Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1668357.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 11x^{3} + x^{2} + 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.117900\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.56570 | −1.59463 | −0.797316 | − | 0.603563i | \(-0.793747\pi\) | ||||
−0.797316 | + | 0.603563i | \(0.793747\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.117900 | −0.0445620 | −0.0222810 | − | 0.999752i | \(-0.507093\pi\) | ||||
−0.0222810 | + | 0.999752i | \(0.507093\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.56570 | 1.12757 | ||||||||
\(11\) | 6.11159 | 1.84271 | 0.921356 | − | 0.388719i | \(-0.127082\pi\) | ||||
0.921356 | + | 0.388719i | \(0.127082\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.74796 | 1.03950 | 0.519749 | − | 0.854319i | \(-0.326025\pi\) | ||||
0.519749 | + | 0.854319i | \(0.326025\pi\) | |||||||
\(14\) | 0.117900 | 0.0315101 | ||||||||
\(15\) | −3.56570 | −0.920661 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.663784 | −0.152282 | −0.0761412 | − | 0.997097i | \(-0.524260\pi\) | ||||
−0.0761412 | + | 0.997097i | \(0.524260\pi\) | |||||||
\(20\) | −3.56570 | −0.797316 | ||||||||
\(21\) | −0.117900 | −0.0257279 | ||||||||
\(22\) | −6.11159 | −1.30299 | ||||||||
\(23\) | 8.53198 | 1.77904 | 0.889521 | − | 0.456895i | \(-0.151038\pi\) | ||||
0.889521 | + | 0.456895i | \(0.151038\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 7.71424 | 1.54285 | ||||||||
\(26\) | −3.74796 | −0.735036 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.117900 | −0.0222810 | ||||||||
\(29\) | 7.62248 | 1.41546 | 0.707729 | − | 0.706484i | \(-0.249720\pi\) | ||||
0.707729 | + | 0.706484i | \(0.249720\pi\) | |||||||
\(30\) | 3.56570 | 0.651005 | ||||||||
\(31\) | −7.73406 | −1.38908 | −0.694539 | − | 0.719455i | \(-0.744392\pi\) | ||||
−0.694539 | + | 0.719455i | \(0.744392\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.11159 | 1.06389 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0.420396 | 0.0710599 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.71732 | −0.446725 | −0.223363 | − | 0.974735i | \(-0.571703\pi\) | ||||
−0.223363 | + | 0.974735i | \(0.571703\pi\) | |||||||
\(38\) | 0.663784 | 0.107680 | ||||||||
\(39\) | 3.74796 | 0.600154 | ||||||||
\(40\) | 3.56570 | 0.563787 | ||||||||
\(41\) | −4.76778 | −0.744603 | −0.372301 | − | 0.928112i | \(-0.621431\pi\) | ||||
−0.372301 | + | 0.928112i | \(0.621431\pi\) | |||||||
\(42\) | 0.117900 | 0.0181923 | ||||||||
\(43\) | 0.835224 | 0.127370 | 0.0636852 | − | 0.997970i | \(-0.479715\pi\) | ||||
0.0636852 | + | 0.997970i | \(0.479715\pi\) | |||||||
\(44\) | 6.11159 | 0.921356 | ||||||||
\(45\) | −3.56570 | −0.531544 | ||||||||
\(46\) | −8.53198 | −1.25797 | ||||||||
\(47\) | 2.98777 | 0.435811 | 0.217905 | − | 0.975970i | \(-0.430078\pi\) | ||||
0.217905 | + | 0.975970i | \(0.430078\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.98610 | −0.998014 | ||||||||
\(50\) | −7.71424 | −1.09096 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 3.74796 | 0.519749 | ||||||||
\(53\) | 5.50134 | 0.755668 | 0.377834 | − | 0.925873i | \(-0.376669\pi\) | ||||
0.377834 | + | 0.925873i | \(0.376669\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −21.7921 | −2.93845 | ||||||||
\(56\) | 0.117900 | 0.0157550 | ||||||||
\(57\) | −0.663784 | −0.0879203 | ||||||||
\(58\) | −7.62248 | −1.00088 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −3.56570 | −0.460330 | ||||||||
\(61\) | 5.26321 | 0.673885 | 0.336942 | − | 0.941525i | \(-0.390607\pi\) | ||||
0.336942 | + | 0.941525i | \(0.390607\pi\) | |||||||
\(62\) | 7.73406 | 0.982227 | ||||||||
\(63\) | −0.117900 | −0.0148540 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −13.3641 | −1.65762 | ||||||||
\(66\) | −6.11159 | −0.752284 | ||||||||
\(67\) | 13.6706 | 1.67013 | 0.835065 | − | 0.550152i | \(-0.185430\pi\) | ||||
0.835065 | + | 0.550152i | \(0.185430\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 8.53198 | 1.02713 | ||||||||
\(70\) | −0.420396 | −0.0502469 | ||||||||
\(71\) | 3.38434 | 0.401647 | 0.200824 | − | 0.979627i | \(-0.435638\pi\) | ||||
0.200824 | + | 0.979627i | \(0.435638\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −16.0203 | −1.87504 | −0.937518 | − | 0.347936i | \(-0.886883\pi\) | ||||
−0.937518 | + | 0.347936i | \(0.886883\pi\) | |||||||
\(74\) | 2.71732 | 0.315882 | ||||||||
\(75\) | 7.71424 | 0.890764 | ||||||||
\(76\) | −0.663784 | −0.0761412 | ||||||||
\(77\) | −0.720555 | −0.0821149 | ||||||||
\(78\) | −3.74796 | −0.424373 | ||||||||
\(79\) | 0.152544 | 0.0171626 | 0.00858129 | − | 0.999963i | \(-0.497268\pi\) | ||||
0.00858129 | + | 0.999963i | \(0.497268\pi\) | |||||||
\(80\) | −3.56570 | −0.398658 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.76778 | 0.526514 | ||||||||
\(83\) | 6.37444 | 0.699686 | 0.349843 | − | 0.936808i | \(-0.386235\pi\) | ||||
0.349843 | + | 0.936808i | \(0.386235\pi\) | |||||||
\(84\) | −0.117900 | −0.0128639 | ||||||||
\(85\) | 3.56570 | 0.386755 | ||||||||
\(86\) | −0.835224 | −0.0900645 | ||||||||
\(87\) | 7.62248 | 0.817215 | ||||||||
\(88\) | −6.11159 | −0.651497 | ||||||||
\(89\) | −3.96986 | −0.420805 | −0.210402 | − | 0.977615i | \(-0.567477\pi\) | ||||
−0.210402 | + | 0.977615i | \(0.567477\pi\) | |||||||
\(90\) | 3.56570 | 0.375858 | ||||||||
\(91\) | −0.441884 | −0.0463221 | ||||||||
\(92\) | 8.53198 | 0.889521 | ||||||||
\(93\) | −7.73406 | −0.801985 | ||||||||
\(94\) | −2.98777 | −0.308165 | ||||||||
\(95\) | 2.36686 | 0.242834 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 2.65620 | 0.269696 | 0.134848 | − | 0.990866i | \(-0.456945\pi\) | ||||
0.134848 | + | 0.990866i | \(0.456945\pi\) | |||||||
\(98\) | 6.98610 | 0.705703 | ||||||||
\(99\) | 6.11159 | 0.614238 | ||||||||
\(100\) | 7.71424 | 0.771424 | ||||||||
\(101\) | 12.3259 | 1.22647 | 0.613236 | − | 0.789899i | \(-0.289867\pi\) | ||||
0.613236 | + | 0.789899i | \(0.289867\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −17.3019 | −1.70481 | −0.852405 | − | 0.522882i | \(-0.824857\pi\) | ||||
−0.852405 | + | 0.522882i | \(0.824857\pi\) | |||||||
\(104\) | −3.74796 | −0.367518 | ||||||||
\(105\) | 0.420396 | 0.0410264 | ||||||||
\(106\) | −5.50134 | −0.534338 | ||||||||
\(107\) | −7.61744 | −0.736406 | −0.368203 | − | 0.929746i | \(-0.620027\pi\) | ||||
−0.368203 | + | 0.929746i | \(0.620027\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −4.84838 | −0.464391 | −0.232195 | − | 0.972669i | \(-0.574591\pi\) | ||||
−0.232195 | + | 0.972669i | \(0.574591\pi\) | |||||||
\(110\) | 21.7921 | 2.07780 | ||||||||
\(111\) | −2.71732 | −0.257917 | ||||||||
\(112\) | −0.117900 | −0.0111405 | ||||||||
\(113\) | 9.80909 | 0.922762 | 0.461381 | − | 0.887202i | \(-0.347354\pi\) | ||||
0.461381 | + | 0.887202i | \(0.347354\pi\) | |||||||
\(114\) | 0.663784 | 0.0621690 | ||||||||
\(115\) | −30.4225 | −2.83692 | ||||||||
\(116\) | 7.62248 | 0.707729 | ||||||||
\(117\) | 3.74796 | 0.346499 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | 0.117900 | 0.0108079 | ||||||||
\(120\) | 3.56570 | 0.325503 | ||||||||
\(121\) | 26.3515 | 2.39559 | ||||||||
\(122\) | −5.26321 | −0.476508 | ||||||||
\(123\) | −4.76778 | −0.429897 | ||||||||
\(124\) | −7.73406 | −0.694539 | ||||||||
\(125\) | −9.67819 | −0.865643 | ||||||||
\(126\) | 0.117900 | 0.0105034 | ||||||||
\(127\) | −8.67239 | −0.769550 | −0.384775 | − | 0.923010i | \(-0.625721\pi\) | ||||
−0.384775 | + | 0.923010i | \(0.625721\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.835224 | 0.0735373 | ||||||||
\(130\) | 13.3641 | 1.17211 | ||||||||
\(131\) | 12.2080 | 1.06662 | 0.533309 | − | 0.845921i | \(-0.320948\pi\) | ||||
0.533309 | + | 0.845921i | \(0.320948\pi\) | |||||||
\(132\) | 6.11159 | 0.531945 | ||||||||
\(133\) | 0.0782600 | 0.00678600 | ||||||||
\(134\) | −13.6706 | −1.18096 | ||||||||
\(135\) | −3.56570 | −0.306887 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −22.0193 | −1.88123 | −0.940616 | − | 0.339472i | \(-0.889752\pi\) | ||||
−0.940616 | + | 0.339472i | \(0.889752\pi\) | |||||||
\(138\) | −8.53198 | −0.726291 | ||||||||
\(139\) | −5.98287 | −0.507460 | −0.253730 | − | 0.967275i | \(-0.581658\pi\) | ||||
−0.253730 | + | 0.967275i | \(0.581658\pi\) | |||||||
\(140\) | 0.420396 | 0.0355299 | ||||||||
\(141\) | 2.98777 | 0.251615 | ||||||||
\(142\) | −3.38434 | −0.284007 | ||||||||
\(143\) | 22.9060 | 1.91550 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −27.1795 | −2.25713 | ||||||||
\(146\) | 16.0203 | 1.32585 | ||||||||
\(147\) | −6.98610 | −0.576204 | ||||||||
\(148\) | −2.71732 | −0.223363 | ||||||||
\(149\) | −0.239031 | −0.0195822 | −0.00979109 | − | 0.999952i | \(-0.503117\pi\) | ||||
−0.00979109 | + | 0.999952i | \(0.503117\pi\) | |||||||
\(150\) | −7.71424 | −0.629865 | ||||||||
\(151\) | −4.91184 | −0.399720 | −0.199860 | − | 0.979824i | \(-0.564049\pi\) | ||||
−0.199860 | + | 0.979824i | \(0.564049\pi\) | |||||||
\(152\) | 0.663784 | 0.0538400 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0.720555 | 0.0580640 | ||||||||
\(155\) | 27.5774 | 2.21507 | ||||||||
\(156\) | 3.74796 | 0.300077 | ||||||||
\(157\) | 2.51989 | 0.201109 | 0.100554 | − | 0.994932i | \(-0.467938\pi\) | ||||
0.100554 | + | 0.994932i | \(0.467938\pi\) | |||||||
\(158\) | −0.152544 | −0.0121358 | ||||||||
\(159\) | 5.50134 | 0.436285 | ||||||||
\(160\) | 3.56570 | 0.281894 | ||||||||
\(161\) | −1.00592 | −0.0792776 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 6.47521 | 0.507178 | 0.253589 | − | 0.967312i | \(-0.418389\pi\) | ||||
0.253589 | + | 0.967312i | \(0.418389\pi\) | |||||||
\(164\) | −4.76778 | −0.372301 | ||||||||
\(165\) | −21.7921 | −1.69651 | ||||||||
\(166\) | −6.37444 | −0.494753 | ||||||||
\(167\) | −21.3686 | −1.65355 | −0.826777 | − | 0.562529i | \(-0.809828\pi\) | ||||
−0.826777 | + | 0.562529i | \(0.809828\pi\) | |||||||
\(168\) | 0.117900 | 0.00909617 | ||||||||
\(169\) | 1.04723 | 0.0805560 | ||||||||
\(170\) | −3.56570 | −0.273477 | ||||||||
\(171\) | −0.663784 | −0.0507608 | ||||||||
\(172\) | 0.835224 | 0.0636852 | ||||||||
\(173\) | 4.59815 | 0.349591 | 0.174795 | − | 0.984605i | \(-0.444074\pi\) | ||||
0.174795 | + | 0.984605i | \(0.444074\pi\) | |||||||
\(174\) | −7.62248 | −0.577858 | ||||||||
\(175\) | −0.909508 | −0.0687523 | ||||||||
\(176\) | 6.11159 | 0.460678 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | 3.96986 | 0.297554 | ||||||||
\(179\) | −13.2291 | −0.988789 | −0.494394 | − | 0.869238i | \(-0.664610\pi\) | ||||
−0.494394 | + | 0.869238i | \(0.664610\pi\) | |||||||
\(180\) | −3.56570 | −0.265772 | ||||||||
\(181\) | −3.72222 | −0.276671 | −0.138335 | − | 0.990385i | \(-0.544175\pi\) | ||||
−0.138335 | + | 0.990385i | \(0.544175\pi\) | |||||||
\(182\) | 0.441884 | 0.0327546 | ||||||||
\(183\) | 5.26321 | 0.389068 | ||||||||
\(184\) | −8.53198 | −0.628986 | ||||||||
\(185\) | 9.68917 | 0.712362 | ||||||||
\(186\) | 7.73406 | 0.567089 | ||||||||
\(187\) | −6.11159 | −0.446924 | ||||||||
\(188\) | 2.98777 | 0.217905 | ||||||||
\(189\) | −0.117900 | −0.00857595 | ||||||||
\(190\) | −2.36686 | −0.171710 | ||||||||
\(191\) | 19.3258 | 1.39836 | 0.699182 | − | 0.714944i | \(-0.253548\pi\) | ||||
0.699182 | + | 0.714944i | \(0.253548\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −3.37044 | −0.242609 | −0.121305 | − | 0.992615i | \(-0.538708\pi\) | ||||
−0.121305 | + | 0.992615i | \(0.538708\pi\) | |||||||
\(194\) | −2.65620 | −0.190704 | ||||||||
\(195\) | −13.3641 | −0.957025 | ||||||||
\(196\) | −6.98610 | −0.499007 | ||||||||
\(197\) | 14.7678 | 1.05216 | 0.526080 | − | 0.850435i | \(-0.323661\pi\) | ||||
0.526080 | + | 0.850435i | \(0.323661\pi\) | |||||||
\(198\) | −6.11159 | −0.434332 | ||||||||
\(199\) | 9.14722 | 0.648429 | 0.324215 | − | 0.945984i | \(-0.394900\pi\) | ||||
0.324215 | + | 0.945984i | \(0.394900\pi\) | |||||||
\(200\) | −7.71424 | −0.545479 | ||||||||
\(201\) | 13.6706 | 0.964250 | ||||||||
\(202\) | −12.3259 | −0.867247 | ||||||||
\(203\) | −0.898689 | −0.0630756 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 17.0005 | 1.18737 | ||||||||
\(206\) | 17.3019 | 1.20548 | ||||||||
\(207\) | 8.53198 | 0.593014 | ||||||||
\(208\) | 3.74796 | 0.259874 | ||||||||
\(209\) | −4.05677 | −0.280613 | ||||||||
\(210\) | −0.420396 | −0.0290101 | ||||||||
\(211\) | 25.5797 | 1.76098 | 0.880490 | − | 0.474065i | \(-0.157214\pi\) | ||||
0.880490 | + | 0.474065i | \(0.157214\pi\) | |||||||
\(212\) | 5.50134 | 0.377834 | ||||||||
\(213\) | 3.38434 | 0.231891 | ||||||||
\(214\) | 7.61744 | 0.520717 | ||||||||
\(215\) | −2.97816 | −0.203109 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.911845 | 0.0619001 | ||||||||
\(218\) | 4.84838 | 0.328374 | ||||||||
\(219\) | −16.0203 | −1.08255 | ||||||||
\(220\) | −21.7921 | −1.46922 | ||||||||
\(221\) | −3.74796 | −0.252115 | ||||||||
\(222\) | 2.71732 | 0.182375 | ||||||||
\(223\) | 23.7681 | 1.59163 | 0.795816 | − | 0.605539i | \(-0.207042\pi\) | ||||
0.795816 | + | 0.605539i | \(0.207042\pi\) | |||||||
\(224\) | 0.117900 | 0.00787752 | ||||||||
\(225\) | 7.71424 | 0.514283 | ||||||||
\(226\) | −9.80909 | −0.652491 | ||||||||
\(227\) | 14.6124 | 0.969860 | 0.484930 | − | 0.874553i | \(-0.338845\pi\) | ||||
0.484930 | + | 0.874553i | \(0.338845\pi\) | |||||||
\(228\) | −0.663784 | −0.0439601 | ||||||||
\(229\) | 22.3800 | 1.47891 | 0.739455 | − | 0.673206i | \(-0.235083\pi\) | ||||
0.739455 | + | 0.673206i | \(0.235083\pi\) | |||||||
\(230\) | 30.4225 | 2.00600 | ||||||||
\(231\) | −0.720555 | −0.0474091 | ||||||||
\(232\) | −7.62248 | −0.500440 | ||||||||
\(233\) | 16.9609 | 1.11114 | 0.555572 | − | 0.831469i | \(-0.312500\pi\) | ||||
0.555572 | + | 0.831469i | \(0.312500\pi\) | |||||||
\(234\) | −3.74796 | −0.245012 | ||||||||
\(235\) | −10.6535 | −0.694957 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 0.152544 | 0.00990882 | ||||||||
\(238\) | −0.117900 | −0.00764231 | ||||||||
\(239\) | −9.32948 | −0.603474 | −0.301737 | − | 0.953391i | \(-0.597566\pi\) | ||||
−0.301737 | + | 0.953391i | \(0.597566\pi\) | |||||||
\(240\) | −3.56570 | −0.230165 | ||||||||
\(241\) | 6.64255 | 0.427884 | 0.213942 | − | 0.976846i | \(-0.431370\pi\) | ||||
0.213942 | + | 0.976846i | \(0.431370\pi\) | |||||||
\(242\) | −26.3515 | −1.69394 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.26321 | 0.336942 | ||||||||
\(245\) | 24.9104 | 1.59146 | ||||||||
\(246\) | 4.76778 | 0.303983 | ||||||||
\(247\) | −2.48784 | −0.158297 | ||||||||
\(248\) | 7.73406 | 0.491113 | ||||||||
\(249\) | 6.37444 | 0.403964 | ||||||||
\(250\) | 9.67819 | 0.612102 | ||||||||
\(251\) | 4.91450 | 0.310201 | 0.155100 | − | 0.987899i | \(-0.450430\pi\) | ||||
0.155100 | + | 0.987899i | \(0.450430\pi\) | |||||||
\(252\) | −0.117900 | −0.00742699 | ||||||||
\(253\) | 52.1440 | 3.27826 | ||||||||
\(254\) | 8.67239 | 0.544154 | ||||||||
\(255\) | 3.56570 | 0.223293 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.6585 | −1.53815 | −0.769077 | − | 0.639156i | \(-0.779284\pi\) | ||||
−0.769077 | + | 0.639156i | \(0.779284\pi\) | |||||||
\(258\) | −0.835224 | −0.0519988 | ||||||||
\(259\) | 0.320372 | 0.0199070 | ||||||||
\(260\) | −13.3641 | −0.828808 | ||||||||
\(261\) | 7.62248 | 0.471819 | ||||||||
\(262\) | −12.2080 | −0.754213 | ||||||||
\(263\) | −6.42580 | −0.396232 | −0.198116 | − | 0.980179i | \(-0.563482\pi\) | ||||
−0.198116 | + | 0.980179i | \(0.563482\pi\) | |||||||
\(264\) | −6.11159 | −0.376142 | ||||||||
\(265\) | −19.6162 | −1.20501 | ||||||||
\(266\) | −0.0782600 | −0.00479843 | ||||||||
\(267\) | −3.96986 | −0.242952 | ||||||||
\(268\) | 13.6706 | 0.835065 | ||||||||
\(269\) | 0.159710 | 0.00973769 | 0.00486884 | − | 0.999988i | \(-0.498450\pi\) | ||||
0.00486884 | + | 0.999988i | \(0.498450\pi\) | |||||||
\(270\) | 3.56570 | 0.217002 | ||||||||
\(271\) | 1.81105 | 0.110013 | 0.0550066 | − | 0.998486i | \(-0.482482\pi\) | ||||
0.0550066 | + | 0.998486i | \(0.482482\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −0.441884 | −0.0267441 | ||||||||
\(274\) | 22.0193 | 1.33023 | ||||||||
\(275\) | 47.1463 | 2.84303 | ||||||||
\(276\) | 8.53198 | 0.513565 | ||||||||
\(277\) | 27.4820 | 1.65123 | 0.825617 | − | 0.564230i | \(-0.190827\pi\) | ||||
0.825617 | + | 0.564230i | \(0.190827\pi\) | |||||||
\(278\) | 5.98287 | 0.358829 | ||||||||
\(279\) | −7.73406 | −0.463026 | ||||||||
\(280\) | −0.420396 | −0.0251235 | ||||||||
\(281\) | 31.2878 | 1.86647 | 0.933236 | − | 0.359263i | \(-0.116972\pi\) | ||||
0.933236 | + | 0.359263i | \(0.116972\pi\) | |||||||
\(282\) | −2.98777 | −0.177919 | ||||||||
\(283\) | −16.0077 | −0.951561 | −0.475781 | − | 0.879564i | \(-0.657834\pi\) | ||||
−0.475781 | + | 0.879564i | \(0.657834\pi\) | |||||||
\(284\) | 3.38434 | 0.200824 | ||||||||
\(285\) | 2.36686 | 0.140200 | ||||||||
\(286\) | −22.9060 | −1.35446 | ||||||||
\(287\) | 0.562121 | 0.0331809 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 27.1795 | 1.59603 | ||||||||
\(291\) | 2.65620 | 0.155709 | ||||||||
\(292\) | −16.0203 | −0.937518 | ||||||||
\(293\) | 19.2486 | 1.12451 | 0.562257 | − | 0.826963i | \(-0.309933\pi\) | ||||
0.562257 | + | 0.826963i | \(0.309933\pi\) | |||||||
\(294\) | 6.98610 | 0.407438 | ||||||||
\(295\) | 3.56570 | 0.207603 | ||||||||
\(296\) | 2.71732 | 0.157941 | ||||||||
\(297\) | 6.11159 | 0.354630 | ||||||||
\(298\) | 0.239031 | 0.0138467 | ||||||||
\(299\) | 31.9776 | 1.84931 | ||||||||
\(300\) | 7.71424 | 0.445382 | ||||||||
\(301\) | −0.0984727 | −0.00567587 | ||||||||
\(302\) | 4.91184 | 0.282645 | ||||||||
\(303\) | 12.3259 | 0.708104 | ||||||||
\(304\) | −0.663784 | −0.0380706 | ||||||||
\(305\) | −18.7670 | −1.07460 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | −6.54982 | −0.373818 | −0.186909 | − | 0.982377i | \(-0.559847\pi\) | ||||
−0.186909 | + | 0.982377i | \(0.559847\pi\) | |||||||
\(308\) | −0.720555 | −0.0410574 | ||||||||
\(309\) | −17.3019 | −0.984273 | ||||||||
\(310\) | −27.5774 | −1.56629 | ||||||||
\(311\) | 27.1871 | 1.54164 | 0.770820 | − | 0.637053i | \(-0.219847\pi\) | ||||
0.770820 | + | 0.637053i | \(0.219847\pi\) | |||||||
\(312\) | −3.74796 | −0.212187 | ||||||||
\(313\) | 21.1346 | 1.19460 | 0.597299 | − | 0.802019i | \(-0.296241\pi\) | ||||
0.597299 | + | 0.802019i | \(0.296241\pi\) | |||||||
\(314\) | −2.51989 | −0.142206 | ||||||||
\(315\) | 0.420396 | 0.0236866 | ||||||||
\(316\) | 0.152544 | 0.00858129 | ||||||||
\(317\) | −17.5500 | −0.985706 | −0.492853 | − | 0.870113i | \(-0.664046\pi\) | ||||
−0.492853 | + | 0.870113i | \(0.664046\pi\) | |||||||
\(318\) | −5.50134 | −0.308500 | ||||||||
\(319\) | 46.5854 | 2.60828 | ||||||||
\(320\) | −3.56570 | −0.199329 | ||||||||
\(321\) | −7.61744 | −0.425164 | ||||||||
\(322\) | 1.00592 | 0.0560577 | ||||||||
\(323\) | 0.663784 | 0.0369339 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 28.9127 | 1.60379 | ||||||||
\(326\) | −6.47521 | −0.358629 | ||||||||
\(327\) | −4.84838 | −0.268116 | ||||||||
\(328\) | 4.76778 | 0.263257 | ||||||||
\(329\) | −0.352257 | −0.0194206 | ||||||||
\(330\) | 21.7921 | 1.19962 | ||||||||
\(331\) | −31.1646 | −1.71296 | −0.856480 | − | 0.516181i | \(-0.827353\pi\) | ||||
−0.856480 | + | 0.516181i | \(0.827353\pi\) | |||||||
\(332\) | 6.37444 | 0.349843 | ||||||||
\(333\) | −2.71732 | −0.148908 | ||||||||
\(334\) | 21.3686 | 1.16924 | ||||||||
\(335\) | −48.7453 | −2.66324 | ||||||||
\(336\) | −0.117900 | −0.00643196 | ||||||||
\(337\) | 3.30735 | 0.180163 | 0.0900815 | − | 0.995934i | \(-0.471287\pi\) | ||||
0.0900815 | + | 0.995934i | \(0.471287\pi\) | |||||||
\(338\) | −1.04723 | −0.0569617 | ||||||||
\(339\) | 9.80909 | 0.532757 | ||||||||
\(340\) | 3.56570 | 0.193377 | ||||||||
\(341\) | −47.2674 | −2.55967 | ||||||||
\(342\) | 0.663784 | 0.0358933 | ||||||||
\(343\) | 1.64896 | 0.0890354 | ||||||||
\(344\) | −0.835224 | −0.0450322 | ||||||||
\(345\) | −30.4225 | −1.63789 | ||||||||
\(346\) | −4.59815 | −0.247198 | ||||||||
\(347\) | 20.2791 | 1.08864 | 0.544318 | − | 0.838879i | \(-0.316788\pi\) | ||||
0.544318 | + | 0.838879i | \(0.316788\pi\) | |||||||
\(348\) | 7.62248 | 0.408608 | ||||||||
\(349\) | −9.39605 | −0.502959 | −0.251480 | − | 0.967863i | \(-0.580917\pi\) | ||||
−0.251480 | + | 0.967863i | \(0.580917\pi\) | |||||||
\(350\) | 0.909508 | 0.0486153 | ||||||||
\(351\) | 3.74796 | 0.200051 | ||||||||
\(352\) | −6.11159 | −0.325749 | ||||||||
\(353\) | 28.4262 | 1.51297 | 0.756486 | − | 0.654009i | \(-0.226914\pi\) | ||||
0.756486 | + | 0.654009i | \(0.226914\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | −12.0675 | −0.640479 | ||||||||
\(356\) | −3.96986 | −0.210402 | ||||||||
\(357\) | 0.117900 | 0.00623992 | ||||||||
\(358\) | 13.2291 | 0.699179 | ||||||||
\(359\) | 1.57637 | 0.0831978 | 0.0415989 | − | 0.999134i | \(-0.486755\pi\) | ||||
0.0415989 | + | 0.999134i | \(0.486755\pi\) | |||||||
\(360\) | 3.56570 | 0.187929 | ||||||||
\(361\) | −18.5594 | −0.976810 | ||||||||
\(362\) | 3.72222 | 0.195636 | ||||||||
\(363\) | 26.3515 | 1.38310 | ||||||||
\(364\) | −0.441884 | −0.0231610 | ||||||||
\(365\) | 57.1237 | 2.98999 | ||||||||
\(366\) | −5.26321 | −0.275112 | ||||||||
\(367\) | −14.0577 | −0.733804 | −0.366902 | − | 0.930260i | \(-0.619582\pi\) | ||||
−0.366902 | + | 0.930260i | \(0.619582\pi\) | |||||||
\(368\) | 8.53198 | 0.444760 | ||||||||
\(369\) | −4.76778 | −0.248201 | ||||||||
\(370\) | −9.68917 | −0.503716 | ||||||||
\(371\) | −0.648608 | −0.0336740 | ||||||||
\(372\) | −7.73406 | −0.400992 | ||||||||
\(373\) | 3.23349 | 0.167424 | 0.0837119 | − | 0.996490i | \(-0.473322\pi\) | ||||
0.0837119 | + | 0.996490i | \(0.473322\pi\) | |||||||
\(374\) | 6.11159 | 0.316023 | ||||||||
\(375\) | −9.67819 | −0.499779 | ||||||||
\(376\) | −2.98777 | −0.154082 | ||||||||
\(377\) | 28.5688 | 1.47137 | ||||||||
\(378\) | 0.117900 | 0.00606411 | ||||||||
\(379\) | −24.4567 | −1.25626 | −0.628129 | − | 0.778109i | \(-0.716179\pi\) | ||||
−0.628129 | + | 0.778109i | \(0.716179\pi\) | |||||||
\(380\) | 2.36686 | 0.121417 | ||||||||
\(381\) | −8.67239 | −0.444300 | ||||||||
\(382\) | −19.3258 | −0.988792 | ||||||||
\(383\) | −20.6255 | −1.05392 | −0.526958 | − | 0.849892i | \(-0.676667\pi\) | ||||
−0.526958 | + | 0.849892i | \(0.676667\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 2.56929 | 0.130943 | ||||||||
\(386\) | 3.37044 | 0.171551 | ||||||||
\(387\) | 0.835224 | 0.0424568 | ||||||||
\(388\) | 2.65620 | 0.134848 | ||||||||
\(389\) | 21.8541 | 1.10805 | 0.554024 | − | 0.832501i | \(-0.313091\pi\) | ||||
0.554024 | + | 0.832501i | \(0.313091\pi\) | |||||||
\(390\) | 13.3641 | 0.676719 | ||||||||
\(391\) | −8.53198 | −0.431481 | ||||||||
\(392\) | 6.98610 | 0.352851 | ||||||||
\(393\) | 12.2080 | 0.615812 | ||||||||
\(394\) | −14.7678 | −0.743990 | ||||||||
\(395\) | −0.543928 | −0.0273680 | ||||||||
\(396\) | 6.11159 | 0.307119 | ||||||||
\(397\) | 6.27040 | 0.314702 | 0.157351 | − | 0.987543i | \(-0.449705\pi\) | ||||
0.157351 | + | 0.987543i | \(0.449705\pi\) | |||||||
\(398\) | −9.14722 | −0.458509 | ||||||||
\(399\) | 0.0782600 | 0.00391790 | ||||||||
\(400\) | 7.71424 | 0.385712 | ||||||||
\(401\) | 26.2543 | 1.31108 | 0.655539 | − | 0.755161i | \(-0.272441\pi\) | ||||
0.655539 | + | 0.755161i | \(0.272441\pi\) | |||||||
\(402\) | −13.6706 | −0.681827 | ||||||||
\(403\) | −28.9870 | −1.44394 | ||||||||
\(404\) | 12.3259 | 0.613236 | ||||||||
\(405\) | −3.56570 | −0.177181 | ||||||||
\(406\) | 0.898689 | 0.0446012 | ||||||||
\(407\) | −16.6072 | −0.823186 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 13.2838 | 0.656841 | 0.328420 | − | 0.944532i | \(-0.393484\pi\) | ||||
0.328420 | + | 0.944532i | \(0.393484\pi\) | |||||||
\(410\) | −17.0005 | −0.839595 | ||||||||
\(411\) | −22.0193 | −1.08613 | ||||||||
\(412\) | −17.3019 | −0.852405 | ||||||||
\(413\) | 0.117900 | 0.00580147 | ||||||||
\(414\) | −8.53198 | −0.419324 | ||||||||
\(415\) | −22.7294 | −1.11574 | ||||||||
\(416\) | −3.74796 | −0.183759 | ||||||||
\(417\) | −5.98287 | −0.292982 | ||||||||
\(418\) | 4.05677 | 0.198423 | ||||||||
\(419\) | 28.0142 | 1.36858 | 0.684292 | − | 0.729208i | \(-0.260111\pi\) | ||||
0.684292 | + | 0.729208i | \(0.260111\pi\) | |||||||
\(420\) | 0.420396 | 0.0205132 | ||||||||
\(421\) | 40.2124 | 1.95983 | 0.979917 | − | 0.199404i | \(-0.0639005\pi\) | ||||
0.979917 | + | 0.199404i | \(0.0639005\pi\) | |||||||
\(422\) | −25.5797 | −1.24520 | ||||||||
\(423\) | 2.98777 | 0.145270 | ||||||||
\(424\) | −5.50134 | −0.267169 | ||||||||
\(425\) | −7.71424 | −0.374196 | ||||||||
\(426\) | −3.38434 | −0.163972 | ||||||||
\(427\) | −0.620531 | −0.0300296 | ||||||||
\(428\) | −7.61744 | −0.368203 | ||||||||
\(429\) | 22.9060 | 1.10591 | ||||||||
\(430\) | 2.97816 | 0.143620 | ||||||||
\(431\) | −14.1361 | −0.680912 | −0.340456 | − | 0.940260i | \(-0.610581\pi\) | ||||
−0.340456 | + | 0.940260i | \(0.610581\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 14.1754 | 0.681225 | 0.340613 | − | 0.940204i | \(-0.389366\pi\) | ||||
0.340613 | + | 0.940204i | \(0.389366\pi\) | |||||||
\(434\) | −0.911845 | −0.0437700 | ||||||||
\(435\) | −27.1795 | −1.30316 | ||||||||
\(436\) | −4.84838 | −0.232195 | ||||||||
\(437\) | −5.66339 | −0.270917 | ||||||||
\(438\) | 16.0203 | 0.765481 | ||||||||
\(439\) | 9.57975 | 0.457217 | 0.228608 | − | 0.973518i | \(-0.426582\pi\) | ||||
0.228608 | + | 0.973518i | \(0.426582\pi\) | |||||||
\(440\) | 21.7921 | 1.03890 | ||||||||
\(441\) | −6.98610 | −0.332671 | ||||||||
\(442\) | 3.74796 | 0.178272 | ||||||||
\(443\) | 6.70989 | 0.318796 | 0.159398 | − | 0.987214i | \(-0.449045\pi\) | ||||
0.159398 | + | 0.987214i | \(0.449045\pi\) | |||||||
\(444\) | −2.71732 | −0.128958 | ||||||||
\(445\) | 14.1554 | 0.671028 | ||||||||
\(446\) | −23.7681 | −1.12545 | ||||||||
\(447\) | −0.239031 | −0.0113058 | ||||||||
\(448\) | −0.117900 | −0.00557024 | ||||||||
\(449\) | −12.7988 | −0.604011 | −0.302006 | − | 0.953306i | \(-0.597656\pi\) | ||||
−0.302006 | + | 0.953306i | \(0.597656\pi\) | |||||||
\(450\) | −7.71424 | −0.363653 | ||||||||
\(451\) | −29.1387 | −1.37209 | ||||||||
\(452\) | 9.80909 | 0.461381 | ||||||||
\(453\) | −4.91184 | −0.230779 | ||||||||
\(454\) | −14.6124 | −0.685795 | ||||||||
\(455\) | 1.57563 | 0.0738666 | ||||||||
\(456\) | 0.663784 | 0.0310845 | ||||||||
\(457\) | 24.8047 | 1.16032 | 0.580158 | − | 0.814504i | \(-0.302991\pi\) | ||||
0.580158 | + | 0.814504i | \(0.302991\pi\) | |||||||
\(458\) | −22.3800 | −1.04575 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −30.4225 | −1.41846 | ||||||||
\(461\) | −10.1639 | −0.473378 | −0.236689 | − | 0.971585i | \(-0.576062\pi\) | ||||
−0.236689 | + | 0.971585i | \(0.576062\pi\) | |||||||
\(462\) | 0.720555 | 0.0335233 | ||||||||
\(463\) | 2.29746 | 0.106772 | 0.0533860 | − | 0.998574i | \(-0.482999\pi\) | ||||
0.0533860 | + | 0.998574i | \(0.482999\pi\) | |||||||
\(464\) | 7.62248 | 0.353865 | ||||||||
\(465\) | 27.5774 | 1.27887 | ||||||||
\(466\) | −16.9609 | −0.785697 | ||||||||
\(467\) | −28.7497 | −1.33038 | −0.665189 | − | 0.746675i | \(-0.731649\pi\) | ||||
−0.665189 | + | 0.746675i | \(0.731649\pi\) | |||||||
\(468\) | 3.74796 | 0.173250 | ||||||||
\(469\) | −1.61176 | −0.0744242 | ||||||||
\(470\) | 10.6535 | 0.491409 | ||||||||
\(471\) | 2.51989 | 0.116110 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | 5.10454 | 0.234707 | ||||||||
\(474\) | −0.152544 | −0.00700659 | ||||||||
\(475\) | −5.12059 | −0.234949 | ||||||||
\(476\) | 0.117900 | 0.00540393 | ||||||||
\(477\) | 5.50134 | 0.251889 | ||||||||
\(478\) | 9.32948 | 0.426721 | ||||||||
\(479\) | −27.2878 | −1.24681 | −0.623405 | − | 0.781899i | \(-0.714251\pi\) | ||||
−0.623405 | + | 0.781899i | \(0.714251\pi\) | |||||||
\(480\) | 3.56570 | 0.162751 | ||||||||
\(481\) | −10.1844 | −0.464370 | ||||||||
\(482\) | −6.64255 | −0.302560 | ||||||||
\(483\) | −1.00592 | −0.0457709 | ||||||||
\(484\) | 26.3515 | 1.19780 | ||||||||
\(485\) | −9.47121 | −0.430065 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 5.51322 | 0.249828 | 0.124914 | − | 0.992168i | \(-0.460134\pi\) | ||||
0.124914 | + | 0.992168i | \(0.460134\pi\) | |||||||
\(488\) | −5.26321 | −0.238254 | ||||||||
\(489\) | 6.47521 | 0.292819 | ||||||||
\(490\) | −24.9104 | −1.12534 | ||||||||
\(491\) | −32.8749 | −1.48362 | −0.741811 | − | 0.670609i | \(-0.766033\pi\) | ||||
−0.741811 | + | 0.670609i | \(0.766033\pi\) | |||||||
\(492\) | −4.76778 | −0.214948 | ||||||||
\(493\) | −7.62248 | −0.343299 | ||||||||
\(494\) | 2.48784 | 0.111933 | ||||||||
\(495\) | −21.7921 | −0.979483 | ||||||||
\(496\) | −7.73406 | −0.347270 | ||||||||
\(497\) | −0.399013 | −0.0178982 | ||||||||
\(498\) | −6.37444 | −0.285646 | ||||||||
\(499\) | −14.9760 | −0.670420 | −0.335210 | − | 0.942144i | \(-0.608807\pi\) | ||||
−0.335210 | + | 0.942144i | \(0.608807\pi\) | |||||||
\(500\) | −9.67819 | −0.432822 | ||||||||
\(501\) | −21.3686 | −0.954680 | ||||||||
\(502\) | −4.91450 | −0.219345 | ||||||||
\(503\) | 34.6732 | 1.54600 | 0.773001 | − | 0.634404i | \(-0.218755\pi\) | ||||
0.773001 | + | 0.634404i | \(0.218755\pi\) | |||||||
\(504\) | 0.117900 | 0.00525168 | ||||||||
\(505\) | −43.9505 | −1.95577 | ||||||||
\(506\) | −52.1440 | −2.31808 | ||||||||
\(507\) | 1.04723 | 0.0465090 | ||||||||
\(508\) | −8.67239 | −0.384775 | ||||||||
\(509\) | −36.4780 | −1.61686 | −0.808430 | − | 0.588592i | \(-0.799682\pi\) | ||||
−0.808430 | + | 0.588592i | \(0.799682\pi\) | |||||||
\(510\) | −3.56570 | −0.157892 | ||||||||
\(511\) | 1.88879 | 0.0835553 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.663784 | −0.0293068 | ||||||||
\(514\) | 24.6585 | 1.08764 | ||||||||
\(515\) | 61.6936 | 2.71854 | ||||||||
\(516\) | 0.835224 | 0.0367687 | ||||||||
\(517\) | 18.2600 | 0.803074 | ||||||||
\(518\) | −0.320372 | −0.0140763 | ||||||||
\(519\) | 4.59815 | 0.201836 | ||||||||
\(520\) | 13.3641 | 0.586056 | ||||||||
\(521\) | −15.8453 | −0.694196 | −0.347098 | − | 0.937829i | \(-0.612833\pi\) | ||||
−0.347098 | + | 0.937829i | \(0.612833\pi\) | |||||||
\(522\) | −7.62248 | −0.333627 | ||||||||
\(523\) | −5.05585 | −0.221077 | −0.110538 | − | 0.993872i | \(-0.535258\pi\) | ||||
−0.110538 | + | 0.993872i | \(0.535258\pi\) | |||||||
\(524\) | 12.2080 | 0.533309 | ||||||||
\(525\) | −0.909508 | −0.0396942 | ||||||||
\(526\) | 6.42580 | 0.280178 | ||||||||
\(527\) | 7.73406 | 0.336901 | ||||||||
\(528\) | 6.11159 | 0.265973 | ||||||||
\(529\) | 49.7947 | 2.16499 | ||||||||
\(530\) | 19.6162 | 0.852072 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 0.0782600 | 0.00339300 | ||||||||
\(533\) | −17.8695 | −0.774013 | ||||||||
\(534\) | 3.96986 | 0.171793 | ||||||||
\(535\) | 27.1615 | 1.17430 | ||||||||
\(536\) | −13.6706 | −0.590480 | ||||||||
\(537\) | −13.2291 | −0.570878 | ||||||||
\(538\) | −0.159710 | −0.00688558 | ||||||||
\(539\) | −42.6962 | −1.83905 | ||||||||
\(540\) | −3.56570 | −0.153443 | ||||||||
\(541\) | −17.6490 | −0.758790 | −0.379395 | − | 0.925235i | \(-0.623868\pi\) | ||||
−0.379395 | + | 0.925235i | \(0.623868\pi\) | |||||||
\(542\) | −1.81105 | −0.0777911 | ||||||||
\(543\) | −3.72222 | −0.159736 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 17.2879 | 0.740532 | ||||||||
\(546\) | 0.441884 | 0.0189109 | ||||||||
\(547\) | −10.0749 | −0.430773 | −0.215386 | − | 0.976529i | \(-0.569101\pi\) | ||||
−0.215386 | + | 0.976529i | \(0.569101\pi\) | |||||||
\(548\) | −22.0193 | −0.940616 | ||||||||
\(549\) | 5.26321 | 0.224628 | ||||||||
\(550\) | −47.1463 | −2.01032 | ||||||||
\(551\) | −5.05967 | −0.215549 | ||||||||
\(552\) | −8.53198 | −0.363145 | ||||||||
\(553\) | −0.0179850 | −0.000764798 0 | ||||||||
\(554\) | −27.4820 | −1.16760 | ||||||||
\(555\) | 9.68917 | 0.411282 | ||||||||
\(556\) | −5.98287 | −0.253730 | ||||||||
\(557\) | −3.90423 | −0.165427 | −0.0827137 | − | 0.996573i | \(-0.526359\pi\) | ||||
−0.0827137 | + | 0.996573i | \(0.526359\pi\) | |||||||
\(558\) | 7.73406 | 0.327409 | ||||||||
\(559\) | 3.13039 | 0.132401 | ||||||||
\(560\) | 0.420396 | 0.0177650 | ||||||||
\(561\) | −6.11159 | −0.258031 | ||||||||
\(562\) | −31.2878 | −1.31980 | ||||||||
\(563\) | −8.95057 | −0.377222 | −0.188611 | − | 0.982052i | \(-0.560398\pi\) | ||||
−0.188611 | + | 0.982052i | \(0.560398\pi\) | |||||||
\(564\) | 2.98777 | 0.125808 | ||||||||
\(565\) | −34.9763 | −1.47146 | ||||||||
\(566\) | 16.0077 | 0.672855 | ||||||||
\(567\) | −0.117900 | −0.00495133 | ||||||||
\(568\) | −3.38434 | −0.142004 | ||||||||
\(569\) | −14.8522 | −0.622635 | −0.311318 | − | 0.950306i | \(-0.600770\pi\) | ||||
−0.311318 | + | 0.950306i | \(0.600770\pi\) | |||||||
\(570\) | −2.36686 | −0.0991367 | ||||||||
\(571\) | −37.2762 | −1.55996 | −0.779979 | − | 0.625805i | \(-0.784770\pi\) | ||||
−0.779979 | + | 0.625805i | \(0.784770\pi\) | |||||||
\(572\) | 22.9060 | 0.957748 | ||||||||
\(573\) | 19.3258 | 0.807345 | ||||||||
\(574\) | −0.562121 | −0.0234625 | ||||||||
\(575\) | 65.8178 | 2.74479 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −12.3110 | −0.512513 | −0.256256 | − | 0.966609i | \(-0.582489\pi\) | ||||
−0.256256 | + | 0.966609i | \(0.582489\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −3.37044 | −0.140071 | ||||||||
\(580\) | −27.1795 | −1.12857 | ||||||||
\(581\) | −0.751546 | −0.0311794 | ||||||||
\(582\) | −2.65620 | −0.110103 | ||||||||
\(583\) | 33.6219 | 1.39248 | ||||||||
\(584\) | 16.0203 | 0.662926 | ||||||||
\(585\) | −13.3641 | −0.552539 | ||||||||
\(586\) | −19.2486 | −0.795151 | ||||||||
\(587\) | −17.4677 | −0.720967 | −0.360484 | − | 0.932766i | \(-0.617388\pi\) | ||||
−0.360484 | + | 0.932766i | \(0.617388\pi\) | |||||||
\(588\) | −6.98610 | −0.288102 | ||||||||
\(589\) | 5.13374 | 0.211532 | ||||||||
\(590\) | −3.56570 | −0.146798 | ||||||||
\(591\) | 14.7678 | 0.607465 | ||||||||
\(592\) | −2.71732 | −0.111681 | ||||||||
\(593\) | −0.890571 | −0.0365714 | −0.0182857 | − | 0.999833i | \(-0.505821\pi\) | ||||
−0.0182857 | + | 0.999833i | \(0.505821\pi\) | |||||||
\(594\) | −6.11159 | −0.250761 | ||||||||
\(595\) | −0.420396 | −0.0172346 | ||||||||
\(596\) | −0.239031 | −0.00979109 | ||||||||
\(597\) | 9.14722 | 0.374371 | ||||||||
\(598\) | −31.9776 | −1.30766 | ||||||||
\(599\) | 4.93280 | 0.201549 | 0.100774 | − | 0.994909i | \(-0.467868\pi\) | ||||
0.100774 | + | 0.994909i | \(0.467868\pi\) | |||||||
\(600\) | −7.71424 | −0.314933 | ||||||||
\(601\) | 7.69602 | 0.313927 | 0.156964 | − | 0.987604i | \(-0.449829\pi\) | ||||
0.156964 | + | 0.987604i | \(0.449829\pi\) | |||||||
\(602\) | 0.0984727 | 0.00401345 | ||||||||
\(603\) | 13.6706 | 0.556710 | ||||||||
\(604\) | −4.91184 | −0.199860 | ||||||||
\(605\) | −93.9616 | −3.82008 | ||||||||
\(606\) | −12.3259 | −0.500705 | ||||||||
\(607\) | 15.6840 | 0.636593 | 0.318297 | − | 0.947991i | \(-0.396889\pi\) | ||||
0.318297 | + | 0.947991i | \(0.396889\pi\) | |||||||
\(608\) | 0.663784 | 0.0269200 | ||||||||
\(609\) | −0.898689 | −0.0364167 | ||||||||
\(610\) | 18.7670 | 0.759855 | ||||||||
\(611\) | 11.1980 | 0.453024 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 25.5268 | 1.03102 | 0.515508 | − | 0.856885i | \(-0.327603\pi\) | ||||
0.515508 | + | 0.856885i | \(0.327603\pi\) | |||||||
\(614\) | 6.54982 | 0.264329 | ||||||||
\(615\) | 17.0005 | 0.685526 | ||||||||
\(616\) | 0.720555 | 0.0290320 | ||||||||
\(617\) | 5.49917 | 0.221388 | 0.110694 | − | 0.993855i | \(-0.464693\pi\) | ||||
0.110694 | + | 0.993855i | \(0.464693\pi\) | |||||||
\(618\) | 17.3019 | 0.695986 | ||||||||
\(619\) | −24.4214 | −0.981580 | −0.490790 | − | 0.871278i | \(-0.663292\pi\) | ||||
−0.490790 | + | 0.871278i | \(0.663292\pi\) | |||||||
\(620\) | 27.5774 | 1.10753 | ||||||||
\(621\) | 8.53198 | 0.342377 | ||||||||
\(622\) | −27.1871 | −1.09010 | ||||||||
\(623\) | 0.468046 | 0.0187519 | ||||||||
\(624\) | 3.74796 | 0.150039 | ||||||||
\(625\) | −4.06167 | −0.162467 | ||||||||
\(626\) | −21.1346 | −0.844708 | ||||||||
\(627\) | −4.05677 | −0.162012 | ||||||||
\(628\) | 2.51989 | 0.100554 | ||||||||
\(629\) | 2.71732 | 0.108347 | ||||||||
\(630\) | −0.420396 | −0.0167490 | ||||||||
\(631\) | 41.7809 | 1.66327 | 0.831635 | − | 0.555323i | \(-0.187405\pi\) | ||||
0.831635 | + | 0.555323i | \(0.187405\pi\) | |||||||
\(632\) | −0.152544 | −0.00606789 | ||||||||
\(633\) | 25.5797 | 1.01670 | ||||||||
\(634\) | 17.5500 | 0.696999 | ||||||||
\(635\) | 30.9232 | 1.22715 | ||||||||
\(636\) | 5.50134 | 0.218142 | ||||||||
\(637\) | −26.1836 | −1.03743 | ||||||||
\(638\) | −46.5854 | −1.84433 | ||||||||
\(639\) | 3.38434 | 0.133882 | ||||||||
\(640\) | 3.56570 | 0.140947 | ||||||||
\(641\) | −40.3832 | −1.59504 | −0.797521 | − | 0.603291i | \(-0.793856\pi\) | ||||
−0.797521 | + | 0.603291i | \(0.793856\pi\) | |||||||
\(642\) | 7.61744 | 0.300636 | ||||||||
\(643\) | −12.6028 | −0.497007 | −0.248503 | − | 0.968631i | \(-0.579939\pi\) | ||||
−0.248503 | + | 0.968631i | \(0.579939\pi\) | |||||||
\(644\) | −1.00592 | −0.0396388 | ||||||||
\(645\) | −2.97816 | −0.117265 | ||||||||
\(646\) | −0.663784 | −0.0261162 | ||||||||
\(647\) | 40.8528 | 1.60609 | 0.803044 | − | 0.595919i | \(-0.203212\pi\) | ||||
0.803044 | + | 0.595919i | \(0.203212\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −6.11159 | −0.239901 | ||||||||
\(650\) | −28.9127 | −1.13405 | ||||||||
\(651\) | 0.911845 | 0.0357380 | ||||||||
\(652\) | 6.47521 | 0.253589 | ||||||||
\(653\) | 3.94004 | 0.154186 | 0.0770928 | − | 0.997024i | \(-0.475436\pi\) | ||||
0.0770928 | + | 0.997024i | \(0.475436\pi\) | |||||||
\(654\) | 4.84838 | 0.189587 | ||||||||
\(655\) | −43.5301 | −1.70086 | ||||||||
\(656\) | −4.76778 | −0.186151 | ||||||||
\(657\) | −16.0203 | −0.625012 | ||||||||
\(658\) | 0.352257 | 0.0137324 | ||||||||
\(659\) | 11.3329 | 0.441469 | 0.220734 | − | 0.975334i | \(-0.429155\pi\) | ||||
0.220734 | + | 0.975334i | \(0.429155\pi\) | |||||||
\(660\) | −21.7921 | −0.848257 | ||||||||
\(661\) | −35.6357 | −1.38607 | −0.693035 | − | 0.720904i | \(-0.743727\pi\) | ||||
−0.693035 | + | 0.720904i | \(0.743727\pi\) | |||||||
\(662\) | 31.1646 | 1.21125 | ||||||||
\(663\) | −3.74796 | −0.145559 | ||||||||
\(664\) | −6.37444 | −0.247376 | ||||||||
\(665\) | −0.279052 | −0.0108212 | ||||||||
\(666\) | 2.71732 | 0.105294 | ||||||||
\(667\) | 65.0348 | 2.51816 | ||||||||
\(668\) | −21.3686 | −0.826777 | ||||||||
\(669\) | 23.7681 | 0.918929 | ||||||||
\(670\) | 48.7453 | 1.88320 | ||||||||
\(671\) | 32.1666 | 1.24178 | ||||||||
\(672\) | 0.117900 | 0.00454809 | ||||||||
\(673\) | 36.0148 | 1.38827 | 0.694133 | − | 0.719846i | \(-0.255788\pi\) | ||||
0.694133 | + | 0.719846i | \(0.255788\pi\) | |||||||
\(674\) | −3.30735 | −0.127395 | ||||||||
\(675\) | 7.71424 | 0.296921 | ||||||||
\(676\) | 1.04723 | 0.0402780 | ||||||||
\(677\) | −25.3463 | −0.974138 | −0.487069 | − | 0.873363i | \(-0.661934\pi\) | ||||
−0.487069 | + | 0.873363i | \(0.661934\pi\) | |||||||
\(678\) | −9.80909 | −0.376716 | ||||||||
\(679\) | −0.313165 | −0.0120182 | ||||||||
\(680\) | −3.56570 | −0.136738 | ||||||||
\(681\) | 14.6124 | 0.559949 | ||||||||
\(682\) | 47.2674 | 1.80996 | ||||||||
\(683\) | 48.3320 | 1.84937 | 0.924686 | − | 0.380732i | \(-0.124328\pi\) | ||||
0.924686 | + | 0.380732i | \(0.124328\pi\) | |||||||
\(684\) | −0.663784 | −0.0253804 | ||||||||
\(685\) | 78.5142 | 2.99987 | ||||||||
\(686\) | −1.64896 | −0.0629575 | ||||||||
\(687\) | 22.3800 | 0.853849 | ||||||||
\(688\) | 0.835224 | 0.0318426 | ||||||||
\(689\) | 20.6188 | 0.785515 | ||||||||
\(690\) | 30.4225 | 1.15817 | ||||||||
\(691\) | 7.97994 | 0.303571 | 0.151786 | − | 0.988413i | \(-0.451498\pi\) | ||||
0.151786 | + | 0.988413i | \(0.451498\pi\) | |||||||
\(692\) | 4.59815 | 0.174795 | ||||||||
\(693\) | −0.720555 | −0.0273716 | ||||||||
\(694\) | −20.2791 | −0.769782 | ||||||||
\(695\) | 21.3331 | 0.809212 | ||||||||
\(696\) | −7.62248 | −0.288929 | ||||||||
\(697\) | 4.76778 | 0.180593 | ||||||||
\(698\) | 9.39605 | 0.355646 | ||||||||
\(699\) | 16.9609 | 0.641519 | ||||||||
\(700\) | −0.909508 | −0.0343762 | ||||||||
\(701\) | 21.9629 | 0.829526 | 0.414763 | − | 0.909929i | \(-0.363864\pi\) | ||||
0.414763 | + | 0.909929i | \(0.363864\pi\) | |||||||
\(702\) | −3.74796 | −0.141458 | ||||||||
\(703\) | 1.80372 | 0.0680284 | ||||||||
\(704\) | 6.11159 | 0.230339 | ||||||||
\(705\) | −10.6535 | −0.401234 | ||||||||
\(706\) | −28.4262 | −1.06983 | ||||||||
\(707\) | −1.45322 | −0.0546540 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | −17.8180 | −0.669171 | −0.334585 | − | 0.942365i | \(-0.608596\pi\) | ||||
−0.334585 | + | 0.942365i | \(0.608596\pi\) | |||||||
\(710\) | 12.0675 | 0.452887 | ||||||||
\(711\) | 0.152544 | 0.00572086 | ||||||||
\(712\) | 3.96986 | 0.148777 | ||||||||
\(713\) | −65.9869 | −2.47123 | ||||||||
\(714\) | −0.117900 | −0.00441229 | ||||||||
\(715\) | −81.6760 | −3.05451 | ||||||||
\(716\) | −13.2291 | −0.494394 | ||||||||
\(717\) | −9.32948 | −0.348416 | ||||||||
\(718\) | −1.57637 | −0.0588297 | ||||||||
\(719\) | −2.83486 | −0.105722 | −0.0528612 | − | 0.998602i | \(-0.516834\pi\) | ||||
−0.0528612 | + | 0.998602i | \(0.516834\pi\) | |||||||
\(720\) | −3.56570 | −0.132886 | ||||||||
\(721\) | 2.03990 | 0.0759697 | ||||||||
\(722\) | 18.5594 | 0.690709 | ||||||||
\(723\) | 6.64255 | 0.247039 | ||||||||
\(724\) | −3.72222 | −0.138335 | ||||||||
\(725\) | 58.8016 | 2.18384 | ||||||||
\(726\) | −26.3515 | −0.977996 | ||||||||
\(727\) | 2.41297 | 0.0894923 | 0.0447461 | − | 0.998998i | \(-0.485752\pi\) | ||||
0.0447461 | + | 0.998998i | \(0.485752\pi\) | |||||||
\(728\) | 0.441884 | 0.0163773 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −57.1237 | −2.11424 | ||||||||
\(731\) | −0.835224 | −0.0308919 | ||||||||
\(732\) | 5.26321 | 0.194534 | ||||||||
\(733\) | 28.3155 | 1.04586 | 0.522929 | − | 0.852376i | \(-0.324839\pi\) | ||||
0.522929 | + | 0.852376i | \(0.324839\pi\) | |||||||
\(734\) | 14.0577 | 0.518878 | ||||||||
\(735\) | 24.9104 | 0.918833 | ||||||||
\(736\) | −8.53198 | −0.314493 | ||||||||
\(737\) | 83.5491 | 3.07757 | ||||||||
\(738\) | 4.76778 | 0.175505 | ||||||||
\(739\) | −18.2325 | −0.670694 | −0.335347 | − | 0.942095i | \(-0.608854\pi\) | ||||
−0.335347 | + | 0.942095i | \(0.608854\pi\) | |||||||
\(740\) | 9.68917 | 0.356181 | ||||||||
\(741\) | −2.48784 | −0.0913930 | ||||||||
\(742\) | 0.648608 | 0.0238111 | ||||||||
\(743\) | 38.2654 | 1.40382 | 0.701911 | − | 0.712264i | \(-0.252330\pi\) | ||||
0.701911 | + | 0.712264i | \(0.252330\pi\) | |||||||
\(744\) | 7.73406 | 0.283544 | ||||||||
\(745\) | 0.852314 | 0.0312264 | ||||||||
\(746\) | −3.23349 | −0.118387 | ||||||||
\(747\) | 6.37444 | 0.233229 | ||||||||
\(748\) | −6.11159 | −0.223462 | ||||||||
\(749\) | 0.898095 | 0.0328157 | ||||||||
\(750\) | 9.67819 | 0.353397 | ||||||||
\(751\) | −8.02423 | −0.292808 | −0.146404 | − | 0.989225i | \(-0.546770\pi\) | ||||
−0.146404 | + | 0.989225i | \(0.546770\pi\) | |||||||
\(752\) | 2.98777 | 0.108953 | ||||||||
\(753\) | 4.91450 | 0.179094 | ||||||||
\(754\) | −28.5688 | −1.04041 | ||||||||
\(755\) | 17.5142 | 0.637406 | ||||||||
\(756\) | −0.117900 | −0.00428798 | ||||||||
\(757\) | 37.1116 | 1.34884 | 0.674422 | − | 0.738346i | \(-0.264393\pi\) | ||||
0.674422 | + | 0.738346i | \(0.264393\pi\) | |||||||
\(758\) | 24.4567 | 0.888309 | ||||||||
\(759\) | 52.1440 | 1.89271 | ||||||||
\(760\) | −2.36686 | −0.0858549 | ||||||||
\(761\) | −39.6545 | −1.43747 | −0.718737 | − | 0.695282i | \(-0.755279\pi\) | ||||
−0.718737 | + | 0.695282i | \(0.755279\pi\) | |||||||
\(762\) | 8.67239 | 0.314168 | ||||||||
\(763\) | 0.571623 | 0.0206942 | ||||||||
\(764\) | 19.3258 | 0.699182 | ||||||||
\(765\) | 3.56570 | 0.128918 | ||||||||
\(766\) | 20.6255 | 0.745231 | ||||||||
\(767\) | −3.74796 | −0.135331 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −15.3864 | −0.554846 | −0.277423 | − | 0.960748i | \(-0.589480\pi\) | ||||
−0.277423 | + | 0.960748i | \(0.589480\pi\) | |||||||
\(770\) | −2.56929 | −0.0925907 | ||||||||
\(771\) | −24.6585 | −0.888053 | ||||||||
\(772\) | −3.37044 | −0.121305 | ||||||||
\(773\) | 29.1421 | 1.04817 | 0.524084 | − | 0.851667i | \(-0.324408\pi\) | ||||
0.524084 | + | 0.851667i | \(0.324408\pi\) | |||||||
\(774\) | −0.835224 | −0.0300215 | ||||||||
\(775\) | −59.6624 | −2.14314 | ||||||||
\(776\) | −2.65620 | −0.0953519 | ||||||||
\(777\) | 0.320372 | 0.0114933 | ||||||||
\(778\) | −21.8541 | −0.783509 | ||||||||
\(779\) | 3.16478 | 0.113390 | ||||||||
\(780\) | −13.3641 | −0.478512 | ||||||||
\(781\) | 20.6837 | 0.740120 | ||||||||
\(782\) | 8.53198 | 0.305103 | ||||||||
\(783\) | 7.62248 | 0.272405 | ||||||||
\(784\) | −6.98610 | −0.249504 | ||||||||
\(785\) | −8.98518 | −0.320695 | ||||||||
\(786\) | −12.2080 | −0.435445 | ||||||||
\(787\) | −42.2725 | −1.50685 | −0.753425 | − | 0.657533i | \(-0.771600\pi\) | ||||
−0.753425 | + | 0.657533i | \(0.771600\pi\) | |||||||
\(788\) | 14.7678 | 0.526080 | ||||||||
\(789\) | −6.42580 | −0.228764 | ||||||||
\(790\) | 0.543928 | 0.0193521 | ||||||||
\(791\) | −1.15649 | −0.0411201 | ||||||||
\(792\) | −6.11159 | −0.217166 | ||||||||
\(793\) | 19.7263 | 0.700502 | ||||||||
\(794\) | −6.27040 | −0.222528 | ||||||||
\(795\) | −19.6162 | −0.695714 | ||||||||
\(796\) | 9.14722 | 0.324215 | ||||||||
\(797\) | 37.4616 | 1.32696 | 0.663478 | − | 0.748196i | \(-0.269080\pi\) | ||||
0.663478 | + | 0.748196i | \(0.269080\pi\) | |||||||
\(798\) | −0.0782600 | −0.00277037 | ||||||||
\(799\) | −2.98777 | −0.105700 | ||||||||
\(800\) | −7.71424 | −0.272740 | ||||||||
\(801\) | −3.96986 | −0.140268 | ||||||||
\(802\) | −26.2543 | −0.927072 | ||||||||
\(803\) | −97.9096 | −3.45515 | ||||||||
\(804\) | 13.6706 | 0.482125 | ||||||||
\(805\) | 3.58681 | 0.126418 | ||||||||
\(806\) | 28.9870 | 1.02102 | ||||||||
\(807\) | 0.159710 | 0.00562206 | ||||||||
\(808\) | −12.3259 | −0.433624 | ||||||||
\(809\) | −37.3291 | −1.31242 | −0.656210 | − | 0.754578i | \(-0.727841\pi\) | ||||
−0.656210 | + | 0.754578i | \(0.727841\pi\) | |||||||
\(810\) | 3.56570 | 0.125286 | ||||||||
\(811\) | 52.5876 | 1.84660 | 0.923301 | − | 0.384078i | \(-0.125480\pi\) | ||||
0.923301 | + | 0.384078i | \(0.125480\pi\) | |||||||
\(812\) | −0.898689 | −0.0315378 | ||||||||
\(813\) | 1.81105 | 0.0635162 | ||||||||
\(814\) | 16.6072 | 0.582081 | ||||||||
\(815\) | −23.0887 | −0.808761 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −0.554408 | −0.0193963 | ||||||||
\(818\) | −13.2838 | −0.464457 | ||||||||
\(819\) | −0.441884 | −0.0154407 | ||||||||
\(820\) | 17.0005 | 0.593683 | ||||||||
\(821\) | −41.0047 | −1.43107 | −0.715537 | − | 0.698575i | \(-0.753818\pi\) | ||||
−0.715537 | + | 0.698575i | \(0.753818\pi\) | |||||||
\(822\) | 22.0193 | 0.768010 | ||||||||
\(823\) | 11.4903 | 0.400526 | 0.200263 | − | 0.979742i | \(-0.435820\pi\) | ||||
0.200263 | + | 0.979742i | \(0.435820\pi\) | |||||||
\(824\) | 17.3019 | 0.602742 | ||||||||
\(825\) | 47.1463 | 1.64142 | ||||||||
\(826\) | −0.117900 | −0.00410226 | ||||||||
\(827\) | −0.973551 | −0.0338537 | −0.0169268 | − | 0.999857i | \(-0.505388\pi\) | ||||
−0.0169268 | + | 0.999857i | \(0.505388\pi\) | |||||||
\(828\) | 8.53198 | 0.296507 | ||||||||
\(829\) | 1.33152 | 0.0462455 | 0.0231228 | − | 0.999733i | \(-0.492639\pi\) | ||||
0.0231228 | + | 0.999733i | \(0.492639\pi\) | |||||||
\(830\) | 22.7294 | 0.788948 | ||||||||
\(831\) | 27.4820 | 0.953341 | ||||||||
\(832\) | 3.74796 | 0.129937 | ||||||||
\(833\) | 6.98610 | 0.242054 | ||||||||
\(834\) | 5.98287 | 0.207170 | ||||||||
\(835\) | 76.1942 | 2.63681 | ||||||||
\(836\) | −4.05677 | −0.140306 | ||||||||
\(837\) | −7.73406 | −0.267328 | ||||||||
\(838\) | −28.0142 | −0.967735 | ||||||||
\(839\) | 18.8915 | 0.652206 | 0.326103 | − | 0.945334i | \(-0.394264\pi\) | ||||
0.326103 | + | 0.945334i | \(0.394264\pi\) | |||||||
\(840\) | −0.420396 | −0.0145050 | ||||||||
\(841\) | 29.1021 | 1.00352 | ||||||||
\(842\) | −40.2124 | −1.38581 | ||||||||
\(843\) | 31.2878 | 1.07761 | ||||||||
\(844\) | 25.5797 | 0.880490 | ||||||||
\(845\) | −3.73410 | −0.128457 | ||||||||
\(846\) | −2.98777 | −0.102722 | ||||||||
\(847\) | −3.10684 | −0.106752 | ||||||||
\(848\) | 5.50134 | 0.188917 | ||||||||
\(849\) | −16.0077 | −0.549384 | ||||||||
\(850\) | 7.71424 | 0.264596 | ||||||||
\(851\) | −23.1842 | −0.794743 | ||||||||
\(852\) | 3.38434 | 0.115946 | ||||||||
\(853\) | 15.8034 | 0.541099 | 0.270549 | − | 0.962706i | \(-0.412795\pi\) | ||||
0.270549 | + | 0.962706i | \(0.412795\pi\) | |||||||
\(854\) | 0.620531 | 0.0212341 | ||||||||
\(855\) | 2.36686 | 0.0809448 | ||||||||
\(856\) | 7.61744 | 0.260359 | ||||||||
\(857\) | −45.4881 | −1.55385 | −0.776923 | − | 0.629596i | \(-0.783220\pi\) | ||||
−0.776923 | + | 0.629596i | \(0.783220\pi\) | |||||||
\(858\) | −22.9060 | −0.781998 | ||||||||
\(859\) | 26.4544 | 0.902613 | 0.451306 | − | 0.892369i | \(-0.350958\pi\) | ||||
0.451306 | + | 0.892369i | \(0.350958\pi\) | |||||||
\(860\) | −2.97816 | −0.101554 | ||||||||
\(861\) | 0.562121 | 0.0191570 | ||||||||
\(862\) | 14.1361 | 0.481477 | ||||||||
\(863\) | 8.00293 | 0.272423 | 0.136212 | − | 0.990680i | \(-0.456507\pi\) | ||||
0.136212 | + | 0.990680i | \(0.456507\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −16.3956 | −0.557468 | ||||||||
\(866\) | −14.1754 | −0.481699 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0.911845 | 0.0309500 | ||||||||
\(869\) | 0.932288 | 0.0316257 | ||||||||
\(870\) | 27.1795 | 0.921471 | ||||||||
\(871\) | 51.2369 | 1.73610 | ||||||||
\(872\) | 4.84838 | 0.164187 | ||||||||
\(873\) | 2.65620 | 0.0898986 | ||||||||
\(874\) | 5.66339 | 0.191567 | ||||||||
\(875\) | 1.14106 | 0.0385748 | ||||||||
\(876\) | −16.0203 | −0.541277 | ||||||||
\(877\) | −24.1230 | −0.814577 | −0.407289 | − | 0.913299i | \(-0.633526\pi\) | ||||
−0.407289 | + | 0.913299i | \(0.633526\pi\) | |||||||
\(878\) | −9.57975 | −0.323301 | ||||||||
\(879\) | 19.2486 | 0.649238 | ||||||||
\(880\) | −21.7921 | −0.734612 | ||||||||
\(881\) | −2.82944 | −0.0953263 | −0.0476632 | − | 0.998863i | \(-0.515177\pi\) | ||||
−0.0476632 | + | 0.998863i | \(0.515177\pi\) | |||||||
\(882\) | 6.98610 | 0.235234 | ||||||||
\(883\) | −55.7913 | −1.87753 | −0.938764 | − | 0.344561i | \(-0.888028\pi\) | ||||
−0.938764 | + | 0.344561i | \(0.888028\pi\) | |||||||
\(884\) | −3.74796 | −0.126058 | ||||||||
\(885\) | 3.56570 | 0.119860 | ||||||||
\(886\) | −6.70989 | −0.225423 | ||||||||
\(887\) | −16.8000 | −0.564089 | −0.282044 | − | 0.959401i | \(-0.591013\pi\) | ||||
−0.282044 | + | 0.959401i | \(0.591013\pi\) | |||||||
\(888\) | 2.71732 | 0.0911874 | ||||||||
\(889\) | 1.02247 | 0.0342927 | ||||||||
\(890\) | −14.1554 | −0.474489 | ||||||||
\(891\) | 6.11159 | 0.204746 | ||||||||
\(892\) | 23.7681 | 0.795816 | ||||||||
\(893\) | −1.98323 | −0.0663663 | ||||||||
\(894\) | 0.239031 | 0.00799440 | ||||||||
\(895\) | 47.1710 | 1.57675 | ||||||||
\(896\) | 0.117900 | 0.00393876 | ||||||||
\(897\) | 31.9776 | 1.06770 | ||||||||
\(898\) | 12.7988 | 0.427101 | ||||||||
\(899\) | −58.9527 | −1.96618 | ||||||||
\(900\) | 7.71424 | 0.257141 | ||||||||
\(901\) | −5.50134 | −0.183276 | ||||||||
\(902\) | 29.1387 | 0.970213 | ||||||||
\(903\) | −0.0984727 | −0.00327697 | ||||||||
\(904\) | −9.80909 | −0.326246 | ||||||||
\(905\) | 13.2723 | 0.441188 | ||||||||
\(906\) | 4.91184 | 0.163185 | ||||||||
\(907\) | 16.6671 | 0.553422 | 0.276711 | − | 0.960953i | \(-0.410756\pi\) | ||||
0.276711 | + | 0.960953i | \(0.410756\pi\) | |||||||
\(908\) | 14.6124 | 0.484930 | ||||||||
\(909\) | 12.3259 | 0.408824 | ||||||||
\(910\) | −1.57563 | −0.0522316 | ||||||||
\(911\) | −57.3455 | −1.89994 | −0.949971 | − | 0.312339i | \(-0.898888\pi\) | ||||
−0.949971 | + | 0.312339i | \(0.898888\pi\) | |||||||
\(912\) | −0.663784 | −0.0219801 | ||||||||
\(913\) | 38.9580 | 1.28932 | ||||||||
\(914\) | −24.8047 | −0.820467 | ||||||||
\(915\) | −18.7670 | −0.620419 | ||||||||
\(916\) | 22.3800 | 0.739455 | ||||||||
\(917\) | −1.43932 | −0.0475306 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −8.93042 | −0.294587 | −0.147294 | − | 0.989093i | \(-0.547056\pi\) | ||||
−0.147294 | + | 0.989093i | \(0.547056\pi\) | |||||||
\(920\) | 30.4225 | 1.00300 | ||||||||
\(921\) | −6.54982 | −0.215824 | ||||||||
\(922\) | 10.1639 | 0.334729 | ||||||||
\(923\) | 12.6844 | 0.417511 | ||||||||
\(924\) | −0.720555 | −0.0237045 | ||||||||
\(925\) | −20.9621 | −0.689229 | ||||||||
\(926\) | −2.29746 | −0.0754992 | ||||||||
\(927\) | −17.3019 | −0.568270 | ||||||||
\(928\) | −7.62248 | −0.250220 | ||||||||
\(929\) | −16.6158 | −0.545148 | −0.272574 | − | 0.962135i | \(-0.587875\pi\) | ||||
−0.272574 | + | 0.962135i | \(0.587875\pi\) | |||||||
\(930\) | −27.5774 | −0.904298 | ||||||||
\(931\) | 4.63726 | 0.151980 | ||||||||
\(932\) | 16.9609 | 0.555572 | ||||||||
\(933\) | 27.1871 | 0.890066 | ||||||||
\(934\) | 28.7497 | 0.940719 | ||||||||
\(935\) | 21.7921 | 0.712678 | ||||||||
\(936\) | −3.74796 | −0.122506 | ||||||||
\(937\) | −4.59473 | −0.150103 | −0.0750517 | − | 0.997180i | \(-0.523912\pi\) | ||||
−0.0750517 | + | 0.997180i | \(0.523912\pi\) | |||||||
\(938\) | 1.61176 | 0.0526259 | ||||||||
\(939\) | 21.1346 | 0.689702 | ||||||||
\(940\) | −10.6535 | −0.347479 | ||||||||
\(941\) | −37.9517 | −1.23719 | −0.618595 | − | 0.785710i | \(-0.712298\pi\) | ||||
−0.618595 | + | 0.785710i | \(0.712298\pi\) | |||||||
\(942\) | −2.51989 | −0.0821024 | ||||||||
\(943\) | −40.6786 | −1.32468 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | 0.420396 | 0.0136755 | ||||||||
\(946\) | −5.10454 | −0.165963 | ||||||||
\(947\) | 32.5996 | 1.05935 | 0.529673 | − | 0.848202i | \(-0.322315\pi\) | ||||
0.529673 | + | 0.848202i | \(0.322315\pi\) | |||||||
\(948\) | 0.152544 | 0.00495441 | ||||||||
\(949\) | −60.0436 | −1.94910 | ||||||||
\(950\) | 5.12059 | 0.166134 | ||||||||
\(951\) | −17.5500 | −0.569098 | ||||||||
\(952\) | −0.117900 | −0.00382116 | ||||||||
\(953\) | 10.4092 | 0.337186 | 0.168593 | − | 0.985686i | \(-0.446078\pi\) | ||||
0.168593 | + | 0.985686i | \(0.446078\pi\) | |||||||
\(954\) | −5.50134 | −0.178113 | ||||||||
\(955\) | −68.9099 | −2.22987 | ||||||||
\(956\) | −9.32948 | −0.301737 | ||||||||
\(957\) | 46.5854 | 1.50589 | ||||||||
\(958\) | 27.2878 | 0.881628 | ||||||||
\(959\) | 2.59607 | 0.0838314 | ||||||||
\(960\) | −3.56570 | −0.115083 | ||||||||
\(961\) | 28.8157 | 0.929540 | ||||||||
\(962\) | 10.1844 | 0.328359 | ||||||||
\(963\) | −7.61744 | −0.245469 | ||||||||
\(964\) | 6.64255 | 0.213942 | ||||||||
\(965\) | 12.0180 | 0.386873 | ||||||||
\(966\) | 1.00592 | 0.0323649 | ||||||||
\(967\) | −13.4260 | −0.431750 | −0.215875 | − | 0.976421i | \(-0.569260\pi\) | ||||
−0.215875 | + | 0.976421i | \(0.569260\pi\) | |||||||
\(968\) | −26.3515 | −0.846969 | ||||||||
\(969\) | 0.663784 | 0.0213238 | ||||||||
\(970\) | 9.47121 | 0.304102 | ||||||||
\(971\) | −27.0066 | −0.866682 | −0.433341 | − | 0.901230i | \(-0.642665\pi\) | ||||
−0.433341 | + | 0.901230i | \(0.642665\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0.705379 | 0.0226134 | ||||||||
\(974\) | −5.51322 | −0.176655 | ||||||||
\(975\) | 28.9127 | 0.925947 | ||||||||
\(976\) | 5.26321 | 0.168471 | ||||||||
\(977\) | 28.9880 | 0.927408 | 0.463704 | − | 0.885990i | \(-0.346520\pi\) | ||||
0.463704 | + | 0.885990i | \(0.346520\pi\) | |||||||
\(978\) | −6.47521 | −0.207054 | ||||||||
\(979\) | −24.2622 | −0.775422 | ||||||||
\(980\) | 24.9104 | 0.795732 | ||||||||
\(981\) | −4.84838 | −0.154797 | ||||||||
\(982\) | 32.8749 | 1.04908 | ||||||||
\(983\) | 34.0619 | 1.08641 | 0.543203 | − | 0.839602i | \(-0.317212\pi\) | ||||
0.543203 | + | 0.839602i | \(0.317212\pi\) | |||||||
\(984\) | 4.76778 | 0.151991 | ||||||||
\(985\) | −52.6575 | −1.67781 | ||||||||
\(986\) | 7.62248 | 0.242749 | ||||||||
\(987\) | −0.352257 | −0.0112125 | ||||||||
\(988\) | −2.48784 | −0.0791486 | ||||||||
\(989\) | 7.12611 | 0.226597 | ||||||||
\(990\) | 21.7921 | 0.692599 | ||||||||
\(991\) | −45.5896 | −1.44820 | −0.724100 | − | 0.689695i | \(-0.757745\pi\) | ||||
−0.724100 | + | 0.689695i | \(0.757745\pi\) | |||||||
\(992\) | 7.73406 | 0.245557 | ||||||||
\(993\) | −31.1646 | −0.988978 | ||||||||
\(994\) | 0.399013 | 0.0126559 | ||||||||
\(995\) | −32.6163 | −1.03401 | ||||||||
\(996\) | 6.37444 | 0.201982 | ||||||||
\(997\) | 39.0015 | 1.23519 | 0.617595 | − | 0.786497i | \(-0.288107\pi\) | ||||
0.617595 | + | 0.786497i | \(0.288107\pi\) | |||||||
\(998\) | 14.9760 | 0.474058 | ||||||||
\(999\) | −2.71732 | −0.0859723 |
(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 | 6018.2.a.p.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.p.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial |