Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,28,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 28, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 28);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 28 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), not 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: | \(115.463893710\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{18209})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9105x^{2} + 20720704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{6}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.4 | ||
Root | \(-66.9704i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.28.b.a.24.1 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 18713.6i | 1.61530i | 0.589664 | + | 0.807648i | \(0.299260\pi\) | ||||
−0.589664 | + | 0.807648i | \(0.700740\pi\) | |||||||
\(3\) | − 3.44127e6i | − 1.24618i | −0.782149 | − | 0.623092i | \(-0.785876\pi\) | ||||
0.782149 | − | 0.623092i | \(-0.214124\pi\) | |||||||
\(4\) | −2.15981e8 | −1.60918 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.43986e10 | 2.01296 | ||||||||
\(7\) | 1.96873e11i | 0.768004i | 0.923332 | + | 0.384002i | \(0.125454\pi\) | ||||
−0.923332 | + | 0.384002i | \(0.874546\pi\) | |||||||
\(8\) | − 1.53009e12i | − 0.984013i | ||||||||
\(9\) | −4.21675e12 | −0.552973 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.06714e14 | 1.80538 | 0.902691 | − | 0.430290i | \(-0.141589\pi\) | ||||
0.902691 | + | 0.430290i | \(0.141589\pi\) | |||||||
\(12\) | 7.43249e14i | 2.00534i | ||||||||
\(13\) | − 1.66656e14i | − 0.152611i | −0.997084 | − | 0.0763057i | \(-0.975688\pi\) | ||||
0.997084 | − | 0.0763057i | \(-0.0243125\pi\) | |||||||
\(14\) | −3.68421e15 | −1.24055 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.55072e14 | −0.0197105 | ||||||||
\(17\) | 5.47219e15i | 0.133999i | 0.997753 | + | 0.0669994i | \(0.0213425\pi\) | ||||
−0.997753 | + | 0.0669994i | \(0.978657\pi\) | |||||||
\(18\) | − 7.89105e16i | − 0.893215i | ||||||||
\(19\) | −1.61471e17 | −0.880891 | −0.440445 | − | 0.897779i | \(-0.645179\pi\) | ||||
−0.440445 | + | 0.897779i | \(0.645179\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.77495e17 | 0.957074 | ||||||||
\(22\) | 3.86837e18i | 2.91623i | ||||||||
\(23\) | 2.80341e18i | 1.15974i | 0.814709 | + | 0.579870i | \(0.196897\pi\) | ||||
−0.814709 | + | 0.579870i | \(0.803103\pi\) | |||||||
\(24\) | −5.26544e18 | −1.22626 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.11874e18 | 0.246513 | ||||||||
\(27\) | − 1.17308e19i | − 0.557078i | ||||||||
\(28\) | − 4.25209e19i | − 1.23586i | ||||||||
\(29\) | 2.99842e18 | 0.0542650 | 0.0271325 | − | 0.999632i | \(-0.491362\pi\) | ||||
0.0271325 | + | 0.999632i | \(0.491362\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.09190e19 | 0.668763 | 0.334381 | − | 0.942438i | \(-0.391473\pi\) | ||||
0.334381 | + | 0.942438i | \(0.391473\pi\) | |||||||
\(32\) | − 2.12009e20i | − 1.01585i | ||||||||
\(33\) | − 7.11360e20i | − 2.24984i | ||||||||
\(34\) | −1.02404e20 | −0.216448 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.10738e20 | 0.889835 | ||||||||
\(37\) | − 1.50001e21i | − 1.01244i | −0.862404 | − | 0.506220i | \(-0.831042\pi\) | ||||
0.862404 | − | 0.506220i | \(-0.168958\pi\) | |||||||
\(38\) | − 3.02171e21i | − 1.42290i | ||||||||
\(39\) | −5.73510e20 | −0.190182 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.47146e21 | 0.923679 | 0.461840 | − | 0.886963i | \(-0.347190\pi\) | ||||
0.461840 | + | 0.886963i | \(0.347190\pi\) | |||||||
\(42\) | 1.26784e22i | 1.54596i | ||||||||
\(43\) | − 6.81035e21i | − 0.604429i | −0.953240 | − | 0.302215i | \(-0.902274\pi\) | ||||
0.953240 | − | 0.302215i | \(-0.0977259\pi\) | |||||||
\(44\) | −4.46463e22 | −2.90519 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.24619e22 | −1.87333 | ||||||||
\(47\) | 9.41657e21i | 0.251520i | 0.992061 | + | 0.125760i | \(0.0401369\pi\) | ||||
−0.992061 | + | 0.125760i | \(0.959863\pi\) | |||||||
\(48\) | 1.22190e21i | 0.0245628i | ||||||||
\(49\) | 2.69532e22 | 0.410169 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.88313e22 | 0.166987 | ||||||||
\(52\) | 3.59946e22i | 0.245580i | ||||||||
\(53\) | − 5.35936e22i | − 0.282741i | −0.989957 | − | 0.141370i | \(-0.954849\pi\) | ||||
0.989957 | − | 0.141370i | \(-0.0451509\pi\) | |||||||
\(54\) | 2.19525e23 | 0.899846 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.01233e23 | 0.755726 | ||||||||
\(57\) | 5.55667e23i | 1.09775i | ||||||||
\(58\) | 5.61113e22i | 0.0876541i | ||||||||
\(59\) | −9.16258e23 | −1.13636 | −0.568180 | − | 0.822904i | \(-0.692352\pi\) | ||||
−0.568180 | + | 0.822904i | \(0.692352\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.47362e24 | 1.16529 | 0.582643 | − | 0.812728i | \(-0.302019\pi\) | ||||
0.582643 | + | 0.812728i | \(0.302019\pi\) | |||||||
\(62\) | 1.70142e24i | 1.08025i | ||||||||
\(63\) | − 8.30166e23i | − 0.424685i | ||||||||
\(64\) | 3.91980e24 | 1.62119 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.33121e25 | 3.63415 | ||||||||
\(67\) | 3.21915e24i | 0.717349i | 0.933463 | + | 0.358675i | \(0.116771\pi\) | ||||
−0.933463 | + | 0.358675i | \(0.883229\pi\) | |||||||
\(68\) | − 1.18189e24i | − 0.215629i | ||||||||
\(69\) | 9.64729e24 | 1.44525 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.38255e24 | 0.344554 | 0.172277 | − | 0.985049i | \(-0.444888\pi\) | ||||
0.172277 | + | 0.985049i | \(0.444888\pi\) | |||||||
\(72\) | 6.45199e24i | 0.544133i | ||||||||
\(73\) | 1.32172e25i | 0.925295i | 0.886542 | + | 0.462648i | \(0.153100\pi\) | ||||
−0.886542 | + | 0.462648i | \(0.846900\pi\) | |||||||
\(74\) | 2.80705e25 | 1.63539 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.48748e25 | 1.41752 | ||||||||
\(77\) | 4.06965e25i | 1.38654i | ||||||||
\(78\) | − 1.07324e25i | − 0.307200i | ||||||||
\(79\) | −4.66230e25 | −1.12366 | −0.561830 | − | 0.827253i | \(-0.689902\pi\) | ||||
−0.561830 | + | 0.827253i | \(0.689902\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.25240e25 | −1.24719 | ||||||||
\(82\) | 1.02391e26i | 1.49202i | ||||||||
\(83\) | 7.14690e25i | 0.884226i | 0.896959 | + | 0.442113i | \(0.145771\pi\) | ||||
−0.896959 | + | 0.442113i | \(0.854229\pi\) | |||||||
\(84\) | −1.46326e26 | −1.54011 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.27446e26 | 0.976332 | ||||||||
\(87\) | − 1.03184e25i | − 0.0676242i | ||||||||
\(88\) | − 3.16290e26i | − 1.77652i | ||||||||
\(89\) | 1.40708e26 | 0.678504 | 0.339252 | − | 0.940696i | \(-0.389826\pi\) | ||||
0.339252 | + | 0.940696i | \(0.389826\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.28102e25 | 0.117206 | ||||||||
\(92\) | − 6.05484e26i | − 1.86624i | ||||||||
\(93\) | − 3.12877e26i | − 0.833401i | ||||||||
\(94\) | −1.76218e26 | −0.406279 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.29582e26 | −1.26594 | ||||||||
\(97\) | − 3.77568e26i | − 0.569609i | −0.958586 | − | 0.284805i | \(-0.908071\pi\) | ||||
0.958586 | − | 0.284805i | \(-0.0919287\pi\) | |||||||
\(98\) | 5.04391e26i | 0.662545i | ||||||||
\(99\) | −8.71662e26 | −0.998327 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.82546e27 | −1.59600 | −0.798002 | − | 0.602654i | \(-0.794110\pi\) | ||||
−0.798002 | + | 0.602654i | \(0.794110\pi\) | |||||||
\(102\) | 3.52401e26i | 0.269734i | ||||||||
\(103\) | 2.87048e27i | 1.92598i | 0.269534 | + | 0.962991i | \(0.413130\pi\) | ||||
−0.269534 | + | 0.962991i | \(0.586870\pi\) | |||||||
\(104\) | −2.54999e26 | −0.150172 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00293e27 | 0.456710 | ||||||||
\(107\) | 1.31331e27i | 0.526849i | 0.964680 | + | 0.263425i | \(0.0848520\pi\) | ||||
−0.964680 | + | 0.263425i | \(0.915148\pi\) | |||||||
\(108\) | 2.53362e27i | 0.896441i | ||||||||
\(109\) | 3.16013e27 | 0.987296 | 0.493648 | − | 0.869662i | \(-0.335663\pi\) | ||||
0.493648 | + | 0.869662i | \(0.335663\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.16192e27 | −1.26169 | ||||||||
\(112\) | − 6.99043e25i | − 0.0151377i | ||||||||
\(113\) | 3.68033e27i | 0.706851i | 0.935463 | + | 0.353425i | \(0.114983\pi\) | ||||
−0.935463 | + | 0.353425i | \(0.885017\pi\) | |||||||
\(114\) | −1.03985e28 | −1.77319 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.47603e26 | −0.0873224 | ||||||||
\(117\) | 7.02748e26i | 0.0843899i | ||||||||
\(118\) | − 1.71465e28i | − 1.83556i | ||||||||
\(119\) | −1.07733e27 | −0.102912 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.96208e28 | 2.25940 | ||||||||
\(122\) | 2.75767e28i | 1.88228i | ||||||||
\(123\) | − 1.88288e28i | − 1.15107i | ||||||||
\(124\) | −1.96368e28 | −1.07616 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.55354e28 | 0.685993 | ||||||||
\(127\) | 2.69227e28i | 1.06849i | 0.845331 | + | 0.534243i | \(0.179403\pi\) | ||||
−0.845331 | + | 0.534243i | \(0.820597\pi\) | |||||||
\(128\) | 4.48982e28i | 1.60285i | ||||||||
\(129\) | −2.34363e28 | −0.753229 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.17810e28 | 0.829860 | 0.414930 | − | 0.909853i | \(-0.363806\pi\) | ||||
0.414930 | + | 0.909853i | \(0.363806\pi\) | |||||||
\(132\) | 1.53640e29i | 3.62040i | ||||||||
\(133\) | − 3.17894e28i | − 0.676528i | ||||||||
\(134\) | −6.02418e28 | −1.15873 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.37292e27 | 0.131857 | ||||||||
\(137\) | − 2.13194e28i | − 0.304122i | −0.988371 | − | 0.152061i | \(-0.951409\pi\) | ||||
0.988371 | − | 0.152061i | \(-0.0485910\pi\) | |||||||
\(138\) | 1.80536e29i | 2.33451i | ||||||||
\(139\) | 1.15969e29 | 1.36032 | 0.680161 | − | 0.733062i | \(-0.261910\pi\) | ||||
0.680161 | + | 0.733062i | \(0.261910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.24050e28 | 0.313439 | ||||||||
\(142\) | 6.32998e28i | 0.556557i | ||||||||
\(143\) | − 3.44502e28i | − 0.275522i | ||||||||
\(144\) | 1.49725e27 | 0.0108993 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.47341e29 | −1.49463 | ||||||||
\(147\) | − 9.27533e28i | − 0.511146i | ||||||||
\(148\) | 3.23973e29i | 1.62920i | ||||||||
\(149\) | −2.70481e29 | −1.24200 | −0.621000 | − | 0.783810i | \(-0.713273\pi\) | ||||
−0.621000 | + | 0.783810i | \(0.713273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.43669e28 | 0.246873 | 0.123437 | − | 0.992352i | \(-0.460608\pi\) | ||||
0.123437 | + | 0.992352i | \(0.460608\pi\) | |||||||
\(152\) | 2.47065e29i | 0.866808i | ||||||||
\(153\) | − 2.30748e28i | − 0.0740977i | ||||||||
\(154\) | −7.61579e29 | −2.23968 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.23867e29 | 0.306037 | ||||||||
\(157\) | 7.36476e29i | 1.66922i | 0.550842 | + | 0.834609i | \(0.314307\pi\) | ||||
−0.550842 | + | 0.834609i | \(0.685693\pi\) | |||||||
\(158\) | − 8.72484e29i | − 1.81504i | ||||||||
\(159\) | −1.84430e29 | −0.352347 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.51917e29 | −0.890686 | ||||||||
\(162\) | − 1.35718e30i | − 2.01459i | ||||||||
\(163\) | 4.91659e29i | 0.671632i | 0.941928 | + | 0.335816i | \(0.109012\pi\) | ||||
−0.941928 | + | 0.335816i | \(0.890988\pi\) | |||||||
\(164\) | −1.18173e30 | −1.48637 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.33744e30 | −1.42829 | ||||||||
\(167\) | − 6.37427e29i | − 0.627709i | −0.949471 | − | 0.313854i | \(-0.898380\pi\) | ||||
0.949471 | − | 0.313854i | \(-0.101620\pi\) | |||||||
\(168\) | − 1.03663e30i | − 0.941774i | ||||||||
\(169\) | 1.16476e30 | 0.976710 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.80884e29 | 0.487109 | ||||||||
\(172\) | 1.47091e30i | 0.972638i | ||||||||
\(173\) | 2.71145e30i | 1.65798i | 0.559265 | + | 0.828989i | \(0.311083\pi\) | ||||
−0.559265 | + | 0.828989i | \(0.688917\pi\) | |||||||
\(174\) | 1.93094e29 | 0.109233 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.33984e28 | −0.0355849 | ||||||||
\(177\) | 3.15309e30i | 1.41611i | ||||||||
\(178\) | 2.63315e30i | 1.09599i | ||||||||
\(179\) | 1.65055e30 | 0.636961 | 0.318481 | − | 0.947929i | \(-0.396827\pi\) | ||||
0.318481 | + | 0.947929i | \(0.396827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.30260e30 | 1.42913 | 0.714563 | − | 0.699571i | \(-0.246626\pi\) | ||||
0.714563 | + | 0.699571i | \(0.246626\pi\) | |||||||
\(182\) | 6.13997e29i | 0.189323i | ||||||||
\(183\) | − 5.07112e30i | − 1.45216i | ||||||||
\(184\) | 4.28946e30 | 1.14120 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.85506e30 | 1.34619 | ||||||||
\(187\) | 1.13118e30i | 0.241919i | ||||||||
\(188\) | − 2.03380e30i | − 0.404741i | ||||||||
\(189\) | 2.30948e30 | 0.427838 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.35850e30 | 0.861177 | 0.430589 | − | 0.902548i | \(-0.358306\pi\) | ||||
0.430589 | + | 0.902548i | \(0.358306\pi\) | |||||||
\(192\) | − 1.34891e31i | − 2.02030i | ||||||||
\(193\) | 2.47114e30i | 0.345044i | 0.985006 | + | 0.172522i | \(0.0551915\pi\) | ||||
−0.985006 | + | 0.172522i | \(0.944808\pi\) | |||||||
\(194\) | 7.06566e30 | 0.920088 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.82138e30 | −0.660038 | ||||||||
\(197\) | 4.41349e30i | 0.467185i | 0.972335 | + | 0.233592i | \(0.0750481\pi\) | ||||
−0.972335 | + | 0.233592i | \(0.924952\pi\) | |||||||
\(198\) | − 1.63119e31i | − 1.61259i | ||||||||
\(199\) | 1.58034e31 | 1.45960 | 0.729802 | − | 0.683658i | \(-0.239612\pi\) | ||||
0.729802 | + | 0.683658i | \(0.239612\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.10780e31 | 0.893949 | ||||||||
\(202\) | − 3.41610e31i | − 2.57802i | ||||||||
\(203\) | 5.90310e29i | 0.0416758i | ||||||||
\(204\) | −4.06720e30 | −0.268713 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.37170e31 | −3.11103 | ||||||||
\(207\) | − 1.18213e31i | − 0.641305i | ||||||||
\(208\) | 5.91750e28i | 0.00300804i | ||||||||
\(209\) | −3.33784e31 | −1.59034 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.50086e31 | −0.628820 | −0.314410 | − | 0.949287i | \(-0.601807\pi\) | ||||
−0.314410 | + | 0.949287i | \(0.601807\pi\) | |||||||
\(212\) | 1.15752e31i | 0.454982i | ||||||||
\(213\) | − 1.16403e31i | − 0.429377i | ||||||||
\(214\) | −2.45768e31 | −0.851018 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.79491e31 | −0.548172 | ||||||||
\(217\) | 1.78995e31i | 0.513613i | ||||||||
\(218\) | 5.91374e31i | 1.59478i | ||||||||
\(219\) | 4.54839e31 | 1.15309 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.11975e29 | 0.0204497 | ||||||||
\(222\) | − 9.65982e31i | − 2.03800i | ||||||||
\(223\) | − 1.04534e31i | − 0.207559i | −0.994600 | − | 0.103779i | \(-0.966906\pi\) | ||||
0.994600 | − | 0.103779i | \(-0.0330936\pi\) | |||||||
\(224\) | 4.17390e31 | 0.780178 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.88722e31 | −1.14177 | ||||||||
\(227\) | − 9.45028e31i | − 1.47603i | −0.674783 | − | 0.738016i | \(-0.735763\pi\) | ||||
0.674783 | − | 0.738016i | \(-0.264237\pi\) | |||||||
\(228\) | − 1.20013e32i | − 1.76648i | ||||||||
\(229\) | 6.26689e31 | 0.869508 | 0.434754 | − | 0.900549i | \(-0.356835\pi\) | ||||
0.434754 | + | 0.900549i | \(0.356835\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.40048e32 | 1.72788 | ||||||||
\(232\) | − 4.58785e30i | − 0.0533975i | ||||||||
\(233\) | 7.87335e31i | 0.864678i | 0.901711 | + | 0.432339i | \(0.142312\pi\) | ||||
−0.901711 | + | 0.432339i | \(0.857688\pi\) | |||||||
\(234\) | −1.31509e31 | −0.136315 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.97894e32 | 1.82861 | ||||||||
\(237\) | 1.60442e32i | 1.40029i | ||||||||
\(238\) | − 2.01607e31i | − 0.166233i | ||||||||
\(239\) | 5.65108e30 | 0.0440311 | 0.0220156 | − | 0.999758i | \(-0.492992\pi\) | ||||
0.0220156 | + | 0.999758i | \(0.492992\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.42939e31 | −0.308400 | −0.154200 | − | 0.988040i | \(-0.549280\pi\) | ||||
−0.154200 | + | 0.988040i | \(0.549280\pi\) | |||||||
\(242\) | 5.54311e32i | 3.64961i | ||||||||
\(243\) | 1.60121e32i | 0.997154i | ||||||||
\(244\) | −3.18274e32 | −1.87516 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.52354e32 | 1.85933 | ||||||||
\(247\) | 2.69102e31i | 0.134434i | ||||||||
\(248\) | − 1.39114e32i | − 0.658071i | ||||||||
\(249\) | 2.45944e32 | 1.10191 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.28116e32 | −1.31957 | −0.659785 | − | 0.751454i | \(-0.729353\pi\) | ||||
−0.659785 | + | 0.751454i | \(0.729353\pi\) | |||||||
\(252\) | 1.79300e32i | 0.683397i | ||||||||
\(253\) | 5.79505e32i | 2.09377i | ||||||||
\(254\) | −5.03822e32 | −1.72592 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.14099e32 | −0.967894 | ||||||||
\(257\) | − 3.48288e31i | − 0.101822i | −0.998703 | − | 0.0509109i | \(-0.983788\pi\) | ||||
0.998703 | − | 0.0509109i | \(-0.0162125\pi\) | |||||||
\(258\) | − 4.38577e32i | − 1.21669i | ||||||||
\(259\) | 2.95311e32 | 0.777559 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.26436e31 | −0.0300071 | ||||||||
\(262\) | 5.94736e32i | 1.34047i | ||||||||
\(263\) | 3.82694e31i | 0.0819311i | 0.999161 | + | 0.0409656i | \(0.0130434\pi\) | ||||
−0.999161 | + | 0.0409656i | \(0.986957\pi\) | |||||||
\(264\) | −1.08844e33 | −2.21387 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.94895e32 | 1.09279 | ||||||||
\(267\) | − 4.84213e32i | − 0.845541i | ||||||||
\(268\) | − 6.95274e32i | − 1.15435i | ||||||||
\(269\) | 4.44965e31 | 0.0702539 | 0.0351269 | − | 0.999383i | \(-0.488816\pi\) | ||||
0.0351269 | + | 0.999383i | \(0.488816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.62870e32 | 0.518401 | 0.259200 | − | 0.965824i | \(-0.416541\pi\) | ||||
0.259200 | + | 0.965824i | \(0.416541\pi\) | |||||||
\(272\) | − 1.94302e30i | − 0.00264118i | ||||||||
\(273\) | − 1.12909e32i | − 0.146060i | ||||||||
\(274\) | 3.98963e32 | 0.491247 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.08363e33 | −2.32567 | ||||||||
\(277\) | − 1.40758e33i | − 1.49622i | −0.663574 | − | 0.748111i | \(-0.730961\pi\) | ||||
0.663574 | − | 0.748111i | \(-0.269039\pi\) | |||||||
\(278\) | 2.17020e33i | 2.19733i | ||||||||
\(279\) | −3.83383e32 | −0.369808 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.59534e32 | 0.314924 | 0.157462 | − | 0.987525i | \(-0.449669\pi\) | ||||
0.157462 | + | 0.987525i | \(0.449669\pi\) | |||||||
\(282\) | 6.06414e32i | 0.506298i | ||||||||
\(283\) | − 3.59177e32i | − 0.285885i | −0.989731 | − | 0.142943i | \(-0.954344\pi\) | ||||
0.989731 | − | 0.142943i | \(-0.0456565\pi\) | |||||||
\(284\) | −7.30568e32 | −0.554451 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.44688e32 | 0.445049 | ||||||||
\(287\) | 1.07719e33i | 0.709390i | ||||||||
\(288\) | 8.93990e32i | 0.561738i | ||||||||
\(289\) | 1.63777e33 | 0.982044 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.29931e33 | −0.709838 | ||||||||
\(292\) | − 2.85466e33i | − 1.48897i | ||||||||
\(293\) | 3.51312e32i | 0.174976i | 0.996166 | + | 0.0874882i | \(0.0278840\pi\) | ||||
−0.996166 | + | 0.0874882i | \(0.972116\pi\) | |||||||
\(294\) | 1.73575e33 | 0.825653 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.29514e33 | −0.996255 | ||||||||
\(297\) | − 2.42492e33i | − 1.00574i | ||||||||
\(298\) | − 5.06167e33i | − 2.00620i | ||||||||
\(299\) | 4.67206e32 | 0.176990 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.34078e33 | 0.464204 | ||||||||
\(302\) | 1.20454e33i | 0.398773i | ||||||||
\(303\) | 6.28191e33i | 1.98891i | ||||||||
\(304\) | 5.73340e31 | 0.0173628 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.31813e32 | 0.119690 | ||||||||
\(307\) | 6.75654e32i | 0.179208i | 0.995977 | + | 0.0896038i | \(0.0285601\pi\) | ||||
−0.995977 | + | 0.0896038i | \(0.971440\pi\) | |||||||
\(308\) | − 8.78968e33i | − 2.23120i | ||||||||
\(309\) | 9.87810e33 | 2.40013 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.16690e33 | 1.15071 | 0.575354 | − | 0.817905i | \(-0.304864\pi\) | ||||
0.575354 | + | 0.817905i | \(0.304864\pi\) | |||||||
\(312\) | 8.77519e32i | 0.187141i | ||||||||
\(313\) | − 1.10679e33i | − 0.226056i | −0.993592 | − | 0.113028i | \(-0.963945\pi\) | ||||
0.993592 | − | 0.113028i | \(-0.0360551\pi\) | |||||||
\(314\) | −1.37821e34 | −2.69628 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.00697e34 | 1.80817 | ||||||||
\(317\) | 9.49991e33i | 1.63463i | 0.576191 | + | 0.817315i | \(0.304539\pi\) | ||||
−0.576191 | + | 0.817315i | \(0.695461\pi\) | |||||||
\(318\) | − 3.45135e33i | − 0.569145i | ||||||||
\(319\) | 6.19817e32 | 0.0979691 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.51946e33 | 0.656551 | ||||||||
\(322\) | − 1.03284e34i | − 1.43872i | ||||||||
\(323\) | − 8.83602e32i | − 0.118038i | ||||||||
\(324\) | 1.56638e34 | 2.00696 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.20072e33 | −1.08489 | ||||||||
\(327\) | − 1.08749e34i | − 1.23035i | ||||||||
\(328\) | − 8.37180e33i | − 0.908913i | ||||||||
\(329\) | −1.85387e33 | −0.193168 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.25351e34 | −1.20351 | −0.601757 | − | 0.798679i | \(-0.705533\pi\) | ||||
−0.601757 | + | 0.798679i | \(0.705533\pi\) | |||||||
\(332\) | − 1.54359e34i | − 1.42288i | ||||||||
\(333\) | 6.32514e33i | 0.559852i | ||||||||
\(334\) | 1.19286e34 | 1.01394 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.40560e32 | −0.0188644 | ||||||||
\(337\) | 3.36740e33i | 0.253683i | 0.991923 | + | 0.126842i | \(0.0404840\pi\) | ||||
−0.991923 | + | 0.126842i | \(0.959516\pi\) | |||||||
\(338\) | 2.17968e34i | 1.57768i | ||||||||
\(339\) | 1.26650e34 | 0.880865 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.87943e34 | 1.20737 | ||||||||
\(342\) | 1.27418e34i | 0.786825i | ||||||||
\(343\) | 1.82434e34i | 1.08302i | ||||||||
\(344\) | −1.04204e34 | −0.594766 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.07409e34 | −2.67813 | ||||||||
\(347\) | 1.91545e34i | 0.972353i | 0.873861 | + | 0.486177i | \(0.161609\pi\) | ||||
−0.873861 | + | 0.486177i | \(0.838391\pi\) | |||||||
\(348\) | 2.22858e33i | 0.108820i | ||||||||
\(349\) | −1.45433e34 | −0.683158 | −0.341579 | − | 0.939853i | \(-0.610962\pi\) | ||||
−0.341579 | + | 0.939853i | \(0.610962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.95501e33 | −0.0850164 | ||||||||
\(352\) | − 4.38253e34i | − 1.83400i | ||||||||
\(353\) | − 4.39359e33i | − 0.176954i | −0.996078 | − | 0.0884772i | \(-0.971800\pi\) | ||||
0.996078 | − | 0.0884772i | \(-0.0282000\pi\) | |||||||
\(354\) | −5.90057e34 | −2.28744 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.03902e34 | −1.09184 | ||||||||
\(357\) | 3.70738e33i | 0.128247i | ||||||||
\(358\) | 3.08877e34i | 1.02888i | ||||||||
\(359\) | −2.60550e34 | −0.835828 | −0.417914 | − | 0.908487i | \(-0.637239\pi\) | ||||
−0.417914 | + | 0.908487i | \(0.637239\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.52760e33 | −0.224032 | ||||||||
\(362\) | 8.05172e34i | 2.30846i | ||||||||
\(363\) | − 1.01933e35i | − 2.81563i | ||||||||
\(364\) | −7.08639e33 | −0.188606 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.48990e34 | 2.34567 | ||||||||
\(367\) | − 3.50053e34i | − 0.833953i | −0.908917 | − | 0.416977i | \(-0.863090\pi\) | ||||
0.908917 | − | 0.416977i | \(-0.136910\pi\) | |||||||
\(368\) | − 9.95413e32i | − 0.0228590i | ||||||||
\(369\) | −2.30718e34 | −0.510770 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.05512e34 | 0.217146 | ||||||||
\(372\) | 6.75755e34i | 1.34110i | ||||||||
\(373\) | − 2.06100e34i | − 0.394464i | −0.980357 | − | 0.197232i | \(-0.936805\pi\) | ||||
0.980357 | − | 0.197232i | \(-0.0631953\pi\) | |||||||
\(374\) | −2.11684e34 | −0.390771 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.44082e34 | 0.247499 | ||||||||
\(377\) | − 4.99707e32i | − 0.00828146i | ||||||||
\(378\) | 4.32186e34i | 0.691086i | ||||||||
\(379\) | 3.69120e34 | 0.569559 | 0.284779 | − | 0.958593i | \(-0.408080\pi\) | ||||
0.284779 | + | 0.958593i | \(0.408080\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.26485e34 | 1.33153 | ||||||||
\(382\) | 1.00277e35i | 1.39106i | ||||||||
\(383\) | 6.12833e34i | 0.820652i | 0.911939 | + | 0.410326i | \(0.134585\pi\) | ||||
−0.911939 | + | 0.410326i | \(0.865415\pi\) | |||||||
\(384\) | 1.54507e35 | 1.99745 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.62439e34 | −0.557348 | ||||||||
\(387\) | 2.87175e34i | 0.334233i | ||||||||
\(388\) | 8.15476e34i | 0.916606i | ||||||||
\(389\) | −5.65060e34 | −0.613444 | −0.306722 | − | 0.951799i | \(-0.599232\pi\) | ||||
−0.306722 | + | 0.951799i | \(0.599232\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.53408e34 | −0.155404 | ||||||||
\(392\) | − 4.12407e34i | − 0.403612i | ||||||||
\(393\) | − 1.09367e35i | − 1.03416i | ||||||||
\(394\) | −8.25924e34 | −0.754642 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.88262e35 | 1.60649 | ||||||||
\(397\) | 2.20649e35i | 1.81983i | 0.414794 | + | 0.909915i | \(0.363854\pi\) | ||||
−0.414794 | + | 0.909915i | \(0.636146\pi\) | |||||||
\(398\) | 2.95739e35i | 2.35769i | ||||||||
\(399\) | −1.09396e35 | −0.843078 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.87612e35 | −1.35148 | −0.675741 | − | 0.737139i | \(-0.736176\pi\) | ||||
−0.675741 | + | 0.737139i | \(0.736176\pi\) | |||||||
\(402\) | 2.07308e35i | 1.44399i | ||||||||
\(403\) | − 1.51522e34i | − 0.102061i | ||||||||
\(404\) | 3.94265e35 | 2.56827 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.10468e34 | −0.0673188 | ||||||||
\(407\) | − 3.10072e35i | − 1.82784i | ||||||||
\(408\) | − 2.88135e34i | − 0.164317i | ||||||||
\(409\) | −2.22853e35 | −1.22957 | −0.614786 | − | 0.788694i | \(-0.710758\pi\) | ||||
−0.614786 | + | 0.788694i | \(0.710758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.33658e34 | −0.378991 | ||||||||
\(412\) | − 6.19970e35i | − 3.09926i | ||||||||
\(413\) | − 1.80387e35i | − 0.872729i | ||||||||
\(414\) | 2.21219e35 | 1.03590 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.53327e34 | −0.155030 | ||||||||
\(417\) | − 3.99081e35i | − 1.69521i | ||||||||
\(418\) | − 6.24631e35i | − 2.56888i | ||||||||
\(419\) | 5.47879e34 | 0.218170 | 0.109085 | − | 0.994032i | \(-0.465208\pi\) | ||||
0.109085 | + | 0.994032i | \(0.465208\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.97758e35 | −0.738458 | −0.369229 | − | 0.929338i | \(-0.620378\pi\) | ||||
−0.369229 | + | 0.929338i | \(0.620378\pi\) | |||||||
\(422\) | − 2.80864e35i | − 1.01573i | ||||||||
\(423\) | − 3.97073e34i | − 0.139083i | ||||||||
\(424\) | −8.20028e34 | −0.278221 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.17832e35 | 0.693572 | ||||||||
\(427\) | 2.90116e35i | 0.894945i | ||||||||
\(428\) | − 2.83650e35i | − 0.847798i | ||||||||
\(429\) | −1.18553e35 | −0.343350 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.94928e35 | −1.34617 | −0.673083 | − | 0.739567i | \(-0.735030\pi\) | ||||
−0.673083 | + | 0.739567i | \(0.735030\pi\) | |||||||
\(432\) | 4.16527e33i | 0.0109803i | ||||||||
\(433\) | 3.12882e35i | 0.799454i | 0.916634 | + | 0.399727i | \(0.130895\pi\) | ||||
−0.916634 | + | 0.399727i | \(0.869105\pi\) | |||||||
\(434\) | −3.34965e35 | −0.829637 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.82528e35 | −1.58874 | ||||||||
\(437\) | − 4.52671e35i | − 1.02160i | ||||||||
\(438\) | 8.51168e35i | 1.86258i | ||||||||
\(439\) | −7.22790e35 | −1.53370 | −0.766852 | − | 0.641824i | \(-0.778178\pi\) | ||||
−0.766852 | + | 0.641824i | \(0.778178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.13655e35 | −0.226813 | ||||||||
\(442\) | 1.70663e34i | 0.0330324i | ||||||||
\(443\) | − 7.68142e35i | − 1.44209i | −0.692891 | − | 0.721043i | \(-0.743663\pi\) | ||||
0.692891 | − | 0.721043i | \(-0.256337\pi\) | |||||||
\(444\) | 1.11488e36 | 2.03029 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.95620e35 | 0.335269 | ||||||||
\(447\) | 9.30798e35i | 1.54776i | ||||||||
\(448\) | 7.71705e35i | 1.24508i | ||||||||
\(449\) | 6.52536e35 | 1.02160 | 0.510798 | − | 0.859701i | \(-0.329350\pi\) | ||||
0.510798 | + | 0.859701i | \(0.329350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.13103e36 | 1.66759 | ||||||||
\(452\) | − 7.94881e35i | − 1.13745i | ||||||||
\(453\) | − 2.21504e35i | − 0.307649i | ||||||||
\(454\) | 1.76849e36 | 2.38423 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.50218e35 | 1.08020 | ||||||||
\(457\) | − 6.21081e35i | − 0.766090i | −0.923730 | − | 0.383045i | \(-0.874875\pi\) | ||||
0.923730 | − | 0.383045i | \(-0.125125\pi\) | |||||||
\(458\) | 1.17276e36i | 1.40451i | ||||||||
\(459\) | 6.41930e34 | 0.0746477 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.02161e36 | 1.12027 | 0.560133 | − | 0.828402i | \(-0.310750\pi\) | ||||
0.560133 | + | 0.828402i | \(0.310750\pi\) | |||||||
\(462\) | 2.62080e36i | 2.79105i | ||||||||
\(463\) | − 1.10341e36i | − 1.14129i | −0.821199 | − | 0.570643i | \(-0.806694\pi\) | ||||
0.821199 | − | 0.570643i | \(-0.193306\pi\) | |||||||
\(464\) | −1.06466e33 | −0.00106959 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.47339e36 | −1.39671 | ||||||||
\(467\) | − 8.66440e35i | − 0.797922i | −0.916968 | − | 0.398961i | \(-0.869371\pi\) | ||||
0.916968 | − | 0.398961i | \(-0.130629\pi\) | |||||||
\(468\) | − 1.51780e35i | − 0.135799i | ||||||||
\(469\) | −6.33764e35 | −0.550927 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.53441e36 | 2.08015 | ||||||||
\(472\) | 1.40195e36i | 1.11819i | ||||||||
\(473\) | − 1.40780e36i | − 1.09123i | ||||||||
\(474\) | −3.00246e36 | −2.26188 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.32683e35 | 0.165604 | ||||||||
\(477\) | 2.25991e35i | 0.156348i | ||||||||
\(478\) | 1.05752e35i | 0.0711234i | ||||||||
\(479\) | 2.57345e36 | 1.68262 | 0.841311 | − | 0.540552i | \(-0.181785\pi\) | ||||
0.841311 | + | 0.540552i | \(0.181785\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.49985e35 | −0.154510 | ||||||||
\(482\) | − 8.28899e35i | − 0.498157i | ||||||||
\(483\) | 1.89930e36i | 1.10996i | ||||||||
\(484\) | −6.39752e36 | −3.63580 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.99643e36 | −1.61070 | ||||||||
\(487\) | 2.28927e36i | 1.19690i | 0.801162 | + | 0.598448i | \(0.204216\pi\) | ||||
−0.801162 | + | 0.598448i | \(0.795784\pi\) | |||||||
\(488\) | − 2.25476e36i | − 1.14666i | ||||||||
\(489\) | 1.69193e36 | 0.836977 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.74114e36 | 0.815142 | 0.407571 | − | 0.913174i | \(-0.366376\pi\) | ||||
0.407571 | + | 0.913174i | \(0.366376\pi\) | |||||||
\(492\) | 4.06666e36i | 1.85229i | ||||||||
\(493\) | 1.64079e34i | 0.00727145i | ||||||||
\(494\) | −5.03587e35 | −0.217151 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.22828e34 | −0.0131816 | ||||||||
\(497\) | 6.65935e35i | 0.264619i | ||||||||
\(498\) | 4.60250e36i | 1.77991i | ||||||||
\(499\) | −2.80174e36 | −1.05456 | −0.527278 | − | 0.849693i | \(-0.676787\pi\) | ||||
−0.527278 | + | 0.849693i | \(0.676787\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.19356e36 | −0.782240 | ||||||||
\(502\) | − 6.14024e36i | − 2.13150i | ||||||||
\(503\) | 3.44032e36i | 1.16260i | 0.813688 | + | 0.581301i | \(0.197456\pi\) | ||||
−0.813688 | + | 0.581301i | \(0.802544\pi\) | |||||||
\(504\) | −1.27022e36 | −0.417896 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.08446e37 | −3.38207 | ||||||||
\(507\) | − 4.00825e36i | − 1.21716i | ||||||||
\(508\) | − 5.81480e36i | − 1.71939i | ||||||||
\(509\) | −1.50719e35 | −0.0433989 | −0.0216995 | − | 0.999765i | \(-0.506908\pi\) | ||||
−0.0216995 | + | 0.999765i | \(0.506908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.60211e36 | −0.710631 | ||||||||
\(512\) | 1.48198e35i | 0.0394183i | ||||||||
\(513\) | 1.89418e36i | 0.490725i | ||||||||
\(514\) | 6.51772e35 | 0.164473 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.06179e36 | 1.21208 | ||||||||
\(517\) | 1.94654e36i | 0.454089i | ||||||||
\(518\) | 5.52634e36i | 1.25599i | ||||||||
\(519\) | 9.33082e36 | 2.06614 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.14778e36 | 1.71289 | 0.856446 | − | 0.516236i | \(-0.172667\pi\) | ||||
0.856446 | + | 0.516236i | \(0.172667\pi\) | |||||||
\(522\) | − 2.36607e35i | − 0.0484704i | ||||||||
\(523\) | − 4.14380e36i | − 0.827229i | −0.910452 | − | 0.413615i | \(-0.864266\pi\) | ||||
0.910452 | − | 0.413615i | \(-0.135734\pi\) | |||||||
\(524\) | −6.86409e36 | −1.33540 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.16158e35 | −0.132343 | ||||||||
\(527\) | 4.97526e35i | 0.0896133i | ||||||||
\(528\) | 2.52584e35i | 0.0443453i | ||||||||
\(529\) | −2.01590e36 | −0.344999 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.86363e36 | 0.628376 | ||||||||
\(532\) | 6.86591e36i | 1.08866i | ||||||||
\(533\) | − 9.11854e35i | − 0.140964i | ||||||||
\(534\) | 9.06137e36 | 1.36580 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.92557e36 | 0.705881 | ||||||||
\(537\) | − 5.67999e36i | − 0.793770i | ||||||||
\(538\) | 8.32690e35i | 0.113481i | ||||||||
\(539\) | 5.57161e36 | 0.740512 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.06017e37 | 1.34033 | 0.670163 | − | 0.742214i | \(-0.266224\pi\) | ||||
0.670163 | + | 0.742214i | \(0.266224\pi\) | |||||||
\(542\) | 6.79060e36i | 0.837371i | ||||||||
\(543\) | − 1.48064e37i | − 1.78095i | ||||||||
\(544\) | 1.16016e36 | 0.136123 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.11293e36 | 0.235931 | ||||||||
\(547\) | − 8.42305e36i | − 0.917573i | −0.888547 | − | 0.458786i | \(-0.848284\pi\) | ||||
0.888547 | − | 0.458786i | \(-0.151716\pi\) | |||||||
\(548\) | 4.60459e36i | 0.489388i | ||||||||
\(549\) | −6.21388e36 | −0.644371 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.84160e35 | −0.0478016 | ||||||||
\(552\) | − 1.47612e37i | − 1.42214i | ||||||||
\(553\) | − 9.17883e36i | − 0.862975i | ||||||||
\(554\) | 2.63409e37 | 2.41684 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.50471e37 | −2.18901 | ||||||||
\(557\) | 5.59363e36i | 0.477143i | 0.971125 | + | 0.238571i | \(0.0766791\pi\) | ||||
−0.971125 | + | 0.238571i | \(0.923321\pi\) | |||||||
\(558\) | − 7.17447e36i | − 0.597349i | ||||||||
\(559\) | −1.13499e36 | −0.0922427 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.89269e36 | 0.301475 | ||||||||
\(562\) | 6.72818e36i | 0.508695i | ||||||||
\(563\) | 2.06136e37i | 1.52157i | 0.649006 | + | 0.760783i | \(0.275185\pi\) | ||||
−0.649006 | + | 0.760783i | \(0.724815\pi\) | |||||||
\(564\) | −6.99886e36 | −0.504382 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.72150e36 | 0.461790 | ||||||||
\(567\) | − 1.42780e37i | − 0.957850i | ||||||||
\(568\) | − 5.17560e36i | − 0.339046i | ||||||||
\(569\) | −4.96854e36 | −0.317844 | −0.158922 | − | 0.987291i | \(-0.550802\pi\) | ||||
−0.158922 | + | 0.987291i | \(0.550802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.02940e36 | 0.0628055 | 0.0314028 | − | 0.999507i | \(-0.490003\pi\) | ||||
0.0314028 | + | 0.999507i | \(0.490003\pi\) | |||||||
\(572\) | 7.44060e36i | 0.443365i | ||||||||
\(573\) | − 1.84400e37i | − 1.07318i | ||||||||
\(574\) | −2.01580e37 | −1.14587 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.65288e37 | −0.896475 | ||||||||
\(577\) | 4.63258e36i | 0.245442i | 0.992441 | + | 0.122721i | \(0.0391620\pi\) | ||||
−0.992441 | + | 0.122721i | \(0.960838\pi\) | |||||||
\(578\) | 3.06485e37i | 1.58629i | ||||||||
\(579\) | 8.50387e36 | 0.429987 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.40703e37 | −0.679090 | ||||||||
\(582\) | − 2.43149e37i | − 1.14660i | ||||||||
\(583\) | − 1.10786e37i | − 0.510455i | ||||||||
\(584\) | 2.02234e37 | 0.910503 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.57430e36 | −0.282639 | ||||||||
\(587\) | − 2.64137e36i | − 0.110972i | −0.998459 | − | 0.0554862i | \(-0.982329\pi\) | ||||
0.998459 | − | 0.0554862i | \(-0.0176709\pi\) | |||||||
\(588\) | 2.00330e37i | 0.822529i | ||||||||
\(589\) | −1.46808e37 | −0.589107 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.51880e37 | 0.582198 | ||||||||
\(592\) | 5.32610e35i | 0.0199557i | ||||||||
\(593\) | − 3.52090e37i | − 1.28948i | −0.764401 | − | 0.644741i | \(-0.776965\pi\) | ||||
0.764401 | − | 0.644741i | \(-0.223035\pi\) | |||||||
\(594\) | 4.53789e37 | 1.62457 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.84187e37 | 1.99861 | ||||||||
\(597\) | − 5.43839e37i | − 1.81893i | ||||||||
\(598\) | 8.74311e36i | 0.285891i | ||||||||
\(599\) | −4.76915e37 | −1.52468 | −0.762341 | − | 0.647176i | \(-0.775950\pi\) | ||||
−0.762341 | + | 0.647176i | \(0.775950\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.39124e37 | −0.730831 | −0.365416 | − | 0.930844i | \(-0.619073\pi\) | ||||
−0.365416 | + | 0.930844i | \(0.619073\pi\) | |||||||
\(602\) | 2.50908e37i | 0.749827i | ||||||||
\(603\) | − 1.35743e37i | − 0.396675i | ||||||||
\(604\) | −1.39020e37 | −0.397264 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.17557e38 | −3.21269 | ||||||||
\(607\) | − 3.35424e37i | − 0.896493i | −0.893910 | − | 0.448246i | \(-0.852049\pi\) | ||||
0.893910 | − | 0.448246i | \(-0.147951\pi\) | |||||||
\(608\) | 3.42334e37i | 0.894854i | ||||||||
\(609\) | 2.03142e36 | 0.0519357 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.56933e36 | 0.0383847 | ||||||||
\(612\) | 4.98373e36i | 0.119237i | ||||||||
\(613\) | − 6.25036e37i | − 1.46281i | −0.681942 | − | 0.731407i | \(-0.738864\pi\) | ||||
0.681942 | − | 0.731407i | \(-0.261136\pi\) | |||||||
\(614\) | −1.26439e37 | −0.289474 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.22692e37 | 1.36437 | ||||||||
\(617\) | 6.57455e37i | 1.40934i | 0.709534 | + | 0.704671i | \(0.248906\pi\) | ||||
−0.709534 | + | 0.704671i | \(0.751094\pi\) | |||||||
\(618\) | 1.84855e38i | 3.87692i | ||||||||
\(619\) | −2.39694e37 | −0.491851 | −0.245926 | − | 0.969289i | \(-0.579092\pi\) | ||||
−0.245926 | + | 0.969289i | \(0.579092\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.28862e37 | 0.646066 | ||||||||
\(622\) | 9.66913e37i | 1.85873i | ||||||||
\(623\) | 2.77016e37i | 0.521094i | ||||||||
\(624\) | 2.03637e35 | 0.00374857 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.07120e37 | 0.365148 | ||||||||
\(627\) | 1.14864e38i | 1.98186i | ||||||||
\(628\) | − 1.59065e38i | − 2.68608i | ||||||||
\(629\) | 8.20831e36 | 0.135666 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.72032e37 | −0.430748 | −0.215374 | − | 0.976532i | \(-0.569097\pi\) | ||||
−0.215374 | + | 0.976532i | \(0.569097\pi\) | |||||||
\(632\) | 7.13372e37i | 1.10570i | ||||||||
\(633\) | 5.16486e37i | 0.783625i | ||||||||
\(634\) | −1.77778e38 | −2.64041 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.98334e37 | 0.566991 | ||||||||
\(637\) | − 4.49192e36i | − 0.0625965i | ||||||||
\(638\) | 1.15990e37i | 0.158249i | ||||||||
\(639\) | −1.42634e37 | −0.190529 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.03099e37 | 0.772334 | 0.386167 | − | 0.922429i | \(-0.373799\pi\) | ||||
0.386167 | + | 0.922429i | \(0.373799\pi\) | |||||||
\(642\) | 8.45753e37i | 1.06052i | ||||||||
\(643\) | − 1.01937e38i | − 1.25165i | −0.779965 | − | 0.625823i | \(-0.784763\pi\) | ||||
0.779965 | − | 0.625823i | \(-0.215237\pi\) | |||||||
\(644\) | 1.19204e38 | 1.43328 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.65354e37 | 0.190667 | ||||||||
\(647\) | − 1.38190e36i | − 0.0156052i | −0.999970 | − | 0.00780260i | \(-0.997516\pi\) | ||||
0.999970 | − | 0.00780260i | \(-0.00248367\pi\) | |||||||
\(648\) | 1.10968e38i | 1.22726i | ||||||||
\(649\) | −1.89404e38 | −2.05156 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.15972e37 | 0.640055 | ||||||||
\(652\) | − 1.06189e38i | − 1.08078i | ||||||||
\(653\) | − 1.67383e38i | − 1.66872i | −0.551224 | − | 0.834358i | \(-0.685839\pi\) | ||||
0.551224 | − | 0.834358i | \(-0.314161\pi\) | |||||||
\(654\) | 2.03508e38 | 1.98738 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.94276e36 | −0.0182061 | ||||||||
\(657\) | − 5.57335e37i | − 0.511663i | ||||||||
\(658\) | − 3.46926e37i | − 0.312024i | ||||||||
\(659\) | 1.83021e38 | 1.61268 | 0.806339 | − | 0.591454i | \(-0.201446\pi\) | ||||
0.806339 | + | 0.591454i | \(0.201446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.09366e37 | 0.515417 | 0.257708 | − | 0.966223i | \(-0.417033\pi\) | ||||
0.257708 | + | 0.966223i | \(0.417033\pi\) | |||||||
\(662\) | − 2.34578e38i | − 1.94403i | ||||||||
\(663\) | − 3.13835e36i | − 0.0254841i | ||||||||
\(664\) | 1.09354e38 | 0.870090 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.18366e38 | −0.904327 | ||||||||
\(667\) | 8.40581e36i | 0.0629334i | ||||||||
\(668\) | 1.37672e38i | 1.01010i | ||||||||
\(669\) | −3.59729e37 | −0.258656 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.04618e38 | 2.10379 | ||||||||
\(672\) | − 1.43635e38i | − 0.972245i | ||||||||
\(673\) | − 6.36340e37i | − 0.422168i | −0.977468 | − | 0.211084i | \(-0.932301\pi\) | ||||
0.977468 | − | 0.211084i | \(-0.0676994\pi\) | |||||||
\(674\) | −6.30163e37 | −0.409774 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.51566e38 | −1.57171 | ||||||||
\(677\) | 5.37104e37i | 0.328936i | 0.986382 | + | 0.164468i | \(0.0525907\pi\) | ||||
−0.986382 | + | 0.164468i | \(0.947409\pi\) | |||||||
\(678\) | 2.37008e38i | 1.42286i | ||||||||
\(679\) | 7.43332e37 | 0.437462 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.25210e38 | −1.83941 | ||||||||
\(682\) | 3.51708e38i | 1.95026i | ||||||||
\(683\) | 1.59190e38i | 0.865437i | 0.901529 | + | 0.432718i | \(0.142446\pi\) | ||||
−0.901529 | + | 0.432718i | \(0.857554\pi\) | |||||||
\(684\) | −1.47058e38 | −0.783847 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.41399e38 | −1.74939 | ||||||||
\(687\) | − 2.15661e38i | − 1.08357i | ||||||||
\(688\) | 2.41817e36i | 0.0119136i | ||||||||
\(689\) | −8.93171e36 | −0.0431495 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.11503e38 | −0.518006 | −0.259003 | − | 0.965877i | \(-0.583394\pi\) | ||||
−0.259003 | + | 0.965877i | \(0.583394\pi\) | |||||||
\(692\) | − 5.85621e38i | − 2.66799i | ||||||||
\(693\) | − 1.71607e38i | − 0.766719i | ||||||||
\(694\) | −3.58451e38 | −1.57064 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.57880e37 | −0.0665431 | ||||||||
\(697\) | 2.99409e37i | 0.123772i | ||||||||
\(698\) | − 2.72158e38i | − 1.10350i | ||||||||
\(699\) | 2.70943e38 | 1.07755 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.04824e37 | 0.346235 | 0.173117 | − | 0.984901i | \(-0.444616\pi\) | ||||
0.173117 | + | 0.984901i | \(0.444616\pi\) | |||||||
\(702\) | − 3.65852e37i | − 0.137327i | ||||||||
\(703\) | 2.42208e38i | 0.891849i | ||||||||
\(704\) | 8.10278e38 | 2.92687 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.22199e37 | 0.285834 | ||||||||
\(707\) | − 3.59385e38i | − 1.22574i | ||||||||
\(708\) | − 6.81008e38i | − 2.27879i | ||||||||
\(709\) | −2.52263e38 | −0.828190 | −0.414095 | − | 0.910234i | \(-0.635902\pi\) | ||||
−0.414095 | + | 0.910234i | \(0.635902\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.96598e38 | 0.621353 | ||||||||
\(712\) | − 2.15295e38i | − 0.667657i | ||||||||
\(713\) | 2.54883e38i | 0.775591i | ||||||||
\(714\) | −6.93784e37 | −0.207157 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.56488e38 | −1.02499 | ||||||||
\(717\) | − 1.94469e37i | − 0.0548709i | ||||||||
\(718\) | − 4.87584e38i | − 1.35011i | ||||||||
\(719\) | 2.15368e38 | 0.585249 | 0.292624 | − | 0.956227i | \(-0.405471\pi\) | ||||
0.292624 | + | 0.956227i | \(0.405471\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.65122e38 | −1.47916 | ||||||||
\(722\) | − 1.40869e38i | − 0.361878i | ||||||||
\(723\) | 1.52427e38i | 0.384323i | ||||||||
\(724\) | −9.29280e38 | −2.29973 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.90753e39 | 4.54808 | ||||||||
\(727\) | 6.18554e38i | 1.44765i | 0.689985 | + | 0.723824i | \(0.257617\pi\) | ||||
−0.689985 | + | 0.723824i | \(0.742383\pi\) | |||||||
\(728\) | − 5.02025e37i | − 0.115332i | ||||||||
\(729\) | −2.02058e36 | −0.00455675 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.72675e37 | 0.0809927 | ||||||||
\(732\) | 1.09527e39i | 2.33679i | ||||||||
\(733\) | − 5.13013e36i | − 0.0107455i | −0.999986 | − | 0.00537273i | \(-0.998290\pi\) | ||||
0.999986 | − | 0.00537273i | \(-0.00171020\pi\) | |||||||
\(734\) | 6.55075e38 | 1.34708 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.94349e38 | 1.17812 | ||||||||
\(737\) | 6.65443e38i | 1.29509i | ||||||||
\(738\) | − 4.31756e38i | − 0.825044i | ||||||||
\(739\) | 5.22466e38 | 0.980298 | 0.490149 | − | 0.871639i | \(-0.336942\pi\) | ||||
0.490149 | + | 0.871639i | \(0.336942\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.26054e37 | 0.167529 | ||||||||
\(742\) | 1.97450e38i | 0.350756i | ||||||||
\(743\) | 1.00984e39i | 1.76158i | 0.473509 | + | 0.880789i | \(0.342987\pi\) | ||||
−0.473509 | + | 0.880789i | \(0.657013\pi\) | |||||||
\(744\) | −4.78729e38 | −0.820077 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.85686e38 | 0.637177 | ||||||||
\(747\) | − 3.01367e38i | − 0.488953i | ||||||||
\(748\) | − 2.44313e38i | − 0.389292i | ||||||||
\(749\) | −2.58556e38 | −0.404622 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.44629e38 | −0.671210 | −0.335605 | − | 0.942003i | \(-0.608941\pi\) | ||||
−0.335605 | + | 0.942003i | \(0.608941\pi\) | |||||||
\(752\) | − 3.34356e36i | − 0.00495757i | ||||||||
\(753\) | 1.12914e39i | 1.64443i | ||||||||
\(754\) | 9.35131e36 | 0.0133770 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.98803e38 | −0.688470 | ||||||||
\(757\) | − 8.24934e38i | − 1.11847i | −0.829009 | − | 0.559235i | \(-0.811095\pi\) | ||||
0.829009 | − | 0.559235i | \(-0.188905\pi\) | |||||||
\(758\) | 6.90757e38i | 0.920007i | ||||||||
\(759\) | 1.99423e39 | 2.60923 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.69669e38 | −0.719333 | −0.359666 | − | 0.933081i | \(-0.617109\pi\) | ||||
−0.359666 | + | 0.933081i | \(0.617109\pi\) | |||||||
\(762\) | 1.73379e39i | 2.15082i | ||||||||
\(763\) | 6.22146e38i | 0.758248i | ||||||||
\(764\) | −1.15733e39 | −1.38579 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.14683e39 | −1.32560 | ||||||||
\(767\) | 1.52700e38i | 0.173421i | ||||||||
\(768\) | 1.08090e39i | 1.20617i | ||||||||
\(769\) | −1.47938e39 | −1.62209 | −0.811043 | − | 0.584986i | \(-0.801100\pi\) | ||||
−0.811043 | + | 0.584986i | \(0.801100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.19855e38 | −0.126889 | ||||||||
\(772\) | − 5.33720e38i | − 0.555239i | ||||||||
\(773\) | − 1.83758e39i | − 1.87855i | −0.343160 | − | 0.939277i | \(-0.611497\pi\) | ||||
0.343160 | − | 0.939277i | \(-0.388503\pi\) | |||||||
\(774\) | −5.37408e38 | −0.539885 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.77712e38 | −0.560503 | ||||||||
\(777\) | − 1.01625e39i | − 0.968981i | ||||||||
\(778\) | − 1.05743e39i | − 0.990894i | ||||||||
\(779\) | −8.83484e38 | −0.813660 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.99222e38 | 0.622051 | ||||||||
\(782\) | − 2.87081e38i | − 0.251023i | ||||||||
\(783\) | − 3.51738e37i | − 0.0302298i | ||||||||
\(784\) | −9.57033e36 | −0.00808463 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.04665e39 | 1.67047 | ||||||||
\(787\) | 3.93218e38i | 0.315482i | 0.987481 | + | 0.157741i | \(0.0504210\pi\) | ||||
−0.987481 | + | 0.157741i | \(0.949579\pi\) | |||||||
\(788\) | − 9.53231e38i | − 0.751786i | ||||||||
\(789\) | 1.31695e38 | 0.102101 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.24559e38 | −0.542864 | ||||||||
\(792\) | 1.33372e39i | 0.982367i | ||||||||
\(793\) | − 2.45588e38i | − 0.177836i | ||||||||
\(794\) | −4.12914e39 | −2.93957 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.41324e39 | −2.34877 | ||||||||
\(797\) | 1.32458e39i | 0.896168i | 0.893991 | + | 0.448084i | \(0.147893\pi\) | ||||
−0.893991 | + | 0.448084i | \(0.852107\pi\) | |||||||
\(798\) | − 2.04719e39i | − 1.36182i | ||||||||
\(799\) | −5.15293e37 | −0.0337033 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.93329e38 | −0.375194 | ||||||||
\(802\) | − 3.51089e39i | − 2.18305i | ||||||||
\(803\) | 2.73218e39i | 1.67051i | ||||||||
\(804\) | −2.39263e39 | −1.43853 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.83553e38 | 0.164858 | ||||||||
\(807\) | − 1.53125e38i | − 0.0875492i | ||||||||
\(808\) | 2.79311e39i | 1.57049i | ||||||||
\(809\) | 2.19258e39 | 1.21241 | 0.606206 | − | 0.795308i | \(-0.292691\pi\) | ||||
0.606206 | + | 0.795308i | \(0.292691\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.76373e39 | 1.47813 | 0.739066 | − | 0.673633i | \(-0.235267\pi\) | ||||
0.739066 | + | 0.673633i | \(0.235267\pi\) | |||||||
\(812\) | − 1.27496e38i | − 0.0670640i | ||||||||
\(813\) | − 1.24873e39i | − 0.646022i | ||||||||
\(814\) | 5.80257e39 | 2.95251 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.68646e36 | −0.00329139 | ||||||||
\(817\) | 1.09968e39i | 0.532436i | ||||||||
\(818\) | − 4.17038e39i | − 1.98612i | ||||||||
\(819\) | −1.38352e38 | −0.0648118 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.42212e38 | −0.427087 | −0.213543 | − | 0.976934i | \(-0.568500\pi\) | ||||
−0.213543 | + | 0.976934i | \(0.568500\pi\) | |||||||
\(822\) | − 1.37294e39i | − 0.612183i | ||||||||
\(823\) | 2.17900e39i | 0.955782i | 0.878419 | + | 0.477891i | \(0.158599\pi\) | ||||
−0.878419 | + | 0.477891i | \(0.841401\pi\) | |||||||
\(824\) | 4.39208e39 | 1.89519 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.37569e39 | 1.40972 | ||||||||
\(827\) | 8.15484e38i | 0.335036i | 0.985869 | + | 0.167518i | \(0.0535752\pi\) | ||||
−0.985869 | + | 0.167518i | \(0.946425\pi\) | |||||||
\(828\) | 2.55317e39i | 1.03198i | ||||||||
\(829\) | −1.51577e39 | −0.602763 | −0.301382 | − | 0.953504i | \(-0.597448\pi\) | ||||
−0.301382 | + | 0.953504i | \(0.597448\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.84386e39 | −1.86457 | ||||||||
\(832\) | − 6.53260e38i | − 0.247412i | ||||||||
\(833\) | 1.47493e38i | 0.0549622i | ||||||||
\(834\) | 7.46823e39 | 2.73827 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.20911e39 | 2.55916 | ||||||||
\(837\) | − 1.06655e39i | − 0.372553i | ||||||||
\(838\) | 1.02528e39i | 0.352409i | ||||||||
\(839\) | −3.04177e39 | −1.02882 | −0.514410 | − | 0.857544i | \(-0.671989\pi\) | ||||
−0.514410 | + | 0.857544i | \(0.671989\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.04414e39 | −0.997055 | ||||||||
\(842\) | − 3.70077e39i | − 1.19283i | ||||||||
\(843\) | − 1.23726e39i | − 0.392453i | ||||||||
\(844\) | 3.24157e39 | 1.01189 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.43067e38 | 0.224661 | ||||||||
\(847\) | 5.83154e39i | 1.73523i | ||||||||
\(848\) | 1.90296e37i | 0.00557295i | ||||||||
\(849\) | −1.23603e39 | −0.356266 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.20513e39 | 1.17417 | ||||||||
\(852\) | 2.51408e39i | 0.690947i | ||||||||
\(853\) | − 9.78044e38i | − 0.264574i | −0.991211 | − | 0.132287i | \(-0.957768\pi\) | ||||
0.991211 | − | 0.132287i | \(-0.0422320\pi\) | |||||||
\(854\) | −5.42912e39 | −1.44560 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.00948e39 | 0.518427 | ||||||||
\(857\) | 6.93851e39i | 1.76208i | 0.473044 | + | 0.881039i | \(0.343155\pi\) | ||||
−0.473044 | + | 0.881039i | \(0.656845\pi\) | |||||||
\(858\) | − 2.21855e39i | − 0.554613i | ||||||||
\(859\) | 6.79141e39 | 1.67129 | 0.835646 | − | 0.549268i | \(-0.185093\pi\) | ||||
0.835646 | + | 0.549268i | \(0.185093\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.70689e39 | 0.884030 | ||||||||
\(862\) | − 9.26188e39i | − 2.17446i | ||||||||
\(863\) | − 5.27048e38i | − 0.121816i | −0.998143 | − | 0.0609080i | \(-0.980600\pi\) | ||||
0.998143 | − | 0.0609080i | \(-0.0193996\pi\) | |||||||
\(864\) | −2.48703e39 | −0.565908 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.85514e39 | −1.29136 | ||||||||
\(867\) | − 5.63600e39i | − 1.22381i | ||||||||
\(868\) | − 3.86596e39i | − 0.826497i | ||||||||
\(869\) | −9.63764e39 | −2.02863 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.36491e38 | 0.109476 | ||||||||
\(872\) | − 4.83527e39i | − 0.971512i | ||||||||
\(873\) | 1.59211e39i | 0.314978i | ||||||||
\(874\) | 8.47110e39 | 1.65019 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.82366e39 | −1.85553 | ||||||||
\(877\) | − 3.42049e39i | − 0.636200i | −0.948057 | − | 0.318100i | \(-0.896955\pi\) | ||||
0.948057 | − | 0.318100i | \(-0.103045\pi\) | |||||||
\(878\) | − 1.35260e40i | − 2.47739i | ||||||||
\(879\) | 1.20896e39 | 0.218053 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.31752e39 | −1.27994 | −0.639969 | − | 0.768401i | \(-0.721053\pi\) | ||||
−0.639969 | + | 0.768401i | \(0.721053\pi\) | |||||||
\(882\) | − 2.12689e39i | − 0.366370i | ||||||||
\(883\) | − 2.06213e39i | − 0.349821i | −0.984584 | − | 0.174910i | \(-0.944036\pi\) | ||||
0.984584 | − | 0.174910i | \(-0.0559636\pi\) | |||||||
\(884\) | −1.96969e38 | −0.0329074 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.43747e40 | 2.32940 | ||||||||
\(887\) | − 6.98969e39i | − 1.11555i | −0.829992 | − | 0.557775i | \(-0.811655\pi\) | ||||
0.829992 | − | 0.557775i | \(-0.188345\pi\) | |||||||
\(888\) | 7.89819e39i | 1.24152i | ||||||||
\(889\) | −5.30037e39 | −0.820602 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.49917e40 | −2.25166 | ||||||||
\(892\) | 2.25773e39i | 0.334000i | ||||||||
\(893\) | − 1.52051e39i | − 0.221561i | ||||||||
\(894\) | −1.74186e40 | −2.50009 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.83926e39 | −1.23100 | ||||||||
\(897\) | − 1.60778e39i | − 0.220561i | ||||||||
\(898\) | 1.22113e40i | 1.65018i | ||||||||
\(899\) | 2.72614e38 | 0.0362904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.93274e38 | 0.0378869 | ||||||||
\(902\) | 2.11656e40i | 2.69366i | ||||||||
\(903\) | − 4.61398e39i | − 0.578483i | ||||||||
\(904\) | 5.63122e39 | 0.695550 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.14514e39 | 0.496945 | ||||||||
\(907\) | 2.28488e39i | 0.269876i | 0.990854 | + | 0.134938i | \(0.0430835\pi\) | ||||
−0.990854 | + | 0.134938i | \(0.956916\pi\) | |||||||
\(908\) | 2.04108e40i | 2.37521i | ||||||||
\(909\) | 7.69751e39 | 0.882547 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.51662e39 | 0.836612 | 0.418306 | − | 0.908306i | \(-0.362624\pi\) | ||||
0.418306 | + | 0.908306i | \(0.362624\pi\) | |||||||
\(912\) | − 1.97302e38i | − 0.0216372i | ||||||||
\(913\) | 1.47737e40i | 1.59637i | ||||||||
\(914\) | 1.16227e40 | 1.23746 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.35353e40 | −1.39920 | ||||||||
\(917\) | 6.25683e39i | 0.637336i | ||||||||
\(918\) | 1.20128e39i | 0.120578i | ||||||||
\(919\) | −5.26405e39 | −0.520668 | −0.260334 | − | 0.965519i | \(-0.583833\pi\) | ||||
−0.260334 | + | 0.965519i | \(0.583833\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.32511e39 | 0.223326 | ||||||||
\(922\) | 1.91179e40i | 1.80956i | ||||||||
\(923\) | − 5.63724e38i | − 0.0525828i | ||||||||
\(924\) | −3.02477e40 | −2.78048 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.06488e40 | 1.84351 | ||||||||
\(927\) | − 1.21041e40i | − 1.06502i | ||||||||
\(928\) | − 6.35694e38i | − 0.0551252i | ||||||||
\(929\) | 2.48177e39 | 0.212104 | 0.106052 | − | 0.994361i | \(-0.466179\pi\) | ||||
0.106052 | + | 0.994361i | \(0.466179\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.35217e39 | −0.361314 | ||||||||
\(932\) | − 1.70049e40i | − 1.39143i | ||||||||
\(933\) | − 1.77807e40i | − 1.43399i | ||||||||
\(934\) | 1.62142e40 | 1.28888 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.07526e39 | 0.0830408 | ||||||||
\(937\) | 2.96211e39i | 0.225485i | 0.993624 | + | 0.112742i | \(0.0359635\pi\) | ||||
−0.993624 | + | 0.112742i | \(0.964037\pi\) | |||||||
\(938\) | − 1.18600e40i | − 0.889911i | ||||||||
\(939\) | −3.80877e39 | −0.281708 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.23582e40 | 0.888168 | 0.444084 | − | 0.895985i | \(-0.353529\pi\) | ||||
0.444084 | + | 0.895985i | \(0.353529\pi\) | |||||||
\(942\) | 4.74280e40i | 3.36006i | ||||||||
\(943\) | 1.53388e40i | 1.07123i | ||||||||
\(944\) | 3.25338e38 | 0.0223982 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.63449e40 | 1.76265 | ||||||||
\(947\) | − 3.62546e39i | − 0.239132i | −0.992826 | − | 0.119566i | \(-0.961850\pi\) | ||||
0.992826 | − | 0.119566i | \(-0.0381503\pi\) | |||||||
\(948\) | − 3.46525e40i | − 2.25332i | ||||||||
\(949\) | 2.20273e39 | 0.141210 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.26918e40 | 2.03705 | ||||||||
\(952\) | 1.64841e39i | 0.101266i | ||||||||
\(953\) | − 2.05559e40i | − 1.24504i | −0.782605 | − | 0.622519i | \(-0.786109\pi\) | ||||
0.782605 | − | 0.622519i | \(-0.213891\pi\) | |||||||
\(954\) | −4.22910e39 | −0.252548 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.22053e39 | −0.0708542 | ||||||||
\(957\) | − 2.13296e39i | − 0.122087i | ||||||||
\(958\) | 4.81585e40i | 2.71793i | ||||||||
\(959\) | 4.19722e39 | 0.233567 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.02164e40 | −0.552757 | ||||||||
\(962\) | − 4.67813e39i | − 0.249579i | ||||||||
\(963\) | − 5.53790e39i | − 0.291333i | ||||||||
\(964\) | 9.56665e39 | 0.496272 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.55427e40 | −1.79291 | ||||||||
\(967\) | 2.81961e40i | 1.40259i | 0.712871 | + | 0.701296i | \(0.247395\pi\) | ||||
−0.712871 | + | 0.701296i | \(0.752605\pi\) | |||||||
\(968\) | − 4.53223e40i | − 2.22328i | ||||||||
\(969\) | −3.04071e39 | −0.147097 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.81766e40 | −0.855170 | −0.427585 | − | 0.903975i | \(-0.640636\pi\) | ||||
−0.427585 | + | 0.903975i | \(0.640636\pi\) | |||||||
\(972\) | − 3.45830e40i | − 1.60461i | ||||||||
\(973\) | 2.28312e40i | 1.04473i | ||||||||
\(974\) | −4.28405e40 | −1.93334 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.23241e38 | −0.0229683 | ||||||||
\(977\) | − 2.03258e40i | − 0.879974i | −0.898004 | − | 0.439987i | \(-0.854983\pi\) | ||||
0.898004 | − | 0.439987i | \(-0.145017\pi\) | |||||||
\(978\) | 3.16622e40i | 1.35197i | ||||||||
\(979\) | 2.90863e40 | 1.22496 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.33255e40 | −0.545948 | ||||||||
\(982\) | 3.25830e40i | 1.31670i | ||||||||
\(983\) | 7.72807e39i | 0.308034i | 0.988068 | + | 0.154017i | \(0.0492210\pi\) | ||||
−0.988068 | + | 0.154017i | \(0.950779\pi\) | |||||||
\(984\) | −2.88096e40 | −1.13267 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.07052e38 | −0.0117455 | ||||||||
\(987\) | 6.37968e39i | 0.240723i | ||||||||
\(988\) | − 5.81210e39i | − 0.216329i | ||||||||
\(989\) | 1.90922e40 | 0.700981 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.25885e40 | 0.449758 | 0.224879 | − | 0.974387i | \(-0.427801\pi\) | ||||
0.224879 | + | 0.974387i | \(0.427801\pi\) | |||||||
\(992\) | − 1.92757e40i | − 0.679364i | ||||||||
\(993\) | 4.31368e40i | 1.49980i | ||||||||
\(994\) | −1.24620e40 | −0.427438 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.31193e40 | −1.77317 | ||||||||
\(997\) | − 4.50833e40i | − 1.48467i | −0.670028 | − | 0.742336i | \(-0.733718\pi\) | ||||
0.670028 | − | 0.742336i | \(-0.266282\pi\) | |||||||
\(998\) | − 5.24306e40i | − 1.70342i | ||||||||
\(999\) | −1.75962e40 | −0.564008 |
(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 | 25.28.b.a.24.4 | 4 | ||
5.2 | odd | 4 | 1.28.a.a.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 25.28.a.a.1.2 | 2 | |||
5.4 | even | 2 | inner | 25.28.b.a.24.1 | 4 | ||
15.2 | even | 4 | 9.28.a.d.1.2 | 2 | |||
20.7 | even | 4 | 16.28.a.d.1.2 | 2 | |||
35.27 | even | 4 | 49.28.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.28.a.a.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
9.28.a.d.1.2 | 2 | 15.2 | even | 4 | |||
16.28.a.d.1.2 | 2 | 20.7 | even | 4 | |||
25.28.a.a.1.2 | 2 | 5.3 | odd | 4 | |||
25.28.b.a.24.1 | 4 | 5.4 | even | 2 | inner | ||
25.28.b.a.24.4 | 4 | 1.1 | even | 1 | trivial | ||
49.28.a.b.1.1 | 2 | 35.27 | even | 4 |