Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73023 | −1.93056 | −0.965281 | − | 0.261212i | \(-0.915878\pi\) | ||||
−0.965281 | + | 0.261212i | \(0.915878\pi\) | |||||||
\(3\) | −3.10574 | −1.79310 | −0.896550 | − | 0.442943i | \(-0.853934\pi\) | ||||
−0.896550 | + | 0.442943i | \(0.853934\pi\) | |||||||
\(4\) | 5.45415 | 2.72707 | ||||||||
\(5\) | −3.71411 | −1.66100 | −0.830500 | − | 0.557019i | \(-0.811945\pi\) | ||||
−0.830500 | + | 0.557019i | \(0.811945\pi\) | |||||||
\(6\) | 8.47938 | 3.46169 | ||||||||
\(7\) | 1.88828 | 0.713702 | 0.356851 | − | 0.934161i | \(-0.383850\pi\) | ||||
0.356851 | + | 0.934161i | \(0.383850\pi\) | |||||||
\(8\) | −9.43061 | −3.33422 | ||||||||
\(9\) | 6.64562 | 2.21521 | ||||||||
\(10\) | 10.1404 | 3.20666 | ||||||||
\(11\) | 0.489363 | 0.147549 | 0.0737743 | − | 0.997275i | \(-0.476496\pi\) | ||||
0.0737743 | + | 0.997275i | \(0.476496\pi\) | |||||||
\(12\) | −16.9392 | −4.88991 | ||||||||
\(13\) | 5.48712 | 1.52185 | 0.760927 | − | 0.648838i | \(-0.224745\pi\) | ||||
0.760927 | + | 0.648838i | \(0.224745\pi\) | |||||||
\(14\) | −5.15543 | −1.37785 | ||||||||
\(15\) | 11.5351 | 2.97834 | ||||||||
\(16\) | 14.8394 | 3.70986 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −18.1441 | −4.27660 | ||||||||
\(19\) | −0.332704 | −0.0763276 | −0.0381638 | − | 0.999271i | \(-0.512151\pi\) | ||||
−0.0381638 | + | 0.999271i | \(0.512151\pi\) | |||||||
\(20\) | −20.2573 | −4.52967 | ||||||||
\(21\) | −5.86450 | −1.27974 | ||||||||
\(22\) | −1.33607 | −0.284852 | ||||||||
\(23\) | 8.82357 | 1.83984 | 0.919921 | − | 0.392104i | \(-0.128253\pi\) | ||||
0.919921 | + | 0.392104i | \(0.128253\pi\) | |||||||
\(24\) | 29.2890 | 5.97860 | ||||||||
\(25\) | 8.79459 | 1.75892 | ||||||||
\(26\) | −14.9811 | −2.93803 | ||||||||
\(27\) | −11.3223 | −2.17899 | ||||||||
\(28\) | 10.2989 | 1.94632 | ||||||||
\(29\) | 0.482276 | 0.0895564 | 0.0447782 | − | 0.998997i | \(-0.485742\pi\) | ||||
0.0447782 | + | 0.998997i | \(0.485742\pi\) | |||||||
\(30\) | −31.4933 | −5.74987 | ||||||||
\(31\) | −5.74916 | −1.03258 | −0.516290 | − | 0.856414i | \(-0.672687\pi\) | ||||
−0.516290 | + | 0.856414i | \(0.672687\pi\) | |||||||
\(32\) | −21.6538 | −3.82789 | ||||||||
\(33\) | −1.51984 | −0.264569 | ||||||||
\(34\) | −2.73023 | −0.468230 | ||||||||
\(35\) | −7.01326 | −1.18546 | ||||||||
\(36\) | 36.2462 | 6.04103 | ||||||||
\(37\) | 8.83875 | 1.45308 | 0.726541 | − | 0.687124i | \(-0.241127\pi\) | ||||
0.726541 | + | 0.687124i | \(0.241127\pi\) | |||||||
\(38\) | 0.908359 | 0.147355 | ||||||||
\(39\) | −17.0416 | −2.72883 | ||||||||
\(40\) | 35.0263 | 5.53814 | ||||||||
\(41\) | −4.82872 | −0.754120 | −0.377060 | − | 0.926189i | \(-0.623065\pi\) | ||||
−0.377060 | + | 0.926189i | \(0.623065\pi\) | |||||||
\(42\) | 16.0114 | 2.47061 | ||||||||
\(43\) | 4.70608 | 0.717671 | 0.358836 | − | 0.933401i | \(-0.383174\pi\) | ||||
0.358836 | + | 0.933401i | \(0.383174\pi\) | |||||||
\(44\) | 2.66906 | 0.402376 | ||||||||
\(45\) | −24.6825 | −3.67946 | ||||||||
\(46\) | −24.0904 | −3.55193 | ||||||||
\(47\) | −9.37780 | −1.36789 | −0.683947 | − | 0.729532i | \(-0.739738\pi\) | ||||
−0.683947 | + | 0.729532i | \(0.739738\pi\) | |||||||
\(48\) | −46.0874 | −6.65214 | ||||||||
\(49\) | −3.43441 | −0.490630 | ||||||||
\(50\) | −24.0112 | −3.39570 | ||||||||
\(51\) | −3.10574 | −0.434891 | ||||||||
\(52\) | 29.9276 | 4.15021 | ||||||||
\(53\) | 6.17027 | 0.847552 | 0.423776 | − | 0.905767i | \(-0.360704\pi\) | ||||
0.423776 | + | 0.905767i | \(0.360704\pi\) | |||||||
\(54\) | 30.9126 | 4.20667 | ||||||||
\(55\) | −1.81755 | −0.245078 | ||||||||
\(56\) | −17.8076 | −2.37964 | ||||||||
\(57\) | 1.03329 | 0.136863 | ||||||||
\(58\) | −1.31672 | −0.172894 | ||||||||
\(59\) | 1.46121 | 0.190234 | 0.0951170 | − | 0.995466i | \(-0.469677\pi\) | ||||
0.0951170 | + | 0.995466i | \(0.469677\pi\) | |||||||
\(60\) | 62.9139 | 8.12214 | ||||||||
\(61\) | −6.01970 | −0.770744 | −0.385372 | − | 0.922761i | \(-0.625927\pi\) | ||||
−0.385372 | + | 0.922761i | \(0.625927\pi\) | |||||||
\(62\) | 15.6965 | 1.99346 | ||||||||
\(63\) | 12.5488 | 1.58100 | ||||||||
\(64\) | 29.4409 | 3.68012 | ||||||||
\(65\) | −20.3798 | −2.52780 | ||||||||
\(66\) | 4.14950 | 0.510768 | ||||||||
\(67\) | 6.95743 | 0.849986 | 0.424993 | − | 0.905197i | \(-0.360277\pi\) | ||||
0.424993 | + | 0.905197i | \(0.360277\pi\) | |||||||
\(68\) | 5.45415 | 0.661412 | ||||||||
\(69\) | −27.4037 | −3.29902 | ||||||||
\(70\) | 19.1478 | 2.28860 | ||||||||
\(71\) | −10.4009 | −1.23436 | −0.617181 | − | 0.786821i | \(-0.711726\pi\) | ||||
−0.617181 | + | 0.786821i | \(0.711726\pi\) | |||||||
\(72\) | −62.6722 | −7.38599 | ||||||||
\(73\) | −14.5071 | −1.69793 | −0.848963 | − | 0.528452i | \(-0.822773\pi\) | ||||
−0.848963 | + | 0.528452i | \(0.822773\pi\) | |||||||
\(74\) | −24.1318 | −2.80526 | ||||||||
\(75\) | −27.3137 | −3.15392 | ||||||||
\(76\) | −1.81462 | −0.208151 | ||||||||
\(77\) | 0.924054 | 0.105306 | ||||||||
\(78\) | 46.5274 | 5.26819 | ||||||||
\(79\) | 3.18488 | 0.358327 | 0.179163 | − | 0.983819i | \(-0.442661\pi\) | ||||
0.179163 | + | 0.983819i | \(0.442661\pi\) | |||||||
\(80\) | −55.1152 | −6.16207 | ||||||||
\(81\) | 15.2274 | 1.69193 | ||||||||
\(82\) | 13.1835 | 1.45588 | ||||||||
\(83\) | −7.61897 | −0.836290 | −0.418145 | − | 0.908380i | \(-0.637320\pi\) | ||||
−0.418145 | + | 0.908380i | \(0.637320\pi\) | |||||||
\(84\) | −31.9858 | −3.48994 | ||||||||
\(85\) | −3.71411 | −0.402852 | ||||||||
\(86\) | −12.8487 | −1.38551 | ||||||||
\(87\) | −1.49782 | −0.160583 | ||||||||
\(88\) | −4.61500 | −0.491960 | ||||||||
\(89\) | −10.6162 | −1.12531 | −0.562657 | − | 0.826690i | \(-0.690221\pi\) | ||||
−0.562657 | + | 0.826690i | \(0.690221\pi\) | |||||||
\(90\) | 67.3890 | 7.10342 | ||||||||
\(91\) | 10.3612 | 1.08615 | ||||||||
\(92\) | 48.1250 | 5.01738 | ||||||||
\(93\) | 17.8554 | 1.85152 | ||||||||
\(94\) | 25.6035 | 2.64080 | ||||||||
\(95\) | 1.23570 | 0.126780 | ||||||||
\(96\) | 67.2510 | 6.86378 | ||||||||
\(97\) | −13.5666 | −1.37747 | −0.688737 | − | 0.725011i | \(-0.741835\pi\) | ||||
−0.688737 | + | 0.725011i | \(0.741835\pi\) | |||||||
\(98\) | 9.37672 | 0.947192 | ||||||||
\(99\) | 3.25212 | 0.326851 | ||||||||
\(100\) | 47.9670 | 4.79670 | ||||||||
\(101\) | 17.6559 | 1.75682 | 0.878412 | − | 0.477905i | \(-0.158604\pi\) | ||||
0.878412 | + | 0.477905i | \(0.158604\pi\) | |||||||
\(102\) | 8.47938 | 0.839584 | ||||||||
\(103\) | 5.54877 | 0.546737 | 0.273368 | − | 0.961909i | \(-0.411862\pi\) | ||||
0.273368 | + | 0.961909i | \(0.411862\pi\) | |||||||
\(104\) | −51.7469 | −5.07420 | ||||||||
\(105\) | 21.7814 | 2.12564 | ||||||||
\(106\) | −16.8462 | −1.63625 | ||||||||
\(107\) | −6.62995 | −0.640942 | −0.320471 | − | 0.947258i | \(-0.603841\pi\) | ||||
−0.320471 | + | 0.947258i | \(0.603841\pi\) | |||||||
\(108\) | −61.7537 | −5.94225 | ||||||||
\(109\) | 3.56639 | 0.341598 | 0.170799 | − | 0.985306i | \(-0.445365\pi\) | ||||
0.170799 | + | 0.985306i | \(0.445365\pi\) | |||||||
\(110\) | 4.96232 | 0.473139 | ||||||||
\(111\) | −27.4508 | −2.60552 | ||||||||
\(112\) | 28.0209 | 2.64773 | ||||||||
\(113\) | 12.7847 | 1.20268 | 0.601341 | − | 0.798993i | \(-0.294633\pi\) | ||||
0.601341 | + | 0.798993i | \(0.294633\pi\) | |||||||
\(114\) | −2.82113 | −0.264223 | ||||||||
\(115\) | −32.7717 | −3.05598 | ||||||||
\(116\) | 2.63040 | 0.244227 | ||||||||
\(117\) | 36.4653 | 3.37122 | ||||||||
\(118\) | −3.98945 | −0.367259 | ||||||||
\(119\) | 1.88828 | 0.173098 | ||||||||
\(120\) | −108.783 | −9.93044 | ||||||||
\(121\) | −10.7605 | −0.978229 | ||||||||
\(122\) | 16.4352 | 1.48797 | ||||||||
\(123\) | 14.9968 | 1.35221 | ||||||||
\(124\) | −31.3568 | −2.81592 | ||||||||
\(125\) | −14.0935 | −1.26056 | ||||||||
\(126\) | −34.2610 | −3.05221 | ||||||||
\(127\) | 4.13427 | 0.366857 | 0.183428 | − | 0.983033i | \(-0.441280\pi\) | ||||
0.183428 | + | 0.983033i | \(0.441280\pi\) | |||||||
\(128\) | −37.0729 | −3.27682 | ||||||||
\(129\) | −14.6159 | −1.28686 | ||||||||
\(130\) | 55.6414 | 4.88007 | ||||||||
\(131\) | −2.51700 | −0.219911 | −0.109956 | − | 0.993937i | \(-0.535071\pi\) | ||||
−0.109956 | + | 0.993937i | \(0.535071\pi\) | |||||||
\(132\) | −8.28941 | −0.721500 | ||||||||
\(133\) | −0.628238 | −0.0544751 | ||||||||
\(134\) | −18.9954 | −1.64095 | ||||||||
\(135\) | 42.0524 | 3.61929 | ||||||||
\(136\) | −9.43061 | −0.808668 | ||||||||
\(137\) | −4.34490 | −0.371210 | −0.185605 | − | 0.982624i | \(-0.559424\pi\) | ||||
−0.185605 | + | 0.982624i | \(0.559424\pi\) | |||||||
\(138\) | 74.8184 | 6.36896 | ||||||||
\(139\) | −14.4175 | −1.22287 | −0.611437 | − | 0.791293i | \(-0.709408\pi\) | ||||
−0.611437 | + | 0.791293i | \(0.709408\pi\) | |||||||
\(140\) | −38.2514 | −3.23283 | ||||||||
\(141\) | 29.1250 | 2.45277 | ||||||||
\(142\) | 28.3969 | 2.38302 | ||||||||
\(143\) | 2.68520 | 0.224547 | ||||||||
\(144\) | 98.6171 | 8.21810 | ||||||||
\(145\) | −1.79122 | −0.148753 | ||||||||
\(146\) | 39.6077 | 3.27795 | ||||||||
\(147\) | 10.6664 | 0.879748 | ||||||||
\(148\) | 48.2078 | 3.96266 | ||||||||
\(149\) | 8.91601 | 0.730428 | 0.365214 | − | 0.930924i | \(-0.380996\pi\) | ||||
0.365214 | + | 0.930924i | \(0.380996\pi\) | |||||||
\(150\) | 74.5727 | 6.08883 | ||||||||
\(151\) | −23.3970 | −1.90402 | −0.952012 | − | 0.306062i | \(-0.900988\pi\) | ||||
−0.952012 | + | 0.306062i | \(0.900988\pi\) | |||||||
\(152\) | 3.13760 | 0.254493 | ||||||||
\(153\) | 6.64562 | 0.537266 | ||||||||
\(154\) | −2.52288 | −0.203299 | ||||||||
\(155\) | 21.3530 | 1.71511 | ||||||||
\(156\) | −92.9472 | −7.44173 | ||||||||
\(157\) | −7.57057 | −0.604197 | −0.302098 | − | 0.953277i | \(-0.597687\pi\) | ||||
−0.302098 | + | 0.953277i | \(0.597687\pi\) | |||||||
\(158\) | −8.69545 | −0.691773 | ||||||||
\(159\) | −19.1633 | −1.51974 | ||||||||
\(160\) | 80.4245 | 6.35812 | ||||||||
\(161\) | 16.6613 | 1.31310 | ||||||||
\(162\) | −41.5743 | −3.26638 | ||||||||
\(163\) | −22.9019 | −1.79381 | −0.896907 | − | 0.442219i | \(-0.854192\pi\) | ||||
−0.896907 | + | 0.442219i | \(0.854192\pi\) | |||||||
\(164\) | −26.3366 | −2.05654 | ||||||||
\(165\) | 5.64483 | 0.439450 | ||||||||
\(166\) | 20.8015 | 1.61451 | ||||||||
\(167\) | −5.06068 | −0.391607 | −0.195803 | − | 0.980643i | \(-0.562731\pi\) | ||||
−0.195803 | + | 0.980643i | \(0.562731\pi\) | |||||||
\(168\) | 55.3058 | 4.26693 | ||||||||
\(169\) | 17.1085 | 1.31604 | ||||||||
\(170\) | 10.1404 | 0.777730 | ||||||||
\(171\) | −2.21103 | −0.169081 | ||||||||
\(172\) | 25.6677 | 1.95714 | ||||||||
\(173\) | 14.9806 | 1.13895 | 0.569477 | − | 0.822007i | \(-0.307146\pi\) | ||||
0.569477 | + | 0.822007i | \(0.307146\pi\) | |||||||
\(174\) | 4.08940 | 0.310017 | ||||||||
\(175\) | 16.6066 | 1.25534 | ||||||||
\(176\) | 7.26187 | 0.547384 | ||||||||
\(177\) | −4.53815 | −0.341108 | ||||||||
\(178\) | 28.9846 | 2.17249 | ||||||||
\(179\) | −2.28495 | −0.170785 | −0.0853924 | − | 0.996347i | \(-0.527214\pi\) | ||||
−0.0853924 | + | 0.996347i | \(0.527214\pi\) | |||||||
\(180\) | −134.622 | −10.0341 | ||||||||
\(181\) | −9.98093 | −0.741877 | −0.370938 | − | 0.928657i | \(-0.620964\pi\) | ||||
−0.370938 | + | 0.928657i | \(0.620964\pi\) | |||||||
\(182\) | −28.2885 | −2.09688 | ||||||||
\(183\) | 18.6956 | 1.38202 | ||||||||
\(184\) | −83.2116 | −6.13444 | ||||||||
\(185\) | −32.8281 | −2.41357 | ||||||||
\(186\) | −48.7493 | −3.57447 | ||||||||
\(187\) | 0.489363 | 0.0357858 | ||||||||
\(188\) | −51.1479 | −3.73035 | ||||||||
\(189\) | −21.3797 | −1.55515 | ||||||||
\(190\) | −3.37374 | −0.244757 | ||||||||
\(191\) | 9.37472 | 0.678331 | 0.339166 | − | 0.940727i | \(-0.389855\pi\) | ||||
0.339166 | + | 0.940727i | \(0.389855\pi\) | |||||||
\(192\) | −91.4359 | −6.59882 | ||||||||
\(193\) | −3.57459 | −0.257305 | −0.128652 | − | 0.991690i | \(-0.541065\pi\) | ||||
−0.128652 | + | 0.991690i | \(0.541065\pi\) | |||||||
\(194\) | 37.0398 | 2.65930 | ||||||||
\(195\) | 63.2942 | 4.53259 | ||||||||
\(196\) | −18.7318 | −1.33798 | ||||||||
\(197\) | −3.72825 | −0.265627 | −0.132814 | − | 0.991141i | \(-0.542401\pi\) | ||||
−0.132814 | + | 0.991141i | \(0.542401\pi\) | |||||||
\(198\) | −8.87904 | −0.631006 | ||||||||
\(199\) | 16.2589 | 1.15257 | 0.576283 | − | 0.817250i | \(-0.304503\pi\) | ||||
0.576283 | + | 0.817250i | \(0.304503\pi\) | |||||||
\(200\) | −82.9384 | −5.86463 | ||||||||
\(201\) | −21.6080 | −1.52411 | ||||||||
\(202\) | −48.2045 | −3.39166 | ||||||||
\(203\) | 0.910670 | 0.0639165 | ||||||||
\(204\) | −16.9392 | −1.18598 | ||||||||
\(205\) | 17.9344 | 1.25259 | ||||||||
\(206\) | −15.1494 | −1.05551 | ||||||||
\(207\) | 58.6381 | 4.07563 | ||||||||
\(208\) | 81.4257 | 5.64586 | ||||||||
\(209\) | −0.162813 | −0.0112620 | ||||||||
\(210\) | −59.4681 | −4.10369 | ||||||||
\(211\) | −17.6162 | −1.21275 | −0.606375 | − | 0.795179i | \(-0.707377\pi\) | ||||
−0.606375 | + | 0.795179i | \(0.707377\pi\) | |||||||
\(212\) | 33.6536 | 2.31134 | ||||||||
\(213\) | 32.3026 | 2.21334 | ||||||||
\(214\) | 18.1013 | 1.23738 | ||||||||
\(215\) | −17.4789 | −1.19205 | ||||||||
\(216\) | 106.777 | 7.26523 | ||||||||
\(217\) | −10.8560 | −0.736954 | ||||||||
\(218\) | −9.73705 | −0.659476 | ||||||||
\(219\) | 45.0552 | 3.04455 | ||||||||
\(220\) | −9.91318 | −0.668346 | ||||||||
\(221\) | 5.48712 | 0.369104 | ||||||||
\(222\) | 74.9471 | 5.03012 | ||||||||
\(223\) | 21.3039 | 1.42662 | 0.713308 | − | 0.700851i | \(-0.247196\pi\) | ||||
0.713308 | + | 0.700851i | \(0.247196\pi\) | |||||||
\(224\) | −40.8884 | −2.73197 | ||||||||
\(225\) | 58.4455 | 3.89637 | ||||||||
\(226\) | −34.9051 | −2.32185 | ||||||||
\(227\) | −23.3592 | −1.55040 | −0.775201 | − | 0.631715i | \(-0.782351\pi\) | ||||
−0.775201 | + | 0.631715i | \(0.782351\pi\) | |||||||
\(228\) | 5.63573 | 0.373236 | ||||||||
\(229\) | 24.0406 | 1.58865 | 0.794324 | − | 0.607494i | \(-0.207825\pi\) | ||||
0.794324 | + | 0.607494i | \(0.207825\pi\) | |||||||
\(230\) | 89.4742 | 5.89975 | ||||||||
\(231\) | −2.86987 | −0.188824 | ||||||||
\(232\) | −4.54815 | −0.298601 | ||||||||
\(233\) | 24.7168 | 1.61925 | 0.809626 | − | 0.586946i | \(-0.199670\pi\) | ||||
0.809626 | + | 0.586946i | \(0.199670\pi\) | |||||||
\(234\) | −99.5586 | −6.50835 | ||||||||
\(235\) | 34.8302 | 2.27207 | ||||||||
\(236\) | 7.96968 | 0.518782 | ||||||||
\(237\) | −9.89141 | −0.642516 | ||||||||
\(238\) | −5.15543 | −0.334177 | ||||||||
\(239\) | 15.3728 | 0.994386 | 0.497193 | − | 0.867640i | \(-0.334364\pi\) | ||||
0.497193 | + | 0.867640i | \(0.334364\pi\) | |||||||
\(240\) | 171.173 | 11.0492 | ||||||||
\(241\) | −2.36423 | −0.152294 | −0.0761468 | − | 0.997097i | \(-0.524262\pi\) | ||||
−0.0761468 | + | 0.997097i | \(0.524262\pi\) | |||||||
\(242\) | 29.3787 | 1.88853 | ||||||||
\(243\) | −13.3253 | −0.854818 | ||||||||
\(244\) | −32.8323 | −2.10187 | ||||||||
\(245\) | 12.7558 | 0.814936 | ||||||||
\(246\) | −40.9446 | −2.61053 | ||||||||
\(247\) | −1.82559 | −0.116159 | ||||||||
\(248\) | 54.2181 | 3.44285 | ||||||||
\(249\) | 23.6625 | 1.49955 | ||||||||
\(250\) | 38.4785 | 2.43360 | ||||||||
\(251\) | −4.03403 | −0.254626 | −0.127313 | − | 0.991863i | \(-0.540635\pi\) | ||||
−0.127313 | + | 0.991863i | \(0.540635\pi\) | |||||||
\(252\) | 68.4428 | 4.31149 | ||||||||
\(253\) | 4.31793 | 0.271466 | ||||||||
\(254\) | −11.2875 | −0.708240 | ||||||||
\(255\) | 11.5351 | 0.722353 | ||||||||
\(256\) | 42.3357 | 2.64598 | ||||||||
\(257\) | −20.6869 | −1.29041 | −0.645207 | − | 0.764008i | \(-0.723229\pi\) | ||||
−0.645207 | + | 0.764008i | \(0.723229\pi\) | |||||||
\(258\) | 39.9047 | 2.48436 | ||||||||
\(259\) | 16.6900 | 1.03707 | ||||||||
\(260\) | −111.154 | −6.89349 | ||||||||
\(261\) | 3.20502 | 0.198386 | ||||||||
\(262\) | 6.87198 | 0.424552 | ||||||||
\(263\) | 4.81240 | 0.296745 | 0.148373 | − | 0.988932i | \(-0.452597\pi\) | ||||
0.148373 | + | 0.988932i | \(0.452597\pi\) | |||||||
\(264\) | 14.3330 | 0.882134 | ||||||||
\(265\) | −22.9170 | −1.40778 | ||||||||
\(266\) | 1.71523 | 0.105168 | ||||||||
\(267\) | 32.9711 | 2.01780 | ||||||||
\(268\) | 37.9469 | 2.31797 | ||||||||
\(269\) | −21.4166 | −1.30579 | −0.652896 | − | 0.757448i | \(-0.726446\pi\) | ||||
−0.652896 | + | 0.757448i | \(0.726446\pi\) | |||||||
\(270\) | −114.813 | −6.98728 | ||||||||
\(271\) | 9.59117 | 0.582622 | 0.291311 | − | 0.956628i | \(-0.405908\pi\) | ||||
0.291311 | + | 0.956628i | \(0.405908\pi\) | |||||||
\(272\) | 14.8394 | 0.899772 | ||||||||
\(273\) | −32.1792 | −1.94757 | ||||||||
\(274\) | 11.8626 | 0.716644 | ||||||||
\(275\) | 4.30375 | 0.259526 | ||||||||
\(276\) | −149.464 | −8.99667 | ||||||||
\(277\) | 25.2227 | 1.51549 | 0.757744 | − | 0.652552i | \(-0.226302\pi\) | ||||
0.757744 | + | 0.652552i | \(0.226302\pi\) | |||||||
\(278\) | 39.3630 | 2.36084 | ||||||||
\(279\) | −38.2067 | −2.28738 | ||||||||
\(280\) | 66.1393 | 3.95258 | ||||||||
\(281\) | −28.2834 | −1.68725 | −0.843623 | − | 0.536935i | \(-0.819582\pi\) | ||||
−0.843623 | + | 0.536935i | \(0.819582\pi\) | |||||||
\(282\) | −79.5179 | −4.73523 | ||||||||
\(283\) | −6.79798 | −0.404098 | −0.202049 | − | 0.979375i | \(-0.564760\pi\) | ||||
−0.202049 | + | 0.979375i | \(0.564760\pi\) | |||||||
\(284\) | −56.7282 | −3.36620 | ||||||||
\(285\) | −3.83776 | −0.227329 | ||||||||
\(286\) | −7.33120 | −0.433503 | ||||||||
\(287\) | −9.11797 | −0.538217 | ||||||||
\(288\) | −143.903 | −8.47956 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 4.89045 | 0.287177 | ||||||||
\(291\) | 42.1342 | 2.46995 | ||||||||
\(292\) | −79.1238 | −4.63037 | ||||||||
\(293\) | 25.8654 | 1.51107 | 0.755536 | − | 0.655107i | \(-0.227376\pi\) | ||||
0.755536 | + | 0.655107i | \(0.227376\pi\) | |||||||
\(294\) | −29.1217 | −1.69841 | ||||||||
\(295\) | −5.42711 | −0.315978 | ||||||||
\(296\) | −83.3548 | −4.84490 | ||||||||
\(297\) | −5.54074 | −0.321506 | ||||||||
\(298\) | −24.3427 | −1.41014 | ||||||||
\(299\) | 48.4160 | 2.79997 | ||||||||
\(300\) | −148.973 | −8.60096 | ||||||||
\(301\) | 8.88639 | 0.512203 | ||||||||
\(302\) | 63.8792 | 3.67584 | ||||||||
\(303\) | −54.8345 | −3.15016 | ||||||||
\(304\) | −4.93714 | −0.283164 | ||||||||
\(305\) | 22.3578 | 1.28020 | ||||||||
\(306\) | −18.1441 | −1.03723 | ||||||||
\(307\) | −2.79061 | −0.159268 | −0.0796342 | − | 0.996824i | \(-0.525375\pi\) | ||||
−0.0796342 | + | 0.996824i | \(0.525375\pi\) | |||||||
\(308\) | 5.03992 | 0.287176 | ||||||||
\(309\) | −17.2330 | −0.980353 | ||||||||
\(310\) | −58.2986 | −3.31114 | ||||||||
\(311\) | 15.4616 | 0.876749 | 0.438375 | − | 0.898792i | \(-0.355554\pi\) | ||||
0.438375 | + | 0.898792i | \(0.355554\pi\) | |||||||
\(312\) | 160.712 | 9.09855 | ||||||||
\(313\) | −15.3716 | −0.868851 | −0.434426 | − | 0.900708i | \(-0.643049\pi\) | ||||
−0.434426 | + | 0.900708i | \(0.643049\pi\) | |||||||
\(314\) | 20.6694 | 1.16644 | ||||||||
\(315\) | −46.6075 | −2.62603 | ||||||||
\(316\) | 17.3708 | 0.977184 | ||||||||
\(317\) | 8.42410 | 0.473145 | 0.236572 | − | 0.971614i | \(-0.423976\pi\) | ||||
0.236572 | + | 0.971614i | \(0.423976\pi\) | |||||||
\(318\) | 52.3201 | 2.93396 | ||||||||
\(319\) | 0.236008 | 0.0132139 | ||||||||
\(320\) | −109.347 | −6.11267 | ||||||||
\(321\) | 20.5909 | 1.14927 | ||||||||
\(322\) | −45.4893 | −2.53502 | ||||||||
\(323\) | −0.332704 | −0.0185122 | ||||||||
\(324\) | 83.0524 | 4.61402 | ||||||||
\(325\) | 48.2570 | 2.67682 | ||||||||
\(326\) | 62.5274 | 3.46307 | ||||||||
\(327\) | −11.0763 | −0.612519 | ||||||||
\(328\) | 45.5378 | 2.51440 | ||||||||
\(329\) | −17.7079 | −0.976268 | ||||||||
\(330\) | −15.4117 | −0.848385 | ||||||||
\(331\) | −0.912109 | −0.0501341 | −0.0250670 | − | 0.999686i | \(-0.507980\pi\) | ||||
−0.0250670 | + | 0.999686i | \(0.507980\pi\) | |||||||
\(332\) | −41.5550 | −2.28062 | ||||||||
\(333\) | 58.7390 | 3.21887 | ||||||||
\(334\) | 13.8168 | 0.756022 | ||||||||
\(335\) | −25.8407 | −1.41183 | ||||||||
\(336\) | −87.0257 | −4.74764 | ||||||||
\(337\) | 4.59478 | 0.250294 | 0.125147 | − | 0.992138i | \(-0.460060\pi\) | ||||
0.125147 | + | 0.992138i | \(0.460060\pi\) | |||||||
\(338\) | −46.7101 | −2.54069 | ||||||||
\(339\) | −39.7059 | −2.15653 | ||||||||
\(340\) | −20.2573 | −1.09861 | ||||||||
\(341\) | −2.81343 | −0.152356 | ||||||||
\(342\) | 6.03661 | 0.326422 | ||||||||
\(343\) | −19.7031 | −1.06387 | ||||||||
\(344\) | −44.3812 | −2.39288 | ||||||||
\(345\) | 101.780 | 5.47967 | ||||||||
\(346\) | −40.9004 | −2.19882 | ||||||||
\(347\) | −25.7120 | −1.38029 | −0.690147 | − | 0.723669i | \(-0.742454\pi\) | ||||
−0.690147 | + | 0.723669i | \(0.742454\pi\) | |||||||
\(348\) | −8.16935 | −0.437923 | ||||||||
\(349\) | −17.9258 | −0.959544 | −0.479772 | − | 0.877393i | \(-0.659281\pi\) | ||||
−0.479772 | + | 0.877393i | \(0.659281\pi\) | |||||||
\(350\) | −45.3399 | −2.42352 | ||||||||
\(351\) | −62.1271 | −3.31610 | ||||||||
\(352\) | −10.5966 | −0.564799 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | 12.3902 | 0.658531 | ||||||||
\(355\) | 38.6302 | 2.05028 | ||||||||
\(356\) | −57.9023 | −3.06881 | ||||||||
\(357\) | −5.86450 | −0.310382 | ||||||||
\(358\) | 6.23842 | 0.329711 | ||||||||
\(359\) | −1.81147 | −0.0956059 | −0.0478029 | − | 0.998857i | \(-0.515222\pi\) | ||||
−0.0478029 | + | 0.998857i | \(0.515222\pi\) | |||||||
\(360\) | 232.771 | 12.2681 | ||||||||
\(361\) | −18.8893 | −0.994174 | ||||||||
\(362\) | 27.2502 | 1.43224 | ||||||||
\(363\) | 33.4194 | 1.75406 | ||||||||
\(364\) | 56.5115 | 2.96201 | ||||||||
\(365\) | 53.8809 | 2.82025 | ||||||||
\(366\) | −51.0433 | −2.66808 | ||||||||
\(367\) | −16.0234 | −0.836416 | −0.418208 | − | 0.908351i | \(-0.637342\pi\) | ||||
−0.418208 | + | 0.908351i | \(0.637342\pi\) | |||||||
\(368\) | 130.937 | 6.82555 | ||||||||
\(369\) | −32.0899 | −1.67053 | ||||||||
\(370\) | 89.6281 | 4.65954 | ||||||||
\(371\) | 11.6512 | 0.604899 | ||||||||
\(372\) | 97.3860 | 5.04923 | ||||||||
\(373\) | 26.3507 | 1.36439 | 0.682194 | − | 0.731171i | \(-0.261026\pi\) | ||||
0.682194 | + | 0.731171i | \(0.261026\pi\) | |||||||
\(374\) | −1.33607 | −0.0690867 | ||||||||
\(375\) | 43.7708 | 2.26032 | ||||||||
\(376\) | 88.4384 | 4.56086 | ||||||||
\(377\) | 2.64631 | 0.136292 | ||||||||
\(378\) | 58.3715 | 3.00231 | ||||||||
\(379\) | 17.1585 | 0.881374 | 0.440687 | − | 0.897661i | \(-0.354735\pi\) | ||||
0.440687 | + | 0.897661i | \(0.354735\pi\) | |||||||
\(380\) | 6.73969 | 0.345739 | ||||||||
\(381\) | −12.8400 | −0.657811 | ||||||||
\(382\) | −25.5951 | −1.30956 | ||||||||
\(383\) | −24.1693 | −1.23499 | −0.617497 | − | 0.786574i | \(-0.711853\pi\) | ||||
−0.617497 | + | 0.786574i | \(0.711853\pi\) | |||||||
\(384\) | 115.139 | 5.87566 | ||||||||
\(385\) | −3.43203 | −0.174913 | ||||||||
\(386\) | 9.75946 | 0.496743 | ||||||||
\(387\) | 31.2748 | 1.58979 | ||||||||
\(388\) | −73.9940 | −3.75647 | ||||||||
\(389\) | −38.4853 | −1.95128 | −0.975640 | − | 0.219378i | \(-0.929597\pi\) | ||||
−0.975640 | + | 0.219378i | \(0.929597\pi\) | |||||||
\(390\) | −172.808 | −8.75046 | ||||||||
\(391\) | 8.82357 | 0.446227 | ||||||||
\(392\) | 32.3886 | 1.63587 | ||||||||
\(393\) | 7.81714 | 0.394323 | ||||||||
\(394\) | 10.1790 | 0.512810 | ||||||||
\(395\) | −11.8290 | −0.595181 | ||||||||
\(396\) | 17.7376 | 0.891346 | ||||||||
\(397\) | 18.6066 | 0.933839 | 0.466919 | − | 0.884300i | \(-0.345364\pi\) | ||||
0.466919 | + | 0.884300i | \(0.345364\pi\) | |||||||
\(398\) | −44.3906 | −2.22510 | ||||||||
\(399\) | 1.95114 | 0.0976794 | ||||||||
\(400\) | 130.507 | 6.52533 | ||||||||
\(401\) | −34.1431 | −1.70503 | −0.852513 | − | 0.522706i | \(-0.824922\pi\) | ||||
−0.852513 | + | 0.522706i | \(0.824922\pi\) | |||||||
\(402\) | 58.9947 | 2.94239 | ||||||||
\(403\) | −31.5464 | −1.57144 | ||||||||
\(404\) | 96.2976 | 4.79099 | ||||||||
\(405\) | −56.5562 | −2.81030 | ||||||||
\(406\) | −2.48634 | −0.123395 | ||||||||
\(407\) | 4.32536 | 0.214400 | ||||||||
\(408\) | 29.2890 | 1.45002 | ||||||||
\(409\) | −17.0858 | −0.844838 | −0.422419 | − | 0.906401i | \(-0.638819\pi\) | ||||
−0.422419 | + | 0.906401i | \(0.638819\pi\) | |||||||
\(410\) | −48.9650 | −2.41821 | ||||||||
\(411\) | 13.4941 | 0.665616 | ||||||||
\(412\) | 30.2638 | 1.49099 | ||||||||
\(413\) | 2.75918 | 0.135770 | ||||||||
\(414\) | −160.095 | −7.86826 | ||||||||
\(415\) | 28.2977 | 1.38908 | ||||||||
\(416\) | −118.817 | −5.82548 | ||||||||
\(417\) | 44.7769 | 2.19274 | ||||||||
\(418\) | 0.444518 | 0.0217421 | ||||||||
\(419\) | 18.4805 | 0.902831 | 0.451415 | − | 0.892314i | \(-0.350919\pi\) | ||||
0.451415 | + | 0.892314i | \(0.350919\pi\) | |||||||
\(420\) | 118.799 | 5.79679 | ||||||||
\(421\) | −33.3756 | −1.62663 | −0.813314 | − | 0.581825i | \(-0.802339\pi\) | ||||
−0.813314 | + | 0.581825i | \(0.802339\pi\) | |||||||
\(422\) | 48.0963 | 2.34129 | ||||||||
\(423\) | −62.3213 | −3.03017 | ||||||||
\(424\) | −58.1894 | −2.82593 | ||||||||
\(425\) | 8.79459 | 0.426600 | ||||||||
\(426\) | −88.1934 | −4.27298 | ||||||||
\(427\) | −11.3669 | −0.550081 | ||||||||
\(428\) | −36.1607 | −1.74789 | ||||||||
\(429\) | −8.33952 | −0.402636 | ||||||||
\(430\) | 47.7214 | 2.30133 | ||||||||
\(431\) | 31.4371 | 1.51427 | 0.757135 | − | 0.653259i | \(-0.226599\pi\) | ||||
0.757135 | + | 0.653259i | \(0.226599\pi\) | |||||||
\(432\) | −168.017 | −8.08372 | ||||||||
\(433\) | 39.5437 | 1.90035 | 0.950175 | − | 0.311716i | \(-0.100904\pi\) | ||||
0.950175 | + | 0.311716i | \(0.100904\pi\) | |||||||
\(434\) | 29.6394 | 1.42274 | ||||||||
\(435\) | 5.56308 | 0.266729 | ||||||||
\(436\) | 19.4516 | 0.931562 | ||||||||
\(437\) | −2.93564 | −0.140431 | ||||||||
\(438\) | −123.011 | −5.87770 | ||||||||
\(439\) | −12.6570 | −0.604084 | −0.302042 | − | 0.953295i | \(-0.597668\pi\) | ||||
−0.302042 | + | 0.953295i | \(0.597668\pi\) | |||||||
\(440\) | 17.1406 | 0.817145 | ||||||||
\(441\) | −22.8238 | −1.08685 | ||||||||
\(442\) | −14.9811 | −0.712578 | ||||||||
\(443\) | −7.99741 | −0.379968 | −0.189984 | − | 0.981787i | \(-0.560844\pi\) | ||||
−0.189984 | + | 0.981787i | \(0.560844\pi\) | |||||||
\(444\) | −149.721 | −7.10544 | ||||||||
\(445\) | 39.4297 | 1.86915 | ||||||||
\(446\) | −58.1646 | −2.75417 | ||||||||
\(447\) | −27.6908 | −1.30973 | ||||||||
\(448\) | 55.5927 | 2.62651 | ||||||||
\(449\) | −2.48995 | −0.117508 | −0.0587541 | − | 0.998272i | \(-0.518713\pi\) | ||||
−0.0587541 | + | 0.998272i | \(0.518713\pi\) | |||||||
\(450\) | −159.570 | −7.52218 | ||||||||
\(451\) | −2.36300 | −0.111269 | ||||||||
\(452\) | 69.7295 | 3.27980 | ||||||||
\(453\) | 72.6651 | 3.41410 | ||||||||
\(454\) | 63.7758 | 2.99315 | ||||||||
\(455\) | −38.4826 | −1.80409 | ||||||||
\(456\) | −9.74458 | −0.456332 | ||||||||
\(457\) | 1.67177 | 0.0782022 | 0.0391011 | − | 0.999235i | \(-0.487551\pi\) | ||||
0.0391011 | + | 0.999235i | \(0.487551\pi\) | |||||||
\(458\) | −65.6364 | −3.06699 | ||||||||
\(459\) | −11.3223 | −0.528482 | ||||||||
\(460\) | −178.742 | −8.33387 | ||||||||
\(461\) | −7.96759 | −0.371088 | −0.185544 | − | 0.982636i | \(-0.559405\pi\) | ||||
−0.185544 | + | 0.982636i | \(0.559405\pi\) | |||||||
\(462\) | 7.83540 | 0.364536 | ||||||||
\(463\) | −3.44446 | −0.160078 | −0.0800389 | − | 0.996792i | \(-0.525504\pi\) | ||||
−0.0800389 | + | 0.996792i | \(0.525504\pi\) | |||||||
\(464\) | 7.15669 | 0.332241 | ||||||||
\(465\) | −66.3169 | −3.07537 | ||||||||
\(466\) | −67.4825 | −3.12607 | ||||||||
\(467\) | −19.0809 | −0.882960 | −0.441480 | − | 0.897271i | \(-0.645546\pi\) | ||||
−0.441480 | + | 0.897271i | \(0.645546\pi\) | |||||||
\(468\) | 198.887 | 9.19356 | ||||||||
\(469\) | 13.1376 | 0.606636 | ||||||||
\(470\) | −95.0943 | −4.38637 | ||||||||
\(471\) | 23.5122 | 1.08339 | ||||||||
\(472\) | −13.7801 | −0.634283 | ||||||||
\(473\) | 2.30299 | 0.105891 | ||||||||
\(474\) | 27.0058 | 1.24042 | ||||||||
\(475\) | −2.92600 | −0.134254 | ||||||||
\(476\) | 10.2989 | 0.472051 | ||||||||
\(477\) | 41.0053 | 1.87750 | ||||||||
\(478\) | −41.9714 | −1.91973 | ||||||||
\(479\) | −0.317062 | −0.0144869 | −0.00724346 | − | 0.999974i | \(-0.502306\pi\) | ||||
−0.00724346 | + | 0.999974i | \(0.502306\pi\) | |||||||
\(480\) | −249.778 | −11.4007 | ||||||||
\(481\) | 48.4993 | 2.21138 | ||||||||
\(482\) | 6.45490 | 0.294013 | ||||||||
\(483\) | −51.7458 | −2.35452 | ||||||||
\(484\) | −58.6895 | −2.66770 | ||||||||
\(485\) | 50.3876 | 2.28798 | ||||||||
\(486\) | 36.3811 | 1.65028 | ||||||||
\(487\) | −36.3431 | −1.64686 | −0.823431 | − | 0.567416i | \(-0.807943\pi\) | ||||
−0.823431 | + | 0.567416i | \(0.807943\pi\) | |||||||
\(488\) | 56.7694 | 2.56983 | ||||||||
\(489\) | 71.1273 | 3.21649 | ||||||||
\(490\) | −34.8262 | −1.57329 | ||||||||
\(491\) | 23.0676 | 1.04103 | 0.520514 | − | 0.853853i | \(-0.325740\pi\) | ||||
0.520514 | + | 0.853853i | \(0.325740\pi\) | |||||||
\(492\) | 81.7945 | 3.68758 | ||||||||
\(493\) | 0.482276 | 0.0217206 | ||||||||
\(494\) | 4.98427 | 0.224253 | ||||||||
\(495\) | −12.0787 | −0.542899 | ||||||||
\(496\) | −85.3143 | −3.83072 | ||||||||
\(497\) | −19.6398 | −0.880967 | ||||||||
\(498\) | −64.6041 | −2.89498 | ||||||||
\(499\) | 35.8699 | 1.60576 | 0.802879 | − | 0.596142i | \(-0.203300\pi\) | ||||
0.802879 | + | 0.596142i | \(0.203300\pi\) | |||||||
\(500\) | −76.8682 | −3.43765 | ||||||||
\(501\) | 15.7171 | 0.702190 | ||||||||
\(502\) | 11.0138 | 0.491571 | ||||||||
\(503\) | −12.3750 | −0.551776 | −0.275888 | − | 0.961190i | \(-0.588972\pi\) | ||||
−0.275888 | + | 0.961190i | \(0.588972\pi\) | |||||||
\(504\) | −118.343 | −5.27140 | ||||||||
\(505\) | −65.5758 | −2.91808 | ||||||||
\(506\) | −11.7889 | −0.524082 | ||||||||
\(507\) | −53.1345 | −2.35979 | ||||||||
\(508\) | 22.5489 | 1.00045 | ||||||||
\(509\) | −22.9858 | −1.01883 | −0.509414 | − | 0.860522i | \(-0.670138\pi\) | ||||
−0.509414 | + | 0.860522i | \(0.670138\pi\) | |||||||
\(510\) | −31.4933 | −1.39455 | ||||||||
\(511\) | −27.3934 | −1.21181 | ||||||||
\(512\) | −41.4402 | −1.83141 | ||||||||
\(513\) | 3.76699 | 0.166317 | ||||||||
\(514\) | 56.4800 | 2.49123 | ||||||||
\(515\) | −20.6087 | −0.908129 | ||||||||
\(516\) | −79.7171 | −3.50935 | ||||||||
\(517\) | −4.58915 | −0.201831 | ||||||||
\(518\) | −45.5675 | −2.00212 | ||||||||
\(519\) | −46.5258 | −2.04226 | ||||||||
\(520\) | 192.193 | 8.42824 | ||||||||
\(521\) | −2.92055 | −0.127952 | −0.0639758 | − | 0.997951i | \(-0.520378\pi\) | ||||
−0.0639758 | + | 0.997951i | \(0.520378\pi\) | |||||||
\(522\) | −8.75044 | −0.382996 | ||||||||
\(523\) | −9.77817 | −0.427569 | −0.213785 | − | 0.976881i | \(-0.568579\pi\) | ||||
−0.213785 | + | 0.976881i | \(0.568579\pi\) | |||||||
\(524\) | −13.7281 | −0.599714 | ||||||||
\(525\) | −51.5759 | −2.25096 | ||||||||
\(526\) | −13.1389 | −0.572885 | ||||||||
\(527\) | −5.74916 | −0.250437 | ||||||||
\(528\) | −22.5535 | −0.981514 | ||||||||
\(529\) | 54.8554 | 2.38502 | ||||||||
\(530\) | 62.5688 | 2.71781 | ||||||||
\(531\) | 9.71068 | 0.421408 | ||||||||
\(532\) | −3.42650 | −0.148558 | ||||||||
\(533\) | −26.4958 | −1.14766 | ||||||||
\(534\) | −90.0187 | −3.89549 | ||||||||
\(535\) | 24.6244 | 1.06460 | ||||||||
\(536\) | −65.6128 | −2.83404 | ||||||||
\(537\) | 7.09645 | 0.306234 | ||||||||
\(538\) | 58.4721 | 2.52091 | ||||||||
\(539\) | −1.68067 | −0.0723918 | ||||||||
\(540\) | 229.360 | 9.87008 | ||||||||
\(541\) | −5.62524 | −0.241848 | −0.120924 | − | 0.992662i | \(-0.538586\pi\) | ||||
−0.120924 | + | 0.992662i | \(0.538586\pi\) | |||||||
\(542\) | −26.1861 | −1.12479 | ||||||||
\(543\) | 30.9982 | 1.33026 | ||||||||
\(544\) | −21.6538 | −0.928399 | ||||||||
\(545\) | −13.2459 | −0.567394 | ||||||||
\(546\) | 87.8566 | 3.75991 | ||||||||
\(547\) | −19.7322 | −0.843686 | −0.421843 | − | 0.906669i | \(-0.638617\pi\) | ||||
−0.421843 | + | 0.906669i | \(0.638617\pi\) | |||||||
\(548\) | −23.6977 | −1.01232 | ||||||||
\(549\) | −40.0046 | −1.70736 | ||||||||
\(550\) | −11.7502 | −0.501031 | ||||||||
\(551\) | −0.160455 | −0.00683562 | ||||||||
\(552\) | 258.434 | 10.9997 | ||||||||
\(553\) | 6.01393 | 0.255739 | ||||||||
\(554\) | −68.8638 | −2.92574 | ||||||||
\(555\) | 101.955 | 4.32777 | ||||||||
\(556\) | −78.6350 | −3.33487 | ||||||||
\(557\) | 27.0923 | 1.14794 | 0.573970 | − | 0.818877i | \(-0.305403\pi\) | ||||
0.573970 | + | 0.818877i | \(0.305403\pi\) | |||||||
\(558\) | 104.313 | 4.41593 | ||||||||
\(559\) | 25.8229 | 1.09219 | ||||||||
\(560\) | −104.073 | −4.39788 | ||||||||
\(561\) | −1.51984 | −0.0641675 | ||||||||
\(562\) | 77.2202 | 3.25734 | ||||||||
\(563\) | −7.40450 | −0.312063 | −0.156031 | − | 0.987752i | \(-0.549870\pi\) | ||||
−0.156031 | + | 0.987752i | \(0.549870\pi\) | |||||||
\(564\) | 158.852 | 6.68888 | ||||||||
\(565\) | −47.4837 | −1.99765 | ||||||||
\(566\) | 18.5600 | 0.780137 | ||||||||
\(567\) | 28.7535 | 1.20754 | ||||||||
\(568\) | 98.0871 | 4.11564 | ||||||||
\(569\) | −27.7703 | −1.16419 | −0.582096 | − | 0.813120i | \(-0.697767\pi\) | ||||
−0.582096 | + | 0.813120i | \(0.697767\pi\) | |||||||
\(570\) | 10.4780 | 0.438874 | ||||||||
\(571\) | −11.5386 | −0.482876 | −0.241438 | − | 0.970416i | \(-0.577619\pi\) | ||||
−0.241438 | + | 0.970416i | \(0.577619\pi\) | |||||||
\(572\) | 14.6455 | 0.612357 | ||||||||
\(573\) | −29.1154 | −1.21632 | ||||||||
\(574\) | 24.8941 | 1.03906 | ||||||||
\(575\) | 77.5997 | 3.23613 | ||||||||
\(576\) | 195.653 | 8.15222 | ||||||||
\(577\) | −32.1425 | −1.33811 | −0.669055 | − | 0.743213i | \(-0.733301\pi\) | ||||
−0.669055 | + | 0.743213i | \(0.733301\pi\) | |||||||
\(578\) | −2.73023 | −0.113563 | ||||||||
\(579\) | 11.1018 | 0.461373 | ||||||||
\(580\) | −9.76960 | −0.405660 | ||||||||
\(581\) | −14.3867 | −0.596862 | ||||||||
\(582\) | −115.036 | −4.76839 | ||||||||
\(583\) | 3.01950 | 0.125055 | ||||||||
\(584\) | 136.811 | 5.66127 | ||||||||
\(585\) | −135.436 | −5.59959 | ||||||||
\(586\) | −70.6185 | −2.91722 | ||||||||
\(587\) | 7.24354 | 0.298973 | 0.149486 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149486 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(588\) | 58.1760 | 2.39914 | ||||||||
\(589\) | 1.91277 | 0.0788144 | ||||||||
\(590\) | 14.8172 | 0.610016 | ||||||||
\(591\) | 11.5790 | 0.476296 | ||||||||
\(592\) | 131.162 | 5.39072 | ||||||||
\(593\) | 14.1958 | 0.582951 | 0.291476 | − | 0.956578i | \(-0.405854\pi\) | ||||
0.291476 | + | 0.956578i | \(0.405854\pi\) | |||||||
\(594\) | 15.1275 | 0.620688 | ||||||||
\(595\) | −7.01326 | −0.287516 | ||||||||
\(596\) | 48.6292 | 1.99193 | ||||||||
\(597\) | −50.4960 | −2.06666 | ||||||||
\(598\) | −132.187 | −5.40552 | ||||||||
\(599\) | −41.0042 | −1.67539 | −0.837693 | − | 0.546142i | \(-0.816096\pi\) | ||||
−0.837693 | + | 0.546142i | \(0.816096\pi\) | |||||||
\(600\) | 257.585 | 10.5159 | ||||||||
\(601\) | −19.2506 | −0.785250 | −0.392625 | − | 0.919699i | \(-0.628433\pi\) | ||||
−0.392625 | + | 0.919699i | \(0.628433\pi\) | |||||||
\(602\) | −24.2619 | −0.988840 | ||||||||
\(603\) | 46.2364 | 1.88289 | ||||||||
\(604\) | −127.611 | −5.19241 | ||||||||
\(605\) | 39.9657 | 1.62484 | ||||||||
\(606\) | 149.711 | 6.08158 | ||||||||
\(607\) | −22.0815 | −0.896259 | −0.448130 | − | 0.893969i | \(-0.647910\pi\) | ||||
−0.448130 | + | 0.893969i | \(0.647910\pi\) | |||||||
\(608\) | 7.20431 | 0.292173 | ||||||||
\(609\) | −2.82830 | −0.114609 | ||||||||
\(610\) | −61.0419 | −2.47152 | ||||||||
\(611\) | −51.4571 | −2.08173 | ||||||||
\(612\) | 36.2462 | 1.46516 | ||||||||
\(613\) | −22.8577 | −0.923214 | −0.461607 | − | 0.887085i | \(-0.652727\pi\) | ||||
−0.461607 | + | 0.887085i | \(0.652727\pi\) | |||||||
\(614\) | 7.61900 | 0.307478 | ||||||||
\(615\) | −55.6996 | −2.24602 | ||||||||
\(616\) | −8.71439 | −0.351113 | ||||||||
\(617\) | −26.1765 | −1.05383 | −0.526913 | − | 0.849919i | \(-0.676651\pi\) | ||||
−0.526913 | + | 0.849919i | \(0.676651\pi\) | |||||||
\(618\) | 47.0501 | 1.89263 | ||||||||
\(619\) | 17.5333 | 0.704724 | 0.352362 | − | 0.935864i | \(-0.385379\pi\) | ||||
0.352362 | + | 0.935864i | \(0.385379\pi\) | |||||||
\(620\) | 116.462 | 4.67724 | ||||||||
\(621\) | −99.9035 | −4.00899 | ||||||||
\(622\) | −42.2138 | −1.69262 | ||||||||
\(623\) | −20.0463 | −0.803139 | ||||||||
\(624\) | −252.887 | −10.1236 | ||||||||
\(625\) | 8.37191 | 0.334876 | ||||||||
\(626\) | 41.9678 | 1.67737 | ||||||||
\(627\) | 0.505656 | 0.0201940 | ||||||||
\(628\) | −41.2910 | −1.64769 | ||||||||
\(629\) | 8.83875 | 0.352424 | ||||||||
\(630\) | 127.249 | 5.06972 | ||||||||
\(631\) | 0.116003 | 0.00461802 | 0.00230901 | − | 0.999997i | \(-0.499265\pi\) | ||||
0.00230901 | + | 0.999997i | \(0.499265\pi\) | |||||||
\(632\) | −30.0354 | −1.19474 | ||||||||
\(633\) | 54.7114 | 2.17458 | ||||||||
\(634\) | −22.9997 | −0.913435 | ||||||||
\(635\) | −15.3551 | −0.609349 | ||||||||
\(636\) | −104.519 | −4.14446 | ||||||||
\(637\) | −18.8450 | −0.746667 | ||||||||
\(638\) | −0.644356 | −0.0255103 | ||||||||
\(639\) | −69.1206 | −2.73437 | ||||||||
\(640\) | 137.693 | 5.44279 | ||||||||
\(641\) | 31.7091 | 1.25243 | 0.626216 | − | 0.779649i | \(-0.284603\pi\) | ||||
0.626216 | + | 0.779649i | \(0.284603\pi\) | |||||||
\(642\) | −56.2179 | −2.21874 | ||||||||
\(643\) | 4.04807 | 0.159640 | 0.0798202 | − | 0.996809i | \(-0.474565\pi\) | ||||
0.0798202 | + | 0.996809i | \(0.474565\pi\) | |||||||
\(644\) | 90.8734 | 3.58091 | ||||||||
\(645\) | 54.2849 | 2.13747 | ||||||||
\(646\) | 0.908359 | 0.0357389 | ||||||||
\(647\) | 39.8631 | 1.56718 | 0.783590 | − | 0.621279i | \(-0.213386\pi\) | ||||
0.783590 | + | 0.621279i | \(0.213386\pi\) | |||||||
\(648\) | −143.604 | −5.64128 | ||||||||
\(649\) | 0.715065 | 0.0280688 | ||||||||
\(650\) | −131.753 | −5.16776 | ||||||||
\(651\) | 33.7159 | 1.32143 | ||||||||
\(652\) | −124.910 | −4.89186 | ||||||||
\(653\) | −17.4076 | −0.681212 | −0.340606 | − | 0.940206i | \(-0.610632\pi\) | ||||
−0.340606 | + | 0.940206i | \(0.610632\pi\) | |||||||
\(654\) | 30.2407 | 1.18251 | ||||||||
\(655\) | 9.34840 | 0.365272 | ||||||||
\(656\) | −71.6555 | −2.79768 | ||||||||
\(657\) | −96.4086 | −3.76126 | ||||||||
\(658\) | 48.3466 | 1.88475 | ||||||||
\(659\) | −18.7947 | −0.732138 | −0.366069 | − | 0.930588i | \(-0.619297\pi\) | ||||
−0.366069 | + | 0.930588i | \(0.619297\pi\) | |||||||
\(660\) | 30.7877 | 1.19841 | ||||||||
\(661\) | −4.61400 | −0.179464 | −0.0897320 | − | 0.995966i | \(-0.528601\pi\) | ||||
−0.0897320 | + | 0.995966i | \(0.528601\pi\) | |||||||
\(662\) | 2.49027 | 0.0967870 | ||||||||
\(663\) | −17.0416 | −0.661840 | ||||||||
\(664\) | 71.8515 | 2.78838 | ||||||||
\(665\) | 2.33334 | 0.0904832 | ||||||||
\(666\) | −160.371 | −6.21424 | ||||||||
\(667\) | 4.25539 | 0.164770 | ||||||||
\(668\) | −27.6017 | −1.06794 | ||||||||
\(669\) | −66.1644 | −2.55807 | ||||||||
\(670\) | 70.5509 | 2.72562 | ||||||||
\(671\) | −2.94582 | −0.113722 | ||||||||
\(672\) | 126.989 | 4.89869 | ||||||||
\(673\) | −18.9647 | −0.731037 | −0.365518 | − | 0.930804i | \(-0.619108\pi\) | ||||
−0.365518 | + | 0.930804i | \(0.619108\pi\) | |||||||
\(674\) | −12.5448 | −0.483208 | ||||||||
\(675\) | −99.5754 | −3.83266 | ||||||||
\(676\) | 93.3122 | 3.58893 | ||||||||
\(677\) | 12.8848 | 0.495203 | 0.247601 | − | 0.968862i | \(-0.420358\pi\) | ||||
0.247601 | + | 0.968862i | \(0.420358\pi\) | |||||||
\(678\) | 108.406 | 4.16331 | ||||||||
\(679\) | −25.6174 | −0.983106 | ||||||||
\(680\) | 35.0263 | 1.34320 | ||||||||
\(681\) | 72.5474 | 2.78002 | ||||||||
\(682\) | 7.68131 | 0.294132 | ||||||||
\(683\) | −13.3476 | −0.510731 | −0.255366 | − | 0.966845i | \(-0.582196\pi\) | ||||
−0.255366 | + | 0.966845i | \(0.582196\pi\) | |||||||
\(684\) | −12.0593 | −0.461097 | ||||||||
\(685\) | 16.1374 | 0.616579 | ||||||||
\(686\) | 53.7938 | 2.05386 | ||||||||
\(687\) | −74.6639 | −2.84861 | ||||||||
\(688\) | 69.8356 | 2.66246 | ||||||||
\(689\) | 33.8570 | 1.28985 | ||||||||
\(690\) | −277.884 | −10.5788 | ||||||||
\(691\) | 26.1747 | 0.995734 | 0.497867 | − | 0.867253i | \(-0.334117\pi\) | ||||
0.497867 | + | 0.867253i | \(0.334117\pi\) | |||||||
\(692\) | 81.7064 | 3.10601 | ||||||||
\(693\) | 6.14091 | 0.233274 | ||||||||
\(694\) | 70.1997 | 2.66474 | ||||||||
\(695\) | 53.5480 | 2.03119 | ||||||||
\(696\) | 14.1254 | 0.535421 | ||||||||
\(697\) | −4.82872 | −0.182901 | ||||||||
\(698\) | 48.9414 | 1.85246 | ||||||||
\(699\) | −76.7640 | −2.90348 | ||||||||
\(700\) | 90.5750 | 3.42341 | ||||||||
\(701\) | 9.87840 | 0.373102 | 0.186551 | − | 0.982445i | \(-0.440269\pi\) | ||||
0.186551 | + | 0.982445i | \(0.440269\pi\) | |||||||
\(702\) | 169.621 | 6.40193 | ||||||||
\(703\) | −2.94069 | −0.110910 | ||||||||
\(704\) | 14.4073 | 0.542996 | ||||||||
\(705\) | −108.173 | −4.07405 | ||||||||
\(706\) | −2.73023 | −0.102753 | ||||||||
\(707\) | 33.3391 | 1.25385 | ||||||||
\(708\) | −24.7518 | −0.930228 | ||||||||
\(709\) | −33.9452 | −1.27484 | −0.637419 | − | 0.770518i | \(-0.719998\pi\) | ||||
−0.637419 | + | 0.770518i | \(0.719998\pi\) | |||||||
\(710\) | −105.469 | −3.95819 | ||||||||
\(711\) | 21.1655 | 0.793768 | ||||||||
\(712\) | 100.117 | 3.75205 | ||||||||
\(713\) | −50.7281 | −1.89978 | ||||||||
\(714\) | 16.0114 | 0.599212 | ||||||||
\(715\) | −9.97311 | −0.372973 | ||||||||
\(716\) | −12.4624 | −0.465743 | ||||||||
\(717\) | −47.7440 | −1.78303 | ||||||||
\(718\) | 4.94573 | 0.184573 | ||||||||
\(719\) | −32.9145 | −1.22750 | −0.613752 | − | 0.789499i | \(-0.710340\pi\) | ||||
−0.613752 | + | 0.789499i | \(0.710340\pi\) | |||||||
\(720\) | −366.275 | −13.6503 | ||||||||
\(721\) | 10.4776 | 0.390207 | ||||||||
\(722\) | 51.5721 | 1.91932 | ||||||||
\(723\) | 7.34269 | 0.273078 | ||||||||
\(724\) | −54.4375 | −2.02315 | ||||||||
\(725\) | 4.24142 | 0.157522 | ||||||||
\(726\) | −91.2425 | −3.38633 | ||||||||
\(727\) | 11.4999 | 0.426508 | 0.213254 | − | 0.976997i | \(-0.431594\pi\) | ||||
0.213254 | + | 0.976997i | \(0.431594\pi\) | |||||||
\(728\) | −97.7125 | −3.62146 | ||||||||
\(729\) | −4.29729 | −0.159159 | ||||||||
\(730\) | −147.107 | −5.44468 | ||||||||
\(731\) | 4.70608 | 0.174061 | ||||||||
\(732\) | 101.969 | 3.76887 | ||||||||
\(733\) | 8.26852 | 0.305405 | 0.152702 | − | 0.988272i | \(-0.451202\pi\) | ||||
0.152702 | + | 0.988272i | \(0.451202\pi\) | |||||||
\(734\) | 43.7476 | 1.61475 | ||||||||
\(735\) | −39.6161 | −1.46126 | ||||||||
\(736\) | −191.064 | −7.04270 | ||||||||
\(737\) | 3.40471 | 0.125414 | ||||||||
\(738\) | 87.6126 | 3.22507 | ||||||||
\(739\) | −41.6012 | −1.53032 | −0.765162 | − | 0.643837i | \(-0.777341\pi\) | ||||
−0.765162 | + | 0.643837i | \(0.777341\pi\) | |||||||
\(740\) | −179.049 | −6.58197 | ||||||||
\(741\) | 5.66980 | 0.208285 | ||||||||
\(742\) | −31.8104 | −1.16780 | ||||||||
\(743\) | −13.8321 | −0.507450 | −0.253725 | − | 0.967276i | \(-0.581656\pi\) | ||||
−0.253725 | + | 0.967276i | \(0.581656\pi\) | |||||||
\(744\) | −168.387 | −6.17338 | ||||||||
\(745\) | −33.1150 | −1.21324 | ||||||||
\(746\) | −71.9435 | −2.63404 | ||||||||
\(747\) | −50.6327 | −1.85256 | ||||||||
\(748\) | 2.66906 | 0.0975905 | ||||||||
\(749\) | −12.5192 | −0.457441 | ||||||||
\(750\) | −119.504 | −4.36368 | ||||||||
\(751\) | −16.5109 | −0.602491 | −0.301245 | − | 0.953547i | \(-0.597402\pi\) | ||||
−0.301245 | + | 0.953547i | \(0.597402\pi\) | |||||||
\(752\) | −139.161 | −5.07469 | ||||||||
\(753\) | 12.5287 | 0.456570 | ||||||||
\(754\) | −7.22502 | −0.263120 | ||||||||
\(755\) | 86.8991 | 3.16258 | ||||||||
\(756\) | −116.608 | −4.24100 | ||||||||
\(757\) | −16.7520 | −0.608863 | −0.304432 | − | 0.952534i | \(-0.598467\pi\) | ||||
−0.304432 | + | 0.952534i | \(0.598467\pi\) | |||||||
\(758\) | −46.8467 | −1.70155 | ||||||||
\(759\) | −13.4104 | −0.486766 | ||||||||
\(760\) | −11.6534 | −0.422713 | ||||||||
\(761\) | 43.9955 | 1.59483 | 0.797417 | − | 0.603429i | \(-0.206199\pi\) | ||||
0.797417 | + | 0.603429i | \(0.206199\pi\) | |||||||
\(762\) | 35.0560 | 1.26995 | ||||||||
\(763\) | 6.73433 | 0.243799 | ||||||||
\(764\) | 51.1311 | 1.84986 | ||||||||
\(765\) | −24.6825 | −0.892399 | ||||||||
\(766\) | 65.9877 | 2.38423 | ||||||||
\(767\) | 8.01786 | 0.289508 | ||||||||
\(768\) | −131.484 | −4.74450 | ||||||||
\(769\) | 33.2541 | 1.19917 | 0.599587 | − | 0.800309i | \(-0.295331\pi\) | ||||
0.599587 | + | 0.800309i | \(0.295331\pi\) | |||||||
\(770\) | 9.37024 | 0.337680 | ||||||||
\(771\) | 64.2482 | 2.31384 | ||||||||
\(772\) | −19.4964 | −0.701689 | ||||||||
\(773\) | −18.5456 | −0.667039 | −0.333520 | − | 0.942743i | \(-0.608236\pi\) | ||||
−0.333520 | + | 0.942743i | \(0.608236\pi\) | |||||||
\(774\) | −85.3875 | −3.06919 | ||||||||
\(775\) | −50.5616 | −1.81622 | ||||||||
\(776\) | 127.941 | 4.59281 | ||||||||
\(777\) | −51.8348 | −1.85956 | ||||||||
\(778\) | 105.074 | 3.76707 | ||||||||
\(779\) | 1.60654 | 0.0575602 | ||||||||
\(780\) | 345.216 | 12.3607 | ||||||||
\(781\) | −5.08983 | −0.182129 | ||||||||
\(782\) | −24.0904 | −0.861470 | ||||||||
\(783\) | −5.46049 | −0.195142 | ||||||||
\(784\) | −50.9647 | −1.82017 | ||||||||
\(785\) | 28.1179 | 1.00357 | ||||||||
\(786\) | −21.3426 | −0.761265 | ||||||||
\(787\) | −13.0023 | −0.463482 | −0.231741 | − | 0.972778i | \(-0.574442\pi\) | ||||
−0.231741 | + | 0.972778i | \(0.574442\pi\) | |||||||
\(788\) | −20.3344 | −0.724385 | ||||||||
\(789\) | −14.9461 | −0.532094 | ||||||||
\(790\) | 32.2958 | 1.14903 | ||||||||
\(791\) | 24.1410 | 0.858356 | ||||||||
\(792\) | −30.6695 | −1.08979 | ||||||||
\(793\) | −33.0308 | −1.17296 | ||||||||
\(794\) | −50.8003 | −1.80283 | ||||||||
\(795\) | 71.1744 | 2.52430 | ||||||||
\(796\) | 88.6786 | 3.14313 | ||||||||
\(797\) | 10.8613 | 0.384729 | 0.192364 | − | 0.981324i | \(-0.438384\pi\) | ||||
0.192364 | + | 0.981324i | \(0.438384\pi\) | |||||||
\(798\) | −5.32707 | −0.188576 | ||||||||
\(799\) | −9.37780 | −0.331763 | ||||||||
\(800\) | −190.436 | −6.73294 | ||||||||
\(801\) | −70.5512 | −2.49280 | ||||||||
\(802\) | 93.2185 | 3.29166 | ||||||||
\(803\) | −7.09924 | −0.250527 | ||||||||
\(804\) | −117.853 | −4.15636 | ||||||||
\(805\) | −61.8820 | −2.18105 | ||||||||
\(806\) | 86.1287 | 3.03376 | ||||||||
\(807\) | 66.5143 | 2.34141 | ||||||||
\(808\) | −166.505 | −5.85764 | ||||||||
\(809\) | −12.1153 | −0.425953 | −0.212976 | − | 0.977057i | \(-0.568316\pi\) | ||||
−0.212976 | + | 0.977057i | \(0.568316\pi\) | |||||||
\(810\) | 154.411 | 5.42546 | ||||||||
\(811\) | −1.56410 | −0.0549230 | −0.0274615 | − | 0.999623i | \(-0.508742\pi\) | ||||
−0.0274615 | + | 0.999623i | \(0.508742\pi\) | |||||||
\(812\) | 4.96693 | 0.174305 | ||||||||
\(813\) | −29.7877 | −1.04470 | ||||||||
\(814\) | −11.8092 | −0.413913 | ||||||||
\(815\) | 85.0601 | 2.97952 | ||||||||
\(816\) | −46.0874 | −1.61338 | ||||||||
\(817\) | −1.56573 | −0.0547781 | ||||||||
\(818\) | 46.6481 | 1.63101 | ||||||||
\(819\) | 68.8566 | 2.40604 | ||||||||
\(820\) | 97.8168 | 3.41591 | ||||||||
\(821\) | 37.1552 | 1.29672 | 0.648362 | − | 0.761332i | \(-0.275454\pi\) | ||||
0.648362 | + | 0.761332i | \(0.275454\pi\) | |||||||
\(822\) | −36.8420 | −1.28501 | ||||||||
\(823\) | −34.0078 | −1.18544 | −0.592719 | − | 0.805409i | \(-0.701945\pi\) | ||||
−0.592719 | + | 0.805409i | \(0.701945\pi\) | |||||||
\(824\) | −52.3283 | −1.82294 | ||||||||
\(825\) | −13.3663 | −0.465356 | ||||||||
\(826\) | −7.53319 | −0.262113 | ||||||||
\(827\) | −39.5015 | −1.37360 | −0.686801 | − | 0.726845i | \(-0.740986\pi\) | ||||
−0.686801 | + | 0.726845i | \(0.740986\pi\) | |||||||
\(828\) | 319.821 | 11.1145 | ||||||||
\(829\) | −55.2152 | −1.91770 | −0.958852 | − | 0.283906i | \(-0.908370\pi\) | ||||
−0.958852 | + | 0.283906i | \(0.908370\pi\) | |||||||
\(830\) | −77.2591 | −2.68170 | ||||||||
\(831\) | −78.3353 | −2.71742 | ||||||||
\(832\) | 161.546 | 5.60060 | ||||||||
\(833\) | −3.43441 | −0.118995 | ||||||||
\(834\) | −122.251 | −4.23321 | ||||||||
\(835\) | 18.7959 | 0.650459 | ||||||||
\(836\) | −0.888008 | −0.0307124 | ||||||||
\(837\) | 65.0940 | 2.24998 | ||||||||
\(838\) | −50.4560 | −1.74297 | ||||||||
\(839\) | 16.5066 | 0.569871 | 0.284935 | − | 0.958547i | \(-0.408028\pi\) | ||||
0.284935 | + | 0.958547i | \(0.408028\pi\) | |||||||
\(840\) | −205.412 | −7.08737 | ||||||||
\(841\) | −28.7674 | −0.991980 | ||||||||
\(842\) | 91.1230 | 3.14031 | ||||||||
\(843\) | 87.8409 | 3.02540 | ||||||||
\(844\) | −96.0814 | −3.30726 | ||||||||
\(845\) | −63.5428 | −2.18594 | ||||||||
\(846\) | 170.151 | 5.84993 | ||||||||
\(847\) | −20.3188 | −0.698164 | ||||||||
\(848\) | 91.5632 | 3.14429 | ||||||||
\(849\) | 21.1128 | 0.724588 | ||||||||
\(850\) | −24.0112 | −0.823579 | ||||||||
\(851\) | 77.9893 | 2.67344 | ||||||||
\(852\) | 176.183 | 6.03593 | ||||||||
\(853\) | 45.0347 | 1.54196 | 0.770979 | − | 0.636860i | \(-0.219767\pi\) | ||||
0.770979 | + | 0.636860i | \(0.219767\pi\) | |||||||
\(854\) | 31.0341 | 1.06197 | ||||||||
\(855\) | 8.21199 | 0.280844 | ||||||||
\(856\) | 62.5245 | 2.13704 | ||||||||
\(857\) | 29.9362 | 1.02260 | 0.511301 | − | 0.859402i | \(-0.329164\pi\) | ||||
0.511301 | + | 0.859402i | \(0.329164\pi\) | |||||||
\(858\) | 22.7688 | 0.777314 | ||||||||
\(859\) | 45.5819 | 1.55523 | 0.777617 | − | 0.628738i | \(-0.216428\pi\) | ||||
0.777617 | + | 0.628738i | \(0.216428\pi\) | |||||||
\(860\) | −95.3325 | −3.25081 | ||||||||
\(861\) | 28.3180 | 0.965076 | ||||||||
\(862\) | −85.8303 | −2.92339 | ||||||||
\(863\) | 23.0996 | 0.786320 | 0.393160 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393160 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(864\) | 245.172 | 8.34091 | ||||||||
\(865\) | −55.6395 | −1.89180 | ||||||||
\(866\) | −107.963 | −3.66875 | ||||||||
\(867\) | −3.10574 | −0.105476 | ||||||||
\(868\) | −59.2103 | −2.00973 | ||||||||
\(869\) | 1.55856 | 0.0528706 | ||||||||
\(870\) | −15.1885 | −0.514937 | ||||||||
\(871\) | 38.1763 | 1.29355 | ||||||||
\(872\) | −33.6332 | −1.13896 | ||||||||
\(873\) | −90.1581 | −3.05139 | ||||||||
\(874\) | 8.01497 | 0.271110 | ||||||||
\(875\) | −26.6125 | −0.899666 | ||||||||
\(876\) | 245.738 | 8.30271 | ||||||||
\(877\) | 6.42386 | 0.216918 | 0.108459 | − | 0.994101i | \(-0.465408\pi\) | ||||
0.108459 | + | 0.994101i | \(0.465408\pi\) | |||||||
\(878\) | 34.5564 | 1.16622 | ||||||||
\(879\) | −80.3312 | −2.70950 | ||||||||
\(880\) | −26.9714 | −0.909205 | ||||||||
\(881\) | 32.9297 | 1.10943 | 0.554715 | − | 0.832040i | \(-0.312827\pi\) | ||||
0.554715 | + | 0.832040i | \(0.312827\pi\) | |||||||
\(882\) | 62.3141 | 2.09823 | ||||||||
\(883\) | 20.2052 | 0.679960 | 0.339980 | − | 0.940433i | \(-0.389580\pi\) | ||||
0.339980 | + | 0.940433i | \(0.389580\pi\) | |||||||
\(884\) | 29.9276 | 1.00657 | ||||||||
\(885\) | 16.8552 | 0.566581 | ||||||||
\(886\) | 21.8348 | 0.733553 | ||||||||
\(887\) | 10.2533 | 0.344271 | 0.172135 | − | 0.985073i | \(-0.444933\pi\) | ||||
0.172135 | + | 0.985073i | \(0.444933\pi\) | |||||||
\(888\) | 258.878 | 8.68738 | ||||||||
\(889\) | 7.80664 | 0.261826 | ||||||||
\(890\) | −107.652 | −3.60850 | ||||||||
\(891\) | 7.45173 | 0.249642 | ||||||||
\(892\) | 116.195 | 3.89049 | ||||||||
\(893\) | 3.12004 | 0.104408 | ||||||||
\(894\) | 75.6022 | 2.52852 | ||||||||
\(895\) | 8.48653 | 0.283673 | ||||||||
\(896\) | −70.0040 | −2.33867 | ||||||||
\(897\) | −150.367 | −5.02062 | ||||||||
\(898\) | 6.79814 | 0.226857 | ||||||||
\(899\) | −2.77268 | −0.0924741 | ||||||||
\(900\) | 318.770 | 10.6257 | ||||||||
\(901\) | 6.17027 | 0.205562 | ||||||||
\(902\) | 6.45153 | 0.214812 | ||||||||
\(903\) | −27.5988 | −0.918431 | ||||||||
\(904\) | −120.567 | −4.01001 | ||||||||
\(905\) | 37.0703 | 1.23226 | ||||||||
\(906\) | −198.392 | −6.59114 | ||||||||
\(907\) | −20.5685 | −0.682966 | −0.341483 | − | 0.939888i | \(-0.610929\pi\) | ||||
−0.341483 | + | 0.939888i | \(0.610929\pi\) | |||||||
\(908\) | −127.404 | −4.22806 | ||||||||
\(909\) | 117.334 | 3.89173 | ||||||||
\(910\) | 105.066 | 3.48292 | ||||||||
\(911\) | −45.9796 | −1.52337 | −0.761685 | − | 0.647947i | \(-0.775628\pi\) | ||||
−0.761685 | + | 0.647947i | \(0.775628\pi\) | |||||||
\(912\) | 15.3335 | 0.507742 | ||||||||
\(913\) | −3.72844 | −0.123393 | ||||||||
\(914\) | −4.56432 | −0.150974 | ||||||||
\(915\) | −69.4375 | −2.29553 | ||||||||
\(916\) | 131.121 | 4.33236 | ||||||||
\(917\) | −4.75279 | −0.156951 | ||||||||
\(918\) | 30.9126 | 1.02027 | ||||||||
\(919\) | 14.9234 | 0.492278 | 0.246139 | − | 0.969235i | \(-0.420838\pi\) | ||||
0.246139 | + | 0.969235i | \(0.420838\pi\) | |||||||
\(920\) | 309.057 | 10.1893 | ||||||||
\(921\) | 8.66690 | 0.285584 | ||||||||
\(922\) | 21.7533 | 0.716408 | ||||||||
\(923\) | −57.0711 | −1.87852 | ||||||||
\(924\) | −15.6527 | −0.514936 | ||||||||
\(925\) | 77.7332 | 2.55585 | ||||||||
\(926\) | 9.40417 | 0.309040 | ||||||||
\(927\) | 36.8750 | 1.21113 | ||||||||
\(928\) | −10.4431 | −0.342812 | ||||||||
\(929\) | 53.1100 | 1.74248 | 0.871241 | − | 0.490855i | \(-0.163315\pi\) | ||||
0.871241 | + | 0.490855i | \(0.163315\pi\) | |||||||
\(930\) | 181.060 | 5.93720 | ||||||||
\(931\) | 1.14264 | 0.0374486 | ||||||||
\(932\) | 134.809 | 4.41582 | ||||||||
\(933\) | −48.0198 | −1.57210 | ||||||||
\(934\) | 52.0953 | 1.70461 | ||||||||
\(935\) | −1.81755 | −0.0594402 | ||||||||
\(936\) | −343.890 | −11.2404 | ||||||||
\(937\) | 26.7036 | 0.872369 | 0.436184 | − | 0.899857i | \(-0.356330\pi\) | ||||
0.436184 | + | 0.899857i | \(0.356330\pi\) | |||||||
\(938\) | −35.8685 | −1.17115 | ||||||||
\(939\) | 47.7400 | 1.55794 | ||||||||
\(940\) | 189.969 | 6.19610 | ||||||||
\(941\) | −0.757355 | −0.0246891 | −0.0123445 | − | 0.999924i | \(-0.503929\pi\) | ||||
−0.0123445 | + | 0.999924i | \(0.503929\pi\) | |||||||
\(942\) | −64.1937 | −2.09154 | ||||||||
\(943\) | −42.6066 | −1.38746 | ||||||||
\(944\) | 21.6836 | 0.705741 | ||||||||
\(945\) | 79.4066 | 2.58310 | ||||||||
\(946\) | −6.28768 | −0.204430 | ||||||||
\(947\) | 13.5317 | 0.439722 | 0.219861 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219861 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(948\) | −53.9492 | −1.75219 | ||||||||
\(949\) | −79.6021 | −2.58399 | ||||||||
\(950\) | 7.98865 | 0.259186 | ||||||||
\(951\) | −26.1631 | −0.848395 | ||||||||
\(952\) | −17.8076 | −0.577148 | ||||||||
\(953\) | −50.2605 | −1.62810 | −0.814048 | − | 0.580798i | \(-0.802741\pi\) | ||||
−0.814048 | + | 0.580798i | \(0.802741\pi\) | |||||||
\(954\) | −111.954 | −3.62464 | ||||||||
\(955\) | −34.8187 | −1.12671 | ||||||||
\(956\) | 83.8457 | 2.71176 | ||||||||
\(957\) | −0.732980 | −0.0236939 | ||||||||
\(958\) | 0.865651 | 0.0279679 | ||||||||
\(959\) | −8.20437 | −0.264933 | ||||||||
\(960\) | 339.603 | 10.9606 | ||||||||
\(961\) | 2.05288 | 0.0662218 | ||||||||
\(962\) | −132.414 | −4.26920 | ||||||||
\(963\) | −44.0601 | −1.41982 | ||||||||
\(964\) | −12.8949 | −0.415316 | ||||||||
\(965\) | 13.2764 | 0.427383 | ||||||||
\(966\) | 141.278 | 4.54554 | ||||||||
\(967\) | 60.4776 | 1.94483 | 0.972414 | − | 0.233262i | \(-0.0749401\pi\) | ||||
0.972414 | + | 0.233262i | \(0.0749401\pi\) | |||||||
\(968\) | 101.478 | 3.26164 | ||||||||
\(969\) | 1.03329 | 0.0331942 | ||||||||
\(970\) | −137.570 | −4.41710 | ||||||||
\(971\) | 23.4587 | 0.752825 | 0.376413 | − | 0.926452i | \(-0.377157\pi\) | ||||
0.376413 | + | 0.926452i | \(0.377157\pi\) | |||||||
\(972\) | −72.6781 | −2.33115 | ||||||||
\(973\) | −27.2242 | −0.872767 | ||||||||
\(974\) | 99.2249 | 3.17937 | ||||||||
\(975\) | −149.874 | −4.79980 | ||||||||
\(976\) | −89.3289 | −2.85935 | ||||||||
\(977\) | −24.5612 | −0.785784 | −0.392892 | − | 0.919585i | \(-0.628525\pi\) | ||||
−0.392892 | + | 0.919585i | \(0.628525\pi\) | |||||||
\(978\) | −194.194 | −6.20963 | ||||||||
\(979\) | −5.19518 | −0.166039 | ||||||||
\(980\) | 69.5718 | 2.22239 | ||||||||
\(981\) | 23.7008 | 0.756710 | ||||||||
\(982\) | −62.9799 | −2.00977 | ||||||||
\(983\) | −19.2821 | −0.615003 | −0.307502 | − | 0.951548i | \(-0.599493\pi\) | ||||
−0.307502 | + | 0.951548i | \(0.599493\pi\) | |||||||
\(984\) | −141.429 | −4.50858 | ||||||||
\(985\) | 13.8471 | 0.441207 | ||||||||
\(986\) | −1.31672 | −0.0419330 | ||||||||
\(987\) | 54.9961 | 1.75055 | ||||||||
\(988\) | −9.95703 | −0.316775 | ||||||||
\(989\) | 41.5245 | 1.32040 | ||||||||
\(990\) | 32.9777 | 1.04810 | ||||||||
\(991\) | 27.2784 | 0.866528 | 0.433264 | − | 0.901267i | \(-0.357362\pi\) | ||||
0.433264 | + | 0.901267i | \(0.357362\pi\) | |||||||
\(992\) | 124.491 | 3.95260 | ||||||||
\(993\) | 2.83277 | 0.0898954 | ||||||||
\(994\) | 53.6212 | 1.70076 | ||||||||
\(995\) | −60.3874 | −1.91441 | ||||||||
\(996\) | 129.059 | 4.08939 | ||||||||
\(997\) | 40.6600 | 1.28771 | 0.643857 | − | 0.765146i | \(-0.277333\pi\) | ||||
0.643857 | + | 0.765146i | \(0.277333\pi\) | |||||||
\(998\) | −97.9331 | −3.10002 | ||||||||
\(999\) | −100.075 | −3.16624 |
(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 | 6001.2.a.b.1.4 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.4 | ✓ | 114 | 1.1 | even | 1 | trivial |