Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(249,1400)]
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, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.bh (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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 849.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.849 |
Dual form | 1400.2.bh.d.249.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 1.73205 | − | 1.00000i | 1.00000 | − | 0.577350i | 0.0917517 | − | 0.995782i | \(-0.470753\pi\) |
0.908248 | + | 0.418432i | \(0.137420\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59808 | − | 0.500000i | 0.981981 | − | 0.188982i | ||||
\(8\) | 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 | ||||||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.59808 | − | 1.50000i | 0.630126 | − | 0.363803i | −0.150675 | − | 0.988583i | \(-0.548145\pi\) |
0.780801 | + | 0.624780i | \(0.214811\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | −2.59808 | − | 1.50000i | −0.541736 | − | 0.312772i | 0.204046 | − | 0.978961i | \(-0.434591\pi\) |
−0.745782 | + | 0.666190i | \(0.767924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | −6.92820 | − | 4.00000i | −1.20605 | − | 0.696311i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | − | 6.00000i | − | 0.914991i | −0.889212 | − | 0.457496i | \(-0.848747\pi\) | ||
0.889212 | − | 0.457496i | \(-0.151253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.79423 | + | 4.50000i | 1.13691 | + | 0.656392i | 0.945662 | − | 0.325150i | \(-0.105415\pi\) |
0.191243 | + | 0.981543i | \(0.438748\pi\) | |||||||
\(48\) | 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 | ||||||||
\(53\) | −5.19615 | + | 3.00000i | −0.713746 | + | 0.412082i | −0.812447 | − | 0.583036i | \(-0.801865\pi\) |
0.0987002 | + | 0.995117i | \(0.468532\pi\) | |||||||
\(54\) | 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 | \(0.00768307\pi\) |
−0.478953 | + | 0.877841i | \(0.658984\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 0.866025 | − | 2.50000i | 0.109109 | − | 0.314970i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.1244 | + | 7.00000i | −1.48123 | + | 0.855186i | −0.999773 | − | 0.0212861i | \(-0.993224\pi\) |
−0.481452 | + | 0.876472i | \(0.659891\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −1.73205 | + | 1.00000i | −0.202721 | + | 0.117041i | −0.597924 | − | 0.801553i | \(-0.704008\pi\) |
0.395203 | + | 0.918594i | \(0.370674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.92820 | − | 8.00000i | −0.789542 | − | 0.911685i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50000 | − | 7.79423i | 0.506290 | − | 0.876919i | −0.493684 | − | 0.869641i | \(-0.664350\pi\) |
0.999974 | − | 0.00727784i | \(-0.00231663\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.3923 | − | 6.00000i | 1.11417 | − | 0.643268i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.50000 | − | 9.52628i | 0.582999 | − | 1.00978i | −0.412123 | − | 0.911128i | \(-0.635213\pi\) |
0.995122 | − | 0.0986553i | \(-0.0314541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | − | 5.19615i | −0.104828 | − | 0.544705i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.5885 | − | 9.00000i | −1.61645 | − | 0.933257i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0000i | 1.11688i | 0.829545 | + | 0.558440i | \(0.188600\pi\) | ||||
−0.829545 | + | 0.558440i | \(0.811400\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | −12.9904 | − | 7.50000i | −1.27998 | − | 0.738997i | −0.303136 | − | 0.952947i | \(-0.598034\pi\) |
−0.976845 | + | 0.213950i | \(0.931367\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92820 | + | 4.00000i | 0.669775 | + | 0.386695i | 0.795991 | − | 0.605308i | \(-0.206950\pi\) |
−0.126217 | + | 0.992003i | \(0.540283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | − | 12.1244i | −0.670478 | − | 1.16130i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) |
0.307290 | − | 0.951616i | \(-0.400578\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.0000i | 1.41108i | 0.708669 | + | 0.705541i | \(0.249296\pi\) | ||||
−0.708669 | + | 0.705541i | \(0.750704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.73205 | − | 1.00000i | −0.160128 | − | 0.0924500i | ||||
\(118\) | 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 | ||||||||
\(123\) | 8.66025 | − | 5.00000i | 0.780869 | − | 0.450835i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 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 | ||||||||
\(137\) | −14.7224 | + | 8.50000i | −1.25782 | + | 0.726204i | −0.972651 | − | 0.232273i | \(-0.925384\pi\) |
−0.285171 | + | 0.958477i | \(0.592051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.00000 | 0.508913 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.0000 | 1.51587 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.92820 | + | 4.00000i | −0.579365 | + | 0.334497i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.66025 | − | 11.0000i | 0.714286 | − | 0.907265i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.0000 | + | 17.3205i | −0.819232 | + | 1.41895i | 0.0870170 | + | 0.996207i | \(0.472267\pi\) |
−0.906249 | + | 0.422744i | \(0.861067\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | − | 3.00000i | − | 0.242536i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.66025 | + | 5.00000i | −0.691164 | + | 0.399043i | −0.804048 | − | 0.594565i | \(-0.797324\pi\) |
0.112884 | + | 0.993608i | \(0.463991\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | 20.7846 | + | 12.0000i | 1.62798 | + | 0.939913i | 0.984696 | + | 0.174282i | \(0.0557604\pi\) |
0.643280 | + | 0.765631i | \(0.277573\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8564 | − | 8.00000i | −1.05348 | − | 0.608229i | −0.129861 | − | 0.991532i | \(-0.541453\pi\) |
−0.923622 | + | 0.383304i | \(0.874786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.8564 | + | 8.00000i | 1.04151 | + | 0.601317i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000 | + | 3.46410i | 0.149487 | + | 0.258919i | 0.931038 | − | 0.364922i | \(-0.118904\pi\) |
−0.781551 | + | 0.623841i | \(0.785571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.00000 | −0.594635 | −0.297318 | − | 0.954779i | \(-0.596092\pi\) | ||||
−0.297318 | + | 0.954779i | \(0.596092\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.0000i | 1.18275i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.3923 | − | 6.00000i | −0.759961 | − | 0.438763i | ||||
\(188\) | 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 | ||||||||
\(193\) | 4.33013 | − | 2.50000i | 0.311689 | − | 0.179954i | −0.335993 | − | 0.941865i | \(-0.609072\pi\) |
0.647682 | + | 0.761911i | \(0.275738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5000 | + | 18.1865i | 0.744325 | + | 1.28921i | 0.950509 | + | 0.310696i | \(0.100562\pi\) |
−0.206184 | + | 0.978513i | \(0.566105\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.0000 | + | 24.2487i | −0.987484 | + | 1.71037i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.5885 | − | 3.00000i | 1.09410 | − | 0.210559i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.59808 | + | 1.50000i | −0.180579 | + | 0.104257i | ||||
\(208\) | 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 | ||||||||
\(213\) | 19.0526 | − | 11.0000i | 1.30546 | − | 0.753708i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.5885 | − | 18.0000i | −1.05821 | − | 1.22192i | ||||
\(218\) | 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 | ||||||||
\(223\) | 11.0000i | 0.736614i | 0.929704 | + | 0.368307i | \(0.120063\pi\) | ||||
−0.929704 | + | 0.368307i | \(0.879937\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.0526 | − | 11.0000i | 1.26456 | − | 0.730096i | 0.290609 | − | 0.956842i | \(-0.406142\pi\) |
0.973954 | + | 0.226746i | \(0.0728088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.00000 | + | 6.92820i | −0.264327 | + | 0.457829i | −0.967387 | − | 0.253302i | \(-0.918483\pi\) |
0.703060 | + | 0.711131i | \(0.251817\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −20.0000 | − | 6.92820i | −1.31590 | − | 0.455842i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.0526 | + | 11.0000i | 1.24817 | + | 0.720634i | 0.970745 | − | 0.240112i | \(-0.0771842\pi\) |
0.277429 | + | 0.960746i | \(0.410518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 18.0000i | − | 1.16923i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0000 | −0.711531 | −0.355765 | − | 0.934575i | \(-0.615780\pi\) | ||||
−0.355765 | + | 0.934575i | \(0.615780\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 8.66025 | + | 5.00000i | 0.555556 | + | 0.320750i | ||||
\(244\) | 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 | ||||||||
\(253\) | 12.0000i | 0.754434i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.5885 | + | 9.00000i | 0.972381 | + | 0.561405i | 0.899961 | − | 0.435970i | \(-0.143595\pi\) |
0.0724199 | + | 0.997374i | \(0.476928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.59808 | + | 1.50000i | −0.160204 | + | 0.0924940i | −0.577959 | − | 0.816066i | \(-0.696151\pi\) |
0.417755 | + | 0.908560i | \(0.362817\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 22.0000i | − | 1.34638i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.00000 | − | 1.73205i | −0.0609711 | − | 0.105605i | 0.833929 | − | 0.551872i | \(-0.186086\pi\) |
−0.894900 | + | 0.446267i | \(0.852753\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | −6.92820 | − | 8.00000i | −0.419314 | − | 0.484182i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.92820 | + | 4.00000i | −0.416275 | + | 0.240337i | −0.693482 | − | 0.720473i | \(-0.743925\pi\) |
0.277207 | + | 0.960810i | \(0.410591\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 1.73205 | − | 1.00000i | 0.102960 | − | 0.0594438i | −0.447636 | − | 0.894216i | \(-0.647734\pi\) |
0.550596 | + | 0.834772i | \(0.314401\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.9904 | − | 2.50000i | 0.766798 | − | 0.147570i | ||||
\(288\) | 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 | ||||||||
\(293\) | 14.0000i | 0.817889i | 0.912559 | + | 0.408944i | \(0.134103\pi\) | ||||
−0.912559 | + | 0.408944i | \(0.865897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.8564 | − | 8.00000i | 0.804030 | − | 0.464207i | ||||
\(298\) | 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 | ||||||||
\(303\) | 13.8564 | + | 8.00000i | 0.796030 | + | 0.459588i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.0000i | 1.36975i | 0.728659 | + | 0.684876i | \(0.240144\pi\) | ||||
−0.728659 | + | 0.684876i | \(0.759856\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 26.8468 | + | 15.5000i | 1.51747 | + | 0.876112i | 0.999789 | + | 0.0205381i | \(0.00653795\pi\) |
0.517681 | + | 0.855574i | \(0.326795\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.3923 | − | 6.00000i | −0.583690 | − | 0.336994i | 0.178908 | − | 0.983866i | \(-0.442743\pi\) |
−0.762598 | + | 0.646872i | \(0.776077\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | −24.2487 | − | 14.0000i | −1.34096 | − | 0.774202i | ||||
\(328\) | 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 | ||||||||
\(337\) | 29.0000i | 1.57973i | 0.613280 | + | 0.789865i | \(0.289850\pi\) | ||||
−0.613280 | + | 0.789865i | \(0.710150\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.73205 | + | 1.00000i | −0.0929814 | + | 0.0536828i | −0.545770 | − | 0.837935i | \(-0.683763\pi\) |
0.452788 | + | 0.891618i | \(0.350429\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.00000 | 0.427008 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9904 | − | 7.50000i | 0.691408 | − | 0.399185i | −0.112731 | − | 0.993626i | \(-0.535960\pi\) |
0.804139 | + | 0.594441i | \(0.202627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.19615 | − | 15.0000i | 0.275010 | − | 0.793884i | ||||
\(358\) | 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 | ||||||||
\(363\) | 10.0000i | 0.524864i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.8564 | + | 8.00000i | −0.723299 | + | 0.417597i | −0.815966 | − | 0.578101i | \(-0.803794\pi\) |
0.0926670 | + | 0.995697i | \(0.470461\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | −5.19615 | − | 3.00000i | −0.269047 | − | 0.155334i | 0.359408 | − | 0.933181i | \(-0.382979\pi\) |
−0.628454 | + | 0.777847i | \(0.716312\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.00000 | − | 13.8564i | −0.409852 | − | 0.709885i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.1865 | − | 10.5000i | −0.929288 | − | 0.536525i | −0.0427020 | − | 0.999088i | \(-0.513597\pi\) |
−0.886586 | + | 0.462563i | \(0.846930\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.19615 | − | 3.00000i | −0.264135 | − | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.0000 | + | 29.4449i | 0.861934 | + | 1.49291i | 0.870059 | + | 0.492947i | \(0.164080\pi\) |
−0.00812520 | + | 0.999967i | \(0.502586\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.0000i | 1.21064i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.9090 | − | 19.0000i | −1.65165 | − | 0.953583i | −0.976392 | − | 0.216004i | \(-0.930698\pi\) |
−0.675261 | − | 0.737579i | \(-0.735969\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | −15.5885 | + | 9.00000i | −0.776516 | + | 0.448322i | ||||
\(404\) | 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 | \(-0.888700\pi\) |
0.173064 | − | 0.984911i | \(-0.444633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.0000 | + | 29.4449i | −0.838548 | + | 1.45241i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.8564 | + | 16.0000i | 0.681829 | + | 0.787309i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.3923 | − | 6.00000i | 0.508913 | − | 0.293821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0000 | −1.46560 | −0.732798 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732798 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.79423 | − | 4.50000i | 0.378968 | − | 0.218797i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.92820 | + | 20.0000i | −0.335279 | + | 0.967868i | ||||
\(428\) | 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 | ||||||||
\(433\) | 21.0000i | 1.00920i | 0.863355 | + | 0.504598i | \(0.168359\pi\) | ||||
−0.863355 | + | 0.504598i | \(0.831641\pi\) | |||||||
\(434\) | 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 | \(-0.518668\pi\) |
0.893843 | − | 0.448379i | \(-0.147999\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3923 | − | 6.00000i | −0.493753 | − | 0.285069i | 0.232377 | − | 0.972626i | \(-0.425350\pi\) |
−0.726130 | + | 0.687557i | \(0.758683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 40.0000i | 1.89194i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.0000 | 1.27421 | 0.637104 | − | 0.770778i | \(-0.280132\pi\) | ||||
0.637104 | + | 0.770778i | \(0.280132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0000 | − | 17.3205i | −0.470882 | − | 0.815591i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −34.6410 | − | 20.0000i | −1.62758 | − | 0.939682i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.73205 | + | 1.00000i | 0.0810219 | + | 0.0467780i | 0.539964 | − | 0.841688i | \(-0.318438\pi\) |
−0.458942 | + | 0.888466i | \(0.651771\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 11.0000i | 0.511213i | 0.966781 | + | 0.255607i | \(0.0822752\pi\) | ||||
−0.966781 | + | 0.255607i | \(0.917725\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.9808 | − | 15.0000i | −1.20225 | − | 0.694117i | −0.241192 | − | 0.970477i | \(-0.577538\pi\) |
−0.961054 | + | 0.276360i | \(0.910872\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | −20.7846 | + | 12.0000i | −0.955677 | + | 0.551761i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000i | 0.274721i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.50000 | + | 7.79423i | 0.205610 | + | 0.356127i | 0.950327 | − | 0.311253i | \(-0.100749\pi\) |
−0.744717 | + | 0.667381i | \(0.767415\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.5885 | + | 3.00000i | −0.709299 | + | 0.136505i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.9186 | + | 11.5000i | −0.902597 | + | 0.521115i | −0.878042 | − | 0.478584i | \(-0.841150\pi\) |
−0.0245553 | + | 0.999698i | \(0.507817\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 15.5885 | − | 9.00000i | 0.702069 | − | 0.405340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.5788 | − | 5.50000i | 1.28194 | − | 0.246709i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.0000 | − | 32.9090i | 0.850557 | − | 1.47321i | −0.0301498 | − | 0.999545i | \(-0.509598\pi\) |
0.880707 | − | 0.473662i | \(-0.157068\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 16.0000i | − | 0.713405i | −0.934218 | − | 0.356702i | \(-0.883901\pi\) | ||
0.934218 | − | 0.356702i | \(-0.116099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.5885 | − | 9.00000i | 0.692308 | − | 0.399704i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.00000 | − | 10.3923i | 0.265945 | − | 0.460631i | −0.701866 | − | 0.712309i | \(-0.747649\pi\) |
0.967811 | + | 0.251679i | \(0.0809826\pi\) | |||||||
\(510\) | 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 | ||||||||
\(517\) | − | 36.0000i | − | 1.58328i | ||||||
\(518\) | 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 | ||||||||
\(523\) | −19.0526 | − | 11.0000i | −0.833110 | − | 0.480996i | 0.0218062 | − | 0.999762i | \(-0.493058\pi\) |
−0.854916 | + | 0.518766i | \(0.826392\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.3827 | − | 13.5000i | −1.01857 | − | 0.588069i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.0000i | − | 0.433148i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.92820 | + | 4.00000i | 0.298974 | + | 0.172613i | ||||
\(538\) | 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 | ||||||||
\(543\) | −13.8564 | + | 8.00000i | −0.594635 | + | 0.343313i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.0000i | 1.71028i | 0.518400 | + | 0.855138i | \(0.326528\pi\) | ||||
−0.518400 | + | 0.855138i | \(0.673472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.00000 | + | 6.92820i | 0.170716 | + | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.79423 | − | 22.5000i | 0.331444 | − | 0.956797i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.1769 | − | 18.0000i | 1.32101 | − | 0.762684i | 0.337119 | − | 0.941462i | \(-0.390548\pi\) |
0.983890 | + | 0.178778i | \(0.0572143\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.5167 | + | 13.0000i | −0.948964 | + | 0.547885i | −0.892759 | − | 0.450535i | \(-0.851233\pi\) |
−0.0562051 | + | 0.998419i | \(0.517900\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.0526 | + | 22.0000i | 0.800132 | + | 0.923913i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.50000 | + | 9.52628i | −0.230572 | + | 0.399362i | −0.957977 | − | 0.286846i | \(-0.907393\pi\) |
0.727405 | + | 0.686209i | \(0.240726\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | − | 26.0000i | − | 1.08617i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.1244 | + | 7.00000i | −0.504744 | + | 0.291414i | −0.730670 | − | 0.682730i | \(-0.760792\pi\) |
0.225927 | + | 0.974144i | \(0.427459\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | 20.7846 | + | 12.0000i | 0.860811 | + | 0.496989i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.00000i | − | 0.330195i | −0.986277 | − | 0.165098i | \(-0.947206\pi\) | ||
0.986277 | − | 0.165098i | \(-0.0527939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | + | 31.1769i | 0.740421 | + | 1.28245i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.2583 | + | 6.50000i | 0.462324 | + | 0.266923i | 0.713021 | − | 0.701143i | \(-0.247326\pi\) |
−0.250697 | + | 0.968066i | \(0.580660\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.3731 | + | 21.0000i | 1.48865 | + | 0.859473i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.50000 | + | 7.79423i | 0.183865 | + | 0.318464i | 0.943193 | − | 0.332244i | \(-0.107806\pi\) |
−0.759328 | + | 0.650708i | \(0.774472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0000i | 0.570124i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2583 | − | 6.50000i | −0.456962 | − | 0.263827i | 0.253804 | − | 0.967256i | \(-0.418318\pi\) |
−0.710766 | + | 0.703429i | \(0.751651\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | 22.5167 | − | 13.0000i | 0.909439 | − | 0.525065i | 0.0291886 | − | 0.999574i | \(-0.490708\pi\) |
0.880251 | + | 0.474509i | \(0.157374\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.0000i | 0.684394i | 0.939628 | + | 0.342197i | \(0.111171\pi\) | ||||
−0.939628 | + | 0.342197i | \(0.888829\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.00000 | − | 8.66025i | −0.200967 | − | 0.348085i | 0.747873 | − | 0.663842i | \(-0.231075\pi\) |
−0.948840 | + | 0.315757i | \(0.897742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.00000 | − | 10.3923i | 0.240772 | − | 0.417029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.52628 | − | 27.5000i | 0.381662 | − | 1.10176i | ||||
\(624\) | 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 | ||||||||
\(633\) | 38.1051 | − | 22.0000i | 1.51454 | − | 0.874421i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.19615 | − | 13.0000i | −0.205879 | − | 0.515079i | ||||
\(638\) | 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 | ||||||||
\(643\) | − | 16.0000i | − | 0.630978i | −0.948929 | − | 0.315489i | \(-0.897831\pi\) | ||
0.948929 | − | 0.315489i | \(-0.102169\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.5692 | − | 24.0000i | 1.63425 | − | 0.943537i | 0.651494 | − | 0.758654i | \(-0.274142\pi\) |
0.982760 | − | 0.184884i | \(-0.0591909\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | −25.9808 | − | 15.0000i | −1.01671 | − | 0.586995i | −0.103558 | − | 0.994623i | \(-0.533023\pi\) |
−0.913148 | + | 0.407628i | \(0.866356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000i | 0.0780274i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.0000 | −0.545363 | −0.272681 | − | 0.962104i | \(-0.587910\pi\) | ||||
−0.272681 | + | 0.962104i | \(0.587910\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −10.3923 | − | 6.00000i | −0.403604 | − | 0.233021i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.5885 | − | 9.00000i | −0.603587 | − | 0.348481i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.0000 | + | 19.0526i | 0.425285 | + | 0.736614i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.0000 | 1.23535 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 43.0000i | − | 1.65753i | −0.559598 | − | 0.828764i | \(-0.689045\pi\) | ||
0.559598 | − | 0.828764i | \(-0.310955\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.19615 | − | 3.00000i | −0.199704 | − | 0.115299i | 0.396813 | − | 0.917899i | \(-0.370116\pi\) |
−0.596518 | + | 0.802600i | \(0.703449\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | −12.1244 | + | 7.00000i | −0.463926 | + | 0.267848i | −0.713693 | − | 0.700458i | \(-0.752979\pi\) |
0.249768 | + | 0.968306i | \(0.419646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.0000i | 0.610438i | ||||||||
\(688\) | 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 | ||||||||
\(693\) | −10.3923 | + | 2.00000i | −0.394771 | + | 0.0759737i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.9904 | − | 7.50000i | 0.492046 | − | 0.284083i | ||||
\(698\) | 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 | ||||||||
\(707\) | 13.8564 | + | 16.0000i | 0.521124 | + | 0.601742i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | + | 6.92820i | −0.150223 | + | 0.260194i | −0.931309 | − | 0.364229i | \(-0.881333\pi\) |
0.781086 | + | 0.624423i | \(0.214666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.50000 | − | 7.79423i | −0.168763 | − | 0.292306i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.0000i | 1.01116i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.0526 | + | 11.0000i | −0.711531 | + | 0.410803i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.5000 | − | 25.1147i | 0.540759 | − | 0.936622i | −0.458102 | − | 0.888900i | \(-0.651471\pi\) |
0.998861 | − | 0.0477220i | \(-0.0151961\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.5000 | − | 12.9904i | −1.39657 | − | 0.483787i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −31.1769 | − | 18.0000i | −1.15948 | − | 0.669427i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 29.0000i | − | 1.07555i | −0.843088 | − | 0.537775i | \(-0.819265\pi\) | ||
0.843088 | − | 0.537775i | \(-0.180735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.00000 | − | 15.5885i | −0.332877 | − | 0.576560i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.1244 | − | 7.00000i | −0.447823 | − | 0.258551i | 0.259087 | − | 0.965854i | \(-0.416578\pi\) |
−0.706910 | + | 0.707303i | \(0.749912\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.4974 | + | 28.0000i | 1.78643 | + | 1.03139i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.00000 | − | 13.8564i | −0.294285 | − | 0.509716i | 0.680534 | − | 0.732717i | \(-0.261748\pi\) |
−0.974818 | + | 0.223001i | \(0.928415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27.0000i | − | 0.990534i | −0.868741 | − | 0.495267i | \(-0.835070\pi\) | ||
0.868741 | − | 0.495267i | \(-0.164930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.19615 | − | 3.00000i | −0.190117 | − | 0.109764i | ||||
\(748\) | 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 | ||||||||
\(753\) | −27.7128 | + | 16.0000i | −1.00991 | + | 0.583072i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0000i | 1.23575i | 0.786276 | + | 0.617876i | \(0.212006\pi\) | ||||
−0.786276 | + | 0.617876i | \(0.787994\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −24.2487 | − | 28.0000i | −0.877862 | − | 1.01367i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.8564 | − | 8.00000i | 0.500326 | − | 0.288863i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.0000 | 1.29651 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.3205 | + | 10.0000i | −0.622975 | + | 0.359675i | −0.778027 | − | 0.628231i | \(-0.783779\pi\) |
0.155051 | + | 0.987906i | \(0.450446\pi\) | |||||||
\(774\) | 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 | ||||||||
\(783\) | 24.0000i | 0.857690i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.92820 | + | 4.00000i | −0.246964 | + | 0.142585i | −0.618373 | − | 0.785885i | \(-0.712208\pi\) |
0.371409 | + | 0.928469i | \(0.378875\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | 13.8564 | + | 8.00000i | 0.492055 | + | 0.284088i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 8.00000i | − | 0.283375i | −0.989911 | − | 0.141687i | \(-0.954747\pi\) | ||
0.989911 | − | 0.141687i | \(-0.0452527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.0000 | 0.955191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.50000 | − | 9.52628i | −0.194333 | − | 0.336595i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.92820 | + | 4.00000i | 0.244491 | + | 0.141157i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.46410 | − | 2.00000i | −0.121942 | − | 0.0704033i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.00000 | + | 8.66025i | 0.175791 | + | 0.304478i | 0.940435 | − | 0.339975i | \(-0.110418\pi\) |
−0.764644 | + | 0.644453i | \(0.777085\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.0000 | −0.351147 | −0.175574 | − | 0.984466i | \(-0.556178\pi\) | ||||
−0.175574 | + | 0.984466i | \(0.556178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0000i | 0.491001i | ||||||||
\(814\) | 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 | ||||||||
\(823\) | −3.46410 | + | 2.00000i | −0.120751 | + | 0.0697156i | −0.559159 | − | 0.829060i | \(-0.688876\pi\) |
0.438408 | + | 0.898776i | \(0.355543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14.0000i | − | 0.486828i | −0.969923 | − | 0.243414i | \(-0.921733\pi\) | ||
0.969923 | − | 0.243414i | \(-0.0782673\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.0000 | − | 27.7128i | −0.555703 | − | 0.962506i | −0.997848 | − | 0.0655624i | \(-0.979116\pi\) |
0.442145 | − | 0.896943i | \(-0.354217\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.00000 | + | 13.8564i | −0.277517 | + | 0.480673i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.9904 | − | 16.5000i | 0.450090 | − | 0.571691i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.1769 | − | 18.0000i | 1.07763 | − | 0.622171i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.0000 | 1.00119 | 0.500596 | − | 0.865681i | \(-0.333114\pi\) | ||||
0.500596 | + | 0.865681i | \(0.333114\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.5167 | + | 13.0000i | −0.775515 | + | 0.447744i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.33013 | + | 12.5000i | −0.148785 | + | 0.429505i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.00000 | − | 3.46410i | 0.0686398 | − | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38.0000i | − | 1.30110i | −0.759465 | − | 0.650548i | \(-0.774539\pi\) | ||
0.759465 | − | 0.650548i | \(-0.225461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.0526 | + | 11.0000i | −0.650823 | + | 0.375753i | −0.788771 | − | 0.614687i | \(-0.789283\pi\) |
0.137948 | + | 0.990439i | \(0.455949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0000 | − | 17.3205i | 0.341196 | − | 0.590968i | −0.643459 | − | 0.765480i | \(-0.722501\pi\) |
0.984655 | + | 0.174512i | \(0.0558348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0000 | − | 17.3205i | 0.681598 | − | 0.590281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.06218 | + | 3.50000i | 0.206359 | + | 0.119141i | 0.599618 | − | 0.800286i | \(-0.295319\pi\) |
−0.393259 | + | 0.919428i | \(0.628652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.0000i | 0.543388i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.0000 | −1.22122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.0000 | + | 24.2487i | 0.474372 | + | 0.821636i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.52628 | + | 5.50000i | 0.322416 | + | 0.186147i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.46410 | − | 2.00000i | −0.116974 | − | 0.0675352i | 0.440371 | − | 0.897816i | \(-0.354847\pi\) |
−0.557346 | + | 0.830281i | \(0.688180\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 2.00000i | 0.0673054i | 0.999434 | + | 0.0336527i | \(0.0107140\pi\) | ||||
−0.999434 | + | 0.0336527i | \(0.989286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.3205 | − | 10.0000i | −0.581566 | − | 0.335767i | 0.180190 | − | 0.983632i | \(-0.442329\pi\) |
−0.761755 | + | 0.647865i | \(0.775662\pi\) | |||||||
\(888\) | 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 | ||||||||
\(897\) | 12.0000i | 0.400668i | ||||||||
\(898\) | 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 | ||||||||
\(903\) | −20.7846 | − | 24.0000i | −0.691669 | − | 0.798670i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.3923 | − | 6.00000i | 0.345071 | − | 0.199227i | −0.317441 | − | 0.948278i | \(-0.602824\pi\) |
0.662512 | + | 0.749051i | \(0.269490\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −20.7846 | + | 12.0000i | −0.687870 | + | 0.397142i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3923 | + | 30.0000i | −0.343184 | + | 0.990687i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.50000 | − | 6.06218i | 0.115454 | − | 0.199973i | −0.802507 | − | 0.596643i | \(-0.796501\pi\) |
0.917961 | + | 0.396670i | \(0.129834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.0000 | + | 41.5692i | 0.790827 | + | 1.36975i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 22.0000i | − | 0.724139i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.9904 | + | 7.50000i | −0.426660 | + | 0.246332i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.00000 | + | 5.19615i | −0.0984268 | + | 0.170480i | −0.911034 | − | 0.412332i | \(-0.864714\pi\) |
0.812607 | + | 0.582812i | \(0.198048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.73205 | − | 1.00000i | −0.0567048 | − | 0.0327385i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000i | 0.0653372i | 0.999466 | + | 0.0326686i | \(0.0104006\pi\) | ||||
−0.999466 | + | 0.0326686i | \(0.989599\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −12.9904 | − | 7.50000i | −0.423025 | − | 0.244234i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.46410 | − | 2.00000i | −0.112568 | − | 0.0649913i | 0.442659 | − | 0.896690i | \(-0.354035\pi\) |
−0.555227 | + | 0.831699i | \(0.687369\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.00000 | + | 3.46410i | 0.0649227 | + | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 10.0000i | − | 0.323932i | −0.986796 | − | 0.161966i | \(-0.948217\pi\) | ||
0.986796 | − | 0.161966i | \(-0.0517835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −41.5692 | − | 24.0000i | −1.34374 | − | 0.775810i | ||||
\(958\) | 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 | ||||||||
\(963\) | 6.92820 | − | 4.00000i | 0.223258 | − | 0.128898i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 13.0000i | − | 0.418052i | −0.977910 | − | 0.209026i | \(-0.932971\pi\) | ||
0.977910 | − | 0.209026i | \(-0.0670293\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | 15.5885 | − | 3.00000i | 0.499743 | − | 0.0961756i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.59808 | − | 1.50000i | 0.0831198 | − | 0.0479893i | −0.457864 | − | 0.889022i | \(-0.651385\pi\) |
0.540984 | + | 0.841033i | \(0.318052\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.0000 | −1.40625 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0000 | −0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.5692 | − | 24.0000i | 1.32585 | − | 0.765481i | 0.341197 | − | 0.939992i | \(-0.389168\pi\) |
0.984655 | + | 0.174511i | \(0.0558344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 46.7654 | − | 9.00000i | 1.48856 | − | 0.286473i | ||||
\(988\) | 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 | ||||||||
\(993\) | − | 4.00000i | − | 0.126936i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.1051 | + | 22.0000i | −1.20680 | + | 0.696747i | −0.962059 | − | 0.272841i | \(-0.912037\pi\) |
−0.244742 | + | 0.969588i | \(0.578703\pi\) | |||||||
\(998\) | 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.bh.d.849.2 | 4 | ||
5.2 | odd | 4 | 1400.2.q.b.401.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1400.2.q.f.401.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1400.2.bh.d.849.1 | 4 | ||
7.4 | even | 3 | inner | 1400.2.bh.d.249.1 | 4 | ||
35.2 | odd | 12 | 9800.2.a.bm.1.1 | 1 | |||
35.4 | even | 6 | inner | 1400.2.bh.d.249.2 | 4 | ||
35.12 | even | 12 | 9800.2.a.k.1.1 | 1 | |||
35.18 | odd | 12 | 1400.2.q.f.1201.1 | yes | 2 | ||
35.23 | odd | 12 | 9800.2.a.j.1.1 | 1 | |||
35.32 | odd | 12 | 1400.2.q.b.1201.1 | yes | 2 | ||
35.33 | even | 12 | 9800.2.a.bl.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.q.b.401.1 | ✓ | 2 | 5.2 | odd | 4 | ||
1400.2.q.b.1201.1 | yes | 2 | 35.32 | odd | 12 | ||
1400.2.q.f.401.1 | yes | 2 | 5.3 | odd | 4 | ||
1400.2.q.f.1201.1 | yes | 2 | 35.18 | odd | 12 | ||
1400.2.bh.d.249.1 | 4 | 7.4 | even | 3 | inner | ||
1400.2.bh.d.249.2 | 4 | 35.4 | even | 6 | inner | ||
1400.2.bh.d.849.1 | 4 | 5.4 | even | 2 | inner | ||
1400.2.bh.d.849.2 | 4 | 1.1 | even | 1 | trivial | ||
9800.2.a.j.1.1 | 1 | 35.23 | odd | 12 | |||
9800.2.a.k.1.1 | 1 | 35.12 | even | 12 | |||
9800.2.a.bl.1.1 | 1 | 35.33 | even | 12 | |||
9800.2.a.bm.1.1 | 1 | 35.2 | odd | 12 |