Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.487315 | −0.344584 | −0.172292 | − | 0.985046i | \(-0.555117\pi\) | ||||
−0.172292 | + | 0.985046i | \(0.555117\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.76252 | −0.881262 | ||||||||
\(5\) | 0.708639 | 0.316913 | 0.158456 | − | 0.987366i | \(-0.449348\pi\) | ||||
0.158456 | + | 0.987366i | \(0.449348\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.83353 | 0.648252 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.345330 | −0.109203 | ||||||||
\(11\) | 4.44553 | 1.34038 | 0.670189 | − | 0.742190i | \(-0.266213\pi\) | ||||
0.670189 | + | 0.742190i | \(0.266213\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.01971 | −1.11487 | −0.557433 | − | 0.830222i | \(-0.688214\pi\) | ||||
−0.557433 | + | 0.830222i | \(0.688214\pi\) | |||||||
\(14\) | 0.487315 | 0.130240 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.63154 | 0.657885 | ||||||||
\(17\) | 1.16643 | 0.282900 | 0.141450 | − | 0.989945i | \(-0.454824\pi\) | ||||
0.141450 | + | 0.989945i | \(0.454824\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.231089 | 0.0530155 | 0.0265078 | − | 0.999649i | \(-0.491561\pi\) | ||||
0.0265078 | + | 0.999649i | \(0.491561\pi\) | |||||||
\(20\) | −1.24899 | −0.279283 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.16638 | −0.461873 | ||||||||
\(23\) | 6.97361 | 1.45410 | 0.727049 | − | 0.686585i | \(-0.240891\pi\) | ||||
0.727049 | + | 0.686585i | \(0.240891\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.49783 | −0.899566 | ||||||||
\(26\) | 1.95886 | 0.384165 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.76252 | 0.333086 | ||||||||
\(29\) | 0.276783 | 0.0513973 | 0.0256986 | − | 0.999670i | \(-0.491819\pi\) | ||||
0.0256986 | + | 0.999670i | \(0.491819\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.86349 | −1.23272 | −0.616360 | − | 0.787465i | \(-0.711393\pi\) | ||||
−0.616360 | + | 0.787465i | \(0.711393\pi\) | |||||||
\(32\) | −4.94946 | −0.874949 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.568417 | −0.0974827 | ||||||||
\(35\) | −0.708639 | −0.119782 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.38389 | −0.556307 | −0.278154 | − | 0.960537i | \(-0.589722\pi\) | ||||
−0.278154 | + | 0.960537i | \(0.589722\pi\) | |||||||
\(38\) | −0.112613 | −0.0182683 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.29931 | 0.205440 | ||||||||
\(41\) | 7.55759 | 1.18030 | 0.590148 | − | 0.807295i | \(-0.299069\pi\) | ||||
0.590148 | + | 0.807295i | \(0.299069\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.27833 | 0.804938 | 0.402469 | − | 0.915434i | \(-0.368152\pi\) | ||||
0.402469 | + | 0.915434i | \(0.368152\pi\) | |||||||
\(44\) | −7.83536 | −1.18122 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.39835 | −0.501059 | ||||||||
\(47\) | −5.93194 | −0.865263 | −0.432632 | − | 0.901571i | \(-0.642415\pi\) | ||||
−0.432632 | + | 0.901571i | \(0.642415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.19186 | 0.309976 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.08483 | 0.982489 | ||||||||
\(53\) | 10.2985 | 1.41461 | 0.707305 | − | 0.706908i | \(-0.249911\pi\) | ||||
0.707305 | + | 0.706908i | \(0.249911\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.15028 | 0.424783 | ||||||||
\(56\) | −1.83353 | −0.245016 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.134880 | −0.0177107 | ||||||||
\(59\) | 9.69255 | 1.26186 | 0.630932 | − | 0.775839i | \(-0.282673\pi\) | ||||
0.630932 | + | 0.775839i | \(0.282673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.65994 | 1.23683 | 0.618414 | − | 0.785852i | \(-0.287775\pi\) | ||||
0.618414 | + | 0.785852i | \(0.287775\pi\) | |||||||
\(62\) | 3.34468 | 0.424775 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.85113 | −0.356391 | ||||||||
\(65\) | −2.84852 | −0.353316 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.37876 | −0.657120 | −0.328560 | − | 0.944483i | \(-0.606563\pi\) | ||||
−0.328560 | + | 0.944483i | \(0.606563\pi\) | |||||||
\(68\) | −2.05585 | −0.249309 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.345330 | 0.0412749 | ||||||||
\(71\) | 2.44937 | 0.290687 | 0.145344 | − | 0.989381i | \(-0.453571\pi\) | ||||
0.145344 | + | 0.989381i | \(0.453571\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1674 | −1.19000 | −0.595000 | − | 0.803725i | \(-0.702848\pi\) | ||||
−0.595000 | + | 0.803725i | \(0.702848\pi\) | |||||||
\(74\) | 1.64902 | 0.191695 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.407300 | −0.0467206 | ||||||||
\(77\) | −4.44553 | −0.506615 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.67284 | 1.08828 | 0.544140 | − | 0.838995i | \(-0.316856\pi\) | ||||
0.544140 | + | 0.838995i | \(0.316856\pi\) | |||||||
\(80\) | 1.86481 | 0.208492 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.68293 | −0.406711 | ||||||||
\(83\) | −4.65761 | −0.511239 | −0.255619 | − | 0.966777i | \(-0.582279\pi\) | ||||
−0.255619 | + | 0.966777i | \(0.582279\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.826575 | 0.0896546 | ||||||||
\(86\) | −2.57221 | −0.277369 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.15104 | 0.868904 | ||||||||
\(89\) | 2.71373 | 0.287655 | 0.143827 | − | 0.989603i | \(-0.454059\pi\) | ||||
0.143827 | + | 0.989603i | \(0.454059\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.01971 | 0.421380 | ||||||||
\(92\) | −12.2912 | −1.28144 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.89073 | 0.298156 | ||||||||
\(95\) | 0.163759 | 0.0168013 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.35612 | 0.543831 | 0.271916 | − | 0.962321i | \(-0.412343\pi\) | ||||
0.271916 | + | 0.962321i | \(0.412343\pi\) | |||||||
\(98\) | −0.487315 | −0.0492263 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.92753 | 0.792753 | ||||||||
\(101\) | 8.03179 | 0.799193 | 0.399596 | − | 0.916691i | \(-0.369150\pi\) | ||||
0.399596 | + | 0.916691i | \(0.369150\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1212 | −1.19433 | −0.597167 | − | 0.802117i | \(-0.703707\pi\) | ||||
−0.597167 | + | 0.802117i | \(0.703707\pi\) | |||||||
\(104\) | −7.37028 | −0.722715 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.01862 | −0.487452 | ||||||||
\(107\) | −11.1977 | −1.08252 | −0.541262 | − | 0.840854i | \(-0.682053\pi\) | ||||
−0.541262 | + | 0.840854i | \(0.682053\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4591 | −1.00180 | −0.500900 | − | 0.865505i | \(-0.666997\pi\) | ||||
−0.500900 | + | 0.865505i | \(0.666997\pi\) | |||||||
\(110\) | −1.53518 | −0.146373 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.63154 | −0.248657 | ||||||||
\(113\) | −7.87867 | −0.741163 | −0.370582 | − | 0.928800i | \(-0.620842\pi\) | ||||
−0.370582 | + | 0.928800i | \(0.620842\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.94177 | 0.460823 | ||||||||
\(116\) | −0.487836 | −0.0452945 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.72333 | −0.434818 | ||||||||
\(119\) | −1.16643 | −0.106926 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.76276 | 0.796614 | ||||||||
\(122\) | −4.70743 | −0.426191 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.0971 | 1.08635 | ||||||||
\(125\) | −6.73053 | −0.601997 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 11.2883 | 0.997756 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.38813 | 0.121747 | ||||||||
\(131\) | 6.58055 | 0.574946 | 0.287473 | − | 0.957789i | \(-0.407185\pi\) | ||||
0.287473 | + | 0.957789i | \(0.407185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.231089 | −0.0200380 | ||||||||
\(134\) | 2.62115 | 0.226433 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.13868 | 0.183391 | ||||||||
\(137\) | −19.1658 | −1.63744 | −0.818721 | − | 0.574191i | \(-0.805317\pi\) | ||||
−0.818721 | + | 0.574191i | \(0.805317\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.15283 | −0.437057 | −0.218529 | − | 0.975831i | \(-0.570126\pi\) | ||||
−0.218529 | + | 0.975831i | \(0.570126\pi\) | |||||||
\(140\) | 1.24899 | 0.105559 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.19362 | −0.100166 | ||||||||
\(143\) | −17.8697 | −1.49434 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.196139 | 0.0162885 | ||||||||
\(146\) | 4.95471 | 0.410055 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.96418 | 0.490252 | ||||||||
\(149\) | 4.97869 | 0.407870 | 0.203935 | − | 0.978984i | \(-0.434627\pi\) | ||||
0.203935 | + | 0.978984i | \(0.434627\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.9375 | −1.86663 | −0.933314 | − | 0.359061i | \(-0.883097\pi\) | ||||
−0.933314 | + | 0.359061i | \(0.883097\pi\) | |||||||
\(152\) | 0.423710 | 0.0343674 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.16638 | 0.174571 | ||||||||
\(155\) | −4.86374 | −0.390665 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.3926 | 1.30827 | 0.654135 | − | 0.756377i | \(-0.273033\pi\) | ||||
0.654135 | + | 0.756377i | \(0.273033\pi\) | |||||||
\(158\) | −4.71372 | −0.375003 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.50738 | −0.277283 | ||||||||
\(161\) | −6.97361 | −0.549598 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.5481 | −1.60945 | −0.804724 | − | 0.593649i | \(-0.797687\pi\) | ||||
−0.804724 | + | 0.593649i | \(0.797687\pi\) | |||||||
\(164\) | −13.3204 | −1.04015 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.26972 | 0.176165 | ||||||||
\(167\) | 9.17092 | 0.709667 | 0.354834 | − | 0.934929i | \(-0.384538\pi\) | ||||
0.354834 | + | 0.934929i | \(0.384538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.15805 | 0.242927 | ||||||||
\(170\) | −0.402802 | −0.0308935 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.30319 | −0.709361 | ||||||||
\(173\) | 12.6056 | 0.958386 | 0.479193 | − | 0.877710i | \(-0.340929\pi\) | ||||
0.479193 | + | 0.877710i | \(0.340929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.49783 | 0.340004 | ||||||||
\(176\) | 11.6986 | 0.881814 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.32244 | −0.0991212 | ||||||||
\(179\) | −3.02510 | −0.226107 | −0.113053 | − | 0.993589i | \(-0.536063\pi\) | ||||
−0.113053 | + | 0.993589i | \(0.536063\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.3615 | 0.844494 | 0.422247 | − | 0.906481i | \(-0.361241\pi\) | ||||
0.422247 | + | 0.906481i | \(0.361241\pi\) | |||||||
\(182\) | −1.95886 | −0.145201 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.7864 | 0.942623 | ||||||||
\(185\) | −2.39795 | −0.176301 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.18538 | 0.379193 | ||||||||
\(188\) | 10.4552 | 0.762523 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0798022 | −0.00578946 | ||||||||
\(191\) | 12.3592 | 0.894278 | 0.447139 | − | 0.894464i | \(-0.352443\pi\) | ||||
0.447139 | + | 0.894464i | \(0.352443\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.9860 | 1.58259 | 0.791294 | − | 0.611436i | \(-0.209408\pi\) | ||||
0.791294 | + | 0.611436i | \(0.209408\pi\) | |||||||
\(194\) | −2.61012 | −0.187395 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.76252 | −0.125895 | ||||||||
\(197\) | −10.2498 | −0.730270 | −0.365135 | − | 0.930955i | \(-0.618977\pi\) | ||||
−0.365135 | + | 0.930955i | \(0.618977\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.1527 | 0.790595 | 0.395298 | − | 0.918553i | \(-0.370641\pi\) | ||||
0.395298 | + | 0.918553i | \(0.370641\pi\) | |||||||
\(200\) | −8.24693 | −0.583146 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.91401 | −0.275389 | ||||||||
\(203\) | −0.276783 | −0.0194263 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.35560 | 0.374051 | ||||||||
\(206\) | 5.90683 | 0.411549 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.5780 | −0.733454 | ||||||||
\(209\) | 1.02732 | 0.0710609 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8010 | 1.15663 | 0.578315 | − | 0.815814i | \(-0.303710\pi\) | ||||
0.578315 | + | 0.815814i | \(0.303710\pi\) | |||||||
\(212\) | −18.1514 | −1.24664 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.45682 | 0.373021 | ||||||||
\(215\) | 3.74043 | 0.255095 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.86349 | 0.465924 | ||||||||
\(218\) | 5.09687 | 0.345204 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.55244 | −0.374345 | ||||||||
\(221\) | −4.68869 | −0.315396 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.3679 | 0.962148 | 0.481074 | − | 0.876680i | \(-0.340247\pi\) | ||||
0.481074 | + | 0.876680i | \(0.340247\pi\) | |||||||
\(224\) | 4.94946 | 0.330700 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.83940 | 0.255393 | ||||||||
\(227\) | 25.0501 | 1.66263 | 0.831316 | − | 0.555801i | \(-0.187588\pi\) | ||||
0.831316 | + | 0.555801i | \(0.187588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3121 | 0.813609 | 0.406804 | − | 0.913515i | \(-0.366643\pi\) | ||||
0.406804 | + | 0.913515i | \(0.366643\pi\) | |||||||
\(230\) | −2.40820 | −0.158792 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.507491 | 0.0333184 | ||||||||
\(233\) | 12.9128 | 0.845944 | 0.422972 | − | 0.906143i | \(-0.360987\pi\) | ||||
0.422972 | + | 0.906143i | \(0.360987\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.20361 | −0.274213 | ||||||||
\(236\) | −17.0834 | −1.11203 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.568417 | 0.0368450 | ||||||||
\(239\) | −22.9286 | −1.48313 | −0.741564 | − | 0.670883i | \(-0.765915\pi\) | ||||
−0.741564 | + | 0.670883i | \(0.765915\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.93591 | 0.253534 | 0.126767 | − | 0.991933i | \(-0.459540\pi\) | ||||
0.126767 | + | 0.991933i | \(0.459540\pi\) | |||||||
\(242\) | −4.27022 | −0.274500 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −17.0259 | −1.08997 | ||||||||
\(245\) | 0.708639 | 0.0452733 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.928912 | −0.0591052 | ||||||||
\(248\) | −12.5844 | −0.799113 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.27989 | 0.207438 | ||||||||
\(251\) | 24.9566 | 1.57524 | 0.787622 | − | 0.616159i | \(-0.211312\pi\) | ||||
0.787622 | + | 0.616159i | \(0.211312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.0014 | 1.94904 | ||||||||
\(254\) | −0.487315 | −0.0305769 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.201294 | 0.0125809 | ||||||||
\(257\) | −1.87577 | −0.117007 | −0.0585037 | − | 0.998287i | \(-0.518633\pi\) | ||||
−0.0585037 | + | 0.998287i | \(0.518633\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.38389 | 0.210264 | ||||||||
\(260\) | 5.02059 | 0.311364 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.20680 | −0.198117 | ||||||||
\(263\) | −22.3178 | −1.37618 | −0.688088 | − | 0.725628i | \(-0.741550\pi\) | ||||
−0.688088 | + | 0.725628i | \(0.741550\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.29793 | 0.448308 | ||||||||
\(266\) | 0.112613 | 0.00690477 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.48019 | 0.579095 | ||||||||
\(269\) | −3.14560 | −0.191790 | −0.0958952 | − | 0.995391i | \(-0.530571\pi\) | ||||
−0.0958952 | + | 0.995391i | \(0.530571\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4088 | 1.42198 | 0.710991 | − | 0.703201i | \(-0.248247\pi\) | ||||
0.710991 | + | 0.703201i | \(0.248247\pi\) | |||||||
\(272\) | 3.06949 | 0.186115 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.33977 | 0.564236 | ||||||||
\(275\) | −19.9953 | −1.20576 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.3914 | −0.744525 | −0.372263 | − | 0.928127i | \(-0.621418\pi\) | ||||
−0.372263 | + | 0.928127i | \(0.621418\pi\) | |||||||
\(278\) | 2.51105 | 0.150603 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.29931 | −0.0776489 | ||||||||
\(281\) | −0.509059 | −0.0303679 | −0.0151840 | − | 0.999885i | \(-0.504833\pi\) | ||||
−0.0151840 | + | 0.999885i | \(0.504833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.4598 | 0.859547 | 0.429773 | − | 0.902937i | \(-0.358593\pi\) | ||||
0.429773 | + | 0.902937i | \(0.358593\pi\) | |||||||
\(284\) | −4.31708 | −0.256172 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.70820 | 0.514926 | ||||||||
\(287\) | −7.55759 | −0.446110 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6395 | −0.919968 | ||||||||
\(290\) | −0.0955815 | −0.00561274 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.9202 | 1.04870 | ||||||||
\(293\) | 10.0307 | 0.586002 | 0.293001 | − | 0.956112i | \(-0.405346\pi\) | ||||
0.293001 | + | 0.956112i | \(0.405346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.86852 | 0.399901 | ||||||||
\(296\) | −6.20447 | −0.360628 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.42619 | −0.140545 | ||||||||
\(299\) | −28.0319 | −1.62113 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.27833 | −0.304238 | ||||||||
\(302\) | 11.1778 | 0.643210 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.608120 | 0.0348781 | ||||||||
\(305\) | 6.84541 | 0.391967 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.70954 | 0.0975688 | 0.0487844 | − | 0.998809i | \(-0.484465\pi\) | ||||
0.0487844 | + | 0.998809i | \(0.484465\pi\) | |||||||
\(308\) | 7.83536 | 0.446461 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.37017 | 0.134617 | ||||||||
\(311\) | −10.1740 | −0.576912 | −0.288456 | − | 0.957493i | \(-0.593142\pi\) | ||||
−0.288456 | + | 0.957493i | \(0.593142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2723 | 0.580627 | 0.290314 | − | 0.956932i | \(-0.406240\pi\) | ||||
0.290314 | + | 0.956932i | \(0.406240\pi\) | |||||||
\(314\) | −7.98836 | −0.450809 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.0486 | −0.959059 | ||||||||
\(317\) | 9.81675 | 0.551364 | 0.275682 | − | 0.961249i | \(-0.411096\pi\) | ||||
0.275682 | + | 0.961249i | \(0.411096\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.23045 | 0.0688918 | ||||||||
\(320\) | −2.02042 | −0.112945 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.39835 | 0.189382 | ||||||||
\(323\) | 0.269549 | 0.0149981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.0800 | 1.00290 | ||||||||
\(326\) | 10.0134 | 0.554590 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.8571 | 0.765130 | ||||||||
\(329\) | 5.93194 | 0.327039 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.1848 | 0.779669 | 0.389834 | − | 0.920885i | \(-0.372532\pi\) | ||||
0.389834 | + | 0.920885i | \(0.372532\pi\) | |||||||
\(332\) | 8.20914 | 0.450535 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.46913 | −0.244540 | ||||||||
\(335\) | −3.81160 | −0.208250 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.58219 | −0.521975 | −0.260988 | − | 0.965342i | \(-0.584048\pi\) | ||||
−0.260988 | + | 0.965342i | \(0.584048\pi\) | |||||||
\(338\) | −1.53897 | −0.0837088 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.45686 | −0.0790092 | ||||||||
\(341\) | −30.5119 | −1.65231 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 9.67801 | 0.521803 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.14290 | −0.330244 | ||||||||
\(347\) | 6.57274 | 0.352843 | 0.176421 | − | 0.984315i | \(-0.443548\pi\) | ||||
0.176421 | + | 0.984315i | \(0.443548\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.4702 | −0.667513 | −0.333757 | − | 0.942659i | \(-0.608316\pi\) | ||||
−0.333757 | + | 0.942659i | \(0.608316\pi\) | |||||||
\(350\) | −2.19186 | −0.117160 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −22.0030 | −1.17276 | ||||||||
\(353\) | 30.6990 | 1.63394 | 0.816971 | − | 0.576679i | \(-0.195652\pi\) | ||||
0.816971 | + | 0.576679i | \(0.195652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.73572 | 0.0921225 | ||||||||
\(356\) | −4.78301 | −0.253499 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.47418 | 0.0779127 | ||||||||
\(359\) | −10.9313 | −0.576930 | −0.288465 | − | 0.957490i | \(-0.593145\pi\) | ||||
−0.288465 | + | 0.957490i | \(0.593145\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9466 | −0.997189 | ||||||||
\(362\) | −5.53663 | −0.290999 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.08483 | −0.371346 | ||||||||
\(365\) | −7.20499 | −0.377127 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.3619 | 0.749687 | 0.374843 | − | 0.927088i | \(-0.377697\pi\) | ||||
0.374843 | + | 0.927088i | \(0.377697\pi\) | |||||||
\(368\) | 18.3513 | 0.956629 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.16856 | 0.0607505 | ||||||||
\(371\) | −10.2985 | −0.534672 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.52175 | 0.337683 | 0.168842 | − | 0.985643i | \(-0.445997\pi\) | ||||
0.168842 | + | 0.985643i | \(0.445997\pi\) | |||||||
\(374\) | −2.52692 | −0.130664 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.8764 | −0.560909 | ||||||||
\(377\) | −1.11259 | −0.0573011 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.56819 | −0.337385 | −0.168693 | − | 0.985669i | \(-0.553954\pi\) | ||||
−0.168693 | + | 0.985669i | \(0.553954\pi\) | |||||||
\(380\) | −0.288629 | −0.0148063 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.02281 | −0.308154 | ||||||||
\(383\) | 17.8013 | 0.909604 | 0.454802 | − | 0.890592i | \(-0.349710\pi\) | ||||
0.454802 | + | 0.890592i | \(0.349710\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.15028 | −0.160553 | ||||||||
\(386\) | −10.7141 | −0.545334 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.44028 | −0.479258 | ||||||||
\(389\) | 26.8008 | 1.35885 | 0.679427 | − | 0.733743i | \(-0.262228\pi\) | ||||
0.679427 | + | 0.733743i | \(0.262228\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.13420 | 0.411364 | ||||||||
\(392\) | 1.83353 | 0.0926075 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.99489 | 0.251639 | ||||||||
\(395\) | 6.85455 | 0.344890 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.3047 | 0.717932 | 0.358966 | − | 0.933351i | \(-0.383129\pi\) | ||||
0.358966 | + | 0.933351i | \(0.383129\pi\) | |||||||
\(398\) | −5.43489 | −0.272426 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.8362 | −0.591811 | ||||||||
\(401\) | 7.72247 | 0.385642 | 0.192821 | − | 0.981234i | \(-0.438236\pi\) | ||||
0.192821 | + | 0.981234i | \(0.438236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.5892 | 1.37432 | ||||||||
\(404\) | −14.1562 | −0.704298 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.134880 | 0.00669400 | ||||||||
\(407\) | −15.0432 | −0.745662 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.41265 | −0.119298 | −0.0596488 | − | 0.998219i | \(-0.518998\pi\) | ||||
−0.0596488 | + | 0.998219i | \(0.518998\pi\) | |||||||
\(410\) | −2.60987 | −0.128892 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21.3639 | 1.05252 | ||||||||
\(413\) | −9.69255 | −0.476939 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.30056 | −0.162018 | ||||||||
\(416\) | 19.8954 | 0.975451 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.500626 | −0.0244864 | ||||||||
\(419\) | 18.1299 | 0.885705 | 0.442852 | − | 0.896594i | \(-0.353967\pi\) | ||||
0.442852 | + | 0.896594i | \(0.353967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.2093 | 1.08242 | 0.541208 | − | 0.840889i | \(-0.317967\pi\) | ||||
0.541208 | + | 0.840889i | \(0.317967\pi\) | |||||||
\(422\) | −8.18739 | −0.398556 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.8827 | 0.917024 | ||||||||
\(425\) | −5.24639 | −0.254487 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.65994 | −0.467477 | ||||||||
\(428\) | 19.7363 | 0.953988 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.82277 | −0.0879017 | ||||||||
\(431\) | −4.43053 | −0.213411 | −0.106706 | − | 0.994291i | \(-0.534030\pi\) | ||||
−0.106706 | + | 0.994291i | \(0.534030\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7205 | −0.563251 | −0.281625 | − | 0.959524i | \(-0.590874\pi\) | ||||
−0.281625 | + | 0.959524i | \(0.590874\pi\) | |||||||
\(434\) | −3.34468 | −0.160550 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.4344 | 0.882848 | ||||||||
\(437\) | 1.61153 | 0.0770898 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.6460 | 1.41492 | 0.707462 | − | 0.706751i | \(-0.249840\pi\) | ||||
0.707462 | + | 0.706751i | \(0.249840\pi\) | |||||||
\(440\) | 5.77614 | 0.275367 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.28487 | 0.108680 | ||||||||
\(443\) | 25.1045 | 1.19275 | 0.596376 | − | 0.802706i | \(-0.296607\pi\) | ||||
0.596376 | + | 0.802706i | \(0.296607\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.92305 | 0.0911615 | ||||||||
\(446\) | −7.00171 | −0.331541 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.85113 | 0.134703 | ||||||||
\(449\) | 0.786336 | 0.0371095 | 0.0185548 | − | 0.999828i | \(-0.494093\pi\) | ||||
0.0185548 | + | 0.999828i | \(0.494093\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.5975 | 1.58204 | ||||||||
\(452\) | 13.8864 | 0.653159 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.2073 | −0.572916 | ||||||||
\(455\) | 2.84852 | 0.133541 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5485 | 0.493440 | 0.246720 | − | 0.969087i | \(-0.420647\pi\) | ||||
0.246720 | + | 0.969087i | \(0.420647\pi\) | |||||||
\(458\) | −5.99989 | −0.280356 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.70999 | −0.406105 | ||||||||
\(461\) | 29.7725 | 1.38664 | 0.693322 | − | 0.720628i | \(-0.256147\pi\) | ||||
0.693322 | + | 0.720628i | \(0.256147\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0991 | 0.748187 | 0.374093 | − | 0.927391i | \(-0.377954\pi\) | ||||
0.374093 | + | 0.927391i | \(0.377954\pi\) | |||||||
\(464\) | 0.728364 | 0.0338135 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.29259 | −0.291499 | ||||||||
\(467\) | −23.4876 | −1.08688 | −0.543438 | − | 0.839450i | \(-0.682878\pi\) | ||||
−0.543438 | + | 0.839450i | \(0.682878\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.37876 | 0.248368 | ||||||||
\(470\) | 2.04848 | 0.0944894 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17.7716 | 0.818006 | ||||||||
\(473\) | 23.4650 | 1.07892 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.03940 | −0.0476910 | ||||||||
\(476\) | 2.05585 | 0.0942299 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.1735 | 0.511062 | ||||||||
\(479\) | 29.7558 | 1.35958 | 0.679788 | − | 0.733409i | \(-0.262072\pi\) | ||||
0.679788 | + | 0.733409i | \(0.262072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.6022 | 0.620208 | ||||||||
\(482\) | −1.91803 | −0.0873637 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15.4446 | −0.702026 | ||||||||
\(485\) | 3.79555 | 0.172347 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.06984 | −0.184422 | −0.0922110 | − | 0.995739i | \(-0.529393\pi\) | ||||
−0.0922110 | + | 0.995739i | \(0.529393\pi\) | |||||||
\(488\) | 17.7118 | 0.801777 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.345330 | −0.0156004 | ||||||||
\(491\) | −21.5351 | −0.971867 | −0.485934 | − | 0.873996i | \(-0.661520\pi\) | ||||
−0.485934 | + | 0.873996i | \(0.661520\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.322847 | 0.0145403 | ||||||||
\(494\) | 0.452673 | 0.0203667 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.0615 | −0.810987 | ||||||||
\(497\) | −2.44937 | −0.109869 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.9904 | 0.715830 | 0.357915 | − | 0.933754i | \(-0.383488\pi\) | ||||
0.357915 | + | 0.933754i | \(0.383488\pi\) | |||||||
\(500\) | 11.8627 | 0.530517 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.1617 | −0.542804 | ||||||||
\(503\) | −2.47442 | −0.110329 | −0.0551645 | − | 0.998477i | \(-0.517568\pi\) | ||||
−0.0551645 | + | 0.998477i | \(0.517568\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.69164 | 0.253274 | ||||||||
\(506\) | −15.1075 | −0.671609 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.76252 | −0.0781994 | ||||||||
\(509\) | 12.3113 | 0.545689 | 0.272845 | − | 0.962058i | \(-0.412035\pi\) | ||||
0.272845 | + | 0.962058i | \(0.412035\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.1674 | 0.449778 | ||||||||
\(512\) | −22.6747 | −1.00209 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.914092 | 0.0403189 | ||||||||
\(515\) | −8.58954 | −0.378500 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.3707 | −1.15978 | ||||||||
\(518\) | −1.64902 | −0.0724537 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.22286 | −0.229038 | ||||||||
\(521\) | 10.6667 | 0.467315 | 0.233657 | − | 0.972319i | \(-0.424931\pi\) | ||||
0.233657 | + | 0.972319i | \(0.424931\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.8109 | −1.47845 | −0.739223 | − | 0.673461i | \(-0.764807\pi\) | ||||
−0.739223 | + | 0.673461i | \(0.764807\pi\) | |||||||
\(524\) | −11.5984 | −0.506678 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.8758 | 0.474208 | ||||||||
\(527\) | −8.00575 | −0.348736 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.6313 | 1.11440 | ||||||||
\(530\) | −3.55639 | −0.154480 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.407300 | 0.0176587 | ||||||||
\(533\) | −30.3793 | −1.31587 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.93514 | −0.343066 | ||||||||
\(536\) | −9.86214 | −0.425980 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.53290 | 0.0660879 | ||||||||
\(539\) | 4.44553 | 0.191483 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.9095 | 1.28591 | 0.642955 | − | 0.765904i | \(-0.277708\pi\) | ||||
0.642955 | + | 0.765904i | \(0.277708\pi\) | |||||||
\(542\) | −11.4074 | −0.489992 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.77318 | −0.247523 | ||||||||
\(545\) | −7.41172 | −0.317483 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.75633 | 0.203366 | 0.101683 | − | 0.994817i | \(-0.467577\pi\) | ||||
0.101683 | + | 0.994817i | \(0.467577\pi\) | |||||||
\(548\) | 33.7801 | 1.44302 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.74399 | 0.415485 | ||||||||
\(551\) | 0.0639615 | 0.00272485 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.67284 | −0.411331 | ||||||||
\(554\) | 6.03850 | 0.256551 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.08199 | 0.385162 | ||||||||
\(557\) | 21.0394 | 0.891467 | 0.445733 | − | 0.895166i | \(-0.352943\pi\) | ||||
0.445733 | + | 0.895166i | \(0.352943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.2174 | −0.897399 | ||||||||
\(560\) | −1.86481 | −0.0788026 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.248072 | 0.0104643 | ||||||||
\(563\) | −0.979301 | −0.0412726 | −0.0206363 | − | 0.999787i | \(-0.506569\pi\) | ||||
−0.0206363 | + | 0.999787i | \(0.506569\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.58313 | −0.234884 | ||||||||
\(566\) | −7.04649 | −0.296186 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.49101 | 0.188439 | ||||||||
\(569\) | 30.7127 | 1.28754 | 0.643772 | − | 0.765217i | \(-0.277368\pi\) | ||||
0.643772 | + | 0.765217i | \(0.277368\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.9175 | −1.62865 | −0.814324 | − | 0.580410i | \(-0.802892\pi\) | ||||
−0.814324 | + | 0.580410i | \(0.802892\pi\) | |||||||
\(572\) | 31.4959 | 1.31691 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.68293 | 0.153722 | ||||||||
\(575\) | −31.3661 | −1.30806 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.38437 | −0.0992628 | −0.0496314 | − | 0.998768i | \(-0.515805\pi\) | ||||
−0.0496314 | + | 0.998768i | \(0.515805\pi\) | |||||||
\(578\) | 7.62134 | 0.317006 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.345700 | −0.0143544 | ||||||||
\(581\) | 4.65761 | 0.193230 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.7824 | 1.89611 | ||||||||
\(584\) | −18.6422 | −0.771421 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.88813 | −0.201927 | ||||||||
\(587\) | −40.0906 | −1.65472 | −0.827358 | − | 0.561675i | \(-0.810157\pi\) | ||||
−0.827358 | + | 0.561675i | \(0.810157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.58608 | −0.0653533 | ||||||||
\(590\) | −3.34713 | −0.137799 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.90482 | −0.365986 | ||||||||
\(593\) | −14.8133 | −0.608309 | −0.304155 | − | 0.952623i | \(-0.598374\pi\) | ||||
−0.304155 | + | 0.952623i | \(0.598374\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.826575 | −0.0338863 | ||||||||
\(596\) | −8.77506 | −0.359440 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.6604 | 0.558614 | ||||||||
\(599\) | 8.30624 | 0.339384 | 0.169692 | − | 0.985497i | \(-0.445723\pi\) | ||||
0.169692 | + | 0.985497i | \(0.445723\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.6167 | −1.16730 | −0.583649 | − | 0.812006i | \(-0.698376\pi\) | ||||
−0.583649 | + | 0.812006i | \(0.698376\pi\) | |||||||
\(602\) | 2.57221 | 0.104836 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 40.4279 | 1.64499 | ||||||||
\(605\) | 6.20963 | 0.252457 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.28776 | −0.376979 | −0.188489 | − | 0.982075i | \(-0.560359\pi\) | ||||
−0.188489 | + | 0.982075i | \(0.560359\pi\) | |||||||
\(608\) | −1.14377 | −0.0463859 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.33587 | −0.135065 | ||||||||
\(611\) | 23.8447 | 0.964653 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.36950 | −0.136093 | −0.0680465 | − | 0.997682i | \(-0.521677\pi\) | ||||
−0.0680465 | + | 0.997682i | \(0.521677\pi\) | |||||||
\(614\) | −0.833087 | −0.0336206 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.15104 | −0.328415 | ||||||||
\(617\) | 5.44174 | 0.219076 | 0.109538 | − | 0.993983i | \(-0.465063\pi\) | ||||
0.109538 | + | 0.993983i | \(0.465063\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.7609 | 0.955032 | 0.477516 | − | 0.878623i | \(-0.341537\pi\) | ||||
0.477516 | + | 0.878623i | \(0.341537\pi\) | |||||||
\(620\) | 8.57245 | 0.344278 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.95792 | 0.198795 | ||||||||
\(623\) | −2.71373 | −0.108723 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.7196 | 0.708786 | ||||||||
\(626\) | −5.00587 | −0.200075 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.8923 | −1.15293 | ||||||||
\(629\) | −3.94705 | −0.157379 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.82905 | 0.351479 | 0.175740 | − | 0.984437i | \(-0.443768\pi\) | ||||
0.175740 | + | 0.984437i | \(0.443768\pi\) | |||||||
\(632\) | 17.7355 | 0.705480 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.78385 | −0.189991 | ||||||||
\(635\) | 0.708639 | 0.0281215 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.01971 | −0.159267 | ||||||||
\(638\) | −0.599615 | −0.0237390 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.99934 | 0.316202 | ||||||||
\(641\) | 10.2756 | 0.405864 | 0.202932 | − | 0.979193i | \(-0.434953\pi\) | ||||
0.202932 | + | 0.979193i | \(0.434953\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.8800 | 0.862865 | 0.431432 | − | 0.902145i | \(-0.358008\pi\) | ||||
0.431432 | + | 0.902145i | \(0.358008\pi\) | |||||||
\(644\) | 12.2912 | 0.484339 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.131355 | −0.00516810 | ||||||||
\(647\) | 39.7972 | 1.56459 | 0.782295 | − | 0.622908i | \(-0.214049\pi\) | ||||
0.782295 | + | 0.622908i | \(0.214049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.0886 | 1.69137 | ||||||||
\(650\) | −8.81064 | −0.345582 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 36.2164 | 1.41835 | ||||||||
\(653\) | −19.3461 | −0.757073 | −0.378537 | − | 0.925586i | \(-0.623573\pi\) | ||||
−0.378537 | + | 0.925586i | \(0.623573\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.66324 | 0.182208 | ||||||||
\(656\) | 19.8881 | 0.776499 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.89073 | −0.112692 | ||||||||
\(659\) | −23.2178 | −0.904438 | −0.452219 | − | 0.891907i | \(-0.649368\pi\) | ||||
−0.452219 | + | 0.891907i | \(0.649368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.0273 | 1.67357 | 0.836784 | − | 0.547533i | \(-0.184433\pi\) | ||||
0.836784 | + | 0.547533i | \(0.184433\pi\) | |||||||
\(662\) | −6.91248 | −0.268661 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.53989 | −0.331412 | ||||||||
\(665\) | −0.163759 | −0.00635030 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.93018 | 0.0747367 | ||||||||
\(668\) | −16.1640 | −0.625403 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.85745 | 0.0717595 | ||||||||
\(671\) | 42.9436 | 1.65782 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.5855 | −1.10189 | −0.550945 | − | 0.834542i | \(-0.685733\pi\) | ||||
−0.550945 | + | 0.834542i | \(0.685733\pi\) | |||||||
\(674\) | 4.66955 | 0.179864 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.56615 | −0.214083 | ||||||||
\(677\) | −30.3041 | −1.16468 | −0.582340 | − | 0.812945i | \(-0.697863\pi\) | ||||
−0.582340 | + | 0.812945i | \(0.697863\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.35612 | −0.205549 | ||||||||
\(680\) | 1.51555 | 0.0581188 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14.8689 | 0.569359 | ||||||||
\(683\) | 21.5333 | 0.823949 | 0.411974 | − | 0.911195i | \(-0.364839\pi\) | ||||
0.411974 | + | 0.911195i | \(0.364839\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.5816 | −0.518927 | ||||||||
\(686\) | 0.487315 | 0.0186058 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.8901 | 0.529557 | ||||||||
\(689\) | −41.3970 | −1.57710 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.2050 | 1.37730 | 0.688651 | − | 0.725093i | \(-0.258203\pi\) | ||||
0.688651 | + | 0.725093i | \(0.258203\pi\) | |||||||
\(692\) | −22.2177 | −0.844589 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.20299 | −0.121584 | ||||||||
\(695\) | −3.65150 | −0.138509 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.81537 | 0.333906 | ||||||||
\(698\) | 6.07690 | 0.230014 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.92753 | −0.299633 | ||||||||
\(701\) | 28.5639 | 1.07884 | 0.539422 | − | 0.842035i | \(-0.318643\pi\) | ||||
0.539422 | + | 0.842035i | \(0.318643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.781980 | −0.0294929 | ||||||||
\(704\) | −12.6748 | −0.477699 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.9601 | −0.563030 | ||||||||
\(707\) | −8.03179 | −0.302066 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.3923 | 1.44185 | 0.720927 | − | 0.693011i | \(-0.243716\pi\) | ||||
0.720927 | + | 0.693011i | \(0.243716\pi\) | |||||||
\(710\) | −0.845843 | −0.0317439 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.97572 | 0.186473 | ||||||||
\(713\) | −47.8633 | −1.79250 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.6632 | −0.473577 | ||||||||
\(716\) | 5.33181 | 0.199259 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.32697 | 0.198801 | ||||||||
\(719\) | −19.6881 | −0.734241 | −0.367121 | − | 0.930173i | \(-0.619656\pi\) | ||||
−0.367121 | + | 0.930173i | \(0.619656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.1212 | 0.451416 | ||||||||
\(722\) | 9.23296 | 0.343615 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.0249 | −0.744220 | ||||||||
\(725\) | −1.24492 | −0.0462352 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.1351 | −1.63688 | −0.818440 | − | 0.574592i | \(-0.805161\pi\) | ||||
−0.818440 | + | 0.574592i | \(0.805161\pi\) | |||||||
\(728\) | 7.37028 | 0.273161 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.51110 | 0.129952 | ||||||||
\(731\) | 6.15679 | 0.227717 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.12685 | −0.0416213 | −0.0208106 | − | 0.999783i | \(-0.506625\pi\) | ||||
−0.0208106 | + | 0.999783i | \(0.506625\pi\) | |||||||
\(734\) | −6.99879 | −0.258330 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34.5156 | −1.27226 | ||||||||
\(737\) | −23.9114 | −0.880789 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.372615 | 0.0137069 | 0.00685344 | − | 0.999977i | \(-0.497818\pi\) | ||||
0.00685344 | + | 0.999977i | \(0.497818\pi\) | |||||||
\(740\) | 4.22645 | 0.155367 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.01862 | 0.184239 | ||||||||
\(743\) | 43.0807 | 1.58048 | 0.790239 | − | 0.612798i | \(-0.209956\pi\) | ||||
0.790239 | + | 0.612798i | \(0.209956\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.52809 | 0.129259 | ||||||||
\(746\) | −3.17815 | −0.116360 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.13936 | −0.334168 | ||||||||
\(749\) | 11.1977 | 0.409156 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.9812 | −1.34946 | −0.674732 | − | 0.738063i | \(-0.735741\pi\) | ||||
−0.674732 | + | 0.738063i | \(0.735741\pi\) | |||||||
\(752\) | −15.6101 | −0.569243 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.542180 | 0.0197450 | ||||||||
\(755\) | −16.2544 | −0.591559 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.1174 | −0.440416 | −0.220208 | − | 0.975453i | \(-0.570674\pi\) | ||||
−0.220208 | + | 0.975453i | \(0.570674\pi\) | |||||||
\(758\) | 3.20078 | 0.116257 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.300258 | 0.0108915 | ||||||||
\(761\) | −20.3956 | −0.739341 | −0.369670 | − | 0.929163i | \(-0.620529\pi\) | ||||
−0.369670 | + | 0.929163i | \(0.620529\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.4591 | 0.378645 | ||||||||
\(764\) | −21.7833 | −0.788093 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.67485 | −0.313435 | ||||||||
\(767\) | −38.9612 | −1.40681 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.8100 | 1.86832 | 0.934159 | − | 0.356857i | \(-0.116152\pi\) | ||||
0.934159 | + | 0.356857i | \(0.116152\pi\) | |||||||
\(770\) | 1.53518 | 0.0553240 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −38.7509 | −1.39467 | ||||||||
\(773\) | 7.84456 | 0.282149 | 0.141075 | − | 0.989999i | \(-0.454944\pi\) | ||||
0.141075 | + | 0.989999i | \(0.454944\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.8708 | 1.10891 | ||||||||
\(776\) | 9.82063 | 0.352540 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.0604 | −0.468239 | ||||||||
\(779\) | 1.74648 | 0.0625741 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.8888 | 0.389631 | ||||||||
\(782\) | −3.96392 | −0.141749 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.63154 | 0.0939835 | ||||||||
\(785\) | 11.6164 | 0.414608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.0806 | 0.894028 | 0.447014 | − | 0.894527i | \(-0.352487\pi\) | ||||
0.447014 | + | 0.894527i | \(0.352487\pi\) | |||||||
\(788\) | 18.0656 | 0.643559 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.34033 | −0.118843 | ||||||||
\(791\) | 7.87867 | 0.280133 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.8301 | −1.37890 | ||||||||
\(794\) | −6.97089 | −0.247388 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.6569 | −0.696722 | ||||||||
\(797\) | 31.9270 | 1.13091 | 0.565456 | − | 0.824778i | \(-0.308700\pi\) | ||||
0.565456 | + | 0.824778i | \(0.308700\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.91917 | −0.244783 | ||||||||
\(800\) | 22.2618 | 0.787074 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.76328 | −0.132886 | ||||||||
\(803\) | −45.1994 | −1.59505 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.94177 | −0.174175 | ||||||||
\(806\) | −13.4446 | −0.473568 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.7266 | 0.518079 | ||||||||
\(809\) | 36.2961 | 1.27610 | 0.638052 | − | 0.769993i | \(-0.279740\pi\) | ||||
0.638052 | + | 0.769993i | \(0.279740\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.8823 | −1.11954 | −0.559770 | − | 0.828648i | \(-0.689111\pi\) | ||||
−0.559770 | + | 0.828648i | \(0.689111\pi\) | |||||||
\(812\) | 0.487836 | 0.0171197 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.33077 | 0.256943 | ||||||||
\(815\) | −14.5612 | −0.510055 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.21977 | 0.0426742 | ||||||||
\(818\) | 1.17572 | 0.0411081 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.43937 | −0.329637 | ||||||||
\(821\) | −11.7624 | −0.410510 | −0.205255 | − | 0.978709i | \(-0.565802\pi\) | ||||
−0.205255 | + | 0.978709i | \(0.565802\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.3668 | 0.640226 | 0.320113 | − | 0.947379i | \(-0.396279\pi\) | ||||
0.320113 | + | 0.947379i | \(0.396279\pi\) | |||||||
\(824\) | −22.2246 | −0.774231 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.72333 | 0.164346 | ||||||||
\(827\) | −13.4858 | −0.468946 | −0.234473 | − | 0.972123i | \(-0.575337\pi\) | ||||
−0.234473 | + | 0.972123i | \(0.575337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.1638 | −0.873974 | −0.436987 | − | 0.899468i | \(-0.643954\pi\) | ||||
−0.436987 | + | 0.899468i | \(0.643954\pi\) | |||||||
\(830\) | 1.60841 | 0.0558289 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.4607 | 0.397329 | ||||||||
\(833\) | 1.16643 | 0.0404143 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.49887 | 0.224903 | ||||||||
\(836\) | −1.81067 | −0.0626232 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.83499 | −0.305200 | ||||||||
\(839\) | −5.43112 | −0.187503 | −0.0937515 | − | 0.995596i | \(-0.529886\pi\) | ||||
−0.0937515 | + | 0.995596i | \(0.529886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9234 | −0.997358 | ||||||||
\(842\) | −10.8229 | −0.372983 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −29.6122 | −1.01929 | ||||||||
\(845\) | 2.23792 | 0.0769868 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.76276 | −0.301092 | ||||||||
\(848\) | 27.1009 | 0.930650 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.55664 | 0.0876922 | ||||||||
\(851\) | −23.5979 | −0.808926 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.7990 | −1.02030 | −0.510149 | − | 0.860086i | \(-0.670410\pi\) | ||||
−0.510149 | + | 0.860086i | \(0.670410\pi\) | |||||||
\(854\) | 4.70743 | 0.161085 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.5314 | −0.701749 | ||||||||
\(857\) | 28.3224 | 0.967474 | 0.483737 | − | 0.875213i | \(-0.339279\pi\) | ||||
0.483737 | + | 0.875213i | \(0.339279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.73816 | 0.229903 | 0.114951 | − | 0.993371i | \(-0.463329\pi\) | ||||
0.114951 | + | 0.993371i | \(0.463329\pi\) | |||||||
\(860\) | −6.59260 | −0.224806 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.15907 | 0.0735381 | ||||||||
\(863\) | 41.1313 | 1.40013 | 0.700063 | − | 0.714081i | \(-0.253155\pi\) | ||||
0.700063 | + | 0.714081i | \(0.253155\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.93282 | 0.303725 | ||||||||
\(866\) | 5.71157 | 0.194087 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.0971 | −0.410601 | ||||||||
\(869\) | 43.0009 | 1.45871 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.6210 | 0.732601 | ||||||||
\(872\) | −19.1771 | −0.649419 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.785322 | −0.0265639 | ||||||||
\(875\) | 6.73053 | 0.227533 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.5769 | 1.20135 | 0.600673 | − | 0.799495i | \(-0.294899\pi\) | ||||
0.600673 | + | 0.799495i | \(0.294899\pi\) | |||||||
\(878\) | −14.4469 | −0.487560 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.29007 | 0.279458 | ||||||||
\(881\) | −55.0792 | −1.85566 | −0.927832 | − | 0.372999i | \(-0.878330\pi\) | ||||
−0.927832 | + | 0.372999i | \(0.878330\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.28813 | 0.110655 | 0.0553273 | − | 0.998468i | \(-0.482380\pi\) | ||||
0.0553273 | + | 0.998468i | \(0.482380\pi\) | |||||||
\(884\) | 8.26393 | 0.277946 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.2338 | −0.411003 | ||||||||
\(887\) | 50.0083 | 1.67912 | 0.839558 | − | 0.543270i | \(-0.182814\pi\) | ||||
0.839558 | + | 0.543270i | \(0.182814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −0.937133 | −0.0314128 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.3238 | −0.847904 | ||||||||
\(893\) | −1.37081 | −0.0458724 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.14370 | −0.0716561 | ||||||||
\(896\) | −11.2883 | −0.377116 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.383194 | −0.0127873 | ||||||||
\(899\) | −1.89970 | −0.0633584 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0125 | 0.400193 | ||||||||
\(902\) | −16.3726 | −0.545147 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.4458 | −0.480461 | ||||||||
\(905\) | 8.05120 | 0.267631 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.57167 | 0.185004 | 0.0925022 | − | 0.995712i | \(-0.470513\pi\) | ||||
0.0925022 | + | 0.995712i | \(0.470513\pi\) | |||||||
\(908\) | −44.1513 | −1.46521 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.38813 | −0.0460160 | ||||||||
\(911\) | −41.4104 | −1.37199 | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||||
−0.685994 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.7055 | −0.685254 | ||||||||
\(914\) | −5.14046 | −0.170031 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.7004 | −0.717002 | ||||||||
\(917\) | −6.58055 | −0.217309 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.9610 | −0.691440 | −0.345720 | − | 0.938338i | \(-0.612365\pi\) | ||||
−0.345720 | + | 0.938338i | \(0.612365\pi\) | |||||||
\(920\) | 9.06091 | 0.298729 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.5086 | −0.477815 | ||||||||
\(923\) | −9.84577 | −0.324077 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.2201 | 0.500435 | ||||||||
\(926\) | −7.84532 | −0.257813 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.36992 | −0.0449700 | ||||||||
\(929\) | 43.7964 | 1.43691 | 0.718457 | − | 0.695571i | \(-0.244849\pi\) | ||||
0.718457 | + | 0.695571i | \(0.244849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.231089 | 0.00757365 | ||||||||
\(932\) | −22.7591 | −0.745499 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.4458 | 0.374520 | ||||||||
\(935\) | 3.67456 | 0.120171 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.5238 | −0.997168 | −0.498584 | − | 0.866841i | \(-0.666147\pi\) | ||||
−0.498584 | + | 0.866841i | \(0.666147\pi\) | |||||||
\(938\) | −2.62115 | −0.0855836 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.40896 | 0.241654 | ||||||||
\(941\) | 14.2779 | 0.465446 | 0.232723 | − | 0.972543i | \(-0.425236\pi\) | ||||
0.232723 | + | 0.972543i | \(0.425236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.7037 | 1.71627 | ||||||||
\(944\) | 25.5063 | 0.830160 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.4349 | −0.371779 | ||||||||
\(947\) | 12.8467 | 0.417461 | 0.208730 | − | 0.977973i | \(-0.433067\pi\) | ||||
0.208730 | + | 0.977973i | \(0.433067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.8699 | 1.32669 | ||||||||
\(950\) | 0.506516 | 0.0164335 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.13868 | −0.0693151 | ||||||||
\(953\) | 54.6449 | 1.77012 | 0.885061 | − | 0.465475i | \(-0.154117\pi\) | ||||
0.885061 | + | 0.465475i | \(0.154117\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.75819 | 0.283408 | ||||||||
\(956\) | 40.4122 | 1.30702 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.5004 | −0.468488 | ||||||||
\(959\) | 19.1658 | 0.618895 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.1075 | 0.519597 | ||||||||
\(962\) | −6.62857 | −0.213714 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.93713 | −0.223430 | ||||||||
\(965\) | 15.5801 | 0.501543 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.4172 | −1.52483 | −0.762417 | − | 0.647086i | \(-0.775988\pi\) | ||||
−0.762417 | + | 0.647086i | \(0.775988\pi\) | |||||||
\(968\) | 16.0668 | 0.516407 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.84963 | −0.0593880 | ||||||||
\(971\) | 32.8849 | 1.05533 | 0.527663 | − | 0.849454i | \(-0.323068\pi\) | ||||
0.527663 | + | 0.849454i | \(0.323068\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.15283 | 0.165192 | ||||||||
\(974\) | 1.98329 | 0.0635488 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25.4205 | 0.813690 | ||||||||
\(977\) | −16.2482 | −0.519827 | −0.259914 | − | 0.965632i | \(-0.583694\pi\) | ||||
−0.259914 | + | 0.965632i | \(0.583694\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0640 | 0.385566 | ||||||||
\(980\) | −1.24899 | −0.0398976 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.4944 | 0.334890 | ||||||||
\(983\) | −48.0077 | −1.53121 | −0.765603 | − | 0.643313i | \(-0.777559\pi\) | ||||
−0.765603 | + | 0.643313i | \(0.777559\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.26342 | −0.231432 | ||||||||
\(986\) | −0.157328 | −0.00501034 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.63723 | 0.0520872 | ||||||||
\(989\) | 36.8090 | 1.17046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.59145 | 0.177618 | 0.0888091 | − | 0.996049i | \(-0.471694\pi\) | ||||
0.0888091 | + | 0.996049i | \(0.471694\pi\) | |||||||
\(992\) | 33.9706 | 1.07857 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.19362 | 0.0378592 | ||||||||
\(995\) | 7.90325 | 0.250550 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.4008 | −1.37452 | −0.687259 | − | 0.726413i | \(-0.741186\pi\) | ||||
−0.687259 | + | 0.726413i | \(0.741186\pi\) | |||||||
\(998\) | −7.79238 | −0.246663 | ||||||||
\(999\) | 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 | 8001.2.a.y.1.13 | ✓ | 28 | |
3.2 | odd | 2 | inner | 8001.2.a.y.1.16 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.y.1.13 | ✓ | 28 | 1.1 | even | 1 | trivial | |
8001.2.a.y.1.16 | yes | 28 | 3.2 | odd | 2 | inner |