Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(449,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.cu (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 18 x^{18} + 232 x^{17} + 208 x^{16} - 3152 x^{15} - 2732 x^{14} + 24552 x^{13} + \cdots + 414864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.7 | ||
Root | \(-0.561107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.521 |
Dual form | 1368.2.cu.b.449.7 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.524572 | + | 0.302862i | 0.234596 | + | 0.135444i | 0.612690 | − | 0.790323i | \(-0.290087\pi\) |
−0.378095 | + | 0.925767i | \(0.623421\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.37361 | 1.65307 | 0.826535 | − | 0.562885i | \(-0.190309\pi\) | ||||
0.826535 | + | 0.562885i | \(0.190309\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.96560i | − | 1.49718i | −0.663031 | − | 0.748592i | \(-0.730730\pi\) | ||
0.663031 | − | 0.748592i | \(-0.269270\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.91196 | − | 1.10387i | 0.530282 | − | 0.306158i | −0.210850 | − | 0.977519i | \(-0.567623\pi\) |
0.741131 | + | 0.671360i | \(0.234290\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.80061 | − | 1.61693i | −0.679247 | − | 0.392163i | 0.120325 | − | 0.992735i | \(-0.461606\pi\) |
−0.799571 | + | 0.600571i | \(0.794940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.965553 | − | 4.25061i | −0.221513 | − | 0.975157i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.27590 | − | 0.736640i | 0.266043 | − | 0.153600i | −0.361045 | − | 0.932548i | \(-0.617580\pi\) |
0.627088 | + | 0.778948i | \(0.284247\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.31655 | − | 4.01238i | −0.463310 | − | 0.802476i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.05366 | − | 1.82499i | −0.195660 | − | 0.338893i | 0.751457 | − | 0.659782i | \(-0.229352\pi\) |
−0.947117 | + | 0.320889i | \(0.896018\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.85749i | 1.77046i | 0.465157 | + | 0.885228i | \(0.345998\pi\) | ||||
−0.465157 | + | 0.885228i | \(0.654002\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.29427 | + | 1.32460i | 0.387803 | + | 0.223898i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.03086i | 0.827069i | 0.910488 | + | 0.413534i | \(0.135706\pi\) | ||||
−0.910488 | + | 0.413534i | \(0.864294\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.79948 | − | 6.58090i | 0.593379 | − | 1.02776i | −0.400394 | − | 0.916343i | \(-0.631127\pi\) |
0.993773 | − | 0.111420i | \(-0.0355399\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.50446 | − | 2.60580i | 0.229428 | − | 0.397381i | −0.728211 | − | 0.685353i | \(-0.759648\pi\) |
0.957639 | + | 0.287972i | \(0.0929811\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.40077 | + | 5.42754i | −1.37124 | + | 0.791687i | −0.991085 | − | 0.133234i | \(-0.957464\pi\) |
−0.380158 | + | 0.924921i | \(0.624130\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.1285 | 1.73264 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.08442 | + | 1.87827i | 0.148957 | + | 0.258000i | 0.930842 | − | 0.365422i | \(-0.119075\pi\) |
−0.781885 | + | 0.623422i | \(0.785742\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.50389 | − | 2.60481i | 0.202784 | − | 0.351233i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.306301 | + | 0.530529i | −0.0398770 | + | 0.0690690i | −0.885275 | − | 0.465068i | \(-0.846030\pi\) |
0.845398 | + | 0.534137i | \(0.179363\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.45845 | − | 7.72227i | −0.570846 | − | 0.988735i | −0.996479 | − | 0.0838390i | \(-0.973282\pi\) |
0.425633 | − | 0.904896i | \(-0.360051\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.33728 | 0.165869 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7394 | − | 6.77776i | 1.43420 | − | 0.828035i | 0.436761 | − | 0.899578i | \(-0.356126\pi\) |
0.997438 | + | 0.0715426i | \(0.0227922\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.90222 | + | 3.29475i | −0.225752 | + | 0.391014i | −0.956545 | − | 0.291585i | \(-0.905817\pi\) |
0.730793 | + | 0.682600i | \(0.239151\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.75981 | + | 3.04808i | −0.205970 | + | 0.356751i | −0.950441 | − | 0.310904i | \(-0.899368\pi\) |
0.744471 | + | 0.667655i | \(0.232702\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 21.7176i | − | 2.47495i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7950 | + | 7.96456i | 1.55206 | + | 0.896083i | 0.997974 | + | 0.0636245i | \(0.0202660\pi\) |
0.554087 | + | 0.832458i | \(0.313067\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.1763i | 1.55606i | 0.628230 | + | 0.778028i | \(0.283780\pi\) | ||||
−0.628230 | + | 0.778028i | \(0.716220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.979412 | − | 1.69639i | −0.106232 | − | 0.183999i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.78655 | − | 11.7546i | −0.719373 | − | 1.24599i | −0.961249 | − | 0.275683i | \(-0.911096\pi\) |
0.241876 | − | 0.970307i | \(-0.422237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.36216 | − | 4.82790i | 0.876593 | − | 0.506101i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.780846 | − | 2.52218i | 0.0801131 | − | 0.258770i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.12989 | + | 1.80704i | 0.317792 | + | 0.183478i | 0.650408 | − | 0.759585i | \(-0.274598\pi\) |
−0.332616 | + | 0.943062i | \(0.607931\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.6728 | − | 9.62603i | 1.65900 | − | 0.957826i | 0.685826 | − | 0.727765i | \(-0.259441\pi\) |
0.973176 | − | 0.230060i | \(-0.0738923\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.29310i | 0.324479i | 0.986751 | + | 0.162239i | \(0.0518717\pi\) | ||||
−0.986751 | + | 0.162239i | \(0.948128\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.00308 | 0.193645 | 0.0968224 | − | 0.995302i | \(-0.469132\pi\) | ||||
0.0968224 | + | 0.995302i | \(0.469132\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.514531 | + | 0.297065i | 0.0492832 | + | 0.0284536i | 0.524439 | − | 0.851448i | \(-0.324275\pi\) |
−0.475156 | + | 0.879902i | \(0.657608\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.13975 | −0.671651 | −0.335825 | − | 0.941924i | \(-0.609015\pi\) | ||||
−0.335825 | + | 0.941924i | \(0.609015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.892400 | 0.0832167 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.2488 | − | 7.07183i | −1.12284 | − | 0.648273i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.6572 | −1.24156 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.83499i | − | 0.521898i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.79592 | − | 5.65568i | 0.869247 | − | 0.501860i | 0.00214915 | − | 0.999998i | \(-0.499316\pi\) |
0.867098 | + | 0.498138i | \(0.165983\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.84637 | − | 2.79805i | −0.423430 | − | 0.244467i | 0.273114 | − | 0.961982i | \(-0.411946\pi\) |
−0.696544 | + | 0.717515i | \(0.745280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.22295 | − | 18.5905i | −0.366176 | − | 1.61200i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.97602 | + | 4.02761i | −0.596002 | + | 0.344102i | −0.767467 | − | 0.641088i | \(-0.778483\pi\) |
0.171465 | + | 0.985190i | \(0.445150\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.58012 | + | 11.3971i | 0.558118 | + | 0.966689i | 0.997654 | + | 0.0684640i | \(0.0218098\pi\) |
−0.439535 | + | 0.898225i | \(0.644857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.48137 | − | 9.49401i | −0.458375 | − | 0.793929i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.27645i | − | 0.106004i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.6556 | + | 11.3482i | 1.61025 | + | 0.929679i | 0.989311 | + | 0.145820i | \(0.0465820\pi\) |
0.620939 | + | 0.783859i | \(0.286751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4226i | 0.929556i | 0.885427 | + | 0.464778i | \(0.153866\pi\) | ||||
−0.885427 | + | 0.464778i | \(0.846134\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.98545 | + | 5.17096i | −0.239797 | + | 0.415341i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.15228 | + | 7.19197i | −0.331388 | + | 0.573981i | −0.982784 | − | 0.184757i | \(-0.940850\pi\) |
0.651396 | + | 0.758738i | \(0.274184\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.58028 | − | 3.22178i | 0.439788 | − | 0.253912i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.1546 | −1.03035 | −0.515173 | − | 0.857086i | \(-0.672272\pi\) | ||||
−0.515173 | + | 0.857086i | \(0.672272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.1178 | + | 19.2567i | 0.860324 | + | 1.49013i | 0.871616 | + | 0.490189i | \(0.163072\pi\) |
−0.0112920 | + | 0.999936i | \(0.503594\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.06295 | + | 7.03723i | −0.312534 | + | 0.541325i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.63651 | + | 9.76272i | −0.428536 | + | 0.742246i | −0.996743 | − | 0.0806396i | \(-0.974304\pi\) |
0.568208 | + | 0.822885i | \(0.307637\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.1317 | − | 17.5486i | −0.765884 | − | 1.32655i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.0361 | 1.87128 | 0.935642 | − | 0.352951i | \(-0.114822\pi\) | ||||
0.935642 | + | 0.352951i | \(0.114822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.39225 | − | 3.69057i | 0.475132 | − | 0.274318i | −0.243254 | − | 0.969963i | \(-0.578215\pi\) |
0.718386 | + | 0.695645i | \(0.244881\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.52366 | + | 2.63905i | −0.112021 | + | 0.194027i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.02903 | + | 13.9067i | −0.587141 | + | 1.01696i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.4138i | 1.33237i | 0.745785 | + | 0.666187i | \(0.232075\pi\) | ||||
−0.745785 | + | 0.666187i | \(0.767925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0421 | − | 6.95252i | −0.866811 | − | 0.500454i | −0.000523893 | − | 1.00000i | \(-0.500167\pi\) |
−0.866287 | + | 0.499546i | \(0.833500\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.26259i | 0.659932i | 0.943993 | + | 0.329966i | \(0.107037\pi\) | ||||
−0.943993 | + | 0.329966i | \(0.892963\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.97107 | − | 12.0743i | −0.494166 | − | 0.855921i | 0.505811 | − | 0.862644i | \(-0.331193\pi\) |
−0.999977 | + | 0.00672315i | \(0.997860\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.60830 | − | 7.98181i | −0.323439 | − | 0.560214i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.98620 | − | 2.30143i | 0.278408 | − | 0.160739i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.1068 | + | 4.79455i | −1.45999 | + | 0.331646i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.223008 | − | 0.128754i | −0.0153525 | − | 0.00886378i | 0.492304 | − | 0.870423i | \(-0.336155\pi\) |
−0.507657 | + | 0.861559i | \(0.669488\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.57839 | − | 0.911286i | 0.107646 | − | 0.0621492i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 43.1128i | 2.92669i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.13952 | −0.480256 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3860 | − | 7.72842i | −0.896394 | − | 0.517533i | −0.0203653 | − | 0.999793i | \(-0.506483\pi\) |
−0.876028 | + | 0.482259i | \(0.839816\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.51731 | −0.233452 | −0.116726 | − | 0.993164i | \(-0.537240\pi\) | ||||
−0.116726 | + | 0.993164i | \(0.537240\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.1834 | −1.00335 | −0.501674 | − | 0.865057i | \(-0.667282\pi\) | ||||
−0.501674 | + | 0.865057i | \(0.667282\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.6888 | + | 6.17117i | 0.700246 | + | 0.404287i | 0.807439 | − | 0.589951i | \(-0.200853\pi\) |
−0.107193 | + | 0.994238i | \(0.534186\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.57517 | −0.428917 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.8027i | 1.28093i | 0.767986 | + | 0.640466i | \(0.221259\pi\) | ||||
−0.767986 | + | 0.640466i | \(0.778741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.7113 | − | 7.33884i | 0.818804 | − | 0.472737i | −0.0312001 | − | 0.999513i | \(-0.509933\pi\) |
0.850004 | + | 0.526777i | \(0.176600\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.36226 | + | 3.67325i | 0.406470 | + | 0.234675i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.53822 | − | 7.06115i | −0.416017 | − | 0.449290i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.82239 | + | 2.20686i | −0.241267 | + | 0.139296i | −0.615759 | − | 0.787935i | \(-0.711150\pi\) |
0.374492 | + | 0.927230i | \(0.377817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.65786 | − | 6.33560i | −0.229968 | − | 0.398316i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.90044 | + | 10.2199i | 0.368059 | + | 0.637497i | 0.989262 | − | 0.146153i | \(-0.0466890\pi\) |
−0.621203 | + | 0.783650i | \(0.713356\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.0030i | 1.36720i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.83830 | − | 3.94810i | −0.421668 | − | 0.243450i | 0.274123 | − | 0.961695i | \(-0.411613\pi\) |
−0.695791 | + | 0.718245i | \(0.744946\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.31372i | 0.0807010i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.3294 | − | 24.8193i | 0.873681 | − | 1.51326i | 0.0155207 | − | 0.999880i | \(-0.495059\pi\) |
0.858161 | − | 0.513381i | \(-0.171607\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.13683 | + | 5.43315i | −0.190549 | + | 0.330040i | −0.945432 | − | 0.325819i | \(-0.894360\pi\) |
0.754883 | + | 0.655859i | \(0.227693\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.9239 | + | 11.5031i | −1.20146 | + | 0.693660i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.56534 | −0.454557 | −0.227279 | − | 0.973830i | \(-0.572983\pi\) | ||||
−0.227279 | + | 0.973830i | \(0.572983\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.1342 | − | 21.0171i | −0.723867 | − | 1.25377i | −0.959439 | − | 0.281917i | \(-0.909030\pi\) |
0.235572 | − | 0.971857i | \(-0.424304\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.151128 | + | 0.261761i | −0.00898362 | + | 0.0155601i | −0.870482 | − | 0.492200i | \(-0.836193\pi\) |
0.861499 | + | 0.507760i | \(0.169526\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.6175 | − | 28.7823i | 0.980898 | − | 1.69896i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.27107 | − | 5.66567i | −0.192416 | − | 0.333274i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.09526 | −0.0639860 | −0.0319930 | − | 0.999488i | \(-0.510185\pi\) | ||||
−0.0319930 | + | 0.999488i | \(0.510185\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.321354 | + | 0.185534i | −0.0187099 | + | 0.0108022i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.62631 | − | 2.81685i | 0.0940519 | − | 0.162903i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.57992 | − | 11.3968i | 0.379260 | − | 0.656898i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.40118i | − | 0.309270i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.19400 | + | 3.57611i | 0.353510 | + | 0.204099i | 0.666230 | − | 0.745746i | \(-0.267907\pi\) |
−0.312720 | + | 0.949845i | \(0.601240\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.76798i | 0.156958i | 0.996916 | + | 0.0784789i | \(0.0250063\pi\) | ||||
−0.996916 | + | 0.0784789i | \(0.974994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.28875 | − | 9.16039i | −0.298938 | − | 0.517776i | 0.676955 | − | 0.736024i | \(-0.263299\pi\) |
−0.975893 | + | 0.218248i | \(0.929966\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.32100 | + | 16.1444i | 0.523519 | + | 0.906762i | 0.999625 | + | 0.0273741i | \(0.00871453\pi\) |
−0.476106 | + | 0.879388i | \(0.657952\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.06219 | + | 5.23206i | −0.507385 | + | 0.292939i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.16881 | + | 13.4655i | −0.231959 | + | 0.749242i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.85829 | − | 5.11434i | −0.491369 | − | 0.283692i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −41.1153 | + | 23.7379i | −2.26676 | + | 1.30871i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.01912i | − | 0.0560161i | −0.999608 | − | 0.0280081i | \(-0.991084\pi\) | ||
0.999608 | − | 0.0280081i | \(-0.00891641\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.21089 | 0.448609 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.2415 | + | 8.22233i | 0.775784 | + | 0.447899i | 0.834934 | − | 0.550350i | \(-0.185506\pi\) |
−0.0591502 | + | 0.998249i | \(0.518839\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.9483 | 2.65070 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.4300 | 1.21111 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.18410 | − | 4.72509i | −0.439346 | − | 0.253656i | 0.263974 | − | 0.964530i | \(-0.414967\pi\) |
−0.703320 | + | 0.710873i | \(0.748300\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.6715 | −1.21358 | −0.606790 | − | 0.794863i | \(-0.707543\pi\) | ||||
−0.606790 | + | 0.794863i | \(0.707543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.5827i | 0.669708i | 0.942270 | + | 0.334854i | \(0.108687\pi\) | ||||
−0.942270 | + | 0.334854i | \(0.891313\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.99570 | + | 1.15222i | −0.105921 | + | 0.0611535i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.4835 | + | 10.0941i | 0.922743 | + | 0.532746i | 0.884509 | − | 0.466523i | \(-0.154494\pi\) |
0.0382336 | + | 0.999269i | \(0.487827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1354 | + | 8.20838i | −0.901864 | + | 0.432020i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.84629 | + | 1.06596i | −0.0966394 | + | 0.0557948i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.61388 | − | 7.99148i | −0.240843 | − | 0.417152i | 0.720112 | − | 0.693858i | \(-0.244090\pi\) |
−0.960955 | + | 0.276706i | \(0.910757\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.74283 | + | 8.21483i | 0.246236 | + | 0.426493i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.81744i | − | 0.145881i | −0.997336 | − | 0.0729407i | \(-0.976762\pi\) | ||
0.997336 | − | 0.0729407i | \(-0.0232384\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.02911 | − | 2.32621i | −0.207510 | − | 0.119806i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.9290i | 0.664116i | 0.943259 | + | 0.332058i | \(0.107743\pi\) | ||||
−0.943259 | + | 0.332058i | \(0.892257\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.52287 | + | 13.0300i | −0.384401 | + | 0.665801i | −0.991686 | − | 0.128683i | \(-0.958925\pi\) |
0.607285 | + | 0.794484i | \(0.292259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.57743 | − | 11.3924i | 0.335217 | − | 0.580612i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.0322 | + | 6.94677i | −0.610054 | + | 0.352215i | −0.772987 | − | 0.634422i | \(-0.781238\pi\) |
0.162932 | + | 0.986637i | \(0.447905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.76438 | −0.240945 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.82432 | + | 8.35597i | 0.242738 | + | 0.420434i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.0494 | + | 17.4060i | −0.504364 | + | 0.873585i | 0.495623 | + | 0.868538i | \(0.334940\pi\) |
−0.999987 | + | 0.00504676i | \(0.998394\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.20805 | + | 14.2168i | −0.409890 | + | 0.709951i | −0.994877 | − | 0.101092i | \(-0.967766\pi\) |
0.584987 | + | 0.811043i | \(0.301100\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.8814 | + | 18.8471i | 0.542040 | + | 0.938841i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.9812 | 1.23827 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.3916 | + | 17.5466i | −1.50277 | + | 0.867623i | −0.502773 | + | 0.864419i | \(0.667687\pi\) |
−0.999995 | + | 0.00320474i | \(0.998980\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.33964 | + | 2.32033i | −0.0659195 | + | 0.114176i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.29347 | + | 7.43650i | −0.210758 | + | 0.365044i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.77786i | 0.477680i | 0.971059 | + | 0.238840i | \(0.0767671\pi\) | ||||
−0.971059 | + | 0.238840i | \(0.923233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.1421 | − | 10.4744i | −0.884192 | − | 0.510489i | −0.0121540 | − | 0.999926i | \(-0.503869\pi\) |
−0.872038 | + | 0.489437i | \(0.837202\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.9828i | 0.726772i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.4995 | − | 33.7742i | −0.943649 | − | 1.63445i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.2100 | − | 21.1484i | −0.588137 | − | 1.01868i | −0.994476 | − | 0.104961i | \(-0.966528\pi\) |
0.406339 | − | 0.913722i | \(-0.366805\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.1998 | + | 11.0850i | −0.922685 | + | 0.532712i | −0.884491 | − | 0.466558i | \(-0.845494\pi\) |
−0.0381943 | + | 0.999270i | \(0.512161\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.36312 | − | 4.71208i | −0.208716 | − | 0.225410i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.89573 | + | 2.24920i | 0.185933 | + | 0.107349i | 0.590077 | − | 0.807347i | \(-0.299097\pi\) |
−0.404144 | + | 0.914695i | \(0.632431\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.6836 | + | 9.05495i | −0.745152 | + | 0.430214i | −0.823940 | − | 0.566678i | \(-0.808228\pi\) |
0.0787875 | + | 0.996891i | \(0.474895\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 8.22154i | − | 0.389738i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.9207 | 1.60082 | 0.800409 | − | 0.599454i | \(-0.204615\pi\) | ||||
0.800409 | + | 0.599454i | \(0.204615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.6781 | − | 18.8667i | −1.53875 | − | 0.888398i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.84874 | 0.274193 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.7160 | 1.48361 | 0.741807 | − | 0.670614i | \(-0.233969\pi\) | ||||
0.741807 | + | 0.670614i | \(0.233969\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.65156 | − | 3.26293i | −0.263219 | − | 0.151970i | 0.362583 | − | 0.931952i | \(-0.381895\pi\) |
−0.625802 | + | 0.779982i | \(0.715228\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.5365 | −1.09383 | −0.546916 | − | 0.837187i | \(-0.684198\pi\) | ||||
−0.546916 | + | 0.837187i | \(0.684198\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 27.7992i | − | 1.28639i | −0.765701 | − | 0.643196i | \(-0.777608\pi\) | ||
0.765701 | − | 0.643196i | \(-0.222392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51.3437 | − | 29.6433i | 2.37083 | − | 1.36880i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.9394 | − | 7.47054i | −0.594952 | − | 0.343496i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.8183 | + | 13.7209i | −0.679912 | + | 0.629559i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.7896 | − | 6.22939i | 0.492991 | − | 0.284628i | −0.232824 | − | 0.972519i | \(-0.574797\pi\) |
0.725814 | + | 0.687891i | \(0.241463\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.55342 | + | 9.61880i | 0.253214 | + | 0.438579i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.09457 | + | 1.89585i | 0.0497018 | + | 0.0860860i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 19.2572i | − | 0.872628i | −0.899794 | − | 0.436314i | \(-0.856284\pi\) | ||
0.899794 | − | 0.436314i | \(-0.143716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.6394 | − | 14.2256i | −1.11196 | − | 0.641991i | −0.172624 | − | 0.984988i | \(-0.555225\pi\) |
−0.939337 | + | 0.342997i | \(0.888558\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.81478i | 0.306922i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.31958 | + | 14.4099i | −0.373184 | + | 0.646374i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.1417 | − | 29.6903i | 0.767367 | − | 1.32912i | −0.171618 | − | 0.985164i | \(-0.554900\pi\) |
0.938986 | − | 0.343956i | \(-0.111767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.7949 | − | 9.11919i | 0.704260 | − | 0.406605i | −0.104672 | − | 0.994507i | \(-0.533379\pi\) |
0.808932 | + | 0.587902i | \(0.200046\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.6614 | 0.518926 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.00706242 | + | 0.0122325i | 0.000313036 | + | 0.000542195i | 0.866182 | − | 0.499729i | \(-0.166567\pi\) |
−0.865869 | + | 0.500271i | \(0.833234\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.69673 | + | 13.3311i | −0.340483 | + | 0.589734i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.997353 | + | 1.72747i | −0.0439486 | + | 0.0761213i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.9510 | + | 46.6804i | 1.18530 | + | 2.05300i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.7469 | −1.04037 | −0.520186 | − | 0.854053i | \(-0.674137\pi\) | ||||
−0.520186 | + | 0.854053i | \(0.674137\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.6145 | + | 15.3659i | −1.16377 | + | 0.671905i | −0.952205 | − | 0.305459i | \(-0.901190\pi\) |
−0.211567 | + | 0.977363i | \(0.567857\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.9389 | − | 27.6069i | 0.694308 | − | 1.20258i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.4147 | + | 18.0388i | −0.452814 | + | 0.784297i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 16.7765i | − | 0.726672i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.05076 | + | 0.606655i | 0.0454282 | + | 0.0262280i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 60.2252i | − | 2.59408i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1670 | − | 22.8060i | −0.566096 | − | 0.980506i | −0.996947 | − | 0.0780835i | \(-0.975120\pi\) |
0.430851 | − | 0.902423i | \(-0.358213\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.179939 | + | 0.311663i | 0.00770774 | + | 0.0133502i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.7124 | − | 13.1130i | 0.971113 | − | 0.560672i | 0.0715375 | − | 0.997438i | \(-0.477209\pi\) |
0.899575 | + | 0.436766i | \(0.143876\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.73998 | + | 6.24083i | −0.287133 | + | 0.265868i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.3341 | + | 34.8339i | 2.56567 | + | 1.48129i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.8083 | − | 14.9004i | 1.09353 | − | 0.631352i | 0.159018 | − | 0.987276i | \(-0.449167\pi\) |
0.934515 | + | 0.355924i | \(0.115834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.64291i | − | 0.280965i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.09466 | 0.214714 | 0.107357 | − | 0.994221i | \(-0.465761\pi\) | ||||
0.107357 | + | 0.994221i | \(0.465761\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.74531 | − | 2.16236i | −0.157566 | − | 0.0909710i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.90540 | −0.121801 | −0.0609003 | − | 0.998144i | \(-0.519397\pi\) | ||||
−0.0609003 | + | 0.998144i | \(0.519397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.5319 | 1.52881 | 0.764406 | − | 0.644735i | \(-0.223032\pi\) | ||||
0.764406 | + | 0.644735i | \(0.223032\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.91136 | − | 3.41293i | −0.246521 | − | 0.142329i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.6393 | 1.69184 | 0.845919 | − | 0.533312i | \(-0.179053\pi\) | ||||
0.845919 | + | 0.533312i | \(0.179053\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 62.0018i | 2.57227i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.32674 | − | 5.38480i | 0.386274 | − | 0.223016i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.1443 | + | 9.89826i | 0.707620 | + | 0.408545i | 0.810179 | − | 0.586182i | \(-0.199370\pi\) |
−0.102559 | + | 0.994727i | \(0.532703\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.9004 | − | 9.51792i | 1.72647 | − | 0.392179i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.51318 | + | 0.873633i | −0.0621387 | + | 0.0358758i | −0.530747 | − | 0.847530i | \(-0.678089\pi\) |
0.468609 | + | 0.883406i | \(0.344755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.28357 | − | 7.41936i | −0.175609 | − | 0.304164i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.607867 | + | 1.05286i | 0.0248368 | + | 0.0430186i | 0.878177 | − | 0.478336i | \(-0.158760\pi\) |
−0.853340 | + | 0.521355i | \(0.825427\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 39.9166i | − | 1.62823i | −0.580703 | − | 0.814116i | \(-0.697222\pi\) | ||
0.580703 | − | 0.814116i | \(-0.302778\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.16417 | − | 4.13623i | −0.291265 | − | 0.168162i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.1840i | 0.941008i | 0.882398 | + | 0.470504i | \(0.155928\pi\) | ||||
−0.882398 | + | 0.470504i | \(0.844072\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.9826 | + | 20.7544i | −0.484763 | + | 0.839635i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7145 | − | 32.4145i | 0.755872 | − | 1.30921i | −0.189068 | − | 0.981964i | \(-0.560547\pi\) |
0.944940 | − | 0.327244i | \(-0.106120\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.1965 | + | 13.9699i | −0.974115 | + | 0.562406i | −0.900488 | − | 0.434880i | \(-0.856791\pi\) |
−0.0736271 | + | 0.997286i | \(0.523457\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.3728 | −0.818850 | −0.409425 | − | 0.912344i | \(-0.634271\pi\) | ||||
−0.409425 | + | 0.912344i | \(0.634271\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.6817 | − | 51.4103i | −1.18917 | − | 2.05971i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.81555 | + | 17.0010i | −0.392622 | + | 0.680042i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.13455 | − | 14.0895i | 0.324346 | − | 0.561784i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.12585 | + | 12.3423i | 0.283676 | + | 0.491341i | 0.972287 | − | 0.233790i | \(-0.0751128\pi\) |
−0.688611 | + | 0.725130i | \(0.741779\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.85155 | 0.271895 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.1891 | − | 13.3883i | 0.918787 | − | 0.530462i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.7247 | + | 35.8962i | −0.818575 | + | 1.41781i | 0.0881571 | + | 0.996107i | \(0.471902\pi\) |
−0.906732 | + | 0.421707i | \(0.861431\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.3938 | − | 42.2512i | 0.961996 | − | 1.66623i | 0.244519 | − | 0.969644i | \(-0.421370\pi\) |
0.717477 | − | 0.696582i | \(-0.245297\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 24.1855i | − | 0.950829i | −0.879762 | − | 0.475414i | \(-0.842298\pi\) | ||
0.879762 | − | 0.475414i | \(-0.157702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.63440 | + | 1.52097i | 0.103409 | + | 0.0597032i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 19.3902i | − | 0.758797i | −0.925233 | − | 0.379399i | \(-0.876131\pi\) | ||
0.925233 | − | 0.379399i | \(-0.123869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.69485 | − | 2.93556i | −0.0662231 | − | 0.114702i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.1706 | − | 28.0083i | −0.629918 | − | 1.09105i | −0.987568 | − | 0.157194i | \(-0.949755\pi\) |
0.357650 | − | 0.933856i | \(-0.383578\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.2738 | − | 9.97301i | 0.671872 | − | 0.387905i | −0.124914 | − | 0.992168i | \(-0.539865\pi\) |
0.796785 | + | 0.604262i | \(0.206532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.41512 | − | 11.0310i | 0.132433 | − | 0.427765i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.68873 | − | 1.55234i | −0.104108 | − | 0.0601068i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.3457 | + | 22.1389i | −1.48032 | + | 0.854662i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.5000i | 0.597480i | 0.954335 | + | 0.298740i | \(0.0965663\pi\) | ||||
−0.954335 | + | 0.298740i | \(0.903434\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.6896 | −0.987332 | −0.493666 | − | 0.869652i | \(-0.664343\pi\) | ||||
−0.493666 | + | 0.869652i | \(0.664343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.6889 | + | 7.90331i | 0.525333 | + | 0.303301i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.9201 | 1.48924 | 0.744618 | − | 0.667491i | \(-0.232632\pi\) | ||||
0.744618 | + | 0.667491i | \(0.232632\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.87923 | −0.186426 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.14673 | + | 2.39412i | 0.157978 | + | 0.0912086i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.29825 | −0.239597 | −0.119798 | − | 0.992798i | \(-0.538225\pi\) | ||||
−0.119798 | + | 0.992798i | \(0.538225\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.97146i | 0.302375i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.2817 | + | 12.2870i | −0.806102 | + | 0.465403i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.2523 | + | 15.1568i | 0.991537 | + | 0.572464i | 0.905733 | − | 0.423848i | \(-0.139321\pi\) |
0.0858038 | + | 0.996312i | \(0.472654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.3843 | − | 4.85756i | 0.806522 | − | 0.183206i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 72.9202 | − | 42.1005i | 2.74245 | − | 1.58335i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.526628 | − | 0.912146i | −0.0197779 | − | 0.0342564i | 0.855967 | − | 0.517030i | \(-0.172963\pi\) |
−0.875745 | + | 0.482774i | \(0.839629\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.26142 | + | 12.5772i | 0.271942 | + | 0.471018i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 6.64039i | − | 0.248336i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.0751 | + | 10.4356i | 0.674086 | + | 0.389184i | 0.797623 | − | 0.603156i | \(-0.206090\pi\) |
−0.123537 | + | 0.992340i | \(0.539424\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.4027i | 0.536386i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.88171 | + | 8.45538i | −0.181302 | + | 0.314025i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.50923 | + | 11.2743i | −0.241414 | + | 0.418141i | −0.961117 | − | 0.276141i | \(-0.910944\pi\) |
0.719703 | + | 0.694282i | \(0.244278\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.42679 | + | 4.86521i | −0.311676 | + | 0.179946i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −52.1956 | −1.92789 | −0.963944 | − | 0.266104i | \(-0.914263\pi\) | ||||
−0.963944 | + | 0.266104i | \(0.914263\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.6556 | − | 58.2933i | −1.23972 | − | 2.14726i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.41460 | + | 9.37837i | −0.199179 | + | 0.344989i | −0.948263 | − | 0.317487i | \(-0.897161\pi\) |
0.749083 | + | 0.662476i | \(0.230494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.7477 | − | 32.4720i | 0.687786 | − | 1.19128i | −0.284766 | − | 0.958597i | \(-0.591916\pi\) |
0.972552 | − | 0.232684i | \(-0.0747507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.87385 | + | 11.9059i | 0.251838 | + | 0.436197i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.76068 | 0.320108 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.3564 | + | 23.8771i | −1.50912 | + | 0.871289i | −0.509174 | + | 0.860664i | \(0.670049\pi\) |
−0.999944 | + | 0.0106254i | \(0.996618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.45946 | + | 5.99196i | −0.125903 | + | 0.218070i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.28153 | − | 9.14788i | 0.191960 | − | 0.332485i | −0.753939 | − | 0.656944i | \(-0.771849\pi\) |
0.945900 | + | 0.324459i | \(0.105182\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 17.4566i | − | 0.632801i | −0.948626 | − | 0.316400i | \(-0.897526\pi\) | ||
0.948626 | − | 0.316400i | \(-0.102474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.25036 | + | 1.29925i | 0.0814685 | + | 0.0470359i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.35247i | 0.0488347i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.34837 | − | 4.06750i | −0.0846844 | − | 0.146678i | 0.820572 | − | 0.571543i | \(-0.193655\pi\) |
−0.905257 | + | 0.424865i | \(0.860322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.20124 | − | 10.7409i | −0.223043 | − | 0.386322i | 0.732687 | − | 0.680565i | \(-0.238266\pi\) |
−0.955731 | + | 0.294243i | \(0.904932\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.5520 | − | 22.8354i | 1.42075 | − | 0.820270i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.6414 | − | 9.79592i | −1.13367 | − | 0.350975i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.3604 | + | 9.44567i | 0.585421 | + | 0.337993i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.35634 | + | 2.51513i | −0.155484 | + | 0.0897690i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.833723i | 0.0297190i | 0.999890 | + | 0.0148595i | \(0.00473010\pi\) | ||||
−0.999890 | + | 0.0148595i | \(0.995270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.2265 | −1.11029 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.0487 | − | 9.84310i | −0.605419 | − | 0.349539i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.8381 | 1.41114 | 0.705569 | − | 0.708641i | \(-0.250691\pi\) | ||||
0.705569 | + | 0.708641i | \(0.250691\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.1038 | 1.24188 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.1355 | + | 8.73851i | 0.534122 | + | 0.308375i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.90301 | 0.137563 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.2719i | 1.02914i | 0.857447 | + | 0.514572i | \(0.172049\pi\) | ||||
−0.857447 | + | 0.514572i | \(0.827951\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.6197 | − | 9.59539i | 0.583597 | − | 0.336940i | −0.178965 | − | 0.983856i | \(-0.557275\pi\) |
0.762562 | + | 0.646916i | \(0.223941\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.90052 | − | 3.98402i | −0.241715 | − | 0.139554i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.5289 | − | 3.87884i | −0.438330 | − | 0.135703i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.0207 | + | 10.9816i | −0.663828 | + | 0.383261i | −0.793734 | − | 0.608265i | \(-0.791866\pi\) |
0.129906 | + | 0.991526i | \(0.458532\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.18570 | − | 5.51779i | −0.111046 | − | 0.192338i | 0.805146 | − | 0.593077i | \(-0.202087\pi\) |
−0.916192 | + | 0.400739i | \(0.868754\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.935401 | + | 1.62016i | 0.0325271 | + | 0.0563386i | 0.881831 | − | 0.471566i | \(-0.156311\pi\) |
−0.849304 | + | 0.527905i | \(0.822978\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.41224i | 0.0837806i | 0.999122 | + | 0.0418903i | \(0.0133380\pi\) | ||||
−0.999122 | + | 0.0418903i | \(0.986662\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.9671 | − | 19.6109i | −1.17689 | − | 0.679478i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.4687i | 0.466102i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.12136 | + | 15.7987i | −0.314904 | + | 0.545430i | −0.979417 | − | 0.201847i | \(-0.935306\pi\) |
0.664513 | + | 0.747277i | \(0.268639\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.2796 | − | 21.2689i | 0.423434 | − | 0.733410i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.26261 | + | 2.46102i | −0.146638 | + | 0.0846617i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −59.7312 | −2.05239 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.70594 | + | 6.41887i | 0.127038 | + | 0.220036i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.34815 | + | 10.9953i | −0.217357 | + | 0.376473i | −0.953999 | − | 0.299810i | \(-0.903077\pi\) |
0.736642 | + | 0.676283i | \(0.236410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.78818 | − | 10.0254i | 0.197720 | − | 0.342462i | −0.750069 | − | 0.661360i | \(-0.769980\pi\) |
0.947789 | + | 0.318898i | \(0.103313\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.8563 | − | 20.5357i | −0.404532 | − | 0.700669i | 0.589735 | − | 0.807597i | \(-0.299232\pi\) |
−0.994267 | + | 0.106927i | \(0.965899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.59563 | −0.258558 | −0.129279 | − | 0.991608i | \(-0.541266\pi\) | ||||
−0.129279 | + | 0.991608i | \(0.541266\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.91350 | + | 3.41416i | −0.201065 | + | 0.116085i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.5488 | − | 68.5005i | 1.34160 | − | 2.32372i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.9635 | − | 25.9176i | 0.507019 | − | 0.878183i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 25.5200i | − | 0.862733i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.21952 | − | 5.32289i | −0.311321 | − | 0.179741i | 0.336196 | − | 0.941792i | \(-0.390859\pi\) |
−0.647518 | + | 0.762051i | \(0.724193\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.9276i | 1.61472i | 0.590058 | + | 0.807361i | \(0.299105\pi\) | ||||
−0.590058 | + | 0.807361i | \(0.700895\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.9331 | + | 43.1854i | 0.839067 | + | 1.45331i | 0.890676 | + | 0.454639i | \(0.150232\pi\) |
−0.0516094 | + | 0.998667i | \(0.516435\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.4328 | + | 23.2663i | 0.451030 | + | 0.781206i | 0.998450 | − | 0.0556514i | \(-0.0177235\pi\) |
−0.547421 | + | 0.836858i | \(0.684390\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.8435 | − | 24.7357i | 1.43693 | − | 0.829610i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.1473 | + | 34.7184i | 1.07577 | + | 1.16181i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.1332 | + | 7.58246i | 0.438995 | + | 0.253454i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.9899 | − | 10.3864i | 0.599995 | − | 0.346407i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 7.01373i | − | 0.233661i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.47092 | 0.148619 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.3174 | + | 28.4734i | 1.63756 | + | 0.945444i | 0.981671 | + | 0.190585i | \(0.0610385\pi\) |
0.655887 | + | 0.754859i | \(0.272295\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.3317 | −1.56817 | −0.784084 | − | 0.620655i | \(-0.786867\pi\) | ||||
−0.784084 | + | 0.620655i | \(0.786867\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 70.3940 | 2.32970 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.1962 | − | 12.2376i | −0.699959 | − | 0.404121i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.8656 | 0.853229 | 0.426614 | − | 0.904434i | \(-0.359706\pi\) | ||||
0.426614 | + | 0.904434i | \(0.359706\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.39922i | 0.276464i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.1857 | − | 11.6542i | 0.663703 | − | 0.383189i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.6190 | − | 6.70826i | −0.381209 | − | 0.220091i | 0.297135 | − | 0.954835i | \(-0.403969\pi\) |
−0.678344 | + | 0.734744i | \(0.737302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.7107 | − | 51.5535i | −0.383802 | − | 1.68960i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.42360 | + | 4.86337i | −0.275481 | + | 0.159049i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5622 | − | 18.2943i | −0.345053 | − | 0.597649i | 0.640310 | − | 0.768116i | \(-0.278806\pi\) |
−0.985363 | + | 0.170467i | \(0.945472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.45798 | + | 7.72145i | 0.145326 | + | 0.251712i | 0.929495 | − | 0.368836i | \(-0.120244\pi\) |
−0.784168 | + | 0.620548i | \(0.786910\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 11.1954i | − | 0.364573i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.3309 | + | 22.1303i | 1.24559 | + | 0.719139i | 0.970226 | − | 0.242202i | \(-0.0778698\pi\) |
0.275360 | + | 0.961341i | \(0.411203\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.77040i | 0.252238i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.4711 | − | 37.1890i | 0.695517 | − | 1.20467i | −0.274490 | − | 0.961590i | \(-0.588509\pi\) |
0.970006 | − | 0.243080i | \(-0.0781577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.57683 | + | 9.65935i | −0.180462 | + | 0.312569i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.5104 | + | 17.6152i | −0.985233 | + | 0.568824i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −66.1700 | −2.13452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.21130 | − | 7.29419i | −0.135567 | − | 0.234808i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.84907 | + | 11.8629i | −0.220251 | + | 0.381486i | −0.954884 | − | 0.296978i | \(-0.904021\pi\) |
0.734633 | + | 0.678465i | \(0.237354\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.0241 | − | 26.0224i | 0.482145 | − | 0.835100i | −0.517645 | − | 0.855596i | \(-0.673191\pi\) |
0.999790 | + | 0.0204959i | \(0.00652451\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.7789 | + | 49.8465i | 0.922609 | + | 1.59801i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.06375 | 0.257982 | 0.128991 | − | 0.991646i | \(-0.458826\pi\) | ||||
0.128991 | + | 0.991646i | \(0.458826\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −58.3689 | + | 33.6993i | −1.86548 | + | 1.07703i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.7029 | + | 53.1790i | −0.979271 | + | 1.69615i | −0.314216 | + | 0.949352i | \(0.601742\pi\) |
−0.665055 | + | 0.746795i | \(0.731592\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.80528 | + | 4.85889i | −0.0893838 | + | 0.154817i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 4.43298i | − | 0.140961i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.12690 | − | 5.26942i | −0.289926 | − | 0.167389i | 0.347983 | − | 0.937501i | \(-0.386867\pi\) |
−0.637908 | + | 0.770112i | \(0.720200\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 8.44508i | − | 0.267727i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.1468 | − | 27.9670i | −0.511373 | − | 0.885724i | −0.999913 | − | 0.0131823i | \(-0.995804\pi\) |
0.488540 | − | 0.872541i | \(-0.337530\pi\) | |||||||
\(998\) | 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 | 1368.2.cu.b.521.7 | yes | 20 | |
3.2 | odd | 2 | 1368.2.cu.a.521.4 | yes | 20 | ||
4.3 | odd | 2 | 2736.2.dc.f.1889.7 | 20 | |||
12.11 | even | 2 | 2736.2.dc.e.1889.4 | 20 | |||
19.12 | odd | 6 | 1368.2.cu.a.449.4 | ✓ | 20 | ||
57.50 | even | 6 | inner | 1368.2.cu.b.449.7 | yes | 20 | |
76.31 | even | 6 | 2736.2.dc.e.449.4 | 20 | |||
228.107 | odd | 6 | 2736.2.dc.f.449.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.cu.a.449.4 | ✓ | 20 | 19.12 | odd | 6 | ||
1368.2.cu.a.521.4 | yes | 20 | 3.2 | odd | 2 | ||
1368.2.cu.b.449.7 | yes | 20 | 57.50 | even | 6 | inner | |
1368.2.cu.b.521.7 | yes | 20 | 1.1 | even | 1 | trivial | |
2736.2.dc.e.449.4 | 20 | 76.31 | even | 6 | |||
2736.2.dc.e.1889.4 | 20 | 12.11 | even | 2 | |||
2736.2.dc.f.449.7 | 20 | 228.107 | odd | 6 | |||
2736.2.dc.f.1889.7 | 20 | 4.3 | odd | 2 |