Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3920,2,Mod(1,3920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3920.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: | \(31.3013575923\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1960) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.87996\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3920.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.87996 | 1.66275 | 0.831373 | − | 0.555715i | \(-0.187555\pi\) | ||||
0.831373 | + | 0.555715i | \(0.187555\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.29417 | 1.76472 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.46575 | −0.441939 | −0.220970 | − | 0.975281i | \(-0.570922\pi\) | ||||
−0.220970 | + | 0.975281i | \(0.570922\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.22129 | −0.616076 | −0.308038 | − | 0.951374i | \(-0.599672\pi\) | ||||
−0.308038 | + | 0.951374i | \(0.599672\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.87996 | −0.743603 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.26580 | −1.76221 | −0.881107 | − | 0.472916i | \(-0.843201\pi\) | ||||
−0.881107 | + | 0.472916i | \(0.843201\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.48709 | −1.25883 | −0.629413 | − | 0.777071i | \(-0.716705\pi\) | ||||
−0.629413 | + | 0.777071i | \(0.716705\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.51547 | −0.524512 | −0.262256 | − | 0.964998i | \(-0.584466\pi\) | ||||
−0.262256 | + | 0.964998i | \(0.584466\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.60713 | 1.27154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.12260 | −1.32263 | −0.661317 | − | 0.750107i | \(-0.730002\pi\) | ||||
−0.661317 | + | 0.750107i | \(0.730002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.51547 | −1.17021 | −0.585106 | − | 0.810957i | \(-0.698947\pi\) | ||||
−0.585106 | + | 0.810957i | \(0.698947\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.22129 | −0.734833 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.90131 | 1.13457 | 0.567284 | − | 0.823522i | \(-0.307994\pi\) | ||||
0.567284 | + | 0.823522i | \(0.307994\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.39724 | −1.02438 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.3199 | 1.76787 | 0.883935 | − | 0.467609i | \(-0.154885\pi\) | ||||
0.883935 | + | 0.467609i | \(0.154885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.31733 | −0.505888 | −0.252944 | − | 0.967481i | \(-0.581399\pi\) | ||||
−0.252944 | + | 0.967481i | \(0.581399\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.29417 | −0.789209 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.36705 | −1.22046 | −0.610230 | − | 0.792224i | \(-0.708923\pi\) | ||||
−0.610230 | + | 0.792224i | \(0.708923\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −20.9252 | −2.93012 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.00437 | −0.962125 | −0.481062 | − | 0.876686i | \(-0.659749\pi\) | ||||
−0.481062 | + | 0.876686i | \(0.659749\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.46575 | 0.197641 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.8026 | −2.09311 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.07107 | 1.18095 | 0.590476 | − | 0.807055i | \(-0.298940\pi\) | ||||
0.590476 | + | 0.807055i | \(0.298940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2143 | −1.43584 | −0.717920 | − | 0.696126i | \(-0.754906\pi\) | ||||
−0.717920 | + | 0.696126i | \(0.754906\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.22129 | 0.275518 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.41240 | 0.783400 | 0.391700 | − | 0.920093i | \(-0.371887\pi\) | ||||
0.391700 | + | 0.920093i | \(0.371887\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.24445 | −0.872130 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5316 | 1.24987 | 0.624935 | − | 0.780677i | \(-0.285125\pi\) | ||||
0.624935 | + | 0.780677i | \(0.285125\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5217 | −1.23147 | −0.615733 | − | 0.787955i | \(-0.711140\pi\) | ||||
−0.615733 | + | 0.787955i | \(0.711140\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.87996 | 0.332549 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.1911 | −1.14659 | −0.573295 | − | 0.819349i | \(-0.694335\pi\) | ||||
−0.573295 | + | 0.819349i | \(0.694335\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.14576 | 0.349529 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.4186 | 1.80217 | 0.901087 | − | 0.433638i | \(-0.142770\pi\) | ||||
0.901087 | + | 0.433638i | \(0.142770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.26580 | 0.788086 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.5128 | −2.19920 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.83024 | −1.04200 | −0.521002 | − | 0.853556i | \(-0.674441\pi\) | ||||
−0.521002 | + | 0.853556i | \(0.674441\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.7643 | −1.94577 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.48709 | 0.562964 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.09423 | 0.212636 | 0.106318 | − | 0.994332i | \(-0.466094\pi\) | ||||
0.106318 | + | 0.994332i | \(0.466094\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.75992 | −0.779901 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6656 | 1.35978 | 0.679889 | − | 0.733315i | \(-0.262028\pi\) | ||||
0.679889 | + | 0.733315i | \(0.262028\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0239 | 0.987685 | 0.493843 | − | 0.869551i | \(-0.335592\pi\) | ||||
0.493843 | + | 0.869551i | \(0.335592\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.42040 | 0.910704 | 0.455352 | − | 0.890311i | \(-0.349513\pi\) | ||||
0.455352 | + | 0.890311i | \(0.349513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.98559 | −0.860663 | −0.430332 | − | 0.902671i | \(-0.641603\pi\) | ||||
−0.430332 | + | 0.902671i | \(0.641603\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.8755 | 1.88650 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9476 | 1.02987 | 0.514933 | − | 0.857231i | \(-0.327817\pi\) | ||||
0.514933 | + | 0.857231i | \(0.327817\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.51547 | 0.234569 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.7599 | −1.08721 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85158 | −0.804690 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 32.6009 | 2.93952 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.44696 | 0.483340 | 0.241670 | − | 0.970359i | \(-0.422305\pi\) | ||||
0.241670 | + | 0.970359i | \(0.422305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.55379 | −0.841164 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.17414 | 0.801548 | 0.400774 | − | 0.916177i | \(-0.368741\pi\) | ||||
0.400774 | + | 0.916177i | \(0.368741\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.60713 | −0.568651 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3137 | 0.966595 | 0.483298 | − | 0.875456i | \(-0.339439\pi\) | ||||
0.483298 | + | 0.875456i | \(0.339439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.83099 | −0.579397 | −0.289698 | − | 0.957118i | \(-0.593555\pi\) | ||||
−0.289698 | + | 0.957118i | \(0.593555\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.0968 | −2.02932 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.25586 | 0.272268 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.12260 | 0.591500 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.96243 | −0.160769 | −0.0803844 | − | 0.996764i | \(-0.525615\pi\) | ||||
−0.0803844 | + | 0.996764i | \(0.525615\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.32511 | 0.596109 | 0.298055 | − | 0.954549i | \(-0.403662\pi\) | ||||
0.298055 | + | 0.954549i | \(0.403662\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −38.4664 | −3.10982 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.51547 | 0.523335 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.46309 | 0.595620 | 0.297810 | − | 0.954625i | \(-0.403744\pi\) | ||||
0.297810 | + | 0.954625i | \(0.403744\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.1723 | −1.59977 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2790 | 0.961767 | 0.480883 | − | 0.876785i | \(-0.340316\pi\) | ||||
0.480883 | + | 0.876785i | \(0.340316\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.22129 | 0.328627 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.2300 | −1.41068 | −0.705342 | − | 0.708868i | \(-0.749206\pi\) | ||||
−0.705342 | + | 0.708868i | \(0.749206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.06585 | −0.620450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29.0496 | −2.22148 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.9245 | −1.36277 | −0.681386 | − | 0.731924i | \(-0.738622\pi\) | ||||
−0.681386 | + | 0.731924i | \(0.738622\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.1243 | 1.96362 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.0375672 | −0.00280791 | −0.00140395 | − | 0.999999i | \(-0.500447\pi\) | ||||
−0.00140395 | + | 0.999999i | \(0.500447\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.82105 | 0.507004 | 0.253502 | − | 0.967335i | \(-0.418417\pi\) | ||||
0.253502 | + | 0.967335i | \(0.418417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −32.2966 | −2.38744 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.90131 | −0.507394 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.6498 | 0.778792 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.86202 | 0.424161 | 0.212080 | − | 0.977252i | \(-0.431976\pi\) | ||||
0.212080 | + | 0.977252i | \(0.431976\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.77168 | −0.343473 | −0.171736 | − | 0.985143i | \(-0.554938\pi\) | ||||
−0.171736 | + | 0.985143i | \(0.554938\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.39724 | 0.458116 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.28714 | −0.661682 | −0.330841 | − | 0.943687i | \(-0.607332\pi\) | ||||
−0.330841 | + | 0.943687i | \(0.607332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.20176 | −0.226967 | −0.113483 | − | 0.993540i | \(-0.536201\pi\) | ||||
−0.113483 | + | 0.993540i | \(0.536201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.4675 | 1.30259 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.3199 | −0.790616 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.3173 | −0.925619 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.04269 | 0.556325 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.1055 | 1.79718 | 0.898590 | − | 0.438790i | \(-0.144593\pi\) | ||||
0.898590 | + | 0.438790i | \(0.144593\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 30.3306 | 2.07822 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.31733 | 0.226240 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −30.3020 | −2.04762 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.1395 | 1.08566 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.8214 | −1.59520 | −0.797599 | − | 0.603188i | \(-0.793897\pi\) | ||||
−0.797599 | + | 0.603188i | \(0.793897\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.29417 | 0.352945 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.42199 | −0.625360 | −0.312680 | − | 0.949859i | \(-0.601227\pi\) | ||||
−0.312680 | + | 0.949859i | \(0.601227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.93587 | −0.656581 | −0.328290 | − | 0.944577i | \(-0.606472\pi\) | ||||
−0.328290 | + | 0.944577i | \(0.606472\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.23707 | 0.0810434 | 0.0405217 | − | 0.999179i | \(-0.487098\pi\) | ||||
0.0405217 | + | 0.999179i | \(0.487098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.36705 | 0.545806 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29.3500 | −1.90649 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.05710 | −0.0683782 | −0.0341891 | − | 0.999415i | \(-0.510885\pi\) | ||||
−0.0341891 | + | 0.999415i | \(0.510885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.52903 | −0.291741 | −0.145870 | − | 0.989304i | \(-0.546598\pi\) | ||||
−0.145870 | + | 0.989304i | \(0.546598\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.7617 | −0.690366 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1885 | 0.775533 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 47.2849 | 2.99656 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.74198 | 0.299311 | 0.149656 | − | 0.988738i | \(-0.452184\pi\) | ||||
0.149656 | + | 0.988738i | \(0.452184\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.68704 | 0.231802 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.9252 | 1.31039 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.9297 | −0.993666 | −0.496833 | − | 0.867846i | \(-0.665504\pi\) | ||||
−0.496833 | + | 0.867846i | \(0.665504\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −37.7083 | −2.33408 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.2746 | 0.818549 | 0.409275 | − | 0.912411i | \(-0.365782\pi\) | ||||
0.409275 | + | 0.912411i | \(0.365782\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.00437 | 0.430275 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.3107 | −1.73259 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.8601 | −1.51575 | −0.757874 | − | 0.652401i | \(-0.773762\pi\) | ||||
−0.757874 | + | 0.652401i | \(0.773762\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.4285 | −1.84840 | −0.924201 | − | 0.381907i | \(-0.875267\pi\) | ||||
−0.924201 | + | 0.381907i | \(0.875267\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.46575 | −0.0883879 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.7297 | −1.30561 | −0.652807 | − | 0.757525i | \(-0.726409\pi\) | ||||
−0.652807 | + | 0.757525i | \(0.726409\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −34.4940 | −2.06510 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.285426 | −0.0170271 | −0.00851354 | − | 0.999964i | \(-0.502710\pi\) | ||||
−0.00851354 | + | 0.999964i | \(0.502710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.51463 | 0.327810 | 0.163905 | − | 0.986476i | \(-0.447591\pi\) | ||||
0.163905 | + | 0.986476i | \(0.447591\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.8026 | 0.936066 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.7918 | 2.10540 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.03129 | 0.353560 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.5777 | −1.02690 | −0.513450 | − | 0.858120i | \(-0.671633\pi\) | ||||
−0.513450 | + | 0.858120i | \(0.671633\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.07107 | −0.528138 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.68439 | −0.561945 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.58760 | 0.323139 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 39.3564 | 2.26097 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.2143 | 0.642127 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.4771 | −1.45405 | −0.727026 | − | 0.686610i | \(-0.759098\pi\) | ||||
−0.727026 | + | 0.686610i | \(0.759098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.8685 | 1.64227 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.5662 | 1.22290 | 0.611452 | − | 0.791281i | \(-0.290586\pi\) | ||||
0.611452 | + | 0.791281i | \(0.290586\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.97940 | −0.168406 | −0.0842030 | − | 0.996449i | \(-0.526834\pi\) | ||||
−0.0842030 | + | 0.996449i | \(0.526834\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.99638 | −0.449121 | −0.224561 | − | 0.974460i | \(-0.572095\pi\) | ||||
−0.224561 | + | 0.974460i | \(0.572095\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4399 | 0.584524 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.1304 | 1.51427 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.8681 | 2.21832 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.22129 | −0.123215 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −25.8781 | −1.43106 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.2966 | −1.88511 | −0.942557 | − | 0.334045i | \(-0.891586\pi\) | ||||
−0.942557 | + | 0.334045i | \(0.891586\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 36.5367 | 2.00220 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.41240 | −0.350347 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8719 | 1.30038 | 0.650192 | − | 0.759770i | \(-0.274689\pi\) | ||||
0.650192 | + | 0.759770i | \(0.274689\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.5287 | 1.71241 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.55003 | 0.517163 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.24445 | 0.390028 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.35565 | −0.341189 | −0.170595 | − | 0.985341i | \(-0.554569\pi\) | ||||
−0.170595 | + | 0.985341i | \(0.554569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.24821 | 0.495045 | 0.247523 | − | 0.968882i | \(-0.420384\pi\) | ||||
0.247523 | + | 0.968882i | \(0.420384\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.6764 | −0.783368 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.9608 | −0.955959 | −0.477979 | − | 0.878371i | \(-0.658631\pi\) | ||||
−0.477979 | + | 0.878371i | \(0.658631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.5316 | −0.558959 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.2843 | 1.07056 | 0.535281 | − | 0.844674i | \(-0.320206\pi\) | ||||
0.535281 | + | 0.844674i | \(0.320206\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.1082 | 0.584642 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.4922 | −1.33799 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.5217 | 0.550729 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.1439 | 1.31250 | 0.656249 | − | 0.754544i | \(-0.272142\pi\) | ||||
0.656249 | + | 0.754544i | \(0.272142\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 59.9295 | 3.11980 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.737732 | 0.0381983 | 0.0190992 | − | 0.999818i | \(-0.493920\pi\) | ||||
0.0190992 | + | 0.999818i | \(0.493920\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.87996 | −0.148721 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.8214 | 0.814843 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.11120 | 0.365278 | 0.182639 | − | 0.983180i | \(-0.441536\pi\) | ||||
0.182639 | + | 0.983180i | \(0.441536\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.6870 | 0.803672 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.6842 | 1.46569 | 0.732846 | − | 0.680394i | \(-0.238191\pi\) | ||||
0.732846 | + | 0.680394i | \(0.238191\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.5625 | −0.892754 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.5189 | 0.685434 | 0.342717 | − | 0.939439i | \(-0.388653\pi\) | ||||
0.342717 | + | 0.939439i | \(0.388653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.2769 | 0.924302 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.4212 | 1.33277 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.1911 | 0.512770 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.02391 | −0.201954 | −0.100977 | − | 0.994889i | \(-0.532197\pi\) | ||||
−0.100977 | + | 0.994889i | \(0.532197\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.3796 | −1.21746 | −0.608729 | − | 0.793379i | \(-0.708320\pi\) | ||||
−0.608729 | + | 0.793379i | \(0.708320\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.4728 | 0.720940 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.14576 | −0.156314 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.1156 | −0.501410 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.49522 | −0.420062 | −0.210031 | − | 0.977695i | \(-0.567356\pi\) | ||||
−0.210031 | + | 0.977695i | \(0.567356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.5830 | 1.60720 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.4186 | −0.805957 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.6730 | −0.963390 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.07469 | 0.150209 | 0.0751043 | − | 0.997176i | \(-0.476071\pi\) | ||||
0.0751043 | + | 0.997176i | \(0.476071\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.4790 | 1.09556 | 0.547780 | − | 0.836623i | \(-0.315473\pi\) | ||||
0.547780 | + | 0.836623i | \(0.315473\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −44.2966 | −2.15378 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.26580 | −0.352443 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.37674 | 0.452713 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.17254 | 0.249153 | 0.124576 | − | 0.992210i | \(-0.460243\pi\) | ||||
0.124576 | + | 0.992210i | \(0.460243\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.78030 | −0.0855557 | −0.0427779 | − | 0.999085i | \(-0.513621\pi\) | ||||
−0.0427779 | + | 0.999085i | \(0.513621\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.5128 | 0.983514 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.8026 | 0.660269 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.7865 | −1.23072 | −0.615361 | − | 0.788245i | \(-0.710990\pi\) | ||||
−0.615361 | + | 0.788245i | \(0.710990\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.4426 | 0.591165 | 0.295583 | − | 0.955317i | \(-0.404486\pi\) | ||||
0.295583 | + | 0.955317i | \(0.404486\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.83024 | 0.465998 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.65173 | −0.267318 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.3574 | −1.19669 | −0.598344 | − | 0.801239i | \(-0.704174\pi\) | ||||
−0.598344 | + | 0.801239i | \(0.704174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.5921 | −0.781292 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.0960 | 0.991178 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.7039 | −1.62338 | −0.811690 | − | 0.584088i | \(-0.801452\pi\) | ||||
−0.811690 | + | 0.584088i | \(0.801452\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −48.0061 | −2.24073 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.8762 | 1.90380 | 0.951898 | − | 0.306414i | \(-0.0991293\pi\) | ||||
0.951898 | + | 0.306414i | \(0.0991293\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.1236 | 1.16759 | 0.583796 | − | 0.811901i | \(-0.301567\pi\) | ||||
0.583796 | + | 0.811901i | \(0.301567\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.7643 | 0.870173 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.1766 | −1.25758 | −0.628792 | − | 0.777574i | \(-0.716450\pi\) | ||||
−0.628792 | + | 0.777574i | \(0.716450\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.4934 | 0.990364 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.86237 | 0.223572 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.48709 | −0.251765 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −37.0824 | −1.69789 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.07288 | −0.0947123 | −0.0473561 | − | 0.998878i | \(-0.515080\pi\) | ||||
−0.0473561 | + | 0.998878i | \(0.515080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.3298 | −0.698980 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.09423 | −0.0950939 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.3490 | −1.51119 | −0.755594 | − | 0.655040i | \(-0.772652\pi\) | ||||
−0.755594 | + | 0.655040i | \(0.772652\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 35.3631 | 1.59917 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.4487 | −1.64491 | −0.822453 | − | 0.568833i | \(-0.807395\pi\) | ||||
−0.822453 | + | 0.568833i | \(0.807395\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 51.7514 | 2.33077 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.75992 | 0.348783 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.49368 | 0.335463 | 0.167732 | − | 0.985833i | \(-0.446356\pi\) | ||||
0.167732 | + | 0.985833i | \(0.446356\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −52.5018 | −2.34561 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6381 | −0.697267 | −0.348634 | − | 0.937259i | \(-0.613354\pi\) | ||||
−0.348634 | + | 0.937259i | \(0.613354\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.6656 | −0.608111 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.2293 | −1.03165 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.21051 | −0.319600 | −0.159800 | − | 0.987149i | \(-0.551085\pi\) | ||||
−0.159800 | + | 0.987149i | \(0.551085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −36.2540 | −1.60065 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.0239 | −0.441706 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2640 | 0.539370 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −51.6218 | −2.26594 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8236 | −0.649434 | −0.324717 | − | 0.945811i | \(-0.605269\pi\) | ||||
−0.324717 | + | 0.945811i | \(0.605269\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.27283 | −0.186838 | −0.0934189 | − | 0.995627i | \(-0.529780\pi\) | ||||
−0.0934189 | + | 0.995627i | \(0.529780\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.3401 | 2.06217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6724 | −0.724888 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 48.0238 | 2.08406 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.1448 | −1.08914 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.42040 | −0.407279 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.108192 | −0.00466883 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.942899 | −0.0405384 | −0.0202692 | − | 0.999795i | \(-0.506452\pi\) | ||||
−0.0202692 | + | 0.999795i | \(0.506452\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.6444 | 0.843020 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.98559 | 0.384900 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.1871 | 0.478327 | 0.239164 | − | 0.970979i | \(-0.423127\pi\) | ||||
0.239164 | + | 0.970979i | \(0.423127\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −59.3703 | −2.53386 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 39.0824 | 1.66497 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.8755 | −0.843668 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.7305 | 1.21735 | 0.608675 | − | 0.793420i | \(-0.291701\pi\) | ||||
0.608675 | + | 0.793420i | \(0.291701\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.36877 | 0.311666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.6711 | 1.29493 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.44741 | 0.103146 | 0.0515729 | − | 0.998669i | \(-0.483577\pi\) | ||||
0.0515729 | + | 0.998669i | \(0.483577\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.9476 | −0.460570 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.5058 | 1.48848 | 0.744240 | − | 0.667912i | \(-0.232812\pi\) | ||||
0.744240 | + | 0.667912i | \(0.232812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.78874 | −0.242251 | −0.121126 | − | 0.992637i | \(-0.538650\pi\) | ||||
−0.121126 | + | 0.992637i | \(0.538650\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.8824 | 0.705272 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.51547 | −0.104902 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.20773 | −0.0919090 | −0.0459545 | − | 0.998944i | \(-0.514633\pi\) | ||||
−0.0459545 | + | 0.998944i | \(0.514633\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.7422 | −0.571108 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.2666 | 0.425201 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.7599 | 0.486213 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.6719 | 1.63744 | 0.818718 | − | 0.574196i | \(-0.194685\pi\) | ||||
0.818718 | + | 0.574196i | \(0.194685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.7510 | 1.47309 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.7466 | −1.10021 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.93309 | 0.366838 | 0.183419 | − | 0.983035i | \(-0.441283\pi\) | ||||
0.183419 | + | 0.983035i | \(0.441283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.22095 | −0.377388 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.3900 | −0.751395 | −0.375697 | − | 0.926742i | \(-0.622597\pi\) | ||||
−0.375697 | + | 0.926742i | \(0.622597\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5063 | −0.714096 | −0.357048 | − | 0.934086i | \(-0.616217\pi\) | ||||
−0.357048 | + | 0.934086i | \(0.616217\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.9484 | 1.38248 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.85158 | 0.359868 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.1439 | −1.83233 | −0.916166 | − | 0.400798i | \(-0.868733\pi\) | ||||
−0.916166 | + | 0.400798i | \(0.868733\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.5857 | 0.751897 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.8557 | −0.478849 | −0.239424 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239424 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −32.6009 | −1.31459 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.8174 | −0.838078 | −0.419039 | − | 0.907968i | \(-0.637633\pi\) | ||||
−0.419039 | + | 0.907968i | \(0.637633\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.78149 | −0.352958 | −0.176479 | − | 0.984304i | \(-0.556471\pi\) | ||||
−0.176479 | + | 0.984304i | \(0.556471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.6200 | −0.666939 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.1626 | 0.925027 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.1435 | −1.99935 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.1004 | −0.879803 | −0.439902 | − | 0.898046i | \(-0.644987\pi\) | ||||
−0.439902 | + | 0.898046i | \(0.644987\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 75.1829 | 2.98825 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.44696 | −0.216156 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 55.7561 | 2.20568 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.8577 | −1.73227 | −0.866137 | − | 0.499807i | \(-0.833404\pi\) | ||||
−0.866137 | + | 0.499807i | \(0.833404\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.9895 | 1.49816 | 0.749079 | − | 0.662480i | \(-0.230496\pi\) | ||||
0.749079 | + | 0.662480i | \(0.230496\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.55379 | 0.376180 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.3705 | 1.31193 | 0.655964 | − | 0.754792i | \(-0.272262\pi\) | ||||
0.655964 | + | 0.754792i | \(0.272262\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.2959 | −0.521909 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.0632 | 0.589468 | 0.294734 | − | 0.955579i | \(-0.404769\pi\) | ||||
0.294734 | + | 0.955579i | \(0.404769\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.17414 | −0.358463 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −55.7035 | −2.17320 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.153540 | 0.00598106 | 0.00299053 | − | 0.999996i | \(-0.499048\pi\) | ||||
0.00299053 | + | 0.999996i | \(0.499048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.3056 | −0.478632 | −0.239316 | − | 0.970942i | \(-0.576923\pi\) | ||||
−0.239316 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 46.4811 | 1.80518 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.9167 | 0.693737 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −68.6047 | −2.65241 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.4373 | 0.634554 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.82480 | 0.185983 | 0.0929913 | − | 0.995667i | \(-0.470357\pi\) | ||||
0.0929913 | + | 0.995667i | \(0.470357\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.60713 | 0.254309 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.5041 | −0.634303 | −0.317151 | − | 0.948375i | \(-0.602726\pi\) | ||||
−0.317151 | + | 0.948375i | \(0.602726\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.1350 | −1.03981 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.3621 | −1.23830 | −0.619152 | − | 0.785272i | \(-0.712523\pi\) | ||||
−0.619152 | + | 0.785272i | \(0.712523\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.3137 | −0.432275 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.6149 | −1.09173 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.5588 | 0.592742 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.32446 | 0.0884265 | 0.0442132 | − | 0.999022i | \(-0.485922\pi\) | ||||
0.0442132 | + | 0.999022i | \(0.485922\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.83099 | 0.259114 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −82.2481 | −3.11537 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.56272 | 0.134755 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.77071 | −0.255726 | −0.127863 | − | 0.991792i | \(-0.540812\pi\) | ||||
−0.127863 | + | 0.991792i | \(0.540812\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.8681 | −1.42822 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.0968 | 0.907538 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.23742 | −0.234251 | −0.117126 | − | 0.993117i | \(-0.537368\pi\) | ||||
−0.117126 | + | 0.993117i | \(0.537368\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −53.9535 | −2.02341 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.3895 | 0.613790 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.25586 | −0.121762 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.04441 | −0.113696 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.94931 | 0.184578 | 0.0922891 | − | 0.995732i | \(-0.470582\pi\) | ||||
0.0922891 | + | 0.995732i | \(0.470582\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.0434 | −0.485091 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.12260 | −0.264527 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.5847 | −0.689269 | −0.344635 | − | 0.938737i | \(-0.611997\pi\) | ||||
−0.344635 | + | 0.938737i | \(0.611997\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.4306 | −1.49743 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.1031 | 0.891484 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5696 | 0.907498 | 0.453749 | − | 0.891130i | \(-0.350086\pi\) | ||||
0.453749 | + | 0.891130i | \(0.350086\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.39896 | −0.346215 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.42950 | 0.310084 | 0.155042 | − | 0.987908i | \(-0.450449\pi\) | ||||
0.155042 | + | 0.987908i | \(0.450449\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.1023 | 1.28951 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.4705 | 0.420811 | 0.210405 | − | 0.977614i | \(-0.432522\pi\) | ||||
0.210405 | + | 0.977614i | \(0.432522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.96243 | 0.0718980 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 86.9229 | 3.18034 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.3029 | 0.594902 | 0.297451 | − | 0.954737i | \(-0.403863\pi\) | ||||
0.297451 | + | 0.954737i | \(0.403863\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.6567 | 0.497679 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.32511 | −0.266588 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0875 | 0.911821 | 0.455910 | − | 0.890026i | \(-0.349314\pi\) | ||||
0.455910 | + | 0.890026i | \(0.349314\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.6185 | 0.385428 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.0849 | −1.77933 | −0.889664 | − | 0.456616i | \(-0.849061\pi\) | ||||
−0.889664 | + | 0.456616i | \(0.849061\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 38.4664 | 1.39076 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.1495 | −0.727557 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.0548 | 0.975619 | 0.487810 | − | 0.872950i | \(-0.337796\pi\) | ||||
0.487810 | + | 0.872950i | \(0.337796\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.8769 | −1.65221 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.0828 | 1.47764 | 0.738822 | − | 0.673900i | \(-0.235382\pi\) | ||||
0.738822 | + | 0.673900i | \(0.235382\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.51547 | −0.234043 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −62.1133 | −2.22544 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.4367 | −0.552367 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −47.0600 | −1.68179 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.46309 | −0.266369 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.7475 | −0.703921 | −0.351960 | − | 0.936015i | \(-0.614485\pi\) | ||||
−0.351960 | + | 0.936015i | \(0.614485\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38.2304 | 1.36104 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.9102 | 0.884587 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.1723 | 0.715439 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.9488 | 1.27337 | 0.636685 | − | 0.771124i | \(-0.280305\pi\) | ||||
0.636685 | + | 0.771124i | \(0.280305\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.7933 | 2.15071 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −52.0430 | −1.83885 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.4221 | 0.544234 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −71.5962 | −2.52030 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.1137 | 1.37516 | 0.687582 | − | 0.726107i | \(-0.258672\pi\) | ||||
0.687582 | + | 0.726107i | \(0.258672\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.4017 | 1.52404 | 0.762019 | − | 0.647555i | \(-0.224208\pi\) | ||||
0.762019 | + | 0.647555i | \(0.224208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −87.6330 | −3.07342 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.2790 | −0.430115 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.2025 | 0.636825 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.0135 | 0.454175 | 0.227088 | − | 0.973874i | \(-0.427080\pi\) | ||||
0.227088 | + | 0.973874i | \(0.427080\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0590066 | 0.00205684 | 0.00102842 | − | 0.999999i | \(-0.499673\pi\) | ||||
0.00102842 | + | 0.999999i | \(0.499673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.22129 | −0.146967 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.519093 | −0.0180506 | −0.00902531 | − | 0.999959i | \(-0.502873\pi\) | ||||
−0.00902531 | + | 0.999959i | \(0.502873\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.1574 | −1.74204 | −0.871019 | − | 0.491250i | \(-0.836540\pi\) | ||||
−0.871019 | + | 0.491250i | \(0.836540\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −62.5808 | −2.17090 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.2300 | 0.630877 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43.0486 | −1.48798 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.44696 | 0.326145 | 0.163073 | − | 0.986614i | \(-0.447859\pi\) | ||||
0.163073 | + | 0.986614i | \(0.447859\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.7315 | 0.749360 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.822016 | −0.0283117 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.06585 | 0.277474 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.8819 | 0.545066 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.3600 | −0.595094 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.2482 | −0.727525 | −0.363762 | − | 0.931492i | \(-0.618508\pi\) | ||||
−0.363762 | + | 0.931492i | \(0.618508\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.0496 | 0.993476 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.56435 | −0.224234 | −0.112117 | − | 0.993695i | \(-0.535763\pi\) | ||||
−0.112117 | + | 0.993695i | \(0.535763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.2506 | 0.725062 | 0.362531 | − | 0.931972i | \(-0.381913\pi\) | ||||
0.362531 | + | 0.931972i | \(0.381913\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.43459 | 0.0488341 | 0.0244170 | − | 0.999702i | \(-0.492227\pi\) | ||||
0.0244170 | + | 0.999702i | \(0.492227\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.9245 | 0.609450 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 103.079 | 3.50075 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.9376 | 0.506723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.2438 | −0.482634 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.0872 | 0.375245 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.6039 | 0.763280 | 0.381640 | − | 0.924311i | \(-0.375359\pi\) | ||||
0.381640 | + | 0.924311i | \(0.375359\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −50.6231 | −1.70747 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.2167 | −0.849572 | −0.424786 | − | 0.905294i | \(-0.639651\pi\) | ||||
−0.424786 | + | 0.905294i | \(0.639651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.0869 | 1.41634 | 0.708168 | − | 0.706044i | \(-0.249522\pi\) | ||||
0.708168 | + | 0.706044i | \(0.249522\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.1243 | −0.878159 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.0721 | 0.774686 | 0.387343 | − | 0.921936i | \(-0.373393\pi\) | ||||
0.387343 | + | 0.921936i | \(0.373393\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.61089 | −0.154471 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.9108 | 1.53635 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0375672 | 0.00125573 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0921 | 0.537298 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.4071 | 1.54776 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.8924 | 1.69547 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.82105 | −0.226739 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.3923 | −0.743525 | −0.371763 | − | 0.928328i | \(-0.621246\pi\) | ||||
−0.371763 | + | 0.928328i | \(0.621246\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 72.3481 | 2.39963 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.7584 | 1.81423 | 0.907114 | − | 0.420886i | \(-0.138281\pi\) | ||||
0.907114 | + | 0.420886i | \(0.138281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0655 | −0.796452 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.2966 | 1.06769 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.0590 | −1.84922 | −0.924608 | − | 0.380919i | \(-0.875608\pi\) | ||||
−0.924608 | + | 0.380919i | \(0.875608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −73.3729 | −2.41772 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.3938 | −0.770016 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.90131 | 0.226914 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 53.0683 | 1.74299 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.5879 | −1.23322 | −0.616610 | − | 0.787269i | \(-0.711494\pi\) | ||||
−0.616610 | + | 0.787269i | \(0.711494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 62.1097 | 2.03338 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.6498 | −0.348286 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.4322 | 1.81089 | 0.905446 | − | 0.424461i | \(-0.139536\pi\) | ||||
0.905446 | + | 0.424461i | \(0.139536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.58057 | −0.280016 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.1539 | −0.494003 | −0.247001 | − | 0.969015i | \(-0.579445\pi\) | ||||
−0.247001 | + | 0.969015i | \(0.579445\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.4748 | −0.927269 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.6907 | 0.639861 | 0.319930 | − | 0.947441i | \(-0.396340\pi\) | ||||
0.319930 | + | 0.947441i | \(0.396340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.3717 | 0.758677 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.0293 | −0.746775 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.8194 | 1.45184 | 0.725921 | − | 0.687778i | \(-0.241414\pi\) | ||||
0.725921 | + | 0.687778i | \(0.241414\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.86202 | −0.189691 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.0666 | 0.971915 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.4513 | 0.369398 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 49.8732 | 1.60714 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.77168 | 0.153606 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.3195 | −1.03932 | −0.519662 | − | 0.854372i | \(-0.673942\pi\) | ||||
−0.519662 | + | 0.854372i | \(0.673942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 114.819 | 3.68851 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.5807 | 0.403733 | 0.201866 | − | 0.979413i | \(-0.435299\pi\) | ||||
0.201866 | + | 0.979413i | \(0.435299\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.39724 | −0.204876 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.1169 | 1.34744 | 0.673720 | − | 0.738987i | \(-0.264695\pi\) | ||||
0.673720 | + | 0.738987i | \(0.264695\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.4086 | 0.460502 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −47.5713 | −1.51883 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.7102 | 0.851923 | 0.425962 | − | 0.904741i | \(-0.359936\pi\) | ||||
0.425962 | + | 0.904741i | \(0.359936\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.28714 | 0.295913 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.34465 | 0.265344 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.44903 | 0.236626 | 0.118313 | − | 0.992976i | \(-0.462251\pi\) | ||||
0.118313 | + | 0.992976i | \(0.462251\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −98.7730 | −3.13447 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.20176 | 0.101503 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.9068 | −1.70724 | −0.853622 | − | 0.520892i | \(-0.825599\pi\) | ||||
−0.853622 | + | 0.520892i | \(0.825599\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.5978 | 1.44265 |
(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 | 3920.2.a.ce.1.4 | 4 | ||
4.3 | odd | 2 | 1960.2.a.x.1.1 | ✓ | 4 | ||
7.6 | odd | 2 | 3920.2.a.cd.1.1 | 4 | |||
20.19 | odd | 2 | 9800.2.a.cs.1.4 | 4 | |||
28.3 | even | 6 | 1960.2.q.x.961.1 | 8 | |||
28.11 | odd | 6 | 1960.2.q.y.961.4 | 8 | |||
28.19 | even | 6 | 1960.2.q.x.361.1 | 8 | |||
28.23 | odd | 6 | 1960.2.q.y.361.4 | 8 | |||
28.27 | even | 2 | 1960.2.a.y.1.4 | yes | 4 | ||
140.139 | even | 2 | 9800.2.a.cl.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.x.1.1 | ✓ | 4 | 4.3 | odd | 2 | ||
1960.2.a.y.1.4 | yes | 4 | 28.27 | even | 2 | ||
1960.2.q.x.361.1 | 8 | 28.19 | even | 6 | |||
1960.2.q.x.961.1 | 8 | 28.3 | even | 6 | |||
1960.2.q.y.361.4 | 8 | 28.23 | odd | 6 | |||
1960.2.q.y.961.4 | 8 | 28.11 | odd | 6 | |||
3920.2.a.cd.1.1 | 4 | 7.6 | odd | 2 | |||
3920.2.a.ce.1.4 | 4 | 1.1 | even | 1 | trivial | ||
9800.2.a.cl.1.1 | 4 | 140.139 | even | 2 | |||
9800.2.a.cs.1.4 | 4 | 20.19 | odd | 2 |