Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,12,Mod(1,25)]
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([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(19.2085795140\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 24.0000 | 0.530330 | 0.265165 | − | 0.964203i | \(-0.414574\pi\) | ||||
0.265165 | + | 0.964203i | \(0.414574\pi\) | |||||||
\(3\) | −252.000 | −0.598734 | −0.299367 | − | 0.954138i | \(-0.596775\pi\) | ||||
−0.299367 | + | 0.954138i | \(0.596775\pi\) | |||||||
\(4\) | −1472.00 | −0.718750 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6048.00 | −0.317526 | ||||||||
\(7\) | 16744.0 | 0.376548 | 0.188274 | − | 0.982117i | \(-0.439711\pi\) | ||||
0.188274 | + | 0.982117i | \(0.439711\pi\) | |||||||
\(8\) | −84480.0 | −0.911505 | ||||||||
\(9\) | −113643. | −0.641518 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 534612. | 1.00087 | 0.500436 | − | 0.865773i | \(-0.333173\pi\) | ||||
0.500436 | + | 0.865773i | \(0.333173\pi\) | |||||||
\(12\) | 370944. | 0.430340 | ||||||||
\(13\) | 577738. | 0.431561 | 0.215781 | − | 0.976442i | \(-0.430770\pi\) | ||||
0.215781 | + | 0.976442i | \(0.430770\pi\) | |||||||
\(14\) | 401856. | 0.199695 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 987136. | 0.235352 | ||||||||
\(17\) | 6.90593e6 | 1.17965 | 0.589825 | − | 0.807531i | \(-0.299197\pi\) | ||||
0.589825 | + | 0.807531i | \(0.299197\pi\) | |||||||
\(18\) | −2.72743e6 | −0.340216 | ||||||||
\(19\) | 1.06614e7 | 0.987803 | 0.493901 | − | 0.869518i | \(-0.335570\pi\) | ||||
0.493901 | + | 0.869518i | \(0.335570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.21949e6 | −0.225452 | ||||||||
\(22\) | 1.28307e7 | 0.530793 | ||||||||
\(23\) | −1.86433e7 | −0.603975 | −0.301988 | − | 0.953312i | \(-0.597650\pi\) | ||||
−0.301988 | + | 0.953312i | \(0.597650\pi\) | |||||||
\(24\) | 2.12890e7 | 0.545749 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.38657e7 | 0.228870 | ||||||||
\(27\) | 7.32791e7 | 0.982832 | ||||||||
\(28\) | −2.46472e7 | −0.270644 | ||||||||
\(29\) | 1.28407e8 | 1.16251 | 0.581257 | − | 0.813720i | \(-0.302561\pi\) | ||||
0.581257 | + | 0.813720i | \(0.302561\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.28432e7 | −0.331512 | −0.165756 | − | 0.986167i | \(-0.553006\pi\) | ||||
−0.165756 | + | 0.986167i | \(0.553006\pi\) | |||||||
\(32\) | 1.96706e8 | 1.03632 | ||||||||
\(33\) | −1.34722e8 | −0.599256 | ||||||||
\(34\) | 1.65742e8 | 0.625604 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.67282e8 | 0.461091 | ||||||||
\(37\) | 1.82213e8 | 0.431987 | 0.215993 | − | 0.976395i | \(-0.430701\pi\) | ||||
0.215993 | + | 0.976395i | \(0.430701\pi\) | |||||||
\(38\) | 2.55874e8 | 0.523862 | ||||||||
\(39\) | −1.45590e8 | −0.258390 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.08120e8 | 0.415345 | 0.207673 | − | 0.978198i | \(-0.433411\pi\) | ||||
0.207673 | + | 0.978198i | \(0.433411\pi\) | |||||||
\(42\) | −1.01268e8 | −0.119564 | ||||||||
\(43\) | 1.71257e7 | 0.0177653 | 0.00888264 | − | 0.999961i | \(-0.497173\pi\) | ||||
0.00888264 | + | 0.999961i | \(0.497173\pi\) | |||||||
\(44\) | −7.86949e8 | −0.719377 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.47439e8 | −0.320306 | ||||||||
\(47\) | −2.68735e9 | −1.70917 | −0.854586 | − | 0.519310i | \(-0.826189\pi\) | ||||
−0.854586 | + | 0.519310i | \(0.826189\pi\) | |||||||
\(48\) | −2.48758e8 | −0.140913 | ||||||||
\(49\) | −1.69697e9 | −0.858212 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.74030e9 | −0.706296 | ||||||||
\(52\) | −8.50430e8 | −0.310185 | ||||||||
\(53\) | 1.59606e9 | 0.524241 | 0.262120 | − | 0.965035i | \(-0.415578\pi\) | ||||
0.262120 | + | 0.965035i | \(0.415578\pi\) | |||||||
\(54\) | 1.75870e9 | 0.521225 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.41453e9 | −0.343225 | ||||||||
\(57\) | −2.68668e9 | −0.591431 | ||||||||
\(58\) | 3.08176e9 | 0.616517 | ||||||||
\(59\) | −5.18920e9 | −0.944963 | −0.472481 | − | 0.881341i | \(-0.656642\pi\) | ||||
−0.472481 | + | 0.881341i | \(0.656642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.95648e9 | 1.05457 | 0.527285 | − | 0.849689i | \(-0.323210\pi\) | ||||
0.527285 | + | 0.849689i | \(0.323210\pi\) | |||||||
\(62\) | −1.26824e9 | −0.175811 | ||||||||
\(63\) | −1.90284e9 | −0.241562 | ||||||||
\(64\) | 2.69930e9 | 0.314240 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.23333e9 | −0.317804 | ||||||||
\(67\) | 1.54818e10 | 1.40091 | 0.700456 | − | 0.713696i | \(-0.252980\pi\) | ||||
0.700456 | + | 0.713696i | \(0.252980\pi\) | |||||||
\(68\) | −1.01655e10 | −0.847874 | ||||||||
\(69\) | 4.69810e9 | 0.361620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.79149e9 | 0.644062 | 0.322031 | − | 0.946729i | \(-0.395634\pi\) | ||||
0.322031 | + | 0.946729i | \(0.395634\pi\) | |||||||
\(72\) | 9.60056e9 | 0.584747 | ||||||||
\(73\) | −1.46379e9 | −0.0826425 | −0.0413212 | − | 0.999146i | \(-0.513157\pi\) | ||||
−0.0413212 | + | 0.999146i | \(0.513157\pi\) | |||||||
\(74\) | 4.37312e9 | 0.229096 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.56936e10 | −0.709983 | ||||||||
\(77\) | 8.95154e9 | 0.376876 | ||||||||
\(78\) | −3.49416e9 | −0.137032 | ||||||||
\(79\) | 3.81168e10 | 1.39370 | 0.696848 | − | 0.717219i | \(-0.254585\pi\) | ||||
0.696848 | + | 0.717219i | \(0.254585\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.66519e9 | 0.0530635 | ||||||||
\(82\) | 7.39489e9 | 0.220270 | ||||||||
\(83\) | 2.93351e10 | 0.817444 | 0.408722 | − | 0.912659i | \(-0.365975\pi\) | ||||
0.408722 | + | 0.912659i | \(0.365975\pi\) | |||||||
\(84\) | 6.21109e9 | 0.162043 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.11017e8 | 0.00942146 | ||||||||
\(87\) | −3.23585e10 | −0.696037 | ||||||||
\(88\) | −4.51640e10 | −0.912300 | ||||||||
\(89\) | −2.49929e10 | −0.474430 | −0.237215 | − | 0.971457i | \(-0.576235\pi\) | ||||
−0.237215 | + | 0.971457i | \(0.576235\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.67365e9 | 0.162503 | ||||||||
\(92\) | 2.74429e10 | 0.434107 | ||||||||
\(93\) | 1.33165e10 | 0.198488 | ||||||||
\(94\) | −6.44964e10 | −0.906425 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.95700e10 | −0.620479 | ||||||||
\(97\) | −7.50136e10 | −0.886942 | −0.443471 | − | 0.896289i | \(-0.646253\pi\) | ||||
−0.443471 | + | 0.896289i | \(0.646253\pi\) | |||||||
\(98\) | −4.07272e10 | −0.455136 | ||||||||
\(99\) | −6.07549e10 | −0.642078 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.17430e10 | 0.773896 | 0.386948 | − | 0.922101i | \(-0.373529\pi\) | ||||
0.386948 | + | 0.922101i | \(0.373529\pi\) | |||||||
\(102\) | −4.17671e10 | −0.374570 | ||||||||
\(103\) | 2.25755e11 | 1.91881 | 0.959407 | − | 0.282025i | \(-0.0910061\pi\) | ||||
0.959407 | + | 0.282025i | \(0.0910061\pi\) | |||||||
\(104\) | −4.88073e10 | −0.393370 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.83053e10 | 0.278021 | ||||||||
\(107\) | −9.02413e10 | −0.622006 | −0.311003 | − | 0.950409i | \(-0.600665\pi\) | ||||
−0.311003 | + | 0.950409i | \(0.600665\pi\) | |||||||
\(108\) | −1.07867e11 | −0.706411 | ||||||||
\(109\) | 7.34827e10 | 0.457445 | 0.228723 | − | 0.973492i | \(-0.426545\pi\) | ||||
0.228723 | + | 0.973492i | \(0.426545\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.59178e10 | −0.258645 | ||||||||
\(112\) | 1.65286e10 | 0.0886211 | ||||||||
\(113\) | 8.51469e10 | 0.434748 | 0.217374 | − | 0.976088i | \(-0.430251\pi\) | ||||
0.217374 | + | 0.976088i | \(0.430251\pi\) | |||||||
\(114\) | −6.44803e10 | −0.313654 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.89015e11 | −0.835557 | ||||||||
\(117\) | −6.56559e10 | −0.276854 | ||||||||
\(118\) | −1.24541e11 | −0.501142 | ||||||||
\(119\) | 1.15633e11 | 0.444195 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.98320e8 | 0.00174658 | ||||||||
\(122\) | 1.66955e11 | 0.559270 | ||||||||
\(123\) | −7.76464e10 | −0.248681 | ||||||||
\(124\) | 7.77851e10 | 0.238274 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.56681e10 | −0.128108 | ||||||||
\(127\) | 2.62717e11 | 0.705615 | 0.352808 | − | 0.935696i | \(-0.385227\pi\) | ||||
0.352808 | + | 0.935696i | \(0.385227\pi\) | |||||||
\(128\) | −3.38071e11 | −0.869668 | ||||||||
\(129\) | −4.31568e9 | −0.0106367 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.31529e11 | 1.43021 | 0.715107 | − | 0.699015i | \(-0.246378\pi\) | ||||
0.715107 | + | 0.699015i | \(0.246378\pi\) | |||||||
\(132\) | 1.98311e11 | 0.430715 | ||||||||
\(133\) | 1.78515e11 | 0.371955 | ||||||||
\(134\) | 3.71564e11 | 0.742946 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.83413e11 | −1.07526 | ||||||||
\(137\) | 2.97199e11 | 0.526119 | 0.263059 | − | 0.964780i | \(-0.415268\pi\) | ||||
0.263059 | + | 0.964780i | \(0.415268\pi\) | |||||||
\(138\) | 1.12755e11 | 0.191778 | ||||||||
\(139\) | 5.96794e11 | 0.975535 | 0.487767 | − | 0.872974i | \(-0.337811\pi\) | ||||
0.487767 | + | 0.872974i | \(0.337811\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.77212e11 | 1.02334 | ||||||||
\(142\) | 2.34996e11 | 0.341565 | ||||||||
\(143\) | 3.08866e11 | 0.431938 | ||||||||
\(144\) | −1.12181e11 | −0.150982 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.51310e10 | −0.0438278 | ||||||||
\(147\) | 4.27635e11 | 0.513840 | ||||||||
\(148\) | −2.68218e11 | −0.310491 | ||||||||
\(149\) | −1.11543e12 | −1.24428 | −0.622142 | − | 0.782905i | \(-0.713737\pi\) | ||||
−0.622142 | + | 0.782905i | \(0.713737\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.24447e11 | −0.854653 | −0.427326 | − | 0.904097i | \(-0.640544\pi\) | ||||
−0.427326 | + | 0.904097i | \(0.640544\pi\) | |||||||
\(152\) | −9.00677e11 | −0.900387 | ||||||||
\(153\) | −7.84811e11 | −0.756767 | ||||||||
\(154\) | 2.14837e11 | 0.199869 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.14308e11 | 0.185718 | ||||||||
\(157\) | −1.31512e12 | −1.10031 | −0.550156 | − | 0.835062i | \(-0.685432\pi\) | ||||
−0.550156 | + | 0.835062i | \(0.685432\pi\) | |||||||
\(158\) | 9.14804e11 | 0.739119 | ||||||||
\(159\) | −4.02206e11 | −0.313881 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.12163e11 | −0.227425 | ||||||||
\(162\) | 3.99645e10 | 0.0281412 | ||||||||
\(163\) | 3.57833e11 | 0.243584 | 0.121792 | − | 0.992556i | \(-0.461136\pi\) | ||||
0.121792 | + | 0.992556i | \(0.461136\pi\) | |||||||
\(164\) | −4.53553e11 | −0.298529 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.04042e11 | 0.433515 | ||||||||
\(167\) | −2.75483e12 | −1.64117 | −0.820587 | − | 0.571521i | \(-0.806354\pi\) | ||||
−0.820587 | + | 0.571521i | \(0.806354\pi\) | |||||||
\(168\) | 3.56462e11 | 0.205500 | ||||||||
\(169\) | −1.45838e12 | −0.813755 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.21160e12 | −0.633693 | ||||||||
\(172\) | −2.52090e10 | −0.0127688 | ||||||||
\(173\) | 9.50387e11 | 0.466280 | 0.233140 | − | 0.972443i | \(-0.425100\pi\) | ||||
0.233140 | + | 0.972443i | \(0.425100\pi\) | |||||||
\(174\) | −7.76603e11 | −0.369129 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.27735e11 | 0.235557 | ||||||||
\(177\) | 1.30768e12 | 0.565781 | ||||||||
\(178\) | −5.99830e11 | −0.251604 | ||||||||
\(179\) | 1.68138e12 | 0.683873 | 0.341936 | − | 0.939723i | \(-0.388917\pi\) | ||||
0.341936 | + | 0.939723i | \(0.388917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.96774e11 | −0.381386 | −0.190693 | − | 0.981650i | \(-0.561073\pi\) | ||||
−0.190693 | + | 0.981650i | \(0.561073\pi\) | |||||||
\(182\) | 2.32167e11 | 0.0861804 | ||||||||
\(183\) | −1.75303e12 | −0.631406 | ||||||||
\(184\) | 1.57498e12 | 0.550526 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.19595e11 | 0.105264 | ||||||||
\(187\) | 3.69200e12 | 1.18068 | ||||||||
\(188\) | 3.95578e12 | 1.22847 | ||||||||
\(189\) | 1.22698e12 | 0.370083 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.76240e12 | 0.786328 | 0.393164 | − | 0.919468i | \(-0.371381\pi\) | ||||
0.393164 | + | 0.919468i | \(0.371381\pi\) | |||||||
\(192\) | −6.80223e11 | −0.188146 | ||||||||
\(193\) | −5.44239e12 | −1.46293 | −0.731466 | − | 0.681878i | \(-0.761164\pi\) | ||||
−0.731466 | + | 0.681878i | \(0.761164\pi\) | |||||||
\(194\) | −1.80033e12 | −0.470372 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.49793e12 | 0.616840 | ||||||||
\(197\) | 2.87609e12 | 0.690619 | 0.345309 | − | 0.938489i | \(-0.387774\pi\) | ||||
0.345309 | + | 0.938489i | \(0.387774\pi\) | |||||||
\(198\) | −1.45812e12 | −0.340513 | ||||||||
\(199\) | 7.28391e11 | 0.165452 | 0.0827262 | − | 0.996572i | \(-0.473637\pi\) | ||||
0.0827262 | + | 0.996572i | \(0.473637\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.90142e12 | −0.838773 | ||||||||
\(202\) | 1.96183e12 | 0.410421 | ||||||||
\(203\) | 2.15004e12 | 0.437742 | ||||||||
\(204\) | 2.56171e12 | 0.507651 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.41812e12 | 1.01760 | ||||||||
\(207\) | 2.11868e12 | 0.387461 | ||||||||
\(208\) | 5.70306e11 | 0.101569 | ||||||||
\(209\) | 5.69972e12 | 0.988665 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.79317e12 | −1.11820 | −0.559099 | − | 0.829101i | \(-0.688853\pi\) | ||||
−0.559099 | + | 0.829101i | \(0.688853\pi\) | |||||||
\(212\) | −2.34939e12 | −0.376798 | ||||||||
\(213\) | −2.46745e12 | −0.385622 | ||||||||
\(214\) | −2.16579e12 | −0.329868 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.19062e12 | −0.895856 | ||||||||
\(217\) | −8.84806e11 | −0.124830 | ||||||||
\(218\) | 1.76358e12 | 0.242597 | ||||||||
\(219\) | 3.68875e11 | 0.0494808 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.98982e12 | 0.509092 | ||||||||
\(222\) | −1.10203e12 | −0.137167 | ||||||||
\(223\) | −7.33486e12 | −0.890667 | −0.445333 | − | 0.895365i | \(-0.646915\pi\) | ||||
−0.445333 | + | 0.895365i | \(0.646915\pi\) | |||||||
\(224\) | 3.29365e12 | 0.390223 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.04352e12 | 0.230560 | ||||||||
\(227\) | 1.35984e12 | 0.149743 | 0.0748713 | − | 0.997193i | \(-0.476145\pi\) | ||||
0.0748713 | + | 0.997193i | \(0.476145\pi\) | |||||||
\(228\) | 3.95479e12 | 0.425091 | ||||||||
\(229\) | −1.18244e13 | −1.24075 | −0.620375 | − | 0.784305i | \(-0.713020\pi\) | ||||
−0.620375 | + | 0.784305i | \(0.713020\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.25579e12 | −0.225649 | ||||||||
\(232\) | −1.08478e13 | −1.05964 | ||||||||
\(233\) | 1.75634e13 | 1.67552 | 0.837761 | − | 0.546038i | \(-0.183865\pi\) | ||||
0.837761 | + | 0.546038i | \(0.183865\pi\) | |||||||
\(234\) | −1.57574e12 | −0.146824 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.63851e12 | 0.679192 | ||||||||
\(237\) | −9.60545e12 | −0.834452 | ||||||||
\(238\) | 2.77519e12 | 0.235570 | ||||||||
\(239\) | −7.13958e12 | −0.592221 | −0.296111 | − | 0.955154i | \(-0.595690\pi\) | ||||
−0.296111 | + | 0.955154i | \(0.595690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.31307e11 | −0.0183271 | −0.00916357 | − | 0.999958i | \(-0.502917\pi\) | ||||
−0.00916357 | + | 0.999958i | \(0.502917\pi\) | |||||||
\(242\) | 1.19597e10 | 0.000926264 0 | ||||||||
\(243\) | −1.34008e13 | −1.01460 | ||||||||
\(244\) | −1.02399e13 | −0.757972 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.86351e12 | −0.131883 | ||||||||
\(247\) | 6.15951e12 | 0.426297 | ||||||||
\(248\) | 4.46419e12 | 0.302175 | ||||||||
\(249\) | −7.39245e12 | −0.489431 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.29831e13 | 0.822567 | 0.411284 | − | 0.911507i | \(-0.365081\pi\) | ||||
0.411284 | + | 0.911507i | \(0.365081\pi\) | |||||||
\(252\) | 2.80098e12 | 0.173623 | ||||||||
\(253\) | −9.96692e12 | −0.604502 | ||||||||
\(254\) | 6.30521e12 | 0.374209 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.36419e13 | −0.775451 | ||||||||
\(257\) | −2.39612e13 | −1.33314 | −0.666571 | − | 0.745442i | \(-0.732239\pi\) | ||||
−0.666571 | + | 0.745442i | \(0.732239\pi\) | |||||||
\(258\) | −1.03576e11 | −0.00564095 | ||||||||
\(259\) | 3.05098e12 | 0.162664 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.45925e13 | −0.745774 | ||||||||
\(262\) | 1.51567e13 | 0.758485 | ||||||||
\(263\) | 2.42737e13 | 1.18954 | 0.594771 | − | 0.803895i | \(-0.297243\pi\) | ||||
0.594771 | + | 0.803895i | \(0.297243\pi\) | |||||||
\(264\) | 1.13813e13 | 0.546225 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.28436e12 | 0.197259 | ||||||||
\(267\) | 6.29822e12 | 0.284057 | ||||||||
\(268\) | −2.27892e13 | −1.00691 | ||||||||
\(269\) | 2.58377e13 | 1.11845 | 0.559225 | − | 0.829016i | \(-0.311099\pi\) | ||||
0.559225 | + | 0.829016i | \(0.311099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.76793e12 | −0.156593 | −0.0782964 | − | 0.996930i | \(-0.524948\pi\) | ||||
−0.0782964 | + | 0.996930i | \(0.524948\pi\) | |||||||
\(272\) | 6.81710e12 | 0.277633 | ||||||||
\(273\) | −2.43776e12 | −0.0972963 | ||||||||
\(274\) | 7.13277e12 | 0.279017 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.91561e12 | −0.259915 | ||||||||
\(277\) | 1.64189e13 | 0.604931 | 0.302466 | − | 0.953160i | \(-0.402190\pi\) | ||||
0.302466 | + | 0.953160i | \(0.402190\pi\) | |||||||
\(278\) | 1.43230e13 | 0.517355 | ||||||||
\(279\) | 6.00526e12 | 0.212671 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.10357e13 | 0.716263 | 0.358132 | − | 0.933671i | \(-0.383414\pi\) | ||||
0.358132 | + | 0.933671i | \(0.383414\pi\) | |||||||
\(282\) | 1.62531e13 | 0.542707 | ||||||||
\(283\) | −1.67132e13 | −0.547310 | −0.273655 | − | 0.961828i | \(-0.588233\pi\) | ||||
−0.273655 | + | 0.961828i | \(0.588233\pi\) | |||||||
\(284\) | −1.44131e13 | −0.462920 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.41278e12 | 0.229070 | ||||||||
\(287\) | 5.15917e12 | 0.156397 | ||||||||
\(288\) | −2.23543e13 | −0.664817 | ||||||||
\(289\) | 1.34200e13 | 0.391575 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.89034e13 | 0.531042 | ||||||||
\(292\) | 2.15470e12 | 0.0593993 | ||||||||
\(293\) | 2.39269e13 | 0.647312 | 0.323656 | − | 0.946175i | \(-0.395088\pi\) | ||||
0.323656 | + | 0.946175i | \(0.395088\pi\) | |||||||
\(294\) | 1.02632e13 | 0.272505 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.53934e13 | −0.393758 | ||||||||
\(297\) | 3.91759e13 | 0.983690 | ||||||||
\(298\) | −2.67704e13 | −0.659881 | ||||||||
\(299\) | −1.07709e13 | −0.260652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.86753e11 | 0.00668947 | ||||||||
\(302\) | −1.97867e13 | −0.453248 | ||||||||
\(303\) | −2.05992e13 | −0.463358 | ||||||||
\(304\) | 1.05243e13 | 0.232481 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.88355e13 | −0.401336 | ||||||||
\(307\) | −1.53111e13 | −0.320439 | −0.160219 | − | 0.987081i | \(-0.551220\pi\) | ||||
−0.160219 | + | 0.987081i | \(0.551220\pi\) | |||||||
\(308\) | −1.31767e13 | −0.270880 | ||||||||
\(309\) | −5.68903e13 | −1.14886 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.98752e13 | 0.972080 | 0.486040 | − | 0.873936i | \(-0.338441\pi\) | ||||
0.486040 | + | 0.873936i | \(0.338441\pi\) | |||||||
\(312\) | 1.22994e13 | 0.235524 | ||||||||
\(313\) | 9.94808e13 | 1.87174 | 0.935870 | − | 0.352345i | \(-0.114616\pi\) | ||||
0.935870 | + | 0.352345i | \(0.114616\pi\) | |||||||
\(314\) | −3.15628e13 | −0.583529 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.61080e13 | −1.00172 | ||||||||
\(317\) | −8.33692e13 | −1.46278 | −0.731392 | − | 0.681958i | \(-0.761129\pi\) | ||||
−0.731392 | + | 0.681958i | \(0.761129\pi\) | |||||||
\(318\) | −9.65294e12 | −0.166460 | ||||||||
\(319\) | 6.86477e13 | 1.16353 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.27408e13 | 0.372416 | ||||||||
\(322\) | −7.49191e12 | −0.120611 | ||||||||
\(323\) | 7.36271e13 | 1.16526 | ||||||||
\(324\) | −2.45116e12 | −0.0381394 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.58799e12 | 0.129180 | ||||||||
\(327\) | −1.85176e13 | −0.273888 | ||||||||
\(328\) | −2.60300e13 | −0.378589 | ||||||||
\(329\) | −4.49970e13 | −0.643585 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.35840e13 | −0.879618 | −0.439809 | − | 0.898091i | \(-0.644954\pi\) | ||||
−0.439809 | + | 0.898091i | \(0.644954\pi\) | |||||||
\(332\) | −4.31813e13 | −0.587538 | ||||||||
\(333\) | −2.07073e13 | −0.277127 | ||||||||
\(334\) | −6.61160e13 | −0.870364 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.16521e12 | −0.0530604 | ||||||||
\(337\) | −1.21001e14 | −1.51644 | −0.758221 | − | 0.651997i | \(-0.773931\pi\) | ||||
−0.758221 | + | 0.651997i | \(0.773931\pi\) | |||||||
\(338\) | −3.50011e13 | −0.431559 | ||||||||
\(339\) | −2.14570e13 | −0.260298 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.82506e13 | −0.331802 | ||||||||
\(342\) | −2.90783e13 | −0.336067 | ||||||||
\(343\) | −6.15223e13 | −0.699705 | ||||||||
\(344\) | −1.44678e12 | −0.0161931 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.28093e13 | 0.247283 | ||||||||
\(347\) | 1.55662e14 | 1.66100 | 0.830499 | − | 0.557020i | \(-0.188055\pi\) | ||||
0.830499 | + | 0.557020i | \(0.188055\pi\) | |||||||
\(348\) | 4.76317e13 | 0.500276 | ||||||||
\(349\) | −2.56430e13 | −0.265112 | −0.132556 | − | 0.991176i | \(-0.542318\pi\) | ||||
−0.132556 | + | 0.991176i | \(0.542318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.23361e13 | 0.424152 | ||||||||
\(352\) | 1.05162e14 | 1.03722 | ||||||||
\(353\) | −2.49098e13 | −0.241885 | −0.120943 | − | 0.992659i | \(-0.538592\pi\) | ||||
−0.120943 | + | 0.992659i | \(0.538592\pi\) | |||||||
\(354\) | 3.13843e13 | 0.300051 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.67896e13 | 0.340996 | ||||||||
\(357\) | −2.91395e13 | −0.265954 | ||||||||
\(358\) | 4.03532e13 | 0.362678 | ||||||||
\(359\) | 1.57584e14 | 1.39474 | 0.697370 | − | 0.716712i | \(-0.254354\pi\) | ||||
0.697370 | + | 0.716712i | \(0.254354\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.82438e12 | −0.0242457 | ||||||||
\(362\) | −2.39226e13 | −0.202260 | ||||||||
\(363\) | −1.25577e11 | −0.00104574 | ||||||||
\(364\) | −1.42396e13 | −0.116799 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.20728e13 | −0.334854 | ||||||||
\(367\) | 1.77901e14 | 1.39481 | 0.697406 | − | 0.716676i | \(-0.254338\pi\) | ||||
0.697406 | + | 0.716676i | \(0.254338\pi\) | |||||||
\(368\) | −1.84034e13 | −0.142146 | ||||||||
\(369\) | −3.50157e13 | −0.266452 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.67244e13 | 0.197402 | ||||||||
\(372\) | −1.96019e13 | −0.142663 | ||||||||
\(373\) | 5.51617e13 | 0.395585 | 0.197792 | − | 0.980244i | \(-0.436623\pi\) | ||||
0.197792 | + | 0.980244i | \(0.436623\pi\) | |||||||
\(374\) | 8.86079e13 | 0.626150 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.27027e14 | 1.55792 | ||||||||
\(377\) | 7.41854e13 | 0.501696 | ||||||||
\(378\) | 2.94476e13 | 0.196266 | ||||||||
\(379\) | 1.46463e14 | 0.962083 | 0.481042 | − | 0.876698i | \(-0.340259\pi\) | ||||
0.481042 | + | 0.876698i | \(0.340259\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.62047e13 | −0.422476 | ||||||||
\(382\) | 6.62977e13 | 0.417013 | ||||||||
\(383\) | −2.31450e14 | −1.43504 | −0.717519 | − | 0.696539i | \(-0.754722\pi\) | ||||
−0.717519 | + | 0.696539i | \(0.754722\pi\) | |||||||
\(384\) | 8.51940e13 | 0.520700 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.30617e14 | −0.775837 | ||||||||
\(387\) | −1.94622e12 | −0.0113967 | ||||||||
\(388\) | 1.10420e14 | 0.637490 | ||||||||
\(389\) | −1.49872e14 | −0.853093 | −0.426547 | − | 0.904466i | \(-0.640270\pi\) | ||||
−0.426547 | + | 0.904466i | \(0.640270\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.28749e14 | −0.712480 | ||||||||
\(392\) | 1.43360e14 | 0.782264 | ||||||||
\(393\) | −1.59145e14 | −0.856317 | ||||||||
\(394\) | 6.90262e13 | 0.366256 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.94312e13 | 0.461494 | ||||||||
\(397\) | −2.08111e14 | −1.05912 | −0.529562 | − | 0.848271i | \(-0.677644\pi\) | ||||
−0.529562 | + | 0.848271i | \(0.677644\pi\) | |||||||
\(398\) | 1.74814e13 | 0.0877443 | ||||||||
\(399\) | −4.49857e13 | −0.222702 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.33408e14 | −0.642521 | −0.321261 | − | 0.946991i | \(-0.604107\pi\) | ||||
−0.321261 | + | 0.946991i | \(0.604107\pi\) | |||||||
\(402\) | −9.36341e13 | −0.444827 | ||||||||
\(403\) | −3.05295e13 | −0.143068 | ||||||||
\(404\) | −1.20326e14 | −0.556238 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.16010e13 | 0.232148 | ||||||||
\(407\) | 9.74134e13 | 0.432364 | ||||||||
\(408\) | 1.47020e14 | 0.643793 | ||||||||
\(409\) | −2.06168e14 | −0.890722 | −0.445361 | − | 0.895351i | \(-0.646925\pi\) | ||||
−0.445361 | + | 0.895351i | \(0.646925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.48941e13 | −0.315005 | ||||||||
\(412\) | −3.32312e14 | −1.37915 | ||||||||
\(413\) | −8.68880e13 | −0.355824 | ||||||||
\(414\) | 5.08483e13 | 0.205482 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.13645e14 | 0.447235 | ||||||||
\(417\) | −1.50392e14 | −0.584085 | ||||||||
\(418\) | 1.36793e14 | 0.524319 | ||||||||
\(419\) | 7.34035e13 | 0.277677 | 0.138838 | − | 0.990315i | \(-0.455663\pi\) | ||||
0.138838 | + | 0.990315i | \(0.455663\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.71112e14 | 0.630563 | 0.315282 | − | 0.948998i | \(-0.397901\pi\) | ||||
0.315282 | + | 0.948998i | \(0.397901\pi\) | |||||||
\(422\) | −1.63036e14 | −0.593014 | ||||||||
\(423\) | 3.05398e14 | 1.09646 | ||||||||
\(424\) | −1.34835e14 | −0.477848 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.92189e13 | −0.204507 | ||||||||
\(427\) | 1.16479e14 | 0.397096 | ||||||||
\(428\) | 1.32835e14 | 0.447067 | ||||||||
\(429\) | −7.78341e13 | −0.258616 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.17758e13 | −0.232463 | −0.116231 | − | 0.993222i | \(-0.537081\pi\) | ||||
−0.116231 | + | 0.993222i | \(0.537081\pi\) | |||||||
\(432\) | 7.23364e13 | 0.231311 | ||||||||
\(433\) | −9.98812e13 | −0.315356 | −0.157678 | − | 0.987491i | \(-0.550401\pi\) | ||||
−0.157678 | + | 0.987491i | \(0.550401\pi\) | |||||||
\(434\) | −2.12353e13 | −0.0662012 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.08166e14 | −0.328789 | ||||||||
\(437\) | −1.98764e14 | −0.596608 | ||||||||
\(438\) | 8.85301e12 | 0.0262412 | ||||||||
\(439\) | −2.90312e13 | −0.0849788 | −0.0424894 | − | 0.999097i | \(-0.513529\pi\) | ||||
−0.0424894 | + | 0.999097i | \(0.513529\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.92848e14 | 0.550558 | ||||||||
\(442\) | 9.57557e13 | 0.269987 | ||||||||
\(443\) | −3.28370e14 | −0.914414 | −0.457207 | − | 0.889360i | \(-0.651150\pi\) | ||||
−0.457207 | + | 0.889360i | \(0.651150\pi\) | |||||||
\(444\) | 6.75909e13 | 0.185901 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.76037e14 | −0.472347 | ||||||||
\(447\) | 2.81089e14 | 0.744994 | ||||||||
\(448\) | 4.51970e13 | 0.118326 | ||||||||
\(449\) | −6.12368e14 | −1.58364 | −0.791822 | − | 0.610752i | \(-0.790867\pi\) | ||||
−0.791822 | + | 0.610752i | \(0.790867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.64725e14 | 0.415708 | ||||||||
\(452\) | −1.25336e14 | −0.312475 | ||||||||
\(453\) | 2.07761e14 | 0.511709 | ||||||||
\(454\) | 3.26361e13 | 0.0794130 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.26971e14 | 0.539092 | ||||||||
\(457\) | −3.03483e14 | −0.712189 | −0.356095 | − | 0.934450i | \(-0.615892\pi\) | ||||
−0.356095 | + | 0.934450i | \(0.615892\pi\) | |||||||
\(458\) | −2.83786e14 | −0.658007 | ||||||||
\(459\) | 5.06060e14 | 1.15940 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.29308e14 | −1.63138 | −0.815691 | − | 0.578487i | \(-0.803643\pi\) | ||||
−0.815691 | + | 0.578487i | \(0.803643\pi\) | |||||||
\(462\) | −5.41389e13 | −0.119668 | ||||||||
\(463\) | −1.22188e14 | −0.266891 | −0.133445 | − | 0.991056i | \(-0.542604\pi\) | ||||
−0.133445 | + | 0.991056i | \(0.542604\pi\) | |||||||
\(464\) | 1.26755e14 | 0.273600 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.21520e14 | 0.888579 | ||||||||
\(467\) | 6.17381e14 | 1.28621 | 0.643103 | − | 0.765780i | \(-0.277647\pi\) | ||||
0.643103 | + | 0.765780i | \(0.277647\pi\) | |||||||
\(468\) | 9.66455e13 | 0.198989 | ||||||||
\(469\) | 2.59228e14 | 0.527510 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.31409e14 | 0.658794 | ||||||||
\(472\) | 4.38384e14 | 0.861338 | ||||||||
\(473\) | 9.15561e12 | 0.0177808 | ||||||||
\(474\) | −2.30531e14 | −0.442535 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.70212e14 | −0.319265 | ||||||||
\(477\) | −1.81381e14 | −0.336310 | ||||||||
\(478\) | −1.71350e14 | −0.314073 | ||||||||
\(479\) | 1.05084e15 | 1.90410 | 0.952052 | − | 0.305938i | \(-0.0989700\pi\) | ||||
0.952052 | + | 0.305938i | \(0.0989700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.05272e14 | 0.186429 | ||||||||
\(482\) | −5.55137e12 | −0.00971944 | ||||||||
\(483\) | 7.86651e13 | 0.136167 | ||||||||
\(484\) | −7.33527e11 | −0.00125536 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.21619e14 | −0.538074 | ||||||||
\(487\) | 2.19910e14 | 0.363777 | 0.181889 | − | 0.983319i | \(-0.441779\pi\) | ||||
0.181889 | + | 0.983319i | \(0.441779\pi\) | |||||||
\(488\) | −5.87683e14 | −0.961246 | ||||||||
\(489\) | −9.01739e13 | −0.145842 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.83863e14 | −0.765199 | −0.382599 | − | 0.923914i | \(-0.624971\pi\) | ||||
−0.382599 | + | 0.923914i | \(0.624971\pi\) | |||||||
\(492\) | 1.14295e14 | 0.178740 | ||||||||
\(493\) | 8.86768e14 | 1.37136 | ||||||||
\(494\) | 1.47828e14 | 0.226078 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.21634e13 | −0.0780219 | ||||||||
\(497\) | 1.63949e14 | 0.242520 | ||||||||
\(498\) | −1.77419e14 | −0.259560 | ||||||||
\(499\) | −1.08878e14 | −0.157538 | −0.0787691 | − | 0.996893i | \(-0.525099\pi\) | ||||
−0.0787691 | + | 0.996893i | \(0.525099\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.94218e14 | 0.982626 | ||||||||
\(502\) | 3.11593e14 | 0.436232 | ||||||||
\(503\) | −5.06588e14 | −0.701506 | −0.350753 | − | 0.936468i | \(-0.614074\pi\) | ||||
−0.350753 | + | 0.936468i | \(0.614074\pi\) | |||||||
\(504\) | 1.60752e14 | 0.220185 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.39206e14 | −0.320586 | ||||||||
\(507\) | 3.67512e14 | 0.487222 | ||||||||
\(508\) | −3.86720e14 | −0.507161 | ||||||||
\(509\) | 8.57534e13 | 0.111251 | 0.0556254 | − | 0.998452i | \(-0.482285\pi\) | ||||
0.0556254 | + | 0.998452i | \(0.482285\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.45097e13 | −0.0311188 | ||||||||
\(512\) | 3.64965e14 | 0.458423 | ||||||||
\(513\) | 7.81259e14 | 0.970844 | ||||||||
\(514\) | −5.75069e14 | −0.707005 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.35268e12 | 0.00764511 | ||||||||
\(517\) | −1.43669e15 | −1.71066 | ||||||||
\(518\) | 7.32235e13 | 0.0862654 | ||||||||
\(519\) | −2.39498e14 | −0.279178 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.27575e14 | 1.05862 | 0.529312 | − | 0.848428i | \(-0.322450\pi\) | ||||
0.529312 | + | 0.848428i | \(0.322450\pi\) | |||||||
\(522\) | −3.50220e14 | −0.395506 | ||||||||
\(523\) | 2.18187e13 | 0.0243820 | 0.0121910 | − | 0.999926i | \(-0.496119\pi\) | ||||
0.0121910 | + | 0.999926i | \(0.496119\pi\) | |||||||
\(524\) | −9.29610e14 | −1.02797 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.82569e14 | 0.630850 | ||||||||
\(527\) | −3.64931e14 | −0.391069 | ||||||||
\(528\) | −1.32989e14 | −0.141036 | ||||||||
\(529\) | −6.05238e14 | −0.635214 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.89717e14 | 0.606211 | ||||||||
\(532\) | −2.62774e14 | −0.267343 | ||||||||
\(533\) | 1.78013e14 | 0.179247 | ||||||||
\(534\) | 1.51157e14 | 0.150644 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.30790e15 | −1.27694 | ||||||||
\(537\) | −4.23709e14 | −0.409458 | ||||||||
\(538\) | 6.20105e14 | 0.593147 | ||||||||
\(539\) | −9.07218e14 | −0.858961 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.69527e15 | −1.57273 | −0.786363 | − | 0.617765i | \(-0.788038\pi\) | ||||
−0.786363 | + | 0.617765i | \(0.788038\pi\) | |||||||
\(542\) | −9.04304e13 | −0.0830459 | ||||||||
\(543\) | 2.51187e14 | 0.228349 | ||||||||
\(544\) | 1.35844e15 | 1.22249 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.85062e13 | −0.0515991 | ||||||||
\(547\) | −7.52145e14 | −0.656706 | −0.328353 | − | 0.944555i | \(-0.606494\pi\) | ||||
−0.328353 | + | 0.944555i | \(0.606494\pi\) | |||||||
\(548\) | −4.37477e14 | −0.378148 | ||||||||
\(549\) | −7.90555e14 | −0.676526 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.36900e15 | 1.14834 | ||||||||
\(552\) | −3.96896e14 | −0.329619 | ||||||||
\(553\) | 6.38228e14 | 0.524793 | ||||||||
\(554\) | 3.94054e14 | 0.320813 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.78480e14 | −0.701166 | ||||||||
\(557\) | −1.87489e14 | −0.148174 | −0.0740870 | − | 0.997252i | \(-0.523604\pi\) | ||||
−0.0740870 | + | 0.997252i | \(0.523604\pi\) | |||||||
\(558\) | 1.44126e14 | 0.112786 | ||||||||
\(559\) | 9.89417e12 | 0.00766681 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.30383e14 | −0.706913 | ||||||||
\(562\) | 5.04857e14 | 0.379856 | ||||||||
\(563\) | −2.44971e14 | −0.182524 | −0.0912618 | − | 0.995827i | \(-0.529090\pi\) | ||||
−0.0912618 | + | 0.995827i | \(0.529090\pi\) | |||||||
\(564\) | −9.96856e14 | −0.735525 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.01116e14 | −0.290255 | ||||||||
\(567\) | 2.78819e13 | 0.0199809 | ||||||||
\(568\) | −8.27185e14 | −0.587066 | ||||||||
\(569\) | 1.35243e15 | 0.950596 | 0.475298 | − | 0.879825i | \(-0.342340\pi\) | ||||
0.475298 | + | 0.879825i | \(0.342340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.43223e15 | 0.987447 | 0.493723 | − | 0.869619i | \(-0.335636\pi\) | ||||
0.493723 | + | 0.869619i | \(0.335636\pi\) | |||||||
\(572\) | −4.54650e14 | −0.310455 | ||||||||
\(573\) | −6.96126e14 | −0.470801 | ||||||||
\(574\) | 1.23820e14 | 0.0829422 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.06756e14 | −0.201590 | ||||||||
\(577\) | 8.77659e14 | 0.571293 | 0.285647 | − | 0.958335i | \(-0.407792\pi\) | ||||
0.285647 | + | 0.958335i | \(0.407792\pi\) | |||||||
\(578\) | 3.22081e14 | 0.207664 | ||||||||
\(579\) | 1.37148e15 | 0.875907 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.91187e14 | 0.307807 | ||||||||
\(582\) | 4.53682e14 | 0.281628 | ||||||||
\(583\) | 8.53271e14 | 0.524698 | ||||||||
\(584\) | 1.23661e14 | 0.0753290 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.74245e14 | 0.343289 | ||||||||
\(587\) | 2.43425e15 | 1.44164 | 0.720818 | − | 0.693124i | \(-0.243766\pi\) | ||||
0.720818 | + | 0.693124i | \(0.243766\pi\) | |||||||
\(588\) | −6.29479e14 | −0.369323 | ||||||||
\(589\) | −5.63383e14 | −0.327469 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.24775e14 | −0.413497 | ||||||||
\(592\) | 1.79869e14 | 0.101669 | ||||||||
\(593\) | 3.03318e14 | 0.169863 | 0.0849313 | − | 0.996387i | \(-0.472933\pi\) | ||||
0.0849313 | + | 0.996387i | \(0.472933\pi\) | |||||||
\(594\) | 9.40221e14 | 0.521680 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.64192e15 | 0.894329 | ||||||||
\(597\) | −1.83555e14 | −0.0990619 | ||||||||
\(598\) | −2.58502e14 | −0.138232 | ||||||||
\(599\) | −1.70198e15 | −0.901795 | −0.450898 | − | 0.892576i | \(-0.648896\pi\) | ||||
−0.450898 | + | 0.892576i | \(0.648896\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.33922e15 | 1.21692 | 0.608458 | − | 0.793586i | \(-0.291788\pi\) | ||||
0.608458 | + | 0.793586i | \(0.291788\pi\) | |||||||
\(602\) | 6.88207e12 | 0.00354763 | ||||||||
\(603\) | −1.75940e15 | −0.898710 | ||||||||
\(604\) | 1.21359e15 | 0.614282 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.94381e14 | −0.245733 | ||||||||
\(607\) | 2.49607e15 | 1.22947 | 0.614737 | − | 0.788732i | \(-0.289262\pi\) | ||||
0.614737 | + | 0.788732i | \(0.289262\pi\) | |||||||
\(608\) | 2.09717e15 | 1.02368 | ||||||||
\(609\) | −5.41810e14 | −0.262091 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.55258e15 | −0.737612 | ||||||||
\(612\) | 1.15524e15 | 0.543926 | ||||||||
\(613\) | −2.47301e15 | −1.15397 | −0.576983 | − | 0.816756i | \(-0.695770\pi\) | ||||
−0.576983 | + | 0.816756i | \(0.695770\pi\) | |||||||
\(614\) | −3.67466e14 | −0.169938 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.56226e14 | −0.343525 | ||||||||
\(617\) | −2.43368e13 | −0.0109571 | −0.00547854 | − | 0.999985i | \(-0.501744\pi\) | ||||
−0.00547854 | + | 0.999985i | \(0.501744\pi\) | |||||||
\(618\) | −1.36537e15 | −0.609274 | ||||||||
\(619\) | 4.22545e15 | 1.86885 | 0.934425 | − | 0.356160i | \(-0.115914\pi\) | ||||
0.934425 | + | 0.356160i | \(0.115914\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.36616e15 | −0.593606 | ||||||||
\(622\) | 1.19700e15 | 0.515523 | ||||||||
\(623\) | −4.18481e14 | −0.178645 | ||||||||
\(624\) | −1.43717e14 | −0.0608126 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.38754e15 | 0.992640 | ||||||||
\(627\) | −1.43633e15 | −0.591947 | ||||||||
\(628\) | 1.93585e15 | 0.790850 | ||||||||
\(629\) | 1.25835e15 | 0.509594 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.26326e15 | −1.69660 | −0.848302 | − | 0.529513i | \(-0.822375\pi\) | ||||
−0.848302 | + | 0.529513i | \(0.822375\pi\) | |||||||
\(632\) | −3.22011e15 | −1.27036 | ||||||||
\(633\) | 1.71188e15 | 0.669503 | ||||||||
\(634\) | −2.00086e15 | −0.775758 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.92047e14 | 0.225602 | ||||||||
\(637\) | −9.80401e14 | −0.370371 | ||||||||
\(638\) | 1.64755e15 | 0.617055 | ||||||||
\(639\) | −1.11273e15 | −0.413177 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.00830e15 | 0.368018 | 0.184009 | − | 0.982925i | \(-0.441092\pi\) | ||||
0.184009 | + | 0.982925i | \(0.441092\pi\) | |||||||
\(642\) | 5.45779e14 | 0.197503 | ||||||||
\(643\) | −3.03982e14 | −0.109066 | −0.0545328 | − | 0.998512i | \(-0.517367\pi\) | ||||
−0.0545328 | + | 0.998512i | \(0.517367\pi\) | |||||||
\(644\) | 4.59504e14 | 0.163462 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.76705e15 | 0.617974 | ||||||||
\(647\) | −3.43583e15 | −1.19140 | −0.595700 | − | 0.803207i | \(-0.703125\pi\) | ||||
−0.595700 | + | 0.803207i | \(0.703125\pi\) | |||||||
\(648\) | −1.40675e14 | −0.0483676 | ||||||||
\(649\) | −2.77421e15 | −0.945788 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.22971e14 | 0.0747400 | ||||||||
\(652\) | −5.26730e14 | −0.175076 | ||||||||
\(653\) | 1.18539e15 | 0.390695 | 0.195347 | − | 0.980734i | \(-0.437417\pi\) | ||||
0.195347 | + | 0.980734i | \(0.437417\pi\) | |||||||
\(654\) | −4.44423e14 | −0.145251 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.04157e14 | 0.0977522 | ||||||||
\(657\) | 1.66350e14 | 0.0530167 | ||||||||
\(658\) | −1.07993e15 | −0.341312 | ||||||||
\(659\) | −2.26510e15 | −0.709934 | −0.354967 | − | 0.934879i | \(-0.615508\pi\) | ||||
−0.354967 | + | 0.934879i | \(0.615508\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.33012e15 | −1.64297 | −0.821484 | − | 0.570232i | \(-0.806853\pi\) | ||||
−0.821484 | + | 0.570232i | \(0.806853\pi\) | |||||||
\(662\) | −1.52602e15 | −0.466488 | ||||||||
\(663\) | −1.00543e15 | −0.304810 | ||||||||
\(664\) | −2.47823e15 | −0.745104 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.96974e14 | −0.146969 | ||||||||
\(667\) | −2.39392e15 | −0.702130 | ||||||||
\(668\) | 4.05512e15 | 1.17959 | ||||||||
\(669\) | 1.84839e15 | 0.533272 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.71902e15 | 1.05549 | ||||||||
\(672\) | −8.30000e14 | −0.233640 | ||||||||
\(673\) | −4.74120e15 | −1.32375 | −0.661874 | − | 0.749615i | \(-0.730239\pi\) | ||||
−0.661874 | + | 0.749615i | \(0.730239\pi\) | |||||||
\(674\) | −2.90403e15 | −0.804215 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.14673e15 | 0.584886 | ||||||||
\(677\) | 1.41307e15 | 0.381880 | 0.190940 | − | 0.981602i | \(-0.438846\pi\) | ||||
0.190940 | + | 0.981602i | \(0.438846\pi\) | |||||||
\(678\) | −5.14968e14 | −0.138044 | ||||||||
\(679\) | −1.25603e15 | −0.333976 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.42680e14 | −0.0896559 | ||||||||
\(682\) | −6.78014e14 | −0.175964 | ||||||||
\(683\) | 3.03116e15 | 0.780359 | 0.390180 | − | 0.920739i | \(-0.372413\pi\) | ||||
0.390180 | + | 0.920739i | \(0.372413\pi\) | |||||||
\(684\) | 1.78347e15 | 0.455467 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.47654e15 | −0.371075 | ||||||||
\(687\) | 2.97975e15 | 0.742879 | ||||||||
\(688\) | 1.69054e13 | 0.00418109 | ||||||||
\(689\) | 9.22102e14 | 0.226242 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.74731e15 | −0.663405 | −0.331703 | − | 0.943384i | \(-0.607623\pi\) | ||||
−0.331703 | + | 0.943384i | \(0.607623\pi\) | |||||||
\(692\) | −1.39897e15 | −0.335139 | ||||||||
\(693\) | −1.01728e15 | −0.241773 | ||||||||
\(694\) | 3.73588e15 | 0.880878 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.73364e15 | 0.634441 | ||||||||
\(697\) | 2.12786e15 | 0.489962 | ||||||||
\(698\) | −6.15433e14 | −0.140597 | ||||||||
\(699\) | −4.42597e15 | −1.00319 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.72747e15 | 1.27795 | 0.638974 | − | 0.769228i | \(-0.279359\pi\) | ||||
0.638974 | + | 0.769228i | \(0.279359\pi\) | |||||||
\(702\) | 1.01607e15 | 0.224941 | ||||||||
\(703\) | 1.94265e15 | 0.426718 | ||||||||
\(704\) | 1.44308e15 | 0.314514 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.97836e14 | −0.128279 | ||||||||
\(707\) | 1.36870e15 | 0.291409 | ||||||||
\(708\) | −1.92490e15 | −0.406655 | ||||||||
\(709\) | 6.98326e14 | 0.146388 | 0.0731938 | − | 0.997318i | \(-0.476681\pi\) | ||||
0.0731938 | + | 0.997318i | \(0.476681\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.33171e15 | −0.894081 | ||||||||
\(712\) | 2.11140e15 | 0.432445 | ||||||||
\(713\) | 9.85170e14 | 0.200225 | ||||||||
\(714\) | −6.99348e14 | −0.141044 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.47500e15 | −0.491534 | ||||||||
\(717\) | 1.79917e15 | 0.354583 | ||||||||
\(718\) | 3.78202e15 | 0.739672 | ||||||||
\(719\) | 9.70979e15 | 1.88452 | 0.942260 | − | 0.334882i | \(-0.108696\pi\) | ||||
0.942260 | + | 0.334882i | \(0.108696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.78004e15 | 0.722525 | ||||||||
\(722\) | −6.77852e13 | −0.0128582 | ||||||||
\(723\) | 5.82893e13 | 0.0109731 | ||||||||
\(724\) | 1.46725e15 | 0.274121 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.01384e12 | −0.000554586 0 | ||||||||
\(727\) | −2.46469e15 | −0.450114 | −0.225057 | − | 0.974346i | \(-0.572257\pi\) | ||||
−0.225057 | + | 0.974346i | \(0.572257\pi\) | |||||||
\(728\) | −8.17230e14 | −0.148123 | ||||||||
\(729\) | 3.08202e15 | 0.554413 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.18269e14 | 0.0209568 | ||||||||
\(732\) | 2.58046e15 | 0.453823 | ||||||||
\(733\) | −7.91285e15 | −1.38121 | −0.690607 | − | 0.723230i | \(-0.742657\pi\) | ||||
−0.690607 | + | 0.723230i | \(0.742657\pi\) | |||||||
\(734\) | 4.26963e15 | 0.739711 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.66725e15 | −0.625911 | ||||||||
\(737\) | 8.27677e15 | 1.40213 | ||||||||
\(738\) | −8.40378e14 | −0.141307 | ||||||||
\(739\) | −8.40694e15 | −1.40312 | −0.701558 | − | 0.712613i | \(-0.747512\pi\) | ||||
−0.701558 | + | 0.712613i | \(0.747512\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.55220e15 | −0.255239 | ||||||||
\(742\) | 6.41385e14 | 0.104688 | ||||||||
\(743\) | −1.36287e15 | −0.220809 | −0.110404 | − | 0.993887i | \(-0.535215\pi\) | ||||
−0.110404 | + | 0.993887i | \(0.535215\pi\) | |||||||
\(744\) | −1.12498e15 | −0.180922 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.32388e15 | 0.209790 | ||||||||
\(747\) | −3.33373e15 | −0.524405 | ||||||||
\(748\) | −5.43462e15 | −0.848614 | ||||||||
\(749\) | −1.51100e15 | −0.234215 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.81722e15 | 1.04133 | 0.520664 | − | 0.853762i | \(-0.325684\pi\) | ||||
0.520664 | + | 0.853762i | \(0.325684\pi\) | |||||||
\(752\) | −2.65278e15 | −0.402256 | ||||||||
\(753\) | −3.27173e15 | −0.492499 | ||||||||
\(754\) | 1.78045e15 | 0.266065 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.80612e15 | −0.265997 | ||||||||
\(757\) | 6.67049e14 | 0.0975282 | 0.0487641 | − | 0.998810i | \(-0.484472\pi\) | ||||
0.0487641 | + | 0.998810i | \(0.484472\pi\) | |||||||
\(758\) | 3.51511e15 | 0.510222 | ||||||||
\(759\) | 2.51166e15 | 0.361936 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.74408e15 | −1.09990 | −0.549951 | − | 0.835197i | \(-0.685354\pi\) | ||||
−0.549951 | + | 0.835197i | \(0.685354\pi\) | |||||||
\(762\) | −1.58891e15 | −0.224052 | ||||||||
\(763\) | 1.23039e15 | 0.172250 | ||||||||
\(764\) | −4.06626e15 | −0.565173 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.55479e15 | −0.761043 | ||||||||
\(767\) | −2.99800e15 | −0.407809 | ||||||||
\(768\) | 3.43775e15 | 0.464288 | ||||||||
\(769\) | 2.52411e15 | 0.338465 | 0.169232 | − | 0.985576i | \(-0.445871\pi\) | ||||
0.169232 | + | 0.985576i | \(0.445871\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.03822e15 | 0.798197 | ||||||||
\(772\) | 8.01119e15 | 1.05148 | ||||||||
\(773\) | 1.11453e16 | 1.45246 | 0.726229 | − | 0.687453i | \(-0.241271\pi\) | ||||
0.726229 | + | 0.687453i | \(0.241271\pi\) | |||||||
\(774\) | −4.67092e13 | −0.00604404 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.33715e15 | 0.808452 | ||||||||
\(777\) | −7.68847e14 | −0.0973922 | ||||||||
\(778\) | −3.59692e15 | −0.452421 | ||||||||
\(779\) | 3.28500e15 | 0.410279 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.23465e15 | 0.644624 | ||||||||
\(782\) | −3.08998e15 | −0.377849 | ||||||||
\(783\) | 9.40952e15 | 1.14256 | ||||||||
\(784\) | −1.67514e15 | −0.201981 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.81949e15 | −0.454131 | ||||||||
\(787\) | −1.32271e16 | −1.56172 | −0.780861 | − | 0.624705i | \(-0.785219\pi\) | ||||
−0.780861 | + | 0.624705i | \(0.785219\pi\) | |||||||
\(788\) | −4.23361e15 | −0.496382 | ||||||||
\(789\) | −6.11698e15 | −0.712219 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.42570e15 | 0.163703 | ||||||||
\(792\) | 5.13257e15 | 0.585257 | ||||||||
\(793\) | 4.01902e15 | 0.455112 | ||||||||
\(794\) | −4.99466e15 | −0.561685 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.07219e15 | −0.118919 | ||||||||
\(797\) | −2.30248e15 | −0.253615 | −0.126807 | − | 0.991927i | \(-0.540473\pi\) | ||||
−0.126807 | + | 0.991927i | \(0.540473\pi\) | |||||||
\(798\) | −1.07966e15 | −0.118106 | ||||||||
\(799\) | −1.85587e16 | −2.01623 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.84027e15 | 0.304355 | ||||||||
\(802\) | −3.20179e15 | −0.340748 | ||||||||
\(803\) | −7.82560e14 | −0.0827146 | ||||||||
\(804\) | 5.74289e15 | 0.602868 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.32708e14 | −0.0758732 | ||||||||
\(807\) | −6.51110e15 | −0.669653 | ||||||||
\(808\) | −6.90565e15 | −0.705410 | ||||||||
\(809\) | 5.60472e15 | 0.568639 | 0.284320 | − | 0.958730i | \(-0.408232\pi\) | ||||
0.284320 | + | 0.958730i | \(0.408232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.08516e15 | −0.508968 | −0.254484 | − | 0.967077i | \(-0.581906\pi\) | ||||
−0.254484 | + | 0.967077i | \(0.581906\pi\) | |||||||
\(812\) | −3.16486e15 | −0.314627 | ||||||||
\(813\) | 9.49519e14 | 0.0937574 | ||||||||
\(814\) | 2.33792e15 | 0.229296 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.71791e15 | −0.166228 | ||||||||
\(817\) | 1.82584e14 | 0.0175486 | ||||||||
\(818\) | −4.94802e15 | −0.472377 | ||||||||
\(819\) | −1.09934e15 | −0.104249 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.79111e14 | 0.0261150 | 0.0130575 | − | 0.999915i | \(-0.495844\pi\) | ||||
0.0130575 | + | 0.999915i | \(0.495844\pi\) | |||||||
\(822\) | −1.79746e15 | −0.167057 | ||||||||
\(823\) | 1.35265e16 | 1.24878 | 0.624391 | − | 0.781112i | \(-0.285347\pi\) | ||||
0.624391 | + | 0.781112i | \(0.285347\pi\) | |||||||
\(824\) | −1.90718e16 | −1.74901 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.08531e15 | −0.188704 | ||||||||
\(827\) | −2.72544e14 | −0.0244994 | −0.0122497 | − | 0.999925i | \(-0.503899\pi\) | ||||
−0.0122497 | + | 0.999925i | \(0.503899\pi\) | |||||||
\(828\) | −3.11869e15 | −0.278488 | ||||||||
\(829\) | 1.80459e16 | 1.60077 | 0.800385 | − | 0.599486i | \(-0.204628\pi\) | ||||
0.800385 | + | 0.599486i | \(0.204628\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.13757e15 | −0.362193 | ||||||||
\(832\) | 1.55949e15 | 0.135614 | ||||||||
\(833\) | −1.17191e16 | −1.01239 | ||||||||
\(834\) | −3.60941e15 | −0.309758 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.38999e15 | −0.710603 | ||||||||
\(837\) | −3.87230e15 | −0.325821 | ||||||||
\(838\) | 1.76168e15 | 0.147260 | ||||||||
\(839\) | −7.96183e15 | −0.661184 | −0.330592 | − | 0.943774i | \(-0.607248\pi\) | ||||
−0.330592 | + | 0.943774i | \(0.607248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.28775e15 | 0.351440 | ||||||||
\(842\) | 4.10669e15 | 0.334407 | ||||||||
\(843\) | −5.30100e15 | −0.428851 | ||||||||
\(844\) | 9.99954e15 | 0.803705 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.32956e15 | 0.581488 | ||||||||
\(847\) | 8.34387e12 | 0.000657671 0 | ||||||||
\(848\) | 1.57552e15 | 0.123381 | ||||||||
\(849\) | 4.21172e15 | 0.327693 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.39705e15 | −0.260909 | ||||||||
\(852\) | 3.63209e15 | 0.277165 | ||||||||
\(853\) | 1.49826e16 | 1.13598 | 0.567988 | − | 0.823037i | \(-0.307722\pi\) | ||||
0.567988 | + | 0.823037i | \(0.307722\pi\) | |||||||
\(854\) | 2.79550e15 | 0.210592 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.62358e15 | 0.566961 | ||||||||
\(857\) | 2.22561e16 | 1.64458 | 0.822290 | − | 0.569068i | \(-0.192696\pi\) | ||||
0.822290 | + | 0.569068i | \(0.192696\pi\) | |||||||
\(858\) | −1.86802e15 | −0.137152 | ||||||||
\(859\) | 5.44237e15 | 0.397032 | 0.198516 | − | 0.980098i | \(-0.436388\pi\) | ||||
0.198516 | + | 0.980098i | \(0.436388\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.30011e15 | −0.0936403 | ||||||||
\(862\) | −1.72262e15 | −0.123282 | ||||||||
\(863\) | −1.08110e16 | −0.768787 | −0.384393 | − | 0.923169i | \(-0.625589\pi\) | ||||
−0.384393 | + | 0.923169i | \(0.625589\pi\) | |||||||
\(864\) | 1.44145e16 | 1.01853 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.39715e15 | −0.167243 | ||||||||
\(867\) | −3.38185e15 | −0.234449 | ||||||||
\(868\) | 1.30243e15 | 0.0897217 | ||||||||
\(869\) | 2.03777e16 | 1.39491 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.94444e15 | 0.604579 | ||||||||
\(872\) | −6.20782e15 | −0.416964 | ||||||||
\(873\) | 8.52477e15 | 0.568989 | ||||||||
\(874\) | −4.77033e15 | −0.316399 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.42985e14 | −0.0355644 | ||||||||
\(877\) | 2.81024e16 | 1.82914 | 0.914568 | − | 0.404431i | \(-0.132530\pi\) | ||||
0.914568 | + | 0.404431i | \(0.132530\pi\) | |||||||
\(878\) | −6.96749e14 | −0.0450668 | ||||||||
\(879\) | −6.02957e15 | −0.387568 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.22209e15 | 0.268016 | 0.134008 | − | 0.990980i | \(-0.457215\pi\) | ||||
0.134008 | + | 0.990980i | \(0.457215\pi\) | |||||||
\(882\) | 4.62836e15 | 0.291978 | ||||||||
\(883\) | −5.16092e14 | −0.0323551 | −0.0161776 | − | 0.999869i | \(-0.505150\pi\) | ||||
−0.0161776 | + | 0.999869i | \(0.505150\pi\) | |||||||
\(884\) | −5.87302e15 | −0.365910 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.88088e15 | −0.484941 | ||||||||
\(887\) | −5.71906e15 | −0.349740 | −0.174870 | − | 0.984592i | \(-0.555950\pi\) | ||||
−0.174870 | + | 0.984592i | \(0.555950\pi\) | |||||||
\(888\) | 3.87913e15 | 0.235756 | ||||||||
\(889\) | 4.39894e15 | 0.265698 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.90230e14 | 0.0531098 | ||||||||
\(892\) | 1.07969e16 | 0.640167 | ||||||||
\(893\) | −2.86510e16 | −1.68832 | ||||||||
\(894\) | 6.74614e15 | 0.395093 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.66067e15 | −0.327472 | ||||||||
\(897\) | 2.71427e15 | 0.156061 | ||||||||
\(898\) | −1.46968e16 | −0.839854 | ||||||||
\(899\) | −6.78541e15 | −0.385388 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.10223e16 | 0.618421 | ||||||||
\(902\) | 3.95340e15 | 0.220462 | ||||||||
\(903\) | −7.22617e13 | −0.00400521 | ||||||||
\(904\) | −7.19321e15 | −0.396275 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.98626e15 | 0.271375 | ||||||||
\(907\) | 8.43778e13 | 0.00456445 | 0.00228222 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228222 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(908\) | −2.00168e15 | −0.107628 | ||||||||
\(909\) | −9.28952e15 | −0.496468 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.10091e16 | −0.581298 | −0.290649 | − | 0.956830i | \(-0.593871\pi\) | ||||
−0.290649 | + | 0.956830i | \(0.593871\pi\) | |||||||
\(912\) | −2.65212e15 | −0.139194 | ||||||||
\(913\) | 1.56829e16 | 0.818158 | ||||||||
\(914\) | −7.28359e15 | −0.377695 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.74055e16 | 0.891789 | ||||||||
\(917\) | 1.05743e16 | 0.538544 | ||||||||
\(918\) | 1.21455e16 | 0.614864 | ||||||||
\(919\) | −4.86351e15 | −0.244746 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.85840e15 | 0.191857 | ||||||||
\(922\) | −1.75034e16 | −0.865171 | ||||||||
\(923\) | 5.65691e15 | 0.277952 | ||||||||
\(924\) | 3.32052e15 | 0.162185 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.93252e15 | −0.141540 | ||||||||
\(927\) | −2.56555e16 | −1.23095 | ||||||||
\(928\) | 2.52584e16 | 1.20474 | ||||||||
\(929\) | 3.57534e15 | 0.169524 | 0.0847620 | − | 0.996401i | \(-0.472987\pi\) | ||||
0.0847620 | + | 0.996401i | \(0.472987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.80921e16 | −0.847744 | ||||||||
\(932\) | −2.58533e16 | −1.20428 | ||||||||
\(933\) | −1.25685e16 | −0.582017 | ||||||||
\(934\) | 1.48171e16 | 0.682113 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.54661e15 | 0.252354 | ||||||||
\(937\) | −3.86373e16 | −1.74759 | −0.873795 | − | 0.486295i | \(-0.838348\pi\) | ||||
−0.873795 | + | 0.486295i | \(0.838348\pi\) | |||||||
\(938\) | 6.22147e15 | 0.279754 | ||||||||
\(939\) | −2.50692e16 | −1.12067 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.48997e16 | −1.54198 | −0.770991 | − | 0.636846i | \(-0.780239\pi\) | ||||
−0.770991 | + | 0.636846i | \(0.780239\pi\) | |||||||
\(942\) | 7.95383e15 | 0.349378 | ||||||||
\(943\) | −5.74437e15 | −0.250858 | ||||||||
\(944\) | −5.12245e15 | −0.222398 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.19735e14 | 0.00942969 | ||||||||
\(947\) | 2.85123e16 | 1.21649 | 0.608243 | − | 0.793751i | \(-0.291875\pi\) | ||||
0.608243 | + | 0.793751i | \(0.291875\pi\) | |||||||
\(948\) | 1.41392e16 | 0.599763 | ||||||||
\(949\) | −8.45688e14 | −0.0356653 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.10091e16 | 0.875817 | ||||||||
\(952\) | −9.76867e15 | −0.404886 | ||||||||
\(953\) | −4.00334e16 | −1.64973 | −0.824863 | − | 0.565332i | \(-0.808748\pi\) | ||||
−0.824863 | + | 0.565332i | \(0.808748\pi\) | |||||||
\(954\) | −4.35313e15 | −0.178355 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.05095e16 | 0.425659 | ||||||||
\(957\) | −1.72992e16 | −0.696644 | ||||||||
\(958\) | 2.52201e16 | 1.00980 | ||||||||
\(959\) | 4.97630e15 | 0.198109 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.26161e16 | −0.890100 | ||||||||
\(962\) | 2.52652e15 | 0.0988688 | ||||||||
\(963\) | 1.02553e16 | 0.399028 | ||||||||
\(964\) | 3.40484e14 | 0.0131726 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.88796e15 | 0.0722136 | ||||||||
\(967\) | −1.84953e16 | −0.703422 | −0.351711 | − | 0.936109i | \(-0.614400\pi\) | ||||
−0.351711 | + | 0.936109i | \(0.614400\pi\) | |||||||
\(968\) | −4.20981e13 | −0.00159202 | ||||||||
\(969\) | −1.85540e16 | −0.697682 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.14877e16 | −0.798884 | −0.399442 | − | 0.916759i | \(-0.630796\pi\) | ||||
−0.399442 | + | 0.916759i | \(0.630796\pi\) | |||||||
\(972\) | 1.97260e16 | 0.729246 | ||||||||
\(973\) | 9.99271e15 | 0.367335 | ||||||||
\(974\) | 5.27784e15 | 0.192922 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.86699e15 | 0.248195 | ||||||||
\(977\) | 8.73880e15 | 0.314074 | 0.157037 | − | 0.987593i | \(-0.449806\pi\) | ||||
0.157037 | + | 0.987593i | \(0.449806\pi\) | |||||||
\(978\) | −2.16417e15 | −0.0773443 | ||||||||
\(979\) | −1.33615e16 | −0.474844 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.35079e15 | −0.293459 | ||||||||
\(982\) | −1.16127e16 | −0.405808 | ||||||||
\(983\) | −1.18924e16 | −0.413263 | −0.206631 | − | 0.978419i | \(-0.566250\pi\) | ||||
−0.206631 | + | 0.978419i | \(0.566250\pi\) | |||||||
\(984\) | 6.55956e15 | 0.226674 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.12824e16 | 0.727274 | ||||||||
\(987\) | 1.13392e16 | 0.385336 | ||||||||
\(988\) | −9.06679e15 | −0.306401 | ||||||||
\(989\) | −3.19279e14 | −0.0107298 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.34409e16 | 0.779056 | 0.389528 | − | 0.921015i | \(-0.372638\pi\) | ||||
0.389528 | + | 0.921015i | \(0.372638\pi\) | |||||||
\(992\) | −1.03946e16 | −0.343552 | ||||||||
\(993\) | 1.60232e16 | 0.526657 | ||||||||
\(994\) | 3.93477e15 | 0.128616 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.08817e16 | 0.351779 | ||||||||
\(997\) | 2.14004e16 | 0.688016 | 0.344008 | − | 0.938967i | \(-0.388215\pi\) | ||||
0.344008 | + | 0.938967i | \(0.388215\pi\) | |||||||
\(998\) | −2.61307e15 | −0.0835473 | ||||||||
\(999\) | 1.33524e16 | 0.424571 |
(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 | 25.12.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 225.12.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 25.12.b.b.24.2 | 2 | |||
5.3 | odd | 4 | 25.12.b.b.24.1 | 2 | |||
5.4 | even | 2 | 1.12.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 225.12.b.d.199.1 | 2 | |||
15.8 | even | 4 | 225.12.b.d.199.2 | 2 | |||
15.14 | odd | 2 | 9.12.a.b.1.1 | 1 | |||
20.19 | odd | 2 | 16.12.a.a.1.1 | 1 | |||
35.4 | even | 6 | 49.12.c.b.30.1 | 2 | |||
35.9 | even | 6 | 49.12.c.b.18.1 | 2 | |||
35.19 | odd | 6 | 49.12.c.c.18.1 | 2 | |||
35.24 | odd | 6 | 49.12.c.c.30.1 | 2 | |||
35.34 | odd | 2 | 49.12.a.a.1.1 | 1 | |||
40.19 | odd | 2 | 64.12.a.f.1.1 | 1 | |||
40.29 | even | 2 | 64.12.a.b.1.1 | 1 | |||
45.4 | even | 6 | 81.12.c.d.55.1 | 2 | |||
45.14 | odd | 6 | 81.12.c.b.55.1 | 2 | |||
45.29 | odd | 6 | 81.12.c.b.28.1 | 2 | |||
45.34 | even | 6 | 81.12.c.d.28.1 | 2 | |||
55.54 | odd | 2 | 121.12.a.b.1.1 | 1 | |||
60.59 | even | 2 | 144.12.a.d.1.1 | 1 | |||
65.64 | even | 2 | 169.12.a.a.1.1 | 1 | |||
80.19 | odd | 4 | 256.12.b.c.129.1 | 2 | |||
80.29 | even | 4 | 256.12.b.e.129.2 | 2 | |||
80.59 | odd | 4 | 256.12.b.c.129.2 | 2 | |||
80.69 | even | 4 | 256.12.b.e.129.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.12.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
9.12.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
16.12.a.a.1.1 | 1 | 20.19 | odd | 2 | |||
25.12.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
25.12.b.b.24.1 | 2 | 5.3 | odd | 4 | |||
25.12.b.b.24.2 | 2 | 5.2 | odd | 4 | |||
49.12.a.a.1.1 | 1 | 35.34 | odd | 2 | |||
49.12.c.b.18.1 | 2 | 35.9 | even | 6 | |||
49.12.c.b.30.1 | 2 | 35.4 | even | 6 | |||
49.12.c.c.18.1 | 2 | 35.19 | odd | 6 | |||
49.12.c.c.30.1 | 2 | 35.24 | odd | 6 | |||
64.12.a.b.1.1 | 1 | 40.29 | even | 2 | |||
64.12.a.f.1.1 | 1 | 40.19 | odd | 2 | |||
81.12.c.b.28.1 | 2 | 45.29 | odd | 6 | |||
81.12.c.b.55.1 | 2 | 45.14 | odd | 6 | |||
81.12.c.d.28.1 | 2 | 45.34 | even | 6 | |||
81.12.c.d.55.1 | 2 | 45.4 | even | 6 | |||
121.12.a.b.1.1 | 1 | 55.54 | odd | 2 | |||
144.12.a.d.1.1 | 1 | 60.59 | even | 2 | |||
169.12.a.a.1.1 | 1 | 65.64 | even | 2 | |||
225.12.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
225.12.b.d.199.1 | 2 | 15.2 | even | 4 | |||
225.12.b.d.199.2 | 2 | 15.8 | even | 4 | |||
256.12.b.c.129.1 | 2 | 80.19 | odd | 4 | |||
256.12.b.c.129.2 | 2 | 80.59 | odd | 4 | |||
256.12.b.e.129.1 | 2 | 80.69 | even | 4 | |||
256.12.b.e.129.2 | 2 | 80.29 | even | 4 |