Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
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, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(189.798744245\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −126.798 | −1.40094 | −0.700469 | − | 0.713683i | \(-0.747026\pi\) | ||||
−0.700469 | + | 0.713683i | \(0.747026\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 7885.84 | 0.962627 | ||||||||
\(5\) | 57088.2 | 1.63396 | 0.816980 | − | 0.576666i | \(-0.195647\pi\) | ||||
0.816980 | + | 0.576666i | \(0.195647\pi\) | |||||||
\(6\) | −92436.0 | −0.808832 | ||||||||
\(7\) | 543807. | 1.74706 | 0.873529 | − | 0.486772i | \(-0.161826\pi\) | ||||
0.873529 | + | 0.486772i | \(0.161826\pi\) | |||||||
\(8\) | 38821.0 | 0.0523578 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −7.23869e6 | −2.28908 | ||||||||
\(11\) | 4.27310e6 | 0.727261 | 0.363630 | − | 0.931543i | \(-0.381537\pi\) | ||||
0.363630 | + | 0.931543i | \(0.381537\pi\) | |||||||
\(12\) | 5.74878e6 | 0.555773 | ||||||||
\(13\) | 1.89254e7 | 1.08746 | 0.543730 | − | 0.839260i | \(-0.317012\pi\) | ||||
0.543730 | + | 0.839260i | \(0.317012\pi\) | |||||||
\(14\) | −6.89538e7 | −2.44752 | ||||||||
\(15\) | 4.16173e7 | 0.943367 | ||||||||
\(16\) | −6.95232e7 | −1.03598 | ||||||||
\(17\) | 6.68663e7 | 0.671876 | 0.335938 | − | 0.941884i | \(-0.390947\pi\) | ||||
0.335938 | + | 0.941884i | \(0.390947\pi\) | |||||||
\(18\) | −6.73859e7 | −0.466979 | ||||||||
\(19\) | −1.27598e8 | −0.622224 | −0.311112 | − | 0.950373i | \(-0.600701\pi\) | ||||
−0.311112 | + | 0.950373i | \(0.600701\pi\) | |||||||
\(20\) | 4.50188e8 | 1.57289 | ||||||||
\(21\) | 3.96435e8 | 1.00866 | ||||||||
\(22\) | −5.41822e8 | −1.01885 | ||||||||
\(23\) | −1.18294e9 | −1.66622 | −0.833112 | − | 0.553105i | \(-0.813443\pi\) | ||||
−0.833112 | + | 0.553105i | \(0.813443\pi\) | |||||||
\(24\) | 2.83005e7 | 0.0302288 | ||||||||
\(25\) | 2.03836e9 | 1.66982 | ||||||||
\(26\) | −2.39971e9 | −1.52346 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 4.28837e9 | 1.68176 | ||||||||
\(29\) | −4.39611e8 | −0.137240 | −0.0686201 | − | 0.997643i | \(-0.521860\pi\) | ||||
−0.0686201 | + | 0.997643i | \(0.521860\pi\) | |||||||
\(30\) | −5.27701e9 | −1.32160 | ||||||||
\(31\) | −4.50096e8 | −0.0910864 | −0.0455432 | − | 0.998962i | \(-0.514502\pi\) | ||||
−0.0455432 | + | 0.998962i | \(0.514502\pi\) | |||||||
\(32\) | 8.49741e9 | 1.39898 | ||||||||
\(33\) | 3.11509e9 | 0.419884 | ||||||||
\(34\) | −8.47854e9 | −0.941257 | ||||||||
\(35\) | 3.10449e10 | 2.85462 | ||||||||
\(36\) | 4.19086e9 | 0.320876 | ||||||||
\(37\) | −1.47236e10 | −0.943414 | −0.471707 | − | 0.881755i | \(-0.656362\pi\) | ||||
−0.471707 | + | 0.881755i | \(0.656362\pi\) | |||||||
\(38\) | 1.61793e10 | 0.871697 | ||||||||
\(39\) | 1.37966e10 | 0.627845 | ||||||||
\(40\) | 2.21622e9 | 0.0855505 | ||||||||
\(41\) | −1.44432e10 | −0.474863 | −0.237431 | − | 0.971404i | \(-0.576305\pi\) | ||||
−0.237431 | + | 0.971404i | \(0.576305\pi\) | |||||||
\(42\) | −5.02673e10 | −1.41308 | ||||||||
\(43\) | −6.17662e9 | −0.149007 | −0.0745033 | − | 0.997221i | \(-0.523737\pi\) | ||||
−0.0745033 | + | 0.997221i | \(0.523737\pi\) | |||||||
\(44\) | 3.36969e10 | 0.700080 | ||||||||
\(45\) | 3.03390e10 | 0.544653 | ||||||||
\(46\) | 1.49995e11 | 2.33427 | ||||||||
\(47\) | 1.00774e11 | 1.36367 | 0.681837 | − | 0.731504i | \(-0.261181\pi\) | ||||
0.681837 | + | 0.731504i | \(0.261181\pi\) | |||||||
\(48\) | −5.06824e10 | −0.598121 | ||||||||
\(49\) | 1.98837e11 | 2.05221 | ||||||||
\(50\) | −2.58461e11 | −2.33932 | ||||||||
\(51\) | 4.87455e10 | 0.387908 | ||||||||
\(52\) | 1.49243e11 | 1.04682 | ||||||||
\(53\) | 3.49052e10 | 0.216320 | 0.108160 | − | 0.994133i | \(-0.465504\pi\) | ||||
0.108160 | + | 0.994133i | \(0.465504\pi\) | |||||||
\(54\) | −4.91243e10 | −0.269611 | ||||||||
\(55\) | 2.43943e11 | 1.18831 | ||||||||
\(56\) | 2.11111e10 | 0.0914721 | ||||||||
\(57\) | −9.30192e10 | −0.359241 | ||||||||
\(58\) | 5.57419e10 | 0.192265 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | 3.28187e11 | 0.908110 | ||||||||
\(61\) | 4.06898e11 | 1.01121 | 0.505605 | − | 0.862765i | \(-0.331269\pi\) | ||||
0.505605 | + | 0.862765i | \(0.331269\pi\) | |||||||
\(62\) | 5.70714e10 | 0.127606 | ||||||||
\(63\) | 2.89001e11 | 0.582353 | ||||||||
\(64\) | −5.07924e11 | −0.923909 | ||||||||
\(65\) | 1.08042e12 | 1.77687 | ||||||||
\(66\) | −3.94988e11 | −0.588232 | ||||||||
\(67\) | 1.91805e11 | 0.259044 | 0.129522 | − | 0.991577i | \(-0.458656\pi\) | ||||
0.129522 | + | 0.991577i | \(0.458656\pi\) | |||||||
\(68\) | 5.27297e11 | 0.646766 | ||||||||
\(69\) | −8.62366e11 | −0.961994 | ||||||||
\(70\) | −3.93645e12 | −3.99915 | ||||||||
\(71\) | −1.26723e12 | −1.17403 | −0.587013 | − | 0.809578i | \(-0.699696\pi\) | ||||
−0.587013 | + | 0.809578i | \(0.699696\pi\) | |||||||
\(72\) | 2.06310e10 | 0.0174526 | ||||||||
\(73\) | 7.26492e11 | 0.561865 | 0.280933 | − | 0.959727i | \(-0.409356\pi\) | ||||
0.280933 | + | 0.959727i | \(0.409356\pi\) | |||||||
\(74\) | 1.86693e12 | 1.32166 | ||||||||
\(75\) | 1.48596e12 | 0.964073 | ||||||||
\(76\) | −1.00622e12 | −0.598970 | ||||||||
\(77\) | 2.32374e12 | 1.27057 | ||||||||
\(78\) | −1.74939e12 | −0.879572 | ||||||||
\(79\) | 1.13147e12 | 0.523679 | 0.261839 | − | 0.965111i | \(-0.415671\pi\) | ||||
0.261839 | + | 0.965111i | \(0.415671\pi\) | |||||||
\(80\) | −3.96896e12 | −1.69274 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 1.83137e12 | 0.665253 | ||||||||
\(83\) | 4.87459e12 | 1.63655 | 0.818277 | − | 0.574824i | \(-0.194929\pi\) | ||||
0.818277 | + | 0.574824i | \(0.194929\pi\) | |||||||
\(84\) | 3.12622e12 | 0.970967 | ||||||||
\(85\) | 3.81728e12 | 1.09782 | ||||||||
\(86\) | 7.83185e11 | 0.208749 | ||||||||
\(87\) | −3.20476e11 | −0.0792357 | ||||||||
\(88\) | 1.65886e11 | 0.0380778 | ||||||||
\(89\) | 3.48139e12 | 0.742536 | 0.371268 | − | 0.928526i | \(-0.378923\pi\) | ||||
0.371268 | + | 0.928526i | \(0.378923\pi\) | |||||||
\(90\) | −3.84694e12 | −0.763025 | ||||||||
\(91\) | 1.02918e13 | 1.89986 | ||||||||
\(92\) | −9.32850e12 | −1.60395 | ||||||||
\(93\) | −3.28120e11 | −0.0525888 | ||||||||
\(94\) | −1.27779e13 | −1.91042 | ||||||||
\(95\) | −7.28436e12 | −1.01669 | ||||||||
\(96\) | 6.19461e12 | 0.807702 | ||||||||
\(97\) | 1.18763e13 | 1.44765 | 0.723826 | − | 0.689983i | \(-0.242382\pi\) | ||||
0.723826 | + | 0.689983i | \(0.242382\pi\) | |||||||
\(98\) | −2.52122e13 | −2.87502 | ||||||||
\(99\) | 2.27090e12 | 0.242420 | ||||||||
\(100\) | 1.60742e13 | 1.60742 | ||||||||
\(101\) | −1.57426e13 | −1.47567 | −0.737834 | − | 0.674982i | \(-0.764151\pi\) | ||||
−0.737834 | + | 0.674982i | \(0.764151\pi\) | |||||||
\(102\) | −6.18086e12 | −0.543435 | ||||||||
\(103\) | 1.25174e12 | 0.103293 | 0.0516466 | − | 0.998665i | \(-0.483553\pi\) | ||||
0.0516466 | + | 0.998665i | \(0.483553\pi\) | |||||||
\(104\) | 7.34702e11 | 0.0569370 | ||||||||
\(105\) | 2.26318e13 | 1.64812 | ||||||||
\(106\) | −4.42593e12 | −0.303051 | ||||||||
\(107\) | −1.64026e13 | −1.05662 | −0.528308 | − | 0.849053i | \(-0.677173\pi\) | ||||
−0.528308 | + | 0.849053i | \(0.677173\pi\) | |||||||
\(108\) | 3.05513e12 | 0.185258 | ||||||||
\(109\) | −2.54712e13 | −1.45471 | −0.727356 | − | 0.686261i | \(-0.759251\pi\) | ||||
−0.727356 | + | 0.686261i | \(0.759251\pi\) | |||||||
\(110\) | −3.09316e13 | −1.66475 | ||||||||
\(111\) | −1.07335e13 | −0.544680 | ||||||||
\(112\) | −3.78072e13 | −1.80991 | ||||||||
\(113\) | 7.02449e11 | 0.0317398 | 0.0158699 | − | 0.999874i | \(-0.494948\pi\) | ||||
0.0158699 | + | 0.999874i | \(0.494948\pi\) | |||||||
\(114\) | 1.17947e13 | 0.503275 | ||||||||
\(115\) | −6.75321e13 | −2.72254 | ||||||||
\(116\) | −3.46670e12 | −0.132111 | ||||||||
\(117\) | 1.00577e13 | 0.362487 | ||||||||
\(118\) | 5.34842e12 | 0.182387 | ||||||||
\(119\) | 3.63623e13 | 1.17381 | ||||||||
\(120\) | 1.61562e12 | 0.0493926 | ||||||||
\(121\) | −1.62634e13 | −0.471092 | ||||||||
\(122\) | −5.15940e13 | −1.41664 | ||||||||
\(123\) | −1.05291e13 | −0.274162 | ||||||||
\(124\) | −3.54938e12 | −0.0876822 | ||||||||
\(125\) | 4.66785e13 | 1.09447 | ||||||||
\(126\) | −3.66449e13 | −0.815840 | ||||||||
\(127\) | −2.17612e13 | −0.460213 | −0.230107 | − | 0.973165i | \(-0.573907\pi\) | ||||
−0.230107 | + | 0.973165i | \(0.573907\pi\) | |||||||
\(128\) | −5.20682e12 | −0.104642 | ||||||||
\(129\) | −4.50275e12 | −0.0860290 | ||||||||
\(130\) | −1.36995e14 | −2.48928 | ||||||||
\(131\) | 5.05864e13 | 0.874520 | 0.437260 | − | 0.899335i | \(-0.355949\pi\) | ||||
0.437260 | + | 0.899335i | \(0.355949\pi\) | |||||||
\(132\) | 2.45651e13 | 0.404192 | ||||||||
\(133\) | −6.93889e13 | −1.08706 | ||||||||
\(134\) | −2.43205e13 | −0.362904 | ||||||||
\(135\) | 2.21171e13 | 0.314456 | ||||||||
\(136\) | 2.59581e12 | 0.0351780 | ||||||||
\(137\) | 9.19406e13 | 1.18802 | 0.594010 | − | 0.804458i | \(-0.297544\pi\) | ||||
0.594010 | + | 0.804458i | \(0.297544\pi\) | |||||||
\(138\) | 1.09347e14 | 1.34769 | ||||||||
\(139\) | −8.25654e13 | −0.970961 | −0.485480 | − | 0.874248i | \(-0.661355\pi\) | ||||
−0.485480 | + | 0.874248i | \(0.661355\pi\) | |||||||
\(140\) | 2.44815e14 | 2.74793 | ||||||||
\(141\) | 7.34639e13 | 0.787317 | ||||||||
\(142\) | 1.60683e14 | 1.64474 | ||||||||
\(143\) | 8.08700e13 | 0.790867 | ||||||||
\(144\) | −3.69475e13 | −0.345326 | ||||||||
\(145\) | −2.50966e13 | −0.224245 | ||||||||
\(146\) | −9.21180e13 | −0.787138 | ||||||||
\(147\) | 1.44952e14 | 1.18484 | ||||||||
\(148\) | −1.16108e14 | −0.908156 | ||||||||
\(149\) | −1.15044e14 | −0.861301 | −0.430650 | − | 0.902519i | \(-0.641716\pi\) | ||||
−0.430650 | + | 0.902519i | \(0.641716\pi\) | |||||||
\(150\) | −1.88418e14 | −1.35061 | ||||||||
\(151\) | 2.30382e14 | 1.58161 | 0.790805 | − | 0.612069i | \(-0.209662\pi\) | ||||
0.790805 | + | 0.612069i | \(0.209662\pi\) | |||||||
\(152\) | −4.95349e12 | −0.0325783 | ||||||||
\(153\) | 3.55355e13 | 0.223959 | ||||||||
\(154\) | −2.94646e14 | −1.77998 | ||||||||
\(155\) | −2.56951e13 | −0.148832 | ||||||||
\(156\) | 1.08798e14 | 0.604381 | ||||||||
\(157\) | −2.00111e14 | −1.06641 | −0.533204 | − | 0.845987i | \(-0.679012\pi\) | ||||
−0.533204 | + | 0.845987i | \(0.679012\pi\) | |||||||
\(158\) | −1.43468e14 | −0.733642 | ||||||||
\(159\) | 2.54459e13 | 0.124893 | ||||||||
\(160\) | 4.85102e14 | 2.28588 | ||||||||
\(161\) | −6.43293e14 | −2.91099 | ||||||||
\(162\) | −3.58116e13 | −0.155660 | ||||||||
\(163\) | −2.91103e14 | −1.21570 | −0.607852 | − | 0.794050i | \(-0.707969\pi\) | ||||
−0.607852 | + | 0.794050i | \(0.707969\pi\) | |||||||
\(164\) | −1.13897e14 | −0.457115 | ||||||||
\(165\) | 1.77835e14 | 0.686074 | ||||||||
\(166\) | −6.18090e14 | −2.29271 | ||||||||
\(167\) | 1.80557e14 | 0.644106 | 0.322053 | − | 0.946722i | \(-0.395627\pi\) | ||||
0.322053 | + | 0.946722i | \(0.395627\pi\) | |||||||
\(168\) | 1.53900e13 | 0.0528114 | ||||||||
\(169\) | 5.52956e13 | 0.182569 | ||||||||
\(170\) | −4.84025e14 | −1.53798 | ||||||||
\(171\) | −6.78110e13 | −0.207408 | ||||||||
\(172\) | −4.87078e13 | −0.143438 | ||||||||
\(173\) | 4.92993e14 | 1.39811 | 0.699054 | − | 0.715069i | \(-0.253605\pi\) | ||||
0.699054 | + | 0.715069i | \(0.253605\pi\) | |||||||
\(174\) | 4.06359e13 | 0.111004 | ||||||||
\(175\) | 1.10847e15 | 2.91728 | ||||||||
\(176\) | −2.97079e14 | −0.753425 | ||||||||
\(177\) | −3.07496e13 | −0.0751646 | ||||||||
\(178\) | −4.41435e14 | −1.04025 | ||||||||
\(179\) | 4.21410e14 | 0.957548 | 0.478774 | − | 0.877938i | \(-0.341081\pi\) | ||||
0.478774 | + | 0.877938i | \(0.341081\pi\) | |||||||
\(180\) | 2.39248e14 | 0.524298 | ||||||||
\(181\) | 4.22654e14 | 0.893459 | 0.446729 | − | 0.894669i | \(-0.352589\pi\) | ||||
0.446729 | + | 0.894669i | \(0.352589\pi\) | |||||||
\(182\) | −1.30498e15 | −2.66158 | ||||||||
\(183\) | 2.96628e14 | 0.583822 | ||||||||
\(184\) | −4.59230e13 | −0.0872398 | ||||||||
\(185\) | −8.40543e14 | −1.54150 | ||||||||
\(186\) | 4.16051e13 | 0.0736736 | ||||||||
\(187\) | 2.85726e14 | 0.488629 | ||||||||
\(188\) | 7.94684e14 | 1.31271 | ||||||||
\(189\) | 2.10682e14 | 0.336221 | ||||||||
\(190\) | 9.23646e14 | 1.42432 | ||||||||
\(191\) | 1.04831e15 | 1.56233 | 0.781163 | − | 0.624327i | \(-0.214627\pi\) | ||||
0.781163 | + | 0.624327i | \(0.214627\pi\) | |||||||
\(192\) | −3.70277e14 | −0.533419 | ||||||||
\(193\) | −2.77452e14 | −0.386425 | −0.193213 | − | 0.981157i | \(-0.561891\pi\) | ||||
−0.193213 | + | 0.981157i | \(0.561891\pi\) | |||||||
\(194\) | −1.50589e15 | −2.02807 | ||||||||
\(195\) | 7.87624e14 | 1.02587 | ||||||||
\(196\) | 1.56799e15 | 1.97551 | ||||||||
\(197\) | 1.09387e14 | 0.133333 | 0.0666664 | − | 0.997775i | \(-0.478764\pi\) | ||||
0.0666664 | + | 0.997775i | \(0.478764\pi\) | |||||||
\(198\) | −2.87946e14 | −0.339616 | ||||||||
\(199\) | 9.79714e14 | 1.11829 | 0.559145 | − | 0.829070i | \(-0.311129\pi\) | ||||
0.559145 | + | 0.829070i | \(0.311129\pi\) | |||||||
\(200\) | 7.91311e13 | 0.0874283 | ||||||||
\(201\) | 1.39826e14 | 0.149559 | ||||||||
\(202\) | 1.99614e15 | 2.06732 | ||||||||
\(203\) | −2.39063e14 | −0.239767 | ||||||||
\(204\) | 3.84399e14 | 0.373411 | ||||||||
\(205\) | −8.24536e14 | −0.775906 | ||||||||
\(206\) | −1.58718e14 | −0.144707 | ||||||||
\(207\) | −6.28665e14 | −0.555408 | ||||||||
\(208\) | −1.31575e15 | −1.12658 | ||||||||
\(209\) | −5.45240e14 | −0.452519 | ||||||||
\(210\) | −2.86967e15 | −2.30891 | ||||||||
\(211\) | 2.38723e14 | 0.186234 | 0.0931168 | − | 0.995655i | \(-0.470317\pi\) | ||||
0.0931168 | + | 0.995655i | \(0.470317\pi\) | |||||||
\(212\) | 2.75257e14 | 0.208236 | ||||||||
\(213\) | −9.23813e14 | −0.677824 | ||||||||
\(214\) | 2.07982e15 | 1.48025 | ||||||||
\(215\) | −3.52612e14 | −0.243471 | ||||||||
\(216\) | 1.50400e13 | 0.0100763 | ||||||||
\(217\) | −2.44765e14 | −0.159133 | ||||||||
\(218\) | 3.22971e15 | 2.03796 | ||||||||
\(219\) | 5.29613e14 | 0.324393 | ||||||||
\(220\) | 1.92370e15 | 1.14390 | ||||||||
\(221\) | 1.26547e15 | 0.730639 | ||||||||
\(222\) | 1.36099e15 | 0.763063 | ||||||||
\(223\) | 1.03581e15 | 0.564024 | 0.282012 | − | 0.959411i | \(-0.408998\pi\) | ||||
0.282012 | + | 0.959411i | \(0.408998\pi\) | |||||||
\(224\) | 4.62095e15 | 2.44410 | ||||||||
\(225\) | 1.08327e15 | 0.556608 | ||||||||
\(226\) | −8.90694e13 | −0.0444655 | ||||||||
\(227\) | 2.68518e15 | 1.30258 | 0.651290 | − | 0.758829i | \(-0.274228\pi\) | ||||
0.651290 | + | 0.758829i | \(0.274228\pi\) | |||||||
\(228\) | −7.33535e14 | −0.345815 | ||||||||
\(229\) | −1.19812e15 | −0.548995 | −0.274497 | − | 0.961588i | \(-0.588512\pi\) | ||||
−0.274497 | + | 0.961588i | \(0.588512\pi\) | |||||||
\(230\) | 8.56297e15 | 3.81411 | ||||||||
\(231\) | 1.69400e15 | 0.733562 | ||||||||
\(232\) | −1.70661e13 | −0.00718559 | ||||||||
\(233\) | −3.97777e15 | −1.62865 | −0.814323 | − | 0.580412i | \(-0.802892\pi\) | ||||
−0.814323 | + | 0.580412i | \(0.802892\pi\) | |||||||
\(234\) | −1.27530e15 | −0.507821 | ||||||||
\(235\) | 5.75298e15 | 2.22819 | ||||||||
\(236\) | −3.32629e14 | −0.125323 | ||||||||
\(237\) | 8.24838e14 | 0.302346 | ||||||||
\(238\) | −4.61069e15 | −1.64443 | ||||||||
\(239\) | 4.96261e15 | 1.72236 | 0.861179 | − | 0.508302i | \(-0.169727\pi\) | ||||
0.861179 | + | 0.508302i | \(0.169727\pi\) | |||||||
\(240\) | −2.89337e15 | −0.977306 | ||||||||
\(241\) | 1.37022e15 | 0.450484 | 0.225242 | − | 0.974303i | \(-0.427683\pi\) | ||||
0.225242 | + | 0.974303i | \(0.427683\pi\) | |||||||
\(242\) | 2.06217e15 | 0.659970 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 3.20873e15 | 0.973417 | ||||||||
\(245\) | 1.13512e16 | 3.35323 | ||||||||
\(246\) | 1.33507e15 | 0.384084 | ||||||||
\(247\) | −2.41485e15 | −0.676644 | ||||||||
\(248\) | −1.74731e13 | −0.00476908 | ||||||||
\(249\) | 3.55358e15 | 0.944865 | ||||||||
\(250\) | −5.91876e15 | −1.53328 | ||||||||
\(251\) | −2.25218e15 | −0.568491 | −0.284246 | − | 0.958752i | \(-0.591743\pi\) | ||||
−0.284246 | + | 0.958752i | \(0.591743\pi\) | |||||||
\(252\) | 2.27902e15 | 0.560588 | ||||||||
\(253\) | −5.05483e15 | −1.21178 | ||||||||
\(254\) | 2.75929e15 | 0.644730 | ||||||||
\(255\) | 2.78280e15 | 0.633826 | ||||||||
\(256\) | 4.82113e15 | 1.07051 | ||||||||
\(257\) | −6.59299e15 | −1.42731 | −0.713653 | − | 0.700499i | \(-0.752961\pi\) | ||||
−0.713653 | + | 0.700499i | \(0.752961\pi\) | |||||||
\(258\) | 5.70942e14 | 0.120521 | ||||||||
\(259\) | −8.00678e15 | −1.64820 | ||||||||
\(260\) | 8.51999e15 | 1.71046 | ||||||||
\(261\) | −2.33627e14 | −0.0457467 | ||||||||
\(262\) | −6.41427e15 | −1.22515 | ||||||||
\(263\) | −5.78677e15 | −1.07826 | −0.539131 | − | 0.842222i | \(-0.681247\pi\) | ||||
−0.539131 | + | 0.842222i | \(0.681247\pi\) | |||||||
\(264\) | 1.20931e14 | 0.0219842 | ||||||||
\(265\) | 1.99268e15 | 0.353459 | ||||||||
\(266\) | 8.79840e15 | 1.52291 | ||||||||
\(267\) | 2.53793e15 | 0.428703 | ||||||||
\(268\) | 1.51254e15 | 0.249362 | ||||||||
\(269\) | 1.19272e16 | 1.91933 | 0.959664 | − | 0.281148i | \(-0.0907153\pi\) | ||||
0.959664 | + | 0.281148i | \(0.0907153\pi\) | |||||||
\(270\) | −2.80442e15 | −0.440533 | ||||||||
\(271\) | 5.02154e15 | 0.770081 | 0.385040 | − | 0.922900i | \(-0.374187\pi\) | ||||
0.385040 | + | 0.922900i | \(0.374187\pi\) | |||||||
\(272\) | −4.64876e15 | −0.696048 | ||||||||
\(273\) | 7.50269e15 | 1.09688 | ||||||||
\(274\) | −1.16579e16 | −1.66434 | ||||||||
\(275\) | 8.71010e15 | 1.21440 | ||||||||
\(276\) | −6.80048e15 | −0.926041 | ||||||||
\(277\) | −1.26988e16 | −1.68906 | −0.844530 | − | 0.535508i | \(-0.820120\pi\) | ||||
−0.844530 | + | 0.535508i | \(0.820120\pi\) | |||||||
\(278\) | 1.04692e16 | 1.36026 | ||||||||
\(279\) | −2.39199e14 | −0.0303621 | ||||||||
\(280\) | 1.20519e15 | 0.149462 | ||||||||
\(281\) | 1.22023e16 | 1.47860 | 0.739302 | − | 0.673374i | \(-0.235156\pi\) | ||||
0.739302 | + | 0.673374i | \(0.235156\pi\) | |||||||
\(282\) | −9.31510e15 | −1.10298 | ||||||||
\(283\) | −6.35053e15 | −0.734849 | −0.367424 | − | 0.930053i | \(-0.619760\pi\) | ||||
−0.367424 | + | 0.930053i | \(0.619760\pi\) | |||||||
\(284\) | −9.99320e15 | −1.13015 | ||||||||
\(285\) | −5.31030e15 | −0.586986 | ||||||||
\(286\) | −1.02542e16 | −1.10796 | ||||||||
\(287\) | −7.85430e15 | −0.829612 | ||||||||
\(288\) | 4.51587e15 | 0.466327 | ||||||||
\(289\) | −5.43347e15 | −0.548582 | ||||||||
\(290\) | 3.18221e15 | 0.314153 | ||||||||
\(291\) | 8.65781e15 | 0.835802 | ||||||||
\(292\) | 5.72900e15 | 0.540867 | ||||||||
\(293\) | 4.85848e15 | 0.448601 | 0.224301 | − | 0.974520i | \(-0.427990\pi\) | ||||
0.224301 | + | 0.974520i | \(0.427990\pi\) | |||||||
\(294\) | −1.83797e16 | −1.65989 | ||||||||
\(295\) | −2.40801e15 | −0.212723 | ||||||||
\(296\) | −5.71584e14 | −0.0493951 | ||||||||
\(297\) | 1.65548e15 | 0.139961 | ||||||||
\(298\) | 1.45874e16 | 1.20663 | ||||||||
\(299\) | −2.23877e16 | −1.81195 | ||||||||
\(300\) | 1.17181e16 | 0.928043 | ||||||||
\(301\) | −3.35888e15 | −0.260323 | ||||||||
\(302\) | −2.92121e16 | −2.21574 | ||||||||
\(303\) | −1.14764e16 | −0.851977 | ||||||||
\(304\) | 8.87105e15 | 0.644610 | ||||||||
\(305\) | 2.32290e16 | 1.65228 | ||||||||
\(306\) | −4.50584e15 | −0.313752 | ||||||||
\(307\) | −1.26430e16 | −0.861888 | −0.430944 | − | 0.902379i | \(-0.641819\pi\) | ||||
−0.430944 | + | 0.902379i | \(0.641819\pi\) | |||||||
\(308\) | 1.83246e16 | 1.22308 | ||||||||
\(309\) | 9.12517e14 | 0.0596363 | ||||||||
\(310\) | 3.25810e15 | 0.208504 | ||||||||
\(311\) | −2.08567e16 | −1.30708 | −0.653541 | − | 0.756891i | \(-0.726717\pi\) | ||||
−0.653541 | + | 0.756891i | \(0.726717\pi\) | |||||||
\(312\) | 5.35598e14 | 0.0328726 | ||||||||
\(313\) | 2.10378e16 | 1.26463 | 0.632314 | − | 0.774712i | \(-0.282105\pi\) | ||||
0.632314 | + | 0.774712i | \(0.282105\pi\) | |||||||
\(314\) | 2.53738e16 | 1.49397 | ||||||||
\(315\) | 1.64986e16 | 0.951541 | ||||||||
\(316\) | 8.92255e15 | 0.504107 | ||||||||
\(317\) | 1.96726e15 | 0.108887 | 0.0544437 | − | 0.998517i | \(-0.482661\pi\) | ||||
0.0544437 | + | 0.998517i | \(0.482661\pi\) | |||||||
\(318\) | −3.22650e15 | −0.174967 | ||||||||
\(319\) | −1.87850e15 | −0.0998094 | ||||||||
\(320\) | −2.89965e16 | −1.50963 | ||||||||
\(321\) | −1.19575e16 | −0.610037 | ||||||||
\(322\) | 8.15685e16 | 4.07811 | ||||||||
\(323\) | −8.53204e15 | −0.418058 | ||||||||
\(324\) | 2.22719e15 | 0.106959 | ||||||||
\(325\) | 3.85768e16 | 1.81587 | ||||||||
\(326\) | 3.69115e16 | 1.70313 | ||||||||
\(327\) | −1.85685e16 | −0.839878 | ||||||||
\(328\) | −5.60698e14 | −0.0248628 | ||||||||
\(329\) | 5.48013e16 | 2.38242 | ||||||||
\(330\) | −2.25492e16 | −0.961147 | ||||||||
\(331\) | −1.13113e16 | −0.472748 | −0.236374 | − | 0.971662i | \(-0.575959\pi\) | ||||
−0.236374 | + | 0.971662i | \(0.575959\pi\) | |||||||
\(332\) | 3.84402e16 | 1.57539 | ||||||||
\(333\) | −7.82472e15 | −0.314471 | ||||||||
\(334\) | −2.28943e16 | −0.902352 | ||||||||
\(335\) | 1.09498e16 | 0.423267 | ||||||||
\(336\) | −2.75614e16 | −1.04495 | ||||||||
\(337\) | −3.98649e16 | −1.48251 | −0.741253 | − | 0.671225i | \(-0.765768\pi\) | ||||
−0.741253 | + | 0.671225i | \(0.765768\pi\) | |||||||
\(338\) | −7.01139e15 | −0.255768 | ||||||||
\(339\) | 5.12085e14 | 0.0183250 | ||||||||
\(340\) | 3.01024e16 | 1.05679 | ||||||||
\(341\) | −1.92330e15 | −0.0662436 | ||||||||
\(342\) | 8.59833e15 | 0.290566 | ||||||||
\(343\) | 5.54398e16 | 1.83827 | ||||||||
\(344\) | −2.39782e14 | −0.00780166 | ||||||||
\(345\) | −4.92309e16 | −1.57186 | ||||||||
\(346\) | −6.25107e16 | −1.95866 | ||||||||
\(347\) | −2.60771e16 | −0.801894 | −0.400947 | − | 0.916101i | \(-0.631319\pi\) | ||||
−0.400947 | + | 0.916101i | \(0.631319\pi\) | |||||||
\(348\) | −2.52722e15 | −0.0762743 | ||||||||
\(349\) | −5.55368e16 | −1.64519 | −0.822594 | − | 0.568629i | \(-0.807474\pi\) | ||||
−0.822594 | + | 0.568629i | \(0.807474\pi\) | |||||||
\(350\) | −1.40553e17 | −4.08693 | ||||||||
\(351\) | 7.33209e15 | 0.209282 | ||||||||
\(352\) | 3.63102e16 | 1.01742 | ||||||||
\(353\) | 3.77223e16 | 1.03768 | 0.518838 | − | 0.854872i | \(-0.326365\pi\) | ||||
0.518838 | + | 0.854872i | \(0.326365\pi\) | |||||||
\(354\) | 3.89900e15 | 0.105301 | ||||||||
\(355\) | −7.23441e16 | −1.91831 | ||||||||
\(356\) | 2.74537e16 | 0.714785 | ||||||||
\(357\) | 2.65081e16 | 0.677698 | ||||||||
\(358\) | −5.34342e16 | −1.34147 | ||||||||
\(359\) | 3.81306e16 | 0.940069 | 0.470035 | − | 0.882648i | \(-0.344241\pi\) | ||||
0.470035 | + | 0.882648i | \(0.344241\pi\) | |||||||
\(360\) | 1.17779e15 | 0.0285168 | ||||||||
\(361\) | −2.57716e16 | −0.612837 | ||||||||
\(362\) | −5.35919e16 | −1.25168 | ||||||||
\(363\) | −1.18560e16 | −0.271985 | ||||||||
\(364\) | 8.11591e16 | 1.82885 | ||||||||
\(365\) | 4.14741e16 | 0.918065 | ||||||||
\(366\) | −3.76120e16 | −0.817898 | ||||||||
\(367\) | 1.07064e16 | 0.228725 | 0.114363 | − | 0.993439i | \(-0.463517\pi\) | ||||
0.114363 | + | 0.993439i | \(0.463517\pi\) | |||||||
\(368\) | 8.22420e16 | 1.72617 | ||||||||
\(369\) | −7.67570e15 | −0.158288 | ||||||||
\(370\) | 1.06580e17 | 2.15955 | ||||||||
\(371\) | 1.89817e16 | 0.377924 | ||||||||
\(372\) | −2.58750e15 | −0.0506234 | ||||||||
\(373\) | −9.62522e16 | −1.85056 | −0.925280 | − | 0.379285i | \(-0.876170\pi\) | ||||
−0.925280 | + | 0.379285i | \(0.876170\pi\) | |||||||
\(374\) | −3.62296e16 | −0.684539 | ||||||||
\(375\) | 3.40286e16 | 0.631890 | ||||||||
\(376\) | 3.91212e15 | 0.0713989 | ||||||||
\(377\) | −8.31981e15 | −0.149243 | ||||||||
\(378\) | −2.67141e16 | −0.471025 | ||||||||
\(379\) | −6.96076e16 | −1.20643 | −0.603215 | − | 0.797579i | \(-0.706114\pi\) | ||||
−0.603215 | + | 0.797579i | \(0.706114\pi\) | |||||||
\(380\) | −5.74433e16 | −0.978692 | ||||||||
\(381\) | −1.58639e16 | −0.265704 | ||||||||
\(382\) | −1.32924e17 | −2.18872 | ||||||||
\(383\) | 1.73851e15 | 0.0281439 | 0.0140720 | − | 0.999901i | \(-0.495521\pi\) | ||||
0.0140720 | + | 0.999901i | \(0.495521\pi\) | |||||||
\(384\) | −3.79577e15 | −0.0604153 | ||||||||
\(385\) | 1.32658e17 | 2.07605 | ||||||||
\(386\) | 3.51805e16 | 0.541358 | ||||||||
\(387\) | −3.28251e15 | −0.0496689 | ||||||||
\(388\) | 9.36544e16 | 1.39355 | ||||||||
\(389\) | −8.31322e16 | −1.21646 | −0.608228 | − | 0.793762i | \(-0.708119\pi\) | ||||
−0.608228 | + | 0.793762i | \(0.708119\pi\) | |||||||
\(390\) | −9.98695e16 | −1.43719 | ||||||||
\(391\) | −7.90991e16 | −1.11950 | ||||||||
\(392\) | 7.71903e15 | 0.107449 | ||||||||
\(393\) | 3.68775e16 | 0.504905 | ||||||||
\(394\) | −1.38702e16 | −0.186791 | ||||||||
\(395\) | 6.45933e16 | 0.855670 | ||||||||
\(396\) | 1.79079e16 | 0.233360 | ||||||||
\(397\) | −9.57949e16 | −1.22802 | −0.614008 | − | 0.789300i | \(-0.710444\pi\) | ||||
−0.614008 | + | 0.789300i | \(0.710444\pi\) | |||||||
\(398\) | −1.24226e17 | −1.56665 | ||||||||
\(399\) | −5.05845e16 | −0.627615 | ||||||||
\(400\) | −1.41713e17 | −1.72990 | ||||||||
\(401\) | 1.00372e17 | 1.20552 | 0.602761 | − | 0.797922i | \(-0.294067\pi\) | ||||
0.602761 | + | 0.797922i | \(0.294067\pi\) | |||||||
\(402\) | −1.77297e16 | −0.209523 | ||||||||
\(403\) | −8.51824e15 | −0.0990528 | ||||||||
\(404\) | −1.24144e17 | −1.42052 | ||||||||
\(405\) | 1.61234e16 | 0.181551 | ||||||||
\(406\) | 3.03128e16 | 0.335898 | ||||||||
\(407\) | −6.29153e16 | −0.686108 | ||||||||
\(408\) | 1.89235e15 | 0.0203100 | ||||||||
\(409\) | −1.05825e17 | −1.11786 | −0.558928 | − | 0.829216i | \(-0.688787\pi\) | ||||
−0.558928 | + | 0.829216i | \(0.688787\pi\) | |||||||
\(410\) | 1.04550e17 | 1.08700 | ||||||||
\(411\) | 6.70247e16 | 0.685904 | ||||||||
\(412\) | 9.87100e15 | 0.0994327 | ||||||||
\(413\) | −2.29381e16 | −0.227448 | ||||||||
\(414\) | 7.97137e16 | 0.778092 | ||||||||
\(415\) | 2.78282e17 | 2.67406 | ||||||||
\(416\) | 1.60817e17 | 1.52134 | ||||||||
\(417\) | −6.01902e16 | −0.560585 | ||||||||
\(418\) | 6.91356e16 | 0.633951 | ||||||||
\(419\) | 2.06263e17 | 1.86222 | 0.931108 | − | 0.364745i | \(-0.118844\pi\) | ||||
0.931108 | + | 0.364745i | \(0.118844\pi\) | |||||||
\(420\) | 1.78470e17 | 1.58652 | ||||||||
\(421\) | 1.85110e17 | 1.62031 | 0.810153 | − | 0.586218i | \(-0.199384\pi\) | ||||
0.810153 | + | 0.586218i | \(0.199384\pi\) | |||||||
\(422\) | −3.02697e16 | −0.260902 | ||||||||
\(423\) | 5.35552e16 | 0.454558 | ||||||||
\(424\) | 1.35505e15 | 0.0113261 | ||||||||
\(425\) | 1.36298e17 | 1.12192 | ||||||||
\(426\) | 1.17138e17 | 0.949589 | ||||||||
\(427\) | 2.21274e17 | 1.76664 | ||||||||
\(428\) | −1.29348e17 | −1.01713 | ||||||||
\(429\) | 5.89542e16 | 0.456607 | ||||||||
\(430\) | 4.47106e16 | 0.341088 | ||||||||
\(431\) | 9.02699e16 | 0.678329 | 0.339165 | − | 0.940727i | \(-0.389856\pi\) | ||||
0.339165 | + | 0.940727i | \(0.389856\pi\) | |||||||
\(432\) | −2.69347e16 | −0.199374 | ||||||||
\(433\) | 5.35452e16 | 0.390436 | 0.195218 | − | 0.980760i | \(-0.437459\pi\) | ||||
0.195218 | + | 0.980760i | \(0.437459\pi\) | |||||||
\(434\) | 3.10358e16 | 0.222936 | ||||||||
\(435\) | −1.82954e16 | −0.129468 | ||||||||
\(436\) | −2.00862e17 | −1.40034 | ||||||||
\(437\) | 1.50942e17 | 1.03676 | ||||||||
\(438\) | −6.71540e16 | −0.454455 | ||||||||
\(439\) | 5.80855e16 | 0.387300 | 0.193650 | − | 0.981071i | \(-0.437967\pi\) | ||||
0.193650 | + | 0.981071i | \(0.437967\pi\) | |||||||
\(440\) | 9.47011e15 | 0.0622175 | ||||||||
\(441\) | 1.05670e17 | 0.684070 | ||||||||
\(442\) | −1.60460e17 | −1.02358 | ||||||||
\(443\) | −4.83363e16 | −0.303843 | −0.151921 | − | 0.988393i | \(-0.548546\pi\) | ||||
−0.151921 | + | 0.988393i | \(0.548546\pi\) | |||||||
\(444\) | −8.46426e16 | −0.524324 | ||||||||
\(445\) | 1.98746e17 | 1.21327 | ||||||||
\(446\) | −1.31339e17 | −0.790163 | ||||||||
\(447\) | −8.38674e16 | −0.497272 | ||||||||
\(448\) | −2.76213e17 | −1.61412 | ||||||||
\(449\) | −1.25262e17 | −0.721470 | −0.360735 | − | 0.932668i | \(-0.617474\pi\) | ||||
−0.360735 | + | 0.932668i | \(0.617474\pi\) | |||||||
\(450\) | −1.37357e17 | −0.779773 | ||||||||
\(451\) | −6.17171e16 | −0.345349 | ||||||||
\(452\) | 5.53940e15 | 0.0305536 | ||||||||
\(453\) | 1.67949e17 | 0.913143 | ||||||||
\(454\) | −3.40476e17 | −1.82483 | ||||||||
\(455\) | 5.87538e17 | 3.10429 | ||||||||
\(456\) | −3.61110e15 | −0.0188091 | ||||||||
\(457\) | −1.02986e17 | −0.528839 | −0.264420 | − | 0.964408i | \(-0.585180\pi\) | ||||
−0.264420 | + | 0.964408i | \(0.585180\pi\) | |||||||
\(458\) | 1.51919e17 | 0.769108 | ||||||||
\(459\) | 2.59054e16 | 0.129303 | ||||||||
\(460\) | −5.32547e17 | −2.62079 | ||||||||
\(461\) | 1.65942e17 | 0.805194 | 0.402597 | − | 0.915377i | \(-0.368108\pi\) | ||||
0.402597 | + | 0.915377i | \(0.368108\pi\) | |||||||
\(462\) | −2.14797e17 | −1.02767 | ||||||||
\(463\) | −8.22815e16 | −0.388173 | −0.194087 | − | 0.980984i | \(-0.562174\pi\) | ||||
−0.194087 | + | 0.980984i | \(0.562174\pi\) | |||||||
\(464\) | 3.05631e16 | 0.142178 | ||||||||
\(465\) | −1.87318e16 | −0.0859279 | ||||||||
\(466\) | 5.04376e17 | 2.28163 | ||||||||
\(467\) | −2.57308e17 | −1.14787 | −0.573935 | − | 0.818901i | \(-0.694584\pi\) | ||||
−0.573935 | + | 0.818901i | \(0.694584\pi\) | |||||||
\(468\) | 7.93136e16 | 0.348939 | ||||||||
\(469\) | 1.04305e17 | 0.452564 | ||||||||
\(470\) | −7.29469e17 | −3.12155 | ||||||||
\(471\) | −1.45881e17 | −0.615691 | ||||||||
\(472\) | −1.63749e15 | −0.00681640 | ||||||||
\(473\) | −2.63933e16 | −0.108367 | ||||||||
\(474\) | −1.04588e17 | −0.423568 | ||||||||
\(475\) | −2.60091e17 | −1.03900 | ||||||||
\(476\) | 2.86748e17 | 1.12994 | ||||||||
\(477\) | 1.85501e16 | 0.0721068 | ||||||||
\(478\) | −6.29251e17 | −2.41292 | ||||||||
\(479\) | −3.59462e17 | −1.35979 | −0.679895 | − | 0.733309i | \(-0.737975\pi\) | ||||
−0.679895 | + | 0.733309i | \(0.737975\pi\) | |||||||
\(480\) | 3.53639e17 | 1.31975 | ||||||||
\(481\) | −2.78650e17 | −1.02593 | ||||||||
\(482\) | −1.73742e17 | −0.631100 | ||||||||
\(483\) | −4.68960e17 | −1.68066 | ||||||||
\(484\) | −1.28250e17 | −0.453486 | ||||||||
\(485\) | 6.77995e17 | 2.36540 | ||||||||
\(486\) | −2.61067e16 | −0.0898702 | ||||||||
\(487\) | −2.15348e17 | −0.731481 | −0.365741 | − | 0.930717i | \(-0.619184\pi\) | ||||
−0.365741 | + | 0.930717i | \(0.619184\pi\) | |||||||
\(488\) | 1.57962e16 | 0.0529447 | ||||||||
\(489\) | −2.12214e17 | −0.701887 | ||||||||
\(490\) | −1.43932e18 | −4.69767 | ||||||||
\(491\) | 3.08298e17 | 0.992981 | 0.496491 | − | 0.868042i | \(-0.334622\pi\) | ||||
0.496491 | + | 0.868042i | \(0.334622\pi\) | |||||||
\(492\) | −8.30306e16 | −0.263916 | ||||||||
\(493\) | −2.93951e16 | −0.0922084 | ||||||||
\(494\) | 3.06199e17 | 0.947936 | ||||||||
\(495\) | 1.29641e17 | 0.396105 | ||||||||
\(496\) | 3.12921e16 | 0.0943634 | ||||||||
\(497\) | −6.89130e17 | −2.05109 | ||||||||
\(498\) | −4.50588e17 | −1.32370 | ||||||||
\(499\) | −4.63642e17 | −1.34440 | −0.672200 | − | 0.740369i | \(-0.734651\pi\) | ||||
−0.672200 | + | 0.740369i | \(0.734651\pi\) | |||||||
\(500\) | 3.68099e17 | 1.05356 | ||||||||
\(501\) | 1.31626e17 | 0.371875 | ||||||||
\(502\) | 2.85573e17 | 0.796421 | ||||||||
\(503\) | 2.03093e17 | 0.559117 | 0.279558 | − | 0.960129i | \(-0.409812\pi\) | ||||
0.279558 | + | 0.960129i | \(0.409812\pi\) | |||||||
\(504\) | 1.12193e16 | 0.0304907 | ||||||||
\(505\) | −8.98719e17 | −2.41118 | ||||||||
\(506\) | 6.40945e17 | 1.69763 | ||||||||
\(507\) | 4.03105e16 | 0.105406 | ||||||||
\(508\) | −1.71605e17 | −0.443013 | ||||||||
\(509\) | 6.29871e16 | 0.160541 | 0.0802705 | − | 0.996773i | \(-0.474422\pi\) | ||||
0.0802705 | + | 0.996773i | \(0.474422\pi\) | |||||||
\(510\) | −3.52854e17 | −0.887951 | ||||||||
\(511\) | 3.95071e17 | 0.981611 | ||||||||
\(512\) | −5.68658e17 | −1.39507 | ||||||||
\(513\) | −4.94342e16 | −0.119747 | ||||||||
\(514\) | 8.35981e17 | 1.99957 | ||||||||
\(515\) | 7.14595e16 | 0.168777 | ||||||||
\(516\) | −3.55080e16 | −0.0828138 | ||||||||
\(517\) | 4.30615e17 | 0.991746 | ||||||||
\(518\) | 1.01525e18 | 2.30902 | ||||||||
\(519\) | 3.59392e17 | 0.807198 | ||||||||
\(520\) | 4.19428e16 | 0.0930327 | ||||||||
\(521\) | 3.40065e17 | 0.744932 | 0.372466 | − | 0.928046i | \(-0.378512\pi\) | ||||
0.372466 | + | 0.928046i | \(0.378512\pi\) | |||||||
\(522\) | 2.96236e16 | 0.0640883 | ||||||||
\(523\) | −6.59434e16 | −0.140900 | −0.0704499 | − | 0.997515i | \(-0.522443\pi\) | ||||
−0.0704499 | + | 0.997515i | \(0.522443\pi\) | |||||||
\(524\) | 3.98916e17 | 0.841837 | ||||||||
\(525\) | 8.08077e17 | 1.68429 | ||||||||
\(526\) | 7.33753e17 | 1.51058 | ||||||||
\(527\) | −3.00962e16 | −0.0611988 | ||||||||
\(528\) | −2.16571e17 | −0.434990 | ||||||||
\(529\) | 8.95319e17 | 1.77630 | ||||||||
\(530\) | −2.52668e17 | −0.495174 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | −5.47189e17 | −1.04643 | ||||||||
\(533\) | −2.73343e17 | −0.516394 | ||||||||
\(534\) | −3.21806e17 | −0.600587 | ||||||||
\(535\) | −9.36393e17 | −1.72647 | ||||||||
\(536\) | 7.44604e15 | 0.0135629 | ||||||||
\(537\) | 3.07208e17 | 0.552841 | ||||||||
\(538\) | −1.51235e18 | −2.68886 | ||||||||
\(539\) | 8.49648e17 | 1.49249 | ||||||||
\(540\) | 1.74412e17 | 0.302703 | ||||||||
\(541\) | −5.08956e17 | −0.872767 | −0.436383 | − | 0.899761i | \(-0.643741\pi\) | ||||
−0.436383 | + | 0.899761i | \(0.643741\pi\) | |||||||
\(542\) | −6.36723e17 | −1.07884 | ||||||||
\(543\) | 3.08115e17 | 0.515839 | ||||||||
\(544\) | 5.68191e17 | 0.939942 | ||||||||
\(545\) | −1.45410e18 | −2.37694 | ||||||||
\(546\) | −9.51329e17 | −1.53666 | ||||||||
\(547\) | 7.78960e17 | 1.24336 | 0.621681 | − | 0.783271i | \(-0.286450\pi\) | ||||
0.621681 | + | 0.783271i | \(0.286450\pi\) | |||||||
\(548\) | 7.25029e17 | 1.14362 | ||||||||
\(549\) | 2.16242e17 | 0.337070 | ||||||||
\(550\) | −1.10443e18 | −1.70130 | ||||||||
\(551\) | 5.60936e16 | 0.0853942 | ||||||||
\(552\) | −3.34779e16 | −0.0503679 | ||||||||
\(553\) | 6.15298e17 | 0.914897 | ||||||||
\(554\) | 1.61019e18 | 2.36627 | ||||||||
\(555\) | −6.12756e17 | −0.889986 | ||||||||
\(556\) | −6.51097e17 | −0.934673 | ||||||||
\(557\) | −1.22662e18 | −1.74040 | −0.870201 | − | 0.492696i | \(-0.836011\pi\) | ||||
−0.870201 | + | 0.492696i | \(0.836011\pi\) | |||||||
\(558\) | 3.03301e16 | 0.0425355 | ||||||||
\(559\) | −1.16895e17 | −0.162039 | ||||||||
\(560\) | −2.15834e18 | −2.95732 | ||||||||
\(561\) | 2.08294e17 | 0.282110 | ||||||||
\(562\) | −1.54724e18 | −2.07143 | ||||||||
\(563\) | −1.24151e18 | −1.64303 | −0.821515 | − | 0.570187i | \(-0.806871\pi\) | ||||
−0.821515 | + | 0.570187i | \(0.806871\pi\) | |||||||
\(564\) | 5.79324e17 | 0.757892 | ||||||||
\(565\) | 4.01015e16 | 0.0518616 | ||||||||
\(566\) | 8.05237e17 | 1.02948 | ||||||||
\(567\) | 1.53587e17 | 0.194118 | ||||||||
\(568\) | −4.91952e16 | −0.0614694 | ||||||||
\(569\) | −8.02977e17 | −0.991913 | −0.495956 | − | 0.868347i | \(-0.665182\pi\) | ||||
−0.495956 | + | 0.868347i | \(0.665182\pi\) | |||||||
\(570\) | 6.73338e17 | 0.822331 | ||||||||
\(571\) | 1.26137e18 | 1.52303 | 0.761517 | − | 0.648145i | \(-0.224455\pi\) | ||||
0.761517 | + | 0.648145i | \(0.224455\pi\) | |||||||
\(572\) | 6.37728e17 | 0.761309 | ||||||||
\(573\) | 7.64216e17 | 0.902010 | ||||||||
\(574\) | 9.95913e17 | 1.16224 | ||||||||
\(575\) | −2.41126e18 | −2.78230 | ||||||||
\(576\) | −2.69932e17 | −0.307970 | ||||||||
\(577\) | −2.66138e17 | −0.300237 | −0.150118 | − | 0.988668i | \(-0.547965\pi\) | ||||
−0.150118 | + | 0.988668i | \(0.547965\pi\) | |||||||
\(578\) | 6.88956e17 | 0.768529 | ||||||||
\(579\) | −2.02263e17 | −0.223103 | ||||||||
\(580\) | −1.97908e17 | −0.215864 | ||||||||
\(581\) | 2.65083e18 | 2.85916 | ||||||||
\(582\) | −1.09780e18 | −1.17091 | ||||||||
\(583\) | 1.49153e17 | 0.157321 | ||||||||
\(584\) | 2.82031e16 | 0.0294180 | ||||||||
\(585\) | 5.74178e17 | 0.592288 | ||||||||
\(586\) | −6.16047e17 | −0.628462 | ||||||||
\(587\) | −5.96616e15 | −0.00601932 | −0.00300966 | − | 0.999995i | \(-0.500958\pi\) | ||||
−0.00300966 | + | 0.999995i | \(0.500958\pi\) | |||||||
\(588\) | 1.14307e18 | 1.14056 | ||||||||
\(589\) | 5.74315e16 | 0.0566762 | ||||||||
\(590\) | 3.05332e17 | 0.298012 | ||||||||
\(591\) | 7.97435e16 | 0.0769798 | ||||||||
\(592\) | 1.02363e18 | 0.977355 | ||||||||
\(593\) | −2.05384e17 | −0.193959 | −0.0969796 | − | 0.995286i | \(-0.530918\pi\) | ||||
−0.0969796 | + | 0.995286i | \(0.530918\pi\) | |||||||
\(594\) | −2.09913e17 | −0.196077 | ||||||||
\(595\) | 2.07586e18 | 1.91795 | ||||||||
\(596\) | −9.07221e17 | −0.829111 | ||||||||
\(597\) | 7.14212e17 | 0.645645 | ||||||||
\(598\) | 2.83872e18 | 2.53843 | ||||||||
\(599\) | 1.54318e18 | 1.36503 | 0.682514 | − | 0.730873i | \(-0.260887\pi\) | ||||
0.682514 | + | 0.730873i | \(0.260887\pi\) | |||||||
\(600\) | 5.76865e16 | 0.0504767 | ||||||||
\(601\) | −1.24282e18 | −1.07578 | −0.537890 | − | 0.843015i | \(-0.680778\pi\) | ||||
−0.537890 | + | 0.843015i | \(0.680778\pi\) | |||||||
\(602\) | 4.25901e17 | 0.364697 | ||||||||
\(603\) | 1.01933e17 | 0.0863478 | ||||||||
\(604\) | 1.81676e18 | 1.52250 | ||||||||
\(605\) | −9.28447e17 | −0.769745 | ||||||||
\(606\) | 1.45519e18 | 1.19357 | ||||||||
\(607\) | −1.15880e18 | −0.940331 | −0.470166 | − | 0.882578i | \(-0.655806\pi\) | ||||
−0.470166 | + | 0.882578i | \(0.655806\pi\) | |||||||
\(608\) | −1.08426e18 | −0.870480 | ||||||||
\(609\) | −1.74277e17 | −0.138429 | ||||||||
\(610\) | −2.94541e18 | −2.31474 | ||||||||
\(611\) | 1.90718e18 | 1.48294 | ||||||||
\(612\) | 2.80227e17 | 0.215589 | ||||||||
\(613\) | 1.10886e18 | 0.844083 | 0.422042 | − | 0.906576i | \(-0.361314\pi\) | ||||
0.422042 | + | 0.906576i | \(0.361314\pi\) | |||||||
\(614\) | 1.60311e18 | 1.20745 | ||||||||
\(615\) | −6.01086e17 | −0.447970 | ||||||||
\(616\) | 9.02097e16 | 0.0665240 | ||||||||
\(617\) | 2.55361e18 | 1.86338 | 0.931689 | − | 0.363256i | \(-0.118335\pi\) | ||||
0.931689 | + | 0.363256i | \(0.118335\pi\) | |||||||
\(618\) | −1.15706e17 | −0.0835468 | ||||||||
\(619\) | −2.51856e18 | −1.79955 | −0.899775 | − | 0.436355i | \(-0.856269\pi\) | ||||
−0.899775 | + | 0.436355i | \(0.856269\pi\) | |||||||
\(620\) | −2.02628e17 | −0.143269 | ||||||||
\(621\) | −4.58297e17 | −0.320665 | ||||||||
\(622\) | 2.64459e18 | 1.83114 | ||||||||
\(623\) | 1.89320e18 | 1.29725 | ||||||||
\(624\) | −9.59185e17 | −0.650433 | ||||||||
\(625\) | 1.76561e17 | 0.118488 | ||||||||
\(626\) | −2.66756e18 | −1.77166 | ||||||||
\(627\) | −3.97480e17 | −0.261262 | ||||||||
\(628\) | −1.57804e18 | −1.02655 | ||||||||
\(629\) | −9.84512e17 | −0.633858 | ||||||||
\(630\) | −2.09199e18 | −1.33305 | ||||||||
\(631\) | 2.66852e18 | 1.68298 | 0.841490 | − | 0.540272i | \(-0.181679\pi\) | ||||
0.841490 | + | 0.540272i | \(0.181679\pi\) | |||||||
\(632\) | 4.39246e16 | 0.0274187 | ||||||||
\(633\) | 1.74029e17 | 0.107522 | ||||||||
\(634\) | −2.49446e17 | −0.152544 | ||||||||
\(635\) | −1.24231e18 | −0.751970 | ||||||||
\(636\) | 2.00662e17 | 0.120225 | ||||||||
\(637\) | 3.76306e18 | 2.23170 | ||||||||
\(638\) | 2.38191e17 | 0.139827 | ||||||||
\(639\) | −6.73460e17 | −0.391342 | ||||||||
\(640\) | −2.97248e17 | −0.170982 | ||||||||
\(641\) | 3.06517e18 | 1.74533 | 0.872665 | − | 0.488319i | \(-0.162390\pi\) | ||||
0.872665 | + | 0.488319i | \(0.162390\pi\) | |||||||
\(642\) | 1.51619e18 | 0.854624 | ||||||||
\(643\) | −9.10555e17 | −0.508083 | −0.254042 | − | 0.967193i | \(-0.581760\pi\) | ||||
−0.254042 | + | 0.967193i | \(0.581760\pi\) | |||||||
\(644\) | −5.07290e18 | −2.80219 | ||||||||
\(645\) | −2.57054e17 | −0.140568 | ||||||||
\(646\) | 1.08185e18 | 0.585673 | ||||||||
\(647\) | −1.71798e18 | −0.920749 | −0.460375 | − | 0.887725i | \(-0.652285\pi\) | ||||
−0.460375 | + | 0.887725i | \(0.652285\pi\) | |||||||
\(648\) | 1.09642e16 | 0.00581753 | ||||||||
\(649\) | −1.80241e17 | −0.0946813 | ||||||||
\(650\) | −4.89147e18 | −2.54392 | ||||||||
\(651\) | −1.78434e17 | −0.0918756 | ||||||||
\(652\) | −2.29559e18 | −1.17027 | ||||||||
\(653\) | −2.37148e18 | −1.19697 | −0.598487 | − | 0.801133i | \(-0.704231\pi\) | ||||
−0.598487 | + | 0.801133i | \(0.704231\pi\) | |||||||
\(654\) | 2.35446e18 | 1.17662 | ||||||||
\(655\) | 2.88788e18 | 1.42893 | ||||||||
\(656\) | 1.00414e18 | 0.491947 | ||||||||
\(657\) | 3.86088e17 | 0.187288 | ||||||||
\(658\) | −6.94872e18 | −3.33762 | ||||||||
\(659\) | −1.83481e18 | −0.872639 | −0.436320 | − | 0.899792i | \(-0.643718\pi\) | ||||
−0.436320 | + | 0.899792i | \(0.643718\pi\) | |||||||
\(660\) | 1.40238e18 | 0.660433 | ||||||||
\(661\) | −2.23094e18 | −1.04035 | −0.520174 | − | 0.854060i | \(-0.674133\pi\) | ||||
−0.520174 | + | 0.854060i | \(0.674133\pi\) | |||||||
\(662\) | 1.43425e18 | 0.662290 | ||||||||
\(663\) | 9.22529e17 | 0.421834 | ||||||||
\(664\) | 1.89236e17 | 0.0856864 | ||||||||
\(665\) | −3.96129e18 | −1.77621 | ||||||||
\(666\) | 9.92162e17 | 0.440555 | ||||||||
\(667\) | 5.20035e17 | 0.228673 | ||||||||
\(668\) | 1.42384e18 | 0.620034 | ||||||||
\(669\) | 7.55104e17 | 0.325640 | ||||||||
\(670\) | −1.38841e18 | −0.592970 | ||||||||
\(671\) | 1.73871e18 | 0.735413 | ||||||||
\(672\) | 3.36867e18 | 1.41110 | ||||||||
\(673\) | 2.05076e18 | 0.850781 | 0.425390 | − | 0.905010i | \(-0.360137\pi\) | ||||
0.425390 | + | 0.905010i | \(0.360137\pi\) | |||||||
\(674\) | 5.05481e18 | 2.07690 | ||||||||
\(675\) | 7.89702e17 | 0.321358 | ||||||||
\(676\) | 4.36052e17 | 0.175746 | ||||||||
\(677\) | 1.55946e18 | 0.622511 | 0.311255 | − | 0.950326i | \(-0.399251\pi\) | ||||
0.311255 | + | 0.950326i | \(0.399251\pi\) | |||||||
\(678\) | −6.49316e16 | −0.0256722 | ||||||||
\(679\) | 6.45840e18 | 2.52913 | ||||||||
\(680\) | 1.48190e17 | 0.0574794 | ||||||||
\(681\) | 1.95749e18 | 0.752045 | ||||||||
\(682\) | 2.43872e17 | 0.0928031 | ||||||||
\(683\) | 9.55275e17 | 0.360076 | 0.180038 | − | 0.983660i | \(-0.442378\pi\) | ||||
0.180038 | + | 0.983660i | \(0.442378\pi\) | |||||||
\(684\) | −5.34747e17 | −0.199657 | ||||||||
\(685\) | 5.24873e18 | 1.94118 | ||||||||
\(686\) | −7.02968e18 | −2.57531 | ||||||||
\(687\) | −8.73427e17 | −0.316962 | ||||||||
\(688\) | 4.29418e17 | 0.154367 | ||||||||
\(689\) | 6.60595e17 | 0.235240 | ||||||||
\(690\) | 6.24240e18 | 2.20208 | ||||||||
\(691\) | −3.41134e18 | −1.19212 | −0.596058 | − | 0.802942i | \(-0.703267\pi\) | ||||
−0.596058 | + | 0.802942i | \(0.703267\pi\) | |||||||
\(692\) | 3.88766e18 | 1.34586 | ||||||||
\(693\) | 1.23493e18 | 0.423522 | ||||||||
\(694\) | 3.30653e18 | 1.12340 | ||||||||
\(695\) | −4.71351e18 | −1.58651 | ||||||||
\(696\) | −1.24412e16 | −0.00414860 | ||||||||
\(697\) | −9.65763e17 | −0.319049 | ||||||||
\(698\) | 7.04198e18 | 2.30481 | ||||||||
\(699\) | −2.89980e18 | −0.940299 | ||||||||
\(700\) | 8.74124e18 | 2.80825 | ||||||||
\(701\) | −9.69972e17 | −0.308740 | −0.154370 | − | 0.988013i | \(-0.549335\pi\) | ||||
−0.154370 | + | 0.988013i | \(0.549335\pi\) | |||||||
\(702\) | −9.29697e17 | −0.293191 | ||||||||
\(703\) | 1.87871e18 | 0.587015 | ||||||||
\(704\) | −2.17041e18 | −0.671922 | ||||||||
\(705\) | 4.19392e18 | 1.28644 | ||||||||
\(706\) | −4.78312e18 | −1.45372 | ||||||||
\(707\) | −8.56095e18 | −2.57808 | ||||||||
\(708\) | −2.42486e17 | −0.0723554 | ||||||||
\(709\) | −1.85546e18 | −0.548595 | −0.274297 | − | 0.961645i | \(-0.588445\pi\) | ||||
−0.274297 | + | 0.961645i | \(0.588445\pi\) | |||||||
\(710\) | 9.17312e18 | 2.68743 | ||||||||
\(711\) | 6.01307e17 | 0.174560 | ||||||||
\(712\) | 1.35151e17 | 0.0388775 | ||||||||
\(713\) | 5.32438e17 | 0.151770 | ||||||||
\(714\) | −3.36119e18 | −0.949412 | ||||||||
\(715\) | 4.61672e18 | 1.29224 | ||||||||
\(716\) | 3.32317e18 | 0.921761 | ||||||||
\(717\) | 3.61774e18 | 0.994404 | ||||||||
\(718\) | −4.83490e18 | −1.31698 | ||||||||
\(719\) | −5.00313e17 | −0.135053 | −0.0675264 | − | 0.997717i | \(-0.521511\pi\) | ||||
−0.0675264 | + | 0.997717i | \(0.521511\pi\) | |||||||
\(720\) | −2.10927e18 | −0.564248 | ||||||||
\(721\) | 6.80703e17 | 0.180459 | ||||||||
\(722\) | 3.26780e18 | 0.858547 | ||||||||
\(723\) | 9.98891e17 | 0.260087 | ||||||||
\(724\) | 3.33298e18 | 0.860067 | ||||||||
\(725\) | −8.96085e17 | −0.229167 | ||||||||
\(726\) | 1.50332e18 | 0.381034 | ||||||||
\(727\) | 3.88274e18 | 0.975359 | 0.487679 | − | 0.873023i | \(-0.337843\pi\) | ||||
0.487679 | + | 0.873023i | \(0.337843\pi\) | |||||||
\(728\) | 3.99536e17 | 0.0994722 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −5.25885e18 | −1.28615 | ||||||||
\(731\) | −4.13008e17 | −0.100114 | ||||||||
\(732\) | 2.33916e18 | 0.562003 | ||||||||
\(733\) | 2.86795e18 | 0.682961 | 0.341480 | − | 0.939889i | \(-0.389072\pi\) | ||||
0.341480 | + | 0.939889i | \(0.389072\pi\) | |||||||
\(734\) | −1.35756e18 | −0.320430 | ||||||||
\(735\) | 8.27504e18 | 1.93599 | ||||||||
\(736\) | −1.00520e19 | −2.33101 | ||||||||
\(737\) | 8.19599e17 | 0.188392 | ||||||||
\(738\) | 9.73267e17 | 0.221751 | ||||||||
\(739\) | 7.23182e18 | 1.63327 | 0.816636 | − | 0.577152i | \(-0.195836\pi\) | ||||
0.816636 | + | 0.577152i | \(0.195836\pi\) | |||||||
\(740\) | −6.62839e18 | −1.48389 | ||||||||
\(741\) | −1.76043e18 | −0.390660 | ||||||||
\(742\) | −2.40685e18 | −0.529448 | ||||||||
\(743\) | 2.64189e18 | 0.576087 | 0.288044 | − | 0.957617i | \(-0.406995\pi\) | ||||
0.288044 | + | 0.957617i | \(0.406995\pi\) | |||||||
\(744\) | −1.27379e16 | −0.00275343 | ||||||||
\(745\) | −6.56768e18 | −1.40733 | ||||||||
\(746\) | 1.22046e19 | 2.59252 | ||||||||
\(747\) | 2.59056e18 | 0.545518 | ||||||||
\(748\) | 2.25319e18 | 0.470368 | ||||||||
\(749\) | −8.91982e18 | −1.84597 | ||||||||
\(750\) | −4.31478e18 | −0.885238 | ||||||||
\(751\) | −7.29114e18 | −1.48298 | −0.741490 | − | 0.670963i | \(-0.765881\pi\) | ||||
−0.741490 | + | 0.670963i | \(0.765881\pi\) | |||||||
\(752\) | −7.00610e18 | −1.41273 | ||||||||
\(753\) | −1.64184e18 | −0.328218 | ||||||||
\(754\) | 1.05494e18 | 0.209080 | ||||||||
\(755\) | 1.31521e19 | 2.58429 | ||||||||
\(756\) | 1.66140e18 | 0.323656 | ||||||||
\(757\) | 4.76634e18 | 0.920580 | 0.460290 | − | 0.887769i | \(-0.347745\pi\) | ||||
0.460290 | + | 0.887769i | \(0.347745\pi\) | |||||||
\(758\) | 8.82614e18 | 1.69013 | ||||||||
\(759\) | −3.68497e18 | −0.699621 | ||||||||
\(760\) | −2.82786e17 | −0.0532316 | ||||||||
\(761\) | −7.10313e18 | −1.32571 | −0.662857 | − | 0.748746i | \(-0.730656\pi\) | ||||
−0.662857 | + | 0.748746i | \(0.730656\pi\) | |||||||
\(762\) | 2.01152e18 | 0.372235 | ||||||||
\(763\) | −1.38514e19 | −2.54147 | ||||||||
\(764\) | 8.26678e18 | 1.50394 | ||||||||
\(765\) | 2.02866e18 | 0.365940 | ||||||||
\(766\) | −2.20440e17 | −0.0394279 | ||||||||
\(767\) | −7.98283e17 | −0.141575 | ||||||||
\(768\) | 3.51460e18 | 0.618057 | ||||||||
\(769\) | −1.21414e18 | −0.211714 | −0.105857 | − | 0.994381i | \(-0.533759\pi\) | ||||
−0.105857 | + | 0.994381i | \(0.533759\pi\) | |||||||
\(770\) | −1.68208e19 | −2.90842 | ||||||||
\(771\) | −4.80629e18 | −0.824056 | ||||||||
\(772\) | −2.18794e18 | −0.371983 | ||||||||
\(773\) | 5.39991e18 | 0.910373 | 0.455187 | − | 0.890396i | \(-0.349573\pi\) | ||||
0.455187 | + | 0.890396i | \(0.349573\pi\) | |||||||
\(774\) | 4.16217e17 | 0.0695830 | ||||||||
\(775\) | −9.17457e17 | −0.152098 | ||||||||
\(776\) | 4.61048e17 | 0.0757958 | ||||||||
\(777\) | −5.83695e18 | −0.951588 | ||||||||
\(778\) | 1.05410e19 | 1.70418 | ||||||||
\(779\) | 1.84293e18 | 0.295471 | ||||||||
\(780\) | 6.21107e18 | 0.987533 | ||||||||
\(781\) | −5.41501e18 | −0.853822 | ||||||||
\(782\) | 1.00296e19 | 1.56834 | ||||||||
\(783\) | −1.70314e17 | −0.0264119 | ||||||||
\(784\) | −1.38238e19 | −2.12604 | ||||||||
\(785\) | −1.14240e19 | −1.74247 | ||||||||
\(786\) | −4.67600e18 | −0.707340 | ||||||||
\(787\) | −2.01405e18 | −0.302159 | −0.151079 | − | 0.988522i | \(-0.548275\pi\) | ||||
−0.151079 | + | 0.988522i | \(0.548275\pi\) | |||||||
\(788\) | 8.62612e17 | 0.128350 | ||||||||
\(789\) | −4.21856e18 | −0.622534 | ||||||||
\(790\) | −8.19033e18 | −1.19874 | ||||||||
\(791\) | 3.81996e17 | 0.0554513 | ||||||||
\(792\) | 8.81584e16 | 0.0126926 | ||||||||
\(793\) | 7.70070e18 | 1.09965 | ||||||||
\(794\) | 1.21466e19 | 1.72037 | ||||||||
\(795\) | 1.45266e18 | 0.204070 | ||||||||
\(796\) | 7.72587e18 | 1.07650 | ||||||||
\(797\) | 5.61457e17 | 0.0775956 | 0.0387978 | − | 0.999247i | \(-0.487647\pi\) | ||||
0.0387978 | + | 0.999247i | \(0.487647\pi\) | |||||||
\(798\) | 6.41403e18 | 0.879250 | ||||||||
\(799\) | 6.73835e18 | 0.916220 | ||||||||
\(800\) | 1.73208e19 | 2.33605 | ||||||||
\(801\) | 1.85015e18 | 0.247512 | ||||||||
\(802\) | −1.27270e19 | −1.68886 | ||||||||
\(803\) | 3.10437e18 | 0.408623 | ||||||||
\(804\) | 1.10264e18 | 0.143969 | ||||||||
\(805\) | −3.67244e19 | −4.75644 | ||||||||
\(806\) | 1.08010e18 | 0.138767 | ||||||||
\(807\) | 8.69494e18 | 1.10812 | ||||||||
\(808\) | −6.11144e17 | −0.0772627 | ||||||||
\(809\) | −8.15503e18 | −1.02273 | −0.511364 | − | 0.859364i | \(-0.670860\pi\) | ||||
−0.511364 | + | 0.859364i | \(0.670860\pi\) | |||||||
\(810\) | −2.04442e18 | −0.254342 | ||||||||
\(811\) | −1.12812e19 | −1.39226 | −0.696130 | − | 0.717916i | \(-0.745096\pi\) | ||||
−0.696130 | + | 0.717916i | \(0.745096\pi\) | |||||||
\(812\) | −1.88521e18 | −0.230806 | ||||||||
\(813\) | 3.66070e18 | 0.444606 | ||||||||
\(814\) | 7.97756e18 | 0.961195 | ||||||||
\(815\) | −1.66186e19 | −1.98641 | ||||||||
\(816\) | −3.38895e18 | −0.401864 | ||||||||
\(817\) | 7.88126e17 | 0.0927155 | ||||||||
\(818\) | 1.34184e19 | 1.56605 | ||||||||
\(819\) | 5.46946e18 | 0.633285 | ||||||||
\(820\) | −6.50215e18 | −0.746908 | ||||||||
\(821\) | 1.25463e18 | 0.142983 | 0.0714916 | − | 0.997441i | \(-0.477224\pi\) | ||||
0.0714916 | + | 0.997441i | \(0.477224\pi\) | |||||||
\(822\) | −8.49863e18 | −0.960909 | ||||||||
\(823\) | −1.27294e19 | −1.42794 | −0.713971 | − | 0.700175i | \(-0.753105\pi\) | ||||
−0.713971 | + | 0.700175i | \(0.753105\pi\) | |||||||
\(824\) | 4.85937e16 | 0.00540820 | ||||||||
\(825\) | 6.34967e18 | 0.701133 | ||||||||
\(826\) | 2.90851e18 | 0.318640 | ||||||||
\(827\) | 5.71850e18 | 0.621579 | 0.310790 | − | 0.950479i | \(-0.399407\pi\) | ||||
0.310790 | + | 0.950479i | \(0.399407\pi\) | |||||||
\(828\) | −4.95755e18 | −0.534650 | ||||||||
\(829\) | 3.94703e18 | 0.422344 | 0.211172 | − | 0.977449i | \(-0.432272\pi\) | ||||
0.211172 | + | 0.977449i | \(0.432272\pi\) | |||||||
\(830\) | −3.52857e19 | −3.74620 | ||||||||
\(831\) | −9.25745e18 | −0.975179 | ||||||||
\(832\) | −9.61267e18 | −1.00471 | ||||||||
\(833\) | 1.32955e19 | 1.37883 | ||||||||
\(834\) | 7.63202e18 | 0.785344 | ||||||||
\(835\) | 1.03077e19 | 1.05244 | ||||||||
\(836\) | −4.29968e18 | −0.435607 | ||||||||
\(837\) | −1.74376e17 | −0.0175296 | ||||||||
\(838\) | −2.61538e19 | −2.60885 | ||||||||
\(839\) | −1.24102e19 | −1.22836 | −0.614180 | − | 0.789166i | \(-0.710513\pi\) | ||||
−0.614180 | + | 0.789166i | \(0.710513\pi\) | |||||||
\(840\) | 8.78587e17 | 0.0862917 | ||||||||
\(841\) | −1.00674e19 | −0.981165 | ||||||||
\(842\) | −2.34717e19 | −2.26995 | ||||||||
\(843\) | 8.89550e18 | 0.853673 | ||||||||
\(844\) | 1.88253e18 | 0.179273 | ||||||||
\(845\) | 3.15672e18 | 0.298310 | ||||||||
\(846\) | −6.79071e18 | −0.636807 | ||||||||
\(847\) | −8.84413e18 | −0.823025 | ||||||||
\(848\) | −2.42672e18 | −0.224103 | ||||||||
\(849\) | −4.62953e18 | −0.424265 | ||||||||
\(850\) | −1.72823e19 | −1.57173 | ||||||||
\(851\) | 1.74172e19 | 1.57194 | ||||||||
\(852\) | −7.28504e18 | −0.652491 | ||||||||
\(853\) | −1.51135e19 | −1.34337 | −0.671685 | − | 0.740837i | \(-0.734429\pi\) | ||||
−0.671685 | + | 0.740837i | \(0.734429\pi\) | |||||||
\(854\) | −2.80571e19 | −2.47495 | ||||||||
\(855\) | −3.87121e18 | −0.338896 | ||||||||
\(856\) | −6.36763e17 | −0.0553221 | ||||||||
\(857\) | −7.32167e18 | −0.631299 | −0.315649 | − | 0.948876i | \(-0.602222\pi\) | ||||
−0.315649 | + | 0.948876i | \(0.602222\pi\) | |||||||
\(858\) | −7.47530e18 | −0.639678 | ||||||||
\(859\) | 1.59872e19 | 1.35774 | 0.678870 | − | 0.734258i | \(-0.262470\pi\) | ||||
0.678870 | + | 0.734258i | \(0.262470\pi\) | |||||||
\(860\) | −2.78064e18 | −0.234372 | ||||||||
\(861\) | −5.72579e18 | −0.478977 | ||||||||
\(862\) | −1.14461e19 | −0.950297 | ||||||||
\(863\) | 8.34284e18 | 0.687454 | 0.343727 | − | 0.939070i | \(-0.388310\pi\) | ||||
0.343727 | + | 0.939070i | \(0.388310\pi\) | |||||||
\(864\) | 3.29207e18 | 0.269234 | ||||||||
\(865\) | 2.81441e19 | 2.28445 | ||||||||
\(866\) | −6.78945e18 | −0.546976 | ||||||||
\(867\) | −3.96100e18 | −0.316724 | ||||||||
\(868\) | −1.93018e18 | −0.153186 | ||||||||
\(869\) | 4.83486e18 | 0.380851 | ||||||||
\(870\) | 2.31983e18 | 0.181376 | ||||||||
\(871\) | 3.62998e18 | 0.281699 | ||||||||
\(872\) | −9.88816e17 | −0.0761655 | ||||||||
\(873\) | 6.31154e18 | 0.482551 | ||||||||
\(874\) | −1.91392e19 | −1.45244 | ||||||||
\(875\) | 2.53841e19 | 1.91209 | ||||||||
\(876\) | 4.17644e18 | 0.312269 | ||||||||
\(877\) | 1.23699e19 | 0.918057 | 0.459029 | − | 0.888421i | \(-0.348197\pi\) | ||||
0.459029 | + | 0.888421i | \(0.348197\pi\) | |||||||
\(878\) | −7.36514e18 | −0.542584 | ||||||||
\(879\) | 3.54183e18 | 0.259000 | ||||||||
\(880\) | −1.69597e19 | −1.23107 | ||||||||
\(881\) | 8.10626e17 | 0.0584086 | 0.0292043 | − | 0.999573i | \(-0.490703\pi\) | ||||
0.0292043 | + | 0.999573i | \(0.490703\pi\) | |||||||
\(882\) | −1.33988e19 | −0.958340 | ||||||||
\(883\) | 1.06000e19 | 0.752593 | 0.376296 | − | 0.926499i | \(-0.377197\pi\) | ||||
0.376296 | + | 0.926499i | \(0.377197\pi\) | |||||||
\(884\) | 9.97930e18 | 0.703332 | ||||||||
\(885\) | −1.75544e18 | −0.122816 | ||||||||
\(886\) | 6.12896e18 | 0.425665 | ||||||||
\(887\) | 2.00306e19 | 1.38099 | 0.690494 | − | 0.723338i | \(-0.257393\pi\) | ||||
0.690494 | + | 0.723338i | \(0.257393\pi\) | |||||||
\(888\) | −4.16684e17 | −0.0285183 | ||||||||
\(889\) | −1.18339e19 | −0.804019 | ||||||||
\(890\) | −2.52007e19 | −1.69972 | ||||||||
\(891\) | 1.20685e18 | 0.0808067 | ||||||||
\(892\) | 8.16822e18 | 0.542945 | ||||||||
\(893\) | −1.28585e19 | −0.848511 | ||||||||
\(894\) | 1.06342e19 | 0.696647 | ||||||||
\(895\) | 2.40576e19 | 1.56460 | ||||||||
\(896\) | −2.83150e18 | −0.182816 | ||||||||
\(897\) | −1.63206e19 | −1.04613 | ||||||||
\(898\) | 1.58830e19 | 1.01073 | ||||||||
\(899\) | 1.97867e17 | 0.0125007 | ||||||||
\(900\) | 8.54247e18 | 0.535806 | ||||||||
\(901\) | 2.33398e18 | 0.145341 | ||||||||
\(902\) | 7.82563e18 | 0.483812 | ||||||||
\(903\) | −2.44863e18 | −0.150298 | ||||||||
\(904\) | 2.72697e16 | 0.00166183 | ||||||||
\(905\) | 2.41286e19 | 1.45988 | ||||||||
\(906\) | −2.12956e19 | −1.27926 | ||||||||
\(907\) | −1.31339e19 | −0.783332 | −0.391666 | − | 0.920107i | \(-0.628101\pi\) | ||||
−0.391666 | + | 0.920107i | \(0.628101\pi\) | |||||||
\(908\) | 2.11749e19 | 1.25390 | ||||||||
\(909\) | −8.36629e18 | −0.491889 | ||||||||
\(910\) | −7.44989e19 | −4.34891 | ||||||||
\(911\) | −1.45501e19 | −0.843326 | −0.421663 | − | 0.906753i | \(-0.638554\pi\) | ||||
−0.421663 | + | 0.906753i | \(0.638554\pi\) | |||||||
\(912\) | 6.46700e18 | 0.372166 | ||||||||
\(913\) | 2.08296e19 | 1.19020 | ||||||||
\(914\) | 1.30585e19 | 0.740871 | ||||||||
\(915\) | 1.69340e19 | 0.953942 | ||||||||
\(916\) | −9.44815e18 | −0.528477 | ||||||||
\(917\) | 2.75092e19 | 1.52784 | ||||||||
\(918\) | −3.28476e18 | −0.181145 | ||||||||
\(919\) | 5.02915e18 | 0.275387 | 0.137693 | − | 0.990475i | \(-0.456031\pi\) | ||||
0.137693 | + | 0.990475i | \(0.456031\pi\) | |||||||
\(920\) | −2.62166e18 | −0.142546 | ||||||||
\(921\) | −9.21675e18 | −0.497611 | ||||||||
\(922\) | −2.10412e19 | −1.12803 | ||||||||
\(923\) | −2.39829e19 | −1.27671 | ||||||||
\(924\) | 1.33586e19 | 0.706146 | ||||||||
\(925\) | −3.00120e19 | −1.57534 | ||||||||
\(926\) | 1.04332e19 | 0.543807 | ||||||||
\(927\) | 6.65225e17 | 0.0344310 | ||||||||
\(928\) | −3.73555e18 | −0.191996 | ||||||||
\(929\) | 2.60627e19 | 1.33020 | 0.665099 | − | 0.746755i | \(-0.268389\pi\) | ||||
0.665099 | + | 0.746755i | \(0.268389\pi\) | |||||||
\(930\) | 2.37516e18 | 0.120380 | ||||||||
\(931\) | −2.53712e19 | −1.27694 | ||||||||
\(932\) | −3.13681e19 | −1.56778 | ||||||||
\(933\) | −1.52045e19 | −0.754644 | ||||||||
\(934\) | 3.26262e19 | 1.60810 | ||||||||
\(935\) | 1.63116e19 | 0.798400 | ||||||||
\(936\) | 3.90451e17 | 0.0189790 | ||||||||
\(937\) | 5.36747e18 | 0.259097 | 0.129548 | − | 0.991573i | \(-0.458647\pi\) | ||||
0.129548 | + | 0.991573i | \(0.458647\pi\) | |||||||
\(938\) | −1.32257e19 | −0.634014 | ||||||||
\(939\) | 1.53366e19 | 0.730133 | ||||||||
\(940\) | 4.53671e19 | 2.14491 | ||||||||
\(941\) | −1.16226e19 | −0.545721 | −0.272860 | − | 0.962054i | \(-0.587970\pi\) | ||||
−0.272860 | + | 0.962054i | \(0.587970\pi\) | |||||||
\(942\) | 1.84975e19 | 0.862545 | ||||||||
\(943\) | 1.70855e19 | 0.791227 | ||||||||
\(944\) | 2.93253e18 | 0.134873 | ||||||||
\(945\) | 1.20274e19 | 0.549372 | ||||||||
\(946\) | 3.34662e18 | 0.151815 | ||||||||
\(947\) | −1.69017e19 | −0.761476 | −0.380738 | − | 0.924683i | \(-0.624330\pi\) | ||||
−0.380738 | + | 0.924683i | \(0.624330\pi\) | |||||||
\(948\) | 6.50454e18 | 0.291046 | ||||||||
\(949\) | 1.37491e19 | 0.611006 | ||||||||
\(950\) | 3.29792e19 | 1.45558 | ||||||||
\(951\) | 1.43414e18 | 0.0628661 | ||||||||
\(952\) | 1.41162e18 | 0.0614579 | ||||||||
\(953\) | 1.64360e19 | 0.710711 | 0.355356 | − | 0.934731i | \(-0.384360\pi\) | ||||
0.355356 | + | 0.934731i | \(0.384360\pi\) | |||||||
\(954\) | −2.35212e18 | −0.101017 | ||||||||
\(955\) | 5.98460e19 | 2.55278 | ||||||||
\(956\) | 3.91343e19 | 1.65799 | ||||||||
\(957\) | −1.36943e18 | −0.0576250 | ||||||||
\(958\) | 4.55792e19 | 1.90498 | ||||||||
\(959\) | 4.99979e19 | 2.07554 | ||||||||
\(960\) | −2.11384e19 | −0.871585 | ||||||||
\(961\) | −2.42150e19 | −0.991703 | ||||||||
\(962\) | 3.53323e19 | 1.43726 | ||||||||
\(963\) | −8.71699e18 | −0.352205 | ||||||||
\(964\) | 1.08053e19 | 0.433648 | ||||||||
\(965\) | −1.58392e19 | −0.631404 | ||||||||
\(966\) | 5.94634e19 | 2.35450 | ||||||||
\(967\) | −4.36155e19 | −1.71541 | −0.857707 | − | 0.514139i | \(-0.828111\pi\) | ||||
−0.857707 | + | 0.514139i | \(0.828111\pi\) | |||||||
\(968\) | −6.31360e17 | −0.0246653 | ||||||||
\(969\) | −6.21985e18 | −0.241366 | ||||||||
\(970\) | −8.59687e19 | −3.31378 | ||||||||
\(971\) | −4.79427e19 | −1.83568 | −0.917842 | − | 0.396947i | \(-0.870070\pi\) | ||||
−0.917842 | + | 0.396947i | \(0.870070\pi\) | |||||||
\(972\) | 1.62362e18 | 0.0617525 | ||||||||
\(973\) | −4.48996e19 | −1.69632 | ||||||||
\(974\) | 2.73058e19 | 1.02476 | ||||||||
\(975\) | 2.81225e19 | 1.04839 | ||||||||
\(976\) | −2.82888e19 | −1.04759 | ||||||||
\(977\) | −3.37789e18 | −0.124260 | −0.0621300 | − | 0.998068i | \(-0.519789\pi\) | ||||
−0.0621300 | + | 0.998068i | \(0.519789\pi\) | |||||||
\(978\) | 2.69085e19 | 0.983300 | ||||||||
\(979\) | 1.48763e19 | 0.540017 | ||||||||
\(980\) | 8.95139e19 | 3.22791 | ||||||||
\(981\) | −1.35364e19 | −0.484904 | ||||||||
\(982\) | −3.90917e19 | −1.39110 | ||||||||
\(983\) | −3.79740e19 | −1.34242 | −0.671210 | − | 0.741267i | \(-0.734225\pi\) | ||||
−0.671210 | + | 0.741267i | \(0.734225\pi\) | |||||||
\(984\) | −4.08749e17 | −0.0143545 | ||||||||
\(985\) | 6.24473e18 | 0.217860 | ||||||||
\(986\) | 3.72726e18 | 0.129178 | ||||||||
\(987\) | 3.99502e19 | 1.37549 | ||||||||
\(988\) | −1.90431e19 | −0.651355 | ||||||||
\(989\) | 7.30659e18 | 0.248278 | ||||||||
\(990\) | −1.64383e19 | −0.554918 | ||||||||
\(991\) | 1.37136e19 | 0.459911 | 0.229956 | − | 0.973201i | \(-0.426142\pi\) | ||||
0.229956 | + | 0.973201i | \(0.426142\pi\) | |||||||
\(992\) | −3.82465e18 | −0.127428 | ||||||||
\(993\) | −8.24592e18 | −0.272941 | ||||||||
\(994\) | 8.73806e19 | 2.87345 | ||||||||
\(995\) | 5.59301e19 | 1.82724 | ||||||||
\(996\) | 2.80229e19 | 0.909552 | ||||||||
\(997\) | 2.06934e19 | 0.667288 | 0.333644 | − | 0.942699i | \(-0.391722\pi\) | ||||
0.333644 | + | 0.942699i | \(0.391722\pi\) | |||||||
\(998\) | 5.87890e19 | 1.88342 | ||||||||
\(999\) | −5.70422e18 | −0.181560 |
(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 | 177.14.a.c.1.4 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.c.1.4 | ✓ | 31 | 1.1 | even | 1 | trivial |