Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7569,2,Mod(1,7569)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7569, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7569.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7569 = 3^{2} \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7569.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: | \(60.4387692899\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{9} - 4x^{8} - 6x^{7} + 33x^{6} + 6x^{5} - 90x^{4} + 21x^{3} + 84x^{2} - 36x - 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 87) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.58860\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7569.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58860 | −1.83042 | −0.915210 | − | 0.402978i | \(-0.867975\pi\) | ||||
−0.915210 | + | 0.402978i | \(0.867975\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.70087 | 2.35043 | ||||||||
\(5\) | 1.14894 | 0.513823 | 0.256911 | − | 0.966435i | \(-0.417295\pi\) | ||||
0.256911 | + | 0.966435i | \(0.417295\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.76526 | 1.04517 | 0.522585 | − | 0.852587i | \(-0.324968\pi\) | ||||
0.522585 | + | 0.852587i | \(0.324968\pi\) | |||||||
\(8\) | −6.99148 | −2.47186 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.97416 | −0.940511 | ||||||||
\(11\) | 4.35418 | 1.31283 | 0.656417 | − | 0.754399i | \(-0.272071\pi\) | ||||
0.656417 | + | 0.754399i | \(0.272071\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.62914 | 1.56124 | 0.780621 | − | 0.625005i | \(-0.214903\pi\) | ||||
0.780621 | + | 0.625005i | \(0.214903\pi\) | |||||||
\(14\) | −7.15816 | −1.91310 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.69643 | 2.17411 | ||||||||
\(17\) | −2.41516 | −0.585763 | −0.292881 | − | 0.956149i | \(-0.594614\pi\) | ||||
−0.292881 | + | 0.956149i | \(0.594614\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.87296 | 0.429686 | 0.214843 | − | 0.976649i | \(-0.431076\pi\) | ||||
0.214843 | + | 0.976649i | \(0.431076\pi\) | |||||||
\(20\) | 5.40103 | 1.20771 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.2712 | −2.40304 | ||||||||
\(23\) | 8.82048 | 1.83920 | 0.919598 | − | 0.392860i | \(-0.128514\pi\) | ||||
0.919598 | + | 0.392860i | \(0.128514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.67993 | −0.735986 | ||||||||
\(26\) | −14.5716 | −2.85773 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 12.9991 | 2.45660 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.56053 | 0.280280 | 0.140140 | − | 0.990132i | \(-0.455245\pi\) | ||||
0.140140 | + | 0.990132i | \(0.455245\pi\) | |||||||
\(32\) | −8.52865 | −1.50767 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.25190 | 1.07219 | ||||||||
\(35\) | 3.17713 | 0.537032 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.76330 | 1.27628 | 0.638139 | − | 0.769921i | \(-0.279705\pi\) | ||||
0.638139 | + | 0.769921i | \(0.279705\pi\) | |||||||
\(38\) | −4.84834 | −0.786505 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.03281 | −1.27010 | ||||||||
\(41\) | −3.16072 | −0.493622 | −0.246811 | − | 0.969064i | \(-0.579383\pi\) | ||||
−0.246811 | + | 0.969064i | \(0.579383\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.46397 | −0.223254 | −0.111627 | − | 0.993750i | \(-0.535606\pi\) | ||||
−0.111627 | + | 0.993750i | \(0.535606\pi\) | |||||||
\(44\) | 20.4684 | 3.08573 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −22.8327 | −3.36650 | ||||||||
\(47\) | −0.357351 | −0.0521250 | −0.0260625 | − | 0.999660i | \(-0.508297\pi\) | ||||
−0.0260625 | + | 0.999660i | \(0.508297\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.646666 | 0.0923809 | ||||||||
\(50\) | 9.52588 | 1.34716 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 26.4618 | 3.66960 | ||||||||
\(53\) | 1.63498 | 0.224582 | 0.112291 | − | 0.993675i | \(-0.464181\pi\) | ||||
0.112291 | + | 0.993675i | \(0.464181\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00270 | 0.674563 | ||||||||
\(56\) | −19.3333 | −2.58352 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.85026 | 0.631450 | 0.315725 | − | 0.948851i | \(-0.397752\pi\) | ||||
0.315725 | + | 0.948851i | \(0.397752\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.55510 | 0.199110 | 0.0995551 | − | 0.995032i | \(-0.468258\pi\) | ||||
0.0995551 | + | 0.995032i | \(0.468258\pi\) | |||||||
\(62\) | −4.03961 | −0.513030 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.68444 | 0.585555 | ||||||||
\(65\) | 6.46755 | 0.802201 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.66950 | −1.18132 | −0.590659 | − | 0.806922i | \(-0.701132\pi\) | ||||
−0.590659 | + | 0.806922i | \(0.701132\pi\) | |||||||
\(68\) | −11.3534 | −1.37680 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.22432 | −0.982994 | ||||||||
\(71\) | 8.18108 | 0.970915 | 0.485458 | − | 0.874260i | \(-0.338653\pi\) | ||||
0.485458 | + | 0.874260i | \(0.338653\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3786 | 1.33177 | 0.665884 | − | 0.746055i | \(-0.268054\pi\) | ||||
0.665884 | + | 0.746055i | \(0.268054\pi\) | |||||||
\(74\) | −20.0961 | −2.33612 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.80452 | 1.00995 | ||||||||
\(77\) | 12.0404 | 1.37213 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.13075 | −0.914781 | −0.457391 | − | 0.889266i | \(-0.651216\pi\) | ||||
−0.457391 | + | 0.889266i | \(0.651216\pi\) | |||||||
\(80\) | 9.99170 | 1.11711 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.18185 | 0.903535 | ||||||||
\(83\) | 0.481835 | 0.0528882 | 0.0264441 | − | 0.999650i | \(-0.491582\pi\) | ||||
0.0264441 | + | 0.999650i | \(0.491582\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.77488 | −0.300978 | ||||||||
\(86\) | 3.78965 | 0.408648 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −30.4421 | −3.24514 | ||||||||
\(89\) | 1.99621 | 0.211598 | 0.105799 | − | 0.994388i | \(-0.466260\pi\) | ||||
0.105799 | + | 0.994388i | \(0.466260\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.5660 | 1.63176 | ||||||||
\(92\) | 41.4639 | 4.32291 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.925040 | 0.0954106 | ||||||||
\(95\) | 2.15192 | 0.220782 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.63516 | 0.470629 | 0.235315 | − | 0.971919i | \(-0.424388\pi\) | ||||
0.235315 | + | 0.971919i | \(0.424388\pi\) | |||||||
\(98\) | −1.67396 | −0.169096 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −17.2989 | −1.72989 | ||||||||
\(101\) | 1.89907 | 0.188964 | 0.0944822 | − | 0.995527i | \(-0.469880\pi\) | ||||
0.0944822 | + | 0.995527i | \(0.469880\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.22122 | −0.810061 | −0.405030 | − | 0.914303i | \(-0.632739\pi\) | ||||
−0.405030 | + | 0.914303i | \(0.632739\pi\) | |||||||
\(104\) | −39.3560 | −3.85917 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.23233 | −0.411080 | ||||||||
\(107\) | −4.45778 | −0.430950 | −0.215475 | − | 0.976509i | \(-0.569130\pi\) | ||||
−0.215475 | + | 0.976509i | \(0.569130\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.5256 | 1.67865 | 0.839324 | − | 0.543631i | \(-0.182951\pi\) | ||||
0.839324 | + | 0.543631i | \(0.182951\pi\) | |||||||
\(110\) | −12.9500 | −1.23473 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 24.0479 | 2.27231 | ||||||||
\(113\) | −7.93117 | −0.746102 | −0.373051 | − | 0.927811i | \(-0.621688\pi\) | ||||
−0.373051 | + | 0.927811i | \(0.621688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.1342 | 0.945021 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.5554 | −1.15582 | ||||||||
\(119\) | −6.67855 | −0.612222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.95884 | 0.723531 | ||||||||
\(122\) | −4.02554 | −0.364455 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.33587 | 0.658780 | ||||||||
\(125\) | −9.97274 | −0.891989 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.35542 | −0.297745 | −0.148873 | − | 0.988856i | \(-0.547564\pi\) | ||||
−0.148873 | + | 0.988856i | \(0.547564\pi\) | |||||||
\(128\) | 4.93114 | 0.435855 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −16.7419 | −1.46836 | ||||||||
\(131\) | 8.69320 | 0.759528 | 0.379764 | − | 0.925083i | \(-0.376005\pi\) | ||||
0.379764 | + | 0.925083i | \(0.376005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.17921 | 0.449095 | ||||||||
\(134\) | 25.0305 | 2.16231 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.8856 | 1.44792 | ||||||||
\(137\) | −3.22382 | −0.275429 | −0.137715 | − | 0.990472i | \(-0.543976\pi\) | ||||
−0.137715 | + | 0.990472i | \(0.543976\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.4884 | −1.90744 | −0.953721 | − | 0.300693i | \(-0.902782\pi\) | ||||
−0.953721 | + | 0.300693i | \(0.902782\pi\) | |||||||
\(140\) | 14.9352 | 1.26226 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −21.1776 | −1.77718 | ||||||||
\(143\) | 24.5102 | 2.04965 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −29.4548 | −2.43769 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 36.4942 | 2.99981 | ||||||||
\(149\) | −1.28934 | −0.105627 | −0.0528133 | − | 0.998604i | \(-0.516819\pi\) | ||||
−0.0528133 | + | 0.998604i | \(0.516819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.55195 | 0.533190 | 0.266595 | − | 0.963809i | \(-0.414101\pi\) | ||||
0.266595 | + | 0.963809i | \(0.414101\pi\) | |||||||
\(152\) | −13.0947 | −1.06212 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −31.1679 | −2.51158 | ||||||||
\(155\) | 1.79296 | 0.144014 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.1178 | −1.92481 | −0.962407 | − | 0.271612i | \(-0.912443\pi\) | ||||
−0.962407 | + | 0.271612i | \(0.912443\pi\) | |||||||
\(158\) | 21.0473 | 1.67443 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.79893 | −0.774674 | ||||||||
\(161\) | 24.3909 | 1.92227 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.1434 | 1.26445 | 0.632223 | − | 0.774786i | \(-0.282143\pi\) | ||||
0.632223 | + | 0.774786i | \(0.282143\pi\) | |||||||
\(164\) | −14.8581 | −1.16023 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.24728 | −0.0968076 | ||||||||
\(167\) | 5.42045 | 0.419447 | 0.209723 | − | 0.977761i | \(-0.432744\pi\) | ||||
0.209723 | + | 0.977761i | \(0.432744\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.6872 | 1.43747 | ||||||||
\(170\) | 7.18307 | 0.550916 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.88195 | −0.524744 | ||||||||
\(173\) | 11.2923 | 0.858537 | 0.429268 | − | 0.903177i | \(-0.358771\pi\) | ||||
0.429268 | + | 0.903177i | \(0.358771\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.1760 | −0.769231 | ||||||||
\(176\) | 37.8658 | 2.85424 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.16739 | −0.387312 | ||||||||
\(179\) | 10.6541 | 0.796323 | 0.398161 | − | 0.917315i | \(-0.369648\pi\) | ||||
0.398161 | + | 0.917315i | \(0.369648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2934 | −0.913763 | −0.456882 | − | 0.889527i | \(-0.651034\pi\) | ||||
−0.456882 | + | 0.889527i | \(0.651034\pi\) | |||||||
\(182\) | −40.2943 | −2.98681 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −61.6682 | −4.54624 | ||||||||
\(185\) | 8.91958 | 0.655781 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.5160 | −0.769009 | ||||||||
\(188\) | −1.67986 | −0.122516 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.57047 | −0.404124 | ||||||||
\(191\) | 1.68311 | 0.121786 | 0.0608929 | − | 0.998144i | \(-0.480605\pi\) | ||||
0.0608929 | + | 0.998144i | \(0.480605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5761 | 0.761284 | 0.380642 | − | 0.924722i | \(-0.375703\pi\) | ||||
0.380642 | + | 0.924722i | \(0.375703\pi\) | |||||||
\(194\) | −11.9986 | −0.861449 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.03989 | 0.217135 | ||||||||
\(197\) | 12.1150 | 0.863161 | 0.431581 | − | 0.902074i | \(-0.357956\pi\) | ||||
0.431581 | + | 0.902074i | \(0.357956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.99592 | 0.354151 | 0.177076 | − | 0.984197i | \(-0.443336\pi\) | ||||
0.177076 | + | 0.984197i | \(0.443336\pi\) | |||||||
\(200\) | 25.7282 | 1.81926 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.91594 | −0.345884 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.63149 | −0.253634 | ||||||||
\(206\) | 21.2815 | 1.48275 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 48.9534 | 3.39431 | ||||||||
\(209\) | 8.15518 | 0.564106 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.2108 | −1.32253 | −0.661263 | − | 0.750154i | \(-0.729979\pi\) | ||||
−0.661263 | + | 0.750154i | \(0.729979\pi\) | |||||||
\(212\) | 7.68585 | 0.527866 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.5394 | 0.788819 | ||||||||
\(215\) | −1.68202 | −0.114713 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.31528 | 0.292941 | ||||||||
\(218\) | −45.3668 | −3.07263 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 23.5170 | 1.58552 | ||||||||
\(221\) | −13.5953 | −0.914517 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.2442 | −1.42262 | −0.711308 | − | 0.702881i | \(-0.751897\pi\) | ||||
−0.711308 | + | 0.702881i | \(0.751897\pi\) | |||||||
\(224\) | −23.5840 | −1.57577 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.5307 | 1.36568 | ||||||||
\(227\) | −19.7559 | −1.31125 | −0.655624 | − | 0.755088i | \(-0.727594\pi\) | ||||
−0.655624 | + | 0.755088i | \(0.727594\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.7139 | 1.36881 | 0.684405 | − | 0.729102i | \(-0.260062\pi\) | ||||
0.684405 | + | 0.729102i | \(0.260062\pi\) | |||||||
\(230\) | −26.2335 | −1.72978 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.7745 | −1.36098 | −0.680492 | − | 0.732756i | \(-0.738234\pi\) | ||||
−0.680492 | + | 0.732756i | \(0.738234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.410576 | −0.0267830 | ||||||||
\(236\) | 22.8004 | 1.48418 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.2881 | 1.12062 | ||||||||
\(239\) | 2.27481 | 0.147145 | 0.0735727 | − | 0.997290i | \(-0.476560\pi\) | ||||
0.0735727 | + | 0.997290i | \(0.476560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7783 | 0.758706 | 0.379353 | − | 0.925252i | \(-0.376147\pi\) | ||||
0.379353 | + | 0.925252i | \(0.376147\pi\) | |||||||
\(242\) | −20.6023 | −1.32437 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.31032 | 0.467995 | ||||||||
\(245\) | 0.742982 | 0.0474674 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.5431 | 0.670843 | ||||||||
\(248\) | −10.9104 | −0.692814 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 25.8155 | 1.63271 | ||||||||
\(251\) | 1.42714 | 0.0900805 | 0.0450402 | − | 0.998985i | \(-0.485658\pi\) | ||||
0.0450402 | + | 0.998985i | \(0.485658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 38.4059 | 2.41456 | ||||||||
\(254\) | 8.68585 | 0.544999 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −22.1337 | −1.38335 | ||||||||
\(257\) | 28.6450 | 1.78683 | 0.893414 | − | 0.449234i | \(-0.148303\pi\) | ||||
0.893414 | + | 0.449234i | \(0.148303\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.4675 | 1.33393 | ||||||||
\(260\) | 30.4031 | 1.88552 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −22.5032 | −1.39025 | ||||||||
\(263\) | −18.5023 | −1.14090 | −0.570451 | − | 0.821332i | \(-0.693231\pi\) | ||||
−0.570451 | + | 0.821332i | \(0.693231\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.87850 | 0.115396 | ||||||||
\(266\) | −13.4069 | −0.822032 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −45.4550 | −2.77661 | ||||||||
\(269\) | 28.7074 | 1.75032 | 0.875160 | − | 0.483834i | \(-0.160756\pi\) | ||||
0.875160 | + | 0.483834i | \(0.160756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.80441 | 0.109610 | 0.0548050 | − | 0.998497i | \(-0.482546\pi\) | ||||
0.0548050 | + | 0.998497i | \(0.482546\pi\) | |||||||
\(272\) | −21.0033 | −1.27351 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.34518 | 0.504151 | ||||||||
\(275\) | −16.0231 | −0.966227 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1949 | −0.852890 | −0.426445 | − | 0.904513i | \(-0.640234\pi\) | ||||
−0.426445 | + | 0.904513i | \(0.640234\pi\) | |||||||
\(278\) | 58.2136 | 3.49142 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −22.2128 | −1.32747 | ||||||||
\(281\) | −18.8216 | −1.12280 | −0.561400 | − | 0.827545i | \(-0.689737\pi\) | ||||
−0.561400 | + | 0.827545i | \(0.689737\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.8832 | 1.30082 | 0.650410 | − | 0.759584i | \(-0.274597\pi\) | ||||
0.650410 | + | 0.759584i | \(0.274597\pi\) | |||||||
\(284\) | 38.4582 | 2.28207 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −63.4473 | −3.75172 | ||||||||
\(287\) | −8.74022 | −0.515919 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1670 | −0.656882 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 53.4895 | 3.13023 | ||||||||
\(293\) | −0.00776592 | −0.000453690 0 | −0.000226845 | − | 1.00000i | \(-0.500072\pi\) | ||||
−0.000226845 | 1.00000i | \(0.500072\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.57267 | 0.324453 | ||||||||
\(296\) | −54.2769 | −3.15478 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.33758 | 0.193341 | ||||||||
\(299\) | 49.6517 | 2.87143 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.04827 | −0.233338 | ||||||||
\(302\) | −16.9604 | −0.975961 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.2880 | 0.934183 | ||||||||
\(305\) | 1.78672 | 0.102307 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.214941 | 0.0122673 | 0.00613367 | − | 0.999981i | \(-0.498048\pi\) | ||||
0.00613367 | + | 0.999981i | \(0.498048\pi\) | |||||||
\(308\) | 56.6005 | 3.22511 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.64127 | −0.263607 | ||||||||
\(311\) | −28.2266 | −1.60058 | −0.800291 | − | 0.599612i | \(-0.795322\pi\) | ||||
−0.800291 | + | 0.599612i | \(0.795322\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.2302 | −0.578244 | −0.289122 | − | 0.957292i | \(-0.593363\pi\) | ||||
−0.289122 | + | 0.957292i | \(0.593363\pi\) | |||||||
\(314\) | 62.4316 | 3.52322 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −38.2216 | −2.15013 | ||||||||
\(317\) | −23.7789 | −1.33555 | −0.667777 | − | 0.744361i | \(-0.732754\pi\) | ||||
−0.667777 | + | 0.744361i | \(0.732754\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 5.38216 | 0.300872 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −63.1384 | −3.51857 | ||||||||
\(323\) | −4.52349 | −0.251694 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.7148 | −1.14905 | ||||||||
\(326\) | −41.7888 | −2.31447 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 22.0981 | 1.22016 | ||||||||
\(329\) | −0.988168 | −0.0544795 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.07856 | −0.389073 | −0.194536 | − | 0.980895i | \(-0.562320\pi\) | ||||
−0.194536 | + | 0.980895i | \(0.562320\pi\) | |||||||
\(332\) | 2.26504 | 0.124310 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.0314 | −0.767763 | ||||||||
\(335\) | −11.1097 | −0.606987 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.02402 | −0.382623 | −0.191311 | − | 0.981529i | \(-0.561274\pi\) | ||||
−0.191311 | + | 0.981529i | \(0.561274\pi\) | |||||||
\(338\) | −48.3737 | −2.63118 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.0444 | −0.707429 | ||||||||
\(341\) | 6.79484 | 0.367961 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.5686 | −0.948617 | ||||||||
\(344\) | 10.2353 | 0.551852 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −29.2313 | −1.57148 | ||||||||
\(347\) | −10.0795 | −0.541094 | −0.270547 | − | 0.962707i | \(-0.587205\pi\) | ||||
−0.270547 | + | 0.962707i | \(0.587205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.64246 | −0.0879187 | −0.0439593 | − | 0.999033i | \(-0.513997\pi\) | ||||
−0.0439593 | + | 0.999033i | \(0.513997\pi\) | |||||||
\(350\) | 26.3416 | 1.40802 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −37.1353 | −1.97932 | ||||||||
\(353\) | −24.1232 | −1.28395 | −0.641975 | − | 0.766726i | \(-0.721885\pi\) | ||||
−0.641975 | + | 0.766726i | \(0.721885\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.39959 | 0.498878 | ||||||||
\(356\) | 9.38391 | 0.497346 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −27.5792 | −1.45760 | ||||||||
\(359\) | 12.8958 | 0.680612 | 0.340306 | − | 0.940315i | \(-0.389469\pi\) | ||||
0.340306 | + | 0.940315i | \(0.389469\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.4920 | −0.815370 | ||||||||
\(362\) | 31.8228 | 1.67257 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 73.1739 | 3.83535 | ||||||||
\(365\) | 13.0734 | 0.684293 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.7420 | −1.65692 | −0.828459 | − | 0.560050i | \(-0.810782\pi\) | ||||
−0.828459 | + | 0.560050i | \(0.810782\pi\) | |||||||
\(368\) | 76.7067 | 3.99861 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −23.0893 | −1.20035 | ||||||||
\(371\) | 4.52116 | 0.234727 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.75511 | 0.246210 | 0.123105 | − | 0.992394i | \(-0.460715\pi\) | ||||
0.123105 | + | 0.992394i | \(0.460715\pi\) | |||||||
\(374\) | 27.2218 | 1.40761 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.49841 | 0.128846 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.11960 | 0.108877 | 0.0544383 | − | 0.998517i | \(-0.482663\pi\) | ||||
0.0544383 | + | 0.998517i | \(0.482663\pi\) | |||||||
\(380\) | 10.1159 | 0.518934 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.35691 | −0.222919 | ||||||||
\(383\) | −14.6407 | −0.748103 | −0.374051 | − | 0.927408i | \(-0.622032\pi\) | ||||
−0.374051 | + | 0.927408i | \(0.622032\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.8338 | 0.705034 | ||||||||
\(386\) | −27.3773 | −1.39347 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.7893 | 1.10618 | ||||||||
\(389\) | −1.93401 | −0.0980583 | −0.0490292 | − | 0.998797i | \(-0.515613\pi\) | ||||
−0.0490292 | + | 0.998797i | \(0.515613\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.3029 | −1.07733 | ||||||||
\(392\) | −4.52115 | −0.228353 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −31.3611 | −1.57995 | ||||||||
\(395\) | −9.34177 | −0.470035 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.0191 | −1.50662 | −0.753309 | − | 0.657667i | \(-0.771543\pi\) | ||||
−0.753309 | + | 0.657667i | \(0.771543\pi\) | |||||||
\(398\) | −12.9324 | −0.648245 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −32.0023 | −1.60011 | ||||||||
\(401\) | −15.7085 | −0.784444 | −0.392222 | − | 0.919871i | \(-0.628293\pi\) | ||||
−0.392222 | + | 0.919871i | \(0.628293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.78446 | 0.437585 | ||||||||
\(404\) | 8.92728 | 0.444149 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.8027 | 1.67554 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.87216 | −0.240913 | −0.120456 | − | 0.992719i | \(-0.538436\pi\) | ||||
−0.120456 | + | 0.992719i | \(0.538436\pi\) | |||||||
\(410\) | 9.40048 | 0.464257 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −38.6469 | −1.90399 | ||||||||
\(413\) | 13.4122 | 0.659973 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.553600 | 0.0271752 | ||||||||
\(416\) | −48.0090 | −2.35383 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.1105 | −1.03255 | ||||||||
\(419\) | −19.0131 | −0.928853 | −0.464426 | − | 0.885612i | \(-0.653739\pi\) | ||||
−0.464426 | + | 0.885612i | \(0.653739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5171 | 0.610047 | 0.305023 | − | 0.952345i | \(-0.401336\pi\) | ||||
0.305023 | + | 0.952345i | \(0.401336\pi\) | |||||||
\(422\) | 49.7292 | 2.42078 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.4310 | −0.555136 | ||||||||
\(425\) | 8.88763 | 0.431113 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.30026 | 0.208104 | ||||||||
\(428\) | −20.9554 | −1.01292 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.35409 | 0.209973 | ||||||||
\(431\) | −35.3970 | −1.70501 | −0.852507 | − | 0.522716i | \(-0.824919\pi\) | ||||
−0.852507 | + | 0.522716i | \(0.824919\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.85494 | 0.281371 | 0.140685 | − | 0.990054i | \(-0.455069\pi\) | ||||
0.140685 | + | 0.990054i | \(0.455069\pi\) | |||||||
\(434\) | −11.1706 | −0.536204 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 82.3856 | 3.94555 | ||||||||
\(437\) | 16.5204 | 0.790277 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.8297 | 1.18506 | 0.592530 | − | 0.805549i | \(-0.298129\pi\) | ||||
0.592530 | + | 0.805549i | \(0.298129\pi\) | |||||||
\(440\) | −34.9762 | −1.66743 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.1928 | 1.67395 | ||||||||
\(443\) | −23.7488 | −1.12834 | −0.564170 | − | 0.825659i | \(-0.690804\pi\) | ||||
−0.564170 | + | 0.825659i | \(0.690804\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.29353 | 0.108724 | ||||||||
\(446\) | 54.9928 | 2.60398 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.9537 | 0.612005 | ||||||||
\(449\) | −6.44854 | −0.304325 | −0.152163 | − | 0.988355i | \(-0.548624\pi\) | ||||
−0.152163 | + | 0.988355i | \(0.548624\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.7623 | −0.648043 | ||||||||
\(452\) | −37.2834 | −1.75366 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 51.1403 | 2.40013 | ||||||||
\(455\) | 17.8845 | 0.838437 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.62569 | −0.122824 | −0.0614122 | − | 0.998112i | \(-0.519560\pi\) | ||||
−0.0614122 | + | 0.998112i | \(0.519560\pi\) | |||||||
\(458\) | −53.6200 | −2.50550 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 47.6396 | 2.22121 | ||||||||
\(461\) | 7.15794 | 0.333378 | 0.166689 | − | 0.986009i | \(-0.446692\pi\) | ||||
0.166689 | + | 0.986009i | \(0.446692\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.2411 | −0.847737 | −0.423868 | − | 0.905724i | \(-0.639328\pi\) | ||||
−0.423868 | + | 0.905724i | \(0.639328\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 53.7770 | 2.49117 | ||||||||
\(467\) | −35.4677 | −1.64125 | −0.820624 | − | 0.571468i | \(-0.806374\pi\) | ||||
−0.820624 | + | 0.571468i | \(0.806374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.7387 | −1.23468 | ||||||||
\(470\) | 1.06282 | 0.0490241 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −33.9105 | −1.56086 | ||||||||
\(473\) | −6.37440 | −0.293095 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.89235 | −0.316243 | ||||||||
\(476\) | −31.3950 | −1.43899 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.88859 | −0.269338 | ||||||||
\(479\) | −26.1004 | −1.19256 | −0.596280 | − | 0.802777i | \(-0.703355\pi\) | ||||
−0.596280 | + | 0.802777i | \(0.703355\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 43.7006 | 1.99258 | ||||||||
\(482\) | −30.4893 | −1.38875 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 37.4135 | 1.70061 | ||||||||
\(485\) | 5.32553 | 0.241820 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.1493 | 1.00368 | 0.501839 | − | 0.864961i | \(-0.332657\pi\) | ||||
0.501839 | + | 0.864961i | \(0.332657\pi\) | |||||||
\(488\) | −10.8724 | −0.492173 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.92329 | −0.0868852 | ||||||||
\(491\) | 11.7483 | 0.530193 | 0.265096 | − | 0.964222i | \(-0.414596\pi\) | ||||
0.265096 | + | 0.964222i | \(0.414596\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −27.2920 | −1.22792 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.5711 | 0.609359 | ||||||||
\(497\) | 22.6228 | 1.01477 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.3753 | −0.733060 | −0.366530 | − | 0.930406i | \(-0.619454\pi\) | ||||
−0.366530 | + | 0.930406i | \(0.619454\pi\) | |||||||
\(500\) | −46.8805 | −2.09656 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.69431 | −0.164885 | ||||||||
\(503\) | −14.8354 | −0.661476 | −0.330738 | − | 0.943723i | \(-0.607298\pi\) | ||||
−0.330738 | + | 0.943723i | \(0.607298\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.18192 | 0.0970942 | ||||||||
\(506\) | −99.4177 | −4.41965 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.7734 | −0.699831 | ||||||||
\(509\) | −31.5733 | −1.39946 | −0.699732 | − | 0.714406i | \(-0.746697\pi\) | ||||
−0.699732 | + | 0.714406i | \(0.746697\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.4649 | 1.39192 | ||||||||
\(512\) | 47.4330 | 2.09626 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −74.1507 | −3.27065 | ||||||||
\(515\) | −9.44571 | −0.416228 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.55597 | −0.0684314 | ||||||||
\(518\) | −55.5709 | −2.44165 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −45.2178 | −1.98293 | ||||||||
\(521\) | 8.03875 | 0.352184 | 0.176092 | − | 0.984374i | \(-0.443654\pi\) | ||||
0.176092 | + | 0.984374i | \(0.443654\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.48633 | −0.0649927 | −0.0324963 | − | 0.999472i | \(-0.510346\pi\) | ||||
−0.0324963 | + | 0.999472i | \(0.510346\pi\) | |||||||
\(524\) | 40.8656 | 1.78522 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 47.8951 | 2.08833 | ||||||||
\(527\) | −3.76894 | −0.164178 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.8008 | 2.38264 | ||||||||
\(530\) | −4.86270 | −0.211222 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.3468 | 1.05557 | ||||||||
\(533\) | −17.7921 | −0.770663 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.12173 | −0.221432 | ||||||||
\(536\) | 67.6041 | 2.92005 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −74.3120 | −3.20382 | ||||||||
\(539\) | 2.81570 | 0.121281 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.8306 | 1.66946 | 0.834728 | − | 0.550662i | \(-0.185625\pi\) | ||||
0.834728 | + | 0.550662i | \(0.185625\pi\) | |||||||
\(542\) | −4.67090 | −0.200632 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.5981 | 0.883135 | ||||||||
\(545\) | 20.1359 | 0.862528 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.3495 | −0.741809 | −0.370905 | − | 0.928671i | \(-0.620952\pi\) | ||||
−0.370905 | + | 0.928671i | \(0.620952\pi\) | |||||||
\(548\) | −15.1547 | −0.647378 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 41.4774 | 1.76860 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.4837 | −0.956102 | ||||||||
\(554\) | 36.7450 | 1.56115 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −105.715 | −4.48332 | ||||||||
\(557\) | −30.4259 | −1.28919 | −0.644593 | − | 0.764526i | \(-0.722973\pi\) | ||||
−0.644593 | + | 0.764526i | \(0.722973\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.24091 | −0.348553 | ||||||||
\(560\) | 27.6296 | 1.16757 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 48.7215 | 2.05519 | ||||||||
\(563\) | 12.1911 | 0.513793 | 0.256897 | − | 0.966439i | \(-0.417300\pi\) | ||||
0.256897 | + | 0.966439i | \(0.417300\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.11246 | −0.383364 | ||||||||
\(566\) | −56.6469 | −2.38104 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −57.1978 | −2.39997 | ||||||||
\(569\) | 3.15785 | 0.132384 | 0.0661920 | − | 0.997807i | \(-0.478915\pi\) | ||||
0.0661920 | + | 0.997807i | \(0.478915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.3414 | 1.01865 | 0.509327 | − | 0.860573i | \(-0.329894\pi\) | ||||
0.509327 | + | 0.860573i | \(0.329894\pi\) | |||||||
\(572\) | 115.219 | 4.81757 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 22.6250 | 0.944347 | ||||||||
\(575\) | −32.4588 | −1.35362 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.99079 | 0.332661 | 0.166330 | − | 0.986070i | \(-0.446808\pi\) | ||||
0.166330 | + | 0.986070i | \(0.446808\pi\) | |||||||
\(578\) | 28.9069 | 1.20237 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.33240 | 0.0552772 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.11901 | 0.294839 | ||||||||
\(584\) | −79.5535 | −3.29195 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.0201029 | 0.000830443 0 | ||||||||
\(587\) | 42.3655 | 1.74861 | 0.874305 | − | 0.485377i | \(-0.161318\pi\) | ||||
0.874305 | + | 0.485377i | \(0.161318\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.92281 | 0.120432 | ||||||||
\(590\) | −14.4254 | −0.593886 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 67.5130 | 2.77477 | ||||||||
\(593\) | 26.3761 | 1.08314 | 0.541569 | − | 0.840656i | \(-0.317831\pi\) | ||||
0.541569 | + | 0.840656i | \(0.317831\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.67327 | −0.314573 | ||||||||
\(596\) | −6.06100 | −0.248268 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −128.528 | −5.25592 | ||||||||
\(599\) | −6.35768 | −0.259768 | −0.129884 | − | 0.991529i | \(-0.541460\pi\) | ||||
−0.129884 | + | 0.991529i | \(0.541460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9016 | −0.689430 | −0.344715 | − | 0.938707i | \(-0.612024\pi\) | ||||
−0.344715 | + | 0.938707i | \(0.612024\pi\) | |||||||
\(602\) | 10.4794 | 0.427107 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 30.7999 | 1.25323 | ||||||||
\(605\) | 9.14425 | 0.371767 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.41550 | −0.300986 | −0.150493 | − | 0.988611i | \(-0.548086\pi\) | ||||
−0.150493 | + | 0.988611i | \(0.548086\pi\) | |||||||
\(608\) | −15.9738 | −0.647823 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.62511 | −0.187265 | ||||||||
\(611\) | −2.01158 | −0.0813797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.9255 | −1.16829 | −0.584145 | − | 0.811649i | \(-0.698570\pi\) | ||||
−0.584145 | + | 0.811649i | \(0.698570\pi\) | |||||||
\(614\) | −0.556398 | −0.0224544 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −84.1804 | −3.39173 | ||||||||
\(617\) | 34.9128 | 1.40554 | 0.702768 | − | 0.711419i | \(-0.251947\pi\) | ||||
0.702768 | + | 0.711419i | \(0.251947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.1342 | 1.81410 | 0.907048 | − | 0.421028i | \(-0.138331\pi\) | ||||
0.907048 | + | 0.421028i | \(0.138331\pi\) | |||||||
\(620\) | 8.42849 | 0.338496 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 73.0674 | 2.92974 | ||||||||
\(623\) | 5.52003 | 0.221155 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.94155 | 0.277662 | ||||||||
\(626\) | 26.4819 | 1.05843 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −113.375 | −4.52415 | ||||||||
\(629\) | −18.7496 | −0.747596 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.2602 | 1.16483 | 0.582415 | − | 0.812892i | \(-0.302108\pi\) | ||||
0.582415 | + | 0.812892i | \(0.302108\pi\) | |||||||
\(632\) | 56.8460 | 2.26121 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 61.5540 | 2.44462 | ||||||||
\(635\) | −3.85518 | −0.152988 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.64017 | 0.144229 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.66560 | 0.223952 | ||||||||
\(641\) | −17.7234 | −0.700031 | −0.350016 | − | 0.936744i | \(-0.613824\pi\) | ||||
−0.350016 | + | 0.936744i | \(0.613824\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.4443 | 1.51609 | 0.758047 | − | 0.652200i | \(-0.226154\pi\) | ||||
0.758047 | + | 0.652200i | \(0.226154\pi\) | |||||||
\(644\) | 114.659 | 4.51818 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.7095 | 0.460705 | ||||||||
\(647\) | −40.5910 | −1.59580 | −0.797899 | − | 0.602792i | \(-0.794055\pi\) | ||||
−0.797899 | + | 0.602792i | \(0.794055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.1189 | 0.828989 | ||||||||
\(650\) | 53.6225 | 2.10325 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 75.8879 | 2.97200 | ||||||||
\(653\) | 26.6169 | 1.04160 | 0.520800 | − | 0.853679i | \(-0.325634\pi\) | ||||
0.520800 | + | 0.853679i | \(0.325634\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.98798 | 0.390263 | ||||||||
\(656\) | −27.4870 | −1.07319 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.55798 | 0.0997203 | ||||||||
\(659\) | 23.1105 | 0.900259 | 0.450130 | − | 0.892963i | \(-0.351378\pi\) | ||||
0.450130 | + | 0.892963i | \(0.351378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.4613 | 0.912537 | 0.456269 | − | 0.889842i | \(-0.349186\pi\) | ||||
0.456269 | + | 0.889842i | \(0.349186\pi\) | |||||||
\(662\) | 18.3236 | 0.712166 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.36874 | −0.130732 | ||||||||
\(665\) | 5.95062 | 0.230755 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 25.4808 | 0.985882 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 28.7586 | 1.11104 | ||||||||
\(671\) | 6.77118 | 0.261398 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.9621 | −1.03931 | −0.519656 | − | 0.854376i | \(-0.673940\pi\) | ||||
−0.519656 | + | 0.854376i | \(0.673940\pi\) | |||||||
\(674\) | 18.1824 | 0.700360 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 87.8460 | 3.37869 | ||||||||
\(677\) | −33.5314 | −1.28872 | −0.644358 | − | 0.764724i | \(-0.722875\pi\) | ||||
−0.644358 | + | 0.764724i | \(0.722875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.8174 | 0.491888 | ||||||||
\(680\) | 19.4005 | 0.743976 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17.5891 | −0.673523 | ||||||||
\(683\) | 12.3343 | 0.471957 | 0.235979 | − | 0.971758i | \(-0.424170\pi\) | ||||
0.235979 | + | 0.971758i | \(0.424170\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.70398 | −0.141522 | ||||||||
\(686\) | 45.4782 | 1.73637 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.7313 | −0.485378 | ||||||||
\(689\) | 9.20355 | 0.350627 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.02123 | 0.0768913 | 0.0384457 | − | 0.999261i | \(-0.487759\pi\) | ||||
0.0384457 | + | 0.999261i | \(0.487759\pi\) | |||||||
\(692\) | 53.0836 | 2.01793 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.0918 | 0.990429 | ||||||||
\(695\) | −25.8379 | −0.980087 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.63365 | 0.289145 | ||||||||
\(698\) | 4.25167 | 0.160928 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −47.8359 | −1.80803 | ||||||||
\(701\) | 33.6980 | 1.27275 | 0.636377 | − | 0.771378i | \(-0.280432\pi\) | ||||
0.636377 | + | 0.771378i | \(0.280432\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.5403 | 0.548398 | ||||||||
\(704\) | 20.3969 | 0.768737 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 62.4455 | 2.35017 | ||||||||
\(707\) | 5.25142 | 0.197500 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.6531 | 0.475198 | 0.237599 | − | 0.971363i | \(-0.423640\pi\) | ||||
0.237599 | + | 0.971363i | \(0.423640\pi\) | |||||||
\(710\) | −24.3318 | −0.913157 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.9564 | −0.523040 | ||||||||
\(713\) | 13.7647 | 0.515490 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.1609 | 1.05316 | ||||||||
\(716\) | 50.0834 | 1.87170 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.3820 | −1.24581 | ||||||||
\(719\) | −13.3377 | −0.497411 | −0.248706 | − | 0.968579i | \(-0.580005\pi\) | ||||
−0.248706 | + | 0.968579i | \(0.580005\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.7338 | −0.846651 | ||||||||
\(722\) | 40.1027 | 1.49247 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −57.7898 | −2.14774 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.7683 | −1.54910 | −0.774551 | − | 0.632512i | \(-0.782024\pi\) | ||||
−0.774551 | + | 0.632512i | \(0.782024\pi\) | |||||||
\(728\) | −108.830 | −4.03349 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −33.8418 | −1.25254 | ||||||||
\(731\) | 3.53573 | 0.130774 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.5635 | −1.57212 | −0.786059 | − | 0.618152i | \(-0.787882\pi\) | ||||
−0.786059 | + | 0.618152i | \(0.787882\pi\) | |||||||
\(734\) | 82.1674 | 3.03285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −75.2268 | −2.77290 | ||||||||
\(737\) | −42.1027 | −1.55087 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.2405 | 0.818129 | 0.409064 | − | 0.912506i | \(-0.365855\pi\) | ||||
0.409064 | + | 0.912506i | \(0.365855\pi\) | |||||||
\(740\) | 41.9298 | 1.54137 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.7035 | −0.429648 | ||||||||
\(743\) | 28.0714 | 1.02984 | 0.514920 | − | 0.857238i | \(-0.327822\pi\) | ||||
0.514920 | + | 0.857238i | \(0.327822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.48137 | −0.0542733 | ||||||||
\(746\) | −12.3091 | −0.450668 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −49.4345 | −1.80750 | ||||||||
\(749\) | −12.3269 | −0.450416 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.5813 | 1.04295 | 0.521473 | − | 0.853268i | \(-0.325383\pi\) | ||||
0.521473 | + | 0.853268i | \(0.325383\pi\) | |||||||
\(752\) | −3.10768 | −0.113325 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.52781 | 0.273965 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.4521 | −0.779689 | −0.389844 | − | 0.920881i | \(-0.627471\pi\) | ||||
−0.389844 | + | 0.920881i | \(0.627471\pi\) | |||||||
\(758\) | −5.48680 | −0.199290 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.0451 | −0.545743 | ||||||||
\(761\) | 21.4222 | 0.776553 | 0.388277 | − | 0.921543i | \(-0.373071\pi\) | ||||
0.388277 | + | 0.921543i | \(0.373071\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.4629 | 1.75447 | ||||||||
\(764\) | 7.91209 | 0.286249 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.8989 | 1.36934 | ||||||||
\(767\) | 27.3028 | 0.985846 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.7152 | −0.819130 | −0.409565 | − | 0.912281i | \(-0.634320\pi\) | ||||
−0.409565 | + | 0.912281i | \(0.634320\pi\) | |||||||
\(770\) | −35.8101 | −1.29051 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 49.7168 | 1.78935 | ||||||||
\(773\) | 0.180228 | 0.00648235 | 0.00324118 | − | 0.999995i | \(-0.498968\pi\) | ||||
0.00324118 | + | 0.999995i | \(0.498968\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.74266 | −0.206282 | ||||||||
\(776\) | −32.4066 | −1.16333 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.00639 | 0.179488 | ||||||||
\(779\) | −5.91989 | −0.212102 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.6219 | 1.27465 | ||||||||
\(782\) | 55.1447 | 1.97197 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.62369 | 0.200846 | ||||||||
\(785\) | −27.7100 | −0.989013 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.4923 | 1.58598 | 0.792989 | − | 0.609236i | \(-0.208524\pi\) | ||||
0.792989 | + | 0.609236i | \(0.208524\pi\) | |||||||
\(788\) | 56.9513 | 2.02880 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.1821 | 0.860362 | ||||||||
\(791\) | −21.9318 | −0.779803 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.75387 | 0.310859 | ||||||||
\(794\) | 77.7076 | 2.75774 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.4851 | 0.832409 | ||||||||
\(797\) | 2.28072 | 0.0807872 | 0.0403936 | − | 0.999184i | \(-0.487139\pi\) | ||||
0.0403936 | + | 0.999184i | \(0.487139\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.863060 | 0.0305329 | ||||||||
\(800\) | 31.3849 | 1.10962 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 40.6630 | 1.43586 | ||||||||
\(803\) | 49.5446 | 1.74839 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.0238 | 0.987708 | ||||||||
\(806\) | −22.7395 | −0.800964 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.2773 | −0.467094 | ||||||||
\(809\) | −11.4774 | −0.403523 | −0.201761 | − | 0.979435i | \(-0.564667\pi\) | ||||
−0.201761 | + | 0.979435i | \(0.564667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.4524 | 0.963985 | 0.481993 | − | 0.876175i | \(-0.339913\pi\) | ||||
0.481993 | + | 0.876175i | \(0.339913\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −87.5019 | −3.06694 | ||||||||
\(815\) | 18.5478 | 0.649701 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.74196 | −0.0959290 | ||||||||
\(818\) | 12.6121 | 0.440971 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.0711 | −0.596150 | ||||||||
\(821\) | 25.1785 | 0.878734 | 0.439367 | − | 0.898308i | \(-0.355203\pi\) | ||||
0.439367 | + | 0.898308i | \(0.355203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.12913 | 0.0742169 | 0.0371085 | − | 0.999311i | \(-0.488185\pi\) | ||||
0.0371085 | + | 0.999311i | \(0.488185\pi\) | |||||||
\(824\) | 57.4785 | 2.00236 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −34.7190 | −1.20803 | ||||||||
\(827\) | 18.3427 | 0.637837 | 0.318918 | − | 0.947782i | \(-0.396680\pi\) | ||||
0.318918 | + | 0.947782i | \(0.396680\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.9373 | 1.83859 | 0.919295 | − | 0.393570i | \(-0.128760\pi\) | ||||
0.919295 | + | 0.393570i | \(0.128760\pi\) | |||||||
\(830\) | −1.43305 | −0.0497419 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 26.3694 | 0.914194 | ||||||||
\(833\) | −1.56180 | −0.0541133 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.22778 | 0.215521 | ||||||||
\(836\) | 38.3364 | 1.32589 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 49.2175 | 1.70019 | ||||||||
\(839\) | 26.8505 | 0.926984 | 0.463492 | − | 0.886101i | \(-0.346596\pi\) | ||||
0.463492 | + | 0.886101i | \(0.346596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −32.4018 | −1.11664 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −90.3075 | −3.10851 | ||||||||
\(845\) | 21.4705 | 0.738607 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.0083 | 0.756213 | ||||||||
\(848\) | 14.2185 | 0.488266 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −23.0065 | −0.789118 | ||||||||
\(851\) | 68.4760 | 2.34733 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.8554 | 1.36462 | 0.682311 | − | 0.731062i | \(-0.260975\pi\) | ||||
0.682311 | + | 0.731062i | \(0.260975\pi\) | |||||||
\(854\) | −11.1317 | −0.380918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31.1665 | 1.06525 | ||||||||
\(857\) | −50.9827 | −1.74154 | −0.870768 | − | 0.491694i | \(-0.836378\pi\) | ||||
−0.870768 | + | 0.491694i | \(0.836378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.8714 | 0.507404 | 0.253702 | − | 0.967282i | \(-0.418352\pi\) | ||||
0.253702 | + | 0.967282i | \(0.418352\pi\) | |||||||
\(860\) | −7.90696 | −0.269625 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 91.6288 | 3.12089 | ||||||||
\(863\) | 20.4603 | 0.696478 | 0.348239 | − | 0.937406i | \(-0.386780\pi\) | ||||
0.348239 | + | 0.937406i | \(0.386780\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.9742 | 0.441136 | ||||||||
\(866\) | −15.1561 | −0.515026 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.2856 | 0.688538 | ||||||||
\(869\) | −35.4027 | −1.20096 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54.4309 | −1.84432 | ||||||||
\(872\) | −122.530 | −4.14939 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −42.7647 | −1.44654 | ||||||||
\(875\) | −27.5772 | −0.932280 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.4211 | −0.520732 | −0.260366 | − | 0.965510i | \(-0.583843\pi\) | ||||
−0.260366 | + | 0.965510i | \(0.583843\pi\) | |||||||
\(878\) | −64.2744 | −2.16916 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 43.5056 | 1.46657 | ||||||||
\(881\) | −55.0390 | −1.85431 | −0.927155 | − | 0.374678i | \(-0.877753\pi\) | ||||
−0.927155 | + | 0.374678i | \(0.877753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.9954 | 1.27865 | 0.639324 | − | 0.768938i | \(-0.279214\pi\) | ||||
0.639324 | + | 0.768938i | \(0.279214\pi\) | |||||||
\(884\) | −63.9096 | −2.14951 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 61.4762 | 2.06533 | ||||||||
\(887\) | −18.2699 | −0.613444 | −0.306722 | − | 0.951799i | \(-0.599232\pi\) | ||||
−0.306722 | + | 0.951799i | \(0.599232\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.27861 | −0.311195 | ||||||||
\(890\) | −5.93703 | −0.199010 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −99.8661 | −3.34376 | ||||||||
\(893\) | −0.669303 | −0.0223974 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.2409 | 0.409169 | ||||||||
\(896\) | 13.6359 | 0.455543 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.6927 | 0.557043 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.94875 | −0.131552 | ||||||||
\(902\) | 35.6252 | 1.18619 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 55.4506 | 1.84426 | ||||||||
\(905\) | −14.1244 | −0.469512 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.2735 | 0.839192 | 0.419596 | − | 0.907711i | \(-0.362172\pi\) | ||||
0.419596 | + | 0.907711i | \(0.362172\pi\) | |||||||
\(908\) | −92.8701 | −3.08200 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −46.2958 | −1.53469 | ||||||||
\(911\) | −34.3336 | −1.13752 | −0.568762 | − | 0.822502i | \(-0.692578\pi\) | ||||
−0.568762 | + | 0.822502i | \(0.692578\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.09799 | 0.0694334 | ||||||||
\(914\) | 6.79686 | 0.224820 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 97.3731 | 3.21730 | ||||||||
\(917\) | 24.0390 | 0.793836 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.8764 | −0.886572 | −0.443286 | − | 0.896380i | \(-0.646187\pi\) | ||||
−0.443286 | + | 0.896380i | \(0.646187\pi\) | |||||||
\(920\) | −70.8532 | −2.33596 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.5291 | −0.610222 | ||||||||
\(923\) | 46.0524 | 1.51583 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.5684 | −0.939323 | ||||||||
\(926\) | 47.2190 | 1.55171 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.4218 | 0.899679 | 0.449839 | − | 0.893109i | \(-0.351481\pi\) | ||||
0.449839 | + | 0.893109i | \(0.351481\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.21118 | 0.0396947 | ||||||||
\(932\) | −97.6582 | −3.19890 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 91.8118 | 3.00417 | ||||||||
\(935\) | −12.0823 | −0.395134 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.3107 | −0.336836 | −0.168418 | − | 0.985716i | \(-0.553866\pi\) | ||||
−0.168418 | + | 0.985716i | \(0.553866\pi\) | |||||||
\(938\) | 69.2158 | 2.25998 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.93006 | −0.0629517 | ||||||||
\(941\) | −16.9225 | −0.551657 | −0.275828 | − | 0.961207i | \(-0.588952\pi\) | ||||
−0.275828 | + | 0.961207i | \(0.588952\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.8791 | −0.907867 | ||||||||
\(944\) | 42.1800 | 1.37284 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.5008 | 0.536487 | ||||||||
\(947\) | 21.2231 | 0.689659 | 0.344829 | − | 0.938665i | \(-0.387937\pi\) | ||||
0.344829 | + | 0.938665i | \(0.387937\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 64.0519 | 2.07921 | ||||||||
\(950\) | 17.8416 | 0.578857 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 46.6929 | 1.51333 | ||||||||
\(953\) | 8.78444 | 0.284556 | 0.142278 | − | 0.989827i | \(-0.454557\pi\) | ||||
0.142278 | + | 0.989827i | \(0.454557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.93380 | 0.0625763 | ||||||||
\(956\) | 10.6936 | 0.345856 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 67.5637 | 2.18288 | ||||||||
\(959\) | −8.91469 | −0.287870 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5647 | −0.921443 | ||||||||
\(962\) | −113.124 | −3.64725 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 55.3682 | 1.78329 | ||||||||
\(965\) | 12.1513 | 0.391165 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.9334 | −0.833961 | −0.416981 | − | 0.908915i | \(-0.636912\pi\) | ||||
−0.416981 | + | 0.908915i | \(0.636912\pi\) | |||||||
\(968\) | −55.6441 | −1.78847 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.7857 | −0.442632 | ||||||||
\(971\) | 58.1391 | 1.86577 | 0.932886 | − | 0.360172i | \(-0.117282\pi\) | ||||
0.932886 | + | 0.360172i | \(0.117282\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62.1863 | −1.99360 | ||||||||
\(974\) | −57.3357 | −1.83715 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.5238 | 0.432887 | ||||||||
\(977\) | −29.9259 | −0.957414 | −0.478707 | − | 0.877975i | \(-0.658894\pi\) | ||||
−0.478707 | + | 0.877975i | \(0.658894\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.69184 | 0.277792 | ||||||||
\(980\) | 3.49266 | 0.111569 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.4117 | −0.970475 | ||||||||
\(983\) | 40.2091 | 1.28247 | 0.641236 | − | 0.767344i | \(-0.278422\pi\) | ||||
0.641236 | + | 0.767344i | \(0.278422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.9195 | 0.443512 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 49.5619 | 1.57677 | ||||||||
\(989\) | −12.9129 | −0.410608 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.1707 | 1.24430 | 0.622149 | − | 0.782898i | \(-0.286260\pi\) | ||||
0.622149 | + | 0.782898i | \(0.286260\pi\) | |||||||
\(992\) | −13.3093 | −0.422569 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −58.5615 | −1.85746 | ||||||||
\(995\) | 5.74002 | 0.181971 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.4756 | 1.09185 | 0.545927 | − | 0.837833i | \(-0.316177\pi\) | ||||
0.545927 | + | 0.837833i | \(0.316177\pi\) | |||||||
\(998\) | 42.3892 | 1.34181 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7569.2.a.bj.1.2 | 9 | ||
3.2 | odd | 2 | 2523.2.a.r.1.8 | 9 | |||
29.16 | even | 7 | 261.2.k.c.82.1 | 18 | |||
29.20 | even | 7 | 261.2.k.c.226.1 | 18 | |||
29.28 | even | 2 | 7569.2.a.bm.1.8 | 9 | |||
87.20 | odd | 14 | 87.2.g.a.52.3 | ✓ | 18 | ||
87.74 | odd | 14 | 87.2.g.a.82.3 | yes | 18 | ||
87.86 | odd | 2 | 2523.2.a.o.1.2 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.2.g.a.52.3 | ✓ | 18 | 87.20 | odd | 14 | ||
87.2.g.a.82.3 | yes | 18 | 87.74 | odd | 14 | ||
261.2.k.c.82.1 | 18 | 29.16 | even | 7 | |||
261.2.k.c.226.1 | 18 | 29.20 | even | 7 | |||
2523.2.a.o.1.2 | 9 | 87.86 | odd | 2 | |||
2523.2.a.r.1.8 | 9 | 3.2 | odd | 2 | |||
7569.2.a.bj.1.2 | 9 | 1.1 | even | 1 | trivial | ||
7569.2.a.bm.1.8 | 9 | 29.28 | even | 2 |