Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.36450\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36450 | −0.964845 | −0.482422 | − | 0.875939i | \(-0.660243\pi\) | ||||
−0.482422 | + | 0.875939i | \(0.660243\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.138150 | −0.0690748 | ||||||||
\(5\) | −3.32059 | −1.48501 | −0.742506 | − | 0.669839i | \(-0.766363\pi\) | ||||
−0.742506 | + | 0.669839i | \(0.766363\pi\) | |||||||
\(6\) | 1.36450 | 0.557053 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.91750 | 1.03149 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.53093 | 1.43281 | ||||||||
\(11\) | 1.11378 | 0.335818 | 0.167909 | − | 0.985803i | \(-0.446299\pi\) | ||||
0.167909 | + | 0.985803i | \(0.446299\pi\) | |||||||
\(12\) | 0.138150 | 0.0398803 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.36450 | 0.364677 | ||||||||
\(15\) | 3.32059 | 0.857372 | ||||||||
\(16\) | −3.70462 | −0.926154 | ||||||||
\(17\) | 0.665810 | 0.161483 | 0.0807413 | − | 0.996735i | \(-0.474271\pi\) | ||||
0.0807413 | + | 0.996735i | \(0.474271\pi\) | |||||||
\(18\) | −1.36450 | −0.321615 | ||||||||
\(19\) | 3.22931 | 0.740855 | 0.370428 | − | 0.928861i | \(-0.379211\pi\) | ||||
0.370428 | + | 0.928861i | \(0.379211\pi\) | |||||||
\(20\) | 0.458738 | 0.102577 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.51975 | −0.324012 | ||||||||
\(23\) | 5.07298 | 1.05779 | 0.528895 | − | 0.848687i | \(-0.322606\pi\) | ||||
0.528895 | + | 0.848687i | \(0.322606\pi\) | |||||||
\(24\) | −2.91750 | −0.595532 | ||||||||
\(25\) | 6.02631 | 1.20526 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.138150 | 0.0261078 | ||||||||
\(29\) | −0.615375 | −0.114272 | −0.0571361 | − | 0.998366i | \(-0.518197\pi\) | ||||
−0.0571361 | + | 0.998366i | \(0.518197\pi\) | |||||||
\(30\) | −4.53093 | −0.827231 | ||||||||
\(31\) | −8.84343 | −1.58833 | −0.794163 | − | 0.607704i | \(-0.792091\pi\) | ||||
−0.794163 | + | 0.607704i | \(0.792091\pi\) | |||||||
\(32\) | −0.780060 | −0.137896 | ||||||||
\(33\) | −1.11378 | −0.193885 | ||||||||
\(34\) | −0.908495 | −0.155806 | ||||||||
\(35\) | 3.32059 | 0.561282 | ||||||||
\(36\) | −0.138150 | −0.0230249 | ||||||||
\(37\) | −3.79560 | −0.623992 | −0.311996 | − | 0.950083i | \(-0.600998\pi\) | ||||
−0.311996 | + | 0.950083i | \(0.600998\pi\) | |||||||
\(38\) | −4.40639 | −0.714810 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.68781 | −1.53178 | ||||||||
\(41\) | 0.916015 | 0.143058 | 0.0715288 | − | 0.997439i | \(-0.477212\pi\) | ||||
0.0715288 | + | 0.997439i | \(0.477212\pi\) | |||||||
\(42\) | −1.36450 | −0.210546 | ||||||||
\(43\) | 8.09576 | 1.23459 | 0.617296 | − | 0.786731i | \(-0.288228\pi\) | ||||
0.617296 | + | 0.786731i | \(0.288228\pi\) | |||||||
\(44\) | −0.153868 | −0.0231965 | ||||||||
\(45\) | −3.32059 | −0.495004 | ||||||||
\(46\) | −6.92207 | −1.02060 | ||||||||
\(47\) | −13.0955 | −1.91018 | −0.955090 | − | 0.296316i | \(-0.904242\pi\) | ||||
−0.955090 | + | 0.296316i | \(0.904242\pi\) | |||||||
\(48\) | 3.70462 | 0.534715 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.22287 | −1.16289 | ||||||||
\(51\) | −0.665810 | −0.0932320 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.52862 | 0.484694 | 0.242347 | − | 0.970190i | \(-0.422083\pi\) | ||||
0.242347 | + | 0.970190i | \(0.422083\pi\) | |||||||
\(54\) | 1.36450 | 0.185684 | ||||||||
\(55\) | −3.69841 | −0.498694 | ||||||||
\(56\) | −2.91750 | −0.389867 | ||||||||
\(57\) | −3.22931 | −0.427733 | ||||||||
\(58\) | 0.839676 | 0.110255 | ||||||||
\(59\) | 5.48952 | 0.714674 | 0.357337 | − | 0.933975i | \(-0.383685\pi\) | ||||
0.357337 | + | 0.933975i | \(0.383685\pi\) | |||||||
\(60\) | −0.458738 | −0.0592228 | ||||||||
\(61\) | −14.1106 | −1.80667 | −0.903336 | − | 0.428934i | \(-0.858889\pi\) | ||||
−0.903336 | + | 0.428934i | \(0.858889\pi\) | |||||||
\(62\) | 12.0668 | 1.53249 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 8.47362 | 1.05920 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.51975 | 0.187069 | ||||||||
\(67\) | −3.47625 | −0.424691 | −0.212345 | − | 0.977195i | \(-0.568110\pi\) | ||||
−0.212345 | + | 0.977195i | \(0.568110\pi\) | |||||||
\(68\) | −0.0919813 | −0.0111544 | ||||||||
\(69\) | −5.07298 | −0.610716 | ||||||||
\(70\) | −4.53093 | −0.541550 | ||||||||
\(71\) | 4.77075 | 0.566184 | 0.283092 | − | 0.959093i | \(-0.408640\pi\) | ||||
0.283092 | + | 0.959093i | \(0.408640\pi\) | |||||||
\(72\) | 2.91750 | 0.343830 | ||||||||
\(73\) | −7.86139 | −0.920106 | −0.460053 | − | 0.887892i | \(-0.652170\pi\) | ||||
−0.460053 | + | 0.887892i | \(0.652170\pi\) | |||||||
\(74\) | 5.17908 | 0.602056 | ||||||||
\(75\) | −6.02631 | −0.695858 | ||||||||
\(76\) | −0.446128 | −0.0511744 | ||||||||
\(77\) | −1.11378 | −0.126927 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.8320 | −1.33120 | −0.665601 | − | 0.746307i | \(-0.731825\pi\) | ||||
−0.665601 | + | 0.746307i | \(0.731825\pi\) | |||||||
\(80\) | 12.3015 | 1.37535 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.24990 | −0.138028 | ||||||||
\(83\) | −16.4426 | −1.80481 | −0.902406 | − | 0.430887i | \(-0.858201\pi\) | ||||
−0.902406 | + | 0.430887i | \(0.858201\pi\) | |||||||
\(84\) | −0.138150 | −0.0150733 | ||||||||
\(85\) | −2.21088 | −0.239804 | ||||||||
\(86\) | −11.0466 | −1.19119 | ||||||||
\(87\) | 0.615375 | 0.0659751 | ||||||||
\(88\) | 3.24946 | 0.346393 | ||||||||
\(89\) | 16.1871 | 1.71583 | 0.857913 | − | 0.513796i | \(-0.171761\pi\) | ||||
0.857913 | + | 0.513796i | \(0.171761\pi\) | |||||||
\(90\) | 4.53093 | 0.477602 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.700830 | −0.0730666 | ||||||||
\(93\) | 8.84343 | 0.917021 | ||||||||
\(94\) | 17.8688 | 1.84303 | ||||||||
\(95\) | −10.7232 | −1.10018 | ||||||||
\(96\) | 0.780060 | 0.0796145 | ||||||||
\(97\) | −1.42122 | −0.144303 | −0.0721516 | − | 0.997394i | \(-0.522987\pi\) | ||||
−0.0721516 | + | 0.997394i | \(0.522987\pi\) | |||||||
\(98\) | −1.36450 | −0.137835 | ||||||||
\(99\) | 1.11378 | 0.111939 | ||||||||
\(100\) | −0.832531 | −0.0832531 | ||||||||
\(101\) | −0.720751 | −0.0717174 | −0.0358587 | − | 0.999357i | \(-0.511417\pi\) | ||||
−0.0358587 | + | 0.999357i | \(0.511417\pi\) | |||||||
\(102\) | 0.908495 | 0.0899544 | ||||||||
\(103\) | 14.9632 | 1.47437 | 0.737186 | − | 0.675690i | \(-0.236154\pi\) | ||||
0.737186 | + | 0.675690i | \(0.236154\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.32059 | −0.324056 | ||||||||
\(106\) | −4.81479 | −0.467654 | ||||||||
\(107\) | 11.6187 | 1.12323 | 0.561613 | − | 0.827400i | \(-0.310181\pi\) | ||||
0.561613 | + | 0.827400i | \(0.310181\pi\) | |||||||
\(108\) | 0.138150 | 0.0132934 | ||||||||
\(109\) | −4.94550 | −0.473693 | −0.236846 | − | 0.971547i | \(-0.576114\pi\) | ||||
−0.236846 | + | 0.971547i | \(0.576114\pi\) | |||||||
\(110\) | 5.04647 | 0.481162 | ||||||||
\(111\) | 3.79560 | 0.360262 | ||||||||
\(112\) | 3.70462 | 0.350053 | ||||||||
\(113\) | 16.2144 | 1.52532 | 0.762661 | − | 0.646798i | \(-0.223892\pi\) | ||||
0.762661 | + | 0.646798i | \(0.223892\pi\) | |||||||
\(114\) | 4.40639 | 0.412696 | ||||||||
\(115\) | −16.8453 | −1.57083 | ||||||||
\(116\) | 0.0850137 | 0.00789332 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.49043 | −0.689550 | ||||||||
\(119\) | −0.665810 | −0.0610347 | ||||||||
\(120\) | 9.68781 | 0.884372 | ||||||||
\(121\) | −9.75949 | −0.887226 | ||||||||
\(122\) | 19.2538 | 1.74316 | ||||||||
\(123\) | −0.916015 | −0.0825943 | ||||||||
\(124\) | 1.22172 | 0.109713 | ||||||||
\(125\) | −3.40794 | −0.304815 | ||||||||
\(126\) | 1.36450 | 0.121559 | ||||||||
\(127\) | −11.4819 | −1.01886 | −0.509429 | − | 0.860513i | \(-0.670143\pi\) | ||||
−0.509429 | + | 0.860513i | \(0.670143\pi\) | |||||||
\(128\) | −10.0021 | −0.884070 | ||||||||
\(129\) | −8.09576 | −0.712792 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.3232 | −1.60090 | −0.800451 | − | 0.599398i | \(-0.795407\pi\) | ||||
−0.800451 | + | 0.599398i | \(0.795407\pi\) | |||||||
\(132\) | 0.153868 | 0.0133925 | ||||||||
\(133\) | −3.22931 | −0.280017 | ||||||||
\(134\) | 4.74332 | 0.409761 | ||||||||
\(135\) | 3.32059 | 0.285791 | ||||||||
\(136\) | 1.94250 | 0.166568 | ||||||||
\(137\) | −13.5829 | −1.16047 | −0.580233 | − | 0.814451i | \(-0.697038\pi\) | ||||
−0.580233 | + | 0.814451i | \(0.697038\pi\) | |||||||
\(138\) | 6.92207 | 0.589246 | ||||||||
\(139\) | −0.226772 | −0.0192345 | −0.00961726 | − | 0.999954i | \(-0.503061\pi\) | ||||
−0.00961726 | + | 0.999954i | \(0.503061\pi\) | |||||||
\(140\) | −0.458738 | −0.0387704 | ||||||||
\(141\) | 13.0955 | 1.10284 | ||||||||
\(142\) | −6.50967 | −0.546279 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.70462 | −0.308718 | ||||||||
\(145\) | 2.04341 | 0.169696 | ||||||||
\(146\) | 10.7268 | 0.887759 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0.524360 | 0.0431021 | ||||||||
\(149\) | 7.17188 | 0.587543 | 0.293772 | − | 0.955876i | \(-0.405089\pi\) | ||||
0.293772 | + | 0.955876i | \(0.405089\pi\) | |||||||
\(150\) | 8.22287 | 0.671395 | ||||||||
\(151\) | −7.19280 | −0.585342 | −0.292671 | − | 0.956213i | \(-0.594544\pi\) | ||||
−0.292671 | + | 0.956213i | \(0.594544\pi\) | |||||||
\(152\) | 9.42151 | 0.764186 | ||||||||
\(153\) | 0.665810 | 0.0538275 | ||||||||
\(154\) | 1.51975 | 0.122465 | ||||||||
\(155\) | 29.3654 | 2.35868 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.18613 | 0.573515 | 0.286758 | − | 0.958003i | \(-0.407423\pi\) | ||||
0.286758 | + | 0.958003i | \(0.407423\pi\) | |||||||
\(158\) | 16.1447 | 1.28440 | ||||||||
\(159\) | −3.52862 | −0.279838 | ||||||||
\(160\) | 2.59026 | 0.204778 | ||||||||
\(161\) | −5.07298 | −0.399807 | ||||||||
\(162\) | −1.36450 | −0.107205 | ||||||||
\(163\) | −22.1597 | −1.73568 | −0.867839 | − | 0.496845i | \(-0.834492\pi\) | ||||
−0.867839 | + | 0.496845i | \(0.834492\pi\) | |||||||
\(164\) | −0.126547 | −0.00988167 | ||||||||
\(165\) | 3.69841 | 0.287921 | ||||||||
\(166\) | 22.4359 | 1.74136 | ||||||||
\(167\) | 14.9897 | 1.15994 | 0.579969 | − | 0.814638i | \(-0.303064\pi\) | ||||
0.579969 | + | 0.814638i | \(0.303064\pi\) | |||||||
\(168\) | 2.91750 | 0.225090 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.01674 | 0.231373 | ||||||||
\(171\) | 3.22931 | 0.246952 | ||||||||
\(172\) | −1.11843 | −0.0852791 | ||||||||
\(173\) | 0.425335 | 0.0323376 | 0.0161688 | − | 0.999869i | \(-0.494853\pi\) | ||||
0.0161688 | + | 0.999869i | \(0.494853\pi\) | |||||||
\(174\) | −0.839676 | −0.0636557 | ||||||||
\(175\) | −6.02631 | −0.455546 | ||||||||
\(176\) | −4.12614 | −0.311019 | ||||||||
\(177\) | −5.48952 | −0.412617 | ||||||||
\(178\) | −22.0872 | −1.65550 | ||||||||
\(179\) | 13.7825 | 1.03015 | 0.515076 | − | 0.857145i | \(-0.327764\pi\) | ||||
0.515076 | + | 0.857145i | \(0.327764\pi\) | |||||||
\(180\) | 0.458738 | 0.0341923 | ||||||||
\(181\) | 21.8738 | 1.62587 | 0.812933 | − | 0.582357i | \(-0.197870\pi\) | ||||
0.812933 | + | 0.582357i | \(0.197870\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.1106 | 1.04308 | ||||||||
\(184\) | 14.8004 | 1.09110 | ||||||||
\(185\) | 12.6036 | 0.926636 | ||||||||
\(186\) | −12.0668 | −0.884783 | ||||||||
\(187\) | 0.741567 | 0.0542287 | ||||||||
\(188\) | 1.80914 | 0.131945 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 14.6318 | 1.06150 | ||||||||
\(191\) | 10.8936 | 0.788231 | 0.394115 | − | 0.919061i | \(-0.371051\pi\) | ||||
0.394115 | + | 0.919061i | \(0.371051\pi\) | |||||||
\(192\) | −8.47362 | −0.611531 | ||||||||
\(193\) | 17.0935 | 1.23042 | 0.615208 | − | 0.788365i | \(-0.289072\pi\) | ||||
0.615208 | + | 0.788365i | \(0.289072\pi\) | |||||||
\(194\) | 1.93925 | 0.139230 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.138150 | −0.00986782 | ||||||||
\(197\) | 4.58665 | 0.326785 | 0.163393 | − | 0.986561i | \(-0.447756\pi\) | ||||
0.163393 | + | 0.986561i | \(0.447756\pi\) | |||||||
\(198\) | −1.51975 | −0.108004 | ||||||||
\(199\) | 6.08803 | 0.431569 | 0.215785 | − | 0.976441i | \(-0.430769\pi\) | ||||
0.215785 | + | 0.976441i | \(0.430769\pi\) | |||||||
\(200\) | 17.5817 | 1.24322 | ||||||||
\(201\) | 3.47625 | 0.245195 | ||||||||
\(202\) | 0.983462 | 0.0691961 | ||||||||
\(203\) | 0.615375 | 0.0431908 | ||||||||
\(204\) | 0.0919813 | 0.00643998 | ||||||||
\(205\) | −3.04171 | −0.212442 | ||||||||
\(206\) | −20.4173 | −1.42254 | ||||||||
\(207\) | 5.07298 | 0.352597 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.59675 | 0.248793 | ||||||||
\(210\) | 4.53093 | 0.312664 | ||||||||
\(211\) | 10.3803 | 0.714606 | 0.357303 | − | 0.933988i | \(-0.383696\pi\) | ||||
0.357303 | + | 0.933988i | \(0.383696\pi\) | |||||||
\(212\) | −0.487478 | −0.0334801 | ||||||||
\(213\) | −4.77075 | −0.326886 | ||||||||
\(214\) | −15.8537 | −1.08374 | ||||||||
\(215\) | −26.8827 | −1.83338 | ||||||||
\(216\) | −2.91750 | −0.198511 | ||||||||
\(217\) | 8.84343 | 0.600331 | ||||||||
\(218\) | 6.74811 | 0.457040 | ||||||||
\(219\) | 7.86139 | 0.531223 | ||||||||
\(220\) | 0.510934 | 0.0344471 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.17908 | −0.347597 | ||||||||
\(223\) | −12.7655 | −0.854840 | −0.427420 | − | 0.904053i | \(-0.640577\pi\) | ||||
−0.427420 | + | 0.904053i | \(0.640577\pi\) | |||||||
\(224\) | 0.780060 | 0.0521199 | ||||||||
\(225\) | 6.02631 | 0.401754 | ||||||||
\(226\) | −22.1245 | −1.47170 | ||||||||
\(227\) | 13.3301 | 0.884747 | 0.442374 | − | 0.896831i | \(-0.354136\pi\) | ||||
0.442374 | + | 0.896831i | \(0.354136\pi\) | |||||||
\(228\) | 0.446128 | 0.0295456 | ||||||||
\(229\) | −9.63903 | −0.636965 | −0.318482 | − | 0.947929i | \(-0.603173\pi\) | ||||
−0.318482 | + | 0.947929i | \(0.603173\pi\) | |||||||
\(230\) | 22.9853 | 1.51561 | ||||||||
\(231\) | 1.11378 | 0.0732815 | ||||||||
\(232\) | −1.79535 | −0.117871 | ||||||||
\(233\) | −22.0553 | −1.44489 | −0.722444 | − | 0.691429i | \(-0.756981\pi\) | ||||
−0.722444 | + | 0.691429i | \(0.756981\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 43.4849 | 2.83664 | ||||||||
\(236\) | −0.758374 | −0.0493659 | ||||||||
\(237\) | 11.8320 | 0.768570 | ||||||||
\(238\) | 0.908495 | 0.0588890 | ||||||||
\(239\) | 23.6972 | 1.53285 | 0.766424 | − | 0.642335i | \(-0.222034\pi\) | ||||
0.766424 | + | 0.642335i | \(0.222034\pi\) | |||||||
\(240\) | −12.3015 | −0.794059 | ||||||||
\(241\) | 17.5586 | 1.13105 | 0.565525 | − | 0.824731i | \(-0.308673\pi\) | ||||
0.565525 | + | 0.824731i | \(0.308673\pi\) | |||||||
\(242\) | 13.3168 | 0.856036 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.94937 | 0.124795 | ||||||||
\(245\) | −3.32059 | −0.212145 | ||||||||
\(246\) | 1.24990 | 0.0796907 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −25.8007 | −1.63834 | ||||||||
\(249\) | 16.4426 | 1.04201 | ||||||||
\(250\) | 4.65012 | 0.294099 | ||||||||
\(251\) | 30.2065 | 1.90662 | 0.953310 | − | 0.301994i | \(-0.0976522\pi\) | ||||
0.953310 | + | 0.301994i | \(0.0976522\pi\) | |||||||
\(252\) | 0.138150 | 0.00870260 | ||||||||
\(253\) | 5.65020 | 0.355225 | ||||||||
\(254\) | 15.6671 | 0.983039 | ||||||||
\(255\) | 2.21088 | 0.138451 | ||||||||
\(256\) | −3.29940 | −0.206213 | ||||||||
\(257\) | −4.98163 | −0.310746 | −0.155373 | − | 0.987856i | \(-0.549658\pi\) | ||||
−0.155373 | + | 0.987856i | \(0.549658\pi\) | |||||||
\(258\) | 11.0466 | 0.687733 | ||||||||
\(259\) | 3.79560 | 0.235847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.615375 | −0.0380907 | ||||||||
\(262\) | 25.0019 | 1.54462 | ||||||||
\(263\) | −12.5614 | −0.774571 | −0.387286 | − | 0.921960i | \(-0.626587\pi\) | ||||
−0.387286 | + | 0.921960i | \(0.626587\pi\) | |||||||
\(264\) | −3.24946 | −0.199990 | ||||||||
\(265\) | −11.7171 | −0.719776 | ||||||||
\(266\) | 4.40639 | 0.270173 | ||||||||
\(267\) | −16.1871 | −0.990632 | ||||||||
\(268\) | 0.480242 | 0.0293354 | ||||||||
\(269\) | −1.45811 | −0.0889028 | −0.0444514 | − | 0.999012i | \(-0.514154\pi\) | ||||
−0.0444514 | + | 0.999012i | \(0.514154\pi\) | |||||||
\(270\) | −4.53093 | −0.275744 | ||||||||
\(271\) | −15.5702 | −0.945820 | −0.472910 | − | 0.881111i | \(-0.656797\pi\) | ||||
−0.472910 | + | 0.881111i | \(0.656797\pi\) | |||||||
\(272\) | −2.46657 | −0.149558 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.5338 | 1.11967 | ||||||||
\(275\) | 6.71199 | 0.404748 | ||||||||
\(276\) | 0.700830 | 0.0421850 | ||||||||
\(277\) | −18.0174 | −1.08256 | −0.541280 | − | 0.840842i | \(-0.682060\pi\) | ||||
−0.541280 | + | 0.840842i | \(0.682060\pi\) | |||||||
\(278\) | 0.309429 | 0.0185583 | ||||||||
\(279\) | −8.84343 | −0.529442 | ||||||||
\(280\) | 9.68781 | 0.578957 | ||||||||
\(281\) | 25.8821 | 1.54400 | 0.771999 | − | 0.635624i | \(-0.219257\pi\) | ||||
0.771999 | + | 0.635624i | \(0.219257\pi\) | |||||||
\(282\) | −17.8688 | −1.06407 | ||||||||
\(283\) | 9.98839 | 0.593748 | 0.296874 | − | 0.954917i | \(-0.404056\pi\) | ||||
0.296874 | + | 0.954917i | \(0.404056\pi\) | |||||||
\(284\) | −0.659077 | −0.0391090 | ||||||||
\(285\) | 10.7232 | 0.635189 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.916015 | −0.0540707 | ||||||||
\(288\) | −0.780060 | −0.0459655 | ||||||||
\(289\) | −16.5567 | −0.973923 | ||||||||
\(290\) | −2.78822 | −0.163730 | ||||||||
\(291\) | 1.42122 | 0.0833135 | ||||||||
\(292\) | 1.08605 | 0.0635561 | ||||||||
\(293\) | −3.60381 | −0.210537 | −0.105268 | − | 0.994444i | \(-0.533570\pi\) | ||||
−0.105268 | + | 0.994444i | \(0.533570\pi\) | |||||||
\(294\) | 1.36450 | 0.0795790 | ||||||||
\(295\) | −18.2284 | −1.06130 | ||||||||
\(296\) | −11.0736 | −0.643642 | ||||||||
\(297\) | −1.11378 | −0.0646282 | ||||||||
\(298\) | −9.78600 | −0.566888 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.832531 | 0.0480662 | ||||||||
\(301\) | −8.09576 | −0.466632 | ||||||||
\(302\) | 9.81455 | 0.564764 | ||||||||
\(303\) | 0.720751 | 0.0414061 | ||||||||
\(304\) | −11.9634 | −0.686146 | ||||||||
\(305\) | 46.8553 | 2.68293 | ||||||||
\(306\) | −0.908495 | −0.0519352 | ||||||||
\(307\) | 17.4426 | 0.995500 | 0.497750 | − | 0.867321i | \(-0.334160\pi\) | ||||
0.497750 | + | 0.867321i | \(0.334160\pi\) | |||||||
\(308\) | 0.153868 | 0.00876747 | ||||||||
\(309\) | −14.9632 | −0.851229 | ||||||||
\(310\) | −40.0690 | −2.27576 | ||||||||
\(311\) | −22.3025 | −1.26466 | −0.632330 | − | 0.774699i | \(-0.717901\pi\) | ||||
−0.632330 | + | 0.774699i | \(0.717901\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.792995 | 0.0448227 | 0.0224114 | − | 0.999749i | \(-0.492866\pi\) | ||||
0.0224114 | + | 0.999749i | \(0.492866\pi\) | |||||||
\(314\) | −9.80545 | −0.553353 | ||||||||
\(315\) | 3.32059 | 0.187094 | ||||||||
\(316\) | 1.63458 | 0.0919525 | ||||||||
\(317\) | 8.48350 | 0.476481 | 0.238240 | − | 0.971206i | \(-0.423429\pi\) | ||||
0.238240 | + | 0.971206i | \(0.423429\pi\) | |||||||
\(318\) | 4.81479 | 0.270000 | ||||||||
\(319\) | −0.685393 | −0.0383747 | ||||||||
\(320\) | −28.1374 | −1.57293 | ||||||||
\(321\) | −11.6187 | −0.648495 | ||||||||
\(322\) | 6.92207 | 0.385752 | ||||||||
\(323\) | 2.15011 | 0.119635 | ||||||||
\(324\) | −0.138150 | −0.00767497 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 30.2368 | 1.67466 | ||||||||
\(327\) | 4.94550 | 0.273487 | ||||||||
\(328\) | 2.67247 | 0.147563 | ||||||||
\(329\) | 13.0955 | 0.721980 | ||||||||
\(330\) | −5.04647 | −0.277799 | ||||||||
\(331\) | 33.5170 | 1.84226 | 0.921130 | − | 0.389256i | \(-0.127268\pi\) | ||||
0.921130 | + | 0.389256i | \(0.127268\pi\) | |||||||
\(332\) | 2.27154 | 0.124667 | ||||||||
\(333\) | −3.79560 | −0.207997 | ||||||||
\(334\) | −20.4534 | −1.11916 | ||||||||
\(335\) | 11.5432 | 0.630671 | ||||||||
\(336\) | −3.70462 | −0.202103 | ||||||||
\(337\) | −19.4227 | −1.05802 | −0.529012 | − | 0.848614i | \(-0.677437\pi\) | ||||
−0.529012 | + | 0.848614i | \(0.677437\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.2144 | −0.880645 | ||||||||
\(340\) | 0.305432 | 0.0165644 | ||||||||
\(341\) | −9.84965 | −0.533389 | ||||||||
\(342\) | −4.40639 | −0.238270 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 23.6194 | 1.27347 | ||||||||
\(345\) | 16.8453 | 0.906920 | ||||||||
\(346\) | −0.580368 | −0.0312008 | ||||||||
\(347\) | −11.1748 | −0.599896 | −0.299948 | − | 0.953956i | \(-0.596969\pi\) | ||||
−0.299948 | + | 0.953956i | \(0.596969\pi\) | |||||||
\(348\) | −0.0850137 | −0.00455721 | ||||||||
\(349\) | −36.8109 | −1.97044 | −0.985222 | − | 0.171281i | \(-0.945209\pi\) | ||||
−0.985222 | + | 0.171281i | \(0.945209\pi\) | |||||||
\(350\) | 8.22287 | 0.439531 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.868817 | −0.0463081 | ||||||||
\(353\) | −17.5115 | −0.932041 | −0.466021 | − | 0.884774i | \(-0.654313\pi\) | ||||
−0.466021 | + | 0.884774i | \(0.654313\pi\) | |||||||
\(354\) | 7.49043 | 0.398112 | ||||||||
\(355\) | −15.8417 | −0.840790 | ||||||||
\(356\) | −2.23623 | −0.118520 | ||||||||
\(357\) | 0.665810 | 0.0352384 | ||||||||
\(358\) | −18.8062 | −0.993936 | ||||||||
\(359\) | −8.15731 | −0.430527 | −0.215263 | − | 0.976556i | \(-0.569061\pi\) | ||||
−0.215263 | + | 0.976556i | \(0.569061\pi\) | |||||||
\(360\) | −9.68781 | −0.510592 | ||||||||
\(361\) | −8.57154 | −0.451133 | ||||||||
\(362\) | −29.8467 | −1.56871 | ||||||||
\(363\) | 9.75949 | 0.512240 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.1044 | 1.36637 | ||||||||
\(366\) | −19.2538 | −1.00641 | ||||||||
\(367\) | 15.8536 | 0.827552 | 0.413776 | − | 0.910379i | \(-0.364210\pi\) | ||||
0.413776 | + | 0.910379i | \(0.364210\pi\) | |||||||
\(368\) | −18.7935 | −0.979677 | ||||||||
\(369\) | 0.916015 | 0.0476859 | ||||||||
\(370\) | −17.1976 | −0.894060 | ||||||||
\(371\) | −3.52862 | −0.183197 | ||||||||
\(372\) | −1.22172 | −0.0633430 | ||||||||
\(373\) | 11.3075 | 0.585482 | 0.292741 | − | 0.956192i | \(-0.405433\pi\) | ||||
0.292741 | + | 0.956192i | \(0.405433\pi\) | |||||||
\(374\) | −1.01187 | −0.0523223 | ||||||||
\(375\) | 3.40794 | 0.175985 | ||||||||
\(376\) | −38.2062 | −1.97033 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.36450 | −0.0701821 | ||||||||
\(379\) | −14.8591 | −0.763262 | −0.381631 | − | 0.924315i | \(-0.624638\pi\) | ||||
−0.381631 | + | 0.924315i | \(0.624638\pi\) | |||||||
\(380\) | 1.48141 | 0.0759946 | ||||||||
\(381\) | 11.4819 | 0.588238 | ||||||||
\(382\) | −14.8642 | −0.760520 | ||||||||
\(383\) | −19.5528 | −0.999101 | −0.499551 | − | 0.866285i | \(-0.666502\pi\) | ||||
−0.499551 | + | 0.866285i | \(0.666502\pi\) | |||||||
\(384\) | 10.0021 | 0.510418 | ||||||||
\(385\) | 3.69841 | 0.188489 | ||||||||
\(386\) | −23.3240 | −1.18716 | ||||||||
\(387\) | 8.09576 | 0.411531 | ||||||||
\(388\) | 0.196341 | 0.00996771 | ||||||||
\(389\) | 15.4987 | 0.785815 | 0.392907 | − | 0.919578i | \(-0.371469\pi\) | ||||
0.392907 | + | 0.919578i | \(0.371469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.37764 | 0.170815 | ||||||||
\(392\) | 2.91750 | 0.147356 | ||||||||
\(393\) | 18.3232 | 0.924281 | ||||||||
\(394\) | −6.25847 | −0.315297 | ||||||||
\(395\) | 39.2892 | 1.97685 | ||||||||
\(396\) | −0.153868 | −0.00773218 | ||||||||
\(397\) | 23.2126 | 1.16501 | 0.582503 | − | 0.812828i | \(-0.302073\pi\) | ||||
0.582503 | + | 0.812828i | \(0.302073\pi\) | |||||||
\(398\) | −8.30710 | −0.416397 | ||||||||
\(399\) | 3.22931 | 0.161668 | ||||||||
\(400\) | −22.3251 | −1.11626 | ||||||||
\(401\) | 39.2538 | 1.96024 | 0.980121 | − | 0.198403i | \(-0.0635754\pi\) | ||||
0.980121 | + | 0.198403i | \(0.0635754\pi\) | |||||||
\(402\) | −4.74332 | −0.236576 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.0995714 | 0.00495386 | ||||||||
\(405\) | −3.32059 | −0.165001 | ||||||||
\(406\) | −0.839676 | −0.0416724 | ||||||||
\(407\) | −4.22747 | −0.209548 | ||||||||
\(408\) | −1.94250 | −0.0961680 | ||||||||
\(409\) | 19.5916 | 0.968743 | 0.484371 | − | 0.874862i | \(-0.339048\pi\) | ||||
0.484371 | + | 0.874862i | \(0.339048\pi\) | |||||||
\(410\) | 4.15040 | 0.204974 | ||||||||
\(411\) | 13.5829 | 0.669995 | ||||||||
\(412\) | −2.06716 | −0.101842 | ||||||||
\(413\) | −5.48952 | −0.270121 | ||||||||
\(414\) | −6.92207 | −0.340201 | ||||||||
\(415\) | 54.5992 | 2.68017 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.226772 | 0.0111051 | ||||||||
\(418\) | −4.90775 | −0.240046 | ||||||||
\(419\) | 8.42940 | 0.411803 | 0.205902 | − | 0.978573i | \(-0.433987\pi\) | ||||
0.205902 | + | 0.978573i | \(0.433987\pi\) | |||||||
\(420\) | 0.458738 | 0.0223841 | ||||||||
\(421\) | −2.84921 | −0.138862 | −0.0694309 | − | 0.997587i | \(-0.522118\pi\) | ||||
−0.0694309 | + | 0.997587i | \(0.522118\pi\) | |||||||
\(422\) | −14.1638 | −0.689484 | ||||||||
\(423\) | −13.0955 | −0.636727 | ||||||||
\(424\) | 10.2948 | 0.499957 | ||||||||
\(425\) | 4.01237 | 0.194629 | ||||||||
\(426\) | 6.50967 | 0.315394 | ||||||||
\(427\) | 14.1106 | 0.682858 | ||||||||
\(428\) | −1.60512 | −0.0775865 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 36.6813 | 1.76893 | ||||||||
\(431\) | −35.8018 | −1.72451 | −0.862257 | − | 0.506472i | \(-0.830950\pi\) | ||||
−0.862257 | + | 0.506472i | \(0.830950\pi\) | |||||||
\(432\) | 3.70462 | 0.178238 | ||||||||
\(433\) | 8.92560 | 0.428937 | 0.214468 | − | 0.976731i | \(-0.431198\pi\) | ||||
0.214468 | + | 0.976731i | \(0.431198\pi\) | |||||||
\(434\) | −12.0668 | −0.579226 | ||||||||
\(435\) | −2.04341 | −0.0979738 | ||||||||
\(436\) | 0.683218 | 0.0327202 | ||||||||
\(437\) | 16.3823 | 0.783670 | ||||||||
\(438\) | −10.7268 | −0.512548 | ||||||||
\(439\) | −4.92169 | −0.234899 | −0.117450 | − | 0.993079i | \(-0.537472\pi\) | ||||
−0.117450 | + | 0.993079i | \(0.537472\pi\) | |||||||
\(440\) | −10.7901 | −0.514398 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.96252 | −0.235776 | −0.117888 | − | 0.993027i | \(-0.537612\pi\) | ||||
−0.117888 | + | 0.993027i | \(0.537612\pi\) | |||||||
\(444\) | −0.524360 | −0.0248850 | ||||||||
\(445\) | −53.7506 | −2.54802 | ||||||||
\(446\) | 17.4185 | 0.824788 | ||||||||
\(447\) | −7.17188 | −0.339218 | ||||||||
\(448\) | −8.47362 | −0.400341 | ||||||||
\(449\) | 17.9792 | 0.848492 | 0.424246 | − | 0.905547i | \(-0.360539\pi\) | ||||
0.424246 | + | 0.905547i | \(0.360539\pi\) | |||||||
\(450\) | −8.22287 | −0.387630 | ||||||||
\(451\) | 1.02024 | 0.0480413 | ||||||||
\(452\) | −2.24001 | −0.105361 | ||||||||
\(453\) | 7.19280 | 0.337947 | ||||||||
\(454\) | −18.1888 | −0.853644 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.42151 | −0.441203 | ||||||||
\(457\) | 27.8074 | 1.30078 | 0.650389 | − | 0.759602i | \(-0.274606\pi\) | ||||
0.650389 | + | 0.759602i | \(0.274606\pi\) | |||||||
\(458\) | 13.1524 | 0.614572 | ||||||||
\(459\) | −0.665810 | −0.0310773 | ||||||||
\(460\) | 2.32717 | 0.108505 | ||||||||
\(461\) | −16.5862 | −0.772496 | −0.386248 | − | 0.922395i | \(-0.626229\pi\) | ||||
−0.386248 | + | 0.922395i | \(0.626229\pi\) | |||||||
\(462\) | −1.51975 | −0.0707053 | ||||||||
\(463\) | 42.4947 | 1.97490 | 0.987449 | − | 0.157940i | \(-0.0504853\pi\) | ||||
0.987449 | + | 0.157940i | \(0.0504853\pi\) | |||||||
\(464\) | 2.27973 | 0.105834 | ||||||||
\(465\) | −29.3654 | −1.36179 | ||||||||
\(466\) | 30.0943 | 1.39409 | ||||||||
\(467\) | −1.30217 | −0.0602575 | −0.0301287 | − | 0.999546i | \(-0.509592\pi\) | ||||
−0.0301287 | + | 0.999546i | \(0.509592\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.47625 | 0.160518 | ||||||||
\(470\) | −59.3349 | −2.73692 | ||||||||
\(471\) | −7.18613 | −0.331119 | ||||||||
\(472\) | 16.0157 | 0.737180 | ||||||||
\(473\) | 9.01691 | 0.414598 | ||||||||
\(474\) | −16.1447 | −0.741551 | ||||||||
\(475\) | 19.4608 | 0.892924 | ||||||||
\(476\) | 0.0919813 | 0.00421595 | ||||||||
\(477\) | 3.52862 | 0.161565 | ||||||||
\(478\) | −32.3348 | −1.47896 | ||||||||
\(479\) | 8.28495 | 0.378549 | 0.189274 | − | 0.981924i | \(-0.439386\pi\) | ||||
0.189274 | + | 0.981924i | \(0.439386\pi\) | |||||||
\(480\) | −2.59026 | −0.118229 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −23.9587 | −1.09129 | ||||||||
\(483\) | 5.07298 | 0.230829 | ||||||||
\(484\) | 1.34827 | 0.0612849 | ||||||||
\(485\) | 4.71929 | 0.214292 | ||||||||
\(486\) | 1.36450 | 0.0618948 | ||||||||
\(487\) | 43.5629 | 1.97402 | 0.987011 | − | 0.160651i | \(-0.0513595\pi\) | ||||
0.987011 | + | 0.160651i | \(0.0513595\pi\) | |||||||
\(488\) | −41.1675 | −1.86357 | ||||||||
\(489\) | 22.1597 | 1.00209 | ||||||||
\(490\) | 4.53093 | 0.204687 | ||||||||
\(491\) | 41.8051 | 1.88664 | 0.943318 | − | 0.331890i | \(-0.107686\pi\) | ||||
0.943318 | + | 0.331890i | \(0.107686\pi\) | |||||||
\(492\) | 0.126547 | 0.00570518 | ||||||||
\(493\) | −0.409722 | −0.0184530 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.69841 | −0.166231 | ||||||||
\(496\) | 32.7615 | 1.47103 | ||||||||
\(497\) | −4.77075 | −0.213997 | ||||||||
\(498\) | −22.4359 | −1.00538 | ||||||||
\(499\) | 6.28962 | 0.281562 | 0.140781 | − | 0.990041i | \(-0.455039\pi\) | ||||
0.140781 | + | 0.990041i | \(0.455039\pi\) | |||||||
\(500\) | 0.470805 | 0.0210550 | ||||||||
\(501\) | −14.9897 | −0.669691 | ||||||||
\(502\) | −41.2167 | −1.83959 | ||||||||
\(503\) | 18.5950 | 0.829109 | 0.414554 | − | 0.910025i | \(-0.363937\pi\) | ||||
0.414554 | + | 0.910025i | \(0.363937\pi\) | |||||||
\(504\) | −2.91750 | −0.129956 | ||||||||
\(505\) | 2.39332 | 0.106501 | ||||||||
\(506\) | −7.70968 | −0.342737 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.58622 | 0.0703773 | ||||||||
\(509\) | 2.87537 | 0.127448 | 0.0637242 | − | 0.997968i | \(-0.479702\pi\) | ||||
0.0637242 | + | 0.997968i | \(0.479702\pi\) | |||||||
\(510\) | −3.01674 | −0.133583 | ||||||||
\(511\) | 7.86139 | 0.347767 | ||||||||
\(512\) | 24.5062 | 1.08303 | ||||||||
\(513\) | −3.22931 | −0.142578 | ||||||||
\(514\) | 6.79742 | 0.299821 | ||||||||
\(515\) | −49.6868 | −2.18946 | ||||||||
\(516\) | 1.11843 | 0.0492359 | ||||||||
\(517\) | −14.5856 | −0.641473 | ||||||||
\(518\) | −5.17908 | −0.227556 | ||||||||
\(519\) | −0.425335 | −0.0186701 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.3937 | 0.805843 | 0.402922 | − | 0.915234i | \(-0.367995\pi\) | ||||
0.402922 | + | 0.915234i | \(0.367995\pi\) | |||||||
\(522\) | 0.839676 | 0.0367516 | ||||||||
\(523\) | 2.24583 | 0.0982031 | 0.0491016 | − | 0.998794i | \(-0.484364\pi\) | ||||
0.0491016 | + | 0.998794i | \(0.484364\pi\) | |||||||
\(524\) | 2.53134 | 0.110582 | ||||||||
\(525\) | 6.02631 | 0.263010 | ||||||||
\(526\) | 17.1400 | 0.747341 | ||||||||
\(527\) | −5.88804 | −0.256487 | ||||||||
\(528\) | 4.12614 | 0.179567 | ||||||||
\(529\) | 2.73517 | 0.118920 | ||||||||
\(530\) | 15.9879 | 0.694472 | ||||||||
\(531\) | 5.48952 | 0.238225 | ||||||||
\(532\) | 0.446128 | 0.0193421 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 22.0872 | 0.955806 | ||||||||
\(535\) | −38.5810 | −1.66800 | ||||||||
\(536\) | −10.1419 | −0.438065 | ||||||||
\(537\) | −13.7825 | −0.594758 | ||||||||
\(538\) | 1.98959 | 0.0857774 | ||||||||
\(539\) | 1.11378 | 0.0479740 | ||||||||
\(540\) | −0.458738 | −0.0197409 | ||||||||
\(541\) | 22.4028 | 0.963170 | 0.481585 | − | 0.876399i | \(-0.340061\pi\) | ||||
0.481585 | + | 0.876399i | \(0.340061\pi\) | |||||||
\(542\) | 21.2454 | 0.912570 | ||||||||
\(543\) | −21.8738 | −0.938694 | ||||||||
\(544\) | −0.519371 | −0.0222679 | ||||||||
\(545\) | 16.4220 | 0.703440 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.5948 | −0.966084 | −0.483042 | − | 0.875597i | \(-0.660468\pi\) | ||||
−0.483042 | + | 0.875597i | \(0.660468\pi\) | |||||||
\(548\) | 1.87647 | 0.0801589 | ||||||||
\(549\) | −14.1106 | −0.602224 | ||||||||
\(550\) | −9.15849 | −0.390519 | ||||||||
\(551\) | −1.98724 | −0.0846591 | ||||||||
\(552\) | −14.8004 | −0.629948 | ||||||||
\(553\) | 11.8320 | 0.503147 | ||||||||
\(554\) | 24.5847 | 1.04450 | ||||||||
\(555\) | −12.6036 | −0.534994 | ||||||||
\(556\) | 0.0313284 | 0.00132862 | ||||||||
\(557\) | 18.0550 | 0.765014 | 0.382507 | − | 0.923953i | \(-0.375061\pi\) | ||||
0.382507 | + | 0.923953i | \(0.375061\pi\) | |||||||
\(558\) | 12.0668 | 0.510829 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −12.3015 | −0.519833 | ||||||||
\(561\) | −0.741567 | −0.0313090 | ||||||||
\(562\) | −35.3161 | −1.48972 | ||||||||
\(563\) | 11.9664 | 0.504322 | 0.252161 | − | 0.967685i | \(-0.418859\pi\) | ||||
0.252161 | + | 0.967685i | \(0.418859\pi\) | |||||||
\(564\) | −1.80914 | −0.0761786 | ||||||||
\(565\) | −53.8413 | −2.26512 | ||||||||
\(566\) | −13.6291 | −0.572875 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 13.9186 | 0.584013 | ||||||||
\(569\) | 35.7491 | 1.49868 | 0.749339 | − | 0.662186i | \(-0.230371\pi\) | ||||
0.749339 | + | 0.662186i | \(0.230371\pi\) | |||||||
\(570\) | −14.6318 | −0.612858 | ||||||||
\(571\) | 18.4132 | 0.770570 | 0.385285 | − | 0.922798i | \(-0.374103\pi\) | ||||
0.385285 | + | 0.922798i | \(0.374103\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.8936 | −0.455085 | ||||||||
\(574\) | 1.24990 | 0.0521698 | ||||||||
\(575\) | 30.5714 | 1.27491 | ||||||||
\(576\) | 8.47362 | 0.353068 | ||||||||
\(577\) | −27.4531 | −1.14289 | −0.571444 | − | 0.820641i | \(-0.693617\pi\) | ||||
−0.571444 | + | 0.820641i | \(0.693617\pi\) | |||||||
\(578\) | 22.5916 | 0.939685 | ||||||||
\(579\) | −17.0935 | −0.710381 | ||||||||
\(580\) | −0.282295 | −0.0117217 | ||||||||
\(581\) | 16.4426 | 0.682155 | ||||||||
\(582\) | −1.93925 | −0.0803846 | ||||||||
\(583\) | 3.93012 | 0.162769 | ||||||||
\(584\) | −22.9356 | −0.949081 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.91738 | 0.203135 | ||||||||
\(587\) | −23.5141 | −0.970531 | −0.485265 | − | 0.874367i | \(-0.661277\pi\) | ||||
−0.485265 | + | 0.874367i | \(0.661277\pi\) | |||||||
\(588\) | 0.138150 | 0.00569719 | ||||||||
\(589\) | −28.5582 | −1.17672 | ||||||||
\(590\) | 24.8726 | 1.02399 | ||||||||
\(591\) | −4.58665 | −0.188670 | ||||||||
\(592\) | 14.0612 | 0.577913 | ||||||||
\(593\) | 31.0493 | 1.27504 | 0.637520 | − | 0.770433i | \(-0.279960\pi\) | ||||
0.637520 | + | 0.770433i | \(0.279960\pi\) | |||||||
\(594\) | 1.51975 | 0.0623562 | ||||||||
\(595\) | 2.21088 | 0.0906372 | ||||||||
\(596\) | −0.990792 | −0.0405844 | ||||||||
\(597\) | −6.08803 | −0.249167 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.3733 | −0.955007 | −0.477503 | − | 0.878630i | \(-0.658458\pi\) | ||||
−0.477503 | + | 0.878630i | \(0.658458\pi\) | |||||||
\(600\) | −17.5817 | −0.717771 | ||||||||
\(601\) | −25.5738 | −1.04318 | −0.521588 | − | 0.853197i | \(-0.674660\pi\) | ||||
−0.521588 | + | 0.853197i | \(0.674660\pi\) | |||||||
\(602\) | 11.0466 | 0.450227 | ||||||||
\(603\) | −3.47625 | −0.141564 | ||||||||
\(604\) | 0.993682 | 0.0404323 | ||||||||
\(605\) | 32.4072 | 1.31754 | ||||||||
\(606\) | −0.983462 | −0.0399504 | ||||||||
\(607\) | −31.2846 | −1.26980 | −0.634902 | − | 0.772593i | \(-0.718959\pi\) | ||||
−0.634902 | + | 0.772593i | \(0.718959\pi\) | |||||||
\(608\) | −2.51906 | −0.102161 | ||||||||
\(609\) | −0.615375 | −0.0249362 | ||||||||
\(610\) | −63.9339 | −2.58861 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.0919813 | −0.00371812 | ||||||||
\(613\) | −8.72726 | −0.352491 | −0.176245 | − | 0.984346i | \(-0.556395\pi\) | ||||
−0.176245 | + | 0.984346i | \(0.556395\pi\) | |||||||
\(614\) | −23.8003 | −0.960502 | ||||||||
\(615\) | 3.04171 | 0.122654 | ||||||||
\(616\) | −3.24946 | −0.130924 | ||||||||
\(617\) | −19.2871 | −0.776470 | −0.388235 | − | 0.921560i | \(-0.626915\pi\) | ||||
−0.388235 | + | 0.921560i | \(0.626915\pi\) | |||||||
\(618\) | 20.4173 | 0.821304 | ||||||||
\(619\) | 42.3279 | 1.70130 | 0.850650 | − | 0.525732i | \(-0.176209\pi\) | ||||
0.850650 | + | 0.525732i | \(0.176209\pi\) | |||||||
\(620\) | −4.05681 | −0.162926 | ||||||||
\(621\) | −5.07298 | −0.203572 | ||||||||
\(622\) | 30.4317 | 1.22020 | ||||||||
\(623\) | −16.1871 | −0.648521 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.8152 | −0.752607 | ||||||||
\(626\) | −1.08204 | −0.0432470 | ||||||||
\(627\) | −3.59675 | −0.143640 | ||||||||
\(628\) | −0.992760 | −0.0396154 | ||||||||
\(629\) | −2.52714 | −0.100764 | ||||||||
\(630\) | −4.53093 | −0.180517 | ||||||||
\(631\) | 15.0098 | 0.597531 | 0.298766 | − | 0.954326i | \(-0.403425\pi\) | ||||
0.298766 | + | 0.954326i | \(0.403425\pi\) | |||||||
\(632\) | −34.5198 | −1.37312 | ||||||||
\(633\) | −10.3803 | −0.412578 | ||||||||
\(634\) | −11.5757 | −0.459730 | ||||||||
\(635\) | 38.1268 | 1.51302 | ||||||||
\(636\) | 0.487478 | 0.0193297 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.935217 | 0.0370256 | ||||||||
\(639\) | 4.77075 | 0.188728 | ||||||||
\(640\) | 33.2129 | 1.31285 | ||||||||
\(641\) | 24.5344 | 0.969050 | 0.484525 | − | 0.874777i | \(-0.338992\pi\) | ||||
0.484525 | + | 0.874777i | \(0.338992\pi\) | |||||||
\(642\) | 15.8537 | 0.625697 | ||||||||
\(643\) | −29.4303 | −1.16062 | −0.580309 | − | 0.814396i | \(-0.697068\pi\) | ||||
−0.580309 | + | 0.814396i | \(0.697068\pi\) | |||||||
\(644\) | 0.700830 | 0.0276166 | ||||||||
\(645\) | 26.8827 | 1.05850 | ||||||||
\(646\) | −2.93381 | −0.115429 | ||||||||
\(647\) | −8.01884 | −0.315253 | −0.157627 | − | 0.987499i | \(-0.550384\pi\) | ||||
−0.157627 | + | 0.987499i | \(0.550384\pi\) | |||||||
\(648\) | 2.91750 | 0.114610 | ||||||||
\(649\) | 6.11413 | 0.240000 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.84343 | −0.346601 | ||||||||
\(652\) | 3.06135 | 0.119892 | ||||||||
\(653\) | 5.06783 | 0.198320 | 0.0991598 | − | 0.995072i | \(-0.468385\pi\) | ||||
0.0991598 | + | 0.995072i | \(0.468385\pi\) | |||||||
\(654\) | −6.74811 | −0.263872 | ||||||||
\(655\) | 60.8437 | 2.37736 | ||||||||
\(656\) | −3.39348 | −0.132493 | ||||||||
\(657\) | −7.86139 | −0.306702 | ||||||||
\(658\) | −17.8688 | −0.696599 | ||||||||
\(659\) | −16.9404 | −0.659904 | −0.329952 | − | 0.943998i | \(-0.607033\pi\) | ||||
−0.329952 | + | 0.943998i | \(0.607033\pi\) | |||||||
\(660\) | −0.510934 | −0.0198881 | ||||||||
\(661\) | 36.7741 | 1.43035 | 0.715174 | − | 0.698947i | \(-0.246348\pi\) | ||||
0.715174 | + | 0.698947i | \(0.246348\pi\) | |||||||
\(662\) | −45.7338 | −1.77749 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −47.9713 | −1.86165 | ||||||||
\(665\) | 10.7232 | 0.415829 | ||||||||
\(666\) | 5.17908 | 0.200685 | ||||||||
\(667\) | −3.12179 | −0.120876 | ||||||||
\(668\) | −2.07082 | −0.0801225 | ||||||||
\(669\) | 12.7655 | 0.493542 | ||||||||
\(670\) | −15.7506 | −0.608500 | ||||||||
\(671\) | −15.7161 | −0.606713 | ||||||||
\(672\) | −0.780060 | −0.0300915 | ||||||||
\(673\) | −45.5657 | −1.75643 | −0.878214 | − | 0.478268i | \(-0.841265\pi\) | ||||
−0.878214 | + | 0.478268i | \(0.841265\pi\) | |||||||
\(674\) | 26.5023 | 1.02083 | ||||||||
\(675\) | −6.02631 | −0.231953 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.9937 | 0.460956 | 0.230478 | − | 0.973077i | \(-0.425971\pi\) | ||||
0.230478 | + | 0.973077i | \(0.425971\pi\) | |||||||
\(678\) | 22.1245 | 0.849686 | ||||||||
\(679\) | 1.42122 | 0.0545415 | ||||||||
\(680\) | −6.45023 | −0.247355 | ||||||||
\(681\) | −13.3301 | −0.510809 | ||||||||
\(682\) | 13.4398 | 0.514637 | ||||||||
\(683\) | −23.9577 | −0.916716 | −0.458358 | − | 0.888768i | \(-0.651562\pi\) | ||||
−0.458358 | + | 0.888768i | \(0.651562\pi\) | |||||||
\(684\) | −0.446128 | −0.0170581 | ||||||||
\(685\) | 45.1032 | 1.72331 | ||||||||
\(686\) | 1.36450 | 0.0520967 | ||||||||
\(687\) | 9.63903 | 0.367752 | ||||||||
\(688\) | −29.9917 | −1.14342 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −22.9853 | −0.875037 | ||||||||
\(691\) | 23.9462 | 0.910958 | 0.455479 | − | 0.890247i | \(-0.349468\pi\) | ||||
0.455479 | + | 0.890247i | \(0.349468\pi\) | |||||||
\(692\) | −0.0587598 | −0.00223371 | ||||||||
\(693\) | −1.11378 | −0.0423091 | ||||||||
\(694\) | 15.2480 | 0.578806 | ||||||||
\(695\) | 0.753015 | 0.0285635 | ||||||||
\(696\) | 1.79535 | 0.0680527 | ||||||||
\(697\) | 0.609892 | 0.0231013 | ||||||||
\(698\) | 50.2284 | 1.90117 | ||||||||
\(699\) | 22.0553 | 0.834207 | ||||||||
\(700\) | 0.832531 | 0.0314667 | ||||||||
\(701\) | −20.6807 | −0.781099 | −0.390550 | − | 0.920582i | \(-0.627715\pi\) | ||||
−0.390550 | + | 0.920582i | \(0.627715\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.2572 | −0.462288 | ||||||||
\(704\) | 9.43777 | 0.355699 | ||||||||
\(705\) | −43.4849 | −1.63773 | ||||||||
\(706\) | 23.8943 | 0.899275 | ||||||||
\(707\) | 0.720751 | 0.0271066 | ||||||||
\(708\) | 0.758374 | 0.0285014 | ||||||||
\(709\) | 16.0902 | 0.604281 | 0.302141 | − | 0.953263i | \(-0.402299\pi\) | ||||
0.302141 | + | 0.953263i | \(0.402299\pi\) | |||||||
\(710\) | 21.6159 | 0.811231 | ||||||||
\(711\) | −11.8320 | −0.443734 | ||||||||
\(712\) | 47.2257 | 1.76986 | ||||||||
\(713\) | −44.8626 | −1.68012 | ||||||||
\(714\) | −0.908495 | −0.0339996 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.90404 | −0.0711575 | ||||||||
\(717\) | −23.6972 | −0.884990 | ||||||||
\(718\) | 11.1306 | 0.415391 | ||||||||
\(719\) | −8.10172 | −0.302143 | −0.151072 | − | 0.988523i | \(-0.548272\pi\) | ||||
−0.151072 | + | 0.988523i | \(0.548272\pi\) | |||||||
\(720\) | 12.3015 | 0.458450 | ||||||||
\(721\) | −14.9632 | −0.557260 | ||||||||
\(722\) | 11.6958 | 0.435274 | ||||||||
\(723\) | −17.5586 | −0.653012 | ||||||||
\(724\) | −3.02185 | −0.112306 | ||||||||
\(725\) | −3.70843 | −0.137728 | ||||||||
\(726\) | −13.3168 | −0.494232 | ||||||||
\(727\) | −8.37621 | −0.310657 | −0.155328 | − | 0.987863i | \(-0.549644\pi\) | ||||
−0.155328 | + | 0.987863i | \(0.549644\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −35.6194 | −1.31833 | ||||||||
\(731\) | 5.39023 | 0.199365 | ||||||||
\(732\) | −1.94937 | −0.0720506 | ||||||||
\(733\) | −13.7644 | −0.508399 | −0.254199 | − | 0.967152i | \(-0.581812\pi\) | ||||
−0.254199 | + | 0.967152i | \(0.581812\pi\) | |||||||
\(734\) | −21.6322 | −0.798460 | ||||||||
\(735\) | 3.32059 | 0.122482 | ||||||||
\(736\) | −3.95723 | −0.145865 | ||||||||
\(737\) | −3.87178 | −0.142619 | ||||||||
\(738\) | −1.24990 | −0.0460094 | ||||||||
\(739\) | 39.2848 | 1.44511 | 0.722557 | − | 0.691311i | \(-0.242967\pi\) | ||||
0.722557 | + | 0.691311i | \(0.242967\pi\) | |||||||
\(740\) | −1.74118 | −0.0640072 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.81479 | 0.176757 | ||||||||
\(743\) | −3.96163 | −0.145338 | −0.0726690 | − | 0.997356i | \(-0.523152\pi\) | ||||
−0.0726690 | + | 0.997356i | \(0.523152\pi\) | |||||||
\(744\) | 25.8007 | 0.945899 | ||||||||
\(745\) | −23.8149 | −0.872509 | ||||||||
\(746\) | −15.4291 | −0.564899 | ||||||||
\(747\) | −16.4426 | −0.601604 | ||||||||
\(748\) | −0.102447 | −0.00374584 | ||||||||
\(749\) | −11.6187 | −0.424539 | ||||||||
\(750\) | −4.65012 | −0.169798 | ||||||||
\(751\) | −12.3197 | −0.449553 | −0.224776 | − | 0.974410i | \(-0.572165\pi\) | ||||
−0.224776 | + | 0.974410i | \(0.572165\pi\) | |||||||
\(752\) | 48.5139 | 1.76912 | ||||||||
\(753\) | −30.2065 | −1.10079 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.8843 | 0.869239 | ||||||||
\(756\) | −0.138150 | −0.00502445 | ||||||||
\(757\) | 27.1281 | 0.985988 | 0.492994 | − | 0.870033i | \(-0.335902\pi\) | ||||
0.492994 | + | 0.870033i | \(0.335902\pi\) | |||||||
\(758\) | 20.2752 | 0.736430 | ||||||||
\(759\) | −5.65020 | −0.205089 | ||||||||
\(760\) | −31.2850 | −1.13482 | ||||||||
\(761\) | −8.01574 | −0.290570 | −0.145285 | − | 0.989390i | \(-0.546410\pi\) | ||||
−0.145285 | + | 0.989390i | \(0.546410\pi\) | |||||||
\(762\) | −15.6671 | −0.567558 | ||||||||
\(763\) | 4.94550 | 0.179039 | ||||||||
\(764\) | −1.50494 | −0.0544468 | ||||||||
\(765\) | −2.21088 | −0.0799345 | ||||||||
\(766\) | 26.6797 | 0.963978 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.29940 | 0.119057 | ||||||||
\(769\) | 31.3627 | 1.13097 | 0.565484 | − | 0.824759i | \(-0.308689\pi\) | ||||
0.565484 | + | 0.824759i | \(0.308689\pi\) | |||||||
\(770\) | −5.04647 | −0.181862 | ||||||||
\(771\) | 4.98163 | 0.179409 | ||||||||
\(772\) | −2.36146 | −0.0849907 | ||||||||
\(773\) | −4.00669 | −0.144111 | −0.0720553 | − | 0.997401i | \(-0.522956\pi\) | ||||
−0.0720553 | + | 0.997401i | \(0.522956\pi\) | |||||||
\(774\) | −11.0466 | −0.397063 | ||||||||
\(775\) | −53.2932 | −1.91435 | ||||||||
\(776\) | −4.14641 | −0.148847 | ||||||||
\(777\) | −3.79560 | −0.136166 | ||||||||
\(778\) | −21.1479 | −0.758189 | ||||||||
\(779\) | 2.95810 | 0.105985 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.31357 | 0.190135 | ||||||||
\(782\) | −4.60878 | −0.164810 | ||||||||
\(783\) | 0.615375 | 0.0219917 | ||||||||
\(784\) | −3.70462 | −0.132308 | ||||||||
\(785\) | −23.8622 | −0.851677 | ||||||||
\(786\) | −25.0019 | −0.891788 | ||||||||
\(787\) | 10.2148 | 0.364117 | 0.182058 | − | 0.983288i | \(-0.441724\pi\) | ||||
0.182058 | + | 0.983288i | \(0.441724\pi\) | |||||||
\(788\) | −0.633644 | −0.0225726 | ||||||||
\(789\) | 12.5614 | 0.447199 | ||||||||
\(790\) | −53.6099 | −1.90736 | ||||||||
\(791\) | −16.2144 | −0.576518 | ||||||||
\(792\) | 3.24946 | 0.115464 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −31.6735 | −1.12405 | ||||||||
\(795\) | 11.7171 | 0.415563 | ||||||||
\(796\) | −0.841059 | −0.0298105 | ||||||||
\(797\) | −15.5770 | −0.551767 | −0.275884 | − | 0.961191i | \(-0.588970\pi\) | ||||
−0.275884 | + | 0.961191i | \(0.588970\pi\) | |||||||
\(798\) | −4.40639 | −0.155984 | ||||||||
\(799\) | −8.71913 | −0.308461 | ||||||||
\(800\) | −4.70088 | −0.166201 | ||||||||
\(801\) | 16.1871 | 0.571942 | ||||||||
\(802\) | −53.5617 | −1.89133 | ||||||||
\(803\) | −8.75587 | −0.308988 | ||||||||
\(804\) | −0.480242 | −0.0169368 | ||||||||
\(805\) | 16.8453 | 0.593718 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.45811 | 0.0513281 | ||||||||
\(808\) | −2.10279 | −0.0739758 | ||||||||
\(809\) | −30.9360 | −1.08765 | −0.543826 | − | 0.839198i | \(-0.683025\pi\) | ||||
−0.543826 | + | 0.839198i | \(0.683025\pi\) | |||||||
\(810\) | 4.53093 | 0.159201 | ||||||||
\(811\) | 14.2471 | 0.500284 | 0.250142 | − | 0.968209i | \(-0.419523\pi\) | ||||
0.250142 | + | 0.968209i | \(0.419523\pi\) | |||||||
\(812\) | −0.0850137 | −0.00298340 | ||||||||
\(813\) | 15.5702 | 0.546070 | ||||||||
\(814\) | 5.76837 | 0.202181 | ||||||||
\(815\) | 73.5831 | 2.57750 | ||||||||
\(816\) | 2.46657 | 0.0863472 | ||||||||
\(817\) | 26.1437 | 0.914654 | ||||||||
\(818\) | −26.7327 | −0.934686 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.420211 | 0.0146744 | ||||||||
\(821\) | −8.23270 | −0.287323 | −0.143662 | − | 0.989627i | \(-0.545888\pi\) | ||||
−0.143662 | + | 0.989627i | \(0.545888\pi\) | |||||||
\(822\) | −18.5338 | −0.646441 | ||||||||
\(823\) | −7.03818 | −0.245336 | −0.122668 | − | 0.992448i | \(-0.539145\pi\) | ||||
−0.122668 | + | 0.992448i | \(0.539145\pi\) | |||||||
\(824\) | 43.6552 | 1.52080 | ||||||||
\(825\) | −6.71199 | −0.233682 | ||||||||
\(826\) | 7.49043 | 0.260625 | ||||||||
\(827\) | 43.3827 | 1.50856 | 0.754282 | − | 0.656550i | \(-0.227985\pi\) | ||||
0.754282 | + | 0.656550i | \(0.227985\pi\) | |||||||
\(828\) | −0.700830 | −0.0243555 | ||||||||
\(829\) | 32.7843 | 1.13865 | 0.569323 | − | 0.822114i | \(-0.307206\pi\) | ||||
0.569323 | + | 0.822114i | \(0.307206\pi\) | |||||||
\(830\) | −74.5004 | −2.58594 | ||||||||
\(831\) | 18.0174 | 0.625016 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.665810 | 0.0230689 | ||||||||
\(834\) | −0.309429 | −0.0107147 | ||||||||
\(835\) | −49.7747 | −1.72252 | ||||||||
\(836\) | −0.496889 | −0.0171853 | ||||||||
\(837\) | 8.84343 | 0.305674 | ||||||||
\(838\) | −11.5019 | −0.397326 | ||||||||
\(839\) | 26.5096 | 0.915212 | 0.457606 | − | 0.889155i | \(-0.348707\pi\) | ||||
0.457606 | + | 0.889155i | \(0.348707\pi\) | |||||||
\(840\) | −9.68781 | −0.334261 | ||||||||
\(841\) | −28.6213 | −0.986942 | ||||||||
\(842\) | 3.88773 | 0.133980 | ||||||||
\(843\) | −25.8821 | −0.891427 | ||||||||
\(844\) | −1.43403 | −0.0493613 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.8688 | 0.614342 | ||||||||
\(847\) | 9.75949 | 0.335340 | ||||||||
\(848\) | −13.0722 | −0.448901 | ||||||||
\(849\) | −9.98839 | −0.342801 | ||||||||
\(850\) | −5.47487 | −0.187786 | ||||||||
\(851\) | −19.2550 | −0.660053 | ||||||||
\(852\) | 0.659077 | 0.0225796 | ||||||||
\(853\) | −23.0901 | −0.790589 | −0.395295 | − | 0.918554i | \(-0.629357\pi\) | ||||
−0.395295 | + | 0.918554i | \(0.629357\pi\) | |||||||
\(854\) | −19.2538 | −0.658851 | ||||||||
\(855\) | −10.7232 | −0.366726 | ||||||||
\(856\) | 33.8976 | 1.15860 | ||||||||
\(857\) | 0.861504 | 0.0294284 | 0.0147142 | − | 0.999892i | \(-0.495316\pi\) | ||||
0.0147142 | + | 0.999892i | \(0.495316\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.6223 | −0.635386 | −0.317693 | − | 0.948194i | \(-0.602908\pi\) | ||||
−0.317693 | + | 0.948194i | \(0.602908\pi\) | |||||||
\(860\) | 3.71383 | 0.126641 | ||||||||
\(861\) | 0.916015 | 0.0312177 | ||||||||
\(862\) | 48.8515 | 1.66389 | ||||||||
\(863\) | −22.5310 | −0.766965 | −0.383482 | − | 0.923548i | \(-0.625275\pi\) | ||||
−0.383482 | + | 0.923548i | \(0.625275\pi\) | |||||||
\(864\) | 0.780060 | 0.0265382 | ||||||||
\(865\) | −1.41236 | −0.0480218 | ||||||||
\(866\) | −12.1789 | −0.413858 | ||||||||
\(867\) | 16.5567 | 0.562295 | ||||||||
\(868\) | −1.22172 | −0.0414677 | ||||||||
\(869\) | −13.1783 | −0.447042 | ||||||||
\(870\) | 2.78822 | 0.0945295 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −14.4285 | −0.488610 | ||||||||
\(873\) | −1.42122 | −0.0481011 | ||||||||
\(874\) | −22.3535 | −0.756119 | ||||||||
\(875\) | 3.40794 | 0.115209 | ||||||||
\(876\) | −1.08605 | −0.0366941 | ||||||||
\(877\) | −46.8180 | −1.58093 | −0.790466 | − | 0.612506i | \(-0.790161\pi\) | ||||
−0.790466 | + | 0.612506i | \(0.790161\pi\) | |||||||
\(878\) | 6.71563 | 0.226641 | ||||||||
\(879\) | 3.60381 | 0.121553 | ||||||||
\(880\) | 13.7012 | 0.461867 | ||||||||
\(881\) | −12.3276 | −0.415326 | −0.207663 | − | 0.978200i | \(-0.566586\pi\) | ||||
−0.207663 | + | 0.978200i | \(0.566586\pi\) | |||||||
\(882\) | −1.36450 | −0.0459450 | ||||||||
\(883\) | −20.2249 | −0.680622 | −0.340311 | − | 0.940313i | \(-0.610532\pi\) | ||||
−0.340311 | + | 0.940313i | \(0.610532\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.2284 | 0.612742 | ||||||||
\(886\) | 6.77134 | 0.227488 | ||||||||
\(887\) | −41.4430 | −1.39152 | −0.695760 | − | 0.718274i | \(-0.744932\pi\) | ||||
−0.695760 | + | 0.718274i | \(0.744932\pi\) | |||||||
\(888\) | 11.0736 | 0.371607 | ||||||||
\(889\) | 11.4819 | 0.385092 | ||||||||
\(890\) | 73.3425 | 2.45844 | ||||||||
\(891\) | 1.11378 | 0.0373131 | ||||||||
\(892\) | 1.76355 | 0.0590479 | ||||||||
\(893\) | −42.2896 | −1.41517 | ||||||||
\(894\) | 9.78600 | 0.327293 | ||||||||
\(895\) | −45.7660 | −1.52979 | ||||||||
\(896\) | 10.0021 | 0.334147 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.5326 | −0.818663 | ||||||||
\(899\) | 5.44202 | 0.181502 | ||||||||
\(900\) | −0.832531 | −0.0277510 | ||||||||
\(901\) | 2.34939 | 0.0782696 | ||||||||
\(902\) | −1.39212 | −0.0463524 | ||||||||
\(903\) | 8.09576 | 0.269410 | ||||||||
\(904\) | 47.3055 | 1.57336 | ||||||||
\(905\) | −72.6338 | −2.41443 | ||||||||
\(906\) | −9.81455 | −0.326067 | ||||||||
\(907\) | 18.4094 | 0.611275 | 0.305638 | − | 0.952148i | \(-0.401130\pi\) | ||||
0.305638 | + | 0.952148i | \(0.401130\pi\) | |||||||
\(908\) | −1.84154 | −0.0611137 | ||||||||
\(909\) | −0.720751 | −0.0239058 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.7759 | 1.21844 | 0.609220 | − | 0.793001i | \(-0.291483\pi\) | ||||
0.609220 | + | 0.793001i | \(0.291483\pi\) | |||||||
\(912\) | 11.9634 | 0.396147 | ||||||||
\(913\) | −18.3135 | −0.606088 | ||||||||
\(914\) | −37.9432 | −1.25505 | ||||||||
\(915\) | −46.8553 | −1.54899 | ||||||||
\(916\) | 1.33163 | 0.0439982 | ||||||||
\(917\) | 18.3232 | 0.605084 | ||||||||
\(918\) | 0.908495 | 0.0299848 | ||||||||
\(919\) | 55.6734 | 1.83649 | 0.918247 | − | 0.396008i | \(-0.129605\pi\) | ||||
0.918247 | + | 0.396008i | \(0.129605\pi\) | |||||||
\(920\) | −49.1461 | −1.62030 | ||||||||
\(921\) | −17.4426 | −0.574752 | ||||||||
\(922\) | 22.6318 | 0.745339 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.153868 | −0.00506190 | ||||||||
\(925\) | −22.8734 | −0.752074 | ||||||||
\(926\) | −57.9839 | −1.90547 | ||||||||
\(927\) | 14.9632 | 0.491457 | ||||||||
\(928\) | 0.480029 | 0.0157577 | ||||||||
\(929\) | −34.2055 | −1.12224 | −0.561122 | − | 0.827733i | \(-0.689630\pi\) | ||||
−0.561122 | + | 0.827733i | \(0.689630\pi\) | |||||||
\(930\) | 40.0690 | 1.31391 | ||||||||
\(931\) | 3.22931 | 0.105836 | ||||||||
\(932\) | 3.04692 | 0.0998053 | ||||||||
\(933\) | 22.3025 | 0.730152 | ||||||||
\(934\) | 1.77681 | 0.0581391 | ||||||||
\(935\) | −2.46244 | −0.0805303 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.2091 | −1.64026 | −0.820130 | − | 0.572177i | \(-0.806099\pi\) | ||||
−0.820130 | + | 0.572177i | \(0.806099\pi\) | |||||||
\(938\) | −4.74332 | −0.154875 | ||||||||
\(939\) | −0.792995 | −0.0258784 | ||||||||
\(940\) | −6.00741 | −0.195940 | ||||||||
\(941\) | 3.12662 | 0.101925 | 0.0509625 | − | 0.998701i | \(-0.483771\pi\) | ||||
0.0509625 | + | 0.998701i | \(0.483771\pi\) | |||||||
\(942\) | 9.80545 | 0.319479 | ||||||||
\(943\) | 4.64693 | 0.151325 | ||||||||
\(944\) | −20.3366 | −0.661898 | ||||||||
\(945\) | −3.32059 | −0.108019 | ||||||||
\(946\) | −12.3035 | −0.400023 | ||||||||
\(947\) | −2.54412 | −0.0826729 | −0.0413364 | − | 0.999145i | \(-0.513162\pi\) | ||||
−0.0413364 | + | 0.999145i | \(0.513162\pi\) | |||||||
\(948\) | −1.63458 | −0.0530888 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −26.5542 | −0.861533 | ||||||||
\(951\) | −8.48350 | −0.275096 | ||||||||
\(952\) | −1.94250 | −0.0629567 | ||||||||
\(953\) | 42.2175 | 1.36756 | 0.683780 | − | 0.729688i | \(-0.260335\pi\) | ||||
0.683780 | + | 0.729688i | \(0.260335\pi\) | |||||||
\(954\) | −4.81479 | −0.155885 | ||||||||
\(955\) | −36.1730 | −1.17053 | ||||||||
\(956\) | −3.27376 | −0.105881 | ||||||||
\(957\) | 0.685393 | 0.0221556 | ||||||||
\(958\) | −11.3048 | −0.365241 | ||||||||
\(959\) | 13.5829 | 0.438615 | ||||||||
\(960\) | 28.1374 | 0.908131 | ||||||||
\(961\) | 47.2062 | 1.52278 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.6187 | 0.374409 | ||||||||
\(964\) | −2.42572 | −0.0781270 | ||||||||
\(965\) | −56.7604 | −1.82718 | ||||||||
\(966\) | −6.92207 | −0.222714 | ||||||||
\(967\) | 38.3214 | 1.23233 | 0.616166 | − | 0.787616i | \(-0.288685\pi\) | ||||
0.616166 | + | 0.787616i | \(0.288685\pi\) | |||||||
\(968\) | −28.4733 | −0.915166 | ||||||||
\(969\) | −2.15011 | −0.0690714 | ||||||||
\(970\) | −6.43946 | −0.206759 | ||||||||
\(971\) | 8.66075 | 0.277937 | 0.138968 | − | 0.990297i | \(-0.455621\pi\) | ||||
0.138968 | + | 0.990297i | \(0.455621\pi\) | |||||||
\(972\) | 0.138150 | 0.00443115 | ||||||||
\(973\) | 0.226772 | 0.00726997 | ||||||||
\(974\) | −59.4414 | −1.90463 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 52.2742 | 1.67326 | ||||||||
\(977\) | −11.2083 | −0.358585 | −0.179292 | − | 0.983796i | \(-0.557381\pi\) | ||||
−0.179292 | + | 0.983796i | \(0.557381\pi\) | |||||||
\(978\) | −30.2368 | −0.966865 | ||||||||
\(979\) | 18.0289 | 0.576205 | ||||||||
\(980\) | 0.458738 | 0.0146538 | ||||||||
\(981\) | −4.94550 | −0.157898 | ||||||||
\(982\) | −57.0429 | −1.82031 | ||||||||
\(983\) | 24.8347 | 0.792102 | 0.396051 | − | 0.918228i | \(-0.370380\pi\) | ||||
0.396051 | + | 0.918228i | \(0.370380\pi\) | |||||||
\(984\) | −2.67247 | −0.0851953 | ||||||||
\(985\) | −15.2304 | −0.485280 | ||||||||
\(986\) | 0.559065 | 0.0178042 | ||||||||
\(987\) | −13.0955 | −0.416835 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.0697 | 1.30594 | ||||||||
\(990\) | 5.04647 | 0.160387 | ||||||||
\(991\) | 22.6526 | 0.719585 | 0.359793 | − | 0.933032i | \(-0.382847\pi\) | ||||
0.359793 | + | 0.933032i | \(0.382847\pi\) | |||||||
\(992\) | 6.89840 | 0.219025 | ||||||||
\(993\) | −33.5170 | −1.06363 | ||||||||
\(994\) | 6.50967 | 0.206474 | ||||||||
\(995\) | −20.2159 | −0.640886 | ||||||||
\(996\) | −2.27154 | −0.0719765 | ||||||||
\(997\) | 39.1382 | 1.23952 | 0.619760 | − | 0.784791i | \(-0.287230\pi\) | ||||
0.619760 | + | 0.784791i | \(0.287230\pi\) | |||||||
\(998\) | −8.58217 | −0.271664 | ||||||||
\(999\) | 3.79560 | 0.120087 |
(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 | 3549.2.a.bf.1.3 | yes | 9 | |
13.12 | even | 2 | 3549.2.a.be.1.7 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.be.1.7 | ✓ | 9 | 13.12 | even | 2 | ||
3549.2.a.bf.1.3 | yes | 9 | 1.1 | even | 1 | trivial |