Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, 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("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 7 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 462) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.64575 | 1.18322 | 0.591608 | − | 0.806226i | \(-0.298493\pi\) | ||||
0.591608 | + | 0.806226i | \(0.298493\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.64575 | −0.836660 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.64575 | −0.683130 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.29150 | 1.21395 | 0.606977 | − | 0.794719i | \(-0.292382\pi\) | ||||
0.606977 | + | 0.794719i | \(0.292382\pi\) | |||||||
\(20\) | 2.64575 | 0.591608 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −2.64575 | −0.551677 | −0.275839 | − | 0.961204i | \(-0.588956\pi\) | ||||
−0.275839 | + | 0.961204i | \(0.588956\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 2.64575 | 0.483046 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.29150 | 0.212322 | 0.106161 | − | 0.994349i | \(-0.466144\pi\) | ||||
0.106161 | + | 0.994349i | \(0.466144\pi\) | |||||||
\(38\) | −5.29150 | −0.858395 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | −2.64575 | −0.418330 | ||||||||
\(41\) | 9.00000 | 1.40556 | 0.702782 | − | 0.711405i | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.29150 | 1.41694 | 0.708470 | − | 0.705740i | \(-0.249386\pi\) | ||||
0.708470 | + | 0.705740i | \(0.249386\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 2.64575 | 0.394405 | ||||||||
\(46\) | 2.64575 | 0.390095 | ||||||||
\(47\) | −3.93725 | −0.574308 | −0.287154 | − | 0.957885i | \(-0.592709\pi\) | ||||
−0.287154 | + | 0.957885i | \(0.592709\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.00000 | −0.282843 | ||||||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.64575 | 0.356753 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.29150 | −0.700877 | ||||||||
\(58\) | −2.00000 | −0.262613 | ||||||||
\(59\) | 6.58301 | 0.857034 | 0.428517 | − | 0.903534i | \(-0.359036\pi\) | ||||
0.428517 | + | 0.903534i | \(0.359036\pi\) | |||||||
\(60\) | −2.64575 | −0.341565 | ||||||||
\(61\) | 11.9373 | 1.52841 | 0.764204 | − | 0.644974i | \(-0.223132\pi\) | ||||
0.764204 | + | 0.644974i | \(0.223132\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.5830 | −1.31266 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 7.58301 | 0.926412 | 0.463206 | − | 0.886251i | \(-0.346699\pi\) | ||||
0.463206 | + | 0.886251i | \(0.346699\pi\) | |||||||
\(68\) | −3.00000 | −0.363803 | ||||||||
\(69\) | 2.64575 | 0.318511 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.70850 | −0.321440 | −0.160720 | − | 0.987000i | \(-0.551382\pi\) | ||||
−0.160720 | + | 0.987000i | \(0.551382\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −15.2915 | −1.78974 | −0.894868 | − | 0.446332i | \(-0.852730\pi\) | ||||
−0.894868 | + | 0.446332i | \(0.852730\pi\) | |||||||
\(74\) | −1.29150 | −0.150134 | ||||||||
\(75\) | −2.00000 | −0.230940 | ||||||||
\(76\) | 5.29150 | 0.606977 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | 10.6458 | 1.19774 | 0.598870 | − | 0.800846i | \(-0.295616\pi\) | ||||
0.598870 | + | 0.800846i | \(0.295616\pi\) | |||||||
\(80\) | 2.64575 | 0.295804 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.00000 | −0.993884 | ||||||||
\(83\) | 15.5830 | 1.71046 | 0.855229 | − | 0.518251i | \(-0.173417\pi\) | ||||
0.855229 | + | 0.518251i | \(0.173417\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.93725 | −0.860916 | ||||||||
\(86\) | −9.29150 | −1.00193 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 2.70850 | 0.287100 | 0.143550 | − | 0.989643i | \(-0.454148\pi\) | ||||
0.143550 | + | 0.989643i | \(0.454148\pi\) | |||||||
\(90\) | −2.64575 | −0.278887 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.64575 | −0.275839 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 3.93725 | 0.406097 | ||||||||
\(95\) | 14.0000 | 1.43637 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −11.5830 | −1.17608 | −0.588038 | − | 0.808833i | \(-0.700099\pi\) | ||||
−0.588038 | + | 0.808833i | \(0.700099\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | 7.29150 | 0.725532 | 0.362766 | − | 0.931880i | \(-0.381832\pi\) | ||||
0.362766 | + | 0.931880i | \(0.381832\pi\) | |||||||
\(102\) | −3.00000 | −0.297044 | ||||||||
\(103\) | −10.0000 | −0.985329 | −0.492665 | − | 0.870219i | \(-0.663977\pi\) | ||||
−0.492665 | + | 0.870219i | \(0.663977\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | 9.00000 | 0.870063 | 0.435031 | − | 0.900415i | \(-0.356737\pi\) | ||||
0.435031 | + | 0.900415i | \(0.356737\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −3.93725 | −0.377121 | −0.188560 | − | 0.982062i | \(-0.560382\pi\) | ||||
−0.188560 | + | 0.982062i | \(0.560382\pi\) | |||||||
\(110\) | −2.64575 | −0.252262 | ||||||||
\(111\) | −1.29150 | −0.122584 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.5830 | 1.18371 | 0.591855 | − | 0.806045i | \(-0.298396\pi\) | ||||
0.591855 | + | 0.806045i | \(0.298396\pi\) | |||||||
\(114\) | 5.29150 | 0.495595 | ||||||||
\(115\) | −7.00000 | −0.652753 | ||||||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | −4.00000 | −0.369800 | ||||||||
\(118\) | −6.58301 | −0.606015 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.64575 | 0.241523 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −11.9373 | −1.08075 | ||||||||
\(123\) | −9.00000 | −0.811503 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | −7.93725 | −0.709930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.64575 | 0.234772 | 0.117386 | − | 0.993086i | \(-0.462548\pi\) | ||||
0.117386 | + | 0.993086i | \(0.462548\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.29150 | −0.818071 | ||||||||
\(130\) | 10.5830 | 0.928191 | ||||||||
\(131\) | −18.5830 | −1.62360 | −0.811802 | − | 0.583932i | \(-0.801513\pi\) | ||||
−0.811802 | + | 0.583932i | \(0.801513\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.58301 | −0.655072 | ||||||||
\(135\) | −2.64575 | −0.227710 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | −13.2915 | −1.13557 | −0.567785 | − | 0.823177i | \(-0.692199\pi\) | ||||
−0.567785 | + | 0.823177i | \(0.692199\pi\) | |||||||
\(138\) | −2.64575 | −0.225221 | ||||||||
\(139\) | −12.5830 | −1.06728 | −0.533638 | − | 0.845713i | \(-0.679176\pi\) | ||||
−0.533638 | + | 0.845713i | \(0.679176\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.93725 | 0.331577 | ||||||||
\(142\) | 2.70850 | 0.227292 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.29150 | 0.439435 | ||||||||
\(146\) | 15.2915 | 1.26553 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.29150 | 0.106161 | ||||||||
\(149\) | 19.8745 | 1.62818 | 0.814092 | − | 0.580737i | \(-0.197235\pi\) | ||||
0.814092 | + | 0.580737i | \(0.197235\pi\) | |||||||
\(150\) | 2.00000 | 0.163299 | ||||||||
\(151\) | 22.6458 | 1.84289 | 0.921443 | − | 0.388515i | \(-0.127012\pi\) | ||||
0.921443 | + | 0.388515i | \(0.127012\pi\) | |||||||
\(152\) | −5.29150 | −0.429198 | ||||||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.5830 | −0.850047 | ||||||||
\(156\) | 4.00000 | 0.320256 | ||||||||
\(157\) | −0.708497 | −0.0565442 | −0.0282721 | − | 0.999600i | \(-0.509000\pi\) | ||||
−0.0282721 | + | 0.999600i | \(0.509000\pi\) | |||||||
\(158\) | −10.6458 | −0.846931 | ||||||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | −2.64575 | −0.209165 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.58301 | −0.437295 | −0.218647 | − | 0.975804i | \(-0.570164\pi\) | ||||
−0.218647 | + | 0.975804i | \(0.570164\pi\) | |||||||
\(164\) | 9.00000 | 0.702782 | ||||||||
\(165\) | −2.64575 | −0.205971 | ||||||||
\(166\) | −15.5830 | −1.20948 | ||||||||
\(167\) | 8.70850 | 0.673884 | 0.336942 | − | 0.941525i | \(-0.390607\pi\) | ||||
0.336942 | + | 0.941525i | \(0.390607\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 7.93725 | 0.608760 | ||||||||
\(171\) | 5.29150 | 0.404651 | ||||||||
\(172\) | 9.29150 | 0.708470 | ||||||||
\(173\) | 4.00000 | 0.304114 | 0.152057 | − | 0.988372i | \(-0.451410\pi\) | ||||
0.152057 | + | 0.988372i | \(0.451410\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −6.58301 | −0.494809 | ||||||||
\(178\) | −2.70850 | −0.203010 | ||||||||
\(179\) | 4.70850 | 0.351930 | 0.175965 | − | 0.984396i | \(-0.443696\pi\) | ||||
0.175965 | + | 0.984396i | \(0.443696\pi\) | |||||||
\(180\) | 2.64575 | 0.197203 | ||||||||
\(181\) | −5.29150 | −0.393314 | −0.196657 | − | 0.980472i | \(-0.563009\pi\) | ||||
−0.196657 | + | 0.980472i | \(0.563009\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.9373 | −0.882427 | ||||||||
\(184\) | 2.64575 | 0.195047 | ||||||||
\(185\) | 3.41699 | 0.251222 | ||||||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | −3.00000 | −0.219382 | ||||||||
\(188\) | −3.93725 | −0.287154 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.0000 | −1.01567 | ||||||||
\(191\) | 6.70850 | 0.485410 | 0.242705 | − | 0.970100i | \(-0.421965\pi\) | ||||
0.242705 | + | 0.970100i | \(0.421965\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −15.8745 | −1.14267 | −0.571336 | − | 0.820716i | \(-0.693575\pi\) | ||||
−0.571336 | + | 0.820716i | \(0.693575\pi\) | |||||||
\(194\) | 11.5830 | 0.831611 | ||||||||
\(195\) | 10.5830 | 0.757865 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.8745 | 1.55849 | 0.779247 | − | 0.626717i | \(-0.215602\pi\) | ||||
0.779247 | + | 0.626717i | \(0.215602\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −19.1660 | −1.35864 | −0.679321 | − | 0.733841i | \(-0.737726\pi\) | ||||
−0.679321 | + | 0.733841i | \(0.737726\pi\) | |||||||
\(200\) | −2.00000 | −0.141421 | ||||||||
\(201\) | −7.58301 | −0.534864 | ||||||||
\(202\) | −7.29150 | −0.513028 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.00000 | 0.210042 | ||||||||
\(205\) | 23.8118 | 1.66309 | ||||||||
\(206\) | 10.0000 | 0.696733 | ||||||||
\(207\) | −2.64575 | −0.183892 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 5.29150 | 0.366021 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.2915 | 1.46577 | 0.732884 | − | 0.680354i | \(-0.238174\pi\) | ||||
0.732884 | + | 0.680354i | \(0.238174\pi\) | |||||||
\(212\) | 4.00000 | 0.274721 | ||||||||
\(213\) | 2.70850 | 0.185583 | ||||||||
\(214\) | −9.00000 | −0.615227 | ||||||||
\(215\) | 24.5830 | 1.67655 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.93725 | 0.266664 | ||||||||
\(219\) | 15.2915 | 1.03330 | ||||||||
\(220\) | 2.64575 | 0.178377 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 1.29150 | 0.0866800 | ||||||||
\(223\) | 28.4575 | 1.90566 | 0.952828 | − | 0.303511i | \(-0.0981588\pi\) | ||||
0.952828 | + | 0.303511i | \(0.0981588\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.00000 | 0.133333 | ||||||||
\(226\) | −12.5830 | −0.837009 | ||||||||
\(227\) | 2.41699 | 0.160422 | 0.0802108 | − | 0.996778i | \(-0.474441\pi\) | ||||
0.0802108 | + | 0.996778i | \(0.474441\pi\) | |||||||
\(228\) | −5.29150 | −0.350438 | ||||||||
\(229\) | 6.70850 | 0.443310 | 0.221655 | − | 0.975125i | \(-0.428854\pi\) | ||||
0.221655 | + | 0.975125i | \(0.428854\pi\) | |||||||
\(230\) | 7.00000 | 0.461566 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | 20.1660 | 1.32112 | 0.660560 | − | 0.750774i | \(-0.270319\pi\) | ||||
0.660560 | + | 0.750774i | \(0.270319\pi\) | |||||||
\(234\) | 4.00000 | 0.261488 | ||||||||
\(235\) | −10.4170 | −0.679530 | ||||||||
\(236\) | 6.58301 | 0.428517 | ||||||||
\(237\) | −10.6458 | −0.691516 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.70850 | 0.175198 | 0.0875991 | − | 0.996156i | \(-0.472081\pi\) | ||||
0.0875991 | + | 0.996156i | \(0.472081\pi\) | |||||||
\(240\) | −2.64575 | −0.170783 | ||||||||
\(241\) | −27.1660 | −1.74992 | −0.874958 | − | 0.484198i | \(-0.839111\pi\) | ||||
−0.874958 | + | 0.484198i | \(0.839111\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.9373 | 0.764204 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | −21.1660 | −1.34676 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −15.5830 | −0.987533 | ||||||||
\(250\) | 7.93725 | 0.501996 | ||||||||
\(251\) | 23.2915 | 1.47015 | 0.735073 | − | 0.677988i | \(-0.237148\pi\) | ||||
0.735073 | + | 0.677988i | \(0.237148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.64575 | −0.166337 | ||||||||
\(254\) | −2.64575 | −0.166009 | ||||||||
\(255\) | 7.93725 | 0.497050 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.29150 | 0.579588 | 0.289794 | − | 0.957089i | \(-0.406413\pi\) | ||||
0.289794 | + | 0.957089i | \(0.406413\pi\) | |||||||
\(258\) | 9.29150 | 0.578464 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −10.5830 | −0.656330 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 18.5830 | 1.14806 | ||||||||
\(263\) | 21.8745 | 1.34884 | 0.674420 | − | 0.738348i | \(-0.264394\pi\) | ||||
0.674420 | + | 0.738348i | \(0.264394\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 10.5830 | 0.650109 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.70850 | −0.165757 | ||||||||
\(268\) | 7.58301 | 0.463206 | ||||||||
\(269\) | −10.6458 | −0.649083 | −0.324541 | − | 0.945871i | \(-0.605210\pi\) | ||||
−0.324541 | + | 0.945871i | \(0.605210\pi\) | |||||||
\(270\) | 2.64575 | 0.161015 | ||||||||
\(271\) | 9.29150 | 0.564419 | 0.282209 | − | 0.959353i | \(-0.408933\pi\) | ||||
0.282209 | + | 0.959353i | \(0.408933\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.2915 | 0.802969 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | 2.64575 | 0.159256 | ||||||||
\(277\) | −17.1660 | −1.03141 | −0.515703 | − | 0.856768i | \(-0.672469\pi\) | ||||
−0.515703 | + | 0.856768i | \(0.672469\pi\) | |||||||
\(278\) | 12.5830 | 0.754679 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.00000 | −0.178965 | −0.0894825 | − | 0.995988i | \(-0.528521\pi\) | ||||
−0.0894825 | + | 0.995988i | \(0.528521\pi\) | |||||||
\(282\) | −3.93725 | −0.234460 | ||||||||
\(283\) | 30.4575 | 1.81051 | 0.905256 | − | 0.424867i | \(-0.139679\pi\) | ||||
0.905256 | + | 0.424867i | \(0.139679\pi\) | |||||||
\(284\) | −2.70850 | −0.160720 | ||||||||
\(285\) | −14.0000 | −0.829288 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | −5.29150 | −0.310728 | ||||||||
\(291\) | 11.5830 | 0.679008 | ||||||||
\(292\) | −15.2915 | −0.894868 | ||||||||
\(293\) | −14.5830 | −0.851948 | −0.425974 | − | 0.904735i | \(-0.640069\pi\) | ||||
−0.425974 | + | 0.904735i | \(0.640069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4170 | 1.01406 | ||||||||
\(296\) | −1.29150 | −0.0750671 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −19.8745 | −1.15130 | ||||||||
\(299\) | 10.5830 | 0.612031 | ||||||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −22.6458 | −1.30312 | ||||||||
\(303\) | −7.29150 | −0.418886 | ||||||||
\(304\) | 5.29150 | 0.303488 | ||||||||
\(305\) | 31.5830 | 1.80844 | ||||||||
\(306\) | 3.00000 | 0.171499 | ||||||||
\(307\) | −11.4170 | −0.651602 | −0.325801 | − | 0.945438i | \(-0.605634\pi\) | ||||
−0.325801 | + | 0.945438i | \(0.605634\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0000 | 0.568880 | ||||||||
\(310\) | 10.5830 | 0.601074 | ||||||||
\(311\) | 22.5203 | 1.27701 | 0.638503 | − | 0.769619i | \(-0.279554\pi\) | ||||
0.638503 | + | 0.769619i | \(0.279554\pi\) | |||||||
\(312\) | −4.00000 | −0.226455 | ||||||||
\(313\) | −20.5830 | −1.16342 | −0.581710 | − | 0.813396i | \(-0.697616\pi\) | ||||
−0.581710 | + | 0.813396i | \(0.697616\pi\) | |||||||
\(314\) | 0.708497 | 0.0399828 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.6458 | 0.598870 | ||||||||
\(317\) | 9.22876 | 0.518339 | 0.259169 | − | 0.965832i | \(-0.416551\pi\) | ||||
0.259169 | + | 0.965832i | \(0.416551\pi\) | |||||||
\(318\) | 4.00000 | 0.224309 | ||||||||
\(319\) | 2.00000 | 0.111979 | ||||||||
\(320\) | 2.64575 | 0.147902 | ||||||||
\(321\) | −9.00000 | −0.502331 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.8745 | −0.883281 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −8.00000 | −0.443760 | ||||||||
\(326\) | 5.58301 | 0.309214 | ||||||||
\(327\) | 3.93725 | 0.217731 | ||||||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.64575 | 0.145644 | ||||||||
\(331\) | 13.0000 | 0.714545 | 0.357272 | − | 0.934000i | \(-0.383707\pi\) | ||||
0.357272 | + | 0.934000i | \(0.383707\pi\) | |||||||
\(332\) | 15.5830 | 0.855229 | ||||||||
\(333\) | 1.29150 | 0.0707739 | ||||||||
\(334\) | −8.70850 | −0.476508 | ||||||||
\(335\) | 20.0627 | 1.09614 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.70850 | 0.365435 | 0.182718 | − | 0.983165i | \(-0.441511\pi\) | ||||
0.182718 | + | 0.983165i | \(0.441511\pi\) | |||||||
\(338\) | −3.00000 | −0.163178 | ||||||||
\(339\) | −12.5830 | −0.683415 | ||||||||
\(340\) | −7.93725 | −0.430458 | ||||||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | −5.29150 | −0.286132 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.29150 | −0.500964 | ||||||||
\(345\) | 7.00000 | 0.376867 | ||||||||
\(346\) | −4.00000 | −0.215041 | ||||||||
\(347\) | 29.5830 | 1.58810 | 0.794049 | − | 0.607853i | \(-0.207969\pi\) | ||||
0.794049 | + | 0.607853i | \(0.207969\pi\) | |||||||
\(348\) | −2.00000 | −0.107211 | ||||||||
\(349\) | −13.2288 | −0.708119 | −0.354060 | − | 0.935223i | \(-0.615199\pi\) | ||||
−0.354060 | + | 0.935223i | \(0.615199\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −23.2915 | −1.23968 | −0.619841 | − | 0.784728i | \(-0.712803\pi\) | ||||
−0.619841 | + | 0.784728i | \(0.712803\pi\) | |||||||
\(354\) | 6.58301 | 0.349883 | ||||||||
\(355\) | −7.16601 | −0.380332 | ||||||||
\(356\) | 2.70850 | 0.143550 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.70850 | −0.248852 | ||||||||
\(359\) | 20.5830 | 1.08633 | 0.543165 | − | 0.839626i | \(-0.317226\pi\) | ||||
0.543165 | + | 0.839626i | \(0.317226\pi\) | |||||||
\(360\) | −2.64575 | −0.139443 | ||||||||
\(361\) | 9.00000 | 0.473684 | ||||||||
\(362\) | 5.29150 | 0.278115 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.4575 | −2.11764 | ||||||||
\(366\) | 11.9373 | 0.623970 | ||||||||
\(367\) | 10.7085 | 0.558979 | 0.279490 | − | 0.960149i | \(-0.409835\pi\) | ||||
0.279490 | + | 0.960149i | \(0.409835\pi\) | |||||||
\(368\) | −2.64575 | −0.137919 | ||||||||
\(369\) | 9.00000 | 0.468521 | ||||||||
\(370\) | −3.41699 | −0.177641 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | −15.8118 | −0.818702 | −0.409351 | − | 0.912377i | \(-0.634245\pi\) | ||||
−0.409351 | + | 0.912377i | \(0.634245\pi\) | |||||||
\(374\) | 3.00000 | 0.155126 | ||||||||
\(375\) | 7.93725 | 0.409878 | ||||||||
\(376\) | 3.93725 | 0.203048 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.5830 | −1.41684 | −0.708422 | − | 0.705789i | \(-0.750593\pi\) | ||||
−0.708422 | + | 0.705789i | \(0.750593\pi\) | |||||||
\(380\) | 14.0000 | 0.718185 | ||||||||
\(381\) | −2.64575 | −0.135546 | ||||||||
\(382\) | −6.70850 | −0.343237 | ||||||||
\(383\) | 18.7085 | 0.955960 | 0.477980 | − | 0.878371i | \(-0.341369\pi\) | ||||
0.477980 | + | 0.878371i | \(0.341369\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.8745 | 0.807991 | ||||||||
\(387\) | 9.29150 | 0.472314 | ||||||||
\(388\) | −11.5830 | −0.588038 | ||||||||
\(389\) | 31.9373 | 1.61928 | 0.809642 | − | 0.586925i | \(-0.199662\pi\) | ||||
0.809642 | + | 0.586925i | \(0.199662\pi\) | |||||||
\(390\) | −10.5830 | −0.535891 | ||||||||
\(391\) | 7.93725 | 0.401404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.5830 | 0.937389 | ||||||||
\(394\) | −21.8745 | −1.10202 | ||||||||
\(395\) | 28.1660 | 1.41719 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 6.00000 | 0.301131 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(398\) | 19.1660 | 0.960705 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | 0.100000 | ||||||||
\(401\) | −35.8745 | −1.79149 | −0.895744 | − | 0.444571i | \(-0.853356\pi\) | ||||
−0.895744 | + | 0.444571i | \(0.853356\pi\) | |||||||
\(402\) | 7.58301 | 0.378206 | ||||||||
\(403\) | 16.0000 | 0.797017 | ||||||||
\(404\) | 7.29150 | 0.362766 | ||||||||
\(405\) | 2.64575 | 0.131468 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.29150 | 0.0640174 | ||||||||
\(408\) | −3.00000 | −0.148522 | ||||||||
\(409\) | 35.8745 | 1.77388 | 0.886940 | − | 0.461884i | \(-0.152827\pi\) | ||||
0.886940 | + | 0.461884i | \(0.152827\pi\) | |||||||
\(410\) | −23.8118 | −1.17598 | ||||||||
\(411\) | 13.2915 | 0.655621 | ||||||||
\(412\) | −10.0000 | −0.492665 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.64575 | 0.130032 | ||||||||
\(415\) | 41.2288 | 2.02384 | ||||||||
\(416\) | 4.00000 | 0.196116 | ||||||||
\(417\) | 12.5830 | 0.616192 | ||||||||
\(418\) | −5.29150 | −0.258816 | ||||||||
\(419\) | −9.87451 | −0.482401 | −0.241201 | − | 0.970475i | \(-0.577541\pi\) | ||||
−0.241201 | + | 0.970475i | \(0.577541\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.12549 | 0.298538 | 0.149269 | − | 0.988797i | \(-0.452308\pi\) | ||||
0.149269 | + | 0.988797i | \(0.452308\pi\) | |||||||
\(422\) | −21.2915 | −1.03645 | ||||||||
\(423\) | −3.93725 | −0.191436 | ||||||||
\(424\) | −4.00000 | −0.194257 | ||||||||
\(425\) | −6.00000 | −0.291043 | ||||||||
\(426\) | −2.70850 | −0.131227 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.00000 | 0.435031 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | −24.5830 | −1.18550 | ||||||||
\(431\) | −17.2915 | −0.832902 | −0.416451 | − | 0.909158i | \(-0.636726\pi\) | ||||
−0.416451 | + | 0.909158i | \(0.636726\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 1.58301 | 0.0760744 | 0.0380372 | − | 0.999276i | \(-0.487889\pi\) | ||||
0.0380372 | + | 0.999276i | \(0.487889\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.29150 | −0.253708 | ||||||||
\(436\) | −3.93725 | −0.188560 | ||||||||
\(437\) | −14.0000 | −0.669711 | ||||||||
\(438\) | −15.2915 | −0.730656 | ||||||||
\(439\) | −9.35425 | −0.446454 | −0.223227 | − | 0.974766i | \(-0.571659\pi\) | ||||
−0.223227 | + | 0.974766i | \(0.571659\pi\) | |||||||
\(440\) | −2.64575 | −0.126131 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | −31.1660 | −1.48074 | −0.740371 | − | 0.672199i | \(-0.765350\pi\) | ||||
−0.740371 | + | 0.672199i | \(0.765350\pi\) | |||||||
\(444\) | −1.29150 | −0.0612920 | ||||||||
\(445\) | 7.16601 | 0.339701 | ||||||||
\(446\) | −28.4575 | −1.34750 | ||||||||
\(447\) | −19.8745 | −0.940032 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.4575 | 1.43738 | 0.718689 | − | 0.695331i | \(-0.244742\pi\) | ||||
0.718689 | + | 0.695331i | \(0.244742\pi\) | |||||||
\(450\) | −2.00000 | −0.0942809 | ||||||||
\(451\) | 9.00000 | 0.423793 | ||||||||
\(452\) | 12.5830 | 0.591855 | ||||||||
\(453\) | −22.6458 | −1.06399 | ||||||||
\(454\) | −2.41699 | −0.113435 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.29150 | 0.247797 | ||||||||
\(457\) | −40.5830 | −1.89839 | −0.949196 | − | 0.314684i | \(-0.898101\pi\) | ||||
−0.949196 | + | 0.314684i | \(0.898101\pi\) | |||||||
\(458\) | −6.70850 | −0.313467 | ||||||||
\(459\) | 3.00000 | 0.140028 | ||||||||
\(460\) | −7.00000 | −0.326377 | ||||||||
\(461\) | −24.5830 | −1.14494 | −0.572472 | − | 0.819924i | \(-0.694016\pi\) | ||||
−0.572472 | + | 0.819924i | \(0.694016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.0405 | 1.81437 | 0.907183 | − | 0.420735i | \(-0.138228\pi\) | ||||
0.907183 | + | 0.420735i | \(0.138228\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 10.5830 | 0.490775 | ||||||||
\(466\) | −20.1660 | −0.934172 | ||||||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | −4.00000 | −0.184900 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.4170 | 0.480500 | ||||||||
\(471\) | 0.708497 | 0.0326458 | ||||||||
\(472\) | −6.58301 | −0.303007 | ||||||||
\(473\) | 9.29150 | 0.427224 | ||||||||
\(474\) | 10.6458 | 0.488976 | ||||||||
\(475\) | 10.5830 | 0.485582 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.00000 | 0.183147 | ||||||||
\(478\) | −2.70850 | −0.123884 | ||||||||
\(479\) | −33.8745 | −1.54777 | −0.773883 | − | 0.633329i | \(-0.781688\pi\) | ||||
−0.773883 | + | 0.633329i | \(0.781688\pi\) | |||||||
\(480\) | 2.64575 | 0.120761 | ||||||||
\(481\) | −5.16601 | −0.235550 | ||||||||
\(482\) | 27.1660 | 1.23738 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −30.6458 | −1.39155 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 21.8745 | 0.991229 | 0.495614 | − | 0.868543i | \(-0.334943\pi\) | ||||
0.495614 | + | 0.868543i | \(0.334943\pi\) | |||||||
\(488\) | −11.9373 | −0.540374 | ||||||||
\(489\) | 5.58301 | 0.252472 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.00000 | −0.0451294 | −0.0225647 | − | 0.999745i | \(-0.507183\pi\) | ||||
−0.0225647 | + | 0.999745i | \(0.507183\pi\) | |||||||
\(492\) | −9.00000 | −0.405751 | ||||||||
\(493\) | −6.00000 | −0.270226 | ||||||||
\(494\) | 21.1660 | 0.952304 | ||||||||
\(495\) | 2.64575 | 0.118918 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15.5830 | 0.698291 | ||||||||
\(499\) | −18.5830 | −0.831890 | −0.415945 | − | 0.909390i | \(-0.636549\pi\) | ||||
−0.415945 | + | 0.909390i | \(0.636549\pi\) | |||||||
\(500\) | −7.93725 | −0.354965 | ||||||||
\(501\) | −8.70850 | −0.389067 | ||||||||
\(502\) | −23.2915 | −1.03955 | ||||||||
\(503\) | −1.29150 | −0.0575853 | −0.0287926 | − | 0.999585i | \(-0.509166\pi\) | ||||
−0.0287926 | + | 0.999585i | \(0.509166\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.2915 | 0.858461 | ||||||||
\(506\) | 2.64575 | 0.117618 | ||||||||
\(507\) | −3.00000 | −0.133235 | ||||||||
\(508\) | 2.64575 | 0.117386 | ||||||||
\(509\) | 25.1660 | 1.11546 | 0.557732 | − | 0.830021i | \(-0.311672\pi\) | ||||
0.557732 | + | 0.830021i | \(0.311672\pi\) | |||||||
\(510\) | −7.93725 | −0.351468 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.29150 | −0.233626 | ||||||||
\(514\) | −9.29150 | −0.409831 | ||||||||
\(515\) | −26.4575 | −1.16586 | ||||||||
\(516\) | −9.29150 | −0.409036 | ||||||||
\(517\) | −3.93725 | −0.173160 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.00000 | −0.175581 | ||||||||
\(520\) | 10.5830 | 0.464095 | ||||||||
\(521\) | 42.0000 | 1.84005 | 0.920027 | − | 0.391856i | \(-0.128167\pi\) | ||||
0.920027 | + | 0.391856i | \(0.128167\pi\) | |||||||
\(522\) | −2.00000 | −0.0875376 | ||||||||
\(523\) | 2.70850 | 0.118434 | 0.0592172 | − | 0.998245i | \(-0.481140\pi\) | ||||
0.0592172 | + | 0.998245i | \(0.481140\pi\) | |||||||
\(524\) | −18.5830 | −0.811802 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.8745 | −0.953774 | ||||||||
\(527\) | 12.0000 | 0.522728 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −16.0000 | −0.695652 | ||||||||
\(530\) | −10.5830 | −0.459696 | ||||||||
\(531\) | 6.58301 | 0.285678 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.0000 | −1.55933 | ||||||||
\(534\) | 2.70850 | 0.117208 | ||||||||
\(535\) | 23.8118 | 1.02947 | ||||||||
\(536\) | −7.58301 | −0.327536 | ||||||||
\(537\) | −4.70850 | −0.203187 | ||||||||
\(538\) | 10.6458 | 0.458971 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.64575 | −0.113855 | ||||||||
\(541\) | 3.81176 | 0.163880 | 0.0819402 | − | 0.996637i | \(-0.473888\pi\) | ||||
0.0819402 | + | 0.996637i | \(0.473888\pi\) | |||||||
\(542\) | −9.29150 | −0.399104 | ||||||||
\(543\) | 5.29150 | 0.227080 | ||||||||
\(544\) | 3.00000 | 0.128624 | ||||||||
\(545\) | −10.4170 | −0.446215 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7085 | 0.628890 | 0.314445 | − | 0.949276i | \(-0.398182\pi\) | ||||
0.314445 | + | 0.949276i | \(0.398182\pi\) | |||||||
\(548\) | −13.2915 | −0.567785 | ||||||||
\(549\) | 11.9373 | 0.509470 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | 10.5830 | 0.450851 | ||||||||
\(552\) | −2.64575 | −0.112611 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 17.1660 | 0.729314 | ||||||||
\(555\) | −3.41699 | −0.145043 | ||||||||
\(556\) | −12.5830 | −0.533638 | ||||||||
\(557\) | −19.2915 | −0.817407 | −0.408704 | − | 0.912667i | \(-0.634019\pi\) | ||||
−0.408704 | + | 0.912667i | \(0.634019\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | −37.1660 | −1.57195 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | 3.00000 | 0.126547 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 3.93725 | 0.165788 | ||||||||
\(565\) | 33.2915 | 1.40058 | ||||||||
\(566\) | −30.4575 | −1.28022 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.70850 | 0.113646 | ||||||||
\(569\) | −15.1660 | −0.635792 | −0.317896 | − | 0.948126i | \(-0.602976\pi\) | ||||
−0.317896 | + | 0.948126i | \(0.602976\pi\) | |||||||
\(570\) | 14.0000 | 0.586395 | ||||||||
\(571\) | −29.7490 | −1.24496 | −0.622479 | − | 0.782637i | \(-0.713874\pi\) | ||||
−0.622479 | + | 0.782637i | \(0.713874\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | −6.70850 | −0.280251 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.29150 | −0.220671 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 22.7490 | 0.947054 | 0.473527 | − | 0.880779i | \(-0.342981\pi\) | ||||
0.473527 | + | 0.880779i | \(0.342981\pi\) | |||||||
\(578\) | 8.00000 | 0.332756 | ||||||||
\(579\) | 15.8745 | 0.659722 | ||||||||
\(580\) | 5.29150 | 0.219718 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.5830 | −0.480131 | ||||||||
\(583\) | 4.00000 | 0.165663 | ||||||||
\(584\) | 15.2915 | 0.632767 | ||||||||
\(585\) | −10.5830 | −0.437553 | ||||||||
\(586\) | 14.5830 | 0.602418 | ||||||||
\(587\) | 9.87451 | 0.407565 | 0.203782 | − | 0.979016i | \(-0.434677\pi\) | ||||
0.203782 | + | 0.979016i | \(0.434677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.1660 | −0.872130 | ||||||||
\(590\) | −17.4170 | −0.717046 | ||||||||
\(591\) | −21.8745 | −0.899797 | ||||||||
\(592\) | 1.29150 | 0.0530804 | ||||||||
\(593\) | −25.7490 | −1.05739 | −0.528693 | − | 0.848813i | \(-0.677318\pi\) | ||||
−0.528693 | + | 0.848813i | \(0.677318\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.8745 | 0.814092 | ||||||||
\(597\) | 19.1660 | 0.784413 | ||||||||
\(598\) | −10.5830 | −0.432771 | ||||||||
\(599\) | 29.3542 | 1.19938 | 0.599691 | − | 0.800232i | \(-0.295290\pi\) | ||||
0.599691 | + | 0.800232i | \(0.295290\pi\) | |||||||
\(600\) | 2.00000 | 0.0816497 | ||||||||
\(601\) | −38.5830 | −1.57383 | −0.786917 | − | 0.617059i | \(-0.788324\pi\) | ||||
−0.786917 | + | 0.617059i | \(0.788324\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.58301 | 0.308804 | ||||||||
\(604\) | 22.6458 | 0.921443 | ||||||||
\(605\) | 2.64575 | 0.107565 | ||||||||
\(606\) | 7.29150 | 0.296197 | ||||||||
\(607\) | −13.1033 | −0.531845 | −0.265923 | − | 0.963994i | \(-0.585677\pi\) | ||||
−0.265923 | + | 0.963994i | \(0.585677\pi\) | |||||||
\(608\) | −5.29150 | −0.214599 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −31.5830 | −1.27876 | ||||||||
\(611\) | 15.7490 | 0.637137 | ||||||||
\(612\) | −3.00000 | −0.121268 | ||||||||
\(613\) | 7.81176 | 0.315514 | 0.157757 | − | 0.987478i | \(-0.449574\pi\) | ||||
0.157757 | + | 0.987478i | \(0.449574\pi\) | |||||||
\(614\) | 11.4170 | 0.460752 | ||||||||
\(615\) | −23.8118 | −0.960183 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.7085 | −0.592142 | −0.296071 | − | 0.955166i | \(-0.595676\pi\) | ||||
−0.296071 | + | 0.955166i | \(0.595676\pi\) | |||||||
\(618\) | −10.0000 | −0.402259 | ||||||||
\(619\) | −41.0000 | −1.64793 | −0.823965 | − | 0.566641i | \(-0.808243\pi\) | ||||
−0.823965 | + | 0.566641i | \(0.808243\pi\) | |||||||
\(620\) | −10.5830 | −0.425024 | ||||||||
\(621\) | 2.64575 | 0.106170 | ||||||||
\(622\) | −22.5203 | −0.902980 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 20.5830 | 0.822662 | ||||||||
\(627\) | −5.29150 | −0.211322 | ||||||||
\(628\) | −0.708497 | −0.0282721 | ||||||||
\(629\) | −3.87451 | −0.154487 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.8745 | 1.66700 | 0.833499 | − | 0.552521i | \(-0.186334\pi\) | ||||
0.833499 | + | 0.552521i | \(0.186334\pi\) | |||||||
\(632\) | −10.6458 | −0.423465 | ||||||||
\(633\) | −21.2915 | −0.846261 | ||||||||
\(634\) | −9.22876 | −0.366521 | ||||||||
\(635\) | 7.00000 | 0.277787 | ||||||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | −2.70850 | −0.107147 | ||||||||
\(640\) | −2.64575 | −0.104583 | ||||||||
\(641\) | −26.5830 | −1.04997 | −0.524983 | − | 0.851113i | \(-0.675928\pi\) | ||||
−0.524983 | + | 0.851113i | \(0.675928\pi\) | |||||||
\(642\) | 9.00000 | 0.355202 | ||||||||
\(643\) | −1.16601 | −0.0459830 | −0.0229915 | − | 0.999736i | \(-0.507319\pi\) | ||||
−0.0229915 | + | 0.999736i | \(0.507319\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.5830 | −0.967955 | ||||||||
\(646\) | 15.8745 | 0.624574 | ||||||||
\(647\) | −26.3948 | −1.03769 | −0.518843 | − | 0.854870i | \(-0.673637\pi\) | ||||
−0.518843 | + | 0.854870i | \(0.673637\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 6.58301 | 0.258406 | ||||||||
\(650\) | 8.00000 | 0.313786 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.58301 | −0.218647 | ||||||||
\(653\) | −45.1033 | −1.76503 | −0.882514 | − | 0.470287i | \(-0.844150\pi\) | ||||
−0.882514 | + | 0.470287i | \(0.844150\pi\) | |||||||
\(654\) | −3.93725 | −0.153959 | ||||||||
\(655\) | −49.1660 | −1.92107 | ||||||||
\(656\) | 9.00000 | 0.351391 | ||||||||
\(657\) | −15.2915 | −0.596578 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.1660 | −0.941374 | −0.470687 | − | 0.882300i | \(-0.655994\pi\) | ||||
−0.470687 | + | 0.882300i | \(0.655994\pi\) | |||||||
\(660\) | −2.64575 | −0.102986 | ||||||||
\(661\) | 20.7085 | 0.805467 | 0.402734 | − | 0.915317i | \(-0.368060\pi\) | ||||
0.402734 | + | 0.915317i | \(0.368060\pi\) | |||||||
\(662\) | −13.0000 | −0.505259 | ||||||||
\(663\) | −12.0000 | −0.466041 | ||||||||
\(664\) | −15.5830 | −0.604738 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.29150 | −0.0500447 | ||||||||
\(667\) | −5.29150 | −0.204888 | ||||||||
\(668\) | 8.70850 | 0.336942 | ||||||||
\(669\) | −28.4575 | −1.10023 | ||||||||
\(670\) | −20.0627 | −0.775092 | ||||||||
\(671\) | 11.9373 | 0.460833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.4170 | −0.748470 | −0.374235 | − | 0.927334i | \(-0.622095\pi\) | ||||
−0.374235 | + | 0.927334i | \(0.622095\pi\) | |||||||
\(674\) | −6.70850 | −0.258402 | ||||||||
\(675\) | −2.00000 | −0.0769800 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −8.12549 | −0.312288 | −0.156144 | − | 0.987734i | \(-0.549906\pi\) | ||||
−0.156144 | + | 0.987734i | \(0.549906\pi\) | |||||||
\(678\) | 12.5830 | 0.483247 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.93725 | 0.304380 | ||||||||
\(681\) | −2.41699 | −0.0926194 | ||||||||
\(682\) | 4.00000 | 0.153168 | ||||||||
\(683\) | −17.1660 | −0.656839 | −0.328420 | − | 0.944532i | \(-0.606516\pi\) | ||||
−0.328420 | + | 0.944532i | \(0.606516\pi\) | |||||||
\(684\) | 5.29150 | 0.202326 | ||||||||
\(685\) | −35.1660 | −1.34362 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.70850 | −0.255945 | ||||||||
\(688\) | 9.29150 | 0.354235 | ||||||||
\(689\) | −16.0000 | −0.609551 | ||||||||
\(690\) | −7.00000 | −0.266485 | ||||||||
\(691\) | 14.1660 | 0.538900 | 0.269450 | − | 0.963014i | \(-0.413158\pi\) | ||||
0.269450 | + | 0.963014i | \(0.413158\pi\) | |||||||
\(692\) | 4.00000 | 0.152057 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.5830 | −1.12296 | ||||||||
\(695\) | −33.2915 | −1.26282 | ||||||||
\(696\) | 2.00000 | 0.0758098 | ||||||||
\(697\) | −27.0000 | −1.02270 | ||||||||
\(698\) | 13.2288 | 0.500716 | ||||||||
\(699\) | −20.1660 | −0.762749 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.4575 | 1.60360 | 0.801799 | − | 0.597594i | \(-0.203876\pi\) | ||||
0.801799 | + | 0.597594i | \(0.203876\pi\) | |||||||
\(702\) | −4.00000 | −0.150970 | ||||||||
\(703\) | 6.83399 | 0.257749 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 10.4170 | 0.392327 | ||||||||
\(706\) | 23.2915 | 0.876587 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.58301 | −0.247404 | ||||||||
\(709\) | 15.7490 | 0.591467 | 0.295733 | − | 0.955271i | \(-0.404436\pi\) | ||||
0.295733 | + | 0.955271i | \(0.404436\pi\) | |||||||
\(710\) | 7.16601 | 0.268936 | ||||||||
\(711\) | 10.6458 | 0.399247 | ||||||||
\(712\) | −2.70850 | −0.101505 | ||||||||
\(713\) | 10.5830 | 0.396337 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5830 | −0.395782 | ||||||||
\(716\) | 4.70850 | 0.175965 | ||||||||
\(717\) | −2.70850 | −0.101151 | ||||||||
\(718\) | −20.5830 | −0.768151 | ||||||||
\(719\) | −28.0627 | −1.04656 | −0.523282 | − | 0.852160i | \(-0.675293\pi\) | ||||
−0.523282 | + | 0.852160i | \(0.675293\pi\) | |||||||
\(720\) | 2.64575 | 0.0986013 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.00000 | −0.334945 | ||||||||
\(723\) | 27.1660 | 1.01031 | ||||||||
\(724\) | −5.29150 | −0.196657 | ||||||||
\(725\) | 4.00000 | 0.148556 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −2.00000 | −0.0741759 | −0.0370879 | − | 0.999312i | \(-0.511808\pi\) | ||||
−0.0370879 | + | 0.999312i | \(0.511808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 40.4575 | 1.49740 | ||||||||
\(731\) | −27.8745 | −1.03098 | ||||||||
\(732\) | −11.9373 | −0.441214 | ||||||||
\(733\) | 11.9373 | 0.440913 | 0.220456 | − | 0.975397i | \(-0.429245\pi\) | ||||
0.220456 | + | 0.975397i | \(0.429245\pi\) | |||||||
\(734\) | −10.7085 | −0.395258 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.64575 | 0.0975237 | ||||||||
\(737\) | 7.58301 | 0.279324 | ||||||||
\(738\) | −9.00000 | −0.331295 | ||||||||
\(739\) | −24.5830 | −0.904300 | −0.452150 | − | 0.891942i | \(-0.649343\pi\) | ||||
−0.452150 | + | 0.891942i | \(0.649343\pi\) | |||||||
\(740\) | 3.41699 | 0.125611 | ||||||||
\(741\) | 21.1660 | 0.777553 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.7085 | −0.686348 | −0.343174 | − | 0.939272i | \(-0.611502\pi\) | ||||
−0.343174 | + | 0.939272i | \(0.611502\pi\) | |||||||
\(744\) | −4.00000 | −0.146647 | ||||||||
\(745\) | 52.5830 | 1.92649 | ||||||||
\(746\) | 15.8118 | 0.578910 | ||||||||
\(747\) | 15.5830 | 0.570152 | ||||||||
\(748\) | −3.00000 | −0.109691 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.93725 | −0.289828 | ||||||||
\(751\) | −29.2915 | −1.06886 | −0.534431 | − | 0.845212i | \(-0.679474\pi\) | ||||
−0.534431 | + | 0.845212i | \(0.679474\pi\) | |||||||
\(752\) | −3.93725 | −0.143577 | ||||||||
\(753\) | −23.2915 | −0.848790 | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 59.9150 | 2.18053 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.5830 | −1.18425 | −0.592125 | − | 0.805846i | \(-0.701711\pi\) | ||||
−0.592125 | + | 0.805846i | \(0.701711\pi\) | |||||||
\(758\) | 27.5830 | 1.00186 | ||||||||
\(759\) | 2.64575 | 0.0960347 | ||||||||
\(760\) | −14.0000 | −0.507833 | ||||||||
\(761\) | 47.5830 | 1.72488 | 0.862441 | − | 0.506157i | \(-0.168934\pi\) | ||||
0.862441 | + | 0.506157i | \(0.168934\pi\) | |||||||
\(762\) | 2.64575 | 0.0958455 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.70850 | 0.242705 | ||||||||
\(765\) | −7.93725 | −0.286972 | ||||||||
\(766\) | −18.7085 | −0.675965 | ||||||||
\(767\) | −26.3320 | −0.950794 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −30.7085 | −1.10738 | −0.553688 | − | 0.832724i | \(-0.686780\pi\) | ||||
−0.553688 | + | 0.832724i | \(0.686780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.29150 | −0.334625 | ||||||||
\(772\) | −15.8745 | −0.571336 | ||||||||
\(773\) | −8.06275 | −0.289997 | −0.144998 | − | 0.989432i | \(-0.546318\pi\) | ||||
−0.144998 | + | 0.989432i | \(0.546318\pi\) | |||||||
\(774\) | −9.29150 | −0.333976 | ||||||||
\(775\) | −8.00000 | −0.287368 | ||||||||
\(776\) | 11.5830 | 0.415806 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.9373 | −1.14501 | ||||||||
\(779\) | 47.6235 | 1.70629 | ||||||||
\(780\) | 10.5830 | 0.378932 | ||||||||
\(781\) | −2.70850 | −0.0969177 | ||||||||
\(782\) | −7.93725 | −0.283836 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.87451 | −0.0669041 | ||||||||
\(786\) | −18.5830 | −0.662834 | ||||||||
\(787\) | 9.29150 | 0.331206 | 0.165603 | − | 0.986192i | \(-0.447043\pi\) | ||||
0.165603 | + | 0.986192i | \(0.447043\pi\) | |||||||
\(788\) | 21.8745 | 0.779247 | ||||||||
\(789\) | −21.8745 | −0.778753 | ||||||||
\(790\) | −28.1660 | −1.00210 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | −47.7490 | −1.69562 | ||||||||
\(794\) | −6.00000 | −0.212932 | ||||||||
\(795\) | −10.5830 | −0.375341 | ||||||||
\(796\) | −19.1660 | −0.679321 | ||||||||
\(797\) | 45.1033 | 1.59764 | 0.798820 | − | 0.601570i | \(-0.205458\pi\) | ||||
0.798820 | + | 0.601570i | \(0.205458\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.8118 | 0.417870 | ||||||||
\(800\) | −2.00000 | −0.0707107 | ||||||||
\(801\) | 2.70850 | 0.0957000 | ||||||||
\(802\) | 35.8745 | 1.26677 | ||||||||
\(803\) | −15.2915 | −0.539625 | ||||||||
\(804\) | −7.58301 | −0.267432 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.0000 | −0.563576 | ||||||||
\(807\) | 10.6458 | 0.374748 | ||||||||
\(808\) | −7.29150 | −0.256514 | ||||||||
\(809\) | 45.3320 | 1.59379 | 0.796894 | − | 0.604119i | \(-0.206475\pi\) | ||||
0.796894 | + | 0.604119i | \(0.206475\pi\) | |||||||
\(810\) | −2.64575 | −0.0929622 | ||||||||
\(811\) | 16.5830 | 0.582308 | 0.291154 | − | 0.956676i | \(-0.405961\pi\) | ||||
0.291154 | + | 0.956676i | \(0.405961\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.29150 | −0.325867 | ||||||||
\(814\) | −1.29150 | −0.0452671 | ||||||||
\(815\) | −14.7712 | −0.517414 | ||||||||
\(816\) | 3.00000 | 0.105021 | ||||||||
\(817\) | 49.1660 | 1.72010 | ||||||||
\(818\) | −35.8745 | −1.25432 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.8118 | 0.831543 | ||||||||
\(821\) | −30.3320 | −1.05859 | −0.529297 | − | 0.848436i | \(-0.677544\pi\) | ||||
−0.529297 | + | 0.848436i | \(0.677544\pi\) | |||||||
\(822\) | −13.2915 | −0.463594 | ||||||||
\(823\) | −12.1255 | −0.422668 | −0.211334 | − | 0.977414i | \(-0.567781\pi\) | ||||
−0.211334 | + | 0.977414i | \(0.567781\pi\) | |||||||
\(824\) | 10.0000 | 0.348367 | ||||||||
\(825\) | −2.00000 | −0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.3320 | 1.22861 | 0.614307 | − | 0.789067i | \(-0.289435\pi\) | ||||
0.614307 | + | 0.789067i | \(0.289435\pi\) | |||||||
\(828\) | −2.64575 | −0.0919462 | ||||||||
\(829\) | 19.8745 | 0.690270 | 0.345135 | − | 0.938553i | \(-0.387833\pi\) | ||||
0.345135 | + | 0.938553i | \(0.387833\pi\) | |||||||
\(830\) | −41.2288 | −1.43107 | ||||||||
\(831\) | 17.1660 | 0.595482 | ||||||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12.5830 | −0.435714 | ||||||||
\(835\) | 23.0405 | 0.797350 | ||||||||
\(836\) | 5.29150 | 0.183010 | ||||||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | 9.87451 | 0.341109 | ||||||||
\(839\) | −37.1033 | −1.28095 | −0.640473 | − | 0.767980i | \(-0.721262\pi\) | ||||
−0.640473 | + | 0.767980i | \(0.721262\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −6.12549 | −0.211098 | ||||||||
\(843\) | 3.00000 | 0.103325 | ||||||||
\(844\) | 21.2915 | 0.732884 | ||||||||
\(845\) | 7.93725 | 0.273050 | ||||||||
\(846\) | 3.93725 | 0.135366 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.00000 | 0.137361 | ||||||||
\(849\) | −30.4575 | −1.04530 | ||||||||
\(850\) | 6.00000 | 0.205798 | ||||||||
\(851\) | −3.41699 | −0.117133 | ||||||||
\(852\) | 2.70850 | 0.0927916 | ||||||||
\(853\) | 14.5203 | 0.497164 | 0.248582 | − | 0.968611i | \(-0.420035\pi\) | ||||
0.248582 | + | 0.968611i | \(0.420035\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.0000 | 0.478790 | ||||||||
\(856\) | −9.00000 | −0.307614 | ||||||||
\(857\) | 9.83399 | 0.335923 | 0.167961 | − | 0.985794i | \(-0.446282\pi\) | ||||
0.167961 | + | 0.985794i | \(0.446282\pi\) | |||||||
\(858\) | −4.00000 | −0.136558 | ||||||||
\(859\) | 48.7490 | 1.66329 | 0.831647 | − | 0.555304i | \(-0.187398\pi\) | ||||
0.831647 | + | 0.555304i | \(0.187398\pi\) | |||||||
\(860\) | 24.5830 | 0.838274 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.2915 | 0.588951 | ||||||||
\(863\) | −33.1033 | −1.12685 | −0.563424 | − | 0.826168i | \(-0.690516\pi\) | ||||
−0.563424 | + | 0.826168i | \(0.690516\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 10.5830 | 0.359833 | ||||||||
\(866\) | −1.58301 | −0.0537927 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.6458 | 0.361132 | ||||||||
\(870\) | 5.29150 | 0.179399 | ||||||||
\(871\) | −30.3320 | −1.02776 | ||||||||
\(872\) | 3.93725 | 0.133332 | ||||||||
\(873\) | −11.5830 | −0.392025 | ||||||||
\(874\) | 14.0000 | 0.473557 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.2915 | 0.516652 | ||||||||
\(877\) | 10.7712 | 0.363719 | 0.181860 | − | 0.983325i | \(-0.441788\pi\) | ||||
0.181860 | + | 0.983325i | \(0.441788\pi\) | |||||||
\(878\) | 9.35425 | 0.315691 | ||||||||
\(879\) | 14.5830 | 0.491873 | ||||||||
\(880\) | 2.64575 | 0.0891883 | ||||||||
\(881\) | 23.1660 | 0.780483 | 0.390241 | − | 0.920713i | \(-0.372392\pi\) | ||||
0.390241 | + | 0.920713i | \(0.372392\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.4170 | −1.15822 | −0.579112 | − | 0.815248i | \(-0.696601\pi\) | ||||
−0.579112 | + | 0.815248i | \(0.696601\pi\) | |||||||
\(884\) | 12.0000 | 0.403604 | ||||||||
\(885\) | −17.4170 | −0.585466 | ||||||||
\(886\) | 31.1660 | 1.04704 | ||||||||
\(887\) | −31.0405 | −1.04224 | −0.521119 | − | 0.853484i | \(-0.674485\pi\) | ||||
−0.521119 | + | 0.853484i | \(0.674485\pi\) | |||||||
\(888\) | 1.29150 | 0.0433400 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.16601 | −0.240205 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 28.4575 | 0.952828 | ||||||||
\(893\) | −20.8340 | −0.697183 | ||||||||
\(894\) | 19.8745 | 0.664703 | ||||||||
\(895\) | 12.4575 | 0.416409 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.5830 | −0.353356 | ||||||||
\(898\) | −30.4575 | −1.01638 | ||||||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | 2.00000 | 0.0666667 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | −9.00000 | −0.299667 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.5830 | −0.418505 | ||||||||
\(905\) | −14.0000 | −0.465376 | ||||||||
\(906\) | 22.6458 | 0.752355 | ||||||||
\(907\) | −15.8340 | −0.525759 | −0.262879 | − | 0.964829i | \(-0.584672\pi\) | ||||
−0.262879 | + | 0.964829i | \(0.584672\pi\) | |||||||
\(908\) | 2.41699 | 0.0802108 | ||||||||
\(909\) | 7.29150 | 0.241844 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.3948 | −0.609446 | −0.304723 | − | 0.952441i | \(-0.598564\pi\) | ||||
−0.304723 | + | 0.952441i | \(0.598564\pi\) | |||||||
\(912\) | −5.29150 | −0.175219 | ||||||||
\(913\) | 15.5830 | 0.515722 | ||||||||
\(914\) | 40.5830 | 1.34237 | ||||||||
\(915\) | −31.5830 | −1.04410 | ||||||||
\(916\) | 6.70850 | 0.221655 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.00000 | −0.0990148 | ||||||||
\(919\) | 9.35425 | 0.308568 | 0.154284 | − | 0.988027i | \(-0.450693\pi\) | ||||
0.154284 | + | 0.988027i | \(0.450693\pi\) | |||||||
\(920\) | 7.00000 | 0.230783 | ||||||||
\(921\) | 11.4170 | 0.376203 | ||||||||
\(922\) | 24.5830 | 0.809598 | ||||||||
\(923\) | 10.8340 | 0.356605 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.58301 | 0.0849287 | ||||||||
\(926\) | −39.0405 | −1.28295 | ||||||||
\(927\) | −10.0000 | −0.328443 | ||||||||
\(928\) | −2.00000 | −0.0656532 | ||||||||
\(929\) | −34.4575 | −1.13051 | −0.565257 | − | 0.824915i | \(-0.691223\pi\) | ||||
−0.565257 | + | 0.824915i | \(0.691223\pi\) | |||||||
\(930\) | −10.5830 | −0.347030 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.1660 | 0.660560 | ||||||||
\(933\) | −22.5203 | −0.737280 | ||||||||
\(934\) | −8.00000 | −0.261768 | ||||||||
\(935\) | −7.93725 | −0.259576 | ||||||||
\(936\) | 4.00000 | 0.130744 | ||||||||
\(937\) | 50.0000 | 1.63343 | 0.816714 | − | 0.577042i | \(-0.195793\pi\) | ||||
0.816714 | + | 0.577042i | \(0.195793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.5830 | 0.671701 | ||||||||
\(940\) | −10.4170 | −0.339765 | ||||||||
\(941\) | 3.41699 | 0.111391 | 0.0556954 | − | 0.998448i | \(-0.482262\pi\) | ||||
0.0556954 | + | 0.998448i | \(0.482262\pi\) | |||||||
\(942\) | −0.708497 | −0.0230841 | ||||||||
\(943\) | −23.8118 | −0.775418 | ||||||||
\(944\) | 6.58301 | 0.214259 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.29150 | −0.302093 | ||||||||
\(947\) | −15.4170 | −0.500985 | −0.250493 | − | 0.968119i | \(-0.580593\pi\) | ||||
−0.250493 | + | 0.968119i | \(0.580593\pi\) | |||||||
\(948\) | −10.6458 | −0.345758 | ||||||||
\(949\) | 61.1660 | 1.98553 | ||||||||
\(950\) | −10.5830 | −0.343358 | ||||||||
\(951\) | −9.22876 | −0.299263 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.7490 | 0.866486 | 0.433243 | − | 0.901277i | \(-0.357369\pi\) | ||||
0.433243 | + | 0.901277i | \(0.357369\pi\) | |||||||
\(954\) | −4.00000 | −0.129505 | ||||||||
\(955\) | 17.7490 | 0.574345 | ||||||||
\(956\) | 2.70850 | 0.0875991 | ||||||||
\(957\) | −2.00000 | −0.0646508 | ||||||||
\(958\) | 33.8745 | 1.09444 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.64575 | −0.0853913 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 5.16601 | 0.166559 | ||||||||
\(963\) | 9.00000 | 0.290021 | ||||||||
\(964\) | −27.1660 | −0.874958 | ||||||||
\(965\) | −42.0000 | −1.35203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.0627 | 1.28833 | 0.644166 | − | 0.764886i | \(-0.277205\pi\) | ||||
0.644166 | + | 0.764886i | \(0.277205\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 15.8745 | 0.509963 | ||||||||
\(970\) | 30.6458 | 0.983976 | ||||||||
\(971\) | 6.00000 | 0.192549 | 0.0962746 | − | 0.995355i | \(-0.469307\pi\) | ||||
0.0962746 | + | 0.995355i | \(0.469307\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −21.8745 | −0.700904 | ||||||||
\(975\) | 8.00000 | 0.256205 | ||||||||
\(976\) | 11.9373 | 0.382102 | ||||||||
\(977\) | 13.1660 | 0.421218 | 0.210609 | − | 0.977570i | \(-0.432455\pi\) | ||||
0.210609 | + | 0.977570i | \(0.432455\pi\) | |||||||
\(978\) | −5.58301 | −0.178525 | ||||||||
\(979\) | 2.70850 | 0.0865640 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.93725 | −0.125707 | ||||||||
\(982\) | 1.00000 | 0.0319113 | ||||||||
\(983\) | 42.5203 | 1.35619 | 0.678093 | − | 0.734976i | \(-0.262807\pi\) | ||||
0.678093 | + | 0.734976i | \(0.262807\pi\) | |||||||
\(984\) | 9.00000 | 0.286910 | ||||||||
\(985\) | 57.8745 | 1.84404 | ||||||||
\(986\) | 6.00000 | 0.191079 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.1660 | −0.673380 | ||||||||
\(989\) | −24.5830 | −0.781694 | ||||||||
\(990\) | −2.64575 | −0.0840875 | ||||||||
\(991\) | −43.8745 | −1.39372 | −0.696860 | − | 0.717207i | \(-0.745420\pi\) | ||||
−0.696860 | + | 0.717207i | \(0.745420\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | −13.0000 | −0.412543 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −50.7085 | −1.60757 | ||||||||
\(996\) | −15.5830 | −0.493766 | ||||||||
\(997\) | 6.83399 | 0.216435 | 0.108217 | − | 0.994127i | \(-0.465486\pi\) | ||||
0.108217 | + | 0.994127i | \(0.465486\pi\) | |||||||
\(998\) | 18.5830 | 0.588235 | ||||||||
\(999\) | −1.29150 | −0.0408613 |
(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 | 3234.2.a.w.1.2 | 2 | ||
3.2 | odd | 2 | 9702.2.a.db.1.1 | 2 | |||
7.2 | even | 3 | 462.2.i.e.67.1 | ✓ | 4 | ||
7.4 | even | 3 | 462.2.i.e.331.1 | yes | 4 | ||
7.6 | odd | 2 | 3234.2.a.ba.1.1 | 2 | |||
21.2 | odd | 6 | 1386.2.k.r.991.2 | 4 | |||
21.11 | odd | 6 | 1386.2.k.r.793.2 | 4 | |||
21.20 | even | 2 | 9702.2.a.dm.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.e.67.1 | ✓ | 4 | 7.2 | even | 3 | ||
462.2.i.e.331.1 | yes | 4 | 7.4 | even | 3 | ||
1386.2.k.r.793.2 | 4 | 21.11 | odd | 6 | |||
1386.2.k.r.991.2 | 4 | 21.2 | odd | 6 | |||
3234.2.a.w.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3234.2.a.ba.1.1 | 2 | 7.6 | odd | 2 | |||
9702.2.a.db.1.1 | 2 | 3.2 | odd | 2 | |||
9702.2.a.dm.1.2 | 2 | 21.20 | even | 2 |