Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(257,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.r (of order \(4\), 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: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.6040479020157644046336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.8 | ||
Root | \(0.912166 - 1.47240i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.257 |
Dual form | 600.2.r.f.593.8 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 1.73122 | − | 0.0537601i | 0.999518 | − | 0.0310384i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.560232 | + | 0.560232i | 0.211748 | + | 0.211748i | 0.805010 | − | 0.593262i | \(-0.202160\pi\) |
−0.593262 | + | 0.805010i | \(0.702160\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.99422 | − | 0.186141i | 0.998073 | − | 0.0620469i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.939764i | − | 0.283349i | −0.989913 | − | 0.141675i | \(-0.954751\pi\) | ||
0.989913 | − | 0.141675i | \(-0.0452487\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.13018 | − | 4.13018i | 1.14551 | − | 1.14551i | 0.158081 | − | 0.987426i | \(-0.449469\pi\) |
0.987426 | − | 0.158081i | \(-0.0505307\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.50588 | + | 4.50588i | −1.09284 | + | 1.09284i | −0.0976128 | + | 0.995224i | \(0.531121\pi\) |
−0.995224 | + | 0.0976128i | \(0.968879\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.74456i | − | 0.859062i | −0.903052 | − | 0.429531i | \(-0.858679\pi\) | ||
0.903052 | − | 0.429531i | \(-0.141321\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | + | 0.939764i | 0.218218 | + | 0.205073i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.18334 | + | 6.18334i | 1.28932 | + | 1.28932i | 0.935203 | + | 0.354113i | \(0.115217\pi\) |
0.354113 | + | 0.935203i | \(0.384783\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.17364 | − | 0.483219i | 0.995667 | − | 0.0929956i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.16915 | 0.588496 | 0.294248 | − | 0.955729i | \(-0.404931\pi\) | ||||
0.294248 | + | 0.955729i | \(0.404931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.37228 | −0.964890 | −0.482445 | − | 0.875926i | \(-0.660251\pi\) | ||||
−0.482445 | + | 0.875926i | \(0.660251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0505218 | − | 1.62693i | −0.00879471 | − | 0.283213i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.56995 | + | 3.56995i | 0.586897 | + | 0.586897i | 0.936790 | − | 0.349893i | \(-0.113782\pi\) |
−0.349893 | + | 0.936790i | \(0.613782\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.92820 | − | 7.37228i | 1.10940 | − | 1.18051i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.15759i | − | 1.43017i | −0.699035 | − | 0.715087i | \(-0.746387\pi\) | ||
0.699035 | − | 0.715087i | \(-0.253613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.33875 | + | 4.33875i | −0.661653 | + | 0.661653i | −0.955770 | − | 0.294117i | \(-0.904975\pi\) |
0.294117 | + | 0.955770i | \(0.404975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65685 | + | 5.65685i | −0.825137 | + | 0.825137i | −0.986840 | − | 0.161703i | \(-0.948301\pi\) |
0.161703 | + | 0.986840i | \(0.448301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.37228i | − | 0.910326i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.55842 | + | 8.04290i | −1.05839 | + | 1.12623i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.526485 | − | 0.526485i | −0.0723183 | − | 0.0723183i | 0.670022 | − | 0.742341i | \(-0.266284\pi\) |
−0.742341 | + | 0.670022i | \(0.766284\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.201308 | − | 6.48265i | −0.0266639 | − | 0.858648i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.9769 | −1.55926 | −0.779628 | − | 0.626242i | \(-0.784592\pi\) | ||||
−0.779628 | + | 0.626242i | \(0.784592\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.37228 | 0.175703 | 0.0878513 | − | 0.996134i | \(-0.472000\pi\) | ||||
0.0878513 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.78174 | + | 1.57317i | 0.224478 | + | 0.198201i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.22474 | − | 1.22474i | −0.149626 | − | 0.149626i | 0.628325 | − | 0.777951i | \(-0.283741\pi\) |
−0.777951 | + | 0.628325i | \(0.783741\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.0371 | + | 10.3723i | 1.32871 | + | 1.24868i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.16915i | 0.376109i | 0.982159 | + | 0.188054i | \(0.0602181\pi\) | ||||
−0.982159 | + | 0.188054i | \(0.939782\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.56349 | − | 5.56349i | 0.651158 | − | 0.651158i | −0.302114 | − | 0.953272i | \(-0.597692\pi\) |
0.953272 | + | 0.302114i | \(0.0976924\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.526485 | − | 0.526485i | 0.0599986 | − | 0.0599986i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.74456i | 0.983840i | 0.870640 | + | 0.491920i | \(0.163705\pi\) | ||||
−0.870640 | + | 0.491920i | \(0.836295\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.93070 | − | 1.11469i | 0.992300 | − | 0.123855i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.97940 | − | 3.97940i | −0.436796 | − | 0.436796i | 0.454136 | − | 0.890932i | \(-0.349948\pi\) |
−0.890932 | + | 0.454136i | \(0.849948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.48648 | − | 0.170374i | 0.588212 | − | 0.0182660i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.0858 | −1.70509 | −0.852545 | − | 0.522654i | \(-0.824942\pi\) | ||||
−0.852545 | + | 0.522654i | \(0.824942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.62772 | 0.485117 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.30058 | + | 0.288814i | −0.964425 | + | 0.0299486i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.25065 | − | 5.25065i | −0.533122 | − | 0.533122i | 0.388378 | − | 0.921500i | \(-0.373036\pi\) |
−0.921500 | + | 0.388378i | \(0.873036\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.174928 | − | 2.81386i | −0.0175810 | − | 0.282804i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.80773i | − | 0.876402i | −0.898877 | − | 0.438201i | \(-0.855616\pi\) | ||
0.898877 | − | 0.438201i | \(-0.144384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.26037 | + | 8.26037i | −0.813918 | + | 0.813918i | −0.985219 | − | 0.171301i | \(-0.945203\pi\) |
0.171301 | + | 0.985219i | \(0.445203\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.15097 | + | 1.15097i | −0.111269 | + | 0.111269i | −0.760549 | − | 0.649280i | \(-0.775070\pi\) |
0.649280 | + | 0.760549i | \(0.275070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.8614i | 1.04033i | 0.854065 | + | 0.520167i | \(0.174130\pi\) | ||||
−0.854065 | + | 0.520167i | \(0.825870\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.37228 | + | 5.98844i | 0.604830 | + | 0.568398i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.67746 | − | 1.67746i | −0.157802 | − | 0.157802i | 0.623790 | − | 0.781592i | \(-0.285592\pi\) |
−0.781592 | + | 0.623790i | \(0.785592\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.5979 | − | 13.1355i | 1.07222 | − | 1.21438i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.04868 | −0.462811 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1168 | 0.919713 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.492313 | − | 15.8538i | −0.0443903 | − | 1.42949i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.58940 | − | 9.58940i | −0.850921 | − | 0.850921i | 0.139325 | − | 0.990247i | \(-0.455507\pi\) |
−0.990247 | + | 0.139325i | \(0.955507\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.27806 | + | 7.74456i | −0.640797 | + | 0.681871i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.04868i | 0.441105i | 0.975375 | + | 0.220552i | \(0.0707860\pi\) | ||||
−0.975375 | + | 0.220552i | \(0.929214\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.09782 | − | 2.09782i | 0.181904 | − | 0.181904i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.03237 | + | 5.03237i | −0.429944 | + | 0.429944i | −0.888609 | − | 0.458665i | \(-0.848328\pi\) |
0.458665 | + | 0.888609i | \(0.348328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.1168i | 1.28219i | 0.767460 | + | 0.641097i | \(0.221520\pi\) | ||||
−0.767460 | + | 0.641097i | \(0.778480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.48913 | + | 10.0974i | −0.799129 | + | 0.850350i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.88140 | − | 3.88140i | −0.324579 | − | 0.324579i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.342574 | − | 11.0318i | −0.0282551 | − | 0.909887i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.75906 | −0.307954 | −0.153977 | − | 0.988074i | \(-0.549208\pi\) | ||||
−0.153977 | + | 0.988074i | \(0.549208\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.62772 | −0.213841 | −0.106920 | − | 0.994268i | \(-0.534099\pi\) | ||||
−0.106920 | + | 0.994268i | \(0.534099\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.6529 | + | 14.3303i | −1.02292 | + | 1.15854i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.23773 | + | 9.23773i | 0.737251 | + | 0.737251i | 0.972045 | − | 0.234794i | \(-0.0754416\pi\) |
−0.234794 | + | 0.972045i | \(0.575442\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.939764 | − | 0.883156i | −0.0745281 | − | 0.0700388i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820i | 0.546019i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.2636 | + | 13.2636i | −1.03889 | + | 1.03889i | −0.0396750 | + | 0.999213i | \(0.512632\pi\) |
−0.999213 | + | 0.0396750i | \(0.987368\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.82843 | − | 2.82843i | 0.218870 | − | 0.218870i | −0.589152 | − | 0.808022i | \(-0.700538\pi\) |
0.808022 | + | 0.589152i | \(0.200538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 21.1168i | − | 1.62437i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.697015 | − | 11.2120i | −0.0533021 | − | 0.857406i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.48528 | − | 8.48528i | −0.645124 | − | 0.645124i | 0.306687 | − | 0.951811i | \(-0.400780\pi\) |
−0.951811 | + | 0.306687i | \(0.900780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.7346 | + | 0.643878i | −1.55851 | + | 0.0483968i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.98844 | −0.447597 | −0.223798 | − | 0.974635i | \(-0.571846\pi\) | ||||
−0.223798 | + | 0.974635i | \(0.571846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.1168 | −1.49527 | −0.747637 | − | 0.664108i | \(-0.768811\pi\) | ||||
−0.747637 | + | 0.664108i | \(0.768811\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.37572 | − | 0.0737740i | 0.175618 | − | 0.00545353i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.23447 | + | 4.23447i | 0.309655 | + | 0.309655i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.16915 | + | 2.62772i | 0.230522 | + | 0.191138i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 25.2434i | − | 1.82655i | −0.407347 | − | 0.913273i | \(-0.633546\pi\) | ||
0.407347 | − | 0.913273i | \(-0.366454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.36465 | + | 8.36465i | −0.602101 | + | 0.602101i | −0.940870 | − | 0.338769i | \(-0.889990\pi\) |
0.338769 | + | 0.940870i | \(0.389990\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0647 | − | 10.0647i | 0.717083 | − | 0.717083i | −0.250924 | − | 0.968007i | \(-0.580734\pi\) |
0.968007 | + | 0.250924i | \(0.0807344\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.62772i | 0.328050i | 0.986456 | + | 0.164025i | \(0.0524478\pi\) | ||||
−0.986456 | + | 0.164025i | \(0.947552\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.18614 | − | 2.05446i | −0.154198 | − | 0.144910i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.77546 | + | 1.77546i | 0.124613 | + | 0.124613i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.6652 | + | 17.3633i | 1.36683 | + | 1.20683i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.51900 | −0.243415 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.74456 | 0.670843 | 0.335422 | − | 0.942068i | \(-0.391121\pi\) | ||||
0.335422 | + | 0.942068i | \(0.391121\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.170374 | + | 5.48648i | 0.0116738 | + | 0.375927i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00972 | − | 3.00972i | −0.204313 | − | 0.204313i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.33252 | − | 9.93070i | 0.630633 | − | 0.671055i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 37.2203i | 2.50371i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3906 | − | 12.3906i | 0.829733 | − | 0.829733i | −0.157747 | − | 0.987480i | \(-0.550423\pi\) |
0.987480 | + | 0.157747i | \(0.0504230\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.82843 | − | 2.82843i | 0.187729 | − | 0.187729i | −0.606984 | − | 0.794714i | \(-0.707621\pi\) |
0.794714 | + | 0.606984i | \(0.207621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.62772i | − | 0.305808i | −0.988241 | − | 0.152904i | \(-0.951137\pi\) | ||
0.988241 | − | 0.152904i | \(-0.0488626\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.883156 | − | 0.939764i | 0.0581074 | − | 0.0618319i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.8932 | + | 12.8932i | 0.844659 | + | 0.844659i | 0.989461 | − | 0.144801i | \(-0.0462543\pi\) |
−0.144801 | + | 0.989461i | \(0.546254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.470108 | + | 15.1387i | 0.0305368 | + | 0.983366i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.2665 | 0.858138 | 0.429069 | − | 0.903272i | \(-0.358842\pi\) | ||||
0.429069 | + | 0.903272i | \(0.358842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2337 | −0.852457 | −0.426228 | − | 0.904616i | \(-0.640158\pi\) | ||||
−0.426228 | + | 0.904616i | \(0.640158\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4011 | − | 2.40989i | 0.987978 | − | 0.154594i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.4657 | − | 15.4657i | −0.984061 | − | 0.984061i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.10313 | − | 6.67527i | −0.450143 | − | 0.423028i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 10.4472i | − | 0.659422i | −0.944082 | − | 0.329711i | \(-0.893049\pi\) | ||
0.944082 | − | 0.329711i | \(-0.106951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.81088 | − | 5.81088i | 0.365327 | − | 0.365327i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.0647 | + | 10.0647i | −0.627821 | + | 0.627821i | −0.947519 | − | 0.319698i | \(-0.896418\pi\) |
0.319698 | + | 0.947519i | \(0.396418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000i | 0.248548i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.48913 | − | 0.589907i | 0.587362 | − | 0.0365143i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.7872 | − | 10.7872i | −0.665169 | − | 0.665169i | 0.291425 | − | 0.956594i | \(-0.405871\pi\) |
−0.956594 | + | 0.291425i | \(0.905871\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.8480 | + | 0.864773i | −1.70427 | + | 0.0529233i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.1229 | 1.65371 | 0.826856 | − | 0.562413i | \(-0.190127\pi\) | ||||
0.826856 | + | 0.562413i | \(0.190127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.2337 | 1.10762 | 0.553809 | − | 0.832644i | \(-0.313174\pi\) | ||||
0.553809 | + | 0.832644i | \(0.313174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.01158 | − | 0.248787i | 0.484883 | − | 0.0150572i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.6315 | + | 14.6315i | 0.879120 | + | 0.879120i | 0.993444 | − | 0.114323i | \(-0.0364700\pi\) |
−0.114323 | + | 0.993444i | \(0.536470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.0858 | + | 1.00000i | −0.963031 | + | 0.0598684i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.7846i | − | 1.23991i | −0.784639 | − | 0.619953i | \(-0.787152\pi\) | ||
0.784639 | − | 0.619953i | \(-0.212848\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.7455 | − | 17.7455i | 1.05486 | − | 1.05486i | 0.0564542 | − | 0.998405i | \(-0.482021\pi\) |
0.998405 | − | 0.0564542i | \(-0.0179795\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.13037 | − | 5.13037i | 0.302836 | − | 0.302836i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 23.6060i | − | 1.38859i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.37228 | − | 8.80773i | −0.549413 | − | 0.516318i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.3784 | + | 21.3784i | 1.24894 | + | 1.24894i | 0.956188 | + | 0.292754i | \(0.0945719\pi\) |
0.292754 | + | 0.956188i | \(0.405428\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.454112 | − | 4.86199i | −0.0263502 | − | 0.282122i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 51.0767 | 2.95384 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.86141 | −0.280207 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.473504 | − | 15.2481i | −0.0272021 | − | 0.875980i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.4916 | + | 19.4916i | 1.11245 | + | 1.11245i | 0.992819 | + | 0.119628i | \(0.0381701\pi\) |
0.119628 | + | 0.992819i | \(0.461830\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.8564 | + | 14.7446i | −0.788263 | + | 0.838789i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.8333i | 1.46487i | 0.680836 | + | 0.732436i | \(0.261617\pi\) | ||||
−0.680836 | + | 0.732436i | \(0.738383\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.02916 | − | 9.02916i | 0.510359 | − | 0.510359i | −0.404278 | − | 0.914636i | \(-0.632477\pi\) |
0.914636 | + | 0.404278i | \(0.132477\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.70982 | − | 6.70982i | 0.376861 | − | 0.376861i | −0.493107 | − | 0.869969i | \(-0.664139\pi\) |
0.869969 | + | 0.493107i | \(0.164139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.97825i | − | 0.166750i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.93070 | + | 2.05446i | −0.107761 | + | 0.114669i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.8726 | + | 16.8726i | 0.938814 | + | 0.938814i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.583910 | + | 18.8034i | 0.0322903 | + | 1.03983i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.33830 | −0.349442 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.3723 | 1.44955 | 0.724776 | − | 0.688985i | \(-0.241943\pi\) | ||||
0.724776 | + | 0.688985i | \(0.241943\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.3537 | + | 10.0247i | 0.622181 | + | 0.549351i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.67423 | + | 3.67423i | 0.200148 | + | 0.200148i | 0.800064 | − | 0.599915i | \(-0.204799\pi\) |
−0.599915 | + | 0.800064i | \(0.704799\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.99422 | − | 2.81386i | −0.162624 | − | 0.152828i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.04868i | 0.273401i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.49157 | − | 7.49157i | 0.404507 | − | 0.404507i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.38728 | + | 8.38728i | −0.450253 | + | 0.450253i | −0.895438 | − | 0.445186i | \(-0.853138\pi\) |
0.445186 | + | 0.895438i | \(0.353138\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.51087i | 0.241462i | 0.992685 | + | 0.120731i | \(0.0385238\pi\) | ||||
−0.992685 | + | 0.120731i | \(0.961476\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.3723 | − | 23.3639i | 1.03402 | − | 1.24707i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.13037 | − | 5.13037i | −0.273062 | − | 0.273062i | 0.557270 | − | 0.830332i | \(-0.311849\pi\) |
−0.830332 | + | 0.557270i | \(0.811849\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.74035 | + | 0.271417i | −0.462588 | + | 0.0143649i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.04868 | −0.266459 | −0.133229 | − | 0.991085i | \(-0.542535\pi\) | ||||
−0.133229 | + | 0.991085i | \(0.542535\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.97825 | 0.262013 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.5144 | − | 0.543882i | 0.919270 | − | 0.0285464i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.02916 | − | 9.02916i | −0.471319 | − | 0.471319i | 0.431023 | − | 0.902341i | \(-0.358153\pi\) |
−0.902341 | + | 0.431023i | \(0.858153\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.70460 | − | 27.4198i | −0.0887379 | − | 1.42742i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.589907i | − | 0.0306265i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.560232 | − | 0.560232i | 0.0290077 | − | 0.0290077i | −0.692454 | − | 0.721462i | \(-0.743471\pi\) |
0.721462 | + | 0.692454i | \(0.243471\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.0892 | − | 13.0892i | 0.674126 | − | 0.674126i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.51087i | − | 0.180342i | −0.995926 | − | 0.0901708i | \(-0.971259\pi\) | ||
0.995926 | − | 0.0901708i | \(-0.0287413\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.1168 | − | 16.0858i | −0.876922 | − | 0.824100i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.0647 | − | 10.0647i | −0.514284 | − | 0.514284i | 0.401552 | − | 0.915836i | \(-0.368471\pi\) |
−0.915836 | + | 0.401552i | \(0.868471\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.1835 | + | 13.7988i | −0.619325 | + | 0.701432i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.0024 | 1.47048 | 0.735241 | − | 0.677806i | \(-0.237069\pi\) | ||||
0.735241 | + | 0.677806i | \(0.237069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −55.7228 | −2.81802 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.271417 | + | 8.74035i | 0.0136912 | + | 0.440892i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.66777 | − | 5.66777i | −0.284457 | − | 0.284457i | 0.550426 | − | 0.834884i | \(-0.314465\pi\) |
−0.834884 | + | 0.550426i | \(0.814465\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.51900 | − | 3.74456i | 0.176171 | − | 0.187463i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.6757i | 0.832745i | 0.909194 | + | 0.416372i | \(0.136699\pi\) | ||||
−0.909194 | + | 0.416372i | \(0.863301\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.1885 | + | 22.1885i | −1.10529 | + | 1.10529i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.35491 | − | 3.35491i | 0.166297 | − | 0.166297i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.48913i | 0.123079i | 0.998105 | + | 0.0615397i | \(0.0196011\pi\) | ||||
−0.998105 | + | 0.0615397i | \(0.980399\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.44158 | + | 8.98266i | −0.416392 | + | 0.443082i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.70982 | − | 6.70982i | −0.330169 | − | 0.330169i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.812683 | + | 26.1705i | 0.0397972 | + | 1.28158i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.81929 | 0.137731 | 0.0688657 | − | 0.997626i | \(-0.478062\pi\) | ||||
0.0688657 | + | 0.997626i | \(0.478062\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.25544 | −0.256134 | −0.128067 | − | 0.991765i | \(-0.540877\pi\) | ||||
−0.128067 | + | 0.991765i | \(0.540877\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.8849 | + | 17.9908i | −0.772350 | + | 0.874744i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.768795 | + | 0.768795i | 0.0372046 | + | 0.0372046i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.92820 | − | 6.51087i | −0.334497 | − | 0.314348i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.6641i | 1.09169i | 0.837885 | + | 0.545847i | \(0.183792\pi\) | ||||
−0.837885 | + | 0.545847i | \(0.816208\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.12372 | + | 6.12372i | −0.294287 | + | 0.294287i | −0.838771 | − | 0.544484i | \(-0.816726\pi\) |
0.544484 | + | 0.838771i | \(0.316726\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.1539 | − | 23.1539i | 1.10760 | − | 1.10760i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.62772i | − | 0.411779i | −0.978575 | − | 0.205889i | \(-0.933991\pi\) | ||
0.978575 | − | 0.205889i | \(-0.0660087\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.18614 | − | 19.0800i | −0.0564829 | − | 0.908572i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.0559 | − | 23.0559i | −1.09542 | − | 1.09542i | −0.994939 | − | 0.100480i | \(-0.967962\pi\) |
−0.100480 | − | 0.994939i | \(-0.532038\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.50774 | + | 0.202087i | −0.307805 | + | 0.00955839i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.22938 | 0.105211 | 0.0526056 | − | 0.998615i | \(-0.483247\pi\) | ||||
0.0526056 | + | 0.998615i | \(0.483247\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.60597 | −0.405239 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.54915 | + | 0.141266i | −0.213738 | + | 0.00663727i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.3744 | − | 11.3744i | −0.532071 | − | 0.532071i | 0.389117 | − | 0.921188i | \(-0.372780\pi\) |
−0.921188 | + | 0.389117i | \(0.872780\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.1345 | + | 25.4891i | −0.986472 | + | 1.18973i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.0256i | − | 0.792959i | −0.918044 | − | 0.396480i | \(-0.870232\pi\) | ||
0.918044 | − | 0.396480i | \(-0.129768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.43657 | − | 6.43657i | 0.299133 | − | 0.299133i | −0.541541 | − | 0.840674i | \(-0.682159\pi\) |
0.840674 | + | 0.541541i | \(0.182159\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.82843 | − | 2.82843i | 0.130884 | − | 0.130884i | −0.638630 | − | 0.769514i | \(-0.720499\pi\) |
0.769514 | + | 0.638630i | \(0.220499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.37228i | − | 0.0633661i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.4891 | + | 15.4959i | 0.759779 | + | 0.714013i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.07740 | + | 4.07740i | 0.187479 | + | 0.187479i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.67441 | − | 1.47841i | −0.0766661 | − | 0.0676919i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.45877 | −0.203726 | −0.101863 | − | 0.994798i | \(-0.532480\pi\) | ||||
−0.101863 | + | 0.994798i | \(0.532480\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.4891 | 1.34459 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.372461 | + | 11.9942i | 0.0169476 | + | 0.545756i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.94106 | + | 9.94106i | 0.450473 | + | 0.450473i | 0.895511 | − | 0.445039i | \(-0.146810\pi\) |
−0.445039 | + | 0.895511i | \(0.646810\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.2492 | + | 23.6753i | −1.00614 | + | 1.07063i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.45877i | − | 0.201221i | −0.994926 | − | 0.100611i | \(-0.967920\pi\) | ||
0.994926 | − | 0.100611i | \(-0.0320797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.2798 | + | 14.2798i | −0.643130 | + | 0.643130i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.77546 | + | 1.77546i | −0.0796401 | + | 0.0796401i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 23.3723i | − | 1.04629i | −0.852245 | − | 0.523144i | \(-0.824759\pi\) | ||
0.852245 | − | 0.523144i | \(-0.175241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.74456 | − | 5.04868i | 0.211971 | − | 0.225558i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.2481 | + | 16.2481i | 0.724466 | + | 0.724466i | 0.969512 | − | 0.245046i | \(-0.0788029\pi\) |
−0.245046 | + | 0.969512i | \(0.578803\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.13524 | − | 36.5578i | −0.0504179 | − | 1.62359i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.0742 | −0.978423 | −0.489212 | − | 0.872165i | \(-0.662715\pi\) | ||||
−0.489212 | + | 0.872165i | \(0.662715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.23369 | 0.275762 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.80944 | − | 19.3730i | −0.0798889 | − | 0.855339i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.31611 | + | 5.31611i | 0.233802 | + | 0.233802i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.1460 | − | 14.2337i | −0.664837 | − | 0.624790i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.6757i | 0.730576i | 0.930895 | + | 0.365288i | \(0.119029\pi\) | ||||
−0.930895 | + | 0.365288i | \(0.880971\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.8465 | + | 12.8465i | −0.561738 | + | 0.561738i | −0.929801 | − | 0.368063i | \(-0.880021\pi\) |
0.368063 | + | 0.929801i | \(0.380021\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.2069 | − | 24.2069i | 1.05447 | − | 1.05447i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.4674i | 2.32467i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.8614 | + | 2.22938i | −1.55625 | + | 0.0967470i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −37.8225 | − | 37.8225i | −1.63828 | − | 1.63828i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.3673 | + | 0.321939i | −0.447381 | + | 0.0138927i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.98844 | −0.257940 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.88316 | 0.252937 | 0.126468 | − | 0.991971i | \(-0.459636\pi\) | ||||
0.126468 | + | 0.991971i | \(0.459636\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −34.8266 | + | 1.08148i | −1.49455 | + | 0.0464109i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.53113 | + | 3.53113i | 0.150980 | + | 0.150980i | 0.778556 | − | 0.627575i | \(-0.215953\pi\) |
−0.627575 | + | 0.778556i | \(0.715953\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.10891 | − | 0.255437i | 0.175364 | − | 0.0109018i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11.8671i | − | 0.505554i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.89898 | + | 4.89898i | −0.208326 | + | 0.208326i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.7334 | + | 24.7334i | −1.04799 | + | 1.04799i | −0.0491969 | + | 0.998789i | \(0.515666\pi\) |
−0.998789 | + | 0.0491969i | \(0.984334\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.8397i | 1.51586i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.55842 | + | 7.10313i | 0.319117 | + | 0.299894i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.9579 | + | 22.9579i | 0.967560 | + | 0.967560i | 0.999490 | − | 0.0319299i | \(-0.0101653\pi\) |
−0.0319299 | + | 0.999490i | \(0.510165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.62775 | + | 4.37878i | 0.236343 | + | 0.183891i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.9909 | 1.46689 | 0.733447 | − | 0.679747i | \(-0.237910\pi\) | ||||
0.733447 | + | 0.679747i | \(0.237910\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.8397 | 1.33245 | 0.666224 | − | 0.745752i | \(-0.267909\pi\) | ||||
0.666224 | + | 0.745752i | \(0.267909\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.35709 | − | 43.7017i | −0.0566931 | − | 1.82567i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.2144 | − | 26.2144i | −1.09132 | − | 1.09132i | −0.995388 | − | 0.0959325i | \(-0.969417\pi\) |
−0.0959325 | − | 0.995388i | \(-0.530583\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.0313 | + | 14.9307i | −0.583122 | + | 0.620499i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.45877i | − | 0.184981i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.494772 | + | 0.494772i | −0.0204914 | + | 0.0204914i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.8726 | − | 16.8726i | 0.696405 | − | 0.696405i | −0.267228 | − | 0.963633i | \(-0.586108\pi\) |
0.963633 | + | 0.267228i | \(0.0861077\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.1168i | 0.828900i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.8832 | − | 17.9653i | 0.694480 | − | 0.738994i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.5177 | − | 13.5177i | −0.555103 | − | 0.555103i | 0.372806 | − | 0.927909i | \(-0.378396\pi\) |
−0.927909 | + | 0.372806i | \(0.878396\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.248787 | + | 8.01158i | 0.0101822 | + | 0.327892i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.4125 | −1.16090 | −0.580452 | − | 0.814294i | \(-0.697124\pi\) | ||||
−0.580452 | + | 0.814294i | \(0.697124\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.74456 | −0.152744 | −0.0763719 | − | 0.997079i | \(-0.524334\pi\) | ||||
−0.0763719 | + | 0.997079i | \(0.524334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.89513 | − | 3.43918i | −0.158622 | − | 0.140054i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.4755 | − | 18.4755i | −0.749896 | − | 0.749896i | 0.224564 | − | 0.974459i | \(-0.427904\pi\) |
−0.974459 | + | 0.224564i | \(0.927904\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.16915 | + | 2.97825i | 0.128420 | + | 0.120685i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.7277i | 1.89040i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.88606 | − | 8.88606i | 0.358905 | − | 0.358905i | −0.504504 | − | 0.863409i | \(-0.668325\pi\) |
0.863409 | + | 0.504504i | \(0.168325\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.9461 | − | 13.9461i | 0.561450 | − | 0.561450i | −0.368269 | − | 0.929719i | \(-0.620049\pi\) |
0.929719 | + | 0.368269i | \(0.120049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12.8614i | − | 0.516944i | −0.966019 | − | 0.258472i | \(-0.916781\pi\) | ||
0.966019 | − | 0.258472i | \(-0.0832189\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.9783 | + | 29.0024i | 1.40363 | + | 1.16383i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.01177 | − | 9.01177i | −0.361049 | − | 0.361049i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.09216 | + | 0.189182i | −0.243297 | + | 0.00755520i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.1716 | −1.28276 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.6060 | −1.01936 | −0.509679 | − | 0.860365i | \(-0.670236\pi\) | ||||
−0.509679 | + | 0.860365i | \(0.670236\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.8699 | − | 0.523868i | 0.670520 | − | 0.0208219i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.3187 | − | 26.3187i | −1.04278 | − | 1.04278i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.589907 | + | 9.48913i | 0.0233364 | + | 0.375384i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 23.9538i | − | 0.946117i | −0.881031 | − | 0.473058i | \(-0.843150\pi\) | ||
0.881031 | − | 0.473058i | \(-0.156850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.10754 | − | 5.10754i | 0.201422 | − | 0.201422i | −0.599187 | − | 0.800609i | \(-0.704509\pi\) |
0.800609 | + | 0.599187i | \(0.204509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2554i | 0.441815i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.37228 | − | 5.04868i | −0.210556 | − | 0.197873i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.90583 | + | 6.90583i | 0.270246 | + | 0.270246i | 0.829199 | − | 0.558953i | \(-0.188797\pi\) |
−0.558953 | + | 0.829199i | \(0.688797\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.6227 | − | 17.6939i | 0.609501 | − | 0.690305i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.6906 | −1.39031 | −0.695154 | − | 0.718861i | \(-0.744664\pi\) | ||||
−0.695154 | + | 0.718861i | \(0.744664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.2337 | 1.56491 | 0.782455 | − | 0.622708i | \(-0.213967\pi\) | ||||
0.782455 | + | 0.622708i | \(0.213967\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.00096 | + | 64.4363i | 0.0777110 | + | 2.50250i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.5959 | + | 19.5959i | 0.758757 | + | 0.758757i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.7846 | − | 22.1168i | 0.803579 | − | 0.855087i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.28962i | − | 0.0497852i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.82380 | − | 1.82380i | 0.0703023 | − | 0.0703023i | −0.671081 | − | 0.741384i | \(-0.734170\pi\) |
0.741384 | + | 0.671081i | \(0.234170\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.2481 | + | 16.2481i | −0.624464 | + | 0.624464i | −0.946670 | − | 0.322205i | \(-0.895576\pi\) |
0.322205 | + | 0.946670i | \(0.395576\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 5.88316i | − | 0.225775i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.74456 | − | 5.04868i | 0.181812 | − | 0.193466i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.3990 | − | 17.3990i | −0.665756 | − | 0.665756i | 0.290975 | − | 0.956731i | \(-0.406020\pi\) |
−0.956731 | + | 0.290975i | \(0.906020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.248787 | − | 8.01158i | −0.00949180 | − | 0.305661i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.34896 | −0.165682 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.3505 | −0.812213 | −0.406106 | − | 0.913826i | \(-0.633114\pi\) | ||||
−0.406106 | + | 0.913826i | \(0.633114\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.47841 | − | 1.67441i | 0.0561602 | − | 0.0636057i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.2630 | + | 41.2630i | 1.56295 | + | 1.56295i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.0140 | + | 21.6277i | 0.870469 | + | 0.818035i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.2665i | − | 0.501069i | −0.968108 | − | 0.250534i | \(-0.919394\pi\) | ||
0.968108 | − | 0.250534i | \(-0.0806063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.3679 | − | 13.3679i | 0.504180 | − | 0.504180i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.93437 | − | 4.93437i | 0.185576 | − | 0.185576i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.861407i | 0.0323508i | 0.999869 | + | 0.0161754i | \(0.00514902\pi\) | ||||
−0.999869 | + | 0.0161754i | \(0.994851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.62772 | + | 26.1831i | 0.0610442 | + | 0.981945i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33.2186 | − | 33.2186i | −1.24405 | − | 1.24405i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.9672 | − | 0.713208i | 0.857725 | − | 0.0266352i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.8226 | 1.03761 | 0.518804 | − | 0.854893i | \(-0.326377\pi\) | ||||
0.518804 | + | 0.854893i | \(0.326377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.25544 | −0.344690 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.9104 | + | 0.711444i | −0.852046 | + | 0.0264589i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.5668 | + | 10.5668i | 0.391899 | + | 0.391899i | 0.875364 | − | 0.483465i | \(-0.160622\pi\) |
−0.483465 | + | 0.875364i | \(0.660622\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.5330 | − | 5.00000i | 0.982704 | − | 0.185185i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 39.0998i | − | 1.44616i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.2929 | + | 34.2929i | −1.26664 | + | 1.26664i | −0.318820 | + | 0.947815i | \(0.603287\pi\) |
−0.947815 | + | 0.318820i | \(0.896713\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.15097 | + | 1.15097i | −0.0423966 | + | 0.0423966i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 44.4674i | − | 1.63576i | −0.575390 | − | 0.817879i | \(-0.695150\pi\) | ||
0.575390 | − | 0.817879i | \(-0.304850\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.6060 | − | 25.9431i | −1.01413 | − | 0.953043i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.6922 | + | 32.6922i | 1.19936 | + | 1.19936i | 0.974359 | + | 0.225000i | \(0.0722382\pi\) |
0.225000 | + | 0.974359i | \(0.427762\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.6559 | − | 11.1745i | −0.463056 | − | 0.408852i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.28962 | −0.0471217 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.0000 | −1.60558 | −0.802791 | − | 0.596260i | \(-0.796653\pi\) | ||||
−0.802791 | + | 0.596260i | \(0.796653\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.561643 | − | 18.0864i | −0.0204674 | − | 0.659104i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.6251 | − | 28.6251i | −1.04040 | − | 1.04040i | −0.999149 | − | 0.0412473i | \(-0.986867\pi\) |
−0.0412473 | − | 0.999149i | \(-0.513133\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.74749 | − | 10.3723i | 0.353812 | − | 0.376490i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.2063i | 0.514977i | 0.966281 | + | 0.257488i | \(0.0828949\pi\) | ||||
−0.966281 | + | 0.257488i | \(0.917105\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.08490 | + | 6.08490i | −0.220288 | + | 0.220288i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −49.4667 | + | 49.4667i | −1.78614 | + | 1.78614i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.51087i | 0.270849i | 0.990788 | + | 0.135425i | \(0.0432398\pi\) | ||||
−0.990788 | + | 0.135425i | \(0.956760\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.8832 | + | 17.9653i | −0.608032 | + | 0.647005i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.7696 | + | 36.7696i | 1.32251 | + | 1.32251i | 0.911739 | + | 0.410770i | \(0.134740\pi\) |
0.410770 | + | 0.911739i | \(0.365260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.215040 | + | 6.92487i | 0.00771453 | + | 0.248428i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −34.2912 | −1.22861 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.97825 | 0.106570 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.3960 | − | 1.53139i | 0.585946 | − | 0.0547275i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.560232 | − | 0.560232i | −0.0199701 | − | 0.0199701i | 0.697051 | − | 0.717021i | \(-0.254495\pi\) |
−0.717021 | + | 0.697051i | \(0.754495\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.2549 | − | 18.0951i | −0.685494 | − | 0.644202i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.87953i | − | 0.0668283i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.66777 | − | 5.66777i | 0.201269 | − | 0.201269i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.0647 | + | 10.0647i | −0.356511 | + | 0.356511i | −0.862525 | − | 0.506014i | \(-0.831118\pi\) |
0.506014 | + | 0.862525i | \(0.331118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 50.9783i | − | 1.80348i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.1644 | + | 2.99422i | −1.70181 | + | 0.105796i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.22837 | − | 5.22837i | −0.184505 | − | 0.184505i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.9556 | − | 1.45813i | 1.65292 | − | 0.0513286i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.74839 | 0.202103 | 0.101051 | − | 0.994881i | \(-0.467779\pi\) | ||||
0.101051 | + | 0.994881i | \(0.467779\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.6277 | 1.14571 | 0.572857 | − | 0.819655i | \(-0.305835\pi\) | ||||
0.572857 | + | 0.819655i | \(0.305835\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.5665 | − | 0.980245i | 1.10708 | − | 0.0343787i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.2467 | + | 16.2467i | 0.568401 | + | 0.568401i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.8564 | − | 0.861407i | 0.484182 | − | 0.0301000i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 25.8333i | − | 0.901588i | −0.892628 | − | 0.450794i | \(-0.851141\pi\) | ||
0.892628 | − | 0.450794i | \(-0.148859\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.59259 | + | 2.59259i | −0.0903721 | + | 0.0903721i | −0.750848 | − | 0.660475i | \(-0.770355\pi\) |
0.660475 | + | 0.750848i | \(0.270355\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2157 | + | 11.2157i | −0.390008 | + | 0.390008i | −0.874690 | − | 0.484682i | \(-0.838935\pi\) |
0.484682 | + | 0.874690i | \(0.338935\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.2554i | 0.460380i | 0.973146 | + | 0.230190i | \(0.0739348\pi\) | ||||
−0.973146 | + | 0.230190i | \(0.926065\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.1168 | + | 24.5437i | 0.905983 | + | 0.851410i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.7128 | + | 28.7128i | 0.994838 | + | 0.994838i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.7942 | + | 2.59599i | −0.960709 | + | 0.0897305i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.9793 | 1.41476 | 0.707381 | − | 0.706832i | \(-0.249876\pi\) | ||||
0.707381 | + | 0.706832i | \(0.249876\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9565 | −0.653672 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.11738 | − | 35.9827i | −0.0384847 | − | 1.23931i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.66777 | + | 5.66777i | 0.194747 | + | 0.194747i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.7673 | − | 31.6753i | 1.02161 | − | 1.08709i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.1485i | 1.51339i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.5823 | − | 27.5823i | 0.944399 | − | 0.944399i | −0.0541349 | − | 0.998534i | \(-0.517240\pi\) |
0.998534 | + | 0.0541349i | \(0.0172401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.2401 | + | 14.2401i | −0.486434 | + | 0.486434i | −0.907179 | − | 0.420745i | \(-0.861769\pi\) |
0.420745 | + | 0.907179i | \(0.361769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.8614i | 0.404706i | 0.979313 | + | 0.202353i | \(0.0648588\pi\) | ||||
−0.979313 | + | 0.202353i | \(0.935141\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.60597 | − | 9.15759i | 0.293291 | − | 0.312090i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.65685 | + | 5.65685i | 0.192562 | + | 0.192562i | 0.796802 | − | 0.604240i | \(-0.206523\pi\) |
−0.604240 | + | 0.796802i | \(0.706523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.26906 | − | 40.8670i | −0.0430995 | − | 1.38792i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.21782 | 0.278771 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.1168 | −0.342796 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.6990 | − | 14.7442i | −0.565174 | − | 0.499017i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.768795 | − | 0.768795i | −0.0259604 | − | 0.0259604i | 0.694007 | − | 0.719968i | \(-0.255843\pi\) |
−0.719968 | + | 0.694007i | \(0.755843\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.1600 | + | 35.8614i | 1.28711 | + | 1.20958i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 17.6155i | − | 0.593480i | −0.954958 | − | 0.296740i | \(-0.904101\pi\) | ||
0.954958 | − | 0.296740i | \(-0.0958995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.28947 | − | 5.28947i | 0.178005 | − | 0.178005i | −0.612481 | − | 0.790486i | \(-0.709828\pi\) |
0.790486 | + | 0.612481i | \(0.209828\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.6274 | + | 22.6274i | −0.759754 | + | 0.759754i | −0.976277 | − | 0.216523i | \(-0.930528\pi\) |
0.216523 | + | 0.976277i | \(0.430528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.7446i | − | 0.360361i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.04755 | − | 8.39275i | −0.0350942 | − | 0.281168i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.1824 | + | 21.1824i | 0.708843 | + | 0.708843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 88.4248 | − | 2.74589i | 2.95242 | − | 0.0916825i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.0256 | −0.567834 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.74456 | 0.158064 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.41615 | + | 0.261350i | −0.280072 | + | 0.00869717i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.4910 | + | 35.4910i | 1.17846 | + | 1.17846i | 0.980137 | + | 0.198321i | \(0.0635488\pi\) |
0.198321 | + | 0.980137i | \(0.436451\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.63948 | − | 26.3723i | −0.0543780 | − | 0.874713i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 54.2458i | − | 1.79724i | −0.438724 | − | 0.898622i | \(-0.644569\pi\) | ||
0.438724 | − | 0.898622i | \(-0.355431\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.73969 | + | 3.73969i | −0.123766 | + | 0.123766i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.82843 | + | 2.82843i | −0.0934029 | + | 0.0934029i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 33.8397i | − | 1.11627i | −0.829751 | − | 0.558134i | \(-0.811518\pi\) | ||
0.829751 | − | 0.558134i | \(-0.188482\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.7921 | + | 32.6964i | 1.14644 | + | 1.07738i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.0892 | + | 13.0892i | 0.430835 | + | 0.430835i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.1958 | + | 26.2709i | −0.761849 | + | 0.862851i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.16915 | 0.103976 | 0.0519882 | − | 0.998648i | \(-0.483444\pi\) | ||||
0.0519882 | + | 0.998648i | \(0.483444\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.8614 | −0.782026 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.38880 | + | 44.7230i | 0.0454673 | + | 1.46417i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.67423 | − | 3.67423i | −0.120032 | − | 0.120032i | 0.644539 | − | 0.764571i | \(-0.277049\pi\) |
−0.764571 | + | 0.644539i | \(0.777049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.1460 | − | 16.1168i | 0.494272 | − | 0.525953i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 30.2921i | − | 0.987493i | −0.869606 | − | 0.493746i | \(-0.835627\pi\) | ||
0.869606 | − | 0.493746i | \(-0.164373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.6245 | − | 56.6245i | 1.84395 | − | 1.84395i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.8520 | + | 20.8520i | −0.677598 | + | 0.677598i | −0.959456 | − | 0.281858i | \(-0.909049\pi\) |
0.281858 | + | 0.959456i | \(0.409049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 45.9565i | − | 1.49181i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.2554 | − | 11.9769i | 0.364983 | − | 0.388377i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.3990 | + | 17.3990i | 0.563610 | + | 0.563610i | 0.930331 | − | 0.366721i | \(-0.119520\pi\) |
−0.366721 | + | 0.930331i | \(0.619520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.160111 | − | 5.15600i | −0.00517565 | − | 0.166670i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.63858 | −0.182079 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.13859 | −0.0689869 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.23202 | + | 3.66050i | −0.104150 | + | 0.117958i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.1361 | − | 42.1361i | −1.35501 | − | 1.35501i | −0.879963 | − | 0.475043i | \(-0.842433\pi\) |
−0.475043 | − | 0.879963i | \(-0.657567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.1171 | + | 28.3030i | 0.967501 | + | 0.909223i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 22.4241i | − | 0.719623i | −0.933025 | − | 0.359812i | \(-0.882841\pi\) | ||
0.933025 | − | 0.359812i | \(-0.117159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.46893 | + | 8.46893i | −0.271502 | + | 0.271502i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.33431 | − | 7.33431i | 0.234645 | − | 0.234645i | −0.579983 | − | 0.814628i | \(-0.696941\pi\) |
0.814628 | + | 0.579983i | \(0.196941\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.1168i | 0.483136i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.02175 | + | 32.5214i | 0.0645495 | + | 1.03833i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.95880 | − | 7.95880i | −0.253846 | − | 0.253846i | 0.568699 | − | 0.822545i | \(-0.307447\pi\) |
−0.822545 | + | 0.568699i | \(0.807447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.9730 | + | 0.340747i | −0.349273 | + | 0.0108461i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.6559 | −1.70616 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.8397 | 1.83734 | 0.918669 | − | 0.395029i | \(-0.129265\pi\) | ||||
0.918669 | + | 0.395029i | \(0.129265\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.6561 | − | 1.41778i | 1.44885 | − | 0.0449918i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.06472 | − | 4.06472i | −0.128731 | − | 0.128731i | 0.639806 | − | 0.768537i | \(-0.279015\pi\) |
−0.768537 | + | 0.639806i | \(0.779015\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.1947 | + | 16.7446i | 0.638932 | + | 0.529775i |
(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 | 600.2.r.f.257.8 | yes | 16 | |
3.2 | odd | 2 | inner | 600.2.r.f.257.5 | yes | 16 | |
4.3 | odd | 2 | 1200.2.v.m.257.1 | 16 | |||
5.2 | odd | 4 | inner | 600.2.r.f.593.4 | yes | 16 | |
5.3 | odd | 4 | inner | 600.2.r.f.593.5 | yes | 16 | |
5.4 | even | 2 | inner | 600.2.r.f.257.1 | ✓ | 16 | |
12.11 | even | 2 | 1200.2.v.m.257.4 | 16 | |||
15.2 | even | 4 | inner | 600.2.r.f.593.1 | yes | 16 | |
15.8 | even | 4 | inner | 600.2.r.f.593.8 | yes | 16 | |
15.14 | odd | 2 | inner | 600.2.r.f.257.4 | yes | 16 | |
20.3 | even | 4 | 1200.2.v.m.593.4 | 16 | |||
20.7 | even | 4 | 1200.2.v.m.593.5 | 16 | |||
20.19 | odd | 2 | 1200.2.v.m.257.8 | 16 | |||
60.23 | odd | 4 | 1200.2.v.m.593.1 | 16 | |||
60.47 | odd | 4 | 1200.2.v.m.593.8 | 16 | |||
60.59 | even | 2 | 1200.2.v.m.257.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.2.r.f.257.1 | ✓ | 16 | 5.4 | even | 2 | inner | |
600.2.r.f.257.4 | yes | 16 | 15.14 | odd | 2 | inner | |
600.2.r.f.257.5 | yes | 16 | 3.2 | odd | 2 | inner | |
600.2.r.f.257.8 | yes | 16 | 1.1 | even | 1 | trivial | |
600.2.r.f.593.1 | yes | 16 | 15.2 | even | 4 | inner | |
600.2.r.f.593.4 | yes | 16 | 5.2 | odd | 4 | inner | |
600.2.r.f.593.5 | yes | 16 | 5.3 | odd | 4 | inner | |
600.2.r.f.593.8 | yes | 16 | 15.8 | even | 4 | inner | |
1200.2.v.m.257.1 | 16 | 4.3 | odd | 2 | |||
1200.2.v.m.257.4 | 16 | 12.11 | even | 2 | |||
1200.2.v.m.257.5 | 16 | 60.59 | even | 2 | |||
1200.2.v.m.257.8 | 16 | 20.19 | odd | 2 | |||
1200.2.v.m.593.1 | 16 | 60.23 | odd | 4 | |||
1200.2.v.m.593.4 | 16 | 20.3 | even | 4 | |||
1200.2.v.m.593.5 | 16 | 20.7 | even | 4 | |||
1200.2.v.m.593.8 | 16 | 60.47 | odd | 4 |