Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} + \cdots - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.67335\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67335 | 1.18324 | 0.591619 | − | 0.806218i | \(-0.298489\pi\) | ||||
0.591619 | + | 0.806218i | \(0.298489\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.800100 | 0.400050 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.67335 | 0.683142 | ||||||||
\(7\) | −2.75180 | −1.04008 | −0.520041 | − | 0.854141i | \(-0.674084\pi\) | ||||
−0.520041 | + | 0.854141i | \(0.674084\pi\) | |||||||
\(8\) | −2.00785 | −0.709883 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.09151 | −0.932126 | −0.466063 | − | 0.884752i | \(-0.654328\pi\) | ||||
−0.466063 | + | 0.884752i | \(0.654328\pi\) | |||||||
\(12\) | 0.800100 | 0.230969 | ||||||||
\(13\) | 4.10277 | 1.13790 | 0.568951 | − | 0.822371i | \(-0.307349\pi\) | ||||
0.568951 | + | 0.822371i | \(0.307349\pi\) | |||||||
\(14\) | −4.60473 | −1.23066 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.96004 | −1.24001 | ||||||||
\(17\) | 4.07070 | 0.987290 | 0.493645 | − | 0.869664i | \(-0.335664\pi\) | ||||
0.493645 | + | 0.869664i | \(0.335664\pi\) | |||||||
\(18\) | 1.67335 | 0.394412 | ||||||||
\(19\) | 5.75557 | 1.32042 | 0.660210 | − | 0.751081i | \(-0.270467\pi\) | ||||
0.660210 | + | 0.751081i | \(0.270467\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.75180 | −0.600492 | ||||||||
\(22\) | −5.17318 | −1.10293 | ||||||||
\(23\) | 6.80592 | 1.41913 | 0.709567 | − | 0.704638i | \(-0.248891\pi\) | ||||
0.709567 | + | 0.704638i | \(0.248891\pi\) | |||||||
\(24\) | −2.00785 | −0.409851 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.86536 | 1.34641 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.20171 | −0.416085 | ||||||||
\(29\) | 1.81214 | 0.336506 | 0.168253 | − | 0.985744i | \(-0.446187\pi\) | ||||
0.168253 | + | 0.985744i | \(0.446187\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.24850 | 0.583448 | 0.291724 | − | 0.956503i | \(-0.405771\pi\) | ||||
0.291724 | + | 0.956503i | \(0.405771\pi\) | |||||||
\(32\) | −4.28418 | −0.757342 | ||||||||
\(33\) | −3.09151 | −0.538163 | ||||||||
\(34\) | 6.81170 | 1.16820 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.800100 | 0.133350 | ||||||||
\(37\) | −5.48507 | −0.901741 | −0.450870 | − | 0.892589i | \(-0.648886\pi\) | ||||
−0.450870 | + | 0.892589i | \(0.648886\pi\) | |||||||
\(38\) | 9.63109 | 1.56237 | ||||||||
\(39\) | 4.10277 | 0.656968 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.31661 | 0.205620 | 0.102810 | − | 0.994701i | \(-0.467217\pi\) | ||||
0.102810 | + | 0.994701i | \(0.467217\pi\) | |||||||
\(42\) | −4.60473 | −0.710524 | ||||||||
\(43\) | 8.65847 | 1.32040 | 0.660202 | − | 0.751088i | \(-0.270471\pi\) | ||||
0.660202 | + | 0.751088i | \(0.270471\pi\) | |||||||
\(44\) | −2.47352 | −0.372897 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.3887 | 1.67917 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | −4.96004 | −0.715920 | ||||||||
\(49\) | 0.572406 | 0.0817723 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.07070 | 0.570012 | ||||||||
\(52\) | 3.28262 | 0.455218 | ||||||||
\(53\) | −5.58252 | −0.766819 | −0.383409 | − | 0.923579i | \(-0.625250\pi\) | ||||
−0.383409 | + | 0.923579i | \(0.625250\pi\) | |||||||
\(54\) | 1.67335 | 0.227714 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.52521 | 0.738337 | ||||||||
\(57\) | 5.75557 | 0.762344 | ||||||||
\(58\) | 3.03234 | 0.398166 | ||||||||
\(59\) | 0.623977 | 0.0812349 | 0.0406175 | − | 0.999175i | \(-0.487067\pi\) | ||||
0.0406175 | + | 0.999175i | \(0.487067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.04084 | 0.773451 | 0.386725 | − | 0.922195i | \(-0.373606\pi\) | ||||
0.386725 | + | 0.922195i | \(0.373606\pi\) | |||||||
\(62\) | 5.43588 | 0.690357 | ||||||||
\(63\) | −2.75180 | −0.346694 | ||||||||
\(64\) | 2.75115 | 0.343894 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.17318 | −0.636774 | ||||||||
\(67\) | −4.05619 | −0.495542 | −0.247771 | − | 0.968819i | \(-0.579698\pi\) | ||||
−0.247771 | + | 0.968819i | \(0.579698\pi\) | |||||||
\(68\) | 3.25696 | 0.394965 | ||||||||
\(69\) | 6.80592 | 0.819337 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.1185 | 1.79423 | 0.897117 | − | 0.441794i | \(-0.145658\pi\) | ||||
0.897117 | + | 0.441794i | \(0.145658\pi\) | |||||||
\(72\) | −2.00785 | −0.236628 | ||||||||
\(73\) | 3.81119 | 0.446067 | 0.223033 | − | 0.974811i | \(-0.428404\pi\) | ||||
0.223033 | + | 0.974811i | \(0.428404\pi\) | |||||||
\(74\) | −9.17845 | −1.06697 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.60503 | 0.528233 | ||||||||
\(77\) | 8.50722 | 0.969488 | ||||||||
\(78\) | 6.86536 | 0.777349 | ||||||||
\(79\) | −5.60887 | −0.631047 | −0.315523 | − | 0.948918i | \(-0.602180\pi\) | ||||
−0.315523 | + | 0.948918i | \(0.602180\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.20315 | 0.243297 | ||||||||
\(83\) | 4.45627 | 0.489139 | 0.244570 | − | 0.969632i | \(-0.421353\pi\) | ||||
0.244570 | + | 0.969632i | \(0.421353\pi\) | |||||||
\(84\) | −2.20171 | −0.240227 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.4886 | 1.56235 | ||||||||
\(87\) | 1.81214 | 0.194282 | ||||||||
\(88\) | 6.20730 | 0.661700 | ||||||||
\(89\) | −2.86645 | −0.303844 | −0.151922 | − | 0.988393i | \(-0.548546\pi\) | ||||
−0.151922 | + | 0.988393i | \(0.548546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.2900 | −1.18351 | ||||||||
\(92\) | 5.44542 | 0.567724 | ||||||||
\(93\) | 3.24850 | 0.336854 | ||||||||
\(94\) | 1.67335 | 0.172593 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.28418 | −0.437252 | ||||||||
\(97\) | 6.01711 | 0.610945 | 0.305473 | − | 0.952201i | \(-0.401186\pi\) | ||||
0.305473 | + | 0.952201i | \(0.401186\pi\) | |||||||
\(98\) | 0.957836 | 0.0967561 | ||||||||
\(99\) | −3.09151 | −0.310709 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.07572 | 0.903068 | 0.451534 | − | 0.892254i | \(-0.350877\pi\) | ||||
0.451534 | + | 0.892254i | \(0.350877\pi\) | |||||||
\(102\) | 6.81170 | 0.674459 | ||||||||
\(103\) | −8.36703 | −0.824428 | −0.412214 | − | 0.911087i | \(-0.635244\pi\) | ||||
−0.412214 | + | 0.911087i | \(0.635244\pi\) | |||||||
\(104\) | −8.23775 | −0.807778 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.34151 | −0.907328 | ||||||||
\(107\) | 9.99601 | 0.966350 | 0.483175 | − | 0.875524i | \(-0.339483\pi\) | ||||
0.483175 | + | 0.875524i | \(0.339483\pi\) | |||||||
\(108\) | 0.800100 | 0.0769896 | ||||||||
\(109\) | 8.75321 | 0.838406 | 0.419203 | − | 0.907893i | \(-0.362310\pi\) | ||||
0.419203 | + | 0.907893i | \(0.362310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.48507 | −0.520620 | ||||||||
\(112\) | 13.6490 | 1.28971 | ||||||||
\(113\) | 14.6778 | 1.38078 | 0.690388 | − | 0.723439i | \(-0.257440\pi\) | ||||
0.690388 | + | 0.723439i | \(0.257440\pi\) | |||||||
\(114\) | 9.63109 | 0.902034 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.44989 | 0.134619 | ||||||||
\(117\) | 4.10277 | 0.379301 | ||||||||
\(118\) | 1.04413 | 0.0961202 | ||||||||
\(119\) | −11.2018 | −1.02686 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.44256 | −0.131142 | ||||||||
\(122\) | 10.1084 | 0.915176 | ||||||||
\(123\) | 1.31661 | 0.118715 | ||||||||
\(124\) | 2.59912 | 0.233408 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.60473 | −0.410222 | ||||||||
\(127\) | −20.1493 | −1.78796 | −0.893979 | − | 0.448109i | \(-0.852098\pi\) | ||||
−0.893979 | + | 0.448109i | \(0.852098\pi\) | |||||||
\(128\) | 13.1720 | 1.16425 | ||||||||
\(129\) | 8.65847 | 0.762336 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.7317 | −1.63660 | −0.818299 | − | 0.574793i | \(-0.805083\pi\) | ||||
−0.818299 | + | 0.574793i | \(0.805083\pi\) | |||||||
\(132\) | −2.47352 | −0.215292 | ||||||||
\(133\) | −15.8382 | −1.37335 | ||||||||
\(134\) | −6.78742 | −0.586344 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.17337 | −0.700860 | ||||||||
\(137\) | 13.3070 | 1.13689 | 0.568447 | − | 0.822720i | \(-0.307545\pi\) | ||||
0.568447 | + | 0.822720i | \(0.307545\pi\) | |||||||
\(138\) | 11.3887 | 0.969470 | ||||||||
\(139\) | −2.40184 | −0.203721 | −0.101861 | − | 0.994799i | \(-0.532480\pi\) | ||||
−0.101861 | + | 0.994799i | \(0.532480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | 25.2985 | 2.12300 | ||||||||
\(143\) | −12.6837 | −1.06067 | ||||||||
\(144\) | −4.96004 | −0.413337 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.37746 | 0.527803 | ||||||||
\(147\) | 0.572406 | 0.0472113 | ||||||||
\(148\) | −4.38861 | −0.360741 | ||||||||
\(149\) | −2.94723 | −0.241447 | −0.120723 | − | 0.992686i | \(-0.538521\pi\) | ||||
−0.120723 | + | 0.992686i | \(0.538521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.3477 | 1.65587 | 0.827935 | − | 0.560824i | \(-0.189516\pi\) | ||||
0.827935 | + | 0.560824i | \(0.189516\pi\) | |||||||
\(152\) | −11.5563 | −0.937343 | ||||||||
\(153\) | 4.07070 | 0.329097 | ||||||||
\(154\) | 14.2356 | 1.14713 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.28262 | 0.262820 | ||||||||
\(157\) | −16.7571 | −1.33736 | −0.668681 | − | 0.743549i | \(-0.733141\pi\) | ||||
−0.668681 | + | 0.743549i | \(0.733141\pi\) | |||||||
\(158\) | −9.38560 | −0.746678 | ||||||||
\(159\) | −5.58252 | −0.442723 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.7285 | −1.47602 | ||||||||
\(162\) | 1.67335 | 0.131471 | ||||||||
\(163\) | 14.5503 | 1.13967 | 0.569835 | − | 0.821759i | \(-0.307007\pi\) | ||||
0.569835 | + | 0.821759i | \(0.307007\pi\) | |||||||
\(164\) | 1.05342 | 0.0822583 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.45690 | 0.578768 | ||||||||
\(167\) | −7.15918 | −0.553994 | −0.276997 | − | 0.960871i | \(-0.589339\pi\) | ||||
−0.276997 | + | 0.960871i | \(0.589339\pi\) | |||||||
\(168\) | 5.52521 | 0.426279 | ||||||||
\(169\) | 3.83269 | 0.294822 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.75557 | 0.440140 | ||||||||
\(172\) | 6.92764 | 0.528227 | ||||||||
\(173\) | −10.8401 | −0.824161 | −0.412081 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412081 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(174\) | 3.03234 | 0.229881 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.3340 | 1.15584 | ||||||||
\(177\) | 0.623977 | 0.0469010 | ||||||||
\(178\) | −4.79658 | −0.359519 | ||||||||
\(179\) | 10.0976 | 0.754731 | 0.377366 | − | 0.926064i | \(-0.376830\pi\) | ||||
0.377366 | + | 0.926064i | \(0.376830\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.18508 | −0.311075 | −0.155537 | − | 0.987830i | \(-0.549711\pi\) | ||||
−0.155537 | + | 0.987830i | \(0.549711\pi\) | |||||||
\(182\) | −18.8921 | −1.40038 | ||||||||
\(183\) | 6.04084 | 0.446552 | ||||||||
\(184\) | −13.6653 | −1.00742 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.43588 | 0.398578 | ||||||||
\(187\) | −12.5846 | −0.920278 | ||||||||
\(188\) | 0.800100 | 0.0583533 | ||||||||
\(189\) | −2.75180 | −0.200164 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.2288 | −1.39135 | −0.695673 | − | 0.718358i | \(-0.744894\pi\) | ||||
−0.695673 | + | 0.718358i | \(0.744894\pi\) | |||||||
\(192\) | 2.75115 | 0.198548 | ||||||||
\(193\) | −25.7747 | −1.85530 | −0.927652 | − | 0.373445i | \(-0.878177\pi\) | ||||
−0.927652 | + | 0.373445i | \(0.878177\pi\) | |||||||
\(194\) | 10.0687 | 0.722893 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.457982 | 0.0327130 | ||||||||
\(197\) | −21.7824 | −1.55193 | −0.775966 | − | 0.630775i | \(-0.782737\pi\) | ||||
−0.775966 | + | 0.630775i | \(0.782737\pi\) | |||||||
\(198\) | −5.17318 | −0.367642 | ||||||||
\(199\) | 17.3880 | 1.23260 | 0.616301 | − | 0.787511i | \(-0.288630\pi\) | ||||
0.616301 | + | 0.787511i | \(0.288630\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.05619 | −0.286101 | ||||||||
\(202\) | 15.1869 | 1.06854 | ||||||||
\(203\) | −4.98665 | −0.349994 | ||||||||
\(204\) | 3.25696 | 0.228033 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.0010 | −0.975494 | ||||||||
\(207\) | 6.80592 | 0.473044 | ||||||||
\(208\) | −20.3499 | −1.41101 | ||||||||
\(209\) | −17.7934 | −1.23080 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2661 | 1.18864 | 0.594322 | − | 0.804227i | \(-0.297420\pi\) | ||||
0.594322 | + | 0.804227i | \(0.297420\pi\) | |||||||
\(212\) | −4.46657 | −0.306766 | ||||||||
\(213\) | 15.1185 | 1.03590 | ||||||||
\(214\) | 16.7268 | 1.14342 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.00785 | −0.136617 | ||||||||
\(217\) | −8.93923 | −0.606834 | ||||||||
\(218\) | 14.6472 | 0.992033 | ||||||||
\(219\) | 3.81119 | 0.257537 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.7011 | 1.12344 | ||||||||
\(222\) | −9.17845 | −0.616017 | ||||||||
\(223\) | −7.59823 | −0.508815 | −0.254407 | − | 0.967097i | \(-0.581880\pi\) | ||||
−0.254407 | + | 0.967097i | \(0.581880\pi\) | |||||||
\(224\) | 11.7892 | 0.787699 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.5612 | 1.63379 | ||||||||
\(227\) | 13.0082 | 0.863387 | 0.431694 | − | 0.902020i | \(-0.357916\pi\) | ||||
0.431694 | + | 0.902020i | \(0.357916\pi\) | |||||||
\(228\) | 4.60503 | 0.304976 | ||||||||
\(229\) | −4.17490 | −0.275885 | −0.137942 | − | 0.990440i | \(-0.544049\pi\) | ||||
−0.137942 | + | 0.990440i | \(0.544049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.50722 | 0.559734 | ||||||||
\(232\) | −3.63851 | −0.238880 | ||||||||
\(233\) | −26.2804 | −1.72169 | −0.860844 | − | 0.508870i | \(-0.830064\pi\) | ||||
−0.860844 | + | 0.508870i | \(0.830064\pi\) | |||||||
\(234\) | 6.86536 | 0.448803 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.499244 | 0.0324980 | ||||||||
\(237\) | −5.60887 | −0.364335 | ||||||||
\(238\) | −18.7444 | −1.21502 | ||||||||
\(239\) | −1.61063 | −0.104183 | −0.0520915 | − | 0.998642i | \(-0.516589\pi\) | ||||
−0.0520915 | + | 0.998642i | \(0.516589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.95494 | −0.319176 | −0.159588 | − | 0.987184i | \(-0.551017\pi\) | ||||
−0.159588 | + | 0.987184i | \(0.551017\pi\) | |||||||
\(242\) | −2.41391 | −0.155172 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.83328 | 0.309419 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.20315 | 0.140468 | ||||||||
\(247\) | 23.6138 | 1.50251 | ||||||||
\(248\) | −6.52251 | −0.414180 | ||||||||
\(249\) | 4.45627 | 0.282405 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.3337 | −0.652260 | −0.326130 | − | 0.945325i | \(-0.605745\pi\) | ||||
−0.326130 | + | 0.945325i | \(0.605745\pi\) | |||||||
\(252\) | −2.20171 | −0.138695 | ||||||||
\(253\) | −21.0406 | −1.32281 | ||||||||
\(254\) | −33.7168 | −2.11558 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.5390 | 1.03369 | ||||||||
\(257\) | −17.4871 | −1.09082 | −0.545408 | − | 0.838171i | \(-0.683625\pi\) | ||||
−0.545408 | + | 0.838171i | \(0.683625\pi\) | |||||||
\(258\) | 14.4886 | 0.902024 | ||||||||
\(259\) | 15.0938 | 0.937885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.81214 | 0.112169 | ||||||||
\(262\) | −31.3447 | −1.93648 | ||||||||
\(263\) | 12.2487 | 0.755290 | 0.377645 | − | 0.925951i | \(-0.376734\pi\) | ||||
0.377645 | + | 0.925951i | \(0.376734\pi\) | |||||||
\(264\) | 6.20730 | 0.382033 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −26.5028 | −1.62499 | ||||||||
\(267\) | −2.86645 | −0.175424 | ||||||||
\(268\) | −3.24535 | −0.198242 | ||||||||
\(269\) | −4.24499 | −0.258822 | −0.129411 | − | 0.991591i | \(-0.541309\pi\) | ||||
−0.129411 | + | 0.991591i | \(0.541309\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5778 | 0.885541 | 0.442770 | − | 0.896635i | \(-0.353996\pi\) | ||||
0.442770 | + | 0.896635i | \(0.353996\pi\) | |||||||
\(272\) | −20.1908 | −1.22425 | ||||||||
\(273\) | −11.2900 | −0.683301 | ||||||||
\(274\) | 22.2673 | 1.34521 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.44542 | 0.327776 | ||||||||
\(277\) | 27.7778 | 1.66900 | 0.834502 | − | 0.551005i | \(-0.185756\pi\) | ||||
0.834502 | + | 0.551005i | \(0.185756\pi\) | |||||||
\(278\) | −4.01912 | −0.241051 | ||||||||
\(279\) | 3.24850 | 0.194483 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0720 | 0.779807 | 0.389904 | − | 0.920856i | \(-0.372508\pi\) | ||||
0.389904 | + | 0.920856i | \(0.372508\pi\) | |||||||
\(282\) | 1.67335 | 0.0996465 | ||||||||
\(283\) | −15.1027 | −0.897763 | −0.448881 | − | 0.893591i | \(-0.648177\pi\) | ||||
−0.448881 | + | 0.893591i | \(0.648177\pi\) | |||||||
\(284\) | 12.0963 | 0.717783 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −21.2243 | −1.25502 | ||||||||
\(287\) | −3.62305 | −0.213862 | ||||||||
\(288\) | −4.28418 | −0.252447 | ||||||||
\(289\) | −0.429409 | −0.0252593 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.01711 | 0.352729 | ||||||||
\(292\) | 3.04934 | 0.178449 | ||||||||
\(293\) | −11.9208 | −0.696423 | −0.348212 | − | 0.937416i | \(-0.613211\pi\) | ||||
−0.348212 | + | 0.937416i | \(0.613211\pi\) | |||||||
\(294\) | 0.957836 | 0.0558621 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.0132 | 0.640131 | ||||||||
\(297\) | −3.09151 | −0.179388 | ||||||||
\(298\) | −4.93175 | −0.285688 | ||||||||
\(299\) | 27.9231 | 1.61484 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.8264 | −1.37333 | ||||||||
\(302\) | 34.0488 | 1.95929 | ||||||||
\(303\) | 9.07572 | 0.521386 | ||||||||
\(304\) | −28.5479 | −1.63733 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.81170 | 0.389399 | ||||||||
\(307\) | −25.3094 | −1.44448 | −0.722242 | − | 0.691641i | \(-0.756888\pi\) | ||||
−0.722242 | + | 0.691641i | \(0.756888\pi\) | |||||||
\(308\) | 6.80662 | 0.387843 | ||||||||
\(309\) | −8.36703 | −0.475984 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.2759 | 1.26315 | 0.631575 | − | 0.775315i | \(-0.282409\pi\) | ||||
0.631575 | + | 0.775315i | \(0.282409\pi\) | |||||||
\(312\) | −8.23775 | −0.466371 | ||||||||
\(313\) | −8.85418 | −0.500468 | −0.250234 | − | 0.968185i | \(-0.580508\pi\) | ||||
−0.250234 | + | 0.968185i | \(0.580508\pi\) | |||||||
\(314\) | −28.0405 | −1.58242 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.48765 | −0.252450 | ||||||||
\(317\) | −25.6447 | −1.44035 | −0.720174 | − | 0.693793i | \(-0.755938\pi\) | ||||
−0.720174 | + | 0.693793i | \(0.755938\pi\) | |||||||
\(318\) | −9.34151 | −0.523846 | ||||||||
\(319\) | −5.60225 | −0.313666 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.99601 | 0.557923 | ||||||||
\(322\) | −31.3394 | −1.74648 | ||||||||
\(323\) | 23.4292 | 1.30364 | ||||||||
\(324\) | 0.800100 | 0.0444500 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.3478 | 1.34850 | ||||||||
\(327\) | 8.75321 | 0.484054 | ||||||||
\(328\) | −2.64356 | −0.145966 | ||||||||
\(329\) | −2.75180 | −0.151712 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.7383 | 1.63456 | 0.817282 | − | 0.576237i | \(-0.195480\pi\) | ||||
0.817282 | + | 0.576237i | \(0.195480\pi\) | |||||||
\(332\) | 3.56546 | 0.195680 | ||||||||
\(333\) | −5.48507 | −0.300580 | ||||||||
\(334\) | −11.9798 | −0.655506 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 13.6490 | 0.744616 | ||||||||
\(337\) | −16.4731 | −0.897344 | −0.448672 | − | 0.893696i | \(-0.648103\pi\) | ||||
−0.448672 | + | 0.893696i | \(0.648103\pi\) | |||||||
\(338\) | 6.41343 | 0.348844 | ||||||||
\(339\) | 14.6778 | 0.797191 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.0428 | −0.543847 | ||||||||
\(342\) | 9.63109 | 0.520790 | ||||||||
\(343\) | 17.6875 | 0.955033 | ||||||||
\(344\) | −17.3849 | −0.937333 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.1394 | −0.975178 | ||||||||
\(347\) | −10.8365 | −0.581734 | −0.290867 | − | 0.956763i | \(-0.593944\pi\) | ||||
−0.290867 | + | 0.956763i | \(0.593944\pi\) | |||||||
\(348\) | 1.44989 | 0.0777224 | ||||||||
\(349\) | 5.80101 | 0.310521 | 0.155260 | − | 0.987874i | \(-0.450378\pi\) | ||||
0.155260 | + | 0.987874i | \(0.450378\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.10277 | 0.218989 | ||||||||
\(352\) | 13.2446 | 0.705938 | ||||||||
\(353\) | 14.9999 | 0.798364 | 0.399182 | − | 0.916872i | \(-0.369294\pi\) | ||||
0.399182 | + | 0.916872i | \(0.369294\pi\) | |||||||
\(354\) | 1.04413 | 0.0554950 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.29345 | −0.121553 | ||||||||
\(357\) | −11.2018 | −0.592860 | ||||||||
\(358\) | 16.8968 | 0.893026 | ||||||||
\(359\) | −10.7284 | −0.566223 | −0.283112 | − | 0.959087i | \(-0.591367\pi\) | ||||
−0.283112 | + | 0.959087i | \(0.591367\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.1266 | 0.743506 | ||||||||
\(362\) | −7.00311 | −0.368075 | ||||||||
\(363\) | −1.44256 | −0.0757148 | ||||||||
\(364\) | −9.03312 | −0.473464 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.1084 | 0.528377 | ||||||||
\(367\) | −28.5989 | −1.49285 | −0.746425 | − | 0.665470i | \(-0.768231\pi\) | ||||
−0.746425 | + | 0.665470i | \(0.768231\pi\) | |||||||
\(368\) | −33.7577 | −1.75974 | ||||||||
\(369\) | 1.31661 | 0.0685400 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.3620 | 0.797555 | ||||||||
\(372\) | 2.59912 | 0.134758 | ||||||||
\(373\) | −6.36548 | −0.329592 | −0.164796 | − | 0.986328i | \(-0.552697\pi\) | ||||
−0.164796 | + | 0.986328i | \(0.552697\pi\) | |||||||
\(374\) | −21.0585 | −1.08891 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.00785 | −0.103547 | ||||||||
\(377\) | 7.43478 | 0.382911 | ||||||||
\(378\) | −4.60473 | −0.236841 | ||||||||
\(379\) | −30.3510 | −1.55903 | −0.779513 | − | 0.626386i | \(-0.784534\pi\) | ||||
−0.779513 | + | 0.626386i | \(0.784534\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.1493 | −1.03228 | ||||||||
\(382\) | −32.1765 | −1.64629 | ||||||||
\(383\) | 30.9748 | 1.58274 | 0.791370 | − | 0.611338i | \(-0.209368\pi\) | ||||
0.791370 | + | 0.611338i | \(0.209368\pi\) | |||||||
\(384\) | 13.1720 | 0.672181 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −43.1301 | −2.19527 | ||||||||
\(387\) | 8.65847 | 0.440135 | ||||||||
\(388\) | 4.81429 | 0.244409 | ||||||||
\(389\) | 26.6200 | 1.34969 | 0.674843 | − | 0.737962i | \(-0.264211\pi\) | ||||
0.674843 | + | 0.737962i | \(0.264211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.7049 | 1.40110 | ||||||||
\(392\) | −1.14931 | −0.0580488 | ||||||||
\(393\) | −18.7317 | −0.944890 | ||||||||
\(394\) | −36.4496 | −1.83630 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.47352 | −0.124299 | ||||||||
\(397\) | 31.2708 | 1.56944 | 0.784719 | − | 0.619851i | \(-0.212807\pi\) | ||||
0.784719 | + | 0.619851i | \(0.212807\pi\) | |||||||
\(398\) | 29.0962 | 1.45846 | ||||||||
\(399\) | −15.8382 | −0.792901 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1993 | 0.559266 | 0.279633 | − | 0.960107i | \(-0.409787\pi\) | ||||
0.279633 | + | 0.960107i | \(0.409787\pi\) | |||||||
\(402\) | −6.78742 | −0.338526 | ||||||||
\(403\) | 13.3278 | 0.663907 | ||||||||
\(404\) | 7.26148 | 0.361272 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.34440 | −0.414126 | ||||||||
\(407\) | 16.9572 | 0.840536 | ||||||||
\(408\) | −8.17337 | −0.404642 | ||||||||
\(409\) | −25.7028 | −1.27092 | −0.635462 | − | 0.772132i | \(-0.719190\pi\) | ||||
−0.635462 | + | 0.772132i | \(0.719190\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.3070 | 0.656386 | ||||||||
\(412\) | −6.69446 | −0.329812 | ||||||||
\(413\) | −1.71706 | −0.0844911 | ||||||||
\(414\) | 11.3887 | 0.559724 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −17.5770 | −0.861782 | ||||||||
\(417\) | −2.40184 | −0.117619 | ||||||||
\(418\) | −29.7746 | −1.45632 | ||||||||
\(419\) | 26.7057 | 1.30466 | 0.652329 | − | 0.757936i | \(-0.273792\pi\) | ||||
0.652329 | + | 0.757936i | \(0.273792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.7159 | 0.765947 | 0.382973 | − | 0.923759i | \(-0.374900\pi\) | ||||
0.382973 | + | 0.923759i | \(0.374900\pi\) | |||||||
\(422\) | 28.8921 | 1.40645 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | 11.2089 | 0.544352 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 25.2985 | 1.22572 | ||||||||
\(427\) | −16.6232 | −0.804453 | ||||||||
\(428\) | 7.99780 | 0.386588 | ||||||||
\(429\) | −12.6837 | −0.612377 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.9696 | −1.44358 | −0.721792 | − | 0.692110i | \(-0.756681\pi\) | ||||
−0.721792 | + | 0.692110i | \(0.756681\pi\) | |||||||
\(432\) | −4.96004 | −0.238640 | ||||||||
\(433\) | −16.0442 | −0.771033 | −0.385517 | − | 0.922701i | \(-0.625977\pi\) | ||||
−0.385517 | + | 0.922701i | \(0.625977\pi\) | |||||||
\(434\) | −14.9585 | −0.718029 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.00344 | 0.335404 | ||||||||
\(437\) | 39.1720 | 1.87385 | ||||||||
\(438\) | 6.37746 | 0.304727 | ||||||||
\(439\) | −5.53502 | −0.264172 | −0.132086 | − | 0.991238i | \(-0.542168\pi\) | ||||
−0.132086 | + | 0.991238i | \(0.542168\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.572406 | 0.0272574 | ||||||||
\(442\) | 27.9468 | 1.32929 | ||||||||
\(443\) | 8.49669 | 0.403690 | 0.201845 | − | 0.979417i | \(-0.435306\pi\) | ||||
0.201845 | + | 0.979417i | \(0.435306\pi\) | |||||||
\(444\) | −4.38861 | −0.208274 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.7145 | −0.602049 | ||||||||
\(447\) | −2.94723 | −0.139399 | ||||||||
\(448\) | −7.57063 | −0.357679 | ||||||||
\(449\) | 6.82306 | 0.322000 | 0.161000 | − | 0.986954i | \(-0.448528\pi\) | ||||
0.161000 | + | 0.986954i | \(0.448528\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.07032 | −0.191664 | ||||||||
\(452\) | 11.7437 | 0.552379 | ||||||||
\(453\) | 20.3477 | 0.956017 | ||||||||
\(454\) | 21.7673 | 1.02159 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11.5563 | −0.541175 | ||||||||
\(457\) | 40.7763 | 1.90743 | 0.953717 | − | 0.300706i | \(-0.0972222\pi\) | ||||
0.953717 | + | 0.300706i | \(0.0972222\pi\) | |||||||
\(458\) | −6.98606 | −0.326437 | ||||||||
\(459\) | 4.07070 | 0.190004 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.8707 | −1.06519 | −0.532597 | − | 0.846369i | \(-0.678784\pi\) | ||||
−0.532597 | + | 0.846369i | \(0.678784\pi\) | |||||||
\(462\) | 14.2356 | 0.662298 | ||||||||
\(463\) | 25.9393 | 1.20550 | 0.602752 | − | 0.797929i | \(-0.294071\pi\) | ||||
0.602752 | + | 0.797929i | \(0.294071\pi\) | |||||||
\(464\) | −8.98828 | −0.417271 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −43.9763 | −2.03716 | ||||||||
\(467\) | 20.3302 | 0.940768 | 0.470384 | − | 0.882462i | \(-0.344115\pi\) | ||||
0.470384 | + | 0.882462i | \(0.344115\pi\) | |||||||
\(468\) | 3.28262 | 0.151739 | ||||||||
\(469\) | 11.1618 | 0.515405 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.7571 | −0.772127 | ||||||||
\(472\) | −1.25286 | −0.0576673 | ||||||||
\(473\) | −26.7677 | −1.23078 | ||||||||
\(474\) | −9.38560 | −0.431095 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.96252 | −0.410796 | ||||||||
\(477\) | −5.58252 | −0.255606 | ||||||||
\(478\) | −2.69515 | −0.123273 | ||||||||
\(479\) | 15.5445 | 0.710247 | 0.355123 | − | 0.934819i | \(-0.384439\pi\) | ||||
0.355123 | + | 0.934819i | \(0.384439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.5040 | −1.02609 | ||||||||
\(482\) | −8.29135 | −0.377661 | ||||||||
\(483\) | −18.7285 | −0.852178 | ||||||||
\(484\) | −1.15419 | −0.0524633 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.67335 | 0.0759047 | ||||||||
\(487\) | −42.3974 | −1.92121 | −0.960605 | − | 0.277919i | \(-0.910355\pi\) | ||||
−0.960605 | + | 0.277919i | \(0.910355\pi\) | |||||||
\(488\) | −12.1291 | −0.549060 | ||||||||
\(489\) | 14.5503 | 0.657988 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.8996 | 1.25909 | 0.629546 | − | 0.776963i | \(-0.283241\pi\) | ||||
0.629546 | + | 0.776963i | \(0.283241\pi\) | |||||||
\(492\) | 1.05342 | 0.0474918 | ||||||||
\(493\) | 7.37667 | 0.332229 | ||||||||
\(494\) | 39.5141 | 1.77782 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.1127 | −0.723481 | ||||||||
\(497\) | −41.6030 | −1.86615 | ||||||||
\(498\) | 7.45690 | 0.334152 | ||||||||
\(499\) | 4.67712 | 0.209377 | 0.104688 | − | 0.994505i | \(-0.466616\pi\) | ||||
0.104688 | + | 0.994505i | \(0.466616\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.15918 | −0.319849 | ||||||||
\(502\) | −17.2920 | −0.771778 | ||||||||
\(503\) | −34.3219 | −1.53034 | −0.765168 | − | 0.643830i | \(-0.777344\pi\) | ||||
−0.765168 | + | 0.643830i | \(0.777344\pi\) | |||||||
\(504\) | 5.52521 | 0.246112 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −35.2083 | −1.56520 | ||||||||
\(507\) | 3.83269 | 0.170216 | ||||||||
\(508\) | −16.1214 | −0.715272 | ||||||||
\(509\) | 31.2751 | 1.38625 | 0.693123 | − | 0.720819i | \(-0.256234\pi\) | ||||
0.693123 | + | 0.720819i | \(0.256234\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.4876 | −0.463946 | ||||||||
\(512\) | 1.33162 | 0.0588499 | ||||||||
\(513\) | 5.75557 | 0.254115 | ||||||||
\(514\) | −29.2620 | −1.29069 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.92764 | 0.304972 | ||||||||
\(517\) | −3.09151 | −0.135964 | ||||||||
\(518\) | 25.2573 | 1.10974 | ||||||||
\(519\) | −10.8401 | −0.475830 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.4663 | 1.11570 | 0.557849 | − | 0.829942i | \(-0.311627\pi\) | ||||
0.557849 | + | 0.829942i | \(0.311627\pi\) | |||||||
\(522\) | 3.03234 | 0.132722 | ||||||||
\(523\) | −20.9218 | −0.914848 | −0.457424 | − | 0.889249i | \(-0.651228\pi\) | ||||
−0.457424 | + | 0.889249i | \(0.651228\pi\) | |||||||
\(524\) | −14.9872 | −0.654721 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.4964 | 0.893687 | ||||||||
\(527\) | 13.2237 | 0.576032 | ||||||||
\(528\) | 15.3340 | 0.667327 | ||||||||
\(529\) | 23.3206 | 1.01394 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.623977 | 0.0270783 | ||||||||
\(532\) | −12.6721 | −0.549406 | ||||||||
\(533\) | 5.40175 | 0.233976 | ||||||||
\(534\) | −4.79658 | −0.207568 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.14423 | 0.351777 | ||||||||
\(537\) | 10.0976 | 0.435744 | ||||||||
\(538\) | −7.10335 | −0.306247 | ||||||||
\(539\) | −1.76960 | −0.0762221 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.461908 | −0.0198590 | −0.00992948 | − | 0.999951i | \(-0.503161\pi\) | ||||
−0.00992948 | + | 0.999951i | \(0.503161\pi\) | |||||||
\(542\) | 24.3938 | 1.04780 | ||||||||
\(543\) | −4.18508 | −0.179599 | ||||||||
\(544\) | −17.4396 | −0.747716 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18.8921 | −0.808508 | ||||||||
\(547\) | −23.3606 | −0.998827 | −0.499413 | − | 0.866364i | \(-0.666451\pi\) | ||||
−0.499413 | + | 0.866364i | \(0.666451\pi\) | |||||||
\(548\) | 10.6469 | 0.454814 | ||||||||
\(549\) | 6.04084 | 0.257817 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.4299 | 0.444329 | ||||||||
\(552\) | −13.6653 | −0.581634 | ||||||||
\(553\) | 15.4345 | 0.656341 | ||||||||
\(554\) | 46.4819 | 1.97483 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.92171 | −0.0814987 | ||||||||
\(557\) | −22.3707 | −0.947877 | −0.473939 | − | 0.880558i | \(-0.657168\pi\) | ||||
−0.473939 | + | 0.880558i | \(0.657168\pi\) | |||||||
\(558\) | 5.43588 | 0.230119 | ||||||||
\(559\) | 35.5237 | 1.50249 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.5846 | −0.531323 | ||||||||
\(562\) | 21.8740 | 0.922697 | ||||||||
\(563\) | 47.1758 | 1.98822 | 0.994112 | − | 0.108362i | \(-0.0345606\pi\) | ||||
0.994112 | + | 0.108362i | \(0.0345606\pi\) | |||||||
\(564\) | 0.800100 | 0.0336903 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25.2721 | −1.06227 | ||||||||
\(567\) | −2.75180 | −0.115565 | ||||||||
\(568\) | −30.3557 | −1.27370 | ||||||||
\(569\) | 14.1917 | 0.594945 | 0.297473 | − | 0.954730i | \(-0.403856\pi\) | ||||
0.297473 | + | 0.954730i | \(0.403856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.4724 | −0.438256 | −0.219128 | − | 0.975696i | \(-0.570321\pi\) | ||||
−0.219128 | + | 0.975696i | \(0.570321\pi\) | |||||||
\(572\) | −10.1483 | −0.424320 | ||||||||
\(573\) | −19.2288 | −0.803294 | ||||||||
\(574\) | −6.06263 | −0.253049 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.75115 | 0.114631 | ||||||||
\(577\) | −15.7927 | −0.657458 | −0.328729 | − | 0.944424i | \(-0.606620\pi\) | ||||
−0.328729 | + | 0.944424i | \(0.606620\pi\) | |||||||
\(578\) | −0.718551 | −0.0298878 | ||||||||
\(579\) | −25.7747 | −1.07116 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.2628 | −0.508746 | ||||||||
\(582\) | 10.0687 | 0.417363 | ||||||||
\(583\) | 17.2584 | 0.714771 | ||||||||
\(584\) | −7.65232 | −0.316655 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.9477 | −0.824034 | ||||||||
\(587\) | −43.0436 | −1.77660 | −0.888300 | − | 0.459264i | \(-0.848113\pi\) | ||||
−0.888300 | + | 0.459264i | \(0.848113\pi\) | |||||||
\(588\) | 0.457982 | 0.0188869 | ||||||||
\(589\) | 18.6970 | 0.770396 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.7824 | −0.896008 | ||||||||
\(592\) | 27.2062 | 1.11817 | ||||||||
\(593\) | −15.8784 | −0.652049 | −0.326025 | − | 0.945361i | \(-0.605709\pi\) | ||||
−0.326025 | + | 0.945361i | \(0.605709\pi\) | |||||||
\(594\) | −5.17318 | −0.212258 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.35808 | −0.0965907 | ||||||||
\(597\) | 17.3880 | 0.711643 | ||||||||
\(598\) | 46.7251 | 1.91073 | ||||||||
\(599\) | 42.2747 | 1.72730 | 0.863649 | − | 0.504094i | \(-0.168173\pi\) | ||||
0.863649 | + | 0.504094i | \(0.168173\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.9712 | −1.91600 | −0.957998 | − | 0.286776i | \(-0.907416\pi\) | ||||
−0.957998 | + | 0.286776i | \(0.907416\pi\) | |||||||
\(602\) | −39.8699 | −1.62497 | ||||||||
\(603\) | −4.05619 | −0.165181 | ||||||||
\(604\) | 16.2802 | 0.662431 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 15.1869 | 0.616924 | ||||||||
\(607\) | 37.6395 | 1.52774 | 0.763870 | − | 0.645371i | \(-0.223297\pi\) | ||||
0.763870 | + | 0.645371i | \(0.223297\pi\) | |||||||
\(608\) | −24.6579 | −1.00001 | ||||||||
\(609\) | −4.98665 | −0.202069 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.10277 | 0.165980 | ||||||||
\(612\) | 3.25696 | 0.131655 | ||||||||
\(613\) | −30.7507 | −1.24201 | −0.621005 | − | 0.783807i | \(-0.713275\pi\) | ||||
−0.621005 | + | 0.783807i | \(0.713275\pi\) | |||||||
\(614\) | −42.3515 | −1.70917 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17.0812 | −0.688223 | ||||||||
\(617\) | 17.0417 | 0.686073 | 0.343037 | − | 0.939322i | \(-0.388545\pi\) | ||||
0.343037 | + | 0.939322i | \(0.388545\pi\) | |||||||
\(618\) | −14.0010 | −0.563202 | ||||||||
\(619\) | 42.9648 | 1.72690 | 0.863450 | − | 0.504435i | \(-0.168299\pi\) | ||||
0.863450 | + | 0.504435i | \(0.168299\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.80592 | 0.273112 | ||||||||
\(622\) | 37.2753 | 1.49461 | ||||||||
\(623\) | 7.88791 | 0.316022 | ||||||||
\(624\) | −20.3499 | −0.814647 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.8161 | −0.592172 | ||||||||
\(627\) | −17.7934 | −0.710601 | ||||||||
\(628\) | −13.4074 | −0.535012 | ||||||||
\(629\) | −22.3281 | −0.890279 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.7446 | 0.586972 | 0.293486 | − | 0.955963i | \(-0.405185\pi\) | ||||
0.293486 | + | 0.955963i | \(0.405185\pi\) | |||||||
\(632\) | 11.2618 | 0.447970 | ||||||||
\(633\) | 17.2661 | 0.686264 | ||||||||
\(634\) | −42.9125 | −1.70427 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.46657 | −0.177111 | ||||||||
\(637\) | 2.34845 | 0.0930490 | ||||||||
\(638\) | −9.37452 | −0.371141 | ||||||||
\(639\) | 15.1185 | 0.598078 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.488794 | 0.0193062 | 0.00965311 | − | 0.999953i | \(-0.496927\pi\) | ||||
0.00965311 | + | 0.999953i | \(0.496927\pi\) | |||||||
\(642\) | 16.7268 | 0.660155 | ||||||||
\(643\) | −37.6682 | −1.48549 | −0.742744 | − | 0.669576i | \(-0.766476\pi\) | ||||
−0.742744 | + | 0.669576i | \(0.766476\pi\) | |||||||
\(644\) | −14.9847 | −0.590480 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 39.2053 | 1.54251 | ||||||||
\(647\) | −15.9964 | −0.628884 | −0.314442 | − | 0.949277i | \(-0.601817\pi\) | ||||
−0.314442 | + | 0.949277i | \(0.601817\pi\) | |||||||
\(648\) | −2.00785 | −0.0788759 | ||||||||
\(649\) | −1.92903 | −0.0757212 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.93923 | −0.350356 | ||||||||
\(652\) | 11.6417 | 0.455924 | ||||||||
\(653\) | 1.45400 | 0.0568993 | 0.0284496 | − | 0.999595i | \(-0.490943\pi\) | ||||
0.0284496 | + | 0.999595i | \(0.490943\pi\) | |||||||
\(654\) | 14.6472 | 0.572750 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.53044 | −0.254971 | ||||||||
\(657\) | 3.81119 | 0.148689 | ||||||||
\(658\) | −4.60473 | −0.179511 | ||||||||
\(659\) | 44.3803 | 1.72881 | 0.864406 | − | 0.502795i | \(-0.167695\pi\) | ||||
0.864406 | + | 0.502795i | \(0.167695\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.2944 | −0.867152 | −0.433576 | − | 0.901117i | \(-0.642748\pi\) | ||||
−0.433576 | + | 0.901117i | \(0.642748\pi\) | |||||||
\(662\) | 49.7626 | 1.93408 | ||||||||
\(663\) | 16.7011 | 0.648618 | ||||||||
\(664\) | −8.94754 | −0.347232 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.17845 | −0.355658 | ||||||||
\(667\) | 12.3333 | 0.477547 | ||||||||
\(668\) | −5.72806 | −0.221625 | ||||||||
\(669\) | −7.59823 | −0.293764 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.6753 | −0.720953 | ||||||||
\(672\) | 11.7892 | 0.454778 | ||||||||
\(673\) | 32.3309 | 1.24626 | 0.623132 | − | 0.782117i | \(-0.285860\pi\) | ||||
0.623132 | + | 0.782117i | \(0.285860\pi\) | |||||||
\(674\) | −27.5652 | −1.06177 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.06653 | 0.117944 | ||||||||
\(677\) | 18.7864 | 0.722021 | 0.361011 | − | 0.932562i | \(-0.382432\pi\) | ||||
0.361011 | + | 0.932562i | \(0.382432\pi\) | |||||||
\(678\) | 24.5612 | 0.943266 | ||||||||
\(679\) | −16.5579 | −0.635434 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.0082 | 0.498477 | ||||||||
\(682\) | −16.8051 | −0.643500 | ||||||||
\(683\) | 29.3802 | 1.12420 | 0.562102 | − | 0.827068i | \(-0.309993\pi\) | ||||
0.562102 | + | 0.827068i | \(0.309993\pi\) | |||||||
\(684\) | 4.60503 | 0.176078 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 29.5973 | 1.13003 | ||||||||
\(687\) | −4.17490 | −0.159282 | ||||||||
\(688\) | −42.9463 | −1.63731 | ||||||||
\(689\) | −22.9038 | −0.872565 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.2695 | −0.428710 | −0.214355 | − | 0.976756i | \(-0.568765\pi\) | ||||
−0.214355 | + | 0.976756i | \(0.568765\pi\) | |||||||
\(692\) | −8.67320 | −0.329705 | ||||||||
\(693\) | 8.50722 | 0.323163 | ||||||||
\(694\) | −18.1333 | −0.688330 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.63851 | −0.137917 | ||||||||
\(697\) | 5.35953 | 0.203007 | ||||||||
\(698\) | 9.70711 | 0.367420 | ||||||||
\(699\) | −26.2804 | −0.994017 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.0991 | −0.796901 | −0.398451 | − | 0.917190i | \(-0.630452\pi\) | ||||
−0.398451 | + | 0.917190i | \(0.630452\pi\) | |||||||
\(702\) | 6.86536 | 0.259116 | ||||||||
\(703\) | −31.5697 | −1.19068 | ||||||||
\(704\) | −8.50523 | −0.320553 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.1001 | 0.944653 | ||||||||
\(707\) | −24.9746 | −0.939265 | ||||||||
\(708\) | 0.499244 | 0.0187627 | ||||||||
\(709\) | −24.0964 | −0.904961 | −0.452481 | − | 0.891774i | \(-0.649461\pi\) | ||||
−0.452481 | + | 0.891774i | \(0.649461\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.60887 | −0.210349 | ||||||||
\(712\) | 5.75542 | 0.215693 | ||||||||
\(713\) | 22.1090 | 0.827990 | ||||||||
\(714\) | −18.7444 | −0.701493 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.07910 | 0.301930 | ||||||||
\(717\) | −1.61063 | −0.0601501 | ||||||||
\(718\) | −17.9524 | −0.669976 | ||||||||
\(719\) | −17.5539 | −0.654649 | −0.327325 | − | 0.944912i | \(-0.606147\pi\) | ||||
−0.327325 | + | 0.944912i | \(0.606147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.0244 | 0.857474 | ||||||||
\(722\) | 23.6388 | 0.879744 | ||||||||
\(723\) | −4.95494 | −0.184276 | ||||||||
\(724\) | −3.34848 | −0.124445 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.41391 | −0.0895886 | ||||||||
\(727\) | −39.1878 | −1.45340 | −0.726698 | − | 0.686958i | \(-0.758946\pi\) | ||||
−0.726698 | + | 0.686958i | \(0.758946\pi\) | |||||||
\(728\) | 22.6686 | 0.840156 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.2460 | 1.30362 | ||||||||
\(732\) | 4.83328 | 0.178643 | ||||||||
\(733\) | −5.50231 | −0.203232 | −0.101616 | − | 0.994824i | \(-0.532401\pi\) | ||||
−0.101616 | + | 0.994824i | \(0.532401\pi\) | |||||||
\(734\) | −47.8559 | −1.76639 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.1578 | −1.07477 | ||||||||
\(737\) | 12.5397 | 0.461907 | ||||||||
\(738\) | 2.20315 | 0.0810991 | ||||||||
\(739\) | 2.23210 | 0.0821090 | 0.0410545 | − | 0.999157i | \(-0.486928\pi\) | ||||
0.0410545 | + | 0.999157i | \(0.486928\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.6138 | 0.867473 | ||||||||
\(742\) | 25.7060 | 0.943696 | ||||||||
\(743\) | −48.9867 | −1.79715 | −0.898573 | − | 0.438823i | \(-0.855395\pi\) | ||||
−0.898573 | + | 0.438823i | \(0.855395\pi\) | |||||||
\(744\) | −6.52251 | −0.239127 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.6517 | −0.389985 | ||||||||
\(747\) | 4.45627 | 0.163046 | ||||||||
\(748\) | −10.0689 | −0.368157 | ||||||||
\(749\) | −27.5070 | −1.00508 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.2338 | 1.43166 | 0.715831 | − | 0.698274i | \(-0.246048\pi\) | ||||
0.715831 | + | 0.698274i | \(0.246048\pi\) | |||||||
\(752\) | −4.96004 | −0.180874 | ||||||||
\(753\) | −10.3337 | −0.376582 | ||||||||
\(754\) | 12.4410 | 0.453074 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.20171 | −0.0800756 | ||||||||
\(757\) | −31.3025 | −1.13771 | −0.568854 | − | 0.822439i | \(-0.692613\pi\) | ||||
−0.568854 | + | 0.822439i | \(0.692613\pi\) | |||||||
\(758\) | −50.7879 | −1.84470 | ||||||||
\(759\) | −21.0406 | −0.763725 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.6565 | −0.422548 | −0.211274 | − | 0.977427i | \(-0.567761\pi\) | ||||
−0.211274 | + | 0.977427i | \(0.567761\pi\) | |||||||
\(762\) | −33.7168 | −1.22143 | ||||||||
\(763\) | −24.0871 | −0.872012 | ||||||||
\(764\) | −15.3849 | −0.556608 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 51.8317 | 1.87276 | ||||||||
\(767\) | 2.56003 | 0.0924375 | ||||||||
\(768\) | 16.5390 | 0.596801 | ||||||||
\(769\) | −40.4684 | −1.45933 | −0.729664 | − | 0.683806i | \(-0.760324\pi\) | ||||
−0.729664 | + | 0.683806i | \(0.760324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.4871 | −0.629782 | ||||||||
\(772\) | −20.6223 | −0.742214 | ||||||||
\(773\) | 28.4120 | 1.02191 | 0.510955 | − | 0.859608i | \(-0.329292\pi\) | ||||
0.510955 | + | 0.859608i | \(0.329292\pi\) | |||||||
\(774\) | 14.4886 | 0.520784 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.0815 | −0.433700 | ||||||||
\(777\) | 15.0938 | 0.541488 | ||||||||
\(778\) | 44.5445 | 1.59700 | ||||||||
\(779\) | 7.57785 | 0.271505 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −46.7389 | −1.67245 | ||||||||
\(782\) | 46.3599 | 1.65783 | ||||||||
\(783\) | 1.81214 | 0.0647606 | ||||||||
\(784\) | −2.83916 | −0.101399 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −31.3447 | −1.11803 | ||||||||
\(787\) | 37.2934 | 1.32937 | 0.664683 | − | 0.747126i | \(-0.268567\pi\) | ||||
0.664683 | + | 0.747126i | \(0.268567\pi\) | |||||||
\(788\) | −17.4281 | −0.620850 | ||||||||
\(789\) | 12.2487 | 0.436067 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −40.3905 | −1.43612 | ||||||||
\(792\) | 6.20730 | 0.220567 | ||||||||
\(793\) | 24.7842 | 0.880112 | ||||||||
\(794\) | 52.3271 | 1.85702 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.9121 | 0.493102 | ||||||||
\(797\) | −36.9191 | −1.30774 | −0.653870 | − | 0.756607i | \(-0.726856\pi\) | ||||
−0.653870 | + | 0.756607i | \(0.726856\pi\) | |||||||
\(798\) | −26.5028 | −0.938190 | ||||||||
\(799\) | 4.07070 | 0.144011 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.86645 | −0.101281 | ||||||||
\(802\) | 18.7403 | 0.661744 | ||||||||
\(803\) | −11.7824 | −0.415790 | ||||||||
\(804\) | −3.24535 | −0.114455 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 22.3021 | 0.785559 | ||||||||
\(807\) | −4.24499 | −0.149431 | ||||||||
\(808\) | −18.2227 | −0.641073 | ||||||||
\(809\) | −47.8896 | −1.68371 | −0.841854 | − | 0.539706i | \(-0.818535\pi\) | ||||
−0.841854 | + | 0.539706i | \(0.818535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.9542 | 1.50833 | 0.754163 | − | 0.656687i | \(-0.228043\pi\) | ||||
0.754163 | + | 0.656687i | \(0.228043\pi\) | |||||||
\(812\) | −3.98981 | −0.140015 | ||||||||
\(813\) | 14.5778 | 0.511267 | ||||||||
\(814\) | 28.3753 | 0.994553 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.1908 | −0.706820 | ||||||||
\(817\) | 49.8344 | 1.74349 | ||||||||
\(818\) | −43.0098 | −1.50380 | ||||||||
\(819\) | −11.2900 | −0.394504 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.99177 | 0.139314 | 0.0696569 | − | 0.997571i | \(-0.477810\pi\) | ||||
0.0696569 | + | 0.997571i | \(0.477810\pi\) | |||||||
\(822\) | 22.2673 | 0.776660 | ||||||||
\(823\) | 5.89579 | 0.205514 | 0.102757 | − | 0.994706i | \(-0.467234\pi\) | ||||
0.102757 | + | 0.994706i | \(0.467234\pi\) | |||||||
\(824\) | 16.7998 | 0.585248 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.87324 | −0.0999730 | ||||||||
\(827\) | −16.7716 | −0.583204 | −0.291602 | − | 0.956540i | \(-0.594188\pi\) | ||||
−0.291602 | + | 0.956540i | \(0.594188\pi\) | |||||||
\(828\) | 5.44542 | 0.189241 | ||||||||
\(829\) | −42.2432 | −1.46717 | −0.733583 | − | 0.679599i | \(-0.762154\pi\) | ||||
−0.733583 | + | 0.679599i | \(0.762154\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.7778 | 0.963600 | ||||||||
\(832\) | 11.2873 | 0.391318 | ||||||||
\(833\) | 2.33009 | 0.0807330 | ||||||||
\(834\) | −4.01912 | −0.139171 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −14.2365 | −0.492380 | ||||||||
\(837\) | 3.24850 | 0.112285 | ||||||||
\(838\) | 44.6880 | 1.54372 | ||||||||
\(839\) | −1.08010 | −0.0372891 | −0.0186445 | − | 0.999826i | \(-0.505935\pi\) | ||||
−0.0186445 | + | 0.999826i | \(0.505935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.7162 | −0.886764 | ||||||||
\(842\) | 26.2982 | 0.906297 | ||||||||
\(843\) | 13.0720 | 0.450222 | ||||||||
\(844\) | 13.8146 | 0.475517 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.67335 | 0.0575310 | ||||||||
\(847\) | 3.96964 | 0.136398 | ||||||||
\(848\) | 27.6895 | 0.950863 | ||||||||
\(849\) | −15.1027 | −0.518323 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.3310 | −1.27969 | ||||||||
\(852\) | 12.0963 | 0.414412 | ||||||||
\(853\) | 11.3175 | 0.387503 | 0.193751 | − | 0.981051i | \(-0.437935\pi\) | ||||
0.193751 | + | 0.981051i | \(0.437935\pi\) | |||||||
\(854\) | −27.8164 | −0.951859 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.0705 | −0.685996 | ||||||||
\(857\) | 52.2813 | 1.78589 | 0.892947 | − | 0.450162i | \(-0.148634\pi\) | ||||
0.892947 | + | 0.450162i | \(0.148634\pi\) | |||||||
\(858\) | −21.2243 | −0.724587 | ||||||||
\(859\) | −20.2984 | −0.692574 | −0.346287 | − | 0.938129i | \(-0.612558\pi\) | ||||
−0.346287 | + | 0.938129i | \(0.612558\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.62305 | −0.123473 | ||||||||
\(862\) | −50.1496 | −1.70810 | ||||||||
\(863\) | 37.2057 | 1.26650 | 0.633249 | − | 0.773948i | \(-0.281721\pi\) | ||||
0.633249 | + | 0.773948i | \(0.281721\pi\) | |||||||
\(864\) | −4.28418 | −0.145751 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −26.8475 | −0.912315 | ||||||||
\(867\) | −0.429409 | −0.0145835 | ||||||||
\(868\) | −7.15227 | −0.242764 | ||||||||
\(869\) | 17.3399 | 0.588215 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.6416 | −0.563879 | ||||||||
\(872\) | −17.5752 | −0.595170 | ||||||||
\(873\) | 6.01711 | 0.203648 | ||||||||
\(874\) | 65.5485 | 2.21721 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.04934 | 0.103028 | ||||||||
\(877\) | −35.9906 | −1.21532 | −0.607659 | − | 0.794198i | \(-0.707891\pi\) | ||||
−0.607659 | + | 0.794198i | \(0.707891\pi\) | |||||||
\(878\) | −9.26203 | −0.312578 | ||||||||
\(879\) | −11.9208 | −0.402080 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.2664 | 1.08708 | 0.543541 | − | 0.839382i | \(-0.317083\pi\) | ||||
0.543541 | + | 0.839382i | \(0.317083\pi\) | |||||||
\(882\) | 0.957836 | 0.0322520 | ||||||||
\(883\) | 18.6132 | 0.626383 | 0.313192 | − | 0.949690i | \(-0.398602\pi\) | ||||
0.313192 | + | 0.949690i | \(0.398602\pi\) | |||||||
\(884\) | 13.3626 | 0.449432 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.2179 | 0.477661 | ||||||||
\(887\) | −25.5149 | −0.856705 | −0.428353 | − | 0.903612i | \(-0.640906\pi\) | ||||
−0.428353 | + | 0.903612i | \(0.640906\pi\) | |||||||
\(888\) | 11.0132 | 0.369580 | ||||||||
\(889\) | 55.4467 | 1.85962 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.09151 | −0.103570 | ||||||||
\(892\) | −6.07934 | −0.203551 | ||||||||
\(893\) | 5.75557 | 0.192603 | ||||||||
\(894\) | −4.93175 | −0.164942 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −36.2467 | −1.21092 | ||||||||
\(897\) | 27.9231 | 0.932326 | ||||||||
\(898\) | 11.4174 | 0.381002 | ||||||||
\(899\) | 5.88674 | 0.196334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.7248 | −0.757072 | ||||||||
\(902\) | −6.81106 | −0.226784 | ||||||||
\(903\) | −23.8264 | −0.792892 | ||||||||
\(904\) | −29.4710 | −0.980190 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 34.0488 | 1.13119 | ||||||||
\(907\) | −47.4369 | −1.57512 | −0.787559 | − | 0.616240i | \(-0.788655\pi\) | ||||
−0.787559 | + | 0.616240i | \(0.788655\pi\) | |||||||
\(908\) | 10.4079 | 0.345398 | ||||||||
\(909\) | 9.07572 | 0.301023 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.9807 | −1.09270 | −0.546350 | − | 0.837557i | \(-0.683983\pi\) | ||||
−0.546350 | + | 0.837557i | \(0.683983\pi\) | |||||||
\(912\) | −28.5479 | −0.945314 | ||||||||
\(913\) | −13.7766 | −0.455939 | ||||||||
\(914\) | 68.2330 | 2.25695 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.34033 | −0.110368 | ||||||||
\(917\) | 51.5460 | 1.70220 | ||||||||
\(918\) | 6.81170 | 0.224820 | ||||||||
\(919\) | 25.7949 | 0.850895 | 0.425447 | − | 0.904983i | \(-0.360117\pi\) | ||||
0.425447 | + | 0.904983i | \(0.360117\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.3094 | −0.833973 | ||||||||
\(922\) | −38.2707 | −1.26038 | ||||||||
\(923\) | 62.0276 | 2.04166 | ||||||||
\(924\) | 6.80662 | 0.223922 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 43.4056 | 1.42640 | ||||||||
\(927\) | −8.36703 | −0.274809 | ||||||||
\(928\) | −7.76352 | −0.254850 | ||||||||
\(929\) | 33.8137 | 1.10939 | 0.554696 | − | 0.832053i | \(-0.312835\pi\) | ||||
0.554696 | + | 0.832053i | \(0.312835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.29453 | 0.107974 | ||||||||
\(932\) | −21.0270 | −0.688761 | ||||||||
\(933\) | 22.2759 | 0.729280 | ||||||||
\(934\) | 34.0195 | 1.11315 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.23775 | −0.269259 | ||||||||
\(937\) | 19.6956 | 0.643427 | 0.321714 | − | 0.946837i | \(-0.395741\pi\) | ||||
0.321714 | + | 0.946837i | \(0.395741\pi\) | |||||||
\(938\) | 18.6776 | 0.609846 | ||||||||
\(939\) | −8.85418 | −0.288945 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.4267 | 1.67646 | 0.838231 | − | 0.545315i | \(-0.183590\pi\) | ||||
0.838231 | + | 0.545315i | \(0.183590\pi\) | |||||||
\(942\) | −28.0405 | −0.913609 | ||||||||
\(943\) | 8.96075 | 0.291802 | ||||||||
\(944\) | −3.09495 | −0.100732 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.7918 | −1.45631 | ||||||||
\(947\) | 2.31054 | 0.0750825 | 0.0375413 | − | 0.999295i | \(-0.488047\pi\) | ||||
0.0375413 | + | 0.999295i | \(0.488047\pi\) | |||||||
\(948\) | −4.48765 | −0.145752 | ||||||||
\(949\) | 15.6364 | 0.507580 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.6447 | −0.831585 | ||||||||
\(952\) | 22.4915 | 0.728953 | ||||||||
\(953\) | 18.2392 | 0.590825 | 0.295413 | − | 0.955370i | \(-0.404543\pi\) | ||||
0.295413 | + | 0.955370i | \(0.404543\pi\) | |||||||
\(954\) | −9.34151 | −0.302443 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.28866 | −0.0416784 | ||||||||
\(957\) | −5.60225 | −0.181095 | ||||||||
\(958\) | 26.0114 | 0.840390 | ||||||||
\(959\) | −36.6182 | −1.18246 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.4472 | −0.659589 | ||||||||
\(962\) | −37.6570 | −1.21411 | ||||||||
\(963\) | 9.99601 | 0.322117 | ||||||||
\(964\) | −3.96445 | −0.127686 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −31.3394 | −1.00833 | ||||||||
\(967\) | 19.6701 | 0.632548 | 0.316274 | − | 0.948668i | \(-0.397568\pi\) | ||||
0.316274 | + | 0.948668i | \(0.397568\pi\) | |||||||
\(968\) | 2.89645 | 0.0930955 | ||||||||
\(969\) | 23.4292 | 0.752655 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.6396 | 1.24000 | 0.620002 | − | 0.784600i | \(-0.287132\pi\) | ||||
0.620002 | + | 0.784600i | \(0.287132\pi\) | |||||||
\(972\) | 0.800100 | 0.0256632 | ||||||||
\(973\) | 6.60938 | 0.211887 | ||||||||
\(974\) | −70.9457 | −2.27325 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.9628 | −0.959087 | ||||||||
\(977\) | 32.9862 | 1.05532 | 0.527662 | − | 0.849455i | \(-0.323069\pi\) | ||||
0.527662 | + | 0.849455i | \(0.323069\pi\) | |||||||
\(978\) | 24.3478 | 0.778556 | ||||||||
\(979\) | 8.86167 | 0.283220 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.75321 | 0.279469 | ||||||||
\(982\) | 46.6858 | 1.48980 | ||||||||
\(983\) | 3.94238 | 0.125742 | 0.0628711 | − | 0.998022i | \(-0.479974\pi\) | ||||
0.0628711 | + | 0.998022i | \(0.479974\pi\) | |||||||
\(984\) | −2.64356 | −0.0842736 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12.3438 | 0.393105 | ||||||||
\(987\) | −2.75180 | −0.0875908 | ||||||||
\(988\) | 18.8934 | 0.601078 | ||||||||
\(989\) | 58.9289 | 1.87383 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.0682 | 0.383360 | 0.191680 | − | 0.981457i | \(-0.438606\pi\) | ||||
0.191680 | + | 0.981457i | \(0.438606\pi\) | |||||||
\(992\) | −13.9171 | −0.441870 | ||||||||
\(993\) | 29.7383 | 0.943716 | ||||||||
\(994\) | −69.6164 | −2.20810 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.56546 | 0.112976 | ||||||||
\(997\) | 2.87188 | 0.0909535 | 0.0454767 | − | 0.998965i | \(-0.485519\pi\) | ||||
0.0454767 | + | 0.998965i | \(0.485519\pi\) | |||||||
\(998\) | 7.82646 | 0.247742 | ||||||||
\(999\) | −5.48507 | −0.173540 |
(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 | 3525.2.a.bi.1.10 | 13 | ||
5.2 | odd | 4 | 705.2.c.c.424.20 | yes | 26 | ||
5.3 | odd | 4 | 705.2.c.c.424.7 | ✓ | 26 | ||
5.4 | even | 2 | 3525.2.a.bh.1.4 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.c.c.424.7 | ✓ | 26 | 5.3 | odd | 4 | ||
705.2.c.c.424.20 | yes | 26 | 5.2 | odd | 4 | ||
3525.2.a.bh.1.4 | 13 | 5.4 | even | 2 | |||
3525.2.a.bi.1.10 | 13 | 1.1 | even | 1 | trivial |