Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7225,2,Mod(1,7225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7225 = 5^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7225.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: | \(57.6919154604\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 425) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 7225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.903848 | −0.639117 | −0.319558 | − | 0.947567i | \(-0.603535\pi\) | ||||
−0.319558 | + | 0.947567i | \(0.603535\pi\) | |||||||
\(3\) | 2.88161 | 1.66370 | 0.831849 | − | 0.555002i | \(-0.187282\pi\) | ||||
0.831849 | + | 0.555002i | \(0.187282\pi\) | |||||||
\(4\) | −1.18306 | −0.591530 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.60454 | −1.06330 | ||||||||
\(7\) | 0.726991 | 0.274777 | 0.137388 | − | 0.990517i | \(-0.456129\pi\) | ||||
0.137388 | + | 0.990517i | \(0.456129\pi\) | |||||||
\(8\) | 2.87700 | 1.01717 | ||||||||
\(9\) | 5.30368 | 1.76789 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50358 | 0.754859 | 0.377430 | − | 0.926038i | \(-0.376808\pi\) | ||||
0.377430 | + | 0.926038i | \(0.376808\pi\) | |||||||
\(12\) | −3.40912 | −0.984127 | ||||||||
\(13\) | −6.29663 | −1.74637 | −0.873186 | − | 0.487388i | \(-0.837950\pi\) | ||||
−0.873186 | + | 0.487388i | \(0.837950\pi\) | |||||||
\(14\) | −0.657089 | −0.175614 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.234252 | −0.0585630 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −4.79372 | −1.12989 | ||||||||
\(19\) | 0.202859 | 0.0465391 | 0.0232696 | − | 0.999729i | \(-0.492592\pi\) | ||||
0.0232696 | + | 0.999729i | \(0.492592\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.09490 | 0.457146 | ||||||||
\(22\) | −2.26286 | −0.482443 | ||||||||
\(23\) | −0.666914 | −0.139061 | −0.0695306 | − | 0.997580i | \(-0.522150\pi\) | ||||
−0.0695306 | + | 0.997580i | \(0.522150\pi\) | |||||||
\(24\) | 8.29040 | 1.69227 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.69120 | 1.11614 | ||||||||
\(27\) | 6.63830 | 1.27754 | ||||||||
\(28\) | −0.860073 | −0.162539 | ||||||||
\(29\) | −7.93568 | −1.47362 | −0.736809 | − | 0.676101i | \(-0.763668\pi\) | ||||
−0.736809 | + | 0.676101i | \(0.763668\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.56241 | 0.999038 | 0.499519 | − | 0.866303i | \(-0.333510\pi\) | ||||
0.499519 | + | 0.866303i | \(0.333510\pi\) | |||||||
\(32\) | −5.54227 | −0.979745 | ||||||||
\(33\) | 7.21436 | 1.25586 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.27457 | −1.04576 | ||||||||
\(37\) | −7.94487 | −1.30613 | −0.653064 | − | 0.757303i | \(-0.726517\pi\) | ||||
−0.653064 | + | 0.757303i | \(0.726517\pi\) | |||||||
\(38\) | −0.183354 | −0.0297439 | ||||||||
\(39\) | −18.1444 | −2.90544 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.12655 | −0.800633 | −0.400316 | − | 0.916377i | \(-0.631100\pi\) | ||||
−0.400316 | + | 0.916377i | \(0.631100\pi\) | |||||||
\(42\) | −1.89347 | −0.292169 | ||||||||
\(43\) | −11.9561 | −1.82329 | −0.911647 | − | 0.410975i | \(-0.865188\pi\) | ||||
−0.911647 | + | 0.410975i | \(0.865188\pi\) | |||||||
\(44\) | −2.96189 | −0.446522 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.602789 | 0.0888763 | ||||||||
\(47\) | −10.9207 | −1.59294 | −0.796472 | − | 0.604675i | \(-0.793303\pi\) | ||||
−0.796472 | + | 0.604675i | \(0.793303\pi\) | |||||||
\(48\) | −0.675023 | −0.0974312 | ||||||||
\(49\) | −6.47148 | −0.924498 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.44929 | 1.03303 | ||||||||
\(53\) | 3.87580 | 0.532383 | 0.266191 | − | 0.963920i | \(-0.414235\pi\) | ||||
0.266191 | + | 0.963920i | \(0.414235\pi\) | |||||||
\(54\) | −6.00002 | −0.816499 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.09155 | 0.279496 | ||||||||
\(57\) | 0.584562 | 0.0774271 | ||||||||
\(58\) | 7.17264 | 0.941814 | ||||||||
\(59\) | −3.37248 | −0.439060 | −0.219530 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219530 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.13465 | 0.145277 | 0.0726386 | − | 0.997358i | \(-0.476858\pi\) | ||||
0.0726386 | + | 0.997358i | \(0.476858\pi\) | |||||||
\(62\) | −5.02757 | −0.638502 | ||||||||
\(63\) | 3.85573 | 0.485776 | ||||||||
\(64\) | 5.47788 | 0.684734 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.52068 | −0.802640 | ||||||||
\(67\) | −5.61946 | −0.686526 | −0.343263 | − | 0.939239i | \(-0.611532\pi\) | ||||
−0.343263 | + | 0.939239i | \(0.611532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.92179 | −0.231356 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.96368 | −0.470402 | −0.235201 | − | 0.971947i | \(-0.575575\pi\) | ||||
−0.235201 | + | 0.971947i | \(0.575575\pi\) | |||||||
\(72\) | 15.2587 | 1.79825 | ||||||||
\(73\) | 5.18908 | 0.607336 | 0.303668 | − | 0.952778i | \(-0.401789\pi\) | ||||
0.303668 | + | 0.952778i | \(0.401789\pi\) | |||||||
\(74\) | 7.18095 | 0.834768 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.239995 | −0.0275293 | ||||||||
\(77\) | 1.82008 | 0.207418 | ||||||||
\(78\) | 16.3998 | 1.85691 | ||||||||
\(79\) | −14.0406 | −1.57969 | −0.789847 | − | 0.613304i | \(-0.789840\pi\) | ||||
−0.789847 | + | 0.613304i | \(0.789840\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.21797 | 0.357552 | ||||||||
\(82\) | 4.63362 | 0.511698 | ||||||||
\(83\) | 12.3494 | 1.35552 | 0.677762 | − | 0.735282i | \(-0.262950\pi\) | ||||
0.677762 | + | 0.735282i | \(0.262950\pi\) | |||||||
\(84\) | −2.47840 | −0.270415 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.8065 | 1.16530 | ||||||||
\(87\) | −22.8675 | −2.45166 | ||||||||
\(88\) | 7.20282 | 0.767823 | ||||||||
\(89\) | 13.0419 | 1.38244 | 0.691221 | − | 0.722644i | \(-0.257073\pi\) | ||||
0.691221 | + | 0.722644i | \(0.257073\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.57759 | −0.479862 | ||||||||
\(92\) | 0.788999 | 0.0822588 | ||||||||
\(93\) | 16.0287 | 1.66210 | ||||||||
\(94\) | 9.87063 | 1.01808 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −15.9707 | −1.63000 | ||||||||
\(97\) | 11.9245 | 1.21075 | 0.605374 | − | 0.795942i | \(-0.293024\pi\) | ||||
0.605374 | + | 0.795942i | \(0.293024\pi\) | |||||||
\(98\) | 5.84924 | 0.590862 | ||||||||
\(99\) | 13.2782 | 1.33451 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0642 | 1.00143 | 0.500713 | − | 0.865613i | \(-0.333071\pi\) | ||||
0.500713 | + | 0.865613i | \(0.333071\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.80719 | 0.966331 | 0.483166 | − | 0.875529i | \(-0.339487\pi\) | ||||
0.483166 | + | 0.875529i | \(0.339487\pi\) | |||||||
\(104\) | −18.1154 | −1.77636 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.50314 | −0.340255 | ||||||||
\(107\) | −3.81498 | −0.368808 | −0.184404 | − | 0.982851i | \(-0.559035\pi\) | ||||
−0.184404 | + | 0.982851i | \(0.559035\pi\) | |||||||
\(108\) | −7.85351 | −0.755704 | ||||||||
\(109\) | −3.20733 | −0.307207 | −0.153603 | − | 0.988133i | \(-0.549088\pi\) | ||||
−0.153603 | + | 0.988133i | \(0.549088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.8940 | −2.17300 | ||||||||
\(112\) | −0.170299 | −0.0160918 | ||||||||
\(113\) | 0.403282 | 0.0379376 | 0.0189688 | − | 0.999820i | \(-0.493962\pi\) | ||||
0.0189688 | + | 0.999820i | \(0.493962\pi\) | |||||||
\(114\) | −0.528355 | −0.0494850 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.38838 | 0.871689 | ||||||||
\(117\) | −33.3953 | −3.08740 | ||||||||
\(118\) | 3.04821 | 0.280610 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.73206 | −0.430187 | ||||||||
\(122\) | −1.02555 | −0.0928491 | ||||||||
\(123\) | −14.7727 | −1.33201 | ||||||||
\(124\) | −6.58066 | −0.590961 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.48499 | −0.310467 | ||||||||
\(127\) | 2.16112 | 0.191769 | 0.0958844 | − | 0.995392i | \(-0.469432\pi\) | ||||
0.0958844 | + | 0.995392i | \(0.469432\pi\) | |||||||
\(128\) | 6.13338 | 0.542119 | ||||||||
\(129\) | −34.4529 | −3.03341 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.04478 | 0.702876 | 0.351438 | − | 0.936211i | \(-0.385693\pi\) | ||||
0.351438 | + | 0.936211i | \(0.385693\pi\) | |||||||
\(132\) | −8.53501 | −0.742877 | ||||||||
\(133\) | 0.147477 | 0.0127879 | ||||||||
\(134\) | 5.07913 | 0.438770 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.87082 | −0.672450 | −0.336225 | − | 0.941782i | \(-0.609150\pi\) | ||||
−0.336225 | + | 0.941782i | \(0.609150\pi\) | |||||||
\(138\) | 1.73700 | 0.147863 | ||||||||
\(139\) | −17.4627 | −1.48117 | −0.740583 | − | 0.671965i | \(-0.765451\pi\) | ||||
−0.740583 | + | 0.671965i | \(0.765451\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31.4691 | −2.65018 | ||||||||
\(142\) | 3.58256 | 0.300642 | ||||||||
\(143\) | −15.7642 | −1.31826 | ||||||||
\(144\) | −1.24240 | −0.103533 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.69014 | −0.388159 | ||||||||
\(147\) | −18.6483 | −1.53809 | ||||||||
\(148\) | 9.39925 | 0.772613 | ||||||||
\(149\) | 7.42906 | 0.608613 | 0.304306 | − | 0.952574i | \(-0.401575\pi\) | ||||
0.304306 | + | 0.952574i | \(0.401575\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5132 | −1.09969 | −0.549844 | − | 0.835267i | \(-0.685313\pi\) | ||||
−0.549844 | + | 0.835267i | \(0.685313\pi\) | |||||||
\(152\) | 0.583627 | 0.0473384 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.64508 | −0.132564 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 21.4659 | 1.71865 | ||||||||
\(157\) | 2.75786 | 0.220101 | 0.110051 | − | 0.993926i | \(-0.464899\pi\) | ||||
0.110051 | + | 0.993926i | \(0.464899\pi\) | |||||||
\(158\) | 12.6906 | 1.00961 | ||||||||
\(159\) | 11.1686 | 0.885724 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.484840 | −0.0382108 | ||||||||
\(162\) | −2.90856 | −0.228518 | ||||||||
\(163\) | 1.38371 | 0.108381 | 0.0541905 | − | 0.998531i | \(-0.482742\pi\) | ||||
0.0541905 | + | 0.998531i | \(0.482742\pi\) | |||||||
\(164\) | 6.06501 | 0.473598 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.1620 | −0.866338 | ||||||||
\(167\) | −14.6843 | −1.13630 | −0.568151 | − | 0.822924i | \(-0.692341\pi\) | ||||
−0.568151 | + | 0.822924i | \(0.692341\pi\) | |||||||
\(168\) | 6.02704 | 0.464996 | ||||||||
\(169\) | 26.6476 | 2.04981 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.07590 | 0.0822762 | ||||||||
\(172\) | 14.1448 | 1.07853 | ||||||||
\(173\) | −14.7492 | −1.12136 | −0.560681 | − | 0.828032i | \(-0.689461\pi\) | ||||
−0.560681 | + | 0.828032i | \(0.689461\pi\) | |||||||
\(174\) | 20.6688 | 1.56689 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.586470 | −0.0442068 | ||||||||
\(177\) | −9.71818 | −0.730463 | ||||||||
\(178\) | −11.7879 | −0.883542 | ||||||||
\(179\) | 14.2764 | 1.06707 | 0.533534 | − | 0.845779i | \(-0.320864\pi\) | ||||
0.533534 | + | 0.845779i | \(0.320864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.02407 | −0.447766 | −0.223883 | − | 0.974616i | \(-0.571873\pi\) | ||||
−0.223883 | + | 0.974616i | \(0.571873\pi\) | |||||||
\(182\) | 4.13745 | 0.306688 | ||||||||
\(183\) | 3.26962 | 0.241698 | ||||||||
\(184\) | −1.91871 | −0.141449 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −14.4875 | −1.06227 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.9198 | 0.942274 | ||||||||
\(189\) | 4.82599 | 0.351039 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.1379 | 1.02298 | 0.511492 | − | 0.859288i | \(-0.329093\pi\) | ||||
0.511492 | + | 0.859288i | \(0.329093\pi\) | |||||||
\(192\) | 15.7851 | 1.13919 | ||||||||
\(193\) | −23.2770 | −1.67552 | −0.837758 | − | 0.546042i | \(-0.816134\pi\) | ||||
−0.837758 | + | 0.546042i | \(0.816134\pi\) | |||||||
\(194\) | −10.7779 | −0.773809 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.65615 | 0.546868 | ||||||||
\(197\) | −9.29796 | −0.662452 | −0.331226 | − | 0.943551i | \(-0.607462\pi\) | ||||
−0.331226 | + | 0.943551i | \(0.607462\pi\) | |||||||
\(198\) | −12.0015 | −0.852908 | ||||||||
\(199\) | −7.56226 | −0.536075 | −0.268037 | − | 0.963409i | \(-0.586375\pi\) | ||||
−0.268037 | + | 0.963409i | \(0.586375\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.1931 | −1.14217 | ||||||||
\(202\) | −9.09652 | −0.640029 | ||||||||
\(203\) | −5.76916 | −0.404916 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.86421 | −0.617598 | ||||||||
\(207\) | −3.53710 | −0.245845 | ||||||||
\(208\) | 1.47500 | 0.102273 | ||||||||
\(209\) | 0.507876 | 0.0351305 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.9647 | 1.71864 | 0.859322 | − | 0.511435i | \(-0.170886\pi\) | ||||
0.859322 | + | 0.511435i | \(0.170886\pi\) | |||||||
\(212\) | −4.58531 | −0.314920 | ||||||||
\(213\) | −11.4218 | −0.782607 | ||||||||
\(214\) | 3.44816 | 0.235711 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 19.0984 | 1.29948 | ||||||||
\(217\) | 4.04382 | 0.274512 | ||||||||
\(218\) | 2.89894 | 0.196341 | ||||||||
\(219\) | 14.9529 | 1.01042 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 20.6927 | 1.38880 | ||||||||
\(223\) | −12.1685 | −0.814860 | −0.407430 | − | 0.913236i | \(-0.633575\pi\) | ||||
−0.407430 | + | 0.913236i | \(0.633575\pi\) | |||||||
\(224\) | −4.02918 | −0.269211 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.364506 | −0.0242466 | ||||||||
\(227\) | −1.98651 | −0.131850 | −0.0659248 | − | 0.997825i | \(-0.521000\pi\) | ||||
−0.0659248 | + | 0.997825i | \(0.521000\pi\) | |||||||
\(228\) | −0.691571 | −0.0458004 | ||||||||
\(229\) | 2.29201 | 0.151460 | 0.0757302 | − | 0.997128i | \(-0.475871\pi\) | ||||
0.0757302 | + | 0.997128i | \(0.475871\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.24477 | 0.345081 | ||||||||
\(232\) | −22.8309 | −1.49893 | ||||||||
\(233\) | 22.7030 | 1.48732 | 0.743662 | − | 0.668555i | \(-0.233087\pi\) | ||||
0.743662 | + | 0.668555i | \(0.233087\pi\) | |||||||
\(234\) | 30.1843 | 1.97321 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.98984 | 0.259717 | ||||||||
\(237\) | −40.4596 | −2.62813 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.2285 | 0.855683 | 0.427841 | − | 0.903854i | \(-0.359274\pi\) | ||||
0.427841 | + | 0.903854i | \(0.359274\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.89925 | 0.186757 | 0.0933787 | − | 0.995631i | \(-0.470233\pi\) | ||||
0.0933787 | + | 0.995631i | \(0.470233\pi\) | |||||||
\(242\) | 4.27706 | 0.274940 | ||||||||
\(243\) | −10.6420 | −0.682683 | ||||||||
\(244\) | −1.34236 | −0.0859358 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.3523 | 0.851311 | ||||||||
\(247\) | −1.27733 | −0.0812746 | ||||||||
\(248\) | 16.0031 | 1.01619 | ||||||||
\(249\) | 35.5862 | 2.25518 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.85445 | 0.622008 | 0.311004 | − | 0.950409i | \(-0.399335\pi\) | ||||
0.311004 | + | 0.950409i | \(0.399335\pi\) | |||||||
\(252\) | −4.56155 | −0.287351 | ||||||||
\(253\) | −1.66968 | −0.104972 | ||||||||
\(254\) | −1.95333 | −0.122563 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.4994 | −1.03121 | ||||||||
\(257\) | 5.28936 | 0.329941 | 0.164970 | − | 0.986299i | \(-0.447247\pi\) | ||||
0.164970 | + | 0.986299i | \(0.447247\pi\) | |||||||
\(258\) | 31.1402 | 1.93870 | ||||||||
\(259\) | −5.77584 | −0.358893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −42.0883 | −2.60520 | ||||||||
\(262\) | −7.27126 | −0.449220 | ||||||||
\(263\) | −12.5802 | −0.775726 | −0.387863 | − | 0.921717i | \(-0.626787\pi\) | ||||
−0.387863 | + | 0.921717i | \(0.626787\pi\) | |||||||
\(264\) | 20.7557 | 1.27743 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.133297 | −0.00817294 | ||||||||
\(267\) | 37.5817 | 2.29997 | ||||||||
\(268\) | 6.64815 | 0.406101 | ||||||||
\(269\) | −9.20257 | −0.561091 | −0.280545 | − | 0.959841i | \(-0.590515\pi\) | ||||
−0.280545 | + | 0.959841i | \(0.590515\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.6023 | 0.887028 | 0.443514 | − | 0.896267i | \(-0.353732\pi\) | ||||
0.443514 | + | 0.896267i | \(0.353732\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.1908 | −0.798346 | ||||||||
\(274\) | 7.11403 | 0.429774 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.27359 | 0.136854 | ||||||||
\(277\) | −13.0658 | −0.785050 | −0.392525 | − | 0.919741i | \(-0.628398\pi\) | ||||
−0.392525 | + | 0.919741i | \(0.628398\pi\) | |||||||
\(278\) | 15.7836 | 0.946638 | ||||||||
\(279\) | 29.5012 | 1.76619 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.56115 | −0.451060 | −0.225530 | − | 0.974236i | \(-0.572411\pi\) | ||||
−0.225530 | + | 0.974236i | \(0.572411\pi\) | |||||||
\(282\) | 28.4433 | 1.69377 | ||||||||
\(283\) | 4.11802 | 0.244791 | 0.122396 | − | 0.992481i | \(-0.460942\pi\) | ||||
0.122396 | + | 0.992481i | \(0.460942\pi\) | |||||||
\(284\) | 4.68927 | 0.278257 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.2484 | 0.842525 | ||||||||
\(287\) | −3.72696 | −0.219995 | ||||||||
\(288\) | −29.3944 | −1.73208 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 34.3617 | 2.01432 | ||||||||
\(292\) | −6.13899 | −0.359257 | ||||||||
\(293\) | 18.5803 | 1.08547 | 0.542736 | − | 0.839903i | \(-0.317388\pi\) | ||||
0.542736 | + | 0.839903i | \(0.317388\pi\) | |||||||
\(294\) | 16.8552 | 0.983016 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −22.8574 | −1.32856 | ||||||||
\(297\) | 16.6196 | 0.964365 | ||||||||
\(298\) | −6.71474 | −0.388975 | ||||||||
\(299\) | 4.19931 | 0.242852 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.69200 | −0.500998 | ||||||||
\(302\) | 12.2139 | 0.702829 | ||||||||
\(303\) | 29.0011 | 1.66607 | ||||||||
\(304\) | −0.0475202 | −0.00272547 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.82624 | −0.560813 | −0.280407 | − | 0.959881i | \(-0.590469\pi\) | ||||
−0.280407 | + | 0.959881i | \(0.590469\pi\) | |||||||
\(308\) | −2.15327 | −0.122694 | ||||||||
\(309\) | 28.2605 | 1.60768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.6883 | 1.62676 | 0.813382 | − | 0.581729i | \(-0.197624\pi\) | ||||
0.813382 | + | 0.581729i | \(0.197624\pi\) | |||||||
\(312\) | −52.2016 | −2.95533 | ||||||||
\(313\) | 0.968645 | 0.0547511 | 0.0273755 | − | 0.999625i | \(-0.491285\pi\) | ||||
0.0273755 | + | 0.999625i | \(0.491285\pi\) | |||||||
\(314\) | −2.49268 | −0.140670 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.6109 | 0.934436 | ||||||||
\(317\) | −26.5248 | −1.48978 | −0.744892 | − | 0.667185i | \(-0.767499\pi\) | ||||
−0.744892 | + | 0.667185i | \(0.767499\pi\) | |||||||
\(318\) | −10.0947 | −0.566081 | ||||||||
\(319\) | −19.8676 | −1.11237 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.9933 | −0.613585 | ||||||||
\(322\) | 0.438222 | 0.0244211 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3.80705 | −0.211503 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.25067 | −0.0692681 | ||||||||
\(327\) | −9.24228 | −0.511099 | ||||||||
\(328\) | −14.7491 | −0.814383 | ||||||||
\(329\) | −7.93923 | −0.437704 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.12601 | 0.336716 | 0.168358 | − | 0.985726i | \(-0.446154\pi\) | ||||
0.168358 | + | 0.985726i | \(0.446154\pi\) | |||||||
\(332\) | −14.6101 | −0.801832 | ||||||||
\(333\) | −42.1370 | −2.30909 | ||||||||
\(334\) | 13.2723 | 0.726230 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.490736 | −0.0267718 | ||||||||
\(337\) | −15.8752 | −0.864777 | −0.432388 | − | 0.901687i | \(-0.642329\pi\) | ||||
−0.432388 | + | 0.901687i | \(0.642329\pi\) | |||||||
\(338\) | −24.0853 | −1.31007 | ||||||||
\(339\) | 1.16210 | 0.0631167 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.9260 | 0.754133 | ||||||||
\(342\) | −0.972451 | −0.0525841 | ||||||||
\(343\) | −9.79364 | −0.528807 | ||||||||
\(344\) | −34.3978 | −1.85461 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.3310 | 0.716681 | ||||||||
\(347\) | 1.70339 | 0.0914428 | 0.0457214 | − | 0.998954i | \(-0.485441\pi\) | ||||
0.0457214 | + | 0.998954i | \(0.485441\pi\) | |||||||
\(348\) | 27.0536 | 1.45023 | ||||||||
\(349\) | −35.2541 | −1.88711 | −0.943553 | − | 0.331221i | \(-0.892540\pi\) | ||||
−0.943553 | + | 0.331221i | \(0.892540\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −41.7990 | −2.23106 | ||||||||
\(352\) | −13.8756 | −0.739569 | ||||||||
\(353\) | −22.4928 | −1.19717 | −0.598586 | − | 0.801059i | \(-0.704270\pi\) | ||||
−0.598586 | + | 0.801059i | \(0.704270\pi\) | |||||||
\(354\) | 8.78375 | 0.466851 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.4294 | −0.817755 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.9037 | −0.681981 | ||||||||
\(359\) | 18.0039 | 0.950208 | 0.475104 | − | 0.879930i | \(-0.342410\pi\) | ||||
0.475104 | + | 0.879930i | \(0.342410\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9588 | −0.997834 | ||||||||
\(362\) | 5.44485 | 0.286175 | ||||||||
\(363\) | −13.6360 | −0.715702 | ||||||||
\(364\) | 5.41556 | 0.283853 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.95524 | −0.154473 | ||||||||
\(367\) | 31.2820 | 1.63291 | 0.816454 | − | 0.577411i | \(-0.195937\pi\) | ||||
0.816454 | + | 0.577411i | \(0.195937\pi\) | |||||||
\(368\) | 0.156226 | 0.00814384 | ||||||||
\(369\) | −27.1896 | −1.41543 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.81767 | 0.146286 | ||||||||
\(372\) | −18.9629 | −0.983180 | ||||||||
\(373\) | 24.3521 | 1.26091 | 0.630453 | − | 0.776228i | \(-0.282869\pi\) | ||||
0.630453 | + | 0.776228i | \(0.282869\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −31.4188 | −1.62030 | ||||||||
\(377\) | 49.9680 | 2.57348 | ||||||||
\(378\) | −4.36196 | −0.224355 | ||||||||
\(379\) | 6.54787 | 0.336341 | 0.168171 | − | 0.985758i | \(-0.446214\pi\) | ||||
0.168171 | + | 0.985758i | \(0.446214\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.22752 | 0.319045 | ||||||||
\(382\) | −12.7785 | −0.653806 | ||||||||
\(383\) | −18.3898 | −0.939675 | −0.469838 | − | 0.882753i | \(-0.655688\pi\) | ||||
−0.469838 | + | 0.882753i | \(0.655688\pi\) | |||||||
\(384\) | 17.6740 | 0.901923 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.0389 | 1.07085 | ||||||||
\(387\) | −63.4115 | −3.22339 | ||||||||
\(388\) | −14.1074 | −0.716193 | ||||||||
\(389\) | 2.15031 | 0.109025 | 0.0545124 | − | 0.998513i | \(-0.482640\pi\) | ||||
0.0545124 | + | 0.998513i | \(0.482640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −18.6185 | −0.940375 | ||||||||
\(393\) | 23.1819 | 1.16937 | ||||||||
\(394\) | 8.40394 | 0.423384 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −15.7089 | −0.789402 | ||||||||
\(397\) | 0.387651 | 0.0194556 | 0.00972782 | − | 0.999953i | \(-0.496903\pi\) | ||||
0.00972782 | + | 0.999953i | \(0.496903\pi\) | |||||||
\(398\) | 6.83513 | 0.342614 | ||||||||
\(399\) | 0.424971 | 0.0212752 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.7192 | 0.834917 | 0.417458 | − | 0.908696i | \(-0.362921\pi\) | ||||
0.417458 | + | 0.908696i | \(0.362921\pi\) | |||||||
\(402\) | 14.6361 | 0.729982 | ||||||||
\(403\) | −35.0244 | −1.74469 | ||||||||
\(404\) | −11.9066 | −0.592374 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.21444 | 0.258789 | ||||||||
\(407\) | −19.8906 | −0.985943 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.7306 | −0.777828 | −0.388914 | − | 0.921274i | \(-0.627150\pi\) | ||||
−0.388914 | + | 0.921274i | \(0.627150\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.6807 | −1.11875 | ||||||||
\(412\) | −11.6025 | −0.571613 | ||||||||
\(413\) | −2.45176 | −0.120643 | ||||||||
\(414\) | 3.19700 | 0.157124 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 34.8977 | 1.71100 | ||||||||
\(417\) | −50.3207 | −2.46421 | ||||||||
\(418\) | −0.459042 | −0.0224525 | ||||||||
\(419\) | 10.6214 | 0.518888 | 0.259444 | − | 0.965758i | \(-0.416461\pi\) | ||||
0.259444 | + | 0.965758i | \(0.416461\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0231 | −0.829656 | −0.414828 | − | 0.909900i | \(-0.636158\pi\) | ||||
−0.414828 | + | 0.909900i | \(0.636158\pi\) | |||||||
\(422\) | −22.5643 | −1.09841 | ||||||||
\(423\) | −57.9198 | −2.81615 | ||||||||
\(424\) | 11.1507 | 0.541526 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.3235 | 0.500178 | ||||||||
\(427\) | 0.824881 | 0.0399188 | ||||||||
\(428\) | 4.51334 | 0.218161 | ||||||||
\(429\) | −45.4261 | −2.19320 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.6907 | −0.948467 | −0.474234 | − | 0.880399i | \(-0.657275\pi\) | ||||
−0.474234 | + | 0.880399i | \(0.657275\pi\) | |||||||
\(432\) | −1.55504 | −0.0748167 | ||||||||
\(433\) | −21.9579 | −1.05523 | −0.527614 | − | 0.849484i | \(-0.676913\pi\) | ||||
−0.527614 | + | 0.849484i | \(0.676913\pi\) | |||||||
\(434\) | −3.65500 | −0.175445 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.79446 | 0.181722 | ||||||||
\(437\) | −0.135290 | −0.00647179 | ||||||||
\(438\) | −13.5152 | −0.645779 | ||||||||
\(439\) | 8.49879 | 0.405625 | 0.202813 | − | 0.979218i | \(-0.434992\pi\) | ||||
0.202813 | + | 0.979218i | \(0.434992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −34.3227 | −1.63441 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.70952 | 0.223756 | 0.111878 | − | 0.993722i | \(-0.464313\pi\) | ||||
0.111878 | + | 0.993722i | \(0.464313\pi\) | |||||||
\(444\) | 27.0850 | 1.28540 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.9984 | 0.520791 | ||||||||
\(447\) | 21.4077 | 1.01255 | ||||||||
\(448\) | 3.98236 | 0.188149 | ||||||||
\(449\) | −26.2370 | −1.23820 | −0.619101 | − | 0.785311i | \(-0.712503\pi\) | ||||
−0.619101 | + | 0.785311i | \(0.712503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8348 | −0.604365 | ||||||||
\(452\) | −0.477107 | −0.0224412 | ||||||||
\(453\) | −38.9398 | −1.82955 | ||||||||
\(454\) | 1.79551 | 0.0842673 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.68178 | 0.0787568 | ||||||||
\(457\) | 20.6825 | 0.967485 | 0.483743 | − | 0.875210i | \(-0.339277\pi\) | ||||
0.483743 | + | 0.875210i | \(0.339277\pi\) | |||||||
\(458\) | −2.07163 | −0.0968009 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.94101 | 0.0904020 | 0.0452010 | − | 0.998978i | \(-0.485607\pi\) | ||||
0.0452010 | + | 0.998978i | \(0.485607\pi\) | |||||||
\(462\) | −4.74047 | −0.220547 | ||||||||
\(463\) | −10.6872 | −0.496676 | −0.248338 | − | 0.968673i | \(-0.579884\pi\) | ||||
−0.248338 | + | 0.968673i | \(0.579884\pi\) | |||||||
\(464\) | 1.85895 | 0.0862995 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.5201 | −0.950574 | ||||||||
\(467\) | 4.85368 | 0.224602 | 0.112301 | − | 0.993674i | \(-0.464178\pi\) | ||||
0.112301 | + | 0.993674i | \(0.464178\pi\) | |||||||
\(468\) | 39.5086 | 1.82629 | ||||||||
\(469\) | −4.08529 | −0.188641 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.94707 | 0.366182 | ||||||||
\(472\) | −9.70263 | −0.446600 | ||||||||
\(473\) | −29.9332 | −1.37633 | ||||||||
\(474\) | 36.5693 | 1.67969 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.5560 | 0.941196 | ||||||||
\(478\) | −11.9566 | −0.546881 | ||||||||
\(479\) | 7.60904 | 0.347666 | 0.173833 | − | 0.984775i | \(-0.444385\pi\) | ||||
0.173833 | + | 0.984775i | \(0.444385\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.0259 | 2.28098 | ||||||||
\(482\) | −2.62048 | −0.119360 | ||||||||
\(483\) | −1.39712 | −0.0635712 | ||||||||
\(484\) | 5.59831 | 0.254469 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.61872 | 0.436314 | ||||||||
\(487\) | 0.425586 | 0.0192851 | 0.00964257 | − | 0.999954i | \(-0.496931\pi\) | ||||
0.00964257 | + | 0.999954i | \(0.496931\pi\) | |||||||
\(488\) | 3.26439 | 0.147772 | ||||||||
\(489\) | 3.98733 | 0.180313 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.279220 | 0.0126010 | 0.00630052 | − | 0.999980i | \(-0.497994\pi\) | ||||
0.00630052 | + | 0.999980i | \(0.497994\pi\) | |||||||
\(492\) | 17.4770 | 0.787924 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.15451 | 0.0519440 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.30301 | −0.0585067 | ||||||||
\(497\) | −2.88156 | −0.129256 | ||||||||
\(498\) | −32.1645 | −1.44132 | ||||||||
\(499\) | 18.5254 | 0.829311 | 0.414655 | − | 0.909979i | \(-0.363902\pi\) | ||||
0.414655 | + | 0.909979i | \(0.363902\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.3143 | −1.89046 | ||||||||
\(502\) | −8.90693 | −0.397536 | ||||||||
\(503\) | 8.12470 | 0.362262 | 0.181131 | − | 0.983459i | \(-0.442024\pi\) | ||||
0.181131 | + | 0.983459i | \(0.442024\pi\) | |||||||
\(504\) | 11.0929 | 0.494118 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.50913 | 0.0670891 | ||||||||
\(507\) | 76.7879 | 3.41027 | ||||||||
\(508\) | −2.55674 | −0.113437 | ||||||||
\(509\) | −15.1877 | −0.673181 | −0.336590 | − | 0.941651i | \(-0.609274\pi\) | ||||
−0.336590 | + | 0.941651i | \(0.609274\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.77241 | 0.166882 | ||||||||
\(512\) | 2.64618 | 0.116946 | ||||||||
\(513\) | 1.34664 | 0.0594557 | ||||||||
\(514\) | −4.78077 | −0.210871 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 40.7598 | 1.79435 | ||||||||
\(517\) | −27.3408 | −1.20245 | ||||||||
\(518\) | 5.22048 | 0.229375 | ||||||||
\(519\) | −42.5015 | −1.86561 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.3496 | 1.63631 | 0.818157 | − | 0.574995i | \(-0.194996\pi\) | ||||
0.818157 | + | 0.574995i | \(0.194996\pi\) | |||||||
\(522\) | 38.0414 | 1.66503 | ||||||||
\(523\) | 8.03541 | 0.351364 | 0.175682 | − | 0.984447i | \(-0.443787\pi\) | ||||
0.175682 | + | 0.984447i | \(0.443787\pi\) | |||||||
\(524\) | −9.51745 | −0.415772 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.3706 | 0.495780 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.68998 | −0.0735469 | ||||||||
\(529\) | −22.5552 | −0.980662 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.8866 | −0.776210 | ||||||||
\(532\) | −0.174474 | −0.00756440 | ||||||||
\(533\) | 32.2800 | 1.39820 | ||||||||
\(534\) | −33.9682 | −1.46995 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −16.1672 | −0.698316 | ||||||||
\(537\) | 41.1390 | 1.77528 | ||||||||
\(538\) | 8.31772 | 0.358603 | ||||||||
\(539\) | −16.2019 | −0.697866 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.3264 | −0.701929 | −0.350964 | − | 0.936389i | \(-0.614146\pi\) | ||||
−0.350964 | + | 0.936389i | \(0.614146\pi\) | |||||||
\(542\) | −13.1983 | −0.566915 | ||||||||
\(543\) | −17.3590 | −0.744947 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.9225 | 0.510236 | ||||||||
\(547\) | 28.8042 | 1.23158 | 0.615789 | − | 0.787911i | \(-0.288838\pi\) | ||||
0.615789 | + | 0.787911i | \(0.288838\pi\) | |||||||
\(548\) | 9.31165 | 0.397774 | ||||||||
\(549\) | 6.01783 | 0.256835 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.60983 | −0.0685809 | ||||||||
\(552\) | −5.52898 | −0.235329 | ||||||||
\(553\) | −10.2074 | −0.434063 | ||||||||
\(554\) | 11.8095 | 0.501738 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.6594 | 0.876154 | ||||||||
\(557\) | 7.64838 | 0.324072 | 0.162036 | − | 0.986785i | \(-0.448194\pi\) | ||||
0.162036 | + | 0.986785i | \(0.448194\pi\) | |||||||
\(558\) | −26.6646 | −1.12880 | ||||||||
\(559\) | 75.2834 | 3.18415 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.83413 | 0.288280 | ||||||||
\(563\) | −42.3891 | −1.78649 | −0.893244 | − | 0.449572i | \(-0.851577\pi\) | ||||
−0.893244 | + | 0.449572i | \(0.851577\pi\) | |||||||
\(564\) | 37.2298 | 1.56766 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.72207 | −0.156450 | ||||||||
\(567\) | 2.33944 | 0.0982471 | ||||||||
\(568\) | −11.4035 | −0.478481 | ||||||||
\(569\) | −30.8191 | −1.29200 | −0.646001 | − | 0.763336i | \(-0.723560\pi\) | ||||
−0.646001 | + | 0.763336i | \(0.723560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0459 | 0.922594 | 0.461297 | − | 0.887246i | \(-0.347384\pi\) | ||||
0.461297 | + | 0.887246i | \(0.347384\pi\) | |||||||
\(572\) | 18.6499 | 0.779793 | ||||||||
\(573\) | 40.7400 | 1.70194 | ||||||||
\(574\) | 3.36860 | 0.140603 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 29.0529 | 1.21054 | ||||||||
\(577\) | 20.2437 | 0.842755 | 0.421378 | − | 0.906885i | \(-0.361547\pi\) | ||||
0.421378 | + | 0.906885i | \(0.361547\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −67.0753 | −2.78755 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.97790 | 0.372466 | ||||||||
\(582\) | −31.0577 | −1.28738 | ||||||||
\(583\) | 9.70341 | 0.401874 | ||||||||
\(584\) | 14.9290 | 0.617766 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.7938 | −0.693744 | ||||||||
\(587\) | −12.7637 | −0.526812 | −0.263406 | − | 0.964685i | \(-0.584846\pi\) | ||||
−0.263406 | + | 0.964685i | \(0.584846\pi\) | |||||||
\(588\) | 22.0620 | 0.909823 | ||||||||
\(589\) | 1.12839 | 0.0464944 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.7931 | −1.10212 | ||||||||
\(592\) | 1.86110 | 0.0764908 | ||||||||
\(593\) | −2.87908 | −0.118230 | −0.0591148 | − | 0.998251i | \(-0.518828\pi\) | ||||
−0.0591148 | + | 0.998251i | \(0.518828\pi\) | |||||||
\(594\) | −15.0216 | −0.616342 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.78902 | −0.360012 | ||||||||
\(597\) | −21.7915 | −0.891867 | ||||||||
\(598\) | −3.79554 | −0.155211 | ||||||||
\(599\) | −12.6720 | −0.517762 | −0.258881 | − | 0.965909i | \(-0.583354\pi\) | ||||
−0.258881 | + | 0.965909i | \(0.583354\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.7248 | −0.559846 | −0.279923 | − | 0.960022i | \(-0.590309\pi\) | ||||
−0.279923 | + | 0.960022i | \(0.590309\pi\) | |||||||
\(602\) | 7.85624 | 0.320197 | ||||||||
\(603\) | −29.8038 | −1.21370 | ||||||||
\(604\) | 15.9869 | 0.650498 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −26.2126 | −1.06481 | ||||||||
\(607\) | −7.80403 | −0.316756 | −0.158378 | − | 0.987379i | \(-0.550626\pi\) | ||||
−0.158378 | + | 0.987379i | \(0.550626\pi\) | |||||||
\(608\) | −1.12430 | −0.0455965 | ||||||||
\(609\) | −16.6245 | −0.673658 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 68.7635 | 2.78187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.7999 | 1.80945 | 0.904726 | − | 0.425994i | \(-0.140076\pi\) | ||||
0.904726 | + | 0.425994i | \(0.140076\pi\) | |||||||
\(614\) | 8.88142 | 0.358425 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.23638 | 0.210980 | ||||||||
\(617\) | 21.5816 | 0.868843 | 0.434422 | − | 0.900710i | \(-0.356953\pi\) | ||||
0.434422 | + | 0.900710i | \(0.356953\pi\) | |||||||
\(618\) | −25.5432 | −1.02750 | ||||||||
\(619\) | 38.5766 | 1.55052 | 0.775262 | − | 0.631640i | \(-0.217618\pi\) | ||||
0.775262 | + | 0.631640i | \(0.217618\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.42718 | −0.177657 | ||||||||
\(622\) | −25.9299 | −1.03969 | ||||||||
\(623\) | 9.48136 | 0.379863 | ||||||||
\(624\) | 4.25037 | 0.170151 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.875508 | −0.0349923 | ||||||||
\(627\) | 1.46350 | 0.0584466 | ||||||||
\(628\) | −3.26271 | −0.130196 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.2230 | −0.964304 | −0.482152 | − | 0.876088i | \(-0.660145\pi\) | ||||
−0.482152 | + | 0.876088i | \(0.660145\pi\) | |||||||
\(632\) | −40.3949 | −1.60682 | ||||||||
\(633\) | 71.9387 | 2.85931 | ||||||||
\(634\) | 23.9744 | 0.952146 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.2131 | −0.523932 | ||||||||
\(637\) | 40.7486 | 1.61452 | ||||||||
\(638\) | 17.9573 | 0.710937 | ||||||||
\(639\) | −21.0221 | −0.831621 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.4317 | −1.71545 | −0.857725 | − | 0.514108i | \(-0.828123\pi\) | ||||
−0.857725 | + | 0.514108i | \(0.828123\pi\) | |||||||
\(642\) | 9.93625 | 0.392152 | ||||||||
\(643\) | 35.4825 | 1.39929 | 0.699646 | − | 0.714490i | \(-0.253341\pi\) | ||||
0.699646 | + | 0.714490i | \(0.253341\pi\) | |||||||
\(644\) | 0.573595 | 0.0226028 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.2269 | 1.10971 | 0.554857 | − | 0.831946i | \(-0.312773\pi\) | ||||
0.554857 | + | 0.831946i | \(0.312773\pi\) | |||||||
\(648\) | 9.25811 | 0.363693 | ||||||||
\(649\) | −8.44329 | −0.331428 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.6527 | 0.456706 | ||||||||
\(652\) | −1.63702 | −0.0641105 | ||||||||
\(653\) | −3.72898 | −0.145926 | −0.0729632 | − | 0.997335i | \(-0.523246\pi\) | ||||
−0.0729632 | + | 0.997335i | \(0.523246\pi\) | |||||||
\(654\) | 8.35361 | 0.326652 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.20091 | 0.0468875 | ||||||||
\(657\) | 27.5212 | 1.07371 | ||||||||
\(658\) | 7.17585 | 0.279744 | ||||||||
\(659\) | −16.0238 | −0.624200 | −0.312100 | − | 0.950049i | \(-0.601032\pi\) | ||||
−0.312100 | + | 0.950049i | \(0.601032\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.5405 | −1.07120 | −0.535601 | − | 0.844471i | \(-0.679915\pi\) | ||||
−0.535601 | + | 0.844471i | \(0.679915\pi\) | |||||||
\(662\) | −5.53698 | −0.215201 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 35.5292 | 1.37880 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 38.0854 | 1.47578 | ||||||||
\(667\) | 5.29241 | 0.204923 | ||||||||
\(668\) | 17.3723 | 0.672156 | ||||||||
\(669\) | −35.0648 | −1.35568 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.84070 | 0.109664 | ||||||||
\(672\) | −11.6105 | −0.447886 | ||||||||
\(673\) | −18.9406 | −0.730106 | −0.365053 | − | 0.930987i | \(-0.618949\pi\) | ||||
−0.365053 | + | 0.930987i | \(0.618949\pi\) | |||||||
\(674\) | 14.3488 | 0.552693 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −31.5257 | −1.21253 | ||||||||
\(677\) | −10.5909 | −0.407042 | −0.203521 | − | 0.979071i | \(-0.565238\pi\) | ||||
−0.203521 | + | 0.979071i | \(0.565238\pi\) | |||||||
\(678\) | −1.05036 | −0.0403390 | ||||||||
\(679\) | 8.66898 | 0.332685 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.72436 | −0.219358 | ||||||||
\(682\) | −12.5869 | −0.481979 | ||||||||
\(683\) | −45.0651 | −1.72437 | −0.862184 | − | 0.506596i | \(-0.830904\pi\) | ||||
−0.862184 | + | 0.506596i | \(0.830904\pi\) | |||||||
\(684\) | −1.27285 | −0.0486688 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.85196 | 0.337970 | ||||||||
\(687\) | 6.60469 | 0.251985 | ||||||||
\(688\) | 2.80075 | 0.106778 | ||||||||
\(689\) | −24.4045 | −0.929738 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0470 | 0.496332 | 0.248166 | − | 0.968718i | \(-0.420172\pi\) | ||||
0.248166 | + | 0.968718i | \(0.420172\pi\) | |||||||
\(692\) | 17.4492 | 0.663319 | ||||||||
\(693\) | 9.65314 | 0.366692 | ||||||||
\(694\) | −1.53961 | −0.0584426 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −65.7899 | −2.49376 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 31.8643 | 1.20608 | ||||||||
\(699\) | 65.4213 | 2.47446 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.42228 | 0.167027 | 0.0835136 | − | 0.996507i | \(-0.473386\pi\) | ||||
0.0835136 | + | 0.996507i | \(0.473386\pi\) | |||||||
\(702\) | 37.7799 | 1.42591 | ||||||||
\(703\) | −1.61169 | −0.0607861 | ||||||||
\(704\) | 13.7143 | 0.516878 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.3301 | 0.765132 | ||||||||
\(707\) | 7.31659 | 0.275169 | ||||||||
\(708\) | 11.4972 | 0.432090 | ||||||||
\(709\) | 32.0483 | 1.20360 | 0.601800 | − | 0.798647i | \(-0.294451\pi\) | ||||
0.601800 | + | 0.798647i | \(0.294451\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −74.4670 | −2.79273 | ||||||||
\(712\) | 37.5216 | 1.40618 | ||||||||
\(713\) | −3.70965 | −0.138927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.8898 | −0.631202 | ||||||||
\(717\) | 38.1195 | 1.42360 | ||||||||
\(718\) | −16.2728 | −0.607294 | ||||||||
\(719\) | 27.7269 | 1.03404 | 0.517020 | − | 0.855973i | \(-0.327041\pi\) | ||||
0.517020 | + | 0.855973i | \(0.327041\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.12973 | 0.265525 | ||||||||
\(722\) | 17.1359 | 0.637733 | ||||||||
\(723\) | 8.35452 | 0.310708 | ||||||||
\(724\) | 7.12684 | 0.264867 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.3248 | 0.457417 | ||||||||
\(727\) | 10.5407 | 0.390934 | 0.195467 | − | 0.980710i | \(-0.437378\pi\) | ||||
0.195467 | + | 0.980710i | \(0.437378\pi\) | |||||||
\(728\) | −13.1697 | −0.488103 | ||||||||
\(729\) | −40.3199 | −1.49333 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.86816 | −0.142971 | ||||||||
\(733\) | −16.4227 | −0.606585 | −0.303293 | − | 0.952898i | \(-0.598086\pi\) | ||||
−0.303293 | + | 0.952898i | \(0.598086\pi\) | |||||||
\(734\) | −28.2742 | −1.04362 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.69622 | 0.136244 | ||||||||
\(737\) | −14.0688 | −0.518231 | ||||||||
\(738\) | 24.5752 | 0.904627 | ||||||||
\(739\) | 1.80904 | 0.0665467 | 0.0332733 | − | 0.999446i | \(-0.489407\pi\) | ||||
0.0332733 | + | 0.999446i | \(0.489407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.68077 | −0.135216 | ||||||||
\(742\) | −2.54675 | −0.0934941 | ||||||||
\(743\) | −43.1045 | −1.58135 | −0.790676 | − | 0.612235i | \(-0.790271\pi\) | ||||
−0.790676 | + | 0.612235i | \(0.790271\pi\) | |||||||
\(744\) | 46.1146 | 1.69064 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −22.0106 | −0.805866 | ||||||||
\(747\) | 65.4973 | 2.39642 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.77345 | −0.101340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.3004 | −1.06919 | −0.534593 | − | 0.845110i | \(-0.679535\pi\) | ||||
−0.534593 | + | 0.845110i | \(0.679535\pi\) | |||||||
\(752\) | 2.55819 | 0.0932876 | ||||||||
\(753\) | 28.3967 | 1.03483 | ||||||||
\(754\) | −45.1635 | −1.64476 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.70943 | −0.207650 | ||||||||
\(757\) | 10.3516 | 0.376234 | 0.188117 | − | 0.982147i | \(-0.439762\pi\) | ||||
0.188117 | + | 0.982147i | \(0.439762\pi\) | |||||||
\(758\) | −5.91828 | −0.214961 | ||||||||
\(759\) | −4.81136 | −0.174641 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.0677 | −1.45245 | −0.726227 | − | 0.687455i | \(-0.758728\pi\) | ||||
−0.726227 | + | 0.687455i | \(0.758728\pi\) | |||||||
\(762\) | −5.62873 | −0.203907 | ||||||||
\(763\) | −2.33170 | −0.0844132 | ||||||||
\(764\) | −16.7260 | −0.605125 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.6216 | 0.600562 | ||||||||
\(767\) | 21.2353 | 0.766761 | ||||||||
\(768\) | −47.5448 | −1.71563 | ||||||||
\(769\) | 40.8532 | 1.47320 | 0.736602 | − | 0.676327i | \(-0.236429\pi\) | ||||
0.736602 | + | 0.676327i | \(0.236429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.2419 | 0.548922 | ||||||||
\(772\) | 27.5381 | 0.991117 | ||||||||
\(773\) | −17.1111 | −0.615442 | −0.307721 | − | 0.951477i | \(-0.599566\pi\) | ||||
−0.307721 | + | 0.951477i | \(0.599566\pi\) | |||||||
\(774\) | 57.3143 | 2.06012 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 34.3067 | 1.23154 | ||||||||
\(777\) | −16.6437 | −0.597091 | ||||||||
\(778\) | −1.94355 | −0.0696796 | ||||||||
\(779\) | −1.03997 | −0.0372608 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.92341 | −0.355087 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −52.6794 | −1.88261 | ||||||||
\(784\) | 1.51596 | 0.0541414 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −20.9529 | −0.747366 | ||||||||
\(787\) | −18.4210 | −0.656639 | −0.328320 | − | 0.944567i | \(-0.606482\pi\) | ||||
−0.328320 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(788\) | 11.0000 | 0.391860 | ||||||||
\(789\) | −36.2511 | −1.29057 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.293182 | 0.0104244 | ||||||||
\(792\) | 38.2014 | 1.35743 | ||||||||
\(793\) | −7.14448 | −0.253708 | ||||||||
\(794\) | −0.350377 | −0.0124344 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.94661 | 0.317104 | ||||||||
\(797\) | −28.5994 | −1.01304 | −0.506521 | − | 0.862228i | \(-0.669069\pi\) | ||||
−0.506521 | + | 0.862228i | \(0.669069\pi\) | |||||||
\(798\) | −0.384109 | −0.0135973 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 69.1702 | 2.44401 | ||||||||
\(802\) | −15.1116 | −0.533609 | ||||||||
\(803\) | 12.9913 | 0.458453 | ||||||||
\(804\) | 19.1574 | 0.675629 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 31.6568 | 1.11506 | ||||||||
\(807\) | −26.5182 | −0.933486 | ||||||||
\(808\) | 28.9547 | 1.01862 | ||||||||
\(809\) | 27.1783 | 0.955537 | 0.477769 | − | 0.878486i | \(-0.341446\pi\) | ||||
0.477769 | + | 0.878486i | \(0.341446\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.0265 | −0.668111 | −0.334055 | − | 0.942553i | \(-0.608417\pi\) | ||||
−0.334055 | + | 0.942553i | \(0.608417\pi\) | |||||||
\(812\) | 6.82526 | 0.239520 | ||||||||
\(813\) | 42.0782 | 1.47575 | ||||||||
\(814\) | 17.9781 | 0.630133 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.42541 | −0.0848545 | ||||||||
\(818\) | 14.2181 | 0.497123 | ||||||||
\(819\) | −24.2781 | −0.848345 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.8147 | −1.00564 | −0.502819 | − | 0.864392i | \(-0.667704\pi\) | ||||
−0.502819 | + | 0.864392i | \(0.667704\pi\) | |||||||
\(822\) | 20.4999 | 0.715015 | ||||||||
\(823\) | −41.7187 | −1.45422 | −0.727112 | − | 0.686519i | \(-0.759138\pi\) | ||||
−0.727112 | + | 0.686519i | \(0.759138\pi\) | |||||||
\(824\) | 28.2153 | 0.982926 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.21602 | 0.0771052 | ||||||||
\(827\) | −27.0696 | −0.941302 | −0.470651 | − | 0.882319i | \(-0.655981\pi\) | ||||
−0.470651 | + | 0.882319i | \(0.655981\pi\) | |||||||
\(828\) | 4.18460 | 0.145425 | ||||||||
\(829\) | 21.8341 | 0.758331 | 0.379165 | − | 0.925329i | \(-0.376211\pi\) | ||||
0.379165 | + | 0.925329i | \(0.376211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −37.6506 | −1.30609 | ||||||||
\(832\) | −34.4922 | −1.19580 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 45.4822 | 1.57492 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.600847 | −0.0207807 | ||||||||
\(837\) | 36.9250 | 1.27631 | ||||||||
\(838\) | −9.60010 | −0.331630 | ||||||||
\(839\) | 45.6890 | 1.57736 | 0.788680 | − | 0.614805i | \(-0.210765\pi\) | ||||
0.788680 | + | 0.614805i | \(0.210765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.9750 | 1.17155 | ||||||||
\(842\) | 15.3863 | 0.530247 | ||||||||
\(843\) | −21.7883 | −0.750428 | ||||||||
\(844\) | −29.5348 | −1.01663 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 52.3506 | 1.79985 | ||||||||
\(847\) | −3.44017 | −0.118205 | ||||||||
\(848\) | −0.907915 | −0.0311779 | ||||||||
\(849\) | 11.8665 | 0.407259 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.29854 | 0.181632 | ||||||||
\(852\) | 13.5126 | 0.462935 | ||||||||
\(853\) | 0.0970449 | 0.00332276 | 0.00166138 | − | 0.999999i | \(-0.499471\pi\) | ||||
0.00166138 | + | 0.999999i | \(0.499471\pi\) | |||||||
\(854\) | −0.745567 | −0.0255128 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.9757 | −0.375141 | ||||||||
\(857\) | −46.7682 | −1.59757 | −0.798786 | − | 0.601616i | \(-0.794524\pi\) | ||||
−0.798786 | + | 0.601616i | \(0.794524\pi\) | |||||||
\(858\) | 41.0583 | 1.40171 | ||||||||
\(859\) | 26.3135 | 0.897806 | 0.448903 | − | 0.893580i | \(-0.351815\pi\) | ||||
0.448903 | + | 0.893580i | \(0.351815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.7396 | −0.366006 | ||||||||
\(862\) | 17.7974 | 0.606182 | ||||||||
\(863\) | −33.5202 | −1.14104 | −0.570520 | − | 0.821284i | \(-0.693258\pi\) | ||||
−0.570520 | + | 0.821284i | \(0.693258\pi\) | |||||||
\(864\) | −36.7913 | −1.25167 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.8466 | 0.674414 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.78408 | −0.162382 | ||||||||
\(869\) | −35.1519 | −1.19245 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.3837 | 1.19893 | ||||||||
\(872\) | −9.22749 | −0.312482 | ||||||||
\(873\) | 63.2436 | 2.14047 | ||||||||
\(874\) | 0.122281 | 0.00413623 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.6902 | −0.597696 | ||||||||
\(877\) | −3.96792 | −0.133987 | −0.0669936 | − | 0.997753i | \(-0.521341\pi\) | ||||
−0.0669936 | + | 0.997753i | \(0.521341\pi\) | |||||||
\(878\) | −7.68162 | −0.259242 | ||||||||
\(879\) | 53.5412 | 1.80590 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7632 | 1.50811 | 0.754056 | − | 0.656811i | \(-0.228095\pi\) | ||||
0.754056 | + | 0.656811i | \(0.228095\pi\) | |||||||
\(882\) | 31.0225 | 1.04458 | ||||||||
\(883\) | 6.22372 | 0.209445 | 0.104722 | − | 0.994501i | \(-0.466605\pi\) | ||||
0.104722 | + | 0.994501i | \(0.466605\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.25669 | −0.143006 | ||||||||
\(887\) | −16.8428 | −0.565526 | −0.282763 | − | 0.959190i | \(-0.591251\pi\) | ||||
−0.282763 | + | 0.959190i | \(0.591251\pi\) | |||||||
\(888\) | −65.8661 | −2.21032 | ||||||||
\(889\) | 1.57112 | 0.0526936 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.05647 | 0.269902 | ||||||||
\(892\) | 14.3960 | 0.482014 | ||||||||
\(893\) | −2.21536 | −0.0741342 | ||||||||
\(894\) | −19.3493 | −0.647136 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.45891 | 0.148962 | ||||||||
\(897\) | 12.1008 | 0.404033 | ||||||||
\(898\) | 23.7143 | 0.791356 | ||||||||
\(899\) | −44.1415 | −1.47220 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 11.6007 | 0.386260 | ||||||||
\(903\) | −25.0469 | −0.833510 | ||||||||
\(904\) | 1.16024 | 0.0385891 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 35.1956 | 1.16930 | ||||||||
\(907\) | −28.9372 | −0.960845 | −0.480422 | − | 0.877037i | \(-0.659517\pi\) | ||||
−0.480422 | + | 0.877037i | \(0.659517\pi\) | |||||||
\(908\) | 2.35016 | 0.0779929 | ||||||||
\(909\) | 53.3774 | 1.77041 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.3748 | −0.509389 | −0.254694 | − | 0.967022i | \(-0.581975\pi\) | ||||
−0.254694 | + | 0.967022i | \(0.581975\pi\) | |||||||
\(912\) | −0.136935 | −0.00453436 | ||||||||
\(913\) | 30.9178 | 1.02323 | ||||||||
\(914\) | −18.6938 | −0.618336 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.71159 | −0.0895933 | ||||||||
\(917\) | 5.84848 | 0.193134 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.89298 | 0.326339 | 0.163170 | − | 0.986598i | \(-0.447828\pi\) | ||||
0.163170 | + | 0.986598i | \(0.447828\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.3154 | −0.933024 | ||||||||
\(922\) | −1.75438 | −0.0577774 | ||||||||
\(923\) | 24.9578 | 0.821497 | ||||||||
\(924\) | −6.20487 | −0.204125 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.65959 | 0.317434 | ||||||||
\(927\) | 52.0142 | 1.70837 | ||||||||
\(928\) | 43.9817 | 1.44377 | ||||||||
\(929\) | 7.21578 | 0.236742 | 0.118371 | − | 0.992969i | \(-0.462233\pi\) | ||||
0.118371 | + | 0.992969i | \(0.462233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.31280 | −0.0430253 | ||||||||
\(932\) | −26.8590 | −0.879797 | ||||||||
\(933\) | 82.6685 | 2.70645 | ||||||||
\(934\) | −4.38699 | −0.143547 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −96.0783 | −3.14042 | ||||||||
\(937\) | 4.90678 | 0.160298 | 0.0801488 | − | 0.996783i | \(-0.474460\pi\) | ||||
0.0801488 | + | 0.996783i | \(0.474460\pi\) | |||||||
\(938\) | 3.69248 | 0.120564 | ||||||||
\(939\) | 2.79126 | 0.0910892 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.2958 | 0.857218 | 0.428609 | − | 0.903490i | \(-0.359004\pi\) | ||||
0.428609 | + | 0.903490i | \(0.359004\pi\) | |||||||
\(942\) | −7.18294 | −0.234033 | ||||||||
\(943\) | 3.41897 | 0.111337 | ||||||||
\(944\) | 0.790011 | 0.0257127 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.0550 | 0.879636 | ||||||||
\(947\) | 33.0347 | 1.07348 | 0.536742 | − | 0.843746i | \(-0.319655\pi\) | ||||
0.536742 | + | 0.843746i | \(0.319655\pi\) | |||||||
\(948\) | 47.8661 | 1.55462 | ||||||||
\(949\) | −32.6737 | −1.06063 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −76.4343 | −2.47855 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.4399 | −1.66630 | −0.833151 | − | 0.553046i | \(-0.813465\pi\) | ||||
−0.833151 | + | 0.553046i | \(0.813465\pi\) | |||||||
\(954\) | −18.5795 | −0.601534 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.6501 | −0.506162 | ||||||||
\(957\) | −57.2508 | −1.85066 | ||||||||
\(958\) | −6.87741 | −0.222199 | ||||||||
\(959\) | −5.72202 | −0.184774 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.0596155 | −0.00192308 | ||||||||
\(962\) | −45.2158 | −1.45782 | ||||||||
\(963\) | −20.2334 | −0.652013 | ||||||||
\(964\) | −3.42999 | −0.110472 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.26278 | 0.0406294 | ||||||||
\(967\) | 30.2986 | 0.974337 | 0.487169 | − | 0.873308i | \(-0.338030\pi\) | ||||
0.487169 | + | 0.873308i | \(0.338030\pi\) | |||||||
\(968\) | −13.6141 | −0.437575 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.8251 | 1.11759 | 0.558796 | − | 0.829305i | \(-0.311264\pi\) | ||||
0.558796 | + | 0.829305i | \(0.311264\pi\) | |||||||
\(972\) | 12.5901 | 0.403827 | ||||||||
\(973\) | −12.6952 | −0.406990 | ||||||||
\(974\) | −0.384665 | −0.0123255 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.265795 | −0.00850788 | ||||||||
\(977\) | −20.6989 | −0.662215 | −0.331108 | − | 0.943593i | \(-0.607422\pi\) | ||||
−0.331108 | + | 0.943593i | \(0.607422\pi\) | |||||||
\(978\) | −3.60394 | −0.115241 | ||||||||
\(979\) | 32.6516 | 1.04355 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.0106 | −0.543108 | ||||||||
\(982\) | −0.252373 | −0.00805354 | ||||||||
\(983\) | −44.3237 | −1.41371 | −0.706853 | − | 0.707360i | \(-0.749886\pi\) | ||||
−0.706853 | + | 0.707360i | \(0.749886\pi\) | |||||||
\(984\) | −42.5011 | −1.35489 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.8778 | −0.728207 | ||||||||
\(988\) | 1.51116 | 0.0480763 | ||||||||
\(989\) | 7.97371 | 0.253549 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.1318 | 0.830103 | 0.415051 | − | 0.909798i | \(-0.363764\pi\) | ||||
0.415051 | + | 0.909798i | \(0.363764\pi\) | |||||||
\(992\) | −30.8284 | −0.978802 | ||||||||
\(993\) | 17.6528 | 0.560193 | ||||||||
\(994\) | 2.60449 | 0.0826094 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −42.1005 | −1.33401 | ||||||||
\(997\) | −26.2757 | −0.832160 | −0.416080 | − | 0.909328i | \(-0.636596\pi\) | ||||
−0.416080 | + | 0.909328i | \(0.636596\pi\) | |||||||
\(998\) | −16.7441 | −0.530026 | ||||||||
\(999\) | −52.7404 | −1.66863 |
(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 | 7225.2.a.bx.1.12 | 24 | ||
5.4 | even | 2 | 7225.2.a.cb.1.13 | 24 | |||
17.10 | odd | 16 | 425.2.m.c.151.4 | yes | 24 | ||
17.12 | odd | 16 | 425.2.m.c.76.4 | ✓ | 24 | ||
17.16 | even | 2 | inner | 7225.2.a.bx.1.11 | 24 | ||
85.12 | even | 16 | 425.2.n.d.399.4 | 24 | |||
85.27 | even | 16 | 425.2.n.e.49.3 | 24 | |||
85.29 | odd | 16 | 425.2.m.d.76.3 | yes | 24 | ||
85.44 | odd | 16 | 425.2.m.d.151.3 | yes | 24 | ||
85.63 | even | 16 | 425.2.n.e.399.3 | 24 | |||
85.78 | even | 16 | 425.2.n.d.49.4 | 24 | |||
85.84 | even | 2 | 7225.2.a.cb.1.14 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
425.2.m.c.76.4 | ✓ | 24 | 17.12 | odd | 16 | ||
425.2.m.c.151.4 | yes | 24 | 17.10 | odd | 16 | ||
425.2.m.d.76.3 | yes | 24 | 85.29 | odd | 16 | ||
425.2.m.d.151.3 | yes | 24 | 85.44 | odd | 16 | ||
425.2.n.d.49.4 | 24 | 85.78 | even | 16 | |||
425.2.n.d.399.4 | 24 | 85.12 | even | 16 | |||
425.2.n.e.49.3 | 24 | 85.27 | even | 16 | |||
425.2.n.e.399.3 | 24 | 85.63 | even | 16 | |||
7225.2.a.bx.1.11 | 24 | 17.16 | even | 2 | inner | ||
7225.2.a.bx.1.12 | 24 | 1.1 | even | 1 | trivial | ||
7225.2.a.cb.1.13 | 24 | 5.4 | even | 2 | |||
7225.2.a.cb.1.14 | 24 | 85.84 | even | 2 |