Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(101,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.y (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.3 | ||
Root | \(-1.27597 - 0.609843i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.901 |
Dual form | 1300.2.y.b.101.3 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.800098 | − | 1.38581i | 0.461937 | − | 0.800098i | −0.537121 | − | 0.843505i | \(-0.680488\pi\) |
0.999057 | + | 0.0434075i | \(0.0138214\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.75184 | + | 2.16612i | −1.41806 | + | 0.818718i | −0.996128 | − | 0.0879098i | \(-0.971981\pi\) |
−0.421932 | + | 0.906627i | \(0.638648\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.219687 | + | 0.380509i | 0.0732290 | + | 0.126836i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 0.866025i | 0.452267 | + | 0.261116i | 0.708787 | − | 0.705422i | \(-0.249243\pi\) |
−0.256520 | + | 0.966539i | \(0.582576\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.11256 | − | 1.81988i | 0.863269 | − | 0.504745i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.75184 | − | 6.49837i | −0.909954 | − | 1.57609i | −0.814126 | − | 0.580688i | \(-0.802784\pi\) |
−0.0958278 | − | 0.995398i | \(-0.530550\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.65213 | − | 2.68591i | 1.06727 | − | 0.616190i | 0.139837 | − | 0.990175i | \(-0.455342\pi\) |
0.927435 | + | 0.373985i | \(0.122009\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.93244i | 1.51278i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.580411 | − | 1.00530i | 0.121024 | − | 0.209620i | −0.799148 | − | 0.601135i | \(-0.794716\pi\) |
0.920172 | + | 0.391515i | \(0.128049\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.50367 | 1.05918 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.01236 | − | 1.75347i | 0.187991 | − | 0.325610i | −0.756589 | − | 0.653891i | \(-0.773136\pi\) |
0.944580 | + | 0.328280i | \(0.106469\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.86488i | − | 1.41257i | −0.707925 | − | 0.706287i | \(-0.750369\pi\) | ||
0.707925 | − | 0.706287i | \(-0.249631\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.40029 | − | 1.38581i | 0.417837 | − | 0.241239i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.25551 | + | 4.76632i | 1.35720 | + | 0.783578i | 0.989245 | − | 0.146267i | \(-0.0467258\pi\) |
0.367952 | + | 0.929845i | \(0.380059\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0316594 | − | 5.76950i | −0.00506956 | − | 0.923860i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.69615 | + | 3.86603i | 1.04576 | + | 0.603772i | 0.921460 | − | 0.388473i | \(-0.126997\pi\) |
0.124303 | + | 0.992244i | \(0.460331\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.09277 | − | 3.62479i | −0.319145 | − | 0.552776i | 0.661165 | − | 0.750241i | \(-0.270062\pi\) |
−0.980310 | + | 0.197465i | \(0.936729\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.46410i | 0.505291i | 0.967559 | + | 0.252646i | \(0.0813007\pi\) | ||||
−0.967559 | + | 0.252646i | \(0.918699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.88418 | − | 10.1917i | 0.840597 | − | 1.45596i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.0073 | −1.68136 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.6471 | 1.73721 | 0.868607 | − | 0.495502i | \(-0.165016\pi\) | ||||
0.868607 | + | 0.495502i | \(0.165016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 8.59596i | − | 1.13856i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.49674 | − | 3.17354i | 0.715615 | − | 0.413160i | −0.0975219 | − | 0.995233i | \(-0.531092\pi\) |
0.813136 | + | 0.582073i | \(0.197758\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.85154 | − | 3.20696i | −0.237066 | − | 0.410610i | 0.722805 | − | 0.691052i | \(-0.242852\pi\) |
−0.959871 | + | 0.280442i | \(0.909519\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.64846 | − | 0.951738i | −0.207686 | − | 0.119908i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.55568 | + | 2.63022i | 0.556565 | + | 0.321333i | 0.751766 | − | 0.659430i | \(-0.229202\pi\) |
−0.195200 | + | 0.980763i | \(0.562536\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.928771 | − | 1.60868i | −0.111811 | − | 0.193662i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8377 | + | 6.25714i | −1.28620 | + | 0.742586i | −0.977974 | − | 0.208729i | \(-0.933067\pi\) |
−0.308222 | + | 0.951314i | \(0.599734\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.23898i | − | 0.613177i | −0.951842 | − | 0.306588i | \(-0.900813\pi\) | ||
0.951842 | − | 0.306588i | \(-0.0991875\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.50367 | −0.855123 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.16719 | −0.918880 | −0.459440 | − | 0.888209i | \(-0.651950\pi\) | ||||
−0.459440 | + | 0.888209i | \(0.651950\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.74441 | − | 6.48552i | 0.416046 | − | 0.720613i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 0.456760i | − | 0.0501359i | −0.999686 | − | 0.0250679i | \(-0.992020\pi\) | ||
0.999686 | − | 0.0250679i | \(-0.00798021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.61998 | − | 2.80589i | −0.173680 | − | 0.300823i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.4967 | − | 6.63765i | −1.21865 | − | 0.703589i | −0.254022 | − | 0.967198i | \(-0.581754\pi\) |
−0.964630 | + | 0.263609i | \(0.915087\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.73572 | + | 13.5701i | −0.810924 | + | 1.42253i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.8992 | − | 6.29268i | −1.13020 | − | 0.652520i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.43371 | − | 1.40511i | 0.247106 | − | 0.142667i | −0.371332 | − | 0.928500i | \(-0.621099\pi\) |
0.618439 | + | 0.785833i | \(0.287766\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.761018i | 0.0764852i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.31988 | + | 5.75021i | −0.330341 | + | 0.572167i | −0.982579 | − | 0.185847i | \(-0.940497\pi\) |
0.652238 | + | 0.758014i | \(0.273830\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.37605 | −0.726784 | −0.363392 | − | 0.931636i | \(-0.618381\pi\) | ||||
−0.363392 | + | 0.931636i | \(0.618381\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.95668 | + | 6.85317i | −0.382507 | + | 0.662521i | −0.991420 | − | 0.130716i | \(-0.958272\pi\) |
0.608913 | + | 0.793237i | \(0.291606\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.18301i | 0.879572i | 0.898102 | + | 0.439786i | \(0.144946\pi\) | ||||
−0.898102 | + | 0.439786i | \(0.855054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.2104 | − | 7.62704i | 1.25388 | − | 0.723927i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.88793 | − | 5.00204i | −0.271674 | − | 0.470552i | 0.697617 | − | 0.716471i | \(-0.254244\pi\) |
−0.969291 | + | 0.245919i | \(0.920910\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.37627 | + | 0.784552i | 0.127236 | + | 0.0725319i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28.1525 | + | 16.2539i | 2.58074 | + | 1.48999i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | − | 6.92820i | −0.363636 | − | 0.629837i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.7152 | − | 6.18640i | 0.966153 | − | 0.557809i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.48389 | + | 16.4266i | −0.841559 | + | 1.45762i | 0.0470176 | + | 0.998894i | \(0.485028\pi\) |
−0.888576 | + | 0.458729i | \(0.848305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.69770 | −0.589699 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.34637 | −0.117633 | −0.0588165 | − | 0.998269i | \(-0.518733\pi\) | ||||
−0.0588165 | + | 0.998269i | \(0.518733\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.6360 | + | 20.1542i | −1.00897 | + | 1.74759i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.7152 | − | 6.18640i | 0.915457 | − | 0.528540i | 0.0332744 | − | 0.999446i | \(-0.489406\pi\) |
0.882183 | + | 0.470907i | \(0.156073\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.38418 | − | 7.59362i | −0.371861 | − | 0.644083i | 0.617991 | − | 0.786185i | \(-0.287947\pi\) |
−0.989852 | + | 0.142103i | \(0.954614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.80059 | + | 2.77162i | 0.404282 | + | 0.233413i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.24490 | − | 0.0342681i | 0.522225 | − | 0.00286565i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.41584 | − | 16.3087i | −0.776605 | − | 1.34512i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.10443 | − | 2.36970i | 0.336248 | − | 0.194133i | −0.322363 | − | 0.946616i | \(-0.604477\pi\) |
0.658612 | + | 0.752483i | \(0.271144\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.56063i | 0.127002i | 0.997982 | + | 0.0635010i | \(0.0202266\pi\) | ||||
−0.997982 | + | 0.0635010i | \(0.979773\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.64846 | − | 2.85521i | 0.133270 | − | 0.230830i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.15332 | 0.730515 | 0.365257 | − | 0.930907i | \(-0.380981\pi\) | ||||
0.365257 | + | 0.930907i | \(0.380981\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.1189 | − | 17.5265i | 0.802483 | − | 1.38994i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.02897i | 0.396338i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.28893 | + | 1.32151i | −0.179283 | + | 0.103509i | −0.586956 | − | 0.809619i | \(-0.699674\pi\) |
0.407673 | + | 0.913128i | \(0.366340\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.71515 | − | 4.45435i | −0.597017 | − | 0.344688i | 0.170850 | − | 0.985297i | \(-0.445349\pi\) |
−0.767867 | + | 0.640609i | \(0.778682\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.37605 | − | 11.3290i | 0.490466 | − | 0.871460i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.04402 | + | 1.18012i | 0.156310 | + | 0.0902458i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.90396 | − | 11.9580i | −0.524899 | − | 0.909151i | −0.999580 | − | 0.0289933i | \(-0.990770\pi\) |
0.474681 | − | 0.880158i | \(-0.342563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 10.1566i | − | 0.763416i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.1751 | + | 21.0879i | −0.910009 | + | 1.57618i | −0.0959612 | + | 0.995385i | \(0.530592\pi\) |
−0.814048 | + | 0.580797i | \(0.802741\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8336 | 1.84587 | 0.922935 | − | 0.384956i | \(-0.125783\pi\) | ||||
0.922935 | + | 0.384956i | \(0.125783\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.92566 | −0.438037 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 12.9967i | − | 0.950416i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −20.6489 | + | 11.9216i | −1.50198 | + | 0.867171i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.98438 | − | 5.16909i | −0.215942 | − | 0.374022i | 0.737622 | − | 0.675214i | \(-0.235949\pi\) |
−0.953564 | + | 0.301192i | \(0.902615\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.83988 | + | 4.52636i | 0.564327 | + | 0.325814i | 0.754880 | − | 0.655862i | \(-0.227695\pi\) |
−0.190553 | + | 0.981677i | \(0.561028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.86320 | + | 5.69452i | 0.702724 | + | 0.405718i | 0.808361 | − | 0.588687i | \(-0.200355\pi\) |
−0.105637 | + | 0.994405i | \(0.533688\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.38863 | + | 9.33339i | 0.381990 | + | 0.661626i | 0.991347 | − | 0.131270i | \(-0.0419055\pi\) |
−0.609357 | + | 0.792896i | \(0.708572\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.28998 | − | 4.20887i | 0.514196 | − | 0.296871i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.77162i | 0.615647i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.510035 | 0.0354499 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.30426 | 0.643589 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.61256 | − | 2.79304i | 0.111013 | − | 0.192280i | −0.805166 | − | 0.593050i | \(-0.797924\pi\) |
0.916179 | + | 0.400769i | \(0.131257\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.0253i | 1.37211i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.0363 | + | 29.5078i | 1.15650 | + | 2.00312i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.26023 | − | 4.19170i | −0.490601 | − | 0.283249i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.5041 | − | 13.3987i | −1.58106 | − | 0.901292i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7046 | + | 8.48968i | 0.984690 | + | 0.568511i | 0.903683 | − | 0.428203i | \(-0.140853\pi\) |
0.0810069 | + | 0.996714i | \(0.474186\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.07891 | + | 1.20026i | −0.137982 | + | 0.0796641i | −0.567402 | − | 0.823441i | \(-0.692051\pi\) |
0.429420 | + | 0.903105i | \(0.358718\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.35671i | 0.486145i | 0.970008 | + | 0.243073i | \(0.0781553\pi\) | ||||
−0.970008 | + | 0.243073i | \(0.921845\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.00367 | + | 10.3987i | −0.395013 | + | 0.684182i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.37410 | 0.221045 | 0.110522 | − | 0.993874i | \(-0.464748\pi\) | ||||
0.110522 | + | 0.993874i | \(0.464748\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.53455 | + | 11.3182i | −0.424464 | + | 0.735194i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.7807i | 1.53824i | 0.639103 | + | 0.769121i | \(0.279306\pi\) | ||||
−0.639103 | + | 0.769121i | \(0.720694\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.3307 | − | 11.1606i | 1.24520 | − | 0.718918i | 0.275054 | − | 0.961429i | \(-0.411304\pi\) |
0.970149 | + | 0.242511i | \(0.0779709\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.26371 | + | 3.92086i | 0.145217 | + | 0.251523i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.59199 | − | 16.8264i | 0.610324 | − | 1.07064i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.632982 | − | 0.365452i | −0.0401136 | − | 0.0231596i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.31119 | − | 4.00310i | −0.145881 | − | 0.252673i | 0.783820 | − | 0.620988i | \(-0.213268\pi\) |
−0.929701 | + | 0.368314i | \(0.879935\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.74123 | − | 1.00530i | 0.109470 | − | 0.0632028i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.9320 | + | 18.9347i | −0.681916 | + | 1.18111i | 0.292479 | + | 0.956272i | \(0.405520\pi\) |
−0.974395 | + | 0.224842i | \(0.927813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −41.2977 | −2.56612 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.889612 | 0.0550656 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.0895 | + | 17.4756i | −0.622146 | + | 1.07759i | 0.366939 | + | 0.930245i | \(0.380406\pi\) |
−0.989085 | + | 0.147344i | \(0.952928\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.3970 | + | 10.6215i | −1.12588 | + | 0.650027i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.64344 | − | 6.31062i | −0.222144 | − | 0.384765i | 0.733315 | − | 0.679889i | \(-0.237972\pi\) |
−0.955459 | + | 0.295124i | \(0.904639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.23650 | − | 2.44595i | −0.257349 | − | 0.148581i | 0.365775 | − | 0.930703i | \(-0.380804\pi\) |
−0.623125 | + | 0.782122i | \(0.714137\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.6162 | + | 21.5776i | 0.763569 | + | 1.30594i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.40029 | − | 7.62153i | −0.264388 | − | 0.457933i | 0.703015 | − | 0.711175i | \(-0.251837\pi\) |
−0.967403 | + | 0.253241i | \(0.918503\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.99266 | − | 1.72781i | 0.179166 | − | 0.103441i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.6085i | − | 0.752161i | −0.926587 | − | 0.376081i | \(-0.877272\pi\) | ||
0.926587 | − | 0.376081i | \(-0.122728\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.4505 | − | 18.1007i | 0.621216 | − | 1.07598i | −0.368044 | − | 0.929808i | \(-0.619972\pi\) |
0.989260 | − | 0.146169i | \(-0.0466943\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.4972 | −1.97727 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.6525 | + | 34.0392i | −1.15603 | + | 2.00231i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 4.49689i | − | 0.263612i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.599706 | − | 0.346241i | 0.0350352 | − | 0.0202276i | −0.482380 | − | 0.875962i | \(-0.660228\pi\) |
0.517415 | + | 0.855734i | \(0.326894\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.25551 | + | 4.76632i | 0.479033 | + | 0.276570i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0229665 | − | 4.18534i | −0.00132819 | − | 0.242044i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.7035 | + | 9.06642i | 0.905134 | + | 0.522580i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.31246 | + | 9.20145i | 0.305193 | + | 0.528610i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.83168i | − | 0.504051i | −0.967721 | − | 0.252025i | \(-0.918903\pi\) | ||
0.967721 | − | 0.252025i | \(-0.0810966\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.90157 | + | 10.2218i | −0.335728 | + | 0.581499i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3958 | −0.646198 | −0.323099 | − | 0.946365i | \(-0.604725\pi\) | ||||
−0.323099 | + | 0.946365i | \(0.604725\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.38496 | 0.191329 | 0.0956647 | − | 0.995414i | \(-0.469502\pi\) | ||||
0.0956647 | + | 0.995414i | \(0.469502\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.557104i | 0.0312901i | 0.999878 | + | 0.0156450i | \(0.00498017\pi\) | ||||
−0.999878 | + | 0.0156450i | \(0.995020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.03709 | − | 1.75347i | 0.170044 | − | 0.0981752i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.33146 | + | 10.9664i | 0.353388 | + | 0.612086i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −34.9080 | − | 20.1542i | −1.94234 | − | 1.12141i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.7259 | + | 7.34730i | 0.703744 | + | 0.406307i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.50367 | − | 12.9967i | −0.413691 | − | 0.716533i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.43266 | − | 1.98185i | 0.188676 | − | 0.108932i | −0.402687 | − | 0.915338i | \(-0.631924\pi\) |
0.591363 | + | 0.806406i | \(0.298590\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.18839i | 0.229522i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.7243 | −0.911030 | −0.455515 | − | 0.890228i | \(-0.650545\pi\) | ||||
−0.455515 | + | 0.890228i | \(0.650545\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.24251 | −0.501984 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.81119 | − | 11.7973i | 0.368847 | − | 0.638861i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.6577i | 1.11541i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.79043 | + | 6.56521i | 0.203481 | + | 0.352439i | 0.949648 | − | 0.313320i | \(-0.101441\pi\) |
−0.746167 | + | 0.665759i | \(0.768108\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.6733 | + | 13.6678i | 1.26720 | + | 0.731621i | 0.974458 | − | 0.224569i | \(-0.0720975\pi\) |
0.292746 | + | 0.956190i | \(0.405431\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.1305 | − | 10.0160i | 0.914359 | − | 0.534616i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.5964 | − | 13.0461i | −1.20269 | − | 0.694372i | −0.241536 | − | 0.970392i | \(-0.577651\pi\) |
−0.961152 | + | 0.276020i | \(0.910984\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 45.0496 | − | 26.0094i | 2.38428 | − | 1.37656i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.694176i | 0.0366372i | 0.999832 | + | 0.0183186i | \(0.00583132\pi\) | ||||
−0.999832 | + | 0.0183186i | \(0.994169\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.92820 | − | 8.53590i | 0.259379 | − | 0.449258i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.8016 | −0.671908 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.4109 | − | 19.7643i | 0.595644 | − | 1.03169i | −0.397812 | − | 0.917467i | \(-0.630230\pi\) |
0.993456 | − | 0.114218i | \(-0.0364364\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.39726i | 0.176854i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −47.4499 | + | 27.3952i | −2.46347 | + | 1.42229i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.94065 | − | 6.82540i | −0.204039 | − | 0.353406i | 0.745787 | − | 0.666184i | \(-0.232074\pi\) |
−0.949826 | + | 0.312779i | \(0.898740\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0400587 | − | 7.30015i | −0.00206313 | − | 0.375977i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.9703 | + | 15.5713i | 1.38537 | + | 0.799843i | 0.992789 | − | 0.119875i | \(-0.0382494\pi\) |
0.392580 | + | 0.919718i | \(0.371583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.1761 | + | 26.2857i | 0.777494 | + | 1.34666i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.8885 | + | 17.2561i | −1.52723 | + | 0.881747i | −0.527754 | + | 0.849397i | \(0.676966\pi\) |
−0.999477 | + | 0.0323495i | \(0.989701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.919510 | − | 1.59264i | 0.0467413 | − | 0.0809584i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.18414 | −0.313548 | −0.156774 | − | 0.987634i | \(-0.550109\pi\) | ||||
−0.156774 | + | 0.987634i | \(0.550109\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.71043 | −0.440505 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.07723 | + | 1.86582i | −0.0543390 | + | 0.0941179i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.6209 | + | 11.3281i | −0.984745 | + | 0.568543i | −0.903699 | − | 0.428167i | \(-0.859159\pi\) |
−0.0810459 | + | 0.996710i | \(0.525826\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.6199 | + | 32.2506i | 0.932161 | + | 1.61455i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.35847 | + | 1.93902i | 0.167714 | + | 0.0968298i | 0.581508 | − | 0.813541i | \(-0.302463\pi\) |
−0.413793 | + | 0.910371i | \(0.635796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.3132 | − | 24.4799i | −0.712990 | − | 1.21943i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.25551 | + | 14.2990i | 0.409210 | + | 0.708773i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0037 | − | 6.93032i | 0.593543 | − | 0.342682i | −0.172954 | − | 0.984930i | \(-0.555331\pi\) |
0.766497 | + | 0.642248i | \(0.221998\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 19.7989i | − | 0.976607i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.7486 | + | 23.8132i | −0.676523 | + | 1.17177i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.0311 | −0.687106 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.1751 | − | 26.2840i | 0.741352 | − | 1.28406i | −0.210528 | − | 0.977588i | \(-0.567518\pi\) |
0.951880 | − | 0.306471i | \(-0.0991484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.608516i | 0.0296573i | 0.999890 | + | 0.0148286i | \(0.00472027\pi\) | ||||
−0.999890 | + | 0.0148286i | \(0.995280\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.31812 | + | 0.761018i | −0.0640892 | + | 0.0370019i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.8934 | + | 8.02134i | 0.672347 | + | 0.388180i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.94905 | − | 8.68167i | 0.238942 | − | 0.419155i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.0819 | − | 19.6772i | −1.64167 | − | 0.947818i | −0.980240 | − | 0.197810i | \(-0.936617\pi\) |
−0.661429 | − | 0.750008i | \(-0.730050\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.21474 | − | 5.56810i | −0.154491 | − | 0.267586i | 0.778383 | − | 0.627790i | \(-0.216040\pi\) |
−0.932873 | + | 0.360204i | \(0.882707\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.23572i | − | 0.298295i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.735722 | − | 1.27431i | 0.0351141 | − | 0.0608194i | −0.847934 | − | 0.530101i | \(-0.822154\pi\) |
0.883048 | + | 0.469282i | \(0.155487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.17071 | 0.246224 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9193 | 0.803860 | 0.401930 | − | 0.915670i | \(-0.368340\pi\) | ||||
0.401930 | + | 0.915670i | \(0.368340\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 7.58396i | − | 0.358709i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.89557 | + | 4.55851i | −0.372615 | + | 0.215129i | −0.674600 | − | 0.738183i | \(-0.735684\pi\) |
0.301985 | + | 0.953313i | \(0.402351\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.69615 | + | 11.5981i | 0.315310 | + | 0.546132i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.16273 | + | 1.24865i | 0.101614 | + | 0.0586669i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.2041 | + | 8.77811i | 0.711220 | + | 0.410623i | 0.811512 | − | 0.584335i | \(-0.198645\pi\) |
−0.100293 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.6489 | − | 35.7649i | −0.963807 | − | 1.66936i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.2973 | + | 7.67722i | −0.619318 | + | 0.357564i | −0.776604 | − | 0.629990i | \(-0.783059\pi\) |
0.157285 | + | 0.987553i | \(0.449726\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.8614i | 0.876562i | 0.898838 | + | 0.438281i | \(0.144412\pi\) | ||||
−0.898838 | + | 0.438281i | \(0.855588\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.9302 | −1.52383 | −0.761913 | − | 0.647679i | \(-0.775740\pi\) | ||||
−0.761913 | + | 0.647679i | \(0.775740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.7896 | −1.05232 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.32355 | − | 12.6848i | 0.337452 | − | 0.584483i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.24958i | − | 0.333336i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.77840 | + | 4.81234i | 0.127214 | + | 0.220342i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.9368 | − | 8.62378i | −0.682481 | − | 0.394031i | 0.118308 | − | 0.992977i | \(-0.462253\pi\) |
−0.800789 | + | 0.598946i | \(0.795586\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.3699 | − | 0.188601i | 1.56713 | − | 0.00859944i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.96919 | + | 4.02367i | 0.317109 | + | 0.183083i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5663 | − | 8.98720i | 0.705376 | − | 0.407249i | −0.103971 | − | 0.994580i | \(-0.533155\pi\) |
0.809346 | + | 0.587331i | \(0.199822\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.22936i | 0.191258i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.0977 | − | 22.6858i | 0.591089 | − | 1.02380i | −0.402997 | − | 0.915201i | \(-0.632032\pi\) |
0.994086 | − | 0.108595i | \(-0.0346350\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.1929 | −0.684253 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.1075 | − | 46.9515i | 1.21594 | − | 2.10606i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.3428i | − | 0.821139i | −0.911829 | − | 0.410569i | \(-0.865330\pi\) | ||
0.911829 | − | 0.410569i | \(-0.134670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.3458 | + | 7.12783i | −0.551568 | + | 0.318448i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.12811 | − | 12.3462i | −0.317827 | − | 0.550492i | 0.662208 | − | 0.749320i | \(-0.269620\pi\) |
−0.980034 | + | 0.198829i | \(0.936286\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.5984 | − | 17.9003i | −0.470690 | − | 0.794980i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.5380 | + | 15.8991i | 1.22060 | + | 0.704714i | 0.965046 | − | 0.262081i | \(-0.0844086\pi\) |
0.255555 | + | 0.966795i | \(0.417742\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.3483 | + | 19.6558i | 0.502018 | + | 0.869521i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 25.6038 | − | 14.7824i | 1.13043 | − | 0.652657i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.00000 | + | 5.19615i | −0.131940 | + | 0.228527i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.0954 | −0.969880 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −45.1676 | −1.97883 | −0.989414 | − | 0.145122i | \(-0.953642\pi\) | ||||
−0.989414 | + | 0.145122i | \(0.953642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0573 | − | 22.6159i | 0.570955 | − | 0.988924i | −0.425513 | − | 0.904952i | \(-0.639906\pi\) |
0.996468 | − | 0.0839712i | \(-0.0267604\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.1089 | + | 29.5078i | −2.22634 | + | 1.28538i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8262 | + | 18.7516i | 0.470706 | + | 0.815287i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.41512 | + | 1.39437i | 0.104807 | + | 0.0605106i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.8779 | − | 0.152976i | 1.20753 | − | 0.00662615i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.4825 | + | 33.7447i | 0.840733 | + | 1.45619i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.6525 | − | 10.1917i | 0.760349 | − | 0.438988i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.4750i | 1.35321i | 0.736344 | + | 0.676607i | \(0.236550\pi\) | ||||
−0.736344 | + | 0.676607i | \(0.763450\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.8693 | − | 34.4147i | 0.852675 | − | 1.47688i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.70391 | 0.243881 | 0.121941 | − | 0.992537i | \(-0.461088\pi\) | ||||
0.121941 | + | 0.992537i | \(0.461088\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.813519 | − | 1.40906i | 0.0347201 | − | 0.0601370i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.8765i | − | 0.463353i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.6419 | − | 17.6911i | 1.30303 | − | 0.752303i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.0757 | − | 10.4360i | −0.765890 | − | 0.442187i | 0.0655165 | − | 0.997851i | \(-0.479130\pi\) |
−0.831406 | + | 0.555665i | \(0.812464\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.1106 | − | 7.47378i | −0.554519 | − | 0.316107i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0110 | − | 10.3987i | −0.760426 | − | 0.439032i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.6157 | + | 28.7793i | 0.700270 | + | 1.21290i | 0.968372 | + | 0.249513i | \(0.0802704\pi\) |
−0.268102 | + | 0.963391i | \(0.586396\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 32.4435i | 1.36250i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.0336 | + | 34.6992i | −0.839851 | + | 1.45466i | 0.0501680 | + | 0.998741i | \(0.484024\pi\) |
−0.890019 | + | 0.455924i | \(0.849309\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.53590 | −0.189821 | −0.0949107 | − | 0.995486i | \(-0.530257\pi\) | ||||
−0.0949107 | + | 0.995486i | \(0.530257\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.55117 | −0.399006 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.2706i | 1.46834i | 0.678968 | + | 0.734168i | \(0.262427\pi\) | ||||
−0.678968 | + | 0.734168i | \(0.737573\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.5453 | − | 7.24306i | 0.521367 | − | 0.301011i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.989397 | + | 1.71369i | 0.0410471 | + | 0.0710957i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.9707 | + | 10.9527i | 0.785684 | + | 0.453615i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.6511 | + | 20.5832i | 1.47148 | + | 0.849558i | 0.999486 | − | 0.0320457i | \(-0.0102022\pi\) |
0.471991 | + | 0.881603i | \(0.343536\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.1244 | − | 36.5885i | −0.870414 | − | 1.50760i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.7831 | − | 9.11235i | 0.649228 | − | 0.374832i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 9.39726i | − | 0.385899i | −0.981209 | − | 0.192950i | \(-0.938195\pi\) | ||
0.981209 | − | 0.192950i | \(-0.0618054\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.2457 | 0.705821 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.7881 | 0.890239 | 0.445119 | − | 0.895471i | \(-0.353161\pi\) | ||||
0.445119 | + | 0.895471i | \(0.353161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5481 | + | 21.7340i | −0.511848 | + | 0.886547i | 0.488058 | + | 0.872811i | \(0.337706\pi\) |
−0.999906 | + | 0.0137352i | \(0.995628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.31130i | 0.0941236i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.9888 | − | 29.4254i | −0.689552 | − | 1.19434i | −0.971983 | − | 0.235052i | \(-0.924474\pi\) |
0.282431 | − | 0.959288i | \(-0.408859\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.1558 | + | 7.01815i | 0.492578 | + | 0.284390i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.30426 | + | 10.7822i | 0.255043 | + | 0.436202i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.5736 | − | 10.7235i | −0.750182 | − | 0.433118i | 0.0755778 | − | 0.997140i | \(-0.475920\pi\) |
−0.825760 | + | 0.564022i | \(0.809253\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.5092 | + | 17.0372i | −1.18800 | + | 0.685890i | −0.957851 | − | 0.287266i | \(-0.907254\pi\) |
−0.230146 | + | 0.973156i | \(0.573920\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 26.9791i | − | 1.08438i | −0.840256 | − | 0.542191i | \(-0.817595\pi\) | ||
0.840256 | − | 0.542191i | \(-0.182405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.19439 | − | 5.53285i | 0.128186 | − | 0.222026i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 57.5118 | 2.30416 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.44432 | − | 12.8939i | 0.297297 | − | 0.514934i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 71.5298i | − | 2.85208i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.8863 | + | 18.9869i | −1.30918 | + | 0.755857i | −0.981960 | − | 0.189090i | \(-0.939446\pi\) |
−0.327223 | + | 0.944947i | \(0.606113\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.58041 | − | 4.46940i | −0.102562 | − | 0.177643i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.232834 | − | 42.4308i | −0.00922521 | − | 1.68117i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.76179 | − | 2.74922i | −0.188374 | − | 0.108758i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.12590 | − | 7.14627i | −0.162963 | − | 0.282261i | 0.772967 | − | 0.634446i | \(-0.218772\pi\) |
−0.935930 | + | 0.352186i | \(0.885439\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.6992 | + | 24.0750i | −1.64446 | + | 0.949427i | −0.665233 | + | 0.746636i | \(0.731668\pi\) |
−0.979222 | + | 0.202791i | \(0.934999\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.08951 | − | 1.88709i | 0.0428332 | − | 0.0741893i | −0.843814 | − | 0.536636i | \(-0.819695\pi\) |
0.886647 | + | 0.462446i | \(0.153028\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.9935 | 0.431532 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 54.5229 | 2.13692 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.9341 | − | 29.3308i | 0.662684 | − | 1.14780i | −0.317224 | − | 0.948351i | \(-0.602751\pi\) |
0.979908 | − | 0.199451i | \(-0.0639159\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.99348 | − | 1.15094i | 0.0777730 | − | 0.0449023i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.2246 | − | 22.9056i | −0.515155 | − | 0.892275i | −0.999845 | − | 0.0175892i | \(-0.994401\pi\) |
0.484690 | − | 0.874686i | \(-0.338932\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.3259 | − | 15.1993i | −1.02396 | − | 0.591182i | −0.108710 | − | 0.994074i | \(-0.534672\pi\) |
−0.915248 | + | 0.402891i | \(0.868005\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −37.3736 | + | 21.8520i | −1.45147 | + | 0.848660i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.17517 | − | 2.03546i | −0.0455029 | − | 0.0788134i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.5302 | − | 13.5851i | 0.909729 | − | 0.525232i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 6.41393i | − | 0.247607i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.1976 | − | 31.5192i | 0.701467 | − | 1.21498i | −0.266485 | − | 0.963839i | \(-0.585862\pi\) |
0.967952 | − | 0.251137i | \(-0.0808044\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.0043 | −1.38376 | −0.691880 | − | 0.722013i | \(-0.743217\pi\) | ||||
−0.691880 | + | 0.722013i | \(0.743217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.08726 | + | 10.5435i | −0.233608 | + | 0.404620i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.84130i | 0.147199i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.1107 | − | 6.41478i | 0.425140 | − | 0.245455i | −0.272134 | − | 0.962259i | \(-0.587729\pi\) |
0.697274 | + | 0.716805i | \(0.254396\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.1950 | + | 5.88609i | 0.388964 | + | 0.224568i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.3649 | − | 23.0162i | 1.49968 | − | 0.876849i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.5608 | + | 16.4896i | 1.08650 | + | 0.627294i | 0.932644 | − | 0.360799i | \(-0.117496\pi\) |
0.153861 | + | 0.988092i | \(0.450829\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.64846 | − | 2.85521i | −0.0626197 | − | 0.108461i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 58.0188i | − | 2.19762i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.69961 | − | 4.67586i | 0.102109 | − | 0.176857i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.7352 | 1.53855 | 0.769273 | − | 0.638921i | \(-0.220619\pi\) | ||||
0.769273 | + | 0.638921i | \(0.220619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 51.2076 | 1.93133 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 28.7651i | − | 1.08182i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.2932 | + | 8.82956i | −0.574350 | + | 0.331601i | −0.758885 | − | 0.651225i | \(-0.774255\pi\) |
0.184535 | + | 0.982826i | \(0.440922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.79422 | − | 3.10769i | −0.0672886 | − | 0.116547i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.90658 | − | 4.56487i | −0.296104 | − | 0.170956i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.9555 | + | 19.0269i | 1.23074 | + | 0.710571i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.7836 | + | 42.9265i | 0.924273 | + | 1.60089i | 0.792727 | + | 0.609577i | \(0.208661\pi\) |
0.131546 | + | 0.991310i | \(0.458006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.6737 | − | 15.9774i | 1.03062 | − | 0.595031i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 35.7183i | − | 1.32838i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.4738 | 1.35274 | 0.676370 | − | 0.736562i | \(-0.263552\pi\) | ||||
0.676370 | + | 0.736562i | \(0.263552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7112 | 1.10042 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.7035 | + | 27.1993i | −0.580815 | + | 1.00600i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.8491i | 1.06556i | 0.846252 | + | 0.532782i | \(0.178854\pi\) | ||||
−0.846252 | + | 0.532782i | \(0.821146\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.55568 | + | 7.89067i | 0.167811 | + | 0.290657i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.1330 | + | 9.89173i | 0.630247 | + | 0.363873i | 0.780848 | − | 0.624721i | \(-0.214787\pi\) |
−0.150601 | + | 0.988595i | \(0.548121\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.6436 | − | 26.7554i | −0.574683 | − | 0.982885i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.8635 | + | 13.2003i | 0.838781 | + | 0.484271i | 0.856850 | − | 0.515566i | \(-0.172418\pi\) |
−0.0180685 | + | 0.999837i | \(0.505752\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.173801 | − | 0.100344i | 0.00635905 | − | 0.00367140i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 34.2826i | − | 1.25266i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.90171 | + | 11.9541i | −0.251847 | + | 0.436212i | −0.964034 | − | 0.265778i | \(-0.914371\pi\) |
0.712187 | + | 0.701990i | \(0.247705\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.39671 | −0.269551 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.59080 | + | 4.48739i | −0.0941642 | + | 0.163097i | −0.909259 | − | 0.416230i | \(-0.863351\pi\) |
0.815095 | + | 0.579327i | \(0.196685\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 3.21736i | − | 0.116783i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.00743288 | − | 0.00429137i | 0.000269442 | − | 0.000155562i | −0.499865 | − | 0.866103i | \(-0.666617\pi\) |
0.500135 | + | 0.865948i | \(0.333284\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.8915 | − | 34.4531i | −0.720121 | − | 1.24729i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.3335 | − | 19.8813i | 0.409227 | − | 0.717871i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.2610 | + | 5.92417i | 0.370020 | + | 0.213631i | 0.673467 | − | 0.739217i | \(-0.264804\pi\) |
−0.303447 | + | 0.952848i | \(0.598138\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.4933 | + | 30.2992i | 0.630005 | + | 1.09120i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.2262 | − | 10.5229i | 0.655550 | − | 0.378482i | −0.135030 | − | 0.990842i | \(-0.543113\pi\) |
0.790579 | + | 0.612360i | \(0.209780\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −33.0422 | + | 57.2308i | −1.18538 | + | 2.05314i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41.5352 | 1.48815 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.6754 | −0.775605 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.57172 | − | 9.65050i | 0.199117 | − | 0.344881i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.34029 | − | 2.50587i | 0.154715 | − | 0.0893246i | −0.420644 | − | 0.907226i | \(-0.638196\pi\) |
0.575359 | + | 0.817901i | \(0.304862\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.1452 | + | 27.9643i | 0.574784 | + | 0.995556i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.6701 | + | 12.5112i | 0.770499 | + | 0.444848i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.5993 | − | 6.61228i | −0.411904 | − | 0.234809i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.3283 | − | 35.2096i | −0.720065 | − | 1.24719i | −0.960973 | − | 0.276641i | \(-0.910779\pi\) |
0.240909 | − | 0.970548i | \(-0.422555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.5110 | − | 12.9967i | 0.796382 | − | 0.459792i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 5.83281i | − | 0.206092i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.53709 | − | 7.85847i | 0.160110 | − | 0.277320i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.6604 | −0.410466 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.70676 | + | 4.68824i | −0.0951644 | + | 0.164830i | −0.909677 | − | 0.415316i | \(-0.863671\pi\) |
0.814513 | + | 0.580146i | \(0.197004\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.616994i | 0.0216656i | 0.999941 | + | 0.0108328i | \(0.00344825\pi\) | ||||
−0.999941 | + | 0.0108328i | \(0.996552\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.77924 | + | 3.91399i | −0.237758 | + | 0.137270i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.4717 | − | 11.2420i | −0.681229 | − | 0.393308i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.86297 | + | 0.0376597i | −0.239812 | + | 0.00131594i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.8377 | − | 11.4533i | −0.692340 | − | 0.399723i | 0.112148 | − | 0.993691i | \(-0.464227\pi\) |
−0.804488 | + | 0.593969i | \(0.797560\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.82928 | − | 8.36456i | −0.168338 | − | 0.291570i | 0.769498 | − | 0.638650i | \(-0.220507\pi\) |
−0.937836 | + | 0.347080i | \(0.887173\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.2602i | 0.739289i | 0.929173 | + | 0.369645i | \(0.120521\pi\) | ||||
−0.929173 | + | 0.369645i | \(0.879479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.9948 | + | 20.7755i | −0.416595 | + | 0.721564i | −0.995594 | − | 0.0937639i | \(-0.970110\pi\) |
0.578999 | + | 0.815328i | \(0.303443\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.0827 | −0.488522 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −88.3059 | −3.05962 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 43.2857i | − | 1.49617i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.4511 | + | 10.6527i | −0.637003 | + | 0.367774i | −0.783459 | − | 0.621443i | \(-0.786547\pi\) |
0.146456 | + | 0.989217i | \(0.453213\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.4502 | + | 21.5644i | 0.429319 | + | 0.743602i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.4730 | − | 10.0880i | −0.601802 | − | 0.347451i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.0147 | + | 17.3290i | 1.03132 | + | 0.595431i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.7228 | − | 28.9647i | −0.573925 | − | 0.994067i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.58317 | − | 5.53285i | 0.328507 | − | 0.189664i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.1098i | 0.414631i | 0.978274 | + | 0.207315i | \(0.0664726\pi\) | ||||
−0.978274 | + | 0.207315i | \(0.933527\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.4491 | −1.21092 | −0.605459 | − | 0.795876i | \(-0.707010\pi\) | ||||
−0.605459 | + | 0.795876i | \(0.707010\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.4600 | −1.61931 | −0.809657 | − | 0.586904i | \(-0.800347\pi\) | ||||
−0.809657 | + | 0.586904i | \(0.800347\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26.8010 | + | 46.4207i | −0.913376 | + | 1.58201i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 18.7268i | − | 0.637467i | −0.947844 | − | 0.318733i | \(-0.896743\pi\) | ||
0.947844 | − | 0.318733i | \(-0.103257\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.4479 | + | 54.4694i | 1.06803 | + | 1.84988i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.2508 | − | 7.07299i | −0.415579 | − | 0.239935i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.9665 | − | 0.104077i | 0.642657 | − | 0.00352650i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.06931 | + | 0.617367i | 0.0361907 | + | 0.0208947i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.57198 | + | 0.907583i | −0.0530820 | + | 0.0306469i | −0.526306 | − | 0.850295i | \(-0.676423\pi\) |
0.473224 | + | 0.880942i | \(0.343090\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1.10811i | − | 0.0373755i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.1718 | + | 43.5989i | −0.848061 | + | 1.46888i | 0.0348758 | + | 0.999392i | \(0.488896\pi\) |
−0.882936 | + | 0.469493i | \(0.844437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.42003 | −0.148746 | −0.0743729 | − | 0.997230i | \(-0.523696\pi\) | ||||
−0.0743729 | + | 0.997230i | \(0.523696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.34567 | − | 2.33076i | 0.0451831 | − | 0.0782594i | −0.842549 | − | 0.538619i | \(-0.818946\pi\) |
0.887732 | + | 0.460360i | \(0.152280\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 82.1731i | − | 2.75600i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.2332 | − | 6.48552i | 0.376328 | − | 0.217273i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.30426 | + | 16.1154i | 0.311355 | + | 0.539283i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.81846 | − | 3.31685i | −0.194273 | − | 0.110747i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.7908 | − | 7.96213i | −0.459949 | − | 0.265552i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47.4499 | − | 82.1856i | −1.58078 | − | 2.73800i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.1287 | − | 14.5080i | 0.836230 | − | 0.482797i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.20083 | + | 12.4722i | −0.239100 | + | 0.414133i | −0.960456 | − | 0.278431i | \(-0.910186\pi\) |
0.721356 | + | 0.692564i | \(0.243519\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.91734 | −0.0967620 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.88723 | −0.294447 | −0.147223 | − | 0.989103i | \(-0.547034\pi\) | ||||
−0.147223 | + | 0.989103i | \(0.547034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.395565 | − | 0.685139i | 0.0130913 | − | 0.0226748i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.05137 | − | 2.91641i | 0.166811 | − | 0.0963083i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.4873 | + | 37.2171i | 0.708802 | + | 1.22768i | 0.965302 | + | 0.261136i | \(0.0840972\pi\) |
−0.256500 | + | 0.966544i | \(0.582569\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.2390 | − | 7.06621i | −0.403290 | − | 0.232839i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.3457 | + | 39.1990i | −0.735517 | + | 1.29025i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.62042 | − | 2.80665i | −0.0532217 | − | 0.0921826i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.7537 | + | 14.8689i | −0.844952 | + | 0.487833i | −0.858944 | − | 0.512069i | \(-0.828879\pi\) |
0.0139925 | + | 0.999902i | \(0.495546\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 63.2175i | − | 2.07187i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.11778 | + | 15.7925i | −0.298503 | + | 0.517022i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.1355 | −0.559793 | −0.279896 | − | 0.960030i | \(-0.590300\pi\) | ||||
−0.279896 | + | 0.960030i | \(0.590300\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.70830 | − | 4.69092i | 0.0883821 | − | 0.153082i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.5767i | 0.768580i | 0.923212 | + | 0.384290i | \(0.125554\pi\) | ||||
−0.923212 | + | 0.384290i | \(0.874446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.77304 | − | 4.48777i | 0.253125 | − | 0.146142i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.2656 | − | 8.81360i | −0.496066 | − | 0.286404i | 0.231022 | − | 0.972949i | \(-0.425793\pi\) |
−0.727087 | + | 0.686545i | \(0.759126\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.53433 | − | 16.3066i | −0.309498 | − | 0.529336i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.772040 | + | 0.445737i | 0.0250351 | + | 0.0144540i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.3816 | + | 50.8903i | 0.951762 | + | 1.64850i | 0.741610 | + | 0.670831i | \(0.234063\pi\) |
0.210152 | + | 0.977669i | \(0.432604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 5.61178i | − | 0.181403i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.8010 | + | 46.4207i | −0.865449 | + | 1.49900i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8564 | −0.995368 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.47692 | −0.112042 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.92168i | − | 0.0939550i | −0.998896 | − | 0.0469775i | \(-0.985041\pi\) | ||
0.998896 | − | 0.0469775i | \(-0.0149589\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −55.8597 | + | 32.2506i | −1.79447 | + | 1.03604i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.00693 | + | 8.67226i | 0.160680 | + | 0.278306i | 0.935113 | − | 0.354350i | \(-0.115298\pi\) |
−0.774433 | + | 0.632656i | \(0.781965\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.8974 | + | 18.9933i | 1.05464 | + | 0.608899i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.9757 | + | 13.2650i | 0.735058 | + | 0.424386i | 0.820270 | − | 0.571977i | \(-0.193823\pi\) |
−0.0852116 | + | 0.996363i | \(0.527157\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.4967 | − | 19.9129i | −0.367437 | − | 0.636420i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.49421 | + | 2.01739i | −0.111562 | + | 0.0644102i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 4.69317i | − | 0.149689i | −0.997195 | − | 0.0748445i | \(-0.976154\pi\) | ||
0.997195 | − | 0.0748445i | \(-0.0238460\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.0147 | −0.764396 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.85868 | −0.154497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.4601 | − | 19.8494i | 0.364041 | − | 0.630537i | −0.624581 | − | 0.780960i | \(-0.714730\pi\) |
0.988622 | + | 0.150423i | \(0.0480636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 6.34268i | − | 0.201279i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.7213 | + | 42.8186i | 0.782932 | + | 1.35608i | 0.930227 | + | 0.366985i | \(0.119610\pi\) |
−0.147295 | + | 0.989093i | \(0.547057\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.4356 | + | 26.2323i | 1.43752 | + | 0.829952i |
(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 | 1300.2.y.b.901.3 | 8 | ||
5.2 | odd | 4 | 1300.2.ba.c.849.1 | 8 | |||
5.3 | odd | 4 | 1300.2.ba.b.849.4 | 8 | |||
5.4 | even | 2 | 260.2.x.a.121.2 | yes | 8 | ||
13.10 | even | 6 | inner | 1300.2.y.b.101.3 | 8 | ||
15.14 | odd | 2 | 2340.2.dj.d.901.4 | 8 | |||
20.19 | odd | 2 | 1040.2.da.c.641.3 | 8 | |||
65.4 | even | 6 | 3380.2.f.i.3041.6 | 8 | |||
65.9 | even | 6 | 3380.2.f.i.3041.5 | 8 | |||
65.19 | odd | 12 | 3380.2.a.p.1.3 | 4 | |||
65.23 | odd | 12 | 1300.2.ba.c.49.1 | 8 | |||
65.49 | even | 6 | 260.2.x.a.101.2 | ✓ | 8 | ||
65.59 | odd | 12 | 3380.2.a.q.1.3 | 4 | |||
65.62 | odd | 12 | 1300.2.ba.b.49.4 | 8 | |||
195.179 | odd | 6 | 2340.2.dj.d.361.2 | 8 | |||
260.179 | odd | 6 | 1040.2.da.c.881.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.x.a.101.2 | ✓ | 8 | 65.49 | even | 6 | ||
260.2.x.a.121.2 | yes | 8 | 5.4 | even | 2 | ||
1040.2.da.c.641.3 | 8 | 20.19 | odd | 2 | |||
1040.2.da.c.881.3 | 8 | 260.179 | odd | 6 | |||
1300.2.y.b.101.3 | 8 | 13.10 | even | 6 | inner | ||
1300.2.y.b.901.3 | 8 | 1.1 | even | 1 | trivial | ||
1300.2.ba.b.49.4 | 8 | 65.62 | odd | 12 | |||
1300.2.ba.b.849.4 | 8 | 5.3 | odd | 4 | |||
1300.2.ba.c.49.1 | 8 | 65.23 | odd | 12 | |||
1300.2.ba.c.849.1 | 8 | 5.2 | odd | 4 | |||
2340.2.dj.d.361.2 | 8 | 195.179 | odd | 6 | |||
2340.2.dj.d.901.4 | 8 | 15.14 | odd | 2 | |||
3380.2.a.p.1.3 | 4 | 65.19 | odd | 12 | |||
3380.2.a.q.1.3 | 4 | 65.59 | odd | 12 | |||
3380.2.f.i.3041.5 | 8 | 65.9 | even | 6 | |||
3380.2.f.i.3041.6 | 8 | 65.4 | even | 6 |