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: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50188 | −1.06199 | −0.530994 | − | 0.847375i | \(-0.678181\pi\) | ||||
−0.530994 | + | 0.847375i | \(0.678181\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.255640 | 0.127820 | ||||||||
\(5\) | −0.915140 | −0.409263 | −0.204632 | − | 0.978839i | \(-0.565600\pi\) | ||||
−0.204632 | + | 0.978839i | \(0.565600\pi\) | |||||||
\(6\) | −1.50188 | −0.613139 | ||||||||
\(7\) | −3.11181 | −1.17616 | −0.588078 | − | 0.808804i | \(-0.700115\pi\) | ||||
−0.588078 | + | 0.808804i | \(0.700115\pi\) | |||||||
\(8\) | 2.61982 | 0.926245 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.37443 | 0.434633 | ||||||||
\(11\) | 1.83124 | 0.552139 | 0.276069 | − | 0.961138i | \(-0.410968\pi\) | ||||
0.276069 | + | 0.961138i | \(0.410968\pi\) | |||||||
\(12\) | 0.255640 | 0.0737970 | ||||||||
\(13\) | −4.69886 | −1.30323 | −0.651614 | − | 0.758550i | \(-0.725908\pi\) | ||||
−0.651614 | + | 0.758550i | \(0.725908\pi\) | |||||||
\(14\) | 4.67357 | 1.24906 | ||||||||
\(15\) | −0.915140 | −0.236288 | ||||||||
\(16\) | −4.44593 | −1.11148 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.50188 | −0.353996 | ||||||||
\(19\) | 4.81296 | 1.10417 | 0.552084 | − | 0.833789i | \(-0.313833\pi\) | ||||
0.552084 | + | 0.833789i | \(0.313833\pi\) | |||||||
\(20\) | −0.233947 | −0.0523120 | ||||||||
\(21\) | −3.11181 | −0.679054 | ||||||||
\(22\) | −2.75030 | −0.586365 | ||||||||
\(23\) | −2.49596 | −0.520443 | −0.260222 | − | 0.965549i | \(-0.583796\pi\) | ||||
−0.260222 | + | 0.965549i | \(0.583796\pi\) | |||||||
\(24\) | 2.61982 | 0.534768 | ||||||||
\(25\) | −4.16252 | −0.832504 | ||||||||
\(26\) | 7.05712 | 1.38401 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.795505 | −0.150336 | ||||||||
\(29\) | 4.17081 | 0.774500 | 0.387250 | − | 0.921975i | \(-0.373425\pi\) | ||||
0.387250 | + | 0.921975i | \(0.373425\pi\) | |||||||
\(30\) | 1.37443 | 0.250935 | ||||||||
\(31\) | 7.38733 | 1.32680 | 0.663402 | − | 0.748264i | \(-0.269112\pi\) | ||||
0.663402 | + | 0.748264i | \(0.269112\pi\) | |||||||
\(32\) | 1.43761 | 0.254136 | ||||||||
\(33\) | 1.83124 | 0.318777 | ||||||||
\(34\) | 1.50188 | 0.257570 | ||||||||
\(35\) | 2.84775 | 0.481357 | ||||||||
\(36\) | 0.255640 | 0.0426067 | ||||||||
\(37\) | −5.82140 | −0.957032 | −0.478516 | − | 0.878079i | \(-0.658825\pi\) | ||||
−0.478516 | + | 0.878079i | \(0.658825\pi\) | |||||||
\(38\) | −7.22848 | −1.17261 | ||||||||
\(39\) | −4.69886 | −0.752420 | ||||||||
\(40\) | −2.39750 | −0.379078 | ||||||||
\(41\) | 3.73781 | 0.583748 | 0.291874 | − | 0.956457i | \(-0.405721\pi\) | ||||
0.291874 | + | 0.956457i | \(0.405721\pi\) | |||||||
\(42\) | 4.67357 | 0.721147 | ||||||||
\(43\) | −3.88336 | −0.592206 | −0.296103 | − | 0.955156i | \(-0.595687\pi\) | ||||
−0.296103 | + | 0.955156i | \(0.595687\pi\) | |||||||
\(44\) | 0.468138 | 0.0705744 | ||||||||
\(45\) | −0.915140 | −0.136421 | ||||||||
\(46\) | 3.74863 | 0.552705 | ||||||||
\(47\) | 3.13382 | 0.457114 | 0.228557 | − | 0.973530i | \(-0.426599\pi\) | ||||
0.228557 | + | 0.973530i | \(0.426599\pi\) | |||||||
\(48\) | −4.44593 | −0.641715 | ||||||||
\(49\) | 2.68339 | 0.383342 | ||||||||
\(50\) | 6.25160 | 0.884110 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −1.20122 | −0.166579 | ||||||||
\(53\) | 12.4806 | 1.71434 | 0.857172 | − | 0.515030i | \(-0.172219\pi\) | ||||
0.857172 | + | 0.515030i | \(0.172219\pi\) | |||||||
\(54\) | −1.50188 | −0.204380 | ||||||||
\(55\) | −1.67584 | −0.225970 | ||||||||
\(56\) | −8.15239 | −1.08941 | ||||||||
\(57\) | 4.81296 | 0.637492 | ||||||||
\(58\) | −6.26405 | −0.822511 | ||||||||
\(59\) | 3.86590 | 0.503297 | 0.251648 | − | 0.967819i | \(-0.419027\pi\) | ||||
0.251648 | + | 0.967819i | \(0.419027\pi\) | |||||||
\(60\) | −0.233947 | −0.0302024 | ||||||||
\(61\) | 4.04555 | 0.517980 | 0.258990 | − | 0.965880i | \(-0.416610\pi\) | ||||
0.258990 | + | 0.965880i | \(0.416610\pi\) | |||||||
\(62\) | −11.0949 | −1.40905 | ||||||||
\(63\) | −3.11181 | −0.392052 | ||||||||
\(64\) | 6.73274 | 0.841592 | ||||||||
\(65\) | 4.30011 | 0.533363 | ||||||||
\(66\) | −2.75030 | −0.338538 | ||||||||
\(67\) | −10.2633 | −1.25386 | −0.626928 | − | 0.779077i | \(-0.715688\pi\) | ||||
−0.626928 | + | 0.779077i | \(0.715688\pi\) | |||||||
\(68\) | −0.255640 | −0.0310009 | ||||||||
\(69\) | −2.49596 | −0.300478 | ||||||||
\(70\) | −4.27697 | −0.511196 | ||||||||
\(71\) | 4.17445 | 0.495416 | 0.247708 | − | 0.968835i | \(-0.420323\pi\) | ||||
0.247708 | + | 0.968835i | \(0.420323\pi\) | |||||||
\(72\) | 2.61982 | 0.308748 | ||||||||
\(73\) | 3.90172 | 0.456662 | 0.228331 | − | 0.973584i | \(-0.426673\pi\) | ||||
0.228331 | + | 0.973584i | \(0.426673\pi\) | |||||||
\(74\) | 8.74304 | 1.01636 | ||||||||
\(75\) | −4.16252 | −0.480646 | ||||||||
\(76\) | 1.23039 | 0.141135 | ||||||||
\(77\) | −5.69847 | −0.649401 | ||||||||
\(78\) | 7.05712 | 0.799061 | ||||||||
\(79\) | −1.84040 | −0.207061 | −0.103530 | − | 0.994626i | \(-0.533014\pi\) | ||||
−0.103530 | + | 0.994626i | \(0.533014\pi\) | |||||||
\(80\) | 4.06865 | 0.454889 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.61374 | −0.619934 | ||||||||
\(83\) | −2.87241 | −0.315288 | −0.157644 | − | 0.987496i | \(-0.550390\pi\) | ||||
−0.157644 | + | 0.987496i | \(0.550390\pi\) | |||||||
\(84\) | −0.795505 | −0.0867967 | ||||||||
\(85\) | 0.915140 | 0.0992609 | ||||||||
\(86\) | 5.83233 | 0.628917 | ||||||||
\(87\) | 4.17081 | 0.447158 | ||||||||
\(88\) | 4.79751 | 0.511416 | ||||||||
\(89\) | −10.5142 | −1.11451 | −0.557253 | − | 0.830343i | \(-0.688145\pi\) | ||||
−0.557253 | + | 0.830343i | \(0.688145\pi\) | |||||||
\(90\) | 1.37443 | 0.144878 | ||||||||
\(91\) | 14.6220 | 1.53280 | ||||||||
\(92\) | −0.638067 | −0.0665231 | ||||||||
\(93\) | 7.38733 | 0.766030 | ||||||||
\(94\) | −4.70661 | −0.485450 | ||||||||
\(95\) | −4.40453 | −0.451895 | ||||||||
\(96\) | 1.43761 | 0.146726 | ||||||||
\(97\) | 5.66576 | 0.575271 | 0.287635 | − | 0.957740i | \(-0.407131\pi\) | ||||
0.287635 | + | 0.957740i | \(0.407131\pi\) | |||||||
\(98\) | −4.03013 | −0.407104 | ||||||||
\(99\) | 1.83124 | 0.184046 | ||||||||
\(100\) | −1.06411 | −0.106411 | ||||||||
\(101\) | −15.9150 | −1.58361 | −0.791803 | − | 0.610777i | \(-0.790857\pi\) | ||||
−0.791803 | + | 0.610777i | \(0.790857\pi\) | |||||||
\(102\) | 1.50188 | 0.148708 | ||||||||
\(103\) | −16.7480 | −1.65023 | −0.825114 | − | 0.564967i | \(-0.808889\pi\) | ||||
−0.825114 | + | 0.564967i | \(0.808889\pi\) | |||||||
\(104\) | −12.3101 | −1.20711 | ||||||||
\(105\) | 2.84775 | 0.277912 | ||||||||
\(106\) | −18.7444 | −1.82061 | ||||||||
\(107\) | 10.0590 | 0.972438 | 0.486219 | − | 0.873837i | \(-0.338376\pi\) | ||||
0.486219 | + | 0.873837i | \(0.338376\pi\) | |||||||
\(108\) | 0.255640 | 0.0245990 | ||||||||
\(109\) | 10.6498 | 1.02007 | 0.510033 | − | 0.860155i | \(-0.329633\pi\) | ||||
0.510033 | + | 0.860155i | \(0.329633\pi\) | |||||||
\(110\) | 2.51691 | 0.239978 | ||||||||
\(111\) | −5.82140 | −0.552543 | ||||||||
\(112\) | 13.8349 | 1.30728 | ||||||||
\(113\) | 10.9013 | 1.02550 | 0.512752 | − | 0.858537i | \(-0.328626\pi\) | ||||
0.512752 | + | 0.858537i | \(0.328626\pi\) | |||||||
\(114\) | −7.22848 | −0.677009 | ||||||||
\(115\) | 2.28415 | 0.212998 | ||||||||
\(116\) | 1.06623 | 0.0989967 | ||||||||
\(117\) | −4.69886 | −0.434410 | ||||||||
\(118\) | −5.80611 | −0.534496 | ||||||||
\(119\) | 3.11181 | 0.285260 | ||||||||
\(120\) | −2.39750 | −0.218861 | ||||||||
\(121\) | −7.64657 | −0.695143 | ||||||||
\(122\) | −6.07593 | −0.550089 | ||||||||
\(123\) | 3.73781 | 0.337027 | ||||||||
\(124\) | 1.88850 | 0.169592 | ||||||||
\(125\) | 8.38499 | 0.749976 | ||||||||
\(126\) | 4.67357 | 0.416355 | ||||||||
\(127\) | 18.9120 | 1.67817 | 0.839084 | − | 0.544001i | \(-0.183091\pi\) | ||||
0.839084 | + | 0.544001i | \(0.183091\pi\) | |||||||
\(128\) | −12.9870 | −1.14790 | ||||||||
\(129\) | −3.88336 | −0.341911 | ||||||||
\(130\) | −6.45825 | −0.566426 | ||||||||
\(131\) | 15.5951 | 1.36255 | 0.681276 | − | 0.732026i | \(-0.261425\pi\) | ||||
0.681276 | + | 0.732026i | \(0.261425\pi\) | |||||||
\(132\) | 0.468138 | 0.0407462 | ||||||||
\(133\) | −14.9770 | −1.29867 | ||||||||
\(134\) | 15.4142 | 1.33158 | ||||||||
\(135\) | −0.915140 | −0.0787627 | ||||||||
\(136\) | −2.61982 | −0.224647 | ||||||||
\(137\) | −14.0854 | −1.20340 | −0.601698 | − | 0.798724i | \(-0.705509\pi\) | ||||
−0.601698 | + | 0.798724i | \(0.705509\pi\) | |||||||
\(138\) | 3.74863 | 0.319104 | ||||||||
\(139\) | −18.8607 | −1.59974 | −0.799871 | − | 0.600172i | \(-0.795099\pi\) | ||||
−0.799871 | + | 0.600172i | \(0.795099\pi\) | |||||||
\(140\) | 0.727998 | 0.0615271 | ||||||||
\(141\) | 3.13382 | 0.263915 | ||||||||
\(142\) | −6.26952 | −0.526126 | ||||||||
\(143\) | −8.60472 | −0.719563 | ||||||||
\(144\) | −4.44593 | −0.370494 | ||||||||
\(145\) | −3.81688 | −0.316974 | ||||||||
\(146\) | −5.85991 | −0.484970 | ||||||||
\(147\) | 2.68339 | 0.221322 | ||||||||
\(148\) | −1.48818 | −0.122328 | ||||||||
\(149\) | −4.02889 | −0.330059 | −0.165030 | − | 0.986289i | \(-0.552772\pi\) | ||||
−0.165030 | + | 0.986289i | \(0.552772\pi\) | |||||||
\(150\) | 6.25160 | 0.510441 | ||||||||
\(151\) | 8.06088 | 0.655985 | 0.327993 | − | 0.944680i | \(-0.393628\pi\) | ||||
0.327993 | + | 0.944680i | \(0.393628\pi\) | |||||||
\(152\) | 12.6091 | 1.02273 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 8.55841 | 0.689657 | ||||||||
\(155\) | −6.76044 | −0.543011 | ||||||||
\(156\) | −1.20122 | −0.0961743 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 2.76405 | 0.219896 | ||||||||
\(159\) | 12.4806 | 0.989777 | ||||||||
\(160\) | −1.31562 | −0.104009 | ||||||||
\(161\) | 7.76696 | 0.612122 | ||||||||
\(162\) | −1.50188 | −0.117999 | ||||||||
\(163\) | −18.2135 | −1.42659 | −0.713297 | − | 0.700861i | \(-0.752799\pi\) | ||||
−0.713297 | + | 0.700861i | \(0.752799\pi\) | |||||||
\(164\) | 0.955535 | 0.0746147 | ||||||||
\(165\) | −1.67584 | −0.130464 | ||||||||
\(166\) | 4.31401 | 0.334832 | ||||||||
\(167\) | −18.6021 | −1.43947 | −0.719735 | − | 0.694248i | \(-0.755737\pi\) | ||||
−0.719735 | + | 0.694248i | \(0.755737\pi\) | |||||||
\(168\) | −8.15239 | −0.628970 | ||||||||
\(169\) | 9.07927 | 0.698405 | ||||||||
\(170\) | −1.37443 | −0.105414 | ||||||||
\(171\) | 4.81296 | 0.368056 | ||||||||
\(172\) | −0.992742 | −0.0756959 | ||||||||
\(173\) | 3.81136 | 0.289773 | 0.144886 | − | 0.989448i | \(-0.453718\pi\) | ||||
0.144886 | + | 0.989448i | \(0.453718\pi\) | |||||||
\(174\) | −6.26405 | −0.474877 | ||||||||
\(175\) | 12.9530 | 0.979154 | ||||||||
\(176\) | −8.14155 | −0.613692 | ||||||||
\(177\) | 3.86590 | 0.290579 | ||||||||
\(178\) | 15.7911 | 1.18359 | ||||||||
\(179\) | −21.3262 | −1.59400 | −0.796998 | − | 0.603982i | \(-0.793580\pi\) | ||||
−0.796998 | + | 0.603982i | \(0.793580\pi\) | |||||||
\(180\) | −0.233947 | −0.0174373 | ||||||||
\(181\) | 17.5474 | 1.30429 | 0.652145 | − | 0.758094i | \(-0.273869\pi\) | ||||
0.652145 | + | 0.758094i | \(0.273869\pi\) | |||||||
\(182\) | −21.9604 | −1.62782 | ||||||||
\(183\) | 4.04555 | 0.299056 | ||||||||
\(184\) | −6.53896 | −0.482058 | ||||||||
\(185\) | 5.32740 | 0.391678 | ||||||||
\(186\) | −11.0949 | −0.813515 | ||||||||
\(187\) | −1.83124 | −0.133913 | ||||||||
\(188\) | 0.801130 | 0.0584284 | ||||||||
\(189\) | −3.11181 | −0.226351 | ||||||||
\(190\) | 6.61507 | 0.479907 | ||||||||
\(191\) | 22.2002 | 1.60635 | 0.803175 | − | 0.595744i | \(-0.203143\pi\) | ||||
0.803175 | + | 0.595744i | \(0.203143\pi\) | |||||||
\(192\) | 6.73274 | 0.485894 | ||||||||
\(193\) | 11.2600 | 0.810515 | 0.405258 | − | 0.914202i | \(-0.367182\pi\) | ||||
0.405258 | + | 0.914202i | \(0.367182\pi\) | |||||||
\(194\) | −8.50929 | −0.610931 | ||||||||
\(195\) | 4.30011 | 0.307938 | ||||||||
\(196\) | 0.685983 | 0.0489988 | ||||||||
\(197\) | −11.4265 | −0.814104 | −0.407052 | − | 0.913405i | \(-0.633443\pi\) | ||||
−0.407052 | + | 0.913405i | \(0.633443\pi\) | |||||||
\(198\) | −2.75030 | −0.195455 | ||||||||
\(199\) | −9.58517 | −0.679475 | −0.339737 | − | 0.940520i | \(-0.610338\pi\) | ||||
−0.339737 | + | 0.940520i | \(0.610338\pi\) | |||||||
\(200\) | −10.9050 | −0.771103 | ||||||||
\(201\) | −10.2633 | −0.723914 | ||||||||
\(202\) | 23.9025 | 1.68177 | ||||||||
\(203\) | −12.9788 | −0.910933 | ||||||||
\(204\) | −0.255640 | −0.0178984 | ||||||||
\(205\) | −3.42062 | −0.238906 | ||||||||
\(206\) | 25.1534 | 1.75252 | ||||||||
\(207\) | −2.49596 | −0.173481 | ||||||||
\(208\) | 20.8908 | 1.44852 | ||||||||
\(209\) | 8.81366 | 0.609654 | ||||||||
\(210\) | −4.27697 | −0.295139 | ||||||||
\(211\) | 15.8365 | 1.09023 | 0.545116 | − | 0.838360i | \(-0.316485\pi\) | ||||
0.545116 | + | 0.838360i | \(0.316485\pi\) | |||||||
\(212\) | 3.19055 | 0.219128 | ||||||||
\(213\) | 4.17445 | 0.286029 | ||||||||
\(214\) | −15.1074 | −1.03272 | ||||||||
\(215\) | 3.55382 | 0.242368 | ||||||||
\(216\) | 2.61982 | 0.178256 | ||||||||
\(217\) | −22.9880 | −1.56053 | ||||||||
\(218\) | −15.9947 | −1.08330 | ||||||||
\(219\) | 3.90172 | 0.263654 | ||||||||
\(220\) | −0.428412 | −0.0288835 | ||||||||
\(221\) | 4.69886 | 0.316079 | ||||||||
\(222\) | 8.74304 | 0.586794 | ||||||||
\(223\) | 7.95027 | 0.532389 | 0.266195 | − | 0.963919i | \(-0.414234\pi\) | ||||
0.266195 | + | 0.963919i | \(0.414234\pi\) | |||||||
\(224\) | −4.47358 | −0.298904 | ||||||||
\(225\) | −4.16252 | −0.277501 | ||||||||
\(226\) | −16.3724 | −1.08907 | ||||||||
\(227\) | −16.8738 | −1.11996 | −0.559978 | − | 0.828508i | \(-0.689190\pi\) | ||||
−0.559978 | + | 0.828508i | \(0.689190\pi\) | |||||||
\(228\) | 1.23039 | 0.0814842 | ||||||||
\(229\) | 17.6968 | 1.16944 | 0.584719 | − | 0.811236i | \(-0.301205\pi\) | ||||
0.584719 | + | 0.811236i | \(0.301205\pi\) | |||||||
\(230\) | −3.43052 | −0.226202 | ||||||||
\(231\) | −5.69847 | −0.374932 | ||||||||
\(232\) | 10.9268 | 0.717377 | ||||||||
\(233\) | −3.99403 | −0.261658 | −0.130829 | − | 0.991405i | \(-0.541764\pi\) | ||||
−0.130829 | + | 0.991405i | \(0.541764\pi\) | |||||||
\(234\) | 7.05712 | 0.461338 | ||||||||
\(235\) | −2.86788 | −0.187080 | ||||||||
\(236\) | 0.988278 | 0.0643314 | ||||||||
\(237\) | −1.84040 | −0.119547 | ||||||||
\(238\) | −4.67357 | −0.302942 | ||||||||
\(239\) | 12.5749 | 0.813401 | 0.406701 | − | 0.913562i | \(-0.366679\pi\) | ||||
0.406701 | + | 0.913562i | \(0.366679\pi\) | |||||||
\(240\) | 4.06865 | 0.262630 | ||||||||
\(241\) | 0.414955 | 0.0267296 | 0.0133648 | − | 0.999911i | \(-0.495746\pi\) | ||||
0.0133648 | + | 0.999911i | \(0.495746\pi\) | |||||||
\(242\) | 11.4842 | 0.738234 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.03421 | 0.0662083 | ||||||||
\(245\) | −2.45568 | −0.156888 | ||||||||
\(246\) | −5.61374 | −0.357919 | ||||||||
\(247\) | −22.6154 | −1.43898 | ||||||||
\(248\) | 19.3534 | 1.22895 | ||||||||
\(249\) | −2.87241 | −0.182032 | ||||||||
\(250\) | −12.5932 | −0.796466 | ||||||||
\(251\) | 7.38317 | 0.466022 | 0.233011 | − | 0.972474i | \(-0.425142\pi\) | ||||
0.233011 | + | 0.972474i | \(0.425142\pi\) | |||||||
\(252\) | −0.795505 | −0.0501121 | ||||||||
\(253\) | −4.57069 | −0.287357 | ||||||||
\(254\) | −28.4035 | −1.78220 | ||||||||
\(255\) | 0.915140 | 0.0573083 | ||||||||
\(256\) | 6.03940 | 0.377462 | ||||||||
\(257\) | 2.48429 | 0.154966 | 0.0774828 | − | 0.996994i | \(-0.475312\pi\) | ||||
0.0774828 | + | 0.996994i | \(0.475312\pi\) | |||||||
\(258\) | 5.83233 | 0.363105 | ||||||||
\(259\) | 18.1151 | 1.12562 | ||||||||
\(260\) | 1.09928 | 0.0681746 | ||||||||
\(261\) | 4.17081 | 0.258167 | ||||||||
\(262\) | −23.4220 | −1.44702 | ||||||||
\(263\) | −14.0861 | −0.868583 | −0.434292 | − | 0.900772i | \(-0.643001\pi\) | ||||
−0.434292 | + | 0.900772i | \(0.643001\pi\) | |||||||
\(264\) | 4.79751 | 0.295266 | ||||||||
\(265\) | −11.4215 | −0.701618 | ||||||||
\(266\) | 22.4937 | 1.37918 | ||||||||
\(267\) | −10.5142 | −0.643460 | ||||||||
\(268\) | −2.62370 | −0.160268 | ||||||||
\(269\) | 26.1809 | 1.59628 | 0.798138 | − | 0.602475i | \(-0.205819\pi\) | ||||
0.798138 | + | 0.602475i | \(0.205819\pi\) | |||||||
\(270\) | 1.37443 | 0.0836451 | ||||||||
\(271\) | −1.66508 | −0.101147 | −0.0505733 | − | 0.998720i | \(-0.516105\pi\) | ||||
−0.0505733 | + | 0.998720i | \(0.516105\pi\) | |||||||
\(272\) | 4.44593 | 0.269574 | ||||||||
\(273\) | 14.6220 | 0.884962 | ||||||||
\(274\) | 21.1546 | 1.27799 | ||||||||
\(275\) | −7.62256 | −0.459658 | ||||||||
\(276\) | −0.638067 | −0.0384071 | ||||||||
\(277\) | 5.21404 | 0.313282 | 0.156641 | − | 0.987656i | \(-0.449934\pi\) | ||||
0.156641 | + | 0.987656i | \(0.449934\pi\) | |||||||
\(278\) | 28.3265 | 1.69891 | ||||||||
\(279\) | 7.38733 | 0.442268 | ||||||||
\(280\) | 7.46057 | 0.445855 | ||||||||
\(281\) | −21.5851 | −1.28766 | −0.643830 | − | 0.765168i | \(-0.722656\pi\) | ||||
−0.643830 | + | 0.765168i | \(0.722656\pi\) | |||||||
\(282\) | −4.70661 | −0.280275 | ||||||||
\(283\) | −19.8556 | −1.18029 | −0.590145 | − | 0.807297i | \(-0.700930\pi\) | ||||
−0.590145 | + | 0.807297i | \(0.700930\pi\) | |||||||
\(284\) | 1.06716 | 0.0633241 | ||||||||
\(285\) | −4.40453 | −0.260902 | ||||||||
\(286\) | 12.9233 | 0.764168 | ||||||||
\(287\) | −11.6314 | −0.686578 | ||||||||
\(288\) | 1.43761 | 0.0847121 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 5.73249 | 0.336623 | ||||||||
\(291\) | 5.66576 | 0.332133 | ||||||||
\(292\) | 0.997437 | 0.0583706 | ||||||||
\(293\) | −30.9786 | −1.80979 | −0.904894 | − | 0.425638i | \(-0.860050\pi\) | ||||
−0.904894 | + | 0.425638i | \(0.860050\pi\) | |||||||
\(294\) | −4.03013 | −0.235042 | ||||||||
\(295\) | −3.53784 | −0.205981 | ||||||||
\(296\) | −15.2510 | −0.886447 | ||||||||
\(297\) | 1.83124 | 0.106259 | ||||||||
\(298\) | 6.05090 | 0.350519 | ||||||||
\(299\) | 11.7282 | 0.678257 | ||||||||
\(300\) | −1.06411 | −0.0614363 | ||||||||
\(301\) | 12.0843 | 0.696527 | ||||||||
\(302\) | −12.1065 | −0.696649 | ||||||||
\(303\) | −15.9150 | −0.914295 | ||||||||
\(304\) | −21.3981 | −1.22726 | ||||||||
\(305\) | −3.70225 | −0.211990 | ||||||||
\(306\) | 1.50188 | 0.0858567 | ||||||||
\(307\) | −31.1940 | −1.78034 | −0.890169 | − | 0.455631i | \(-0.849414\pi\) | ||||
−0.890169 | + | 0.455631i | \(0.849414\pi\) | |||||||
\(308\) | −1.45676 | −0.0830065 | ||||||||
\(309\) | −16.7480 | −0.952759 | ||||||||
\(310\) | 10.1534 | 0.576672 | ||||||||
\(311\) | −19.7758 | −1.12138 | −0.560691 | − | 0.828025i | \(-0.689464\pi\) | ||||
−0.560691 | + | 0.828025i | \(0.689464\pi\) | |||||||
\(312\) | −12.3101 | −0.696925 | ||||||||
\(313\) | −14.9782 | −0.846618 | −0.423309 | − | 0.905985i | \(-0.639132\pi\) | ||||
−0.423309 | + | 0.905985i | \(0.639132\pi\) | |||||||
\(314\) | −1.50188 | −0.0847559 | ||||||||
\(315\) | 2.84775 | 0.160452 | ||||||||
\(316\) | −0.470480 | −0.0264665 | ||||||||
\(317\) | 9.00178 | 0.505590 | 0.252795 | − | 0.967520i | \(-0.418650\pi\) | ||||
0.252795 | + | 0.967520i | \(0.418650\pi\) | |||||||
\(318\) | −18.7444 | −1.05113 | ||||||||
\(319\) | 7.63774 | 0.427632 | ||||||||
\(320\) | −6.16140 | −0.344433 | ||||||||
\(321\) | 10.0590 | 0.561437 | ||||||||
\(322\) | −11.6650 | −0.650067 | ||||||||
\(323\) | −4.81296 | −0.267800 | ||||||||
\(324\) | 0.255640 | 0.0142022 | ||||||||
\(325\) | 19.5591 | 1.08494 | ||||||||
\(326\) | 27.3545 | 1.51503 | ||||||||
\(327\) | 10.6498 | 0.588935 | ||||||||
\(328\) | 9.79238 | 0.540694 | ||||||||
\(329\) | −9.75186 | −0.537637 | ||||||||
\(330\) | 2.51691 | 0.138551 | ||||||||
\(331\) | 13.0512 | 0.717359 | 0.358680 | − | 0.933461i | \(-0.383227\pi\) | ||||
0.358680 | + | 0.933461i | \(0.383227\pi\) | |||||||
\(332\) | −0.734304 | −0.0403002 | ||||||||
\(333\) | −5.82140 | −0.319011 | ||||||||
\(334\) | 27.9380 | 1.52870 | ||||||||
\(335\) | 9.39231 | 0.513157 | ||||||||
\(336\) | 13.8349 | 0.754756 | ||||||||
\(337\) | −28.5224 | −1.55372 | −0.776858 | − | 0.629676i | \(-0.783188\pi\) | ||||
−0.776858 | + | 0.629676i | \(0.783188\pi\) | |||||||
\(338\) | −13.6360 | −0.741699 | ||||||||
\(339\) | 10.9013 | 0.592075 | ||||||||
\(340\) | 0.233947 | 0.0126875 | ||||||||
\(341\) | 13.5279 | 0.732579 | ||||||||
\(342\) | −7.22848 | −0.390871 | ||||||||
\(343\) | 13.4325 | 0.725286 | ||||||||
\(344\) | −10.1737 | −0.548528 | ||||||||
\(345\) | 2.28415 | 0.122975 | ||||||||
\(346\) | −5.72421 | −0.307735 | ||||||||
\(347\) | −31.2471 | −1.67743 | −0.838715 | − | 0.544570i | \(-0.816693\pi\) | ||||
−0.838715 | + | 0.544570i | \(0.816693\pi\) | |||||||
\(348\) | 1.06623 | 0.0571558 | ||||||||
\(349\) | 28.3573 | 1.51793 | 0.758967 | − | 0.651129i | \(-0.225704\pi\) | ||||
0.758967 | + | 0.651129i | \(0.225704\pi\) | |||||||
\(350\) | −19.4538 | −1.03985 | ||||||||
\(351\) | −4.69886 | −0.250807 | ||||||||
\(352\) | 2.63261 | 0.140318 | ||||||||
\(353\) | −19.4903 | −1.03736 | −0.518682 | − | 0.854968i | \(-0.673577\pi\) | ||||
−0.518682 | + | 0.854968i | \(0.673577\pi\) | |||||||
\(354\) | −5.80611 | −0.308591 | ||||||||
\(355\) | −3.82021 | −0.202755 | ||||||||
\(356\) | −2.68786 | −0.142456 | ||||||||
\(357\) | 3.11181 | 0.164695 | ||||||||
\(358\) | 32.0294 | 1.69281 | ||||||||
\(359\) | −31.8602 | −1.68151 | −0.840757 | − | 0.541412i | \(-0.817890\pi\) | ||||
−0.840757 | + | 0.541412i | \(0.817890\pi\) | |||||||
\(360\) | −2.39750 | −0.126359 | ||||||||
\(361\) | 4.16454 | 0.219186 | ||||||||
\(362\) | −26.3541 | −1.38514 | ||||||||
\(363\) | −7.64657 | −0.401341 | ||||||||
\(364\) | 3.73797 | 0.195923 | ||||||||
\(365\) | −3.57062 | −0.186895 | ||||||||
\(366\) | −6.07593 | −0.317594 | ||||||||
\(367\) | 35.3160 | 1.84348 | 0.921741 | − | 0.387805i | \(-0.126767\pi\) | ||||
0.921741 | + | 0.387805i | \(0.126767\pi\) | |||||||
\(368\) | 11.0969 | 0.578463 | ||||||||
\(369\) | 3.73781 | 0.194583 | ||||||||
\(370\) | −8.00110 | −0.415958 | ||||||||
\(371\) | −38.8374 | −2.01634 | ||||||||
\(372\) | 1.88850 | 0.0979141 | ||||||||
\(373\) | 3.36495 | 0.174231 | 0.0871153 | − | 0.996198i | \(-0.472235\pi\) | ||||
0.0871153 | + | 0.996198i | \(0.472235\pi\) | |||||||
\(374\) | 2.75030 | 0.142214 | ||||||||
\(375\) | 8.38499 | 0.432999 | ||||||||
\(376\) | 8.21003 | 0.423400 | ||||||||
\(377\) | −19.5981 | −1.00935 | ||||||||
\(378\) | 4.67357 | 0.240382 | ||||||||
\(379\) | 12.8544 | 0.660288 | 0.330144 | − | 0.943931i | \(-0.392903\pi\) | ||||
0.330144 | + | 0.943931i | \(0.392903\pi\) | |||||||
\(380\) | −1.12597 | −0.0577613 | ||||||||
\(381\) | 18.9120 | 0.968891 | ||||||||
\(382\) | −33.3420 | −1.70592 | ||||||||
\(383\) | 6.75149 | 0.344985 | 0.172492 | − | 0.985011i | \(-0.444818\pi\) | ||||
0.172492 | + | 0.985011i | \(0.444818\pi\) | |||||||
\(384\) | −12.9870 | −0.662739 | ||||||||
\(385\) | 5.21490 | 0.265776 | ||||||||
\(386\) | −16.9112 | −0.860758 | ||||||||
\(387\) | −3.88336 | −0.197402 | ||||||||
\(388\) | 1.44840 | 0.0735312 | ||||||||
\(389\) | −10.0817 | −0.511162 | −0.255581 | − | 0.966788i | \(-0.582267\pi\) | ||||
−0.255581 | + | 0.966788i | \(0.582267\pi\) | |||||||
\(390\) | −6.45825 | −0.327026 | ||||||||
\(391\) | 2.49596 | 0.126226 | ||||||||
\(392\) | 7.02999 | 0.355068 | ||||||||
\(393\) | 15.5951 | 0.786670 | ||||||||
\(394\) | 17.1612 | 0.864569 | ||||||||
\(395\) | 1.68422 | 0.0847424 | ||||||||
\(396\) | 0.468138 | 0.0235248 | ||||||||
\(397\) | −2.78465 | −0.139758 | −0.0698789 | − | 0.997555i | \(-0.522261\pi\) | ||||
−0.0698789 | + | 0.997555i | \(0.522261\pi\) | |||||||
\(398\) | 14.3958 | 0.721595 | ||||||||
\(399\) | −14.9770 | −0.749789 | ||||||||
\(400\) | 18.5063 | 0.925313 | ||||||||
\(401\) | 0.965042 | 0.0481919 | 0.0240959 | − | 0.999710i | \(-0.492329\pi\) | ||||
0.0240959 | + | 0.999710i | \(0.492329\pi\) | |||||||
\(402\) | 15.4142 | 0.768789 | ||||||||
\(403\) | −34.7120 | −1.72913 | ||||||||
\(404\) | −4.06852 | −0.202417 | ||||||||
\(405\) | −0.915140 | −0.0454737 | ||||||||
\(406\) | 19.4926 | 0.967400 | ||||||||
\(407\) | −10.6604 | −0.528415 | ||||||||
\(408\) | −2.61982 | −0.129700 | ||||||||
\(409\) | −35.9049 | −1.77538 | −0.887692 | − | 0.460437i | \(-0.847693\pi\) | ||||
−0.887692 | + | 0.460437i | \(0.847693\pi\) | |||||||
\(410\) | 5.13736 | 0.253716 | ||||||||
\(411\) | −14.0854 | −0.694781 | ||||||||
\(412\) | −4.28146 | −0.210932 | ||||||||
\(413\) | −12.0300 | −0.591955 | ||||||||
\(414\) | 3.74863 | 0.184235 | ||||||||
\(415\) | 2.62866 | 0.129036 | ||||||||
\(416\) | −6.75514 | −0.331198 | ||||||||
\(417\) | −18.8607 | −0.923611 | ||||||||
\(418\) | −13.2371 | −0.647445 | ||||||||
\(419\) | −5.08050 | −0.248199 | −0.124099 | − | 0.992270i | \(-0.539604\pi\) | ||||
−0.124099 | + | 0.992270i | \(0.539604\pi\) | |||||||
\(420\) | 0.727998 | 0.0355227 | ||||||||
\(421\) | −10.7271 | −0.522807 | −0.261403 | − | 0.965230i | \(-0.584185\pi\) | ||||
−0.261403 | + | 0.965230i | \(0.584185\pi\) | |||||||
\(422\) | −23.7846 | −1.15782 | ||||||||
\(423\) | 3.13382 | 0.152371 | ||||||||
\(424\) | 32.6969 | 1.58790 | ||||||||
\(425\) | 4.16252 | 0.201912 | ||||||||
\(426\) | −6.26952 | −0.303759 | ||||||||
\(427\) | −12.5890 | −0.609225 | ||||||||
\(428\) | 2.57148 | 0.124297 | ||||||||
\(429\) | −8.60472 | −0.415440 | ||||||||
\(430\) | −5.33740 | −0.257392 | ||||||||
\(431\) | −8.95163 | −0.431185 | −0.215593 | − | 0.976483i | \(-0.569168\pi\) | ||||
−0.215593 | + | 0.976483i | \(0.569168\pi\) | |||||||
\(432\) | −4.44593 | −0.213905 | ||||||||
\(433\) | 18.8978 | 0.908172 | 0.454086 | − | 0.890958i | \(-0.349966\pi\) | ||||
0.454086 | + | 0.890958i | \(0.349966\pi\) | |||||||
\(434\) | 34.5252 | 1.65726 | ||||||||
\(435\) | −3.81688 | −0.183005 | ||||||||
\(436\) | 2.72252 | 0.130385 | ||||||||
\(437\) | −12.0129 | −0.574657 | ||||||||
\(438\) | −5.85991 | −0.279997 | ||||||||
\(439\) | −36.3004 | −1.73253 | −0.866263 | − | 0.499589i | \(-0.833484\pi\) | ||||
−0.866263 | + | 0.499589i | \(0.833484\pi\) | |||||||
\(440\) | −4.39039 | −0.209304 | ||||||||
\(441\) | 2.68339 | 0.127781 | ||||||||
\(442\) | −7.05712 | −0.335673 | ||||||||
\(443\) | −33.2829 | −1.58132 | −0.790660 | − | 0.612256i | \(-0.790262\pi\) | ||||
−0.790660 | + | 0.612256i | \(0.790262\pi\) | |||||||
\(444\) | −1.48818 | −0.0706261 | ||||||||
\(445\) | 9.62199 | 0.456126 | ||||||||
\(446\) | −11.9403 | −0.565392 | ||||||||
\(447\) | −4.02889 | −0.190560 | ||||||||
\(448\) | −20.9510 | −0.989843 | ||||||||
\(449\) | −33.2779 | −1.57048 | −0.785241 | − | 0.619190i | \(-0.787461\pi\) | ||||
−0.785241 | + | 0.619190i | \(0.787461\pi\) | |||||||
\(450\) | 6.25160 | 0.294703 | ||||||||
\(451\) | 6.84482 | 0.322310 | ||||||||
\(452\) | 2.78680 | 0.131080 | ||||||||
\(453\) | 8.06088 | 0.378733 | ||||||||
\(454\) | 25.3425 | 1.18938 | ||||||||
\(455\) | −13.3812 | −0.627318 | ||||||||
\(456\) | 12.6091 | 0.590473 | ||||||||
\(457\) | 5.36358 | 0.250898 | 0.125449 | − | 0.992100i | \(-0.459963\pi\) | ||||
0.125449 | + | 0.992100i | \(0.459963\pi\) | |||||||
\(458\) | −26.5785 | −1.24193 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 0.583921 | 0.0272255 | ||||||||
\(461\) | 15.4815 | 0.721047 | 0.360523 | − | 0.932750i | \(-0.382598\pi\) | ||||
0.360523 | + | 0.932750i | \(0.382598\pi\) | |||||||
\(462\) | 8.55841 | 0.398173 | ||||||||
\(463\) | 11.1458 | 0.517988 | 0.258994 | − | 0.965879i | \(-0.416609\pi\) | ||||
0.258994 | + | 0.965879i | \(0.416609\pi\) | |||||||
\(464\) | −18.5431 | −0.860843 | ||||||||
\(465\) | −6.76044 | −0.313508 | ||||||||
\(466\) | 5.99856 | 0.277878 | ||||||||
\(467\) | −24.9412 | −1.15414 | −0.577072 | − | 0.816693i | \(-0.695805\pi\) | ||||
−0.577072 | + | 0.816693i | \(0.695805\pi\) | |||||||
\(468\) | −1.20122 | −0.0555263 | ||||||||
\(469\) | 31.9373 | 1.47473 | ||||||||
\(470\) | 4.30721 | 0.198677 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 10.1279 | 0.466176 | ||||||||
\(473\) | −7.11135 | −0.326980 | ||||||||
\(474\) | 2.76405 | 0.126957 | ||||||||
\(475\) | −20.0340 | −0.919224 | ||||||||
\(476\) | 0.795505 | 0.0364619 | ||||||||
\(477\) | 12.4806 | 0.571448 | ||||||||
\(478\) | −18.8859 | −0.863823 | ||||||||
\(479\) | −4.34821 | −0.198675 | −0.0993375 | − | 0.995054i | \(-0.531672\pi\) | ||||
−0.0993375 | + | 0.995054i | \(0.531672\pi\) | |||||||
\(480\) | −1.31562 | −0.0600494 | ||||||||
\(481\) | 27.3539 | 1.24723 | ||||||||
\(482\) | −0.623212 | −0.0283865 | ||||||||
\(483\) | 7.76696 | 0.353409 | ||||||||
\(484\) | −1.95477 | −0.0888532 | ||||||||
\(485\) | −5.18496 | −0.235437 | ||||||||
\(486\) | −1.50188 | −0.0681266 | ||||||||
\(487\) | −27.3229 | −1.23812 | −0.619060 | − | 0.785344i | \(-0.712486\pi\) | ||||
−0.619060 | + | 0.785344i | \(0.712486\pi\) | |||||||
\(488\) | 10.5986 | 0.479776 | ||||||||
\(489\) | −18.2135 | −0.823645 | ||||||||
\(490\) | 3.68813 | 0.166613 | ||||||||
\(491\) | −4.23577 | −0.191158 | −0.0955788 | − | 0.995422i | \(-0.530470\pi\) | ||||
−0.0955788 | + | 0.995422i | \(0.530470\pi\) | |||||||
\(492\) | 0.955535 | 0.0430788 | ||||||||
\(493\) | −4.17081 | −0.187844 | ||||||||
\(494\) | 33.9656 | 1.52818 | ||||||||
\(495\) | −1.67584 | −0.0753233 | ||||||||
\(496\) | −32.8435 | −1.47472 | ||||||||
\(497\) | −12.9901 | −0.582686 | ||||||||
\(498\) | 4.31401 | 0.193316 | ||||||||
\(499\) | −19.6122 | −0.877961 | −0.438981 | − | 0.898496i | \(-0.644660\pi\) | ||||
−0.438981 | + | 0.898496i | \(0.644660\pi\) | |||||||
\(500\) | 2.14354 | 0.0958620 | ||||||||
\(501\) | −18.6021 | −0.831079 | ||||||||
\(502\) | −11.0886 | −0.494910 | ||||||||
\(503\) | 7.71947 | 0.344194 | 0.172097 | − | 0.985080i | \(-0.444946\pi\) | ||||
0.172097 | + | 0.985080i | \(0.444946\pi\) | |||||||
\(504\) | −8.15239 | −0.363136 | ||||||||
\(505\) | 14.5645 | 0.648111 | ||||||||
\(506\) | 6.86463 | 0.305170 | ||||||||
\(507\) | 9.07927 | 0.403225 | ||||||||
\(508\) | 4.83467 | 0.214504 | ||||||||
\(509\) | −29.3330 | −1.30016 | −0.650081 | − | 0.759865i | \(-0.725265\pi\) | ||||
−0.650081 | + | 0.759865i | \(0.725265\pi\) | |||||||
\(510\) | −1.37443 | −0.0608608 | ||||||||
\(511\) | −12.1414 | −0.537105 | ||||||||
\(512\) | 16.9035 | 0.747037 | ||||||||
\(513\) | 4.81296 | 0.212497 | ||||||||
\(514\) | −3.73110 | −0.164572 | ||||||||
\(515\) | 15.3267 | 0.675377 | ||||||||
\(516\) | −0.992742 | −0.0437030 | ||||||||
\(517\) | 5.73876 | 0.252391 | ||||||||
\(518\) | −27.2067 | −1.19539 | ||||||||
\(519\) | 3.81136 | 0.167300 | ||||||||
\(520\) | 11.2655 | 0.494025 | ||||||||
\(521\) | 24.6332 | 1.07920 | 0.539600 | − | 0.841921i | \(-0.318575\pi\) | ||||
0.539600 | + | 0.841921i | \(0.318575\pi\) | |||||||
\(522\) | −6.26405 | −0.274170 | ||||||||
\(523\) | −14.4385 | −0.631351 | −0.315675 | − | 0.948867i | \(-0.602231\pi\) | ||||
−0.315675 | + | 0.948867i | \(0.602231\pi\) | |||||||
\(524\) | 3.98674 | 0.174162 | ||||||||
\(525\) | 12.9530 | 0.565315 | ||||||||
\(526\) | 21.1555 | 0.922426 | ||||||||
\(527\) | −7.38733 | −0.321797 | ||||||||
\(528\) | −8.14155 | −0.354315 | ||||||||
\(529\) | −16.7702 | −0.729139 | ||||||||
\(530\) | 17.1537 | 0.745110 | ||||||||
\(531\) | 3.86590 | 0.167766 | ||||||||
\(532\) | −3.82873 | −0.165997 | ||||||||
\(533\) | −17.5634 | −0.760757 | ||||||||
\(534\) | 15.7911 | 0.683347 | ||||||||
\(535\) | −9.20537 | −0.397983 | ||||||||
\(536\) | −26.8878 | −1.16138 | ||||||||
\(537\) | −21.3262 | −0.920294 | ||||||||
\(538\) | −39.3205 | −1.69523 | ||||||||
\(539\) | 4.91393 | 0.211658 | ||||||||
\(540\) | −0.233947 | −0.0100675 | ||||||||
\(541\) | −13.8201 | −0.594173 | −0.297086 | − | 0.954851i | \(-0.596015\pi\) | ||||
−0.297086 | + | 0.954851i | \(0.596015\pi\) | |||||||
\(542\) | 2.50075 | 0.107416 | ||||||||
\(543\) | 17.5474 | 0.753032 | ||||||||
\(544\) | −1.43761 | −0.0616371 | ||||||||
\(545\) | −9.74605 | −0.417475 | ||||||||
\(546\) | −21.9604 | −0.939820 | ||||||||
\(547\) | 41.3531 | 1.76813 | 0.884065 | − | 0.467364i | \(-0.154796\pi\) | ||||
0.884065 | + | 0.467364i | \(0.154796\pi\) | |||||||
\(548\) | −3.60079 | −0.153818 | ||||||||
\(549\) | 4.04555 | 0.172660 | ||||||||
\(550\) | 11.4482 | 0.488151 | ||||||||
\(551\) | 20.0739 | 0.855178 | ||||||||
\(552\) | −6.53896 | −0.278316 | ||||||||
\(553\) | 5.72698 | 0.243536 | ||||||||
\(554\) | −7.83086 | −0.332701 | ||||||||
\(555\) | 5.32740 | 0.226135 | ||||||||
\(556\) | −4.82155 | −0.204479 | ||||||||
\(557\) | 8.36064 | 0.354252 | 0.177126 | − | 0.984188i | \(-0.443320\pi\) | ||||
0.177126 | + | 0.984188i | \(0.443320\pi\) | |||||||
\(558\) | −11.0949 | −0.469683 | ||||||||
\(559\) | 18.2473 | 0.771780 | ||||||||
\(560\) | −12.6609 | −0.535020 | ||||||||
\(561\) | −1.83124 | −0.0773149 | ||||||||
\(562\) | 32.4182 | 1.36748 | ||||||||
\(563\) | 15.6157 | 0.658124 | 0.329062 | − | 0.944308i | \(-0.393268\pi\) | ||||
0.329062 | + | 0.944308i | \(0.393268\pi\) | |||||||
\(564\) | 0.801130 | 0.0337337 | ||||||||
\(565\) | −9.97618 | −0.419701 | ||||||||
\(566\) | 29.8207 | 1.25346 | ||||||||
\(567\) | −3.11181 | −0.130684 | ||||||||
\(568\) | 10.9363 | 0.458877 | ||||||||
\(569\) | −21.5052 | −0.901546 | −0.450773 | − | 0.892639i | \(-0.648852\pi\) | ||||
−0.450773 | + | 0.892639i | \(0.648852\pi\) | |||||||
\(570\) | 6.61507 | 0.277075 | ||||||||
\(571\) | 22.6781 | 0.949049 | 0.474524 | − | 0.880242i | \(-0.342620\pi\) | ||||
0.474524 | + | 0.880242i | \(0.342620\pi\) | |||||||
\(572\) | −2.19971 | −0.0919746 | ||||||||
\(573\) | 22.2002 | 0.927426 | ||||||||
\(574\) | 17.4689 | 0.729138 | ||||||||
\(575\) | 10.3895 | 0.433271 | ||||||||
\(576\) | 6.73274 | 0.280531 | ||||||||
\(577\) | 14.4168 | 0.600178 | 0.300089 | − | 0.953911i | \(-0.402984\pi\) | ||||
0.300089 | + | 0.953911i | \(0.402984\pi\) | |||||||
\(578\) | −1.50188 | −0.0624699 | ||||||||
\(579\) | 11.2600 | 0.467951 | ||||||||
\(580\) | −0.975747 | −0.0405157 | ||||||||
\(581\) | 8.93841 | 0.370828 | ||||||||
\(582\) | −8.50929 | −0.352721 | ||||||||
\(583\) | 22.8550 | 0.946556 | ||||||||
\(584\) | 10.2218 | 0.422981 | ||||||||
\(585\) | 4.30011 | 0.177788 | ||||||||
\(586\) | 46.5261 | 1.92197 | ||||||||
\(587\) | −26.2285 | −1.08257 | −0.541283 | − | 0.840840i | \(-0.682061\pi\) | ||||
−0.541283 | + | 0.840840i | \(0.682061\pi\) | |||||||
\(588\) | 0.685983 | 0.0282895 | ||||||||
\(589\) | 35.5549 | 1.46501 | ||||||||
\(590\) | 5.31340 | 0.218749 | ||||||||
\(591\) | −11.4265 | −0.470023 | ||||||||
\(592\) | 25.8815 | 1.06372 | ||||||||
\(593\) | 37.7746 | 1.55122 | 0.775608 | − | 0.631215i | \(-0.217444\pi\) | ||||
0.775608 | + | 0.631215i | \(0.217444\pi\) | |||||||
\(594\) | −2.75030 | −0.112846 | ||||||||
\(595\) | −2.84775 | −0.116746 | ||||||||
\(596\) | −1.02995 | −0.0421882 | ||||||||
\(597\) | −9.58517 | −0.392295 | ||||||||
\(598\) | −17.6143 | −0.720301 | ||||||||
\(599\) | −27.8240 | −1.13686 | −0.568429 | − | 0.822733i | \(-0.692448\pi\) | ||||
−0.568429 | + | 0.822733i | \(0.692448\pi\) | |||||||
\(600\) | −10.9050 | −0.445196 | ||||||||
\(601\) | 11.0182 | 0.449443 | 0.224722 | − | 0.974423i | \(-0.427853\pi\) | ||||
0.224722 | + | 0.974423i | \(0.427853\pi\) | |||||||
\(602\) | −18.1491 | −0.739704 | ||||||||
\(603\) | −10.2633 | −0.417952 | ||||||||
\(604\) | 2.06069 | 0.0838481 | ||||||||
\(605\) | 6.99768 | 0.284496 | ||||||||
\(606\) | 23.9025 | 0.970971 | ||||||||
\(607\) | 2.12634 | 0.0863055 | 0.0431527 | − | 0.999068i | \(-0.486260\pi\) | ||||
0.0431527 | + | 0.999068i | \(0.486260\pi\) | |||||||
\(608\) | 6.91916 | 0.280609 | ||||||||
\(609\) | −12.9788 | −0.525927 | ||||||||
\(610\) | 5.56033 | 0.225131 | ||||||||
\(611\) | −14.7254 | −0.595725 | ||||||||
\(612\) | −0.255640 | −0.0103336 | ||||||||
\(613\) | 23.4373 | 0.946625 | 0.473312 | − | 0.880895i | \(-0.343058\pi\) | ||||
0.473312 | + | 0.880895i | \(0.343058\pi\) | |||||||
\(614\) | 46.8497 | 1.89070 | ||||||||
\(615\) | −3.42062 | −0.137933 | ||||||||
\(616\) | −14.9290 | −0.601505 | ||||||||
\(617\) | 20.3337 | 0.818606 | 0.409303 | − | 0.912399i | \(-0.365772\pi\) | ||||
0.409303 | + | 0.912399i | \(0.365772\pi\) | |||||||
\(618\) | 25.1534 | 1.01182 | ||||||||
\(619\) | 11.5193 | 0.463000 | 0.231500 | − | 0.972835i | \(-0.425637\pi\) | ||||
0.231500 | + | 0.972835i | \(0.425637\pi\) | |||||||
\(620\) | −1.72824 | −0.0694078 | ||||||||
\(621\) | −2.49596 | −0.100159 | ||||||||
\(622\) | 29.7008 | 1.19089 | ||||||||
\(623\) | 32.7183 | 1.31083 | ||||||||
\(624\) | 20.8908 | 0.836301 | ||||||||
\(625\) | 13.1392 | 0.525566 | ||||||||
\(626\) | 22.4955 | 0.899099 | ||||||||
\(627\) | 8.81366 | 0.351984 | ||||||||
\(628\) | 0.255640 | 0.0102012 | ||||||||
\(629\) | 5.82140 | 0.232114 | ||||||||
\(630\) | −4.27697 | −0.170399 | ||||||||
\(631\) | 3.62641 | 0.144365 | 0.0721826 | − | 0.997391i | \(-0.477004\pi\) | ||||
0.0721826 | + | 0.997391i | \(0.477004\pi\) | |||||||
\(632\) | −4.82150 | −0.191789 | ||||||||
\(633\) | 15.8365 | 0.629446 | ||||||||
\(634\) | −13.5196 | −0.536931 | ||||||||
\(635\) | −17.3071 | −0.686813 | ||||||||
\(636\) | 3.19055 | 0.126513 | ||||||||
\(637\) | −12.6089 | −0.499582 | ||||||||
\(638\) | −11.4710 | −0.454140 | ||||||||
\(639\) | 4.17445 | 0.165139 | ||||||||
\(640\) | 11.8849 | 0.469792 | ||||||||
\(641\) | −13.0015 | −0.513530 | −0.256765 | − | 0.966474i | \(-0.582657\pi\) | ||||
−0.256765 | + | 0.966474i | \(0.582657\pi\) | |||||||
\(642\) | −15.1074 | −0.596240 | ||||||||
\(643\) | −32.0750 | −1.26491 | −0.632457 | − | 0.774595i | \(-0.717953\pi\) | ||||
−0.632457 | + | 0.774595i | \(0.717953\pi\) | |||||||
\(644\) | 1.98555 | 0.0782415 | ||||||||
\(645\) | 3.55382 | 0.139931 | ||||||||
\(646\) | 7.22848 | 0.284401 | ||||||||
\(647\) | 30.9965 | 1.21860 | 0.609299 | − | 0.792940i | \(-0.291451\pi\) | ||||
0.609299 | + | 0.792940i | \(0.291451\pi\) | |||||||
\(648\) | 2.61982 | 0.102916 | ||||||||
\(649\) | 7.07937 | 0.277890 | ||||||||
\(650\) | −29.3754 | −1.15220 | ||||||||
\(651\) | −22.9880 | −0.900970 | ||||||||
\(652\) | −4.65611 | −0.182348 | ||||||||
\(653\) | −2.30916 | −0.0903646 | −0.0451823 | − | 0.998979i | \(-0.514387\pi\) | ||||
−0.0451823 | + | 0.998979i | \(0.514387\pi\) | |||||||
\(654\) | −15.9947 | −0.625442 | ||||||||
\(655\) | −14.2717 | −0.557642 | ||||||||
\(656\) | −16.6180 | −0.648825 | ||||||||
\(657\) | 3.90172 | 0.152221 | ||||||||
\(658\) | 14.6461 | 0.570965 | ||||||||
\(659\) | −6.79254 | −0.264600 | −0.132300 | − | 0.991210i | \(-0.542236\pi\) | ||||
−0.132300 | + | 0.991210i | \(0.542236\pi\) | |||||||
\(660\) | −0.428412 | −0.0166759 | ||||||||
\(661\) | −31.4243 | −1.22226 | −0.611132 | − | 0.791529i | \(-0.709286\pi\) | ||||
−0.611132 | + | 0.791529i | \(0.709286\pi\) | |||||||
\(662\) | −19.6013 | −0.761827 | ||||||||
\(663\) | 4.69886 | 0.182489 | ||||||||
\(664\) | −7.52519 | −0.292034 | ||||||||
\(665\) | 13.7061 | 0.531499 | ||||||||
\(666\) | 8.74304 | 0.338786 | ||||||||
\(667\) | −10.4102 | −0.403084 | ||||||||
\(668\) | −4.75544 | −0.183993 | ||||||||
\(669\) | 7.95027 | 0.307375 | ||||||||
\(670\) | −14.1061 | −0.544967 | ||||||||
\(671\) | 7.40837 | 0.285997 | ||||||||
\(672\) | −4.47358 | −0.172572 | ||||||||
\(673\) | 30.1465 | 1.16206 | 0.581032 | − | 0.813881i | \(-0.302649\pi\) | ||||
0.581032 | + | 0.813881i | \(0.302649\pi\) | |||||||
\(674\) | 42.8372 | 1.65003 | ||||||||
\(675\) | −4.16252 | −0.160215 | ||||||||
\(676\) | 2.32103 | 0.0892703 | ||||||||
\(677\) | 1.85605 | 0.0713339 | 0.0356670 | − | 0.999364i | \(-0.488644\pi\) | ||||
0.0356670 | + | 0.999364i | \(0.488644\pi\) | |||||||
\(678\) | −16.3724 | −0.628778 | ||||||||
\(679\) | −17.6308 | −0.676608 | ||||||||
\(680\) | 2.39750 | 0.0919399 | ||||||||
\(681\) | −16.8738 | −0.646607 | ||||||||
\(682\) | −20.3173 | −0.777991 | ||||||||
\(683\) | −42.0446 | −1.60879 | −0.804395 | − | 0.594094i | \(-0.797511\pi\) | ||||
−0.804395 | + | 0.594094i | \(0.797511\pi\) | |||||||
\(684\) | 1.23039 | 0.0470449 | ||||||||
\(685\) | 12.8901 | 0.492506 | ||||||||
\(686\) | −20.1740 | −0.770246 | ||||||||
\(687\) | 17.6968 | 0.675175 | ||||||||
\(688\) | 17.2651 | 0.658227 | ||||||||
\(689\) | −58.6446 | −2.23418 | ||||||||
\(690\) | −3.43052 | −0.130598 | ||||||||
\(691\) | −20.4108 | −0.776463 | −0.388232 | − | 0.921562i | \(-0.626914\pi\) | ||||
−0.388232 | + | 0.921562i | \(0.626914\pi\) | |||||||
\(692\) | 0.974338 | 0.0370388 | ||||||||
\(693\) | −5.69847 | −0.216467 | ||||||||
\(694\) | 46.9293 | 1.78141 | ||||||||
\(695\) | 17.2602 | 0.654715 | ||||||||
\(696\) | 10.9268 | 0.414178 | ||||||||
\(697\) | −3.73781 | −0.141580 | ||||||||
\(698\) | −42.5893 | −1.61203 | ||||||||
\(699\) | −3.99403 | −0.151068 | ||||||||
\(700\) | 3.31130 | 0.125156 | ||||||||
\(701\) | −28.4942 | −1.07621 | −0.538106 | − | 0.842877i | \(-0.680860\pi\) | ||||
−0.538106 | + | 0.842877i | \(0.680860\pi\) | |||||||
\(702\) | 7.05712 | 0.266354 | ||||||||
\(703\) | −28.0181 | −1.05672 | ||||||||
\(704\) | 12.3292 | 0.464676 | ||||||||
\(705\) | −2.86788 | −0.108011 | ||||||||
\(706\) | 29.2720 | 1.10167 | ||||||||
\(707\) | 49.5246 | 1.86257 | ||||||||
\(708\) | 0.988278 | 0.0371418 | ||||||||
\(709\) | 23.1444 | 0.869207 | 0.434604 | − | 0.900622i | \(-0.356889\pi\) | ||||
0.434604 | + | 0.900622i | \(0.356889\pi\) | |||||||
\(710\) | 5.73749 | 0.215324 | ||||||||
\(711\) | −1.84040 | −0.0690203 | ||||||||
\(712\) | −27.5453 | −1.03231 | ||||||||
\(713\) | −18.4385 | −0.690526 | ||||||||
\(714\) | −4.67357 | −0.174904 | ||||||||
\(715\) | 7.87453 | 0.294491 | ||||||||
\(716\) | −5.45184 | −0.203745 | ||||||||
\(717\) | 12.5749 | 0.469617 | ||||||||
\(718\) | 47.8501 | 1.78575 | ||||||||
\(719\) | −19.1557 | −0.714387 | −0.357194 | − | 0.934030i | \(-0.616266\pi\) | ||||
−0.357194 | + | 0.934030i | \(0.616266\pi\) | |||||||
\(720\) | 4.06865 | 0.151630 | ||||||||
\(721\) | 52.1166 | 1.94092 | ||||||||
\(722\) | −6.25464 | −0.232773 | ||||||||
\(723\) | 0.414955 | 0.0154323 | ||||||||
\(724\) | 4.48583 | 0.166714 | ||||||||
\(725\) | −17.3611 | −0.644774 | ||||||||
\(726\) | 11.4842 | 0.426219 | ||||||||
\(727\) | −12.6329 | −0.468527 | −0.234264 | − | 0.972173i | \(-0.575268\pi\) | ||||
−0.234264 | + | 0.972173i | \(0.575268\pi\) | |||||||
\(728\) | 38.3069 | 1.41975 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.36264 | 0.198480 | ||||||||
\(731\) | 3.88336 | 0.143631 | ||||||||
\(732\) | 1.03421 | 0.0382254 | ||||||||
\(733\) | 31.6526 | 1.16911 | 0.584557 | − | 0.811352i | \(-0.301268\pi\) | ||||
0.584557 | + | 0.811352i | \(0.301268\pi\) | |||||||
\(734\) | −53.0404 | −1.95776 | ||||||||
\(735\) | −2.45568 | −0.0905791 | ||||||||
\(736\) | −3.58822 | −0.132264 | ||||||||
\(737\) | −18.7945 | −0.692302 | ||||||||
\(738\) | −5.61374 | −0.206645 | ||||||||
\(739\) | −16.3722 | −0.602262 | −0.301131 | − | 0.953583i | \(-0.597364\pi\) | ||||
−0.301131 | + | 0.953583i | \(0.597364\pi\) | |||||||
\(740\) | 1.36190 | 0.0500643 | ||||||||
\(741\) | −22.6154 | −0.830797 | ||||||||
\(742\) | 58.3290 | 2.14133 | ||||||||
\(743\) | −27.4874 | −1.00841 | −0.504207 | − | 0.863583i | \(-0.668215\pi\) | ||||
−0.504207 | + | 0.863583i | \(0.668215\pi\) | |||||||
\(744\) | 19.3534 | 0.709532 | ||||||||
\(745\) | 3.68700 | 0.135081 | ||||||||
\(746\) | −5.05375 | −0.185031 | ||||||||
\(747\) | −2.87241 | −0.105096 | ||||||||
\(748\) | −0.468138 | −0.0171168 | ||||||||
\(749\) | −31.3017 | −1.14374 | ||||||||
\(750\) | −12.5932 | −0.459840 | ||||||||
\(751\) | 18.2375 | 0.665495 | 0.332748 | − | 0.943016i | \(-0.392024\pi\) | ||||
0.332748 | + | 0.943016i | \(0.392024\pi\) | |||||||
\(752\) | −13.9327 | −0.508074 | ||||||||
\(753\) | 7.38317 | 0.269058 | ||||||||
\(754\) | 29.4339 | 1.07192 | ||||||||
\(755\) | −7.37684 | −0.268471 | ||||||||
\(756\) | −0.795505 | −0.0289322 | ||||||||
\(757\) | −44.7603 | −1.62684 | −0.813420 | − | 0.581677i | \(-0.802397\pi\) | ||||
−0.813420 | + | 0.581677i | \(0.802397\pi\) | |||||||
\(758\) | −19.3058 | −0.701219 | ||||||||
\(759\) | −4.57069 | −0.165906 | ||||||||
\(760\) | −11.5391 | −0.418566 | ||||||||
\(761\) | 38.5692 | 1.39813 | 0.699066 | − | 0.715057i | \(-0.253599\pi\) | ||||
0.699066 | + | 0.715057i | \(0.253599\pi\) | |||||||
\(762\) | −28.4035 | −1.02895 | ||||||||
\(763\) | −33.1402 | −1.19976 | ||||||||
\(764\) | 5.67526 | 0.205324 | ||||||||
\(765\) | 0.915140 | 0.0330870 | ||||||||
\(766\) | −10.1399 | −0.366370 | ||||||||
\(767\) | −18.1653 | −0.655911 | ||||||||
\(768\) | 6.03940 | 0.217928 | ||||||||
\(769\) | −24.0629 | −0.867729 | −0.433864 | − | 0.900978i | \(-0.642850\pi\) | ||||
−0.433864 | + | 0.900978i | \(0.642850\pi\) | |||||||
\(770\) | −7.83215 | −0.282251 | ||||||||
\(771\) | 2.48429 | 0.0894694 | ||||||||
\(772\) | 2.87852 | 0.103600 | ||||||||
\(773\) | −0.696648 | −0.0250567 | −0.0125283 | − | 0.999922i | \(-0.503988\pi\) | ||||
−0.0125283 | + | 0.999922i | \(0.503988\pi\) | |||||||
\(774\) | 5.83233 | 0.209639 | ||||||||
\(775\) | −30.7499 | −1.10457 | ||||||||
\(776\) | 14.8433 | 0.532842 | ||||||||
\(777\) | 18.1151 | 0.649876 | ||||||||
\(778\) | 15.1415 | 0.542848 | ||||||||
\(779\) | 17.9899 | 0.644556 | ||||||||
\(780\) | 1.09928 | 0.0393606 | ||||||||
\(781\) | 7.64441 | 0.273538 | ||||||||
\(782\) | −3.74863 | −0.134051 | ||||||||
\(783\) | 4.17081 | 0.149053 | ||||||||
\(784\) | −11.9302 | −0.426077 | ||||||||
\(785\) | −0.915140 | −0.0326627 | ||||||||
\(786\) | −23.4220 | −0.835435 | ||||||||
\(787\) | −27.7211 | −0.988150 | −0.494075 | − | 0.869419i | \(-0.664493\pi\) | ||||
−0.494075 | + | 0.869419i | \(0.664493\pi\) | |||||||
\(788\) | −2.92107 | −0.104059 | ||||||||
\(789\) | −14.0861 | −0.501477 | ||||||||
\(790\) | −2.52950 | −0.0899954 | ||||||||
\(791\) | −33.9227 | −1.20615 | ||||||||
\(792\) | 4.79751 | 0.170472 | ||||||||
\(793\) | −19.0095 | −0.675046 | ||||||||
\(794\) | 4.18221 | 0.148421 | ||||||||
\(795\) | −11.4215 | −0.405079 | ||||||||
\(796\) | −2.45036 | −0.0868506 | ||||||||
\(797\) | 28.8795 | 1.02297 | 0.511483 | − | 0.859294i | \(-0.329096\pi\) | ||||
0.511483 | + | 0.859294i | \(0.329096\pi\) | |||||||
\(798\) | 22.4937 | 0.796268 | ||||||||
\(799\) | −3.13382 | −0.110867 | ||||||||
\(800\) | −5.98409 | −0.211569 | ||||||||
\(801\) | −10.5142 | −0.371502 | ||||||||
\(802\) | −1.44938 | −0.0511792 | ||||||||
\(803\) | 7.14498 | 0.252141 | ||||||||
\(804\) | −2.62370 | −0.0925308 | ||||||||
\(805\) | −7.10786 | −0.250519 | ||||||||
\(806\) | 52.1332 | 1.83631 | ||||||||
\(807\) | 26.1809 | 0.921610 | ||||||||
\(808\) | −41.6945 | −1.46681 | ||||||||
\(809\) | 30.5648 | 1.07460 | 0.537300 | − | 0.843391i | \(-0.319444\pi\) | ||||
0.537300 | + | 0.843391i | \(0.319444\pi\) | |||||||
\(810\) | 1.37443 | 0.0482925 | ||||||||
\(811\) | 17.1111 | 0.600853 | 0.300426 | − | 0.953805i | \(-0.402871\pi\) | ||||
0.300426 | + | 0.953805i | \(0.402871\pi\) | |||||||
\(812\) | −3.31790 | −0.116436 | ||||||||
\(813\) | −1.66508 | −0.0583970 | ||||||||
\(814\) | 16.0106 | 0.561170 | ||||||||
\(815\) | 16.6679 | 0.583853 | ||||||||
\(816\) | 4.44593 | 0.155639 | ||||||||
\(817\) | −18.6904 | −0.653895 | ||||||||
\(818\) | 53.9249 | 1.88544 | ||||||||
\(819\) | 14.6220 | 0.510933 | ||||||||
\(820\) | −0.874448 | −0.0305370 | ||||||||
\(821\) | −18.0481 | −0.629884 | −0.314942 | − | 0.949111i | \(-0.601985\pi\) | ||||
−0.314942 | + | 0.949111i | \(0.601985\pi\) | |||||||
\(822\) | 21.1546 | 0.737850 | ||||||||
\(823\) | −19.5413 | −0.681167 | −0.340583 | − | 0.940214i | \(-0.610625\pi\) | ||||
−0.340583 | + | 0.940214i | \(0.610625\pi\) | |||||||
\(824\) | −43.8766 | −1.52851 | ||||||||
\(825\) | −7.62256 | −0.265383 | ||||||||
\(826\) | 18.0675 | 0.628650 | ||||||||
\(827\) | 43.2662 | 1.50451 | 0.752257 | − | 0.658870i | \(-0.228965\pi\) | ||||
0.752257 | + | 0.658870i | \(0.228965\pi\) | |||||||
\(828\) | −0.638067 | −0.0221744 | ||||||||
\(829\) | −39.0073 | −1.35478 | −0.677389 | − | 0.735625i | \(-0.736889\pi\) | ||||
−0.677389 | + | 0.735625i | \(0.736889\pi\) | |||||||
\(830\) | −3.94793 | −0.137035 | ||||||||
\(831\) | 5.21404 | 0.180873 | ||||||||
\(832\) | −31.6362 | −1.09679 | ||||||||
\(833\) | −2.68339 | −0.0929740 | ||||||||
\(834\) | 28.3265 | 0.980865 | ||||||||
\(835\) | 17.0235 | 0.589122 | ||||||||
\(836\) | 2.25313 | 0.0779260 | ||||||||
\(837\) | 7.38733 | 0.255343 | ||||||||
\(838\) | 7.63030 | 0.263584 | ||||||||
\(839\) | −48.1734 | −1.66313 | −0.831566 | − | 0.555426i | \(-0.812555\pi\) | ||||
−0.831566 | + | 0.555426i | \(0.812555\pi\) | |||||||
\(840\) | 7.46057 | 0.257414 | ||||||||
\(841\) | −11.6043 | −0.400149 | ||||||||
\(842\) | 16.1108 | 0.555215 | ||||||||
\(843\) | −21.5851 | −0.743431 | ||||||||
\(844\) | 4.04846 | 0.139354 | ||||||||
\(845\) | −8.30880 | −0.285832 | ||||||||
\(846\) | −4.70661 | −0.161817 | ||||||||
\(847\) | 23.7947 | 0.817596 | ||||||||
\(848\) | −55.4879 | −1.90546 | ||||||||
\(849\) | −19.8556 | −0.681441 | ||||||||
\(850\) | −6.25160 | −0.214428 | ||||||||
\(851\) | 14.5300 | 0.498081 | ||||||||
\(852\) | 1.06716 | 0.0365602 | ||||||||
\(853\) | −47.2449 | −1.61763 | −0.808817 | − | 0.588061i | \(-0.799892\pi\) | ||||
−0.808817 | + | 0.588061i | \(0.799892\pi\) | |||||||
\(854\) | 18.9072 | 0.646990 | ||||||||
\(855\) | −4.40453 | −0.150632 | ||||||||
\(856\) | 26.3527 | 0.900716 | ||||||||
\(857\) | −44.4208 | −1.51738 | −0.758692 | − | 0.651449i | \(-0.774161\pi\) | ||||
−0.758692 | + | 0.651449i | \(0.774161\pi\) | |||||||
\(858\) | 12.9233 | 0.441193 | ||||||||
\(859\) | 10.6719 | 0.364121 | 0.182060 | − | 0.983287i | \(-0.441723\pi\) | ||||
0.182060 | + | 0.983287i | \(0.441723\pi\) | |||||||
\(860\) | 0.908498 | 0.0309795 | ||||||||
\(861\) | −11.6314 | −0.396396 | ||||||||
\(862\) | 13.4443 | 0.457914 | ||||||||
\(863\) | 46.3561 | 1.57798 | 0.788990 | − | 0.614406i | \(-0.210604\pi\) | ||||
0.788990 | + | 0.614406i | \(0.210604\pi\) | |||||||
\(864\) | 1.43761 | 0.0489086 | ||||||||
\(865\) | −3.48793 | −0.118593 | ||||||||
\(866\) | −28.3822 | −0.964468 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −5.87666 | −0.199467 | ||||||||
\(869\) | −3.37020 | −0.114326 | ||||||||
\(870\) | 5.73249 | 0.194349 | ||||||||
\(871\) | 48.2256 | 1.63406 | ||||||||
\(872\) | 27.9005 | 0.944830 | ||||||||
\(873\) | 5.66576 | 0.191757 | ||||||||
\(874\) | 18.0420 | 0.610279 | ||||||||
\(875\) | −26.0925 | −0.882088 | ||||||||
\(876\) | 0.997437 | 0.0337003 | ||||||||
\(877\) | −29.8111 | −1.00665 | −0.503325 | − | 0.864097i | \(-0.667890\pi\) | ||||
−0.503325 | + | 0.864097i | \(0.667890\pi\) | |||||||
\(878\) | 54.5189 | 1.83992 | ||||||||
\(879\) | −30.9786 | −1.04488 | ||||||||
\(880\) | 7.45066 | 0.251162 | ||||||||
\(881\) | −29.5075 | −0.994132 | −0.497066 | − | 0.867713i | \(-0.665589\pi\) | ||||
−0.497066 | + | 0.867713i | \(0.665589\pi\) | |||||||
\(882\) | −4.03013 | −0.135701 | ||||||||
\(883\) | −4.60611 | −0.155008 | −0.0775040 | − | 0.996992i | \(-0.524695\pi\) | ||||
−0.0775040 | + | 0.996992i | \(0.524695\pi\) | |||||||
\(884\) | 1.20122 | 0.0404013 | ||||||||
\(885\) | −3.53784 | −0.118923 | ||||||||
\(886\) | 49.9869 | 1.67934 | ||||||||
\(887\) | 23.1898 | 0.778636 | 0.389318 | − | 0.921103i | \(-0.372711\pi\) | ||||
0.389318 | + | 0.921103i | \(0.372711\pi\) | |||||||
\(888\) | −15.2510 | −0.511790 | ||||||||
\(889\) | −58.8507 | −1.97379 | ||||||||
\(890\) | −14.4511 | −0.484401 | ||||||||
\(891\) | 1.83124 | 0.0613488 | ||||||||
\(892\) | 2.03241 | 0.0680501 | ||||||||
\(893\) | 15.0829 | 0.504731 | ||||||||
\(894\) | 6.05090 | 0.202372 | ||||||||
\(895\) | 19.5165 | 0.652364 | ||||||||
\(896\) | 40.4131 | 1.35011 | ||||||||
\(897\) | 11.7282 | 0.391592 | ||||||||
\(898\) | 49.9794 | 1.66783 | ||||||||
\(899\) | 30.8111 | 1.02761 | ||||||||
\(900\) | −1.06411 | −0.0354702 | ||||||||
\(901\) | −12.4806 | −0.415790 | ||||||||
\(902\) | −10.2801 | −0.342289 | ||||||||
\(903\) | 12.0843 | 0.402140 | ||||||||
\(904\) | 28.5593 | 0.949869 | ||||||||
\(905\) | −16.0584 | −0.533798 | ||||||||
\(906\) | −12.1065 | −0.402211 | ||||||||
\(907\) | −28.1937 | −0.936157 | −0.468078 | − | 0.883687i | \(-0.655054\pi\) | ||||
−0.468078 | + | 0.883687i | \(0.655054\pi\) | |||||||
\(908\) | −4.31363 | −0.143153 | ||||||||
\(909\) | −15.9150 | −0.527868 | ||||||||
\(910\) | 20.0969 | 0.666205 | ||||||||
\(911\) | −28.1315 | −0.932038 | −0.466019 | − | 0.884775i | \(-0.654312\pi\) | ||||
−0.466019 | + | 0.884775i | \(0.654312\pi\) | |||||||
\(912\) | −21.3981 | −0.708560 | ||||||||
\(913\) | −5.26007 | −0.174083 | ||||||||
\(914\) | −8.05545 | −0.266450 | ||||||||
\(915\) | −3.70225 | −0.122393 | ||||||||
\(916\) | 4.52402 | 0.149478 | ||||||||
\(917\) | −48.5291 | −1.60257 | ||||||||
\(918\) | 1.50188 | 0.0495694 | ||||||||
\(919\) | −5.37789 | −0.177400 | −0.0887001 | − | 0.996058i | \(-0.528271\pi\) | ||||
−0.0887001 | + | 0.996058i | \(0.528271\pi\) | |||||||
\(920\) | 5.98406 | 0.197289 | ||||||||
\(921\) | −31.1940 | −1.02788 | ||||||||
\(922\) | −23.2514 | −0.765744 | ||||||||
\(923\) | −19.6151 | −0.645640 | ||||||||
\(924\) | −1.45676 | −0.0479238 | ||||||||
\(925\) | 24.2317 | 0.796733 | ||||||||
\(926\) | −16.7396 | −0.550097 | ||||||||
\(927\) | −16.7480 | −0.550076 | ||||||||
\(928\) | 5.99601 | 0.196829 | ||||||||
\(929\) | −7.80116 | −0.255948 | −0.127974 | − | 0.991778i | \(-0.540847\pi\) | ||||
−0.127974 | + | 0.991778i | \(0.540847\pi\) | |||||||
\(930\) | 10.1534 | 0.332942 | ||||||||
\(931\) | 12.9150 | 0.423273 | ||||||||
\(932\) | −1.02104 | −0.0334451 | ||||||||
\(933\) | −19.7758 | −0.647430 | ||||||||
\(934\) | 37.4587 | 1.22569 | ||||||||
\(935\) | 1.67584 | 0.0548058 | ||||||||
\(936\) | −12.3101 | −0.402370 | ||||||||
\(937\) | −36.3746 | −1.18831 | −0.594154 | − | 0.804352i | \(-0.702513\pi\) | ||||
−0.594154 | + | 0.804352i | \(0.702513\pi\) | |||||||
\(938\) | −47.9660 | −1.56615 | ||||||||
\(939\) | −14.9782 | −0.488795 | ||||||||
\(940\) | −0.733146 | −0.0239126 | ||||||||
\(941\) | −60.4168 | −1.96953 | −0.984766 | − | 0.173887i | \(-0.944367\pi\) | ||||
−0.984766 | + | 0.173887i | \(0.944367\pi\) | |||||||
\(942\) | −1.50188 | −0.0489339 | ||||||||
\(943\) | −9.32942 | −0.303808 | ||||||||
\(944\) | −17.1875 | −0.559405 | ||||||||
\(945\) | 2.84775 | 0.0926372 | ||||||||
\(946\) | 10.6804 | 0.347249 | ||||||||
\(947\) | −38.6064 | −1.25454 | −0.627270 | − | 0.778802i | \(-0.715828\pi\) | ||||
−0.627270 | + | 0.778802i | \(0.715828\pi\) | |||||||
\(948\) | −0.470480 | −0.0152805 | ||||||||
\(949\) | −18.3336 | −0.595135 | ||||||||
\(950\) | 30.0887 | 0.976205 | ||||||||
\(951\) | 9.00178 | 0.291903 | ||||||||
\(952\) | 8.15239 | 0.264220 | ||||||||
\(953\) | 34.3529 | 1.11280 | 0.556400 | − | 0.830915i | \(-0.312182\pi\) | ||||
0.556400 | + | 0.830915i | \(0.312182\pi\) | |||||||
\(954\) | −18.7444 | −0.606871 | ||||||||
\(955\) | −20.3163 | −0.657419 | ||||||||
\(956\) | 3.21464 | 0.103969 | ||||||||
\(957\) | 7.63774 | 0.246893 | ||||||||
\(958\) | 6.53049 | 0.210991 | ||||||||
\(959\) | 43.8311 | 1.41538 | ||||||||
\(960\) | −6.16140 | −0.198858 | ||||||||
\(961\) | 23.5726 | 0.760406 | ||||||||
\(962\) | −41.0823 | −1.32455 | ||||||||
\(963\) | 10.0590 | 0.324146 | ||||||||
\(964\) | 0.106079 | 0.00341658 | ||||||||
\(965\) | −10.3045 | −0.331714 | ||||||||
\(966\) | −11.6650 | −0.375316 | ||||||||
\(967\) | −4.19285 | −0.134833 | −0.0674165 | − | 0.997725i | \(-0.521476\pi\) | ||||
−0.0674165 | + | 0.997725i | \(0.521476\pi\) | |||||||
\(968\) | −20.0326 | −0.643873 | ||||||||
\(969\) | −4.81296 | −0.154614 | ||||||||
\(970\) | 7.78719 | 0.250032 | ||||||||
\(971\) | 11.3531 | 0.364339 | 0.182169 | − | 0.983267i | \(-0.441688\pi\) | ||||
0.182169 | + | 0.983267i | \(0.441688\pi\) | |||||||
\(972\) | 0.255640 | 0.00819966 | ||||||||
\(973\) | 58.6909 | 1.88155 | ||||||||
\(974\) | 41.0357 | 1.31487 | ||||||||
\(975\) | 19.5591 | 0.626392 | ||||||||
\(976\) | −17.9862 | −0.575725 | ||||||||
\(977\) | 9.32622 | 0.298372 | 0.149186 | − | 0.988809i | \(-0.452335\pi\) | ||||
0.149186 | + | 0.988809i | \(0.452335\pi\) | |||||||
\(978\) | 27.3545 | 0.874702 | ||||||||
\(979\) | −19.2540 | −0.615362 | ||||||||
\(980\) | −0.627770 | −0.0200534 | ||||||||
\(981\) | 10.6498 | 0.340022 | ||||||||
\(982\) | 6.36161 | 0.203007 | ||||||||
\(983\) | 7.93673 | 0.253142 | 0.126571 | − | 0.991958i | \(-0.459603\pi\) | ||||
0.126571 | + | 0.991958i | \(0.459603\pi\) | |||||||
\(984\) | 9.79238 | 0.312170 | ||||||||
\(985\) | 10.4568 | 0.333183 | ||||||||
\(986\) | 6.26405 | 0.199488 | ||||||||
\(987\) | −9.75186 | −0.310405 | ||||||||
\(988\) | −5.78141 | −0.183931 | ||||||||
\(989\) | 9.69270 | 0.308210 | ||||||||
\(990\) | 2.51691 | 0.0799925 | ||||||||
\(991\) | −31.3797 | −0.996809 | −0.498404 | − | 0.866945i | \(-0.666080\pi\) | ||||
−0.498404 | + | 0.866945i | \(0.666080\pi\) | |||||||
\(992\) | 10.6201 | 0.337189 | ||||||||
\(993\) | 13.0512 | 0.414167 | ||||||||
\(994\) | 19.5096 | 0.618806 | ||||||||
\(995\) | 8.77178 | 0.278084 | ||||||||
\(996\) | −0.734304 | −0.0232673 | ||||||||
\(997\) | −12.8996 | −0.408533 | −0.204266 | − | 0.978915i | \(-0.565481\pi\) | ||||
−0.204266 | + | 0.978915i | \(0.565481\pi\) | |||||||
\(998\) | 29.4551 | 0.932385 | ||||||||
\(999\) | −5.82140 | −0.184181 |
(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.e.1.13 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.13 | ✓ | 46 | 1.1 | even | 1 | trivial |