Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7350,2,Mod(1,7350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7350, 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("7350.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7350.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: | \(58.6900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2700.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 15x - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.61323\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7350.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.78426 | −1.44251 | −0.721254 | − | 0.692670i | \(-0.756434\pi\) | ||||
−0.721254 | + | 0.692670i | \(0.756434\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.17103 | 0.879485 | 0.439743 | − | 0.898124i | \(-0.355070\pi\) | ||||
0.439743 | + | 0.898124i | \(0.355070\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.22646 | −1.26760 | −0.633801 | − | 0.773496i | \(-0.718506\pi\) | ||||
−0.633801 | + | 0.773496i | \(0.718506\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −3.17103 | −0.727484 | −0.363742 | − | 0.931500i | \(-0.618501\pi\) | ||||
−0.363742 | + | 0.931500i | \(0.618501\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.78426 | 1.02001 | ||||||||
\(23\) | −7.17103 | −1.49526 | −0.747632 | − | 0.664114i | \(-0.768809\pi\) | ||||
−0.747632 | + | 0.664114i | \(0.768809\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.17103 | −0.621890 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.38677 | 0.443212 | 0.221606 | − | 0.975136i | \(-0.428870\pi\) | ||||
0.221606 | + | 0.975136i | \(0.428870\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.17103 | 0.749139 | 0.374570 | − | 0.927199i | \(-0.377791\pi\) | ||||
0.374570 | + | 0.927199i | \(0.377791\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.78426 | 0.832833 | ||||||||
\(34\) | 5.22646 | 0.896330 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.17103 | −1.17891 | −0.589455 | − | 0.807801i | \(-0.700657\pi\) | ||||
−0.589455 | + | 0.807801i | \(0.700657\pi\) | |||||||
\(38\) | 3.17103 | 0.514409 | ||||||||
\(39\) | −3.17103 | −0.507771 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.05543 | −0.321004 | −0.160502 | − | 0.987035i | \(-0.551311\pi\) | ||||
−0.160502 | + | 0.987035i | \(0.551311\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | −4.78426 | −0.721254 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.17103 | 1.05731 | ||||||||
\(47\) | −11.5131 | −1.67936 | −0.839678 | − | 0.543084i | \(-0.817256\pi\) | ||||
−0.839678 | + | 0.543084i | \(0.817256\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.22646 | 0.731851 | ||||||||
\(52\) | 3.17103 | 0.439743 | ||||||||
\(53\) | 8.11560 | 1.11476 | 0.557382 | − | 0.830256i | \(-0.311806\pi\) | ||||
0.557382 | + | 0.830256i | \(0.311806\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.17103 | 0.420013 | ||||||||
\(58\) | −2.38677 | −0.313398 | ||||||||
\(59\) | −10.7288 | −1.39677 | −0.698387 | − | 0.715720i | \(-0.746099\pi\) | ||||
−0.698387 | + | 0.715720i | \(0.746099\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.11560 | 0.911059 | 0.455530 | − | 0.890221i | \(-0.349450\pi\) | ||||
0.455530 | + | 0.890221i | \(0.349450\pi\) | |||||||
\(62\) | −4.17103 | −0.529721 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.78426 | −0.588902 | ||||||||
\(67\) | −9.56852 | −1.16898 | −0.584490 | − | 0.811401i | \(-0.698706\pi\) | ||||
−0.584490 | + | 0.811401i | \(0.698706\pi\) | |||||||
\(68\) | −5.22646 | −0.633801 | ||||||||
\(69\) | 7.17103 | 0.863291 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 7.17103 | 0.833615 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.17103 | −0.363742 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.17103 | 0.359048 | ||||||||
\(79\) | 12.1710 | 1.36935 | 0.684674 | − | 0.728850i | \(-0.259945\pi\) | ||||
0.684674 | + | 0.728850i | \(0.259945\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.05543 | 0.226984 | ||||||||
\(83\) | 3.39749 | 0.372923 | 0.186461 | − | 0.982462i | \(-0.440298\pi\) | ||||
0.186461 | + | 0.982462i | \(0.440298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | −2.38677 | −0.255889 | ||||||||
\(88\) | 4.78426 | 0.510004 | ||||||||
\(89\) | 9.56852 | 1.01426 | 0.507131 | − | 0.861869i | \(-0.330706\pi\) | ||||
0.507131 | + | 0.861869i | \(0.330706\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.17103 | −0.747632 | ||||||||
\(93\) | −4.17103 | −0.432516 | ||||||||
\(94\) | 11.5131 | 1.18748 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.27117 | 0.129068 | 0.0645339 | − | 0.997916i | \(-0.479444\pi\) | ||||
0.0645339 | + | 0.997916i | \(0.479444\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.78426 | −0.480836 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.00000 | −0.796030 | −0.398015 | − | 0.917379i | \(-0.630301\pi\) | ||||
−0.398015 | + | 0.917379i | \(0.630301\pi\) | |||||||
\(102\) | −5.22646 | −0.517497 | ||||||||
\(103\) | 11.2265 | 1.10618 | 0.553088 | − | 0.833123i | \(-0.313449\pi\) | ||||
0.553088 | + | 0.833123i | \(0.313449\pi\) | |||||||
\(104\) | −3.17103 | −0.310945 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.11560 | −0.788257 | ||||||||
\(107\) | 1.39749 | 0.135100 | 0.0675502 | − | 0.997716i | \(-0.478482\pi\) | ||||
0.0675502 | + | 0.997716i | \(0.478482\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 12.4529 | 1.19277 | 0.596387 | − | 0.802697i | \(-0.296603\pi\) | ||||
0.596387 | + | 0.802697i | \(0.296603\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.17103 | 0.680644 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.34206 | −0.596611 | −0.298305 | − | 0.954470i | \(-0.596421\pi\) | ||||
−0.298305 | + | 0.954470i | \(0.596421\pi\) | |||||||
\(114\) | −3.17103 | −0.296994 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.38677 | 0.221606 | ||||||||
\(117\) | 3.17103 | 0.293162 | ||||||||
\(118\) | 10.7288 | 0.987669 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8891 | 1.08083 | ||||||||
\(122\) | −7.11560 | −0.644216 | ||||||||
\(123\) | 2.05543 | 0.185332 | ||||||||
\(124\) | 4.17103 | 0.374570 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.0107 | −1.59819 | −0.799096 | − | 0.601203i | \(-0.794688\pi\) | ||||
−0.799096 | + | 0.601203i | \(0.794688\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.00000 | −0.176090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.55780 | −0.485587 | −0.242794 | − | 0.970078i | \(-0.578064\pi\) | ||||
−0.242794 | + | 0.970078i | \(0.578064\pi\) | |||||||
\(132\) | 4.78426 | 0.416416 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.56852 | 0.826594 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.22646 | 0.448165 | ||||||||
\(137\) | 14.7950 | 1.26402 | 0.632010 | − | 0.774960i | \(-0.282230\pi\) | ||||
0.632010 | + | 0.774960i | \(0.282230\pi\) | |||||||
\(138\) | −7.17103 | −0.610439 | ||||||||
\(139\) | 3.65794 | 0.310262 | 0.155131 | − | 0.987894i | \(-0.450420\pi\) | ||||
0.155131 | + | 0.987894i | \(0.450420\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.5131 | 0.969577 | ||||||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | −15.1710 | −1.26867 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.00000 | 0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.17103 | −0.589455 | ||||||||
\(149\) | 22.3421 | 1.83033 | 0.915166 | − | 0.403076i | \(-0.132059\pi\) | ||||
0.915166 | + | 0.403076i | \(0.132059\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.5131 | 1.34382 | 0.671908 | − | 0.740635i | \(-0.265475\pi\) | ||||
0.671908 | + | 0.740635i | \(0.265475\pi\) | |||||||
\(152\) | 3.17103 | 0.257204 | ||||||||
\(153\) | −5.22646 | −0.422534 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.17103 | −0.253886 | ||||||||
\(157\) | −9.94457 | −0.793663 | −0.396832 | − | 0.917891i | \(-0.629890\pi\) | ||||
−0.396832 | + | 0.917891i | \(0.629890\pi\) | |||||||
\(158\) | −12.1710 | −0.968275 | ||||||||
\(159\) | −8.11560 | −0.643609 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −2.88440 | −0.225924 | −0.112962 | − | 0.993599i | \(-0.536034\pi\) | ||||
−0.112962 | + | 0.993599i | \(0.536034\pi\) | |||||||
\(164\) | −2.05543 | −0.160502 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.39749 | −0.263696 | ||||||||
\(167\) | −4.05543 | −0.313819 | −0.156909 | − | 0.987613i | \(-0.550153\pi\) | ||||
−0.156909 | + | 0.987613i | \(0.550153\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.94457 | −0.226505 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.17103 | −0.242495 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | −6.39749 | −0.486392 | −0.243196 | − | 0.969977i | \(-0.578196\pi\) | ||||
−0.243196 | + | 0.969977i | \(0.578196\pi\) | |||||||
\(174\) | 2.38677 | 0.180941 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.78426 | −0.360627 | ||||||||
\(177\) | 10.7288 | 0.806428 | ||||||||
\(178\) | −9.56852 | −0.717191 | ||||||||
\(179\) | 19.5131 | 1.45848 | 0.729238 | − | 0.684260i | \(-0.239875\pi\) | ||||
0.729238 | + | 0.684260i | \(0.239875\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.0262 | −1.71152 | −0.855761 | − | 0.517371i | \(-0.826911\pi\) | ||||
−0.855761 | + | 0.517371i | \(0.826911\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.11560 | −0.526000 | ||||||||
\(184\) | 7.17103 | 0.528655 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.17103 | 0.305835 | ||||||||
\(187\) | 25.0047 | 1.82853 | ||||||||
\(188\) | −11.5131 | −0.839678 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2312 | −0.740304 | −0.370152 | − | 0.928971i | \(-0.620694\pi\) | ||||
−0.370152 | + | 0.928971i | \(0.620694\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 11.6132 | 0.835939 | 0.417969 | − | 0.908461i | \(-0.362742\pi\) | ||||
0.417969 | + | 0.908461i | \(0.362742\pi\) | |||||||
\(194\) | −1.27117 | −0.0912647 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.39749 | 0.170814 | 0.0854070 | − | 0.996346i | \(-0.472781\pi\) | ||||
0.0854070 | + | 0.996346i | \(0.472781\pi\) | |||||||
\(198\) | 4.78426 | 0.340003 | ||||||||
\(199\) | −18.3421 | −1.30023 | −0.650117 | − | 0.759834i | \(-0.725280\pi\) | ||||
−0.650117 | + | 0.759834i | \(0.725280\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.56852 | 0.674911 | ||||||||
\(202\) | 8.00000 | 0.562878 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.22646 | 0.365925 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.2265 | −0.782185 | ||||||||
\(207\) | −7.17103 | −0.498421 | ||||||||
\(208\) | 3.17103 | 0.219871 | ||||||||
\(209\) | 15.1710 | 1.04940 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.82897 | −0.194754 | −0.0973772 | − | 0.995248i | \(-0.531045\pi\) | ||||
−0.0973772 | + | 0.995248i | \(0.531045\pi\) | |||||||
\(212\) | 8.11560 | 0.557382 | ||||||||
\(213\) | −6.00000 | −0.411113 | ||||||||
\(214\) | −1.39749 | −0.0955304 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.4529 | −0.843418 | ||||||||
\(219\) | 4.00000 | 0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.5733 | −1.11484 | ||||||||
\(222\) | −7.17103 | −0.481288 | ||||||||
\(223\) | −14.2973 | −0.957421 | −0.478711 | − | 0.877973i | \(-0.658896\pi\) | ||||
−0.478711 | + | 0.877973i | \(0.658896\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.34206 | 0.421868 | ||||||||
\(227\) | −11.0554 | −0.733775 | −0.366887 | − | 0.930265i | \(-0.619577\pi\) | ||||
−0.366887 | + | 0.930265i | \(0.619577\pi\) | |||||||
\(228\) | 3.17103 | 0.210007 | ||||||||
\(229\) | −18.4529 | −1.21940 | −0.609702 | − | 0.792631i | \(-0.708711\pi\) | ||||
−0.609702 | + | 0.792631i | \(0.708711\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.38677 | −0.156699 | ||||||||
\(233\) | 9.11560 | 0.597183 | 0.298591 | − | 0.954381i | \(-0.403483\pi\) | ||||
0.298591 | + | 0.954381i | \(0.403483\pi\) | |||||||
\(234\) | −3.17103 | −0.207297 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.7288 | −0.698387 | ||||||||
\(237\) | −12.1710 | −0.790593 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1156 | 0.848378 | 0.424189 | − | 0.905574i | \(-0.360559\pi\) | ||||
0.424189 | + | 0.905574i | \(0.360559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.34206 | −0.344112 | −0.172056 | − | 0.985087i | \(-0.555041\pi\) | ||||
−0.172056 | + | 0.985087i | \(0.555041\pi\) | |||||||
\(242\) | −11.8891 | −0.764263 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.11560 | 0.455530 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.05543 | −0.131049 | ||||||||
\(247\) | −10.0554 | −0.639812 | ||||||||
\(248\) | −4.17103 | −0.264861 | ||||||||
\(249\) | −3.39749 | −0.215307 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.9213 | 1.76238 | 0.881188 | − | 0.472765i | \(-0.156744\pi\) | ||||
0.881188 | + | 0.472765i | \(0.156744\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.3081 | 2.15693 | ||||||||
\(254\) | 18.0107 | 1.13009 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.1370 | 1.31849 | 0.659246 | − | 0.751927i | \(-0.270876\pi\) | ||||
0.659246 | + | 0.751927i | \(0.270876\pi\) | |||||||
\(258\) | 2.00000 | 0.124515 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.38677 | 0.147737 | ||||||||
\(262\) | 5.55780 | 0.343362 | ||||||||
\(263\) | −11.9106 | −0.734438 | −0.367219 | − | 0.930135i | \(-0.619690\pi\) | ||||
−0.367219 | + | 0.930135i | \(0.619690\pi\) | |||||||
\(264\) | −4.78426 | −0.294451 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.56852 | −0.585584 | ||||||||
\(268\) | −9.56852 | −0.584490 | ||||||||
\(269\) | −3.27117 | −0.199447 | −0.0997234 | − | 0.995015i | \(-0.531796\pi\) | ||||
−0.0997234 | + | 0.995015i | \(0.531796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.623949 | 0.0379022 | 0.0189511 | − | 0.999820i | \(-0.493967\pi\) | ||||
0.0189511 | + | 0.999820i | \(0.493967\pi\) | |||||||
\(272\) | −5.22646 | −0.316901 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.7950 | −0.893797 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.17103 | 0.431645 | ||||||||
\(277\) | 28.7950 | 1.73012 | 0.865061 | − | 0.501666i | \(-0.167279\pi\) | ||||
0.865061 | + | 0.501666i | \(0.167279\pi\) | |||||||
\(278\) | −3.65794 | −0.219389 | ||||||||
\(279\) | 4.17103 | 0.249713 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.82897 | 0.168762 | 0.0843811 | − | 0.996434i | \(-0.473109\pi\) | ||||
0.0843811 | + | 0.996434i | \(0.473109\pi\) | |||||||
\(282\) | −11.5131 | −0.685594 | ||||||||
\(283\) | 25.1370 | 1.49424 | 0.747121 | − | 0.664688i | \(-0.231436\pi\) | ||||
0.747121 | + | 0.664688i | \(0.231436\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.1710 | 0.897082 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 10.3159 | 0.606817 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.27117 | −0.0745173 | ||||||||
\(292\) | −4.00000 | −0.234082 | ||||||||
\(293\) | −10.2265 | −0.597436 | −0.298718 | − | 0.954341i | \(-0.596559\pi\) | ||||
−0.298718 | + | 0.954341i | \(0.596559\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.17103 | 0.416808 | ||||||||
\(297\) | 4.78426 | 0.277611 | ||||||||
\(298\) | −22.3421 | −1.29424 | ||||||||
\(299\) | −22.7395 | −1.31506 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.5131 | −0.950222 | ||||||||
\(303\) | 8.00000 | 0.459588 | ||||||||
\(304\) | −3.17103 | −0.181871 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.22646 | 0.298777 | ||||||||
\(307\) | 23.4577 | 1.33880 | 0.669400 | − | 0.742902i | \(-0.266551\pi\) | ||||
0.669400 | + | 0.742902i | \(0.266551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.2265 | −0.638651 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.65794 | −0.320832 | −0.160416 | − | 0.987049i | \(-0.551284\pi\) | ||||
−0.160416 | + | 0.987049i | \(0.551284\pi\) | |||||||
\(312\) | 3.17103 | 0.179524 | ||||||||
\(313\) | 16.3868 | 0.926235 | 0.463118 | − | 0.886297i | \(-0.346731\pi\) | ||||
0.463118 | + | 0.886297i | \(0.346731\pi\) | |||||||
\(314\) | 9.94457 | 0.561205 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.1710 | 0.684674 | ||||||||
\(317\) | −4.51309 | −0.253480 | −0.126740 | − | 0.991936i | \(-0.540451\pi\) | ||||
−0.126740 | + | 0.991936i | \(0.540451\pi\) | |||||||
\(318\) | 8.11560 | 0.455100 | ||||||||
\(319\) | −11.4189 | −0.639337 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.39749 | −0.0780003 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.5733 | 0.922161 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.88440 | 0.159752 | ||||||||
\(327\) | −12.4529 | −0.688648 | ||||||||
\(328\) | 2.05543 | 0.113492 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0816 | −0.719030 | −0.359515 | − | 0.933139i | \(-0.617058\pi\) | ||||
−0.359515 | + | 0.933139i | \(0.617058\pi\) | |||||||
\(332\) | 3.39749 | 0.186461 | ||||||||
\(333\) | −7.17103 | −0.392970 | ||||||||
\(334\) | 4.05543 | 0.221903 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.2973 | −1.10567 | −0.552834 | − | 0.833292i | \(-0.686453\pi\) | ||||
−0.552834 | + | 0.833292i | \(0.686453\pi\) | |||||||
\(338\) | 2.94457 | 0.160163 | ||||||||
\(339\) | 6.34206 | 0.344453 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.9553 | −1.08064 | ||||||||
\(342\) | 3.17103 | 0.171470 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.39749 | 0.343931 | ||||||||
\(347\) | −14.4529 | −0.775873 | −0.387937 | − | 0.921686i | \(-0.626812\pi\) | ||||
−0.387937 | + | 0.921686i | \(0.626812\pi\) | |||||||
\(348\) | −2.38677 | −0.127944 | ||||||||
\(349\) | 13.8891 | 0.743469 | 0.371734 | − | 0.928339i | \(-0.378763\pi\) | ||||
0.371734 | + | 0.928339i | \(0.378763\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.17103 | −0.169257 | ||||||||
\(352\) | 4.78426 | 0.255002 | ||||||||
\(353\) | 6.45292 | 0.343454 | 0.171727 | − | 0.985145i | \(-0.445065\pi\) | ||||
0.171727 | + | 0.985145i | \(0.445065\pi\) | |||||||
\(354\) | −10.7288 | −0.570231 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.56852 | 0.507131 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.5131 | −1.03130 | ||||||||
\(359\) | 7.22646 | 0.381398 | 0.190699 | − | 0.981649i | \(-0.438925\pi\) | ||||
0.190699 | + | 0.981649i | \(0.438925\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.94457 | −0.470767 | ||||||||
\(362\) | 23.0262 | 1.21023 | ||||||||
\(363\) | −11.8891 | −0.624018 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.11560 | 0.371938 | ||||||||
\(367\) | 2.10014 | 0.109626 | 0.0548132 | − | 0.998497i | \(-0.482544\pi\) | ||||
0.0548132 | + | 0.998497i | \(0.482544\pi\) | |||||||
\(368\) | −7.17103 | −0.373816 | ||||||||
\(369\) | −2.05543 | −0.107001 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.17103 | −0.216258 | ||||||||
\(373\) | 23.2479 | 1.20373 | 0.601865 | − | 0.798598i | \(-0.294424\pi\) | ||||
0.601865 | + | 0.798598i | \(0.294424\pi\) | |||||||
\(374\) | −25.0047 | −1.29296 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.5131 | 0.593742 | ||||||||
\(377\) | 7.56852 | 0.389799 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.16629 | 0.111275 | 0.0556374 | − | 0.998451i | \(-0.482281\pi\) | ||||
0.0556374 | + | 0.998451i | \(0.482281\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0107 | 0.922717 | ||||||||
\(382\) | 10.2312 | 0.523474 | ||||||||
\(383\) | 8.05543 | 0.411613 | 0.205807 | − | 0.978593i | \(-0.434018\pi\) | ||||
0.205807 | + | 0.978593i | \(0.434018\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.6132 | −0.591098 | ||||||||
\(387\) | 2.00000 | 0.101666 | ||||||||
\(388\) | 1.27117 | 0.0645339 | ||||||||
\(389\) | 11.8891 | 0.602803 | 0.301402 | − | 0.953497i | \(-0.402545\pi\) | ||||
0.301402 | + | 0.953497i | \(0.402545\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.4791 | 1.89540 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.55780 | 0.280354 | ||||||||
\(394\) | −2.39749 | −0.120784 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.78426 | −0.240418 | ||||||||
\(397\) | 16.1109 | 0.808581 | 0.404290 | − | 0.914631i | \(-0.367519\pi\) | ||||
0.404290 | + | 0.914631i | \(0.367519\pi\) | |||||||
\(398\) | 18.3421 | 0.919404 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.9707 | 1.24698 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(402\) | −9.56852 | −0.477234 | ||||||||
\(403\) | 13.2265 | 0.658857 | ||||||||
\(404\) | −8.00000 | −0.398015 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.3081 | 1.70059 | ||||||||
\(408\) | −5.22646 | −0.258748 | ||||||||
\(409\) | 3.05543 | 0.151081 | 0.0755406 | − | 0.997143i | \(-0.475932\pi\) | ||||
0.0755406 | + | 0.997143i | \(0.475932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.7950 | −0.729782 | ||||||||
\(412\) | 11.2265 | 0.553088 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.17103 | 0.352437 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.17103 | −0.155473 | ||||||||
\(417\) | −3.65794 | −0.179130 | ||||||||
\(418\) | −15.1710 | −0.742039 | ||||||||
\(419\) | −20.1972 | −0.986698 | −0.493349 | − | 0.869831i | \(-0.664227\pi\) | ||||
−0.493349 | + | 0.869831i | \(0.664227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.3635 | −1.47983 | −0.739913 | − | 0.672702i | \(-0.765133\pi\) | ||||
−0.739913 | + | 0.672702i | \(0.765133\pi\) | |||||||
\(422\) | 2.82897 | 0.137712 | ||||||||
\(423\) | −11.5131 | −0.559786 | ||||||||
\(424\) | −8.11560 | −0.394128 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.39749 | 0.0675502 | ||||||||
\(429\) | 15.1710 | 0.732464 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.5733 | 1.18365 | 0.591826 | − | 0.806066i | \(-0.298407\pi\) | ||||
0.591826 | + | 0.806066i | \(0.298407\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −4.68412 | −0.225104 | −0.112552 | − | 0.993646i | \(-0.535903\pi\) | ||||
−0.112552 | + | 0.993646i | \(0.535903\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.4529 | 0.596387 | ||||||||
\(437\) | 22.7395 | 1.08778 | ||||||||
\(438\) | −4.00000 | −0.191127 | ||||||||
\(439\) | −30.5131 | −1.45631 | −0.728155 | − | 0.685412i | \(-0.759622\pi\) | ||||
−0.728155 | + | 0.685412i | \(0.759622\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.5733 | 0.788310 | ||||||||
\(443\) | 9.50835 | 0.451755 | 0.225878 | − | 0.974156i | \(-0.427475\pi\) | ||||
0.225878 | + | 0.974156i | \(0.427475\pi\) | |||||||
\(444\) | 7.17103 | 0.340322 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.2973 | 0.676999 | ||||||||
\(447\) | −22.3421 | −1.05674 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.6239 | 0.831726 | 0.415863 | − | 0.909427i | \(-0.363480\pi\) | ||||
0.415863 | + | 0.909427i | \(0.363480\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.83371 | 0.463051 | ||||||||
\(452\) | −6.34206 | −0.298305 | ||||||||
\(453\) | −16.5131 | −0.775853 | ||||||||
\(454\) | 11.0554 | 0.518857 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.17103 | −0.148497 | ||||||||
\(457\) | −0.386770 | −0.0180923 | −0.00904617 | − | 0.999959i | \(-0.502880\pi\) | ||||
−0.00904617 | + | 0.999959i | \(0.502880\pi\) | |||||||
\(458\) | 18.4529 | 0.862248 | ||||||||
\(459\) | 5.22646 | 0.243950 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.3682 | −1.74041 | −0.870206 | − | 0.492688i | \(-0.836014\pi\) | ||||
−0.870206 | + | 0.492688i | \(0.836014\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.3081 | −1.12969 | −0.564846 | − | 0.825196i | \(-0.691064\pi\) | ||||
−0.564846 | + | 0.825196i | \(0.691064\pi\) | |||||||
\(464\) | 2.38677 | 0.110803 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.11560 | −0.422272 | ||||||||
\(467\) | −28.5733 | −1.32221 | −0.661106 | − | 0.750292i | \(-0.729913\pi\) | ||||
−0.661106 | + | 0.750292i | \(0.729913\pi\) | |||||||
\(468\) | 3.17103 | 0.146581 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.94457 | 0.458222 | ||||||||
\(472\) | 10.7288 | 0.493834 | ||||||||
\(473\) | −9.56852 | −0.439961 | ||||||||
\(474\) | 12.1710 | 0.559034 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.11560 | 0.371588 | ||||||||
\(478\) | −13.1156 | −0.599894 | ||||||||
\(479\) | −8.56378 | −0.391289 | −0.195645 | − | 0.980675i | \(-0.562680\pi\) | ||||
−0.195645 | + | 0.980675i | \(0.562680\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.7395 | −1.03683 | ||||||||
\(482\) | 5.34206 | 0.243324 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.8891 | 0.540415 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 31.8444 | 1.44301 | 0.721504 | − | 0.692410i | \(-0.243451\pi\) | ||||
0.721504 | + | 0.692410i | \(0.243451\pi\) | |||||||
\(488\) | −7.11560 | −0.322108 | ||||||||
\(489\) | 2.88440 | 0.130437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.49763 | 0.202975 | 0.101488 | − | 0.994837i | \(-0.467640\pi\) | ||||
0.101488 | + | 0.994837i | \(0.467640\pi\) | |||||||
\(492\) | 2.05543 | 0.0926659 | ||||||||
\(493\) | −12.4744 | −0.561817 | ||||||||
\(494\) | 10.0554 | 0.452415 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.17103 | 0.187285 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.39749 | 0.152245 | ||||||||
\(499\) | −0.342060 | −0.0153127 | −0.00765634 | − | 0.999971i | \(-0.502437\pi\) | ||||
−0.00765634 | + | 0.999971i | \(0.502437\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.05543 | 0.181183 | ||||||||
\(502\) | −27.9213 | −1.24619 | ||||||||
\(503\) | 7.56852 | 0.337464 | 0.168732 | − | 0.985662i | \(-0.446033\pi\) | ||||
0.168732 | + | 0.985662i | \(0.446033\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −34.3081 | −1.52518 | ||||||||
\(507\) | 2.94457 | 0.130773 | ||||||||
\(508\) | −18.0107 | −0.799096 | ||||||||
\(509\) | 30.9600 | 1.37228 | 0.686140 | − | 0.727470i | \(-0.259304\pi\) | ||||
0.686140 | + | 0.727470i | \(0.259304\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.17103 | 0.140004 | ||||||||
\(514\) | −21.1370 | −0.932315 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.00000 | −0.0880451 | ||||||||
\(517\) | 55.0816 | 2.42249 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.39749 | 0.280819 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.85041 | 0.212500 | 0.106250 | − | 0.994339i | \(-0.466116\pi\) | ||||
0.106250 | + | 0.994339i | \(0.466116\pi\) | |||||||
\(522\) | −2.38677 | −0.104466 | ||||||||
\(523\) | −4.25264 | −0.185955 | −0.0929774 | − | 0.995668i | \(-0.529638\pi\) | ||||
−0.0929774 | + | 0.995668i | \(0.529638\pi\) | |||||||
\(524\) | −5.55780 | −0.242794 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.9106 | 0.519326 | ||||||||
\(527\) | −21.7997 | −0.949611 | ||||||||
\(528\) | 4.78426 | 0.208208 | ||||||||
\(529\) | 28.4237 | 1.23581 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.7288 | −0.465592 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.51783 | −0.282319 | ||||||||
\(534\) | 9.56852 | 0.414070 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.56852 | 0.413297 | ||||||||
\(537\) | −19.5131 | −0.842052 | ||||||||
\(538\) | 3.27117 | 0.141030 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.3635 | 1.64938 | 0.824688 | − | 0.565588i | \(-0.191351\pi\) | ||||
0.824688 | + | 0.565588i | \(0.191351\pi\) | |||||||
\(542\) | −0.623949 | −0.0268009 | ||||||||
\(543\) | 23.0262 | 0.988148 | ||||||||
\(544\) | 5.22646 | 0.224083 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.44818 | 0.0619197 | 0.0309598 | − | 0.999521i | \(-0.490144\pi\) | ||||
0.0309598 | + | 0.999521i | \(0.490144\pi\) | |||||||
\(548\) | 14.7950 | 0.632010 | ||||||||
\(549\) | 7.11560 | 0.303686 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.56852 | −0.322430 | ||||||||
\(552\) | −7.17103 | −0.305219 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −28.7950 | −1.22338 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.65794 | 0.155131 | ||||||||
\(557\) | −13.0214 | −0.551736 | −0.275868 | − | 0.961196i | \(-0.588965\pi\) | ||||
−0.275868 | + | 0.961196i | \(0.588965\pi\) | |||||||
\(558\) | −4.17103 | −0.176574 | ||||||||
\(559\) | 6.34206 | 0.268241 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.0047 | −1.05570 | ||||||||
\(562\) | −2.82897 | −0.119333 | ||||||||
\(563\) | −5.85041 | −0.246565 | −0.123283 | − | 0.992372i | \(-0.539342\pi\) | ||||
−0.123283 | + | 0.992372i | \(0.539342\pi\) | |||||||
\(564\) | 11.5131 | 0.484789 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25.1370 | −1.05659 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | −40.6501 | −1.70414 | −0.852071 | − | 0.523426i | \(-0.824654\pi\) | ||||
−0.852071 | + | 0.523426i | \(0.824654\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.22646 | −0.135023 | −0.0675116 | − | 0.997718i | \(-0.521506\pi\) | ||||
−0.0675116 | + | 0.997718i | \(0.521506\pi\) | |||||||
\(572\) | −15.1710 | −0.634333 | ||||||||
\(573\) | 10.2312 | 0.427415 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −11.6347 | −0.484358 | −0.242179 | − | 0.970232i | \(-0.577862\pi\) | ||||
−0.242179 | + | 0.970232i | \(0.577862\pi\) | |||||||
\(578\) | −10.3159 | −0.429084 | ||||||||
\(579\) | −11.6132 | −0.482629 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.27117 | 0.0526917 | ||||||||
\(583\) | −38.8271 | −1.60806 | ||||||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.2265 | 0.422451 | ||||||||
\(587\) | −28.9446 | −1.19467 | −0.597335 | − | 0.801992i | \(-0.703774\pi\) | ||||
−0.597335 | + | 0.801992i | \(0.703774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.2265 | −0.544987 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.39749 | −0.0986195 | ||||||||
\(592\) | −7.17103 | −0.294728 | ||||||||
\(593\) | 11.4577 | 0.470510 | 0.235255 | − | 0.971934i | \(-0.424408\pi\) | ||||
0.235255 | + | 0.971934i | \(0.424408\pi\) | |||||||
\(594\) | −4.78426 | −0.196301 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.3421 | 0.915166 | ||||||||
\(597\) | 18.3421 | 0.750691 | ||||||||
\(598\) | 22.7395 | 0.929889 | ||||||||
\(599\) | −3.00474 | −0.122770 | −0.0613852 | − | 0.998114i | \(-0.519552\pi\) | ||||
−0.0613852 | + | 0.998114i | \(0.519552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.0816 | 1.63496 | 0.817481 | − | 0.575955i | \(-0.195370\pi\) | ||||
0.817481 | + | 0.575955i | \(0.195370\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.56852 | −0.389660 | ||||||||
\(604\) | 16.5131 | 0.671908 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.00000 | −0.324978 | ||||||||
\(607\) | 26.1216 | 1.06024 | 0.530121 | − | 0.847922i | \(-0.322146\pi\) | ||||
0.530121 | + | 0.847922i | \(0.322146\pi\) | |||||||
\(608\) | 3.17103 | 0.128602 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.5083 | −1.47697 | ||||||||
\(612\) | −5.22646 | −0.211267 | ||||||||
\(613\) | 41.5131 | 1.67670 | 0.838349 | − | 0.545134i | \(-0.183521\pi\) | ||||
0.838349 | + | 0.545134i | \(0.183521\pi\) | |||||||
\(614\) | −23.4577 | −0.946674 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.1156 | 1.25267 | 0.626333 | − | 0.779555i | \(-0.284555\pi\) | ||||
0.626333 | + | 0.779555i | \(0.284555\pi\) | |||||||
\(618\) | 11.2265 | 0.451594 | ||||||||
\(619\) | 32.9922 | 1.32607 | 0.663034 | − | 0.748589i | \(-0.269268\pi\) | ||||
0.663034 | + | 0.748589i | \(0.269268\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.17103 | 0.287764 | ||||||||
\(622\) | 5.65794 | 0.226863 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.17103 | −0.126943 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.3868 | −0.654947 | ||||||||
\(627\) | −15.1710 | −0.605873 | ||||||||
\(628\) | −9.94457 | −0.396832 | ||||||||
\(629\) | 37.4791 | 1.49439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.6501 | 1.89692 | 0.948461 | − | 0.316894i | \(-0.102640\pi\) | ||||
0.948461 | + | 0.316894i | \(0.102640\pi\) | |||||||
\(632\) | −12.1710 | −0.484138 | ||||||||
\(633\) | 2.82897 | 0.112441 | ||||||||
\(634\) | 4.51309 | 0.179238 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.11560 | −0.321804 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11.4189 | 0.452080 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.2866 | 0.406297 | 0.203149 | − | 0.979148i | \(-0.434883\pi\) | ||||
0.203149 | + | 0.979148i | \(0.434883\pi\) | |||||||
\(642\) | 1.39749 | 0.0551545 | ||||||||
\(643\) | 38.9368 | 1.53552 | 0.767758 | − | 0.640740i | \(-0.221372\pi\) | ||||
0.767758 | + | 0.640740i | \(0.221372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.5733 | −0.652066 | ||||||||
\(647\) | 33.8551 | 1.33098 | 0.665492 | − | 0.746405i | \(-0.268222\pi\) | ||||
0.665492 | + | 0.746405i | \(0.268222\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 51.3295 | 2.01486 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.88440 | −0.112962 | ||||||||
\(653\) | −5.36350 | −0.209890 | −0.104945 | − | 0.994478i | \(-0.533467\pi\) | ||||
−0.104945 | + | 0.994478i | \(0.533467\pi\) | |||||||
\(654\) | 12.4529 | 0.486948 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.05543 | −0.0802511 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.2265 | 0.904774 | 0.452387 | − | 0.891822i | \(-0.350573\pi\) | ||||
0.452387 | + | 0.891822i | \(0.350573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.5947 | −1.42337 | −0.711684 | − | 0.702499i | \(-0.752067\pi\) | ||||
−0.711684 | + | 0.702499i | \(0.752067\pi\) | |||||||
\(662\) | 13.0816 | 0.508431 | ||||||||
\(663\) | 16.5733 | 0.643652 | ||||||||
\(664\) | −3.39749 | −0.131848 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.17103 | 0.277872 | ||||||||
\(667\) | −17.1156 | −0.662719 | ||||||||
\(668\) | −4.05543 | −0.156909 | ||||||||
\(669\) | 14.2973 | 0.552767 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.0429 | −1.31421 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.7336 | 0.683579 | 0.341789 | − | 0.939777i | \(-0.388967\pi\) | ||||
0.341789 | + | 0.939777i | \(0.388967\pi\) | |||||||
\(674\) | 20.2973 | 0.781825 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.94457 | −0.113253 | ||||||||
\(677\) | −26.2265 | −1.00796 | −0.503982 | − | 0.863714i | \(-0.668132\pi\) | ||||
−0.503982 | + | 0.863714i | \(0.668132\pi\) | |||||||
\(678\) | −6.34206 | −0.243565 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0554 | 0.423645 | ||||||||
\(682\) | 19.9553 | 0.764128 | ||||||||
\(683\) | 49.2186 | 1.88330 | 0.941650 | − | 0.336595i | \(-0.109275\pi\) | ||||
0.941650 | + | 0.336595i | \(0.109275\pi\) | |||||||
\(684\) | −3.17103 | −0.121247 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.4529 | 0.704023 | ||||||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | 25.7348 | 0.980418 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.90584 | 0.338794 | 0.169397 | − | 0.985548i | \(-0.445818\pi\) | ||||
0.169397 | + | 0.985548i | \(0.445818\pi\) | |||||||
\(692\) | −6.39749 | −0.243196 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.4529 | 0.548625 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.38677 | 0.0904703 | ||||||||
\(697\) | 10.7426 | 0.406906 | ||||||||
\(698\) | −13.8891 | −0.525712 | ||||||||
\(699\) | −9.11560 | −0.344784 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.9553 | 0.451545 | 0.225773 | − | 0.974180i | \(-0.427509\pi\) | ||||
0.225773 | + | 0.974180i | \(0.427509\pi\) | |||||||
\(702\) | 3.17103 | 0.119683 | ||||||||
\(703\) | 22.7395 | 0.857638 | ||||||||
\(704\) | −4.78426 | −0.180314 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.45292 | −0.242859 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.7288 | 0.403214 | ||||||||
\(709\) | 52.1632 | 1.95903 | 0.979515 | − | 0.201369i | \(-0.0645392\pi\) | ||||
0.979515 | + | 0.201369i | \(0.0645392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.1710 | 0.456449 | ||||||||
\(712\) | −9.56852 | −0.358595 | ||||||||
\(713\) | −29.9106 | −1.12016 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.5131 | 0.729238 | ||||||||
\(717\) | −13.1156 | −0.489811 | ||||||||
\(718\) | −7.22646 | −0.269689 | ||||||||
\(719\) | 25.7902 | 0.961814 | 0.480907 | − | 0.876772i | \(-0.340308\pi\) | ||||
0.480907 | + | 0.876772i | \(0.340308\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.94457 | 0.332882 | ||||||||
\(723\) | 5.34206 | 0.198673 | ||||||||
\(724\) | −23.0262 | −0.855761 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.8891 | 0.441247 | ||||||||
\(727\) | −34.6054 | −1.28344 | −0.641722 | − | 0.766937i | \(-0.721780\pi\) | ||||
−0.641722 | + | 0.766937i | \(0.721780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.4529 | −0.386615 | ||||||||
\(732\) | −7.11560 | −0.263000 | ||||||||
\(733\) | 30.9707 | 1.14393 | 0.571965 | − | 0.820278i | \(-0.306181\pi\) | ||||
0.571965 | + | 0.820278i | \(0.306181\pi\) | |||||||
\(734\) | −2.10014 | −0.0775176 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.17103 | 0.264328 | ||||||||
\(737\) | 45.7783 | 1.68626 | ||||||||
\(738\) | 2.05543 | 0.0756614 | ||||||||
\(739\) | −2.17577 | −0.0800370 | −0.0400185 | − | 0.999199i | \(-0.512742\pi\) | ||||
−0.0400185 | + | 0.999199i | \(0.512742\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.0554 | 0.369395 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.9446 | 1.17193 | 0.585966 | − | 0.810335i | \(-0.300715\pi\) | ||||
0.585966 | + | 0.810335i | \(0.300715\pi\) | |||||||
\(744\) | 4.17103 | 0.152917 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.2479 | −0.851166 | ||||||||
\(747\) | 3.39749 | 0.124308 | ||||||||
\(748\) | 25.0047 | 0.914264 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.60725 | −0.204611 | −0.102306 | − | 0.994753i | \(-0.532622\pi\) | ||||
−0.102306 | + | 0.994753i | \(0.532622\pi\) | |||||||
\(752\) | −11.5131 | −0.419839 | ||||||||
\(753\) | −27.9213 | −1.01751 | ||||||||
\(754\) | −7.56852 | −0.275629 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.2312 | 0.880698 | 0.440349 | − | 0.897827i | \(-0.354855\pi\) | ||||
0.440349 | + | 0.897827i | \(0.354855\pi\) | |||||||
\(758\) | −2.16629 | −0.0786832 | ||||||||
\(759\) | −34.3081 | −1.24530 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.8551 | 1.44475 | 0.722374 | − | 0.691503i | \(-0.243051\pi\) | ||||
0.722374 | + | 0.691503i | \(0.243051\pi\) | |||||||
\(762\) | −18.0107 | −0.652460 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.2312 | −0.370152 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.05543 | −0.291055 | ||||||||
\(767\) | −34.0214 | −1.22844 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 29.7950 | 1.07443 | 0.537217 | − | 0.843444i | \(-0.319476\pi\) | ||||
0.537217 | + | 0.843444i | \(0.319476\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.1370 | −0.761232 | ||||||||
\(772\) | 11.6132 | 0.417969 | ||||||||
\(773\) | −0.166290 | −0.00598102 | −0.00299051 | − | 0.999996i | \(-0.500952\pi\) | ||||
−0.00299051 | + | 0.999996i | \(0.500952\pi\) | |||||||
\(774\) | −2.00000 | −0.0718885 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.27117 | −0.0456324 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.8891 | −0.426246 | ||||||||
\(779\) | 6.51783 | 0.233525 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.7056 | −1.02717 | ||||||||
\(782\) | −37.4791 | −1.34025 | ||||||||
\(783\) | −2.38677 | −0.0852962 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.55780 | −0.198240 | ||||||||
\(787\) | 28.4529 | 1.01424 | 0.507119 | − | 0.861876i | \(-0.330711\pi\) | ||||
0.507119 | + | 0.861876i | \(0.330711\pi\) | |||||||
\(788\) | 2.39749 | 0.0854070 | ||||||||
\(789\) | 11.9106 | 0.424028 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.78426 | 0.170001 | ||||||||
\(793\) | 22.5638 | 0.801263 | ||||||||
\(794\) | −16.1109 | −0.571753 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.3421 | −0.650117 | ||||||||
\(797\) | −36.6334 | −1.29762 | −0.648811 | − | 0.760949i | \(-0.724734\pi\) | ||||
−0.648811 | + | 0.760949i | \(0.724734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.1727 | 2.12876 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.56852 | 0.338087 | ||||||||
\(802\) | −24.9707 | −0.881748 | ||||||||
\(803\) | 19.1370 | 0.675331 | ||||||||
\(804\) | 9.56852 | 0.337456 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.2265 | −0.465882 | ||||||||
\(807\) | 3.27117 | 0.115151 | ||||||||
\(808\) | 8.00000 | 0.281439 | ||||||||
\(809\) | −20.2866 | −0.713240 | −0.356620 | − | 0.934250i | \(-0.616071\pi\) | ||||
−0.356620 | + | 0.934250i | \(0.616071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.38079 | 0.0484861 | 0.0242431 | − | 0.999706i | \(-0.492282\pi\) | ||||
0.0242431 | + | 0.999706i | \(0.492282\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.623949 | −0.0218829 | ||||||||
\(814\) | −34.3081 | −1.20250 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.22646 | 0.182963 | ||||||||
\(817\) | −6.34206 | −0.221881 | ||||||||
\(818\) | −3.05543 | −0.106831 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.4129 | −0.607716 | −0.303858 | − | 0.952717i | \(-0.598275\pi\) | ||||
−0.303858 | + | 0.952717i | \(0.598275\pi\) | |||||||
\(822\) | 14.7950 | 0.516034 | ||||||||
\(823\) | −20.5947 | −0.717886 | −0.358943 | − | 0.933359i | \(-0.616863\pi\) | ||||
−0.358943 | + | 0.933359i | \(0.616863\pi\) | |||||||
\(824\) | −11.2265 | −0.391092 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.8504 | −0.481626 | −0.240813 | − | 0.970572i | \(-0.577414\pi\) | ||||
−0.240813 | + | 0.970572i | \(0.577414\pi\) | |||||||
\(828\) | −7.17103 | −0.249211 | ||||||||
\(829\) | −1.22646 | −0.0425967 | −0.0212984 | − | 0.999773i | \(-0.506780\pi\) | ||||
−0.0212984 | + | 0.999773i | \(0.506780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.7950 | −0.998887 | ||||||||
\(832\) | 3.17103 | 0.109936 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.65794 | 0.126664 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 15.1710 | 0.524701 | ||||||||
\(837\) | −4.17103 | −0.144172 | ||||||||
\(838\) | 20.1972 | 0.697701 | ||||||||
\(839\) | 29.9106 | 1.03263 | 0.516314 | − | 0.856399i | \(-0.327304\pi\) | ||||
0.516314 | + | 0.856399i | \(0.327304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.3033 | −0.803563 | ||||||||
\(842\) | 30.3635 | 1.04640 | ||||||||
\(843\) | −2.82897 | −0.0974349 | ||||||||
\(844\) | −2.82897 | −0.0973772 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.5131 | 0.395828 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.11560 | 0.278691 | ||||||||
\(849\) | −25.1370 | −0.862701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.4237 | 1.76278 | ||||||||
\(852\) | −6.00000 | −0.205557 | ||||||||
\(853\) | 10.7181 | 0.366981 | 0.183491 | − | 0.983021i | \(-0.441260\pi\) | ||||
0.183491 | + | 0.983021i | \(0.441260\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.39749 | −0.0477652 | ||||||||
\(857\) | −39.6889 | −1.35575 | −0.677873 | − | 0.735179i | \(-0.737098\pi\) | ||||
−0.677873 | + | 0.735179i | \(0.737098\pi\) | |||||||
\(858\) | −15.1710 | −0.517930 | ||||||||
\(859\) | 11.0047 | 0.375477 | 0.187738 | − | 0.982219i | \(-0.439884\pi\) | ||||
0.187738 | + | 0.982219i | \(0.439884\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.5733 | −0.836969 | ||||||||
\(863\) | −8.62869 | −0.293724 | −0.146862 | − | 0.989157i | \(-0.546917\pi\) | ||||
−0.146862 | + | 0.989157i | \(0.546917\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.68412 | 0.159173 | ||||||||
\(867\) | −10.3159 | −0.350346 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −58.2294 | −1.97530 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.3421 | −1.02810 | ||||||||
\(872\) | −12.4529 | −0.421709 | ||||||||
\(873\) | 1.27117 | 0.0430226 | ||||||||
\(874\) | −22.7395 | −0.769177 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000 | 0.135147 | ||||||||
\(877\) | 38.7395 | 1.30814 | 0.654071 | − | 0.756433i | \(-0.273060\pi\) | ||||
0.654071 | + | 0.756433i | \(0.273060\pi\) | |||||||
\(878\) | 30.5131 | 1.02977 | ||||||||
\(879\) | 10.2265 | 0.344930 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.03399 | −0.203290 | −0.101645 | − | 0.994821i | \(-0.532411\pi\) | ||||
−0.101645 | + | 0.994821i | \(0.532411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.77828 | −0.261760 | −0.130880 | − | 0.991398i | \(-0.541780\pi\) | ||||
−0.130880 | + | 0.991398i | \(0.541780\pi\) | |||||||
\(884\) | −16.5733 | −0.557419 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.50835 | −0.319439 | ||||||||
\(887\) | 24.8939 | 0.835855 | 0.417927 | − | 0.908480i | \(-0.362757\pi\) | ||||
0.417927 | + | 0.908480i | \(0.362757\pi\) | |||||||
\(888\) | −7.17103 | −0.240644 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.78426 | −0.160279 | ||||||||
\(892\) | −14.2973 | −0.478711 | ||||||||
\(893\) | 36.5083 | 1.22171 | ||||||||
\(894\) | 22.3421 | 0.747230 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.7395 | 0.759251 | ||||||||
\(898\) | −17.6239 | −0.588119 | ||||||||
\(899\) | 9.95529 | 0.332027 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.4159 | −1.41308 | ||||||||
\(902\) | −9.83371 | −0.327427 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.34206 | 0.210934 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 16.5131 | 0.548611 | ||||||||
\(907\) | 46.7056 | 1.55083 | 0.775416 | − | 0.631450i | \(-0.217540\pi\) | ||||
0.775416 | + | 0.631450i | \(0.217540\pi\) | |||||||
\(908\) | −11.0554 | −0.366887 | ||||||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 3.17103 | 0.105003 | ||||||||
\(913\) | −16.2545 | −0.537944 | ||||||||
\(914\) | 0.386770 | 0.0127932 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.4529 | −0.609702 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.22646 | −0.172499 | ||||||||
\(919\) | −34.2312 | −1.12918 | −0.564592 | − | 0.825370i | \(-0.690966\pi\) | ||||
−0.564592 | + | 0.825370i | \(0.690966\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.4577 | −0.772956 | ||||||||
\(922\) | 37.3682 | 1.23066 | ||||||||
\(923\) | 19.0262 | 0.626254 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24.3081 | 0.798813 | ||||||||
\(927\) | 11.2265 | 0.368725 | ||||||||
\(928\) | −2.38677 | −0.0783496 | ||||||||
\(929\) | −27.6549 | −0.907327 | −0.453663 | − | 0.891173i | \(-0.649883\pi\) | ||||
−0.453663 | + | 0.891173i | \(0.649883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.11560 | 0.298591 | ||||||||
\(933\) | 5.65794 | 0.185233 | ||||||||
\(934\) | 28.5733 | 0.934946 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.17103 | −0.103648 | ||||||||
\(937\) | 38.8397 | 1.26884 | 0.634419 | − | 0.772990i | \(-0.281240\pi\) | ||||
0.634419 | + | 0.772990i | \(0.281240\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.3868 | −0.534762 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.7550 | −0.643995 | −0.321997 | − | 0.946741i | \(-0.604354\pi\) | ||||
−0.321997 | + | 0.946741i | \(0.604354\pi\) | |||||||
\(942\) | −9.94457 | −0.324012 | ||||||||
\(943\) | 14.7395 | 0.479986 | ||||||||
\(944\) | −10.7288 | −0.349194 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.56852 | 0.311099 | ||||||||
\(947\) | 38.0524 | 1.23654 | 0.618268 | − | 0.785968i | \(-0.287835\pi\) | ||||
0.618268 | + | 0.785968i | \(0.287835\pi\) | |||||||
\(948\) | −12.1710 | −0.395297 | ||||||||
\(949\) | −12.6841 | −0.411744 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.51309 | 0.146347 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.5947 | −1.70371 | −0.851855 | − | 0.523778i | \(-0.824522\pi\) | ||||
−0.851855 | + | 0.523778i | \(0.824522\pi\) | |||||||
\(954\) | −8.11560 | −0.262752 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.1156 | 0.424189 | ||||||||
\(957\) | 11.4189 | 0.369122 | ||||||||
\(958\) | 8.56378 | 0.276683 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.6025 | −0.438791 | ||||||||
\(962\) | 22.7395 | 0.733152 | ||||||||
\(963\) | 1.39749 | 0.0450335 | ||||||||
\(964\) | −5.34206 | −0.172056 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.61797 | 0.148504 | 0.0742520 | − | 0.997240i | \(-0.476343\pi\) | ||||
0.0742520 | + | 0.997240i | \(0.476343\pi\) | |||||||
\(968\) | −11.8891 | −0.382131 | ||||||||
\(969\) | −16.5733 | −0.532410 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.9046 | 1.24851 | 0.624254 | − | 0.781221i | \(-0.285403\pi\) | ||||
0.624254 | + | 0.781221i | \(0.285403\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31.8444 | −1.02036 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.11560 | 0.227765 | ||||||||
\(977\) | 16.0214 | 0.512571 | 0.256286 | − | 0.966601i | \(-0.417501\pi\) | ||||
0.256286 | + | 0.966601i | \(0.417501\pi\) | |||||||
\(978\) | −2.88440 | −0.0922329 | ||||||||
\(979\) | −45.7783 | −1.46308 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.4529 | 0.397591 | ||||||||
\(982\) | −4.49763 | −0.143525 | ||||||||
\(983\) | 2.05543 | 0.0655580 | 0.0327790 | − | 0.999463i | \(-0.489564\pi\) | ||||
0.0327790 | + | 0.999463i | \(0.489564\pi\) | |||||||
\(984\) | −2.05543 | −0.0655247 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12.4744 | 0.397264 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.0554 | −0.319906 | ||||||||
\(989\) | −14.3421 | −0.456051 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.1972 | −0.863948 | −0.431974 | − | 0.901886i | \(-0.642183\pi\) | ||||
−0.431974 | + | 0.901886i | \(0.642183\pi\) | |||||||
\(992\) | −4.17103 | −0.132430 | ||||||||
\(993\) | 13.0816 | 0.415132 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.39749 | −0.107654 | ||||||||
\(997\) | 18.4744 | 0.585089 | 0.292544 | − | 0.956252i | \(-0.405498\pi\) | ||||
0.292544 | + | 0.956252i | \(0.405498\pi\) | |||||||
\(998\) | 0.342060 | 0.0108277 | ||||||||
\(999\) | 7.17103 | 0.226881 |
(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 | 7350.2.a.dn.1.1 | 3 | ||
5.2 | odd | 4 | 1470.2.g.i.589.2 | 6 | |||
5.3 | odd | 4 | 1470.2.g.i.589.5 | 6 | |||
5.4 | even | 2 | 7350.2.a.dq.1.1 | 3 | |||
7.2 | even | 3 | 1050.2.i.v.151.2 | 6 | |||
7.4 | even | 3 | 1050.2.i.v.751.2 | 6 | |||
7.6 | odd | 2 | 7350.2.a.do.1.1 | 3 | |||
35.2 | odd | 12 | 210.2.n.b.109.3 | yes | 12 | ||
35.3 | even | 12 | 1470.2.n.j.79.1 | 12 | |||
35.4 | even | 6 | 1050.2.i.u.751.2 | 6 | |||
35.9 | even | 6 | 1050.2.i.u.151.2 | 6 | |||
35.12 | even | 12 | 1470.2.n.j.949.1 | 12 | |||
35.13 | even | 4 | 1470.2.g.h.589.5 | 6 | |||
35.17 | even | 12 | 1470.2.n.j.79.6 | 12 | |||
35.18 | odd | 12 | 210.2.n.b.79.3 | ✓ | 12 | ||
35.23 | odd | 12 | 210.2.n.b.109.4 | yes | 12 | ||
35.27 | even | 4 | 1470.2.g.h.589.2 | 6 | |||
35.32 | odd | 12 | 210.2.n.b.79.4 | yes | 12 | ||
35.33 | even | 12 | 1470.2.n.j.949.6 | 12 | |||
35.34 | odd | 2 | 7350.2.a.dp.1.1 | 3 | |||
105.2 | even | 12 | 630.2.u.f.109.4 | 12 | |||
105.23 | even | 12 | 630.2.u.f.109.3 | 12 | |||
105.32 | even | 12 | 630.2.u.f.289.3 | 12 | |||
105.53 | even | 12 | 630.2.u.f.289.4 | 12 | |||
140.23 | even | 12 | 1680.2.di.c.529.1 | 12 | |||
140.67 | even | 12 | 1680.2.di.c.289.1 | 12 | |||
140.107 | even | 12 | 1680.2.di.c.529.6 | 12 | |||
140.123 | even | 12 | 1680.2.di.c.289.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.n.b.79.3 | ✓ | 12 | 35.18 | odd | 12 | ||
210.2.n.b.79.4 | yes | 12 | 35.32 | odd | 12 | ||
210.2.n.b.109.3 | yes | 12 | 35.2 | odd | 12 | ||
210.2.n.b.109.4 | yes | 12 | 35.23 | odd | 12 | ||
630.2.u.f.109.3 | 12 | 105.23 | even | 12 | |||
630.2.u.f.109.4 | 12 | 105.2 | even | 12 | |||
630.2.u.f.289.3 | 12 | 105.32 | even | 12 | |||
630.2.u.f.289.4 | 12 | 105.53 | even | 12 | |||
1050.2.i.u.151.2 | 6 | 35.9 | even | 6 | |||
1050.2.i.u.751.2 | 6 | 35.4 | even | 6 | |||
1050.2.i.v.151.2 | 6 | 7.2 | even | 3 | |||
1050.2.i.v.751.2 | 6 | 7.4 | even | 3 | |||
1470.2.g.h.589.2 | 6 | 35.27 | even | 4 | |||
1470.2.g.h.589.5 | 6 | 35.13 | even | 4 | |||
1470.2.g.i.589.2 | 6 | 5.2 | odd | 4 | |||
1470.2.g.i.589.5 | 6 | 5.3 | odd | 4 | |||
1470.2.n.j.79.1 | 12 | 35.3 | even | 12 | |||
1470.2.n.j.79.6 | 12 | 35.17 | even | 12 | |||
1470.2.n.j.949.1 | 12 | 35.12 | even | 12 | |||
1470.2.n.j.949.6 | 12 | 35.33 | even | 12 | |||
1680.2.di.c.289.1 | 12 | 140.67 | even | 12 | |||
1680.2.di.c.289.6 | 12 | 140.123 | even | 12 | |||
1680.2.di.c.529.1 | 12 | 140.23 | even | 12 | |||
1680.2.di.c.529.6 | 12 | 140.107 | even | 12 | |||
7350.2.a.dn.1.1 | 3 | 1.1 | even | 1 | trivial | ||
7350.2.a.do.1.1 | 3 | 7.6 | odd | 2 | |||
7350.2.a.dp.1.1 | 3 | 35.34 | odd | 2 | |||
7350.2.a.dq.1.1 | 3 | 5.4 | even | 2 |