Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.79702 | 1.27068 | 0.635342 | − | 0.772230i | \(-0.280859\pi\) | ||||
0.635342 | + | 0.772230i | \(0.280859\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.22928 | 0.614640 | ||||||||
\(5\) | −4.13243 | −1.84808 | −0.924039 | − | 0.382298i | \(-0.875133\pi\) | ||||
−0.924039 | + | 0.382298i | \(0.875133\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.22858 | 1.59825 | 0.799127 | − | 0.601162i | \(-0.205295\pi\) | ||||
0.799127 | + | 0.601162i | \(0.205295\pi\) | |||||||
\(8\) | −1.38500 | −0.489671 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.42606 | −2.34833 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.95009 | −1.65026 | −0.825130 | − | 0.564944i | \(-0.808898\pi\) | ||||
−0.825130 | + | 0.564944i | \(0.808898\pi\) | |||||||
\(14\) | 7.59885 | 2.03088 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.94743 | −1.23686 | ||||||||
\(17\) | 6.87502 | 1.66744 | 0.833718 | − | 0.552190i | \(-0.186208\pi\) | ||||
0.833718 | + | 0.552190i | \(0.186208\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.114410 | −0.0262474 | −0.0131237 | − | 0.999914i | \(-0.504178\pi\) | ||||
−0.0131237 | + | 0.999914i | \(0.504178\pi\) | |||||||
\(20\) | −5.07992 | −1.13590 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.79702 | 0.383126 | ||||||||
\(23\) | 3.90616 | 0.814490 | 0.407245 | − | 0.913319i | \(-0.366490\pi\) | ||||
0.407245 | + | 0.913319i | \(0.366490\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.0770 | 2.41539 | ||||||||
\(26\) | −10.6924 | −2.09696 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.19812 | 0.982351 | ||||||||
\(29\) | 1.80774 | 0.335689 | 0.167845 | − | 0.985813i | \(-0.446319\pi\) | ||||
0.167845 | + | 0.985813i | \(0.446319\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.12966 | −1.46013 | −0.730065 | − | 0.683378i | \(-0.760510\pi\) | ||||
−0.730065 | + | 0.683378i | \(0.760510\pi\) | |||||||
\(32\) | −6.12063 | −1.08199 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.3545 | 2.11879 | ||||||||
\(35\) | −17.4743 | −2.95370 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.76890 | −0.784002 | −0.392001 | − | 0.919965i | \(-0.628217\pi\) | ||||
−0.392001 | + | 0.919965i | \(0.628217\pi\) | |||||||
\(38\) | −0.205597 | −0.0333522 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.72341 | 0.904950 | ||||||||
\(41\) | −1.81748 | −0.283843 | −0.141921 | − | 0.989878i | \(-0.545328\pi\) | ||||
−0.141921 | + | 0.989878i | \(0.545328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.000598963 0 | 9.13411e−5 0 | 4.56705e−5 | − | 1.00000i | \(-0.499985\pi\) | ||||
4.56705e−5 | 1.00000i | \(0.499985\pi\) | ||||||||
\(44\) | 1.22928 | 0.185321 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.01944 | 1.03496 | ||||||||
\(47\) | −6.87638 | −1.00302 | −0.501512 | − | 0.865151i | \(-0.667223\pi\) | ||||
−0.501512 | + | 0.865151i | \(0.667223\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.8809 | 1.55442 | ||||||||
\(50\) | 21.7026 | 3.06921 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.31433 | −1.01432 | ||||||||
\(53\) | 10.2253 | 1.40455 | 0.702275 | − | 0.711906i | \(-0.252168\pi\) | ||||
0.702275 | + | 0.711906i | \(0.252168\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.13243 | −0.557217 | ||||||||
\(56\) | −5.85658 | −0.782618 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.24855 | 0.426555 | ||||||||
\(59\) | 6.58478 | 0.857266 | 0.428633 | − | 0.903479i | \(-0.358995\pi\) | ||||
0.428633 | + | 0.903479i | \(0.358995\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −14.6092 | −1.85537 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.10404 | −0.138005 | ||||||||
\(65\) | 24.5883 | 3.04981 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.06126 | −1.10701 | −0.553505 | − | 0.832846i | \(-0.686710\pi\) | ||||
−0.553505 | + | 0.832846i | \(0.686710\pi\) | |||||||
\(68\) | 8.45132 | 1.02487 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −31.4017 | −3.75322 | ||||||||
\(71\) | 12.7148 | 1.50897 | 0.754485 | − | 0.656318i | \(-0.227887\pi\) | ||||
0.754485 | + | 0.656318i | \(0.227887\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9759 | 1.51871 | 0.759357 | − | 0.650674i | \(-0.225514\pi\) | ||||
0.759357 | + | 0.650674i | \(0.225514\pi\) | |||||||
\(74\) | −8.56980 | −0.996219 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.140642 | −0.0161327 | ||||||||
\(77\) | 4.22858 | 0.481892 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.35873 | 0.940431 | 0.470215 | − | 0.882552i | \(-0.344176\pi\) | ||||
0.470215 | + | 0.882552i | \(0.344176\pi\) | |||||||
\(80\) | 20.4449 | 2.28581 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.26605 | −0.360675 | ||||||||
\(83\) | −2.71294 | −0.297784 | −0.148892 | − | 0.988853i | \(-0.547571\pi\) | ||||
−0.148892 | + | 0.988853i | \(0.547571\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.4105 | −3.08155 | ||||||||
\(86\) | 0.00107635 | 0.000116066 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.38500 | −0.147641 | ||||||||
\(89\) | 16.6064 | 1.76028 | 0.880138 | − | 0.474718i | \(-0.157450\pi\) | ||||
0.880138 | + | 0.474718i | \(0.157450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.1605 | −2.63753 | ||||||||
\(92\) | 4.80176 | 0.500618 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.3570 | −1.27453 | ||||||||
\(95\) | 0.472791 | 0.0485073 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1502 | 1.74133 | 0.870667 | − | 0.491873i | \(-0.163687\pi\) | ||||
0.870667 | + | 0.491873i | \(0.163687\pi\) | |||||||
\(98\) | 19.5532 | 1.97517 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 14.8460 | 1.48460 | ||||||||
\(101\) | 15.5825 | 1.55051 | 0.775256 | − | 0.631647i | \(-0.217621\pi\) | ||||
0.775256 | + | 0.631647i | \(0.217621\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1112 | −1.19335 | −0.596677 | − | 0.802482i | \(-0.703513\pi\) | ||||
−0.596677 | + | 0.802482i | \(0.703513\pi\) | |||||||
\(104\) | 8.24087 | 0.808084 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.3750 | 1.78474 | ||||||||
\(107\) | −1.87666 | −0.181424 | −0.0907120 | − | 0.995877i | \(-0.528914\pi\) | ||||
−0.0907120 | + | 0.995877i | \(0.528914\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9578 | 1.24113 | 0.620567 | − | 0.784153i | \(-0.286902\pi\) | ||||
0.620567 | + | 0.784153i | \(0.286902\pi\) | |||||||
\(110\) | −7.42606 | −0.708047 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −20.9206 | −1.97681 | ||||||||
\(113\) | −1.15087 | −0.108265 | −0.0541325 | − | 0.998534i | \(-0.517239\pi\) | ||||
−0.0541325 | + | 0.998534i | \(0.517239\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.1419 | −1.50524 | ||||||||
\(116\) | 2.22222 | 0.206328 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.8330 | 1.08931 | ||||||||
\(119\) | 29.0716 | 2.66499 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.79702 | −0.162695 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.99363 | −0.897455 | ||||||||
\(125\) | −29.2451 | −2.61576 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.4814 | −1.28502 | −0.642509 | − | 0.766278i | \(-0.722107\pi\) | ||||
−0.642509 | + | 0.766278i | \(0.722107\pi\) | |||||||
\(128\) | 10.2573 | 0.906624 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 44.1857 | 3.87535 | ||||||||
\(131\) | −3.43385 | −0.300017 | −0.150008 | − | 0.988685i | \(-0.547930\pi\) | ||||
−0.150008 | + | 0.988685i | \(0.547930\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.483792 | −0.0419501 | ||||||||
\(134\) | −16.2833 | −1.40666 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.52188 | −0.816495 | ||||||||
\(137\) | 14.0878 | 1.20360 | 0.601799 | − | 0.798648i | \(-0.294451\pi\) | ||||
0.601799 | + | 0.798648i | \(0.294451\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.7447 | 0.911358 | 0.455679 | − | 0.890144i | \(-0.349397\pi\) | ||||
0.455679 | + | 0.890144i | \(0.349397\pi\) | |||||||
\(140\) | −21.4808 | −1.81546 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 22.8487 | 1.91742 | ||||||||
\(143\) | −5.95009 | −0.497572 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.47037 | −0.620380 | ||||||||
\(146\) | 23.3179 | 1.92981 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.86231 | −0.481879 | ||||||||
\(149\) | 21.7408 | 1.78108 | 0.890539 | − | 0.454906i | \(-0.150327\pi\) | ||||
0.890539 | + | 0.454906i | \(0.150327\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.01304 | 0.407955 | 0.203978 | − | 0.978976i | \(-0.434613\pi\) | ||||
0.203978 | + | 0.978976i | \(0.434613\pi\) | |||||||
\(152\) | 0.158457 | 0.0128526 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.59885 | 0.612333 | ||||||||
\(155\) | 33.5952 | 2.69844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.11572 | 0.647705 | 0.323853 | − | 0.946108i | \(-0.395022\pi\) | ||||
0.323853 | + | 0.946108i | \(0.395022\pi\) | |||||||
\(158\) | 15.0208 | 1.19499 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 25.2931 | 1.99959 | ||||||||
\(161\) | 16.5175 | 1.30176 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.6507 | −1.53916 | −0.769579 | − | 0.638551i | \(-0.779534\pi\) | ||||
−0.769579 | + | 0.638551i | \(0.779534\pi\) | |||||||
\(164\) | −2.23419 | −0.174461 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.87521 | −0.378390 | ||||||||
\(167\) | 9.43965 | 0.730462 | 0.365231 | − | 0.930917i | \(-0.380990\pi\) | ||||
0.365231 | + | 0.930917i | \(0.380990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.4036 | 1.72336 | ||||||||
\(170\) | −51.0543 | −3.91568 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.000736294 0 | 5.61419e−5 0 | ||||||||
\(173\) | −14.8804 | −1.13134 | −0.565668 | − | 0.824633i | \(-0.691381\pi\) | ||||
−0.565668 | + | 0.824633i | \(0.691381\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 51.0685 | 3.86041 | ||||||||
\(176\) | −4.94743 | −0.372927 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 29.8421 | 2.23676 | ||||||||
\(179\) | −3.80389 | −0.284316 | −0.142158 | − | 0.989844i | \(-0.545404\pi\) | ||||
−0.142158 | + | 0.989844i | \(0.545404\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.450976 | −0.0335208 | −0.0167604 | − | 0.999860i | \(-0.505335\pi\) | ||||
−0.0167604 | + | 0.999860i | \(0.505335\pi\) | |||||||
\(182\) | −45.2139 | −3.35147 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.41002 | −0.398832 | ||||||||
\(185\) | 19.7071 | 1.44890 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.87502 | 0.502751 | ||||||||
\(188\) | −8.45300 | −0.616498 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.849614 | 0.0616375 | ||||||||
\(191\) | 10.9248 | 0.790494 | 0.395247 | − | 0.918575i | \(-0.370659\pi\) | ||||
0.395247 | + | 0.918575i | \(0.370659\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.24835 | 0.449766 | 0.224883 | − | 0.974386i | \(-0.427800\pi\) | ||||
0.224883 | + | 0.974386i | \(0.427800\pi\) | |||||||
\(194\) | 30.8192 | 2.21269 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.3757 | 0.955407 | ||||||||
\(197\) | −11.3428 | −0.808143 | −0.404072 | − | 0.914727i | \(-0.632405\pi\) | ||||
−0.404072 | + | 0.914727i | \(0.632405\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.57964 | 0.679083 | 0.339541 | − | 0.940591i | \(-0.389728\pi\) | ||||
0.339541 | + | 0.940591i | \(0.389728\pi\) | |||||||
\(200\) | −16.7266 | −1.18275 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 28.0020 | 1.97021 | ||||||||
\(203\) | 7.64419 | 0.536517 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.51060 | 0.524563 | ||||||||
\(206\) | −21.7641 | −1.51638 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 29.4377 | 2.04114 | ||||||||
\(209\) | −0.114410 | −0.00791390 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.4885 | 1.47933 | 0.739663 | − | 0.672977i | \(-0.234985\pi\) | ||||
0.739663 | + | 0.672977i | \(0.234985\pi\) | |||||||
\(212\) | 12.5697 | 0.863293 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.37240 | −0.230533 | ||||||||
\(215\) | −0.00247517 | −0.000168805 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −34.3769 | −2.33366 | ||||||||
\(218\) | 23.2855 | 1.57709 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.07992 | −0.342488 | ||||||||
\(221\) | −40.9070 | −2.75170 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.87993 | −0.192854 | −0.0964271 | − | 0.995340i | \(-0.530741\pi\) | ||||
−0.0964271 | + | 0.995340i | \(0.530741\pi\) | |||||||
\(224\) | −25.8816 | −1.72929 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.06814 | −0.137571 | ||||||||
\(227\) | 25.7966 | 1.71218 | 0.856089 | − | 0.516828i | \(-0.172887\pi\) | ||||
0.856089 | + | 0.516828i | \(0.172887\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.5014 | −0.892200 | −0.446100 | − | 0.894983i | \(-0.647187\pi\) | ||||
−0.446100 | + | 0.894983i | \(0.647187\pi\) | |||||||
\(230\) | −29.0073 | −1.91269 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.50372 | −0.164377 | ||||||||
\(233\) | −6.77150 | −0.443616 | −0.221808 | − | 0.975090i | \(-0.571196\pi\) | ||||
−0.221808 | + | 0.975090i | \(0.571196\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.4162 | 1.85367 | ||||||||
\(236\) | 8.09455 | 0.526910 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 52.2422 | 3.38636 | ||||||||
\(239\) | −5.72817 | −0.370525 | −0.185262 | − | 0.982689i | \(-0.559314\pi\) | ||||
−0.185262 | + | 0.982689i | \(0.559314\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.3348 | −1.24546 | −0.622731 | − | 0.782436i | \(-0.713977\pi\) | ||||
−0.622731 | + | 0.782436i | \(0.713977\pi\) | |||||||
\(242\) | 1.79702 | 0.115517 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.22928 | −0.0786966 | ||||||||
\(245\) | −44.9646 | −2.87268 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.680750 | 0.0433151 | ||||||||
\(248\) | 11.2596 | 0.714983 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −52.5540 | −3.32381 | ||||||||
\(251\) | −24.5158 | −1.54742 | −0.773711 | − | 0.633539i | \(-0.781602\pi\) | ||||
−0.773711 | + | 0.633539i | \(0.781602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.90616 | 0.245578 | ||||||||
\(254\) | −26.0234 | −1.63285 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.6406 | 1.29004 | ||||||||
\(257\) | −6.58361 | −0.410674 | −0.205337 | − | 0.978691i | \(-0.565829\pi\) | ||||
−0.205337 | + | 0.978691i | \(0.565829\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.1657 | −1.25303 | ||||||||
\(260\) | 30.2260 | 1.87454 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.17069 | −0.381227 | ||||||||
\(263\) | 1.91765 | 0.118247 | 0.0591236 | − | 0.998251i | \(-0.481169\pi\) | ||||
0.0591236 | + | 0.998251i | \(0.481169\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −42.2552 | −2.59572 | ||||||||
\(266\) | −0.869383 | −0.0533053 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.1388 | −0.680412 | ||||||||
\(269\) | 3.53464 | 0.215511 | 0.107755 | − | 0.994177i | \(-0.465634\pi\) | ||||
0.107755 | + | 0.994177i | \(0.465634\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.8059 | −0.777901 | −0.388951 | − | 0.921259i | \(-0.627162\pi\) | ||||
−0.388951 | + | 0.921259i | \(0.627162\pi\) | |||||||
\(272\) | −34.0137 | −2.06238 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.3160 | 1.52939 | ||||||||
\(275\) | 12.0770 | 0.728269 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0569 | 0.784510 | 0.392255 | − | 0.919856i | \(-0.371695\pi\) | ||||
0.392255 | + | 0.919856i | \(0.371695\pi\) | |||||||
\(278\) | 19.3085 | 1.15805 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 24.2019 | 1.44634 | ||||||||
\(281\) | 23.0464 | 1.37483 | 0.687415 | − | 0.726264i | \(-0.258745\pi\) | ||||
0.687415 | + | 0.726264i | \(0.258745\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7644 | 0.818207 | 0.409103 | − | 0.912488i | \(-0.365842\pi\) | ||||
0.409103 | + | 0.912488i | \(0.365842\pi\) | |||||||
\(284\) | 15.6301 | 0.927473 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.6924 | −0.632257 | ||||||||
\(287\) | −7.68536 | −0.453653 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.2658 | 1.78034 | ||||||||
\(290\) | −13.4244 | −0.788308 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.9510 | 0.933463 | ||||||||
\(293\) | −10.7562 | −0.628384 | −0.314192 | − | 0.949359i | \(-0.601734\pi\) | ||||
−0.314192 | + | 0.949359i | \(0.601734\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.2112 | −1.58429 | ||||||||
\(296\) | 6.60491 | 0.383903 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 39.0687 | 2.26319 | ||||||||
\(299\) | −23.2420 | −1.34412 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.00253277 | 0.000145986 0 | ||||||||
\(302\) | 9.00853 | 0.518383 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.566035 | 0.0324643 | ||||||||
\(305\) | 4.13243 | 0.236622 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.0831 | −1.20328 | −0.601639 | − | 0.798768i | \(-0.705485\pi\) | ||||
−0.601639 | + | 0.798768i | \(0.705485\pi\) | |||||||
\(308\) | 5.19812 | 0.296190 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 60.3713 | 3.42886 | ||||||||
\(311\) | −5.47069 | −0.310214 | −0.155107 | − | 0.987898i | \(-0.549572\pi\) | ||||
−0.155107 | + | 0.987898i | \(0.549572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.5030 | −1.32847 | −0.664234 | − | 0.747524i | \(-0.731242\pi\) | ||||
−0.664234 | + | 0.747524i | \(0.731242\pi\) | |||||||
\(314\) | 14.5841 | 0.823029 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.2752 | 0.578027 | ||||||||
\(317\) | −15.5042 | −0.870802 | −0.435401 | − | 0.900237i | \(-0.643393\pi\) | ||||
−0.435401 | + | 0.900237i | \(0.643393\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.80774 | 0.101214 | ||||||||
\(320\) | 4.56237 | 0.255044 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 29.6823 | 1.65413 | ||||||||
\(323\) | −0.786570 | −0.0437659 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −71.8591 | −3.98603 | ||||||||
\(326\) | −35.3126 | −1.95579 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.51721 | 0.138989 | ||||||||
\(329\) | −29.0773 | −1.60309 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4645 | −0.740077 | −0.370038 | − | 0.929016i | \(-0.620655\pi\) | ||||
−0.370038 | + | 0.929016i | \(0.620655\pi\) | |||||||
\(332\) | −3.33497 | −0.183030 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.9632 | 0.928187 | ||||||||
\(335\) | 37.4450 | 2.04584 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.25582 | 0.122882 | 0.0614411 | − | 0.998111i | \(-0.480430\pi\) | ||||
0.0614411 | + | 0.998111i | \(0.480430\pi\) | |||||||
\(338\) | 40.2597 | 2.18984 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −34.9245 | −1.89405 | ||||||||
\(341\) | −8.12966 | −0.440246 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4108 | 0.886098 | ||||||||
\(344\) | −0.000829563 0 | −4.47270e−5 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −26.7404 | −1.43757 | ||||||||
\(347\) | 6.94172 | 0.372651 | 0.186325 | − | 0.982488i | \(-0.440342\pi\) | ||||
0.186325 | + | 0.982488i | \(0.440342\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.2568 | −1.03079 | −0.515396 | − | 0.856952i | \(-0.672355\pi\) | ||||
−0.515396 | + | 0.856952i | \(0.672355\pi\) | |||||||
\(350\) | 91.7711 | 4.90537 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.12063 | −0.326231 | ||||||||
\(353\) | 17.2457 | 0.917895 | 0.458947 | − | 0.888463i | \(-0.348227\pi\) | ||||
0.458947 | + | 0.888463i | \(0.348227\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −52.5430 | −2.78869 | ||||||||
\(356\) | 20.4139 | 1.08194 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.83566 | −0.361276 | ||||||||
\(359\) | 7.01416 | 0.370193 | 0.185097 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185097 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9869 | −0.999311 | ||||||||
\(362\) | −0.810413 | −0.0425944 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −30.9293 | −1.62113 | ||||||||
\(365\) | −53.6220 | −2.80670 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.793430 | −0.0414167 | −0.0207084 | − | 0.999786i | \(-0.506592\pi\) | ||||
−0.0207084 | + | 0.999786i | \(0.506592\pi\) | |||||||
\(368\) | −19.3254 | −1.00741 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 35.4141 | 1.84109 | ||||||||
\(371\) | 43.2384 | 2.24483 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.5789 | 1.11731 | 0.558656 | − | 0.829399i | \(-0.311317\pi\) | ||||
0.558656 | + | 0.829399i | \(0.311317\pi\) | |||||||
\(374\) | 12.3545 | 0.638838 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.52377 | 0.491151 | ||||||||
\(377\) | −10.7562 | −0.553975 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.364682 | −0.0187325 | −0.00936623 | − | 0.999956i | \(-0.502981\pi\) | ||||
−0.00936623 | + | 0.999956i | \(0.502981\pi\) | |||||||
\(380\) | 0.581193 | 0.0298145 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.6322 | 1.00447 | ||||||||
\(383\) | 5.90918 | 0.301945 | 0.150973 | − | 0.988538i | \(-0.451759\pi\) | ||||
0.150973 | + | 0.988538i | \(0.451759\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.4743 | −0.890574 | ||||||||
\(386\) | 11.2284 | 0.571511 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.0824 | 1.07029 | ||||||||
\(389\) | −0.0700961 | −0.00355401 | −0.00177701 | − | 0.999998i | \(-0.500566\pi\) | ||||
−0.00177701 | + | 0.999998i | \(0.500566\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.8549 | 1.35811 | ||||||||
\(392\) | −15.0700 | −0.761152 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.3833 | −1.02690 | ||||||||
\(395\) | −34.5419 | −1.73799 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.10974 | 0.457205 | 0.228602 | − | 0.973520i | \(-0.426584\pi\) | ||||
0.228602 | + | 0.973520i | \(0.426584\pi\) | |||||||
\(398\) | 17.2148 | 0.862900 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −59.7500 | −2.98750 | ||||||||
\(401\) | 30.5240 | 1.52429 | 0.762147 | − | 0.647404i | \(-0.224145\pi\) | ||||
0.762147 | + | 0.647404i | \(0.224145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 48.3722 | 2.40959 | ||||||||
\(404\) | 19.1552 | 0.953007 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.7368 | 0.681744 | ||||||||
\(407\) | −4.76890 | −0.236385 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.0857 | 0.993173 | 0.496587 | − | 0.867987i | \(-0.334586\pi\) | ||||
0.496587 | + | 0.867987i | \(0.334586\pi\) | |||||||
\(410\) | 13.4967 | 0.666555 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.8881 | −0.733483 | ||||||||
\(413\) | 27.8443 | 1.37013 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.2110 | 0.550329 | ||||||||
\(416\) | 36.4184 | 1.78556 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.205597 | −0.0100561 | ||||||||
\(419\) | −20.3405 | −0.993700 | −0.496850 | − | 0.867836i | \(-0.665510\pi\) | ||||
−0.496850 | + | 0.867836i | \(0.665510\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0548 | 0.636254 | 0.318127 | − | 0.948048i | \(-0.396946\pi\) | ||||
0.318127 | + | 0.948048i | \(0.396946\pi\) | |||||||
\(422\) | 38.6152 | 1.87976 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.1620 | −0.687767 | ||||||||
\(425\) | 83.0294 | 4.02752 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.22858 | −0.204635 | ||||||||
\(428\) | −2.30695 | −0.111510 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.00444794 | −0.000214499 0 | ||||||||
\(431\) | −19.6386 | −0.945959 | −0.472979 | − | 0.881073i | \(-0.656822\pi\) | ||||
−0.472979 | + | 0.881073i | \(0.656822\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.252308 | 0.0121251 | 0.00606256 | − | 0.999982i | \(-0.498070\pi\) | ||||
0.00606256 | + | 0.999982i | \(0.498070\pi\) | |||||||
\(434\) | −61.7761 | −2.96535 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.9288 | 0.762851 | ||||||||
\(437\) | −0.446903 | −0.0213783 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.0439 | −1.00437 | −0.502186 | − | 0.864760i | \(-0.667471\pi\) | ||||
−0.502186 | + | 0.864760i | \(0.667471\pi\) | |||||||
\(440\) | 5.72341 | 0.272853 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −73.5107 | −3.49655 | ||||||||
\(443\) | −34.5338 | −1.64075 | −0.820376 | − | 0.571824i | \(-0.806236\pi\) | ||||
−0.820376 | + | 0.571824i | \(0.806236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −68.6248 | −3.25313 | ||||||||
\(446\) | −5.17528 | −0.245057 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.66853 | −0.220567 | ||||||||
\(449\) | 37.4052 | 1.76526 | 0.882630 | − | 0.470069i | \(-0.155771\pi\) | ||||
0.882630 | + | 0.470069i | \(0.155771\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.81748 | −0.0855818 | ||||||||
\(452\) | −1.41475 | −0.0665441 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 46.3570 | 2.17564 | ||||||||
\(455\) | 103.974 | 4.87437 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.9860 | −1.40269 | −0.701344 | − | 0.712823i | \(-0.747416\pi\) | ||||
−0.701344 | + | 0.712823i | \(0.747416\pi\) | |||||||
\(458\) | −24.2623 | −1.13371 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −19.8429 | −0.925182 | ||||||||
\(461\) | −9.54911 | −0.444746 | −0.222373 | − | 0.974962i | \(-0.571380\pi\) | ||||
−0.222373 | + | 0.974962i | \(0.571380\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.3600 | 0.946209 | 0.473104 | − | 0.881006i | \(-0.343133\pi\) | ||||
0.473104 | + | 0.881006i | \(0.343133\pi\) | |||||||
\(464\) | −8.94368 | −0.415200 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.1685 | −0.563696 | ||||||||
\(467\) | 15.9468 | 0.737930 | 0.368965 | − | 0.929443i | \(-0.379712\pi\) | ||||
0.368965 | + | 0.929443i | \(0.379712\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −38.3163 | −1.76928 | ||||||||
\(470\) | 51.0644 | 2.35543 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.11991 | −0.419778 | ||||||||
\(473\) | 0.000598963 0 | 2.75404e−5 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.38172 | −0.0633979 | ||||||||
\(476\) | 35.7371 | 1.63801 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.2936 | −0.470820 | ||||||||
\(479\) | −40.2343 | −1.83835 | −0.919176 | − | 0.393847i | \(-0.871144\pi\) | ||||
−0.919176 | + | 0.393847i | \(0.871144\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.3754 | 1.29381 | ||||||||
\(482\) | −34.7450 | −1.58259 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.22928 | 0.0558764 | ||||||||
\(485\) | −70.8718 | −3.21812 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.969646 | 0.0439388 | 0.0219694 | − | 0.999759i | \(-0.493006\pi\) | ||||
0.0219694 | + | 0.999759i | \(0.493006\pi\) | |||||||
\(488\) | 1.38500 | 0.0626959 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −80.8023 | −3.65028 | ||||||||
\(491\) | −5.83295 | −0.263238 | −0.131619 | − | 0.991300i | \(-0.542017\pi\) | ||||
−0.131619 | + | 0.991300i | \(0.542017\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.4283 | 0.559741 | ||||||||
\(494\) | 1.22332 | 0.0550398 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 40.2209 | 1.80597 | ||||||||
\(497\) | 53.7656 | 2.41172 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.7460 | 0.883954 | 0.441977 | − | 0.897026i | \(-0.354277\pi\) | ||||
0.441977 | + | 0.897026i | \(0.354277\pi\) | |||||||
\(500\) | −35.9504 | −1.60775 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −44.0553 | −1.96629 | ||||||||
\(503\) | −14.4566 | −0.644588 | −0.322294 | − | 0.946640i | \(-0.604454\pi\) | ||||
−0.322294 | + | 0.946640i | \(0.604454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −64.3934 | −2.86547 | ||||||||
\(506\) | 7.01944 | 0.312052 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.8017 | −0.789824 | ||||||||
\(509\) | 3.47334 | 0.153953 | 0.0769766 | − | 0.997033i | \(-0.475473\pi\) | ||||
0.0769766 | + | 0.997033i | \(0.475473\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 54.8697 | 2.42729 | ||||||||
\(512\) | 16.5771 | 0.732609 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.8309 | −0.521838 | ||||||||
\(515\) | 50.0487 | 2.20541 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.87638 | −0.302423 | ||||||||
\(518\) | −36.2381 | −1.59221 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −34.0548 | −1.49340 | ||||||||
\(521\) | 14.4838 | 0.634546 | 0.317273 | − | 0.948334i | \(-0.397233\pi\) | ||||
0.317273 | + | 0.948334i | \(0.397233\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.4917 | −1.20213 | −0.601065 | − | 0.799200i | \(-0.705257\pi\) | ||||
−0.601065 | + | 0.799200i | \(0.705257\pi\) | |||||||
\(524\) | −4.22116 | −0.184402 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.44605 | 0.150255 | ||||||||
\(527\) | −55.8915 | −2.43467 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.74194 | −0.336606 | ||||||||
\(530\) | −75.9335 | −3.29834 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.594716 | −0.0257842 | ||||||||
\(533\) | 10.8142 | 0.468414 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.75518 | 0.335286 | ||||||||
\(536\) | 12.5498 | 0.542070 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.35182 | 0.273846 | ||||||||
\(539\) | 10.8809 | 0.468674 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.05357 | 0.260263 | 0.130132 | − | 0.991497i | \(-0.458460\pi\) | ||||
0.130132 | + | 0.991497i | \(0.458460\pi\) | |||||||
\(542\) | −23.0124 | −0.988467 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −42.0795 | −1.80414 | ||||||||
\(545\) | −53.5473 | −2.29371 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.9576 | 1.40916 | 0.704582 | − | 0.709622i | \(-0.251134\pi\) | ||||
0.704582 | + | 0.709622i | \(0.251134\pi\) | |||||||
\(548\) | 17.3178 | 0.739780 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.7026 | 0.925400 | ||||||||
\(551\) | −0.206824 | −0.00881098 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.3456 | 1.50305 | ||||||||
\(554\) | 23.4634 | 0.996866 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.2083 | 0.560157 | ||||||||
\(557\) | 12.4314 | 0.526735 | 0.263367 | − | 0.964696i | \(-0.415167\pi\) | ||||
0.263367 | + | 0.964696i | \(0.415167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.00356389 | −0.000150736 0 | ||||||||
\(560\) | 86.4530 | 3.65331 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 41.4148 | 1.74698 | ||||||||
\(563\) | 5.86096 | 0.247010 | 0.123505 | − | 0.992344i | \(-0.460586\pi\) | ||||
0.123505 | + | 0.992344i | \(0.460586\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.75590 | 0.200082 | ||||||||
\(566\) | 24.7348 | 1.03968 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.6100 | −0.738898 | ||||||||
\(569\) | −35.8528 | −1.50303 | −0.751514 | − | 0.659718i | \(-0.770676\pi\) | ||||
−0.751514 | + | 0.659718i | \(0.770676\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.0482 | 1.59227 | 0.796134 | − | 0.605120i | \(-0.206875\pi\) | ||||
0.796134 | + | 0.605120i | \(0.206875\pi\) | |||||||
\(572\) | −7.31433 | −0.305828 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.8107 | −0.576450 | ||||||||
\(575\) | 47.1745 | 1.96731 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.4611 | 0.602024 | 0.301012 | − | 0.953620i | \(-0.402676\pi\) | ||||
0.301012 | + | 0.953620i | \(0.402676\pi\) | |||||||
\(578\) | 54.3883 | 2.26226 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.18318 | −0.381311 | ||||||||
\(581\) | −11.4719 | −0.475935 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.2253 | 0.423488 | ||||||||
\(584\) | −17.9716 | −0.743670 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.3291 | −0.798478 | ||||||||
\(587\) | −12.5605 | −0.518429 | −0.259214 | − | 0.965820i | \(-0.583464\pi\) | ||||
−0.259214 | + | 0.965820i | \(0.583464\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.930114 | 0.0383247 | ||||||||
\(590\) | −48.8990 | −2.01314 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.5938 | 0.969699 | ||||||||
\(593\) | 21.6528 | 0.889175 | 0.444588 | − | 0.895735i | \(-0.353350\pi\) | ||||
0.444588 | + | 0.895735i | \(0.353350\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −120.136 | −4.92510 | ||||||||
\(596\) | 26.7256 | 1.09472 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −41.7663 | −1.70795 | ||||||||
\(599\) | −8.14091 | −0.332629 | −0.166314 | − | 0.986073i | \(-0.553187\pi\) | ||||
−0.166314 | + | 0.986073i | \(0.553187\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.887153 | −0.0361877 | −0.0180939 | − | 0.999836i | \(-0.505760\pi\) | ||||
−0.0180939 | + | 0.999836i | \(0.505760\pi\) | |||||||
\(602\) | 0.00455143 | 0.000185502 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.16243 | 0.250746 | ||||||||
\(605\) | −4.13243 | −0.168007 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.16751 | 0.128565 | 0.0642827 | − | 0.997932i | \(-0.479524\pi\) | ||||
0.0642827 | + | 0.997932i | \(0.479524\pi\) | |||||||
\(608\) | 0.700261 | 0.0283993 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.42606 | 0.300672 | ||||||||
\(611\) | 40.9151 | 1.65525 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.3632 | 1.02441 | 0.512205 | − | 0.858863i | \(-0.328829\pi\) | ||||
0.512205 | + | 0.858863i | \(0.328829\pi\) | |||||||
\(614\) | −37.8868 | −1.52899 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.85658 | −0.235968 | ||||||||
\(617\) | −8.47573 | −0.341220 | −0.170610 | − | 0.985339i | \(-0.554574\pi\) | ||||
−0.170610 | + | 0.985339i | \(0.554574\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.5870 | −0.666687 | −0.333344 | − | 0.942805i | \(-0.608177\pi\) | ||||
−0.333344 | + | 0.942805i | \(0.608177\pi\) | |||||||
\(620\) | 41.2980 | 1.65857 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.83093 | −0.394184 | ||||||||
\(623\) | 70.2216 | 2.81337 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 60.4684 | 2.41874 | ||||||||
\(626\) | −42.2354 | −1.68807 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.97650 | 0.398106 | ||||||||
\(629\) | −32.7862 | −1.30727 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.9136 | 0.593700 | 0.296850 | − | 0.954924i | \(-0.404064\pi\) | ||||
0.296850 | + | 0.954924i | \(0.404064\pi\) | |||||||
\(632\) | −11.5768 | −0.460502 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −27.8613 | −1.10652 | ||||||||
\(635\) | 59.8434 | 2.37481 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −64.7425 | −2.56519 | ||||||||
\(638\) | 3.24855 | 0.128611 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −42.3875 | −1.67551 | ||||||||
\(641\) | −0.0827782 | −0.00326954 | −0.00163477 | − | 0.999999i | \(-0.500520\pi\) | ||||
−0.00163477 | + | 0.999999i | \(0.500520\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.8688 | 0.783547 | 0.391774 | − | 0.920062i | \(-0.371862\pi\) | ||||
0.391774 | + | 0.920062i | \(0.371862\pi\) | |||||||
\(644\) | 20.3046 | 0.800115 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.41348 | −0.0556127 | ||||||||
\(647\) | 13.9341 | 0.547807 | 0.273904 | − | 0.961757i | \(-0.411685\pi\) | ||||
0.273904 | + | 0.961757i | \(0.411685\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.58478 | 0.258475 | ||||||||
\(650\) | −129.132 | −5.06498 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.1562 | −0.946029 | ||||||||
\(653\) | 17.9089 | 0.700830 | 0.350415 | − | 0.936594i | \(-0.386041\pi\) | ||||
0.350415 | + | 0.936594i | \(0.386041\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.1901 | 0.554454 | ||||||||
\(656\) | 8.99185 | 0.351073 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −52.2526 | −2.03702 | ||||||||
\(659\) | 7.08434 | 0.275967 | 0.137983 | − | 0.990435i | \(-0.455938\pi\) | ||||
0.137983 | + | 0.990435i | \(0.455938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.3330 | 1.64656 | 0.823282 | − | 0.567633i | \(-0.192141\pi\) | ||||
0.823282 | + | 0.567633i | \(0.192141\pi\) | |||||||
\(662\) | −24.1960 | −0.940405 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.75742 | 0.145816 | ||||||||
\(665\) | 1.99924 | 0.0775270 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.06133 | 0.273416 | ||||||||
\(668\) | 11.6040 | 0.448971 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 67.2894 | 2.59962 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.2241 | 1.78181 | 0.890904 | − | 0.454192i | \(-0.150072\pi\) | ||||
0.890904 | + | 0.454192i | \(0.150072\pi\) | |||||||
\(674\) | 4.05375 | 0.156145 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 27.5403 | 1.05924 | ||||||||
\(677\) | 8.24391 | 0.316839 | 0.158420 | − | 0.987372i | \(-0.449360\pi\) | ||||
0.158420 | + | 0.987372i | \(0.449360\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 72.5208 | 2.78309 | ||||||||
\(680\) | 39.3485 | 1.50895 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.6092 | −0.559414 | ||||||||
\(683\) | 38.3645 | 1.46798 | 0.733989 | − | 0.679162i | \(-0.237657\pi\) | ||||
0.733989 | + | 0.679162i | \(0.237657\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −58.2166 | −2.22434 | ||||||||
\(686\) | 29.4905 | 1.12595 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.00296333 | −0.000112976 0 | ||||||||
\(689\) | −60.8413 | −2.31787 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.4049 | −1.57512 | −0.787558 | − | 0.616240i | \(-0.788655\pi\) | ||||
−0.787558 | + | 0.616240i | \(0.788655\pi\) | |||||||
\(692\) | −18.2922 | −0.695364 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.4744 | 0.473522 | ||||||||
\(695\) | −44.4019 | −1.68426 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.4952 | −0.473289 | ||||||||
\(698\) | −34.6049 | −1.30981 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 62.7775 | 2.37277 | ||||||||
\(701\) | −27.8921 | −1.05347 | −0.526735 | − | 0.850029i | \(-0.676584\pi\) | ||||
−0.526735 | + | 0.850029i | \(0.676584\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.545609 | 0.0205780 | ||||||||
\(704\) | −1.10404 | −0.0416101 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.9908 | 1.16636 | ||||||||
\(707\) | 65.8917 | 2.47811 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.19632 | −0.157596 | −0.0787980 | − | 0.996891i | \(-0.525108\pi\) | ||||
−0.0787980 | + | 0.996891i | \(0.525108\pi\) | |||||||
\(710\) | −94.4208 | −3.54355 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −22.9999 | −0.861956 | ||||||||
\(713\) | −31.7557 | −1.18926 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.5883 | 0.919552 | ||||||||
\(716\) | −4.67605 | −0.174752 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.6046 | 0.470399 | ||||||||
\(719\) | −48.7664 | −1.81868 | −0.909339 | − | 0.416055i | \(-0.863412\pi\) | ||||
−0.909339 | + | 0.416055i | \(0.863412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −51.2133 | −1.90728 | ||||||||
\(722\) | −34.1199 | −1.26981 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.554376 | −0.0206032 | ||||||||
\(725\) | 21.8321 | 0.810822 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.3367 | −1.19930 | −0.599652 | − | 0.800261i | \(-0.704694\pi\) | ||||
−0.599652 | + | 0.800261i | \(0.704694\pi\) | |||||||
\(728\) | 34.8472 | 1.29152 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −96.3598 | −3.56643 | ||||||||
\(731\) | 0.00411788 | 0.000152305 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.1274 | −1.22359 | −0.611795 | − | 0.791017i | \(-0.709552\pi\) | ||||
−0.611795 | + | 0.791017i | \(0.709552\pi\) | |||||||
\(734\) | −1.42581 | −0.0526276 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23.9082 | −0.881266 | ||||||||
\(737\) | −9.06126 | −0.333776 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.1344 | 0.446372 | 0.223186 | − | 0.974776i | \(-0.428354\pi\) | ||||
0.223186 | + | 0.974776i | \(0.428354\pi\) | |||||||
\(740\) | 24.2256 | 0.890550 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 77.7003 | 2.85247 | ||||||||
\(743\) | −43.8579 | −1.60899 | −0.804496 | − | 0.593958i | \(-0.797564\pi\) | ||||
−0.804496 | + | 0.593958i | \(0.797564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −89.8425 | −3.29157 | ||||||||
\(746\) | 38.7777 | 1.41975 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.45132 | 0.309011 | ||||||||
\(749\) | −7.93563 | −0.289962 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.4328 | −0.636130 | −0.318065 | − | 0.948069i | \(-0.603033\pi\) | ||||
−0.318065 | + | 0.948069i | \(0.603033\pi\) | |||||||
\(752\) | 34.0204 | 1.24060 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19.3292 | −0.703927 | ||||||||
\(755\) | −20.7160 | −0.753934 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.6697 | −0.387796 | −0.193898 | − | 0.981022i | \(-0.562113\pi\) | ||||
−0.193898 | + | 0.981022i | \(0.562113\pi\) | |||||||
\(758\) | −0.655341 | −0.0238031 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.654814 | −0.0237526 | ||||||||
\(761\) | 25.4388 | 0.922154 | 0.461077 | − | 0.887360i | \(-0.347463\pi\) | ||||
0.461077 | + | 0.887360i | \(0.347463\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 54.7932 | 1.98365 | ||||||||
\(764\) | 13.4297 | 0.485870 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.6189 | 0.383677 | ||||||||
\(767\) | −39.1801 | −1.41471 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.2863 | −1.20033 | −0.600167 | − | 0.799875i | \(-0.704899\pi\) | ||||
−0.600167 | + | 0.799875i | \(0.704899\pi\) | |||||||
\(770\) | −31.4017 | −1.13164 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.68097 | 0.276444 | ||||||||
\(773\) | 25.8479 | 0.929686 | 0.464843 | − | 0.885393i | \(-0.346111\pi\) | ||||
0.464843 | + | 0.885393i | \(0.346111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −98.1817 | −3.52679 | ||||||||
\(776\) | −23.7529 | −0.852681 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.125964 | −0.00451603 | ||||||||
\(779\) | 0.207938 | 0.00745014 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.7148 | 0.454971 | ||||||||
\(782\) | 48.2588 | 1.72573 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −53.8326 | −1.92259 | ||||||||
\(785\) | −33.5376 | −1.19701 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.1813 | 1.18279 | 0.591393 | − | 0.806384i | \(-0.298578\pi\) | ||||
0.591393 | + | 0.806384i | \(0.298578\pi\) | |||||||
\(788\) | −13.9435 | −0.496717 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −62.0724 | −2.20844 | ||||||||
\(791\) | −4.86656 | −0.173035 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.95009 | 0.211294 | ||||||||
\(794\) | 16.3704 | 0.580963 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.7761 | 0.417392 | ||||||||
\(797\) | −35.7596 | −1.26667 | −0.633335 | − | 0.773878i | \(-0.718314\pi\) | ||||
−0.633335 | + | 0.773878i | \(0.718314\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.2752 | −1.67248 | ||||||||
\(800\) | −73.9187 | −2.61342 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 54.8522 | 1.93690 | ||||||||
\(803\) | 12.9759 | 0.457909 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −68.2574 | −2.40576 | ||||||||
\(806\) | 86.9259 | 3.06183 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.5817 | −0.759241 | ||||||||
\(809\) | −20.5071 | −0.720993 | −0.360496 | − | 0.932761i | \(-0.617393\pi\) | ||||
−0.360496 | + | 0.932761i | \(0.617393\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.3261 | −1.34581 | −0.672906 | − | 0.739728i | \(-0.734954\pi\) | ||||
−0.672906 | + | 0.739728i | \(0.734954\pi\) | |||||||
\(812\) | 9.39686 | 0.329765 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.56980 | −0.300371 | ||||||||
\(815\) | 81.2050 | 2.84449 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.85273e−5 0 | −2.39747e−6 0 | ||||||||
\(818\) | 36.0944 | 1.26201 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.23264 | 0.322418 | ||||||||
\(821\) | 11.9912 | 0.418496 | 0.209248 | − | 0.977863i | \(-0.432898\pi\) | ||||
0.209248 | + | 0.977863i | \(0.432898\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.7456 | −0.792861 | −0.396430 | − | 0.918065i | \(-0.629751\pi\) | ||||
−0.396430 | + | 0.918065i | \(0.629751\pi\) | |||||||
\(824\) | 16.7740 | 0.584350 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 50.0368 | 1.74100 | ||||||||
\(827\) | 20.5343 | 0.714047 | 0.357024 | − | 0.934095i | \(-0.383792\pi\) | ||||
0.357024 | + | 0.934095i | \(0.383792\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.48682 | 0.329491 | 0.164746 | − | 0.986336i | \(-0.447320\pi\) | ||||
0.164746 | + | 0.986336i | \(0.447320\pi\) | |||||||
\(830\) | 20.1465 | 0.699294 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.56915 | 0.227744 | ||||||||
\(833\) | 74.8065 | 2.59189 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.0087 | −1.34995 | ||||||||
\(836\) | −0.140642 | −0.00486420 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −36.5523 | −1.26268 | ||||||||
\(839\) | 40.8237 | 1.40939 | 0.704695 | − | 0.709510i | \(-0.251084\pi\) | ||||
0.704695 | + | 0.709510i | \(0.251084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.7321 | −0.887313 | ||||||||
\(842\) | 23.4598 | 0.808479 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 26.4153 | 0.909253 | ||||||||
\(845\) | −92.5814 | −3.18490 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.22858 | 0.145296 | ||||||||
\(848\) | −50.5888 | −1.73723 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 149.205 | 5.11770 | ||||||||
\(851\) | −18.6281 | −0.638561 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.6419 | 0.501329 | 0.250665 | − | 0.968074i | \(-0.419351\pi\) | ||||
0.250665 | + | 0.968074i | \(0.419351\pi\) | |||||||
\(854\) | −7.59885 | −0.260027 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.59918 | 0.0888380 | ||||||||
\(857\) | −3.14537 | −0.107444 | −0.0537219 | − | 0.998556i | \(-0.517108\pi\) | ||||
−0.0537219 | + | 0.998556i | \(0.517108\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.53158 | 0.188735 | 0.0943675 | − | 0.995537i | \(-0.469917\pi\) | ||||
0.0943675 | + | 0.995537i | \(0.469917\pi\) | |||||||
\(860\) | −0.00304268 | −0.000103755 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −35.2910 | −1.20202 | ||||||||
\(863\) | −21.2821 | −0.724452 | −0.362226 | − | 0.932090i | \(-0.617983\pi\) | ||||
−0.362226 | + | 0.932090i | \(0.617983\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 61.4922 | 2.09080 | ||||||||
\(866\) | 0.453402 | 0.0154072 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −42.2589 | −1.43436 | ||||||||
\(869\) | 8.35873 | 0.283551 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53.9153 | 1.82685 | ||||||||
\(872\) | −17.9466 | −0.607747 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.803093 | −0.0271650 | ||||||||
\(875\) | −123.665 | −4.18065 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.0646 | −1.79186 | −0.895931 | − | 0.444192i | \(-0.853491\pi\) | ||||
−0.895931 | + | 0.444192i | \(0.853491\pi\) | |||||||
\(878\) | −37.8163 | −1.27624 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 20.4449 | 0.689198 | ||||||||
\(881\) | −40.9268 | −1.37886 | −0.689430 | − | 0.724353i | \(-0.742139\pi\) | ||||
−0.689430 | + | 0.724353i | \(0.742139\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.5469 | 0.624153 | 0.312076 | − | 0.950057i | \(-0.398975\pi\) | ||||
0.312076 | + | 0.950057i | \(0.398975\pi\) | |||||||
\(884\) | −50.2862 | −1.69131 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −62.0580 | −2.08488 | ||||||||
\(887\) | −3.31658 | −0.111360 | −0.0556800 | − | 0.998449i | \(-0.517733\pi\) | ||||
−0.0556800 | + | 0.998449i | \(0.517733\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −61.2359 | −2.05379 | ||||||||
\(890\) | −123.320 | −4.13370 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.54024 | −0.118536 | ||||||||
\(893\) | 0.786726 | 0.0263268 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.7193 | 0.525438 | ||||||||
\(896\) | 43.3738 | 1.44902 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 67.2178 | 2.24309 | ||||||||
\(899\) | −14.6963 | −0.490150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 70.2989 | 2.34200 | ||||||||
\(902\) | −3.26605 | −0.108747 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.59396 | 0.0530142 | ||||||||
\(905\) | 1.86363 | 0.0619491 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.6886 | 1.58347 | 0.791737 | − | 0.610862i | \(-0.209177\pi\) | ||||
0.791737 | + | 0.610862i | \(0.209177\pi\) | |||||||
\(908\) | 31.7112 | 1.05237 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 186.843 | 6.19379 | ||||||||
\(911\) | −10.3974 | −0.344480 | −0.172240 | − | 0.985055i | \(-0.555100\pi\) | ||||
−0.172240 | + | 0.985055i | \(0.555100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.71294 | −0.0897853 | ||||||||
\(914\) | −53.8855 | −1.78237 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.5971 | −0.548382 | ||||||||
\(917\) | −14.5203 | −0.479503 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −59.9521 | −1.97764 | −0.988818 | − | 0.149128i | \(-0.952353\pi\) | ||||
−0.988818 | + | 0.149128i | \(0.952353\pi\) | |||||||
\(920\) | 22.3565 | 0.737073 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.1599 | −0.565133 | ||||||||
\(923\) | −75.6543 | −2.49019 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −57.5938 | −1.89367 | ||||||||
\(926\) | 36.5873 | 1.20233 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11.0645 | −0.363211 | ||||||||
\(929\) | 3.13584 | 0.102884 | 0.0514418 | − | 0.998676i | \(-0.483618\pi\) | ||||
0.0514418 | + | 0.998676i | \(0.483618\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.24488 | −0.0407994 | ||||||||
\(932\) | −8.32407 | −0.272664 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.6567 | 0.937676 | ||||||||
\(935\) | −28.4105 | −0.929123 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55.4987 | −1.81306 | −0.906531 | − | 0.422139i | \(-0.861279\pi\) | ||||
−0.906531 | + | 0.422139i | \(0.861279\pi\) | |||||||
\(938\) | −68.8551 | −2.24820 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 34.9314 | 1.13934 | ||||||||
\(941\) | −0.0229290 | −0.000747463 0 | −0.000373731 | − | 1.00000i | \(-0.500119\pi\) | ||||
−0.000373731 | 1.00000i | \(0.500119\pi\) | ||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.09936 | −0.231187 | ||||||||
\(944\) | −32.5778 | −1.06032 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.00107635 | 3.49951e−5 0 | ||||||||
\(947\) | 11.9133 | 0.387129 | 0.193565 | − | 0.981088i | \(-0.437995\pi\) | ||||
0.193565 | + | 0.981088i | \(0.437995\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −77.2078 | −2.50627 | ||||||||
\(950\) | −2.48299 | −0.0805587 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −40.2641 | −1.30497 | ||||||||
\(953\) | −38.9528 | −1.26180 | −0.630902 | − | 0.775862i | \(-0.717315\pi\) | ||||
−0.630902 | + | 0.775862i | \(0.717315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −45.1462 | −1.46090 | ||||||||
\(956\) | −7.04153 | −0.227739 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −72.3018 | −2.33597 | ||||||||
\(959\) | 59.5712 | 1.92366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.0914 | 1.13198 | ||||||||
\(962\) | 50.9911 | 1.64402 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.7678 | −0.765511 | ||||||||
\(965\) | −25.8209 | −0.831203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.5683 | −0.983009 | −0.491504 | − | 0.870875i | \(-0.663553\pi\) | ||||
−0.491504 | + | 0.870875i | \(0.663553\pi\) | |||||||
\(968\) | −1.38500 | −0.0445155 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −127.358 | −4.08922 | ||||||||
\(971\) | 13.5495 | 0.434823 | 0.217412 | − | 0.976080i | \(-0.430239\pi\) | ||||
0.217412 | + | 0.976080i | \(0.430239\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.4351 | 1.45658 | ||||||||
\(974\) | 1.74247 | 0.0558324 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.94743 | 0.158363 | ||||||||
\(977\) | 47.4768 | 1.51892 | 0.759459 | − | 0.650555i | \(-0.225464\pi\) | ||||
0.759459 | + | 0.650555i | \(0.225464\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.6064 | 0.530743 | ||||||||
\(980\) | −55.2741 | −1.76567 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.4819 | −0.334492 | ||||||||
\(983\) | 38.2094 | 1.21869 | 0.609345 | − | 0.792905i | \(-0.291432\pi\) | ||||
0.609345 | + | 0.792905i | \(0.291432\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.8734 | 1.49351 | ||||||||
\(986\) | 22.3338 | 0.711254 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.836832 | 0.0266232 | ||||||||
\(989\) | 0.00233964 | 7.43964e−5 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.55647 | −0.144741 | −0.0723705 | − | 0.997378i | \(-0.523056\pi\) | ||||
−0.0723705 | + | 0.997378i | \(0.523056\pi\) | |||||||
\(992\) | 49.7587 | 1.57984 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 96.6178 | 3.06453 | ||||||||
\(995\) | −39.5872 | −1.25500 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.2658 | 1.27523 | 0.637616 | − | 0.770354i | \(-0.279921\pi\) | ||||
0.637616 | + | 0.770354i | \(0.279921\pi\) | |||||||
\(998\) | 35.4840 | 1.12323 | ||||||||
\(999\) | 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 | 6039.2.a.o.1.20 | yes | 25 | |
3.2 | odd | 2 | 6039.2.a.n.1.6 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.n.1.6 | ✓ | 25 | 3.2 | odd | 2 | ||
6039.2.a.o.1.20 | yes | 25 | 1.1 | even | 1 | trivial |