Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,6,Mod(1,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.a (trivial) |
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: | yes |
Analytic conductor: | \(25.9821788097\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.125628.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 63x + 159 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 18) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.81933\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −66.0868 | −1.18220 | −0.591099 | − | 0.806599i | \(-0.701306\pi\) | ||||
−0.591099 | + | 0.806599i | \(0.701306\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 114.190 | 0.880814 | 0.440407 | − | 0.897798i | \(-0.354834\pi\) | ||||
0.440407 | + | 0.897798i | \(0.354834\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −264.347 | −0.835940 | ||||||||
\(11\) | −385.625 | −0.960911 | −0.480455 | − | 0.877019i | \(-0.659529\pi\) | ||||
−0.480455 | + | 0.877019i | \(0.659529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1032.57 | 1.69458 | 0.847292 | − | 0.531128i | \(-0.178232\pi\) | ||||
0.847292 | + | 0.531128i | \(0.178232\pi\) | |||||||
\(14\) | 456.762 | 0.622830 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 959.020 | 0.804832 | 0.402416 | − | 0.915457i | \(-0.368171\pi\) | ||||
0.402416 | + | 0.915457i | \(0.368171\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −464.576 | −0.295239 | −0.147619 | − | 0.989044i | \(-0.547161\pi\) | ||||
−0.147619 | + | 0.989044i | \(0.547161\pi\) | |||||||
\(20\) | −1057.39 | −0.591099 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1542.50 | −0.679466 | ||||||||
\(23\) | 2303.41 | 0.907927 | 0.453963 | − | 0.891020i | \(-0.350010\pi\) | ||||
0.453963 | + | 0.891020i | \(0.350010\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1242.47 | 0.397590 | ||||||||
\(26\) | 4130.30 | 1.19825 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1827.05 | 0.440407 | ||||||||
\(29\) | 7098.27 | 1.56732 | 0.783659 | − | 0.621191i | \(-0.213351\pi\) | ||||
0.783659 | + | 0.621191i | \(0.213351\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7763.06 | 1.45087 | 0.725435 | − | 0.688291i | \(-0.241639\pi\) | ||||
0.725435 | + | 0.688291i | \(0.241639\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3836.08 | 0.569102 | ||||||||
\(35\) | −7546.48 | −1.04130 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9317.57 | 1.11892 | 0.559459 | − | 0.828858i | \(-0.311009\pi\) | ||||
0.559459 | + | 0.828858i | \(0.311009\pi\) | |||||||
\(38\) | −1858.31 | −0.208765 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4229.56 | −0.417970 | ||||||||
\(41\) | −13323.3 | −1.23780 | −0.618901 | − | 0.785469i | \(-0.712422\pi\) | ||||
−0.618901 | + | 0.785469i | \(0.712422\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2112.58 | −0.174238 | −0.0871190 | − | 0.996198i | \(-0.527766\pi\) | ||||
−0.0871190 | + | 0.996198i | \(0.527766\pi\) | |||||||
\(44\) | −6169.99 | −0.480455 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9213.62 | 0.642001 | ||||||||
\(47\) | 2494.80 | 0.164737 | 0.0823686 | − | 0.996602i | \(-0.473752\pi\) | ||||
0.0823686 | + | 0.996602i | \(0.473752\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3767.56 | −0.224166 | ||||||||
\(50\) | 4969.88 | 0.281139 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16521.2 | 0.847292 | ||||||||
\(53\) | −10044.2 | −0.491163 | −0.245582 | − | 0.969376i | \(-0.578979\pi\) | ||||
−0.245582 | + | 0.969376i | \(0.578979\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 25484.7 | 1.13599 | ||||||||
\(56\) | 7308.18 | 0.311415 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 28393.1 | 1.10826 | ||||||||
\(59\) | 5440.66 | 0.203480 | 0.101740 | − | 0.994811i | \(-0.467559\pi\) | ||||
0.101740 | + | 0.994811i | \(0.467559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34188.8 | 1.17641 | 0.588206 | − | 0.808711i | \(-0.299834\pi\) | ||||
0.588206 | + | 0.808711i | \(0.299834\pi\) | |||||||
\(62\) | 31052.2 | 1.02592 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −68239.6 | −2.00333 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 53585.2 | 1.45834 | 0.729169 | − | 0.684334i | \(-0.239907\pi\) | ||||
0.729169 | + | 0.684334i | \(0.239907\pi\) | |||||||
\(68\) | 15344.3 | 0.402416 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −30185.9 | −0.736308 | ||||||||
\(71\) | −970.010 | −0.0228365 | −0.0114183 | − | 0.999935i | \(-0.503635\pi\) | ||||
−0.0114183 | + | 0.999935i | \(0.503635\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −72400.3 | −1.59013 | −0.795066 | − | 0.606523i | \(-0.792564\pi\) | ||||
−0.795066 | + | 0.606523i | \(0.792564\pi\) | |||||||
\(74\) | 37270.3 | 0.791195 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7433.22 | −0.147619 | ||||||||
\(77\) | −44034.6 | −0.846384 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32197.7 | 0.580440 | 0.290220 | − | 0.956960i | \(-0.406271\pi\) | ||||
0.290220 | + | 0.956960i | \(0.406271\pi\) | |||||||
\(80\) | −16918.2 | −0.295549 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −53293.1 | −0.875258 | ||||||||
\(83\) | −36093.2 | −0.575082 | −0.287541 | − | 0.957768i | \(-0.592838\pi\) | ||||
−0.287541 | + | 0.957768i | \(0.592838\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −63378.6 | −0.951470 | ||||||||
\(86\) | −8450.34 | −0.123205 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −24680.0 | −0.339733 | ||||||||
\(89\) | 42622.2 | 0.570375 | 0.285188 | − | 0.958472i | \(-0.407944\pi\) | ||||
0.285188 | + | 0.958472i | \(0.407944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 117910. | 1.49261 | ||||||||
\(92\) | 36854.5 | 0.453963 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9979.21 | 0.116487 | ||||||||
\(95\) | 30702.4 | 0.349030 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −43853.9 | −0.473237 | −0.236618 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236618 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(98\) | −15070.2 | −0.158509 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 19879.5 | 0.198795 | ||||||||
\(101\) | 24113.3 | 0.235209 | 0.117604 | − | 0.993061i | \(-0.462478\pi\) | ||||
0.117604 | + | 0.993061i | \(0.462478\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −137221. | −1.27446 | −0.637231 | − | 0.770673i | \(-0.719920\pi\) | ||||
−0.637231 | + | 0.770673i | \(0.719920\pi\) | |||||||
\(104\) | 66084.8 | 0.599126 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −40176.8 | −0.347305 | ||||||||
\(107\) | −167979. | −1.41839 | −0.709195 | − | 0.705012i | \(-0.750941\pi\) | ||||
−0.709195 | + | 0.705012i | \(0.750941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −21224.0 | −0.171104 | −0.0855521 | − | 0.996334i | \(-0.527265\pi\) | ||||
−0.0855521 | + | 0.996334i | \(0.527265\pi\) | |||||||
\(110\) | 101939. | 0.803263 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 29232.7 | 0.220204 | ||||||||
\(113\) | −28841.6 | −0.212482 | −0.106241 | − | 0.994340i | \(-0.533882\pi\) | ||||
−0.106241 | + | 0.994340i | \(0.533882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −152225. | −1.07335 | ||||||||
\(116\) | 113572. | 0.783659 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 21762.6 | 0.143882 | ||||||||
\(119\) | 109511. | 0.708908 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12344.7 | −0.0766509 | ||||||||
\(122\) | 136755. | 0.831849 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 124209. | 0.725435 | ||||||||
\(125\) | 124410. | 0.712167 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −215062. | −1.18319 | −0.591594 | − | 0.806236i | \(-0.701501\pi\) | ||||
−0.591594 | + | 0.806236i | \(0.701501\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −272958. | −1.41657 | ||||||||
\(131\) | −189309. | −0.963815 | −0.481908 | − | 0.876222i | \(-0.660056\pi\) | ||||
−0.481908 | + | 0.876222i | \(0.660056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −53050.2 | −0.260050 | ||||||||
\(134\) | 214341. | 1.03120 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 61377.3 | 0.284551 | ||||||||
\(137\) | −3619.56 | −0.0164761 | −0.00823805 | − | 0.999966i | \(-0.502622\pi\) | ||||
−0.00823805 | + | 0.999966i | \(0.502622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 120880. | 0.530662 | 0.265331 | − | 0.964157i | \(-0.414519\pi\) | ||||
0.265331 | + | 0.964157i | \(0.414519\pi\) | |||||||
\(140\) | −120744. | −0.520648 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3880.04 | −0.0161479 | ||||||||
\(143\) | −398186. | −1.62834 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −469102. | −1.85288 | ||||||||
\(146\) | −289601. | −1.12439 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 149081. | 0.559459 | ||||||||
\(149\) | 74816.3 | 0.276077 | 0.138039 | − | 0.990427i | \(-0.455920\pi\) | ||||
0.138039 | + | 0.990427i | \(0.455920\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −359953. | −1.28470 | −0.642352 | − | 0.766410i | \(-0.722041\pi\) | ||||
−0.642352 | + | 0.766410i | \(0.722041\pi\) | |||||||
\(152\) | −29732.9 | −0.104383 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −176138. | −0.598484 | ||||||||
\(155\) | −513036. | −1.71521 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 47966.6 | 0.155307 | 0.0776533 | − | 0.996980i | \(-0.475257\pi\) | ||||
0.0776533 | + | 0.996980i | \(0.475257\pi\) | |||||||
\(158\) | 128791. | 0.410433 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −67672.9 | −0.208985 | ||||||||
\(161\) | 263027. | 0.799715 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 361063. | 1.06442 | 0.532212 | − | 0.846611i | \(-0.321361\pi\) | ||||
0.532212 | + | 0.846611i | \(0.321361\pi\) | |||||||
\(164\) | −213172. | −0.618901 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −144373. | −0.406644 | ||||||||
\(167\) | 116466. | 0.323154 | 0.161577 | − | 0.986860i | \(-0.448342\pi\) | ||||
0.161577 | + | 0.986860i | \(0.448342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 694917. | 1.87161 | ||||||||
\(170\) | −253514. | −0.672791 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −33801.4 | −0.0871190 | ||||||||
\(173\) | 103526. | 0.262987 | 0.131493 | − | 0.991317i | \(-0.458023\pi\) | ||||
0.131493 | + | 0.991317i | \(0.458023\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 141878. | 0.350203 | ||||||||
\(176\) | −98719.9 | −0.240228 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 170489. | 0.403316 | ||||||||
\(179\) | −78941.2 | −0.184150 | −0.0920748 | − | 0.995752i | \(-0.529350\pi\) | ||||
−0.0920748 | + | 0.995752i | \(0.529350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 586108. | 1.32978 | 0.664892 | − | 0.746940i | \(-0.268478\pi\) | ||||
0.664892 | + | 0.746940i | \(0.268478\pi\) | |||||||
\(182\) | 471640. | 1.05544 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 147418. | 0.321001 | ||||||||
\(185\) | −615769. | −1.32278 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −369822. | −0.773372 | ||||||||
\(188\) | 39916.8 | 0.0823686 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 122810. | 0.246802 | ||||||||
\(191\) | 772053. | 1.53131 | 0.765656 | − | 0.643251i | \(-0.222415\pi\) | ||||
0.765656 | + | 0.643251i | \(0.222415\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17439.3 | −0.0337005 | −0.0168503 | − | 0.999858i | \(-0.505364\pi\) | ||||
−0.0168503 | + | 0.999858i | \(0.505364\pi\) | |||||||
\(194\) | −175416. | −0.334629 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −60280.9 | −0.112083 | ||||||||
\(197\) | 340729. | 0.625524 | 0.312762 | − | 0.949832i | \(-0.398746\pi\) | ||||
0.312762 | + | 0.949832i | \(0.398746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14239.7 | 0.0254899 | 0.0127450 | − | 0.999919i | \(-0.495943\pi\) | ||||
0.0127450 | + | 0.999919i | \(0.495943\pi\) | |||||||
\(200\) | 79518.1 | 0.140569 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 96453.4 | 0.166318 | ||||||||
\(203\) | 810554. | 1.38052 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 880493. | 1.46333 | ||||||||
\(206\) | −548883. | −0.901181 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 264339. | 0.423646 | ||||||||
\(209\) | 179152. | 0.283698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −48098.4 | −0.0743745 | −0.0371873 | − | 0.999308i | \(-0.511840\pi\) | ||||
−0.0371873 | + | 0.999308i | \(0.511840\pi\) | |||||||
\(212\) | −160707. | −0.245582 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −671916. | −1.00295 | ||||||||
\(215\) | 139614. | 0.205984 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 886466. | 1.27795 | ||||||||
\(218\) | −84896.0 | −0.120989 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 407755. | 0.567993 | ||||||||
\(221\) | 990259. | 1.36386 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 783977. | 1.05570 | 0.527851 | − | 0.849337i | \(-0.322998\pi\) | ||||
0.527851 | + | 0.849337i | \(0.322998\pi\) | |||||||
\(224\) | 116931. | 0.155707 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −115366. | −0.150248 | ||||||||
\(227\) | −555796. | −0.715898 | −0.357949 | − | 0.933741i | \(-0.616524\pi\) | ||||
−0.357949 | + | 0.933741i | \(0.616524\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 114692. | 0.144526 | 0.0722630 | − | 0.997386i | \(-0.476978\pi\) | ||||
0.0722630 | + | 0.997386i | \(0.476978\pi\) | |||||||
\(230\) | −608899. | −0.758972 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 454289. | 0.554131 | ||||||||
\(233\) | −111177. | −0.134161 | −0.0670805 | − | 0.997748i | \(-0.521368\pi\) | ||||
−0.0670805 | + | 0.997748i | \(0.521368\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −164874. | −0.194752 | ||||||||
\(236\) | 87050.6 | 0.101740 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 438043. | 0.501274 | ||||||||
\(239\) | −739047. | −0.836907 | −0.418453 | − | 0.908238i | \(-0.637428\pi\) | ||||
−0.418453 | + | 0.908238i | \(0.637428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.29036e6 | −1.43109 | −0.715547 | − | 0.698564i | \(-0.753823\pi\) | ||||
−0.715547 | + | 0.698564i | \(0.753823\pi\) | |||||||
\(242\) | −49378.8 | −0.0542004 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 547021. | 0.588206 | ||||||||
\(245\) | 248986. | 0.265008 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −479710. | −0.500307 | ||||||||
\(248\) | 496836. | 0.512960 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 497642. | 0.503578 | ||||||||
\(251\) | 1.29383e6 | 1.29626 | 0.648129 | − | 0.761530i | \(-0.275552\pi\) | ||||
0.648129 | + | 0.761530i | \(0.275552\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −888250. | −0.872437 | ||||||||
\(254\) | −860247. | −0.836640 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 624362. | 0.589663 | 0.294831 | − | 0.955549i | \(-0.404737\pi\) | ||||
0.294831 | + | 0.955549i | \(0.404737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.06398e6 | 0.985559 | ||||||||
\(260\) | −1.09183e6 | −1.00167 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −757237. | −0.681520 | ||||||||
\(263\) | −1.16499e6 | −1.03856 | −0.519281 | − | 0.854603i | \(-0.673800\pi\) | ||||
−0.519281 | + | 0.854603i | \(0.673800\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 663790. | 0.580652 | ||||||||
\(266\) | −212201. | −0.183883 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 857363. | 0.729169 | ||||||||
\(269\) | 1.58951e6 | 1.33932 | 0.669659 | − | 0.742669i | \(-0.266440\pi\) | ||||
0.669659 | + | 0.742669i | \(0.266440\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −977878. | −0.808837 | −0.404419 | − | 0.914574i | \(-0.632526\pi\) | ||||
−0.404419 | + | 0.914574i | \(0.632526\pi\) | |||||||
\(272\) | 245509. | 0.201208 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14478.2 | −0.0116504 | ||||||||
\(275\) | −479127. | −0.382049 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.29049e6 | −1.01054 | −0.505271 | − | 0.862961i | \(-0.668607\pi\) | ||||
−0.505271 | + | 0.862961i | \(0.668607\pi\) | |||||||
\(278\) | 483521. | 0.375235 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −482975. | −0.368154 | ||||||||
\(281\) | 1.66732e6 | 1.25966 | 0.629831 | − | 0.776732i | \(-0.283124\pi\) | ||||
0.629831 | + | 0.776732i | \(0.283124\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.12914e6 | 0.838070 | 0.419035 | − | 0.907970i | \(-0.362368\pi\) | ||||
0.419035 | + | 0.907970i | \(0.362368\pi\) | |||||||
\(284\) | −15520.2 | −0.0114183 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.59274e6 | −1.15141 | ||||||||
\(287\) | −1.52139e6 | −1.09027 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −500138. | −0.352245 | ||||||||
\(290\) | −1.87641e6 | −1.31018 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.15840e6 | −0.795066 | ||||||||
\(293\) | 2.05631e6 | 1.39933 | 0.699663 | − | 0.714473i | \(-0.253334\pi\) | ||||
0.699663 | + | 0.714473i | \(0.253334\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −359556. | −0.240553 | ||||||||
\(296\) | 596324. | 0.395597 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 299265. | 0.195216 | ||||||||
\(299\) | 2.37844e6 | 1.53856 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −241237. | −0.153471 | ||||||||
\(302\) | −1.43981e6 | −0.908423 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −118932. | −0.0738097 | ||||||||
\(305\) | −2.25943e6 | −1.39075 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.52149e6 | 0.921346 | 0.460673 | − | 0.887570i | \(-0.347608\pi\) | ||||
0.460673 | + | 0.887570i | \(0.347608\pi\) | |||||||
\(308\) | −704554. | −0.423192 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.05214e6 | −1.21284 | ||||||||
\(311\) | −2.70840e6 | −1.58786 | −0.793928 | − | 0.608011i | \(-0.791968\pi\) | ||||
−0.793928 | + | 0.608011i | \(0.791968\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −651166. | −0.375691 | −0.187845 | − | 0.982199i | \(-0.560150\pi\) | ||||
−0.187845 | + | 0.982199i | \(0.560150\pi\) | |||||||
\(314\) | 191866. | 0.109818 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 515164. | 0.290220 | ||||||||
\(317\) | −116111. | −0.0648969 | −0.0324484 | − | 0.999473i | \(-0.510330\pi\) | ||||
−0.0324484 | + | 0.999473i | \(0.510330\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.73727e6 | −1.50605 | ||||||||
\(320\) | −270692. | −0.147775 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.05211e6 | 0.565484 | ||||||||
\(323\) | −445538. | −0.237618 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.28294e6 | 0.673750 | ||||||||
\(326\) | 1.44425e6 | 0.752661 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −852689. | −0.437629 | ||||||||
\(329\) | 284882. | 0.145103 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 317657. | 0.159363 | 0.0796816 | − | 0.996820i | \(-0.474610\pi\) | ||||
0.0796816 | + | 0.996820i | \(0.474610\pi\) | |||||||
\(332\) | −577491. | −0.287541 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 465866. | 0.228504 | ||||||||
\(335\) | −3.54128e6 | −1.72404 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 430550. | 0.206514 | 0.103257 | − | 0.994655i | \(-0.467074\pi\) | ||||
0.103257 | + | 0.994655i | \(0.467074\pi\) | |||||||
\(338\) | 2.77967e6 | 1.32343 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.01406e6 | −0.475735 | ||||||||
\(341\) | −2.99363e6 | −1.39416 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.34942e6 | −1.07826 | ||||||||
\(344\) | −135205. | −0.0616024 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 414103. | 0.185960 | ||||||||
\(347\) | −4.14039e6 | −1.84594 | −0.922971 | − | 0.384870i | \(-0.874246\pi\) | ||||
−0.922971 | + | 0.384870i | \(0.874246\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.46095e6 | −1.52101 | −0.760505 | − | 0.649332i | \(-0.775049\pi\) | ||||
−0.760505 | + | 0.649332i | \(0.775049\pi\) | |||||||
\(350\) | 567512. | 0.247631 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −394880. | −0.169867 | ||||||||
\(353\) | 2.64457e6 | 1.12958 | 0.564792 | − | 0.825233i | \(-0.308956\pi\) | ||||
0.564792 | + | 0.825233i | \(0.308956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 64104.9 | 0.0269973 | ||||||||
\(356\) | 681955. | 0.285188 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −315765. | −0.130213 | ||||||||
\(359\) | 2.13123e6 | 0.872761 | 0.436380 | − | 0.899762i | \(-0.356260\pi\) | ||||
0.436380 | + | 0.899762i | \(0.356260\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.26027e6 | −0.912834 | ||||||||
\(362\) | 2.34443e6 | 0.940299 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.88656e6 | 0.746307 | ||||||||
\(365\) | 4.78471e6 | 1.87985 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.28007e6 | −0.496099 | −0.248049 | − | 0.968747i | \(-0.579790\pi\) | ||||
−0.248049 | + | 0.968747i | \(0.579790\pi\) | |||||||
\(368\) | 589672. | 0.226982 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.46307e6 | −0.935348 | ||||||||
\(371\) | −1.14695e6 | −0.432624 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.89466e6 | −1.44943 | −0.724716 | − | 0.689048i | \(-0.758029\pi\) | ||||
−0.724716 | + | 0.689048i | \(0.758029\pi\) | |||||||
\(374\) | −1.47929e6 | −0.546856 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 159667. | 0.0582434 | ||||||||
\(377\) | 7.32949e6 | 2.65595 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.83335e6 | −1.01322 | −0.506609 | − | 0.862176i | \(-0.669101\pi\) | ||||
−0.506609 | + | 0.862176i | \(0.669101\pi\) | |||||||
\(380\) | 491238. | 0.174515 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.08821e6 | 1.08280 | ||||||||
\(383\) | 2.36499e6 | 0.823819 | 0.411909 | − | 0.911225i | \(-0.364862\pi\) | ||||
0.411909 | + | 0.911225i | \(0.364862\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.91011e6 | 1.00059 | ||||||||
\(386\) | −69757.3 | −0.0238299 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −701662. | −0.236618 | ||||||||
\(389\) | −1.74338e6 | −0.584143 | −0.292071 | − | 0.956397i | \(-0.594344\pi\) | ||||
−0.292071 | + | 0.956397i | \(0.594344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.20901e6 | 0.730729 | ||||||||
\(392\) | −241124. | −0.0792546 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.36292e6 | 0.442312 | ||||||||
\(395\) | −2.12785e6 | −0.686195 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.81109e6 | 1.53203 | 0.766015 | − | 0.642823i | \(-0.222237\pi\) | ||||
0.766015 | + | 0.642823i | \(0.222237\pi\) | |||||||
\(398\) | 56958.9 | 0.0180241 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 318072. | 0.0993976 | ||||||||
\(401\) | −4.55407e6 | −1.41429 | −0.707145 | − | 0.707068i | \(-0.750017\pi\) | ||||
−0.707145 | + | 0.707068i | \(0.750017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.01593e6 | 2.45862 | ||||||||
\(404\) | 385813. | 0.117604 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.24221e6 | 0.976173 | ||||||||
\(407\) | −3.59308e6 | −1.07518 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.91283e6 | 0.565416 | 0.282708 | − | 0.959206i | \(-0.408767\pi\) | ||||
0.282708 | + | 0.959206i | \(0.408767\pi\) | |||||||
\(410\) | 3.52197e6 | 1.03473 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.19553e6 | −0.637231 | ||||||||
\(413\) | 621271. | 0.179228 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.38528e6 | 0.679860 | ||||||||
\(416\) | 1.05736e6 | 0.299563 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 716608. | 0.200605 | ||||||||
\(419\) | 4.41395e6 | 1.22826 | 0.614132 | − | 0.789203i | \(-0.289506\pi\) | ||||
0.614132 | + | 0.789203i | \(0.289506\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.74451e6 | −0.479697 | −0.239848 | − | 0.970810i | \(-0.577098\pi\) | ||||
−0.239848 | + | 0.970810i | \(0.577098\pi\) | |||||||
\(422\) | −192393. | −0.0525907 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −642829. | −0.173652 | ||||||||
\(425\) | 1.19155e6 | 0.319993 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.90403e6 | 1.03620 | ||||||||
\(428\) | −2.68766e6 | −0.709195 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 558456. | 0.145652 | ||||||||
\(431\) | −2.21740e6 | −0.574976 | −0.287488 | − | 0.957784i | \(-0.592820\pi\) | ||||
−0.287488 | + | 0.957784i | \(0.592820\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.63511e6 | −0.931746 | −0.465873 | − | 0.884851i | \(-0.654260\pi\) | ||||
−0.465873 | + | 0.884851i | \(0.654260\pi\) | |||||||
\(434\) | 3.54587e6 | 0.903645 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −339584. | −0.0855521 | ||||||||
\(437\) | −1.07011e6 | −0.268055 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.08827e6 | −0.764810 | −0.382405 | − | 0.923995i | \(-0.624904\pi\) | ||||
−0.382405 | + | 0.923995i | \(0.624904\pi\) | |||||||
\(440\) | 1.63102e6 | 0.401632 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.96104e6 | 0.964391 | ||||||||
\(443\) | −7.00097e6 | −1.69492 | −0.847459 | − | 0.530861i | \(-0.821869\pi\) | ||||
−0.847459 | + | 0.530861i | \(0.821869\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.81677e6 | −0.674296 | ||||||||
\(446\) | 3.13591e6 | 0.746493 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 467724. | 0.110102 | ||||||||
\(449\) | −5.00196e6 | −1.17091 | −0.585456 | − | 0.810704i | \(-0.699084\pi\) | ||||
−0.585456 | + | 0.810704i | \(0.699084\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.13778e6 | 1.18942 | ||||||||
\(452\) | −461465. | −0.106241 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.22319e6 | −0.506216 | ||||||||
\(455\) | −7.79230e6 | −1.76456 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.57162e6 | 0.799971 | 0.399985 | − | 0.916521i | \(-0.369015\pi\) | ||||
0.399985 | + | 0.916521i | \(0.369015\pi\) | |||||||
\(458\) | 458770. | 0.102195 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.43560e6 | −0.536674 | ||||||||
\(461\) | 5.50122e6 | 1.20561 | 0.602805 | − | 0.797888i | \(-0.294050\pi\) | ||||
0.602805 | + | 0.797888i | \(0.294050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.85416e6 | −0.618765 | −0.309382 | − | 0.950938i | \(-0.600122\pi\) | ||||
−0.309382 | + | 0.950938i | \(0.600122\pi\) | |||||||
\(464\) | 1.81716e6 | 0.391830 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −444709. | −0.0948662 | ||||||||
\(467\) | −7.16552e6 | −1.52039 | −0.760196 | − | 0.649694i | \(-0.774897\pi\) | ||||
−0.760196 | + | 0.649694i | \(0.774897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.11892e6 | 1.28452 | ||||||||
\(470\) | −659494. | −0.137710 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 348202. | 0.0719410 | ||||||||
\(473\) | 814664. | 0.167427 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −577222. | −0.117384 | ||||||||
\(476\) | 1.75217e6 | 0.354454 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.95619e6 | −0.591782 | ||||||||
\(479\) | 3.28370e6 | 0.653921 | 0.326961 | − | 0.945038i | \(-0.393976\pi\) | ||||
0.326961 | + | 0.945038i | \(0.393976\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.62108e6 | 1.89610 | ||||||||
\(482\) | −5.16144e6 | −1.01194 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −197515. | −0.0383255 | ||||||||
\(485\) | 2.89816e6 | 0.559459 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.18097e6 | 0.416704 | 0.208352 | − | 0.978054i | \(-0.433190\pi\) | ||||
0.208352 | + | 0.978054i | \(0.433190\pi\) | |||||||
\(488\) | 2.18808e6 | 0.415925 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 995944. | 0.187389 | ||||||||
\(491\) | −9.93949e6 | −1.86063 | −0.930315 | − | 0.366760i | \(-0.880467\pi\) | ||||
−0.930315 | + | 0.366760i | \(0.880467\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.80738e6 | 1.26143 | ||||||||
\(494\) | −1.91884e6 | −0.353770 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.98734e6 | 0.362718 | ||||||||
\(497\) | −110766. | −0.0201148 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.52772e6 | −0.814007 | −0.407004 | − | 0.913427i | \(-0.633426\pi\) | ||||
−0.407004 | + | 0.913427i | \(0.633426\pi\) | |||||||
\(500\) | 1.99057e6 | 0.356084 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.17530e6 | 0.916593 | ||||||||
\(503\) | −4.40282e6 | −0.775909 | −0.387955 | − | 0.921679i | \(-0.626818\pi\) | ||||
−0.387955 | + | 0.921679i | \(0.626818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.59357e6 | −0.278063 | ||||||||
\(506\) | −3.55300e6 | −0.616906 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.44099e6 | −0.591594 | ||||||||
\(509\) | 5.82125e6 | 0.995915 | 0.497957 | − | 0.867202i | \(-0.334084\pi\) | ||||
0.497957 | + | 0.867202i | \(0.334084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.26742e6 | −1.40061 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.49745e6 | 0.416954 | ||||||||
\(515\) | 9.06849e6 | 1.50667 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −962057. | −0.158298 | ||||||||
\(518\) | 4.25591e6 | 0.696896 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.36733e6 | −0.708285 | ||||||||
\(521\) | 1.09649e7 | 1.76975 | 0.884875 | − | 0.465829i | \(-0.154244\pi\) | ||||
0.884875 | + | 0.465829i | \(0.154244\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.83705e6 | −0.613399 | −0.306700 | − | 0.951806i | \(-0.599225\pi\) | ||||
−0.306700 | + | 0.951806i | \(0.599225\pi\) | |||||||
\(524\) | −3.02895e6 | −0.481908 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.65996e6 | −0.734374 | ||||||||
\(527\) | 7.44493e6 | 1.16771 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.13066e6 | −0.175669 | ||||||||
\(530\) | 2.65516e6 | 0.410583 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −848803. | −0.130025 | ||||||||
\(533\) | −1.37573e7 | −2.09756 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.11012e7 | 1.67682 | ||||||||
\(536\) | 3.42945e6 | 0.515600 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.35805e6 | 0.947040 | ||||||||
\(539\) | 1.45286e6 | 0.215403 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.88767e6 | −0.717974 | −0.358987 | − | 0.933343i | \(-0.616878\pi\) | ||||
−0.358987 | + | 0.933343i | \(0.616878\pi\) | |||||||
\(542\) | −3.91151e6 | −0.571934 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 982036. | 0.142276 | ||||||||
\(545\) | 1.40263e6 | 0.202279 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.93344e6 | −0.990788 | −0.495394 | − | 0.868668i | \(-0.664976\pi\) | ||||
−0.495394 | + | 0.868668i | \(0.664976\pi\) | |||||||
\(548\) | −57913.0 | −0.00823805 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.91651e6 | −0.270149 | ||||||||
\(551\) | −3.29769e6 | −0.462733 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.67667e6 | 0.511260 | ||||||||
\(554\) | −5.16195e6 | −0.714561 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.93408e6 | 0.265331 | ||||||||
\(557\) | −9.83771e6 | −1.34356 | −0.671778 | − | 0.740752i | \(-0.734469\pi\) | ||||
−0.671778 | + | 0.740752i | \(0.734469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.18140e6 | −0.295261 | ||||||||
\(560\) | −1.93190e6 | −0.260324 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.66930e6 | 0.890716 | ||||||||
\(563\) | 2.73217e6 | 0.363277 | 0.181638 | − | 0.983365i | \(-0.441860\pi\) | ||||
0.181638 | + | 0.983365i | \(0.441860\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.90605e6 | 0.251196 | ||||||||
\(566\) | 4.51654e6 | 0.592605 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −62080.7 | −0.00807394 | ||||||||
\(569\) | 9.43997e6 | 1.22233 | 0.611167 | − | 0.791502i | \(-0.290700\pi\) | ||||
0.611167 | + | 0.791502i | \(0.290700\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.26790e7 | −1.62740 | −0.813698 | − | 0.581288i | \(-0.802549\pi\) | ||||
−0.813698 | + | 0.581288i | \(0.802549\pi\) | |||||||
\(572\) | −6.37098e6 | −0.814172 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.08556e6 | −0.770940 | ||||||||
\(575\) | 2.86191e6 | 0.360983 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.51657e7 | −1.89637 | −0.948187 | − | 0.317712i | \(-0.897086\pi\) | ||||
−0.948187 | + | 0.317712i | \(0.897086\pi\) | |||||||
\(578\) | −2.00055e6 | −0.249075 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.50563e6 | −0.926440 | ||||||||
\(581\) | −4.12149e6 | −0.506540 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.87329e6 | 0.471964 | ||||||||
\(584\) | −4.63362e6 | −0.562197 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.22522e6 | 0.989472 | ||||||||
\(587\) | 1.82340e6 | 0.218417 | 0.109209 | − | 0.994019i | \(-0.465168\pi\) | ||||
0.109209 | + | 0.994019i | \(0.465168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.60653e6 | −0.428353 | ||||||||
\(590\) | −1.43822e6 | −0.170097 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.38530e6 | 0.279730 | ||||||||
\(593\) | 1.27957e7 | 1.49427 | 0.747133 | − | 0.664674i | \(-0.231430\pi\) | ||||
0.747133 | + | 0.664674i | \(0.231430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.23723e6 | −0.838069 | ||||||||
\(596\) | 1.19706e6 | 0.138039 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.51375e6 | 1.08792 | ||||||||
\(599\) | 8.76425e6 | 0.998039 | 0.499020 | − | 0.866591i | \(-0.333694\pi\) | ||||
0.499020 | + | 0.866591i | \(0.333694\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.66959e6 | 0.188548 | 0.0942741 | − | 0.995546i | \(-0.469947\pi\) | ||||
0.0942741 | + | 0.995546i | \(0.469947\pi\) | |||||||
\(602\) | −964947. | −0.108521 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.75924e6 | −0.642352 | ||||||||
\(605\) | 815822. | 0.0906165 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.01707e7 | −1.12042 | −0.560208 | − | 0.828352i | \(-0.689279\pi\) | ||||
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(608\) | −475726. | −0.0521913 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.03772e6 | −0.983410 | ||||||||
\(611\) | 2.57607e6 | 0.279161 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.37829e7 | 1.48146 | 0.740730 | − | 0.671803i | \(-0.234480\pi\) | ||||
0.740730 | + | 0.671803i | \(0.234480\pi\) | |||||||
\(614\) | 6.08595e6 | 0.651490 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.81822e6 | −0.299242 | ||||||||
\(617\) | −1.21082e7 | −1.28046 | −0.640230 | − | 0.768184i | \(-0.721161\pi\) | ||||
−0.640230 | + | 0.768184i | \(0.721161\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.69733e7 | −1.78049 | −0.890245 | − | 0.455481i | \(-0.849467\pi\) | ||||
−0.890245 | + | 0.455481i | \(0.849467\pi\) | |||||||
\(620\) | −8.20857e6 | −0.857607 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.08336e7 | −1.12278 | ||||||||
\(623\) | 4.86704e6 | 0.502395 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.21046e7 | −1.23951 | ||||||||
\(626\) | −2.60466e6 | −0.265654 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 767466. | 0.0776533 | ||||||||
\(629\) | 8.93574e6 | 0.900541 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.90092e6 | 0.789958 | 0.394979 | − | 0.918690i | \(-0.370752\pi\) | ||||
0.394979 | + | 0.918690i | \(0.370752\pi\) | |||||||
\(632\) | 2.06065e6 | 0.205217 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −464443. | −0.0458890 | ||||||||
\(635\) | 1.42127e7 | 1.39876 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.89028e6 | −0.379868 | ||||||||
\(638\) | −1.09491e7 | −1.06494 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.08277e6 | −0.104492 | ||||||||
\(641\) | 1.06761e7 | 1.02629 | 0.513144 | − | 0.858302i | \(-0.328481\pi\) | ||||
0.513144 | + | 0.858302i | \(0.328481\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.37769e6 | 0.894476 | 0.447238 | − | 0.894415i | \(-0.352408\pi\) | ||||
0.447238 | + | 0.894415i | \(0.352408\pi\) | |||||||
\(644\) | 4.20843e6 | 0.399858 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.78215e6 | −0.168021 | ||||||||
\(647\) | −9.44013e6 | −0.886579 | −0.443289 | − | 0.896379i | \(-0.646189\pi\) | ||||
−0.443289 | + | 0.896379i | \(0.646189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.09805e6 | −0.195526 | ||||||||
\(650\) | 5.13177e6 | 0.476413 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.77701e6 | 0.532212 | ||||||||
\(653\) | 1.48891e7 | 1.36642 | 0.683212 | − | 0.730220i | \(-0.260582\pi\) | ||||
0.683212 | + | 0.730220i | \(0.260582\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.25109e7 | 1.13942 | ||||||||
\(656\) | −3.41076e6 | −0.309451 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.13953e6 | 0.102603 | ||||||||
\(659\) | −7.64781e6 | −0.685999 | −0.343000 | − | 0.939336i | \(-0.611443\pi\) | ||||
−0.343000 | + | 0.939336i | \(0.611443\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.00539e6 | −0.445588 | −0.222794 | − | 0.974866i | \(-0.571518\pi\) | ||||
−0.222794 | + | 0.974866i | \(0.571518\pi\) | |||||||
\(662\) | 1.27063e6 | 0.112687 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.30996e6 | −0.203322 | ||||||||
\(665\) | 3.50592e6 | 0.307431 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.63502e7 | 1.42301 | ||||||||
\(668\) | 1.86346e6 | 0.161577 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.41651e7 | −1.21908 | ||||||||
\(671\) | −1.31840e7 | −1.13043 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.14440e6 | 0.182502 | 0.0912511 | − | 0.995828i | \(-0.470913\pi\) | ||||
0.0912511 | + | 0.995828i | \(0.470913\pi\) | |||||||
\(674\) | 1.72220e6 | 0.146027 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.11187e7 | 0.935807 | ||||||||
\(677\) | −9.50926e6 | −0.797398 | −0.398699 | − | 0.917082i | \(-0.630538\pi\) | ||||
−0.398699 | + | 0.917082i | \(0.630538\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.00769e6 | −0.416834 | ||||||||
\(680\) | −4.05623e6 | −0.336396 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.19745e7 | −0.985817 | ||||||||
\(683\) | −5.47266e6 | −0.448897 | −0.224449 | − | 0.974486i | \(-0.572058\pi\) | ||||
−0.224449 | + | 0.974486i | \(0.572058\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 239205. | 0.0194780 | ||||||||
\(686\) | −9.39767e6 | −0.762447 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −540822. | −0.0435595 | ||||||||
\(689\) | −1.03714e7 | −0.832317 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.88167e6 | 0.548276 | 0.274138 | − | 0.961690i | \(-0.411608\pi\) | ||||
0.274138 | + | 0.961690i | \(0.411608\pi\) | |||||||
\(692\) | 1.65641e6 | 0.131493 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.65616e7 | −1.30528 | ||||||||
\(695\) | −7.98859e6 | −0.627348 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.27773e7 | −0.996223 | ||||||||
\(698\) | −1.38438e7 | −1.07552 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.27005e6 | 0.175102 | ||||||||
\(701\) | 5.19615e6 | 0.399380 | 0.199690 | − | 0.979859i | \(-0.436006\pi\) | ||||
0.199690 | + | 0.979859i | \(0.436006\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.32872e6 | −0.330348 | ||||||||
\(704\) | −1.57952e6 | −0.120114 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.05783e7 | 0.798737 | ||||||||
\(707\) | 2.75351e6 | 0.207175 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 574821. | 0.0429454 | 0.0214727 | − | 0.999769i | \(-0.493164\pi\) | ||||
0.0214727 | + | 0.999769i | \(0.493164\pi\) | |||||||
\(710\) | 256420. | 0.0190900 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.72782e6 | 0.201658 | ||||||||
\(713\) | 1.78815e7 | 1.31728 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.63149e7 | 1.92502 | ||||||||
\(716\) | −1.26306e6 | −0.0920748 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.52494e6 | 0.617135 | ||||||||
\(719\) | −400906. | −0.0289215 | −0.0144607 | − | 0.999895i | \(-0.504603\pi\) | ||||
−0.0144607 | + | 0.999895i | \(0.504603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.56693e7 | −1.12256 | ||||||||
\(722\) | −9.04107e6 | −0.645471 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.37772e6 | 0.664892 | ||||||||
\(725\) | 8.81938e6 | 0.623151 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.05431e7 | 0.739830 | 0.369915 | − | 0.929066i | \(-0.379387\pi\) | ||||
0.369915 | + | 0.929066i | \(0.379387\pi\) | |||||||
\(728\) | 7.54624e6 | 0.527719 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.91388e7 | 1.32925 | ||||||||
\(731\) | −2.02601e6 | −0.140232 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.39374e7 | 0.958122 | 0.479061 | − | 0.877782i | \(-0.340977\pi\) | ||||
0.479061 | + | 0.877782i | \(0.340977\pi\) | |||||||
\(734\) | −5.12028e6 | −0.350795 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.35869e6 | 0.160500 | ||||||||
\(737\) | −2.06638e7 | −1.40133 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.88034e6 | −0.665519 | −0.332760 | − | 0.943012i | \(-0.607980\pi\) | ||||
−0.332760 | + | 0.943012i | \(0.607980\pi\) | |||||||
\(740\) | −9.85230e6 | −0.661391 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.58781e6 | −0.305911 | ||||||||
\(743\) | −9.33390e6 | −0.620285 | −0.310142 | − | 0.950690i | \(-0.600377\pi\) | ||||
−0.310142 | + | 0.950690i | \(0.600377\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.94438e6 | −0.326378 | ||||||||
\(746\) | −1.55787e7 | −1.02490 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.91715e6 | −0.386686 | ||||||||
\(749\) | −1.91816e7 | −1.24934 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.87522e7 | 1.86025 | 0.930124 | − | 0.367245i | \(-0.119699\pi\) | ||||
0.930124 | + | 0.367245i | \(0.119699\pi\) | |||||||
\(752\) | 638669. | 0.0411843 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.93179e7 | 1.87804 | ||||||||
\(755\) | 2.37881e7 | 1.51877 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.94587e6 | −0.313691 | −0.156846 | − | 0.987623i | \(-0.550133\pi\) | ||||
−0.156846 | + | 0.987623i | \(0.550133\pi\) | |||||||
\(758\) | −1.13334e7 | −0.716453 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.96495e6 | 0.123401 | ||||||||
\(761\) | 9.13658e6 | 0.571902 | 0.285951 | − | 0.958244i | \(-0.407690\pi\) | ||||
0.285951 | + | 0.958244i | \(0.407690\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.42358e6 | −0.150711 | ||||||||
\(764\) | 1.23528e7 | 0.765656 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.45995e6 | 0.582528 | ||||||||
\(767\) | 5.61789e6 | 0.344814 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.65244e7 | 1.00765 | 0.503826 | − | 0.863805i | \(-0.331925\pi\) | ||||
0.503826 | + | 0.863805i | \(0.331925\pi\) | |||||||
\(770\) | 1.16404e7 | 0.707526 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −279029. | −0.0168503 | ||||||||
\(773\) | 1.01763e7 | 0.612550 | 0.306275 | − | 0.951943i | \(-0.400917\pi\) | ||||
0.306275 | + | 0.951943i | \(0.400917\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.64536e6 | 0.576852 | ||||||||
\(776\) | −2.80665e6 | −0.167315 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.97353e6 | −0.413051 | ||||||||
\(779\) | 6.18968e6 | 0.365447 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 374060. | 0.0219439 | ||||||||
\(782\) | 8.83605e6 | 0.516703 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −964495. | −0.0560415 | ||||||||
\(785\) | −3.16996e6 | −0.183603 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.87635e7 | −1.07988 | −0.539941 | − | 0.841703i | \(-0.681553\pi\) | ||||
−0.539941 | + | 0.841703i | \(0.681553\pi\) | |||||||
\(788\) | 5.45167e6 | 0.312762 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.51138e6 | −0.485213 | ||||||||
\(791\) | −3.29343e6 | −0.187158 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.53025e7 | 1.99353 | ||||||||
\(794\) | 1.92444e7 | 1.08331 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 227835. | 0.0127450 | ||||||||
\(797\) | −2.47965e6 | −0.138275 | −0.0691376 | − | 0.997607i | \(-0.522025\pi\) | ||||
−0.0691376 | + | 0.997607i | \(0.522025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.39257e6 | 0.132586 | ||||||||
\(800\) | 1.27229e6 | 0.0702847 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.82163e7 | −1.00005 | ||||||||
\(803\) | 2.79193e7 | 1.52797 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.73826e7 | −0.945421 | ||||||||
\(806\) | 3.20637e7 | 1.73851 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.54325e6 | 0.0831589 | ||||||||
\(809\) | −2.50880e7 | −1.34770 | −0.673852 | − | 0.738867i | \(-0.735361\pi\) | ||||
−0.673852 | + | 0.738867i | \(0.735361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.28465e6 | −0.228751 | −0.114376 | − | 0.993438i | \(-0.536487\pi\) | ||||
−0.114376 | + | 0.993438i | \(0.536487\pi\) | |||||||
\(812\) | 1.29689e7 | 0.690258 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.43723e7 | −0.760267 | ||||||||
\(815\) | −2.38615e7 | −1.25836 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 981457. | 0.0514418 | ||||||||
\(818\) | 7.65132e6 | 0.399809 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.40879e7 | 0.731663 | ||||||||
\(821\) | 2.03127e7 | 1.05174 | 0.525871 | − | 0.850564i | \(-0.323739\pi\) | ||||
0.525871 | + | 0.850564i | \(0.323739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.31663e7 | −0.677583 | −0.338792 | − | 0.940861i | \(-0.610018\pi\) | ||||
−0.338792 | + | 0.940861i | \(0.610018\pi\) | |||||||
\(824\) | −8.78213e6 | −0.450590 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.48508e6 | 0.126733 | ||||||||
\(827\) | 2.82859e7 | 1.43816 | 0.719079 | − | 0.694928i | \(-0.244564\pi\) | ||||
0.719079 | + | 0.694928i | \(0.244564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.36608e7 | 0.690381 | 0.345190 | − | 0.938533i | \(-0.387814\pi\) | ||||
0.345190 | + | 0.938533i | \(0.387814\pi\) | |||||||
\(830\) | 9.54113e6 | 0.480734 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.22942e6 | 0.211823 | ||||||||
\(833\) | −3.61316e6 | −0.180416 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.69690e6 | −0.382032 | ||||||||
\(836\) | 2.86643e6 | 0.141849 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.76558e7 | 0.868514 | ||||||||
\(839\) | −151283. | −0.00741969 | −0.00370984 | − | 0.999993i | \(-0.501181\pi\) | ||||
−0.00370984 | + | 0.999993i | \(0.501181\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.98742e7 | 1.45649 | ||||||||
\(842\) | −6.97802e6 | −0.339197 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −769574. | −0.0371873 | ||||||||
\(845\) | −4.59249e7 | −2.21262 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.40965e6 | −0.0675152 | ||||||||
\(848\) | −2.57132e6 | −0.122791 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.76621e6 | 0.226270 | ||||||||
\(851\) | 2.14621e7 | 1.01590 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.77662e7 | −1.30660 | −0.653301 | − | 0.757098i | \(-0.726616\pi\) | ||||
−0.653301 | + | 0.757098i | \(0.726616\pi\) | |||||||
\(854\) | 1.56161e7 | 0.732705 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.07507e7 | −0.501477 | ||||||||
\(857\) | −3.52272e7 | −1.63842 | −0.819212 | − | 0.573491i | \(-0.805589\pi\) | ||||
−0.819212 | + | 0.573491i | \(0.805589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.04681e7 | −1.87124 | −0.935622 | − | 0.353005i | \(-0.885160\pi\) | ||||
−0.935622 | + | 0.353005i | \(0.885160\pi\) | |||||||
\(860\) | 2.23382e6 | 0.102992 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.86958e6 | −0.406570 | ||||||||
\(863\) | −1.96865e7 | −0.899789 | −0.449895 | − | 0.893082i | \(-0.648538\pi\) | ||||
−0.449895 | + | 0.893082i | \(0.648538\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.84170e6 | −0.310902 | ||||||||
\(866\) | −1.45404e7 | −0.658844 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.41835e7 | 0.638974 | ||||||||
\(869\) | −1.24162e7 | −0.557751 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.53307e7 | 2.47127 | ||||||||
\(872\) | −1.35834e6 | −0.0604945 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.28043e6 | −0.189544 | ||||||||
\(875\) | 1.42065e7 | 0.627287 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.62442e7 | 1.15222 | 0.576109 | − | 0.817373i | \(-0.304570\pi\) | ||||
0.576109 | + | 0.817373i | \(0.304570\pi\) | |||||||
\(878\) | −1.23531e7 | −0.540802 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.52408e6 | 0.283996 | ||||||||
\(881\) | −1.29423e7 | −0.561786 | −0.280893 | − | 0.959739i | \(-0.590631\pi\) | ||||
−0.280893 | + | 0.959739i | \(0.590631\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.39097e6 | 0.146360 | 0.0731800 | − | 0.997319i | \(-0.476685\pi\) | ||||
0.0731800 | + | 0.997319i | \(0.476685\pi\) | |||||||
\(884\) | 1.58442e7 | 0.681928 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.80039e7 | −1.19849 | ||||||||
\(887\) | 7.67591e6 | 0.327583 | 0.163791 | − | 0.986495i | \(-0.447628\pi\) | ||||
0.163791 | + | 0.986495i | \(0.447628\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.45580e7 | −1.04217 | ||||||||
\(890\) | −1.12671e7 | −0.476799 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.25436e7 | 0.527851 | ||||||||
\(893\) | −1.15903e6 | −0.0486368 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.21697e6 | 0.217701 | ||||||||
\(896\) | 1.87090e6 | 0.0778537 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.00078e7 | −0.827959 | ||||||||
\(899\) | 5.51042e7 | 2.27398 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.63260e6 | −0.395304 | ||||||||
\(902\) | 2.05511e7 | 0.841045 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.84586e6 | −0.0751239 | ||||||||
\(905\) | −3.87340e7 | −1.57207 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.08887e7 | 0.439499 | 0.219750 | − | 0.975556i | \(-0.429476\pi\) | ||||
0.219750 | + | 0.975556i | \(0.429476\pi\) | |||||||
\(908\) | −8.89274e6 | −0.357949 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.11692e7 | −1.24773 | ||||||||
\(911\) | −180478. | −0.00720492 | −0.00360246 | − | 0.999994i | \(-0.501147\pi\) | ||||
−0.00360246 | + | 0.999994i | \(0.501147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.39184e7 | 0.552602 | ||||||||
\(914\) | 1.42865e7 | 0.565665 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.83508e6 | 0.0722630 | ||||||||
\(917\) | −2.16173e7 | −0.848942 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.24831e7 | −0.878148 | −0.439074 | − | 0.898451i | \(-0.644693\pi\) | ||||
−0.439074 | + | 0.898451i | \(0.644693\pi\) | |||||||
\(920\) | −9.74239e6 | −0.379486 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.20049e7 | 0.852495 | ||||||||
\(923\) | −1.00161e6 | −0.0386984 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.15768e7 | 0.444871 | ||||||||
\(926\) | −1.14166e7 | −0.437533 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.26862e6 | 0.277065 | ||||||||
\(929\) | −4.13240e7 | −1.57095 | −0.785477 | − | 0.618891i | \(-0.787582\pi\) | ||||
−0.785477 | + | 0.618891i | \(0.787582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.75032e6 | 0.0661824 | ||||||||
\(932\) | −1.77884e6 | −0.0670805 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.86621e7 | −1.07508 | ||||||||
\(935\) | 2.44403e7 | 0.914278 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.56470e7 | 0.954305 | 0.477153 | − | 0.878820i | \(-0.341669\pi\) | ||||
0.477153 | + | 0.878820i | \(0.341669\pi\) | |||||||
\(938\) | 2.44757e7 | 0.908296 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.63798e6 | −0.0973759 | ||||||||
\(941\) | 1.79976e7 | 0.662583 | 0.331292 | − | 0.943528i | \(-0.392516\pi\) | ||||
0.331292 | + | 0.943528i | \(0.392516\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.06889e7 | −1.12383 | ||||||||
\(944\) | 1.39281e6 | 0.0508700 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.25866e6 | 0.118389 | ||||||||
\(947\) | −4.50796e7 | −1.63345 | −0.816723 | − | 0.577030i | \(-0.804211\pi\) | ||||
−0.816723 | + | 0.577030i | \(0.804211\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.47587e7 | −2.69461 | ||||||||
\(950\) | −2.30889e6 | −0.0830030 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.00869e6 | 0.250637 | ||||||||
\(953\) | 2.21374e7 | 0.789577 | 0.394788 | − | 0.918772i | \(-0.370818\pi\) | ||||
0.394788 | + | 0.918772i | \(0.370818\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.10225e7 | −1.81031 | ||||||||
\(956\) | −1.18247e7 | −0.418453 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.31348e7 | 0.462392 | ||||||||
\(959\) | −413319. | −0.0145124 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.16359e7 | 1.10502 | ||||||||
\(962\) | 3.84843e7 | 1.34075 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.06458e7 | −0.715547 | ||||||||
\(965\) | 1.15251e6 | 0.0398407 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.96323e7 | −0.675156 | −0.337578 | − | 0.941297i | \(-0.609608\pi\) | ||||
−0.337578 | + | 0.941297i | \(0.609608\pi\) | |||||||
\(968\) | −790061. | −0.0271002 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.15927e7 | 0.395598 | ||||||||
\(971\) | −3.46539e7 | −1.17952 | −0.589758 | − | 0.807580i | \(-0.700777\pi\) | ||||
−0.589758 | + | 0.807580i | \(0.700777\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.38034e7 | 0.467415 | ||||||||
\(974\) | 8.72389e6 | 0.294654 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.75234e6 | 0.294103 | ||||||||
\(977\) | 2.68013e7 | 0.898296 | 0.449148 | − | 0.893457i | \(-0.351728\pi\) | ||||
0.449148 | + | 0.893457i | \(0.351728\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.64362e7 | −0.548080 | ||||||||
\(980\) | 3.98377e6 | 0.132504 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.97579e7 | −1.31566 | ||||||||
\(983\) | −2.38080e7 | −0.785849 | −0.392924 | − | 0.919571i | \(-0.628537\pi\) | ||||
−0.392924 | + | 0.919571i | \(0.628537\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.25177e7 | −0.739492 | ||||||||
\(986\) | 2.72295e7 | 0.891965 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.67536e6 | −0.250153 | ||||||||
\(989\) | −4.86614e6 | −0.158195 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.37156e7 | −0.767096 | −0.383548 | − | 0.923521i | \(-0.625298\pi\) | ||||
−0.383548 | + | 0.923521i | \(0.625298\pi\) | |||||||
\(992\) | 7.94937e6 | 0.256480 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −443063. | −0.0142233 | ||||||||
\(995\) | −941058. | −0.0301341 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.08340e7 | −1.30102 | −0.650511 | − | 0.759497i | \(-0.725445\pi\) | ||||
−0.650511 | + | 0.759497i | \(0.725445\pi\) | |||||||
\(998\) | −1.81109e7 | −0.575590 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 162.6.a.j.1.1 | 3 | ||
3.2 | odd | 2 | 162.6.a.i.1.3 | 3 | |||
9.2 | odd | 6 | 54.6.c.b.37.1 | 6 | |||
9.4 | even | 3 | 18.6.c.b.7.3 | ✓ | 6 | ||
9.5 | odd | 6 | 54.6.c.b.19.1 | 6 | |||
9.7 | even | 3 | 18.6.c.b.13.3 | yes | 6 | ||
36.7 | odd | 6 | 144.6.i.b.49.1 | 6 | |||
36.11 | even | 6 | 432.6.i.b.145.1 | 6 | |||
36.23 | even | 6 | 432.6.i.b.289.1 | 6 | |||
36.31 | odd | 6 | 144.6.i.b.97.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.6.c.b.7.3 | ✓ | 6 | 9.4 | even | 3 | ||
18.6.c.b.13.3 | yes | 6 | 9.7 | even | 3 | ||
54.6.c.b.19.1 | 6 | 9.5 | odd | 6 | |||
54.6.c.b.37.1 | 6 | 9.2 | odd | 6 | |||
144.6.i.b.49.1 | 6 | 36.7 | odd | 6 | |||
144.6.i.b.97.1 | 6 | 36.31 | odd | 6 | |||
162.6.a.i.1.3 | 3 | 3.2 | odd | 2 | |||
162.6.a.j.1.1 | 3 | 1.1 | even | 1 | trivial | ||
432.6.i.b.145.1 | 6 | 36.11 | even | 6 | |||
432.6.i.b.289.1 | 6 | 36.23 | even | 6 |