Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,9,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(72.1060139808\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.7 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.9.c.a.58.74 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 28.1432i | − | 1.75895i | −0.475946 | − | 0.879475i | \(-0.657894\pi\) | ||
0.475946 | − | 0.879475i | \(-0.342106\pi\) | |||||||
\(3\) | −46.7654 | −0.577350 | ||||||||
\(4\) | −536.039 | −2.09390 | ||||||||
\(5\) | −406.960 | −0.651135 | −0.325568 | − | 0.945519i | \(-0.605555\pi\) | ||||
−0.325568 | + | 0.945519i | \(0.605555\pi\) | |||||||
\(6\) | 1316.13i | 1.01553i | ||||||||
\(7\) | 2744.16 | 1.14292 | 0.571461 | − | 0.820629i | \(-0.306377\pi\) | ||||
0.571461 | + | 0.820629i | \(0.306377\pi\) | |||||||
\(8\) | 7881.18i | 1.92412i | ||||||||
\(9\) | 2187.00 | 0.333333 | ||||||||
\(10\) | 11453.1i | 1.14531i | ||||||||
\(11\) | − | 5707.50i | − | 0.389830i | −0.980820 | − | 0.194915i | \(-0.937557\pi\) | ||
0.980820 | − | 0.194915i | \(-0.0624431\pi\) | |||||||
\(12\) | 25068.1 | 1.20891 | ||||||||
\(13\) | − | 49047.0i | − | 1.71727i | −0.512586 | − | 0.858636i | \(-0.671312\pi\) | ||
0.512586 | − | 0.858636i | \(-0.328688\pi\) | |||||||
\(14\) | − | 77229.3i | − | 2.01034i | ||||||
\(15\) | 19031.6 | 0.375933 | ||||||||
\(16\) | 84575.7 | 1.29052 | ||||||||
\(17\) | −62224.1 | −0.745012 | −0.372506 | − | 0.928030i | \(-0.621501\pi\) | ||||
−0.372506 | + | 0.928030i | \(0.621501\pi\) | |||||||
\(18\) | − | 61549.1i | − | 0.586316i | ||||||
\(19\) | 167552. | 1.28568 | 0.642842 | − | 0.765999i | \(-0.277755\pi\) | ||||
0.642842 | + | 0.765999i | \(0.277755\pi\) | |||||||
\(20\) | 218146. | 1.36341 | ||||||||
\(21\) | −128332. | −0.659867 | ||||||||
\(22\) | −160627. | −0.685691 | ||||||||
\(23\) | − | 321556.i | − | 1.14907i | −0.818482 | − | 0.574533i | \(-0.805184\pi\) | ||
0.818482 | − | 0.574533i | \(-0.194816\pi\) | |||||||
\(24\) | − | 368567.i | − | 1.11089i | ||||||
\(25\) | −225009. | −0.576023 | ||||||||
\(26\) | −1.38034e6 | −3.02059 | ||||||||
\(27\) | −102276. | −0.192450 | ||||||||
\(28\) | −1.47097e6 | −2.39317 | ||||||||
\(29\) | −340144. | −0.480918 | −0.240459 | − | 0.970659i | \(-0.577298\pi\) | ||||
−0.240459 | + | 0.970659i | \(0.577298\pi\) | |||||||
\(30\) | − | 535610.i | − | 0.661247i | ||||||
\(31\) | − | 822696.i | − | 0.890825i | −0.895325 | − | 0.445413i | \(-0.853057\pi\) | ||
0.895325 | − | 0.445413i | \(-0.146943\pi\) | |||||||
\(32\) | − | 362646.i | − | 0.345846i | ||||||
\(33\) | 266913.i | 0.225068i | ||||||||
\(34\) | 1.75118e6i | 1.31044i | ||||||||
\(35\) | −1.11676e6 | −0.744197 | ||||||||
\(36\) | −1.17232e6 | −0.697967 | ||||||||
\(37\) | − | 506510.i | − | 0.270260i | −0.990828 | − | 0.135130i | \(-0.956855\pi\) | ||
0.990828 | − | 0.135130i | \(-0.0431451\pi\) | |||||||
\(38\) | − | 4.71543e6i | − | 2.26145i | ||||||
\(39\) | 2.29370e6i | 0.991467i | ||||||||
\(40\) | − | 3.20732e6i | − | 1.25286i | ||||||
\(41\) | 2.70031e6 | 0.955604 | 0.477802 | − | 0.878467i | \(-0.341434\pi\) | ||||
0.477802 | + | 0.878467i | \(0.341434\pi\) | |||||||
\(42\) | 3.61166e6i | 1.16067i | ||||||||
\(43\) | − | 2.76851e6i | − | 0.809788i | −0.914364 | − | 0.404894i | \(-0.867308\pi\) | ||
0.914364 | − | 0.404894i | \(-0.132692\pi\) | |||||||
\(44\) | 3.05944e6i | 0.816265i | ||||||||
\(45\) | −890021. | −0.217045 | ||||||||
\(46\) | −9.04960e6 | −2.02115 | ||||||||
\(47\) | 71974.2i | 0.0147498i | 0.999973 | + | 0.00737489i | \(0.00234752\pi\) | ||||
−0.999973 | + | 0.00737489i | \(0.997652\pi\) | |||||||
\(48\) | −3.95521e6 | −0.745084 | ||||||||
\(49\) | 1.76559e6 | 0.306271 | ||||||||
\(50\) | 6.33247e6i | 1.01319i | ||||||||
\(51\) | 2.90993e6 | 0.430133 | ||||||||
\(52\) | 2.62911e7i | 3.59580i | ||||||||
\(53\) | 2.39637e6 | 0.303704 | 0.151852 | − | 0.988403i | \(-0.451476\pi\) | ||||
0.151852 | + | 0.988403i | \(0.451476\pi\) | |||||||
\(54\) | 2.87837e6i | 0.338510i | ||||||||
\(55\) | 2.32272e6i | 0.253832i | ||||||||
\(56\) | 2.16272e7i | 2.19912i | ||||||||
\(57\) | −7.83561e6 | −0.742290 | ||||||||
\(58\) | 9.57275e6i | 0.845911i | ||||||||
\(59\) | 6.01191e6 | − | 1.05208e7i | 0.496141 | − | 0.868242i | ||||
\(60\) | −1.02017e7 | −0.787167 | ||||||||
\(61\) | − | 5.73423e6i | − | 0.414148i | −0.978325 | − | 0.207074i | \(-0.933606\pi\) | ||
0.978325 | − | 0.207074i | \(-0.0663941\pi\) | |||||||
\(62\) | −2.31533e7 | −1.56692 | ||||||||
\(63\) | 6.00147e6 | 0.380974 | ||||||||
\(64\) | 1.14454e7 | 0.682197 | ||||||||
\(65\) | 1.99601e7i | 1.11818i | ||||||||
\(66\) | 7.51179e6 | 0.395884 | ||||||||
\(67\) | − | 1.33867e7i | − | 0.664315i | −0.943224 | − | 0.332157i | \(-0.892223\pi\) | ||
0.943224 | − | 0.332157i | \(-0.107777\pi\) | |||||||
\(68\) | 3.33545e7 | 1.55998 | ||||||||
\(69\) | 1.50377e7i | 0.663413i | ||||||||
\(70\) | 3.14292e7i | 1.30900i | ||||||||
\(71\) | −2.76871e7 | −1.08954 | −0.544771 | − | 0.838585i | \(-0.683384\pi\) | ||||
−0.544771 | + | 0.838585i | \(0.683384\pi\) | |||||||
\(72\) | 1.72362e7i | 0.641372i | ||||||||
\(73\) | 1.83891e6i | 0.0647545i | 0.999476 | + | 0.0323772i | \(0.0103078\pi\) | ||||
−0.999476 | + | 0.0323772i | \(0.989692\pi\) | |||||||
\(74\) | −1.42548e7 | −0.475373 | ||||||||
\(75\) | 1.05226e7 | 0.332567 | ||||||||
\(76\) | −8.98141e7 | −2.69209 | ||||||||
\(77\) | − | 1.56623e7i | − | 0.445545i | ||||||
\(78\) | 6.45521e7 | 1.74394 | ||||||||
\(79\) | −3.52171e7 | −0.904160 | −0.452080 | − | 0.891977i | \(-0.649318\pi\) | ||||
−0.452080 | + | 0.891977i | \(0.649318\pi\) | |||||||
\(80\) | −3.44189e7 | −0.840305 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | − | 7.59953e7i | − | 1.68086i | ||||||
\(83\) | 3.28542e7i | 0.692275i | 0.938184 | + | 0.346137i | \(0.112507\pi\) | ||||
−0.938184 | + | 0.346137i | \(0.887493\pi\) | |||||||
\(84\) | 6.87907e7 | 1.38170 | ||||||||
\(85\) | 2.53227e7 | 0.485103 | ||||||||
\(86\) | −7.79145e7 | −1.42438 | ||||||||
\(87\) | 1.59070e7 | 0.277658 | ||||||||
\(88\) | 4.49818e7 | 0.750078 | ||||||||
\(89\) | 8.29411e7i | 1.32193i | 0.750415 | + | 0.660967i | \(0.229854\pi\) | ||||
−0.750415 | + | 0.660967i | \(0.770146\pi\) | |||||||
\(90\) | 2.50480e7i | 0.381771i | ||||||||
\(91\) | − | 1.34593e8i | − | 1.96271i | ||||||
\(92\) | 1.72366e8i | 2.40603i | ||||||||
\(93\) | 3.84737e7i | 0.514318i | ||||||||
\(94\) | 2.02558e6 | 0.0259441 | ||||||||
\(95\) | −6.81867e7 | −0.837154 | ||||||||
\(96\) | 1.69593e7i | 0.199674i | ||||||||
\(97\) | − | 2.69493e6i | − | 0.0304411i | −0.999884 | − | 0.0152205i | \(-0.995155\pi\) | ||
0.999884 | − | 0.0152205i | \(-0.00484503\pi\) | |||||||
\(98\) | − | 4.96894e7i | − | 0.538716i | ||||||
\(99\) | − | 1.24823e7i | − | 0.129943i | ||||||
\(100\) | 1.20614e8 | 1.20614 | ||||||||
\(101\) | 8.66455e7i | 0.832646i | 0.909217 | + | 0.416323i | \(0.136681\pi\) | ||||
−0.909217 | + | 0.416323i | \(0.863319\pi\) | |||||||
\(102\) | − | 8.18948e7i | − | 0.756581i | ||||||
\(103\) | − | 1.48893e8i | − | 1.32290i | −0.749990 | − | 0.661449i | \(-0.769942\pi\) | ||
0.749990 | − | 0.661449i | \(-0.230058\pi\) | |||||||
\(104\) | 3.86549e8 | 3.30423 | ||||||||
\(105\) | 5.22257e7 | 0.429662 | ||||||||
\(106\) | − | 6.74416e7i | − | 0.534201i | ||||||
\(107\) | −3.68069e7 | −0.280798 | −0.140399 | − | 0.990095i | \(-0.544839\pi\) | ||||
−0.140399 | + | 0.990095i | \(0.544839\pi\) | |||||||
\(108\) | 5.48238e7 | 0.402972 | ||||||||
\(109\) | − | 8.91124e7i | − | 0.631295i | −0.948877 | − | 0.315647i | \(-0.897778\pi\) | ||
0.948877 | − | 0.315647i | \(-0.102222\pi\) | |||||||
\(110\) | 6.53687e7 | 0.446477 | ||||||||
\(111\) | 2.36871e7i | 0.156034i | ||||||||
\(112\) | 2.32089e8 | 1.47497 | ||||||||
\(113\) | 3.04104e8i | 1.86513i | 0.361007 | + | 0.932563i | \(0.382433\pi\) | ||||
−0.361007 | + | 0.932563i | \(0.617567\pi\) | |||||||
\(114\) | 2.20519e8i | 1.30565i | ||||||||
\(115\) | 1.30860e8i | 0.748197i | ||||||||
\(116\) | 1.82331e8 | 1.00700 | ||||||||
\(117\) | − | 1.07266e8i | − | 0.572424i | ||||||
\(118\) | −2.96089e8 | − | 1.69194e8i | −1.52719 | − | 0.872686i | ||||
\(119\) | −1.70753e8 | −0.851490 | ||||||||
\(120\) | 1.49992e8i | 0.723340i | ||||||||
\(121\) | 1.81783e8 | 0.848033 | ||||||||
\(122\) | −1.61379e8 | −0.728465 | ||||||||
\(123\) | −1.26281e8 | −0.551718 | ||||||||
\(124\) | 4.40997e8i | 1.86530i | ||||||||
\(125\) | 2.50538e8 | 1.02620 | ||||||||
\(126\) | − | 1.68900e8i | − | 0.670114i | ||||||
\(127\) | 2.83628e8 | 1.09027 | 0.545135 | − | 0.838349i | \(-0.316479\pi\) | ||||
0.545135 | + | 0.838349i | \(0.316479\pi\) | |||||||
\(128\) | − | 4.14946e8i | − | 1.54580i | ||||||
\(129\) | 1.29470e8i | 0.467531i | ||||||||
\(130\) | 5.61742e8 | 1.96682 | ||||||||
\(131\) | 2.19846e8i | 0.746506i | 0.927730 | + | 0.373253i | \(0.121758\pi\) | ||||
−0.927730 | + | 0.373253i | \(0.878242\pi\) | |||||||
\(132\) | − | 1.43076e8i | − | 0.471271i | ||||||
\(133\) | 4.59788e8 | 1.46944 | ||||||||
\(134\) | −3.76744e8 | −1.16850 | ||||||||
\(135\) | 4.16221e7 | 0.125311 | ||||||||
\(136\) | − | 4.90400e8i | − | 1.43349i | ||||||
\(137\) | −1.43138e8 | −0.406324 | −0.203162 | − | 0.979145i | \(-0.565122\pi\) | ||||
−0.203162 | + | 0.979145i | \(0.565122\pi\) | |||||||
\(138\) | 4.23208e8 | 1.16691 | ||||||||
\(139\) | 1.34149e8 | 0.359358 | 0.179679 | − | 0.983725i | \(-0.442494\pi\) | ||||
0.179679 | + | 0.983725i | \(0.442494\pi\) | |||||||
\(140\) | 5.98627e8 | 1.55828 | ||||||||
\(141\) | − | 3.36590e6i | − | 0.00851578i | ||||||
\(142\) | 7.79204e8i | 1.91645i | ||||||||
\(143\) | −2.79936e8 | −0.669444 | ||||||||
\(144\) | 1.84967e8 | 0.430174 | ||||||||
\(145\) | 1.38425e8 | 0.313143 | ||||||||
\(146\) | 5.17529e7 | 0.113900 | ||||||||
\(147\) | −8.25687e7 | −0.176826 | ||||||||
\(148\) | 2.71509e8i | 0.565897i | ||||||||
\(149\) | − | 2.11758e8i | − | 0.429629i | −0.976655 | − | 0.214815i | \(-0.931085\pi\) | ||
0.976655 | − | 0.214815i | \(-0.0689147\pi\) | |||||||
\(150\) | − | 2.96140e8i | − | 0.584968i | ||||||
\(151\) | 9.10554e8i | 1.75145i | 0.482809 | + | 0.875726i | \(0.339617\pi\) | ||||
−0.482809 | + | 0.875726i | \(0.660383\pi\) | |||||||
\(152\) | 1.32050e9i | 2.47381i | ||||||||
\(153\) | −1.36084e8 | −0.248337 | ||||||||
\(154\) | −4.40786e8 | −0.783691 | ||||||||
\(155\) | 3.34804e8i | 0.580048i | ||||||||
\(156\) | − | 1.22951e9i | − | 2.07604i | ||||||
\(157\) | − | 1.77008e8i | − | 0.291337i | −0.989333 | − | 0.145668i | \(-0.953467\pi\) | ||
0.989333 | − | 0.145668i | \(-0.0465333\pi\) | |||||||
\(158\) | 9.91121e8i | 1.59037i | ||||||||
\(159\) | −1.12067e8 | −0.175344 | ||||||||
\(160\) | 1.47582e8i | 0.225193i | ||||||||
\(161\) | − | 8.82399e8i | − | 1.31329i | ||||||
\(162\) | − | 1.34608e8i | − | 0.195439i | ||||||
\(163\) | −9.70750e8 | −1.37517 | −0.687586 | − | 0.726103i | \(-0.741330\pi\) | ||||
−0.687586 | + | 0.726103i | \(0.741330\pi\) | |||||||
\(164\) | −1.44747e9 | −2.00094 | ||||||||
\(165\) | − | 1.08623e8i | − | 0.146550i | ||||||
\(166\) | 9.24622e8 | 1.21768 | ||||||||
\(167\) | −1.28578e9 | −1.65311 | −0.826556 | − | 0.562855i | \(-0.809703\pi\) | ||||
−0.826556 | + | 0.562855i | \(0.809703\pi\) | |||||||
\(168\) | − | 1.01140e9i | − | 1.26966i | ||||||
\(169\) | −1.58988e9 | −1.94902 | ||||||||
\(170\) | − | 7.12661e8i | − | 0.853272i | ||||||
\(171\) | 3.66435e8 | 0.428561 | ||||||||
\(172\) | 1.48403e9i | 1.69562i | ||||||||
\(173\) | 1.10174e9i | 1.22997i | 0.788539 | + | 0.614984i | \(0.210838\pi\) | ||||
−0.788539 | + | 0.614984i | \(0.789162\pi\) | |||||||
\(174\) | − | 4.47673e8i | − | 0.488387i | ||||||
\(175\) | −6.17460e8 | −0.658349 | ||||||||
\(176\) | − | 4.82715e8i | − | 0.503084i | ||||||
\(177\) | −2.81149e8 | + | 4.92009e8i | −0.286447 | + | 0.501280i | ||||
\(178\) | 2.33423e9 | 2.32521 | ||||||||
\(179\) | − | 2.16436e8i | − | 0.210823i | −0.994429 | − | 0.105411i | \(-0.966384\pi\) | ||
0.994429 | − | 0.105411i | \(-0.0336159\pi\) | |||||||
\(180\) | 4.77086e8 | 0.454471 | ||||||||
\(181\) | −7.17258e8 | −0.668284 | −0.334142 | − | 0.942523i | \(-0.608447\pi\) | ||||
−0.334142 | + | 0.942523i | \(0.608447\pi\) | |||||||
\(182\) | −3.78787e9 | −3.45230 | ||||||||
\(183\) | 2.68163e8i | 0.239108i | ||||||||
\(184\) | 2.53424e9 | 2.21094 | ||||||||
\(185\) | 2.06129e8i | 0.175976i | ||||||||
\(186\) | 1.08277e9 | 0.904660 | ||||||||
\(187\) | 3.55144e8i | 0.290428i | ||||||||
\(188\) | − | 3.85810e7i | − | 0.0308846i | ||||||
\(189\) | −2.80661e8 | −0.219956 | ||||||||
\(190\) | 1.91899e9i | 1.47251i | ||||||||
\(191\) | − | 8.84331e8i | − | 0.664479i | −0.943195 | − | 0.332240i | \(-0.892196\pi\) | ||
0.943195 | − | 0.332240i | \(-0.107804\pi\) | |||||||
\(192\) | −5.35247e8 | −0.393867 | ||||||||
\(193\) | 1.45097e9 | 1.04576 | 0.522878 | − | 0.852408i | \(-0.324858\pi\) | ||||
0.522878 | + | 0.852408i | \(0.324858\pi\) | |||||||
\(194\) | −7.58438e7 | −0.0535443 | ||||||||
\(195\) | − | 9.33444e8i | − | 0.645579i | ||||||
\(196\) | −9.46427e8 | −0.641302 | ||||||||
\(197\) | −2.08279e9 | −1.38287 | −0.691434 | − | 0.722440i | \(-0.743021\pi\) | ||||
−0.691434 | + | 0.722440i | \(0.743021\pi\) | |||||||
\(198\) | −3.51292e8 | −0.228564 | ||||||||
\(199\) | 1.28765e9 | 0.821078 | 0.410539 | − | 0.911843i | \(-0.365341\pi\) | ||||
0.410539 | + | 0.911843i | \(0.365341\pi\) | |||||||
\(200\) | − | 1.77334e9i | − | 1.10834i | ||||||
\(201\) | 6.26033e8i | 0.383542i | ||||||||
\(202\) | 2.43848e9 | 1.46458 | ||||||||
\(203\) | −9.33410e8 | −0.549652 | ||||||||
\(204\) | −1.55984e9 | −0.900655 | ||||||||
\(205\) | −1.09892e9 | −0.622228 | ||||||||
\(206\) | −4.19033e9 | −2.32691 | ||||||||
\(207\) | − | 7.03242e8i | − | 0.383022i | ||||||
\(208\) | − | 4.14818e9i | − | 2.21618i | ||||||
\(209\) | − | 9.56300e8i | − | 0.501198i | ||||||
\(210\) | − | 1.46980e9i | − | 0.755754i | ||||||
\(211\) | 1.38402e9i | 0.698253i | 0.937076 | + | 0.349127i | \(0.113522\pi\) | ||||
−0.937076 | + | 0.349127i | \(0.886478\pi\) | |||||||
\(212\) | −1.28455e9 | −0.635927 | ||||||||
\(213\) | 1.29480e9 | 0.629048 | ||||||||
\(214\) | 1.03586e9i | 0.493909i | ||||||||
\(215\) | 1.12667e9i | 0.527282i | ||||||||
\(216\) | − | 8.06055e8i | − | 0.370297i | ||||||
\(217\) | − | 2.25761e9i | − | 1.01814i | ||||||
\(218\) | −2.50791e9 | −1.11042 | ||||||||
\(219\) | − | 8.59975e7i | − | 0.0373860i | ||||||
\(220\) | − | 1.24507e9i | − | 0.531499i | ||||||
\(221\) | 3.05191e9i | 1.27939i | ||||||||
\(222\) | 6.66631e8 | 0.274457 | ||||||||
\(223\) | −4.49221e9 | −1.81652 | −0.908261 | − | 0.418403i | \(-0.862590\pi\) | ||||
−0.908261 | + | 0.418403i | \(0.862590\pi\) | |||||||
\(224\) | − | 9.95157e8i | − | 0.395275i | ||||||
\(225\) | −4.92094e8 | −0.192008 | ||||||||
\(226\) | 8.55845e9 | 3.28066 | ||||||||
\(227\) | 2.37194e9i | 0.893304i | 0.894708 | + | 0.446652i | \(0.147384\pi\) | ||||
−0.894708 | + | 0.446652i | \(0.852616\pi\) | |||||||
\(228\) | 4.20019e9 | 1.55428 | ||||||||
\(229\) | 1.73293e9i | 0.630142i | 0.949068 | + | 0.315071i | \(0.102028\pi\) | ||||
−0.949068 | + | 0.315071i | \(0.897972\pi\) | |||||||
\(230\) | 3.68282e9 | 1.31604 | ||||||||
\(231\) | 7.32452e8i | 0.257236i | ||||||||
\(232\) | − | 2.68074e9i | − | 0.925343i | ||||||
\(233\) | 9.85201e8i | 0.334273i | 0.985934 | + | 0.167136i | \(0.0534520\pi\) | ||||
−0.985934 | + | 0.167136i | \(0.946548\pi\) | |||||||
\(234\) | −3.01880e9 | −1.00686 | ||||||||
\(235\) | − | 2.92906e7i | − | 0.00960410i | ||||||
\(236\) | −3.22262e9 | + | 5.63956e9i | −1.03887 | + | 1.81801i | ||||
\(237\) | 1.64694e9 | 0.522017 | ||||||||
\(238\) | 4.80553e9i | 1.49773i | ||||||||
\(239\) | −1.03515e9 | −0.317258 | −0.158629 | − | 0.987338i | \(-0.550707\pi\) | ||||
−0.158629 | + | 0.987338i | \(0.550707\pi\) | |||||||
\(240\) | 1.60961e9 | 0.485150 | ||||||||
\(241\) | −4.76332e9 | −1.41202 | −0.706012 | − | 0.708200i | \(-0.749507\pi\) | ||||
−0.706012 | + | 0.708200i | \(0.749507\pi\) | |||||||
\(242\) | − | 5.11596e9i | − | 1.49165i | ||||||
\(243\) | −2.23677e8 | −0.0641500 | ||||||||
\(244\) | 3.07377e9i | 0.867185i | ||||||||
\(245\) | −7.18525e8 | −0.199424 | ||||||||
\(246\) | 3.55395e9i | 0.970444i | ||||||||
\(247\) | − | 8.21790e9i | − | 2.20787i | ||||||
\(248\) | 6.48382e9 | 1.71405 | ||||||||
\(249\) | − | 1.53644e9i | − | 0.399685i | ||||||
\(250\) | − | 7.05094e9i | − | 1.80504i | ||||||
\(251\) | 7.08834e9 | 1.78587 | 0.892935 | − | 0.450186i | \(-0.148642\pi\) | ||||
0.892935 | + | 0.450186i | \(0.148642\pi\) | |||||||
\(252\) | −3.21702e9 | −0.797722 | ||||||||
\(253\) | −1.83528e9 | −0.447940 | ||||||||
\(254\) | − | 7.98219e9i | − | 1.91773i | ||||||
\(255\) | −1.18423e9 | −0.280075 | ||||||||
\(256\) | −8.74790e9 | −2.03678 | ||||||||
\(257\) | 3.07457e9 | 0.704778 | 0.352389 | − | 0.935854i | \(-0.385369\pi\) | ||||
0.352389 | + | 0.935854i | \(0.385369\pi\) | |||||||
\(258\) | 3.64370e9 | 0.822364 | ||||||||
\(259\) | − | 1.38994e9i | − | 0.308886i | ||||||
\(260\) | − | 1.06994e10i | − | 2.34135i | ||||||
\(261\) | −7.43896e8 | −0.160306 | ||||||||
\(262\) | 6.18716e9 | 1.31307 | ||||||||
\(263\) | −4.06444e9 | −0.849527 | −0.424764 | − | 0.905304i | \(-0.639643\pi\) | ||||
−0.424764 | + | 0.905304i | \(0.639643\pi\) | |||||||
\(264\) | −2.10359e9 | −0.433058 | ||||||||
\(265\) | −9.75227e8 | −0.197753 | ||||||||
\(266\) | − | 1.29399e10i | − | 2.58466i | ||||||
\(267\) | − | 3.87877e9i | − | 0.763219i | ||||||
\(268\) | 7.17578e9i | 1.39101i | ||||||||
\(269\) | 1.25437e9i | 0.239562i | 0.992800 | + | 0.119781i | \(0.0382192\pi\) | ||||
−0.992800 | + | 0.119781i | \(0.961781\pi\) | |||||||
\(270\) | − | 1.17138e9i | − | 0.220416i | ||||||
\(271\) | 1.02476e10 | 1.89996 | 0.949981 | − | 0.312308i | \(-0.101102\pi\) | ||||
0.949981 | + | 0.312308i | \(0.101102\pi\) | |||||||
\(272\) | −5.26265e9 | −0.961454 | ||||||||
\(273\) | 6.29428e9i | 1.13317i | ||||||||
\(274\) | 4.02836e9i | 0.714704i | ||||||||
\(275\) | 1.28424e9i | 0.224551i | ||||||||
\(276\) | − | 8.06077e9i | − | 1.38912i | ||||||
\(277\) | −9.16453e9 | −1.55665 | −0.778325 | − | 0.627861i | \(-0.783930\pi\) | ||||
−0.778325 | + | 0.627861i | \(0.783930\pi\) | |||||||
\(278\) | − | 3.77538e9i | − | 0.632093i | ||||||
\(279\) | − | 1.79924e9i | − | 0.296942i | ||||||
\(280\) | − | 8.80140e9i | − | 1.43192i | ||||||
\(281\) | 1.18401e10 | 1.89902 | 0.949511 | − | 0.313735i | \(-0.101580\pi\) | ||||
0.949511 | + | 0.313735i | \(0.101580\pi\) | |||||||
\(282\) | −9.47271e7 | −0.0149788 | ||||||||
\(283\) | − | 9.34560e9i | − | 1.45701i | −0.685043 | − | 0.728503i | \(-0.740217\pi\) | ||
0.685043 | − | 0.728503i | \(-0.259783\pi\) | |||||||
\(284\) | 1.48414e10 | 2.28140 | ||||||||
\(285\) | 3.18878e9 | 0.483331 | ||||||||
\(286\) | 7.87828e9i | 1.17752i | ||||||||
\(287\) | 7.41007e9 | 1.09218 | ||||||||
\(288\) | − | 7.93107e8i | − | 0.115282i | ||||||
\(289\) | −3.10392e9 | −0.444958 | ||||||||
\(290\) | − | 3.89572e9i | − | 0.550802i | ||||||
\(291\) | 1.26029e8i | 0.0175752i | ||||||||
\(292\) | − | 9.85729e8i | − | 0.135590i | ||||||
\(293\) | −4.31608e9 | −0.585625 | −0.292812 | − | 0.956170i | \(-0.594591\pi\) | ||||
−0.292812 | + | 0.956170i | \(0.594591\pi\) | |||||||
\(294\) | 2.32375e9i | 0.311028i | ||||||||
\(295\) | −2.44661e9 | + | 4.28154e9i | −0.323055 | + | 0.565343i | ||||
\(296\) | 3.99190e9 | 0.520011 | ||||||||
\(297\) | 5.83739e8i | 0.0750228i | ||||||||
\(298\) | −5.95953e9 | −0.755696 | ||||||||
\(299\) | −1.57713e10 | −1.97326 | ||||||||
\(300\) | −5.64054e9 | −0.696362 | ||||||||
\(301\) | − | 7.59721e9i | − | 0.925525i | ||||||
\(302\) | 2.56259e10 | 3.08071 | ||||||||
\(303\) | − | 4.05201e9i | − | 0.480728i | ||||||
\(304\) | 1.41708e10 | 1.65920 | ||||||||
\(305\) | 2.33360e9i | 0.269666i | ||||||||
\(306\) | 3.82984e9i | 0.436812i | ||||||||
\(307\) | −3.72885e9 | −0.419780 | −0.209890 | − | 0.977725i | \(-0.567311\pi\) | ||||
−0.209890 | + | 0.977725i | \(0.567311\pi\) | |||||||
\(308\) | 8.39558e9i | 0.932928i | ||||||||
\(309\) | 6.96305e9i | 0.763775i | ||||||||
\(310\) | 9.42245e9 | 1.02027 | ||||||||
\(311\) | −1.78526e10 | −1.90835 | −0.954177 | − | 0.299242i | \(-0.903266\pi\) | ||||
−0.954177 | + | 0.299242i | \(0.903266\pi\) | |||||||
\(312\) | −1.80771e10 | −1.90770 | ||||||||
\(313\) | 1.65765e10i | 1.72710i | 0.504266 | + | 0.863548i | \(0.331763\pi\) | ||||
−0.504266 | + | 0.863548i | \(0.668237\pi\) | |||||||
\(314\) | −4.98158e9 | −0.512447 | ||||||||
\(315\) | −2.44236e9 | −0.248066 | ||||||||
\(316\) | 1.88777e10 | 1.89322 | ||||||||
\(317\) | −5.90897e9 | −0.585160 | −0.292580 | − | 0.956241i | \(-0.594514\pi\) | ||||
−0.292580 | + | 0.956241i | \(0.594514\pi\) | |||||||
\(318\) | 3.15393e9i | 0.308421i | ||||||||
\(319\) | 1.94137e9i | 0.187476i | ||||||||
\(320\) | −4.65780e9 | −0.444202 | ||||||||
\(321\) | 1.72129e9 | 0.162119 | ||||||||
\(322\) | −2.48335e10 | −2.31001 | ||||||||
\(323\) | −1.04257e10 | −0.957849 | ||||||||
\(324\) | −2.56386e9 | −0.232656 | ||||||||
\(325\) | 1.10360e10i | 0.989188i | ||||||||
\(326\) | 2.73200e10i | 2.41886i | ||||||||
\(327\) | 4.16738e9i | 0.364478i | ||||||||
\(328\) | 2.12816e10i | 1.83869i | ||||||||
\(329\) | 1.97508e8i | 0.0168578i | ||||||||
\(330\) | −3.05699e9 | −0.257774 | ||||||||
\(331\) | 8.74322e9 | 0.728382 | 0.364191 | − | 0.931324i | \(-0.381345\pi\) | ||||
0.364191 | + | 0.931324i | \(0.381345\pi\) | |||||||
\(332\) | − | 1.76111e10i | − | 1.44955i | ||||||
\(333\) | − | 1.10774e9i | − | 0.0900865i | ||||||
\(334\) | 3.61861e10i | 2.90774i | ||||||||
\(335\) | 5.44784e9i | 0.432559i | ||||||||
\(336\) | −1.08537e10 | −0.851573 | ||||||||
\(337\) | − | 9.50740e9i | − | 0.737126i | −0.929603 | − | 0.368563i | \(-0.879850\pi\) | ||
0.929603 | − | 0.368563i | \(-0.120150\pi\) | |||||||
\(338\) | 4.47442e10i | 3.42823i | ||||||||
\(339\) | − | 1.42215e10i | − | 1.07683i | ||||||
\(340\) | −1.35740e10 | −1.01576 | ||||||||
\(341\) | −4.69553e9 | −0.347270 | ||||||||
\(342\) | − | 1.03127e10i | − | 0.753817i | ||||||
\(343\) | −1.09744e10 | −0.792878 | ||||||||
\(344\) | 2.18191e10 | 1.55813 | ||||||||
\(345\) | − | 6.11972e9i | − | 0.431972i | ||||||
\(346\) | 3.10064e10 | 2.16345 | ||||||||
\(347\) | − | 1.56359e10i | − | 1.07846i | −0.842157 | − | 0.539232i | \(-0.818714\pi\) | ||
0.842157 | − | 0.539232i | \(-0.181286\pi\) | |||||||
\(348\) | −8.52676e9 | −0.581389 | ||||||||
\(349\) | 1.05023e10i | 0.707918i | 0.935261 | + | 0.353959i | \(0.115165\pi\) | ||||
−0.935261 | + | 0.353959i | \(0.884835\pi\) | |||||||
\(350\) | 1.73773e10i | 1.15800i | ||||||||
\(351\) | 5.01633e9i | 0.330489i | ||||||||
\(352\) | −2.06980e9 | −0.134821 | ||||||||
\(353\) | − | 1.77402e10i | − | 1.14251i | −0.820773 | − | 0.571254i | \(-0.806457\pi\) | ||
0.820773 | − | 0.571254i | \(-0.193543\pi\) | |||||||
\(354\) | 1.38467e10 | + | 7.91244e9i | 0.881726 | + | 0.503845i | ||||
\(355\) | 1.12675e10 | 0.709440 | ||||||||
\(356\) | − | 4.44597e10i | − | 2.76800i | ||||||
\(357\) | 7.98531e9 | 0.491608 | ||||||||
\(358\) | −6.09119e9 | −0.370826 | ||||||||
\(359\) | −1.55105e10 | −0.933787 | −0.466894 | − | 0.884313i | \(-0.654627\pi\) | ||||
−0.466894 | + | 0.884313i | \(0.654627\pi\) | |||||||
\(360\) | − | 7.01442e9i | − | 0.417620i | ||||||
\(361\) | 1.10900e10 | 0.652982 | ||||||||
\(362\) | 2.01859e10i | 1.17548i | ||||||||
\(363\) | −8.50117e9 | −0.489612 | ||||||||
\(364\) | 7.21469e10i | 4.10972i | ||||||||
\(365\) | − | 7.48363e8i | − | 0.0421639i | ||||||
\(366\) | 7.54697e9 | 0.420579 | ||||||||
\(367\) | − | 3.08457e10i | − | 1.70032i | −0.526527 | − | 0.850158i | \(-0.676506\pi\) | ||
0.526527 | − | 0.850158i | \(-0.323494\pi\) | |||||||
\(368\) | − | 2.71958e10i | − | 1.48289i | ||||||
\(369\) | 5.90558e9 | 0.318535 | ||||||||
\(370\) | 5.80113e9 | 0.309532 | ||||||||
\(371\) | 6.57603e9 | 0.347111 | ||||||||
\(372\) | − | 2.06234e10i | − | 1.07693i | ||||||
\(373\) | −1.50923e10 | −0.779687 | −0.389844 | − | 0.920881i | \(-0.627471\pi\) | ||||
−0.389844 | + | 0.920881i | \(0.627471\pi\) | |||||||
\(374\) | 9.99488e9 | 0.510847 | ||||||||
\(375\) | −1.17165e10 | −0.592479 | ||||||||
\(376\) | −5.67242e8 | −0.0283803 | ||||||||
\(377\) | 1.66831e10i | 0.825868i | ||||||||
\(378\) | 7.89869e9i | 0.386891i | ||||||||
\(379\) | 2.73541e10 | 1.32576 | 0.662882 | − | 0.748724i | \(-0.269333\pi\) | ||||
0.662882 | + | 0.748724i | \(0.269333\pi\) | |||||||
\(380\) | 3.65507e10 | 1.75292 | ||||||||
\(381\) | −1.32640e10 | −0.629467 | ||||||||
\(382\) | −2.48879e10 | −1.16879 | ||||||||
\(383\) | 1.55369e10 | 0.722053 | 0.361026 | − | 0.932556i | \(-0.382426\pi\) | ||||
0.361026 | + | 0.932556i | \(0.382426\pi\) | |||||||
\(384\) | 1.94051e10i | 0.892466i | ||||||||
\(385\) | 6.37391e9i | 0.290110i | ||||||||
\(386\) | − | 4.08350e10i | − | 1.83943i | ||||||
\(387\) | − | 6.05472e9i | − | 0.269929i | ||||||
\(388\) | 1.44459e9i | 0.0637406i | ||||||||
\(389\) | −1.05981e10 | −0.462840 | −0.231420 | − | 0.972854i | \(-0.574337\pi\) | ||||
−0.231420 | + | 0.972854i | \(0.574337\pi\) | |||||||
\(390\) | −2.62701e10 | −1.13554 | ||||||||
\(391\) | 2.00085e10i | 0.856067i | ||||||||
\(392\) | 1.39150e10i | 0.589302i | ||||||||
\(393\) | − | 1.02812e10i | − | 0.430995i | ||||||
\(394\) | 5.86163e10i | 2.43239i | ||||||||
\(395\) | 1.43319e10 | 0.588730 | ||||||||
\(396\) | 6.69099e9i | 0.272088i | ||||||||
\(397\) | − | 2.46311e10i | − | 0.991565i | −0.868447 | − | 0.495783i | \(-0.834881\pi\) | ||
0.868447 | − | 0.495783i | \(-0.165119\pi\) | |||||||
\(398\) | − | 3.62385e10i | − | 1.44423i | ||||||
\(399\) | −2.15021e10 | −0.848379 | ||||||||
\(400\) | −1.90303e10 | −0.743370 | ||||||||
\(401\) | 3.11202e9i | 0.120355i | 0.998188 | + | 0.0601777i | \(0.0191667\pi\) | ||||
−0.998188 | + | 0.0601777i | \(0.980833\pi\) | |||||||
\(402\) | 1.76186e10 | 0.674631 | ||||||||
\(403\) | −4.03508e10 | −1.52979 | ||||||||
\(404\) | − | 4.64453e10i | − | 1.74348i | ||||||
\(405\) | −1.94648e9 | −0.0723484 | ||||||||
\(406\) | 2.62691e10i | 0.966810i | ||||||||
\(407\) | −2.89090e9 | −0.105355 | ||||||||
\(408\) | 2.29337e10i | 0.827626i | ||||||||
\(409\) | − | 1.95746e10i | − | 0.699521i | −0.936839 | − | 0.349760i | \(-0.886263\pi\) | ||
0.936839 | − | 0.349760i | \(-0.113737\pi\) | |||||||
\(410\) | 3.09270e10i | 1.09447i | ||||||||
\(411\) | 6.69391e9 | 0.234592 | ||||||||
\(412\) | 7.98126e10i | 2.77002i | ||||||||
\(413\) | 1.64976e10 | − | 2.88707e10i | 0.567050 | − | 0.992333i | ||||
\(414\) | −1.97915e10 | −0.673716 | ||||||||
\(415\) | − | 1.33703e10i | − | 0.450764i | ||||||
\(416\) | −1.77867e10 | −0.593912 | ||||||||
\(417\) | −6.27352e9 | −0.207476 | ||||||||
\(418\) | −2.69133e10 | −0.881581 | ||||||||
\(419\) | − | 5.13543e10i | − | 1.66617i | −0.553142 | − | 0.833087i | \(-0.686571\pi\) | ||
0.553142 | − | 0.833087i | \(-0.313429\pi\) | |||||||
\(420\) | −2.79950e10 | −0.899671 | ||||||||
\(421\) | 2.58050e10i | 0.821439i | 0.911762 | + | 0.410720i | \(0.134722\pi\) | ||||
−0.911762 | + | 0.410720i | \(0.865278\pi\) | |||||||
\(422\) | 3.89508e10 | 1.22819 | ||||||||
\(423\) | 1.57408e8i | 0.00491659i | ||||||||
\(424\) | 1.88863e10i | 0.584363i | ||||||||
\(425\) | 1.40010e10 | 0.429144 | ||||||||
\(426\) | − | 3.64397e10i | − | 1.10646i | ||||||
\(427\) | − | 1.57356e10i | − | 0.473339i | ||||||
\(428\) | 1.97299e10 | 0.587963 | ||||||||
\(429\) | 1.30913e10 | 0.386503 | ||||||||
\(430\) | 3.17081e10 | 0.927462 | ||||||||
\(431\) | − | 2.35267e10i | − | 0.681793i | −0.940101 | − | 0.340897i | \(-0.889269\pi\) | ||
0.940101 | − | 0.340897i | \(-0.110731\pi\) | |||||||
\(432\) | −8.65005e9 | −0.248361 | ||||||||
\(433\) | 2.29758e10 | 0.653612 | 0.326806 | − | 0.945091i | \(-0.394028\pi\) | ||||
0.326806 | + | 0.945091i | \(0.394028\pi\) | |||||||
\(434\) | −6.35362e10 | −1.79086 | ||||||||
\(435\) | −6.47350e9 | −0.180793 | ||||||||
\(436\) | 4.77677e10i | 1.32187i | ||||||||
\(437\) | − | 5.38771e10i | − | 1.47733i | ||||||
\(438\) | −2.42024e9 | −0.0657601 | ||||||||
\(439\) | 4.42515e10 | 1.19143 | 0.595717 | − | 0.803194i | \(-0.296868\pi\) | ||||
0.595717 | + | 0.803194i | \(0.296868\pi\) | |||||||
\(440\) | −1.83058e10 | −0.488402 | ||||||||
\(441\) | 3.86135e9 | 0.102090 | ||||||||
\(442\) | 8.58904e10 | 2.25038 | ||||||||
\(443\) | − | 1.02222e9i | − | 0.0265417i | −0.999912 | − | 0.0132708i | \(-0.995776\pi\) | ||
0.999912 | − | 0.0132708i | \(-0.00422436\pi\) | |||||||
\(444\) | − | 1.26972e10i | − | 0.326721i | ||||||
\(445\) | − | 3.37537e10i | − | 0.860758i | ||||||
\(446\) | 1.26425e11i | 3.19517i | ||||||||
\(447\) | 9.90292e9i | 0.248047i | ||||||||
\(448\) | 3.14079e10 | 0.779698 | ||||||||
\(449\) | 3.67444e10 | 0.904079 | 0.452039 | − | 0.891998i | \(-0.350697\pi\) | ||||
0.452039 | + | 0.891998i | \(0.350697\pi\) | |||||||
\(450\) | 1.38491e10i | 0.337732i | ||||||||
\(451\) | − | 1.54120e10i | − | 0.372523i | ||||||
\(452\) | − | 1.63012e11i | − | 3.90539i | ||||||
\(453\) | − | 4.25824e10i | − | 1.01120i | ||||||
\(454\) | 6.67538e10 | 1.57128 | ||||||||
\(455\) | 5.47738e10i | 1.27799i | ||||||||
\(456\) | − | 6.17539e10i | − | 1.42825i | ||||||
\(457\) | − | 4.00848e10i | − | 0.918999i | −0.888178 | − | 0.459499i | \(-0.848029\pi\) | ||
0.888178 | − | 0.459499i | \(-0.151971\pi\) | |||||||
\(458\) | 4.87701e10 | 1.10839 | ||||||||
\(459\) | 6.36403e9 | 0.143378 | ||||||||
\(460\) | − | 7.01461e10i | − | 1.56665i | ||||||
\(461\) | 4.68445e10 | 1.03718 | 0.518591 | − | 0.855022i | \(-0.326457\pi\) | ||||
0.518591 | + | 0.855022i | \(0.326457\pi\) | |||||||
\(462\) | 2.06135e10 | 0.452464 | ||||||||
\(463\) | 2.50947e10i | 0.546082i | 0.962002 | + | 0.273041i | \(0.0880294\pi\) | ||||
−0.962002 | + | 0.273041i | \(0.911971\pi\) | |||||||
\(464\) | −2.87679e10 | −0.620636 | ||||||||
\(465\) | − | 1.56572e10i | − | 0.334891i | ||||||
\(466\) | 2.77267e10 | 0.587969 | ||||||||
\(467\) | 2.89237e10i | 0.608115i | 0.952654 | + | 0.304058i | \(0.0983416\pi\) | ||||
−0.952654 | + | 0.304058i | \(0.901658\pi\) | |||||||
\(468\) | 5.74986e10i | 1.19860i | ||||||||
\(469\) | − | 3.67352e10i | − | 0.759260i | ||||||
\(470\) | −8.24330e8 | −0.0168931 | ||||||||
\(471\) | 8.27787e9i | 0.168203i | ||||||||
\(472\) | 8.29164e10 | + | 4.73810e10i | 1.67060 | + | 0.954633i | ||||
\(473\) | −1.58012e10 | −0.315680 | ||||||||
\(474\) | − | 4.63502e10i | − | 0.918201i | ||||||
\(475\) | −3.77006e10 | −0.740583 | ||||||||
\(476\) | 9.15301e10 | 1.78294 | ||||||||
\(477\) | 5.24087e9 | 0.101235 | ||||||||
\(478\) | 2.91324e10i | 0.558040i | ||||||||
\(479\) | −6.00874e10 | −1.14141 | −0.570704 | − | 0.821156i | \(-0.693330\pi\) | ||||
−0.570704 | + | 0.821156i | \(0.693330\pi\) | |||||||
\(480\) | − | 6.90174e9i | − | 0.130015i | ||||||
\(481\) | −2.48428e10 | −0.464109 | ||||||||
\(482\) | 1.34055e11i | 2.48368i | ||||||||
\(483\) | 4.12657e10i | 0.758230i | ||||||||
\(484\) | −9.74429e10 | −1.77570 | ||||||||
\(485\) | 1.09673e9i | 0.0198213i | ||||||||
\(486\) | 6.29499e9i | 0.112837i | ||||||||
\(487\) | 8.08677e10 | 1.43767 | 0.718835 | − | 0.695181i | \(-0.244676\pi\) | ||||
0.718835 | + | 0.695181i | \(0.244676\pi\) | |||||||
\(488\) | 4.51925e10 | 0.796869 | ||||||||
\(489\) | 4.53975e10 | 0.793956 | ||||||||
\(490\) | 2.02216e10i | 0.350777i | ||||||||
\(491\) | 2.29280e9 | 0.0394493 | 0.0197247 | − | 0.999805i | \(-0.493721\pi\) | ||||
0.0197247 | + | 0.999805i | \(0.493721\pi\) | |||||||
\(492\) | 6.76915e10 | 1.15524 | ||||||||
\(493\) | 2.11652e10 | 0.358290 | ||||||||
\(494\) | −2.31278e11 | −3.88353 | ||||||||
\(495\) | 5.07979e9i | 0.0846106i | ||||||||
\(496\) | − | 6.95801e10i | − | 1.14963i | ||||||
\(497\) | −7.59778e10 | −1.24526 | ||||||||
\(498\) | −4.32403e10 | −0.703025 | ||||||||
\(499\) | 9.12096e10 | 1.47109 | 0.735544 | − | 0.677477i | \(-0.236927\pi\) | ||||
0.735544 | + | 0.677477i | \(0.236927\pi\) | |||||||
\(500\) | −1.34298e11 | −2.14877 | ||||||||
\(501\) | 6.01302e10 | 0.954424 | ||||||||
\(502\) | − | 1.99488e11i | − | 3.14125i | ||||||
\(503\) | − | 4.30436e10i | − | 0.672414i | −0.941788 | − | 0.336207i | \(-0.890856\pi\) | ||
0.941788 | − | 0.336207i | \(-0.109144\pi\) | |||||||
\(504\) | 4.72987e10i | 0.733039i | ||||||||
\(505\) | − | 3.52612e10i | − | 0.542165i | ||||||
\(506\) | 5.16505e10i | 0.787903i | ||||||||
\(507\) | 7.43512e10 | 1.12527 | ||||||||
\(508\) | −1.52035e11 | −2.28292 | ||||||||
\(509\) | 4.82412e10i | 0.718699i | 0.933203 | + | 0.359350i | \(0.117001\pi\) | ||||
−0.933203 | + | 0.359350i | \(0.882999\pi\) | |||||||
\(510\) | 3.33279e10i | 0.492637i | ||||||||
\(511\) | 5.04627e9i | 0.0740093i | ||||||||
\(512\) | 1.39967e11i | 2.03679i | ||||||||
\(513\) | −1.71365e10 | −0.247430 | ||||||||
\(514\) | − | 8.65282e10i | − | 1.23967i | ||||||
\(515\) | 6.05936e10i | 0.861386i | ||||||||
\(516\) | − | 6.94010e10i | − | 0.978965i | ||||||
\(517\) | 4.10792e8 | 0.00574990 | ||||||||
\(518\) | −3.91174e10 | −0.543314 | ||||||||
\(519\) | − | 5.15232e10i | − | 0.710123i | ||||||
\(520\) | −1.57310e11 | −2.15150 | ||||||||
\(521\) | −5.59642e10 | −0.759555 | −0.379777 | − | 0.925078i | \(-0.623999\pi\) | ||||
−0.379777 | + | 0.925078i | \(0.623999\pi\) | |||||||
\(522\) | 2.09356e10i | 0.281970i | ||||||||
\(523\) | 9.80172e10 | 1.31007 | 0.655037 | − | 0.755597i | \(-0.272653\pi\) | ||||
0.655037 | + | 0.755597i | \(0.272653\pi\) | |||||||
\(524\) | − | 1.17846e11i | − | 1.56311i | ||||||
\(525\) | 2.88757e10 | 0.380098 | ||||||||
\(526\) | 1.14386e11i | 1.49428i | ||||||||
\(527\) | 5.11915e10i | 0.663675i | ||||||||
\(528\) | 2.25744e10i | 0.290456i | ||||||||
\(529\) | −2.50870e10 | −0.320350 | ||||||||
\(530\) | 2.74460e10i | 0.347837i | ||||||||
\(531\) | 1.31481e10 | − | 2.30090e10i | 0.165380 | − | 0.289414i | ||||
\(532\) | −2.46464e11 | −3.07686 | ||||||||
\(533\) | − | 1.32442e11i | − | 1.64103i | ||||||
\(534\) | −1.09161e11 | −1.34246 | ||||||||
\(535\) | 1.49789e10 | 0.182837 | ||||||||
\(536\) | 1.05503e11 | 1.27822 | ||||||||
\(537\) | 1.01217e10i | 0.121718i | ||||||||
\(538\) | 3.53020e10 | 0.421377 | ||||||||
\(539\) | − | 1.00771e10i | − | 0.119394i | ||||||
\(540\) | −2.23111e10 | −0.262389 | ||||||||
\(541\) | 8.07791e10i | 0.942997i | 0.881867 | + | 0.471498i | \(0.156287\pi\) | ||||
−0.881867 | + | 0.471498i | \(0.843713\pi\) | |||||||
\(542\) | − | 2.88400e11i | − | 3.34194i | ||||||
\(543\) | 3.35429e10 | 0.385834 | ||||||||
\(544\) | 2.25653e10i | 0.257659i | ||||||||
\(545\) | 3.62652e10i | 0.411058i | ||||||||
\(546\) | 1.77141e11 | 1.99319 | ||||||||
\(547\) | 1.74965e9 | 0.0195435 | 0.00977176 | − | 0.999952i | \(-0.496890\pi\) | ||||
0.00977176 | + | 0.999952i | \(0.496890\pi\) | |||||||
\(548\) | 7.67276e10 | 0.850803 | ||||||||
\(549\) | − | 1.25408e10i | − | 0.138049i | ||||||
\(550\) | 3.61425e10 | 0.394973 | ||||||||
\(551\) | −5.69917e10 | −0.618309 | ||||||||
\(552\) | −1.18515e11 | −1.27648 | ||||||||
\(553\) | −9.66412e10 | −1.03338 | ||||||||
\(554\) | 2.57919e11i | 2.73807i | ||||||||
\(555\) | − | 9.63970e9i | − | 0.101600i | ||||||
\(556\) | −7.19090e10 | −0.752461 | ||||||||
\(557\) | −1.10540e11 | −1.14841 | −0.574207 | − | 0.818710i | \(-0.694690\pi\) | ||||
−0.574207 | + | 0.818710i | \(0.694690\pi\) | |||||||
\(558\) | −5.06362e10 | −0.522305 | ||||||||
\(559\) | −1.35787e11 | −1.39063 | ||||||||
\(560\) | −9.44508e10 | −0.960403 | ||||||||
\(561\) | − | 1.66084e10i | − | 0.167678i | ||||||
\(562\) | − | 3.33218e11i | − | 3.34028i | ||||||
\(563\) | 5.32954e10i | 0.530464i | 0.964185 | + | 0.265232i | \(0.0854485\pi\) | ||||
−0.964185 | + | 0.265232i | \(0.914551\pi\) | |||||||
\(564\) | 1.80425e9i | 0.0178312i | ||||||||
\(565\) | − | 1.23758e11i | − | 1.21445i | ||||||
\(566\) | −2.63015e11 | −2.56280 | ||||||||
\(567\) | 1.31252e10 | 0.126991 | ||||||||
\(568\) | − | 2.18207e11i | − | 2.09641i | ||||||
\(569\) | − | 5.27709e10i | − | 0.503437i | −0.967800 | − | 0.251719i | \(-0.919004\pi\) | ||
0.967800 | − | 0.251719i | \(-0.0809957\pi\) | |||||||
\(570\) | − | 8.97423e10i | − | 0.850155i | ||||||
\(571\) | − | 8.72877e10i | − | 0.821124i | −0.911833 | − | 0.410562i | \(-0.865333\pi\) | ||
0.911833 | − | 0.410562i | \(-0.134667\pi\) | |||||||
\(572\) | 1.50056e11 | 1.40175 | ||||||||
\(573\) | 4.13561e10i | 0.383637i | ||||||||
\(574\) | − | 2.08543e11i | − | 1.92109i | ||||||
\(575\) | 7.23529e10i | 0.661888i | ||||||||
\(576\) | 2.50310e10 | 0.227399 | ||||||||
\(577\) | −7.68360e8 | −0.00693205 | −0.00346602 | − | 0.999994i | \(-0.501103\pi\) | ||||
−0.00346602 | + | 0.999994i | \(0.501103\pi\) | |||||||
\(578\) | 8.73541e10i | 0.782658i | ||||||||
\(579\) | −6.78553e10 | −0.603768 | ||||||||
\(580\) | −7.42012e10 | −0.655691 | ||||||||
\(581\) | 9.01570e10i | 0.791216i | ||||||||
\(582\) | 3.54686e9 | 0.0309138 | ||||||||
\(583\) | − | 1.36773e10i | − | 0.118393i | ||||||
\(584\) | −1.44928e10 | −0.124595 | ||||||||
\(585\) | 4.36528e10i | 0.372725i | ||||||||
\(586\) | 1.21468e11i | 1.03008i | ||||||||
\(587\) | − | 7.08101e10i | − | 0.596407i | −0.954502 | − | 0.298203i | \(-0.903613\pi\) | ||
0.954502 | − | 0.298203i | \(-0.0963874\pi\) | |||||||
\(588\) | 4.42600e10 | 0.370256 | ||||||||
\(589\) | − | 1.37844e11i | − | 1.14532i | ||||||
\(590\) | 1.20496e11 | + | 6.88553e10i | 0.994410 | + | 0.568237i | ||||
\(591\) | 9.74024e10 | 0.798399 | ||||||||
\(592\) | − | 4.28384e10i | − | 0.348776i | ||||||
\(593\) | −7.38587e10 | −0.597287 | −0.298643 | − | 0.954365i | \(-0.596534\pi\) | ||||
−0.298643 | + | 0.954365i | \(0.596534\pi\) | |||||||
\(594\) | 1.64283e10 | 0.131961 | ||||||||
\(595\) | 6.94895e10 | 0.554435 | ||||||||
\(596\) | 1.13510e11i | 0.899601i | ||||||||
\(597\) | −6.02173e10 | −0.474050 | ||||||||
\(598\) | 4.43856e11i | 3.47086i | ||||||||
\(599\) | −6.39782e10 | −0.496963 | −0.248482 | − | 0.968637i | \(-0.579932\pi\) | ||||
−0.248482 | + | 0.968637i | \(0.579932\pi\) | |||||||
\(600\) | 8.29307e10i | 0.639898i | ||||||||
\(601\) | − | 4.79700e10i | − | 0.367682i | −0.982956 | − | 0.183841i | \(-0.941147\pi\) | ||
0.982956 | − | 0.183841i | \(-0.0588531\pi\) | |||||||
\(602\) | −2.13810e11 | −1.62795 | ||||||||
\(603\) | − | 2.92767e10i | − | 0.221438i | ||||||
\(604\) | − | 4.88093e11i | − | 3.66737i | ||||||
\(605\) | −7.39785e10 | −0.552184 | ||||||||
\(606\) | −1.14036e11 | −0.845577 | ||||||||
\(607\) | −1.76542e11 | −1.30045 | −0.650223 | − | 0.759743i | \(-0.725325\pi\) | ||||
−0.650223 | + | 0.759743i | \(0.725325\pi\) | |||||||
\(608\) | − | 6.07619e10i | − | 0.444649i | ||||||
\(609\) | 4.36512e10 | 0.317342 | ||||||||
\(610\) | 6.56749e10 | 0.474329 | ||||||||
\(611\) | 3.53012e9 | 0.0253294 | ||||||||
\(612\) | 7.29464e10 | 0.519994 | ||||||||
\(613\) | 1.62572e11i | 1.15134i | 0.817681 | + | 0.575672i | \(0.195259\pi\) | ||||
−0.817681 | + | 0.575672i | \(0.804741\pi\) | |||||||
\(614\) | 1.04942e11i | 0.738372i | ||||||||
\(615\) | 5.13912e10 | 0.359243 | ||||||||
\(616\) | 1.23437e11 | 0.857281 | ||||||||
\(617\) | −9.33035e10 | −0.643809 | −0.321905 | − | 0.946772i | \(-0.604323\pi\) | ||||
−0.321905 | + | 0.946772i | \(0.604323\pi\) | |||||||
\(618\) | 1.95962e11 | 1.34344 | ||||||||
\(619\) | 2.34361e11 | 1.59633 | 0.798165 | − | 0.602439i | \(-0.205804\pi\) | ||||
0.798165 | + | 0.602439i | \(0.205804\pi\) | |||||||
\(620\) | − | 1.79468e11i | − | 1.21456i | ||||||
\(621\) | 3.28874e10i | 0.221138i | ||||||||
\(622\) | 5.02428e11i | 3.35670i | ||||||||
\(623\) | 2.27603e11i | 1.51087i | ||||||||
\(624\) | 1.93991e11i | 1.27951i | ||||||||
\(625\) | −1.40648e10 | −0.0921750 | ||||||||
\(626\) | 4.66517e11 | 3.03787 | ||||||||
\(627\) | 4.47217e10i | 0.289367i | ||||||||
\(628\) | 9.48834e10i | 0.610031i | ||||||||
\(629\) | 3.15171e10i | 0.201346i | ||||||||
\(630\) | 6.87357e10i | 0.436335i | ||||||||
\(631\) | −4.43112e10 | −0.279509 | −0.139755 | − | 0.990186i | \(-0.544631\pi\) | ||||
−0.139755 | + | 0.990186i | \(0.544631\pi\) | |||||||
\(632\) | − | 2.77552e11i | − | 1.73971i | ||||||
\(633\) | − | 6.47243e10i | − | 0.403137i | ||||||
\(634\) | 1.66297e11i | 1.02927i | ||||||||
\(635\) | −1.15425e11 | −0.709913 | ||||||||
\(636\) | 6.00724e10 | 0.367153 | ||||||||
\(637\) | − | 8.65971e10i | − | 0.525951i | ||||||
\(638\) | 5.46364e10 | 0.329761 | ||||||||
\(639\) | −6.05517e10 | −0.363181 | ||||||||
\(640\) | 1.68866e11i | 1.00652i | ||||||||
\(641\) | −1.26538e11 | −0.749528 | −0.374764 | − | 0.927120i | \(-0.622276\pi\) | ||||
−0.374764 | + | 0.927120i | \(0.622276\pi\) | |||||||
\(642\) | − | 4.84425e10i | − | 0.285159i | ||||||
\(643\) | 1.67234e11 | 0.978317 | 0.489158 | − | 0.872195i | \(-0.337304\pi\) | ||||
0.489158 | + | 0.872195i | \(0.337304\pi\) | |||||||
\(644\) | 4.73000e11i | 2.74990i | ||||||||
\(645\) | − | 5.26891e10i | − | 0.304426i | ||||||
\(646\) | 2.93414e11i | 1.68481i | ||||||||
\(647\) | 1.60905e10 | 0.0918233 | 0.0459116 | − | 0.998946i | \(-0.485381\pi\) | ||||
0.0459116 | + | 0.998946i | \(0.485381\pi\) | |||||||
\(648\) | 3.76955e10i | 0.213791i | ||||||||
\(649\) | −6.00475e10 | − | 3.43130e10i | −0.338467 | − | 0.193410i | ||||
\(650\) | 3.10589e11 | 1.73993 | ||||||||
\(651\) | 1.05578e11i | 0.587826i | ||||||||
\(652\) | 5.20360e11 | 2.87948 | ||||||||
\(653\) | 1.82713e11 | 1.00489 | 0.502444 | − | 0.864610i | \(-0.332434\pi\) | ||||
0.502444 | + | 0.864610i | \(0.332434\pi\) | |||||||
\(654\) | 1.17283e11 | 0.641099 | ||||||||
\(655\) | − | 8.94684e10i | − | 0.486076i | ||||||
\(656\) | 2.28381e11 | 1.23323 | ||||||||
\(657\) | 4.02170e9i | 0.0215848i | ||||||||
\(658\) | 5.55852e9 | 0.0296521 | ||||||||
\(659\) | 1.16823e11i | 0.619425i | 0.950830 | + | 0.309712i | \(0.100233\pi\) | ||||
−0.950830 | + | 0.309712i | \(0.899767\pi\) | |||||||
\(660\) | 5.82261e10i | 0.306861i | ||||||||
\(661\) | −2.78164e10 | −0.145712 | −0.0728560 | − | 0.997342i | \(-0.523211\pi\) | ||||
−0.0728560 | + | 0.997342i | \(0.523211\pi\) | |||||||
\(662\) | − | 2.46062e11i | − | 1.28119i | ||||||
\(663\) | − | 1.42724e11i | − | 0.738655i | ||||||
\(664\) | −2.58930e11 | −1.33202 | ||||||||
\(665\) | −1.87115e11 | −0.956802 | ||||||||
\(666\) | −3.11752e10 | −0.158458 | ||||||||
\(667\) | 1.09375e11i | 0.552606i | ||||||||
\(668\) | 6.89230e11 | 3.46145 | ||||||||
\(669\) | 2.10080e11 | 1.04877 | ||||||||
\(670\) | 1.53320e11 | 0.760849 | ||||||||
\(671\) | −3.27281e10 | −0.161447 | ||||||||
\(672\) | 4.65389e10i | 0.228212i | ||||||||
\(673\) | − | 1.70203e11i | − | 0.829675i | −0.909896 | − | 0.414837i | \(-0.863838\pi\) | ||
0.909896 | − | 0.414837i | \(-0.136162\pi\) | |||||||
\(674\) | −2.67568e11 | −1.29657 | ||||||||
\(675\) | 2.30130e10 | 0.110856 | ||||||||
\(676\) | 8.52236e11 | 4.08106 | ||||||||
\(677\) | −1.60157e11 | −0.762413 | −0.381207 | − | 0.924490i | \(-0.624491\pi\) | ||||
−0.381207 | + | 0.924490i | \(0.624491\pi\) | |||||||
\(678\) | −4.00239e11 | −1.89409 | ||||||||
\(679\) | − | 7.39530e9i | − | 0.0347918i | ||||||
\(680\) | 1.99573e11i | 0.933396i | ||||||||
\(681\) | − | 1.10924e11i | − | 0.515749i | ||||||
\(682\) | 1.32147e11i | 0.610831i | ||||||||
\(683\) | − | 3.49843e11i | − | 1.60765i | −0.594868 | − | 0.803823i | \(-0.702796\pi\) | ||
0.594868 | − | 0.803823i | \(-0.297204\pi\) | |||||||
\(684\) | −1.96424e11 | −0.897365 | ||||||||
\(685\) | 5.82514e10 | 0.264572 | ||||||||
\(686\) | 3.08856e11i | 1.39463i | ||||||||
\(687\) | − | 8.10410e10i | − | 0.363813i | ||||||
\(688\) | − | 2.34148e11i | − | 1.04505i | ||||||
\(689\) | − | 1.17535e11i | − | 0.521543i | ||||||
\(690\) | −1.72228e11 | −0.759816 | ||||||||
\(691\) | 1.43170e11i | 0.627973i | 0.949427 | + | 0.313987i | \(0.101665\pi\) | ||||
−0.949427 | + | 0.313987i | \(0.898335\pi\) | |||||||
\(692\) | − | 5.90575e11i | − | 2.57543i | ||||||
\(693\) | − | 3.42534e10i | − | 0.148515i | ||||||
\(694\) | −4.40045e11 | −1.89696 | ||||||||
\(695\) | −5.45931e10 | −0.233991 | ||||||||
\(696\) | 1.25366e11i | 0.534247i | ||||||||
\(697\) | −1.68024e11 | −0.711936 | ||||||||
\(698\) | 2.95568e11 | 1.24519 | ||||||||
\(699\) | − | 4.60733e10i | − | 0.192992i | ||||||
\(700\) | 3.30982e11 | 1.37852 | ||||||||
\(701\) | − | 1.34207e11i | − | 0.555781i | −0.960613 | − | 0.277891i | \(-0.910365\pi\) | ||
0.960613 | − | 0.277891i | \(-0.0896353\pi\) | |||||||
\(702\) | 1.41175e11 | 0.581314 | ||||||||
\(703\) | − | 8.48665e10i | − | 0.347468i | ||||||
\(704\) | − | 6.53244e10i | − | 0.265941i | ||||||
\(705\) | 1.36978e9i | 0.00554493i | ||||||||
\(706\) | −4.99265e11 | −2.00961 | ||||||||
\(707\) | 2.37769e11i | 0.951650i | ||||||||
\(708\) | 1.50707e11 | − | 2.63736e11i | 0.599792 | − | 1.04963i | ||||
\(709\) | 2.30261e11 | 0.911245 | 0.455623 | − | 0.890173i | \(-0.349417\pi\) | ||||
0.455623 | + | 0.890173i | \(0.349417\pi\) | |||||||
\(710\) | − | 3.17104e11i | − | 1.24787i | ||||||
\(711\) | −7.70198e10 | −0.301387 | ||||||||
\(712\) | −6.53674e11 | −2.54356 | ||||||||
\(713\) | −2.64542e11 | −1.02362 | ||||||||
\(714\) | − | 2.24732e11i | − | 0.864714i | ||||||
\(715\) | 1.13922e11 | 0.435898 | ||||||||
\(716\) | 1.16018e11i | 0.441442i | ||||||||
\(717\) | 4.84092e10 | 0.183169 | ||||||||
\(718\) | 4.36515e11i | 1.64248i | ||||||||
\(719\) | 3.23619e11i | 1.21093i | 0.795873 | + | 0.605464i | \(0.207012\pi\) | ||||
−0.795873 | + | 0.605464i | \(0.792988\pi\) | |||||||
\(720\) | −7.52741e10 | −0.280102 | ||||||||
\(721\) | − | 4.08587e11i | − | 1.51197i | ||||||
\(722\) | − | 3.12107e11i | − | 1.14856i | ||||||
\(723\) | 2.22759e11 | 0.815232 | ||||||||
\(724\) | 3.84478e11 | 1.39932 | ||||||||
\(725\) | 7.65355e10 | 0.277020 | ||||||||
\(726\) | 2.39250e11i | 0.861203i | ||||||||
\(727\) | −8.18255e10 | −0.292921 | −0.146461 | − | 0.989216i | \(-0.546788\pi\) | ||||
−0.146461 | + | 0.989216i | \(0.546788\pi\) | |||||||
\(728\) | 1.06075e12 | 3.77648 | ||||||||
\(729\) | 1.04604e10 | 0.0370370 | ||||||||
\(730\) | −2.10613e10 | −0.0741642 | ||||||||
\(731\) | 1.72268e11i | 0.603302i | ||||||||
\(732\) | − | 1.43746e11i | − | 0.500669i | ||||||
\(733\) | −5.06458e10 | −0.175440 | −0.0877198 | − | 0.996145i | \(-0.527958\pi\) | ||||
−0.0877198 | + | 0.996145i | \(0.527958\pi\) | |||||||
\(734\) | −8.68095e11 | −2.99077 | ||||||||
\(735\) | 3.36021e10 | 0.115138 | ||||||||
\(736\) | −1.16611e11 | −0.397400 | ||||||||
\(737\) | −7.64045e10 | −0.258970 | ||||||||
\(738\) | − | 1.66202e11i | − | 0.560286i | ||||||
\(739\) | 2.40198e11i | 0.805363i | 0.915340 | + | 0.402682i | \(0.131922\pi\) | ||||
−0.915340 | + | 0.402682i | \(0.868078\pi\) | |||||||
\(740\) | − | 1.10493e11i | − | 0.368475i | ||||||
\(741\) | 3.84313e11i | 1.27471i | ||||||||
\(742\) | − | 1.85070e11i | − | 0.610550i | ||||||
\(743\) | −7.18154e10 | −0.235647 | −0.117824 | − | 0.993035i | \(-0.537592\pi\) | ||||
−0.117824 | + | 0.993035i | \(0.537592\pi\) | |||||||
\(744\) | −3.03218e11 | −0.989609 | ||||||||
\(745\) | 8.61768e10i | 0.279747i | ||||||||
\(746\) | 4.24746e11i | 1.37143i | ||||||||
\(747\) | 7.18521e10i | 0.230758i | ||||||||
\(748\) | − | 1.90371e11i | − | 0.608127i | ||||||
\(749\) | −1.01004e11 | −0.320930 | ||||||||
\(750\) | 3.29740e11i | 1.04214i | ||||||||
\(751\) | 2.61941e11i | 0.823461i | 0.911306 | + | 0.411731i | \(0.135076\pi\) | ||||
−0.911306 | + | 0.411731i | \(0.864924\pi\) | |||||||
\(752\) | 6.08727e9i | 0.0190349i | ||||||||
\(753\) | −3.31489e11 | −1.03107 | ||||||||
\(754\) | 4.69515e11 | 1.45266 | ||||||||
\(755\) | − | 3.70559e11i | − | 1.14043i | ||||||
\(756\) | 1.50445e11 | 0.460565 | ||||||||
\(757\) | −2.95970e11 | −0.901290 | −0.450645 | − | 0.892703i | \(-0.648806\pi\) | ||||
−0.450645 | + | 0.892703i | \(0.648806\pi\) | |||||||
\(758\) | − | 7.69832e11i | − | 2.33195i | ||||||
\(759\) | 8.58274e10 | 0.258618 | ||||||||
\(760\) | − | 5.37392e11i | − | 1.61078i | ||||||
\(761\) | 2.40603e11 | 0.717402 | 0.358701 | − | 0.933453i | \(-0.383220\pi\) | ||||
0.358701 | + | 0.933453i | \(0.383220\pi\) | |||||||
\(762\) | 3.73290e11i | 1.10720i | ||||||||
\(763\) | − | 2.44538e11i | − | 0.721521i | ||||||
\(764\) | 4.74036e11i | 1.39135i | ||||||||
\(765\) | 5.53807e10 | 0.161701 | ||||||||
\(766\) | − | 4.37258e11i | − | 1.27005i | ||||||
\(767\) | −5.16014e11 | − | 2.94866e11i | −1.49101 | − | 0.852008i | ||||
\(768\) | 4.09099e11 | 1.17593 | ||||||||
\(769\) | − | 5.22952e11i | − | 1.49540i | −0.664038 | − | 0.747699i | \(-0.731159\pi\) | ||
0.664038 | − | 0.747699i | \(-0.268841\pi\) | |||||||
\(770\) | 1.79382e11 | 0.510289 | ||||||||
\(771\) | −1.43784e11 | −0.406904 | ||||||||
\(772\) | −7.77778e11 | −2.18971 | ||||||||
\(773\) | − | 2.34322e11i | − | 0.656289i | −0.944628 | − | 0.328144i | \(-0.893577\pi\) | ||
0.944628 | − | 0.328144i | \(-0.106423\pi\) | |||||||
\(774\) | −1.70399e11 | −0.474792 | ||||||||
\(775\) | 1.85114e11i | 0.513136i | ||||||||
\(776\) | 2.12392e10 | 0.0585722 | ||||||||
\(777\) | 6.50012e10i | 0.178335i | ||||||||
\(778\) | 2.98265e11i | 0.814111i | ||||||||
\(779\) | 4.52441e11 | 1.22860 | ||||||||
\(780\) | 5.00362e11i | 1.35178i | ||||||||
\(781\) | 1.58024e11i | 0.424736i | ||||||||
\(782\) | 5.63103e11 | 1.50578 | ||||||||
\(783\) | 3.47886e10 | 0.0925528 | ||||||||
\(784\) | 1.49326e11 | 0.395250 | ||||||||
\(785\) | 7.20353e10i | 0.189700i | ||||||||
\(786\) | −2.89345e11 | −0.758099 | ||||||||
\(787\) | −6.84094e11 | −1.78327 | −0.891635 | − | 0.452756i | \(-0.850441\pi\) | ||||
−0.891635 | + | 0.452756i | \(0.850441\pi\) | |||||||
\(788\) | 1.11646e12 | 2.89559 | ||||||||
\(789\) | 1.90075e11 | 0.490475 | ||||||||
\(790\) | − | 4.03346e11i | − | 1.03555i | ||||||
\(791\) | 8.34509e11i | 2.13169i | ||||||||
\(792\) | 9.83753e10 | 0.250026 | ||||||||
\(793\) | −2.81247e11 | −0.711205 | ||||||||
\(794\) | −6.93197e11 | −1.74411 | ||||||||
\(795\) | 4.56069e10 | 0.114173 | ||||||||
\(796\) | −6.90229e11 | −1.71926 | ||||||||
\(797\) | 4.90056e11i | 1.21454i | 0.794495 | + | 0.607270i | \(0.207736\pi\) | ||||
−0.794495 | + | 0.607270i | \(0.792264\pi\) | |||||||
\(798\) | 6.05139e11i | 1.49226i | ||||||||
\(799\) | − | 4.47853e9i | − | 0.0109888i | ||||||
\(800\) | 8.15986e10i | 0.199215i | ||||||||
\(801\) | 1.81392e11i | 0.440645i | ||||||||
\(802\) | 8.75823e10 | 0.211699 | ||||||||
\(803\) | 1.04956e10 | 0.0252432 | ||||||||
\(804\) | − | 3.35578e11i | − | 0.803100i | ||||||
\(805\) | 3.59101e11i | 0.855131i | ||||||||
\(806\) | 1.13560e12i | 2.69082i | ||||||||
\(807\) | − | 5.86612e10i | − | 0.138311i | ||||||
\(808\) | −6.82869e11 | −1.60211 | ||||||||
\(809\) | 7.40132e11i | 1.72789i | 0.503589 | + | 0.863943i | \(0.332013\pi\) | ||||
−0.503589 | + | 0.863943i | \(0.667987\pi\) | |||||||
\(810\) | 5.47800e10i | 0.127257i | ||||||||
\(811\) | 5.04910e11i | 1.16716i | 0.812056 | + | 0.583580i | \(0.198348\pi\) | ||||
−0.812056 | + | 0.583580i | \(0.801652\pi\) | |||||||
\(812\) | 5.00344e11 | 1.15092 | ||||||||
\(813\) | −4.79233e11 | −1.09694 | ||||||||
\(814\) | 8.13592e10i | 0.185314i | ||||||||
\(815\) | 3.95056e11 | 0.895423 | ||||||||
\(816\) | 2.46110e11 | 0.555096 | ||||||||
\(817\) | − | 4.63867e11i | − | 1.04113i | ||||||
\(818\) | −5.50893e11 | −1.23042 | ||||||||
\(819\) | − | 2.94354e11i | − | 0.654236i | ||||||
\(820\) | 5.89062e11 | 1.30288 | ||||||||
\(821\) | 4.65143e11i | 1.02380i | 0.859046 | + | 0.511898i | \(0.171057\pi\) | ||||
−0.859046 | + | 0.511898i | \(0.828943\pi\) | |||||||
\(822\) | − | 1.88388e11i | − | 0.412635i | ||||||
\(823\) | 4.75117e11i | 1.03562i | 0.855495 | + | 0.517811i | \(0.173253\pi\) | ||||
−0.855495 | + | 0.517811i | \(0.826747\pi\) | |||||||
\(824\) | 1.17346e12 | 2.54541 | ||||||||
\(825\) | − | 6.00578e10i | − | 0.129644i | ||||||
\(826\) | −8.12514e11 | − | 4.64296e11i | −1.74546 | − | 0.997412i | ||||
\(827\) | −3.93701e11 | −0.841675 | −0.420838 | − | 0.907136i | \(-0.638264\pi\) | ||||
−0.420838 | + | 0.907136i | \(0.638264\pi\) | |||||||
\(828\) | 3.76965e11i | 0.802010i | ||||||||
\(829\) | −2.28295e11 | −0.483368 | −0.241684 | − | 0.970355i | \(-0.577700\pi\) | ||||
−0.241684 | + | 0.970355i | \(0.577700\pi\) | |||||||
\(830\) | −3.76284e11 | −0.792872 | ||||||||
\(831\) | 4.28583e11 | 0.898732 | ||||||||
\(832\) | − | 5.61361e11i | − | 1.17152i | ||||||
\(833\) | −1.09863e11 | −0.228176 | ||||||||
\(834\) | 1.76557e11i | 0.364939i | ||||||||
\(835\) | 5.23262e11 | 1.07640 | ||||||||
\(836\) | 5.12614e11i | 1.04946i | ||||||||
\(837\) | 8.41419e10i | 0.171439i | ||||||||
\(838\) | −1.44527e12 | −2.93072 | ||||||||
\(839\) | − | 7.99134e11i | − | 1.61277i | −0.591392 | − | 0.806384i | \(-0.701421\pi\) | ||
0.591392 | − | 0.806384i | \(-0.298579\pi\) | |||||||
\(840\) | 4.11601e11i | 0.826721i | ||||||||
\(841\) | −3.84548e11 | −0.768718 | ||||||||
\(842\) | 7.26235e11 | 1.44487 | ||||||||
\(843\) | −5.53706e11 | −1.09640 | ||||||||
\(844\) | − | 7.41889e11i | − | 1.46207i | ||||||
\(845\) | 6.47016e11 | 1.26908 | ||||||||
\(846\) | 4.42995e9 | 0.00864803 | ||||||||
\(847\) | 4.98842e11 | 0.969236 | ||||||||
\(848\) | 2.02675e11 | 0.391937 | ||||||||
\(849\) | 4.37050e11i | 0.841203i | ||||||||
\(850\) | − | 3.94032e11i | − | 0.754842i | ||||||
\(851\) | −1.62871e11 | −0.310546 | ||||||||
\(852\) | −6.94062e11 | −1.31716 | ||||||||
\(853\) | 3.39922e11 | 0.642072 | 0.321036 | − | 0.947067i | \(-0.395969\pi\) | ||||
0.321036 | + | 0.947067i | \(0.395969\pi\) | |||||||
\(854\) | −4.42850e11 | −0.832579 | ||||||||
\(855\) | −1.49124e11 | −0.279051 | ||||||||
\(856\) | − | 2.90082e11i | − | 0.540288i | ||||||
\(857\) | − | 5.65338e11i | − | 1.04806i | −0.851701 | − | 0.524029i | \(-0.824428\pi\) | ||
0.851701 | − | 0.524029i | \(-0.175572\pi\) | |||||||
\(858\) | − | 3.68431e11i | − | 0.679840i | ||||||
\(859\) | 9.28491e11i | 1.70532i | 0.522468 | + | 0.852659i | \(0.325011\pi\) | ||||
−0.522468 | + | 0.852659i | \(0.674989\pi\) | |||||||
\(860\) | − | 6.03939e11i | − | 1.10408i | ||||||
\(861\) | −3.46535e11 | −0.630571 | ||||||||
\(862\) | −6.62118e11 | −1.19924 | ||||||||
\(863\) | 9.50068e11i | 1.71282i | 0.516297 | + | 0.856410i | \(0.327310\pi\) | ||||
−0.516297 | + | 0.856410i | \(0.672690\pi\) | |||||||
\(864\) | 3.70899e10i | 0.0665581i | ||||||||
\(865\) | − | 4.48363e11i | − | 0.800876i | ||||||
\(866\) | − | 6.46613e11i | − | 1.14967i | ||||||
\(867\) | 1.45156e11 | 0.256896 | ||||||||
\(868\) | 1.21016e12i | 2.13189i | ||||||||
\(869\) | 2.01001e11i | 0.352468i | ||||||||
\(870\) | 1.82185e11i | 0.318006i | ||||||||
\(871\) | −6.56577e11 | −1.14081 | ||||||||
\(872\) | 7.02311e11 | 1.21469 | ||||||||
\(873\) | − | 5.89380e9i | − | 0.0101470i | ||||||
\(874\) | −1.51627e12 | −2.59856 | ||||||||
\(875\) | 6.87516e11 | 1.17287 | ||||||||
\(876\) | 4.60980e10i | 0.0782826i | ||||||||
\(877\) | 5.13352e11 | 0.867795 | 0.433898 | − | 0.900962i | \(-0.357138\pi\) | ||||
0.433898 | + | 0.900962i | \(0.357138\pi\) | |||||||
\(878\) | − | 1.24538e12i | − | 2.09567i | ||||||
\(879\) | 2.01843e11 | 0.338111 | ||||||||
\(880\) | 1.96446e11i | 0.327576i | ||||||||
\(881\) | − | 2.13360e11i | − | 0.354168i | −0.984196 | − | 0.177084i | \(-0.943334\pi\) | ||
0.984196 | − | 0.177084i | \(-0.0566665\pi\) | |||||||
\(882\) | − | 1.08671e11i | − | 0.179572i | ||||||
\(883\) | −1.11489e12 | −1.83396 | −0.916979 | − | 0.398936i | \(-0.869380\pi\) | ||||
−0.916979 | + | 0.398936i | \(0.869380\pi\) | |||||||
\(884\) | − | 1.63594e12i | − | 2.67891i | ||||||
\(885\) | 1.14416e11 | − | 2.00228e11i | 0.186516 | − | 0.326401i | ||||
\(886\) | −2.87684e10 | −0.0466854 | ||||||||
\(887\) | − | 2.59056e10i | − | 0.0418504i | −0.999781 | − | 0.0209252i | \(-0.993339\pi\) | ||
0.999781 | − | 0.0209252i | \(-0.00666119\pi\) | |||||||
\(888\) | −1.86683e11 | −0.300228 | ||||||||
\(889\) | 7.78319e11 | 1.24609 | ||||||||
\(890\) | −9.49936e11 | −1.51403 | ||||||||
\(891\) | − | 2.72988e10i | − | 0.0433144i | ||||||
\(892\) | 2.40800e12 | 3.80362 | ||||||||
\(893\) | 1.20594e10i | 0.0189635i | ||||||||
\(894\) | 2.78700e11 | 0.436301 | ||||||||
\(895\) | 8.80806e10i | 0.137274i | ||||||||
\(896\) | − | 1.13868e12i | − | 1.76672i | ||||||
\(897\) | 7.37552e11 | 1.13926 | ||||||||
\(898\) | − | 1.03411e12i | − | 1.59023i | ||||||
\(899\) | 2.79835e11i | 0.428414i | ||||||||
\(900\) | 2.63782e11 | 0.402045 | ||||||||
\(901\) | −1.49112e11 | −0.226263 | ||||||||
\(902\) | −4.33743e11 | −0.655249 | ||||||||
\(903\) | 3.55286e11i | 0.534352i | ||||||||
\(904\) | −2.39670e12 | −3.58872 | ||||||||
\(905\) | 2.91895e11 | 0.435144 | ||||||||
\(906\) | −1.19840e12 | −1.77865 | ||||||||
\(907\) | 1.30006e12 | 1.92103 | 0.960516 | − | 0.278224i | \(-0.0897458\pi\) | ||||
0.960516 | + | 0.278224i | \(0.0897458\pi\) | |||||||
\(908\) | − | 1.27145e12i | − | 1.87049i | ||||||
\(909\) | 1.89494e11i | 0.277549i | ||||||||
\(910\) | 1.54151e12 | 2.24792 | ||||||||
\(911\) | −1.22667e12 | −1.78096 | −0.890478 | − | 0.455026i | \(-0.849630\pi\) | ||||
−0.890478 | + | 0.455026i | \(0.849630\pi\) | |||||||
\(912\) | −6.62702e11 | −0.957942 | ||||||||
\(913\) | 1.87515e11 | 0.269869 | ||||||||
\(914\) | −1.12811e12 | −1.61647 | ||||||||
\(915\) | − | 1.09132e11i | − | 0.155692i | ||||||
\(916\) | − | 9.28917e11i | − | 1.31946i | ||||||
\(917\) | 6.03291e11i | 0.853198i | ||||||||
\(918\) | − | 1.79104e11i | − | 0.252194i | ||||||
\(919\) | − | 1.29291e12i | − | 1.81262i | −0.422618 | − | 0.906308i | \(-0.638889\pi\) | ||
0.422618 | − | 0.906308i | \(-0.361111\pi\) | |||||||
\(920\) | −1.03133e12 | −1.43962 | ||||||||
\(921\) | 1.74381e11 | 0.242360 | ||||||||
\(922\) | − | 1.31835e12i | − | 1.82435i | ||||||
\(923\) | 1.35797e12i | 1.87104i | ||||||||
\(924\) | − | 3.92622e11i | − | 0.538626i | ||||||
\(925\) | 1.13969e11i | 0.155676i | ||||||||
\(926\) | 7.06244e11 | 0.960530 | ||||||||
\(927\) | − | 3.25630e11i | − | 0.440966i | ||||||
\(928\) | 1.23352e11i | 0.166324i | ||||||||
\(929\) | 5.20893e11i | 0.699336i | 0.936874 | + | 0.349668i | \(0.113706\pi\) | ||||
−0.936874 | + | 0.349668i | \(0.886294\pi\) | |||||||
\(930\) | −4.40644e11 | −0.589056 | ||||||||
\(931\) | 2.95828e11 | 0.393768 | ||||||||
\(932\) | − | 5.28106e11i | − | 0.699934i | ||||||
\(933\) | 8.34882e11 | 1.10179 | ||||||||
\(934\) | 8.14004e11 | 1.06964 | ||||||||
\(935\) | − | 1.44529e11i | − | 0.189108i | ||||||
\(936\) | 8.45382e11 | 1.10141 | ||||||||
\(937\) | − | 1.15219e12i | − | 1.49474i | −0.664408 | − | 0.747370i | \(-0.731316\pi\) | ||
0.664408 | − | 0.747370i | \(-0.268684\pi\) | |||||||
\(938\) | −1.03384e12 | −1.33550 | ||||||||
\(939\) | − | 7.75208e11i | − | 0.997140i | ||||||
\(940\) | 1.57009e10i | 0.0201100i | ||||||||
\(941\) | − | 2.92866e11i | − | 0.373518i | −0.982406 | − | 0.186759i | \(-0.940202\pi\) | ||
0.982406 | − | 0.186759i | \(-0.0597983\pi\) | |||||||
\(942\) | 2.32966e11 | 0.295861 | ||||||||
\(943\) | − | 8.68299e11i | − | 1.09805i | ||||||
\(944\) | 5.08462e11 | − | 8.89804e11i | 0.640281 | − | 1.12049i | ||||
\(945\) | 1.14218e11 | 0.143221 | ||||||||
\(946\) | 4.44697e11i | 0.555264i | ||||||||
\(947\) | 1.73015e11 | 0.215121 | 0.107560 | − | 0.994199i | \(-0.465696\pi\) | ||||
0.107560 | + | 0.994199i | \(0.465696\pi\) | |||||||
\(948\) | −8.82824e11 | −1.09305 | ||||||||
\(949\) | 9.01932e10 | 0.111201 | ||||||||
\(950\) | 1.06101e12i | 1.30265i | ||||||||
\(951\) | 2.76335e11 | 0.337842 | ||||||||
\(952\) | − | 1.34573e12i | − | 1.63837i | ||||||
\(953\) | 8.31729e11 | 1.00835 | 0.504174 | − | 0.863602i | \(-0.331797\pi\) | ||||
0.504174 | + | 0.863602i | \(0.331797\pi\) | |||||||
\(954\) | − | 1.47495e11i | − | 0.178067i | ||||||
\(955\) | 3.59887e11i | 0.432666i | ||||||||
\(956\) | 5.54881e11 | 0.664306 | ||||||||
\(957\) | − | 9.07890e10i | − | 0.108239i | ||||||
\(958\) | 1.69105e12i | 2.00768i | ||||||||
\(959\) | −3.92793e11 | −0.464397 | ||||||||
\(960\) | 2.17824e11 | 0.256460 | ||||||||
\(961\) | 1.76062e11 | 0.206430 | ||||||||
\(962\) | 6.99155e11i | 0.816344i | ||||||||
\(963\) | −8.04966e10 | −0.0935993 | ||||||||
\(964\) | 2.55333e12 | 2.95664 | ||||||||
\(965\) | −5.90488e11 | −0.680929 | ||||||||
\(966\) | 1.16135e12 | 1.33369 | ||||||||
\(967\) | − | 2.17787e11i | − | 0.249073i | −0.992215 | − | 0.124537i | \(-0.960256\pi\) | ||
0.992215 | − | 0.124537i | \(-0.0397444\pi\) | |||||||
\(968\) | 1.43267e12i | 1.63171i | ||||||||
\(969\) | 4.87564e11 | 0.553014 | ||||||||
\(970\) | 3.08654e10 | 0.0348646 | ||||||||
\(971\) | 2.95639e11 | 0.332571 | 0.166286 | − | 0.986078i | \(-0.446823\pi\) | ||||
0.166286 | + | 0.986078i | \(0.446823\pi\) | |||||||
\(972\) | 1.19900e11 | 0.134324 | ||||||||
\(973\) | 3.68125e11 | 0.410719 | ||||||||
\(974\) | − | 2.27587e12i | − | 2.52879i | ||||||
\(975\) | − | 5.16103e11i | − | 0.571108i | ||||||
\(976\) | − | 4.84976e11i | − | 0.534467i | ||||||
\(977\) | − | 6.13007e11i | − | 0.672801i | −0.941719 | − | 0.336401i | \(-0.890790\pi\) | ||
0.941719 | − | 0.336401i | \(-0.109210\pi\) | |||||||
\(978\) | − | 1.27763e12i | − | 1.39653i | ||||||
\(979\) | 4.73386e11 | 0.515329 | ||||||||
\(980\) | 3.85158e11 | 0.417575 | ||||||||
\(981\) | − | 1.94889e11i | − | 0.210432i | ||||||
\(982\) | − | 6.45266e10i | − | 0.0693894i | ||||||
\(983\) | 1.50377e11i | 0.161053i | 0.996752 | + | 0.0805263i | \(0.0256601\pi\) | ||||
−0.996752 | + | 0.0805263i | \(0.974340\pi\) | |||||||
\(984\) | − | 9.95244e11i | − | 1.06157i | ||||||
\(985\) | 8.47611e11 | 0.900434 | ||||||||
\(986\) | − | 5.95656e11i | − | 0.630213i | ||||||
\(987\) | − | 9.23655e9i | − | 0.00973288i | ||||||
\(988\) | 4.40511e12i | 4.62306i | ||||||||
\(989\) | −8.90228e11 | −0.930499 | ||||||||
\(990\) | 1.42961e11 | 0.148826 | ||||||||
\(991\) | − | 3.90397e11i | − | 0.404773i | −0.979306 | − | 0.202387i | \(-0.935130\pi\) | ||
0.979306 | − | 0.202387i | \(-0.0648698\pi\) | |||||||
\(992\) | −2.98347e11 | −0.308089 | ||||||||
\(993\) | −4.08880e11 | −0.420532 | ||||||||
\(994\) | 2.13826e12i | 2.19035i | ||||||||
\(995\) | −5.24020e11 | −0.534633 | ||||||||
\(996\) | 8.23591e11i | 0.836901i | ||||||||
\(997\) | 2.66999e11 | 0.270227 | 0.135113 | − | 0.990830i | \(-0.456860\pi\) | ||||
0.135113 | + | 0.990830i | \(0.456860\pi\) | |||||||
\(998\) | − | 2.56693e12i | − | 2.58757i | ||||||
\(999\) | 5.18037e10i | 0.0520115i |
(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 | 177.9.c.a.58.7 | ✓ | 80 | |
59.58 | odd | 2 | inner | 177.9.c.a.58.74 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.9.c.a.58.7 | ✓ | 80 | 1.1 | even | 1 | trivial | |
177.9.c.a.58.74 | yes | 80 | 59.58 | odd | 2 | inner |