Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,8,Mod(1,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.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: | \(23.1164918858\) |
Analytic rank: | \(1\) |
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: |
\( x^{4} - 2x^{3} - 2177x^{2} - 14018x + 634476 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(47.8378\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | 22.3907 | 0.478788 | 0.239394 | − | 0.970922i | \(-0.423051\pi\) | ||||
0.239394 | + | 0.970922i | \(0.423051\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −504.619 | −1.80538 | −0.902689 | − | 0.430293i | \(-0.858410\pi\) | ||||
−0.902689 | + | 0.430293i | \(0.858410\pi\) | |||||||
\(6\) | 179.126 | 0.338554 | ||||||||
\(7\) | 892.385 | 0.983352 | 0.491676 | − | 0.870778i | \(-0.336384\pi\) | ||||
0.491676 | + | 0.870778i | \(0.336384\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | −1685.66 | −0.770762 | ||||||||
\(10\) | −4036.95 | −1.27660 | ||||||||
\(11\) | 4703.14 | 1.06540 | 0.532701 | − | 0.846303i | \(-0.321177\pi\) | ||||
0.532701 | + | 0.846303i | \(0.321177\pi\) | |||||||
\(12\) | 1433.01 | 0.239394 | ||||||||
\(13\) | −11843.3 | −1.49511 | −0.747553 | − | 0.664202i | \(-0.768771\pi\) | ||||
−0.747553 | + | 0.664202i | \(0.768771\pi\) | |||||||
\(14\) | 7139.08 | 0.695335 | ||||||||
\(15\) | −11298.8 | −0.864394 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −22642.5 | −1.11777 | −0.558885 | − | 0.829245i | \(-0.688771\pi\) | ||||
−0.558885 | + | 0.829245i | \(0.688771\pi\) | |||||||
\(18\) | −13485.2 | −0.545011 | ||||||||
\(19\) | −51600.8 | −1.72591 | −0.862956 | − | 0.505279i | \(-0.831390\pi\) | ||||
−0.862956 | + | 0.505279i | \(0.831390\pi\) | |||||||
\(20\) | −32295.6 | −0.902689 | ||||||||
\(21\) | 19981.1 | 0.470818 | ||||||||
\(22\) | 37625.1 | 0.753353 | ||||||||
\(23\) | −72804.0 | −1.24769 | −0.623847 | − | 0.781547i | \(-0.714431\pi\) | ||||
−0.623847 | + | 0.781547i | \(0.714431\pi\) | |||||||
\(24\) | 11464.0 | 0.169277 | ||||||||
\(25\) | 176515. | 2.25939 | ||||||||
\(26\) | −94746.6 | −1.05720 | ||||||||
\(27\) | −86711.5 | −0.847820 | ||||||||
\(28\) | 57112.7 | 0.491676 | ||||||||
\(29\) | 162871. | 1.24008 | 0.620041 | − | 0.784570i | \(-0.287116\pi\) | ||||
0.620041 | + | 0.784570i | \(0.287116\pi\) | |||||||
\(30\) | −90390.2 | −0.611219 | ||||||||
\(31\) | −20354.2 | −0.122712 | −0.0613560 | − | 0.998116i | \(-0.519543\pi\) | ||||
−0.0613560 | + | 0.998116i | \(0.519543\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | 105307. | 0.510102 | ||||||||
\(34\) | −181140. | −0.790383 | ||||||||
\(35\) | −450314. | −1.77532 | ||||||||
\(36\) | −107882. | −0.385381 | ||||||||
\(37\) | −50653.0 | −0.164399 | ||||||||
\(38\) | −412806. | −1.22040 | ||||||||
\(39\) | −265180. | −0.715839 | ||||||||
\(40\) | −258365. | −0.638298 | ||||||||
\(41\) | −540030. | −1.22370 | −0.611849 | − | 0.790975i | \(-0.709574\pi\) | ||||
−0.611849 | + | 0.790975i | \(0.709574\pi\) | |||||||
\(42\) | 159849. | 0.332918 | ||||||||
\(43\) | 158658. | 0.304314 | 0.152157 | − | 0.988356i | \(-0.451378\pi\) | ||||
0.152157 | + | 0.988356i | \(0.451378\pi\) | |||||||
\(44\) | 301001. | 0.532701 | ||||||||
\(45\) | 850613. | 1.39152 | ||||||||
\(46\) | −582432. | −0.882252 | ||||||||
\(47\) | 470210. | 0.660617 | 0.330308 | − | 0.943873i | \(-0.392847\pi\) | ||||
0.330308 | + | 0.943873i | \(0.392847\pi\) | |||||||
\(48\) | 91712.4 | 0.119697 | ||||||||
\(49\) | −27191.7 | −0.0330179 | ||||||||
\(50\) | 1.41212e6 | 1.59763 | ||||||||
\(51\) | −506981. | −0.535175 | ||||||||
\(52\) | −757973. | −0.747553 | ||||||||
\(53\) | 1.52235e6 | 1.40458 | 0.702292 | − | 0.711889i | \(-0.252160\pi\) | ||||
0.702292 | + | 0.711889i | \(0.252160\pi\) | |||||||
\(54\) | −693692. | −0.599499 | ||||||||
\(55\) | −2.37329e6 | −1.92346 | ||||||||
\(56\) | 456901. | 0.347668 | ||||||||
\(57\) | −1.15538e6 | −0.826346 | ||||||||
\(58\) | 1.30297e6 | 0.876870 | ||||||||
\(59\) | 1.33575e6 | 0.846725 | 0.423362 | − | 0.905960i | \(-0.360850\pi\) | ||||
0.423362 | + | 0.905960i | \(0.360850\pi\) | |||||||
\(60\) | −723121. | −0.432197 | ||||||||
\(61\) | −3.08165e6 | −1.73832 | −0.869159 | − | 0.494532i | \(-0.835339\pi\) | ||||
−0.869159 | + | 0.494532i | \(0.835339\pi\) | |||||||
\(62\) | −162833. | −0.0867705 | ||||||||
\(63\) | −1.50425e6 | −0.757930 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 5.97636e6 | 2.69923 | ||||||||
\(66\) | 842454. | 0.360697 | ||||||||
\(67\) | 202860. | 0.0824015 | 0.0412008 | − | 0.999151i | \(-0.486882\pi\) | ||||
0.0412008 | + | 0.999151i | \(0.486882\pi\) | |||||||
\(68\) | −1.44912e6 | −0.558885 | ||||||||
\(69\) | −1.63013e6 | −0.597381 | ||||||||
\(70\) | −3.60251e6 | −1.25534 | ||||||||
\(71\) | −1.68686e6 | −0.559338 | −0.279669 | − | 0.960096i | \(-0.590225\pi\) | ||||
−0.279669 | + | 0.960096i | \(0.590225\pi\) | |||||||
\(72\) | −863056. | −0.272505 | ||||||||
\(73\) | 3.90554e6 | 1.17504 | 0.587518 | − | 0.809211i | \(-0.300105\pi\) | ||||
0.587518 | + | 0.809211i | \(0.300105\pi\) | |||||||
\(74\) | −405224. | −0.116248 | ||||||||
\(75\) | 3.95230e6 | 1.08177 | ||||||||
\(76\) | −3.30245e6 | −0.862956 | ||||||||
\(77\) | 4.19702e6 | 1.04767 | ||||||||
\(78\) | −2.12144e6 | −0.506175 | ||||||||
\(79\) | 4.25515e6 | 0.971001 | 0.485501 | − | 0.874236i | \(-0.338637\pi\) | ||||
0.485501 | + | 0.874236i | \(0.338637\pi\) | |||||||
\(80\) | −2.06692e6 | −0.451345 | ||||||||
\(81\) | 1.74500e6 | 0.364835 | ||||||||
\(82\) | −4.32024e6 | −0.865285 | ||||||||
\(83\) | 2.69308e6 | 0.516982 | 0.258491 | − | 0.966014i | \(-0.416775\pi\) | ||||
0.258491 | + | 0.966014i | \(0.416775\pi\) | |||||||
\(84\) | 1.27879e6 | 0.235409 | ||||||||
\(85\) | 1.14258e7 | 2.01800 | ||||||||
\(86\) | 1.26926e6 | 0.215182 | ||||||||
\(87\) | 3.64679e6 | 0.593736 | ||||||||
\(88\) | 2.40801e6 | 0.376677 | ||||||||
\(89\) | 6.50359e6 | 0.977885 | 0.488943 | − | 0.872316i | \(-0.337383\pi\) | ||||
0.488943 | + | 0.872316i | \(0.337383\pi\) | |||||||
\(90\) | 6.80491e6 | 0.983951 | ||||||||
\(91\) | −1.05688e7 | −1.47022 | ||||||||
\(92\) | −4.65946e6 | −0.623847 | ||||||||
\(93\) | −455744. | −0.0587531 | ||||||||
\(94\) | 3.76168e6 | 0.467127 | ||||||||
\(95\) | 2.60387e7 | 3.11592 | ||||||||
\(96\) | 733699. | 0.0846386 | ||||||||
\(97\) | −7.24155e6 | −0.805620 | −0.402810 | − | 0.915284i | \(-0.631966\pi\) | ||||
−0.402810 | + | 0.915284i | \(0.631966\pi\) | |||||||
\(98\) | −217533. | −0.0233472 | ||||||||
\(99\) | −7.92788e6 | −0.821172 | ||||||||
\(100\) | 1.12970e7 | 1.12970 | ||||||||
\(101\) | −1.45545e7 | −1.40563 | −0.702815 | − | 0.711372i | \(-0.748074\pi\) | ||||
−0.702815 | + | 0.711372i | \(0.748074\pi\) | |||||||
\(102\) | −4.05585e6 | −0.378426 | ||||||||
\(103\) | −1.89626e7 | −1.70989 | −0.854946 | − | 0.518717i | \(-0.826410\pi\) | ||||
−0.854946 | + | 0.518717i | \(0.826410\pi\) | |||||||
\(104\) | −6.06378e6 | −0.528600 | ||||||||
\(105\) | −1.00829e7 | −0.850004 | ||||||||
\(106\) | 1.21788e7 | 0.993191 | ||||||||
\(107\) | 1.11941e6 | 0.0883374 | 0.0441687 | − | 0.999024i | \(-0.485936\pi\) | ||||
0.0441687 | + | 0.999024i | \(0.485936\pi\) | |||||||
\(108\) | −5.54954e6 | −0.423910 | ||||||||
\(109\) | 4.69508e6 | 0.347256 | 0.173628 | − | 0.984811i | \(-0.444451\pi\) | ||||
0.173628 | + | 0.984811i | \(0.444451\pi\) | |||||||
\(110\) | −1.89863e7 | −1.36009 | ||||||||
\(111\) | −1.13416e6 | −0.0787123 | ||||||||
\(112\) | 3.65521e6 | 0.245838 | ||||||||
\(113\) | 1.57905e7 | 1.02949 | 0.514745 | − | 0.857343i | \(-0.327887\pi\) | ||||
0.514745 | + | 0.857343i | \(0.327887\pi\) | |||||||
\(114\) | −9.24303e6 | −0.584315 | ||||||||
\(115\) | 3.67383e7 | 2.25256 | ||||||||
\(116\) | 1.04237e7 | 0.620041 | ||||||||
\(117\) | 1.99638e7 | 1.15237 | ||||||||
\(118\) | 1.06860e7 | 0.598725 | ||||||||
\(119\) | −2.02058e7 | −1.09916 | ||||||||
\(120\) | −5.78497e6 | −0.305609 | ||||||||
\(121\) | 2.63238e6 | 0.135083 | ||||||||
\(122\) | −2.46532e7 | −1.22918 | ||||||||
\(123\) | −1.20916e7 | −0.585892 | ||||||||
\(124\) | −1.30267e6 | −0.0613560 | ||||||||
\(125\) | −4.96494e7 | −2.27368 | ||||||||
\(126\) | −1.20340e7 | −0.535938 | ||||||||
\(127\) | −2.06929e7 | −0.896415 | −0.448208 | − | 0.893930i | \(-0.647937\pi\) | ||||
−0.448208 | + | 0.893930i | \(0.647937\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | 3.55246e6 | 0.145702 | ||||||||
\(130\) | 4.78109e7 | 1.90864 | ||||||||
\(131\) | 1.60306e7 | 0.623017 | 0.311508 | − | 0.950243i | \(-0.399166\pi\) | ||||
0.311508 | + | 0.950243i | \(0.399166\pi\) | |||||||
\(132\) | 6.73963e6 | 0.255051 | ||||||||
\(133\) | −4.60478e7 | −1.69718 | ||||||||
\(134\) | 1.62288e6 | 0.0582667 | ||||||||
\(135\) | 4.37563e7 | 1.53064 | ||||||||
\(136\) | −1.15929e7 | −0.395192 | ||||||||
\(137\) | −3.82499e7 | −1.27089 | −0.635446 | − | 0.772145i | \(-0.719184\pi\) | ||||
−0.635446 | + | 0.772145i | \(0.719184\pi\) | |||||||
\(138\) | −1.30411e7 | −0.422412 | ||||||||
\(139\) | 2.59639e7 | 0.820009 | 0.410004 | − | 0.912084i | \(-0.365527\pi\) | ||||
0.410004 | + | 0.912084i | \(0.365527\pi\) | |||||||
\(140\) | −2.88201e7 | −0.887662 | ||||||||
\(141\) | 1.05283e7 | 0.316296 | ||||||||
\(142\) | −1.34949e7 | −0.395512 | ||||||||
\(143\) | −5.57008e7 | −1.59289 | ||||||||
\(144\) | −6.90445e6 | −0.192690 | ||||||||
\(145\) | −8.21876e7 | −2.23882 | ||||||||
\(146\) | 3.12443e7 | 0.830876 | ||||||||
\(147\) | −608840. | −0.0158086 | ||||||||
\(148\) | −3.24179e6 | −0.0821995 | ||||||||
\(149\) | 2.14478e7 | 0.531168 | 0.265584 | − | 0.964088i | \(-0.414435\pi\) | ||||
0.265584 | + | 0.964088i | \(0.414435\pi\) | |||||||
\(150\) | 3.16184e7 | 0.764927 | ||||||||
\(151\) | −7.61861e7 | −1.80076 | −0.900382 | − | 0.435101i | \(-0.856713\pi\) | ||||
−0.900382 | + | 0.435101i | \(0.856713\pi\) | |||||||
\(152\) | −2.64196e7 | −0.610202 | ||||||||
\(153\) | 3.81674e7 | 0.861535 | ||||||||
\(154\) | 3.35761e7 | 0.740812 | ||||||||
\(155\) | 1.02711e7 | 0.221542 | ||||||||
\(156\) | −1.69715e7 | −0.357920 | ||||||||
\(157\) | 4.99325e6 | 0.102976 | 0.0514878 | − | 0.998674i | \(-0.483604\pi\) | ||||
0.0514878 | + | 0.998674i | \(0.483604\pi\) | |||||||
\(158\) | 3.40412e7 | 0.686602 | ||||||||
\(159\) | 3.40864e7 | 0.672499 | ||||||||
\(160\) | −1.65353e7 | −0.319149 | ||||||||
\(161\) | −6.49692e7 | −1.22692 | ||||||||
\(162\) | 1.39600e7 | 0.257978 | ||||||||
\(163\) | −7.53673e7 | −1.36310 | −0.681548 | − | 0.731774i | \(-0.738693\pi\) | ||||
−0.681548 | + | 0.731774i | \(0.738693\pi\) | |||||||
\(164\) | −3.45619e7 | −0.611849 | ||||||||
\(165\) | −5.31397e7 | −0.920928 | ||||||||
\(166\) | 2.15446e7 | 0.365562 | ||||||||
\(167\) | 1.76591e7 | 0.293401 | 0.146701 | − | 0.989181i | \(-0.453135\pi\) | ||||
0.146701 | + | 0.989181i | \(0.453135\pi\) | |||||||
\(168\) | 1.02303e7 | 0.166459 | ||||||||
\(169\) | 7.75158e7 | 1.23534 | ||||||||
\(170\) | 9.14065e7 | 1.42694 | ||||||||
\(171\) | 8.69812e7 | 1.33027 | ||||||||
\(172\) | 1.01541e7 | 0.152157 | ||||||||
\(173\) | 5.17704e7 | 0.760187 | 0.380093 | − | 0.924948i | \(-0.375892\pi\) | ||||
0.380093 | + | 0.924948i | \(0.375892\pi\) | |||||||
\(174\) | 2.91743e7 | 0.419835 | ||||||||
\(175\) | 1.57519e8 | 2.22178 | ||||||||
\(176\) | 1.92641e7 | 0.266351 | ||||||||
\(177\) | 2.99083e7 | 0.405402 | ||||||||
\(178\) | 5.20287e7 | 0.691469 | ||||||||
\(179\) | 3.40585e7 | 0.443853 | 0.221927 | − | 0.975063i | \(-0.428765\pi\) | ||||
0.221927 | + | 0.975063i | \(0.428765\pi\) | |||||||
\(180\) | 5.44393e7 | 0.695758 | ||||||||
\(181\) | 9.39883e7 | 1.17814 | 0.589072 | − | 0.808080i | \(-0.299493\pi\) | ||||
0.589072 | + | 0.808080i | \(0.299493\pi\) | |||||||
\(182\) | −8.45505e7 | −1.03960 | ||||||||
\(183\) | −6.90004e7 | −0.832287 | ||||||||
\(184\) | −3.72756e7 | −0.441126 | ||||||||
\(185\) | 2.55604e7 | 0.296802 | ||||||||
\(186\) | −3.64595e6 | −0.0415447 | ||||||||
\(187\) | −1.06491e8 | −1.19088 | ||||||||
\(188\) | 3.00935e7 | 0.330308 | ||||||||
\(189\) | −7.73801e7 | −0.833706 | ||||||||
\(190\) | 2.08310e8 | 2.20329 | ||||||||
\(191\) | −7.50093e7 | −0.778930 | −0.389465 | − | 0.921041i | \(-0.627340\pi\) | ||||
−0.389465 | + | 0.921041i | \(0.627340\pi\) | |||||||
\(192\) | 5.86959e6 | 0.0598485 | ||||||||
\(193\) | −4.91473e7 | −0.492095 | −0.246047 | − | 0.969258i | \(-0.579132\pi\) | ||||
−0.246047 | + | 0.969258i | \(0.579132\pi\) | |||||||
\(194\) | −5.79324e7 | −0.569659 | ||||||||
\(195\) | 1.33815e8 | 1.29236 | ||||||||
\(196\) | −1.74027e6 | −0.0165089 | ||||||||
\(197\) | −1.33349e8 | −1.24268 | −0.621339 | − | 0.783542i | \(-0.713411\pi\) | ||||
−0.621339 | + | 0.783542i | \(0.713411\pi\) | |||||||
\(198\) | −6.34231e7 | −0.580656 | ||||||||
\(199\) | −8.34957e7 | −0.751066 | −0.375533 | − | 0.926809i | \(-0.622540\pi\) | ||||
−0.375533 | + | 0.926809i | \(0.622540\pi\) | |||||||
\(200\) | 9.03756e7 | 0.798815 | ||||||||
\(201\) | 4.54219e6 | 0.0394529 | ||||||||
\(202\) | −1.16436e8 | −0.993931 | ||||||||
\(203\) | 1.45343e8 | 1.21944 | ||||||||
\(204\) | −3.24468e7 | −0.267588 | ||||||||
\(205\) | 2.72509e8 | 2.20924 | ||||||||
\(206\) | −1.51701e8 | −1.20908 | ||||||||
\(207\) | 1.22722e8 | 0.961674 | ||||||||
\(208\) | −4.85103e7 | −0.373776 | ||||||||
\(209\) | −2.42686e8 | −1.83879 | ||||||||
\(210\) | −8.06628e7 | −0.601044 | ||||||||
\(211\) | −5.17239e7 | −0.379056 | −0.189528 | − | 0.981875i | \(-0.560696\pi\) | ||||
−0.189528 | + | 0.981875i | \(0.560696\pi\) | |||||||
\(212\) | 9.74302e7 | 0.702292 | ||||||||
\(213\) | −3.77700e7 | −0.267805 | ||||||||
\(214\) | 8.95525e6 | 0.0624640 | ||||||||
\(215\) | −8.00617e7 | −0.549402 | ||||||||
\(216\) | −4.43963e7 | −0.299750 | ||||||||
\(217\) | −1.81637e7 | −0.120669 | ||||||||
\(218\) | 3.75606e7 | 0.245547 | ||||||||
\(219\) | 8.74478e7 | 0.562593 | ||||||||
\(220\) | −1.51891e8 | −0.961728 | ||||||||
\(221\) | 2.68162e8 | 1.67119 | ||||||||
\(222\) | −9.07325e6 | −0.0556580 | ||||||||
\(223\) | −1.88593e8 | −1.13883 | −0.569414 | − | 0.822051i | \(-0.692830\pi\) | ||||
−0.569414 | + | 0.822051i | \(0.692830\pi\) | |||||||
\(224\) | 2.92417e7 | 0.173834 | ||||||||
\(225\) | −2.97543e8 | −1.74145 | ||||||||
\(226\) | 1.26324e8 | 0.727959 | ||||||||
\(227\) | 3.12875e8 | 1.77533 | 0.887667 | − | 0.460486i | \(-0.152325\pi\) | ||||
0.887667 | + | 0.460486i | \(0.152325\pi\) | |||||||
\(228\) | −7.39442e7 | −0.413173 | ||||||||
\(229\) | −2.14457e8 | −1.18009 | −0.590046 | − | 0.807370i | \(-0.700890\pi\) | ||||
−0.590046 | + | 0.807370i | \(0.700890\pi\) | |||||||
\(230\) | 2.93906e8 | 1.59280 | ||||||||
\(231\) | 9.39742e7 | 0.501610 | ||||||||
\(232\) | 8.33898e7 | 0.438435 | ||||||||
\(233\) | 7.68437e7 | 0.397981 | 0.198991 | − | 0.980001i | \(-0.436234\pi\) | ||||
0.198991 | + | 0.980001i | \(0.436234\pi\) | |||||||
\(234\) | 1.59710e8 | 0.814849 | ||||||||
\(235\) | −2.37277e8 | −1.19266 | ||||||||
\(236\) | 8.54878e7 | 0.423362 | ||||||||
\(237\) | 9.52758e7 | 0.464904 | ||||||||
\(238\) | −1.61646e8 | −0.777225 | ||||||||
\(239\) | −1.96745e8 | −0.932206 | −0.466103 | − | 0.884730i | \(-0.654342\pi\) | ||||
−0.466103 | + | 0.884730i | \(0.654342\pi\) | |||||||
\(240\) | −4.62798e7 | −0.216099 | ||||||||
\(241\) | 1.30039e8 | 0.598430 | 0.299215 | − | 0.954186i | \(-0.403275\pi\) | ||||
0.299215 | + | 0.954186i | \(0.403275\pi\) | |||||||
\(242\) | 2.10591e7 | 0.0955181 | ||||||||
\(243\) | 2.28710e8 | 1.02250 | ||||||||
\(244\) | −1.97226e8 | −0.869159 | ||||||||
\(245\) | 1.37214e7 | 0.0596098 | ||||||||
\(246\) | −9.67332e7 | −0.414288 | ||||||||
\(247\) | 6.11125e8 | 2.58042 | ||||||||
\(248\) | −1.04213e7 | −0.0433853 | ||||||||
\(249\) | 6.03000e7 | 0.247525 | ||||||||
\(250\) | −3.97195e8 | −1.60773 | ||||||||
\(251\) | −4.56690e8 | −1.82290 | −0.911452 | − | 0.411406i | \(-0.865038\pi\) | ||||
−0.911452 | + | 0.411406i | \(0.865038\pi\) | |||||||
\(252\) | −9.62723e7 | −0.378965 | ||||||||
\(253\) | −3.42408e8 | −1.32930 | ||||||||
\(254\) | −1.65544e8 | −0.633861 | ||||||||
\(255\) | 2.55832e8 | 0.966194 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 9.55782e7 | 0.351231 | 0.175616 | − | 0.984459i | \(-0.443808\pi\) | ||||
0.175616 | + | 0.984459i | \(0.443808\pi\) | |||||||
\(258\) | 2.84197e7 | 0.103027 | ||||||||
\(259\) | −4.52020e7 | −0.161662 | ||||||||
\(260\) | 3.82487e8 | 1.34962 | ||||||||
\(261\) | −2.74544e8 | −0.955807 | ||||||||
\(262\) | 1.28245e8 | 0.440539 | ||||||||
\(263\) | −3.48809e8 | −1.18234 | −0.591170 | − | 0.806547i | \(-0.701334\pi\) | ||||
−0.591170 | + | 0.806547i | \(0.701334\pi\) | |||||||
\(264\) | 5.39170e7 | 0.180348 | ||||||||
\(265\) | −7.68204e8 | −2.53581 | ||||||||
\(266\) | −3.68382e8 | −1.20009 | ||||||||
\(267\) | 1.45620e8 | 0.468200 | ||||||||
\(268\) | 1.29831e7 | 0.0412008 | ||||||||
\(269\) | 5.90362e7 | 0.184921 | 0.0924604 | − | 0.995716i | \(-0.470527\pi\) | ||||
0.0924604 | + | 0.995716i | \(0.470527\pi\) | |||||||
\(270\) | 3.50050e8 | 1.08232 | ||||||||
\(271\) | 2.36805e8 | 0.722767 | 0.361384 | − | 0.932417i | \(-0.382304\pi\) | ||||
0.361384 | + | 0.932417i | \(0.382304\pi\) | |||||||
\(272\) | −9.27436e7 | −0.279443 | ||||||||
\(273\) | −2.36643e8 | −0.703922 | ||||||||
\(274\) | −3.05999e8 | −0.898656 | ||||||||
\(275\) | 8.30175e8 | 2.40716 | ||||||||
\(276\) | −1.04329e8 | −0.298690 | ||||||||
\(277\) | 8.74196e7 | 0.247132 | 0.123566 | − | 0.992336i | \(-0.460567\pi\) | ||||
0.123566 | + | 0.992336i | \(0.460567\pi\) | |||||||
\(278\) | 2.07711e8 | 0.579834 | ||||||||
\(279\) | 3.43101e7 | 0.0945818 | ||||||||
\(280\) | −2.30561e8 | −0.627672 | ||||||||
\(281\) | 6.81033e6 | 0.0183103 | 0.00915516 | − | 0.999958i | \(-0.497086\pi\) | ||||
0.00915516 | + | 0.999958i | \(0.497086\pi\) | |||||||
\(282\) | 8.42268e7 | 0.223655 | ||||||||
\(283\) | 3.29675e8 | 0.864636 | 0.432318 | − | 0.901721i | \(-0.357696\pi\) | ||||
0.432318 | + | 0.901721i | \(0.357696\pi\) | |||||||
\(284\) | −1.07959e8 | −0.279669 | ||||||||
\(285\) | 5.83025e8 | 1.49187 | ||||||||
\(286\) | −4.45607e8 | −1.12634 | ||||||||
\(287\) | −4.81914e8 | −1.20333 | ||||||||
\(288\) | −5.52356e7 | −0.136253 | ||||||||
\(289\) | 1.02343e8 | 0.249411 | ||||||||
\(290\) | −6.57501e8 | −1.58308 | ||||||||
\(291\) | −1.62143e8 | −0.385721 | ||||||||
\(292\) | 2.49955e8 | 0.587518 | ||||||||
\(293\) | −5.11505e6 | −0.0118799 | −0.00593995 | − | 0.999982i | \(-0.501891\pi\) | ||||
−0.00593995 | + | 0.999982i | \(0.501891\pi\) | |||||||
\(294\) | −4.87072e6 | −0.0111784 | ||||||||
\(295\) | −6.74043e8 | −1.52866 | ||||||||
\(296\) | −2.59343e7 | −0.0581238 | ||||||||
\(297\) | −4.07817e8 | −0.903270 | ||||||||
\(298\) | 1.71583e8 | 0.375592 | ||||||||
\(299\) | 8.62241e8 | 1.86543 | ||||||||
\(300\) | 2.52947e8 | 0.540885 | ||||||||
\(301\) | 1.41584e8 | 0.299248 | ||||||||
\(302\) | −6.09489e8 | −1.27333 | ||||||||
\(303\) | −3.25885e8 | −0.672999 | ||||||||
\(304\) | −2.11357e8 | −0.431478 | ||||||||
\(305\) | 1.55506e9 | 3.13832 | ||||||||
\(306\) | 3.05339e8 | 0.609197 | ||||||||
\(307\) | 4.03860e7 | 0.0796611 | 0.0398305 | − | 0.999206i | \(-0.487318\pi\) | ||||
0.0398305 | + | 0.999206i | \(0.487318\pi\) | |||||||
\(308\) | 2.68609e8 | 0.523833 | ||||||||
\(309\) | −4.24587e8 | −0.818676 | ||||||||
\(310\) | 8.21687e7 | 0.156654 | ||||||||
\(311\) | −2.00657e8 | −0.378262 | −0.189131 | − | 0.981952i | \(-0.560567\pi\) | ||||
−0.189131 | + | 0.981952i | \(0.560567\pi\) | |||||||
\(312\) | −1.35772e8 | −0.253087 | ||||||||
\(313\) | −5.11656e8 | −0.943133 | −0.471566 | − | 0.881831i | \(-0.656311\pi\) | ||||
−0.471566 | + | 0.881831i | \(0.656311\pi\) | |||||||
\(314\) | 3.99460e7 | 0.0728148 | ||||||||
\(315\) | 7.59075e8 | 1.36835 | ||||||||
\(316\) | 2.72329e8 | 0.485501 | ||||||||
\(317\) | −9.61366e8 | −1.69504 | −0.847522 | − | 0.530760i | \(-0.821907\pi\) | ||||
−0.847522 | + | 0.530760i | \(0.821907\pi\) | |||||||
\(318\) | 2.72691e8 | 0.475528 | ||||||||
\(319\) | 7.66004e8 | 1.32119 | ||||||||
\(320\) | −1.32283e8 | −0.225672 | ||||||||
\(321\) | 2.50643e7 | 0.0422949 | ||||||||
\(322\) | −5.19754e8 | −0.867565 | ||||||||
\(323\) | 1.16837e9 | 1.92917 | ||||||||
\(324\) | 1.11680e8 | 0.182418 | ||||||||
\(325\) | −2.09052e9 | −3.37803 | ||||||||
\(326\) | −6.02938e8 | −0.963854 | ||||||||
\(327\) | 1.05126e8 | 0.166262 | ||||||||
\(328\) | −2.76495e8 | −0.432642 | ||||||||
\(329\) | 4.19609e8 | 0.649619 | ||||||||
\(330\) | −4.25118e8 | −0.651194 | ||||||||
\(331\) | −4.03400e8 | −0.611417 | −0.305709 | − | 0.952125i | \(-0.598893\pi\) | ||||
−0.305709 | + | 0.952125i | \(0.598893\pi\) | |||||||
\(332\) | 1.72357e8 | 0.258491 | ||||||||
\(333\) | 8.53835e7 | 0.126712 | ||||||||
\(334\) | 1.41273e8 | 0.207466 | ||||||||
\(335\) | −1.02367e8 | −0.148766 | ||||||||
\(336\) | 8.18428e7 | 0.117704 | ||||||||
\(337\) | −3.99976e8 | −0.569285 | −0.284643 | − | 0.958634i | \(-0.591875\pi\) | ||||
−0.284643 | + | 0.958634i | \(0.591875\pi\) | |||||||
\(338\) | 6.20126e8 | 0.873518 | ||||||||
\(339\) | 3.53561e8 | 0.492908 | ||||||||
\(340\) | 7.31252e8 | 1.00900 | ||||||||
\(341\) | −9.57285e7 | −0.130738 | ||||||||
\(342\) | 6.95849e8 | 0.940641 | ||||||||
\(343\) | −7.59183e8 | −1.01582 | ||||||||
\(344\) | 8.12328e7 | 0.107591 | ||||||||
\(345\) | 8.22596e8 | 1.07850 | ||||||||
\(346\) | 4.14163e8 | 0.537533 | ||||||||
\(347\) | 7.68302e8 | 0.987140 | 0.493570 | − | 0.869706i | \(-0.335692\pi\) | ||||
0.493570 | + | 0.869706i | \(0.335692\pi\) | |||||||
\(348\) | 2.33395e8 | 0.296868 | ||||||||
\(349\) | 1.39255e8 | 0.175357 | 0.0876783 | − | 0.996149i | \(-0.472055\pi\) | ||||
0.0876783 | + | 0.996149i | \(0.472055\pi\) | |||||||
\(350\) | 1.26015e9 | 1.57103 | ||||||||
\(351\) | 1.02695e9 | 1.26758 | ||||||||
\(352\) | 1.54113e8 | 0.188338 | ||||||||
\(353\) | 3.62036e8 | 0.438067 | 0.219034 | − | 0.975717i | \(-0.429710\pi\) | ||||
0.219034 | + | 0.975717i | \(0.429710\pi\) | |||||||
\(354\) | 2.39267e8 | 0.286662 | ||||||||
\(355\) | 8.51220e8 | 1.00982 | ||||||||
\(356\) | 4.16230e8 | 0.488943 | ||||||||
\(357\) | −4.52422e8 | −0.526266 | ||||||||
\(358\) | 2.72468e8 | 0.313852 | ||||||||
\(359\) | −6.39521e8 | −0.729498 | −0.364749 | − | 0.931106i | \(-0.618845\pi\) | ||||
−0.364749 | + | 0.931106i | \(0.618845\pi\) | |||||||
\(360\) | 4.35514e8 | 0.491975 | ||||||||
\(361\) | 1.76877e9 | 1.97877 | ||||||||
\(362\) | 7.51906e8 | 0.833074 | ||||||||
\(363\) | 5.89410e7 | 0.0646761 | ||||||||
\(364\) | −6.76404e8 | −0.735108 | ||||||||
\(365\) | −1.97081e9 | −2.12138 | ||||||||
\(366\) | −5.52003e8 | −0.588516 | ||||||||
\(367\) | −1.56742e9 | −1.65521 | −0.827605 | − | 0.561311i | \(-0.810297\pi\) | ||||
−0.827605 | + | 0.561311i | \(0.810297\pi\) | |||||||
\(368\) | −2.98205e8 | −0.311923 | ||||||||
\(369\) | 9.10304e8 | 0.943179 | ||||||||
\(370\) | 2.04484e8 | 0.209871 | ||||||||
\(371\) | 1.35852e9 | 1.38120 | ||||||||
\(372\) | −2.91676e7 | −0.0293765 | ||||||||
\(373\) | −6.28913e8 | −0.627494 | −0.313747 | − | 0.949507i | \(-0.601584\pi\) | ||||
−0.313747 | + | 0.949507i | \(0.601584\pi\) | |||||||
\(374\) | −8.51926e8 | −0.842076 | ||||||||
\(375\) | −1.11169e9 | −1.08861 | ||||||||
\(376\) | 2.40748e8 | 0.233563 | ||||||||
\(377\) | −1.92893e9 | −1.85405 | ||||||||
\(378\) | −6.19041e8 | −0.589519 | ||||||||
\(379\) | −4.65760e8 | −0.439466 | −0.219733 | − | 0.975560i | \(-0.570519\pi\) | ||||
−0.219733 | + | 0.975560i | \(0.570519\pi\) | |||||||
\(380\) | 1.66648e9 | 1.55796 | ||||||||
\(381\) | −4.63330e8 | −0.429193 | ||||||||
\(382\) | −6.00074e8 | −0.550787 | ||||||||
\(383\) | 1.35682e9 | 1.23403 | 0.617014 | − | 0.786952i | \(-0.288342\pi\) | ||||
0.617014 | + | 0.786952i | \(0.288342\pi\) | |||||||
\(384\) | 4.69567e7 | 0.0423193 | ||||||||
\(385\) | −2.11789e9 | −1.89143 | ||||||||
\(386\) | −3.93178e8 | −0.347963 | ||||||||
\(387\) | −2.67442e8 | −0.234553 | ||||||||
\(388\) | −4.63459e8 | −0.402810 | ||||||||
\(389\) | 9.47602e8 | 0.816211 | 0.408105 | − | 0.912935i | \(-0.366190\pi\) | ||||
0.408105 | + | 0.912935i | \(0.366190\pi\) | |||||||
\(390\) | 1.07052e9 | 0.913837 | ||||||||
\(391\) | 1.64846e9 | 1.39463 | ||||||||
\(392\) | −1.39221e7 | −0.0116736 | ||||||||
\(393\) | 3.58936e8 | 0.298293 | ||||||||
\(394\) | −1.06679e9 | −0.878706 | ||||||||
\(395\) | −2.14723e9 | −1.75302 | ||||||||
\(396\) | −5.07384e8 | −0.410586 | ||||||||
\(397\) | 1.61811e9 | 1.29790 | 0.648951 | − | 0.760830i | \(-0.275208\pi\) | ||||
0.648951 | + | 0.760830i | \(0.275208\pi\) | |||||||
\(398\) | −6.67965e8 | −0.531084 | ||||||||
\(399\) | −1.03104e9 | −0.812590 | ||||||||
\(400\) | 7.23005e8 | 0.564848 | ||||||||
\(401\) | 1.47928e9 | 1.14563 | 0.572816 | − | 0.819684i | \(-0.305851\pi\) | ||||
0.572816 | + | 0.819684i | \(0.305851\pi\) | |||||||
\(402\) | 3.63375e7 | 0.0278974 | ||||||||
\(403\) | 2.41061e8 | 0.183467 | ||||||||
\(404\) | −9.31485e8 | −0.702815 | ||||||||
\(405\) | −8.80558e8 | −0.658666 | ||||||||
\(406\) | 1.16275e9 | 0.862272 | ||||||||
\(407\) | −2.38228e8 | −0.175151 | ||||||||
\(408\) | −2.59574e8 | −0.189213 | ||||||||
\(409\) | 1.53241e9 | 1.10750 | 0.553750 | − | 0.832683i | \(-0.313196\pi\) | ||||
0.553750 | + | 0.832683i | \(0.313196\pi\) | |||||||
\(410\) | 2.18007e9 | 1.56217 | ||||||||
\(411\) | −8.56443e8 | −0.608488 | ||||||||
\(412\) | −1.21361e9 | −0.854946 | ||||||||
\(413\) | 1.19200e9 | 0.832629 | ||||||||
\(414\) | 9.81780e8 | 0.680006 | ||||||||
\(415\) | −1.35898e9 | −0.933349 | ||||||||
\(416\) | −3.88082e8 | −0.264300 | ||||||||
\(417\) | 5.81351e8 | 0.392611 | ||||||||
\(418\) | −1.94149e9 | −1.30022 | ||||||||
\(419\) | 5.61884e8 | 0.373162 | 0.186581 | − | 0.982440i | \(-0.440259\pi\) | ||||
0.186581 | + | 0.982440i | \(0.440259\pi\) | |||||||
\(420\) | −6.45303e8 | −0.425002 | ||||||||
\(421\) | −8.61751e6 | −0.00562853 | −0.00281426 | − | 0.999996i | \(-0.500896\pi\) | ||||
−0.00281426 | + | 0.999996i | \(0.500896\pi\) | |||||||
\(422\) | −4.13791e8 | −0.268033 | ||||||||
\(423\) | −7.92613e8 | −0.509178 | ||||||||
\(424\) | 7.79441e8 | 0.496596 | ||||||||
\(425\) | −3.99674e9 | −2.52548 | ||||||||
\(426\) | −3.02160e8 | −0.189366 | ||||||||
\(427\) | −2.75002e9 | −1.70938 | ||||||||
\(428\) | 7.16420e7 | 0.0441687 | ||||||||
\(429\) | −1.24718e9 | −0.762657 | ||||||||
\(430\) | −6.40493e8 | −0.388486 | ||||||||
\(431\) | −4.27833e8 | −0.257397 | −0.128699 | − | 0.991684i | \(-0.541080\pi\) | ||||
−0.128699 | + | 0.991684i | \(0.541080\pi\) | |||||||
\(432\) | −3.55170e8 | −0.211955 | ||||||||
\(433\) | 1.56113e9 | 0.924127 | 0.462064 | − | 0.886847i | \(-0.347109\pi\) | ||||
0.462064 | + | 0.886847i | \(0.347109\pi\) | |||||||
\(434\) | −1.45310e8 | −0.0853260 | ||||||||
\(435\) | −1.84024e9 | −1.07192 | ||||||||
\(436\) | 3.00485e8 | 0.173628 | ||||||||
\(437\) | 3.75674e9 | 2.15341 | ||||||||
\(438\) | 6.99582e8 | 0.397814 | ||||||||
\(439\) | 1.63407e9 | 0.921817 | 0.460908 | − | 0.887448i | \(-0.347524\pi\) | ||||
0.460908 | + | 0.887448i | \(0.347524\pi\) | |||||||
\(440\) | −1.21513e9 | −0.680044 | ||||||||
\(441\) | 4.58358e7 | 0.0254489 | ||||||||
\(442\) | 2.14530e9 | 1.18171 | ||||||||
\(443\) | −6.21106e8 | −0.339432 | −0.169716 | − | 0.985493i | \(-0.554285\pi\) | ||||
−0.169716 | + | 0.985493i | \(0.554285\pi\) | |||||||
\(444\) | −7.25860e7 | −0.0393562 | ||||||||
\(445\) | −3.28183e9 | −1.76545 | ||||||||
\(446\) | −1.50874e9 | −0.805273 | ||||||||
\(447\) | 4.80233e8 | 0.254317 | ||||||||
\(448\) | 2.33933e8 | 0.122919 | ||||||||
\(449\) | 2.16788e8 | 0.113024 | 0.0565122 | − | 0.998402i | \(-0.482002\pi\) | ||||
0.0565122 | + | 0.998402i | \(0.482002\pi\) | |||||||
\(450\) | −2.38035e9 | −1.23139 | ||||||||
\(451\) | −2.53984e9 | −1.30373 | ||||||||
\(452\) | 1.01059e9 | 0.514745 | ||||||||
\(453\) | −1.70586e9 | −0.862184 | ||||||||
\(454\) | 2.50300e9 | 1.25535 | ||||||||
\(455\) | 5.33322e9 | 2.65430 | ||||||||
\(456\) | −5.91554e8 | −0.292158 | ||||||||
\(457\) | −3.59868e9 | −1.76375 | −0.881874 | − | 0.471485i | \(-0.843718\pi\) | ||||
−0.881874 | + | 0.471485i | \(0.843718\pi\) | |||||||
\(458\) | −1.71565e9 | −0.834451 | ||||||||
\(459\) | 1.96336e9 | 0.947668 | ||||||||
\(460\) | 2.35125e9 | 1.12628 | ||||||||
\(461\) | −4.44676e8 | −0.211393 | −0.105696 | − | 0.994398i | \(-0.533707\pi\) | ||||
−0.105696 | + | 0.994398i | \(0.533707\pi\) | |||||||
\(462\) | 7.51793e8 | 0.354692 | ||||||||
\(463\) | −1.08602e9 | −0.508517 | −0.254258 | − | 0.967136i | \(-0.581831\pi\) | ||||
−0.254258 | + | 0.967136i | \(0.581831\pi\) | |||||||
\(464\) | 6.67119e8 | 0.310020 | ||||||||
\(465\) | 2.29977e8 | 0.106072 | ||||||||
\(466\) | 6.14750e8 | 0.281415 | ||||||||
\(467\) | 3.61227e9 | 1.64124 | 0.820619 | − | 0.571476i | \(-0.193629\pi\) | ||||
0.820619 | + | 0.571476i | \(0.193629\pi\) | |||||||
\(468\) | 1.27768e9 | 0.576185 | ||||||||
\(469\) | 1.81030e8 | 0.0810298 | ||||||||
\(470\) | −1.89822e9 | −0.843340 | ||||||||
\(471\) | 1.11802e8 | 0.0493036 | ||||||||
\(472\) | 6.83903e8 | 0.299362 | ||||||||
\(473\) | 7.46190e8 | 0.324217 | ||||||||
\(474\) | 7.62206e8 | 0.328737 | ||||||||
\(475\) | −9.10831e9 | −3.89951 | ||||||||
\(476\) | −1.29317e9 | −0.549581 | ||||||||
\(477\) | −2.56615e9 | −1.08260 | ||||||||
\(478\) | −1.57396e9 | −0.659169 | ||||||||
\(479\) | 3.95907e9 | 1.64596 | 0.822978 | − | 0.568073i | \(-0.192311\pi\) | ||||
0.822978 | + | 0.568073i | \(0.192311\pi\) | |||||||
\(480\) | −3.70238e8 | −0.152805 | ||||||||
\(481\) | 5.99900e8 | 0.245794 | ||||||||
\(482\) | 1.04031e9 | 0.423154 | ||||||||
\(483\) | −1.45471e9 | −0.587436 | ||||||||
\(484\) | 1.68473e8 | 0.0675415 | ||||||||
\(485\) | 3.65422e9 | 1.45445 | ||||||||
\(486\) | 1.82968e9 | 0.723016 | ||||||||
\(487\) | 4.30023e9 | 1.68710 | 0.843549 | − | 0.537052i | \(-0.180462\pi\) | ||||
0.843549 | + | 0.537052i | \(0.180462\pi\) | |||||||
\(488\) | −1.57781e9 | −0.614588 | ||||||||
\(489\) | −1.68753e9 | −0.652634 | ||||||||
\(490\) | 1.09771e8 | 0.0421505 | ||||||||
\(491\) | −2.54704e9 | −0.971072 | −0.485536 | − | 0.874217i | \(-0.661375\pi\) | ||||
−0.485536 | + | 0.874217i | \(0.661375\pi\) | |||||||
\(492\) | −7.73865e8 | −0.292946 | ||||||||
\(493\) | −3.68780e9 | −1.38613 | ||||||||
\(494\) | 4.88900e9 | 1.82463 | ||||||||
\(495\) | 4.00056e9 | 1.48253 | ||||||||
\(496\) | −8.33706e7 | −0.0306780 | ||||||||
\(497\) | −1.50533e9 | −0.550027 | ||||||||
\(498\) | 4.82400e8 | 0.175027 | ||||||||
\(499\) | −3.13518e9 | −1.12956 | −0.564782 | − | 0.825240i | \(-0.691040\pi\) | ||||
−0.564782 | + | 0.825240i | \(0.691040\pi\) | |||||||
\(500\) | −3.17756e9 | −1.13684 | ||||||||
\(501\) | 3.95401e8 | 0.140477 | ||||||||
\(502\) | −3.65352e9 | −1.28899 | ||||||||
\(503\) | 8.10436e7 | 0.0283943 | 0.0141971 | − | 0.999899i | \(-0.495481\pi\) | ||||
0.0141971 | + | 0.999899i | \(0.495481\pi\) | |||||||
\(504\) | −7.70178e8 | −0.267969 | ||||||||
\(505\) | 7.34445e9 | 2.53769 | ||||||||
\(506\) | −2.73926e9 | −0.939954 | ||||||||
\(507\) | 1.73563e9 | 0.591467 | ||||||||
\(508\) | −1.32435e9 | −0.448208 | ||||||||
\(509\) | 1.83771e9 | 0.617683 | 0.308841 | − | 0.951114i | \(-0.400059\pi\) | ||||
0.308841 | + | 0.951114i | \(0.400059\pi\) | |||||||
\(510\) | 2.04666e9 | 0.683202 | ||||||||
\(511\) | 3.48525e9 | 1.15547 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 4.47438e9 | 1.46326 | ||||||||
\(514\) | 7.64626e8 | 0.248358 | ||||||||
\(515\) | 9.56891e9 | 3.08700 | ||||||||
\(516\) | 2.27357e8 | 0.0728510 | ||||||||
\(517\) | 2.21147e9 | 0.703823 | ||||||||
\(518\) | −3.61616e8 | −0.114312 | ||||||||
\(519\) | 1.15918e9 | 0.363968 | ||||||||
\(520\) | 3.05990e9 | 0.954322 | ||||||||
\(521\) | −3.26147e9 | −1.01037 | −0.505186 | − | 0.863011i | \(-0.668576\pi\) | ||||
−0.505186 | + | 0.863011i | \(0.668576\pi\) | |||||||
\(522\) | −2.19635e9 | −0.675858 | ||||||||
\(523\) | 1.51622e9 | 0.463454 | 0.231727 | − | 0.972781i | \(-0.425562\pi\) | ||||
0.231727 | + | 0.972781i | \(0.425562\pi\) | |||||||
\(524\) | 1.02596e9 | 0.311508 | ||||||||
\(525\) | 3.52697e9 | 1.06376 | ||||||||
\(526\) | −2.79047e9 | −0.836041 | ||||||||
\(527\) | 4.60868e8 | 0.137164 | ||||||||
\(528\) | 4.31336e8 | 0.127526 | ||||||||
\(529\) | 1.89560e9 | 0.556738 | ||||||||
\(530\) | −6.14563e9 | −1.79309 | ||||||||
\(531\) | −2.25161e9 | −0.652623 | ||||||||
\(532\) | −2.94706e9 | −0.848590 | ||||||||
\(533\) | 6.39575e9 | 1.82956 | ||||||||
\(534\) | 1.16496e9 | 0.331067 | ||||||||
\(535\) | −5.64873e8 | −0.159482 | ||||||||
\(536\) | 1.03864e8 | 0.0291333 | ||||||||
\(537\) | 7.62593e8 | 0.212512 | ||||||||
\(538\) | 4.72290e8 | 0.130759 | ||||||||
\(539\) | −1.27886e8 | −0.0351774 | ||||||||
\(540\) | 2.80040e9 | 0.765318 | ||||||||
\(541\) | −8.73876e8 | −0.237279 | −0.118640 | − | 0.992937i | \(-0.537853\pi\) | ||||
−0.118640 | + | 0.992937i | \(0.537853\pi\) | |||||||
\(542\) | 1.89444e9 | 0.511074 | ||||||||
\(543\) | 2.10446e9 | 0.564082 | ||||||||
\(544\) | −7.41949e8 | −0.197596 | ||||||||
\(545\) | −2.36922e9 | −0.626929 | ||||||||
\(546\) | −1.89314e9 | −0.497748 | ||||||||
\(547\) | −1.08535e9 | −0.283541 | −0.141770 | − | 0.989900i | \(-0.545279\pi\) | ||||
−0.141770 | + | 0.989900i | \(0.545279\pi\) | |||||||
\(548\) | −2.44800e9 | −0.635446 | ||||||||
\(549\) | 5.19461e9 | 1.33983 | ||||||||
\(550\) | 6.64140e9 | 1.70212 | ||||||||
\(551\) | −8.40426e9 | −2.14027 | ||||||||
\(552\) | −8.34628e8 | −0.211206 | ||||||||
\(553\) | 3.79723e9 | 0.954837 | ||||||||
\(554\) | 6.99356e8 | 0.174749 | ||||||||
\(555\) | 5.72317e8 | 0.142106 | ||||||||
\(556\) | 1.66169e9 | 0.410004 | ||||||||
\(557\) | −6.40646e9 | −1.57081 | −0.785407 | − | 0.618980i | \(-0.787546\pi\) | ||||
−0.785407 | + | 0.618980i | \(0.787546\pi\) | |||||||
\(558\) | 2.74481e8 | 0.0668794 | ||||||||
\(559\) | −1.87904e9 | −0.454981 | ||||||||
\(560\) | −1.84449e9 | −0.443831 | ||||||||
\(561\) | −2.38440e9 | −0.570177 | ||||||||
\(562\) | 5.44826e7 | 0.0129473 | ||||||||
\(563\) | −7.36885e8 | −0.174028 | −0.0870142 | − | 0.996207i | \(-0.527733\pi\) | ||||
−0.0870142 | + | 0.996207i | \(0.527733\pi\) | |||||||
\(564\) | 6.73814e8 | 0.158148 | ||||||||
\(565\) | −7.96820e9 | −1.85862 | ||||||||
\(566\) | 2.63740e9 | 0.611390 | ||||||||
\(567\) | 1.55721e9 | 0.358762 | ||||||||
\(568\) | −8.63672e8 | −0.197756 | ||||||||
\(569\) | 2.26466e9 | 0.515360 | 0.257680 | − | 0.966230i | \(-0.417042\pi\) | ||||
0.257680 | + | 0.966230i | \(0.417042\pi\) | |||||||
\(570\) | 4.66420e9 | 1.05491 | ||||||||
\(571\) | 1.77146e9 | 0.398202 | 0.199101 | − | 0.979979i | \(-0.436198\pi\) | ||||
0.199101 | + | 0.979979i | \(0.436198\pi\) | |||||||
\(572\) | −3.56485e9 | −0.796445 | ||||||||
\(573\) | −1.67951e9 | −0.372942 | ||||||||
\(574\) | −3.85532e9 | −0.850880 | ||||||||
\(575\) | −1.28510e10 | −2.81903 | ||||||||
\(576\) | −4.41885e8 | −0.0963452 | ||||||||
\(577\) | 4.19705e9 | 0.909554 | 0.454777 | − | 0.890605i | \(-0.349719\pi\) | ||||
0.454777 | + | 0.890605i | \(0.349719\pi\) | |||||||
\(578\) | 8.18744e8 | 0.176360 | ||||||||
\(579\) | −1.10044e9 | −0.235609 | ||||||||
\(580\) | −5.26001e9 | −1.11941 | ||||||||
\(581\) | 2.40326e9 | 0.508376 | ||||||||
\(582\) | −1.29715e9 | −0.272746 | ||||||||
\(583\) | 7.15981e9 | 1.49645 | ||||||||
\(584\) | 1.99964e9 | 0.415438 | ||||||||
\(585\) | −1.00741e10 | −2.08046 | ||||||||
\(586\) | −4.09204e7 | −0.00840036 | ||||||||
\(587\) | 6.47404e9 | 1.32112 | 0.660560 | − | 0.750773i | \(-0.270319\pi\) | ||||
0.660560 | + | 0.750773i | \(0.270319\pi\) | |||||||
\(588\) | −3.89658e7 | −0.00790429 | ||||||||
\(589\) | 1.05029e9 | 0.211790 | ||||||||
\(590\) | −5.39234e9 | −1.08092 | ||||||||
\(591\) | −2.98578e9 | −0.594979 | ||||||||
\(592\) | −2.07475e8 | −0.0410997 | ||||||||
\(593\) | −9.00131e9 | −1.77261 | −0.886307 | − | 0.463098i | \(-0.846738\pi\) | ||||
−0.886307 | + | 0.463098i | \(0.846738\pi\) | |||||||
\(594\) | −3.26253e9 | −0.638708 | ||||||||
\(595\) | 1.01962e10 | 1.98440 | ||||||||
\(596\) | 1.37266e9 | 0.265584 | ||||||||
\(597\) | −1.86953e9 | −0.359602 | ||||||||
\(598\) | 6.89793e9 | 1.31906 | ||||||||
\(599\) | 2.07040e9 | 0.393604 | 0.196802 | − | 0.980443i | \(-0.436944\pi\) | ||||
0.196802 | + | 0.980443i | \(0.436944\pi\) | |||||||
\(600\) | 2.02358e9 | 0.382463 | ||||||||
\(601\) | −4.27425e9 | −0.803155 | −0.401577 | − | 0.915825i | \(-0.631538\pi\) | ||||
−0.401577 | + | 0.915825i | \(0.631538\pi\) | |||||||
\(602\) | 1.13267e9 | 0.211600 | ||||||||
\(603\) | −3.41953e8 | −0.0635120 | ||||||||
\(604\) | −4.87591e9 | −0.900382 | ||||||||
\(605\) | −1.32835e9 | −0.243876 | ||||||||
\(606\) | −2.60708e9 | −0.475882 | ||||||||
\(607\) | −9.36384e9 | −1.69939 | −0.849696 | − | 0.527272i | \(-0.823215\pi\) | ||||
−0.849696 | + | 0.527272i | \(0.823215\pi\) | |||||||
\(608\) | −1.69085e9 | −0.305101 | ||||||||
\(609\) | 3.25434e9 | 0.583852 | ||||||||
\(610\) | 1.24405e10 | 2.21913 | ||||||||
\(611\) | −5.56885e9 | −0.987692 | ||||||||
\(612\) | 2.44272e9 | 0.430767 | ||||||||
\(613\) | −6.35668e8 | −0.111460 | −0.0557299 | − | 0.998446i | \(-0.517749\pi\) | ||||
−0.0557299 | + | 0.998446i | \(0.517749\pi\) | |||||||
\(614\) | 3.23088e8 | 0.0563289 | ||||||||
\(615\) | 6.10167e9 | 1.05776 | ||||||||
\(616\) | 2.14887e9 | 0.370406 | ||||||||
\(617\) | −3.37951e9 | −0.579237 | −0.289618 | − | 0.957142i | \(-0.593528\pi\) | ||||
−0.289618 | + | 0.957142i | \(0.593528\pi\) | |||||||
\(618\) | −3.39670e9 | −0.578892 | ||||||||
\(619\) | −7.37657e9 | −1.25008 | −0.625039 | − | 0.780593i | \(-0.714917\pi\) | ||||
−0.625039 | + | 0.780593i | \(0.714917\pi\) | |||||||
\(620\) | 6.57350e8 | 0.110771 | ||||||||
\(621\) | 6.31295e9 | 1.05782 | ||||||||
\(622\) | −1.60526e9 | −0.267472 | ||||||||
\(623\) | 5.80370e9 | 0.961606 | ||||||||
\(624\) | −1.08618e9 | −0.178960 | ||||||||
\(625\) | 1.12638e10 | 1.84546 | ||||||||
\(626\) | −4.09325e9 | −0.666896 | ||||||||
\(627\) | −5.43391e9 | −0.880392 | ||||||||
\(628\) | 3.19568e8 | 0.0514878 | ||||||||
\(629\) | 1.14691e9 | 0.183760 | ||||||||
\(630\) | 6.07260e9 | 0.967571 | ||||||||
\(631\) | −8.76066e9 | −1.38814 | −0.694071 | − | 0.719906i | \(-0.744185\pi\) | ||||
−0.694071 | + | 0.719906i | \(0.744185\pi\) | |||||||
\(632\) | 2.17864e9 | 0.343301 | ||||||||
\(633\) | −1.15814e9 | −0.181487 | ||||||||
\(634\) | −7.69092e9 | −1.19858 | ||||||||
\(635\) | 1.04420e10 | 1.61837 | ||||||||
\(636\) | 2.18153e9 | 0.336249 | ||||||||
\(637\) | 3.22040e8 | 0.0493652 | ||||||||
\(638\) | 6.12804e9 | 0.934219 | ||||||||
\(639\) | 2.84346e9 | 0.431117 | ||||||||
\(640\) | −1.05826e9 | −0.159574 | ||||||||
\(641\) | −5.91406e9 | −0.886916 | −0.443458 | − | 0.896295i | \(-0.646248\pi\) | ||||
−0.443458 | + | 0.896295i | \(0.646248\pi\) | |||||||
\(642\) | 2.00514e8 | 0.0299070 | ||||||||
\(643\) | 1.21681e9 | 0.180504 | 0.0902518 | − | 0.995919i | \(-0.471233\pi\) | ||||
0.0902518 | + | 0.995919i | \(0.471233\pi\) | |||||||
\(644\) | −4.15803e9 | −0.613461 | ||||||||
\(645\) | −1.79264e9 | −0.263047 | ||||||||
\(646\) | 9.34695e9 | 1.36413 | ||||||||
\(647\) | −4.35488e9 | −0.632137 | −0.316068 | − | 0.948736i | \(-0.602363\pi\) | ||||
−0.316068 | + | 0.948736i | \(0.602363\pi\) | |||||||
\(648\) | 8.93438e8 | 0.128989 | ||||||||
\(649\) | 6.28221e9 | 0.902103 | ||||||||
\(650\) | −1.67242e10 | −2.38863 | ||||||||
\(651\) | −4.06699e8 | −0.0577750 | ||||||||
\(652\) | −4.82351e9 | −0.681548 | ||||||||
\(653\) | −2.37363e9 | −0.333594 | −0.166797 | − | 0.985991i | \(-0.553342\pi\) | ||||
−0.166797 | + | 0.985991i | \(0.553342\pi\) | |||||||
\(654\) | 8.41009e8 | 0.117565 | ||||||||
\(655\) | −8.08933e9 | −1.12478 | ||||||||
\(656\) | −2.21196e9 | −0.305924 | ||||||||
\(657\) | −6.58340e9 | −0.905672 | ||||||||
\(658\) | 3.35687e9 | 0.459350 | ||||||||
\(659\) | −3.03953e9 | −0.413721 | −0.206861 | − | 0.978370i | \(-0.566325\pi\) | ||||
−0.206861 | + | 0.978370i | \(0.566325\pi\) | |||||||
\(660\) | −3.40094e9 | −0.460464 | ||||||||
\(661\) | −1.60589e9 | −0.216277 | −0.108138 | − | 0.994136i | \(-0.534489\pi\) | ||||
−0.108138 | + | 0.994136i | \(0.534489\pi\) | |||||||
\(662\) | −3.22720e9 | −0.432337 | ||||||||
\(663\) | 6.00434e9 | 0.800144 | ||||||||
\(664\) | 1.37886e9 | 0.182781 | ||||||||
\(665\) | 2.32366e10 | 3.06405 | ||||||||
\(666\) | 6.83068e8 | 0.0895992 | ||||||||
\(667\) | −1.18576e10 | −1.54724 | ||||||||
\(668\) | 1.13019e9 | 0.146701 | ||||||||
\(669\) | −4.22273e9 | −0.545257 | ||||||||
\(670\) | −8.18937e8 | −0.105193 | ||||||||
\(671\) | −1.44935e10 | −1.85201 | ||||||||
\(672\) | 6.54742e8 | 0.0832296 | ||||||||
\(673\) | 1.06339e10 | 1.34474 | 0.672371 | − | 0.740214i | \(-0.265276\pi\) | ||||
0.672371 | + | 0.740214i | \(0.265276\pi\) | |||||||
\(674\) | −3.19981e9 | −0.402545 | ||||||||
\(675\) | −1.53059e10 | −1.91556 | ||||||||
\(676\) | 4.96101e9 | 0.617670 | ||||||||
\(677\) | 1.12699e10 | 1.39591 | 0.697957 | − | 0.716139i | \(-0.254093\pi\) | ||||
0.697957 | + | 0.716139i | \(0.254093\pi\) | |||||||
\(678\) | 2.82849e9 | 0.348538 | ||||||||
\(679\) | −6.46225e9 | −0.792208 | ||||||||
\(680\) | 5.85002e9 | 0.713470 | ||||||||
\(681\) | 7.00549e9 | 0.850009 | ||||||||
\(682\) | −7.65828e8 | −0.0924455 | ||||||||
\(683\) | −7.09950e9 | −0.852619 | −0.426310 | − | 0.904577i | \(-0.640187\pi\) | ||||
−0.426310 | + | 0.904577i | \(0.640187\pi\) | |||||||
\(684\) | 5.56679e9 | 0.665133 | ||||||||
\(685\) | 1.93016e10 | 2.29444 | ||||||||
\(686\) | −6.07346e9 | −0.718294 | ||||||||
\(687\) | −4.80184e9 | −0.565014 | ||||||||
\(688\) | 6.49862e8 | 0.0760785 | ||||||||
\(689\) | −1.80296e10 | −2.10000 | ||||||||
\(690\) | 6.58076e9 | 0.762614 | ||||||||
\(691\) | −8.79291e9 | −1.01382 | −0.506909 | − | 0.862000i | \(-0.669212\pi\) | ||||
−0.506909 | + | 0.862000i | \(0.669212\pi\) | |||||||
\(692\) | 3.31331e9 | 0.380093 | ||||||||
\(693\) | −7.07472e9 | −0.807501 | ||||||||
\(694\) | 6.14641e9 | 0.698013 | ||||||||
\(695\) | −1.31019e10 | −1.48043 | ||||||||
\(696\) | 1.86716e9 | 0.209917 | ||||||||
\(697\) | 1.22276e10 | 1.36781 | ||||||||
\(698\) | 1.11404e9 | 0.123996 | ||||||||
\(699\) | 1.72059e9 | 0.190549 | ||||||||
\(700\) | 1.00812e10 | 1.11089 | ||||||||
\(701\) | −2.64063e9 | −0.289530 | −0.144765 | − | 0.989466i | \(-0.546243\pi\) | ||||
−0.144765 | + | 0.989466i | \(0.546243\pi\) | |||||||
\(702\) | 8.21562e9 | 0.896315 | ||||||||
\(703\) | 2.61373e9 | 0.283738 | ||||||||
\(704\) | 1.23290e9 | 0.133175 | ||||||||
\(705\) | −5.31280e9 | −0.571033 | ||||||||
\(706\) | 2.89629e9 | 0.309760 | ||||||||
\(707\) | −1.29882e10 | −1.38223 | ||||||||
\(708\) | 1.91413e9 | 0.202701 | ||||||||
\(709\) | 9.19450e9 | 0.968872 | 0.484436 | − | 0.874827i | \(-0.339025\pi\) | ||||
0.484436 | + | 0.874827i | \(0.339025\pi\) | |||||||
\(710\) | 6.80976e9 | 0.714049 | ||||||||
\(711\) | −7.17272e9 | −0.748411 | ||||||||
\(712\) | 3.32984e9 | 0.345735 | ||||||||
\(713\) | 1.48186e9 | 0.153107 | ||||||||
\(714\) | −3.61938e9 | −0.372126 | ||||||||
\(715\) | 2.81077e10 | 2.87577 | ||||||||
\(716\) | 2.17974e9 | 0.221927 | ||||||||
\(717\) | −4.40527e9 | −0.446329 | ||||||||
\(718\) | −5.11617e9 | −0.515833 | ||||||||
\(719\) | 2.41418e9 | 0.242225 | 0.121112 | − | 0.992639i | \(-0.461354\pi\) | ||||
0.121112 | + | 0.992639i | \(0.461354\pi\) | |||||||
\(720\) | 3.48411e9 | 0.347879 | ||||||||
\(721\) | −1.69220e10 | −1.68143 | ||||||||
\(722\) | 1.41501e10 | 1.39920 | ||||||||
\(723\) | 2.91166e9 | 0.286521 | ||||||||
\(724\) | 6.01525e9 | 0.589072 | ||||||||
\(725\) | 2.87491e10 | 2.80183 | ||||||||
\(726\) | 4.71528e8 | 0.0457329 | ||||||||
\(727\) | 7.98519e9 | 0.770753 | 0.385376 | − | 0.922760i | \(-0.374072\pi\) | ||||
0.385376 | + | 0.922760i | \(0.374072\pi\) | |||||||
\(728\) | −5.41123e9 | −0.519800 | ||||||||
\(729\) | 1.30467e9 | 0.124725 | ||||||||
\(730\) | −1.57665e10 | −1.50004 | ||||||||
\(731\) | −3.59240e9 | −0.340153 | ||||||||
\(732\) | −4.41603e9 | −0.416143 | ||||||||
\(733\) | 6.97965e9 | 0.654591 | 0.327295 | − | 0.944922i | \(-0.393863\pi\) | ||||
0.327295 | + | 0.944922i | \(0.393863\pi\) | |||||||
\(734\) | −1.25393e10 | −1.17041 | ||||||||
\(735\) | 3.07232e8 | 0.0285405 | ||||||||
\(736\) | −2.38564e9 | −0.220563 | ||||||||
\(737\) | 9.54081e8 | 0.0877908 | ||||||||
\(738\) | 7.28243e9 | 0.666928 | ||||||||
\(739\) | 2.04231e9 | 0.186151 | 0.0930757 | − | 0.995659i | \(-0.470330\pi\) | ||||
0.0930757 | + | 0.995659i | \(0.470330\pi\) | |||||||
\(740\) | 1.63587e9 | 0.148401 | ||||||||
\(741\) | 1.36835e10 | 1.23548 | ||||||||
\(742\) | 1.08682e10 | 0.976657 | ||||||||
\(743\) | −1.55097e10 | −1.38721 | −0.693604 | − | 0.720357i | \(-0.743978\pi\) | ||||
−0.693604 | + | 0.720357i | \(0.743978\pi\) | |||||||
\(744\) | −2.33341e8 | −0.0207724 | ||||||||
\(745\) | −1.08230e10 | −0.958959 | ||||||||
\(746\) | −5.03131e9 | −0.443706 | ||||||||
\(747\) | −4.53960e9 | −0.398470 | ||||||||
\(748\) | −6.81541e9 | −0.595438 | ||||||||
\(749\) | 9.98942e8 | 0.0868668 | ||||||||
\(750\) | −8.89348e9 | −0.769764 | ||||||||
\(751\) | −7.67830e9 | −0.661493 | −0.330746 | − | 0.943720i | \(-0.607300\pi\) | ||||
−0.330746 | + | 0.943720i | \(0.607300\pi\) | |||||||
\(752\) | 1.92598e9 | 0.165154 | ||||||||
\(753\) | −1.02256e10 | −0.872785 | ||||||||
\(754\) | −1.54314e10 | −1.31101 | ||||||||
\(755\) | 3.84449e10 | 3.25106 | ||||||||
\(756\) | −4.95233e9 | −0.416853 | ||||||||
\(757\) | 1.30345e9 | 0.109209 | 0.0546047 | − | 0.998508i | \(-0.482610\pi\) | ||||
0.0546047 | + | 0.998508i | \(0.482610\pi\) | |||||||
\(758\) | −3.72608e9 | −0.310749 | ||||||||
\(759\) | −7.66675e9 | −0.636451 | ||||||||
\(760\) | 1.33318e10 | 1.10165 | ||||||||
\(761\) | −1.93614e9 | −0.159254 | −0.0796269 | − | 0.996825i | \(-0.525373\pi\) | ||||
−0.0796269 | + | 0.996825i | \(0.525373\pi\) | |||||||
\(762\) | −3.70664e9 | −0.303485 | ||||||||
\(763\) | 4.18982e9 | 0.341475 | ||||||||
\(764\) | −4.80060e9 | −0.389465 | ||||||||
\(765\) | −1.92600e10 | −1.55540 | ||||||||
\(766\) | 1.08545e10 | 0.872590 | ||||||||
\(767\) | −1.58197e10 | −1.26594 | ||||||||
\(768\) | 3.75654e8 | 0.0299243 | ||||||||
\(769\) | 1.86998e9 | 0.148284 | 0.0741422 | − | 0.997248i | \(-0.476378\pi\) | ||||
0.0741422 | + | 0.997248i | \(0.476378\pi\) | |||||||
\(770\) | −1.69431e10 | −1.33745 | ||||||||
\(771\) | 2.14006e9 | 0.168165 | ||||||||
\(772\) | −3.14542e9 | −0.246047 | ||||||||
\(773\) | 1.89091e10 | 1.47246 | 0.736228 | − | 0.676734i | \(-0.236605\pi\) | ||||
0.736228 | + | 0.676734i | \(0.236605\pi\) | |||||||
\(774\) | −2.13954e9 | −0.165854 | ||||||||
\(775\) | −3.59281e9 | −0.277255 | ||||||||
\(776\) | −3.70767e9 | −0.284830 | ||||||||
\(777\) | −1.01210e9 | −0.0774019 | ||||||||
\(778\) | 7.58082e9 | 0.577148 | ||||||||
\(779\) | 2.78659e10 | 2.11199 | ||||||||
\(780\) | 8.56416e9 | 0.646180 | ||||||||
\(781\) | −7.93354e9 | −0.595921 | ||||||||
\(782\) | 1.31877e10 | 0.986156 | ||||||||
\(783\) | −1.41228e10 | −1.05137 | ||||||||
\(784\) | −1.11377e8 | −0.00825447 | ||||||||
\(785\) | −2.51969e9 | −0.185910 | ||||||||
\(786\) | 2.87149e9 | 0.210925 | ||||||||
\(787\) | −6.44240e9 | −0.471125 | −0.235563 | − | 0.971859i | \(-0.575693\pi\) | ||||
−0.235563 | + | 0.971859i | \(0.575693\pi\) | |||||||
\(788\) | −8.53434e9 | −0.621339 | ||||||||
\(789\) | −7.81008e9 | −0.566091 | ||||||||
\(790\) | −1.71778e10 | −1.23958 | ||||||||
\(791\) | 1.40912e10 | 1.01235 | ||||||||
\(792\) | −4.05908e9 | −0.290328 | ||||||||
\(793\) | 3.64970e10 | 2.59897 | ||||||||
\(794\) | 1.29449e10 | 0.917755 | ||||||||
\(795\) | −1.72006e10 | −1.21411 | ||||||||
\(796\) | −5.34372e9 | −0.375533 | ||||||||
\(797\) | −6.22130e9 | −0.435288 | −0.217644 | − | 0.976028i | \(-0.569837\pi\) | ||||
−0.217644 | + | 0.976028i | \(0.569837\pi\) | |||||||
\(798\) | −8.24834e9 | −0.574588 | ||||||||
\(799\) | −1.06467e10 | −0.738418 | ||||||||
\(800\) | 5.78404e9 | 0.399408 | ||||||||
\(801\) | −1.09628e10 | −0.753717 | ||||||||
\(802\) | 1.18342e10 | 0.810084 | ||||||||
\(803\) | 1.83683e10 | 1.25189 | ||||||||
\(804\) | 2.90700e8 | 0.0197264 | ||||||||
\(805\) | 3.27847e10 | 2.21506 | ||||||||
\(806\) | 1.92849e9 | 0.129731 | ||||||||
\(807\) | 1.32186e9 | 0.0885379 | ||||||||
\(808\) | −7.45188e9 | −0.496965 | ||||||||
\(809\) | −5.70480e6 | −0.000378809 0 | −0.000189404 | − | 1.00000i | \(-0.500060\pi\) | ||||
−0.000189404 | 1.00000i | \(0.500060\pi\) | ||||||||
\(810\) | −7.04446e9 | −0.465747 | ||||||||
\(811\) | 1.35122e10 | 0.889514 | 0.444757 | − | 0.895651i | \(-0.353290\pi\) | ||||
0.444757 | + | 0.895651i | \(0.353290\pi\) | |||||||
\(812\) | 9.30198e9 | 0.609718 | ||||||||
\(813\) | 5.30224e9 | 0.346053 | ||||||||
\(814\) | −1.90583e9 | −0.123851 | ||||||||
\(815\) | 3.80317e10 | 2.46090 | ||||||||
\(816\) | −2.07659e9 | −0.133794 | ||||||||
\(817\) | −8.18686e9 | −0.525219 | ||||||||
\(818\) | 1.22593e10 | 0.783120 | ||||||||
\(819\) | 1.78154e10 | 1.13319 | ||||||||
\(820\) | 1.74406e10 | 1.10462 | ||||||||
\(821\) | −2.04061e10 | −1.28694 | −0.643472 | − | 0.765470i | \(-0.722507\pi\) | ||||
−0.643472 | + | 0.765470i | \(0.722507\pi\) | |||||||
\(822\) | −6.85155e9 | −0.430266 | ||||||||
\(823\) | 1.31164e10 | 0.820191 | 0.410095 | − | 0.912043i | \(-0.365495\pi\) | ||||
0.410095 | + | 0.912043i | \(0.365495\pi\) | |||||||
\(824\) | −9.70888e9 | −0.604538 | ||||||||
\(825\) | 1.85882e10 | 1.15252 | ||||||||
\(826\) | 9.53601e9 | 0.588758 | ||||||||
\(827\) | 1.00525e10 | 0.618021 | 0.309010 | − | 0.951059i | \(-0.400002\pi\) | ||||
0.309010 | + | 0.951059i | \(0.400002\pi\) | |||||||
\(828\) | 7.85424e9 | 0.480837 | ||||||||
\(829\) | −2.39621e10 | −1.46078 | −0.730389 | − | 0.683031i | \(-0.760661\pi\) | ||||
−0.730389 | + | 0.683031i | \(0.760661\pi\) | |||||||
\(830\) | −1.08718e10 | −0.659977 | ||||||||
\(831\) | 1.95739e9 | 0.118324 | ||||||||
\(832\) | −3.10466e9 | −0.186888 | ||||||||
\(833\) | 6.15686e8 | 0.0369064 | ||||||||
\(834\) | 4.65081e9 | 0.277618 | ||||||||
\(835\) | −8.91113e9 | −0.529700 | ||||||||
\(836\) | −1.55319e10 | −0.919396 | ||||||||
\(837\) | 1.76494e9 | 0.104038 | ||||||||
\(838\) | 4.49507e9 | 0.263865 | ||||||||
\(839\) | 2.73604e9 | 0.159939 | 0.0799697 | − | 0.996797i | \(-0.474518\pi\) | ||||
0.0799697 | + | 0.996797i | \(0.474518\pi\) | |||||||
\(840\) | −5.16242e9 | −0.300522 | ||||||||
\(841\) | 9.27700e9 | 0.537801 | ||||||||
\(842\) | −6.89401e7 | −0.00397997 | ||||||||
\(843\) | 1.52488e8 | 0.00876676 | ||||||||
\(844\) | −3.31033e9 | −0.189528 | ||||||||
\(845\) | −3.91159e10 | −2.23026 | ||||||||
\(846\) | −6.34090e9 | −0.360043 | ||||||||
\(847\) | 2.34910e9 | 0.132834 | ||||||||
\(848\) | 6.23553e9 | 0.351146 | ||||||||
\(849\) | 7.38166e9 | 0.413978 | ||||||||
\(850\) | −3.19739e10 | −1.78578 | ||||||||
\(851\) | 3.68774e9 | 0.205119 | ||||||||
\(852\) | −2.41728e9 | −0.133902 | ||||||||
\(853\) | −1.75500e10 | −0.968181 | −0.484090 | − | 0.875018i | \(-0.660849\pi\) | ||||
−0.484090 | + | 0.875018i | \(0.660849\pi\) | |||||||
\(854\) | −2.20002e10 | −1.20871 | ||||||||
\(855\) | −4.38923e10 | −2.40164 | ||||||||
\(856\) | 5.73136e8 | 0.0312320 | ||||||||
\(857\) | 1.35123e9 | 0.0733327 | 0.0366663 | − | 0.999328i | \(-0.488326\pi\) | ||||
0.0366663 | + | 0.999328i | \(0.488326\pi\) | |||||||
\(858\) | −9.97745e9 | −0.539280 | ||||||||
\(859\) | 1.07334e10 | 0.577777 | 0.288888 | − | 0.957363i | \(-0.406714\pi\) | ||||
0.288888 | + | 0.957363i | \(0.406714\pi\) | |||||||
\(860\) | −5.12395e9 | −0.274701 | ||||||||
\(861\) | −1.07904e10 | −0.576138 | ||||||||
\(862\) | −3.42267e9 | −0.182007 | ||||||||
\(863\) | −1.85843e10 | −0.984257 | −0.492129 | − | 0.870523i | \(-0.663781\pi\) | ||||
−0.492129 | + | 0.870523i | \(0.663781\pi\) | |||||||
\(864\) | −2.84136e9 | −0.149875 | ||||||||
\(865\) | −2.61243e10 | −1.37242 | ||||||||
\(866\) | 1.24891e10 | 0.653457 | ||||||||
\(867\) | 2.29153e9 | 0.119415 | ||||||||
\(868\) | −1.16248e9 | −0.0603346 | ||||||||
\(869\) | 2.00126e10 | 1.03451 | ||||||||
\(870\) | −1.47219e10 | −0.757961 | ||||||||
\(871\) | −2.40254e9 | −0.123199 | ||||||||
\(872\) | 2.40388e9 | 0.122774 | ||||||||
\(873\) | 1.22068e10 | 0.620941 | ||||||||
\(874\) | 3.00539e10 | 1.52269 | ||||||||
\(875\) | −4.43064e10 | −2.23583 | ||||||||
\(876\) | 5.59666e9 | 0.281297 | ||||||||
\(877\) | −1.63802e10 | −0.820012 | −0.410006 | − | 0.912083i | \(-0.634473\pi\) | ||||
−0.410006 | + | 0.912083i | \(0.634473\pi\) | |||||||
\(878\) | 1.30726e10 | 0.651823 | ||||||||
\(879\) | −1.14530e8 | −0.00568796 | ||||||||
\(880\) | −9.72101e9 | −0.480864 | ||||||||
\(881\) | 2.64570e10 | 1.30354 | 0.651771 | − | 0.758416i | \(-0.274026\pi\) | ||||
0.651771 | + | 0.758416i | \(0.274026\pi\) | |||||||
\(882\) | 3.66686e8 | 0.0179951 | ||||||||
\(883\) | 1.20676e10 | 0.589874 | 0.294937 | − | 0.955517i | \(-0.404701\pi\) | ||||
0.294937 | + | 0.955517i | \(0.404701\pi\) | |||||||
\(884\) | 1.71624e10 | 0.835593 | ||||||||
\(885\) | −1.50923e10 | −0.731904 | ||||||||
\(886\) | −4.96885e9 | −0.240015 | ||||||||
\(887\) | 5.29007e9 | 0.254524 | 0.127262 | − | 0.991869i | \(-0.459381\pi\) | ||||
0.127262 | + | 0.991869i | \(0.459381\pi\) | |||||||
\(888\) | −5.80688e8 | −0.0278290 | ||||||||
\(889\) | −1.84661e10 | −0.881492 | ||||||||
\(890\) | −2.62546e10 | −1.24836 | ||||||||
\(891\) | 8.20697e9 | 0.388697 | ||||||||
\(892\) | −1.20699e10 | −0.569414 | ||||||||
\(893\) | −2.42632e10 | −1.14017 | ||||||||
\(894\) | 3.84186e9 | 0.179829 | ||||||||
\(895\) | −1.71865e10 | −0.801323 | ||||||||
\(896\) | 1.87147e9 | 0.0869169 | ||||||||
\(897\) | 1.93062e10 | 0.893147 | ||||||||
\(898\) | 1.73430e9 | 0.0799204 | ||||||||
\(899\) | −3.31510e9 | −0.152173 | ||||||||
\(900\) | −1.90428e10 | −0.870726 | ||||||||
\(901\) | −3.44697e10 | −1.57000 | ||||||||
\(902\) | −2.03187e10 | −0.921877 | ||||||||
\(903\) | 3.17016e9 | 0.143276 | ||||||||
\(904\) | 8.08475e9 | 0.363980 | ||||||||
\(905\) | −4.74282e10 | −2.12700 | ||||||||
\(906\) | −1.36469e10 | −0.609656 | ||||||||
\(907\) | 4.35182e9 | 0.193663 | 0.0968313 | − | 0.995301i | \(-0.469129\pi\) | ||||
0.0968313 | + | 0.995301i | \(0.469129\pi\) | |||||||
\(908\) | 2.00240e10 | 0.887667 | ||||||||
\(909\) | 2.45338e10 | 1.08341 | ||||||||
\(910\) | 4.26657e10 | 1.87687 | ||||||||
\(911\) | −8.14092e9 | −0.356746 | −0.178373 | − | 0.983963i | \(-0.557083\pi\) | ||||
−0.178373 | + | 0.983963i | \(0.557083\pi\) | |||||||
\(912\) | −4.73243e9 | −0.206587 | ||||||||
\(913\) | 1.26659e10 | 0.550794 | ||||||||
\(914\) | −2.87894e10 | −1.24716 | ||||||||
\(915\) | 3.48189e10 | 1.50259 | ||||||||
\(916\) | −1.37252e10 | −0.590046 | ||||||||
\(917\) | 1.43055e10 | 0.612645 | ||||||||
\(918\) | 1.57069e10 | 0.670103 | ||||||||
\(919\) | −4.36837e10 | −1.85659 | −0.928293 | − | 0.371850i | \(-0.878723\pi\) | ||||
−0.928293 | + | 0.371850i | \(0.878723\pi\) | |||||||
\(920\) | 1.88100e10 | 0.796400 | ||||||||
\(921\) | 9.04271e8 | 0.0381408 | ||||||||
\(922\) | −3.55741e9 | −0.149477 | ||||||||
\(923\) | 1.99780e10 | 0.836270 | ||||||||
\(924\) | 6.01435e9 | 0.250805 | ||||||||
\(925\) | −8.94101e9 | −0.371442 | ||||||||
\(926\) | −8.68818e9 | −0.359576 | ||||||||
\(927\) | 3.19645e10 | 1.31792 | ||||||||
\(928\) | 5.33695e9 | 0.219217 | ||||||||
\(929\) | −7.35357e9 | −0.300915 | −0.150457 | − | 0.988617i | \(-0.548075\pi\) | ||||
−0.150457 | + | 0.988617i | \(0.548075\pi\) | |||||||
\(930\) | 1.83982e9 | 0.0750039 | ||||||||
\(931\) | 1.40311e9 | 0.0569860 | ||||||||
\(932\) | 4.91800e9 | 0.198991 | ||||||||
\(933\) | −4.49285e9 | −0.181107 | ||||||||
\(934\) | 2.88982e10 | 1.16053 | ||||||||
\(935\) | 5.37372e10 | 2.14998 | ||||||||
\(936\) | 1.02214e10 | 0.407424 | ||||||||
\(937\) | −1.44717e10 | −0.574688 | −0.287344 | − | 0.957827i | \(-0.592772\pi\) | ||||
−0.287344 | + | 0.957827i | \(0.592772\pi\) | |||||||
\(938\) | 1.44824e9 | 0.0572967 | ||||||||
\(939\) | −1.14563e10 | −0.451561 | ||||||||
\(940\) | −1.51857e10 | −0.596332 | ||||||||
\(941\) | 1.33141e9 | 0.0520894 | 0.0260447 | − | 0.999661i | \(-0.491709\pi\) | ||||
0.0260447 | + | 0.999661i | \(0.491709\pi\) | |||||||
\(942\) | 8.94420e8 | 0.0348629 | ||||||||
\(943\) | 3.93163e10 | 1.52680 | ||||||||
\(944\) | 5.47122e9 | 0.211681 | ||||||||
\(945\) | 3.90474e10 | 1.50515 | ||||||||
\(946\) | 5.96952e9 | 0.229256 | ||||||||
\(947\) | 1.16271e10 | 0.444882 | 0.222441 | − | 0.974946i | \(-0.428598\pi\) | ||||
0.222441 | + | 0.974946i | \(0.428598\pi\) | |||||||
\(948\) | 6.09765e9 | 0.232452 | ||||||||
\(949\) | −4.62546e10 | −1.75680 | ||||||||
\(950\) | −7.28665e10 | −2.75737 | ||||||||
\(951\) | −2.15257e10 | −0.811568 | ||||||||
\(952\) | −1.03454e10 | −0.388613 | ||||||||
\(953\) | 9.52377e7 | 0.00356438 | 0.00178219 | − | 0.999998i | \(-0.499433\pi\) | ||||
0.00178219 | + | 0.999998i | \(0.499433\pi\) | |||||||
\(954\) | −2.05292e10 | −0.765514 | ||||||||
\(955\) | 3.78511e10 | 1.40626 | ||||||||
\(956\) | −1.25917e10 | −0.466103 | ||||||||
\(957\) | 1.71514e10 | 0.632568 | ||||||||
\(958\) | 3.16725e10 | 1.16387 | ||||||||
\(959\) | −3.41337e10 | −1.24973 | ||||||||
\(960\) | −2.96190e9 | −0.108049 | ||||||||
\(961\) | −2.70983e10 | −0.984942 | ||||||||
\(962\) | 4.79920e9 | 0.173802 | ||||||||
\(963\) | −1.88693e9 | −0.0680871 | ||||||||
\(964\) | 8.32249e9 | 0.299215 | ||||||||
\(965\) | 2.48006e10 | 0.888417 | ||||||||
\(966\) | −1.16377e10 | −0.415380 | ||||||||
\(967\) | 4.10715e10 | 1.46066 | 0.730328 | − | 0.683096i | \(-0.239367\pi\) | ||||
0.730328 | + | 0.683096i | \(0.239367\pi\) | |||||||
\(968\) | 1.34778e9 | 0.0477590 | ||||||||
\(969\) | 2.61606e10 | 0.923666 | ||||||||
\(970\) | 2.92338e10 | 1.02845 | ||||||||
\(971\) | 1.43880e10 | 0.504350 | 0.252175 | − | 0.967682i | \(-0.418854\pi\) | ||||
0.252175 | + | 0.967682i | \(0.418854\pi\) | |||||||
\(972\) | 1.46374e10 | 0.511249 | ||||||||
\(973\) | 2.31698e10 | 0.806358 | ||||||||
\(974\) | 3.44019e10 | 1.19296 | ||||||||
\(975\) | −4.68083e10 | −1.61736 | ||||||||
\(976\) | −1.26225e10 | −0.434580 | ||||||||
\(977\) | 6.76985e9 | 0.232246 | 0.116123 | − | 0.993235i | \(-0.462953\pi\) | ||||
0.116123 | + | 0.993235i | \(0.462953\pi\) | |||||||
\(978\) | −1.35002e10 | −0.461482 | ||||||||
\(979\) | 3.05873e10 | 1.04184 | ||||||||
\(980\) | 8.78170e8 | 0.0298049 | ||||||||
\(981\) | −7.91428e9 | −0.267652 | ||||||||
\(982\) | −2.03764e10 | −0.686651 | ||||||||
\(983\) | 4.81556e10 | 1.61700 | 0.808498 | − | 0.588498i | \(-0.200281\pi\) | ||||
0.808498 | + | 0.588498i | \(0.200281\pi\) | |||||||
\(984\) | −6.19092e9 | −0.207144 | ||||||||
\(985\) | 6.72905e10 | 2.24350 | ||||||||
\(986\) | −2.95024e10 | −0.980139 | ||||||||
\(987\) | 9.39534e9 | 0.311030 | ||||||||
\(988\) | 3.91120e10 | 1.29021 | ||||||||
\(989\) | −1.15509e10 | −0.379690 | ||||||||
\(990\) | 3.20045e10 | 1.04830 | ||||||||
\(991\) | 1.81773e10 | 0.593296 | 0.296648 | − | 0.954987i | \(-0.404131\pi\) | ||||
0.296648 | + | 0.954987i | \(0.404131\pi\) | |||||||
\(992\) | −6.66965e8 | −0.0216926 | ||||||||
\(993\) | −9.03241e9 | −0.292740 | ||||||||
\(994\) | −1.20426e10 | −0.388928 | ||||||||
\(995\) | 4.21335e10 | 1.35596 | ||||||||
\(996\) | 3.85920e9 | 0.123763 | ||||||||
\(997\) | 3.32870e10 | 1.06376 | 0.531878 | − | 0.846821i | \(-0.321487\pi\) | ||||
0.531878 | + | 0.846821i | \(0.321487\pi\) | |||||||
\(998\) | −2.50815e10 | −0.798723 | ||||||||
\(999\) | 4.39220e9 | 0.139381 |
(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 | 74.8.a.b.1.4 | ✓ | 4 | |
4.3 | odd | 2 | 592.8.a.a.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.8.a.b.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
592.8.a.a.1.1 | 4 | 4.3 | odd | 2 |