Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(401,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.q (of order \(3\), degree \(2\), 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: | \(11.1790562830\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 401.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.401 |
Dual form | 1400.2.q.f.1201.1 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | + | 1.73205i | 0.577350 | + | 1.00000i | 0.995782 | + | 0.0917517i | \(0.0292466\pi\) |
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 2.59808i | −0.188982 | − | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | − | 3.46410i | −0.603023 | − | 1.04447i | −0.992361 | − | 0.123371i | \(-0.960630\pi\) |
0.389338 | − | 0.921095i | \(-0.372704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | − | 3.46410i | 0.872872 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50000 | − | 2.59808i | 0.312772 | − | 0.541736i | −0.666190 | − | 0.745782i | \(-0.732076\pi\) |
0.978961 | + | 0.204046i | \(0.0654092\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50000 | − | 7.79423i | −0.808224 | − | 1.39988i | −0.914093 | − | 0.405505i | \(-0.867096\pi\) |
0.105869 | − | 0.994380i | \(-0.466238\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.00000 | − | 6.92820i | 0.696311 | − | 1.20605i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | + | 3.46410i | 0.320256 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000 | 0.780869 | 0.390434 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390434 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | 0.914991 | 0.457496 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457496 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.50000 | − | 7.79423i | 0.656392 | − | 1.13691i | −0.325150 | − | 0.945662i | \(-0.605415\pi\) |
0.981543 | − | 0.191243i | \(-0.0612518\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | − | 5.19615i | 0.420084 | − | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | − | 6.92820i | −0.520756 | − | 0.901975i | −0.999709 | − | 0.0241347i | \(-0.992317\pi\) |
0.478953 | − | 0.877841i | \(-0.341016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.50000 | + | 0.866025i | 0.314970 | + | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00000 | + | 12.1244i | 0.855186 | + | 1.48123i | 0.876472 | + | 0.481452i | \(0.159891\pi\) |
−0.0212861 | + | 0.999773i | \(0.506776\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0000 | 1.30546 | 0.652730 | − | 0.757591i | \(-0.273624\pi\) | ||||
0.652730 | + | 0.757591i | \(0.273624\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | − | 1.73205i | −0.117041 | − | 0.202721i | 0.801553 | − | 0.597924i | \(-0.204008\pi\) |
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.00000 | + | 6.92820i | −0.911685 | + | 0.789542i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.50000 | + | 7.79423i | −0.506290 | + | 0.876919i | 0.493684 | + | 0.869641i | \(0.335650\pi\) |
−0.999974 | + | 0.00727784i | \(0.997683\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.00000 | − | 10.3923i | −0.643268 | − | 1.11417i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.50000 | + | 9.52628i | −0.582999 | + | 1.00978i | 0.412123 | + | 0.911128i | \(0.364787\pi\) |
−0.995122 | + | 0.0986553i | \(0.968546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | − | 5.19615i | −0.104828 | − | 0.544705i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.00000 | − | 15.5885i | 0.933257 | − | 1.61645i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0000 | 1.11688 | 0.558440 | − | 0.829545i | \(-0.311400\pi\) | ||||
0.558440 | + | 0.829545i | \(0.311400\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.00000 | + | 6.92820i | 0.398015 | + | 0.689382i | 0.993481 | − | 0.113998i | \(-0.0363659\pi\) |
−0.595466 | + | 0.803380i | \(0.703033\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.50000 | − | 12.9904i | 0.738997 | − | 1.27998i | −0.213950 | − | 0.976845i | \(-0.568633\pi\) |
0.952947 | − | 0.303136i | \(-0.0980336\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | − | 6.92820i | 0.386695 | − | 0.669775i | −0.605308 | − | 0.795991i | \(-0.706950\pi\) |
0.992003 | + | 0.126217i | \(0.0402834\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | + | 12.1244i | 0.670478 | + | 1.16130i | 0.977769 | + | 0.209687i | \(0.0672444\pi\) |
−0.307290 | + | 0.951616i | \(0.599422\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0000 | −1.41108 | −0.705541 | − | 0.708669i | \(-0.749296\pi\) | ||||
−0.705541 | + | 0.708669i | \(0.749296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | + | 1.73205i | −0.0924500 | + | 0.160128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | + | 5.19615i | −0.550019 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.00000 | + | 8.66025i | 0.450835 | + | 0.780869i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | + | 10.3923i | 0.528271 | + | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.50000 | + | 14.7224i | 0.726204 | + | 1.25782i | 0.958477 | + | 0.285171i | \(0.0920506\pi\) |
−0.232273 | + | 0.972651i | \(0.574616\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | −0.508913 | −0.254457 | − | 0.967084i | \(-0.581897\pi\) | ||||
−0.254457 | + | 0.967084i | \(0.581897\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.0000 | 1.51587 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00000 | − | 6.92820i | −0.334497 | − | 0.579365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.0000 | − | 8.66025i | −0.907265 | − | 0.714286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0000 | − | 17.3205i | 0.819232 | − | 1.41895i | −0.0870170 | − | 0.996207i | \(-0.527733\pi\) |
0.906249 | − | 0.422744i | \(-0.138933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | − | 17.3205i | −0.813788 | − | 1.40952i | −0.910195 | − | 0.414181i | \(-0.864068\pi\) |
0.0964061 | − | 0.995342i | \(-0.469265\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.00000 | 0.242536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000 | + | 8.66025i | 0.399043 | + | 0.691164i | 0.993608 | − | 0.112884i | \(-0.0360089\pi\) |
−0.594565 | + | 0.804048i | \(0.702676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | − | 10.3923i | 0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.50000 | − | 2.59808i | −0.591083 | − | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | + | 20.7846i | −0.939913 | + | 1.62798i | −0.174282 | + | 0.984696i | \(0.555760\pi\) |
−0.765631 | + | 0.643280i | \(0.777573\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.00000 | − | 13.8564i | 0.608229 | − | 1.05348i | −0.383304 | − | 0.923622i | \(-0.625214\pi\) |
0.991532 | − | 0.129861i | \(-0.0414530\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000 | − | 13.8564i | 0.601317 | − | 1.04151i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.00000 | − | 3.46410i | −0.149487 | − | 0.258919i | 0.781551 | − | 0.623841i | \(-0.214429\pi\) |
−0.931038 | + | 0.364922i | \(0.881096\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.00000 | −0.594635 | −0.297318 | − | 0.954779i | \(-0.596092\pi\) | ||||
−0.297318 | + | 0.954779i | \(0.596092\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.0000 | −1.18275 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | + | 10.3923i | −0.438763 | + | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.00000 | − | 10.3923i | −0.145479 | − | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.50000 | − | 11.2583i | 0.470323 | − | 0.814624i | −0.529101 | − | 0.848559i | \(-0.677471\pi\) |
0.999424 | + | 0.0339349i | \(0.0108039\pi\) | |||||||
\(192\) | 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 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.5000 | − | 18.1865i | −0.744325 | − | 1.28921i | −0.950509 | − | 0.310696i | \(-0.899438\pi\) |
0.206184 | − | 0.978513i | \(-0.433895\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.0000 | + | 24.2487i | −0.987484 | + | 1.71037i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.00000 | + | 15.5885i | 0.210559 | + | 1.09410i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.50000 | + | 2.59808i | 0.104257 | + | 0.180579i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.0000 | 1.51454 | 0.757271 | − | 0.653101i | \(-0.226532\pi\) | ||||
0.757271 | + | 0.653101i | \(0.226532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.0000 | + | 19.0526i | 0.753708 | + | 1.30546i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.0000 | + | 15.5885i | −1.22192 | + | 1.05821i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000 | − | 3.46410i | 0.135147 | − | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0000 | −0.736614 | −0.368307 | − | 0.929704i | \(-0.620063\pi\) | ||||
−0.368307 | + | 0.929704i | \(0.620063\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.0000 | − | 19.0526i | −0.730096 | − | 1.26456i | −0.956842 | − | 0.290609i | \(-0.906142\pi\) |
0.226746 | − | 0.973954i | \(-0.427191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000 | − | 6.92820i | 0.264327 | − | 0.457829i | −0.703060 | − | 0.711131i | \(-0.748183\pi\) |
0.967387 | + | 0.253302i | \(0.0815167\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −20.0000 | − | 6.92820i | −1.31590 | − | 0.455842i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.0000 | + | 19.0526i | −0.720634 | + | 1.24817i | 0.240112 | + | 0.970745i | \(0.422816\pi\) |
−0.960746 | + | 0.277429i | \(0.910518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.0000 | −1.16923 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0000 | 0.711531 | 0.355765 | − | 0.934575i | \(-0.384220\pi\) | ||||
0.355765 | + | 0.934575i | \(0.384220\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.00000 | − | 15.5885i | −0.579741 | − | 1.00414i | −0.995509 | − | 0.0946700i | \(-0.969820\pi\) |
0.415768 | − | 0.909471i | \(-0.363513\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.00000 | + | 8.66025i | −0.320750 | + | 0.555556i | ||||
\(244\) | 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 | ||||||||
\(251\) | −16.0000 | −1.00991 | −0.504956 | − | 0.863145i | \(-0.668491\pi\) | ||||
−0.504956 | + | 0.863145i | \(0.668491\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.00000 | − | 15.5885i | 0.561405 | − | 0.972381i | −0.435970 | − | 0.899961i | \(-0.643595\pi\) |
0.997374 | − | 0.0724199i | \(-0.0230722\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.50000 | − | 2.59808i | −0.0924940 | − | 0.160204i | 0.816066 | − | 0.577959i | \(-0.196151\pi\) |
−0.908560 | + | 0.417755i | \(0.862817\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.0000 | −1.34638 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.00000 | + | 1.73205i | 0.0609711 | + | 0.105605i | 0.894900 | − | 0.446267i | \(-0.147247\pi\) |
−0.833929 | + | 0.551872i | \(0.813914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.50000 | + | 6.06218i | −0.212610 | + | 0.368251i | −0.952531 | − | 0.304443i | \(-0.901530\pi\) |
0.739921 | + | 0.672694i | \(0.234863\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00000 | − | 6.92820i | 0.484182 | − | 0.419314i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00000 | + | 6.92820i | 0.240337 | + | 0.416275i | 0.960810 | − | 0.277207i | \(-0.0894088\pi\) |
−0.720473 | + | 0.693482i | \(0.756075\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.00000 | 0.538816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0000 | −0.775515 | −0.387757 | − | 0.921761i | \(-0.626750\pi\) | ||||
−0.387757 | + | 0.921761i | \(0.626750\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.00000 | + | 1.73205i | 0.0594438 | + | 0.102960i | 0.894216 | − | 0.447636i | \(-0.147734\pi\) |
−0.834772 | + | 0.550596i | \(0.814401\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.50000 | − | 12.9904i | −0.147570 | − | 0.766798i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.0000 | + | 19.0526i | 0.644831 | + | 1.11688i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.00000 | − | 13.8564i | −0.464207 | − | 0.804030i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | − | 15.5885i | −0.172917 | − | 0.898504i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.00000 | + | 13.8564i | −0.459588 | + | 0.796030i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.0000 | 1.36975 | 0.684876 | − | 0.728659i | \(-0.259856\pi\) | ||||
0.684876 | + | 0.728659i | \(0.259856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.0000 | 1.70664 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.500000 | − | 0.866025i | −0.0283524 | − | 0.0491078i | 0.851501 | − | 0.524353i | \(-0.175693\pi\) |
−0.879853 | + | 0.475245i | \(0.842359\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5000 | + | 26.8468i | −0.876112 | + | 1.51747i | −0.0205381 | + | 0.999789i | \(0.506538\pi\) |
−0.855574 | + | 0.517681i | \(0.826795\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.00000 | + | 10.3923i | −0.336994 | + | 0.583690i | −0.983866 | − | 0.178908i | \(-0.942743\pi\) |
0.646872 | + | 0.762598i | \(0.276077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | + | 20.7846i | 0.671871 | + | 1.16371i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.0000 | 0.893033 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.0000 | + | 24.2487i | −0.774202 | + | 1.34096i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.5000 | − | 7.79423i | −1.24047 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.00000 | − | 1.73205i | 0.0549650 | − | 0.0952021i | −0.837234 | − | 0.546845i | \(-0.815829\pi\) |
0.892199 | + | 0.451643i | \(0.149162\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.0000 | 1.57973 | 0.789865 | − | 0.613280i | \(-0.210150\pi\) | ||||
0.789865 | + | 0.613280i | \(0.210150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.0000 | − | 25.9808i | −0.814688 | − | 1.41108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.0000 | + | 31.1769i | −0.974755 | + | 1.68832i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.00000 | + | 1.73205i | 0.0536828 | + | 0.0929814i | 0.891618 | − | 0.452788i | \(-0.149571\pi\) |
−0.837935 | + | 0.545770i | \(0.816237\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.00000 | 0.427008 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.50000 | + | 12.9904i | 0.399185 | + | 0.691408i | 0.993626 | − | 0.112731i | \(-0.0359599\pi\) |
−0.594441 | + | 0.804139i | \(0.702627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.0000 | − | 5.19615i | −0.793884 | − | 0.275010i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | + | 16.4545i | 0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | + | 13.8564i | 0.417597 | + | 0.723299i | 0.995697 | − | 0.0926670i | \(-0.0295392\pi\) |
−0.578101 | + | 0.815966i | \(0.696206\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.50000 | + | 4.33013i | −0.130145 | + | 0.225417i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | + | 10.3923i | −0.623009 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.00000 | − | 5.19615i | 0.155334 | − | 0.269047i | −0.777847 | − | 0.628454i | \(-0.783688\pi\) |
0.933181 | + | 0.359408i | \(0.117021\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.00000 | − | 13.8564i | −0.409852 | − | 0.709885i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.5000 | − | 18.1865i | 0.536525 | − | 0.929288i | −0.462563 | − | 0.886586i | \(-0.653070\pi\) |
0.999088 | − | 0.0427020i | \(-0.0135966\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.00000 | + | 5.19615i | −0.152499 | + | 0.264135i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.0000 | − | 29.4449i | −0.861934 | − | 1.49291i | −0.870059 | − | 0.492947i | \(-0.835920\pi\) |
0.00812520 | − | 0.999967i | \(-0.497414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.0000 | −1.21064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.0000 | + | 32.9090i | −0.953583 | + | 1.65165i | −0.216004 | + | 0.976392i | \(0.569302\pi\) |
−0.737579 | + | 0.675261i | \(0.764031\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.00000 | + | 15.5885i | −0.449439 | + | 0.778450i | −0.998350 | − | 0.0574304i | \(-0.981709\pi\) |
0.548911 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00000 | − | 15.5885i | −0.448322 | − | 0.776516i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.5000 | + | 26.8468i | 0.766426 | + | 1.32749i | 0.939490 | + | 0.342578i | \(0.111300\pi\) |
−0.173064 | + | 0.984911i | \(0.555367\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.0000 | + | 29.4449i | −0.838548 | + | 1.45241i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.0000 | + | 13.8564i | −0.787309 | + | 0.681829i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.00000 | − | 10.3923i | −0.293821 | − | 0.508913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0000 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.50000 | + | 7.79423i | 0.218797 | + | 0.378968i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0000 | + | 6.92820i | 0.967868 | + | 0.335279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.00000 | − | 13.8564i | 0.386244 | − | 0.668994i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.5000 | + | 26.8468i | 0.746609 | + | 1.29316i | 0.949439 | + | 0.313950i | \(0.101653\pi\) |
−0.202831 | + | 0.979214i | \(0.565014\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.0000 | −1.00920 | −0.504598 | − | 0.863355i | \(-0.668359\pi\) | ||||
−0.504598 | + | 0.863355i | \(0.668359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.5000 | + | 30.3109i | −0.835229 | + | 1.44666i | 0.0586141 | + | 0.998281i | \(0.481332\pi\) |
−0.893843 | + | 0.448379i | \(0.852001\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.00000 | − | 10.3923i | 0.285069 | − | 0.493753i | −0.687557 | − | 0.726130i | \(-0.741317\pi\) |
0.972626 | + | 0.232377i | \(0.0746503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 40.0000 | 1.89194 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.0000 | −1.27421 | −0.637104 | − | 0.770778i | \(-0.719868\pi\) | ||||
−0.637104 | + | 0.770778i | \(0.719868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0000 | − | 17.3205i | −0.470882 | − | 0.815591i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.0000 | − | 34.6410i | 0.939682 | − | 1.62758i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00000 | − | 1.73205i | 0.0467780 | − | 0.0810219i | −0.841688 | − | 0.539964i | \(-0.818438\pi\) |
0.888466 | + | 0.458942i | \(0.151771\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.00000 | − | 10.3923i | −0.280056 | − | 0.485071i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.0000 | 1.11779 | 0.558896 | − | 0.829238i | \(-0.311225\pi\) | ||||
0.558896 | + | 0.829238i | \(0.311225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.0000 | −0.511213 | −0.255607 | − | 0.966781i | \(-0.582275\pi\) | ||||
−0.255607 | + | 0.966781i | \(0.582275\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.0000 | + | 25.9808i | −0.694117 | + | 1.20225i | 0.276360 | + | 0.961054i | \(0.410872\pi\) |
−0.970477 | + | 0.241192i | \(0.922462\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.0000 | − | 24.2487i | 1.29292 | − | 1.11970i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0000 | + | 17.3205i | −0.460776 | + | 0.798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.0000 | − | 20.7846i | −0.551761 | − | 0.955677i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | −3.00000 | − | 15.5885i | −0.136505 | − | 0.709299i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.5000 | + | 19.9186i | 0.521115 | + | 0.902597i | 0.999698 | + | 0.0245553i | \(0.00781698\pi\) |
−0.478584 | + | 0.878042i | \(0.658850\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −48.0000 | −2.17064 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0000 | 1.35388 | 0.676941 | − | 0.736038i | \(-0.263305\pi\) | ||||
0.676941 | + | 0.736038i | \(0.263305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | + | 15.5885i | 0.405340 | + | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.50000 | − | 28.5788i | −0.246709 | − | 1.28194i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.0000 | + | 32.9090i | −0.850557 | + | 1.47321i | 0.0301498 | + | 0.999545i | \(0.490402\pi\) |
−0.880707 | + | 0.473662i | \(0.842932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0000 | 0.713405 | 0.356702 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356702 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | − | 15.5885i | −0.399704 | − | 0.692308i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.00000 | + | 10.3923i | −0.265945 | + | 0.460631i | −0.967811 | − | 0.251679i | \(-0.919017\pi\) |
0.701866 | + | 0.712309i | \(0.252351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | + | 3.46410i | −0.176950 | + | 0.153243i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.0000 | −1.58328 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.0000 | 1.40464 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.5000 | − | 38.9711i | −0.985743 | − | 1.70736i | −0.638588 | − | 0.769549i | \(-0.720481\pi\) |
−0.347155 | − | 0.937808i | \(-0.612852\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0000 | − | 19.0526i | 0.480996 | − | 0.833110i | −0.518766 | − | 0.854916i | \(-0.673608\pi\) |
0.999762 | + | 0.0218062i | \(0.00694167\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.5000 | + | 23.3827i | −0.588069 | + | 1.01857i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.0000 | 0.433148 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.00000 | − | 6.92820i | 0.172613 | − | 0.298974i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.0000 | + | 17.3205i | 0.947607 | + | 0.746047i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.0000 | − | 25.9808i | 0.644900 | − | 1.11700i | −0.339424 | − | 0.940633i | \(-0.610232\pi\) |
0.984325 | − | 0.176367i | \(-0.0564345\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.00000 | − | 13.8564i | −0.343313 | − | 0.594635i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.0000 | 1.71028 | 0.855138 | − | 0.518400i | \(-0.173472\pi\) | ||||
0.855138 | + | 0.518400i | \(0.173472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.00000 | − | 6.92820i | −0.170716 | − | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.5000 | + | 7.79423i | 0.956797 | + | 0.331444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.0000 | − | 31.1769i | −0.762684 | − | 1.32101i | −0.941462 | − | 0.337119i | \(-0.890548\pi\) |
0.178778 | − | 0.983890i | \(-0.442786\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0000 | 0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.0000 | − | 22.5167i | −0.547885 | − | 0.948964i | −0.998419 | − | 0.0562051i | \(-0.982100\pi\) |
0.450535 | − | 0.892759i | \(-0.351233\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.0000 | − | 19.0526i | 0.923913 | − | 0.800132i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.50000 | − | 9.52628i | 0.230572 | − | 0.399362i | −0.727405 | − | 0.686209i | \(-0.759274\pi\) |
0.957977 | + | 0.286846i | \(0.0926069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.00000 | + | 10.3923i | 0.251092 | + | 0.434904i | 0.963827 | − | 0.266529i | \(-0.0858769\pi\) |
−0.712735 | + | 0.701434i | \(0.752544\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.0000 | 1.08617 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00000 | + | 12.1244i | 0.291414 | + | 0.504744i | 0.974144 | − | 0.225927i | \(-0.0725410\pi\) |
−0.682730 | + | 0.730670i | \(0.739208\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.00000 | + | 8.66025i | −0.207793 | + | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.00000 | − | 15.5885i | −0.124461 | − | 0.646718i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | + | 20.7846i | −0.496989 | + | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.00000 | −0.330195 | −0.165098 | − | 0.986277i | \(-0.552794\pi\) | ||||
−0.165098 | + | 0.986277i | \(0.552794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | + | 31.1769i | 0.740421 | + | 1.28245i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.50000 | + | 11.2583i | −0.266923 | + | 0.462324i | −0.968066 | − | 0.250697i | \(-0.919340\pi\) |
0.701143 | + | 0.713021i | \(0.252674\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.0000 | − | 36.3731i | 0.859473 | − | 1.48865i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.50000 | − | 7.79423i | −0.183865 | − | 0.318464i | 0.759328 | − | 0.650708i | \(-0.225528\pi\) |
−0.943193 | + | 0.332244i | \(0.892194\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.0000 | −0.570124 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.50000 | + | 11.2583i | −0.263827 | + | 0.456962i | −0.967256 | − | 0.253804i | \(-0.918318\pi\) |
0.703429 | + | 0.710766i | \(0.251651\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.0000 | + | 20.7846i | −0.972529 | + | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.00000 | − | 15.5885i | 0.364101 | − | 0.630641i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.0000 | + | 22.5167i | 0.525065 | + | 0.909439i | 0.999574 | + | 0.0291886i | \(0.00929235\pi\) |
−0.474509 | + | 0.880251i | \(0.657374\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.0000 | 0.684394 | 0.342197 | − | 0.939628i | \(-0.388829\pi\) | ||||
0.342197 | + | 0.939628i | \(0.388829\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.00000 | + | 8.66025i | 0.200967 | + | 0.348085i | 0.948840 | − | 0.315757i | \(-0.102258\pi\) |
−0.747873 | + | 0.663842i | \(0.768925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.00000 | − | 10.3923i | 0.240772 | − | 0.417029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.5000 | + | 9.52628i | 1.10176 | + | 0.381662i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.0000 | −0.597141 | −0.298570 | − | 0.954388i | \(-0.596510\pi\) | ||||
−0.298570 | + | 0.954388i | \(0.596510\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.0000 | + | 38.1051i | 0.874421 | + | 1.51454i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.0000 | + | 5.19615i | −0.515079 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.50000 | + | 9.52628i | −0.217577 | + | 0.376854i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.5000 | + | 30.3109i | 0.691208 | + | 1.19721i | 0.971442 | + | 0.237276i | \(0.0762547\pi\) |
−0.280234 | + | 0.959932i | \(0.590412\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.0000 | 0.630978 | 0.315489 | − | 0.948929i | \(-0.397831\pi\) | ||||
0.315489 | + | 0.948929i | \(0.397831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0000 | − | 41.5692i | −0.943537 | − | 1.63425i | −0.758654 | − | 0.651494i | \(-0.774142\pi\) |
−0.184884 | − | 0.982760i | \(-0.559191\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.0000 | + | 27.7128i | −0.628055 | + | 1.08782i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45.0000 | − | 15.5885i | −1.76369 | − | 0.610960i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.0000 | − | 25.9808i | 0.586995 | − | 1.01671i | −0.407628 | − | 0.913148i | \(-0.633644\pi\) |
0.994623 | − | 0.103558i | \(-0.0330227\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.0000 | 0.545363 | 0.272681 | − | 0.962104i | \(-0.412090\pi\) | ||||
0.272681 | + | 0.962104i | \(0.412090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0000 | − | 38.1051i | −0.855701 | − | 1.48212i | −0.875993 | − | 0.482323i | \(-0.839793\pi\) |
0.0202925 | − | 0.999794i | \(-0.493540\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.00000 | − | 10.3923i | 0.233021 | − | 0.403604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | + | 15.5885i | −0.348481 | + | 0.603587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.0000 | − | 19.0526i | −0.425285 | − | 0.736614i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.0000 | 1.23535 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.0000 | 1.65753 | 0.828764 | − | 0.559598i | \(-0.189045\pi\) | ||||
0.828764 | + | 0.559598i | \(0.189045\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.00000 | + | 5.19615i | −0.115299 | + | 0.199704i | −0.917899 | − | 0.396813i | \(-0.870116\pi\) |
0.802600 | + | 0.596518i | \(0.203449\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.50000 | − | 28.5788i | −0.211071 | − | 1.09676i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.0000 | − | 38.1051i | 0.843042 | − | 1.46019i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.00000 | − | 12.1244i | −0.267848 | − | 0.463926i | 0.700458 | − | 0.713693i | \(-0.252979\pi\) |
−0.968306 | + | 0.249768i | \(0.919646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.0000 | 0.610438 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.0000 | − | 19.0526i | 0.418460 | − | 0.724793i | −0.577325 | − | 0.816514i | \(-0.695903\pi\) |
0.995785 | + | 0.0917209i | \(0.0292368\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.00000 | − | 10.3923i | −0.0759737 | − | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.50000 | − | 12.9904i | −0.284083 | − | 0.492046i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −44.0000 | −1.66423 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.0000 | − | 13.8564i | 0.601742 | − | 0.521124i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000 | − | 6.92820i | 0.150223 | − | 0.260194i | −0.781086 | − | 0.624423i | \(-0.785334\pi\) |
0.931309 | + | 0.364229i | \(0.118667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.50000 | − | 7.79423i | −0.168763 | − | 0.292306i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.0000 | −1.01116 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.0000 | + | 19.0526i | 0.410803 | + | 0.711531i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.5000 | + | 25.1147i | −0.540759 | + | 0.936622i | 0.458102 | + | 0.888900i | \(0.348529\pi\) |
−0.998861 | + | 0.0477220i | \(0.984804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.5000 | − | 12.9904i | −1.39657 | − | 0.483787i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.0000 | − | 31.1769i | 0.669427 | − | 1.15948i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.0000 | −1.07555 | −0.537775 | − | 0.843088i | \(-0.680735\pi\) | ||||
−0.537775 | + | 0.843088i | \(0.680735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.00000 | − | 15.5885i | −0.332877 | − | 0.576560i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.00000 | − | 12.1244i | 0.258551 | − | 0.447823i | −0.707303 | − | 0.706910i | \(-0.750088\pi\) |
0.965854 | + | 0.259087i | \(0.0834217\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.0000 | − | 48.4974i | 1.03139 | − | 1.78643i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.00000 | + | 13.8564i | 0.294285 | + | 0.509716i | 0.974818 | − | 0.223001i | \(-0.0715853\pi\) |
−0.680534 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.0000 | 0.990534 | 0.495267 | − | 0.868741i | \(-0.335070\pi\) | ||||
0.495267 | + | 0.868741i | \(0.335070\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.00000 | + | 5.19615i | −0.109764 | + | 0.190117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.0000 | − | 6.92820i | −0.730784 | − | 0.253151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | − | 27.7128i | 0.583848 | − | 1.01125i | −0.411170 | − | 0.911559i | \(-0.634880\pi\) |
0.995018 | − | 0.0996961i | \(-0.0317870\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.0000 | − | 27.7128i | −0.583072 | − | 1.00991i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0000 | 1.23575 | 0.617876 | − | 0.786276i | \(-0.287994\pi\) | ||||
0.617876 | + | 0.786276i | \(0.287994\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.0000 | − | 20.7846i | −0.435572 | − | 0.754434i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.5000 | − | 37.2391i | 0.779374 | − | 1.34992i | −0.152928 | − | 0.988237i | \(-0.548870\pi\) |
0.932303 | − | 0.361679i | \(-0.117796\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.0000 | − | 24.2487i | 1.01367 | − | 0.877862i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.00000 | − | 13.8564i | −0.288863 | − | 0.500326i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.0000 | 1.29651 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.0000 | − | 17.3205i | −0.359675 | − | 0.622975i | 0.628231 | − | 0.778027i | \(-0.283779\pi\) |
−0.987906 | + | 0.155051i | \(0.950446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.0000 | − | 38.1051i | −0.787222 | − | 1.36351i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.0000 | −0.857690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.00000 | + | 6.92820i | 0.142585 | + | 0.246964i | 0.928469 | − | 0.371409i | \(-0.121125\pi\) |
−0.785885 | + | 0.618373i | \(0.787792\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.00000 | − | 5.19615i | 0.106803 | − | 0.184988i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.50000 | + | 38.9711i | 0.266669 | + | 1.38565i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | + | 13.8564i | −0.284088 | + | 0.492055i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.00000 | −0.283375 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.0000 | −0.955191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.50000 | − | 9.52628i | −0.194333 | − | 0.336595i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.00000 | + | 6.92820i | −0.141157 | + | 0.244491i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.00000 | + | 3.46410i | −0.0704033 | + | 0.121942i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.00000 | − | 8.66025i | −0.175791 | − | 0.304478i | 0.764644 | − | 0.644453i | \(-0.222915\pi\) |
−0.940435 | + | 0.339975i | \(0.889582\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.0000 | −0.351147 | −0.175574 | − | 0.984466i | \(-0.556178\pi\) | ||||
−0.175574 | + | 0.984466i | \(0.556178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.0000 | −0.491001 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.00000 | + | 1.73205i | 0.174714 | + | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0000 | + | 17.3205i | −0.349002 | + | 0.604490i | −0.986073 | − | 0.166316i | \(-0.946813\pi\) |
0.637070 | + | 0.770806i | \(0.280146\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.00000 | − | 3.46410i | −0.0697156 | − | 0.120751i | 0.829060 | − | 0.559159i | \(-0.188876\pi\) |
−0.898776 | + | 0.438408i | \(0.855543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.0000 | −0.486828 | −0.243414 | − | 0.969923i | \(-0.578267\pi\) | ||||
−0.243414 | + | 0.969923i | \(0.578267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.0000 | + | 27.7128i | 0.555703 | + | 0.962506i | 0.997848 | + | 0.0655624i | \(0.0208842\pi\) |
−0.442145 | + | 0.896943i | \(0.645783\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.00000 | + | 13.8564i | −0.277517 | + | 0.480673i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.5000 | + | 12.9904i | 0.571691 | + | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.0000 | − | 31.1769i | −0.622171 | − | 1.07763i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.0000 | −1.00119 | −0.500596 | − | 0.865681i | \(-0.666886\pi\) | ||||
−0.500596 | + | 0.865681i | \(0.666886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.0000 | − | 22.5167i | −0.447744 | − | 0.775515i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.5000 | + | 4.33013i | 0.429505 | + | 0.148785i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.00000 | + | 3.46410i | −0.0686398 | + | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.0000 | 1.30110 | 0.650548 | − | 0.759465i | \(-0.274539\pi\) | ||||
0.650548 | + | 0.759465i | \(0.274539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.0000 | + | 19.0526i | 0.375753 | + | 0.650823i | 0.990439 | − | 0.137948i | \(-0.0440508\pi\) |
−0.614687 | + | 0.788771i | \(0.710717\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0000 | + | 17.3205i | −0.341196 | + | 0.590968i | −0.984655 | − | 0.174512i | \(-0.944165\pi\) |
0.643459 | + | 0.765480i | \(0.277499\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0000 | − | 17.3205i | 0.681598 | − | 0.590281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.50000 | + | 6.06218i | −0.119141 | + | 0.206359i | −0.919428 | − | 0.393259i | \(-0.871348\pi\) |
0.800286 | + | 0.599618i | \(0.204681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.0000 | 0.543388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.0000 | 1.22122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.0000 | + | 24.2487i | 0.474372 | + | 0.821636i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.50000 | + | 9.52628i | −0.186147 | + | 0.322416i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.00000 | + | 3.46410i | −0.0675352 | + | 0.116974i | −0.897816 | − | 0.440371i | \(-0.854847\pi\) |
0.830281 | + | 0.557346i | \(0.188180\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.0000 | − | 24.2487i | −0.472208 | − | 0.817889i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.0000 | −1.24656 | −0.623281 | − | 0.781998i | \(-0.714201\pi\) | ||||
−0.623281 | + | 0.781998i | \(0.714201\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.0000 | + | 17.3205i | −0.335767 | + | 0.581566i | −0.983632 | − | 0.180190i | \(-0.942329\pi\) |
0.647865 | + | 0.761755i | \(0.275662\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.00000 | + | 20.7846i | 0.134156 | + | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.0000 | − | 38.1051i | 0.737028 | − | 1.27657i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.0000 | + | 46.7654i | 0.900500 | + | 1.55971i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | + | 15.5885i | −0.299833 | + | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.0000 | − | 20.7846i | 0.798670 | − | 0.691669i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.00000 | − | 10.3923i | −0.199227 | − | 0.345071i | 0.749051 | − | 0.662512i | \(-0.230510\pi\) |
−0.948278 | + | 0.317441i | \(0.897176\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.0000 | 1.55718 | 0.778590 | − | 0.627533i | \(-0.215935\pi\) | ||||
0.778590 | + | 0.627533i | \(0.215935\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | − | 20.7846i | −0.397142 | − | 0.687870i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.0000 | + | 10.3923i | 0.990687 | + | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.50000 | + | 6.06218i | −0.115454 | + | 0.199973i | −0.917961 | − | 0.396670i | \(-0.870166\pi\) |
0.802507 | + | 0.596643i | \(0.203499\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.0000 | + | 41.5692i | 0.790827 | + | 1.36975i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.0000 | 0.724139 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.50000 | + | 12.9904i | 0.246332 | + | 0.426660i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.00000 | − | 5.19615i | 0.0984268 | − | 0.170480i | −0.812607 | − | 0.582812i | \(-0.801952\pi\) |
0.911034 | + | 0.412332i | \(0.135286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.00000 | − | 1.73205i | 0.0327385 | − | 0.0567048i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −62.0000 | −2.02329 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.0000 | + | 22.5167i | 0.423788 | + | 0.734022i | 0.996306 | − | 0.0858697i | \(-0.0273669\pi\) |
−0.572518 | + | 0.819892i | \(0.694034\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.50000 | − | 12.9904i | 0.244234 | − | 0.423025i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.00000 | + | 3.46410i | −0.0649913 | + | 0.112568i | −0.896690 | − | 0.442659i | \(-0.854035\pi\) |
0.831699 | + | 0.555227i | \(0.187369\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.00000 | − | 3.46410i | −0.0649227 | − | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.0000 | 0.323932 | 0.161966 | − | 0.986796i | \(-0.448217\pi\) | ||||
0.161966 | + | 0.986796i | \(0.448217\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.0000 | + | 41.5692i | −0.775810 | + | 1.34374i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.0000 | − | 29.4449i | 1.09792 | − | 0.950824i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0000 | + | 43.3013i | −0.806452 | + | 1.39682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000 | + | 6.92820i | 0.128898 | + | 0.223258i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0000 | −0.418052 | −0.209026 | − | 0.977910i | \(-0.567029\pi\) | ||||
−0.209026 | + | 0.977910i | \(0.567029\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.0000 | + | 19.0526i | −0.353007 | + | 0.611426i | −0.986775 | − | 0.162098i | \(-0.948174\pi\) |
0.633768 | + | 0.773523i | \(0.281507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.00000 | + | 15.5885i | 0.0961756 | + | 0.499743i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.50000 | − | 2.59808i | −0.0479893 | − | 0.0831198i | 0.841033 | − | 0.540984i | \(-0.181948\pi\) |
−0.889022 | + | 0.457864i | \(0.848615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.0000 | 1.40625 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0000 | −0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.0000 | + | 41.5692i | 0.765481 | + | 1.32585i | 0.939992 | + | 0.341197i | \(0.110832\pi\) |
−0.174511 | + | 0.984655i | \(0.555834\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.00000 | − | 46.7654i | −0.286473 | − | 1.48856i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.00000 | − | 15.5885i | 0.286183 | − | 0.495684i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.5000 | + | 26.8468i | 0.492374 | + | 0.852816i | 0.999961 | − | 0.00878379i | \(-0.00279600\pi\) |
−0.507588 | + | 0.861600i | \(0.669463\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.0000 | + | 38.1051i | 0.696747 | + | 1.20680i | 0.969588 | + | 0.244742i | \(0.0787033\pi\) |
−0.272841 | + | 0.962059i | \(0.587963\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1400.2.q.f.401.1 | yes | 2 | |
5.2 | odd | 4 | 1400.2.bh.d.849.2 | 4 | |||
5.3 | odd | 4 | 1400.2.bh.d.849.1 | 4 | |||
5.4 | even | 2 | 1400.2.q.b.401.1 | ✓ | 2 | ||
7.2 | even | 3 | 9800.2.a.j.1.1 | 1 | |||
7.4 | even | 3 | inner | 1400.2.q.f.1201.1 | yes | 2 | |
7.5 | odd | 6 | 9800.2.a.bl.1.1 | 1 | |||
35.4 | even | 6 | 1400.2.q.b.1201.1 | yes | 2 | ||
35.9 | even | 6 | 9800.2.a.bm.1.1 | 1 | |||
35.18 | odd | 12 | 1400.2.bh.d.249.2 | 4 | |||
35.19 | odd | 6 | 9800.2.a.k.1.1 | 1 | |||
35.32 | odd | 12 | 1400.2.bh.d.249.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.q.b.401.1 | ✓ | 2 | 5.4 | even | 2 | ||
1400.2.q.b.1201.1 | yes | 2 | 35.4 | even | 6 | ||
1400.2.q.f.401.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1400.2.q.f.1201.1 | yes | 2 | 7.4 | even | 3 | inner | |
1400.2.bh.d.249.1 | 4 | 35.32 | odd | 12 | |||
1400.2.bh.d.249.2 | 4 | 35.18 | odd | 12 | |||
1400.2.bh.d.849.1 | 4 | 5.3 | odd | 4 | |||
1400.2.bh.d.849.2 | 4 | 5.2 | odd | 4 | |||
9800.2.a.j.1.1 | 1 | 7.2 | even | 3 | |||
9800.2.a.k.1.1 | 1 | 35.19 | odd | 6 | |||
9800.2.a.bl.1.1 | 1 | 7.5 | odd | 6 | |||
9800.2.a.bm.1.1 | 1 | 35.9 | even | 6 |