Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.684852 | 0.484263 | 0.242132 | − | 0.970243i | \(-0.422153\pi\) | ||||
0.242132 | + | 0.970243i | \(0.422153\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.53098 | −0.765489 | ||||||||
\(5\) | 0.182709 | 0.0817100 | 0.0408550 | − | 0.999165i | \(-0.486992\pi\) | ||||
0.0408550 | + | 0.999165i | \(0.486992\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.41820 | −0.854962 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.125129 | 0.0395692 | ||||||||
\(11\) | −4.23638 | −1.27732 | −0.638658 | − | 0.769491i | \(-0.720510\pi\) | ||||
−0.638658 | + | 0.769491i | \(0.720510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.25646 | 0.903179 | 0.451589 | − | 0.892226i | \(-0.350857\pi\) | ||||
0.451589 | + | 0.892226i | \(0.350857\pi\) | |||||||
\(14\) | 0.684852 | 0.183034 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.40585 | 0.351462 | ||||||||
\(17\) | 2.73216 | 0.662646 | 0.331323 | − | 0.943517i | \(-0.392505\pi\) | ||||
0.331323 | + | 0.943517i | \(0.392505\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.66272 | 1.29912 | 0.649558 | − | 0.760312i | \(-0.274954\pi\) | ||||
0.649558 | + | 0.760312i | \(0.274954\pi\) | |||||||
\(20\) | −0.279724 | −0.0625481 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.90129 | −0.618557 | ||||||||
\(23\) | −3.08998 | −0.644306 | −0.322153 | − | 0.946688i | \(-0.604407\pi\) | ||||
−0.322153 | + | 0.946688i | \(0.604407\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96662 | −0.993323 | ||||||||
\(26\) | 2.23019 | 0.437376 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.53098 | −0.289328 | ||||||||
\(29\) | 6.70003 | 1.24417 | 0.622083 | − | 0.782952i | \(-0.286287\pi\) | ||||
0.622083 | + | 0.782952i | \(0.286287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.55396 | −1.71594 | −0.857971 | − | 0.513698i | \(-0.828275\pi\) | ||||
−0.857971 | + | 0.513698i | \(0.828275\pi\) | |||||||
\(32\) | 5.79919 | 1.02516 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.87112 | 0.320895 | ||||||||
\(35\) | 0.182709 | 0.0308835 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.75698 | −1.27524 | −0.637620 | − | 0.770351i | \(-0.720081\pi\) | ||||
−0.637620 | + | 0.770351i | \(0.720081\pi\) | |||||||
\(38\) | 3.87812 | 0.629115 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.441827 | −0.0698590 | ||||||||
\(41\) | −0.852638 | −0.133160 | −0.0665798 | − | 0.997781i | \(-0.521209\pi\) | ||||
−0.0665798 | + | 0.997781i | \(0.521209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.16565 | −1.24525 | −0.622625 | − | 0.782521i | \(-0.713934\pi\) | ||||
−0.622625 | + | 0.782521i | \(0.713934\pi\) | |||||||
\(44\) | 6.48580 | 0.977771 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.11618 | −0.312014 | ||||||||
\(47\) | −5.27194 | −0.768991 | −0.384496 | − | 0.923127i | \(-0.625625\pi\) | ||||
−0.384496 | + | 0.923127i | \(0.625625\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.40140 | −0.481030 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.98556 | −0.691373 | ||||||||
\(53\) | 5.94870 | 0.817116 | 0.408558 | − | 0.912732i | \(-0.366032\pi\) | ||||
0.408558 | + | 0.912732i | \(0.366032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.774025 | −0.104370 | ||||||||
\(56\) | −2.41820 | −0.323145 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.58853 | 0.602504 | ||||||||
\(59\) | 7.70514 | 1.00312 | 0.501562 | − | 0.865122i | \(-0.332759\pi\) | ||||
0.501562 | + | 0.865122i | \(0.332759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.28184 | −0.932345 | −0.466172 | − | 0.884694i | \(-0.654367\pi\) | ||||
−0.466172 | + | 0.884694i | \(0.654367\pi\) | |||||||
\(62\) | −6.54305 | −0.830968 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.15989 | 0.144986 | ||||||||
\(65\) | 0.594985 | 0.0737988 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.52437 | 1.04142 | 0.520709 | − | 0.853734i | \(-0.325668\pi\) | ||||
0.520709 | + | 0.853734i | \(0.325668\pi\) | |||||||
\(68\) | −4.18288 | −0.507248 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.125129 | 0.0149557 | ||||||||
\(71\) | 7.08011 | 0.840254 | 0.420127 | − | 0.907465i | \(-0.361986\pi\) | ||||
0.420127 | + | 0.907465i | \(0.361986\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.43264 | −0.167678 | −0.0838388 | − | 0.996479i | \(-0.526718\pi\) | ||||
−0.0838388 | + | 0.996479i | \(0.526718\pi\) | |||||||
\(74\) | −5.31238 | −0.617552 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.66950 | −0.994459 | ||||||||
\(77\) | −4.23638 | −0.482780 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5663 | 1.41382 | 0.706910 | − | 0.707303i | \(-0.250089\pi\) | ||||
0.706910 | + | 0.707303i | \(0.250089\pi\) | |||||||
\(80\) | 0.256862 | 0.0287180 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.583930 | −0.0644843 | ||||||||
\(83\) | 11.1087 | 1.21934 | 0.609670 | − | 0.792655i | \(-0.291302\pi\) | ||||
0.609670 | + | 0.792655i | \(0.291302\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.499191 | 0.0541448 | ||||||||
\(86\) | −5.59226 | −0.603029 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.2444 | 1.09206 | ||||||||
\(89\) | 9.91467 | 1.05095 | 0.525476 | − | 0.850808i | \(-0.323887\pi\) | ||||
0.525476 | + | 0.850808i | \(0.323887\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.25646 | 0.341369 | ||||||||
\(92\) | 4.73069 | 0.493209 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.61050 | −0.372394 | ||||||||
\(95\) | 1.03463 | 0.106151 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.39495 | −0.750843 | −0.375422 | − | 0.926854i | \(-0.622502\pi\) | ||||
−0.375422 | + | 0.926854i | \(0.622502\pi\) | |||||||
\(98\) | 0.684852 | 0.0691805 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.60378 | 0.760378 | ||||||||
\(101\) | −12.5594 | −1.24971 | −0.624853 | − | 0.780742i | \(-0.714841\pi\) | ||||
−0.624853 | + | 0.780742i | \(0.714841\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.37085 | −0.135074 | −0.0675369 | − | 0.997717i | \(-0.521514\pi\) | ||||
−0.0675369 | + | 0.997717i | \(0.521514\pi\) | |||||||
\(104\) | −7.87475 | −0.772183 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.07398 | 0.395700 | ||||||||
\(107\) | −7.25917 | −0.701771 | −0.350885 | − | 0.936418i | \(-0.614119\pi\) | ||||
−0.350885 | + | 0.936418i | \(0.614119\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.47375 | 0.524290 | 0.262145 | − | 0.965028i | \(-0.415570\pi\) | ||||
0.262145 | + | 0.965028i | \(0.415570\pi\) | |||||||
\(110\) | −0.530093 | −0.0505423 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.40585 | 0.132840 | ||||||||
\(113\) | 6.45405 | 0.607146 | 0.303573 | − | 0.952808i | \(-0.401820\pi\) | ||||
0.303573 | + | 0.952808i | \(0.401820\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.564568 | −0.0526463 | ||||||||
\(116\) | −10.2576 | −0.952395 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.27688 | 0.485776 | ||||||||
\(119\) | 2.73216 | 0.250457 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.94689 | 0.631536 | ||||||||
\(122\) | −4.98698 | −0.451500 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.6269 | 1.31354 | ||||||||
\(125\) | −1.82099 | −0.162875 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −10.8040 | −0.954951 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.407476 | 0.0357380 | ||||||||
\(131\) | −19.0900 | −1.66790 | −0.833951 | − | 0.551839i | \(-0.813926\pi\) | ||||
−0.833951 | + | 0.551839i | \(0.813926\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.66272 | 0.491020 | ||||||||
\(134\) | 5.83793 | 0.504321 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.60690 | −0.566537 | ||||||||
\(137\) | −8.01951 | −0.685153 | −0.342576 | − | 0.939490i | \(-0.611300\pi\) | ||||
−0.342576 | + | 0.939490i | \(0.611300\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3101 | −0.959306 | −0.479653 | − | 0.877458i | \(-0.659237\pi\) | ||||
−0.479653 | + | 0.877458i | \(0.659237\pi\) | |||||||
\(140\) | −0.279724 | −0.0236410 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.84882 | 0.406904 | ||||||||
\(143\) | −13.7956 | −1.15364 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.22416 | 0.101661 | ||||||||
\(146\) | −0.981145 | −0.0812001 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.8758 | 0.976182 | ||||||||
\(149\) | 1.63779 | 0.134173 | 0.0670866 | − | 0.997747i | \(-0.478630\pi\) | ||||
0.0670866 | + | 0.997747i | \(0.478630\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.2446 | −1.72886 | −0.864429 | − | 0.502756i | \(-0.832320\pi\) | ||||
−0.864429 | + | 0.502756i | \(0.832320\pi\) | |||||||
\(152\) | −13.6936 | −1.11069 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.90129 | −0.233793 | ||||||||
\(155\) | −1.74560 | −0.140210 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.3492 | −1.30481 | −0.652405 | − | 0.757870i | \(-0.726240\pi\) | ||||
−0.652405 | + | 0.757870i | \(0.726240\pi\) | |||||||
\(158\) | 8.60606 | 0.684661 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.05957 | 0.0837660 | ||||||||
\(161\) | −3.08998 | −0.243525 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.20865 | 0.721277 | 0.360638 | − | 0.932706i | \(-0.382559\pi\) | ||||
0.360638 | + | 0.932706i | \(0.382559\pi\) | |||||||
\(164\) | 1.30537 | 0.101932 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.60782 | 0.590482 | ||||||||
\(167\) | −11.5029 | −0.890120 | −0.445060 | − | 0.895501i | \(-0.646818\pi\) | ||||
−0.445060 | + | 0.895501i | \(0.646818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.39549 | −0.184268 | ||||||||
\(170\) | 0.341872 | 0.0262204 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.5014 | 0.953225 | ||||||||
\(173\) | 23.7780 | 1.80781 | 0.903903 | − | 0.427737i | \(-0.140689\pi\) | ||||
0.903903 | + | 0.427737i | \(0.140689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.96662 | −0.375441 | ||||||||
\(176\) | −5.95571 | −0.448928 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.79008 | 0.508938 | ||||||||
\(179\) | −19.0210 | −1.42169 | −0.710846 | − | 0.703347i | \(-0.751688\pi\) | ||||
−0.710846 | + | 0.703347i | \(0.751688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1013 | −0.825151 | −0.412575 | − | 0.910923i | \(-0.635371\pi\) | ||||
−0.412575 | + | 0.910923i | \(0.635371\pi\) | |||||||
\(182\) | 2.23019 | 0.165313 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.47219 | 0.550857 | ||||||||
\(185\) | −1.41727 | −0.104200 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.5745 | −0.846408 | ||||||||
\(188\) | 8.07122 | 0.588654 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.708569 | 0.0514050 | ||||||||
\(191\) | 17.3402 | 1.25469 | 0.627347 | − | 0.778740i | \(-0.284141\pi\) | ||||
0.627347 | + | 0.778740i | \(0.284141\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.7667 | −1.20689 | −0.603445 | − | 0.797404i | \(-0.706206\pi\) | ||||
−0.603445 | + | 0.797404i | \(0.706206\pi\) | |||||||
\(194\) | −5.06445 | −0.363606 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.53098 | −0.109356 | ||||||||
\(197\) | −5.78061 | −0.411852 | −0.205926 | − | 0.978568i | \(-0.566021\pi\) | ||||
−0.205926 | + | 0.978568i | \(0.566021\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.52069 | −0.178687 | −0.0893433 | − | 0.996001i | \(-0.528477\pi\) | ||||
−0.0893433 | + | 0.996001i | \(0.528477\pi\) | |||||||
\(200\) | 12.0103 | 0.849254 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.60133 | −0.605187 | ||||||||
\(203\) | 6.70003 | 0.470250 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.155785 | −0.0108805 | ||||||||
\(206\) | −0.938829 | −0.0654113 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.57809 | 0.317433 | ||||||||
\(209\) | −23.9894 | −1.65938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.8740 | −0.817437 | −0.408719 | − | 0.912660i | \(-0.634024\pi\) | ||||
−0.408719 | + | 0.912660i | \(0.634024\pi\) | |||||||
\(212\) | −9.10732 | −0.625494 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.97146 | −0.339842 | ||||||||
\(215\) | −1.49194 | −0.101749 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.55396 | −0.648565 | ||||||||
\(218\) | 3.74871 | 0.253894 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.18502 | 0.0798937 | ||||||||
\(221\) | 8.89716 | 0.598488 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.7449 | −1.79097 | −0.895485 | − | 0.445092i | \(-0.853171\pi\) | ||||
−0.895485 | + | 0.445092i | \(0.853171\pi\) | |||||||
\(224\) | 5.79919 | 0.387475 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.42007 | 0.294018 | ||||||||
\(227\) | −25.5670 | −1.69694 | −0.848472 | − | 0.529241i | \(-0.822477\pi\) | ||||
−0.848472 | + | 0.529241i | \(0.822477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.4599 | −1.74852 | −0.874261 | − | 0.485457i | \(-0.838653\pi\) | ||||
−0.874261 | + | 0.485457i | \(0.838653\pi\) | |||||||
\(230\) | −0.386646 | −0.0254947 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.2020 | −1.06371 | ||||||||
\(233\) | 10.1130 | 0.662526 | 0.331263 | − | 0.943538i | \(-0.392525\pi\) | ||||
0.331263 | + | 0.943538i | \(0.392525\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.963231 | −0.0628343 | ||||||||
\(236\) | −11.7964 | −0.767880 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.87112 | 0.121287 | ||||||||
\(239\) | −5.64416 | −0.365090 | −0.182545 | − | 0.983197i | \(-0.558434\pi\) | ||||
−0.182545 | + | 0.983197i | \(0.558434\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.78563 | −0.179438 | −0.0897192 | − | 0.995967i | \(-0.528597\pi\) | ||||
−0.0897192 | + | 0.995967i | \(0.528597\pi\) | |||||||
\(242\) | 4.75759 | 0.305830 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.1483 | 0.713699 | ||||||||
\(245\) | 0.182709 | 0.0116729 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.4404 | 1.17333 | ||||||||
\(248\) | 23.1034 | 1.46707 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.24711 | −0.0788742 | ||||||||
\(251\) | −15.8489 | −1.00038 | −0.500188 | − | 0.865917i | \(-0.666736\pi\) | ||||
−0.500188 | + | 0.865917i | \(0.666736\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.0903 | 0.822982 | ||||||||
\(254\) | 0.684852 | 0.0429714 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.71894 | −0.607434 | ||||||||
\(257\) | 23.0355 | 1.43691 | 0.718457 | − | 0.695571i | \(-0.244849\pi\) | ||||
0.718457 | + | 0.695571i | \(0.244849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.75698 | −0.481995 | ||||||||
\(260\) | −0.910908 | −0.0564921 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.0738 | −0.807704 | ||||||||
\(263\) | −21.0237 | −1.29638 | −0.648189 | − | 0.761479i | \(-0.724473\pi\) | ||||
−0.648189 | + | 0.761479i | \(0.724473\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.08688 | 0.0667666 | ||||||||
\(266\) | 3.87812 | 0.237783 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.0506 | −0.797194 | ||||||||
\(269\) | −25.1761 | −1.53501 | −0.767507 | − | 0.641040i | \(-0.778503\pi\) | ||||
−0.767507 | + | 0.641040i | \(0.778503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.93418 | 0.481967 | 0.240983 | − | 0.970529i | \(-0.422530\pi\) | ||||
0.240983 | + | 0.970529i | \(0.422530\pi\) | |||||||
\(272\) | 3.84100 | 0.232895 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.49217 | −0.331794 | ||||||||
\(275\) | 21.0405 | 1.26879 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.7272 | −0.824786 | −0.412393 | − | 0.911006i | \(-0.635307\pi\) | ||||
−0.412393 | + | 0.911006i | \(0.635307\pi\) | |||||||
\(278\) | −7.74571 | −0.464557 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.441827 | −0.0264042 | ||||||||
\(281\) | 10.3547 | 0.617711 | 0.308855 | − | 0.951109i | \(-0.400054\pi\) | ||||
0.308855 | + | 0.951109i | \(0.400054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3223 | 0.673038 | 0.336519 | − | 0.941677i | \(-0.390750\pi\) | ||||
0.336519 | + | 0.941677i | \(0.390750\pi\) | |||||||
\(284\) | −10.8395 | −0.643205 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.44793 | −0.558668 | ||||||||
\(287\) | −0.852638 | −0.0503296 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.53530 | −0.560900 | ||||||||
\(290\) | 0.838367 | 0.0492306 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.19334 | 0.128355 | ||||||||
\(293\) | 0.941792 | 0.0550200 | 0.0275100 | − | 0.999622i | \(-0.491242\pi\) | ||||
0.0275100 | + | 0.999622i | \(0.491242\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.40780 | 0.0819653 | ||||||||
\(296\) | 18.7579 | 1.09028 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.12165 | 0.0649752 | ||||||||
\(299\) | −10.0624 | −0.581923 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.16565 | −0.470660 | ||||||||
\(302\) | −14.5494 | −0.837222 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.96093 | 0.456590 | ||||||||
\(305\) | −1.33046 | −0.0761819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0831 | −0.575473 | −0.287737 | − | 0.957710i | \(-0.592903\pi\) | ||||
−0.287737 | + | 0.957710i | \(0.592903\pi\) | |||||||
\(308\) | 6.48580 | 0.369563 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.19548 | −0.0678984 | ||||||||
\(311\) | −6.79471 | −0.385292 | −0.192646 | − | 0.981268i | \(-0.561707\pi\) | ||||
−0.192646 | + | 0.981268i | \(0.561707\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.80105 | 0.214848 | 0.107424 | − | 0.994213i | \(-0.465740\pi\) | ||||
0.107424 | + | 0.994213i | \(0.465740\pi\) | |||||||
\(314\) | −11.1968 | −0.631872 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.2387 | −1.08226 | ||||||||
\(317\) | 0.0825552 | 0.00463676 | 0.00231838 | − | 0.999997i | \(-0.499262\pi\) | ||||
0.00231838 | + | 0.999997i | \(0.499262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.3839 | −1.58919 | ||||||||
\(320\) | 0.211922 | 0.0118468 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.11618 | −0.117930 | ||||||||
\(323\) | 15.4714 | 0.860854 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.1736 | −0.897149 | ||||||||
\(326\) | 6.30656 | 0.349288 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.06185 | 0.113846 | ||||||||
\(329\) | −5.27194 | −0.290651 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.6223 | −1.73812 | −0.869059 | − | 0.494709i | \(-0.835275\pi\) | ||||
−0.869059 | + | 0.494709i | \(0.835275\pi\) | |||||||
\(332\) | −17.0072 | −0.933391 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.87777 | −0.431053 | ||||||||
\(335\) | 1.55748 | 0.0850943 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.0391 | 1.14607 | 0.573037 | − | 0.819530i | \(-0.305765\pi\) | ||||
0.573037 | + | 0.819530i | \(0.305765\pi\) | |||||||
\(338\) | −1.64055 | −0.0892344 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.764250 | −0.0414473 | ||||||||
\(341\) | 40.4742 | 2.19180 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 19.7461 | 1.06464 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.2844 | 0.875454 | ||||||||
\(347\) | 0.860099 | 0.0461725 | 0.0230863 | − | 0.999733i | \(-0.492651\pi\) | ||||
0.0230863 | + | 0.999733i | \(0.492651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.72368 | −0.359910 | −0.179955 | − | 0.983675i | \(-0.557595\pi\) | ||||
−0.179955 | + | 0.983675i | \(0.557595\pi\) | |||||||
\(350\) | −3.40140 | −0.181812 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −24.5676 | −1.30946 | ||||||||
\(353\) | −7.98795 | −0.425156 | −0.212578 | − | 0.977144i | \(-0.568186\pi\) | ||||
−0.212578 | + | 0.977144i | \(0.568186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.29360 | 0.0686572 | ||||||||
\(356\) | −15.1791 | −0.804492 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.0265 | −0.688474 | ||||||||
\(359\) | −23.6994 | −1.25080 | −0.625402 | − | 0.780302i | \(-0.715065\pi\) | ||||
−0.625402 | + | 0.780302i | \(0.715065\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0664 | 0.687704 | ||||||||
\(362\) | −7.60273 | −0.399590 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.98556 | −0.261315 | ||||||||
\(365\) | −0.261756 | −0.0137009 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.85990 | 0.514683 | 0.257341 | − | 0.966321i | \(-0.417154\pi\) | ||||
0.257341 | + | 0.966321i | \(0.417154\pi\) | |||||||
\(368\) | −4.34405 | −0.226449 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.970621 | −0.0504602 | ||||||||
\(371\) | 5.94870 | 0.308841 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.6669 | −0.862982 | −0.431491 | − | 0.902117i | \(-0.642012\pi\) | ||||
−0.431491 | + | 0.902117i | \(0.642012\pi\) | |||||||
\(374\) | −7.92679 | −0.409885 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.7486 | 0.657458 | ||||||||
\(377\) | 21.8184 | 1.12370 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.6371 | 0.700491 | 0.350245 | − | 0.936658i | \(-0.386098\pi\) | ||||
0.350245 | + | 0.936658i | \(0.386098\pi\) | |||||||
\(380\) | −1.58400 | −0.0812573 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.8755 | 0.607603 | ||||||||
\(383\) | −12.0694 | −0.616718 | −0.308359 | − | 0.951270i | \(-0.599780\pi\) | ||||
−0.308359 | + | 0.951270i | \(0.599780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.774025 | −0.0394480 | ||||||||
\(386\) | −11.4827 | −0.584453 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.3215 | 0.574762 | ||||||||
\(389\) | 30.2684 | 1.53467 | 0.767335 | − | 0.641246i | \(-0.221582\pi\) | ||||
0.767335 | + | 0.641246i | \(0.221582\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.44233 | −0.426947 | ||||||||
\(392\) | −2.41820 | −0.122137 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.95886 | −0.199445 | ||||||||
\(395\) | 2.29598 | 0.115523 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.2326 | 0.513561 | 0.256780 | − | 0.966470i | \(-0.417338\pi\) | ||||
0.256780 | + | 0.966470i | \(0.417338\pi\) | |||||||
\(398\) | −1.72630 | −0.0865314 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.98231 | −0.349116 | ||||||||
\(401\) | 22.6896 | 1.13307 | 0.566533 | − | 0.824039i | \(-0.308284\pi\) | ||||
0.566533 | + | 0.824039i | \(0.308284\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.1121 | −1.54980 | ||||||||
\(404\) | 19.2282 | 0.956637 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.58853 | 0.227725 | ||||||||
\(407\) | 32.8615 | 1.62888 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.9744 | 1.48214 | 0.741069 | − | 0.671429i | \(-0.234319\pi\) | ||||
0.741069 | + | 0.671429i | \(0.234319\pi\) | |||||||
\(410\) | −0.106689 | −0.00526902 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.09874 | 0.103397 | ||||||||
\(413\) | 7.70514 | 0.379145 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.02966 | 0.0996323 | ||||||||
\(416\) | 18.8848 | 0.925904 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16.4292 | −0.803578 | ||||||||
\(419\) | −2.69907 | −0.131858 | −0.0659290 | − | 0.997824i | \(-0.521001\pi\) | ||||
−0.0659290 | + | 0.997824i | \(0.521001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.141470 | −0.00689482 | −0.00344741 | − | 0.999994i | \(-0.501097\pi\) | ||||
−0.00344741 | + | 0.999994i | \(0.501097\pi\) | |||||||
\(422\) | −8.13191 | −0.395855 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.3851 | −0.698603 | ||||||||
\(425\) | −13.5696 | −0.658222 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.28184 | −0.352393 | ||||||||
\(428\) | 11.1136 | 0.537198 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.02176 | −0.0492735 | ||||||||
\(431\) | −30.3884 | −1.46376 | −0.731880 | − | 0.681434i | \(-0.761357\pi\) | ||||
−0.731880 | + | 0.681434i | \(0.761357\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.7113 | 0.658923 | 0.329461 | − | 0.944169i | \(-0.393133\pi\) | ||||
0.329461 | + | 0.944169i | \(0.393133\pi\) | |||||||
\(434\) | −6.54305 | −0.314076 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.38019 | −0.401338 | ||||||||
\(437\) | −17.4977 | −0.837028 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.3026 | 0.968992 | 0.484496 | − | 0.874794i | \(-0.339003\pi\) | ||||
0.484496 | + | 0.874794i | \(0.339003\pi\) | |||||||
\(440\) | 1.87175 | 0.0892320 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.09324 | 0.289826 | ||||||||
\(443\) | −37.7781 | −1.79489 | −0.897445 | − | 0.441126i | \(-0.854579\pi\) | ||||
−0.897445 | + | 0.441126i | \(0.854579\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.81150 | 0.0858734 | ||||||||
\(446\) | −18.3163 | −0.867301 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.15989 | 0.0547996 | ||||||||
\(449\) | 4.11605 | 0.194248 | 0.0971242 | − | 0.995272i | \(-0.469036\pi\) | ||||
0.0971242 | + | 0.995272i | \(0.469036\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.61209 | 0.170087 | ||||||||
\(452\) | −9.88100 | −0.464763 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.5096 | −0.821767 | ||||||||
\(455\) | 0.594985 | 0.0278933 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.6147 | −0.496533 | −0.248267 | − | 0.968692i | \(-0.579861\pi\) | ||||
−0.248267 | + | 0.968692i | \(0.579861\pi\) | |||||||
\(458\) | −18.1211 | −0.846745 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.864342 | 0.0403001 | ||||||||
\(461\) | 36.1999 | 1.68600 | 0.842998 | − | 0.537916i | \(-0.180788\pi\) | ||||
0.842998 | + | 0.537916i | \(0.180788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.39773 | −0.157906 | −0.0789530 | − | 0.996878i | \(-0.525158\pi\) | ||||
−0.0789530 | + | 0.996878i | \(0.525158\pi\) | |||||||
\(464\) | 9.41924 | 0.437277 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.92592 | 0.320837 | ||||||||
\(467\) | 25.8244 | 1.19501 | 0.597506 | − | 0.801865i | \(-0.296159\pi\) | ||||
0.597506 | + | 0.801865i | \(0.296159\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.52437 | 0.393619 | ||||||||
\(470\) | −0.659671 | −0.0304283 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.6326 | −0.857633 | ||||||||
\(473\) | 34.5928 | 1.59058 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.1246 | −1.29044 | ||||||||
\(476\) | −4.18288 | −0.191722 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.86541 | −0.176800 | ||||||||
\(479\) | 0.309258 | 0.0141304 | 0.00706518 | − | 0.999975i | \(-0.497751\pi\) | ||||
0.00706518 | + | 0.999975i | \(0.497751\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.2603 | −1.15177 | ||||||||
\(482\) | −1.90775 | −0.0868954 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.6355 | −0.483434 | ||||||||
\(485\) | −1.35113 | −0.0613514 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.17161 | −0.189034 | −0.0945169 | − | 0.995523i | \(-0.530131\pi\) | ||||
−0.0945169 | + | 0.995523i | \(0.530131\pi\) | |||||||
\(488\) | 17.6089 | 0.797119 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.125129 | 0.00565274 | ||||||||
\(491\) | 40.2311 | 1.81560 | 0.907801 | − | 0.419401i | \(-0.137760\pi\) | ||||
0.907801 | + | 0.419401i | \(0.137760\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.3056 | 0.824441 | ||||||||
\(494\) | 12.6289 | 0.568203 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.4314 | −0.603089 | ||||||||
\(497\) | 7.08011 | 0.317586 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.20374 | 0.322484 | 0.161242 | − | 0.986915i | \(-0.448450\pi\) | ||||
0.161242 | + | 0.986915i | \(0.448450\pi\) | |||||||
\(500\) | 2.78790 | 0.124679 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.8542 | −0.484445 | ||||||||
\(503\) | −10.8960 | −0.485830 | −0.242915 | − | 0.970048i | \(-0.578104\pi\) | ||||
−0.242915 | + | 0.970048i | \(0.578104\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.29472 | −0.102114 | ||||||||
\(506\) | 8.96494 | 0.398540 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.53098 | −0.0679262 | ||||||||
\(509\) | −7.55836 | −0.335019 | −0.167509 | − | 0.985871i | \(-0.553572\pi\) | ||||
−0.167509 | + | 0.985871i | \(0.553572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.43264 | −0.0633762 | ||||||||
\(512\) | 14.9520 | 0.660793 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.7759 | 0.695845 | ||||||||
\(515\) | −0.250467 | −0.0110369 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.3339 | 0.982244 | ||||||||
\(518\) | −5.31238 | −0.233413 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.43879 | −0.0630951 | ||||||||
\(521\) | −7.79661 | −0.341576 | −0.170788 | − | 0.985308i | \(-0.554631\pi\) | ||||
−0.170788 | + | 0.985308i | \(0.554631\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.65311 | −0.203466 | −0.101733 | − | 0.994812i | \(-0.532439\pi\) | ||||
−0.101733 | + | 0.994812i | \(0.532439\pi\) | |||||||
\(524\) | 29.2264 | 1.27676 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.3981 | −0.627789 | ||||||||
\(527\) | −26.1030 | −1.13706 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.4520 | −0.584870 | ||||||||
\(530\) | 0.744353 | 0.0323326 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.66950 | −0.375870 | ||||||||
\(533\) | −2.77658 | −0.120267 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.32632 | −0.0573417 | ||||||||
\(536\) | −20.6136 | −0.890372 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.2419 | −0.743351 | ||||||||
\(539\) | −4.23638 | −0.182474 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.1327 | 0.822578 | 0.411289 | − | 0.911505i | \(-0.365079\pi\) | ||||
0.411289 | + | 0.911505i | \(0.365079\pi\) | |||||||
\(542\) | 5.43374 | 0.233399 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15.8443 | 0.679320 | ||||||||
\(545\) | 1.00010 | 0.0428398 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.3544 | 1.21235 | 0.606173 | − | 0.795333i | \(-0.292704\pi\) | ||||
0.606173 | + | 0.795333i | \(0.292704\pi\) | |||||||
\(548\) | 12.2777 | 0.524477 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.4096 | 0.614428 | ||||||||
\(551\) | 37.9404 | 1.61632 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.5663 | 0.534374 | ||||||||
\(554\) | −9.40108 | −0.399414 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.3154 | 0.734338 | ||||||||
\(557\) | 9.66963 | 0.409715 | 0.204858 | − | 0.978792i | \(-0.434327\pi\) | ||||
0.204858 | + | 0.978792i | \(0.434327\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.5911 | −1.12468 | ||||||||
\(560\) | 0.256862 | 0.0108544 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.09145 | 0.299135 | ||||||||
\(563\) | 8.16696 | 0.344196 | 0.172098 | − | 0.985080i | \(-0.444945\pi\) | ||||
0.172098 | + | 0.985080i | \(0.444945\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.17921 | 0.0496099 | ||||||||
\(566\) | 7.75406 | 0.325928 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.1211 | −0.718385 | ||||||||
\(569\) | −30.6856 | −1.28641 | −0.643203 | − | 0.765696i | \(-0.722395\pi\) | ||||
−0.643203 | + | 0.765696i | \(0.722395\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.06856 | −0.212113 | −0.106056 | − | 0.994360i | \(-0.533822\pi\) | ||||
−0.106056 | + | 0.994360i | \(0.533822\pi\) | |||||||
\(572\) | 21.1207 | 0.883102 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.583930 | −0.0243728 | ||||||||
\(575\) | 15.3468 | 0.640004 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.50282 | −0.187455 | −0.0937274 | − | 0.995598i | \(-0.529878\pi\) | ||||
−0.0937274 | + | 0.995598i | \(0.529878\pi\) | |||||||
\(578\) | −6.53027 | −0.271623 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.87416 | −0.0778202 | ||||||||
\(581\) | 11.1087 | 0.460867 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.2009 | −1.04372 | ||||||||
\(584\) | 3.46440 | 0.143358 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.644988 | 0.0266442 | ||||||||
\(587\) | −26.0055 | −1.07336 | −0.536681 | − | 0.843785i | \(-0.680322\pi\) | ||||
−0.536681 | + | 0.843785i | \(0.680322\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −54.1014 | −2.22921 | ||||||||
\(590\) | 0.964135 | 0.0396928 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.9051 | −0.448199 | ||||||||
\(593\) | 48.2944 | 1.98321 | 0.991607 | − | 0.129291i | \(-0.0412703\pi\) | ||||
0.991607 | + | 0.129291i | \(0.0412703\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.499191 | 0.0204648 | ||||||||
\(596\) | −2.50743 | −0.102708 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.89125 | −0.281804 | ||||||||
\(599\) | 14.1896 | 0.579772 | 0.289886 | − | 0.957061i | \(-0.406383\pi\) | ||||
0.289886 | + | 0.957061i | \(0.406383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.2962 | −0.501572 | −0.250786 | − | 0.968043i | \(-0.580689\pi\) | ||||
−0.250786 | + | 0.968043i | \(0.580689\pi\) | |||||||
\(602\) | −5.59226 | −0.227923 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 32.5249 | 1.32342 | ||||||||
\(605\) | 1.26926 | 0.0516028 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.2861 | 0.863978 | 0.431989 | − | 0.901879i | \(-0.357812\pi\) | ||||
0.431989 | + | 0.901879i | \(0.357812\pi\) | |||||||
\(608\) | 32.8392 | 1.33180 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.911168 | −0.0368921 | ||||||||
\(611\) | −17.1678 | −0.694536 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.9001 | −0.924928 | −0.462464 | − | 0.886638i | \(-0.653034\pi\) | ||||
−0.462464 | + | 0.886638i | \(0.653034\pi\) | |||||||
\(614\) | −6.90543 | −0.278681 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.2444 | 0.412758 | ||||||||
\(617\) | 26.1239 | 1.05171 | 0.525854 | − | 0.850575i | \(-0.323746\pi\) | ||||
0.525854 | + | 0.850575i | \(0.323746\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.74080 | 0.110162 | 0.0550811 | − | 0.998482i | \(-0.482458\pi\) | ||||
0.0550811 | + | 0.998482i | \(0.482458\pi\) | |||||||
\(620\) | 2.67247 | 0.107329 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.65337 | −0.186583 | ||||||||
\(623\) | 9.91467 | 0.397223 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5004 | 0.980015 | ||||||||
\(626\) | 2.60315 | 0.104043 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 25.0303 | 0.998818 | ||||||||
\(629\) | −21.1933 | −0.845032 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.8494 | −0.750381 | −0.375191 | − | 0.926948i | \(-0.622423\pi\) | ||||
−0.375191 | + | 0.926948i | \(0.622423\pi\) | |||||||
\(632\) | −30.3878 | −1.20876 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.0565381 | 0.00224541 | ||||||||
\(635\) | 0.182709 | 0.00725059 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.25646 | 0.129026 | ||||||||
\(638\) | −19.4387 | −0.769587 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.97400 | −0.0780290 | ||||||||
\(641\) | −9.48946 | −0.374811 | −0.187406 | − | 0.982283i | \(-0.560008\pi\) | ||||
−0.187406 | + | 0.982283i | \(0.560008\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.4153 | −0.923408 | −0.461704 | − | 0.887034i | \(-0.652762\pi\) | ||||
−0.461704 | + | 0.887034i | \(0.652762\pi\) | |||||||
\(644\) | 4.73069 | 0.186415 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.5957 | 0.416880 | ||||||||
\(647\) | −16.1609 | −0.635352 | −0.317676 | − | 0.948199i | \(-0.602902\pi\) | ||||
−0.317676 | + | 0.948199i | \(0.602902\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.6419 | −1.28131 | ||||||||
\(650\) | −11.0765 | −0.434456 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.0982 | −0.552129 | ||||||||
\(653\) | −48.0044 | −1.87856 | −0.939279 | − | 0.343156i | \(-0.888504\pi\) | ||||
−0.939279 | + | 0.343156i | \(0.888504\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.48792 | −0.136284 | ||||||||
\(656\) | −1.19868 | −0.0468006 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.61050 | −0.140752 | ||||||||
\(659\) | −22.3312 | −0.869899 | −0.434949 | − | 0.900455i | \(-0.643234\pi\) | ||||
−0.434949 | + | 0.900455i | \(0.643234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.5861 | −0.567335 | −0.283667 | − | 0.958923i | \(-0.591551\pi\) | ||||
−0.283667 | + | 0.958923i | \(0.591551\pi\) | |||||||
\(662\) | −21.6566 | −0.841707 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −26.8631 | −1.04249 | ||||||||
\(665\) | 1.03463 | 0.0401213 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.7030 | −0.801623 | ||||||||
\(668\) | 17.6107 | 0.681377 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.06664 | 0.0412081 | ||||||||
\(671\) | 30.8486 | 1.19090 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.1286 | 1.35411 | 0.677054 | − | 0.735933i | \(-0.263256\pi\) | ||||
0.677054 | + | 0.735933i | \(0.263256\pi\) | |||||||
\(674\) | 14.4087 | 0.555002 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.66744 | 0.141055 | ||||||||
\(677\) | −38.9180 | −1.49574 | −0.747871 | − | 0.663844i | \(-0.768924\pi\) | ||||
−0.747871 | + | 0.663844i | \(0.768924\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.39495 | −0.283792 | ||||||||
\(680\) | −1.20714 | −0.0462918 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.7188 | 1.06141 | ||||||||
\(683\) | 18.3659 | 0.702751 | 0.351376 | − | 0.936235i | \(-0.385714\pi\) | ||||
0.351376 | + | 0.936235i | \(0.385714\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.46524 | −0.0559839 | ||||||||
\(686\) | 0.684852 | 0.0261478 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.4797 | −0.437658 | ||||||||
\(689\) | 19.3717 | 0.738002 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.9973 | −0.684650 | −0.342325 | − | 0.939582i | \(-0.611214\pi\) | ||||
−0.342325 | + | 0.939582i | \(0.611214\pi\) | |||||||
\(692\) | −36.4036 | −1.38386 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.589040 | 0.0223597 | ||||||||
\(695\) | −2.06645 | −0.0783849 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.32954 | −0.0882377 | ||||||||
\(698\) | −4.60472 | −0.174291 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.60378 | 0.287396 | ||||||||
\(701\) | −21.7226 | −0.820451 | −0.410226 | − | 0.911984i | \(-0.634550\pi\) | ||||
−0.410226 | + | 0.911984i | \(0.634550\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43.9256 | −1.65668 | ||||||||
\(704\) | −4.91373 | −0.185193 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.47056 | −0.205887 | ||||||||
\(707\) | −12.5594 | −0.472345 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5399 | 0.433392 | 0.216696 | − | 0.976239i | \(-0.430472\pi\) | ||||
0.216696 | + | 0.976239i | \(0.430472\pi\) | |||||||
\(710\) | 0.885925 | 0.0332482 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23.9756 | −0.898524 | ||||||||
\(713\) | 29.5216 | 1.10559 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.52058 | −0.0942643 | ||||||||
\(716\) | 29.1207 | 1.08829 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16.2306 | −0.605719 | ||||||||
\(719\) | 7.43315 | 0.277210 | 0.138605 | − | 0.990348i | \(-0.455738\pi\) | ||||
0.138605 | + | 0.990348i | \(0.455738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.37085 | −0.0510531 | ||||||||
\(722\) | 8.94853 | 0.333030 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.9958 | 0.631644 | ||||||||
\(725\) | −33.2765 | −1.23586 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.16165 | 0.154347 | 0.0771736 | − | 0.997018i | \(-0.475410\pi\) | ||||
0.0771736 | + | 0.997018i | \(0.475410\pi\) | |||||||
\(728\) | −7.87475 | −0.291858 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.179264 | −0.00663486 | ||||||||
\(731\) | −22.3098 | −0.825160 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.6578 | −0.689143 | −0.344571 | − | 0.938760i | \(-0.611976\pi\) | ||||
−0.344571 | + | 0.938760i | \(0.611976\pi\) | |||||||
\(734\) | 6.75257 | 0.249242 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.9194 | −0.660518 | ||||||||
\(737\) | −36.1125 | −1.33022 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.7826 | 1.46343 | 0.731713 | − | 0.681613i | \(-0.238721\pi\) | ||||
0.731713 | + | 0.681613i | \(0.238721\pi\) | |||||||
\(740\) | 2.16981 | 0.0797638 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.07398 | 0.149560 | ||||||||
\(743\) | −30.1346 | −1.10553 | −0.552765 | − | 0.833337i | \(-0.686427\pi\) | ||||
−0.552765 | + | 0.833337i | \(0.686427\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.299240 | 0.0109633 | ||||||||
\(746\) | −11.4144 | −0.417911 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.7202 | 0.647916 | ||||||||
\(749\) | −7.25917 | −0.265244 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.66769 | 0.0973454 | 0.0486727 | − | 0.998815i | \(-0.484501\pi\) | ||||
0.0486727 | + | 0.998815i | \(0.484501\pi\) | |||||||
\(752\) | −7.41155 | −0.270271 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.9424 | 0.544168 | ||||||||
\(755\) | −3.88158 | −0.141265 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.7069 | −0.716259 | −0.358130 | − | 0.933672i | \(-0.616585\pi\) | ||||
−0.358130 | + | 0.933672i | \(0.616585\pi\) | |||||||
\(758\) | 9.33939 | 0.339222 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.50194 | −0.0907549 | ||||||||
\(761\) | −11.8208 | −0.428502 | −0.214251 | − | 0.976779i | \(-0.568731\pi\) | ||||
−0.214251 | + | 0.976779i | \(0.568731\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.47375 | 0.198163 | ||||||||
\(764\) | −26.5475 | −0.960455 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.26575 | −0.298654 | ||||||||
\(767\) | 25.0915 | 0.906000 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.0031 | −1.11800 | −0.559001 | − | 0.829167i | \(-0.688815\pi\) | ||||
−0.559001 | + | 0.829167i | \(0.688815\pi\) | |||||||
\(770\) | −0.530093 | −0.0191032 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.6694 | 0.923861 | ||||||||
\(773\) | −25.2317 | −0.907520 | −0.453760 | − | 0.891124i | \(-0.649918\pi\) | ||||
−0.453760 | + | 0.891124i | \(0.649918\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 47.4509 | 1.70449 | ||||||||
\(776\) | 17.8824 | 0.641942 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.7294 | 0.743185 | ||||||||
\(779\) | −4.82825 | −0.172990 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.9940 | −1.07327 | ||||||||
\(782\) | −5.78174 | −0.206755 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.40585 | 0.0502089 | ||||||||
\(785\) | −2.98716 | −0.106616 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.2540 | 1.54184 | 0.770920 | − | 0.636932i | \(-0.219797\pi\) | ||||
0.770920 | + | 0.636932i | \(0.219797\pi\) | |||||||
\(788\) | 8.84999 | 0.315268 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.57241 | 0.0559437 | ||||||||
\(791\) | 6.45405 | 0.229480 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.7130 | −0.842074 | ||||||||
\(794\) | 7.00783 | 0.248699 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.85911 | 0.136783 | ||||||||
\(797\) | 47.4345 | 1.68022 | 0.840108 | − | 0.542419i | \(-0.182492\pi\) | ||||
0.840108 | + | 0.542419i | \(0.182492\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.4038 | −0.509569 | ||||||||
\(800\) | −28.8024 | −1.01832 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.5390 | 0.548702 | ||||||||
\(803\) | 6.06919 | 0.214177 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.564568 | −0.0198984 | ||||||||
\(806\) | −21.3072 | −0.750513 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 30.3711 | 1.06845 | ||||||||
\(809\) | −21.8218 | −0.767212 | −0.383606 | − | 0.923497i | \(-0.625318\pi\) | ||||
−0.383606 | + | 0.923497i | \(0.625318\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.8994 | 0.874336 | 0.437168 | − | 0.899380i | \(-0.355982\pi\) | ||||
0.437168 | + | 0.899380i | \(0.355982\pi\) | |||||||
\(812\) | −10.2576 | −0.359971 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.5053 | 0.788809 | ||||||||
\(815\) | 1.68250 | 0.0589356 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.2397 | −1.61772 | ||||||||
\(818\) | 20.5280 | 0.717745 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.238503 | 0.00832888 | ||||||||
\(821\) | 38.3151 | 1.33721 | 0.668603 | − | 0.743619i | \(-0.266892\pi\) | ||||
0.668603 | + | 0.743619i | \(0.266892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.09096 | −0.247175 | −0.123588 | − | 0.992334i | \(-0.539440\pi\) | ||||
−0.123588 | + | 0.992334i | \(0.539440\pi\) | |||||||
\(824\) | 3.31498 | 0.115483 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.27688 | 0.183606 | ||||||||
\(827\) | 16.2005 | 0.563346 | 0.281673 | − | 0.959510i | \(-0.409111\pi\) | ||||
0.281673 | + | 0.959510i | \(0.409111\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.9552 | 0.484684 | 0.242342 | − | 0.970191i | \(-0.422084\pi\) | ||||
0.242342 | + | 0.970191i | \(0.422084\pi\) | |||||||
\(830\) | 1.39002 | 0.0482483 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.77713 | 0.130948 | ||||||||
\(833\) | 2.73216 | 0.0946637 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.10168 | −0.0727317 | ||||||||
\(836\) | 36.7273 | 1.27024 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.84846 | −0.0638540 | ||||||||
\(839\) | 28.7918 | 0.994004 | 0.497002 | − | 0.867749i | \(-0.334434\pi\) | ||||
0.497002 | + | 0.867749i | \(0.334434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.8905 | 0.547947 | ||||||||
\(842\) | −0.0968860 | −0.00333891 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.1788 | 0.625739 | ||||||||
\(845\) | −0.437678 | −0.0150566 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.94689 | 0.238698 | ||||||||
\(848\) | 8.36297 | 0.287186 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.29316 | −0.318753 | ||||||||
\(851\) | 23.9689 | 0.821644 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.3538 | −0.696902 | −0.348451 | − | 0.937327i | \(-0.613292\pi\) | ||||
−0.348451 | + | 0.937327i | \(0.613292\pi\) | |||||||
\(854\) | −4.98698 | −0.170651 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.5541 | 0.599987 | ||||||||
\(857\) | −2.41015 | −0.0823291 | −0.0411645 | − | 0.999152i | \(-0.513107\pi\) | ||||
−0.0411645 | + | 0.999152i | \(0.513107\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.00391 | −0.170731 | −0.0853656 | − | 0.996350i | \(-0.527206\pi\) | ||||
−0.0853656 | + | 0.996350i | \(0.527206\pi\) | |||||||
\(860\) | 2.28413 | 0.0778880 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.8116 | −0.708845 | ||||||||
\(863\) | 53.9732 | 1.83727 | 0.918634 | − | 0.395110i | \(-0.129293\pi\) | ||||
0.918634 | + | 0.395110i | \(0.129293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.34446 | 0.147716 | ||||||||
\(866\) | 9.39021 | 0.319092 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.6269 | 0.496470 | ||||||||
\(869\) | −53.2356 | −1.80589 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.7593 | 0.940586 | ||||||||
\(872\) | −13.2366 | −0.448248 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.9833 | −0.405342 | ||||||||
\(875\) | −1.82099 | −0.0615608 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.77331 | −0.296254 | −0.148127 | − | 0.988968i | \(-0.547324\pi\) | ||||
−0.148127 | + | 0.988968i | \(0.547324\pi\) | |||||||
\(878\) | 13.9043 | 0.469247 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.08816 | −0.0366820 | ||||||||
\(881\) | −59.0141 | −1.98823 | −0.994117 | − | 0.108311i | \(-0.965456\pi\) | ||||
−0.994117 | + | 0.108311i | \(0.965456\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.4425 | −1.29369 | −0.646847 | − | 0.762620i | \(-0.723913\pi\) | ||||
−0.646847 | + | 0.762620i | \(0.723913\pi\) | |||||||
\(884\) | −13.6214 | −0.458136 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.8724 | −0.869200 | ||||||||
\(887\) | −46.8555 | −1.57325 | −0.786627 | − | 0.617428i | \(-0.788175\pi\) | ||||
−0.786627 | + | 0.617428i | \(0.788175\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 1.24061 | 0.0415853 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 40.9458 | 1.37097 | ||||||||
\(893\) | −29.8535 | −0.999009 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.47530 | −0.116167 | ||||||||
\(896\) | −10.8040 | −0.360937 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.81889 | 0.0940674 | ||||||||
\(899\) | −64.0119 | −2.13492 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.2528 | 0.541459 | ||||||||
\(902\) | 2.47375 | 0.0823669 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.6072 | −0.519086 | ||||||||
\(905\) | −2.02830 | −0.0674231 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.3917 | −1.14196 | −0.570979 | − | 0.820965i | \(-0.693436\pi\) | ||||
−0.570979 | + | 0.820965i | \(0.693436\pi\) | |||||||
\(908\) | 39.1426 | 1.29899 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.407476 | 0.0135077 | ||||||||
\(911\) | −5.39247 | −0.178661 | −0.0893303 | − | 0.996002i | \(-0.528473\pi\) | ||||
−0.0893303 | + | 0.996002i | \(0.528473\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47.0607 | −1.55748 | ||||||||
\(914\) | −7.26948 | −0.240453 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 40.5096 | 1.33847 | ||||||||
\(917\) | −19.0900 | −0.630407 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.62144 | −0.152447 | −0.0762236 | − | 0.997091i | \(-0.524286\pi\) | ||||
−0.0762236 | + | 0.997091i | \(0.524286\pi\) | |||||||
\(920\) | 1.36524 | 0.0450105 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.7916 | 0.816466 | ||||||||
\(923\) | 23.0561 | 0.758900 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.5259 | 1.26673 | ||||||||
\(926\) | −2.32694 | −0.0764681 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 38.8548 | 1.27547 | ||||||||
\(929\) | 39.2036 | 1.28623 | 0.643115 | − | 0.765770i | \(-0.277642\pi\) | ||||
0.643115 | + | 0.765770i | \(0.277642\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.66272 | 0.185588 | ||||||||
\(932\) | −15.4828 | −0.507157 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.6859 | 0.578700 | ||||||||
\(935\) | −2.11476 | −0.0691601 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.9890 | 0.849024 | 0.424512 | − | 0.905422i | \(-0.360446\pi\) | ||||
0.424512 | + | 0.905422i | \(0.360446\pi\) | |||||||
\(938\) | 5.83793 | 0.190615 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.47469 | 0.0480990 | ||||||||
\(941\) | 50.0404 | 1.63127 | 0.815635 | − | 0.578566i | \(-0.196388\pi\) | ||||
0.815635 | + | 0.578566i | \(0.196388\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.63463 | 0.0857955 | ||||||||
\(944\) | 10.8323 | 0.352560 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.6909 | 0.770258 | ||||||||
\(947\) | 34.5608 | 1.12307 | 0.561537 | − | 0.827452i | \(-0.310210\pi\) | ||||
0.561537 | + | 0.827452i | \(0.310210\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.66532 | −0.151443 | ||||||||
\(950\) | −19.2612 | −0.624914 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.60690 | −0.214131 | ||||||||
\(953\) | 49.0514 | 1.58893 | 0.794465 | − | 0.607310i | \(-0.207752\pi\) | ||||
0.794465 | + | 0.607310i | \(0.207752\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.16822 | 0.102521 | ||||||||
\(956\) | 8.64108 | 0.279472 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.211796 | 0.00684281 | ||||||||
\(959\) | −8.01951 | −0.258963 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.2782 | 1.94446 | ||||||||
\(962\) | −17.2995 | −0.557760 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.26474 | 0.137358 | ||||||||
\(965\) | −3.06342 | −0.0986151 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.4155 | 0.752992 | 0.376496 | − | 0.926418i | \(-0.377129\pi\) | ||||
0.376496 | + | 0.926418i | \(0.377129\pi\) | |||||||
\(968\) | −16.7990 | −0.539939 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.925321 | −0.0297103 | ||||||||
\(971\) | 2.89055 | 0.0927623 | 0.0463811 | − | 0.998924i | \(-0.485231\pi\) | ||||
0.0463811 | + | 0.998924i | \(0.485231\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.3101 | −0.362584 | ||||||||
\(974\) | −2.85694 | −0.0915421 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.2372 | −0.327684 | ||||||||
\(977\) | −8.69803 | −0.278275 | −0.139137 | − | 0.990273i | \(-0.544433\pi\) | ||||
−0.139137 | + | 0.990273i | \(0.544433\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.0023 | −1.34240 | ||||||||
\(980\) | −0.279724 | −0.00893545 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27.5523 | 0.879230 | ||||||||
\(983\) | −37.6232 | −1.20000 | −0.599998 | − | 0.800002i | \(-0.704832\pi\) | ||||
−0.599998 | + | 0.800002i | \(0.704832\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.05617 | −0.0336524 | ||||||||
\(986\) | 12.5366 | 0.399247 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −28.2318 | −0.898174 | ||||||||
\(989\) | 25.2317 | 0.802321 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.3616 | −1.12330 | −0.561650 | − | 0.827375i | \(-0.689833\pi\) | ||||
−0.561650 | + | 0.827375i | \(0.689833\pi\) | |||||||
\(992\) | −55.4053 | −1.75912 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.84882 | 0.153795 | ||||||||
\(995\) | −0.460552 | −0.0146005 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.4674 | 0.838231 | 0.419115 | − | 0.907933i | \(-0.362340\pi\) | ||||
0.419115 | + | 0.907933i | \(0.362340\pi\) | |||||||
\(998\) | 4.93349 | 0.156167 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.x.1.14 | yes | 22 | |
3.2 | odd | 2 | inner | 8001.2.a.x.1.9 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.x.1.9 | ✓ | 22 | 3.2 | odd | 2 | inner | |
8001.2.a.x.1.14 | yes | 22 | 1.1 | even | 1 | trivial |