Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(626,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.626");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.f (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 626.4 | ||
Character | \(\chi\) | \(=\) | 1045.626 |
Dual form | 1045.2.f.a.626.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52972 | −1.78878 | −0.894391 | − | 0.447287i | \(-0.852390\pi\) | ||||
−0.894391 | + | 0.447287i | \(0.852390\pi\) | |||||||
\(3\) | 0.384887i | 0.222215i | 0.993808 | + | 0.111107i | \(0.0354398\pi\) | ||||
−0.993808 | + | 0.111107i | \(0.964560\pi\) | |||||||
\(4\) | 4.39948 | 2.19974 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | − | 0.973657i | − | 0.397494i | ||||||
\(7\) | − | 1.35297i | − | 0.511376i | −0.966759 | − | 0.255688i | \(-0.917698\pi\) | ||
0.966759 | − | 0.255688i | \(-0.0823020\pi\) | |||||||
\(8\) | −6.07000 | −2.14607 | ||||||||
\(9\) | 2.85186 | 0.950621 | ||||||||
\(10\) | 2.52972 | 0.799967 | ||||||||
\(11\) | 1.95002 | − | 2.68280i | 0.587952 | − | 0.808896i | ||||
\(12\) | 1.69330i | 0.488815i | ||||||||
\(13\) | 2.33668 | 0.648078 | 0.324039 | − | 0.946044i | \(-0.394959\pi\) | ||||
0.324039 | + | 0.946044i | \(0.394959\pi\) | |||||||
\(14\) | 3.42264i | 0.914740i | ||||||||
\(15\) | − | 0.384887i | − | 0.0993775i | ||||||
\(16\) | 6.55645 | 1.63911 | ||||||||
\(17\) | 5.43006i | 1.31698i | 0.752588 | + | 0.658492i | \(0.228805\pi\) | ||||
−0.752588 | + | 0.658492i | \(0.771195\pi\) | |||||||
\(18\) | −7.21441 | −1.70045 | ||||||||
\(19\) | 0.531936 | − | 4.32632i | 0.122035 | − | 0.992526i | ||||
\(20\) | −4.39948 | −0.983753 | ||||||||
\(21\) | 0.520743 | 0.113635 | ||||||||
\(22\) | −4.93299 | + | 6.78674i | −1.05172 | + | 1.44694i | ||||
\(23\) | 0.981945 | 0.204750 | 0.102375 | − | 0.994746i | \(-0.467356\pi\) | ||||
0.102375 | + | 0.994746i | \(0.467356\pi\) | |||||||
\(24\) | − | 2.33627i | − | 0.476889i | ||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.91114 | −1.15927 | ||||||||
\(27\) | 2.25231i | 0.433457i | ||||||||
\(28\) | − | 5.95238i | − | 1.12489i | ||||||
\(29\) | −3.04589 | −0.565608 | −0.282804 | − | 0.959178i | \(-0.591265\pi\) | ||||
−0.282804 | + | 0.959178i | \(0.591265\pi\) | |||||||
\(30\) | 0.973657i | 0.177765i | ||||||||
\(31\) | − | 8.09312i | − | 1.45357i | −0.686866 | − | 0.726784i | \(-0.741014\pi\) | ||
0.686866 | − | 0.726784i | \(-0.258986\pi\) | |||||||
\(32\) | −4.44597 | −0.785943 | ||||||||
\(33\) | 1.03258 | + | 0.750537i | 0.179749 | + | 0.130652i | ||||
\(34\) | − | 13.7365i | − | 2.35580i | ||||||
\(35\) | 1.35297i | 0.228694i | ||||||||
\(36\) | 12.5467 | 2.09112 | ||||||||
\(37\) | 1.40295i | 0.230644i | 0.993328 | + | 0.115322i | \(0.0367899\pi\) | ||||
−0.993328 | + | 0.115322i | \(0.963210\pi\) | |||||||
\(38\) | −1.34565 | + | 10.9444i | −0.218293 | + | 1.77541i | ||||
\(39\) | 0.899359i | 0.144013i | ||||||||
\(40\) | 6.07000 | 0.959752 | ||||||||
\(41\) | 1.12340 | 0.175445 | 0.0877226 | − | 0.996145i | \(-0.472041\pi\) | ||||
0.0877226 | + | 0.996145i | \(0.472041\pi\) | |||||||
\(42\) | −1.31733 | −0.203269 | ||||||||
\(43\) | − | 2.01890i | − | 0.307879i | −0.988080 | − | 0.153939i | \(-0.950804\pi\) | ||
0.988080 | − | 0.153939i | \(-0.0491960\pi\) | |||||||
\(44\) | 8.57905 | − | 11.8029i | 1.29334 | − | 1.77936i | ||||
\(45\) | −2.85186 | −0.425130 | ||||||||
\(46\) | −2.48404 | −0.366252 | ||||||||
\(47\) | −12.2984 | −1.79390 | −0.896950 | − | 0.442131i | \(-0.854222\pi\) | ||||
−0.896950 | + | 0.442131i | \(0.854222\pi\) | |||||||
\(48\) | 2.52350i | 0.364235i | ||||||||
\(49\) | 5.16946 | 0.738495 | ||||||||
\(50\) | −2.52972 | −0.357756 | ||||||||
\(51\) | −2.08996 | −0.292653 | ||||||||
\(52\) | 10.2802 | 1.42560 | ||||||||
\(53\) | − | 3.95467i | − | 0.543216i | −0.962408 | − | 0.271608i | \(-0.912445\pi\) | ||
0.962408 | − | 0.271608i | \(-0.0875555\pi\) | |||||||
\(54\) | − | 5.69771i | − | 0.775360i | ||||||
\(55\) | −1.95002 | + | 2.68280i | −0.262940 | + | 0.361749i | ||||
\(56\) | 8.21255i | 1.09745i | ||||||||
\(57\) | 1.66515 | + | 0.204736i | 0.220554 | + | 0.0271179i | ||||
\(58\) | 7.70526 | 1.01175 | ||||||||
\(59\) | 1.26044i | 0.164095i | 0.996628 | + | 0.0820474i | \(0.0261459\pi\) | ||||
−0.996628 | + | 0.0820474i | \(0.973854\pi\) | |||||||
\(60\) | − | 1.69330i | − | 0.218605i | ||||||
\(61\) | 9.55786i | 1.22376i | 0.790951 | + | 0.611879i | \(0.209586\pi\) | ||||
−0.790951 | + | 0.611879i | \(0.790414\pi\) | |||||||
\(62\) | 20.4733i | 2.60011i | ||||||||
\(63\) | − | 3.85849i | − | 0.486124i | ||||||
\(64\) | −1.86586 | −0.233232 | ||||||||
\(65\) | −2.33668 | −0.289829 | ||||||||
\(66\) | −2.61213 | − | 1.89865i | −0.321531 | − | 0.233707i | ||||
\(67\) | − | 13.2712i | − | 1.62134i | −0.585505 | − | 0.810669i | \(-0.699104\pi\) | ||
0.585505 | − | 0.810669i | \(-0.300896\pi\) | |||||||
\(68\) | 23.8894i | 2.89702i | ||||||||
\(69\) | 0.377938i | 0.0454984i | ||||||||
\(70\) | − | 3.42264i | − | 0.409084i | ||||||
\(71\) | 14.3607i | 1.70431i | 0.523292 | + | 0.852154i | \(0.324704\pi\) | ||||
−0.523292 | + | 0.852154i | \(0.675296\pi\) | |||||||
\(72\) | −17.3108 | −2.04010 | ||||||||
\(73\) | 2.05840i | 0.240918i | 0.992718 | + | 0.120459i | \(0.0384366\pi\) | ||||
−0.992718 | + | 0.120459i | \(0.961563\pi\) | |||||||
\(74\) | − | 3.54907i | − | 0.412571i | ||||||
\(75\) | 0.384887i | 0.0444430i | ||||||||
\(76\) | 2.34024 | − | 19.0335i | 0.268444 | − | 2.18330i | ||||
\(77\) | −3.62976 | − | 2.63832i | −0.413650 | − | 0.300665i | ||||
\(78\) | − | 2.27512i | − | 0.257607i | ||||||
\(79\) | 9.57041 | 1.07676 | 0.538378 | − | 0.842704i | \(-0.319037\pi\) | ||||
0.538378 | + | 0.842704i | \(0.319037\pi\) | |||||||
\(80\) | −6.55645 | −0.733033 | ||||||||
\(81\) | 7.68870 | 0.854300 | ||||||||
\(82\) | −2.84188 | −0.313833 | ||||||||
\(83\) | − | 10.1838i | − | 1.11782i | −0.829230 | − | 0.558908i | \(-0.811221\pi\) | ||
0.829230 | − | 0.558908i | \(-0.188779\pi\) | |||||||
\(84\) | 2.29100 | 0.249968 | ||||||||
\(85\) | − | 5.43006i | − | 0.588973i | ||||||
\(86\) | 5.10724i | 0.550728i | ||||||||
\(87\) | − | 1.17233i | − | 0.125687i | ||||||
\(88\) | −11.8366 | + | 16.2846i | −1.26179 | + | 1.73595i | ||||
\(89\) | − | 12.3375i | − | 1.30777i | −0.756594 | − | 0.653885i | \(-0.773138\pi\) | ||
0.756594 | − | 0.653885i | \(-0.226862\pi\) | |||||||
\(90\) | 7.21441 | 0.760465 | ||||||||
\(91\) | − | 3.16147i | − | 0.331412i | ||||||
\(92\) | 4.32004 | 0.450396 | ||||||||
\(93\) | 3.11494 | 0.323004 | ||||||||
\(94\) | 31.1114 | 3.20890 | ||||||||
\(95\) | −0.531936 | + | 4.32632i | −0.0545755 | + | 0.443871i | ||||
\(96\) | − | 1.71120i | − | 0.174648i | ||||||
\(97\) | − | 2.23673i | − | 0.227106i | −0.993532 | − | 0.113553i | \(-0.963777\pi\) | ||
0.993532 | − | 0.113553i | \(-0.0362231\pi\) | |||||||
\(98\) | −13.0773 | −1.32101 | ||||||||
\(99\) | 5.56118 | − | 7.65098i | 0.558919 | − | 0.768953i | ||||
\(100\) | 4.39948 | 0.439948 | ||||||||
\(101\) | 5.08567i | 0.506043i | 0.967461 | + | 0.253022i | \(0.0814244\pi\) | ||||
−0.967461 | + | 0.253022i | \(0.918576\pi\) | |||||||
\(102\) | 5.28702 | 0.523493 | ||||||||
\(103\) | − | 6.81557i | − | 0.671558i | −0.941941 | − | 0.335779i | \(-0.891000\pi\) | ||
0.941941 | − | 0.335779i | \(-0.109000\pi\) | |||||||
\(104\) | −14.1837 | −1.39082 | ||||||||
\(105\) | −0.520743 | −0.0508193 | ||||||||
\(106\) | 10.0042i | 0.971695i | ||||||||
\(107\) | 17.4233 | 1.68438 | 0.842188 | − | 0.539184i | \(-0.181267\pi\) | ||||
0.842188 | + | 0.539184i | \(0.181267\pi\) | |||||||
\(108\) | 9.90898i | 0.953492i | ||||||||
\(109\) | 16.9175 | 1.62040 | 0.810201 | − | 0.586152i | \(-0.199358\pi\) | ||||
0.810201 | + | 0.586152i | \(0.199358\pi\) | |||||||
\(110\) | 4.93299 | − | 6.78674i | 0.470342 | − | 0.647090i | ||||
\(111\) | −0.539978 | −0.0512524 | ||||||||
\(112\) | − | 8.87070i | − | 0.838203i | ||||||
\(113\) | − | 9.65154i | − | 0.907940i | −0.891017 | − | 0.453970i | \(-0.850007\pi\) | ||
0.891017 | − | 0.453970i | \(-0.149993\pi\) | |||||||
\(114\) | −4.21235 | − | 0.517924i | −0.394523 | − | 0.0485080i | ||||
\(115\) | −0.981945 | −0.0915668 | ||||||||
\(116\) | −13.4003 | −1.24419 | ||||||||
\(117\) | 6.66389 | 0.616077 | ||||||||
\(118\) | − | 3.18855i | − | 0.293530i | ||||||
\(119\) | 7.34673 | 0.673474 | ||||||||
\(120\) | 2.33627i | 0.213271i | ||||||||
\(121\) | −3.39487 | − | 10.4630i | −0.308625 | − | 0.951184i | ||||
\(122\) | − | 24.1787i | − | 2.18904i | ||||||
\(123\) | 0.432382i | 0.0389865i | ||||||||
\(124\) | − | 35.6055i | − | 3.19747i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 9.76090i | 0.869570i | ||||||||
\(127\) | 11.1944 | 0.993347 | 0.496673 | − | 0.867938i | \(-0.334555\pi\) | ||||
0.496673 | + | 0.867938i | \(0.334555\pi\) | |||||||
\(128\) | 13.6120 | 1.20314 | ||||||||
\(129\) | 0.777048 | 0.0684152 | ||||||||
\(130\) | 5.91114 | 0.518442 | ||||||||
\(131\) | − | 11.7600i | − | 1.02748i | −0.857947 | − | 0.513738i | \(-0.828260\pi\) | ||
0.857947 | − | 0.513738i | \(-0.171740\pi\) | |||||||
\(132\) | 4.54280 | + | 3.30197i | 0.395400 | + | 0.287400i | ||||
\(133\) | −5.85340 | − | 0.719696i | −0.507554 | − | 0.0624055i | ||||
\(134\) | 33.5725i | 2.90022i | ||||||||
\(135\) | − | 2.25231i | − | 0.193848i | ||||||
\(136\) | − | 32.9605i | − | 2.82634i | ||||||
\(137\) | 5.82804 | 0.497923 | 0.248962 | − | 0.968513i | \(-0.419911\pi\) | ||||
0.248962 | + | 0.968513i | \(0.419911\pi\) | |||||||
\(138\) | − | 0.956078i | − | 0.0813867i | ||||||
\(139\) | − | 1.94056i | − | 0.164596i | −0.996608 | − | 0.0822980i | \(-0.973774\pi\) | ||
0.996608 | − | 0.0822980i | \(-0.0262259\pi\) | |||||||
\(140\) | 5.95238i | 0.503068i | ||||||||
\(141\) | − | 4.73349i | − | 0.398631i | ||||||
\(142\) | − | 36.3287i | − | 3.04863i | ||||||
\(143\) | 4.55656 | − | 6.26885i | 0.381039 | − | 0.524228i | ||||
\(144\) | 18.6981 | 1.55817 | ||||||||
\(145\) | 3.04589 | 0.252948 | ||||||||
\(146\) | − | 5.20718i | − | 0.430950i | ||||||
\(147\) | 1.98966i | 0.164105i | ||||||||
\(148\) | 6.17225i | 0.507356i | ||||||||
\(149\) | − | 9.35580i | − | 0.766457i | −0.923654 | − | 0.383228i | \(-0.874812\pi\) | ||
0.923654 | − | 0.383228i | \(-0.125188\pi\) | |||||||
\(150\) | − | 0.973657i | − | 0.0794988i | ||||||
\(151\) | −9.35512 | −0.761309 | −0.380655 | − | 0.924717i | \(-0.624301\pi\) | ||||
−0.380655 | + | 0.924717i | \(0.624301\pi\) | |||||||
\(152\) | −3.22886 | + | 26.2608i | −0.261895 | + | 2.13003i | ||||
\(153\) | 15.4858i | 1.25195i | ||||||||
\(154\) | 9.18228 | + | 6.67421i | 0.739929 | + | 0.537823i | ||||
\(155\) | 8.09312i | 0.650055i | ||||||||
\(156\) | 3.95671i | 0.316790i | ||||||||
\(157\) | 6.63790 | 0.529762 | 0.264881 | − | 0.964281i | \(-0.414667\pi\) | ||||
0.264881 | + | 0.964281i | \(0.414667\pi\) | |||||||
\(158\) | −24.2104 | −1.92608 | ||||||||
\(159\) | 1.52210 | 0.120711 | ||||||||
\(160\) | 4.44597 | 0.351484 | ||||||||
\(161\) | − | 1.32855i | − | 0.104704i | ||||||
\(162\) | −19.4502 | −1.52816 | ||||||||
\(163\) | 14.1577 | 1.10892 | 0.554458 | − | 0.832212i | \(-0.312926\pi\) | ||||
0.554458 | + | 0.832212i | \(0.312926\pi\) | |||||||
\(164\) | 4.94236 | 0.385934 | ||||||||
\(165\) | −1.03258 | − | 0.750537i | −0.0803861 | − | 0.0584292i | ||||
\(166\) | 25.7621i | 1.99953i | ||||||||
\(167\) | 2.40922 | 0.186431 | 0.0932155 | − | 0.995646i | \(-0.470285\pi\) | ||||
0.0932155 | + | 0.995646i | \(0.470285\pi\) | |||||||
\(168\) | −3.16091 | −0.243869 | ||||||||
\(169\) | −7.53993 | −0.579994 | ||||||||
\(170\) | 13.7365i | 1.05354i | ||||||||
\(171\) | 1.51701 | − | 12.3381i | 0.116009 | − | 0.943515i | ||||
\(172\) | − | 8.88209i | − | 0.677253i | ||||||
\(173\) | −10.2515 | −0.779410 | −0.389705 | − | 0.920940i | \(-0.627423\pi\) | ||||
−0.389705 | + | 0.920940i | \(0.627423\pi\) | |||||||
\(174\) | 2.96566i | 0.224826i | ||||||||
\(175\) | − | 1.35297i | − | 0.102275i | ||||||
\(176\) | 12.7852 | − | 17.5897i | 0.963720 | − | 1.32587i | ||||
\(177\) | −0.485126 | −0.0364643 | ||||||||
\(178\) | 31.2103i | 2.33931i | ||||||||
\(179\) | − | 16.5494i | − | 1.23696i | −0.785799 | − | 0.618482i | \(-0.787748\pi\) | ||
0.785799 | − | 0.618482i | \(-0.212252\pi\) | |||||||
\(180\) | −12.5467 | −0.935176 | ||||||||
\(181\) | 17.2195i | 1.27992i | 0.768410 | + | 0.639958i | \(0.221048\pi\) | ||||
−0.768410 | + | 0.639958i | \(0.778952\pi\) | |||||||
\(182\) | 7.99762i | 0.592823i | ||||||||
\(183\) | −3.67870 | −0.271937 | ||||||||
\(184\) | −5.96041 | −0.439407 | ||||||||
\(185\) | − | 1.40295i | − | 0.103147i | ||||||
\(186\) | −7.87993 | −0.577784 | ||||||||
\(187\) | 14.5678 | + | 10.5887i | 1.06530 | + | 0.774323i | ||||
\(188\) | −54.1064 | −3.94611 | ||||||||
\(189\) | 3.04731 | 0.221659 | ||||||||
\(190\) | 1.34565 | − | 10.9444i | 0.0976237 | − | 0.793988i | ||||
\(191\) | 10.7378 | 0.776960 | 0.388480 | − | 0.921457i | \(-0.373000\pi\) | ||||
0.388480 | + | 0.921457i | \(0.373000\pi\) | |||||||
\(192\) | − | 0.718145i | − | 0.0518276i | ||||||
\(193\) | −11.7328 | −0.844543 | −0.422272 | − | 0.906469i | \(-0.638767\pi\) | ||||
−0.422272 | + | 0.906469i | \(0.638767\pi\) | |||||||
\(194\) | 5.65830i | 0.406242i | ||||||||
\(195\) | − | 0.899359i | − | 0.0644044i | ||||||
\(196\) | 22.7429 | 1.62450 | ||||||||
\(197\) | − | 10.9577i | − | 0.780704i | −0.920666 | − | 0.390352i | \(-0.872353\pi\) | ||
0.920666 | − | 0.390352i | \(-0.127647\pi\) | |||||||
\(198\) | −14.0682 | + | 19.3548i | −0.999785 | + | 1.37549i | ||||
\(199\) | 15.9815 | 1.13290 | 0.566448 | − | 0.824098i | \(-0.308317\pi\) | ||||
0.566448 | + | 0.824098i | \(0.308317\pi\) | |||||||
\(200\) | −6.07000 | −0.429214 | ||||||||
\(201\) | 5.10793 | 0.360285 | ||||||||
\(202\) | − | 12.8653i | − | 0.905201i | ||||||
\(203\) | 4.12101i | 0.289238i | ||||||||
\(204\) | −9.19475 | −0.643761 | ||||||||
\(205\) | −1.12340 | −0.0784615 | ||||||||
\(206\) | 17.2415i | 1.20127i | ||||||||
\(207\) | 2.80037 | 0.194639 | ||||||||
\(208\) | 15.3203 | 1.06227 | ||||||||
\(209\) | −10.5694 | − | 9.86348i | −0.731099 | − | 0.682271i | ||||
\(210\) | 1.31733 | 0.0909046 | ||||||||
\(211\) | −24.8040 | −1.70758 | −0.853790 | − | 0.520617i | \(-0.825702\pi\) | ||||
−0.853790 | + | 0.520617i | \(0.825702\pi\) | |||||||
\(212\) | − | 17.3985i | − | 1.19493i | ||||||
\(213\) | −5.52727 | −0.378722 | ||||||||
\(214\) | −44.0761 | −3.01298 | ||||||||
\(215\) | 2.01890i | 0.137688i | ||||||||
\(216\) | − | 13.6715i | − | 0.930229i | ||||||
\(217\) | −10.9498 | −0.743319 | ||||||||
\(218\) | −42.7965 | −2.89855 | ||||||||
\(219\) | −0.792254 | −0.0535356 | ||||||||
\(220\) | −8.57905 | + | 11.8029i | −0.578400 | + | 0.795754i | ||||
\(221\) | 12.6883i | 0.853509i | ||||||||
\(222\) | 1.36599 | 0.0916794 | ||||||||
\(223\) | 26.5583i | 1.77848i | 0.457442 | + | 0.889239i | \(0.348766\pi\) | ||||
−0.457442 | + | 0.889239i | \(0.651234\pi\) | |||||||
\(224\) | 6.01527i | 0.401912i | ||||||||
\(225\) | 2.85186 | 0.190124 | ||||||||
\(226\) | 24.4157i | 1.62411i | ||||||||
\(227\) | −3.31971 | −0.220337 | −0.110168 | − | 0.993913i | \(-0.535139\pi\) | ||||
−0.110168 | + | 0.993913i | \(0.535139\pi\) | |||||||
\(228\) | 7.32577 | + | 0.900730i | 0.485161 | + | 0.0596523i | ||||
\(229\) | 2.71143 | 0.179177 | 0.0895883 | − | 0.995979i | \(-0.471445\pi\) | ||||
0.0895883 | + | 0.995979i | \(0.471445\pi\) | |||||||
\(230\) | 2.48404 | 0.163793 | ||||||||
\(231\) | 1.01546 | − | 1.39705i | 0.0668121 | − | 0.0919191i | ||||
\(232\) | 18.4886 | 1.21384 | ||||||||
\(233\) | − | 2.91234i | − | 0.190794i | −0.995439 | − | 0.0953970i | \(-0.969588\pi\) | ||
0.995439 | − | 0.0953970i | \(-0.0304120\pi\) | |||||||
\(234\) | −16.8578 | −1.10203 | ||||||||
\(235\) | 12.2984 | 0.802257 | ||||||||
\(236\) | 5.54526i | 0.360966i | ||||||||
\(237\) | 3.68353i | 0.239271i | ||||||||
\(238\) | −18.5852 | −1.20470 | ||||||||
\(239\) | 20.7111i | 1.33969i | 0.742502 | + | 0.669843i | \(0.233639\pi\) | ||||
−0.742502 | + | 0.669843i | \(0.766361\pi\) | |||||||
\(240\) | − | 2.52350i | − | 0.162891i | ||||||
\(241\) | −6.54934 | −0.421880 | −0.210940 | − | 0.977499i | \(-0.567652\pi\) | ||||
−0.210940 | + | 0.977499i | \(0.567652\pi\) | |||||||
\(242\) | 8.58807 | + | 26.4685i | 0.552062 | + | 1.70146i | ||||
\(243\) | 9.71621i | 0.623295i | ||||||||
\(244\) | 42.0496i | 2.69195i | ||||||||
\(245\) | −5.16946 | −0.330265 | ||||||||
\(246\) | − | 1.09380i | − | 0.0697384i | ||||||
\(247\) | 1.24296 | − | 10.1092i | 0.0790879 | − | 0.643234i | ||||
\(248\) | 49.1253i | 3.11946i | ||||||||
\(249\) | 3.91961 | 0.248395 | ||||||||
\(250\) | 2.52972 | 0.159993 | ||||||||
\(251\) | −8.69353 | −0.548731 | −0.274365 | − | 0.961626i | \(-0.588468\pi\) | ||||
−0.274365 | + | 0.961626i | \(0.588468\pi\) | |||||||
\(252\) | − | 16.9754i | − | 1.06935i | ||||||
\(253\) | 1.91481 | − | 2.63437i | 0.120383 | − | 0.165621i | ||||
\(254\) | −28.3188 | −1.77688 | ||||||||
\(255\) | 2.08996 | 0.130879 | ||||||||
\(256\) | −30.7029 | −1.91893 | ||||||||
\(257\) | − | 17.6353i | − | 1.10006i | −0.835145 | − | 0.550030i | \(-0.814616\pi\) | ||
0.835145 | − | 0.550030i | \(-0.185384\pi\) | |||||||
\(258\) | −1.96571 | −0.122380 | ||||||||
\(259\) | 1.89815 | 0.117946 | ||||||||
\(260\) | −10.2802 | −0.637549 | ||||||||
\(261\) | −8.68647 | −0.537679 | ||||||||
\(262\) | 29.7495i | 1.83793i | ||||||||
\(263\) | 24.9750i | 1.54002i | 0.638030 | + | 0.770012i | \(0.279750\pi\) | ||||
−0.638030 | + | 0.770012i | \(0.720250\pi\) | |||||||
\(264\) | −6.26775 | − | 4.55576i | −0.385753 | − | 0.280388i | ||||
\(265\) | 3.95467i | 0.242934i | ||||||||
\(266\) | 14.8074 | + | 1.82063i | 0.907903 | + | 0.111630i | ||||
\(267\) | 4.74854 | 0.290606 | ||||||||
\(268\) | − | 58.3864i | − | 3.56652i | ||||||
\(269\) | 14.4347i | 0.880096i | 0.897974 | + | 0.440048i | \(0.145039\pi\) | ||||
−0.897974 | + | 0.440048i | \(0.854961\pi\) | |||||||
\(270\) | 5.69771i | 0.346751i | ||||||||
\(271\) | − | 3.81840i | − | 0.231951i | −0.993252 | − | 0.115976i | \(-0.963001\pi\) | ||
0.993252 | − | 0.115976i | \(-0.0369994\pi\) | |||||||
\(272\) | 35.6019i | 2.15868i | ||||||||
\(273\) | 1.21681 | 0.0736446 | ||||||||
\(274\) | −14.7433 | −0.890676 | ||||||||
\(275\) | 1.95002 | − | 2.68280i | 0.117590 | − | 0.161779i | ||||
\(276\) | 1.66273i | 0.100085i | ||||||||
\(277\) | − | 8.53684i | − | 0.512929i | −0.966554 | − | 0.256464i | \(-0.917442\pi\) | ||
0.966554 | − | 0.256464i | \(-0.0825577\pi\) | |||||||
\(278\) | 4.90907i | 0.294426i | ||||||||
\(279\) | − | 23.0805i | − | 1.38179i | ||||||
\(280\) | − | 8.21255i | − | 0.490794i | ||||||
\(281\) | 11.5517 | 0.689114 | 0.344557 | − | 0.938765i | \(-0.388029\pi\) | ||||
0.344557 | + | 0.938765i | \(0.388029\pi\) | |||||||
\(282\) | 11.9744i | 0.713064i | ||||||||
\(283\) | − | 23.1870i | − | 1.37833i | −0.724606 | − | 0.689163i | \(-0.757978\pi\) | ||
0.724606 | − | 0.689163i | \(-0.242022\pi\) | |||||||
\(284\) | 63.1798i | 3.74903i | ||||||||
\(285\) | −1.66515 | − | 0.204736i | −0.0986348 | − | 0.0121275i | ||||
\(286\) | −11.5268 | + | 15.8584i | −0.681596 | + | 0.937729i | ||||
\(287\) | − | 1.51993i | − | 0.0897185i | ||||||
\(288\) | −12.6793 | −0.747134 | ||||||||
\(289\) | −12.4856 | −0.734446 | ||||||||
\(290\) | −7.70526 | −0.452468 | ||||||||
\(291\) | 0.860890 | 0.0504663 | ||||||||
\(292\) | 9.05590i | 0.529957i | ||||||||
\(293\) | 24.5380 | 1.43353 | 0.716763 | − | 0.697317i | \(-0.245623\pi\) | ||||
0.716763 | + | 0.697317i | \(0.245623\pi\) | |||||||
\(294\) | − | 5.03328i | − | 0.293547i | ||||||
\(295\) | − | 1.26044i | − | 0.0733854i | ||||||
\(296\) | − | 8.51591i | − | 0.494977i | ||||||
\(297\) | 6.04250 | + | 4.39204i | 0.350621 | + | 0.254852i | ||||
\(298\) | 23.6675i | 1.37102i | ||||||||
\(299\) | 2.29449 | 0.132694 | ||||||||
\(300\) | 1.69330i | 0.0977629i | ||||||||
\(301\) | −2.73151 | −0.157442 | ||||||||
\(302\) | 23.6658 | 1.36182 | ||||||||
\(303\) | −1.95741 | −0.112450 | ||||||||
\(304\) | 3.48761 | − | 28.3653i | 0.200028 | − | 1.62686i | ||||
\(305\) | − | 9.55786i | − | 0.547281i | ||||||
\(306\) | − | 39.1747i | − | 2.23947i | ||||||
\(307\) | −21.7400 | −1.24077 | −0.620384 | − | 0.784298i | \(-0.713023\pi\) | ||||
−0.620384 | + | 0.784298i | \(0.713023\pi\) | |||||||
\(308\) | −15.9691 | − | 11.6072i | −0.909921 | − | 0.661383i | ||||
\(309\) | 2.62323 | 0.149230 | ||||||||
\(310\) | − | 20.4733i | − | 1.16281i | ||||||
\(311\) | −1.75399 | −0.0994594 | −0.0497297 | − | 0.998763i | \(-0.515836\pi\) | ||||
−0.0497297 | + | 0.998763i | \(0.515836\pi\) | |||||||
\(312\) | − | 5.45911i | − | 0.309061i | ||||||
\(313\) | 9.69040 | 0.547734 | 0.273867 | − | 0.961768i | \(-0.411697\pi\) | ||||
0.273867 | + | 0.961768i | \(0.411697\pi\) | |||||||
\(314\) | −16.7920 | −0.947629 | ||||||||
\(315\) | 3.85849i | 0.217401i | ||||||||
\(316\) | 42.1048 | 2.36858 | ||||||||
\(317\) | − | 1.24283i | − | 0.0698042i | −0.999391 | − | 0.0349021i | \(-0.988888\pi\) | ||
0.999391 | − | 0.0349021i | \(-0.0111119\pi\) | |||||||
\(318\) | −3.85050 | −0.215925 | ||||||||
\(319\) | −5.93954 | + | 8.17154i | −0.332551 | + | 0.457518i | ||||
\(320\) | 1.86586 | 0.104305 | ||||||||
\(321\) | 6.70602i | 0.374293i | ||||||||
\(322\) | 3.36085i | 0.187293i | ||||||||
\(323\) | 23.4922 | + | 2.88845i | 1.30714 | + | 0.160718i | ||||
\(324\) | 33.8263 | 1.87924 | ||||||||
\(325\) | 2.33668 | 0.129616 | ||||||||
\(326\) | −35.8150 | −1.98361 | ||||||||
\(327\) | 6.51133i | 0.360078i | ||||||||
\(328\) | −6.81903 | −0.376518 | ||||||||
\(329\) | 16.6394i | 0.917357i | ||||||||
\(330\) | 2.61213 | + | 1.89865i | 0.143793 | + | 0.104517i | ||||
\(331\) | 33.0877i | 1.81866i | 0.416073 | + | 0.909331i | \(0.363406\pi\) | ||||
−0.416073 | + | 0.909331i | \(0.636594\pi\) | |||||||
\(332\) | − | 44.8033i | − | 2.45890i | ||||||
\(333\) | 4.00102i | 0.219255i | ||||||||
\(334\) | −6.09465 | −0.333484 | ||||||||
\(335\) | 13.2712i | 0.725084i | ||||||||
\(336\) | 3.41422 | 0.186261 | ||||||||
\(337\) | −0.317131 | −0.0172752 | −0.00863760 | − | 0.999963i | \(-0.502749\pi\) | ||||
−0.00863760 | + | 0.999963i | \(0.502749\pi\) | |||||||
\(338\) | 19.0739 | 1.03748 | ||||||||
\(339\) | 3.71476 | 0.201758 | ||||||||
\(340\) | − | 23.8894i | − | 1.29559i | ||||||
\(341\) | −21.7123 | − | 15.7817i | −1.17578 | − | 0.854628i | ||||
\(342\) | −3.83761 | + | 31.2118i | −0.207514 | + | 1.68774i | ||||
\(343\) | − | 16.4650i | − | 0.889024i | ||||||
\(344\) | 12.2547i | 0.660729i | ||||||||
\(345\) | − | 0.377938i | − | 0.0203475i | ||||||
\(346\) | 25.9335 | 1.39419 | ||||||||
\(347\) | 10.3945i | 0.558008i | 0.960290 | + | 0.279004i | \(0.0900043\pi\) | ||||
−0.960290 | + | 0.279004i | \(0.909996\pi\) | |||||||
\(348\) | − | 5.15763i | − | 0.276478i | ||||||
\(349\) | − | 14.6428i | − | 0.783812i | −0.920005 | − | 0.391906i | \(-0.871816\pi\) | ||
0.920005 | − | 0.391906i | \(-0.128184\pi\) | |||||||
\(350\) | 3.42264i | 0.182948i | ||||||||
\(351\) | 5.26292i | 0.280914i | ||||||||
\(352\) | −8.66971 | + | 11.9277i | −0.462097 | + | 0.635746i | ||||
\(353\) | 10.5498 | 0.561507 | 0.280753 | − | 0.959780i | \(-0.409416\pi\) | ||||
0.280753 | + | 0.959780i | \(0.409416\pi\) | |||||||
\(354\) | 1.22723 | 0.0652267 | ||||||||
\(355\) | − | 14.3607i | − | 0.762189i | ||||||
\(356\) | − | 54.2784i | − | 2.87675i | ||||||
\(357\) | 2.82766i | 0.149656i | ||||||||
\(358\) | 41.8654i | 2.21266i | ||||||||
\(359\) | − | 20.9700i | − | 1.10675i | −0.832931 | − | 0.553376i | \(-0.813339\pi\) | ||
0.832931 | − | 0.553376i | \(-0.186661\pi\) | |||||||
\(360\) | 17.3108 | 0.912360 | ||||||||
\(361\) | −18.4341 | − | 4.60265i | −0.970215 | − | 0.242245i | ||||
\(362\) | − | 43.5605i | − | 2.28949i | ||||||
\(363\) | 4.02709 | − | 1.30664i | 0.211367 | − | 0.0685810i | ||||
\(364\) | − | 13.9088i | − | 0.729019i | ||||||
\(365\) | − | 2.05840i | − | 0.107742i | ||||||
\(366\) | 9.30608 | 0.486437 | ||||||||
\(367\) | −18.1151 | −0.945599 | −0.472799 | − | 0.881170i | \(-0.656757\pi\) | ||||
−0.472799 | + | 0.881170i | \(0.656757\pi\) | |||||||
\(368\) | 6.43807 | 0.335608 | ||||||||
\(369\) | 3.20377 | 0.166782 | ||||||||
\(370\) | 3.54907i | 0.184507i | ||||||||
\(371\) | −5.35057 | −0.277788 | ||||||||
\(372\) | 13.7041 | 0.710525 | ||||||||
\(373\) | −22.2513 | −1.15213 | −0.576064 | − | 0.817405i | \(-0.695412\pi\) | ||||
−0.576064 | + | 0.817405i | \(0.695412\pi\) | |||||||
\(374\) | −36.8524 | − | 26.7865i | −1.90559 | − | 1.38510i | ||||
\(375\) | − | 0.384887i | − | 0.0198755i | ||||||
\(376\) | 74.6511 | 3.84984 | ||||||||
\(377\) | −7.11728 | −0.366559 | ||||||||
\(378\) | −7.70885 | −0.396500 | ||||||||
\(379\) | 21.0036i | 1.07888i | 0.842024 | + | 0.539441i | \(0.181364\pi\) | ||||
−0.842024 | + | 0.539441i | \(0.818636\pi\) | |||||||
\(380\) | −2.34024 | + | 19.0335i | −0.120052 | + | 0.976400i | ||||
\(381\) | 4.30860i | 0.220736i | ||||||||
\(382\) | −27.1636 | −1.38981 | ||||||||
\(383\) | − | 17.6182i | − | 0.900249i | −0.892966 | − | 0.450125i | \(-0.851380\pi\) | ||
0.892966 | − | 0.450125i | \(-0.148620\pi\) | |||||||
\(384\) | 5.23910i | 0.267357i | ||||||||
\(385\) | 3.62976 | + | 2.63832i | 0.184990 | + | 0.134461i | ||||
\(386\) | 29.6806 | 1.51070 | ||||||||
\(387\) | − | 5.75761i | − | 0.292676i | ||||||
\(388\) | − | 9.84045i | − | 0.499573i | ||||||
\(389\) | −12.7126 | −0.644555 | −0.322278 | − | 0.946645i | \(-0.604448\pi\) | ||||
−0.322278 | + | 0.946645i | \(0.604448\pi\) | |||||||
\(390\) | 2.27512i | 0.115205i | ||||||||
\(391\) | 5.33202i | 0.269652i | ||||||||
\(392\) | −31.3787 | −1.58486 | ||||||||
\(393\) | 4.52628 | 0.228321 | ||||||||
\(394\) | 27.7199i | 1.39651i | ||||||||
\(395\) | −9.57041 | −0.481540 | ||||||||
\(396\) | 24.4663 | − | 33.6603i | 1.22948 | − | 1.69150i | ||||
\(397\) | −3.16750 | −0.158972 | −0.0794862 | − | 0.996836i | \(-0.525328\pi\) | ||||
−0.0794862 | + | 0.996836i | \(0.525328\pi\) | |||||||
\(398\) | −40.4286 | −2.02650 | ||||||||
\(399\) | 0.277002 | − | 2.25290i | 0.0138674 | − | 0.112786i | ||||
\(400\) | 6.55645 | 0.327822 | ||||||||
\(401\) | 10.7406i | 0.536358i | 0.963369 | + | 0.268179i | \(0.0864219\pi\) | ||||
−0.963369 | + | 0.268179i | \(0.913578\pi\) | |||||||
\(402\) | −12.9216 | −0.644472 | ||||||||
\(403\) | − | 18.9110i | − | 0.942026i | ||||||
\(404\) | 22.3743i | 1.11316i | ||||||||
\(405\) | −7.68870 | −0.382055 | ||||||||
\(406\) | − | 10.4250i | − | 0.517384i | ||||||
\(407\) | 3.76384 | + | 2.73578i | 0.186567 | + | 0.135607i | ||||
\(408\) | 12.6861 | 0.628055 | ||||||||
\(409\) | −16.5390 | −0.817801 | −0.408900 | − | 0.912579i | \(-0.634088\pi\) | ||||
−0.408900 | + | 0.912579i | \(0.634088\pi\) | |||||||
\(410\) | 2.84188 | 0.140350 | ||||||||
\(411\) | 2.24314i | 0.110646i | ||||||||
\(412\) | − | 29.9849i | − | 1.47725i | ||||||
\(413\) | 1.70534 | 0.0839141 | ||||||||
\(414\) | −7.08415 | −0.348167 | ||||||||
\(415\) | 10.1838i | 0.499902i | ||||||||
\(416\) | −10.3888 | −0.509353 | ||||||||
\(417\) | 0.746897 | 0.0365757 | ||||||||
\(418\) | 26.7376 | + | 24.9518i | 1.30778 | + | 1.22043i | ||||
\(419\) | 7.71720 | 0.377010 | 0.188505 | − | 0.982072i | \(-0.439636\pi\) | ||||
0.188505 | + | 0.982072i | \(0.439636\pi\) | |||||||
\(420\) | −2.29100 | −0.111789 | ||||||||
\(421\) | − | 25.5946i | − | 1.24740i | −0.781662 | − | 0.623702i | \(-0.785628\pi\) | ||
0.781662 | − | 0.623702i | \(-0.214372\pi\) | |||||||
\(422\) | 62.7473 | 3.05449 | ||||||||
\(423\) | −35.0732 | −1.70532 | ||||||||
\(424\) | 24.0049i | 1.16578i | ||||||||
\(425\) | 5.43006i | 0.263397i | ||||||||
\(426\) | 13.9824 | 0.677452 | ||||||||
\(427\) | 12.9315 | 0.625801 | ||||||||
\(428\) | 76.6535 | 3.70519 | ||||||||
\(429\) | 2.41280 | + | 1.75376i | 0.116491 | + | 0.0846725i | ||||
\(430\) | − | 5.10724i | − | 0.246293i | ||||||
\(431\) | −33.3982 | −1.60873 | −0.804367 | − | 0.594133i | \(-0.797495\pi\) | ||||
−0.804367 | + | 0.594133i | \(0.797495\pi\) | |||||||
\(432\) | 14.7671i | 0.710485i | ||||||||
\(433\) | 24.2308i | 1.16446i | 0.813025 | + | 0.582228i | \(0.197819\pi\) | ||||
−0.813025 | + | 0.582228i | \(0.802181\pi\) | |||||||
\(434\) | 27.6999 | 1.32964 | ||||||||
\(435\) | 1.17233i | 0.0562088i | ||||||||
\(436\) | 74.4282 | 3.56446 | ||||||||
\(437\) | 0.522332 | − | 4.24821i | 0.0249865 | − | 0.203219i | ||||
\(438\) | 2.00418 | 0.0957634 | ||||||||
\(439\) | 30.2441 | 1.44347 | 0.721737 | − | 0.692167i | \(-0.243344\pi\) | ||||
0.721737 | + | 0.692167i | \(0.243344\pi\) | |||||||
\(440\) | 11.8366 | − | 16.2846i | 0.564288 | − | 0.776339i | ||||
\(441\) | 14.7426 | 0.702028 | ||||||||
\(442\) | − | 32.0979i | − | 1.52674i | ||||||
\(443\) | −2.75876 | −0.131073 | −0.0655363 | − | 0.997850i | \(-0.520876\pi\) | ||||
−0.0655363 | + | 0.997850i | \(0.520876\pi\) | |||||||
\(444\) | −2.37562 | −0.112742 | ||||||||
\(445\) | 12.3375i | 0.584852i | ||||||||
\(446\) | − | 67.1852i | − | 3.18131i | ||||||
\(447\) | 3.60093 | 0.170318 | ||||||||
\(448\) | 2.52445i | 0.119269i | ||||||||
\(449\) | 32.7641i | 1.54623i | 0.634265 | + | 0.773116i | \(0.281303\pi\) | ||||
−0.634265 | + | 0.773116i | \(0.718697\pi\) | |||||||
\(450\) | −7.21441 | −0.340090 | ||||||||
\(451\) | 2.19064 | − | 3.01386i | 0.103153 | − | 0.141917i | ||||
\(452\) | − | 42.4617i | − | 1.99723i | ||||||
\(453\) | − | 3.60067i | − | 0.169174i | ||||||
\(454\) | 8.39793 | 0.394134 | ||||||||
\(455\) | 3.16147i | 0.148212i | ||||||||
\(456\) | −10.1074 | − | 1.24275i | −0.473325 | − | 0.0581969i | ||||
\(457\) | 13.2581i | 0.620186i | 0.950706 | + | 0.310093i | \(0.100360\pi\) | ||||
−0.950706 | + | 0.310093i | \(0.899640\pi\) | |||||||
\(458\) | −6.85916 | −0.320508 | ||||||||
\(459\) | −12.2302 | −0.570856 | ||||||||
\(460\) | −4.32004 | −0.201423 | ||||||||
\(461\) | 23.8716i | 1.11181i | 0.831246 | + | 0.555905i | \(0.187628\pi\) | ||||
−0.831246 | + | 0.555905i | \(0.812372\pi\) | |||||||
\(462\) | −2.56882 | + | 3.53414i | −0.119512 | + | 0.164423i | ||||
\(463\) | 7.08380 | 0.329212 | 0.164606 | − | 0.986359i | \(-0.447365\pi\) | ||||
0.164606 | + | 0.986359i | \(0.447365\pi\) | |||||||
\(464\) | −19.9703 | −0.927096 | ||||||||
\(465\) | −3.11494 | −0.144452 | ||||||||
\(466\) | 7.36741i | 0.341289i | ||||||||
\(467\) | 0.535622 | 0.0247856 | 0.0123928 | − | 0.999923i | \(-0.496055\pi\) | ||||
0.0123928 | + | 0.999923i | \(0.496055\pi\) | |||||||
\(468\) | 29.3176 | 1.35521 | ||||||||
\(469\) | −17.9556 | −0.829113 | ||||||||
\(470\) | −31.1114 | −1.43506 | ||||||||
\(471\) | 2.55485i | 0.117721i | ||||||||
\(472\) | − | 7.65085i | − | 0.352159i | ||||||
\(473\) | −5.41630 | − | 3.93688i | −0.249042 | − | 0.181018i | ||||
\(474\) | − | 9.31830i | − | 0.428004i | ||||||
\(475\) | 0.531936 | − | 4.32632i | 0.0244069 | − | 0.198505i | ||||
\(476\) | 32.3218 | 1.48147 | ||||||||
\(477\) | − | 11.2782i | − | 0.516393i | ||||||
\(478\) | − | 52.3931i | − | 2.39641i | ||||||
\(479\) | − | 19.4054i | − | 0.886657i | −0.896359 | − | 0.443329i | \(-0.853797\pi\) | ||
0.896359 | − | 0.443329i | \(-0.146203\pi\) | |||||||
\(480\) | 1.71120i | 0.0781051i | ||||||||
\(481\) | 3.27824i | 0.149475i | ||||||||
\(482\) | 16.5680 | 0.754651 | ||||||||
\(483\) | 0.511340 | 0.0232668 | ||||||||
\(484\) | −14.9357 | − | 46.0318i | −0.678894 | − | 2.09236i | ||||
\(485\) | 2.23673i | 0.101565i | ||||||||
\(486\) | − | 24.5793i | − | 1.11494i | ||||||
\(487\) | 7.55916i | 0.342538i | 0.985224 | + | 0.171269i | \(0.0547867\pi\) | ||||
−0.985224 | + | 0.171269i | \(0.945213\pi\) | |||||||
\(488\) | − | 58.0163i | − | 2.62627i | ||||||
\(489\) | 5.44912i | 0.246418i | ||||||||
\(490\) | 13.0773 | 0.590772 | ||||||||
\(491\) | − | 30.9535i | − | 1.39691i | −0.715654 | − | 0.698455i | \(-0.753871\pi\) | ||
0.715654 | − | 0.698455i | \(-0.246129\pi\) | |||||||
\(492\) | 1.90225i | 0.0857602i | ||||||||
\(493\) | − | 16.5394i | − | 0.744897i | ||||||
\(494\) | −3.14435 | + | 25.5735i | −0.141471 | + | 1.15061i | ||||
\(495\) | −5.56118 | + | 7.65098i | −0.249956 | + | 0.343886i | ||||
\(496\) | − | 53.0621i | − | 2.38256i | ||||||
\(497\) | 19.4297 | 0.871542 | ||||||||
\(498\) | −9.91551 | −0.444325 | ||||||||
\(499\) | 40.9890 | 1.83492 | 0.917459 | − | 0.397831i | \(-0.130237\pi\) | ||||
0.917459 | + | 0.397831i | \(0.130237\pi\) | |||||||
\(500\) | −4.39948 | −0.196751 | ||||||||
\(501\) | 0.927278i | 0.0414277i | ||||||||
\(502\) | 21.9922 | 0.981559 | ||||||||
\(503\) | 17.7033i | 0.789350i | 0.918821 | + | 0.394675i | \(0.129143\pi\) | ||||
−0.918821 | + | 0.394675i | \(0.870857\pi\) | |||||||
\(504\) | 23.4211i | 1.04326i | ||||||||
\(505\) | − | 5.08567i | − | 0.226310i | ||||||
\(506\) | −4.84393 | + | 6.66420i | −0.215339 | + | 0.296260i | ||||
\(507\) | − | 2.90202i | − | 0.128883i | ||||||
\(508\) | 49.2497 | 2.18510 | ||||||||
\(509\) | − | 40.5717i | − | 1.79831i | −0.437630 | − | 0.899155i | \(-0.644182\pi\) | ||
0.437630 | − | 0.899155i | \(-0.355818\pi\) | |||||||
\(510\) | −5.28702 | −0.234113 | ||||||||
\(511\) | 2.78497 | 0.123200 | ||||||||
\(512\) | 50.4456 | 2.22940 | ||||||||
\(513\) | 9.74421 | + | 1.19808i | 0.430217 | + | 0.0528967i | ||||
\(514\) | 44.6124i | 1.96777i | ||||||||
\(515\) | 6.81557i | 0.300330i | ||||||||
\(516\) | 3.41860 | 0.150496 | ||||||||
\(517\) | −23.9820 | + | 32.9941i | −1.05473 | + | 1.45108i | ||||
\(518\) | −4.80180 | −0.210979 | ||||||||
\(519\) | − | 3.94569i | − | 0.173196i | ||||||
\(520\) | 14.1837 | 0.621994 | ||||||||
\(521\) | 28.1322i | 1.23249i | 0.787553 | + | 0.616247i | \(0.211348\pi\) | ||||
−0.787553 | + | 0.616247i | \(0.788652\pi\) | |||||||
\(522\) | 21.9743 | 0.961790 | ||||||||
\(523\) | −13.7730 | −0.602252 | −0.301126 | − | 0.953584i | \(-0.597362\pi\) | ||||
−0.301126 | + | 0.953584i | \(0.597362\pi\) | |||||||
\(524\) | − | 51.7379i | − | 2.26018i | ||||||
\(525\) | 0.520743 | 0.0227271 | ||||||||
\(526\) | − | 63.1797i | − | 2.75477i | ||||||
\(527\) | 43.9462 | 1.91432 | ||||||||
\(528\) | 6.77004 | + | 4.92086i | 0.294628 | + | 0.214153i | ||||
\(529\) | −22.0358 | −0.958078 | ||||||||
\(530\) | − | 10.0042i | − | 0.434555i | ||||||
\(531\) | 3.59459i | 0.155992i | ||||||||
\(532\) | −25.7519 | − | 3.16628i | −1.11649 | − | 0.137276i | ||||
\(533\) | 2.62502 | 0.113702 | ||||||||
\(534\) | −12.0125 | −0.519830 | ||||||||
\(535\) | −17.4233 | −0.753276 | ||||||||
\(536\) | 80.5564i | 3.47951i | ||||||||
\(537\) | 6.36967 | 0.274872 | ||||||||
\(538\) | − | 36.5156i | − | 1.57430i | ||||||
\(539\) | 10.0805 | − | 13.8687i | 0.434200 | − | 0.597365i | ||||
\(540\) | − | 9.90898i | − | 0.426415i | ||||||
\(541\) | 19.7937i | 0.850996i | 0.904959 | + | 0.425498i | \(0.139901\pi\) | ||||
−0.904959 | + | 0.425498i | \(0.860099\pi\) | |||||||
\(542\) | 9.65947i | 0.414910i | ||||||||
\(543\) | −6.62757 | −0.284416 | ||||||||
\(544\) | − | 24.1419i | − | 1.03507i | ||||||
\(545\) | −16.9175 | −0.724666 | ||||||||
\(546\) | −3.07818 | −0.131734 | ||||||||
\(547\) | 38.3756 | 1.64082 | 0.820411 | − | 0.571774i | \(-0.193744\pi\) | ||||
0.820411 | + | 0.571774i | \(0.193744\pi\) | |||||||
\(548\) | 25.6403 | 1.09530 | ||||||||
\(549\) | 27.2577i | 1.16333i | ||||||||
\(550\) | −4.93299 | + | 6.78674i | −0.210344 | + | 0.289388i | ||||
\(551\) | −1.62022 | + | 13.1775i | −0.0690238 | + | 0.561381i | ||||
\(552\) | − | 2.29409i | − | 0.0976428i | ||||||
\(553\) | − | 12.9485i | − | 0.550627i | ||||||
\(554\) | 21.5958i | 0.917518i | ||||||||
\(555\) | 0.539978 | 0.0229208 | ||||||||
\(556\) | − | 8.53744i | − | 0.362068i | ||||||
\(557\) | 17.2554i | 0.731136i | 0.930785 | + | 0.365568i | \(0.119125\pi\) | ||||
−0.930785 | + | 0.365568i | \(0.880875\pi\) | |||||||
\(558\) | 58.3871i | 2.47172i | ||||||||
\(559\) | − | 4.71751i | − | 0.199529i | ||||||
\(560\) | 8.87070i | 0.374856i | ||||||||
\(561\) | −4.07546 | + | 5.60696i | −0.172066 | + | 0.236726i | ||||
\(562\) | −29.2224 | −1.23267 | ||||||||
\(563\) | 27.2632 | 1.14901 | 0.574503 | − | 0.818502i | \(-0.305195\pi\) | ||||
0.574503 | + | 0.818502i | \(0.305195\pi\) | |||||||
\(564\) | − | 20.8249i | − | 0.876885i | ||||||
\(565\) | 9.65154i | 0.406043i | ||||||||
\(566\) | 58.6567i | 2.46553i | ||||||||
\(567\) | − | 10.4026i | − | 0.436868i | ||||||
\(568\) | − | 87.1698i | − | 3.65756i | ||||||
\(569\) | 28.1885 | 1.18172 | 0.590862 | − | 0.806772i | \(-0.298788\pi\) | ||||
0.590862 | + | 0.806772i | \(0.298788\pi\) | |||||||
\(570\) | 4.21235 | + | 0.517924i | 0.176436 | + | 0.0216934i | ||||
\(571\) | 20.8031i | 0.870581i | 0.900290 | + | 0.435290i | \(0.143354\pi\) | ||||
−0.900290 | + | 0.435290i | \(0.856646\pi\) | |||||||
\(572\) | 20.0465 | − | 27.5797i | 0.838186 | − | 1.15316i | ||||
\(573\) | 4.13284i | 0.172652i | ||||||||
\(574\) | 3.84499i | 0.160487i | ||||||||
\(575\) | 0.981945 | 0.0409499 | ||||||||
\(576\) | −5.32116 | −0.221715 | ||||||||
\(577\) | −43.6723 | −1.81810 | −0.909051 | − | 0.416685i | \(-0.863192\pi\) | ||||
−0.909051 | + | 0.416685i | \(0.863192\pi\) | |||||||
\(578\) | 31.5850 | 1.31376 | ||||||||
\(579\) | − | 4.51580i | − | 0.187670i | ||||||
\(580\) | 13.4003 | 0.556419 | ||||||||
\(581\) | −13.7784 | −0.571624 | ||||||||
\(582\) | −2.17781 | −0.0902731 | ||||||||
\(583\) | −10.6096 | − | 7.71168i | −0.439405 | − | 0.319385i | ||||
\(584\) | − | 12.4945i | − | 0.517027i | ||||||
\(585\) | −6.66389 | −0.275518 | ||||||||
\(586\) | −62.0743 | −2.56426 | ||||||||
\(587\) | −27.5563 | −1.13737 | −0.568685 | − | 0.822555i | \(-0.692548\pi\) | ||||
−0.568685 | + | 0.822555i | \(0.692548\pi\) | |||||||
\(588\) | 8.75347i | 0.360987i | ||||||||
\(589\) | −35.0134 | − | 4.30502i | −1.44270 | − | 0.177385i | ||||
\(590\) | 3.18855i | 0.131270i | ||||||||
\(591\) | 4.21748 | 0.173484 | ||||||||
\(592\) | 9.19837i | 0.378051i | ||||||||
\(593\) | − | 17.1694i | − | 0.705063i | −0.935800 | − | 0.352531i | \(-0.885321\pi\) | ||
0.935800 | − | 0.352531i | \(-0.114679\pi\) | |||||||
\(594\) | −15.2858 | − | 11.1106i | −0.627185 | − | 0.455874i | ||||
\(595\) | −7.34673 | −0.301187 | ||||||||
\(596\) | − | 41.1606i | − | 1.68600i | ||||||
\(597\) | 6.15106i | 0.251746i | ||||||||
\(598\) | −5.80442 | −0.237360 | ||||||||
\(599\) | 6.49020i | 0.265182i | 0.991171 | + | 0.132591i | \(0.0423297\pi\) | ||||
−0.991171 | + | 0.132591i | \(0.957670\pi\) | |||||||
\(600\) | − | 2.33627i | − | 0.0953778i | ||||||
\(601\) | −44.8595 | −1.82986 | −0.914928 | − | 0.403618i | \(-0.867753\pi\) | ||||
−0.914928 | + | 0.403618i | \(0.867753\pi\) | |||||||
\(602\) | 6.90996 | 0.281629 | ||||||||
\(603\) | − | 37.8477i | − | 1.54128i | ||||||
\(604\) | −41.1577 | −1.67468 | ||||||||
\(605\) | 3.39487 | + | 10.4630i | 0.138021 | + | 0.425382i | ||||
\(606\) | 4.95170 | 0.201149 | ||||||||
\(607\) | −30.0795 | −1.22089 | −0.610446 | − | 0.792058i | \(-0.709010\pi\) | ||||
−0.610446 | + | 0.792058i | \(0.709010\pi\) | |||||||
\(608\) | −2.36497 | + | 19.2347i | −0.0959122 | + | 0.780069i | ||||
\(609\) | −1.58613 | −0.0642731 | ||||||||
\(610\) | 24.1787i | 0.978967i | ||||||||
\(611\) | −28.7373 | −1.16259 | ||||||||
\(612\) | 68.1294i | 2.75397i | ||||||||
\(613\) | 13.4630i | 0.543764i | 0.962331 | + | 0.271882i | \(0.0876460\pi\) | ||||
−0.962331 | + | 0.271882i | \(0.912354\pi\) | |||||||
\(614\) | 54.9962 | 2.21946 | ||||||||
\(615\) | − | 0.432382i | − | 0.0174353i | ||||||
\(616\) | 22.0327 | + | 16.0146i | 0.887722 | + | 0.645247i | ||||
\(617\) | 9.32634 | 0.375464 | 0.187732 | − | 0.982220i | \(-0.439886\pi\) | ||||
0.187732 | + | 0.982220i | \(0.439886\pi\) | |||||||
\(618\) | −6.63603 | −0.266940 | ||||||||
\(619\) | 17.9855 | 0.722899 | 0.361449 | − | 0.932392i | \(-0.382282\pi\) | ||||
0.361449 | + | 0.932392i | \(0.382282\pi\) | |||||||
\(620\) | 35.6055i | 1.42995i | ||||||||
\(621\) | 2.21164i | 0.0887502i | ||||||||
\(622\) | 4.43709 | 0.177911 | ||||||||
\(623\) | −16.6923 | −0.668762 | ||||||||
\(624\) | 5.89660i | 0.236053i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −24.5140 | −0.979776 | ||||||||
\(627\) | 3.79633 | − | 4.06802i | 0.151611 | − | 0.162461i | ||||
\(628\) | 29.2033 | 1.16534 | ||||||||
\(629\) | −7.61811 | −0.303754 | ||||||||
\(630\) | − | 9.76090i | − | 0.388884i | ||||||
\(631\) | 10.4925 | 0.417701 | 0.208850 | − | 0.977948i | \(-0.433028\pi\) | ||||
0.208850 | + | 0.977948i | \(0.433028\pi\) | |||||||
\(632\) | −58.0924 | −2.31079 | ||||||||
\(633\) | − | 9.54677i | − | 0.379450i | ||||||
\(634\) | 3.14401i | 0.124864i | ||||||||
\(635\) | −11.1944 | −0.444238 | ||||||||
\(636\) | 6.69647 | 0.265532 | ||||||||
\(637\) | 12.0794 | 0.478602 | ||||||||
\(638\) | 15.0254 | − | 20.6717i | 0.594860 | − | 0.818400i | ||||
\(639\) | 40.9549i | 1.62015i | ||||||||
\(640\) | −13.6120 | −0.538062 | ||||||||
\(641\) | 6.59173i | 0.260358i | 0.991491 | + | 0.130179i | \(0.0415551\pi\) | ||||
−0.991491 | + | 0.130179i | \(0.958445\pi\) | |||||||
\(642\) | − | 16.9643i | − | 0.669529i | ||||||
\(643\) | 42.3494 | 1.67010 | 0.835049 | − | 0.550176i | \(-0.185439\pi\) | ||||
0.835049 | + | 0.550176i | \(0.185439\pi\) | |||||||
\(644\) | − | 5.84491i | − | 0.230322i | ||||||
\(645\) | −0.777048 | −0.0305962 | ||||||||
\(646\) | −59.4286 | − | 7.30696i | −2.33819 | − | 0.287488i | ||||
\(647\) | −37.6226 | −1.47910 | −0.739549 | − | 0.673103i | \(-0.764961\pi\) | ||||
−0.739549 | + | 0.673103i | \(0.764961\pi\) | |||||||
\(648\) | −46.6704 | −1.83339 | ||||||||
\(649\) | 3.38150 | + | 2.45787i | 0.132736 | + | 0.0964798i | ||||
\(650\) | −5.91114 | −0.231854 | ||||||||
\(651\) | − | 4.21443i | − | 0.165177i | ||||||
\(652\) | 62.2864 | 2.43932 | ||||||||
\(653\) | 2.79930 | 0.109545 | 0.0547726 | − | 0.998499i | \(-0.482557\pi\) | ||||
0.0547726 | + | 0.998499i | \(0.482557\pi\) | |||||||
\(654\) | − | 16.4718i | − | 0.644100i | ||||||
\(655\) | 11.7600i | 0.459501i | ||||||||
\(656\) | 7.36550 | 0.287574 | ||||||||
\(657\) | 5.87028i | 0.229022i | ||||||||
\(658\) | − | 42.0929i | − | 1.64095i | ||||||
\(659\) | −28.1649 | −1.09715 | −0.548574 | − | 0.836102i | \(-0.684829\pi\) | ||||
−0.548574 | + | 0.836102i | \(0.684829\pi\) | |||||||
\(660\) | −4.54280 | − | 3.30197i | −0.176828 | − | 0.128529i | ||||
\(661\) | 23.2863i | 0.905731i | 0.891579 | + | 0.452865i | \(0.149598\pi\) | ||||
−0.891579 | + | 0.452865i | \(0.850402\pi\) | |||||||
\(662\) | − | 83.7025i | − | 3.25319i | ||||||
\(663\) | −4.88357 | −0.189662 | ||||||||
\(664\) | 61.8156i | 2.39891i | ||||||||
\(665\) | 5.85340 | + | 0.719696i | 0.226985 | + | 0.0279086i | ||||
\(666\) | − | 10.1215i | − | 0.392198i | ||||||
\(667\) | −2.99090 | −0.115808 | ||||||||
\(668\) | 10.5993 | 0.410099 | ||||||||
\(669\) | −10.2220 | −0.395204 | ||||||||
\(670\) | − | 33.5725i | − | 1.29702i | ||||||
\(671\) | 25.6419 | + | 18.6380i | 0.989893 | + | 0.719511i | ||||
\(672\) | −2.31520 | −0.0893109 | ||||||||
\(673\) | 21.5800 | 0.831847 | 0.415924 | − | 0.909400i | \(-0.363458\pi\) | ||||
0.415924 | + | 0.909400i | \(0.363458\pi\) | |||||||
\(674\) | 0.802251 | 0.0309016 | ||||||||
\(675\) | 2.25231i | 0.0866914i | ||||||||
\(676\) | −33.1717 | −1.27584 | ||||||||
\(677\) | 40.3794 | 1.55190 | 0.775952 | − | 0.630791i | \(-0.217270\pi\) | ||||
0.775952 | + | 0.630791i | \(0.217270\pi\) | |||||||
\(678\) | −9.39729 | −0.360901 | ||||||||
\(679\) | −3.02624 | −0.116136 | ||||||||
\(680\) | 32.9605i | 1.26398i | ||||||||
\(681\) | − | 1.27771i | − | 0.0489621i | ||||||
\(682\) | 54.9259 | + | 39.9233i | 2.10322 | + | 1.52874i | ||||
\(683\) | − | 36.7147i | − | 1.40485i | −0.711758 | − | 0.702424i | \(-0.752101\pi\) | ||
0.711758 | − | 0.702424i | \(-0.247899\pi\) | |||||||
\(684\) | 6.67405 | − | 54.2810i | 0.255189 | − | 2.07549i | ||||
\(685\) | −5.82804 | −0.222678 | ||||||||
\(686\) | 41.6517i | 1.59027i | ||||||||
\(687\) | 1.04360i | 0.0398157i | ||||||||
\(688\) | − | 13.2368i | − | 0.504648i | ||||||
\(689\) | − | 9.24081i | − | 0.352047i | ||||||
\(690\) | 0.956078i | 0.0363973i | ||||||||
\(691\) | 13.6882 | 0.520724 | 0.260362 | − | 0.965511i | \(-0.416158\pi\) | ||||
0.260362 | + | 0.965511i | \(0.416158\pi\) | |||||||
\(692\) | −45.1014 | −1.71450 | ||||||||
\(693\) | −10.3516 | − | 7.52412i | −0.393224 | − | 0.285818i | ||||
\(694\) | − | 26.2953i | − | 0.998155i | ||||||
\(695\) | 1.94056i | 0.0736096i | ||||||||
\(696\) | 7.11603i | 0.269732i | ||||||||
\(697\) | 6.10012i | 0.231059i | ||||||||
\(698\) | 37.0422i | 1.40207i | ||||||||
\(699\) | 1.12092 | 0.0423972 | ||||||||
\(700\) | − | 5.95238i | − | 0.224979i | ||||||
\(701\) | 28.9116i | 1.09197i | 0.837793 | + | 0.545987i | \(0.183845\pi\) | ||||
−0.837793 | + | 0.545987i | \(0.816155\pi\) | |||||||
\(702\) | − | 13.3137i | − | 0.502494i | ||||||
\(703\) | 6.06961 | + | 0.746280i | 0.228920 | + | 0.0281465i | ||||
\(704\) | −3.63845 | + | 5.00573i | −0.137129 | + | 0.188660i | ||||
\(705\) | 4.73349i | 0.178273i | ||||||||
\(706\) | −26.6879 | −1.00441 | ||||||||
\(707\) | 6.88078 | 0.258778 | ||||||||
\(708\) | −2.13430 | −0.0802119 | ||||||||
\(709\) | 16.2679 | 0.610954 | 0.305477 | − | 0.952199i | \(-0.401184\pi\) | ||||
0.305477 | + | 0.952199i | \(0.401184\pi\) | |||||||
\(710\) | 36.3287i | 1.36339i | ||||||||
\(711\) | 27.2935 | 1.02359 | ||||||||
\(712\) | 74.8885i | 2.80657i | ||||||||
\(713\) | − | 7.94700i | − | 0.297617i | ||||||
\(714\) | − | 7.15320i | − | 0.267702i | ||||||
\(715\) | −4.55656 | + | 6.26885i | −0.170406 | + | 0.234442i | ||||
\(716\) | − | 72.8089i | − | 2.72100i | ||||||
\(717\) | −7.97143 | −0.297698 | ||||||||
\(718\) | 53.0481i | 1.97974i | ||||||||
\(719\) | −9.82583 | −0.366442 | −0.183221 | − | 0.983072i | \(-0.558652\pi\) | ||||
−0.183221 | + | 0.983072i | \(0.558652\pi\) | |||||||
\(720\) | −18.6981 | −0.696837 | ||||||||
\(721\) | −9.22128 | −0.343418 | ||||||||
\(722\) | 46.6331 | + | 11.6434i | 1.73550 | + | 0.433323i | ||||
\(723\) | − | 2.52076i | − | 0.0937480i | ||||||
\(724\) | 75.7568i | 2.81548i | ||||||||
\(725\) | −3.04589 | −0.113122 | ||||||||
\(726\) | −10.1874 | + | 3.30544i | −0.378090 | + | 0.122676i | ||||
\(727\) | −29.2149 | −1.08352 | −0.541760 | − | 0.840533i | \(-0.682242\pi\) | ||||
−0.541760 | + | 0.840533i | \(0.682242\pi\) | |||||||
\(728\) | 19.1901i | 0.711233i | ||||||||
\(729\) | 19.3265 | 0.715795 | ||||||||
\(730\) | 5.20718i | 0.192727i | ||||||||
\(731\) | 10.9627 | 0.405471 | ||||||||
\(732\) | −16.1844 | −0.598191 | ||||||||
\(733\) | − | 27.2427i | − | 1.00623i | −0.864219 | − | 0.503116i | \(-0.832187\pi\) | ||
0.864219 | − | 0.503116i | \(-0.167813\pi\) | |||||||
\(734\) | 45.8260 | 1.69147 | ||||||||
\(735\) | − | 1.98966i | − | 0.0733898i | ||||||
\(736\) | −4.36569 | −0.160922 | ||||||||
\(737\) | −35.6041 | − | 25.8791i | −1.31149 | − | 0.953269i | ||||
\(738\) | −8.10465 | −0.298336 | ||||||||
\(739\) | 12.3404i | 0.453950i | 0.973901 | + | 0.226975i | \(0.0728835\pi\) | ||||
−0.973901 | + | 0.226975i | \(0.927116\pi\) | |||||||
\(740\) | − | 6.17225i | − | 0.226896i | ||||||
\(741\) | 3.89091 | + | 0.478402i | 0.142936 | + | 0.0175745i | ||||
\(742\) | 13.5354 | 0.496901 | ||||||||
\(743\) | −16.2242 | −0.595207 | −0.297603 | − | 0.954690i | \(-0.596187\pi\) | ||||
−0.297603 | + | 0.954690i | \(0.596187\pi\) | |||||||
\(744\) | −18.9077 | −0.693190 | ||||||||
\(745\) | 9.35580i | 0.342770i | ||||||||
\(746\) | 56.2895 | 2.06090 | ||||||||
\(747\) | − | 29.0427i | − | 1.06262i | ||||||
\(748\) | 64.0907 | + | 46.5848i | 2.34339 | + | 1.70331i | ||||
\(749\) | − | 23.5733i | − | 0.861349i | ||||||
\(750\) | 0.973657i | 0.0355529i | ||||||||
\(751\) | − | 5.85396i | − | 0.213614i | −0.994280 | − | 0.106807i | \(-0.965937\pi\) | ||
0.994280 | − | 0.106807i | \(-0.0340627\pi\) | |||||||
\(752\) | −80.6336 | −2.94040 | ||||||||
\(753\) | − | 3.34603i | − | 0.121936i | ||||||
\(754\) | 18.0047 | 0.655693 | ||||||||
\(755\) | 9.35512 | 0.340468 | ||||||||
\(756\) | 13.4066 | 0.487593 | ||||||||
\(757\) | −40.7510 | −1.48112 | −0.740561 | − | 0.671989i | \(-0.765440\pi\) | ||||
−0.740561 | + | 0.671989i | \(0.765440\pi\) | |||||||
\(758\) | − | 53.1331i | − | 1.92988i | ||||||
\(759\) | 1.01393 | + | 0.736986i | 0.0368035 | + | 0.0267509i | ||||
\(760\) | 3.22886 | − | 26.2608i | 0.117123 | − | 0.952579i | ||||
\(761\) | − | 12.3774i | − | 0.448681i | −0.974511 | − | 0.224340i | \(-0.927977\pi\) | ||
0.974511 | − | 0.224340i | \(-0.0720227\pi\) | |||||||
\(762\) | − | 10.8996i | − | 0.394849i | ||||||
\(763\) | − | 22.8889i | − | 0.828635i | ||||||
\(764\) | 47.2407 | 1.70911 | ||||||||
\(765\) | − | 15.4858i | − | 0.559890i | ||||||
\(766\) | 44.5691i | 1.61035i | ||||||||
\(767\) | 2.94523i | 0.106346i | ||||||||
\(768\) | − | 11.8172i | − | 0.426415i | ||||||
\(769\) | 27.3673i | 0.986889i | 0.869777 | + | 0.493444i | \(0.164262\pi\) | ||||
−0.869777 | + | 0.493444i | \(0.835738\pi\) | |||||||
\(770\) | −9.18228 | − | 6.67421i | −0.330906 | − | 0.240522i | ||||
\(771\) | 6.78761 | 0.244450 | ||||||||
\(772\) | −51.6181 | −1.85778 | ||||||||
\(773\) | 44.5435i | 1.60212i | 0.598586 | + | 0.801059i | \(0.295729\pi\) | ||||
−0.598586 | + | 0.801059i | \(0.704271\pi\) | |||||||
\(774\) | 14.5651i | 0.523533i | ||||||||
\(775\) | − | 8.09312i | − | 0.290714i | ||||||
\(776\) | 13.5770i | 0.487385i | ||||||||
\(777\) | 0.730576i | 0.0262093i | ||||||||
\(778\) | 32.1593 | 1.15297 | ||||||||
\(779\) | 0.597576 | − | 4.86018i | 0.0214104 | − | 0.174134i | ||||
\(780\) | − | 3.95671i | − | 0.141673i | ||||||
\(781\) | 38.5271 | + | 28.0037i | 1.37861 | + | 1.00205i | ||||
\(782\) | − | 13.4885i | − | 0.482348i | ||||||
\(783\) | − | 6.86029i | − | 0.245167i | ||||||
\(784\) | 33.8933 | 1.21048 | ||||||||
\(785\) | −6.63790 | −0.236917 | ||||||||
\(786\) | −11.4502 | −0.408416 | ||||||||
\(787\) | −14.5204 | −0.517596 | −0.258798 | − | 0.965932i | \(-0.583326\pi\) | ||||
−0.258798 | + | 0.965932i | \(0.583326\pi\) | |||||||
\(788\) | − | 48.2082i | − | 1.71734i | ||||||
\(789\) | −9.61256 | −0.342216 | ||||||||
\(790\) | 24.2104 | 0.861369 | ||||||||
\(791\) | −13.0583 | −0.464299 | ||||||||
\(792\) | −33.7564 | + | 46.4415i | −1.19948 | + | 1.65023i | ||||
\(793\) | 22.3337i | 0.793091i | ||||||||
\(794\) | 8.01289 | 0.284367 | ||||||||
\(795\) | −1.52210 | −0.0539835 | ||||||||
\(796\) | 70.3101 | 2.49207 | ||||||||
\(797\) | 4.45183i | 0.157692i | 0.996887 | + | 0.0788459i | \(0.0251235\pi\) | ||||
−0.996887 | + | 0.0788459i | \(0.974876\pi\) | |||||||
\(798\) | −0.700737 | + | 5.69920i | −0.0248058 | + | 0.201750i | ||||
\(799\) | − | 66.7809i | − | 2.36254i | ||||||
\(800\) | −4.44597 | −0.157189 | ||||||||
\(801\) | − | 35.1848i | − | 1.24319i | ||||||
\(802\) | − | 27.1706i | − | 0.959428i | ||||||
\(803\) | 5.52229 | + | 4.01392i | 0.194878 | + | 0.141648i | ||||
\(804\) | 22.4722 | 0.792534 | ||||||||
\(805\) | 1.32855i | 0.0468251i | ||||||||
\(806\) | 47.8396i | 1.68508i | ||||||||
\(807\) | −5.55572 | −0.195571 | ||||||||
\(808\) | − | 30.8701i | − | 1.08600i | ||||||
\(809\) | − | 44.2999i | − | 1.55750i | −0.627334 | − | 0.778750i | \(-0.715854\pi\) | ||
0.627334 | − | 0.778750i | \(-0.284146\pi\) | |||||||
\(810\) | 19.4502 | 0.683412 | ||||||||
\(811\) | 23.0013 | 0.807683 | 0.403842 | − | 0.914829i | \(-0.367675\pi\) | ||||
0.403842 | + | 0.914829i | \(0.367675\pi\) | |||||||
\(812\) | 18.1303i | 0.636249i | ||||||||
\(813\) | 1.46965 | 0.0515430 | ||||||||
\(814\) | −9.52146 | − | 6.92074i | −0.333727 | − | 0.242572i | ||||
\(815\) | −14.1577 | −0.495922 | ||||||||
\(816\) | −13.7027 | −0.479692 | ||||||||
\(817\) | −8.73439 | − | 1.07392i | −0.305578 | − | 0.0375718i | ||||
\(818\) | 41.8390 | 1.46287 | ||||||||
\(819\) | − | 9.01606i | − | 0.315047i | ||||||
\(820\) | −4.94236 | −0.172595 | ||||||||
\(821\) | 27.6565i | 0.965218i | 0.875836 | + | 0.482609i | \(0.160311\pi\) | ||||
−0.875836 | + | 0.482609i | \(0.839689\pi\) | |||||||
\(822\) | − | 5.67451i | − | 0.197921i | ||||||
\(823\) | 11.9083 | 0.415098 | 0.207549 | − | 0.978225i | \(-0.433451\pi\) | ||||
0.207549 | + | 0.978225i | \(0.433451\pi\) | |||||||
\(824\) | 41.3705i | 1.44121i | ||||||||
\(825\) | 1.03258 | + | 0.750537i | 0.0359497 | + | 0.0261303i | ||||
\(826\) | −4.31402 | −0.150104 | ||||||||
\(827\) | 11.4708 | 0.398879 | 0.199440 | − | 0.979910i | \(-0.436088\pi\) | ||||
0.199440 | + | 0.979910i | \(0.436088\pi\) | |||||||
\(828\) | 12.3202 | 0.428156 | ||||||||
\(829\) | 39.9028i | 1.38588i | 0.720995 | + | 0.692941i | \(0.243685\pi\) | ||||
−0.720995 | + | 0.692941i | \(0.756315\pi\) | |||||||
\(830\) | − | 25.7621i | − | 0.894216i | ||||||
\(831\) | 3.28572 | 0.113980 | ||||||||
\(832\) | −4.35991 | −0.151153 | ||||||||
\(833\) | 28.0705i | 0.972586i | ||||||||
\(834\) | −1.88944 | −0.0654259 | ||||||||
\(835\) | −2.40922 | −0.0833745 | ||||||||
\(836\) | −46.4998 | − | 43.3941i | −1.60823 | − | 1.50082i | ||||
\(837\) | 18.2282 | 0.630059 | ||||||||
\(838\) | −19.5223 | −0.674388 | ||||||||
\(839\) | − | 31.4430i | − | 1.08553i | −0.839884 | − | 0.542766i | \(-0.817377\pi\) | ||
0.839884 | − | 0.542766i | \(-0.182623\pi\) | |||||||
\(840\) | 3.16091 | 0.109062 | ||||||||
\(841\) | −19.7225 | −0.680087 | ||||||||
\(842\) | 64.7471i | 2.23133i | ||||||||
\(843\) | 4.44609i | 0.153131i | ||||||||
\(844\) | −109.125 | −3.75623 | ||||||||
\(845\) | 7.53993 | 0.259381 | ||||||||
\(846\) | 88.7254 | 3.05044 | ||||||||
\(847\) | −14.1562 | + | 4.59317i | −0.486412 | + | 0.157823i | ||||
\(848\) | − | 25.9286i | − | 0.890393i | ||||||
\(849\) | 8.92440 | 0.306285 | ||||||||
\(850\) | − | 13.7365i | − | 0.471159i | ||||||
\(851\) | 1.37762i | 0.0472242i | ||||||||
\(852\) | −24.3171 | −0.833090 | ||||||||
\(853\) | − | 29.2514i | − | 1.00155i | −0.865578 | − | 0.500775i | \(-0.833049\pi\) | ||
0.865578 | − | 0.500775i | \(-0.166951\pi\) | |||||||
\(854\) | −32.7131 | −1.11942 | ||||||||
\(855\) | −1.51701 | + | 12.3381i | −0.0518806 | + | 0.421953i | ||||
\(856\) | −105.760 | −3.61479 | ||||||||
\(857\) | −3.26967 | −0.111690 | −0.0558449 | − | 0.998439i | \(-0.517785\pi\) | ||||
−0.0558449 | + | 0.998439i | \(0.517785\pi\) | |||||||
\(858\) | −6.10371 | − | 4.43653i | −0.208377 | − | 0.151461i | ||||
\(859\) | 44.4634 | 1.51707 | 0.758536 | − | 0.651631i | \(-0.225915\pi\) | ||||
0.758536 | + | 0.651631i | \(0.225915\pi\) | |||||||
\(860\) | 8.88209i | 0.302877i | ||||||||
\(861\) | 0.585001 | 0.0199368 | ||||||||
\(862\) | 84.4880 | 2.87767 | ||||||||
\(863\) | 24.8514i | 0.845951i | 0.906141 | + | 0.422975i | \(0.139014\pi\) | ||||
−0.906141 | + | 0.422975i | \(0.860986\pi\) | |||||||
\(864\) | − | 10.0137i | − | 0.340672i | ||||||
\(865\) | 10.2515 | 0.348563 | ||||||||
\(866\) | − | 61.2971i | − | 2.08296i | ||||||
\(867\) | − | 4.80555i | − | 0.163205i | ||||||
\(868\) | −48.1733 | −1.63511 | ||||||||
\(869\) | 18.6625 | − | 25.6755i | 0.633081 | − | 0.870983i | ||||
\(870\) | − | 2.96566i | − | 0.100545i | ||||||
\(871\) | − | 31.0106i | − | 1.05075i | ||||||
\(872\) | −102.689 | −3.47750 | ||||||||
\(873\) | − | 6.37885i | − | 0.215891i | ||||||
\(874\) | −1.32135 | + | 10.7468i | −0.0446954 | + | 0.363515i | ||||
\(875\) | 1.35297i | 0.0457388i | ||||||||
\(876\) | −3.48550 | −0.117764 | ||||||||
\(877\) | 1.81191 | 0.0611839 | 0.0305919 | − | 0.999532i | \(-0.490261\pi\) | ||||
0.0305919 | + | 0.999532i | \(0.490261\pi\) | |||||||
\(878\) | −76.5092 | −2.58206 | ||||||||
\(879\) | 9.44437i | 0.318551i | ||||||||
\(880\) | −12.7852 | + | 17.5897i | −0.430989 | + | 0.592948i | ||||
\(881\) | −45.3998 | −1.52956 | −0.764779 | − | 0.644293i | \(-0.777152\pi\) | ||||
−0.764779 | + | 0.644293i | \(0.777152\pi\) | |||||||
\(882\) | −37.2946 | −1.25578 | ||||||||
\(883\) | 31.4299 | 1.05770 | 0.528851 | − | 0.848715i | \(-0.322623\pi\) | ||||
0.528851 | + | 0.848715i | \(0.322623\pi\) | |||||||
\(884\) | 55.8220i | 1.87750i | ||||||||
\(885\) | 0.485126 | 0.0163073 | ||||||||
\(886\) | 6.97889 | 0.234460 | ||||||||
\(887\) | 12.8799 | 0.432464 | 0.216232 | − | 0.976342i | \(-0.430623\pi\) | ||||
0.216232 | + | 0.976342i | \(0.430623\pi\) | |||||||
\(888\) | 3.27767 | 0.109991 | ||||||||
\(889\) | − | 15.1458i | − | 0.507974i | ||||||
\(890\) | − | 31.2103i | − | 1.04617i | ||||||
\(891\) | 14.9931 | − | 20.6273i | 0.502287 | − | 0.691040i | ||||
\(892\) | 116.843i | 3.91219i | ||||||||
\(893\) | −6.54195 | + | 53.2067i | −0.218918 | + | 1.78049i | ||||
\(894\) | −9.10934 | −0.304662 | ||||||||
\(895\) | 16.5494i | 0.553187i | ||||||||
\(896\) | − | 18.4167i | − | 0.615259i | ||||||
\(897\) | 0.883121i | 0.0294865i | ||||||||
\(898\) | − | 82.8839i | − | 2.76587i | ||||||
\(899\) | 24.6508i | 0.822150i | ||||||||
\(900\) | 12.5467 | 0.418223 | ||||||||
\(901\) | 21.4741 | 0.715407 | ||||||||
\(902\) | −5.54171 | + | 7.62421i | −0.184519 | + | 0.253858i | ||||
\(903\) | − | 1.05132i | − | 0.0349859i | ||||||
\(904\) | 58.5849i | 1.94850i | ||||||||
\(905\) | − | 17.2195i | − | 0.572395i | ||||||
\(906\) | 9.10868i | 0.302616i | ||||||||
\(907\) | 45.1329i | 1.49861i | 0.662222 | + | 0.749307i | \(0.269613\pi\) | ||||
−0.662222 | + | 0.749307i | \(0.730387\pi\) | |||||||
\(908\) | −14.6050 | −0.484683 | ||||||||
\(909\) | 14.5036i | 0.481055i | ||||||||
\(910\) | − | 7.99762i | − | 0.265118i | ||||||
\(911\) | − | 45.2270i | − | 1.49844i | −0.662323 | − | 0.749219i | \(-0.730429\pi\) | ||
0.662323 | − | 0.749219i | \(-0.269571\pi\) | |||||||
\(912\) | 10.9174 | + | 1.34234i | 0.361513 | + | 0.0444493i | ||||
\(913\) | −27.3211 | − | 19.8585i | −0.904196 | − | 0.657222i | ||||
\(914\) | − | 33.5392i | − | 1.10938i | ||||||
\(915\) | 3.67870 | 0.121614 | ||||||||
\(916\) | 11.9289 | 0.394142 | ||||||||
\(917\) | −15.9110 | −0.525427 | ||||||||
\(918\) | 30.9389 | 1.02114 | ||||||||
\(919\) | 50.4139i | 1.66300i | 0.555525 | + | 0.831500i | \(0.312517\pi\) | ||||
−0.555525 | + | 0.831500i | \(0.687483\pi\) | |||||||
\(920\) | 5.96041 | 0.196509 | ||||||||
\(921\) | − | 8.36746i | − | 0.275717i | ||||||
\(922\) | − | 60.3884i | − | 1.98879i | ||||||
\(923\) | 33.5565i | 1.10452i | ||||||||
\(924\) | 4.46748 | − | 6.14629i | 0.146969 | − | 0.202198i | ||||
\(925\) | 1.40295i | 0.0461287i | ||||||||
\(926\) | −17.9200 | −0.588889 | ||||||||
\(927\) | − | 19.4371i | − | 0.638397i | ||||||
\(928\) | 13.5419 | 0.444536 | ||||||||
\(929\) | −18.1263 | −0.594704 | −0.297352 | − | 0.954768i | \(-0.596103\pi\) | ||||
−0.297352 | + | 0.954768i | \(0.596103\pi\) | |||||||
\(930\) | 7.87993 | 0.258393 | ||||||||
\(931\) | 2.74982 | − | 22.3648i | 0.0901219 | − | 0.732975i | ||||
\(932\) | − | 12.8128i | − | 0.419697i | ||||||
\(933\) | − | 0.675087i | − | 0.0221014i | ||||||
\(934\) | −1.35497 | −0.0443361 | ||||||||
\(935\) | −14.5678 | − | 10.5887i | −0.476418 | − | 0.346288i | ||||
\(936\) | −40.4498 | −1.32214 | ||||||||
\(937\) | 39.2538i | 1.28237i | 0.767388 | + | 0.641183i | \(0.221556\pi\) | ||||
−0.767388 | + | 0.641183i | \(0.778444\pi\) | |||||||
\(938\) | 45.4226 | 1.48310 | ||||||||
\(939\) | 3.72971i | 0.121715i | ||||||||
\(940\) | 54.1064 | 1.76476 | ||||||||
\(941\) | −19.7778 | −0.644739 | −0.322370 | − | 0.946614i | \(-0.604479\pi\) | ||||
−0.322370 | + | 0.946614i | \(0.604479\pi\) | |||||||
\(942\) | − | 6.46304i | − | 0.210577i | ||||||
\(943\) | 1.10311 | 0.0359224 | ||||||||
\(944\) | 8.26398i | 0.268970i | ||||||||
\(945\) | −3.04731 | −0.0991291 | ||||||||
\(946\) | 13.7017 | + | 9.95920i | 0.445481 | + | 0.323801i | ||||
\(947\) | 14.7874 | 0.480527 | 0.240263 | − | 0.970708i | \(-0.422766\pi\) | ||||
0.240263 | + | 0.970708i | \(0.422766\pi\) | |||||||
\(948\) | 16.2056i | 0.526334i | ||||||||
\(949\) | 4.80983i | 0.156134i | ||||||||
\(950\) | −1.34565 | + | 10.9444i | −0.0436586 | + | 0.355082i | ||||
\(951\) | 0.478349 | 0.0155115 | ||||||||
\(952\) | −44.5947 | −1.44532 | ||||||||
\(953\) | 24.2111 | 0.784274 | 0.392137 | − | 0.919907i | \(-0.371736\pi\) | ||||
0.392137 | + | 0.919907i | \(0.371736\pi\) | |||||||
\(954\) | 28.5306i | 0.923713i | ||||||||
\(955\) | −10.7378 | −0.347467 | ||||||||
\(956\) | 91.1178i | 2.94696i | ||||||||
\(957\) | −3.14512 | − | 2.28606i | −0.101667 | − | 0.0738977i | ||||
\(958\) | 49.0903i | 1.58604i | ||||||||
\(959\) | − | 7.88518i | − | 0.254626i | ||||||
\(960\) | 0.718145i | 0.0231780i | ||||||||
\(961\) | −34.4986 | −1.11286 | ||||||||
\(962\) | − | 8.29304i | − | 0.267378i | ||||||
\(963\) | 49.6889 | 1.60120 | ||||||||
\(964\) | −28.8137 | −0.928026 | ||||||||
\(965\) | 11.7328 | 0.377691 | ||||||||
\(966\) | −1.29355 | −0.0416192 | ||||||||
\(967\) | 0.150839i | 0.00485064i | 0.999997 | + | 0.00242532i | \(0.000772005\pi\) | ||||
−0.999997 | + | 0.00242532i | \(0.999228\pi\) | |||||||
\(968\) | 20.6069 | + | 63.5106i | 0.662330 | + | 2.04131i | ||||
\(969\) | −1.11173 | + | 9.04185i | −0.0357138 | + | 0.290466i | ||||
\(970\) | − | 5.65830i | − | 0.181677i | ||||||
\(971\) | − | 1.13243i | − | 0.0363415i | −0.999835 | − | 0.0181708i | \(-0.994216\pi\) | ||
0.999835 | − | 0.0181708i | \(-0.00578425\pi\) | |||||||
\(972\) | 42.7462i | 1.37109i | ||||||||
\(973\) | −2.62552 | −0.0841704 | ||||||||
\(974\) | − | 19.1225i | − | 0.612726i | ||||||
\(975\) | 0.899359i | 0.0288025i | ||||||||
\(976\) | 62.6656i | 2.00588i | ||||||||
\(977\) | − | 14.0511i | − | 0.449534i | −0.974413 | − | 0.224767i | \(-0.927838\pi\) | ||
0.974413 | − | 0.224767i | \(-0.0721621\pi\) | |||||||
\(978\) | − | 13.7847i | − | 0.440787i | ||||||
\(979\) | −33.0990 | − | 24.0583i | −1.05785 | − | 0.768906i | ||||
\(980\) | −22.7429 | −0.726497 | ||||||||
\(981\) | 48.2464 | 1.54039 | ||||||||
\(982\) | 78.3035i | 2.49877i | ||||||||
\(983\) | 29.6116i | 0.944464i | 0.881474 | + | 0.472232i | \(0.156551\pi\) | ||||
−0.881474 | + | 0.472232i | \(0.843449\pi\) | |||||||
\(984\) | − | 2.62456i | − | 0.0836679i | ||||||
\(985\) | 10.9577i | 0.349141i | ||||||||
\(986\) | 41.8400i | 1.33246i | ||||||||
\(987\) | −6.40428 | −0.203850 | ||||||||
\(988\) | 5.46840 | − | 44.4753i | 0.173973 | − | 1.41495i | ||||
\(989\) | − | 1.98244i | − | 0.0630381i | ||||||
\(990\) | 14.0682 | − | 19.3548i | 0.447117 | − | 0.615137i | ||||
\(991\) | 1.64752i | 0.0523351i | 0.999658 | + | 0.0261675i | \(0.00833034\pi\) | ||||
−0.999658 | + | 0.0261675i | \(0.991670\pi\) | |||||||
\(992\) | 35.9817i | 1.14242i | ||||||||
\(993\) | −12.7350 | −0.404134 | ||||||||
\(994\) | −49.1517 | −1.55900 | ||||||||
\(995\) | −15.9815 | −0.506646 | ||||||||
\(996\) | 17.2442 | 0.546405 | ||||||||
\(997\) | 23.4405i | 0.742369i | 0.928559 | + | 0.371185i | \(0.121048\pi\) | ||||
−0.928559 | + | 0.371185i | \(0.878952\pi\) | |||||||
\(998\) | −103.691 | −3.28227 | ||||||||
\(999\) | −3.15988 | −0.0999741 |
(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 | 1045.2.f.a.626.4 | yes | 40 | |
11.10 | odd | 2 | inner | 1045.2.f.a.626.38 | yes | 40 | |
19.18 | odd | 2 | inner | 1045.2.f.a.626.37 | yes | 40 | |
209.208 | even | 2 | inner | 1045.2.f.a.626.3 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.f.a.626.3 | ✓ | 40 | 209.208 | even | 2 | inner | |
1045.2.f.a.626.4 | yes | 40 | 1.1 | even | 1 | trivial | |
1045.2.f.a.626.37 | yes | 40 | 19.18 | odd | 2 | inner | |
1045.2.f.a.626.38 | yes | 40 | 11.10 | odd | 2 | inner |