Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2056877002\) |
Analytic rank: | \(1\) |
Dimension: | \(243\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63616 | −1.86404 | −0.932022 | − | 0.362403i | \(-0.881957\pi\) | ||||
−0.932022 | + | 0.362403i | \(0.881957\pi\) | |||||||
\(3\) | 2.26078 | 1.30526 | 0.652630 | − | 0.757676i | \(-0.273665\pi\) | ||||
0.652630 | + | 0.757676i | \(0.273665\pi\) | |||||||
\(4\) | 4.94932 | 2.47466 | ||||||||
\(5\) | −3.62229 | −1.61994 | −0.809969 | − | 0.586473i | \(-0.800516\pi\) | ||||
−0.809969 | + | 0.586473i | \(0.800516\pi\) | |||||||
\(6\) | −5.95976 | −2.43306 | ||||||||
\(7\) | 1.87932 | 0.710317 | 0.355158 | − | 0.934806i | \(-0.384427\pi\) | ||||
0.355158 | + | 0.934806i | \(0.384427\pi\) | |||||||
\(8\) | −7.77485 | −2.74883 | ||||||||
\(9\) | 2.11112 | 0.703705 | ||||||||
\(10\) | 9.54892 | 3.01963 | ||||||||
\(11\) | 5.65974 | 1.70648 | 0.853238 | − | 0.521522i | \(-0.174635\pi\) | ||||
0.853238 | + | 0.521522i | \(0.174635\pi\) | |||||||
\(12\) | 11.1893 | 3.23007 | ||||||||
\(13\) | −3.90835 | −1.08398 | −0.541991 | − | 0.840385i | \(-0.682329\pi\) | ||||
−0.541991 | + | 0.840385i | \(0.682329\pi\) | |||||||
\(14\) | −4.95418 | −1.32406 | ||||||||
\(15\) | −8.18920 | −2.11444 | ||||||||
\(16\) | 10.5971 | 2.64927 | ||||||||
\(17\) | −6.51206 | −1.57941 | −0.789703 | − | 0.613490i | \(-0.789765\pi\) | ||||
−0.789703 | + | 0.613490i | \(0.789765\pi\) | |||||||
\(18\) | −5.56523 | −1.31174 | ||||||||
\(19\) | 2.29268 | 0.525977 | 0.262989 | − | 0.964799i | \(-0.415292\pi\) | ||||
0.262989 | + | 0.964799i | \(0.415292\pi\) | |||||||
\(20\) | −17.9279 | −4.00879 | ||||||||
\(21\) | 4.24873 | 0.927149 | ||||||||
\(22\) | −14.9200 | −3.18095 | ||||||||
\(23\) | −4.01981 | −0.838188 | −0.419094 | − | 0.907943i | \(-0.637652\pi\) | ||||
−0.419094 | + | 0.907943i | \(0.637652\pi\) | |||||||
\(24\) | −17.5772 | −3.58793 | ||||||||
\(25\) | 8.12099 | 1.62420 | ||||||||
\(26\) | 10.3030 | 2.02059 | ||||||||
\(27\) | −2.00957 | −0.386742 | ||||||||
\(28\) | 9.30136 | 1.75779 | ||||||||
\(29\) | −8.27055 | −1.53580 | −0.767902 | − | 0.640568i | \(-0.778699\pi\) | ||||
−0.767902 | + | 0.640568i | \(0.778699\pi\) | |||||||
\(30\) | 21.5880 | 3.94141 | ||||||||
\(31\) | 6.34469 | 1.13954 | 0.569770 | − | 0.821804i | \(-0.307032\pi\) | ||||
0.569770 | + | 0.821804i | \(0.307032\pi\) | |||||||
\(32\) | −12.3859 | −2.18953 | ||||||||
\(33\) | 12.7954 | 2.22740 | ||||||||
\(34\) | 17.1668 | 2.94408 | ||||||||
\(35\) | −6.80745 | −1.15067 | ||||||||
\(36\) | 10.4486 | 1.74143 | ||||||||
\(37\) | 4.92743 | 0.810065 | 0.405032 | − | 0.914302i | \(-0.367260\pi\) | ||||
0.405032 | + | 0.914302i | \(0.367260\pi\) | |||||||
\(38\) | −6.04387 | −0.980445 | ||||||||
\(39\) | −8.83591 | −1.41488 | ||||||||
\(40\) | 28.1628 | 4.45293 | ||||||||
\(41\) | 4.52556 | 0.706774 | 0.353387 | − | 0.935477i | \(-0.385030\pi\) | ||||
0.353387 | + | 0.935477i | \(0.385030\pi\) | |||||||
\(42\) | −11.2003 | −1.72825 | ||||||||
\(43\) | 5.35348 | 0.816398 | 0.408199 | − | 0.912893i | \(-0.366157\pi\) | ||||
0.408199 | + | 0.912893i | \(0.366157\pi\) | |||||||
\(44\) | 28.0118 | 4.22294 | ||||||||
\(45\) | −7.64708 | −1.13996 | ||||||||
\(46\) | 10.5968 | 1.56242 | ||||||||
\(47\) | 8.64243 | 1.26063 | 0.630314 | − | 0.776340i | \(-0.282926\pi\) | ||||
0.630314 | + | 0.776340i | \(0.282926\pi\) | |||||||
\(48\) | 23.9577 | 3.45799 | ||||||||
\(49\) | −3.46815 | −0.495450 | ||||||||
\(50\) | −21.4082 | −3.02758 | ||||||||
\(51\) | −14.7223 | −2.06154 | ||||||||
\(52\) | −19.3437 | −2.68248 | ||||||||
\(53\) | 12.7504 | 1.75140 | 0.875702 | − | 0.482852i | \(-0.160399\pi\) | ||||
0.875702 | + | 0.482852i | \(0.160399\pi\) | |||||||
\(54\) | 5.29753 | 0.720903 | ||||||||
\(55\) | −20.5012 | −2.76439 | ||||||||
\(56\) | −14.6115 | −1.95254 | ||||||||
\(57\) | 5.18324 | 0.686538 | ||||||||
\(58\) | 21.8025 | 2.86280 | ||||||||
\(59\) | −4.11361 | −0.535547 | −0.267773 | − | 0.963482i | \(-0.586288\pi\) | ||||
−0.267773 | + | 0.963482i | \(0.586288\pi\) | |||||||
\(60\) | −40.5309 | −5.23252 | ||||||||
\(61\) | 12.5991 | 1.61314 | 0.806572 | − | 0.591136i | \(-0.201320\pi\) | ||||
0.806572 | + | 0.591136i | \(0.201320\pi\) | |||||||
\(62\) | −16.7256 | −2.12415 | ||||||||
\(63\) | 3.96747 | 0.499854 | ||||||||
\(64\) | 11.4569 | 1.43211 | ||||||||
\(65\) | 14.1572 | 1.75598 | ||||||||
\(66\) | −33.7307 | −4.15196 | ||||||||
\(67\) | −12.2384 | −1.49515 | −0.747577 | − | 0.664175i | \(-0.768783\pi\) | ||||
−0.747577 | + | 0.664175i | \(0.768783\pi\) | |||||||
\(68\) | −32.2302 | −3.90849 | ||||||||
\(69\) | −9.08789 | −1.09405 | ||||||||
\(70\) | 17.9455 | 2.14490 | ||||||||
\(71\) | 0.0173576 | 0.00205997 | 0.00102998 | − | 0.999999i | \(-0.499672\pi\) | ||||
0.00102998 | + | 0.999999i | \(0.499672\pi\) | |||||||
\(72\) | −16.4136 | −1.93436 | ||||||||
\(73\) | −8.68355 | −1.01633 | −0.508166 | − | 0.861259i | \(-0.669676\pi\) | ||||
−0.508166 | + | 0.861259i | \(0.669676\pi\) | |||||||
\(74\) | −12.9895 | −1.51000 | ||||||||
\(75\) | 18.3598 | 2.12000 | ||||||||
\(76\) | 11.3472 | 1.30161 | ||||||||
\(77\) | 10.6365 | 1.21214 | ||||||||
\(78\) | 23.2928 | 2.63739 | ||||||||
\(79\) | −15.7173 | −1.76834 | −0.884169 | − | 0.467167i | \(-0.845275\pi\) | ||||
−0.884169 | + | 0.467167i | \(0.845275\pi\) | |||||||
\(80\) | −38.3857 | −4.29166 | ||||||||
\(81\) | −10.8765 | −1.20850 | ||||||||
\(82\) | −11.9301 | −1.31746 | ||||||||
\(83\) | −8.21983 | −0.902243 | −0.451122 | − | 0.892463i | \(-0.648976\pi\) | ||||
−0.451122 | + | 0.892463i | \(0.648976\pi\) | |||||||
\(84\) | 21.0283 | 2.29438 | ||||||||
\(85\) | 23.5886 | 2.55854 | ||||||||
\(86\) | −14.1126 | −1.52180 | ||||||||
\(87\) | −18.6979 | −2.00462 | ||||||||
\(88\) | −44.0037 | −4.69081 | ||||||||
\(89\) | −13.3585 | −1.41599 | −0.707997 | − | 0.706215i | \(-0.750401\pi\) | ||||
−0.707997 | + | 0.706215i | \(0.750401\pi\) | |||||||
\(90\) | 20.1589 | 2.12493 | ||||||||
\(91\) | −7.34505 | −0.769970 | ||||||||
\(92\) | −19.8953 | −2.07423 | ||||||||
\(93\) | 14.3439 | 1.48740 | ||||||||
\(94\) | −22.7828 | −2.34987 | ||||||||
\(95\) | −8.30476 | −0.852051 | ||||||||
\(96\) | −28.0017 | −2.85791 | ||||||||
\(97\) | −7.74671 | −0.786560 | −0.393280 | − | 0.919419i | \(-0.628660\pi\) | ||||
−0.393280 | + | 0.919419i | \(0.628660\pi\) | |||||||
\(98\) | 9.14258 | 0.923540 | ||||||||
\(99\) | 11.9484 | 1.20086 | ||||||||
\(100\) | 40.1934 | 4.01934 | ||||||||
\(101\) | 6.78423 | 0.675056 | 0.337528 | − | 0.941315i | \(-0.390409\pi\) | ||||
0.337528 | + | 0.941315i | \(0.390409\pi\) | |||||||
\(102\) | 38.8103 | 3.84279 | ||||||||
\(103\) | 3.04045 | 0.299584 | 0.149792 | − | 0.988718i | \(-0.452140\pi\) | ||||
0.149792 | + | 0.988718i | \(0.452140\pi\) | |||||||
\(104\) | 30.3868 | 2.97968 | ||||||||
\(105\) | −15.3901 | −1.50192 | ||||||||
\(106\) | −33.6121 | −3.26469 | ||||||||
\(107\) | −16.9705 | −1.64060 | −0.820299 | − | 0.571934i | \(-0.806193\pi\) | ||||
−0.820299 | + | 0.571934i | \(0.806193\pi\) | |||||||
\(108\) | −9.94599 | −0.957053 | ||||||||
\(109\) | 3.61896 | 0.346634 | 0.173317 | − | 0.984866i | \(-0.444552\pi\) | ||||
0.173317 | + | 0.984866i | \(0.444552\pi\) | |||||||
\(110\) | 54.0444 | 5.15293 | ||||||||
\(111\) | 11.1398 | 1.05735 | ||||||||
\(112\) | 19.9153 | 1.88182 | ||||||||
\(113\) | 8.73777 | 0.821980 | 0.410990 | − | 0.911640i | \(-0.365183\pi\) | ||||
0.410990 | + | 0.911640i | \(0.365183\pi\) | |||||||
\(114\) | −13.6638 | −1.27974 | ||||||||
\(115\) | 14.5609 | 1.35781 | ||||||||
\(116\) | −40.9336 | −3.80059 | ||||||||
\(117\) | −8.25098 | −0.762803 | ||||||||
\(118\) | 10.8441 | 0.998282 | ||||||||
\(119\) | −12.2382 | −1.12188 | ||||||||
\(120\) | 63.6698 | 5.81223 | ||||||||
\(121\) | 21.0327 | 1.91206 | ||||||||
\(122\) | −33.2131 | −3.00697 | ||||||||
\(123\) | 10.2313 | 0.922524 | ||||||||
\(124\) | 31.4019 | 2.81997 | ||||||||
\(125\) | −11.3052 | −1.01116 | ||||||||
\(126\) | −10.4589 | −0.931749 | ||||||||
\(127\) | 14.1920 | 1.25933 | 0.629667 | − | 0.776865i | \(-0.283191\pi\) | ||||
0.629667 | + | 0.776865i | \(0.283191\pi\) | |||||||
\(128\) | −5.43042 | −0.479986 | ||||||||
\(129\) | 12.1030 | 1.06561 | ||||||||
\(130\) | −37.3205 | −3.27323 | ||||||||
\(131\) | 2.34418 | 0.204812 | 0.102406 | − | 0.994743i | \(-0.467346\pi\) | ||||
0.102406 | + | 0.994743i | \(0.467346\pi\) | |||||||
\(132\) | 63.3286 | 5.51204 | ||||||||
\(133\) | 4.30869 | 0.373611 | ||||||||
\(134\) | 32.2622 | 2.78703 | ||||||||
\(135\) | 7.27924 | 0.626497 | ||||||||
\(136\) | 50.6303 | 4.34151 | ||||||||
\(137\) | −16.4051 | −1.40158 | −0.700790 | − | 0.713368i | \(-0.747169\pi\) | ||||
−0.700790 | + | 0.713368i | \(0.747169\pi\) | |||||||
\(138\) | 23.9571 | 2.03936 | ||||||||
\(139\) | −11.1497 | −0.945705 | −0.472853 | − | 0.881142i | \(-0.656776\pi\) | ||||
−0.472853 | + | 0.881142i | \(0.656776\pi\) | |||||||
\(140\) | −33.6922 | −2.84751 | ||||||||
\(141\) | 19.5386 | 1.64545 | ||||||||
\(142\) | −0.0457574 | −0.00383987 | ||||||||
\(143\) | −22.1202 | −1.84979 | ||||||||
\(144\) | 22.3717 | 1.86431 | ||||||||
\(145\) | 29.9584 | 2.48791 | ||||||||
\(146\) | 22.8912 | 1.89449 | ||||||||
\(147\) | −7.84072 | −0.646691 | ||||||||
\(148\) | 24.3874 | 2.00463 | ||||||||
\(149\) | −14.4811 | −1.18634 | −0.593171 | − | 0.805077i | \(-0.702124\pi\) | ||||
−0.593171 | + | 0.805077i | \(0.702124\pi\) | |||||||
\(150\) | −48.3992 | −3.95178 | ||||||||
\(151\) | −6.64659 | −0.540892 | −0.270446 | − | 0.962735i | \(-0.587171\pi\) | ||||
−0.270446 | + | 0.962735i | \(0.587171\pi\) | |||||||
\(152\) | −17.8253 | −1.44582 | ||||||||
\(153\) | −13.7477 | −1.11144 | ||||||||
\(154\) | −28.0394 | −2.25948 | ||||||||
\(155\) | −22.9823 | −1.84598 | ||||||||
\(156\) | −43.7317 | −3.50134 | ||||||||
\(157\) | −14.3312 | −1.14376 | −0.571879 | − | 0.820338i | \(-0.693785\pi\) | ||||
−0.571879 | + | 0.820338i | \(0.693785\pi\) | |||||||
\(158\) | 41.4333 | 3.29626 | ||||||||
\(159\) | 28.8259 | 2.28604 | ||||||||
\(160\) | 44.8652 | 3.54691 | ||||||||
\(161\) | −7.55451 | −0.595379 | ||||||||
\(162\) | 28.6722 | 2.25270 | ||||||||
\(163\) | 10.7801 | 0.844360 | 0.422180 | − | 0.906512i | \(-0.361265\pi\) | ||||
0.422180 | + | 0.906512i | \(0.361265\pi\) | |||||||
\(164\) | 22.3984 | 1.74902 | ||||||||
\(165\) | −46.3487 | −3.60824 | ||||||||
\(166\) | 21.6687 | 1.68182 | ||||||||
\(167\) | −14.8919 | −1.15237 | −0.576184 | − | 0.817320i | \(-0.695459\pi\) | ||||
−0.576184 | + | 0.817320i | \(0.695459\pi\) | |||||||
\(168\) | −33.0332 | −2.54857 | ||||||||
\(169\) | 2.27520 | 0.175015 | ||||||||
\(170\) | −62.1831 | −4.76923 | ||||||||
\(171\) | 4.84012 | 0.370133 | ||||||||
\(172\) | 26.4961 | 2.02031 | ||||||||
\(173\) | −11.7849 | −0.895987 | −0.447994 | − | 0.894037i | \(-0.647861\pi\) | ||||
−0.447994 | + | 0.894037i | \(0.647861\pi\) | |||||||
\(174\) | 49.2905 | 3.73670 | ||||||||
\(175\) | 15.2620 | 1.15370 | ||||||||
\(176\) | 59.9768 | 4.52092 | ||||||||
\(177\) | −9.29996 | −0.699028 | ||||||||
\(178\) | 35.2150 | 2.63948 | ||||||||
\(179\) | 25.5644 | 1.91077 | 0.955386 | − | 0.295362i | \(-0.0954401\pi\) | ||||
0.955386 | + | 0.295362i | \(0.0954401\pi\) | |||||||
\(180\) | −37.8478 | −2.82101 | ||||||||
\(181\) | 14.6238 | 1.08698 | 0.543490 | − | 0.839415i | \(-0.317102\pi\) | ||||
0.543490 | + | 0.839415i | \(0.317102\pi\) | |||||||
\(182\) | 19.3627 | 1.43526 | ||||||||
\(183\) | 28.4837 | 2.10557 | ||||||||
\(184\) | 31.2534 | 2.30403 | ||||||||
\(185\) | −17.8486 | −1.31225 | ||||||||
\(186\) | −37.8128 | −2.77257 | ||||||||
\(187\) | −36.8566 | −2.69522 | ||||||||
\(188\) | 42.7741 | 3.11962 | ||||||||
\(189\) | −3.77663 | −0.274709 | ||||||||
\(190\) | 21.8926 | 1.58826 | ||||||||
\(191\) | −16.1504 | −1.16860 | −0.584299 | − | 0.811538i | \(-0.698631\pi\) | ||||
−0.584299 | + | 0.811538i | \(0.698631\pi\) | |||||||
\(192\) | 25.9015 | 1.86928 | ||||||||
\(193\) | −23.4379 | −1.68710 | −0.843550 | − | 0.537051i | \(-0.819538\pi\) | ||||
−0.843550 | + | 0.537051i | \(0.819538\pi\) | |||||||
\(194\) | 20.4215 | 1.46618 | ||||||||
\(195\) | 32.0062 | 2.29201 | ||||||||
\(196\) | −17.1650 | −1.22607 | ||||||||
\(197\) | 5.42090 | 0.386223 | 0.193112 | − | 0.981177i | \(-0.438142\pi\) | ||||
0.193112 | + | 0.981177i | \(0.438142\pi\) | |||||||
\(198\) | −31.4978 | −2.23845 | ||||||||
\(199\) | 11.1628 | 0.791308 | 0.395654 | − | 0.918400i | \(-0.370518\pi\) | ||||
0.395654 | + | 0.918400i | \(0.370518\pi\) | |||||||
\(200\) | −63.1395 | −4.46464 | ||||||||
\(201\) | −27.6682 | −1.95157 | ||||||||
\(202\) | −17.8843 | −1.25833 | ||||||||
\(203\) | −15.5430 | −1.09091 | ||||||||
\(204\) | −72.8654 | −5.10160 | ||||||||
\(205\) | −16.3929 | −1.14493 | ||||||||
\(206\) | −8.01509 | −0.558438 | ||||||||
\(207\) | −8.48628 | −0.589837 | ||||||||
\(208\) | −41.4171 | −2.87176 | ||||||||
\(209\) | 12.9760 | 0.897568 | ||||||||
\(210\) | 40.5708 | 2.79965 | ||||||||
\(211\) | 14.3700 | 0.989269 | 0.494635 | − | 0.869101i | \(-0.335302\pi\) | ||||
0.494635 | + | 0.869101i | \(0.335302\pi\) | |||||||
\(212\) | 63.1058 | 4.33412 | ||||||||
\(213\) | 0.0392417 | 0.00268880 | ||||||||
\(214\) | 44.7368 | 3.05815 | ||||||||
\(215\) | −19.3919 | −1.32251 | ||||||||
\(216\) | 15.6241 | 1.06309 | ||||||||
\(217\) | 11.9237 | 0.809434 | ||||||||
\(218\) | −9.54015 | −0.646140 | ||||||||
\(219\) | −19.6316 | −1.32658 | ||||||||
\(220\) | −101.467 | −6.84091 | ||||||||
\(221\) | 25.4514 | 1.71205 | ||||||||
\(222\) | −29.3663 | −1.97094 | ||||||||
\(223\) | −25.3394 | −1.69685 | −0.848425 | − | 0.529316i | \(-0.822449\pi\) | ||||
−0.848425 | + | 0.529316i | \(0.822449\pi\) | |||||||
\(224\) | −23.2770 | −1.55526 | ||||||||
\(225\) | 17.1444 | 1.14296 | ||||||||
\(226\) | −23.0341 | −1.53221 | ||||||||
\(227\) | 7.42527 | 0.492832 | 0.246416 | − | 0.969164i | \(-0.420747\pi\) | ||||
0.246416 | + | 0.969164i | \(0.420747\pi\) | |||||||
\(228\) | 25.6535 | 1.69895 | ||||||||
\(229\) | 14.3786 | 0.950161 | 0.475081 | − | 0.879942i | \(-0.342419\pi\) | ||||
0.475081 | + | 0.879942i | \(0.342419\pi\) | |||||||
\(230\) | −38.3848 | −2.53102 | ||||||||
\(231\) | 24.0467 | 1.58216 | ||||||||
\(232\) | 64.3023 | 4.22165 | ||||||||
\(233\) | −4.51579 | −0.295839 | −0.147920 | − | 0.988999i | \(-0.547258\pi\) | ||||
−0.147920 | + | 0.988999i | \(0.547258\pi\) | |||||||
\(234\) | 21.7509 | 1.42190 | ||||||||
\(235\) | −31.3054 | −2.04214 | ||||||||
\(236\) | −20.3596 | −1.32529 | ||||||||
\(237\) | −35.5334 | −2.30814 | ||||||||
\(238\) | 32.2619 | 2.09123 | ||||||||
\(239\) | −3.53675 | −0.228774 | −0.114387 | − | 0.993436i | \(-0.536490\pi\) | ||||
−0.114387 | + | 0.993436i | \(0.536490\pi\) | |||||||
\(240\) | −86.7816 | −5.60173 | ||||||||
\(241\) | −1.11636 | −0.0719113 | −0.0359557 | − | 0.999353i | \(-0.511448\pi\) | ||||
−0.0359557 | + | 0.999353i | \(0.511448\pi\) | |||||||
\(242\) | −55.4454 | −3.56416 | ||||||||
\(243\) | −18.5607 | −1.19067 | ||||||||
\(244\) | 62.3567 | 3.99198 | ||||||||
\(245\) | 12.5626 | 0.802598 | ||||||||
\(246\) | −26.9713 | −1.71963 | ||||||||
\(247\) | −8.96060 | −0.570149 | ||||||||
\(248\) | −49.3290 | −3.13240 | ||||||||
\(249\) | −18.5832 | −1.17766 | ||||||||
\(250\) | 29.8021 | 1.88485 | ||||||||
\(251\) | 2.15528 | 0.136040 | 0.0680200 | − | 0.997684i | \(-0.478332\pi\) | ||||
0.0680200 | + | 0.997684i | \(0.478332\pi\) | |||||||
\(252\) | 19.6362 | 1.23697 | ||||||||
\(253\) | −22.7511 | −1.43035 | ||||||||
\(254\) | −37.4122 | −2.34745 | ||||||||
\(255\) | 53.3285 | 3.33956 | ||||||||
\(256\) | −8.59836 | −0.537397 | ||||||||
\(257\) | −29.2570 | −1.82500 | −0.912500 | − | 0.409078i | \(-0.865850\pi\) | ||||
−0.912500 | + | 0.409078i | \(0.865850\pi\) | |||||||
\(258\) | −31.9055 | −1.98635 | ||||||||
\(259\) | 9.26023 | 0.575402 | ||||||||
\(260\) | 70.0683 | 4.34545 | ||||||||
\(261\) | −17.4601 | −1.08075 | ||||||||
\(262\) | −6.17963 | −0.381779 | ||||||||
\(263\) | −11.5637 | −0.713050 | −0.356525 | − | 0.934286i | \(-0.616038\pi\) | ||||
−0.356525 | + | 0.934286i | \(0.616038\pi\) | |||||||
\(264\) | −99.4825 | −6.12272 | ||||||||
\(265\) | −46.1857 | −2.83717 | ||||||||
\(266\) | −11.3584 | −0.696426 | ||||||||
\(267\) | −30.2005 | −1.84824 | ||||||||
\(268\) | −60.5715 | −3.69999 | ||||||||
\(269\) | 6.71699 | 0.409542 | 0.204771 | − | 0.978810i | \(-0.434355\pi\) | ||||
0.204771 | + | 0.978810i | \(0.434355\pi\) | |||||||
\(270\) | −19.1892 | −1.16782 | ||||||||
\(271\) | 10.2717 | 0.623963 | 0.311981 | − | 0.950088i | \(-0.399007\pi\) | ||||
0.311981 | + | 0.950088i | \(0.399007\pi\) | |||||||
\(272\) | −69.0088 | −4.18428 | ||||||||
\(273\) | −16.6055 | −1.00501 | ||||||||
\(274\) | 43.2463 | 2.61261 | ||||||||
\(275\) | 45.9627 | 2.77166 | ||||||||
\(276\) | −44.9788 | −2.70741 | ||||||||
\(277\) | −7.62663 | −0.458240 | −0.229120 | − | 0.973398i | \(-0.573585\pi\) | ||||
−0.229120 | + | 0.973398i | \(0.573585\pi\) | |||||||
\(278\) | 29.3923 | 1.76284 | ||||||||
\(279\) | 13.3944 | 0.801901 | ||||||||
\(280\) | 52.9269 | 3.16299 | ||||||||
\(281\) | 12.9909 | 0.774974 | 0.387487 | − | 0.921875i | \(-0.373343\pi\) | ||||
0.387487 | + | 0.921875i | \(0.373343\pi\) | |||||||
\(282\) | −51.5068 | −3.06719 | ||||||||
\(283\) | −5.55961 | −0.330484 | −0.165242 | − | 0.986253i | \(-0.552841\pi\) | ||||
−0.165242 | + | 0.986253i | \(0.552841\pi\) | |||||||
\(284\) | 0.0859083 | 0.00509772 | ||||||||
\(285\) | −18.7752 | −1.11215 | ||||||||
\(286\) | 58.3124 | 3.44808 | ||||||||
\(287\) | 8.50499 | 0.502033 | ||||||||
\(288\) | −26.1480 | −1.54079 | ||||||||
\(289\) | 25.4069 | 1.49452 | ||||||||
\(290\) | −78.9749 | −4.63756 | ||||||||
\(291\) | −17.5136 | −1.02667 | ||||||||
\(292\) | −42.9776 | −2.51507 | ||||||||
\(293\) | 9.24805 | 0.540277 | 0.270138 | − | 0.962821i | \(-0.412931\pi\) | ||||
0.270138 | + | 0.962821i | \(0.412931\pi\) | |||||||
\(294\) | 20.6693 | 1.20546 | ||||||||
\(295\) | 14.9007 | 0.867553 | ||||||||
\(296\) | −38.3100 | −2.22673 | ||||||||
\(297\) | −11.3736 | −0.659965 | ||||||||
\(298\) | 38.1745 | 2.21139 | ||||||||
\(299\) | 15.7108 | 0.908580 | ||||||||
\(300\) | 90.8683 | 5.24628 | ||||||||
\(301\) | 10.0609 | 0.579902 | ||||||||
\(302\) | 17.5215 | 1.00825 | ||||||||
\(303\) | 15.3376 | 0.881124 | ||||||||
\(304\) | 24.2958 | 1.39346 | ||||||||
\(305\) | −45.6375 | −2.61319 | ||||||||
\(306\) | 36.2411 | 2.07177 | ||||||||
\(307\) | 15.4216 | 0.880159 | 0.440079 | − | 0.897959i | \(-0.354950\pi\) | ||||
0.440079 | + | 0.897959i | \(0.354950\pi\) | |||||||
\(308\) | 52.6433 | 2.99963 | ||||||||
\(309\) | 6.87377 | 0.391035 | ||||||||
\(310\) | 60.5850 | 3.44099 | ||||||||
\(311\) | −0.454415 | −0.0257675 | −0.0128837 | − | 0.999917i | \(-0.504101\pi\) | ||||
−0.0128837 | + | 0.999917i | \(0.504101\pi\) | |||||||
\(312\) | 68.6979 | 3.88925 | ||||||||
\(313\) | 9.15234 | 0.517321 | 0.258661 | − | 0.965968i | \(-0.416719\pi\) | ||||
0.258661 | + | 0.965968i | \(0.416719\pi\) | |||||||
\(314\) | 37.7794 | 2.13201 | ||||||||
\(315\) | −14.3713 | −0.809732 | ||||||||
\(316\) | −77.7900 | −4.37603 | ||||||||
\(317\) | 14.3870 | 0.808052 | 0.404026 | − | 0.914747i | \(-0.367610\pi\) | ||||
0.404026 | + | 0.914747i | \(0.367610\pi\) | |||||||
\(318\) | −75.9894 | −4.26128 | ||||||||
\(319\) | −46.8092 | −2.62081 | ||||||||
\(320\) | −41.5002 | −2.31993 | ||||||||
\(321\) | −38.3665 | −2.14141 | ||||||||
\(322\) | 19.9149 | 1.10981 | ||||||||
\(323\) | −14.9301 | −0.830732 | ||||||||
\(324\) | −53.8314 | −2.99063 | ||||||||
\(325\) | −31.7397 | −1.76060 | ||||||||
\(326\) | −28.4179 | −1.57392 | ||||||||
\(327\) | 8.18167 | 0.452447 | ||||||||
\(328\) | −35.1856 | −1.94280 | ||||||||
\(329\) | 16.2419 | 0.895445 | ||||||||
\(330\) | 122.182 | 6.72592 | ||||||||
\(331\) | −18.3304 | −1.00753 | −0.503765 | − | 0.863841i | \(-0.668052\pi\) | ||||
−0.503765 | + | 0.863841i | \(0.668052\pi\) | |||||||
\(332\) | −40.6825 | −2.23274 | ||||||||
\(333\) | 10.4024 | 0.570047 | ||||||||
\(334\) | 39.2573 | 2.14806 | ||||||||
\(335\) | 44.3309 | 2.42206 | ||||||||
\(336\) | 45.0242 | 2.45627 | ||||||||
\(337\) | −18.6584 | −1.01639 | −0.508194 | − | 0.861243i | \(-0.669687\pi\) | ||||
−0.508194 | + | 0.861243i | \(0.669687\pi\) | |||||||
\(338\) | −5.99777 | −0.326236 | ||||||||
\(339\) | 19.7542 | 1.07290 | ||||||||
\(340\) | 116.747 | 6.33151 | ||||||||
\(341\) | 35.9093 | 1.94460 | ||||||||
\(342\) | −12.7593 | −0.689944 | ||||||||
\(343\) | −19.6730 | −1.06224 | ||||||||
\(344\) | −41.6225 | −2.24414 | ||||||||
\(345\) | 32.9190 | 1.77230 | ||||||||
\(346\) | 31.0668 | 1.67016 | ||||||||
\(347\) | −23.3493 | −1.25345 | −0.626727 | − | 0.779239i | \(-0.715606\pi\) | ||||
−0.626727 | + | 0.779239i | \(0.715606\pi\) | |||||||
\(348\) | −92.5417 | −4.96076 | ||||||||
\(349\) | −29.3355 | −1.57029 | −0.785146 | − | 0.619310i | \(-0.787412\pi\) | ||||
−0.785146 | + | 0.619310i | \(0.787412\pi\) | |||||||
\(350\) | −40.2329 | −2.15054 | ||||||||
\(351\) | 7.85410 | 0.419221 | ||||||||
\(352\) | −70.1008 | −3.73639 | ||||||||
\(353\) | 31.1397 | 1.65740 | 0.828701 | − | 0.559692i | \(-0.189081\pi\) | ||||
0.828701 | + | 0.559692i | \(0.189081\pi\) | |||||||
\(354\) | 24.5162 | 1.30302 | ||||||||
\(355\) | −0.0628743 | −0.00333702 | ||||||||
\(356\) | −66.1153 | −3.50410 | ||||||||
\(357\) | −27.6680 | −1.46434 | ||||||||
\(358\) | −67.3917 | −3.56176 | ||||||||
\(359\) | 10.0063 | 0.528114 | 0.264057 | − | 0.964507i | \(-0.414939\pi\) | ||||
0.264057 | + | 0.964507i | \(0.414939\pi\) | |||||||
\(360\) | 59.4549 | 3.13355 | ||||||||
\(361\) | −13.7436 | −0.723348 | ||||||||
\(362\) | −38.5507 | −2.02618 | ||||||||
\(363\) | 47.5502 | 2.49574 | ||||||||
\(364\) | −36.3529 | −1.90541 | ||||||||
\(365\) | 31.4543 | 1.64640 | ||||||||
\(366\) | −75.0874 | −3.92488 | ||||||||
\(367\) | 25.4067 | 1.32622 | 0.663108 | − | 0.748523i | \(-0.269237\pi\) | ||||
0.663108 | + | 0.748523i | \(0.269237\pi\) | |||||||
\(368\) | −42.5983 | −2.22059 | ||||||||
\(369\) | 9.55399 | 0.497361 | ||||||||
\(370\) | 47.0517 | 2.44610 | ||||||||
\(371\) | 23.9621 | 1.24405 | ||||||||
\(372\) | 70.9927 | 3.68080 | ||||||||
\(373\) | −36.0526 | −1.86673 | −0.933367 | − | 0.358924i | \(-0.883144\pi\) | ||||
−0.933367 | + | 0.358924i | \(0.883144\pi\) | |||||||
\(374\) | 97.1596 | 5.02400 | ||||||||
\(375\) | −25.5584 | −1.31983 | ||||||||
\(376\) | −67.1936 | −3.46525 | ||||||||
\(377\) | 32.3242 | 1.66478 | ||||||||
\(378\) | 9.95577 | 0.512070 | ||||||||
\(379\) | 17.7345 | 0.910960 | 0.455480 | − | 0.890246i | \(-0.349468\pi\) | ||||
0.455480 | + | 0.890246i | \(0.349468\pi\) | |||||||
\(380\) | −41.1029 | −2.10853 | ||||||||
\(381\) | 32.0849 | 1.64376 | ||||||||
\(382\) | 42.5748 | 2.17832 | ||||||||
\(383\) | 11.2834 | 0.576552 | 0.288276 | − | 0.957547i | \(-0.406918\pi\) | ||||
0.288276 | + | 0.957547i | \(0.406918\pi\) | |||||||
\(384\) | −12.2770 | −0.626507 | ||||||||
\(385\) | −38.5284 | −1.96359 | ||||||||
\(386\) | 61.7861 | 3.14483 | ||||||||
\(387\) | 11.3018 | 0.574504 | ||||||||
\(388\) | −38.3409 | −1.94647 | ||||||||
\(389\) | −16.0830 | −0.815440 | −0.407720 | − | 0.913107i | \(-0.633676\pi\) | ||||
−0.407720 | + | 0.913107i | \(0.633676\pi\) | |||||||
\(390\) | −84.3734 | −4.27241 | ||||||||
\(391\) | 26.1772 | 1.32384 | ||||||||
\(392\) | 26.9644 | 1.36191 | ||||||||
\(393\) | 5.29967 | 0.267333 | ||||||||
\(394\) | −14.2903 | −0.719937 | ||||||||
\(395\) | 56.9328 | 2.86460 | ||||||||
\(396\) | 59.1363 | 2.97171 | ||||||||
\(397\) | 2.14160 | 0.107484 | 0.0537419 | − | 0.998555i | \(-0.482885\pi\) | ||||
0.0537419 | + | 0.998555i | \(0.482885\pi\) | |||||||
\(398\) | −29.4268 | −1.47503 | ||||||||
\(399\) | 9.74098 | 0.487659 | ||||||||
\(400\) | 86.0589 | 4.30295 | ||||||||
\(401\) | −21.8289 | −1.09009 | −0.545043 | − | 0.838408i | \(-0.683487\pi\) | ||||
−0.545043 | + | 0.838408i | \(0.683487\pi\) | |||||||
\(402\) | 72.9377 | 3.63780 | ||||||||
\(403\) | −24.7973 | −1.23524 | ||||||||
\(404\) | 33.5773 | 1.67053 | ||||||||
\(405\) | 39.3980 | 1.95770 | ||||||||
\(406\) | 40.9738 | 2.03350 | ||||||||
\(407\) | 27.8880 | 1.38236 | ||||||||
\(408\) | 114.464 | 5.66680 | ||||||||
\(409\) | −32.5747 | −1.61071 | −0.805357 | − | 0.592790i | \(-0.798026\pi\) | ||||
−0.805357 | + | 0.592790i | \(0.798026\pi\) | |||||||
\(410\) | 43.2142 | 2.13420 | ||||||||
\(411\) | −37.0882 | −1.82943 | ||||||||
\(412\) | 15.0481 | 0.741368 | ||||||||
\(413\) | −7.73080 | −0.380408 | ||||||||
\(414\) | 22.3712 | 1.09948 | ||||||||
\(415\) | 29.7746 | 1.46158 | ||||||||
\(416\) | 48.4083 | 2.37341 | ||||||||
\(417\) | −25.2070 | −1.23439 | ||||||||
\(418\) | −34.2067 | −1.67311 | ||||||||
\(419\) | −16.6825 | −0.814992 | −0.407496 | − | 0.913207i | \(-0.633598\pi\) | ||||
−0.407496 | + | 0.913207i | \(0.633598\pi\) | |||||||
\(420\) | −76.1706 | −3.71675 | ||||||||
\(421\) | 19.1114 | 0.931433 | 0.465717 | − | 0.884934i | \(-0.345797\pi\) | ||||
0.465717 | + | 0.884934i | \(0.345797\pi\) | |||||||
\(422\) | −37.8815 | −1.84404 | ||||||||
\(423\) | 18.2452 | 0.887111 | ||||||||
\(424\) | −99.1326 | −4.81430 | ||||||||
\(425\) | −52.8844 | −2.56527 | ||||||||
\(426\) | −0.103447 | −0.00501203 | ||||||||
\(427\) | 23.6777 | 1.14584 | ||||||||
\(428\) | −83.9923 | −4.05992 | ||||||||
\(429\) | −50.0090 | −2.41446 | ||||||||
\(430\) | 51.1200 | 2.46523 | ||||||||
\(431\) | 1.73546 | 0.0835943 | 0.0417971 | − | 0.999126i | \(-0.486692\pi\) | ||||
0.0417971 | + | 0.999126i | \(0.486692\pi\) | |||||||
\(432\) | −21.2956 | −1.02458 | ||||||||
\(433\) | −1.97257 | −0.0947955 | −0.0473978 | − | 0.998876i | \(-0.515093\pi\) | ||||
−0.0473978 | + | 0.998876i | \(0.515093\pi\) | |||||||
\(434\) | −31.4328 | −1.50882 | ||||||||
\(435\) | 67.7292 | 3.24737 | ||||||||
\(436\) | 17.9114 | 0.857800 | ||||||||
\(437\) | −9.21614 | −0.440868 | ||||||||
\(438\) | 51.7519 | 2.47280 | ||||||||
\(439\) | 23.5443 | 1.12371 | 0.561854 | − | 0.827237i | \(-0.310088\pi\) | ||||
0.561854 | + | 0.827237i | \(0.310088\pi\) | |||||||
\(440\) | 159.394 | 7.59881 | ||||||||
\(441\) | −7.32167 | −0.348651 | ||||||||
\(442\) | −67.0938 | −3.19133 | ||||||||
\(443\) | −15.6000 | −0.741179 | −0.370589 | − | 0.928797i | \(-0.620844\pi\) | ||||
−0.370589 | + | 0.928797i | \(0.620844\pi\) | |||||||
\(444\) | 55.1345 | 2.61657 | ||||||||
\(445\) | 48.3883 | 2.29382 | ||||||||
\(446\) | 66.7985 | 3.16300 | ||||||||
\(447\) | −32.7387 | −1.54849 | ||||||||
\(448\) | 21.5312 | 1.01725 | ||||||||
\(449\) | −11.2249 | −0.529734 | −0.264867 | − | 0.964285i | \(-0.585328\pi\) | ||||
−0.264867 | + | 0.964285i | \(0.585328\pi\) | |||||||
\(450\) | −45.1952 | −2.13052 | ||||||||
\(451\) | 25.6135 | 1.20609 | ||||||||
\(452\) | 43.2460 | 2.03412 | ||||||||
\(453\) | −15.0265 | −0.706005 | ||||||||
\(454\) | −19.5742 | −0.918661 | ||||||||
\(455\) | 26.6059 | 1.24730 | ||||||||
\(456\) | −40.2990 | −1.88717 | ||||||||
\(457\) | −18.7227 | −0.875811 | −0.437906 | − | 0.899021i | \(-0.644280\pi\) | ||||
−0.437906 | + | 0.899021i | \(0.644280\pi\) | |||||||
\(458\) | −37.9041 | −1.77114 | ||||||||
\(459\) | 13.0864 | 0.610822 | ||||||||
\(460\) | 72.0665 | 3.36012 | ||||||||
\(461\) | −18.5401 | −0.863501 | −0.431750 | − | 0.901993i | \(-0.642104\pi\) | ||||
−0.431750 | + | 0.901993i | \(0.642104\pi\) | |||||||
\(462\) | −63.3909 | −2.94921 | ||||||||
\(463\) | −24.3339 | −1.13089 | −0.565446 | − | 0.824785i | \(-0.691296\pi\) | ||||
−0.565446 | + | 0.824785i | \(0.691296\pi\) | |||||||
\(464\) | −87.6438 | −4.06876 | ||||||||
\(465\) | −51.9579 | −2.40949 | ||||||||
\(466\) | 11.9043 | 0.551457 | ||||||||
\(467\) | 20.5636 | 0.951568 | 0.475784 | − | 0.879562i | \(-0.342164\pi\) | ||||
0.475784 | + | 0.879562i | \(0.342164\pi\) | |||||||
\(468\) | −40.8367 | −1.88768 | ||||||||
\(469\) | −22.9998 | −1.06203 | ||||||||
\(470\) | 82.5259 | 3.80664 | ||||||||
\(471\) | −32.3997 | −1.49290 | ||||||||
\(472\) | 31.9827 | 1.47212 | ||||||||
\(473\) | 30.2993 | 1.39316 | ||||||||
\(474\) | 93.6716 | 4.30248 | ||||||||
\(475\) | 18.6189 | 0.854292 | ||||||||
\(476\) | −60.5710 | −2.77627 | ||||||||
\(477\) | 26.9176 | 1.23247 | ||||||||
\(478\) | 9.32344 | 0.426444 | ||||||||
\(479\) | −33.0900 | −1.51192 | −0.755961 | − | 0.654617i | \(-0.772830\pi\) | ||||
−0.755961 | + | 0.654617i | \(0.772830\pi\) | |||||||
\(480\) | 101.430 | 4.62964 | ||||||||
\(481\) | −19.2581 | −0.878095 | ||||||||
\(482\) | 2.94291 | 0.134046 | ||||||||
\(483\) | −17.0791 | −0.777125 | ||||||||
\(484\) | 104.097 | 4.73170 | ||||||||
\(485\) | 28.0609 | 1.27418 | ||||||||
\(486\) | 48.9290 | 2.21946 | ||||||||
\(487\) | −6.40332 | −0.290162 | −0.145081 | − | 0.989420i | \(-0.546344\pi\) | ||||
−0.145081 | + | 0.989420i | \(0.546344\pi\) | |||||||
\(488\) | −97.9559 | −4.43425 | ||||||||
\(489\) | 24.3713 | 1.10211 | ||||||||
\(490\) | −33.1171 | −1.49608 | ||||||||
\(491\) | −17.1152 | −0.772400 | −0.386200 | − | 0.922415i | \(-0.626212\pi\) | ||||
−0.386200 | + | 0.922415i | \(0.626212\pi\) | |||||||
\(492\) | 50.6379 | 2.28293 | ||||||||
\(493\) | 53.8583 | 2.42566 | ||||||||
\(494\) | 23.6215 | 1.06278 | ||||||||
\(495\) | −43.2805 | −1.94531 | ||||||||
\(496\) | 67.2353 | 3.01895 | ||||||||
\(497\) | 0.0326205 | 0.00146323 | ||||||||
\(498\) | 48.9882 | 2.19521 | ||||||||
\(499\) | −7.33629 | −0.328417 | −0.164209 | − | 0.986426i | \(-0.552507\pi\) | ||||
−0.164209 | + | 0.986426i | \(0.552507\pi\) | |||||||
\(500\) | −55.9528 | −2.50228 | ||||||||
\(501\) | −33.6672 | −1.50414 | ||||||||
\(502\) | −5.68165 | −0.253585 | ||||||||
\(503\) | −1.73650 | −0.0774268 | −0.0387134 | − | 0.999250i | \(-0.512326\pi\) | ||||
−0.0387134 | + | 0.999250i | \(0.512326\pi\) | |||||||
\(504\) | −30.8465 | −1.37401 | ||||||||
\(505\) | −24.5745 | −1.09355 | ||||||||
\(506\) | 59.9753 | 2.66623 | ||||||||
\(507\) | 5.14371 | 0.228440 | ||||||||
\(508\) | 70.2405 | 3.11642 | ||||||||
\(509\) | −17.2500 | −0.764592 | −0.382296 | − | 0.924040i | \(-0.624866\pi\) | ||||
−0.382296 | + | 0.924040i | \(0.624866\pi\) | |||||||
\(510\) | −140.582 | −6.22509 | ||||||||
\(511\) | −16.3192 | −0.721918 | ||||||||
\(512\) | 33.5275 | 1.48172 | ||||||||
\(513\) | −4.60730 | −0.203417 | ||||||||
\(514\) | 77.1259 | 3.40188 | ||||||||
\(515\) | −11.0134 | −0.485308 | ||||||||
\(516\) | 59.9017 | 2.63703 | ||||||||
\(517\) | 48.9139 | 2.15123 | ||||||||
\(518\) | −24.4114 | −1.07258 | ||||||||
\(519\) | −26.6430 | −1.16950 | ||||||||
\(520\) | −110.070 | −4.82689 | ||||||||
\(521\) | 27.7826 | 1.21718 | 0.608589 | − | 0.793486i | \(-0.291736\pi\) | ||||
0.608589 | + | 0.793486i | \(0.291736\pi\) | |||||||
\(522\) | 46.0275 | 2.01457 | ||||||||
\(523\) | 15.6264 | 0.683296 | 0.341648 | − | 0.939828i | \(-0.389015\pi\) | ||||
0.341648 | + | 0.939828i | \(0.389015\pi\) | |||||||
\(524\) | 11.6021 | 0.506840 | ||||||||
\(525\) | 34.5039 | 1.50587 | ||||||||
\(526\) | 30.4838 | 1.32916 | ||||||||
\(527\) | −41.3170 | −1.79980 | ||||||||
\(528\) | 135.594 | 5.90098 | ||||||||
\(529\) | −6.84115 | −0.297441 | ||||||||
\(530\) | 121.753 | 5.28860 | ||||||||
\(531\) | −8.68432 | −0.376867 | ||||||||
\(532\) | 21.3251 | 0.924558 | ||||||||
\(533\) | −17.6875 | −0.766130 | ||||||||
\(534\) | 79.6133 | 3.44520 | ||||||||
\(535\) | 61.4721 | 2.65767 | ||||||||
\(536\) | 95.1514 | 4.10992 | ||||||||
\(537\) | 57.7954 | 2.49405 | ||||||||
\(538\) | −17.7070 | −0.763404 | ||||||||
\(539\) | −19.6288 | −0.845474 | ||||||||
\(540\) | 36.0273 | 1.55037 | ||||||||
\(541\) | −39.0241 | −1.67778 | −0.838888 | − | 0.544305i | \(-0.816794\pi\) | ||||
−0.838888 | + | 0.544305i | \(0.816794\pi\) | |||||||
\(542\) | −27.0779 | −1.16309 | ||||||||
\(543\) | 33.0612 | 1.41879 | ||||||||
\(544\) | 80.6575 | 3.45816 | ||||||||
\(545\) | −13.1089 | −0.561525 | ||||||||
\(546\) | 43.7747 | 1.87339 | ||||||||
\(547\) | 8.70518 | 0.372207 | 0.186103 | − | 0.982530i | \(-0.440414\pi\) | ||||
0.186103 | + | 0.982530i | \(0.440414\pi\) | |||||||
\(548\) | −81.1939 | −3.46843 | ||||||||
\(549\) | 26.5981 | 1.13518 | ||||||||
\(550\) | −121.165 | −5.16649 | ||||||||
\(551\) | −18.9617 | −0.807798 | ||||||||
\(552\) | 70.6570 | 3.00736 | ||||||||
\(553\) | −29.5379 | −1.25608 | ||||||||
\(554\) | 20.1050 | 0.854179 | ||||||||
\(555\) | −40.3517 | −1.71283 | ||||||||
\(556\) | −55.1834 | −2.34030 | ||||||||
\(557\) | 26.7761 | 1.13454 | 0.567269 | − | 0.823533i | \(-0.308000\pi\) | ||||
0.567269 | + | 0.823533i | \(0.308000\pi\) | |||||||
\(558\) | −35.3097 | −1.49478 | ||||||||
\(559\) | −20.9233 | −0.884961 | ||||||||
\(560\) | −72.1392 | −3.04844 | ||||||||
\(561\) | −83.3245 | −3.51796 | ||||||||
\(562\) | −34.2461 | −1.44459 | ||||||||
\(563\) | −22.5502 | −0.950380 | −0.475190 | − | 0.879883i | \(-0.657621\pi\) | ||||
−0.475190 | + | 0.879883i | \(0.657621\pi\) | |||||||
\(564\) | 96.7028 | 4.07192 | ||||||||
\(565\) | −31.6507 | −1.33156 | ||||||||
\(566\) | 14.6560 | 0.616037 | ||||||||
\(567\) | −20.4405 | −0.858421 | ||||||||
\(568\) | −0.134953 | −0.00566250 | ||||||||
\(569\) | 32.4585 | 1.36073 | 0.680365 | − | 0.732873i | \(-0.261821\pi\) | ||||
0.680365 | + | 0.732873i | \(0.261821\pi\) | |||||||
\(570\) | 49.4944 | 2.07309 | ||||||||
\(571\) | −45.3518 | −1.89791 | −0.948956 | − | 0.315407i | \(-0.897859\pi\) | ||||
−0.948956 | + | 0.315407i | \(0.897859\pi\) | |||||||
\(572\) | −109.480 | −4.57759 | ||||||||
\(573\) | −36.5124 | −1.52533 | ||||||||
\(574\) | −22.4205 | −0.935812 | ||||||||
\(575\) | −32.6448 | −1.36138 | ||||||||
\(576\) | 24.1868 | 1.00779 | ||||||||
\(577\) | −16.5870 | −0.690526 | −0.345263 | − | 0.938506i | \(-0.612210\pi\) | ||||
−0.345263 | + | 0.938506i | \(0.612210\pi\) | |||||||
\(578\) | −66.9765 | −2.78585 | ||||||||
\(579\) | −52.9880 | −2.20211 | ||||||||
\(580\) | 148.273 | 6.15671 | ||||||||
\(581\) | −15.4477 | −0.640878 | ||||||||
\(582\) | 46.1686 | 1.91375 | ||||||||
\(583\) | 72.1640 | 2.98873 | ||||||||
\(584\) | 67.5133 | 2.79372 | ||||||||
\(585\) | 29.8875 | 1.23569 | ||||||||
\(586\) | −24.3793 | −1.00710 | ||||||||
\(587\) | −19.2160 | −0.793129 | −0.396564 | − | 0.918007i | \(-0.629798\pi\) | ||||
−0.396564 | + | 0.918007i | \(0.629798\pi\) | |||||||
\(588\) | −38.8062 | −1.60034 | ||||||||
\(589\) | 14.5464 | 0.599372 | ||||||||
\(590\) | −39.2806 | −1.61716 | ||||||||
\(591\) | 12.2555 | 0.504122 | ||||||||
\(592\) | 52.2164 | 2.14608 | ||||||||
\(593\) | 20.7827 | 0.853443 | 0.426722 | − | 0.904383i | \(-0.359668\pi\) | ||||
0.426722 | + | 0.904383i | \(0.359668\pi\) | |||||||
\(594\) | 29.9827 | 1.23020 | ||||||||
\(595\) | 44.3305 | 1.81737 | ||||||||
\(596\) | −71.6717 | −2.93579 | ||||||||
\(597\) | 25.2365 | 1.03286 | ||||||||
\(598\) | −41.4161 | −1.69363 | ||||||||
\(599\) | −31.3712 | −1.28179 | −0.640897 | − | 0.767627i | \(-0.721437\pi\) | ||||
−0.640897 | + | 0.767627i | \(0.721437\pi\) | |||||||
\(600\) | −142.744 | −5.82752 | ||||||||
\(601\) | 5.03189 | 0.205255 | 0.102627 | − | 0.994720i | \(-0.467275\pi\) | ||||
0.102627 | + | 0.994720i | \(0.467275\pi\) | |||||||
\(602\) | −26.5221 | −1.08096 | ||||||||
\(603\) | −25.8366 | −1.05215 | ||||||||
\(604\) | −32.8961 | −1.33852 | ||||||||
\(605\) | −76.1865 | −3.09742 | ||||||||
\(606\) | −40.4324 | −1.64245 | ||||||||
\(607\) | 25.3974 | 1.03085 | 0.515424 | − | 0.856935i | \(-0.327634\pi\) | ||||
0.515424 | + | 0.856935i | \(0.327634\pi\) | |||||||
\(608\) | −28.3969 | −1.15164 | ||||||||
\(609\) | −35.1393 | −1.42392 | ||||||||
\(610\) | 120.307 | 4.87111 | ||||||||
\(611\) | −33.7776 | −1.36650 | ||||||||
\(612\) | −68.0417 | −2.75042 | ||||||||
\(613\) | 19.5551 | 0.789823 | 0.394911 | − | 0.918719i | \(-0.370775\pi\) | ||||
0.394911 | + | 0.918719i | \(0.370775\pi\) | |||||||
\(614\) | −40.6538 | −1.64065 | ||||||||
\(615\) | −37.0607 | −1.49443 | ||||||||
\(616\) | −82.6970 | −3.33196 | ||||||||
\(617\) | −34.0953 | −1.37262 | −0.686312 | − | 0.727308i | \(-0.740771\pi\) | ||||
−0.686312 | + | 0.727308i | \(0.740771\pi\) | |||||||
\(618\) | −18.1203 | −0.728907 | ||||||||
\(619\) | −31.8931 | −1.28189 | −0.640946 | − | 0.767586i | \(-0.721458\pi\) | ||||
−0.640946 | + | 0.767586i | \(0.721458\pi\) | |||||||
\(620\) | −113.747 | −4.56818 | ||||||||
\(621\) | 8.07808 | 0.324162 | ||||||||
\(622\) | 1.19791 | 0.0480317 | ||||||||
\(623\) | −25.1049 | −1.00580 | ||||||||
\(624\) | −93.6349 | −3.74840 | ||||||||
\(625\) | 0.345580 | 0.0138232 | ||||||||
\(626\) | −24.1270 | −0.964309 | ||||||||
\(627\) | 29.3358 | 1.17156 | ||||||||
\(628\) | −70.9298 | −2.83041 | ||||||||
\(629\) | −32.0877 | −1.27942 | ||||||||
\(630\) | 37.8850 | 1.50938 | ||||||||
\(631\) | −16.1086 | −0.641274 | −0.320637 | − | 0.947202i | \(-0.603897\pi\) | ||||
−0.320637 | + | 0.947202i | \(0.603897\pi\) | |||||||
\(632\) | 122.200 | 4.86085 | ||||||||
\(633\) | 32.4873 | 1.29125 | ||||||||
\(634\) | −37.9263 | −1.50624 | ||||||||
\(635\) | −51.4075 | −2.04004 | ||||||||
\(636\) | 142.668 | 5.65716 | ||||||||
\(637\) | 13.5547 | 0.537058 | ||||||||
\(638\) | 123.396 | 4.88531 | ||||||||
\(639\) | 0.0366439 | 0.00144961 | ||||||||
\(640\) | 19.6706 | 0.777548 | ||||||||
\(641\) | 0.696605 | 0.0275143 | 0.0137571 | − | 0.999905i | \(-0.495621\pi\) | ||||
0.0137571 | + | 0.999905i | \(0.495621\pi\) | |||||||
\(642\) | 101.140 | 3.99168 | ||||||||
\(643\) | −31.0841 | −1.22584 | −0.612918 | − | 0.790146i | \(-0.710005\pi\) | ||||
−0.612918 | + | 0.790146i | \(0.710005\pi\) | |||||||
\(644\) | −37.3897 | −1.47336 | ||||||||
\(645\) | −43.8407 | −1.72623 | ||||||||
\(646\) | 39.3580 | 1.54852 | ||||||||
\(647\) | 18.4732 | 0.726257 | 0.363129 | − | 0.931739i | \(-0.381709\pi\) | ||||
0.363129 | + | 0.931739i | \(0.381709\pi\) | |||||||
\(648\) | 84.5635 | 3.32197 | ||||||||
\(649\) | −23.2820 | −0.913898 | ||||||||
\(650\) | 83.6707 | 3.28184 | ||||||||
\(651\) | 26.9569 | 1.05652 | ||||||||
\(652\) | 53.3540 | 2.08950 | ||||||||
\(653\) | −48.1859 | −1.88566 | −0.942830 | − | 0.333274i | \(-0.891846\pi\) | ||||
−0.942830 | + | 0.333274i | \(0.891846\pi\) | |||||||
\(654\) | −21.5682 | −0.843382 | ||||||||
\(655\) | −8.49131 | −0.331783 | ||||||||
\(656\) | 47.9578 | 1.87244 | ||||||||
\(657\) | −18.3320 | −0.715199 | ||||||||
\(658\) | −42.8162 | −1.66915 | ||||||||
\(659\) | 21.4031 | 0.833748 | 0.416874 | − | 0.908964i | \(-0.363126\pi\) | ||||
0.416874 | + | 0.908964i | \(0.363126\pi\) | |||||||
\(660\) | −229.394 | −8.92917 | ||||||||
\(661\) | −28.3101 | −1.10114 | −0.550568 | − | 0.834790i | \(-0.685589\pi\) | ||||
−0.550568 | + | 0.834790i | \(0.685589\pi\) | |||||||
\(662\) | 48.3218 | 1.87808 | ||||||||
\(663\) | 57.5399 | 2.23467 | ||||||||
\(664\) | 63.9079 | 2.48011 | ||||||||
\(665\) | −15.6073 | −0.605226 | ||||||||
\(666\) | −27.4223 | −1.06259 | ||||||||
\(667\) | 33.2460 | 1.28729 | ||||||||
\(668\) | −73.7045 | −2.85171 | ||||||||
\(669\) | −57.2867 | −2.21483 | ||||||||
\(670\) | −116.863 | −4.51482 | ||||||||
\(671\) | 71.3074 | 2.75279 | ||||||||
\(672\) | −52.6242 | −2.03002 | ||||||||
\(673\) | −12.0807 | −0.465677 | −0.232838 | − | 0.972515i | \(-0.574801\pi\) | ||||
−0.232838 | + | 0.972515i | \(0.574801\pi\) | |||||||
\(674\) | 49.1864 | 1.89459 | ||||||||
\(675\) | −16.3197 | −0.628145 | ||||||||
\(676\) | 11.2607 | 0.433102 | ||||||||
\(677\) | −19.2366 | −0.739322 | −0.369661 | − | 0.929167i | \(-0.620526\pi\) | ||||
−0.369661 | + | 0.929167i | \(0.620526\pi\) | |||||||
\(678\) | −52.0750 | −1.99993 | ||||||||
\(679\) | −14.5586 | −0.558707 | ||||||||
\(680\) | −183.398 | −7.03298 | ||||||||
\(681\) | 16.7869 | 0.643275 | ||||||||
\(682\) | −94.6625 | −3.62481 | ||||||||
\(683\) | −27.5789 | −1.05528 | −0.527638 | − | 0.849469i | \(-0.676922\pi\) | ||||
−0.527638 | + | 0.849469i | \(0.676922\pi\) | |||||||
\(684\) | 23.9553 | 0.915953 | ||||||||
\(685\) | 59.4239 | 2.27047 | ||||||||
\(686\) | 51.8611 | 1.98007 | ||||||||
\(687\) | 32.5067 | 1.24021 | ||||||||
\(688\) | 56.7313 | 2.16286 | ||||||||
\(689\) | −49.8331 | −1.89849 | ||||||||
\(690\) | −86.7796 | −3.30364 | ||||||||
\(691\) | 4.12930 | 0.157086 | 0.0785431 | − | 0.996911i | \(-0.474973\pi\) | ||||
0.0785431 | + | 0.996911i | \(0.474973\pi\) | |||||||
\(692\) | −58.3270 | −2.21726 | ||||||||
\(693\) | 22.4548 | 0.852989 | ||||||||
\(694\) | 61.5523 | 2.33649 | ||||||||
\(695\) | 40.3875 | 1.53198 | ||||||||
\(696\) | 145.373 | 5.51036 | ||||||||
\(697\) | −29.4707 | −1.11628 | ||||||||
\(698\) | 77.3329 | 2.92709 | ||||||||
\(699\) | −10.2092 | −0.386147 | ||||||||
\(700\) | 75.5363 | 2.85500 | ||||||||
\(701\) | 31.5539 | 1.19177 | 0.595887 | − | 0.803068i | \(-0.296801\pi\) | ||||
0.595887 | + | 0.803068i | \(0.296801\pi\) | |||||||
\(702\) | −20.7046 | −0.781445 | ||||||||
\(703\) | 11.2970 | 0.426076 | ||||||||
\(704\) | 64.8431 | 2.44387 | ||||||||
\(705\) | −70.7745 | −2.66552 | ||||||||
\(706\) | −82.0892 | −3.08947 | ||||||||
\(707\) | 12.7498 | 0.479504 | ||||||||
\(708\) | −46.0285 | −1.72986 | ||||||||
\(709\) | −9.07511 | −0.340823 | −0.170411 | − | 0.985373i | \(-0.554510\pi\) | ||||
−0.170411 | + | 0.985373i | \(0.554510\pi\) | |||||||
\(710\) | 0.165747 | 0.00622036 | ||||||||
\(711\) | −33.1811 | −1.24439 | ||||||||
\(712\) | 103.860 | 3.89232 | ||||||||
\(713\) | −25.5044 | −0.955148 | ||||||||
\(714\) | 72.9370 | 2.72960 | ||||||||
\(715\) | 80.1260 | 2.99654 | ||||||||
\(716\) | 126.526 | 4.72850 | ||||||||
\(717\) | −7.99582 | −0.298609 | ||||||||
\(718\) | −26.3783 | −0.984428 | ||||||||
\(719\) | 38.2747 | 1.42741 | 0.713703 | − | 0.700448i | \(-0.247016\pi\) | ||||
0.713703 | + | 0.700448i | \(0.247016\pi\) | |||||||
\(720\) | −81.0368 | −3.02006 | ||||||||
\(721\) | 5.71398 | 0.212800 | ||||||||
\(722\) | 36.2303 | 1.34835 | ||||||||
\(723\) | −2.52385 | −0.0938630 | ||||||||
\(724\) | 72.3779 | 2.68991 | ||||||||
\(725\) | −67.1651 | −2.49445 | ||||||||
\(726\) | −125.350 | −4.65216 | ||||||||
\(727\) | −18.9948 | −0.704477 | −0.352238 | − | 0.935910i | \(-0.614579\pi\) | ||||
−0.352238 | + | 0.935910i | \(0.614579\pi\) | |||||||
\(728\) | 57.1067 | 2.11651 | ||||||||
\(729\) | −9.33207 | −0.345632 | ||||||||
\(730\) | −82.9185 | −3.06895 | ||||||||
\(731\) | −34.8622 | −1.28942 | ||||||||
\(732\) | 140.975 | 5.21057 | ||||||||
\(733\) | −11.0680 | −0.408806 | −0.204403 | − | 0.978887i | \(-0.565525\pi\) | ||||
−0.204403 | + | 0.978887i | \(0.565525\pi\) | |||||||
\(734\) | −66.9759 | −2.47213 | ||||||||
\(735\) | 28.4014 | 1.04760 | ||||||||
\(736\) | 49.7888 | 1.83524 | ||||||||
\(737\) | −69.2659 | −2.55144 | ||||||||
\(738\) | −25.1858 | −0.927102 | ||||||||
\(739\) | −14.0017 | −0.515060 | −0.257530 | − | 0.966270i | \(-0.582909\pi\) | ||||
−0.257530 | + | 0.966270i | \(0.582909\pi\) | |||||||
\(740\) | −88.3383 | −3.24738 | ||||||||
\(741\) | −20.2579 | −0.744194 | ||||||||
\(742\) | −63.1679 | −2.31897 | ||||||||
\(743\) | 0.580564 | 0.0212988 | 0.0106494 | − | 0.999943i | \(-0.496610\pi\) | ||||
0.0106494 | + | 0.999943i | \(0.496610\pi\) | |||||||
\(744\) | −111.522 | −4.08859 | ||||||||
\(745\) | 52.4549 | 1.92180 | ||||||||
\(746\) | 95.0403 | 3.47967 | ||||||||
\(747\) | −17.3530 | −0.634913 | ||||||||
\(748\) | −182.415 | −6.66974 | ||||||||
\(749\) | −31.8930 | −1.16535 | ||||||||
\(750\) | 67.3760 | 2.46022 | ||||||||
\(751\) | 40.6483 | 1.48328 | 0.741639 | − | 0.670800i | \(-0.234049\pi\) | ||||
0.741639 | + | 0.670800i | \(0.234049\pi\) | |||||||
\(752\) | 91.5846 | 3.33975 | ||||||||
\(753\) | 4.87261 | 0.177568 | ||||||||
\(754\) | −85.2116 | −3.10322 | ||||||||
\(755\) | 24.0759 | 0.876212 | ||||||||
\(756\) | −18.6917 | −0.679811 | ||||||||
\(757\) | 9.13565 | 0.332041 | 0.166020 | − | 0.986122i | \(-0.446908\pi\) | ||||
0.166020 | + | 0.986122i | \(0.446908\pi\) | |||||||
\(758\) | −46.7509 | −1.69807 | ||||||||
\(759\) | −51.4351 | −1.86698 | ||||||||
\(760\) | 64.5683 | 2.34214 | ||||||||
\(761\) | 46.3031 | 1.67849 | 0.839243 | − | 0.543756i | \(-0.182998\pi\) | ||||
0.839243 | + | 0.543756i | \(0.182998\pi\) | |||||||
\(762\) | −84.5808 | −3.06404 | ||||||||
\(763\) | 6.80120 | 0.246220 | ||||||||
\(764\) | −79.9332 | −2.89188 | ||||||||
\(765\) | 49.7982 | 1.80046 | ||||||||
\(766\) | −29.7447 | −1.07472 | ||||||||
\(767\) | 16.0774 | 0.580523 | ||||||||
\(768\) | −19.4390 | −0.701444 | ||||||||
\(769\) | 24.0027 | 0.865558 | 0.432779 | − | 0.901500i | \(-0.357533\pi\) | ||||
0.432779 | + | 0.901500i | \(0.357533\pi\) | |||||||
\(770\) | 101.567 | 3.66022 | ||||||||
\(771\) | −66.1435 | −2.38210 | ||||||||
\(772\) | −116.002 | −4.17499 | ||||||||
\(773\) | 6.36333 | 0.228873 | 0.114437 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114437 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(774\) | −29.7934 | −1.07090 | ||||||||
\(775\) | 51.5252 | 1.85084 | ||||||||
\(776\) | 60.2296 | 2.16212 | ||||||||
\(777\) | 20.9353 | 0.751050 | ||||||||
\(778\) | 42.3972 | 1.52001 | ||||||||
\(779\) | 10.3757 | 0.371747 | ||||||||
\(780\) | 158.409 | 5.67195 | ||||||||
\(781\) | 0.0982396 | 0.00351529 | ||||||||
\(782\) | −69.0072 | −2.46769 | ||||||||
\(783\) | 16.6202 | 0.593959 | ||||||||
\(784\) | −36.7523 | −1.31258 | ||||||||
\(785\) | 51.9119 | 1.85282 | ||||||||
\(786\) | −13.9708 | −0.498321 | ||||||||
\(787\) | −24.8236 | −0.884867 | −0.442433 | − | 0.896801i | \(-0.645885\pi\) | ||||
−0.442433 | + | 0.896801i | \(0.645885\pi\) | |||||||
\(788\) | 26.8297 | 0.955770 | ||||||||
\(789\) | −26.1430 | −0.930716 | ||||||||
\(790\) | −150.084 | −5.33973 | ||||||||
\(791\) | 16.4211 | 0.583866 | ||||||||
\(792\) | −92.8968 | −3.30095 | ||||||||
\(793\) | −49.2415 | −1.74862 | ||||||||
\(794\) | −5.64559 | −0.200355 | ||||||||
\(795\) | −104.416 | −3.70324 | ||||||||
\(796\) | 55.2481 | 1.95822 | ||||||||
\(797\) | 22.6917 | 0.803782 | 0.401891 | − | 0.915688i | \(-0.368353\pi\) | ||||
0.401891 | + | 0.915688i | \(0.368353\pi\) | |||||||
\(798\) | −25.6787 | −0.909018 | ||||||||
\(799\) | −56.2800 | −1.99104 | ||||||||
\(800\) | −100.586 | −3.55624 | ||||||||
\(801\) | −28.2013 | −0.996443 | ||||||||
\(802\) | 57.5445 | 2.03197 | ||||||||
\(803\) | −49.1466 | −1.73435 | ||||||||
\(804\) | −136.939 | −4.82946 | ||||||||
\(805\) | 27.3646 | 0.964477 | ||||||||
\(806\) | 65.3694 | 2.30254 | ||||||||
\(807\) | 15.1856 | 0.534559 | ||||||||
\(808\) | −52.7464 | −1.85561 | ||||||||
\(809\) | −24.5496 | −0.863118 | −0.431559 | − | 0.902085i | \(-0.642036\pi\) | ||||
−0.431559 | + | 0.902085i | \(0.642036\pi\) | |||||||
\(810\) | −103.859 | −3.64924 | ||||||||
\(811\) | 32.2191 | 1.13137 | 0.565683 | − | 0.824623i | \(-0.308613\pi\) | ||||
0.565683 | + | 0.824623i | \(0.308613\pi\) | |||||||
\(812\) | −76.9273 | −2.69962 | ||||||||
\(813\) | 23.2221 | 0.814434 | ||||||||
\(814\) | −73.5170 | −2.57677 | ||||||||
\(815\) | −39.0485 | −1.36781 | ||||||||
\(816\) | −156.014 | −5.46157 | ||||||||
\(817\) | 12.2738 | 0.429407 | ||||||||
\(818\) | 85.8719 | 3.00244 | ||||||||
\(819\) | −15.5062 | −0.541832 | ||||||||
\(820\) | −81.1336 | −2.83331 | ||||||||
\(821\) | 18.7264 | 0.653556 | 0.326778 | − | 0.945101i | \(-0.394037\pi\) | ||||
0.326778 | + | 0.945101i | \(0.394037\pi\) | |||||||
\(822\) | 97.7703 | 3.41013 | ||||||||
\(823\) | 18.0706 | 0.629901 | 0.314950 | − | 0.949108i | \(-0.398012\pi\) | ||||
0.314950 | + | 0.949108i | \(0.398012\pi\) | |||||||
\(824\) | −23.6390 | −0.823505 | ||||||||
\(825\) | 103.912 | 3.61773 | ||||||||
\(826\) | 20.3796 | 0.709097 | ||||||||
\(827\) | 8.98012 | 0.312269 | 0.156135 | − | 0.987736i | \(-0.450097\pi\) | ||||
0.156135 | + | 0.987736i | \(0.450097\pi\) | |||||||
\(828\) | −42.0013 | −1.45965 | ||||||||
\(829\) | 17.2083 | 0.597668 | 0.298834 | − | 0.954305i | \(-0.403402\pi\) | ||||
0.298834 | + | 0.954305i | \(0.403402\pi\) | |||||||
\(830\) | −78.4905 | −2.72444 | ||||||||
\(831\) | −17.2421 | −0.598122 | ||||||||
\(832\) | −44.7776 | −1.55238 | ||||||||
\(833\) | 22.5848 | 0.782517 | ||||||||
\(834\) | 66.4495 | 2.30096 | ||||||||
\(835\) | 53.9427 | 1.86676 | ||||||||
\(836\) | 64.2223 | 2.22117 | ||||||||
\(837\) | −12.7501 | −0.440708 | ||||||||
\(838\) | 43.9776 | 1.51918 | ||||||||
\(839\) | 18.8624 | 0.651203 | 0.325601 | − | 0.945507i | \(-0.394433\pi\) | ||||
0.325601 | + | 0.945507i | \(0.394433\pi\) | |||||||
\(840\) | 119.656 | 4.12853 | ||||||||
\(841\) | 39.4020 | 1.35869 | ||||||||
\(842\) | −50.3806 | −1.73623 | ||||||||
\(843\) | 29.3696 | 1.01154 | ||||||||
\(844\) | 71.1215 | 2.44810 | ||||||||
\(845\) | −8.24142 | −0.283513 | ||||||||
\(846\) | −48.0971 | −1.65361 | ||||||||
\(847\) | 39.5272 | 1.35817 | ||||||||
\(848\) | 135.117 | 4.63995 | ||||||||
\(849\) | −12.5690 | −0.431368 | ||||||||
\(850\) | 139.411 | 4.78177 | ||||||||
\(851\) | −19.8073 | −0.678986 | ||||||||
\(852\) | 0.194220 | 0.00665385 | ||||||||
\(853\) | −16.1285 | −0.552229 | −0.276115 | − | 0.961125i | \(-0.589047\pi\) | ||||
−0.276115 | + | 0.961125i | \(0.589047\pi\) | |||||||
\(854\) | −62.4181 | −2.13590 | ||||||||
\(855\) | −17.5323 | −0.599593 | ||||||||
\(856\) | 131.943 | 4.50972 | ||||||||
\(857\) | 11.8324 | 0.404188 | 0.202094 | − | 0.979366i | \(-0.435225\pi\) | ||||
0.202094 | + | 0.979366i | \(0.435225\pi\) | |||||||
\(858\) | 131.831 | 4.50065 | ||||||||
\(859\) | 3.54913 | 0.121095 | 0.0605473 | − | 0.998165i | \(-0.480715\pi\) | ||||
0.0605473 | + | 0.998165i | \(0.480715\pi\) | |||||||
\(860\) | −95.9765 | −3.27277 | ||||||||
\(861\) | 19.2279 | 0.655285 | ||||||||
\(862\) | −4.57495 | −0.155823 | ||||||||
\(863\) | 13.5205 | 0.460242 | 0.230121 | − | 0.973162i | \(-0.426088\pi\) | ||||
0.230121 | + | 0.973162i | \(0.426088\pi\) | |||||||
\(864\) | 24.8903 | 0.846784 | ||||||||
\(865\) | 42.6882 | 1.45144 | ||||||||
\(866\) | 5.19999 | 0.176703 | ||||||||
\(867\) | 57.4393 | 1.95074 | ||||||||
\(868\) | 59.0142 | 2.00307 | ||||||||
\(869\) | −88.9560 | −3.01763 | ||||||||
\(870\) | −178.545 | −6.05323 | ||||||||
\(871\) | 47.8318 | 1.62072 | ||||||||
\(872\) | −28.1369 | −0.952836 | ||||||||
\(873\) | −16.3542 | −0.553506 | ||||||||
\(874\) | 24.2952 | 0.821797 | ||||||||
\(875\) | −21.2460 | −0.718246 | ||||||||
\(876\) | −97.1628 | −3.28283 | ||||||||
\(877\) | −40.3413 | −1.36223 | −0.681115 | − | 0.732177i | \(-0.738505\pi\) | ||||
−0.681115 | + | 0.732177i | \(0.738505\pi\) | |||||||
\(878\) | −62.0664 | −2.09464 | ||||||||
\(879\) | 20.9078 | 0.705202 | ||||||||
\(880\) | −217.253 | −7.32361 | ||||||||
\(881\) | 8.21663 | 0.276825 | 0.138413 | − | 0.990375i | \(-0.455800\pi\) | ||||
0.138413 | + | 0.990375i | \(0.455800\pi\) | |||||||
\(882\) | 19.3011 | 0.649900 | ||||||||
\(883\) | −11.3747 | −0.382789 | −0.191395 | − | 0.981513i | \(-0.561301\pi\) | ||||
−0.191395 | + | 0.981513i | \(0.561301\pi\) | |||||||
\(884\) | 125.967 | 4.23673 | ||||||||
\(885\) | 33.6872 | 1.13238 | ||||||||
\(886\) | 41.1240 | 1.38159 | ||||||||
\(887\) | 20.7635 | 0.697170 | 0.348585 | − | 0.937277i | \(-0.386662\pi\) | ||||
0.348585 | + | 0.937277i | \(0.386662\pi\) | |||||||
\(888\) | −86.6105 | −2.90646 | ||||||||
\(889\) | 26.6713 | 0.894526 | ||||||||
\(890\) | −127.559 | −4.27579 | ||||||||
\(891\) | −61.5584 | −2.06228 | ||||||||
\(892\) | −125.413 | −4.19912 | ||||||||
\(893\) | 19.8143 | 0.663062 | ||||||||
\(894\) | 86.3042 | 2.88644 | ||||||||
\(895\) | −92.6016 | −3.09533 | ||||||||
\(896\) | −10.2055 | −0.340942 | ||||||||
\(897\) | 35.5186 | 1.18593 | ||||||||
\(898\) | 29.5905 | 0.987447 | ||||||||
\(899\) | −52.4741 | −1.75011 | ||||||||
\(900\) | 84.8529 | 2.82843 | ||||||||
\(901\) | −83.0314 | −2.76618 | ||||||||
\(902\) | −67.5212 | −2.24821 | ||||||||
\(903\) | 22.7455 | 0.756923 | ||||||||
\(904\) | −67.9349 | −2.25948 | ||||||||
\(905\) | −52.9718 | −1.76084 | ||||||||
\(906\) | 39.6121 | 1.31602 | ||||||||
\(907\) | −4.82059 | −0.160065 | −0.0800325 | − | 0.996792i | \(-0.525502\pi\) | ||||
−0.0800325 | + | 0.996792i | \(0.525502\pi\) | |||||||
\(908\) | 36.7500 | 1.21959 | ||||||||
\(909\) | 14.3223 | 0.475041 | ||||||||
\(910\) | −70.1373 | −2.32503 | ||||||||
\(911\) | −32.5713 | −1.07914 | −0.539568 | − | 0.841942i | \(-0.681412\pi\) | ||||
−0.539568 | + | 0.841942i | \(0.681412\pi\) | |||||||
\(912\) | 54.9273 | 1.81883 | ||||||||
\(913\) | −46.5221 | −1.53966 | ||||||||
\(914\) | 49.3560 | 1.63255 | ||||||||
\(915\) | −103.176 | −3.41090 | ||||||||
\(916\) | 71.1640 | 2.35132 | ||||||||
\(917\) | 4.40547 | 0.145481 | ||||||||
\(918\) | −34.4978 | −1.13860 | ||||||||
\(919\) | −16.5653 | −0.546440 | −0.273220 | − | 0.961952i | \(-0.588089\pi\) | ||||
−0.273220 | + | 0.961952i | \(0.588089\pi\) | |||||||
\(920\) | −113.209 | −3.73239 | ||||||||
\(921\) | 34.8649 | 1.14884 | ||||||||
\(922\) | 48.8747 | 1.60960 | ||||||||
\(923\) | −0.0678396 | −0.00223297 | ||||||||
\(924\) | 119.015 | 3.91530 | ||||||||
\(925\) | 40.0156 | 1.31571 | ||||||||
\(926\) | 64.1480 | 2.10803 | ||||||||
\(927\) | 6.41874 | 0.210819 | ||||||||
\(928\) | 102.438 | 3.36269 | ||||||||
\(929\) | 13.3972 | 0.439547 | 0.219774 | − | 0.975551i | \(-0.429468\pi\) | ||||
0.219774 | + | 0.975551i | \(0.429468\pi\) | |||||||
\(930\) | 136.969 | 4.49139 | ||||||||
\(931\) | −7.95137 | −0.260595 | ||||||||
\(932\) | −22.3501 | −0.732100 | ||||||||
\(933\) | −1.02733 | −0.0336333 | ||||||||
\(934\) | −54.2088 | −1.77376 | ||||||||
\(935\) | 133.505 | 4.36609 | ||||||||
\(936\) | 64.1502 | 2.09681 | ||||||||
\(937\) | 14.8426 | 0.484885 | 0.242443 | − | 0.970166i | \(-0.422051\pi\) | ||||
0.242443 | + | 0.970166i | \(0.422051\pi\) | |||||||
\(938\) | 60.6311 | 1.97968 | ||||||||
\(939\) | 20.6914 | 0.675239 | ||||||||
\(940\) | −154.940 | −5.05359 | ||||||||
\(941\) | −52.3156 | −1.70544 | −0.852719 | − | 0.522369i | \(-0.825048\pi\) | ||||
−0.852719 | + | 0.522369i | \(0.825048\pi\) | |||||||
\(942\) | 85.4107 | 2.78283 | ||||||||
\(943\) | −18.1919 | −0.592409 | ||||||||
\(944\) | −43.5923 | −1.41881 | ||||||||
\(945\) | 13.6800 | 0.445012 | ||||||||
\(946\) | −79.8737 | −2.59692 | ||||||||
\(947\) | 37.1252 | 1.20641 | 0.603204 | − | 0.797587i | \(-0.293890\pi\) | ||||
0.603204 | + | 0.797587i | \(0.293890\pi\) | |||||||
\(948\) | −175.866 | −5.71186 | ||||||||
\(949\) | 33.9383 | 1.10169 | ||||||||
\(950\) | −49.0822 | −1.59244 | ||||||||
\(951\) | 32.5257 | 1.05472 | ||||||||
\(952\) | 95.1506 | 3.08385 | ||||||||
\(953\) | −24.3215 | −0.787851 | −0.393926 | − | 0.919142i | \(-0.628883\pi\) | ||||
−0.393926 | + | 0.919142i | \(0.628883\pi\) | |||||||
\(954\) | −70.9590 | −2.29738 | ||||||||
\(955\) | 58.5013 | 1.89306 | ||||||||
\(956\) | −17.5045 | −0.566136 | ||||||||
\(957\) | −105.825 | −3.42084 | ||||||||
\(958\) | 87.2304 | 2.81829 | ||||||||
\(959\) | −30.8304 | −0.995566 | ||||||||
\(960\) | −93.8228 | −3.02812 | ||||||||
\(961\) | 9.25510 | 0.298551 | ||||||||
\(962\) | 50.7674 | 1.63681 | ||||||||
\(963\) | −35.8267 | −1.15450 | ||||||||
\(964\) | −5.52524 | −0.177956 | ||||||||
\(965\) | 84.8991 | 2.73300 | ||||||||
\(966\) | 45.0231 | 1.44859 | ||||||||
\(967\) | 14.4070 | 0.463297 | 0.231649 | − | 0.972800i | \(-0.425588\pi\) | ||||
0.231649 | + | 0.972800i | \(0.425588\pi\) | |||||||
\(968\) | −163.526 | −5.25592 | ||||||||
\(969\) | −33.7536 | −1.08432 | ||||||||
\(970\) | −73.9728 | −2.37512 | ||||||||
\(971\) | −7.10457 | −0.227996 | −0.113998 | − | 0.993481i | \(-0.536366\pi\) | ||||
−0.113998 | + | 0.993481i | \(0.536366\pi\) | |||||||
\(972\) | −91.8629 | −2.94650 | ||||||||
\(973\) | −20.9539 | −0.671750 | ||||||||
\(974\) | 16.8801 | 0.540875 | ||||||||
\(975\) | −71.7564 | −2.29804 | ||||||||
\(976\) | 133.513 | 4.27366 | ||||||||
\(977\) | −6.44172 | −0.206089 | −0.103044 | − | 0.994677i | \(-0.532858\pi\) | ||||
−0.103044 | + | 0.994677i | \(0.532858\pi\) | |||||||
\(978\) | −64.2466 | −2.05438 | ||||||||
\(979\) | −75.6055 | −2.41636 | ||||||||
\(980\) | 62.1765 | 1.98616 | ||||||||
\(981\) | 7.64005 | 0.243928 | ||||||||
\(982\) | 45.1184 | 1.43979 | ||||||||
\(983\) | −36.7902 | −1.17343 | −0.586713 | − | 0.809795i | \(-0.699578\pi\) | ||||
−0.586713 | + | 0.809795i | \(0.699578\pi\) | |||||||
\(984\) | −79.5468 | −2.53586 | ||||||||
\(985\) | −19.6361 | −0.625658 | ||||||||
\(986\) | −141.979 | −4.52153 | ||||||||
\(987\) | 36.7193 | 1.16879 | ||||||||
\(988\) | −44.3488 | −1.41092 | ||||||||
\(989\) | −21.5200 | −0.684295 | ||||||||
\(990\) | 114.094 | 3.62615 | ||||||||
\(991\) | 9.15927 | 0.290954 | 0.145477 | − | 0.989362i | \(-0.453528\pi\) | ||||
0.145477 | + | 0.989362i | \(0.453528\pi\) | |||||||
\(992\) | −78.5845 | −2.49506 | ||||||||
\(993\) | −41.4410 | −1.31509 | ||||||||
\(994\) | −0.0859928 | −0.00272753 | ||||||||
\(995\) | −40.4348 | −1.28187 | ||||||||
\(996\) | −91.9741 | −2.91431 | ||||||||
\(997\) | −32.3907 | −1.02583 | −0.512913 | − | 0.858441i | \(-0.671433\pi\) | ||||
−0.512913 | + | 0.858441i | \(0.671433\pi\) | |||||||
\(998\) | 19.3396 | 0.612184 | ||||||||
\(999\) | −9.90201 | −0.313286 |
(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 | 6037.2.a.a.1.15 | ✓ | 243 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.a.1.15 | ✓ | 243 | 1.1 | even | 1 | trivial |