Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,15,Mod(5,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.5");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.c (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: | \(14.9194761782\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 440x^{2} + 48015 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{9}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(14.1555i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.5 |
Dual form | 12.15.c.b.5.2 |
$q$-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 \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −640.285 | − | 2091.17i | −0.292769 | − | 0.956183i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 68988.7i | 0.883056i | 0.897248 | + | 0.441528i | \(0.145563\pi\) | ||||
−0.897248 | + | 0.441528i | \(0.854437\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.38092e6 | 1.67681 | 0.838404 | − | 0.545050i | \(-0.183489\pi\) | ||||
0.838404 | + | 0.545050i | \(0.183489\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.96304e6 | + | 2.67789e6i | −0.828573 | + | 0.559881i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.70839e7i | − | 1.38983i | −0.719092 | − | 0.694915i | \(-0.755442\pi\) | ||
0.719092 | − | 0.694915i | \(-0.244558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.34588e7 | −0.214488 | −0.107244 | − | 0.994233i | \(-0.534203\pi\) | ||||
−0.107244 | + | 0.994233i | \(0.534203\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.44267e8 | − | 4.41724e7i | 0.844363 | − | 0.258531i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.06850e8i | − | 1.47890i | −0.673211 | − | 0.739451i | \(-0.735085\pi\) | ||
0.673211 | − | 0.739451i | \(-0.264915\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.78604e8 | 0.871046 | 0.435523 | − | 0.900178i | \(-0.356563\pi\) | ||||
0.435523 | + | 0.900178i | \(0.356563\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.84184e8 | − | 2.88775e9i | −0.490917 | − | 1.60334i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.87154e9i | − | 1.13707i | −0.822658 | − | 0.568537i | \(-0.807510\pi\) | ||
0.822658 | − | 0.568537i | \(-0.192490\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.34407e9 | 0.220213 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.13741e9 | + | 6.57279e9i | 0.777929 | + | 0.628352i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.89957e9i | 0.168092i | 0.996462 | + | 0.0840460i | \(0.0267843\pi\) | ||||
−0.996462 | + | 0.0840460i | \(0.973216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.07349e10 | −0.390181 | −0.195091 | − | 0.980785i | \(-0.562500\pi\) | ||||
−0.195091 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.66370e10 | + | 1.73414e10i | −1.32893 | + | 0.406899i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.52681e10i | 1.48071i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.73171e10 | 0.709110 | 0.354555 | − | 0.935035i | \(-0.384632\pi\) | ||||
0.354555 | + | 0.935035i | \(0.384632\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.61748e9 | + | 2.81447e10i | 0.0627954 | + | 0.205090i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.05568e10i | 0.362286i | 0.983457 | + | 0.181143i | \(0.0579797\pi\) | ||||
−0.983457 | + | 0.181143i | \(0.942020\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.53053e10 | −0.0930962 | −0.0465481 | − | 0.998916i | \(-0.514822\pi\) | ||||
−0.0465481 | + | 0.998916i | \(0.514822\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.84744e11 | − | 2.73405e11i | −0.494406 | − | 0.731676i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.91845e11i | − | 1.95776i | −0.204443 | − | 0.978878i | \(-0.565538\pi\) | ||
0.204443 | − | 0.978878i | \(-0.434462\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.22872e12 | 1.81168 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.26903e12 | + | 3.88557e11i | −1.41410 | + | 0.432976i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.88078e11i | − | 0.330360i | −0.986263 | − | 0.165180i | \(-0.947179\pi\) | ||
0.986263 | − | 0.165180i | \(-0.0528205\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.86848e12 | 1.22730 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.98528e11 | − | 1.62819e12i | −0.255015 | − | 0.832880i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.01476e12i | 1.61323i | 0.591079 | + | 0.806614i | \(0.298702\pi\) | ||||
−0.591079 | + | 0.806614i | \(0.701298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.48567e12 | −0.472730 | −0.236365 | − | 0.971664i | \(-0.575956\pi\) | ||||
−0.236365 | + | 0.971664i | \(0.575956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.47265e12 | + | 3.69796e12i | −1.38936 | + | 0.938812i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 9.28506e11i | − | 0.189405i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.96434e12 | 1.47909 | 0.739545 | − | 0.673107i | \(-0.235041\pi\) | ||||
0.739545 | + | 0.673107i | \(0.235041\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.09606e12 | + | 2.47889e12i | −1.08725 | + | 0.332900i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00451e13i | 1.10445i | 0.833694 | + | 0.552227i | \(0.186222\pi\) | ||||
−0.833694 | + | 0.552227i | \(0.813778\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.44494e13 | 1.30795 | 0.653974 | − | 0.756517i | \(-0.273101\pi\) | ||||
0.653974 | + | 0.756517i | \(0.273101\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.60589e11 | − | 2.81069e12i | −0.0644714 | − | 0.210564i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.74007e13i | − | 2.33048i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.81968e13 | −1.46829 | −0.734143 | − | 0.678995i | \(-0.762416\pi\) | ||||
−0.734143 | + | 0.678995i | \(0.762416\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.53457e12 | − | 2.12252e13i | 0.373067 | − | 0.927805i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.17334e13i | 0.432392i | 0.976350 | + | 0.216196i | \(0.0693649\pi\) | ||||
−0.976350 | + | 0.216196i | \(0.930635\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.18658e13 | 1.30595 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.06350e12 | − | 1.85655e12i | 0.160727 | − | 0.0492121i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.95724e12i | 0.0442500i | 0.999755 | + | 0.0221250i | \(0.00704318\pi\) | ||||
−0.999755 | + | 0.0221250i | \(0.992957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.85856e13 | −0.359655 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.87340e12 | + | 2.24485e13i | 0.114233 | + | 0.373085i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.37149e13i | 0.769182i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.49470e14 | −1.84992 | −0.924961 | − | 0.380062i | \(-0.875902\pi\) | ||||
−0.924961 | + | 0.380062i | \(0.875902\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.25277e13 | + | 1.07334e14i | 0.778139 | + | 1.15158i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.42108e13i | − | 0.319090i | −0.987191 | − | 0.159545i | \(-0.948997\pi\) | ||
0.987191 | − | 0.159545i | \(-0.0510027\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.10454e14 | −0.898089 | −0.449044 | − | 0.893509i | \(-0.648235\pi\) | ||||
−0.449044 | + | 0.893509i | \(0.648235\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.99222e14 | − | 6.09987e13i | 1.41583 | − | 0.433507i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.01954e14i | 1.25767i | 0.777540 | + | 0.628834i | \(0.216467\pi\) | ||||
−0.777540 | + | 0.628834i | \(0.783533\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.52716e13 | −0.357058 | −0.178529 | − | 0.983935i | \(-0.557134\pi\) | ||||
−0.178529 | + | 0.983935i | \(0.557134\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.31022e13 | − | 1.40772e14i | −0.207605 | − | 0.678039i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.53710e13i | − | 0.405385i | −0.979242 | − | 0.202692i | \(-0.935031\pi\) | ||
0.979242 | − | 0.202692i | \(-0.0649691\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.67093e14 | 1.00410 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.33378e13 | − | 3.60413e13i | 0.177719 | − | 0.120088i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 8.38014e14i | − | 2.47983i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.53786e14 | −0.931628 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.47546e14 | − | 4.51765e13i | 0.346412 | − | 0.106066i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.13800e14i | 1.07752i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.75936e14 | −0.330163 | −0.165082 | − | 0.986280i | \(-0.552789\pi\) | ||||
−0.165082 | + | 0.986280i | \(0.552789\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.62026e13 | + | 5.29177e13i | 0.0272557 | + | 0.0890171i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.46193e14i | − | 0.220814i | −0.993886 | − | 0.110407i | \(-0.964785\pi\) | ||
0.993886 | − | 0.110407i | \(-0.0352155\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.07519e15 | 1.46058 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.53448e14 | + | 5.61390e14i | −0.554870 | + | 0.686955i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.26878e15i | 1.40069i | 0.713805 | + | 0.700344i | \(0.246970\pi\) | ||||
−0.713805 | + | 0.700344i | \(0.753030\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.80462e14 | 0.279750 | 0.139875 | − | 0.990169i | \(-0.455330\pi\) | ||||
0.139875 | + | 0.990169i | \(0.455330\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.07412e15 | + | 6.35063e14i | −1.87197 | + | 0.573170i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.64517e14i | 0.298102i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00037e14 | −0.148435 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.86734e14 | − | 2.56948e15i | −0.530404 | − | 1.73230i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.24281e14i | 0.137559i | 0.997632 | + | 0.0687795i | \(0.0219105\pi\) | ||||
−0.997632 | + | 0.0687795i | \(0.978089\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.08375e15 | 1.16414 | 0.582072 | − | 0.813137i | \(-0.302242\pi\) | ||||
0.582072 | + | 0.813137i | \(0.302242\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.62508e15 | + | 2.40497e15i | 0.828009 | + | 1.22538i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 7.40587e14i | − | 0.344552i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.86555e13 | −0.0419589 | −0.0209794 | − | 0.999780i | \(-0.506678\pi\) | ||||
−0.0209794 | + | 0.999780i | \(0.506678\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.11537e14 | + | 2.48480e14i | −0.315885 | + | 0.0967191i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.34630e15i | − | 1.90665i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.36626e15 | 1.10112 | 0.550559 | − | 0.834796i | \(-0.314415\pi\) | ||||
0.550559 | + | 0.834796i | \(0.314415\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.19636e15 | − | 3.90732e15i | −0.359314 | − | 1.17352i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.34309e15i | − | 0.370758i | −0.982667 | − | 0.185379i | \(-0.940649\pi\) | ||
0.982667 | − | 0.185379i | \(-0.0593513\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.75624e15 | −0.953995 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.08564e15 | + | 2.08502e15i | −0.721725 | + | 0.487682i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.49540e15i | 0.969272i | 0.874716 | + | 0.484636i | \(0.161048\pi\) | ||||
−0.874716 | + | 0.484636i | \(0.838952\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.85606e15 | 0.369254 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.39556e15 | − | 2.57059e15i | 1.54254 | − | 0.472302i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.21605e15i | 0.885872i | 0.896553 | + | 0.442936i | \(0.146063\pi\) | ||||
−0.896553 | + | 0.442936i | \(0.853937\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.34290e15 | −0.682385 | −0.341193 | − | 0.939993i | \(-0.610831\pi\) | ||||
−0.341193 | + | 0.939993i | \(0.610831\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.51251e14 | + | 3.10679e15i | 0.138400 | + | 0.452016i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.64412e15i | 0.626184i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.64359e16 | −2.05542 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.12371e16 | + | 9.07651e15i | 1.30444 | + | 1.05363i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.52605e15i | 0.380237i | 0.981761 | + | 0.190119i | \(0.0608873\pi\) | ||||
−0.981761 | + | 0.190119i | \(0.939113\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.54539e14 | −0.0255184 | −0.0127592 | − | 0.999919i | \(-0.504061\pi\) | ||||
−0.0127592 | + | 0.999919i | \(0.504061\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.94167e15 | + | 5.94509e14i | −0.181106 | + | 0.0554518i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.33824e16i | − | 1.16217i | −0.813843 | − | 0.581085i | \(-0.802628\pi\) | ||
0.813843 | − | 0.581085i | \(-0.197372\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.45124e15 | 0.198342 | 0.0991711 | − | 0.995070i | \(-0.468381\pi\) | ||||
0.0991711 | + | 0.995070i | \(0.468381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.73973e15 | − | 1.87460e16i | −0.433031 | − | 1.41428i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.00408e15i | 0.281858i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.86762e15 | −0.319919 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.03676e16 | + | 1.53431e16i | 0.636626 | + | 0.942149i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.10876e16i | − | 1.21061i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.26632e16 | 0.680088 | 0.340044 | − | 0.940410i | \(-0.389558\pi\) | ||||
0.340044 | + | 0.940410i | \(0.389558\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.10061e16 | − | 6.43176e15i | 1.05606 | − | 0.323350i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.74578e15i | − | 0.0822091i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.48241e16 | −0.654258 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.25174e15 | − | 3.02162e16i | −0.382926 | − | 1.25064i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.16749e15i | 0.317207i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.59561e16 | 0.946466 | 0.473233 | − | 0.880937i | \(-0.343087\pi\) | ||||
0.473233 | + | 0.880937i | \(0.343087\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.32661e15 | + | 3.59928e15i | −0.182462 | + | 0.123293i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.07499e16i | 0.346117i | 0.984912 | + | 0.173058i | \(0.0553649\pi\) | ||||
−0.984912 | + | 0.173058i | \(0.944635\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.84804e16 | −1.16517 | −0.582587 | − | 0.812768i | \(-0.697960\pi\) | ||||
−0.582587 | + | 0.812768i | \(0.697960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.82114e16 | + | 2.39471e16i | −2.22836 | + | 0.682291i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.43134e16i | 0.383930i | 0.981402 | + | 0.191965i | \(0.0614860\pi\) | ||||
−0.981402 | + | 0.191965i | \(0.938514\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.84261e16 | 1.72881 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.80540e16 | + | 5.89644e16i | 0.429868 | + | 1.40395i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.96828e16i | − | 0.441877i | −0.975288 | − | 0.220938i | \(-0.929088\pi\) | ||
0.975288 | − | 0.220938i | \(-0.0709119\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.49775e16 | 1.37608 | 0.688040 | − | 0.725672i | \(-0.258471\pi\) | ||||
0.688040 | + | 0.725672i | \(0.258471\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.98501e16 | − | 4.25708e15i | −0.996373 | − | 0.0850880i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.47682e16i | 1.59982i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.04791e16 | −0.186829 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.45366e16 | − | 7.51272e15i | 0.413446 | − | 0.126591i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.01654e16i | 0.161961i | 0.996716 | + | 0.0809805i | \(0.0258052\pi\) | ||||
−0.996716 | + | 0.0809805i | \(0.974195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.04856e17 | −1.58034 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.68061e16 | − | 8.75487e16i | −0.382342 | − | 1.24873i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7.68554e16i | − | 1.03787i | −0.854814 | − | 0.518935i | \(-0.826329\pi\) | ||
0.854814 | − | 0.518935i | \(-0.173671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.29598e16 | 1.18904 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.76473e15 | − | 1.14911e16i | −0.0941115 | − | 0.139277i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.41566e17i | − | 1.62656i | −0.581875 | − | 0.813278i | \(-0.697681\pi\) | ||
0.581875 | − | 0.813278i | \(-0.302319\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.67730e16 | 0.291726 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.09292e15 | − | 1.25319e15i | 0.0423111 | − | 0.0129550i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.75053e16i | 0.956670i | 0.878178 | + | 0.478335i | \(0.158759\pi\) | ||||
−0.878178 | + | 0.478335i | \(0.841241\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.31104e17 | 1.22133 | 0.610664 | − | 0.791890i | \(-0.290903\pi\) | ||||
0.610664 | + | 0.791890i | \(0.290903\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.19001e16 | + | 3.88657e16i | 0.105296 | + | 0.343896i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3.64026e16i | − | 0.306058i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.65715e16 | −0.691858 | −0.345929 | − | 0.938261i | \(-0.612436\pi\) | ||||
−0.345929 | + | 0.938261i | \(0.612436\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.25428e16 | − | 2.87469e16i | 0.323293 | − | 0.218455i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.28286e17i | − | 0.927335i | −0.886009 | − | 0.463667i | \(-0.846533\pi\) | ||
0.886009 | − | 0.463667i | \(-0.153467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.43803e17 | −0.989155 | −0.494577 | − | 0.869134i | \(-0.664677\pi\) | ||||
−0.494577 | + | 0.869134i | \(0.664677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.12327e17 | − | 3.43928e16i | 0.735479 | − | 0.225192i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.74335e16i | 0.607484i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.99890e17 | −1.18715 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.57037e16 | + | 3.12569e17i | 0.541599 | + | 1.76886i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.82287e17i | 1.52271i | 0.648336 | + | 0.761355i | \(0.275465\pi\) | ||||
−0.648336 | + | 0.761355i | \(0.724535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.76973e17 | −1.42457 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.78016e17 | − | 2.20393e17i | 0.873303 | − | 1.08119i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.21063e16i | 0.243889i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.49446e16 | −0.156104 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.15406e16 | + | 2.19046e16i | −0.305109 | + | 0.0934196i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.02494e17i | − | 0.417447i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.91381e17 | 1.13368 | 0.566842 | − | 0.823826i | \(-0.308165\pi\) | ||||
0.566842 | + | 0.823826i | \(0.308165\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.07218e16 | + | 2.30978e17i | 0.262932 | + | 0.858737i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.39433e17i | 1.20623i | 0.797653 | + | 0.603117i | \(0.206075\pi\) | ||||
−0.797653 | + | 0.603117i | \(0.793925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00517e17 | −0.341529 | −0.170765 | − | 0.985312i | \(-0.554624\pi\) | ||||
−0.170765 | + | 0.985312i | \(0.554624\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.55118e17 | − | 3.77551e17i | −0.829024 | − | 1.22688i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.05957e16i | − | 0.0951144i | −0.998869 | − | 0.0475572i | \(-0.984856\pi\) | ||
0.998869 | − | 0.0475572i | \(-0.0151436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.85315e16 | 0.233619 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.22321e17 | − | 1.29308e17i | 1.20256 | − | 0.368206i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.72496e17i | − | 1.28819i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.80896e16 | −0.0472330 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.17924e16 | + | 1.36494e17i | 0.104535 | + | 0.341413i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1.36966e18i | − | 3.28278i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.66084e17 | −0.840979 | −0.420490 | − | 0.907297i | \(-0.638142\pi\) | ||||
−0.420490 | + | 0.907297i | \(0.638142\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.66781e17 | + | 1.80268e17i | −0.587549 | + | 0.397017i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.18438e17i | 1.30612i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.55887e17 | 0.518368 | 0.259184 | − | 0.965828i | \(-0.416546\pi\) | ||||
0.259184 | + | 0.965828i | \(0.416546\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.99437e17 | + | 6.10646e16i | −0.387622 | + | 0.118684i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.90742e17i | 0.542285i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.60201e17 | 1.36104 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.71015e17 | − | 5.58537e17i | −0.293969 | − | 0.960103i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.67030e17i | 1.10113i | 0.834792 | + | 0.550565i | \(0.185588\pi\) | ||||
−0.834792 | + | 0.550565i | \(0.814412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.23010e18 | 1.95057 | 0.975285 | − | 0.220953i | \(-0.0709166\pi\) | ||||
0.975285 | + | 0.220953i | \(0.0709166\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.09520e17 | − | 8.84619e16i | −0.166857 | − | 0.134774i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.70227e17i | 0.981294i | 0.871358 | + | 0.490647i | \(0.163240\pi\) | ||||
−0.871358 | + | 0.490647i | \(0.836760\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.93002e17 | −0.975295 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.75243e18 | + | 5.36568e17i | −2.37117 | + | 0.726017i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.07433e17i | − | 0.790382i | −0.918599 | − | 0.395191i | \(-0.870678\pi\) | ||
0.918599 | − | 0.395191i | \(-0.129322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.92783e17 | −0.241279 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.26524e17 | + | 7.39827e17i | 0.272751 | + | 0.890807i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.96847e17i | 1.15499i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.92124e17 | 0.325765 | 0.162883 | − | 0.986645i | \(-0.447921\pi\) | ||||
0.162883 | + | 0.986645i | \(0.447921\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.88944e17 | − | 2.79619e17i | −0.202837 | − | 0.300181i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 5.35905e17i | − | 0.553950i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.04551e18 | −1.04080 | −0.520399 | − | 0.853923i | \(-0.674217\pi\) | ||||
−0.520399 | + | 0.853923i | \(0.674217\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.07444e18 | − | 3.28978e17i | 1.03030 | − | 0.315463i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.90247e16i | − | 0.0360537i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.91356e17 | 0.526471 | 0.263236 | − | 0.964732i | \(-0.415210\pi\) | ||||
0.263236 | + | 0.964732i | \(0.415210\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.12649e17 | + | 3.67913e17i | 0.0966615 | + | 0.315697i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.90949e16i | − | 0.0323392i | −0.999869 | − | 0.0161696i | \(-0.994853\pi\) | ||
0.999869 | − | 0.0161696i | \(-0.00514716\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.58023e18 | 2.05794 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.00286e17 | − | 6.77649e16i | 0.0771370 | − | 0.0521228i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 7.21106e17i | − | 0.534997i | −0.963558 | − | 0.267499i | \(-0.913803\pi\) | ||
0.963558 | − | 0.267499i | \(-0.0861971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.34945e18 | −1.68162 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.05715e17 | + | 9.36051e16i | −0.211139 | + | 0.0646475i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.94526e18i | − | 1.29658i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.54741e17 | 0.0995571 | 0.0497786 | − | 0.998760i | \(-0.484148\pi\) | ||||
0.0497786 | + | 0.998760i | \(0.484148\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.88429e17 | − | 2.24841e18i | −0.427611 | − | 1.39658i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4.78610e17i | − | 0.287059i | −0.989646 | − | 0.143530i | \(-0.954155\pi\) | ||
0.989646 | − | 0.143530i | \(-0.0458452\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.44479e17 | 0.0836892 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.46430e18 | + | 5.88789e17i | 0.819303 | + | 0.329439i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.82321e18i | − | 0.985543i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.72580e18 | −0.901422 | −0.450711 | − | 0.892670i | \(-0.648829\pi\) | ||||
−0.450711 | + | 0.892670i | \(0.648829\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.65323e18 | − | 8.12379e17i | 1.33932 | − | 0.410078i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.54407e18i | 2.70507i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.09472e17 | −0.381826 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.79576e17 | − | 5.86494e17i | −0.0819020 | − | 0.267492i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.39335e17i | 0.193775i | 0.995295 | + | 0.0968875i | \(0.0308887\pi\) | ||||
−0.995295 | + | 0.0968875i | \(0.969111\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.08023e18 | −1.31404 | −0.657020 | − | 0.753873i | \(-0.728183\pi\) | ||||
−0.657020 | + | 0.753873i | \(0.728183\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.65605e18 | + | 3.93072e18i | 1.09611 | + | 1.62214i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 8.15650e17i | − | 0.325673i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.05159e18 | −0.792677 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.62267e17 | − | 2.33395e17i | 0.285040 | − | 0.0872749i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.37699e18i | 0.860373i | 0.902740 | + | 0.430186i | \(0.141552\pi\) | ||||
−0.902740 | + | 0.430186i | \(0.858448\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.02947e18 | 1.06158 | 0.530788 | − | 0.847505i | \(-0.321896\pi\) | ||||
0.530788 | + | 0.847505i | \(0.321896\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.28081e17 | + | 4.18313e17i | 0.0434570 | + | 0.141931i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.01439e18i | − | 0.990444i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.91418e18 | −0.609160 | −0.304580 | − | 0.952487i | \(-0.598516\pi\) | ||||
−0.304580 | + | 0.952487i | \(0.598516\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.86948e18 | + | 3.29039e18i | −1.50111 | + | 1.01433i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.12040e18i | 1.52925i | 0.644477 | + | 0.764624i | \(0.277075\pi\) | ||||
−0.644477 | + | 0.764624i | \(0.722925\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.35027e17 | −0.0390752 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.69011e17 | − | 1.43604e17i | 0.131532 | − | 0.0402730i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.64483e18i | − | 1.26254i | −0.775563 | − | 0.631270i | \(-0.782534\pi\) | ||
0.775563 | − | 0.631270i | \(-0.217466\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.91095e18 | 0.503516 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.33419e18 | − | 4.35748e18i | −0.340825 | − | 1.11313i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.28220e18i | − | 0.317596i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.22480e18 | 0.534413 | 0.267207 | − | 0.963639i | \(-0.413899\pi\) | ||||
0.267207 | + | 0.963639i | \(0.413899\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.98870e18 | − | 4.93819e18i | 0.929271 | − | 1.15048i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.65714e17i | − | 0.150446i | −0.997167 | − | 0.0752231i | \(-0.976033\pi\) | ||
0.997167 | − | 0.0752231i | \(-0.0239669\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.49092e18 | −1.20387 | −0.601933 | − | 0.798546i | \(-0.705603\pi\) | ||||
−0.601933 | + | 0.798546i | \(0.705603\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.54870e18 | + | 4.74187e17i | −0.329454 | + | 0.100874i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.59003e18i | 0.534670i | 0.963604 | + | 0.267335i | \(0.0861431\pi\) | ||||
−0.963604 | + | 0.267335i | \(0.913857\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.23791e19 | 2.48015 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.31676e16 | + | 2.06306e17i | 0.0122842 | + | 0.0401204i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.85365e17i | 0.129388i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.04650e18 | 0.191815 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.03923e18 | + | 1.53797e18i | 0.184962 | + | 0.273727i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 9.62912e18i | − | 1.66432i | −0.554532 | − | 0.832162i | \(-0.687103\pi\) | ||
0.554532 | − | 0.832162i | \(-0.312897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.06009e17 | −0.152096 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.11800e19 | + | 3.42315e18i | −1.82311 | + | 0.558209i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.03118e19i | − | 1.63358i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.64749e18 | 0.561424 | 0.280712 | − | 0.959792i | \(-0.409429\pi\) | ||||
0.280712 | + | 0.959792i | \(0.409429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.15536e18 | − | 7.03943e18i | −0.322373 | − | 1.05287i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.94505e18i | 1.15485i | 0.816443 | + | 0.577426i | \(0.195943\pi\) | ||||
−0.816443 | + | 0.577426i | \(0.804057\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.75960e18 | 0.248592 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.40486e18 | + | 5.00359e18i | −1.01691 | + | 0.687140i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.38716e19i | 1.85196i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.03402e18 | −0.264029 | −0.132014 | − | 0.991248i | \(-0.542144\pi\) | ||||
−0.132014 | + | 0.991248i | \(0.542144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.80864e18 | + | 8.59962e17i | −0.354513 | + | 0.108546i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.75970e18i | 1.19801i | 0.800745 | + | 0.599005i | \(0.204437\pi\) | ||||
−0.800745 | + | 0.599005i | \(0.795563\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.36016e18 | 0.281774 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.40506e18 | + | 7.85494e18i | 0.279300 | + | 0.912194i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 6.39781e18i | − | 0.722781i | −0.932415 | − | 0.361390i | \(-0.882302\pi\) | ||
0.932415 | − | 0.361390i | \(-0.117698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.99535e19 | 2.19318 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.33582e18 | + | 5.11759e18i | 0.677612 | + | 0.547324i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.62005e18i | − | 0.793062i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.68630e19 | −2.72095 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.40066e18 | − | 2.87834e18i | 0.926802 | − | 0.283773i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.54487e19i | 1.48261i | 0.671168 | + | 0.741305i | \(0.265793\pi\) | ||||
−0.671168 | + | 0.741305i | \(0.734207\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.39022e18 | −0.503610 | −0.251805 | − | 0.967778i | \(-0.581024\pi\) | ||||
−0.251805 | + | 0.967778i | \(0.581024\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.18841e18 | − | 3.88134e18i | −0.108106 | − | 0.353075i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.51448e18i | 0.577039i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.39598e18 | −0.292938 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.07511e19 | − | 1.59107e19i | −0.903215 | − | 1.33668i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9.49611e17i | − | 0.0777061i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.39325e19 | −1.11059 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.09077e19 | − | 3.33976e18i | 0.847056 | − | 0.259356i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3.32786e19i | − | 2.51793i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.35219e19 | 1.73417 | 0.867086 | − | 0.498158i | \(-0.165990\pi\) | ||||
0.867086 | + | 0.498158i | \(0.165990\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.78069e18 | + | 9.08175e18i | 0.199781 | + | 0.652485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.50300e18i | − | 0.315302i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.11047e19 | 1.44035 | 0.720176 | − | 0.693792i | \(-0.244061\pi\) | ||||
0.720176 | + | 0.693792i | \(0.244061\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.88776e18 | − | 3.97846e18i | 0.391691 | − | 0.264672i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.25761e18i | 0.146416i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.89376e19 | −2.46203 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.71167e18 | − | 2.97356e18i | 0.598746 | − | 0.183327i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.57942e19i | − | 0.949538i | −0.880110 | − | 0.474769i | \(-0.842532\pi\) | ||
0.880110 | − | 0.474769i | \(-0.157468\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.40579e17 | 0.0199680 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.05236e19 | + | 3.43702e19i | 0.601763 | + | 1.96536i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.39943e18i | 0.301155i | 0.988598 | + | 0.150577i | \(0.0481132\pi\) | ||||
−0.988598 | + | 0.150577i | \(0.951887\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.57953e18 | 0.357977 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.17856e19 | − | 2.93104e19i | 0.625561 | − | 1.55575i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.17179e19i | 0.606825i | 0.952859 | + | 0.303413i | \(0.0981260\pi\) | ||||
−0.952859 | + | 0.303413i | \(0.901874\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.21736e19 | −1.62572 | −0.812862 | − | 0.582456i | \(-0.802092\pi\) | ||||
−0.812862 | + | 0.582456i | \(0.802092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.37358e18 | − | 2.25768e18i | 0.363577 | − | 0.111322i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.20363e18i | − | 0.250398i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.16837e19 | −0.548717 | −0.274358 | − | 0.961627i | \(-0.588465\pi\) | ||||
−0.274358 | + | 0.961627i | \(0.588465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.62977e17 | + | 5.32284e17i | 0.00747097 | + | 0.0244002i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.62029e19i | 0.725037i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.05106e19 | −0.459144 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.48644e18 | + | 3.67971e18i | 0.106044 | + | 0.156936i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.46586e19i | 1.02684i | 0.858139 | + | 0.513418i | \(0.171621\pi\) | ||||
−0.858139 | + | 0.513418i | \(0.828379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.35823e18 | −0.339866 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.79849e19 | + | 8.56854e18i | −1.11125 | + | 0.340247i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.87788e19i | 1.89168i | 0.324630 | + | 0.945841i | \(0.394760\pi\) | ||||
−0.324630 | + | 0.945841i | \(0.605240\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.78135e19 | 2.18983 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.56950e18 | − | 5.12598e18i | −0.0580684 | − | 0.189652i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 2.50684e19i | − | 0.906022i | −0.891505 | − | 0.453011i | \(-0.850350\pi\) | ||
0.891505 | − | 0.453011i | \(-0.149650\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.80139e19 | −0.636042 | −0.318021 | − | 0.948084i | \(-0.603018\pi\) | ||||
−0.318021 | + | 0.948084i | \(0.603018\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.55260e19 | + | 2.40055e19i | −1.22553 | + | 0.828114i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2.44072e19i | − | 0.822679i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.93861e19 | 0.638513 | 0.319256 | − | 0.947668i | \(-0.396567\pi\) | ||||
0.319256 | + | 0.947668i | \(0.396567\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.37322e18 | − | 2.56375e18i | 0.269508 | − | 0.0825192i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.33491e19i | 0.419916i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.46685e19 | 0.758436 | 0.379218 | − | 0.925307i | \(-0.376193\pi\) | ||||
0.379218 | + | 0.925307i | \(0.376193\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.11667e18 | + | 1.01790e19i | 0.0936623 | + | 0.305901i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.13779e19i | − | 0.921780i | −0.887457 | − | 0.460890i | \(-0.847530\pi\) | ||
0.887457 | − | 0.460890i | \(-0.152470\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.72248e19 | 0.781861 | 0.390931 | − | 0.920420i | \(-0.372153\pi\) | ||||
0.390931 | + | 0.920420i | \(0.372153\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.54468e19 | − | 3.15043e19i | 0.714483 | − | 0.884563i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.70279e18i | 0.0741987i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.72428e19 | −0.731294 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.40978e19 | + | 1.35021e19i | −1.15756 | + | 0.354428i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.08514e19i | − | 1.04870i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.02403e18 | 0.0508174 | 0.0254087 | − | 0.999677i | \(-0.491911\pi\) | ||||
0.0254087 | + | 0.999677i | \(0.491911\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.10803e18 | − | 2.64809e19i | −0.199108 | − | 0.650289i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 1.21376e19i | − | 0.291553i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.65372e19 | −0.388584 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.68998e19 | − | 3.98093e19i | −0.618363 | − | 0.915121i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 7.98787e19i | − | 1.79649i | −0.439495 | − | 0.898245i | \(-0.644843\pi\) | ||
0.439495 | − | 0.898245i | \(-0.355157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.79361e19 | 0.834788 | 0.417394 | − | 0.908726i | \(-0.362944\pi\) | ||||
0.417394 | + | 0.908726i | \(0.362944\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.65073e18 | + | 1.11780e18i | −0.0786070 | + | 0.0240683i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.84341e19i | 1.02052i | 0.860021 | + | 0.510259i | \(0.170451\pi\) | ||||
−0.860021 | + | 0.510259i | \(0.829549\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.08735e20 | 2.24211 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.49163e18 | + | 3.09997e19i | 0.191546 | + | 0.625591i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.77183e19i | 0.942524i | 0.881993 | + | 0.471262i | \(0.156201\pi\) | ||||
−0.881993 | + | 0.471262i | \(0.843799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.00857e19 | 0.194991 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.72636e19 | + | 3.86940e19i | −1.08373 | + | 0.732295i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.16539e19i | 0.215911i | 0.994156 | + | 0.107956i | \(0.0344304\pi\) | ||||
−0.994156 | + | 0.107956i | \(0.965570\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.06800e19 | −0.737854 | −0.368927 | − | 0.929458i | \(-0.620275\pi\) | ||||
−0.368927 | + | 0.929458i | \(0.620275\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.70796e19 | − | 5.22952e18i | 0.303308 | − | 0.0928682i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.41761e19i | 1.28977i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.12258e19 | 0.191133 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.66193e19 | − | 5.42786e19i | −0.277096 | − | 0.904995i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.02376e19i | 0.657014i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.17111e19 | 0.986865 | 0.493432 | − | 0.869784i | \(-0.335742\pi\) | ||||
0.493432 | + | 0.869784i | \(0.335742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.09373e19 | + | 8.83429e18i | 0.171310 | + | 0.138371i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.68368e19i | − | 0.258308i | −0.991625 | − | 0.129154i | \(-0.958774\pi\) | ||
0.991625 | − | 0.129154i | \(-0.0412261\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.06407e20 | −3.10196 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.24798e19 | − | 6.88298e18i | 0.330951 | − | 0.101332i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4.05494e19i | − | 0.584843i | −0.956290 | − | 0.292421i | \(-0.905539\pi\) | ||
0.956290 | − | 0.292421i | \(-0.0944610\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.75314e19 | −1.23689 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.46384e19 | + | 8.04691e19i | 0.341126 | + | 1.11412i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.22306e18i | 0.0708583i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.30948e19 | −0.572900 | −0.286450 | − | 0.958095i | \(-0.592475\pi\) | ||||
−0.286450 | + | 0.958095i | \(0.592475\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.00155e20 | + | 1.48221e20i | 1.30479 | + | 1.93097i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.93487e19i | 0.247035i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.28174e19 | 0.535786 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.99318e19 | − | 9.16467e18i | 0.367107 | − | 0.112403i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.96929e19i | − | 0.356966i | −0.983943 | − | 0.178483i | \(-0.942881\pi\) | ||
0.983943 | − | 0.178483i | \(-0.0571190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.24134e19 | 0.617668 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.38122e19 | − | 1.43091e20i | −0.506141 | − | 1.65306i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.72424e19i | − | 0.535053i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.03569e19 | 1.00332 | 0.501658 | − | 0.865066i | \(-0.332724\pi\) | ||||
0.501658 | + | 0.865066i | \(0.332724\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.11745e20 | − | 7.55081e19i | 1.21658 | − | 0.822065i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.15606e19i | 0.443665i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.51475e19 | −0.263241 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.11601e19 | + | 1.26026e19i | −0.422515 | + | 0.129368i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 3.52487e19i | − | 0.354847i | −0.984135 | − | 0.177424i | \(-0.943224\pi\) | ||
0.984135 | − | 0.177424i | \(-0.0567763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.52528e20 | −1.50592 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.16041e19 | − | 1.35879e20i | −0.402873 | − | 1.31579i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.89723e18i | 0.0370160i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.84164e19 | 0.637411 | 0.318705 | − | 0.947854i | \(-0.396752\pi\) | ||||
0.318705 | + | 0.947854i | \(0.396752\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.30160e19 | + | 1.06971e20i | 0.210347 | + | 0.977627i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.53565e19i | 0.137680i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.32414e20 | −1.16468 | −0.582341 | − | 0.812944i | \(-0.697863\pi\) | ||||
−0.582341 | + | 0.812944i | \(0.697863\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.77265e20 | − | 5.42758e19i | 1.52972 | − | 0.468376i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.42789e20i | − | 2.05568i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.21190e19 | 0.100683 | 0.0503413 | − | 0.998732i | \(-0.483969\pi\) | ||||
0.0503413 | + | 0.998732i | \(0.483969\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.70960e18 | + | 2.19136e19i | 0.0546977 | + | 0.178643i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.67371e20i | − | 1.33893i | −0.742844 | − | 0.669465i | \(-0.766524\pi\) | ||
0.742844 | − | 0.669465i | \(-0.233476\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.54729e19 | −0.121472 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.14208e19 | − | 4.64999e19i | −0.242088 | − | 0.358268i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.78883e20i | 2.10887i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.05322e19 | −0.226610 | −0.113305 | − | 0.993560i | \(-0.536144\pi\) | ||||
−0.113305 | + | 0.993560i | \(0.536144\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.12577e19 | − | 6.50878e18i | 0.154864 | − | 0.0474171i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.43755e20i | 1.02800i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.88353e19 | 0.272618 | 0.136309 | − | 0.990666i | \(-0.456476\pi\) | ||||
0.136309 | + | 0.990666i | \(0.456476\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.71379e19 | + | 2.19272e20i | 0.462674 | + | 1.51109i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.43742e19i | 0.503187i | 0.967833 | + | 0.251594i | \(0.0809547\pi\) | ||||
−0.967833 | + | 0.251594i | \(0.919045\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.01350e19 | −0.598717 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.65916e20 | + | 1.12112e20i | −1.08208 | + | 0.731178i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5.40339e19i | − | 0.346018i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.13892e20 | 1.34496 | 0.672481 | − | 0.740115i | \(-0.265229\pi\) | ||||
0.672481 | + | 0.740115i | \(0.265229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.60718e20 | + | 4.92094e19i | −0.992393 | + | 0.303856i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.15894e20i | 0.702756i | 0.936234 | + | 0.351378i | \(0.114287\pi\) | ||||
−0.936234 | + | 0.351378i | \(0.885713\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.44285e19 | −0.0859228 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.95208e19 | − | 1.94395e20i | −0.348114 | − | 1.13694i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.49358e19i | 0.315568i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.72061e20 | 1.53500 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.90582e19 | + | 2.35950e19i | −0.105621 | + | 0.130764i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 6.80612e18i | − | 0.0370520i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.00050e20 | 0.535051 | 0.267526 | − | 0.963551i | \(-0.413794\pi\) | ||||
0.267526 | + | 0.963551i | \(0.413794\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.96039e20 | + | 9.06427e19i | −1.55529 | + | 0.476205i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.31700e20i | − | 0.679752i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.99953e19 | 0.101395 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.71423e19 | − | 5.59869e19i | −0.0854083 | − | 0.278944i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.77847e20i | 1.84973i | 0.380300 | + | 0.924863i | \(0.375821\pi\) | ||||
−0.380300 | + | 0.924863i | \(0.624179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.01902e20 | −2.89533 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.24127e18 | − | 7.75661e18i | −0.0247747 | − | 0.0366644i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 3.91346e20i | − | 1.81782i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.68834e20 | 1.68368 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.03900e20 | − | 6.24312e19i | 0.914752 | − | 0.280083i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.21152e20i | − | 0.975104i | −0.873094 | − | 0.487552i | \(-0.837890\pi\) | ||
0.873094 | − | 0.487552i | \(-0.162110\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.29020e20 | 1.42586 | 0.712929 | − | 0.701236i | \(-0.247368\pi\) | ||||
0.712929 | + | 0.701236i | \(0.247368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.39442e19 | − | 2.74162e20i | −0.357567 | − | 1.16781i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.32234e20i | 0.972349i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.97028e19 | −0.0810911 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.36554e19 | − | 4.97702e19i | 0.298001 | − | 0.201364i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 3.23812e20i | − | 1.28792i | −0.765057 | − | 0.643962i | \(-0.777289\pi\) | ||
0.765057 | − | 0.643962i | \(-0.222711\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.05331e20 | 1.19391 | 0.596956 | − | 0.802274i | \(-0.296377\pi\) | ||||
0.596956 | + | 0.802274i | \(0.296377\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.61242e19 | + | 2.33081e19i | −0.292648 | + | 0.0896043i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.32658e20i | 1.63533i | 0.575692 | + | 0.817666i | \(0.304733\pi\) | ||||
−0.575692 | + | 0.817666i | \(0.695267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.40970e20 | −0.523897 | −0.261949 | − | 0.965082i | \(-0.584365\pi\) | ||||
−0.261949 | + | 0.965082i | \(0.584365\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.54305e19 | + | 1.81036e20i | 0.202554 | + | 0.661543i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 7.45652e20i | − | 2.67930i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.26582e19 | 0.327400 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.73543e19 | − | 7.05582e19i | −0.303533 | − | 0.245171i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.14846e20i | 1.07588i | 0.842982 | + | 0.537941i | \(0.180798\pi\) | ||||
−0.842982 | + | 0.537941i | \(0.819202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.89151e20 | 0.971745 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.68269e20 | + | 8.21399e19i | −0.886702 | + | 0.271494i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 2.59138e20i | − | 0.842431i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.88551e20 | −1.56216 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.20752e19 | + | 3.00718e20i | 0.289593 | + | 0.945813i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.60621e20i | − | 0.806311i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.02131e20 | −1.22384 | −0.611919 | − | 0.790920i | \(-0.709602\pi\) | ||||
−0.611919 | + | 0.790920i | \(0.709602\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.43843e20 | − | 2.12874e20i | −0.430651 | − | 0.637324i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.24590e20i | 0.366960i | 0.983023 | + | 0.183480i | \(0.0587362\pi\) | ||||
−0.983023 | + | 0.183480i | \(0.941264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.48728e20 | 0.720731 | 0.360365 | − | 0.932811i | \(-0.382652\pi\) | ||||
0.360365 | + | 0.932811i | \(0.382652\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.03750e20 | − | 6.23852e19i | 0.580866 | − | 0.177852i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.83129e20i | 0.794162i | 0.917784 | + | 0.397081i | \(0.129977\pi\) | ||||
−0.917784 | + | 0.397081i | \(0.870023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.10132e20 | −0.855922 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.27986e20 | + | 4.18004e20i | 0.347560 | + | 1.13513i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.63679e20i | 2.04067i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.20649e20 | −0.317247 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.92357e20 | − | 4.00266e20i | 1.53280 | − | 1.03574i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.09518e20i | 1.80679i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.14867e20 | −0.287870 | −0.143935 | − | 0.989587i | \(-0.545976\pi\) | ||||
−0.143935 | + | 0.989587i | \(0.545976\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.90310e20 | − | 1.80744e20i | 1.45599 | − | 0.445801i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.03422e20i | 1.46484i | 0.680853 | + | 0.732420i | \(0.261609\pi\) | ||||
−0.680853 | + | 0.732420i | \(0.738391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.17121e20 | −0.757706 | −0.378853 | − | 0.925457i | \(-0.623681\pi\) | ||||
−0.378853 | + | 0.925457i | \(0.623681\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.77342e20 | + | 5.79199e20i | 0.417069 | + | 1.36215i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 6.63312e20i | − | 1.53551i | −0.640744 | − | 0.767754i | \(-0.721374\pi\) | ||
0.640744 | − | 0.767754i | \(-0.278626\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.42954e20 | −0.553620 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.74860e20 | − | 2.31149e20i | −1.28949 | − | 0.518499i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7.72254e20i | − | 1.70530i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.59849e20 | −0.782274 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.08963e20 | − | 3.33629e19i | 0.233203 | − | 0.0714030i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 3.11266e19i | − | 0.0655863i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.35505e20 | −0.488570 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.23745e19 | + | 7.30753e19i | 0.0457025 | + | 0.149264i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.99611e20i | − | 0.602584i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.54603e20 | 1.49440 | 0.747201 | − | 0.664598i | \(-0.231397\pi\) | ||||
0.747201 | + | 0.664598i | \(0.231397\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.16128e19 | + | 1.35579e20i | 0.178652 | + | 0.264389i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.26952e20i | − | 0.435819i | −0.975969 | − | 0.217909i | \(-0.930076\pi\) | ||
0.975969 | − | 0.217909i | \(-0.0699237\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.17786e20 | 0.600951 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.14333e20 | + | 6.56256e19i | −0.399156 | + | 0.122215i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.01881e20i | − | 0.370263i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.30333e20 | −1.31921 | −0.659603 | − | 0.751614i | \(-0.729276\pi\) | ||||
−0.659603 | + | 0.751614i | \(0.729276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.86567e20 | − | 6.09327e20i | −0.331907 | − | 1.08401i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.35196e20i | − | 0.236892i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.04791e19 | 0.156155 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.37732e20 | − | 2.95783e20i | 0.744132 | − | 0.502823i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.36475e20i | 0.898337i | 0.893447 | + | 0.449169i | \(0.148280\pi\) | ||||
−0.893447 | + | 0.449169i | \(0.851720\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.56690e20 | 1.57806 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.09814e20 | − | 2.17334e20i | 1.15338 | − | 0.353148i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.13389e21i | − | 1.81505i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.70668e20 | −0.584531 | −0.292266 | − | 0.956337i | \(-0.594409\pi\) | ||||
−0.292266 | + | 0.956337i | \(0.594409\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.43593e19 | + | 2.10198e20i | 0.0999890 | + | 0.326564i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.25213e20i | 0.344720i | 0.985034 | + | 0.172360i | \(0.0551393\pi\) | ||||
−0.985034 | + | 0.172360i | \(0.944861\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.73163e20 | 0.411946 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.26177e20 | + | 7.75236e20i | −0.930410 | + | 1.15189i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1.02524e21i | − | 1.50099i | −0.660877 | − | 0.750494i | \(-0.729816\pi\) | ||
0.660877 | − | 0.750494i | \(-0.270184\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.94472e20 | −0.280539 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.39810e19 | + | 1.95900e19i | −0.0909468 | + | 0.0278465i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.14513e21i | 1.60400i | 0.597324 | + | 0.802000i | \(0.296231\pi\) | ||||
−0.597324 | + | 0.802000i | \(0.703769\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.43258e20 | −0.335771 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.02825e19 | − | 1.64223e20i | −0.0683964 | − | 0.223383i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.75208e21i | 2.34868i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.41706e20 | −0.847759 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.40811e20 | − | 8.00351e20i | −0.704144 | − | 1.04207i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.75603e19i | − | 0.0225341i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.47587e21 | 1.86665 | 0.933327 | − | 0.359026i | \(-0.116891\pi\) | ||||
0.933327 | + | 0.359026i | \(0.116891\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.88071e20 | + | 3.02532e20i | −1.23175 | + | 0.377142i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 7.59504e20i | − | 0.933245i | −0.884457 | − | 0.466623i | \(-0.845471\pi\) | ||
0.884457 | − | 0.466623i | \(-0.154529\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.87296e20 | 0.469087 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.15825e19 | + | 3.78285e19i | 0.0138283 | + | 0.0451634i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 5.70330e18i | − | 0.00671219i | −0.999994 | − | 0.00335610i | \(-0.998932\pi\) | ||
0.999994 | − | 0.00335610i | \(-0.00106828\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.30095e19 | 0.0615000 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.58674e20 | − | 1.74790e20i | 0.295848 | − | 0.199910i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.23409e21i | 1.39147i | 0.718299 | + | 0.695735i | \(0.244921\pi\) | ||||
−0.718299 | + | 0.695735i | \(0.755079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.23233e20 | 1.02626 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.86420e21 | + | 8.76974e20i | −3.13894 | + | 0.961095i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.79704e19i | 0.105857i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.93368e20 | −0.419067 | −0.209533 | − | 0.977802i | \(-0.567194\pi\) | ||||
−0.209533 | + | 0.977802i | \(0.567194\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.34398e20 | + | 7.65546e20i | 0.246212 | + | 0.804131i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.69108e20i | 0.175147i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.62481e20 | −0.982938 | −0.491469 | − | 0.870895i | \(-0.663540\pi\) | ||||
−0.491469 | + | 0.870895i | \(0.663540\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.47787e20 | + | 4.42461e20i | 0.551637 | + | 0.445571i |
(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 | 12.15.c.b.5.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 12.15.c.b.5.2 | yes | 4 | |
4.3 | odd | 2 | 48.15.e.c.17.4 | 4 | |||
12.11 | even | 2 | 48.15.e.c.17.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.15.c.b.5.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
12.15.c.b.5.2 | yes | 4 | 3.2 | odd | 2 | inner | |
48.15.e.c.17.3 | 4 | 12.11 | even | 2 | |||
48.15.e.c.17.4 | 4 | 4.3 | odd | 2 |