Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6015,2,Mod(1,6015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6015 = 3 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6015.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: | \(48.0300168158\) |
Analytic rank: | \(0\) |
Dimension: | \(43\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.211503 | −0.149556 | −0.0747778 | − | 0.997200i | \(-0.523825\pi\) | ||||
−0.0747778 | + | 0.997200i | \(0.523825\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.95527 | −0.977633 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.211503 | −0.0863459 | ||||||||
\(7\) | 3.03461 | 1.14697 | 0.573487 | − | 0.819214i | \(-0.305590\pi\) | ||||
0.573487 | + | 0.819214i | \(0.305590\pi\) | |||||||
\(8\) | 0.836552 | 0.295766 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.211503 | −0.0668833 | ||||||||
\(11\) | 2.42289 | 0.730528 | 0.365264 | − | 0.930904i | \(-0.380979\pi\) | ||||
0.365264 | + | 0.930904i | \(0.380979\pi\) | |||||||
\(12\) | −1.95527 | −0.564437 | ||||||||
\(13\) | 5.84813 | 1.62198 | 0.810989 | − | 0.585061i | \(-0.198929\pi\) | ||||
0.810989 | + | 0.585061i | \(0.198929\pi\) | |||||||
\(14\) | −0.641830 | −0.171536 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 3.73360 | 0.933400 | ||||||||
\(17\) | −0.920871 | −0.223344 | −0.111672 | − | 0.993745i | \(-0.535621\pi\) | ||||
−0.111672 | + | 0.993745i | \(0.535621\pi\) | |||||||
\(18\) | −0.211503 | −0.0498518 | ||||||||
\(19\) | 2.43117 | 0.557750 | 0.278875 | − | 0.960327i | \(-0.410039\pi\) | ||||
0.278875 | + | 0.960327i | \(0.410039\pi\) | |||||||
\(20\) | −1.95527 | −0.437211 | ||||||||
\(21\) | 3.03461 | 0.662206 | ||||||||
\(22\) | −0.512449 | −0.109254 | ||||||||
\(23\) | 0.265985 | 0.0554618 | 0.0277309 | − | 0.999615i | \(-0.491172\pi\) | ||||
0.0277309 | + | 0.999615i | \(0.491172\pi\) | |||||||
\(24\) | 0.836552 | 0.170761 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.23690 | −0.242576 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −5.93347 | −1.12132 | ||||||||
\(29\) | −0.369226 | −0.0685636 | −0.0342818 | − | 0.999412i | \(-0.510914\pi\) | ||||
−0.0342818 | + | 0.999412i | \(0.510914\pi\) | |||||||
\(30\) | −0.211503 | −0.0386151 | ||||||||
\(31\) | 6.48890 | 1.16544 | 0.582720 | − | 0.812673i | \(-0.301988\pi\) | ||||
0.582720 | + | 0.812673i | \(0.301988\pi\) | |||||||
\(32\) | −2.46277 | −0.435361 | ||||||||
\(33\) | 2.42289 | 0.421770 | ||||||||
\(34\) | 0.194767 | 0.0334023 | ||||||||
\(35\) | 3.03461 | 0.512943 | ||||||||
\(36\) | −1.95527 | −0.325878 | ||||||||
\(37\) | 8.25624 | 1.35732 | 0.678659 | − | 0.734454i | \(-0.262561\pi\) | ||||
0.678659 | + | 0.734454i | \(0.262561\pi\) | |||||||
\(38\) | −0.514202 | −0.0834145 | ||||||||
\(39\) | 5.84813 | 0.936450 | ||||||||
\(40\) | 0.836552 | 0.132271 | ||||||||
\(41\) | −5.57053 | −0.869971 | −0.434986 | − | 0.900437i | \(-0.643247\pi\) | ||||
−0.434986 | + | 0.900437i | \(0.643247\pi\) | |||||||
\(42\) | −0.641830 | −0.0990366 | ||||||||
\(43\) | 6.44720 | 0.983189 | 0.491594 | − | 0.870824i | \(-0.336414\pi\) | ||||
0.491594 | + | 0.870824i | \(0.336414\pi\) | |||||||
\(44\) | −4.73739 | −0.714188 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −0.0562568 | −0.00829462 | ||||||||
\(47\) | −0.0721234 | −0.0105203 | −0.00526014 | − | 0.999986i | \(-0.501674\pi\) | ||||
−0.00526014 | + | 0.999986i | \(0.501674\pi\) | |||||||
\(48\) | 3.73360 | 0.538899 | ||||||||
\(49\) | 2.20886 | 0.315551 | ||||||||
\(50\) | −0.211503 | −0.0299111 | ||||||||
\(51\) | −0.920871 | −0.128948 | ||||||||
\(52\) | −11.4346 | −1.58570 | ||||||||
\(53\) | −10.5984 | −1.45580 | −0.727899 | − | 0.685684i | \(-0.759503\pi\) | ||||
−0.727899 | + | 0.685684i | \(0.759503\pi\) | |||||||
\(54\) | −0.211503 | −0.0287820 | ||||||||
\(55\) | 2.42289 | 0.326702 | ||||||||
\(56\) | 2.53861 | 0.339236 | ||||||||
\(57\) | 2.43117 | 0.322017 | ||||||||
\(58\) | 0.0780926 | 0.0102541 | ||||||||
\(59\) | 2.31999 | 0.302037 | 0.151018 | − | 0.988531i | \(-0.451745\pi\) | ||||
0.151018 | + | 0.988531i | \(0.451745\pi\) | |||||||
\(60\) | −1.95527 | −0.252424 | ||||||||
\(61\) | −0.801821 | −0.102663 | −0.0513313 | − | 0.998682i | \(-0.516346\pi\) | ||||
−0.0513313 | + | 0.998682i | \(0.516346\pi\) | |||||||
\(62\) | −1.37242 | −0.174298 | ||||||||
\(63\) | 3.03461 | 0.382325 | ||||||||
\(64\) | −6.94631 | −0.868289 | ||||||||
\(65\) | 5.84813 | 0.725371 | ||||||||
\(66\) | −0.512449 | −0.0630781 | ||||||||
\(67\) | 10.1489 | 1.23989 | 0.619945 | − | 0.784645i | \(-0.287155\pi\) | ||||
0.619945 | + | 0.784645i | \(0.287155\pi\) | |||||||
\(68\) | 1.80055 | 0.218348 | ||||||||
\(69\) | 0.265985 | 0.0320209 | ||||||||
\(70\) | −0.641830 | −0.0767134 | ||||||||
\(71\) | 5.98942 | 0.710813 | 0.355406 | − | 0.934712i | \(-0.384342\pi\) | ||||
0.355406 | + | 0.934712i | \(0.384342\pi\) | |||||||
\(72\) | 0.836552 | 0.0985886 | ||||||||
\(73\) | −14.0198 | −1.64089 | −0.820446 | − | 0.571724i | \(-0.806275\pi\) | ||||
−0.820446 | + | 0.571724i | \(0.806275\pi\) | |||||||
\(74\) | −1.74622 | −0.202994 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −4.75359 | −0.545274 | ||||||||
\(77\) | 7.35252 | 0.837897 | ||||||||
\(78\) | −1.23690 | −0.140051 | ||||||||
\(79\) | −1.32234 | −0.148775 | −0.0743874 | − | 0.997229i | \(-0.523700\pi\) | ||||
−0.0743874 | + | 0.997229i | \(0.523700\pi\) | |||||||
\(80\) | 3.73360 | 0.417429 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.17819 | 0.130109 | ||||||||
\(83\) | −3.93580 | −0.432010 | −0.216005 | − | 0.976392i | \(-0.569303\pi\) | ||||
−0.216005 | + | 0.976392i | \(0.569303\pi\) | |||||||
\(84\) | −5.93347 | −0.647395 | ||||||||
\(85\) | −0.920871 | −0.0998825 | ||||||||
\(86\) | −1.36360 | −0.147041 | ||||||||
\(87\) | −0.369226 | −0.0395852 | ||||||||
\(88\) | 2.02687 | 0.216065 | ||||||||
\(89\) | −10.4647 | −1.10926 | −0.554630 | − | 0.832097i | \(-0.687140\pi\) | ||||
−0.554630 | + | 0.832097i | \(0.687140\pi\) | |||||||
\(90\) | −0.211503 | −0.0222944 | ||||||||
\(91\) | 17.7468 | 1.86037 | ||||||||
\(92\) | −0.520072 | −0.0542213 | ||||||||
\(93\) | 6.48890 | 0.672867 | ||||||||
\(94\) | 0.0152543 | 0.00157337 | ||||||||
\(95\) | 2.43117 | 0.249433 | ||||||||
\(96\) | −2.46277 | −0.251356 | ||||||||
\(97\) | 0.184517 | 0.0187349 | 0.00936745 | − | 0.999956i | \(-0.497018\pi\) | ||||
0.00936745 | + | 0.999956i | \(0.497018\pi\) | |||||||
\(98\) | −0.467182 | −0.0471925 | ||||||||
\(99\) | 2.42289 | 0.243509 | ||||||||
\(100\) | −1.95527 | −0.195527 | ||||||||
\(101\) | −4.35727 | −0.433565 | −0.216782 | − | 0.976220i | \(-0.569556\pi\) | ||||
−0.216782 | + | 0.976220i | \(0.569556\pi\) | |||||||
\(102\) | 0.194767 | 0.0192848 | ||||||||
\(103\) | −7.68993 | −0.757712 | −0.378856 | − | 0.925456i | \(-0.623682\pi\) | ||||
−0.378856 | + | 0.925456i | \(0.623682\pi\) | |||||||
\(104\) | 4.89226 | 0.479726 | ||||||||
\(105\) | 3.03461 | 0.296148 | ||||||||
\(106\) | 2.24159 | 0.217723 | ||||||||
\(107\) | −0.224002 | −0.0216551 | −0.0108276 | − | 0.999941i | \(-0.503447\pi\) | ||||
−0.0108276 | + | 0.999941i | \(0.503447\pi\) | |||||||
\(108\) | −1.95527 | −0.188146 | ||||||||
\(109\) | −10.7052 | −1.02538 | −0.512688 | − | 0.858575i | \(-0.671350\pi\) | ||||
−0.512688 | + | 0.858575i | \(0.671350\pi\) | |||||||
\(110\) | −0.512449 | −0.0488601 | ||||||||
\(111\) | 8.25624 | 0.783648 | ||||||||
\(112\) | 11.3300 | 1.07059 | ||||||||
\(113\) | −6.84989 | −0.644383 | −0.322192 | − | 0.946674i | \(-0.604420\pi\) | ||||
−0.322192 | + | 0.946674i | \(0.604420\pi\) | |||||||
\(114\) | −0.514202 | −0.0481594 | ||||||||
\(115\) | 0.265985 | 0.0248033 | ||||||||
\(116\) | 0.721936 | 0.0670300 | ||||||||
\(117\) | 5.84813 | 0.540660 | ||||||||
\(118\) | −0.490685 | −0.0451712 | ||||||||
\(119\) | −2.79448 | −0.256170 | ||||||||
\(120\) | 0.836552 | 0.0763664 | ||||||||
\(121\) | −5.12962 | −0.466329 | ||||||||
\(122\) | 0.169588 | 0.0153538 | ||||||||
\(123\) | −5.57053 | −0.502278 | ||||||||
\(124\) | −12.6875 | −1.13937 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.641830 | −0.0571788 | ||||||||
\(127\) | −5.47964 | −0.486239 | −0.243120 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243120 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(128\) | 6.39472 | 0.565218 | ||||||||
\(129\) | 6.44720 | 0.567644 | ||||||||
\(130\) | −1.23690 | −0.108483 | ||||||||
\(131\) | 17.0298 | 1.48790 | 0.743952 | − | 0.668233i | \(-0.232949\pi\) | ||||
0.743952 | + | 0.668233i | \(0.232949\pi\) | |||||||
\(132\) | −4.73739 | −0.412337 | ||||||||
\(133\) | 7.37767 | 0.639725 | ||||||||
\(134\) | −2.14654 | −0.185432 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −0.770357 | −0.0660575 | ||||||||
\(137\) | −18.1250 | −1.54852 | −0.774260 | − | 0.632867i | \(-0.781878\pi\) | ||||
−0.774260 | + | 0.632867i | \(0.781878\pi\) | |||||||
\(138\) | −0.0562568 | −0.00478890 | ||||||||
\(139\) | −15.1610 | −1.28594 | −0.642971 | − | 0.765890i | \(-0.722298\pi\) | ||||
−0.642971 | + | 0.765890i | \(0.722298\pi\) | |||||||
\(140\) | −5.93347 | −0.501470 | ||||||||
\(141\) | −0.0721234 | −0.00607389 | ||||||||
\(142\) | −1.26678 | −0.106306 | ||||||||
\(143\) | 14.1693 | 1.18490 | ||||||||
\(144\) | 3.73360 | 0.311133 | ||||||||
\(145\) | −0.369226 | −0.0306626 | ||||||||
\(146\) | 2.96523 | 0.245404 | ||||||||
\(147\) | 2.20886 | 0.182184 | ||||||||
\(148\) | −16.1432 | −1.32696 | ||||||||
\(149\) | −1.85053 | −0.151601 | −0.0758007 | − | 0.997123i | \(-0.524151\pi\) | ||||
−0.0758007 | + | 0.997123i | \(0.524151\pi\) | |||||||
\(150\) | −0.211503 | −0.0172692 | ||||||||
\(151\) | 11.4334 | 0.930437 | 0.465219 | − | 0.885196i | \(-0.345976\pi\) | ||||
0.465219 | + | 0.885196i | \(0.345976\pi\) | |||||||
\(152\) | 2.03380 | 0.164963 | ||||||||
\(153\) | −0.920871 | −0.0744480 | ||||||||
\(154\) | −1.55508 | −0.125312 | ||||||||
\(155\) | 6.48890 | 0.521201 | ||||||||
\(156\) | −11.4346 | −0.915504 | ||||||||
\(157\) | −3.26069 | −0.260232 | −0.130116 | − | 0.991499i | \(-0.541535\pi\) | ||||
−0.130116 | + | 0.991499i | \(0.541535\pi\) | |||||||
\(158\) | 0.279679 | 0.0222501 | ||||||||
\(159\) | −10.5984 | −0.840505 | ||||||||
\(160\) | −2.46277 | −0.194699 | ||||||||
\(161\) | 0.807162 | 0.0636133 | ||||||||
\(162\) | −0.211503 | −0.0166173 | ||||||||
\(163\) | 10.8738 | 0.851699 | 0.425850 | − | 0.904794i | \(-0.359975\pi\) | ||||
0.425850 | + | 0.904794i | \(0.359975\pi\) | |||||||
\(164\) | 10.8919 | 0.850513 | ||||||||
\(165\) | 2.42289 | 0.188621 | ||||||||
\(166\) | 0.832435 | 0.0646095 | ||||||||
\(167\) | −10.0862 | −0.780494 | −0.390247 | − | 0.920710i | \(-0.627610\pi\) | ||||
−0.390247 | + | 0.920710i | \(0.627610\pi\) | |||||||
\(168\) | 2.53861 | 0.195858 | ||||||||
\(169\) | 21.2006 | 1.63081 | ||||||||
\(170\) | 0.194767 | 0.0149380 | ||||||||
\(171\) | 2.43117 | 0.185917 | ||||||||
\(172\) | −12.6060 | −0.961198 | ||||||||
\(173\) | 16.8481 | 1.28093 | 0.640467 | − | 0.767985i | \(-0.278741\pi\) | ||||
0.640467 | + | 0.767985i | \(0.278741\pi\) | |||||||
\(174\) | 0.0780926 | 0.00592019 | ||||||||
\(175\) | 3.03461 | 0.229395 | ||||||||
\(176\) | 9.04609 | 0.681874 | ||||||||
\(177\) | 2.31999 | 0.174381 | ||||||||
\(178\) | 2.21333 | 0.165896 | ||||||||
\(179\) | −22.9185 | −1.71301 | −0.856504 | − | 0.516140i | \(-0.827368\pi\) | ||||
−0.856504 | + | 0.516140i | \(0.827368\pi\) | |||||||
\(180\) | −1.95527 | −0.145737 | ||||||||
\(181\) | −11.1785 | −0.830888 | −0.415444 | − | 0.909619i | \(-0.636374\pi\) | ||||
−0.415444 | + | 0.909619i | \(0.636374\pi\) | |||||||
\(182\) | −3.75351 | −0.278228 | ||||||||
\(183\) | −0.801821 | −0.0592723 | ||||||||
\(184\) | 0.222511 | 0.0164037 | ||||||||
\(185\) | 8.25624 | 0.607011 | ||||||||
\(186\) | −1.37242 | −0.100631 | ||||||||
\(187\) | −2.23117 | −0.163159 | ||||||||
\(188\) | 0.141020 | 0.0102850 | ||||||||
\(189\) | 3.03461 | 0.220735 | ||||||||
\(190\) | −0.514202 | −0.0373041 | ||||||||
\(191\) | −16.3225 | −1.18105 | −0.590526 | − | 0.807018i | \(-0.701080\pi\) | ||||
−0.590526 | + | 0.807018i | \(0.701080\pi\) | |||||||
\(192\) | −6.94631 | −0.501307 | ||||||||
\(193\) | 13.9218 | 1.00211 | 0.501057 | − | 0.865414i | \(-0.332945\pi\) | ||||
0.501057 | + | 0.865414i | \(0.332945\pi\) | |||||||
\(194\) | −0.0390260 | −0.00280191 | ||||||||
\(195\) | 5.84813 | 0.418793 | ||||||||
\(196\) | −4.31891 | −0.308494 | ||||||||
\(197\) | 9.62146 | 0.685501 | 0.342750 | − | 0.939427i | \(-0.388641\pi\) | ||||
0.342750 | + | 0.939427i | \(0.388641\pi\) | |||||||
\(198\) | −0.512449 | −0.0364181 | ||||||||
\(199\) | −21.0696 | −1.49359 | −0.746794 | − | 0.665056i | \(-0.768408\pi\) | ||||
−0.746794 | + | 0.665056i | \(0.768408\pi\) | |||||||
\(200\) | 0.836552 | 0.0591532 | ||||||||
\(201\) | 10.1489 | 0.715851 | ||||||||
\(202\) | 0.921578 | 0.0648420 | ||||||||
\(203\) | −1.12046 | −0.0786407 | ||||||||
\(204\) | 1.80055 | 0.126064 | ||||||||
\(205\) | −5.57053 | −0.389063 | ||||||||
\(206\) | 1.62645 | 0.113320 | ||||||||
\(207\) | 0.265985 | 0.0184873 | ||||||||
\(208\) | 21.8346 | 1.51395 | ||||||||
\(209\) | 5.89046 | 0.407452 | ||||||||
\(210\) | −0.641830 | −0.0442905 | ||||||||
\(211\) | 10.1585 | 0.699338 | 0.349669 | − | 0.936873i | \(-0.386294\pi\) | ||||
0.349669 | + | 0.936873i | \(0.386294\pi\) | |||||||
\(212\) | 20.7226 | 1.42324 | ||||||||
\(213\) | 5.98942 | 0.410388 | ||||||||
\(214\) | 0.0473773 | 0.00323864 | ||||||||
\(215\) | 6.44720 | 0.439695 | ||||||||
\(216\) | 0.836552 | 0.0569202 | ||||||||
\(217\) | 19.6913 | 1.33673 | ||||||||
\(218\) | 2.26419 | 0.153351 | ||||||||
\(219\) | −14.0198 | −0.947369 | ||||||||
\(220\) | −4.73739 | −0.319395 | ||||||||
\(221\) | −5.38537 | −0.362259 | ||||||||
\(222\) | −1.74622 | −0.117199 | ||||||||
\(223\) | 12.6691 | 0.848382 | 0.424191 | − | 0.905573i | \(-0.360558\pi\) | ||||
0.424191 | + | 0.905573i | \(0.360558\pi\) | |||||||
\(224\) | −7.47356 | −0.499348 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 1.44877 | 0.0963711 | ||||||||
\(227\) | 15.5838 | 1.03433 | 0.517166 | − | 0.855885i | \(-0.326987\pi\) | ||||
0.517166 | + | 0.855885i | \(0.326987\pi\) | |||||||
\(228\) | −4.75359 | −0.314814 | ||||||||
\(229\) | 6.10570 | 0.403476 | 0.201738 | − | 0.979440i | \(-0.435341\pi\) | ||||
0.201738 | + | 0.979440i | \(0.435341\pi\) | |||||||
\(230\) | −0.0562568 | −0.00370947 | ||||||||
\(231\) | 7.35252 | 0.483760 | ||||||||
\(232\) | −0.308877 | −0.0202788 | ||||||||
\(233\) | −7.81283 | −0.511835 | −0.255918 | − | 0.966699i | \(-0.582378\pi\) | ||||
−0.255918 | + | 0.966699i | \(0.582378\pi\) | |||||||
\(234\) | −1.23690 | −0.0808586 | ||||||||
\(235\) | −0.0721234 | −0.00470481 | ||||||||
\(236\) | −4.53619 | −0.295281 | ||||||||
\(237\) | −1.32234 | −0.0858952 | ||||||||
\(238\) | 0.591043 | 0.0383116 | ||||||||
\(239\) | −18.3863 | −1.18931 | −0.594656 | − | 0.803980i | \(-0.702712\pi\) | ||||
−0.594656 | + | 0.803980i | \(0.702712\pi\) | |||||||
\(240\) | 3.73360 | 0.241003 | ||||||||
\(241\) | −17.4321 | −1.12290 | −0.561449 | − | 0.827511i | \(-0.689756\pi\) | ||||
−0.561449 | + | 0.827511i | \(0.689756\pi\) | |||||||
\(242\) | 1.08493 | 0.0697421 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.56777 | 0.100366 | ||||||||
\(245\) | 2.20886 | 0.141119 | ||||||||
\(246\) | 1.17819 | 0.0751185 | ||||||||
\(247\) | 14.2178 | 0.904658 | ||||||||
\(248\) | 5.42830 | 0.344697 | ||||||||
\(249\) | −3.93580 | −0.249421 | ||||||||
\(250\) | −0.211503 | −0.0133767 | ||||||||
\(251\) | 19.7790 | 1.24844 | 0.624219 | − | 0.781250i | \(-0.285417\pi\) | ||||
0.624219 | + | 0.781250i | \(0.285417\pi\) | |||||||
\(252\) | −5.93347 | −0.373774 | ||||||||
\(253\) | 0.644452 | 0.0405164 | ||||||||
\(254\) | 1.15896 | 0.0727198 | ||||||||
\(255\) | −0.920871 | −0.0576672 | ||||||||
\(256\) | 12.5401 | 0.783758 | ||||||||
\(257\) | 25.4638 | 1.58839 | 0.794194 | − | 0.607664i | \(-0.207893\pi\) | ||||
0.794194 | + | 0.607664i | \(0.207893\pi\) | |||||||
\(258\) | −1.36360 | −0.0848943 | ||||||||
\(259\) | 25.0545 | 1.55681 | ||||||||
\(260\) | −11.4346 | −0.709147 | ||||||||
\(261\) | −0.369226 | −0.0228545 | ||||||||
\(262\) | −3.60187 | −0.222524 | ||||||||
\(263\) | −4.94984 | −0.305220 | −0.152610 | − | 0.988286i | \(-0.548768\pi\) | ||||
−0.152610 | + | 0.988286i | \(0.548768\pi\) | |||||||
\(264\) | 2.02687 | 0.124745 | ||||||||
\(265\) | −10.5984 | −0.651053 | ||||||||
\(266\) | −1.56040 | −0.0956744 | ||||||||
\(267\) | −10.4647 | −0.640432 | ||||||||
\(268\) | −19.8439 | −1.21216 | ||||||||
\(269\) | 29.9145 | 1.82392 | 0.911960 | − | 0.410279i | \(-0.134569\pi\) | ||||
0.911960 | + | 0.410279i | \(0.134569\pi\) | |||||||
\(270\) | −0.211503 | −0.0128717 | ||||||||
\(271\) | 16.8727 | 1.02494 | 0.512471 | − | 0.858704i | \(-0.328730\pi\) | ||||
0.512471 | + | 0.858704i | \(0.328730\pi\) | |||||||
\(272\) | −3.43816 | −0.208469 | ||||||||
\(273\) | 17.7468 | 1.07408 | ||||||||
\(274\) | 3.83349 | 0.231590 | ||||||||
\(275\) | 2.42289 | 0.146106 | ||||||||
\(276\) | −0.520072 | −0.0313047 | ||||||||
\(277\) | 29.6902 | 1.78391 | 0.891956 | − | 0.452122i | \(-0.149333\pi\) | ||||
0.891956 | + | 0.452122i | \(0.149333\pi\) | |||||||
\(278\) | 3.20661 | 0.192320 | ||||||||
\(279\) | 6.48890 | 0.388480 | ||||||||
\(280\) | 2.53861 | 0.151711 | ||||||||
\(281\) | −9.05519 | −0.540187 | −0.270094 | − | 0.962834i | \(-0.587055\pi\) | ||||
−0.270094 | + | 0.962834i | \(0.587055\pi\) | |||||||
\(282\) | 0.0152543 | 0.000908383 0 | ||||||||
\(283\) | −2.42399 | −0.144091 | −0.0720457 | − | 0.997401i | \(-0.522953\pi\) | ||||
−0.0720457 | + | 0.997401i | \(0.522953\pi\) | |||||||
\(284\) | −11.7109 | −0.694914 | ||||||||
\(285\) | 2.43117 | 0.144010 | ||||||||
\(286\) | −2.99687 | −0.177208 | ||||||||
\(287\) | −16.9044 | −0.997835 | ||||||||
\(288\) | −2.46277 | −0.145120 | ||||||||
\(289\) | −16.1520 | −0.950117 | ||||||||
\(290\) | 0.0780926 | 0.00458576 | ||||||||
\(291\) | 0.184517 | 0.0108166 | ||||||||
\(292\) | 27.4124 | 1.60419 | ||||||||
\(293\) | 11.7098 | 0.684092 | 0.342046 | − | 0.939683i | \(-0.388880\pi\) | ||||
0.342046 | + | 0.939683i | \(0.388880\pi\) | |||||||
\(294\) | −0.467182 | −0.0272466 | ||||||||
\(295\) | 2.31999 | 0.135075 | ||||||||
\(296\) | 6.90678 | 0.401448 | ||||||||
\(297\) | 2.42289 | 0.140590 | ||||||||
\(298\) | 0.391393 | 0.0226728 | ||||||||
\(299\) | 1.55552 | 0.0899579 | ||||||||
\(300\) | −1.95527 | −0.112887 | ||||||||
\(301\) | 19.5647 | 1.12769 | ||||||||
\(302\) | −2.41820 | −0.139152 | ||||||||
\(303\) | −4.35727 | −0.250319 | ||||||||
\(304\) | 9.07703 | 0.520603 | ||||||||
\(305\) | −0.801821 | −0.0459121 | ||||||||
\(306\) | 0.194767 | 0.0111341 | ||||||||
\(307\) | −4.24442 | −0.242242 | −0.121121 | − | 0.992638i | \(-0.538649\pi\) | ||||
−0.121121 | + | 0.992638i | \(0.538649\pi\) | |||||||
\(308\) | −14.3761 | −0.819156 | ||||||||
\(309\) | −7.68993 | −0.437465 | ||||||||
\(310\) | −1.37242 | −0.0779484 | ||||||||
\(311\) | −12.3533 | −0.700493 | −0.350246 | − | 0.936658i | \(-0.613902\pi\) | ||||
−0.350246 | + | 0.936658i | \(0.613902\pi\) | |||||||
\(312\) | 4.89226 | 0.276970 | ||||||||
\(313\) | 7.57303 | 0.428053 | 0.214026 | − | 0.976828i | \(-0.431342\pi\) | ||||
0.214026 | + | 0.976828i | \(0.431342\pi\) | |||||||
\(314\) | 0.689648 | 0.0389191 | ||||||||
\(315\) | 3.03461 | 0.170981 | ||||||||
\(316\) | 2.58553 | 0.145447 | ||||||||
\(317\) | −8.60857 | −0.483505 | −0.241753 | − | 0.970338i | \(-0.577722\pi\) | ||||
−0.241753 | + | 0.970338i | \(0.577722\pi\) | |||||||
\(318\) | 2.24159 | 0.125702 | ||||||||
\(319\) | −0.894593 | −0.0500876 | ||||||||
\(320\) | −6.94631 | −0.388311 | ||||||||
\(321\) | −0.224002 | −0.0125026 | ||||||||
\(322\) | −0.170718 | −0.00951372 | ||||||||
\(323\) | −2.23880 | −0.124570 | ||||||||
\(324\) | −1.95527 | −0.108626 | ||||||||
\(325\) | 5.84813 | 0.324396 | ||||||||
\(326\) | −2.29984 | −0.127376 | ||||||||
\(327\) | −10.7052 | −0.592001 | ||||||||
\(328\) | −4.66004 | −0.257308 | ||||||||
\(329\) | −0.218866 | −0.0120665 | ||||||||
\(330\) | −0.512449 | −0.0282094 | ||||||||
\(331\) | −23.1407 | −1.27193 | −0.635965 | − | 0.771718i | \(-0.719398\pi\) | ||||
−0.635965 | + | 0.771718i | \(0.719398\pi\) | |||||||
\(332\) | 7.69553 | 0.422347 | ||||||||
\(333\) | 8.25624 | 0.452439 | ||||||||
\(334\) | 2.13327 | 0.116727 | ||||||||
\(335\) | 10.1489 | 0.554496 | ||||||||
\(336\) | 11.3300 | 0.618103 | ||||||||
\(337\) | −9.24214 | −0.503451 | −0.251726 | − | 0.967799i | \(-0.580998\pi\) | ||||
−0.251726 | + | 0.967799i | \(0.580998\pi\) | |||||||
\(338\) | −4.48400 | −0.243897 | ||||||||
\(339\) | −6.84989 | −0.372035 | ||||||||
\(340\) | 1.80055 | 0.0976484 | ||||||||
\(341\) | 15.7219 | 0.851386 | ||||||||
\(342\) | −0.514202 | −0.0278048 | ||||||||
\(343\) | −14.5392 | −0.785045 | ||||||||
\(344\) | 5.39342 | 0.290794 | ||||||||
\(345\) | 0.265985 | 0.0143202 | ||||||||
\(346\) | −3.56342 | −0.191571 | ||||||||
\(347\) | −5.09499 | −0.273513 | −0.136757 | − | 0.990605i | \(-0.543668\pi\) | ||||
−0.136757 | + | 0.990605i | \(0.543668\pi\) | |||||||
\(348\) | 0.721936 | 0.0386998 | ||||||||
\(349\) | −28.7025 | −1.53641 | −0.768205 | − | 0.640204i | \(-0.778850\pi\) | ||||
−0.768205 | + | 0.640204i | \(0.778850\pi\) | |||||||
\(350\) | −0.641830 | −0.0343073 | ||||||||
\(351\) | 5.84813 | 0.312150 | ||||||||
\(352\) | −5.96702 | −0.318043 | ||||||||
\(353\) | 9.05416 | 0.481904 | 0.240952 | − | 0.970537i | \(-0.422540\pi\) | ||||
0.240952 | + | 0.970537i | \(0.422540\pi\) | |||||||
\(354\) | −0.490685 | −0.0260796 | ||||||||
\(355\) | 5.98942 | 0.317885 | ||||||||
\(356\) | 20.4613 | 1.08445 | ||||||||
\(357\) | −2.79448 | −0.147900 | ||||||||
\(358\) | 4.84734 | 0.256190 | ||||||||
\(359\) | 25.1956 | 1.32977 | 0.664886 | − | 0.746945i | \(-0.268480\pi\) | ||||
0.664886 | + | 0.746945i | \(0.268480\pi\) | |||||||
\(360\) | 0.836552 | 0.0440902 | ||||||||
\(361\) | −13.0894 | −0.688915 | ||||||||
\(362\) | 2.36428 | 0.124264 | ||||||||
\(363\) | −5.12962 | −0.269235 | ||||||||
\(364\) | −34.6997 | −1.81876 | ||||||||
\(365\) | −14.0198 | −0.733829 | ||||||||
\(366\) | 0.169588 | 0.00886450 | ||||||||
\(367\) | 11.8528 | 0.618712 | 0.309356 | − | 0.950946i | \(-0.399887\pi\) | ||||
0.309356 | + | 0.950946i | \(0.399887\pi\) | |||||||
\(368\) | 0.993083 | 0.0517680 | ||||||||
\(369\) | −5.57053 | −0.289990 | ||||||||
\(370\) | −1.74622 | −0.0907818 | ||||||||
\(371\) | −32.1619 | −1.66976 | ||||||||
\(372\) | −12.6875 | −0.657817 | ||||||||
\(373\) | −1.34905 | −0.0698512 | −0.0349256 | − | 0.999390i | \(-0.511119\pi\) | ||||
−0.0349256 | + | 0.999390i | \(0.511119\pi\) | |||||||
\(374\) | 0.471899 | 0.0244013 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −0.0603350 | −0.00311154 | ||||||||
\(377\) | −2.15928 | −0.111209 | ||||||||
\(378\) | −0.641830 | −0.0330122 | ||||||||
\(379\) | 1.90003 | 0.0975979 | 0.0487990 | − | 0.998809i | \(-0.484461\pi\) | ||||
0.0487990 | + | 0.998809i | \(0.484461\pi\) | |||||||
\(380\) | −4.75359 | −0.243854 | ||||||||
\(381\) | −5.47964 | −0.280730 | ||||||||
\(382\) | 3.45226 | 0.176633 | ||||||||
\(383\) | 14.2734 | 0.729336 | 0.364668 | − | 0.931138i | \(-0.381182\pi\) | ||||
0.364668 | + | 0.931138i | \(0.381182\pi\) | |||||||
\(384\) | 6.39472 | 0.326329 | ||||||||
\(385\) | 7.35252 | 0.374719 | ||||||||
\(386\) | −2.94451 | −0.149872 | ||||||||
\(387\) | 6.44720 | 0.327730 | ||||||||
\(388\) | −0.360780 | −0.0183159 | ||||||||
\(389\) | 30.4225 | 1.54248 | 0.771241 | − | 0.636544i | \(-0.219636\pi\) | ||||
0.771241 | + | 0.636544i | \(0.219636\pi\) | |||||||
\(390\) | −1.23690 | −0.0626328 | ||||||||
\(391\) | −0.244938 | −0.0123871 | ||||||||
\(392\) | 1.84783 | 0.0933294 | ||||||||
\(393\) | 17.0298 | 0.859041 | ||||||||
\(394\) | −2.03497 | −0.102520 | ||||||||
\(395\) | −1.32234 | −0.0665341 | ||||||||
\(396\) | −4.73739 | −0.238063 | ||||||||
\(397\) | 1.15575 | 0.0580055 | 0.0290028 | − | 0.999579i | \(-0.490767\pi\) | ||||
0.0290028 | + | 0.999579i | \(0.490767\pi\) | |||||||
\(398\) | 4.45630 | 0.223374 | ||||||||
\(399\) | 7.37767 | 0.369345 | ||||||||
\(400\) | 3.73360 | 0.186680 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | −2.14654 | −0.107059 | ||||||||
\(403\) | 37.9479 | 1.89032 | ||||||||
\(404\) | 8.51963 | 0.423867 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0.236981 | 0.0117612 | ||||||||
\(407\) | 20.0039 | 0.991558 | ||||||||
\(408\) | −0.770357 | −0.0381383 | ||||||||
\(409\) | −16.7064 | −0.826077 | −0.413038 | − | 0.910714i | \(-0.635532\pi\) | ||||
−0.413038 | + | 0.910714i | \(0.635532\pi\) | |||||||
\(410\) | 1.17819 | 0.0581865 | ||||||||
\(411\) | −18.1250 | −0.894039 | ||||||||
\(412\) | 15.0359 | 0.740764 | ||||||||
\(413\) | 7.04026 | 0.346429 | ||||||||
\(414\) | −0.0562568 | −0.00276487 | ||||||||
\(415\) | −3.93580 | −0.193201 | ||||||||
\(416\) | −14.4026 | −0.706146 | ||||||||
\(417\) | −15.1610 | −0.742439 | ||||||||
\(418\) | −1.24585 | −0.0609366 | ||||||||
\(419\) | 24.3068 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(420\) | −5.93347 | −0.289524 | ||||||||
\(421\) | 17.4587 | 0.850886 | 0.425443 | − | 0.904985i | \(-0.360118\pi\) | ||||
0.425443 | + | 0.904985i | \(0.360118\pi\) | |||||||
\(422\) | −2.14855 | −0.104590 | ||||||||
\(423\) | −0.0721234 | −0.00350676 | ||||||||
\(424\) | −8.86609 | −0.430575 | ||||||||
\(425\) | −0.920871 | −0.0446688 | ||||||||
\(426\) | −1.26678 | −0.0613758 | ||||||||
\(427\) | −2.43322 | −0.117752 | ||||||||
\(428\) | 0.437984 | 0.0211708 | ||||||||
\(429\) | 14.1693 | 0.684103 | ||||||||
\(430\) | −1.36360 | −0.0657589 | ||||||||
\(431\) | 22.1901 | 1.06886 | 0.534431 | − | 0.845212i | \(-0.320526\pi\) | ||||
0.534431 | + | 0.845212i | \(0.320526\pi\) | |||||||
\(432\) | 3.73360 | 0.179633 | ||||||||
\(433\) | 14.4121 | 0.692603 | 0.346301 | − | 0.938123i | \(-0.387438\pi\) | ||||
0.346301 | + | 0.938123i | \(0.387438\pi\) | |||||||
\(434\) | −4.16477 | −0.199915 | ||||||||
\(435\) | −0.369226 | −0.0177030 | ||||||||
\(436\) | 20.9316 | 1.00244 | ||||||||
\(437\) | 0.646657 | 0.0309338 | ||||||||
\(438\) | 2.96523 | 0.141684 | ||||||||
\(439\) | −36.6471 | −1.74907 | −0.874536 | − | 0.484961i | \(-0.838834\pi\) | ||||
−0.874536 | + | 0.484961i | \(0.838834\pi\) | |||||||
\(440\) | 2.02687 | 0.0966273 | ||||||||
\(441\) | 2.20886 | 0.105184 | ||||||||
\(442\) | 1.13902 | 0.0541779 | ||||||||
\(443\) | −13.4046 | −0.636870 | −0.318435 | − | 0.947945i | \(-0.603157\pi\) | ||||
−0.318435 | + | 0.947945i | \(0.603157\pi\) | |||||||
\(444\) | −16.1432 | −0.766120 | ||||||||
\(445\) | −10.4647 | −0.496076 | ||||||||
\(446\) | −2.67955 | −0.126880 | ||||||||
\(447\) | −1.85053 | −0.0875271 | ||||||||
\(448\) | −21.0794 | −0.995906 | ||||||||
\(449\) | −32.1891 | −1.51910 | −0.759550 | − | 0.650449i | \(-0.774581\pi\) | ||||
−0.759550 | + | 0.650449i | \(0.774581\pi\) | |||||||
\(450\) | −0.211503 | −0.00997037 | ||||||||
\(451\) | −13.4968 | −0.635538 | ||||||||
\(452\) | 13.3934 | 0.629971 | ||||||||
\(453\) | 11.4334 | 0.537188 | ||||||||
\(454\) | −3.29602 | −0.154690 | ||||||||
\(455\) | 17.7468 | 0.831982 | ||||||||
\(456\) | 2.03380 | 0.0952416 | ||||||||
\(457\) | 3.86165 | 0.180640 | 0.0903201 | − | 0.995913i | \(-0.471211\pi\) | ||||
0.0903201 | + | 0.995913i | \(0.471211\pi\) | |||||||
\(458\) | −1.29138 | −0.0603421 | ||||||||
\(459\) | −0.920871 | −0.0429826 | ||||||||
\(460\) | −0.520072 | −0.0242485 | ||||||||
\(461\) | 0.462987 | 0.0215634 | 0.0107817 | − | 0.999942i | \(-0.496568\pi\) | ||||
0.0107817 | + | 0.999942i | \(0.496568\pi\) | |||||||
\(462\) | −1.55508 | −0.0723490 | ||||||||
\(463\) | 30.6724 | 1.42547 | 0.712734 | − | 0.701434i | \(-0.247457\pi\) | ||||
0.712734 | + | 0.701434i | \(0.247457\pi\) | |||||||
\(464\) | −1.37854 | −0.0639972 | ||||||||
\(465\) | 6.48890 | 0.300915 | ||||||||
\(466\) | 1.65244 | 0.0765478 | ||||||||
\(467\) | −35.5085 | −1.64314 | −0.821569 | − | 0.570109i | \(-0.806901\pi\) | ||||
−0.821569 | + | 0.570109i | \(0.806901\pi\) | |||||||
\(468\) | −11.4346 | −0.528567 | ||||||||
\(469\) | 30.7981 | 1.42212 | ||||||||
\(470\) | 0.0152543 | 0.000703631 0 | ||||||||
\(471\) | −3.26069 | −0.150245 | ||||||||
\(472\) | 1.94079 | 0.0893322 | ||||||||
\(473\) | 15.6208 | 0.718247 | ||||||||
\(474\) | 0.279679 | 0.0128461 | ||||||||
\(475\) | 2.43117 | 0.111550 | ||||||||
\(476\) | 5.46396 | 0.250440 | ||||||||
\(477\) | −10.5984 | −0.485266 | ||||||||
\(478\) | 3.88877 | 0.177868 | ||||||||
\(479\) | 18.5970 | 0.849717 | 0.424859 | − | 0.905260i | \(-0.360324\pi\) | ||||
0.424859 | + | 0.905260i | \(0.360324\pi\) | |||||||
\(480\) | −2.46277 | −0.112410 | ||||||||
\(481\) | 48.2836 | 2.20154 | ||||||||
\(482\) | 3.68694 | 0.167936 | ||||||||
\(483\) | 0.807162 | 0.0367272 | ||||||||
\(484\) | 10.0298 | 0.455899 | ||||||||
\(485\) | 0.184517 | 0.00837850 | ||||||||
\(486\) | −0.211503 | −0.00959399 | ||||||||
\(487\) | 18.8938 | 0.856158 | 0.428079 | − | 0.903741i | \(-0.359190\pi\) | ||||
0.428079 | + | 0.903741i | \(0.359190\pi\) | |||||||
\(488\) | −0.670765 | −0.0303641 | ||||||||
\(489\) | 10.8738 | 0.491729 | ||||||||
\(490\) | −0.467182 | −0.0211051 | ||||||||
\(491\) | 16.5401 | 0.746445 | 0.373222 | − | 0.927742i | \(-0.378253\pi\) | ||||
0.373222 | + | 0.927742i | \(0.378253\pi\) | |||||||
\(492\) | 10.8919 | 0.491044 | ||||||||
\(493\) | 0.340010 | 0.0153133 | ||||||||
\(494\) | −3.00712 | −0.135297 | ||||||||
\(495\) | 2.42289 | 0.108901 | ||||||||
\(496\) | 24.2269 | 1.08782 | ||||||||
\(497\) | 18.1755 | 0.815285 | ||||||||
\(498\) | 0.832435 | 0.0373023 | ||||||||
\(499\) | 35.4985 | 1.58913 | 0.794565 | − | 0.607179i | \(-0.207699\pi\) | ||||
0.794565 | + | 0.607179i | \(0.207699\pi\) | |||||||
\(500\) | −1.95527 | −0.0874422 | ||||||||
\(501\) | −10.0862 | −0.450619 | ||||||||
\(502\) | −4.18332 | −0.186711 | ||||||||
\(503\) | 7.75457 | 0.345759 | 0.172880 | − | 0.984943i | \(-0.444693\pi\) | ||||
0.172880 | + | 0.984943i | \(0.444693\pi\) | |||||||
\(504\) | 2.53861 | 0.113079 | ||||||||
\(505\) | −4.35727 | −0.193896 | ||||||||
\(506\) | −0.136304 | −0.00605945 | ||||||||
\(507\) | 21.2006 | 0.941551 | ||||||||
\(508\) | 10.7142 | 0.475364 | ||||||||
\(509\) | −9.24652 | −0.409845 | −0.204922 | − | 0.978778i | \(-0.565694\pi\) | ||||
−0.204922 | + | 0.978778i | \(0.565694\pi\) | |||||||
\(510\) | 0.194767 | 0.00862444 | ||||||||
\(511\) | −42.5446 | −1.88206 | ||||||||
\(512\) | −15.4417 | −0.682434 | ||||||||
\(513\) | 2.43117 | 0.107339 | ||||||||
\(514\) | −5.38568 | −0.237552 | ||||||||
\(515\) | −7.68993 | −0.338859 | ||||||||
\(516\) | −12.6060 | −0.554948 | ||||||||
\(517\) | −0.174747 | −0.00768536 | ||||||||
\(518\) | −5.29911 | −0.232829 | ||||||||
\(519\) | 16.8481 | 0.739548 | ||||||||
\(520\) | 4.89226 | 0.214540 | ||||||||
\(521\) | −21.1535 | −0.926753 | −0.463376 | − | 0.886162i | \(-0.653362\pi\) | ||||
−0.463376 | + | 0.886162i | \(0.653362\pi\) | |||||||
\(522\) | 0.0780926 | 0.00341802 | ||||||||
\(523\) | 19.6153 | 0.857718 | 0.428859 | − | 0.903371i | \(-0.358916\pi\) | ||||
0.428859 | + | 0.903371i | \(0.358916\pi\) | |||||||
\(524\) | −33.2979 | −1.45462 | ||||||||
\(525\) | 3.03461 | 0.132441 | ||||||||
\(526\) | 1.04691 | 0.0456473 | ||||||||
\(527\) | −5.97544 | −0.260294 | ||||||||
\(528\) | 9.04609 | 0.393680 | ||||||||
\(529\) | −22.9293 | −0.996924 | ||||||||
\(530\) | 2.24159 | 0.0973685 | ||||||||
\(531\) | 2.31999 | 0.100679 | ||||||||
\(532\) | −14.4253 | −0.625416 | ||||||||
\(533\) | −32.5772 | −1.41107 | ||||||||
\(534\) | 2.21333 | 0.0957801 | ||||||||
\(535\) | −0.224002 | −0.00968447 | ||||||||
\(536\) | 8.49012 | 0.366717 | ||||||||
\(537\) | −22.9185 | −0.989006 | ||||||||
\(538\) | −6.32702 | −0.272777 | ||||||||
\(539\) | 5.35182 | 0.230519 | ||||||||
\(540\) | −1.95527 | −0.0841413 | ||||||||
\(541\) | 35.5697 | 1.52926 | 0.764631 | − | 0.644469i | \(-0.222921\pi\) | ||||
0.764631 | + | 0.644469i | \(0.222921\pi\) | |||||||
\(542\) | −3.56863 | −0.153286 | ||||||||
\(543\) | −11.1785 | −0.479713 | ||||||||
\(544\) | 2.26790 | 0.0972353 | ||||||||
\(545\) | −10.7052 | −0.458562 | ||||||||
\(546\) | −3.75351 | −0.160635 | ||||||||
\(547\) | −20.8798 | −0.892755 | −0.446377 | − | 0.894845i | \(-0.647286\pi\) | ||||
−0.446377 | + | 0.894845i | \(0.647286\pi\) | |||||||
\(548\) | 35.4391 | 1.51389 | ||||||||
\(549\) | −0.801821 | −0.0342209 | ||||||||
\(550\) | −0.512449 | −0.0218509 | ||||||||
\(551\) | −0.897653 | −0.0382413 | ||||||||
\(552\) | 0.222511 | 0.00947069 | ||||||||
\(553\) | −4.01278 | −0.170641 | ||||||||
\(554\) | −6.27958 | −0.266794 | ||||||||
\(555\) | 8.25624 | 0.350458 | ||||||||
\(556\) | 29.6439 | 1.25718 | ||||||||
\(557\) | −20.6420 | −0.874629 | −0.437315 | − | 0.899309i | \(-0.644070\pi\) | ||||
−0.437315 | + | 0.899309i | \(0.644070\pi\) | |||||||
\(558\) | −1.37242 | −0.0580993 | ||||||||
\(559\) | 37.7040 | 1.59471 | ||||||||
\(560\) | 11.3300 | 0.478781 | ||||||||
\(561\) | −2.23117 | −0.0941999 | ||||||||
\(562\) | 1.91520 | 0.0807880 | ||||||||
\(563\) | −23.3531 | −0.984218 | −0.492109 | − | 0.870534i | \(-0.663774\pi\) | ||||
−0.492109 | + | 0.870534i | \(0.663774\pi\) | |||||||
\(564\) | 0.141020 | 0.00593803 | ||||||||
\(565\) | −6.84989 | −0.288177 | ||||||||
\(566\) | 0.512682 | 0.0215497 | ||||||||
\(567\) | 3.03461 | 0.127442 | ||||||||
\(568\) | 5.01046 | 0.210234 | ||||||||
\(569\) | 4.22051 | 0.176933 | 0.0884664 | − | 0.996079i | \(-0.471803\pi\) | ||||
0.0884664 | + | 0.996079i | \(0.471803\pi\) | |||||||
\(570\) | −0.514202 | −0.0215375 | ||||||||
\(571\) | −27.5757 | −1.15401 | −0.577004 | − | 0.816742i | \(-0.695778\pi\) | ||||
−0.577004 | + | 0.816742i | \(0.695778\pi\) | |||||||
\(572\) | −27.7048 | −1.15840 | ||||||||
\(573\) | −16.3225 | −0.681881 | ||||||||
\(574\) | 3.57534 | 0.149232 | ||||||||
\(575\) | 0.265985 | 0.0110924 | ||||||||
\(576\) | −6.94631 | −0.289430 | ||||||||
\(577\) | −8.44884 | −0.351730 | −0.175865 | − | 0.984414i | \(-0.556272\pi\) | ||||
−0.175865 | + | 0.984414i | \(0.556272\pi\) | |||||||
\(578\) | 3.41620 | 0.142095 | ||||||||
\(579\) | 13.9218 | 0.578571 | ||||||||
\(580\) | 0.721936 | 0.0299767 | ||||||||
\(581\) | −11.9436 | −0.495505 | ||||||||
\(582\) | −0.0390260 | −0.00161768 | ||||||||
\(583\) | −25.6786 | −1.06350 | ||||||||
\(584\) | −11.7283 | −0.485320 | ||||||||
\(585\) | 5.84813 | 0.241790 | ||||||||
\(586\) | −2.47666 | −0.102310 | ||||||||
\(587\) | −23.5838 | −0.973409 | −0.486705 | − | 0.873567i | \(-0.661801\pi\) | ||||
−0.486705 | + | 0.873567i | \(0.661801\pi\) | |||||||
\(588\) | −4.31891 | −0.178109 | ||||||||
\(589\) | 15.7756 | 0.650024 | ||||||||
\(590\) | −0.490685 | −0.0202012 | ||||||||
\(591\) | 9.62146 | 0.395774 | ||||||||
\(592\) | 30.8255 | 1.26692 | ||||||||
\(593\) | −16.4635 | −0.676073 | −0.338037 | − | 0.941133i | \(-0.609763\pi\) | ||||
−0.338037 | + | 0.941133i | \(0.609763\pi\) | |||||||
\(594\) | −0.512449 | −0.0210260 | ||||||||
\(595\) | −2.79448 | −0.114563 | ||||||||
\(596\) | 3.61828 | 0.148211 | ||||||||
\(597\) | −21.0696 | −0.862323 | ||||||||
\(598\) | −0.328997 | −0.0134537 | ||||||||
\(599\) | −42.1650 | −1.72281 | −0.861407 | − | 0.507915i | \(-0.830416\pi\) | ||||
−0.861407 | + | 0.507915i | \(0.830416\pi\) | |||||||
\(600\) | 0.836552 | 0.0341521 | ||||||||
\(601\) | −7.03460 | −0.286947 | −0.143474 | − | 0.989654i | \(-0.545827\pi\) | ||||
−0.143474 | + | 0.989654i | \(0.545827\pi\) | |||||||
\(602\) | −4.13801 | −0.168653 | ||||||||
\(603\) | 10.1489 | 0.413297 | ||||||||
\(604\) | −22.3553 | −0.909626 | ||||||||
\(605\) | −5.12962 | −0.208549 | ||||||||
\(606\) | 0.921578 | 0.0374366 | ||||||||
\(607\) | 26.6821 | 1.08299 | 0.541496 | − | 0.840703i | \(-0.317858\pi\) | ||||
0.541496 | + | 0.840703i | \(0.317858\pi\) | |||||||
\(608\) | −5.98743 | −0.242822 | ||||||||
\(609\) | −1.12046 | −0.0454032 | ||||||||
\(610\) | 0.169588 | 0.00686641 | ||||||||
\(611\) | −0.421787 | −0.0170637 | ||||||||
\(612\) | 1.80055 | 0.0727828 | ||||||||
\(613\) | 24.5956 | 0.993406 | 0.496703 | − | 0.867921i | \(-0.334544\pi\) | ||||
0.496703 | + | 0.867921i | \(0.334544\pi\) | |||||||
\(614\) | 0.897710 | 0.0362286 | ||||||||
\(615\) | −5.57053 | −0.224626 | ||||||||
\(616\) | 6.15076 | 0.247821 | ||||||||
\(617\) | −18.7309 | −0.754078 | −0.377039 | − | 0.926197i | \(-0.623058\pi\) | ||||
−0.377039 | + | 0.926197i | \(0.623058\pi\) | |||||||
\(618\) | 1.62645 | 0.0654253 | ||||||||
\(619\) | −15.1561 | −0.609175 | −0.304588 | − | 0.952484i | \(-0.598519\pi\) | ||||
−0.304588 | + | 0.952484i | \(0.598519\pi\) | |||||||
\(620\) | −12.6875 | −0.509543 | ||||||||
\(621\) | 0.265985 | 0.0106736 | ||||||||
\(622\) | 2.61277 | 0.104763 | ||||||||
\(623\) | −31.7564 | −1.27229 | ||||||||
\(624\) | 21.8346 | 0.874082 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −1.60172 | −0.0640177 | ||||||||
\(627\) | 5.89046 | 0.235242 | ||||||||
\(628\) | 6.37552 | 0.254411 | ||||||||
\(629\) | −7.60293 | −0.303149 | ||||||||
\(630\) | −0.641830 | −0.0255711 | ||||||||
\(631\) | 21.4986 | 0.855847 | 0.427924 | − | 0.903815i | \(-0.359245\pi\) | ||||
0.427924 | + | 0.903815i | \(0.359245\pi\) | |||||||
\(632\) | −1.10621 | −0.0440025 | ||||||||
\(633\) | 10.1585 | 0.403763 | ||||||||
\(634\) | 1.82074 | 0.0723109 | ||||||||
\(635\) | −5.47964 | −0.217453 | ||||||||
\(636\) | 20.7226 | 0.821706 | ||||||||
\(637\) | 12.9177 | 0.511818 | ||||||||
\(638\) | 0.189210 | 0.00749088 | ||||||||
\(639\) | 5.98942 | 0.236938 | ||||||||
\(640\) | 6.39472 | 0.252773 | ||||||||
\(641\) | 22.4259 | 0.885768 | 0.442884 | − | 0.896579i | \(-0.353955\pi\) | ||||
0.442884 | + | 0.896579i | \(0.353955\pi\) | |||||||
\(642\) | 0.0473773 | 0.00186983 | ||||||||
\(643\) | 20.1049 | 0.792859 | 0.396429 | − | 0.918065i | \(-0.370249\pi\) | ||||
0.396429 | + | 0.918065i | \(0.370249\pi\) | |||||||
\(644\) | −1.57822 | −0.0621905 | ||||||||
\(645\) | 6.44720 | 0.253858 | ||||||||
\(646\) | 0.473513 | 0.0186301 | ||||||||
\(647\) | −23.7482 | −0.933637 | −0.466819 | − | 0.884353i | \(-0.654600\pi\) | ||||
−0.466819 | + | 0.884353i | \(0.654600\pi\) | |||||||
\(648\) | 0.836552 | 0.0328629 | ||||||||
\(649\) | 5.62107 | 0.220646 | ||||||||
\(650\) | −1.23690 | −0.0485152 | ||||||||
\(651\) | 19.6913 | 0.771762 | ||||||||
\(652\) | −21.2611 | −0.832650 | ||||||||
\(653\) | 21.3475 | 0.835391 | 0.417695 | − | 0.908587i | \(-0.362838\pi\) | ||||
0.417695 | + | 0.908587i | \(0.362838\pi\) | |||||||
\(654\) | 2.26419 | 0.0885370 | ||||||||
\(655\) | 17.0298 | 0.665411 | ||||||||
\(656\) | −20.7981 | −0.812031 | ||||||||
\(657\) | −14.0198 | −0.546964 | ||||||||
\(658\) | 0.0462910 | 0.00180461 | ||||||||
\(659\) | 7.69749 | 0.299852 | 0.149926 | − | 0.988697i | \(-0.452097\pi\) | ||||
0.149926 | + | 0.988697i | \(0.452097\pi\) | |||||||
\(660\) | −4.73739 | −0.184403 | ||||||||
\(661\) | 43.2616 | 1.68268 | 0.841341 | − | 0.540505i | \(-0.181767\pi\) | ||||
0.841341 | + | 0.540505i | \(0.181767\pi\) | |||||||
\(662\) | 4.89434 | 0.190224 | ||||||||
\(663\) | −5.38537 | −0.209150 | ||||||||
\(664\) | −3.29250 | −0.127774 | ||||||||
\(665\) | 7.37767 | 0.286094 | ||||||||
\(666\) | −1.74622 | −0.0676648 | ||||||||
\(667\) | −0.0982088 | −0.00380266 | ||||||||
\(668\) | 19.7212 | 0.763037 | ||||||||
\(669\) | 12.6691 | 0.489814 | ||||||||
\(670\) | −2.14654 | −0.0829279 | ||||||||
\(671\) | −1.94272 | −0.0749979 | ||||||||
\(672\) | −7.47356 | −0.288299 | ||||||||
\(673\) | −28.4016 | −1.09480 | −0.547400 | − | 0.836871i | \(-0.684382\pi\) | ||||
−0.547400 | + | 0.836871i | \(0.684382\pi\) | |||||||
\(674\) | 1.95474 | 0.0752939 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −41.4528 | −1.59434 | ||||||||
\(677\) | −27.8235 | −1.06935 | −0.534673 | − | 0.845059i | \(-0.679565\pi\) | ||||
−0.534673 | + | 0.845059i | \(0.679565\pi\) | |||||||
\(678\) | 1.44877 | 0.0556399 | ||||||||
\(679\) | 0.559938 | 0.0214885 | ||||||||
\(680\) | −0.770357 | −0.0295418 | ||||||||
\(681\) | 15.5838 | 0.597172 | ||||||||
\(682\) | −3.32523 | −0.127330 | ||||||||
\(683\) | −9.73555 | −0.372521 | −0.186260 | − | 0.982500i | \(-0.559637\pi\) | ||||
−0.186260 | + | 0.982500i | \(0.559637\pi\) | |||||||
\(684\) | −4.75359 | −0.181758 | ||||||||
\(685\) | −18.1250 | −0.692520 | ||||||||
\(686\) | 3.07510 | 0.117408 | ||||||||
\(687\) | 6.10570 | 0.232947 | ||||||||
\(688\) | 24.0713 | 0.917708 | ||||||||
\(689\) | −61.9806 | −2.36127 | ||||||||
\(690\) | −0.0562568 | −0.00214166 | ||||||||
\(691\) | −4.52388 | −0.172096 | −0.0860482 | − | 0.996291i | \(-0.527424\pi\) | ||||
−0.0860482 | + | 0.996291i | \(0.527424\pi\) | |||||||
\(692\) | −32.9425 | −1.25228 | ||||||||
\(693\) | 7.35252 | 0.279299 | ||||||||
\(694\) | 1.07761 | 0.0409054 | ||||||||
\(695\) | −15.1610 | −0.575091 | ||||||||
\(696\) | −0.308877 | −0.0117080 | ||||||||
\(697\) | 5.12974 | 0.194303 | ||||||||
\(698\) | 6.07068 | 0.229779 | ||||||||
\(699\) | −7.81283 | −0.295508 | ||||||||
\(700\) | −5.93347 | −0.224264 | ||||||||
\(701\) | 46.2086 | 1.74527 | 0.872636 | − | 0.488370i | \(-0.162408\pi\) | ||||
0.872636 | + | 0.488370i | \(0.162408\pi\) | |||||||
\(702\) | −1.23690 | −0.0466837 | ||||||||
\(703\) | 20.0724 | 0.757044 | ||||||||
\(704\) | −16.8301 | −0.634309 | ||||||||
\(705\) | −0.0721234 | −0.00271633 | ||||||||
\(706\) | −1.91499 | −0.0720715 | ||||||||
\(707\) | −13.2226 | −0.497288 | ||||||||
\(708\) | −4.53619 | −0.170481 | ||||||||
\(709\) | −28.8628 | −1.08396 | −0.541982 | − | 0.840390i | \(-0.682326\pi\) | ||||
−0.541982 | + | 0.840390i | \(0.682326\pi\) | |||||||
\(710\) | −1.26678 | −0.0475415 | ||||||||
\(711\) | −1.32234 | −0.0495916 | ||||||||
\(712\) | −8.75430 | −0.328081 | ||||||||
\(713\) | 1.72595 | 0.0646374 | ||||||||
\(714\) | 0.591043 | 0.0221192 | ||||||||
\(715\) | 14.1693 | 0.529904 | ||||||||
\(716\) | 44.8117 | 1.67469 | ||||||||
\(717\) | −18.3863 | −0.686650 | ||||||||
\(718\) | −5.32895 | −0.198875 | ||||||||
\(719\) | 21.4317 | 0.799267 | 0.399633 | − | 0.916675i | \(-0.369137\pi\) | ||||
0.399633 | + | 0.916675i | \(0.369137\pi\) | |||||||
\(720\) | 3.73360 | 0.139143 | ||||||||
\(721\) | −23.3360 | −0.869076 | ||||||||
\(722\) | 2.76845 | 0.103031 | ||||||||
\(723\) | −17.4321 | −0.648305 | ||||||||
\(724\) | 21.8569 | 0.812304 | ||||||||
\(725\) | −0.369226 | −0.0137127 | ||||||||
\(726\) | 1.08493 | 0.0402656 | ||||||||
\(727\) | −25.2662 | −0.937071 | −0.468536 | − | 0.883445i | \(-0.655218\pi\) | ||||
−0.468536 | + | 0.883445i | \(0.655218\pi\) | |||||||
\(728\) | 14.8461 | 0.550234 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.96523 | 0.109748 | ||||||||
\(731\) | −5.93704 | −0.219589 | ||||||||
\(732\) | 1.56777 | 0.0579466 | ||||||||
\(733\) | −11.6821 | −0.431489 | −0.215745 | − | 0.976450i | \(-0.569218\pi\) | ||||
−0.215745 | + | 0.976450i | \(0.569218\pi\) | |||||||
\(734\) | −2.50691 | −0.0925318 | ||||||||
\(735\) | 2.20886 | 0.0814750 | ||||||||
\(736\) | −0.655062 | −0.0241459 | ||||||||
\(737\) | 24.5897 | 0.905775 | ||||||||
\(738\) | 1.17819 | 0.0433697 | ||||||||
\(739\) | −31.8904 | −1.17311 | −0.586554 | − | 0.809910i | \(-0.699516\pi\) | ||||
−0.586554 | + | 0.809910i | \(0.699516\pi\) | |||||||
\(740\) | −16.1432 | −0.593434 | ||||||||
\(741\) | 14.2178 | 0.522304 | ||||||||
\(742\) | 6.80236 | 0.249722 | ||||||||
\(743\) | −40.3014 | −1.47851 | −0.739257 | − | 0.673424i | \(-0.764823\pi\) | ||||
−0.739257 | + | 0.673424i | \(0.764823\pi\) | |||||||
\(744\) | 5.42830 | 0.199011 | ||||||||
\(745\) | −1.85053 | −0.0677982 | ||||||||
\(746\) | 0.285329 | 0.0104466 | ||||||||
\(747\) | −3.93580 | −0.144003 | ||||||||
\(748\) | 4.36252 | 0.159510 | ||||||||
\(749\) | −0.679760 | −0.0248379 | ||||||||
\(750\) | −0.211503 | −0.00772301 | ||||||||
\(751\) | −27.7590 | −1.01294 | −0.506470 | − | 0.862258i | \(-0.669050\pi\) | ||||
−0.506470 | + | 0.862258i | \(0.669050\pi\) | |||||||
\(752\) | −0.269280 | −0.00981963 | ||||||||
\(753\) | 19.7790 | 0.720786 | ||||||||
\(754\) | 0.456696 | 0.0166319 | ||||||||
\(755\) | 11.4334 | 0.416104 | ||||||||
\(756\) | −5.93347 | −0.215798 | ||||||||
\(757\) | 26.2546 | 0.954240 | 0.477120 | − | 0.878838i | \(-0.341681\pi\) | ||||
0.477120 | + | 0.878838i | \(0.341681\pi\) | |||||||
\(758\) | −0.401862 | −0.0145963 | ||||||||
\(759\) | 0.644452 | 0.0233921 | ||||||||
\(760\) | 2.03380 | 0.0737738 | ||||||||
\(761\) | −11.0992 | −0.402347 | −0.201173 | − | 0.979556i | \(-0.564475\pi\) | ||||
−0.201173 | + | 0.979556i | \(0.564475\pi\) | |||||||
\(762\) | 1.15896 | 0.0419848 | ||||||||
\(763\) | −32.4862 | −1.17608 | ||||||||
\(764\) | 31.9148 | 1.15464 | ||||||||
\(765\) | −0.920871 | −0.0332942 | ||||||||
\(766\) | −3.01887 | −0.109076 | ||||||||
\(767\) | 13.5676 | 0.489897 | ||||||||
\(768\) | 12.5401 | 0.452503 | ||||||||
\(769\) | 10.0998 | 0.364209 | 0.182105 | − | 0.983279i | \(-0.441709\pi\) | ||||
0.182105 | + | 0.983279i | \(0.441709\pi\) | |||||||
\(770\) | −1.55508 | −0.0560413 | ||||||||
\(771\) | 25.4638 | 0.917056 | ||||||||
\(772\) | −27.2209 | −0.979701 | ||||||||
\(773\) | −26.6875 | −0.959881 | −0.479941 | − | 0.877301i | \(-0.659342\pi\) | ||||
−0.479941 | + | 0.877301i | \(0.659342\pi\) | |||||||
\(774\) | −1.36360 | −0.0490138 | ||||||||
\(775\) | 6.48890 | 0.233088 | ||||||||
\(776\) | 0.154358 | 0.00554114 | ||||||||
\(777\) | 25.0545 | 0.898825 | ||||||||
\(778\) | −6.43446 | −0.230687 | ||||||||
\(779\) | −13.5429 | −0.485226 | ||||||||
\(780\) | −11.4346 | −0.409426 | ||||||||
\(781\) | 14.5117 | 0.519268 | ||||||||
\(782\) | 0.0518053 | 0.00185255 | ||||||||
\(783\) | −0.369226 | −0.0131951 | ||||||||
\(784\) | 8.24700 | 0.294536 | ||||||||
\(785\) | −3.26069 | −0.116379 | ||||||||
\(786\) | −3.60187 | −0.128474 | ||||||||
\(787\) | 43.5061 | 1.55083 | 0.775413 | − | 0.631454i | \(-0.217542\pi\) | ||||
0.775413 | + | 0.631454i | \(0.217542\pi\) | |||||||
\(788\) | −18.8125 | −0.670168 | ||||||||
\(789\) | −4.94984 | −0.176219 | ||||||||
\(790\) | 0.279679 | 0.00995054 | ||||||||
\(791\) | −20.7867 | −0.739092 | ||||||||
\(792\) | 2.02687 | 0.0720217 | ||||||||
\(793\) | −4.68915 | −0.166517 | ||||||||
\(794\) | −0.244445 | −0.00867504 | ||||||||
\(795\) | −10.5984 | −0.375885 | ||||||||
\(796\) | 41.1968 | 1.46018 | ||||||||
\(797\) | −50.3062 | −1.78194 | −0.890969 | − | 0.454064i | \(-0.849974\pi\) | ||||
−0.890969 | + | 0.454064i | \(0.849974\pi\) | |||||||
\(798\) | −1.56040 | −0.0552376 | ||||||||
\(799\) | 0.0664164 | 0.00234964 | ||||||||
\(800\) | −2.46277 | −0.0870722 | ||||||||
\(801\) | −10.4647 | −0.369753 | ||||||||
\(802\) | −0.211503 | −0.00746845 | ||||||||
\(803\) | −33.9683 | −1.19872 | ||||||||
\(804\) | −19.8439 | −0.699840 | ||||||||
\(805\) | 0.807162 | 0.0284487 | ||||||||
\(806\) | −8.02611 | −0.282708 | ||||||||
\(807\) | 29.9145 | 1.05304 | ||||||||
\(808\) | −3.64509 | −0.128234 | ||||||||
\(809\) | 1.54720 | 0.0543967 | 0.0271983 | − | 0.999630i | \(-0.491341\pi\) | ||||
0.0271983 | + | 0.999630i | \(0.491341\pi\) | |||||||
\(810\) | −0.211503 | −0.00743147 | ||||||||
\(811\) | 24.6350 | 0.865052 | 0.432526 | − | 0.901622i | \(-0.357622\pi\) | ||||
0.432526 | + | 0.901622i | \(0.357622\pi\) | |||||||
\(812\) | 2.19079 | 0.0768818 | ||||||||
\(813\) | 16.8727 | 0.591751 | ||||||||
\(814\) | −4.23090 | −0.148293 | ||||||||
\(815\) | 10.8738 | 0.380892 | ||||||||
\(816\) | −3.43816 | −0.120360 | ||||||||
\(817\) | 15.6743 | 0.548373 | ||||||||
\(818\) | 3.53345 | 0.123544 | ||||||||
\(819\) | 17.7468 | 0.620123 | ||||||||
\(820\) | 10.8919 | 0.380361 | ||||||||
\(821\) | 2.59844 | 0.0906860 | 0.0453430 | − | 0.998971i | \(-0.485562\pi\) | ||||
0.0453430 | + | 0.998971i | \(0.485562\pi\) | |||||||
\(822\) | 3.83349 | 0.133708 | ||||||||
\(823\) | −41.2340 | −1.43733 | −0.718664 | − | 0.695358i | \(-0.755246\pi\) | ||||
−0.718664 | + | 0.695358i | \(0.755246\pi\) | |||||||
\(824\) | −6.43303 | −0.224105 | ||||||||
\(825\) | 2.42289 | 0.0843541 | ||||||||
\(826\) | −1.48904 | −0.0518103 | ||||||||
\(827\) | −20.5095 | −0.713186 | −0.356593 | − | 0.934260i | \(-0.616062\pi\) | ||||
−0.356593 | + | 0.934260i | \(0.616062\pi\) | |||||||
\(828\) | −0.520072 | −0.0180738 | ||||||||
\(829\) | −5.45389 | −0.189421 | −0.0947107 | − | 0.995505i | \(-0.530193\pi\) | ||||
−0.0947107 | + | 0.995505i | \(0.530193\pi\) | |||||||
\(830\) | 0.832435 | 0.0288942 | ||||||||
\(831\) | 29.6902 | 1.02994 | ||||||||
\(832\) | −40.6229 | −1.40835 | ||||||||
\(833\) | −2.03408 | −0.0704765 | ||||||||
\(834\) | 3.20661 | 0.111036 | ||||||||
\(835\) | −10.0862 | −0.349048 | ||||||||
\(836\) | −11.5174 | −0.398338 | ||||||||
\(837\) | 6.48890 | 0.224289 | ||||||||
\(838\) | −5.14097 | −0.177592 | ||||||||
\(839\) | 20.3373 | 0.702123 | 0.351061 | − | 0.936352i | \(-0.385821\pi\) | ||||
0.351061 | + | 0.936352i | \(0.385821\pi\) | |||||||
\(840\) | 2.53861 | 0.0875904 | ||||||||
\(841\) | −28.8637 | −0.995299 | ||||||||
\(842\) | −3.69258 | −0.127255 | ||||||||
\(843\) | −9.05519 | −0.311877 | ||||||||
\(844\) | −19.8625 | −0.683696 | ||||||||
\(845\) | 21.2006 | 0.729322 | ||||||||
\(846\) | 0.0152543 | 0.000524455 0 | ||||||||
\(847\) | −15.5664 | −0.534868 | ||||||||
\(848\) | −39.5701 | −1.35884 | ||||||||
\(849\) | −2.42399 | −0.0831912 | ||||||||
\(850\) | 0.194767 | 0.00668046 | ||||||||
\(851\) | 2.19604 | 0.0752793 | ||||||||
\(852\) | −11.7109 | −0.401209 | ||||||||
\(853\) | −9.03803 | −0.309456 | −0.154728 | − | 0.987957i | \(-0.549450\pi\) | ||||
−0.154728 | + | 0.987957i | \(0.549450\pi\) | |||||||
\(854\) | 0.514633 | 0.0176104 | ||||||||
\(855\) | 2.43117 | 0.0831444 | ||||||||
\(856\) | −0.187390 | −0.00640485 | ||||||||
\(857\) | 1.87095 | 0.0639105 | 0.0319553 | − | 0.999489i | \(-0.489827\pi\) | ||||
0.0319553 | + | 0.999489i | \(0.489827\pi\) | |||||||
\(858\) | −2.99687 | −0.102311 | ||||||||
\(859\) | 9.11687 | 0.311064 | 0.155532 | − | 0.987831i | \(-0.450291\pi\) | ||||
0.155532 | + | 0.987831i | \(0.450291\pi\) | |||||||
\(860\) | −12.6060 | −0.429861 | ||||||||
\(861\) | −16.9044 | −0.576100 | ||||||||
\(862\) | −4.69329 | −0.159854 | ||||||||
\(863\) | −45.5201 | −1.54952 | −0.774761 | − | 0.632255i | \(-0.782130\pi\) | ||||
−0.774761 | + | 0.632255i | \(0.782130\pi\) | |||||||
\(864\) | −2.46277 | −0.0837853 | ||||||||
\(865\) | 16.8481 | 0.572852 | ||||||||
\(866\) | −3.04821 | −0.103583 | ||||||||
\(867\) | −16.1520 | −0.548551 | ||||||||
\(868\) | −38.5017 | −1.30683 | ||||||||
\(869\) | −3.20388 | −0.108684 | ||||||||
\(870\) | 0.0780926 | 0.00264759 | ||||||||
\(871\) | 59.3523 | 2.01108 | ||||||||
\(872\) | −8.95549 | −0.303271 | ||||||||
\(873\) | 0.184517 | 0.00624497 | ||||||||
\(874\) | −0.136770 | −0.00462632 | ||||||||
\(875\) | 3.03461 | 0.102589 | ||||||||
\(876\) | 27.4124 | 0.926180 | ||||||||
\(877\) | 12.9307 | 0.436640 | 0.218320 | − | 0.975877i | \(-0.429942\pi\) | ||||
0.218320 | + | 0.975877i | \(0.429942\pi\) | |||||||
\(878\) | 7.75099 | 0.261583 | ||||||||
\(879\) | 11.7098 | 0.394961 | ||||||||
\(880\) | 9.04609 | 0.304943 | ||||||||
\(881\) | −39.7481 | −1.33915 | −0.669574 | − | 0.742745i | \(-0.733523\pi\) | ||||
−0.669574 | + | 0.742745i | \(0.733523\pi\) | |||||||
\(882\) | −0.467182 | −0.0157308 | ||||||||
\(883\) | 20.4010 | 0.686548 | 0.343274 | − | 0.939235i | \(-0.388464\pi\) | ||||
0.343274 | + | 0.939235i | \(0.388464\pi\) | |||||||
\(884\) | 10.5298 | 0.354157 | ||||||||
\(885\) | 2.31999 | 0.0779855 | ||||||||
\(886\) | 2.83511 | 0.0952475 | ||||||||
\(887\) | −21.7993 | −0.731948 | −0.365974 | − | 0.930625i | \(-0.619264\pi\) | ||||
−0.365974 | + | 0.930625i | \(0.619264\pi\) | |||||||
\(888\) | 6.90678 | 0.231776 | ||||||||
\(889\) | −16.6286 | −0.557704 | ||||||||
\(890\) | 2.21333 | 0.0741909 | ||||||||
\(891\) | 2.42289 | 0.0811697 | ||||||||
\(892\) | −24.7714 | −0.829407 | ||||||||
\(893\) | −0.175345 | −0.00586768 | ||||||||
\(894\) | 0.391393 | 0.0130902 | ||||||||
\(895\) | −22.9185 | −0.766081 | ||||||||
\(896\) | 19.4055 | 0.648291 | ||||||||
\(897\) | 1.55552 | 0.0519372 | ||||||||
\(898\) | 6.80811 | 0.227190 | ||||||||
\(899\) | −2.39587 | −0.0799068 | ||||||||
\(900\) | −1.95527 | −0.0651755 | ||||||||
\(901\) | 9.75973 | 0.325144 | ||||||||
\(902\) | 2.85461 | 0.0950482 | ||||||||
\(903\) | 19.5647 | 0.651074 | ||||||||
\(904\) | −5.73029 | −0.190587 | ||||||||
\(905\) | −11.1785 | −0.371584 | ||||||||
\(906\) | −2.41820 | −0.0803394 | ||||||||
\(907\) | −13.0315 | −0.432702 | −0.216351 | − | 0.976316i | \(-0.569416\pi\) | ||||
−0.216351 | + | 0.976316i | \(0.569416\pi\) | |||||||
\(908\) | −30.4704 | −1.01120 | ||||||||
\(909\) | −4.35727 | −0.144522 | ||||||||
\(910\) | −3.75351 | −0.124428 | ||||||||
\(911\) | −7.43704 | −0.246400 | −0.123200 | − | 0.992382i | \(-0.539316\pi\) | ||||
−0.123200 | + | 0.992382i | \(0.539316\pi\) | |||||||
\(912\) | 9.07703 | 0.300570 | ||||||||
\(913\) | −9.53599 | −0.315595 | ||||||||
\(914\) | −0.816752 | −0.0270157 | ||||||||
\(915\) | −0.801821 | −0.0265074 | ||||||||
\(916\) | −11.9383 | −0.394452 | ||||||||
\(917\) | 51.6789 | 1.70659 | ||||||||
\(918\) | 0.194767 | 0.00642828 | ||||||||
\(919\) | 27.3370 | 0.901765 | 0.450882 | − | 0.892583i | \(-0.351109\pi\) | ||||
0.450882 | + | 0.892583i | \(0.351109\pi\) | |||||||
\(920\) | 0.222511 | 0.00733596 | ||||||||
\(921\) | −4.24442 | −0.139858 | ||||||||
\(922\) | −0.0979233 | −0.00322493 | ||||||||
\(923\) | 35.0269 | 1.15292 | ||||||||
\(924\) | −14.3761 | −0.472940 | ||||||||
\(925\) | 8.25624 | 0.271464 | ||||||||
\(926\) | −6.48732 | −0.213187 | ||||||||
\(927\) | −7.68993 | −0.252571 | ||||||||
\(928\) | 0.909321 | 0.0298499 | ||||||||
\(929\) | 35.0498 | 1.14995 | 0.574973 | − | 0.818172i | \(-0.305013\pi\) | ||||
0.574973 | + | 0.818172i | \(0.305013\pi\) | |||||||
\(930\) | −1.37242 | −0.0450035 | ||||||||
\(931\) | 5.37012 | 0.175999 | ||||||||
\(932\) | 15.2762 | 0.500387 | ||||||||
\(933\) | −12.3533 | −0.404430 | ||||||||
\(934\) | 7.51017 | 0.245740 | ||||||||
\(935\) | −2.23117 | −0.0729669 | ||||||||
\(936\) | 4.89226 | 0.159909 | ||||||||
\(937\) | 34.9984 | 1.14335 | 0.571674 | − | 0.820481i | \(-0.306294\pi\) | ||||
0.571674 | + | 0.820481i | \(0.306294\pi\) | |||||||
\(938\) | −6.51390 | −0.212686 | ||||||||
\(939\) | 7.57303 | 0.247136 | ||||||||
\(940\) | 0.141020 | 0.00459958 | ||||||||
\(941\) | 55.7197 | 1.81641 | 0.908205 | − | 0.418526i | \(-0.137453\pi\) | ||||
0.908205 | + | 0.418526i | \(0.137453\pi\) | |||||||
\(942\) | 0.689648 | 0.0224699 | ||||||||
\(943\) | −1.48168 | −0.0482502 | ||||||||
\(944\) | 8.66190 | 0.281921 | ||||||||
\(945\) | 3.03461 | 0.0987159 | ||||||||
\(946\) | −3.30386 | −0.107418 | ||||||||
\(947\) | 5.51743 | 0.179292 | 0.0896461 | − | 0.995974i | \(-0.471426\pi\) | ||||
0.0896461 | + | 0.995974i | \(0.471426\pi\) | |||||||
\(948\) | 2.58553 | 0.0839740 | ||||||||
\(949\) | −81.9895 | −2.66149 | ||||||||
\(950\) | −0.514202 | −0.0166829 | ||||||||
\(951\) | −8.60857 | −0.279152 | ||||||||
\(952\) | −2.33773 | −0.0757663 | ||||||||
\(953\) | −55.7412 | −1.80563 | −0.902817 | − | 0.430026i | \(-0.858504\pi\) | ||||
−0.902817 | + | 0.430026i | \(0.858504\pi\) | |||||||
\(954\) | 2.24159 | 0.0725742 | ||||||||
\(955\) | −16.3225 | −0.528183 | ||||||||
\(956\) | 35.9502 | 1.16271 | ||||||||
\(957\) | −0.894593 | −0.0289181 | ||||||||
\(958\) | −3.93332 | −0.127080 | ||||||||
\(959\) | −55.0022 | −1.77611 | ||||||||
\(960\) | −6.94631 | −0.224191 | ||||||||
\(961\) | 11.1058 | 0.358251 | ||||||||
\(962\) | −10.2121 | −0.329253 | ||||||||
\(963\) | −0.224002 | −0.00721838 | ||||||||
\(964\) | 34.0843 | 1.09778 | ||||||||
\(965\) | 13.9218 | 0.448159 | ||||||||
\(966\) | −0.170718 | −0.00549275 | ||||||||
\(967\) | 22.3789 | 0.719658 | 0.359829 | − | 0.933018i | \(-0.382835\pi\) | ||||
0.359829 | + | 0.933018i | \(0.382835\pi\) | |||||||
\(968\) | −4.29120 | −0.137924 | ||||||||
\(969\) | −2.23880 | −0.0719205 | ||||||||
\(970\) | −0.0390260 | −0.00125305 | ||||||||
\(971\) | 46.0083 | 1.47648 | 0.738239 | − | 0.674539i | \(-0.235658\pi\) | ||||
0.738239 | + | 0.674539i | \(0.235658\pi\) | |||||||
\(972\) | −1.95527 | −0.0627152 | ||||||||
\(973\) | −46.0078 | −1.47494 | ||||||||
\(974\) | −3.99610 | −0.128043 | ||||||||
\(975\) | 5.84813 | 0.187290 | ||||||||
\(976\) | −2.99368 | −0.0958253 | ||||||||
\(977\) | 0.229801 | 0.00735199 | 0.00367600 | − | 0.999993i | \(-0.498830\pi\) | ||||
0.00367600 | + | 0.999993i | \(0.498830\pi\) | |||||||
\(978\) | −2.29984 | −0.0735408 | ||||||||
\(979\) | −25.3549 | −0.810345 | ||||||||
\(980\) | −4.31891 | −0.137963 | ||||||||
\(981\) | −10.7052 | −0.341792 | ||||||||
\(982\) | −3.49829 | −0.111635 | ||||||||
\(983\) | −19.6189 | −0.625747 | −0.312873 | − | 0.949795i | \(-0.601292\pi\) | ||||
−0.312873 | + | 0.949795i | \(0.601292\pi\) | |||||||
\(984\) | −4.66004 | −0.148557 | ||||||||
\(985\) | 9.62146 | 0.306565 | ||||||||
\(986\) | −0.0719132 | −0.00229018 | ||||||||
\(987\) | −0.218866 | −0.00696660 | ||||||||
\(988\) | −27.7996 | −0.884424 | ||||||||
\(989\) | 1.71486 | 0.0545294 | ||||||||
\(990\) | −0.512449 | −0.0162867 | ||||||||
\(991\) | 25.8041 | 0.819695 | 0.409848 | − | 0.912154i | \(-0.365582\pi\) | ||||
0.409848 | + | 0.912154i | \(0.365582\pi\) | |||||||
\(992\) | −15.9807 | −0.507387 | ||||||||
\(993\) | −23.1407 | −0.734349 | ||||||||
\(994\) | −3.84419 | −0.121930 | ||||||||
\(995\) | −21.0696 | −0.667952 | ||||||||
\(996\) | 7.69553 | 0.243842 | ||||||||
\(997\) | −6.05796 | −0.191857 | −0.0959287 | − | 0.995388i | \(-0.530582\pi\) | ||||
−0.0959287 | + | 0.995388i | \(0.530582\pi\) | |||||||
\(998\) | −7.50805 | −0.237663 | ||||||||
\(999\) | 8.25624 | 0.261216 |
(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 | 6015.2.a.i.1.20 | ✓ | 43 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6015.2.a.i.1.20 | ✓ | 43 | 1.1 | even | 1 | trivial |