Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.99322 | 1.40942 | 0.704708 | − | 0.709497i | \(-0.251078\pi\) | ||||
0.704708 | + | 0.709497i | \(0.251078\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.97291 | 0.986453 | ||||||||
\(5\) | −0.735105 | −0.328749 | −0.164375 | − | 0.986398i | \(-0.552561\pi\) | ||||
−0.164375 | + | 0.986398i | \(0.552561\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.83374 | −1.44902 | −0.724510 | − | 0.689265i | \(-0.757934\pi\) | ||||
−0.724510 | + | 0.689265i | \(0.757934\pi\) | |||||||
\(8\) | −0.0540029 | −0.0190929 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.46522 | −0.463344 | ||||||||
\(11\) | −0.205441 | −0.0619428 | −0.0309714 | − | 0.999520i | \(-0.509860\pi\) | ||||
−0.0309714 | + | 0.999520i | \(0.509860\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.99499 | 1.94006 | 0.970031 | − | 0.242981i | \(-0.0781253\pi\) | ||||
0.970031 | + | 0.242981i | \(0.0781253\pi\) | |||||||
\(14\) | −7.64148 | −2.04227 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.05345 | −1.01336 | ||||||||
\(17\) | −3.70930 | −0.899638 | −0.449819 | − | 0.893120i | \(-0.648511\pi\) | ||||
−0.449819 | + | 0.893120i | \(0.648511\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.87904 | 1.11933 | 0.559664 | − | 0.828720i | \(-0.310930\pi\) | ||||
0.559664 | + | 0.828720i | \(0.310930\pi\) | |||||||
\(20\) | −1.45029 | −0.324296 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.409488 | −0.0873032 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.45962 | −0.891924 | ||||||||
\(26\) | 13.9425 | 2.73435 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.56362 | −1.42939 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.25291 | 0.943450 | 0.471725 | − | 0.881746i | \(-0.343632\pi\) | ||||
0.471725 | + | 0.881746i | \(0.343632\pi\) | |||||||
\(32\) | −7.97140 | −1.40916 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.39344 | −1.26796 | ||||||||
\(35\) | 2.81821 | 0.476364 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.20377 | 0.691096 | 0.345548 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345548 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(38\) | 9.72497 | 1.57760 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0396978 | 0.00627678 | ||||||||
\(41\) | −11.5860 | −1.80942 | −0.904712 | − | 0.426023i | \(-0.859914\pi\) | ||||
−0.904712 | + | 0.426023i | \(0.859914\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.44126 | 0.982283 | 0.491141 | − | 0.871080i | \(-0.336580\pi\) | ||||
0.491141 | + | 0.871080i | \(0.336580\pi\) | |||||||
\(44\) | −0.405316 | −0.0611037 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.99322 | −0.293884 | ||||||||
\(47\) | 0.322866 | 0.0470948 | 0.0235474 | − | 0.999723i | \(-0.492504\pi\) | ||||
0.0235474 | + | 0.999723i | \(0.492504\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.69760 | 1.09966 | ||||||||
\(50\) | −8.88898 | −1.25709 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.8005 | 1.91378 | ||||||||
\(53\) | 12.4026 | 1.70362 | 0.851812 | − | 0.523847i | \(-0.175504\pi\) | ||||
0.851812 | + | 0.523847i | \(0.175504\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.151021 | 0.0203636 | ||||||||
\(56\) | 0.207033 | 0.0276660 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.99322 | 0.261722 | ||||||||
\(59\) | 8.24981 | 1.07403 | 0.537017 | − | 0.843571i | \(-0.319551\pi\) | ||||
0.537017 | + | 0.843571i | \(0.319551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3425 | 1.45226 | 0.726131 | − | 0.687556i | \(-0.241316\pi\) | ||||
0.726131 | + | 0.687556i | \(0.241316\pi\) | |||||||
\(62\) | 10.4702 | 1.32971 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.78180 | −0.972726 | ||||||||
\(65\) | −5.14206 | −0.637794 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.87929 | 0.962609 | 0.481304 | − | 0.876554i | \(-0.340163\pi\) | ||||
0.481304 | + | 0.876554i | \(0.340163\pi\) | |||||||
\(68\) | −7.31811 | −0.887451 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.61729 | 0.671395 | ||||||||
\(71\) | 8.34336 | 0.990174 | 0.495087 | − | 0.868843i | \(-0.335136\pi\) | ||||
0.495087 | + | 0.868843i | \(0.335136\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.72520 | 0.201919 | 0.100960 | − | 0.994891i | \(-0.467809\pi\) | ||||
0.100960 | + | 0.994891i | \(0.467809\pi\) | |||||||
\(74\) | 8.37902 | 0.974042 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.62589 | 1.10416 | ||||||||
\(77\) | 0.787608 | 0.0897563 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.27322 | −0.255758 | −0.127879 | − | 0.991790i | \(-0.540817\pi\) | ||||
−0.127879 | + | 0.991790i | \(0.540817\pi\) | |||||||
\(80\) | 2.97971 | 0.333142 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −23.0933 | −2.55023 | ||||||||
\(83\) | 2.31436 | 0.254034 | 0.127017 | − | 0.991901i | \(-0.459460\pi\) | ||||
0.127017 | + | 0.991901i | \(0.459460\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.72673 | 0.295755 | ||||||||
\(86\) | 12.8388 | 1.38444 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0110944 | 0.00118267 | ||||||||
\(89\) | 9.00709 | 0.954749 | 0.477375 | − | 0.878700i | \(-0.341589\pi\) | ||||
0.477375 | + | 0.878700i | \(0.341589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.8170 | −2.81119 | ||||||||
\(92\) | −1.97291 | −0.205690 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.643541 | 0.0663761 | ||||||||
\(95\) | −3.58661 | −0.367978 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.7302 | 1.59716 | 0.798580 | − | 0.601889i | \(-0.205585\pi\) | ||||
0.798580 | + | 0.601889i | \(0.205585\pi\) | |||||||
\(98\) | 15.3430 | 1.54987 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.79841 | −0.879841 | ||||||||
\(101\) | −15.1163 | −1.50413 | −0.752066 | − | 0.659087i | \(-0.770943\pi\) | ||||
−0.752066 | + | 0.659087i | \(0.770943\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.1194 | −1.88389 | −0.941944 | − | 0.335770i | \(-0.891003\pi\) | ||||
−0.941944 | + | 0.335770i | \(0.891003\pi\) | |||||||
\(104\) | −0.377750 | −0.0370414 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.7210 | 2.40112 | ||||||||
\(107\) | 4.51704 | 0.436679 | 0.218339 | − | 0.975873i | \(-0.429936\pi\) | ||||
0.218339 | + | 0.975873i | \(0.429936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.24986 | −0.119715 | −0.0598573 | − | 0.998207i | \(-0.519065\pi\) | ||||
−0.0598573 | + | 0.998207i | \(0.519065\pi\) | |||||||
\(110\) | 0.301017 | 0.0287008 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15.5399 | 1.46838 | ||||||||
\(113\) | 1.73750 | 0.163450 | 0.0817252 | − | 0.996655i | \(-0.473957\pi\) | ||||
0.0817252 | + | 0.996655i | \(0.473957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.735105 | 0.0685489 | ||||||||
\(116\) | 1.97291 | 0.183180 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.4437 | 1.51376 | ||||||||
\(119\) | 14.2205 | 1.30359 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9578 | −0.996163 | ||||||||
\(122\) | 22.6081 | 2.04684 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.3635 | 0.930669 | ||||||||
\(125\) | 6.95382 | 0.621968 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.77512 | −0.689930 | −0.344965 | − | 0.938615i | \(-0.612109\pi\) | ||||
−0.344965 | + | 0.938615i | \(0.612109\pi\) | |||||||
\(128\) | 0.431984 | 0.0381823 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.2492 | −0.898916 | ||||||||
\(131\) | −7.77889 | −0.679645 | −0.339822 | − | 0.940490i | \(-0.610367\pi\) | ||||
−0.339822 | + | 0.940490i | \(0.610367\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.7050 | −1.62193 | ||||||||
\(134\) | 15.7051 | 1.35672 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.200313 | 0.0171767 | ||||||||
\(137\) | 21.8734 | 1.86877 | 0.934383 | − | 0.356269i | \(-0.115951\pi\) | ||||
0.934383 | + | 0.356269i | \(0.115951\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.10387 | 0.178448 | 0.0892239 | − | 0.996012i | \(-0.471561\pi\) | ||||
0.0892239 | + | 0.996012i | \(0.471561\pi\) | |||||||
\(140\) | 5.56006 | 0.469911 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.6301 | 1.39557 | ||||||||
\(143\) | −1.43706 | −0.120173 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.735105 | −0.0610472 | ||||||||
\(146\) | 3.43870 | 0.284589 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.29365 | 0.681734 | ||||||||
\(149\) | −2.90681 | −0.238135 | −0.119067 | − | 0.992886i | \(-0.537990\pi\) | ||||
−0.119067 | + | 0.992886i | \(0.537990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7679 | 1.20179 | 0.600896 | − | 0.799327i | \(-0.294811\pi\) | ||||
0.600896 | + | 0.799327i | \(0.294811\pi\) | |||||||
\(152\) | −0.263482 | −0.0213712 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.56987 | 0.126504 | ||||||||
\(155\) | −3.86144 | −0.310158 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.71893 | −0.296803 | −0.148401 | − | 0.988927i | \(-0.547413\pi\) | ||||
−0.148401 | + | 0.988927i | \(0.547413\pi\) | |||||||
\(158\) | −4.53102 | −0.360469 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.85982 | 0.463259 | ||||||||
\(161\) | 3.83374 | 0.302141 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.3418 | 1.74994 | 0.874972 | − | 0.484173i | \(-0.160880\pi\) | ||||
0.874972 | + | 0.484173i | \(0.160880\pi\) | |||||||
\(164\) | −22.8580 | −1.78491 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.61302 | 0.358040 | ||||||||
\(167\) | −10.6214 | −0.821910 | −0.410955 | − | 0.911656i | \(-0.634805\pi\) | ||||
−0.410955 | + | 0.911656i | \(0.634805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.9299 | 2.76384 | ||||||||
\(170\) | 5.43495 | 0.416842 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.7080 | 0.968976 | ||||||||
\(173\) | 2.93433 | 0.223093 | 0.111546 | − | 0.993759i | \(-0.464420\pi\) | ||||
0.111546 | + | 0.993759i | \(0.464420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.0970 | 1.29242 | ||||||||
\(176\) | 0.832746 | 0.0627706 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.9531 | 1.34564 | ||||||||
\(179\) | 9.64171 | 0.720655 | 0.360328 | − | 0.932826i | \(-0.382665\pi\) | ||||
0.360328 | + | 0.932826i | \(0.382665\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7004 | 0.795355 | 0.397678 | − | 0.917525i | \(-0.369816\pi\) | ||||
0.397678 | + | 0.917525i | \(0.369816\pi\) | |||||||
\(182\) | −53.4521 | −3.96213 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.0540029 | 0.00398115 | ||||||||
\(185\) | −3.09022 | −0.227197 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.762043 | 0.0557261 | ||||||||
\(188\) | 0.636984 | 0.0464568 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.14888 | −0.518634 | ||||||||
\(191\) | 17.0137 | 1.23107 | 0.615536 | − | 0.788109i | \(-0.288940\pi\) | ||||
0.615536 | + | 0.788109i | \(0.288940\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.184988 | −0.0133157 | −0.00665786 | − | 0.999978i | \(-0.502119\pi\) | ||||
−0.00665786 | + | 0.999978i | \(0.502119\pi\) | |||||||
\(194\) | 31.3537 | 2.25106 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.1866 | 1.08476 | ||||||||
\(197\) | −27.5520 | −1.96300 | −0.981500 | − | 0.191461i | \(-0.938678\pi\) | ||||
−0.981500 | + | 0.191461i | \(0.938678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.23085 | 0.654358 | 0.327179 | − | 0.944962i | \(-0.393902\pi\) | ||||
0.327179 | + | 0.944962i | \(0.393902\pi\) | |||||||
\(200\) | 0.240832 | 0.0170294 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −30.1301 | −2.11995 | ||||||||
\(203\) | −3.83374 | −0.269076 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.51691 | 0.594847 | ||||||||
\(206\) | −38.1090 | −2.65518 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −28.3539 | −1.96599 | ||||||||
\(209\) | −1.00235 | −0.0693343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5991 | −1.07388 | −0.536941 | − | 0.843619i | \(-0.680420\pi\) | ||||
−0.536941 | + | 0.843619i | \(0.680420\pi\) | |||||||
\(212\) | 24.4691 | 1.68055 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.00344 | 0.615462 | ||||||||
\(215\) | −4.73500 | −0.322924 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.1383 | −1.36708 | ||||||||
\(218\) | −2.49123 | −0.168728 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.297950 | 0.0200878 | ||||||||
\(221\) | −25.9465 | −1.74535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.52483 | 0.503900 | 0.251950 | − | 0.967740i | \(-0.418928\pi\) | ||||
0.251950 | + | 0.967740i | \(0.418928\pi\) | |||||||
\(224\) | 30.5603 | 2.04190 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.46321 | 0.230370 | ||||||||
\(227\) | 11.5656 | 0.767635 | 0.383818 | − | 0.923409i | \(-0.374609\pi\) | ||||
0.383818 | + | 0.923409i | \(0.374609\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.91669 | −0.324904 | −0.162452 | − | 0.986716i | \(-0.551940\pi\) | ||||
−0.162452 | + | 0.986716i | \(0.551940\pi\) | |||||||
\(230\) | 1.46522 | 0.0966139 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.0540029 | −0.00354546 | ||||||||
\(233\) | −4.86391 | −0.318645 | −0.159323 | − | 0.987227i | \(-0.550931\pi\) | ||||
−0.159323 | + | 0.987227i | \(0.550931\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.237340 | −0.0154824 | ||||||||
\(236\) | 16.2761 | 1.05948 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 28.3445 | 1.83730 | ||||||||
\(239\) | 13.1237 | 0.848899 | 0.424450 | − | 0.905452i | \(-0.360468\pi\) | ||||
0.424450 | + | 0.905452i | \(0.360468\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.35922 | −0.474049 | −0.237025 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237025 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(242\) | −21.8412 | −1.40401 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.3778 | 1.43259 | ||||||||
\(245\) | −5.65854 | −0.361511 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.1288 | 2.17157 | ||||||||
\(248\) | −0.283672 | −0.0180132 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.8605 | 0.876612 | ||||||||
\(251\) | 7.85155 | 0.495585 | 0.247793 | − | 0.968813i | \(-0.420295\pi\) | ||||
0.247793 | + | 0.968813i | \(0.420295\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.205441 | 0.0129160 | ||||||||
\(254\) | −15.4975 | −0.972399 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.4246 | 1.02654 | ||||||||
\(257\) | −4.43790 | −0.276829 | −0.138414 | − | 0.990374i | \(-0.544201\pi\) | ||||
−0.138414 | + | 0.990374i | \(0.544201\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.1162 | −1.00141 | ||||||||
\(260\) | −10.1448 | −0.629154 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.5050 | −0.957902 | ||||||||
\(263\) | −23.1392 | −1.42682 | −0.713411 | − | 0.700746i | \(-0.752851\pi\) | ||||
−0.713411 | + | 0.700746i | \(0.752851\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.11720 | −0.560065 | ||||||||
\(266\) | −37.2831 | −2.28597 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.5451 | 0.949568 | ||||||||
\(269\) | 19.1142 | 1.16541 | 0.582706 | − | 0.812683i | \(-0.301994\pi\) | ||||
0.582706 | + | 0.812683i | \(0.301994\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.26721 | 0.380706 | 0.190353 | − | 0.981716i | \(-0.439037\pi\) | ||||
0.190353 | + | 0.981716i | \(0.439037\pi\) | |||||||
\(272\) | 15.0355 | 0.911660 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 43.5983 | 2.63387 | ||||||||
\(275\) | 0.916189 | 0.0552483 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.29983 | −0.438604 | −0.219302 | − | 0.975657i | \(-0.570378\pi\) | ||||
−0.219302 | + | 0.975657i | \(0.570378\pi\) | |||||||
\(278\) | 4.19346 | 0.251507 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.152191 | −0.00909517 | ||||||||
\(281\) | 8.88233 | 0.529875 | 0.264938 | − | 0.964266i | \(-0.414649\pi\) | ||||
0.264938 | + | 0.964266i | \(0.414649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.70543 | −0.458040 | −0.229020 | − | 0.973422i | \(-0.573552\pi\) | ||||
−0.229020 | + | 0.973422i | \(0.573552\pi\) | |||||||
\(284\) | 16.4607 | 0.976761 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.86437 | −0.169374 | ||||||||
\(287\) | 44.4177 | 2.62189 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.24108 | −0.190652 | ||||||||
\(290\) | −1.46522 | −0.0860409 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.40366 | 0.199184 | ||||||||
\(293\) | 0.218722 | 0.0127779 | 0.00638894 | − | 0.999980i | \(-0.497966\pi\) | ||||
0.00638894 | + | 0.999980i | \(0.497966\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.06448 | −0.353088 | ||||||||
\(296\) | −0.227016 | −0.0131950 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.79389 | −0.335631 | ||||||||
\(299\) | −6.99499 | −0.404531 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.6941 | −1.42335 | ||||||||
\(302\) | 29.4355 | 1.69382 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −19.7769 | −1.13429 | ||||||||
\(305\) | −8.33796 | −0.477430 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.1831 | −1.66557 | −0.832784 | − | 0.553598i | \(-0.813255\pi\) | ||||
−0.832784 | + | 0.553598i | \(0.813255\pi\) | |||||||
\(308\) | 1.55388 | 0.0885404 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.69668 | −0.437142 | ||||||||
\(311\) | −18.9236 | −1.07306 | −0.536528 | − | 0.843882i | \(-0.680265\pi\) | ||||
−0.536528 | + | 0.843882i | \(0.680265\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.13022 | 0.346500 | 0.173250 | − | 0.984878i | \(-0.444573\pi\) | ||||
0.173250 | + | 0.984878i | \(0.444573\pi\) | |||||||
\(314\) | −7.41262 | −0.418319 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.48486 | −0.252293 | ||||||||
\(317\) | −16.3437 | −0.917953 | −0.458976 | − | 0.888448i | \(-0.651784\pi\) | ||||
−0.458976 | + | 0.888448i | \(0.651784\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.205441 | −0.0115025 | ||||||||
\(320\) | 5.72045 | 0.319783 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.64148 | 0.425843 | ||||||||
\(323\) | −18.0978 | −1.00699 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −31.1950 | −1.73039 | ||||||||
\(326\) | 44.5320 | 2.46640 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.625676 | 0.0345472 | ||||||||
\(329\) | −1.23778 | −0.0682412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5579 | −0.855139 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(332\) | 4.56602 | 0.250593 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −21.1708 | −1.15841 | ||||||||
\(335\) | −5.79211 | −0.316457 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.7973 | 1.62316 | 0.811580 | − | 0.584241i | \(-0.198608\pi\) | ||||
0.811580 | + | 0.584241i | \(0.198608\pi\) | |||||||
\(338\) | 71.6161 | 3.89540 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.37958 | 0.291749 | ||||||||
\(341\) | −1.07916 | −0.0584399 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.67440 | −0.144404 | ||||||||
\(344\) | −0.347847 | −0.0187546 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.84875 | 0.314431 | ||||||||
\(347\) | −22.5165 | −1.20875 | −0.604374 | − | 0.796701i | \(-0.706577\pi\) | ||||
−0.604374 | + | 0.796701i | \(0.706577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.53805 | 0.0823298 | 0.0411649 | − | 0.999152i | \(-0.486893\pi\) | ||||
0.0411649 | + | 0.999152i | \(0.486893\pi\) | |||||||
\(350\) | 34.0781 | 1.82155 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.63765 | 0.0872872 | ||||||||
\(353\) | 15.1412 | 0.805883 | 0.402942 | − | 0.915226i | \(-0.367988\pi\) | ||||
0.402942 | + | 0.915226i | \(0.367988\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.13325 | −0.325519 | ||||||||
\(356\) | 17.7701 | 0.941815 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.2180 | 1.01570 | ||||||||
\(359\) | −7.91870 | −0.417933 | −0.208966 | − | 0.977923i | \(-0.567010\pi\) | ||||
−0.208966 | + | 0.977923i | \(0.567010\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.80501 | 0.252895 | ||||||||
\(362\) | 21.3282 | 1.12099 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −52.9075 | −2.77310 | ||||||||
\(365\) | −1.26820 | −0.0663808 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.7861 | −1.71142 | −0.855709 | − | 0.517457i | \(-0.826879\pi\) | ||||
−0.855709 | + | 0.517457i | \(0.826879\pi\) | |||||||
\(368\) | 4.05345 | 0.211301 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.15946 | −0.320215 | ||||||||
\(371\) | −47.5483 | −2.46858 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.5365 | 1.01156 | 0.505780 | − | 0.862662i | \(-0.331205\pi\) | ||||
0.505780 | + | 0.862662i | \(0.331205\pi\) | |||||||
\(374\) | 1.51892 | 0.0785412 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0174357 | −0.000899177 0 | ||||||||
\(377\) | 6.99499 | 0.360260 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.2511 | −0.937494 | −0.468747 | − | 0.883332i | \(-0.655294\pi\) | ||||
−0.468747 | + | 0.883332i | \(0.655294\pi\) | |||||||
\(380\) | −7.07604 | −0.362993 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 33.9121 | 1.73509 | ||||||||
\(383\) | −15.1886 | −0.776103 | −0.388052 | − | 0.921638i | \(-0.626852\pi\) | ||||
−0.388052 | + | 0.921638i | \(0.626852\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.578975 | −0.0295073 | ||||||||
\(386\) | −0.368721 | −0.0187674 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 31.0342 | 1.57552 | ||||||||
\(389\) | 24.2781 | 1.23095 | 0.615474 | − | 0.788158i | \(-0.288965\pi\) | ||||
0.615474 | + | 0.788158i | \(0.288965\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.70930 | 0.187587 | ||||||||
\(392\) | −0.415693 | −0.0209956 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −54.9171 | −2.76668 | ||||||||
\(395\) | 1.67106 | 0.0840801 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.3709 | 1.27333 | 0.636665 | − | 0.771141i | \(-0.280314\pi\) | ||||
0.636665 | + | 0.771141i | \(0.280314\pi\) | |||||||
\(398\) | 18.3991 | 0.922262 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.0769 | 0.903843 | ||||||||
\(401\) | 16.2577 | 0.811873 | 0.405936 | − | 0.913901i | \(-0.366945\pi\) | ||||
0.405936 | + | 0.913901i | \(0.366945\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.7440 | 1.83035 | ||||||||
\(404\) | −29.8231 | −1.48376 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.64148 | −0.379240 | ||||||||
\(407\) | −0.863627 | −0.0428084 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.6830 | 0.627136 | 0.313568 | − | 0.949566i | \(-0.398476\pi\) | ||||
0.313568 | + | 0.949566i | \(0.398476\pi\) | |||||||
\(410\) | 16.9760 | 0.838387 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −37.7207 | −1.85837 | ||||||||
\(413\) | −31.6277 | −1.55630 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.70130 | −0.0835136 | ||||||||
\(416\) | −55.7599 | −2.73385 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.99791 | −0.0977209 | ||||||||
\(419\) | 1.53634 | 0.0750553 | 0.0375277 | − | 0.999296i | \(-0.488052\pi\) | ||||
0.0375277 | + | 0.999296i | \(0.488052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.8697 | 1.21207 | 0.606037 | − | 0.795437i | \(-0.292758\pi\) | ||||
0.606037 | + | 0.795437i | \(0.292758\pi\) | |||||||
\(422\) | −31.0923 | −1.51355 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.669775 | −0.0325272 | ||||||||
\(425\) | 16.5421 | 0.802409 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43.4844 | −2.10436 | ||||||||
\(428\) | 8.91170 | 0.430763 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.43788 | −0.455135 | ||||||||
\(431\) | −34.5459 | −1.66402 | −0.832008 | − | 0.554763i | \(-0.812809\pi\) | ||||
−0.832008 | + | 0.554763i | \(0.812809\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.9295 | 1.91889 | 0.959444 | − | 0.281898i | \(-0.0909641\pi\) | ||||
0.959444 | + | 0.281898i | \(0.0909641\pi\) | |||||||
\(434\) | −40.1400 | −1.92678 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.46585 | −0.118093 | ||||||||
\(437\) | −4.87904 | −0.233396 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.95513 | −0.188768 | −0.0943841 | − | 0.995536i | \(-0.530088\pi\) | ||||
−0.0943841 | + | 0.995536i | \(0.530088\pi\) | |||||||
\(440\) | −0.00815556 | −0.000388801 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −51.7170 | −2.45993 | ||||||||
\(443\) | −2.46202 | −0.116974 | −0.0584871 | − | 0.998288i | \(-0.518628\pi\) | ||||
−0.0584871 | + | 0.998288i | \(0.518628\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.62116 | −0.313873 | ||||||||
\(446\) | 14.9986 | 0.710204 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 29.8334 | 1.40950 | ||||||||
\(449\) | 19.4807 | 0.919349 | 0.459675 | − | 0.888087i | \(-0.347966\pi\) | ||||
0.459675 | + | 0.888087i | \(0.347966\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.38023 | 0.112081 | ||||||||
\(452\) | 3.42793 | 0.161236 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23.0527 | 1.08192 | ||||||||
\(455\) | 19.7133 | 0.924175 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.32011 | 0.155308 | 0.0776541 | − | 0.996980i | \(-0.475257\pi\) | ||||
0.0776541 | + | 0.996980i | \(0.475257\pi\) | |||||||
\(458\) | −9.80002 | −0.457925 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.45029 | 0.0676203 | ||||||||
\(461\) | −16.9011 | −0.787162 | −0.393581 | − | 0.919290i | \(-0.628764\pi\) | ||||
−0.393581 | + | 0.919290i | \(0.628764\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.3580 | −1.41086 | −0.705429 | − | 0.708781i | \(-0.749246\pi\) | ||||
−0.705429 | + | 0.708781i | \(0.749246\pi\) | |||||||
\(464\) | −4.05345 | −0.188177 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.69482 | −0.449104 | ||||||||
\(467\) | 7.99095 | 0.369777 | 0.184888 | − | 0.982760i | \(-0.440808\pi\) | ||||
0.184888 | + | 0.982760i | \(0.440808\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.2072 | −1.39484 | ||||||||
\(470\) | −0.473070 | −0.0218211 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.445514 | −0.0205064 | ||||||||
\(473\) | −1.32330 | −0.0608453 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.7587 | −0.998356 | ||||||||
\(476\) | 28.0557 | 1.28593 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.1583 | 1.19645 | ||||||||
\(479\) | 7.02146 | 0.320819 | 0.160409 | − | 0.987051i | \(-0.448719\pi\) | ||||
0.160409 | + | 0.987051i | \(0.448719\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.4054 | 1.34077 | ||||||||
\(482\) | −14.6685 | −0.668132 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.6187 | −0.982668 | ||||||||
\(485\) | −11.5634 | −0.525065 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.5212 | 1.38305 | 0.691524 | − | 0.722353i | \(-0.256940\pi\) | ||||
0.691524 | + | 0.722353i | \(0.256940\pi\) | |||||||
\(488\) | −0.612530 | −0.0277279 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.2787 | −0.509519 | ||||||||
\(491\) | −38.6997 | −1.74649 | −0.873245 | − | 0.487281i | \(-0.837989\pi\) | ||||
−0.873245 | + | 0.487281i | \(0.837989\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.70930 | −0.167059 | ||||||||
\(494\) | 68.0261 | 3.06064 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.2924 | −0.956057 | ||||||||
\(497\) | −31.9863 | −1.43478 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.85466 | −0.217325 | −0.108662 | − | 0.994079i | \(-0.534657\pi\) | ||||
−0.108662 | + | 0.994079i | \(0.534657\pi\) | |||||||
\(500\) | 13.7192 | 0.613543 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.6498 | 0.698486 | ||||||||
\(503\) | −22.5078 | −1.00357 | −0.501786 | − | 0.864992i | \(-0.667324\pi\) | ||||
−0.501786 | + | 0.864992i | \(0.667324\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.1121 | 0.494482 | ||||||||
\(506\) | 0.409488 | 0.0182040 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.3396 | −0.680584 | ||||||||
\(509\) | −39.7724 | −1.76288 | −0.881441 | − | 0.472294i | \(-0.843426\pi\) | ||||
−0.881441 | + | 0.472294i | \(0.843426\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.61398 | −0.292585 | ||||||||
\(512\) | 31.8739 | 1.40864 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.84570 | −0.390167 | ||||||||
\(515\) | 14.0548 | 0.619326 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0663298 | −0.00291718 | ||||||||
\(518\) | −32.1230 | −1.41141 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.277686 | 0.0121773 | ||||||||
\(521\) | −18.9327 | −0.829458 | −0.414729 | − | 0.909945i | \(-0.636124\pi\) | ||||
−0.414729 | + | 0.909945i | \(0.636124\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.97995 | −0.174031 | −0.0870155 | − | 0.996207i | \(-0.527733\pi\) | ||||
−0.0870155 | + | 0.996207i | \(0.527733\pi\) | |||||||
\(524\) | −15.3470 | −0.670438 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −46.1213 | −2.01099 | ||||||||
\(527\) | −19.4846 | −0.848763 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −18.1725 | −0.789364 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −36.9032 | −1.59996 | ||||||||
\(533\) | −81.0438 | −3.51040 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.32050 | −0.143558 | ||||||||
\(536\) | −0.425505 | −0.0183790 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 38.0987 | 1.64255 | ||||||||
\(539\) | −1.58140 | −0.0681158 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1909 | 0.567123 | 0.283561 | − | 0.958954i | \(-0.408484\pi\) | ||||
0.283561 | + | 0.958954i | \(0.408484\pi\) | |||||||
\(542\) | 12.4919 | 0.536573 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 29.5683 | 1.26773 | ||||||||
\(545\) | 0.918777 | 0.0393561 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.0821 | −1.15795 | −0.578974 | − | 0.815346i | \(-0.696547\pi\) | ||||
−0.578974 | + | 0.815346i | \(0.696547\pi\) | |||||||
\(548\) | 43.1541 | 1.84345 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.82616 | 0.0778678 | ||||||||
\(551\) | 4.87904 | 0.207854 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.71496 | 0.370598 | ||||||||
\(554\) | −14.5501 | −0.618175 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.15074 | 0.176030 | ||||||||
\(557\) | 16.5268 | 0.700263 | 0.350131 | − | 0.936701i | \(-0.386137\pi\) | ||||
0.350131 | + | 0.936701i | \(0.386137\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.0565 | 1.90569 | ||||||||
\(560\) | −11.4235 | −0.482729 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.7044 | 0.746815 | ||||||||
\(563\) | −19.3926 | −0.817302 | −0.408651 | − | 0.912691i | \(-0.634001\pi\) | ||||
−0.408651 | + | 0.912691i | \(0.634001\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.27725 | −0.0537342 | ||||||||
\(566\) | −15.3586 | −0.645569 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.450566 | −0.0189053 | ||||||||
\(569\) | 37.0098 | 1.55153 | 0.775766 | − | 0.631020i | \(-0.217364\pi\) | ||||
0.775766 | + | 0.631020i | \(0.217364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9624 | −1.00279 | −0.501397 | − | 0.865217i | \(-0.667180\pi\) | ||||
−0.501397 | + | 0.865217i | \(0.667180\pi\) | |||||||
\(572\) | −2.83518 | −0.118545 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 88.5339 | 3.69534 | ||||||||
\(575\) | 4.45962 | 0.185979 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.93076 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(578\) | −6.46017 | −0.268707 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.45029 | −0.0602202 | ||||||||
\(581\) | −8.87268 | −0.368101 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.54800 | −0.105527 | ||||||||
\(584\) | −0.0931659 | −0.00385523 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.435960 | 0.0180094 | ||||||||
\(587\) | 42.7864 | 1.76599 | 0.882993 | − | 0.469387i | \(-0.155525\pi\) | ||||
0.882993 | + | 0.469387i | \(0.155525\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.6291 | 1.05603 | ||||||||
\(590\) | −12.0878 | −0.497648 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.0398 | −0.700331 | ||||||||
\(593\) | −27.1472 | −1.11480 | −0.557401 | − | 0.830244i | \(-0.688201\pi\) | ||||
−0.557401 | + | 0.830244i | \(0.688201\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4536 | −0.428555 | ||||||||
\(596\) | −5.73486 | −0.234909 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.9425 | −0.570152 | ||||||||
\(599\) | 29.0030 | 1.18503 | 0.592514 | − | 0.805560i | \(-0.298135\pi\) | ||||
0.592514 | + | 0.805560i | \(0.298135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5526 | 0.756778 | 0.378389 | − | 0.925647i | \(-0.376478\pi\) | ||||
0.378389 | + | 0.925647i | \(0.376478\pi\) | |||||||
\(602\) | −49.2207 | −2.00609 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 29.1356 | 1.18551 | ||||||||
\(605\) | 8.05513 | 0.327488 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.8252 | −0.561149 | −0.280575 | − | 0.959832i | \(-0.590525\pi\) | ||||
−0.280575 | + | 0.959832i | \(0.590525\pi\) | |||||||
\(608\) | −38.8928 | −1.57731 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.6193 | −0.672898 | ||||||||
\(611\) | 2.25844 | 0.0913668 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.3288 | 1.02302 | 0.511510 | − | 0.859277i | \(-0.329086\pi\) | ||||
0.511510 | + | 0.859277i | \(0.329086\pi\) | |||||||
\(614\) | −58.1682 | −2.34748 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0425331 | −0.00171371 | ||||||||
\(617\) | −37.9401 | −1.52741 | −0.763705 | − | 0.645565i | \(-0.776622\pi\) | ||||
−0.763705 | + | 0.645565i | \(0.776622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.1030 | 0.808006 | 0.404003 | − | 0.914758i | \(-0.367619\pi\) | ||||
0.404003 | + | 0.914758i | \(0.367619\pi\) | |||||||
\(620\) | −7.61826 | −0.305957 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −37.7187 | −1.51238 | ||||||||
\(623\) | −34.5309 | −1.38345 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.1863 | 0.687453 | ||||||||
\(626\) | 12.2188 | 0.488363 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.33710 | −0.292782 | ||||||||
\(629\) | −15.5931 | −0.621736 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.8881 | −1.18983 | −0.594913 | − | 0.803790i | \(-0.702814\pi\) | ||||
−0.594913 | + | 0.803790i | \(0.702814\pi\) | |||||||
\(632\) | 0.122761 | 0.00488316 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −32.5765 | −1.29378 | ||||||||
\(635\) | 5.71553 | 0.226814 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 53.8446 | 2.13340 | ||||||||
\(638\) | −0.409488 | −0.0162118 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.317553 | −0.0125524 | ||||||||
\(641\) | −29.4363 | −1.16267 | −0.581333 | − | 0.813666i | \(-0.697468\pi\) | ||||
−0.581333 | + | 0.813666i | \(0.697468\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.7604 | −0.542659 | −0.271329 | − | 0.962487i | \(-0.587463\pi\) | ||||
−0.271329 | + | 0.962487i | \(0.587463\pi\) | |||||||
\(644\) | 7.56362 | 0.298048 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36.0729 | −1.41927 | ||||||||
\(647\) | −16.6878 | −0.656067 | −0.328034 | − | 0.944666i | \(-0.606386\pi\) | ||||
−0.328034 | + | 0.944666i | \(0.606386\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.69485 | −0.0665287 | ||||||||
\(650\) | −62.1784 | −2.43884 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 44.0783 | 1.72624 | ||||||||
\(653\) | 6.84989 | 0.268057 | 0.134028 | − | 0.990977i | \(-0.457209\pi\) | ||||
0.134028 | + | 0.990977i | \(0.457209\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.71830 | 0.223433 | ||||||||
\(656\) | 46.9632 | 1.83360 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.46717 | −0.0961803 | ||||||||
\(659\) | −38.8758 | −1.51439 | −0.757193 | − | 0.653191i | \(-0.773430\pi\) | ||||
−0.757193 | + | 0.653191i | \(0.773430\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.4123 | −0.793947 | −0.396974 | − | 0.917830i | \(-0.629940\pi\) | ||||
−0.396974 | + | 0.917830i | \(0.629940\pi\) | |||||||
\(662\) | −31.0102 | −1.20525 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.124982 | −0.00485026 | ||||||||
\(665\) | 13.7501 | 0.533207 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −20.9551 | −0.810775 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.5449 | −0.446019 | ||||||||
\(671\) | −2.33022 | −0.0899572 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0139 | 0.771479 | 0.385739 | − | 0.922608i | \(-0.373946\pi\) | ||||
0.385739 | + | 0.922608i | \(0.373946\pi\) | |||||||
\(674\) | 59.3924 | 2.28771 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 70.8864 | 2.72640 | ||||||||
\(677\) | −5.46125 | −0.209893 | −0.104946 | − | 0.994478i | \(-0.533467\pi\) | ||||
−0.104946 | + | 0.994478i | \(0.533467\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −60.3056 | −2.31432 | ||||||||
\(680\) | −0.147251 | −0.00564683 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.15100 | −0.0823661 | ||||||||
\(683\) | 26.5878 | 1.01735 | 0.508677 | − | 0.860957i | \(-0.330135\pi\) | ||||
0.508677 | + | 0.860957i | \(0.330135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.0792 | −0.614355 | ||||||||
\(686\) | −5.33066 | −0.203525 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.1093 | −0.995409 | ||||||||
\(689\) | 86.7559 | 3.30514 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.3723 | 1.57388 | 0.786939 | − | 0.617031i | \(-0.211665\pi\) | ||||
0.786939 | + | 0.617031i | \(0.211665\pi\) | |||||||
\(692\) | 5.78916 | 0.220071 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −44.8802 | −1.70363 | ||||||||
\(695\) | −1.54656 | −0.0586645 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.9759 | 1.62783 | ||||||||
\(698\) | 3.06566 | 0.116037 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 33.7309 | 1.27491 | ||||||||
\(701\) | −47.6825 | −1.80094 | −0.900472 | − | 0.434915i | \(-0.856779\pi\) | ||||
−0.900472 | + | 0.434915i | \(0.856779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.5104 | 0.773563 | ||||||||
\(704\) | 1.59870 | 0.0602533 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.1796 | 1.13582 | ||||||||
\(707\) | 57.9522 | 2.17952 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.7799 | −1.11841 | −0.559203 | − | 0.829030i | \(-0.688893\pi\) | ||||
−0.559203 | + | 0.829030i | \(0.688893\pi\) | |||||||
\(710\) | −12.2249 | −0.458792 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.486409 | −0.0182289 | ||||||||
\(713\) | −5.25291 | −0.196723 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.05639 | 0.0395067 | ||||||||
\(716\) | 19.0222 | 0.710893 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.7837 | −0.589041 | ||||||||
\(719\) | 36.0592 | 1.34478 | 0.672390 | − | 0.740197i | \(-0.265268\pi\) | ||||
0.672390 | + | 0.740197i | \(0.265268\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 73.2988 | 2.72979 | ||||||||
\(722\) | 9.57742 | 0.356435 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.1109 | 0.784581 | ||||||||
\(725\) | −4.45962 | −0.165626 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.1159 | −1.33947 | −0.669733 | − | 0.742602i | \(-0.733591\pi\) | ||||
−0.669733 | + | 0.742602i | \(0.733591\pi\) | |||||||
\(728\) | 1.44820 | 0.0536737 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.52780 | −0.0935582 | ||||||||
\(731\) | −23.8926 | −0.883699 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.7470 | 1.24647 | 0.623237 | − | 0.782033i | \(-0.285817\pi\) | ||||
0.623237 | + | 0.782033i | \(0.285817\pi\) | |||||||
\(734\) | −65.3497 | −2.41210 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.97140 | 0.293830 | ||||||||
\(737\) | −1.61873 | −0.0596267 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.8229 | −0.582055 | −0.291028 | − | 0.956715i | \(-0.593997\pi\) | ||||
−0.291028 | + | 0.956715i | \(0.593997\pi\) | |||||||
\(740\) | −6.09671 | −0.224119 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −94.7740 | −3.47926 | ||||||||
\(743\) | −32.1252 | −1.17856 | −0.589279 | − | 0.807930i | \(-0.700588\pi\) | ||||
−0.589279 | + | 0.807930i | \(0.700588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.13681 | 0.0782866 | ||||||||
\(746\) | 38.9404 | 1.42571 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.50344 | 0.0549712 | ||||||||
\(749\) | −17.3172 | −0.632756 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.88696 | 0.360780 | 0.180390 | − | 0.983595i | \(-0.442264\pi\) | ||||
0.180390 | + | 0.983595i | \(0.442264\pi\) | |||||||
\(752\) | −1.30872 | −0.0477241 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.9425 | 0.507757 | ||||||||
\(755\) | −10.8559 | −0.395088 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.9982 | 1.92625 | 0.963126 | − | 0.269050i | \(-0.0867095\pi\) | ||||
0.963126 | + | 0.269050i | \(0.0867095\pi\) | |||||||
\(758\) | −36.3783 | −1.32132 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.193687 | 0.00702577 | ||||||||
\(761\) | 35.1393 | 1.27380 | 0.636900 | − | 0.770946i | \(-0.280216\pi\) | ||||
0.636900 | + | 0.770946i | \(0.280216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.79163 | 0.173469 | ||||||||
\(764\) | 33.5665 | 1.21439 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.2742 | −1.09385 | ||||||||
\(767\) | 57.7074 | 2.08369 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.2896 | −0.803784 | −0.401892 | − | 0.915687i | \(-0.631647\pi\) | ||||
−0.401892 | + | 0.915687i | \(0.631647\pi\) | |||||||
\(770\) | −1.15402 | −0.0415881 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.364964 | −0.0131353 | ||||||||
\(773\) | −20.5040 | −0.737479 | −0.368740 | − | 0.929533i | \(-0.620211\pi\) | ||||
−0.368740 | + | 0.929533i | \(0.620211\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.4260 | −0.841485 | ||||||||
\(776\) | −0.849477 | −0.0304944 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 48.3914 | 1.73492 | ||||||||
\(779\) | −56.5284 | −2.02534 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.71407 | −0.0613342 | ||||||||
\(782\) | 7.39344 | 0.264389 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −31.2018 | −1.11435 | ||||||||
\(785\) | 2.73380 | 0.0975736 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.2891 | 0.723227 | 0.361613 | − | 0.932328i | \(-0.382226\pi\) | ||||
0.361613 | + | 0.932328i | \(0.382226\pi\) | |||||||
\(788\) | −54.3576 | −1.93641 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.33078 | 0.118504 | ||||||||
\(791\) | −6.66114 | −0.236843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 79.3410 | 2.81748 | ||||||||
\(794\) | 50.5697 | 1.79465 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.2116 | 0.645493 | ||||||||
\(797\) | 33.8001 | 1.19726 | 0.598630 | − | 0.801025i | \(-0.295712\pi\) | ||||
0.598630 | + | 0.801025i | \(0.295712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.19761 | −0.0423683 | ||||||||
\(800\) | 35.5494 | 1.25686 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 32.4052 | 1.14427 | ||||||||
\(803\) | −0.354427 | −0.0125075 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.81821 | −0.0993287 | ||||||||
\(806\) | 73.2388 | 2.57973 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.816327 | 0.0287183 | ||||||||
\(809\) | −15.1078 | −0.531163 | −0.265582 | − | 0.964088i | \(-0.585564\pi\) | ||||
−0.265582 | + | 0.964088i | \(0.585564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.9409 | −0.419300 | −0.209650 | − | 0.977776i | \(-0.567232\pi\) | ||||
−0.209650 | + | 0.977776i | \(0.567232\pi\) | |||||||
\(812\) | −7.56362 | −0.265431 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.72140 | −0.0603349 | ||||||||
\(815\) | −16.4236 | −0.575292 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.4271 | 1.09950 | ||||||||
\(818\) | 25.2800 | 0.883896 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.8031 | 0.586789 | ||||||||
\(821\) | 33.0975 | 1.15511 | 0.577555 | − | 0.816352i | \(-0.304007\pi\) | ||||
0.577555 | + | 0.816352i | \(0.304007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.7692 | 1.94399 | 0.971997 | − | 0.234994i | \(-0.0755071\pi\) | ||||
0.971997 | + | 0.234994i | \(0.0755071\pi\) | |||||||
\(824\) | 1.03250 | 0.0359689 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −63.0408 | −2.19347 | ||||||||
\(827\) | −26.6159 | −0.925524 | −0.462762 | − | 0.886483i | \(-0.653142\pi\) | ||||
−0.462762 | + | 0.886483i | \(0.653142\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.3734 | 0.638133 | 0.319066 | − | 0.947732i | \(-0.396631\pi\) | ||||
0.319066 | + | 0.947732i | \(0.396631\pi\) | |||||||
\(830\) | −3.39106 | −0.117705 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −54.4337 | −1.88715 | ||||||||
\(833\) | −28.5527 | −0.989293 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.80786 | 0.270202 | ||||||||
\(836\) | −1.97755 | −0.0683951 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.06226 | 0.105784 | ||||||||
\(839\) | 7.56762 | 0.261263 | 0.130632 | − | 0.991431i | \(-0.458299\pi\) | ||||
0.130632 | + | 0.991431i | \(0.458299\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 49.5706 | 1.70832 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30.7755 | −1.05934 | ||||||||
\(845\) | −26.4123 | −0.908610 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.0094 | 1.44346 | ||||||||
\(848\) | −50.2732 | −1.72639 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 32.9719 | 1.13093 | ||||||||
\(851\) | −4.20377 | −0.144103 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.153744 | −0.00526409 | −0.00263205 | − | 0.999997i | \(-0.500838\pi\) | ||||
−0.00263205 | + | 0.999997i | \(0.500838\pi\) | |||||||
\(854\) | −86.6737 | −2.96591 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.243933 | −0.00833747 | ||||||||
\(857\) | 2.17376 | 0.0742544 | 0.0371272 | − | 0.999311i | \(-0.488179\pi\) | ||||
0.0371272 | + | 0.999311i | \(0.488179\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.80983 | −0.129990 | −0.0649948 | − | 0.997886i | \(-0.520703\pi\) | ||||
−0.0649948 | + | 0.997886i | \(0.520703\pi\) | |||||||
\(860\) | −9.34172 | −0.318550 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −68.8574 | −2.34529 | ||||||||
\(863\) | −12.2177 | −0.415897 | −0.207948 | − | 0.978140i | \(-0.566679\pi\) | ||||
−0.207948 | + | 0.978140i | \(0.566679\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.15704 | −0.0733416 | ||||||||
\(866\) | 79.5881 | 2.70451 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −39.7310 | −1.34856 | ||||||||
\(869\) | 0.467013 | 0.0158423 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.1156 | 1.86752 | ||||||||
\(872\) | 0.0674959 | 0.00228570 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.72497 | −0.328952 | ||||||||
\(875\) | −26.6592 | −0.901244 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.6753 | 0.394248 | 0.197124 | − | 0.980379i | \(-0.436840\pi\) | ||||
0.197124 | + | 0.980379i | \(0.436840\pi\) | |||||||
\(878\) | −7.88343 | −0.266053 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.612156 | −0.0206358 | ||||||||
\(881\) | −6.52745 | −0.219915 | −0.109958 | − | 0.993936i | \(-0.535072\pi\) | ||||
−0.109958 | + | 0.993936i | \(0.535072\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.949789 | 0.0319629 | 0.0159815 | − | 0.999872i | \(-0.494913\pi\) | ||||
0.0159815 | + | 0.999872i | \(0.494913\pi\) | |||||||
\(884\) | −51.1901 | −1.72171 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.90734 | −0.164865 | ||||||||
\(887\) | 26.4928 | 0.889540 | 0.444770 | − | 0.895645i | \(-0.353285\pi\) | ||||
0.444770 | + | 0.895645i | \(0.353285\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.8078 | 0.999722 | ||||||||
\(890\) | −13.1974 | −0.442377 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.8458 | 0.497073 | ||||||||
\(893\) | 1.57527 | 0.0527145 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.08767 | −0.236915 | ||||||||
\(896\) | −1.65611 | −0.0553269 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 38.8292 | 1.29575 | ||||||||
\(899\) | 5.25291 | 0.175194 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.0049 | −1.53264 | ||||||||
\(902\) | 4.74432 | 0.157969 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.0938301 | −0.00312074 | ||||||||
\(905\) | −7.86593 | −0.261472 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.79751 | 0.258912 | 0.129456 | − | 0.991585i | \(-0.458677\pi\) | ||||
0.129456 | + | 0.991585i | \(0.458677\pi\) | |||||||
\(908\) | 22.8178 | 0.757236 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 39.2929 | 1.30255 | ||||||||
\(911\) | −14.4227 | −0.477845 | −0.238923 | − | 0.971039i | \(-0.576794\pi\) | ||||
−0.238923 | + | 0.971039i | \(0.576794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.475465 | −0.0157356 | ||||||||
\(914\) | 6.61770 | 0.218894 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.70017 | −0.320503 | ||||||||
\(917\) | 29.8223 | 0.984818 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.48607 | 0.0490211 | 0.0245105 | − | 0.999700i | \(-0.492197\pi\) | ||||
0.0245105 | + | 0.999700i | \(0.492197\pi\) | |||||||
\(920\) | −0.0396978 | −0.00130880 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33.6875 | −1.10944 | ||||||||
\(923\) | 58.3617 | 1.92100 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.7472 | −0.616405 | ||||||||
\(926\) | −60.5101 | −1.98849 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.97140 | −0.261674 | ||||||||
\(929\) | 35.0529 | 1.15005 | 0.575025 | − | 0.818136i | \(-0.304992\pi\) | ||||
0.575025 | + | 0.818136i | \(0.304992\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.5569 | 1.23088 | ||||||||
\(932\) | −9.59604 | −0.314329 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.9277 | 0.521169 | ||||||||
\(935\) | −0.560182 | −0.0183199 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.4594 | 0.635711 | 0.317855 | − | 0.948139i | \(-0.397037\pi\) | ||||
0.317855 | + | 0.948139i | \(0.397037\pi\) | |||||||
\(938\) | −60.2094 | −1.96591 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.468250 | −0.0152726 | ||||||||
\(941\) | 8.80006 | 0.286874 | 0.143437 | − | 0.989659i | \(-0.454185\pi\) | ||||
0.143437 | + | 0.989659i | \(0.454185\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.5860 | 0.377291 | ||||||||
\(944\) | −33.4402 | −1.08839 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.63762 | −0.0857564 | ||||||||
\(947\) | −15.9958 | −0.519794 | −0.259897 | − | 0.965636i | \(-0.583689\pi\) | ||||
−0.259897 | + | 0.965636i | \(0.583689\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0678 | 0.391736 | ||||||||
\(950\) | −43.3697 | −1.40710 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.767949 | −0.0248894 | ||||||||
\(953\) | 27.3967 | 0.887465 | 0.443733 | − | 0.896159i | \(-0.353654\pi\) | ||||
0.443733 | + | 0.896159i | \(0.353654\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.5069 | −0.404714 | ||||||||
\(956\) | 25.8918 | 0.837400 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.9953 | 0.452167 | ||||||||
\(959\) | −83.8568 | −2.70788 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.40699 | −0.109903 | ||||||||
\(962\) | 58.6112 | 1.88970 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.5191 | −0.467627 | ||||||||
\(965\) | 0.135986 | 0.00437753 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.6368 | 0.985212 | 0.492606 | − | 0.870253i | \(-0.336044\pi\) | ||||
0.492606 | + | 0.870253i | \(0.336044\pi\) | |||||||
\(968\) | 0.591753 | 0.0190197 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.0483 | −0.740035 | ||||||||
\(971\) | 3.20546 | 0.102868 | 0.0514340 | − | 0.998676i | \(-0.483621\pi\) | ||||
0.0514340 | + | 0.998676i | \(0.483621\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.06569 | −0.258574 | ||||||||
\(974\) | 60.8353 | 1.94929 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −45.9764 | −1.47167 | ||||||||
\(977\) | −39.8395 | −1.27458 | −0.637290 | − | 0.770624i | \(-0.719945\pi\) | ||||
−0.637290 | + | 0.770624i | \(0.719945\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.85042 | −0.0591398 | ||||||||
\(980\) | −11.1638 | −0.356614 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −77.1367 | −2.46153 | ||||||||
\(983\) | −15.3920 | −0.490928 | −0.245464 | − | 0.969406i | \(-0.578940\pi\) | ||||
−0.245464 | + | 0.969406i | \(0.578940\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.2536 | 0.645335 | ||||||||
\(986\) | −7.39344 | −0.235455 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 67.3330 | 2.14215 | ||||||||
\(989\) | −6.44126 | −0.204820 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.0357 | −1.14471 | −0.572355 | − | 0.820006i | \(-0.693970\pi\) | ||||
−0.572355 | + | 0.820006i | \(0.693970\pi\) | |||||||
\(992\) | −41.8730 | −1.32947 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −63.7556 | −2.02220 | ||||||||
\(995\) | −6.78565 | −0.215119 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.8316 | −1.22981 | −0.614904 | − | 0.788602i | \(-0.710805\pi\) | ||||
−0.614904 | + | 0.788602i | \(0.710805\pi\) | |||||||
\(998\) | −9.67639 | −0.306301 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.w.1.25 | yes | 30 | |
3.2 | odd | 2 | 6003.2.a.v.1.6 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.v.1.6 | ✓ | 30 | 3.2 | odd | 2 | ||
6003.2.a.w.1.25 | yes | 30 | 1.1 | even | 1 | trivial |