Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 55 x^{10} + 32 x^{9} - 266 x^{8} + 13 x^{7} + 534 x^{6} - 141 x^{5} - 404 x^{4} + 98 x^{3} + 118 x^{2} - 16 x - 11 \) |
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 | 1.13 | ||
Root | \(2.62425\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.62425 | 1.85562 | 0.927812 | − | 0.373047i | \(-0.121687\pi\) | ||||
0.927812 | + | 0.373047i | \(0.121687\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.88668 | 2.44334 | ||||||||
\(5\) | 0.233370 | 0.104366 | 0.0521831 | − | 0.998638i | \(-0.483382\pi\) | ||||
0.0521831 | + | 0.998638i | \(0.483382\pi\) | |||||||
\(6\) | 2.62425 | 1.07135 | ||||||||
\(7\) | 1.03556 | 0.391404 | 0.195702 | − | 0.980663i | \(-0.437301\pi\) | ||||
0.195702 | + | 0.980663i | \(0.437301\pi\) | |||||||
\(8\) | 7.57538 | 2.67830 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.612421 | 0.193664 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 4.88668 | 1.41066 | ||||||||
\(13\) | 3.46134 | 0.960004 | 0.480002 | − | 0.877267i | \(-0.340636\pi\) | ||||
0.480002 | + | 0.877267i | \(0.340636\pi\) | |||||||
\(14\) | 2.71756 | 0.726300 | ||||||||
\(15\) | 0.233370 | 0.0602558 | ||||||||
\(16\) | 10.1063 | 2.52658 | ||||||||
\(17\) | 0.866180 | 0.210080 | 0.105040 | − | 0.994468i | \(-0.466503\pi\) | ||||
0.105040 | + | 0.994468i | \(0.466503\pi\) | |||||||
\(18\) | 2.62425 | 0.618541 | ||||||||
\(19\) | −6.81869 | −1.56431 | −0.782157 | − | 0.623081i | \(-0.785880\pi\) | ||||
−0.782157 | + | 0.623081i | \(0.785880\pi\) | |||||||
\(20\) | 1.14041 | 0.255002 | ||||||||
\(21\) | 1.03556 | 0.225977 | ||||||||
\(22\) | −2.62425 | −0.559492 | ||||||||
\(23\) | −2.06167 | −0.429888 | −0.214944 | − | 0.976626i | \(-0.568957\pi\) | ||||
−0.214944 | + | 0.976626i | \(0.568957\pi\) | |||||||
\(24\) | 7.57538 | 1.54632 | ||||||||
\(25\) | −4.94554 | −0.989108 | ||||||||
\(26\) | 9.08343 | 1.78141 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 5.06045 | 0.956335 | ||||||||
\(29\) | −6.06446 | −1.12614 | −0.563071 | − | 0.826408i | \(-0.690380\pi\) | ||||
−0.563071 | + | 0.826408i | \(0.690380\pi\) | |||||||
\(30\) | 0.612421 | 0.111812 | ||||||||
\(31\) | 0.640968 | 0.115121 | 0.0575606 | − | 0.998342i | \(-0.481668\pi\) | ||||
0.0575606 | + | 0.998342i | \(0.481668\pi\) | |||||||
\(32\) | 11.3707 | 2.01008 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 2.27307 | 0.389829 | ||||||||
\(35\) | 0.241668 | 0.0408494 | ||||||||
\(36\) | 4.88668 | 0.814447 | ||||||||
\(37\) | 6.49171 | 1.06723 | 0.533615 | − | 0.845728i | \(-0.320833\pi\) | ||||
0.533615 | + | 0.845728i | \(0.320833\pi\) | |||||||
\(38\) | −17.8939 | −2.90278 | ||||||||
\(39\) | 3.46134 | 0.554259 | ||||||||
\(40\) | 1.76787 | 0.279524 | ||||||||
\(41\) | −0.461254 | −0.0720357 | −0.0360178 | − | 0.999351i | \(-0.511467\pi\) | ||||
−0.0360178 | + | 0.999351i | \(0.511467\pi\) | |||||||
\(42\) | 2.71756 | 0.419329 | ||||||||
\(43\) | −5.84824 | −0.891849 | −0.445924 | − | 0.895071i | \(-0.647125\pi\) | ||||
−0.445924 | + | 0.895071i | \(0.647125\pi\) | |||||||
\(44\) | −4.88668 | −0.736695 | ||||||||
\(45\) | 0.233370 | 0.0347887 | ||||||||
\(46\) | −5.41033 | −0.797710 | ||||||||
\(47\) | 10.8361 | 1.58061 | 0.790307 | − | 0.612711i | \(-0.209921\pi\) | ||||
0.790307 | + | 0.612711i | \(0.209921\pi\) | |||||||
\(48\) | 10.1063 | 1.45872 | ||||||||
\(49\) | −5.92762 | −0.846803 | ||||||||
\(50\) | −12.9783 | −1.83541 | ||||||||
\(51\) | 0.866180 | 0.121290 | ||||||||
\(52\) | 16.9145 | 2.34562 | ||||||||
\(53\) | 5.93238 | 0.814875 | 0.407437 | − | 0.913233i | \(-0.366422\pi\) | ||||
0.407437 | + | 0.913233i | \(0.366422\pi\) | |||||||
\(54\) | 2.62425 | 0.357115 | ||||||||
\(55\) | −0.233370 | −0.0314676 | ||||||||
\(56\) | 7.84475 | 1.04830 | ||||||||
\(57\) | −6.81869 | −0.903157 | ||||||||
\(58\) | −15.9147 | −2.08970 | ||||||||
\(59\) | −13.8895 | −1.80826 | −0.904131 | − | 0.427256i | \(-0.859480\pi\) | ||||
−0.904131 | + | 0.427256i | \(0.859480\pi\) | |||||||
\(60\) | 1.14041 | 0.147226 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 1.68206 | 0.213622 | ||||||||
\(63\) | 1.03556 | 0.130468 | ||||||||
\(64\) | 9.62701 | 1.20338 | ||||||||
\(65\) | 0.807774 | 0.100192 | ||||||||
\(66\) | −2.62425 | −0.323023 | ||||||||
\(67\) | 5.49525 | 0.671352 | 0.335676 | − | 0.941978i | \(-0.391035\pi\) | ||||
0.335676 | + | 0.941978i | \(0.391035\pi\) | |||||||
\(68\) | 4.23275 | 0.513296 | ||||||||
\(69\) | −2.06167 | −0.248196 | ||||||||
\(70\) | 0.634198 | 0.0758011 | ||||||||
\(71\) | 10.9720 | 1.30213 | 0.651067 | − | 0.759020i | \(-0.274322\pi\) | ||||
0.651067 | + | 0.759020i | \(0.274322\pi\) | |||||||
\(72\) | 7.57538 | 0.892767 | ||||||||
\(73\) | −15.4334 | −1.80634 | −0.903172 | − | 0.429280i | \(-0.858767\pi\) | ||||
−0.903172 | + | 0.429280i | \(0.858767\pi\) | |||||||
\(74\) | 17.0359 | 1.98038 | ||||||||
\(75\) | −4.94554 | −0.571062 | ||||||||
\(76\) | −33.3208 | −3.82215 | ||||||||
\(77\) | −1.03556 | −0.118013 | ||||||||
\(78\) | 9.08343 | 1.02850 | ||||||||
\(79\) | 12.4523 | 1.40100 | 0.700498 | − | 0.713654i | \(-0.252961\pi\) | ||||
0.700498 | + | 0.713654i | \(0.252961\pi\) | |||||||
\(80\) | 2.35851 | 0.263689 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.21044 | −0.133671 | ||||||||
\(83\) | 4.62807 | 0.507997 | 0.253998 | − | 0.967205i | \(-0.418254\pi\) | ||||
0.253998 | + | 0.967205i | \(0.418254\pi\) | |||||||
\(84\) | 5.06045 | 0.552140 | ||||||||
\(85\) | 0.202140 | 0.0219252 | ||||||||
\(86\) | −15.3473 | −1.65494 | ||||||||
\(87\) | −6.06446 | −0.650179 | ||||||||
\(88\) | −7.57538 | −0.807538 | ||||||||
\(89\) | 4.71761 | 0.500066 | 0.250033 | − | 0.968237i | \(-0.419559\pi\) | ||||
0.250033 | + | 0.968237i | \(0.419559\pi\) | |||||||
\(90\) | 0.612421 | 0.0645548 | ||||||||
\(91\) | 3.58443 | 0.375750 | ||||||||
\(92\) | −10.0747 | −1.05036 | ||||||||
\(93\) | 0.640968 | 0.0664653 | ||||||||
\(94\) | 28.4368 | 2.93303 | ||||||||
\(95\) | −1.59128 | −0.163261 | ||||||||
\(96\) | 11.3707 | 1.16052 | ||||||||
\(97\) | −0.332084 | −0.0337180 | −0.0168590 | − | 0.999858i | \(-0.505367\pi\) | ||||
−0.0168590 | + | 0.999858i | \(0.505367\pi\) | |||||||
\(98\) | −15.5555 | −1.57135 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −24.1673 | −2.41673 | ||||||||
\(101\) | 12.3590 | 1.22977 | 0.614883 | − | 0.788618i | \(-0.289203\pi\) | ||||
0.614883 | + | 0.788618i | \(0.289203\pi\) | |||||||
\(102\) | 2.27307 | 0.225068 | ||||||||
\(103\) | 14.4756 | 1.42633 | 0.713163 | − | 0.700998i | \(-0.247262\pi\) | ||||
0.713163 | + | 0.700998i | \(0.247262\pi\) | |||||||
\(104\) | 26.2210 | 2.57118 | ||||||||
\(105\) | 0.241668 | 0.0235844 | ||||||||
\(106\) | 15.5680 | 1.51210 | ||||||||
\(107\) | −2.13786 | −0.206675 | −0.103337 | − | 0.994646i | \(-0.532952\pi\) | ||||
−0.103337 | + | 0.994646i | \(0.532952\pi\) | |||||||
\(108\) | 4.88668 | 0.470221 | ||||||||
\(109\) | −1.66386 | −0.159369 | −0.0796844 | − | 0.996820i | \(-0.525391\pi\) | ||||
−0.0796844 | + | 0.996820i | \(0.525391\pi\) | |||||||
\(110\) | −0.612421 | −0.0583920 | ||||||||
\(111\) | 6.49171 | 0.616165 | ||||||||
\(112\) | 10.4657 | 0.988914 | ||||||||
\(113\) | −16.6819 | −1.56930 | −0.784652 | − | 0.619936i | \(-0.787158\pi\) | ||||
−0.784652 | + | 0.619936i | \(0.787158\pi\) | |||||||
\(114\) | −17.8939 | −1.67592 | ||||||||
\(115\) | −0.481132 | −0.0448657 | ||||||||
\(116\) | −29.6351 | −2.75155 | ||||||||
\(117\) | 3.46134 | 0.320001 | ||||||||
\(118\) | −36.4496 | −3.35545 | ||||||||
\(119\) | 0.896981 | 0.0822261 | ||||||||
\(120\) | 1.76787 | 0.161383 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.62425 | −0.237588 | ||||||||
\(123\) | −0.461254 | −0.0415898 | ||||||||
\(124\) | 3.13221 | 0.281281 | ||||||||
\(125\) | −2.32099 | −0.207596 | ||||||||
\(126\) | 2.71756 | 0.242100 | ||||||||
\(127\) | −6.27466 | −0.556786 | −0.278393 | − | 0.960467i | \(-0.589802\pi\) | ||||
−0.278393 | + | 0.960467i | \(0.589802\pi\) | |||||||
\(128\) | 2.52221 | 0.222934 | ||||||||
\(129\) | −5.84824 | −0.514909 | ||||||||
\(130\) | 2.11980 | 0.185919 | ||||||||
\(131\) | 18.4332 | 1.61052 | 0.805259 | − | 0.592923i | \(-0.202026\pi\) | ||||
0.805259 | + | 0.592923i | \(0.202026\pi\) | |||||||
\(132\) | −4.88668 | −0.425331 | ||||||||
\(133\) | −7.06115 | −0.612279 | ||||||||
\(134\) | 14.4209 | 1.24578 | ||||||||
\(135\) | 0.233370 | 0.0200853 | ||||||||
\(136\) | 6.56165 | 0.562657 | ||||||||
\(137\) | −15.5912 | −1.33204 | −0.666022 | − | 0.745932i | \(-0.732004\pi\) | ||||
−0.666022 | + | 0.745932i | \(0.732004\pi\) | |||||||
\(138\) | −5.41033 | −0.460558 | ||||||||
\(139\) | −18.1623 | −1.54051 | −0.770255 | − | 0.637736i | \(-0.779871\pi\) | ||||
−0.770255 | + | 0.637736i | \(0.779871\pi\) | |||||||
\(140\) | 1.18096 | 0.0998090 | ||||||||
\(141\) | 10.8361 | 0.912568 | ||||||||
\(142\) | 28.7932 | 2.41627 | ||||||||
\(143\) | −3.46134 | −0.289452 | ||||||||
\(144\) | 10.1063 | 0.842193 | ||||||||
\(145\) | −1.41526 | −0.117531 | ||||||||
\(146\) | −40.5011 | −3.35189 | ||||||||
\(147\) | −5.92762 | −0.488902 | ||||||||
\(148\) | 31.7229 | 2.60761 | ||||||||
\(149\) | 8.50275 | 0.696573 | 0.348286 | − | 0.937388i | \(-0.386764\pi\) | ||||
0.348286 | + | 0.937388i | \(0.386764\pi\) | |||||||
\(150\) | −12.9783 | −1.05968 | ||||||||
\(151\) | −23.5234 | −1.91430 | −0.957152 | − | 0.289585i | \(-0.906483\pi\) | ||||
−0.957152 | + | 0.289585i | \(0.906483\pi\) | |||||||
\(152\) | −51.6541 | −4.18970 | ||||||||
\(153\) | 0.866180 | 0.0700265 | ||||||||
\(154\) | −2.71756 | −0.218988 | ||||||||
\(155\) | 0.149583 | 0.0120148 | ||||||||
\(156\) | 16.9145 | 1.35424 | ||||||||
\(157\) | −15.5352 | −1.23984 | −0.619922 | − | 0.784663i | \(-0.712836\pi\) | ||||
−0.619922 | + | 0.784663i | \(0.712836\pi\) | |||||||
\(158\) | 32.6780 | 2.59972 | ||||||||
\(159\) | 5.93238 | 0.470468 | ||||||||
\(160\) | 2.65359 | 0.209785 | ||||||||
\(161\) | −2.13498 | −0.168260 | ||||||||
\(162\) | 2.62425 | 0.206180 | ||||||||
\(163\) | 3.93029 | 0.307844 | 0.153922 | − | 0.988083i | \(-0.450809\pi\) | ||||
0.153922 | + | 0.988083i | \(0.450809\pi\) | |||||||
\(164\) | −2.25400 | −0.176008 | ||||||||
\(165\) | −0.233370 | −0.0181678 | ||||||||
\(166\) | 12.1452 | 0.942651 | ||||||||
\(167\) | −1.83634 | −0.142100 | −0.0710502 | − | 0.997473i | \(-0.522635\pi\) | ||||
−0.0710502 | + | 0.997473i | \(0.522635\pi\) | |||||||
\(168\) | 7.84475 | 0.605236 | ||||||||
\(169\) | −1.01910 | −0.0783920 | ||||||||
\(170\) | 0.530467 | 0.0406850 | ||||||||
\(171\) | −6.81869 | −0.521438 | ||||||||
\(172\) | −28.5785 | −2.17909 | ||||||||
\(173\) | 10.3886 | 0.789834 | 0.394917 | − | 0.918717i | \(-0.370773\pi\) | ||||
0.394917 | + | 0.918717i | \(0.370773\pi\) | |||||||
\(174\) | −15.9147 | −1.20649 | ||||||||
\(175\) | −5.12140 | −0.387141 | ||||||||
\(176\) | −10.1063 | −0.761792 | ||||||||
\(177\) | −13.8895 | −1.04400 | ||||||||
\(178\) | 12.3802 | 0.927934 | ||||||||
\(179\) | 17.4905 | 1.30730 | 0.653652 | − | 0.756795i | \(-0.273236\pi\) | ||||
0.653652 | + | 0.756795i | \(0.273236\pi\) | |||||||
\(180\) | 1.14041 | 0.0850008 | ||||||||
\(181\) | −14.8136 | −1.10108 | −0.550542 | − | 0.834807i | \(-0.685579\pi\) | ||||
−0.550542 | + | 0.834807i | \(0.685579\pi\) | |||||||
\(182\) | 9.40643 | 0.697251 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −15.6179 | −1.15137 | ||||||||
\(185\) | 1.51497 | 0.111383 | ||||||||
\(186\) | 1.68206 | 0.123335 | ||||||||
\(187\) | −0.866180 | −0.0633414 | ||||||||
\(188\) | 52.9528 | 3.86198 | ||||||||
\(189\) | 1.03556 | 0.0753258 | ||||||||
\(190\) | −4.17591 | −0.302952 | ||||||||
\(191\) | −6.59920 | −0.477501 | −0.238751 | − | 0.971081i | \(-0.576738\pi\) | ||||
−0.238751 | + | 0.971081i | \(0.576738\pi\) | |||||||
\(192\) | 9.62701 | 0.694770 | ||||||||
\(193\) | −18.6461 | −1.34218 | −0.671089 | − | 0.741377i | \(-0.734173\pi\) | ||||
−0.671089 | + | 0.741377i | \(0.734173\pi\) | |||||||
\(194\) | −0.871471 | −0.0625680 | ||||||||
\(195\) | 0.807774 | 0.0578459 | ||||||||
\(196\) | −28.9664 | −2.06903 | ||||||||
\(197\) | 4.09897 | 0.292039 | 0.146020 | − | 0.989282i | \(-0.453354\pi\) | ||||
0.146020 | + | 0.989282i | \(0.453354\pi\) | |||||||
\(198\) | −2.62425 | −0.186497 | ||||||||
\(199\) | 13.0650 | 0.926151 | 0.463076 | − | 0.886319i | \(-0.346746\pi\) | ||||
0.463076 | + | 0.886319i | \(0.346746\pi\) | |||||||
\(200\) | −37.4643 | −2.64913 | ||||||||
\(201\) | 5.49525 | 0.387605 | ||||||||
\(202\) | 32.4331 | 2.28198 | ||||||||
\(203\) | −6.28011 | −0.440777 | ||||||||
\(204\) | 4.23275 | 0.296352 | ||||||||
\(205\) | −0.107643 | −0.00751809 | ||||||||
\(206\) | 37.9876 | 2.64672 | ||||||||
\(207\) | −2.06167 | −0.143296 | ||||||||
\(208\) | 34.9814 | 2.42553 | ||||||||
\(209\) | 6.81869 | 0.471658 | ||||||||
\(210\) | 0.634198 | 0.0437638 | ||||||||
\(211\) | 25.2541 | 1.73856 | 0.869281 | − | 0.494318i | \(-0.164582\pi\) | ||||
0.869281 | + | 0.494318i | \(0.164582\pi\) | |||||||
\(212\) | 28.9897 | 1.99102 | ||||||||
\(213\) | 10.9720 | 0.751787 | ||||||||
\(214\) | −5.61028 | −0.383511 | ||||||||
\(215\) | −1.36480 | −0.0930789 | ||||||||
\(216\) | 7.57538 | 0.515439 | ||||||||
\(217\) | 0.663760 | 0.0450590 | ||||||||
\(218\) | −4.36638 | −0.295729 | ||||||||
\(219\) | −15.4334 | −1.04289 | ||||||||
\(220\) | −1.14041 | −0.0768861 | ||||||||
\(221\) | 2.99815 | 0.201677 | ||||||||
\(222\) | 17.0359 | 1.14337 | ||||||||
\(223\) | 0.184928 | 0.0123837 | 0.00619186 | − | 0.999981i | \(-0.498029\pi\) | ||||
0.00619186 | + | 0.999981i | \(0.498029\pi\) | |||||||
\(224\) | 11.7751 | 0.786755 | ||||||||
\(225\) | −4.94554 | −0.329703 | ||||||||
\(226\) | −43.7775 | −2.91204 | ||||||||
\(227\) | −10.8433 | −0.719698 | −0.359849 | − | 0.933011i | \(-0.617172\pi\) | ||||
−0.359849 | + | 0.933011i | \(0.617172\pi\) | |||||||
\(228\) | −33.3208 | −2.20672 | ||||||||
\(229\) | 9.68390 | 0.639930 | 0.319965 | − | 0.947429i | \(-0.396329\pi\) | ||||
0.319965 | + | 0.947429i | \(0.396329\pi\) | |||||||
\(230\) | −1.26261 | −0.0832540 | ||||||||
\(231\) | −1.03556 | −0.0681348 | ||||||||
\(232\) | −45.9406 | −3.01615 | ||||||||
\(233\) | −10.8919 | −0.713555 | −0.356778 | − | 0.934189i | \(-0.616125\pi\) | ||||
−0.356778 | + | 0.934189i | \(0.616125\pi\) | |||||||
\(234\) | 9.08343 | 0.593802 | ||||||||
\(235\) | 2.52883 | 0.164963 | ||||||||
\(236\) | −67.8737 | −4.41820 | ||||||||
\(237\) | 12.4523 | 0.808866 | ||||||||
\(238\) | 2.35390 | 0.152581 | ||||||||
\(239\) | 7.56308 | 0.489215 | 0.244607 | − | 0.969622i | \(-0.421341\pi\) | ||||
0.244607 | + | 0.969622i | \(0.421341\pi\) | |||||||
\(240\) | 2.35851 | 0.152241 | ||||||||
\(241\) | 12.1001 | 0.779439 | 0.389720 | − | 0.920934i | \(-0.372572\pi\) | ||||
0.389720 | + | 0.920934i | \(0.372572\pi\) | |||||||
\(242\) | 2.62425 | 0.168693 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.88668 | −0.312838 | ||||||||
\(245\) | −1.38333 | −0.0883776 | ||||||||
\(246\) | −1.21044 | −0.0771751 | ||||||||
\(247\) | −23.6018 | −1.50175 | ||||||||
\(248\) | 4.85558 | 0.308329 | ||||||||
\(249\) | 4.62807 | 0.293292 | ||||||||
\(250\) | −6.09085 | −0.385219 | ||||||||
\(251\) | −14.5210 | −0.916557 | −0.458278 | − | 0.888809i | \(-0.651534\pi\) | ||||
−0.458278 | + | 0.888809i | \(0.651534\pi\) | |||||||
\(252\) | 5.06045 | 0.318778 | ||||||||
\(253\) | 2.06167 | 0.129616 | ||||||||
\(254\) | −16.4663 | −1.03319 | ||||||||
\(255\) | 0.202140 | 0.0126585 | ||||||||
\(256\) | −12.6351 | −0.789695 | ||||||||
\(257\) | −1.95557 | −0.121985 | −0.0609924 | − | 0.998138i | \(-0.519427\pi\) | ||||
−0.0609924 | + | 0.998138i | \(0.519427\pi\) | |||||||
\(258\) | −15.3473 | −0.955478 | ||||||||
\(259\) | 6.72254 | 0.417718 | ||||||||
\(260\) | 3.94733 | 0.244803 | ||||||||
\(261\) | −6.06446 | −0.375381 | ||||||||
\(262\) | 48.3734 | 2.98852 | ||||||||
\(263\) | −5.37410 | −0.331381 | −0.165691 | − | 0.986178i | \(-0.552985\pi\) | ||||
−0.165691 | + | 0.986178i | \(0.552985\pi\) | |||||||
\(264\) | −7.57538 | −0.466232 | ||||||||
\(265\) | 1.38444 | 0.0850454 | ||||||||
\(266\) | −18.5302 | −1.13616 | ||||||||
\(267\) | 4.71761 | 0.288713 | ||||||||
\(268\) | 26.8536 | 1.64034 | ||||||||
\(269\) | −14.9982 | −0.914459 | −0.457229 | − | 0.889349i | \(-0.651158\pi\) | ||||
−0.457229 | + | 0.889349i | \(0.651158\pi\) | |||||||
\(270\) | 0.612421 | 0.0372707 | ||||||||
\(271\) | 20.1090 | 1.22153 | 0.610766 | − | 0.791811i | \(-0.290862\pi\) | ||||
0.610766 | + | 0.791811i | \(0.290862\pi\) | |||||||
\(272\) | 8.75389 | 0.530783 | ||||||||
\(273\) | 3.58443 | 0.216939 | ||||||||
\(274\) | −40.9151 | −2.47177 | ||||||||
\(275\) | 4.94554 | 0.298227 | ||||||||
\(276\) | −10.0747 | −0.606427 | ||||||||
\(277\) | −9.56683 | −0.574815 | −0.287408 | − | 0.957808i | \(-0.592793\pi\) | ||||
−0.287408 | + | 0.957808i | \(0.592793\pi\) | |||||||
\(278\) | −47.6625 | −2.85861 | ||||||||
\(279\) | 0.640968 | 0.0383738 | ||||||||
\(280\) | 1.83073 | 0.109407 | ||||||||
\(281\) | 27.4378 | 1.63680 | 0.818402 | − | 0.574646i | \(-0.194860\pi\) | ||||
0.818402 | + | 0.574646i | \(0.194860\pi\) | |||||||
\(282\) | 28.4368 | 1.69338 | ||||||||
\(283\) | 21.0886 | 1.25358 | 0.626792 | − | 0.779186i | \(-0.284367\pi\) | ||||
0.626792 | + | 0.779186i | \(0.284367\pi\) | |||||||
\(284\) | 53.6166 | 3.18156 | ||||||||
\(285\) | −1.59128 | −0.0942591 | ||||||||
\(286\) | −9.08343 | −0.537114 | ||||||||
\(287\) | −0.477655 | −0.0281951 | ||||||||
\(288\) | 11.3707 | 0.670027 | ||||||||
\(289\) | −16.2497 | −0.955867 | ||||||||
\(290\) | −3.71400 | −0.218094 | ||||||||
\(291\) | −0.332084 | −0.0194671 | ||||||||
\(292\) | −75.4182 | −4.41351 | ||||||||
\(293\) | 10.8811 | 0.635679 | 0.317840 | − | 0.948144i | \(-0.397043\pi\) | ||||
0.317840 | + | 0.948144i | \(0.397043\pi\) | |||||||
\(294\) | −15.5555 | −0.907218 | ||||||||
\(295\) | −3.24140 | −0.188721 | ||||||||
\(296\) | 49.1771 | 2.85836 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 22.3133 | 1.29258 | ||||||||
\(299\) | −7.13615 | −0.412694 | ||||||||
\(300\) | −24.1673 | −1.39530 | ||||||||
\(301\) | −6.05620 | −0.349074 | ||||||||
\(302\) | −61.7312 | −3.55223 | ||||||||
\(303\) | 12.3590 | 0.710006 | ||||||||
\(304\) | −68.9118 | −3.95236 | ||||||||
\(305\) | −0.233370 | −0.0133627 | ||||||||
\(306\) | 2.27307 | 0.129943 | ||||||||
\(307\) | −7.26799 | −0.414806 | −0.207403 | − | 0.978256i | \(-0.566501\pi\) | ||||
−0.207403 | + | 0.978256i | \(0.566501\pi\) | |||||||
\(308\) | −5.06045 | −0.288346 | ||||||||
\(309\) | 14.4756 | 0.823490 | ||||||||
\(310\) | 0.392542 | 0.0222949 | ||||||||
\(311\) | −0.304014 | −0.0172391 | −0.00861953 | − | 0.999963i | \(-0.502744\pi\) | ||||
−0.00861953 | + | 0.999963i | \(0.502744\pi\) | |||||||
\(312\) | 26.2210 | 1.48447 | ||||||||
\(313\) | 30.5243 | 1.72533 | 0.862667 | − | 0.505773i | \(-0.168792\pi\) | ||||
0.862667 | + | 0.505773i | \(0.168792\pi\) | |||||||
\(314\) | −40.7683 | −2.30069 | ||||||||
\(315\) | 0.241668 | 0.0136165 | ||||||||
\(316\) | 60.8506 | 3.42311 | ||||||||
\(317\) | 0.909394 | 0.0510767 | 0.0255383 | − | 0.999674i | \(-0.491870\pi\) | ||||
0.0255383 | + | 0.999674i | \(0.491870\pi\) | |||||||
\(318\) | 15.5680 | 0.873012 | ||||||||
\(319\) | 6.06446 | 0.339545 | ||||||||
\(320\) | 2.24665 | 0.125592 | ||||||||
\(321\) | −2.13786 | −0.119324 | ||||||||
\(322\) | −5.60272 | −0.312227 | ||||||||
\(323\) | −5.90621 | −0.328630 | ||||||||
\(324\) | 4.88668 | 0.271482 | ||||||||
\(325\) | −17.1182 | −0.949548 | ||||||||
\(326\) | 10.3141 | 0.571244 | ||||||||
\(327\) | −1.66386 | −0.0920116 | ||||||||
\(328\) | −3.49417 | −0.192933 | ||||||||
\(329\) | 11.2215 | 0.618659 | ||||||||
\(330\) | −0.612421 | −0.0337127 | ||||||||
\(331\) | 20.7795 | 1.14215 | 0.571073 | − | 0.820899i | \(-0.306527\pi\) | ||||
0.571073 | + | 0.820899i | \(0.306527\pi\) | |||||||
\(332\) | 22.6159 | 1.24121 | ||||||||
\(333\) | 6.49171 | 0.355743 | ||||||||
\(334\) | −4.81902 | −0.263685 | ||||||||
\(335\) | 1.28243 | 0.0700664 | ||||||||
\(336\) | 10.4657 | 0.570950 | ||||||||
\(337\) | −7.77395 | −0.423474 | −0.211737 | − | 0.977327i | \(-0.567912\pi\) | ||||
−0.211737 | + | 0.977327i | \(0.567912\pi\) | |||||||
\(338\) | −2.67436 | −0.145466 | ||||||||
\(339\) | −16.6819 | −0.906038 | ||||||||
\(340\) | 0.987797 | 0.0535708 | ||||||||
\(341\) | −0.640968 | −0.0347104 | ||||||||
\(342\) | −17.8939 | −0.967593 | ||||||||
\(343\) | −13.3873 | −0.722847 | ||||||||
\(344\) | −44.3027 | −2.38864 | ||||||||
\(345\) | −0.481132 | −0.0259033 | ||||||||
\(346\) | 27.2624 | 1.46564 | ||||||||
\(347\) | 12.8645 | 0.690602 | 0.345301 | − | 0.938492i | \(-0.387777\pi\) | ||||
0.345301 | + | 0.938492i | \(0.387777\pi\) | |||||||
\(348\) | −29.6351 | −1.58861 | ||||||||
\(349\) | 14.3781 | 0.769644 | 0.384822 | − | 0.922991i | \(-0.374263\pi\) | ||||
0.384822 | + | 0.922991i | \(0.374263\pi\) | |||||||
\(350\) | −13.4398 | −0.718388 | ||||||||
\(351\) | 3.46134 | 0.184753 | ||||||||
\(352\) | −11.3707 | −0.606062 | ||||||||
\(353\) | 1.41907 | 0.0755294 | 0.0377647 | − | 0.999287i | \(-0.487976\pi\) | ||||
0.0377647 | + | 0.999287i | \(0.487976\pi\) | |||||||
\(354\) | −36.4496 | −1.93727 | ||||||||
\(355\) | 2.56053 | 0.135899 | ||||||||
\(356\) | 23.0535 | 1.22183 | ||||||||
\(357\) | 0.896981 | 0.0474733 | ||||||||
\(358\) | 45.8995 | 2.42587 | ||||||||
\(359\) | −0.867127 | −0.0457652 | −0.0228826 | − | 0.999738i | \(-0.507284\pi\) | ||||
−0.0228826 | + | 0.999738i | \(0.507284\pi\) | |||||||
\(360\) | 1.76787 | 0.0931747 | ||||||||
\(361\) | 27.4945 | 1.44708 | ||||||||
\(362\) | −38.8745 | −2.04320 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 17.5160 | 0.918085 | ||||||||
\(365\) | −3.60169 | −0.188521 | ||||||||
\(366\) | −2.62425 | −0.137172 | ||||||||
\(367\) | 37.3721 | 1.95081 | 0.975405 | − | 0.220421i | \(-0.0707432\pi\) | ||||
0.975405 | + | 0.220421i | \(0.0707432\pi\) | |||||||
\(368\) | −20.8359 | −1.08615 | ||||||||
\(369\) | −0.461254 | −0.0240119 | ||||||||
\(370\) | 3.97566 | 0.206685 | ||||||||
\(371\) | 6.14333 | 0.318946 | ||||||||
\(372\) | 3.13221 | 0.162397 | ||||||||
\(373\) | −18.3417 | −0.949695 | −0.474848 | − | 0.880068i | \(-0.657497\pi\) | ||||
−0.474848 | + | 0.880068i | \(0.657497\pi\) | |||||||
\(374\) | −2.27307 | −0.117538 | ||||||||
\(375\) | −2.32099 | −0.119855 | ||||||||
\(376\) | 82.0879 | 4.23336 | ||||||||
\(377\) | −20.9912 | −1.08110 | ||||||||
\(378\) | 2.71756 | 0.139776 | ||||||||
\(379\) | −8.69436 | −0.446599 | −0.223300 | − | 0.974750i | \(-0.571683\pi\) | ||||
−0.223300 | + | 0.974750i | \(0.571683\pi\) | |||||||
\(380\) | −7.77606 | −0.398904 | ||||||||
\(381\) | −6.27466 | −0.321460 | ||||||||
\(382\) | −17.3179 | −0.886063 | ||||||||
\(383\) | −19.6485 | −1.00399 | −0.501997 | − | 0.864870i | \(-0.667401\pi\) | ||||
−0.501997 | + | 0.864870i | \(0.667401\pi\) | |||||||
\(384\) | 2.52221 | 0.128711 | ||||||||
\(385\) | −0.241668 | −0.0123166 | ||||||||
\(386\) | −48.9321 | −2.49058 | ||||||||
\(387\) | −5.84824 | −0.297283 | ||||||||
\(388\) | −1.62279 | −0.0823847 | ||||||||
\(389\) | 27.9899 | 1.41914 | 0.709571 | − | 0.704633i | \(-0.248889\pi\) | ||||
0.709571 | + | 0.704633i | \(0.248889\pi\) | |||||||
\(390\) | 2.11980 | 0.107340 | ||||||||
\(391\) | −1.78578 | −0.0903107 | ||||||||
\(392\) | −44.9040 | −2.26799 | ||||||||
\(393\) | 18.4332 | 0.929833 | ||||||||
\(394\) | 10.7567 | 0.541915 | ||||||||
\(395\) | 2.90600 | 0.146217 | ||||||||
\(396\) | −4.88668 | −0.245565 | ||||||||
\(397\) | 5.52183 | 0.277133 | 0.138566 | − | 0.990353i | \(-0.455751\pi\) | ||||
0.138566 | + | 0.990353i | \(0.455751\pi\) | |||||||
\(398\) | 34.2858 | 1.71859 | ||||||||
\(399\) | −7.06115 | −0.353500 | ||||||||
\(400\) | −49.9812 | −2.49906 | ||||||||
\(401\) | 14.3933 | 0.718768 | 0.359384 | − | 0.933190i | \(-0.382987\pi\) | ||||
0.359384 | + | 0.933190i | \(0.382987\pi\) | |||||||
\(402\) | 14.4209 | 0.719249 | ||||||||
\(403\) | 2.21861 | 0.110517 | ||||||||
\(404\) | 60.3945 | 3.00474 | ||||||||
\(405\) | 0.233370 | 0.0115962 | ||||||||
\(406\) | −16.4806 | −0.817917 | ||||||||
\(407\) | −6.49171 | −0.321782 | ||||||||
\(408\) | 6.56165 | 0.324850 | ||||||||
\(409\) | 17.9215 | 0.886160 | 0.443080 | − | 0.896482i | \(-0.353886\pi\) | ||||
0.443080 | + | 0.896482i | \(0.353886\pi\) | |||||||
\(410\) | −0.282481 | −0.0139508 | ||||||||
\(411\) | −15.5912 | −0.769056 | ||||||||
\(412\) | 70.7378 | 3.48500 | ||||||||
\(413\) | −14.3834 | −0.707761 | ||||||||
\(414\) | −5.41033 | −0.265903 | ||||||||
\(415\) | 1.08005 | 0.0530177 | ||||||||
\(416\) | 39.3580 | 1.92969 | ||||||||
\(417\) | −18.1623 | −0.889414 | ||||||||
\(418\) | 17.8939 | 0.875221 | ||||||||
\(419\) | 26.7628 | 1.30745 | 0.653724 | − | 0.756733i | \(-0.273206\pi\) | ||||
0.653724 | + | 0.756733i | \(0.273206\pi\) | |||||||
\(420\) | 1.18096 | 0.0576248 | ||||||||
\(421\) | −27.0091 | −1.31634 | −0.658172 | − | 0.752867i | \(-0.728670\pi\) | ||||
−0.658172 | + | 0.752867i | \(0.728670\pi\) | |||||||
\(422\) | 66.2730 | 3.22612 | ||||||||
\(423\) | 10.8361 | 0.526872 | ||||||||
\(424\) | 44.9400 | 2.18248 | ||||||||
\(425\) | −4.28373 | −0.207791 | ||||||||
\(426\) | 28.7932 | 1.39504 | ||||||||
\(427\) | −1.03556 | −0.0501142 | ||||||||
\(428\) | −10.4471 | −0.504978 | ||||||||
\(429\) | −3.46134 | −0.167115 | ||||||||
\(430\) | −3.58159 | −0.172719 | ||||||||
\(431\) | −6.61296 | −0.318535 | −0.159267 | − | 0.987235i | \(-0.550913\pi\) | ||||
−0.159267 | + | 0.987235i | \(0.550913\pi\) | |||||||
\(432\) | 10.1063 | 0.486240 | ||||||||
\(433\) | 6.98921 | 0.335880 | 0.167940 | − | 0.985797i | \(-0.446289\pi\) | ||||
0.167940 | + | 0.985797i | \(0.446289\pi\) | |||||||
\(434\) | 1.74187 | 0.0836125 | ||||||||
\(435\) | −1.41526 | −0.0678567 | ||||||||
\(436\) | −8.13075 | −0.389392 | ||||||||
\(437\) | 14.0579 | 0.672479 | ||||||||
\(438\) | −40.5011 | −1.93522 | ||||||||
\(439\) | 4.82441 | 0.230256 | 0.115128 | − | 0.993351i | \(-0.463272\pi\) | ||||
0.115128 | + | 0.993351i | \(0.463272\pi\) | |||||||
\(440\) | −1.76787 | −0.0842797 | ||||||||
\(441\) | −5.92762 | −0.282268 | ||||||||
\(442\) | 7.86789 | 0.374237 | ||||||||
\(443\) | −7.14384 | −0.339414 | −0.169707 | − | 0.985495i | \(-0.554282\pi\) | ||||
−0.169707 | + | 0.985495i | \(0.554282\pi\) | |||||||
\(444\) | 31.7229 | 1.50550 | ||||||||
\(445\) | 1.10095 | 0.0521900 | ||||||||
\(446\) | 0.485298 | 0.0229795 | ||||||||
\(447\) | 8.50275 | 0.402166 | ||||||||
\(448\) | 9.96933 | 0.471007 | ||||||||
\(449\) | −2.81996 | −0.133082 | −0.0665410 | − | 0.997784i | \(-0.521196\pi\) | ||||
−0.0665410 | + | 0.997784i | \(0.521196\pi\) | |||||||
\(450\) | −12.9783 | −0.611804 | ||||||||
\(451\) | 0.461254 | 0.0217196 | ||||||||
\(452\) | −81.5193 | −3.83435 | ||||||||
\(453\) | −23.5234 | −1.10522 | ||||||||
\(454\) | −28.4556 | −1.33549 | ||||||||
\(455\) | 0.836497 | 0.0392156 | ||||||||
\(456\) | −51.6541 | −2.41893 | ||||||||
\(457\) | −21.3915 | −1.00065 | −0.500326 | − | 0.865837i | \(-0.666786\pi\) | ||||
−0.500326 | + | 0.865837i | \(0.666786\pi\) | |||||||
\(458\) | 25.4130 | 1.18747 | ||||||||
\(459\) | 0.866180 | 0.0404298 | ||||||||
\(460\) | −2.35114 | −0.109622 | ||||||||
\(461\) | 2.40884 | 0.112191 | 0.0560954 | − | 0.998425i | \(-0.482135\pi\) | ||||
0.0560954 | + | 0.998425i | \(0.482135\pi\) | |||||||
\(462\) | −2.71756 | −0.126433 | ||||||||
\(463\) | −27.7917 | −1.29159 | −0.645794 | − | 0.763512i | \(-0.723474\pi\) | ||||
−0.645794 | + | 0.763512i | \(0.723474\pi\) | |||||||
\(464\) | −61.2894 | −2.84529 | ||||||||
\(465\) | 0.149583 | 0.00693673 | ||||||||
\(466\) | −28.5832 | −1.32409 | ||||||||
\(467\) | −6.65416 | −0.307918 | −0.153959 | − | 0.988077i | \(-0.549202\pi\) | ||||
−0.153959 | + | 0.988077i | \(0.549202\pi\) | |||||||
\(468\) | 16.9145 | 0.781873 | ||||||||
\(469\) | 5.69065 | 0.262770 | ||||||||
\(470\) | 6.63628 | 0.306109 | ||||||||
\(471\) | −15.5352 | −0.715825 | ||||||||
\(472\) | −105.218 | −4.84307 | ||||||||
\(473\) | 5.84824 | 0.268903 | ||||||||
\(474\) | 32.6780 | 1.50095 | ||||||||
\(475\) | 33.7221 | 1.54727 | ||||||||
\(476\) | 4.38326 | 0.200906 | ||||||||
\(477\) | 5.93238 | 0.271625 | ||||||||
\(478\) | 19.8474 | 0.907799 | ||||||||
\(479\) | 9.11561 | 0.416503 | 0.208251 | − | 0.978075i | \(-0.433223\pi\) | ||||
0.208251 | + | 0.978075i | \(0.433223\pi\) | |||||||
\(480\) | 2.65359 | 0.121119 | ||||||||
\(481\) | 22.4700 | 1.02455 | ||||||||
\(482\) | 31.7538 | 1.44635 | ||||||||
\(483\) | −2.13498 | −0.0971449 | ||||||||
\(484\) | 4.88668 | 0.222122 | ||||||||
\(485\) | −0.0774984 | −0.00351902 | ||||||||
\(486\) | 2.62425 | 0.119038 | ||||||||
\(487\) | −4.97655 | −0.225509 | −0.112755 | − | 0.993623i | \(-0.535967\pi\) | ||||
−0.112755 | + | 0.993623i | \(0.535967\pi\) | |||||||
\(488\) | −7.57538 | −0.342921 | ||||||||
\(489\) | 3.93029 | 0.177734 | ||||||||
\(490\) | −3.63020 | −0.163996 | ||||||||
\(491\) | −0.371810 | −0.0167795 | −0.00838977 | − | 0.999965i | \(-0.502671\pi\) | ||||
−0.00838977 | + | 0.999965i | \(0.502671\pi\) | |||||||
\(492\) | −2.25400 | −0.101618 | ||||||||
\(493\) | −5.25292 | −0.236580 | ||||||||
\(494\) | −61.9371 | −2.78668 | ||||||||
\(495\) | −0.233370 | −0.0104892 | ||||||||
\(496\) | 6.47783 | 0.290863 | ||||||||
\(497\) | 11.3621 | 0.509661 | ||||||||
\(498\) | 12.1452 | 0.544240 | ||||||||
\(499\) | −24.9013 | −1.11474 | −0.557368 | − | 0.830266i | \(-0.688189\pi\) | ||||
−0.557368 | + | 0.830266i | \(0.688189\pi\) | |||||||
\(500\) | −11.3419 | −0.507227 | ||||||||
\(501\) | −1.83634 | −0.0820417 | ||||||||
\(502\) | −38.1067 | −1.70078 | ||||||||
\(503\) | −4.42508 | −0.197305 | −0.0986524 | − | 0.995122i | \(-0.531453\pi\) | ||||
−0.0986524 | + | 0.995122i | \(0.531453\pi\) | |||||||
\(504\) | 7.84475 | 0.349433 | ||||||||
\(505\) | 2.88422 | 0.128346 | ||||||||
\(506\) | 5.41033 | 0.240519 | ||||||||
\(507\) | −1.01910 | −0.0452596 | ||||||||
\(508\) | −30.6623 | −1.36042 | ||||||||
\(509\) | 32.5147 | 1.44119 | 0.720595 | − | 0.693356i | \(-0.243869\pi\) | ||||
0.720595 | + | 0.693356i | \(0.243869\pi\) | |||||||
\(510\) | 0.530467 | 0.0234895 | ||||||||
\(511\) | −15.9822 | −0.707011 | ||||||||
\(512\) | −38.2021 | −1.68831 | ||||||||
\(513\) | −6.81869 | −0.301052 | ||||||||
\(514\) | −5.13189 | −0.226358 | ||||||||
\(515\) | 3.37818 | 0.148860 | ||||||||
\(516\) | −28.5785 | −1.25810 | ||||||||
\(517\) | −10.8361 | −0.476573 | ||||||||
\(518\) | 17.6416 | 0.775129 | ||||||||
\(519\) | 10.3886 | 0.456011 | ||||||||
\(520\) | 6.11919 | 0.268344 | ||||||||
\(521\) | 39.4030 | 1.72628 | 0.863139 | − | 0.504967i | \(-0.168495\pi\) | ||||
0.863139 | + | 0.504967i | \(0.168495\pi\) | |||||||
\(522\) | −15.9147 | −0.696566 | ||||||||
\(523\) | −6.69006 | −0.292536 | −0.146268 | − | 0.989245i | \(-0.546726\pi\) | ||||
−0.146268 | + | 0.989245i | \(0.546726\pi\) | |||||||
\(524\) | 90.0773 | 3.93505 | ||||||||
\(525\) | −5.12140 | −0.223516 | ||||||||
\(526\) | −14.1030 | −0.614919 | ||||||||
\(527\) | 0.555194 | 0.0241846 | ||||||||
\(528\) | −10.1063 | −0.439821 | ||||||||
\(529\) | −18.7495 | −0.815197 | ||||||||
\(530\) | 3.63311 | 0.157812 | ||||||||
\(531\) | −13.8895 | −0.602754 | ||||||||
\(532\) | −34.5056 | −1.49601 | ||||||||
\(533\) | −1.59656 | −0.0691546 | ||||||||
\(534\) | 12.3802 | 0.535743 | ||||||||
\(535\) | −0.498913 | −0.0215699 | ||||||||
\(536\) | 41.6286 | 1.79808 | ||||||||
\(537\) | 17.4905 | 0.754773 | ||||||||
\(538\) | −39.3591 | −1.69689 | ||||||||
\(539\) | 5.92762 | 0.255321 | ||||||||
\(540\) | 1.14041 | 0.0490752 | ||||||||
\(541\) | −32.7099 | −1.40631 | −0.703154 | − | 0.711038i | \(-0.748226\pi\) | ||||
−0.703154 | + | 0.711038i | \(0.748226\pi\) | |||||||
\(542\) | 52.7709 | 2.26670 | ||||||||
\(543\) | −14.8136 | −0.635711 | ||||||||
\(544\) | 9.84911 | 0.422277 | ||||||||
\(545\) | −0.388295 | −0.0166327 | ||||||||
\(546\) | 9.40643 | 0.402558 | ||||||||
\(547\) | −22.7993 | −0.974830 | −0.487415 | − | 0.873171i | \(-0.662060\pi\) | ||||
−0.487415 | + | 0.873171i | \(0.662060\pi\) | |||||||
\(548\) | −76.1892 | −3.25464 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 12.9783 | 0.553398 | ||||||||
\(551\) | 41.3517 | 1.76164 | ||||||||
\(552\) | −15.6179 | −0.664743 | ||||||||
\(553\) | 12.8951 | 0.548356 | ||||||||
\(554\) | −25.1058 | −1.06664 | ||||||||
\(555\) | 1.51497 | 0.0643068 | ||||||||
\(556\) | −88.7536 | −3.76399 | ||||||||
\(557\) | 32.5746 | 1.38023 | 0.690115 | − | 0.723700i | \(-0.257560\pi\) | ||||
0.690115 | + | 0.723700i | \(0.257560\pi\) | |||||||
\(558\) | 1.68206 | 0.0712073 | ||||||||
\(559\) | −20.2428 | −0.856179 | ||||||||
\(560\) | 2.44238 | 0.103209 | ||||||||
\(561\) | −0.866180 | −0.0365702 | ||||||||
\(562\) | 72.0037 | 3.03729 | ||||||||
\(563\) | −4.76382 | −0.200771 | −0.100386 | − | 0.994949i | \(-0.532008\pi\) | ||||
−0.100386 | + | 0.994949i | \(0.532008\pi\) | |||||||
\(564\) | 52.9528 | 2.22972 | ||||||||
\(565\) | −3.89306 | −0.163782 | ||||||||
\(566\) | 55.3416 | 2.32618 | ||||||||
\(567\) | 1.03556 | 0.0434894 | ||||||||
\(568\) | 83.1169 | 3.48751 | ||||||||
\(569\) | −36.9691 | −1.54982 | −0.774912 | − | 0.632069i | \(-0.782206\pi\) | ||||
−0.774912 | + | 0.632069i | \(0.782206\pi\) | |||||||
\(570\) | −4.17591 | −0.174909 | ||||||||
\(571\) | −18.7090 | −0.782949 | −0.391474 | − | 0.920189i | \(-0.628035\pi\) | ||||
−0.391474 | + | 0.920189i | \(0.628035\pi\) | |||||||
\(572\) | −16.9145 | −0.707231 | ||||||||
\(573\) | −6.59920 | −0.275685 | ||||||||
\(574\) | −1.25349 | −0.0523195 | ||||||||
\(575\) | 10.1961 | 0.425205 | ||||||||
\(576\) | 9.62701 | 0.401125 | ||||||||
\(577\) | 34.5793 | 1.43956 | 0.719779 | − | 0.694204i | \(-0.244243\pi\) | ||||
0.719779 | + | 0.694204i | \(0.244243\pi\) | |||||||
\(578\) | −42.6433 | −1.77373 | ||||||||
\(579\) | −18.6461 | −0.774907 | ||||||||
\(580\) | −6.91594 | −0.287169 | ||||||||
\(581\) | 4.79264 | 0.198832 | ||||||||
\(582\) | −0.871471 | −0.0361236 | ||||||||
\(583\) | −5.93238 | −0.245694 | ||||||||
\(584\) | −116.914 | −4.83793 | ||||||||
\(585\) | 0.807774 | 0.0333973 | ||||||||
\(586\) | 28.5547 | 1.17958 | ||||||||
\(587\) | 40.4240 | 1.66848 | 0.834238 | − | 0.551405i | \(-0.185908\pi\) | ||||
0.834238 | + | 0.551405i | \(0.185908\pi\) | |||||||
\(588\) | −28.9664 | −1.19455 | ||||||||
\(589\) | −4.37056 | −0.180086 | ||||||||
\(590\) | −8.50623 | −0.350196 | ||||||||
\(591\) | 4.09897 | 0.168609 | ||||||||
\(592\) | 65.6072 | 2.69644 | ||||||||
\(593\) | −19.3560 | −0.794854 | −0.397427 | − | 0.917634i | \(-0.630097\pi\) | ||||
−0.397427 | + | 0.917634i | \(0.630097\pi\) | |||||||
\(594\) | −2.62425 | −0.107674 | ||||||||
\(595\) | 0.209328 | 0.00858162 | ||||||||
\(596\) | 41.5503 | 1.70197 | ||||||||
\(597\) | 13.0650 | 0.534714 | ||||||||
\(598\) | −18.7270 | −0.765805 | ||||||||
\(599\) | 15.4274 | 0.630348 | 0.315174 | − | 0.949034i | \(-0.397937\pi\) | ||||
0.315174 | + | 0.949034i | \(0.397937\pi\) | |||||||
\(600\) | −37.4643 | −1.52948 | ||||||||
\(601\) | 15.3065 | 0.624364 | 0.312182 | − | 0.950022i | \(-0.398940\pi\) | ||||
0.312182 | + | 0.950022i | \(0.398940\pi\) | |||||||
\(602\) | −15.8930 | −0.647750 | ||||||||
\(603\) | 5.49525 | 0.223784 | ||||||||
\(604\) | −114.951 | −4.67730 | ||||||||
\(605\) | 0.233370 | 0.00948784 | ||||||||
\(606\) | 32.4331 | 1.31750 | ||||||||
\(607\) | −40.9891 | −1.66370 | −0.831848 | − | 0.555003i | \(-0.812717\pi\) | ||||
−0.831848 | + | 0.555003i | \(0.812717\pi\) | |||||||
\(608\) | −77.5335 | −3.14440 | ||||||||
\(609\) | −6.28011 | −0.254483 | ||||||||
\(610\) | −0.612421 | −0.0247962 | ||||||||
\(611\) | 37.5076 | 1.51740 | ||||||||
\(612\) | 4.23275 | 0.171099 | ||||||||
\(613\) | 7.15889 | 0.289145 | 0.144573 | − | 0.989494i | \(-0.453819\pi\) | ||||
0.144573 | + | 0.989494i | \(0.453819\pi\) | |||||||
\(614\) | −19.0730 | −0.769725 | ||||||||
\(615\) | −0.107643 | −0.00434057 | ||||||||
\(616\) | −7.84475 | −0.316074 | ||||||||
\(617\) | 11.2849 | 0.454315 | 0.227157 | − | 0.973858i | \(-0.427057\pi\) | ||||
0.227157 | + | 0.973858i | \(0.427057\pi\) | |||||||
\(618\) | 37.9876 | 1.52809 | ||||||||
\(619\) | 5.57451 | 0.224058 | 0.112029 | − | 0.993705i | \(-0.464265\pi\) | ||||
0.112029 | + | 0.993705i | \(0.464265\pi\) | |||||||
\(620\) | 0.730963 | 0.0293562 | ||||||||
\(621\) | −2.06167 | −0.0827319 | ||||||||
\(622\) | −0.797809 | −0.0319892 | ||||||||
\(623\) | 4.88536 | 0.195728 | ||||||||
\(624\) | 34.9814 | 1.40038 | ||||||||
\(625\) | 24.1860 | 0.967442 | ||||||||
\(626\) | 80.1033 | 3.20157 | ||||||||
\(627\) | 6.81869 | 0.272312 | ||||||||
\(628\) | −75.9157 | −3.02937 | ||||||||
\(629\) | 5.62299 | 0.224203 | ||||||||
\(630\) | 0.634198 | 0.0252670 | ||||||||
\(631\) | −28.2662 | −1.12526 | −0.562630 | − | 0.826709i | \(-0.690210\pi\) | ||||
−0.562630 | + | 0.826709i | \(0.690210\pi\) | |||||||
\(632\) | 94.3311 | 3.75229 | ||||||||
\(633\) | 25.2541 | 1.00376 | ||||||||
\(634\) | 2.38648 | 0.0947791 | ||||||||
\(635\) | −1.46432 | −0.0581096 | ||||||||
\(636\) | 28.9897 | 1.14951 | ||||||||
\(637\) | −20.5175 | −0.812934 | ||||||||
\(638\) | 15.9147 | 0.630067 | ||||||||
\(639\) | 10.9720 | 0.434045 | ||||||||
\(640\) | 0.588607 | 0.0232667 | ||||||||
\(641\) | −23.9009 | −0.944028 | −0.472014 | − | 0.881591i | \(-0.656473\pi\) | ||||
−0.472014 | + | 0.881591i | \(0.656473\pi\) | |||||||
\(642\) | −5.61028 | −0.221420 | ||||||||
\(643\) | 24.9816 | 0.985179 | 0.492589 | − | 0.870262i | \(-0.336050\pi\) | ||||
0.492589 | + | 0.870262i | \(0.336050\pi\) | |||||||
\(644\) | −10.4330 | −0.411117 | ||||||||
\(645\) | −1.36480 | −0.0537391 | ||||||||
\(646\) | −15.4994 | −0.609815 | ||||||||
\(647\) | 24.5879 | 0.966650 | 0.483325 | − | 0.875441i | \(-0.339429\pi\) | ||||
0.483325 | + | 0.875441i | \(0.339429\pi\) | |||||||
\(648\) | 7.57538 | 0.297589 | ||||||||
\(649\) | 13.8895 | 0.545211 | ||||||||
\(650\) | −44.9225 | −1.76200 | ||||||||
\(651\) | 0.663760 | 0.0260148 | ||||||||
\(652\) | 19.2061 | 0.752169 | ||||||||
\(653\) | 13.5911 | 0.531861 | 0.265931 | − | 0.963992i | \(-0.414321\pi\) | ||||
0.265931 | + | 0.963992i | \(0.414321\pi\) | |||||||
\(654\) | −4.36638 | −0.170739 | ||||||||
\(655\) | 4.30176 | 0.168084 | ||||||||
\(656\) | −4.66157 | −0.182004 | ||||||||
\(657\) | −15.4334 | −0.602114 | ||||||||
\(658\) | 29.4479 | 1.14800 | ||||||||
\(659\) | 12.8127 | 0.499114 | 0.249557 | − | 0.968360i | \(-0.419715\pi\) | ||||
0.249557 | + | 0.968360i | \(0.419715\pi\) | |||||||
\(660\) | −1.14041 | −0.0443902 | ||||||||
\(661\) | 7.66063 | 0.297964 | 0.148982 | − | 0.988840i | \(-0.452400\pi\) | ||||
0.148982 | + | 0.988840i | \(0.452400\pi\) | |||||||
\(662\) | 54.5307 | 2.11939 | ||||||||
\(663\) | 2.99815 | 0.116438 | ||||||||
\(664\) | 35.0594 | 1.36057 | ||||||||
\(665\) | −1.64786 | −0.0639013 | ||||||||
\(666\) | 17.0359 | 0.660126 | ||||||||
\(667\) | 12.5029 | 0.484115 | ||||||||
\(668\) | −8.97362 | −0.347200 | ||||||||
\(669\) | 0.184928 | 0.00714975 | ||||||||
\(670\) | 3.36541 | 0.130017 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 11.7751 | 0.454233 | ||||||||
\(673\) | −15.7132 | −0.605698 | −0.302849 | − | 0.953038i | \(-0.597938\pi\) | ||||
−0.302849 | + | 0.953038i | \(0.597938\pi\) | |||||||
\(674\) | −20.4008 | −0.785809 | ||||||||
\(675\) | −4.94554 | −0.190354 | ||||||||
\(676\) | −4.98000 | −0.191539 | ||||||||
\(677\) | −19.2713 | −0.740655 | −0.370327 | − | 0.928901i | \(-0.620755\pi\) | ||||
−0.370327 | + | 0.928901i | \(0.620755\pi\) | |||||||
\(678\) | −43.7775 | −1.68127 | ||||||||
\(679\) | −0.343892 | −0.0131974 | ||||||||
\(680\) | 1.53129 | 0.0587223 | ||||||||
\(681\) | −10.8433 | −0.415518 | ||||||||
\(682\) | −1.68206 | −0.0644094 | ||||||||
\(683\) | 45.1825 | 1.72886 | 0.864430 | − | 0.502753i | \(-0.167680\pi\) | ||||
0.864430 | + | 0.502753i | \(0.167680\pi\) | |||||||
\(684\) | −33.3208 | −1.27405 | ||||||||
\(685\) | −3.63851 | −0.139020 | ||||||||
\(686\) | −35.1316 | −1.34133 | ||||||||
\(687\) | 9.68390 | 0.369464 | ||||||||
\(688\) | −59.1042 | −2.25333 | ||||||||
\(689\) | 20.5340 | 0.782283 | ||||||||
\(690\) | −1.26261 | −0.0480667 | ||||||||
\(691\) | 0.659628 | 0.0250934 | 0.0125467 | − | 0.999921i | \(-0.496006\pi\) | ||||
0.0125467 | + | 0.999921i | \(0.496006\pi\) | |||||||
\(692\) | 50.7660 | 1.92983 | ||||||||
\(693\) | −1.03556 | −0.0393376 | ||||||||
\(694\) | 33.7596 | 1.28150 | ||||||||
\(695\) | −4.23854 | −0.160777 | ||||||||
\(696\) | −45.9406 | −1.74137 | ||||||||
\(697\) | −0.399529 | −0.0151332 | ||||||||
\(698\) | 37.7318 | 1.42817 | ||||||||
\(699\) | −10.8919 | −0.411971 | ||||||||
\(700\) | −25.0266 | −0.945918 | ||||||||
\(701\) | 11.8645 | 0.448116 | 0.224058 | − | 0.974576i | \(-0.428070\pi\) | ||||
0.224058 | + | 0.974576i | \(0.428070\pi\) | |||||||
\(702\) | 9.08343 | 0.342832 | ||||||||
\(703\) | −44.2649 | −1.66948 | ||||||||
\(704\) | −9.62701 | −0.362832 | ||||||||
\(705\) | 2.52883 | 0.0952413 | ||||||||
\(706\) | 3.72399 | 0.140154 | ||||||||
\(707\) | 12.7985 | 0.481336 | ||||||||
\(708\) | −67.8737 | −2.55085 | ||||||||
\(709\) | 7.38312 | 0.277279 | 0.138640 | − | 0.990343i | \(-0.455727\pi\) | ||||
0.138640 | + | 0.990343i | \(0.455727\pi\) | |||||||
\(710\) | 6.71947 | 0.252177 | ||||||||
\(711\) | 12.4523 | 0.466999 | ||||||||
\(712\) | 35.7377 | 1.33933 | ||||||||
\(713\) | −1.32146 | −0.0494892 | ||||||||
\(714\) | 2.35390 | 0.0880925 | ||||||||
\(715\) | −0.807774 | −0.0302090 | ||||||||
\(716\) | 85.4708 | 3.19419 | ||||||||
\(717\) | 7.56308 | 0.282448 | ||||||||
\(718\) | −2.27556 | −0.0849230 | ||||||||
\(719\) | 12.2824 | 0.458057 | 0.229028 | − | 0.973420i | \(-0.426445\pi\) | ||||
0.229028 | + | 0.973420i | \(0.426445\pi\) | |||||||
\(720\) | 2.35851 | 0.0878965 | ||||||||
\(721\) | 14.9904 | 0.558270 | ||||||||
\(722\) | 72.1524 | 2.68523 | ||||||||
\(723\) | 12.1001 | 0.450009 | ||||||||
\(724\) | −72.3893 | −2.69033 | ||||||||
\(725\) | 29.9920 | 1.11388 | ||||||||
\(726\) | 2.62425 | 0.0973950 | ||||||||
\(727\) | 8.68056 | 0.321944 | 0.160972 | − | 0.986959i | \(-0.448537\pi\) | ||||
0.160972 | + | 0.986959i | \(0.448537\pi\) | |||||||
\(728\) | 27.1534 | 1.00637 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.45174 | −0.349824 | ||||||||
\(731\) | −5.06564 | −0.187359 | ||||||||
\(732\) | −4.88668 | −0.180617 | ||||||||
\(733\) | 11.5763 | 0.427582 | 0.213791 | − | 0.976879i | \(-0.431419\pi\) | ||||
0.213791 | + | 0.976879i | \(0.431419\pi\) | |||||||
\(734\) | 98.0738 | 3.61997 | ||||||||
\(735\) | −1.38333 | −0.0510248 | ||||||||
\(736\) | −23.4427 | −0.864109 | ||||||||
\(737\) | −5.49525 | −0.202420 | ||||||||
\(738\) | −1.21044 | −0.0445571 | ||||||||
\(739\) | −6.65608 | −0.244848 | −0.122424 | − | 0.992478i | \(-0.539067\pi\) | ||||
−0.122424 | + | 0.992478i | \(0.539067\pi\) | |||||||
\(740\) | 7.40317 | 0.272146 | ||||||||
\(741\) | −23.6018 | −0.867035 | ||||||||
\(742\) | 16.1216 | 0.591843 | ||||||||
\(743\) | 0.134338 | 0.00492837 | 0.00246418 | − | 0.999997i | \(-0.499216\pi\) | ||||
0.00246418 | + | 0.999997i | \(0.499216\pi\) | |||||||
\(744\) | 4.85558 | 0.178014 | ||||||||
\(745\) | 1.98429 | 0.0726986 | ||||||||
\(746\) | −48.1331 | −1.76228 | ||||||||
\(747\) | 4.62807 | 0.169332 | ||||||||
\(748\) | −4.23275 | −0.154765 | ||||||||
\(749\) | −2.21388 | −0.0808935 | ||||||||
\(750\) | −6.09085 | −0.222407 | ||||||||
\(751\) | 28.5757 | 1.04274 | 0.521372 | − | 0.853330i | \(-0.325420\pi\) | ||||
0.521372 | + | 0.853330i | \(0.325420\pi\) | |||||||
\(752\) | 109.514 | 3.99355 | ||||||||
\(753\) | −14.5210 | −0.529174 | ||||||||
\(754\) | −55.0861 | −2.00612 | ||||||||
\(755\) | −5.48965 | −0.199789 | ||||||||
\(756\) | 5.06045 | 0.184047 | ||||||||
\(757\) | 23.9955 | 0.872131 | 0.436065 | − | 0.899915i | \(-0.356372\pi\) | ||||
0.436065 | + | 0.899915i | \(0.356372\pi\) | |||||||
\(758\) | −22.8162 | −0.828721 | ||||||||
\(759\) | 2.06167 | 0.0748339 | ||||||||
\(760\) | −12.0545 | −0.437263 | ||||||||
\(761\) | −15.1346 | −0.548628 | −0.274314 | − | 0.961640i | \(-0.588451\pi\) | ||||
−0.274314 | + | 0.961640i | \(0.588451\pi\) | |||||||
\(762\) | −16.4663 | −0.596510 | ||||||||
\(763\) | −1.72302 | −0.0623776 | ||||||||
\(764\) | −32.2482 | −1.16670 | ||||||||
\(765\) | 0.202140 | 0.00730840 | ||||||||
\(766\) | −51.5627 | −1.86303 | ||||||||
\(767\) | −48.0764 | −1.73594 | ||||||||
\(768\) | −12.6351 | −0.455931 | ||||||||
\(769\) | −50.1531 | −1.80857 | −0.904283 | − | 0.426934i | \(-0.859594\pi\) | ||||
−0.904283 | + | 0.426934i | \(0.859594\pi\) | |||||||
\(770\) | −0.634198 | −0.0228549 | ||||||||
\(771\) | −1.95557 | −0.0704280 | ||||||||
\(772\) | −91.1178 | −3.27940 | ||||||||
\(773\) | 4.15446 | 0.149426 | 0.0747128 | − | 0.997205i | \(-0.476196\pi\) | ||||
0.0747128 | + | 0.997205i | \(0.476196\pi\) | |||||||
\(774\) | −15.3473 | −0.551646 | ||||||||
\(775\) | −3.16993 | −0.113867 | ||||||||
\(776\) | −2.51566 | −0.0903070 | ||||||||
\(777\) | 6.72254 | 0.241170 | ||||||||
\(778\) | 73.4524 | 2.63340 | ||||||||
\(779\) | 3.14514 | 0.112686 | ||||||||
\(780\) | 3.94733 | 0.141337 | ||||||||
\(781\) | −10.9720 | −0.392608 | ||||||||
\(782\) | −4.68633 | −0.167583 | ||||||||
\(783\) | −6.06446 | −0.216726 | ||||||||
\(784\) | −59.9064 | −2.13951 | ||||||||
\(785\) | −3.62545 | −0.129398 | ||||||||
\(786\) | 48.3734 | 1.72542 | ||||||||
\(787\) | 26.2406 | 0.935377 | 0.467689 | − | 0.883893i | \(-0.345087\pi\) | ||||
0.467689 | + | 0.883893i | \(0.345087\pi\) | |||||||
\(788\) | 20.0304 | 0.713552 | ||||||||
\(789\) | −5.37410 | −0.191323 | ||||||||
\(790\) | 7.62606 | 0.271323 | ||||||||
\(791\) | −17.2751 | −0.614232 | ||||||||
\(792\) | −7.57538 | −0.269179 | ||||||||
\(793\) | −3.46134 | −0.122916 | ||||||||
\(794\) | 14.4907 | 0.514254 | ||||||||
\(795\) | 1.38444 | 0.0491010 | ||||||||
\(796\) | 63.8444 | 2.26291 | ||||||||
\(797\) | 2.88176 | 0.102077 | 0.0510386 | − | 0.998697i | \(-0.483747\pi\) | ||||
0.0510386 | + | 0.998697i | \(0.483747\pi\) | |||||||
\(798\) | −18.5302 | −0.655963 | ||||||||
\(799\) | 9.38606 | 0.332055 | ||||||||
\(800\) | −56.2344 | −1.98819 | ||||||||
\(801\) | 4.71761 | 0.166689 | ||||||||
\(802\) | 37.7716 | 1.33376 | ||||||||
\(803\) | 15.4334 | 0.544633 | ||||||||
\(804\) | 26.8536 | 0.947052 | ||||||||
\(805\) | −0.498240 | −0.0175607 | ||||||||
\(806\) | 5.82219 | 0.205078 | ||||||||
\(807\) | −14.9982 | −0.527963 | ||||||||
\(808\) | 93.6241 | 3.29368 | ||||||||
\(809\) | −25.0212 | −0.879697 | −0.439849 | − | 0.898072i | \(-0.644968\pi\) | ||||
−0.439849 | + | 0.898072i | \(0.644968\pi\) | |||||||
\(810\) | 0.612421 | 0.0215183 | ||||||||
\(811\) | −24.9051 | −0.874538 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(812\) | −30.6889 | −1.07697 | ||||||||
\(813\) | 20.1090 | 0.705252 | ||||||||
\(814\) | −17.0359 | −0.597106 | ||||||||
\(815\) | 0.917212 | 0.0321285 | ||||||||
\(816\) | 8.75389 | 0.306448 | ||||||||
\(817\) | 39.8773 | 1.39513 | ||||||||
\(818\) | 47.0304 | 1.64438 | ||||||||
\(819\) | 3.58443 | 0.125250 | ||||||||
\(820\) | −0.526016 | −0.0183693 | ||||||||
\(821\) | 18.3839 | 0.641603 | 0.320802 | − | 0.947146i | \(-0.396048\pi\) | ||||
0.320802 | + | 0.947146i | \(0.396048\pi\) | |||||||
\(822\) | −40.9151 | −1.42708 | ||||||||
\(823\) | 40.4252 | 1.40913 | 0.704567 | − | 0.709638i | \(-0.251141\pi\) | ||||
0.704567 | + | 0.709638i | \(0.251141\pi\) | |||||||
\(824\) | 109.658 | 3.82013 | ||||||||
\(825\) | 4.94554 | 0.172182 | ||||||||
\(826\) | −37.7457 | −1.31334 | ||||||||
\(827\) | −17.3687 | −0.603969 | −0.301984 | − | 0.953313i | \(-0.597649\pi\) | ||||
−0.301984 | + | 0.953313i | \(0.597649\pi\) | |||||||
\(828\) | −10.0747 | −0.350121 | ||||||||
\(829\) | 28.4250 | 0.987241 | 0.493620 | − | 0.869678i | \(-0.335673\pi\) | ||||
0.493620 | + | 0.869678i | \(0.335673\pi\) | |||||||
\(830\) | 2.83433 | 0.0983809 | ||||||||
\(831\) | −9.56683 | −0.331870 | ||||||||
\(832\) | 33.3224 | 1.15525 | ||||||||
\(833\) | −5.13439 | −0.177896 | ||||||||
\(834\) | −47.6625 | −1.65042 | ||||||||
\(835\) | −0.428547 | −0.0148305 | ||||||||
\(836\) | 33.3208 | 1.15242 | ||||||||
\(837\) | 0.640968 | 0.0221551 | ||||||||
\(838\) | 70.2323 | 2.42613 | ||||||||
\(839\) | 48.0557 | 1.65907 | 0.829534 | − | 0.558456i | \(-0.188606\pi\) | ||||
0.829534 | + | 0.558456i | \(0.188606\pi\) | |||||||
\(840\) | 1.83073 | 0.0631661 | ||||||||
\(841\) | 7.77770 | 0.268197 | ||||||||
\(842\) | −70.8787 | −2.44264 | ||||||||
\(843\) | 27.4378 | 0.945009 | ||||||||
\(844\) | 123.409 | 4.24790 | ||||||||
\(845\) | −0.237826 | −0.00818148 | ||||||||
\(846\) | 28.4368 | 0.977676 | ||||||||
\(847\) | 1.03556 | 0.0355822 | ||||||||
\(848\) | 59.9545 | 2.05885 | ||||||||
\(849\) | 21.0886 | 0.723757 | ||||||||
\(850\) | −11.2416 | −0.385583 | ||||||||
\(851\) | −13.3838 | −0.458789 | ||||||||
\(852\) | 53.6166 | 1.83687 | ||||||||
\(853\) | −43.8113 | −1.50007 | −0.750035 | − | 0.661398i | \(-0.769963\pi\) | ||||
−0.750035 | + | 0.661398i | \(0.769963\pi\) | |||||||
\(854\) | −2.71756 | −0.0929931 | ||||||||
\(855\) | −1.59128 | −0.0544205 | ||||||||
\(856\) | −16.1951 | −0.553538 | ||||||||
\(857\) | −21.6329 | −0.738967 | −0.369484 | − | 0.929237i | \(-0.620465\pi\) | ||||
−0.369484 | + | 0.929237i | \(0.620465\pi\) | |||||||
\(858\) | −9.08343 | −0.310103 | ||||||||
\(859\) | −47.8429 | −1.63238 | −0.816190 | − | 0.577784i | \(-0.803918\pi\) | ||||
−0.816190 | + | 0.577784i | \(0.803918\pi\) | |||||||
\(860\) | −6.66937 | −0.227424 | ||||||||
\(861\) | −0.477655 | −0.0162784 | ||||||||
\(862\) | −17.3540 | −0.591081 | ||||||||
\(863\) | −46.6138 | −1.58675 | −0.793377 | − | 0.608731i | \(-0.791679\pi\) | ||||
−0.793377 | + | 0.608731i | \(0.791679\pi\) | |||||||
\(864\) | 11.3707 | 0.386840 | ||||||||
\(865\) | 2.42440 | 0.0824320 | ||||||||
\(866\) | 18.3414 | 0.623267 | ||||||||
\(867\) | −16.2497 | −0.551870 | ||||||||
\(868\) | 3.24359 | 0.110094 | ||||||||
\(869\) | −12.4523 | −0.422416 | ||||||||
\(870\) | −3.71400 | −0.125916 | ||||||||
\(871\) | 19.0210 | 0.644500 | ||||||||
\(872\) | −12.6044 | −0.426838 | ||||||||
\(873\) | −0.332084 | −0.0112393 | ||||||||
\(874\) | 36.8914 | 1.24787 | ||||||||
\(875\) | −2.40352 | −0.0812538 | ||||||||
\(876\) | −75.4182 | −2.54814 | ||||||||
\(877\) | −13.1502 | −0.444049 | −0.222025 | − | 0.975041i | \(-0.571267\pi\) | ||||
−0.222025 | + | 0.975041i | \(0.571267\pi\) | |||||||
\(878\) | 12.6605 | 0.427270 | ||||||||
\(879\) | 10.8811 | 0.367010 | ||||||||
\(880\) | −2.35851 | −0.0795054 | ||||||||
\(881\) | 14.2325 | 0.479504 | 0.239752 | − | 0.970834i | \(-0.422934\pi\) | ||||
0.239752 | + | 0.970834i | \(0.422934\pi\) | |||||||
\(882\) | −15.5555 | −0.523783 | ||||||||
\(883\) | −19.9158 | −0.670221 | −0.335111 | − | 0.942179i | \(-0.608774\pi\) | ||||
−0.335111 | + | 0.942179i | \(0.608774\pi\) | |||||||
\(884\) | 14.6510 | 0.492767 | ||||||||
\(885\) | −3.24140 | −0.108958 | ||||||||
\(886\) | −18.7472 | −0.629825 | ||||||||
\(887\) | 27.9231 | 0.937566 | 0.468783 | − | 0.883313i | \(-0.344693\pi\) | ||||
0.468783 | + | 0.883313i | \(0.344693\pi\) | |||||||
\(888\) | 49.1771 | 1.65028 | ||||||||
\(889\) | −6.49777 | −0.217928 | ||||||||
\(890\) | 2.88916 | 0.0968450 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0.903687 | 0.0302577 | ||||||||
\(893\) | −73.8883 | −2.47258 | ||||||||
\(894\) | 22.3133 | 0.746270 | ||||||||
\(895\) | 4.08177 | 0.136438 | ||||||||
\(896\) | 2.61189 | 0.0872572 | ||||||||
\(897\) | −7.13615 | −0.238269 | ||||||||
\(898\) | −7.40027 | −0.246950 | ||||||||
\(899\) | −3.88713 | −0.129643 | ||||||||
\(900\) | −24.1673 | −0.805576 | ||||||||
\(901\) | 5.13851 | 0.171189 | ||||||||
\(902\) | 1.21044 | 0.0403034 | ||||||||
\(903\) | −6.05620 | −0.201538 | ||||||||
\(904\) | −126.372 | −4.20307 | ||||||||
\(905\) | −3.45704 | −0.114916 | ||||||||
\(906\) | −61.7312 | −2.05088 | ||||||||
\(907\) | 37.3959 | 1.24171 | 0.620856 | − | 0.783925i | \(-0.286785\pi\) | ||||
0.620856 | + | 0.783925i | \(0.286785\pi\) | |||||||
\(908\) | −52.9880 | −1.75847 | ||||||||
\(909\) | 12.3590 | 0.409922 | ||||||||
\(910\) | 2.19518 | 0.0727694 | ||||||||
\(911\) | 52.2628 | 1.73154 | 0.865771 | − | 0.500440i | \(-0.166828\pi\) | ||||
0.865771 | + | 0.500440i | \(0.166828\pi\) | |||||||
\(912\) | −68.9118 | −2.28190 | ||||||||
\(913\) | −4.62807 | −0.153167 | ||||||||
\(914\) | −56.1366 | −1.85683 | ||||||||
\(915\) | −0.233370 | −0.00771497 | ||||||||
\(916\) | 47.3222 | 1.56357 | ||||||||
\(917\) | 19.0887 | 0.630364 | ||||||||
\(918\) | 2.27307 | 0.0750226 | ||||||||
\(919\) | −34.2063 | −1.12836 | −0.564182 | − | 0.825651i | \(-0.690808\pi\) | ||||
−0.564182 | + | 0.825651i | \(0.690808\pi\) | |||||||
\(920\) | −3.64475 | −0.120164 | ||||||||
\(921\) | −7.26799 | −0.239488 | ||||||||
\(922\) | 6.32139 | 0.208184 | ||||||||
\(923\) | 37.9778 | 1.25005 | ||||||||
\(924\) | −5.06045 | −0.166477 | ||||||||
\(925\) | −32.1050 | −1.05561 | ||||||||
\(926\) | −72.9323 | −2.39670 | ||||||||
\(927\) | 14.4756 | 0.475442 | ||||||||
\(928\) | −68.9574 | −2.26364 | ||||||||
\(929\) | −26.6684 | −0.874963 | −0.437482 | − | 0.899227i | \(-0.644130\pi\) | ||||
−0.437482 | + | 0.899227i | \(0.644130\pi\) | |||||||
\(930\) | 0.392542 | 0.0128720 | ||||||||
\(931\) | 40.4186 | 1.32467 | ||||||||
\(932\) | −53.2255 | −1.74346 | ||||||||
\(933\) | −0.304014 | −0.00995298 | ||||||||
\(934\) | −17.4622 | −0.571380 | ||||||||
\(935\) | −0.202140 | −0.00661070 | ||||||||
\(936\) | 26.2210 | 0.857060 | ||||||||
\(937\) | 11.0117 | 0.359736 | 0.179868 | − | 0.983691i | \(-0.442433\pi\) | ||||
0.179868 | + | 0.983691i | \(0.442433\pi\) | |||||||
\(938\) | 14.9337 | 0.487602 | ||||||||
\(939\) | 30.5243 | 0.996122 | ||||||||
\(940\) | 12.3576 | 0.403060 | ||||||||
\(941\) | 41.5013 | 1.35290 | 0.676451 | − | 0.736487i | \(-0.263517\pi\) | ||||
0.676451 | + | 0.736487i | \(0.263517\pi\) | |||||||
\(942\) | −40.7683 | −1.32830 | ||||||||
\(943\) | 0.950952 | 0.0309673 | ||||||||
\(944\) | −140.372 | −4.56872 | ||||||||
\(945\) | 0.241668 | 0.00786147 | ||||||||
\(946\) | 15.3473 | 0.498982 | ||||||||
\(947\) | −6.86498 | −0.223082 | −0.111541 | − | 0.993760i | \(-0.535579\pi\) | ||||
−0.111541 | + | 0.993760i | \(0.535579\pi\) | |||||||
\(948\) | 60.8506 | 1.97634 | ||||||||
\(949\) | −53.4203 | −1.73410 | ||||||||
\(950\) | 88.4951 | 2.87116 | ||||||||
\(951\) | 0.909394 | 0.0294891 | ||||||||
\(952\) | 6.79497 | 0.220226 | ||||||||
\(953\) | 50.1428 | 1.62429 | 0.812143 | − | 0.583458i | \(-0.198301\pi\) | ||||
0.812143 | + | 0.583458i | \(0.198301\pi\) | |||||||
\(954\) | 15.5680 | 0.504034 | ||||||||
\(955\) | −1.54005 | −0.0498350 | ||||||||
\(956\) | 36.9584 | 1.19532 | ||||||||
\(957\) | 6.06446 | 0.196036 | ||||||||
\(958\) | 23.9216 | 0.772873 | ||||||||
\(959\) | −16.1456 | −0.521368 | ||||||||
\(960\) | 2.24665 | 0.0725105 | ||||||||
\(961\) | −30.5892 | −0.986747 | ||||||||
\(962\) | 58.9670 | 1.90117 | ||||||||
\(963\) | −2.13786 | −0.0688916 | ||||||||
\(964\) | 59.1296 | 1.90444 | ||||||||
\(965\) | −4.35145 | −0.140078 | ||||||||
\(966\) | −5.60272 | −0.180265 | ||||||||
\(967\) | −38.7157 | −1.24501 | −0.622506 | − | 0.782615i | \(-0.713885\pi\) | ||||
−0.622506 | + | 0.782615i | \(0.713885\pi\) | |||||||
\(968\) | 7.57538 | 0.243482 | ||||||||
\(969\) | −5.90621 | −0.189735 | ||||||||
\(970\) | −0.203375 | −0.00652998 | ||||||||
\(971\) | −8.40355 | −0.269683 | −0.134841 | − | 0.990867i | \(-0.543053\pi\) | ||||
−0.134841 | + | 0.990867i | \(0.543053\pi\) | |||||||
\(972\) | 4.88668 | 0.156740 | ||||||||
\(973\) | −18.8082 | −0.602962 | ||||||||
\(974\) | −13.0597 | −0.418460 | ||||||||
\(975\) | −17.1182 | −0.548222 | ||||||||
\(976\) | −10.1063 | −0.323495 | ||||||||
\(977\) | −32.3670 | −1.03551 | −0.517756 | − | 0.855528i | \(-0.673233\pi\) | ||||
−0.517756 | + | 0.855528i | \(0.673233\pi\) | |||||||
\(978\) | 10.3141 | 0.329808 | ||||||||
\(979\) | −4.71761 | −0.150776 | ||||||||
\(980\) | −6.75989 | −0.215937 | ||||||||
\(981\) | −1.66386 | −0.0531229 | ||||||||
\(982\) | −0.975722 | −0.0311365 | ||||||||
\(983\) | 35.2337 | 1.12378 | 0.561890 | − | 0.827212i | \(-0.310075\pi\) | ||||
0.561890 | + | 0.827212i | \(0.310075\pi\) | |||||||
\(984\) | −3.49417 | −0.111390 | ||||||||
\(985\) | 0.956576 | 0.0304790 | ||||||||
\(986\) | −13.7850 | −0.439003 | ||||||||
\(987\) | 11.2215 | 0.357183 | ||||||||
\(988\) | −115.335 | −3.66928 | ||||||||
\(989\) | 12.0571 | 0.383395 | ||||||||
\(990\) | −0.612421 | −0.0194640 | ||||||||
\(991\) | 61.5964 | 1.95667 | 0.978336 | − | 0.207022i | \(-0.0663771\pi\) | ||||
0.978336 | + | 0.207022i | \(0.0663771\pi\) | |||||||
\(992\) | 7.28828 | 0.231403 | ||||||||
\(993\) | 20.7795 | 0.659418 | ||||||||
\(994\) | 29.8170 | 0.945739 | ||||||||
\(995\) | 3.04897 | 0.0966589 | ||||||||
\(996\) | 22.6159 | 0.716613 | ||||||||
\(997\) | 22.2950 | 0.706090 | 0.353045 | − | 0.935606i | \(-0.385146\pi\) | ||||
0.353045 | + | 0.935606i | \(0.385146\pi\) | |||||||
\(998\) | −65.3472 | −2.06853 | ||||||||
\(999\) | 6.49171 | 0.205388 |
(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 | 2013.2.a.f.1.13 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.g.1.1 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.f.1.13 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.g.1.1 | 13 | 3.2 | odd | 2 |