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 | 593.4 | ||
Root | \(1.47240 + 0.912166i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.593 |
Dual form | 600.2.r.f.257.4 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.0537601 | − | 1.73122i | −0.0310384 | − | 0.999518i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.560232 | + | 0.560232i | −0.211748 | + | 0.211748i | −0.805010 | − | 0.593262i | \(-0.797840\pi\) |
0.593262 | + | 0.805010i | \(0.297840\pi\) | |||||||
\(8\) | 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 | −0.987426 | − | 0.158081i | \(-0.949469\pi\) |
−0.158081 | − | 0.987426i | \(-0.550531\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.50588 | − | 4.50588i | −1.09284 | − | 1.09284i | −0.995224 | − | 0.0976128i | \(-0.968879\pi\) |
−0.0976128 | − | 0.995224i | \(-0.531121\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.74456i | 0.859062i | 0.903052 | + | 0.429531i | \(0.141321\pi\) | ||||
−0.903052 | + | 0.429531i | \(0.858679\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | + | 0.939764i | 0.218218 | + | 0.205073i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.18334 | − | 6.18334i | 1.28932 | − | 1.28932i | 0.354113 | − | 0.935203i | \(-0.384783\pi\) |
0.935203 | − | 0.354113i | \(-0.115217\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.483219 | + | 5.17364i | 0.0929956 | + | 0.995667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.16915 | −0.588496 | −0.294248 | − | 0.955729i | \(-0.595069\pi\) | ||||
−0.294248 | + | 0.955729i | \(0.595069\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.37228 | −0.964890 | −0.482445 | − | 0.875926i | \(-0.660251\pi\) | ||||
−0.482445 | + | 0.875926i | \(0.660251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.62693 | + | 0.0505218i | −0.283213 | + | 0.00879471i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.56995 | + | 3.56995i | −0.586897 | + | 0.586897i | −0.936790 | − | 0.349893i | \(-0.886218\pi\) |
0.349893 | + | 0.936790i | \(0.386218\pi\) | |||||||
\(38\) | 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 | \(-0.0950254\pi\) |
−0.294117 | + | 0.955770i | \(0.595025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65685 | − | 5.65685i | −0.825137 | − | 0.825137i | 0.161703 | − | 0.986840i | \(-0.448301\pi\) |
−0.986840 | + | 0.161703i | \(0.948301\pi\) | |||||||
\(48\) | 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 | −0.742341 | − | 0.670022i | \(-0.766284\pi\) |
0.670022 | + | 0.742341i | \(0.266284\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.48265 | − | 0.201308i | 0.858648 | − | 0.0266639i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.9769 | 1.55926 | 0.779628 | − | 0.626242i | \(-0.215408\pi\) | ||||
0.779628 | + | 0.626242i | \(0.215408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.37228 | 0.175703 | 0.0878513 | − | 0.996134i | \(-0.472000\pi\) | ||||
0.0878513 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.57317 | − | 1.78174i | 0.198201 | − | 0.224478i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.22474 | − | 1.22474i | 0.149626 | − | 0.149626i | −0.628325 | − | 0.777951i | \(-0.716259\pi\) |
0.777951 | + | 0.628325i | \(0.216259\pi\) | |||||||
\(68\) | 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 | \(-0.402308\pi\) |
−0.953272 | + | 0.302114i | \(0.902308\pi\) | |||||||
\(74\) | 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 | \(-0.836295\pi\) | ||
0.870640 | − | 0.491920i | \(-0.163705\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.93070 | − | 1.11469i | 0.992300 | − | 0.123855i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.97940 | + | 3.97940i | −0.436796 | + | 0.436796i | −0.890932 | − | 0.454136i | \(-0.849948\pi\) |
0.454136 | + | 0.890932i | \(0.349948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.170374 | + | 5.48648i | 0.0182660 | + | 0.588212i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.0858 | 1.70509 | 0.852545 | − | 0.522654i | \(-0.175058\pi\) | ||||
0.852545 | + | 0.522654i | \(0.175058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.62772 | 0.485117 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.288814 | + | 9.30058i | 0.0299486 | + | 0.964425i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.25065 | − | 5.25065i | 0.533122 | − | 0.533122i | −0.388378 | − | 0.921500i | \(-0.626964\pi\) |
0.921500 | + | 0.388378i | \(0.126964\pi\) | |||||||
\(98\) | 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 | \(-0.0547969\pi\) |
−0.171301 | + | 0.985219i | \(0.554797\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.15097 | − | 1.15097i | −0.111269 | − | 0.111269i | 0.649280 | − | 0.760549i | \(-0.275070\pi\) |
−0.760549 | + | 0.649280i | \(0.775070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.8614i | − | 1.04033i | −0.854065 | − | 0.520167i | \(-0.825870\pi\) | ||
0.854065 | − | 0.520167i | \(-0.174130\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.37228 | + | 5.98844i | 0.604830 | + | 0.568398i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.67746 | + | 1.67746i | −0.157802 | + | 0.157802i | −0.781592 | − | 0.623790i | \(-0.785592\pi\) |
0.623790 | + | 0.781592i | \(0.285592\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.1355 | + | 11.5979i | 1.21438 | + | 1.07222i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.04868 | 0.462811 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1168 | 0.919713 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.8538 | + | 0.492313i | −1.42949 | + | 0.0443903i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.58940 | − | 9.58940i | 0.850921 | − | 0.850921i | −0.139325 | − | 0.990247i | \(-0.544493\pi\) |
0.990247 | + | 0.139325i | \(0.0444934\pi\) | |||||||
\(128\) | 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 | 0.458665 | − | 0.888609i | \(-0.348328\pi\) |
−0.888609 | + | 0.458665i | \(0.848328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.1168i | − | 1.28219i | −0.767460 | − | 0.641097i | \(-0.778480\pi\) | ||
0.767460 | − | 0.641097i | \(-0.221520\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 11.0318 | − | 0.342574i | 0.909887 | − | 0.0282551i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.75906 | 0.307954 | 0.153977 | − | 0.988074i | \(-0.450792\pi\) | ||||
0.153977 | + | 0.988074i | \(0.450792\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.62772 | −0.213841 | −0.106920 | − | 0.994268i | \(-0.534099\pi\) | ||||
−0.106920 | + | 0.994268i | \(0.534099\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.3303 | + | 12.6529i | 1.15854 | + | 1.02292i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.23773 | + | 9.23773i | −0.737251 | + | 0.737251i | −0.972045 | − | 0.234794i | \(-0.924558\pi\) |
0.234794 | + | 0.972045i | \(0.424558\pi\) | |||||||
\(158\) | 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 | 0.999213 | + | 0.0396750i | \(0.0126323\pi\) |
0.0396750 | + | 0.999213i | \(0.487368\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.82843 | + | 2.82843i | 0.218870 | + | 0.218870i | 0.808022 | − | 0.589152i | \(-0.200538\pi\) |
−0.589152 | + | 0.808022i | \(0.700538\pi\) | |||||||
\(168\) | 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 | −0.951811 | − | 0.306687i | \(-0.900780\pi\) |
0.306687 | + | 0.951811i | \(0.400780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.643878 | − | 20.7346i | −0.0483968 | − | 1.55851i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.98844 | 0.447597 | 0.223798 | − | 0.974635i | \(-0.428154\pi\) | ||||
0.223798 | + | 0.974635i | \(0.428154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.1168 | −1.49527 | −0.747637 | − | 0.664108i | \(-0.768811\pi\) | ||||
−0.747637 | + | 0.664108i | \(0.768811\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0737740 | − | 2.37572i | −0.00545353 | − | 0.175618i | ||||
\(184\) | 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 | \(-0.110010\pi\) |
−0.338769 | + | 0.940870i | \(0.610010\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0647 | + | 10.0647i | 0.717083 | + | 0.717083i | 0.968007 | − | 0.250924i | \(-0.0807344\pi\) |
−0.250924 | + | 0.968007i | \(0.580734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.62772i | − | 0.328050i | −0.986456 | − | 0.164025i | \(-0.947552\pi\) | ||
0.986456 | − | 0.164025i | \(-0.0524478\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | −17.3633 | + | 19.6652i | −1.20683 | + | 1.36683i | ||||
\(208\) | 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 | ||||||||
\(213\) | 5.48648 | − | 0.170374i | 0.375927 | − | 0.0116738i | ||||
\(214\) | 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 | \(-0.449577\pi\) |
−0.987480 | + | 0.157747i | \(0.949577\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.82843 | + | 2.82843i | 0.187729 | + | 0.187729i | 0.794714 | − | 0.606984i | \(-0.207621\pi\) |
−0.606984 | + | 0.794714i | \(0.707621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.62772i | 0.305808i | 0.988241 | + | 0.152904i | \(0.0488626\pi\) | ||||
−0.988241 | + | 0.152904i | \(0.951137\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.883156 | − | 0.939764i | 0.0581074 | − | 0.0618319i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.8932 | − | 12.8932i | 0.844659 | − | 0.844659i | −0.144801 | − | 0.989461i | \(-0.546254\pi\) |
0.989461 | + | 0.144801i | \(0.0462543\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.1387 | + | 0.470108i | −0.983366 | + | 0.0305368i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.2665 | −0.858138 | −0.429069 | − | 0.903272i | \(-0.641158\pi\) | ||||
−0.429069 | + | 0.903272i | \(0.641158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2337 | −0.852457 | −0.426228 | − | 0.904616i | \(-0.640158\pi\) | ||||
−0.426228 | + | 0.904616i | \(0.640158\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.40989 | − | 15.4011i | −0.154594 | − | 0.987978i | ||||
\(244\) | 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 | 0.319698 | − | 0.947519i | \(-0.396418\pi\) |
−0.947519 | + | 0.319698i | \(0.896418\pi\) | |||||||
\(258\) | 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 | −0.956594 | − | 0.291425i | \(-0.905871\pi\) |
0.291425 | + | 0.956594i | \(0.405871\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.864773 | − | 27.8480i | −0.0529233 | − | 1.70427i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.1229 | −1.65371 | −0.826856 | − | 0.562413i | \(-0.809873\pi\) | ||||
−0.826856 | + | 0.562413i | \(0.809873\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.2337 | 1.10762 | 0.553809 | − | 0.832644i | \(-0.313174\pi\) | ||||
0.553809 | + | 0.832644i | \(0.313174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.248787 | − | 8.01158i | −0.0150572 | − | 0.484883i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.6315 | + | 14.6315i | −0.879120 | + | 0.879120i | −0.993444 | − | 0.114323i | \(-0.963530\pi\) |
0.114323 | + | 0.993444i | \(0.463530\pi\) | |||||||
\(278\) | 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 | −0.998405 | − | 0.0564542i | \(-0.982021\pi\) |
−0.0564542 | − | 0.998405i | \(-0.517979\pi\) | |||||||
\(284\) | 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 | 0.292754 | − | 0.956188i | \(-0.405428\pi\) |
0.956188 | − | 0.292754i | \(-0.0945719\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.86199 | − | 0.454112i | 0.282122 | − | 0.0263502i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −51.0767 | −2.95384 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.86141 | −0.280207 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.2481 | + | 0.473504i | −0.875980 | + | 0.0272021i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.4916 | + | 19.4916i | −1.11245 | + | 1.11245i | −0.119628 | + | 0.992819i | \(0.538170\pi\) |
−0.992819 | + | 0.119628i | \(0.961830\pi\) | |||||||
\(308\) | 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 | \(-0.367523\pi\) |
−0.914636 | + | 0.404278i | \(0.867523\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.70982 | + | 6.70982i | 0.376861 | + | 0.376861i | 0.869969 | − | 0.493107i | \(-0.164139\pi\) |
−0.493107 | + | 0.869969i | \(0.664139\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | −18.8034 | + | 0.583910i | −1.03983 | + | 0.0322903i | ||||
\(328\) | 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 | ||||||||
\(333\) | 10.0247 | − | 11.3537i | 0.549351 | − | 0.622181i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.67423 | + | 3.67423i | −0.200148 | + | 0.200148i | −0.800064 | − | 0.599915i | \(-0.795201\pi\) |
0.599915 | + | 0.800064i | \(0.295201\pi\) | |||||||
\(338\) | 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 | 0.445186 | − | 0.895438i | \(-0.353138\pi\) |
−0.895438 | + | 0.445186i | \(0.853138\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.51087i | − | 0.241462i | −0.992685 | − | 0.120731i | \(-0.961476\pi\) | ||
0.992685 | − | 0.120731i | \(-0.0385238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.3723 | − | 23.3639i | 1.03402 | − | 1.24707i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.13037 | + | 5.13037i | −0.273062 | + | 0.273062i | −0.830332 | − | 0.557270i | \(-0.811849\pi\) |
0.557270 | + | 0.830332i | \(0.311849\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.271417 | − | 8.74035i | −0.0143649 | − | 0.462588i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.04868 | 0.266459 | 0.133229 | − | 0.991085i | \(-0.457465\pi\) | ||||
0.133229 | + | 0.991085i | \(0.457465\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.97825 | 0.262013 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.543882 | − | 17.5144i | −0.0285464 | − | 0.919270i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.02916 | − | 9.02916i | 0.471319 | − | 0.471319i | −0.431023 | − | 0.902341i | \(-0.641847\pi\) |
0.902341 | + | 0.431023i | \(0.141847\pi\) | |||||||
\(368\) | 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 | \(-0.256529\pi\) |
−0.721462 | + | 0.692454i | \(0.756529\pi\) | |||||||
\(374\) | 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 | \(0.0287413\pi\) | ||||
−0.995926 | + | 0.0901708i | \(0.971259\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.1168 | − | 16.0858i | −0.876922 | − | 0.824100i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.0647 | + | 10.0647i | −0.514284 | + | 0.514284i | −0.915836 | − | 0.401552i | \(-0.868471\pi\) |
0.401552 | + | 0.915836i | \(0.368471\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.7988 | − | 12.1835i | −0.701432 | − | 0.619325i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.0024 | −1.47048 | −0.735241 | − | 0.677806i | \(-0.762931\pi\) | ||||
−0.735241 | + | 0.677806i | \(0.762931\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −55.7228 | −2.81802 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.74035 | − | 0.271417i | 0.440892 | − | 0.0136912i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.66777 | − | 5.66777i | 0.284457 | − | 0.284457i | −0.550426 | − | 0.834884i | \(-0.685535\pi\) |
0.834884 | + | 0.550426i | \(0.185535\pi\) | |||||||
\(398\) | 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 | \(-0.980399\pi\) | ||
0.998105 | − | 0.0615397i | \(-0.0196011\pi\) | |||||||
\(410\) | 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 | ||||||||
\(417\) | −26.1705 | + | 0.812683i | −1.28158 | + | 0.0397972i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.81929 | −0.137731 | −0.0688657 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688657 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.25544 | −0.256134 | −0.128067 | − | 0.991765i | \(-0.540877\pi\) | ||||
−0.128067 | + | 0.991765i | \(0.540877\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.9908 | + | 15.8849i | 0.874744 | + | 0.772350i | ||||
\(424\) | 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 | \(-0.183274\pi\) |
−0.544484 | + | 0.838771i | \(0.683274\pi\) | |||||||
\(434\) | 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 | \(0.0660087\pi\) | ||||
−0.978575 | + | 0.205889i | \(0.933991\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.18614 | − | 19.0800i | −0.0564829 | − | 0.908572i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.0559 | + | 23.0559i | −1.09542 | + | 1.09542i | −0.100480 | + | 0.994939i | \(0.532038\pi\) |
−0.994939 | + | 0.100480i | \(0.967962\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.202087 | − | 6.50774i | −0.00955839 | − | 0.307805i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.22938 | −0.105211 | −0.0526056 | − | 0.998615i | \(-0.516753\pi\) | ||||
−0.0526056 | + | 0.998615i | \(0.516753\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.60597 | −0.405239 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.141266 | + | 4.54915i | 0.00663727 | + | 0.213738i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3744 | − | 11.3744i | 0.532071 | − | 0.532071i | −0.389117 | − | 0.921188i | \(-0.627220\pi\) |
0.921188 | + | 0.389117i | \(0.127220\pi\) | |||||||
\(458\) | 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 | \(-0.317841\pi\) |
−0.840674 | + | 0.541541i | \(0.817841\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.82843 | + | 2.82843i | 0.130884 | + | 0.130884i | 0.769514 | − | 0.638630i | \(-0.220499\pi\) |
−0.638630 | + | 0.769514i | \(0.720499\pi\) | |||||||
\(468\) | 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 | ||||||||
\(477\) | 1.47841 | − | 1.67441i | 0.0676919 | − | 0.0766661i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.45877 | 0.203726 | 0.101863 | − | 0.994798i | \(-0.467520\pi\) | ||||
0.101863 | + | 0.994798i | \(0.467520\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.4891 | 1.34459 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.9942 | − | 0.372461i | 0.545756 | − | 0.0169476i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.94106 | + | 9.94106i | −0.450473 | + | 0.450473i | −0.895511 | − | 0.445039i | \(-0.853190\pi\) |
0.445039 | + | 0.895511i | \(0.353190\pi\) | |||||||
\(488\) | 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 | \(0.175241\pi\) | ||||
−0.852245 | + | 0.523144i | \(0.824759\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.74456 | − | 5.04868i | 0.211971 | − | 0.225558i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.2481 | − | 16.2481i | 0.724466 | − | 0.724466i | −0.245046 | − | 0.969512i | \(-0.578803\pi\) |
0.969512 | + | 0.245046i | \(0.0788029\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 36.5578 | − | 1.13524i | 1.62359 | − | 0.0504179i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.0742 | 0.978423 | 0.489212 | − | 0.872165i | \(-0.337285\pi\) | ||||
0.489212 | + | 0.872165i | \(0.337285\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.23369 | 0.275762 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.3730 | + | 1.80944i | −0.855339 | + | 0.0798889i | ||||
\(514\) | 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 | \(-0.119979\pi\) |
−0.368063 | + | 0.929801i | \(0.619979\pi\) | |||||||
\(524\) | 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 | ||||||||
\(537\) | −0.321939 | − | 10.3673i | −0.0138927 | − | 0.447381i | ||||
\(538\) | 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 | ||||||||
\(543\) | 1.08148 | + | 34.8266i | 0.0464109 | + | 1.49455i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.53113 | + | 3.53113i | −0.150980 | + | 0.150980i | −0.778556 | − | 0.627575i | \(-0.784047\pi\) |
0.627575 | + | 0.778556i | \(0.284047\pi\) | |||||||
\(548\) | 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 | −0.998789 | − | 0.0491969i | \(-0.984334\pi\) |
−0.0491969 | − | 0.998789i | \(-0.515666\pi\) | |||||||
\(558\) | 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 | −0.0319299 | − | 0.999490i | \(-0.510165\pi\) |
0.999490 | + | 0.0319299i | \(0.0101653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.37878 | + | 5.62775i | −0.183891 | + | 0.236343i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.9909 | −1.46689 | −0.733447 | − | 0.679747i | \(-0.762090\pi\) | ||||
−0.733447 | + | 0.679747i | \(0.762090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.8397 | 1.33245 | 0.666224 | − | 0.745752i | \(-0.267909\pi\) | ||||
0.666224 | + | 0.745752i | \(0.267909\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −43.7017 | + | 1.35709i | −1.82567 | + | 0.0566931i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.2144 | − | 26.2144i | 1.09132 | − | 1.09132i | 0.0959325 | − | 0.995388i | \(-0.469417\pi\) |
0.995388 | − | 0.0959325i | \(-0.0305833\pi\) | |||||||
\(578\) | 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 | 0.963633 | − | 0.267228i | \(-0.0861077\pi\) |
−0.267228 | + | 0.963633i | \(0.586108\pi\) | |||||||
\(588\) | 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 | −0.927909 | − | 0.372806i | \(-0.878396\pi\) |
0.372806 | + | 0.927909i | \(0.378396\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.01158 | + | 0.248787i | −0.327892 | + | 0.0101822i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.4125 | 1.16090 | 0.580452 | − | 0.814294i | \(-0.302876\pi\) | ||||
0.580452 | + | 0.814294i | \(0.302876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.74456 | −0.152744 | −0.0763719 | − | 0.997079i | \(-0.524334\pi\) | ||||
−0.0763719 | + | 0.997079i | \(0.524334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.43918 | + | 3.89513i | −0.140054 | + | 0.158622i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.4755 | − | 18.4755i | 0.749896 | − | 0.749896i | −0.224564 | − | 0.974459i | \(-0.572096\pi\) |
0.974459 | + | 0.224564i | \(0.0720957\pi\) | |||||||
\(608\) | 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 | \(-0.331675\pi\) |
−0.863409 | + | 0.504504i | \(0.831675\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.9461 | + | 13.9461i | 0.561450 | + | 0.561450i | 0.929719 | − | 0.368269i | \(-0.120049\pi\) |
−0.368269 | + | 0.929719i | \(0.620049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.8614i | 0.516944i | 0.966019 | + | 0.258472i | \(0.0832189\pi\) | ||||
−0.966019 | + | 0.258472i | \(0.916781\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | −0.189182 | − | 6.09216i | −0.00755520 | − | 0.243297i | ||||
\(628\) | 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 | ||||||||
\(633\) | −0.523868 | − | 16.8699i | −0.0208219 | − | 0.670520i | ||||
\(634\) | 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 | \(-0.295491\pi\) |
−0.800609 | + | 0.599187i | \(0.795491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | 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 | −0.558953 | − | 0.829199i | \(-0.688797\pi\) |
0.829199 | + | 0.558953i | \(0.188797\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.6939 | + | 15.6227i | 0.690305 | + | 0.609501i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.6906 | 1.39031 | 0.695154 | − | 0.718861i | \(-0.255336\pi\) | ||||
0.695154 | + | 0.718861i | \(0.255336\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.2337 | 1.56491 | 0.782455 | − | 0.622708i | \(-0.213967\pi\) | ||||
0.782455 | + | 0.622708i | \(0.213967\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 64.4363 | − | 2.00096i | 2.50250 | − | 0.0777110i | ||||
\(664\) | 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 | \(-0.265830\pi\) |
−0.741384 | + | 0.671081i | \(0.765830\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.2481 | − | 16.2481i | −0.624464 | − | 0.624464i | 0.322205 | − | 0.946670i | \(-0.395576\pi\) |
−0.946670 | + | 0.322205i | \(0.895576\pi\) | |||||||
\(678\) | 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 | −0.956731 | − | 0.290975i | \(-0.906020\pi\) |
0.290975 | + | 0.956731i | \(0.406020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.01158 | − | 0.248787i | 0.305661 | − | 0.00949180i | ||||
\(688\) | 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 | ||||||||
\(693\) | −1.67441 | − | 1.47841i | −0.0636057 | − | 0.0561602i | ||||
\(694\) | 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 | \(-0.994851\pi\) | ||
0.999869 | − | 0.0161754i | \(-0.00514902\pi\) | |||||||
\(710\) | 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 | ||||||||
\(717\) | 0.713208 | + | 22.9672i | 0.0266352 | + | 0.857725i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.8226 | −1.03761 | −0.518804 | − | 0.854893i | \(-0.673623\pi\) | ||||
−0.518804 | + | 0.854893i | \(0.673623\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.25544 | −0.344690 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.711444 | + | 22.9104i | 0.0264589 | + | 0.852046i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.5668 | + | 10.5668i | −0.391899 | + | 0.391899i | −0.875364 | − | 0.483465i | \(-0.839378\pi\) |
0.483465 | + | 0.875364i | \(0.339378\pi\) | |||||||
\(728\) | 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 | 0.947815 | + | 0.318820i | \(0.103287\pi\) |
0.318820 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(734\) | 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 | \(0.304850\pi\) | ||||
−0.575390 | + | 0.817879i | \(0.695150\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.6060 | − | 25.9431i | −1.01413 | − | 0.953043i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.6922 | − | 32.6922i | 1.19936 | − | 1.19936i | 0.225000 | − | 0.974359i | \(-0.427762\pi\) |
0.974359 | − | 0.225000i | \(-0.0722382\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.1745 | − | 12.6559i | 0.408852 | − | 0.463056i | ||||
\(748\) | 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 | ||||||||
\(753\) | −18.0864 | + | 0.561643i | −0.659104 | + | 0.0204674i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.6251 | − | 28.6251i | 1.04040 | − | 1.04040i | 0.0412473 | − | 0.999149i | \(-0.486867\pi\) |
0.999149 | − | 0.0412473i | \(-0.0131332\pi\) | |||||||
\(758\) | 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 | \(-0.956760\pi\) | ||
0.990788 | − | 0.135425i | \(-0.0432398\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.8832 | + | 17.9653i | −0.608032 | + | 0.647005i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.7696 | − | 36.7696i | 1.32251 | − | 1.32251i | 0.410770 | − | 0.911739i | \(-0.365260\pi\) |
0.911739 | − | 0.410770i | \(-0.134740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.92487 | + | 0.215040i | −0.248428 | + | 0.00771453i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.2912 | 1.22861 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.97825 | 0.106570 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.53139 | − | 16.3960i | −0.0547275 | − | 0.585946i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.560232 | − | 0.560232i | 0.0199701 | − | 0.0199701i | −0.697051 | − | 0.717021i | \(-0.745505\pi\) |
0.717021 | + | 0.697051i | \(0.245505\pi\) | |||||||
\(788\) | 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 | 0.506014 | − | 0.862525i | \(-0.331118\pi\) |
−0.862525 | + | 0.506014i | \(0.831118\pi\) | |||||||
\(798\) | 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 | ||||||||
\(807\) | 1.45813 | + | 46.9556i | 0.0513286 | + | 1.65292i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.74839 | −0.202103 | −0.101051 | − | 0.994881i | \(-0.532221\pi\) | ||||
−0.101051 | + | 0.994881i | \(0.532221\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.6277 | 1.14571 | 0.572857 | − | 0.819655i | \(-0.305835\pi\) | ||||
0.572857 | + | 0.819655i | \(0.305835\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.980245 | − | 31.5665i | −0.0343787 | − | 1.10708i | ||||
\(814\) | 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 | \(-0.229645\pi\) |
−0.660475 | + | 0.750848i | \(0.729645\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2157 | − | 11.2157i | −0.390008 | − | 0.390008i | 0.484682 | − | 0.874690i | \(-0.338935\pi\) |
−0.874690 | + | 0.484682i | \(0.838935\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 13.2554i | − | 0.460380i | −0.973146 | − | 0.230190i | \(-0.926065\pi\) | ||
0.973146 | − | 0.230190i | \(-0.0739348\pi\) | |||||||
\(830\) | 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 | ||||||||
\(837\) | −2.59599 | − | 27.7942i | −0.0897305 | − | 0.960709i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.9793 | −1.41476 | −0.707381 | − | 0.706832i | \(-0.750124\pi\) | ||||
−0.707381 | + | 0.706832i | \(0.750124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9565 | −0.653672 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.9827 | + | 1.11738i | −1.23931 | + | 0.0384847i | ||||
\(844\) | 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 | \(-0.482760\pi\) |
−0.998534 | + | 0.0541349i | \(0.982760\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.2401 | − | 14.2401i | −0.486434 | − | 0.486434i | 0.420745 | − | 0.907179i | \(-0.361769\pi\) |
−0.907179 | + | 0.420745i | \(0.861769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 11.8614i | − | 0.404706i | −0.979313 | − | 0.202353i | \(-0.935141\pi\) | ||
0.979313 | − | 0.202353i | \(-0.0648588\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.60597 | − | 9.15759i | 0.293291 | − | 0.312090i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.65685 | − | 5.65685i | 0.192562 | − | 0.192562i | −0.604240 | − | 0.796802i | \(-0.706523\pi\) |
0.796802 | + | 0.604240i | \(0.206523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.8670 | − | 1.26906i | 1.38792 | − | 0.0430995i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.21782 | −0.278771 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.1168 | −0.342796 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.7442 | + | 16.6990i | −0.499017 | + | 0.565174i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.768795 | − | 0.768795i | 0.0259604 | − | 0.0259604i | −0.694007 | − | 0.719968i | \(-0.744157\pi\) |
0.719968 | + | 0.694007i | \(0.244157\pi\) | |||||||
\(878\) | 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 | \(-0.290172\pi\) |
−0.790486 | + | 0.612481i | \(0.790172\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.6274 | − | 22.6274i | −0.759754 | − | 0.759754i | 0.216523 | − | 0.976277i | \(-0.430528\pi\) |
−0.976277 | + | 0.216523i | \(0.930528\pi\) | |||||||
\(888\) | 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 | ||||||||
\(897\) | 2.74589 | + | 88.4248i | 0.0916825 | + | 2.95242i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.0256 | 0.567834 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.74456 | 0.158064 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.261350 | + | 8.41615i | 0.00869717 | + | 0.280072i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.4910 | + | 35.4910i | −1.17846 | + | 1.17846i | −0.198321 | + | 0.980137i | \(0.563549\pi\) |
−0.980137 | + | 0.198321i | \(0.936451\pi\) | |||||||
\(908\) | 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 | \(0.188482\pi\) | ||||
−0.829751 | + | 0.558134i | \(0.811518\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | −26.2709 | − | 23.1958i | −0.862851 | − | 0.761849i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.16915 | −0.103976 | −0.0519882 | − | 0.998648i | \(-0.516556\pi\) | ||||
−0.0519882 | + | 0.998648i | \(0.516556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.8614 | −0.782026 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 44.7230 | − | 1.38880i | 1.46417 | − | 0.0454673i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.67423 | − | 3.67423i | 0.120032 | − | 0.120032i | −0.644539 | − | 0.764571i | \(-0.722951\pi\) |
0.764571 | + | 0.644539i | \(0.222951\pi\) | |||||||
\(938\) | 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 | 0.281858 | − | 0.959456i | \(-0.409049\pi\) |
−0.959456 | + | 0.281858i | \(0.909049\pi\) | |||||||
\(948\) | 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 | −0.366721 | − | 0.930331i | \(-0.619520\pi\) |
0.930331 | + | 0.366721i | \(0.119520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.15600 | − | 0.160111i | 0.166670 | − | 0.00517565i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.63858 | 0.182079 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.13859 | −0.0689869 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.66050 | + | 3.23202i | 0.117958 | + | 0.104150i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.1361 | − | 42.1361i | 1.35501 | − | 1.35501i | 0.475043 | − | 0.879963i | \(-0.342433\pi\) |
0.879963 | − | 0.475043i | \(-0.157567\pi\) | |||||||
\(968\) | 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 | 0.814628 | − | 0.579983i | \(-0.196941\pi\) |
−0.579983 | + | 0.814628i | \(0.696941\pi\) | |||||||
\(978\) | 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 | −0.822545 | − | 0.568699i | \(-0.807447\pi\) |
0.568699 | + | 0.822545i | \(0.307447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.340747 | − | 10.9730i | −0.0108461 | − | 0.349273i | ||||
\(988\) | 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 | ||||||||
\(993\) | −1.41778 | − | 45.6561i | −0.0449918 | − | 1.44885i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.06472 | − | 4.06472i | 0.128731 | − | 0.128731i | −0.639806 | − | 0.768537i | \(-0.720985\pi\) |
0.768537 | + | 0.639806i | \(0.220985\pi\) | |||||||
\(998\) | 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.593.4 | yes | 16 | |
3.2 | odd | 2 | inner | 600.2.r.f.593.1 | yes | 16 | |
4.3 | odd | 2 | 1200.2.v.m.593.5 | 16 | |||
5.2 | odd | 4 | inner | 600.2.r.f.257.1 | ✓ | 16 | |
5.3 | odd | 4 | inner | 600.2.r.f.257.8 | yes | 16 | |
5.4 | even | 2 | inner | 600.2.r.f.593.5 | yes | 16 | |
12.11 | even | 2 | 1200.2.v.m.593.8 | 16 | |||
15.2 | even | 4 | inner | 600.2.r.f.257.4 | yes | 16 | |
15.8 | even | 4 | inner | 600.2.r.f.257.5 | yes | 16 | |
15.14 | odd | 2 | inner | 600.2.r.f.593.8 | yes | 16 | |
20.3 | even | 4 | 1200.2.v.m.257.1 | 16 | |||
20.7 | even | 4 | 1200.2.v.m.257.8 | 16 | |||
20.19 | odd | 2 | 1200.2.v.m.593.4 | 16 | |||
60.23 | odd | 4 | 1200.2.v.m.257.4 | 16 | |||
60.47 | odd | 4 | 1200.2.v.m.257.5 | 16 | |||
60.59 | even | 2 | 1200.2.v.m.593.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.2.r.f.257.1 | ✓ | 16 | 5.2 | odd | 4 | inner | |
600.2.r.f.257.4 | yes | 16 | 15.2 | even | 4 | inner | |
600.2.r.f.257.5 | yes | 16 | 15.8 | even | 4 | inner | |
600.2.r.f.257.8 | yes | 16 | 5.3 | odd | 4 | inner | |
600.2.r.f.593.1 | yes | 16 | 3.2 | odd | 2 | inner | |
600.2.r.f.593.4 | yes | 16 | 1.1 | even | 1 | trivial | |
600.2.r.f.593.5 | yes | 16 | 5.4 | even | 2 | inner | |
600.2.r.f.593.8 | yes | 16 | 15.14 | odd | 2 | inner | |
1200.2.v.m.257.1 | 16 | 20.3 | even | 4 | |||
1200.2.v.m.257.4 | 16 | 60.23 | odd | 4 | |||
1200.2.v.m.257.5 | 16 | 60.47 | odd | 4 | |||
1200.2.v.m.257.8 | 16 | 20.7 | even | 4 | |||
1200.2.v.m.593.1 | 16 | 60.59 | even | 2 | |||
1200.2.v.m.593.4 | 16 | 20.19 | odd | 2 | |||
1200.2.v.m.593.5 | 16 | 4.3 | odd | 2 | |||
1200.2.v.m.593.8 | 16 | 12.11 | even | 2 |