Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,26,Mod(1,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(23.7598067971\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4096.00 | −0.707107 | ||||||||
\(3\) | 531441. | 0.577350 | ||||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 5.90426e8 | 1.08153 | 0.540767 | − | 0.841172i | \(-0.318134\pi\) | ||||
0.540767 | + | 0.841172i | \(0.318134\pi\) | |||||||
\(6\) | −2.17678e9 | −0.408248 | ||||||||
\(7\) | 5.78574e10 | 1.57991 | 0.789957 | − | 0.613162i | \(-0.210103\pi\) | ||||
0.789957 | + | 0.613162i | \(0.210103\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | 2.82430e11 | 0.333333 | ||||||||
\(10\) | −2.41838e12 | −0.764760 | ||||||||
\(11\) | 9.49427e12 | 0.912122 | 0.456061 | − | 0.889949i | \(-0.349260\pi\) | ||||
0.456061 | + | 0.889949i | \(0.349260\pi\) | |||||||
\(12\) | 8.91610e12 | 0.288675 | ||||||||
\(13\) | −1.34968e14 | −1.60672 | −0.803358 | − | 0.595497i | \(-0.796955\pi\) | ||||
−0.803358 | + | 0.595497i | \(0.796955\pi\) | |||||||
\(14\) | −2.36984e14 | −1.11717 | ||||||||
\(15\) | 3.13776e14 | 0.624424 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −2.52611e15 | −1.05158 | −0.525789 | − | 0.850615i | \(-0.676230\pi\) | ||||
−0.525789 | + | 0.850615i | \(0.676230\pi\) | |||||||
\(18\) | −1.15683e15 | −0.235702 | ||||||||
\(19\) | 1.14688e16 | 1.18877 | 0.594383 | − | 0.804182i | \(-0.297396\pi\) | ||||
0.594383 | + | 0.804182i | \(0.297396\pi\) | |||||||
\(20\) | 9.90570e15 | 0.540767 | ||||||||
\(21\) | 3.07478e16 | 0.912164 | ||||||||
\(22\) | −3.88885e16 | −0.644968 | ||||||||
\(23\) | 1.13343e17 | 1.07844 | 0.539219 | − | 0.842165i | \(-0.318719\pi\) | ||||
0.539219 | + | 0.842165i | \(0.318719\pi\) | |||||||
\(24\) | −3.65203e16 | −0.204124 | ||||||||
\(25\) | 5.05793e16 | 0.169716 | ||||||||
\(26\) | 5.52829e17 | 1.13612 | ||||||||
\(27\) | 1.50095e17 | 0.192450 | ||||||||
\(28\) | 9.70686e17 | 0.789957 | ||||||||
\(29\) | 1.08135e18 | 0.567533 | 0.283766 | − | 0.958893i | \(-0.408416\pi\) | ||||
0.283766 | + | 0.958893i | \(0.408416\pi\) | |||||||
\(30\) | −1.28523e18 | −0.441534 | ||||||||
\(31\) | 4.64909e18 | 1.06010 | 0.530050 | − | 0.847966i | \(-0.322173\pi\) | ||||
0.530050 | + | 0.847966i | \(0.322173\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | 5.04564e18 | 0.526614 | ||||||||
\(34\) | 1.03470e19 | 0.743578 | ||||||||
\(35\) | 3.41605e19 | 1.70873 | ||||||||
\(36\) | 4.73838e18 | 0.166667 | ||||||||
\(37\) | −4.60934e19 | −1.15111 | −0.575555 | − | 0.817763i | \(-0.695214\pi\) | ||||
−0.575555 | + | 0.817763i | \(0.695214\pi\) | |||||||
\(38\) | −4.69760e19 | −0.840585 | ||||||||
\(39\) | −7.17275e19 | −0.927638 | ||||||||
\(40\) | −4.05737e19 | −0.382380 | ||||||||
\(41\) | 5.14492e19 | 0.356107 | 0.178054 | − | 0.984021i | \(-0.443020\pi\) | ||||
0.178054 | + | 0.984021i | \(0.443020\pi\) | |||||||
\(42\) | −1.25943e20 | −0.644997 | ||||||||
\(43\) | −3.69343e20 | −1.40953 | −0.704764 | − | 0.709442i | \(-0.748947\pi\) | ||||
−0.704764 | + | 0.709442i | \(0.748947\pi\) | |||||||
\(44\) | 1.59287e20 | 0.456061 | ||||||||
\(45\) | 1.66754e20 | 0.360511 | ||||||||
\(46\) | −4.64251e20 | −0.762571 | ||||||||
\(47\) | −4.91066e19 | −0.0616477 | −0.0308239 | − | 0.999525i | \(-0.509813\pi\) | ||||
−0.0308239 | + | 0.999525i | \(0.509813\pi\) | |||||||
\(48\) | 1.49587e20 | 0.144338 | ||||||||
\(49\) | 2.00641e21 | 1.49613 | ||||||||
\(50\) | −2.07173e20 | −0.120007 | ||||||||
\(51\) | −1.34248e21 | −0.607129 | ||||||||
\(52\) | −2.26439e21 | −0.803358 | ||||||||
\(53\) | 4.44008e21 | 1.24149 | 0.620744 | − | 0.784014i | \(-0.286831\pi\) | ||||
0.620744 | + | 0.784014i | \(0.286831\pi\) | |||||||
\(54\) | −6.14788e20 | −0.136083 | ||||||||
\(55\) | 5.60566e21 | 0.986491 | ||||||||
\(56\) | −3.97593e21 | −0.558584 | ||||||||
\(57\) | 6.09497e21 | 0.686334 | ||||||||
\(58\) | −4.42921e21 | −0.401306 | ||||||||
\(59\) | 2.25493e22 | 1.65000 | 0.825000 | − | 0.565133i | \(-0.191175\pi\) | ||||
0.825000 | + | 0.565133i | \(0.191175\pi\) | |||||||
\(60\) | 5.26430e21 | 0.312212 | ||||||||
\(61\) | −1.23106e22 | −0.593824 | −0.296912 | − | 0.954905i | \(-0.595957\pi\) | ||||
−0.296912 | + | 0.954905i | \(0.595957\pi\) | |||||||
\(62\) | −1.90427e22 | −0.749604 | ||||||||
\(63\) | 1.63406e22 | 0.526638 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | −7.96886e22 | −1.73772 | ||||||||
\(66\) | −2.06670e22 | −0.372372 | ||||||||
\(67\) | 6.38592e21 | 0.0953429 | 0.0476715 | − | 0.998863i | \(-0.484820\pi\) | ||||
0.0476715 | + | 0.998863i | \(0.484820\pi\) | |||||||
\(68\) | −4.23812e22 | −0.525789 | ||||||||
\(69\) | 6.02349e22 | 0.622637 | ||||||||
\(70\) | −1.39921e23 | −1.20826 | ||||||||
\(71\) | 6.02768e22 | 0.435934 | 0.217967 | − | 0.975956i | \(-0.430058\pi\) | ||||
0.217967 | + | 0.975956i | \(0.430058\pi\) | |||||||
\(72\) | −1.94084e22 | −0.117851 | ||||||||
\(73\) | −2.68812e23 | −1.37377 | −0.686883 | − | 0.726768i | \(-0.741022\pi\) | ||||
−0.686883 | + | 0.726768i | \(0.741022\pi\) | |||||||
\(74\) | 1.88798e23 | 0.813958 | ||||||||
\(75\) | 2.68799e22 | 0.0979856 | ||||||||
\(76\) | 1.92414e23 | 0.594383 | ||||||||
\(77\) | 5.49314e23 | 1.44107 | ||||||||
\(78\) | 2.93796e23 | 0.655939 | ||||||||
\(79\) | −2.62861e23 | −0.500481 | −0.250241 | − | 0.968184i | \(-0.580510\pi\) | ||||
−0.250241 | + | 0.968184i | \(0.580510\pi\) | |||||||
\(80\) | 1.66190e23 | 0.270384 | ||||||||
\(81\) | 7.97664e22 | 0.111111 | ||||||||
\(82\) | −2.10736e23 | −0.251806 | ||||||||
\(83\) | 6.88506e23 | 0.707020 | 0.353510 | − | 0.935431i | \(-0.384988\pi\) | ||||
0.353510 | + | 0.935431i | \(0.384988\pi\) | |||||||
\(84\) | 5.15863e23 | 0.456082 | ||||||||
\(85\) | −1.49148e24 | −1.13732 | ||||||||
\(86\) | 1.51283e24 | 0.996687 | ||||||||
\(87\) | 5.74673e23 | 0.327665 | ||||||||
\(88\) | −6.52441e23 | −0.322484 | ||||||||
\(89\) | −2.55875e24 | −1.09813 | −0.549064 | − | 0.835780i | \(-0.685016\pi\) | ||||
−0.549064 | + | 0.835780i | \(0.685016\pi\) | |||||||
\(90\) | −6.83023e23 | −0.254920 | ||||||||
\(91\) | −7.80890e24 | −2.53847 | ||||||||
\(92\) | 1.90157e24 | 0.539219 | ||||||||
\(93\) | 2.47072e24 | 0.612049 | ||||||||
\(94\) | 2.01141e23 | 0.0435915 | ||||||||
\(95\) | 6.77145e24 | 1.28569 | ||||||||
\(96\) | −6.12710e23 | −0.102062 | ||||||||
\(97\) | 2.59521e24 | 0.379774 | 0.189887 | − | 0.981806i | \(-0.439188\pi\) | ||||
0.189887 | + | 0.981806i | \(0.439188\pi\) | |||||||
\(98\) | −8.21826e24 | −1.05792 | ||||||||
\(99\) | 2.68146e24 | 0.304041 | ||||||||
\(100\) | 8.48580e23 | 0.0848580 | ||||||||
\(101\) | −1.74742e25 | −1.54305 | −0.771524 | − | 0.636200i | \(-0.780505\pi\) | ||||
−0.771524 | + | 0.636200i | \(0.780505\pi\) | |||||||
\(102\) | 5.49880e24 | 0.429305 | ||||||||
\(103\) | −1.32798e25 | −0.917756 | −0.458878 | − | 0.888499i | \(-0.651748\pi\) | ||||
−0.458878 | + | 0.888499i | \(0.651748\pi\) | |||||||
\(104\) | 9.27493e24 | 0.568060 | ||||||||
\(105\) | 1.81543e25 | 0.986536 | ||||||||
\(106\) | −1.81866e25 | −0.877864 | ||||||||
\(107\) | 4.17957e25 | 1.79405 | 0.897025 | − | 0.441980i | \(-0.145724\pi\) | ||||
0.897025 | + | 0.441980i | \(0.145724\pi\) | |||||||
\(108\) | 2.51817e24 | 0.0962250 | ||||||||
\(109\) | 4.64640e25 | 1.58229 | 0.791143 | − | 0.611631i | \(-0.209486\pi\) | ||||
0.791143 | + | 0.611631i | \(0.209486\pi\) | |||||||
\(110\) | −2.29608e25 | −0.697554 | ||||||||
\(111\) | −2.44959e25 | −0.664594 | ||||||||
\(112\) | 1.62854e25 | 0.394979 | ||||||||
\(113\) | 3.27395e25 | 0.710544 | 0.355272 | − | 0.934763i | \(-0.384388\pi\) | ||||
0.355272 | + | 0.934763i | \(0.384388\pi\) | |||||||
\(114\) | −2.49650e25 | −0.485312 | ||||||||
\(115\) | 6.69204e25 | 1.16637 | ||||||||
\(116\) | 1.81420e25 | 0.283766 | ||||||||
\(117\) | −3.81190e25 | −0.535572 | ||||||||
\(118\) | −9.23621e25 | −1.16673 | ||||||||
\(119\) | −1.46154e26 | −1.66140 | ||||||||
\(120\) | −2.15626e25 | −0.220767 | ||||||||
\(121\) | −1.82060e25 | −0.168034 | ||||||||
\(122\) | 5.04244e25 | 0.419897 | ||||||||
\(123\) | 2.73422e25 | 0.205599 | ||||||||
\(124\) | 7.79988e25 | 0.530050 | ||||||||
\(125\) | −1.46097e26 | −0.897980 | ||||||||
\(126\) | −6.69313e25 | −0.372389 | ||||||||
\(127\) | −1.69226e26 | −0.852944 | −0.426472 | − | 0.904501i | \(-0.640244\pi\) | ||||
−0.426472 | + | 0.904501i | \(0.640244\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | −1.96284e26 | −0.813791 | ||||||||
\(130\) | 3.26404e26 | 1.22875 | ||||||||
\(131\) | 1.90262e25 | 0.0650821 | 0.0325410 | − | 0.999470i | \(-0.489640\pi\) | ||||
0.0325410 | + | 0.999470i | \(0.489640\pi\) | |||||||
\(132\) | 8.46518e25 | 0.263307 | ||||||||
\(133\) | 6.63553e26 | 1.87815 | ||||||||
\(134\) | −2.61567e25 | −0.0674176 | ||||||||
\(135\) | 8.86197e25 | 0.208141 | ||||||||
\(136\) | 1.73593e26 | 0.371789 | ||||||||
\(137\) | −3.48433e25 | −0.0680945 | −0.0340473 | − | 0.999420i | \(-0.510840\pi\) | ||||
−0.0340473 | + | 0.999420i | \(0.510840\pi\) | |||||||
\(138\) | −2.46722e26 | −0.440271 | ||||||||
\(139\) | 1.79180e26 | 0.292150 | 0.146075 | − | 0.989274i | \(-0.453336\pi\) | ||||
0.146075 | + | 0.989274i | \(0.453336\pi\) | |||||||
\(140\) | 5.73118e26 | 0.854366 | ||||||||
\(141\) | −2.60973e25 | −0.0355923 | ||||||||
\(142\) | −2.46894e26 | −0.308252 | ||||||||
\(143\) | −1.28142e27 | −1.46552 | ||||||||
\(144\) | 7.94968e25 | 0.0833333 | ||||||||
\(145\) | 6.38456e26 | 0.613806 | ||||||||
\(146\) | 1.10105e27 | 0.971400 | ||||||||
\(147\) | 1.06629e27 | 0.863791 | ||||||||
\(148\) | −7.73318e26 | −0.575555 | ||||||||
\(149\) | −2.46268e27 | −1.68492 | −0.842459 | − | 0.538760i | \(-0.818893\pi\) | ||||
−0.842459 | + | 0.538760i | \(0.818893\pi\) | |||||||
\(150\) | −1.10100e26 | −0.0692863 | ||||||||
\(151\) | 4.33646e26 | 0.251144 | 0.125572 | − | 0.992084i | \(-0.459923\pi\) | ||||
0.125572 | + | 0.992084i | \(0.459923\pi\) | |||||||
\(152\) | −7.88127e26 | −0.420292 | ||||||||
\(153\) | −7.13449e26 | −0.350526 | ||||||||
\(154\) | −2.24999e27 | −1.01899 | ||||||||
\(155\) | 2.74494e27 | 1.14653 | ||||||||
\(156\) | −1.20339e27 | −0.463819 | ||||||||
\(157\) | −3.54008e27 | −1.25970 | −0.629850 | − | 0.776717i | \(-0.716884\pi\) | ||||
−0.629850 | + | 0.776717i | \(0.716884\pi\) | |||||||
\(158\) | 1.07668e27 | 0.353894 | ||||||||
\(159\) | 2.35964e27 | 0.716773 | ||||||||
\(160\) | −6.80715e26 | −0.191190 | ||||||||
\(161\) | 6.55771e27 | 1.70384 | ||||||||
\(162\) | −3.26723e26 | −0.0785674 | ||||||||
\(163\) | −6.45978e27 | −1.43838 | −0.719189 | − | 0.694815i | \(-0.755486\pi\) | ||||
−0.719189 | + | 0.694815i | \(0.755486\pi\) | |||||||
\(164\) | 8.63175e26 | 0.178054 | ||||||||
\(165\) | 2.97908e27 | 0.569551 | ||||||||
\(166\) | −2.82012e27 | −0.499938 | ||||||||
\(167\) | −4.48432e27 | −0.737463 | −0.368732 | − | 0.929536i | \(-0.620208\pi\) | ||||
−0.368732 | + | 0.929536i | \(0.620208\pi\) | |||||||
\(168\) | −2.11297e27 | −0.322499 | ||||||||
\(169\) | 1.11600e28 | 1.58153 | ||||||||
\(170\) | 6.10911e27 | 0.804205 | ||||||||
\(171\) | 3.23912e27 | 0.396255 | ||||||||
\(172\) | −6.19654e27 | −0.704764 | ||||||||
\(173\) | 1.21973e27 | 0.129029 | 0.0645147 | − | 0.997917i | \(-0.479450\pi\) | ||||
0.0645147 | + | 0.997917i | \(0.479450\pi\) | |||||||
\(174\) | −2.35386e27 | −0.231694 | ||||||||
\(175\) | 2.92639e27 | 0.268137 | ||||||||
\(176\) | 2.67240e27 | 0.228030 | ||||||||
\(177\) | 1.19836e28 | 0.952628 | ||||||||
\(178\) | 1.04806e28 | 0.776493 | ||||||||
\(179\) | −2.09258e28 | −1.44550 | −0.722751 | − | 0.691109i | \(-0.757122\pi\) | ||||
−0.722751 | + | 0.691109i | \(0.757122\pi\) | |||||||
\(180\) | 2.79766e27 | 0.180256 | ||||||||
\(181\) | −1.48896e27 | −0.0895158 | −0.0447579 | − | 0.998998i | \(-0.514252\pi\) | ||||
−0.0447579 | + | 0.998998i | \(0.514252\pi\) | |||||||
\(182\) | 3.19853e28 | 1.79497 | ||||||||
\(183\) | −6.54238e27 | −0.342844 | ||||||||
\(184\) | −7.78885e27 | −0.381286 | ||||||||
\(185\) | −2.72147e28 | −1.24496 | ||||||||
\(186\) | −1.01201e28 | −0.432784 | ||||||||
\(187\) | −2.39836e28 | −0.959167 | ||||||||
\(188\) | −8.23873e26 | −0.0308239 | ||||||||
\(189\) | 8.68409e27 | 0.304055 | ||||||||
\(190\) | −2.77359e28 | −0.909121 | ||||||||
\(191\) | −3.19546e28 | −0.980880 | −0.490440 | − | 0.871475i | \(-0.663164\pi\) | ||||
−0.490440 | + | 0.871475i | \(0.663164\pi\) | |||||||
\(192\) | 2.50966e27 | 0.0721688 | ||||||||
\(193\) | 3.16427e28 | 0.852721 | 0.426361 | − | 0.904553i | \(-0.359795\pi\) | ||||
0.426361 | + | 0.904553i | \(0.359795\pi\) | |||||||
\(194\) | −1.06300e28 | −0.268541 | ||||||||
\(195\) | −4.23498e28 | −1.00327 | ||||||||
\(196\) | 3.36620e28 | 0.748065 | ||||||||
\(197\) | −4.82083e28 | −1.00530 | −0.502649 | − | 0.864491i | \(-0.667641\pi\) | ||||
−0.502649 | + | 0.864491i | \(0.667641\pi\) | |||||||
\(198\) | −1.09833e28 | −0.214989 | ||||||||
\(199\) | 9.63887e28 | 1.77159 | 0.885793 | − | 0.464080i | \(-0.153615\pi\) | ||||
0.885793 | + | 0.464080i | \(0.153615\pi\) | |||||||
\(200\) | −3.47578e27 | −0.0600037 | ||||||||
\(201\) | 3.39374e27 | 0.0550463 | ||||||||
\(202\) | 7.15742e28 | 1.09110 | ||||||||
\(203\) | 6.25641e28 | 0.896653 | ||||||||
\(204\) | −2.25231e28 | −0.303564 | ||||||||
\(205\) | 3.03770e28 | 0.385142 | ||||||||
\(206\) | 5.43942e28 | 0.648951 | ||||||||
\(207\) | 3.20113e28 | 0.359479 | ||||||||
\(208\) | −3.79901e28 | −0.401679 | ||||||||
\(209\) | 1.08887e29 | 1.08430 | ||||||||
\(210\) | −7.43600e28 | −0.697587 | ||||||||
\(211\) | −7.22567e28 | −0.638774 | −0.319387 | − | 0.947624i | \(-0.603477\pi\) | ||||
−0.319387 | + | 0.947624i | \(0.603477\pi\) | |||||||
\(212\) | 7.44921e28 | 0.620744 | ||||||||
\(213\) | 3.20335e28 | 0.251687 | ||||||||
\(214\) | −1.71195e29 | −1.26859 | ||||||||
\(215\) | −2.18069e29 | −1.52445 | ||||||||
\(216\) | −1.03144e28 | −0.0680414 | ||||||||
\(217\) | 2.68984e29 | 1.67487 | ||||||||
\(218\) | −1.90316e29 | −1.11885 | ||||||||
\(219\) | −1.42858e29 | −0.793145 | ||||||||
\(220\) | 9.40474e28 | 0.493245 | ||||||||
\(221\) | 3.40945e29 | 1.68959 | ||||||||
\(222\) | 1.00335e29 | 0.469939 | ||||||||
\(223\) | −7.19979e28 | −0.318793 | −0.159396 | − | 0.987215i | \(-0.550955\pi\) | ||||
−0.159396 | + | 0.987215i | \(0.550955\pi\) | |||||||
\(224\) | −6.67051e28 | −0.279292 | ||||||||
\(225\) | 1.42851e28 | 0.0565720 | ||||||||
\(226\) | −1.34101e29 | −0.502431 | ||||||||
\(227\) | −4.13856e29 | −1.46732 | −0.733662 | − | 0.679514i | \(-0.762191\pi\) | ||||
−0.733662 | + | 0.679514i | \(0.762191\pi\) | |||||||
\(228\) | 1.02257e29 | 0.343167 | ||||||||
\(229\) | −4.93767e29 | −1.56884 | −0.784420 | − | 0.620230i | \(-0.787039\pi\) | ||||
−0.784420 | + | 0.620230i | \(0.787039\pi\) | |||||||
\(230\) | −2.74106e29 | −0.824747 | ||||||||
\(231\) | 2.91928e29 | 0.832005 | ||||||||
\(232\) | −7.43097e28 | −0.200653 | ||||||||
\(233\) | 2.65749e29 | 0.680020 | 0.340010 | − | 0.940422i | \(-0.389569\pi\) | ||||
0.340010 | + | 0.940422i | \(0.389569\pi\) | |||||||
\(234\) | 1.56135e29 | 0.378706 | ||||||||
\(235\) | −2.89938e28 | −0.0666741 | ||||||||
\(236\) | 3.78315e29 | 0.825000 | ||||||||
\(237\) | −1.39695e29 | −0.288953 | ||||||||
\(238\) | 5.98649e29 | 1.17479 | ||||||||
\(239\) | −2.43722e29 | −0.453859 | −0.226929 | − | 0.973911i | \(-0.572869\pi\) | ||||
−0.226929 | + | 0.973911i | \(0.572869\pi\) | |||||||
\(240\) | 8.83202e28 | 0.156106 | ||||||||
\(241\) | −2.75488e29 | −0.462263 | −0.231132 | − | 0.972922i | \(-0.574243\pi\) | ||||
−0.231132 | + | 0.972922i | \(0.574243\pi\) | |||||||
\(242\) | 7.45716e28 | 0.118818 | ||||||||
\(243\) | 4.23912e28 | 0.0641500 | ||||||||
\(244\) | −2.06538e29 | −0.296912 | ||||||||
\(245\) | 1.18464e30 | 1.61811 | ||||||||
\(246\) | −1.11994e29 | −0.145380 | ||||||||
\(247\) | −1.54792e30 | −1.91001 | ||||||||
\(248\) | −3.19483e29 | −0.374802 | ||||||||
\(249\) | 3.65900e29 | 0.408198 | ||||||||
\(250\) | 5.98414e29 | 0.634968 | ||||||||
\(251\) | 1.20863e30 | 1.22004 | 0.610018 | − | 0.792387i | \(-0.291162\pi\) | ||||
0.610018 | + | 0.792387i | \(0.291162\pi\) | |||||||
\(252\) | 2.74151e29 | 0.263319 | ||||||||
\(253\) | 1.07611e30 | 0.983667 | ||||||||
\(254\) | 6.93150e29 | 0.603123 | ||||||||
\(255\) | −7.92635e29 | −0.656630 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | −2.27637e29 | −0.171032 | −0.0855162 | − | 0.996337i | \(-0.527254\pi\) | ||||
−0.0855162 | + | 0.996337i | \(0.527254\pi\) | |||||||
\(258\) | 8.03979e29 | 0.575437 | ||||||||
\(259\) | −2.66684e30 | −1.81866 | ||||||||
\(260\) | −1.33695e30 | −0.868859 | ||||||||
\(261\) | 3.05405e29 | 0.189178 | ||||||||
\(262\) | −7.79314e28 | −0.0460200 | ||||||||
\(263\) | 7.19227e28 | 0.0404966 | 0.0202483 | − | 0.999795i | \(-0.493554\pi\) | ||||
0.0202483 | + | 0.999795i | \(0.493554\pi\) | |||||||
\(264\) | −3.46734e29 | −0.186186 | ||||||||
\(265\) | 2.62154e30 | 1.34271 | ||||||||
\(266\) | −2.71791e30 | −1.32805 | ||||||||
\(267\) | −1.35982e30 | −0.634004 | ||||||||
\(268\) | 1.07138e29 | 0.0476715 | ||||||||
\(269\) | 2.58878e29 | 0.109949 | 0.0549745 | − | 0.998488i | \(-0.482492\pi\) | ||||
0.0549745 | + | 0.998488i | \(0.482492\pi\) | |||||||
\(270\) | −3.62986e29 | −0.147178 | ||||||||
\(271\) | −1.02532e30 | −0.396955 | −0.198478 | − | 0.980105i | \(-0.563600\pi\) | ||||
−0.198478 | + | 0.980105i | \(0.563600\pi\) | |||||||
\(272\) | −7.11038e29 | −0.262894 | ||||||||
\(273\) | −4.14997e30 | −1.46559 | ||||||||
\(274\) | 1.42718e29 | 0.0481501 | ||||||||
\(275\) | 4.80214e29 | 0.154802 | ||||||||
\(276\) | 1.01057e30 | 0.311318 | ||||||||
\(277\) | 4.94719e30 | 1.45667 | 0.728336 | − | 0.685220i | \(-0.240294\pi\) | ||||
0.728336 | + | 0.685220i | \(0.240294\pi\) | |||||||
\(278\) | −7.33923e29 | −0.206581 | ||||||||
\(279\) | 1.31304e30 | 0.353367 | ||||||||
\(280\) | −2.34749e30 | −0.604128 | ||||||||
\(281\) | −3.59090e30 | −0.883842 | −0.441921 | − | 0.897054i | \(-0.645703\pi\) | ||||
−0.441921 | + | 0.897054i | \(0.645703\pi\) | |||||||
\(282\) | 1.06894e29 | 0.0251676 | ||||||||
\(283\) | 4.52174e30 | 1.01853 | 0.509266 | − | 0.860609i | \(-0.329917\pi\) | ||||
0.509266 | + | 0.860609i | \(0.329917\pi\) | |||||||
\(284\) | 1.01128e30 | 0.217967 | ||||||||
\(285\) | 3.59863e30 | 0.742294 | ||||||||
\(286\) | 5.24871e30 | 1.03628 | ||||||||
\(287\) | 2.97672e30 | 0.562619 | ||||||||
\(288\) | −3.25619e29 | −0.0589256 | ||||||||
\(289\) | 6.10625e29 | 0.105816 | ||||||||
\(290\) | −2.61512e30 | −0.434026 | ||||||||
\(291\) | 1.37920e30 | 0.219263 | ||||||||
\(292\) | −4.50992e30 | −0.686883 | ||||||||
\(293\) | 5.67005e30 | 0.827450 | 0.413725 | − | 0.910402i | \(-0.364227\pi\) | ||||
0.413725 | + | 0.910402i | \(0.364227\pi\) | |||||||
\(294\) | −4.36752e30 | −0.610792 | ||||||||
\(295\) | 1.33137e31 | 1.78453 | ||||||||
\(296\) | 3.16751e30 | 0.406979 | ||||||||
\(297\) | 1.42504e30 | 0.175538 | ||||||||
\(298\) | 1.00871e31 | 1.19142 | ||||||||
\(299\) | −1.52976e31 | −1.73274 | ||||||||
\(300\) | 4.50970e29 | 0.0489928 | ||||||||
\(301\) | −2.13692e31 | −2.22693 | ||||||||
\(302\) | −1.77621e30 | −0.177586 | ||||||||
\(303\) | −9.28650e30 | −0.890880 | ||||||||
\(304\) | 3.22817e30 | 0.297192 | ||||||||
\(305\) | −7.26852e30 | −0.642241 | ||||||||
\(306\) | 2.92229e30 | 0.247859 | ||||||||
\(307\) | −2.05241e31 | −1.67122 | −0.835611 | − | 0.549322i | \(-0.814886\pi\) | ||||
−0.835611 | + | 0.549322i | \(0.814886\pi\) | |||||||
\(308\) | 9.21596e30 | 0.720537 | ||||||||
\(309\) | −7.05745e30 | −0.529867 | ||||||||
\(310\) | −1.12433e31 | −0.810722 | ||||||||
\(311\) | 2.33797e31 | 1.61933 | 0.809663 | − | 0.586895i | \(-0.199650\pi\) | ||||
0.809663 | + | 0.586895i | \(0.199650\pi\) | |||||||
\(312\) | 4.92908e30 | 0.327969 | ||||||||
\(313\) | −3.96767e30 | −0.253648 | −0.126824 | − | 0.991925i | \(-0.540478\pi\) | ||||
−0.126824 | + | 0.991925i | \(0.540478\pi\) | |||||||
\(314\) | 1.45002e31 | 0.890742 | ||||||||
\(315\) | 9.64794e30 | 0.569577 | ||||||||
\(316\) | −4.41008e30 | −0.250241 | ||||||||
\(317\) | −6.40482e30 | −0.349354 | −0.174677 | − | 0.984626i | \(-0.555888\pi\) | ||||
−0.174677 | + | 0.984626i | \(0.555888\pi\) | |||||||
\(318\) | −9.66508e30 | −0.506835 | ||||||||
\(319\) | 1.02666e31 | 0.517659 | ||||||||
\(320\) | 2.78821e30 | 0.135192 | ||||||||
\(321\) | 2.22120e31 | 1.03580 | ||||||||
\(322\) | −2.68604e31 | −1.20480 | ||||||||
\(323\) | −2.89714e31 | −1.25008 | ||||||||
\(324\) | 1.33826e30 | 0.0555556 | ||||||||
\(325\) | −6.82659e30 | −0.272685 | ||||||||
\(326\) | 2.64593e31 | 1.01709 | ||||||||
\(327\) | 2.46929e31 | 0.913533 | ||||||||
\(328\) | −3.53556e30 | −0.125903 | ||||||||
\(329\) | −2.84118e30 | −0.0973981 | ||||||||
\(330\) | −1.22023e31 | −0.402733 | ||||||||
\(331\) | 3.45945e31 | 1.09940 | 0.549702 | − | 0.835361i | \(-0.314741\pi\) | ||||
0.549702 | + | 0.835361i | \(0.314741\pi\) | |||||||
\(332\) | 1.15512e31 | 0.353510 | ||||||||
\(333\) | −1.30181e31 | −0.383703 | ||||||||
\(334\) | 1.83678e31 | 0.521465 | ||||||||
\(335\) | 3.77041e30 | 0.103117 | ||||||||
\(336\) | 8.65474e30 | 0.228041 | ||||||||
\(337\) | −2.03336e31 | −0.516228 | −0.258114 | − | 0.966114i | \(-0.583101\pi\) | ||||
−0.258114 | + | 0.966114i | \(0.583101\pi\) | |||||||
\(338\) | −4.57112e31 | −1.11831 | ||||||||
\(339\) | 1.73991e31 | 0.410233 | ||||||||
\(340\) | −2.50229e31 | −0.568659 | ||||||||
\(341\) | 4.41397e31 | 0.966940 | ||||||||
\(342\) | −1.32674e31 | −0.280195 | ||||||||
\(343\) | 3.84951e31 | 0.783842 | ||||||||
\(344\) | 2.53810e31 | 0.498343 | ||||||||
\(345\) | 3.55642e31 | 0.673403 | ||||||||
\(346\) | −4.99603e30 | −0.0912376 | ||||||||
\(347\) | 1.40061e31 | 0.246718 | 0.123359 | − | 0.992362i | \(-0.460633\pi\) | ||||
0.123359 | + | 0.992362i | \(0.460633\pi\) | |||||||
\(348\) | 9.64142e30 | 0.163833 | ||||||||
\(349\) | −1.88041e31 | −0.308273 | −0.154136 | − | 0.988050i | \(-0.549260\pi\) | ||||
−0.154136 | + | 0.988050i | \(0.549260\pi\) | |||||||
\(350\) | −1.19865e31 | −0.189601 | ||||||||
\(351\) | −2.02580e31 | −0.309213 | ||||||||
\(352\) | −1.09461e31 | −0.161242 | ||||||||
\(353\) | −1.05140e32 | −1.49481 | −0.747404 | − | 0.664370i | \(-0.768700\pi\) | ||||
−0.747404 | + | 0.664370i | \(0.768700\pi\) | |||||||
\(354\) | −4.90850e31 | −0.673609 | ||||||||
\(355\) | 3.55890e31 | 0.471477 | ||||||||
\(356\) | −4.29287e31 | −0.549064 | ||||||||
\(357\) | −7.76725e31 | −0.959211 | ||||||||
\(358\) | 8.57119e31 | 1.02212 | ||||||||
\(359\) | −2.39508e31 | −0.275828 | −0.137914 | − | 0.990444i | \(-0.544040\pi\) | ||||
−0.137914 | + | 0.990444i | \(0.544040\pi\) | |||||||
\(360\) | −1.14592e31 | −0.127460 | ||||||||
\(361\) | 3.84559e31 | 0.413165 | ||||||||
\(362\) | 6.09876e30 | 0.0632972 | ||||||||
\(363\) | −9.67540e30 | −0.0970144 | ||||||||
\(364\) | −1.31012e32 | −1.26924 | ||||||||
\(365\) | −1.58714e32 | −1.48578 | ||||||||
\(366\) | 2.67976e31 | 0.242428 | ||||||||
\(367\) | 1.16817e31 | 0.102136 | 0.0510680 | − | 0.998695i | \(-0.483737\pi\) | ||||
0.0510680 | + | 0.998695i | \(0.483737\pi\) | |||||||
\(368\) | 3.19031e31 | 0.269610 | ||||||||
\(369\) | 1.45308e31 | 0.118702 | ||||||||
\(370\) | 1.11471e32 | 0.880323 | ||||||||
\(371\) | 2.56891e32 | 1.96144 | ||||||||
\(372\) | 4.14518e31 | 0.306025 | ||||||||
\(373\) | −6.29652e31 | −0.449511 | −0.224755 | − | 0.974415i | \(-0.572158\pi\) | ||||
−0.224755 | + | 0.974415i | \(0.572158\pi\) | |||||||
\(374\) | 9.82368e31 | 0.678234 | ||||||||
\(375\) | −7.76421e31 | −0.518449 | ||||||||
\(376\) | 3.37458e30 | 0.0217958 | ||||||||
\(377\) | −1.45948e32 | −0.911864 | ||||||||
\(378\) | −3.55700e31 | −0.214999 | ||||||||
\(379\) | 7.98394e31 | 0.466903 | 0.233452 | − | 0.972368i | \(-0.424998\pi\) | ||||
0.233452 | + | 0.972368i | \(0.424998\pi\) | |||||||
\(380\) | 1.13606e32 | 0.642846 | ||||||||
\(381\) | −8.99337e31 | −0.492448 | ||||||||
\(382\) | 1.30886e32 | 0.693587 | ||||||||
\(383\) | 1.16203e32 | 0.595980 | 0.297990 | − | 0.954569i | \(-0.403684\pi\) | ||||
0.297990 | + | 0.954569i | \(0.403684\pi\) | |||||||
\(384\) | −1.02796e31 | −0.0510310 | ||||||||
\(385\) | 3.24329e32 | 1.55857 | ||||||||
\(386\) | −1.29608e32 | −0.602965 | ||||||||
\(387\) | −1.04313e32 | −0.469843 | ||||||||
\(388\) | 4.35404e31 | 0.189887 | ||||||||
\(389\) | 1.94162e32 | 0.819964 | 0.409982 | − | 0.912094i | \(-0.365535\pi\) | ||||
0.409982 | + | 0.912094i | \(0.365535\pi\) | |||||||
\(390\) | 1.73465e32 | 0.709420 | ||||||||
\(391\) | −2.86316e32 | −1.13406 | ||||||||
\(392\) | −1.37880e32 | −0.528962 | ||||||||
\(393\) | 1.01113e31 | 0.0375751 | ||||||||
\(394\) | 1.97461e32 | 0.710852 | ||||||||
\(395\) | −1.55200e32 | −0.541288 | ||||||||
\(396\) | 4.49875e31 | 0.152020 | ||||||||
\(397\) | −1.56136e32 | −0.511237 | −0.255618 | − | 0.966778i | \(-0.582279\pi\) | ||||
−0.255618 | + | 0.966778i | \(0.582279\pi\) | |||||||
\(398\) | −3.94808e32 | −1.25270 | ||||||||
\(399\) | 3.52639e32 | 1.08435 | ||||||||
\(400\) | 1.42368e31 | 0.0424290 | ||||||||
\(401\) | 2.04402e32 | 0.590447 | 0.295223 | − | 0.955428i | \(-0.404606\pi\) | ||||
0.295223 | + | 0.955428i | \(0.404606\pi\) | |||||||
\(402\) | −1.39008e31 | −0.0389236 | ||||||||
\(403\) | −6.27479e32 | −1.70328 | ||||||||
\(404\) | −2.93168e32 | −0.771524 | ||||||||
\(405\) | 4.70962e31 | 0.120170 | ||||||||
\(406\) | −2.56262e32 | −0.634029 | ||||||||
\(407\) | −4.37623e32 | −1.04995 | ||||||||
\(408\) | 9.22546e31 | 0.214652 | ||||||||
\(409\) | −5.80074e32 | −1.30901 | −0.654503 | − | 0.756059i | \(-0.727122\pi\) | ||||
−0.654503 | + | 0.756059i | \(0.727122\pi\) | |||||||
\(410\) | −1.24424e32 | −0.272337 | ||||||||
\(411\) | −1.85172e31 | −0.0393144 | ||||||||
\(412\) | −2.22799e32 | −0.458878 | ||||||||
\(413\) | 1.30465e33 | 2.60686 | ||||||||
\(414\) | −1.31118e32 | −0.254190 | ||||||||
\(415\) | 4.06512e32 | 0.764666 | ||||||||
\(416\) | 1.55608e32 | 0.284030 | ||||||||
\(417\) | 9.52238e31 | 0.168673 | ||||||||
\(418\) | −4.46003e32 | −0.766716 | ||||||||
\(419\) | 9.59622e31 | 0.160112 | 0.0800562 | − | 0.996790i | \(-0.474490\pi\) | ||||
0.0800562 | + | 0.996790i | \(0.474490\pi\) | |||||||
\(420\) | 3.04579e32 | 0.493268 | ||||||||
\(421\) | 8.99240e32 | 1.41367 | 0.706837 | − | 0.707377i | \(-0.250121\pi\) | ||||
0.706837 | + | 0.707377i | \(0.250121\pi\) | |||||||
\(422\) | 2.95963e32 | 0.451682 | ||||||||
\(423\) | −1.38692e31 | −0.0205492 | ||||||||
\(424\) | −3.05120e32 | −0.438932 | ||||||||
\(425\) | −1.27769e32 | −0.178470 | ||||||||
\(426\) | −1.31209e32 | −0.177969 | ||||||||
\(427\) | −7.12262e32 | −0.938191 | ||||||||
\(428\) | 7.01216e32 | 0.897025 | ||||||||
\(429\) | −6.81000e32 | −0.846118 | ||||||||
\(430\) | 8.93212e32 | 1.07795 | ||||||||
\(431\) | 4.87745e31 | 0.0571778 | 0.0285889 | − | 0.999591i | \(-0.490899\pi\) | ||||
0.0285889 | + | 0.999591i | \(0.490899\pi\) | |||||||
\(432\) | 4.22479e31 | 0.0481125 | ||||||||
\(433\) | −3.43563e32 | −0.380109 | −0.190054 | − | 0.981774i | \(-0.560866\pi\) | ||||
−0.190054 | + | 0.981774i | \(0.560866\pi\) | |||||||
\(434\) | −1.10176e33 | −1.18431 | ||||||||
\(435\) | 3.39302e32 | 0.354381 | ||||||||
\(436\) | 7.79536e32 | 0.791143 | ||||||||
\(437\) | 1.29990e33 | 1.28201 | ||||||||
\(438\) | 5.85145e32 | 0.560838 | ||||||||
\(439\) | 9.52703e32 | 0.887465 | 0.443732 | − | 0.896159i | \(-0.353654\pi\) | ||||
0.443732 | + | 0.896159i | \(0.353654\pi\) | |||||||
\(440\) | −3.85218e32 | −0.348777 | ||||||||
\(441\) | 5.66670e32 | 0.498710 | ||||||||
\(442\) | −1.39651e33 | −1.19472 | ||||||||
\(443\) | 3.31350e32 | 0.275576 | 0.137788 | − | 0.990462i | \(-0.456001\pi\) | ||||
0.137788 | + | 0.990462i | \(0.456001\pi\) | |||||||
\(444\) | −4.10973e32 | −0.332297 | ||||||||
\(445\) | −1.51075e33 | −1.18766 | ||||||||
\(446\) | 2.94903e32 | 0.225421 | ||||||||
\(447\) | −1.30877e33 | −0.972788 | ||||||||
\(448\) | 2.73224e32 | 0.197489 | ||||||||
\(449\) | −1.03610e33 | −0.728318 | −0.364159 | − | 0.931337i | \(-0.618644\pi\) | ||||
−0.364159 | + | 0.931337i | \(0.618644\pi\) | |||||||
\(450\) | −5.85117e31 | −0.0400025 | ||||||||
\(451\) | 4.88473e32 | 0.324813 | ||||||||
\(452\) | 5.49277e32 | 0.355272 | ||||||||
\(453\) | 2.30457e32 | 0.144998 | ||||||||
\(454\) | 1.69515e33 | 1.03756 | ||||||||
\(455\) | −4.61058e33 | −2.74544 | ||||||||
\(456\) | −4.18843e32 | −0.242656 | ||||||||
\(457\) | 2.36104e33 | 1.33092 | 0.665458 | − | 0.746436i | \(-0.268236\pi\) | ||||
0.665458 | + | 0.746436i | \(0.268236\pi\) | |||||||
\(458\) | 2.02247e33 | 1.10934 | ||||||||
\(459\) | −3.79156e32 | −0.202376 | ||||||||
\(460\) | 1.12274e33 | 0.583184 | ||||||||
\(461\) | −3.86492e32 | −0.195380 | −0.0976898 | − | 0.995217i | \(-0.531145\pi\) | ||||
−0.0976898 | + | 0.995217i | \(0.531145\pi\) | |||||||
\(462\) | −1.19574e33 | −0.588316 | ||||||||
\(463\) | −1.13691e33 | −0.544456 | −0.272228 | − | 0.962233i | \(-0.587761\pi\) | ||||
−0.272228 | + | 0.962233i | \(0.587761\pi\) | |||||||
\(464\) | 3.04373e32 | 0.141883 | ||||||||
\(465\) | 1.45878e33 | 0.661952 | ||||||||
\(466\) | −1.08851e33 | −0.480847 | ||||||||
\(467\) | −1.38364e33 | −0.595061 | −0.297530 | − | 0.954712i | \(-0.596163\pi\) | ||||
−0.297530 | + | 0.954712i | \(0.596163\pi\) | |||||||
\(468\) | −6.39530e32 | −0.267786 | ||||||||
\(469\) | 3.69473e32 | 0.150634 | ||||||||
\(470\) | 1.18759e32 | 0.0471457 | ||||||||
\(471\) | −1.88134e33 | −0.727288 | ||||||||
\(472\) | −1.54958e33 | −0.583363 | ||||||||
\(473\) | −3.50664e33 | −1.28566 | ||||||||
\(474\) | 5.72192e32 | 0.204321 | ||||||||
\(475\) | 5.80082e32 | 0.201753 | ||||||||
\(476\) | −2.45206e33 | −0.830701 | ||||||||
\(477\) | 1.25401e33 | 0.413829 | ||||||||
\(478\) | 9.98284e32 | 0.320926 | ||||||||
\(479\) | 2.24544e33 | 0.703248 | 0.351624 | − | 0.936141i | \(-0.385630\pi\) | ||||
0.351624 | + | 0.936141i | \(0.385630\pi\) | |||||||
\(480\) | −3.61760e32 | −0.110384 | ||||||||
\(481\) | 6.22113e33 | 1.84951 | ||||||||
\(482\) | 1.12840e33 | 0.326870 | ||||||||
\(483\) | 3.48504e33 | 0.983713 | ||||||||
\(484\) | −3.05445e32 | −0.0840169 | ||||||||
\(485\) | 1.53228e33 | 0.410739 | ||||||||
\(486\) | −1.73634e32 | −0.0453609 | ||||||||
\(487\) | 5.22121e33 | 1.32941 | 0.664706 | − | 0.747105i | \(-0.268557\pi\) | ||||
0.664706 | + | 0.747105i | \(0.268557\pi\) | |||||||
\(488\) | 8.45981e32 | 0.209948 | ||||||||
\(489\) | −3.43299e33 | −0.830448 | ||||||||
\(490\) | −4.85227e33 | −1.14418 | ||||||||
\(491\) | 2.55379e33 | 0.587039 | 0.293519 | − | 0.955953i | \(-0.405173\pi\) | ||||
0.293519 | + | 0.955953i | \(0.405173\pi\) | |||||||
\(492\) | 4.58727e32 | 0.102799 | ||||||||
\(493\) | −2.73161e33 | −0.596805 | ||||||||
\(494\) | 6.34026e33 | 1.35058 | ||||||||
\(495\) | 1.58320e33 | 0.328830 | ||||||||
\(496\) | 1.30860e33 | 0.265025 | ||||||||
\(497\) | 3.48746e33 | 0.688738 | ||||||||
\(498\) | −1.49873e33 | −0.288640 | ||||||||
\(499\) | 7.23080e32 | 0.135809 | 0.0679047 | − | 0.997692i | \(-0.478369\pi\) | ||||
0.0679047 | + | 0.997692i | \(0.478369\pi\) | |||||||
\(500\) | −2.45111e33 | −0.448990 | ||||||||
\(501\) | −2.38315e33 | −0.425775 | ||||||||
\(502\) | −4.95056e33 | −0.862696 | ||||||||
\(503\) | 3.39140e33 | 0.576474 | 0.288237 | − | 0.957559i | \(-0.406931\pi\) | ||||
0.288237 | + | 0.957559i | \(0.406931\pi\) | |||||||
\(504\) | −1.12292e33 | −0.186195 | ||||||||
\(505\) | −1.03172e34 | −1.66886 | ||||||||
\(506\) | −4.40773e33 | −0.695558 | ||||||||
\(507\) | 5.93086e33 | 0.913099 | ||||||||
\(508\) | −2.83914e33 | −0.426472 | ||||||||
\(509\) | 5.96782e31 | 0.00874668 | 0.00437334 | − | 0.999990i | \(-0.498608\pi\) | ||||
0.00437334 | + | 0.999990i | \(0.498608\pi\) | |||||||
\(510\) | 3.24663e33 | 0.464308 | ||||||||
\(511\) | −1.55528e34 | −2.17043 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | 1.72140e33 | 0.228778 | ||||||||
\(514\) | 9.32400e32 | 0.120938 | ||||||||
\(515\) | −7.84075e33 | −0.992584 | ||||||||
\(516\) | −3.29310e33 | −0.406896 | ||||||||
\(517\) | −4.66231e32 | −0.0562302 | ||||||||
\(518\) | 1.09234e34 | 1.28598 | ||||||||
\(519\) | 6.48217e32 | 0.0744952 | ||||||||
\(520\) | 5.47616e33 | 0.614376 | ||||||||
\(521\) | 6.90204e32 | 0.0755972 | 0.0377986 | − | 0.999285i | \(-0.487965\pi\) | ||||
0.0377986 | + | 0.999285i | \(0.487965\pi\) | |||||||
\(522\) | −1.25094e33 | −0.133769 | ||||||||
\(523\) | −8.36286e32 | −0.0873139 | −0.0436570 | − | 0.999047i | \(-0.513901\pi\) | ||||
−0.0436570 | + | 0.999047i | \(0.513901\pi\) | |||||||
\(524\) | 3.19207e32 | 0.0325410 | ||||||||
\(525\) | 1.55520e33 | 0.154809 | ||||||||
\(526\) | −2.94595e32 | −0.0286355 | ||||||||
\(527\) | −1.17441e34 | −1.11478 | ||||||||
\(528\) | 1.42022e33 | 0.131653 | ||||||||
\(529\) | 1.80078e33 | 0.163029 | ||||||||
\(530\) | −1.07378e34 | −0.949440 | ||||||||
\(531\) | 6.36860e33 | 0.550000 | ||||||||
\(532\) | 1.11326e34 | 0.939074 | ||||||||
\(533\) | −6.94400e33 | −0.572163 | ||||||||
\(534\) | 5.56984e33 | 0.448309 | ||||||||
\(535\) | 2.46773e34 | 1.94033 | ||||||||
\(536\) | −4.38837e32 | −0.0337088 | ||||||||
\(537\) | −1.11208e34 | −0.834561 | ||||||||
\(538\) | −1.06036e33 | −0.0777456 | ||||||||
\(539\) | 1.90494e34 | 1.36465 | ||||||||
\(540\) | 1.48679e33 | 0.104071 | ||||||||
\(541\) | −1.79946e34 | −1.23077 | −0.615384 | − | 0.788228i | \(-0.710999\pi\) | ||||
−0.615384 | + | 0.788228i | \(0.710999\pi\) | |||||||
\(542\) | 4.19969e33 | 0.280690 | ||||||||
\(543\) | −7.91292e32 | −0.0516820 | ||||||||
\(544\) | 2.91241e33 | 0.185894 | ||||||||
\(545\) | 2.74335e34 | 1.71130 | ||||||||
\(546\) | 1.69983e34 | 1.03633 | ||||||||
\(547\) | −8.89037e33 | −0.529759 | −0.264879 | − | 0.964282i | \(-0.585332\pi\) | ||||
−0.264879 | + | 0.964282i | \(0.585332\pi\) | |||||||
\(548\) | −5.84573e32 | −0.0340473 | ||||||||
\(549\) | −3.47689e33 | −0.197941 | ||||||||
\(550\) | −1.96695e33 | −0.109461 | ||||||||
\(551\) | 1.24017e34 | 0.674664 | ||||||||
\(552\) | −4.13931e33 | −0.220135 | ||||||||
\(553\) | −1.52085e34 | −0.790718 | ||||||||
\(554\) | −2.02637e34 | −1.03002 | ||||||||
\(555\) | −1.44630e34 | −0.718781 | ||||||||
\(556\) | 3.00615e33 | 0.146075 | ||||||||
\(557\) | −3.01551e34 | −1.43275 | −0.716376 | − | 0.697714i | \(-0.754201\pi\) | ||||
−0.716376 | + | 0.697714i | \(0.754201\pi\) | |||||||
\(558\) | −5.37821e33 | −0.249868 | ||||||||
\(559\) | 4.98494e34 | 2.26471 | ||||||||
\(560\) | 9.61533e33 | 0.427183 | ||||||||
\(561\) | −1.27459e34 | −0.553775 | ||||||||
\(562\) | 1.47083e34 | 0.624970 | ||||||||
\(563\) | −1.95891e34 | −0.814067 | −0.407033 | − | 0.913413i | \(-0.633437\pi\) | ||||
−0.407033 | + | 0.913413i | \(0.633437\pi\) | |||||||
\(564\) | −4.37840e32 | −0.0177962 | ||||||||
\(565\) | 1.93302e34 | 0.768478 | ||||||||
\(566\) | −1.85210e34 | −0.720211 | ||||||||
\(567\) | 4.61508e33 | 0.175546 | ||||||||
\(568\) | −4.14219e33 | −0.154126 | ||||||||
\(569\) | −1.37387e33 | −0.0500085 | −0.0250042 | − | 0.999687i | \(-0.507960\pi\) | ||||
−0.0250042 | + | 0.999687i | \(0.507960\pi\) | |||||||
\(570\) | −1.47400e34 | −0.524881 | ||||||||
\(571\) | −6.79583e33 | −0.236751 | −0.118375 | − | 0.992969i | \(-0.537769\pi\) | ||||
−0.118375 | + | 0.992969i | \(0.537769\pi\) | |||||||
\(572\) | −2.14987e34 | −0.732760 | ||||||||
\(573\) | −1.69820e34 | −0.566311 | ||||||||
\(574\) | −1.21926e34 | −0.397832 | ||||||||
\(575\) | 5.73279e33 | 0.183028 | ||||||||
\(576\) | 1.33374e33 | 0.0416667 | ||||||||
\(577\) | −4.58517e34 | −1.40171 | −0.700855 | − | 0.713304i | \(-0.747198\pi\) | ||||
−0.700855 | + | 0.713304i | \(0.747198\pi\) | |||||||
\(578\) | −2.50112e33 | −0.0748232 | ||||||||
\(579\) | 1.68162e34 | 0.492319 | ||||||||
\(580\) | 1.07115e34 | 0.306903 | ||||||||
\(581\) | 3.98352e34 | 1.11703 | ||||||||
\(582\) | −5.64920e33 | −0.155042 | ||||||||
\(583\) | 4.21553e34 | 1.13239 | ||||||||
\(584\) | 1.84726e34 | 0.485700 | ||||||||
\(585\) | −2.25064e34 | −0.579239 | ||||||||
\(586\) | −2.32245e34 | −0.585096 | ||||||||
\(587\) | 1.77739e34 | 0.438334 | 0.219167 | − | 0.975687i | \(-0.429666\pi\) | ||||
0.219167 | + | 0.975687i | \(0.429666\pi\) | |||||||
\(588\) | 1.78894e34 | 0.431895 | ||||||||
\(589\) | 5.33193e34 | 1.26021 | ||||||||
\(590\) | −5.45330e34 | −1.26185 | ||||||||
\(591\) | −2.56199e34 | −0.580409 | ||||||||
\(592\) | −1.29741e34 | −0.287778 | ||||||||
\(593\) | 8.33392e34 | 1.80995 | 0.904973 | − | 0.425469i | \(-0.139891\pi\) | ||||
0.904973 | + | 0.425469i | \(0.139891\pi\) | |||||||
\(594\) | −5.83696e33 | −0.124124 | ||||||||
\(595\) | −8.62933e34 | −1.79686 | ||||||||
\(596\) | −4.13168e34 | −0.842459 | ||||||||
\(597\) | 5.12249e34 | 1.02283 | ||||||||
\(598\) | 6.26591e34 | 1.22523 | ||||||||
\(599\) | −7.75840e34 | −1.48572 | −0.742860 | − | 0.669447i | \(-0.766531\pi\) | ||||
−0.742860 | + | 0.669447i | \(0.766531\pi\) | |||||||
\(600\) | −1.84717e33 | −0.0346431 | ||||||||
\(601\) | −6.07045e34 | −1.11504 | −0.557519 | − | 0.830164i | \(-0.688247\pi\) | ||||
−0.557519 | + | 0.830164i | \(0.688247\pi\) | |||||||
\(602\) | 8.75283e34 | 1.57468 | ||||||||
\(603\) | 1.80357e33 | 0.0317810 | ||||||||
\(604\) | 7.27537e33 | 0.125572 | ||||||||
\(605\) | −1.07493e34 | −0.181734 | ||||||||
\(606\) | 3.80375e34 | 0.629947 | ||||||||
\(607\) | 1.40609e34 | 0.228116 | 0.114058 | − | 0.993474i | \(-0.463615\pi\) | ||||
0.114058 | + | 0.993474i | \(0.463615\pi\) | |||||||
\(608\) | −1.32226e34 | −0.210146 | ||||||||
\(609\) | 3.32491e34 | 0.517683 | ||||||||
\(610\) | 2.97719e34 | 0.454133 | ||||||||
\(611\) | 6.62783e33 | 0.0990503 | ||||||||
\(612\) | −1.19697e34 | −0.175263 | ||||||||
\(613\) | 1.12382e35 | 1.61229 | 0.806143 | − | 0.591721i | \(-0.201551\pi\) | ||||
0.806143 | + | 0.591721i | \(0.201551\pi\) | |||||||
\(614\) | 8.40666e34 | 1.18173 | ||||||||
\(615\) | 1.61436e34 | 0.222362 | ||||||||
\(616\) | −3.77486e34 | −0.509497 | ||||||||
\(617\) | −5.19277e34 | −0.686807 | −0.343403 | − | 0.939188i | \(-0.611580\pi\) | ||||
−0.343403 | + | 0.939188i | \(0.611580\pi\) | |||||||
\(618\) | 2.89073e34 | 0.374672 | ||||||||
\(619\) | −4.73877e33 | −0.0601911 | −0.0300956 | − | 0.999547i | \(-0.509581\pi\) | ||||
−0.0300956 | + | 0.999547i | \(0.509581\pi\) | |||||||
\(620\) | 4.60525e34 | 0.573267 | ||||||||
\(621\) | 1.70121e34 | 0.207546 | ||||||||
\(622\) | −9.57633e34 | −1.14504 | ||||||||
\(623\) | −1.48043e35 | −1.73495 | ||||||||
\(624\) | −2.01895e34 | −0.231909 | ||||||||
\(625\) | −1.01333e35 | −1.14091 | ||||||||
\(626\) | 1.62516e34 | 0.179356 | ||||||||
\(627\) | 5.78673e34 | 0.626021 | ||||||||
\(628\) | −5.93926e34 | −0.629850 | ||||||||
\(629\) | 1.16437e35 | 1.21048 | ||||||||
\(630\) | −3.95179e34 | −0.402752 | ||||||||
\(631\) | −3.76797e33 | −0.0376479 | −0.0188240 | − | 0.999823i | \(-0.505992\pi\) | ||||
−0.0188240 | + | 0.999823i | \(0.505992\pi\) | |||||||
\(632\) | 1.80637e34 | 0.176947 | ||||||||
\(633\) | −3.84002e34 | −0.368796 | ||||||||
\(634\) | 2.62342e34 | 0.247031 | ||||||||
\(635\) | −9.99154e34 | −0.922488 | ||||||||
\(636\) | 3.95882e34 | 0.358386 | ||||||||
\(637\) | −2.70801e35 | −2.40385 | ||||||||
\(638\) | −4.20521e34 | −0.366040 | ||||||||
\(639\) | 1.70239e34 | 0.145311 | ||||||||
\(640\) | −1.14205e34 | −0.0955950 | ||||||||
\(641\) | 6.21895e34 | 0.510495 | 0.255248 | − | 0.966876i | \(-0.417843\pi\) | ||||
0.255248 | + | 0.966876i | \(0.417843\pi\) | |||||||
\(642\) | −9.09802e34 | −0.732418 | ||||||||
\(643\) | −2.73698e34 | −0.216090 | −0.108045 | − | 0.994146i | \(-0.534459\pi\) | ||||
−0.108045 | + | 0.994146i | \(0.534459\pi\) | |||||||
\(644\) | 1.10020e35 | 0.851920 | ||||||||
\(645\) | −1.15891e35 | −0.880143 | ||||||||
\(646\) | 1.18667e35 | 0.883940 | ||||||||
\(647\) | −1.42584e35 | −1.04176 | −0.520879 | − | 0.853631i | \(-0.674396\pi\) | ||||
−0.520879 | + | 0.853631i | \(0.674396\pi\) | |||||||
\(648\) | −5.48151e33 | −0.0392837 | ||||||||
\(649\) | 2.14089e35 | 1.50500 | ||||||||
\(650\) | 2.79617e34 | 0.192818 | ||||||||
\(651\) | 1.42949e35 | 0.966985 | ||||||||
\(652\) | −1.08377e35 | −0.719189 | ||||||||
\(653\) | 2.51493e35 | 1.63724 | 0.818619 | − | 0.574337i | \(-0.194740\pi\) | ||||
0.818619 | + | 0.574337i | \(0.194740\pi\) | |||||||
\(654\) | −1.01142e35 | −0.645966 | ||||||||
\(655\) | 1.12336e34 | 0.0703885 | ||||||||
\(656\) | 1.44817e34 | 0.0890268 | ||||||||
\(657\) | −7.59205e34 | −0.457922 | ||||||||
\(658\) | 1.16375e34 | 0.0688709 | ||||||||
\(659\) | −1.23988e35 | −0.719968 | −0.359984 | − | 0.932959i | \(-0.617218\pi\) | ||||
−0.359984 | + | 0.932959i | \(0.617218\pi\) | |||||||
\(660\) | 4.99806e34 | 0.284775 | ||||||||
\(661\) | 2.28549e35 | 1.27779 | 0.638896 | − | 0.769293i | \(-0.279391\pi\) | ||||
0.638896 | + | 0.769293i | \(0.279391\pi\) | |||||||
\(662\) | −1.41699e35 | −0.777395 | ||||||||
\(663\) | 1.81192e35 | 0.975483 | ||||||||
\(664\) | −4.73138e34 | −0.249969 | ||||||||
\(665\) | 3.91779e35 | 2.03128 | ||||||||
\(666\) | 5.33223e34 | 0.271319 | ||||||||
\(667\) | 1.22563e35 | 0.612049 | ||||||||
\(668\) | −7.52344e34 | −0.368732 | ||||||||
\(669\) | −3.82626e34 | −0.184055 | ||||||||
\(670\) | −1.54436e34 | −0.0729145 | ||||||||
\(671\) | −1.16881e35 | −0.541640 | ||||||||
\(672\) | −3.54498e34 | −0.161249 | ||||||||
\(673\) | 2.09133e35 | 0.933756 | 0.466878 | − | 0.884322i | \(-0.345379\pi\) | ||||
0.466878 | + | 0.884322i | \(0.345379\pi\) | |||||||
\(674\) | 8.32866e34 | 0.365028 | ||||||||
\(675\) | 7.59169e33 | 0.0326619 | ||||||||
\(676\) | 1.87233e35 | 0.790767 | ||||||||
\(677\) | −3.93166e35 | −1.63011 | −0.815057 | − | 0.579380i | \(-0.803295\pi\) | ||||
−0.815057 | + | 0.579380i | \(0.803295\pi\) | |||||||
\(678\) | −7.12667e34 | −0.290078 | ||||||||
\(679\) | 1.50152e35 | 0.600011 | ||||||||
\(680\) | 1.02494e35 | 0.402102 | ||||||||
\(681\) | −2.19940e35 | −0.847160 | ||||||||
\(682\) | −1.80796e35 | −0.683730 | ||||||||
\(683\) | −1.01629e35 | −0.377364 | −0.188682 | − | 0.982038i | \(-0.560422\pi\) | ||||
−0.188682 | + | 0.982038i | \(0.560422\pi\) | |||||||
\(684\) | 5.43434e34 | 0.198128 | ||||||||
\(685\) | −2.05724e34 | −0.0736465 | ||||||||
\(686\) | −1.57676e35 | −0.554260 | ||||||||
\(687\) | −2.62408e35 | −0.905770 | ||||||||
\(688\) | −1.03961e35 | −0.352382 | ||||||||
\(689\) | −5.99268e35 | −1.99472 | ||||||||
\(690\) | −1.45671e35 | −0.476168 | ||||||||
\(691\) | 4.93084e35 | 1.58287 | 0.791435 | − | 0.611253i | \(-0.209334\pi\) | ||||
0.791435 | + | 0.611253i | \(0.209334\pi\) | |||||||
\(692\) | 2.04637e34 | 0.0645147 | ||||||||
\(693\) | 1.55142e35 | 0.480358 | ||||||||
\(694\) | −5.73692e34 | −0.174456 | ||||||||
\(695\) | 1.05793e35 | 0.315970 | ||||||||
\(696\) | −3.94912e34 | −0.115847 | ||||||||
\(697\) | −1.29967e35 | −0.374474 | ||||||||
\(698\) | 7.70217e34 | 0.217982 | ||||||||
\(699\) | 1.41230e35 | 0.392610 | ||||||||
\(700\) | 4.90967e34 | 0.134068 | ||||||||
\(701\) | 6.82364e35 | 1.83038 | 0.915189 | − | 0.403025i | \(-0.132041\pi\) | ||||
0.915189 | + | 0.403025i | \(0.132041\pi\) | |||||||
\(702\) | 8.29767e34 | 0.218646 | ||||||||
\(703\) | −5.28634e35 | −1.36840 | ||||||||
\(704\) | 4.48354e34 | 0.114015 | ||||||||
\(705\) | −1.54085e34 | −0.0384943 | ||||||||
\(706\) | 4.30655e35 | 1.05699 | ||||||||
\(707\) | −1.01101e36 | −2.43788 | ||||||||
\(708\) | 2.01052e35 | 0.476314 | ||||||||
\(709\) | −2.78374e35 | −0.647964 | −0.323982 | − | 0.946063i | \(-0.605022\pi\) | ||||
−0.323982 | + | 0.946063i | \(0.605022\pi\) | |||||||
\(710\) | −1.45772e35 | −0.333385 | ||||||||
\(711\) | −7.42398e34 | −0.166827 | ||||||||
\(712\) | 1.75836e35 | 0.388247 | ||||||||
\(713\) | 5.26940e35 | 1.14325 | ||||||||
\(714\) | 3.18146e35 | 0.678265 | ||||||||
\(715\) | −7.56585e35 | −1.58501 | ||||||||
\(716\) | −3.51076e35 | −0.722751 | ||||||||
\(717\) | −1.29524e35 | −0.262035 | ||||||||
\(718\) | 9.81024e34 | 0.195040 | ||||||||
\(719\) | 8.78510e35 | 1.71647 | 0.858234 | − | 0.513259i | \(-0.171562\pi\) | ||||
0.858234 | + | 0.513259i | \(0.171562\pi\) | |||||||
\(720\) | 4.69370e34 | 0.0901278 | ||||||||
\(721\) | −7.68337e35 | −1.44998 | ||||||||
\(722\) | −1.57516e35 | −0.292152 | ||||||||
\(723\) | −1.46406e35 | −0.266888 | ||||||||
\(724\) | −2.49805e34 | −0.0447579 | ||||||||
\(725\) | 5.46939e34 | 0.0963194 | ||||||||
\(726\) | 3.96304e34 | 0.0685995 | ||||||||
\(727\) | 8.08759e35 | 1.37607 | 0.688033 | − | 0.725680i | \(-0.258475\pi\) | ||||
0.688033 | + | 0.725680i | \(0.258475\pi\) | |||||||
\(728\) | 5.36624e35 | 0.897486 | ||||||||
\(729\) | 2.25284e34 | 0.0370370 | ||||||||
\(730\) | 6.50091e35 | 1.05060 | ||||||||
\(731\) | 9.33002e35 | 1.48223 | ||||||||
\(732\) | −1.09763e35 | −0.171422 | ||||||||
\(733\) | −2.44873e35 | −0.375960 | −0.187980 | − | 0.982173i | \(-0.560194\pi\) | ||||
−0.187980 | + | 0.982173i | \(0.560194\pi\) | |||||||
\(734\) | −4.78481e34 | −0.0722211 | ||||||||
\(735\) | 6.29565e35 | 0.934219 | ||||||||
\(736\) | −1.30675e35 | −0.190643 | ||||||||
\(737\) | 6.06296e34 | 0.0869644 | ||||||||
\(738\) | −5.95181e34 | −0.0839353 | ||||||||
\(739\) | 9.48378e35 | 1.31500 | 0.657500 | − | 0.753454i | \(-0.271614\pi\) | ||||
0.657500 | + | 0.753454i | \(0.271614\pi\) | |||||||
\(740\) | −4.56587e35 | −0.622482 | ||||||||
\(741\) | −8.22626e35 | −1.10274 | ||||||||
\(742\) | −1.05223e36 | −1.38695 | ||||||||
\(743\) | −5.64636e35 | −0.731827 | −0.365914 | − | 0.930649i | \(-0.619243\pi\) | ||||
−0.365914 | + | 0.930649i | \(0.619243\pi\) | |||||||
\(744\) | −1.69786e35 | −0.216392 | ||||||||
\(745\) | −1.45403e36 | −1.82230 | ||||||||
\(746\) | 2.57905e35 | 0.317852 | ||||||||
\(747\) | 1.94454e35 | 0.235673 | ||||||||
\(748\) | −4.02378e35 | −0.479584 | ||||||||
\(749\) | 2.41819e36 | 2.83445 | ||||||||
\(750\) | 3.18022e35 | 0.366599 | ||||||||
\(751\) | −2.89134e35 | −0.327793 | −0.163897 | − | 0.986478i | \(-0.552406\pi\) | ||||
−0.163897 | + | 0.986478i | \(0.552406\pi\) | |||||||
\(752\) | −1.38223e34 | −0.0154119 | ||||||||
\(753\) | 6.42317e35 | 0.704388 | ||||||||
\(754\) | 5.97801e35 | 0.644785 | ||||||||
\(755\) | 2.56036e35 | 0.271621 | ||||||||
\(756\) | 1.45695e35 | 0.152027 | ||||||||
\(757\) | −1.58236e36 | −1.62408 | −0.812040 | − | 0.583602i | \(-0.801643\pi\) | ||||
−0.812040 | + | 0.583602i | \(0.801643\pi\) | |||||||
\(758\) | −3.27022e35 | −0.330151 | ||||||||
\(759\) | 5.71886e35 | 0.567921 | ||||||||
\(760\) | −4.65331e35 | −0.454560 | ||||||||
\(761\) | −1.92995e36 | −1.85454 | −0.927272 | − | 0.374389i | \(-0.877853\pi\) | ||||
−0.927272 | + | 0.374389i | \(0.877853\pi\) | |||||||
\(762\) | 3.68368e35 | 0.348213 | ||||||||
\(763\) | 2.68828e36 | 2.49988 | ||||||||
\(764\) | −5.36108e35 | −0.490440 | ||||||||
\(765\) | −4.21239e35 | −0.379106 | ||||||||
\(766\) | −4.75966e35 | −0.421422 | ||||||||
\(767\) | −3.04344e36 | −2.65108 | ||||||||
\(768\) | 4.21051e34 | 0.0360844 | ||||||||
\(769\) | 1.00839e35 | 0.0850252 | 0.0425126 | − | 0.999096i | \(-0.486464\pi\) | ||||
0.0425126 | + | 0.999096i | \(0.486464\pi\) | |||||||
\(770\) | −1.32845e36 | −1.10208 | ||||||||
\(771\) | −1.20975e35 | −0.0987456 | ||||||||
\(772\) | 5.30876e35 | 0.426361 | ||||||||
\(773\) | 2.06169e36 | 1.62922 | 0.814610 | − | 0.580009i | \(-0.196951\pi\) | ||||
0.814610 | + | 0.580009i | \(0.196951\pi\) | |||||||
\(774\) | 4.27267e35 | 0.332229 | ||||||||
\(775\) | 2.35148e35 | 0.179916 | ||||||||
\(776\) | −1.78341e35 | −0.134270 | ||||||||
\(777\) | −1.41727e36 | −1.05000 | ||||||||
\(778\) | −7.95288e35 | −0.579802 | ||||||||
\(779\) | 5.90059e35 | 0.423328 | ||||||||
\(780\) | −7.10511e35 | −0.501636 | ||||||||
\(781\) | 5.72284e35 | 0.397625 | ||||||||
\(782\) | 1.17275e36 | 0.801903 | ||||||||
\(783\) | 1.62305e35 | 0.109222 | ||||||||
\(784\) | 5.64755e35 | 0.374032 | ||||||||
\(785\) | −2.09015e36 | −1.36241 | ||||||||
\(786\) | −4.14159e34 | −0.0265696 | ||||||||
\(787\) | −1.65623e36 | −1.04577 | −0.522885 | − | 0.852404i | \(-0.675144\pi\) | ||||
−0.522885 | + | 0.852404i | \(0.675144\pi\) | |||||||
\(788\) | −8.08802e35 | −0.502649 | ||||||||
\(789\) | 3.82227e34 | 0.0233807 | ||||||||
\(790\) | 6.35699e35 | 0.382748 | ||||||||
\(791\) | 1.89422e36 | 1.12260 | ||||||||
\(792\) | −1.84269e35 | −0.107495 | ||||||||
\(793\) | 1.66154e36 | 0.954106 | ||||||||
\(794\) | 6.39534e35 | 0.361499 | ||||||||
\(795\) | 1.39319e36 | 0.775214 | ||||||||
\(796\) | 1.61713e36 | 0.885793 | ||||||||
\(797\) | 1.70830e36 | 0.921163 | 0.460581 | − | 0.887618i | \(-0.347641\pi\) | ||||
0.460581 | + | 0.887618i | \(0.347641\pi\) | |||||||
\(798\) | −1.44441e36 | −0.766751 | ||||||||
\(799\) | 1.24049e35 | 0.0648274 | ||||||||
\(800\) | −5.83140e34 | −0.0300018 | ||||||||
\(801\) | −7.22667e35 | −0.366042 | ||||||||
\(802\) | −8.37231e35 | −0.417509 | ||||||||
\(803\) | −2.55217e36 | −1.25304 | ||||||||
\(804\) | 5.69375e34 | 0.0275231 | ||||||||
\(805\) | 3.87184e36 | 1.84276 | ||||||||
\(806\) | 2.57015e36 | 1.20440 | ||||||||
\(807\) | 1.37578e35 | 0.0634790 | ||||||||
\(808\) | 1.20082e36 | 0.545550 | ||||||||
\(809\) | 1.58337e36 | 0.708314 | 0.354157 | − | 0.935186i | \(-0.384768\pi\) | ||||
0.354157 | + | 0.935186i | \(0.384768\pi\) | |||||||
\(810\) | −1.92906e35 | −0.0849733 | ||||||||
\(811\) | 2.16537e36 | 0.939228 | 0.469614 | − | 0.882872i | \(-0.344393\pi\) | ||||
0.469614 | + | 0.882872i | \(0.344393\pi\) | |||||||
\(812\) | 1.04965e36 | 0.448327 | ||||||||
\(813\) | −5.44895e35 | −0.229182 | ||||||||
\(814\) | 1.79250e36 | 0.742429 | ||||||||
\(815\) | −3.81402e36 | −1.55565 | ||||||||
\(816\) | −3.77875e35 | −0.151782 | ||||||||
\(817\) | −4.23590e36 | −1.67560 | ||||||||
\(818\) | 2.37598e36 | 0.925608 | ||||||||
\(819\) | −2.20546e36 | −0.846158 | ||||||||
\(820\) | 5.09641e35 | 0.192571 | ||||||||
\(821\) | −3.49750e36 | −1.30157 | −0.650785 | − | 0.759262i | \(-0.725560\pi\) | ||||
−0.650785 | + | 0.759262i | \(0.725560\pi\) | |||||||
\(822\) | 7.58463e34 | 0.0277995 | ||||||||
\(823\) | −1.05634e36 | −0.381333 | −0.190666 | − | 0.981655i | \(-0.561065\pi\) | ||||
−0.190666 | + | 0.981655i | \(0.561065\pi\) | |||||||
\(824\) | 9.12583e35 | 0.324476 | ||||||||
\(825\) | 2.55205e35 | 0.0893748 | ||||||||
\(826\) | −5.34383e36 | −1.84333 | ||||||||
\(827\) | −2.02229e35 | −0.0687106 | −0.0343553 | − | 0.999410i | \(-0.510938\pi\) | ||||
−0.0343553 | + | 0.999410i | \(0.510938\pi\) | |||||||
\(828\) | 5.37061e35 | 0.179740 | ||||||||
\(829\) | 2.37604e36 | 0.783288 | 0.391644 | − | 0.920117i | \(-0.371906\pi\) | ||||
0.391644 | + | 0.920117i | \(0.371906\pi\) | |||||||
\(830\) | −1.66507e36 | −0.540700 | ||||||||
\(831\) | 2.62914e36 | 0.841010 | ||||||||
\(832\) | −6.37368e35 | −0.200839 | ||||||||
\(833\) | −5.06843e36 | −1.57330 | ||||||||
\(834\) | −3.90037e35 | −0.119270 | ||||||||
\(835\) | −2.64766e36 | −0.797592 | ||||||||
\(836\) | 1.82683e36 | 0.542150 | ||||||||
\(837\) | 6.97804e35 | 0.204016 | ||||||||
\(838\) | −3.93061e35 | −0.113217 | ||||||||
\(839\) | 2.93630e36 | 0.833252 | 0.416626 | − | 0.909078i | \(-0.363212\pi\) | ||||
0.416626 | + | 0.909078i | \(0.363212\pi\) | |||||||
\(840\) | −1.24755e36 | −0.348793 | ||||||||
\(841\) | −2.46105e36 | −0.677907 | ||||||||
\(842\) | −3.68329e36 | −0.999618 | ||||||||
\(843\) | −1.90835e36 | −0.510286 | ||||||||
\(844\) | −1.21227e36 | −0.319387 | ||||||||
\(845\) | 6.58913e36 | 1.71048 | ||||||||
\(846\) | 5.68081e34 | 0.0145305 | ||||||||
\(847\) | −1.05335e36 | −0.265479 | ||||||||
\(848\) | 1.24977e36 | 0.310372 | ||||||||
\(849\) | 2.40304e36 | 0.588050 | ||||||||
\(850\) | 5.23342e35 | 0.126197 | ||||||||
\(851\) | −5.22434e36 | −1.24140 | ||||||||
\(852\) | 5.37434e35 | 0.125843 | ||||||||
\(853\) | 4.86448e36 | 1.12247 | 0.561234 | − | 0.827657i | \(-0.310327\pi\) | ||||
0.561234 | + | 0.827657i | \(0.310327\pi\) | |||||||
\(854\) | 2.91742e36 | 0.663401 | ||||||||
\(855\) | 1.91246e36 | 0.428564 | ||||||||
\(856\) | −2.87218e36 | −0.634293 | ||||||||
\(857\) | 6.23674e36 | 1.35737 | 0.678684 | − | 0.734430i | \(-0.262551\pi\) | ||||
0.678684 | + | 0.734430i | \(0.262551\pi\) | |||||||
\(858\) | 2.78938e36 | 0.598296 | ||||||||
\(859\) | −2.04246e36 | −0.431758 | −0.215879 | − | 0.976420i | \(-0.569262\pi\) | ||||
−0.215879 | + | 0.976420i | \(0.569262\pi\) | |||||||
\(860\) | −3.65860e36 | −0.762226 | ||||||||
\(861\) | 1.58195e36 | 0.324828 | ||||||||
\(862\) | −1.99780e35 | −0.0404308 | ||||||||
\(863\) | 3.83159e36 | 0.764266 | 0.382133 | − | 0.924107i | \(-0.375190\pi\) | ||||
0.382133 | + | 0.924107i | \(0.375190\pi\) | |||||||
\(864\) | −1.73047e35 | −0.0340207 | ||||||||
\(865\) | 7.20162e35 | 0.139550 | ||||||||
\(866\) | 1.40724e36 | 0.268778 | ||||||||
\(867\) | 3.24511e35 | 0.0610929 | ||||||||
\(868\) | 4.51281e36 | 0.837434 | ||||||||
\(869\) | −2.49567e36 | −0.456500 | ||||||||
\(870\) | −1.38978e36 | −0.250585 | ||||||||
\(871\) | −8.61895e35 | −0.153189 | ||||||||
\(872\) | −3.19298e36 | −0.559423 | ||||||||
\(873\) | 7.32963e35 | 0.126591 | ||||||||
\(874\) | −5.32439e36 | −0.906519 | ||||||||
\(875\) | −8.45281e36 | −1.41873 | ||||||||
\(876\) | −2.39676e36 | −0.396572 | ||||||||
\(877\) | 8.65600e36 | 1.41196 | 0.705980 | − | 0.708232i | \(-0.250507\pi\) | ||||
0.705980 | + | 0.708232i | \(0.250507\pi\) | |||||||
\(878\) | −3.90227e36 | −0.627532 | ||||||||
\(879\) | 3.01330e36 | 0.477729 | ||||||||
\(880\) | 1.57785e36 | 0.246623 | ||||||||
\(881\) | 6.20228e36 | 0.955767 | 0.477884 | − | 0.878423i | \(-0.341404\pi\) | ||||
0.477884 | + | 0.878423i | \(0.341404\pi\) | |||||||
\(882\) | −2.32108e36 | −0.352641 | ||||||||
\(883\) | −1.95836e35 | −0.0293349 | −0.0146675 | − | 0.999892i | \(-0.504669\pi\) | ||||
−0.0146675 | + | 0.999892i | \(0.504669\pi\) | |||||||
\(884\) | 5.72010e36 | 0.844793 | ||||||||
\(885\) | 7.07545e36 | 1.03030 | ||||||||
\(886\) | −1.35721e36 | −0.194861 | ||||||||
\(887\) | 6.06391e36 | 0.858434 | 0.429217 | − | 0.903201i | \(-0.358789\pi\) | ||||
0.429217 | + | 0.903201i | \(0.358789\pi\) | |||||||
\(888\) | 1.68335e36 | 0.234969 | ||||||||
\(889\) | −9.79098e36 | −1.34758 | ||||||||
\(890\) | 6.18804e36 | 0.839804 | ||||||||
\(891\) | 7.57324e35 | 0.101347 | ||||||||
\(892\) | −1.20792e36 | −0.159396 | ||||||||
\(893\) | −5.63192e35 | −0.0732847 | ||||||||
\(894\) | 5.36071e36 | 0.687865 | ||||||||
\(895\) | −1.23551e37 | −1.56336 | ||||||||
\(896\) | −1.11913e36 | −0.139646 | ||||||||
\(897\) | −8.12979e36 | −1.00040 | ||||||||
\(898\) | 4.24385e36 | 0.514999 | ||||||||
\(899\) | 5.02729e36 | 0.601641 | ||||||||
\(900\) | 2.39664e35 | 0.0282860 | ||||||||
\(901\) | −1.12161e37 | −1.30552 | ||||||||
\(902\) | −2.00078e36 | −0.229678 | ||||||||
\(903\) | −1.13565e37 | −1.28572 | ||||||||
\(904\) | −2.24984e36 | −0.251215 | ||||||||
\(905\) | −8.79118e35 | −0.0968144 | ||||||||
\(906\) | −9.43953e35 | −0.102529 | ||||||||
\(907\) | 7.32294e36 | 0.784503 | 0.392251 | − | 0.919858i | \(-0.371696\pi\) | ||||
0.392251 | + | 0.919858i | \(0.371696\pi\) | |||||||
\(908\) | −6.94335e36 | −0.733662 | ||||||||
\(909\) | −4.93522e36 | −0.514350 | ||||||||
\(910\) | 1.88849e37 | 1.94132 | ||||||||
\(911\) | 7.08337e36 | 0.718225 | 0.359112 | − | 0.933294i | \(-0.383079\pi\) | ||||
0.359112 | + | 0.933294i | \(0.383079\pi\) | |||||||
\(912\) | 1.71558e36 | 0.171584 | ||||||||
\(913\) | 6.53686e36 | 0.644888 | ||||||||
\(914\) | −9.67081e36 | −0.941099 | ||||||||
\(915\) | −3.86279e36 | −0.370798 | ||||||||
\(916\) | −8.28404e36 | −0.784420 | ||||||||
\(917\) | 1.10081e36 | 0.102824 | ||||||||
\(918\) | 1.55302e36 | 0.143102 | ||||||||
\(919\) | 6.34698e36 | 0.576930 | 0.288465 | − | 0.957490i | \(-0.406855\pi\) | ||||
0.288465 | + | 0.957490i | \(0.406855\pi\) | |||||||
\(920\) | −4.59874e36 | −0.412373 | ||||||||
\(921\) | −1.09073e37 | −0.964880 | ||||||||
\(922\) | 1.58307e36 | 0.138154 | ||||||||
\(923\) | −8.13544e36 | −0.700422 | ||||||||
\(924\) | 4.89774e36 | 0.416002 | ||||||||
\(925\) | −2.33137e36 | −0.195362 | ||||||||
\(926\) | 4.65678e36 | 0.384989 | ||||||||
\(927\) | −3.75062e36 | −0.305919 | ||||||||
\(928\) | −1.24671e36 | −0.100327 | ||||||||
\(929\) | −2.21142e37 | −1.75580 | −0.877900 | − | 0.478844i | \(-0.841056\pi\) | ||||
−0.877900 | + | 0.478844i | \(0.841056\pi\) | |||||||
\(930\) | −5.97514e36 | −0.468071 | ||||||||
\(931\) | 2.30111e37 | 1.77855 | ||||||||
\(932\) | 4.45852e36 | 0.340010 | ||||||||
\(933\) | 1.24249e37 | 0.934919 | ||||||||
\(934\) | 5.66738e36 | 0.420772 | ||||||||
\(935\) | −1.41605e37 | −1.03737 | ||||||||
\(936\) | 2.61951e36 | 0.189353 | ||||||||
\(937\) | −2.06870e37 | −1.47554 | −0.737772 | − | 0.675050i | \(-0.764122\pi\) | ||||
−0.737772 | + | 0.675050i | \(0.764122\pi\) | |||||||
\(938\) | −1.51336e36 | −0.106514 | ||||||||
\(939\) | −2.10858e36 | −0.146444 | ||||||||
\(940\) | −4.86436e35 | −0.0333371 | ||||||||
\(941\) | 1.47946e37 | 1.00054 | 0.500268 | − | 0.865870i | \(-0.333235\pi\) | ||||
0.500268 | + | 0.865870i | \(0.333235\pi\) | |||||||
\(942\) | 7.70597e36 | 0.514270 | ||||||||
\(943\) | 5.83139e36 | 0.384040 | ||||||||
\(944\) | 6.34708e36 | 0.412500 | ||||||||
\(945\) | 5.12731e36 | 0.328845 | ||||||||
\(946\) | 1.43632e37 | 0.909100 | ||||||||
\(947\) | 1.88544e37 | 1.17771 | 0.588853 | − | 0.808240i | \(-0.299580\pi\) | ||||
0.588853 | + | 0.808240i | \(0.299580\pi\) | |||||||
\(948\) | −2.34370e36 | −0.144477 | ||||||||
\(949\) | 3.62810e37 | 2.20725 | ||||||||
\(950\) | −2.37602e36 | −0.142661 | ||||||||
\(951\) | −3.40379e36 | −0.201700 | ||||||||
\(952\) | 1.00437e37 | 0.587395 | ||||||||
\(953\) | 8.92812e35 | 0.0515346 | 0.0257673 | − | 0.999668i | \(-0.491797\pi\) | ||||
0.0257673 | + | 0.999668i | \(0.491797\pi\) | |||||||
\(954\) | −5.13642e36 | −0.292621 | ||||||||
\(955\) | −1.88668e37 | −1.06085 | ||||||||
\(956\) | −4.08897e36 | −0.226929 | ||||||||
\(957\) | 5.45610e36 | 0.298871 | ||||||||
\(958\) | −9.19734e36 | −0.497271 | ||||||||
\(959\) | −2.01594e36 | −0.107583 | ||||||||
\(960\) | 1.48177e36 | 0.0780530 | ||||||||
\(961\) | 2.38125e36 | 0.123812 | ||||||||
\(962\) | −2.54818e37 | −1.30780 | ||||||||
\(963\) | 1.18043e37 | 0.598017 | ||||||||
\(964\) | −4.62192e36 | −0.231132 | ||||||||
\(965\) | 1.86827e37 | 0.922247 | ||||||||
\(966\) | −1.42747e37 | −0.695590 | ||||||||
\(967\) | −5.32831e36 | −0.256306 | −0.128153 | − | 0.991754i | \(-0.540905\pi\) | ||||
−0.128153 | + | 0.991754i | \(0.540905\pi\) | |||||||
\(968\) | 1.25110e36 | 0.0594089 | ||||||||
\(969\) | −1.53966e37 | −0.721734 | ||||||||
\(970\) | −6.27621e36 | −0.290436 | ||||||||
\(971\) | 3.40804e37 | 1.55691 | 0.778456 | − | 0.627699i | \(-0.216003\pi\) | ||||
0.778456 | + | 0.627699i | \(0.216003\pi\) | |||||||
\(972\) | 7.11206e35 | 0.0320750 | ||||||||
\(973\) | 1.03669e37 | 0.461571 | ||||||||
\(974\) | −2.13861e37 | −0.940036 | ||||||||
\(975\) | −3.62793e36 | −0.157435 | ||||||||
\(976\) | −3.46514e36 | −0.148456 | ||||||||
\(977\) | −4.16179e37 | −1.76035 | −0.880173 | − | 0.474653i | \(-0.842573\pi\) | ||||
−0.880173 | + | 0.474653i | \(0.842573\pi\) | |||||||
\(978\) | 1.40615e37 | 0.587215 | ||||||||
\(979\) | −2.42935e37 | −1.00163 | ||||||||
\(980\) | 1.98749e37 | 0.809057 | ||||||||
\(981\) | 1.31228e37 | 0.527429 | ||||||||
\(982\) | −1.04603e37 | −0.415099 | ||||||||
\(983\) | 1.59521e37 | 0.625026 | 0.312513 | − | 0.949913i | \(-0.398829\pi\) | ||||
0.312513 | + | 0.949913i | \(0.398829\pi\) | |||||||
\(984\) | −1.87894e36 | −0.0726901 | ||||||||
\(985\) | −2.84634e37 | −1.08726 | ||||||||
\(986\) | 1.11887e37 | 0.422005 | ||||||||
\(987\) | −1.50992e36 | −0.0562328 | ||||||||
\(988\) | −2.59697e37 | −0.955004 | ||||||||
\(989\) | −4.18623e37 | −1.52009 | ||||||||
\(990\) | −6.48480e36 | −0.232518 | ||||||||
\(991\) | 3.15449e36 | 0.111689 | 0.0558443 | − | 0.998439i | \(-0.482215\pi\) | ||||
0.0558443 | + | 0.998439i | \(0.482215\pi\) | |||||||
\(992\) | −5.36004e36 | −0.187401 | ||||||||
\(993\) | 1.83849e37 | 0.634741 | ||||||||
\(994\) | −1.42846e37 | −0.487011 | ||||||||
\(995\) | 5.69103e37 | 1.91603 | ||||||||
\(996\) | 6.13879e36 | 0.204099 | ||||||||
\(997\) | 1.19794e37 | 0.393321 | 0.196660 | − | 0.980472i | \(-0.436990\pi\) | ||||
0.196660 | + | 0.980472i | \(0.436990\pi\) | |||||||
\(998\) | −2.96174e36 | −0.0960317 | ||||||||
\(999\) | −6.91837e36 | −0.221531 |
(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 | 6.26.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.26.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 48.26.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.26.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
18.26.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
48.26.a.a.1.1 | 1 | 4.3 | odd | 2 |