Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28460 | −0.908350 | −0.454175 | − | 0.890912i | \(-0.650066\pi\) | ||||
−0.454175 | + | 0.890912i | \(0.650066\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.349799 | −0.174899 | ||||||||
\(5\) | −0.580730 | −0.259710 | −0.129855 | − | 0.991533i | \(-0.541451\pi\) | ||||
−0.129855 | + | 0.991533i | \(0.541451\pi\) | |||||||
\(6\) | 1.28460 | 0.524436 | ||||||||
\(7\) | −1.93204 | −0.730244 | −0.365122 | − | 0.930960i | \(-0.618973\pi\) | ||||
−0.365122 | + | 0.930960i | \(0.618973\pi\) | |||||||
\(8\) | 3.01856 | 1.06722 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.746007 | 0.235908 | ||||||||
\(11\) | 1.58316 | 0.477340 | 0.238670 | − | 0.971101i | \(-0.423289\pi\) | ||||
0.238670 | + | 0.971101i | \(0.423289\pi\) | |||||||
\(12\) | 0.349799 | 0.100978 | ||||||||
\(13\) | −0.419632 | −0.116385 | −0.0581925 | − | 0.998305i | \(-0.518534\pi\) | ||||
−0.0581925 | + | 0.998305i | \(0.518534\pi\) | |||||||
\(14\) | 2.48191 | 0.663317 | ||||||||
\(15\) | 0.580730 | 0.149944 | ||||||||
\(16\) | −3.17804 | −0.794511 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.28460 | −0.302783 | ||||||||
\(19\) | −2.91658 | −0.669109 | −0.334555 | − | 0.942376i | \(-0.608586\pi\) | ||||
−0.334555 | + | 0.942376i | \(0.608586\pi\) | |||||||
\(20\) | 0.203139 | 0.0454232 | ||||||||
\(21\) | 1.93204 | 0.421607 | ||||||||
\(22\) | −2.03372 | −0.433592 | ||||||||
\(23\) | 8.95631 | 1.86752 | 0.933760 | − | 0.357901i | \(-0.116507\pi\) | ||||
0.933760 | + | 0.357901i | \(0.116507\pi\) | |||||||
\(24\) | −3.01856 | −0.616160 | ||||||||
\(25\) | −4.66275 | −0.932551 | ||||||||
\(26\) | 0.539060 | 0.105718 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.675827 | 0.127719 | ||||||||
\(29\) | 4.63895 | 0.861432 | 0.430716 | − | 0.902488i | \(-0.358261\pi\) | ||||
0.430716 | + | 0.902488i | \(0.358261\pi\) | |||||||
\(30\) | −0.746007 | −0.136202 | ||||||||
\(31\) | 1.94626 | 0.349558 | 0.174779 | − | 0.984608i | \(-0.444079\pi\) | ||||
0.174779 | + | 0.984608i | \(0.444079\pi\) | |||||||
\(32\) | −1.95459 | −0.345526 | ||||||||
\(33\) | −1.58316 | −0.275592 | ||||||||
\(34\) | −1.28460 | −0.220307 | ||||||||
\(35\) | 1.12200 | 0.189652 | ||||||||
\(36\) | −0.349799 | −0.0582998 | ||||||||
\(37\) | 8.65463 | 1.42281 | 0.711406 | − | 0.702781i | \(-0.248059\pi\) | ||||
0.711406 | + | 0.702781i | \(0.248059\pi\) | |||||||
\(38\) | 3.74664 | 0.607786 | ||||||||
\(39\) | 0.419632 | 0.0671949 | ||||||||
\(40\) | −1.75297 | −0.277168 | ||||||||
\(41\) | 10.2986 | 1.60837 | 0.804187 | − | 0.594376i | \(-0.202601\pi\) | ||||
0.804187 | + | 0.594376i | \(0.202601\pi\) | |||||||
\(42\) | −2.48191 | −0.382967 | ||||||||
\(43\) | −1.03555 | −0.157920 | −0.0789602 | − | 0.996878i | \(-0.525160\pi\) | ||||
−0.0789602 | + | 0.996878i | \(0.525160\pi\) | |||||||
\(44\) | −0.553786 | −0.0834864 | ||||||||
\(45\) | −0.580730 | −0.0865701 | ||||||||
\(46\) | −11.5053 | −1.69636 | ||||||||
\(47\) | 7.92894 | 1.15656 | 0.578278 | − | 0.815840i | \(-0.303725\pi\) | ||||
0.578278 | + | 0.815840i | \(0.303725\pi\) | |||||||
\(48\) | 3.17804 | 0.458711 | ||||||||
\(49\) | −3.26721 | −0.466744 | ||||||||
\(50\) | 5.98978 | 0.847083 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0.146787 | 0.0203557 | ||||||||
\(53\) | −10.1848 | −1.39898 | −0.699492 | − | 0.714641i | \(-0.746590\pi\) | ||||
−0.699492 | + | 0.714641i | \(0.746590\pi\) | |||||||
\(54\) | 1.28460 | 0.174812 | ||||||||
\(55\) | −0.919386 | −0.123970 | ||||||||
\(56\) | −5.83198 | −0.779331 | ||||||||
\(57\) | 2.91658 | 0.386310 | ||||||||
\(58\) | −5.95921 | −0.782482 | ||||||||
\(59\) | −11.7856 | −1.53436 | −0.767179 | − | 0.641433i | \(-0.778340\pi\) | ||||
−0.767179 | + | 0.641433i | \(0.778340\pi\) | |||||||
\(60\) | −0.203139 | −0.0262251 | ||||||||
\(61\) | −3.15724 | −0.404243 | −0.202121 | − | 0.979360i | \(-0.564784\pi\) | ||||
−0.202121 | + | 0.979360i | \(0.564784\pi\) | |||||||
\(62\) | −2.50016 | −0.317521 | ||||||||
\(63\) | −1.93204 | −0.243415 | ||||||||
\(64\) | 8.86696 | 1.10837 | ||||||||
\(65\) | 0.243693 | 0.0302264 | ||||||||
\(66\) | 2.03372 | 0.250334 | ||||||||
\(67\) | −5.25076 | −0.641482 | −0.320741 | − | 0.947167i | \(-0.603932\pi\) | ||||
−0.320741 | + | 0.947167i | \(0.603932\pi\) | |||||||
\(68\) | −0.349799 | −0.0424193 | ||||||||
\(69\) | −8.95631 | −1.07821 | ||||||||
\(70\) | −1.44132 | −0.172270 | ||||||||
\(71\) | 10.2391 | 1.21515 | 0.607577 | − | 0.794260i | \(-0.292141\pi\) | ||||
0.607577 | + | 0.794260i | \(0.292141\pi\) | |||||||
\(72\) | 3.01856 | 0.355740 | ||||||||
\(73\) | −0.696030 | −0.0814641 | −0.0407321 | − | 0.999170i | \(-0.512969\pi\) | ||||
−0.0407321 | + | 0.999170i | \(0.512969\pi\) | |||||||
\(74\) | −11.1177 | −1.29241 | ||||||||
\(75\) | 4.66275 | 0.538408 | ||||||||
\(76\) | 1.02022 | 0.117027 | ||||||||
\(77\) | −3.05873 | −0.348574 | ||||||||
\(78\) | −0.539060 | −0.0610365 | ||||||||
\(79\) | −4.38503 | −0.493354 | −0.246677 | − | 0.969098i | \(-0.579339\pi\) | ||||
−0.246677 | + | 0.969098i | \(0.579339\pi\) | |||||||
\(80\) | 1.84559 | 0.206343 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.2296 | −1.46097 | ||||||||
\(83\) | −0.402925 | −0.0442268 | −0.0221134 | − | 0.999755i | \(-0.507039\pi\) | ||||
−0.0221134 | + | 0.999755i | \(0.507039\pi\) | |||||||
\(84\) | −0.675827 | −0.0737387 | ||||||||
\(85\) | −0.580730 | −0.0629890 | ||||||||
\(86\) | 1.33027 | 0.143447 | ||||||||
\(87\) | −4.63895 | −0.497348 | ||||||||
\(88\) | 4.77884 | 0.509426 | ||||||||
\(89\) | 3.07805 | 0.326273 | 0.163137 | − | 0.986603i | \(-0.447839\pi\) | ||||
0.163137 | + | 0.986603i | \(0.447839\pi\) | |||||||
\(90\) | 0.746007 | 0.0786360 | ||||||||
\(91\) | 0.810747 | 0.0849894 | ||||||||
\(92\) | −3.13291 | −0.326628 | ||||||||
\(93\) | −1.94626 | −0.201817 | ||||||||
\(94\) | −10.1855 | −1.05056 | ||||||||
\(95\) | 1.69375 | 0.173775 | ||||||||
\(96\) | 1.95459 | 0.199490 | ||||||||
\(97\) | 18.6258 | 1.89117 | 0.945583 | − | 0.325382i | \(-0.105493\pi\) | ||||
0.945583 | + | 0.325382i | \(0.105493\pi\) | |||||||
\(98\) | 4.19706 | 0.423967 | ||||||||
\(99\) | 1.58316 | 0.159113 | ||||||||
\(100\) | 1.63103 | 0.163103 | ||||||||
\(101\) | 17.5565 | 1.74694 | 0.873469 | − | 0.486880i | \(-0.161865\pi\) | ||||
0.873469 | + | 0.486880i | \(0.161865\pi\) | |||||||
\(102\) | 1.28460 | 0.127195 | ||||||||
\(103\) | −4.39526 | −0.433078 | −0.216539 | − | 0.976274i | \(-0.569477\pi\) | ||||
−0.216539 | + | 0.976274i | \(0.569477\pi\) | |||||||
\(104\) | −1.26668 | −0.124208 | ||||||||
\(105\) | −1.12200 | −0.109496 | ||||||||
\(106\) | 13.0833 | 1.27077 | ||||||||
\(107\) | 2.56618 | 0.248082 | 0.124041 | − | 0.992277i | \(-0.460415\pi\) | ||||
0.124041 | + | 0.992277i | \(0.460415\pi\) | |||||||
\(108\) | 0.349799 | 0.0336594 | ||||||||
\(109\) | 5.05854 | 0.484520 | 0.242260 | − | 0.970211i | \(-0.422111\pi\) | ||||
0.242260 | + | 0.970211i | \(0.422111\pi\) | |||||||
\(110\) | 1.18105 | 0.112608 | ||||||||
\(111\) | −8.65463 | −0.821461 | ||||||||
\(112\) | 6.14012 | 0.580187 | ||||||||
\(113\) | 0.902607 | 0.0849102 | 0.0424551 | − | 0.999098i | \(-0.486482\pi\) | ||||
0.0424551 | + | 0.999098i | \(0.486482\pi\) | |||||||
\(114\) | −3.74664 | −0.350905 | ||||||||
\(115\) | −5.20120 | −0.485014 | ||||||||
\(116\) | −1.62270 | −0.150664 | ||||||||
\(117\) | −0.419632 | −0.0387950 | ||||||||
\(118\) | 15.1398 | 1.39374 | ||||||||
\(119\) | −1.93204 | −0.177110 | ||||||||
\(120\) | 1.75297 | 0.160023 | ||||||||
\(121\) | −8.49362 | −0.772147 | ||||||||
\(122\) | 4.05579 | 0.367194 | ||||||||
\(123\) | −10.2986 | −0.928596 | ||||||||
\(124\) | −0.680798 | −0.0611375 | ||||||||
\(125\) | 5.61145 | 0.501903 | ||||||||
\(126\) | 2.48191 | 0.221106 | ||||||||
\(127\) | −8.31090 | −0.737473 | −0.368736 | − | 0.929534i | \(-0.620210\pi\) | ||||
−0.368736 | + | 0.929534i | \(0.620210\pi\) | |||||||
\(128\) | −7.48132 | −0.661262 | ||||||||
\(129\) | 1.03555 | 0.0911754 | ||||||||
\(130\) | −0.313048 | −0.0274561 | ||||||||
\(131\) | −0.701360 | −0.0612781 | −0.0306391 | − | 0.999531i | \(-0.509754\pi\) | ||||
−0.0306391 | + | 0.999531i | \(0.509754\pi\) | |||||||
\(132\) | 0.553786 | 0.0482009 | ||||||||
\(133\) | 5.63496 | 0.488613 | ||||||||
\(134\) | 6.74513 | 0.582690 | ||||||||
\(135\) | 0.580730 | 0.0499813 | ||||||||
\(136\) | 3.01856 | 0.258839 | ||||||||
\(137\) | −17.9637 | −1.53474 | −0.767370 | − | 0.641205i | \(-0.778435\pi\) | ||||
−0.767370 | + | 0.641205i | \(0.778435\pi\) | |||||||
\(138\) | 11.5053 | 0.979395 | ||||||||
\(139\) | −6.77443 | −0.574600 | −0.287300 | − | 0.957841i | \(-0.592758\pi\) | ||||
−0.287300 | + | 0.957841i | \(0.592758\pi\) | |||||||
\(140\) | −0.392473 | −0.0331700 | ||||||||
\(141\) | −7.92894 | −0.667738 | ||||||||
\(142\) | −13.1531 | −1.10379 | ||||||||
\(143\) | −0.664343 | −0.0555551 | ||||||||
\(144\) | −3.17804 | −0.264837 | ||||||||
\(145\) | −2.69398 | −0.223723 | ||||||||
\(146\) | 0.894121 | 0.0739980 | ||||||||
\(147\) | 3.26721 | 0.269475 | ||||||||
\(148\) | −3.02738 | −0.248849 | ||||||||
\(149\) | 12.3459 | 1.01141 | 0.505707 | − | 0.862706i | \(-0.331232\pi\) | ||||
0.505707 | + | 0.862706i | \(0.331232\pi\) | |||||||
\(150\) | −5.98978 | −0.489063 | ||||||||
\(151\) | 19.9042 | 1.61978 | 0.809890 | − | 0.586582i | \(-0.199527\pi\) | ||||
0.809890 | + | 0.586582i | \(0.199527\pi\) | |||||||
\(152\) | −8.80386 | −0.714087 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 3.92925 | 0.316628 | ||||||||
\(155\) | −1.13025 | −0.0907838 | ||||||||
\(156\) | −0.146787 | −0.0117523 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 5.63301 | 0.448138 | ||||||||
\(159\) | 10.1848 | 0.807703 | ||||||||
\(160\) | 1.13509 | 0.0897367 | ||||||||
\(161\) | −17.3040 | −1.36374 | ||||||||
\(162\) | −1.28460 | −0.100928 | ||||||||
\(163\) | −22.4318 | −1.75699 | −0.878496 | − | 0.477749i | \(-0.841453\pi\) | ||||
−0.878496 | + | 0.477749i | \(0.841453\pi\) | |||||||
\(164\) | −3.60245 | −0.281304 | ||||||||
\(165\) | 0.919386 | 0.0715741 | ||||||||
\(166\) | 0.517598 | 0.0401734 | ||||||||
\(167\) | 3.34538 | 0.258873 | 0.129436 | − | 0.991588i | \(-0.458683\pi\) | ||||
0.129436 | + | 0.991588i | \(0.458683\pi\) | |||||||
\(168\) | 5.83198 | 0.449947 | ||||||||
\(169\) | −12.8239 | −0.986455 | ||||||||
\(170\) | 0.746007 | 0.0572161 | ||||||||
\(171\) | −2.91658 | −0.223036 | ||||||||
\(172\) | 0.362235 | 0.0276202 | ||||||||
\(173\) | −14.7573 | −1.12197 | −0.560987 | − | 0.827824i | \(-0.689578\pi\) | ||||
−0.560987 | + | 0.827824i | \(0.689578\pi\) | |||||||
\(174\) | 5.95921 | 0.451766 | ||||||||
\(175\) | 9.00864 | 0.680989 | ||||||||
\(176\) | −5.03134 | −0.379251 | ||||||||
\(177\) | 11.7856 | 0.885862 | ||||||||
\(178\) | −3.95407 | −0.296370 | ||||||||
\(179\) | −16.7116 | −1.24909 | −0.624543 | − | 0.780991i | \(-0.714715\pi\) | ||||
−0.624543 | + | 0.780991i | \(0.714715\pi\) | |||||||
\(180\) | 0.203139 | 0.0151411 | ||||||||
\(181\) | −0.391152 | −0.0290741 | −0.0145371 | − | 0.999894i | \(-0.504627\pi\) | ||||
−0.0145371 | + | 0.999894i | \(0.504627\pi\) | |||||||
\(182\) | −1.04149 | −0.0772002 | ||||||||
\(183\) | 3.15724 | 0.233390 | ||||||||
\(184\) | 27.0351 | 1.99305 | ||||||||
\(185\) | −5.02600 | −0.369519 | ||||||||
\(186\) | 2.50016 | 0.183321 | ||||||||
\(187\) | 1.58316 | 0.115772 | ||||||||
\(188\) | −2.77354 | −0.202281 | ||||||||
\(189\) | 1.93204 | 0.140536 | ||||||||
\(190\) | −2.17579 | −0.157848 | ||||||||
\(191\) | −23.7512 | −1.71857 | −0.859287 | − | 0.511495i | \(-0.829092\pi\) | ||||
−0.859287 | + | 0.511495i | \(0.829092\pi\) | |||||||
\(192\) | −8.86696 | −0.639918 | ||||||||
\(193\) | −15.1485 | −1.09041 | −0.545206 | − | 0.838302i | \(-0.683548\pi\) | ||||
−0.545206 | + | 0.838302i | \(0.683548\pi\) | |||||||
\(194\) | −23.9268 | −1.71784 | ||||||||
\(195\) | −0.243693 | −0.0174512 | ||||||||
\(196\) | 1.14286 | 0.0816332 | ||||||||
\(197\) | −10.6745 | −0.760528 | −0.380264 | − | 0.924878i | \(-0.624167\pi\) | ||||
−0.380264 | + | 0.924878i | \(0.624167\pi\) | |||||||
\(198\) | −2.03372 | −0.144531 | ||||||||
\(199\) | 9.56418 | 0.677987 | 0.338993 | − | 0.940789i | \(-0.389914\pi\) | ||||
0.338993 | + | 0.940789i | \(0.389914\pi\) | |||||||
\(200\) | −14.0748 | −0.995237 | ||||||||
\(201\) | 5.25076 | 0.370360 | ||||||||
\(202\) | −22.5531 | −1.58683 | ||||||||
\(203\) | −8.96266 | −0.629055 | ||||||||
\(204\) | 0.349799 | 0.0244908 | ||||||||
\(205\) | −5.98072 | −0.417712 | ||||||||
\(206\) | 5.64616 | 0.393387 | ||||||||
\(207\) | 8.95631 | 0.622506 | ||||||||
\(208\) | 1.33361 | 0.0924691 | ||||||||
\(209\) | −4.61740 | −0.319392 | ||||||||
\(210\) | 1.44132 | 0.0994604 | ||||||||
\(211\) | 21.5889 | 1.48624 | 0.743122 | − | 0.669156i | \(-0.233344\pi\) | ||||
0.743122 | + | 0.669156i | \(0.233344\pi\) | |||||||
\(212\) | 3.56261 | 0.244681 | ||||||||
\(213\) | −10.2391 | −0.701570 | ||||||||
\(214\) | −3.29652 | −0.225346 | ||||||||
\(215\) | 0.601377 | 0.0410136 | ||||||||
\(216\) | −3.01856 | −0.205387 | ||||||||
\(217\) | −3.76025 | −0.255262 | ||||||||
\(218\) | −6.49821 | −0.440114 | ||||||||
\(219\) | 0.696030 | 0.0470333 | ||||||||
\(220\) | 0.321600 | 0.0216823 | ||||||||
\(221\) | −0.419632 | −0.0282275 | ||||||||
\(222\) | 11.1177 | 0.746175 | ||||||||
\(223\) | 29.2522 | 1.95887 | 0.979436 | − | 0.201757i | \(-0.0646653\pi\) | ||||
0.979436 | + | 0.201757i | \(0.0646653\pi\) | |||||||
\(224\) | 3.77636 | 0.252318 | ||||||||
\(225\) | −4.66275 | −0.310850 | ||||||||
\(226\) | −1.15949 | −0.0771282 | ||||||||
\(227\) | −18.6000 | −1.23452 | −0.617262 | − | 0.786758i | \(-0.711758\pi\) | ||||
−0.617262 | + | 0.786758i | \(0.711758\pi\) | |||||||
\(228\) | −1.02022 | −0.0675655 | ||||||||
\(229\) | −17.4519 | −1.15326 | −0.576628 | − | 0.817007i | \(-0.695632\pi\) | ||||
−0.576628 | + | 0.817007i | \(0.695632\pi\) | |||||||
\(230\) | 6.68147 | 0.440563 | ||||||||
\(231\) | 3.05873 | 0.201249 | ||||||||
\(232\) | 14.0029 | 0.919338 | ||||||||
\(233\) | 16.3122 | 1.06865 | 0.534325 | − | 0.845279i | \(-0.320566\pi\) | ||||
0.534325 | + | 0.845279i | \(0.320566\pi\) | |||||||
\(234\) | 0.539060 | 0.0352394 | ||||||||
\(235\) | −4.60458 | −0.300369 | ||||||||
\(236\) | 4.12260 | 0.268358 | ||||||||
\(237\) | 4.38503 | 0.284838 | ||||||||
\(238\) | 2.48191 | 0.160878 | ||||||||
\(239\) | −10.4899 | −0.678534 | −0.339267 | − | 0.940690i | \(-0.610179\pi\) | ||||
−0.339267 | + | 0.940690i | \(0.610179\pi\) | |||||||
\(240\) | −1.84559 | −0.119132 | ||||||||
\(241\) | 3.20071 | 0.206176 | 0.103088 | − | 0.994672i | \(-0.467128\pi\) | ||||
0.103088 | + | 0.994672i | \(0.467128\pi\) | |||||||
\(242\) | 10.9109 | 0.701380 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.10440 | 0.0707018 | ||||||||
\(245\) | 1.89737 | 0.121218 | ||||||||
\(246\) | 13.2296 | 0.843490 | ||||||||
\(247\) | 1.22389 | 0.0778742 | ||||||||
\(248\) | 5.87488 | 0.373055 | ||||||||
\(249\) | 0.402925 | 0.0255343 | ||||||||
\(250\) | −7.20848 | −0.455904 | ||||||||
\(251\) | −9.17030 | −0.578824 | −0.289412 | − | 0.957205i | \(-0.593460\pi\) | ||||
−0.289412 | + | 0.957205i | \(0.593460\pi\) | |||||||
\(252\) | 0.675827 | 0.0425731 | ||||||||
\(253\) | 14.1792 | 0.891441 | ||||||||
\(254\) | 10.6762 | 0.669884 | ||||||||
\(255\) | 0.580730 | 0.0363667 | ||||||||
\(256\) | −8.12339 | −0.507712 | ||||||||
\(257\) | 17.5100 | 1.09224 | 0.546122 | − | 0.837706i | \(-0.316104\pi\) | ||||
0.546122 | + | 0.837706i | \(0.316104\pi\) | |||||||
\(258\) | −1.33027 | −0.0828192 | ||||||||
\(259\) | −16.7211 | −1.03900 | ||||||||
\(260\) | −0.0852435 | −0.00528658 | ||||||||
\(261\) | 4.63895 | 0.287144 | ||||||||
\(262\) | 0.900969 | 0.0556620 | ||||||||
\(263\) | 14.3398 | 0.884228 | 0.442114 | − | 0.896959i | \(-0.354229\pi\) | ||||
0.442114 | + | 0.896959i | \(0.354229\pi\) | |||||||
\(264\) | −4.77884 | −0.294118 | ||||||||
\(265\) | 5.91459 | 0.363331 | ||||||||
\(266\) | −7.23868 | −0.443832 | ||||||||
\(267\) | −3.07805 | −0.188374 | ||||||||
\(268\) | 1.83671 | 0.112195 | ||||||||
\(269\) | 5.81592 | 0.354603 | 0.177301 | − | 0.984157i | \(-0.443263\pi\) | ||||
0.177301 | + | 0.984157i | \(0.443263\pi\) | |||||||
\(270\) | −0.746007 | −0.0454005 | ||||||||
\(271\) | 4.72990 | 0.287321 | 0.143661 | − | 0.989627i | \(-0.454113\pi\) | ||||
0.143661 | + | 0.989627i | \(0.454113\pi\) | |||||||
\(272\) | −3.17804 | −0.192697 | ||||||||
\(273\) | −0.810747 | −0.0490687 | ||||||||
\(274\) | 23.0762 | 1.39408 | ||||||||
\(275\) | −7.38186 | −0.445143 | ||||||||
\(276\) | 3.13291 | 0.188579 | ||||||||
\(277\) | −9.62977 | −0.578597 | −0.289298 | − | 0.957239i | \(-0.593422\pi\) | ||||
−0.289298 | + | 0.957239i | \(0.593422\pi\) | |||||||
\(278\) | 8.70245 | 0.521938 | ||||||||
\(279\) | 1.94626 | 0.116519 | ||||||||
\(280\) | 3.38681 | 0.202400 | ||||||||
\(281\) | −23.3377 | −1.39221 | −0.696105 | − | 0.717940i | \(-0.745085\pi\) | ||||
−0.696105 | + | 0.717940i | \(0.745085\pi\) | |||||||
\(282\) | 10.1855 | 0.606540 | ||||||||
\(283\) | 10.3845 | 0.617292 | 0.308646 | − | 0.951177i | \(-0.400124\pi\) | ||||
0.308646 | + | 0.951177i | \(0.400124\pi\) | |||||||
\(284\) | −3.58162 | −0.212530 | ||||||||
\(285\) | −1.69375 | −0.100329 | ||||||||
\(286\) | 0.853416 | 0.0504635 | ||||||||
\(287\) | −19.8974 | −1.17451 | ||||||||
\(288\) | −1.95459 | −0.115175 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 3.46069 | 0.203219 | ||||||||
\(291\) | −18.6258 | −1.09186 | ||||||||
\(292\) | 0.243470 | 0.0142480 | ||||||||
\(293\) | 6.43263 | 0.375798 | 0.187899 | − | 0.982188i | \(-0.439832\pi\) | ||||
0.187899 | + | 0.982188i | \(0.439832\pi\) | |||||||
\(294\) | −4.19706 | −0.244777 | ||||||||
\(295\) | 6.84427 | 0.398489 | ||||||||
\(296\) | 26.1245 | 1.51845 | ||||||||
\(297\) | −1.58316 | −0.0918640 | ||||||||
\(298\) | −15.8595 | −0.918718 | ||||||||
\(299\) | −3.75835 | −0.217351 | ||||||||
\(300\) | −1.63103 | −0.0941673 | ||||||||
\(301\) | 2.00074 | 0.115320 | ||||||||
\(302\) | −25.5690 | −1.47133 | ||||||||
\(303\) | −17.5565 | −1.00859 | ||||||||
\(304\) | 9.26902 | 0.531615 | ||||||||
\(305\) | 1.83350 | 0.104986 | ||||||||
\(306\) | −1.28460 | −0.0734358 | ||||||||
\(307\) | 18.5904 | 1.06101 | 0.530504 | − | 0.847682i | \(-0.322003\pi\) | ||||
0.530504 | + | 0.847682i | \(0.322003\pi\) | |||||||
\(308\) | 1.06994 | 0.0609654 | ||||||||
\(309\) | 4.39526 | 0.250038 | ||||||||
\(310\) | 1.45192 | 0.0824635 | ||||||||
\(311\) | −10.0164 | −0.567979 | −0.283989 | − | 0.958827i | \(-0.591658\pi\) | ||||
−0.283989 | + | 0.958827i | \(0.591658\pi\) | |||||||
\(312\) | 1.26668 | 0.0717118 | ||||||||
\(313\) | −30.8487 | −1.74367 | −0.871835 | − | 0.489799i | \(-0.837070\pi\) | ||||
−0.871835 | + | 0.489799i | \(0.837070\pi\) | |||||||
\(314\) | 1.28460 | 0.0724943 | ||||||||
\(315\) | 1.12200 | 0.0632173 | ||||||||
\(316\) | 1.53388 | 0.0862873 | ||||||||
\(317\) | 30.7099 | 1.72484 | 0.862421 | − | 0.506192i | \(-0.168947\pi\) | ||||
0.862421 | + | 0.506192i | \(0.168947\pi\) | |||||||
\(318\) | −13.0833 | −0.733678 | ||||||||
\(319\) | 7.34419 | 0.411195 | ||||||||
\(320\) | −5.14931 | −0.287855 | ||||||||
\(321\) | −2.56618 | −0.143230 | ||||||||
\(322\) | 22.2287 | 1.23876 | ||||||||
\(323\) | −2.91658 | −0.162283 | ||||||||
\(324\) | −0.349799 | −0.0194333 | ||||||||
\(325\) | 1.95664 | 0.108535 | ||||||||
\(326\) | 28.8159 | 1.59597 | ||||||||
\(327\) | −5.05854 | −0.279738 | ||||||||
\(328\) | 31.0870 | 1.71649 | ||||||||
\(329\) | −15.3191 | −0.844568 | ||||||||
\(330\) | −1.18105 | −0.0650144 | ||||||||
\(331\) | 7.37770 | 0.405515 | 0.202758 | − | 0.979229i | \(-0.435010\pi\) | ||||
0.202758 | + | 0.979229i | \(0.435010\pi\) | |||||||
\(332\) | 0.140943 | 0.00773524 | ||||||||
\(333\) | 8.65463 | 0.474271 | ||||||||
\(334\) | −4.29748 | −0.235147 | ||||||||
\(335\) | 3.04927 | 0.166600 | ||||||||
\(336\) | −6.14012 | −0.334971 | ||||||||
\(337\) | 23.5861 | 1.28482 | 0.642408 | − | 0.766363i | \(-0.277936\pi\) | ||||
0.642408 | + | 0.766363i | \(0.277936\pi\) | |||||||
\(338\) | 16.4736 | 0.896046 | ||||||||
\(339\) | −0.902607 | −0.0490229 | ||||||||
\(340\) | 0.203139 | 0.0110167 | ||||||||
\(341\) | 3.08123 | 0.166858 | ||||||||
\(342\) | 3.74664 | 0.202595 | ||||||||
\(343\) | 19.8367 | 1.07108 | ||||||||
\(344\) | −3.12588 | −0.168536 | ||||||||
\(345\) | 5.20120 | 0.280023 | ||||||||
\(346\) | 18.9572 | 1.01915 | ||||||||
\(347\) | −7.99274 | −0.429073 | −0.214536 | − | 0.976716i | \(-0.568824\pi\) | ||||
−0.214536 | + | 0.976716i | \(0.568824\pi\) | |||||||
\(348\) | 1.62270 | 0.0869859 | ||||||||
\(349\) | 2.28026 | 0.122060 | 0.0610298 | − | 0.998136i | \(-0.480562\pi\) | ||||
0.0610298 | + | 0.998136i | \(0.480562\pi\) | |||||||
\(350\) | −11.5725 | −0.618577 | ||||||||
\(351\) | 0.419632 | 0.0223983 | ||||||||
\(352\) | −3.09442 | −0.164933 | ||||||||
\(353\) | 15.6438 | 0.832633 | 0.416317 | − | 0.909220i | \(-0.363321\pi\) | ||||
0.416317 | + | 0.909220i | \(0.363321\pi\) | |||||||
\(354\) | −15.1398 | −0.804673 | ||||||||
\(355\) | −5.94614 | −0.315588 | ||||||||
\(356\) | −1.07670 | −0.0570650 | ||||||||
\(357\) | 1.93204 | 0.102255 | ||||||||
\(358\) | 21.4678 | 1.13461 | ||||||||
\(359\) | 37.0267 | 1.95420 | 0.977098 | − | 0.212791i | \(-0.0682554\pi\) | ||||
0.977098 | + | 0.212791i | \(0.0682554\pi\) | |||||||
\(360\) | −1.75297 | −0.0923894 | ||||||||
\(361\) | −10.4936 | −0.552293 | ||||||||
\(362\) | 0.502475 | 0.0264095 | ||||||||
\(363\) | 8.49362 | 0.445799 | ||||||||
\(364\) | −0.283598 | −0.0148646 | ||||||||
\(365\) | 0.404205 | 0.0211571 | ||||||||
\(366\) | −4.05579 | −0.212000 | ||||||||
\(367\) | 6.04369 | 0.315478 | 0.157739 | − | 0.987481i | \(-0.449580\pi\) | ||||
0.157739 | + | 0.987481i | \(0.449580\pi\) | |||||||
\(368\) | −28.4635 | −1.48376 | ||||||||
\(369\) | 10.2986 | 0.536125 | ||||||||
\(370\) | 6.45641 | 0.335653 | ||||||||
\(371\) | 19.6774 | 1.02160 | ||||||||
\(372\) | 0.680798 | 0.0352977 | ||||||||
\(373\) | −33.3692 | −1.72779 | −0.863896 | − | 0.503670i | \(-0.831983\pi\) | ||||
−0.863896 | + | 0.503670i | \(0.831983\pi\) | |||||||
\(374\) | −2.03372 | −0.105161 | ||||||||
\(375\) | −5.61145 | −0.289774 | ||||||||
\(376\) | 23.9340 | 1.23430 | ||||||||
\(377\) | −1.94665 | −0.100258 | ||||||||
\(378\) | −2.48191 | −0.127656 | ||||||||
\(379\) | 4.49054 | 0.230663 | 0.115332 | − | 0.993327i | \(-0.463207\pi\) | ||||
0.115332 | + | 0.993327i | \(0.463207\pi\) | |||||||
\(380\) | −0.592470 | −0.0303931 | ||||||||
\(381\) | 8.31090 | 0.425780 | ||||||||
\(382\) | 30.5108 | 1.56107 | ||||||||
\(383\) | −31.6450 | −1.61698 | −0.808492 | − | 0.588507i | \(-0.799716\pi\) | ||||
−0.808492 | + | 0.588507i | \(0.799716\pi\) | |||||||
\(384\) | 7.48132 | 0.381780 | ||||||||
\(385\) | 1.77629 | 0.0905284 | ||||||||
\(386\) | 19.4598 | 0.990476 | ||||||||
\(387\) | −1.03555 | −0.0526402 | ||||||||
\(388\) | −6.51529 | −0.330764 | ||||||||
\(389\) | −21.8230 | −1.10647 | −0.553234 | − | 0.833026i | \(-0.686606\pi\) | ||||
−0.553234 | + | 0.833026i | \(0.686606\pi\) | |||||||
\(390\) | 0.313048 | 0.0158518 | ||||||||
\(391\) | 8.95631 | 0.452940 | ||||||||
\(392\) | −9.86224 | −0.498118 | ||||||||
\(393\) | 0.701360 | 0.0353789 | ||||||||
\(394\) | 13.7125 | 0.690826 | ||||||||
\(395\) | 2.54652 | 0.128129 | ||||||||
\(396\) | −0.553786 | −0.0278288 | ||||||||
\(397\) | 3.00144 | 0.150638 | 0.0753191 | − | 0.997159i | \(-0.476002\pi\) | ||||
0.0753191 | + | 0.997159i | \(0.476002\pi\) | |||||||
\(398\) | −12.2862 | −0.615849 | ||||||||
\(399\) | −5.63496 | −0.282101 | ||||||||
\(400\) | 14.8184 | 0.740921 | ||||||||
\(401\) | 8.96913 | 0.447897 | 0.223949 | − | 0.974601i | \(-0.428105\pi\) | ||||
0.223949 | + | 0.974601i | \(0.428105\pi\) | |||||||
\(402\) | −6.74513 | −0.336416 | ||||||||
\(403\) | −0.816711 | −0.0406833 | ||||||||
\(404\) | −6.14125 | −0.305538 | ||||||||
\(405\) | −0.580730 | −0.0288567 | ||||||||
\(406\) | 11.5134 | 0.571403 | ||||||||
\(407\) | 13.7016 | 0.679164 | ||||||||
\(408\) | −3.01856 | −0.149441 | ||||||||
\(409\) | −5.88355 | −0.290923 | −0.145461 | − | 0.989364i | \(-0.546467\pi\) | ||||
−0.145461 | + | 0.989364i | \(0.546467\pi\) | |||||||
\(410\) | 7.68284 | 0.379429 | ||||||||
\(411\) | 17.9637 | 0.886082 | ||||||||
\(412\) | 1.53746 | 0.0757451 | ||||||||
\(413\) | 22.7704 | 1.12046 | ||||||||
\(414\) | −11.5053 | −0.565454 | ||||||||
\(415\) | 0.233991 | 0.0114862 | ||||||||
\(416\) | 0.820209 | 0.0402140 | ||||||||
\(417\) | 6.77443 | 0.331745 | ||||||||
\(418\) | 5.93152 | 0.290120 | ||||||||
\(419\) | 15.5704 | 0.760663 | 0.380332 | − | 0.924850i | \(-0.375810\pi\) | ||||
0.380332 | + | 0.924850i | \(0.375810\pi\) | |||||||
\(420\) | 0.392473 | 0.0191507 | ||||||||
\(421\) | 7.58791 | 0.369812 | 0.184906 | − | 0.982756i | \(-0.440802\pi\) | ||||
0.184906 | + | 0.982756i | \(0.440802\pi\) | |||||||
\(422\) | −27.7332 | −1.35003 | ||||||||
\(423\) | 7.92894 | 0.385518 | ||||||||
\(424\) | −30.7432 | −1.49302 | ||||||||
\(425\) | −4.66275 | −0.226177 | ||||||||
\(426\) | 13.1531 | 0.637271 | ||||||||
\(427\) | 6.09992 | 0.295196 | ||||||||
\(428\) | −0.897647 | −0.0433894 | ||||||||
\(429\) | 0.664343 | 0.0320748 | ||||||||
\(430\) | −0.772530 | −0.0372547 | ||||||||
\(431\) | 17.4846 | 0.842204 | 0.421102 | − | 0.907013i | \(-0.361643\pi\) | ||||
0.421102 | + | 0.907013i | \(0.361643\pi\) | |||||||
\(432\) | 3.17804 | 0.152904 | ||||||||
\(433\) | 7.59170 | 0.364834 | 0.182417 | − | 0.983221i | \(-0.441608\pi\) | ||||
0.182417 | + | 0.983221i | \(0.441608\pi\) | |||||||
\(434\) | 4.83042 | 0.231868 | ||||||||
\(435\) | 2.69398 | 0.129166 | ||||||||
\(436\) | −1.76947 | −0.0847423 | ||||||||
\(437\) | −26.1218 | −1.24957 | ||||||||
\(438\) | −0.894121 | −0.0427227 | ||||||||
\(439\) | 8.08953 | 0.386092 | 0.193046 | − | 0.981190i | \(-0.438163\pi\) | ||||
0.193046 | + | 0.981190i | \(0.438163\pi\) | |||||||
\(440\) | −2.77522 | −0.132303 | ||||||||
\(441\) | −3.26721 | −0.155581 | ||||||||
\(442\) | 0.539060 | 0.0256405 | ||||||||
\(443\) | −15.9530 | −0.757951 | −0.378975 | − | 0.925407i | \(-0.623723\pi\) | ||||
−0.378975 | + | 0.925407i | \(0.623723\pi\) | |||||||
\(444\) | 3.02738 | 0.143673 | ||||||||
\(445\) | −1.78752 | −0.0847365 | ||||||||
\(446\) | −37.5774 | −1.77934 | ||||||||
\(447\) | −12.3459 | −0.583940 | ||||||||
\(448\) | −17.1314 | −0.809380 | ||||||||
\(449\) | 38.0474 | 1.79557 | 0.897784 | − | 0.440435i | \(-0.145176\pi\) | ||||
0.897784 | + | 0.440435i | \(0.145176\pi\) | |||||||
\(450\) | 5.98978 | 0.282361 | ||||||||
\(451\) | 16.3043 | 0.767741 | ||||||||
\(452\) | −0.315731 | −0.0148507 | ||||||||
\(453\) | −19.9042 | −0.935180 | ||||||||
\(454\) | 23.8936 | 1.12138 | ||||||||
\(455\) | −0.470825 | −0.0220726 | ||||||||
\(456\) | 8.80386 | 0.412278 | ||||||||
\(457\) | 23.3400 | 1.09180 | 0.545899 | − | 0.837851i | \(-0.316188\pi\) | ||||
0.545899 | + | 0.837851i | \(0.316188\pi\) | |||||||
\(458\) | 22.4188 | 1.04756 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 1.81937 | 0.0848287 | ||||||||
\(461\) | −19.1263 | −0.890800 | −0.445400 | − | 0.895332i | \(-0.646939\pi\) | ||||
−0.445400 | + | 0.895332i | \(0.646939\pi\) | |||||||
\(462\) | −3.92925 | −0.182805 | ||||||||
\(463\) | −19.7251 | −0.916703 | −0.458351 | − | 0.888771i | \(-0.651560\pi\) | ||||
−0.458351 | + | 0.888771i | \(0.651560\pi\) | |||||||
\(464\) | −14.7428 | −0.684417 | ||||||||
\(465\) | 1.13025 | 0.0524141 | ||||||||
\(466\) | −20.9547 | −0.970708 | ||||||||
\(467\) | 22.4299 | 1.03793 | 0.518966 | − | 0.854795i | \(-0.326317\pi\) | ||||
0.518966 | + | 0.854795i | \(0.326317\pi\) | |||||||
\(468\) | 0.146787 | 0.00678522 | ||||||||
\(469\) | 10.1447 | 0.468438 | ||||||||
\(470\) | 5.91505 | 0.272841 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −35.5756 | −1.63750 | ||||||||
\(473\) | −1.63944 | −0.0753817 | ||||||||
\(474\) | −5.63301 | −0.258733 | ||||||||
\(475\) | 13.5993 | 0.623978 | ||||||||
\(476\) | 0.675827 | 0.0309765 | ||||||||
\(477\) | −10.1848 | −0.466328 | ||||||||
\(478\) | 13.4753 | 0.616347 | ||||||||
\(479\) | 0.871785 | 0.0398329 | 0.0199164 | − | 0.999802i | \(-0.493660\pi\) | ||||
0.0199164 | + | 0.999802i | \(0.493660\pi\) | |||||||
\(480\) | −1.13509 | −0.0518095 | ||||||||
\(481\) | −3.63176 | −0.165594 | ||||||||
\(482\) | −4.11164 | −0.187280 | ||||||||
\(483\) | 17.3040 | 0.787358 | ||||||||
\(484\) | 2.97106 | 0.135048 | ||||||||
\(485\) | −10.8166 | −0.491155 | ||||||||
\(486\) | 1.28460 | 0.0582707 | ||||||||
\(487\) | 14.2150 | 0.644144 | 0.322072 | − | 0.946715i | \(-0.395621\pi\) | ||||
0.322072 | + | 0.946715i | \(0.395621\pi\) | |||||||
\(488\) | −9.53029 | −0.431416 | ||||||||
\(489\) | 22.4318 | 1.01440 | ||||||||
\(490\) | −2.43736 | −0.110109 | ||||||||
\(491\) | 1.41434 | 0.0638284 | 0.0319142 | − | 0.999491i | \(-0.489840\pi\) | ||||
0.0319142 | + | 0.999491i | \(0.489840\pi\) | |||||||
\(492\) | 3.60245 | 0.162411 | ||||||||
\(493\) | 4.63895 | 0.208928 | ||||||||
\(494\) | −1.57221 | −0.0707371 | ||||||||
\(495\) | −0.919386 | −0.0413233 | ||||||||
\(496\) | −6.18528 | −0.277727 | ||||||||
\(497\) | −19.7823 | −0.887359 | ||||||||
\(498\) | −0.517598 | −0.0231941 | ||||||||
\(499\) | −11.3148 | −0.506519 | −0.253259 | − | 0.967398i | \(-0.581503\pi\) | ||||
−0.253259 | + | 0.967398i | \(0.581503\pi\) | |||||||
\(500\) | −1.96288 | −0.0877826 | ||||||||
\(501\) | −3.34538 | −0.149460 | ||||||||
\(502\) | 11.7802 | 0.525775 | ||||||||
\(503\) | 7.36129 | 0.328224 | 0.164112 | − | 0.986442i | \(-0.447524\pi\) | ||||
0.164112 | + | 0.986442i | \(0.447524\pi\) | |||||||
\(504\) | −5.83198 | −0.259777 | ||||||||
\(505\) | −10.1956 | −0.453698 | ||||||||
\(506\) | −18.2147 | −0.809741 | ||||||||
\(507\) | 12.8239 | 0.569530 | ||||||||
\(508\) | 2.90714 | 0.128984 | ||||||||
\(509\) | 39.5981 | 1.75515 | 0.877577 | − | 0.479436i | \(-0.159159\pi\) | ||||
0.877577 | + | 0.479436i | \(0.159159\pi\) | |||||||
\(510\) | −0.746007 | −0.0330337 | ||||||||
\(511\) | 1.34476 | 0.0594887 | ||||||||
\(512\) | 25.3980 | 1.12244 | ||||||||
\(513\) | 2.91658 | 0.128770 | ||||||||
\(514\) | −22.4934 | −0.992140 | ||||||||
\(515\) | 2.55246 | 0.112475 | ||||||||
\(516\) | −0.362235 | −0.0159465 | ||||||||
\(517\) | 12.5528 | 0.552070 | ||||||||
\(518\) | 21.4800 | 0.943776 | ||||||||
\(519\) | 14.7573 | 0.647772 | ||||||||
\(520\) | 0.735600 | 0.0322582 | ||||||||
\(521\) | 36.4594 | 1.59732 | 0.798658 | − | 0.601785i | \(-0.205543\pi\) | ||||
0.798658 | + | 0.601785i | \(0.205543\pi\) | |||||||
\(522\) | −5.95921 | −0.260827 | ||||||||
\(523\) | −0.196520 | −0.00859323 | −0.00429661 | − | 0.999991i | \(-0.501368\pi\) | ||||
−0.00429661 | + | 0.999991i | \(0.501368\pi\) | |||||||
\(524\) | 0.245335 | 0.0107175 | ||||||||
\(525\) | −9.00864 | −0.393169 | ||||||||
\(526\) | −18.4209 | −0.803189 | ||||||||
\(527\) | 1.94626 | 0.0847802 | ||||||||
\(528\) | 5.03134 | 0.218961 | ||||||||
\(529\) | 57.2154 | 2.48763 | ||||||||
\(530\) | −7.59790 | −0.330031 | ||||||||
\(531\) | −11.7856 | −0.511453 | ||||||||
\(532\) | −1.97110 | −0.0854581 | ||||||||
\(533\) | −4.32163 | −0.187191 | ||||||||
\(534\) | 3.95407 | 0.171110 | ||||||||
\(535\) | −1.49026 | −0.0644295 | ||||||||
\(536\) | −15.8497 | −0.684603 | ||||||||
\(537\) | 16.7116 | 0.721160 | ||||||||
\(538\) | −7.47113 | −0.322103 | ||||||||
\(539\) | −5.17250 | −0.222795 | ||||||||
\(540\) | −0.203139 | −0.00874170 | ||||||||
\(541\) | 21.9594 | 0.944110 | 0.472055 | − | 0.881569i | \(-0.343512\pi\) | ||||
0.472055 | + | 0.881569i | \(0.343512\pi\) | |||||||
\(542\) | −6.07604 | −0.260988 | ||||||||
\(543\) | 0.391152 | 0.0167859 | ||||||||
\(544\) | −1.95459 | −0.0838024 | ||||||||
\(545\) | −2.93765 | −0.125835 | ||||||||
\(546\) | 1.04149 | 0.0445715 | ||||||||
\(547\) | 42.7422 | 1.82753 | 0.913763 | − | 0.406248i | \(-0.133163\pi\) | ||||
0.913763 | + | 0.406248i | \(0.133163\pi\) | |||||||
\(548\) | 6.28367 | 0.268425 | ||||||||
\(549\) | −3.15724 | −0.134748 | ||||||||
\(550\) | 9.48276 | 0.404346 | ||||||||
\(551\) | −13.5299 | −0.576392 | ||||||||
\(552\) | −27.0351 | −1.15069 | ||||||||
\(553\) | 8.47206 | 0.360269 | ||||||||
\(554\) | 12.3704 | 0.525569 | ||||||||
\(555\) | 5.02600 | 0.213342 | ||||||||
\(556\) | 2.36969 | 0.100497 | ||||||||
\(557\) | 30.0082 | 1.27149 | 0.635745 | − | 0.771900i | \(-0.280693\pi\) | ||||
0.635745 | + | 0.771900i | \(0.280693\pi\) | |||||||
\(558\) | −2.50016 | −0.105840 | ||||||||
\(559\) | 0.434551 | 0.0183796 | ||||||||
\(560\) | −3.56575 | −0.150681 | ||||||||
\(561\) | −1.58316 | −0.0668409 | ||||||||
\(562\) | 29.9797 | 1.26462 | ||||||||
\(563\) | −46.6016 | −1.96402 | −0.982012 | − | 0.188819i | \(-0.939534\pi\) | ||||
−0.982012 | + | 0.188819i | \(0.939534\pi\) | |||||||
\(564\) | 2.77354 | 0.116787 | ||||||||
\(565\) | −0.524171 | −0.0220521 | ||||||||
\(566\) | −13.3399 | −0.560717 | ||||||||
\(567\) | −1.93204 | −0.0811382 | ||||||||
\(568\) | 30.9072 | 1.29684 | ||||||||
\(569\) | 28.5846 | 1.19833 | 0.599164 | − | 0.800626i | \(-0.295500\pi\) | ||||
0.599164 | + | 0.800626i | \(0.295500\pi\) | |||||||
\(570\) | 2.17579 | 0.0911337 | ||||||||
\(571\) | −27.9481 | −1.16959 | −0.584797 | − | 0.811180i | \(-0.698826\pi\) | ||||
−0.584797 | + | 0.811180i | \(0.698826\pi\) | |||||||
\(572\) | 0.232386 | 0.00971656 | ||||||||
\(573\) | 23.7512 | 0.992219 | ||||||||
\(574\) | 25.5602 | 1.06686 | ||||||||
\(575\) | −41.7610 | −1.74156 | ||||||||
\(576\) | 8.86696 | 0.369457 | ||||||||
\(577\) | 32.3210 | 1.34554 | 0.672770 | − | 0.739852i | \(-0.265104\pi\) | ||||
0.672770 | + | 0.739852i | \(0.265104\pi\) | |||||||
\(578\) | −1.28460 | −0.0534324 | ||||||||
\(579\) | 15.1485 | 0.629549 | ||||||||
\(580\) | 0.942351 | 0.0391290 | ||||||||
\(581\) | 0.778469 | 0.0322963 | ||||||||
\(582\) | 23.9268 | 0.991796 | ||||||||
\(583\) | −16.1241 | −0.667790 | ||||||||
\(584\) | −2.10100 | −0.0869402 | ||||||||
\(585\) | 0.243693 | 0.0100755 | ||||||||
\(586\) | −8.26336 | −0.341356 | ||||||||
\(587\) | 11.0951 | 0.457945 | 0.228972 | − | 0.973433i | \(-0.426463\pi\) | ||||
0.228972 | + | 0.973433i | \(0.426463\pi\) | |||||||
\(588\) | −1.14286 | −0.0471310 | ||||||||
\(589\) | −5.67641 | −0.233892 | ||||||||
\(590\) | −8.79216 | −0.361968 | ||||||||
\(591\) | 10.6745 | 0.439091 | ||||||||
\(592\) | −27.5048 | −1.13044 | ||||||||
\(593\) | −18.8893 | −0.775692 | −0.387846 | − | 0.921724i | \(-0.626781\pi\) | ||||
−0.387846 | + | 0.921724i | \(0.626781\pi\) | |||||||
\(594\) | 2.03372 | 0.0834447 | ||||||||
\(595\) | 1.12200 | 0.0459974 | ||||||||
\(596\) | −4.31857 | −0.176896 | ||||||||
\(597\) | −9.56418 | −0.391436 | ||||||||
\(598\) | 4.82798 | 0.197431 | ||||||||
\(599\) | −36.1983 | −1.47902 | −0.739510 | − | 0.673145i | \(-0.764943\pi\) | ||||
−0.739510 | + | 0.673145i | \(0.764943\pi\) | |||||||
\(600\) | 14.0748 | 0.574600 | ||||||||
\(601\) | −0.160125 | −0.00653163 | −0.00326582 | − | 0.999995i | \(-0.501040\pi\) | ||||
−0.00326582 | + | 0.999995i | \(0.501040\pi\) | |||||||
\(602\) | −2.57015 | −0.104751 | ||||||||
\(603\) | −5.25076 | −0.213827 | ||||||||
\(604\) | −6.96246 | −0.283299 | ||||||||
\(605\) | 4.93250 | 0.200535 | ||||||||
\(606\) | 22.5531 | 0.916158 | ||||||||
\(607\) | 43.5689 | 1.76841 | 0.884204 | − | 0.467102i | \(-0.154702\pi\) | ||||
0.884204 | + | 0.467102i | \(0.154702\pi\) | |||||||
\(608\) | 5.70072 | 0.231195 | ||||||||
\(609\) | 8.96266 | 0.363185 | ||||||||
\(610\) | −2.35532 | −0.0953641 | ||||||||
\(611\) | −3.32724 | −0.134606 | ||||||||
\(612\) | −0.349799 | −0.0141398 | ||||||||
\(613\) | 39.9136 | 1.61209 | 0.806047 | − | 0.591851i | \(-0.201603\pi\) | ||||
0.806047 | + | 0.591851i | \(0.201603\pi\) | |||||||
\(614\) | −23.8812 | −0.963768 | ||||||||
\(615\) | 5.98072 | 0.241166 | ||||||||
\(616\) | −9.23294 | −0.372006 | ||||||||
\(617\) | 22.0134 | 0.886224 | 0.443112 | − | 0.896466i | \(-0.353874\pi\) | ||||
0.443112 | + | 0.896466i | \(0.353874\pi\) | |||||||
\(618\) | −5.64616 | −0.227122 | ||||||||
\(619\) | 0.629398 | 0.0252976 | 0.0126488 | − | 0.999920i | \(-0.495974\pi\) | ||||
0.0126488 | + | 0.999920i | \(0.495974\pi\) | |||||||
\(620\) | 0.395360 | 0.0158780 | ||||||||
\(621\) | −8.95631 | −0.359404 | ||||||||
\(622\) | 12.8671 | 0.515924 | ||||||||
\(623\) | −5.94694 | −0.238259 | ||||||||
\(624\) | −1.33361 | −0.0533871 | ||||||||
\(625\) | 20.0550 | 0.802201 | ||||||||
\(626\) | 39.6283 | 1.58386 | ||||||||
\(627\) | 4.61740 | 0.184401 | ||||||||
\(628\) | 0.349799 | 0.0139585 | ||||||||
\(629\) | 8.65463 | 0.345083 | ||||||||
\(630\) | −1.44132 | −0.0574235 | ||||||||
\(631\) | 30.9936 | 1.23384 | 0.616919 | − | 0.787027i | \(-0.288381\pi\) | ||||
0.616919 | + | 0.787027i | \(0.288381\pi\) | |||||||
\(632\) | −13.2364 | −0.526517 | ||||||||
\(633\) | −21.5889 | −0.858083 | ||||||||
\(634\) | −39.4500 | −1.56676 | ||||||||
\(635\) | 4.82639 | 0.191529 | ||||||||
\(636\) | −3.56261 | −0.141267 | ||||||||
\(637\) | 1.37102 | 0.0543219 | ||||||||
\(638\) | −9.43435 | −0.373510 | ||||||||
\(639\) | 10.2391 | 0.405052 | ||||||||
\(640\) | 4.34463 | 0.171737 | ||||||||
\(641\) | −1.27589 | −0.0503946 | −0.0251973 | − | 0.999682i | \(-0.508021\pi\) | ||||
−0.0251973 | + | 0.999682i | \(0.508021\pi\) | |||||||
\(642\) | 3.29652 | 0.130103 | ||||||||
\(643\) | −17.5334 | −0.691451 | −0.345725 | − | 0.938336i | \(-0.612367\pi\) | ||||
−0.345725 | + | 0.938336i | \(0.612367\pi\) | |||||||
\(644\) | 6.05291 | 0.238518 | ||||||||
\(645\) | −0.601377 | −0.0236792 | ||||||||
\(646\) | 3.74664 | 0.147410 | ||||||||
\(647\) | 40.3844 | 1.58767 | 0.793837 | − | 0.608131i | \(-0.208080\pi\) | ||||
0.793837 | + | 0.608131i | \(0.208080\pi\) | |||||||
\(648\) | 3.01856 | 0.118580 | ||||||||
\(649\) | −18.6585 | −0.732410 | ||||||||
\(650\) | −2.51350 | −0.0985877 | ||||||||
\(651\) | 3.76025 | 0.147376 | ||||||||
\(652\) | 7.84661 | 0.307297 | ||||||||
\(653\) | −2.29700 | −0.0898887 | −0.0449444 | − | 0.998989i | \(-0.514311\pi\) | ||||
−0.0449444 | + | 0.998989i | \(0.514311\pi\) | |||||||
\(654\) | 6.49821 | 0.254100 | ||||||||
\(655\) | 0.407301 | 0.0159146 | ||||||||
\(656\) | −32.7295 | −1.27787 | ||||||||
\(657\) | −0.696030 | −0.0271547 | ||||||||
\(658\) | 19.6789 | 0.767163 | ||||||||
\(659\) | −10.5022 | −0.409108 | −0.204554 | − | 0.978855i | \(-0.565574\pi\) | ||||
−0.204554 | + | 0.978855i | \(0.565574\pi\) | |||||||
\(660\) | −0.321600 | −0.0125183 | ||||||||
\(661\) | −22.8718 | −0.889611 | −0.444805 | − | 0.895627i | \(-0.646727\pi\) | ||||
−0.444805 | + | 0.895627i | \(0.646727\pi\) | |||||||
\(662\) | −9.47741 | −0.368350 | ||||||||
\(663\) | 0.419632 | 0.0162972 | ||||||||
\(664\) | −1.21625 | −0.0471997 | ||||||||
\(665\) | −3.27239 | −0.126898 | ||||||||
\(666\) | −11.1177 | −0.430804 | ||||||||
\(667\) | 41.5479 | 1.60874 | ||||||||
\(668\) | −1.17021 | −0.0452767 | ||||||||
\(669\) | −29.2522 | −1.13095 | ||||||||
\(670\) | −3.91710 | −0.151331 | ||||||||
\(671\) | −4.99840 | −0.192961 | ||||||||
\(672\) | −3.77636 | −0.145676 | ||||||||
\(673\) | 21.1862 | 0.816667 | 0.408333 | − | 0.912833i | \(-0.366110\pi\) | ||||
0.408333 | + | 0.912833i | \(0.366110\pi\) | |||||||
\(674\) | −30.2987 | −1.16706 | ||||||||
\(675\) | 4.66275 | 0.179469 | ||||||||
\(676\) | 4.48579 | 0.172530 | ||||||||
\(677\) | 32.2338 | 1.23885 | 0.619423 | − | 0.785057i | \(-0.287367\pi\) | ||||
0.619423 | + | 0.785057i | \(0.287367\pi\) | |||||||
\(678\) | 1.15949 | 0.0445300 | ||||||||
\(679\) | −35.9859 | −1.38101 | ||||||||
\(680\) | −1.75297 | −0.0672232 | ||||||||
\(681\) | 18.6000 | 0.712753 | ||||||||
\(682\) | −3.95815 | −0.151565 | ||||||||
\(683\) | −1.30901 | −0.0500878 | −0.0250439 | − | 0.999686i | \(-0.507973\pi\) | ||||
−0.0250439 | + | 0.999686i | \(0.507973\pi\) | |||||||
\(684\) | 1.02022 | 0.0390089 | ||||||||
\(685\) | 10.4320 | 0.398588 | ||||||||
\(686\) | −25.4822 | −0.972917 | ||||||||
\(687\) | 17.4519 | 0.665832 | ||||||||
\(688\) | 3.29103 | 0.125470 | ||||||||
\(689\) | 4.27385 | 0.162821 | ||||||||
\(690\) | −6.68147 | −0.254359 | ||||||||
\(691\) | −16.2990 | −0.620044 | −0.310022 | − | 0.950729i | \(-0.600336\pi\) | ||||
−0.310022 | + | 0.950729i | \(0.600336\pi\) | |||||||
\(692\) | 5.16208 | 0.196233 | ||||||||
\(693\) | −3.05873 | −0.116191 | ||||||||
\(694\) | 10.2675 | 0.389748 | ||||||||
\(695\) | 3.93412 | 0.149230 | ||||||||
\(696\) | −14.0029 | −0.530780 | ||||||||
\(697\) | 10.2986 | 0.390088 | ||||||||
\(698\) | −2.92923 | −0.110873 | ||||||||
\(699\) | −16.3122 | −0.616985 | ||||||||
\(700\) | −3.15121 | −0.119105 | ||||||||
\(701\) | −27.0494 | −1.02164 | −0.510822 | − | 0.859687i | \(-0.670659\pi\) | ||||
−0.510822 | + | 0.859687i | \(0.670659\pi\) | |||||||
\(702\) | −0.539060 | −0.0203455 | ||||||||
\(703\) | −25.2419 | −0.952017 | ||||||||
\(704\) | 14.0378 | 0.529069 | ||||||||
\(705\) | 4.60458 | 0.173418 | ||||||||
\(706\) | −20.0960 | −0.756323 | ||||||||
\(707\) | −33.9199 | −1.27569 | ||||||||
\(708\) | −4.12260 | −0.154937 | ||||||||
\(709\) | 35.3361 | 1.32708 | 0.663538 | − | 0.748143i | \(-0.269054\pi\) | ||||
0.663538 | + | 0.748143i | \(0.269054\pi\) | |||||||
\(710\) | 7.63842 | 0.286665 | ||||||||
\(711\) | −4.38503 | −0.164451 | ||||||||
\(712\) | 9.29128 | 0.348205 | ||||||||
\(713\) | 17.4313 | 0.652806 | ||||||||
\(714\) | −2.48191 | −0.0928830 | ||||||||
\(715\) | 0.385804 | 0.0144282 | ||||||||
\(716\) | 5.84571 | 0.218464 | ||||||||
\(717\) | 10.4899 | 0.391752 | ||||||||
\(718\) | −47.5646 | −1.77509 | ||||||||
\(719\) | −12.0611 | −0.449802 | −0.224901 | − | 0.974382i | \(-0.572206\pi\) | ||||
−0.224901 | + | 0.974382i | \(0.572206\pi\) | |||||||
\(720\) | 1.84559 | 0.0687809 | ||||||||
\(721\) | 8.49184 | 0.316253 | ||||||||
\(722\) | 13.4800 | 0.501675 | ||||||||
\(723\) | −3.20071 | −0.119036 | ||||||||
\(724\) | 0.136825 | 0.00508505 | ||||||||
\(725\) | −21.6303 | −0.803329 | ||||||||
\(726\) | −10.9109 | −0.404942 | ||||||||
\(727\) | −30.9749 | −1.14880 | −0.574399 | − | 0.818576i | \(-0.694764\pi\) | ||||
−0.574399 | + | 0.818576i | \(0.694764\pi\) | |||||||
\(728\) | 2.44729 | 0.0907024 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.519243 | −0.0192180 | ||||||||
\(731\) | −1.03555 | −0.0383013 | ||||||||
\(732\) | −1.10440 | −0.0408197 | ||||||||
\(733\) | −11.5014 | −0.424814 | −0.212407 | − | 0.977181i | \(-0.568130\pi\) | ||||
−0.212407 | + | 0.977181i | \(0.568130\pi\) | |||||||
\(734\) | −7.76373 | −0.286565 | ||||||||
\(735\) | −1.89737 | −0.0699854 | ||||||||
\(736\) | −17.5059 | −0.645277 | ||||||||
\(737\) | −8.31277 | −0.306205 | ||||||||
\(738\) | −13.2296 | −0.486989 | ||||||||
\(739\) | −44.0418 | −1.62010 | −0.810052 | − | 0.586358i | \(-0.800561\pi\) | ||||
−0.810052 | + | 0.586358i | \(0.800561\pi\) | |||||||
\(740\) | 1.75809 | 0.0646287 | ||||||||
\(741\) | −1.22389 | −0.0449607 | ||||||||
\(742\) | −25.2776 | −0.927970 | ||||||||
\(743\) | 42.9094 | 1.57419 | 0.787096 | − | 0.616830i | \(-0.211583\pi\) | ||||
0.787096 | + | 0.616830i | \(0.211583\pi\) | |||||||
\(744\) | −5.87488 | −0.215384 | ||||||||
\(745\) | −7.16962 | −0.262675 | ||||||||
\(746\) | 42.8661 | 1.56944 | ||||||||
\(747\) | −0.402925 | −0.0147423 | ||||||||
\(748\) | −0.553786 | −0.0202484 | ||||||||
\(749\) | −4.95798 | −0.181160 | ||||||||
\(750\) | 7.20848 | 0.263216 | ||||||||
\(751\) | −2.33818 | −0.0853215 | −0.0426607 | − | 0.999090i | \(-0.513583\pi\) | ||||
−0.0426607 | + | 0.999090i | \(0.513583\pi\) | |||||||
\(752\) | −25.1985 | −0.918896 | ||||||||
\(753\) | 9.17030 | 0.334184 | ||||||||
\(754\) | 2.50067 | 0.0910691 | ||||||||
\(755\) | −11.5590 | −0.420674 | ||||||||
\(756\) | −0.675827 | −0.0245796 | ||||||||
\(757\) | 31.0994 | 1.13033 | 0.565164 | − | 0.824979i | \(-0.308813\pi\) | ||||
0.565164 | + | 0.824979i | \(0.308813\pi\) | |||||||
\(758\) | −5.76855 | −0.209523 | ||||||||
\(759\) | −14.1792 | −0.514673 | ||||||||
\(760\) | 5.11267 | 0.185456 | ||||||||
\(761\) | −3.11941 | −0.113079 | −0.0565393 | − | 0.998400i | \(-0.518007\pi\) | ||||
−0.0565393 | + | 0.998400i | \(0.518007\pi\) | |||||||
\(762\) | −10.6762 | −0.386758 | ||||||||
\(763\) | −9.77332 | −0.353818 | ||||||||
\(764\) | 8.30812 | 0.300577 | ||||||||
\(765\) | −0.580730 | −0.0209963 | ||||||||
\(766\) | 40.6512 | 1.46879 | ||||||||
\(767\) | 4.94563 | 0.178576 | ||||||||
\(768\) | 8.12339 | 0.293128 | ||||||||
\(769\) | −3.95661 | −0.142679 | −0.0713396 | − | 0.997452i | \(-0.522727\pi\) | ||||
−0.0713396 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(770\) | −2.28183 | −0.0822315 | ||||||||
\(771\) | −17.5100 | −0.630607 | ||||||||
\(772\) | 5.29892 | 0.190712 | ||||||||
\(773\) | 11.8318 | 0.425560 | 0.212780 | − | 0.977100i | \(-0.431748\pi\) | ||||
0.212780 | + | 0.977100i | \(0.431748\pi\) | |||||||
\(774\) | 1.33027 | 0.0478157 | ||||||||
\(775\) | −9.07491 | −0.325980 | ||||||||
\(776\) | 56.2231 | 2.01829 | ||||||||
\(777\) | 16.7211 | 0.599867 | ||||||||
\(778\) | 28.0338 | 1.00506 | ||||||||
\(779\) | −30.0368 | −1.07618 | ||||||||
\(780\) | 0.0852435 | 0.00305221 | ||||||||
\(781\) | 16.2101 | 0.580041 | ||||||||
\(782\) | −11.5053 | −0.411428 | ||||||||
\(783\) | −4.63895 | −0.165783 | ||||||||
\(784\) | 10.3833 | 0.370833 | ||||||||
\(785\) | 0.580730 | 0.0207271 | ||||||||
\(786\) | −0.900969 | −0.0321365 | ||||||||
\(787\) | 31.3642 | 1.11801 | 0.559007 | − | 0.829163i | \(-0.311183\pi\) | ||||
0.559007 | + | 0.829163i | \(0.311183\pi\) | |||||||
\(788\) | 3.73393 | 0.133016 | ||||||||
\(789\) | −14.3398 | −0.510509 | ||||||||
\(790\) | −3.27126 | −0.116386 | ||||||||
\(791\) | −1.74388 | −0.0620051 | ||||||||
\(792\) | 4.77884 | 0.169809 | ||||||||
\(793\) | 1.32488 | 0.0470478 | ||||||||
\(794\) | −3.85566 | −0.136832 | ||||||||
\(795\) | −5.91459 | −0.209769 | ||||||||
\(796\) | −3.34554 | −0.118579 | ||||||||
\(797\) | 24.4835 | 0.867250 | 0.433625 | − | 0.901093i | \(-0.357234\pi\) | ||||
0.433625 | + | 0.901093i | \(0.357234\pi\) | |||||||
\(798\) | 7.23868 | 0.256246 | ||||||||
\(799\) | 7.92894 | 0.280506 | ||||||||
\(800\) | 9.11378 | 0.322221 | ||||||||
\(801\) | 3.07805 | 0.108758 | ||||||||
\(802\) | −11.5218 | −0.406848 | ||||||||
\(803\) | −1.10192 | −0.0388860 | ||||||||
\(804\) | −1.83671 | −0.0647757 | ||||||||
\(805\) | 10.0489 | 0.354179 | ||||||||
\(806\) | 1.04915 | 0.0369547 | ||||||||
\(807\) | −5.81592 | −0.204730 | ||||||||
\(808\) | 52.9953 | 1.86437 | ||||||||
\(809\) | −18.3096 | −0.643731 | −0.321866 | − | 0.946785i | \(-0.604310\pi\) | ||||
−0.321866 | + | 0.946785i | \(0.604310\pi\) | |||||||
\(810\) | 0.746007 | 0.0262120 | ||||||||
\(811\) | −38.1005 | −1.33789 | −0.668945 | − | 0.743312i | \(-0.733254\pi\) | ||||
−0.668945 | + | 0.743312i | \(0.733254\pi\) | |||||||
\(812\) | 3.13513 | 0.110021 | ||||||||
\(813\) | −4.72990 | −0.165885 | ||||||||
\(814\) | −17.6011 | −0.616919 | ||||||||
\(815\) | 13.0268 | 0.456309 | ||||||||
\(816\) | 3.17804 | 0.111254 | ||||||||
\(817\) | 3.02027 | 0.105666 | ||||||||
\(818\) | 7.55801 | 0.264260 | ||||||||
\(819\) | 0.810747 | 0.0283298 | ||||||||
\(820\) | 2.09205 | 0.0730575 | ||||||||
\(821\) | 16.7676 | 0.585195 | 0.292597 | − | 0.956236i | \(-0.405480\pi\) | ||||
0.292597 | + | 0.956236i | \(0.405480\pi\) | |||||||
\(822\) | −23.0762 | −0.804873 | ||||||||
\(823\) | −2.29394 | −0.0799617 | −0.0399809 | − | 0.999200i | \(-0.512730\pi\) | ||||
−0.0399809 | + | 0.999200i | \(0.512730\pi\) | |||||||
\(824\) | −13.2673 | −0.462190 | ||||||||
\(825\) | 7.38186 | 0.257004 | ||||||||
\(826\) | −29.2508 | −1.01777 | ||||||||
\(827\) | 20.3470 | 0.707534 | 0.353767 | − | 0.935334i | \(-0.384901\pi\) | ||||
0.353767 | + | 0.935334i | \(0.384901\pi\) | |||||||
\(828\) | −3.13291 | −0.108876 | ||||||||
\(829\) | 11.8751 | 0.412439 | 0.206220 | − | 0.978506i | \(-0.433884\pi\) | ||||
0.206220 | + | 0.978506i | \(0.433884\pi\) | |||||||
\(830\) | −0.300585 | −0.0104335 | ||||||||
\(831\) | 9.62977 | 0.334053 | ||||||||
\(832\) | −3.72086 | −0.128998 | ||||||||
\(833\) | −3.26721 | −0.113202 | ||||||||
\(834\) | −8.70245 | −0.301341 | ||||||||
\(835\) | −1.94276 | −0.0672320 | ||||||||
\(836\) | 1.61516 | 0.0558615 | ||||||||
\(837\) | −1.94626 | −0.0672724 | ||||||||
\(838\) | −20.0017 | −0.690949 | ||||||||
\(839\) | −35.7098 | −1.23284 | −0.616420 | − | 0.787418i | \(-0.711417\pi\) | ||||
−0.616420 | + | 0.787418i | \(0.711417\pi\) | |||||||
\(840\) | −3.38681 | −0.116856 | ||||||||
\(841\) | −7.48012 | −0.257935 | ||||||||
\(842\) | −9.74744 | −0.335919 | ||||||||
\(843\) | 23.3377 | 0.803793 | ||||||||
\(844\) | −7.55178 | −0.259943 | ||||||||
\(845\) | 7.44723 | 0.256193 | ||||||||
\(846\) | −10.1855 | −0.350186 | ||||||||
\(847\) | 16.4100 | 0.563856 | ||||||||
\(848\) | 32.3676 | 1.11151 | ||||||||
\(849\) | −10.3845 | −0.356393 | ||||||||
\(850\) | 5.98978 | 0.205448 | ||||||||
\(851\) | 77.5135 | 2.65713 | ||||||||
\(852\) | 3.58162 | 0.122704 | ||||||||
\(853\) | 1.39229 | 0.0476712 | 0.0238356 | − | 0.999716i | \(-0.492412\pi\) | ||||
0.0238356 | + | 0.999716i | \(0.492412\pi\) | |||||||
\(854\) | −7.83597 | −0.268141 | ||||||||
\(855\) | 1.69375 | 0.0579249 | ||||||||
\(856\) | 7.74616 | 0.264758 | ||||||||
\(857\) | −36.6477 | −1.25186 | −0.625932 | − | 0.779878i | \(-0.715281\pi\) | ||||
−0.625932 | + | 0.779878i | \(0.715281\pi\) | |||||||
\(858\) | −0.853416 | −0.0291351 | ||||||||
\(859\) | −2.53062 | −0.0863436 | −0.0431718 | − | 0.999068i | \(-0.513746\pi\) | ||||
−0.0431718 | + | 0.999068i | \(0.513746\pi\) | |||||||
\(860\) | −0.210361 | −0.00717325 | ||||||||
\(861\) | 19.8974 | 0.678101 | ||||||||
\(862\) | −22.4607 | −0.765016 | ||||||||
\(863\) | 1.06128 | 0.0361264 | 0.0180632 | − | 0.999837i | \(-0.494250\pi\) | ||||
0.0180632 | + | 0.999837i | \(0.494250\pi\) | |||||||
\(864\) | 1.95459 | 0.0664965 | ||||||||
\(865\) | 8.56999 | 0.291389 | ||||||||
\(866\) | −9.75231 | −0.331397 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 1.31533 | 0.0446453 | ||||||||
\(869\) | −6.94218 | −0.235497 | ||||||||
\(870\) | −3.46069 | −0.117328 | ||||||||
\(871\) | 2.20338 | 0.0746588 | ||||||||
\(872\) | 15.2695 | 0.517090 | ||||||||
\(873\) | 18.6258 | 0.630388 | ||||||||
\(874\) | 33.5561 | 1.13505 | ||||||||
\(875\) | −10.8416 | −0.366512 | ||||||||
\(876\) | −0.243470 | −0.00822610 | ||||||||
\(877\) | 25.1578 | 0.849517 | 0.424759 | − | 0.905307i | \(-0.360359\pi\) | ||||
0.424759 | + | 0.905307i | \(0.360359\pi\) | |||||||
\(878\) | −10.3918 | −0.350707 | ||||||||
\(879\) | −6.43263 | −0.216967 | ||||||||
\(880\) | 2.92185 | 0.0984955 | ||||||||
\(881\) | −15.5299 | −0.523216 | −0.261608 | − | 0.965174i | \(-0.584253\pi\) | ||||
−0.261608 | + | 0.965174i | \(0.584253\pi\) | |||||||
\(882\) | 4.19706 | 0.141322 | ||||||||
\(883\) | −22.0705 | −0.742730 | −0.371365 | − | 0.928487i | \(-0.621110\pi\) | ||||
−0.371365 | + | 0.928487i | \(0.621110\pi\) | |||||||
\(884\) | 0.146787 | 0.00493697 | ||||||||
\(885\) | −6.84427 | −0.230068 | ||||||||
\(886\) | 20.4933 | 0.688485 | ||||||||
\(887\) | −35.8404 | −1.20340 | −0.601701 | − | 0.798721i | \(-0.705510\pi\) | ||||
−0.601701 | + | 0.798721i | \(0.705510\pi\) | |||||||
\(888\) | −26.1245 | −0.876680 | ||||||||
\(889\) | 16.0570 | 0.538535 | ||||||||
\(890\) | 2.29625 | 0.0769705 | ||||||||
\(891\) | 1.58316 | 0.0530377 | ||||||||
\(892\) | −10.2324 | −0.342605 | ||||||||
\(893\) | −23.1254 | −0.773862 | ||||||||
\(894\) | 15.8595 | 0.530422 | ||||||||
\(895\) | 9.70494 | 0.324400 | ||||||||
\(896\) | 14.4542 | 0.482883 | ||||||||
\(897\) | 3.75835 | 0.125488 | ||||||||
\(898\) | −48.8758 | −1.63101 | ||||||||
\(899\) | 9.02859 | 0.301120 | ||||||||
\(900\) | 1.63103 | 0.0543675 | ||||||||
\(901\) | −10.1848 | −0.339303 | ||||||||
\(902\) | −20.9446 | −0.697378 | ||||||||
\(903\) | −2.00074 | −0.0665803 | ||||||||
\(904\) | 2.72457 | 0.0906179 | ||||||||
\(905\) | 0.227154 | 0.00755085 | ||||||||
\(906\) | 25.5690 | 0.849472 | ||||||||
\(907\) | 48.3005 | 1.60379 | 0.801896 | − | 0.597464i | \(-0.203825\pi\) | ||||
0.801896 | + | 0.597464i | \(0.203825\pi\) | |||||||
\(908\) | 6.50625 | 0.215917 | ||||||||
\(909\) | 17.5565 | 0.582313 | ||||||||
\(910\) | 0.604823 | 0.0200497 | ||||||||
\(911\) | 16.5488 | 0.548287 | 0.274144 | − | 0.961689i | \(-0.411606\pi\) | ||||
0.274144 | + | 0.961689i | \(0.411606\pi\) | |||||||
\(912\) | −9.26902 | −0.306928 | ||||||||
\(913\) | −0.637893 | −0.0211112 | ||||||||
\(914\) | −29.9826 | −0.991736 | ||||||||
\(915\) | −1.83350 | −0.0606137 | ||||||||
\(916\) | 6.10466 | 0.201704 | ||||||||
\(917\) | 1.35506 | 0.0447480 | ||||||||
\(918\) | 1.28460 | 0.0423982 | ||||||||
\(919\) | −18.0335 | −0.594870 | −0.297435 | − | 0.954742i | \(-0.596131\pi\) | ||||
−0.297435 | + | 0.954742i | \(0.596131\pi\) | |||||||
\(920\) | −15.7001 | −0.517617 | ||||||||
\(921\) | −18.5904 | −0.612574 | ||||||||
\(922\) | 24.5697 | 0.809159 | ||||||||
\(923\) | −4.29664 | −0.141426 | ||||||||
\(924\) | −1.06994 | −0.0351984 | ||||||||
\(925\) | −40.3544 | −1.32684 | ||||||||
\(926\) | 25.3389 | 0.832688 | ||||||||
\(927\) | −4.39526 | −0.144359 | ||||||||
\(928\) | −9.06726 | −0.297647 | ||||||||
\(929\) | −51.8467 | −1.70104 | −0.850518 | − | 0.525946i | \(-0.823711\pi\) | ||||
−0.850518 | + | 0.525946i | \(0.823711\pi\) | |||||||
\(930\) | −1.45192 | −0.0476103 | ||||||||
\(931\) | 9.52907 | 0.312303 | ||||||||
\(932\) | −5.70600 | −0.186906 | ||||||||
\(933\) | 10.0164 | 0.327923 | ||||||||
\(934\) | −28.8135 | −0.942807 | ||||||||
\(935\) | −0.919386 | −0.0300672 | ||||||||
\(936\) | −1.26668 | −0.0414028 | ||||||||
\(937\) | −11.6436 | −0.380381 | −0.190190 | − | 0.981747i | \(-0.560911\pi\) | ||||
−0.190190 | + | 0.981747i | \(0.560911\pi\) | |||||||
\(938\) | −13.0319 | −0.425506 | ||||||||
\(939\) | 30.8487 | 1.00671 | ||||||||
\(940\) | 1.61068 | 0.0525344 | ||||||||
\(941\) | −12.3134 | −0.401406 | −0.200703 | − | 0.979652i | \(-0.564323\pi\) | ||||
−0.200703 | + | 0.979652i | \(0.564323\pi\) | |||||||
\(942\) | −1.28460 | −0.0418546 | ||||||||
\(943\) | 92.2376 | 3.00367 | ||||||||
\(944\) | 37.4552 | 1.21906 | ||||||||
\(945\) | −1.12200 | −0.0364985 | ||||||||
\(946\) | 2.10603 | 0.0684730 | ||||||||
\(947\) | 20.8079 | 0.676166 | 0.338083 | − | 0.941116i | \(-0.390222\pi\) | ||||
0.338083 | + | 0.941116i | \(0.390222\pi\) | |||||||
\(948\) | −1.53388 | −0.0498180 | ||||||||
\(949\) | 0.292076 | 0.00948120 | ||||||||
\(950\) | −17.4697 | −0.566791 | ||||||||
\(951\) | −30.7099 | −0.995838 | ||||||||
\(952\) | −5.83198 | −0.189016 | ||||||||
\(953\) | −12.1442 | −0.393389 | −0.196694 | − | 0.980465i | \(-0.563021\pi\) | ||||
−0.196694 | + | 0.980465i | \(0.563021\pi\) | |||||||
\(954\) | 13.0833 | 0.423589 | ||||||||
\(955\) | 13.7930 | 0.446331 | ||||||||
\(956\) | 3.66935 | 0.118675 | ||||||||
\(957\) | −7.34419 | −0.237404 | ||||||||
\(958\) | −1.11990 | −0.0361822 | ||||||||
\(959\) | 34.7066 | 1.12073 | ||||||||
\(960\) | 5.14931 | 0.166193 | ||||||||
\(961\) | −27.2121 | −0.877809 | ||||||||
\(962\) | 4.66536 | 0.150417 | ||||||||
\(963\) | 2.56618 | 0.0826940 | ||||||||
\(964\) | −1.11960 | −0.0360600 | ||||||||
\(965\) | 8.79718 | 0.283191 | ||||||||
\(966\) | −22.2287 | −0.715197 | ||||||||
\(967\) | 44.4464 | 1.42930 | 0.714649 | − | 0.699483i | \(-0.246586\pi\) | ||||
0.714649 | + | 0.699483i | \(0.246586\pi\) | |||||||
\(968\) | −25.6385 | −0.824051 | ||||||||
\(969\) | 2.91658 | 0.0936940 | ||||||||
\(970\) | 13.8950 | 0.446141 | ||||||||
\(971\) | −26.0163 | −0.834904 | −0.417452 | − | 0.908699i | \(-0.637077\pi\) | ||||
−0.417452 | + | 0.908699i | \(0.637077\pi\) | |||||||
\(972\) | 0.349799 | 0.0112198 | ||||||||
\(973\) | 13.0885 | 0.419598 | ||||||||
\(974\) | −18.2606 | −0.585109 | ||||||||
\(975\) | −1.95664 | −0.0626626 | ||||||||
\(976\) | 10.0338 | 0.321175 | ||||||||
\(977\) | −1.97570 | −0.0632084 | −0.0316042 | − | 0.999500i | \(-0.510062\pi\) | ||||
−0.0316042 | + | 0.999500i | \(0.510062\pi\) | |||||||
\(978\) | −28.8159 | −0.921431 | ||||||||
\(979\) | 4.87304 | 0.155743 | ||||||||
\(980\) | −0.663696 | −0.0212010 | ||||||||
\(981\) | 5.05854 | 0.161507 | ||||||||
\(982\) | −1.81687 | −0.0579785 | ||||||||
\(983\) | −12.8906 | −0.411148 | −0.205574 | − | 0.978642i | \(-0.565906\pi\) | ||||
−0.205574 | + | 0.978642i | \(0.565906\pi\) | |||||||
\(984\) | −31.0870 | −0.991016 | ||||||||
\(985\) | 6.19902 | 0.197517 | ||||||||
\(986\) | −5.95921 | −0.189780 | ||||||||
\(987\) | 15.3191 | 0.487611 | ||||||||
\(988\) | −0.428115 | −0.0136202 | ||||||||
\(989\) | −9.27474 | −0.294919 | ||||||||
\(990\) | 1.18105 | 0.0375361 | ||||||||
\(991\) | 12.7498 | 0.405011 | 0.202506 | − | 0.979281i | \(-0.435092\pi\) | ||||
0.202506 | + | 0.979281i | \(0.435092\pi\) | |||||||
\(992\) | −3.80413 | −0.120781 | ||||||||
\(993\) | −7.37770 | −0.234124 | ||||||||
\(994\) | 25.4124 | 0.806033 | ||||||||
\(995\) | −5.55421 | −0.176080 | ||||||||
\(996\) | −0.140943 | −0.00446594 | ||||||||
\(997\) | 33.3101 | 1.05494 | 0.527470 | − | 0.849573i | \(-0.323141\pi\) | ||||
0.527470 | + | 0.849573i | \(0.323141\pi\) | |||||||
\(998\) | 14.5350 | 0.460097 | ||||||||
\(999\) | −8.65463 | −0.273820 |
(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 | 8007.2.a.j.1.20 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.20 | ✓ | 64 | 1.1 | even | 1 | trivial |