Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(143,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.z (of order \(12\), degree \(4\), 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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 719.20 | ||
Character | \(\chi\) | \(=\) | 1728.719 |
Dual form | 1728.2.z.a.1007.20 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.759273 | + | 2.83365i | 0.339557 | + | 1.26725i | 0.898843 | + | 0.438270i | \(0.144409\pi\) |
−0.559286 | + | 0.828975i | \(0.688925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41719 | − | 2.45465i | −0.535648 | − | 0.927769i | −0.999132 | − | 0.0416640i | \(-0.986734\pi\) |
0.463484 | − | 0.886105i | \(-0.346599\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.212907 | − | 0.794578i | 0.0641937 | − | 0.239574i | −0.926373 | − | 0.376608i | \(-0.877090\pi\) |
0.990566 | + | 0.137034i | \(0.0437569\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.864050 | − | 3.22468i | −0.239644 | − | 0.894365i | −0.976000 | − | 0.217770i | \(-0.930122\pi\) |
0.736356 | − | 0.676595i | \(-0.236545\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.28589i | 1.76709i | 0.468348 | + | 0.883544i | \(0.344849\pi\) | ||||
−0.468348 | + | 0.883544i | \(0.655151\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.951758 | + | 0.951758i | 0.218348 | + | 0.218348i | 0.807802 | − | 0.589454i | \(-0.200657\pi\) |
−0.589454 | + | 0.807802i | \(0.700657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.13217 | + | 2.96306i | 1.07013 | + | 0.617841i | 0.928218 | − | 0.372038i | \(-0.121341\pi\) |
0.141915 | + | 0.989879i | \(0.454674\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.12293 | + | 1.80302i | −0.624585 | + | 0.360605i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.473770 | − | 1.76813i | 0.0879768 | − | 0.328334i | −0.907884 | − | 0.419221i | \(-0.862303\pi\) |
0.995861 | + | 0.0908866i | \(0.0289701\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.05610 | + | 1.18709i | 0.369286 | + | 0.213207i | 0.673147 | − | 0.739509i | \(-0.264942\pi\) |
−0.303860 | + | 0.952717i | \(0.598276\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.87957 | − | 5.87957i | 0.993828 | − | 0.993828i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.03704 | + | 6.03704i | 0.992483 | + | 0.992483i | 0.999972 | − | 0.00748933i | \(-0.00238395\pi\) |
−0.00748933 | + | 0.999972i | \(0.502384\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.60866 | + | 7.98243i | −0.719751 | + | 1.24665i | 0.241347 | + | 0.970439i | \(0.422411\pi\) |
−0.961098 | + | 0.276207i | \(0.910923\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.50209 | + | 0.402483i | 0.229066 | + | 0.0613780i | 0.371526 | − | 0.928423i | \(-0.378835\pi\) |
−0.142460 | + | 0.989801i | \(0.545501\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.85832 | + | 4.95075i | 0.416928 | + | 0.722141i | 0.995629 | − | 0.0933994i | \(-0.0297733\pi\) |
−0.578701 | + | 0.815540i | \(0.696440\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.516861 | + | 0.895230i | −0.0738373 | + | 0.127890i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50856 | − | 4.50856i | 0.619298 | − | 0.619298i | −0.326053 | − | 0.945351i | \(-0.605719\pi\) |
0.945351 | + | 0.326053i | \(0.105719\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.41321 | 0.325397 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.6553 | + | 2.85508i | −1.38720 | + | 0.371700i | −0.873732 | − | 0.486407i | \(-0.838307\pi\) |
−0.513471 | + | 0.858107i | \(0.671640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.08106 | + | 2.16531i | 1.03467 | + | 0.277240i | 0.735904 | − | 0.677086i | \(-0.236757\pi\) |
0.298769 | + | 0.954325i | \(0.403424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.48155 | − | 4.89682i | 1.05201 | − | 0.607376i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1746 | + | 2.99423i | −1.36520 | + | 0.365804i | −0.865723 | − | 0.500524i | \(-0.833141\pi\) |
−0.499476 | + | 0.866328i | \(0.666474\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.98978i | 0.354821i | 0.984137 | + | 0.177411i | \(0.0567721\pi\) | ||||
−0.984137 | + | 0.177411i | \(0.943228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7280i | 1.48970i | 0.667229 | + | 0.744852i | \(0.267480\pi\) | ||||
−0.667229 | + | 0.744852i | \(0.732520\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.25214 | + | 0.603459i | −0.256655 | + | 0.0687705i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.94529 | + | 5.16457i | −1.00642 | + | 0.581059i | −0.910143 | − | 0.414295i | \(-0.864028\pi\) |
−0.0962815 | + | 0.995354i | \(0.530695\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.74713 | − | 1.00404i | −0.411301 | − | 0.110208i | 0.0472343 | − | 0.998884i | \(-0.484959\pi\) |
−0.458536 | + | 0.888676i | \(0.651626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.6456 | + | 5.53198i | −2.23933 | + | 0.600028i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.25017 | 0.980516 | 0.490258 | − | 0.871577i | \(-0.336903\pi\) | ||||
0.490258 | + | 0.871577i | \(0.336903\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.69092 | + | 6.69092i | −0.701399 | + | 0.701399i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.97430 | + | 3.41959i | −0.202559 | + | 0.350843i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.148868 | + | 0.257847i | 0.0151153 | + | 0.0261804i | 0.873484 | − | 0.486853i | \(-0.161855\pi\) |
−0.858369 | + | 0.513033i | \(0.828522\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.90610 | − | 2.11843i | −0.786687 | − | 0.210792i | −0.156956 | − | 0.987606i | \(-0.550168\pi\) |
−0.629731 | + | 0.776814i | \(0.716835\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.72414 | − | 9.91450i | 0.564016 | − | 0.976905i | −0.433124 | − | 0.901334i | \(-0.642589\pi\) |
0.997140 | − | 0.0755707i | \(-0.0240779\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.174948 | + | 0.174948i | 0.0169128 | + | 0.0169128i | 0.715513 | − | 0.698600i | \(-0.246193\pi\) |
−0.698600 | + | 0.715513i | \(0.746193\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.50900 | − | 1.50900i | 0.144536 | − | 0.144536i | −0.631136 | − | 0.775672i | \(-0.717411\pi\) |
0.775672 | + | 0.631136i | \(0.217411\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.513633 | + | 0.296546i | 0.0483185 | + | 0.0278967i | 0.523965 | − | 0.851740i | \(-0.324452\pi\) |
−0.475646 | + | 0.879637i | \(0.657786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.49955 | + | 16.7925i | −0.419585 | + | 1.56591i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.8843 | − | 10.3255i | 1.63945 | − | 0.946537i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.94025 | + | 5.16166i | 0.812750 | + | 0.469242i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.89158 | + | 2.89158i | 0.258631 | + | 0.258631i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.1816i | − | 1.25841i | −0.777240 | − | 0.629205i | \(-0.783381\pi\) | ||
0.777240 | − | 0.629205i | \(-0.216619\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.03481 | + | 3.86197i | 0.0904119 | + | 0.337422i | 0.996284 | − | 0.0861298i | \(-0.0274500\pi\) |
−0.905872 | + | 0.423551i | \(0.860783\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.987407 | − | 3.68505i | 0.0856190 | − | 0.319535i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.98207 | + | 6.89714i | 0.340211 | + | 0.589262i | 0.984472 | − | 0.175543i | \(-0.0561682\pi\) |
−0.644261 | + | 0.764806i | \(0.722835\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.76404 | + | 10.3155i | 0.234443 | + | 0.874952i | 0.978399 | + | 0.206724i | \(0.0662803\pi\) |
−0.743957 | + | 0.668228i | \(0.767053\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.74622 | −0.229651 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.36998 | 0.445953 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.13642 | − | 4.24117i | −0.0930990 | − | 0.347450i | 0.903625 | − | 0.428324i | \(-0.140896\pi\) |
−0.996724 | + | 0.0808734i | \(0.974229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.93783 | + | 12.0167i | 0.564592 | + | 0.977903i | 0.997087 | + | 0.0762664i | \(0.0242999\pi\) |
−0.432495 | + | 0.901636i | \(0.642367\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.80265 | + | 6.72758i | −0.144792 | + | 0.540372i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.61187 | − | 6.01560i | −0.128642 | − | 0.480097i | 0.871302 | − | 0.490748i | \(-0.163276\pi\) |
−0.999943 | + | 0.0106509i | \(0.996610\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 16.7969i | − | 1.32378i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.39010 | − | 3.39010i | −0.265533 | − | 0.265533i | 0.561764 | − | 0.827297i | \(-0.310123\pi\) |
−0.827297 | + | 0.561764i | \(0.810123\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.58610 | + | 4.95718i | 0.664412 | + | 0.383598i | 0.793956 | − | 0.607975i | \(-0.208018\pi\) |
−0.129544 | + | 0.991574i | \(0.541351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.60636 | − | 0.927433i | 0.123566 | − | 0.0713410i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.94330 | − | 7.25249i | 0.147746 | − | 0.551396i | −0.851872 | − | 0.523751i | \(-0.824532\pi\) |
0.999618 | − | 0.0276457i | \(-0.00880101\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.85157 | + | 5.11046i | 0.669116 | + | 0.386314i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.604756 | − | 0.604756i | 0.0452016 | − | 0.0452016i | −0.684145 | − | 0.729346i | \(-0.739824\pi\) |
0.729346 | + | 0.684145i | \(0.239824\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1716 | − | 10.1716i | −0.756048 | − | 0.756048i | 0.219553 | − | 0.975601i | \(-0.429540\pi\) |
−0.975601 | + | 0.219553i | \(0.929540\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.5231 | + | 21.6906i | −0.920714 | + | 1.59472i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.78921 | + | 1.55121i | 0.423349 | + | 0.113436i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.80282 | − | 10.0508i | −0.419877 | − | 0.727249i | 0.576049 | − | 0.817415i | \(-0.304594\pi\) |
−0.995927 | + | 0.0901660i | \(0.971260\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.09572 | − | 8.82605i | 0.366798 | − | 0.635313i | −0.622265 | − | 0.782807i | \(-0.713787\pi\) |
0.989063 | + | 0.147494i | \(0.0471206\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.32430 | − | 4.32430i | 0.308094 | − | 0.308094i | −0.536076 | − | 0.844170i | \(-0.680094\pi\) |
0.844170 | + | 0.536076i | \(0.180094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.7260 | 1.96544 | 0.982720 | − | 0.185097i | \(-0.0592599\pi\) | ||||
0.982720 | + | 0.185097i | \(0.0592599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.01156 | + | 1.34284i | −0.351743 | + | 0.0942492i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.1186 | − | 6.99846i | −1.82420 | − | 0.488793i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.958882 | − | 0.553611i | 0.0663272 | − | 0.0382940i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0391 | − | 5.10152i | 1.31071 | − | 0.351203i | 0.465219 | − | 0.885196i | \(-0.345976\pi\) |
0.845489 | + | 0.533993i | \(0.179309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.56197i | 0.311124i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.72933i | − | 0.456817i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.4947 | − | 6.29538i | 1.58042 | − | 0.423473i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.9074 | + | 6.29741i | −0.730416 | + | 0.421706i | −0.818574 | − | 0.574401i | \(-0.805235\pi\) |
0.0881582 | + | 0.996106i | \(0.471902\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.6445 | − | 3.12014i | −0.772874 | − | 0.207091i | −0.149233 | − | 0.988802i | \(-0.547680\pi\) |
−0.623641 | + | 0.781711i | \(0.714347\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.47149 | + | 1.46608i | −0.361566 | + | 0.0968814i | −0.435029 | − | 0.900417i | \(-0.643262\pi\) |
0.0734624 | + | 0.997298i | \(0.476595\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.1291 | −0.663580 | −0.331790 | − | 0.943353i | \(-0.607653\pi\) | ||||
−0.331790 | + | 0.943353i | \(0.607653\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.8584 | + | 11.8584i | −0.773558 | + | 0.773558i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.263562 | − | 0.456503i | 0.0170484 | − | 0.0295287i | −0.857375 | − | 0.514692i | \(-0.827906\pi\) |
0.874424 | + | 0.485163i | \(0.161240\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.74338 | + | 16.8760i | 0.627626 | + | 1.08708i | 0.988027 | + | 0.154283i | \(0.0493068\pi\) |
−0.360400 | + | 0.932798i | \(0.617360\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.92920 | − | 0.784878i | −0.187140 | − | 0.0501440i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.24675 | − | 3.89148i | 0.142957 | − | 0.247609i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.9199 | + | 17.9199i | 1.13110 | + | 1.13110i | 0.989995 | + | 0.141101i | \(0.0450643\pi\) |
0.141101 | + | 0.989995i | \(0.454936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.44706 | − | 3.44706i | 0.216715 | − | 0.216715i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.6152 | − | 8.43809i | −0.911671 | − | 0.526353i | −0.0307025 | − | 0.999529i | \(-0.509774\pi\) |
−0.880968 | + | 0.473175i | \(0.843108\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.26316 | − | 23.3744i | 0.389174 | − | 1.45242i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.8065 | + | 10.8579i | −1.15966 | + | 0.669528i | −0.951222 | − | 0.308508i | \(-0.900170\pi\) |
−0.208435 | + | 0.978036i | \(0.566837\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.1989 | + | 9.35243i | 0.995090 | + | 0.574515i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.50729 | + | 3.50729i | 0.213843 | + | 0.213843i | 0.805898 | − | 0.592055i | \(-0.201683\pi\) |
−0.592055 | + | 0.805898i | \(0.701683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.25749i | 0.137133i | 0.997647 | + | 0.0685665i | \(0.0218425\pi\) | ||||
−0.997647 | + | 0.0685665i | \(0.978157\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.767751 | + | 2.86529i | 0.0462971 | + | 0.172783i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.75826 | − | 17.7581i | 0.285896 | − | 1.06698i | −0.662286 | − | 0.749251i | \(-0.730414\pi\) |
0.948182 | − | 0.317727i | \(-0.102920\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.38270 | − | 7.59106i | −0.261450 | − | 0.452845i | 0.705177 | − | 0.709031i | \(-0.250867\pi\) |
−0.966627 | + | 0.256186i | \(0.917534\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.18474 | − | 15.6177i | −0.248757 | − | 0.928375i | −0.971458 | − | 0.237213i | \(-0.923766\pi\) |
0.722700 | − | 0.691161i | \(-0.242901\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.1254 | 1.54213 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −36.0842 | −2.12260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.24540 | − | 12.1120i | −0.189598 | − | 0.707589i | −0.993599 | − | 0.112962i | \(-0.963966\pi\) |
0.804001 | − | 0.594628i | \(-0.202700\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.1806 | − | 28.0256i | −0.942070 | − | 1.63171i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.12047 | − | 19.1098i | 0.296124 | − | 1.10515i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.14079 | − | 4.25749i | −0.0657540 | − | 0.245397i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.5429i | 1.40532i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.9168 | − | 18.9168i | −1.07964 | − | 1.07964i | −0.996542 | − | 0.0830950i | \(-0.973519\pi\) |
−0.0830950 | − | 0.996542i | \(-0.526481\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.08666 | − | 2.93678i | −0.288438 | − | 0.166530i | 0.348799 | − | 0.937197i | \(-0.386589\pi\) |
−0.637237 | + | 0.770668i | \(0.719923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3490 | − | 8.28438i | 0.811051 | − | 0.468261i | −0.0362694 | − | 0.999342i | \(-0.511547\pi\) |
0.847321 | + | 0.531081i | \(0.178214\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.80531 | − | 6.73750i | 0.101396 | − | 0.378416i | −0.896515 | − | 0.443013i | \(-0.853910\pi\) |
0.997911 | + | 0.0645973i | \(0.0205763\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.30405 | − | 0.752894i | −0.0730128 | − | 0.0421540i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.93441 | + | 6.93441i | −0.385841 | + | 0.385841i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.51253 | + | 8.51253i | 0.472190 | + | 0.472190i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.10156 | − | 14.0323i | 0.446653 | − | 0.773626i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.7853 | + | 5.83736i | 1.19743 | + | 0.320850i | 0.801819 | − | 0.597567i | \(-0.203866\pi\) |
0.395612 | + | 0.918418i | \(0.370533\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.9692 | − | 29.3915i | −0.927126 | − | 1.60583i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.04210 | − | 8.73317i | 0.274661 | − | 0.475726i | −0.695389 | − | 0.718634i | \(-0.744768\pi\) |
0.970049 | + | 0.242908i | \(0.0781012\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.38099 | − | 1.38099i | 0.0747849 | − | 0.0747849i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9107 | −0.913093 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.7569 | + | 7.70540i | −1.54375 | + | 0.413647i | −0.927476 | − | 0.373882i | \(-0.878026\pi\) |
−0.616277 | + | 0.787530i | \(0.711360\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.65259 | + | 2.31845i | 0.463163 | + | 0.124104i | 0.482852 | − | 0.875702i | \(-0.339601\pi\) |
−0.0196892 | + | 0.999806i | \(0.506268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.1794 | + | 16.2694i | −1.49984 | + | 0.865933i | −1.00000 | 0.000184008i | \(-0.999941\pi\) | |
−0.499841 | + | 0.866117i | \(0.666608\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.47197 | + | 2.27006i | −0.449645 | + | 0.120482i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.581843i | 0.0307085i | 0.999882 | + | 0.0153542i | \(0.00488760\pi\) | ||||
−0.999882 | + | 0.0153542i | \(0.995112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 17.1883i | − | 0.904648i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −36.0668 | + | 9.66406i | −1.88782 | + | 0.505840i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.68240 | − | 2.12603i | 0.192220 | − | 0.110978i | −0.400802 | − | 0.916165i | \(-0.631268\pi\) |
0.593021 | + | 0.805187i | \(0.297935\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.4564 | − | 4.67743i | −0.906291 | − | 0.242840i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.02298 | − | 1.61385i | 0.311858 | − | 0.0835621i | −0.0994955 | − | 0.995038i | \(-0.531723\pi\) |
0.411353 | + | 0.911476i | \(0.365056\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.11102 | −0.314733 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.99791 | − | 8.99791i | 0.462192 | − | 0.462192i | −0.437182 | − | 0.899373i | \(-0.644023\pi\) |
0.899373 | + | 0.437182i | \(0.144023\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.35960 | + | 7.55105i | −0.222765 | + | 0.385840i | −0.955647 | − | 0.294516i | \(-0.904842\pi\) |
0.732882 | + | 0.680356i | \(0.238175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.41998 | − | 5.92357i | −0.174298 | − | 0.301893i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.9041 | − | 7.20893i | −1.36409 | − | 0.365507i | −0.498774 | − | 0.866732i | \(-0.666216\pi\) |
−0.865317 | + | 0.501225i | \(0.832883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.5886 | + | 37.3925i | −1.09178 | + | 1.89102i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.4265 | − | 21.4265i | −1.07808 | − | 1.07808i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.82319 | − | 3.82319i | 0.191880 | − | 0.191880i | −0.604628 | − | 0.796508i | \(-0.706678\pi\) |
0.796508 | + | 0.604628i | \(0.206678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.9442 | + | 14.4015i | 1.24565 | + | 0.719178i | 0.970239 | − | 0.242148i | \(-0.0778518\pi\) |
0.275414 | + | 0.961326i | \(0.411185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.05141 | − | 7.65596i | 0.102188 | − | 0.381371i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.08222 | − | 3.51157i | 0.301485 | − | 0.174062i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.11179 | − | 5.26069i | −0.450549 | − | 0.260125i | 0.257513 | − | 0.966275i | \(-0.417097\pi\) |
−0.708062 | + | 0.706150i | \(0.750430\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.1088 | + | 22.1088i | 1.08790 | + | 1.08790i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.3804i | − | 0.558642i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.32320 | − | 12.4024i | −0.162349 | − | 0.605895i | −0.998363 | − | 0.0571875i | \(-0.981787\pi\) |
0.836014 | − | 0.548708i | \(-0.184880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.46909 | − | 9.21476i | 0.120336 | − | 0.449100i | −0.879295 | − | 0.476278i | \(-0.841985\pi\) |
0.999631 | + | 0.0271782i | \(0.00865216\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.1366 | − | 22.7533i | −0.637220 | − | 1.10370i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.13732 | − | 22.9048i | −0.297006 | − | 1.10844i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.4451 | 0.792131 | 0.396065 | − | 0.918222i | \(-0.370375\pi\) | ||||
0.396065 | + | 0.918222i | \(0.370375\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.51715 | −0.169023 | −0.0845116 | − | 0.996422i | \(-0.526933\pi\) | ||||
−0.0845116 | + | 0.996422i | \(0.526933\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.06447 | + | 7.70471i | 0.0987570 | + | 0.368566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4483 | − | 18.0969i | −0.498668 | − | 0.863719i | 0.501331 | − | 0.865256i | \(-0.332844\pi\) |
−0.999999 | + | 0.00153725i | \(0.999511\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.86151 | − | 10.6793i | 0.135954 | − | 0.507389i | −0.864038 | − | 0.503427i | \(-0.832072\pi\) |
0.999992 | − | 0.00396162i | \(-0.00126103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.02341 | + | 26.2117i | 0.332941 | + | 1.24255i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.5860i | − | 0.829933i | −0.909837 | − | 0.414966i | \(-0.863793\pi\) | ||
0.909837 | − | 0.414966i | \(-0.136207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.36145 | + | 5.36145i | 0.252461 | + | 0.252461i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.0399 | − | 13.8795i | −1.12701 | − | 0.650680i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.6606 | + | 10.7737i | −0.872905 | + | 0.503972i | −0.868313 | − | 0.496017i | \(-0.834795\pi\) |
−0.00459262 | + | 0.999989i | \(0.501462\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.55312 | − | 16.9925i | 0.212060 | − | 0.791419i | −0.775121 | − | 0.631813i | \(-0.782311\pi\) |
0.987181 | − | 0.159606i | \(-0.0510223\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.4389 | + | 10.6457i | 0.856930 | + | 0.494749i | 0.862983 | − | 0.505233i | \(-0.168593\pi\) |
−0.00605328 | + | 0.999982i | \(0.501927\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.62864 | − | 2.62864i | 0.121639 | − | 0.121639i | −0.643667 | − | 0.765306i | \(-0.722588\pi\) |
0.765306 | + | 0.643667i | \(0.222588\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.1864 | + | 23.1864i | 1.07065 | + | 1.07065i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.639608 | − | 1.10783i | 0.0294092 | − | 0.0509382i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.68831 | − | 1.25623i | −0.215115 | − | 0.0576398i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.7530 | + | 18.6247i | 0.491317 | + | 0.850986i | 0.999950 | − | 0.00999740i | \(-0.00318233\pi\) |
−0.508633 | + | 0.860983i | \(0.669849\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2512 | − | 24.6838i | 0.649799 | − | 1.12548i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.617616 | + | 0.617616i | −0.0280445 | + | 0.0280445i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.6445 | 0.663607 | 0.331804 | − | 0.943348i | \(-0.392343\pi\) | ||||
0.331804 | + | 0.943348i | \(0.392343\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.2317 | − | 11.3160i | 1.90589 | − | 0.510682i | 0.910658 | − | 0.413161i | \(-0.135575\pi\) |
0.995233 | − | 0.0975209i | \(-0.0310913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.8824 | + | 3.45183i | 0.580195 | + | 0.155463i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.33885 | − | 4.23708i | 0.329192 | − | 0.190059i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.91419 | + | 2.12060i | −0.354288 | + | 0.0949311i | −0.431573 | − | 0.902078i | \(-0.642041\pi\) |
0.0772856 | + | 0.997009i | \(0.475375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.90408i | − | 0.0848988i | −0.999099 | − | 0.0424494i | \(-0.986484\pi\) | ||
0.999099 | − | 0.0424494i | \(-0.0135161\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 24.0116i | − | 1.06850i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.27785 | − | 1.95009i | 0.322585 | − | 0.0864364i | −0.0938926 | − | 0.995582i | \(-0.529931\pi\) |
0.416478 | + | 0.909146i | \(0.363264\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.2428 | − | 18.0381i | 1.38210 | − | 0.797957i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.4404 | + | 8.69237i | 1.42949 | + | 0.383032i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.54231 | − | 1.21711i | 0.199771 | − | 0.0535284i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.5974 | 1.29669 | 0.648343 | − | 0.761349i | \(-0.275462\pi\) | ||||
0.648343 | + | 0.761349i | \(0.275462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.1710 | + | 29.1710i | −1.27556 | + | 1.27556i | −0.332431 | + | 0.943128i | \(0.607869\pi\) |
−0.943128 | + | 0.332431i | \(0.892131\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.64900 | + | 14.9805i | −0.376756 | + | 0.652561i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.05948 | + | 10.4953i | 0.263456 | + | 0.456318i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.7229 | + | 7.96422i | 1.28744 | + | 0.344969i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.362907 | + | 0.628573i | −0.0156898 | + | 0.0271756i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.601287 | + | 0.601287i | 0.0258993 | + | 0.0258993i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.87135 | − | 7.87135i | 0.338416 | − | 0.338416i | −0.517355 | − | 0.855771i | \(-0.673083\pi\) |
0.855771 | + | 0.517355i | \(0.173083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.42173 | + | 3.13024i | 0.232241 | + | 0.134085i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.817385 | − | 3.05052i | 0.0349488 | − | 0.130431i | −0.946247 | − | 0.323444i | \(-0.895159\pi\) |
0.981196 | + | 0.193013i | \(0.0618260\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.13375 | − | 1.23192i | 0.0909007 | − | 0.0524816i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.3544 | + | 14.6384i | 1.07818 | + | 0.622486i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.4110 | − | 22.4110i | −0.949583 | − | 0.949583i | 0.0492055 | − | 0.998789i | \(-0.484331\pi\) |
−0.998789 | + | 0.0492055i | \(0.984331\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.19151i | − | 0.219577i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.11646 | − | 30.2910i | −0.342068 | − | 1.27661i | −0.896000 | − | 0.444053i | \(-0.853540\pi\) |
0.553933 | − | 0.832561i | \(-0.313127\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.450319 | + | 1.68061i | −0.0189450 | + | 0.0707039i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.78787 | − | 4.82873i | −0.116874 | − | 0.202431i | 0.801654 | − | 0.597789i | \(-0.203954\pi\) |
−0.918527 | + | 0.395358i | \(0.870621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.39076 | − | 20.1186i | −0.225596 | − | 0.841937i | −0.982165 | − | 0.188023i | \(-0.939792\pi\) |
0.756568 | − | 0.653915i | \(-0.226874\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.3699 | −0.891185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3551 | 0.847394 | 0.423697 | − | 0.905804i | \(-0.360732\pi\) | ||||
0.423697 | + | 0.905804i | \(0.360732\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.84584 | + | 10.6208i | 0.118065 | + | 0.440626i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.62250 | − | 4.54230i | −0.108613 | − | 0.188123i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.19230 | + | 30.5741i | −0.338132 | + | 1.26193i | 0.562301 | + | 0.826933i | \(0.309916\pi\) |
−0.900433 | + | 0.434994i | \(0.856750\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.827087 | + | 3.08673i | 0.0340795 | + | 0.127186i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.8148i | − | 0.772633i | −0.922366 | − | 0.386317i | \(-0.873747\pi\) | ||
0.922366 | − | 0.386317i | \(-0.126253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 42.8379 | + | 42.8379i | 1.75618 | + | 1.75618i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.618276 | + | 0.356962i | 0.0252621 | + | 0.0145851i | 0.512578 | − | 0.858641i | \(-0.328691\pi\) |
−0.487316 | + | 0.873226i | \(0.662024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.9427 | + | 23.0610i | −1.62930 | + | 0.940676i | −0.644996 | + | 0.764186i | \(0.723141\pi\) |
−0.984302 | + | 0.176490i | \(0.943526\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.83822 | + | 29.2526i | −0.318669 | + | 1.18929i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.9512 | − | 14.9830i | −1.05333 | − | 0.608139i | −0.129749 | − | 0.991547i | \(-0.541417\pi\) |
−0.923579 | + | 0.383408i | \(0.874750\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.4948 | − | 13.4948i | 0.545943 | − | 0.545943i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.31839 | − | 4.31839i | −0.174418 | − | 0.174418i | 0.614499 | − | 0.788917i | \(-0.289358\pi\) |
−0.788917 | + | 0.614499i | \(0.789358\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3245 | − | 24.8108i | 0.576683 | − | 0.998844i | −0.419174 | − | 0.907906i | \(-0.637680\pi\) |
0.995857 | − | 0.0909377i | \(-0.0289864\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.5053 | + | 8.44181i | 1.26630 | + | 0.339305i | 0.828614 | − | 0.559821i | \(-0.189130\pi\) |
0.437690 | + | 0.899126i | \(0.355797\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.1093 | − | 22.7059i | −0.525211 | − | 0.909693i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.0133 | + | 26.0039i | −0.600533 | + | 1.04015i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.9852 | + | 43.9852i | −1.75380 | + | 1.75380i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.5062 | −0.776529 | −0.388265 | − | 0.921548i | \(-0.626925\pi\) | ||||
−0.388265 | + | 0.921548i | \(0.626925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 40.1855 | − | 10.7677i | 1.59471 | − | 0.427302i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.33342 | + | 0.893188i | 0.132075 | + | 0.0353894i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.569361 | + | 0.328721i | −0.0224884 | + | 0.0129837i | −0.511202 | − | 0.859461i | \(-0.670800\pi\) |
0.488714 | + | 0.872444i | \(0.337466\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.4845 | + | 6.29265i | −0.926138 | + | 0.248158i | −0.690207 | − | 0.723612i | \(-0.742481\pi\) |
−0.235931 | + | 0.971770i | \(0.575814\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 21.5984i | − | 0.849122i | −0.905399 | − | 0.424561i | \(-0.860428\pi\) | ||
0.905399 | − | 0.424561i | \(-0.139572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.07434i | 0.356199i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −38.1014 | + | 10.2092i | −1.49102 | + | 0.399519i | −0.910082 | − | 0.414427i | \(-0.863982\pi\) |
−0.580941 | + | 0.813946i | \(0.697315\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.1577 | + | 5.86458i | −0.396896 | + | 0.229148i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.5220 | + | 3.62321i | 0.526742 | + | 0.141140i | 0.512383 | − | 0.858757i | \(-0.328763\pi\) |
0.0143586 | + | 0.999897i | \(0.495429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.1488 | + | 10.7578i | −1.56161 | + | 0.418432i | −0.933172 | − | 0.359430i | \(-0.882971\pi\) |
−0.628436 | + | 0.777861i | \(0.716305\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.1918 | 0.434001 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.67055 | − | 7.67055i | 0.297005 | − | 0.297005i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.44102 | − | 5.96002i | 0.132839 | − | 0.230084i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.88063 | + | 4.98940i | 0.111040 | + | 0.192327i | 0.916190 | − | 0.400744i | \(-0.131248\pi\) |
−0.805150 | + | 0.593072i | \(0.797915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.1438 | + | 7.27316i | 1.04322 | + | 0.279530i | 0.739447 | − | 0.673214i | \(-0.235087\pi\) |
0.303773 | + | 0.952744i | \(0.401754\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.421949 | − | 0.730837i | 0.0161929 | − | 0.0280469i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.50875 | + | 4.50875i | 0.172522 | + | 0.172522i | 0.788087 | − | 0.615564i | \(-0.211072\pi\) |
−0.615564 | + | 0.788087i | \(0.711072\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.5206 | + | 16.5206i | −0.631219 | + | 0.631219i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.4343 | − | 10.6430i | −0.702290 | − | 0.405467i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.65522 | − | 9.90941i | 0.101009 | − | 0.376972i | −0.896853 | − | 0.442329i | \(-0.854152\pi\) |
0.997862 | + | 0.0653578i | \(0.0208189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.1319 | + | 15.6646i | −1.02917 | + | 0.594193i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −58.1591 | − | 33.5782i | −2.20293 | − | 1.27186i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.5518 | − | 16.5518i | −0.625154 | − | 0.625154i | 0.321691 | − | 0.946845i | \(-0.395749\pi\) |
−0.946845 | + | 0.321691i | \(0.895749\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.4916i | 0.433414i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00445 | + | 22.4089i | 0.225821 | + | 0.842774i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.7915 | − | 40.2743i | 0.405282 | − | 1.51253i | −0.398253 | − | 0.917276i | \(-0.630383\pi\) |
0.803535 | − | 0.595257i | \(-0.202950\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.03484 | + | 12.1847i | 0.263457 | + | 0.456320i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.08513 | − | 7.78182i | −0.0779795 | − | 0.291023i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.8494 | −1.00131 | −0.500656 | − | 0.865646i | \(-0.666908\pi\) | ||||
−0.500656 | + | 0.865646i | \(0.666908\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.4488 | −1.20846 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.70843 | + | 6.37597i | 0.0634497 | + | 0.236797i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.1681 | + | 21.0758i | 0.451290 | + | 0.781657i | 0.998466 | − | 0.0553600i | \(-0.0176306\pi\) |
−0.547176 | + | 0.837017i | \(0.684297\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.93245 | + | 10.9440i | −0.108460 | + | 0.404780i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.85501 | + | 21.8512i | 0.216260 | + | 0.807093i | 0.985719 | + | 0.168397i | \(0.0538591\pi\) |
−0.769459 | + | 0.638696i | \(0.779474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.51661i | 0.350549i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.6742 | + | 12.6742i | 0.466230 | + | 0.466230i | 0.900691 | − | 0.434461i | \(-0.143061\pi\) |
−0.434461 | + | 0.900691i | \(0.643061\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.2864 | + | 14.5991i | 0.927667 | + | 0.535589i | 0.886073 | − | 0.463546i | \(-0.153423\pi\) |
0.0415943 | + | 0.999135i | \(0.486756\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.1551 | − | 6.44042i | 0.408692 | − | 0.235959i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.181500 | − | 0.677369i | 0.00663188 | − | 0.0247505i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.9864 | + | 13.8486i | 0.875277 | + | 0.505341i | 0.869098 | − | 0.494639i | \(-0.164700\pi\) |
0.00617885 | + | 0.999981i | \(0.498033\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.7833 | + | 28.7833i | −1.04753 | + | 1.04753i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.84906 | − | 6.84906i | −0.248933 | − | 0.248933i | 0.571599 | − | 0.820533i | \(-0.306323\pi\) |
−0.820533 | + | 0.571599i | \(0.806323\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.92685 | − | 11.9977i | 0.251098 | − | 0.434915i | −0.712730 | − | 0.701438i | \(-0.752542\pi\) |
0.963828 | + | 0.266523i | \(0.0858750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.84262 | − | 1.56553i | −0.211517 | − | 0.0566758i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.4134 | + | 31.8930i | 0.664871 | + | 1.15159i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.15368 | − | 8.92644i | 0.185846 | − | 0.321896i | −0.758015 | − | 0.652237i | \(-0.773831\pi\) |
0.943861 | + | 0.330342i | \(0.107164\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.0684 | − | 29.0684i | 1.04552 | − | 1.04552i | 0.0466043 | − | 0.998913i | \(-0.485160\pi\) |
0.998913 | − | 0.0466043i | \(-0.0148400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.56139 | −0.307534 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.9837 | + | 3.21101i | −0.429359 | + | 0.115046i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.37561 | + | 0.636543i | 0.0850060 | + | 0.0227773i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.8222 | − | 9.13496i | 0.564719 | − | 0.326041i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.9593 | − | 9.63526i | 1.28181 | − | 0.343460i | 0.447266 | − | 0.894401i | \(-0.352398\pi\) |
0.834544 | + | 0.550941i | \(0.185731\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.68105i | − | 0.0597712i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 27.9297i | − | 0.991814i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.38318 | + | 2.51421i | −0.332369 | + | 0.0890580i | −0.421144 | − | 0.906994i | \(-0.638371\pi\) |
0.0887752 | + | 0.996052i | \(0.471705\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.0706 | + | 20.8254i | −1.27609 | + | 0.736749i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.1134 | + | 2.70988i | 0.356895 | + | 0.0956297i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 47.5965 | − | 12.7534i | 1.67756 | − | 0.449500i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.1867 | −0.463620 | −0.231810 | − | 0.972761i | \(-0.574465\pi\) | ||||
−0.231810 | + | 0.972761i | \(0.574465\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0093 | − | 11.0093i | 0.386587 | − | 0.386587i | −0.486881 | − | 0.873468i | \(-0.661865\pi\) |
0.873468 | + | 0.486881i | \(0.161865\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.03233 | − | 12.1804i | 0.246332 | − | 0.426659i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.04656 | + | 1.81269i | 0.0366144 | + | 0.0634179i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.17943 | + | 1.11987i | 0.145863 | + | 0.0390839i | 0.331012 | − | 0.943627i | \(-0.392610\pi\) |
−0.185149 | + | 0.982711i | \(0.559277\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.8576 | + | 41.3225i | −0.831622 | + | 1.44041i | 0.0651287 | + | 0.997877i | \(0.479254\pi\) |
−0.896751 | + | 0.442535i | \(0.854079\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.38625 | − | 1.38625i | −0.0482045 | − | 0.0482045i | 0.682594 | − | 0.730798i | \(-0.260852\pi\) |
−0.730798 | + | 0.682594i | \(0.760852\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.8345 | + | 21.8345i | −0.758345 | + | 0.758345i | −0.976021 | − | 0.217676i | \(-0.930152\pi\) |
0.217676 | + | 0.976021i | \(0.430152\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.52255 | − | 3.76580i | −0.225993 | − | 0.130477i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.52771 | + | 28.0938i | −0.260507 | + | 0.972227i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.8914 | + | 16.1031i | −0.962916 | + | 0.555940i | −0.897069 | − | 0.441890i | \(-0.854308\pi\) |
−0.0658470 | + | 0.997830i | \(0.520975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2129 | + | 12.8246i | 0.765962 | + | 0.442228i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.84768 | + | 3.84768i | 0.132364 | + | 0.132364i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 29.2602i | − | 1.00539i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.0950 | + | 48.8712i | 0.448891 | + | 1.67528i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.0354 | + | 44.9166i | −0.412083 | + | 1.53791i | 0.378525 | + | 0.925591i | \(0.376431\pi\) |
−0.790608 | + | 0.612323i | \(0.790235\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0139 | + | 17.3446i | 0.342068 | + | 0.592480i | 0.984817 | − | 0.173598i | \(-0.0555392\pi\) |
−0.642748 | + | 0.766077i | \(0.722206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.47358 | + | 16.6956i | 0.152637 | + | 0.569648i | 0.999296 | + | 0.0375129i | \(0.0119435\pi\) |
−0.846659 | + | 0.532135i | \(0.821390\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.4242 | −0.831410 | −0.415705 | − | 0.909499i | \(-0.636465\pi\) | ||||
−0.415705 | + | 0.909499i | \(0.636465\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.0265 | 0.748923 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.19914 | + | 8.20731i | 0.0746007 | + | 0.278414i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.3109 | + | 33.4474i | 0.654324 | + | 1.13332i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.99989 | − | 11.1957i | 0.101415 | − | 0.378485i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.26415 | − | 34.5743i | −0.312828 | − | 1.16749i | −0.925995 | − | 0.377537i | \(-0.876771\pi\) |
0.613167 | − | 0.789954i | \(-0.289895\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.8264i | 1.54393i | 0.635664 | + | 0.771966i | \(0.280726\pi\) | ||||
−0.635664 | + | 0.771966i | \(0.719274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.22790 | − | 7.22790i | −0.243238 | − | 0.243238i | 0.574950 | − | 0.818188i | \(-0.305021\pi\) |
−0.818188 | + | 0.574950i | \(0.805021\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.9502 | − | 21.3332i | −1.24067 | − | 0.716300i | −0.271438 | − | 0.962456i | \(-0.587499\pi\) |
−0.969230 | + | 0.246156i | \(0.920832\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.8107 | + | 20.0980i | −1.16751 | + | 0.674065i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.99149 | + | 7.43234i | −0.0666426 | + | 0.248714i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.17284 | + | 1.25449i | 0.0726300 | + | 0.0419330i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.07305 | − | 3.07305i | 0.102492 | − | 0.102492i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.8489 | + | 32.8489i | 1.09435 | + | 1.09435i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.0997 | − | 36.5457i | 0.701376 | − | 1.21482i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.9844 | − | 10.4458i | −1.29445 | − | 0.346848i | −0.455104 | − | 0.890438i | \(-0.650398\pi\) |
−0.839351 | + | 0.543590i | \(0.817065\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.6553 | + | 39.2402i | 0.750605 | + | 1.30009i | 0.947530 | + | 0.319667i | \(0.103571\pi\) |
−0.196925 | + | 0.980419i | \(0.563095\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.59558 | + | 2.76362i | −0.0528060 | + | 0.0914626i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.01324 | − | 8.01324i | 0.264621 | − | 0.264621i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.91688 | 0.129206 | 0.0646030 | − | 0.997911i | \(-0.479422\pi\) | ||||
0.0646030 | + | 0.997911i | \(0.479422\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.64107 | − | 2.58332i | 0.317340 | − | 0.0850309i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.7381 | − | 7.96831i | −0.977784 | − | 0.261996i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.7214 | − | 7.92207i | 0.450185 | − | 0.259915i | −0.257723 | − | 0.966219i | \(-0.582972\pi\) |
0.707908 | + | 0.706304i | \(0.249639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.34397 | + | 0.360116i | −0.0440468 | + | 0.0118023i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.5824i | 0.575005i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.0380i | − | 1.24265i | −0.783554 | − | 0.621324i | \(-0.786595\pi\) | ||
0.783554 | − | 0.621324i | \(-0.213405\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.4756 | − | 13.2570i | 1.61286 | − | 0.432164i | 0.663966 | − | 0.747762i | \(-0.268872\pi\) |
0.948893 | + | 0.315598i | \(0.102205\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.3048 | + | 27.3115i | −1.54046 | + | 0.889384i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.8269 | + | 4.24080i | 0.514305 | + | 0.137808i | 0.506631 | − | 0.862163i | \(-0.330891\pi\) |
0.00767376 | + | 0.999971i | \(0.497557\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.0438 | − | 10.9977i | 1.33234 | − | 0.356999i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.2107 | −0.622295 | −0.311147 | − | 0.950362i | \(-0.600713\pi\) | ||||
−0.311147 | + | 0.950362i | \(0.600713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0744 | − | 24.0744i | 0.779030 | − | 0.779030i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.2867 | − | 19.5491i | 0.364466 | − | 0.631274i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.6816 | − | 21.9652i | −0.409085 | − | 0.708556i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.8789 | + | 7.73809i | 0.929646 | + | 0.249098i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.0779 | − | 29.5798i | 0.549188 | − | 0.951222i | −0.449142 | − | 0.893460i | \(-0.648270\pi\) |
0.998330 | − | 0.0577615i | \(-0.0183963\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.2022 | + | 20.2022i | 0.648318 | + | 0.648318i | 0.952586 | − | 0.304268i | \(-0.0984119\pi\) |
−0.304268 | + | 0.952586i | \(0.598412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.4038 | − | 21.4038i | 0.686175 | − | 0.686175i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.37615 | + | 4.25862i | 0.235984 | + | 0.136245i | 0.613329 | − | 0.789827i | \(-0.289830\pi\) |
−0.377346 | + | 0.926072i | \(0.623163\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.96942 | − | 7.34998i | 0.0629430 | − | 0.234906i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.6844 | − | 27.5306i | 1.52090 | − | 0.878090i | 0.521200 | − | 0.853435i | \(-0.325485\pi\) |
0.999696 | − | 0.0246553i | \(-0.00784881\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.5369 | + | 8.97021i | 0.495045 | + | 0.285815i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.51638 | + | 6.51638i | 0.207209 | + | 0.207209i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.9180i | 1.96689i | 0.181210 | + | 0.983444i | \(0.441999\pi\) | ||||
−0.181210 | + | 0.983444i | \(0.558001\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.0516 | + | 78.5655i | 0.667380 | + | 2.49069i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.65375 | + | 17.3680i | −0.147386 | + | 0.550051i | 0.852252 | + | 0.523132i | \(0.175236\pi\) |
−0.999638 | + | 0.0269194i | \(0.991430\pi\) | |||||||
\(998\) | 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 | 1728.2.z.a.719.20 | 88 | ||
3.2 | odd | 2 | 576.2.y.a.527.15 | 88 | |||
4.3 | odd | 2 | 432.2.v.a.395.12 | 88 | |||
9.2 | odd | 6 | inner | 1728.2.z.a.143.20 | 88 | ||
9.7 | even | 3 | 576.2.y.a.335.19 | 88 | |||
12.11 | even | 2 | 144.2.u.a.59.11 | yes | 88 | ||
16.3 | odd | 4 | inner | 1728.2.z.a.1583.20 | 88 | ||
16.13 | even | 4 | 432.2.v.a.179.5 | 88 | |||
36.7 | odd | 6 | 144.2.u.a.11.18 | ✓ | 88 | ||
36.11 | even | 6 | 432.2.v.a.251.5 | 88 | |||
48.29 | odd | 4 | 144.2.u.a.131.18 | yes | 88 | ||
48.35 | even | 4 | 576.2.y.a.239.19 | 88 | |||
144.29 | odd | 12 | 432.2.v.a.35.12 | 88 | |||
144.61 | even | 12 | 144.2.u.a.83.11 | yes | 88 | ||
144.83 | even | 12 | inner | 1728.2.z.a.1007.20 | 88 | ||
144.115 | odd | 12 | 576.2.y.a.47.15 | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.u.a.11.18 | ✓ | 88 | 36.7 | odd | 6 | ||
144.2.u.a.59.11 | yes | 88 | 12.11 | even | 2 | ||
144.2.u.a.83.11 | yes | 88 | 144.61 | even | 12 | ||
144.2.u.a.131.18 | yes | 88 | 48.29 | odd | 4 | ||
432.2.v.a.35.12 | 88 | 144.29 | odd | 12 | |||
432.2.v.a.179.5 | 88 | 16.13 | even | 4 | |||
432.2.v.a.251.5 | 88 | 36.11 | even | 6 | |||
432.2.v.a.395.12 | 88 | 4.3 | odd | 2 | |||
576.2.y.a.47.15 | 88 | 144.115 | odd | 12 | |||
576.2.y.a.239.19 | 88 | 48.35 | even | 4 | |||
576.2.y.a.335.19 | 88 | 9.7 | even | 3 | |||
576.2.y.a.527.15 | 88 | 3.2 | odd | 2 | |||
1728.2.z.a.143.20 | 88 | 9.2 | odd | 6 | inner | ||
1728.2.z.a.719.20 | 88 | 1.1 | even | 1 | trivial | ||
1728.2.z.a.1007.20 | 88 | 144.83 | even | 12 | inner | ||
1728.2.z.a.1583.20 | 88 | 16.3 | odd | 4 | inner |