Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1502,2,Mod(1,1502)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1502, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1502.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1502 = 2 \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1502.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: | \(11.9935303836\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4x^{10} - 9x^{9} + 58x^{8} - 40x^{7} - 146x^{6} + 237x^{5} - 47x^{4} - 89x^{3} + 39x^{2} - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.90813\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1502.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.785790 | 0.453676 | 0.226838 | − | 0.973933i | \(-0.427161\pi\) | ||||
0.226838 | + | 0.973933i | \(0.427161\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.57015 | 0.702192 | 0.351096 | − | 0.936339i | \(-0.385809\pi\) | ||||
0.351096 | + | 0.936339i | \(0.385809\pi\) | |||||||
\(6\) | −0.785790 | −0.320797 | ||||||||
\(7\) | −1.48223 | −0.560230 | −0.280115 | − | 0.959966i | \(-0.590373\pi\) | ||||
−0.280115 | + | 0.959966i | \(0.590373\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.38253 | −0.794178 | ||||||||
\(10\) | −1.57015 | −0.496525 | ||||||||
\(11\) | 1.12323 | 0.338667 | 0.169333 | − | 0.985559i | \(-0.445839\pi\) | ||||
0.169333 | + | 0.985559i | \(0.445839\pi\) | |||||||
\(12\) | 0.785790 | 0.226838 | ||||||||
\(13\) | −1.20114 | −0.333137 | −0.166568 | − | 0.986030i | \(-0.553269\pi\) | ||||
−0.166568 | + | 0.986030i | \(0.553269\pi\) | |||||||
\(14\) | 1.48223 | 0.396143 | ||||||||
\(15\) | 1.23381 | 0.318568 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.99848 | −1.21231 | −0.606155 | − | 0.795347i | \(-0.707289\pi\) | ||||
−0.606155 | + | 0.795347i | \(0.707289\pi\) | |||||||
\(18\) | 2.38253 | 0.561569 | ||||||||
\(19\) | −0.148967 | −0.0341753 | −0.0170877 | − | 0.999854i | \(-0.505439\pi\) | ||||
−0.0170877 | + | 0.999854i | \(0.505439\pi\) | |||||||
\(20\) | 1.57015 | 0.351096 | ||||||||
\(21\) | −1.16472 | −0.254163 | ||||||||
\(22\) | −1.12323 | −0.239474 | ||||||||
\(23\) | −4.44505 | −0.926856 | −0.463428 | − | 0.886134i | \(-0.653381\pi\) | ||||
−0.463428 | + | 0.886134i | \(0.653381\pi\) | |||||||
\(24\) | −0.785790 | −0.160399 | ||||||||
\(25\) | −2.53463 | −0.506926 | ||||||||
\(26\) | 1.20114 | 0.235563 | ||||||||
\(27\) | −4.22954 | −0.813975 | ||||||||
\(28\) | −1.48223 | −0.280115 | ||||||||
\(29\) | 1.85331 | 0.344151 | 0.172076 | − | 0.985084i | \(-0.444953\pi\) | ||||
0.172076 | + | 0.985084i | \(0.444953\pi\) | |||||||
\(30\) | −1.23381 | −0.225261 | ||||||||
\(31\) | 1.46107 | 0.262416 | 0.131208 | − | 0.991355i | \(-0.458114\pi\) | ||||
0.131208 | + | 0.991355i | \(0.458114\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.882623 | 0.153645 | ||||||||
\(34\) | 4.99848 | 0.857233 | ||||||||
\(35\) | −2.32732 | −0.393389 | ||||||||
\(36\) | −2.38253 | −0.397089 | ||||||||
\(37\) | 0.802290 | 0.131896 | 0.0659479 | − | 0.997823i | \(-0.478993\pi\) | ||||
0.0659479 | + | 0.997823i | \(0.478993\pi\) | |||||||
\(38\) | 0.148967 | 0.0241656 | ||||||||
\(39\) | −0.943844 | −0.151136 | ||||||||
\(40\) | −1.57015 | −0.248262 | ||||||||
\(41\) | 3.17134 | 0.495280 | 0.247640 | − | 0.968852i | \(-0.420345\pi\) | ||||
0.247640 | + | 0.968852i | \(0.420345\pi\) | |||||||
\(42\) | 1.16472 | 0.179720 | ||||||||
\(43\) | −8.91837 | −1.36004 | −0.680020 | − | 0.733194i | \(-0.738029\pi\) | ||||
−0.680020 | + | 0.733194i | \(0.738029\pi\) | |||||||
\(44\) | 1.12323 | 0.169333 | ||||||||
\(45\) | −3.74093 | −0.557665 | ||||||||
\(46\) | 4.44505 | 0.655386 | ||||||||
\(47\) | −8.64624 | −1.26118 | −0.630592 | − | 0.776114i | \(-0.717188\pi\) | ||||
−0.630592 | + | 0.776114i | \(0.717188\pi\) | |||||||
\(48\) | 0.785790 | 0.113419 | ||||||||
\(49\) | −4.80299 | −0.686142 | ||||||||
\(50\) | 2.53463 | 0.358451 | ||||||||
\(51\) | −3.92776 | −0.549996 | ||||||||
\(52\) | −1.20114 | −0.166568 | ||||||||
\(53\) | −7.34095 | −1.00836 | −0.504179 | − | 0.863599i | \(-0.668205\pi\) | ||||
−0.504179 | + | 0.863599i | \(0.668205\pi\) | |||||||
\(54\) | 4.22954 | 0.575568 | ||||||||
\(55\) | 1.76364 | 0.237809 | ||||||||
\(56\) | 1.48223 | 0.198071 | ||||||||
\(57\) | −0.117057 | −0.0155045 | ||||||||
\(58\) | −1.85331 | −0.243352 | ||||||||
\(59\) | 14.6115 | 1.90226 | 0.951128 | − | 0.308798i | \(-0.0999268\pi\) | ||||
0.951128 | + | 0.308798i | \(0.0999268\pi\) | |||||||
\(60\) | 1.23381 | 0.159284 | ||||||||
\(61\) | 0.497909 | 0.0637507 | 0.0318754 | − | 0.999492i | \(-0.489852\pi\) | ||||
0.0318754 | + | 0.999492i | \(0.489852\pi\) | |||||||
\(62\) | −1.46107 | −0.185556 | ||||||||
\(63\) | 3.53146 | 0.444923 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.88597 | −0.233926 | ||||||||
\(66\) | −0.882623 | −0.108643 | ||||||||
\(67\) | −11.0619 | −1.35143 | −0.675715 | − | 0.737163i | \(-0.736165\pi\) | ||||
−0.675715 | + | 0.737163i | \(0.736165\pi\) | |||||||
\(68\) | −4.99848 | −0.606155 | ||||||||
\(69\) | −3.49287 | −0.420492 | ||||||||
\(70\) | 2.32732 | 0.278168 | ||||||||
\(71\) | −9.04210 | −1.07310 | −0.536550 | − | 0.843869i | \(-0.680273\pi\) | ||||
−0.536550 | + | 0.843869i | \(0.680273\pi\) | |||||||
\(72\) | 2.38253 | 0.280784 | ||||||||
\(73\) | 9.34359 | 1.09358 | 0.546792 | − | 0.837268i | \(-0.315849\pi\) | ||||
0.546792 | + | 0.837268i | \(0.315849\pi\) | |||||||
\(74\) | −0.802290 | −0.0932644 | ||||||||
\(75\) | −1.99169 | −0.229980 | ||||||||
\(76\) | −0.148967 | −0.0170877 | ||||||||
\(77\) | −1.66489 | −0.189731 | ||||||||
\(78\) | 0.943844 | 0.106869 | ||||||||
\(79\) | 0.787071 | 0.0885524 | 0.0442762 | − | 0.999019i | \(-0.485902\pi\) | ||||
0.0442762 | + | 0.999019i | \(0.485902\pi\) | |||||||
\(80\) | 1.57015 | 0.175548 | ||||||||
\(81\) | 3.82407 | 0.424897 | ||||||||
\(82\) | −3.17134 | −0.350216 | ||||||||
\(83\) | 5.96427 | 0.654664 | 0.327332 | − | 0.944909i | \(-0.393851\pi\) | ||||
0.327332 | + | 0.944909i | \(0.393851\pi\) | |||||||
\(84\) | −1.16472 | −0.127081 | ||||||||
\(85\) | −7.84836 | −0.851274 | ||||||||
\(86\) | 8.91837 | 0.961693 | ||||||||
\(87\) | 1.45631 | 0.156133 | ||||||||
\(88\) | −1.12323 | −0.119737 | ||||||||
\(89\) | 6.02962 | 0.639139 | 0.319569 | − | 0.947563i | \(-0.396462\pi\) | ||||
0.319569 | + | 0.947563i | \(0.396462\pi\) | |||||||
\(90\) | 3.74093 | 0.394329 | ||||||||
\(91\) | 1.78037 | 0.186633 | ||||||||
\(92\) | −4.44505 | −0.463428 | ||||||||
\(93\) | 1.14809 | 0.119052 | ||||||||
\(94\) | 8.64624 | 0.891792 | ||||||||
\(95\) | −0.233900 | −0.0239977 | ||||||||
\(96\) | −0.785790 | −0.0801993 | ||||||||
\(97\) | 12.8889 | 1.30867 | 0.654335 | − | 0.756204i | \(-0.272948\pi\) | ||||
0.654335 | + | 0.756204i | \(0.272948\pi\) | |||||||
\(98\) | 4.80299 | 0.485176 | ||||||||
\(99\) | −2.67614 | −0.268962 | ||||||||
\(100\) | −2.53463 | −0.253463 | ||||||||
\(101\) | 7.26692 | 0.723085 | 0.361543 | − | 0.932356i | \(-0.382250\pi\) | ||||
0.361543 | + | 0.932356i | \(0.382250\pi\) | |||||||
\(102\) | 3.92776 | 0.388906 | ||||||||
\(103\) | 13.4787 | 1.32810 | 0.664048 | − | 0.747690i | \(-0.268837\pi\) | ||||
0.664048 | + | 0.747690i | \(0.268837\pi\) | |||||||
\(104\) | 1.20114 | 0.117782 | ||||||||
\(105\) | −1.82879 | −0.178471 | ||||||||
\(106\) | 7.34095 | 0.713016 | ||||||||
\(107\) | 3.25270 | 0.314450 | 0.157225 | − | 0.987563i | \(-0.449745\pi\) | ||||
0.157225 | + | 0.987563i | \(0.449745\pi\) | |||||||
\(108\) | −4.22954 | −0.406988 | ||||||||
\(109\) | −13.2735 | −1.27138 | −0.635688 | − | 0.771946i | \(-0.719283\pi\) | ||||
−0.635688 | + | 0.771946i | \(0.719283\pi\) | |||||||
\(110\) | −1.76364 | −0.168156 | ||||||||
\(111\) | 0.630432 | 0.0598379 | ||||||||
\(112\) | −1.48223 | −0.140058 | ||||||||
\(113\) | −12.1726 | −1.14510 | −0.572549 | − | 0.819870i | \(-0.694045\pi\) | ||||
−0.572549 | + | 0.819870i | \(0.694045\pi\) | |||||||
\(114\) | 0.117057 | 0.0109634 | ||||||||
\(115\) | −6.97939 | −0.650831 | ||||||||
\(116\) | 1.85331 | 0.172076 | ||||||||
\(117\) | 2.86176 | 0.264570 | ||||||||
\(118\) | −14.6115 | −1.34510 | ||||||||
\(119\) | 7.40890 | 0.679173 | ||||||||
\(120\) | −1.23381 | −0.112631 | ||||||||
\(121\) | −9.73835 | −0.885305 | ||||||||
\(122\) | −0.497909 | −0.0450786 | ||||||||
\(123\) | 2.49201 | 0.224697 | ||||||||
\(124\) | 1.46107 | 0.131208 | ||||||||
\(125\) | −11.8305 | −1.05815 | ||||||||
\(126\) | −3.53146 | −0.314608 | ||||||||
\(127\) | 6.81461 | 0.604699 | 0.302350 | − | 0.953197i | \(-0.402229\pi\) | ||||
0.302350 | + | 0.953197i | \(0.402229\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.00797 | −0.617017 | ||||||||
\(130\) | 1.88597 | 0.165411 | ||||||||
\(131\) | −6.88715 | −0.601733 | −0.300867 | − | 0.953666i | \(-0.597276\pi\) | ||||
−0.300867 | + | 0.953666i | \(0.597276\pi\) | |||||||
\(132\) | 0.882623 | 0.0768225 | ||||||||
\(133\) | 0.220803 | 0.0191461 | ||||||||
\(134\) | 11.0619 | 0.955605 | ||||||||
\(135\) | −6.64101 | −0.571567 | ||||||||
\(136\) | 4.99848 | 0.428616 | ||||||||
\(137\) | −15.8789 | −1.35663 | −0.678313 | − | 0.734773i | \(-0.737289\pi\) | ||||
−0.678313 | + | 0.734773i | \(0.737289\pi\) | |||||||
\(138\) | 3.49287 | 0.297333 | ||||||||
\(139\) | −16.8630 | −1.43030 | −0.715152 | − | 0.698969i | \(-0.753642\pi\) | ||||
−0.715152 | + | 0.698969i | \(0.753642\pi\) | |||||||
\(140\) | −2.32732 | −0.196695 | ||||||||
\(141\) | −6.79413 | −0.572169 | ||||||||
\(142\) | 9.04210 | 0.758796 | ||||||||
\(143\) | −1.34916 | −0.112822 | ||||||||
\(144\) | −2.38253 | −0.198545 | ||||||||
\(145\) | 2.90998 | 0.241660 | ||||||||
\(146\) | −9.34359 | −0.773281 | ||||||||
\(147\) | −3.77414 | −0.311286 | ||||||||
\(148\) | 0.802290 | 0.0659479 | ||||||||
\(149\) | 10.4664 | 0.857444 | 0.428722 | − | 0.903437i | \(-0.358964\pi\) | ||||
0.428722 | + | 0.903437i | \(0.358964\pi\) | |||||||
\(150\) | 1.99169 | 0.162621 | ||||||||
\(151\) | −11.6911 | −0.951410 | −0.475705 | − | 0.879605i | \(-0.657807\pi\) | ||||
−0.475705 | + | 0.879605i | \(0.657807\pi\) | |||||||
\(152\) | 0.148967 | 0.0120828 | ||||||||
\(153\) | 11.9091 | 0.962790 | ||||||||
\(154\) | 1.66489 | 0.134160 | ||||||||
\(155\) | 2.29410 | 0.184266 | ||||||||
\(156\) | −0.943844 | −0.0755680 | ||||||||
\(157\) | −21.5212 | −1.71758 | −0.858791 | − | 0.512326i | \(-0.828784\pi\) | ||||
−0.858791 | + | 0.512326i | \(0.828784\pi\) | |||||||
\(158\) | −0.787071 | −0.0626160 | ||||||||
\(159\) | −5.76844 | −0.457467 | ||||||||
\(160\) | −1.57015 | −0.124131 | ||||||||
\(161\) | 6.58858 | 0.519253 | ||||||||
\(162\) | −3.82407 | −0.300448 | ||||||||
\(163\) | 19.6349 | 1.53793 | 0.768963 | − | 0.639293i | \(-0.220773\pi\) | ||||
0.768963 | + | 0.639293i | \(0.220773\pi\) | |||||||
\(164\) | 3.17134 | 0.247640 | ||||||||
\(165\) | 1.38585 | 0.107888 | ||||||||
\(166\) | −5.96427 | −0.462917 | ||||||||
\(167\) | 2.68307 | 0.207622 | 0.103811 | − | 0.994597i | \(-0.466896\pi\) | ||||
0.103811 | + | 0.994597i | \(0.466896\pi\) | |||||||
\(168\) | 1.16472 | 0.0898602 | ||||||||
\(169\) | −11.5573 | −0.889020 | ||||||||
\(170\) | 7.84836 | 0.601942 | ||||||||
\(171\) | 0.354919 | 0.0271413 | ||||||||
\(172\) | −8.91837 | −0.680020 | ||||||||
\(173\) | −25.7024 | −1.95412 | −0.977060 | − | 0.212963i | \(-0.931689\pi\) | ||||
−0.977060 | + | 0.212963i | \(0.931689\pi\) | |||||||
\(174\) | −1.45631 | −0.110403 | ||||||||
\(175\) | 3.75691 | 0.283996 | ||||||||
\(176\) | 1.12323 | 0.0846667 | ||||||||
\(177\) | 11.4816 | 0.863007 | ||||||||
\(178\) | −6.02962 | −0.451939 | ||||||||
\(179\) | 20.2662 | 1.51477 | 0.757384 | − | 0.652970i | \(-0.226477\pi\) | ||||
0.757384 | + | 0.652970i | \(0.226477\pi\) | |||||||
\(180\) | −3.74093 | −0.278833 | ||||||||
\(181\) | −17.2363 | −1.28116 | −0.640582 | − | 0.767890i | \(-0.721307\pi\) | ||||
−0.640582 | + | 0.767890i | \(0.721307\pi\) | |||||||
\(182\) | −1.78037 | −0.131970 | ||||||||
\(183\) | 0.391252 | 0.0289222 | ||||||||
\(184\) | 4.44505 | 0.327693 | ||||||||
\(185\) | 1.25972 | 0.0926161 | ||||||||
\(186\) | −1.14809 | −0.0841824 | ||||||||
\(187\) | −5.61445 | −0.410569 | ||||||||
\(188\) | −8.64624 | −0.630592 | ||||||||
\(189\) | 6.26915 | 0.456014 | ||||||||
\(190\) | 0.233900 | 0.0169689 | ||||||||
\(191\) | 4.91472 | 0.355617 | 0.177809 | − | 0.984065i | \(-0.443099\pi\) | ||||
0.177809 | + | 0.984065i | \(0.443099\pi\) | |||||||
\(192\) | 0.785790 | 0.0567095 | ||||||||
\(193\) | −8.26154 | −0.594678 | −0.297339 | − | 0.954772i | \(-0.596099\pi\) | ||||
−0.297339 | + | 0.954772i | \(0.596099\pi\) | |||||||
\(194\) | −12.8889 | −0.925370 | ||||||||
\(195\) | −1.48198 | −0.106127 | ||||||||
\(196\) | −4.80299 | −0.343071 | ||||||||
\(197\) | 2.47513 | 0.176346 | 0.0881729 | − | 0.996105i | \(-0.471897\pi\) | ||||
0.0881729 | + | 0.996105i | \(0.471897\pi\) | |||||||
\(198\) | 2.67614 | 0.190185 | ||||||||
\(199\) | 14.8076 | 1.04968 | 0.524841 | − | 0.851200i | \(-0.324125\pi\) | ||||
0.524841 | + | 0.851200i | \(0.324125\pi\) | |||||||
\(200\) | 2.53463 | 0.179226 | ||||||||
\(201\) | −8.69235 | −0.613111 | ||||||||
\(202\) | −7.26692 | −0.511298 | ||||||||
\(203\) | −2.74703 | −0.192804 | ||||||||
\(204\) | −3.92776 | −0.274998 | ||||||||
\(205\) | 4.97948 | 0.347782 | ||||||||
\(206\) | −13.4787 | −0.939106 | ||||||||
\(207\) | 10.5905 | 0.736089 | ||||||||
\(208\) | −1.20114 | −0.0832842 | ||||||||
\(209\) | −0.167324 | −0.0115741 | ||||||||
\(210\) | 1.82879 | 0.126198 | ||||||||
\(211\) | −16.7938 | −1.15613 | −0.578067 | − | 0.815989i | \(-0.696193\pi\) | ||||
−0.578067 | + | 0.815989i | \(0.696193\pi\) | |||||||
\(212\) | −7.34095 | −0.504179 | ||||||||
\(213\) | −7.10519 | −0.486840 | ||||||||
\(214\) | −3.25270 | −0.222350 | ||||||||
\(215\) | −14.0032 | −0.955008 | ||||||||
\(216\) | 4.22954 | 0.287784 | ||||||||
\(217\) | −2.16564 | −0.147013 | ||||||||
\(218\) | 13.2735 | 0.898998 | ||||||||
\(219\) | 7.34209 | 0.496133 | ||||||||
\(220\) | 1.76364 | 0.118905 | ||||||||
\(221\) | 6.00388 | 0.403865 | ||||||||
\(222\) | −0.630432 | −0.0423118 | ||||||||
\(223\) | 23.4951 | 1.57335 | 0.786675 | − | 0.617368i | \(-0.211801\pi\) | ||||
0.786675 | + | 0.617368i | \(0.211801\pi\) | |||||||
\(224\) | 1.48223 | 0.0990357 | ||||||||
\(225\) | 6.03885 | 0.402590 | ||||||||
\(226\) | 12.1726 | 0.809707 | ||||||||
\(227\) | 21.8781 | 1.45210 | 0.726049 | − | 0.687643i | \(-0.241355\pi\) | ||||
0.726049 | + | 0.687643i | \(0.241355\pi\) | |||||||
\(228\) | −0.117057 | −0.00775227 | ||||||||
\(229\) | −26.4789 | −1.74978 | −0.874888 | − | 0.484325i | \(-0.839065\pi\) | ||||
−0.874888 | + | 0.484325i | \(0.839065\pi\) | |||||||
\(230\) | 6.97939 | 0.460207 | ||||||||
\(231\) | −1.30825 | −0.0860766 | ||||||||
\(232\) | −1.85331 | −0.121676 | ||||||||
\(233\) | 3.58171 | 0.234645 | 0.117323 | − | 0.993094i | \(-0.462569\pi\) | ||||
0.117323 | + | 0.993094i | \(0.462569\pi\) | |||||||
\(234\) | −2.86176 | −0.187079 | ||||||||
\(235\) | −13.5759 | −0.885594 | ||||||||
\(236\) | 14.6115 | 0.951128 | ||||||||
\(237\) | 0.618472 | 0.0401741 | ||||||||
\(238\) | −7.40890 | −0.480248 | ||||||||
\(239\) | 20.3035 | 1.31332 | 0.656661 | − | 0.754186i | \(-0.271968\pi\) | ||||
0.656661 | + | 0.754186i | \(0.271968\pi\) | |||||||
\(240\) | 1.23381 | 0.0796419 | ||||||||
\(241\) | 6.95275 | 0.447866 | 0.223933 | − | 0.974605i | \(-0.428110\pi\) | ||||
0.223933 | + | 0.974605i | \(0.428110\pi\) | |||||||
\(242\) | 9.73835 | 0.626005 | ||||||||
\(243\) | 15.6935 | 1.00674 | ||||||||
\(244\) | 0.497909 | 0.0318754 | ||||||||
\(245\) | −7.54142 | −0.481803 | ||||||||
\(246\) | −2.49201 | −0.158885 | ||||||||
\(247\) | 0.178930 | 0.0113851 | ||||||||
\(248\) | −1.46107 | −0.0927781 | ||||||||
\(249\) | 4.68666 | 0.297005 | ||||||||
\(250\) | 11.8305 | 0.748226 | ||||||||
\(251\) | −1.48232 | −0.0935633 | −0.0467816 | − | 0.998905i | \(-0.514896\pi\) | ||||
−0.0467816 | + | 0.998905i | \(0.514896\pi\) | |||||||
\(252\) | 3.53146 | 0.222461 | ||||||||
\(253\) | −4.99281 | −0.313895 | ||||||||
\(254\) | −6.81461 | −0.427587 | ||||||||
\(255\) | −6.16716 | −0.386203 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.8974 | −1.11641 | −0.558204 | − | 0.829703i | \(-0.688510\pi\) | ||||
−0.558204 | + | 0.829703i | \(0.688510\pi\) | |||||||
\(258\) | 7.00797 | 0.436297 | ||||||||
\(259\) | −1.18918 | −0.0738920 | ||||||||
\(260\) | −1.88597 | −0.116963 | ||||||||
\(261\) | −4.41558 | −0.273318 | ||||||||
\(262\) | 6.88715 | 0.425490 | ||||||||
\(263\) | 0.192075 | 0.0118439 | 0.00592193 | − | 0.999982i | \(-0.498115\pi\) | ||||
0.00592193 | + | 0.999982i | \(0.498115\pi\) | |||||||
\(264\) | −0.882623 | −0.0543217 | ||||||||
\(265\) | −11.5264 | −0.708060 | ||||||||
\(266\) | −0.220803 | −0.0135383 | ||||||||
\(267\) | 4.73801 | 0.289962 | ||||||||
\(268\) | −11.0619 | −0.675715 | ||||||||
\(269\) | 19.7300 | 1.20296 | 0.601480 | − | 0.798888i | \(-0.294578\pi\) | ||||
0.601480 | + | 0.798888i | \(0.294578\pi\) | |||||||
\(270\) | 6.64101 | 0.404159 | ||||||||
\(271\) | −13.0350 | −0.791823 | −0.395911 | − | 0.918289i | \(-0.629571\pi\) | ||||
−0.395911 | + | 0.918289i | \(0.629571\pi\) | |||||||
\(272\) | −4.99848 | −0.303077 | ||||||||
\(273\) | 1.39899 | 0.0846710 | ||||||||
\(274\) | 15.8789 | 0.959280 | ||||||||
\(275\) | −2.84698 | −0.171679 | ||||||||
\(276\) | −3.49287 | −0.210246 | ||||||||
\(277\) | −2.94260 | −0.176804 | −0.0884018 | − | 0.996085i | \(-0.528176\pi\) | ||||
−0.0884018 | + | 0.996085i | \(0.528176\pi\) | |||||||
\(278\) | 16.8630 | 1.01138 | ||||||||
\(279\) | −3.48105 | −0.208405 | ||||||||
\(280\) | 2.32732 | 0.139084 | ||||||||
\(281\) | 30.2505 | 1.80459 | 0.902296 | − | 0.431117i | \(-0.141880\pi\) | ||||
0.902296 | + | 0.431117i | \(0.141880\pi\) | |||||||
\(282\) | 6.79413 | 0.404585 | ||||||||
\(283\) | −5.98578 | −0.355818 | −0.177909 | − | 0.984047i | \(-0.556933\pi\) | ||||
−0.177909 | + | 0.984047i | \(0.556933\pi\) | |||||||
\(284\) | −9.04210 | −0.536550 | ||||||||
\(285\) | −0.183796 | −0.0108872 | ||||||||
\(286\) | 1.34916 | 0.0797774 | ||||||||
\(287\) | −4.70066 | −0.277471 | ||||||||
\(288\) | 2.38253 | 0.140392 | ||||||||
\(289\) | 7.98482 | 0.469695 | ||||||||
\(290\) | −2.90998 | −0.170880 | ||||||||
\(291\) | 10.1280 | 0.593712 | ||||||||
\(292\) | 9.34359 | 0.546792 | ||||||||
\(293\) | 33.6330 | 1.96486 | 0.982432 | − | 0.186622i | \(-0.0597540\pi\) | ||||
0.982432 | + | 0.186622i | \(0.0597540\pi\) | |||||||
\(294\) | 3.77414 | 0.220113 | ||||||||
\(295\) | 22.9422 | 1.33575 | ||||||||
\(296\) | −0.802290 | −0.0466322 | ||||||||
\(297\) | −4.75075 | −0.275666 | ||||||||
\(298\) | −10.4664 | −0.606304 | ||||||||
\(299\) | 5.33913 | 0.308770 | ||||||||
\(300\) | −1.99169 | −0.114990 | ||||||||
\(301\) | 13.2191 | 0.761935 | ||||||||
\(302\) | 11.6911 | 0.672749 | ||||||||
\(303\) | 5.71027 | 0.328046 | ||||||||
\(304\) | −0.148967 | −0.00854384 | ||||||||
\(305\) | 0.781791 | 0.0447652 | ||||||||
\(306\) | −11.9091 | −0.680795 | ||||||||
\(307\) | −20.1738 | −1.15138 | −0.575691 | − | 0.817667i | \(-0.695267\pi\) | ||||
−0.575691 | + | 0.817667i | \(0.695267\pi\) | |||||||
\(308\) | −1.66489 | −0.0948657 | ||||||||
\(309\) | 10.5914 | 0.602525 | ||||||||
\(310\) | −2.29410 | −0.130296 | ||||||||
\(311\) | 26.8279 | 1.52127 | 0.760635 | − | 0.649179i | \(-0.224888\pi\) | ||||
0.760635 | + | 0.649179i | \(0.224888\pi\) | |||||||
\(312\) | 0.943844 | 0.0534347 | ||||||||
\(313\) | 6.99439 | 0.395346 | 0.197673 | − | 0.980268i | \(-0.436662\pi\) | ||||
0.197673 | + | 0.980268i | \(0.436662\pi\) | |||||||
\(314\) | 21.5212 | 1.21451 | ||||||||
\(315\) | 5.54492 | 0.312421 | ||||||||
\(316\) | 0.787071 | 0.0442762 | ||||||||
\(317\) | 9.55367 | 0.536588 | 0.268294 | − | 0.963337i | \(-0.413540\pi\) | ||||
0.268294 | + | 0.963337i | \(0.413540\pi\) | |||||||
\(318\) | 5.76844 | 0.323478 | ||||||||
\(319\) | 2.08170 | 0.116553 | ||||||||
\(320\) | 1.57015 | 0.0877740 | ||||||||
\(321\) | 2.55594 | 0.142659 | ||||||||
\(322\) | −6.58858 | −0.367167 | ||||||||
\(323\) | 0.744608 | 0.0414311 | ||||||||
\(324\) | 3.82407 | 0.212449 | ||||||||
\(325\) | 3.04445 | 0.168876 | ||||||||
\(326\) | −19.6349 | −1.08748 | ||||||||
\(327\) | −10.4302 | −0.576792 | ||||||||
\(328\) | −3.17134 | −0.175108 | ||||||||
\(329\) | 12.8157 | 0.706554 | ||||||||
\(330\) | −1.38585 | −0.0762885 | ||||||||
\(331\) | 0.274676 | 0.0150976 | 0.00754878 | − | 0.999972i | \(-0.497597\pi\) | ||||
0.00754878 | + | 0.999972i | \(0.497597\pi\) | |||||||
\(332\) | 5.96427 | 0.327332 | ||||||||
\(333\) | −1.91148 | −0.104749 | ||||||||
\(334\) | −2.68307 | −0.146811 | ||||||||
\(335\) | −17.3689 | −0.948963 | ||||||||
\(336\) | −1.16472 | −0.0635407 | ||||||||
\(337\) | −11.7834 | −0.641883 | −0.320942 | − | 0.947099i | \(-0.603999\pi\) | ||||
−0.320942 | + | 0.947099i | \(0.603999\pi\) | |||||||
\(338\) | 11.5573 | 0.628632 | ||||||||
\(339\) | −9.56508 | −0.519504 | ||||||||
\(340\) | −7.84836 | −0.425637 | ||||||||
\(341\) | 1.64112 | 0.0888716 | ||||||||
\(342\) | −0.354919 | −0.0191918 | ||||||||
\(343\) | 17.4948 | 0.944628 | ||||||||
\(344\) | 8.91837 | 0.480846 | ||||||||
\(345\) | −5.48433 | −0.295266 | ||||||||
\(346\) | 25.7024 | 1.38177 | ||||||||
\(347\) | −5.55057 | −0.297970 | −0.148985 | − | 0.988839i | \(-0.547601\pi\) | ||||
−0.148985 | + | 0.988839i | \(0.547601\pi\) | |||||||
\(348\) | 1.45631 | 0.0780666 | ||||||||
\(349\) | 8.41635 | 0.450517 | 0.225259 | − | 0.974299i | \(-0.427677\pi\) | ||||
0.225259 | + | 0.974299i | \(0.427677\pi\) | |||||||
\(350\) | −3.75691 | −0.200815 | ||||||||
\(351\) | 5.08028 | 0.271165 | ||||||||
\(352\) | −1.12323 | −0.0598684 | ||||||||
\(353\) | 3.26567 | 0.173814 | 0.0869069 | − | 0.996216i | \(-0.472302\pi\) | ||||
0.0869069 | + | 0.996216i | \(0.472302\pi\) | |||||||
\(354\) | −11.4816 | −0.610238 | ||||||||
\(355\) | −14.1974 | −0.753522 | ||||||||
\(356\) | 6.02962 | 0.319569 | ||||||||
\(357\) | 5.82184 | 0.308124 | ||||||||
\(358\) | −20.2662 | −1.07110 | ||||||||
\(359\) | −1.47094 | −0.0776331 | −0.0388165 | − | 0.999246i | \(-0.512359\pi\) | ||||
−0.0388165 | + | 0.999246i | \(0.512359\pi\) | |||||||
\(360\) | 3.74093 | 0.197165 | ||||||||
\(361\) | −18.9778 | −0.998832 | ||||||||
\(362\) | 17.2363 | 0.905920 | ||||||||
\(363\) | −7.65230 | −0.401641 | ||||||||
\(364\) | 1.78037 | 0.0933166 | ||||||||
\(365\) | 14.6708 | 0.767906 | ||||||||
\(366\) | −0.391252 | −0.0204511 | ||||||||
\(367\) | −23.2050 | −1.21129 | −0.605645 | − | 0.795735i | \(-0.707085\pi\) | ||||
−0.605645 | + | 0.795735i | \(0.707085\pi\) | |||||||
\(368\) | −4.44505 | −0.231714 | ||||||||
\(369\) | −7.55583 | −0.393341 | ||||||||
\(370\) | −1.25972 | −0.0654895 | ||||||||
\(371\) | 10.8810 | 0.564912 | ||||||||
\(372\) | 1.14809 | 0.0595259 | ||||||||
\(373\) | 32.6930 | 1.69278 | 0.846390 | − | 0.532564i | \(-0.178771\pi\) | ||||
0.846390 | + | 0.532564i | \(0.178771\pi\) | |||||||
\(374\) | 5.61445 | 0.290316 | ||||||||
\(375\) | −9.29628 | −0.480058 | ||||||||
\(376\) | 8.64624 | 0.445896 | ||||||||
\(377\) | −2.22609 | −0.114649 | ||||||||
\(378\) | −6.26915 | −0.322450 | ||||||||
\(379\) | −10.4963 | −0.539157 | −0.269578 | − | 0.962978i | \(-0.586884\pi\) | ||||
−0.269578 | + | 0.962978i | \(0.586884\pi\) | |||||||
\(380\) | −0.233900 | −0.0119988 | ||||||||
\(381\) | 5.35485 | 0.274337 | ||||||||
\(382\) | −4.91472 | −0.251459 | ||||||||
\(383\) | 23.9917 | 1.22592 | 0.612958 | − | 0.790115i | \(-0.289979\pi\) | ||||
0.612958 | + | 0.790115i | \(0.289979\pi\) | |||||||
\(384\) | −0.785790 | −0.0400997 | ||||||||
\(385\) | −2.61412 | −0.133228 | ||||||||
\(386\) | 8.26154 | 0.420501 | ||||||||
\(387\) | 21.2483 | 1.08011 | ||||||||
\(388\) | 12.8889 | 0.654335 | ||||||||
\(389\) | −10.1775 | −0.516019 | −0.258010 | − | 0.966142i | \(-0.583067\pi\) | ||||
−0.258010 | + | 0.966142i | \(0.583067\pi\) | |||||||
\(390\) | 1.48198 | 0.0750428 | ||||||||
\(391\) | 22.2185 | 1.12364 | ||||||||
\(392\) | 4.80299 | 0.242588 | ||||||||
\(393\) | −5.41185 | −0.272992 | ||||||||
\(394\) | −2.47513 | −0.124695 | ||||||||
\(395\) | 1.23582 | 0.0621808 | ||||||||
\(396\) | −2.67614 | −0.134481 | ||||||||
\(397\) | −25.6974 | −1.28972 | −0.644858 | − | 0.764303i | \(-0.723083\pi\) | ||||
−0.644858 | + | 0.764303i | \(0.723083\pi\) | |||||||
\(398\) | −14.8076 | −0.742237 | ||||||||
\(399\) | 0.173505 | 0.00868611 | ||||||||
\(400\) | −2.53463 | −0.126732 | ||||||||
\(401\) | −6.43327 | −0.321262 | −0.160631 | − | 0.987015i | \(-0.551353\pi\) | ||||
−0.160631 | + | 0.987015i | \(0.551353\pi\) | |||||||
\(402\) | 8.69235 | 0.433535 | ||||||||
\(403\) | −1.75495 | −0.0874204 | ||||||||
\(404\) | 7.26692 | 0.361543 | ||||||||
\(405\) | 6.00436 | 0.298359 | ||||||||
\(406\) | 2.74703 | 0.136333 | ||||||||
\(407\) | 0.901157 | 0.0446687 | ||||||||
\(408\) | 3.92776 | 0.194453 | ||||||||
\(409\) | 35.9996 | 1.78007 | 0.890034 | − | 0.455895i | \(-0.150681\pi\) | ||||
0.890034 | + | 0.455895i | \(0.150681\pi\) | |||||||
\(410\) | −4.97948 | −0.245919 | ||||||||
\(411\) | −12.4775 | −0.615469 | ||||||||
\(412\) | 13.4787 | 0.664048 | ||||||||
\(413\) | −21.6576 | −1.06570 | ||||||||
\(414\) | −10.5905 | −0.520494 | ||||||||
\(415\) | 9.36479 | 0.459700 | ||||||||
\(416\) | 1.20114 | 0.0588908 | ||||||||
\(417\) | −13.2508 | −0.648894 | ||||||||
\(418\) | 0.167324 | 0.00818409 | ||||||||
\(419\) | −6.88795 | −0.336499 | −0.168249 | − | 0.985744i | \(-0.553811\pi\) | ||||
−0.168249 | + | 0.985744i | \(0.553811\pi\) | |||||||
\(420\) | −1.82879 | −0.0892356 | ||||||||
\(421\) | −3.65448 | −0.178109 | −0.0890543 | − | 0.996027i | \(-0.528384\pi\) | ||||
−0.0890543 | + | 0.996027i | \(0.528384\pi\) | |||||||
\(422\) | 16.7938 | 0.817511 | ||||||||
\(423\) | 20.6000 | 1.00161 | ||||||||
\(424\) | 7.34095 | 0.356508 | ||||||||
\(425\) | 12.6693 | 0.614552 | ||||||||
\(426\) | 7.10519 | 0.344248 | ||||||||
\(427\) | −0.738016 | −0.0357151 | ||||||||
\(428\) | 3.25270 | 0.157225 | ||||||||
\(429\) | −1.06015 | −0.0511848 | ||||||||
\(430\) | 14.0032 | 0.675293 | ||||||||
\(431\) | 33.2769 | 1.60289 | 0.801445 | − | 0.598068i | \(-0.204065\pi\) | ||||
0.801445 | + | 0.598068i | \(0.204065\pi\) | |||||||
\(432\) | −4.22954 | −0.203494 | ||||||||
\(433\) | −28.7825 | −1.38320 | −0.691599 | − | 0.722281i | \(-0.743094\pi\) | ||||
−0.691599 | + | 0.722281i | \(0.743094\pi\) | |||||||
\(434\) | 2.16564 | 0.103954 | ||||||||
\(435\) | 2.28663 | 0.109635 | ||||||||
\(436\) | −13.2735 | −0.635688 | ||||||||
\(437\) | 0.662165 | 0.0316756 | ||||||||
\(438\) | −7.34209 | −0.350819 | ||||||||
\(439\) | 16.3681 | 0.781208 | 0.390604 | − | 0.920559i | \(-0.372266\pi\) | ||||
0.390604 | + | 0.920559i | \(0.372266\pi\) | |||||||
\(440\) | −1.76364 | −0.0840782 | ||||||||
\(441\) | 11.4433 | 0.544919 | ||||||||
\(442\) | −6.00388 | −0.285576 | ||||||||
\(443\) | −1.62213 | −0.0770699 | −0.0385350 | − | 0.999257i | \(-0.512269\pi\) | ||||
−0.0385350 | + | 0.999257i | \(0.512269\pi\) | |||||||
\(444\) | 0.630432 | 0.0299190 | ||||||||
\(445\) | 9.46740 | 0.448798 | ||||||||
\(446\) | −23.4951 | −1.11253 | ||||||||
\(447\) | 8.22442 | 0.389002 | ||||||||
\(448\) | −1.48223 | −0.0700288 | ||||||||
\(449\) | −4.57903 | −0.216098 | −0.108049 | − | 0.994146i | \(-0.534460\pi\) | ||||
−0.108049 | + | 0.994146i | \(0.534460\pi\) | |||||||
\(450\) | −6.03885 | −0.284674 | ||||||||
\(451\) | 3.56215 | 0.167735 | ||||||||
\(452\) | −12.1726 | −0.572549 | ||||||||
\(453\) | −9.18677 | −0.431632 | ||||||||
\(454\) | −21.8781 | −1.02679 | ||||||||
\(455\) | 2.79544 | 0.131052 | ||||||||
\(456\) | 0.117057 | 0.00548168 | ||||||||
\(457\) | −8.95623 | −0.418955 | −0.209477 | − | 0.977813i | \(-0.567176\pi\) | ||||
−0.209477 | + | 0.977813i | \(0.567176\pi\) | |||||||
\(458\) | 26.4789 | 1.23728 | ||||||||
\(459\) | 21.1413 | 0.986791 | ||||||||
\(460\) | −6.97939 | −0.325416 | ||||||||
\(461\) | 2.61266 | 0.121684 | 0.0608418 | − | 0.998147i | \(-0.480621\pi\) | ||||
0.0608418 | + | 0.998147i | \(0.480621\pi\) | |||||||
\(462\) | 1.30825 | 0.0608653 | ||||||||
\(463\) | −39.3068 | −1.82674 | −0.913370 | − | 0.407130i | \(-0.866530\pi\) | ||||
−0.913370 | + | 0.407130i | \(0.866530\pi\) | |||||||
\(464\) | 1.85331 | 0.0860378 | ||||||||
\(465\) | 1.80268 | 0.0835973 | ||||||||
\(466\) | −3.58171 | −0.165919 | ||||||||
\(467\) | 15.6584 | 0.724586 | 0.362293 | − | 0.932064i | \(-0.381994\pi\) | ||||
0.362293 | + | 0.932064i | \(0.381994\pi\) | |||||||
\(468\) | 2.86176 | 0.132285 | ||||||||
\(469\) | 16.3963 | 0.757112 | ||||||||
\(470\) | 13.5759 | 0.626209 | ||||||||
\(471\) | −16.9112 | −0.779226 | ||||||||
\(472\) | −14.6115 | −0.672549 | ||||||||
\(473\) | −10.0174 | −0.460600 | ||||||||
\(474\) | −0.618472 | −0.0284074 | ||||||||
\(475\) | 0.377576 | 0.0173244 | ||||||||
\(476\) | 7.40890 | 0.339586 | ||||||||
\(477\) | 17.4901 | 0.800815 | ||||||||
\(478\) | −20.3035 | −0.928659 | ||||||||
\(479\) | 20.5117 | 0.937204 | 0.468602 | − | 0.883409i | \(-0.344758\pi\) | ||||
0.468602 | + | 0.883409i | \(0.344758\pi\) | |||||||
\(480\) | −1.23381 | −0.0563153 | ||||||||
\(481\) | −0.963664 | −0.0439393 | ||||||||
\(482\) | −6.95275 | −0.316689 | ||||||||
\(483\) | 5.17724 | 0.235573 | ||||||||
\(484\) | −9.73835 | −0.442652 | ||||||||
\(485\) | 20.2375 | 0.918938 | ||||||||
\(486\) | −15.6935 | −0.711873 | ||||||||
\(487\) | 38.7408 | 1.75551 | 0.877757 | − | 0.479105i | \(-0.159039\pi\) | ||||
0.877757 | + | 0.479105i | \(0.159039\pi\) | |||||||
\(488\) | −0.497909 | −0.0225393 | ||||||||
\(489\) | 15.4289 | 0.697720 | ||||||||
\(490\) | 7.54142 | 0.340686 | ||||||||
\(491\) | −18.7683 | −0.847000 | −0.423500 | − | 0.905896i | \(-0.639199\pi\) | ||||
−0.423500 | + | 0.905896i | \(0.639199\pi\) | |||||||
\(492\) | 2.49201 | 0.112348 | ||||||||
\(493\) | −9.26375 | −0.417218 | ||||||||
\(494\) | −0.178930 | −0.00805045 | ||||||||
\(495\) | −4.20193 | −0.188863 | ||||||||
\(496\) | 1.46107 | 0.0656040 | ||||||||
\(497\) | 13.4025 | 0.601183 | ||||||||
\(498\) | −4.68666 | −0.210014 | ||||||||
\(499\) | −24.8176 | −1.11099 | −0.555495 | − | 0.831520i | \(-0.687471\pi\) | ||||
−0.555495 | + | 0.831520i | \(0.687471\pi\) | |||||||
\(500\) | −11.8305 | −0.529076 | ||||||||
\(501\) | 2.10833 | 0.0941931 | ||||||||
\(502\) | 1.48232 | 0.0661592 | ||||||||
\(503\) | 1.03716 | 0.0462445 | 0.0231223 | − | 0.999733i | \(-0.492639\pi\) | ||||
0.0231223 | + | 0.999733i | \(0.492639\pi\) | |||||||
\(504\) | −3.53146 | −0.157304 | ||||||||
\(505\) | 11.4101 | 0.507745 | ||||||||
\(506\) | 4.99281 | 0.221958 | ||||||||
\(507\) | −9.08158 | −0.403327 | ||||||||
\(508\) | 6.81461 | 0.302350 | ||||||||
\(509\) | −1.80453 | −0.0799843 | −0.0399922 | − | 0.999200i | \(-0.512733\pi\) | ||||
−0.0399922 | + | 0.999200i | \(0.512733\pi\) | |||||||
\(510\) | 6.16716 | 0.273087 | ||||||||
\(511\) | −13.8493 | −0.612659 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.630061 | 0.0278179 | ||||||||
\(514\) | 17.8974 | 0.789420 | ||||||||
\(515\) | 21.1636 | 0.932578 | ||||||||
\(516\) | −7.00797 | −0.308509 | ||||||||
\(517\) | −9.71173 | −0.427121 | ||||||||
\(518\) | 1.18918 | 0.0522495 | ||||||||
\(519\) | −20.1967 | −0.886537 | ||||||||
\(520\) | 1.88597 | 0.0827053 | ||||||||
\(521\) | 8.13398 | 0.356356 | 0.178178 | − | 0.983998i | \(-0.442980\pi\) | ||||
0.178178 | + | 0.983998i | \(0.442980\pi\) | |||||||
\(522\) | 4.41558 | 0.193265 | ||||||||
\(523\) | 16.3135 | 0.713339 | 0.356670 | − | 0.934231i | \(-0.383912\pi\) | ||||
0.356670 | + | 0.934231i | \(0.383912\pi\) | |||||||
\(524\) | −6.88715 | −0.300867 | ||||||||
\(525\) | 2.95214 | 0.128842 | ||||||||
\(526\) | −0.192075 | −0.00837488 | ||||||||
\(527\) | −7.30314 | −0.318130 | ||||||||
\(528\) | 0.882623 | 0.0384112 | ||||||||
\(529\) | −3.24155 | −0.140937 | ||||||||
\(530\) | 11.5264 | 0.500674 | ||||||||
\(531\) | −34.8124 | −1.51073 | ||||||||
\(532\) | 0.220803 | 0.00957303 | ||||||||
\(533\) | −3.80923 | −0.164996 | ||||||||
\(534\) | −4.73801 | −0.205034 | ||||||||
\(535\) | 5.10722 | 0.220805 | ||||||||
\(536\) | 11.0619 | 0.477802 | ||||||||
\(537\) | 15.9250 | 0.687214 | ||||||||
\(538\) | −19.7300 | −0.850621 | ||||||||
\(539\) | −5.39487 | −0.232374 | ||||||||
\(540\) | −6.64101 | −0.285784 | ||||||||
\(541\) | 5.25232 | 0.225815 | 0.112907 | − | 0.993606i | \(-0.463984\pi\) | ||||
0.112907 | + | 0.993606i | \(0.463984\pi\) | |||||||
\(542\) | 13.0350 | 0.559903 | ||||||||
\(543\) | −13.5441 | −0.581233 | ||||||||
\(544\) | 4.99848 | 0.214308 | ||||||||
\(545\) | −20.8414 | −0.892750 | ||||||||
\(546\) | −1.39899 | −0.0598714 | ||||||||
\(547\) | −19.9484 | −0.852932 | −0.426466 | − | 0.904503i | \(-0.640242\pi\) | ||||
−0.426466 | + | 0.904503i | \(0.640242\pi\) | |||||||
\(548\) | −15.8789 | −0.678313 | ||||||||
\(549\) | −1.18629 | −0.0506294 | ||||||||
\(550\) | 2.84698 | 0.121395 | ||||||||
\(551\) | −0.276082 | −0.0117615 | ||||||||
\(552\) | 3.49287 | 0.148667 | ||||||||
\(553\) | −1.16662 | −0.0496097 | ||||||||
\(554\) | 2.94260 | 0.125019 | ||||||||
\(555\) | 0.989872 | 0.0420177 | ||||||||
\(556\) | −16.8630 | −0.715152 | ||||||||
\(557\) | 7.44153 | 0.315308 | 0.157654 | − | 0.987494i | \(-0.449607\pi\) | ||||
0.157654 | + | 0.987494i | \(0.449607\pi\) | |||||||
\(558\) | 3.48105 | 0.147365 | ||||||||
\(559\) | 10.7122 | 0.453079 | ||||||||
\(560\) | −2.32732 | −0.0983473 | ||||||||
\(561\) | −4.41178 | −0.186265 | ||||||||
\(562\) | −30.2505 | −1.27604 | ||||||||
\(563\) | −2.74939 | −0.115873 | −0.0579364 | − | 0.998320i | \(-0.518452\pi\) | ||||
−0.0579364 | + | 0.998320i | \(0.518452\pi\) | |||||||
\(564\) | −6.79413 | −0.286085 | ||||||||
\(565\) | −19.1127 | −0.804079 | ||||||||
\(566\) | 5.98578 | 0.251601 | ||||||||
\(567\) | −5.66816 | −0.238040 | ||||||||
\(568\) | 9.04210 | 0.379398 | ||||||||
\(569\) | −0.292119 | −0.0122463 | −0.00612313 | − | 0.999981i | \(-0.501949\pi\) | ||||
−0.00612313 | + | 0.999981i | \(0.501949\pi\) | |||||||
\(570\) | 0.183796 | 0.00769838 | ||||||||
\(571\) | 29.0098 | 1.21402 | 0.607011 | − | 0.794693i | \(-0.292368\pi\) | ||||
0.607011 | + | 0.794693i | \(0.292368\pi\) | |||||||
\(572\) | −1.34916 | −0.0564111 | ||||||||
\(573\) | 3.86194 | 0.161335 | ||||||||
\(574\) | 4.70066 | 0.196202 | ||||||||
\(575\) | 11.2666 | 0.469848 | ||||||||
\(576\) | −2.38253 | −0.0992723 | ||||||||
\(577\) | −46.4267 | −1.93277 | −0.966384 | − | 0.257103i | \(-0.917232\pi\) | ||||
−0.966384 | + | 0.257103i | \(0.917232\pi\) | |||||||
\(578\) | −7.98482 | −0.332125 | ||||||||
\(579\) | −6.49183 | −0.269791 | ||||||||
\(580\) | 2.90998 | 0.120830 | ||||||||
\(581\) | −8.84042 | −0.366762 | ||||||||
\(582\) | −10.1280 | −0.419818 | ||||||||
\(583\) | −8.24558 | −0.341497 | ||||||||
\(584\) | −9.34359 | −0.386640 | ||||||||
\(585\) | 4.49339 | 0.185779 | ||||||||
\(586\) | −33.6330 | −1.38937 | ||||||||
\(587\) | 23.7548 | 0.980466 | 0.490233 | − | 0.871591i | \(-0.336912\pi\) | ||||
0.490233 | + | 0.871591i | \(0.336912\pi\) | |||||||
\(588\) | −3.77414 | −0.155643 | ||||||||
\(589\) | −0.217651 | −0.00896816 | ||||||||
\(590\) | −22.9422 | −0.944517 | ||||||||
\(591\) | 1.94493 | 0.0800039 | ||||||||
\(592\) | 0.802290 | 0.0329739 | ||||||||
\(593\) | 2.17984 | 0.0895153 | 0.0447577 | − | 0.998998i | \(-0.485748\pi\) | ||||
0.0447577 | + | 0.998998i | \(0.485748\pi\) | |||||||
\(594\) | 4.75075 | 0.194926 | ||||||||
\(595\) | 11.6331 | 0.476910 | ||||||||
\(596\) | 10.4664 | 0.428722 | ||||||||
\(597\) | 11.6356 | 0.476215 | ||||||||
\(598\) | −5.33913 | −0.218333 | ||||||||
\(599\) | −16.8553 | −0.688689 | −0.344345 | − | 0.938843i | \(-0.611899\pi\) | ||||
−0.344345 | + | 0.938843i | \(0.611899\pi\) | |||||||
\(600\) | 1.99169 | 0.0813103 | ||||||||
\(601\) | 40.1943 | 1.63956 | 0.819780 | − | 0.572678i | \(-0.194096\pi\) | ||||
0.819780 | + | 0.572678i | \(0.194096\pi\) | |||||||
\(602\) | −13.2191 | −0.538769 | ||||||||
\(603\) | 26.3554 | 1.07328 | ||||||||
\(604\) | −11.6911 | −0.475705 | ||||||||
\(605\) | −15.2907 | −0.621654 | ||||||||
\(606\) | −5.71027 | −0.231964 | ||||||||
\(607\) | 11.3885 | 0.462245 | 0.231122 | − | 0.972925i | \(-0.425760\pi\) | ||||
0.231122 | + | 0.972925i | \(0.425760\pi\) | |||||||
\(608\) | 0.148967 | 0.00604140 | ||||||||
\(609\) | −2.15859 | −0.0874705 | ||||||||
\(610\) | −0.781791 | −0.0316538 | ||||||||
\(611\) | 10.3854 | 0.420147 | ||||||||
\(612\) | 11.9091 | 0.481395 | ||||||||
\(613\) | 3.87769 | 0.156618 | 0.0783092 | − | 0.996929i | \(-0.475048\pi\) | ||||
0.0783092 | + | 0.996929i | \(0.475048\pi\) | |||||||
\(614\) | 20.1738 | 0.814150 | ||||||||
\(615\) | 3.91282 | 0.157780 | ||||||||
\(616\) | 1.66489 | 0.0670802 | ||||||||
\(617\) | −24.4375 | −0.983817 | −0.491909 | − | 0.870647i | \(-0.663701\pi\) | ||||
−0.491909 | + | 0.870647i | \(0.663701\pi\) | |||||||
\(618\) | −10.5914 | −0.426050 | ||||||||
\(619\) | 32.0429 | 1.28791 | 0.643956 | − | 0.765062i | \(-0.277292\pi\) | ||||
0.643956 | + | 0.765062i | \(0.277292\pi\) | |||||||
\(620\) | 2.29410 | 0.0921332 | ||||||||
\(621\) | 18.8005 | 0.754438 | ||||||||
\(622\) | −26.8279 | −1.07570 | ||||||||
\(623\) | −8.93728 | −0.358065 | ||||||||
\(624\) | −0.943844 | −0.0377840 | ||||||||
\(625\) | −5.90248 | −0.236099 | ||||||||
\(626\) | −6.99439 | −0.279552 | ||||||||
\(627\) | −0.131482 | −0.00525087 | ||||||||
\(628\) | −21.5212 | −0.858791 | ||||||||
\(629\) | −4.01023 | −0.159899 | ||||||||
\(630\) | −5.54492 | −0.220915 | ||||||||
\(631\) | 10.0949 | 0.401873 | 0.200937 | − | 0.979604i | \(-0.435601\pi\) | ||||
0.200937 | + | 0.979604i | \(0.435601\pi\) | |||||||
\(632\) | −0.787071 | −0.0313080 | ||||||||
\(633\) | −13.1964 | −0.524510 | ||||||||
\(634\) | −9.55367 | −0.379425 | ||||||||
\(635\) | 10.7000 | 0.424615 | ||||||||
\(636\) | −5.76844 | −0.228734 | ||||||||
\(637\) | 5.76907 | 0.228579 | ||||||||
\(638\) | −2.08170 | −0.0824152 | ||||||||
\(639\) | 21.5431 | 0.852232 | ||||||||
\(640\) | −1.57015 | −0.0620656 | ||||||||
\(641\) | −3.55134 | −0.140269 | −0.0701347 | − | 0.997538i | \(-0.522343\pi\) | ||||
−0.0701347 | + | 0.997538i | \(0.522343\pi\) | |||||||
\(642\) | −2.55594 | −0.100875 | ||||||||
\(643\) | −13.4316 | −0.529689 | −0.264844 | − | 0.964291i | \(-0.585321\pi\) | ||||
−0.264844 | + | 0.964291i | \(0.585321\pi\) | |||||||
\(644\) | 6.58858 | 0.259627 | ||||||||
\(645\) | −11.0036 | −0.433264 | ||||||||
\(646\) | −0.744608 | −0.0292962 | ||||||||
\(647\) | −30.0156 | −1.18003 | −0.590017 | − | 0.807391i | \(-0.700879\pi\) | ||||
−0.590017 | + | 0.807391i | \(0.700879\pi\) | |||||||
\(648\) | −3.82407 | −0.150224 | ||||||||
\(649\) | 16.4121 | 0.644231 | ||||||||
\(650\) | −3.04445 | −0.119413 | ||||||||
\(651\) | −1.70174 | −0.0666965 | ||||||||
\(652\) | 19.6349 | 0.768963 | ||||||||
\(653\) | −15.8159 | −0.618922 | −0.309461 | − | 0.950912i | \(-0.600149\pi\) | ||||
−0.309461 | + | 0.950912i | \(0.600149\pi\) | |||||||
\(654\) | 10.4302 | 0.407854 | ||||||||
\(655\) | −10.8139 | −0.422532 | ||||||||
\(656\) | 3.17134 | 0.123820 | ||||||||
\(657\) | −22.2614 | −0.868500 | ||||||||
\(658\) | −12.8157 | −0.499609 | ||||||||
\(659\) | −39.3464 | −1.53272 | −0.766359 | − | 0.642412i | \(-0.777934\pi\) | ||||
−0.766359 | + | 0.642412i | \(0.777934\pi\) | |||||||
\(660\) | 1.38585 | 0.0539441 | ||||||||
\(661\) | −30.4640 | −1.18491 | −0.592456 | − | 0.805603i | \(-0.701841\pi\) | ||||
−0.592456 | + | 0.805603i | \(0.701841\pi\) | |||||||
\(662\) | −0.274676 | −0.0106756 | ||||||||
\(663\) | 4.71779 | 0.183224 | ||||||||
\(664\) | −5.96427 | −0.231459 | ||||||||
\(665\) | 0.346694 | 0.0134442 | ||||||||
\(666\) | 1.91148 | 0.0740685 | ||||||||
\(667\) | −8.23806 | −0.318979 | ||||||||
\(668\) | 2.68307 | 0.103811 | ||||||||
\(669\) | 18.4622 | 0.713791 | ||||||||
\(670\) | 17.3689 | 0.671018 | ||||||||
\(671\) | 0.559267 | 0.0215902 | ||||||||
\(672\) | 1.16472 | 0.0449301 | ||||||||
\(673\) | 36.3713 | 1.40201 | 0.701005 | − | 0.713156i | \(-0.252735\pi\) | ||||
0.701005 | + | 0.713156i | \(0.252735\pi\) | |||||||
\(674\) | 11.7834 | 0.453880 | ||||||||
\(675\) | 10.7203 | 0.412626 | ||||||||
\(676\) | −11.5573 | −0.444510 | ||||||||
\(677\) | 3.81303 | 0.146547 | 0.0732733 | − | 0.997312i | \(-0.476655\pi\) | ||||
0.0732733 | + | 0.997312i | \(0.476655\pi\) | |||||||
\(678\) | 9.56508 | 0.367345 | ||||||||
\(679\) | −19.1043 | −0.733157 | ||||||||
\(680\) | 7.84836 | 0.300971 | ||||||||
\(681\) | 17.1916 | 0.658782 | ||||||||
\(682\) | −1.64112 | −0.0628417 | ||||||||
\(683\) | 40.6149 | 1.55408 | 0.777042 | − | 0.629448i | \(-0.216719\pi\) | ||||
0.777042 | + | 0.629448i | \(0.216719\pi\) | |||||||
\(684\) | 0.354919 | 0.0135707 | ||||||||
\(685\) | −24.9322 | −0.952612 | ||||||||
\(686\) | −17.4948 | −0.667953 | ||||||||
\(687\) | −20.8069 | −0.793831 | ||||||||
\(688\) | −8.91837 | −0.340010 | ||||||||
\(689\) | 8.81752 | 0.335921 | ||||||||
\(690\) | 5.48433 | 0.208785 | ||||||||
\(691\) | −48.7181 | −1.85332 | −0.926662 | − | 0.375895i | \(-0.877335\pi\) | ||||
−0.926662 | + | 0.375895i | \(0.877335\pi\) | |||||||
\(692\) | −25.7024 | −0.977060 | ||||||||
\(693\) | 3.96665 | 0.150681 | ||||||||
\(694\) | 5.55057 | 0.210697 | ||||||||
\(695\) | −26.4775 | −1.00435 | ||||||||
\(696\) | −1.45631 | −0.0552014 | ||||||||
\(697\) | −15.8519 | −0.600433 | ||||||||
\(698\) | −8.41635 | −0.318564 | ||||||||
\(699\) | 2.81447 | 0.106453 | ||||||||
\(700\) | 3.75691 | 0.141998 | ||||||||
\(701\) | −30.7570 | −1.16168 | −0.580838 | − | 0.814019i | \(-0.697275\pi\) | ||||
−0.580838 | + | 0.814019i | \(0.697275\pi\) | |||||||
\(702\) | −5.08028 | −0.191743 | ||||||||
\(703\) | −0.119515 | −0.00450758 | ||||||||
\(704\) | 1.12323 | 0.0423333 | ||||||||
\(705\) | −10.6678 | −0.401772 | ||||||||
\(706\) | −3.26567 | −0.122905 | ||||||||
\(707\) | −10.7712 | −0.405094 | ||||||||
\(708\) | 11.4816 | 0.431504 | ||||||||
\(709\) | 8.06076 | 0.302728 | 0.151364 | − | 0.988478i | \(-0.451633\pi\) | ||||
0.151364 | + | 0.988478i | \(0.451633\pi\) | |||||||
\(710\) | 14.1974 | 0.532821 | ||||||||
\(711\) | −1.87522 | −0.0703264 | ||||||||
\(712\) | −6.02962 | −0.225970 | ||||||||
\(713\) | −6.49453 | −0.243222 | ||||||||
\(714\) | −5.82184 | −0.217877 | ||||||||
\(715\) | −2.11838 | −0.0792229 | ||||||||
\(716\) | 20.2662 | 0.757384 | ||||||||
\(717\) | 15.9543 | 0.595823 | ||||||||
\(718\) | 1.47094 | 0.0548949 | ||||||||
\(719\) | 16.1017 | 0.600491 | 0.300245 | − | 0.953862i | \(-0.402931\pi\) | ||||
0.300245 | + | 0.953862i | \(0.402931\pi\) | |||||||
\(720\) | −3.74093 | −0.139416 | ||||||||
\(721\) | −19.9785 | −0.744039 | ||||||||
\(722\) | 18.9778 | 0.706281 | ||||||||
\(723\) | 5.46340 | 0.203186 | ||||||||
\(724\) | −17.2363 | −0.640582 | ||||||||
\(725\) | −4.69746 | −0.174459 | ||||||||
\(726\) | 7.65230 | 0.284003 | ||||||||
\(727\) | −19.9152 | −0.738615 | −0.369307 | − | 0.929307i | \(-0.620405\pi\) | ||||
−0.369307 | + | 0.929307i | \(0.620405\pi\) | |||||||
\(728\) | −1.78037 | −0.0659848 | ||||||||
\(729\) | 0.859603 | 0.0318371 | ||||||||
\(730\) | −14.6708 | −0.542991 | ||||||||
\(731\) | 44.5783 | 1.64879 | ||||||||
\(732\) | 0.391252 | 0.0144611 | ||||||||
\(733\) | 34.8344 | 1.28664 | 0.643320 | − | 0.765598i | \(-0.277557\pi\) | ||||
0.643320 | + | 0.765598i | \(0.277557\pi\) | |||||||
\(734\) | 23.2050 | 0.856511 | ||||||||
\(735\) | −5.92597 | −0.218583 | ||||||||
\(736\) | 4.44505 | 0.163847 | ||||||||
\(737\) | −12.4251 | −0.457684 | ||||||||
\(738\) | 7.55583 | 0.278134 | ||||||||
\(739\) | 11.6653 | 0.429115 | 0.214557 | − | 0.976711i | \(-0.431169\pi\) | ||||
0.214557 | + | 0.976711i | \(0.431169\pi\) | |||||||
\(740\) | 1.25972 | 0.0463081 | ||||||||
\(741\) | 0.140602 | 0.00516513 | ||||||||
\(742\) | −10.8810 | −0.399453 | ||||||||
\(743\) | 18.5705 | 0.681287 | 0.340644 | − | 0.940193i | \(-0.389355\pi\) | ||||
0.340644 | + | 0.940193i | \(0.389355\pi\) | |||||||
\(744\) | −1.14809 | −0.0420912 | ||||||||
\(745\) | 16.4339 | 0.602090 | ||||||||
\(746\) | −32.6930 | −1.19698 | ||||||||
\(747\) | −14.2101 | −0.519920 | ||||||||
\(748\) | −5.61445 | −0.205285 | ||||||||
\(749\) | −4.82125 | −0.176165 | ||||||||
\(750\) | 9.29628 | 0.339452 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | −8.64624 | −0.315296 | ||||||||
\(753\) | −1.16479 | −0.0424474 | ||||||||
\(754\) | 2.22609 | 0.0810694 | ||||||||
\(755\) | −18.3568 | −0.668073 | ||||||||
\(756\) | 6.26915 | 0.228007 | ||||||||
\(757\) | 10.5801 | 0.384540 | 0.192270 | − | 0.981342i | \(-0.438415\pi\) | ||||
0.192270 | + | 0.981342i | \(0.438415\pi\) | |||||||
\(758\) | 10.4963 | 0.381242 | ||||||||
\(759\) | −3.92330 | −0.142407 | ||||||||
\(760\) | 0.233900 | 0.00848445 | ||||||||
\(761\) | −46.0458 | −1.66916 | −0.834580 | − | 0.550887i | \(-0.814289\pi\) | ||||
−0.834580 | + | 0.550887i | \(0.814289\pi\) | |||||||
\(762\) | −5.35485 | −0.193986 | ||||||||
\(763\) | 19.6745 | 0.712263 | ||||||||
\(764\) | 4.91472 | 0.177809 | ||||||||
\(765\) | 18.6990 | 0.676063 | ||||||||
\(766\) | −23.9917 | −0.866854 | ||||||||
\(767\) | −17.5505 | −0.633711 | ||||||||
\(768\) | 0.785790 | 0.0283547 | ||||||||
\(769\) | −48.8308 | −1.76088 | −0.880442 | − | 0.474154i | \(-0.842754\pi\) | ||||
−0.880442 | + | 0.474154i | \(0.842754\pi\) | |||||||
\(770\) | 2.61412 | 0.0942063 | ||||||||
\(771\) | −14.0636 | −0.506488 | ||||||||
\(772\) | −8.26154 | −0.297339 | ||||||||
\(773\) | −29.0119 | −1.04349 | −0.521743 | − | 0.853103i | \(-0.674718\pi\) | ||||
−0.521743 | + | 0.853103i | \(0.674718\pi\) | |||||||
\(774\) | −21.2483 | −0.763755 | ||||||||
\(775\) | −3.70328 | −0.133026 | ||||||||
\(776\) | −12.8889 | −0.462685 | ||||||||
\(777\) | −0.934445 | −0.0335230 | ||||||||
\(778\) | 10.1775 | 0.364881 | ||||||||
\(779\) | −0.472425 | −0.0169264 | ||||||||
\(780\) | −1.48198 | −0.0530633 | ||||||||
\(781\) | −10.1564 | −0.363423 | ||||||||
\(782\) | −22.2185 | −0.794532 | ||||||||
\(783\) | −7.83866 | −0.280131 | ||||||||
\(784\) | −4.80299 | −0.171536 | ||||||||
\(785\) | −33.7916 | −1.20607 | ||||||||
\(786\) | 5.41185 | 0.193034 | ||||||||
\(787\) | −5.14685 | −0.183465 | −0.0917327 | − | 0.995784i | \(-0.529241\pi\) | ||||
−0.0917327 | + | 0.995784i | \(0.529241\pi\) | |||||||
\(788\) | 2.47513 | 0.0881729 | ||||||||
\(789\) | 0.150931 | 0.00537328 | ||||||||
\(790\) | −1.23582 | −0.0439685 | ||||||||
\(791\) | 18.0425 | 0.641519 | ||||||||
\(792\) | 2.67614 | 0.0950923 | ||||||||
\(793\) | −0.598059 | −0.0212377 | ||||||||
\(794\) | 25.6974 | 0.911966 | ||||||||
\(795\) | −9.05732 | −0.321230 | ||||||||
\(796\) | 14.8076 | 0.524841 | ||||||||
\(797\) | −11.2392 | −0.398112 | −0.199056 | − | 0.979988i | \(-0.563788\pi\) | ||||
−0.199056 | + | 0.979988i | \(0.563788\pi\) | |||||||
\(798\) | −0.173505 | −0.00614201 | ||||||||
\(799\) | 43.2181 | 1.52895 | ||||||||
\(800\) | 2.53463 | 0.0896128 | ||||||||
\(801\) | −14.3658 | −0.507590 | ||||||||
\(802\) | 6.43327 | 0.227167 | ||||||||
\(803\) | 10.4950 | 0.370361 | ||||||||
\(804\) | −8.69235 | −0.306555 | ||||||||
\(805\) | 10.3451 | 0.364615 | ||||||||
\(806\) | 1.75495 | 0.0618156 | ||||||||
\(807\) | 15.5036 | 0.545754 | ||||||||
\(808\) | −7.26692 | −0.255649 | ||||||||
\(809\) | −44.4379 | −1.56235 | −0.781176 | − | 0.624310i | \(-0.785380\pi\) | ||||
−0.781176 | + | 0.624310i | \(0.785380\pi\) | |||||||
\(810\) | −6.00436 | −0.210972 | ||||||||
\(811\) | 36.2901 | 1.27432 | 0.637159 | − | 0.770732i | \(-0.280110\pi\) | ||||
0.637159 | + | 0.770732i | \(0.280110\pi\) | |||||||
\(812\) | −2.74703 | −0.0964020 | ||||||||
\(813\) | −10.2428 | −0.359231 | ||||||||
\(814\) | −0.901157 | −0.0315855 | ||||||||
\(815\) | 30.8298 | 1.07992 | ||||||||
\(816\) | −3.92776 | −0.137499 | ||||||||
\(817\) | 1.32854 | 0.0464798 | ||||||||
\(818\) | −35.9996 | −1.25870 | ||||||||
\(819\) | −4.24179 | −0.148220 | ||||||||
\(820\) | 4.97948 | 0.173891 | ||||||||
\(821\) | −36.3438 | −1.26841 | −0.634204 | − | 0.773166i | \(-0.718672\pi\) | ||||
−0.634204 | + | 0.773166i | \(0.718672\pi\) | |||||||
\(822\) | 12.4775 | 0.435202 | ||||||||
\(823\) | −17.3625 | −0.605219 | −0.302610 | − | 0.953115i | \(-0.597858\pi\) | ||||
−0.302610 | + | 0.953115i | \(0.597858\pi\) | |||||||
\(824\) | −13.4787 | −0.469553 | ||||||||
\(825\) | −2.23713 | −0.0778867 | ||||||||
\(826\) | 21.6576 | 0.753564 | ||||||||
\(827\) | −30.9284 | −1.07548 | −0.537742 | − | 0.843109i | \(-0.680723\pi\) | ||||
−0.537742 | + | 0.843109i | \(0.680723\pi\) | |||||||
\(828\) | 10.5905 | 0.368045 | ||||||||
\(829\) | 32.2258 | 1.11925 | 0.559624 | − | 0.828747i | \(-0.310946\pi\) | ||||
0.559624 | + | 0.828747i | \(0.310946\pi\) | |||||||
\(830\) | −9.36479 | −0.325057 | ||||||||
\(831\) | −2.31226 | −0.0802115 | ||||||||
\(832\) | −1.20114 | −0.0416421 | ||||||||
\(833\) | 24.0077 | 0.831817 | ||||||||
\(834\) | 13.2508 | 0.458837 | ||||||||
\(835\) | 4.21282 | 0.145790 | ||||||||
\(836\) | −0.167324 | −0.00578703 | ||||||||
\(837\) | −6.17966 | −0.213600 | ||||||||
\(838\) | 6.88795 | 0.237940 | ||||||||
\(839\) | −12.9114 | −0.445750 | −0.222875 | − | 0.974847i | \(-0.571544\pi\) | ||||
−0.222875 | + | 0.974847i | \(0.571544\pi\) | |||||||
\(840\) | 1.82879 | 0.0630991 | ||||||||
\(841\) | −25.5652 | −0.881560 | ||||||||
\(842\) | 3.65448 | 0.125942 | ||||||||
\(843\) | 23.7705 | 0.818700 | ||||||||
\(844\) | −16.7938 | −0.578067 | ||||||||
\(845\) | −18.1466 | −0.624263 | ||||||||
\(846\) | −20.6000 | −0.708242 | ||||||||
\(847\) | 14.4345 | 0.495975 | ||||||||
\(848\) | −7.34095 | −0.252089 | ||||||||
\(849\) | −4.70356 | −0.161426 | ||||||||
\(850\) | −12.6693 | −0.434554 | ||||||||
\(851\) | −3.56622 | −0.122248 | ||||||||
\(852\) | −7.10519 | −0.243420 | ||||||||
\(853\) | 10.4481 | 0.357737 | 0.178869 | − | 0.983873i | \(-0.442756\pi\) | ||||
0.178869 | + | 0.983873i | \(0.442756\pi\) | |||||||
\(854\) | 0.738016 | 0.0252544 | ||||||||
\(855\) | 0.557275 | 0.0190584 | ||||||||
\(856\) | −3.25270 | −0.111175 | ||||||||
\(857\) | −16.8262 | −0.574773 | −0.287386 | − | 0.957815i | \(-0.592786\pi\) | ||||
−0.287386 | + | 0.957815i | \(0.592786\pi\) | |||||||
\(858\) | 1.06015 | 0.0361931 | ||||||||
\(859\) | −2.39566 | −0.0817388 | −0.0408694 | − | 0.999164i | \(-0.513013\pi\) | ||||
−0.0408694 | + | 0.999164i | \(0.513013\pi\) | |||||||
\(860\) | −14.0032 | −0.477504 | ||||||||
\(861\) | −3.69373 | −0.125882 | ||||||||
\(862\) | −33.2769 | −1.13342 | ||||||||
\(863\) | 16.1019 | 0.548114 | 0.274057 | − | 0.961714i | \(-0.411634\pi\) | ||||
0.274057 | + | 0.961714i | \(0.411634\pi\) | |||||||
\(864\) | 4.22954 | 0.143892 | ||||||||
\(865\) | −40.3567 | −1.37217 | ||||||||
\(866\) | 28.7825 | 0.978069 | ||||||||
\(867\) | 6.27439 | 0.213090 | ||||||||
\(868\) | −2.16564 | −0.0735067 | ||||||||
\(869\) | 0.884062 | 0.0299898 | ||||||||
\(870\) | −2.28663 | −0.0775240 | ||||||||
\(871\) | 13.2869 | 0.450211 | ||||||||
\(872\) | 13.2735 | 0.449499 | ||||||||
\(873\) | −30.7083 | −1.03932 | ||||||||
\(874\) | −0.662165 | −0.0223981 | ||||||||
\(875\) | 17.5355 | 0.592809 | ||||||||
\(876\) | 7.34209 | 0.248066 | ||||||||
\(877\) | −32.3171 | −1.09127 | −0.545635 | − | 0.838023i | \(-0.683712\pi\) | ||||
−0.545635 | + | 0.838023i | \(0.683712\pi\) | |||||||
\(878\) | −16.3681 | −0.552397 | ||||||||
\(879\) | 26.4285 | 0.891411 | ||||||||
\(880\) | 1.76364 | 0.0594523 | ||||||||
\(881\) | 33.6465 | 1.13358 | 0.566789 | − | 0.823863i | \(-0.308186\pi\) | ||||
0.566789 | + | 0.823863i | \(0.308186\pi\) | |||||||
\(882\) | −11.4433 | −0.385316 | ||||||||
\(883\) | −23.4966 | −0.790725 | −0.395363 | − | 0.918525i | \(-0.629381\pi\) | ||||
−0.395363 | + | 0.918525i | \(0.629381\pi\) | |||||||
\(884\) | 6.00388 | 0.201932 | ||||||||
\(885\) | 18.0278 | 0.605997 | ||||||||
\(886\) | 1.62213 | 0.0544967 | ||||||||
\(887\) | 17.2265 | 0.578408 | 0.289204 | − | 0.957267i | \(-0.406609\pi\) | ||||
0.289204 | + | 0.957267i | \(0.406609\pi\) | |||||||
\(888\) | −0.630432 | −0.0211559 | ||||||||
\(889\) | −10.1008 | −0.338771 | ||||||||
\(890\) | −9.46740 | −0.317348 | ||||||||
\(891\) | 4.29532 | 0.143899 | ||||||||
\(892\) | 23.4951 | 0.786675 | ||||||||
\(893\) | 1.28800 | 0.0431014 | ||||||||
\(894\) | −8.22442 | −0.275066 | ||||||||
\(895\) | 31.8210 | 1.06366 | ||||||||
\(896\) | 1.48223 | 0.0495178 | ||||||||
\(897\) | 4.19543 | 0.140081 | ||||||||
\(898\) | 4.57903 | 0.152804 | ||||||||
\(899\) | 2.70782 | 0.0903109 | ||||||||
\(900\) | 6.03885 | 0.201295 | ||||||||
\(901\) | 36.6936 | 1.22244 | ||||||||
\(902\) | −3.56215 | −0.118607 | ||||||||
\(903\) | 10.3874 | 0.345672 | ||||||||
\(904\) | 12.1726 | 0.404853 | ||||||||
\(905\) | −27.0636 | −0.899623 | ||||||||
\(906\) | 9.18677 | 0.305210 | ||||||||
\(907\) | −11.4601 | −0.380526 | −0.190263 | − | 0.981733i | \(-0.560934\pi\) | ||||
−0.190263 | + | 0.981733i | \(0.560934\pi\) | |||||||
\(908\) | 21.8781 | 0.726049 | ||||||||
\(909\) | −17.3137 | −0.574258 | ||||||||
\(910\) | −2.79544 | −0.0926680 | ||||||||
\(911\) | −9.82328 | −0.325460 | −0.162730 | − | 0.986671i | \(-0.552030\pi\) | ||||
−0.162730 | + | 0.986671i | \(0.552030\pi\) | |||||||
\(912\) | −0.117057 | −0.00387613 | ||||||||
\(913\) | 6.69925 | 0.221713 | ||||||||
\(914\) | 8.95623 | 0.296246 | ||||||||
\(915\) | 0.614324 | 0.0203089 | ||||||||
\(916\) | −26.4789 | −0.874888 | ||||||||
\(917\) | 10.2083 | 0.337109 | ||||||||
\(918\) | −21.1413 | −0.697766 | ||||||||
\(919\) | 28.8611 | 0.952040 | 0.476020 | − | 0.879434i | \(-0.342079\pi\) | ||||
0.476020 | + | 0.879434i | \(0.342079\pi\) | |||||||
\(920\) | 6.97939 | 0.230104 | ||||||||
\(921\) | −15.8524 | −0.522354 | ||||||||
\(922\) | −2.61266 | −0.0860433 | ||||||||
\(923\) | 10.8608 | 0.357489 | ||||||||
\(924\) | −1.30825 | −0.0430383 | ||||||||
\(925\) | −2.03351 | −0.0668614 | ||||||||
\(926\) | 39.3068 | 1.29170 | ||||||||
\(927\) | −32.1135 | −1.05474 | ||||||||
\(928\) | −1.85331 | −0.0608379 | ||||||||
\(929\) | 27.6531 | 0.907267 | 0.453634 | − | 0.891188i | \(-0.350127\pi\) | ||||
0.453634 | + | 0.891188i | \(0.350127\pi\) | |||||||
\(930\) | −1.80268 | −0.0591122 | ||||||||
\(931\) | 0.715487 | 0.0234491 | ||||||||
\(932\) | 3.58171 | 0.117323 | ||||||||
\(933\) | 21.0811 | 0.690164 | ||||||||
\(934\) | −15.6584 | −0.512360 | ||||||||
\(935\) | −8.81552 | −0.288298 | ||||||||
\(936\) | −2.86176 | −0.0935396 | ||||||||
\(937\) | −2.27959 | −0.0744709 | −0.0372354 | − | 0.999307i | \(-0.511855\pi\) | ||||
−0.0372354 | + | 0.999307i | \(0.511855\pi\) | |||||||
\(938\) | −16.3963 | −0.535359 | ||||||||
\(939\) | 5.49612 | 0.179359 | ||||||||
\(940\) | −13.5759 | −0.442797 | ||||||||
\(941\) | 11.8877 | 0.387526 | 0.193763 | − | 0.981048i | \(-0.437931\pi\) | ||||
0.193763 | + | 0.981048i | \(0.437931\pi\) | |||||||
\(942\) | 16.9112 | 0.550996 | ||||||||
\(943\) | −14.0968 | −0.459054 | ||||||||
\(944\) | 14.6115 | 0.475564 | ||||||||
\(945\) | 9.84350 | 0.320209 | ||||||||
\(946\) | 10.0174 | 0.325693 | ||||||||
\(947\) | −43.4093 | −1.41061 | −0.705306 | − | 0.708903i | \(-0.749191\pi\) | ||||
−0.705306 | + | 0.708903i | \(0.749191\pi\) | |||||||
\(948\) | 0.618472 | 0.0200870 | ||||||||
\(949\) | −11.2230 | −0.364313 | ||||||||
\(950\) | −0.377576 | −0.0122502 | ||||||||
\(951\) | 7.50718 | 0.243437 | ||||||||
\(952\) | −7.40890 | −0.240124 | ||||||||
\(953\) | −29.9829 | −0.971240 | −0.485620 | − | 0.874170i | \(-0.661406\pi\) | ||||
−0.485620 | + | 0.874170i | \(0.661406\pi\) | |||||||
\(954\) | −17.4901 | −0.566262 | ||||||||
\(955\) | 7.71685 | 0.249711 | ||||||||
\(956\) | 20.3035 | 0.656661 | ||||||||
\(957\) | 1.63578 | 0.0528771 | ||||||||
\(958\) | −20.5117 | −0.662703 | ||||||||
\(959\) | 23.5362 | 0.760023 | ||||||||
\(960\) | 1.23381 | 0.0398209 | ||||||||
\(961\) | −28.8653 | −0.931138 | ||||||||
\(962\) | 0.963664 | 0.0310698 | ||||||||
\(963\) | −7.74967 | −0.249730 | ||||||||
\(964\) | 6.95275 | 0.223933 | ||||||||
\(965\) | −12.9718 | −0.417578 | ||||||||
\(966\) | −5.17724 | −0.166575 | ||||||||
\(967\) | −3.59526 | −0.115616 | −0.0578078 | − | 0.998328i | \(-0.518411\pi\) | ||||
−0.0578078 | + | 0.998328i | \(0.518411\pi\) | |||||||
\(968\) | 9.73835 | 0.313003 | ||||||||
\(969\) | 0.585106 | 0.0187963 | ||||||||
\(970\) | −20.2375 | −0.649787 | ||||||||
\(971\) | 8.95642 | 0.287425 | 0.143713 | − | 0.989619i | \(-0.454096\pi\) | ||||
0.143713 | + | 0.989619i | \(0.454096\pi\) | |||||||
\(972\) | 15.6935 | 0.503371 | ||||||||
\(973\) | 24.9949 | 0.801299 | ||||||||
\(974\) | −38.7408 | −1.24134 | ||||||||
\(975\) | 2.39230 | 0.0766149 | ||||||||
\(976\) | 0.497909 | 0.0159377 | ||||||||
\(977\) | −33.3802 | −1.06793 | −0.533964 | − | 0.845507i | \(-0.679298\pi\) | ||||
−0.533964 | + | 0.845507i | \(0.679298\pi\) | |||||||
\(978\) | −15.4289 | −0.493363 | ||||||||
\(979\) | 6.77265 | 0.216455 | ||||||||
\(980\) | −7.54142 | −0.240902 | ||||||||
\(981\) | 31.6247 | 1.00970 | ||||||||
\(982\) | 18.7683 | 0.598919 | ||||||||
\(983\) | −5.74063 | −0.183098 | −0.0915489 | − | 0.995801i | \(-0.529182\pi\) | ||||
−0.0915489 | + | 0.995801i | \(0.529182\pi\) | |||||||
\(984\) | −2.49201 | −0.0794423 | ||||||||
\(985\) | 3.88633 | 0.123829 | ||||||||
\(986\) | 9.26375 | 0.295018 | ||||||||
\(987\) | 10.0705 | 0.320546 | ||||||||
\(988\) | 0.178930 | 0.00569253 | ||||||||
\(989\) | 39.6426 | 1.26056 | ||||||||
\(990\) | 4.20193 | 0.133546 | ||||||||
\(991\) | −18.4615 | −0.586450 | −0.293225 | − | 0.956044i | \(-0.594728\pi\) | ||||
−0.293225 | + | 0.956044i | \(0.594728\pi\) | |||||||
\(992\) | −1.46107 | −0.0463891 | ||||||||
\(993\) | 0.215838 | 0.00684940 | ||||||||
\(994\) | −13.4025 | −0.425101 | ||||||||
\(995\) | 23.2501 | 0.737078 | ||||||||
\(996\) | 4.68666 | 0.148503 | ||||||||
\(997\) | 11.5448 | 0.365629 | 0.182815 | − | 0.983147i | \(-0.441479\pi\) | ||||
0.182815 | + | 0.983147i | \(0.441479\pi\) | |||||||
\(998\) | 24.8176 | 0.785589 | ||||||||
\(999\) | −3.39332 | −0.107360 |
(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 | 1502.2.a.e.1.8 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1502.2.a.e.1.8 | ✓ | 11 | 1.1 | even | 1 | trivial |