Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.87978 | −1.32920 | −0.664601 | − | 0.747198i | \(-0.731399\pi\) | ||||
−0.664601 | + | 0.747198i | \(0.731399\pi\) | |||||||
\(3\) | 3.08968 | 1.78383 | 0.891915 | − | 0.452203i | \(-0.149362\pi\) | ||||
0.891915 | + | 0.452203i | \(0.149362\pi\) | |||||||
\(4\) | 1.53356 | 0.766779 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −5.80791 | −2.37107 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.876807 | 0.309998 | ||||||||
\(9\) | 6.54615 | 2.18205 | ||||||||
\(10\) | −1.87978 | −0.594437 | ||||||||
\(11\) | −4.11760 | −1.24150 | −0.620752 | − | 0.784007i | \(-0.713173\pi\) | ||||
−0.620752 | + | 0.784007i | \(0.713173\pi\) | |||||||
\(12\) | 4.73821 | 1.36780 | ||||||||
\(13\) | 0.273088 | 0.0757409 | 0.0378705 | − | 0.999283i | \(-0.487943\pi\) | ||||
0.0378705 | + | 0.999283i | \(0.487943\pi\) | |||||||
\(14\) | 1.87978 | 0.502391 | ||||||||
\(15\) | 3.08968 | 0.797753 | ||||||||
\(16\) | −4.71532 | −1.17883 | ||||||||
\(17\) | 4.88218 | 1.18410 | 0.592052 | − | 0.805900i | \(-0.298318\pi\) | ||||
0.592052 | + | 0.805900i | \(0.298318\pi\) | |||||||
\(18\) | −12.3053 | −2.90038 | ||||||||
\(19\) | −2.85217 | −0.654333 | −0.327167 | − | 0.944967i | \(-0.606094\pi\) | ||||
−0.327167 | + | 0.944967i | \(0.606094\pi\) | |||||||
\(20\) | 1.53356 | 0.342914 | ||||||||
\(21\) | −3.08968 | −0.674224 | ||||||||
\(22\) | 7.74017 | 1.65021 | ||||||||
\(23\) | −7.60448 | −1.58564 | −0.792822 | − | 0.609453i | \(-0.791389\pi\) | ||||
−0.792822 | + | 0.609453i | \(0.791389\pi\) | |||||||
\(24\) | 2.70906 | 0.552984 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.513344 | −0.100675 | ||||||||
\(27\) | 10.9565 | 2.10857 | ||||||||
\(28\) | −1.53356 | −0.289815 | ||||||||
\(29\) | 0.390236 | 0.0724650 | 0.0362325 | − | 0.999343i | \(-0.488464\pi\) | ||||
0.0362325 | + | 0.999343i | \(0.488464\pi\) | |||||||
\(30\) | −5.80791 | −1.06038 | ||||||||
\(31\) | 3.68320 | 0.661522 | 0.330761 | − | 0.943715i | \(-0.392695\pi\) | ||||
0.330761 | + | 0.943715i | \(0.392695\pi\) | |||||||
\(32\) | 7.11012 | 1.25690 | ||||||||
\(33\) | −12.7221 | −2.21463 | ||||||||
\(34\) | −9.17741 | −1.57391 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 10.0389 | 1.67315 | ||||||||
\(37\) | −10.8320 | −1.78077 | −0.890386 | − | 0.455205i | \(-0.849566\pi\) | ||||
−0.890386 | + | 0.455205i | \(0.849566\pi\) | |||||||
\(38\) | 5.36144 | 0.869741 | ||||||||
\(39\) | 0.843755 | 0.135109 | ||||||||
\(40\) | 0.876807 | 0.138635 | ||||||||
\(41\) | −11.3586 | −1.77391 | −0.886954 | − | 0.461858i | \(-0.847183\pi\) | ||||
−0.886954 | + | 0.461858i | \(0.847183\pi\) | |||||||
\(42\) | 5.80791 | 0.896181 | ||||||||
\(43\) | 0.586083 | 0.0893769 | 0.0446884 | − | 0.999001i | \(-0.485770\pi\) | ||||
0.0446884 | + | 0.999001i | \(0.485770\pi\) | |||||||
\(44\) | −6.31458 | −0.951958 | ||||||||
\(45\) | 6.54615 | 0.975842 | ||||||||
\(46\) | 14.2947 | 2.10764 | ||||||||
\(47\) | 1.17774 | 0.171791 | 0.0858956 | − | 0.996304i | \(-0.472625\pi\) | ||||
0.0858956 | + | 0.996304i | \(0.472625\pi\) | |||||||
\(48\) | −14.5688 | −2.10283 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.87978 | −0.265840 | ||||||||
\(51\) | 15.0844 | 2.11224 | ||||||||
\(52\) | 0.418796 | 0.0580765 | ||||||||
\(53\) | −5.64463 | −0.775349 | −0.387674 | − | 0.921796i | \(-0.626722\pi\) | ||||
−0.387674 | + | 0.921796i | \(0.626722\pi\) | |||||||
\(54\) | −20.5957 | −2.80272 | ||||||||
\(55\) | −4.11760 | −0.555217 | ||||||||
\(56\) | −0.876807 | −0.117168 | ||||||||
\(57\) | −8.81231 | −1.16722 | ||||||||
\(58\) | −0.733556 | −0.0963207 | ||||||||
\(59\) | −9.44277 | −1.22934 | −0.614672 | − | 0.788783i | \(-0.710711\pi\) | ||||
−0.614672 | + | 0.788783i | \(0.710711\pi\) | |||||||
\(60\) | 4.73821 | 0.611700 | ||||||||
\(61\) | −7.72166 | −0.988657 | −0.494329 | − | 0.869275i | \(-0.664586\pi\) | ||||
−0.494329 | + | 0.869275i | \(0.664586\pi\) | |||||||
\(62\) | −6.92359 | −0.879296 | ||||||||
\(63\) | −6.54615 | −0.824737 | ||||||||
\(64\) | −3.93481 | −0.491851 | ||||||||
\(65\) | 0.273088 | 0.0338724 | ||||||||
\(66\) | 23.9147 | 2.94369 | ||||||||
\(67\) | 10.3534 | 1.26487 | 0.632435 | − | 0.774613i | \(-0.282056\pi\) | ||||
0.632435 | + | 0.774613i | \(0.282056\pi\) | |||||||
\(68\) | 7.48711 | 0.907945 | ||||||||
\(69\) | −23.4954 | −2.82852 | ||||||||
\(70\) | 1.87978 | 0.224676 | ||||||||
\(71\) | 11.7403 | 1.39332 | 0.696661 | − | 0.717401i | \(-0.254668\pi\) | ||||
0.696661 | + | 0.717401i | \(0.254668\pi\) | |||||||
\(72\) | 5.73971 | 0.676431 | ||||||||
\(73\) | −11.6305 | −1.36125 | −0.680624 | − | 0.732633i | \(-0.738291\pi\) | ||||
−0.680624 | + | 0.732633i | \(0.738291\pi\) | |||||||
\(74\) | 20.3618 | 2.36701 | ||||||||
\(75\) | 3.08968 | 0.356766 | ||||||||
\(76\) | −4.37397 | −0.501729 | ||||||||
\(77\) | 4.11760 | 0.469244 | ||||||||
\(78\) | −1.58607 | −0.179587 | ||||||||
\(79\) | −2.29928 | −0.258690 | −0.129345 | − | 0.991600i | \(-0.541287\pi\) | ||||
−0.129345 | + | 0.991600i | \(0.541287\pi\) | |||||||
\(80\) | −4.71532 | −0.527188 | ||||||||
\(81\) | 14.2136 | 1.57929 | ||||||||
\(82\) | 21.3515 | 2.35788 | ||||||||
\(83\) | −0.722398 | −0.0792934 | −0.0396467 | − | 0.999214i | \(-0.512623\pi\) | ||||
−0.0396467 | + | 0.999214i | \(0.512623\pi\) | |||||||
\(84\) | −4.73821 | −0.516981 | ||||||||
\(85\) | 4.88218 | 0.529547 | ||||||||
\(86\) | −1.10171 | −0.118800 | ||||||||
\(87\) | 1.20571 | 0.129265 | ||||||||
\(88\) | −3.61034 | −0.384864 | ||||||||
\(89\) | 7.10098 | 0.752702 | 0.376351 | − | 0.926477i | \(-0.377179\pi\) | ||||
0.376351 | + | 0.926477i | \(0.377179\pi\) | |||||||
\(90\) | −12.3053 | −1.29709 | ||||||||
\(91\) | −0.273088 | −0.0286274 | ||||||||
\(92\) | −11.6619 | −1.21584 | ||||||||
\(93\) | 11.3799 | 1.18004 | ||||||||
\(94\) | −2.21389 | −0.228345 | ||||||||
\(95\) | −2.85217 | −0.292627 | ||||||||
\(96\) | 21.9680 | 2.24210 | ||||||||
\(97\) | −15.4305 | −1.56673 | −0.783363 | − | 0.621565i | \(-0.786497\pi\) | ||||
−0.783363 | + | 0.621565i | \(0.786497\pi\) | |||||||
\(98\) | −1.87978 | −0.189886 | ||||||||
\(99\) | −26.9544 | −2.70902 | ||||||||
\(100\) | 1.53356 | 0.153356 | ||||||||
\(101\) | −11.1085 | −1.10534 | −0.552668 | − | 0.833402i | \(-0.686390\pi\) | ||||
−0.552668 | + | 0.833402i | \(0.686390\pi\) | |||||||
\(102\) | −28.3553 | −2.80759 | ||||||||
\(103\) | −18.9383 | −1.86605 | −0.933023 | − | 0.359818i | \(-0.882839\pi\) | ||||
−0.933023 | + | 0.359818i | \(0.882839\pi\) | |||||||
\(104\) | 0.239445 | 0.0234795 | ||||||||
\(105\) | −3.08968 | −0.301522 | ||||||||
\(106\) | 10.6106 | 1.03060 | ||||||||
\(107\) | −10.9789 | −1.06137 | −0.530686 | − | 0.847569i | \(-0.678066\pi\) | ||||
−0.530686 | + | 0.847569i | \(0.678066\pi\) | |||||||
\(108\) | 16.8024 | 1.61681 | ||||||||
\(109\) | 7.35037 | 0.704038 | 0.352019 | − | 0.935993i | \(-0.385495\pi\) | ||||
0.352019 | + | 0.935993i | \(0.385495\pi\) | |||||||
\(110\) | 7.74017 | 0.737996 | ||||||||
\(111\) | −33.4675 | −3.17660 | ||||||||
\(112\) | 4.71532 | 0.445556 | ||||||||
\(113\) | 17.3099 | 1.62838 | 0.814190 | − | 0.580599i | \(-0.197181\pi\) | ||||
0.814190 | + | 0.580599i | \(0.197181\pi\) | |||||||
\(114\) | 16.5652 | 1.55147 | ||||||||
\(115\) | −7.60448 | −0.709122 | ||||||||
\(116\) | 0.598450 | 0.0555646 | ||||||||
\(117\) | 1.78767 | 0.165270 | ||||||||
\(118\) | 17.7503 | 1.63405 | ||||||||
\(119\) | −4.88218 | −0.447549 | ||||||||
\(120\) | 2.70906 | 0.247302 | ||||||||
\(121\) | 5.95464 | 0.541331 | ||||||||
\(122\) | 14.5150 | 1.31413 | ||||||||
\(123\) | −35.0943 | −3.16435 | ||||||||
\(124\) | 5.64839 | 0.507241 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 12.3053 | 1.09624 | ||||||||
\(127\) | 15.6918 | 1.39242 | 0.696210 | − | 0.717838i | \(-0.254868\pi\) | ||||
0.696210 | + | 0.717838i | \(0.254868\pi\) | |||||||
\(128\) | −6.82369 | −0.603135 | ||||||||
\(129\) | 1.81081 | 0.159433 | ||||||||
\(130\) | −0.513344 | −0.0450232 | ||||||||
\(131\) | 14.8642 | 1.29869 | 0.649345 | − | 0.760494i | \(-0.275043\pi\) | ||||
0.649345 | + | 0.760494i | \(0.275043\pi\) | |||||||
\(132\) | −19.5101 | −1.69813 | ||||||||
\(133\) | 2.85217 | 0.247315 | ||||||||
\(134\) | −19.4621 | −1.68127 | ||||||||
\(135\) | 10.9565 | 0.942983 | ||||||||
\(136\) | 4.28073 | 0.367070 | ||||||||
\(137\) | −20.1741 | −1.72359 | −0.861797 | − | 0.507254i | \(-0.830661\pi\) | ||||
−0.861797 | + | 0.507254i | \(0.830661\pi\) | |||||||
\(138\) | 44.1662 | 3.75967 | ||||||||
\(139\) | −6.10706 | −0.517994 | −0.258997 | − | 0.965878i | \(-0.583392\pi\) | ||||
−0.258997 | + | 0.965878i | \(0.583392\pi\) | |||||||
\(140\) | −1.53356 | −0.129609 | ||||||||
\(141\) | 3.63885 | 0.306446 | ||||||||
\(142\) | −22.0692 | −1.85201 | ||||||||
\(143\) | −1.12447 | −0.0940326 | ||||||||
\(144\) | −30.8672 | −2.57226 | ||||||||
\(145\) | 0.390236 | 0.0324073 | ||||||||
\(146\) | 21.8627 | 1.80937 | ||||||||
\(147\) | 3.08968 | 0.254833 | ||||||||
\(148\) | −16.6115 | −1.36546 | ||||||||
\(149\) | 10.6447 | 0.872047 | 0.436023 | − | 0.899935i | \(-0.356387\pi\) | ||||
0.436023 | + | 0.899935i | \(0.356387\pi\) | |||||||
\(150\) | −5.80791 | −0.474214 | ||||||||
\(151\) | 9.46042 | 0.769878 | 0.384939 | − | 0.922942i | \(-0.374222\pi\) | ||||
0.384939 | + | 0.922942i | \(0.374222\pi\) | |||||||
\(152\) | −2.50081 | −0.202842 | ||||||||
\(153\) | 31.9595 | 2.58377 | ||||||||
\(154\) | −7.74017 | −0.623720 | ||||||||
\(155\) | 3.68320 | 0.295842 | ||||||||
\(156\) | 1.29395 | 0.103599 | ||||||||
\(157\) | 23.5609 | 1.88037 | 0.940183 | − | 0.340671i | \(-0.110654\pi\) | ||||
0.940183 | + | 0.340671i | \(0.110654\pi\) | |||||||
\(158\) | 4.32214 | 0.343851 | ||||||||
\(159\) | −17.4401 | −1.38309 | ||||||||
\(160\) | 7.11012 | 0.562105 | ||||||||
\(161\) | 7.60448 | 0.599317 | ||||||||
\(162\) | −26.7184 | −2.09920 | ||||||||
\(163\) | −12.8723 | −1.00824 | −0.504119 | − | 0.863634i | \(-0.668183\pi\) | ||||
−0.504119 | + | 0.863634i | \(0.668183\pi\) | |||||||
\(164\) | −17.4190 | −1.36019 | ||||||||
\(165\) | −12.7221 | −0.990413 | ||||||||
\(166\) | 1.35795 | 0.105397 | ||||||||
\(167\) | −11.6269 | −0.899719 | −0.449859 | − | 0.893099i | \(-0.648526\pi\) | ||||
−0.449859 | + | 0.893099i | \(0.648526\pi\) | |||||||
\(168\) | −2.70906 | −0.209008 | ||||||||
\(169\) | −12.9254 | −0.994263 | ||||||||
\(170\) | −9.17741 | −0.703875 | ||||||||
\(171\) | −18.6707 | −1.42779 | ||||||||
\(172\) | 0.898793 | 0.0685323 | ||||||||
\(173\) | 1.76293 | 0.134033 | 0.0670167 | − | 0.997752i | \(-0.478652\pi\) | ||||
0.0670167 | + | 0.997752i | \(0.478652\pi\) | |||||||
\(174\) | −2.26646 | −0.171820 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 19.4158 | 1.46352 | ||||||||
\(177\) | −29.1752 | −2.19294 | ||||||||
\(178\) | −13.3482 | −1.00049 | ||||||||
\(179\) | −11.3007 | −0.844650 | −0.422325 | − | 0.906444i | \(-0.638786\pi\) | ||||
−0.422325 | + | 0.906444i | \(0.638786\pi\) | |||||||
\(180\) | 10.0389 | 0.748255 | ||||||||
\(181\) | 0.438301 | 0.0325786 | 0.0162893 | − | 0.999867i | \(-0.494815\pi\) | ||||
0.0162893 | + | 0.999867i | \(0.494815\pi\) | |||||||
\(182\) | 0.513344 | 0.0380516 | ||||||||
\(183\) | −23.8575 | −1.76360 | ||||||||
\(184\) | −6.66767 | −0.491547 | ||||||||
\(185\) | −10.8320 | −0.796386 | ||||||||
\(186\) | −21.3917 | −1.56851 | ||||||||
\(187\) | −20.1029 | −1.47007 | ||||||||
\(188\) | 1.80613 | 0.131726 | ||||||||
\(189\) | −10.9565 | −0.796966 | ||||||||
\(190\) | 5.36144 | 0.388960 | ||||||||
\(191\) | 13.0163 | 0.941828 | 0.470914 | − | 0.882179i | \(-0.343924\pi\) | ||||
0.470914 | + | 0.882179i | \(0.343924\pi\) | |||||||
\(192\) | −12.1573 | −0.877378 | ||||||||
\(193\) | 10.3764 | 0.746910 | 0.373455 | − | 0.927648i | \(-0.378173\pi\) | ||||
0.373455 | + | 0.927648i | \(0.378173\pi\) | |||||||
\(194\) | 29.0058 | 2.08250 | ||||||||
\(195\) | 0.843755 | 0.0604225 | ||||||||
\(196\) | 1.53356 | 0.109540 | ||||||||
\(197\) | −4.03627 | −0.287573 | −0.143786 | − | 0.989609i | \(-0.545928\pi\) | ||||
−0.143786 | + | 0.989609i | \(0.545928\pi\) | |||||||
\(198\) | 50.6683 | 3.60084 | ||||||||
\(199\) | −8.14506 | −0.577388 | −0.288694 | − | 0.957421i | \(-0.593221\pi\) | ||||
−0.288694 | + | 0.957421i | \(0.593221\pi\) | |||||||
\(200\) | 0.876807 | 0.0619997 | ||||||||
\(201\) | 31.9888 | 2.25631 | ||||||||
\(202\) | 20.8815 | 1.46921 | ||||||||
\(203\) | −0.390236 | −0.0273892 | ||||||||
\(204\) | 23.1328 | 1.61962 | ||||||||
\(205\) | −11.3586 | −0.793316 | ||||||||
\(206\) | 35.5997 | 2.48035 | ||||||||
\(207\) | −49.7801 | −3.45995 | ||||||||
\(208\) | −1.28770 | −0.0892856 | ||||||||
\(209\) | 11.7441 | 0.812357 | ||||||||
\(210\) | 5.80791 | 0.400784 | ||||||||
\(211\) | 7.51833 | 0.517583 | 0.258792 | − | 0.965933i | \(-0.416676\pi\) | ||||
0.258792 | + | 0.965933i | \(0.416676\pi\) | |||||||
\(212\) | −8.65636 | −0.594521 | ||||||||
\(213\) | 36.2739 | 2.48545 | ||||||||
\(214\) | 20.6379 | 1.41078 | ||||||||
\(215\) | 0.586083 | 0.0399706 | ||||||||
\(216\) | 9.60672 | 0.653655 | ||||||||
\(217\) | −3.68320 | −0.250032 | ||||||||
\(218\) | −13.8171 | −0.935809 | ||||||||
\(219\) | −35.9346 | −2.42823 | ||||||||
\(220\) | −6.31458 | −0.425729 | ||||||||
\(221\) | 1.33326 | 0.0896850 | ||||||||
\(222\) | 62.9114 | 4.22234 | ||||||||
\(223\) | 15.8612 | 1.06214 | 0.531071 | − | 0.847327i | \(-0.321790\pi\) | ||||
0.531071 | + | 0.847327i | \(0.321790\pi\) | |||||||
\(224\) | −7.11012 | −0.475065 | ||||||||
\(225\) | 6.54615 | 0.436410 | ||||||||
\(226\) | −32.5388 | −2.16445 | ||||||||
\(227\) | −19.5954 | −1.30059 | −0.650297 | − | 0.759680i | \(-0.725356\pi\) | ||||
−0.650297 | + | 0.759680i | \(0.725356\pi\) | |||||||
\(228\) | −13.5142 | −0.894999 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 14.2947 | 0.942566 | ||||||||
\(231\) | 12.7221 | 0.837052 | ||||||||
\(232\) | 0.342162 | 0.0224640 | ||||||||
\(233\) | 6.27293 | 0.410953 | 0.205477 | − | 0.978662i | \(-0.434126\pi\) | ||||
0.205477 | + | 0.978662i | \(0.434126\pi\) | |||||||
\(234\) | −3.36042 | −0.219678 | ||||||||
\(235\) | 1.17774 | 0.0768273 | ||||||||
\(236\) | −14.4810 | −0.942634 | ||||||||
\(237\) | −7.10406 | −0.461458 | ||||||||
\(238\) | 9.17741 | 0.594883 | ||||||||
\(239\) | 4.46549 | 0.288849 | 0.144424 | − | 0.989516i | \(-0.453867\pi\) | ||||
0.144424 | + | 0.989516i | \(0.453867\pi\) | |||||||
\(240\) | −14.5688 | −0.940414 | ||||||||
\(241\) | 9.26330 | 0.596702 | 0.298351 | − | 0.954456i | \(-0.403563\pi\) | ||||
0.298351 | + | 0.954456i | \(0.403563\pi\) | |||||||
\(242\) | −11.1934 | −0.719538 | ||||||||
\(243\) | 11.0461 | 0.708609 | ||||||||
\(244\) | −11.8416 | −0.758081 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 65.9695 | 4.20606 | ||||||||
\(247\) | −0.778893 | −0.0495598 | ||||||||
\(248\) | 3.22945 | 0.205071 | ||||||||
\(249\) | −2.23198 | −0.141446 | ||||||||
\(250\) | −1.87978 | −0.118887 | ||||||||
\(251\) | −7.16465 | −0.452229 | −0.226114 | − | 0.974101i | \(-0.572602\pi\) | ||||
−0.226114 | + | 0.974101i | \(0.572602\pi\) | |||||||
\(252\) | −10.0389 | −0.632391 | ||||||||
\(253\) | 31.3122 | 1.96858 | ||||||||
\(254\) | −29.4970 | −1.85081 | ||||||||
\(255\) | 15.0844 | 0.944622 | ||||||||
\(256\) | 20.6966 | 1.29354 | ||||||||
\(257\) | −15.3430 | −0.957067 | −0.478534 | − | 0.878069i | \(-0.658831\pi\) | ||||
−0.478534 | + | 0.878069i | \(0.658831\pi\) | |||||||
\(258\) | −3.40392 | −0.211919 | ||||||||
\(259\) | 10.8320 | 0.673069 | ||||||||
\(260\) | 0.418796 | 0.0259726 | ||||||||
\(261\) | 2.55454 | 0.158122 | ||||||||
\(262\) | −27.9413 | −1.72622 | ||||||||
\(263\) | 4.44327 | 0.273984 | 0.136992 | − | 0.990572i | \(-0.456257\pi\) | ||||
0.136992 | + | 0.990572i | \(0.456257\pi\) | |||||||
\(264\) | −11.1548 | −0.686532 | ||||||||
\(265\) | −5.64463 | −0.346747 | ||||||||
\(266\) | −5.36144 | −0.328731 | ||||||||
\(267\) | 21.9398 | 1.34269 | ||||||||
\(268\) | 15.8775 | 0.969875 | ||||||||
\(269\) | −5.07697 | −0.309548 | −0.154774 | − | 0.987950i | \(-0.549465\pi\) | ||||
−0.154774 | + | 0.987950i | \(0.549465\pi\) | |||||||
\(270\) | −20.5957 | −1.25342 | ||||||||
\(271\) | −29.7934 | −1.80982 | −0.904911 | − | 0.425601i | \(-0.860063\pi\) | ||||
−0.904911 | + | 0.425601i | \(0.860063\pi\) | |||||||
\(272\) | −23.0210 | −1.39586 | ||||||||
\(273\) | −0.843755 | −0.0510664 | ||||||||
\(274\) | 37.9229 | 2.29100 | ||||||||
\(275\) | −4.11760 | −0.248301 | ||||||||
\(276\) | −36.0316 | −2.16885 | ||||||||
\(277\) | 9.02010 | 0.541965 | 0.270983 | − | 0.962584i | \(-0.412651\pi\) | ||||
0.270983 | + | 0.962584i | \(0.412651\pi\) | |||||||
\(278\) | 11.4799 | 0.688519 | ||||||||
\(279\) | 24.1108 | 1.44347 | ||||||||
\(280\) | −0.876807 | −0.0523993 | ||||||||
\(281\) | −11.1578 | −0.665616 | −0.332808 | − | 0.942995i | \(-0.607996\pi\) | ||||
−0.332808 | + | 0.942995i | \(0.607996\pi\) | |||||||
\(282\) | −6.84022 | −0.407329 | ||||||||
\(283\) | 11.6501 | 0.692529 | 0.346264 | − | 0.938137i | \(-0.387450\pi\) | ||||
0.346264 | + | 0.938137i | \(0.387450\pi\) | |||||||
\(284\) | 18.0045 | 1.06837 | ||||||||
\(285\) | −8.81231 | −0.521996 | ||||||||
\(286\) | 2.11374 | 0.124988 | ||||||||
\(287\) | 11.3586 | 0.670474 | ||||||||
\(288\) | 46.5439 | 2.74263 | ||||||||
\(289\) | 6.83570 | 0.402100 | ||||||||
\(290\) | −0.733556 | −0.0430759 | ||||||||
\(291\) | −47.6752 | −2.79477 | ||||||||
\(292\) | −17.8361 | −1.04378 | ||||||||
\(293\) | 8.75204 | 0.511299 | 0.255650 | − | 0.966769i | \(-0.417711\pi\) | ||||
0.255650 | + | 0.966769i | \(0.417711\pi\) | |||||||
\(294\) | −5.80791 | −0.338724 | ||||||||
\(295\) | −9.44277 | −0.549779 | ||||||||
\(296\) | −9.49760 | −0.552037 | ||||||||
\(297\) | −45.1144 | −2.61780 | ||||||||
\(298\) | −20.0096 | −1.15913 | ||||||||
\(299\) | −2.07669 | −0.120098 | ||||||||
\(300\) | 4.73821 | 0.273561 | ||||||||
\(301\) | −0.586083 | −0.0337813 | ||||||||
\(302\) | −17.7835 | −1.02332 | ||||||||
\(303\) | −34.3217 | −1.97173 | ||||||||
\(304\) | 13.4489 | 0.771347 | ||||||||
\(305\) | −7.72166 | −0.442141 | ||||||||
\(306\) | −60.0767 | −3.43435 | ||||||||
\(307\) | 5.16995 | 0.295065 | 0.147532 | − | 0.989057i | \(-0.452867\pi\) | ||||
0.147532 | + | 0.989057i | \(0.452867\pi\) | |||||||
\(308\) | 6.31458 | 0.359806 | ||||||||
\(309\) | −58.5133 | −3.32871 | ||||||||
\(310\) | −6.92359 | −0.393233 | ||||||||
\(311\) | 1.16283 | 0.0659379 | 0.0329689 | − | 0.999456i | \(-0.489504\pi\) | ||||
0.0329689 | + | 0.999456i | \(0.489504\pi\) | |||||||
\(312\) | 0.739811 | 0.0418835 | ||||||||
\(313\) | −16.9049 | −0.955523 | −0.477761 | − | 0.878490i | \(-0.658552\pi\) | ||||
−0.477761 | + | 0.878490i | \(0.658552\pi\) | |||||||
\(314\) | −44.2892 | −2.49939 | ||||||||
\(315\) | −6.54615 | −0.368834 | ||||||||
\(316\) | −3.52608 | −0.198358 | ||||||||
\(317\) | −2.24685 | −0.126196 | −0.0630979 | − | 0.998007i | \(-0.520098\pi\) | ||||
−0.0630979 | + | 0.998007i | \(0.520098\pi\) | |||||||
\(318\) | 32.7835 | 1.83841 | ||||||||
\(319\) | −1.60684 | −0.0899656 | ||||||||
\(320\) | −3.93481 | −0.219962 | ||||||||
\(321\) | −33.9214 | −1.89331 | ||||||||
\(322\) | −14.2947 | −0.796614 | ||||||||
\(323\) | −13.9248 | −0.774798 | ||||||||
\(324\) | 21.7974 | 1.21097 | ||||||||
\(325\) | 0.273088 | 0.0151482 | ||||||||
\(326\) | 24.1971 | 1.34015 | ||||||||
\(327\) | 22.7103 | 1.25588 | ||||||||
\(328\) | −9.95926 | −0.549908 | ||||||||
\(329\) | −1.17774 | −0.0649309 | ||||||||
\(330\) | 23.9147 | 1.31646 | ||||||||
\(331\) | −0.994093 | −0.0546403 | −0.0273202 | − | 0.999627i | \(-0.508697\pi\) | ||||
−0.0273202 | + | 0.999627i | \(0.508697\pi\) | |||||||
\(332\) | −1.10784 | −0.0608005 | ||||||||
\(333\) | −70.9080 | −3.88573 | ||||||||
\(334\) | 21.8560 | 1.19591 | ||||||||
\(335\) | 10.3534 | 0.565667 | ||||||||
\(336\) | 14.5688 | 0.794795 | ||||||||
\(337\) | 2.49224 | 0.135761 | 0.0678804 | − | 0.997693i | \(-0.478376\pi\) | ||||
0.0678804 | + | 0.997693i | \(0.478376\pi\) | |||||||
\(338\) | 24.2969 | 1.32158 | ||||||||
\(339\) | 53.4822 | 2.90475 | ||||||||
\(340\) | 7.48711 | 0.406045 | ||||||||
\(341\) | −15.1659 | −0.821282 | ||||||||
\(342\) | 35.0968 | 1.89782 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.513882 | 0.0277067 | ||||||||
\(345\) | −23.4954 | −1.26495 | ||||||||
\(346\) | −3.31392 | −0.178158 | ||||||||
\(347\) | 21.5213 | 1.15533 | 0.577663 | − | 0.816275i | \(-0.303965\pi\) | ||||
0.577663 | + | 0.816275i | \(0.303965\pi\) | |||||||
\(348\) | 1.84902 | 0.0991179 | ||||||||
\(349\) | −14.5825 | −0.780583 | −0.390292 | − | 0.920691i | \(-0.627626\pi\) | ||||
−0.390292 | + | 0.920691i | \(0.627626\pi\) | |||||||
\(350\) | 1.87978 | 0.100478 | ||||||||
\(351\) | 2.99208 | 0.159705 | ||||||||
\(352\) | −29.2767 | −1.56045 | ||||||||
\(353\) | −6.56600 | −0.349473 | −0.174737 | − | 0.984615i | \(-0.555907\pi\) | ||||
−0.174737 | + | 0.984615i | \(0.555907\pi\) | |||||||
\(354\) | 54.8428 | 2.91486 | ||||||||
\(355\) | 11.7403 | 0.623112 | ||||||||
\(356\) | 10.8898 | 0.577156 | ||||||||
\(357\) | −15.0844 | −0.798351 | ||||||||
\(358\) | 21.2427 | 1.12271 | ||||||||
\(359\) | 1.24490 | 0.0657034 | 0.0328517 | − | 0.999460i | \(-0.489541\pi\) | ||||
0.0328517 | + | 0.999460i | \(0.489541\pi\) | |||||||
\(360\) | 5.73971 | 0.302509 | ||||||||
\(361\) | −10.8651 | −0.571848 | ||||||||
\(362\) | −0.823907 | −0.0433036 | ||||||||
\(363\) | 18.3980 | 0.965642 | ||||||||
\(364\) | −0.418796 | −0.0219509 | ||||||||
\(365\) | −11.6305 | −0.608769 | ||||||||
\(366\) | 44.8467 | 2.34418 | ||||||||
\(367\) | −15.7248 | −0.820827 | −0.410414 | − | 0.911899i | \(-0.634616\pi\) | ||||
−0.410414 | + | 0.911899i | \(0.634616\pi\) | |||||||
\(368\) | 35.8575 | 1.86920 | ||||||||
\(369\) | −74.3547 | −3.87075 | ||||||||
\(370\) | 20.3618 | 1.05856 | ||||||||
\(371\) | 5.64463 | 0.293054 | ||||||||
\(372\) | 17.4518 | 0.904831 | ||||||||
\(373\) | −28.3215 | −1.46643 | −0.733215 | − | 0.679997i | \(-0.761981\pi\) | ||||
−0.733215 | + | 0.679997i | \(0.761981\pi\) | |||||||
\(374\) | 37.7889 | 1.95402 | ||||||||
\(375\) | 3.08968 | 0.159551 | ||||||||
\(376\) | 1.03265 | 0.0532549 | ||||||||
\(377\) | 0.106569 | 0.00548857 | ||||||||
\(378\) | 20.5957 | 1.05933 | ||||||||
\(379\) | 26.5688 | 1.36475 | 0.682374 | − | 0.731004i | \(-0.260948\pi\) | ||||
0.682374 | + | 0.731004i | \(0.260948\pi\) | |||||||
\(380\) | −4.37397 | −0.224380 | ||||||||
\(381\) | 48.4826 | 2.48384 | ||||||||
\(382\) | −24.4678 | −1.25188 | ||||||||
\(383\) | −2.67497 | −0.136685 | −0.0683423 | − | 0.997662i | \(-0.521771\pi\) | ||||
−0.0683423 | + | 0.997662i | \(0.521771\pi\) | |||||||
\(384\) | −21.0831 | −1.07589 | ||||||||
\(385\) | 4.11760 | 0.209852 | ||||||||
\(386\) | −19.5053 | −0.992795 | ||||||||
\(387\) | 3.83659 | 0.195025 | ||||||||
\(388\) | −23.6635 | −1.20133 | ||||||||
\(389\) | −15.7293 | −0.797509 | −0.398754 | − | 0.917058i | \(-0.630557\pi\) | ||||
−0.398754 | + | 0.917058i | \(0.630557\pi\) | |||||||
\(390\) | −1.58607 | −0.0803138 | ||||||||
\(391\) | −37.1265 | −1.87757 | ||||||||
\(392\) | 0.876807 | 0.0442855 | ||||||||
\(393\) | 45.9256 | 2.31664 | ||||||||
\(394\) | 7.58729 | 0.382242 | ||||||||
\(395\) | −2.29928 | −0.115689 | ||||||||
\(396\) | −41.3362 | −2.07722 | ||||||||
\(397\) | 1.32960 | 0.0667305 | 0.0333652 | − | 0.999443i | \(-0.489378\pi\) | ||||
0.0333652 | + | 0.999443i | \(0.489378\pi\) | |||||||
\(398\) | 15.3109 | 0.767466 | ||||||||
\(399\) | 8.81231 | 0.441167 | ||||||||
\(400\) | −4.71532 | −0.235766 | ||||||||
\(401\) | −13.1006 | −0.654212 | −0.327106 | − | 0.944988i | \(-0.606073\pi\) | ||||
−0.327106 | + | 0.944988i | \(0.606073\pi\) | |||||||
\(402\) | −60.1317 | −2.99910 | ||||||||
\(403\) | 1.00584 | 0.0501043 | ||||||||
\(404\) | −17.0355 | −0.847547 | ||||||||
\(405\) | 14.2136 | 0.706280 | ||||||||
\(406\) | 0.733556 | 0.0364058 | ||||||||
\(407\) | 44.6019 | 2.21084 | ||||||||
\(408\) | 13.2261 | 0.654790 | ||||||||
\(409\) | −7.20693 | −0.356360 | −0.178180 | − | 0.983998i | \(-0.557021\pi\) | ||||
−0.178180 | + | 0.983998i | \(0.557021\pi\) | |||||||
\(410\) | 21.3515 | 1.05448 | ||||||||
\(411\) | −62.3317 | −3.07460 | ||||||||
\(412\) | −29.0430 | −1.43084 | ||||||||
\(413\) | 9.44277 | 0.464648 | ||||||||
\(414\) | 93.5754 | 4.59898 | ||||||||
\(415\) | −0.722398 | −0.0354611 | ||||||||
\(416\) | 1.94169 | 0.0951991 | ||||||||
\(417\) | −18.8689 | −0.924014 | ||||||||
\(418\) | −22.0763 | −1.07979 | ||||||||
\(419\) | 17.1308 | 0.836894 | 0.418447 | − | 0.908241i | \(-0.362575\pi\) | ||||
0.418447 | + | 0.908241i | \(0.362575\pi\) | |||||||
\(420\) | −4.73821 | −0.231201 | ||||||||
\(421\) | −40.3820 | −1.96810 | −0.984050 | − | 0.177891i | \(-0.943073\pi\) | ||||
−0.984050 | + | 0.177891i | \(0.943073\pi\) | |||||||
\(422\) | −14.1328 | −0.687973 | ||||||||
\(423\) | 7.70966 | 0.374857 | ||||||||
\(424\) | −4.94925 | −0.240357 | ||||||||
\(425\) | 4.88218 | 0.236821 | ||||||||
\(426\) | −68.1869 | −3.30366 | ||||||||
\(427\) | 7.72166 | 0.373677 | ||||||||
\(428\) | −16.8368 | −0.813837 | ||||||||
\(429\) | −3.47425 | −0.167738 | ||||||||
\(430\) | −1.10171 | −0.0531290 | ||||||||
\(431\) | 3.59873 | 0.173345 | 0.0866725 | − | 0.996237i | \(-0.472377\pi\) | ||||
0.0866725 | + | 0.996237i | \(0.472377\pi\) | |||||||
\(432\) | −51.6633 | −2.48565 | ||||||||
\(433\) | 28.1791 | 1.35420 | 0.677100 | − | 0.735891i | \(-0.263236\pi\) | ||||
0.677100 | + | 0.735891i | \(0.263236\pi\) | |||||||
\(434\) | 6.92359 | 0.332343 | ||||||||
\(435\) | 1.20571 | 0.0578092 | ||||||||
\(436\) | 11.2722 | 0.539841 | ||||||||
\(437\) | 21.6893 | 1.03754 | ||||||||
\(438\) | 67.5490 | 3.22762 | ||||||||
\(439\) | 25.4740 | 1.21581 | 0.607904 | − | 0.794010i | \(-0.292011\pi\) | ||||
0.607904 | + | 0.794010i | \(0.292011\pi\) | |||||||
\(440\) | −3.61034 | −0.172116 | ||||||||
\(441\) | 6.54615 | 0.311721 | ||||||||
\(442\) | −2.50624 | −0.119210 | ||||||||
\(443\) | 19.4683 | 0.924968 | 0.462484 | − | 0.886628i | \(-0.346958\pi\) | ||||
0.462484 | + | 0.886628i | \(0.346958\pi\) | |||||||
\(444\) | −51.3244 | −2.43575 | ||||||||
\(445\) | 7.10098 | 0.336619 | ||||||||
\(446\) | −29.8154 | −1.41180 | ||||||||
\(447\) | 32.8887 | 1.55558 | ||||||||
\(448\) | 3.93481 | 0.185902 | ||||||||
\(449\) | 4.41952 | 0.208570 | 0.104285 | − | 0.994547i | \(-0.466745\pi\) | ||||
0.104285 | + | 0.994547i | \(0.466745\pi\) | |||||||
\(450\) | −12.3053 | −0.580077 | ||||||||
\(451\) | 46.7700 | 2.20231 | ||||||||
\(452\) | 26.5457 | 1.24861 | ||||||||
\(453\) | 29.2297 | 1.37333 | ||||||||
\(454\) | 36.8350 | 1.72875 | ||||||||
\(455\) | −0.273088 | −0.0128026 | ||||||||
\(456\) | −7.72670 | −0.361836 | ||||||||
\(457\) | −11.2328 | −0.525450 | −0.262725 | − | 0.964871i | \(-0.584621\pi\) | ||||
−0.262725 | + | 0.964871i | \(0.584621\pi\) | |||||||
\(458\) | −1.87978 | −0.0878362 | ||||||||
\(459\) | 53.4915 | 2.49677 | ||||||||
\(460\) | −11.6619 | −0.543739 | ||||||||
\(461\) | 29.6531 | 1.38108 | 0.690542 | − | 0.723292i | \(-0.257372\pi\) | ||||
0.690542 | + | 0.723292i | \(0.257372\pi\) | |||||||
\(462\) | −23.9147 | −1.11261 | ||||||||
\(463\) | −30.8834 | −1.43527 | −0.717637 | − | 0.696418i | \(-0.754776\pi\) | ||||
−0.717637 | + | 0.696418i | \(0.754776\pi\) | |||||||
\(464\) | −1.84009 | −0.0854239 | ||||||||
\(465\) | 11.3799 | 0.527731 | ||||||||
\(466\) | −11.7917 | −0.546240 | ||||||||
\(467\) | −28.8611 | −1.33553 | −0.667766 | − | 0.744371i | \(-0.732749\pi\) | ||||
−0.667766 | + | 0.744371i | \(0.732749\pi\) | |||||||
\(468\) | 2.74150 | 0.126726 | ||||||||
\(469\) | −10.3534 | −0.478076 | ||||||||
\(470\) | −2.21389 | −0.102119 | ||||||||
\(471\) | 72.7958 | 3.35425 | ||||||||
\(472\) | −8.27949 | −0.381094 | ||||||||
\(473\) | −2.41326 | −0.110962 | ||||||||
\(474\) | 13.3540 | 0.613371 | ||||||||
\(475\) | −2.85217 | −0.130867 | ||||||||
\(476\) | −7.48711 | −0.343171 | ||||||||
\(477\) | −36.9506 | −1.69185 | ||||||||
\(478\) | −8.39412 | −0.383938 | ||||||||
\(479\) | −2.78355 | −0.127184 | −0.0635919 | − | 0.997976i | \(-0.520256\pi\) | ||||
−0.0635919 | + | 0.997976i | \(0.520256\pi\) | |||||||
\(480\) | 21.9680 | 1.00270 | ||||||||
\(481\) | −2.95809 | −0.134877 | ||||||||
\(482\) | −17.4129 | −0.793137 | ||||||||
\(483\) | 23.4954 | 1.06908 | ||||||||
\(484\) | 9.13178 | 0.415081 | ||||||||
\(485\) | −15.4305 | −0.700661 | ||||||||
\(486\) | −20.7642 | −0.941885 | ||||||||
\(487\) | 35.3405 | 1.60143 | 0.800715 | − | 0.599046i | \(-0.204453\pi\) | ||||
0.800715 | + | 0.599046i | \(0.204453\pi\) | |||||||
\(488\) | −6.77041 | −0.306482 | ||||||||
\(489\) | −39.7714 | −1.79852 | ||||||||
\(490\) | −1.87978 | −0.0849196 | ||||||||
\(491\) | 0.205490 | 0.00927361 | 0.00463681 | − | 0.999989i | \(-0.498524\pi\) | ||||
0.00463681 | + | 0.999989i | \(0.498524\pi\) | |||||||
\(492\) | −53.8192 | −2.42636 | ||||||||
\(493\) | 1.90520 | 0.0858061 | ||||||||
\(494\) | 1.46414 | 0.0658750 | ||||||||
\(495\) | −26.9544 | −1.21151 | ||||||||
\(496\) | −17.3674 | −0.779821 | ||||||||
\(497\) | −11.7403 | −0.526626 | ||||||||
\(498\) | 4.19562 | 0.188010 | ||||||||
\(499\) | −13.9276 | −0.623487 | −0.311743 | − | 0.950166i | \(-0.600913\pi\) | ||||
−0.311743 | + | 0.950166i | \(0.600913\pi\) | |||||||
\(500\) | 1.53356 | 0.0685828 | ||||||||
\(501\) | −35.9235 | −1.60495 | ||||||||
\(502\) | 13.4679 | 0.601103 | ||||||||
\(503\) | 40.5982 | 1.81018 | 0.905091 | − | 0.425217i | \(-0.139802\pi\) | ||||
0.905091 | + | 0.425217i | \(0.139802\pi\) | |||||||
\(504\) | −5.73971 | −0.255667 | ||||||||
\(505\) | −11.1085 | −0.494321 | ||||||||
\(506\) | −58.8600 | −2.61664 | ||||||||
\(507\) | −39.9355 | −1.77360 | ||||||||
\(508\) | 24.0642 | 1.06768 | ||||||||
\(509\) | −12.4269 | −0.550813 | −0.275406 | − | 0.961328i | \(-0.588812\pi\) | ||||
−0.275406 | + | 0.961328i | \(0.588812\pi\) | |||||||
\(510\) | −28.3553 | −1.25559 | ||||||||
\(511\) | 11.6305 | 0.514503 | ||||||||
\(512\) | −25.2576 | −1.11624 | ||||||||
\(513\) | −31.2498 | −1.37971 | ||||||||
\(514\) | 28.8413 | 1.27214 | ||||||||
\(515\) | −18.9383 | −0.834521 | ||||||||
\(516\) | 2.77699 | 0.122250 | ||||||||
\(517\) | −4.84947 | −0.213279 | ||||||||
\(518\) | −20.3618 | −0.894645 | ||||||||
\(519\) | 5.44691 | 0.239093 | ||||||||
\(520\) | 0.239445 | 0.0105004 | ||||||||
\(521\) | 44.7863 | 1.96212 | 0.981062 | − | 0.193693i | \(-0.0620467\pi\) | ||||
0.981062 | + | 0.193693i | \(0.0620467\pi\) | |||||||
\(522\) | −4.80197 | −0.210176 | ||||||||
\(523\) | −29.8999 | −1.30743 | −0.653715 | − | 0.756741i | \(-0.726790\pi\) | ||||
−0.653715 | + | 0.756741i | \(0.726790\pi\) | |||||||
\(524\) | 22.7951 | 0.995807 | ||||||||
\(525\) | −3.08968 | −0.134845 | ||||||||
\(526\) | −8.35236 | −0.364180 | ||||||||
\(527\) | 17.9820 | 0.783310 | ||||||||
\(528\) | 59.9887 | 2.61067 | ||||||||
\(529\) | 34.8281 | 1.51427 | ||||||||
\(530\) | 10.6106 | 0.460896 | ||||||||
\(531\) | −61.8137 | −2.68249 | ||||||||
\(532\) | 4.37397 | 0.189636 | ||||||||
\(533\) | −3.10188 | −0.134357 | ||||||||
\(534\) | −41.2419 | −1.78471 | ||||||||
\(535\) | −10.9789 | −0.474660 | ||||||||
\(536\) | 9.07794 | 0.392107 | ||||||||
\(537\) | −34.9154 | −1.50671 | ||||||||
\(538\) | 9.54356 | 0.411452 | ||||||||
\(539\) | −4.11760 | −0.177358 | ||||||||
\(540\) | 16.8024 | 0.723060 | ||||||||
\(541\) | 26.7008 | 1.14796 | 0.573979 | − | 0.818870i | \(-0.305399\pi\) | ||||
0.573979 | + | 0.818870i | \(0.305399\pi\) | |||||||
\(542\) | 56.0050 | 2.40562 | ||||||||
\(543\) | 1.35421 | 0.0581147 | ||||||||
\(544\) | 34.7129 | 1.48830 | ||||||||
\(545\) | 7.35037 | 0.314855 | ||||||||
\(546\) | 1.58607 | 0.0678775 | ||||||||
\(547\) | −42.0148 | −1.79642 | −0.898212 | − | 0.439563i | \(-0.855133\pi\) | ||||
−0.898212 | + | 0.439563i | \(0.855133\pi\) | |||||||
\(548\) | −30.9382 | −1.32161 | ||||||||
\(549\) | −50.5471 | −2.15730 | ||||||||
\(550\) | 7.74017 | 0.330042 | ||||||||
\(551\) | −1.11302 | −0.0474163 | ||||||||
\(552\) | −20.6010 | −0.876836 | ||||||||
\(553\) | 2.29928 | 0.0977755 | ||||||||
\(554\) | −16.9558 | −0.720381 | ||||||||
\(555\) | −33.4675 | −1.42062 | ||||||||
\(556\) | −9.36553 | −0.397187 | ||||||||
\(557\) | 6.64563 | 0.281585 | 0.140792 | − | 0.990039i | \(-0.455035\pi\) | ||||
0.140792 | + | 0.990039i | \(0.455035\pi\) | |||||||
\(558\) | −45.3228 | −1.91867 | ||||||||
\(559\) | 0.160052 | 0.00676949 | ||||||||
\(560\) | 4.71532 | 0.199258 | ||||||||
\(561\) | −62.1115 | −2.62235 | ||||||||
\(562\) | 20.9741 | 0.884738 | ||||||||
\(563\) | 36.2031 | 1.52578 | 0.762890 | − | 0.646529i | \(-0.223780\pi\) | ||||
0.762890 | + | 0.646529i | \(0.223780\pi\) | |||||||
\(564\) | 5.58038 | 0.234976 | ||||||||
\(565\) | 17.3099 | 0.728234 | ||||||||
\(566\) | −21.8996 | −0.920511 | ||||||||
\(567\) | −14.2136 | −0.596915 | ||||||||
\(568\) | 10.2940 | 0.431927 | ||||||||
\(569\) | 14.9868 | 0.628281 | 0.314141 | − | 0.949376i | \(-0.398284\pi\) | ||||
0.314141 | + | 0.949376i | \(0.398284\pi\) | |||||||
\(570\) | 16.5652 | 0.693839 | ||||||||
\(571\) | 18.4057 | 0.770256 | 0.385128 | − | 0.922863i | \(-0.374157\pi\) | ||||
0.385128 | + | 0.922863i | \(0.374157\pi\) | |||||||
\(572\) | −1.72443 | −0.0721022 | ||||||||
\(573\) | 40.2163 | 1.68006 | ||||||||
\(574\) | −21.3515 | −0.891196 | ||||||||
\(575\) | −7.60448 | −0.317129 | ||||||||
\(576\) | −25.7578 | −1.07324 | ||||||||
\(577\) | −8.86999 | −0.369262 | −0.184631 | − | 0.982808i | \(-0.559109\pi\) | ||||
−0.184631 | + | 0.982808i | \(0.559109\pi\) | |||||||
\(578\) | −12.8496 | −0.534472 | ||||||||
\(579\) | 32.0598 | 1.33236 | ||||||||
\(580\) | 0.598450 | 0.0248493 | ||||||||
\(581\) | 0.722398 | 0.0299701 | ||||||||
\(582\) | 89.6188 | 3.71482 | ||||||||
\(583\) | 23.2423 | 0.962598 | ||||||||
\(584\) | −10.1977 | −0.421984 | ||||||||
\(585\) | 1.78767 | 0.0739112 | ||||||||
\(586\) | −16.4519 | −0.679620 | ||||||||
\(587\) | 23.6884 | 0.977724 | 0.488862 | − | 0.872361i | \(-0.337412\pi\) | ||||
0.488862 | + | 0.872361i | \(0.337412\pi\) | |||||||
\(588\) | 4.73821 | 0.195400 | ||||||||
\(589\) | −10.5051 | −0.432856 | ||||||||
\(590\) | 17.7503 | 0.730768 | ||||||||
\(591\) | −12.4708 | −0.512981 | ||||||||
\(592\) | 51.0764 | 2.09923 | ||||||||
\(593\) | 18.9734 | 0.779142 | 0.389571 | − | 0.920996i | \(-0.372623\pi\) | ||||
0.389571 | + | 0.920996i | \(0.372623\pi\) | |||||||
\(594\) | 84.8050 | 3.47959 | ||||||||
\(595\) | −4.88218 | −0.200150 | ||||||||
\(596\) | 16.3242 | 0.668667 | ||||||||
\(597\) | −25.1657 | −1.02996 | ||||||||
\(598\) | 3.90371 | 0.159635 | ||||||||
\(599\) | −34.3412 | −1.40314 | −0.701572 | − | 0.712599i | \(-0.747518\pi\) | ||||
−0.701572 | + | 0.712599i | \(0.747518\pi\) | |||||||
\(600\) | 2.70906 | 0.110597 | ||||||||
\(601\) | −10.3442 | −0.421948 | −0.210974 | − | 0.977492i | \(-0.567664\pi\) | ||||
−0.210974 | + | 0.977492i | \(0.567664\pi\) | |||||||
\(602\) | 1.10171 | 0.0449022 | ||||||||
\(603\) | 67.7749 | 2.76001 | ||||||||
\(604\) | 14.5081 | 0.590326 | ||||||||
\(605\) | 5.95464 | 0.242091 | ||||||||
\(606\) | 64.5171 | 2.62083 | ||||||||
\(607\) | −27.2104 | −1.10444 | −0.552219 | − | 0.833699i | \(-0.686219\pi\) | ||||
−0.552219 | + | 0.833699i | \(0.686219\pi\) | |||||||
\(608\) | −20.2793 | −0.822434 | ||||||||
\(609\) | −1.20571 | −0.0488577 | ||||||||
\(610\) | 14.5150 | 0.587695 | ||||||||
\(611\) | 0.321626 | 0.0130116 | ||||||||
\(612\) | 49.0117 | 1.98118 | ||||||||
\(613\) | 32.3076 | 1.30489 | 0.652445 | − | 0.757836i | \(-0.273743\pi\) | ||||
0.652445 | + | 0.757836i | \(0.273743\pi\) | |||||||
\(614\) | −9.71835 | −0.392201 | ||||||||
\(615\) | −35.0943 | −1.41514 | ||||||||
\(616\) | 3.61034 | 0.145465 | ||||||||
\(617\) | −8.43779 | −0.339693 | −0.169846 | − | 0.985471i | \(-0.554327\pi\) | ||||
−0.169846 | + | 0.985471i | \(0.554327\pi\) | |||||||
\(618\) | 109.992 | 4.42452 | ||||||||
\(619\) | −29.4777 | −1.18481 | −0.592405 | − | 0.805641i | \(-0.701821\pi\) | ||||
−0.592405 | + | 0.805641i | \(0.701821\pi\) | |||||||
\(620\) | 5.64839 | 0.226845 | ||||||||
\(621\) | −83.3183 | −3.34345 | ||||||||
\(622\) | −2.18585 | −0.0876448 | ||||||||
\(623\) | −7.10098 | −0.284495 | ||||||||
\(624\) | −3.97857 | −0.159270 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 31.7775 | 1.27008 | ||||||||
\(627\) | 36.2856 | 1.44911 | ||||||||
\(628\) | 36.1320 | 1.44182 | ||||||||
\(629\) | −52.8839 | −2.10862 | ||||||||
\(630\) | 12.3053 | 0.490255 | ||||||||
\(631\) | 42.2443 | 1.68172 | 0.840859 | − | 0.541254i | \(-0.182050\pi\) | ||||
0.840859 | + | 0.541254i | \(0.182050\pi\) | |||||||
\(632\) | −2.01603 | −0.0801933 | ||||||||
\(633\) | 23.2293 | 0.923281 | ||||||||
\(634\) | 4.22358 | 0.167740 | ||||||||
\(635\) | 15.6918 | 0.622709 | ||||||||
\(636\) | −26.7454 | −1.06052 | ||||||||
\(637\) | 0.273088 | 0.0108201 | ||||||||
\(638\) | 3.02049 | 0.119582 | ||||||||
\(639\) | 76.8540 | 3.04030 | ||||||||
\(640\) | −6.82369 | −0.269730 | ||||||||
\(641\) | −5.62034 | −0.221990 | −0.110995 | − | 0.993821i | \(-0.535404\pi\) | ||||
−0.110995 | + | 0.993821i | \(0.535404\pi\) | |||||||
\(642\) | 63.7646 | 2.51659 | ||||||||
\(643\) | −25.1007 | −0.989875 | −0.494937 | − | 0.868929i | \(-0.664809\pi\) | ||||
−0.494937 | + | 0.868929i | \(0.664809\pi\) | |||||||
\(644\) | 11.6619 | 0.459544 | ||||||||
\(645\) | 1.81081 | 0.0713007 | ||||||||
\(646\) | 26.1755 | 1.02986 | ||||||||
\(647\) | 10.2646 | 0.403544 | 0.201772 | − | 0.979432i | \(-0.435330\pi\) | ||||
0.201772 | + | 0.979432i | \(0.435330\pi\) | |||||||
\(648\) | 12.4626 | 0.489577 | ||||||||
\(649\) | 38.8815 | 1.52623 | ||||||||
\(650\) | −0.513344 | −0.0201350 | ||||||||
\(651\) | −11.3799 | −0.446014 | ||||||||
\(652\) | −19.7404 | −0.773095 | ||||||||
\(653\) | 38.0884 | 1.49052 | 0.745258 | − | 0.666777i | \(-0.232327\pi\) | ||||
0.745258 | + | 0.666777i | \(0.232327\pi\) | |||||||
\(654\) | −42.6903 | −1.66932 | ||||||||
\(655\) | 14.8642 | 0.580791 | ||||||||
\(656\) | 53.5592 | 2.09113 | ||||||||
\(657\) | −76.1350 | −2.97031 | ||||||||
\(658\) | 2.21389 | 0.0863064 | ||||||||
\(659\) | 27.7386 | 1.08054 | 0.540271 | − | 0.841491i | \(-0.318322\pi\) | ||||
0.540271 | + | 0.841491i | \(0.318322\pi\) | |||||||
\(660\) | −19.5101 | −0.759428 | ||||||||
\(661\) | −21.5170 | −0.836913 | −0.418456 | − | 0.908237i | \(-0.637429\pi\) | ||||
−0.418456 | + | 0.908237i | \(0.637429\pi\) | |||||||
\(662\) | 1.86867 | 0.0726280 | ||||||||
\(663\) | 4.11936 | 0.159983 | ||||||||
\(664\) | −0.633404 | −0.0245808 | ||||||||
\(665\) | 2.85217 | 0.110602 | ||||||||
\(666\) | 133.291 | 5.16493 | ||||||||
\(667\) | −2.96754 | −0.114904 | ||||||||
\(668\) | −17.8306 | −0.689885 | ||||||||
\(669\) | 49.0060 | 1.89468 | ||||||||
\(670\) | −19.4621 | −0.751886 | ||||||||
\(671\) | 31.7947 | 1.22742 | ||||||||
\(672\) | −21.9680 | −0.847435 | ||||||||
\(673\) | −25.3568 | −0.977431 | −0.488716 | − | 0.872443i | \(-0.662534\pi\) | ||||
−0.488716 | + | 0.872443i | \(0.662534\pi\) | |||||||
\(674\) | −4.68485 | −0.180454 | ||||||||
\(675\) | 10.9565 | 0.421715 | ||||||||
\(676\) | −19.8219 | −0.762380 | ||||||||
\(677\) | 39.3176 | 1.51110 | 0.755550 | − | 0.655091i | \(-0.227370\pi\) | ||||
0.755550 | + | 0.655091i | \(0.227370\pi\) | |||||||
\(678\) | −100.534 | −3.86100 | ||||||||
\(679\) | 15.4305 | 0.592167 | ||||||||
\(680\) | 4.28073 | 0.164159 | ||||||||
\(681\) | −60.5437 | −2.32004 | ||||||||
\(682\) | 28.5086 | 1.09165 | ||||||||
\(683\) | −27.4837 | −1.05163 | −0.525817 | − | 0.850598i | \(-0.676240\pi\) | ||||
−0.525817 | + | 0.850598i | \(0.676240\pi\) | |||||||
\(684\) | −28.6327 | −1.09480 | ||||||||
\(685\) | −20.1741 | −0.770814 | ||||||||
\(686\) | 1.87978 | 0.0717702 | ||||||||
\(687\) | 3.08968 | 0.117879 | ||||||||
\(688\) | −2.76357 | −0.105360 | ||||||||
\(689\) | −1.54148 | −0.0587256 | ||||||||
\(690\) | 44.1662 | 1.68138 | ||||||||
\(691\) | −18.1517 | −0.690523 | −0.345261 | − | 0.938507i | \(-0.612210\pi\) | ||||
−0.345261 | + | 0.938507i | \(0.612210\pi\) | |||||||
\(692\) | 2.70356 | 0.102774 | ||||||||
\(693\) | 26.9544 | 1.02391 | ||||||||
\(694\) | −40.4553 | −1.53566 | ||||||||
\(695\) | −6.10706 | −0.231654 | ||||||||
\(696\) | 1.05717 | 0.0400720 | ||||||||
\(697\) | −55.4545 | −2.10049 | ||||||||
\(698\) | 27.4118 | 1.03755 | ||||||||
\(699\) | 19.3814 | 0.733071 | ||||||||
\(700\) | −1.53356 | −0.0579630 | ||||||||
\(701\) | 50.6862 | 1.91439 | 0.957196 | − | 0.289441i | \(-0.0934695\pi\) | ||||
0.957196 | + | 0.289441i | \(0.0934695\pi\) | |||||||
\(702\) | −5.62444 | −0.212281 | ||||||||
\(703\) | 30.8948 | 1.16522 | ||||||||
\(704\) | 16.2020 | 0.610634 | ||||||||
\(705\) | 3.63885 | 0.137047 | ||||||||
\(706\) | 12.3426 | 0.464520 | ||||||||
\(707\) | 11.1085 | 0.417777 | ||||||||
\(708\) | −44.7418 | −1.68150 | ||||||||
\(709\) | 9.07369 | 0.340770 | 0.170385 | − | 0.985378i | \(-0.445499\pi\) | ||||
0.170385 | + | 0.985378i | \(0.445499\pi\) | |||||||
\(710\) | −22.0692 | −0.828242 | ||||||||
\(711\) | −15.0514 | −0.564473 | ||||||||
\(712\) | 6.22619 | 0.233336 | ||||||||
\(713\) | −28.0088 | −1.04894 | ||||||||
\(714\) | 28.3553 | 1.06117 | ||||||||
\(715\) | −1.12447 | −0.0420527 | ||||||||
\(716\) | −17.3302 | −0.647660 | ||||||||
\(717\) | 13.7970 | 0.515257 | ||||||||
\(718\) | −2.34013 | −0.0873330 | ||||||||
\(719\) | −25.6189 | −0.955425 | −0.477713 | − | 0.878516i | \(-0.658534\pi\) | ||||
−0.477713 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(720\) | −30.8672 | −1.15035 | ||||||||
\(721\) | 18.9383 | 0.705299 | ||||||||
\(722\) | 20.4240 | 0.760102 | ||||||||
\(723\) | 28.6207 | 1.06441 | ||||||||
\(724\) | 0.672159 | 0.0249806 | ||||||||
\(725\) | 0.390236 | 0.0144930 | ||||||||
\(726\) | −34.5840 | −1.28353 | ||||||||
\(727\) | 17.6612 | 0.655016 | 0.327508 | − | 0.944848i | \(-0.393791\pi\) | ||||
0.327508 | + | 0.944848i | \(0.393791\pi\) | |||||||
\(728\) | −0.239445 | −0.00887444 | ||||||||
\(729\) | −8.51178 | −0.315251 | ||||||||
\(730\) | 21.8627 | 0.809177 | ||||||||
\(731\) | 2.86137 | 0.105831 | ||||||||
\(732\) | −36.5868 | −1.35229 | ||||||||
\(733\) | −24.3988 | −0.901190 | −0.450595 | − | 0.892729i | \(-0.648788\pi\) | ||||
−0.450595 | + | 0.892729i | \(0.648788\pi\) | |||||||
\(734\) | 29.5591 | 1.09105 | ||||||||
\(735\) | 3.08968 | 0.113965 | ||||||||
\(736\) | −54.0688 | −1.99300 | ||||||||
\(737\) | −42.6312 | −1.57034 | ||||||||
\(738\) | 139.770 | 5.14501 | ||||||||
\(739\) | −28.3385 | −1.04245 | −0.521224 | − | 0.853420i | \(-0.674525\pi\) | ||||
−0.521224 | + | 0.853420i | \(0.674525\pi\) | |||||||
\(740\) | −16.6115 | −0.610652 | ||||||||
\(741\) | −2.40653 | −0.0884062 | ||||||||
\(742\) | −10.6106 | −0.389529 | ||||||||
\(743\) | −20.3300 | −0.745837 | −0.372918 | − | 0.927864i | \(-0.621643\pi\) | ||||
−0.372918 | + | 0.927864i | \(0.621643\pi\) | |||||||
\(744\) | 9.97800 | 0.365811 | ||||||||
\(745\) | 10.6447 | 0.389991 | ||||||||
\(746\) | 53.2380 | 1.94918 | ||||||||
\(747\) | −4.72892 | −0.173022 | ||||||||
\(748\) | −30.8289 | −1.12722 | ||||||||
\(749\) | 10.9789 | 0.401161 | ||||||||
\(750\) | −5.80791 | −0.212075 | ||||||||
\(751\) | 30.1256 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(752\) | −5.55342 | −0.202512 | ||||||||
\(753\) | −22.1365 | −0.806699 | ||||||||
\(754\) | −0.200325 | −0.00729542 | ||||||||
\(755\) | 9.46042 | 0.344300 | ||||||||
\(756\) | −16.8024 | −0.611097 | ||||||||
\(757\) | −3.23180 | −0.117462 | −0.0587309 | − | 0.998274i | \(-0.518705\pi\) | ||||
−0.0587309 | + | 0.998274i | \(0.518705\pi\) | |||||||
\(758\) | −49.9434 | −1.81403 | ||||||||
\(759\) | 96.7449 | 3.51162 | ||||||||
\(760\) | −2.50081 | −0.0907138 | ||||||||
\(761\) | 25.0613 | 0.908471 | 0.454235 | − | 0.890882i | \(-0.349913\pi\) | ||||
0.454235 | + | 0.890882i | \(0.349913\pi\) | |||||||
\(762\) | −91.1365 | −3.30153 | ||||||||
\(763\) | −7.35037 | −0.266101 | ||||||||
\(764\) | 19.9613 | 0.722174 | ||||||||
\(765\) | 31.9595 | 1.15550 | ||||||||
\(766\) | 5.02834 | 0.181681 | ||||||||
\(767\) | −2.57870 | −0.0931116 | ||||||||
\(768\) | 63.9460 | 2.30745 | ||||||||
\(769\) | −36.6145 | −1.32035 | −0.660176 | − | 0.751111i | \(-0.729518\pi\) | ||||
−0.660176 | + | 0.751111i | \(0.729518\pi\) | |||||||
\(770\) | −7.74017 | −0.278936 | ||||||||
\(771\) | −47.4049 | −1.70724 | ||||||||
\(772\) | 15.9128 | 0.572715 | ||||||||
\(773\) | −32.8600 | −1.18189 | −0.590947 | − | 0.806711i | \(-0.701246\pi\) | ||||
−0.590947 | + | 0.806711i | \(0.701246\pi\) | |||||||
\(774\) | −7.21193 | −0.259227 | ||||||||
\(775\) | 3.68320 | 0.132304 | ||||||||
\(776\) | −13.5295 | −0.485682 | ||||||||
\(777\) | 33.4675 | 1.20064 | ||||||||
\(778\) | 29.5676 | 1.06005 | ||||||||
\(779\) | 32.3965 | 1.16073 | ||||||||
\(780\) | 1.29395 | 0.0463307 | ||||||||
\(781\) | −48.3420 | −1.72981 | ||||||||
\(782\) | 69.7894 | 2.49567 | ||||||||
\(783\) | 4.27561 | 0.152798 | ||||||||
\(784\) | −4.71532 | −0.168404 | ||||||||
\(785\) | 23.5609 | 0.840925 | ||||||||
\(786\) | −86.3299 | −3.07928 | ||||||||
\(787\) | −15.6961 | −0.559504 | −0.279752 | − | 0.960072i | \(-0.590252\pi\) | ||||
−0.279752 | + | 0.960072i | \(0.590252\pi\) | |||||||
\(788\) | −6.18986 | −0.220505 | ||||||||
\(789\) | 13.7283 | 0.488741 | ||||||||
\(790\) | 4.32214 | 0.153775 | ||||||||
\(791\) | −17.3099 | −0.615470 | ||||||||
\(792\) | −23.6338 | −0.839792 | ||||||||
\(793\) | −2.10869 | −0.0748818 | ||||||||
\(794\) | −2.49934 | −0.0886983 | ||||||||
\(795\) | −17.4401 | −0.618537 | ||||||||
\(796\) | −12.4909 | −0.442729 | ||||||||
\(797\) | 41.4649 | 1.46876 | 0.734381 | − | 0.678738i | \(-0.237473\pi\) | ||||
0.734381 | + | 0.678738i | \(0.237473\pi\) | |||||||
\(798\) | −16.5652 | −0.586401 | ||||||||
\(799\) | 5.74994 | 0.203418 | ||||||||
\(800\) | 7.11012 | 0.251381 | ||||||||
\(801\) | 46.4840 | 1.64243 | ||||||||
\(802\) | 24.6262 | 0.869580 | ||||||||
\(803\) | 47.8898 | 1.68999 | ||||||||
\(804\) | 49.0566 | 1.73009 | ||||||||
\(805\) | 7.60448 | 0.268023 | ||||||||
\(806\) | −1.89075 | −0.0665987 | ||||||||
\(807\) | −15.6862 | −0.552181 | ||||||||
\(808\) | −9.74000 | −0.342652 | ||||||||
\(809\) | 1.49560 | 0.0525826 | 0.0262913 | − | 0.999654i | \(-0.491630\pi\) | ||||
0.0262913 | + | 0.999654i | \(0.491630\pi\) | |||||||
\(810\) | −26.7184 | −0.938789 | ||||||||
\(811\) | 24.9790 | 0.877132 | 0.438566 | − | 0.898699i | \(-0.355487\pi\) | ||||
0.438566 | + | 0.898699i | \(0.355487\pi\) | |||||||
\(812\) | −0.598450 | −0.0210015 | ||||||||
\(813\) | −92.0523 | −3.22841 | ||||||||
\(814\) | −83.8416 | −2.93865 | ||||||||
\(815\) | −12.8723 | −0.450898 | ||||||||
\(816\) | −71.1277 | −2.48997 | ||||||||
\(817\) | −1.67161 | −0.0584823 | ||||||||
\(818\) | 13.5474 | 0.473674 | ||||||||
\(819\) | −1.78767 | −0.0624663 | ||||||||
\(820\) | −17.4190 | −0.608297 | ||||||||
\(821\) | −47.4480 | −1.65595 | −0.827974 | − | 0.560766i | \(-0.810507\pi\) | ||||
−0.827974 | + | 0.560766i | \(0.810507\pi\) | |||||||
\(822\) | 117.170 | 4.08676 | ||||||||
\(823\) | −9.52464 | −0.332008 | −0.166004 | − | 0.986125i | \(-0.553086\pi\) | ||||
−0.166004 | + | 0.986125i | \(0.553086\pi\) | |||||||
\(824\) | −16.6052 | −0.578471 | ||||||||
\(825\) | −12.7221 | −0.442926 | ||||||||
\(826\) | −17.7503 | −0.617611 | ||||||||
\(827\) | 46.1669 | 1.60538 | 0.802691 | − | 0.596396i | \(-0.203401\pi\) | ||||
0.802691 | + | 0.596396i | \(0.203401\pi\) | |||||||
\(828\) | −76.3406 | −2.65302 | ||||||||
\(829\) | 7.82929 | 0.271922 | 0.135961 | − | 0.990714i | \(-0.456588\pi\) | ||||
0.135961 | + | 0.990714i | \(0.456588\pi\) | |||||||
\(830\) | 1.35795 | 0.0471350 | ||||||||
\(831\) | 27.8693 | 0.966774 | ||||||||
\(832\) | −1.07455 | −0.0372532 | ||||||||
\(833\) | 4.88218 | 0.169158 | ||||||||
\(834\) | 35.4693 | 1.22820 | ||||||||
\(835\) | −11.6269 | −0.402366 | ||||||||
\(836\) | 18.0103 | 0.622898 | ||||||||
\(837\) | 40.3549 | 1.39487 | ||||||||
\(838\) | −32.2020 | −1.11240 | ||||||||
\(839\) | 33.9127 | 1.17080 | 0.585399 | − | 0.810745i | \(-0.300938\pi\) | ||||
0.585399 | + | 0.810745i | \(0.300938\pi\) | |||||||
\(840\) | −2.70906 | −0.0934714 | ||||||||
\(841\) | −28.8477 | −0.994749 | ||||||||
\(842\) | 75.9092 | 2.61600 | ||||||||
\(843\) | −34.4739 | −1.18735 | ||||||||
\(844\) | 11.5298 | 0.396872 | ||||||||
\(845\) | −12.9254 | −0.444648 | ||||||||
\(846\) | −14.4924 | −0.498260 | ||||||||
\(847\) | −5.95464 | −0.204604 | ||||||||
\(848\) | 26.6162 | 0.914004 | ||||||||
\(849\) | 35.9952 | 1.23535 | ||||||||
\(850\) | −9.17741 | −0.314782 | ||||||||
\(851\) | 82.3719 | 2.82367 | ||||||||
\(852\) | 55.6282 | 1.90579 | ||||||||
\(853\) | 7.84264 | 0.268527 | 0.134263 | − | 0.990946i | \(-0.457133\pi\) | ||||
0.134263 | + | 0.990946i | \(0.457133\pi\) | |||||||
\(854\) | −14.5150 | −0.496693 | ||||||||
\(855\) | −18.6707 | −0.638526 | ||||||||
\(856\) | −9.62640 | −0.329023 | ||||||||
\(857\) | 21.8165 | 0.745236 | 0.372618 | − | 0.927985i | \(-0.378460\pi\) | ||||
0.372618 | + | 0.927985i | \(0.378460\pi\) | |||||||
\(858\) | 6.53080 | 0.222958 | ||||||||
\(859\) | −41.9910 | −1.43271 | −0.716357 | − | 0.697734i | \(-0.754192\pi\) | ||||
−0.716357 | + | 0.697734i | \(0.754192\pi\) | |||||||
\(860\) | 0.898793 | 0.0306486 | ||||||||
\(861\) | 35.0943 | 1.19601 | ||||||||
\(862\) | −6.76481 | −0.230410 | ||||||||
\(863\) | 39.2439 | 1.33588 | 0.667939 | − | 0.744216i | \(-0.267177\pi\) | ||||
0.667939 | + | 0.744216i | \(0.267177\pi\) | |||||||
\(864\) | 77.9019 | 2.65028 | ||||||||
\(865\) | 1.76293 | 0.0599416 | ||||||||
\(866\) | −52.9704 | −1.80001 | ||||||||
\(867\) | 21.1202 | 0.717278 | ||||||||
\(868\) | −5.64839 | −0.191719 | ||||||||
\(869\) | 9.46753 | 0.321164 | ||||||||
\(870\) | −2.26646 | −0.0768401 | ||||||||
\(871\) | 2.82739 | 0.0958024 | ||||||||
\(872\) | 6.44486 | 0.218251 | ||||||||
\(873\) | −101.010 | −3.41867 | ||||||||
\(874\) | −40.7710 | −1.37910 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −55.1078 | −1.86192 | ||||||||
\(877\) | 14.8513 | 0.501492 | 0.250746 | − | 0.968053i | \(-0.419324\pi\) | ||||
0.250746 | + | 0.968053i | \(0.419324\pi\) | |||||||
\(878\) | −47.8854 | −1.61605 | ||||||||
\(879\) | 27.0410 | 0.912071 | ||||||||
\(880\) | 19.4158 | 0.654506 | ||||||||
\(881\) | −54.3354 | −1.83061 | −0.915303 | − | 0.402765i | \(-0.868049\pi\) | ||||
−0.915303 | + | 0.402765i | \(0.868049\pi\) | |||||||
\(882\) | −12.3053 | −0.414341 | ||||||||
\(883\) | −44.8923 | −1.51074 | −0.755372 | − | 0.655296i | \(-0.772544\pi\) | ||||
−0.755372 | + | 0.655296i | \(0.772544\pi\) | |||||||
\(884\) | 2.04464 | 0.0687686 | ||||||||
\(885\) | −29.1752 | −0.980712 | ||||||||
\(886\) | −36.5961 | −1.22947 | ||||||||
\(887\) | −12.2076 | −0.409892 | −0.204946 | − | 0.978773i | \(-0.565702\pi\) | ||||
−0.204946 | + | 0.978773i | \(0.565702\pi\) | |||||||
\(888\) | −29.3446 | −0.984739 | ||||||||
\(889\) | −15.6918 | −0.526285 | ||||||||
\(890\) | −13.3482 | −0.447434 | ||||||||
\(891\) | −58.5260 | −1.96069 | ||||||||
\(892\) | 24.3240 | 0.814428 | ||||||||
\(893\) | −3.35912 | −0.112409 | ||||||||
\(894\) | −61.8234 | −2.06768 | ||||||||
\(895\) | −11.3007 | −0.377739 | ||||||||
\(896\) | 6.82369 | 0.227964 | ||||||||
\(897\) | −6.41632 | −0.214235 | ||||||||
\(898\) | −8.30770 | −0.277232 | ||||||||
\(899\) | 1.43732 | 0.0479372 | ||||||||
\(900\) | 10.0389 | 0.334630 | ||||||||
\(901\) | −27.5581 | −0.918093 | ||||||||
\(902\) | −87.9171 | −2.92732 | ||||||||
\(903\) | −1.81081 | −0.0602601 | ||||||||
\(904\) | 15.1775 | 0.504795 | ||||||||
\(905\) | 0.438301 | 0.0145696 | ||||||||
\(906\) | −54.9453 | −1.82544 | ||||||||
\(907\) | 12.1831 | 0.404532 | 0.202266 | − | 0.979331i | \(-0.435169\pi\) | ||||
0.202266 | + | 0.979331i | \(0.435169\pi\) | |||||||
\(908\) | −30.0507 | −0.997268 | ||||||||
\(909\) | −72.7178 | −2.41190 | ||||||||
\(910\) | 0.513344 | 0.0170172 | ||||||||
\(911\) | 8.19262 | 0.271434 | 0.135717 | − | 0.990748i | \(-0.456666\pi\) | ||||
0.135717 | + | 0.990748i | \(0.456666\pi\) | |||||||
\(912\) | 41.5528 | 1.37595 | ||||||||
\(913\) | 2.97454 | 0.0984431 | ||||||||
\(914\) | 21.1152 | 0.698429 | ||||||||
\(915\) | −23.8575 | −0.788704 | ||||||||
\(916\) | 1.53356 | 0.0506702 | ||||||||
\(917\) | −14.8642 | −0.490858 | ||||||||
\(918\) | −100.552 | −3.31871 | ||||||||
\(919\) | 12.8789 | 0.424837 | 0.212419 | − | 0.977179i | \(-0.431866\pi\) | ||||
0.212419 | + | 0.977179i | \(0.431866\pi\) | |||||||
\(920\) | −6.66767 | −0.219826 | ||||||||
\(921\) | 15.9735 | 0.526345 | ||||||||
\(922\) | −55.7412 | −1.83574 | ||||||||
\(923\) | 3.20614 | 0.105531 | ||||||||
\(924\) | 19.5101 | 0.641834 | ||||||||
\(925\) | −10.8320 | −0.356155 | ||||||||
\(926\) | 58.0539 | 1.90777 | ||||||||
\(927\) | −123.973 | −4.07180 | ||||||||
\(928\) | 2.77463 | 0.0910816 | ||||||||
\(929\) | −58.4248 | −1.91686 | −0.958428 | − | 0.285335i | \(-0.907895\pi\) | ||||
−0.958428 | + | 0.285335i | \(0.907895\pi\) | |||||||
\(930\) | −21.3917 | −0.701461 | ||||||||
\(931\) | −2.85217 | −0.0934762 | ||||||||
\(932\) | 9.61990 | 0.315110 | ||||||||
\(933\) | 3.59277 | 0.117622 | ||||||||
\(934\) | 54.2524 | 1.77519 | ||||||||
\(935\) | −20.1029 | −0.657434 | ||||||||
\(936\) | 1.56744 | 0.0512335 | ||||||||
\(937\) | 43.9779 | 1.43669 | 0.718347 | − | 0.695684i | \(-0.244899\pi\) | ||||
0.718347 | + | 0.695684i | \(0.244899\pi\) | |||||||
\(938\) | 19.4621 | 0.635460 | ||||||||
\(939\) | −52.2309 | −1.70449 | ||||||||
\(940\) | 1.80613 | 0.0589096 | ||||||||
\(941\) | −24.3846 | −0.794915 | −0.397457 | − | 0.917621i | \(-0.630107\pi\) | ||||
−0.397457 | + | 0.917621i | \(0.630107\pi\) | |||||||
\(942\) | −136.840 | −4.45848 | ||||||||
\(943\) | 86.3759 | 2.81279 | ||||||||
\(944\) | 44.5256 | 1.44919 | ||||||||
\(945\) | −10.9565 | −0.356414 | ||||||||
\(946\) | 4.53638 | 0.147491 | ||||||||
\(947\) | 21.3477 | 0.693707 | 0.346854 | − | 0.937919i | \(-0.387250\pi\) | ||||
0.346854 | + | 0.937919i | \(0.387250\pi\) | |||||||
\(948\) | −10.8945 | −0.353836 | ||||||||
\(949\) | −3.17615 | −0.103102 | ||||||||
\(950\) | 5.36144 | 0.173948 | ||||||||
\(951\) | −6.94207 | −0.225112 | ||||||||
\(952\) | −4.28073 | −0.138739 | ||||||||
\(953\) | −50.6737 | −1.64148 | −0.820741 | − | 0.571300i | \(-0.806439\pi\) | ||||
−0.820741 | + | 0.571300i | \(0.806439\pi\) | |||||||
\(954\) | 69.4588 | 2.24881 | ||||||||
\(955\) | 13.0163 | 0.421198 | ||||||||
\(956\) | 6.84809 | 0.221483 | ||||||||
\(957\) | −4.96462 | −0.160483 | ||||||||
\(958\) | 5.23246 | 0.169053 | ||||||||
\(959\) | 20.1741 | 0.651457 | ||||||||
\(960\) | −12.1573 | −0.392375 | ||||||||
\(961\) | −17.4341 | −0.562389 | ||||||||
\(962\) | 5.56055 | 0.179279 | ||||||||
\(963\) | −71.8696 | −2.31597 | ||||||||
\(964\) | 14.2058 | 0.457538 | ||||||||
\(965\) | 10.3764 | 0.334028 | ||||||||
\(966\) | −44.1662 | −1.42102 | ||||||||
\(967\) | −4.17101 | −0.134131 | −0.0670654 | − | 0.997749i | \(-0.521364\pi\) | ||||
−0.0670654 | + | 0.997749i | \(0.521364\pi\) | |||||||
\(968\) | 5.22107 | 0.167812 | ||||||||
\(969\) | −43.0233 | −1.38211 | ||||||||
\(970\) | 29.0058 | 0.931320 | ||||||||
\(971\) | 24.7362 | 0.793823 | 0.396911 | − | 0.917857i | \(-0.370082\pi\) | ||||
0.396911 | + | 0.917857i | \(0.370082\pi\) | |||||||
\(972\) | 16.9399 | 0.543347 | ||||||||
\(973\) | 6.10706 | 0.195783 | ||||||||
\(974\) | −66.4321 | −2.12862 | ||||||||
\(975\) | 0.843755 | 0.0270218 | ||||||||
\(976\) | 36.4101 | 1.16546 | ||||||||
\(977\) | −20.3057 | −0.649637 | −0.324818 | − | 0.945776i | \(-0.605303\pi\) | ||||
−0.324818 | + | 0.945776i | \(0.605303\pi\) | |||||||
\(978\) | 74.7613 | 2.39060 | ||||||||
\(979\) | −29.2390 | −0.934482 | ||||||||
\(980\) | 1.53356 | 0.0489877 | ||||||||
\(981\) | 48.1166 | 1.53625 | ||||||||
\(982\) | −0.386274 | −0.0123265 | ||||||||
\(983\) | 58.4313 | 1.86367 | 0.931834 | − | 0.362884i | \(-0.118208\pi\) | ||||
0.931834 | + | 0.362884i | \(0.118208\pi\) | |||||||
\(984\) | −30.7710 | −0.980943 | ||||||||
\(985\) | −4.03627 | −0.128606 | ||||||||
\(986\) | −3.58136 | −0.114054 | ||||||||
\(987\) | −3.63885 | −0.115826 | ||||||||
\(988\) | −1.19448 | −0.0380014 | ||||||||
\(989\) | −4.45686 | −0.141720 | ||||||||
\(990\) | 50.6683 | 1.61034 | ||||||||
\(991\) | −0.405886 | −0.0128934 | −0.00644670 | − | 0.999979i | \(-0.502052\pi\) | ||||
−0.00644670 | + | 0.999979i | \(0.502052\pi\) | |||||||
\(992\) | 26.1880 | 0.831469 | ||||||||
\(993\) | −3.07143 | −0.0974690 | ||||||||
\(994\) | 22.0692 | 0.699993 | ||||||||
\(995\) | −8.14506 | −0.258216 | ||||||||
\(996\) | −3.42287 | −0.108458 | ||||||||
\(997\) | −60.8518 | −1.92720 | −0.963598 | − | 0.267355i | \(-0.913850\pi\) | ||||
−0.963598 | + | 0.267355i | \(0.913850\pi\) | |||||||
\(998\) | 26.1808 | 0.828740 | ||||||||
\(999\) | −118.681 | −3.75489 |
(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 | 8015.2.a.i.1.8 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.i.1.8 | ✓ | 44 | 1.1 | even | 1 | trivial |