Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [285,10,Mod(1,285)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(285, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("285.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 285 = 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 285.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: | \(146.785213307\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 4398 x^{10} + 4080 x^{9} + 7026370 x^{8} + 7294322 x^{7} - 5023445596 x^{6} + \cdots + 49\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-14.0719\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 285.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −17.0719 | −0.754480 | −0.377240 | − | 0.926116i | \(-0.623127\pi\) | ||||
−0.377240 | + | 0.926116i | \(0.623127\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −220.549 | −0.430761 | ||||||||
\(5\) | 625.000 | 0.447214 | ||||||||
\(6\) | 1382.83 | 0.435599 | ||||||||
\(7\) | 11804.8 | 1.85831 | 0.929153 | − | 0.369695i | \(-0.120538\pi\) | ||||
0.929153 | + | 0.369695i | \(0.120538\pi\) | |||||||
\(8\) | 12506.0 | 1.07948 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −10670.0 | −0.337413 | ||||||||
\(11\) | 10723.5 | 0.220837 | 0.110418 | − | 0.993885i | \(-0.464781\pi\) | ||||
0.110418 | + | 0.993885i | \(0.464781\pi\) | |||||||
\(12\) | 17864.5 | 0.248700 | ||||||||
\(13\) | 55804.2 | 0.541903 | 0.270952 | − | 0.962593i | \(-0.412662\pi\) | ||||
0.270952 | + | 0.962593i | \(0.412662\pi\) | |||||||
\(14\) | −201531. | −1.40205 | ||||||||
\(15\) | −50625.0 | −0.258199 | ||||||||
\(16\) | −100581. | −0.383685 | ||||||||
\(17\) | 39049.4 | 0.113395 | 0.0566976 | − | 0.998391i | \(-0.481943\pi\) | ||||
0.0566976 | + | 0.998391i | \(0.481943\pi\) | |||||||
\(18\) | −112009. | −0.251493 | ||||||||
\(19\) | 130321. | 0.229416 | ||||||||
\(20\) | −137843. | −0.192642 | ||||||||
\(21\) | −956188. | −1.07289 | ||||||||
\(22\) | −183072. | −0.166617 | ||||||||
\(23\) | 85590.2 | 0.0637748 | 0.0318874 | − | 0.999491i | \(-0.489848\pi\) | ||||
0.0318874 | + | 0.999491i | \(0.489848\pi\) | |||||||
\(24\) | −1.01299e6 | −0.623238 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | −952685. | −0.408855 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −2.60354e6 | −0.800485 | ||||||||
\(29\) | −4.91333e6 | −1.28998 | −0.644992 | − | 0.764189i | \(-0.723139\pi\) | ||||
−0.644992 | + | 0.764189i | \(0.723139\pi\) | |||||||
\(30\) | 864266. | 0.194806 | ||||||||
\(31\) | −7.66372e6 | −1.49043 | −0.745216 | − | 0.666823i | \(-0.767654\pi\) | ||||
−0.745216 | + | 0.666823i | \(0.767654\pi\) | |||||||
\(32\) | −4.68598e6 | −0.789997 | ||||||||
\(33\) | −868607. | −0.127500 | ||||||||
\(34\) | −666649. | −0.0855543 | ||||||||
\(35\) | 7.37800e6 | 0.831060 | ||||||||
\(36\) | −1.44702e6 | −0.143587 | ||||||||
\(37\) | −1.74637e7 | −1.53189 | −0.765944 | − | 0.642907i | \(-0.777728\pi\) | ||||
−0.765944 | + | 0.642907i | \(0.777728\pi\) | |||||||
\(38\) | −2.22483e6 | −0.173089 | ||||||||
\(39\) | −4.52014e6 | −0.312868 | ||||||||
\(40\) | 7.81627e6 | 0.482758 | ||||||||
\(41\) | 2.56765e7 | 1.41908 | 0.709541 | − | 0.704664i | \(-0.248902\pi\) | ||||
0.709541 | + | 0.704664i | \(0.248902\pi\) | |||||||
\(42\) | 1.63240e7 | 0.809476 | ||||||||
\(43\) | −3.52977e7 | −1.57449 | −0.787243 | − | 0.616643i | \(-0.788492\pi\) | ||||
−0.787243 | + | 0.616643i | \(0.788492\pi\) | |||||||
\(44\) | −2.36507e6 | −0.0951278 | ||||||||
\(45\) | 4.10062e6 | 0.149071 | ||||||||
\(46\) | −1.46119e6 | −0.0481168 | ||||||||
\(47\) | −9.69853e6 | −0.289912 | −0.144956 | − | 0.989438i | \(-0.546304\pi\) | ||||
−0.144956 | + | 0.989438i | \(0.546304\pi\) | |||||||
\(48\) | 8.14703e6 | 0.221520 | ||||||||
\(49\) | 9.89996e7 | 2.45330 | ||||||||
\(50\) | −6.66872e6 | −0.150896 | ||||||||
\(51\) | −3.16300e6 | −0.0654687 | ||||||||
\(52\) | −1.23076e7 | −0.233431 | ||||||||
\(53\) | −6.79387e7 | −1.18270 | −0.591352 | − | 0.806414i | \(-0.701406\pi\) | ||||
−0.591352 | + | 0.806414i | \(0.701406\pi\) | |||||||
\(54\) | 9.07272e6 | 0.145200 | ||||||||
\(55\) | 6.70222e6 | 0.0987612 | ||||||||
\(56\) | 1.47631e8 | 2.00600 | ||||||||
\(57\) | −1.05560e7 | −0.132453 | ||||||||
\(58\) | 8.38799e7 | 0.973267 | ||||||||
\(59\) | −2.56493e7 | −0.275576 | −0.137788 | − | 0.990462i | \(-0.543999\pi\) | ||||
−0.137788 | + | 0.990462i | \(0.543999\pi\) | |||||||
\(60\) | 1.11653e7 | 0.111222 | ||||||||
\(61\) | −7.01660e6 | −0.0648847 | −0.0324424 | − | 0.999474i | \(-0.510329\pi\) | ||||
−0.0324424 | + | 0.999474i | \(0.510329\pi\) | |||||||
\(62\) | 1.30835e8 | 1.12450 | ||||||||
\(63\) | 7.74513e7 | 0.619435 | ||||||||
\(64\) | 1.31496e8 | 0.979721 | ||||||||
\(65\) | 3.48776e7 | 0.242347 | ||||||||
\(66\) | 1.48288e7 | 0.0961963 | ||||||||
\(67\) | −1.24277e8 | −0.753451 | −0.376725 | − | 0.926325i | \(-0.622950\pi\) | ||||
−0.376725 | + | 0.926325i | \(0.622950\pi\) | |||||||
\(68\) | −8.61233e6 | −0.0488462 | ||||||||
\(69\) | −6.93281e6 | −0.0368204 | ||||||||
\(70\) | −1.25957e8 | −0.627018 | ||||||||
\(71\) | 6.68509e7 | 0.312208 | 0.156104 | − | 0.987741i | \(-0.450106\pi\) | ||||
0.156104 | + | 0.987741i | \(0.450106\pi\) | |||||||
\(72\) | 8.20520e7 | 0.359827 | ||||||||
\(73\) | 4.31812e8 | 1.77968 | 0.889839 | − | 0.456275i | \(-0.150817\pi\) | ||||
0.889839 | + | 0.456275i | \(0.150817\pi\) | |||||||
\(74\) | 2.98138e8 | 1.15578 | ||||||||
\(75\) | −3.16406e7 | −0.115470 | ||||||||
\(76\) | −2.87422e7 | −0.0988233 | ||||||||
\(77\) | 1.26589e8 | 0.410382 | ||||||||
\(78\) | 7.71675e7 | 0.236053 | ||||||||
\(79\) | −1.81702e8 | −0.524853 | −0.262427 | − | 0.964952i | \(-0.584523\pi\) | ||||
−0.262427 | + | 0.964952i | \(0.584523\pi\) | |||||||
\(80\) | −6.28629e7 | −0.171589 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −4.38346e8 | −1.07067 | ||||||||
\(83\) | −6.01036e8 | −1.39011 | −0.695055 | − | 0.718956i | \(-0.744620\pi\) | ||||
−0.695055 | + | 0.718956i | \(0.744620\pi\) | |||||||
\(84\) | 2.10887e8 | 0.462160 | ||||||||
\(85\) | 2.44059e7 | 0.0507118 | ||||||||
\(86\) | 6.02600e8 | 1.18792 | ||||||||
\(87\) | 3.97979e8 | 0.744773 | ||||||||
\(88\) | 1.34109e8 | 0.238389 | ||||||||
\(89\) | −4.69609e8 | −0.793380 | −0.396690 | − | 0.917953i | \(-0.629841\pi\) | ||||
−0.396690 | + | 0.917953i | \(0.629841\pi\) | |||||||
\(90\) | −7.00056e7 | −0.112471 | ||||||||
\(91\) | 6.58757e8 | 1.00702 | ||||||||
\(92\) | −1.88769e7 | −0.0274717 | ||||||||
\(93\) | 6.20762e8 | 0.860501 | ||||||||
\(94\) | 1.65573e8 | 0.218732 | ||||||||
\(95\) | 8.14506e7 | 0.102598 | ||||||||
\(96\) | 3.79565e8 | 0.456105 | ||||||||
\(97\) | −3.63557e8 | −0.416966 | −0.208483 | − | 0.978026i | \(-0.566853\pi\) | ||||
−0.208483 | + | 0.978026i | \(0.566853\pi\) | |||||||
\(98\) | −1.69011e9 | −1.85097 | ||||||||
\(99\) | 7.03572e7 | 0.0736123 | ||||||||
\(100\) | −8.61521e7 | −0.0861521 | ||||||||
\(101\) | −1.10033e9 | −1.05215 | −0.526074 | − | 0.850439i | \(-0.676336\pi\) | ||||
−0.526074 | + | 0.850439i | \(0.676336\pi\) | |||||||
\(102\) | 5.39985e7 | 0.0493948 | ||||||||
\(103\) | −4.43205e8 | −0.388005 | −0.194002 | − | 0.981001i | \(-0.562147\pi\) | ||||
−0.194002 | + | 0.981001i | \(0.562147\pi\) | |||||||
\(104\) | 6.97889e8 | 0.584974 | ||||||||
\(105\) | −5.97618e8 | −0.479813 | ||||||||
\(106\) | 1.15984e9 | 0.892326 | ||||||||
\(107\) | −1.53314e9 | −1.13072 | −0.565360 | − | 0.824844i | \(-0.691263\pi\) | ||||
−0.565360 | + | 0.824844i | \(0.691263\pi\) | |||||||
\(108\) | 1.17209e8 | 0.0828999 | ||||||||
\(109\) | −1.91067e9 | −1.29648 | −0.648240 | − | 0.761436i | \(-0.724495\pi\) | ||||
−0.648240 | + | 0.761436i | \(0.724495\pi\) | |||||||
\(110\) | −1.14420e8 | −0.0745133 | ||||||||
\(111\) | 1.41456e9 | 0.884436 | ||||||||
\(112\) | −1.18733e9 | −0.713004 | ||||||||
\(113\) | 1.84040e9 | 1.06184 | 0.530919 | − | 0.847423i | \(-0.321847\pi\) | ||||
0.530919 | + | 0.847423i | \(0.321847\pi\) | |||||||
\(114\) | 1.80211e8 | 0.0999333 | ||||||||
\(115\) | 5.34939e7 | 0.0285209 | ||||||||
\(116\) | 1.08363e9 | 0.555675 | ||||||||
\(117\) | 3.66131e8 | 0.180634 | ||||||||
\(118\) | 4.37883e8 | 0.207916 | ||||||||
\(119\) | 4.60970e8 | 0.210723 | ||||||||
\(120\) | −6.33118e8 | −0.278720 | ||||||||
\(121\) | −2.24295e9 | −0.951231 | ||||||||
\(122\) | 1.19787e8 | 0.0489542 | ||||||||
\(123\) | −2.07979e9 | −0.819308 | ||||||||
\(124\) | 1.69023e9 | 0.642020 | ||||||||
\(125\) | 2.44141e8 | 0.0894427 | ||||||||
\(126\) | −1.32224e9 | −0.467351 | ||||||||
\(127\) | 1.51876e9 | 0.518049 | 0.259025 | − | 0.965871i | \(-0.416599\pi\) | ||||
0.259025 | + | 0.965871i | \(0.416599\pi\) | |||||||
\(128\) | 1.54333e8 | 0.0508177 | ||||||||
\(129\) | 2.85912e9 | 0.909030 | ||||||||
\(130\) | −5.95428e8 | −0.182845 | ||||||||
\(131\) | 5.54699e9 | 1.64565 | 0.822823 | − | 0.568298i | \(-0.192398\pi\) | ||||
0.822823 | + | 0.568298i | \(0.192398\pi\) | |||||||
\(132\) | 1.91571e8 | 0.0549221 | ||||||||
\(133\) | 1.53841e9 | 0.426325 | ||||||||
\(134\) | 2.12165e9 | 0.568463 | ||||||||
\(135\) | −3.32151e8 | −0.0860663 | ||||||||
\(136\) | 4.88353e8 | 0.122408 | ||||||||
\(137\) | 6.74188e8 | 0.163508 | 0.0817539 | − | 0.996653i | \(-0.473948\pi\) | ||||
0.0817539 | + | 0.996653i | \(0.473948\pi\) | |||||||
\(138\) | 1.18356e8 | 0.0277802 | ||||||||
\(139\) | 3.90541e9 | 0.887360 | 0.443680 | − | 0.896185i | \(-0.353673\pi\) | ||||
0.443680 | + | 0.896185i | \(0.353673\pi\) | |||||||
\(140\) | −1.62721e9 | −0.357988 | ||||||||
\(141\) | 7.85581e8 | 0.167381 | ||||||||
\(142\) | −1.14127e9 | −0.235555 | ||||||||
\(143\) | 5.98419e8 | 0.119672 | ||||||||
\(144\) | −6.59909e8 | −0.127895 | ||||||||
\(145\) | −3.07083e9 | −0.576899 | ||||||||
\(146\) | −7.37185e9 | −1.34273 | ||||||||
\(147\) | −8.01897e9 | −1.41641 | ||||||||
\(148\) | 3.85160e9 | 0.659877 | ||||||||
\(149\) | −3.80714e9 | −0.632791 | −0.316396 | − | 0.948627i | \(-0.602473\pi\) | ||||
−0.316396 | + | 0.948627i | \(0.602473\pi\) | |||||||
\(150\) | 5.40166e8 | 0.0871198 | ||||||||
\(151\) | −5.03611e9 | −0.788314 | −0.394157 | − | 0.919043i | \(-0.628963\pi\) | ||||
−0.394157 | + | 0.919043i | \(0.628963\pi\) | |||||||
\(152\) | 1.62980e9 | 0.247650 | ||||||||
\(153\) | 2.56203e8 | 0.0377984 | ||||||||
\(154\) | −2.16112e9 | −0.309625 | ||||||||
\(155\) | −4.78983e9 | −0.666542 | ||||||||
\(156\) | 9.96914e8 | 0.134771 | ||||||||
\(157\) | −1.27343e10 | −1.67273 | −0.836363 | − | 0.548175i | \(-0.815323\pi\) | ||||
−0.836363 | + | 0.548175i | \(0.815323\pi\) | |||||||
\(158\) | 3.10200e9 | 0.395991 | ||||||||
\(159\) | 5.50304e9 | 0.682834 | ||||||||
\(160\) | −2.92874e9 | −0.353298 | ||||||||
\(161\) | 1.01038e9 | 0.118513 | ||||||||
\(162\) | −7.34890e8 | −0.0838311 | ||||||||
\(163\) | −7.30036e9 | −0.810028 | −0.405014 | − | 0.914310i | \(-0.632733\pi\) | ||||
−0.405014 | + | 0.914310i | \(0.632733\pi\) | |||||||
\(164\) | −5.66293e9 | −0.611285 | ||||||||
\(165\) | −5.42880e8 | −0.0570198 | ||||||||
\(166\) | 1.02608e10 | 1.04881 | ||||||||
\(167\) | −1.73438e9 | −0.172552 | −0.0862758 | − | 0.996271i | \(-0.527497\pi\) | ||||
−0.0862758 | + | 0.996271i | \(0.527497\pi\) | |||||||
\(168\) | −1.19581e10 | −1.15817 | ||||||||
\(169\) | −7.49039e9 | −0.706341 | ||||||||
\(170\) | −4.16655e8 | −0.0382611 | ||||||||
\(171\) | 8.55036e8 | 0.0764719 | ||||||||
\(172\) | 7.78489e9 | 0.678226 | ||||||||
\(173\) | −5.91992e9 | −0.502468 | −0.251234 | − | 0.967926i | \(-0.580836\pi\) | ||||
−0.251234 | + | 0.967926i | \(0.580836\pi\) | |||||||
\(174\) | −6.79427e9 | −0.561916 | ||||||||
\(175\) | 4.61125e9 | 0.371661 | ||||||||
\(176\) | −1.07858e9 | −0.0847317 | ||||||||
\(177\) | 2.07759e9 | 0.159104 | ||||||||
\(178\) | 8.01713e9 | 0.598589 | ||||||||
\(179\) | 1.13075e10 | 0.823241 | 0.411620 | − | 0.911355i | \(-0.364963\pi\) | ||||
0.411620 | + | 0.911355i | \(0.364963\pi\) | |||||||
\(180\) | −9.04391e8 | −0.0642140 | ||||||||
\(181\) | −1.96730e10 | −1.36244 | −0.681219 | − | 0.732080i | \(-0.738550\pi\) | ||||
−0.681219 | + | 0.732080i | \(0.738550\pi\) | |||||||
\(182\) | −1.12463e10 | −0.759778 | ||||||||
\(183\) | 5.68344e8 | 0.0374612 | ||||||||
\(184\) | 1.07039e9 | 0.0688436 | ||||||||
\(185\) | −1.09148e10 | −0.685082 | ||||||||
\(186\) | −1.05976e10 | −0.649231 | ||||||||
\(187\) | 4.18748e8 | 0.0250418 | ||||||||
\(188\) | 2.13901e9 | 0.124883 | ||||||||
\(189\) | −6.27355e9 | −0.357631 | ||||||||
\(190\) | −1.39052e9 | −0.0774080 | ||||||||
\(191\) | −8.57929e9 | −0.466446 | −0.233223 | − | 0.972423i | \(-0.574927\pi\) | ||||
−0.233223 | + | 0.972423i | \(0.574927\pi\) | |||||||
\(192\) | −1.06512e10 | −0.565642 | ||||||||
\(193\) | 2.00369e10 | 1.03949 | 0.519747 | − | 0.854320i | \(-0.326026\pi\) | ||||
0.519747 | + | 0.854320i | \(0.326026\pi\) | |||||||
\(194\) | 6.20663e9 | 0.314592 | ||||||||
\(195\) | −2.82509e9 | −0.139919 | ||||||||
\(196\) | −2.18343e10 | −1.05679 | ||||||||
\(197\) | −9.28019e9 | −0.438994 | −0.219497 | − | 0.975613i | \(-0.570442\pi\) | ||||
−0.219497 | + | 0.975613i | \(0.570442\pi\) | |||||||
\(198\) | −1.20113e9 | −0.0555389 | ||||||||
\(199\) | 3.12211e10 | 1.41127 | 0.705635 | − | 0.708576i | \(-0.250662\pi\) | ||||
0.705635 | + | 0.708576i | \(0.250662\pi\) | |||||||
\(200\) | 4.88517e9 | 0.215896 | ||||||||
\(201\) | 1.00665e10 | 0.435005 | ||||||||
\(202\) | 1.87847e10 | 0.793824 | ||||||||
\(203\) | −5.80008e10 | −2.39719 | ||||||||
\(204\) | 6.97599e8 | 0.0282013 | ||||||||
\(205\) | 1.60478e10 | 0.634633 | ||||||||
\(206\) | 7.56636e9 | 0.292742 | ||||||||
\(207\) | 5.61557e8 | 0.0212583 | ||||||||
\(208\) | −5.61282e9 | −0.207920 | ||||||||
\(209\) | 1.39750e9 | 0.0506634 | ||||||||
\(210\) | 1.02025e10 | 0.362009 | ||||||||
\(211\) | 2.95630e10 | 1.02678 | 0.513391 | − | 0.858155i | \(-0.328389\pi\) | ||||
0.513391 | + | 0.858155i | \(0.328389\pi\) | |||||||
\(212\) | 1.49838e10 | 0.509462 | ||||||||
\(213\) | −5.41492e9 | −0.180254 | ||||||||
\(214\) | 2.61737e10 | 0.853105 | ||||||||
\(215\) | −2.20611e10 | −0.704131 | ||||||||
\(216\) | −6.64622e9 | −0.207746 | ||||||||
\(217\) | −9.04687e10 | −2.76968 | ||||||||
\(218\) | 3.26188e10 | 0.978167 | ||||||||
\(219\) | −3.49767e10 | −1.02750 | ||||||||
\(220\) | −1.47817e9 | −0.0425424 | ||||||||
\(221\) | 2.17912e9 | 0.0614492 | ||||||||
\(222\) | −2.41492e10 | −0.667289 | ||||||||
\(223\) | 3.58409e10 | 0.970527 | 0.485263 | − | 0.874368i | \(-0.338724\pi\) | ||||
0.485263 | + | 0.874368i | \(0.338724\pi\) | |||||||
\(224\) | −5.53171e10 | −1.46806 | ||||||||
\(225\) | 2.56289e9 | 0.0666667 | ||||||||
\(226\) | −3.14191e10 | −0.801135 | ||||||||
\(227\) | −7.63678e10 | −1.90895 | −0.954474 | − | 0.298296i | \(-0.903582\pi\) | ||||
−0.954474 | + | 0.298296i | \(0.903582\pi\) | |||||||
\(228\) | 2.32812e9 | 0.0570556 | ||||||||
\(229\) | −7.53272e10 | −1.81006 | −0.905028 | − | 0.425351i | \(-0.860151\pi\) | ||||
−0.905028 | + | 0.425351i | \(0.860151\pi\) | |||||||
\(230\) | −9.13244e8 | −0.0215185 | ||||||||
\(231\) | −1.02537e10 | −0.236934 | ||||||||
\(232\) | −6.14462e10 | −1.39251 | ||||||||
\(233\) | 5.23818e10 | 1.16434 | 0.582168 | − | 0.813068i | \(-0.302205\pi\) | ||||
0.582168 | + | 0.813068i | \(0.302205\pi\) | |||||||
\(234\) | −6.25057e9 | −0.136285 | ||||||||
\(235\) | −6.06158e9 | −0.129652 | ||||||||
\(236\) | 5.65694e9 | 0.118707 | ||||||||
\(237\) | 1.47179e10 | 0.303024 | ||||||||
\(238\) | −7.86965e9 | −0.158986 | ||||||||
\(239\) | −2.49810e10 | −0.495243 | −0.247622 | − | 0.968857i | \(-0.579649\pi\) | ||||
−0.247622 | + | 0.968857i | \(0.579649\pi\) | |||||||
\(240\) | 5.09189e9 | 0.0990669 | ||||||||
\(241\) | 8.94691e10 | 1.70843 | 0.854213 | − | 0.519923i | \(-0.174039\pi\) | ||||
0.854213 | + | 0.519923i | \(0.174039\pi\) | |||||||
\(242\) | 3.82915e10 | 0.717684 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 1.54751e9 | 0.0279498 | ||||||||
\(245\) | 6.18748e10 | 1.09715 | ||||||||
\(246\) | 3.55061e10 | 0.618151 | ||||||||
\(247\) | 7.27246e9 | 0.124321 | ||||||||
\(248\) | −9.58427e10 | −1.60889 | ||||||||
\(249\) | 4.86840e10 | 0.802581 | ||||||||
\(250\) | −4.16795e9 | −0.0674827 | ||||||||
\(251\) | −3.78202e8 | −0.00601440 | −0.00300720 | − | 0.999995i | \(-0.500957\pi\) | ||||
−0.00300720 | + | 0.999995i | \(0.500957\pi\) | |||||||
\(252\) | −1.70818e10 | −0.266828 | ||||||||
\(253\) | 9.17831e8 | 0.0140838 | ||||||||
\(254\) | −2.59281e10 | −0.390858 | ||||||||
\(255\) | −1.97688e9 | −0.0292785 | ||||||||
\(256\) | −6.99607e10 | −1.01806 | ||||||||
\(257\) | −6.92550e10 | −0.990266 | −0.495133 | − | 0.868817i | \(-0.664881\pi\) | ||||
−0.495133 | + | 0.868817i | \(0.664881\pi\) | |||||||
\(258\) | −4.88106e10 | −0.685844 | ||||||||
\(259\) | −2.06155e11 | −2.84672 | ||||||||
\(260\) | −7.69224e9 | −0.104393 | ||||||||
\(261\) | −3.22363e10 | −0.429995 | ||||||||
\(262\) | −9.46977e10 | −1.24161 | ||||||||
\(263\) | 1.22467e11 | 1.57840 | 0.789200 | − | 0.614136i | \(-0.210495\pi\) | ||||
0.789200 | + | 0.614136i | \(0.210495\pi\) | |||||||
\(264\) | −1.08628e10 | −0.137634 | ||||||||
\(265\) | −4.24617e10 | −0.528921 | ||||||||
\(266\) | −2.62637e10 | −0.321653 | ||||||||
\(267\) | 3.80383e10 | 0.458058 | ||||||||
\(268\) | 2.74093e10 | 0.324557 | ||||||||
\(269\) | −2.06902e10 | −0.240924 | −0.120462 | − | 0.992718i | \(-0.538438\pi\) | ||||
−0.120462 | + | 0.992718i | \(0.538438\pi\) | |||||||
\(270\) | 5.67045e9 | 0.0649353 | ||||||||
\(271\) | −3.14415e10 | −0.354113 | −0.177057 | − | 0.984201i | \(-0.556658\pi\) | ||||
−0.177057 | + | 0.984201i | \(0.556658\pi\) | |||||||
\(272\) | −3.92761e9 | −0.0435080 | ||||||||
\(273\) | −5.33593e10 | −0.581405 | ||||||||
\(274\) | −1.15097e10 | −0.123363 | ||||||||
\(275\) | 4.18889e9 | 0.0441674 | ||||||||
\(276\) | 1.52903e9 | 0.0158608 | ||||||||
\(277\) | 1.81200e11 | 1.84926 | 0.924631 | − | 0.380865i | \(-0.124374\pi\) | ||||
0.924631 | + | 0.380865i | \(0.124374\pi\) | |||||||
\(278\) | −6.66729e10 | −0.669495 | ||||||||
\(279\) | −5.02817e10 | −0.496811 | ||||||||
\(280\) | 9.22694e10 | 0.897112 | ||||||||
\(281\) | 1.51008e11 | 1.44485 | 0.722423 | − | 0.691451i | \(-0.243028\pi\) | ||||
0.722423 | + | 0.691451i | \(0.243028\pi\) | |||||||
\(282\) | −1.34114e10 | −0.126285 | ||||||||
\(283\) | −2.02089e11 | −1.87285 | −0.936425 | − | 0.350867i | \(-0.885887\pi\) | ||||
−0.936425 | + | 0.350867i | \(0.885887\pi\) | |||||||
\(284\) | −1.47439e10 | −0.134487 | ||||||||
\(285\) | −6.59750e9 | −0.0592349 | ||||||||
\(286\) | −1.02162e10 | −0.0902902 | ||||||||
\(287\) | 3.03105e11 | 2.63709 | ||||||||
\(288\) | −3.07447e10 | −0.263332 | ||||||||
\(289\) | −1.17063e11 | −0.987142 | ||||||||
\(290\) | 5.24249e10 | 0.435258 | ||||||||
\(291\) | 2.94482e10 | 0.240735 | ||||||||
\(292\) | −9.52358e10 | −0.766615 | ||||||||
\(293\) | 1.59940e11 | 1.26781 | 0.633905 | − | 0.773411i | \(-0.281451\pi\) | ||||
0.633905 | + | 0.773411i | \(0.281451\pi\) | |||||||
\(294\) | 1.36899e11 | 1.06866 | ||||||||
\(295\) | −1.60308e10 | −0.123241 | ||||||||
\(296\) | −2.18401e11 | −1.65364 | ||||||||
\(297\) | −5.69893e9 | −0.0425001 | ||||||||
\(298\) | 6.49952e10 | 0.477428 | ||||||||
\(299\) | 4.77629e9 | 0.0345598 | ||||||||
\(300\) | 6.97832e9 | 0.0497400 | ||||||||
\(301\) | −4.16682e11 | −2.92588 | ||||||||
\(302\) | 8.59761e10 | 0.594766 | ||||||||
\(303\) | 8.91267e10 | 0.607458 | ||||||||
\(304\) | −1.31078e10 | −0.0880233 | ||||||||
\(305\) | −4.38537e9 | −0.0290173 | ||||||||
\(306\) | −4.37388e9 | −0.0285181 | ||||||||
\(307\) | −2.20955e11 | −1.41965 | −0.709826 | − | 0.704378i | \(-0.751226\pi\) | ||||
−0.709826 | + | 0.704378i | \(0.751226\pi\) | |||||||
\(308\) | −2.79192e10 | −0.176777 | ||||||||
\(309\) | 3.58996e10 | 0.224015 | ||||||||
\(310\) | 8.17716e10 | 0.502892 | ||||||||
\(311\) | −8.57467e10 | −0.519752 | −0.259876 | − | 0.965642i | \(-0.583682\pi\) | ||||
−0.259876 | + | 0.965642i | \(0.583682\pi\) | |||||||
\(312\) | −5.65290e10 | −0.337735 | ||||||||
\(313\) | −1.99701e11 | −1.17606 | −0.588031 | − | 0.808838i | \(-0.700097\pi\) | ||||
−0.588031 | + | 0.808838i | \(0.700097\pi\) | |||||||
\(314\) | 2.17398e11 | 1.26204 | ||||||||
\(315\) | 4.84070e10 | 0.277020 | ||||||||
\(316\) | 4.00743e10 | 0.226086 | ||||||||
\(317\) | 1.01674e11 | 0.565513 | 0.282757 | − | 0.959192i | \(-0.408751\pi\) | ||||
0.282757 | + | 0.959192i | \(0.408751\pi\) | |||||||
\(318\) | −9.39474e10 | −0.515184 | ||||||||
\(319\) | −5.26883e10 | −0.284876 | ||||||||
\(320\) | 8.21850e10 | 0.438145 | ||||||||
\(321\) | 1.24184e11 | 0.652821 | ||||||||
\(322\) | −1.72490e10 | −0.0894157 | ||||||||
\(323\) | 5.08896e9 | 0.0260146 | ||||||||
\(324\) | −9.49393e9 | −0.0478623 | ||||||||
\(325\) | 2.17985e10 | 0.108381 | ||||||||
\(326\) | 1.24631e11 | 0.611150 | ||||||||
\(327\) | 1.54764e11 | 0.748523 | ||||||||
\(328\) | 3.21110e11 | 1.53187 | ||||||||
\(329\) | −1.14489e11 | −0.538745 | ||||||||
\(330\) | 9.26800e9 | 0.0430203 | ||||||||
\(331\) | 6.55209e10 | 0.300022 | 0.150011 | − | 0.988684i | \(-0.452069\pi\) | ||||
0.150011 | + | 0.988684i | \(0.452069\pi\) | |||||||
\(332\) | 1.32558e11 | 0.598805 | ||||||||
\(333\) | −1.14579e11 | −0.510630 | ||||||||
\(334\) | 2.96091e10 | 0.130187 | ||||||||
\(335\) | −7.76732e10 | −0.336953 | ||||||||
\(336\) | 9.61740e10 | 0.411653 | ||||||||
\(337\) | −1.63149e11 | −0.689050 | −0.344525 | − | 0.938777i | \(-0.611960\pi\) | ||||
−0.344525 | + | 0.938777i | \(0.611960\pi\) | |||||||
\(338\) | 1.27875e11 | 0.532920 | ||||||||
\(339\) | −1.49072e11 | −0.613052 | ||||||||
\(340\) | −5.38271e9 | −0.0218447 | ||||||||
\(341\) | −8.21823e10 | −0.329142 | ||||||||
\(342\) | −1.45971e10 | −0.0576965 | ||||||||
\(343\) | 6.92304e11 | 2.70068 | ||||||||
\(344\) | −4.41434e11 | −1.69962 | ||||||||
\(345\) | −4.33301e9 | −0.0164666 | ||||||||
\(346\) | 1.01064e11 | 0.379102 | ||||||||
\(347\) | 4.60263e11 | 1.70421 | 0.852105 | − | 0.523370i | \(-0.175325\pi\) | ||||
0.852105 | + | 0.523370i | \(0.175325\pi\) | |||||||
\(348\) | −8.77741e10 | −0.320819 | ||||||||
\(349\) | −1.56693e11 | −0.565372 | −0.282686 | − | 0.959212i | \(-0.591225\pi\) | ||||
−0.282686 | + | 0.959212i | \(0.591225\pi\) | |||||||
\(350\) | −7.87229e10 | −0.280411 | ||||||||
\(351\) | −2.96566e10 | −0.104289 | ||||||||
\(352\) | −5.02504e10 | −0.174461 | ||||||||
\(353\) | 1.39647e11 | 0.478680 | 0.239340 | − | 0.970936i | \(-0.423069\pi\) | ||||
0.239340 | + | 0.970936i | \(0.423069\pi\) | |||||||
\(354\) | −3.54685e10 | −0.120041 | ||||||||
\(355\) | 4.17818e10 | 0.139624 | ||||||||
\(356\) | 1.03572e11 | 0.341757 | ||||||||
\(357\) | −3.73386e10 | −0.121661 | ||||||||
\(358\) | −1.93040e11 | −0.621118 | ||||||||
\(359\) | 3.87102e11 | 1.22999 | 0.614993 | − | 0.788533i | \(-0.289159\pi\) | ||||
0.614993 | + | 0.788533i | \(0.289159\pi\) | |||||||
\(360\) | 5.12825e10 | 0.160919 | ||||||||
\(361\) | 1.69836e10 | 0.0526316 | ||||||||
\(362\) | 3.35856e11 | 1.02793 | ||||||||
\(363\) | 1.81679e11 | 0.549194 | ||||||||
\(364\) | −1.45289e11 | −0.433786 | ||||||||
\(365\) | 2.69882e11 | 0.795896 | ||||||||
\(366\) | −9.70273e9 | −0.0282637 | ||||||||
\(367\) | 3.70839e11 | 1.06706 | 0.533529 | − | 0.845782i | \(-0.320866\pi\) | ||||
0.533529 | + | 0.845782i | \(0.320866\pi\) | |||||||
\(368\) | −8.60872e9 | −0.0244694 | ||||||||
\(369\) | 1.68463e11 | 0.473028 | ||||||||
\(370\) | 1.86336e11 | 0.516880 | ||||||||
\(371\) | −8.02003e11 | −2.19783 | ||||||||
\(372\) | −1.36909e11 | −0.370670 | ||||||||
\(373\) | −1.58356e11 | −0.423590 | −0.211795 | − | 0.977314i | \(-0.567931\pi\) | ||||
−0.211795 | + | 0.977314i | \(0.567931\pi\) | |||||||
\(374\) | −7.14884e9 | −0.0188935 | ||||||||
\(375\) | −1.97754e10 | −0.0516398 | ||||||||
\(376\) | −1.21290e11 | −0.312954 | ||||||||
\(377\) | −2.74184e11 | −0.699047 | ||||||||
\(378\) | 1.07102e11 | 0.269825 | ||||||||
\(379\) | −5.77139e11 | −1.43682 | −0.718412 | − | 0.695617i | \(-0.755131\pi\) | ||||
−0.718412 | + | 0.695617i | \(0.755131\pi\) | |||||||
\(380\) | −1.79639e10 | −0.0441951 | ||||||||
\(381\) | −1.23019e11 | −0.299096 | ||||||||
\(382\) | 1.46465e11 | 0.351924 | ||||||||
\(383\) | 3.76018e11 | 0.892923 | 0.446461 | − | 0.894803i | \(-0.352684\pi\) | ||||
0.446461 | + | 0.894803i | \(0.352684\pi\) | |||||||
\(384\) | −1.25010e10 | −0.0293396 | ||||||||
\(385\) | 7.91183e10 | 0.183529 | ||||||||
\(386\) | −3.42068e11 | −0.784277 | ||||||||
\(387\) | −2.31588e11 | −0.524828 | ||||||||
\(388\) | 8.01824e10 | 0.179612 | ||||||||
\(389\) | 7.59614e11 | 1.68198 | 0.840988 | − | 0.541053i | \(-0.181974\pi\) | ||||
0.840988 | + | 0.541053i | \(0.181974\pi\) | |||||||
\(390\) | 4.82297e10 | 0.105566 | ||||||||
\(391\) | 3.34225e9 | 0.00723175 | ||||||||
\(392\) | 1.23809e12 | 2.64829 | ||||||||
\(393\) | −4.49306e11 | −0.950114 | ||||||||
\(394\) | 1.58431e11 | 0.331212 | ||||||||
\(395\) | −1.13564e11 | −0.234721 | ||||||||
\(396\) | −1.55172e10 | −0.0317093 | ||||||||
\(397\) | 4.42109e11 | 0.893248 | 0.446624 | − | 0.894722i | \(-0.352626\pi\) | ||||
0.446624 | + | 0.894722i | \(0.352626\pi\) | |||||||
\(398\) | −5.33005e11 | −1.06477 | ||||||||
\(399\) | −1.24611e11 | −0.246139 | ||||||||
\(400\) | −3.92893e10 | −0.0767369 | ||||||||
\(401\) | 2.21483e11 | 0.427752 | 0.213876 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213876 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(402\) | −1.71854e11 | −0.328202 | ||||||||
\(403\) | −4.27668e11 | −0.807670 | ||||||||
\(404\) | 2.42677e11 | 0.453224 | ||||||||
\(405\) | 2.69042e10 | 0.0496904 | ||||||||
\(406\) | 9.90185e11 | 1.80863 | ||||||||
\(407\) | −1.87272e11 | −0.338297 | ||||||||
\(408\) | −3.95566e10 | −0.0706721 | ||||||||
\(409\) | −1.65746e11 | −0.292879 | −0.146439 | − | 0.989220i | \(-0.546781\pi\) | ||||
−0.146439 | + | 0.989220i | \(0.546781\pi\) | |||||||
\(410\) | −2.73967e11 | −0.478818 | ||||||||
\(411\) | −5.46092e10 | −0.0944012 | ||||||||
\(412\) | 9.77486e10 | 0.167137 | ||||||||
\(413\) | −3.02785e11 | −0.512105 | ||||||||
\(414\) | −9.58687e9 | −0.0160389 | ||||||||
\(415\) | −3.75648e11 | −0.621676 | ||||||||
\(416\) | −2.61497e11 | −0.428102 | ||||||||
\(417\) | −3.16338e11 | −0.512318 | ||||||||
\(418\) | −2.38581e10 | −0.0382245 | ||||||||
\(419\) | 1.50545e11 | 0.238619 | 0.119309 | − | 0.992857i | \(-0.461932\pi\) | ||||
0.119309 | + | 0.992857i | \(0.461932\pi\) | |||||||
\(420\) | 1.31804e11 | 0.206684 | ||||||||
\(421\) | 1.11582e12 | 1.73111 | 0.865553 | − | 0.500817i | \(-0.166967\pi\) | ||||
0.865553 | + | 0.500817i | \(0.166967\pi\) | |||||||
\(422\) | −5.04698e11 | −0.774686 | ||||||||
\(423\) | −6.36321e10 | −0.0966372 | ||||||||
\(424\) | −8.49643e11 | −1.27670 | ||||||||
\(425\) | 1.52537e10 | 0.0226790 | ||||||||
\(426\) | 9.24431e10 | 0.135998 | ||||||||
\(427\) | −8.28295e10 | −0.120576 | ||||||||
\(428\) | 3.38133e11 | 0.487070 | ||||||||
\(429\) | −4.84719e10 | −0.0690928 | ||||||||
\(430\) | 3.76625e11 | 0.531253 | ||||||||
\(431\) | 5.20796e11 | 0.726976 | 0.363488 | − | 0.931599i | \(-0.381586\pi\) | ||||
0.363488 | + | 0.931599i | \(0.381586\pi\) | |||||||
\(432\) | 5.34527e10 | 0.0738401 | ||||||||
\(433\) | −7.81289e11 | −1.06811 | −0.534055 | − | 0.845450i | \(-0.679333\pi\) | ||||
−0.534055 | + | 0.845450i | \(0.679333\pi\) | |||||||
\(434\) | 1.54447e12 | 2.08967 | ||||||||
\(435\) | 2.48737e11 | 0.333073 | ||||||||
\(436\) | 4.21397e11 | 0.558472 | ||||||||
\(437\) | 1.11542e10 | 0.0146309 | ||||||||
\(438\) | 5.97120e11 | 0.775226 | ||||||||
\(439\) | −5.76901e11 | −0.741328 | −0.370664 | − | 0.928767i | \(-0.620870\pi\) | ||||
−0.370664 | + | 0.928767i | \(0.620870\pi\) | |||||||
\(440\) | 8.38181e10 | 0.106611 | ||||||||
\(441\) | 6.49536e11 | 0.817767 | ||||||||
\(442\) | −3.72018e10 | −0.0463622 | ||||||||
\(443\) | −1.06242e11 | −0.131063 | −0.0655314 | − | 0.997851i | \(-0.520874\pi\) | ||||
−0.0655314 | + | 0.997851i | \(0.520874\pi\) | |||||||
\(444\) | −3.11979e11 | −0.380980 | ||||||||
\(445\) | −2.93506e11 | −0.354810 | ||||||||
\(446\) | −6.11874e11 | −0.732243 | ||||||||
\(447\) | 3.08378e11 | 0.365342 | ||||||||
\(448\) | 1.55228e12 | 1.82062 | ||||||||
\(449\) | 3.68568e11 | 0.427966 | 0.213983 | − | 0.976837i | \(-0.431356\pi\) | ||||
0.213983 | + | 0.976837i | \(0.431356\pi\) | |||||||
\(450\) | −4.37535e10 | −0.0502986 | ||||||||
\(451\) | 2.75343e11 | 0.313386 | ||||||||
\(452\) | −4.05898e11 | −0.457398 | ||||||||
\(453\) | 4.07925e11 | 0.455133 | ||||||||
\(454\) | 1.30375e12 | 1.44026 | ||||||||
\(455\) | 4.11723e11 | 0.450354 | ||||||||
\(456\) | −1.32014e11 | −0.142981 | ||||||||
\(457\) | −6.92422e11 | −0.742588 | −0.371294 | − | 0.928515i | \(-0.621086\pi\) | ||||
−0.371294 | + | 0.928515i | \(0.621086\pi\) | |||||||
\(458\) | 1.28598e12 | 1.36565 | ||||||||
\(459\) | −2.07525e10 | −0.0218229 | ||||||||
\(460\) | −1.17980e10 | −0.0122857 | ||||||||
\(461\) | 1.23633e11 | 0.127491 | 0.0637455 | − | 0.997966i | \(-0.479695\pi\) | ||||
0.0637455 | + | 0.997966i | \(0.479695\pi\) | |||||||
\(462\) | 1.75051e11 | 0.178762 | ||||||||
\(463\) | −5.65668e11 | −0.572067 | −0.286033 | − | 0.958220i | \(-0.592337\pi\) | ||||
−0.286033 | + | 0.958220i | \(0.592337\pi\) | |||||||
\(464\) | 4.94185e11 | 0.494947 | ||||||||
\(465\) | 3.87976e11 | 0.384828 | ||||||||
\(466\) | −8.94257e11 | −0.878468 | ||||||||
\(467\) | 1.11034e12 | 1.08026 | 0.540130 | − | 0.841582i | \(-0.318375\pi\) | ||||
0.540130 | + | 0.841582i | \(0.318375\pi\) | |||||||
\(468\) | −8.07501e10 | −0.0778102 | ||||||||
\(469\) | −1.46707e12 | −1.40014 | ||||||||
\(470\) | 1.03483e11 | 0.0978201 | ||||||||
\(471\) | 1.03147e12 | 0.965749 | ||||||||
\(472\) | −3.20771e11 | −0.297479 | ||||||||
\(473\) | −3.78517e11 | −0.347704 | ||||||||
\(474\) | −2.51262e11 | −0.228625 | ||||||||
\(475\) | 5.09066e10 | 0.0458831 | ||||||||
\(476\) | −1.01667e11 | −0.0907711 | ||||||||
\(477\) | −4.45746e11 | −0.394235 | ||||||||
\(478\) | 4.26473e11 | 0.373651 | ||||||||
\(479\) | −4.59356e11 | −0.398694 | −0.199347 | − | 0.979929i | \(-0.563882\pi\) | ||||
−0.199347 | + | 0.979929i | \(0.563882\pi\) | |||||||
\(480\) | 2.37228e11 | 0.203976 | ||||||||
\(481\) | −9.74545e11 | −0.830136 | ||||||||
\(482\) | −1.52741e12 | −1.28897 | ||||||||
\(483\) | −8.18404e10 | −0.0684236 | ||||||||
\(484\) | 4.94682e11 | 0.409753 | ||||||||
\(485\) | −2.27223e11 | −0.186473 | ||||||||
\(486\) | 5.95261e10 | 0.0483999 | ||||||||
\(487\) | 2.77447e11 | 0.223511 | 0.111756 | − | 0.993736i | \(-0.464353\pi\) | ||||
0.111756 | + | 0.993736i | \(0.464353\pi\) | |||||||
\(488\) | −8.77498e10 | −0.0700417 | ||||||||
\(489\) | 5.91329e11 | 0.467670 | ||||||||
\(490\) | −1.05632e12 | −0.827777 | ||||||||
\(491\) | −8.86757e11 | −0.688554 | −0.344277 | − | 0.938868i | \(-0.611876\pi\) | ||||
−0.344277 | + | 0.938868i | \(0.611876\pi\) | |||||||
\(492\) | 4.58697e11 | 0.352926 | ||||||||
\(493\) | −1.91863e11 | −0.146278 | ||||||||
\(494\) | −1.24155e11 | −0.0937978 | ||||||||
\(495\) | 4.39733e10 | 0.0329204 | ||||||||
\(496\) | 7.70822e11 | 0.571856 | ||||||||
\(497\) | 7.89161e11 | 0.580179 | ||||||||
\(498\) | −8.31129e11 | −0.605531 | ||||||||
\(499\) | −6.77785e11 | −0.489372 | −0.244686 | − | 0.969602i | \(-0.578685\pi\) | ||||
−0.244686 | + | 0.969602i | \(0.578685\pi\) | |||||||
\(500\) | −5.38451e10 | −0.0385284 | ||||||||
\(501\) | 1.40484e11 | 0.0996228 | ||||||||
\(502\) | 6.45664e9 | 0.00453774 | ||||||||
\(503\) | −8.11800e11 | −0.565449 | −0.282724 | − | 0.959201i | \(-0.591238\pi\) | ||||
−0.282724 | + | 0.959201i | \(0.591238\pi\) | |||||||
\(504\) | 9.68608e11 | 0.668668 | ||||||||
\(505\) | −6.87706e11 | −0.470535 | ||||||||
\(506\) | −1.56691e10 | −0.0106260 | ||||||||
\(507\) | 6.06722e11 | 0.407806 | ||||||||
\(508\) | −3.34961e11 | −0.223155 | ||||||||
\(509\) | 1.61730e11 | 0.106797 | 0.0533986 | − | 0.998573i | \(-0.482995\pi\) | ||||
0.0533986 | + | 0.998573i | \(0.482995\pi\) | |||||||
\(510\) | 3.37491e10 | 0.0220900 | ||||||||
\(511\) | 5.09745e12 | 3.30719 | ||||||||
\(512\) | 1.11535e12 | 0.717290 | ||||||||
\(513\) | −6.92579e10 | −0.0441511 | ||||||||
\(514\) | 1.18232e12 | 0.747136 | ||||||||
\(515\) | −2.77003e11 | −0.173521 | ||||||||
\(516\) | −6.30576e11 | −0.391574 | ||||||||
\(517\) | −1.04003e11 | −0.0640232 | ||||||||
\(518\) | 3.51946e12 | 2.14779 | ||||||||
\(519\) | 4.79513e11 | 0.290100 | ||||||||
\(520\) | 4.36181e11 | 0.261608 | ||||||||
\(521\) | −2.87943e12 | −1.71213 | −0.856065 | − | 0.516868i | \(-0.827098\pi\) | ||||
−0.856065 | + | 0.516868i | \(0.827098\pi\) | |||||||
\(522\) | 5.50336e11 | 0.324422 | ||||||||
\(523\) | −1.88151e12 | −1.09963 | −0.549817 | − | 0.835285i | \(-0.685303\pi\) | ||||
−0.549817 | + | 0.835285i | \(0.685303\pi\) | |||||||
\(524\) | −1.22338e12 | −0.708879 | ||||||||
\(525\) | −3.73511e11 | −0.214579 | ||||||||
\(526\) | −2.09074e12 | −1.19087 | ||||||||
\(527\) | −2.99264e11 | −0.169008 | ||||||||
\(528\) | 8.73651e10 | 0.0489199 | ||||||||
\(529\) | −1.79383e12 | −0.995933 | ||||||||
\(530\) | 7.24903e11 | 0.399060 | ||||||||
\(531\) | −1.68285e11 | −0.0918587 | ||||||||
\(532\) | −3.39296e11 | −0.183644 | ||||||||
\(533\) | 1.43285e12 | 0.769006 | ||||||||
\(534\) | −6.49388e11 | −0.345596 | ||||||||
\(535\) | −9.58213e11 | −0.505673 | ||||||||
\(536\) | −1.55421e12 | −0.813335 | ||||||||
\(537\) | −9.15905e11 | −0.475298 | ||||||||
\(538\) | 3.53222e11 | 0.181772 | ||||||||
\(539\) | 1.06163e12 | 0.541779 | ||||||||
\(540\) | 7.32556e10 | 0.0370740 | ||||||||
\(541\) | −1.62100e12 | −0.813568 | −0.406784 | − | 0.913524i | \(-0.633350\pi\) | ||||
−0.406784 | + | 0.913524i | \(0.633350\pi\) | |||||||
\(542\) | 5.36767e11 | 0.267171 | ||||||||
\(543\) | 1.59351e12 | 0.786604 | ||||||||
\(544\) | −1.82985e11 | −0.0895819 | ||||||||
\(545\) | −1.19417e12 | −0.579803 | ||||||||
\(546\) | 9.10946e11 | 0.438658 | ||||||||
\(547\) | 1.76631e12 | 0.843575 | 0.421787 | − | 0.906695i | \(-0.361403\pi\) | ||||
0.421787 | + | 0.906695i | \(0.361403\pi\) | |||||||
\(548\) | −1.48692e11 | −0.0704327 | ||||||||
\(549\) | −4.60359e10 | −0.0216282 | ||||||||
\(550\) | −7.15123e10 | −0.0333234 | ||||||||
\(551\) | −6.40309e11 | −0.295943 | ||||||||
\(552\) | −8.67019e10 | −0.0397469 | ||||||||
\(553\) | −2.14496e12 | −0.975338 | ||||||||
\(554\) | −3.09343e12 | −1.39523 | ||||||||
\(555\) | 8.84097e11 | 0.395532 | ||||||||
\(556\) | −8.61336e11 | −0.382240 | ||||||||
\(557\) | 2.60533e12 | 1.14687 | 0.573435 | − | 0.819251i | \(-0.305610\pi\) | ||||
0.573435 | + | 0.819251i | \(0.305610\pi\) | |||||||
\(558\) | 8.58405e11 | 0.374834 | ||||||||
\(559\) | −1.96976e12 | −0.853219 | ||||||||
\(560\) | −7.42084e11 | −0.318865 | ||||||||
\(561\) | −3.39186e10 | −0.0144579 | ||||||||
\(562\) | −2.57800e12 | −1.09011 | ||||||||
\(563\) | 4.01223e12 | 1.68306 | 0.841528 | − | 0.540214i | \(-0.181657\pi\) | ||||
0.841528 | + | 0.540214i | \(0.181657\pi\) | |||||||
\(564\) | −1.73260e11 | −0.0721010 | ||||||||
\(565\) | 1.15025e12 | 0.474868 | ||||||||
\(566\) | 3.45004e12 | 1.41303 | ||||||||
\(567\) | 5.08158e11 | 0.206478 | ||||||||
\(568\) | 8.36039e11 | 0.337023 | ||||||||
\(569\) | −3.21451e12 | −1.28561 | −0.642806 | − | 0.766029i | \(-0.722230\pi\) | ||||
−0.642806 | + | 0.766029i | \(0.722230\pi\) | |||||||
\(570\) | 1.12632e11 | 0.0446915 | ||||||||
\(571\) | −6.41308e11 | −0.252467 | −0.126233 | − | 0.992001i | \(-0.540289\pi\) | ||||
−0.126233 | + | 0.992001i | \(0.540289\pi\) | |||||||
\(572\) | −1.31981e11 | −0.0515501 | ||||||||
\(573\) | 6.94922e11 | 0.269303 | ||||||||
\(574\) | −5.17459e12 | −1.98963 | ||||||||
\(575\) | 3.34337e10 | 0.0127550 | ||||||||
\(576\) | 8.62745e11 | 0.326574 | ||||||||
\(577\) | −3.87706e12 | −1.45617 | −0.728085 | − | 0.685487i | \(-0.759589\pi\) | ||||
−0.728085 | + | 0.685487i | \(0.759589\pi\) | |||||||
\(578\) | 1.99849e12 | 0.744778 | ||||||||
\(579\) | −1.62299e12 | −0.600152 | ||||||||
\(580\) | 6.77270e11 | 0.248505 | ||||||||
\(581\) | −7.09511e12 | −2.58325 | ||||||||
\(582\) | −5.02737e11 | −0.181630 | ||||||||
\(583\) | −7.28544e11 | −0.261184 | ||||||||
\(584\) | 5.40025e12 | 1.92113 | ||||||||
\(585\) | 2.28832e11 | 0.0807822 | ||||||||
\(586\) | −2.73049e12 | −0.956536 | ||||||||
\(587\) | 3.11635e12 | 1.08336 | 0.541682 | − | 0.840583i | \(-0.317788\pi\) | ||||
0.541682 | + | 0.840583i | \(0.317788\pi\) | |||||||
\(588\) | 1.76858e12 | 0.610136 | ||||||||
\(589\) | −9.98744e11 | −0.341929 | ||||||||
\(590\) | 2.73677e11 | 0.0929831 | ||||||||
\(591\) | 7.51696e11 | 0.253453 | ||||||||
\(592\) | 1.75650e12 | 0.587762 | ||||||||
\(593\) | −1.96777e12 | −0.653475 | −0.326738 | − | 0.945115i | \(-0.605949\pi\) | ||||
−0.326738 | + | 0.945115i | \(0.605949\pi\) | |||||||
\(594\) | 9.72918e10 | 0.0320654 | ||||||||
\(595\) | 2.88107e11 | 0.0942382 | ||||||||
\(596\) | 8.39663e11 | 0.272582 | ||||||||
\(597\) | −2.52891e12 | −0.814797 | ||||||||
\(598\) | −8.15405e10 | −0.0260746 | ||||||||
\(599\) | −2.44774e12 | −0.776864 | −0.388432 | − | 0.921477i | \(-0.626983\pi\) | ||||
−0.388432 | + | 0.921477i | \(0.626983\pi\) | |||||||
\(600\) | −3.95699e11 | −0.124648 | ||||||||
\(601\) | 8.75163e11 | 0.273624 | 0.136812 | − | 0.990597i | \(-0.456314\pi\) | ||||
0.136812 | + | 0.990597i | \(0.456314\pi\) | |||||||
\(602\) | 7.11357e12 | 2.20751 | ||||||||
\(603\) | −8.15383e11 | −0.251150 | ||||||||
\(604\) | 1.11071e12 | 0.339574 | ||||||||
\(605\) | −1.40185e12 | −0.425403 | ||||||||
\(606\) | −1.52156e12 | −0.458314 | ||||||||
\(607\) | −1.87732e12 | −0.561293 | −0.280647 | − | 0.959811i | \(-0.590549\pi\) | ||||
−0.280647 | + | 0.959811i | \(0.590549\pi\) | |||||||
\(608\) | −6.10682e11 | −0.181238 | ||||||||
\(609\) | 4.69807e12 | 1.38402 | ||||||||
\(610\) | 7.48668e10 | 0.0218930 | ||||||||
\(611\) | −5.41219e11 | −0.157104 | ||||||||
\(612\) | −5.65055e10 | −0.0162821 | ||||||||
\(613\) | 2.33539e12 | 0.668017 | 0.334009 | − | 0.942570i | \(-0.391599\pi\) | ||||
0.334009 | + | 0.942570i | \(0.391599\pi\) | |||||||
\(614\) | 3.77213e12 | 1.07110 | ||||||||
\(615\) | −1.29987e12 | −0.366406 | ||||||||
\(616\) | 1.58313e12 | 0.442999 | ||||||||
\(617\) | 4.28203e12 | 1.18951 | 0.594753 | − | 0.803909i | \(-0.297250\pi\) | ||||
0.594753 | + | 0.803909i | \(0.297250\pi\) | |||||||
\(618\) | −6.12875e11 | −0.169014 | ||||||||
\(619\) | −5.25474e12 | −1.43861 | −0.719305 | − | 0.694694i | \(-0.755540\pi\) | ||||
−0.719305 | + | 0.694694i | \(0.755540\pi\) | |||||||
\(620\) | 1.05639e12 | 0.287120 | ||||||||
\(621\) | −4.54862e10 | −0.0122735 | ||||||||
\(622\) | 1.46386e12 | 0.392142 | ||||||||
\(623\) | −5.54364e12 | −1.47434 | ||||||||
\(624\) | 4.54638e11 | 0.120043 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | 3.40928e12 | 0.887315 | ||||||||
\(627\) | −1.13198e11 | −0.0292505 | ||||||||
\(628\) | 2.80853e12 | 0.720545 | ||||||||
\(629\) | −6.81945e11 | −0.173709 | ||||||||
\(630\) | −8.26401e11 | −0.209006 | ||||||||
\(631\) | −1.73310e12 | −0.435202 | −0.217601 | − | 0.976038i | \(-0.569823\pi\) | ||||
−0.217601 | + | 0.976038i | \(0.569823\pi\) | |||||||
\(632\) | −2.27237e12 | −0.566568 | ||||||||
\(633\) | −2.39461e12 | −0.592813 | ||||||||
\(634\) | −1.73577e12 | −0.426668 | ||||||||
\(635\) | 9.49222e11 | 0.231679 | ||||||||
\(636\) | −1.21369e12 | −0.294138 | ||||||||
\(637\) | 5.52459e12 | 1.32945 | ||||||||
\(638\) | 8.99490e11 | 0.214933 | ||||||||
\(639\) | 4.38609e11 | 0.104069 | ||||||||
\(640\) | 9.64583e10 | 0.0227263 | ||||||||
\(641\) | 9.42113e11 | 0.220415 | 0.110208 | − | 0.993909i | \(-0.464848\pi\) | ||||
0.110208 | + | 0.993909i | \(0.464848\pi\) | |||||||
\(642\) | −2.12007e12 | −0.492540 | ||||||||
\(643\) | 1.07698e11 | 0.0248462 | 0.0124231 | − | 0.999923i | \(-0.496046\pi\) | ||||
0.0124231 | + | 0.999923i | \(0.496046\pi\) | |||||||
\(644\) | −2.22838e11 | −0.0510508 | ||||||||
\(645\) | 1.78695e12 | 0.406530 | ||||||||
\(646\) | −8.68783e10 | −0.0196275 | ||||||||
\(647\) | 6.89733e12 | 1.54743 | 0.773717 | − | 0.633532i | \(-0.218395\pi\) | ||||
0.773717 | + | 0.633532i | \(0.218395\pi\) | |||||||
\(648\) | 5.38343e11 | 0.119942 | ||||||||
\(649\) | −2.75051e11 | −0.0608573 | ||||||||
\(650\) | −3.72143e11 | −0.0817710 | ||||||||
\(651\) | 7.32796e12 | 1.59908 | ||||||||
\(652\) | 1.61009e12 | 0.348928 | ||||||||
\(653\) | −6.08371e12 | −1.30936 | −0.654681 | − | 0.755906i | \(-0.727197\pi\) | ||||
−0.654681 | + | 0.755906i | \(0.727197\pi\) | |||||||
\(654\) | −2.64212e12 | −0.564745 | ||||||||
\(655\) | 3.46687e12 | 0.735955 | ||||||||
\(656\) | −2.58255e12 | −0.544480 | ||||||||
\(657\) | 2.83312e12 | 0.593226 | ||||||||
\(658\) | 1.95455e12 | 0.406472 | ||||||||
\(659\) | −7.58358e12 | −1.56635 | −0.783177 | − | 0.621799i | \(-0.786402\pi\) | ||||
−0.783177 | + | 0.621799i | \(0.786402\pi\) | |||||||
\(660\) | 1.19732e11 | 0.0245619 | ||||||||
\(661\) | −4.44191e12 | −0.905030 | −0.452515 | − | 0.891757i | \(-0.649473\pi\) | ||||
−0.452515 | + | 0.891757i | \(0.649473\pi\) | |||||||
\(662\) | −1.11857e12 | −0.226361 | ||||||||
\(663\) | −1.76509e11 | −0.0354777 | ||||||||
\(664\) | −7.51658e12 | −1.50060 | ||||||||
\(665\) | 9.61508e11 | 0.190658 | ||||||||
\(666\) | 1.95608e12 | 0.385260 | ||||||||
\(667\) | −4.20533e11 | −0.0822685 | ||||||||
\(668\) | 3.82516e11 | 0.0743285 | ||||||||
\(669\) | −2.90312e12 | −0.560334 | ||||||||
\(670\) | 1.32603e12 | 0.254224 | ||||||||
\(671\) | −7.52428e10 | −0.0143289 | ||||||||
\(672\) | 4.48068e12 | 0.847583 | ||||||||
\(673\) | −5.95654e12 | −1.11925 | −0.559624 | − | 0.828747i | \(-0.689054\pi\) | ||||
−0.559624 | + | 0.828747i | \(0.689054\pi\) | |||||||
\(674\) | 2.78527e12 | 0.519874 | ||||||||
\(675\) | −2.07594e11 | −0.0384900 | ||||||||
\(676\) | 1.65200e12 | 0.304264 | ||||||||
\(677\) | 3.79342e12 | 0.694036 | 0.347018 | − | 0.937858i | \(-0.387194\pi\) | ||||
0.347018 | + | 0.937858i | \(0.387194\pi\) | |||||||
\(678\) | 2.54495e12 | 0.462535 | ||||||||
\(679\) | −4.29172e12 | −0.774850 | ||||||||
\(680\) | 3.05221e11 | 0.0547424 | ||||||||
\(681\) | 6.18579e12 | 1.10213 | ||||||||
\(682\) | 1.40301e12 | 0.248331 | ||||||||
\(683\) | −8.63237e12 | −1.51788 | −0.758939 | − | 0.651162i | \(-0.774282\pi\) | ||||
−0.758939 | + | 0.651162i | \(0.774282\pi\) | |||||||
\(684\) | −1.88578e11 | −0.0329411 | ||||||||
\(685\) | 4.21367e11 | 0.0731229 | ||||||||
\(686\) | −1.18190e13 | −2.03761 | ||||||||
\(687\) | 6.10150e12 | 1.04504 | ||||||||
\(688\) | 3.55027e12 | 0.604106 | ||||||||
\(689\) | −3.79127e12 | −0.640911 | ||||||||
\(690\) | 7.39727e10 | 0.0124237 | ||||||||
\(691\) | 8.23079e12 | 1.37338 | 0.686689 | − | 0.726951i | \(-0.259063\pi\) | ||||
0.686689 | + | 0.726951i | \(0.259063\pi\) | |||||||
\(692\) | 1.30563e12 | 0.216443 | ||||||||
\(693\) | 8.30552e11 | 0.136794 | ||||||||
\(694\) | −7.85757e12 | −1.28579 | ||||||||
\(695\) | 2.44088e12 | 0.396840 | ||||||||
\(696\) | 4.97714e12 | 0.803967 | ||||||||
\(697\) | 1.00265e12 | 0.160917 | ||||||||
\(698\) | 2.67505e12 | 0.426562 | ||||||||
\(699\) | −4.24292e12 | −0.672230 | ||||||||
\(700\) | −1.01701e12 | −0.160097 | ||||||||
\(701\) | 5.13274e12 | 0.802819 | 0.401410 | − | 0.915899i | \(-0.368520\pi\) | ||||
0.401410 | + | 0.915899i | \(0.368520\pi\) | |||||||
\(702\) | 5.06296e11 | 0.0786842 | ||||||||
\(703\) | −2.27588e12 | −0.351439 | ||||||||
\(704\) | 1.41010e12 | 0.216359 | ||||||||
\(705\) | 4.90988e11 | 0.0748549 | ||||||||
\(706\) | −2.38404e12 | −0.361154 | ||||||||
\(707\) | −1.29892e13 | −1.95521 | ||||||||
\(708\) | −4.58212e11 | −0.0685357 | ||||||||
\(709\) | 3.81960e12 | 0.567688 | 0.283844 | − | 0.958870i | \(-0.408390\pi\) | ||||
0.283844 | + | 0.958870i | \(0.408390\pi\) | |||||||
\(710\) | −7.13296e11 | −0.105343 | ||||||||
\(711\) | −1.19215e12 | −0.174951 | ||||||||
\(712\) | −5.87294e12 | −0.856438 | ||||||||
\(713\) | −6.55940e11 | −0.0950520 | ||||||||
\(714\) | 6.37442e11 | 0.0917907 | ||||||||
\(715\) | 3.74012e11 | 0.0535190 | ||||||||
\(716\) | −2.49386e12 | −0.354620 | ||||||||
\(717\) | 2.02346e12 | 0.285929 | ||||||||
\(718\) | −6.60857e12 | −0.927999 | ||||||||
\(719\) | −1.11913e13 | −1.56172 | −0.780859 | − | 0.624708i | \(-0.785218\pi\) | ||||
−0.780859 | + | 0.624708i | \(0.785218\pi\) | |||||||
\(720\) | −4.12443e11 | −0.0571963 | ||||||||
\(721\) | −5.23194e12 | −0.721032 | ||||||||
\(722\) | −2.89942e11 | −0.0397094 | ||||||||
\(723\) | −7.24700e12 | −0.986360 | ||||||||
\(724\) | 4.33887e12 | 0.586885 | ||||||||
\(725\) | −1.91927e12 | −0.257997 | ||||||||
\(726\) | −3.10161e12 | −0.414355 | ||||||||
\(727\) | −8.48783e12 | −1.12692 | −0.563458 | − | 0.826145i | \(-0.690529\pi\) | ||||
−0.563458 | + | 0.826145i | \(0.690529\pi\) | |||||||
\(728\) | 8.23844e12 | 1.08706 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −4.60741e12 | −0.600487 | ||||||||
\(731\) | −1.37836e12 | −0.178539 | ||||||||
\(732\) | −1.25348e11 | −0.0161368 | ||||||||
\(733\) | 4.12823e12 | 0.528197 | 0.264098 | − | 0.964496i | \(-0.414926\pi\) | ||||
0.264098 | + | 0.964496i | \(0.414926\pi\) | |||||||
\(734\) | −6.33093e12 | −0.805073 | ||||||||
\(735\) | −5.01185e12 | −0.633440 | ||||||||
\(736\) | −4.01074e11 | −0.0503819 | ||||||||
\(737\) | −1.33269e12 | −0.166390 | ||||||||
\(738\) | −2.87599e12 | −0.356890 | ||||||||
\(739\) | 3.52537e12 | 0.434815 | 0.217408 | − | 0.976081i | \(-0.430240\pi\) | ||||
0.217408 | + | 0.976081i | \(0.430240\pi\) | |||||||
\(740\) | 2.40725e12 | 0.295106 | ||||||||
\(741\) | −5.89069e11 | −0.0717768 | ||||||||
\(742\) | 1.36917e13 | 1.65821 | ||||||||
\(743\) | −6.43206e12 | −0.774284 | −0.387142 | − | 0.922020i | \(-0.626538\pi\) | ||||
−0.387142 | + | 0.922020i | \(0.626538\pi\) | |||||||
\(744\) | 7.76326e12 | 0.928894 | ||||||||
\(745\) | −2.37946e12 | −0.282993 | ||||||||
\(746\) | 2.70345e12 | 0.319590 | ||||||||
\(747\) | −3.94340e12 | −0.463370 | ||||||||
\(748\) | −9.23547e10 | −0.0107870 | ||||||||
\(749\) | −1.80984e13 | −2.10122 | ||||||||
\(750\) | 3.37604e11 | 0.0389612 | ||||||||
\(751\) | 1.02373e12 | 0.117437 | 0.0587184 | − | 0.998275i | \(-0.481299\pi\) | ||||
0.0587184 | + | 0.998275i | \(0.481299\pi\) | |||||||
\(752\) | 9.75485e11 | 0.111235 | ||||||||
\(753\) | 3.06344e10 | 0.00347242 | ||||||||
\(754\) | 4.68085e12 | 0.527417 | ||||||||
\(755\) | −3.14757e12 | −0.352545 | ||||||||
\(756\) | 1.38363e12 | 0.154053 | ||||||||
\(757\) | 5.86577e12 | 0.649222 | 0.324611 | − | 0.945848i | \(-0.394767\pi\) | ||||
0.324611 | + | 0.945848i | \(0.394767\pi\) | |||||||
\(758\) | 9.85287e12 | 1.08405 | ||||||||
\(759\) | −7.43443e10 | −0.00813130 | ||||||||
\(760\) | 1.01862e12 | 0.110752 | ||||||||
\(761\) | 6.18495e12 | 0.668506 | 0.334253 | − | 0.942483i | \(-0.391516\pi\) | ||||
0.334253 | + | 0.942483i | \(0.391516\pi\) | |||||||
\(762\) | 2.10017e12 | 0.225662 | ||||||||
\(763\) | −2.25550e13 | −2.40926 | ||||||||
\(764\) | 1.89216e12 | 0.200926 | ||||||||
\(765\) | 1.60127e11 | 0.0169039 | ||||||||
\(766\) | −6.41934e12 | −0.673692 | ||||||||
\(767\) | −1.43134e12 | −0.149336 | ||||||||
\(768\) | 5.66682e12 | 0.587779 | ||||||||
\(769\) | −1.87533e11 | −0.0193379 | −0.00966895 | − | 0.999953i | \(-0.503078\pi\) | ||||
−0.00966895 | + | 0.999953i | \(0.503078\pi\) | |||||||
\(770\) | −1.35070e12 | −0.138469 | ||||||||
\(771\) | 5.60965e12 | 0.571731 | ||||||||
\(772\) | −4.41912e12 | −0.447773 | ||||||||
\(773\) | −3.37329e12 | −0.339818 | −0.169909 | − | 0.985460i | \(-0.554347\pi\) | ||||
−0.169909 | + | 0.985460i | \(0.554347\pi\) | |||||||
\(774\) | 3.95366e12 | 0.395972 | ||||||||
\(775\) | −2.99364e12 | −0.298086 | ||||||||
\(776\) | −4.54666e12 | −0.450106 | ||||||||
\(777\) | 1.66985e13 | 1.64355 | ||||||||
\(778\) | −1.29681e13 | −1.26902 | ||||||||
\(779\) | 3.34618e12 | 0.325560 | ||||||||
\(780\) | 6.23072e11 | 0.0602715 | ||||||||
\(781\) | 7.16879e11 | 0.0689471 | ||||||||
\(782\) | −5.70586e10 | −0.00545621 | ||||||||
\(783\) | 2.61114e12 | 0.248258 | ||||||||
\(784\) | −9.95744e12 | −0.941294 | ||||||||
\(785\) | −7.95891e12 | −0.748066 | ||||||||
\(786\) | 7.67052e12 | 0.716841 | ||||||||
\(787\) | −3.45820e12 | −0.321340 | −0.160670 | − | 0.987008i | \(-0.551365\pi\) | ||||
−0.160670 | + | 0.987008i | \(0.551365\pi\) | |||||||
\(788\) | 2.04674e12 | 0.189101 | ||||||||
\(789\) | −9.91980e12 | −0.911290 | ||||||||
\(790\) | 1.93875e12 | 0.177093 | ||||||||
\(791\) | 2.17255e13 | 1.97322 | ||||||||
\(792\) | 8.79889e11 | 0.0794629 | ||||||||
\(793\) | −3.91556e11 | −0.0351612 | ||||||||
\(794\) | −7.54765e12 | −0.673937 | ||||||||
\(795\) | 3.43940e12 | 0.305373 | ||||||||
\(796\) | −6.88580e12 | −0.607919 | ||||||||
\(797\) | −1.50198e13 | −1.31857 | −0.659284 | − | 0.751894i | \(-0.729141\pi\) | ||||
−0.659284 | + | 0.751894i | \(0.729141\pi\) | |||||||
\(798\) | 2.12736e12 | 0.185707 | ||||||||
\(799\) | −3.78722e11 | −0.0328746 | ||||||||
\(800\) | −1.83046e12 | −0.157999 | ||||||||
\(801\) | −3.08111e12 | −0.264460 | ||||||||
\(802\) | −3.78115e12 | −0.322730 | ||||||||
\(803\) | 4.63055e12 | 0.393018 | ||||||||
\(804\) | −2.22015e12 | −0.187383 | ||||||||
\(805\) | 6.31485e11 | 0.0530007 | ||||||||
\(806\) | 7.30111e12 | 0.609371 | ||||||||
\(807\) | 1.67591e12 | 0.139097 | ||||||||
\(808\) | −1.37608e13 | −1.13577 | ||||||||
\(809\) | −5.19090e12 | −0.426063 | −0.213032 | − | 0.977045i | \(-0.568334\pi\) | ||||
−0.213032 | + | 0.977045i | \(0.568334\pi\) | |||||||
\(810\) | −4.59306e11 | −0.0374904 | ||||||||
\(811\) | 5.64885e11 | 0.0458528 | 0.0229264 | − | 0.999737i | \(-0.492702\pi\) | ||||
0.0229264 | + | 0.999737i | \(0.492702\pi\) | |||||||
\(812\) | 1.27920e13 | 1.03261 | ||||||||
\(813\) | 2.54676e12 | 0.204447 | ||||||||
\(814\) | 3.19710e12 | 0.255238 | ||||||||
\(815\) | −4.56273e12 | −0.362256 | ||||||||
\(816\) | 3.18137e11 | 0.0251193 | ||||||||
\(817\) | −4.60003e12 | −0.361212 | ||||||||
\(818\) | 2.82960e12 | 0.220971 | ||||||||
\(819\) | 4.32211e12 | 0.335674 | ||||||||
\(820\) | −3.53933e12 | −0.273375 | ||||||||
\(821\) | 2.42921e13 | 1.86604 | 0.933020 | − | 0.359826i | \(-0.117164\pi\) | ||||
0.933020 | + | 0.359826i | \(0.117164\pi\) | |||||||
\(822\) | 9.32284e11 | 0.0712238 | ||||||||
\(823\) | −1.33695e13 | −1.01582 | −0.507910 | − | 0.861410i | \(-0.669582\pi\) | ||||
−0.507910 | + | 0.861410i | \(0.669582\pi\) | |||||||
\(824\) | −5.54273e12 | −0.418843 | ||||||||
\(825\) | −3.39300e11 | −0.0255000 | ||||||||
\(826\) | 5.16912e12 | 0.386372 | ||||||||
\(827\) | 4.50524e12 | 0.334922 | 0.167461 | − | 0.985879i | \(-0.446443\pi\) | ||||
0.167461 | + | 0.985879i | \(0.446443\pi\) | |||||||
\(828\) | −1.23851e11 | −0.00915722 | ||||||||
\(829\) | −8.89486e12 | −0.654099 | −0.327050 | − | 0.945007i | \(-0.606054\pi\) | ||||
−0.327050 | + | 0.945007i | \(0.606054\pi\) | |||||||
\(830\) | 6.41303e12 | 0.469042 | ||||||||
\(831\) | −1.46772e13 | −1.06767 | ||||||||
\(832\) | 7.33803e12 | 0.530914 | ||||||||
\(833\) | 3.86588e12 | 0.278193 | ||||||||
\(834\) | 5.40050e12 | 0.386533 | ||||||||
\(835\) | −1.08399e12 | −0.0771675 | ||||||||
\(836\) | −3.08219e11 | −0.0218238 | ||||||||
\(837\) | 4.07282e12 | 0.286834 | ||||||||
\(838\) | −2.57010e12 | −0.180033 | ||||||||
\(839\) | 1.18724e13 | 0.827199 | 0.413599 | − | 0.910459i | \(-0.364271\pi\) | ||||
0.413599 | + | 0.910459i | \(0.364271\pi\) | |||||||
\(840\) | −7.47382e12 | −0.517948 | ||||||||
\(841\) | 9.63362e12 | 0.664060 | ||||||||
\(842\) | −1.90492e13 | −1.30608 | ||||||||
\(843\) | −1.22317e13 | −0.834183 | ||||||||
\(844\) | −6.52011e12 | −0.442297 | ||||||||
\(845\) | −4.68149e12 | −0.315885 | ||||||||
\(846\) | 1.08632e12 | 0.0729108 | ||||||||
\(847\) | −2.64776e13 | −1.76768 | ||||||||
\(848\) | 6.83332e12 | 0.453785 | ||||||||
\(849\) | 1.63692e13 | 1.08129 | ||||||||
\(850\) | −2.60410e11 | −0.0171109 | ||||||||
\(851\) | −1.49472e12 | −0.0976959 | ||||||||
\(852\) | 1.19426e12 | 0.0776462 | ||||||||
\(853\) | 8.65613e12 | 0.559826 | 0.279913 | − | 0.960025i | \(-0.409694\pi\) | ||||
0.279913 | + | 0.960025i | \(0.409694\pi\) | |||||||
\(854\) | 1.41406e12 | 0.0909719 | ||||||||
\(855\) | 5.34398e11 | 0.0341993 | ||||||||
\(856\) | −1.91735e13 | −1.22059 | ||||||||
\(857\) | −2.58026e12 | −0.163399 | −0.0816997 | − | 0.996657i | \(-0.526035\pi\) | ||||
−0.0816997 | + | 0.996657i | \(0.526035\pi\) | |||||||
\(858\) | 8.27509e11 | 0.0521291 | ||||||||
\(859\) | −1.20094e13 | −0.752581 | −0.376291 | − | 0.926502i | \(-0.622801\pi\) | ||||
−0.376291 | + | 0.926502i | \(0.622801\pi\) | |||||||
\(860\) | 4.86556e12 | 0.303312 | ||||||||
\(861\) | −2.45515e13 | −1.52252 | ||||||||
\(862\) | −8.89099e12 | −0.548489 | ||||||||
\(863\) | 2.57711e13 | 1.58156 | 0.790779 | − | 0.612102i | \(-0.209676\pi\) | ||||
0.790779 | + | 0.612102i | \(0.209676\pi\) | |||||||
\(864\) | 2.49032e12 | 0.152035 | ||||||||
\(865\) | −3.69995e12 | −0.224710 | ||||||||
\(866\) | 1.33381e13 | 0.805867 | ||||||||
\(867\) | 9.48210e12 | 0.569926 | ||||||||
\(868\) | 1.99528e13 | 1.19307 | ||||||||
\(869\) | −1.94849e12 | −0.115907 | ||||||||
\(870\) | −4.24642e12 | −0.251296 | ||||||||
\(871\) | −6.93519e12 | −0.408297 | ||||||||
\(872\) | −2.38949e13 | −1.39952 | ||||||||
\(873\) | −2.38530e12 | −0.138989 | ||||||||
\(874\) | −1.90424e11 | −0.0110387 | ||||||||
\(875\) | 2.88203e12 | 0.166212 | ||||||||
\(876\) | 7.71410e12 | 0.442605 | ||||||||
\(877\) | −4.15440e12 | −0.237143 | −0.118571 | − | 0.992946i | \(-0.537831\pi\) | ||||
−0.118571 | + | 0.992946i | \(0.537831\pi\) | |||||||
\(878\) | 9.84880e12 | 0.559317 | ||||||||
\(879\) | −1.29552e13 | −0.731970 | ||||||||
\(880\) | −6.74113e11 | −0.0378932 | ||||||||
\(881\) | 2.65371e13 | 1.48409 | 0.742047 | − | 0.670348i | \(-0.233855\pi\) | ||||
0.742047 | + | 0.670348i | \(0.233855\pi\) | |||||||
\(882\) | −1.10888e13 | −0.616989 | ||||||||
\(883\) | 1.41263e13 | 0.781998 | 0.390999 | − | 0.920391i | \(-0.372130\pi\) | ||||
0.390999 | + | 0.920391i | \(0.372130\pi\) | |||||||
\(884\) | −4.80604e11 | −0.0264699 | ||||||||
\(885\) | 1.29850e12 | 0.0711534 | ||||||||
\(886\) | 1.81376e12 | 0.0988843 | ||||||||
\(887\) | −1.50302e13 | −0.815283 | −0.407642 | − | 0.913142i | \(-0.633649\pi\) | ||||
−0.407642 | + | 0.913142i | \(0.633649\pi\) | |||||||
\(888\) | 1.76905e13 | 0.954731 | ||||||||
\(889\) | 1.79286e13 | 0.962694 | ||||||||
\(890\) | 5.01071e12 | 0.267697 | ||||||||
\(891\) | 4.61614e11 | 0.0245374 | ||||||||
\(892\) | −7.90470e12 | −0.418065 | ||||||||
\(893\) | −1.26392e12 | −0.0665103 | ||||||||
\(894\) | −5.26461e12 | −0.275643 | ||||||||
\(895\) | 7.06717e12 | 0.368164 | ||||||||
\(896\) | 1.82187e12 | 0.0944348 | ||||||||
\(897\) | −3.86880e11 | −0.0199531 | ||||||||
\(898\) | −6.29217e12 | −0.322892 | ||||||||
\(899\) | 3.76544e13 | 1.92263 | ||||||||
\(900\) | −5.65244e11 | −0.0287174 | ||||||||
\(901\) | −2.65297e12 | −0.134113 | ||||||||
\(902\) | −4.70063e12 | −0.236443 | ||||||||
\(903\) | 3.37513e13 | 1.68926 | ||||||||
\(904\) | 2.30160e13 | 1.14623 | ||||||||
\(905\) | −1.22956e13 | −0.609301 | ||||||||
\(906\) | −6.96406e12 | −0.343389 | ||||||||
\(907\) | 2.29165e13 | 1.12439 | 0.562193 | − | 0.827006i | \(-0.309958\pi\) | ||||
0.562193 | + | 0.827006i | \(0.309958\pi\) | |||||||
\(908\) | 1.68429e13 | 0.822299 | ||||||||
\(909\) | −7.21926e12 | −0.350716 | ||||||||
\(910\) | −7.02891e12 | −0.339783 | ||||||||
\(911\) | −7.02130e12 | −0.337742 | −0.168871 | − | 0.985638i | \(-0.554012\pi\) | ||||
−0.168871 | + | 0.985638i | \(0.554012\pi\) | |||||||
\(912\) | 1.06173e12 | 0.0508203 | ||||||||
\(913\) | −6.44524e12 | −0.306988 | ||||||||
\(914\) | 1.18210e13 | 0.560267 | ||||||||
\(915\) | 3.55215e11 | 0.0167532 | ||||||||
\(916\) | 1.66134e13 | 0.779701 | ||||||||
\(917\) | 6.54810e13 | 3.05811 | ||||||||
\(918\) | 3.54284e11 | 0.0164649 | ||||||||
\(919\) | 1.14513e13 | 0.529584 | 0.264792 | − | 0.964306i | \(-0.414697\pi\) | ||||
0.264792 | + | 0.964306i | \(0.414697\pi\) | |||||||
\(920\) | 6.68996e11 | 0.0307878 | ||||||||
\(921\) | 1.78974e13 | 0.819636 | ||||||||
\(922\) | −2.11065e12 | −0.0961893 | ||||||||
\(923\) | 3.73056e12 | 0.169187 | ||||||||
\(924\) | 2.26146e12 | 0.102062 | ||||||||
\(925\) | −6.82174e12 | −0.306378 | ||||||||
\(926\) | 9.65703e12 | 0.431613 | ||||||||
\(927\) | −2.90787e12 | −0.129335 | ||||||||
\(928\) | 2.30238e13 | 1.01908 | ||||||||
\(929\) | −4.07798e13 | −1.79628 | −0.898141 | − | 0.439708i | \(-0.855082\pi\) | ||||
−0.898141 | + | 0.439708i | \(0.855082\pi\) | |||||||
\(930\) | −6.62350e12 | −0.290345 | ||||||||
\(931\) | 1.29017e13 | 0.562826 | ||||||||
\(932\) | −1.15528e13 | −0.501550 | ||||||||
\(933\) | 6.94548e12 | 0.300079 | ||||||||
\(934\) | −1.89556e13 | −0.815034 | ||||||||
\(935\) | 2.61718e11 | 0.0111990 | ||||||||
\(936\) | 4.57885e12 | 0.194991 | ||||||||
\(937\) | 2.76611e12 | 0.117231 | 0.0586153 | − | 0.998281i | \(-0.481331\pi\) | ||||
0.0586153 | + | 0.998281i | \(0.481331\pi\) | |||||||
\(938\) | 2.50456e13 | 1.05638 | ||||||||
\(939\) | 1.61758e13 | 0.679000 | ||||||||
\(940\) | 1.33688e12 | 0.0558492 | ||||||||
\(941\) | 1.33465e13 | 0.554900 | 0.277450 | − | 0.960740i | \(-0.410511\pi\) | ||||
0.277450 | + | 0.960740i | \(0.410511\pi\) | |||||||
\(942\) | −1.76093e13 | −0.728638 | ||||||||
\(943\) | 2.19765e12 | 0.0905017 | ||||||||
\(944\) | 2.57982e12 | 0.105734 | ||||||||
\(945\) | −3.92097e12 | −0.159938 | ||||||||
\(946\) | 6.46201e12 | 0.262336 | ||||||||
\(947\) | −4.79853e13 | −1.93880 | −0.969402 | − | 0.245480i | \(-0.921054\pi\) | ||||
−0.969402 | + | 0.245480i | \(0.921054\pi\) | |||||||
\(948\) | −3.24602e12 | −0.130531 | ||||||||
\(949\) | 2.40969e13 | 0.964413 | ||||||||
\(950\) | −8.69074e11 | −0.0346179 | ||||||||
\(951\) | −8.23558e12 | −0.326499 | ||||||||
\(952\) | 5.76491e12 | 0.227471 | ||||||||
\(953\) | 4.46482e13 | 1.75342 | 0.876710 | − | 0.481020i | \(-0.159733\pi\) | ||||
0.876710 | + | 0.481020i | \(0.159733\pi\) | |||||||
\(954\) | 7.60974e12 | 0.297442 | ||||||||
\(955\) | −5.36205e12 | −0.208601 | ||||||||
\(956\) | 5.50954e12 | 0.213331 | ||||||||
\(957\) | 4.26775e12 | 0.164473 | ||||||||
\(958\) | 7.84209e12 | 0.300806 | ||||||||
\(959\) | 7.95865e12 | 0.303847 | ||||||||
\(960\) | −6.65698e12 | −0.252963 | ||||||||
\(961\) | 3.22930e13 | 1.22139 | ||||||||
\(962\) | 1.66374e13 | 0.626320 | ||||||||
\(963\) | −1.00589e13 | −0.376907 | ||||||||
\(964\) | −1.97324e13 | −0.735923 | ||||||||
\(965\) | 1.25230e13 | 0.464876 | ||||||||
\(966\) | 1.39717e12 | 0.0516242 | ||||||||
\(967\) | −2.18351e13 | −0.803039 | −0.401519 | − | 0.915851i | \(-0.631518\pi\) | ||||
−0.401519 | + | 0.915851i | \(0.631518\pi\) | |||||||
\(968\) | −2.80504e13 | −1.02683 | ||||||||
\(969\) | −4.12206e11 | −0.0150196 | ||||||||
\(970\) | 3.87914e12 | 0.140690 | ||||||||
\(971\) | −1.25175e13 | −0.451888 | −0.225944 | − | 0.974140i | \(-0.572547\pi\) | ||||
−0.225944 | + | 0.974140i | \(0.572547\pi\) | |||||||
\(972\) | 7.69008e11 | 0.0276333 | ||||||||
\(973\) | 4.61026e13 | 1.64899 | ||||||||
\(974\) | −4.73655e12 | −0.168635 | ||||||||
\(975\) | −1.76568e12 | −0.0625736 | ||||||||
\(976\) | 7.05734e11 | 0.0248953 | ||||||||
\(977\) | 3.20249e13 | 1.12451 | 0.562253 | − | 0.826965i | \(-0.309935\pi\) | ||||
0.562253 | + | 0.826965i | \(0.309935\pi\) | |||||||
\(978\) | −1.00951e13 | −0.352847 | ||||||||
\(979\) | −5.03588e12 | −0.175208 | ||||||||
\(980\) | −1.36464e13 | −0.472609 | ||||||||
\(981\) | −1.25359e13 | −0.432160 | ||||||||
\(982\) | 1.51386e13 | 0.519500 | ||||||||
\(983\) | 5.40250e13 | 1.84546 | 0.922728 | − | 0.385452i | \(-0.125954\pi\) | ||||
0.922728 | + | 0.385452i | \(0.125954\pi\) | |||||||
\(984\) | −2.60099e13 | −0.884426 | ||||||||
\(985\) | −5.80012e12 | −0.196324 | ||||||||
\(986\) | 3.27546e12 | 0.110364 | ||||||||
\(987\) | 9.27363e12 | 0.311044 | ||||||||
\(988\) | −1.60394e12 | −0.0535527 | ||||||||
\(989\) | −3.02114e12 | −0.100412 | ||||||||
\(990\) | −7.50708e11 | −0.0248378 | ||||||||
\(991\) | −8.74099e12 | −0.287892 | −0.143946 | − | 0.989586i | \(-0.545979\pi\) | ||||
−0.143946 | + | 0.989586i | \(0.545979\pi\) | |||||||
\(992\) | 3.59121e13 | 1.17744 | ||||||||
\(993\) | −5.30719e12 | −0.173218 | ||||||||
\(994\) | −1.34725e13 | −0.437733 | ||||||||
\(995\) | 1.95132e13 | 0.631139 | ||||||||
\(996\) | −1.07372e13 | −0.345720 | ||||||||
\(997\) | −1.29294e13 | −0.414429 | −0.207214 | − | 0.978296i | \(-0.566440\pi\) | ||||
−0.207214 | + | 0.978296i | \(0.566440\pi\) | |||||||
\(998\) | 1.15711e13 | 0.369221 | ||||||||
\(999\) | 9.28090e12 | 0.294812 |
(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 | 285.10.a.c.1.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.10.a.c.1.5 | ✓ | 12 | 1.1 | even | 1 | trivial |