Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,8,Mod(1,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, 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("175.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.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: | \(54.6673794597\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 706x^{6} + 1459x^{5} + 140610x^{4} - 269712x^{3} - 8960496x^{2} + 18558112x + 98712192 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 5^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-11.2353\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.23526 | 0.816289 | 0.408145 | − | 0.912917i | \(-0.366176\pi\) | ||||
0.408145 | + | 0.912917i | \(0.366176\pi\) | |||||||
\(3\) | 79.3182 | 1.69609 | 0.848044 | − | 0.529926i | \(-0.177780\pi\) | ||||
0.848044 | + | 0.529926i | \(0.177780\pi\) | |||||||
\(4\) | −42.7100 | −0.333672 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 732.524 | 1.38450 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | −1576.55 | −1.08866 | ||||||||
\(9\) | 4104.37 | 1.87671 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7560.19 | 1.71261 | 0.856305 | − | 0.516471i | \(-0.172755\pi\) | ||||
0.856305 | + | 0.516471i | \(0.172755\pi\) | |||||||
\(12\) | −3387.68 | −0.565936 | ||||||||
\(13\) | −6570.26 | −0.829432 | −0.414716 | − | 0.909951i | \(-0.636119\pi\) | ||||
−0.414716 | + | 0.909951i | \(0.636119\pi\) | |||||||
\(14\) | −3167.69 | −0.308528 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −9092.98 | −0.554992 | ||||||||
\(17\) | 38530.0 | 1.90207 | 0.951037 | − | 0.309077i | \(-0.100020\pi\) | ||||
0.951037 | + | 0.309077i | \(0.100020\pi\) | |||||||
\(18\) | 37904.9 | 1.53194 | ||||||||
\(19\) | 27842.9 | 0.931271 | 0.465636 | − | 0.884977i | \(-0.345826\pi\) | ||||
0.465636 | + | 0.884977i | \(0.345826\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −27206.1 | −0.641061 | ||||||||
\(22\) | 69820.3 | 1.39799 | ||||||||
\(23\) | −56508.5 | −0.968426 | −0.484213 | − | 0.874950i | \(-0.660894\pi\) | ||||
−0.484213 | + | 0.874950i | \(0.660894\pi\) | |||||||
\(24\) | −125049. | −1.84647 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −60678.1 | −0.677057 | ||||||||
\(27\) | 152082. | 1.48698 | ||||||||
\(28\) | 14649.5 | 0.126116 | ||||||||
\(29\) | 213939. | 1.62891 | 0.814453 | − | 0.580229i | \(-0.197037\pi\) | ||||
0.814453 | + | 0.580229i | \(0.197037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18914.9 | 0.114035 | 0.0570174 | − | 0.998373i | \(-0.481841\pi\) | ||||
0.0570174 | + | 0.998373i | \(0.481841\pi\) | |||||||
\(32\) | 117822. | 0.635628 | ||||||||
\(33\) | 599660. | 2.90474 | ||||||||
\(34\) | 355834. | 1.55264 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −175297. | −0.626205 | ||||||||
\(37\) | 158204. | 0.513466 | 0.256733 | − | 0.966482i | \(-0.417354\pi\) | ||||
0.256733 | + | 0.966482i | \(0.417354\pi\) | |||||||
\(38\) | 257136. | 0.760187 | ||||||||
\(39\) | −521141. | −1.40679 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 371840. | 0.842582 | 0.421291 | − | 0.906926i | \(-0.361577\pi\) | ||||
0.421291 | + | 0.906926i | \(0.361577\pi\) | |||||||
\(42\) | −251256. | −0.523291 | ||||||||
\(43\) | −39351.7 | −0.0754785 | −0.0377393 | − | 0.999288i | \(-0.512016\pi\) | ||||
−0.0377393 | + | 0.999288i | \(0.512016\pi\) | |||||||
\(44\) | −322895. | −0.571449 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −521871. | −0.790516 | ||||||||
\(47\) | 452269. | 0.635410 | 0.317705 | − | 0.948190i | \(-0.397088\pi\) | ||||
0.317705 | + | 0.948190i | \(0.397088\pi\) | |||||||
\(48\) | −721239. | −0.941314 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.05613e6 | 3.22608 | ||||||||
\(52\) | 280616. | 0.276758 | ||||||||
\(53\) | −1.21612e6 | −1.12204 | −0.561021 | − | 0.827802i | \(-0.689591\pi\) | ||||
−0.561021 | + | 0.827802i | \(0.689591\pi\) | |||||||
\(54\) | 1.40452e6 | 1.21381 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 540757. | 0.411476 | ||||||||
\(57\) | 2.20844e6 | 1.57952 | ||||||||
\(58\) | 1.97578e6 | 1.32966 | ||||||||
\(59\) | −2.62913e6 | −1.66660 | −0.833299 | − | 0.552823i | \(-0.813551\pi\) | ||||
−0.833299 | + | 0.552823i | \(0.813551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 981864. | 0.553856 | 0.276928 | − | 0.960891i | \(-0.410684\pi\) | ||||
0.276928 | + | 0.960891i | \(0.410684\pi\) | |||||||
\(62\) | 174684. | 0.0930854 | ||||||||
\(63\) | −1.40780e6 | −0.709330 | ||||||||
\(64\) | 2.25202e6 | 1.07385 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.53802e6 | 2.37110 | ||||||||
\(67\) | −3.20605e6 | −1.30229 | −0.651147 | − | 0.758952i | \(-0.725712\pi\) | ||||
−0.651147 | + | 0.758952i | \(0.725712\pi\) | |||||||
\(68\) | −1.64561e6 | −0.634668 | ||||||||
\(69\) | −4.48215e6 | −1.64254 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.27584e6 | −0.423049 | −0.211524 | − | 0.977373i | \(-0.567843\pi\) | ||||
−0.211524 | + | 0.977373i | \(0.567843\pi\) | |||||||
\(72\) | −6.47075e6 | −2.04311 | ||||||||
\(73\) | 3.51670e6 | 1.05805 | 0.529023 | − | 0.848607i | \(-0.322558\pi\) | ||||
0.529023 | + | 0.848607i | \(0.322558\pi\) | |||||||
\(74\) | 1.46106e6 | 0.419137 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.18917e6 | −0.310739 | ||||||||
\(77\) | −2.59315e6 | −0.647306 | ||||||||
\(78\) | −4.81287e6 | −1.14835 | ||||||||
\(79\) | 2.45207e6 | 0.559548 | 0.279774 | − | 0.960066i | \(-0.409740\pi\) | ||||
0.279774 | + | 0.960066i | \(0.409740\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.08662e6 | 0.645336 | ||||||||
\(82\) | 3.43404e6 | 0.687791 | ||||||||
\(83\) | −6.84085e6 | −1.31322 | −0.656609 | − | 0.754231i | \(-0.728010\pi\) | ||||
−0.656609 | + | 0.754231i | \(0.728010\pi\) | |||||||
\(84\) | 1.16197e6 | 0.213904 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −363423. | −0.0616123 | ||||||||
\(87\) | 1.69692e7 | 2.76277 | ||||||||
\(88\) | −1.19190e7 | −1.86445 | ||||||||
\(89\) | −7.49365e6 | −1.12675 | −0.563376 | − | 0.826200i | \(-0.690498\pi\) | ||||
−0.563376 | + | 0.826200i | \(0.690498\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.25360e6 | 0.313496 | ||||||||
\(92\) | 2.41348e6 | 0.323136 | ||||||||
\(93\) | 1.50029e6 | 0.193413 | ||||||||
\(94\) | 4.17682e6 | 0.518678 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.34546e6 | 1.07808 | ||||||||
\(97\) | −1.88197e6 | −0.209369 | −0.104685 | − | 0.994505i | \(-0.533383\pi\) | ||||
−0.104685 | + | 0.994505i | \(0.533383\pi\) | |||||||
\(98\) | 1.08652e6 | 0.116613 | ||||||||
\(99\) | 3.10298e7 | 3.21408 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.58480e6 | −0.153056 | −0.0765281 | − | 0.997067i | \(-0.524383\pi\) | ||||
−0.0765281 | + | 0.997067i | \(0.524383\pi\) | |||||||
\(102\) | 2.82241e7 | 2.63342 | ||||||||
\(103\) | −1.34911e7 | −1.21651 | −0.608257 | − | 0.793740i | \(-0.708131\pi\) | ||||
−0.608257 | + | 0.793740i | \(0.708131\pi\) | |||||||
\(104\) | 1.03584e7 | 0.902971 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.12311e7 | −0.915911 | ||||||||
\(107\) | 8.53266e6 | 0.673351 | 0.336675 | − | 0.941621i | \(-0.390698\pi\) | ||||
0.336675 | + | 0.941621i | \(0.390698\pi\) | |||||||
\(108\) | −6.49542e6 | −0.496163 | ||||||||
\(109\) | 4.40208e6 | 0.325586 | 0.162793 | − | 0.986660i | \(-0.447950\pi\) | ||||
0.162793 | + | 0.986660i | \(0.447950\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.25485e7 | 0.870884 | ||||||||
\(112\) | 3.11889e6 | 0.209767 | ||||||||
\(113\) | 2.41828e7 | 1.57664 | 0.788319 | − | 0.615267i | \(-0.210952\pi\) | ||||
0.788319 | + | 0.615267i | \(0.210952\pi\) | |||||||
\(114\) | 2.03956e7 | 1.28934 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.13731e6 | −0.543520 | ||||||||
\(117\) | −2.69668e7 | −1.55661 | ||||||||
\(118\) | −2.42807e7 | −1.36043 | ||||||||
\(119\) | −1.32158e7 | −0.718917 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.76693e7 | 1.93303 | ||||||||
\(122\) | 9.06777e6 | 0.452107 | ||||||||
\(123\) | 2.94936e7 | 1.42909 | ||||||||
\(124\) | −807853. | −0.0380502 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.30014e7 | −0.579019 | ||||||||
\(127\) | 1.10170e7 | 0.477255 | 0.238627 | − | 0.971111i | \(-0.423303\pi\) | ||||
0.238627 | + | 0.971111i | \(0.423303\pi\) | |||||||
\(128\) | 5.71675e6 | 0.240943 | ||||||||
\(129\) | −3.12130e6 | −0.128018 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.45605e7 | 0.565882 | 0.282941 | − | 0.959137i | \(-0.408690\pi\) | ||||
0.282941 | + | 0.959137i | \(0.408690\pi\) | |||||||
\(132\) | −2.56115e7 | −0.969228 | ||||||||
\(133\) | −9.55010e6 | −0.351987 | ||||||||
\(134\) | −2.96087e7 | −1.06305 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.07445e7 | −2.07072 | ||||||||
\(137\) | 8.01376e6 | 0.266265 | 0.133133 | − | 0.991098i | \(-0.457496\pi\) | ||||
0.133133 | + | 0.991098i | \(0.457496\pi\) | |||||||
\(138\) | −4.13938e7 | −1.34078 | ||||||||
\(139\) | −2.56361e7 | −0.809656 | −0.404828 | − | 0.914393i | \(-0.632669\pi\) | ||||
−0.404828 | + | 0.914393i | \(0.632669\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.58731e7 | 1.07771 | ||||||||
\(142\) | −1.17827e7 | −0.345330 | ||||||||
\(143\) | −4.96724e7 | −1.42049 | ||||||||
\(144\) | −3.73210e7 | −1.04156 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.24776e7 | 0.863672 | ||||||||
\(147\) | 9.33170e6 | 0.242298 | ||||||||
\(148\) | −6.75690e6 | −0.171329 | ||||||||
\(149\) | 4.78456e7 | 1.18492 | 0.592461 | − | 0.805599i | \(-0.298156\pi\) | ||||
0.592461 | + | 0.805599i | \(0.298156\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.88885e6 | −0.186464 | −0.0932319 | − | 0.995644i | \(-0.529720\pi\) | ||||
−0.0932319 | + | 0.995644i | \(0.529720\pi\) | |||||||
\(152\) | −4.38957e7 | −1.01384 | ||||||||
\(153\) | 1.58141e8 | 3.56965 | ||||||||
\(154\) | −2.39484e7 | −0.528389 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.22579e7 | 0.469406 | ||||||||
\(157\) | −1.19330e7 | −0.246094 | −0.123047 | − | 0.992401i | \(-0.539267\pi\) | ||||
−0.123047 | + | 0.992401i | \(0.539267\pi\) | |||||||
\(158\) | 2.26455e7 | 0.456753 | ||||||||
\(159\) | −9.64600e7 | −1.90308 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.93824e7 | 0.366031 | ||||||||
\(162\) | 2.85058e7 | 0.526781 | ||||||||
\(163\) | 4.50349e6 | 0.0814503 | 0.0407251 | − | 0.999170i | \(-0.487033\pi\) | ||||
0.0407251 | + | 0.999170i | \(0.487033\pi\) | |||||||
\(164\) | −1.58813e7 | −0.281146 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.31770e7 | −1.07197 | ||||||||
\(167\) | −6.67726e7 | −1.10941 | −0.554703 | − | 0.832048i | \(-0.687168\pi\) | ||||
−0.554703 | + | 0.832048i | \(0.687168\pi\) | |||||||
\(168\) | 4.28918e7 | 0.697898 | ||||||||
\(169\) | −1.95802e7 | −0.312042 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.14277e8 | 1.74773 | ||||||||
\(172\) | 1.68071e6 | 0.0251850 | ||||||||
\(173\) | −6.29382e7 | −0.924173 | −0.462086 | − | 0.886835i | \(-0.652899\pi\) | ||||
−0.462086 | + | 0.886835i | \(0.652899\pi\) | |||||||
\(174\) | 1.56715e8 | 2.25522 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.87447e7 | −0.950484 | ||||||||
\(177\) | −2.08538e8 | −2.82669 | ||||||||
\(178\) | −6.92058e7 | −0.919756 | ||||||||
\(179\) | −1.10967e8 | −1.44613 | −0.723066 | − | 0.690779i | \(-0.757268\pi\) | ||||
−0.723066 | + | 0.690779i | \(0.757268\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.24619e7 | −0.281560 | −0.140780 | − | 0.990041i | \(-0.544961\pi\) | ||||
−0.140780 | + | 0.990041i | \(0.544961\pi\) | |||||||
\(182\) | 2.08126e7 | 0.255903 | ||||||||
\(183\) | 7.78796e7 | 0.939388 | ||||||||
\(184\) | 8.90886e7 | 1.05429 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.38556e7 | 0.157881 | ||||||||
\(187\) | 2.91294e8 | 3.25751 | ||||||||
\(188\) | −1.93164e7 | −0.212018 | ||||||||
\(189\) | −5.21642e7 | −0.562026 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.39656e7 | −0.975780 | −0.487890 | − | 0.872905i | \(-0.662233\pi\) | ||||
−0.487890 | + | 0.872905i | \(0.662233\pi\) | |||||||
\(192\) | 1.78626e8 | 1.82134 | ||||||||
\(193\) | 4.11603e7 | 0.412124 | 0.206062 | − | 0.978539i | \(-0.433935\pi\) | ||||
0.206062 | + | 0.978539i | \(0.433935\pi\) | |||||||
\(194\) | −1.73805e7 | −0.170906 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.02478e6 | −0.0476674 | ||||||||
\(197\) | −1.89027e8 | −1.76154 | −0.880770 | − | 0.473544i | \(-0.842974\pi\) | ||||
−0.880770 | + | 0.473544i | \(0.842974\pi\) | |||||||
\(198\) | 2.86568e8 | 2.62362 | ||||||||
\(199\) | −1.55243e8 | −1.39645 | −0.698225 | − | 0.715878i | \(-0.746027\pi\) | ||||
−0.698225 | + | 0.715878i | \(0.746027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.54298e8 | −2.20880 | ||||||||
\(202\) | −1.46361e7 | −0.124938 | ||||||||
\(203\) | −7.33809e7 | −0.615669 | ||||||||
\(204\) | −1.30527e8 | −1.07645 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.24594e8 | −0.993028 | ||||||||
\(207\) | −2.31932e8 | −1.81746 | ||||||||
\(208\) | 5.97433e7 | 0.460328 | ||||||||
\(209\) | 2.10497e8 | 1.59490 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.66141e8 | −1.21755 | −0.608777 | − | 0.793341i | \(-0.708340\pi\) | ||||
−0.608777 | + | 0.793341i | \(0.708340\pi\) | |||||||
\(212\) | 5.19402e7 | 0.374394 | ||||||||
\(213\) | −1.01197e8 | −0.717528 | ||||||||
\(214\) | 7.88013e7 | 0.549649 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.39765e8 | −1.61882 | ||||||||
\(217\) | −6.48780e6 | −0.0431011 | ||||||||
\(218\) | 4.06544e7 | 0.265772 | ||||||||
\(219\) | 2.78938e8 | 1.79454 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.53152e8 | −1.57764 | ||||||||
\(222\) | 1.15888e8 | 0.710893 | ||||||||
\(223\) | 1.64063e8 | 0.990704 | 0.495352 | − | 0.868692i | \(-0.335039\pi\) | ||||
0.495352 | + | 0.868692i | \(0.335039\pi\) | |||||||
\(224\) | −4.04131e7 | −0.240245 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.23334e8 | 1.28699 | ||||||||
\(227\) | −5.02061e7 | −0.284882 | −0.142441 | − | 0.989803i | \(-0.545495\pi\) | ||||
−0.142441 | + | 0.989803i | \(0.545495\pi\) | |||||||
\(228\) | −9.43226e7 | −0.527040 | ||||||||
\(229\) | 2.77148e8 | 1.52506 | 0.762531 | − | 0.646952i | \(-0.223957\pi\) | ||||
0.762531 | + | 0.646952i | \(0.223957\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.05684e8 | −1.09789 | ||||||||
\(232\) | −3.37285e8 | −1.77333 | ||||||||
\(233\) | 2.11829e7 | 0.109708 | 0.0548542 | − | 0.998494i | \(-0.482531\pi\) | ||||
0.0548542 | + | 0.998494i | \(0.482531\pi\) | |||||||
\(234\) | −2.49045e8 | −1.27064 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.12290e8 | 0.556096 | ||||||||
\(237\) | 1.94493e8 | 0.949042 | ||||||||
\(238\) | −1.22051e8 | −0.586844 | ||||||||
\(239\) | 3.93164e8 | 1.86287 | 0.931433 | − | 0.363913i | \(-0.118560\pi\) | ||||
0.931433 | + | 0.363913i | \(0.118560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.44922e8 | 1.58731 | 0.793654 | − | 0.608369i | \(-0.208176\pi\) | ||||
0.793654 | + | 0.608369i | \(0.208176\pi\) | |||||||
\(242\) | 3.47886e8 | 1.57791 | ||||||||
\(243\) | −8.77786e7 | −0.392434 | ||||||||
\(244\) | −4.19354e7 | −0.184806 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.72381e8 | 1.16655 | ||||||||
\(247\) | −1.82935e8 | −0.772426 | ||||||||
\(248\) | −2.98203e7 | −0.124145 | ||||||||
\(249\) | −5.42604e8 | −2.22733 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.84645e7 | −0.0737021 | −0.0368511 | − | 0.999321i | \(-0.511733\pi\) | ||||
−0.0368511 | + | 0.999321i | \(0.511733\pi\) | |||||||
\(252\) | 6.01270e7 | 0.236683 | ||||||||
\(253\) | −4.27215e8 | −1.65854 | ||||||||
\(254\) | 1.01745e8 | 0.389578 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.35463e8 | −0.877169 | ||||||||
\(257\) | −1.09956e8 | −0.404067 | −0.202033 | − | 0.979379i | \(-0.564755\pi\) | ||||
−0.202033 | + | 0.979379i | \(0.564755\pi\) | |||||||
\(258\) | −2.88260e7 | −0.104500 | ||||||||
\(259\) | −5.42640e7 | −0.194072 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.78083e8 | 3.05699 | ||||||||
\(262\) | 1.34470e8 | 0.461924 | ||||||||
\(263\) | −4.84965e8 | −1.64386 | −0.821931 | − | 0.569587i | \(-0.807103\pi\) | ||||
−0.821931 | + | 0.569587i | \(0.807103\pi\) | |||||||
\(264\) | −9.45395e8 | −3.16228 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.81977e7 | −0.287324 | ||||||||
\(267\) | −5.94383e8 | −1.91107 | ||||||||
\(268\) | 1.36930e8 | 0.434538 | ||||||||
\(269\) | −1.59008e8 | −0.498065 | −0.249033 | − | 0.968495i | \(-0.580113\pi\) | ||||
−0.249033 | + | 0.968495i | \(0.580113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.76177e7 | −0.236902 | −0.118451 | − | 0.992960i | \(-0.537793\pi\) | ||||
−0.118451 | + | 0.992960i | \(0.537793\pi\) | |||||||
\(272\) | −3.50352e8 | −1.05564 | ||||||||
\(273\) | 1.78751e8 | 0.531716 | ||||||||
\(274\) | 7.40092e7 | 0.217350 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.91433e8 | 0.548067 | ||||||||
\(277\) | −2.83761e8 | −0.802183 | −0.401091 | − | 0.916038i | \(-0.631369\pi\) | ||||
−0.401091 | + | 0.916038i | \(0.631369\pi\) | |||||||
\(278\) | −2.36756e8 | −0.660914 | ||||||||
\(279\) | 7.76336e7 | 0.214010 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.17071e8 | 0.314758 | 0.157379 | − | 0.987538i | \(-0.449696\pi\) | ||||
0.157379 | + | 0.987538i | \(0.449696\pi\) | |||||||
\(282\) | 3.31297e8 | 0.879724 | ||||||||
\(283\) | 3.12939e7 | 0.0820743 | 0.0410372 | − | 0.999158i | \(-0.486934\pi\) | ||||
0.0410372 | + | 0.999158i | \(0.486934\pi\) | |||||||
\(284\) | 5.44909e7 | 0.141159 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.58738e8 | −1.15953 | ||||||||
\(287\) | −1.27541e8 | −0.318466 | ||||||||
\(288\) | 4.83587e8 | 1.19289 | ||||||||
\(289\) | 1.07422e9 | 2.61789 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.49275e8 | −0.355108 | ||||||||
\(292\) | −1.50198e8 | −0.353040 | ||||||||
\(293\) | 1.20452e8 | 0.279754 | 0.139877 | − | 0.990169i | \(-0.455329\pi\) | ||||
0.139877 | + | 0.990169i | \(0.455329\pi\) | |||||||
\(294\) | 8.61807e7 | 0.197785 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.49417e8 | −0.558991 | ||||||||
\(297\) | 1.14977e9 | 2.54662 | ||||||||
\(298\) | 4.41867e8 | 0.967240 | ||||||||
\(299\) | 3.71276e8 | 0.803244 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.34976e7 | 0.0285282 | ||||||||
\(302\) | −7.28556e7 | −0.152208 | ||||||||
\(303\) | −1.25704e8 | −0.259597 | ||||||||
\(304\) | −2.53175e8 | −0.516848 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.46048e9 | 2.91386 | ||||||||
\(307\) | 5.66299e8 | 1.11702 | 0.558511 | − | 0.829497i | \(-0.311373\pi\) | ||||
0.558511 | + | 0.829497i | \(0.311373\pi\) | |||||||
\(308\) | 1.10753e8 | 0.215987 | ||||||||
\(309\) | −1.07009e9 | −2.06331 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.71752e8 | 1.45484 | 0.727422 | − | 0.686190i | \(-0.240718\pi\) | ||||
0.727422 | + | 0.686190i | \(0.240718\pi\) | |||||||
\(312\) | 8.21605e8 | 1.53152 | ||||||||
\(313\) | −4.57295e7 | −0.0842930 | −0.0421465 | − | 0.999111i | \(-0.513420\pi\) | ||||
−0.0421465 | + | 0.999111i | \(0.513420\pi\) | |||||||
\(314\) | −1.10204e8 | −0.200884 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.04728e8 | −0.186705 | ||||||||
\(317\) | −1.11428e9 | −1.96466 | −0.982328 | − | 0.187166i | \(-0.940070\pi\) | ||||
−0.982328 | + | 0.187166i | \(0.940070\pi\) | |||||||
\(318\) | −8.90833e8 | −1.55347 | ||||||||
\(319\) | 1.61742e9 | 2.78968 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.76795e8 | 1.14206 | ||||||||
\(322\) | 1.79002e8 | 0.298787 | ||||||||
\(323\) | 1.07278e9 | 1.77135 | ||||||||
\(324\) | −1.31830e8 | −0.215330 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.15909e7 | 0.0664870 | ||||||||
\(327\) | 3.49165e8 | 0.552222 | ||||||||
\(328\) | −5.86224e8 | −0.917287 | ||||||||
\(329\) | −1.55128e8 | −0.240162 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.22898e7 | −0.139880 | −0.0699400 | − | 0.997551i | \(-0.522281\pi\) | ||||
−0.0699400 | + | 0.997551i | \(0.522281\pi\) | |||||||
\(332\) | 2.92172e8 | 0.438183 | ||||||||
\(333\) | 6.49328e8 | 0.963629 | ||||||||
\(334\) | −6.16662e8 | −0.905596 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.47385e8 | 0.355783 | ||||||||
\(337\) | 1.28496e9 | 1.82888 | 0.914441 | − | 0.404720i | \(-0.132631\pi\) | ||||
0.914441 | + | 0.404720i | \(0.132631\pi\) | |||||||
\(338\) | −1.80828e8 | −0.254717 | ||||||||
\(339\) | 1.91814e9 | 2.67412 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.43000e8 | 0.195297 | ||||||||
\(342\) | 1.05538e9 | 1.42665 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | 6.20399e7 | 0.0821706 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.81251e8 | −0.754392 | ||||||||
\(347\) | 4.16453e8 | 0.535073 | 0.267537 | − | 0.963548i | \(-0.413790\pi\) | ||||
0.267537 | + | 0.963548i | \(0.413790\pi\) | |||||||
\(348\) | −7.24755e8 | −0.921857 | ||||||||
\(349\) | −2.99825e7 | −0.0377554 | −0.0188777 | − | 0.999822i | \(-0.506009\pi\) | ||||
−0.0188777 | + | 0.999822i | \(0.506009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.99220e8 | −1.23335 | ||||||||
\(352\) | 8.90760e8 | 1.08858 | ||||||||
\(353\) | −1.57977e9 | −1.91153 | −0.955765 | − | 0.294130i | \(-0.904970\pi\) | ||||
−0.955765 | + | 0.294130i | \(0.904970\pi\) | |||||||
\(354\) | −1.92590e9 | −2.30740 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.20054e8 | 0.375965 | ||||||||
\(357\) | −1.04825e9 | −1.21935 | ||||||||
\(358\) | −1.02481e9 | −1.18046 | ||||||||
\(359\) | −1.33098e9 | −1.51824 | −0.759119 | − | 0.650952i | \(-0.774370\pi\) | ||||
−0.759119 | + | 0.650952i | \(0.774370\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.18647e8 | −0.132734 | ||||||||
\(362\) | −2.07442e8 | −0.229835 | ||||||||
\(363\) | 2.98786e9 | 3.27859 | ||||||||
\(364\) | −9.62512e7 | −0.104605 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.19238e8 | 0.766812 | ||||||||
\(367\) | 1.00006e9 | 1.05607 | 0.528035 | − | 0.849223i | \(-0.322929\pi\) | ||||
0.528035 | + | 0.849223i | \(0.322929\pi\) | |||||||
\(368\) | 5.13831e8 | 0.537469 | ||||||||
\(369\) | 1.52617e9 | 1.58128 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.17127e8 | 0.424092 | ||||||||
\(372\) | −6.40774e7 | −0.0645364 | ||||||||
\(373\) | −1.31150e9 | −1.30854 | −0.654270 | − | 0.756261i | \(-0.727024\pi\) | ||||
−0.654270 | + | 0.756261i | \(0.727024\pi\) | |||||||
\(374\) | 2.69018e9 | 2.65907 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.13024e8 | −0.691746 | ||||||||
\(377\) | −1.40563e9 | −1.35107 | ||||||||
\(378\) | −4.81750e8 | −0.458776 | ||||||||
\(379\) | 7.55529e8 | 0.712876 | 0.356438 | − | 0.934319i | \(-0.383991\pi\) | ||||
0.356438 | + | 0.934319i | \(0.383991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.73848e8 | 0.809466 | ||||||||
\(382\) | −8.67797e8 | −0.796519 | ||||||||
\(383\) | 5.92335e8 | 0.538731 | 0.269365 | − | 0.963038i | \(-0.413186\pi\) | ||||
0.269365 | + | 0.963038i | \(0.413186\pi\) | |||||||
\(384\) | 4.53442e8 | 0.408660 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.80126e8 | 0.336412 | ||||||||
\(387\) | −1.61514e8 | −0.141651 | ||||||||
\(388\) | 8.03791e7 | 0.0698605 | ||||||||
\(389\) | −1.13635e8 | −0.0978784 | −0.0489392 | − | 0.998802i | \(-0.515584\pi\) | ||||
−0.0489392 | + | 0.998802i | \(0.515584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.17727e9 | −1.84202 | ||||||||
\(392\) | −1.85480e8 | −0.155523 | ||||||||
\(393\) | 1.15491e9 | 0.959786 | ||||||||
\(394\) | −1.74572e9 | −1.43793 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.32528e9 | −1.07245 | ||||||||
\(397\) | −1.63458e9 | −1.31111 | −0.655557 | − | 0.755145i | \(-0.727566\pi\) | ||||
−0.655557 | + | 0.755145i | \(0.727566\pi\) | |||||||
\(398\) | −1.43371e9 | −1.13991 | ||||||||
\(399\) | −7.57496e8 | −0.597001 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.10604e8 | 0.550329 | 0.275165 | − | 0.961397i | \(-0.411268\pi\) | ||||
0.275165 | + | 0.961397i | \(0.411268\pi\) | |||||||
\(402\) | −2.34851e9 | −1.80302 | ||||||||
\(403\) | −1.24276e8 | −0.0945841 | ||||||||
\(404\) | 6.76869e7 | 0.0510705 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.77692e8 | −0.502564 | ||||||||
\(407\) | 1.19605e9 | 0.879367 | ||||||||
\(408\) | −4.81814e9 | −3.51212 | ||||||||
\(409\) | −9.79887e8 | −0.708181 | −0.354090 | − | 0.935211i | \(-0.615210\pi\) | ||||
−0.354090 | + | 0.935211i | \(0.615210\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.35637e8 | 0.451609 | ||||||||
\(412\) | 5.76204e8 | 0.405916 | ||||||||
\(413\) | 9.01793e8 | 0.629915 | ||||||||
\(414\) | −2.14195e9 | −1.48357 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.74124e8 | −0.527210 | ||||||||
\(417\) | −2.03341e9 | −1.37325 | ||||||||
\(418\) | 1.94400e9 | 1.30190 | ||||||||
\(419\) | 5.71474e8 | 0.379531 | 0.189766 | − | 0.981829i | \(-0.439227\pi\) | ||||
0.189766 | + | 0.981829i | \(0.439227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.47927e8 | −0.161933 | −0.0809667 | − | 0.996717i | \(-0.525801\pi\) | ||||
−0.0809667 | + | 0.996717i | \(0.525801\pi\) | |||||||
\(422\) | −1.53436e9 | −0.993876 | ||||||||
\(423\) | 1.85628e9 | 1.19248 | ||||||||
\(424\) | 1.91727e9 | 1.22152 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.34580e8 | −0.585710 | ||||||||
\(427\) | −3.36779e8 | −0.209338 | ||||||||
\(428\) | −3.64430e8 | −0.224678 | ||||||||
\(429\) | −3.93993e9 | −2.40928 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.65433e8 | −0.159693 | −0.0798463 | − | 0.996807i | \(-0.525443\pi\) | ||||
−0.0798463 | + | 0.996807i | \(0.525443\pi\) | |||||||
\(432\) | −1.38288e9 | −0.825262 | ||||||||
\(433\) | −1.66732e9 | −0.986989 | −0.493494 | − | 0.869749i | \(-0.664281\pi\) | ||||
−0.493494 | + | 0.869749i | \(0.664281\pi\) | |||||||
\(434\) | −5.99165e7 | −0.0351830 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.88013e8 | −0.108639 | ||||||||
\(437\) | −1.57336e9 | −0.901868 | ||||||||
\(438\) | 2.57606e9 | 1.46486 | ||||||||
\(439\) | −1.21657e9 | −0.686294 | −0.343147 | − | 0.939282i | \(-0.611493\pi\) | ||||
−0.343147 | + | 0.939282i | \(0.611493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.82875e8 | 0.268102 | ||||||||
\(442\) | −2.33792e9 | −1.28781 | ||||||||
\(443\) | −1.24380e9 | −0.679734 | −0.339867 | − | 0.940474i | \(-0.610382\pi\) | ||||
−0.339867 | + | 0.940474i | \(0.610382\pi\) | |||||||
\(444\) | −5.35944e8 | −0.290589 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.51517e9 | 0.808701 | ||||||||
\(447\) | 3.79502e9 | 2.00973 | ||||||||
\(448\) | −7.72444e8 | −0.405876 | ||||||||
\(449\) | 1.95796e8 | 0.102080 | 0.0510402 | − | 0.998697i | \(-0.483746\pi\) | ||||
0.0510402 | + | 0.998697i | \(0.483746\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.81118e9 | 1.44301 | ||||||||
\(452\) | −1.03285e9 | −0.526079 | ||||||||
\(453\) | −6.25729e8 | −0.316259 | ||||||||
\(454\) | −4.63666e8 | −0.232547 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.48172e9 | −1.71956 | ||||||||
\(457\) | 3.69582e9 | 1.81136 | 0.905679 | − | 0.423965i | \(-0.139362\pi\) | ||||
0.905679 | + | 0.423965i | \(0.139362\pi\) | |||||||
\(458\) | 2.55953e9 | 1.24489 | ||||||||
\(459\) | 5.85972e9 | 2.82835 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.05324e9 | −1.45147 | −0.725733 | − | 0.687976i | \(-0.758499\pi\) | ||||
−0.725733 | + | 0.687976i | \(0.758499\pi\) | |||||||
\(462\) | −1.89954e9 | −0.896193 | ||||||||
\(463\) | −9.99765e7 | −0.0468128 | −0.0234064 | − | 0.999726i | \(-0.507451\pi\) | ||||
−0.0234064 | + | 0.999726i | \(0.507451\pi\) | |||||||
\(464\) | −1.94534e9 | −0.904030 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.95630e8 | 0.0895539 | ||||||||
\(467\) | 4.57973e8 | 0.208080 | 0.104040 | − | 0.994573i | \(-0.466823\pi\) | ||||
0.104040 | + | 0.994573i | \(0.466823\pi\) | |||||||
\(468\) | 1.15175e9 | 0.519395 | ||||||||
\(469\) | 1.09968e9 | 0.492221 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.46504e8 | −0.417397 | ||||||||
\(472\) | 4.14496e9 | 1.81436 | ||||||||
\(473\) | −2.97506e8 | −0.129265 | ||||||||
\(474\) | 1.79620e9 | 0.774693 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.64445e8 | 0.239882 | ||||||||
\(477\) | −4.99139e9 | −2.10575 | ||||||||
\(478\) | 3.63098e9 | 1.52064 | ||||||||
\(479\) | 2.97851e9 | 1.23830 | 0.619149 | − | 0.785274i | \(-0.287478\pi\) | ||||
0.619149 | + | 0.785274i | \(0.287478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.03944e9 | −0.425886 | ||||||||
\(482\) | 3.18545e9 | 1.29570 | ||||||||
\(483\) | 1.53738e9 | 0.620820 | ||||||||
\(484\) | −1.60886e9 | −0.644998 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.10658e8 | −0.320340 | ||||||||
\(487\) | 3.51262e9 | 1.37810 | 0.689048 | − | 0.724716i | \(-0.258029\pi\) | ||||
0.689048 | + | 0.724716i | \(0.258029\pi\) | |||||||
\(488\) | −1.54796e9 | −0.602962 | ||||||||
\(489\) | 3.57209e8 | 0.138147 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.13708e9 | 1.19603 | 0.598013 | − | 0.801487i | \(-0.295957\pi\) | ||||
0.598013 | + | 0.801487i | \(0.295957\pi\) | |||||||
\(492\) | −1.25967e9 | −0.476848 | ||||||||
\(493\) | 8.24305e9 | 3.09830 | ||||||||
\(494\) | −1.68945e9 | −0.630524 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.71993e8 | −0.0632884 | ||||||||
\(497\) | 4.37612e8 | 0.159897 | ||||||||
\(498\) | −5.01109e9 | −1.81815 | ||||||||
\(499\) | −2.35673e9 | −0.849097 | −0.424549 | − | 0.905405i | \(-0.639567\pi\) | ||||
−0.424549 | + | 0.905405i | \(0.639567\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.29628e9 | −1.88165 | ||||||||
\(502\) | −1.70525e8 | −0.0601623 | ||||||||
\(503\) | 4.78527e9 | 1.67656 | 0.838279 | − | 0.545242i | \(-0.183562\pi\) | ||||
0.838279 | + | 0.545242i | \(0.183562\pi\) | |||||||
\(504\) | 2.21947e9 | 0.772221 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.94545e9 | −1.35385 | ||||||||
\(507\) | −1.55306e9 | −0.529251 | ||||||||
\(508\) | −4.70536e8 | −0.159246 | ||||||||
\(509\) | −2.10557e9 | −0.707713 | −0.353856 | − | 0.935300i | \(-0.615130\pi\) | ||||
−0.353856 | + | 0.935300i | \(0.615130\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.20623e9 | −0.399904 | ||||||||
\(512\) | −2.90631e9 | −0.956967 | ||||||||
\(513\) | 4.23440e9 | 1.38478 | ||||||||
\(514\) | −1.01547e9 | −0.329836 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.33311e8 | 0.0427160 | ||||||||
\(517\) | 3.41924e9 | 1.08821 | ||||||||
\(518\) | −5.01143e8 | −0.158419 | ||||||||
\(519\) | −4.99214e9 | −1.56748 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.25442e9 | 0.698397 | 0.349198 | − | 0.937049i | \(-0.386454\pi\) | ||||
0.349198 | + | 0.937049i | \(0.386454\pi\) | |||||||
\(522\) | 8.10933e9 | 2.49539 | ||||||||
\(523\) | 3.32175e9 | 1.01534 | 0.507670 | − | 0.861552i | \(-0.330507\pi\) | ||||
0.507670 | + | 0.861552i | \(0.330507\pi\) | |||||||
\(524\) | −6.21877e8 | −0.188819 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.47878e9 | −1.34187 | ||||||||
\(527\) | 7.28789e8 | 0.216903 | ||||||||
\(528\) | −5.45270e9 | −1.61210 | ||||||||
\(529\) | −2.11611e8 | −0.0621502 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.07909e10 | −3.12772 | ||||||||
\(532\) | 4.07884e8 | 0.117448 | ||||||||
\(533\) | −2.44308e9 | −0.698865 | ||||||||
\(534\) | −5.48928e9 | −1.55999 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.05451e9 | 1.41776 | ||||||||
\(537\) | −8.80169e9 | −2.45277 | ||||||||
\(538\) | −1.46848e9 | −0.406565 | ||||||||
\(539\) | 8.89449e8 | 0.244659 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.22668e9 | 0.333074 | 0.166537 | − | 0.986035i | \(-0.446741\pi\) | ||||
0.166537 | + | 0.986035i | \(0.446741\pi\) | |||||||
\(542\) | −7.16820e8 | −0.193380 | ||||||||
\(543\) | −1.78164e9 | −0.477551 | ||||||||
\(544\) | 4.53970e9 | 1.20901 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.65082e9 | 0.434035 | ||||||||
\(547\) | −2.52060e9 | −0.658489 | −0.329244 | − | 0.944245i | \(-0.606794\pi\) | ||||
−0.329244 | + | 0.944245i | \(0.606794\pi\) | |||||||
\(548\) | −3.42268e8 | −0.0888452 | ||||||||
\(549\) | 4.02993e9 | 1.03943 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.95666e9 | 1.51695 | ||||||||
\(552\) | 7.06634e9 | 1.78817 | ||||||||
\(553\) | −8.41059e8 | −0.211489 | ||||||||
\(554\) | −2.62061e9 | −0.654813 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.09492e9 | 0.270159 | ||||||||
\(557\) | −6.27626e9 | −1.53889 | −0.769445 | − | 0.638713i | \(-0.779467\pi\) | ||||
−0.769445 | + | 0.638713i | \(0.779467\pi\) | |||||||
\(558\) | 7.16967e8 | 0.174694 | ||||||||
\(559\) | 2.58551e8 | 0.0626043 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.31049e10 | 5.52502 | ||||||||
\(562\) | 1.08118e9 | 0.256933 | ||||||||
\(563\) | −1.45170e9 | −0.342844 | −0.171422 | − | 0.985198i | \(-0.554836\pi\) | ||||
−0.171422 | + | 0.985198i | \(0.554836\pi\) | |||||||
\(564\) | −1.53214e9 | −0.359601 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.89007e8 | 0.0669964 | ||||||||
\(567\) | −1.05871e9 | −0.243914 | ||||||||
\(568\) | 2.01142e9 | 0.460557 | ||||||||
\(569\) | 5.99543e9 | 1.36436 | 0.682178 | − | 0.731186i | \(-0.261033\pi\) | ||||
0.682178 | + | 0.731186i | \(0.261033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.09750e9 | 0.246705 | 0.123353 | − | 0.992363i | \(-0.460635\pi\) | ||||
0.123353 | + | 0.992363i | \(0.460635\pi\) | |||||||
\(572\) | 2.12151e9 | 0.473978 | ||||||||
\(573\) | −7.45318e9 | −1.65501 | ||||||||
\(574\) | −1.17787e9 | −0.259960 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.24313e9 | 2.01530 | ||||||||
\(577\) | 3.33317e9 | 0.722341 | 0.361170 | − | 0.932500i | \(-0.382377\pi\) | ||||
0.361170 | + | 0.932500i | \(0.382377\pi\) | |||||||
\(578\) | 9.92070e9 | 2.13695 | ||||||||
\(579\) | 3.26476e9 | 0.698998 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.34641e9 | 0.496350 | ||||||||
\(582\) | −1.37859e9 | −0.289871 | ||||||||
\(583\) | −9.19406e9 | −1.92162 | ||||||||
\(584\) | −5.54425e9 | −1.15185 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.11240e9 | 0.228360 | ||||||||
\(587\) | 5.29160e9 | 1.07983 | 0.539913 | − | 0.841721i | \(-0.318457\pi\) | ||||
0.539913 | + | 0.841721i | \(0.318457\pi\) | |||||||
\(588\) | −3.98557e8 | −0.0808480 | ||||||||
\(589\) | 5.26644e8 | 0.106197 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.49933e10 | −2.98773 | ||||||||
\(592\) | −1.43855e9 | −0.284970 | ||||||||
\(593\) | −2.56026e9 | −0.504189 | −0.252094 | − | 0.967703i | \(-0.581119\pi\) | ||||
−0.252094 | + | 0.967703i | \(0.581119\pi\) | |||||||
\(594\) | 1.06184e10 | 2.07878 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.04348e9 | −0.395375 | ||||||||
\(597\) | −1.23136e10 | −2.36850 | ||||||||
\(598\) | 3.42883e9 | 0.655680 | ||||||||
\(599\) | 3.35967e9 | 0.638708 | 0.319354 | − | 0.947636i | \(-0.396534\pi\) | ||||
0.319354 | + | 0.947636i | \(0.396534\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.80116e9 | 0.902164 | 0.451082 | − | 0.892482i | \(-0.351038\pi\) | ||||
0.451082 | + | 0.892482i | \(0.351038\pi\) | |||||||
\(602\) | 1.24654e8 | 0.0232873 | ||||||||
\(603\) | −1.31588e10 | −2.44403 | ||||||||
\(604\) | 3.36933e8 | 0.0622177 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.16091e9 | −0.211906 | ||||||||
\(607\) | −3.29532e9 | −0.598049 | −0.299024 | − | 0.954245i | \(-0.596661\pi\) | ||||
−0.299024 | + | 0.954245i | \(0.596661\pi\) | |||||||
\(608\) | 3.28051e9 | 0.591942 | ||||||||
\(609\) | −5.82044e9 | −1.04423 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.97152e9 | −0.527029 | ||||||||
\(612\) | −6.75421e9 | −1.19109 | ||||||||
\(613\) | −7.72517e9 | −1.35455 | −0.677277 | − | 0.735728i | \(-0.736840\pi\) | ||||
−0.677277 | + | 0.735728i | \(0.736840\pi\) | |||||||
\(614\) | 5.22992e9 | 0.911813 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.08823e9 | 0.704697 | ||||||||
\(617\) | −3.53848e9 | −0.606483 | −0.303242 | − | 0.952914i | \(-0.598069\pi\) | ||||
−0.303242 | + | 0.952914i | \(0.598069\pi\) | |||||||
\(618\) | −9.88255e9 | −1.68426 | ||||||||
\(619\) | −3.48297e9 | −0.590246 | −0.295123 | − | 0.955459i | \(-0.595361\pi\) | ||||
−0.295123 | + | 0.955459i | \(0.595361\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.59394e9 | −1.44003 | ||||||||
\(622\) | 7.12733e9 | 1.18757 | ||||||||
\(623\) | 2.57032e9 | 0.425872 | ||||||||
\(624\) | 4.73873e9 | 0.780757 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.22324e8 | −0.0688075 | ||||||||
\(627\) | 1.66963e10 | 2.70510 | ||||||||
\(628\) | 5.09658e8 | 0.0821146 | ||||||||
\(629\) | 6.09560e9 | 0.976651 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.08998e9 | −0.648065 | −0.324033 | − | 0.946046i | \(-0.605039\pi\) | ||||
−0.324033 | + | 0.946046i | \(0.605039\pi\) | |||||||
\(632\) | −3.86581e9 | −0.609159 | ||||||||
\(633\) | −1.31780e10 | −2.06508 | ||||||||
\(634\) | −1.02907e10 | −1.60373 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.11980e9 | 0.635004 | ||||||||
\(637\) | −7.72985e8 | −0.118490 | ||||||||
\(638\) | 1.49373e10 | 2.27719 | ||||||||
\(639\) | −5.23650e9 | −0.793941 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.42218e9 | 0.363249 | 0.181624 | − | 0.983368i | \(-0.441865\pi\) | ||||
0.181624 | + | 0.983368i | \(0.441865\pi\) | |||||||
\(642\) | 6.25038e9 | 0.932253 | ||||||||
\(643\) | 6.08579e9 | 0.902773 | 0.451387 | − | 0.892328i | \(-0.350930\pi\) | ||||
0.451387 | + | 0.892328i | \(0.350930\pi\) | |||||||
\(644\) | −8.27823e8 | −0.122134 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.90745e9 | 1.44593 | ||||||||
\(647\) | −5.52131e9 | −0.801451 | −0.400726 | − | 0.916198i | \(-0.631242\pi\) | ||||
−0.400726 | + | 0.916198i | \(0.631242\pi\) | |||||||
\(648\) | −4.86622e9 | −0.702553 | ||||||||
\(649\) | −1.98768e10 | −2.85423 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.14600e8 | −0.0731032 | ||||||||
\(652\) | −1.92344e8 | −0.0271776 | ||||||||
\(653\) | 7.06205e9 | 0.992510 | 0.496255 | − | 0.868177i | \(-0.334708\pi\) | ||||
0.496255 | + | 0.868177i | \(0.334708\pi\) | |||||||
\(654\) | 3.22463e9 | 0.450773 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.38113e9 | −0.467626 | ||||||||
\(657\) | 1.44338e10 | 1.98565 | ||||||||
\(658\) | −1.43265e9 | −0.196042 | ||||||||
\(659\) | 3.89902e9 | 0.530709 | 0.265354 | − | 0.964151i | \(-0.414511\pi\) | ||||
0.265354 | + | 0.964151i | \(0.414511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.85556e9 | 0.653934 | 0.326967 | − | 0.945036i | \(-0.393973\pi\) | ||||
0.326967 | + | 0.945036i | \(0.393973\pi\) | |||||||
\(662\) | −8.52320e8 | −0.114183 | ||||||||
\(663\) | −2.00795e10 | −2.67582 | ||||||||
\(664\) | 1.07850e10 | 1.42965 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.99672e9 | 0.786600 | ||||||||
\(667\) | −1.20894e10 | −1.57748 | ||||||||
\(668\) | 2.85185e9 | 0.370177 | ||||||||
\(669\) | 1.30132e10 | 1.68032 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.42308e9 | 0.948539 | ||||||||
\(672\) | −3.20549e9 | −0.407476 | ||||||||
\(673\) | −4.47378e9 | −0.565747 | −0.282873 | − | 0.959157i | \(-0.591288\pi\) | ||||
−0.282873 | + | 0.959157i | \(0.591288\pi\) | |||||||
\(674\) | 1.18670e10 | 1.49290 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.36269e8 | 0.104120 | ||||||||
\(677\) | 2.69889e9 | 0.334291 | 0.167146 | − | 0.985932i | \(-0.446545\pi\) | ||||
0.167146 | + | 0.985932i | \(0.446545\pi\) | |||||||
\(678\) | 1.77145e10 | 2.18285 | ||||||||
\(679\) | 6.45517e8 | 0.0791341 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.98225e9 | −0.483185 | ||||||||
\(682\) | 1.32064e9 | 0.159419 | ||||||||
\(683\) | 1.01893e10 | 1.22370 | 0.611848 | − | 0.790975i | \(-0.290426\pi\) | ||||
0.611848 | + | 0.790975i | \(0.290426\pi\) | |||||||
\(684\) | −4.88078e9 | −0.583167 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.72676e8 | −0.0440755 | ||||||||
\(687\) | 2.19829e10 | 2.58664 | ||||||||
\(688\) | 3.57824e8 | 0.0418900 | ||||||||
\(689\) | 7.99019e9 | 0.930658 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.48923e10 | −1.71707 | −0.858535 | − | 0.512755i | \(-0.828625\pi\) | ||||
−0.858535 | + | 0.512755i | \(0.828625\pi\) | |||||||
\(692\) | 2.68809e9 | 0.308370 | ||||||||
\(693\) | −1.06432e10 | −1.21481 | ||||||||
\(694\) | 3.84605e9 | 0.436775 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.67528e10 | −3.00772 | ||||||||
\(697\) | 1.43270e10 | 1.60265 | ||||||||
\(698\) | −2.76896e8 | −0.0308193 | ||||||||
\(699\) | 1.68019e9 | 0.186075 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.27757e10 | 1.40079 | 0.700395 | − | 0.713755i | \(-0.253007\pi\) | ||||
0.700395 | + | 0.713755i | \(0.253007\pi\) | |||||||
\(702\) | −9.22805e9 | −1.00677 | ||||||||
\(703\) | 4.40486e9 | 0.478177 | ||||||||
\(704\) | 1.70257e10 | 1.83908 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.45895e10 | −1.56036 | ||||||||
\(707\) | 5.43588e8 | 0.0578498 | ||||||||
\(708\) | 8.90665e9 | 0.943188 | ||||||||
\(709\) | −7.19766e9 | −0.758454 | −0.379227 | − | 0.925304i | \(-0.623810\pi\) | ||||
−0.379227 | + | 0.925304i | \(0.623810\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00642e10 | 1.05011 | ||||||||
\(712\) | 1.18141e10 | 1.22665 | ||||||||
\(713\) | −1.06885e9 | −0.110434 | ||||||||
\(714\) | −9.68087e9 | −0.995339 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.73939e9 | 0.482533 | ||||||||
\(717\) | 3.11851e10 | 3.15958 | ||||||||
\(718\) | −1.22919e10 | −1.23932 | ||||||||
\(719\) | −8.05856e9 | −0.808549 | −0.404275 | − | 0.914638i | \(-0.632476\pi\) | ||||
−0.404275 | + | 0.914638i | \(0.632476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.62745e9 | 0.459799 | ||||||||
\(722\) | −1.09574e9 | −0.108349 | ||||||||
\(723\) | 2.73586e10 | 2.69221 | ||||||||
\(724\) | 9.59347e8 | 0.0939487 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.75937e10 | 2.67628 | ||||||||
\(727\) | −1.83829e10 | −1.77437 | −0.887184 | − | 0.461416i | \(-0.847341\pi\) | ||||
−0.887184 | + | 0.461416i | \(0.847341\pi\) | |||||||
\(728\) | −3.55291e9 | −0.341291 | ||||||||
\(729\) | −1.37129e10 | −1.31094 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.51622e9 | −0.143566 | ||||||||
\(732\) | −3.32624e9 | −0.313447 | ||||||||
\(733\) | 1.09787e10 | 1.02964 | 0.514822 | − | 0.857297i | \(-0.327858\pi\) | ||||
0.514822 | + | 0.857297i | \(0.327858\pi\) | |||||||
\(734\) | 9.23577e9 | 0.862059 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.65797e9 | −0.615559 | ||||||||
\(737\) | −2.42384e10 | −2.23032 | ||||||||
\(738\) | 1.40946e10 | 1.29079 | ||||||||
\(739\) | −7.57794e9 | −0.690710 | −0.345355 | − | 0.938472i | \(-0.612242\pi\) | ||||
−0.345355 | + | 0.938472i | \(0.612242\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.45101e10 | −1.31010 | ||||||||
\(742\) | 3.85228e9 | 0.346182 | ||||||||
\(743\) | −1.79243e10 | −1.60318 | −0.801590 | − | 0.597875i | \(-0.796012\pi\) | ||||
−0.801590 | + | 0.597875i | \(0.796012\pi\) | |||||||
\(744\) | −2.36529e9 | −0.210561 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.21120e10 | −1.06815 | ||||||||
\(747\) | −2.80774e10 | −2.46453 | ||||||||
\(748\) | −1.24412e10 | −1.08694 | ||||||||
\(749\) | −2.92670e9 | −0.254503 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.31633e9 | 0.199554 | 0.0997771 | − | 0.995010i | \(-0.468187\pi\) | ||||
0.0997771 | + | 0.995010i | \(0.468187\pi\) | |||||||
\(752\) | −4.11247e9 | −0.352647 | ||||||||
\(753\) | −1.46457e9 | −0.125005 | ||||||||
\(754\) | −1.29814e10 | −1.10286 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.22793e9 | 0.187532 | ||||||||
\(757\) | −3.38357e8 | −0.0283491 | −0.0141746 | − | 0.999900i | \(-0.504512\pi\) | ||||
−0.0141746 | + | 0.999900i | \(0.504512\pi\) | |||||||
\(758\) | 6.97751e9 | 0.581913 | ||||||||
\(759\) | −3.38859e10 | −2.81302 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.74775e10 | 1.43758 | 0.718792 | − | 0.695225i | \(-0.244695\pi\) | ||||
0.718792 | + | 0.695225i | \(0.244695\pi\) | |||||||
\(762\) | 8.07021e9 | 0.660758 | ||||||||
\(763\) | −1.50992e9 | −0.123060 | ||||||||
\(764\) | 4.01327e9 | 0.325590 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.47037e9 | 0.439760 | ||||||||
\(767\) | 1.72741e10 | 1.38233 | ||||||||
\(768\) | −1.86765e10 | −1.48776 | ||||||||
\(769\) | 1.68650e10 | 1.33735 | 0.668673 | − | 0.743557i | \(-0.266863\pi\) | ||||
0.668673 | + | 0.743557i | \(0.266863\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.72151e9 | −0.685333 | ||||||||
\(772\) | −1.75795e9 | −0.137514 | ||||||||
\(773\) | 1.28837e10 | 1.00326 | 0.501630 | − | 0.865082i | \(-0.332734\pi\) | ||||
0.501630 | + | 0.865082i | \(0.332734\pi\) | |||||||
\(774\) | −1.49162e9 | −0.115629 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.96703e9 | 0.227932 | ||||||||
\(777\) | −4.30412e9 | −0.329163 | ||||||||
\(778\) | −1.04944e9 | −0.0798971 | ||||||||
\(779\) | 1.03531e10 | 0.784673 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.64556e9 | −0.724518 | ||||||||
\(782\) | −2.01077e10 | −1.50362 | ||||||||
\(783\) | 3.25363e10 | 2.42215 | ||||||||
\(784\) | −1.06978e9 | −0.0792845 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.06659e10 | 0.783463 | ||||||||
\(787\) | −2.67614e9 | −0.195703 | −0.0978514 | − | 0.995201i | \(-0.531197\pi\) | ||||
−0.0978514 | + | 0.995201i | \(0.531197\pi\) | |||||||
\(788\) | 8.07334e9 | 0.587776 | ||||||||
\(789\) | −3.84665e10 | −2.78813 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.29470e9 | −0.595913 | ||||||||
\(792\) | −4.89201e10 | −3.49904 | ||||||||
\(793\) | −6.45110e9 | −0.459386 | ||||||||
\(794\) | −1.50958e10 | −1.07025 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.63041e9 | 0.465956 | ||||||||
\(797\) | −1.44598e10 | −1.01171 | −0.505857 | − | 0.862617i | \(-0.668824\pi\) | ||||
−0.505857 | + | 0.862617i | \(0.668824\pi\) | |||||||
\(798\) | −6.99568e9 | −0.487326 | ||||||||
\(799\) | 1.74259e10 | 1.20860 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.07567e10 | −2.11459 | ||||||||
\(802\) | 6.56262e9 | 0.449228 | ||||||||
\(803\) | 2.65869e10 | 1.81202 | ||||||||
\(804\) | 1.08611e10 | 0.737015 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.14772e9 | −0.0772080 | ||||||||
\(807\) | −1.26122e10 | −0.844762 | ||||||||
\(808\) | 2.49853e9 | 0.166626 | ||||||||
\(809\) | −1.91699e10 | −1.27292 | −0.636459 | − | 0.771310i | \(-0.719602\pi\) | ||||
−0.636459 | + | 0.771310i | \(0.719602\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.49695e9 | 0.493528 | 0.246764 | − | 0.969076i | \(-0.420633\pi\) | ||||
0.246764 | + | 0.969076i | \(0.420633\pi\) | |||||||
\(812\) | 3.13410e9 | 0.205431 | ||||||||
\(813\) | −6.15649e9 | −0.401806 | ||||||||
\(814\) | 1.10459e10 | 0.717818 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.77893e10 | −1.79045 | ||||||||
\(817\) | −1.09566e9 | −0.0702910 | ||||||||
\(818\) | −9.04951e9 | −0.578081 | ||||||||
\(819\) | 9.24961e9 | 0.588342 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.43321e8 | −0.0531853 | −0.0265927 | − | 0.999646i | \(-0.508466\pi\) | ||||
−0.0265927 | + | 0.999646i | \(0.508466\pi\) | |||||||
\(822\) | 5.87027e9 | 0.368644 | ||||||||
\(823\) | −2.39654e9 | −0.149860 | −0.0749299 | − | 0.997189i | \(-0.523873\pi\) | ||||
−0.0749299 | + | 0.997189i | \(0.523873\pi\) | |||||||
\(824\) | 2.12694e10 | 1.32437 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.32829e9 | 0.514193 | ||||||||
\(827\) | −6.20597e9 | −0.381540 | −0.190770 | − | 0.981635i | \(-0.561099\pi\) | ||||
−0.190770 | + | 0.981635i | \(0.561099\pi\) | |||||||
\(828\) | 9.90580e9 | 0.606434 | ||||||||
\(829\) | −1.30007e10 | −0.792550 | −0.396275 | − | 0.918132i | \(-0.629697\pi\) | ||||
−0.396275 | + | 0.918132i | \(0.629697\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.25074e10 | −1.36057 | ||||||||
\(832\) | −1.47964e10 | −0.890684 | ||||||||
\(833\) | 4.53301e9 | 0.271725 | ||||||||
\(834\) | −1.87791e10 | −1.12097 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.99033e9 | −0.532174 | ||||||||
\(837\) | 2.87661e9 | 0.169567 | ||||||||
\(838\) | 5.27771e9 | 0.309807 | ||||||||
\(839\) | 2.66826e9 | 0.155977 | 0.0779885 | − | 0.996954i | \(-0.475150\pi\) | ||||
0.0779885 | + | 0.996954i | \(0.475150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.85199e10 | 1.65334 | ||||||||
\(842\) | −2.28967e9 | −0.132185 | ||||||||
\(843\) | 9.28584e9 | 0.533857 | ||||||||
\(844\) | 7.09588e9 | 0.406263 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.71432e10 | 0.973410 | ||||||||
\(847\) | −1.29206e10 | −0.730617 | ||||||||
\(848\) | 1.10581e10 | 0.622724 | ||||||||
\(849\) | 2.48217e9 | 0.139205 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.93989e9 | −0.497254 | ||||||||
\(852\) | 4.32212e9 | 0.239419 | ||||||||
\(853\) | −1.74908e9 | −0.0964913 | −0.0482457 | − | 0.998836i | \(-0.515363\pi\) | ||||
−0.0482457 | + | 0.998836i | \(0.515363\pi\) | |||||||
\(854\) | −3.11024e9 | −0.170880 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.34522e10 | −0.733051 | ||||||||
\(857\) | 1.66810e10 | 0.905291 | 0.452645 | − | 0.891691i | \(-0.350480\pi\) | ||||
0.452645 | + | 0.891691i | \(0.350480\pi\) | |||||||
\(858\) | −3.63862e10 | −1.96667 | ||||||||
\(859\) | −1.88459e10 | −1.01447 | −0.507237 | − | 0.861807i | \(-0.669333\pi\) | ||||
−0.507237 | + | 0.861807i | \(0.669333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.01163e10 | −0.540146 | ||||||||
\(862\) | −2.45134e9 | −0.130355 | ||||||||
\(863\) | −2.40431e10 | −1.27336 | −0.636681 | − | 0.771127i | \(-0.719693\pi\) | ||||
−0.636681 | + | 0.771127i | \(0.719693\pi\) | |||||||
\(864\) | 1.79187e10 | 0.945166 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.53982e10 | −0.805668 | ||||||||
\(867\) | 8.52052e10 | 4.44016 | ||||||||
\(868\) | 2.77094e8 | 0.0143816 | ||||||||
\(869\) | 1.85381e10 | 0.958287 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.10646e10 | 1.08016 | ||||||||
\(872\) | −6.94011e9 | −0.354453 | ||||||||
\(873\) | −7.72432e9 | −0.392926 | ||||||||
\(874\) | −1.45304e10 | −0.736185 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.19134e10 | −0.598787 | ||||||||
\(877\) | 1.03189e10 | 0.516576 | 0.258288 | − | 0.966068i | \(-0.416842\pi\) | ||||
0.258288 | + | 0.966068i | \(0.416842\pi\) | |||||||
\(878\) | −1.12353e10 | −0.560215 | ||||||||
\(879\) | 9.55400e9 | 0.474487 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.18216e10 | −1.56786 | −0.783928 | − | 0.620852i | \(-0.786787\pi\) | ||||
−0.783928 | + | 0.620852i | \(0.786787\pi\) | |||||||
\(882\) | 4.45948e9 | 0.218849 | ||||||||
\(883\) | −2.46997e10 | −1.20734 | −0.603669 | − | 0.797235i | \(-0.706295\pi\) | ||||
−0.603669 | + | 0.797235i | \(0.706295\pi\) | |||||||
\(884\) | 1.08121e10 | 0.526414 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.14869e10 | −0.554859 | ||||||||
\(887\) | 4.91222e9 | 0.236344 | 0.118172 | − | 0.992993i | \(-0.462297\pi\) | ||||
0.118172 | + | 0.992993i | \(0.462297\pi\) | |||||||
\(888\) | −1.97833e10 | −0.948098 | ||||||||
\(889\) | −3.77883e9 | −0.180385 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.33355e10 | 1.10521 | ||||||||
\(892\) | −7.00713e9 | −0.330570 | ||||||||
\(893\) | 1.25924e10 | 0.591739 | ||||||||
\(894\) | 3.50480e10 | 1.64052 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.96084e9 | −0.0910678 | ||||||||
\(897\) | 2.94489e10 | 1.36237 | ||||||||
\(898\) | 1.80823e9 | 0.0833272 | ||||||||
\(899\) | 4.04662e9 | 0.185752 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.68569e10 | −2.13421 | ||||||||
\(902\) | 2.59620e10 | 1.17792 | ||||||||
\(903\) | 1.07061e9 | 0.0483863 | ||||||||
\(904\) | −3.81254e10 | −1.71643 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.77877e9 | −0.258159 | ||||||||
\(907\) | −1.04163e10 | −0.463543 | −0.231771 | − | 0.972770i | \(-0.574452\pi\) | ||||
−0.231771 | + | 0.972770i | \(0.574452\pi\) | |||||||
\(908\) | 2.14430e9 | 0.0950572 | ||||||||
\(909\) | −6.50462e9 | −0.287242 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.28934e10 | 1.00322 | 0.501610 | − | 0.865094i | \(-0.332741\pi\) | ||||
0.501610 | + | 0.865094i | \(0.332741\pi\) | |||||||
\(912\) | −2.00813e10 | −0.876619 | ||||||||
\(913\) | −5.17181e10 | −2.24903 | ||||||||
\(914\) | 3.41319e10 | 1.47859 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.18370e10 | −0.508870 | ||||||||
\(917\) | −4.99424e9 | −0.213883 | ||||||||
\(918\) | 5.41161e10 | 2.30875 | ||||||||
\(919\) | 4.97399e9 | 0.211398 | 0.105699 | − | 0.994398i | \(-0.466292\pi\) | ||||
0.105699 | + | 0.994398i | \(0.466292\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.49178e10 | 1.89457 | ||||||||
\(922\) | −2.81974e10 | −1.18482 | ||||||||
\(923\) | 8.38258e9 | 0.350890 | ||||||||
\(924\) | 8.78474e9 | 0.366334 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.23309e8 | −0.0382128 | ||||||||
\(927\) | −5.53725e10 | −2.28305 | ||||||||
\(928\) | 2.52068e10 | 1.03538 | ||||||||
\(929\) | 3.93240e10 | 1.60917 | 0.804587 | − | 0.593835i | \(-0.202387\pi\) | ||||
0.804587 | + | 0.593835i | \(0.202387\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.27568e9 | 0.133039 | ||||||||
\(932\) | −9.04722e8 | −0.0366066 | ||||||||
\(933\) | 6.12140e10 | 2.46754 | ||||||||
\(934\) | 4.22950e9 | 0.169854 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.25145e10 | 1.69462 | ||||||||
\(937\) | 2.39127e9 | 0.0949599 | 0.0474800 | − | 0.998872i | \(-0.484881\pi\) | ||||
0.0474800 | + | 0.998872i | \(0.484881\pi\) | |||||||
\(938\) | 1.01558e10 | 0.401794 | ||||||||
\(939\) | −3.62718e9 | −0.142968 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.09769e10 | 0.820686 | 0.410343 | − | 0.911931i | \(-0.365409\pi\) | ||||
0.410343 | + | 0.911931i | \(0.365409\pi\) | |||||||
\(942\) | −8.74121e9 | −0.340717 | ||||||||
\(943\) | −2.10121e10 | −0.815979 | ||||||||
\(944\) | 2.39067e10 | 0.924948 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.74755e9 | −0.105518 | ||||||||
\(947\) | −1.66975e10 | −0.638891 | −0.319446 | − | 0.947605i | \(-0.603497\pi\) | ||||
−0.319446 | + | 0.947605i | \(0.603497\pi\) | |||||||
\(948\) | −8.30680e9 | −0.316668 | ||||||||
\(949\) | −2.31056e10 | −0.877578 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.83826e10 | −3.33223 | ||||||||
\(952\) | 2.08354e10 | 0.782657 | ||||||||
\(953\) | −3.33403e10 | −1.24780 | −0.623899 | − | 0.781505i | \(-0.714452\pi\) | ||||
−0.623899 | + | 0.781505i | \(0.714452\pi\) | |||||||
\(954\) | −4.60967e10 | −1.71890 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.67920e10 | −0.621585 | ||||||||
\(957\) | 1.28291e11 | 4.73154 | ||||||||
\(958\) | 2.75073e10 | 1.01081 | ||||||||
\(959\) | −2.74872e9 | −0.100639 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.71548e10 | −0.986996 | ||||||||
\(962\) | −9.59953e9 | −0.347646 | ||||||||
\(963\) | 3.50212e10 | 1.26369 | ||||||||
\(964\) | −1.47316e10 | −0.529640 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.41981e10 | 0.506769 | ||||||||
\(967\) | −3.78414e10 | −1.34578 | −0.672892 | − | 0.739741i | \(-0.734948\pi\) | ||||
−0.672892 | + | 0.739741i | \(0.734948\pi\) | |||||||
\(968\) | −5.93876e10 | −2.10442 | ||||||||
\(969\) | 8.50913e10 | 3.00436 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.26402e9 | −0.0793622 | −0.0396811 | − | 0.999212i | \(-0.512634\pi\) | ||||
−0.0396811 | + | 0.999212i | \(0.512634\pi\) | |||||||
\(972\) | 3.74902e9 | 0.130944 | ||||||||
\(973\) | 8.79319e9 | 0.306021 | ||||||||
\(974\) | 3.24399e10 | 1.12493 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.92807e9 | −0.307385 | ||||||||
\(977\) | −2.20843e10 | −0.757622 | −0.378811 | − | 0.925474i | \(-0.623667\pi\) | ||||
−0.378811 | + | 0.925474i | \(0.623667\pi\) | |||||||
\(978\) | 3.29891e9 | 0.112768 | ||||||||
\(979\) | −5.66534e10 | −1.92969 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.80678e10 | 0.611031 | ||||||||
\(982\) | 2.89717e10 | 0.976303 | ||||||||
\(983\) | 6.71759e9 | 0.225567 | 0.112784 | − | 0.993620i | \(-0.464023\pi\) | ||||
0.112784 | + | 0.993620i | \(0.464023\pi\) | |||||||
\(984\) | −4.64982e10 | −1.55580 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.61267e10 | 2.52911 | ||||||||
\(987\) | −1.23045e10 | −0.407336 | ||||||||
\(988\) | 7.81314e9 | 0.257737 | ||||||||
\(989\) | 2.22370e9 | 0.0730954 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.45207e10 | 1.77952 | 0.889761 | − | 0.456427i | \(-0.150871\pi\) | ||||
0.889761 | + | 0.456427i | \(0.150871\pi\) | |||||||
\(992\) | 2.22860e9 | 0.0724837 | ||||||||
\(993\) | −7.32026e9 | −0.237249 | ||||||||
\(994\) | 4.04146e9 | 0.130523 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.31746e10 | 0.743197 | ||||||||
\(997\) | 1.86308e10 | 0.595385 | 0.297692 | − | 0.954662i | \(-0.403783\pi\) | ||||
0.297692 | + | 0.954662i | \(0.403783\pi\) | |||||||
\(998\) | −2.17650e10 | −0.693109 | ||||||||
\(999\) | 2.40600e10 | 0.763514 |
(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 | 175.8.a.i.1.6 | ✓ | 8 | |
5.2 | odd | 4 | 175.8.b.h.99.11 | 16 | |||
5.3 | odd | 4 | 175.8.b.h.99.6 | 16 | |||
5.4 | even | 2 | 175.8.a.j.1.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.8.a.i.1.6 | ✓ | 8 | 1.1 | even | 1 | trivial | |
175.8.a.j.1.3 | yes | 8 | 5.4 | even | 2 | ||
175.8.b.h.99.6 | 16 | 5.3 | odd | 4 | |||
175.8.b.h.99.11 | 16 | 5.2 | odd | 4 |