Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,10,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(38.6276877123\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{79}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 79 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-8.88819\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.223611 | 0.00988231 | 0.00494116 | − | 0.999988i | \(-0.498427\pi\) | ||||
0.00494116 | + | 0.999988i | \(0.498427\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −511.950 | −0.999902 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −18.1125 | −0.00570555 | ||||||||
\(7\) | 580.825 | 0.0914332 | 0.0457166 | − | 0.998954i | \(-0.485443\pi\) | ||||
0.0457166 | + | 0.998954i | \(0.485443\pi\) | |||||||
\(8\) | −228.967 | −0.0197637 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 47275.7 | 0.973578 | 0.486789 | − | 0.873520i | \(-0.338168\pi\) | ||||
0.486789 | + | 0.873520i | \(0.338168\pi\) | |||||||
\(12\) | 41467.9 | 0.577294 | ||||||||
\(13\) | −22367.7 | −0.217208 | −0.108604 | − | 0.994085i | \(-0.534638\pi\) | ||||
−0.108604 | + | 0.994085i | \(0.534638\pi\) | |||||||
\(14\) | 129.879 | 0.000903572 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 262067. | 0.999707 | ||||||||
\(17\) | 244880. | 0.711105 | 0.355552 | − | 0.934656i | \(-0.384293\pi\) | ||||
0.355552 | + | 0.934656i | \(0.384293\pi\) | |||||||
\(18\) | 1467.11 | 0.00329410 | ||||||||
\(19\) | −248536. | −0.437521 | −0.218760 | − | 0.975779i | \(-0.570201\pi\) | ||||
−0.218760 | + | 0.975779i | \(0.570201\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −47046.8 | −0.0527890 | ||||||||
\(22\) | 10571.4 | 0.00962120 | ||||||||
\(23\) | 990208. | 0.737821 | 0.368911 | − | 0.929465i | \(-0.379731\pi\) | ||||
0.368911 | + | 0.929465i | \(0.379731\pi\) | |||||||
\(24\) | 18546.3 | 0.0114106 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5001.67 | −0.00214652 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −297353. | −0.0914243 | ||||||||
\(29\) | −4.35002e6 | −1.14209 | −0.571045 | − | 0.820919i | \(-0.693462\pi\) | ||||
−0.571045 | + | 0.820919i | \(0.693462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.60419e6 | −1.08990 | −0.544948 | − | 0.838470i | \(-0.683451\pi\) | ||||
−0.544948 | + | 0.838470i | \(0.683451\pi\) | |||||||
\(32\) | 175832. | 0.0296431 | ||||||||
\(33\) | −3.82933e6 | −0.562096 | ||||||||
\(34\) | 54758.0 | 0.00702736 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.35890e6 | −0.333301 | ||||||||
\(37\) | 4.73703e6 | 0.415526 | 0.207763 | − | 0.978179i | \(-0.433382\pi\) | ||||
0.207763 | + | 0.978179i | \(0.433382\pi\) | |||||||
\(38\) | −55575.5 | −0.00432372 | ||||||||
\(39\) | 1.81178e6 | 0.125405 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.11568e6 | 0.338000 | 0.169000 | − | 0.985616i | \(-0.445946\pi\) | ||||
0.169000 | + | 0.985616i | \(0.445946\pi\) | |||||||
\(42\) | −10520.2 | −0.000521677 0 | ||||||||
\(43\) | −3.89014e7 | −1.73523 | −0.867614 | − | 0.497238i | \(-0.834348\pi\) | ||||
−0.867614 | + | 0.497238i | \(0.834348\pi\) | |||||||
\(44\) | −2.42028e7 | −0.973483 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 221422. | 0.00729138 | ||||||||
\(47\) | 5.09738e7 | 1.52372 | 0.761862 | − | 0.647739i | \(-0.224285\pi\) | ||||
0.761862 | + | 0.647739i | \(0.224285\pi\) | |||||||
\(48\) | −2.12274e7 | −0.577181 | ||||||||
\(49\) | −4.00162e7 | −0.991640 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.98353e7 | −0.410557 | ||||||||
\(52\) | 1.14511e7 | 0.217187 | ||||||||
\(53\) | 1.16798e7 | 0.203327 | 0.101664 | − | 0.994819i | \(-0.467583\pi\) | ||||
0.101664 | + | 0.994819i | \(0.467583\pi\) | |||||||
\(54\) | −118836. | −0.00190185 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −132990. | −0.00180706 | ||||||||
\(57\) | 2.01314e7 | 0.252603 | ||||||||
\(58\) | −972713. | −0.0112865 | ||||||||
\(59\) | −1.79748e8 | −1.93121 | −0.965607 | − | 0.260006i | \(-0.916275\pi\) | ||||
−0.965607 | + | 0.260006i | \(0.916275\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.24120e8 | −1.14777 | −0.573887 | − | 0.818935i | \(-0.694565\pi\) | ||||
−0.573887 | + | 0.818935i | \(0.694565\pi\) | |||||||
\(62\) | −1.25316e6 | −0.0107707 | ||||||||
\(63\) | 3.81079e6 | 0.0304777 | ||||||||
\(64\) | −1.34139e8 | −0.999414 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −856281. | −0.00555480 | ||||||||
\(67\) | 1.90142e8 | 1.15277 | 0.576383 | − | 0.817180i | \(-0.304464\pi\) | ||||
0.576383 | + | 0.817180i | \(0.304464\pi\) | |||||||
\(68\) | −1.25366e8 | −0.711035 | ||||||||
\(69\) | −8.02068e7 | −0.425981 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.13551e8 | −0.530309 | −0.265155 | − | 0.964206i | \(-0.585423\pi\) | ||||
−0.265155 | + | 0.964206i | \(0.585423\pi\) | |||||||
\(72\) | −1.50225e6 | −0.00658789 | ||||||||
\(73\) | −1.03304e8 | −0.425761 | −0.212881 | − | 0.977078i | \(-0.568285\pi\) | ||||
−0.212881 | + | 0.977078i | \(0.568285\pi\) | |||||||
\(74\) | 1.05925e6 | 0.00410636 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.27238e8 | 0.437478 | ||||||||
\(77\) | 2.74589e7 | 0.0890174 | ||||||||
\(78\) | 405135. | 0.00123929 | ||||||||
\(79\) | −1.94841e7 | −0.0562807 | −0.0281403 | − | 0.999604i | \(-0.508959\pi\) | ||||
−0.0281403 | + | 0.999604i | \(0.508959\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 1.36753e6 | 0.00334023 | ||||||||
\(83\) | −5.52722e8 | −1.27837 | −0.639183 | − | 0.769055i | \(-0.720727\pi\) | ||||
−0.639183 | + | 0.769055i | \(0.720727\pi\) | |||||||
\(84\) | 2.40856e7 | 0.0527839 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.69878e6 | −0.0171481 | ||||||||
\(87\) | 3.52351e8 | 0.659386 | ||||||||
\(88\) | −1.08246e7 | −0.0192415 | ||||||||
\(89\) | 3.25690e8 | 0.550237 | 0.275119 | − | 0.961410i | \(-0.411283\pi\) | ||||
0.275119 | + | 0.961410i | \(0.411283\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.29917e7 | −0.0198601 | ||||||||
\(92\) | −5.06937e8 | −0.737749 | ||||||||
\(93\) | 4.53939e8 | 0.629251 | ||||||||
\(94\) | 1.13983e7 | 0.0150579 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.42424e7 | −0.0171144 | ||||||||
\(97\) | −1.33561e8 | −0.153182 | −0.0765910 | − | 0.997063i | \(-0.524404\pi\) | ||||
−0.0765910 | + | 0.997063i | \(0.524404\pi\) | |||||||
\(98\) | −8.94808e6 | −0.00979969 | ||||||||
\(99\) | 3.10176e8 | 0.324526 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.72460e8 | 0.164908 | 0.0824542 | − | 0.996595i | \(-0.473724\pi\) | ||||
0.0824542 | + | 0.996595i | \(0.473724\pi\) | |||||||
\(102\) | −4.43539e6 | −0.00405725 | ||||||||
\(103\) | 1.72881e9 | 1.51349 | 0.756746 | − | 0.653710i | \(-0.226788\pi\) | ||||
0.756746 | + | 0.653710i | \(0.226788\pi\) | |||||||
\(104\) | 5.12146e6 | 0.00429283 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.61174e6 | 0.00200934 | ||||||||
\(107\) | −2.12656e9 | −1.56838 | −0.784190 | − | 0.620521i | \(-0.786921\pi\) | ||||
−0.784190 | + | 0.620521i | \(0.786921\pi\) | |||||||
\(108\) | 2.72071e8 | 0.192431 | ||||||||
\(109\) | 1.65766e9 | 1.12480 | 0.562402 | − | 0.826864i | \(-0.309877\pi\) | ||||
0.562402 | + | 0.826864i | \(0.309877\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.83700e8 | −0.239904 | ||||||||
\(112\) | 1.52215e8 | 0.0914065 | ||||||||
\(113\) | 1.83857e9 | 1.06079 | 0.530394 | − | 0.847752i | \(-0.322044\pi\) | ||||
0.530394 | + | 0.847752i | \(0.322044\pi\) | |||||||
\(114\) | 4.50161e6 | 0.00249630 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.22699e9 | 1.14198 | ||||||||
\(117\) | −1.46754e8 | −0.0724027 | ||||||||
\(118\) | −4.01937e7 | −0.0190849 | ||||||||
\(119\) | 1.42233e8 | 0.0650186 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.22956e8 | −0.0521454 | ||||||||
\(122\) | −2.77545e7 | −0.0113427 | ||||||||
\(123\) | −4.95370e8 | −0.195145 | ||||||||
\(124\) | 2.86906e9 | 1.08979 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 852136. | 0.000301191 0 | ||||||||
\(127\) | 7.74572e7 | 0.0264207 | 0.0132104 | − | 0.999913i | \(-0.495795\pi\) | ||||
0.0132104 | + | 0.999913i | \(0.495795\pi\) | |||||||
\(128\) | −1.20021e8 | −0.0395196 | ||||||||
\(129\) | 3.15101e9 | 1.00183 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.50478e9 | 1.33645 | 0.668225 | − | 0.743960i | \(-0.267055\pi\) | ||||
0.668225 | + | 0.743960i | \(0.267055\pi\) | |||||||
\(132\) | 1.96043e9 | 0.562041 | ||||||||
\(133\) | −1.44356e8 | −0.0400039 | ||||||||
\(134\) | 4.25178e7 | 0.0113920 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.60694e7 | −0.0140540 | ||||||||
\(137\) | −6.80091e9 | −1.64939 | −0.824697 | − | 0.565575i | \(-0.808654\pi\) | ||||
−0.824697 | + | 0.565575i | \(0.808654\pi\) | |||||||
\(138\) | −1.79351e7 | −0.00420968 | ||||||||
\(139\) | 1.95054e9 | 0.443187 | 0.221594 | − | 0.975139i | \(-0.428874\pi\) | ||||
0.221594 | + | 0.975139i | \(0.428874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.12888e9 | −0.879723 | ||||||||
\(142\) | −2.53913e7 | −0.00524068 | ||||||||
\(143\) | −1.05745e9 | −0.211469 | ||||||||
\(144\) | 1.71942e9 | 0.333236 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.31000e7 | −0.00420751 | ||||||||
\(147\) | 3.24132e9 | 0.572524 | ||||||||
\(148\) | −2.42512e9 | −0.415486 | ||||||||
\(149\) | −1.06040e10 | −1.76251 | −0.881257 | − | 0.472637i | \(-0.843302\pi\) | ||||
−0.881257 | + | 0.472637i | \(0.843302\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.54596e9 | −1.02465 | −0.512327 | − | 0.858791i | \(-0.671216\pi\) | ||||
−0.512327 | + | 0.858791i | \(0.671216\pi\) | |||||||
\(152\) | 5.69065e7 | 0.00864701 | ||||||||
\(153\) | 1.60666e9 | 0.237035 | ||||||||
\(154\) | 6.14012e6 | 0.000879698 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9.27543e8 | −0.125393 | ||||||||
\(157\) | 4.83783e9 | 0.635480 | 0.317740 | − | 0.948178i | \(-0.397076\pi\) | ||||
0.317740 | + | 0.948178i | \(0.397076\pi\) | |||||||
\(158\) | −4.35687e6 | −0.000556183 0 | ||||||||
\(159\) | −9.46068e8 | −0.117391 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.75137e8 | 0.0674614 | ||||||||
\(162\) | 9.62573e6 | 0.00109803 | ||||||||
\(163\) | 5.42724e9 | 0.602191 | 0.301096 | − | 0.953594i | \(-0.402648\pi\) | ||||
0.301096 | + | 0.953594i | \(0.402648\pi\) | |||||||
\(164\) | −3.13092e9 | −0.337967 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.23595e8 | −0.0126332 | ||||||||
\(167\) | −1.36699e10 | −1.36000 | −0.680002 | − | 0.733210i | \(-0.738021\pi\) | ||||
−0.680002 | + | 0.733210i | \(0.738021\pi\) | |||||||
\(168\) | 1.07722e7 | 0.00104330 | ||||||||
\(169\) | −1.01042e10 | −0.952821 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.63065e9 | −0.145840 | ||||||||
\(172\) | 1.99156e10 | 1.73506 | ||||||||
\(173\) | −1.84099e10 | −1.56259 | −0.781294 | − | 0.624163i | \(-0.785440\pi\) | ||||
−0.781294 | + | 0.624163i | \(0.785440\pi\) | |||||||
\(174\) | 7.87897e7 | 0.00651625 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.23894e10 | 0.973293 | ||||||||
\(177\) | 1.45596e10 | 1.11499 | ||||||||
\(178\) | 7.28280e7 | 0.00543762 | ||||||||
\(179\) | −2.21847e10 | −1.61516 | −0.807580 | − | 0.589758i | \(-0.799223\pi\) | ||||
−0.807580 | + | 0.589758i | \(0.799223\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.26287e10 | −0.874593 | −0.437297 | − | 0.899317i | \(-0.644064\pi\) | ||||
−0.437297 | + | 0.899317i | \(0.644064\pi\) | |||||||
\(182\) | −2.90509e6 | −0.000196263 0 | ||||||||
\(183\) | 1.00537e10 | 0.662668 | ||||||||
\(184\) | −2.26725e8 | −0.0145820 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.01506e8 | 0.00621846 | ||||||||
\(187\) | 1.15769e10 | 0.692316 | ||||||||
\(188\) | −2.60960e10 | −1.52358 | ||||||||
\(189\) | −3.08674e8 | −0.0175963 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00606e9 | −0.163436 | −0.0817179 | − | 0.996655i | \(-0.526041\pi\) | ||||
−0.0817179 | + | 0.996655i | \(0.526041\pi\) | |||||||
\(192\) | 1.08653e10 | 0.577012 | ||||||||
\(193\) | −3.17884e9 | −0.164915 | −0.0824576 | − | 0.996595i | \(-0.526277\pi\) | ||||
−0.0824576 | + | 0.996595i | \(0.526277\pi\) | |||||||
\(194\) | −2.98658e7 | −0.00151379 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.04863e10 | 0.991543 | ||||||||
\(197\) | −2.67639e10 | −1.26605 | −0.633026 | − | 0.774131i | \(-0.718187\pi\) | ||||
−0.633026 | + | 0.774131i | \(0.718187\pi\) | |||||||
\(198\) | 6.93588e7 | 0.00320707 | ||||||||
\(199\) | 3.55476e8 | 0.0160684 | 0.00803419 | − | 0.999968i | \(-0.497443\pi\) | ||||
0.00803419 | + | 0.999968i | \(0.497443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.54015e10 | −0.665550 | ||||||||
\(202\) | 3.85640e7 | 0.00162968 | ||||||||
\(203\) | −2.52660e9 | −0.104425 | ||||||||
\(204\) | 1.01547e10 | 0.410516 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.86581e8 | 0.0149568 | ||||||||
\(207\) | 6.49675e9 | 0.245940 | ||||||||
\(208\) | −5.86184e9 | −0.217145 | ||||||||
\(209\) | −1.17497e10 | −0.425961 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.90979e10 | −1.35795 | −0.678973 | − | 0.734164i | \(-0.737574\pi\) | ||||
−0.678973 | + | 0.734164i | \(0.737574\pi\) | |||||||
\(212\) | −5.97950e9 | −0.203307 | ||||||||
\(213\) | 9.19765e9 | 0.306174 | ||||||||
\(214\) | −4.75523e8 | −0.0154992 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.21682e8 | 0.00380352 | ||||||||
\(217\) | −3.25505e9 | −0.0996527 | ||||||||
\(218\) | 3.70672e8 | 0.0111157 | ||||||||
\(219\) | 8.36766e9 | 0.245813 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.47741e9 | −0.154458 | ||||||||
\(222\) | −8.57995e7 | −0.00237081 | ||||||||
\(223\) | 3.00688e10 | 0.814225 | 0.407112 | − | 0.913378i | \(-0.366536\pi\) | ||||
0.407112 | + | 0.913378i | \(0.366536\pi\) | |||||||
\(224\) | 1.02128e8 | 0.00271036 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.11126e8 | 0.0104830 | ||||||||
\(227\) | −5.17270e10 | −1.29301 | −0.646503 | − | 0.762911i | \(-0.723769\pi\) | ||||
−0.646503 | + | 0.762911i | \(0.723769\pi\) | |||||||
\(228\) | −1.03063e10 | −0.252578 | ||||||||
\(229\) | 4.39043e10 | 1.05499 | 0.527494 | − | 0.849559i | \(-0.323132\pi\) | ||||
0.527494 | + | 0.849559i | \(0.323132\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.22417e9 | −0.0513942 | ||||||||
\(232\) | 9.96009e8 | 0.0225719 | ||||||||
\(233\) | 5.20811e10 | 1.15765 | 0.578826 | − | 0.815451i | \(-0.303511\pi\) | ||||
0.578826 | + | 0.815451i | \(0.303511\pi\) | |||||||
\(234\) | −3.28159e7 | −0.000715506 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.20221e10 | 1.93103 | ||||||||
\(237\) | 1.57822e9 | 0.0324937 | ||||||||
\(238\) | 3.18048e7 | 0.000642534 0 | ||||||||
\(239\) | 1.25028e9 | 0.0247866 | 0.0123933 | − | 0.999923i | \(-0.496055\pi\) | ||||
0.0123933 | + | 0.999923i | \(0.496055\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.39086e9 | 0.102939 | 0.0514696 | − | 0.998675i | \(-0.483609\pi\) | ||||
0.0514696 | + | 0.998675i | \(0.483609\pi\) | |||||||
\(242\) | −2.74944e7 | −0.000515317 0 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 6.35431e10 | 1.14766 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.10770e8 | −0.00192848 | ||||||||
\(247\) | 5.55918e9 | 0.0950331 | ||||||||
\(248\) | 1.28317e9 | 0.0215403 | ||||||||
\(249\) | 4.47705e10 | 0.738065 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.79306e10 | 0.603196 | 0.301598 | − | 0.953435i | \(-0.402480\pi\) | ||||
0.301598 | + | 0.953435i | \(0.402480\pi\) | |||||||
\(252\) | −1.95094e9 | −0.0304748 | ||||||||
\(253\) | 4.68128e10 | 0.718327 | ||||||||
\(254\) | 1.73203e7 | 0.000261098 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.86524e10 | 0.999024 | ||||||||
\(257\) | −1.23297e10 | −0.176301 | −0.0881504 | − | 0.996107i | \(-0.528096\pi\) | ||||
−0.0881504 | + | 0.996107i | \(0.528096\pi\) | |||||||
\(258\) | 7.04601e8 | 0.00990044 | ||||||||
\(259\) | 2.75139e9 | 0.0379929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.85405e10 | −0.380696 | ||||||||
\(262\) | 1.00732e9 | 0.0132072 | ||||||||
\(263\) | 8.86491e10 | 1.14255 | 0.571273 | − | 0.820760i | \(-0.306450\pi\) | ||||
0.571273 | + | 0.820760i | \(0.306450\pi\) | |||||||
\(264\) | 8.76789e8 | 0.0111091 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.22796e7 | −0.000395331 0 | ||||||||
\(267\) | −2.63809e10 | −0.317680 | ||||||||
\(268\) | −9.73431e10 | −1.15265 | ||||||||
\(269\) | 6.53334e10 | 0.760764 | 0.380382 | − | 0.924829i | \(-0.375793\pi\) | ||||
0.380382 | + | 0.924829i | \(0.375793\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.43373e10 | −0.499353 | −0.249676 | − | 0.968329i | \(-0.580324\pi\) | ||||
−0.249676 | + | 0.968329i | \(0.580324\pi\) | |||||||
\(272\) | 6.41751e10 | 0.710896 | ||||||||
\(273\) | 1.05233e9 | 0.0114662 | ||||||||
\(274\) | −1.52076e9 | −0.0162998 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.10619e10 | 0.425940 | ||||||||
\(277\) | −1.89388e11 | −1.93283 | −0.966416 | − | 0.256984i | \(-0.917271\pi\) | ||||
−0.966416 | + | 0.256984i | \(0.917271\pi\) | |||||||
\(278\) | 4.36162e8 | 0.00437972 | ||||||||
\(279\) | −3.67691e10 | −0.363298 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.59371e11 | −1.52486 | −0.762432 | − | 0.647068i | \(-0.775995\pi\) | ||||
−0.762432 | + | 0.647068i | \(0.775995\pi\) | |||||||
\(282\) | −9.23263e8 | −0.00869369 | ||||||||
\(283\) | 9.23708e10 | 0.856043 | 0.428022 | − | 0.903769i | \(-0.359211\pi\) | ||||
0.428022 | + | 0.903769i | \(0.359211\pi\) | |||||||
\(284\) | 5.81325e10 | 0.530257 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.36457e8 | −0.00208980 | ||||||||
\(287\) | 3.55214e9 | 0.0309045 | ||||||||
\(288\) | 1.15363e9 | 0.00988102 | ||||||||
\(289\) | −5.86215e10 | −0.494330 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.08185e10 | 0.0884396 | ||||||||
\(292\) | 5.28867e10 | 0.425720 | ||||||||
\(293\) | −1.47354e11 | −1.16804 | −0.584018 | − | 0.811740i | \(-0.698520\pi\) | ||||
−0.584018 | + | 0.811740i | \(0.698520\pi\) | |||||||
\(294\) | 7.24794e8 | 0.00565786 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.08462e9 | −0.00821232 | ||||||||
\(297\) | −2.51242e10 | −0.187365 | ||||||||
\(298\) | −2.37118e9 | −0.0174177 | ||||||||
\(299\) | −2.21487e10 | −0.160261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.25949e10 | −0.158658 | ||||||||
\(302\) | −1.46375e9 | −0.0101259 | ||||||||
\(303\) | −1.39693e10 | −0.0952099 | ||||||||
\(304\) | −6.51332e10 | −0.437392 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.59267e8 | 0.00234245 | ||||||||
\(307\) | 1.85136e11 | 1.18951 | 0.594755 | − | 0.803907i | \(-0.297249\pi\) | ||||
0.594755 | + | 0.803907i | \(0.297249\pi\) | |||||||
\(308\) | −1.40576e10 | −0.0890087 | ||||||||
\(309\) | −1.40034e11 | −0.873814 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.63232e11 | −0.989429 | −0.494715 | − | 0.869055i | \(-0.664727\pi\) | ||||
−0.494715 | + | 0.869055i | \(0.664727\pi\) | |||||||
\(312\) | −4.14838e8 | −0.00247847 | ||||||||
\(313\) | −1.58814e11 | −0.935272 | −0.467636 | − | 0.883921i | \(-0.654894\pi\) | ||||
−0.467636 | + | 0.883921i | \(0.654894\pi\) | |||||||
\(314\) | 1.08179e9 | 0.00628001 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.97491e9 | 0.0562752 | ||||||||
\(317\) | 2.22998e11 | 1.24032 | 0.620161 | − | 0.784474i | \(-0.287067\pi\) | ||||
0.620161 | + | 0.784474i | \(0.287067\pi\) | |||||||
\(318\) | −2.11551e8 | −0.00116010 | ||||||||
\(319\) | −2.05650e11 | −1.11191 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.72252e11 | 0.905504 | ||||||||
\(322\) | 1.28607e8 | 0.000666674 0 | ||||||||
\(323\) | −6.08616e10 | −0.311123 | ||||||||
\(324\) | −2.20378e10 | −0.111100 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.21359e9 | 0.00595104 | ||||||||
\(327\) | −1.34271e11 | −0.649406 | ||||||||
\(328\) | −1.40029e9 | −0.00668012 | ||||||||
\(329\) | 2.96068e10 | 0.139319 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.64535e11 | 1.21131 | 0.605657 | − | 0.795725i | \(-0.292910\pi\) | ||||
0.605657 | + | 0.795725i | \(0.292910\pi\) | |||||||
\(332\) | 2.82966e11 | 1.27824 | ||||||||
\(333\) | 3.10797e10 | 0.138509 | ||||||||
\(334\) | −3.05674e9 | −0.0134400 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.23294e10 | −0.0527735 | ||||||||
\(337\) | −1.13648e11 | −0.479986 | −0.239993 | − | 0.970775i | \(-0.577145\pi\) | ||||
−0.239993 | + | 0.970775i | \(0.577145\pi\) | |||||||
\(338\) | −2.25941e9 | −0.00941607 | ||||||||
\(339\) | −1.48925e11 | −0.612446 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.64942e11 | −1.06110 | ||||||||
\(342\) | −3.64631e8 | −0.00144124 | ||||||||
\(343\) | −4.66808e10 | −0.182102 | ||||||||
\(344\) | 8.90711e9 | 0.0342945 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.11667e9 | −0.0154420 | ||||||||
\(347\) | 3.78341e11 | 1.40088 | 0.700441 | − | 0.713711i | \(-0.252987\pi\) | ||||
0.700441 | + | 0.713711i | \(0.252987\pi\) | |||||||
\(348\) | −1.80386e11 | −0.659321 | ||||||||
\(349\) | −4.60370e11 | −1.66109 | −0.830545 | − | 0.556952i | \(-0.811971\pi\) | ||||
−0.830545 | + | 0.556952i | \(0.811971\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.18871e10 | 0.0418017 | ||||||||
\(352\) | 8.31258e9 | 0.0288598 | ||||||||
\(353\) | 1.01736e11 | 0.348728 | 0.174364 | − | 0.984681i | \(-0.444213\pi\) | ||||
0.174364 | + | 0.984681i | \(0.444213\pi\) | |||||||
\(354\) | 3.25569e9 | 0.0110186 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.66737e11 | −0.550184 | ||||||||
\(357\) | −1.15208e10 | −0.0375385 | ||||||||
\(358\) | −4.96075e9 | −0.0159615 | ||||||||
\(359\) | 6.76144e10 | 0.214839 | 0.107420 | − | 0.994214i | \(-0.465741\pi\) | ||||
0.107420 | + | 0.994214i | \(0.465741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.60917e11 | −0.808576 | ||||||||
\(362\) | −2.82392e9 | −0.00864300 | ||||||||
\(363\) | 9.95945e9 | 0.0301062 | ||||||||
\(364\) | 6.65111e9 | 0.0198581 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.24812e9 | 0.00654869 | ||||||||
\(367\) | −5.81071e11 | −1.67198 | −0.835991 | − | 0.548743i | \(-0.815107\pi\) | ||||
−0.835991 | + | 0.548743i | \(0.815107\pi\) | |||||||
\(368\) | 2.59501e11 | 0.737605 | ||||||||
\(369\) | 4.01250e10 | 0.112667 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.78395e9 | 0.0185909 | ||||||||
\(372\) | −2.32394e11 | −0.629190 | ||||||||
\(373\) | −3.30933e11 | −0.885219 | −0.442610 | − | 0.896714i | \(-0.645947\pi\) | ||||
−0.442610 | + | 0.896714i | \(0.645947\pi\) | |||||||
\(374\) | 2.58872e9 | 0.00684168 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.16713e10 | −0.0301144 | ||||||||
\(377\) | 9.72999e10 | 0.248071 | ||||||||
\(378\) | −6.90230e7 | −0.000173892 0 | ||||||||
\(379\) | 5.19853e11 | 1.29421 | 0.647104 | − | 0.762401i | \(-0.275980\pi\) | ||||
0.647104 | + | 0.762401i | \(0.275980\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.27403e9 | −0.0152540 | ||||||||
\(382\) | −6.72188e8 | −0.00161512 | ||||||||
\(383\) | 4.51303e11 | 1.07170 | 0.535850 | − | 0.844313i | \(-0.319991\pi\) | ||||
0.535850 | + | 0.844313i | \(0.319991\pi\) | |||||||
\(384\) | 9.72170e9 | 0.0228166 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.10824e8 | −0.00162974 | ||||||||
\(387\) | −2.55232e11 | −0.578410 | ||||||||
\(388\) | 6.83767e10 | 0.153167 | ||||||||
\(389\) | 4.61900e11 | 1.02276 | 0.511381 | − | 0.859354i | \(-0.329134\pi\) | ||||
0.511381 | + | 0.859354i | \(0.329134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.42482e11 | 0.524668 | ||||||||
\(392\) | 9.16239e9 | 0.0195984 | ||||||||
\(393\) | −3.64887e11 | −0.771599 | ||||||||
\(394\) | −5.98471e9 | −0.0125115 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.58795e11 | −0.324494 | ||||||||
\(397\) | 4.81112e11 | 0.972052 | 0.486026 | − | 0.873944i | \(-0.338446\pi\) | ||||
0.486026 | + | 0.873944i | \(0.338446\pi\) | |||||||
\(398\) | 7.94885e7 | 0.000158793 0 | ||||||||
\(399\) | 1.16928e10 | 0.0230963 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.12911e11 | 0.797457 | 0.398728 | − | 0.917069i | \(-0.369452\pi\) | ||||
0.398728 | + | 0.917069i | \(0.369452\pi\) | |||||||
\(402\) | −3.44395e9 | −0.00657717 | ||||||||
\(403\) | 1.25353e11 | 0.236734 | ||||||||
\(404\) | −8.82910e10 | −0.164892 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.64976e8 | −0.00103196 | ||||||||
\(407\) | 2.23947e11 | 0.404547 | ||||||||
\(408\) | 4.54162e9 | 0.00811410 | ||||||||
\(409\) | 6.65886e11 | 1.17664 | 0.588322 | − | 0.808627i | \(-0.299789\pi\) | ||||
0.588322 | + | 0.808627i | \(0.299789\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.50874e11 | 0.952278 | ||||||||
\(412\) | −8.85064e11 | −1.51334 | ||||||||
\(413\) | −1.04402e11 | −0.176577 | ||||||||
\(414\) | 1.45275e9 | 0.00243046 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.93296e9 | −0.00643872 | ||||||||
\(417\) | −1.57993e11 | −0.255874 | ||||||||
\(418\) | −2.62737e9 | −0.00420948 | ||||||||
\(419\) | 7.79778e11 | 1.23597 | 0.617985 | − | 0.786190i | \(-0.287949\pi\) | ||||
0.617985 | + | 0.786190i | \(0.287949\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.59110e11 | 1.48799 | 0.743994 | − | 0.668187i | \(-0.232929\pi\) | ||||
0.743994 | + | 0.668187i | \(0.232929\pi\) | |||||||
\(422\) | −8.74272e9 | −0.0134196 | ||||||||
\(423\) | 3.34439e11 | 0.507908 | ||||||||
\(424\) | −2.67430e9 | −0.00401849 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.05670e9 | 0.00302571 | ||||||||
\(427\) | −7.20918e10 | −0.104945 | ||||||||
\(428\) | 1.08869e12 | 1.56823 | ||||||||
\(429\) | 8.56533e10 | 0.122092 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.89582e10 | 0.0264636 | 0.0132318 | − | 0.999912i | \(-0.495788\pi\) | ||||
0.0132318 | + | 0.999912i | \(0.495788\pi\) | |||||||
\(432\) | −1.39273e11 | −0.192394 | ||||||||
\(433\) | 8.39898e11 | 1.14824 | 0.574118 | − | 0.818773i | \(-0.305345\pi\) | ||||
0.574118 | + | 0.818773i | \(0.305345\pi\) | |||||||
\(434\) | −7.27866e8 | −0.000984799 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.48641e11 | −1.12469 | ||||||||
\(437\) | −2.46103e11 | −0.322812 | ||||||||
\(438\) | 1.87110e9 | 0.00242920 | ||||||||
\(439\) | −3.74391e11 | −0.481100 | −0.240550 | − | 0.970637i | \(-0.577328\pi\) | ||||
−0.240550 | + | 0.970637i | \(0.577328\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.62547e11 | −0.330547 | ||||||||
\(442\) | −1.22481e9 | −0.00152640 | ||||||||
\(443\) | −7.04057e11 | −0.868542 | −0.434271 | − | 0.900782i | \(-0.642994\pi\) | ||||
−0.434271 | + | 0.900782i | \(0.642994\pi\) | |||||||
\(444\) | 1.96435e11 | 0.239881 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.72372e9 | 0.00804642 | ||||||||
\(447\) | 8.58926e11 | 1.01759 | ||||||||
\(448\) | −7.79113e10 | −0.0913797 | ||||||||
\(449\) | 3.02133e11 | 0.350824 | 0.175412 | − | 0.984495i | \(-0.443874\pi\) | ||||
0.175412 | + | 0.984495i | \(0.443874\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.89123e11 | 0.329070 | ||||||||
\(452\) | −9.41258e11 | −1.06068 | ||||||||
\(453\) | 5.30223e11 | 0.591584 | ||||||||
\(454\) | −1.15667e10 | −0.0127779 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.60943e9 | −0.00499235 | ||||||||
\(457\) | 2.44866e11 | 0.262607 | 0.131303 | − | 0.991342i | \(-0.458084\pi\) | ||||
0.131303 | + | 0.991342i | \(0.458084\pi\) | |||||||
\(458\) | 9.81749e9 | 0.0104257 | ||||||||
\(459\) | −1.30139e11 | −0.136852 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.68075e11 | −0.585803 | −0.292902 | − | 0.956143i | \(-0.594621\pi\) | ||||
−0.292902 | + | 0.956143i | \(0.594621\pi\) | |||||||
\(462\) | −4.97350e8 | −0.000507894 0 | ||||||||
\(463\) | 3.27020e11 | 0.330720 | 0.165360 | − | 0.986233i | \(-0.447121\pi\) | ||||
0.165360 | + | 0.986233i | \(0.447121\pi\) | |||||||
\(464\) | −1.14000e12 | −1.14175 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.16459e10 | 0.0114403 | ||||||||
\(467\) | −7.11477e11 | −0.692205 | −0.346102 | − | 0.938197i | \(-0.612495\pi\) | ||||
−0.346102 | + | 0.938197i | \(0.612495\pi\) | |||||||
\(468\) | 7.51310e10 | 0.0723957 | ||||||||
\(469\) | 1.10439e11 | 0.105401 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.91864e11 | −0.366894 | ||||||||
\(472\) | 4.11563e10 | 0.0381678 | ||||||||
\(473\) | −1.83909e12 | −1.68938 | ||||||||
\(474\) | 3.52907e8 | 0.000321113 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.28160e10 | −0.0650123 | ||||||||
\(477\) | 7.66315e10 | 0.0677758 | ||||||||
\(478\) | 2.79577e8 | 0.000244949 0 | ||||||||
\(479\) | 3.36653e11 | 0.292195 | 0.146098 | − | 0.989270i | \(-0.453329\pi\) | ||||
0.146098 | + | 0.989270i | \(0.453329\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.05957e11 | −0.0902557 | ||||||||
\(482\) | 1.20546e9 | 0.00101728 | ||||||||
\(483\) | −4.65861e10 | −0.0389488 | ||||||||
\(484\) | 6.29474e10 | 0.0521403 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.79684e8 | −0.000633951 0 | ||||||||
\(487\) | 1.66615e12 | 1.34225 | 0.671127 | − | 0.741342i | \(-0.265810\pi\) | ||||
0.671127 | + | 0.741342i | \(0.265810\pi\) | |||||||
\(488\) | 2.84193e10 | 0.0226842 | ||||||||
\(489\) | −4.39606e11 | −0.347675 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.80759e11 | 0.606248 | 0.303124 | − | 0.952951i | \(-0.401970\pi\) | ||||
0.303124 | + | 0.952951i | \(0.401970\pi\) | |||||||
\(492\) | 2.53605e11 | 0.195126 | ||||||||
\(493\) | −1.06523e12 | −0.812145 | ||||||||
\(494\) | 1.24310e9 | 0.000939146 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.46867e12 | −1.08958 | ||||||||
\(497\) | −6.59534e10 | −0.0484879 | ||||||||
\(498\) | 1.00112e10 | 0.00729378 | ||||||||
\(499\) | −5.98100e11 | −0.431838 | −0.215919 | − | 0.976411i | \(-0.569275\pi\) | ||||
−0.215919 | + | 0.976411i | \(0.569275\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.10726e12 | 0.785199 | ||||||||
\(502\) | 8.48171e9 | 0.00596097 | ||||||||
\(503\) | −2.15422e12 | −1.50050 | −0.750248 | − | 0.661156i | \(-0.770066\pi\) | ||||
−0.750248 | + | 0.661156i | \(0.770066\pi\) | |||||||
\(504\) | −8.72544e8 | −0.000602352 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.04679e10 | 0.00709873 | ||||||||
\(507\) | 8.18439e11 | 0.550111 | ||||||||
\(508\) | −3.96542e10 | −0.0264181 | ||||||||
\(509\) | −2.28931e12 | −1.51173 | −0.755866 | − | 0.654726i | \(-0.772784\pi\) | ||||
−0.755866 | + | 0.654726i | \(0.772784\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00018e10 | −0.0389287 | ||||||||
\(512\) | 7.68022e10 | 0.0493923 | ||||||||
\(513\) | 1.32082e11 | 0.0842009 | ||||||||
\(514\) | −2.75706e9 | −0.00174226 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.61316e12 | −1.00174 | ||||||||
\(517\) | 2.40982e12 | 1.48347 | ||||||||
\(518\) | 6.15241e8 | 0.000375458 0 | ||||||||
\(519\) | 1.49120e12 | 0.902161 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.81335e12 | 1.07823 | 0.539114 | − | 0.842233i | \(-0.318759\pi\) | ||||
0.539114 | + | 0.842233i | \(0.318759\pi\) | |||||||
\(522\) | −6.38197e9 | −0.00376216 | ||||||||
\(523\) | −2.18455e11 | −0.127675 | −0.0638373 | − | 0.997960i | \(-0.520334\pi\) | ||||
−0.0638373 | + | 0.997960i | \(0.520334\pi\) | |||||||
\(524\) | −2.30622e12 | −1.33632 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.98229e10 | 0.0112910 | ||||||||
\(527\) | −1.37235e12 | −0.775030 | ||||||||
\(528\) | −1.00354e12 | −0.561931 | ||||||||
\(529\) | −8.20641e11 | −0.455620 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.17933e12 | −0.643738 | ||||||||
\(532\) | 7.39031e10 | 0.0400000 | ||||||||
\(533\) | −1.36794e11 | −0.0734165 | ||||||||
\(534\) | −5.89907e9 | −0.00313941 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.35361e10 | −0.0227829 | ||||||||
\(537\) | 1.79696e12 | 0.932513 | ||||||||
\(538\) | 1.46093e10 | 0.00751811 | ||||||||
\(539\) | −1.89180e12 | −0.965439 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00780e12 | −0.505811 | −0.252906 | − | 0.967491i | \(-0.581386\pi\) | ||||
−0.252906 | + | 0.967491i | \(0.581386\pi\) | |||||||
\(542\) | −9.91431e9 | −0.00493476 | ||||||||
\(543\) | 1.02293e12 | 0.504947 | ||||||||
\(544\) | 4.30578e10 | 0.0210793 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.35313e8 | 0.000113313 0 | ||||||||
\(547\) | −1.06674e12 | −0.509468 | −0.254734 | − | 0.967011i | \(-0.581988\pi\) | ||||
−0.254734 | + | 0.967011i | \(0.581988\pi\) | |||||||
\(548\) | 3.48173e12 | 1.64923 | ||||||||
\(549\) | −8.14349e11 | −0.382591 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.08114e12 | 0.499688 | ||||||||
\(552\) | 1.83647e10 | 0.00841895 | ||||||||
\(553\) | −1.13169e10 | −0.00514593 | ||||||||
\(554\) | −4.23493e10 | −0.0191008 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.98577e11 | −0.443144 | ||||||||
\(557\) | −2.02018e12 | −0.889286 | −0.444643 | − | 0.895708i | \(-0.646669\pi\) | ||||
−0.444643 | + | 0.895708i | \(0.646669\pi\) | |||||||
\(558\) | −8.22197e9 | −0.00359023 | ||||||||
\(559\) | 8.70134e11 | 0.376906 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.37728e11 | −0.399709 | ||||||||
\(562\) | −3.56372e10 | −0.0150692 | ||||||||
\(563\) | −5.92218e11 | −0.248424 | −0.124212 | − | 0.992256i | \(-0.539640\pi\) | ||||
−0.124212 | + | 0.992256i | \(0.539640\pi\) | |||||||
\(564\) | 2.11378e12 | 0.879637 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.06551e10 | 0.00845968 | ||||||||
\(567\) | 2.50026e10 | 0.0101592 | ||||||||
\(568\) | 2.59994e10 | 0.0104808 | ||||||||
\(569\) | −1.47778e12 | −0.591025 | −0.295512 | − | 0.955339i | \(-0.595490\pi\) | ||||
−0.295512 | + | 0.955339i | \(0.595490\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.63251e11 | 0.0642677 | 0.0321339 | − | 0.999484i | \(-0.489770\pi\) | ||||
0.0321339 | + | 0.999484i | \(0.489770\pi\) | |||||||
\(572\) | 5.41361e11 | 0.211449 | ||||||||
\(573\) | 2.43491e11 | 0.0943597 | ||||||||
\(574\) | 7.94298e8 | 0.000305408 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.80087e11 | −0.333138 | ||||||||
\(577\) | 1.06656e12 | 0.400584 | 0.200292 | − | 0.979736i | \(-0.435811\pi\) | ||||
0.200292 | + | 0.979736i | \(0.435811\pi\) | |||||||
\(578\) | −1.31084e10 | −0.00488512 | ||||||||
\(579\) | 2.57486e11 | 0.0952138 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.21035e11 | −0.116885 | ||||||||
\(582\) | 2.41913e9 | 0.000873988 0 | ||||||||
\(583\) | 5.52173e11 | 0.197955 | ||||||||
\(584\) | 2.36533e10 | 0.00841460 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.29499e10 | −0.0115429 | ||||||||
\(587\) | −2.49441e12 | −0.867153 | −0.433577 | − | 0.901117i | \(-0.642749\pi\) | ||||
−0.433577 | + | 0.901117i | \(0.642749\pi\) | |||||||
\(588\) | −1.65939e12 | −0.572468 | ||||||||
\(589\) | 1.39284e12 | 0.476852 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.16788e12 | 0.730955 | ||||||||
\(592\) | 1.24142e12 | 0.415405 | ||||||||
\(593\) | −1.76944e12 | −0.587610 | −0.293805 | − | 0.955865i | \(-0.594922\pi\) | ||||
−0.293805 | + | 0.955865i | \(0.594922\pi\) | |||||||
\(594\) | −5.61806e9 | −0.00185160 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.42873e12 | 1.76234 | ||||||||
\(597\) | −2.87936e10 | −0.00927708 | ||||||||
\(598\) | −4.95269e9 | −0.00158375 | ||||||||
\(599\) | 5.49741e12 | 1.74477 | 0.872383 | − | 0.488823i | \(-0.162574\pi\) | ||||
0.872383 | + | 0.488823i | \(0.162574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.24474e11 | 0.132714 | 0.0663569 | − | 0.997796i | \(-0.478862\pi\) | ||||
0.0663569 | + | 0.997796i | \(0.478862\pi\) | |||||||
\(602\) | −5.05247e9 | −0.00156790 | ||||||||
\(603\) | 1.24752e12 | 0.384255 | ||||||||
\(604\) | 3.35120e12 | 1.02455 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.12369e9 | −0.000940894 0 | ||||||||
\(607\) | −2.57263e12 | −0.769181 | −0.384590 | − | 0.923087i | \(-0.625657\pi\) | ||||
−0.384590 | + | 0.923087i | \(0.625657\pi\) | |||||||
\(608\) | −4.37006e10 | −0.0129695 | ||||||||
\(609\) | 2.04655e11 | 0.0602898 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.14017e12 | −0.330965 | ||||||||
\(612\) | −8.22529e11 | −0.237012 | ||||||||
\(613\) | 3.01773e12 | 0.863194 | 0.431597 | − | 0.902066i | \(-0.357950\pi\) | ||||
0.431597 | + | 0.902066i | \(0.357950\pi\) | |||||||
\(614\) | 4.13985e10 | 0.0117551 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.28717e9 | −0.00175931 | ||||||||
\(617\) | −2.87854e12 | −0.799631 | −0.399816 | − | 0.916596i | \(-0.630926\pi\) | ||||
−0.399816 | + | 0.916596i | \(0.630926\pi\) | |||||||
\(618\) | −3.13131e10 | −0.00863531 | ||||||||
\(619\) | 5.36553e12 | 1.46894 | 0.734471 | − | 0.678640i | \(-0.237431\pi\) | ||||
0.734471 | + | 0.678640i | \(0.237431\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.26237e11 | −0.141994 | ||||||||
\(622\) | −3.65006e10 | −0.00977785 | ||||||||
\(623\) | 1.89169e11 | 0.0503100 | ||||||||
\(624\) | 4.74809e11 | 0.125368 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.55125e10 | −0.00924265 | ||||||||
\(627\) | 9.51728e11 | 0.245928 | ||||||||
\(628\) | −2.47672e12 | −0.635418 | ||||||||
\(629\) | 1.16001e12 | 0.295483 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.28798e12 | 0.825653 | 0.412826 | − | 0.910810i | \(-0.364542\pi\) | ||||
0.412826 | + | 0.910810i | \(0.364542\pi\) | |||||||
\(632\) | 4.46122e9 | 0.00111231 | ||||||||
\(633\) | 3.16693e12 | 0.784010 | ||||||||
\(634\) | 4.98649e10 | 0.0122573 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.84339e11 | 0.117380 | ||||||||
\(637\) | 8.95071e11 | 0.215392 | ||||||||
\(638\) | −4.59857e10 | −0.0109883 | ||||||||
\(639\) | −7.45009e11 | −0.176770 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.40972e12 | −1.03169 | −0.515846 | − | 0.856681i | \(-0.672522\pi\) | ||||
−0.515846 | + | 0.856681i | \(0.672522\pi\) | |||||||
\(642\) | 3.85174e10 | 0.00894848 | ||||||||
\(643\) | 4.91168e12 | 1.13313 | 0.566566 | − | 0.824016i | \(-0.308272\pi\) | ||||
0.566566 | + | 0.824016i | \(0.308272\pi\) | |||||||
\(644\) | −2.94442e11 | −0.0674548 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.36093e10 | −0.00307461 | ||||||||
\(647\) | −2.80990e12 | −0.630408 | −0.315204 | − | 0.949024i | \(-0.602073\pi\) | ||||
−0.315204 | + | 0.949024i | \(0.602073\pi\) | |||||||
\(648\) | −9.85626e9 | −0.00219596 | ||||||||
\(649\) | −8.49772e12 | −1.88019 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.63659e11 | 0.0575345 | ||||||||
\(652\) | −2.77847e12 | −0.602133 | ||||||||
\(653\) | −2.56025e12 | −0.551028 | −0.275514 | − | 0.961297i | \(-0.588848\pi\) | ||||
−0.275514 | + | 0.961297i | \(0.588848\pi\) | |||||||
\(654\) | −3.00244e10 | −0.00641763 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.60272e12 | 0.337901 | ||||||||
\(657\) | −6.77781e11 | −0.141920 | ||||||||
\(658\) | 6.62042e9 | 0.00137679 | ||||||||
\(659\) | 8.27996e12 | 1.71019 | 0.855094 | − | 0.518472i | \(-0.173499\pi\) | ||||
0.855094 | + | 0.518472i | \(0.173499\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.18671e11 | −0.0649286 | −0.0324643 | − | 0.999473i | \(-0.510336\pi\) | ||||
−0.0324643 | + | 0.999473i | \(0.510336\pi\) | |||||||
\(662\) | 5.91530e10 | 0.0119706 | ||||||||
\(663\) | 4.43670e11 | 0.0891762 | ||||||||
\(664\) | 1.26555e11 | 0.0252652 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.94976e9 | 0.00136879 | ||||||||
\(667\) | −4.30742e12 | −0.842658 | ||||||||
\(668\) | 6.99829e12 | 1.35987 | ||||||||
\(669\) | −2.43557e12 | −0.470093 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.86784e12 | −1.11745 | ||||||||
\(672\) | −8.27234e9 | −0.00156483 | ||||||||
\(673\) | 6.44097e12 | 1.21027 | 0.605136 | − | 0.796122i | \(-0.293119\pi\) | ||||
0.605136 | + | 0.796122i | \(0.293119\pi\) | |||||||
\(674\) | −2.54130e10 | −0.00474337 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.17284e12 | 0.952728 | ||||||||
\(677\) | 7.45494e12 | 1.36394 | 0.681969 | − | 0.731381i | \(-0.261124\pi\) | ||||
0.681969 | + | 0.731381i | \(0.261124\pi\) | |||||||
\(678\) | −3.33012e10 | −0.00605238 | ||||||||
\(679\) | −7.75757e10 | −0.0140059 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.18989e12 | 0.746518 | ||||||||
\(682\) | −5.92439e10 | −0.0104861 | ||||||||
\(683\) | −1.88685e11 | −0.0331776 | −0.0165888 | − | 0.999862i | \(-0.505281\pi\) | ||||
−0.0165888 | + | 0.999862i | \(0.505281\pi\) | |||||||
\(684\) | 8.34809e11 | 0.145826 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.04384e10 | −0.00179959 | ||||||||
\(687\) | −3.55625e12 | −0.609097 | ||||||||
\(688\) | −1.01948e13 | −1.73472 | ||||||||
\(689\) | −2.61251e11 | −0.0441644 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.12572e12 | −0.688412 | −0.344206 | − | 0.938894i | \(-0.611852\pi\) | ||||
−0.344206 | + | 0.938894i | \(0.611852\pi\) | |||||||
\(692\) | 9.42497e12 | 1.56244 | ||||||||
\(693\) | 1.80158e11 | 0.0296725 | ||||||||
\(694\) | 8.46014e10 | 0.0138439 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.06767e10 | −0.0130319 | ||||||||
\(697\) | 1.49761e12 | 0.240354 | ||||||||
\(698\) | −1.02944e11 | −0.0164154 | ||||||||
\(699\) | −4.21857e12 | −0.668371 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.26038e12 | −0.979196 | −0.489598 | − | 0.871948i | \(-0.662857\pi\) | ||||
−0.489598 | + | 0.871948i | \(0.662857\pi\) | |||||||
\(702\) | 2.65809e9 | 0.000413098 0 | ||||||||
\(703\) | −1.17732e12 | −0.181801 | ||||||||
\(704\) | −6.34152e12 | −0.973008 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.27492e10 | 0.00344624 | ||||||||
\(707\) | 1.00169e11 | 0.0150781 | ||||||||
\(708\) | −7.45379e12 | −1.11488 | ||||||||
\(709\) | −8.40293e12 | −1.24888 | −0.624442 | − | 0.781071i | \(-0.714674\pi\) | ||||
−0.624442 | + | 0.781071i | \(0.714674\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.27835e11 | −0.0187602 | ||||||||
\(712\) | −7.45723e10 | −0.0108747 | ||||||||
\(713\) | −5.54931e12 | −0.804148 | ||||||||
\(714\) | −2.57619e9 | −0.000370967 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.13575e13 | 1.61500 | ||||||||
\(717\) | −1.01273e11 | −0.0143105 | ||||||||
\(718\) | 1.51193e10 | 0.00212311 | ||||||||
\(719\) | −3.44185e11 | −0.0480300 | −0.0240150 | − | 0.999712i | \(-0.507645\pi\) | ||||
−0.0240150 | + | 0.999712i | \(0.507645\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.00414e12 | 0.138383 | ||||||||
\(722\) | −5.83440e10 | −0.00799060 | ||||||||
\(723\) | −4.36659e11 | −0.0594320 | ||||||||
\(724\) | 6.46528e12 | 0.874508 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.22704e9 | 0.000297519 0 | ||||||||
\(727\) | 8.67049e12 | 1.15117 | 0.575584 | − | 0.817743i | \(-0.304775\pi\) | ||||
0.575584 | + | 0.817743i | \(0.304775\pi\) | |||||||
\(728\) | 2.97467e9 | 0.000392507 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.52617e12 | −1.23393 | ||||||||
\(732\) | −5.14699e12 | −0.662603 | ||||||||
\(733\) | −1.10927e13 | −1.41929 | −0.709644 | − | 0.704561i | \(-0.751144\pi\) | ||||
−0.709644 | + | 0.704561i | \(0.751144\pi\) | |||||||
\(734\) | −1.29934e11 | −0.0165230 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.74110e11 | 0.0218713 | ||||||||
\(737\) | 8.98909e12 | 1.12231 | ||||||||
\(738\) | 8.97239e9 | 0.00111341 | ||||||||
\(739\) | −6.37409e12 | −0.786173 | −0.393087 | − | 0.919501i | \(-0.628593\pi\) | ||||
−0.393087 | + | 0.919501i | \(0.628593\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.50294e11 | −0.0548674 | ||||||||
\(742\) | 1.51697e9 | 0.000183721 0 | ||||||||
\(743\) | 6.36760e12 | 0.766525 | 0.383263 | − | 0.923639i | \(-0.374800\pi\) | ||||
0.383263 | + | 0.923639i | \(0.374800\pi\) | |||||||
\(744\) | −1.03937e11 | −0.0124363 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.40004e10 | −0.00874801 | ||||||||
\(747\) | −3.62641e12 | −0.426122 | ||||||||
\(748\) | −5.92679e12 | −0.692249 | ||||||||
\(749\) | −1.23516e12 | −0.143402 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.40024e12 | −0.390058 | −0.195029 | − | 0.980797i | \(-0.562480\pi\) | ||||
−0.195029 | + | 0.980797i | \(0.562480\pi\) | |||||||
\(752\) | 1.33586e13 | 1.52328 | ||||||||
\(753\) | −3.07238e12 | −0.348255 | ||||||||
\(754\) | 2.17573e10 | 0.00245152 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.58026e11 | 0.0175946 | ||||||||
\(757\) | −1.38522e13 | −1.53316 | −0.766581 | − | 0.642148i | \(-0.778044\pi\) | ||||
−0.766581 | + | 0.642148i | \(0.778044\pi\) | |||||||
\(758\) | 1.16245e11 | 0.0127898 | ||||||||
\(759\) | −3.79183e12 | −0.414726 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.25728e13 | −1.35894 | −0.679471 | − | 0.733703i | \(-0.737790\pi\) | ||||
−0.679471 | + | 0.733703i | \(0.737790\pi\) | |||||||
\(762\) | −1.40294e9 | −0.000150745 0 | ||||||||
\(763\) | 9.62812e11 | 0.102845 | ||||||||
\(764\) | 1.53895e12 | 0.163420 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.00916e11 | 0.0105909 | ||||||||
\(767\) | 4.02055e12 | 0.419475 | ||||||||
\(768\) | −5.56084e12 | −0.576787 | ||||||||
\(769\) | −1.11440e13 | −1.14914 | −0.574569 | − | 0.818456i | \(-0.694830\pi\) | ||||
−0.574569 | + | 0.818456i | \(0.694830\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.98707e11 | 0.101787 | ||||||||
\(772\) | 1.62741e12 | 0.164899 | ||||||||
\(773\) | 4.40857e12 | 0.444110 | 0.222055 | − | 0.975034i | \(-0.428724\pi\) | ||||
0.222055 | + | 0.975034i | \(0.428724\pi\) | |||||||
\(774\) | −5.70727e10 | −0.00571602 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.05811e10 | 0.00302744 | ||||||||
\(777\) | −2.22862e11 | −0.0219352 | ||||||||
\(778\) | 1.03286e11 | 0.0101073 | ||||||||
\(779\) | −1.51997e12 | −0.147882 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.36821e12 | −0.516297 | ||||||||
\(782\) | 5.42217e10 | 0.00518493 | ||||||||
\(783\) | 2.31178e12 | 0.219795 | ||||||||
\(784\) | −1.04869e13 | −0.991349 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.15928e10 | −0.00762518 | ||||||||
\(787\) | −1.39083e13 | −1.29237 | −0.646186 | − | 0.763180i | \(-0.723637\pi\) | ||||
−0.646186 | + | 0.763180i | \(0.723637\pi\) | |||||||
\(788\) | 1.37018e13 | 1.26593 | ||||||||
\(789\) | −7.18057e12 | −0.659649 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.06789e12 | 0.0969912 | ||||||||
\(792\) | −7.10199e10 | −0.00641382 | ||||||||
\(793\) | 2.77627e12 | 0.249306 | ||||||||
\(794\) | 1.07582e11 | 0.00960612 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.81986e11 | −0.0160668 | ||||||||
\(797\) | 1.11093e13 | 0.975266 | 0.487633 | − | 0.873049i | \(-0.337861\pi\) | ||||
0.487633 | + | 0.873049i | \(0.337861\pi\) | |||||||
\(798\) | 2.61465e9 | 0.000228245 0 | ||||||||
\(799\) | 1.24825e13 | 1.08353 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.13686e12 | 0.183412 | ||||||||
\(802\) | 9.23316e10 | 0.00788072 | ||||||||
\(803\) | −4.88379e12 | −0.414512 | ||||||||
\(804\) | 7.88479e12 | 0.665485 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.80303e10 | 0.00233948 | ||||||||
\(807\) | −5.29201e12 | −0.439227 | ||||||||
\(808\) | −3.94876e10 | −0.00325919 | ||||||||
\(809\) | 8.47032e12 | 0.695235 | 0.347617 | − | 0.937636i | \(-0.386991\pi\) | ||||
0.347617 | + | 0.937636i | \(0.386991\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.98968e13 | 1.61506 | 0.807532 | − | 0.589823i | \(-0.200803\pi\) | ||||
0.807532 | + | 0.589823i | \(0.200803\pi\) | |||||||
\(812\) | 1.29349e12 | 0.104415 | ||||||||
\(813\) | 3.59132e12 | 0.288301 | ||||||||
\(814\) | 5.00769e10 | 0.00399786 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.19818e12 | −0.410436 | ||||||||
\(817\) | 9.66840e12 | 0.759198 | ||||||||
\(818\) | 1.48900e11 | 0.0116280 | ||||||||
\(819\) | −8.52387e10 | −0.00662002 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.94161e11 | −0.0610049 | −0.0305024 | − | 0.999535i | \(-0.509711\pi\) | ||||
−0.0305024 | + | 0.999535i | \(0.509711\pi\) | |||||||
\(822\) | 1.23182e11 | 0.00941071 | ||||||||
\(823\) | 1.36089e13 | 1.03401 | 0.517004 | − | 0.855983i | \(-0.327047\pi\) | ||||
0.517004 | + | 0.855983i | \(0.327047\pi\) | |||||||
\(824\) | −3.95840e11 | −0.0299121 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.33455e10 | −0.00174499 | ||||||||
\(827\) | −1.79571e13 | −1.33494 | −0.667470 | − | 0.744637i | \(-0.732623\pi\) | ||||
−0.667470 | + | 0.744637i | \(0.732623\pi\) | |||||||
\(828\) | −3.32601e12 | −0.245916 | ||||||||
\(829\) | −3.69953e12 | −0.272052 | −0.136026 | − | 0.990705i | \(-0.543433\pi\) | ||||
−0.136026 | + | 0.990705i | \(0.543433\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.53404e13 | 1.11592 | ||||||||
\(832\) | 3.00038e12 | 0.217081 | ||||||||
\(833\) | −9.79919e12 | −0.705160 | ||||||||
\(834\) | −3.53291e10 | −0.00252863 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.01527e12 | 0.425919 | ||||||||
\(837\) | 2.97829e12 | 0.209750 | ||||||||
\(838\) | 1.74367e11 | 0.0122142 | ||||||||
\(839\) | 2.50920e13 | 1.74826 | 0.874132 | − | 0.485688i | \(-0.161431\pi\) | ||||
0.874132 | + | 0.485688i | \(0.161431\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.41551e12 | 0.304368 | ||||||||
\(842\) | 2.14468e11 | 0.0147048 | ||||||||
\(843\) | 1.29091e13 | 0.880381 | ||||||||
\(844\) | 2.00162e13 | 1.35781 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.47843e10 | 0.00501931 | ||||||||
\(847\) | −7.14160e10 | −0.00476782 | ||||||||
\(848\) | 3.06091e12 | 0.203268 | ||||||||
\(849\) | −7.48203e12 | −0.494237 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.69065e12 | 0.306584 | ||||||||
\(852\) | −4.70874e12 | −0.306144 | ||||||||
\(853\) | −6.79534e12 | −0.439481 | −0.219741 | − | 0.975558i | \(-0.570521\pi\) | ||||
−0.219741 | + | 0.975558i | \(0.570521\pi\) | |||||||
\(854\) | −1.61205e10 | −0.00103710 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.86912e11 | 0.0309969 | ||||||||
\(857\) | −1.31867e13 | −0.835070 | −0.417535 | − | 0.908661i | \(-0.637106\pi\) | ||||
−0.417535 | + | 0.908661i | \(0.637106\pi\) | |||||||
\(858\) | 1.91530e10 | 0.00120655 | ||||||||
\(859\) | 1.27461e13 | 0.798747 | 0.399374 | − | 0.916788i | \(-0.369228\pi\) | ||||
0.399374 | + | 0.916788i | \(0.369228\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.87723e11 | −0.0178427 | ||||||||
\(862\) | 4.23926e9 | 0.000261522 0 | ||||||||
\(863\) | −8.12433e12 | −0.498585 | −0.249292 | − | 0.968428i | \(-0.580198\pi\) | ||||
−0.249292 | + | 0.968428i | \(0.580198\pi\) | |||||||
\(864\) | −9.34444e10 | −0.00570481 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.87811e11 | 0.0113472 | ||||||||
\(867\) | 4.74835e12 | 0.285402 | ||||||||
\(868\) | 1.66642e12 | 0.0996429 | ||||||||
\(869\) | −9.21126e11 | −0.0547937 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.25304e12 | −0.250390 | ||||||||
\(872\) | −3.79550e11 | −0.0222303 | ||||||||
\(873\) | −8.76295e11 | −0.0510607 | ||||||||
\(874\) | −5.50313e10 | −0.00319013 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.28382e12 | −0.245789 | ||||||||
\(877\) | −6.46585e12 | −0.369086 | −0.184543 | − | 0.982824i | \(-0.559080\pi\) | ||||
−0.184543 | + | 0.982824i | \(0.559080\pi\) | |||||||
\(878\) | −8.37180e10 | −0.00475438 | ||||||||
\(879\) | 1.19356e13 | 0.674366 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.69271e13 | −0.946653 | −0.473326 | − | 0.880887i | \(-0.656947\pi\) | ||||
−0.473326 | + | 0.880887i | \(0.656947\pi\) | |||||||
\(882\) | −5.87084e10 | −0.00326656 | ||||||||
\(883\) | 3.56100e13 | 1.97128 | 0.985642 | − | 0.168846i | \(-0.0540041\pi\) | ||||
0.985642 | + | 0.168846i | \(0.0540041\pi\) | |||||||
\(884\) | 2.80416e12 | 0.154443 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.57435e11 | −0.00858321 | ||||||||
\(887\) | −2.18278e13 | −1.18400 | −0.592002 | − | 0.805936i | \(-0.701662\pi\) | ||||
−0.592002 | + | 0.805936i | \(0.701662\pi\) | |||||||
\(888\) | 8.78544e10 | 0.00474139 | ||||||||
\(889\) | 4.49891e10 | 0.00241573 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.03506e12 | 0.108175 | ||||||||
\(892\) | −1.53937e13 | −0.814145 | ||||||||
\(893\) | −1.26688e13 | −0.666661 | ||||||||
\(894\) | 1.92066e11 | 0.0100561 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.97112e10 | −0.00361340 | ||||||||
\(897\) | 1.79404e12 | 0.0925266 | ||||||||
\(898\) | 6.75602e10 | 0.00346695 | ||||||||
\(899\) | 2.43783e13 | 1.24476 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.86016e12 | 0.144587 | ||||||||
\(902\) | 6.46511e10 | 0.00325197 | ||||||||
\(903\) | 1.83019e12 | 0.0916010 | ||||||||
\(904\) | −4.20972e11 | −0.0209650 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.18564e11 | 0.00584622 | ||||||||
\(907\) | −4.79737e12 | −0.235380 | −0.117690 | − | 0.993050i | \(-0.537549\pi\) | ||||
−0.117690 | + | 0.993050i | \(0.537549\pi\) | |||||||
\(908\) | 2.64816e13 | 1.29288 | ||||||||
\(909\) | 1.13151e12 | 0.0549695 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.70045e13 | 0.817957 | 0.408979 | − | 0.912544i | \(-0.365885\pi\) | ||||
0.408979 | + | 0.912544i | \(0.365885\pi\) | |||||||
\(912\) | 5.27579e12 | 0.252529 | ||||||||
\(913\) | −2.61303e13 | −1.24459 | ||||||||
\(914\) | 5.47549e10 | 0.00259516 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.24768e13 | −1.05488 | ||||||||
\(917\) | 2.61649e12 | 0.122196 | ||||||||
\(918\) | −2.91006e10 | −0.00135242 | ||||||||
\(919\) | −1.12820e12 | −0.0521756 | −0.0260878 | − | 0.999660i | \(-0.508305\pi\) | ||||
−0.0260878 | + | 0.999660i | \(0.508305\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.49960e13 | −0.686764 | ||||||||
\(922\) | −1.27028e11 | −0.00578909 | ||||||||
\(923\) | 2.53988e12 | 0.115188 | ||||||||
\(924\) | 1.13866e12 | 0.0513892 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.31253e10 | 0.00326827 | ||||||||
\(927\) | 1.13427e13 | 0.504497 | ||||||||
\(928\) | −7.64873e11 | −0.0338550 | ||||||||
\(929\) | −3.97727e13 | −1.75192 | −0.875960 | − | 0.482384i | \(-0.839771\pi\) | ||||
−0.875960 | + | 0.482384i | \(0.839771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.94549e12 | 0.433863 | ||||||||
\(932\) | −2.66629e13 | −1.15754 | ||||||||
\(933\) | 1.32218e13 | 0.571247 | ||||||||
\(934\) | −1.59094e11 | −0.00684058 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.36019e10 | 0.00143094 | ||||||||
\(937\) | 3.91551e13 | 1.65944 | 0.829718 | − | 0.558184i | \(-0.188501\pi\) | ||||
0.829718 | + | 0.558184i | \(0.188501\pi\) | |||||||
\(938\) | 2.46954e10 | 0.00104161 | ||||||||
\(939\) | 1.28639e13 | 0.539980 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.55120e13 | 1.06070 | 0.530348 | − | 0.847780i | \(-0.322061\pi\) | ||||
0.530348 | + | 0.847780i | \(0.322061\pi\) | |||||||
\(942\) | −8.76251e10 | −0.00362577 | ||||||||
\(943\) | 6.05579e12 | 0.249384 | ||||||||
\(944\) | −4.71061e13 | −1.93065 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.11241e11 | −0.0166950 | ||||||||
\(947\) | 1.92093e12 | 0.0776133 | 0.0388066 | − | 0.999247i | \(-0.487644\pi\) | ||||
0.0388066 | + | 0.999247i | \(0.487644\pi\) | |||||||
\(948\) | −8.07967e11 | −0.0324905 | ||||||||
\(949\) | 2.31068e12 | 0.0924789 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.80629e13 | −0.716101 | ||||||||
\(952\) | −3.25665e10 | −0.00128501 | ||||||||
\(953\) | −3.70640e13 | −1.45558 | −0.727788 | − | 0.685802i | \(-0.759451\pi\) | ||||
−0.727788 | + | 0.685802i | \(0.759451\pi\) | |||||||
\(954\) | 1.71357e10 | 0.000669781 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.40081e11 | −0.0247842 | ||||||||
\(957\) | 1.66577e13 | 0.641963 | ||||||||
\(958\) | 7.52794e10 | 0.00288756 | ||||||||
\(959\) | −3.95014e12 | −0.150809 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.96727e12 | 0.187872 | ||||||||
\(962\) | −2.36931e10 | −0.000891935 0 | ||||||||
\(963\) | −1.39524e13 | −0.522793 | ||||||||
\(964\) | −2.75985e12 | −0.102929 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.04172e10 | −0.000384905 0 | ||||||||
\(967\) | 2.97114e13 | 1.09271 | 0.546353 | − | 0.837555i | \(-0.316016\pi\) | ||||
0.546353 | + | 0.837555i | \(0.316016\pi\) | |||||||
\(968\) | 2.81529e10 | 0.00103058 | ||||||||
\(969\) | 4.92979e12 | 0.179627 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.42639e13 | 1.59795 | 0.798975 | − | 0.601364i | \(-0.205376\pi\) | ||||
0.798975 | + | 0.601364i | \(0.205376\pi\) | |||||||
\(972\) | 1.78506e12 | 0.0641438 | ||||||||
\(973\) | 1.13292e12 | 0.0405221 | ||||||||
\(974\) | 3.72571e11 | 0.0132646 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.25277e13 | −1.14744 | ||||||||
\(977\) | 3.02165e12 | 0.106101 | 0.0530503 | − | 0.998592i | \(-0.483106\pi\) | ||||
0.0530503 | + | 0.998592i | \(0.483106\pi\) | |||||||
\(978\) | −9.83008e10 | −0.00343584 | ||||||||
\(979\) | 1.53972e13 | 0.535699 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.08759e13 | 0.374935 | ||||||||
\(982\) | 1.74586e11 | 0.00599113 | ||||||||
\(983\) | 2.56151e13 | 0.874994 | 0.437497 | − | 0.899220i | \(-0.355865\pi\) | ||||
0.437497 | + | 0.899220i | \(0.355865\pi\) | |||||||
\(984\) | 1.13423e11 | 0.00385677 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.38198e11 | −0.00802587 | ||||||||
\(987\) | −2.39815e12 | −0.0804359 | ||||||||
\(988\) | −2.84602e12 | −0.0950238 | ||||||||
\(989\) | −3.85204e13 | −1.28029 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.40641e12 | 0.145129 | 0.0725644 | − | 0.997364i | \(-0.476882\pi\) | ||||
0.0725644 | + | 0.997364i | \(0.476882\pi\) | |||||||
\(992\) | −9.85396e11 | −0.0323079 | ||||||||
\(993\) | −2.14273e13 | −0.699353 | ||||||||
\(994\) | −1.47479e10 | −0.000479172 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.29202e13 | −0.737993 | ||||||||
\(997\) | 4.49122e13 | 1.43958 | 0.719790 | − | 0.694192i | \(-0.244238\pi\) | ||||
0.719790 | + | 0.694192i | \(0.244238\pi\) | |||||||
\(998\) | −1.33742e11 | −0.00426756 | ||||||||
\(999\) | −2.51745e12 | −0.0799681 |
(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 | 75.10.a.h.1.1 | yes | 2 | |
3.2 | odd | 2 | 225.10.a.g.1.2 | 2 | |||
5.2 | odd | 4 | 75.10.b.g.49.3 | 4 | |||
5.3 | odd | 4 | 75.10.b.g.49.2 | 4 | |||
5.4 | even | 2 | 75.10.a.e.1.2 | ✓ | 2 | ||
15.2 | even | 4 | 225.10.b.j.199.2 | 4 | |||
15.8 | even | 4 | 225.10.b.j.199.3 | 4 | |||
15.14 | odd | 2 | 225.10.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.10.a.e.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
75.10.a.h.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
75.10.b.g.49.2 | 4 | 5.3 | odd | 4 | |||
75.10.b.g.49.3 | 4 | 5.2 | odd | 4 | |||
225.10.a.g.1.2 | 2 | 3.2 | odd | 2 | |||
225.10.a.l.1.1 | 2 | 15.14 | odd | 2 | |||
225.10.b.j.199.2 | 4 | 15.2 | even | 4 | |||
225.10.b.j.199.3 | 4 | 15.8 | even | 4 |