Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(31,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.p (of order \(6\), degree \(2\), not 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 607.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.607 |
Dual form | 784.2.p.c.31.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50000 | − | 0.866025i | −0.670820 | − | 0.387298i | 0.125567 | − | 0.992085i | \(-0.459925\pi\) |
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | − | 0.866025i | 0.452267 | − | 0.261116i | −0.256520 | − | 0.966539i | \(-0.582576\pi\) |
0.708787 | + | 0.705422i | \(0.249243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73205i | 0.447214i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.50000 | − | 2.59808i | 1.09141 | − | 0.630126i | 0.157459 | − | 0.987526i | \(-0.449670\pi\) |
0.933952 | + | 0.357400i | \(0.116337\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | + | 6.06218i | −0.802955 | + | 1.39076i | 0.114708 | + | 0.993399i | \(0.463407\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.50000 | − | 4.33013i | −1.56386 | − | 0.902894i | −0.996861 | − | 0.0791743i | \(-0.974772\pi\) |
−0.566997 | − | 0.823720i | \(-0.691895\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | − | 4.33013i | −0.449013 | − | 0.777714i | 0.549309 | − | 0.835619i | \(-0.314891\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | − | 0.866025i | −0.261116 | − | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50000 | − | 4.33013i | 0.410997 | − | 0.711868i | −0.584002 | − | 0.811752i | \(-0.698514\pi\) |
0.994999 | + | 0.0998840i | \(0.0318472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.92820i | − | 1.08200i | −0.841021 | − | 0.541002i | \(-0.818045\pi\) | ||
0.841021 | − | 0.541002i | \(-0.181955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410i | 0.528271i | 0.964486 | + | 0.264135i | \(0.0850865\pi\) | ||||
−0.964486 | + | 0.264135i | \(0.914913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | + | 1.73205i | −0.447214 | + | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.50000 | + | 2.59808i | −0.218797 | + | 0.378968i | −0.954441 | − | 0.298401i | \(-0.903547\pi\) |
0.735643 | + | 0.677369i | \(0.236880\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50000 | − | 2.59808i | −0.630126 | − | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | + | 7.79423i | 0.618123 | + | 1.07062i | 0.989828 | + | 0.142269i | \(0.0454398\pi\) |
−0.371706 | + | 0.928351i | \(0.621227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.00000 | 0.927173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.50000 | − | 7.79423i | −0.585850 | − | 1.01472i | −0.994769 | − | 0.102151i | \(-0.967427\pi\) |
0.408919 | − | 0.912571i | \(-0.365906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.50000 | − | 4.33013i | −0.960277 | − | 0.554416i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.50000 | + | 2.59808i | −0.549762 | + | 0.317406i | −0.749026 | − | 0.662540i | \(-0.769478\pi\) |
0.199264 | + | 0.979946i | \(0.436145\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.66025i | 1.04257i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.46410i | − | 0.411113i | −0.978645 | − | 0.205557i | \(-0.934100\pi\) | ||
0.978645 | − | 0.205557i | \(-0.0659005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.50000 | + | 0.866025i | −0.175562 | + | 0.101361i | −0.585206 | − | 0.810885i | \(-0.698986\pi\) |
0.409644 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | + | 1.73205i | −0.115470 | + | 0.200000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50000 | + | 2.59808i | 0.506290 | + | 0.292306i | 0.731307 | − | 0.682048i | \(-0.238911\pi\) |
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | −0.976187 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | + | 5.19615i | 0.321634 | + | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.5000 | + | 6.06218i | 1.11300 | + | 0.642590i | 0.939604 | − | 0.342263i | \(-0.111193\pi\) |
0.173394 | + | 0.984853i | \(0.444527\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.50000 | + | 4.33013i | −0.259238 | + | 0.449013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.5000 | − | 6.06218i | 1.07728 | − | 0.621966i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.92820i | − | 0.703452i | −0.936103 | − | 0.351726i | \(-0.885595\pi\) | ||
0.936103 | − | 0.351726i | \(-0.114405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.46410i | − | 0.348155i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.50000 | − | 2.59808i | 0.447767 | − | 0.258518i | −0.259120 | − | 0.965845i | \(-0.583432\pi\) |
0.706887 | + | 0.707327i | \(0.250099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.500000 | − | 0.866025i | 0.0492665 | − | 0.0853320i | −0.840341 | − | 0.542059i | \(-0.817645\pi\) |
0.889607 | + | 0.456727i | \(0.150978\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.50000 | + | 2.59808i | 0.435031 | + | 0.251166i | 0.701488 | − | 0.712681i | \(-0.252519\pi\) |
−0.266456 | + | 0.963847i | \(0.585853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.50000 | − | 9.52628i | −0.526804 | − | 0.912452i | −0.999512 | − | 0.0312328i | \(-0.990057\pi\) |
0.472708 | − | 0.881219i | \(-0.343277\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.00000 | −0.474579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.50000 | + | 12.9904i | 0.699379 | + | 1.21136i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | + | 6.92820i | −0.363636 | + | 0.629837i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.00000 | + | 3.46410i | −0.541002 | + | 0.312348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.46410i | − | 0.307389i | −0.988118 | − | 0.153695i | \(-0.950883\pi\) | ||
0.988118 | − | 0.153695i | \(-0.0491172\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.00000 | − | 1.73205i | 0.264135 | − | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.5000 | − | 18.1865i | 0.917389 | − | 1.58896i | 0.114024 | − | 0.993478i | \(-0.463626\pi\) |
0.803365 | − | 0.595487i | \(-0.203041\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.50000 | + | 4.33013i | 0.645497 | + | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.50000 | − | 2.59808i | −0.128154 | − | 0.221969i | 0.794808 | − | 0.606861i | \(-0.207572\pi\) |
−0.922961 | + | 0.384893i | \(0.874238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | + | 5.19615i | 0.747409 | + | 0.431517i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.50000 | − | 7.79423i | 0.368654 | − | 0.638528i | −0.620701 | − | 0.784047i | \(-0.713152\pi\) |
0.989355 | + | 0.145519i | \(0.0464853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5000 | + | 6.06218i | −0.854478 | + | 0.493333i | −0.862159 | − | 0.506637i | \(-0.830888\pi\) |
0.00768132 | + | 0.999970i | \(0.497555\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 10.3923i | − | 0.840168i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.66025i | 0.695608i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.5000 | + | 7.79423i | −1.07742 | + | 0.622047i | −0.930199 | − | 0.367057i | \(-0.880365\pi\) |
−0.147219 | + | 0.989104i | \(0.547032\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.50000 | − | 7.79423i | 0.356873 | − | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.5000 | + | 6.06218i | 0.822423 | + | 0.474826i | 0.851251 | − | 0.524758i | \(-0.175844\pi\) |
−0.0288280 | + | 0.999584i | \(0.509178\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.50000 | + | 2.59808i | 0.116775 | + | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.00000 | + | 12.1244i | 0.535303 | + | 0.927173i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.50000 | − | 4.33013i | −0.570214 | − | 0.329213i | 0.187021 | − | 0.982356i | \(-0.440117\pi\) |
−0.757235 | + | 0.653143i | \(0.773450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.50000 | + | 7.79423i | −0.338241 | + | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.5000 | − | 7.79423i | 1.00904 | − | 0.582568i | 0.0981277 | − | 0.995174i | \(-0.468715\pi\) |
0.910910 | + | 0.412606i | \(0.135381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.66025i | 0.640184i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.50000 | + | 4.33013i | −0.551411 | + | 0.318357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.50000 | − | 7.79423i | 0.329073 | − | 0.569970i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5000 | + | 6.06218i | 0.759753 | + | 0.438644i | 0.829207 | − | 0.558941i | \(-0.188792\pi\) |
−0.0694538 | + | 0.997585i | \(0.522126\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.50000 | + | 4.33013i | 0.179954 | + | 0.311689i | 0.941865 | − | 0.335993i | \(-0.109072\pi\) |
−0.761911 | + | 0.647682i | \(0.775738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.50000 | + | 9.52628i | 0.389885 | + | 0.675300i | 0.992434 | − | 0.122782i | \(-0.0391815\pi\) |
−0.602549 | + | 0.798082i | \(0.705848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.50000 | + | 2.59808i | 0.317406 | + | 0.183254i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | + | 10.3923i | −0.419058 | + | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.0000 | + | 8.66025i | −1.04257 | + | 0.601929i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.1244i | 0.838659i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 24.2487i | − | 1.66935i | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||
0.550743 | − | 0.834675i | \(-0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | + | 1.73205i | −0.205557 | + | 0.118678i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.00000 | − | 5.19615i | 0.204598 | − | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.50000 | + | 0.866025i | 0.101361 | + | 0.0585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5000 | − | 18.1865i | −0.696909 | − | 1.20708i | −0.969533 | − | 0.244962i | \(-0.921225\pi\) |
0.272623 | − | 0.962121i | \(-0.412109\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.5000 | + | 6.06218i | 0.693860 | + | 0.400600i | 0.805056 | − | 0.593198i | \(-0.202135\pi\) |
−0.111197 | + | 0.993798i | \(0.535468\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.50000 | + | 2.59808i | −0.0982683 | + | 0.170206i | −0.910968 | − | 0.412477i | \(-0.864664\pi\) |
0.812700 | + | 0.582683i | \(0.197997\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.50000 | − | 2.59808i | 0.293548 | − | 0.169480i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 5.19615i | − | 0.337526i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5000 | − | 6.06218i | 0.676364 | − | 0.390499i | −0.122119 | − | 0.992515i | \(-0.538969\pi\) |
0.798484 | + | 0.602016i | \(0.205636\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.0000 | −0.943042 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.50000 | + | 7.79423i | 0.281801 | + | 0.488094i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.5000 | + | 9.52628i | 1.02924 | + | 0.594233i | 0.916767 | − | 0.399422i | \(-0.130789\pi\) |
0.112474 | + | 0.993655i | \(0.464122\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | + | 10.3923i | −0.371391 | + | 0.643268i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.50000 | − | 4.33013i | 0.462470 | − | 0.267007i | −0.250612 | − | 0.968088i | \(-0.580632\pi\) |
0.713082 | + | 0.701080i | \(0.247299\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.5885i | − | 0.957591i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.1244i | − | 0.741999i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.50000 | + | 0.866025i | −0.0914566 | + | 0.0528025i | −0.545031 | − | 0.838416i | \(-0.683482\pi\) |
0.453574 | + | 0.891219i | \(0.350149\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.500000 | − | 0.866025i | 0.0303728 | − | 0.0526073i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) |
0.880812 | + | 0.473466i | \(0.156997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.00000 | − | 1.73205i | −0.180907 | − | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.50000 | + | 14.7224i | 0.510716 | + | 0.884585i | 0.999923 | + | 0.0124177i | \(0.00395278\pi\) |
−0.489207 | + | 0.872167i | \(0.662714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.0000 | −0.598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.50000 | + | 9.52628i | 0.326941 | + | 0.566279i | 0.981903 | − | 0.189383i | \(-0.0606488\pi\) |
−0.654962 | + | 0.755662i | \(0.727315\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.5000 | − | 6.06218i | −0.621966 | − | 0.359092i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | − | 8.66025i | 0.294118 | − | 0.509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00000 | + | 3.46410i | −0.351726 | + | 0.203069i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.7846i | 1.21425i | 0.794606 | + | 0.607125i | \(0.207677\pi\) | ||||
−0.794606 | + | 0.607125i | \(0.792323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5885i | 0.907595i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.50000 | + | 4.33013i | −0.435194 | + | 0.251259i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.50000 | − | 2.59808i | −0.258518 | − | 0.149256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.50000 | + | 12.9904i | 0.429449 | + | 0.743827i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.5000 | − | 28.5788i | −0.935629 | − | 1.62056i | −0.773508 | − | 0.633786i | \(-0.781500\pi\) |
−0.162121 | − | 0.986771i | \(-0.551833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.5000 | − | 14.7224i | −1.44135 | − | 0.832161i | −0.443406 | − | 0.896321i | \(-0.646230\pi\) |
−0.997940 | + | 0.0641600i | \(0.979563\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.5000 | − | 18.1865i | 0.589739 | − | 1.02146i | −0.404528 | − | 0.914526i | \(-0.632564\pi\) |
0.994266 | − | 0.106932i | \(-0.0341026\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | + | 5.19615i | −0.503903 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5.19615i | − | 0.290021i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.3731i | 2.02385i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.50000 | + | 9.52628i | −0.304151 | + | 0.526804i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.5000 | − | 14.7224i | −1.40161 | − | 0.809218i | −0.407049 | − | 0.913406i | \(-0.633442\pi\) |
−0.994558 | + | 0.104188i | \(0.966776\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.00000 | − | 8.66025i | −0.273998 | − | 0.474579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.00000 | 0.491723 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.00000 | − | 5.19615i | −0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.50000 | − | 4.33013i | −0.406148 | − | 0.234490i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.50000 | − | 12.9904i | 0.403786 | − | 0.699379i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.50000 | − | 4.33013i | 0.402621 | − | 0.232453i | −0.284993 | − | 0.958530i | \(-0.591991\pi\) |
0.687614 | + | 0.726076i | \(0.258658\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 27.7128i | − | 1.48343i | −0.670714 | − | 0.741716i | \(-0.734012\pi\) | ||
0.670714 | − | 0.741716i | \(-0.265988\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.5000 | − | 9.52628i | 0.878206 | − | 0.507033i | 0.00813978 | − | 0.999967i | \(-0.497409\pi\) |
0.870067 | + | 0.492934i | \(0.164076\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.00000 | + | 5.19615i | −0.159223 | + | 0.275783i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.5000 | − | 7.79423i | −0.712503 | − | 0.411364i | 0.0994843 | − | 0.995039i | \(-0.468281\pi\) |
−0.811987 | + | 0.583675i | \(0.801614\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.00000 | 0.419891 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.00000 | 0.157027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.500000 | − | 0.866025i | −0.0260998 | − | 0.0452062i | 0.852680 | − | 0.522433i | \(-0.174975\pi\) |
−0.878780 | + | 0.477227i | \(0.841642\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.0000 | − | 6.92820i | −0.624695 | − | 0.360668i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.50000 | − | 11.2583i | 0.336557 | − | 0.582934i | −0.647225 | − | 0.762299i | \(-0.724071\pi\) |
0.983783 | + | 0.179364i | \(0.0574041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.5000 | − | 6.06218i | 0.542218 | − | 0.313050i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923i | 0.533817i | 0.963722 | + | 0.266908i | \(0.0860021\pi\) | ||||
−0.963722 | + | 0.266908i | \(0.913998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.00000 | + | 1.73205i | −0.153695 | + | 0.0887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.5000 | + | 23.3827i | −0.689818 | + | 1.19480i | 0.282079 | + | 0.959391i | \(0.408976\pi\) |
−0.971897 | + | 0.235408i | \(0.924357\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.00000 | + | 3.46410i | 0.304997 | + | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.5000 | + | 18.1865i | 0.532371 | + | 0.922094i | 0.999286 | + | 0.0377914i | \(0.0120322\pi\) |
−0.466915 | + | 0.884302i | \(0.654634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.0000 | −2.27575 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.0000 | −1.05931 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.50000 | − | 7.79423i | −0.226420 | − | 0.392170i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.5000 | + | 6.06218i | 0.526980 | + | 0.304252i | 0.739786 | − | 0.672843i | \(-0.234927\pi\) |
−0.212806 | + | 0.977095i | \(0.568260\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.73205i | 0.0860663i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.66025i | − | 0.429273i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.50000 | − | 2.59808i | 0.222511 | − | 0.128467i | −0.384602 | − | 0.923083i | \(-0.625661\pi\) |
0.607112 | + | 0.794616i | \(0.292328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.50000 | + | 2.59808i | −0.0739895 | + | 0.128154i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | − | 10.3923i | −0.883585 | − | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.00000 | + | 3.46410i | 0.0979404 | + | 0.169638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | + | 5.19615i | 0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.00000 | − | 5.19615i | −0.436564 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.5000 | − | 14.7224i | 1.22829 | − | 0.709155i | 0.261619 | − | 0.965171i | \(-0.415743\pi\) |
0.966672 | + | 0.256017i | \(0.0824102\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.6410i | 1.66474i | 0.554220 | + | 0.832370i | \(0.313017\pi\) | ||||
−0.554220 | + | 0.832370i | \(0.686983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 10.3923i | − | 0.498273i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 52.5000 | − | 30.3109i | 2.51142 | − | 1.44997i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.50000 | + | 16.4545i | −0.453410 | + | 0.785330i | −0.998595 | − | 0.0529862i | \(-0.983126\pi\) |
0.545185 | + | 0.838316i | \(0.316459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.5000 | − | 11.2583i | −0.926473 | − | 0.534899i | −0.0407786 | − | 0.999168i | \(-0.512984\pi\) |
−0.885694 | + | 0.464269i | \(0.846317\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.5000 | − | 18.1865i | −0.497748 | − | 0.862124i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.00000 | −0.425685 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | − | 10.3923i | −0.282529 | − | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.5000 | + | 6.06218i | 0.493333 | + | 0.284826i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | − | 0.866025i | 0.0233890 | − | 0.0405110i | −0.854094 | − | 0.520119i | \(-0.825888\pi\) |
0.877483 | + | 0.479608i | \(0.159221\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.5000 | + | 12.9904i | −1.05021 | + | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 27.7128i | − | 1.29071i | −0.763881 | − | 0.645357i | \(-0.776709\pi\) | ||
0.763881 | − | 0.645357i | \(-0.223291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.46410i | − | 0.160990i | −0.996755 | − | 0.0804952i | \(-0.974350\pi\) | ||
0.996755 | − | 0.0804952i | \(-0.0256502\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.50000 | − | 4.33013i | 0.347804 | − | 0.200805i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.50000 | + | 2.59808i | −0.0694117 | + | 0.120225i | −0.898642 | − | 0.438682i | \(-0.855446\pi\) |
0.829231 | + | 0.558906i | \(0.188779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.5000 | + | 7.79423i | 0.622047 | + | 0.359139i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | + | 5.19615i | 0.137940 | + | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.0000 | 0.642364 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0000 | 0.824163 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.50000 | − | 7.79423i | −0.205610 | − | 0.356127i | 0.744717 | − | 0.667381i | \(-0.232585\pi\) |
−0.950327 | + | 0.311253i | \(0.899251\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.00000 | + | 10.3923i | −0.272446 | + | 0.471890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.50000 | − | 4.33013i | 0.339857 | − | 0.196217i | −0.320352 | − | 0.947299i | \(-0.603801\pi\) |
0.660209 | + | 0.751082i | \(0.270468\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 12.1244i | − | 0.548282i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 17.3205i | − | 0.781664i | −0.920462 | − | 0.390832i | \(-0.872187\pi\) | ||
0.920462 | − | 0.390832i | \(-0.127813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.0000 | + | 15.5885i | −1.21602 | + | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.00000 | + | 5.19615i | −0.134840 | + | 0.233550i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.5000 | + | 6.06218i | 0.470045 | + | 0.271380i | 0.716258 | − | 0.697835i | \(-0.245853\pi\) |
−0.246214 | + | 0.969216i | \(0.579187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.00000 | −0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.50000 | − | 11.2583i | −0.288675 | − | 0.500000i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.5000 | − | 7.79423i | −0.598377 | − | 0.345473i | 0.170026 | − | 0.985440i | \(-0.445615\pi\) |
−0.768403 | + | 0.639966i | \(0.778948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.5000 | − | 30.3109i | 0.772644 | − | 1.33826i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.50000 | + | 0.866025i | −0.0660979 | + | 0.0381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.19615i | 0.228527i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.66025i | 0.380143i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.5000 | + | 14.7224i | −1.11718 | + | 0.645001i | −0.940678 | − | 0.339300i | \(-0.889810\pi\) |
−0.176497 | + | 0.984301i | \(0.556477\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.5000 | + | 19.9186i | −0.502860 | + | 0.870979i | 0.497135 | + | 0.867673i | \(0.334385\pi\) |
−0.999995 | + | 0.00330547i | \(0.998948\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.5000 | − | 12.9904i | −0.980115 | − | 0.565870i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26.0000 | + | 45.0333i | 1.13043 | + | 1.95797i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.0000 | −0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.50000 | − | 7.79423i | −0.194552 | − | 0.336974i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.5000 | − | 7.79423i | −0.582568 | − | 0.336346i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.50000 | + | 6.06218i | −0.150477 | + | 0.260633i | −0.931403 | − | 0.363990i | \(-0.881414\pi\) |
0.780926 | + | 0.624623i | \(0.214748\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.00000 | − | 3.46410i | 0.257485 | − | 0.148659i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.0526i | 0.816122i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2487i | 1.03680i | 0.855138 | + | 0.518400i | \(0.173472\pi\) | ||||
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.0000 | + | 8.66025i | −0.640184 | + | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.0000 | − | 36.3731i | 0.894630 | − | 1.54954i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.50000 | + | 4.33013i | 0.318357 | + | 0.183804i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.50000 | − | 2.59808i | −0.0635570 | − | 0.110084i | 0.832496 | − | 0.554031i | \(-0.186911\pi\) |
−0.896053 | + | 0.443947i | \(0.853578\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | −0.379980 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.50000 | + | 12.9904i | 0.316087 | + | 0.547479i | 0.979668 | − | 0.200625i | \(-0.0642974\pi\) |
−0.663581 | + | 0.748105i | \(0.730964\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | − | 5.19615i | −0.378633 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.5000 | + | 33.7750i | −0.817483 | + | 1.41592i | 0.0900490 | + | 0.995937i | \(0.471298\pi\) |
−0.907532 | + | 0.419984i | \(0.862036\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5000 | + | 6.06218i | −0.439411 | + | 0.253694i | −0.703348 | − | 0.710846i | \(-0.748312\pi\) |
0.263937 | + | 0.964540i | \(0.414979\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 12.1244i | − | 0.506502i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.3205i | 0.722315i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.5000 | + | 7.79423i | −0.562012 | + | 0.324478i | −0.753953 | − | 0.656929i | \(-0.771855\pi\) |
0.191940 | + | 0.981407i | \(0.438522\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.50000 | − | 4.33013i | 0.103896 | − | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.5000 | + | 7.79423i | 0.559113 | + | 0.322804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.0000 | 1.44215 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | + | 5.19615i | 0.123404 | + | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.5000 | + | 9.52628i | 0.677574 | + | 0.391197i | 0.798940 | − | 0.601410i | \(-0.205394\pi\) |
−0.121367 | + | 0.992608i | \(0.538728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.50000 | − | 9.52628i | 0.225100 | − | 0.389885i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.5000 | + | 16.4545i | −1.16448 | + | 0.672312i | −0.952373 | − | 0.304935i | \(-0.901365\pi\) |
−0.212105 | + | 0.977247i | \(0.568032\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.92820i | 0.282607i | 0.989966 | + | 0.141304i | \(0.0451294\pi\) | ||||
−0.989966 | + | 0.141304i | \(0.954871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.3923i | 0.423207i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.0000 | − | 6.92820i | 0.487869 | − | 0.281672i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.5000 | − | 25.1147i | 0.588537 | − | 1.01938i | −0.405887 | − | 0.913923i | \(-0.633038\pi\) |
0.994424 | − | 0.105453i | \(-0.0336291\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.50000 | − | 9.52628i | −0.222143 | − | 0.384763i | 0.733316 | − | 0.679888i | \(-0.237972\pi\) |
−0.955458 | + | 0.295126i | \(0.904638\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.0000 | 0.483887 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0000 | −0.724653 | −0.362326 | − | 0.932051i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.50000 | + | 6.06218i | 0.140677 | + | 0.243659i | 0.927752 | − | 0.373198i | \(-0.121739\pi\) |
−0.787075 | + | 0.616858i | \(0.788405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 37.5000 | + | 21.6506i | 1.50482 | + | 0.868810i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.5000 | − | 6.06218i | 0.419330 | − | 0.242100i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 25.9808i | − | 1.03592i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 45.0333i | − | 1.79275i | −0.443298 | − | 0.896374i | \(-0.646192\pi\) | ||
0.443298 | − | 0.896374i | \(-0.353808\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.0000 | + | 12.1244i | −0.834675 | + | 0.481900i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.00000 | + | 5.19615i | −0.119051 | + | 0.206203i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | − | 3.46410i | −0.237356 | − | 0.137038i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.50000 | + | 7.79423i | 0.177739 | + | 0.307854i | 0.941106 | − | 0.338112i | \(-0.109788\pi\) |
−0.763367 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.00000 | 0.157745 | 0.0788723 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788723 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.50000 | + | 12.9904i | 0.294855 | + | 0.510705i | 0.974951 | − | 0.222419i | \(-0.0713952\pi\) |
−0.680096 | + | 0.733123i | \(0.738062\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.5000 | − | 7.79423i | −0.529921 | − | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.50000 | + | 2.59808i | −0.0586995 | + | 0.101671i | −0.893882 | − | 0.448303i | \(-0.852029\pi\) |
0.835182 | + | 0.549973i | \(0.185362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31.5000 | + | 18.1865i | −1.23081 | + | 0.710607i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.46410i | 0.135147i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 24.2487i | − | 0.944596i | −0.881439 | − | 0.472298i | \(-0.843425\pi\) | ||
0.881439 | − | 0.472298i | \(-0.156575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.5000 | − | 19.9186i | 1.34189 | − | 0.774743i | 0.354809 | − | 0.934939i | \(-0.384546\pi\) |
0.987085 | + | 0.160196i | \(0.0512125\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.0000 | + | 25.9808i | 1.74241 | + | 1.00598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00000 | − | 13.8564i | −0.309298 | − | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0000 | −0.579069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.0000 | −1.92736 | −0.963679 | − | 0.267063i | \(-0.913947\pi\) | ||||
−0.963679 | + | 0.267063i | \(0.913947\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000 | + | 8.66025i | 0.192450 | + | 0.333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.5000 | + | 19.9186i | 1.32594 | + | 0.765533i | 0.984669 | − | 0.174431i | \(-0.0558085\pi\) |
0.341273 | + | 0.939964i | \(0.389142\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5000 | + | 18.1865i | −0.402361 | + | 0.696909i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.5000 | − | 21.6506i | 1.43490 | − | 0.828439i | 0.437409 | − | 0.899263i | \(-0.355896\pi\) |
0.997489 | + | 0.0708242i | \(0.0225629\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.19615i | 0.198535i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 12.1244i | − | 0.462573i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.50000 | − | 11.2583i | 0.247272 | − | 0.428287i | −0.715496 | − | 0.698617i | \(-0.753799\pi\) |
0.962768 | + | 0.270330i | \(0.0871327\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.00000 | + | 3.46410i | 0.227593 | + | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | − | 31.1769i | −0.681799 | − | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.00000 | 0.113470 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.5000 | + | 30.3109i | 0.660025 | + | 1.14320i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.50000 | − | 2.59808i | −0.169480 | − | 0.0978492i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.5000 | + | 30.3109i | −0.657226 | + | 1.13835i | 0.324104 | + | 0.946021i | \(0.394937\pi\) |
−0.981331 | + | 0.192328i | \(0.938396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.00000 | − | 5.19615i | 0.337526 | − | 0.194871i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 43.3013i | 1.62165i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.00000 | + | 5.19615i | −0.336111 | + | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.5000 | − | 28.5788i | 0.615346 | − | 1.06581i | −0.374978 | − | 0.927034i | \(-0.622350\pi\) |
0.990324 | − | 0.138777i | \(-0.0443171\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.5000 | − | 6.06218i | −0.390499 | − | 0.225455i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.00000 | + | 10.3923i | 0.222834 | + | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.00000 | + | 15.5885i | 0.332877 | + | 0.576560i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.5000 | + | 9.52628i | 0.609441 | + | 0.351861i | 0.772747 | − | 0.634714i | \(-0.218882\pi\) |
−0.163305 | + | 0.986576i | \(0.552216\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.50000 | + | 7.79423i | −0.165760 | + | 0.287104i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.50000 | − | 0.866025i | 0.0551784 | − | 0.0318573i | −0.472157 | − | 0.881514i | \(-0.656524\pi\) |
0.527335 | + | 0.849657i | \(0.323191\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.1051i | 1.39794i | 0.715150 | + | 0.698971i | \(0.246358\pi\) | ||||
−0.715150 | + | 0.698971i | \(0.753642\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.5000 | + | 7.79423i | −0.494602 | + | 0.285558i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | − | 20.7846i | 0.439057 | − | 0.760469i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.5000 | + | 19.9186i | 1.25892 | + | 0.726839i | 0.972865 | − | 0.231373i | \(-0.0743217\pi\) |
0.286058 | + | 0.958212i | \(0.407655\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.0000 | 0.764268 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.50000 | + | 12.9904i | 0.272233 | + | 0.471521i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.50000 | + | 2.59808i | 0.163125 | + | 0.0941802i | 0.579340 | − | 0.815086i | \(-0.303310\pi\) |
−0.416215 | + | 0.909266i | \(0.636644\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.00000 | + | 15.5885i | −0.325396 | + | 0.563602i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.92820i | 0.249837i | 0.992167 | + | 0.124919i | \(0.0398670\pi\) | ||||
−0.992167 | + | 0.124919i | \(0.960133\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 19.0526i | − | 0.686161i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.50000 | + | 4.33013i | −0.269756 | + | 0.155744i | −0.628777 | − | 0.777586i | \(-0.716444\pi\) |
0.359021 | + | 0.933330i | \(0.383111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.00000 | + | 8.66025i | −0.179605 | + | 0.311086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42.0000 | + | 24.2487i | 1.50481 | + | 0.868800i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.00000 | − | 5.19615i | −0.107348 | − | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.0000 | 1.07211 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.0000 | 0.963671 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.50000 | + | 6.06218i | 0.124762 | + | 0.216093i | 0.921640 | − | 0.388047i | \(-0.126850\pi\) |
−0.796878 | + | 0.604140i | \(0.793517\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.50000 | − | 4.33013i | −0.267007 | − | 0.154157i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.5000 | + | 7.79423i | −0.478796 | + | 0.276433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 13.8564i | − | 0.490819i | −0.969419 | − | 0.245410i | \(-0.921078\pi\) | ||
0.969419 | − | 0.245410i | \(-0.0789224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.5885i | 0.551480i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.0000 | − | 12.1244i | 0.741999 | − | 0.428393i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.50000 | + | 2.59808i | −0.0529339 | + | 0.0916841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.50000 | + | 0.866025i | 0.0528025 | + | 0.0304855i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.50000 | − | 12.9904i | −0.263686 | − | 0.456717i | 0.703533 | − | 0.710663i | \(-0.251605\pi\) |
−0.967219 | + | 0.253946i | \(0.918272\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.00000 | −0.140459 | −0.0702295 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702295 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.00000 | −0.0350715 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.5000 | − | 18.1865i | −0.367799 | − | 0.637046i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.0000 | − | 12.1244i | −0.734697 | − | 0.424178i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.5000 | − | 49.3634i | 0.994657 | − | 1.72280i | 0.407923 | − | 0.913016i | \(-0.366253\pi\) |
0.586734 | − | 0.809780i | \(-0.300414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.5000 | − | 11.2583i | 0.679727 | − | 0.392441i | −0.120025 | − | 0.992771i | \(-0.538297\pi\) |
0.799752 | + | 0.600330i | \(0.204964\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.46410i | 0.120605i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 38.1051i | − | 1.32504i | −0.749042 | − | 0.662522i | \(-0.769486\pi\) | ||
0.749042 | − | 0.662522i | \(-0.230514\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.50000 | + | 4.33013i | −0.260486 | + | 0.150392i | −0.624556 | − | 0.780980i | \(-0.714720\pi\) |
0.364070 | + | 0.931371i | \(0.381387\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.50000 | − | 14.7224i | 0.294862 | − | 0.510716i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.0000 | − | 10.3923i | −0.622916 | − | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.5000 | + | 21.6506i | 0.432063 | + | 0.748355i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.00000 | − | 5.19615i | −0.103325 | − | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.5000 | − | 11.2583i | −0.670820 | − | 0.387298i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.50000 | − | 9.52628i | 0.188760 | − | 0.326941i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.5000 | + | 21.6506i | −1.28548 | + | 0.742174i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.8564i | 0.474434i | 0.971457 | + | 0.237217i | \(0.0762353\pi\) | ||||
−0.971457 | + | 0.237217i | \(0.923765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 24.2487i | − | 0.829288i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.5000 | + | 21.6506i | −1.28098 | + | 0.739572i | −0.977027 | − | 0.213117i | \(-0.931639\pi\) |
−0.303949 | + | 0.952688i | \(0.598305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.5000 | − | 35.5070i | 0.699451 | − | 1.21148i | −0.269206 | − | 0.963083i | \(-0.586761\pi\) |
0.968657 | − | 0.248402i | \(-0.0799054\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.5000 | + | 23.3827i | 1.37864 | + | 0.795956i | 0.991995 | − | 0.126275i | \(-0.0403020\pi\) |
0.386641 | + | 0.922230i | \(0.373635\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.50000 | + | 12.9904i | 0.255008 | + | 0.441686i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.0000 | −0.339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.00000 | 0.305304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.0000 | − | 6.92820i | −0.406138 | − | 0.234484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.5000 | + | 40.7032i | −0.793539 | + | 1.37445i | 0.130224 | + | 0.991485i | \(0.458430\pi\) |
−0.923763 | + | 0.382965i | \(0.874903\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.0000 | − | 10.3923i | 0.607125 | − | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.8564i | 0.466834i | 0.972377 | + | 0.233417i | \(0.0749907\pi\) | ||||
−0.972377 | + | 0.233417i | \(0.925009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.0333i | 1.51549i | 0.652550 | + | 0.757746i | \(0.273699\pi\) | ||||
−0.652550 | + | 0.757746i | \(0.726301\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.5000 | − | 7.79423i | 0.453798 | − | 0.262000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.50000 | + | 2.59808i | −0.0503651 | + | 0.0872349i | −0.890109 | − | 0.455748i | \(-0.849372\pi\) |
0.839744 | + | 0.542983i | \(0.182705\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 0.866025i | −0.0502519 | − | 0.0290129i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.5000 | − | 18.1865i | −0.351369 | − | 0.608589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.0000 | −0.902510 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.0000 | + | 25.9808i | 0.500278 | + | 0.866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.5000 | + | 23.3827i | 1.34925 | + | 0.778990i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.00000 | − | 10.3923i | 0.199447 | − | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.50000 | + | 2.59808i | −0.149420 | + | 0.0862677i | −0.572846 | − | 0.819663i | \(-0.694161\pi\) |
0.423426 | + | 0.905931i | \(0.360827\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 10.3923i | − | 0.344691i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3923i | 0.344312i | 0.985070 | + | 0.172156i | \(0.0550734\pi\) | ||||
−0.985070 | + | 0.172156i | \(0.944927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | − | 10.3923i | 0.595713 | − | 0.343935i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.50000 | − | 12.9904i | 0.247942 | − | 0.429449i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.5000 | − | 21.6506i | −1.23701 | − | 0.714189i | −0.268529 | − | 0.963272i | \(-0.586537\pi\) |
−0.968482 | + | 0.249083i | \(0.919871\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000 | + | 17.3205i | 0.329511 | + | 0.570730i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.00000 | − | 1.73205i | −0.0328443 | − | 0.0568880i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.5000 | + | 12.9904i | 0.738201 | + | 0.426201i | 0.821415 | − | 0.570331i | \(-0.193185\pi\) |
−0.0832138 | + | 0.996532i | \(0.526518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.5000 | + | 28.5788i | −0.540186 | + | 0.935629i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.5000 | + | 7.79423i | −0.441497 | + | 0.254899i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41.5692i | − | 1.35801i | −0.734135 | − | 0.679004i | \(-0.762412\pi\) | ||
0.734135 | − | 0.679004i | \(-0.237588\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.4449i | 0.960897i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.5000 | + | 14.7224i | −0.831276 | + | 0.479938i | −0.854289 | − | 0.519798i | \(-0.826007\pi\) |
0.0230132 | + | 0.999735i | \(0.492674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.0000 | + | 51.9615i | −0.976934 | + | 1.69210i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.5000 | − | 14.7224i | −0.828639 | − | 0.478415i | 0.0247477 | − | 0.999694i | \(-0.492122\pi\) |
−0.853386 | + | 0.521279i | \(0.825455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.0000 | −0.680972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0000 | −0.583077 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.5000 | − | 18.1865i | −0.339772 | − | 0.588502i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.00000 | + | 5.19615i | 0.290929 | + | 0.167968i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.00000 | − | 5.19615i | 0.290021 | − | 0.167444i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 8.66025i | − | 0.278783i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.1769i | − | 1.00258i | −0.865279 | − | 0.501291i | \(-0.832859\pi\) | ||
0.865279 | − | 0.501291i | \(-0.167141\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.5000 | − | 18.1865i | 1.01193 | − | 0.584236i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.50000 | + | 2.59808i | −0.0481373 | + | 0.0833762i | −0.889090 | − | 0.457732i | \(-0.848662\pi\) |
0.840953 | + | 0.541108i | \(0.181995\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.5000 | − | 23.3827i | −0.431903 | − | 0.748078i | 0.565134 | − | 0.824999i | \(-0.308824\pi\) |
−0.997037 | + | 0.0769208i | \(0.975491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.0000 | 0.671163 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.0000 | −0.702406 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.50000 | + | 2.59808i | 0.0478426 | + | 0.0828658i | 0.888955 | − | 0.457995i | \(-0.151432\pi\) |
−0.841112 | + | 0.540860i | \(0.818099\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.00000 | + | 5.19615i | 0.286764 | + | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.0000 | − | 25.9808i | 0.476972 | − | 0.826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.50000 | + | 2.59808i | −0.142947 | + | 0.0825306i | −0.569768 | − | 0.821806i | \(-0.692967\pi\) |
0.426821 | + | 0.904336i | \(0.359634\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.4449i | 0.934405i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 19.0526i | − | 0.604007i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.50000 | + | 0.866025i | −0.0475055 | + | 0.0274273i | −0.523565 | − | 0.851986i | \(-0.675398\pi\) |
0.476059 | + | 0.879413i | \(0.342065\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.5000 | + | 21.6506i | −0.395482 | + | 0.684996i |
(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 | 784.2.p.c.607.1 | 2 | ||
4.3 | odd | 2 | 784.2.p.d.607.1 | 2 | |||
7.2 | even | 3 | 784.2.f.b.783.2 | 2 | |||
7.3 | odd | 6 | 784.2.p.d.31.1 | 2 | |||
7.4 | even | 3 | 112.2.p.a.31.1 | ✓ | 2 | ||
7.5 | odd | 6 | 784.2.f.a.783.1 | 2 | |||
7.6 | odd | 2 | 112.2.p.b.47.1 | yes | 2 | ||
21.2 | odd | 6 | 7056.2.b.m.1567.1 | 2 | |||
21.5 | even | 6 | 7056.2.b.b.1567.2 | 2 | |||
21.11 | odd | 6 | 1008.2.cs.f.703.1 | 2 | |||
21.20 | even | 2 | 1008.2.cs.c.271.1 | 2 | |||
28.3 | even | 6 | inner | 784.2.p.c.31.1 | 2 | ||
28.11 | odd | 6 | 112.2.p.b.31.1 | yes | 2 | ||
28.19 | even | 6 | 784.2.f.b.783.1 | 2 | |||
28.23 | odd | 6 | 784.2.f.a.783.2 | 2 | |||
28.27 | even | 2 | 112.2.p.a.47.1 | yes | 2 | ||
56.5 | odd | 6 | 3136.2.f.b.3135.2 | 2 | |||
56.11 | odd | 6 | 448.2.p.a.255.1 | 2 | |||
56.13 | odd | 2 | 448.2.p.a.383.1 | 2 | |||
56.19 | even | 6 | 3136.2.f.a.3135.2 | 2 | |||
56.27 | even | 2 | 448.2.p.b.383.1 | 2 | |||
56.37 | even | 6 | 3136.2.f.a.3135.1 | 2 | |||
56.51 | odd | 6 | 3136.2.f.b.3135.1 | 2 | |||
56.53 | even | 6 | 448.2.p.b.255.1 | 2 | |||
84.11 | even | 6 | 1008.2.cs.c.703.1 | 2 | |||
84.23 | even | 6 | 7056.2.b.b.1567.1 | 2 | |||
84.47 | odd | 6 | 7056.2.b.m.1567.2 | 2 | |||
84.83 | odd | 2 | 1008.2.cs.f.271.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.p.a.31.1 | ✓ | 2 | 7.4 | even | 3 | ||
112.2.p.a.47.1 | yes | 2 | 28.27 | even | 2 | ||
112.2.p.b.31.1 | yes | 2 | 28.11 | odd | 6 | ||
112.2.p.b.47.1 | yes | 2 | 7.6 | odd | 2 | ||
448.2.p.a.255.1 | 2 | 56.11 | odd | 6 | |||
448.2.p.a.383.1 | 2 | 56.13 | odd | 2 | |||
448.2.p.b.255.1 | 2 | 56.53 | even | 6 | |||
448.2.p.b.383.1 | 2 | 56.27 | even | 2 | |||
784.2.f.a.783.1 | 2 | 7.5 | odd | 6 | |||
784.2.f.a.783.2 | 2 | 28.23 | odd | 6 | |||
784.2.f.b.783.1 | 2 | 28.19 | even | 6 | |||
784.2.f.b.783.2 | 2 | 7.2 | even | 3 | |||
784.2.p.c.31.1 | 2 | 28.3 | even | 6 | inner | ||
784.2.p.c.607.1 | 2 | 1.1 | even | 1 | trivial | ||
784.2.p.d.31.1 | 2 | 7.3 | odd | 6 | |||
784.2.p.d.607.1 | 2 | 4.3 | odd | 2 | |||
1008.2.cs.c.271.1 | 2 | 21.20 | even | 2 | |||
1008.2.cs.c.703.1 | 2 | 84.11 | even | 6 | |||
1008.2.cs.f.271.1 | 2 | 84.83 | odd | 2 | |||
1008.2.cs.f.703.1 | 2 | 21.11 | odd | 6 | |||
3136.2.f.a.3135.1 | 2 | 56.37 | even | 6 | |||
3136.2.f.a.3135.2 | 2 | 56.19 | even | 6 | |||
3136.2.f.b.3135.1 | 2 | 56.51 | odd | 6 | |||
3136.2.f.b.3135.2 | 2 | 56.5 | odd | 6 | |||
7056.2.b.b.1567.1 | 2 | 84.23 | even | 6 | |||
7056.2.b.b.1567.2 | 2 | 21.5 | even | 6 | |||
7056.2.b.m.1567.1 | 2 | 21.2 | odd | 6 | |||
7056.2.b.m.1567.2 | 2 | 84.47 | odd | 6 |