Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4650,2,Mod(1,4650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4650, 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("4650.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4650.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: | \(37.1304369399\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 186) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4650.1 |
$q$-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 | ||||||||
\(7\) | −5.12311 | −1.93635 | −0.968176 | − | 0.250270i | \(-0.919480\pi\) | ||||
−0.968176 | + | 0.250270i | \(0.919480\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56155 | −0.772337 | −0.386169 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386169 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0.561553 | 0.155747 | 0.0778734 | − | 0.996963i | \(-0.475187\pi\) | ||||
0.0778734 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(14\) | 5.12311 | 1.36921 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.68466 | −1.37873 | −0.689366 | − | 0.724413i | \(-0.742111\pi\) | ||||
−0.689366 | + | 0.724413i | \(0.742111\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.56155 | −0.587661 | −0.293830 | − | 0.955858i | \(-0.594930\pi\) | ||||
−0.293830 | + | 0.955858i | \(0.594930\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.12311 | −1.11795 | ||||||||
\(22\) | 2.56155 | 0.546125 | ||||||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.561553 | −0.110130 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −5.12311 | −0.968176 | ||||||||
\(29\) | −7.12311 | −1.32273 | −0.661364 | − | 0.750065i | \(-0.730022\pi\) | ||||
−0.661364 | + | 0.750065i | \(0.730022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.56155 | −0.445909 | ||||||||
\(34\) | 5.68466 | 0.974911 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.24621 | −1.35567 | −0.677834 | − | 0.735215i | \(-0.737081\pi\) | ||||
−0.677834 | + | 0.735215i | \(0.737081\pi\) | |||||||
\(38\) | 2.56155 | 0.415539 | ||||||||
\(39\) | 0.561553 | 0.0899204 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24621 | 0.663147 | 0.331573 | − | 0.943429i | \(-0.392421\pi\) | ||||
0.331573 | + | 0.943429i | \(0.392421\pi\) | |||||||
\(42\) | 5.12311 | 0.790512 | ||||||||
\(43\) | 9.12311 | 1.39126 | 0.695630 | − | 0.718400i | \(-0.255125\pi\) | ||||
0.695630 | + | 0.718400i | \(0.255125\pi\) | |||||||
\(44\) | −2.56155 | −0.386169 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.00000 | −1.17954 | ||||||||
\(47\) | 3.68466 | 0.537463 | 0.268731 | − | 0.963215i | \(-0.413396\pi\) | ||||
0.268731 | + | 0.963215i | \(0.413396\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 19.2462 | 2.74946 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.68466 | −0.796011 | ||||||||
\(52\) | 0.561553 | 0.0778734 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.12311 | 0.684604 | ||||||||
\(57\) | −2.56155 | −0.339286 | ||||||||
\(58\) | 7.12311 | 0.935310 | ||||||||
\(59\) | −1.12311 | −0.146216 | −0.0731079 | − | 0.997324i | \(-0.523292\pi\) | ||||
−0.0731079 | + | 0.997324i | \(0.523292\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.561553 | −0.0718995 | −0.0359497 | − | 0.999354i | \(-0.511446\pi\) | ||||
−0.0359497 | + | 0.999354i | \(0.511446\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | −5.12311 | −0.645451 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.56155 | 0.315305 | ||||||||
\(67\) | −0.315342 | −0.0385251 | −0.0192626 | − | 0.999814i | \(-0.506132\pi\) | ||||
−0.0192626 | + | 0.999814i | \(0.506132\pi\) | |||||||
\(68\) | −5.68466 | −0.689366 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.43845 | −0.170712 | −0.0853561 | − | 0.996351i | \(-0.527203\pi\) | ||||
−0.0853561 | + | 0.996351i | \(0.527203\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 8.24621 | 0.958603 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.56155 | −0.293830 | ||||||||
\(77\) | 13.1231 | 1.49552 | ||||||||
\(78\) | −0.561553 | −0.0635833 | ||||||||
\(79\) | −3.68466 | −0.414556 | −0.207278 | − | 0.978282i | \(-0.566461\pi\) | ||||
−0.207278 | + | 0.978282i | \(0.566461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.24621 | −0.468916 | ||||||||
\(83\) | −12.8078 | −1.40583 | −0.702917 | − | 0.711272i | \(-0.748120\pi\) | ||||
−0.702917 | + | 0.711272i | \(0.748120\pi\) | |||||||
\(84\) | −5.12311 | −0.558977 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.12311 | −0.983770 | ||||||||
\(87\) | −7.12311 | −0.763677 | ||||||||
\(88\) | 2.56155 | 0.273062 | ||||||||
\(89\) | −0.246211 | −0.0260983 | −0.0130492 | − | 0.999915i | \(-0.504154\pi\) | ||||
−0.0130492 | + | 0.999915i | \(0.504154\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.87689 | −0.301580 | ||||||||
\(92\) | 8.00000 | 0.834058 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | −3.68466 | −0.380043 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 14.8078 | 1.50350 | 0.751750 | − | 0.659448i | \(-0.229210\pi\) | ||||
0.751750 | + | 0.659448i | \(0.229210\pi\) | |||||||
\(98\) | −19.2462 | −1.94416 | ||||||||
\(99\) | −2.56155 | −0.257446 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.2462 | 1.61656 | 0.808279 | − | 0.588799i | \(-0.200399\pi\) | ||||
0.808279 | + | 0.588799i | \(0.200399\pi\) | |||||||
\(102\) | 5.68466 | 0.562865 | ||||||||
\(103\) | 5.12311 | 0.504795 | 0.252397 | − | 0.967624i | \(-0.418781\pi\) | ||||
0.252397 | + | 0.967624i | \(0.418781\pi\) | |||||||
\(104\) | −0.561553 | −0.0550648 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.24621 | −0.782696 | ||||||||
\(112\) | −5.12311 | −0.484088 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 2.56155 | 0.239911 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.12311 | −0.661364 | ||||||||
\(117\) | 0.561553 | 0.0519156 | ||||||||
\(118\) | 1.12311 | 0.103390 | ||||||||
\(119\) | 29.1231 | 2.66971 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 0.561553 | 0.0508406 | ||||||||
\(123\) | 4.24621 | 0.382868 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.12311 | 0.456403 | ||||||||
\(127\) | −10.2462 | −0.909204 | −0.454602 | − | 0.890695i | \(-0.650219\pi\) | ||||
−0.454602 | + | 0.890695i | \(0.650219\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 9.12311 | 0.803245 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.1231 | 1.49605 | 0.748026 | − | 0.663669i | \(-0.231002\pi\) | ||||
0.748026 | + | 0.663669i | \(0.231002\pi\) | |||||||
\(132\) | −2.56155 | −0.222955 | ||||||||
\(133\) | 13.1231 | 1.13792 | ||||||||
\(134\) | 0.315342 | 0.0272414 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.68466 | 0.487455 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | −8.00000 | −0.681005 | ||||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.68466 | 0.310304 | ||||||||
\(142\) | 1.43845 | 0.120712 | ||||||||
\(143\) | −1.43845 | −0.120289 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 19.2462 | 1.58740 | ||||||||
\(148\) | −8.24621 | −0.677834 | ||||||||
\(149\) | 9.68466 | 0.793398 | 0.396699 | − | 0.917949i | \(-0.370156\pi\) | ||||
0.396699 | + | 0.917949i | \(0.370156\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.93087 | 0.482647 | 0.241324 | − | 0.970445i | \(-0.422418\pi\) | ||||
0.241324 | + | 0.970445i | \(0.422418\pi\) | |||||||
\(152\) | 2.56155 | 0.207769 | ||||||||
\(153\) | −5.68466 | −0.459577 | ||||||||
\(154\) | −13.1231 | −1.05749 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.561553 | 0.0449602 | ||||||||
\(157\) | 9.36932 | 0.747753 | 0.373876 | − | 0.927479i | \(-0.378028\pi\) | ||||
0.373876 | + | 0.927479i | \(0.378028\pi\) | |||||||
\(158\) | 3.68466 | 0.293136 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −40.9848 | −3.23006 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 23.0540 | 1.80573 | 0.902863 | − | 0.429928i | \(-0.141461\pi\) | ||||
0.902863 | + | 0.429928i | \(0.141461\pi\) | |||||||
\(164\) | 4.24621 | 0.331573 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.8078 | 0.994075 | ||||||||
\(167\) | 5.12311 | 0.396438 | 0.198219 | − | 0.980158i | \(-0.436484\pi\) | ||||
0.198219 | + | 0.980158i | \(0.436484\pi\) | |||||||
\(168\) | 5.12311 | 0.395256 | ||||||||
\(169\) | −12.6847 | −0.975743 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.56155 | −0.195887 | ||||||||
\(172\) | 9.12311 | 0.695630 | ||||||||
\(173\) | −4.56155 | −0.346808 | −0.173404 | − | 0.984851i | \(-0.555477\pi\) | ||||
−0.173404 | + | 0.984851i | \(0.555477\pi\) | |||||||
\(174\) | 7.12311 | 0.540001 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.56155 | −0.193084 | ||||||||
\(177\) | −1.12311 | −0.0844178 | ||||||||
\(178\) | 0.246211 | 0.0184543 | ||||||||
\(179\) | 23.0540 | 1.72314 | 0.861568 | − | 0.507643i | \(-0.169483\pi\) | ||||
0.861568 | + | 0.507643i | \(0.169483\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2462 | −0.910254 | −0.455127 | − | 0.890427i | \(-0.650406\pi\) | ||||
−0.455127 | + | 0.890427i | \(0.650406\pi\) | |||||||
\(182\) | 2.87689 | 0.213250 | ||||||||
\(183\) | −0.561553 | −0.0415112 | ||||||||
\(184\) | −8.00000 | −0.589768 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.00000 | 0.0733236 | ||||||||
\(187\) | 14.5616 | 1.06485 | ||||||||
\(188\) | 3.68466 | 0.268731 | ||||||||
\(189\) | −5.12311 | −0.372651 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0000 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −24.5616 | −1.76798 | −0.883990 | − | 0.467507i | \(-0.845152\pi\) | ||||
−0.883990 | + | 0.467507i | \(0.845152\pi\) | |||||||
\(194\) | −14.8078 | −1.06314 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.2462 | 1.37473 | ||||||||
\(197\) | −8.24621 | −0.587518 | −0.293759 | − | 0.955879i | \(-0.594906\pi\) | ||||
−0.293759 | + | 0.955879i | \(0.594906\pi\) | |||||||
\(198\) | 2.56155 | 0.182042 | ||||||||
\(199\) | 4.31534 | 0.305906 | 0.152953 | − | 0.988233i | \(-0.451122\pi\) | ||||
0.152953 | + | 0.988233i | \(0.451122\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.315342 | −0.0222425 | ||||||||
\(202\) | −16.2462 | −1.14308 | ||||||||
\(203\) | 36.4924 | 2.56127 | ||||||||
\(204\) | −5.68466 | −0.398006 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.12311 | −0.356944 | ||||||||
\(207\) | 8.00000 | 0.556038 | ||||||||
\(208\) | 0.561553 | 0.0389367 | ||||||||
\(209\) | 6.56155 | 0.453872 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.75379 | −0.120736 | −0.0603679 | − | 0.998176i | \(-0.519227\pi\) | ||||
−0.0603679 | + | 0.998176i | \(0.519227\pi\) | |||||||
\(212\) | 2.00000 | 0.137361 | ||||||||
\(213\) | −1.43845 | −0.0985608 | ||||||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.12311 | 0.347779 | ||||||||
\(218\) | −14.0000 | −0.948200 | ||||||||
\(219\) | −10.0000 | −0.675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.19224 | −0.214733 | ||||||||
\(222\) | 8.24621 | 0.553449 | ||||||||
\(223\) | −19.6847 | −1.31818 | −0.659091 | − | 0.752063i | \(-0.729059\pi\) | ||||
−0.659091 | + | 0.752063i | \(0.729059\pi\) | |||||||
\(224\) | 5.12311 | 0.342302 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | 19.3693 | 1.28559 | 0.642793 | − | 0.766040i | \(-0.277775\pi\) | ||||
0.642793 | + | 0.766040i | \(0.277775\pi\) | |||||||
\(228\) | −2.56155 | −0.169643 | ||||||||
\(229\) | 17.6847 | 1.16864 | 0.584318 | − | 0.811525i | \(-0.301362\pi\) | ||||
0.584318 | + | 0.811525i | \(0.301362\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.1231 | 0.863437 | ||||||||
\(232\) | 7.12311 | 0.467655 | ||||||||
\(233\) | −11.6155 | −0.760959 | −0.380479 | − | 0.924789i | \(-0.624241\pi\) | ||||
−0.380479 | + | 0.924789i | \(0.624241\pi\) | |||||||
\(234\) | −0.561553 | −0.0367099 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.12311 | −0.0731079 | ||||||||
\(237\) | −3.68466 | −0.239344 | ||||||||
\(238\) | −29.1231 | −1.88777 | ||||||||
\(239\) | −20.4924 | −1.32554 | −0.662772 | − | 0.748821i | \(-0.730620\pi\) | ||||
−0.662772 | + | 0.748821i | \(0.730620\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.75379 | 0.499465 | 0.249733 | − | 0.968315i | \(-0.419657\pi\) | ||||
0.249733 | + | 0.968315i | \(0.419657\pi\) | |||||||
\(242\) | 4.43845 | 0.285314 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.561553 | −0.0359497 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.24621 | −0.270729 | ||||||||
\(247\) | −1.43845 | −0.0915262 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | −12.8078 | −0.811659 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.0000 | 1.26239 | 0.631194 | − | 0.775625i | \(-0.282565\pi\) | ||||
0.631194 | + | 0.775625i | \(0.282565\pi\) | |||||||
\(252\) | −5.12311 | −0.322725 | ||||||||
\(253\) | −20.4924 | −1.28835 | ||||||||
\(254\) | 10.2462 | 0.642904 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.8769 | 1.05275 | 0.526376 | − | 0.850252i | \(-0.323550\pi\) | ||||
0.526376 | + | 0.850252i | \(0.323550\pi\) | |||||||
\(258\) | −9.12311 | −0.567980 | ||||||||
\(259\) | 42.2462 | 2.62505 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.12311 | −0.440909 | ||||||||
\(262\) | −17.1231 | −1.05787 | ||||||||
\(263\) | 2.24621 | 0.138507 | 0.0692537 | − | 0.997599i | \(-0.477938\pi\) | ||||
0.0692537 | + | 0.997599i | \(0.477938\pi\) | |||||||
\(264\) | 2.56155 | 0.157653 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −13.1231 | −0.804629 | ||||||||
\(267\) | −0.246211 | −0.0150679 | ||||||||
\(268\) | −0.315342 | −0.0192626 | ||||||||
\(269\) | −14.4924 | −0.883619 | −0.441809 | − | 0.897109i | \(-0.645663\pi\) | ||||
−0.441809 | + | 0.897109i | \(0.645663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.68466 | −0.223827 | −0.111914 | − | 0.993718i | \(-0.535698\pi\) | ||||
−0.111914 | + | 0.993718i | \(0.535698\pi\) | |||||||
\(272\) | −5.68466 | −0.344683 | ||||||||
\(273\) | −2.87689 | −0.174118 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.00000 | 0.481543 | ||||||||
\(277\) | −7.43845 | −0.446933 | −0.223466 | − | 0.974712i | \(-0.571737\pi\) | ||||
−0.223466 | + | 0.974712i | \(0.571737\pi\) | |||||||
\(278\) | 12.0000 | 0.719712 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4924 | 0.864545 | 0.432273 | − | 0.901743i | \(-0.357712\pi\) | ||||
0.432273 | + | 0.901743i | \(0.357712\pi\) | |||||||
\(282\) | −3.68466 | −0.219418 | ||||||||
\(283\) | 3.19224 | 0.189759 | 0.0948794 | − | 0.995489i | \(-0.469753\pi\) | ||||
0.0948794 | + | 0.995489i | \(0.469753\pi\) | |||||||
\(284\) | −1.43845 | −0.0853561 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.43845 | 0.0850572 | ||||||||
\(287\) | −21.7538 | −1.28409 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 15.3153 | 0.900902 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.8078 | 0.868047 | ||||||||
\(292\) | −10.0000 | −0.585206 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | −19.2462 | −1.12246 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.24621 | 0.479301 | ||||||||
\(297\) | −2.56155 | −0.148636 | ||||||||
\(298\) | −9.68466 | −0.561017 | ||||||||
\(299\) | 4.49242 | 0.259804 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −46.7386 | −2.69397 | ||||||||
\(302\) | −5.93087 | −0.341283 | ||||||||
\(303\) | 16.2462 | 0.933320 | ||||||||
\(304\) | −2.56155 | −0.146915 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.68466 | 0.324970 | ||||||||
\(307\) | 1.75379 | 0.100094 | 0.0500470 | − | 0.998747i | \(-0.484063\pi\) | ||||
0.0500470 | + | 0.998747i | \(0.484063\pi\) | |||||||
\(308\) | 13.1231 | 0.747758 | ||||||||
\(309\) | 5.12311 | 0.291443 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.9309 | 1.24359 | 0.621793 | − | 0.783182i | \(-0.286405\pi\) | ||||
0.621793 | + | 0.783182i | \(0.286405\pi\) | |||||||
\(312\) | −0.561553 | −0.0317917 | ||||||||
\(313\) | 16.2462 | 0.918290 | 0.459145 | − | 0.888361i | \(-0.348156\pi\) | ||||
0.459145 | + | 0.888361i | \(0.348156\pi\) | |||||||
\(314\) | −9.36932 | −0.528741 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.68466 | −0.207278 | ||||||||
\(317\) | −10.3153 | −0.579367 | −0.289684 | − | 0.957122i | \(-0.593550\pi\) | ||||
−0.289684 | + | 0.957122i | \(0.593550\pi\) | |||||||
\(318\) | −2.00000 | −0.112154 | ||||||||
\(319\) | 18.2462 | 1.02159 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | 40.9848 | 2.28400 | ||||||||
\(323\) | 14.5616 | 0.810226 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.0540 | −1.27684 | ||||||||
\(327\) | 14.0000 | 0.774202 | ||||||||
\(328\) | −4.24621 | −0.234458 | ||||||||
\(329\) | −18.8769 | −1.04072 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | −12.8078 | −0.702917 | ||||||||
\(333\) | −8.24621 | −0.451890 | ||||||||
\(334\) | −5.12311 | −0.280324 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.12311 | −0.279488 | ||||||||
\(337\) | 27.1231 | 1.47749 | 0.738745 | − | 0.673985i | \(-0.235419\pi\) | ||||
0.738745 | + | 0.673985i | \(0.235419\pi\) | |||||||
\(338\) | 12.6847 | 0.689954 | ||||||||
\(339\) | 14.0000 | 0.760376 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.56155 | 0.138716 | ||||||||
\(342\) | 2.56155 | 0.138513 | ||||||||
\(343\) | −62.7386 | −3.38757 | ||||||||
\(344\) | −9.12311 | −0.491885 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.56155 | 0.245231 | ||||||||
\(347\) | −12.1771 | −0.653700 | −0.326850 | − | 0.945076i | \(-0.605987\pi\) | ||||
−0.326850 | + | 0.945076i | \(0.605987\pi\) | |||||||
\(348\) | −7.12311 | −0.381839 | ||||||||
\(349\) | 15.6155 | 0.835880 | 0.417940 | − | 0.908475i | \(-0.362752\pi\) | ||||
0.417940 | + | 0.908475i | \(0.362752\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.561553 | 0.0299735 | ||||||||
\(352\) | 2.56155 | 0.136531 | ||||||||
\(353\) | −18.8078 | −1.00104 | −0.500518 | − | 0.865726i | \(-0.666857\pi\) | ||||
−0.500518 | + | 0.865726i | \(0.666857\pi\) | |||||||
\(354\) | 1.12311 | 0.0596924 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.246211 | −0.0130492 | ||||||||
\(357\) | 29.1231 | 1.54136 | ||||||||
\(358\) | −23.0540 | −1.21844 | ||||||||
\(359\) | 29.3002 | 1.54640 | 0.773202 | − | 0.634159i | \(-0.218654\pi\) | ||||
0.773202 | + | 0.634159i | \(0.218654\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4384 | −0.654655 | ||||||||
\(362\) | 12.2462 | 0.643647 | ||||||||
\(363\) | −4.43845 | −0.232958 | ||||||||
\(364\) | −2.87689 | −0.150790 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.561553 | 0.0293528 | ||||||||
\(367\) | −32.8078 | −1.71255 | −0.856276 | − | 0.516519i | \(-0.827228\pi\) | ||||
−0.856276 | + | 0.516519i | \(0.827228\pi\) | |||||||
\(368\) | 8.00000 | 0.417029 | ||||||||
\(369\) | 4.24621 | 0.221049 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.2462 | −0.531957 | ||||||||
\(372\) | −1.00000 | −0.0518476 | ||||||||
\(373\) | −3.12311 | −0.161708 | −0.0808541 | − | 0.996726i | \(-0.525765\pi\) | ||||
−0.0808541 | + | 0.996726i | \(0.525765\pi\) | |||||||
\(374\) | −14.5616 | −0.752960 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.68466 | −0.190022 | ||||||||
\(377\) | −4.00000 | −0.206010 | ||||||||
\(378\) | 5.12311 | 0.263504 | ||||||||
\(379\) | −17.9309 | −0.921047 | −0.460523 | − | 0.887648i | \(-0.652338\pi\) | ||||
−0.460523 | + | 0.887648i | \(0.652338\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.2462 | −0.524929 | ||||||||
\(382\) | −16.0000 | −0.818631 | ||||||||
\(383\) | 17.6155 | 0.900111 | 0.450056 | − | 0.893000i | \(-0.351404\pi\) | ||||
0.450056 | + | 0.893000i | \(0.351404\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.5616 | 1.25015 | ||||||||
\(387\) | 9.12311 | 0.463754 | ||||||||
\(388\) | 14.8078 | 0.751750 | ||||||||
\(389\) | −12.2462 | −0.620908 | −0.310454 | − | 0.950588i | \(-0.600481\pi\) | ||||
−0.310454 | + | 0.950588i | \(0.600481\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.4773 | −2.29988 | ||||||||
\(392\) | −19.2462 | −0.972080 | ||||||||
\(393\) | 17.1231 | 0.863746 | ||||||||
\(394\) | 8.24621 | 0.415438 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.56155 | −0.128723 | ||||||||
\(397\) | −12.7386 | −0.639334 | −0.319667 | − | 0.947530i | \(-0.603571\pi\) | ||||
−0.319667 | + | 0.947530i | \(0.603571\pi\) | |||||||
\(398\) | −4.31534 | −0.216309 | ||||||||
\(399\) | 13.1231 | 0.656977 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.9309 | −1.39480 | −0.697401 | − | 0.716682i | \(-0.745660\pi\) | ||||
−0.697401 | + | 0.716682i | \(0.745660\pi\) | |||||||
\(402\) | 0.315342 | 0.0157278 | ||||||||
\(403\) | −0.561553 | −0.0279729 | ||||||||
\(404\) | 16.2462 | 0.808279 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −36.4924 | −1.81109 | ||||||||
\(407\) | 21.1231 | 1.04703 | ||||||||
\(408\) | 5.68466 | 0.281433 | ||||||||
\(409\) | 4.24621 | 0.209962 | 0.104981 | − | 0.994474i | \(-0.466522\pi\) | ||||
0.104981 | + | 0.994474i | \(0.466522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 5.12311 | 0.252397 | ||||||||
\(413\) | 5.75379 | 0.283125 | ||||||||
\(414\) | −8.00000 | −0.393179 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.561553 | −0.0275324 | ||||||||
\(417\) | −12.0000 | −0.587643 | ||||||||
\(418\) | −6.56155 | −0.320936 | ||||||||
\(419\) | −6.24621 | −0.305147 | −0.152574 | − | 0.988292i | \(-0.548756\pi\) | ||||
−0.152574 | + | 0.988292i | \(0.548756\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.7386 | −1.20569 | −0.602844 | − | 0.797859i | \(-0.705966\pi\) | ||||
−0.602844 | + | 0.797859i | \(0.705966\pi\) | |||||||
\(422\) | 1.75379 | 0.0853731 | ||||||||
\(423\) | 3.68466 | 0.179154 | ||||||||
\(424\) | −2.00000 | −0.0971286 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.43845 | 0.0696930 | ||||||||
\(427\) | 2.87689 | 0.139223 | ||||||||
\(428\) | 4.00000 | 0.193347 | ||||||||
\(429\) | −1.43845 | −0.0694489 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.9848 | 1.97417 | 0.987085 | − | 0.160196i | \(-0.0512126\pi\) | ||||
0.987085 | + | 0.160196i | \(0.0512126\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −35.6155 | −1.71157 | −0.855787 | − | 0.517329i | \(-0.826926\pi\) | ||||
−0.855787 | + | 0.517329i | \(0.826926\pi\) | |||||||
\(434\) | −5.12311 | −0.245917 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | −20.4924 | −0.980286 | ||||||||
\(438\) | 10.0000 | 0.477818 | ||||||||
\(439\) | −38.7386 | −1.84889 | −0.924447 | − | 0.381310i | \(-0.875473\pi\) | ||||
−0.924447 | + | 0.381310i | \(0.875473\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.2462 | 0.916486 | ||||||||
\(442\) | 3.19224 | 0.151839 | ||||||||
\(443\) | 11.3693 | 0.540173 | 0.270086 | − | 0.962836i | \(-0.412948\pi\) | ||||
0.270086 | + | 0.962836i | \(0.412948\pi\) | |||||||
\(444\) | −8.24621 | −0.391348 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.6847 | 0.932096 | ||||||||
\(447\) | 9.68466 | 0.458069 | ||||||||
\(448\) | −5.12311 | −0.242044 | ||||||||
\(449\) | 2.80776 | 0.132507 | 0.0662533 | − | 0.997803i | \(-0.478895\pi\) | ||||
0.0662533 | + | 0.997803i | \(0.478895\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8769 | −0.512173 | ||||||||
\(452\) | 14.0000 | 0.658505 | ||||||||
\(453\) | 5.93087 | 0.278657 | ||||||||
\(454\) | −19.3693 | −0.909047 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.56155 | 0.119956 | ||||||||
\(457\) | 0.246211 | 0.0115173 | 0.00575864 | − | 0.999983i | \(-0.498167\pi\) | ||||
0.00575864 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(458\) | −17.6847 | −0.826350 | ||||||||
\(459\) | −5.68466 | −0.265337 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.2462 | 1.50186 | 0.750928 | − | 0.660384i | \(-0.229607\pi\) | ||||
0.750928 | + | 0.660384i | \(0.229607\pi\) | |||||||
\(462\) | −13.1231 | −0.610542 | ||||||||
\(463\) | 13.9309 | 0.647422 | 0.323711 | − | 0.946156i | \(-0.395069\pi\) | ||||
0.323711 | + | 0.946156i | \(0.395069\pi\) | |||||||
\(464\) | −7.12311 | −0.330682 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.6155 | 0.538079 | ||||||||
\(467\) | 22.2462 | 1.02943 | 0.514716 | − | 0.857361i | \(-0.327897\pi\) | ||||
0.514716 | + | 0.857361i | \(0.327897\pi\) | |||||||
\(468\) | 0.561553 | 0.0259578 | ||||||||
\(469\) | 1.61553 | 0.0745982 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.36932 | 0.431715 | ||||||||
\(472\) | 1.12311 | 0.0516951 | ||||||||
\(473\) | −23.3693 | −1.07452 | ||||||||
\(474\) | 3.68466 | 0.169242 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 29.1231 | 1.33486 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 20.4924 | 0.937302 | ||||||||
\(479\) | 29.9309 | 1.36758 | 0.683788 | − | 0.729681i | \(-0.260331\pi\) | ||||
0.683788 | + | 0.729681i | \(0.260331\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.63068 | −0.211141 | ||||||||
\(482\) | −7.75379 | −0.353175 | ||||||||
\(483\) | −40.9848 | −1.86488 | ||||||||
\(484\) | −4.43845 | −0.201748 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 11.6847 | 0.529482 | 0.264741 | − | 0.964319i | \(-0.414713\pi\) | ||||
0.264741 | + | 0.964319i | \(0.414713\pi\) | |||||||
\(488\) | 0.561553 | 0.0254203 | ||||||||
\(489\) | 23.0540 | 1.04254 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0000 | 0.902587 | 0.451294 | − | 0.892375i | \(-0.350963\pi\) | ||||
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(492\) | 4.24621 | 0.191434 | ||||||||
\(493\) | 40.4924 | 1.82369 | ||||||||
\(494\) | 1.43845 | 0.0647188 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 7.36932 | 0.330559 | ||||||||
\(498\) | 12.8078 | 0.573930 | ||||||||
\(499\) | 1.75379 | 0.0785104 | 0.0392552 | − | 0.999229i | \(-0.487501\pi\) | ||||
0.0392552 | + | 0.999229i | \(0.487501\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.12311 | 0.228883 | ||||||||
\(502\) | −20.0000 | −0.892644 | ||||||||
\(503\) | 32.1771 | 1.43471 | 0.717353 | − | 0.696710i | \(-0.245354\pi\) | ||||
0.717353 | + | 0.696710i | \(0.245354\pi\) | |||||||
\(504\) | 5.12311 | 0.228201 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.4924 | 0.910999 | ||||||||
\(507\) | −12.6847 | −0.563345 | ||||||||
\(508\) | −10.2462 | −0.454602 | ||||||||
\(509\) | −37.8617 | −1.67819 | −0.839096 | − | 0.543983i | \(-0.816915\pi\) | ||||
−0.839096 | + | 0.543983i | \(0.816915\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 51.2311 | 2.26633 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.56155 | −0.113095 | ||||||||
\(514\) | −16.8769 | −0.744408 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.12311 | 0.401622 | ||||||||
\(517\) | −9.43845 | −0.415102 | ||||||||
\(518\) | −42.2462 | −1.85619 | ||||||||
\(519\) | −4.56155 | −0.200230 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.6155 | −1.03462 | −0.517308 | − | 0.855800i | \(-0.673066\pi\) | ||||
−0.517308 | + | 0.855800i | \(0.673066\pi\) | |||||||
\(522\) | 7.12311 | 0.311770 | ||||||||
\(523\) | 25.1231 | 1.09856 | 0.549278 | − | 0.835639i | \(-0.314903\pi\) | ||||
0.549278 | + | 0.835639i | \(0.314903\pi\) | |||||||
\(524\) | 17.1231 | 0.748026 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.24621 | −0.0979395 | ||||||||
\(527\) | 5.68466 | 0.247628 | ||||||||
\(528\) | −2.56155 | −0.111477 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.12311 | −0.0487386 | ||||||||
\(532\) | 13.1231 | 0.568959 | ||||||||
\(533\) | 2.38447 | 0.103283 | ||||||||
\(534\) | 0.246211 | 0.0106546 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.315342 | 0.0136207 | ||||||||
\(537\) | 23.0540 | 0.994852 | ||||||||
\(538\) | 14.4924 | 0.624813 | ||||||||
\(539\) | −49.3002 | −2.12351 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.3693 | −1.77861 | −0.889303 | − | 0.457319i | \(-0.848810\pi\) | ||||
−0.889303 | + | 0.457319i | \(0.848810\pi\) | |||||||
\(542\) | 3.68466 | 0.158270 | ||||||||
\(543\) | −12.2462 | −0.525535 | ||||||||
\(544\) | 5.68466 | 0.243728 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.87689 | 0.123120 | ||||||||
\(547\) | 26.7386 | 1.14326 | 0.571631 | − | 0.820511i | \(-0.306311\pi\) | ||||
0.571631 | + | 0.820511i | \(0.306311\pi\) | |||||||
\(548\) | 6.00000 | 0.256307 | ||||||||
\(549\) | −0.561553 | −0.0239665 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.2462 | 0.777315 | ||||||||
\(552\) | −8.00000 | −0.340503 | ||||||||
\(553\) | 18.8769 | 0.802727 | ||||||||
\(554\) | 7.43845 | 0.316029 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0000 | −0.508913 | ||||||||
\(557\) | 17.3693 | 0.735962 | 0.367981 | − | 0.929833i | \(-0.380049\pi\) | ||||
0.367981 | + | 0.929833i | \(0.380049\pi\) | |||||||
\(558\) | 1.00000 | 0.0423334 | ||||||||
\(559\) | 5.12311 | 0.216684 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.5616 | 0.614789 | ||||||||
\(562\) | −14.4924 | −0.611326 | ||||||||
\(563\) | 12.0000 | 0.505740 | 0.252870 | − | 0.967500i | \(-0.418626\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(564\) | 3.68466 | 0.155152 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.19224 | −0.134180 | ||||||||
\(567\) | −5.12311 | −0.215150 | ||||||||
\(568\) | 1.43845 | 0.0603559 | ||||||||
\(569\) | 4.24621 | 0.178010 | 0.0890052 | − | 0.996031i | \(-0.471631\pi\) | ||||
0.0890052 | + | 0.996031i | \(0.471631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.9848 | 1.21298 | 0.606489 | − | 0.795092i | \(-0.292577\pi\) | ||||
0.606489 | + | 0.795092i | \(0.292577\pi\) | |||||||
\(572\) | −1.43845 | −0.0601445 | ||||||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | 21.7538 | 0.907986 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 7.43845 | 0.309667 | 0.154833 | − | 0.987941i | \(-0.450516\pi\) | ||||
0.154833 | + | 0.987941i | \(0.450516\pi\) | |||||||
\(578\) | −15.3153 | −0.637034 | ||||||||
\(579\) | −24.5616 | −1.02074 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 65.6155 | 2.72219 | ||||||||
\(582\) | −14.8078 | −0.613802 | ||||||||
\(583\) | −5.12311 | −0.212177 | ||||||||
\(584\) | 10.0000 | 0.413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | −25.3002 | −1.04425 | −0.522125 | − | 0.852869i | \(-0.674861\pi\) | ||||
−0.522125 | + | 0.852869i | \(0.674861\pi\) | |||||||
\(588\) | 19.2462 | 0.793700 | ||||||||
\(589\) | 2.56155 | 0.105547 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.24621 | −0.339204 | ||||||||
\(592\) | −8.24621 | −0.338917 | ||||||||
\(593\) | 34.4924 | 1.41643 | 0.708217 | − | 0.705995i | \(-0.249500\pi\) | ||||
0.708217 | + | 0.705995i | \(0.249500\pi\) | |||||||
\(594\) | 2.56155 | 0.105102 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.68466 | 0.396699 | ||||||||
\(597\) | 4.31534 | 0.176615 | ||||||||
\(598\) | −4.49242 | −0.183709 | ||||||||
\(599\) | −20.3153 | −0.830062 | −0.415031 | − | 0.909807i | \(-0.636229\pi\) | ||||
−0.415031 | + | 0.909807i | \(0.636229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7538 | −0.479447 | −0.239724 | − | 0.970841i | \(-0.577057\pi\) | ||||
−0.239724 | + | 0.970841i | \(0.577057\pi\) | |||||||
\(602\) | 46.7386 | 1.90492 | ||||||||
\(603\) | −0.315342 | −0.0128417 | ||||||||
\(604\) | 5.93087 | 0.241324 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.2462 | −0.659957 | ||||||||
\(607\) | −7.36932 | −0.299111 | −0.149556 | − | 0.988753i | \(-0.547784\pi\) | ||||
−0.149556 | + | 0.988753i | \(0.547784\pi\) | |||||||
\(608\) | 2.56155 | 0.103885 | ||||||||
\(609\) | 36.4924 | 1.47875 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.06913 | 0.0837081 | ||||||||
\(612\) | −5.68466 | −0.229789 | ||||||||
\(613\) | −13.1922 | −0.532829 | −0.266415 | − | 0.963859i | \(-0.585839\pi\) | ||||
−0.266415 | + | 0.963859i | \(0.585839\pi\) | |||||||
\(614\) | −1.75379 | −0.0707772 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.1231 | −0.528745 | ||||||||
\(617\) | 22.0000 | 0.885687 | 0.442843 | − | 0.896599i | \(-0.353970\pi\) | ||||
0.442843 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(618\) | −5.12311 | −0.206082 | ||||||||
\(619\) | 9.75379 | 0.392038 | 0.196019 | − | 0.980600i | \(-0.437199\pi\) | ||||
0.196019 | + | 0.980600i | \(0.437199\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | −21.9309 | −0.879348 | ||||||||
\(623\) | 1.26137 | 0.0505356 | ||||||||
\(624\) | 0.561553 | 0.0224801 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.2462 | −0.649329 | ||||||||
\(627\) | 6.56155 | 0.262043 | ||||||||
\(628\) | 9.36932 | 0.373876 | ||||||||
\(629\) | 46.8769 | 1.86910 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 3.68466 | 0.146568 | ||||||||
\(633\) | −1.75379 | −0.0697068 | ||||||||
\(634\) | 10.3153 | 0.409675 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.00000 | 0.0793052 | ||||||||
\(637\) | 10.8078 | 0.428219 | ||||||||
\(638\) | −18.2462 | −0.722374 | ||||||||
\(639\) | −1.43845 | −0.0569041 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.3153 | −0.407431 | −0.203716 | − | 0.979030i | \(-0.565302\pi\) | ||||
−0.203716 | + | 0.979030i | \(0.565302\pi\) | |||||||
\(642\) | −4.00000 | −0.157867 | ||||||||
\(643\) | 20.0000 | 0.788723 | 0.394362 | − | 0.918955i | \(-0.370966\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(644\) | −40.9848 | −1.61503 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.5616 | −0.572917 | ||||||||
\(647\) | 35.8617 | 1.40987 | 0.704935 | − | 0.709272i | \(-0.250976\pi\) | ||||
0.704935 | + | 0.709272i | \(0.250976\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 2.87689 | 0.112928 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.12311 | 0.200790 | ||||||||
\(652\) | 23.0540 | 0.902863 | ||||||||
\(653\) | 33.5464 | 1.31277 | 0.656386 | − | 0.754425i | \(-0.272084\pi\) | ||||
0.656386 | + | 0.754425i | \(0.272084\pi\) | |||||||
\(654\) | −14.0000 | −0.547443 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.24621 | 0.165787 | ||||||||
\(657\) | −10.0000 | −0.390137 | ||||||||
\(658\) | 18.8769 | 0.735898 | ||||||||
\(659\) | −19.3693 | −0.754521 | −0.377261 | − | 0.926107i | \(-0.623134\pi\) | ||||
−0.377261 | + | 0.926107i | \(0.623134\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.1080 | 1.71560 | 0.857800 | − | 0.513983i | \(-0.171831\pi\) | ||||
0.857800 | + | 0.513983i | \(0.171831\pi\) | |||||||
\(662\) | 12.0000 | 0.466393 | ||||||||
\(663\) | −3.19224 | −0.123976 | ||||||||
\(664\) | 12.8078 | 0.497038 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.24621 | 0.319534 | ||||||||
\(667\) | −56.9848 | −2.20646 | ||||||||
\(668\) | 5.12311 | 0.198219 | ||||||||
\(669\) | −19.6847 | −0.761053 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.43845 | 0.0555306 | ||||||||
\(672\) | 5.12311 | 0.197628 | ||||||||
\(673\) | 0.876894 | 0.0338018 | 0.0169009 | − | 0.999857i | \(-0.494620\pi\) | ||||
0.0169009 | + | 0.999857i | \(0.494620\pi\) | |||||||
\(674\) | −27.1231 | −1.04474 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.6847 | −0.487871 | ||||||||
\(677\) | −0.876894 | −0.0337018 | −0.0168509 | − | 0.999858i | \(-0.505364\pi\) | ||||
−0.0168509 | + | 0.999858i | \(0.505364\pi\) | |||||||
\(678\) | −14.0000 | −0.537667 | ||||||||
\(679\) | −75.8617 | −2.91131 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.3693 | 0.742234 | ||||||||
\(682\) | −2.56155 | −0.0980869 | ||||||||
\(683\) | 50.7386 | 1.94146 | 0.970730 | − | 0.240174i | \(-0.0772044\pi\) | ||||
0.970730 | + | 0.240174i | \(0.0772044\pi\) | |||||||
\(684\) | −2.56155 | −0.0979434 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 62.7386 | 2.39537 | ||||||||
\(687\) | 17.6847 | 0.674712 | ||||||||
\(688\) | 9.12311 | 0.347815 | ||||||||
\(689\) | 1.12311 | 0.0427869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.17708 | −0.158904 | −0.0794518 | − | 0.996839i | \(-0.525317\pi\) | ||||
−0.0794518 | + | 0.996839i | \(0.525317\pi\) | |||||||
\(692\) | −4.56155 | −0.173404 | ||||||||
\(693\) | 13.1231 | 0.498506 | ||||||||
\(694\) | 12.1771 | 0.462236 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.12311 | 0.270001 | ||||||||
\(697\) | −24.1383 | −0.914302 | ||||||||
\(698\) | −15.6155 | −0.591056 | ||||||||
\(699\) | −11.6155 | −0.439340 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.06913 | −0.153689 | −0.0768445 | − | 0.997043i | \(-0.524484\pi\) | ||||
−0.0768445 | + | 0.997043i | \(0.524484\pi\) | |||||||
\(702\) | −0.561553 | −0.0211944 | ||||||||
\(703\) | 21.1231 | 0.796673 | ||||||||
\(704\) | −2.56155 | −0.0965422 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.8078 | 0.707840 | ||||||||
\(707\) | −83.2311 | −3.13023 | ||||||||
\(708\) | −1.12311 | −0.0422089 | ||||||||
\(709\) | −20.4233 | −0.767013 | −0.383506 | − | 0.923538i | \(-0.625284\pi\) | ||||
−0.383506 | + | 0.923538i | \(0.625284\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.68466 | −0.138185 | ||||||||
\(712\) | 0.246211 | 0.00922716 | ||||||||
\(713\) | −8.00000 | −0.299602 | ||||||||
\(714\) | −29.1231 | −1.08990 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23.0540 | 0.861568 | ||||||||
\(717\) | −20.4924 | −0.765304 | ||||||||
\(718\) | −29.3002 | −1.09347 | ||||||||
\(719\) | 4.49242 | 0.167539 | 0.0837695 | − | 0.996485i | \(-0.473304\pi\) | ||||
0.0837695 | + | 0.996485i | \(0.473304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.2462 | −0.977460 | ||||||||
\(722\) | 12.4384 | 0.462911 | ||||||||
\(723\) | 7.75379 | 0.288367 | ||||||||
\(724\) | −12.2462 | −0.455127 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.43845 | 0.164726 | ||||||||
\(727\) | 13.7538 | 0.510100 | 0.255050 | − | 0.966928i | \(-0.417908\pi\) | ||||
0.255050 | + | 0.966928i | \(0.417908\pi\) | |||||||
\(728\) | 2.87689 | 0.106625 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −51.8617 | −1.91818 | ||||||||
\(732\) | −0.561553 | −0.0207556 | ||||||||
\(733\) | −8.24621 | −0.304581 | −0.152290 | − | 0.988336i | \(-0.548665\pi\) | ||||
−0.152290 | + | 0.988336i | \(0.548665\pi\) | |||||||
\(734\) | 32.8078 | 1.21096 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.00000 | −0.294884 | ||||||||
\(737\) | 0.807764 | 0.0297544 | ||||||||
\(738\) | −4.24621 | −0.156305 | ||||||||
\(739\) | 12.0000 | 0.441427 | 0.220714 | − | 0.975339i | \(-0.429161\pi\) | ||||
0.220714 | + | 0.975339i | \(0.429161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.43845 | −0.0528427 | ||||||||
\(742\) | 10.2462 | 0.376150 | ||||||||
\(743\) | 8.00000 | 0.293492 | 0.146746 | − | 0.989174i | \(-0.453120\pi\) | ||||
0.146746 | + | 0.989174i | \(0.453120\pi\) | |||||||
\(744\) | 1.00000 | 0.0366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.12311 | 0.114345 | ||||||||
\(747\) | −12.8078 | −0.468612 | ||||||||
\(748\) | 14.5616 | 0.532423 | ||||||||
\(749\) | −20.4924 | −0.748777 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.8769 | −0.688828 | −0.344414 | − | 0.938818i | \(-0.611922\pi\) | ||||
−0.344414 | + | 0.938818i | \(0.611922\pi\) | |||||||
\(752\) | 3.68466 | 0.134366 | ||||||||
\(753\) | 20.0000 | 0.728841 | ||||||||
\(754\) | 4.00000 | 0.145671 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.12311 | −0.186326 | ||||||||
\(757\) | −40.2462 | −1.46277 | −0.731387 | − | 0.681963i | \(-0.761127\pi\) | ||||
−0.731387 | + | 0.681963i | \(0.761127\pi\) | |||||||
\(758\) | 17.9309 | 0.651279 | ||||||||
\(759\) | −20.4924 | −0.743828 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.4233 | −1.46534 | −0.732672 | − | 0.680582i | \(-0.761727\pi\) | ||||
−0.732672 | + | 0.680582i | \(0.761727\pi\) | |||||||
\(762\) | 10.2462 | 0.371181 | ||||||||
\(763\) | −71.7235 | −2.59656 | ||||||||
\(764\) | 16.0000 | 0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.6155 | −0.636475 | ||||||||
\(767\) | −0.630683 | −0.0227726 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 7.75379 | 0.279609 | 0.139804 | − | 0.990179i | \(-0.455353\pi\) | ||||
0.139804 | + | 0.990179i | \(0.455353\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.8769 | 0.607807 | ||||||||
\(772\) | −24.5616 | −0.883990 | ||||||||
\(773\) | −31.6155 | −1.13713 | −0.568566 | − | 0.822638i | \(-0.692502\pi\) | ||||
−0.568566 | + | 0.822638i | \(0.692502\pi\) | |||||||
\(774\) | −9.12311 | −0.327923 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.8078 | −0.531568 | ||||||||
\(777\) | 42.2462 | 1.51557 | ||||||||
\(778\) | 12.2462 | 0.439048 | ||||||||
\(779\) | −10.8769 | −0.389705 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.68466 | 0.131847 | ||||||||
\(782\) | 45.4773 | 1.62626 | ||||||||
\(783\) | −7.12311 | −0.254559 | ||||||||
\(784\) | 19.2462 | 0.687365 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17.1231 | −0.610761 | ||||||||
\(787\) | 15.5076 | 0.552785 | 0.276393 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276393 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(788\) | −8.24621 | −0.293759 | ||||||||
\(789\) | 2.24621 | 0.0799672 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −71.7235 | −2.55019 | ||||||||
\(792\) | 2.56155 | 0.0910208 | ||||||||
\(793\) | −0.315342 | −0.0111981 | ||||||||
\(794\) | 12.7386 | 0.452077 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.31534 | 0.152953 | ||||||||
\(797\) | −54.3542 | −1.92532 | −0.962662 | − | 0.270708i | \(-0.912742\pi\) | ||||
−0.962662 | + | 0.270708i | \(0.912742\pi\) | |||||||
\(798\) | −13.1231 | −0.464553 | ||||||||
\(799\) | −20.9460 | −0.741017 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.246211 | −0.00869945 | ||||||||
\(802\) | 27.9309 | 0.986273 | ||||||||
\(803\) | 25.6155 | 0.903952 | ||||||||
\(804\) | −0.315342 | −0.0111212 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.561553 | 0.0197799 | ||||||||
\(807\) | −14.4924 | −0.510157 | ||||||||
\(808\) | −16.2462 | −0.571540 | ||||||||
\(809\) | −17.0540 | −0.599586 | −0.299793 | − | 0.954004i | \(-0.596918\pi\) | ||||
−0.299793 | + | 0.954004i | \(0.596918\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.4924 | 0.579127 | 0.289564 | − | 0.957159i | \(-0.406490\pi\) | ||||
0.289564 | + | 0.957159i | \(0.406490\pi\) | |||||||
\(812\) | 36.4924 | 1.28063 | ||||||||
\(813\) | −3.68466 | −0.129227 | ||||||||
\(814\) | −21.1231 | −0.740364 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.68466 | −0.199003 | ||||||||
\(817\) | −23.3693 | −0.817589 | ||||||||
\(818\) | −4.24621 | −0.148465 | ||||||||
\(819\) | −2.87689 | −0.100527 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.00000 | −0.0698005 | −0.0349002 | − | 0.999391i | \(-0.511111\pi\) | ||||
−0.0349002 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(822\) | −6.00000 | −0.209274 | ||||||||
\(823\) | −11.6847 | −0.407302 | −0.203651 | − | 0.979044i | \(-0.565281\pi\) | ||||
−0.203651 | + | 0.979044i | \(0.565281\pi\) | |||||||
\(824\) | −5.12311 | −0.178472 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.75379 | −0.200200 | ||||||||
\(827\) | 30.4233 | 1.05792 | 0.528961 | − | 0.848646i | \(-0.322582\pi\) | ||||
0.528961 | + | 0.848646i | \(0.322582\pi\) | |||||||
\(828\) | 8.00000 | 0.278019 | ||||||||
\(829\) | −4.24621 | −0.147477 | −0.0737385 | − | 0.997278i | \(-0.523493\pi\) | ||||
−0.0737385 | + | 0.997278i | \(0.523493\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.43845 | −0.258037 | ||||||||
\(832\) | 0.561553 | 0.0194683 | ||||||||
\(833\) | −109.408 | −3.79077 | ||||||||
\(834\) | 12.0000 | 0.415526 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.56155 | 0.226936 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 6.24621 | 0.215772 | ||||||||
\(839\) | −13.7538 | −0.474834 | −0.237417 | − | 0.971408i | \(-0.576301\pi\) | ||||
−0.237417 | + | 0.971408i | \(0.576301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.7386 | 0.749608 | ||||||||
\(842\) | 24.7386 | 0.852550 | ||||||||
\(843\) | 14.4924 | 0.499146 | ||||||||
\(844\) | −1.75379 | −0.0603679 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.68466 | −0.126681 | ||||||||
\(847\) | 22.7386 | 0.781309 | ||||||||
\(848\) | 2.00000 | 0.0686803 | ||||||||
\(849\) | 3.19224 | 0.109557 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −65.9697 | −2.26141 | ||||||||
\(852\) | −1.43845 | −0.0492804 | ||||||||
\(853\) | 29.2311 | 1.00085 | 0.500426 | − | 0.865779i | \(-0.333177\pi\) | ||||
0.500426 | + | 0.865779i | \(0.333177\pi\) | |||||||
\(854\) | −2.87689 | −0.0984453 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | 28.1080 | 0.960149 | 0.480075 | − | 0.877228i | \(-0.340610\pi\) | ||||
0.480075 | + | 0.877228i | \(0.340610\pi\) | |||||||
\(858\) | 1.43845 | 0.0491078 | ||||||||
\(859\) | 58.1080 | 1.98262 | 0.991309 | − | 0.131555i | \(-0.0419971\pi\) | ||||
0.991309 | + | 0.131555i | \(0.0419971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.7538 | −0.741367 | ||||||||
\(862\) | −40.9848 | −1.39595 | ||||||||
\(863\) | −17.6155 | −0.599640 | −0.299820 | − | 0.953996i | \(-0.596927\pi\) | ||||
−0.299820 | + | 0.953996i | \(0.596927\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.6155 | 1.21026 | ||||||||
\(867\) | 15.3153 | 0.520136 | ||||||||
\(868\) | 5.12311 | 0.173890 | ||||||||
\(869\) | 9.43845 | 0.320177 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.177081 | −0.00600016 | ||||||||
\(872\) | −14.0000 | −0.474100 | ||||||||
\(873\) | 14.8078 | 0.501167 | ||||||||
\(874\) | 20.4924 | 0.693167 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.0000 | −0.337869 | ||||||||
\(877\) | −31.6155 | −1.06758 | −0.533790 | − | 0.845617i | \(-0.679233\pi\) | ||||
−0.533790 | + | 0.845617i | \(0.679233\pi\) | |||||||
\(878\) | 38.7386 | 1.30737 | ||||||||
\(879\) | −6.00000 | −0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.9309 | 1.61483 | 0.807416 | − | 0.589983i | \(-0.200865\pi\) | ||||
0.807416 | + | 0.589983i | \(0.200865\pi\) | |||||||
\(882\) | −19.2462 | −0.648054 | ||||||||
\(883\) | −14.8769 | −0.500647 | −0.250324 | − | 0.968162i | \(-0.580537\pi\) | ||||
−0.250324 | + | 0.968162i | \(0.580537\pi\) | |||||||
\(884\) | −3.19224 | −0.107367 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.3693 | −0.381960 | ||||||||
\(887\) | −28.4924 | −0.956682 | −0.478341 | − | 0.878174i | \(-0.658762\pi\) | ||||
−0.478341 | + | 0.878174i | \(0.658762\pi\) | |||||||
\(888\) | 8.24621 | 0.276725 | ||||||||
\(889\) | 52.4924 | 1.76054 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.56155 | −0.0858152 | ||||||||
\(892\) | −19.6847 | −0.659091 | ||||||||
\(893\) | −9.43845 | −0.315846 | ||||||||
\(894\) | −9.68466 | −0.323903 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.12311 | 0.171151 | ||||||||
\(897\) | 4.49242 | 0.149998 | ||||||||
\(898\) | −2.80776 | −0.0936963 | ||||||||
\(899\) | 7.12311 | 0.237569 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.3693 | −0.378767 | ||||||||
\(902\) | 10.8769 | 0.362161 | ||||||||
\(903\) | −46.7386 | −1.55536 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.93087 | −0.197040 | ||||||||
\(907\) | −5.43845 | −0.180581 | −0.0902903 | − | 0.995915i | \(-0.528780\pi\) | ||||
−0.0902903 | + | 0.995915i | \(0.528780\pi\) | |||||||
\(908\) | 19.3693 | 0.642793 | ||||||||
\(909\) | 16.2462 | 0.538853 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | −2.56155 | −0.0848215 | ||||||||
\(913\) | 32.8078 | 1.08578 | ||||||||
\(914\) | −0.246211 | −0.00814394 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.6847 | 0.584318 | ||||||||
\(917\) | −87.7235 | −2.89688 | ||||||||
\(918\) | 5.68466 | 0.187622 | ||||||||
\(919\) | 44.4924 | 1.46767 | 0.733835 | − | 0.679328i | \(-0.237729\pi\) | ||||
0.733835 | + | 0.679328i | \(0.237729\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.75379 | 0.0577893 | ||||||||
\(922\) | −32.2462 | −1.06197 | ||||||||
\(923\) | −0.807764 | −0.0265879 | ||||||||
\(924\) | 13.1231 | 0.431718 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.9309 | −0.457797 | ||||||||
\(927\) | 5.12311 | 0.168265 | ||||||||
\(928\) | 7.12311 | 0.233827 | ||||||||
\(929\) | 6.49242 | 0.213009 | 0.106505 | − | 0.994312i | \(-0.466034\pi\) | ||||
0.106505 | + | 0.994312i | \(0.466034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −49.3002 | −1.61575 | ||||||||
\(932\) | −11.6155 | −0.380479 | ||||||||
\(933\) | 21.9309 | 0.717984 | ||||||||
\(934\) | −22.2462 | −0.727918 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.561553 | −0.0183549 | ||||||||
\(937\) | 1.05398 | 0.0344319 | 0.0172159 | − | 0.999852i | \(-0.494520\pi\) | ||||
0.0172159 | + | 0.999852i | \(0.494520\pi\) | |||||||
\(938\) | −1.61553 | −0.0527489 | ||||||||
\(939\) | 16.2462 | 0.530175 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.63068 | −0.0857578 | −0.0428789 | − | 0.999080i | \(-0.513653\pi\) | ||||
−0.0428789 | + | 0.999080i | \(0.513653\pi\) | |||||||
\(942\) | −9.36932 | −0.305269 | ||||||||
\(943\) | 33.9697 | 1.10621 | ||||||||
\(944\) | −1.12311 | −0.0365540 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.3693 | 0.759802 | ||||||||
\(947\) | −34.5616 | −1.12310 | −0.561550 | − | 0.827443i | \(-0.689795\pi\) | ||||
−0.561550 | + | 0.827443i | \(0.689795\pi\) | |||||||
\(948\) | −3.68466 | −0.119672 | ||||||||
\(949\) | −5.61553 | −0.182288 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.3153 | −0.334498 | ||||||||
\(952\) | −29.1231 | −0.943885 | ||||||||
\(953\) | 21.5464 | 0.697956 | 0.348978 | − | 0.937131i | \(-0.386529\pi\) | ||||
0.348978 | + | 0.937131i | \(0.386529\pi\) | |||||||
\(954\) | −2.00000 | −0.0647524 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.4924 | −0.662772 | ||||||||
\(957\) | 18.2462 | 0.589816 | ||||||||
\(958\) | −29.9309 | −0.967023 | ||||||||
\(959\) | −30.7386 | −0.992602 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 4.63068 | 0.149299 | ||||||||
\(963\) | 4.00000 | 0.128898 | ||||||||
\(964\) | 7.75379 | 0.249733 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 40.9848 | 1.31867 | ||||||||
\(967\) | −46.5616 | −1.49732 | −0.748659 | − | 0.662955i | \(-0.769302\pi\) | ||||
−0.748659 | + | 0.662955i | \(0.769302\pi\) | |||||||
\(968\) | 4.43845 | 0.142657 | ||||||||
\(969\) | 14.5616 | 0.467784 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.3845 | −0.589986 | −0.294993 | − | 0.955499i | \(-0.595317\pi\) | ||||
−0.294993 | + | 0.955499i | \(0.595317\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 61.4773 | 1.97087 | ||||||||
\(974\) | −11.6847 | −0.374401 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.561553 | −0.0179749 | ||||||||
\(977\) | −44.2462 | −1.41556 | −0.707781 | − | 0.706432i | \(-0.750304\pi\) | ||||
−0.707781 | + | 0.706432i | \(0.750304\pi\) | |||||||
\(978\) | −23.0540 | −0.737185 | ||||||||
\(979\) | 0.630683 | 0.0201567 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | −20.0000 | −0.638226 | ||||||||
\(983\) | 18.2462 | 0.581964 | 0.290982 | − | 0.956729i | \(-0.406018\pi\) | ||||
0.290982 | + | 0.956729i | \(0.406018\pi\) | |||||||
\(984\) | −4.24621 | −0.135364 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −40.4924 | −1.28954 | ||||||||
\(987\) | −18.8769 | −0.600858 | ||||||||
\(988\) | −1.43845 | −0.0457631 | ||||||||
\(989\) | 72.9848 | 2.32078 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.7386 | 1.48470 | 0.742351 | − | 0.670011i | \(-0.233711\pi\) | ||||
0.742351 | + | 0.670011i | \(0.233711\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | −12.0000 | −0.380808 | ||||||||
\(994\) | −7.36932 | −0.233741 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.8078 | −0.405830 | ||||||||
\(997\) | 26.0000 | 0.823428 | 0.411714 | − | 0.911313i | \(-0.364930\pi\) | ||||
0.411714 | + | 0.911313i | \(0.364930\pi\) | |||||||
\(998\) | −1.75379 | −0.0555152 | ||||||||
\(999\) | −8.24621 | −0.260899 |
(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 | 4650.2.a.cd.1.1 | 2 | ||
5.2 | odd | 4 | 4650.2.d.bc.3349.1 | 4 | |||
5.3 | odd | 4 | 4650.2.d.bc.3349.4 | 4 | |||
5.4 | even | 2 | 186.2.a.d.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 558.2.a.i.1.2 | 2 | |||
20.19 | odd | 2 | 1488.2.a.r.1.1 | 2 | |||
35.34 | odd | 2 | 9114.2.a.be.1.2 | 2 | |||
40.19 | odd | 2 | 5952.2.a.bk.1.2 | 2 | |||
40.29 | even | 2 | 5952.2.a.bs.1.2 | 2 | |||
60.59 | even | 2 | 4464.2.a.bb.1.2 | 2 | |||
155.154 | odd | 2 | 5766.2.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
186.2.a.d.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
558.2.a.i.1.2 | 2 | 15.14 | odd | 2 | |||
1488.2.a.r.1.1 | 2 | 20.19 | odd | 2 | |||
4464.2.a.bb.1.2 | 2 | 60.59 | even | 2 | |||
4650.2.a.cd.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4650.2.d.bc.3349.1 | 4 | 5.2 | odd | 4 | |||
4650.2.d.bc.3349.4 | 4 | 5.3 | odd | 4 | |||
5766.2.a.v.1.1 | 2 | 155.154 | odd | 2 | |||
5952.2.a.bk.1.2 | 2 | 40.19 | odd | 2 | |||
5952.2.a.bs.1.2 | 2 | 40.29 | even | 2 | |||
9114.2.a.be.1.2 | 2 | 35.34 | odd | 2 |