Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.50502 | 0.868924 | 0.434462 | − | 0.900690i | \(-0.356938\pi\) | ||||
0.434462 | + | 0.900690i | \(0.356938\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.72563 | −1.21894 | −0.609469 | − | 0.792810i | \(-0.708617\pi\) | ||||
−0.609469 | + | 0.792810i | \(0.708617\pi\) | |||||||
\(6\) | −1.50502 | −0.614422 | ||||||||
\(7\) | −2.36491 | −0.893851 | −0.446926 | − | 0.894571i | \(-0.647481\pi\) | ||||
−0.446926 | + | 0.894571i | \(0.647481\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.734912 | −0.244971 | ||||||||
\(10\) | 2.72563 | 0.861920 | ||||||||
\(11\) | 3.29273 | 0.992794 | 0.496397 | − | 0.868095i | \(-0.334656\pi\) | ||||
0.496397 | + | 0.868095i | \(0.334656\pi\) | |||||||
\(12\) | 1.50502 | 0.434462 | ||||||||
\(13\) | −0.0258940 | −0.00718171 | −0.00359086 | − | 0.999994i | \(-0.501143\pi\) | ||||
−0.00359086 | + | 0.999994i | \(0.501143\pi\) | |||||||
\(14\) | 2.36491 | 0.632048 | ||||||||
\(15\) | −4.10213 | −1.05917 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.25710 | 0.304891 | 0.152445 | − | 0.988312i | \(-0.451285\pi\) | ||||
0.152445 | + | 0.988312i | \(0.451285\pi\) | |||||||
\(18\) | 0.734912 | 0.173220 | ||||||||
\(19\) | −1.42633 | −0.327223 | −0.163612 | − | 0.986525i | \(-0.552314\pi\) | ||||
−0.163612 | + | 0.986525i | \(0.552314\pi\) | |||||||
\(20\) | −2.72563 | −0.609469 | ||||||||
\(21\) | −3.55924 | −0.776689 | ||||||||
\(22\) | −3.29273 | −0.702012 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.50502 | −0.307211 | ||||||||
\(25\) | 2.42906 | 0.485812 | ||||||||
\(26\) | 0.0258940 | 0.00507824 | ||||||||
\(27\) | −5.62112 | −1.08179 | ||||||||
\(28\) | −2.36491 | −0.446926 | ||||||||
\(29\) | 1.18615 | 0.220263 | 0.110132 | − | 0.993917i | \(-0.464873\pi\) | ||||
0.110132 | + | 0.993917i | \(0.464873\pi\) | |||||||
\(30\) | 4.10213 | 0.748943 | ||||||||
\(31\) | 5.97814 | 1.07371 | 0.536853 | − | 0.843676i | \(-0.319613\pi\) | ||||
0.536853 | + | 0.843676i | \(0.319613\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.95562 | 0.862663 | ||||||||
\(34\) | −1.25710 | −0.215590 | ||||||||
\(35\) | 6.44587 | 1.08955 | ||||||||
\(36\) | −0.734912 | −0.122485 | ||||||||
\(37\) | 6.53848 | 1.07492 | 0.537460 | − | 0.843289i | \(-0.319384\pi\) | ||||
0.537460 | + | 0.843289i | \(0.319384\pi\) | |||||||
\(38\) | 1.42633 | 0.231382 | ||||||||
\(39\) | −0.0389711 | −0.00624036 | ||||||||
\(40\) | 2.72563 | 0.430960 | ||||||||
\(41\) | 1.11334 | 0.173874 | 0.0869370 | − | 0.996214i | \(-0.472292\pi\) | ||||
0.0869370 | + | 0.996214i | \(0.472292\pi\) | |||||||
\(42\) | 3.55924 | 0.549202 | ||||||||
\(43\) | 3.03969 | 0.463549 | 0.231774 | − | 0.972770i | \(-0.425547\pi\) | ||||
0.231774 | + | 0.972770i | \(0.425547\pi\) | |||||||
\(44\) | 3.29273 | 0.496397 | ||||||||
\(45\) | 2.00310 | 0.298604 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 11.9054 | 1.73658 | 0.868288 | − | 0.496061i | \(-0.165221\pi\) | ||||
0.868288 | + | 0.496061i | \(0.165221\pi\) | |||||||
\(48\) | 1.50502 | 0.217231 | ||||||||
\(49\) | −1.40721 | −0.201030 | ||||||||
\(50\) | −2.42906 | −0.343521 | ||||||||
\(51\) | 1.89196 | 0.264927 | ||||||||
\(52\) | −0.0258940 | −0.00359086 | ||||||||
\(53\) | −8.79403 | −1.20795 | −0.603977 | − | 0.797002i | \(-0.706418\pi\) | ||||
−0.603977 | + | 0.797002i | \(0.706418\pi\) | |||||||
\(54\) | 5.62112 | 0.764938 | ||||||||
\(55\) | −8.97475 | −1.21016 | ||||||||
\(56\) | 2.36491 | 0.316024 | ||||||||
\(57\) | −2.14666 | −0.284332 | ||||||||
\(58\) | −1.18615 | −0.155750 | ||||||||
\(59\) | −0.637130 | −0.0829473 | −0.0414737 | − | 0.999140i | \(-0.513205\pi\) | ||||
−0.0414737 | + | 0.999140i | \(0.513205\pi\) | |||||||
\(60\) | −4.10213 | −0.529583 | ||||||||
\(61\) | −10.4294 | −1.33534 | −0.667672 | − | 0.744456i | \(-0.732709\pi\) | ||||
−0.667672 | + | 0.744456i | \(0.732709\pi\) | |||||||
\(62\) | −5.97814 | −0.759225 | ||||||||
\(63\) | 1.73800 | 0.218967 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0705775 | 0.00875407 | ||||||||
\(66\) | −4.95562 | −0.609995 | ||||||||
\(67\) | 4.76854 | 0.582570 | 0.291285 | − | 0.956636i | \(-0.405917\pi\) | ||||
0.291285 | + | 0.956636i | \(0.405917\pi\) | |||||||
\(68\) | 1.25710 | 0.152445 | ||||||||
\(69\) | 1.50502 | 0.181183 | ||||||||
\(70\) | −6.44587 | −0.770428 | ||||||||
\(71\) | −7.69944 | −0.913756 | −0.456878 | − | 0.889529i | \(-0.651032\pi\) | ||||
−0.456878 | + | 0.889529i | \(0.651032\pi\) | |||||||
\(72\) | 0.734912 | 0.0866102 | ||||||||
\(73\) | −6.63515 | −0.776586 | −0.388293 | − | 0.921536i | \(-0.626935\pi\) | ||||
−0.388293 | + | 0.921536i | \(0.626935\pi\) | |||||||
\(74\) | −6.53848 | −0.760083 | ||||||||
\(75\) | 3.65578 | 0.422134 | ||||||||
\(76\) | −1.42633 | −0.163612 | ||||||||
\(77\) | −7.78700 | −0.887411 | ||||||||
\(78\) | 0.0389711 | 0.00441260 | ||||||||
\(79\) | 7.08175 | 0.796760 | 0.398380 | − | 0.917221i | \(-0.369573\pi\) | ||||
0.398380 | + | 0.917221i | \(0.369573\pi\) | |||||||
\(80\) | −2.72563 | −0.304735 | ||||||||
\(81\) | −6.25517 | −0.695019 | ||||||||
\(82\) | −1.11334 | −0.122947 | ||||||||
\(83\) | −13.3908 | −1.46983 | −0.734913 | − | 0.678162i | \(-0.762777\pi\) | ||||
−0.734913 | + | 0.678162i | \(0.762777\pi\) | |||||||
\(84\) | −3.55924 | −0.388345 | ||||||||
\(85\) | −3.42638 | −0.371643 | ||||||||
\(86\) | −3.03969 | −0.327778 | ||||||||
\(87\) | 1.78519 | 0.191392 | ||||||||
\(88\) | −3.29273 | −0.351006 | ||||||||
\(89\) | 11.0810 | 1.17458 | 0.587292 | − | 0.809375i | \(-0.300194\pi\) | ||||
0.587292 | + | 0.809375i | \(0.300194\pi\) | |||||||
\(90\) | −2.00310 | −0.211145 | ||||||||
\(91\) | 0.0612370 | 0.00641938 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 8.99723 | 0.932969 | ||||||||
\(94\) | −11.9054 | −1.22794 | ||||||||
\(95\) | 3.88765 | 0.398865 | ||||||||
\(96\) | −1.50502 | −0.153606 | ||||||||
\(97\) | 2.00602 | 0.203680 | 0.101840 | − | 0.994801i | \(-0.467527\pi\) | ||||
0.101840 | + | 0.994801i | \(0.467527\pi\) | |||||||
\(98\) | 1.40721 | 0.142150 | ||||||||
\(99\) | −2.41986 | −0.243206 | ||||||||
\(100\) | 2.42906 | 0.242906 | ||||||||
\(101\) | −12.6988 | −1.26358 | −0.631790 | − | 0.775140i | \(-0.717679\pi\) | ||||
−0.631790 | + | 0.775140i | \(0.717679\pi\) | |||||||
\(102\) | −1.89196 | −0.187332 | ||||||||
\(103\) | 2.47387 | 0.243758 | 0.121879 | − | 0.992545i | \(-0.461108\pi\) | ||||
0.121879 | + | 0.992545i | \(0.461108\pi\) | |||||||
\(104\) | 0.0258940 | 0.00253912 | ||||||||
\(105\) | 9.70116 | 0.946736 | ||||||||
\(106\) | 8.79403 | 0.854152 | ||||||||
\(107\) | −19.8351 | −1.91753 | −0.958763 | − | 0.284205i | \(-0.908270\pi\) | ||||
−0.958763 | + | 0.284205i | \(0.908270\pi\) | |||||||
\(108\) | −5.62112 | −0.540893 | ||||||||
\(109\) | 1.14841 | 0.109997 | 0.0549987 | − | 0.998486i | \(-0.482485\pi\) | ||||
0.0549987 | + | 0.998486i | \(0.482485\pi\) | |||||||
\(110\) | 8.97475 | 0.855709 | ||||||||
\(111\) | 9.84056 | 0.934024 | ||||||||
\(112\) | −2.36491 | −0.223463 | ||||||||
\(113\) | 20.1469 | 1.89526 | 0.947630 | − | 0.319369i | \(-0.103471\pi\) | ||||
0.947630 | + | 0.319369i | \(0.103471\pi\) | |||||||
\(114\) | 2.14666 | 0.201053 | ||||||||
\(115\) | −2.72563 | −0.254166 | ||||||||
\(116\) | 1.18615 | 0.110132 | ||||||||
\(117\) | 0.0190298 | 0.00175931 | ||||||||
\(118\) | 0.637130 | 0.0586526 | ||||||||
\(119\) | −2.97292 | −0.272527 | ||||||||
\(120\) | 4.10213 | 0.374472 | ||||||||
\(121\) | −0.157950 | −0.0143591 | ||||||||
\(122\) | 10.4294 | 0.944230 | ||||||||
\(123\) | 1.67559 | 0.151083 | ||||||||
\(124\) | 5.97814 | 0.536853 | ||||||||
\(125\) | 7.00744 | 0.626764 | ||||||||
\(126\) | −1.73800 | −0.154833 | ||||||||
\(127\) | 7.11064 | 0.630967 | 0.315484 | − | 0.948931i | \(-0.397833\pi\) | ||||
0.315484 | + | 0.948931i | \(0.397833\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.57480 | 0.402789 | ||||||||
\(130\) | −0.0705775 | −0.00619006 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 4.95562 | 0.431332 | ||||||||
\(133\) | 3.37315 | 0.292489 | ||||||||
\(134\) | −4.76854 | −0.411939 | ||||||||
\(135\) | 15.3211 | 1.31863 | ||||||||
\(136\) | −1.25710 | −0.107795 | ||||||||
\(137\) | −18.3591 | −1.56853 | −0.784264 | − | 0.620427i | \(-0.786959\pi\) | ||||
−0.784264 | + | 0.620427i | \(0.786959\pi\) | |||||||
\(138\) | −1.50502 | −0.128116 | ||||||||
\(139\) | −16.4313 | −1.39368 | −0.696841 | − | 0.717226i | \(-0.745412\pi\) | ||||
−0.696841 | + | 0.717226i | \(0.745412\pi\) | |||||||
\(140\) | 6.44587 | 0.544775 | ||||||||
\(141\) | 17.9178 | 1.50895 | ||||||||
\(142\) | 7.69944 | 0.646123 | ||||||||
\(143\) | −0.0852620 | −0.00712996 | ||||||||
\(144\) | −0.734912 | −0.0612427 | ||||||||
\(145\) | −3.23302 | −0.268488 | ||||||||
\(146\) | 6.63515 | 0.549129 | ||||||||
\(147\) | −2.11788 | −0.174680 | ||||||||
\(148\) | 6.53848 | 0.537460 | ||||||||
\(149\) | −8.63910 | −0.707743 | −0.353871 | − | 0.935294i | \(-0.615135\pi\) | ||||
−0.353871 | + | 0.935294i | \(0.615135\pi\) | |||||||
\(150\) | −3.65578 | −0.298493 | ||||||||
\(151\) | 0.717568 | 0.0583948 | 0.0291974 | − | 0.999574i | \(-0.490705\pi\) | ||||
0.0291974 | + | 0.999574i | \(0.490705\pi\) | |||||||
\(152\) | 1.42633 | 0.115691 | ||||||||
\(153\) | −0.923856 | −0.0746893 | ||||||||
\(154\) | 7.78700 | 0.627494 | ||||||||
\(155\) | −16.2942 | −1.30878 | ||||||||
\(156\) | −0.0389711 | −0.00312018 | ||||||||
\(157\) | −6.64964 | −0.530699 | −0.265349 | − | 0.964152i | \(-0.585487\pi\) | ||||
−0.265349 | + | 0.964152i | \(0.585487\pi\) | |||||||
\(158\) | −7.08175 | −0.563394 | ||||||||
\(159\) | −13.2352 | −1.04962 | ||||||||
\(160\) | 2.72563 | 0.215480 | ||||||||
\(161\) | −2.36491 | −0.186381 | ||||||||
\(162\) | 6.25517 | 0.491452 | ||||||||
\(163\) | −10.6956 | −0.837741 | −0.418871 | − | 0.908046i | \(-0.637574\pi\) | ||||
−0.418871 | + | 0.908046i | \(0.637574\pi\) | |||||||
\(164\) | 1.11334 | 0.0869370 | ||||||||
\(165\) | −13.5072 | −1.05153 | ||||||||
\(166\) | 13.3908 | 1.03932 | ||||||||
\(167\) | 0.226009 | 0.0174891 | 0.00874453 | − | 0.999962i | \(-0.497216\pi\) | ||||
0.00874453 | + | 0.999962i | \(0.497216\pi\) | |||||||
\(168\) | 3.55924 | 0.274601 | ||||||||
\(169\) | −12.9993 | −0.999948 | ||||||||
\(170\) | 3.42638 | 0.262791 | ||||||||
\(171\) | 1.04823 | 0.0801601 | ||||||||
\(172\) | 3.03969 | 0.231774 | ||||||||
\(173\) | 8.60643 | 0.654335 | 0.327167 | − | 0.944966i | \(-0.393906\pi\) | ||||
0.327167 | + | 0.944966i | \(0.393906\pi\) | |||||||
\(174\) | −1.78519 | −0.135335 | ||||||||
\(175\) | −5.74450 | −0.434243 | ||||||||
\(176\) | 3.29273 | 0.248199 | ||||||||
\(177\) | −0.958895 | −0.0720749 | ||||||||
\(178\) | −11.0810 | −0.830556 | ||||||||
\(179\) | 16.1662 | 1.20832 | 0.604159 | − | 0.796864i | \(-0.293509\pi\) | ||||
0.604159 | + | 0.796864i | \(0.293509\pi\) | |||||||
\(180\) | 2.00310 | 0.149302 | ||||||||
\(181\) | −13.0720 | −0.971636 | −0.485818 | − | 0.874060i | \(-0.661478\pi\) | ||||
−0.485818 | + | 0.874060i | \(0.661478\pi\) | |||||||
\(182\) | −0.0612370 | −0.00453919 | ||||||||
\(183\) | −15.6964 | −1.16031 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −17.8215 | −1.31026 | ||||||||
\(186\) | −8.99723 | −0.659709 | ||||||||
\(187\) | 4.13928 | 0.302694 | ||||||||
\(188\) | 11.9054 | 0.868288 | ||||||||
\(189\) | 13.2934 | 0.966955 | ||||||||
\(190\) | −3.88765 | −0.282040 | ||||||||
\(191\) | 26.9462 | 1.94976 | 0.974878 | − | 0.222737i | \(-0.0714993\pi\) | ||||
0.974878 | + | 0.222737i | \(0.0714993\pi\) | |||||||
\(192\) | 1.50502 | 0.108616 | ||||||||
\(193\) | −14.5321 | −1.04604 | −0.523021 | − | 0.852320i | \(-0.675195\pi\) | ||||
−0.523021 | + | 0.852320i | \(0.675195\pi\) | |||||||
\(194\) | −2.00602 | −0.144024 | ||||||||
\(195\) | 0.106221 | 0.00760662 | ||||||||
\(196\) | −1.40721 | −0.100515 | ||||||||
\(197\) | −22.9483 | −1.63500 | −0.817499 | − | 0.575930i | \(-0.804640\pi\) | ||||
−0.817499 | + | 0.575930i | \(0.804640\pi\) | |||||||
\(198\) | 2.41986 | 0.171972 | ||||||||
\(199\) | 12.6803 | 0.898880 | 0.449440 | − | 0.893311i | \(-0.351624\pi\) | ||||
0.449440 | + | 0.893311i | \(0.351624\pi\) | |||||||
\(200\) | −2.42906 | −0.171760 | ||||||||
\(201\) | 7.17676 | 0.506209 | ||||||||
\(202\) | 12.6988 | 0.893485 | ||||||||
\(203\) | −2.80515 | −0.196883 | ||||||||
\(204\) | 1.89196 | 0.132464 | ||||||||
\(205\) | −3.03454 | −0.211942 | ||||||||
\(206\) | −2.47387 | −0.172363 | ||||||||
\(207\) | −0.734912 | −0.0510799 | ||||||||
\(208\) | −0.0258940 | −0.00179543 | ||||||||
\(209\) | −4.69652 | −0.324865 | ||||||||
\(210\) | −9.70116 | −0.669444 | ||||||||
\(211\) | −28.6231 | −1.97050 | −0.985249 | − | 0.171126i | \(-0.945259\pi\) | ||||
−0.985249 | + | 0.171126i | \(0.945259\pi\) | |||||||
\(212\) | −8.79403 | −0.603977 | ||||||||
\(213\) | −11.5878 | −0.793984 | ||||||||
\(214\) | 19.8351 | 1.35590 | ||||||||
\(215\) | −8.28508 | −0.565038 | ||||||||
\(216\) | 5.62112 | 0.382469 | ||||||||
\(217\) | −14.1378 | −0.959733 | ||||||||
\(218\) | −1.14841 | −0.0777799 | ||||||||
\(219\) | −9.98604 | −0.674794 | ||||||||
\(220\) | −8.97475 | −0.605078 | ||||||||
\(221\) | −0.0325513 | −0.00218964 | ||||||||
\(222\) | −9.84056 | −0.660455 | ||||||||
\(223\) | −21.6945 | −1.45277 | −0.726385 | − | 0.687288i | \(-0.758801\pi\) | ||||
−0.726385 | + | 0.687288i | \(0.758801\pi\) | |||||||
\(224\) | 2.36491 | 0.158012 | ||||||||
\(225\) | −1.78514 | −0.119010 | ||||||||
\(226\) | −20.1469 | −1.34015 | ||||||||
\(227\) | −10.9881 | −0.729303 | −0.364652 | − | 0.931144i | \(-0.618812\pi\) | ||||
−0.364652 | + | 0.931144i | \(0.618812\pi\) | |||||||
\(228\) | −2.14666 | −0.142166 | ||||||||
\(229\) | 11.6536 | 0.770089 | 0.385045 | − | 0.922898i | \(-0.374186\pi\) | ||||
0.385045 | + | 0.922898i | \(0.374186\pi\) | |||||||
\(230\) | 2.72563 | 0.179723 | ||||||||
\(231\) | −11.7196 | −0.771093 | ||||||||
\(232\) | −1.18615 | −0.0778749 | ||||||||
\(233\) | 14.5619 | 0.953980 | 0.476990 | − | 0.878909i | \(-0.341728\pi\) | ||||
0.476990 | + | 0.878909i | \(0.341728\pi\) | |||||||
\(234\) | −0.0190298 | −0.00124402 | ||||||||
\(235\) | −32.4496 | −2.11678 | ||||||||
\(236\) | −0.637130 | −0.0414737 | ||||||||
\(237\) | 10.6582 | 0.692324 | ||||||||
\(238\) | 2.97292 | 0.192706 | ||||||||
\(239\) | −23.8632 | −1.54358 | −0.771791 | − | 0.635877i | \(-0.780639\pi\) | ||||
−0.771791 | + | 0.635877i | \(0.780639\pi\) | |||||||
\(240\) | −4.10213 | −0.264791 | ||||||||
\(241\) | −22.7518 | −1.46557 | −0.732786 | − | 0.680459i | \(-0.761780\pi\) | ||||
−0.732786 | + | 0.680459i | \(0.761780\pi\) | |||||||
\(242\) | 0.157950 | 0.0101534 | ||||||||
\(243\) | 7.44920 | 0.477867 | ||||||||
\(244\) | −10.4294 | −0.667672 | ||||||||
\(245\) | 3.83553 | 0.245043 | ||||||||
\(246\) | −1.67559 | −0.106832 | ||||||||
\(247\) | 0.0369335 | 0.00235002 | ||||||||
\(248\) | −5.97814 | −0.379612 | ||||||||
\(249\) | −20.1534 | −1.27717 | ||||||||
\(250\) | −7.00744 | −0.443189 | ||||||||
\(251\) | −21.0619 | −1.32942 | −0.664708 | − | 0.747103i | \(-0.731444\pi\) | ||||
−0.664708 | + | 0.747103i | \(0.731444\pi\) | |||||||
\(252\) | 1.73800 | 0.109484 | ||||||||
\(253\) | 3.29273 | 0.207012 | ||||||||
\(254\) | −7.11064 | −0.446161 | ||||||||
\(255\) | −5.15678 | −0.322930 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.995340 | 0.0620876 | 0.0310438 | − | 0.999518i | \(-0.490117\pi\) | ||||
0.0310438 | + | 0.999518i | \(0.490117\pi\) | |||||||
\(258\) | −4.57480 | −0.284815 | ||||||||
\(259\) | −15.4629 | −0.960819 | ||||||||
\(260\) | 0.0705775 | 0.00437703 | ||||||||
\(261\) | −0.871719 | −0.0539581 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | 19.0437 | 1.17429 | 0.587143 | − | 0.809483i | \(-0.300253\pi\) | ||||
0.587143 | + | 0.809483i | \(0.300253\pi\) | |||||||
\(264\) | −4.95562 | −0.304997 | ||||||||
\(265\) | 23.9693 | 1.47242 | ||||||||
\(266\) | −3.37315 | −0.206821 | ||||||||
\(267\) | 16.6771 | 1.02062 | ||||||||
\(268\) | 4.76854 | 0.291285 | ||||||||
\(269\) | 23.1840 | 1.41355 | 0.706777 | − | 0.707437i | \(-0.250149\pi\) | ||||
0.706777 | + | 0.707437i | \(0.250149\pi\) | |||||||
\(270\) | −15.3211 | −0.932412 | ||||||||
\(271\) | −0.0952327 | −0.00578497 | −0.00289249 | − | 0.999996i | \(-0.500921\pi\) | ||||
−0.00289249 | + | 0.999996i | \(0.500921\pi\) | |||||||
\(272\) | 1.25710 | 0.0762227 | ||||||||
\(273\) | 0.0921630 | 0.00557796 | ||||||||
\(274\) | 18.3591 | 1.10912 | ||||||||
\(275\) | 7.99823 | 0.482311 | ||||||||
\(276\) | 1.50502 | 0.0905916 | ||||||||
\(277\) | −10.8520 | −0.652033 | −0.326016 | − | 0.945364i | \(-0.605706\pi\) | ||||
−0.326016 | + | 0.945364i | \(0.605706\pi\) | |||||||
\(278\) | 16.4313 | 0.985482 | ||||||||
\(279\) | −4.39341 | −0.263026 | ||||||||
\(280\) | −6.44587 | −0.385214 | ||||||||
\(281\) | −8.69946 | −0.518966 | −0.259483 | − | 0.965748i | \(-0.583552\pi\) | ||||
−0.259483 | + | 0.965748i | \(0.583552\pi\) | |||||||
\(282\) | −17.9178 | −1.06699 | ||||||||
\(283\) | −13.0236 | −0.774174 | −0.387087 | − | 0.922043i | \(-0.626519\pi\) | ||||
−0.387087 | + | 0.922043i | \(0.626519\pi\) | |||||||
\(284\) | −7.69944 | −0.456878 | ||||||||
\(285\) | 5.85100 | 0.346583 | ||||||||
\(286\) | 0.0852620 | 0.00504165 | ||||||||
\(287\) | −2.63294 | −0.155417 | ||||||||
\(288\) | 0.734912 | 0.0433051 | ||||||||
\(289\) | −15.4197 | −0.907042 | ||||||||
\(290\) | 3.23302 | 0.189849 | ||||||||
\(291\) | 3.01910 | 0.176983 | ||||||||
\(292\) | −6.63515 | −0.388293 | ||||||||
\(293\) | 13.7640 | 0.804100 | 0.402050 | − | 0.915618i | \(-0.368298\pi\) | ||||
0.402050 | + | 0.915618i | \(0.368298\pi\) | |||||||
\(294\) | 2.11788 | 0.123517 | ||||||||
\(295\) | 1.73658 | 0.101108 | ||||||||
\(296\) | −6.53848 | −0.380042 | ||||||||
\(297\) | −18.5088 | −1.07399 | ||||||||
\(298\) | 8.63910 | 0.500450 | ||||||||
\(299\) | −0.0258940 | −0.00149749 | ||||||||
\(300\) | 3.65578 | 0.211067 | ||||||||
\(301\) | −7.18859 | −0.414344 | ||||||||
\(302\) | −0.717568 | −0.0412914 | ||||||||
\(303\) | −19.1120 | −1.09795 | ||||||||
\(304\) | −1.42633 | −0.0818058 | ||||||||
\(305\) | 28.4266 | 1.62770 | ||||||||
\(306\) | 0.923856 | 0.0528133 | ||||||||
\(307\) | 32.3442 | 1.84598 | 0.922990 | − | 0.384825i | \(-0.125738\pi\) | ||||
0.922990 | + | 0.384825i | \(0.125738\pi\) | |||||||
\(308\) | −7.78700 | −0.443705 | ||||||||
\(309\) | 3.72323 | 0.211807 | ||||||||
\(310\) | 16.2942 | 0.925448 | ||||||||
\(311\) | −4.72919 | −0.268168 | −0.134084 | − | 0.990970i | \(-0.542809\pi\) | ||||
−0.134084 | + | 0.990970i | \(0.542809\pi\) | |||||||
\(312\) | 0.0389711 | 0.00220630 | ||||||||
\(313\) | −21.3739 | −1.20812 | −0.604061 | − | 0.796938i | \(-0.706452\pi\) | ||||
−0.604061 | + | 0.796938i | \(0.706452\pi\) | |||||||
\(314\) | 6.64964 | 0.375261 | ||||||||
\(315\) | −4.73714 | −0.266908 | ||||||||
\(316\) | 7.08175 | 0.398380 | ||||||||
\(317\) | −16.9856 | −0.954006 | −0.477003 | − | 0.878902i | \(-0.658277\pi\) | ||||
−0.477003 | + | 0.878902i | \(0.658277\pi\) | |||||||
\(318\) | 13.2352 | 0.742193 | ||||||||
\(319\) | 3.90568 | 0.218676 | ||||||||
\(320\) | −2.72563 | −0.152367 | ||||||||
\(321\) | −29.8522 | −1.66619 | ||||||||
\(322\) | 2.36491 | 0.131791 | ||||||||
\(323\) | −1.79304 | −0.0997673 | ||||||||
\(324\) | −6.25517 | −0.347509 | ||||||||
\(325\) | −0.0628981 | −0.00348896 | ||||||||
\(326\) | 10.6956 | 0.592373 | ||||||||
\(327\) | 1.72838 | 0.0955794 | ||||||||
\(328\) | −1.11334 | −0.0614737 | ||||||||
\(329\) | −28.1551 | −1.55224 | ||||||||
\(330\) | 13.5072 | 0.743547 | ||||||||
\(331\) | −29.0657 | −1.59760 | −0.798799 | − | 0.601598i | \(-0.794531\pi\) | ||||
−0.798799 | + | 0.601598i | \(0.794531\pi\) | |||||||
\(332\) | −13.3908 | −0.734913 | ||||||||
\(333\) | −4.80521 | −0.263324 | ||||||||
\(334\) | −0.226009 | −0.0123666 | ||||||||
\(335\) | −12.9973 | −0.710117 | ||||||||
\(336\) | −3.55924 | −0.194172 | ||||||||
\(337\) | 19.9216 | 1.08520 | 0.542599 | − | 0.839992i | \(-0.317440\pi\) | ||||
0.542599 | + | 0.839992i | \(0.317440\pi\) | |||||||
\(338\) | 12.9993 | 0.707070 | ||||||||
\(339\) | 30.3215 | 1.64684 | ||||||||
\(340\) | −3.42638 | −0.185822 | ||||||||
\(341\) | 19.6844 | 1.06597 | ||||||||
\(342\) | −1.04823 | −0.0566817 | ||||||||
\(343\) | 19.8823 | 1.07354 | ||||||||
\(344\) | −3.03969 | −0.163889 | ||||||||
\(345\) | −4.10213 | −0.220851 | ||||||||
\(346\) | −8.60643 | −0.462685 | ||||||||
\(347\) | 31.5949 | 1.69610 | 0.848051 | − | 0.529914i | \(-0.177776\pi\) | ||||
0.848051 | + | 0.529914i | \(0.177776\pi\) | |||||||
\(348\) | 1.78519 | 0.0956961 | ||||||||
\(349\) | 2.88986 | 0.154691 | 0.0773454 | − | 0.997004i | \(-0.475356\pi\) | ||||
0.0773454 | + | 0.997004i | \(0.475356\pi\) | |||||||
\(350\) | 5.74450 | 0.307056 | ||||||||
\(351\) | 0.145553 | 0.00776907 | ||||||||
\(352\) | −3.29273 | −0.175503 | ||||||||
\(353\) | −12.6049 | −0.670890 | −0.335445 | − | 0.942060i | \(-0.608887\pi\) | ||||
−0.335445 | + | 0.942060i | \(0.608887\pi\) | |||||||
\(354\) | 0.958895 | 0.0509647 | ||||||||
\(355\) | 20.9858 | 1.11381 | ||||||||
\(356\) | 11.0810 | 0.587292 | ||||||||
\(357\) | −4.47431 | −0.236805 | ||||||||
\(358\) | −16.1662 | −0.854410 | ||||||||
\(359\) | 11.3247 | 0.597697 | 0.298848 | − | 0.954301i | \(-0.403397\pi\) | ||||
0.298848 | + | 0.954301i | \(0.403397\pi\) | |||||||
\(360\) | −2.00310 | −0.105573 | ||||||||
\(361\) | −16.9656 | −0.892925 | ||||||||
\(362\) | 13.0720 | 0.687051 | ||||||||
\(363\) | −0.237719 | −0.0124770 | ||||||||
\(364\) | 0.0612370 | 0.00320969 | ||||||||
\(365\) | 18.0850 | 0.946611 | ||||||||
\(366\) | 15.6964 | 0.820464 | ||||||||
\(367\) | −12.3212 | −0.643162 | −0.321581 | − | 0.946882i | \(-0.604214\pi\) | ||||
−0.321581 | + | 0.946882i | \(0.604214\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −0.818204 | −0.0425940 | ||||||||
\(370\) | 17.8215 | 0.926495 | ||||||||
\(371\) | 20.7971 | 1.07973 | ||||||||
\(372\) | 8.99723 | 0.466484 | ||||||||
\(373\) | −31.4290 | −1.62733 | −0.813667 | − | 0.581331i | \(-0.802532\pi\) | ||||
−0.813667 | + | 0.581331i | \(0.802532\pi\) | |||||||
\(374\) | −4.13928 | −0.214037 | ||||||||
\(375\) | 10.5463 | 0.544610 | ||||||||
\(376\) | −11.9054 | −0.613972 | ||||||||
\(377\) | −0.0307143 | −0.00158187 | ||||||||
\(378\) | −13.2934 | −0.683741 | ||||||||
\(379\) | 4.54449 | 0.233435 | 0.116717 | − | 0.993165i | \(-0.462763\pi\) | ||||
0.116717 | + | 0.993165i | \(0.462763\pi\) | |||||||
\(380\) | 3.88765 | 0.199432 | ||||||||
\(381\) | 10.7017 | 0.548263 | ||||||||
\(382\) | −26.9462 | −1.37869 | ||||||||
\(383\) | 2.24326 | 0.114625 | 0.0573127 | − | 0.998356i | \(-0.481747\pi\) | ||||
0.0573127 | + | 0.998356i | \(0.481747\pi\) | |||||||
\(384\) | −1.50502 | −0.0768028 | ||||||||
\(385\) | 21.2245 | 1.08170 | ||||||||
\(386\) | 14.5321 | 0.739663 | ||||||||
\(387\) | −2.23391 | −0.113556 | ||||||||
\(388\) | 2.00602 | 0.101840 | ||||||||
\(389\) | −18.5644 | −0.941251 | −0.470626 | − | 0.882333i | \(-0.655972\pi\) | ||||
−0.470626 | + | 0.882333i | \(0.655972\pi\) | |||||||
\(390\) | −0.106221 | −0.00537869 | ||||||||
\(391\) | 1.25710 | 0.0635741 | ||||||||
\(392\) | 1.40721 | 0.0710748 | ||||||||
\(393\) | 1.50502 | 0.0759183 | ||||||||
\(394\) | 22.9483 | 1.15612 | ||||||||
\(395\) | −19.3022 | −0.971201 | ||||||||
\(396\) | −2.41986 | −0.121603 | ||||||||
\(397\) | 0.594174 | 0.0298207 | 0.0149104 | − | 0.999889i | \(-0.495254\pi\) | ||||
0.0149104 | + | 0.999889i | \(0.495254\pi\) | |||||||
\(398\) | −12.6803 | −0.635604 | ||||||||
\(399\) | 5.07666 | 0.254151 | ||||||||
\(400\) | 2.42906 | 0.121453 | ||||||||
\(401\) | 0.754936 | 0.0376997 | 0.0188499 | − | 0.999822i | \(-0.494000\pi\) | ||||
0.0188499 | + | 0.999822i | \(0.494000\pi\) | |||||||
\(402\) | −7.17676 | −0.357944 | ||||||||
\(403\) | −0.154798 | −0.00771104 | ||||||||
\(404\) | −12.6988 | −0.631790 | ||||||||
\(405\) | 17.0493 | 0.847185 | ||||||||
\(406\) | 2.80515 | 0.139217 | ||||||||
\(407\) | 21.5294 | 1.06717 | ||||||||
\(408\) | −1.89196 | −0.0936658 | ||||||||
\(409\) | −25.8626 | −1.27882 | −0.639411 | − | 0.768865i | \(-0.720822\pi\) | ||||
−0.639411 | + | 0.768865i | \(0.720822\pi\) | |||||||
\(410\) | 3.03454 | 0.149865 | ||||||||
\(411\) | −27.6309 | −1.36293 | ||||||||
\(412\) | 2.47387 | 0.121879 | ||||||||
\(413\) | 1.50676 | 0.0741426 | ||||||||
\(414\) | 0.734912 | 0.0361190 | ||||||||
\(415\) | 36.4982 | 1.79163 | ||||||||
\(416\) | 0.0258940 | 0.00126956 | ||||||||
\(417\) | −24.7294 | −1.21100 | ||||||||
\(418\) | 4.69652 | 0.229714 | ||||||||
\(419\) | 17.2461 | 0.842525 | 0.421263 | − | 0.906939i | \(-0.361587\pi\) | ||||
0.421263 | + | 0.906939i | \(0.361587\pi\) | |||||||
\(420\) | 9.70116 | 0.473368 | ||||||||
\(421\) | 36.3621 | 1.77218 | 0.886091 | − | 0.463511i | \(-0.153410\pi\) | ||||
0.886091 | + | 0.463511i | \(0.153410\pi\) | |||||||
\(422\) | 28.6231 | 1.39335 | ||||||||
\(423\) | −8.74939 | −0.425410 | ||||||||
\(424\) | 8.79403 | 0.427076 | ||||||||
\(425\) | 3.05356 | 0.148120 | ||||||||
\(426\) | 11.5878 | 0.561432 | ||||||||
\(427\) | 24.6645 | 1.19360 | ||||||||
\(428\) | −19.8351 | −0.958763 | ||||||||
\(429\) | −0.128321 | −0.00619540 | ||||||||
\(430\) | 8.28508 | 0.399542 | ||||||||
\(431\) | −21.9180 | −1.05575 | −0.527875 | − | 0.849322i | \(-0.677011\pi\) | ||||
−0.527875 | + | 0.849322i | \(0.677011\pi\) | |||||||
\(432\) | −5.62112 | −0.270446 | ||||||||
\(433\) | −32.9831 | −1.58507 | −0.792533 | − | 0.609829i | \(-0.791238\pi\) | ||||
−0.792533 | + | 0.609829i | \(0.791238\pi\) | |||||||
\(434\) | 14.1378 | 0.678634 | ||||||||
\(435\) | −4.86576 | −0.233295 | ||||||||
\(436\) | 1.14841 | 0.0549987 | ||||||||
\(437\) | −1.42633 | −0.0682307 | ||||||||
\(438\) | 9.98604 | 0.477152 | ||||||||
\(439\) | 35.6717 | 1.70252 | 0.851260 | − | 0.524744i | \(-0.175839\pi\) | ||||
0.851260 | + | 0.524744i | \(0.175839\pi\) | |||||||
\(440\) | 8.97475 | 0.427855 | ||||||||
\(441\) | 1.03417 | 0.0492464 | ||||||||
\(442\) | 0.0325513 | 0.00154831 | ||||||||
\(443\) | 19.4406 | 0.923653 | 0.461826 | − | 0.886970i | \(-0.347194\pi\) | ||||
0.461826 | + | 0.886970i | \(0.347194\pi\) | |||||||
\(444\) | 9.84056 | 0.467012 | ||||||||
\(445\) | −30.2027 | −1.43175 | ||||||||
\(446\) | 21.6945 | 1.02726 | ||||||||
\(447\) | −13.0020 | −0.614975 | ||||||||
\(448\) | −2.36491 | −0.111731 | ||||||||
\(449\) | −30.5372 | −1.44114 | −0.720571 | − | 0.693382i | \(-0.756120\pi\) | ||||
−0.720571 | + | 0.693382i | \(0.756120\pi\) | |||||||
\(450\) | 1.78514 | 0.0841525 | ||||||||
\(451\) | 3.66591 | 0.172621 | ||||||||
\(452\) | 20.1469 | 0.947630 | ||||||||
\(453\) | 1.07995 | 0.0507407 | ||||||||
\(454\) | 10.9881 | 0.515695 | ||||||||
\(455\) | −0.166909 | −0.00782483 | ||||||||
\(456\) | 2.14666 | 0.100527 | ||||||||
\(457\) | −19.9037 | −0.931055 | −0.465527 | − | 0.885033i | \(-0.654135\pi\) | ||||
−0.465527 | + | 0.885033i | \(0.654135\pi\) | |||||||
\(458\) | −11.6536 | −0.544535 | ||||||||
\(459\) | −7.06629 | −0.329826 | ||||||||
\(460\) | −2.72563 | −0.127083 | ||||||||
\(461\) | −4.60202 | −0.214337 | −0.107169 | − | 0.994241i | \(-0.534178\pi\) | ||||
−0.107169 | + | 0.994241i | \(0.534178\pi\) | |||||||
\(462\) | 11.7196 | 0.545245 | ||||||||
\(463\) | −9.67270 | −0.449528 | −0.224764 | − | 0.974413i | \(-0.572161\pi\) | ||||
−0.224764 | + | 0.974413i | \(0.572161\pi\) | |||||||
\(464\) | 1.18615 | 0.0550659 | ||||||||
\(465\) | −24.5231 | −1.13723 | ||||||||
\(466\) | −14.5619 | −0.674566 | ||||||||
\(467\) | 38.8060 | 1.79573 | 0.897864 | − | 0.440273i | \(-0.145118\pi\) | ||||
0.897864 | + | 0.440273i | \(0.145118\pi\) | |||||||
\(468\) | 0.0190298 | 0.000879654 0 | ||||||||
\(469\) | −11.2772 | −0.520731 | ||||||||
\(470\) | 32.4496 | 1.49679 | ||||||||
\(471\) | −10.0078 | −0.461137 | ||||||||
\(472\) | 0.637130 | 0.0293263 | ||||||||
\(473\) | 10.0089 | 0.460209 | ||||||||
\(474\) | −10.6582 | −0.489547 | ||||||||
\(475\) | −3.46465 | −0.158969 | ||||||||
\(476\) | −2.97292 | −0.136264 | ||||||||
\(477\) | 6.46284 | 0.295913 | ||||||||
\(478\) | 23.8632 | 1.09148 | ||||||||
\(479\) | 21.0216 | 0.960501 | 0.480250 | − | 0.877131i | \(-0.340546\pi\) | ||||
0.480250 | + | 0.877131i | \(0.340546\pi\) | |||||||
\(480\) | 4.10213 | 0.187236 | ||||||||
\(481\) | −0.169308 | −0.00771977 | ||||||||
\(482\) | 22.7518 | 1.03632 | ||||||||
\(483\) | −3.55924 | −0.161951 | ||||||||
\(484\) | −0.157950 | −0.00717956 | ||||||||
\(485\) | −5.46767 | −0.248274 | ||||||||
\(486\) | −7.44920 | −0.337903 | ||||||||
\(487\) | −15.4903 | −0.701934 | −0.350967 | − | 0.936388i | \(-0.614147\pi\) | ||||
−0.350967 | + | 0.936388i | \(0.614147\pi\) | |||||||
\(488\) | 10.4294 | 0.472115 | ||||||||
\(489\) | −16.0970 | −0.727934 | ||||||||
\(490\) | −3.83553 | −0.173272 | ||||||||
\(491\) | −6.46100 | −0.291581 | −0.145791 | − | 0.989315i | \(-0.546573\pi\) | ||||
−0.145791 | + | 0.989315i | \(0.546573\pi\) | |||||||
\(492\) | 1.67559 | 0.0755416 | ||||||||
\(493\) | 1.49111 | 0.0671563 | ||||||||
\(494\) | −0.0369335 | −0.00166172 | ||||||||
\(495\) | 6.59566 | 0.296453 | ||||||||
\(496\) | 5.97814 | 0.268426 | ||||||||
\(497\) | 18.2085 | 0.816762 | ||||||||
\(498\) | 20.1534 | 0.903094 | ||||||||
\(499\) | −35.8164 | −1.60336 | −0.801681 | − | 0.597752i | \(-0.796061\pi\) | ||||
−0.801681 | + | 0.597752i | \(0.796061\pi\) | |||||||
\(500\) | 7.00744 | 0.313382 | ||||||||
\(501\) | 0.340148 | 0.0151967 | ||||||||
\(502\) | 21.0619 | 0.940039 | ||||||||
\(503\) | 7.48407 | 0.333698 | 0.166849 | − | 0.985982i | \(-0.446641\pi\) | ||||
0.166849 | + | 0.985982i | \(0.446641\pi\) | |||||||
\(504\) | −1.73800 | −0.0774167 | ||||||||
\(505\) | 34.6123 | 1.54023 | ||||||||
\(506\) | −3.29273 | −0.146380 | ||||||||
\(507\) | −19.5643 | −0.868879 | ||||||||
\(508\) | 7.11064 | 0.315484 | ||||||||
\(509\) | −43.0640 | −1.90878 | −0.954390 | − | 0.298563i | \(-0.903493\pi\) | ||||
−0.954390 | + | 0.298563i | \(0.903493\pi\) | |||||||
\(510\) | 5.15678 | 0.228346 | ||||||||
\(511\) | 15.6915 | 0.694152 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 8.01759 | 0.353985 | ||||||||
\(514\) | −0.995340 | −0.0439026 | ||||||||
\(515\) | −6.74286 | −0.297126 | ||||||||
\(516\) | 4.57480 | 0.201394 | ||||||||
\(517\) | 39.2011 | 1.72406 | ||||||||
\(518\) | 15.4629 | 0.679402 | ||||||||
\(519\) | 12.9529 | 0.568567 | ||||||||
\(520\) | −0.0705775 | −0.00309503 | ||||||||
\(521\) | −7.08185 | −0.310261 | −0.155131 | − | 0.987894i | \(-0.549580\pi\) | ||||
−0.155131 | + | 0.987894i | \(0.549580\pi\) | |||||||
\(522\) | 0.871719 | 0.0381541 | ||||||||
\(523\) | 12.8597 | 0.562315 | 0.281158 | − | 0.959662i | \(-0.409282\pi\) | ||||
0.281158 | + | 0.959662i | \(0.409282\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | −8.64559 | −0.377325 | ||||||||
\(526\) | −19.0437 | −0.830345 | ||||||||
\(527\) | 7.51510 | 0.327363 | ||||||||
\(528\) | 4.95562 | 0.215666 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −23.9693 | −1.04116 | ||||||||
\(531\) | 0.468235 | 0.0203197 | ||||||||
\(532\) | 3.37315 | 0.146244 | ||||||||
\(533\) | −0.0288288 | −0.00124871 | ||||||||
\(534\) | −16.6771 | −0.721690 | ||||||||
\(535\) | 54.0630 | 2.33735 | ||||||||
\(536\) | −4.76854 | −0.205970 | ||||||||
\(537\) | 24.3305 | 1.04994 | ||||||||
\(538\) | −23.1840 | −0.999533 | ||||||||
\(539\) | −4.63355 | −0.199581 | ||||||||
\(540\) | 15.3211 | 0.659315 | ||||||||
\(541\) | −8.15798 | −0.350739 | −0.175369 | − | 0.984503i | \(-0.556112\pi\) | ||||
−0.175369 | + | 0.984503i | \(0.556112\pi\) | |||||||
\(542\) | 0.0952327 | 0.00409059 | ||||||||
\(543\) | −19.6737 | −0.844278 | ||||||||
\(544\) | −1.25710 | −0.0538976 | ||||||||
\(545\) | −3.13013 | −0.134080 | ||||||||
\(546\) | −0.0921630 | −0.00394421 | ||||||||
\(547\) | −3.69883 | −0.158150 | −0.0790752 | − | 0.996869i | \(-0.525197\pi\) | ||||
−0.0790752 | + | 0.996869i | \(0.525197\pi\) | |||||||
\(548\) | −18.3591 | −0.784264 | ||||||||
\(549\) | 7.66467 | 0.327120 | ||||||||
\(550\) | −7.99823 | −0.341045 | ||||||||
\(551\) | −1.69185 | −0.0720753 | ||||||||
\(552\) | −1.50502 | −0.0640579 | ||||||||
\(553\) | −16.7477 | −0.712185 | ||||||||
\(554\) | 10.8520 | 0.461057 | ||||||||
\(555\) | −26.8217 | −1.13852 | ||||||||
\(556\) | −16.4313 | −0.696841 | ||||||||
\(557\) | 20.0270 | 0.848569 | 0.424285 | − | 0.905529i | \(-0.360526\pi\) | ||||
0.424285 | + | 0.905529i | \(0.360526\pi\) | |||||||
\(558\) | 4.39341 | 0.185988 | ||||||||
\(559\) | −0.0787099 | −0.00332907 | ||||||||
\(560\) | 6.44587 | 0.272388 | ||||||||
\(561\) | 6.22970 | 0.263018 | ||||||||
\(562\) | 8.69946 | 0.366965 | ||||||||
\(563\) | −13.1630 | −0.554755 | −0.277378 | − | 0.960761i | \(-0.589465\pi\) | ||||
−0.277378 | + | 0.960761i | \(0.589465\pi\) | |||||||
\(564\) | 17.9178 | 0.754476 | ||||||||
\(565\) | −54.9130 | −2.31021 | ||||||||
\(566\) | 13.0236 | 0.547424 | ||||||||
\(567\) | 14.7929 | 0.621243 | ||||||||
\(568\) | 7.69944 | 0.323061 | ||||||||
\(569\) | 20.6842 | 0.867129 | 0.433564 | − | 0.901123i | \(-0.357256\pi\) | ||||
0.433564 | + | 0.901123i | \(0.357256\pi\) | |||||||
\(570\) | −5.85100 | −0.245071 | ||||||||
\(571\) | −19.4022 | −0.811958 | −0.405979 | − | 0.913882i | \(-0.633069\pi\) | ||||
−0.405979 | + | 0.913882i | \(0.633069\pi\) | |||||||
\(572\) | −0.0852620 | −0.00356498 | ||||||||
\(573\) | 40.5546 | 1.69419 | ||||||||
\(574\) | 2.63294 | 0.109897 | ||||||||
\(575\) | 2.42906 | 0.101299 | ||||||||
\(576\) | −0.734912 | −0.0306213 | ||||||||
\(577\) | 17.4130 | 0.724912 | 0.362456 | − | 0.932001i | \(-0.381938\pi\) | ||||
0.362456 | + | 0.932001i | \(0.381938\pi\) | |||||||
\(578\) | 15.4197 | 0.641375 | ||||||||
\(579\) | −21.8711 | −0.908930 | ||||||||
\(580\) | −3.23302 | −0.134244 | ||||||||
\(581\) | 31.6679 | 1.31381 | ||||||||
\(582\) | −3.01910 | −0.125146 | ||||||||
\(583\) | −28.9563 | −1.19925 | ||||||||
\(584\) | 6.63515 | 0.274565 | ||||||||
\(585\) | −0.0518683 | −0.00214449 | ||||||||
\(586\) | −13.7640 | −0.568585 | ||||||||
\(587\) | 43.8593 | 1.81027 | 0.905133 | − | 0.425129i | \(-0.139771\pi\) | ||||
0.905133 | + | 0.425129i | \(0.139771\pi\) | |||||||
\(588\) | −2.11788 | −0.0873398 | ||||||||
\(589\) | −8.52682 | −0.351341 | ||||||||
\(590\) | −1.73658 | −0.0714939 | ||||||||
\(591\) | −34.5376 | −1.42069 | ||||||||
\(592\) | 6.53848 | 0.268730 | ||||||||
\(593\) | 42.1191 | 1.72962 | 0.864812 | − | 0.502097i | \(-0.167438\pi\) | ||||
0.864812 | + | 0.502097i | \(0.167438\pi\) | |||||||
\(594\) | 18.5088 | 0.759426 | ||||||||
\(595\) | 8.10308 | 0.332194 | ||||||||
\(596\) | −8.63910 | −0.353871 | ||||||||
\(597\) | 19.0841 | 0.781059 | ||||||||
\(598\) | 0.0258940 | 0.00105889 | ||||||||
\(599\) | −2.44539 | −0.0999160 | −0.0499580 | − | 0.998751i | \(-0.515909\pi\) | ||||
−0.0499580 | + | 0.998751i | \(0.515909\pi\) | |||||||
\(600\) | −3.65578 | −0.149247 | ||||||||
\(601\) | 8.82383 | 0.359932 | 0.179966 | − | 0.983673i | \(-0.442401\pi\) | ||||
0.179966 | + | 0.983673i | \(0.442401\pi\) | |||||||
\(602\) | 7.18859 | 0.292985 | ||||||||
\(603\) | −3.50446 | −0.142713 | ||||||||
\(604\) | 0.717568 | 0.0291974 | ||||||||
\(605\) | 0.430514 | 0.0175029 | ||||||||
\(606\) | 19.1120 | 0.776371 | ||||||||
\(607\) | −15.1174 | −0.613596 | −0.306798 | − | 0.951775i | \(-0.599258\pi\) | ||||
−0.306798 | + | 0.951775i | \(0.599258\pi\) | |||||||
\(608\) | 1.42633 | 0.0578454 | ||||||||
\(609\) | −4.22181 | −0.171076 | ||||||||
\(610\) | −28.4266 | −1.15096 | ||||||||
\(611\) | −0.308278 | −0.0124716 | ||||||||
\(612\) | −0.923856 | −0.0373447 | ||||||||
\(613\) | −37.7298 | −1.52389 | −0.761946 | − | 0.647640i | \(-0.775756\pi\) | ||||
−0.761946 | + | 0.647640i | \(0.775756\pi\) | |||||||
\(614\) | −32.3442 | −1.30530 | ||||||||
\(615\) | −4.56705 | −0.184161 | ||||||||
\(616\) | 7.78700 | 0.313747 | ||||||||
\(617\) | 8.20391 | 0.330277 | 0.165138 | − | 0.986270i | \(-0.447193\pi\) | ||||
0.165138 | + | 0.986270i | \(0.447193\pi\) | |||||||
\(618\) | −3.72323 | −0.149770 | ||||||||
\(619\) | 23.4058 | 0.940760 | 0.470380 | − | 0.882464i | \(-0.344117\pi\) | ||||
0.470380 | + | 0.882464i | \(0.344117\pi\) | |||||||
\(620\) | −16.2942 | −0.654391 | ||||||||
\(621\) | −5.62112 | −0.225568 | ||||||||
\(622\) | 4.72919 | 0.189623 | ||||||||
\(623\) | −26.2055 | −1.04990 | ||||||||
\(624\) | −0.0389711 | −0.00156009 | ||||||||
\(625\) | −31.2450 | −1.24980 | ||||||||
\(626\) | 21.3739 | 0.854271 | ||||||||
\(627\) | −7.06837 | −0.282283 | ||||||||
\(628\) | −6.64964 | −0.265349 | ||||||||
\(629\) | 8.21951 | 0.327733 | ||||||||
\(630\) | 4.73714 | 0.188732 | ||||||||
\(631\) | 7.69701 | 0.306413 | 0.153206 | − | 0.988194i | \(-0.451040\pi\) | ||||
0.153206 | + | 0.988194i | \(0.451040\pi\) | |||||||
\(632\) | −7.08175 | −0.281697 | ||||||||
\(633\) | −43.0784 | −1.71221 | ||||||||
\(634\) | 16.9856 | 0.674584 | ||||||||
\(635\) | −19.3810 | −0.769110 | ||||||||
\(636\) | −13.2352 | −0.524810 | ||||||||
\(637\) | 0.0364383 | 0.00144374 | ||||||||
\(638\) | −3.90568 | −0.154627 | ||||||||
\(639\) | 5.65841 | 0.223843 | ||||||||
\(640\) | 2.72563 | 0.107740 | ||||||||
\(641\) | 5.82604 | 0.230115 | 0.115057 | − | 0.993359i | \(-0.463295\pi\) | ||||
0.115057 | + | 0.993359i | \(0.463295\pi\) | |||||||
\(642\) | 29.8522 | 1.17817 | ||||||||
\(643\) | 14.2332 | 0.561304 | 0.280652 | − | 0.959810i | \(-0.409449\pi\) | ||||
0.280652 | + | 0.959810i | \(0.409449\pi\) | |||||||
\(644\) | −2.36491 | −0.0931904 | ||||||||
\(645\) | −12.4692 | −0.490975 | ||||||||
\(646\) | 1.79304 | 0.0705462 | ||||||||
\(647\) | −26.2737 | −1.03292 | −0.516462 | − | 0.856310i | \(-0.672751\pi\) | ||||
−0.516462 | + | 0.856310i | \(0.672751\pi\) | |||||||
\(648\) | 6.25517 | 0.245726 | ||||||||
\(649\) | −2.09790 | −0.0823496 | ||||||||
\(650\) | 0.0628981 | 0.00246707 | ||||||||
\(651\) | −21.2776 | −0.833936 | ||||||||
\(652\) | −10.6956 | −0.418871 | ||||||||
\(653\) | 42.9247 | 1.67977 | 0.839887 | − | 0.542762i | \(-0.182621\pi\) | ||||
0.839887 | + | 0.542762i | \(0.182621\pi\) | |||||||
\(654\) | −1.72838 | −0.0675849 | ||||||||
\(655\) | −2.72563 | −0.106499 | ||||||||
\(656\) | 1.11334 | 0.0434685 | ||||||||
\(657\) | 4.87625 | 0.190241 | ||||||||
\(658\) | 28.1551 | 1.09760 | ||||||||
\(659\) | −19.0280 | −0.741224 | −0.370612 | − | 0.928788i | \(-0.620852\pi\) | ||||
−0.370612 | + | 0.928788i | \(0.620852\pi\) | |||||||
\(660\) | −13.5072 | −0.525767 | ||||||||
\(661\) | 2.91174 | 0.113253 | 0.0566267 | − | 0.998395i | \(-0.481966\pi\) | ||||
0.0566267 | + | 0.998395i | \(0.481966\pi\) | |||||||
\(662\) | 29.0657 | 1.12967 | ||||||||
\(663\) | −0.0489904 | −0.00190263 | ||||||||
\(664\) | 13.3908 | 0.519662 | ||||||||
\(665\) | −9.19395 | −0.356526 | ||||||||
\(666\) | 4.80521 | 0.186198 | ||||||||
\(667\) | 1.18615 | 0.0459281 | ||||||||
\(668\) | 0.226009 | 0.00874453 | ||||||||
\(669\) | −32.6506 | −1.26235 | ||||||||
\(670\) | 12.9973 | 0.502129 | ||||||||
\(671\) | −34.3410 | −1.32572 | ||||||||
\(672\) | 3.55924 | 0.137301 | ||||||||
\(673\) | 37.1715 | 1.43285 | 0.716427 | − | 0.697662i | \(-0.245776\pi\) | ||||
0.716427 | + | 0.697662i | \(0.245776\pi\) | |||||||
\(674\) | −19.9216 | −0.767350 | ||||||||
\(675\) | −13.6540 | −0.525544 | ||||||||
\(676\) | −12.9993 | −0.499974 | ||||||||
\(677\) | −30.5435 | −1.17388 | −0.586941 | − | 0.809630i | \(-0.699668\pi\) | ||||
−0.586941 | + | 0.809630i | \(0.699668\pi\) | |||||||
\(678\) | −30.3215 | −1.16449 | ||||||||
\(679\) | −4.74405 | −0.182060 | ||||||||
\(680\) | 3.42638 | 0.131396 | ||||||||
\(681\) | −16.5373 | −0.633709 | ||||||||
\(682\) | −19.6844 | −0.753754 | ||||||||
\(683\) | −2.73959 | −0.104827 | −0.0524137 | − | 0.998625i | \(-0.516691\pi\) | ||||
−0.0524137 | + | 0.998625i | \(0.516691\pi\) | |||||||
\(684\) | 1.04823 | 0.0400800 | ||||||||
\(685\) | 50.0402 | 1.91194 | ||||||||
\(686\) | −19.8823 | −0.759109 | ||||||||
\(687\) | 17.5389 | 0.669149 | ||||||||
\(688\) | 3.03969 | 0.115887 | ||||||||
\(689\) | 0.227713 | 0.00867517 | ||||||||
\(690\) | 4.10213 | 0.156165 | ||||||||
\(691\) | −28.5369 | −1.08560 | −0.542798 | − | 0.839863i | \(-0.682635\pi\) | ||||
−0.542798 | + | 0.839863i | \(0.682635\pi\) | |||||||
\(692\) | 8.60643 | 0.327167 | ||||||||
\(693\) | 5.72276 | 0.217390 | ||||||||
\(694\) | −31.5949 | −1.19933 | ||||||||
\(695\) | 44.7856 | 1.69881 | ||||||||
\(696\) | −1.78519 | −0.0676674 | ||||||||
\(697\) | 1.39957 | 0.0530126 | ||||||||
\(698\) | −2.88986 | −0.109383 | ||||||||
\(699\) | 21.9159 | 0.828937 | ||||||||
\(700\) | −5.74450 | −0.217122 | ||||||||
\(701\) | 2.55875 | 0.0966426 | 0.0483213 | − | 0.998832i | \(-0.484613\pi\) | ||||
0.0483213 | + | 0.998832i | \(0.484613\pi\) | |||||||
\(702\) | −0.145553 | −0.00549356 | ||||||||
\(703\) | −9.32605 | −0.351739 | ||||||||
\(704\) | 3.29273 | 0.124099 | ||||||||
\(705\) | −48.8373 | −1.83932 | ||||||||
\(706\) | 12.6049 | 0.474391 | ||||||||
\(707\) | 30.0315 | 1.12945 | ||||||||
\(708\) | −0.958895 | −0.0360375 | ||||||||
\(709\) | 27.6084 | 1.03686 | 0.518428 | − | 0.855121i | \(-0.326517\pi\) | ||||
0.518428 | + | 0.855121i | \(0.326517\pi\) | |||||||
\(710\) | −20.9858 | −0.787584 | ||||||||
\(711\) | −5.20447 | −0.195183 | ||||||||
\(712\) | −11.0810 | −0.415278 | ||||||||
\(713\) | 5.97814 | 0.223883 | ||||||||
\(714\) | 4.47431 | 0.167447 | ||||||||
\(715\) | 0.232393 | 0.00869099 | ||||||||
\(716\) | 16.1662 | 0.604159 | ||||||||
\(717\) | −35.9146 | −1.34126 | ||||||||
\(718\) | −11.3247 | −0.422636 | ||||||||
\(719\) | −27.6135 | −1.02981 | −0.514905 | − | 0.857247i | \(-0.672173\pi\) | ||||
−0.514905 | + | 0.857247i | \(0.672173\pi\) | |||||||
\(720\) | 2.00310 | 0.0746511 | ||||||||
\(721\) | −5.85048 | −0.217883 | ||||||||
\(722\) | 16.9656 | 0.631393 | ||||||||
\(723\) | −34.2419 | −1.27347 | ||||||||
\(724\) | −13.0720 | −0.485818 | ||||||||
\(725\) | 2.88124 | 0.107007 | ||||||||
\(726\) | 0.237719 | 0.00882256 | ||||||||
\(727\) | −1.00716 | −0.0373534 | −0.0186767 | − | 0.999826i | \(-0.505945\pi\) | ||||
−0.0186767 | + | 0.999826i | \(0.505945\pi\) | |||||||
\(728\) | −0.0612370 | −0.00226959 | ||||||||
\(729\) | 29.9767 | 1.11025 | ||||||||
\(730\) | −18.0850 | −0.669355 | ||||||||
\(731\) | 3.82119 | 0.141332 | ||||||||
\(732\) | −15.6964 | −0.580156 | ||||||||
\(733\) | −52.7200 | −1.94726 | −0.973630 | − | 0.228135i | \(-0.926737\pi\) | ||||
−0.973630 | + | 0.228135i | \(0.926737\pi\) | |||||||
\(734\) | 12.3212 | 0.454784 | ||||||||
\(735\) | 5.77255 | 0.212924 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 15.7015 | 0.578372 | ||||||||
\(738\) | 0.818204 | 0.0301185 | ||||||||
\(739\) | 36.1844 | 1.33106 | 0.665532 | − | 0.746369i | \(-0.268205\pi\) | ||||
0.665532 | + | 0.746369i | \(0.268205\pi\) | |||||||
\(740\) | −17.8215 | −0.655131 | ||||||||
\(741\) | 0.0555857 | 0.00204199 | ||||||||
\(742\) | −20.7971 | −0.763485 | ||||||||
\(743\) | 23.9930 | 0.880219 | 0.440109 | − | 0.897944i | \(-0.354940\pi\) | ||||
0.440109 | + | 0.897944i | \(0.354940\pi\) | |||||||
\(744\) | −8.99723 | −0.329854 | ||||||||
\(745\) | 23.5470 | 0.862695 | ||||||||
\(746\) | 31.4290 | 1.15070 | ||||||||
\(747\) | 9.84102 | 0.360064 | ||||||||
\(748\) | 4.13928 | 0.151347 | ||||||||
\(749\) | 46.9081 | 1.71398 | ||||||||
\(750\) | −10.5463 | −0.385098 | ||||||||
\(751\) | 20.9951 | 0.766121 | 0.383061 | − | 0.923723i | \(-0.374870\pi\) | ||||
0.383061 | + | 0.923723i | \(0.374870\pi\) | |||||||
\(752\) | 11.9054 | 0.434144 | ||||||||
\(753\) | −31.6986 | −1.15516 | ||||||||
\(754\) | 0.0307143 | 0.00111855 | ||||||||
\(755\) | −1.95582 | −0.0711797 | ||||||||
\(756\) | 13.2934 | 0.483478 | ||||||||
\(757\) | −53.9004 | −1.95904 | −0.979521 | − | 0.201341i | \(-0.935470\pi\) | ||||
−0.979521 | + | 0.201341i | \(0.935470\pi\) | |||||||
\(758\) | −4.54449 | −0.165063 | ||||||||
\(759\) | 4.95562 | 0.179878 | ||||||||
\(760\) | −3.88765 | −0.141020 | ||||||||
\(761\) | −52.8201 | −1.91473 | −0.957364 | − | 0.288886i | \(-0.906715\pi\) | ||||
−0.957364 | + | 0.288886i | \(0.906715\pi\) | |||||||
\(762\) | −10.7017 | −0.387680 | ||||||||
\(763\) | −2.71588 | −0.0983214 | ||||||||
\(764\) | 26.9462 | 0.974878 | ||||||||
\(765\) | 2.51809 | 0.0910417 | ||||||||
\(766\) | −2.24326 | −0.0810524 | ||||||||
\(767\) | 0.0164979 | 0.000595704 0 | ||||||||
\(768\) | 1.50502 | 0.0543078 | ||||||||
\(769\) | 11.1251 | 0.401180 | 0.200590 | − | 0.979675i | \(-0.435714\pi\) | ||||
0.200590 | + | 0.979675i | \(0.435714\pi\) | |||||||
\(770\) | −21.2245 | −0.764877 | ||||||||
\(771\) | 1.49801 | 0.0539494 | ||||||||
\(772\) | −14.5321 | −0.523021 | ||||||||
\(773\) | −15.4461 | −0.555557 | −0.277779 | − | 0.960645i | \(-0.589598\pi\) | ||||
−0.277779 | + | 0.960645i | \(0.589598\pi\) | |||||||
\(774\) | 2.23391 | 0.0802961 | ||||||||
\(775\) | 14.5213 | 0.521619 | ||||||||
\(776\) | −2.00602 | −0.0720119 | ||||||||
\(777\) | −23.2720 | −0.834879 | ||||||||
\(778\) | 18.5644 | 0.665565 | ||||||||
\(779\) | −1.58799 | −0.0568956 | ||||||||
\(780\) | 0.106221 | 0.00380331 | ||||||||
\(781\) | −25.3522 | −0.907172 | ||||||||
\(782\) | −1.25710 | −0.0449537 | ||||||||
\(783\) | −6.66752 | −0.238278 | ||||||||
\(784\) | −1.40721 | −0.0502574 | ||||||||
\(785\) | 18.1244 | 0.646889 | ||||||||
\(786\) | −1.50502 | −0.0536823 | ||||||||
\(787\) | −29.2598 | −1.04300 | −0.521500 | − | 0.853251i | \(-0.674627\pi\) | ||||
−0.521500 | + | 0.853251i | \(0.674627\pi\) | |||||||
\(788\) | −22.9483 | −0.817499 | ||||||||
\(789\) | 28.6612 | 1.02036 | ||||||||
\(790\) | 19.3022 | 0.686743 | ||||||||
\(791\) | −47.6456 | −1.69408 | ||||||||
\(792\) | 2.41986 | 0.0859862 | ||||||||
\(793\) | 0.270058 | 0.00959005 | ||||||||
\(794\) | −0.594174 | −0.0210864 | ||||||||
\(795\) | 36.0743 | 1.27942 | ||||||||
\(796\) | 12.6803 | 0.449440 | ||||||||
\(797\) | 36.7528 | 1.30185 | 0.650926 | − | 0.759141i | \(-0.274381\pi\) | ||||
0.650926 | + | 0.759141i | \(0.274381\pi\) | |||||||
\(798\) | −5.07666 | −0.179712 | ||||||||
\(799\) | 14.9662 | 0.529466 | ||||||||
\(800\) | −2.42906 | −0.0858802 | ||||||||
\(801\) | −8.14356 | −0.287739 | ||||||||
\(802\) | −0.754936 | −0.0266577 | ||||||||
\(803\) | −21.8477 | −0.770990 | ||||||||
\(804\) | 7.17676 | 0.253105 | ||||||||
\(805\) | 6.44587 | 0.227187 | ||||||||
\(806\) | 0.154798 | 0.00545253 | ||||||||
\(807\) | 34.8924 | 1.22827 | ||||||||
\(808\) | 12.6988 | 0.446743 | ||||||||
\(809\) | 22.0877 | 0.776561 | 0.388280 | − | 0.921541i | \(-0.373069\pi\) | ||||
0.388280 | + | 0.921541i | \(0.373069\pi\) | |||||||
\(810\) | −17.0493 | −0.599050 | ||||||||
\(811\) | −32.2394 | −1.13208 | −0.566039 | − | 0.824378i | \(-0.691525\pi\) | ||||
−0.566039 | + | 0.824378i | \(0.691525\pi\) | |||||||
\(812\) | −2.80515 | −0.0984414 | ||||||||
\(813\) | −0.143327 | −0.00502670 | ||||||||
\(814\) | −21.5294 | −0.754607 | ||||||||
\(815\) | 29.1522 | 1.02116 | ||||||||
\(816\) | 1.89196 | 0.0662318 | ||||||||
\(817\) | −4.33561 | −0.151684 | ||||||||
\(818\) | 25.8626 | 0.904263 | ||||||||
\(819\) | −0.0450038 | −0.00157256 | ||||||||
\(820\) | −3.03454 | −0.105971 | ||||||||
\(821\) | 42.6236 | 1.48757 | 0.743786 | − | 0.668418i | \(-0.233028\pi\) | ||||
0.743786 | + | 0.668418i | \(0.233028\pi\) | |||||||
\(822\) | 27.6309 | 0.963738 | ||||||||
\(823\) | 22.7196 | 0.791955 | 0.395978 | − | 0.918260i | \(-0.370406\pi\) | ||||
0.395978 | + | 0.918260i | \(0.370406\pi\) | |||||||
\(824\) | −2.47387 | −0.0861815 | ||||||||
\(825\) | 12.0375 | 0.419092 | ||||||||
\(826\) | −1.50676 | −0.0524267 | ||||||||
\(827\) | 26.8990 | 0.935368 | 0.467684 | − | 0.883896i | \(-0.345088\pi\) | ||||
0.467684 | + | 0.883896i | \(0.345088\pi\) | |||||||
\(828\) | −0.734912 | −0.0255400 | ||||||||
\(829\) | −22.5320 | −0.782569 | −0.391285 | − | 0.920270i | \(-0.627969\pi\) | ||||
−0.391285 | + | 0.920270i | \(0.627969\pi\) | |||||||
\(830\) | −36.4982 | −1.26687 | ||||||||
\(831\) | −16.3325 | −0.566567 | ||||||||
\(832\) | −0.0258940 | −0.000897714 0 | ||||||||
\(833\) | −1.76900 | −0.0612921 | ||||||||
\(834\) | 24.7294 | 0.856309 | ||||||||
\(835\) | −0.616016 | −0.0213181 | ||||||||
\(836\) | −4.69652 | −0.162433 | ||||||||
\(837\) | −33.6039 | −1.16152 | ||||||||
\(838\) | −17.2461 | −0.595755 | ||||||||
\(839\) | −6.74190 | −0.232756 | −0.116378 | − | 0.993205i | \(-0.537128\pi\) | ||||
−0.116378 | + | 0.993205i | \(0.537128\pi\) | |||||||
\(840\) | −9.70116 | −0.334722 | ||||||||
\(841\) | −27.5930 | −0.951484 | ||||||||
\(842\) | −36.3621 | −1.25312 | ||||||||
\(843\) | −13.0929 | −0.450942 | ||||||||
\(844\) | −28.6231 | −0.985249 | ||||||||
\(845\) | 35.4314 | 1.21888 | ||||||||
\(846\) | 8.74939 | 0.300810 | ||||||||
\(847\) | 0.373538 | 0.0128349 | ||||||||
\(848\) | −8.79403 | −0.301988 | ||||||||
\(849\) | −19.6008 | −0.672698 | ||||||||
\(850\) | −3.05356 | −0.104736 | ||||||||
\(851\) | 6.53848 | 0.224136 | ||||||||
\(852\) | −11.5878 | −0.396992 | ||||||||
\(853\) | 56.3687 | 1.93003 | 0.965013 | − | 0.262200i | \(-0.0844482\pi\) | ||||
0.965013 | + | 0.262200i | \(0.0844482\pi\) | |||||||
\(854\) | −24.6645 | −0.844001 | ||||||||
\(855\) | −2.85708 | −0.0977102 | ||||||||
\(856\) | 19.8351 | 0.677948 | ||||||||
\(857\) | −16.5555 | −0.565524 | −0.282762 | − | 0.959190i | \(-0.591251\pi\) | ||||
−0.282762 | + | 0.959190i | \(0.591251\pi\) | |||||||
\(858\) | 0.128321 | 0.00438081 | ||||||||
\(859\) | −7.21115 | −0.246041 | −0.123021 | − | 0.992404i | \(-0.539258\pi\) | ||||
−0.123021 | + | 0.992404i | \(0.539258\pi\) | |||||||
\(860\) | −8.28508 | −0.282519 | ||||||||
\(861\) | −3.96263 | −0.135046 | ||||||||
\(862\) | 21.9180 | 0.746528 | ||||||||
\(863\) | −40.5122 | −1.37905 | −0.689526 | − | 0.724261i | \(-0.742181\pi\) | ||||
−0.689526 | + | 0.724261i | \(0.742181\pi\) | |||||||
\(864\) | 5.62112 | 0.191234 | ||||||||
\(865\) | −23.4579 | −0.797594 | ||||||||
\(866\) | 32.9831 | 1.12081 | ||||||||
\(867\) | −23.2070 | −0.788150 | ||||||||
\(868\) | −14.1378 | −0.479867 | ||||||||
\(869\) | 23.3183 | 0.791018 | ||||||||
\(870\) | 4.86576 | 0.164965 | ||||||||
\(871\) | −0.123477 | −0.00418385 | ||||||||
\(872\) | −1.14841 | −0.0388900 | ||||||||
\(873\) | −1.47425 | −0.0498957 | ||||||||
\(874\) | 1.42633 | 0.0482464 | ||||||||
\(875\) | −16.5719 | −0.560234 | ||||||||
\(876\) | −9.98604 | −0.337397 | ||||||||
\(877\) | −35.4033 | −1.19549 | −0.597743 | − | 0.801688i | \(-0.703936\pi\) | ||||
−0.597743 | + | 0.801688i | \(0.703936\pi\) | |||||||
\(878\) | −35.6717 | −1.20386 | ||||||||
\(879\) | 20.7151 | 0.698702 | ||||||||
\(880\) | −8.97475 | −0.302539 | ||||||||
\(881\) | −38.3142 | −1.29084 | −0.645418 | − | 0.763829i | \(-0.723317\pi\) | ||||
−0.645418 | + | 0.763829i | \(0.723317\pi\) | |||||||
\(882\) | −1.03417 | −0.0348225 | ||||||||
\(883\) | −5.41348 | −0.182178 | −0.0910891 | − | 0.995843i | \(-0.529035\pi\) | ||||
−0.0910891 | + | 0.995843i | \(0.529035\pi\) | |||||||
\(884\) | −0.0325513 | −0.00109482 | ||||||||
\(885\) | 2.61359 | 0.0878549 | ||||||||
\(886\) | −19.4406 | −0.653121 | ||||||||
\(887\) | 24.3464 | 0.817471 | 0.408736 | − | 0.912653i | \(-0.365970\pi\) | ||||
0.408736 | + | 0.912653i | \(0.365970\pi\) | |||||||
\(888\) | −9.84056 | −0.330227 | ||||||||
\(889\) | −16.8160 | −0.563991 | ||||||||
\(890\) | 30.2027 | 1.01240 | ||||||||
\(891\) | −20.5966 | −0.690011 | ||||||||
\(892\) | −21.6945 | −0.726385 | ||||||||
\(893\) | −16.9810 | −0.568248 | ||||||||
\(894\) | 13.0020 | 0.434853 | ||||||||
\(895\) | −44.0631 | −1.47287 | ||||||||
\(896\) | 2.36491 | 0.0790060 | ||||||||
\(897\) | −0.0389711 | −0.00130121 | ||||||||
\(898\) | 30.5372 | 1.01904 | ||||||||
\(899\) | 7.09100 | 0.236498 | ||||||||
\(900\) | −1.78514 | −0.0595048 | ||||||||
\(901\) | −11.0550 | −0.368294 | ||||||||
\(902\) | −3.66591 | −0.122062 | ||||||||
\(903\) | −10.8190 | −0.360033 | ||||||||
\(904\) | −20.1469 | −0.670076 | ||||||||
\(905\) | 35.6295 | 1.18437 | ||||||||
\(906\) | −1.07995 | −0.0358791 | ||||||||
\(907\) | −36.5304 | −1.21297 | −0.606486 | − | 0.795094i | \(-0.707422\pi\) | ||||
−0.606486 | + | 0.795094i | \(0.707422\pi\) | |||||||
\(908\) | −10.9881 | −0.364652 | ||||||||
\(909\) | 9.33251 | 0.309540 | ||||||||
\(910\) | 0.166909 | 0.00553299 | ||||||||
\(911\) | −42.7219 | −1.41544 | −0.707720 | − | 0.706493i | \(-0.750276\pi\) | ||||
−0.707720 | + | 0.706493i | \(0.750276\pi\) | |||||||
\(912\) | −2.14666 | −0.0710830 | ||||||||
\(913\) | −44.0921 | −1.45923 | ||||||||
\(914\) | 19.9037 | 0.658355 | ||||||||
\(915\) | 42.7826 | 1.41435 | ||||||||
\(916\) | 11.6536 | 0.385045 | ||||||||
\(917\) | −2.36491 | −0.0780962 | ||||||||
\(918\) | 7.06629 | 0.233222 | ||||||||
\(919\) | 41.5850 | 1.37176 | 0.685881 | − | 0.727714i | \(-0.259417\pi\) | ||||
0.685881 | + | 0.727714i | \(0.259417\pi\) | |||||||
\(920\) | 2.72563 | 0.0898614 | ||||||||
\(921\) | 48.6787 | 1.60402 | ||||||||
\(922\) | 4.60202 | 0.151559 | ||||||||
\(923\) | 0.199370 | 0.00656233 | ||||||||
\(924\) | −11.7196 | −0.385546 | ||||||||
\(925\) | 15.8824 | 0.522209 | ||||||||
\(926\) | 9.67270 | 0.317865 | ||||||||
\(927\) | −1.81808 | −0.0597136 | ||||||||
\(928\) | −1.18615 | −0.0389374 | ||||||||
\(929\) | −1.27879 | −0.0419559 | −0.0209780 | − | 0.999780i | \(-0.506678\pi\) | ||||
−0.0209780 | + | 0.999780i | \(0.506678\pi\) | |||||||
\(930\) | 24.5231 | 0.804144 | ||||||||
\(931\) | 2.00715 | 0.0657816 | ||||||||
\(932\) | 14.5619 | 0.476990 | ||||||||
\(933\) | −7.11753 | −0.233018 | ||||||||
\(934\) | −38.8060 | −1.26977 | ||||||||
\(935\) | −11.2821 | −0.368965 | ||||||||
\(936\) | −0.0190298 | −0.000622010 0 | ||||||||
\(937\) | −23.5815 | −0.770375 | −0.385188 | − | 0.922838i | \(-0.625863\pi\) | ||||
−0.385188 | + | 0.922838i | \(0.625863\pi\) | |||||||
\(938\) | 11.2772 | 0.368213 | ||||||||
\(939\) | −32.1681 | −1.04977 | ||||||||
\(940\) | −32.4496 | −1.05839 | ||||||||
\(941\) | 8.58786 | 0.279956 | 0.139978 | − | 0.990155i | \(-0.455297\pi\) | ||||
0.139978 | + | 0.990155i | \(0.455297\pi\) | |||||||
\(942\) | 10.0078 | 0.326073 | ||||||||
\(943\) | 1.11334 | 0.0362552 | ||||||||
\(944\) | −0.637130 | −0.0207368 | ||||||||
\(945\) | −36.2330 | −1.17866 | ||||||||
\(946\) | −10.0089 | −0.325417 | ||||||||
\(947\) | −19.1246 | −0.621465 | −0.310733 | − | 0.950497i | \(-0.600574\pi\) | ||||
−0.310733 | + | 0.950497i | \(0.600574\pi\) | |||||||
\(948\) | 10.6582 | 0.346162 | ||||||||
\(949\) | 0.171811 | 0.00557722 | ||||||||
\(950\) | 3.46465 | 0.112408 | ||||||||
\(951\) | −25.5637 | −0.828959 | ||||||||
\(952\) | 2.97292 | 0.0963529 | ||||||||
\(953\) | 37.7713 | 1.22353 | 0.611766 | − | 0.791038i | \(-0.290459\pi\) | ||||
0.611766 | + | 0.791038i | \(0.290459\pi\) | |||||||
\(954\) | −6.46284 | −0.209242 | ||||||||
\(955\) | −73.4453 | −2.37663 | ||||||||
\(956\) | −23.8632 | −0.771791 | ||||||||
\(957\) | 5.87814 | 0.190013 | ||||||||
\(958\) | −21.0216 | −0.679177 | ||||||||
\(959\) | 43.4177 | 1.40203 | ||||||||
\(960\) | −4.10213 | −0.132396 | ||||||||
\(961\) | 4.73817 | 0.152844 | ||||||||
\(962\) | 0.169308 | 0.00545870 | ||||||||
\(963\) | 14.5770 | 0.469738 | ||||||||
\(964\) | −22.7518 | −0.732786 | ||||||||
\(965\) | 39.6090 | 1.27506 | ||||||||
\(966\) | 3.55924 | 0.114517 | ||||||||
\(967\) | −17.0636 | −0.548728 | −0.274364 | − | 0.961626i | \(-0.588467\pi\) | ||||
−0.274364 | + | 0.961626i | \(0.588467\pi\) | |||||||
\(968\) | 0.157950 | 0.00507672 | ||||||||
\(969\) | −2.69856 | −0.0866903 | ||||||||
\(970\) | 5.46767 | 0.175556 | ||||||||
\(971\) | −36.6032 | −1.17465 | −0.587326 | − | 0.809350i | \(-0.699819\pi\) | ||||
−0.587326 | + | 0.809350i | \(0.699819\pi\) | |||||||
\(972\) | 7.44920 | 0.238933 | ||||||||
\(973\) | 38.8584 | 1.24574 | ||||||||
\(974\) | 15.4903 | 0.496342 | ||||||||
\(975\) | −0.0946630 | −0.00303164 | ||||||||
\(976\) | −10.4294 | −0.333836 | ||||||||
\(977\) | −12.6657 | −0.405212 | −0.202606 | − | 0.979260i | \(-0.564941\pi\) | ||||
−0.202606 | + | 0.979260i | \(0.564941\pi\) | |||||||
\(978\) | 16.0970 | 0.514727 | ||||||||
\(979\) | 36.4867 | 1.16612 | ||||||||
\(980\) | 3.83553 | 0.122521 | ||||||||
\(981\) | −0.843978 | −0.0269462 | ||||||||
\(982\) | 6.46100 | 0.206179 | ||||||||
\(983\) | 16.9931 | 0.541995 | 0.270997 | − | 0.962580i | \(-0.412647\pi\) | ||||
0.270997 | + | 0.962580i | \(0.412647\pi\) | |||||||
\(984\) | −1.67559 | −0.0534160 | ||||||||
\(985\) | 62.5485 | 1.99296 | ||||||||
\(986\) | −1.49111 | −0.0474867 | ||||||||
\(987\) | −42.3740 | −1.34878 | ||||||||
\(988\) | 0.0369335 | 0.00117501 | ||||||||
\(989\) | 3.03969 | 0.0966566 | ||||||||
\(990\) | −6.59566 | −0.209624 | ||||||||
\(991\) | −8.90226 | −0.282790 | −0.141395 | − | 0.989953i | \(-0.545159\pi\) | ||||
−0.141395 | + | 0.989953i | \(0.545159\pi\) | |||||||
\(992\) | −5.97814 | −0.189806 | ||||||||
\(993\) | −43.7446 | −1.38819 | ||||||||
\(994\) | −18.2085 | −0.577538 | ||||||||
\(995\) | −34.5617 | −1.09568 | ||||||||
\(996\) | −20.1534 | −0.638584 | ||||||||
\(997\) | 0.603734 | 0.0191204 | 0.00956022 | − | 0.999954i | \(-0.496957\pi\) | ||||
0.00956022 | + | 0.999954i | \(0.496957\pi\) | |||||||
\(998\) | 35.8164 | 1.13375 | ||||||||
\(999\) | −36.7536 | −1.16283 |
(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 | 6026.2.a.i.1.19 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.i.1.19 | ✓ | 25 | 1.1 | even | 1 | trivial |