Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(7,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
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("75.7");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.f (of order \(4\), degree \(2\), 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: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.151613669376.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 7x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Root | \(1.88713 - 0.662382i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.43 |
Dual form | 75.9.f.c.7.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −12.8476 | + | 12.8476i | −0.802973 | + | 0.802973i | −0.983559 | − | 0.180586i | \(-0.942201\pi\) |
0.180586 | + | 0.983559i | \(0.442201\pi\) | |||||||
\(3\) | 33.0681 | + | 33.0681i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 74.1200i | − | 0.289531i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −849.690 | −0.655625 | ||||||||
\(7\) | −333.082 | + | 333.082i | −0.138726 | + | 0.138726i | −0.773060 | − | 0.634333i | \(-0.781275\pi\) |
0.634333 | + | 0.773060i | \(0.281275\pi\) | |||||||
\(8\) | −2336.72 | − | 2336.72i | −0.570487 | − | 0.570487i | ||||
\(9\) | 2187.00i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9147.48 | 0.624785 | 0.312393 | − | 0.949953i | \(-0.398870\pi\) | ||||
0.312393 | + | 0.949953i | \(0.398870\pi\) | |||||||
\(12\) | 2451.01 | − | 2451.01i | 0.118201 | − | 0.118201i | ||||
\(13\) | −12379.8 | − | 12379.8i | −0.433452 | − | 0.433452i | 0.456349 | − | 0.889801i | \(-0.349157\pi\) |
−0.889801 | + | 0.456349i | \(0.849157\pi\) | |||||||
\(14\) | − | 8558.59i | − | 0.222787i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 79017.0 | 1.20570 | ||||||||
\(17\) | −7869.96 | + | 7869.96i | −0.0942274 | + | 0.0942274i | −0.752649 | − | 0.658422i | \(-0.771224\pi\) |
0.658422 | + | 0.752649i | \(0.271224\pi\) | |||||||
\(18\) | −28097.6 | − | 28097.6i | −0.267658 | − | 0.267658i | ||||
\(19\) | − | 178951.i | − | 1.37316i | −0.727056 | − | 0.686578i | \(-0.759112\pi\) | ||
0.727056 | − | 0.686578i | \(-0.240888\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −22028.8 | −0.113270 | ||||||||
\(22\) | −117523. | + | 117523.i | −0.501686 | + | 0.501686i | ||||
\(23\) | −225841. | − | 225841.i | −0.807035 | − | 0.807035i | 0.177149 | − | 0.984184i | \(-0.443312\pi\) |
−0.984184 | + | 0.177149i | \(0.943312\pi\) | |||||||
\(24\) | − | 154542.i | − | 0.465801i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 318101. | 0.696100 | ||||||||
\(27\) | −72320.0 | + | 72320.0i | −0.136083 | + | 0.136083i | ||||
\(28\) | 24688.1 | + | 24688.1i | 0.0401657 | + | 0.0401657i | ||||
\(29\) | − | 1.02501e6i | − | 1.44923i | −0.689156 | − | 0.724613i | \(-0.742019\pi\) | ||
0.689156 | − | 0.724613i | \(-0.257981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 392156. | 0.424631 | 0.212316 | − | 0.977201i | \(-0.431900\pi\) | ||||
0.212316 | + | 0.977201i | \(0.431900\pi\) | |||||||
\(32\) | −416977. | + | 416977.i | −0.397660 | + | 0.397660i | ||||
\(33\) | 302490. | + | 302490.i | 0.255068 | + | 0.255068i | ||||
\(34\) | − | 202220.i | − | 0.151324i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 162101. | 0.0965105 | ||||||||
\(37\) | −1.29445e6 | + | 1.29445e6i | −0.690684 | + | 0.690684i | −0.962382 | − | 0.271699i | \(-0.912415\pi\) |
0.271699 | + | 0.962382i | \(0.412415\pi\) | |||||||
\(38\) | 2.29909e6 | + | 2.29909e6i | 1.10261 | + | 1.10261i | ||||
\(39\) | − | 818754.i | − | 0.353912i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.20316e6 | 1.13356 | 0.566778 | − | 0.823871i | \(-0.308190\pi\) | ||||
0.566778 | + | 0.823871i | \(0.308190\pi\) | |||||||
\(42\) | 283016. | − | 283016.i | 0.0909525 | − | 0.0909525i | ||||
\(43\) | 2.40065e6 | + | 2.40065e6i | 0.702190 | + | 0.702190i | 0.964880 | − | 0.262690i | \(-0.0846097\pi\) |
−0.262690 | + | 0.964880i | \(0.584610\pi\) | |||||||
\(44\) | − | 678012.i | − | 0.180895i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.80303e6 | 1.29605 | ||||||||
\(47\) | 4.45079e6 | − | 4.45079e6i | 0.912106 | − | 0.912106i | −0.0843316 | − | 0.996438i | \(-0.526876\pi\) |
0.996438 | + | 0.0843316i | \(0.0268755\pi\) | |||||||
\(48\) | 2.61294e6 | + | 2.61294e6i | 0.492226 | + | 0.492226i | ||||
\(49\) | 5.54291e6i | 0.961510i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −520490. | −0.0769363 | ||||||||
\(52\) | −917592. | + | 917592.i | −0.125498 | + | 0.125498i | ||||
\(53\) | 4.09845e6 | + | 4.09845e6i | 0.519417 | + | 0.519417i | 0.917395 | − | 0.397978i | \(-0.130288\pi\) |
−0.397978 | + | 0.917395i | \(0.630288\pi\) | |||||||
\(54\) | − | 1.85827e6i | − | 0.218542i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.55664e6 | 0.158283 | ||||||||
\(57\) | 5.91757e6 | − | 5.91757e6i | 0.560588 | − | 0.560588i | ||||
\(58\) | 1.31689e7 | + | 1.31689e7i | 1.16369 | + | 1.16369i | ||||
\(59\) | − | 1.34059e7i | − | 1.10634i | −0.833068 | − | 0.553171i | \(-0.813418\pi\) | ||
0.833068 | − | 0.553171i | \(-0.186582\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.38886e7 | 1.72532 | 0.862662 | − | 0.505781i | \(-0.168796\pi\) | ||||
0.862662 | + | 0.505781i | \(0.168796\pi\) | |||||||
\(62\) | −5.03825e6 | + | 5.03825e6i | −0.340967 | + | 0.340967i | ||||
\(63\) | −728451. | − | 728451.i | −0.0462421 | − | 0.0462421i | ||||
\(64\) | 9.51407e6i | 0.567083i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.77252e6 | −0.409625 | ||||||||
\(67\) | −1.67129e7 | + | 1.67129e7i | −0.829376 | + | 0.829376i | −0.987430 | − | 0.158054i | \(-0.949478\pi\) |
0.158054 | + | 0.987430i | \(0.449478\pi\) | |||||||
\(68\) | 583322. | + | 583322.i | 0.0272818 | + | 0.0272818i | ||||
\(69\) | − | 1.49363e7i | − | 0.658941i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 263343. | 0.0103631 | 0.00518153 | − | 0.999987i | \(-0.498351\pi\) | ||||
0.00518153 | + | 0.999987i | \(0.498351\pi\) | |||||||
\(72\) | 5.11040e6 | − | 5.11040e6i | 0.190162 | − | 0.190162i | ||||
\(73\) | −3.04968e7 | − | 3.04968e7i | −1.07390 | − | 1.07390i | −0.997042 | − | 0.0768553i | \(-0.975512\pi\) |
−0.0768553 | − | 0.997042i | \(-0.524488\pi\) | |||||||
\(74\) | − | 3.32611e7i | − | 1.10920i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.32639e7 | −0.397572 | ||||||||
\(77\) | −3.04686e6 | + | 3.04686e6i | −0.0866742 | + | 0.0866742i | ||||
\(78\) | 1.05190e7 | + | 1.05190e7i | 0.284182 | + | 0.284182i | ||||
\(79\) | 3.35015e7i | 0.860114i | 0.902802 | + | 0.430057i | \(0.141507\pi\) | ||||
−0.902802 | + | 0.430057i | \(0.858493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.78297e6 | −0.111111 | ||||||||
\(82\) | −4.11528e7 | + | 4.11528e7i | −0.910214 | + | 0.910214i | ||||
\(83\) | −4.97990e7 | − | 4.97990e7i | −1.04932 | − | 1.04932i | −0.998719 | − | 0.0506010i | \(-0.983886\pi\) |
−0.0506010 | − | 0.998719i | \(-0.516114\pi\) | |||||||
\(84\) | 1.63278e6i | 0.0327951i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.16850e7 | −1.12768 | ||||||||
\(87\) | 3.38951e7 | − | 3.38951e7i | 0.591644 | − | 0.591644i | ||||
\(88\) | −2.13751e7 | − | 2.13751e7i | −0.356432 | − | 0.356432i | ||||
\(89\) | − | 6.58761e7i | − | 1.04995i | −0.851118 | − | 0.524974i | \(-0.824075\pi\) | ||
0.851118 | − | 0.524974i | \(-0.175925\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.24699e6 | 0.120262 | ||||||||
\(92\) | −1.67394e7 | + | 1.67394e7i | −0.233662 | + | 0.233662i | ||||
\(93\) | 1.29678e7 | + | 1.29678e7i | 0.173355 | + | 0.173355i | ||||
\(94\) | 1.14364e8i | 1.46479i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.75773e7 | −0.324688 | ||||||||
\(97\) | 8.26311e7 | − | 8.26311e7i | 0.933376 | − | 0.933376i | −0.0645396 | − | 0.997915i | \(-0.520558\pi\) |
0.997915 | + | 0.0645396i | \(0.0205579\pi\) | |||||||
\(98\) | −7.12130e7 | − | 7.12130e7i | −0.772067 | − | 0.772067i | ||||
\(99\) | 2.00055e7i | 0.208262i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.15531e6 | −0.0111023 | −0.00555115 | − | 0.999985i | \(-0.501767\pi\) | ||||
−0.00555115 | + | 0.999985i | \(0.501767\pi\) | |||||||
\(102\) | 6.68703e6 | − | 6.68703e6i | 0.0617778 | − | 0.0617778i | ||||
\(103\) | 1.82085e7 | + | 1.82085e7i | 0.161780 | + | 0.161780i | 0.783355 | − | 0.621575i | \(-0.213507\pi\) |
−0.621575 | + | 0.783355i | \(0.713507\pi\) | |||||||
\(104\) | 5.78562e7i | 0.494557i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.05310e8 | −0.834156 | ||||||||
\(107\) | 1.18148e8 | − | 1.18148e8i | 0.901348 | − | 0.901348i | −0.0942049 | − | 0.995553i | \(-0.530031\pi\) |
0.995553 | + | 0.0942049i | \(0.0300309\pi\) | |||||||
\(108\) | 5.36036e6 | + | 5.36036e6i | 0.0394002 | + | 0.0394002i | ||||
\(109\) | 1.53879e8i | 1.09012i | 0.838398 | + | 0.545059i | \(0.183493\pi\) | ||||
−0.838398 | + | 0.545059i | \(0.816507\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.56102e7 | −0.563941 | ||||||||
\(112\) | −2.63191e7 | + | 2.63191e7i | −0.167263 | + | 0.167263i | ||||
\(113\) | −6.96861e7 | − | 6.96861e7i | −0.427398 | − | 0.427398i | 0.460343 | − | 0.887741i | \(-0.347726\pi\) |
−0.887741 | + | 0.460343i | \(0.847726\pi\) | |||||||
\(114\) | 1.52053e8i | 0.900275i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.59738e7 | −0.419596 | ||||||||
\(117\) | 2.70747e7 | − | 2.70747e7i | 0.144484 | − | 0.144484i | ||||
\(118\) | 1.72234e8 | + | 1.72234e8i | 0.888363 | + | 0.888363i | ||||
\(119\) | − | 5.24269e6i | − | 0.0261436i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.30682e8 | −0.609643 | ||||||||
\(122\) | −3.06910e8 | + | 3.06910e8i | −1.38539 | + | 1.38539i | ||||
\(123\) | 1.05922e8 | + | 1.05922e8i | 0.462772 | + | 0.462772i | ||||
\(124\) | − | 2.90666e7i | − | 0.122944i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.87176e7 | 0.0742624 | ||||||||
\(127\) | 2.28028e8 | − | 2.28028e8i | 0.876542 | − | 0.876542i | −0.116633 | − | 0.993175i | \(-0.537210\pi\) |
0.993175 | + | 0.116633i | \(0.0372103\pi\) | |||||||
\(128\) | −2.28979e8 | − | 2.28979e8i | −0.853012 | − | 0.853012i | ||||
\(129\) | 1.58770e8i | 0.573336i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.11086e8 | 0.716760 | 0.358380 | − | 0.933576i | \(-0.383329\pi\) | ||||
0.358380 | + | 0.933576i | \(0.383329\pi\) | |||||||
\(132\) | 2.24206e7 | − | 2.24206e7i | 0.0738501 | − | 0.0738501i | ||||
\(133\) | 5.96054e7 | + | 5.96054e7i | 0.190493 | + | 0.190493i | ||||
\(134\) | − | 4.29439e8i | − | 1.33193i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.67797e7 | 0.107511 | ||||||||
\(137\) | −1.65084e8 | + | 1.65084e8i | −0.468622 | + | 0.468622i | −0.901468 | − | 0.432846i | \(-0.857509\pi\) |
0.432846 | + | 0.901468i | \(0.357509\pi\) | |||||||
\(138\) | 1.91895e8 | + | 1.91895e8i | 0.529112 | + | 0.529112i | ||||
\(139\) | − | 5.69012e8i | − | 1.52427i | −0.647418 | − | 0.762135i | \(-0.724151\pi\) | ||
0.647418 | − | 0.762135i | \(-0.275849\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.94358e8 | 0.744732 | ||||||||
\(142\) | −3.38332e6 | + | 3.38332e6i | −0.00832126 | + | 0.00832126i | ||||
\(143\) | −1.13244e8 | − | 1.13244e8i | −0.270814 | − | 0.270814i | ||||
\(144\) | 1.72810e8i | 0.401901i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.83620e8 | 1.72462 | ||||||||
\(147\) | −1.83294e8 | + | 1.83294e8i | −0.392535 | + | 0.392535i | ||||
\(148\) | 9.59449e7 | + | 9.59449e7i | 0.199975 | + | 0.199975i | ||||
\(149\) | − | 7.28638e8i | − | 1.47831i | −0.673533 | − | 0.739157i | \(-0.735224\pi\) | ||
0.673533 | − | 0.739157i | \(-0.264776\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.27033e8 | −0.629048 | −0.314524 | − | 0.949250i | \(-0.601845\pi\) | ||||
−0.314524 | + | 0.949250i | \(0.601845\pi\) | |||||||
\(152\) | −4.18158e8 | + | 4.18158e8i | −0.783368 | + | 0.783368i | ||||
\(153\) | −1.72116e7 | − | 1.72116e7i | −0.0314091 | − | 0.0314091i | ||||
\(154\) | − | 7.82895e7i | − | 0.139194i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.06861e7 | −0.102469 | ||||||||
\(157\) | 5.90569e8 | − | 5.90569e8i | 0.972013 | − | 0.972013i | −0.0276064 | − | 0.999619i | \(-0.508788\pi\) |
0.999619 | + | 0.0276064i | \(0.00878849\pi\) | |||||||
\(158\) | −4.30413e8 | − | 4.30413e8i | −0.690648 | − | 0.690648i | ||||
\(159\) | 2.71056e8i | 0.424102i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.50447e8 | 0.223914 | ||||||||
\(162\) | 6.14495e7 | − | 6.14495e7i | 0.0892192 | − | 0.0892192i | ||||
\(163\) | 5.14036e8 | + | 5.14036e8i | 0.728188 | + | 0.728188i | 0.970259 | − | 0.242071i | \(-0.0778267\pi\) |
−0.242071 | + | 0.970259i | \(0.577827\pi\) | |||||||
\(164\) | − | 2.37418e8i | − | 0.328200i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.27959e9 | 1.68515 | ||||||||
\(167\) | −5.60597e8 | + | 5.60597e8i | −0.720750 | + | 0.720750i | −0.968758 | − | 0.248008i | \(-0.920224\pi\) |
0.248008 | + | 0.968758i | \(0.420224\pi\) | |||||||
\(168\) | 5.14750e7 | + | 5.14750e7i | 0.0646189 | + | 0.0646189i | ||||
\(169\) | − | 5.09211e8i | − | 0.624239i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.91366e8 | 0.457719 | ||||||||
\(172\) | 1.77936e8 | − | 1.77936e8i | 0.203306 | − | 0.203306i | ||||
\(173\) | 1.11036e8 | + | 1.11036e8i | 0.123959 | + | 0.123959i | 0.766365 | − | 0.642406i | \(-0.222064\pi\) |
−0.642406 | + | 0.766365i | \(0.722064\pi\) | |||||||
\(174\) | 8.70940e8i | 0.950148i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.22806e8 | 0.753305 | ||||||||
\(177\) | 4.43309e8 | − | 4.43309e8i | 0.451662 | − | 0.451662i | ||||
\(178\) | 8.46348e8 | + | 8.46348e8i | 0.843080 | + | 0.843080i | ||||
\(179\) | − | 9.39164e8i | − | 0.914807i | −0.889259 | − | 0.457403i | \(-0.848780\pi\) | ||
0.889259 | − | 0.457403i | \(-0.151220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.19785e9 | −1.11606 | −0.558030 | − | 0.829821i | \(-0.688443\pi\) | ||||
−0.558030 | + | 0.829821i | \(0.688443\pi\) | |||||||
\(182\) | −1.05954e8 | + | 1.05954e8i | −0.0965675 | + | 0.0965675i | ||||
\(183\) | 7.89950e8 | + | 7.89950e8i | 0.704361 | + | 0.704361i | ||||
\(184\) | 1.05545e9i | 0.920806i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.33211e8 | −0.278399 | ||||||||
\(187\) | −7.19903e7 | + | 7.19903e7i | −0.0588719 | + | 0.0588719i | ||||
\(188\) | −3.29893e8 | − | 3.29893e8i | −0.264083 | − | 0.264083i | ||||
\(189\) | − | 4.81770e7i | − | 0.0377565i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.70668e9 | −1.28239 | −0.641194 | − | 0.767378i | \(-0.721561\pi\) | ||||
−0.641194 | + | 0.767378i | \(0.721561\pi\) | |||||||
\(192\) | −3.14612e8 | + | 3.14612e8i | −0.231511 | + | 0.231511i | ||||
\(193\) | 3.08858e8 | + | 3.08858e8i | 0.222602 | + | 0.222602i | 0.809593 | − | 0.586991i | \(-0.199688\pi\) |
−0.586991 | + | 0.809593i | \(0.699688\pi\) | |||||||
\(194\) | 2.12322e9i | 1.49895i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.10841e8 | 0.278387 | ||||||||
\(197\) | 6.41714e8 | − | 6.41714e8i | 0.426065 | − | 0.426065i | −0.461220 | − | 0.887286i | \(-0.652588\pi\) |
0.887286 | + | 0.461220i | \(0.152588\pi\) | |||||||
\(198\) | −2.57023e8 | − | 2.57023e8i | −0.167229 | − | 0.167229i | ||||
\(199\) | 5.59952e8i | 0.357058i | 0.983935 | + | 0.178529i | \(0.0571338\pi\) | ||||
−0.983935 | + | 0.178529i | \(0.942866\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.10533e9 | −0.677183 | ||||||||
\(202\) | 1.48429e7 | − | 1.48429e7i | 0.00891485 | − | 0.00891485i | ||||
\(203\) | 3.41412e8 | + | 3.41412e8i | 0.201046 | + | 0.201046i | ||||
\(204\) | 3.85787e7i | 0.0222755i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.67870e8 | −0.259810 | ||||||||
\(207\) | 4.93915e8 | − | 4.93915e8i | 0.269012 | − | 0.269012i | ||||
\(208\) | −9.78215e8 | − | 9.78215e8i | −0.522614 | − | 0.522614i | ||||
\(209\) | − | 1.63695e9i | − | 0.857927i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.69992e9 | −1.36214 | −0.681068 | − | 0.732220i | \(-0.738484\pi\) | ||||
−0.681068 | + | 0.732220i | \(0.738484\pi\) | |||||||
\(212\) | 3.03777e8 | − | 3.03777e8i | 0.150388 | − | 0.150388i | ||||
\(213\) | 8.70826e6 | + | 8.70826e6i | 0.00423070 | + | 0.00423070i | ||||
\(214\) | 3.03584e9i | 1.44752i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.37982e8 | 0.155267 | ||||||||
\(217\) | −1.30620e8 | + | 1.30620e8i | −0.0589075 | + | 0.0589075i | ||||
\(218\) | −1.97697e9 | − | 1.97697e9i | −0.875335 | − | 0.875335i | ||||
\(219\) | − | 2.01694e9i | − | 0.876834i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.94857e8 | 0.0816860 | ||||||||
\(222\) | 1.09988e9 | − | 1.09988e9i | 0.452829 | − | 0.452829i | ||||
\(223\) | −3.27835e9 | − | 3.27835e9i | −1.32567 | − | 1.32567i | −0.909107 | − | 0.416564i | \(-0.863234\pi\) |
−0.416564 | − | 0.909107i | \(-0.636766\pi\) | |||||||
\(224\) | − | 2.77775e8i | − | 0.110332i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.79059e9 | 0.686378 | ||||||||
\(227\) | 2.34941e8 | − | 2.34941e8i | 0.0884820 | − | 0.0884820i | −0.661480 | − | 0.749962i | \(-0.730072\pi\) |
0.749962 | + | 0.661480i | \(0.230072\pi\) | |||||||
\(228\) | −4.38611e8 | − | 4.38611e8i | −0.162308 | − | 0.162308i | ||||
\(229\) | 1.85932e9i | 0.676101i | 0.941128 | + | 0.338051i | \(0.109768\pi\) | ||||
−0.941128 | + | 0.338051i | \(0.890232\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.01508e8 | −0.0707692 | ||||||||
\(232\) | −2.39516e9 | + | 2.39516e9i | −0.826764 | + | 0.826764i | ||||
\(233\) | −9.60879e8 | − | 9.60879e8i | −0.326021 | − | 0.326021i | 0.525050 | − | 0.851071i | \(-0.324046\pi\) |
−0.851071 | + | 0.525050i | \(0.824046\pi\) | |||||||
\(234\) | 6.95687e8i | 0.232033i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.93649e8 | −0.320321 | ||||||||
\(237\) | −1.10783e9 | + | 1.10783e9i | −0.351140 | + | 0.351140i | ||||
\(238\) | 6.73558e7 | + | 6.73558e7i | 0.0209926 | + | 0.0209926i | ||||
\(239\) | − | 2.40669e9i | − | 0.737613i | −0.929506 | − | 0.368807i | \(-0.879766\pi\) | ||
0.929506 | − | 0.368807i | \(-0.120234\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.47993e8 | 0.221733 | 0.110866 | − | 0.993835i | \(-0.464637\pi\) | ||||
0.110866 | + | 0.993835i | \(0.464637\pi\) | |||||||
\(242\) | 1.67895e9 | − | 1.67895e9i | 0.489527 | − | 0.489527i | ||||
\(243\) | −1.58164e8 | − | 1.58164e8i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 1.77062e9i | − | 0.499535i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.72169e9 | −0.743187 | ||||||||
\(247\) | −2.21538e9 | + | 2.21538e9i | −0.595197 | + | 0.595197i | ||||
\(248\) | −9.16356e8 | − | 9.16356e8i | −0.242247 | − | 0.242247i | ||||
\(249\) | − | 3.29352e9i | − | 0.856766i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.38810e9 | −0.853615 | −0.426807 | − | 0.904343i | \(-0.640362\pi\) | ||||
−0.426807 | + | 0.904343i | \(0.640362\pi\) | |||||||
\(252\) | −5.39928e7 | + | 5.39928e7i | −0.0133886 | + | 0.0133886i | ||||
\(253\) | −2.06588e9 | − | 2.06588e9i | −0.504223 | − | 0.504223i | ||||
\(254\) | 5.85920e9i | 1.40768i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.44804e9 | 0.802809 | ||||||||
\(257\) | 2.56381e9 | − | 2.56381e9i | 0.587697 | − | 0.587697i | −0.349310 | − | 0.937007i | \(-0.613584\pi\) |
0.937007 | + | 0.349310i | \(0.113584\pi\) | |||||||
\(258\) | −2.03981e9 | − | 2.03981e9i | −0.460373 | − | 0.460373i | ||||
\(259\) | − | 8.62318e8i | − | 0.191632i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.24170e9 | 0.483075 | ||||||||
\(262\) | −2.71194e9 | + | 2.71194e9i | −0.575539 | + | 0.575539i | ||||
\(263\) | 6.04705e9 | + | 6.04705e9i | 1.26392 | + | 1.26392i | 0.949176 | + | 0.314746i | \(0.101919\pi\) |
0.314746 | + | 0.949176i | \(0.398081\pi\) | |||||||
\(264\) | − | 1.41367e9i | − | 0.291025i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.53157e9 | −0.305921 | ||||||||
\(267\) | 2.17840e9 | − | 2.17840e9i | 0.428640 | − | 0.428640i | ||||
\(268\) | 1.23876e9 | + | 1.23876e9i | 0.240130 | + | 0.240130i | ||||
\(269\) | 1.61487e9i | 0.308410i | 0.988039 | + | 0.154205i | \(0.0492817\pi\) | ||||
−0.988039 | + | 0.154205i | \(0.950718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.86096e8 | 0.0345032 | 0.0172516 | − | 0.999851i | \(-0.494508\pi\) | ||||
0.0172516 | + | 0.999851i | \(0.494508\pi\) | |||||||
\(272\) | −6.21860e8 | + | 6.21860e8i | −0.113610 | + | 0.113610i | ||||
\(273\) | 2.72712e8 | + | 2.72712e8i | 0.0490969 | + | 0.0490969i | ||||
\(274\) | − | 4.24185e9i | − | 0.752581i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.10708e9 | −0.190784 | ||||||||
\(277\) | 4.05703e9 | − | 4.05703e9i | 0.689111 | − | 0.689111i | −0.272924 | − | 0.962036i | \(-0.587991\pi\) |
0.962036 | + | 0.272924i | \(0.0879908\pi\) | |||||||
\(278\) | 7.31042e9 | + | 7.31042e9i | 1.22395 | + | 1.22395i | ||||
\(279\) | 8.57645e8i | 0.141544i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.02195e9 | 0.324298 | 0.162149 | − | 0.986766i | \(-0.448157\pi\) | ||||
0.162149 | + | 0.986766i | \(0.448157\pi\) | |||||||
\(282\) | −3.78179e9 | + | 3.78179e9i | −0.597999 | + | 0.597999i | ||||
\(283\) | 1.77537e9 | + | 1.77537e9i | 0.276786 | + | 0.276786i | 0.831825 | − | 0.555039i | \(-0.187297\pi\) |
−0.555039 | + | 0.831825i | \(0.687297\pi\) | |||||||
\(284\) | − | 1.95190e7i | − | 0.00300043i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.90982e9 | 0.434913 | ||||||||
\(287\) | −1.06691e9 | + | 1.06691e9i | −0.157254 | + | 0.157254i | ||||
\(288\) | −9.11928e8 | − | 9.11928e8i | −0.132553 | − | 0.132553i | ||||
\(289\) | 6.85188e9i | 0.982242i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.46491e9 | 0.762098 | ||||||||
\(292\) | −2.26042e9 | + | 2.26042e9i | −0.310927 | + | 0.310927i | ||||
\(293\) | 8.41639e9 | + | 8.41639e9i | 1.14197 | + | 1.14197i | 0.988089 | + | 0.153882i | \(0.0491776\pi\) |
0.153882 | + | 0.988089i | \(0.450822\pi\) | |||||||
\(294\) | − | 4.70976e9i | − | 0.630390i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.04954e9 | 0.788053 | ||||||||
\(297\) | −6.61545e8 | + | 6.61545e8i | −0.0850225 | + | 0.0850225i | ||||
\(298\) | 9.36122e9 | + | 9.36122e9i | 1.18705 | + | 1.18705i | ||||
\(299\) | 5.59175e9i | 0.699621i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.59923e9 | −0.194825 | ||||||||
\(302\) | 4.20158e9 | − | 4.20158e9i | 0.505108 | − | 0.505108i | ||||
\(303\) | −3.82039e7 | − | 3.82039e7i | −0.00453250 | − | 0.00453250i | ||||
\(304\) | − | 1.41402e10i | − | 1.65562i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.42255e8 | 0.0504413 | ||||||||
\(307\) | 6.86322e9 | − | 6.86322e9i | 0.772635 | − | 0.772635i | −0.205932 | − | 0.978566i | \(-0.566022\pi\) |
0.978566 | + | 0.205932i | \(0.0660224\pi\) | |||||||
\(308\) | 2.25834e8 | + | 2.25834e8i | 0.0250949 | + | 0.0250949i | ||||
\(309\) | 1.20424e9i | 0.132093i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.22090e10 | 1.30508 | 0.652540 | − | 0.757754i | \(-0.273703\pi\) | ||||
0.652540 | + | 0.757754i | \(0.273703\pi\) | |||||||
\(312\) | −1.91320e9 | + | 1.91320e9i | −0.201902 | + | 0.201902i | ||||
\(313\) | −8.97892e9 | − | 8.97892e9i | −0.935507 | − | 0.935507i | 0.0625360 | − | 0.998043i | \(-0.480081\pi\) |
−0.998043 | + | 0.0625360i | \(0.980081\pi\) | |||||||
\(314\) | 1.51747e10i | 1.56100i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.48313e9 | 0.249030 | ||||||||
\(317\) | 2.41244e9 | − | 2.41244e9i | 0.238901 | − | 0.238901i | −0.577494 | − | 0.816395i | \(-0.695969\pi\) |
0.816395 | + | 0.577494i | \(0.195969\pi\) | |||||||
\(318\) | −3.48241e9 | − | 3.48241e9i | −0.340543 | − | 0.340543i | ||||
\(319\) | − | 9.37626e9i | − | 0.905455i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.81388e9 | 0.735948 | ||||||||
\(322\) | −1.93288e9 | + | 1.93288e9i | −0.179797 | + | 0.179797i | ||||
\(323\) | 1.40834e9 | + | 1.40834e9i | 0.129389 | + | 0.129389i | ||||
\(324\) | 3.54514e8i | 0.0321702i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.32082e10 | −1.16943 | ||||||||
\(327\) | −5.08849e9 | + | 5.08849e9i | −0.445039 | + | 0.445039i | ||||
\(328\) | −7.48486e9 | − | 7.48486e9i | −0.646679 | − | 0.646679i | ||||
\(329\) | 2.96495e9i | 0.253066i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.31501e9 | −0.109552 | −0.0547758 | − | 0.998499i | \(-0.517444\pi\) | ||||
−0.0547758 | + | 0.998499i | \(0.517444\pi\) | |||||||
\(332\) | −3.69110e9 | + | 3.69110e9i | −0.303811 | + | 0.303811i | ||||
\(333\) | −2.83097e9 | − | 2.83097e9i | −0.230228 | − | 0.230228i | ||||
\(334\) | − | 1.44046e10i | − | 1.15749i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.74065e9 | −0.136570 | ||||||||
\(337\) | 2.89442e9 | − | 2.89442e9i | 0.224410 | − | 0.224410i | −0.585943 | − | 0.810352i | \(-0.699276\pi\) |
0.810352 | + | 0.585943i | \(0.199276\pi\) | |||||||
\(338\) | 6.54213e9 | + | 6.54213e9i | 0.501247 | + | 0.501247i | ||||
\(339\) | − | 4.60878e9i | − | 0.348969i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.58724e9 | 0.265303 | ||||||||
\(342\) | −5.02810e9 | + | 5.02810e9i | −0.367536 | + | 0.367536i | ||||
\(343\) | −3.76640e9 | − | 3.76640e9i | −0.272113 | − | 0.272113i | ||||
\(344\) | − | 1.12193e10i | − | 0.801181i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.85308e9 | −0.199072 | ||||||||
\(347\) | −8.24434e9 | + | 8.24434e9i | −0.568641 | + | 0.568641i | −0.931748 | − | 0.363107i | \(-0.881716\pi\) |
0.363107 | + | 0.931748i | \(0.381716\pi\) | |||||||
\(348\) | −2.51231e9 | − | 2.51231e9i | −0.171299 | − | 0.171299i | ||||
\(349\) | − | 1.52787e10i | − | 1.02987i | −0.857228 | − | 0.514937i | \(-0.827815\pi\) | ||
0.857228 | − | 0.514937i | \(-0.172185\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.79062e9 | 0.117971 | ||||||||
\(352\) | −3.81429e9 | + | 3.81429e9i | −0.248452 | + | 0.248452i | ||||
\(353\) | −1.34106e10 | − | 1.34106e10i | −0.863675 | − | 0.863675i | 0.128088 | − | 0.991763i | \(-0.459116\pi\) |
−0.991763 | + | 0.128088i | \(0.959116\pi\) | |||||||
\(354\) | 1.13909e10i | 0.725345i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.88274e9 | −0.303993 | ||||||||
\(357\) | 1.73366e8 | − | 1.73366e8i | 0.0106731 | − | 0.0106731i | ||||
\(358\) | 1.20660e10 | + | 1.20660e10i | 0.734565 | + | 0.734565i | ||||
\(359\) | 1.41350e10i | 0.850976i | 0.904964 | + | 0.425488i | \(0.139898\pi\) | ||||
−0.904964 | + | 0.425488i | \(0.860102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.50399e10 | −0.885556 | ||||||||
\(362\) | 1.53894e10 | − | 1.53894e10i | 0.896166 | − | 0.896166i | ||||
\(363\) | −4.32142e9 | − | 4.32142e9i | −0.248886 | − | 0.248886i | ||||
\(364\) | − | 6.11267e8i | − | 0.0348197i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.02979e10 | −1.13117 | ||||||||
\(367\) | −5.17117e9 | + | 5.17117e9i | −0.285052 | + | 0.285052i | −0.835120 | − | 0.550068i | \(-0.814602\pi\) |
0.550068 | + | 0.835120i | \(0.314602\pi\) | |||||||
\(368\) | −1.78453e10 | − | 1.78453e10i | −0.973044 | − | 0.973044i | ||||
\(369\) | 7.00530e9i | 0.377852i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.73024e9 | −0.144114 | ||||||||
\(372\) | 9.61178e8 | − | 9.61178e8i | 0.0501917 | − | 0.0501917i | ||||
\(373\) | −1.24174e10 | − | 1.24174e10i | −0.641496 | − | 0.641496i | 0.309427 | − | 0.950923i | \(-0.399863\pi\) |
−0.950923 | + | 0.309427i | \(0.899863\pi\) | |||||||
\(374\) | − | 1.84980e9i | − | 0.0945450i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.08004e10 | −1.04069 | ||||||||
\(377\) | −1.26894e10 | + | 1.26894e10i | −0.628169 | + | 0.628169i | ||||
\(378\) | 6.18957e8 | + | 6.18957e8i | 0.0303175 | + | 0.0303175i | ||||
\(379\) | 2.85775e10i | 1.38506i | 0.721390 | + | 0.692529i | \(0.243504\pi\) | ||||
−0.721390 | + | 0.692529i | \(0.756496\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50809e10 | 0.715693 | ||||||||
\(382\) | 2.19267e10 | − | 2.19267e10i | 1.02972 | − | 1.02972i | ||||
\(383\) | 1.26480e10 | + | 1.26480e10i | 0.587795 | + | 0.587795i | 0.937034 | − | 0.349238i | \(-0.113560\pi\) |
−0.349238 | + | 0.937034i | \(0.613560\pi\) | |||||||
\(384\) | − | 1.51438e10i | − | 0.696481i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.93614e9 | −0.357487 | ||||||||
\(387\) | −5.25022e9 | + | 5.25022e9i | −0.234063 | + | 0.234063i | ||||
\(388\) | −6.12462e9 | − | 6.12462e9i | −0.270242 | − | 0.270242i | ||||
\(389\) | 2.90672e10i | 1.26942i | 0.772751 | + | 0.634709i | \(0.218880\pi\) | ||||
−0.772751 | + | 0.634709i | \(0.781120\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.55473e9 | 0.152089 | ||||||||
\(392\) | 1.29522e10 | − | 1.29522e10i | 0.548529 | − | 0.548529i | ||||
\(393\) | 6.98021e9 | + | 6.98021e9i | 0.292616 | + | 0.292616i | ||||
\(394\) | 1.64889e10i | 0.684238i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.48281e9 | 0.0602983 | ||||||||
\(397\) | −4.58091e9 | + | 4.58091e9i | −0.184412 | + | 0.184412i | −0.793275 | − | 0.608863i | \(-0.791626\pi\) |
0.608863 | + | 0.793275i | \(0.291626\pi\) | |||||||
\(398\) | −7.19403e9 | − | 7.19403e9i | −0.286708 | − | 0.286708i | ||||
\(399\) | 3.94207e9i | 0.155537i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.56775e10 | −0.993060 | −0.496530 | − | 0.868020i | \(-0.665393\pi\) | ||||
−0.496530 | + | 0.868020i | \(0.665393\pi\) | |||||||
\(402\) | 1.42007e10 | − | 1.42007e10i | 0.543760 | − | 0.543760i | ||||
\(403\) | −4.85481e9 | − | 4.85481e9i | −0.184057 | − | 0.184057i | ||||
\(404\) | 8.56316e7i | 0.00321447i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.77264e9 | −0.322869 | ||||||||
\(407\) | −1.18410e10 | + | 1.18410e10i | −0.431529 | + | 0.431529i | ||||
\(408\) | 1.21624e9 | + | 1.21624e9i | 0.0438912 | + | 0.0438912i | ||||
\(409\) | 5.15362e10i | 1.84170i | 0.389916 | + | 0.920850i | \(0.372504\pi\) | ||||
−0.389916 | + | 0.920850i | \(0.627496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.09180e10 | −0.382628 | ||||||||
\(412\) | 1.34961e9 | − | 1.34961e9i | 0.0468404 | − | 0.0468404i | ||||
\(413\) | 4.46528e9 | + | 4.46528e9i | 0.153479 | + | 0.153479i | ||||
\(414\) | 1.26912e10i | 0.432018i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.03242e10 | 0.344733 | ||||||||
\(417\) | 1.88162e10 | − | 1.88162e10i | 0.622281 | − | 0.622281i | ||||
\(418\) | 2.10308e10 | + | 2.10308e10i | 0.688893 | + | 0.688893i | ||||
\(419\) | − | 5.16799e10i | − | 1.67674i | −0.545102 | − | 0.838370i | \(-0.683509\pi\) | ||
0.545102 | − | 0.838370i | \(-0.316491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.90468e10 | 0.924633 | 0.462316 | − | 0.886715i | \(-0.347018\pi\) | ||||
0.462316 | + | 0.886715i | \(0.347018\pi\) | |||||||
\(422\) | 3.46874e10 | − | 3.46874e10i | 1.09376 | − | 1.09376i | ||||
\(423\) | 9.73387e9 | + | 9.73387e9i | 0.304035 | + | 0.304035i | ||||
\(424\) | − | 1.91538e10i | − | 0.592641i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.23760e8 | −0.00679428 | ||||||||
\(427\) | −7.95685e9 | + | 7.95685e9i | −0.239348 | + | 0.239348i | ||||
\(428\) | −8.75716e9 | − | 8.75716e9i | −0.260969 | − | 0.260969i | ||||
\(429\) | − | 7.48954e9i | − | 0.221119i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.38176e9 | −0.0980018 | −0.0490009 | − | 0.998799i | \(-0.515604\pi\) | ||||
−0.0490009 | + | 0.998799i | \(0.515604\pi\) | |||||||
\(432\) | −5.71450e9 | + | 5.71450e9i | −0.164075 | + | 0.164075i | ||||
\(433\) | 4.76643e9 | + | 4.76643e9i | 0.135594 | + | 0.135594i | 0.771646 | − | 0.636052i | \(-0.219434\pi\) |
−0.636052 | + | 0.771646i | \(0.719434\pi\) | |||||||
\(434\) | − | 3.35630e9i | − | 0.0946023i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.14055e10 | 0.315623 | ||||||||
\(437\) | −4.04145e10 | + | 4.04145e10i | −1.10818 | + | 1.10818i | ||||
\(438\) | 2.59128e10 | + | 2.59128e10i | 0.704074 | + | 0.704074i | ||||
\(439\) | 3.12405e10i | 0.841125i | 0.907264 | + | 0.420562i | \(0.138167\pi\) | ||||
−0.907264 | + | 0.420562i | \(0.861833\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.21224e10 | −0.320503 | ||||||||
\(442\) | −2.50344e9 | + | 2.50344e9i | −0.0655917 | + | 0.0655917i | ||||
\(443\) | −1.38928e10 | − | 1.38928e10i | −0.360725 | − | 0.360725i | 0.503355 | − | 0.864080i | \(-0.332099\pi\) |
−0.864080 | + | 0.503355i | \(0.832099\pi\) | |||||||
\(444\) | 6.34543e9i | 0.163279i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.42376e10 | 2.12895 | ||||||||
\(447\) | 2.40947e10 | − | 2.40947e10i | 0.603519 | − | 0.603519i | ||||
\(448\) | −3.16897e9 | − | 3.16897e9i | −0.0786693 | − | 0.0786693i | ||||
\(449\) | − | 7.46158e10i | − | 1.83588i | −0.396715 | − | 0.917942i | \(-0.629850\pi\) | ||
0.396715 | − | 0.917942i | \(-0.370150\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.93008e10 | 0.708229 | ||||||||
\(452\) | −5.16514e9 | + | 5.16514e9i | −0.123745 | + | 0.123745i | ||||
\(453\) | −1.08144e10 | − | 1.08144e10i | −0.256808 | − | 0.256808i | ||||
\(454\) | 6.03684e9i | 0.142097i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.76554e10 | −0.639617 | ||||||||
\(457\) | −3.35344e10 | + | 3.35344e10i | −0.768822 | + | 0.768822i | −0.977899 | − | 0.209077i | \(-0.932954\pi\) |
0.209077 | + | 0.977899i | \(0.432954\pi\) | |||||||
\(458\) | −2.38877e10 | − | 2.38877e10i | −0.542891 | − | 0.542891i | ||||
\(459\) | − | 1.13831e9i | − | 0.0256454i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.49468e10 | −1.88080 | −0.940401 | − | 0.340067i | \(-0.889550\pi\) | ||||
−0.940401 | + | 0.340067i | \(0.889550\pi\) | |||||||
\(462\) | 2.58889e9 | − | 2.58889e9i | 0.0568258 | − | 0.0568258i | ||||
\(463\) | 2.48427e10 | + | 2.48427e10i | 0.540598 | + | 0.540598i | 0.923704 | − | 0.383106i | \(-0.125146\pi\) |
−0.383106 | + | 0.923704i | \(0.625146\pi\) | |||||||
\(464\) | − | 8.09931e10i | − | 1.74734i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.46899e10 | 0.523572 | ||||||||
\(467\) | −3.37883e10 | + | 3.37883e10i | −0.710393 | + | 0.710393i | −0.966617 | − | 0.256224i | \(-0.917521\pi\) |
0.256224 | + | 0.966617i | \(0.417521\pi\) | |||||||
\(468\) | −2.00677e9 | − | 2.00677e9i | −0.0418326 | − | 0.0418326i | ||||
\(469\) | − | 1.11335e10i | − | 0.230113i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.90580e10 | 0.793645 | ||||||||
\(472\) | −3.13259e10 | + | 3.13259e10i | −0.631154 | + | 0.631154i | ||||
\(473\) | 2.19599e10 | + | 2.19599e10i | 0.438718 | + | 0.438718i | ||||
\(474\) | − | 2.84659e10i | − | 0.563912i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.88588e8 | −0.00756941 | ||||||||
\(477\) | −8.96331e9 | + | 8.96331e9i | −0.173139 | + | 0.173139i | ||||
\(478\) | 3.09201e10 | + | 3.09201e10i | 0.592283 | + | 0.592283i | ||||
\(479\) | − | 9.81566e9i | − | 0.186456i | −0.995645 | − | 0.0932282i | \(-0.970281\pi\) | ||
0.995645 | − | 0.0932282i | \(-0.0297186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.20502e10 | 0.598756 | ||||||||
\(482\) | −9.60989e9 | + | 9.60989e9i | −0.178045 | + | 0.178045i | ||||
\(483\) | 4.97501e9 | + | 4.97501e9i | 0.0914125 | + | 0.0914125i | ||||
\(484\) | 9.68619e9i | 0.176511i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.06404e9 | 0.0728472 | ||||||||
\(487\) | −3.83213e9 | + | 3.83213e9i | −0.0681279 | + | 0.0681279i | −0.740350 | − | 0.672222i | \(-0.765340\pi\) |
0.672222 | + | 0.740350i | \(0.265340\pi\) | |||||||
\(488\) | −5.58208e10 | − | 5.58208e10i | −0.984275 | − | 0.984275i | ||||
\(489\) | 3.39964e10i | 0.594563i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.03138e11 | 1.77457 | 0.887287 | − | 0.461218i | \(-0.152587\pi\) | ||||
0.887287 | + | 0.461218i | \(0.152587\pi\) | |||||||
\(492\) | 7.85097e9 | − | 7.85097e9i | 0.133987 | − | 0.133987i | ||||
\(493\) | 8.06679e9 | + | 8.06679e9i | 0.136557 | + | 0.136557i | ||||
\(494\) | − | 5.69245e10i | − | 0.955854i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.09869e10 | 0.511979 | ||||||||
\(497\) | −8.77148e7 | + | 8.77148e7i | −0.00143763 | + | 0.00143763i | ||||
\(498\) | 4.23137e10 | + | 4.23137e10i | 0.687960 | + | 0.687960i | ||||
\(499\) | − | 4.57149e10i | − | 0.737320i | −0.929564 | − | 0.368660i | \(-0.879817\pi\) | ||
0.929564 | − | 0.368660i | \(-0.120183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.70758e10 | −0.588490 | ||||||||
\(502\) | 4.35289e10 | − | 4.35289e10i | 0.685430 | − | 0.685430i | ||||
\(503\) | 4.38110e9 | + | 4.38110e9i | 0.0684402 | + | 0.0684402i | 0.740498 | − | 0.672058i | \(-0.234590\pi\) |
−0.672058 | + | 0.740498i | \(0.734590\pi\) | |||||||
\(504\) | 3.40436e9i | 0.0527611i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.30831e10 | 0.809756 | ||||||||
\(507\) | 1.68387e10 | − | 1.68387e10i | 0.254845 | − | 0.254845i | ||||
\(508\) | −1.69014e10 | − | 1.69014e10i | −0.253786 | − | 0.253786i | ||||
\(509\) | 4.42948e10i | 0.659906i | 0.943997 | + | 0.329953i | \(0.107033\pi\) | ||||
−0.943997 | + | 0.329953i | \(0.892967\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.03159e10 | 0.297956 | ||||||||
\(512\) | 1.43196e10 | − | 1.43196e10i | 0.208378 | − | 0.208378i | ||||
\(513\) | 1.29417e10 | + | 1.29417e10i | 0.186863 | + | 0.186863i | ||||
\(514\) | 6.58775e10i | 0.943809i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.17680e10 | 0.165999 | ||||||||
\(517\) | 4.07135e10 | − | 4.07135e10i | 0.569870 | − | 0.569870i | ||||
\(518\) | 1.10787e10 | + | 1.10787e10i | 0.153875 | + | 0.153875i | ||||
\(519\) | 7.34349e9i | 0.101212i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.25192e10 | −0.441356 | −0.220678 | − | 0.975347i | \(-0.570827\pi\) | ||||
−0.220678 | + | 0.975347i | \(0.570827\pi\) | |||||||
\(522\) | −2.88003e10 | + | 2.88003e10i | −0.387896 | + | 0.387896i | ||||
\(523\) | 4.21601e10 | + | 4.21601e10i | 0.563502 | + | 0.563502i | 0.930300 | − | 0.366799i | \(-0.119546\pi\) |
−0.366799 | + | 0.930300i | \(0.619546\pi\) | |||||||
\(524\) | − | 1.56457e10i | − | 0.207524i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.55380e11 | −2.02979 | ||||||||
\(527\) | −3.08625e9 | + | 3.08625e9i | −0.0400119 | + | 0.0400119i | ||||
\(528\) | 2.39018e10 | + | 2.39018e10i | 0.307536 | + | 0.307536i | ||||
\(529\) | 2.36977e10i | 0.302610i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.93188e10 | 0.368781 | ||||||||
\(532\) | 4.41795e9 | − | 4.41795e9i | 0.0551537 | − | 0.0551537i | ||||
\(533\) | −3.96545e10 | − | 3.96545e10i | −0.491341 | − | 0.491341i | ||||
\(534\) | 5.59743e10i | 0.688372i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.81064e10 | 0.946297 | ||||||||
\(537\) | 3.10564e10 | − | 3.10564e10i | 0.373468 | − | 0.373468i | ||||
\(538\) | −2.07472e10 | − | 2.07472e10i | −0.247645 | − | 0.247645i | ||||
\(539\) | 5.07037e10i | 0.600737i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.13586e11 | −1.32598 | −0.662991 | − | 0.748628i | \(-0.730713\pi\) | ||||
−0.662991 | + | 0.748628i | \(0.730713\pi\) | |||||||
\(542\) | −2.39088e9 | + | 2.39088e9i | −0.0277051 | + | 0.0277051i | ||||
\(543\) | −3.96106e10 | − | 3.96106e10i | −0.455629 | − | 0.455629i | ||||
\(544\) | − | 6.56318e9i | − | 0.0749409i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.00738e9 | −0.0788470 | ||||||||
\(547\) | 9.36616e10 | − | 9.36616e10i | 1.04619 | − | 1.04619i | 0.0473143 | − | 0.998880i | \(-0.484934\pi\) |
0.998880 | − | 0.0473143i | \(-0.0150662\pi\) | |||||||
\(548\) | 1.22360e10 | + | 1.22360e10i | 0.135681 | + | 0.135681i | ||||
\(549\) | 5.22443e10i | 0.575108i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.83427e11 | −1.99001 | ||||||||
\(552\) | −3.49019e10 | + | 3.49019e10i | −0.375917 | + | 0.375917i | ||||
\(553\) | −1.11588e10 | − | 1.11588e10i | −0.119321 | − | 0.119321i | ||||
\(554\) | 1.04246e11i | 1.10668i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.21752e10 | −0.441324 | ||||||||
\(557\) | 3.10922e9 | − | 3.10922e9i | 0.0323021 | − | 0.0323021i | −0.690771 | − | 0.723073i | \(-0.742729\pi\) |
0.723073 | + | 0.690771i | \(0.242729\pi\) | |||||||
\(558\) | −1.10186e10 | − | 1.10186e10i | −0.113656 | − | 0.113656i | ||||
\(559\) | − | 5.94392e10i | − | 0.608731i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.76117e9 | −0.0480687 | ||||||||
\(562\) | −2.59771e10 | + | 2.59771e10i | −0.260402 | + | 0.260402i | ||||
\(563\) | 7.58588e10 | + | 7.58588e10i | 0.755044 | + | 0.755044i | 0.975416 | − | 0.220372i | \(-0.0707271\pi\) |
−0.220372 | + | 0.975416i | \(0.570727\pi\) | |||||||
\(564\) | − | 2.18178e10i | − | 0.215623i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.56184e10 | −0.444503 | ||||||||
\(567\) | 1.59312e9 | − | 1.59312e9i | 0.0154140 | − | 0.0154140i | ||||
\(568\) | −6.15358e8 | − | 6.15358e8i | −0.00591200 | − | 0.00591200i | ||||
\(569\) | 9.33092e10i | 0.890175i | 0.895487 | + | 0.445087i | \(0.146827\pi\) | ||||
−0.895487 | + | 0.445087i | \(0.853173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.94129e11 | 1.82619 | 0.913096 | − | 0.407744i | \(-0.133684\pi\) | ||||
0.913096 | + | 0.407744i | \(0.133684\pi\) | |||||||
\(572\) | −8.39366e9 | + | 8.39366e9i | −0.0784092 | + | 0.0784092i | ||||
\(573\) | −5.64368e10 | − | 5.64368e10i | −0.523533 | − | 0.523533i | ||||
\(574\) | − | 2.74145e10i | − | 0.252541i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.08073e10 | −0.189028 | ||||||||
\(577\) | 7.27282e10 | − | 7.27282e10i | 0.656145 | − | 0.656145i | −0.298321 | − | 0.954466i | \(-0.596427\pi\) |
0.954466 | + | 0.298321i | \(0.0964266\pi\) | |||||||
\(578\) | −8.80301e10 | − | 8.80301e10i | −0.788714 | − | 0.788714i | ||||
\(579\) | 2.04267e10i | 0.181754i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.31743e10 | 0.291137 | ||||||||
\(582\) | −7.02108e10 | + | 7.02108e10i | −0.611944 | + | 0.611944i | ||||
\(583\) | 3.74905e10 | + | 3.74905e10i | 0.324524 | + | 0.324524i | ||||
\(584\) | 1.42525e11i | 1.22529i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.16260e11 | −1.83394 | ||||||||
\(587\) | −4.26547e10 | + | 4.26547e10i | −0.359265 | + | 0.359265i | −0.863542 | − | 0.504277i | \(-0.831759\pi\) |
0.504277 | + | 0.863542i | \(0.331759\pi\) | |||||||
\(588\) | 1.35857e10 | + | 1.35857e10i | 0.113651 | + | 0.113651i | ||||
\(589\) | − | 7.01767e10i | − | 0.583085i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.24405e10 | 0.347881 | ||||||||
\(592\) | −1.02284e11 | + | 1.02284e11i | −0.832760 | + | 0.832760i | ||||
\(593\) | −1.30080e11 | − | 1.30080e11i | −1.05194 | − | 1.05194i | −0.998575 | − | 0.0533661i | \(-0.983005\pi\) |
−0.0533661 | − | 0.998575i | \(-0.516995\pi\) | |||||||
\(594\) | − | 1.69985e10i | − | 0.136542i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.40067e10 | −0.428018 | ||||||||
\(597\) | −1.85166e10 | + | 1.85166e10i | −0.145768 | + | 0.145768i | ||||
\(598\) | −7.18404e10 | − | 7.18404e10i | −0.561777 | − | 0.561777i | ||||
\(599\) | − | 2.34286e11i | − | 1.81986i | −0.414758 | − | 0.909932i | \(-0.636134\pi\) | ||
0.414758 | − | 0.909932i | \(-0.363866\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.22178e11 | −0.936475 | −0.468237 | − | 0.883603i | \(-0.655111\pi\) | ||||
−0.468237 | + | 0.883603i | \(0.655111\pi\) | |||||||
\(602\) | 2.05462e10 | − | 2.05462e10i | 0.156439 | − | 0.156439i | ||||
\(603\) | −3.65510e10 | − | 3.65510e10i | −0.276459 | − | 0.276459i | ||||
\(604\) | 2.42397e10i | 0.182129i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.81655e8 | 0.00727894 | ||||||||
\(607\) | 1.18161e11 | − | 1.18161e11i | 0.870404 | − | 0.870404i | −0.122112 | − | 0.992516i | \(-0.538967\pi\) |
0.992516 | + | 0.122112i | \(0.0389667\pi\) | |||||||
\(608\) | 7.46184e10 | + | 7.46184e10i | 0.546049 | + | 0.546049i | ||||
\(609\) | 2.25797e10i | 0.164153i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.10200e11 | −0.790708 | ||||||||
\(612\) | −1.27573e9 | + | 1.27573e9i | −0.00909393 | + | 0.00909393i | ||||
\(613\) | −1.40772e11 | − | 1.40772e11i | −0.996955 | − | 0.996955i | 0.00304005 | − | 0.999995i | \(-0.499032\pi\) |
−0.999995 | + | 0.00304005i | \(0.999032\pi\) | |||||||
\(614\) | 1.76351e11i | 1.24081i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.42393e10 | 0.0988930 | ||||||||
\(617\) | −5.57976e10 | + | 5.57976e10i | −0.385013 | + | 0.385013i | −0.872904 | − | 0.487892i | \(-0.837766\pi\) |
0.487892 | + | 0.872904i | \(0.337766\pi\) | |||||||
\(618\) | −1.54716e10 | − | 1.54716e10i | −0.106067 | − | 0.106067i | ||||
\(619\) | − | 2.74494e11i | − | 1.86969i | −0.355053 | − | 0.934846i | \(-0.615537\pi\) | ||
0.355053 | − | 0.934846i | \(-0.384463\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.26657e10 | 0.219647 | ||||||||
\(622\) | −1.56856e11 | + | 1.56856e11i | −1.04794 | + | 1.04794i | ||||
\(623\) | 2.19422e10 | + | 2.19422e10i | 0.145656 | + | 0.145656i | ||||
\(624\) | − | 6.46955e10i | − | 0.426713i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.30715e11 | 1.50237 | ||||||||
\(627\) | 5.41309e10 | − | 5.41309e10i | 0.350247 | − | 0.350247i | ||||
\(628\) | −4.37730e10 | − | 4.37730e10i | −0.281428 | − | 0.281428i | ||||
\(629\) | − | 2.03746e10i | − | 0.130163i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.79192e11 | 1.76111 | 0.880554 | − | 0.473946i | \(-0.157171\pi\) | ||||
0.880554 | + | 0.473946i | \(0.157171\pi\) | |||||||
\(632\) | 7.82835e10 | − | 7.82835e10i | 0.490684 | − | 0.490684i | ||||
\(633\) | −8.92812e10 | − | 8.92812e10i | −0.556090 | − | 0.556090i | ||||
\(634\) | 6.19879e10i | 0.383663i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.00907e10 | 0.122791 | ||||||||
\(637\) | 6.86202e10 | − | 6.86202e10i | 0.416768 | − | 0.416768i | ||||
\(638\) | 1.20462e11 | + | 1.20462e11i | 0.727056 | + | 0.727056i | ||||
\(639\) | 5.75931e8i | 0.00345436i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.94406e11 | −1.74387 | −0.871935 | − | 0.489622i | \(-0.837135\pi\) | ||||
−0.871935 | + | 0.489622i | \(0.837135\pi\) | |||||||
\(642\) | −1.00389e11 | + | 1.00389e11i | −0.590946 | + | 0.590946i | ||||
\(643\) | −7.60521e10 | − | 7.60521e10i | −0.444905 | − | 0.444905i | 0.448751 | − | 0.893657i | \(-0.351869\pi\) |
−0.893657 | + | 0.448751i | \(0.851869\pi\) | |||||||
\(644\) | − | 1.11512e10i | − | 0.0648301i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.61874e10 | −0.207791 | ||||||||
\(647\) | 1.14831e11 | − | 1.14831e11i | 0.655302 | − | 0.655302i | −0.298963 | − | 0.954265i | \(-0.596641\pi\) |
0.954265 | + | 0.298963i | \(0.0966407\pi\) | |||||||
\(648\) | 1.11764e10 | + | 1.11764e10i | 0.0633875 | + | 0.0633875i | ||||
\(649\) | − | 1.22631e11i | − | 0.691226i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.63872e9 | −0.0480978 | ||||||||
\(652\) | 3.81004e10 | − | 3.81004e10i | 0.210833 | − | 0.210833i | ||||
\(653\) | 2.21539e11 | + | 2.21539e11i | 1.21842 | + | 1.21842i | 0.968184 | + | 0.250240i | \(0.0805095\pi\) |
0.250240 | + | 0.968184i | \(0.419490\pi\) | |||||||
\(654\) | − | 1.30749e11i | − | 0.714708i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.53104e11 | 1.36673 | ||||||||
\(657\) | 6.66965e10 | − | 6.66965e10i | 0.357966 | − | 0.357966i | ||||
\(658\) | −3.80925e10 | − | 3.80925e10i | −0.203205 | − | 0.203205i | ||||
\(659\) | 2.01867e11i | 1.07034i | 0.844744 | + | 0.535171i | \(0.179753\pi\) | ||||
−0.844744 | + | 0.535171i | \(0.820247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.01557e11 | 0.531993 | 0.265996 | − | 0.963974i | \(-0.414299\pi\) | ||||
0.265996 | + | 0.963974i | \(0.414299\pi\) | |||||||
\(662\) | 1.68947e10 | − | 1.68947e10i | 0.0879669 | − | 0.0879669i | ||||
\(663\) | 6.44356e9 | + | 6.44356e9i | 0.0333482 | + | 0.0333482i | ||||
\(664\) | 2.32732e11i | 1.19725i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.27421e10 | 0.369734 | ||||||||
\(667\) | −2.31490e11 | + | 2.31490e11i | −1.16958 | + | 1.16958i | ||||
\(668\) | 4.15515e10 | + | 4.15515e10i | 0.208680 | + | 0.208680i | ||||
\(669\) | − | 2.16817e11i | − | 1.08241i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.18520e11 | 1.07796 | ||||||||
\(672\) | 9.18549e9 | − | 9.18549e9i | 0.0450428 | − | 0.0450428i | ||||
\(673\) | 1.52057e11 | + | 1.52057e11i | 0.741220 | + | 0.741220i | 0.972813 | − | 0.231593i | \(-0.0743937\pi\) |
−0.231593 | + | 0.972813i | \(0.574394\pi\) | |||||||
\(674\) | 7.43724e10i | 0.360390i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.77428e10 | −0.180737 | ||||||||
\(677\) | 1.50332e11 | − | 1.50332e11i | 0.715643 | − | 0.715643i | −0.252067 | − | 0.967710i | \(-0.581110\pi\) |
0.967710 | + | 0.252067i | \(0.0811103\pi\) | |||||||
\(678\) | 5.92116e10 | + | 5.92116e10i | 0.280213 | + | 0.280213i | ||||
\(679\) | 5.50459e10i | 0.258968i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.55381e10 | 0.0722453 | ||||||||
\(682\) | −4.60873e10 | + | 4.60873e10i | −0.213031 | + | 0.213031i | ||||
\(683\) | 1.99757e11 | + | 1.99757e11i | 0.917952 | + | 0.917952i | 0.996880 | − | 0.0789283i | \(-0.0251498\pi\) |
−0.0789283 | + | 0.996880i | \(0.525150\pi\) | |||||||
\(684\) | − | 2.90081e10i | − | 0.132524i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.67781e10 | 0.436999 | ||||||||
\(687\) | −6.14841e10 | + | 6.14841e10i | −0.276017 | + | 0.276017i | ||||
\(688\) | 1.89692e11 | + | 1.89692e11i | 0.846633 | + | 0.846633i | ||||
\(689\) | − | 1.01476e11i | − | 0.450284i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.62540e11 | 0.712933 | 0.356467 | − | 0.934308i | \(-0.383981\pi\) | ||||
0.356467 | + | 0.934308i | \(0.383981\pi\) | |||||||
\(692\) | 8.22998e9 | − | 8.22998e9i | 0.0358901 | − | 0.0358901i | ||||
\(693\) | −6.66349e9 | − | 6.66349e9i | −0.0288914 | − | 0.0288914i | ||||
\(694\) | − | 2.11840e11i | − | 0.913207i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.58407e11 | −0.675050 | ||||||||
\(697\) | −2.52087e10 | + | 2.52087e10i | −0.106812 | + | 0.106812i | ||||
\(698\) | 1.96294e11 | + | 1.96294e11i | 0.826961 | + | 0.826961i | ||||
\(699\) | − | 6.35489e10i | − | 0.266195i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.42435e11 | −1.83222 | −0.916109 | − | 0.400929i | \(-0.868687\pi\) | ||||
−0.916109 | + | 0.400929i | \(0.868687\pi\) | |||||||
\(702\) | −2.30051e10 | + | 2.30051e10i | −0.0947272 | + | 0.0947272i | ||||
\(703\) | 2.31644e11 | + | 2.31644e11i | 0.948416 | + | 0.948416i | ||||
\(704\) | 8.70298e10i | 0.354305i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.44588e11 | 1.38702 | ||||||||
\(707\) | 3.84813e8 | − | 3.84813e8i | 0.00154018 | − | 0.00154018i | ||||
\(708\) | −3.28581e10 | − | 3.28581e10i | −0.130770 | − | 0.130770i | ||||
\(709\) | 4.15887e11i | 1.64585i | 0.568149 | + | 0.822926i | \(0.307660\pi\) | ||||
−0.568149 | + | 0.822926i | \(0.692340\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.32678e10 | −0.286705 | ||||||||
\(712\) | −1.53934e11 | + | 1.53934e11i | −0.598982 | + | 0.598982i | ||||
\(713\) | −8.85650e10 | − | 8.85650e10i | −0.342692 | − | 0.342692i | ||||
\(714\) | 4.45466e9i | 0.0171404i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.96109e10 | −0.264865 | ||||||||
\(717\) | 7.95847e10 | − | 7.95847e10i | 0.301129 | − | 0.301129i | ||||
\(718\) | −1.81600e11 | − | 1.81600e11i | −0.683311 | − | 0.683311i | ||||
\(719\) | 7.73071e9i | 0.0289270i | 0.999895 | + | 0.0144635i | \(0.00460404\pi\) | ||||
−0.999895 | + | 0.0144635i | \(0.995396\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.21298e10 | −0.0448863 | ||||||||
\(722\) | 1.93226e11 | − | 1.93226e11i | 0.711078 | − | 0.711078i | ||||
\(723\) | 2.47347e10 | + | 2.47347e10i | 0.0905219 | + | 0.0905219i | ||||
\(724\) | 8.87845e10i | 0.323134i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.11040e11 | 0.399697 | ||||||||
\(727\) | −1.02377e11 | + | 1.02377e11i | −0.366492 | + | 0.366492i | −0.866196 | − | 0.499704i | \(-0.833442\pi\) |
0.499704 | + | 0.866196i | \(0.333442\pi\) | |||||||
\(728\) | −1.92709e10 | − | 1.92709e10i | −0.0686081 | − | 0.0686081i | ||||
\(729\) | − | 1.04604e10i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.77860e10 | −0.132331 | ||||||||
\(732\) | 5.85511e10 | − | 5.85511e10i | 0.203935 | − | 0.203935i | ||||
\(733\) | −1.73130e11 | − | 1.73130e11i | −0.599730 | − | 0.599730i | 0.340510 | − | 0.940241i | \(-0.389400\pi\) |
−0.940241 | + | 0.340510i | \(0.889400\pi\) | |||||||
\(734\) | − | 1.32874e11i | − | 0.457778i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.88341e11 | 0.641851 | ||||||||
\(737\) | −1.52881e11 | + | 1.52881e11i | −0.518182 | + | 0.518182i | ||||
\(738\) | −9.00011e10 | − | 9.00011e10i | −0.303405 | − | 0.303405i | ||||
\(739\) | − | 1.63608e11i | − | 0.548563i | −0.961649 | − | 0.274281i | \(-0.911560\pi\) | ||
0.961649 | − | 0.274281i | \(-0.0884400\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.46517e11 | −0.485976 | ||||||||
\(742\) | 3.50769e10 | − | 3.50769e10i | 0.115719 | − | 0.115719i | ||||
\(743\) | 3.99366e11 | + | 3.99366e11i | 1.31044 | + | 1.31044i | 0.921092 | + | 0.389345i | \(0.127299\pi\) |
0.389345 | + | 0.921092i | \(0.372701\pi\) | |||||||
\(744\) | − | 6.06043e10i | − | 0.197793i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.19066e11 | 1.03021 | ||||||||
\(747\) | 1.08910e11 | − | 1.08910e11i | 0.349773 | − | 0.349773i | ||||
\(748\) | 5.33593e9 | + | 5.33593e9i | 0.0170453 | + | 0.0170453i | ||||
\(749\) | 7.87062e10i | 0.250082i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.42899e10 | −0.264982 | −0.132491 | − | 0.991184i | \(-0.542297\pi\) | ||||
−0.132491 | + | 0.991184i | \(0.542297\pi\) | |||||||
\(752\) | 3.51688e11 | − | 3.51688e11i | 1.09973 | − | 1.09973i | ||||
\(753\) | −1.12038e11 | − | 1.12038e11i | −0.348487 | − | 0.348487i | ||||
\(754\) | − | 3.26057e11i | − | 1.00881i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.57088e9 | −0.0109317 | ||||||||
\(757\) | −1.30447e11 | + | 1.30447e11i | −0.397237 | + | 0.397237i | −0.877257 | − | 0.480020i | \(-0.840629\pi\) |
0.480020 | + | 0.877257i | \(0.340629\pi\) | |||||||
\(758\) | −3.67152e11 | − | 3.67152e11i | −1.11216 | − | 1.11216i | ||||
\(759\) | − | 1.36629e11i | − | 0.411697i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.33668e10 | 0.188940 | 0.0944698 | − | 0.995528i | \(-0.469884\pi\) | ||||
0.0944698 | + | 0.995528i | \(0.469884\pi\) | |||||||
\(762\) | −1.93753e11 | + | 1.93753e11i | −0.574682 | + | 0.574682i | ||||
\(763\) | −5.12543e10 | − | 5.12543e10i | −0.151228 | − | 0.151228i | ||||
\(764\) | 1.26500e11i | 0.371292i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.24992e11 | −0.943968 | ||||||||
\(767\) | −1.65963e11 | + | 1.65963e11i | −0.479546 | + | 0.479546i | ||||
\(768\) | 1.14020e11 | + | 1.14020e11i | 0.327745 | + | 0.327745i | ||||
\(769\) | 3.55053e10i | 0.101528i | 0.998711 | + | 0.0507642i | \(0.0161657\pi\) | ||||
−0.998711 | + | 0.0507642i | \(0.983834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.69561e11 | 0.479852 | ||||||||
\(772\) | 2.28926e10 | − | 2.28926e10i | 0.0644503 | − | 0.0644503i | ||||
\(773\) | −2.87747e11 | − | 2.87747e11i | −0.805921 | − | 0.805921i | 0.178093 | − | 0.984014i | \(-0.443007\pi\) |
−0.984014 | + | 0.178093i | \(0.943007\pi\) | |||||||
\(774\) | − | 1.34905e11i | − | 0.375893i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.86171e11 | −1.06496 | ||||||||
\(777\) | 2.85152e10 | − | 2.85152e10i | 0.0782335 | − | 0.0782335i | ||||
\(778\) | −3.73443e11 | − | 3.73443e11i | −1.01931 | − | 1.01931i | ||||
\(779\) | − | 5.73208e11i | − | 1.55655i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.40893e9 | 0.00647469 | ||||||||
\(782\) | −4.56696e10 | + | 4.56696e10i | −0.122124 | + | 0.122124i | ||||
\(783\) | 7.41287e10 | + | 7.41287e10i | 0.197215 | + | 0.197215i | ||||
\(784\) | 4.37984e11i | 1.15930i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.79357e11 | −0.469925 | ||||||||
\(787\) | −6.58669e10 | + | 6.58669e10i | −0.171699 | + | 0.171699i | −0.787726 | − | 0.616026i | \(-0.788741\pi\) |
0.616026 | + | 0.787726i | \(0.288741\pi\) | |||||||
\(788\) | −4.75638e10 | − | 4.75638e10i | −0.123359 | − | 0.123359i | ||||
\(789\) | 3.99929e11i | 1.03199i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.64224e10 | 0.118583 | ||||||||
\(792\) | 4.67473e10 | − | 4.67473e10i | 0.118811 | − | 0.118811i | ||||
\(793\) | −2.95736e11 | − | 2.95736e11i | −0.747845 | − | 0.747845i | ||||
\(794\) | − | 1.17707e11i | − | 0.296156i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.15037e10 | 0.103380 | ||||||||
\(797\) | −3.21177e11 | + | 3.21177e11i | −0.795996 | + | 0.795996i | −0.982462 | − | 0.186465i | \(-0.940297\pi\) |
0.186465 | + | 0.982462i | \(0.440297\pi\) | |||||||
\(798\) | −5.06461e10 | − | 5.06461e10i | −0.124892 | − | 0.124892i | ||||
\(799\) | 7.00551e10i | 0.171891i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.44071e11 | 0.349983 | ||||||||
\(802\) | 3.29893e11 | − | 3.29893e11i | 0.797400 | − | 0.797400i | ||||
\(803\) | −2.78969e11 | − | 2.78969e11i | −0.670955 | − | 0.670955i | ||||
\(804\) | 8.19268e10i | 0.196066i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.24745e11 | 0.295586 | ||||||||
\(807\) | −5.34008e10 | + | 5.34008e10i | −0.125908 | + | 0.125908i | ||||
\(808\) | 2.69963e9 | + | 2.69963e9i | 0.00633372 | + | 0.00633372i | ||||
\(809\) | 5.25661e11i | 1.22719i | 0.789621 | + | 0.613595i | \(0.210277\pi\) | ||||
−0.789621 | + | 0.613595i | \(0.789723\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.31498e11 | −1.22862 | −0.614311 | − | 0.789064i | \(-0.710566\pi\) | ||||
−0.614311 | + | 0.789064i | \(0.710566\pi\) | |||||||
\(812\) | 2.53055e10 | − | 2.53055e10i | 0.0582091 | − | 0.0582091i | ||||
\(813\) | 6.15383e9 | + | 6.15383e9i | 0.0140859 | + | 0.0140859i | ||||
\(814\) | − | 3.04256e11i | − | 0.693013i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.11275e10 | −0.0927623 | ||||||||
\(817\) | 4.29598e11 | − | 4.29598e11i | 0.964216 | − | 0.964216i | ||||
\(818\) | −6.62115e11 | − | 6.62115e11i | −1.47884 | − | 1.47884i | ||||
\(819\) | 1.80362e10i | 0.0400875i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.70252e11 | −1.47525 | −0.737625 | − | 0.675211i | \(-0.764053\pi\) | ||||
−0.737625 | + | 0.675211i | \(0.764053\pi\) | |||||||
\(822\) | 1.40270e11 | − | 1.40270e11i | 0.307240 | − | 0.307240i | ||||
\(823\) | 2.18846e11 | + | 2.18846e11i | 0.477022 | + | 0.477022i | 0.904178 | − | 0.427156i | \(-0.140484\pi\) |
−0.427156 | + | 0.904178i | \(0.640484\pi\) | |||||||
\(824\) | − | 8.50961e10i | − | 0.184587i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.14736e11 | −0.246479 | ||||||||
\(827\) | −3.35456e11 | + | 3.35456e11i | −0.717155 | + | 0.717155i | −0.968022 | − | 0.250867i | \(-0.919284\pi\) |
0.250867 | + | 0.968022i | \(0.419284\pi\) | |||||||
\(828\) | −3.66090e10 | − | 3.66090e10i | −0.0778873 | − | 0.0778873i | ||||
\(829\) | 3.31479e11i | 0.701839i | 0.936406 | + | 0.350920i | \(0.114131\pi\) | ||||
−0.936406 | + | 0.350920i | \(0.885869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.68317e11 | 0.562657 | ||||||||
\(832\) | 1.17782e11 | − | 1.17782e11i | 0.245803 | − | 0.245803i | ||||
\(833\) | −4.36225e10 | − | 4.36225e10i | −0.0906005 | − | 0.0906005i | ||||
\(834\) | 4.83484e11i | 0.999350i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.21331e11 | −0.248397 | ||||||||
\(837\) | −2.83607e10 | + | 2.83607e10i | −0.0577850 | + | 0.0577850i | ||||
\(838\) | 6.63961e11 | + | 6.63961e11i | 1.34638 | + | 1.34638i | ||||
\(839\) | 1.20093e11i | 0.242365i | 0.992630 | + | 0.121183i | \(0.0386687\pi\) | ||||
−0.992630 | + | 0.121183i | \(0.961331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.50398e11 | −1.10025 | ||||||||
\(842\) | −3.73180e11 | + | 3.73180e11i | −0.742455 | + | 0.742455i | ||||
\(843\) | 6.68619e10 | + | 6.68619e10i | 0.132394 | + | 0.132394i | ||||
\(844\) | 2.00118e11i | 0.394381i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.50113e11 | −0.488264 | ||||||||
\(847\) | 4.35280e10 | − | 4.35280e10i | 0.0845736 | − | 0.0845736i | ||||
\(848\) | 3.23847e11 | + | 3.23847e11i | 0.626263 | + | 0.626263i | ||||
\(849\) | 1.17416e11i | 0.225995i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.84682e11 | 1.11481 | ||||||||
\(852\) | 6.45456e8 | − | 6.45456e8i | 0.00122492 | − | 0.00122492i | ||||
\(853\) | −1.17094e11 | − | 1.17094e11i | −0.221176 | − | 0.221176i | 0.587818 | − | 0.808993i | \(-0.299987\pi\) |
−0.808993 | + | 0.587818i | \(0.799987\pi\) | |||||||
\(854\) | − | 2.04452e11i | − | 0.384380i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.52158e11 | −1.02841 | ||||||||
\(857\) | 1.60077e11 | − | 1.60077e11i | 0.296759 | − | 0.296759i | −0.542984 | − | 0.839743i | \(-0.682705\pi\) |
0.839743 | + | 0.542984i | \(0.182705\pi\) | |||||||
\(858\) | 9.62224e10 | + | 9.62224e10i | 0.177553 | + | 0.177553i | ||||
\(859\) | − | 1.81742e10i | − | 0.0333797i | −0.999861 | − | 0.0166898i | \(-0.994687\pi\) | ||
0.999861 | − | 0.0166898i | \(-0.00531278\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.05617e10 | −0.128397 | ||||||||
\(862\) | 4.34474e10 | − | 4.34474e10i | 0.0786928 | − | 0.0786928i | ||||
\(863\) | 5.99083e11 | + | 5.99083e11i | 1.08005 | + | 1.08005i | 0.996504 | + | 0.0835450i | \(0.0266242\pi\) |
0.0835450 | + | 0.996504i | \(0.473376\pi\) | |||||||
\(864\) | − | 6.03115e10i | − | 0.108229i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.22474e11 | −0.217757 | ||||||||
\(867\) | −2.26579e11 | + | 2.26579e11i | −0.400999 | + | 0.400999i | ||||
\(868\) | 9.68156e9 | + | 9.68156e9i | 0.0170556 | + | 0.0170556i | ||||
\(869\) | 3.06454e11i | 0.537387i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.13804e11 | 0.718989 | ||||||||
\(872\) | 3.59571e11 | − | 3.59571e11i | 0.621898 | − | 0.621898i | ||||
\(873\) | 1.80714e11 | + | 1.80714e11i | 0.311125 | + | 0.311125i | ||||
\(874\) | − | 1.03846e12i | − | 1.77968i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.49496e11 | −0.253871 | ||||||||
\(877\) | 5.84260e11 | − | 5.84260e11i | 0.987661 | − | 0.987661i | −0.0122638 | − | 0.999925i | \(-0.503904\pi\) |
0.999925 | + | 0.0122638i | \(0.00390378\pi\) | |||||||
\(878\) | −4.01365e11 | − | 4.01365e11i | −0.675401 | − | 0.675401i | ||||
\(879\) | 5.56628e11i | 0.932416i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.18962e11 | 0.529463 | 0.264732 | − | 0.964322i | \(-0.414717\pi\) | ||||
0.264732 | + | 0.964322i | \(0.414717\pi\) | |||||||
\(882\) | 1.55743e11 | − | 1.55743e11i | 0.257356 | − | 0.257356i | ||||
\(883\) | 3.93523e11 | + | 3.93523e11i | 0.647333 | + | 0.647333i | 0.952348 | − | 0.305015i | \(-0.0986614\pi\) |
−0.305015 | + | 0.952348i | \(0.598661\pi\) | |||||||
\(884\) | − | 1.44428e10i | − | 0.0236507i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.56979e11 | 0.579305 | ||||||||
\(887\) | −1.97346e11 | + | 1.97346e11i | −0.318812 | + | 0.318812i | −0.848311 | − | 0.529499i | \(-0.822380\pi\) |
0.529499 | + | 0.848311i | \(0.322380\pi\) | |||||||
\(888\) | 2.00047e11 | + | 2.00047e11i | 0.321721 | + | 0.321721i | ||||
\(889\) | 1.51904e11i | 0.243199i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.37521e10 | −0.0694206 | ||||||||
\(892\) | −2.42991e11 | + | 2.42991e11i | −0.383823 | + | 0.383823i | ||||
\(893\) | −7.96473e11 | − | 7.96473e11i | −1.25246 | − | 1.25246i | ||||
\(894\) | 6.19116e11i | 0.969219i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.52537e11 | 0.236671 | ||||||||
\(897\) | −1.84909e11 | + | 1.84909e11i | −0.285619 | + | 0.285619i | ||||
\(898\) | 9.58631e11 | + | 9.58631e11i | 1.47417 | + | 1.47417i | ||||
\(899\) | − | 4.01963e11i | − | 0.615386i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.45093e10 | −0.0978866 | ||||||||
\(902\) | −3.76444e11 | + | 3.76444e11i | −0.568688 | + | 0.568688i | ||||
\(903\) | −5.28834e10 | − | 5.28834e10i | −0.0795368 | − | 0.0795368i | ||||
\(904\) | 3.25673e11i | 0.487650i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.77876e11 | 0.412419 | ||||||||
\(907\) | −1.55260e10 | + | 1.55260e10i | −0.0229419 | + | 0.0229419i | −0.718485 | − | 0.695543i | \(-0.755164\pi\) |
0.695543 | + | 0.718485i | \(0.255164\pi\) | |||||||
\(908\) | −1.74138e10 | − | 1.74138e10i | −0.0256183 | − | 0.0256183i | ||||
\(909\) | − | 2.52666e9i | − | 0.00370077i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.70829e11 | 1.40951 | 0.704757 | − | 0.709449i | \(-0.251056\pi\) | ||||
0.704757 | + | 0.709449i | \(0.251056\pi\) | |||||||
\(912\) | 4.67588e11 | − | 4.67588e11i | 0.675903 | − | 0.675903i | ||||
\(913\) | −4.55535e11 | − | 4.55535e11i | −0.655600 | − | 0.655600i | ||||
\(914\) | − | 8.61671e11i | − | 1.23469i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.37813e11 | 0.195753 | ||||||||
\(917\) | −7.03089e10 | + | 7.03089e10i | −0.0994335 | + | 0.0994335i | ||||
\(918\) | 1.46245e10 | + | 1.46245e10i | 0.0205926 | + | 0.0205926i | ||||
\(919\) | 2.16464e11i | 0.303475i | 0.988421 | + | 0.151738i | \(0.0484868\pi\) | ||||
−0.988421 | + | 0.151738i | \(0.951513\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.53907e11 | 0.630854 | ||||||||
\(922\) | 1.09136e12 | − | 1.09136e12i | 1.51023 | − | 1.51023i | ||||
\(923\) | −3.26014e9 | − | 3.26014e9i | −0.00449189 | − | 0.00449189i | ||||
\(924\) | 1.49358e10i | 0.0204899i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.38336e11 | −0.868172 | ||||||||
\(927\) | −3.98220e10 | + | 3.98220e10i | −0.0539267 | + | 0.0539267i | ||||
\(928\) | 4.27405e11 | + | 4.27405e11i | 0.576299 | + | 0.576299i | ||||
\(929\) | − | 2.35669e11i | − | 0.316402i | −0.987407 | − | 0.158201i | \(-0.949431\pi\) | ||
0.987407 | − | 0.158201i | \(-0.0505694\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.91910e11 | 1.32030 | ||||||||
\(932\) | −7.12204e10 | + | 7.12204e10i | −0.0943932 | + | 0.0943932i | ||||
\(933\) | 4.03727e11 | + | 4.03727e11i | 0.532797 | + | 0.532797i | ||||
\(934\) | − | 8.68195e11i | − | 1.14085i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.26532e11 | −0.164852 | ||||||||
\(937\) | −9.84325e11 | + | 9.84325e11i | −1.27697 | + | 1.27697i | −0.334613 | + | 0.942356i | \(0.608606\pi\) |
−0.942356 | + | 0.334613i | \(0.891394\pi\) | |||||||
\(938\) | 1.43039e11 | + | 1.43039e11i | 0.184774 | + | 0.184774i | ||||
\(939\) | − | 5.93832e11i | − | 0.763838i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.48728e12 | 1.89686 | 0.948430 | − | 0.316986i | \(-0.102671\pi\) | ||||
0.948430 | + | 0.316986i | \(0.102671\pi\) | |||||||
\(942\) | −5.01800e11 | + | 5.01800e11i | −0.637275 | + | 0.637275i | ||||
\(943\) | −7.23405e11 | − | 7.23405e11i | −0.914818 | − | 0.914818i | ||||
\(944\) | − | 1.05930e12i | − | 1.33392i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.64262e11 | −0.704558 | ||||||||
\(947\) | −5.61976e11 | + | 5.61976e11i | −0.698743 | + | 0.698743i | −0.964139 | − | 0.265396i | \(-0.914497\pi\) |
0.265396 | + | 0.964139i | \(0.414497\pi\) | |||||||
\(948\) | 8.21125e10 | + | 8.21125e10i | 0.101666 | + | 0.101666i | ||||
\(949\) | 7.55089e11i | 0.930965i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.59549e11 | 0.195062 | ||||||||
\(952\) | −1.22507e10 | + | 1.22507e10i | −0.0149146 | + | 0.0149146i | ||||
\(953\) | −5.83237e11 | − | 5.83237e11i | −0.707088 | − | 0.707088i | 0.258834 | − | 0.965922i | \(-0.416662\pi\) |
−0.965922 | + | 0.258834i | \(0.916662\pi\) | |||||||
\(954\) | − | 2.30313e11i | − | 0.278052i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.78384e11 | −0.213562 | ||||||||
\(957\) | 3.10055e11 | − | 3.10055e11i | 0.369650 | − | 0.369650i | ||||
\(958\) | 1.26107e11 | + | 1.26107e11i | 0.149719 | + | 0.149719i | ||||
\(959\) | − | 1.09973e11i | − | 0.130020i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.99105e11 | −0.819688 | ||||||||
\(962\) | −4.11767e11 | + | 4.11767e11i | −0.480785 | + | 0.480785i | ||||
\(963\) | 2.58390e11 | + | 2.58390e11i | 0.300449 | + | 0.300449i | ||||
\(964\) | − | 5.54413e10i | − | 0.0641985i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.27834e11 | −0.146804 | ||||||||
\(967\) | 1.37758e10 | − | 1.37758e10i | 0.0157547 | − | 0.0157547i | −0.699186 | − | 0.714940i | \(-0.746454\pi\) |
0.714940 | + | 0.699186i | \(0.246454\pi\) | |||||||
\(968\) | 3.05368e11 | + | 3.05368e11i | 0.347794 | + | 0.347794i | ||||
\(969\) | 9.31421e10i | 0.105646i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.31026e11 | 0.597364 | 0.298682 | − | 0.954353i | \(-0.403453\pi\) | ||||
0.298682 | + | 0.954353i | \(0.403453\pi\) | |||||||
\(972\) | −1.17231e10 | + | 1.17231e10i | −0.0131334 | + | 0.0131334i | ||||
\(973\) | 1.89528e11 | + | 1.89528e11i | 0.211457 | + | 0.211457i | ||||
\(974\) | − | 9.84672e10i | − | 0.109410i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.88760e12 | 2.08023 | ||||||||
\(977\) | 7.35034e11 | − | 7.35034e11i | 0.806731 | − | 0.806731i | −0.177406 | − | 0.984138i | \(-0.556771\pi\) |
0.984138 | + | 0.177406i | \(0.0567706\pi\) | |||||||
\(978\) | −4.36771e11 | − | 4.36771e11i | −0.477418 | − | 0.477418i | ||||
\(979\) | − | 6.02601e11i | − | 0.655992i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.36533e11 | −0.363373 | ||||||||
\(982\) | −1.32508e12 | + | 1.32508e12i | −1.42494 | + | 1.42494i | ||||
\(983\) | −1.73787e10 | − | 1.73787e10i | −0.0186124 | − | 0.0186124i | 0.697739 | − | 0.716352i | \(-0.254189\pi\) |
−0.716352 | + | 0.697739i | \(0.754189\pi\) | |||||||
\(984\) | − | 4.95021e11i | − | 0.528011i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.07277e11 | −0.219303 | ||||||||
\(987\) | −9.80455e10 | + | 9.80455e10i | −0.103314 | + | 0.103314i | ||||
\(988\) | 1.64204e11 | + | 1.64204e11i | 0.172328 | + | 0.172328i | ||||
\(989\) | − | 1.08433e12i | − | 1.13338i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.57804e11 | −0.163615 | −0.0818077 | − | 0.996648i | \(-0.526069\pi\) | ||||
−0.0818077 | + | 0.996648i | \(0.526069\pi\) | |||||||
\(992\) | −1.63520e11 | + | 1.63520e11i | −0.168859 | + | 0.168859i | ||||
\(993\) | −4.34850e10 | − | 4.34850e10i | −0.0447242 | − | 0.0447242i | ||||
\(994\) | − | 2.25384e9i | − | 0.00230876i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.44116e11 | −0.248061 | ||||||||
\(997\) | −1.62852e11 | + | 1.62852e11i | −0.164821 | + | 0.164821i | −0.784699 | − | 0.619877i | \(-0.787182\pi\) |
0.619877 | + | 0.784699i | \(0.287182\pi\) | |||||||
\(998\) | 5.87326e11 | + | 5.87326e11i | 0.592048 | + | 0.592048i | ||||
\(999\) | − | 1.87230e11i | − | 0.187980i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 75.9.f.c.43.2 | yes | 8 | |
5.2 | odd | 4 | inner | 75.9.f.c.7.2 | ✓ | 8 | |
5.3 | odd | 4 | inner | 75.9.f.c.7.3 | yes | 8 | |
5.4 | even | 2 | inner | 75.9.f.c.43.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.9.f.c.7.2 | ✓ | 8 | 5.2 | odd | 4 | inner | |
75.9.f.c.7.3 | yes | 8 | 5.3 | odd | 4 | inner | |
75.9.f.c.43.2 | yes | 8 | 1.1 | even | 1 | trivial | |
75.9.f.c.43.3 | yes | 8 | 5.4 | even | 2 | inner |