Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,2,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, 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("547.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(4.36781699056\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-1.87675\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.87675 | 1.32707 | 0.663533 | − | 0.748147i | \(-0.269056\pi\) | ||||
0.663533 | + | 0.748147i | \(0.269056\pi\) | |||||||
\(3\) | −1.13919 | −0.657712 | −0.328856 | − | 0.944380i | \(-0.606663\pi\) | ||||
−0.328856 | + | 0.944380i | \(0.606663\pi\) | |||||||
\(4\) | 1.52220 | 0.761102 | ||||||||
\(5\) | −1.30620 | −0.584152 | −0.292076 | − | 0.956395i | \(-0.594346\pi\) | ||||
−0.292076 | + | 0.956395i | \(0.594346\pi\) | |||||||
\(6\) | −2.13798 | −0.872827 | ||||||||
\(7\) | −1.71403 | −0.647843 | −0.323922 | − | 0.946084i | \(-0.605001\pi\) | ||||
−0.323922 | + | 0.946084i | \(0.605001\pi\) | |||||||
\(8\) | −0.896704 | −0.317033 | ||||||||
\(9\) | −1.70224 | −0.567415 | ||||||||
\(10\) | −2.45142 | −0.775207 | ||||||||
\(11\) | −5.30835 | −1.60053 | −0.800263 | − | 0.599649i | \(-0.795307\pi\) | ||||
−0.800263 | + | 0.599649i | \(0.795307\pi\) | |||||||
\(12\) | −1.73408 | −0.500586 | ||||||||
\(13\) | 2.18823 | 0.606905 | 0.303452 | − | 0.952847i | \(-0.401861\pi\) | ||||
0.303452 | + | 0.952847i | \(0.401861\pi\) | |||||||
\(14\) | −3.21682 | −0.859730 | ||||||||
\(15\) | 1.48801 | 0.384204 | ||||||||
\(16\) | −4.72730 | −1.18183 | ||||||||
\(17\) | 0.392924 | 0.0952980 | 0.0476490 | − | 0.998864i | \(-0.484827\pi\) | ||||
0.0476490 | + | 0.998864i | \(0.484827\pi\) | |||||||
\(18\) | −3.19469 | −0.752996 | ||||||||
\(19\) | 0.498929 | 0.114462 | 0.0572311 | − | 0.998361i | \(-0.481773\pi\) | ||||
0.0572311 | + | 0.998361i | \(0.481773\pi\) | |||||||
\(20\) | −1.98831 | −0.444599 | ||||||||
\(21\) | 1.95261 | 0.426094 | ||||||||
\(22\) | −9.96246 | −2.12400 | ||||||||
\(23\) | 8.33591 | 1.73816 | 0.869079 | − | 0.494674i | \(-0.164713\pi\) | ||||
0.869079 | + | 0.494674i | \(0.164713\pi\) | |||||||
\(24\) | 1.02152 | 0.208516 | ||||||||
\(25\) | −3.29383 | −0.658767 | ||||||||
\(26\) | 4.10676 | 0.805402 | ||||||||
\(27\) | 5.35675 | 1.03091 | ||||||||
\(28\) | −2.60911 | −0.493075 | ||||||||
\(29\) | −4.50948 | −0.837389 | −0.418695 | − | 0.908127i | \(-0.637512\pi\) | ||||
−0.418695 | + | 0.908127i | \(0.637512\pi\) | |||||||
\(30\) | 2.79264 | 0.509863 | ||||||||
\(31\) | −2.96386 | −0.532324 | −0.266162 | − | 0.963928i | \(-0.585756\pi\) | ||||
−0.266162 | + | 0.963928i | \(0.585756\pi\) | |||||||
\(32\) | −7.07857 | −1.25133 | ||||||||
\(33\) | 6.04722 | 1.05269 | ||||||||
\(34\) | 0.737421 | 0.126467 | ||||||||
\(35\) | 2.23887 | 0.378439 | ||||||||
\(36\) | −2.59116 | −0.431861 | ||||||||
\(37\) | 3.06843 | 0.504447 | 0.252223 | − | 0.967669i | \(-0.418838\pi\) | ||||
0.252223 | + | 0.967669i | \(0.418838\pi\) | |||||||
\(38\) | 0.936368 | 0.151899 | ||||||||
\(39\) | −2.49281 | −0.399169 | ||||||||
\(40\) | 1.17128 | 0.185195 | ||||||||
\(41\) | −10.0885 | −1.57556 | −0.787780 | − | 0.615957i | \(-0.788770\pi\) | ||||
−0.787780 | + | 0.615957i | \(0.788770\pi\) | |||||||
\(42\) | 3.66457 | 0.565455 | ||||||||
\(43\) | 9.93284 | 1.51474 | 0.757372 | − | 0.652984i | \(-0.226483\pi\) | ||||
0.757372 | + | 0.652984i | \(0.226483\pi\) | |||||||
\(44\) | −8.08039 | −1.21816 | ||||||||
\(45\) | 2.22348 | 0.331456 | ||||||||
\(46\) | 15.6444 | 2.30665 | ||||||||
\(47\) | 0.714605 | 0.104236 | 0.0521179 | − | 0.998641i | \(-0.483403\pi\) | ||||
0.0521179 | + | 0.998641i | \(0.483403\pi\) | |||||||
\(48\) | 5.38530 | 0.777301 | ||||||||
\(49\) | −4.06209 | −0.580299 | ||||||||
\(50\) | −6.18172 | −0.874227 | ||||||||
\(51\) | −0.447615 | −0.0626787 | ||||||||
\(52\) | 3.33093 | 0.461916 | ||||||||
\(53\) | −10.3693 | −1.42433 | −0.712165 | − | 0.702012i | \(-0.752285\pi\) | ||||
−0.712165 | + | 0.702012i | \(0.752285\pi\) | |||||||
\(54\) | 10.0533 | 1.36808 | ||||||||
\(55\) | 6.93378 | 0.934950 | ||||||||
\(56\) | 1.53698 | 0.205388 | ||||||||
\(57\) | −0.568376 | −0.0752832 | ||||||||
\(58\) | −8.46318 | −1.11127 | ||||||||
\(59\) | −6.58293 | −0.857024 | −0.428512 | − | 0.903536i | \(-0.640962\pi\) | ||||
−0.428512 | + | 0.903536i | \(0.640962\pi\) | |||||||
\(60\) | 2.26506 | 0.292418 | ||||||||
\(61\) | −0.889139 | −0.113843 | −0.0569213 | − | 0.998379i | \(-0.518128\pi\) | ||||
−0.0569213 | + | 0.998379i | \(0.518128\pi\) | |||||||
\(62\) | −5.56243 | −0.706429 | ||||||||
\(63\) | 2.91770 | 0.367596 | ||||||||
\(64\) | −3.83013 | −0.478767 | ||||||||
\(65\) | −2.85827 | −0.354524 | ||||||||
\(66\) | 11.3491 | 1.39698 | ||||||||
\(67\) | 4.67997 | 0.571750 | 0.285875 | − | 0.958267i | \(-0.407716\pi\) | ||||
0.285875 | + | 0.958267i | \(0.407716\pi\) | |||||||
\(68\) | 0.598110 | 0.0725315 | ||||||||
\(69\) | −9.49619 | −1.14321 | ||||||||
\(70\) | 4.20181 | 0.502213 | ||||||||
\(71\) | 11.4239 | 1.35577 | 0.677886 | − | 0.735167i | \(-0.262896\pi\) | ||||
0.677886 | + | 0.735167i | \(0.262896\pi\) | |||||||
\(72\) | 1.52641 | 0.179889 | ||||||||
\(73\) | 5.35047 | 0.626225 | 0.313113 | − | 0.949716i | \(-0.398628\pi\) | ||||
0.313113 | + | 0.949716i | \(0.398628\pi\) | |||||||
\(74\) | 5.75869 | 0.669434 | ||||||||
\(75\) | 3.75231 | 0.433279 | ||||||||
\(76\) | 0.759473 | 0.0871175 | ||||||||
\(77\) | 9.09868 | 1.03689 | ||||||||
\(78\) | −4.67838 | −0.529723 | ||||||||
\(79\) | −7.79987 | −0.877554 | −0.438777 | − | 0.898596i | \(-0.644588\pi\) | ||||
−0.438777 | + | 0.898596i | \(0.644588\pi\) | |||||||
\(80\) | 6.17481 | 0.690365 | ||||||||
\(81\) | −0.995634 | −0.110626 | ||||||||
\(82\) | −18.9336 | −2.09087 | ||||||||
\(83\) | −17.9975 | −1.97548 | −0.987740 | − | 0.156107i | \(-0.950105\pi\) | ||||
−0.987740 | + | 0.156107i | \(0.950105\pi\) | |||||||
\(84\) | 2.97227 | 0.324301 | ||||||||
\(85\) | −0.513238 | −0.0556685 | ||||||||
\(86\) | 18.6415 | 2.01016 | ||||||||
\(87\) | 5.13716 | 0.550761 | ||||||||
\(88\) | 4.76002 | 0.507420 | ||||||||
\(89\) | 13.3683 | 1.41704 | 0.708519 | − | 0.705691i | \(-0.249363\pi\) | ||||
0.708519 | + | 0.705691i | \(0.249363\pi\) | |||||||
\(90\) | 4.17292 | 0.439864 | ||||||||
\(91\) | −3.75069 | −0.393179 | ||||||||
\(92\) | 12.6890 | 1.32292 | ||||||||
\(93\) | 3.37640 | 0.350116 | ||||||||
\(94\) | 1.34114 | 0.138328 | ||||||||
\(95\) | −0.651703 | −0.0668633 | ||||||||
\(96\) | 8.06385 | 0.823013 | ||||||||
\(97\) | −13.2660 | −1.34696 | −0.673480 | − | 0.739206i | \(-0.735201\pi\) | ||||
−0.673480 | + | 0.739206i | \(0.735201\pi\) | |||||||
\(98\) | −7.62355 | −0.770095 | ||||||||
\(99\) | 9.03610 | 0.908162 | ||||||||
\(100\) | −5.01389 | −0.501389 | ||||||||
\(101\) | −5.06820 | −0.504305 | −0.252152 | − | 0.967688i | \(-0.581138\pi\) | ||||
−0.252152 | + | 0.967688i | \(0.581138\pi\) | |||||||
\(102\) | −0.840064 | −0.0831787 | ||||||||
\(103\) | −1.26789 | −0.124929 | −0.0624644 | − | 0.998047i | \(-0.519896\pi\) | ||||
−0.0624644 | + | 0.998047i | \(0.519896\pi\) | |||||||
\(104\) | −1.96219 | −0.192409 | ||||||||
\(105\) | −2.55050 | −0.248904 | ||||||||
\(106\) | −19.4606 | −1.89018 | ||||||||
\(107\) | 11.5228 | 1.11395 | 0.556974 | − | 0.830530i | \(-0.311962\pi\) | ||||
0.556974 | + | 0.830530i | \(0.311962\pi\) | |||||||
\(108\) | 8.15407 | 0.784626 | ||||||||
\(109\) | 1.84704 | 0.176914 | 0.0884570 | − | 0.996080i | \(-0.471806\pi\) | ||||
0.0884570 | + | 0.996080i | \(0.471806\pi\) | |||||||
\(110\) | 13.0130 | 1.24074 | ||||||||
\(111\) | −3.49553 | −0.331781 | ||||||||
\(112\) | 8.10275 | 0.765638 | ||||||||
\(113\) | −10.8186 | −1.01773 | −0.508865 | − | 0.860846i | \(-0.669935\pi\) | ||||
−0.508865 | + | 0.860846i | \(0.669935\pi\) | |||||||
\(114\) | −1.06670 | −0.0999057 | ||||||||
\(115\) | −10.8884 | −1.01535 | ||||||||
\(116\) | −6.86435 | −0.637339 | ||||||||
\(117\) | −3.72489 | −0.344367 | ||||||||
\(118\) | −12.3545 | −1.13733 | ||||||||
\(119\) | −0.673484 | −0.0617382 | ||||||||
\(120\) | −1.33431 | −0.121805 | ||||||||
\(121\) | 17.1786 | 1.56169 | ||||||||
\(122\) | −1.66869 | −0.151077 | ||||||||
\(123\) | 11.4927 | 1.03626 | ||||||||
\(124\) | −4.51159 | −0.405153 | ||||||||
\(125\) | 10.8334 | 0.968971 | ||||||||
\(126\) | 5.47580 | 0.487823 | ||||||||
\(127\) | 16.9759 | 1.50637 | 0.753185 | − | 0.657809i | \(-0.228517\pi\) | ||||
0.753185 | + | 0.657809i | \(0.228517\pi\) | |||||||
\(128\) | 6.96893 | 0.615972 | ||||||||
\(129\) | −11.3154 | −0.996266 | ||||||||
\(130\) | −5.36426 | −0.470477 | ||||||||
\(131\) | 0.273878 | 0.0239289 | 0.0119644 | − | 0.999928i | \(-0.496192\pi\) | ||||
0.0119644 | + | 0.999928i | \(0.496192\pi\) | |||||||
\(132\) | 9.20511 | 0.801202 | ||||||||
\(133\) | −0.855181 | −0.0741536 | ||||||||
\(134\) | 8.78316 | 0.758749 | ||||||||
\(135\) | −6.99701 | −0.602206 | ||||||||
\(136\) | −0.352337 | −0.0302126 | ||||||||
\(137\) | −5.63213 | −0.481185 | −0.240593 | − | 0.970626i | \(-0.577342\pi\) | ||||
−0.240593 | + | 0.970626i | \(0.577342\pi\) | |||||||
\(138\) | −17.8220 | −1.51711 | ||||||||
\(139\) | −22.7017 | −1.92553 | −0.962767 | − | 0.270333i | \(-0.912866\pi\) | ||||
−0.962767 | + | 0.270333i | \(0.912866\pi\) | |||||||
\(140\) | 3.40802 | 0.288030 | ||||||||
\(141\) | −0.814072 | −0.0685572 | ||||||||
\(142\) | 21.4399 | 1.79920 | ||||||||
\(143\) | −11.6159 | −0.971367 | ||||||||
\(144\) | 8.04702 | 0.670585 | ||||||||
\(145\) | 5.89029 | 0.489162 | ||||||||
\(146\) | 10.0415 | 0.831042 | ||||||||
\(147\) | 4.62750 | 0.381670 | ||||||||
\(148\) | 4.67078 | 0.383936 | ||||||||
\(149\) | −3.23862 | −0.265318 | −0.132659 | − | 0.991162i | \(-0.542352\pi\) | ||||
−0.132659 | + | 0.991162i | \(0.542352\pi\) | |||||||
\(150\) | 7.04216 | 0.574990 | ||||||||
\(151\) | 18.3287 | 1.49157 | 0.745783 | − | 0.666189i | \(-0.232076\pi\) | ||||
0.745783 | + | 0.666189i | \(0.232076\pi\) | |||||||
\(152\) | −0.447392 | −0.0362883 | ||||||||
\(153\) | −0.668852 | −0.0540735 | ||||||||
\(154\) | 17.0760 | 1.37602 | ||||||||
\(155\) | 3.87140 | 0.310958 | ||||||||
\(156\) | −3.79456 | −0.303808 | ||||||||
\(157\) | −2.10134 | −0.167705 | −0.0838527 | − | 0.996478i | \(-0.526723\pi\) | ||||
−0.0838527 | + | 0.996478i | \(0.526723\pi\) | |||||||
\(158\) | −14.6384 | −1.16457 | ||||||||
\(159\) | 11.8126 | 0.936799 | ||||||||
\(160\) | 9.24605 | 0.730965 | ||||||||
\(161\) | −14.2880 | −1.12605 | ||||||||
\(162\) | −1.86856 | −0.146808 | ||||||||
\(163\) | −23.0706 | −1.80703 | −0.903514 | − | 0.428558i | \(-0.859022\pi\) | ||||
−0.903514 | + | 0.428558i | \(0.859022\pi\) | |||||||
\(164\) | −15.3568 | −1.19916 | ||||||||
\(165\) | −7.89890 | −0.614928 | ||||||||
\(166\) | −33.7768 | −2.62159 | ||||||||
\(167\) | −11.3441 | −0.877832 | −0.438916 | − | 0.898528i | \(-0.644637\pi\) | ||||
−0.438916 | + | 0.898528i | \(0.644637\pi\) | |||||||
\(168\) | −1.75091 | −0.135086 | ||||||||
\(169\) | −8.21167 | −0.631667 | ||||||||
\(170\) | −0.963222 | −0.0738757 | ||||||||
\(171\) | −0.849299 | −0.0649476 | ||||||||
\(172\) | 15.1198 | 1.15287 | ||||||||
\(173\) | −17.2109 | −1.30852 | −0.654259 | − | 0.756271i | \(-0.727019\pi\) | ||||
−0.654259 | + | 0.756271i | \(0.727019\pi\) | |||||||
\(174\) | 9.64118 | 0.730896 | ||||||||
\(175\) | 5.64574 | 0.426778 | ||||||||
\(176\) | 25.0942 | 1.89154 | ||||||||
\(177\) | 7.49921 | 0.563675 | ||||||||
\(178\) | 25.0890 | 1.88050 | ||||||||
\(179\) | −11.9899 | −0.896168 | −0.448084 | − | 0.893991i | \(-0.647893\pi\) | ||||
−0.448084 | + | 0.893991i | \(0.647893\pi\) | |||||||
\(180\) | 3.38458 | 0.252272 | ||||||||
\(181\) | 1.09690 | 0.0815319 | 0.0407660 | − | 0.999169i | \(-0.487020\pi\) | ||||
0.0407660 | + | 0.999169i | \(0.487020\pi\) | |||||||
\(182\) | −7.03912 | −0.521774 | ||||||||
\(183\) | 1.01290 | 0.0748756 | ||||||||
\(184\) | −7.47485 | −0.551053 | ||||||||
\(185\) | −4.00799 | −0.294673 | ||||||||
\(186\) | 6.33667 | 0.464627 | ||||||||
\(187\) | −2.08578 | −0.152527 | ||||||||
\(188\) | 1.08778 | 0.0793342 | ||||||||
\(189\) | −9.18165 | −0.667867 | ||||||||
\(190\) | −1.22309 | −0.0887320 | ||||||||
\(191\) | 1.44468 | 0.104533 | 0.0522667 | − | 0.998633i | \(-0.483355\pi\) | ||||
0.0522667 | + | 0.998633i | \(0.483355\pi\) | |||||||
\(192\) | 4.36325 | 0.314891 | ||||||||
\(193\) | 1.41359 | 0.101753 | 0.0508763 | − | 0.998705i | \(-0.483799\pi\) | ||||
0.0508763 | + | 0.998705i | \(0.483799\pi\) | |||||||
\(194\) | −24.8970 | −1.78750 | ||||||||
\(195\) | 3.25611 | 0.233175 | ||||||||
\(196\) | −6.18334 | −0.441667 | ||||||||
\(197\) | −5.14237 | −0.366379 | −0.183189 | − | 0.983078i | \(-0.558642\pi\) | ||||
−0.183189 | + | 0.983078i | \(0.558642\pi\) | |||||||
\(198\) | 16.9585 | 1.20519 | ||||||||
\(199\) | −16.7502 | −1.18739 | −0.593695 | − | 0.804690i | \(-0.702332\pi\) | ||||
−0.593695 | + | 0.804690i | \(0.702332\pi\) | |||||||
\(200\) | 2.95360 | 0.208851 | ||||||||
\(201\) | −5.33139 | −0.376047 | ||||||||
\(202\) | −9.51176 | −0.669245 | ||||||||
\(203\) | 7.72939 | 0.542497 | ||||||||
\(204\) | −0.681362 | −0.0477049 | ||||||||
\(205\) | 13.1776 | 0.920366 | ||||||||
\(206\) | −2.37951 | −0.165789 | ||||||||
\(207\) | −14.1897 | −0.986256 | ||||||||
\(208\) | −10.3444 | −0.717255 | ||||||||
\(209\) | −2.64849 | −0.183200 | ||||||||
\(210\) | −4.78667 | −0.330311 | ||||||||
\(211\) | −11.7475 | −0.808734 | −0.404367 | − | 0.914597i | \(-0.632508\pi\) | ||||
−0.404367 | + | 0.914597i | \(0.632508\pi\) | |||||||
\(212\) | −15.7842 | −1.08406 | ||||||||
\(213\) | −13.0141 | −0.891708 | ||||||||
\(214\) | 21.6254 | 1.47828 | ||||||||
\(215\) | −12.9743 | −0.884840 | ||||||||
\(216\) | −4.80343 | −0.326832 | ||||||||
\(217\) | 5.08014 | 0.344863 | ||||||||
\(218\) | 3.46643 | 0.234777 | ||||||||
\(219\) | −6.09521 | −0.411876 | ||||||||
\(220\) | 10.5546 | 0.711593 | ||||||||
\(221\) | 0.859806 | 0.0578368 | ||||||||
\(222\) | −6.56025 | −0.440295 | ||||||||
\(223\) | 26.9958 | 1.80778 | 0.903888 | − | 0.427770i | \(-0.140701\pi\) | ||||
0.903888 | + | 0.427770i | \(0.140701\pi\) | |||||||
\(224\) | 12.1329 | 0.810664 | ||||||||
\(225\) | 5.60691 | 0.373794 | ||||||||
\(226\) | −20.3039 | −1.35059 | ||||||||
\(227\) | −6.16279 | −0.409039 | −0.204519 | − | 0.978863i | \(-0.565563\pi\) | ||||
−0.204519 | + | 0.978863i | \(0.565563\pi\) | |||||||
\(228\) | −0.865184 | −0.0572982 | ||||||||
\(229\) | 5.04203 | 0.333187 | 0.166593 | − | 0.986026i | \(-0.446723\pi\) | ||||
0.166593 | + | 0.986026i | \(0.446723\pi\) | |||||||
\(230\) | −20.4348 | −1.34743 | ||||||||
\(231\) | −10.3651 | −0.681975 | ||||||||
\(232\) | 4.04367 | 0.265480 | ||||||||
\(233\) | −8.21008 | −0.537860 | −0.268930 | − | 0.963160i | \(-0.586670\pi\) | ||||
−0.268930 | + | 0.963160i | \(0.586670\pi\) | |||||||
\(234\) | −6.99071 | −0.456997 | ||||||||
\(235\) | −0.933419 | −0.0608896 | ||||||||
\(236\) | −10.0206 | −0.652283 | ||||||||
\(237\) | 8.88554 | 0.577178 | ||||||||
\(238\) | −1.26396 | −0.0819306 | ||||||||
\(239\) | 25.4229 | 1.64447 | 0.822235 | − | 0.569148i | \(-0.192727\pi\) | ||||
0.822235 | + | 0.569148i | \(0.192727\pi\) | |||||||
\(240\) | −7.03429 | −0.454062 | ||||||||
\(241\) | 26.7739 | 1.72466 | 0.862328 | − | 0.506350i | \(-0.169006\pi\) | ||||
0.862328 | + | 0.506350i | \(0.169006\pi\) | |||||||
\(242\) | 32.2399 | 2.07246 | ||||||||
\(243\) | −14.9360 | −0.958148 | ||||||||
\(244\) | −1.35345 | −0.0866458 | ||||||||
\(245\) | 5.30592 | 0.338983 | ||||||||
\(246\) | 21.5690 | 1.37519 | ||||||||
\(247\) | 1.09177 | 0.0694677 | ||||||||
\(248\) | 2.65770 | 0.168764 | ||||||||
\(249\) | 20.5026 | 1.29930 | ||||||||
\(250\) | 20.3317 | 1.28589 | ||||||||
\(251\) | 23.7572 | 1.49954 | 0.749770 | − | 0.661699i | \(-0.230164\pi\) | ||||
0.749770 | + | 0.661699i | \(0.230164\pi\) | |||||||
\(252\) | 4.44134 | 0.279778 | ||||||||
\(253\) | −44.2499 | −2.78197 | ||||||||
\(254\) | 31.8596 | 1.99905 | ||||||||
\(255\) | 0.584676 | 0.0366138 | ||||||||
\(256\) | 20.7392 | 1.29620 | ||||||||
\(257\) | −6.92184 | −0.431773 | −0.215886 | − | 0.976418i | \(-0.569264\pi\) | ||||
−0.215886 | + | 0.976418i | \(0.569264\pi\) | |||||||
\(258\) | −21.2362 | −1.32211 | ||||||||
\(259\) | −5.25939 | −0.326802 | ||||||||
\(260\) | −4.35087 | −0.269829 | ||||||||
\(261\) | 7.67623 | 0.475147 | ||||||||
\(262\) | 0.514002 | 0.0317551 | ||||||||
\(263\) | −9.02135 | −0.556281 | −0.278140 | − | 0.960540i | \(-0.589718\pi\) | ||||
−0.278140 | + | 0.960540i | \(0.589718\pi\) | |||||||
\(264\) | −5.42257 | −0.333736 | ||||||||
\(265\) | 13.5444 | 0.832025 | ||||||||
\(266\) | −1.60496 | −0.0984066 | ||||||||
\(267\) | −15.2291 | −0.932004 | ||||||||
\(268\) | 7.12388 | 0.435160 | ||||||||
\(269\) | 7.43191 | 0.453131 | 0.226566 | − | 0.973996i | \(-0.427250\pi\) | ||||
0.226566 | + | 0.973996i | \(0.427250\pi\) | |||||||
\(270\) | −13.1317 | −0.799167 | ||||||||
\(271\) | 24.3754 | 1.48070 | 0.740351 | − | 0.672220i | \(-0.234659\pi\) | ||||
0.740351 | + | 0.672220i | \(0.234659\pi\) | |||||||
\(272\) | −1.85747 | −0.112626 | ||||||||
\(273\) | 4.27275 | 0.258599 | ||||||||
\(274\) | −10.5701 | −0.638564 | ||||||||
\(275\) | 17.4848 | 1.05437 | ||||||||
\(276\) | −14.4551 | −0.870098 | ||||||||
\(277\) | 15.8453 | 0.952052 | 0.476026 | − | 0.879431i | \(-0.342077\pi\) | ||||
0.476026 | + | 0.879431i | \(0.342077\pi\) | |||||||
\(278\) | −42.6055 | −2.55531 | ||||||||
\(279\) | 5.04520 | 0.302049 | ||||||||
\(280\) | −2.00761 | −0.119977 | ||||||||
\(281\) | 5.55329 | 0.331281 | 0.165641 | − | 0.986186i | \(-0.447031\pi\) | ||||
0.165641 | + | 0.986186i | \(0.447031\pi\) | |||||||
\(282\) | −1.52781 | −0.0909799 | ||||||||
\(283\) | −21.5322 | −1.27996 | −0.639978 | − | 0.768394i | \(-0.721056\pi\) | ||||
−0.639978 | + | 0.768394i | \(0.721056\pi\) | |||||||
\(284\) | 17.3896 | 1.03188 | ||||||||
\(285\) | 0.742414 | 0.0439768 | ||||||||
\(286\) | −21.8001 | −1.28907 | ||||||||
\(287\) | 17.2920 | 1.02072 | ||||||||
\(288\) | 12.0495 | 0.710021 | ||||||||
\(289\) | −16.8456 | −0.990918 | ||||||||
\(290\) | 11.0546 | 0.649150 | ||||||||
\(291\) | 15.1125 | 0.885912 | ||||||||
\(292\) | 8.14451 | 0.476621 | ||||||||
\(293\) | −23.9442 | −1.39884 | −0.699418 | − | 0.714713i | \(-0.746557\pi\) | ||||
−0.699418 | + | 0.714713i | \(0.746557\pi\) | |||||||
\(294\) | 8.68468 | 0.506501 | ||||||||
\(295\) | 8.59863 | 0.500632 | ||||||||
\(296\) | −2.75148 | −0.159926 | ||||||||
\(297\) | −28.4355 | −1.65000 | ||||||||
\(298\) | −6.07809 | −0.352094 | ||||||||
\(299\) | 18.2408 | 1.05490 | ||||||||
\(300\) | 5.71178 | 0.329770 | ||||||||
\(301\) | −17.0252 | −0.981316 | ||||||||
\(302\) | 34.3984 | 1.97941 | ||||||||
\(303\) | 5.77365 | 0.331687 | ||||||||
\(304\) | −2.35859 | −0.135274 | ||||||||
\(305\) | 1.16140 | 0.0665013 | ||||||||
\(306\) | −1.25527 | −0.0717591 | ||||||||
\(307\) | 1.31760 | 0.0751996 | 0.0375998 | − | 0.999293i | \(-0.488029\pi\) | ||||
0.0375998 | + | 0.999293i | \(0.488029\pi\) | |||||||
\(308\) | 13.8500 | 0.789180 | ||||||||
\(309\) | 1.44437 | 0.0821672 | ||||||||
\(310\) | 7.26566 | 0.412662 | ||||||||
\(311\) | −21.9974 | −1.24736 | −0.623679 | − | 0.781680i | \(-0.714363\pi\) | ||||
−0.623679 | + | 0.781680i | \(0.714363\pi\) | |||||||
\(312\) | 2.23531 | 0.126550 | ||||||||
\(313\) | −0.891821 | −0.0504087 | −0.0252044 | − | 0.999682i | \(-0.508024\pi\) | ||||
−0.0252044 | + | 0.999682i | \(0.508024\pi\) | |||||||
\(314\) | −3.94370 | −0.222556 | ||||||||
\(315\) | −3.81111 | −0.214732 | ||||||||
\(316\) | −11.8730 | −0.667908 | ||||||||
\(317\) | −24.3281 | −1.36640 | −0.683202 | − | 0.730229i | \(-0.739413\pi\) | ||||
−0.683202 | + | 0.730229i | \(0.739413\pi\) | |||||||
\(318\) | 22.1693 | 1.24319 | ||||||||
\(319\) | 23.9379 | 1.34026 | ||||||||
\(320\) | 5.00293 | 0.279672 | ||||||||
\(321\) | −13.1266 | −0.732657 | ||||||||
\(322\) | −26.8151 | −1.49435 | ||||||||
\(323\) | 0.196041 | 0.0109080 | ||||||||
\(324\) | −1.51556 | −0.0841977 | ||||||||
\(325\) | −7.20765 | −0.399809 | ||||||||
\(326\) | −43.2978 | −2.39804 | ||||||||
\(327\) | −2.10413 | −0.116359 | ||||||||
\(328\) | 9.04641 | 0.499504 | ||||||||
\(329\) | −1.22486 | −0.0675285 | ||||||||
\(330\) | −14.8243 | −0.816050 | ||||||||
\(331\) | 27.7538 | 1.52549 | 0.762745 | − | 0.646700i | \(-0.223851\pi\) | ||||
0.762745 | + | 0.646700i | \(0.223851\pi\) | |||||||
\(332\) | −27.3958 | −1.50354 | ||||||||
\(333\) | −5.22322 | −0.286231 | ||||||||
\(334\) | −21.2901 | −1.16494 | ||||||||
\(335\) | −6.11300 | −0.333989 | ||||||||
\(336\) | −9.23058 | −0.503569 | ||||||||
\(337\) | 6.10740 | 0.332691 | 0.166346 | − | 0.986068i | \(-0.446803\pi\) | ||||
0.166346 | + | 0.986068i | \(0.446803\pi\) | |||||||
\(338\) | −15.4113 | −0.838263 | ||||||||
\(339\) | 12.3245 | 0.669374 | ||||||||
\(340\) | −0.781253 | −0.0423694 | ||||||||
\(341\) | 15.7332 | 0.851999 | ||||||||
\(342\) | −1.59393 | −0.0861896 | ||||||||
\(343\) | 18.9608 | 1.02379 | ||||||||
\(344\) | −8.90682 | −0.480224 | ||||||||
\(345\) | 12.4040 | 0.667806 | ||||||||
\(346\) | −32.3005 | −1.73649 | ||||||||
\(347\) | 27.7441 | 1.48938 | 0.744691 | − | 0.667409i | \(-0.232597\pi\) | ||||
0.744691 | + | 0.667409i | \(0.232597\pi\) | |||||||
\(348\) | 7.81981 | 0.419186 | ||||||||
\(349\) | −14.3589 | −0.768616 | −0.384308 | − | 0.923205i | \(-0.625560\pi\) | ||||
−0.384308 | + | 0.923205i | \(0.625560\pi\) | |||||||
\(350\) | 10.5957 | 0.566362 | ||||||||
\(351\) | 11.7218 | 0.625663 | ||||||||
\(352\) | 37.5755 | 2.00278 | ||||||||
\(353\) | 1.89459 | 0.100839 | 0.0504194 | − | 0.998728i | \(-0.483944\pi\) | ||||
0.0504194 | + | 0.998728i | \(0.483944\pi\) | |||||||
\(354\) | 14.0742 | 0.748034 | ||||||||
\(355\) | −14.9220 | −0.791977 | ||||||||
\(356\) | 20.3493 | 1.07851 | ||||||||
\(357\) | 0.767227 | 0.0406060 | ||||||||
\(358\) | −22.5021 | −1.18927 | ||||||||
\(359\) | 10.0371 | 0.529740 | 0.264870 | − | 0.964284i | \(-0.414671\pi\) | ||||
0.264870 | + | 0.964284i | \(0.414671\pi\) | |||||||
\(360\) | −1.99380 | −0.105083 | ||||||||
\(361\) | −18.7511 | −0.986898 | ||||||||
\(362\) | 2.05861 | 0.108198 | ||||||||
\(363\) | −19.5697 | −1.02714 | ||||||||
\(364\) | −5.70931 | −0.299249 | ||||||||
\(365\) | −6.98880 | −0.365810 | ||||||||
\(366\) | 1.90096 | 0.0993649 | ||||||||
\(367\) | 5.02023 | 0.262054 | 0.131027 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131027 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(368\) | −39.4064 | −2.05420 | ||||||||
\(369\) | 17.1731 | 0.893996 | ||||||||
\(370\) | −7.52201 | −0.391051 | ||||||||
\(371\) | 17.7733 | 0.922742 | ||||||||
\(372\) | 5.13957 | 0.266474 | ||||||||
\(373\) | −3.12699 | −0.161910 | −0.0809548 | − | 0.996718i | \(-0.525797\pi\) | ||||
−0.0809548 | + | 0.996718i | \(0.525797\pi\) | |||||||
\(374\) | −3.91449 | −0.202413 | ||||||||
\(375\) | −12.3413 | −0.637304 | ||||||||
\(376\) | −0.640790 | −0.0330462 | ||||||||
\(377\) | −9.86776 | −0.508215 | ||||||||
\(378\) | −17.2317 | −0.886302 | ||||||||
\(379\) | 16.8372 | 0.864867 | 0.432433 | − | 0.901666i | \(-0.357655\pi\) | ||||
0.432433 | + | 0.901666i | \(0.357655\pi\) | |||||||
\(380\) | −0.992025 | −0.0508898 | ||||||||
\(381\) | −19.3388 | −0.990757 | ||||||||
\(382\) | 2.71131 | 0.138723 | ||||||||
\(383\) | −3.31954 | −0.169621 | −0.0848104 | − | 0.996397i | \(-0.527028\pi\) | ||||
−0.0848104 | + | 0.996397i | \(0.527028\pi\) | |||||||
\(384\) | −7.93894 | −0.405132 | ||||||||
\(385\) | −11.8847 | −0.605701 | ||||||||
\(386\) | 2.65297 | 0.135032 | ||||||||
\(387\) | −16.9081 | −0.859488 | ||||||||
\(388\) | −20.1936 | −1.02517 | ||||||||
\(389\) | −13.8035 | −0.699867 | −0.349933 | − | 0.936775i | \(-0.613796\pi\) | ||||
−0.349933 | + | 0.936775i | \(0.613796\pi\) | |||||||
\(390\) | 6.11092 | 0.309438 | ||||||||
\(391\) | 3.27538 | 0.165643 | ||||||||
\(392\) | 3.64250 | 0.183974 | ||||||||
\(393\) | −0.312000 | −0.0157383 | ||||||||
\(394\) | −9.65096 | −0.486208 | ||||||||
\(395\) | 10.1882 | 0.512625 | ||||||||
\(396\) | 13.7548 | 0.691204 | ||||||||
\(397\) | 13.6460 | 0.684875 | 0.342438 | − | 0.939541i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939541i | \(0.388747\pi\) | |||||||
\(398\) | −31.4360 | −1.57574 | ||||||||
\(399\) | 0.974214 | 0.0487717 | ||||||||
\(400\) | 15.5710 | 0.778548 | ||||||||
\(401\) | −4.21927 | −0.210700 | −0.105350 | − | 0.994435i | \(-0.533596\pi\) | ||||
−0.105350 | + | 0.994435i | \(0.533596\pi\) | |||||||
\(402\) | −10.0057 | −0.499039 | ||||||||
\(403\) | −6.48558 | −0.323070 | ||||||||
\(404\) | −7.71484 | −0.383828 | ||||||||
\(405\) | 1.30050 | 0.0646224 | ||||||||
\(406\) | 14.5062 | 0.719929 | ||||||||
\(407\) | −16.2883 | −0.807381 | ||||||||
\(408\) | 0.401379 | 0.0198712 | ||||||||
\(409\) | 3.32926 | 0.164621 | 0.0823105 | − | 0.996607i | \(-0.473770\pi\) | ||||
0.0823105 | + | 0.996607i | \(0.473770\pi\) | |||||||
\(410\) | 24.7312 | 1.22139 | ||||||||
\(411\) | 6.41607 | 0.316481 | ||||||||
\(412\) | −1.92999 | −0.0950836 | ||||||||
\(413\) | 11.2833 | 0.555217 | ||||||||
\(414\) | −26.6307 | −1.30883 | ||||||||
\(415\) | 23.5084 | 1.15398 | ||||||||
\(416\) | −15.4895 | −0.759436 | ||||||||
\(417\) | 25.8616 | 1.26645 | ||||||||
\(418\) | −4.97056 | −0.243118 | ||||||||
\(419\) | −17.2091 | −0.840718 | −0.420359 | − | 0.907358i | \(-0.638096\pi\) | ||||
−0.420359 | + | 0.907358i | \(0.638096\pi\) | |||||||
\(420\) | −3.88239 | −0.189441 | ||||||||
\(421\) | 5.90690 | 0.287884 | 0.143942 | − | 0.989586i | \(-0.454022\pi\) | ||||
0.143942 | + | 0.989586i | \(0.454022\pi\) | |||||||
\(422\) | −22.0472 | −1.07324 | ||||||||
\(423\) | −1.21643 | −0.0591450 | ||||||||
\(424\) | 9.29818 | 0.451559 | ||||||||
\(425\) | −1.29423 | −0.0627792 | ||||||||
\(426\) | −24.4242 | −1.18336 | ||||||||
\(427\) | 1.52401 | 0.0737521 | ||||||||
\(428\) | 17.5400 | 0.847828 | ||||||||
\(429\) | 13.2327 | 0.638880 | ||||||||
\(430\) | −24.3496 | −1.17424 | ||||||||
\(431\) | −27.0646 | −1.30366 | −0.651829 | − | 0.758366i | \(-0.725998\pi\) | ||||
−0.651829 | + | 0.758366i | \(0.725998\pi\) | |||||||
\(432\) | −25.3230 | −1.21835 | ||||||||
\(433\) | −5.65104 | −0.271571 | −0.135786 | − | 0.990738i | \(-0.543356\pi\) | ||||
−0.135786 | + | 0.990738i | \(0.543356\pi\) | |||||||
\(434\) | 9.53418 | 0.457655 | ||||||||
\(435\) | −6.71017 | −0.321728 | ||||||||
\(436\) | 2.81157 | 0.134650 | ||||||||
\(437\) | 4.15903 | 0.198953 | ||||||||
\(438\) | −11.4392 | −0.546586 | ||||||||
\(439\) | −26.7713 | −1.27772 | −0.638861 | − | 0.769322i | \(-0.720594\pi\) | ||||
−0.638861 | + | 0.769322i | \(0.720594\pi\) | |||||||
\(440\) | −6.21755 | −0.296410 | ||||||||
\(441\) | 6.91468 | 0.329270 | ||||||||
\(442\) | 1.61364 | 0.0767532 | ||||||||
\(443\) | 34.1995 | 1.62487 | 0.812435 | − | 0.583052i | \(-0.198142\pi\) | ||||
0.812435 | + | 0.583052i | \(0.198142\pi\) | |||||||
\(444\) | −5.32091 | −0.252519 | ||||||||
\(445\) | −17.4617 | −0.827765 | ||||||||
\(446\) | 50.6646 | 2.39904 | ||||||||
\(447\) | 3.68940 | 0.174503 | ||||||||
\(448\) | 6.56497 | 0.310166 | ||||||||
\(449\) | −7.11797 | −0.335918 | −0.167959 | − | 0.985794i | \(-0.553718\pi\) | ||||
−0.167959 | + | 0.985794i | \(0.553718\pi\) | |||||||
\(450\) | 10.5228 | 0.496049 | ||||||||
\(451\) | 53.5533 | 2.52173 | ||||||||
\(452\) | −16.4682 | −0.774597 | ||||||||
\(453\) | −20.8799 | −0.981021 | ||||||||
\(454\) | −11.5660 | −0.542821 | ||||||||
\(455\) | 4.89916 | 0.229676 | ||||||||
\(456\) | 0.509665 | 0.0238673 | ||||||||
\(457\) | 25.8336 | 1.20845 | 0.604223 | − | 0.796815i | \(-0.293484\pi\) | ||||
0.604223 | + | 0.796815i | \(0.293484\pi\) | |||||||
\(458\) | 9.46265 | 0.442161 | ||||||||
\(459\) | 2.10480 | 0.0982435 | ||||||||
\(460\) | −16.5744 | −0.772783 | ||||||||
\(461\) | −38.8134 | −1.80772 | −0.903860 | − | 0.427829i | \(-0.859279\pi\) | ||||
−0.903860 | + | 0.427829i | \(0.859279\pi\) | |||||||
\(462\) | −19.4528 | −0.905026 | ||||||||
\(463\) | 22.8908 | 1.06383 | 0.531913 | − | 0.846799i | \(-0.321473\pi\) | ||||
0.531913 | + | 0.846799i | \(0.321473\pi\) | |||||||
\(464\) | 21.3177 | 0.989648 | ||||||||
\(465\) | −4.41026 | −0.204521 | ||||||||
\(466\) | −15.4083 | −0.713775 | ||||||||
\(467\) | −12.1901 | −0.564089 | −0.282045 | − | 0.959401i | \(-0.591013\pi\) | ||||
−0.282045 | + | 0.959401i | \(0.591013\pi\) | |||||||
\(468\) | −5.67005 | −0.262098 | ||||||||
\(469\) | −8.02163 | −0.370404 | ||||||||
\(470\) | −1.75180 | −0.0808044 | ||||||||
\(471\) | 2.39383 | 0.110302 | ||||||||
\(472\) | 5.90294 | 0.271705 | ||||||||
\(473\) | −52.7270 | −2.42439 | ||||||||
\(474\) | 16.6760 | 0.765953 | ||||||||
\(475\) | −1.64339 | −0.0754039 | ||||||||
\(476\) | −1.02518 | −0.0469891 | ||||||||
\(477\) | 17.6510 | 0.808186 | ||||||||
\(478\) | 47.7125 | 2.18232 | ||||||||
\(479\) | −35.1228 | −1.60480 | −0.802400 | − | 0.596786i | \(-0.796444\pi\) | ||||
−0.802400 | + | 0.596786i | \(0.796444\pi\) | |||||||
\(480\) | −10.5330 | −0.480764 | ||||||||
\(481\) | 6.71442 | 0.306151 | ||||||||
\(482\) | 50.2479 | 2.28873 | ||||||||
\(483\) | 16.2768 | 0.740619 | ||||||||
\(484\) | 26.1493 | 1.18860 | ||||||||
\(485\) | 17.3281 | 0.786828 | ||||||||
\(486\) | −28.0313 | −1.27152 | ||||||||
\(487\) | 7.59211 | 0.344031 | 0.172016 | − | 0.985094i | \(-0.444972\pi\) | ||||
0.172016 | + | 0.985094i | \(0.444972\pi\) | |||||||
\(488\) | 0.797295 | 0.0360918 | ||||||||
\(489\) | 26.2818 | 1.18850 | ||||||||
\(490\) | 9.95790 | 0.449852 | ||||||||
\(491\) | 18.2927 | 0.825537 | 0.412768 | − | 0.910836i | \(-0.364562\pi\) | ||||
0.412768 | + | 0.910836i | \(0.364562\pi\) | |||||||
\(492\) | 17.4943 | 0.788704 | ||||||||
\(493\) | −1.77188 | −0.0798015 | ||||||||
\(494\) | 2.04898 | 0.0921881 | ||||||||
\(495\) | −11.8030 | −0.530504 | ||||||||
\(496\) | 14.0110 | 0.629114 | ||||||||
\(497\) | −19.5810 | −0.878328 | ||||||||
\(498\) | 38.4783 | 1.72425 | ||||||||
\(499\) | 5.76535 | 0.258093 | 0.129046 | − | 0.991639i | \(-0.458808\pi\) | ||||
0.129046 | + | 0.991639i | \(0.458808\pi\) | |||||||
\(500\) | 16.4907 | 0.737486 | ||||||||
\(501\) | 12.9231 | 0.577361 | ||||||||
\(502\) | 44.5864 | 1.98999 | ||||||||
\(503\) | −21.1805 | −0.944394 | −0.472197 | − | 0.881493i | \(-0.656539\pi\) | ||||
−0.472197 | + | 0.881493i | \(0.656539\pi\) | |||||||
\(504\) | −2.61631 | −0.116540 | ||||||||
\(505\) | 6.62010 | 0.294590 | ||||||||
\(506\) | −83.0462 | −3.69185 | ||||||||
\(507\) | 9.35466 | 0.415455 | ||||||||
\(508\) | 25.8408 | 1.14650 | ||||||||
\(509\) | 18.1907 | 0.806289 | 0.403145 | − | 0.915136i | \(-0.367917\pi\) | ||||
0.403145 | + | 0.915136i | \(0.367917\pi\) | |||||||
\(510\) | 1.09729 | 0.0485890 | ||||||||
\(511\) | −9.17088 | −0.405696 | ||||||||
\(512\) | 24.9846 | 1.10417 | ||||||||
\(513\) | 2.67264 | 0.118000 | ||||||||
\(514\) | −12.9906 | −0.572991 | ||||||||
\(515\) | 1.65612 | 0.0729773 | ||||||||
\(516\) | −17.2244 | −0.758260 | ||||||||
\(517\) | −3.79337 | −0.166832 | ||||||||
\(518\) | −9.87058 | −0.433688 | ||||||||
\(519\) | 19.6065 | 0.860628 | ||||||||
\(520\) | 2.56302 | 0.112396 | ||||||||
\(521\) | 21.4553 | 0.939976 | 0.469988 | − | 0.882673i | \(-0.344258\pi\) | ||||
0.469988 | + | 0.882673i | \(0.344258\pi\) | |||||||
\(522\) | 14.4064 | 0.630551 | ||||||||
\(523\) | 11.6184 | 0.508038 | 0.254019 | − | 0.967199i | \(-0.418247\pi\) | ||||
0.254019 | + | 0.967199i | \(0.418247\pi\) | |||||||
\(524\) | 0.416899 | 0.0182123 | ||||||||
\(525\) | −6.43157 | −0.280697 | ||||||||
\(526\) | −16.9309 | −0.738221 | ||||||||
\(527\) | −1.16457 | −0.0507294 | ||||||||
\(528\) | −28.5870 | −1.24409 | ||||||||
\(529\) | 46.4874 | 2.02119 | ||||||||
\(530\) | 25.4195 | 1.10415 | ||||||||
\(531\) | 11.2057 | 0.486288 | ||||||||
\(532\) | −1.30176 | −0.0564385 | ||||||||
\(533\) | −22.0759 | −0.956214 | ||||||||
\(534\) | −28.5812 | −1.23683 | ||||||||
\(535\) | −15.0511 | −0.650714 | ||||||||
\(536\) | −4.19655 | −0.181264 | ||||||||
\(537\) | 13.6588 | 0.589421 | ||||||||
\(538\) | 13.9479 | 0.601335 | ||||||||
\(539\) | 21.5630 | 0.928785 | ||||||||
\(540\) | −10.6509 | −0.458341 | ||||||||
\(541\) | 15.8443 | 0.681198 | 0.340599 | − | 0.940209i | \(-0.389370\pi\) | ||||
0.340599 | + | 0.940209i | \(0.389370\pi\) | |||||||
\(542\) | 45.7467 | 1.96499 | ||||||||
\(543\) | −1.24958 | −0.0536245 | ||||||||
\(544\) | −2.78134 | −0.119249 | ||||||||
\(545\) | −2.41260 | −0.103345 | ||||||||
\(546\) | 8.01890 | 0.343177 | ||||||||
\(547\) | −1.00000 | −0.0427569 | ||||||||
\(548\) | −8.57325 | −0.366231 | ||||||||
\(549\) | 1.51353 | 0.0645959 | ||||||||
\(550\) | 32.8147 | 1.39922 | ||||||||
\(551\) | −2.24991 | −0.0958495 | ||||||||
\(552\) | 8.51528 | 0.362434 | ||||||||
\(553\) | 13.3692 | 0.568517 | ||||||||
\(554\) | 29.7377 | 1.26343 | ||||||||
\(555\) | 4.56587 | 0.193810 | ||||||||
\(556\) | −34.5566 | −1.46553 | ||||||||
\(557\) | 11.0799 | 0.469471 | 0.234735 | − | 0.972059i | \(-0.424578\pi\) | ||||
0.234735 | + | 0.972059i | \(0.424578\pi\) | |||||||
\(558\) | 9.46861 | 0.400838 | ||||||||
\(559\) | 21.7353 | 0.919305 | ||||||||
\(560\) | −10.5838 | −0.447248 | ||||||||
\(561\) | 2.37610 | 0.100319 | ||||||||
\(562\) | 10.4221 | 0.439632 | ||||||||
\(563\) | 41.1603 | 1.73470 | 0.867351 | − | 0.497697i | \(-0.165821\pi\) | ||||
0.867351 | + | 0.497697i | \(0.165821\pi\) | |||||||
\(564\) | −1.23918 | −0.0521791 | ||||||||
\(565\) | 14.1313 | 0.594509 | ||||||||
\(566\) | −40.4106 | −1.69858 | ||||||||
\(567\) | 1.70655 | 0.0716683 | ||||||||
\(568\) | −10.2439 | −0.429825 | ||||||||
\(569\) | −9.52628 | −0.399363 | −0.199681 | − | 0.979861i | \(-0.563991\pi\) | ||||
−0.199681 | + | 0.979861i | \(0.563991\pi\) | |||||||
\(570\) | 1.39333 | 0.0583601 | ||||||||
\(571\) | 4.76393 | 0.199364 | 0.0996822 | − | 0.995019i | \(-0.468217\pi\) | ||||
0.0996822 | + | 0.995019i | \(0.468217\pi\) | |||||||
\(572\) | −17.6817 | −0.739310 | ||||||||
\(573\) | −1.64577 | −0.0687530 | ||||||||
\(574\) | 32.4529 | 1.35456 | ||||||||
\(575\) | −27.4571 | −1.14504 | ||||||||
\(576\) | 6.51982 | 0.271659 | ||||||||
\(577\) | 33.8345 | 1.40855 | 0.704274 | − | 0.709929i | \(-0.251273\pi\) | ||||
0.704274 | + | 0.709929i | \(0.251273\pi\) | |||||||
\(578\) | −31.6151 | −1.31501 | ||||||||
\(579\) | −1.61035 | −0.0669240 | ||||||||
\(580\) | 8.96623 | 0.372303 | ||||||||
\(581\) | 30.8483 | 1.27980 | ||||||||
\(582\) | 28.3625 | 1.17566 | ||||||||
\(583\) | 55.0437 | 2.27968 | ||||||||
\(584\) | −4.79779 | −0.198534 | ||||||||
\(585\) | 4.86547 | 0.201162 | ||||||||
\(586\) | −44.9374 | −1.85635 | ||||||||
\(587\) | −12.2101 | −0.503964 | −0.251982 | − | 0.967732i | \(-0.581082\pi\) | ||||
−0.251982 | + | 0.967732i | \(0.581082\pi\) | |||||||
\(588\) | 7.04400 | 0.290490 | ||||||||
\(589\) | −1.47875 | −0.0609310 | ||||||||
\(590\) | 16.1375 | 0.664371 | ||||||||
\(591\) | 5.85814 | 0.240972 | ||||||||
\(592\) | −14.5054 | −0.596168 | ||||||||
\(593\) | 32.7830 | 1.34624 | 0.673118 | − | 0.739535i | \(-0.264954\pi\) | ||||
0.673118 | + | 0.739535i | \(0.264954\pi\) | |||||||
\(594\) | −53.3664 | −2.18965 | ||||||||
\(595\) | 0.879707 | 0.0360645 | ||||||||
\(596\) | −4.92984 | −0.201934 | ||||||||
\(597\) | 19.0817 | 0.780961 | ||||||||
\(598\) | 34.2336 | 1.39992 | ||||||||
\(599\) | −26.1846 | −1.06987 | −0.534936 | − | 0.844892i | \(-0.679664\pi\) | ||||
−0.534936 | + | 0.844892i | \(0.679664\pi\) | |||||||
\(600\) | −3.36471 | −0.137364 | ||||||||
\(601\) | −14.1011 | −0.575196 | −0.287598 | − | 0.957751i | \(-0.592857\pi\) | ||||
−0.287598 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(602\) | −31.9521 | −1.30227 | ||||||||
\(603\) | −7.96646 | −0.324419 | ||||||||
\(604\) | 27.9000 | 1.13523 | ||||||||
\(605\) | −22.4387 | −0.912262 | ||||||||
\(606\) | 10.8357 | 0.440171 | ||||||||
\(607\) | 16.3651 | 0.664239 | 0.332120 | − | 0.943237i | \(-0.392236\pi\) | ||||
0.332120 | + | 0.943237i | \(0.392236\pi\) | |||||||
\(608\) | −3.53171 | −0.143230 | ||||||||
\(609\) | −8.80525 | −0.356807 | ||||||||
\(610\) | 2.17965 | 0.0882516 | ||||||||
\(611\) | 1.56372 | 0.0632612 | ||||||||
\(612\) | −1.01813 | −0.0411555 | ||||||||
\(613\) | −13.3441 | −0.538961 | −0.269481 | − | 0.963006i | \(-0.586852\pi\) | ||||
−0.269481 | + | 0.963006i | \(0.586852\pi\) | |||||||
\(614\) | 2.47282 | 0.0997948 | ||||||||
\(615\) | −15.0118 | −0.605336 | ||||||||
\(616\) | −8.15882 | −0.328728 | ||||||||
\(617\) | 34.5802 | 1.39215 | 0.696074 | − | 0.717971i | \(-0.254929\pi\) | ||||
0.696074 | + | 0.717971i | \(0.254929\pi\) | |||||||
\(618\) | 2.71072 | 0.109041 | ||||||||
\(619\) | −20.0240 | −0.804832 | −0.402416 | − | 0.915457i | \(-0.631829\pi\) | ||||
−0.402416 | + | 0.915457i | \(0.631829\pi\) | |||||||
\(620\) | 5.89306 | 0.236671 | ||||||||
\(621\) | 44.6534 | 1.79188 | ||||||||
\(622\) | −41.2837 | −1.65533 | ||||||||
\(623\) | −22.9137 | −0.918019 | ||||||||
\(624\) | 11.7843 | 0.471748 | ||||||||
\(625\) | 2.31852 | 0.0927408 | ||||||||
\(626\) | −1.67373 | −0.0668957 | ||||||||
\(627\) | 3.01714 | 0.120493 | ||||||||
\(628\) | −3.19868 | −0.127641 | ||||||||
\(629\) | 1.20566 | 0.0480728 | ||||||||
\(630\) | −7.15251 | −0.284963 | ||||||||
\(631\) | −1.64737 | −0.0655808 | −0.0327904 | − | 0.999462i | \(-0.510439\pi\) | ||||
−0.0327904 | + | 0.999462i | \(0.510439\pi\) | |||||||
\(632\) | 6.99418 | 0.278213 | ||||||||
\(633\) | 13.3827 | 0.531914 | ||||||||
\(634\) | −45.6579 | −1.81331 | ||||||||
\(635\) | −22.1740 | −0.879948 | ||||||||
\(636\) | 17.9812 | 0.713000 | ||||||||
\(637\) | −8.88878 | −0.352186 | ||||||||
\(638\) | 44.9255 | 1.77862 | ||||||||
\(639\) | −19.4463 | −0.769285 | ||||||||
\(640\) | −9.10283 | −0.359821 | ||||||||
\(641\) | 30.9733 | 1.22337 | 0.611686 | − | 0.791100i | \(-0.290491\pi\) | ||||
0.611686 | + | 0.791100i | \(0.290491\pi\) | |||||||
\(642\) | −24.6354 | −0.972283 | ||||||||
\(643\) | 24.8226 | 0.978907 | 0.489454 | − | 0.872029i | \(-0.337196\pi\) | ||||
0.489454 | + | 0.872029i | \(0.337196\pi\) | |||||||
\(644\) | −21.7493 | −0.857042 | ||||||||
\(645\) | 14.7802 | 0.581970 | ||||||||
\(646\) | 0.367921 | 0.0144757 | ||||||||
\(647\) | 36.5122 | 1.43544 | 0.717721 | − | 0.696331i | \(-0.245185\pi\) | ||||
0.717721 | + | 0.696331i | \(0.245185\pi\) | |||||||
\(648\) | 0.892790 | 0.0350721 | ||||||||
\(649\) | 34.9445 | 1.37169 | ||||||||
\(650\) | −13.5270 | −0.530572 | ||||||||
\(651\) | −5.78725 | −0.226820 | ||||||||
\(652\) | −35.1182 | −1.37533 | ||||||||
\(653\) | −26.5164 | −1.03767 | −0.518834 | − | 0.854875i | \(-0.673634\pi\) | ||||
−0.518834 | + | 0.854875i | \(0.673634\pi\) | |||||||
\(654\) | −3.94893 | −0.154415 | ||||||||
\(655\) | −0.357740 | −0.0139781 | ||||||||
\(656\) | 47.6914 | 1.86204 | ||||||||
\(657\) | −9.10781 | −0.355329 | ||||||||
\(658\) | −2.29875 | −0.0896147 | ||||||||
\(659\) | −25.7938 | −1.00478 | −0.502391 | − | 0.864641i | \(-0.667546\pi\) | ||||
−0.502391 | + | 0.864641i | \(0.667546\pi\) | |||||||
\(660\) | −12.0237 | −0.468023 | ||||||||
\(661\) | −41.9540 | −1.63182 | −0.815910 | − | 0.578179i | \(-0.803764\pi\) | ||||
−0.815910 | + | 0.578179i | \(0.803764\pi\) | |||||||
\(662\) | 52.0871 | 2.02442 | ||||||||
\(663\) | −0.979483 | −0.0380400 | ||||||||
\(664\) | 16.1384 | 0.626292 | ||||||||
\(665\) | 1.11704 | 0.0433169 | ||||||||
\(666\) | −9.80269 | −0.379847 | ||||||||
\(667\) | −37.5906 | −1.45551 | ||||||||
\(668\) | −17.2680 | −0.668120 | ||||||||
\(669\) | −30.7534 | −1.18900 | ||||||||
\(670\) | −11.4726 | −0.443225 | ||||||||
\(671\) | 4.71986 | 0.182208 | ||||||||
\(672\) | −13.8217 | −0.533183 | ||||||||
\(673\) | −3.20648 | −0.123601 | −0.0618003 | − | 0.998089i | \(-0.519684\pi\) | ||||
−0.0618003 | + | 0.998089i | \(0.519684\pi\) | |||||||
\(674\) | 11.4621 | 0.441503 | ||||||||
\(675\) | −17.6443 | −0.679128 | ||||||||
\(676\) | −12.4998 | −0.480763 | ||||||||
\(677\) | 4.84844 | 0.186341 | 0.0931704 | − | 0.995650i | \(-0.470300\pi\) | ||||
0.0931704 | + | 0.995650i | \(0.470300\pi\) | |||||||
\(678\) | 23.1300 | 0.888303 | ||||||||
\(679\) | 22.7384 | 0.872618 | ||||||||
\(680\) | 0.460223 | 0.0176487 | ||||||||
\(681\) | 7.02059 | 0.269030 | ||||||||
\(682\) | 29.5273 | 1.13066 | ||||||||
\(683\) | −32.3263 | −1.23693 | −0.618466 | − | 0.785812i | \(-0.712245\pi\) | ||||
−0.618466 | + | 0.785812i | \(0.712245\pi\) | |||||||
\(684\) | −1.29281 | −0.0494317 | ||||||||
\(685\) | 7.35670 | 0.281085 | ||||||||
\(686\) | 35.5847 | 1.35863 | ||||||||
\(687\) | −5.74384 | −0.219141 | ||||||||
\(688\) | −46.9555 | −1.79016 | ||||||||
\(689\) | −22.6903 | −0.864432 | ||||||||
\(690\) | 23.2792 | 0.886223 | ||||||||
\(691\) | −9.59431 | −0.364985 | −0.182492 | − | 0.983207i | \(-0.558416\pi\) | ||||
−0.182492 | + | 0.983207i | \(0.558416\pi\) | |||||||
\(692\) | −26.1985 | −0.995916 | ||||||||
\(693\) | −15.4882 | −0.588347 | ||||||||
\(694\) | 52.0689 | 1.97651 | ||||||||
\(695\) | 29.6530 | 1.12480 | ||||||||
\(696\) | −4.60651 | −0.174609 | ||||||||
\(697\) | −3.96401 | −0.150148 | ||||||||
\(698\) | −26.9482 | −1.02000 | ||||||||
\(699\) | 9.35285 | 0.353757 | ||||||||
\(700\) | 8.59397 | 0.324821 | ||||||||
\(701\) | −48.0675 | −1.81549 | −0.907743 | − | 0.419527i | \(-0.862196\pi\) | ||||
−0.907743 | + | 0.419527i | \(0.862196\pi\) | |||||||
\(702\) | 21.9989 | 0.830295 | ||||||||
\(703\) | 1.53093 | 0.0577401 | ||||||||
\(704\) | 20.3317 | 0.766279 | ||||||||
\(705\) | 1.06334 | 0.0400478 | ||||||||
\(706\) | 3.55568 | 0.133820 | ||||||||
\(707\) | 8.68706 | 0.326710 | ||||||||
\(708\) | 11.4153 | 0.429014 | ||||||||
\(709\) | 12.6771 | 0.476099 | 0.238049 | − | 0.971253i | \(-0.423492\pi\) | ||||
0.238049 | + | 0.971253i | \(0.423492\pi\) | |||||||
\(710\) | −28.0049 | −1.05100 | ||||||||
\(711\) | 13.2773 | 0.497937 | ||||||||
\(712\) | −11.9874 | −0.449248 | ||||||||
\(713\) | −24.7064 | −0.925263 | ||||||||
\(714\) | 1.43990 | 0.0538867 | ||||||||
\(715\) | 15.1727 | 0.567426 | ||||||||
\(716\) | −18.2511 | −0.682076 | ||||||||
\(717\) | −28.9615 | −1.08159 | ||||||||
\(718\) | 18.8372 | 0.702999 | ||||||||
\(719\) | 14.9369 | 0.557053 | 0.278526 | − | 0.960429i | \(-0.410154\pi\) | ||||
0.278526 | + | 0.960429i | \(0.410154\pi\) | |||||||
\(720\) | −10.5110 | −0.391723 | ||||||||
\(721\) | 2.17320 | 0.0809343 | ||||||||
\(722\) | −35.1911 | −1.30968 | ||||||||
\(723\) | −30.5005 | −1.13433 | ||||||||
\(724\) | 1.66971 | 0.0620541 | ||||||||
\(725\) | 14.8535 | 0.551644 | ||||||||
\(726\) | −36.7274 | −1.36308 | ||||||||
\(727\) | −16.9039 | −0.626932 | −0.313466 | − | 0.949599i | \(-0.601490\pi\) | ||||
−0.313466 | + | 0.949599i | \(0.601490\pi\) | |||||||
\(728\) | 3.36326 | 0.124651 | ||||||||
\(729\) | 20.0019 | 0.740811 | ||||||||
\(730\) | −13.1163 | −0.485454 | ||||||||
\(731\) | 3.90285 | 0.144352 | ||||||||
\(732\) | 1.54184 | 0.0569880 | ||||||||
\(733\) | 17.0731 | 0.630609 | 0.315305 | − | 0.948991i | \(-0.397893\pi\) | ||||
0.315305 | + | 0.948991i | \(0.397893\pi\) | |||||||
\(734\) | 9.42174 | 0.347763 | ||||||||
\(735\) | −6.04445 | −0.222953 | ||||||||
\(736\) | −59.0063 | −2.17500 | ||||||||
\(737\) | −24.8429 | −0.915101 | ||||||||
\(738\) | 32.2297 | 1.18639 | ||||||||
\(739\) | −0.313121 | −0.0115183 | −0.00575917 | − | 0.999983i | \(-0.501833\pi\) | ||||
−0.00575917 | + | 0.999983i | \(0.501833\pi\) | |||||||
\(740\) | −6.10098 | −0.224277 | ||||||||
\(741\) | −1.24373 | −0.0456897 | ||||||||
\(742\) | 33.3561 | 1.22454 | ||||||||
\(743\) | −19.0657 | −0.699451 | −0.349726 | − | 0.936852i | \(-0.613725\pi\) | ||||
−0.349726 | + | 0.936852i | \(0.613725\pi\) | |||||||
\(744\) | −3.02763 | −0.110998 | ||||||||
\(745\) | 4.23029 | 0.154986 | ||||||||
\(746\) | −5.86860 | −0.214865 | ||||||||
\(747\) | 30.6361 | 1.12092 | ||||||||
\(748\) | −3.17498 | −0.116089 | ||||||||
\(749\) | −19.7504 | −0.721663 | ||||||||
\(750\) | −23.1617 | −0.845744 | ||||||||
\(751\) | −14.1901 | −0.517803 | −0.258901 | − | 0.965904i | \(-0.583360\pi\) | ||||
−0.258901 | + | 0.965904i | \(0.583360\pi\) | |||||||
\(752\) | −3.37816 | −0.123189 | ||||||||
\(753\) | −27.0640 | −0.986266 | ||||||||
\(754\) | −18.5194 | −0.674435 | ||||||||
\(755\) | −23.9410 | −0.871301 | ||||||||
\(756\) | −13.9763 | −0.508315 | ||||||||
\(757\) | −32.0979 | −1.16662 | −0.583309 | − | 0.812250i | \(-0.698242\pi\) | ||||
−0.583309 | + | 0.812250i | \(0.698242\pi\) | |||||||
\(758\) | 31.5992 | 1.14773 | ||||||||
\(759\) | 50.4091 | 1.82973 | ||||||||
\(760\) | 0.584385 | 0.0211979 | ||||||||
\(761\) | 27.3107 | 0.990013 | 0.495006 | − | 0.868889i | \(-0.335166\pi\) | ||||
0.495006 | + | 0.868889i | \(0.335166\pi\) | |||||||
\(762\) | −36.2942 | −1.31480 | ||||||||
\(763\) | −3.16588 | −0.114613 | ||||||||
\(764\) | 2.19910 | 0.0795607 | ||||||||
\(765\) | 0.873656 | 0.0315871 | ||||||||
\(766\) | −6.22997 | −0.225098 | ||||||||
\(767\) | −14.4049 | −0.520132 | ||||||||
\(768\) | −23.6259 | −0.852528 | ||||||||
\(769\) | 15.5549 | 0.560923 | 0.280461 | − | 0.959865i | \(-0.409513\pi\) | ||||
0.280461 | + | 0.959865i | \(0.409513\pi\) | |||||||
\(770\) | −22.3047 | −0.803805 | ||||||||
\(771\) | 7.88530 | 0.283982 | ||||||||
\(772\) | 2.15178 | 0.0774442 | ||||||||
\(773\) | −49.6932 | −1.78734 | −0.893670 | − | 0.448724i | \(-0.851878\pi\) | ||||
−0.893670 | + | 0.448724i | \(0.851878\pi\) | |||||||
\(774\) | −31.7324 | −1.14060 | ||||||||
\(775\) | 9.76245 | 0.350678 | ||||||||
\(776\) | 11.8957 | 0.427030 | ||||||||
\(777\) | 5.99145 | 0.214942 | ||||||||
\(778\) | −25.9058 | −0.928769 | ||||||||
\(779\) | −5.03345 | −0.180342 | ||||||||
\(780\) | 4.95647 | 0.177470 | ||||||||
\(781\) | −60.6423 | −2.16995 | ||||||||
\(782\) | 6.14708 | 0.219819 | ||||||||
\(783\) | −24.1562 | −0.863271 | ||||||||
\(784\) | 19.2028 | 0.685813 | ||||||||
\(785\) | 2.74478 | 0.0979654 | ||||||||
\(786\) | −0.585546 | −0.0208858 | ||||||||
\(787\) | −14.9449 | −0.532729 | −0.266365 | − | 0.963872i | \(-0.585823\pi\) | ||||
−0.266365 | + | 0.963872i | \(0.585823\pi\) | |||||||
\(788\) | −7.82774 | −0.278852 | ||||||||
\(789\) | 10.2770 | 0.365873 | ||||||||
\(790\) | 19.1208 | 0.680286 | ||||||||
\(791\) | 18.5435 | 0.659330 | ||||||||
\(792\) | −8.10271 | −0.287917 | ||||||||
\(793\) | −1.94564 | −0.0690916 | ||||||||
\(794\) | 25.6103 | 0.908874 | ||||||||
\(795\) | −15.4296 | −0.547233 | ||||||||
\(796\) | −25.4972 | −0.903726 | ||||||||
\(797\) | −13.1154 | −0.464573 | −0.232286 | − | 0.972647i | \(-0.574621\pi\) | ||||
−0.232286 | + | 0.972647i | \(0.574621\pi\) | |||||||
\(798\) | 1.82836 | 0.0647233 | ||||||||
\(799\) | 0.280785 | 0.00993347 | ||||||||
\(800\) | 23.3157 | 0.824333 | ||||||||
\(801\) | −22.7561 | −0.804049 | ||||||||
\(802\) | −7.91853 | −0.279613 | ||||||||
\(803\) | −28.4022 | −1.00229 | ||||||||
\(804\) | −8.11546 | −0.286210 | ||||||||
\(805\) | 18.6630 | 0.657786 | ||||||||
\(806\) | −12.1718 | −0.428735 | ||||||||
\(807\) | −8.46636 | −0.298030 | ||||||||
\(808\) | 4.54468 | 0.159881 | ||||||||
\(809\) | −19.4909 | −0.685262 | −0.342631 | − | 0.939470i | \(-0.611318\pi\) | ||||
−0.342631 | + | 0.939470i | \(0.611318\pi\) | |||||||
\(810\) | 2.44072 | 0.0857581 | ||||||||
\(811\) | 18.5367 | 0.650912 | 0.325456 | − | 0.945557i | \(-0.394482\pi\) | ||||
0.325456 | + | 0.945557i | \(0.394482\pi\) | |||||||
\(812\) | 11.7657 | 0.412896 | ||||||||
\(813\) | −27.7683 | −0.973876 | ||||||||
\(814\) | −30.5691 | −1.07145 | ||||||||
\(815\) | 30.1349 | 1.05558 | ||||||||
\(816\) | 2.11601 | 0.0740753 | ||||||||
\(817\) | 4.95579 | 0.173381 | ||||||||
\(818\) | 6.24819 | 0.218463 | ||||||||
\(819\) | 6.38459 | 0.223095 | ||||||||
\(820\) | 20.0590 | 0.700492 | ||||||||
\(821\) | −12.1526 | −0.424130 | −0.212065 | − | 0.977256i | \(-0.568019\pi\) | ||||
−0.212065 | + | 0.977256i | \(0.568019\pi\) | |||||||
\(822\) | 12.0414 | 0.419992 | ||||||||
\(823\) | 15.5837 | 0.543214 | 0.271607 | − | 0.962408i | \(-0.412445\pi\) | ||||
0.271607 | + | 0.962408i | \(0.412445\pi\) | |||||||
\(824\) | 1.13692 | 0.0396065 | ||||||||
\(825\) | −19.9185 | −0.693475 | ||||||||
\(826\) | 21.1761 | 0.736809 | ||||||||
\(827\) | 14.2481 | 0.495456 | 0.247728 | − | 0.968830i | \(-0.420316\pi\) | ||||
0.247728 | + | 0.968830i | \(0.420316\pi\) | |||||||
\(828\) | −21.5997 | −0.750641 | ||||||||
\(829\) | 52.8914 | 1.83700 | 0.918498 | − | 0.395426i | \(-0.129403\pi\) | ||||
0.918498 | + | 0.395426i | \(0.129403\pi\) | |||||||
\(830\) | 44.1194 | 1.53141 | ||||||||
\(831\) | −18.0508 | −0.626176 | ||||||||
\(832\) | −8.38120 | −0.290566 | ||||||||
\(833\) | −1.59609 | −0.0553014 | ||||||||
\(834\) | 48.5358 | 1.68066 | ||||||||
\(835\) | 14.8177 | 0.512787 | ||||||||
\(836\) | −4.03154 | −0.139434 | ||||||||
\(837\) | −15.8766 | −0.548777 | ||||||||
\(838\) | −32.2972 | −1.11569 | ||||||||
\(839\) | −25.6169 | −0.884395 | −0.442198 | − | 0.896918i | \(-0.645801\pi\) | ||||
−0.442198 | + | 0.896918i | \(0.645801\pi\) | |||||||
\(840\) | 2.28705 | 0.0789107 | ||||||||
\(841\) | −8.66460 | −0.298779 | ||||||||
\(842\) | 11.0858 | 0.382041 | ||||||||
\(843\) | −6.32625 | −0.217888 | ||||||||
\(844\) | −17.8821 | −0.615529 | ||||||||
\(845\) | 10.7261 | 0.368989 | ||||||||
\(846\) | −2.28294 | −0.0784892 | ||||||||
\(847\) | −29.4446 | −1.01173 | ||||||||
\(848\) | 49.0187 | 1.68331 | ||||||||
\(849\) | 24.5293 | 0.841842 | ||||||||
\(850\) | −2.42894 | −0.0833121 | ||||||||
\(851\) | 25.5782 | 0.876808 | ||||||||
\(852\) | −19.8101 | −0.678681 | ||||||||
\(853\) | 23.7883 | 0.814498 | 0.407249 | − | 0.913317i | \(-0.366488\pi\) | ||||
0.407249 | + | 0.913317i | \(0.366488\pi\) | |||||||
\(854\) | 2.86020 | 0.0978739 | ||||||||
\(855\) | 1.10936 | 0.0379392 | ||||||||
\(856\) | −10.3325 | −0.353158 | ||||||||
\(857\) | −1.27557 | −0.0435727 | −0.0217863 | − | 0.999763i | \(-0.506935\pi\) | ||||
−0.0217863 | + | 0.999763i | \(0.506935\pi\) | |||||||
\(858\) | 24.8345 | 0.847835 | ||||||||
\(859\) | −38.6456 | −1.31857 | −0.659285 | − | 0.751893i | \(-0.729141\pi\) | ||||
−0.659285 | + | 0.751893i | \(0.729141\pi\) | |||||||
\(860\) | −19.7495 | −0.673454 | ||||||||
\(861\) | −19.6989 | −0.671337 | ||||||||
\(862\) | −50.7937 | −1.73004 | ||||||||
\(863\) | 13.3344 | 0.453908 | 0.226954 | − | 0.973905i | \(-0.427123\pi\) | ||||
0.226954 | + | 0.973905i | \(0.427123\pi\) | |||||||
\(864\) | −37.9182 | −1.29000 | ||||||||
\(865\) | 22.4809 | 0.764373 | ||||||||
\(866\) | −10.6056 | −0.360393 | ||||||||
\(867\) | 19.1904 | 0.651739 | ||||||||
\(868\) | 7.73302 | 0.262476 | ||||||||
\(869\) | 41.4044 | 1.40455 | ||||||||
\(870\) | −12.5933 | −0.426954 | ||||||||
\(871\) | 10.2408 | 0.346998 | ||||||||
\(872\) | −1.65625 | −0.0560876 | ||||||||
\(873\) | 22.5820 | 0.764284 | ||||||||
\(874\) | 7.80547 | 0.264024 | ||||||||
\(875\) | −18.5688 | −0.627741 | ||||||||
\(876\) | −9.27815 | −0.313480 | ||||||||
\(877\) | −5.39699 | −0.182244 | −0.0911218 | − | 0.995840i | \(-0.529045\pi\) | ||||
−0.0911218 | + | 0.995840i | \(0.529045\pi\) | |||||||
\(878\) | −50.2431 | −1.69562 | ||||||||
\(879\) | 27.2770 | 0.920031 | ||||||||
\(880\) | −32.7781 | −1.10495 | ||||||||
\(881\) | −5.04786 | −0.170067 | −0.0850333 | − | 0.996378i | \(-0.527100\pi\) | ||||
−0.0850333 | + | 0.996378i | \(0.527100\pi\) | |||||||
\(882\) | 12.9771 | 0.436963 | ||||||||
\(883\) | −36.4145 | −1.22545 | −0.612723 | − | 0.790298i | \(-0.709926\pi\) | ||||
−0.612723 | + | 0.790298i | \(0.709926\pi\) | |||||||
\(884\) | 1.30880 | 0.0440197 | ||||||||
\(885\) | −9.79549 | −0.329272 | ||||||||
\(886\) | 64.1841 | 2.15631 | ||||||||
\(887\) | −24.9346 | −0.837224 | −0.418612 | − | 0.908165i | \(-0.637483\pi\) | ||||
−0.418612 | + | 0.908165i | \(0.637483\pi\) | |||||||
\(888\) | 3.13446 | 0.105185 | ||||||||
\(889\) | −29.0973 | −0.975891 | ||||||||
\(890\) | −32.7714 | −1.09850 | ||||||||
\(891\) | 5.28517 | 0.177060 | ||||||||
\(892\) | 41.0932 | 1.37590 | ||||||||
\(893\) | 0.356538 | 0.0119311 | ||||||||
\(894\) | 6.92410 | 0.231577 | ||||||||
\(895\) | 15.6613 | 0.523498 | ||||||||
\(896\) | −11.9450 | −0.399053 | ||||||||
\(897\) | −20.7798 | −0.693818 | ||||||||
\(898\) | −13.3587 | −0.445785 | ||||||||
\(899\) | 13.3654 | 0.445763 | ||||||||
\(900\) | 8.53486 | 0.284495 | ||||||||
\(901\) | −4.07434 | −0.135736 | ||||||||
\(902\) | 100.506 | 3.34649 | ||||||||
\(903\) | 19.3950 | 0.645424 | ||||||||
\(904\) | 9.70111 | 0.322654 | ||||||||
\(905\) | −1.43277 | −0.0476270 | ||||||||
\(906\) | −39.1863 | −1.30188 | ||||||||
\(907\) | −27.1951 | −0.903000 | −0.451500 | − | 0.892271i | \(-0.649111\pi\) | ||||
−0.451500 | + | 0.892271i | \(0.649111\pi\) | |||||||
\(908\) | −9.38102 | −0.311320 | ||||||||
\(909\) | 8.62731 | 0.286150 | ||||||||
\(910\) | 9.19451 | 0.304795 | ||||||||
\(911\) | −47.9588 | −1.58895 | −0.794473 | − | 0.607299i | \(-0.792253\pi\) | ||||
−0.794473 | + | 0.607299i | \(0.792253\pi\) | |||||||
\(912\) | 2.68688 | 0.0889716 | ||||||||
\(913\) | 95.5369 | 3.16181 | ||||||||
\(914\) | 48.4834 | 1.60369 | ||||||||
\(915\) | −1.32305 | −0.0437387 | ||||||||
\(916\) | 7.67500 | 0.253589 | ||||||||
\(917\) | −0.469436 | −0.0155021 | ||||||||
\(918\) | 3.95018 | 0.130376 | ||||||||
\(919\) | −20.3674 | −0.671857 | −0.335928 | − | 0.941887i | \(-0.609050\pi\) | ||||
−0.335928 | + | 0.941887i | \(0.609050\pi\) | |||||||
\(920\) | 9.76366 | 0.321898 | ||||||||
\(921\) | −1.50100 | −0.0494597 | ||||||||
\(922\) | −72.8432 | −2.39896 | ||||||||
\(923\) | 24.9982 | 0.822825 | ||||||||
\(924\) | −15.7778 | −0.519053 | ||||||||
\(925\) | −10.1069 | −0.332313 | ||||||||
\(926\) | 42.9604 | 1.41177 | ||||||||
\(927\) | 2.15826 | 0.0708864 | ||||||||
\(928\) | 31.9207 | 1.04785 | ||||||||
\(929\) | 3.43001 | 0.112535 | 0.0562675 | − | 0.998416i | \(-0.482080\pi\) | ||||
0.0562675 | + | 0.998416i | \(0.482080\pi\) | |||||||
\(930\) | −8.27697 | −0.271413 | ||||||||
\(931\) | −2.02670 | −0.0664224 | ||||||||
\(932\) | −12.4974 | −0.409367 | ||||||||
\(933\) | 25.0593 | 0.820403 | ||||||||
\(934\) | −22.8778 | −0.748583 | ||||||||
\(935\) | 2.72445 | 0.0890989 | ||||||||
\(936\) | 3.34013 | 0.109176 | ||||||||
\(937\) | −55.8441 | −1.82435 | −0.912173 | − | 0.409805i | \(-0.865597\pi\) | ||||
−0.912173 | + | 0.409805i | \(0.865597\pi\) | |||||||
\(938\) | −15.0546 | −0.491551 | ||||||||
\(939\) | 1.01595 | 0.0331544 | ||||||||
\(940\) | −1.42086 | −0.0463432 | ||||||||
\(941\) | −35.2757 | −1.14996 | −0.574978 | − | 0.818169i | \(-0.694989\pi\) | ||||
−0.574978 | + | 0.818169i | \(0.694989\pi\) | |||||||
\(942\) | 4.49263 | 0.146378 | ||||||||
\(943\) | −84.0969 | −2.73857 | ||||||||
\(944\) | 31.1195 | 1.01285 | ||||||||
\(945\) | 11.9931 | 0.390135 | ||||||||
\(946\) | −98.9555 | −3.21732 | ||||||||
\(947\) | −45.2546 | −1.47058 | −0.735289 | − | 0.677754i | \(-0.762954\pi\) | ||||
−0.735289 | + | 0.677754i | \(0.762954\pi\) | |||||||
\(948\) | 13.5256 | 0.439291 | ||||||||
\(949\) | 11.7080 | 0.380059 | ||||||||
\(950\) | −3.08424 | −0.100066 | ||||||||
\(951\) | 27.7144 | 0.898701 | ||||||||
\(952\) | 0.603916 | 0.0195730 | ||||||||
\(953\) | 39.0690 | 1.26557 | 0.632784 | − | 0.774328i | \(-0.281912\pi\) | ||||
0.632784 | + | 0.774328i | \(0.281912\pi\) | |||||||
\(954\) | 33.1267 | 1.07252 | ||||||||
\(955\) | −1.88705 | −0.0610634 | ||||||||
\(956\) | 38.6988 | 1.25161 | ||||||||
\(957\) | −27.2698 | −0.881508 | ||||||||
\(958\) | −65.9168 | −2.12968 | ||||||||
\(959\) | 9.65365 | 0.311733 | ||||||||
\(960\) | −5.69929 | −0.183944 | ||||||||
\(961\) | −22.2156 | −0.716631 | ||||||||
\(962\) | 12.6013 | 0.406283 | ||||||||
\(963\) | −19.6146 | −0.632070 | ||||||||
\(964\) | 40.7553 | 1.31264 | ||||||||
\(965\) | −1.84644 | −0.0594390 | ||||||||
\(966\) | 30.5475 | 0.982850 | ||||||||
\(967\) | 11.8771 | 0.381942 | 0.190971 | − | 0.981596i | \(-0.438836\pi\) | ||||
0.190971 | + | 0.981596i | \(0.438836\pi\) | |||||||
\(968\) | −15.4041 | −0.495106 | ||||||||
\(969\) | −0.223328 | −0.00717434 | ||||||||
\(970\) | 32.5206 | 1.04417 | ||||||||
\(971\) | −43.3430 | −1.39094 | −0.695471 | − | 0.718554i | \(-0.744804\pi\) | ||||
−0.695471 | + | 0.718554i | \(0.744804\pi\) | |||||||
\(972\) | −22.7357 | −0.729248 | ||||||||
\(973\) | 38.9115 | 1.24744 | ||||||||
\(974\) | 14.2485 | 0.456552 | ||||||||
\(975\) | 8.21089 | 0.262959 | ||||||||
\(976\) | 4.20323 | 0.134542 | ||||||||
\(977\) | 30.9084 | 0.988846 | 0.494423 | − | 0.869221i | \(-0.335379\pi\) | ||||
0.494423 | + | 0.869221i | \(0.335379\pi\) | |||||||
\(978\) | 49.3245 | 1.57722 | ||||||||
\(979\) | −70.9637 | −2.26801 | ||||||||
\(980\) | 8.07669 | 0.258001 | ||||||||
\(981\) | −3.14411 | −0.100384 | ||||||||
\(982\) | 34.3308 | 1.09554 | ||||||||
\(983\) | 35.0128 | 1.11673 | 0.558367 | − | 0.829594i | \(-0.311428\pi\) | ||||
0.558367 | + | 0.829594i | \(0.311428\pi\) | |||||||
\(984\) | −10.3056 | −0.328530 | ||||||||
\(985\) | 6.71698 | 0.214021 | ||||||||
\(986\) | −3.32539 | −0.105902 | ||||||||
\(987\) | 1.39535 | 0.0444143 | ||||||||
\(988\) | 1.66190 | 0.0528720 | ||||||||
\(989\) | 82.7992 | 2.63286 | ||||||||
\(990\) | −22.1513 | −0.704014 | ||||||||
\(991\) | −22.7329 | −0.722135 | −0.361067 | − | 0.932540i | \(-0.617588\pi\) | ||||
−0.361067 | + | 0.932540i | \(0.617588\pi\) | |||||||
\(992\) | 20.9799 | 0.666112 | ||||||||
\(993\) | −31.6169 | −1.00333 | ||||||||
\(994\) | −36.7487 | −1.16560 | ||||||||
\(995\) | 21.8792 | 0.693616 | ||||||||
\(996\) | 31.2091 | 0.988898 | ||||||||
\(997\) | −10.6754 | −0.338095 | −0.169047 | − | 0.985608i | \(-0.554069\pi\) | ||||
−0.169047 | + | 0.985608i | \(0.554069\pi\) | |||||||
\(998\) | 10.8201 | 0.342506 | ||||||||
\(999\) | 16.4368 | 0.520038 |
(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 | 547.2.a.b.1.16 | ✓ | 18 | |
3.2 | odd | 2 | 4923.2.a.l.1.3 | 18 | |||
4.3 | odd | 2 | 8752.2.a.s.1.11 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.2.a.b.1.16 | ✓ | 18 | 1.1 | even | 1 | trivial | |
4923.2.a.l.1.3 | 18 | 3.2 | odd | 2 | |||
8752.2.a.s.1.11 | 18 | 4.3 | odd | 2 |