Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-18.7189\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −18.7189 | −1.65454 | −0.827268 | − | 0.561808i | \(-0.810106\pi\) | ||||
−0.827268 | + | 0.561808i | \(0.810106\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 222.398 | 1.73749 | ||||||||
\(5\) | −443.832 | −1.58790 | −0.793951 | − | 0.607982i | \(-0.791979\pi\) | ||||
−0.793951 | + | 0.607982i | \(0.791979\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1695.79 | −1.86865 | −0.934326 | − | 0.356419i | \(-0.883997\pi\) | ||||
−0.934326 | + | 0.356419i | \(0.883997\pi\) | |||||||
\(8\) | −1767.03 | −1.22020 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8308.06 | 2.62724 | ||||||||
\(11\) | 2763.59 | 0.626036 | 0.313018 | − | 0.949747i | \(-0.398660\pi\) | ||||
0.313018 | + | 0.949747i | \(0.398660\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10956.4 | −1.38314 | −0.691568 | − | 0.722311i | \(-0.743080\pi\) | ||||
−0.691568 | + | 0.722311i | \(0.743080\pi\) | |||||||
\(14\) | 31743.3 | 3.09175 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4610.01 | 0.281373 | ||||||||
\(17\) | 17168.5 | 0.847541 | 0.423771 | − | 0.905770i | \(-0.360706\pi\) | ||||
0.423771 | + | 0.905770i | \(0.360706\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −41280.8 | −1.38074 | −0.690368 | − | 0.723459i | \(-0.742551\pi\) | ||||
−0.690368 | + | 0.723459i | \(0.742551\pi\) | |||||||
\(20\) | −98707.5 | −2.75896 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −51731.4 | −1.03580 | ||||||||
\(23\) | −82535.2 | −1.41446 | −0.707232 | − | 0.706982i | \(-0.750056\pi\) | ||||
−0.707232 | + | 0.706982i | \(0.750056\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 118862. | 1.52143 | ||||||||
\(26\) | 205092. | 2.28845 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −377140. | −3.24676 | ||||||||
\(29\) | −103089. | −0.784912 | −0.392456 | − | 0.919771i | \(-0.628375\pi\) | ||||
−0.392456 | + | 0.919771i | \(0.628375\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −162172. | −0.977709 | −0.488854 | − | 0.872365i | \(-0.662585\pi\) | ||||
−0.488854 | + | 0.872365i | \(0.662585\pi\) | |||||||
\(32\) | 139886. | 0.754656 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −321376. | −1.40229 | ||||||||
\(35\) | 752645. | 2.96724 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 446923. | 1.45053 | 0.725265 | − | 0.688470i | \(-0.241717\pi\) | ||||
0.725265 | + | 0.688470i | \(0.241717\pi\) | |||||||
\(38\) | 772732. | 2.28448 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 784266. | 1.93755 | ||||||||
\(41\) | −371488. | −0.841785 | −0.420893 | − | 0.907111i | \(-0.638283\pi\) | ||||
−0.420893 | + | 0.907111i | \(0.638283\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −790401. | −1.51603 | −0.758015 | − | 0.652237i | \(-0.773831\pi\) | ||||
−0.758015 | + | 0.652237i | \(0.773831\pi\) | |||||||
\(44\) | 614617. | 1.08773 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.54497e6 | 2.34028 | ||||||||
\(47\) | 1.11011e6 | 1.55964 | 0.779818 | − | 0.626007i | \(-0.215312\pi\) | ||||
0.779818 | + | 0.626007i | \(0.215312\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.05215e6 | 2.49186 | ||||||||
\(50\) | −2.22497e6 | −2.51726 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.43668e6 | −2.40318 | ||||||||
\(53\) | 771292. | 0.711628 | 0.355814 | − | 0.934557i | \(-0.384204\pi\) | ||||
0.355814 | + | 0.934557i | \(0.384204\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.22657e6 | −0.994083 | ||||||||
\(56\) | 2.99652e6 | 2.28012 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.92972e6 | 1.29867 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −211813. | −0.119481 | −0.0597403 | − | 0.998214i | \(-0.519027\pi\) | ||||
−0.0597403 | + | 0.998214i | \(0.519027\pi\) | |||||||
\(62\) | 3.03568e6 | 1.61765 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.20860e6 | −1.52998 | ||||||||
\(65\) | 4.86279e6 | 2.19628 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.48116e6 | 0.601644 | 0.300822 | − | 0.953680i | \(-0.402739\pi\) | ||||
0.300822 | + | 0.953680i | \(0.402739\pi\) | |||||||
\(68\) | 3.81824e6 | 1.47259 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.40887e7 | −4.90940 | ||||||||
\(71\) | −3.40336e6 | −1.12851 | −0.564253 | − | 0.825602i | \(-0.690836\pi\) | ||||
−0.564253 | + | 0.825602i | \(0.690836\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.93442e6 | −1.18372 | −0.591862 | − | 0.806040i | \(-0.701607\pi\) | ||||
−0.591862 | + | 0.806040i | \(0.701607\pi\) | |||||||
\(74\) | −8.36592e6 | −2.39995 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.18078e6 | −2.39901 | ||||||||
\(77\) | −4.68646e6 | −1.16984 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.55385e6 | 1.03916 | 0.519582 | − | 0.854421i | \(-0.326088\pi\) | ||||
0.519582 | + | 0.854421i | \(0.326088\pi\) | |||||||
\(80\) | −2.04607e6 | −0.446793 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.95386e6 | 1.39276 | ||||||||
\(83\) | 4.51953e6 | 0.867602 | 0.433801 | − | 0.901009i | \(-0.357172\pi\) | ||||
0.433801 | + | 0.901009i | \(0.357172\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.61992e6 | −1.34581 | ||||||||
\(86\) | 1.47955e7 | 2.50833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.88336e6 | −0.763887 | ||||||||
\(89\) | 4.21568e6 | 0.633874 | 0.316937 | − | 0.948447i | \(-0.397346\pi\) | ||||
0.316937 | + | 0.948447i | \(0.397346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.85797e7 | 2.58460 | ||||||||
\(92\) | −1.83557e7 | −2.45761 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.07800e7 | −2.58047 | ||||||||
\(95\) | 1.83217e7 | 2.19247 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.59925e6 | −0.177916 | −0.0889579 | − | 0.996035i | \(-0.528354\pi\) | ||||
−0.0889579 | + | 0.996035i | \(0.528354\pi\) | |||||||
\(98\) | −3.84141e7 | −4.12287 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.64347e7 | 2.64347 | ||||||||
\(101\) | 1.38691e6 | 0.133944 | 0.0669719 | − | 0.997755i | \(-0.478666\pi\) | ||||
0.0669719 | + | 0.997755i | \(0.478666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.11202e6 | −0.100273 | −0.0501363 | − | 0.998742i | \(-0.515966\pi\) | ||||
−0.0501363 | + | 0.998742i | \(0.515966\pi\) | |||||||
\(104\) | 1.93603e7 | 1.68770 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.44378e7 | −1.17741 | ||||||||
\(107\) | 2.40434e7 | 1.89737 | 0.948685 | − | 0.316223i | \(-0.102415\pi\) | ||||
0.948685 | + | 0.316223i | \(0.102415\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.06281e7 | 0.786070 | 0.393035 | − | 0.919524i | \(-0.371425\pi\) | ||||
0.393035 | + | 0.919524i | \(0.371425\pi\) | |||||||
\(110\) | 2.29601e7 | 1.64475 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.81761e6 | −0.525788 | ||||||||
\(113\) | −1.82364e7 | −1.18895 | −0.594477 | − | 0.804112i | \(-0.702641\pi\) | ||||
−0.594477 | + | 0.804112i | \(0.702641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.66318e7 | 2.24603 | ||||||||
\(116\) | −2.29269e7 | −1.36377 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.84447e6 | 0.215402 | ||||||||
\(119\) | −2.91141e7 | −1.58376 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.18497e7 | −0.608079 | ||||||||
\(122\) | 3.96491e6 | 0.197685 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.60667e7 | −1.69876 | ||||||||
\(125\) | −1.80803e7 | −0.827982 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.28606e7 | 0.557119 | 0.278559 | − | 0.960419i | \(-0.410143\pi\) | ||||
0.278559 | + | 0.960419i | \(0.410143\pi\) | |||||||
\(128\) | 4.21561e7 | 1.77675 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.10262e7 | −3.63383 | ||||||||
\(131\) | 1.03027e7 | 0.400405 | 0.200203 | − | 0.979754i | \(-0.435840\pi\) | ||||
0.200203 | + | 0.979754i | \(0.435840\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.00035e7 | 2.58011 | ||||||||
\(134\) | −2.77257e7 | −0.995442 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.03373e7 | −1.03417 | ||||||||
\(137\) | 4.73008e7 | 1.57161 | 0.785807 | − | 0.618471i | \(-0.212248\pi\) | ||||
0.785807 | + | 0.618471i | \(0.212248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.76637e7 | 1.82117 | 0.910585 | − | 0.413322i | \(-0.135631\pi\) | ||||
0.910585 | + | 0.413322i | \(0.135631\pi\) | |||||||
\(140\) | 1.67387e8 | 5.15553 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.37073e7 | 1.86715 | ||||||||
\(143\) | −3.02789e7 | −0.865893 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.57544e7 | 1.24636 | ||||||||
\(146\) | 7.36480e7 | 1.95851 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.93949e7 | 2.52028 | ||||||||
\(149\) | −9.45541e6 | −0.234168 | −0.117084 | − | 0.993122i | \(-0.537355\pi\) | ||||
−0.117084 | + | 0.993122i | \(0.537355\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.54572e7 | −0.365353 | −0.182677 | − | 0.983173i | \(-0.558476\pi\) | ||||
−0.182677 | + | 0.983173i | \(0.558476\pi\) | |||||||
\(152\) | 7.29446e7 | 1.68477 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.77255e7 | 1.93555 | ||||||||
\(155\) | 7.19770e7 | 1.55251 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.62627e7 | 0.747845 | 0.373922 | − | 0.927460i | \(-0.378013\pi\) | ||||
0.373922 | + | 0.927460i | \(0.378013\pi\) | |||||||
\(158\) | −8.52432e7 | −1.71933 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.20858e7 | −1.19832 | ||||||||
\(161\) | 1.39962e8 | 2.64314 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.27645e7 | 0.954301 | 0.477151 | − | 0.878822i | \(-0.341670\pi\) | ||||
0.477151 | + | 0.878822i | \(0.341670\pi\) | |||||||
\(164\) | −8.26183e7 | −1.46259 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.46008e7 | −1.43548 | ||||||||
\(167\) | 7.36648e6 | 0.122392 | 0.0611959 | − | 0.998126i | \(-0.480509\pi\) | ||||
0.0611959 | + | 0.998126i | \(0.480509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.72936e7 | 0.913066 | ||||||||
\(170\) | 1.42637e8 | 2.22669 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.75784e8 | −2.63408 | ||||||||
\(173\) | −7.87542e7 | −1.15641 | −0.578206 | − | 0.815891i | \(-0.696247\pi\) | ||||
−0.578206 | + | 0.815891i | \(0.696247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.01564e8 | −2.84303 | ||||||||
\(176\) | 1.27402e7 | 0.176149 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.89130e7 | −1.04877 | ||||||||
\(179\) | −2.13413e7 | −0.278121 | −0.139061 | − | 0.990284i | \(-0.544408\pi\) | ||||
−0.139061 | + | 0.990284i | \(0.544408\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.72243e7 | 0.215907 | 0.107953 | − | 0.994156i | \(-0.465570\pi\) | ||||
0.107953 | + | 0.994156i | \(0.465570\pi\) | |||||||
\(182\) | −3.47792e8 | −4.27631 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.45843e8 | 1.72592 | ||||||||
\(185\) | −1.98359e8 | −2.30330 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.74466e7 | 0.530591 | ||||||||
\(188\) | 2.46886e8 | 2.70984 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.42963e8 | −3.62752 | ||||||||
\(191\) | −2.66378e7 | −0.276619 | −0.138309 | − | 0.990389i | \(-0.544167\pi\) | ||||
−0.138309 | + | 0.990389i | \(0.544167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.69658e8 | −1.69873 | −0.849365 | − | 0.527807i | \(-0.823015\pi\) | ||||
−0.849365 | + | 0.527807i | \(0.823015\pi\) | |||||||
\(194\) | 2.99362e7 | 0.294368 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.56396e8 | 4.32957 | ||||||||
\(197\) | −6.41433e7 | −0.597750 | −0.298875 | − | 0.954292i | \(-0.596611\pi\) | ||||
−0.298875 | + | 0.954292i | \(0.596611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.14787e8 | −1.03254 | −0.516269 | − | 0.856427i | \(-0.672679\pi\) | ||||
−0.516269 | + | 0.856427i | \(0.672679\pi\) | |||||||
\(200\) | −2.10033e8 | −1.85645 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.59614e7 | −0.221615 | ||||||||
\(203\) | 1.74818e8 | 1.46673 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.64878e8 | 1.33667 | ||||||||
\(206\) | 2.08158e7 | 0.165905 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.05090e7 | −0.389177 | ||||||||
\(209\) | −1.14083e8 | −0.864389 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.79484e6 | 0.0497956 | 0.0248978 | − | 0.999690i | \(-0.492074\pi\) | ||||
0.0248978 | + | 0.999690i | \(0.492074\pi\) | |||||||
\(212\) | 1.71534e8 | 1.23644 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.50066e8 | −3.13926 | ||||||||
\(215\) | 3.50805e8 | 2.40731 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.75009e8 | 1.82700 | ||||||||
\(218\) | −1.98946e8 | −1.30058 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.72787e8 | −1.72721 | ||||||||
\(221\) | −1.88104e8 | −1.17227 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.78892e8 | 1.68410 | 0.842052 | − | 0.539396i | \(-0.181347\pi\) | ||||
0.842052 | + | 0.539396i | \(0.181347\pi\) | |||||||
\(224\) | −2.37217e8 | −1.41019 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.41367e8 | 1.96717 | ||||||||
\(227\) | −4.19942e7 | −0.238286 | −0.119143 | − | 0.992877i | \(-0.538015\pi\) | ||||
−0.119143 | + | 0.992877i | \(0.538015\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.50761e7 | −0.0829591 | −0.0414795 | − | 0.999139i | \(-0.513207\pi\) | ||||
−0.0414795 | + | 0.999139i | \(0.513207\pi\) | |||||||
\(230\) | −6.85707e8 | −3.71613 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.82163e8 | 0.957748 | ||||||||
\(233\) | −5.24867e7 | −0.271834 | −0.135917 | − | 0.990720i | \(-0.543398\pi\) | ||||
−0.135917 | + | 0.990720i | \(0.543398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.92702e8 | −2.47655 | ||||||||
\(236\) | −4.56759e7 | −0.226201 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.44985e8 | 2.62039 | ||||||||
\(239\) | −1.82265e8 | −0.863597 | −0.431799 | − | 0.901970i | \(-0.642121\pi\) | ||||
−0.431799 | + | 0.901970i | \(0.642121\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.51242e7 | −0.253678 | −0.126839 | − | 0.991923i | \(-0.540483\pi\) | ||||
−0.126839 | + | 0.991923i | \(0.540483\pi\) | |||||||
\(242\) | 2.21815e8 | 1.00609 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.71068e7 | −0.207596 | ||||||||
\(245\) | −9.10812e8 | −3.95683 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.52288e8 | 1.90975 | ||||||||
\(248\) | 2.86563e8 | 1.19300 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.38444e8 | 1.36993 | ||||||||
\(251\) | 3.50809e8 | 1.40027 | 0.700137 | − | 0.714009i | \(-0.253122\pi\) | ||||
0.700137 | + | 0.714009i | \(0.253122\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.28093e8 | −0.885505 | ||||||||
\(254\) | −2.40736e8 | −0.921772 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.78416e8 | −1.40971 | ||||||||
\(257\) | 3.34359e8 | 1.22871 | 0.614353 | − | 0.789032i | \(-0.289417\pi\) | ||||
0.614353 | + | 0.789032i | \(0.289417\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.57886e8 | −2.71053 | ||||||||
\(260\) | 1.08148e9 | 3.81601 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.92855e8 | −0.662485 | ||||||||
\(263\) | 3.99920e8 | 1.35559 | 0.677795 | − | 0.735251i | \(-0.262936\pi\) | ||||
0.677795 | + | 0.735251i | \(0.262936\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.42324e8 | −1.13000 | ||||||||
\(266\) | −1.31039e9 | −4.26889 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.29407e8 | 1.04535 | ||||||||
\(269\) | −1.62396e7 | −0.0508677 | −0.0254338 | − | 0.999677i | \(-0.508097\pi\) | ||||
−0.0254338 | + | 0.999677i | \(0.508097\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.27140e8 | −1.30370 | −0.651851 | − | 0.758347i | \(-0.726007\pi\) | ||||
−0.651851 | + | 0.758347i | \(0.726007\pi\) | |||||||
\(272\) | 7.91470e7 | 0.238475 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.85419e8 | −2.60029 | ||||||||
\(275\) | 3.28485e8 | 0.952470 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.70787e8 | −1.33090 | −0.665449 | − | 0.746443i | \(-0.731760\pi\) | ||||
−0.665449 | + | 0.746443i | \(0.731760\pi\) | |||||||
\(278\) | −1.07940e9 | −3.01319 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.32995e9 | −3.62061 | ||||||||
\(281\) | 3.44673e8 | 0.926692 | 0.463346 | − | 0.886177i | \(-0.346649\pi\) | ||||
0.463346 | + | 0.886177i | \(0.346649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.05838e8 | 0.802120 | 0.401060 | − | 0.916052i | \(-0.368642\pi\) | ||||
0.401060 | + | 0.916052i | \(0.368642\pi\) | |||||||
\(284\) | −7.56902e8 | −1.96076 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.66789e8 | 1.43265 | ||||||||
\(287\) | 6.29965e8 | 1.57300 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.15582e8 | −0.281674 | ||||||||
\(290\) | −8.56473e8 | −2.06215 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.75007e8 | −2.05670 | ||||||||
\(293\) | 8.35017e7 | 0.193936 | 0.0969680 | − | 0.995287i | \(-0.469086\pi\) | ||||
0.0969680 | + | 0.995287i | \(0.469086\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.11538e7 | 0.206727 | ||||||||
\(296\) | −7.89728e8 | −1.76993 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.76995e8 | 0.387440 | ||||||||
\(299\) | 9.04286e8 | 1.95640 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.34035e9 | 2.83293 | ||||||||
\(302\) | 2.89343e8 | 0.604489 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.90305e8 | −0.388502 | ||||||||
\(305\) | 9.40092e7 | 0.189723 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.34193e8 | −1.44819 | −0.724096 | − | 0.689699i | \(-0.757743\pi\) | ||||
−0.724096 | + | 0.689699i | \(0.757743\pi\) | |||||||
\(308\) | −1.04226e9 | −2.03259 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.34733e9 | −2.56867 | ||||||||
\(311\) | −2.34224e7 | −0.0441540 | −0.0220770 | − | 0.999756i | \(-0.507028\pi\) | ||||
−0.0220770 | + | 0.999756i | \(0.507028\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.22581e8 | 0.778941 | 0.389471 | − | 0.921039i | \(-0.372658\pi\) | ||||
0.389471 | + | 0.921039i | \(0.372658\pi\) | |||||||
\(314\) | −6.78799e8 | −1.23734 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.01277e9 | 1.80553 | ||||||||
\(317\) | 1.79803e7 | 0.0317023 | 0.0158511 | − | 0.999874i | \(-0.494954\pi\) | ||||
0.0158511 | + | 0.999874i | \(0.494954\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.84897e8 | −0.491383 | ||||||||
\(320\) | 1.42408e9 | 2.42945 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.61994e9 | −4.37317 | ||||||||
\(323\) | −7.08729e8 | −1.17023 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.30229e9 | −2.10435 | ||||||||
\(326\) | −9.87695e8 | −1.57892 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.56432e8 | 1.02714 | ||||||||
\(329\) | −1.88251e9 | −2.91442 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.19639e8 | −0.332899 | −0.166449 | − | 0.986050i | \(-0.553230\pi\) | ||||
−0.166449 | + | 0.986050i | \(0.553230\pi\) | |||||||
\(332\) | 1.00514e9 | 1.50745 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.37893e8 | −0.202502 | ||||||||
\(335\) | −6.57386e8 | −0.955352 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.32909e7 | 0.0616158 | 0.0308079 | − | 0.999525i | \(-0.490192\pi\) | ||||
0.0308079 | + | 0.999525i | \(0.490192\pi\) | |||||||
\(338\) | −1.07247e9 | −1.51070 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.69466e9 | −2.33833 | ||||||||
\(341\) | −4.48176e8 | −0.612080 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.08346e9 | −2.78777 | ||||||||
\(344\) | 1.39667e9 | 1.84986 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.47419e9 | 1.91332 | ||||||||
\(347\) | −2.07119e8 | −0.266114 | −0.133057 | − | 0.991108i | \(-0.542479\pi\) | ||||
−0.133057 | + | 0.991108i | \(0.542479\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.35268e9 | −1.70336 | −0.851680 | − | 0.524062i | \(-0.824416\pi\) | ||||
−0.851680 | + | 0.524062i | \(0.824416\pi\) | |||||||
\(350\) | 3.77307e9 | 4.70389 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.86587e8 | 0.472442 | ||||||||
\(353\) | 9.24750e8 | 1.11896 | 0.559478 | − | 0.828845i | \(-0.311002\pi\) | ||||
0.559478 | + | 0.828845i | \(0.311002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.51052e9 | 1.79196 | ||||||||
\(356\) | 9.37560e8 | 1.10135 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.99486e8 | 0.460162 | ||||||||
\(359\) | −5.95223e8 | −0.678968 | −0.339484 | − | 0.940612i | \(-0.610252\pi\) | ||||
−0.339484 | + | 0.940612i | \(0.610252\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.10232e8 | 0.906430 | ||||||||
\(362\) | −3.22421e8 | −0.357226 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.13209e9 | 4.49071 | ||||||||
\(365\) | 1.74622e9 | 1.87964 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.60873e8 | 0.592289 | 0.296144 | − | 0.955143i | \(-0.404299\pi\) | ||||
0.296144 | + | 0.955143i | \(0.404299\pi\) | |||||||
\(368\) | −3.80488e8 | −0.397992 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.71306e9 | 3.81089 | ||||||||
\(371\) | −1.30795e9 | −1.32979 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.85459e8 | −0.683912 | −0.341956 | − | 0.939716i | \(-0.611089\pi\) | ||||
−0.341956 | + | 0.939716i | \(0.611089\pi\) | |||||||
\(374\) | −8.88150e8 | −0.877881 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.96160e9 | −1.90306 | ||||||||
\(377\) | 1.12949e9 | 1.08564 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.03369e9 | −0.975337 | −0.487668 | − | 0.873029i | \(-0.662152\pi\) | ||||
−0.487668 | + | 0.873029i | \(0.662152\pi\) | |||||||
\(380\) | 4.07472e9 | 3.80939 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.98632e8 | 0.457676 | ||||||||
\(383\) | −2.09792e9 | −1.90806 | −0.954032 | − | 0.299705i | \(-0.903112\pi\) | ||||
−0.954032 | + | 0.299705i | \(0.903112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.08000e9 | 1.85760 | ||||||||
\(386\) | 3.17582e9 | 2.81061 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.55670e8 | −0.309126 | ||||||||
\(389\) | 6.60600e7 | 0.0569003 | 0.0284502 | − | 0.999595i | \(-0.490943\pi\) | ||||
0.0284502 | + | 0.999595i | \(0.490943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.41700e9 | −1.19882 | ||||||||
\(392\) | −3.62623e9 | −3.04056 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.20069e9 | 0.988998 | ||||||||
\(395\) | −2.02115e9 | −1.65009 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.83981e9 | 1.47573 | 0.737863 | − | 0.674951i | \(-0.235835\pi\) | ||||
0.737863 | + | 0.674951i | \(0.235835\pi\) | |||||||
\(398\) | 2.14868e9 | 1.70837 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.47955e8 | 0.428090 | ||||||||
\(401\) | −1.61549e9 | −1.25112 | −0.625560 | − | 0.780176i | \(-0.715130\pi\) | ||||
−0.625560 | + | 0.780176i | \(0.715130\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.77681e9 | 1.35230 | ||||||||
\(404\) | 3.08446e8 | 0.232726 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.27240e9 | −2.42675 | ||||||||
\(407\) | 1.23511e9 | 0.908083 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.07871e9 | −0.779605 | −0.389802 | − | 0.920899i | \(-0.627457\pi\) | ||||
−0.389802 | + | 0.920899i | \(0.627457\pi\) | |||||||
\(410\) | −3.08634e9 | −2.21157 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.47311e8 | −0.174222 | ||||||||
\(413\) | 3.48279e8 | 0.243278 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.00591e9 | −1.37767 | ||||||||
\(416\) | −1.53264e9 | −1.04379 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.13551e9 | 1.43016 | ||||||||
\(419\) | 8.10783e8 | 0.538463 | 0.269231 | − | 0.963076i | \(-0.413230\pi\) | ||||
0.269231 | + | 0.963076i | \(0.413230\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.13878e9 | −0.743792 | −0.371896 | − | 0.928274i | \(-0.621292\pi\) | ||||
−0.371896 | + | 0.928274i | \(0.621292\pi\) | |||||||
\(422\) | −1.27192e8 | −0.0823886 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.36290e9 | −0.868327 | ||||||||
\(425\) | 2.04068e9 | 1.28948 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.59189e8 | 0.223268 | ||||||||
\(428\) | 5.34720e9 | 3.29665 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.56670e9 | −3.98297 | ||||||||
\(431\) | 2.09869e9 | 1.26263 | 0.631317 | − | 0.775525i | \(-0.282515\pi\) | ||||
0.631317 | + | 0.775525i | \(0.282515\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.85715e9 | 1.09936 | 0.549679 | − | 0.835376i | \(-0.314750\pi\) | ||||
0.549679 | + | 0.835376i | \(0.314750\pi\) | |||||||
\(434\) | −5.14787e9 | −3.02283 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.36366e9 | 1.36579 | ||||||||
\(437\) | 3.40712e9 | 1.95300 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.58145e8 | 0.371275 | 0.185638 | − | 0.982618i | \(-0.440565\pi\) | ||||
0.185638 | + | 0.982618i | \(0.440565\pi\) | |||||||
\(440\) | 2.16739e9 | 1.21298 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.52111e9 | 1.93955 | ||||||||
\(443\) | 2.56332e8 | 0.140084 | 0.0700422 | − | 0.997544i | \(-0.477687\pi\) | ||||
0.0700422 | + | 0.997544i | \(0.477687\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.87105e9 | −1.00653 | ||||||||
\(446\) | −5.22056e9 | −2.78641 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.44110e9 | 2.85900 | ||||||||
\(449\) | −5.70165e8 | −0.297261 | −0.148631 | − | 0.988893i | \(-0.547487\pi\) | ||||
−0.148631 | + | 0.988893i | \(0.547487\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.02664e9 | −0.526987 | ||||||||
\(452\) | −4.05575e9 | −2.06579 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.86086e8 | 0.394253 | ||||||||
\(455\) | −8.24626e9 | −4.10409 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.42553e8 | −0.0698669 | −0.0349334 | − | 0.999390i | \(-0.511122\pi\) | ||||
−0.0349334 | + | 0.999390i | \(0.511122\pi\) | |||||||
\(458\) | 2.82208e8 | 0.137259 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.14684e9 | 3.90245 | ||||||||
\(461\) | −2.44186e9 | −1.16083 | −0.580414 | − | 0.814321i | \(-0.697109\pi\) | ||||
−0.580414 | + | 0.814321i | \(0.697109\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.57981e9 | −1.20796 | −0.603982 | − | 0.796998i | \(-0.706420\pi\) | ||||
−0.603982 | + | 0.796998i | \(0.706420\pi\) | |||||||
\(464\) | −4.75244e8 | −0.220853 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.82495e8 | 0.449759 | ||||||||
\(467\) | 1.03284e9 | 0.469272 | 0.234636 | − | 0.972083i | \(-0.424610\pi\) | ||||
0.234636 | + | 0.972083i | \(0.424610\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.51173e9 | −1.12426 | ||||||||
\(470\) | 9.22285e9 | 4.09753 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.62912e8 | 0.158856 | ||||||||
\(473\) | −2.18434e9 | −0.949089 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.90671e9 | −2.10069 | ||||||||
\(476\) | −6.47493e9 | −2.75176 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.41181e9 | 1.42885 | ||||||||
\(479\) | 2.54815e9 | 1.05938 | 0.529688 | − | 0.848193i | \(-0.322309\pi\) | ||||
0.529688 | + | 0.848193i | \(0.322309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.89665e9 | −2.00628 | ||||||||
\(482\) | 1.03187e9 | 0.419719 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.63536e9 | −1.05653 | ||||||||
\(485\) | 7.09797e8 | 0.282513 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.38050e9 | −0.541608 | −0.270804 | − | 0.962635i | \(-0.587289\pi\) | ||||
−0.270804 | + | 0.962635i | \(0.587289\pi\) | |||||||
\(488\) | 3.74280e8 | 0.145790 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.70494e10 | 6.54671 | ||||||||
\(491\) | −3.40284e9 | −1.29735 | −0.648674 | − | 0.761067i | \(-0.724676\pi\) | ||||
−0.648674 | + | 0.761067i | \(0.724676\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.76989e9 | −0.665246 | ||||||||
\(494\) | −8.46634e9 | −3.15974 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.47614e8 | −0.275101 | ||||||||
\(497\) | 5.77138e9 | 2.10879 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.71570e9 | −0.978430 | −0.489215 | − | 0.872163i | \(-0.662717\pi\) | ||||
−0.489215 | + | 0.872163i | \(0.662717\pi\) | |||||||
\(500\) | −4.02103e9 | −1.43861 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.56677e9 | −2.31680 | ||||||||
\(503\) | 1.12999e9 | 0.395899 | 0.197950 | − | 0.980212i | \(-0.436572\pi\) | ||||
0.197950 | + | 0.980212i | \(0.436572\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.15554e8 | −0.212690 | ||||||||
\(506\) | 4.26966e9 | 1.46510 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.86017e9 | 0.967986 | ||||||||
\(509\) | −2.58498e9 | −0.868849 | −0.434425 | − | 0.900708i | \(-0.643048\pi\) | ||||
−0.434425 | + | 0.900708i | \(0.643048\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.67193e9 | 2.21197 | ||||||||
\(512\) | 1.68757e9 | 0.555670 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.25885e9 | −2.03294 | ||||||||
\(515\) | 4.93550e8 | 0.159223 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.06788e9 | 0.976387 | ||||||||
\(518\) | 1.41868e10 | 4.48467 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.59272e9 | −2.67990 | ||||||||
\(521\) | 1.68355e9 | 0.521546 | 0.260773 | − | 0.965400i | \(-0.416023\pi\) | ||||
0.260773 | + | 0.965400i | \(0.416023\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.47225e9 | −0.755676 | −0.377838 | − | 0.925872i | \(-0.623332\pi\) | ||||
−0.377838 | + | 0.925872i | \(0.623332\pi\) | |||||||
\(524\) | 2.29129e9 | 0.695699 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.48608e9 | −2.24287 | ||||||||
\(527\) | −2.78424e9 | −0.828648 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.40723e9 | 1.00071 | ||||||||
\(530\) | 6.40794e9 | 1.86962 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.55687e10 | 4.48291 | ||||||||
\(533\) | 4.07016e9 | 1.16430 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.06712e10 | −3.01284 | ||||||||
\(536\) | −2.61726e9 | −0.734125 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.03988e8 | 0.0841624 | ||||||||
\(539\) | 5.67131e9 | 1.55999 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.60201e9 | −0.978034 | −0.489017 | − | 0.872274i | \(-0.662644\pi\) | ||||
−0.489017 | + | 0.872274i | \(0.662644\pi\) | |||||||
\(542\) | 7.99561e9 | 2.15702 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.40163e9 | 0.639602 | ||||||||
\(545\) | −4.71707e9 | −1.24820 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.24077e9 | 0.324141 | 0.162071 | − | 0.986779i | \(-0.448183\pi\) | ||||
0.162071 | + | 0.986779i | \(0.448183\pi\) | |||||||
\(548\) | 1.05196e10 | 2.73066 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.14889e9 | −1.57590 | ||||||||
\(551\) | 4.25561e9 | 1.08376 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.72237e9 | −1.94184 | ||||||||
\(554\) | 8.81262e9 | 2.20202 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.28243e10 | 3.16426 | ||||||||
\(557\) | −1.77982e9 | −0.436399 | −0.218200 | − | 0.975904i | \(-0.570018\pi\) | ||||
−0.218200 | + | 0.975904i | \(0.570018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.65993e9 | 2.09688 | ||||||||
\(560\) | 3.46970e9 | 0.834900 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.45192e9 | −1.53325 | ||||||||
\(563\) | 6.60782e9 | 1.56056 | 0.780278 | − | 0.625433i | \(-0.215078\pi\) | ||||
0.780278 | + | 0.625433i | \(0.215078\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.09391e9 | 1.88794 | ||||||||
\(566\) | −5.72496e9 | −1.32714 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.01386e9 | 1.37700 | ||||||||
\(569\) | −4.59260e9 | −1.04512 | −0.522560 | − | 0.852603i | \(-0.675023\pi\) | ||||
−0.522560 | + | 0.852603i | \(0.675023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.76881e9 | 0.847183 | 0.423592 | − | 0.905853i | \(-0.360769\pi\) | ||||
0.423592 | + | 0.905853i | \(0.360769\pi\) | |||||||
\(572\) | −6.73398e9 | −1.50448 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.17923e10 | −2.60259 | ||||||||
\(575\) | −9.81029e9 | −2.15201 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.58209e9 | 0.776284 | 0.388142 | − | 0.921600i | \(-0.373117\pi\) | ||||
0.388142 | + | 0.921600i | \(0.373117\pi\) | |||||||
\(578\) | 2.16357e9 | 0.466040 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.01757e10 | 2.16554 | ||||||||
\(581\) | −7.66417e9 | −1.62125 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.13153e9 | 0.445504 | ||||||||
\(584\) | 6.95225e9 | 1.44438 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.56306e9 | −0.320874 | ||||||||
\(587\) | −3.85835e8 | −0.0787350 | −0.0393675 | − | 0.999225i | \(-0.512534\pi\) | ||||
−0.0393675 | + | 0.999225i | \(0.512534\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.69458e9 | 1.34996 | ||||||||
\(590\) | −1.70630e9 | −0.342037 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.06032e9 | 0.408140 | ||||||||
\(593\) | 1.84467e9 | 0.363267 | 0.181634 | − | 0.983366i | \(-0.441861\pi\) | ||||
0.181634 | + | 0.983366i | \(0.441861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.29218e10 | 2.51485 | ||||||||
\(596\) | −2.10287e9 | −0.406864 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.69273e10 | −3.23693 | ||||||||
\(599\) | −4.66546e9 | −0.886953 | −0.443476 | − | 0.896286i | \(-0.646255\pi\) | ||||
−0.443476 | + | 0.896286i | \(0.646255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.24604e9 | 0.422043 | 0.211021 | − | 0.977481i | \(-0.432321\pi\) | ||||
0.211021 | + | 0.977481i | \(0.432321\pi\) | |||||||
\(602\) | −2.50900e10 | −4.68719 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.43766e9 | −0.634796 | ||||||||
\(605\) | 5.25930e9 | 0.965570 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.43363e9 | 1.71206 | 0.856029 | − | 0.516928i | \(-0.172925\pi\) | ||||
0.856029 | + | 0.516928i | \(0.172925\pi\) | |||||||
\(608\) | −5.77460e9 | −1.04198 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.75975e9 | −0.313904 | ||||||||
\(611\) | −1.21628e10 | −2.15719 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.56081e9 | 0.449020 | 0.224510 | − | 0.974472i | \(-0.427922\pi\) | ||||
0.224510 | + | 0.974472i | \(0.427922\pi\) | |||||||
\(614\) | 1.37433e10 | 2.39608 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.28114e9 | 1.42744 | ||||||||
\(617\) | −2.42876e9 | −0.416281 | −0.208141 | − | 0.978099i | \(-0.566741\pi\) | ||||
−0.208141 | + | 0.978099i | \(0.566741\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.53273e9 | 1.10708 | 0.553538 | − | 0.832824i | \(-0.313277\pi\) | ||||
0.553538 | + | 0.832824i | \(0.313277\pi\) | |||||||
\(620\) | 1.60076e10 | 2.69746 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.38443e8 | 0.0730544 | ||||||||
\(623\) | −7.14890e9 | −1.18449 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.26146e9 | −0.206678 | ||||||||
\(626\) | −7.91026e9 | −1.28879 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.06476e9 | 1.29937 | ||||||||
\(629\) | 7.67299e9 | 1.22938 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.21286e9 | −0.350631 | −0.175315 | − | 0.984512i | \(-0.556095\pi\) | ||||
−0.175315 | + | 0.984512i | \(0.556095\pi\) | |||||||
\(632\) | −8.04681e9 | −1.26799 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.36573e8 | −0.0524525 | ||||||||
\(635\) | −5.70794e9 | −0.884649 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.24842e10 | −3.44658 | ||||||||
\(638\) | 5.33296e9 | 0.813011 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.87102e10 | −2.82130 | ||||||||
\(641\) | −5.20588e9 | −0.780713 | −0.390356 | − | 0.920664i | \(-0.627648\pi\) | ||||
−0.390356 | + | 0.920664i | \(0.627648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.18888e10 | −1.76359 | −0.881796 | − | 0.471631i | \(-0.843665\pi\) | ||||
−0.881796 | + | 0.471631i | \(0.843665\pi\) | |||||||
\(644\) | 3.11274e10 | 4.59242 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.32666e10 | 1.93619 | ||||||||
\(647\) | 6.02914e9 | 0.875166 | 0.437583 | − | 0.899178i | \(-0.355835\pi\) | ||||
0.437583 | + | 0.899178i | \(0.355835\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.67583e8 | −0.0815029 | ||||||||
\(650\) | 2.43776e10 | 3.48172 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.17347e10 | 1.65809 | ||||||||
\(653\) | −2.77068e8 | −0.0389395 | −0.0194697 | − | 0.999810i | \(-0.506198\pi\) | ||||
−0.0194697 | + | 0.999810i | \(0.506198\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.57265e9 | −0.635804 | ||||||||
\(656\) | −1.71256e9 | −0.236856 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.52386e10 | 4.82200 | ||||||||
\(659\) | 1.19887e10 | 1.63182 | 0.815909 | − | 0.578181i | \(-0.196237\pi\) | ||||
0.815909 | + | 0.578181i | \(0.196237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.39523e9 | 0.457261 | 0.228631 | − | 0.973513i | \(-0.426575\pi\) | ||||
0.228631 | + | 0.973513i | \(0.426575\pi\) | |||||||
\(662\) | 4.11142e9 | 0.550793 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.98617e9 | −1.05865 | ||||||||
\(665\) | −3.10698e10 | −4.09697 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.50851e9 | 1.11023 | ||||||||
\(668\) | 1.63829e9 | 0.212654 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.23056e10 | 1.58066 | ||||||||
\(671\) | −5.85363e8 | −0.0747991 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.44306e9 | 1.19415 | 0.597077 | − | 0.802184i | \(-0.296329\pi\) | ||||
0.597077 | + | 0.802184i | \(0.296329\pi\) | |||||||
\(674\) | −8.10359e8 | −0.101945 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.27420e10 | 1.58644 | ||||||||
\(677\) | −2.31127e9 | −0.286279 | −0.143140 | − | 0.989703i | \(-0.545720\pi\) | ||||
−0.143140 | + | 0.989703i | \(0.545720\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.71199e9 | 0.332463 | ||||||||
\(680\) | 1.34647e10 | 1.64216 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.38938e9 | 1.01271 | ||||||||
\(683\) | 1.31138e10 | 1.57491 | 0.787454 | − | 0.616374i | \(-0.211399\pi\) | ||||
0.787454 | + | 0.616374i | \(0.211399\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.09936e10 | −2.49557 | ||||||||
\(686\) | 3.90002e10 | 4.61246 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.64376e9 | −0.426570 | ||||||||
\(689\) | −8.45056e9 | −0.984279 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.33408e9 | 0.960913 | 0.480457 | − | 0.877018i | \(-0.340471\pi\) | ||||
0.480457 | + | 0.877018i | \(0.340471\pi\) | |||||||
\(692\) | −1.75148e10 | −2.00925 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.87705e9 | 0.440295 | ||||||||
\(695\) | −2.55930e10 | −2.89184 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.37789e9 | −0.713448 | ||||||||
\(698\) | 2.53207e10 | 2.81827 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.48276e10 | −4.93972 | ||||||||
\(701\) | 2.09612e9 | 0.229829 | 0.114914 | − | 0.993375i | \(-0.463341\pi\) | ||||
0.114914 | + | 0.993375i | \(0.463341\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.84493e10 | −2.00280 | ||||||||
\(704\) | −8.86724e9 | −0.957821 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.73103e10 | −1.85135 | ||||||||
\(707\) | −2.35190e9 | −0.250294 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.17621e8 | 0.0440069 | 0.0220035 | − | 0.999758i | \(-0.492996\pi\) | ||||
0.0220035 | + | 0.999758i | \(0.492996\pi\) | |||||||
\(710\) | −2.82753e10 | −2.96486 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.44925e9 | −0.773451 | ||||||||
\(713\) | 1.33849e10 | 1.38293 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.34387e10 | 1.37495 | ||||||||
\(716\) | −4.74626e9 | −0.483232 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.11419e10 | 1.12338 | ||||||||
\(719\) | 6.71535e9 | 0.673779 | 0.336890 | − | 0.941544i | \(-0.390625\pi\) | ||||
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.88575e9 | 0.187375 | ||||||||
\(722\) | −1.51667e10 | −1.49972 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.83066e9 | 0.375136 | ||||||||
\(725\) | −1.22534e10 | −1.19419 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.79100e9 | −0.848531 | −0.424266 | − | 0.905538i | \(-0.639468\pi\) | ||||
−0.424266 | + | 0.905538i | \(0.639468\pi\) | |||||||
\(728\) | −3.28309e10 | −3.15372 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.26874e10 | −3.10992 | ||||||||
\(731\) | −1.35700e10 | −1.28490 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.87568e10 | −1.75912 | −0.879560 | − | 0.475787i | \(-0.842163\pi\) | ||||
−0.879560 | + | 0.475787i | \(0.842163\pi\) | |||||||
\(734\) | −1.04989e10 | −0.979963 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.15455e10 | −1.06743 | ||||||||
\(737\) | 4.09331e9 | 0.376651 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.83197e9 | −0.349274 | −0.174637 | − | 0.984633i | \(-0.555875\pi\) | ||||
−0.174637 | + | 0.984633i | \(0.555875\pi\) | |||||||
\(740\) | −4.41146e10 | −4.00195 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.44834e10 | 2.20018 | ||||||||
\(743\) | 1.74075e9 | 0.155695 | 0.0778475 | − | 0.996965i | \(-0.475195\pi\) | ||||
0.0778475 | + | 0.996965i | \(0.475195\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.19661e9 | 0.371836 | ||||||||
\(746\) | 1.28311e10 | 1.13156 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.05521e10 | 0.921895 | ||||||||
\(749\) | −4.07724e10 | −3.54552 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.87554e10 | 1.61580 | 0.807900 | − | 0.589320i | \(-0.200604\pi\) | ||||
0.807900 | + | 0.589320i | \(0.200604\pi\) | |||||||
\(752\) | 5.11762e9 | 0.438839 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.11428e10 | −1.79623 | ||||||||
\(755\) | 6.86042e9 | 0.580145 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.48636e10 | −1.24534 | −0.622671 | − | 0.782483i | \(-0.713953\pi\) | ||||
−0.622671 | + | 0.782483i | \(0.713953\pi\) | |||||||
\(758\) | 1.93496e10 | 1.61373 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.23751e10 | −2.67525 | ||||||||
\(761\) | −2.55852e9 | −0.210446 | −0.105223 | − | 0.994449i | \(-0.533556\pi\) | ||||
−0.105223 | + | 0.994449i | \(0.533556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.80229e10 | −1.46889 | ||||||||
\(764\) | −5.92421e9 | −0.480622 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.92708e10 | 3.15696 | ||||||||
\(767\) | 2.25021e9 | 0.180069 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.98268e10 | 1.57221 | 0.786104 | − | 0.618094i | \(-0.212095\pi\) | ||||
0.786104 | + | 0.618094i | \(0.212095\pi\) | |||||||
\(770\) | −3.89354e10 | −3.07346 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.77317e10 | −2.95152 | ||||||||
\(773\) | 1.29417e10 | 1.00777 | 0.503886 | − | 0.863770i | \(-0.331903\pi\) | ||||
0.503886 | + | 0.863770i | \(0.331903\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.92760e10 | −1.48752 | ||||||||
\(776\) | 2.82593e9 | 0.217092 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.23657e9 | −0.0941436 | ||||||||
\(779\) | 1.53353e10 | 1.16228 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.40549e9 | −0.706485 | ||||||||
\(782\) | 2.65248e10 | 1.98348 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.46046e9 | 0.701142 | ||||||||
\(785\) | −1.60945e10 | −1.18750 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.60328e9 | 0.702276 | 0.351138 | − | 0.936324i | \(-0.385795\pi\) | ||||
0.351138 | + | 0.936324i | \(0.385795\pi\) | |||||||
\(788\) | −1.42654e10 | −1.03858 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.78337e10 | 2.73013 | ||||||||
\(791\) | 3.09251e10 | 2.22174 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.32070e9 | 0.165258 | ||||||||
\(794\) | −3.44392e10 | −2.44164 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.55284e10 | −1.79402 | ||||||||
\(797\) | 9.10764e9 | 0.637238 | 0.318619 | − | 0.947883i | \(-0.396781\pi\) | ||||
0.318619 | + | 0.947883i | \(0.396781\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.90589e10 | 1.32185 | ||||||||
\(800\) | 1.66271e10 | 1.14816 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.02403e10 | 2.07002 | ||||||||
\(803\) | −1.08731e10 | −0.741053 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.21197e10 | −4.19705 | ||||||||
\(806\) | −3.32601e10 | −2.23744 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.45071e9 | −0.163438 | ||||||||
\(809\) | 1.78494e10 | 1.18524 | 0.592618 | − | 0.805484i | \(-0.298094\pi\) | ||||
0.592618 | + | 0.805484i | \(0.298094\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.82320e9 | 0.449174 | 0.224587 | − | 0.974454i | \(-0.427897\pi\) | ||||
0.224587 | + | 0.974454i | \(0.427897\pi\) | |||||||
\(812\) | 3.88792e10 | 2.54842 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.31200e10 | −1.50246 | ||||||||
\(815\) | −2.34186e10 | −1.51534 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.26284e10 | 2.09324 | ||||||||
\(818\) | 2.01924e10 | 1.28988 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.66686e10 | 2.32245 | ||||||||
\(821\) | −7.07763e9 | −0.446362 | −0.223181 | − | 0.974777i | \(-0.571644\pi\) | ||||
−0.223181 | + | 0.974777i | \(0.571644\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.02079e10 | −0.638317 | −0.319159 | − | 0.947701i | \(-0.603400\pi\) | ||||
−0.319159 | + | 0.947701i | \(0.603400\pi\) | |||||||
\(824\) | 1.96498e9 | 0.122352 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.51941e9 | −0.402512 | ||||||||
\(827\) | −2.59808e9 | −0.159729 | −0.0798644 | − | 0.996806i | \(-0.525449\pi\) | ||||
−0.0798644 | + | 0.996806i | \(0.525449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.93686e9 | 0.179037 | 0.0895184 | − | 0.995985i | \(-0.471467\pi\) | ||||
0.0895184 | + | 0.995985i | \(0.471467\pi\) | |||||||
\(830\) | 3.75486e10 | 2.27940 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.51546e10 | 2.11617 | ||||||||
\(833\) | 3.52324e10 | 2.11195 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.26948e9 | −0.194346 | ||||||||
\(836\) | −2.53719e10 | −1.50187 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.51770e10 | −0.890905 | ||||||||
\(839\) | −1.16450e10 | −0.680728 | −0.340364 | − | 0.940294i | \(-0.610550\pi\) | ||||
−0.340364 | + | 0.940294i | \(0.610550\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.62244e9 | −0.383912 | ||||||||
\(842\) | 2.13167e10 | 1.23063 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.51116e9 | 0.0865192 | ||||||||
\(845\) | −2.54287e10 | −1.44986 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00947e10 | 1.13629 | ||||||||
\(848\) | 3.55567e9 | 0.200233 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.81993e10 | −2.13348 | ||||||||
\(851\) | −3.68869e10 | −2.05172 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.63671e10 | 0.902922 | 0.451461 | − | 0.892291i | \(-0.350903\pi\) | ||||
0.451461 | + | 0.892291i | \(0.350903\pi\) | |||||||
\(854\) | −6.72364e9 | −0.369404 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.24854e10 | −2.31517 | ||||||||
\(857\) | 1.66058e10 | 0.901210 | 0.450605 | − | 0.892724i | \(-0.351208\pi\) | ||||
0.450605 | + | 0.892724i | \(0.351208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.88831e10 | −1.01647 | −0.508237 | − | 0.861217i | \(-0.669703\pi\) | ||||
−0.508237 | + | 0.861217i | \(0.669703\pi\) | |||||||
\(860\) | 7.80185e10 | 4.18266 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.92852e10 | −2.08907 | ||||||||
\(863\) | −2.09759e10 | −1.11092 | −0.555461 | − | 0.831543i | \(-0.687458\pi\) | ||||
−0.555461 | + | 0.831543i | \(0.687458\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.49536e10 | 1.83627 | ||||||||
\(866\) | −3.47639e10 | −1.81893 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.11615e10 | 3.17438 | ||||||||
\(869\) | 1.25850e10 | 0.650554 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.62281e10 | −0.832156 | ||||||||
\(872\) | −1.87801e10 | −0.959161 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.37776e10 | −3.23131 | ||||||||
\(875\) | 3.06604e10 | 1.54721 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.68896e10 | 1.84674 | 0.923370 | − | 0.383911i | \(-0.125423\pi\) | ||||
0.923370 | + | 0.383911i | \(0.125423\pi\) | |||||||
\(878\) | −1.23198e10 | −0.614288 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.65450e9 | −0.279708 | ||||||||
\(881\) | 3.57144e10 | 1.75966 | 0.879829 | − | 0.475291i | \(-0.157657\pi\) | ||||
0.879829 | + | 0.475291i | \(0.157657\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.90952e9 | −0.191100 | −0.0955501 | − | 0.995425i | \(-0.530461\pi\) | ||||
−0.0955501 | + | 0.995425i | \(0.530461\pi\) | |||||||
\(884\) | −4.18341e10 | −2.03679 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.79826e9 | −0.231775 | ||||||||
\(887\) | 1.25223e10 | 0.602494 | 0.301247 | − | 0.953546i | \(-0.402597\pi\) | ||||
0.301247 | + | 0.953546i | \(0.402597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.18088e10 | −1.04106 | ||||||||
\(890\) | 3.50241e10 | 1.66534 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.20251e10 | 2.92611 | ||||||||
\(893\) | −4.58262e10 | −2.15344 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.47193e9 | 0.441630 | ||||||||
\(896\) | −7.14878e10 | −3.32012 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.06729e10 | 0.491829 | ||||||||
\(899\) | 1.67182e10 | 0.767416 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.32419e10 | 0.603134 | ||||||||
\(902\) | 1.92176e10 | 0.871919 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.22244e10 | 1.45076 | ||||||||
\(905\) | −7.64470e9 | −0.342839 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.27291e10 | 1.01148 | 0.505739 | − | 0.862687i | \(-0.331220\pi\) | ||||
0.505739 | + | 0.862687i | \(0.331220\pi\) | |||||||
\(908\) | −9.33944e9 | −0.414019 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.54361e11 | 6.79036 | ||||||||
\(911\) | 2.77093e10 | 1.21426 | 0.607129 | − | 0.794603i | \(-0.292321\pi\) | ||||
0.607129 | + | 0.794603i | \(0.292321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.24901e10 | 0.543150 | ||||||||
\(914\) | 2.66845e9 | 0.115597 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.35289e9 | −0.144140 | ||||||||
\(917\) | −1.74711e10 | −0.748218 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.24377e10 | −0.528612 | −0.264306 | − | 0.964439i | \(-0.585143\pi\) | ||||
−0.264306 | + | 0.964439i | \(0.585143\pi\) | |||||||
\(920\) | −6.47296e10 | −2.74060 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.57091e10 | 1.92063 | ||||||||
\(923\) | 3.72885e10 | 1.56088 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.31221e10 | 2.20688 | ||||||||
\(926\) | 4.82913e10 | 1.99862 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.44208e10 | −0.592339 | ||||||||
\(929\) | 3.14739e10 | 1.28794 | 0.643970 | − | 0.765051i | \(-0.277286\pi\) | ||||
0.643970 | + | 0.765051i | \(0.277286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.47146e10 | −3.44060 | ||||||||
\(932\) | −1.16730e10 | −0.472308 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.93337e10 | −0.776428 | ||||||||
\(935\) | −2.10583e10 | −0.842526 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.85637e10 | −1.53140 | −0.765702 | − | 0.643195i | \(-0.777608\pi\) | ||||
−0.765702 | + | 0.643195i | \(0.777608\pi\) | |||||||
\(938\) | 4.70169e10 | 1.86013 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.09576e11 | −4.30297 | ||||||||
\(941\) | −2.15748e10 | −0.844078 | −0.422039 | − | 0.906578i | \(-0.638686\pi\) | ||||
−0.422039 | + | 0.906578i | \(0.638686\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.06608e10 | 1.19067 | ||||||||
\(944\) | −9.46800e8 | −0.0366316 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.08886e10 | 1.57030 | ||||||||
\(947\) | 2.58130e10 | 0.987675 | 0.493838 | − | 0.869554i | \(-0.335594\pi\) | ||||
0.493838 | + | 0.869554i | \(0.335594\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.31069e10 | 1.63725 | ||||||||
\(950\) | 9.18484e10 | 3.47567 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.14457e10 | 1.93250 | ||||||||
\(953\) | −3.92406e10 | −1.46862 | −0.734311 | − | 0.678813i | \(-0.762495\pi\) | ||||
−0.734311 | + | 0.678813i | \(0.762495\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.18227e10 | 0.439244 | ||||||||
\(956\) | −4.05355e10 | −1.50049 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.76986e10 | −1.75278 | ||||||||
\(959\) | −8.02121e10 | −2.93680 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.21292e9 | −0.0440859 | ||||||||
\(962\) | 9.16601e10 | 3.31946 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.22595e10 | −0.440762 | ||||||||
\(965\) | 7.52997e10 | 2.69741 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.78901e9 | −0.0636240 | −0.0318120 | − | 0.999494i | \(-0.510128\pi\) | ||||
−0.0318120 | + | 0.999494i | \(0.510128\pi\) | |||||||
\(968\) | 2.09389e10 | 0.741977 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.32866e10 | −0.467427 | ||||||||
\(971\) | 2.44481e10 | 0.856993 | 0.428497 | − | 0.903543i | \(-0.359043\pi\) | ||||
0.428497 | + | 0.903543i | \(0.359043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.77854e10 | −3.40313 | ||||||||
\(974\) | 2.58415e10 | 0.896109 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.76459e8 | −0.0336186 | ||||||||
\(977\) | −3.42307e10 | −1.17432 | −0.587158 | − | 0.809472i | \(-0.699753\pi\) | ||||
−0.587158 | + | 0.809472i | \(0.699753\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.16504e10 | 0.396827 | ||||||||
\(980\) | −2.02563e11 | −6.87494 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.36975e10 | 2.14651 | ||||||||
\(983\) | 4.53628e10 | 1.52322 | 0.761610 | − | 0.648036i | \(-0.224409\pi\) | ||||
0.761610 | + | 0.648036i | \(0.224409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.84688e10 | 0.949167 | ||||||||
\(986\) | 3.31304e10 | 1.10067 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.00588e11 | 3.31816 | ||||||||
\(989\) | 6.52359e10 | 2.14437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.84050e10 | 0.927123 | 0.463561 | − | 0.886065i | \(-0.346571\pi\) | ||||
0.463561 | + | 0.886065i | \(0.346571\pi\) | |||||||
\(992\) | −2.26855e10 | −0.737834 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.08034e11 | −3.48906 | ||||||||
\(995\) | 5.09460e10 | 1.63957 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.63738e10 | −1.16240 | −0.581201 | − | 0.813760i | \(-0.697417\pi\) | ||||
−0.581201 | + | 0.813760i | \(0.697417\pi\) | |||||||
\(998\) | 5.08350e10 | 1.61885 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.8.a.b.1.2 | 16 | ||
3.2 | odd | 2 | 177.8.a.a.1.15 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.15 | ✓ | 16 | 3.2 | odd | 2 | ||
531.8.a.b.1.2 | 16 | 1.1 | even | 1 | trivial |