Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,12,Mod(1,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.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: | \(161.352067918\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2535805712x^{2} - 66934369575900x - 478525314115194389 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(61281.8\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 32.0000 | 0.707107 | ||||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 1024.00 | 0.500000 | ||||||||
\(5\) | 3125.00 | 0.447214 | ||||||||
\(6\) | 7776.00 | 0.408248 | ||||||||
\(7\) | 16807.0 | 0.377964 | ||||||||
\(8\) | 32768.0 | 0.353553 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 100000. | 0.316228 | ||||||||
\(11\) | 66140.8 | 0.123825 | 0.0619127 | − | 0.998082i | \(-0.480280\pi\) | ||||
0.0619127 | + | 0.998082i | \(0.480280\pi\) | |||||||
\(12\) | 248832. | 0.288675 | ||||||||
\(13\) | −1.66136e6 | −1.24101 | −0.620505 | − | 0.784203i | \(-0.713072\pi\) | ||||
−0.620505 | + | 0.784203i | \(0.713072\pi\) | |||||||
\(14\) | 537824. | 0.267261 | ||||||||
\(15\) | 759375. | 0.258199 | ||||||||
\(16\) | 1.04858e6 | 0.250000 | ||||||||
\(17\) | −2.72893e6 | −0.466148 | −0.233074 | − | 0.972459i | \(-0.574878\pi\) | ||||
−0.233074 | + | 0.972459i | \(0.574878\pi\) | |||||||
\(18\) | 1.88957e6 | 0.235702 | ||||||||
\(19\) | 170139. | 0.0157638 | 0.00788189 | − | 0.999969i | \(-0.497491\pi\) | ||||
0.00788189 | + | 0.999969i | \(0.497491\pi\) | |||||||
\(20\) | 3.20000e6 | 0.223607 | ||||||||
\(21\) | 4.08410e6 | 0.218218 | ||||||||
\(22\) | 2.11651e6 | 0.0875577 | ||||||||
\(23\) | 2.02888e7 | 0.657283 | 0.328642 | − | 0.944455i | \(-0.393409\pi\) | ||||
0.328642 | + | 0.944455i | \(0.393409\pi\) | |||||||
\(24\) | 7.96262e6 | 0.204124 | ||||||||
\(25\) | 9.76562e6 | 0.200000 | ||||||||
\(26\) | −5.31635e7 | −0.877526 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 1.72104e7 | 0.188982 | ||||||||
\(29\) | 1.73752e8 | 1.57305 | 0.786524 | − | 0.617560i | \(-0.211879\pi\) | ||||
0.786524 | + | 0.617560i | \(0.211879\pi\) | |||||||
\(30\) | 2.43000e7 | 0.182574 | ||||||||
\(31\) | 9.43176e7 | 0.591702 | 0.295851 | − | 0.955234i | \(-0.404397\pi\) | ||||
0.295851 | + | 0.955234i | \(0.404397\pi\) | |||||||
\(32\) | 3.35544e7 | 0.176777 | ||||||||
\(33\) | 1.60722e7 | 0.0714906 | ||||||||
\(34\) | −8.73259e7 | −0.329616 | ||||||||
\(35\) | 5.25219e7 | 0.169031 | ||||||||
\(36\) | 6.04662e7 | 0.166667 | ||||||||
\(37\) | 5.05619e8 | 1.19871 | 0.599354 | − | 0.800484i | \(-0.295424\pi\) | ||||
0.599354 | + | 0.800484i | \(0.295424\pi\) | |||||||
\(38\) | 5.44446e6 | 0.0111467 | ||||||||
\(39\) | −4.03710e8 | −0.716497 | ||||||||
\(40\) | 1.02400e8 | 0.158114 | ||||||||
\(41\) | 9.81031e8 | 1.32243 | 0.661213 | − | 0.750198i | \(-0.270042\pi\) | ||||
0.661213 | + | 0.750198i | \(0.270042\pi\) | |||||||
\(42\) | 1.30691e8 | 0.154303 | ||||||||
\(43\) | −6.55889e8 | −0.680383 | −0.340192 | − | 0.940356i | \(-0.610492\pi\) | ||||
−0.340192 | + | 0.940356i | \(0.610492\pi\) | |||||||
\(44\) | 6.77282e7 | 0.0619127 | ||||||||
\(45\) | 1.84528e8 | 0.149071 | ||||||||
\(46\) | 6.49241e8 | 0.464770 | ||||||||
\(47\) | −1.20259e9 | −0.764853 | −0.382426 | − | 0.923986i | \(-0.624911\pi\) | ||||
−0.382426 | + | 0.923986i | \(0.624911\pi\) | |||||||
\(48\) | 2.54804e8 | 0.144338 | ||||||||
\(49\) | 2.82475e8 | 0.142857 | ||||||||
\(50\) | 3.12500e8 | 0.141421 | ||||||||
\(51\) | −6.63131e8 | −0.269131 | ||||||||
\(52\) | −1.70123e9 | −0.620505 | ||||||||
\(53\) | 4.49627e9 | 1.47685 | 0.738423 | − | 0.674338i | \(-0.235571\pi\) | ||||
0.738423 | + | 0.674338i | \(0.235571\pi\) | |||||||
\(54\) | 4.59165e8 | 0.136083 | ||||||||
\(55\) | 2.06690e8 | 0.0553764 | ||||||||
\(56\) | 5.50732e8 | 0.133631 | ||||||||
\(57\) | 4.13439e7 | 0.00910122 | ||||||||
\(58\) | 5.56008e9 | 1.11231 | ||||||||
\(59\) | −3.76456e8 | −0.0685533 | −0.0342766 | − | 0.999412i | \(-0.510913\pi\) | ||||
−0.0342766 | + | 0.999412i | \(0.510913\pi\) | |||||||
\(60\) | 7.77600e8 | 0.129099 | ||||||||
\(61\) | −1.37967e9 | −0.209151 | −0.104575 | − | 0.994517i | \(-0.533348\pi\) | ||||
−0.104575 | + | 0.994517i | \(0.533348\pi\) | |||||||
\(62\) | 3.01816e9 | 0.418397 | ||||||||
\(63\) | 9.92437e8 | 0.125988 | ||||||||
\(64\) | 1.07374e9 | 0.125000 | ||||||||
\(65\) | −5.19175e9 | −0.554996 | ||||||||
\(66\) | 5.14311e8 | 0.0505515 | ||||||||
\(67\) | −4.62132e8 | −0.0418171 | −0.0209086 | − | 0.999781i | \(-0.506656\pi\) | ||||
−0.0209086 | + | 0.999781i | \(0.506656\pi\) | |||||||
\(68\) | −2.79443e9 | −0.233074 | ||||||||
\(69\) | 4.93017e9 | 0.379483 | ||||||||
\(70\) | 1.68070e9 | 0.119523 | ||||||||
\(71\) | 2.61019e10 | 1.71693 | 0.858463 | − | 0.512875i | \(-0.171420\pi\) | ||||
0.858463 | + | 0.512875i | \(0.171420\pi\) | |||||||
\(72\) | 1.93492e9 | 0.117851 | ||||||||
\(73\) | −1.98822e10 | −1.12251 | −0.561254 | − | 0.827644i | \(-0.689681\pi\) | ||||
−0.561254 | + | 0.827644i | \(0.689681\pi\) | |||||||
\(74\) | 1.61798e10 | 0.847615 | ||||||||
\(75\) | 2.37305e9 | 0.115470 | ||||||||
\(76\) | 1.74223e8 | 0.00788189 | ||||||||
\(77\) | 1.11163e9 | 0.0468016 | ||||||||
\(78\) | −1.29187e10 | −0.506640 | ||||||||
\(79\) | 4.05647e10 | 1.48320 | 0.741599 | − | 0.670844i | \(-0.234068\pi\) | ||||
0.741599 | + | 0.670844i | \(0.234068\pi\) | |||||||
\(80\) | 3.27680e9 | 0.111803 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 3.13930e10 | 0.935097 | ||||||||
\(83\) | −3.73268e10 | −1.04014 | −0.520070 | − | 0.854124i | \(-0.674094\pi\) | ||||
−0.520070 | + | 0.854124i | \(0.674094\pi\) | |||||||
\(84\) | 4.18212e9 | 0.109109 | ||||||||
\(85\) | −8.52792e9 | −0.208468 | ||||||||
\(86\) | −2.09884e10 | −0.481104 | ||||||||
\(87\) | 4.22218e10 | 0.908200 | ||||||||
\(88\) | 2.16730e9 | 0.0437789 | ||||||||
\(89\) | −3.35790e10 | −0.637415 | −0.318707 | − | 0.947853i | \(-0.603249\pi\) | ||||
−0.318707 | + | 0.947853i | \(0.603249\pi\) | |||||||
\(90\) | 5.90490e9 | 0.105409 | ||||||||
\(91\) | −2.79225e10 | −0.469057 | ||||||||
\(92\) | 2.07757e10 | 0.328642 | ||||||||
\(93\) | 2.29192e10 | 0.341619 | ||||||||
\(94\) | −3.84827e10 | −0.540833 | ||||||||
\(95\) | 5.31686e8 | 0.00704977 | ||||||||
\(96\) | 8.15373e9 | 0.102062 | ||||||||
\(97\) | −3.04604e10 | −0.360156 | −0.180078 | − | 0.983652i | \(-0.557635\pi\) | ||||
−0.180078 | + | 0.983652i | \(0.557635\pi\) | |||||||
\(98\) | 9.03921e9 | 0.101015 | ||||||||
\(99\) | 3.90555e9 | 0.0412751 | ||||||||
\(100\) | 1.00000e10 | 0.100000 | ||||||||
\(101\) | 1.47836e11 | 1.39963 | 0.699813 | − | 0.714326i | \(-0.253266\pi\) | ||||
0.699813 | + | 0.714326i | \(0.253266\pi\) | |||||||
\(102\) | −2.12202e10 | −0.190304 | ||||||||
\(103\) | 8.87420e10 | 0.754266 | 0.377133 | − | 0.926159i | \(-0.376910\pi\) | ||||
0.377133 | + | 0.926159i | \(0.376910\pi\) | |||||||
\(104\) | −5.44394e10 | −0.438763 | ||||||||
\(105\) | 1.27628e10 | 0.0975900 | ||||||||
\(106\) | 1.43881e11 | 1.04429 | ||||||||
\(107\) | 3.28122e10 | 0.226165 | 0.113082 | − | 0.993586i | \(-0.463928\pi\) | ||||
0.113082 | + | 0.993586i | \(0.463928\pi\) | |||||||
\(108\) | 1.46933e10 | 0.0962250 | ||||||||
\(109\) | 1.54613e11 | 0.962497 | 0.481248 | − | 0.876584i | \(-0.340183\pi\) | ||||
0.481248 | + | 0.876584i | \(0.340183\pi\) | |||||||
\(110\) | 6.61408e9 | 0.0391570 | ||||||||
\(111\) | 1.22865e11 | 0.692075 | ||||||||
\(112\) | 1.76234e10 | 0.0944911 | ||||||||
\(113\) | −2.41500e11 | −1.23306 | −0.616531 | − | 0.787330i | \(-0.711463\pi\) | ||||
−0.616531 | + | 0.787330i | \(0.711463\pi\) | |||||||
\(114\) | 1.32300e9 | 0.00643553 | ||||||||
\(115\) | 6.34024e10 | 0.293946 | ||||||||
\(116\) | 1.77922e11 | 0.786524 | ||||||||
\(117\) | −9.81016e10 | −0.413670 | ||||||||
\(118\) | −1.20466e10 | −0.0484745 | ||||||||
\(119\) | −4.58652e10 | −0.176187 | ||||||||
\(120\) | 2.48832e10 | 0.0912871 | ||||||||
\(121\) | −2.80937e11 | −0.984667 | ||||||||
\(122\) | −4.41493e10 | −0.147892 | ||||||||
\(123\) | 2.38390e11 | 0.763503 | ||||||||
\(124\) | 9.65812e10 | 0.295851 | ||||||||
\(125\) | 3.05176e10 | 0.0894427 | ||||||||
\(126\) | 3.17580e10 | 0.0890871 | ||||||||
\(127\) | −7.42829e10 | −0.199512 | −0.0997558 | − | 0.995012i | \(-0.531806\pi\) | ||||
−0.0997558 | + | 0.995012i | \(0.531806\pi\) | |||||||
\(128\) | 3.43597e10 | 0.0883883 | ||||||||
\(129\) | −1.59381e11 | −0.392819 | ||||||||
\(130\) | −1.66136e11 | −0.392442 | ||||||||
\(131\) | 2.17771e11 | 0.493183 | 0.246592 | − | 0.969119i | \(-0.420689\pi\) | ||||
0.246592 | + | 0.969119i | \(0.420689\pi\) | |||||||
\(132\) | 1.64579e10 | 0.0357453 | ||||||||
\(133\) | 2.85953e9 | 0.00595815 | ||||||||
\(134\) | −1.47882e10 | −0.0295692 | ||||||||
\(135\) | 4.48403e10 | 0.0860663 | ||||||||
\(136\) | −8.94217e10 | −0.164808 | ||||||||
\(137\) | 8.39855e11 | 1.48676 | 0.743381 | − | 0.668868i | \(-0.233221\pi\) | ||||
0.743381 | + | 0.668868i | \(0.233221\pi\) | |||||||
\(138\) | 1.57765e11 | 0.268335 | ||||||||
\(139\) | −2.47328e11 | −0.404289 | −0.202145 | − | 0.979356i | \(-0.564791\pi\) | ||||
−0.202145 | + | 0.979356i | \(0.564791\pi\) | |||||||
\(140\) | 5.37824e10 | 0.0845154 | ||||||||
\(141\) | −2.92228e11 | −0.441588 | ||||||||
\(142\) | 8.35262e11 | 1.21405 | ||||||||
\(143\) | −1.09884e11 | −0.153668 | ||||||||
\(144\) | 6.19174e10 | 0.0833333 | ||||||||
\(145\) | 5.42976e11 | 0.703488 | ||||||||
\(146\) | −6.36231e11 | −0.793732 | ||||||||
\(147\) | 6.86415e10 | 0.0824786 | ||||||||
\(148\) | 5.17754e11 | 0.599354 | ||||||||
\(149\) | −1.41322e11 | −0.157647 | −0.0788236 | − | 0.996889i | \(-0.525116\pi\) | ||||
−0.0788236 | + | 0.996889i | \(0.525116\pi\) | |||||||
\(150\) | 7.59375e10 | 0.0816497 | ||||||||
\(151\) | 1.11781e11 | 0.115876 | 0.0579382 | − | 0.998320i | \(-0.481547\pi\) | ||||
0.0579382 | + | 0.998320i | \(0.481547\pi\) | |||||||
\(152\) | 5.57513e9 | 0.00557333 | ||||||||
\(153\) | −1.61141e11 | −0.155383 | ||||||||
\(154\) | 3.55721e10 | 0.0330937 | ||||||||
\(155\) | 2.94742e11 | 0.264617 | ||||||||
\(156\) | −4.13399e11 | −0.358249 | ||||||||
\(157\) | −2.14126e12 | −1.79152 | −0.895758 | − | 0.444541i | \(-0.853367\pi\) | ||||
−0.895758 | + | 0.444541i | \(0.853367\pi\) | |||||||
\(158\) | 1.29807e12 | 1.04878 | ||||||||
\(159\) | 1.09259e12 | 0.852657 | ||||||||
\(160\) | 1.04858e11 | 0.0790569 | ||||||||
\(161\) | 3.40993e11 | 0.248430 | ||||||||
\(162\) | 1.11577e11 | 0.0785674 | ||||||||
\(163\) | 1.09710e12 | 0.746814 | 0.373407 | − | 0.927668i | \(-0.378189\pi\) | ||||
0.373407 | + | 0.927668i | \(0.378189\pi\) | |||||||
\(164\) | 1.00458e12 | 0.661213 | ||||||||
\(165\) | 5.02257e10 | 0.0319716 | ||||||||
\(166\) | −1.19446e12 | −0.735490 | ||||||||
\(167\) | 1.73886e12 | 1.03591 | 0.517957 | − | 0.855407i | \(-0.326693\pi\) | ||||
0.517957 | + | 0.855407i | \(0.326693\pi\) | |||||||
\(168\) | 1.33828e11 | 0.0771517 | ||||||||
\(169\) | 9.67953e11 | 0.540104 | ||||||||
\(170\) | −2.72893e11 | −0.147409 | ||||||||
\(171\) | 1.00466e10 | 0.00525459 | ||||||||
\(172\) | −6.71630e11 | −0.340192 | ||||||||
\(173\) | 5.88694e11 | 0.288826 | 0.144413 | − | 0.989518i | \(-0.453871\pi\) | ||||
0.144413 | + | 0.989518i | \(0.453871\pi\) | |||||||
\(174\) | 1.35110e12 | 0.642194 | ||||||||
\(175\) | 1.64131e11 | 0.0755929 | ||||||||
\(176\) | 6.93536e10 | 0.0309563 | ||||||||
\(177\) | −9.14788e10 | −0.0395793 | ||||||||
\(178\) | −1.07453e12 | −0.450720 | ||||||||
\(179\) | −3.59513e12 | −1.46226 | −0.731128 | − | 0.682240i | \(-0.761006\pi\) | ||||
−0.731128 | + | 0.682240i | \(0.761006\pi\) | |||||||
\(180\) | 1.88957e11 | 0.0745356 | ||||||||
\(181\) | 2.38944e12 | 0.914247 | 0.457123 | − | 0.889403i | \(-0.348880\pi\) | ||||
0.457123 | + | 0.889403i | \(0.348880\pi\) | |||||||
\(182\) | −8.93519e11 | −0.331674 | ||||||||
\(183\) | −3.35259e11 | −0.120753 | ||||||||
\(184\) | 6.64823e11 | 0.232385 | ||||||||
\(185\) | 1.58006e12 | 0.536079 | ||||||||
\(186\) | 7.33413e11 | 0.241561 | ||||||||
\(187\) | −1.80494e11 | −0.0577209 | ||||||||
\(188\) | −1.23145e12 | −0.382426 | ||||||||
\(189\) | 2.41162e11 | 0.0727393 | ||||||||
\(190\) | 1.70139e10 | 0.00498494 | ||||||||
\(191\) | −3.22923e10 | −0.00919210 | −0.00459605 | − | 0.999989i | \(-0.501463\pi\) | ||||
−0.00459605 | + | 0.999989i | \(0.501463\pi\) | |||||||
\(192\) | 2.60919e11 | 0.0721688 | ||||||||
\(193\) | 2.01541e11 | 0.0541750 | 0.0270875 | − | 0.999633i | \(-0.491377\pi\) | ||||
0.0270875 | + | 0.999633i | \(0.491377\pi\) | |||||||
\(194\) | −9.74731e11 | −0.254669 | ||||||||
\(195\) | −1.26159e12 | −0.320427 | ||||||||
\(196\) | 2.89255e11 | 0.0714286 | ||||||||
\(197\) | −6.83789e12 | −1.64194 | −0.820971 | − | 0.570970i | \(-0.806567\pi\) | ||||
−0.820971 | + | 0.570970i | \(0.806567\pi\) | |||||||
\(198\) | 1.24978e11 | 0.0291859 | ||||||||
\(199\) | 6.86478e12 | 1.55932 | 0.779659 | − | 0.626204i | \(-0.215392\pi\) | ||||
0.779659 | + | 0.626204i | \(0.215392\pi\) | |||||||
\(200\) | 3.20000e11 | 0.0707107 | ||||||||
\(201\) | −1.12298e11 | −0.0241431 | ||||||||
\(202\) | 4.73075e12 | 0.989686 | ||||||||
\(203\) | 2.92026e12 | 0.594556 | ||||||||
\(204\) | −6.79046e11 | −0.134565 | ||||||||
\(205\) | 3.06572e12 | 0.591407 | ||||||||
\(206\) | 2.83974e12 | 0.533346 | ||||||||
\(207\) | 1.19803e12 | 0.219094 | ||||||||
\(208\) | −1.74206e12 | −0.310252 | ||||||||
\(209\) | 1.12532e10 | 0.00195195 | ||||||||
\(210\) | 4.08410e11 | 0.0690066 | ||||||||
\(211\) | 3.64997e12 | 0.600809 | 0.300404 | − | 0.953812i | \(-0.402878\pi\) | ||||
0.300404 | + | 0.953812i | \(0.402878\pi\) | |||||||
\(212\) | 4.60418e12 | 0.738423 | ||||||||
\(213\) | 6.34277e12 | 0.991268 | ||||||||
\(214\) | 1.04999e12 | 0.159923 | ||||||||
\(215\) | −2.04965e12 | −0.304277 | ||||||||
\(216\) | 4.70185e11 | 0.0680414 | ||||||||
\(217\) | 1.58520e12 | 0.223642 | ||||||||
\(218\) | 4.94761e12 | 0.680588 | ||||||||
\(219\) | −4.83138e12 | −0.648080 | ||||||||
\(220\) | 2.11651e11 | 0.0276882 | ||||||||
\(221\) | 4.53374e12 | 0.578494 | ||||||||
\(222\) | 3.93169e12 | 0.489371 | ||||||||
\(223\) | −1.18816e13 | −1.44277 | −0.721386 | − | 0.692533i | \(-0.756495\pi\) | ||||
−0.721386 | + | 0.692533i | \(0.756495\pi\) | |||||||
\(224\) | 5.63949e11 | 0.0668153 | ||||||||
\(225\) | 5.76650e11 | 0.0666667 | ||||||||
\(226\) | −7.72799e12 | −0.871907 | ||||||||
\(227\) | −3.23541e12 | −0.356277 | −0.178138 | − | 0.984005i | \(-0.557007\pi\) | ||||
−0.178138 | + | 0.984005i | \(0.557007\pi\) | |||||||
\(228\) | 4.23361e10 | 0.00455061 | ||||||||
\(229\) | 4.37790e11 | 0.0459378 | 0.0229689 | − | 0.999736i | \(-0.492688\pi\) | ||||
0.0229689 | + | 0.999736i | \(0.492688\pi\) | |||||||
\(230\) | 2.02888e12 | 0.207851 | ||||||||
\(231\) | 2.70126e11 | 0.0270209 | ||||||||
\(232\) | 5.69352e12 | 0.556156 | ||||||||
\(233\) | 2.27567e12 | 0.217096 | 0.108548 | − | 0.994091i | \(-0.465380\pi\) | ||||
0.108548 | + | 0.994091i | \(0.465380\pi\) | |||||||
\(234\) | −3.13925e12 | −0.292509 | ||||||||
\(235\) | −3.75808e12 | −0.342053 | ||||||||
\(236\) | −3.85491e11 | −0.0342766 | ||||||||
\(237\) | 9.85722e12 | 0.856325 | ||||||||
\(238\) | −1.46769e12 | −0.124583 | ||||||||
\(239\) | 1.18415e13 | 0.982239 | 0.491119 | − | 0.871092i | \(-0.336588\pi\) | ||||
0.491119 | + | 0.871092i | \(0.336588\pi\) | |||||||
\(240\) | 7.96262e11 | 0.0645497 | ||||||||
\(241\) | −6.95309e12 | −0.550914 | −0.275457 | − | 0.961313i | \(-0.588829\pi\) | ||||
−0.275457 | + | 0.961313i | \(0.588829\pi\) | |||||||
\(242\) | −8.98999e12 | −0.696265 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | −1.41278e12 | −0.104575 | ||||||||
\(245\) | 8.82735e11 | 0.0638877 | ||||||||
\(246\) | 7.62850e12 | 0.539878 | ||||||||
\(247\) | −2.82663e11 | −0.0195630 | ||||||||
\(248\) | 3.09060e12 | 0.209198 | ||||||||
\(249\) | −9.07042e12 | −0.600525 | ||||||||
\(250\) | 9.76562e11 | 0.0632456 | ||||||||
\(251\) | 1.80184e13 | 1.14159 | 0.570797 | − | 0.821091i | \(-0.306634\pi\) | ||||
0.570797 | + | 0.821091i | \(0.306634\pi\) | |||||||
\(252\) | 1.01626e12 | 0.0629941 | ||||||||
\(253\) | 1.34192e12 | 0.0813884 | ||||||||
\(254\) | −2.37705e12 | −0.141076 | ||||||||
\(255\) | −2.07228e12 | −0.120359 | ||||||||
\(256\) | 1.09951e12 | 0.0625000 | ||||||||
\(257\) | 1.36485e13 | 0.759369 | 0.379685 | − | 0.925116i | \(-0.376033\pi\) | ||||
0.379685 | + | 0.925116i | \(0.376033\pi\) | |||||||
\(258\) | −5.10019e12 | −0.277765 | ||||||||
\(259\) | 8.49793e12 | 0.453069 | ||||||||
\(260\) | −5.31635e12 | −0.277498 | ||||||||
\(261\) | 1.02599e13 | 0.524349 | ||||||||
\(262\) | 6.96868e12 | 0.348733 | ||||||||
\(263\) | −5.43786e11 | −0.0266484 | −0.0133242 | − | 0.999911i | \(-0.504241\pi\) | ||||
−0.0133242 | + | 0.999911i | \(0.504241\pi\) | |||||||
\(264\) | 5.26654e11 | 0.0252757 | ||||||||
\(265\) | 1.40508e13 | 0.660465 | ||||||||
\(266\) | 9.15051e10 | 0.00421304 | ||||||||
\(267\) | −8.15969e12 | −0.368012 | ||||||||
\(268\) | −4.73223e11 | −0.0209086 | ||||||||
\(269\) | 1.28824e13 | 0.557645 | 0.278822 | − | 0.960343i | \(-0.410056\pi\) | ||||
0.278822 | + | 0.960343i | \(0.410056\pi\) | |||||||
\(270\) | 1.43489e12 | 0.0608581 | ||||||||
\(271\) | 1.37500e13 | 0.571440 | 0.285720 | − | 0.958313i | \(-0.407767\pi\) | ||||
0.285720 | + | 0.958313i | \(0.407767\pi\) | |||||||
\(272\) | −2.86149e12 | −0.116537 | ||||||||
\(273\) | −6.78516e12 | −0.270810 | ||||||||
\(274\) | 2.68754e13 | 1.05130 | ||||||||
\(275\) | 6.45906e11 | 0.0247651 | ||||||||
\(276\) | 5.04850e12 | 0.189741 | ||||||||
\(277\) | 3.09874e12 | 0.114168 | 0.0570842 | − | 0.998369i | \(-0.481820\pi\) | ||||
0.0570842 | + | 0.998369i | \(0.481820\pi\) | |||||||
\(278\) | −7.91450e12 | −0.285876 | ||||||||
\(279\) | 5.56936e12 | 0.197234 | ||||||||
\(280\) | 1.72104e12 | 0.0597614 | ||||||||
\(281\) | 4.07746e12 | 0.138837 | 0.0694185 | − | 0.997588i | \(-0.477886\pi\) | ||||
0.0694185 | + | 0.997588i | \(0.477886\pi\) | |||||||
\(282\) | −9.35131e12 | −0.312250 | ||||||||
\(283\) | 4.41972e12 | 0.144733 | 0.0723667 | − | 0.997378i | \(-0.476945\pi\) | ||||
0.0723667 | + | 0.997378i | \(0.476945\pi\) | |||||||
\(284\) | 2.67284e13 | 0.858463 | ||||||||
\(285\) | 1.29200e11 | 0.00407019 | ||||||||
\(286\) | −3.51627e12 | −0.108660 | ||||||||
\(287\) | 1.64882e13 | 0.499830 | ||||||||
\(288\) | 1.98136e12 | 0.0589256 | ||||||||
\(289\) | −2.68248e13 | −0.782706 | ||||||||
\(290\) | 1.73752e13 | 0.497441 | ||||||||
\(291\) | −7.40187e12 | −0.207936 | ||||||||
\(292\) | −2.03594e13 | −0.561254 | ||||||||
\(293\) | 2.07901e13 | 0.562451 | 0.281226 | − | 0.959642i | \(-0.409259\pi\) | ||||
0.281226 | + | 0.959642i | \(0.409259\pi\) | |||||||
\(294\) | 2.19653e12 | 0.0583212 | ||||||||
\(295\) | −1.17643e12 | −0.0306580 | ||||||||
\(296\) | 1.65681e13 | 0.423807 | ||||||||
\(297\) | 9.49048e11 | 0.0238302 | ||||||||
\(298\) | −4.52231e12 | −0.111473 | ||||||||
\(299\) | −3.37069e13 | −0.815695 | ||||||||
\(300\) | 2.43000e12 | 0.0577350 | ||||||||
\(301\) | −1.10235e13 | −0.257161 | ||||||||
\(302\) | 3.57699e12 | 0.0819369 | ||||||||
\(303\) | 3.59241e13 | 0.808075 | ||||||||
\(304\) | 1.78404e11 | 0.00394094 | ||||||||
\(305\) | −4.31146e12 | −0.0935352 | ||||||||
\(306\) | −5.15650e12 | −0.109872 | ||||||||
\(307\) | −2.48567e13 | −0.520213 | −0.260107 | − | 0.965580i | \(-0.583758\pi\) | ||||
−0.260107 | + | 0.965580i | \(0.583758\pi\) | |||||||
\(308\) | 1.13831e12 | 0.0234008 | ||||||||
\(309\) | 2.15643e13 | 0.435475 | ||||||||
\(310\) | 9.43176e12 | 0.187113 | ||||||||
\(311\) | −4.76556e12 | −0.0928821 | −0.0464411 | − | 0.998921i | \(-0.514788\pi\) | ||||
−0.0464411 | + | 0.998921i | \(0.514788\pi\) | |||||||
\(312\) | −1.32288e13 | −0.253320 | ||||||||
\(313\) | 5.20906e13 | 0.980089 | 0.490045 | − | 0.871697i | \(-0.336980\pi\) | ||||
0.490045 | + | 0.871697i | \(0.336980\pi\) | |||||||
\(314\) | −6.85203e13 | −1.26679 | ||||||||
\(315\) | 3.10136e12 | 0.0563436 | ||||||||
\(316\) | 4.15382e13 | 0.741599 | ||||||||
\(317\) | 1.32321e13 | 0.232168 | 0.116084 | − | 0.993239i | \(-0.462966\pi\) | ||||
0.116084 | + | 0.993239i | \(0.462966\pi\) | |||||||
\(318\) | 3.49630e13 | 0.602920 | ||||||||
\(319\) | 1.14921e13 | 0.194783 | ||||||||
\(320\) | 3.35544e12 | 0.0559017 | ||||||||
\(321\) | 7.97337e12 | 0.130576 | ||||||||
\(322\) | 1.09118e13 | 0.175666 | ||||||||
\(323\) | −4.64299e11 | −0.00734825 | ||||||||
\(324\) | 3.57047e12 | 0.0555556 | ||||||||
\(325\) | −1.62242e13 | −0.248202 | ||||||||
\(326\) | 3.51071e13 | 0.528078 | ||||||||
\(327\) | 3.75709e13 | 0.555698 | ||||||||
\(328\) | 3.21464e13 | 0.467548 | ||||||||
\(329\) | −2.02119e13 | −0.289087 | ||||||||
\(330\) | 1.60722e12 | 0.0226073 | ||||||||
\(331\) | −7.72344e13 | −1.06846 | −0.534228 | − | 0.845341i | \(-0.679398\pi\) | ||||
−0.534228 | + | 0.845341i | \(0.679398\pi\) | |||||||
\(332\) | −3.82227e13 | −0.520070 | ||||||||
\(333\) | 2.98563e13 | 0.399570 | ||||||||
\(334\) | 5.56435e13 | 0.732502 | ||||||||
\(335\) | −1.44416e12 | −0.0187012 | ||||||||
\(336\) | 4.28249e12 | 0.0545545 | ||||||||
\(337\) | −1.09778e14 | −1.37579 | −0.687895 | − | 0.725810i | \(-0.741465\pi\) | ||||
−0.687895 | + | 0.725810i | \(0.741465\pi\) | |||||||
\(338\) | 3.09745e13 | 0.381911 | ||||||||
\(339\) | −5.86844e13 | −0.711909 | ||||||||
\(340\) | −8.73259e12 | −0.104234 | ||||||||
\(341\) | 6.23824e12 | 0.0732677 | ||||||||
\(342\) | 3.21490e11 | 0.00371556 | ||||||||
\(343\) | 4.74756e12 | 0.0539949 | ||||||||
\(344\) | −2.14922e13 | −0.240552 | ||||||||
\(345\) | 1.54068e13 | 0.169710 | ||||||||
\(346\) | 1.88382e13 | 0.204231 | ||||||||
\(347\) | 9.79105e13 | 1.04476 | 0.522381 | − | 0.852712i | \(-0.325044\pi\) | ||||
0.522381 | + | 0.852712i | \(0.325044\pi\) | |||||||
\(348\) | 4.32352e13 | 0.454100 | ||||||||
\(349\) | −3.78226e13 | −0.391032 | −0.195516 | − | 0.980701i | \(-0.562638\pi\) | ||||
−0.195516 | + | 0.980701i | \(0.562638\pi\) | |||||||
\(350\) | 5.25219e12 | 0.0534522 | ||||||||
\(351\) | −2.38387e13 | −0.238832 | ||||||||
\(352\) | 2.21932e12 | 0.0218894 | ||||||||
\(353\) | 1.88359e14 | 1.82905 | 0.914523 | − | 0.404533i | \(-0.132566\pi\) | ||||
0.914523 | + | 0.404533i | \(0.132566\pi\) | |||||||
\(354\) | −2.92732e12 | −0.0279868 | ||||||||
\(355\) | 8.15685e13 | 0.767833 | ||||||||
\(356\) | −3.43848e13 | −0.318707 | ||||||||
\(357\) | −1.11452e13 | −0.101722 | ||||||||
\(358\) | −1.15044e14 | −1.03397 | ||||||||
\(359\) | 1.12973e14 | 0.999894 | 0.499947 | − | 0.866056i | \(-0.333353\pi\) | ||||
0.499947 | + | 0.866056i | \(0.333353\pi\) | |||||||
\(360\) | 6.04662e12 | 0.0527046 | ||||||||
\(361\) | −1.16461e14 | −0.999752 | ||||||||
\(362\) | 7.64620e13 | 0.646470 | ||||||||
\(363\) | −6.82677e13 | −0.568498 | ||||||||
\(364\) | −2.85926e13 | −0.234529 | ||||||||
\(365\) | −6.21319e13 | −0.502000 | ||||||||
\(366\) | −1.07283e13 | −0.0853855 | ||||||||
\(367\) | −1.22823e14 | −0.962976 | −0.481488 | − | 0.876453i | \(-0.659904\pi\) | ||||
−0.481488 | + | 0.876453i | \(0.659904\pi\) | |||||||
\(368\) | 2.12743e13 | 0.164321 | ||||||||
\(369\) | 5.79289e13 | 0.440809 | ||||||||
\(370\) | 5.05619e13 | 0.379065 | ||||||||
\(371\) | 7.55688e13 | 0.558195 | ||||||||
\(372\) | 2.34692e13 | 0.170810 | ||||||||
\(373\) | 2.45034e12 | 0.0175723 | 0.00878614 | − | 0.999961i | \(-0.497203\pi\) | ||||
0.00878614 | + | 0.999961i | \(0.497203\pi\) | |||||||
\(374\) | −5.77580e12 | −0.0408149 | ||||||||
\(375\) | 7.41577e12 | 0.0516398 | ||||||||
\(376\) | −3.94063e13 | −0.270416 | ||||||||
\(377\) | −2.88665e14 | −1.95217 | ||||||||
\(378\) | 7.71719e12 | 0.0514344 | ||||||||
\(379\) | 2.46438e12 | 0.0161880 | 0.00809398 | − | 0.999967i | \(-0.497424\pi\) | ||||
0.00809398 | + | 0.999967i | \(0.497424\pi\) | |||||||
\(380\) | 5.44446e11 | 0.00352489 | ||||||||
\(381\) | −1.80507e13 | −0.115188 | ||||||||
\(382\) | −1.03335e12 | −0.00649980 | ||||||||
\(383\) | −2.49930e14 | −1.54962 | −0.774810 | − | 0.632194i | \(-0.782155\pi\) | ||||
−0.774810 | + | 0.632194i | \(0.782155\pi\) | |||||||
\(384\) | 8.34942e12 | 0.0510310 | ||||||||
\(385\) | 3.47384e12 | 0.0209303 | ||||||||
\(386\) | 6.44932e12 | 0.0383075 | ||||||||
\(387\) | −3.87296e13 | −0.226794 | ||||||||
\(388\) | −3.11914e13 | −0.180078 | ||||||||
\(389\) | −2.61748e14 | −1.48991 | −0.744955 | − | 0.667115i | \(-0.767529\pi\) | ||||
−0.744955 | + | 0.667115i | \(0.767529\pi\) | |||||||
\(390\) | −4.03710e13 | −0.226576 | ||||||||
\(391\) | −5.53667e13 | −0.306391 | ||||||||
\(392\) | 9.25615e12 | 0.0505076 | ||||||||
\(393\) | 5.29184e13 | 0.284740 | ||||||||
\(394\) | −2.18812e14 | −1.16103 | ||||||||
\(395\) | 1.26765e14 | 0.663306 | ||||||||
\(396\) | 3.99928e12 | 0.0206376 | ||||||||
\(397\) | 8.24283e13 | 0.419496 | 0.209748 | − | 0.977755i | \(-0.432736\pi\) | ||||
0.209748 | + | 0.977755i | \(0.432736\pi\) | |||||||
\(398\) | 2.19673e14 | 1.10260 | ||||||||
\(399\) | 6.94867e11 | 0.00343994 | ||||||||
\(400\) | 1.02400e13 | 0.0500000 | ||||||||
\(401\) | −1.23889e14 | −0.596675 | −0.298338 | − | 0.954460i | \(-0.596432\pi\) | ||||
−0.298338 | + | 0.954460i | \(0.596432\pi\) | |||||||
\(402\) | −3.59354e12 | −0.0170718 | ||||||||
\(403\) | −1.56695e14 | −0.734308 | ||||||||
\(404\) | 1.51384e14 | 0.699813 | ||||||||
\(405\) | 1.08962e13 | 0.0496904 | ||||||||
\(406\) | 9.34482e13 | 0.420415 | ||||||||
\(407\) | 3.34420e13 | 0.148431 | ||||||||
\(408\) | −2.17295e13 | −0.0951521 | ||||||||
\(409\) | −3.30706e14 | −1.42878 | −0.714389 | − | 0.699749i | \(-0.753295\pi\) | ||||
−0.714389 | + | 0.699749i | \(0.753295\pi\) | |||||||
\(410\) | 9.81031e13 | 0.418188 | ||||||||
\(411\) | 2.04085e14 | 0.858382 | ||||||||
\(412\) | 9.08718e13 | 0.377133 | ||||||||
\(413\) | −6.32710e12 | −0.0259107 | ||||||||
\(414\) | 3.83370e13 | 0.154923 | ||||||||
\(415\) | −1.16646e14 | −0.465164 | ||||||||
\(416\) | −5.57460e13 | −0.219382 | ||||||||
\(417\) | −6.01007e13 | −0.233417 | ||||||||
\(418\) | 3.60101e11 | 0.00138024 | ||||||||
\(419\) | −3.05793e14 | −1.15678 | −0.578389 | − | 0.815761i | \(-0.696318\pi\) | ||||
−0.578389 | + | 0.815761i | \(0.696318\pi\) | |||||||
\(420\) | 1.30691e13 | 0.0487950 | ||||||||
\(421\) | −4.78033e14 | −1.76160 | −0.880798 | − | 0.473492i | \(-0.842993\pi\) | ||||
−0.880798 | + | 0.473492i | \(0.842993\pi\) | |||||||
\(422\) | 1.16799e14 | 0.424836 | ||||||||
\(423\) | −7.10115e13 | −0.254951 | ||||||||
\(424\) | 1.47334e14 | 0.522144 | ||||||||
\(425\) | −2.66497e13 | −0.0932296 | ||||||||
\(426\) | 2.02969e14 | 0.700932 | ||||||||
\(427\) | −2.31880e13 | −0.0790516 | ||||||||
\(428\) | 3.35997e13 | 0.113082 | ||||||||
\(429\) | −2.67017e13 | −0.0887205 | ||||||||
\(430\) | −6.55889e13 | −0.215156 | ||||||||
\(431\) | −2.72466e14 | −0.882445 | −0.441222 | − | 0.897398i | \(-0.645455\pi\) | ||||
−0.441222 | + | 0.897398i | \(0.645455\pi\) | |||||||
\(432\) | 1.50459e13 | 0.0481125 | ||||||||
\(433\) | −3.61376e14 | −1.14097 | −0.570487 | − | 0.821307i | \(-0.693245\pi\) | ||||
−0.570487 | + | 0.821307i | \(0.693245\pi\) | |||||||
\(434\) | 5.07262e13 | 0.158139 | ||||||||
\(435\) | 1.31943e14 | 0.406159 | ||||||||
\(436\) | 1.58323e14 | 0.481248 | ||||||||
\(437\) | 3.45192e12 | 0.0103613 | ||||||||
\(438\) | −1.54604e14 | −0.458262 | ||||||||
\(439\) | −4.05139e14 | −1.18590 | −0.592951 | − | 0.805238i | \(-0.702037\pi\) | ||||
−0.592951 | + | 0.805238i | \(0.702037\pi\) | |||||||
\(440\) | 6.77282e12 | 0.0195785 | ||||||||
\(441\) | 1.66799e13 | 0.0476190 | ||||||||
\(442\) | 1.45080e14 | 0.409057 | ||||||||
\(443\) | −2.89899e14 | −0.807284 | −0.403642 | − | 0.914917i | \(-0.632256\pi\) | ||||
−0.403642 | + | 0.914917i | \(0.632256\pi\) | |||||||
\(444\) | 1.25814e14 | 0.346037 | ||||||||
\(445\) | −1.04934e14 | −0.285061 | ||||||||
\(446\) | −3.80211e14 | −1.02019 | ||||||||
\(447\) | −3.43413e13 | −0.0910176 | ||||||||
\(448\) | 1.80464e13 | 0.0472456 | ||||||||
\(449\) | −6.42021e14 | −1.66033 | −0.830165 | − | 0.557518i | \(-0.811754\pi\) | ||||
−0.830165 | + | 0.557518i | \(0.811754\pi\) | |||||||
\(450\) | 1.84528e13 | 0.0471405 | ||||||||
\(451\) | 6.48861e13 | 0.163750 | ||||||||
\(452\) | −2.47296e14 | −0.616531 | ||||||||
\(453\) | 2.71628e13 | 0.0669012 | ||||||||
\(454\) | −1.03533e14 | −0.251926 | ||||||||
\(455\) | −8.72577e13 | −0.209769 | ||||||||
\(456\) | 1.35476e12 | 0.00321777 | ||||||||
\(457\) | 7.48555e14 | 1.75665 | 0.878324 | − | 0.478066i | \(-0.158662\pi\) | ||||
0.878324 | + | 0.478066i | \(0.158662\pi\) | |||||||
\(458\) | 1.40093e13 | 0.0324830 | ||||||||
\(459\) | −3.91572e13 | −0.0897102 | ||||||||
\(460\) | 6.49241e13 | 0.146973 | ||||||||
\(461\) | −1.97382e14 | −0.441523 | −0.220761 | − | 0.975328i | \(-0.570854\pi\) | ||||
−0.220761 | + | 0.975328i | \(0.570854\pi\) | |||||||
\(462\) | 8.64402e12 | 0.0191067 | ||||||||
\(463\) | 1.52003e14 | 0.332013 | 0.166007 | − | 0.986125i | \(-0.446913\pi\) | ||||
0.166007 | + | 0.986125i | \(0.446913\pi\) | |||||||
\(464\) | 1.82193e14 | 0.393262 | ||||||||
\(465\) | 7.16224e13 | 0.152777 | ||||||||
\(466\) | 7.28216e13 | 0.153510 | ||||||||
\(467\) | −5.83558e14 | −1.21574 | −0.607870 | − | 0.794036i | \(-0.707976\pi\) | ||||
−0.607870 | + | 0.794036i | \(0.707976\pi\) | |||||||
\(468\) | −1.00456e14 | −0.206835 | ||||||||
\(469\) | −7.76705e12 | −0.0158054 | ||||||||
\(470\) | −1.20259e14 | −0.241868 | ||||||||
\(471\) | −5.20326e14 | −1.03433 | ||||||||
\(472\) | −1.23357e13 | −0.0242372 | ||||||||
\(473\) | −4.33810e13 | −0.0842487 | ||||||||
\(474\) | 3.15431e14 | 0.605513 | ||||||||
\(475\) | 1.66152e12 | 0.00315275 | ||||||||
\(476\) | −4.69659e13 | −0.0880937 | ||||||||
\(477\) | 2.65500e14 | 0.492282 | ||||||||
\(478\) | 3.78927e14 | 0.694548 | ||||||||
\(479\) | −1.00235e15 | −1.81624 | −0.908121 | − | 0.418708i | \(-0.862483\pi\) | ||||
−0.908121 | + | 0.418708i | \(0.862483\pi\) | |||||||
\(480\) | 2.54804e13 | 0.0456435 | ||||||||
\(481\) | −8.40014e14 | −1.48761 | ||||||||
\(482\) | −2.22499e14 | −0.389555 | ||||||||
\(483\) | 8.28614e13 | 0.143431 | ||||||||
\(484\) | −2.87680e14 | −0.492334 | ||||||||
\(485\) | −9.51886e13 | −0.161067 | ||||||||
\(486\) | 2.71132e13 | 0.0453609 | ||||||||
\(487\) | −1.92144e14 | −0.317847 | −0.158924 | − | 0.987291i | \(-0.550802\pi\) | ||||
−0.158924 | + | 0.987291i | \(0.550802\pi\) | |||||||
\(488\) | −4.52089e13 | −0.0739460 | ||||||||
\(489\) | 2.66594e14 | 0.431174 | ||||||||
\(490\) | 2.82475e13 | 0.0451754 | ||||||||
\(491\) | −1.03762e15 | −1.64093 | −0.820466 | − | 0.571695i | \(-0.806286\pi\) | ||||
−0.820466 | + | 0.571695i | \(0.806286\pi\) | |||||||
\(492\) | 2.44112e14 | 0.381752 | ||||||||
\(493\) | −4.74159e14 | −0.733273 | ||||||||
\(494\) | −9.04520e12 | −0.0138331 | ||||||||
\(495\) | 1.22048e13 | 0.0184588 | ||||||||
\(496\) | 9.88991e13 | 0.147926 | ||||||||
\(497\) | 4.38695e14 | 0.648937 | ||||||||
\(498\) | −2.90253e14 | −0.424635 | ||||||||
\(499\) | 9.42193e14 | 1.36329 | 0.681643 | − | 0.731685i | \(-0.261266\pi\) | ||||
0.681643 | + | 0.731685i | \(0.261266\pi\) | |||||||
\(500\) | 3.12500e13 | 0.0447214 | ||||||||
\(501\) | 4.22543e14 | 0.598085 | ||||||||
\(502\) | 5.76590e14 | 0.807229 | ||||||||
\(503\) | −3.71104e14 | −0.513891 | −0.256946 | − | 0.966426i | \(-0.582716\pi\) | ||||
−0.256946 | + | 0.966426i | \(0.582716\pi\) | |||||||
\(504\) | 3.25202e13 | 0.0445435 | ||||||||
\(505\) | 4.61987e14 | 0.625932 | ||||||||
\(506\) | 4.29413e13 | 0.0575503 | ||||||||
\(507\) | 2.35213e14 | 0.311829 | ||||||||
\(508\) | −7.60656e13 | −0.0997558 | ||||||||
\(509\) | 6.34591e14 | 0.823278 | 0.411639 | − | 0.911347i | \(-0.364957\pi\) | ||||
0.411639 | + | 0.911347i | \(0.364957\pi\) | |||||||
\(510\) | −6.63131e13 | −0.0851066 | ||||||||
\(511\) | −3.34160e14 | −0.424268 | ||||||||
\(512\) | 3.51844e13 | 0.0441942 | ||||||||
\(513\) | 2.44131e12 | 0.00303374 | ||||||||
\(514\) | 4.36752e14 | 0.536955 | ||||||||
\(515\) | 2.77319e14 | 0.337318 | ||||||||
\(516\) | −1.63206e14 | −0.196410 | ||||||||
\(517\) | −7.95400e13 | −0.0947082 | ||||||||
\(518\) | 2.71934e14 | 0.320368 | ||||||||
\(519\) | 1.43053e14 | 0.166754 | ||||||||
\(520\) | −1.70123e14 | −0.196221 | ||||||||
\(521\) | −5.41628e13 | −0.0618149 | −0.0309075 | − | 0.999522i | \(-0.509840\pi\) | ||||
−0.0309075 | + | 0.999522i | \(0.509840\pi\) | |||||||
\(522\) | 3.28317e14 | 0.370771 | ||||||||
\(523\) | 7.28576e14 | 0.814170 | 0.407085 | − | 0.913390i | \(-0.366545\pi\) | ||||
0.407085 | + | 0.913390i | \(0.366545\pi\) | |||||||
\(524\) | 2.22998e14 | 0.246592 | ||||||||
\(525\) | 3.98838e13 | 0.0436436 | ||||||||
\(526\) | −1.74012e13 | −0.0188433 | ||||||||
\(527\) | −2.57386e14 | −0.275821 | ||||||||
\(528\) | 1.68529e13 | 0.0178726 | ||||||||
\(529\) | −5.41175e14 | −0.567978 | ||||||||
\(530\) | 4.49627e14 | 0.467019 | ||||||||
\(531\) | −2.22294e13 | −0.0228511 | ||||||||
\(532\) | 2.92816e12 | 0.00297907 | ||||||||
\(533\) | −1.62984e15 | −1.64114 | ||||||||
\(534\) | −2.61110e14 | −0.260223 | ||||||||
\(535\) | 1.02538e14 | 0.101144 | ||||||||
\(536\) | −1.51431e13 | −0.0147846 | ||||||||
\(537\) | −8.73618e14 | −0.844234 | ||||||||
\(538\) | 4.12235e14 | 0.394315 | ||||||||
\(539\) | 1.86831e13 | 0.0176893 | ||||||||
\(540\) | 4.59165e13 | 0.0430331 | ||||||||
\(541\) | 2.21419e14 | 0.205414 | 0.102707 | − | 0.994712i | \(-0.467250\pi\) | ||||
0.102707 | + | 0.994712i | \(0.467250\pi\) | |||||||
\(542\) | 4.39999e14 | 0.404069 | ||||||||
\(543\) | 5.80633e14 | 0.527841 | ||||||||
\(544\) | −9.15678e13 | −0.0824041 | ||||||||
\(545\) | 4.83165e14 | 0.430442 | ||||||||
\(546\) | −2.17125e14 | −0.191492 | ||||||||
\(547\) | 9.82674e14 | 0.857984 | 0.428992 | − | 0.903308i | \(-0.358869\pi\) | ||||
0.428992 | + | 0.903308i | \(0.358869\pi\) | |||||||
\(548\) | 8.60012e14 | 0.743381 | ||||||||
\(549\) | −8.14679e13 | −0.0697170 | ||||||||
\(550\) | 2.06690e13 | 0.0175115 | ||||||||
\(551\) | 2.95621e13 | 0.0247972 | ||||||||
\(552\) | 1.61552e14 | 0.134167 | ||||||||
\(553\) | 6.81771e14 | 0.560596 | ||||||||
\(554\) | 9.91596e13 | 0.0807293 | ||||||||
\(555\) | 3.83954e14 | 0.309505 | ||||||||
\(556\) | −2.53264e14 | −0.202145 | ||||||||
\(557\) | 1.30649e15 | 1.03253 | 0.516265 | − | 0.856429i | \(-0.327322\pi\) | ||||
0.516265 | + | 0.856429i | \(0.327322\pi\) | |||||||
\(558\) | 1.78219e14 | 0.139466 | ||||||||
\(559\) | 1.08967e15 | 0.844362 | ||||||||
\(560\) | 5.50732e13 | 0.0422577 | ||||||||
\(561\) | −4.38600e13 | −0.0333252 | ||||||||
\(562\) | 1.30479e14 | 0.0981726 | ||||||||
\(563\) | −1.38691e15 | −1.03336 | −0.516679 | − | 0.856179i | \(-0.672832\pi\) | ||||
−0.516679 | + | 0.856179i | \(0.672832\pi\) | |||||||
\(564\) | −2.99242e14 | −0.220794 | ||||||||
\(565\) | −7.54686e14 | −0.551442 | ||||||||
\(566\) | 1.41431e14 | 0.102342 | ||||||||
\(567\) | 5.86024e13 | 0.0419961 | ||||||||
\(568\) | 8.55308e14 | 0.607025 | ||||||||
\(569\) | −3.74583e14 | −0.263288 | −0.131644 | − | 0.991297i | \(-0.542026\pi\) | ||||
−0.131644 | + | 0.991297i | \(0.542026\pi\) | |||||||
\(570\) | 4.13439e12 | 0.00287806 | ||||||||
\(571\) | 2.71362e15 | 1.87090 | 0.935450 | − | 0.353458i | \(-0.114994\pi\) | ||||
0.935450 | + | 0.353458i | \(0.114994\pi\) | |||||||
\(572\) | −1.12521e14 | −0.0768342 | ||||||||
\(573\) | −7.84702e12 | −0.00530706 | ||||||||
\(574\) | 5.27622e14 | 0.353433 | ||||||||
\(575\) | 1.98133e14 | 0.131457 | ||||||||
\(576\) | 6.34034e13 | 0.0416667 | ||||||||
\(577\) | 1.15722e15 | 0.753268 | 0.376634 | − | 0.926362i | \(-0.377081\pi\) | ||||
0.376634 | + | 0.926362i | \(0.377081\pi\) | |||||||
\(578\) | −8.58394e14 | −0.553457 | ||||||||
\(579\) | 4.89745e13 | 0.0312779 | ||||||||
\(580\) | 5.56008e14 | 0.351744 | ||||||||
\(581\) | −6.27352e14 | −0.393136 | ||||||||
\(582\) | −2.36860e14 | −0.147033 | ||||||||
\(583\) | 2.97387e14 | 0.182871 | ||||||||
\(584\) | −6.51501e14 | −0.396866 | ||||||||
\(585\) | −3.06567e14 | −0.184999 | ||||||||
\(586\) | 6.65283e14 | 0.397713 | ||||||||
\(587\) | 6.58289e12 | 0.00389859 | 0.00194929 | − | 0.999998i | \(-0.499380\pi\) | ||||
0.00194929 | + | 0.999998i | \(0.499380\pi\) | |||||||
\(588\) | 7.02889e13 | 0.0412393 | ||||||||
\(589\) | 1.60471e13 | 0.00932746 | ||||||||
\(590\) | −3.76456e13 | −0.0216785 | ||||||||
\(591\) | −1.66161e15 | −0.947976 | ||||||||
\(592\) | 5.30180e14 | 0.299677 | ||||||||
\(593\) | −6.61462e14 | −0.370428 | −0.185214 | − | 0.982698i | \(-0.559298\pi\) | ||||
−0.185214 | + | 0.982698i | \(0.559298\pi\) | |||||||
\(594\) | 3.03695e13 | 0.0168505 | ||||||||
\(595\) | −1.43329e14 | −0.0787934 | ||||||||
\(596\) | −1.44714e14 | −0.0788236 | ||||||||
\(597\) | 1.66814e15 | 0.900273 | ||||||||
\(598\) | −1.07862e15 | −0.576783 | ||||||||
\(599\) | 1.91973e15 | 1.01717 | 0.508583 | − | 0.861013i | \(-0.330170\pi\) | ||||
0.508583 | + | 0.861013i | \(0.330170\pi\) | |||||||
\(600\) | 7.77600e13 | 0.0408248 | ||||||||
\(601\) | 2.36512e15 | 1.23039 | 0.615196 | − | 0.788374i | \(-0.289077\pi\) | ||||
0.615196 | + | 0.788374i | \(0.289077\pi\) | |||||||
\(602\) | −3.52753e14 | −0.181840 | ||||||||
\(603\) | −2.72884e13 | −0.0139390 | ||||||||
\(604\) | 1.14464e14 | 0.0579382 | ||||||||
\(605\) | −8.77928e14 | −0.440357 | ||||||||
\(606\) | 1.14957e15 | 0.571395 | ||||||||
\(607\) | 3.33310e15 | 1.64176 | 0.820882 | − | 0.571098i | \(-0.193483\pi\) | ||||
0.820882 | + | 0.571098i | \(0.193483\pi\) | |||||||
\(608\) | 5.70893e12 | 0.00278667 | ||||||||
\(609\) | 7.09622e14 | 0.343267 | ||||||||
\(610\) | −1.37967e14 | −0.0661393 | ||||||||
\(611\) | 1.99793e15 | 0.949190 | ||||||||
\(612\) | −1.65008e14 | −0.0776913 | ||||||||
\(613\) | 1.94940e15 | 0.909637 | 0.454819 | − | 0.890584i | \(-0.349704\pi\) | ||||
0.454819 | + | 0.890584i | \(0.349704\pi\) | |||||||
\(614\) | −7.95413e14 | −0.367846 | ||||||||
\(615\) | 7.44970e14 | 0.341449 | ||||||||
\(616\) | 3.64258e13 | 0.0165469 | ||||||||
\(617\) | 1.81576e15 | 0.817503 | 0.408751 | − | 0.912646i | \(-0.365964\pi\) | ||||
0.408751 | + | 0.912646i | \(0.365964\pi\) | |||||||
\(618\) | 6.90058e14 | 0.307928 | ||||||||
\(619\) | 1.78336e15 | 0.788753 | 0.394376 | − | 0.918949i | \(-0.370961\pi\) | ||||
0.394376 | + | 0.918949i | \(0.370961\pi\) | |||||||
\(620\) | 3.01816e14 | 0.132309 | ||||||||
\(621\) | 2.91122e14 | 0.126494 | ||||||||
\(622\) | −1.52498e14 | −0.0656776 | ||||||||
\(623\) | −5.64361e14 | −0.240920 | ||||||||
\(624\) | −4.23321e14 | −0.179124 | ||||||||
\(625\) | 9.53674e13 | 0.0400000 | ||||||||
\(626\) | 1.66690e15 | 0.693028 | ||||||||
\(627\) | 2.73452e12 | 0.00112696 | ||||||||
\(628\) | −2.19265e15 | −0.895758 | ||||||||
\(629\) | −1.37980e15 | −0.558776 | ||||||||
\(630\) | 9.92437e13 | 0.0398410 | ||||||||
\(631\) | −4.41303e15 | −1.75621 | −0.878103 | − | 0.478471i | \(-0.841191\pi\) | ||||
−0.878103 | + | 0.478471i | \(0.841191\pi\) | |||||||
\(632\) | 1.32922e15 | 0.524390 | ||||||||
\(633\) | 8.86943e14 | 0.346877 | ||||||||
\(634\) | 4.23426e14 | 0.164167 | ||||||||
\(635\) | −2.32134e14 | −0.0892243 | ||||||||
\(636\) | 1.11882e15 | 0.426328 | ||||||||
\(637\) | −4.69293e14 | −0.177287 | ||||||||
\(638\) | 3.67748e14 | 0.137733 | ||||||||
\(639\) | 1.54129e15 | 0.572309 | ||||||||
\(640\) | 1.07374e14 | 0.0395285 | ||||||||
\(641\) | −2.49924e15 | −0.912198 | −0.456099 | − | 0.889929i | \(-0.650754\pi\) | ||||
−0.456099 | + | 0.889929i | \(0.650754\pi\) | |||||||
\(642\) | 2.55148e14 | 0.0923313 | ||||||||
\(643\) | −2.04153e15 | −0.732479 | −0.366239 | − | 0.930521i | \(-0.619355\pi\) | ||||
−0.366239 | + | 0.930521i | \(0.619355\pi\) | |||||||
\(644\) | 3.49177e14 | 0.124215 | ||||||||
\(645\) | −4.98065e14 | −0.175674 | ||||||||
\(646\) | −1.48576e13 | −0.00519600 | ||||||||
\(647\) | −1.64063e15 | −0.568902 | −0.284451 | − | 0.958691i | \(-0.591811\pi\) | ||||
−0.284451 | + | 0.958691i | \(0.591811\pi\) | |||||||
\(648\) | 1.14255e14 | 0.0392837 | ||||||||
\(649\) | −2.48991e13 | −0.00848864 | ||||||||
\(650\) | −5.19175e14 | −0.175505 | ||||||||
\(651\) | 3.85202e14 | 0.129120 | ||||||||
\(652\) | 1.12343e15 | 0.373407 | ||||||||
\(653\) | −1.06369e15 | −0.350585 | −0.175293 | − | 0.984516i | \(-0.556087\pi\) | ||||
−0.175293 | + | 0.984516i | \(0.556087\pi\) | |||||||
\(654\) | 1.20227e15 | 0.392938 | ||||||||
\(655\) | 6.80535e14 | 0.220558 | ||||||||
\(656\) | 1.02869e15 | 0.330607 | ||||||||
\(657\) | −1.17403e15 | −0.374169 | ||||||||
\(658\) | −6.46780e14 | −0.204416 | ||||||||
\(659\) | 1.39069e15 | 0.435874 | 0.217937 | − | 0.975963i | \(-0.430067\pi\) | ||||
0.217937 | + | 0.975963i | \(0.430067\pi\) | |||||||
\(660\) | 5.14311e13 | 0.0159858 | ||||||||
\(661\) | 2.83166e15 | 0.872838 | 0.436419 | − | 0.899743i | \(-0.356247\pi\) | ||||
0.436419 | + | 0.899743i | \(0.356247\pi\) | |||||||
\(662\) | −2.47150e15 | −0.755512 | ||||||||
\(663\) | 1.10170e15 | 0.333994 | ||||||||
\(664\) | −1.22313e15 | −0.367745 | ||||||||
\(665\) | 8.93604e12 | 0.00266456 | ||||||||
\(666\) | 9.55401e14 | 0.282538 | ||||||||
\(667\) | 3.52522e15 | 1.03394 | ||||||||
\(668\) | 1.78059e15 | 0.517957 | ||||||||
\(669\) | −2.88723e15 | −0.832985 | ||||||||
\(670\) | −4.62132e13 | −0.0132237 | ||||||||
\(671\) | −9.12522e13 | −0.0258982 | ||||||||
\(672\) | 1.37040e14 | 0.0385758 | ||||||||
\(673\) | −2.97905e15 | −0.831754 | −0.415877 | − | 0.909421i | \(-0.636525\pi\) | ||||
−0.415877 | + | 0.909421i | \(0.636525\pi\) | |||||||
\(674\) | −3.51291e15 | −0.972831 | ||||||||
\(675\) | 1.40126e14 | 0.0384900 | ||||||||
\(676\) | 9.91184e14 | 0.270052 | ||||||||
\(677\) | −7.08685e14 | −0.191521 | −0.0957603 | − | 0.995404i | \(-0.530528\pi\) | ||||
−0.0957603 | + | 0.995404i | \(0.530528\pi\) | |||||||
\(678\) | −1.87790e15 | −0.503396 | ||||||||
\(679\) | −5.11947e14 | −0.136126 | ||||||||
\(680\) | −2.79443e14 | −0.0737045 | ||||||||
\(681\) | −7.86205e14 | −0.205696 | ||||||||
\(682\) | 1.99624e14 | 0.0518081 | ||||||||
\(683\) | −5.19665e15 | −1.33786 | −0.668928 | − | 0.743327i | \(-0.733247\pi\) | ||||
−0.668928 | + | 0.743327i | \(0.733247\pi\) | |||||||
\(684\) | 1.02877e13 | 0.00262730 | ||||||||
\(685\) | 2.62455e15 | 0.664900 | ||||||||
\(686\) | 1.51922e14 | 0.0381802 | ||||||||
\(687\) | 1.06383e14 | 0.0265222 | ||||||||
\(688\) | −6.87749e14 | −0.170096 | ||||||||
\(689\) | −7.46992e15 | −1.83278 | ||||||||
\(690\) | 4.93017e14 | 0.120003 | ||||||||
\(691\) | −1.46449e15 | −0.353637 | −0.176819 | − | 0.984243i | \(-0.556581\pi\) | ||||
−0.176819 | + | 0.984243i | \(0.556581\pi\) | |||||||
\(692\) | 6.02823e14 | 0.144413 | ||||||||
\(693\) | 6.56405e13 | 0.0156005 | ||||||||
\(694\) | 3.13314e15 | 0.738758 | ||||||||
\(695\) | −7.72901e14 | −0.180804 | ||||||||
\(696\) | 1.38353e15 | 0.321097 | ||||||||
\(697\) | −2.67717e15 | −0.616446 | ||||||||
\(698\) | −1.21032e15 | −0.276501 | ||||||||
\(699\) | 5.52989e14 | 0.125341 | ||||||||
\(700\) | 1.68070e14 | 0.0377964 | ||||||||
\(701\) | −6.77879e15 | −1.51253 | −0.756263 | − | 0.654267i | \(-0.772977\pi\) | ||||
−0.756263 | + | 0.654267i | \(0.772977\pi\) | |||||||
\(702\) | −7.62838e14 | −0.168880 | ||||||||
\(703\) | 8.60257e13 | 0.0188962 | ||||||||
\(704\) | 7.10181e13 | 0.0154782 | ||||||||
\(705\) | −9.13214e14 | −0.197484 | ||||||||
\(706\) | 6.02748e15 | 1.29333 | ||||||||
\(707\) | 2.48468e15 | 0.529009 | ||||||||
\(708\) | −9.36743e13 | −0.0197896 | ||||||||
\(709\) | 4.86070e15 | 1.01893 | 0.509466 | − | 0.860491i | \(-0.329843\pi\) | ||||
0.509466 | + | 0.860491i | \(0.329843\pi\) | |||||||
\(710\) | 2.61019e15 | 0.542940 | ||||||||
\(711\) | 2.39530e15 | 0.494399 | ||||||||
\(712\) | −1.10032e15 | −0.225360 | ||||||||
\(713\) | 1.91359e15 | 0.388916 | ||||||||
\(714\) | −3.56648e14 | −0.0719282 | ||||||||
\(715\) | −3.43386e14 | −0.0687226 | ||||||||
\(716\) | −3.68142e15 | −0.731128 | ||||||||
\(717\) | 2.87748e15 | 0.567096 | ||||||||
\(718\) | 3.61513e15 | 0.707032 | ||||||||
\(719\) | −6.11407e14 | −0.118665 | −0.0593324 | − | 0.998238i | \(-0.518897\pi\) | ||||
−0.0593324 | + | 0.998238i | \(0.518897\pi\) | |||||||
\(720\) | 1.93492e14 | 0.0372678 | ||||||||
\(721\) | 1.49149e15 | 0.285086 | ||||||||
\(722\) | −3.72676e15 | −0.706931 | ||||||||
\(723\) | −1.68960e15 | −0.318070 | ||||||||
\(724\) | 2.44678e15 | 0.457123 | ||||||||
\(725\) | 1.69680e15 | 0.314610 | ||||||||
\(726\) | −2.18457e15 | −0.401989 | ||||||||
\(727\) | 5.40192e15 | 0.986526 | 0.493263 | − | 0.869880i | \(-0.335804\pi\) | ||||
0.493263 | + | 0.869880i | \(0.335804\pi\) | |||||||
\(728\) | −9.14963e14 | −0.165837 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −1.98822e15 | −0.354968 | ||||||||
\(731\) | 1.78988e15 | 0.317159 | ||||||||
\(732\) | −3.43305e14 | −0.0603767 | ||||||||
\(733\) | −1.00849e16 | −1.76035 | −0.880176 | − | 0.474647i | \(-0.842576\pi\) | ||||
−0.880176 | + | 0.474647i | \(0.842576\pi\) | |||||||
\(734\) | −3.93033e15 | −0.680927 | ||||||||
\(735\) | 2.14505e14 | 0.0368856 | ||||||||
\(736\) | 6.80778e14 | 0.116192 | ||||||||
\(737\) | −3.05657e13 | −0.00517802 | ||||||||
\(738\) | 1.85372e15 | 0.311699 | ||||||||
\(739\) | 6.32820e15 | 1.05617 | 0.528087 | − | 0.849190i | \(-0.322909\pi\) | ||||
0.528087 | + | 0.849190i | \(0.322909\pi\) | |||||||
\(740\) | 1.61798e15 | 0.268039 | ||||||||
\(741\) | −6.86870e13 | −0.0112947 | ||||||||
\(742\) | 2.41820e15 | 0.394703 | ||||||||
\(743\) | −1.59106e15 | −0.257779 | −0.128890 | − | 0.991659i | \(-0.541141\pi\) | ||||
−0.128890 | + | 0.991659i | \(0.541141\pi\) | |||||||
\(744\) | 7.51015e14 | 0.120781 | ||||||||
\(745\) | −4.41632e14 | −0.0705020 | ||||||||
\(746\) | 7.84109e13 | 0.0124255 | ||||||||
\(747\) | −2.20411e15 | −0.346713 | ||||||||
\(748\) | −1.84826e14 | −0.0288605 | ||||||||
\(749\) | 5.51475e14 | 0.0854822 | ||||||||
\(750\) | 2.37305e14 | 0.0365148 | ||||||||
\(751\) | 2.80993e14 | 0.0429216 | 0.0214608 | − | 0.999770i | \(-0.493168\pi\) | ||||
0.0214608 | + | 0.999770i | \(0.493168\pi\) | |||||||
\(752\) | −1.26100e15 | −0.191213 | ||||||||
\(753\) | 4.37848e15 | 0.659099 | ||||||||
\(754\) | −9.23728e15 | −1.38039 | ||||||||
\(755\) | 3.49316e14 | 0.0518215 | ||||||||
\(756\) | 2.46950e14 | 0.0363696 | ||||||||
\(757\) | 1.75331e15 | 0.256349 | 0.128174 | − | 0.991752i | \(-0.459088\pi\) | ||||
0.128174 | + | 0.991752i | \(0.459088\pi\) | |||||||
\(758\) | 7.88602e13 | 0.0114466 | ||||||||
\(759\) | 3.26085e14 | 0.0469896 | ||||||||
\(760\) | 1.74223e13 | 0.00249247 | ||||||||
\(761\) | −7.72125e15 | −1.09666 | −0.548330 | − | 0.836262i | \(-0.684736\pi\) | ||||
−0.548330 | + | 0.836262i | \(0.684736\pi\) | |||||||
\(762\) | −5.77624e14 | −0.0814503 | ||||||||
\(763\) | 2.59858e15 | 0.363790 | ||||||||
\(764\) | −3.30673e13 | −0.00459605 | ||||||||
\(765\) | −5.03565e14 | −0.0694892 | ||||||||
\(766\) | −7.99777e15 | −1.09575 | ||||||||
\(767\) | 6.25429e14 | 0.0850753 | ||||||||
\(768\) | 2.67181e14 | 0.0360844 | ||||||||
\(769\) | 4.61889e15 | 0.619359 | 0.309679 | − | 0.950841i | \(-0.399778\pi\) | ||||
0.309679 | + | 0.950841i | \(0.399778\pi\) | |||||||
\(770\) | 1.11163e14 | 0.0148000 | ||||||||
\(771\) | 3.31659e15 | 0.438422 | ||||||||
\(772\) | 2.06378e14 | 0.0270875 | ||||||||
\(773\) | −3.76789e15 | −0.491034 | −0.245517 | − | 0.969392i | \(-0.578958\pi\) | ||||
−0.245517 | + | 0.969392i | \(0.578958\pi\) | |||||||
\(774\) | −1.23935e15 | −0.160368 | ||||||||
\(775\) | 9.21070e14 | 0.118340 | ||||||||
\(776\) | −9.98125e14 | −0.127334 | ||||||||
\(777\) | 2.06500e15 | 0.261580 | ||||||||
\(778\) | −8.37592e15 | −1.05353 | ||||||||
\(779\) | 1.66912e14 | 0.0208464 | ||||||||
\(780\) | −1.29187e15 | −0.160214 | ||||||||
\(781\) | 1.72640e15 | 0.212599 | ||||||||
\(782\) | −1.77173e15 | −0.216651 | ||||||||
\(783\) | 2.49316e15 | 0.302733 | ||||||||
\(784\) | 2.96197e14 | 0.0357143 | ||||||||
\(785\) | −6.69143e15 | −0.801191 | ||||||||
\(786\) | 1.69339e15 | 0.201341 | ||||||||
\(787\) | 6.50876e15 | 0.768488 | 0.384244 | − | 0.923231i | \(-0.374462\pi\) | ||||
0.384244 | + | 0.923231i | \(0.374462\pi\) | |||||||
\(788\) | −7.00200e15 | −0.820971 | ||||||||
\(789\) | −1.32140e14 | −0.0153855 | ||||||||
\(790\) | 4.05647e15 | 0.469028 | ||||||||
\(791\) | −4.05889e15 | −0.466054 | ||||||||
\(792\) | 1.27977e14 | 0.0145930 | ||||||||
\(793\) | 2.29212e15 | 0.259558 | ||||||||
\(794\) | 2.63770e15 | 0.296629 | ||||||||
\(795\) | 3.41435e15 | 0.381320 | ||||||||
\(796\) | 7.02954e15 | 0.779659 | ||||||||
\(797\) | 2.41321e14 | 0.0265812 | 0.0132906 | − | 0.999912i | \(-0.495769\pi\) | ||||
0.0132906 | + | 0.999912i | \(0.495769\pi\) | |||||||
\(798\) | 2.22357e13 | 0.00243240 | ||||||||
\(799\) | 3.28178e15 | 0.356535 | ||||||||
\(800\) | 3.27680e14 | 0.0353553 | ||||||||
\(801\) | −1.98280e15 | −0.212472 | ||||||||
\(802\) | −3.96444e15 | −0.421913 | ||||||||
\(803\) | −1.31503e15 | −0.138995 | ||||||||
\(804\) | −1.14993e14 | −0.0120716 | ||||||||
\(805\) | 1.06560e15 | 0.111101 | ||||||||
\(806\) | −5.01425e15 | −0.519234 | ||||||||
\(807\) | 3.13041e15 | 0.321956 | ||||||||
\(808\) | 4.84429e15 | 0.494843 | ||||||||
\(809\) | 7.97869e15 | 0.809496 | 0.404748 | − | 0.914428i | \(-0.367359\pi\) | ||||
0.404748 | + | 0.914428i | \(0.367359\pi\) | |||||||
\(810\) | 3.48678e14 | 0.0351364 | ||||||||
\(811\) | 7.66758e15 | 0.767439 | 0.383720 | − | 0.923450i | \(-0.374643\pi\) | ||||
0.383720 | + | 0.923450i | \(0.374643\pi\) | |||||||
\(812\) | 2.99034e15 | 0.297278 | ||||||||
\(813\) | 3.34124e15 | 0.329921 | ||||||||
\(814\) | 1.07014e15 | 0.104956 | ||||||||
\(815\) | 3.42842e15 | 0.333986 | ||||||||
\(816\) | −6.95343e14 | −0.0672827 | ||||||||
\(817\) | −1.11592e14 | −0.0107254 | ||||||||
\(818\) | −1.05826e16 | −1.01030 | ||||||||
\(819\) | −1.64879e15 | −0.156352 | ||||||||
\(820\) | 3.13930e15 | 0.295703 | ||||||||
\(821\) | −3.56124e15 | −0.333206 | −0.166603 | − | 0.986024i | \(-0.553280\pi\) | ||||
−0.166603 | + | 0.986024i | \(0.553280\pi\) | |||||||
\(822\) | 6.53072e15 | 0.606968 | ||||||||
\(823\) | −6.38018e15 | −0.589025 | −0.294512 | − | 0.955648i | \(-0.595157\pi\) | ||||
−0.294512 | + | 0.955648i | \(0.595157\pi\) | |||||||
\(824\) | 2.90790e15 | 0.266673 | ||||||||
\(825\) | 1.56955e14 | 0.0142981 | ||||||||
\(826\) | −2.02467e14 | −0.0183216 | ||||||||
\(827\) | 2.94158e15 | 0.264424 | 0.132212 | − | 0.991221i | \(-0.457792\pi\) | ||||
0.132212 | + | 0.991221i | \(0.457792\pi\) | |||||||
\(828\) | 1.22678e15 | 0.109547 | ||||||||
\(829\) | 3.48147e15 | 0.308825 | 0.154412 | − | 0.988006i | \(-0.450652\pi\) | ||||
0.154412 | + | 0.988006i | \(0.450652\pi\) | |||||||
\(830\) | −3.73268e15 | −0.328921 | ||||||||
\(831\) | 7.52993e14 | 0.0659152 | ||||||||
\(832\) | −1.78387e15 | −0.155126 | ||||||||
\(833\) | −7.70856e14 | −0.0665926 | ||||||||
\(834\) | −1.92322e15 | −0.165050 | ||||||||
\(835\) | 5.43393e15 | 0.463275 | ||||||||
\(836\) | 1.15232e13 | 0.000975977 0 | ||||||||
\(837\) | 1.35335e15 | 0.113873 | ||||||||
\(838\) | −9.78537e15 | −0.817966 | ||||||||
\(839\) | −7.97328e15 | −0.662135 | −0.331067 | − | 0.943607i | \(-0.607409\pi\) | ||||
−0.331067 | + | 0.943607i | \(0.607409\pi\) | |||||||
\(840\) | 4.18212e14 | 0.0345033 | ||||||||
\(841\) | 1.79894e16 | 1.47448 | ||||||||
\(842\) | −1.52971e16 | −1.24564 | ||||||||
\(843\) | 9.90824e14 | 0.0801576 | ||||||||
\(844\) | 3.73757e15 | 0.300404 | ||||||||
\(845\) | 3.02485e15 | 0.241542 | ||||||||
\(846\) | −2.27237e15 | −0.180278 | ||||||||
\(847\) | −4.72171e15 | −0.372169 | ||||||||
\(848\) | 4.71468e15 | 0.369211 | ||||||||
\(849\) | 1.07399e15 | 0.0835619 | ||||||||
\(850\) | −8.52792e14 | −0.0659233 | ||||||||
\(851\) | 1.02584e16 | 0.787891 | ||||||||
\(852\) | 6.49499e15 | 0.495634 | ||||||||
\(853\) | 4.80230e15 | 0.364108 | 0.182054 | − | 0.983289i | \(-0.441725\pi\) | ||||
0.182054 | + | 0.983289i | \(0.441725\pi\) | |||||||
\(854\) | −7.42017e14 | −0.0558979 | ||||||||
\(855\) | 3.13955e13 | 0.00234992 | ||||||||
\(856\) | 1.07519e15 | 0.0799613 | ||||||||
\(857\) | −1.15145e16 | −0.850847 | −0.425423 | − | 0.904994i | \(-0.639875\pi\) | ||||
−0.425423 | + | 0.904994i | \(0.639875\pi\) | |||||||
\(858\) | −8.54455e14 | −0.0627349 | ||||||||
\(859\) | −5.67712e15 | −0.414158 | −0.207079 | − | 0.978324i | \(-0.566396\pi\) | ||||
−0.207079 | + | 0.978324i | \(0.566396\pi\) | |||||||
\(860\) | −2.09884e15 | −0.152138 | ||||||||
\(861\) | 4.00663e15 | 0.288577 | ||||||||
\(862\) | −8.71892e15 | −0.623983 | ||||||||
\(863\) | −8.65956e15 | −0.615796 | −0.307898 | − | 0.951419i | \(-0.599625\pi\) | ||||
−0.307898 | + | 0.951419i | \(0.599625\pi\) | |||||||
\(864\) | 4.81469e14 | 0.0340207 | ||||||||
\(865\) | 1.83967e15 | 0.129167 | ||||||||
\(866\) | −1.15640e16 | −0.806790 | ||||||||
\(867\) | −6.51843e15 | −0.451896 | ||||||||
\(868\) | 1.62324e15 | 0.111821 | ||||||||
\(869\) | 2.68298e15 | 0.183657 | ||||||||
\(870\) | 4.22218e15 | 0.287198 | ||||||||
\(871\) | 7.67767e14 | 0.0518955 | ||||||||
\(872\) | 5.06635e15 | 0.340294 | ||||||||
\(873\) | −1.79865e15 | −0.120052 | ||||||||
\(874\) | 1.10461e14 | 0.00732652 | ||||||||
\(875\) | 5.12909e14 | 0.0338062 | ||||||||
\(876\) | −4.94733e15 | −0.324040 | ||||||||
\(877\) | −4.62452e15 | −0.301002 | −0.150501 | − | 0.988610i | \(-0.548089\pi\) | ||||
−0.150501 | + | 0.988610i | \(0.548089\pi\) | |||||||
\(878\) | −1.29644e16 | −0.838560 | ||||||||
\(879\) | 5.05200e15 | 0.324731 | ||||||||
\(880\) | 2.16730e14 | 0.0138441 | ||||||||
\(881\) | 6.67369e15 | 0.423642 | 0.211821 | − | 0.977309i | \(-0.432061\pi\) | ||||
0.211821 | + | 0.977309i | \(0.432061\pi\) | |||||||
\(882\) | 5.33756e14 | 0.0336718 | ||||||||
\(883\) | −2.91359e16 | −1.82660 | −0.913302 | − | 0.407282i | \(-0.866477\pi\) | ||||
−0.913302 | + | 0.407282i | \(0.866477\pi\) | |||||||
\(884\) | 4.64255e15 | 0.289247 | ||||||||
\(885\) | −2.85871e14 | −0.0177004 | ||||||||
\(886\) | −9.27677e15 | −0.570836 | ||||||||
\(887\) | −3.07655e16 | −1.88141 | −0.940705 | − | 0.339224i | \(-0.889835\pi\) | ||||
−0.940705 | + | 0.339224i | \(0.889835\pi\) | |||||||
\(888\) | 4.02605e15 | 0.244685 | ||||||||
\(889\) | −1.24847e15 | −0.0754083 | ||||||||
\(890\) | −3.35790e15 | −0.201568 | ||||||||
\(891\) | 2.30619e14 | 0.0137584 | ||||||||
\(892\) | −1.21667e16 | −0.721386 | ||||||||
\(893\) | −2.04607e14 | −0.0120570 | ||||||||
\(894\) | −1.09892e15 | −0.0643592 | ||||||||
\(895\) | −1.12348e16 | −0.653941 | ||||||||
\(896\) | 5.77484e14 | 0.0334077 | ||||||||
\(897\) | −8.19079e15 | −0.470942 | ||||||||
\(898\) | −2.05447e16 | −1.17403 | ||||||||
\(899\) | 1.63879e16 | 0.930776 | ||||||||
\(900\) | 5.90490e14 | 0.0333333 | ||||||||
\(901\) | −1.22700e16 | −0.688428 | ||||||||
\(902\) | 2.07636e15 | 0.115789 | ||||||||
\(903\) | −2.67872e15 | −0.148472 | ||||||||
\(904\) | −7.91346e15 | −0.435953 | ||||||||
\(905\) | 7.46699e15 | 0.408864 | ||||||||
\(906\) | 8.69209e14 | 0.0473063 | ||||||||
\(907\) | 1.61863e16 | 0.875606 | 0.437803 | − | 0.899071i | \(-0.355757\pi\) | ||||
0.437803 | + | 0.899071i | \(0.355757\pi\) | |||||||
\(908\) | −3.31306e15 | −0.178138 | ||||||||
\(909\) | 8.72956e15 | 0.466542 | ||||||||
\(910\) | −2.79225e15 | −0.148329 | ||||||||
\(911\) | −2.78417e16 | −1.47009 | −0.735046 | − | 0.678018i | \(-0.762839\pi\) | ||||
−0.735046 | + | 0.678018i | \(0.762839\pi\) | |||||||
\(912\) | 4.33522e13 | 0.00227530 | ||||||||
\(913\) | −2.46883e15 | −0.128796 | ||||||||
\(914\) | 2.39538e16 | 1.24214 | ||||||||
\(915\) | −1.04768e15 | −0.0540025 | ||||||||
\(916\) | 4.48297e14 | 0.0229689 | ||||||||
\(917\) | 3.66008e15 | 0.186406 | ||||||||
\(918\) | −1.25303e15 | −0.0634347 | ||||||||
\(919\) | 5.36430e15 | 0.269946 | 0.134973 | − | 0.990849i | \(-0.456905\pi\) | ||||
0.134973 | + | 0.990849i | \(0.456905\pi\) | |||||||
\(920\) | 2.07757e15 | 0.103926 | ||||||||
\(921\) | −6.04017e15 | −0.300345 | ||||||||
\(922\) | −6.31623e15 | −0.312204 | ||||||||
\(923\) | −4.33647e16 | −2.13072 | ||||||||
\(924\) | 2.76609e14 | 0.0135105 | ||||||||
\(925\) | 4.93768e15 | 0.239742 | ||||||||
\(926\) | 4.86409e15 | 0.234769 | ||||||||
\(927\) | 5.24012e15 | 0.251422 | ||||||||
\(928\) | 5.83016e15 | 0.278078 | ||||||||
\(929\) | 7.30043e15 | 0.346148 | 0.173074 | − | 0.984909i | \(-0.444630\pi\) | ||||
0.173074 | + | 0.984909i | \(0.444630\pi\) | |||||||
\(930\) | 2.29192e15 | 0.108030 | ||||||||
\(931\) | 4.80602e13 | 0.00225197 | ||||||||
\(932\) | 2.33029e15 | 0.108548 | ||||||||
\(933\) | −1.15803e15 | −0.0536255 | ||||||||
\(934\) | −1.86738e16 | −0.859658 | ||||||||
\(935\) | −5.64043e14 | −0.0258136 | ||||||||
\(936\) | −3.21459e15 | −0.146254 | ||||||||
\(937\) | −2.97740e16 | −1.34670 | −0.673348 | − | 0.739326i | \(-0.735144\pi\) | ||||
−0.673348 | + | 0.739326i | \(0.735144\pi\) | |||||||
\(938\) | −2.48545e14 | −0.0111761 | ||||||||
\(939\) | 1.26580e16 | 0.565855 | ||||||||
\(940\) | −3.84827e15 | −0.171026 | ||||||||
\(941\) | −1.16623e16 | −0.515279 | −0.257640 | − | 0.966241i | \(-0.582945\pi\) | ||||
−0.257640 | + | 0.966241i | \(0.582945\pi\) | |||||||
\(942\) | −1.66504e16 | −0.731384 | ||||||||
\(943\) | 1.99039e16 | 0.869209 | ||||||||
\(944\) | −3.94743e14 | −0.0171383 | ||||||||
\(945\) | 7.53631e14 | 0.0325300 | ||||||||
\(946\) | −1.38819e15 | −0.0595728 | ||||||||
\(947\) | 6.31543e15 | 0.269450 | 0.134725 | − | 0.990883i | \(-0.456985\pi\) | ||||
0.134725 | + | 0.990883i | \(0.456985\pi\) | |||||||
\(948\) | 1.00938e16 | 0.428162 | ||||||||
\(949\) | 3.30315e16 | 1.39304 | ||||||||
\(950\) | 5.31686e13 | 0.00222933 | ||||||||
\(951\) | 3.21539e15 | 0.134042 | ||||||||
\(952\) | −1.50291e15 | −0.0622916 | ||||||||
\(953\) | 4.74094e16 | 1.95368 | 0.976840 | − | 0.213969i | \(-0.0686392\pi\) | ||||
0.976840 | + | 0.213969i | \(0.0686392\pi\) | |||||||
\(954\) | 8.49601e15 | 0.348096 | ||||||||
\(955\) | −1.00913e14 | −0.00411083 | ||||||||
\(956\) | 1.21257e16 | 0.491119 | ||||||||
\(957\) | 2.79259e15 | 0.112458 | ||||||||
\(958\) | −3.20752e16 | −1.28428 | ||||||||
\(959\) | 1.41154e16 | 0.561943 | ||||||||
\(960\) | 8.15373e14 | 0.0322749 | ||||||||
\(961\) | −1.65127e16 | −0.649888 | ||||||||
\(962\) | −2.68805e16 | −1.05190 | ||||||||
\(963\) | 1.93753e15 | 0.0753882 | ||||||||
\(964\) | −7.11996e15 | −0.275457 | ||||||||
\(965\) | 6.29816e14 | 0.0242278 | ||||||||
\(966\) | 2.65156e15 | 0.101421 | ||||||||
\(967\) | 1.60190e16 | 0.609244 | 0.304622 | − | 0.952473i | \(-0.401470\pi\) | ||||
0.304622 | + | 0.952473i | \(0.401470\pi\) | |||||||
\(968\) | −9.20575e15 | −0.348132 | ||||||||
\(969\) | −1.12825e14 | −0.00424251 | ||||||||
\(970\) | −3.04604e15 | −0.113891 | ||||||||
\(971\) | −4.54980e16 | −1.69156 | −0.845778 | − | 0.533534i | \(-0.820863\pi\) | ||||
−0.845778 | + | 0.533534i | \(0.820863\pi\) | |||||||
\(972\) | 8.67624e14 | 0.0320750 | ||||||||
\(973\) | −4.15684e15 | −0.152807 | ||||||||
\(974\) | −6.14862e15 | −0.224752 | ||||||||
\(975\) | −3.94248e15 | −0.143299 | ||||||||
\(976\) | −1.44668e15 | −0.0522877 | ||||||||
\(977\) | 3.50910e16 | 1.26117 | 0.630587 | − | 0.776118i | \(-0.282814\pi\) | ||||
0.630587 | + | 0.776118i | \(0.282814\pi\) | |||||||
\(978\) | 8.53102e15 | 0.304886 | ||||||||
\(979\) | −2.22094e15 | −0.0789281 | ||||||||
\(980\) | 9.03921e14 | 0.0319438 | ||||||||
\(981\) | 9.12972e15 | 0.320832 | ||||||||
\(982\) | −3.32039e16 | −1.16031 | ||||||||
\(983\) | −4.45932e16 | −1.54962 | −0.774808 | − | 0.632197i | \(-0.782153\pi\) | ||||
−0.774808 | + | 0.632197i | \(0.782153\pi\) | |||||||
\(984\) | 7.81158e15 | 0.269939 | ||||||||
\(985\) | −2.13684e16 | −0.734299 | ||||||||
\(986\) | −1.51731e16 | −0.518502 | ||||||||
\(987\) | −4.91148e15 | −0.166905 | ||||||||
\(988\) | −2.89447e14 | −0.00978149 | ||||||||
\(989\) | −1.33072e16 | −0.447205 | ||||||||
\(990\) | 3.90555e14 | 0.0130523 | ||||||||
\(991\) | 2.37035e16 | 0.787783 | 0.393892 | − | 0.919157i | \(-0.371129\pi\) | ||||
0.393892 | + | 0.919157i | \(0.371129\pi\) | |||||||
\(992\) | 3.16477e15 | 0.104599 | ||||||||
\(993\) | −1.87679e16 | −0.616873 | ||||||||
\(994\) | 1.40382e16 | 0.458868 | ||||||||
\(995\) | 2.14524e16 | 0.697349 | ||||||||
\(996\) | −9.28811e15 | −0.300262 | ||||||||
\(997\) | 4.45651e16 | 1.43275 | 0.716376 | − | 0.697714i | \(-0.245799\pi\) | ||||
0.716376 | + | 0.697714i | \(0.245799\pi\) | |||||||
\(998\) | 3.01502e16 | 0.963989 | ||||||||
\(999\) | 7.25508e15 | 0.230692 |
(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 | 210.12.a.p.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.12.a.p.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial |