Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,110,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 110, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 110);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 110 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(75.2394221917\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2 x^{7} + \cdots + 46\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{118}\cdot 3^{40}\cdot 5^{14}\cdot 7^{6}\cdot 11^{3}\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.20500e13\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.02754e15 | −0.0795858 | −0.0397929 | − | 0.999208i | \(-0.512670\pi\) | ||||
−0.0397929 | + | 0.999208i | \(0.512670\pi\) | |||||||
\(3\) | −9.96254e25 | −0.989149 | −0.494575 | − | 0.869135i | \(-0.664676\pi\) | ||||
−0.494575 | + | 0.869135i | \(0.664676\pi\) | |||||||
\(4\) | −6.44926e32 | −0.993666 | ||||||||
\(5\) | −2.14431e38 | −1.72752 | −0.863761 | − | 0.503903i | \(-0.831897\pi\) | ||||
−0.863761 | + | 0.503903i | \(0.831897\pi\) | |||||||
\(6\) | 2.01995e41 | 0.0787222 | ||||||||
\(7\) | −1.47165e46 | −1.28813 | −0.644067 | − | 0.764969i | \(-0.722754\pi\) | ||||
−0.644067 | + | 0.764969i | \(0.722754\pi\) | |||||||
\(8\) | 2.62357e48 | 0.158668 | ||||||||
\(9\) | −2.18949e50 | −0.0215837 | ||||||||
\(10\) | 4.34769e53 | 0.137486 | ||||||||
\(11\) | 5.24987e56 | 0.920974 | 0.460487 | − | 0.887666i | \(-0.347675\pi\) | ||||
0.460487 | + | 0.887666i | \(0.347675\pi\) | |||||||
\(12\) | 6.42510e58 | 0.982884 | ||||||||
\(13\) | −3.46172e60 | −0.675117 | −0.337559 | − | 0.941304i | \(-0.609601\pi\) | ||||
−0.337559 | + | 0.941304i | \(0.609601\pi\) | |||||||
\(14\) | 2.98383e61 | 0.102517 | ||||||||
\(15\) | 2.13628e64 | 1.70878 | ||||||||
\(16\) | 4.13262e65 | 0.981038 | ||||||||
\(17\) | 1.50023e67 | 1.30825 | 0.654125 | − | 0.756386i | \(-0.273037\pi\) | ||||
0.654125 | + | 0.756386i | \(0.273037\pi\) | |||||||
\(18\) | 4.43928e65 | 0.00171775 | ||||||||
\(19\) | −4.60234e69 | −0.935206 | −0.467603 | − | 0.883939i | \(-0.654882\pi\) | ||||
−0.467603 | + | 0.883939i | \(0.654882\pi\) | |||||||
\(20\) | 1.38292e71 | 1.71658 | ||||||||
\(21\) | 1.46614e72 | 1.27416 | ||||||||
\(22\) | −1.06444e72 | −0.0732965 | ||||||||
\(23\) | −1.72378e74 | −1.05273 | −0.526364 | − | 0.850260i | \(-0.676445\pi\) | ||||
−0.526364 | + | 0.850260i | \(0.676445\pi\) | |||||||
\(24\) | −2.61374e74 | −0.156946 | ||||||||
\(25\) | 3.05734e76 | 1.98433 | ||||||||
\(26\) | 7.01879e75 | 0.0537298 | ||||||||
\(27\) | 1.03243e78 | 1.01050 | ||||||||
\(28\) | 9.49105e78 | 1.27997 | ||||||||
\(29\) | −4.10244e79 | −0.817243 | −0.408622 | − | 0.912704i | \(-0.633990\pi\) | ||||
−0.408622 | + | 0.912704i | \(0.633990\pi\) | |||||||
\(30\) | −4.33141e79 | −0.135994 | ||||||||
\(31\) | −8.97441e79 | −0.0471839 | −0.0235919 | − | 0.999722i | \(-0.507510\pi\) | ||||
−0.0235919 | + | 0.999722i | \(0.507510\pi\) | |||||||
\(32\) | −2.54070e81 | −0.236744 | ||||||||
\(33\) | −5.23021e82 | −0.910981 | ||||||||
\(34\) | −3.04178e82 | −0.104118 | ||||||||
\(35\) | 3.15568e84 | 2.22528 | ||||||||
\(36\) | 1.41206e83 | 0.0214470 | ||||||||
\(37\) | −4.96618e85 | −1.69445 | −0.847225 | − | 0.531235i | \(-0.821728\pi\) | ||||
−0.847225 | + | 0.531235i | \(0.821728\pi\) | |||||||
\(38\) | 9.33144e84 | 0.0744291 | ||||||||
\(39\) | 3.44875e86 | 0.667792 | ||||||||
\(40\) | −5.62576e86 | −0.274101 | ||||||||
\(41\) | 5.38189e87 | 0.682676 | 0.341338 | − | 0.939941i | \(-0.389120\pi\) | ||||
0.341338 | + | 0.939941i | \(0.389120\pi\) | |||||||
\(42\) | −2.97266e87 | −0.101405 | ||||||||
\(43\) | 3.74176e88 | 0.354034 | 0.177017 | − | 0.984208i | \(-0.443355\pi\) | ||||
0.177017 | + | 0.984208i | \(0.443355\pi\) | |||||||
\(44\) | −3.38578e89 | −0.915141 | ||||||||
\(45\) | 4.69495e88 | 0.0372863 | ||||||||
\(46\) | 3.49505e89 | 0.0837821 | ||||||||
\(47\) | 1.16615e91 | 0.865804 | 0.432902 | − | 0.901441i | \(-0.357490\pi\) | ||||
0.432902 | + | 0.901441i | \(0.357490\pi\) | |||||||
\(48\) | −4.11714e91 | −0.970393 | ||||||||
\(49\) | 8.60522e91 | 0.659289 | ||||||||
\(50\) | −6.19890e91 | −0.157924 | ||||||||
\(51\) | −1.49461e93 | −1.29405 | ||||||||
\(52\) | 2.23255e93 | 0.670841 | ||||||||
\(53\) | 1.39456e94 | 1.48389 | 0.741946 | − | 0.670459i | \(-0.233903\pi\) | ||||
0.741946 | + | 0.670459i | \(0.233903\pi\) | |||||||
\(54\) | −2.09330e93 | −0.0804213 | ||||||||
\(55\) | −1.12574e95 | −1.59100 | ||||||||
\(56\) | −3.86097e94 | −0.204385 | ||||||||
\(57\) | 4.58510e95 | 0.925058 | ||||||||
\(58\) | 8.31788e94 | 0.0650410 | ||||||||
\(59\) | 2.10352e96 | 0.647905 | 0.323952 | − | 0.946073i | \(-0.394988\pi\) | ||||
0.323952 | + | 0.946073i | \(0.394988\pi\) | |||||||
\(60\) | −1.37774e97 | −1.69795 | ||||||||
\(61\) | 1.91674e97 | 0.959594 | 0.479797 | − | 0.877380i | \(-0.340710\pi\) | ||||
0.479797 | + | 0.877380i | \(0.340710\pi\) | |||||||
\(62\) | 1.81960e95 | 0.00375517 | ||||||||
\(63\) | 3.22215e96 | 0.0278027 | ||||||||
\(64\) | −2.63071e98 | −0.962197 | ||||||||
\(65\) | 7.42302e98 | 1.16628 | ||||||||
\(66\) | 1.06045e98 | 0.0725012 | ||||||||
\(67\) | −2.19176e99 | −0.660262 | −0.330131 | − | 0.943935i | \(-0.607093\pi\) | ||||
−0.330131 | + | 0.943935i | \(0.607093\pi\) | |||||||
\(68\) | −9.67536e99 | −1.29996 | ||||||||
\(69\) | 1.71733e100 | 1.04130 | ||||||||
\(70\) | −6.39828e99 | −0.177101 | ||||||||
\(71\) | −1.48237e100 | −0.189399 | −0.0946993 | − | 0.995506i | \(-0.530189\pi\) | ||||
−0.0946993 | + | 0.995506i | \(0.530189\pi\) | |||||||
\(72\) | −5.74426e98 | −0.00342463 | ||||||||
\(73\) | −4.73812e101 | −1.33202 | −0.666009 | − | 0.745944i | \(-0.731999\pi\) | ||||
−0.666009 | + | 0.745944i | \(0.731999\pi\) | |||||||
\(74\) | 1.00692e101 | 0.134854 | ||||||||
\(75\) | −3.04589e102 | −1.96280 | ||||||||
\(76\) | 2.96817e102 | 0.929282 | ||||||||
\(77\) | −7.72597e102 | −1.18634 | ||||||||
\(78\) | −6.99250e101 | −0.0531468 | ||||||||
\(79\) | −3.66779e103 | −1.39229 | −0.696143 | − | 0.717904i | \(-0.745102\pi\) | ||||
−0.696143 | + | 0.717904i | \(0.745102\pi\) | |||||||
\(80\) | −8.86163e103 | −1.69476 | ||||||||
\(81\) | −1.00635e104 | −0.977950 | ||||||||
\(82\) | −1.09120e103 | −0.0543313 | ||||||||
\(83\) | 1.15763e104 | 0.297724 | 0.148862 | − | 0.988858i | \(-0.452439\pi\) | ||||
0.148862 | + | 0.988858i | \(0.452439\pi\) | |||||||
\(84\) | −9.45550e104 | −1.26609 | ||||||||
\(85\) | −3.21696e105 | −2.26003 | ||||||||
\(86\) | −7.58658e103 | −0.0281761 | ||||||||
\(87\) | 4.08707e105 | 0.808376 | ||||||||
\(88\) | 1.37734e105 | 0.146129 | ||||||||
\(89\) | −7.77888e105 | −0.445822 | −0.222911 | − | 0.974839i | \(-0.571556\pi\) | ||||
−0.222911 | + | 0.974839i | \(0.571556\pi\) | |||||||
\(90\) | −9.51921e103 | −0.00296746 | ||||||||
\(91\) | 5.09444e106 | 0.869642 | ||||||||
\(92\) | 1.11171e107 | 1.04606 | ||||||||
\(93\) | 8.94080e105 | 0.0466719 | ||||||||
\(94\) | −2.36441e106 | −0.0689057 | ||||||||
\(95\) | 9.86886e107 | 1.61559 | ||||||||
\(96\) | 2.53118e107 | 0.234175 | ||||||||
\(97\) | 2.38667e108 | 1.25526 | 0.627629 | − | 0.778513i | \(-0.284026\pi\) | ||||
0.627629 | + | 0.778513i | \(0.284026\pi\) | |||||||
\(98\) | −1.74475e107 | −0.0524700 | ||||||||
\(99\) | −1.14945e107 | −0.0198780 | ||||||||
\(100\) | −1.97176e109 | −1.97176 | ||||||||
\(101\) | 1.79300e109 | 1.04248 | 0.521239 | − | 0.853411i | \(-0.325470\pi\) | ||||
0.521239 | + | 0.853411i | \(0.325470\pi\) | |||||||
\(102\) | 3.03038e108 | 0.102988 | ||||||||
\(103\) | −3.76956e109 | −0.752769 | −0.376385 | − | 0.926464i | \(-0.622833\pi\) | ||||
−0.376385 | + | 0.926464i | \(0.622833\pi\) | |||||||
\(104\) | −9.08206e108 | −0.107119 | ||||||||
\(105\) | −3.14386e110 | −2.20113 | ||||||||
\(106\) | −2.82753e109 | −0.118097 | ||||||||
\(107\) | 2.26052e110 | 0.565968 | 0.282984 | − | 0.959125i | \(-0.408676\pi\) | ||||
0.282984 | + | 0.959125i | \(0.408676\pi\) | |||||||
\(108\) | −6.65842e110 | −1.00410 | ||||||||
\(109\) | 4.65522e110 | 0.424811 | 0.212406 | − | 0.977182i | \(-0.431870\pi\) | ||||
0.212406 | + | 0.977182i | \(0.431870\pi\) | |||||||
\(110\) | 2.28248e110 | 0.126621 | ||||||||
\(111\) | 4.94758e111 | 1.67606 | ||||||||
\(112\) | −6.08176e111 | −1.26371 | ||||||||
\(113\) | 5.07866e111 | 0.650091 | 0.325046 | − | 0.945698i | \(-0.394620\pi\) | ||||
0.325046 | + | 0.945698i | \(0.394620\pi\) | |||||||
\(114\) | −9.29649e110 | −0.0736215 | ||||||||
\(115\) | 3.69634e112 | 1.81861 | ||||||||
\(116\) | 2.64577e112 | 0.812067 | ||||||||
\(117\) | 7.57939e110 | 0.0145715 | ||||||||
\(118\) | −4.26497e111 | −0.0515640 | ||||||||
\(119\) | −2.20781e113 | −1.68520 | ||||||||
\(120\) | 5.60468e112 | 0.271127 | ||||||||
\(121\) | −4.93278e112 | −0.151806 | ||||||||
\(122\) | −3.88628e112 | −0.0763700 | ||||||||
\(123\) | −5.36173e113 | −0.675269 | ||||||||
\(124\) | 5.78783e112 | 0.0468850 | ||||||||
\(125\) | −3.25207e114 | −1.70045 | ||||||||
\(126\) | −6.53306e111 | −0.00221270 | ||||||||
\(127\) | 3.91250e114 | 0.861293 | 0.430647 | − | 0.902521i | \(-0.358285\pi\) | ||||
0.430647 | + | 0.902521i | \(0.358285\pi\) | |||||||
\(128\) | 2.18240e114 | 0.313321 | ||||||||
\(129\) | −3.72774e114 | −0.350193 | ||||||||
\(130\) | −1.50505e114 | −0.0928193 | ||||||||
\(131\) | 2.54602e115 | 1.03413 | 0.517066 | − | 0.855945i | \(-0.327024\pi\) | ||||
0.517066 | + | 0.855945i | \(0.327024\pi\) | |||||||
\(132\) | 3.37310e115 | 0.905211 | ||||||||
\(133\) | 6.77302e115 | 1.20467 | ||||||||
\(134\) | 4.44389e114 | 0.0525475 | ||||||||
\(135\) | −2.21386e116 | −1.74566 | ||||||||
\(136\) | 3.93595e115 | 0.207577 | ||||||||
\(137\) | 1.85339e116 | 0.655686 | 0.327843 | − | 0.944732i | \(-0.393678\pi\) | ||||
0.327843 | + | 0.944732i | \(0.393678\pi\) | |||||||
\(138\) | −3.48196e115 | −0.0828730 | ||||||||
\(139\) | 5.08781e116 | 0.817004 | 0.408502 | − | 0.912757i | \(-0.366051\pi\) | ||||
0.408502 | + | 0.912757i | \(0.366051\pi\) | |||||||
\(140\) | −2.03518e117 | −2.21118 | ||||||||
\(141\) | −1.16178e117 | −0.856410 | ||||||||
\(142\) | 3.00557e115 | 0.0150734 | ||||||||
\(143\) | −1.81736e117 | −0.621766 | ||||||||
\(144\) | −9.04831e115 | −0.0211744 | ||||||||
\(145\) | 8.79692e117 | 1.41181 | ||||||||
\(146\) | 9.60674e116 | 0.106010 | ||||||||
\(147\) | −8.57299e117 | −0.652135 | ||||||||
\(148\) | 3.20282e118 | 1.68372 | ||||||||
\(149\) | −2.95585e118 | −1.07654 | −0.538270 | − | 0.842772i | \(-0.680922\pi\) | ||||
−0.538270 | + | 0.842772i | \(0.680922\pi\) | |||||||
\(150\) | 6.17568e117 | 0.156211 | ||||||||
\(151\) | 9.53184e118 | 1.67855 | 0.839273 | − | 0.543711i | \(-0.182981\pi\) | ||||
0.839273 | + | 0.543711i | \(0.182981\pi\) | |||||||
\(152\) | −1.20745e118 | −0.148387 | ||||||||
\(153\) | −3.28473e117 | −0.0282369 | ||||||||
\(154\) | 1.56647e118 | 0.0944157 | ||||||||
\(155\) | 1.92440e118 | 0.0815112 | ||||||||
\(156\) | −2.22419e119 | −0.663562 | ||||||||
\(157\) | −6.55912e119 | −1.38139 | −0.690693 | − | 0.723148i | \(-0.742694\pi\) | ||||
−0.690693 | + | 0.723148i | \(0.742694\pi\) | |||||||
\(158\) | 7.43661e118 | 0.110806 | ||||||||
\(159\) | −1.38934e120 | −1.46779 | ||||||||
\(160\) | 5.44806e119 | 0.408981 | ||||||||
\(161\) | 2.53680e120 | 1.35605 | ||||||||
\(162\) | 2.04043e119 | 0.0778310 | ||||||||
\(163\) | −3.98860e120 | −1.08792 | −0.543959 | − | 0.839112i | \(-0.683075\pi\) | ||||
−0.543959 | + | 0.839112i | \(0.683075\pi\) | |||||||
\(164\) | −3.47092e120 | −0.678352 | ||||||||
\(165\) | 1.12152e121 | 1.57374 | ||||||||
\(166\) | −2.34715e119 | −0.0236946 | ||||||||
\(167\) | 2.12485e121 | 1.54625 | 0.773126 | − | 0.634253i | \(-0.218692\pi\) | ||||
0.773126 | + | 0.634253i | \(0.218692\pi\) | |||||||
\(168\) | 3.84651e120 | 0.202167 | ||||||||
\(169\) | −1.43086e121 | −0.544216 | ||||||||
\(170\) | 6.52253e120 | 0.179866 | ||||||||
\(171\) | 1.00768e120 | 0.0201852 | ||||||||
\(172\) | −2.41316e121 | −0.351792 | ||||||||
\(173\) | 3.38854e121 | 0.360164 | 0.180082 | − | 0.983652i | \(-0.442364\pi\) | ||||
0.180082 | + | 0.983652i | \(0.442364\pi\) | |||||||
\(174\) | −8.28672e120 | −0.0643352 | ||||||||
\(175\) | −4.49933e122 | −2.55608 | ||||||||
\(176\) | 2.16957e122 | 0.903511 | ||||||||
\(177\) | −2.09564e122 | −0.640875 | ||||||||
\(178\) | 1.57720e121 | 0.0354811 | ||||||||
\(179\) | 2.93078e122 | 0.485840 | 0.242920 | − | 0.970046i | \(-0.421895\pi\) | ||||
0.242920 | + | 0.970046i | \(0.421895\pi\) | |||||||
\(180\) | −3.02789e121 | −0.0370501 | ||||||||
\(181\) | 5.78889e122 | 0.523737 | 0.261868 | − | 0.965104i | \(-0.415661\pi\) | ||||
0.261868 | + | 0.965104i | \(0.415661\pi\) | |||||||
\(182\) | −1.03292e122 | −0.0692111 | ||||||||
\(183\) | −1.90956e123 | −0.949181 | ||||||||
\(184\) | −4.52246e122 | −0.167034 | ||||||||
\(185\) | 1.06491e124 | 2.92720 | ||||||||
\(186\) | −1.81279e121 | −0.00371442 | ||||||||
\(187\) | 7.87600e123 | 1.20487 | ||||||||
\(188\) | −7.52078e123 | −0.860320 | ||||||||
\(189\) | −1.51938e124 | −1.30166 | ||||||||
\(190\) | −2.00095e123 | −0.128578 | ||||||||
\(191\) | −3.20680e124 | −1.54794 | −0.773969 | − | 0.633224i | \(-0.781731\pi\) | ||||
−0.773969 | + | 0.633224i | \(0.781731\pi\) | |||||||
\(192\) | 2.62085e124 | 0.951756 | ||||||||
\(193\) | 1.82650e124 | 0.499742 | 0.249871 | − | 0.968279i | \(-0.419612\pi\) | ||||
0.249871 | + | 0.968279i | \(0.419612\pi\) | |||||||
\(194\) | −4.83908e123 | −0.0999007 | ||||||||
\(195\) | −7.39522e124 | −1.15362 | ||||||||
\(196\) | −5.54973e124 | −0.655113 | ||||||||
\(197\) | 6.94971e124 | 0.621666 | 0.310833 | − | 0.950464i | \(-0.399392\pi\) | ||||
0.310833 | + | 0.950464i | \(0.399392\pi\) | |||||||
\(198\) | 2.33057e122 | 0.00158201 | ||||||||
\(199\) | −3.75935e123 | −0.0193919 | −0.00969595 | − | 0.999953i | \(-0.503086\pi\) | ||||
−0.00969595 | + | 0.999953i | \(0.503086\pi\) | |||||||
\(200\) | 8.02115e124 | 0.314848 | ||||||||
\(201\) | 2.18355e125 | 0.653097 | ||||||||
\(202\) | −3.63540e124 | −0.0829664 | ||||||||
\(203\) | 6.03735e125 | 1.05272 | ||||||||
\(204\) | 9.63912e125 | 1.28586 | ||||||||
\(205\) | −1.15405e126 | −1.17934 | ||||||||
\(206\) | 7.64295e124 | 0.0599097 | ||||||||
\(207\) | 3.77420e124 | 0.0227217 | ||||||||
\(208\) | −1.43060e126 | −0.662316 | ||||||||
\(209\) | −2.41617e126 | −0.861300 | ||||||||
\(210\) | 6.37431e125 | 0.175179 | ||||||||
\(211\) | 3.63035e126 | 0.770112 | 0.385056 | − | 0.922893i | \(-0.374182\pi\) | ||||
0.385056 | + | 0.922893i | \(0.374182\pi\) | |||||||
\(212\) | −8.99388e126 | −1.47449 | ||||||||
\(213\) | 1.47682e126 | 0.187344 | ||||||||
\(214\) | −4.58330e125 | −0.0450430 | ||||||||
\(215\) | −8.02351e126 | −0.611601 | ||||||||
\(216\) | 2.70865e126 | 0.160333 | ||||||||
\(217\) | 1.32072e126 | 0.0607792 | ||||||||
\(218\) | −9.43866e125 | −0.0338089 | ||||||||
\(219\) | 4.72037e127 | 1.31756 | ||||||||
\(220\) | 7.26018e127 | 1.58093 | ||||||||
\(221\) | −5.19337e127 | −0.883223 | ||||||||
\(222\) | −1.00314e127 | −0.133391 | ||||||||
\(223\) | 1.69776e127 | 0.176710 | 0.0883552 | − | 0.996089i | \(-0.471839\pi\) | ||||
0.0883552 | + | 0.996089i | \(0.471839\pi\) | |||||||
\(224\) | 3.73902e127 | 0.304958 | ||||||||
\(225\) | −6.69401e126 | −0.0428291 | ||||||||
\(226\) | −1.02972e127 | −0.0517380 | ||||||||
\(227\) | −2.63698e127 | −0.104159 | −0.0520795 | − | 0.998643i | \(-0.516585\pi\) | ||||
−0.0520795 | + | 0.998643i | \(0.516585\pi\) | |||||||
\(228\) | −2.95705e128 | −0.919199 | ||||||||
\(229\) | −5.95327e128 | −1.45788 | −0.728940 | − | 0.684577i | \(-0.759987\pi\) | ||||
−0.728940 | + | 0.684577i | \(0.759987\pi\) | |||||||
\(230\) | −7.49448e127 | −0.144735 | ||||||||
\(231\) | 7.69703e128 | 1.17347 | ||||||||
\(232\) | −1.07630e128 | −0.129670 | ||||||||
\(233\) | 5.27747e128 | 0.502954 | 0.251477 | − | 0.967863i | \(-0.419084\pi\) | ||||
0.251477 | + | 0.967863i | \(0.419084\pi\) | |||||||
\(234\) | −1.53675e126 | −0.00115969 | ||||||||
\(235\) | −2.50058e129 | −1.49569 | ||||||||
\(236\) | −1.35661e129 | −0.643801 | ||||||||
\(237\) | 3.65405e129 | 1.37718 | ||||||||
\(238\) | 4.47643e128 | 0.134118 | ||||||||
\(239\) | 6.00392e129 | 1.43136 | 0.715681 | − | 0.698427i | \(-0.246116\pi\) | ||||
0.715681 | + | 0.698427i | \(0.246116\pi\) | |||||||
\(240\) | 8.82844e129 | 1.67638 | ||||||||
\(241\) | −6.09889e129 | −0.923255 | −0.461627 | − | 0.887074i | \(-0.652734\pi\) | ||||
−0.461627 | + | 0.887074i | \(0.652734\pi\) | |||||||
\(242\) | 1.00014e128 | 0.0120816 | ||||||||
\(243\) | −4.47323e128 | −0.0431598 | ||||||||
\(244\) | −1.23616e130 | −0.953516 | ||||||||
\(245\) | −1.84523e130 | −1.13894 | ||||||||
\(246\) | 1.08712e129 | 0.0537418 | ||||||||
\(247\) | 1.59320e130 | 0.631374 | ||||||||
\(248\) | −2.35450e128 | −0.00748655 | ||||||||
\(249\) | −1.15329e130 | −0.294494 | ||||||||
\(250\) | 6.59371e129 | 0.135332 | ||||||||
\(251\) | −6.08328e130 | −1.00443 | −0.502215 | − | 0.864743i | \(-0.667482\pi\) | ||||
−0.502215 | + | 0.864743i | \(0.667482\pi\) | |||||||
\(252\) | −2.07805e129 | −0.0276266 | ||||||||
\(253\) | −9.04965e130 | −0.969535 | ||||||||
\(254\) | −7.93276e129 | −0.0685467 | ||||||||
\(255\) | 3.20491e131 | 2.23551 | ||||||||
\(256\) | 1.66318e131 | 0.937261 | ||||||||
\(257\) | −2.64025e131 | −1.20307 | −0.601533 | − | 0.798848i | \(-0.705443\pi\) | ||||
−0.601533 | + | 0.798848i | \(0.705443\pi\) | |||||||
\(258\) | 7.55817e129 | 0.0278704 | ||||||||
\(259\) | 7.30847e131 | 2.18268 | ||||||||
\(260\) | −4.78730e131 | −1.15889 | ||||||||
\(261\) | 8.98224e129 | 0.0176391 | ||||||||
\(262\) | −5.16217e130 | −0.0823023 | ||||||||
\(263\) | 6.99024e131 | 0.905532 | 0.452766 | − | 0.891629i | \(-0.350437\pi\) | ||||
0.452766 | + | 0.891629i | \(0.350437\pi\) | |||||||
\(264\) | −1.37218e131 | −0.144543 | ||||||||
\(265\) | −2.99038e132 | −2.56346 | ||||||||
\(266\) | −1.37326e131 | −0.0958746 | ||||||||
\(267\) | 7.74974e131 | 0.440985 | ||||||||
\(268\) | 1.41352e132 | 0.656080 | ||||||||
\(269\) | −6.91264e131 | −0.261905 | −0.130953 | − | 0.991389i | \(-0.541804\pi\) | ||||
−0.130953 | + | 0.991389i | \(0.541804\pi\) | |||||||
\(270\) | 4.48869e131 | 0.138930 | ||||||||
\(271\) | −7.05558e132 | −1.78528 | −0.892640 | − | 0.450770i | \(-0.851149\pi\) | ||||
−0.892640 | + | 0.450770i | \(0.851149\pi\) | |||||||
\(272\) | 6.19986e132 | 1.28344 | ||||||||
\(273\) | −5.07536e132 | −0.860205 | ||||||||
\(274\) | −3.75783e131 | −0.0521833 | ||||||||
\(275\) | 1.60507e133 | 1.82752 | ||||||||
\(276\) | −1.10755e133 | −1.03471 | ||||||||
\(277\) | 2.41655e133 | 1.85374 | 0.926870 | − | 0.375383i | \(-0.122489\pi\) | ||||
0.926870 | + | 0.375383i | \(0.122489\pi\) | |||||||
\(278\) | −1.03158e132 | −0.0650219 | ||||||||
\(279\) | 1.96494e130 | 0.00101840 | ||||||||
\(280\) | 8.27914e132 | 0.353079 | ||||||||
\(281\) | −1.29415e133 | −0.454453 | −0.227226 | − | 0.973842i | \(-0.572966\pi\) | ||||
−0.227226 | + | 0.973842i | \(0.572966\pi\) | |||||||
\(282\) | 2.35556e132 | 0.0681580 | ||||||||
\(283\) | −1.51288e132 | −0.0360948 | −0.0180474 | − | 0.999837i | \(-0.505745\pi\) | ||||
−0.0180474 | + | 0.999837i | \(0.505745\pi\) | |||||||
\(284\) | 9.56020e132 | 0.188199 | ||||||||
\(285\) | −9.83189e133 | −1.59806 | ||||||||
\(286\) | 3.68478e132 | 0.0494837 | ||||||||
\(287\) | −7.92026e133 | −0.879379 | ||||||||
\(288\) | 5.56282e131 | 0.00510981 | ||||||||
\(289\) | 9.35662e133 | 0.711519 | ||||||||
\(290\) | −1.78362e133 | −0.112360 | ||||||||
\(291\) | −2.37773e134 | −1.24164 | ||||||||
\(292\) | 3.05573e134 | 1.32358 | ||||||||
\(293\) | 2.46161e134 | 0.884980 | 0.442490 | − | 0.896773i | \(-0.354095\pi\) | ||||
0.442490 | + | 0.896773i | \(0.354095\pi\) | |||||||
\(294\) | 1.73821e133 | 0.0519007 | ||||||||
\(295\) | −4.51060e134 | −1.11927 | ||||||||
\(296\) | −1.30291e134 | −0.268854 | ||||||||
\(297\) | 5.42013e134 | 0.930644 | ||||||||
\(298\) | 5.99311e133 | 0.0856773 | ||||||||
\(299\) | 5.96726e134 | 0.710714 | ||||||||
\(300\) | 1.96437e135 | 1.95037 | ||||||||
\(301\) | −5.50656e134 | −0.456043 | ||||||||
\(302\) | −1.93262e134 | −0.133588 | ||||||||
\(303\) | −1.78629e135 | −1.03117 | ||||||||
\(304\) | −1.90197e135 | −0.917473 | ||||||||
\(305\) | −4.11010e135 | −1.65772 | ||||||||
\(306\) | 6.65993e132 | 0.00224725 | ||||||||
\(307\) | 2.70496e134 | 0.0764047 | 0.0382023 | − | 0.999270i | \(-0.487837\pi\) | ||||
0.0382023 | + | 0.999270i | \(0.487837\pi\) | |||||||
\(308\) | 4.98268e135 | 1.17882 | ||||||||
\(309\) | 3.75544e135 | 0.744601 | ||||||||
\(310\) | −3.90180e133 | −0.00648713 | ||||||||
\(311\) | −1.26793e136 | −1.76870 | −0.884349 | − | 0.466826i | \(-0.845397\pi\) | ||||
−0.884349 | + | 0.466826i | \(0.845397\pi\) | |||||||
\(312\) | 9.04804e134 | 0.105957 | ||||||||
\(313\) | −3.22055e134 | −0.0316784 | −0.0158392 | − | 0.999875i | \(-0.505042\pi\) | ||||
−0.0158392 | + | 0.999875i | \(0.505042\pi\) | |||||||
\(314\) | 1.32989e135 | 0.109939 | ||||||||
\(315\) | −6.90931e134 | −0.0480297 | ||||||||
\(316\) | 2.36546e136 | 1.38347 | ||||||||
\(317\) | 1.60712e136 | 0.791258 | 0.395629 | − | 0.918410i | \(-0.370527\pi\) | ||||
0.395629 | + | 0.918410i | \(0.370527\pi\) | |||||||
\(318\) | 2.81694e135 | 0.116815 | ||||||||
\(319\) | −2.15373e136 | −0.752660 | ||||||||
\(320\) | 5.64107e136 | 1.66222 | ||||||||
\(321\) | −2.25205e136 | −0.559827 | ||||||||
\(322\) | −5.14348e135 | −0.107923 | ||||||||
\(323\) | −6.90455e136 | −1.22348 | ||||||||
\(324\) | 6.49023e136 | 0.971756 | ||||||||
\(325\) | −1.05837e137 | −1.33965 | ||||||||
\(326\) | 8.08706e135 | 0.0865828 | ||||||||
\(327\) | −4.63778e136 | −0.420202 | ||||||||
\(328\) | 1.41198e136 | 0.108319 | ||||||||
\(329\) | −1.71616e137 | −1.11527 | ||||||||
\(330\) | −2.27393e136 | −0.125247 | ||||||||
\(331\) | 2.41606e137 | 1.12845 | 0.564226 | − | 0.825621i | \(-0.309175\pi\) | ||||
0.564226 | + | 0.825621i | \(0.309175\pi\) | |||||||
\(332\) | −7.46586e136 | −0.295838 | ||||||||
\(333\) | 1.08734e136 | 0.0365724 | ||||||||
\(334\) | −4.30822e136 | −0.123060 | ||||||||
\(335\) | 4.69982e137 | 1.14062 | ||||||||
\(336\) | 6.05898e137 | 1.25000 | ||||||||
\(337\) | −9.68101e137 | −1.69860 | −0.849300 | − | 0.527911i | \(-0.822975\pi\) | ||||
−0.849300 | + | 0.527911i | \(0.822975\pi\) | |||||||
\(338\) | 2.90113e136 | 0.0433119 | ||||||||
\(339\) | −5.05964e137 | −0.643037 | ||||||||
\(340\) | 2.07470e138 | 2.24572 | ||||||||
\(341\) | −4.71145e136 | −0.0434552 | ||||||||
\(342\) | −2.04311e135 | −0.00160645 | ||||||||
\(343\) | 6.54450e137 | 0.438881 | ||||||||
\(344\) | 9.81676e136 | 0.0561737 | ||||||||
\(345\) | −3.68249e138 | −1.79887 | ||||||||
\(346\) | −6.87042e136 | −0.0286639 | ||||||||
\(347\) | −9.86471e137 | −0.351664 | −0.175832 | − | 0.984420i | \(-0.556262\pi\) | ||||
−0.175832 | + | 0.984420i | \(0.556262\pi\) | |||||||
\(348\) | −2.63586e138 | −0.803255 | ||||||||
\(349\) | 1.74389e138 | 0.454498 | 0.227249 | − | 0.973837i | \(-0.427027\pi\) | ||||
0.227249 | + | 0.973837i | \(0.427027\pi\) | |||||||
\(350\) | 9.12260e137 | 0.203428 | ||||||||
\(351\) | −3.57399e138 | −0.682205 | ||||||||
\(352\) | −1.33384e138 | −0.218035 | ||||||||
\(353\) | 5.89853e137 | 0.0826081 | 0.0413040 | − | 0.999147i | \(-0.486849\pi\) | ||||
0.0413040 | + | 0.999147i | \(0.486849\pi\) | |||||||
\(354\) | 4.24900e137 | 0.0510045 | ||||||||
\(355\) | 3.17867e138 | 0.327190 | ||||||||
\(356\) | 5.01680e138 | 0.442998 | ||||||||
\(357\) | 2.19954e139 | 1.66692 | ||||||||
\(358\) | −5.94229e137 | −0.0386660 | ||||||||
\(359\) | −1.00536e139 | −0.561918 | −0.280959 | − | 0.959720i | \(-0.590653\pi\) | ||||
−0.280959 | + | 0.959720i | \(0.590653\pi\) | |||||||
\(360\) | 1.23175e137 | 0.00591612 | ||||||||
\(361\) | −3.03674e138 | −0.125391 | ||||||||
\(362\) | −1.17372e138 | −0.0416820 | ||||||||
\(363\) | 4.91431e138 | 0.150159 | ||||||||
\(364\) | −3.28554e139 | −0.864133 | ||||||||
\(365\) | 1.01600e140 | 2.30109 | ||||||||
\(366\) | 3.87172e138 | 0.0755413 | ||||||||
\(367\) | −6.47645e139 | −1.08902 | −0.544511 | − | 0.838754i | \(-0.683285\pi\) | ||||
−0.544511 | + | 0.838754i | \(0.683285\pi\) | |||||||
\(368\) | −7.12374e139 | −1.03277 | ||||||||
\(369\) | −1.17836e138 | −0.0147347 | ||||||||
\(370\) | −2.15914e139 | −0.232963 | ||||||||
\(371\) | −2.05230e140 | −1.91145 | ||||||||
\(372\) | −5.76616e138 | −0.0463763 | ||||||||
\(373\) | 4.82923e139 | 0.335542 | 0.167771 | − | 0.985826i | \(-0.446343\pi\) | ||||
0.167771 | + | 0.985826i | \(0.446343\pi\) | |||||||
\(374\) | −1.59689e139 | −0.0958901 | ||||||||
\(375\) | 3.23988e140 | 1.68200 | ||||||||
\(376\) | 3.05946e139 | 0.137375 | ||||||||
\(377\) | 1.42015e140 | 0.551735 | ||||||||
\(378\) | 3.08060e139 | 0.103593 | ||||||||
\(379\) | 4.91466e140 | 1.43106 | 0.715528 | − | 0.698584i | \(-0.246186\pi\) | ||||
0.715528 | + | 0.698584i | \(0.246186\pi\) | |||||||
\(380\) | −6.36469e140 | −1.60535 | ||||||||
\(381\) | −3.89784e140 | −0.851948 | ||||||||
\(382\) | 6.50193e139 | 0.123194 | ||||||||
\(383\) | 4.10831e140 | 0.675040 | 0.337520 | − | 0.941318i | \(-0.390412\pi\) | ||||
0.337520 | + | 0.941318i | \(0.390412\pi\) | |||||||
\(384\) | −2.17422e140 | −0.309922 | ||||||||
\(385\) | 1.65669e141 | 2.04942 | ||||||||
\(386\) | −3.70331e139 | −0.0397724 | ||||||||
\(387\) | −8.19253e138 | −0.00764136 | ||||||||
\(388\) | −1.53923e141 | −1.24731 | ||||||||
\(389\) | −6.99680e140 | −0.492772 | −0.246386 | − | 0.969172i | \(-0.579243\pi\) | ||||
−0.246386 | + | 0.969172i | \(0.579243\pi\) | |||||||
\(390\) | 1.49941e140 | 0.0918121 | ||||||||
\(391\) | −2.58607e141 | −1.37723 | ||||||||
\(392\) | 2.25764e140 | 0.104608 | ||||||||
\(393\) | −2.53648e141 | −1.02291 | ||||||||
\(394\) | −1.40908e140 | −0.0494758 | ||||||||
\(395\) | 7.86490e141 | 2.40520 | ||||||||
\(396\) | 7.41312e139 | 0.0197521 | ||||||||
\(397\) | −7.26167e141 | −1.68637 | −0.843186 | − | 0.537621i | \(-0.819323\pi\) | ||||
−0.843186 | + | 0.537621i | \(0.819323\pi\) | |||||||
\(398\) | 7.62225e138 | 0.00154332 | ||||||||
\(399\) | −6.74765e141 | −1.19160 | ||||||||
\(400\) | 1.26348e142 | 1.94670 | ||||||||
\(401\) | 1.37737e142 | 1.85218 | 0.926090 | − | 0.377302i | \(-0.123148\pi\) | ||||
0.926090 | + | 0.377302i | \(0.123148\pi\) | |||||||
\(402\) | −4.42724e140 | −0.0519773 | ||||||||
\(403\) | 3.10669e140 | 0.0318547 | ||||||||
\(404\) | −1.15636e142 | −1.03587 | ||||||||
\(405\) | 2.15794e142 | 1.68943 | ||||||||
\(406\) | −1.22410e141 | −0.0837815 | ||||||||
\(407\) | −2.60718e142 | −1.56054 | ||||||||
\(408\) | −3.92121e141 | −0.205324 | ||||||||
\(409\) | 8.08649e141 | 0.370544 | 0.185272 | − | 0.982687i | \(-0.440683\pi\) | ||||
0.185272 | + | 0.982687i | \(0.440683\pi\) | |||||||
\(410\) | 2.33988e141 | 0.0938585 | ||||||||
\(411\) | −1.84645e142 | −0.648572 | ||||||||
\(412\) | 2.43109e142 | 0.748001 | ||||||||
\(413\) | −3.09564e142 | −0.834588 | ||||||||
\(414\) | −7.65236e139 | −0.00180833 | ||||||||
\(415\) | −2.48232e142 | −0.514325 | ||||||||
\(416\) | 8.79519e141 | 0.159830 | ||||||||
\(417\) | −5.06875e142 | −0.808139 | ||||||||
\(418\) | 4.89889e141 | 0.0685473 | ||||||||
\(419\) | −1.03306e143 | −1.26900 | −0.634501 | − | 0.772922i | \(-0.718795\pi\) | ||||
−0.634501 | + | 0.772922i | \(0.718795\pi\) | |||||||
\(420\) | 2.02756e143 | 2.18719 | ||||||||
\(421\) | −1.72030e142 | −0.163016 | −0.0815081 | − | 0.996673i | \(-0.525974\pi\) | ||||
−0.0815081 | + | 0.996673i | \(0.525974\pi\) | |||||||
\(422\) | −7.36069e141 | −0.0612900 | ||||||||
\(423\) | −2.55326e141 | −0.0186872 | ||||||||
\(424\) | 3.65872e142 | 0.235445 | ||||||||
\(425\) | 4.58671e143 | 2.59600 | ||||||||
\(426\) | −2.99431e141 | −0.0149099 | ||||||||
\(427\) | −2.82077e143 | −1.23608 | ||||||||
\(428\) | −1.45787e143 | −0.562383 | ||||||||
\(429\) | 1.81055e143 | 0.615019 | ||||||||
\(430\) | 1.62680e142 | 0.0486748 | ||||||||
\(431\) | −3.29879e143 | −0.869647 | −0.434824 | − | 0.900516i | \(-0.643189\pi\) | ||||
−0.434824 | + | 0.900516i | \(0.643189\pi\) | |||||||
\(432\) | 4.26664e143 | 0.991338 | ||||||||
\(433\) | −3.54235e143 | −0.725606 | −0.362803 | − | 0.931866i | \(-0.618180\pi\) | ||||
−0.362803 | + | 0.931866i | \(0.618180\pi\) | |||||||
\(434\) | −2.67782e141 | −0.00483716 | ||||||||
\(435\) | −8.76397e143 | −1.39649 | ||||||||
\(436\) | −3.00227e143 | −0.422121 | ||||||||
\(437\) | 7.93343e143 | 0.984516 | ||||||||
\(438\) | −9.57076e142 | −0.104859 | ||||||||
\(439\) | 1.32418e143 | 0.128124 | 0.0640619 | − | 0.997946i | \(-0.479594\pi\) | ||||
0.0640619 | + | 0.997946i | \(0.479594\pi\) | |||||||
\(440\) | −2.95345e143 | −0.252440 | ||||||||
\(441\) | −1.88410e142 | −0.0142299 | ||||||||
\(442\) | 1.05298e143 | 0.0702920 | ||||||||
\(443\) | −2.49424e142 | −0.0147209 | −0.00736045 | − | 0.999973i | \(-0.502343\pi\) | ||||
−0.00736045 | + | 0.999973i | \(0.502343\pi\) | |||||||
\(444\) | −3.19082e144 | −1.66545 | ||||||||
\(445\) | 1.66804e144 | 0.770167 | ||||||||
\(446\) | −3.44229e142 | −0.0140636 | ||||||||
\(447\) | 2.94478e144 | 1.06486 | ||||||||
\(448\) | 3.87148e144 | 1.23944 | ||||||||
\(449\) | 5.02265e144 | 1.42399 | 0.711996 | − | 0.702184i | \(-0.247792\pi\) | ||||
0.711996 | + | 0.702184i | \(0.247792\pi\) | |||||||
\(450\) | 1.35724e142 | 0.00340859 | ||||||||
\(451\) | 2.82543e144 | 0.628727 | ||||||||
\(452\) | −3.27536e144 | −0.645974 | ||||||||
\(453\) | −9.49614e144 | −1.66033 | ||||||||
\(454\) | 5.34658e142 | 0.00828958 | ||||||||
\(455\) | −1.09241e145 | −1.50232 | ||||||||
\(456\) | 1.20293e144 | 0.146777 | ||||||||
\(457\) | 2.47069e144 | 0.267538 | 0.133769 | − | 0.991013i | \(-0.457292\pi\) | ||||
0.133769 | + | 0.991013i | \(0.457292\pi\) | |||||||
\(458\) | 1.20705e144 | 0.116027 | ||||||||
\(459\) | 1.54888e145 | 1.32199 | ||||||||
\(460\) | −2.38386e145 | −1.80709 | ||||||||
\(461\) | 9.07133e144 | 0.610901 | 0.305450 | − | 0.952208i | \(-0.401193\pi\) | ||||
0.305450 | + | 0.952208i | \(0.401193\pi\) | |||||||
\(462\) | −1.56061e144 | −0.0933912 | ||||||||
\(463\) | −2.19315e144 | −0.116655 | −0.0583277 | − | 0.998297i | \(-0.518577\pi\) | ||||
−0.0583277 | + | 0.998297i | \(0.518577\pi\) | |||||||
\(464\) | −1.69538e145 | −0.801747 | ||||||||
\(465\) | −1.91719e144 | −0.0806267 | ||||||||
\(466\) | −1.07003e144 | −0.0400280 | ||||||||
\(467\) | 7.75309e144 | 0.258051 | 0.129025 | − | 0.991641i | \(-0.458815\pi\) | ||||
0.129025 | + | 0.991641i | \(0.458815\pi\) | |||||||
\(468\) | −4.88815e143 | −0.0144792 | ||||||||
\(469\) | 3.22550e145 | 0.850505 | ||||||||
\(470\) | 5.07004e144 | 0.119036 | ||||||||
\(471\) | 6.53456e145 | 1.36640 | ||||||||
\(472\) | 5.51872e144 | 0.102801 | ||||||||
\(473\) | 1.96438e145 | 0.326056 | ||||||||
\(474\) | −7.40876e144 | −0.109604 | ||||||||
\(475\) | −1.40709e146 | −1.85576 | ||||||||
\(476\) | 1.42387e146 | 1.67453 | ||||||||
\(477\) | −3.05337e144 | −0.0320279 | ||||||||
\(478\) | −1.21732e145 | −0.113916 | ||||||||
\(479\) | −1.24921e146 | −1.04316 | −0.521578 | − | 0.853203i | \(-0.674657\pi\) | ||||
−0.521578 | + | 0.853203i | \(0.674657\pi\) | |||||||
\(480\) | −5.42765e145 | −0.404543 | ||||||||
\(481\) | 1.71915e146 | 1.14395 | ||||||||
\(482\) | 1.23658e145 | 0.0734780 | ||||||||
\(483\) | −2.52730e146 | −1.34134 | ||||||||
\(484\) | 3.18128e145 | 0.150845 | ||||||||
\(485\) | −5.11777e146 | −2.16848 | ||||||||
\(486\) | 9.06966e143 | 0.00343490 | ||||||||
\(487\) | 2.45739e146 | 0.832044 | 0.416022 | − | 0.909354i | \(-0.363424\pi\) | ||||
0.416022 | + | 0.909354i | \(0.363424\pi\) | |||||||
\(488\) | 5.02870e145 | 0.152256 | ||||||||
\(489\) | 3.97366e146 | 1.07611 | ||||||||
\(490\) | 3.74129e145 | 0.0906431 | ||||||||
\(491\) | 2.18529e146 | 0.473771 | 0.236886 | − | 0.971538i | \(-0.423873\pi\) | ||||
0.236886 | + | 0.971538i | \(0.423873\pi\) | |||||||
\(492\) | 3.45792e146 | 0.670992 | ||||||||
\(493\) | −6.15459e146 | −1.06916 | ||||||||
\(494\) | −3.23028e145 | −0.0502484 | ||||||||
\(495\) | 2.46479e145 | 0.0343397 | ||||||||
\(496\) | −3.70878e145 | −0.0462892 | ||||||||
\(497\) | 2.18153e146 | 0.243971 | ||||||||
\(498\) | 2.33836e145 | 0.0234375 | ||||||||
\(499\) | 1.46230e147 | 1.31388 | 0.656942 | − | 0.753941i | \(-0.271850\pi\) | ||||
0.656942 | + | 0.753941i | \(0.271850\pi\) | |||||||
\(500\) | 2.09734e147 | 1.68968 | ||||||||
\(501\) | −2.11689e147 | −1.52947 | ||||||||
\(502\) | 1.23341e146 | 0.0799384 | ||||||||
\(503\) | −8.66865e146 | −0.504076 | −0.252038 | − | 0.967717i | \(-0.581101\pi\) | ||||
−0.252038 | + | 0.967717i | \(0.581101\pi\) | |||||||
\(504\) | 8.45354e144 | 0.00441138 | ||||||||
\(505\) | −3.84477e147 | −1.80090 | ||||||||
\(506\) | 1.83486e146 | 0.0771612 | ||||||||
\(507\) | 1.42550e147 | 0.538311 | ||||||||
\(508\) | −2.52327e147 | −0.855838 | ||||||||
\(509\) | −3.08181e147 | −0.939046 | −0.469523 | − | 0.882920i | \(-0.655574\pi\) | ||||
−0.469523 | + | 0.882920i | \(0.655574\pi\) | |||||||
\(510\) | −6.49810e146 | −0.177915 | ||||||||
\(511\) | 6.97284e147 | 1.71582 | ||||||||
\(512\) | −1.75367e147 | −0.387914 | ||||||||
\(513\) | −4.75159e147 | −0.945024 | ||||||||
\(514\) | 5.35322e146 | 0.0957470 | ||||||||
\(515\) | 8.08312e147 | 1.30042 | ||||||||
\(516\) | 2.40412e147 | 0.347974 | ||||||||
\(517\) | 6.12212e147 | 0.797383 | ||||||||
\(518\) | −1.48183e147 | −0.173710 | ||||||||
\(519\) | −3.37585e147 | −0.356256 | ||||||||
\(520\) | 1.94748e147 | 0.185051 | ||||||||
\(521\) | 5.80957e147 | 0.497151 | 0.248575 | − | 0.968613i | \(-0.420038\pi\) | ||||
0.248575 | + | 0.968613i | \(0.420038\pi\) | |||||||
\(522\) | −1.82119e145 | −0.00140382 | ||||||||
\(523\) | −1.36517e148 | −0.948078 | −0.474039 | − | 0.880504i | \(-0.657204\pi\) | ||||
−0.474039 | + | 0.880504i | \(0.657204\pi\) | |||||||
\(524\) | −1.64199e148 | −1.02758 | ||||||||
\(525\) | 4.48248e148 | 2.52835 | ||||||||
\(526\) | −1.41730e147 | −0.0720675 | ||||||||
\(527\) | −1.34637e147 | −0.0617283 | ||||||||
\(528\) | −2.16145e148 | −0.893708 | ||||||||
\(529\) | 2.90201e147 | 0.108234 | ||||||||
\(530\) | 6.06312e147 | 0.204015 | ||||||||
\(531\) | −4.60562e146 | −0.0139842 | ||||||||
\(532\) | −4.36810e148 | −1.19704 | ||||||||
\(533\) | −1.86306e148 | −0.460887 | ||||||||
\(534\) | −1.57129e147 | −0.0350961 | ||||||||
\(535\) | −4.84726e148 | −0.977722 | ||||||||
\(536\) | −5.75023e147 | −0.104762 | ||||||||
\(537\) | −2.91981e148 | −0.480569 | ||||||||
\(538\) | 1.40157e147 | 0.0208440 | ||||||||
\(539\) | 4.51763e148 | 0.607188 | ||||||||
\(540\) | 1.42777e149 | 1.73460 | ||||||||
\(541\) | 1.34934e149 | 1.48208 | 0.741039 | − | 0.671462i | \(-0.234333\pi\) | ||||
0.741039 | + | 0.671462i | \(0.234333\pi\) | |||||||
\(542\) | 1.43055e148 | 0.142083 | ||||||||
\(543\) | −5.76721e148 | −0.518054 | ||||||||
\(544\) | −3.81163e148 | −0.309721 | ||||||||
\(545\) | −9.98226e148 | −0.733870 | ||||||||
\(546\) | 1.02905e148 | 0.0684601 | ||||||||
\(547\) | 1.50039e149 | 0.903433 | 0.451717 | − | 0.892162i | \(-0.350812\pi\) | ||||
0.451717 | + | 0.892162i | \(0.350812\pi\) | |||||||
\(548\) | −1.19530e149 | −0.651533 | ||||||||
\(549\) | −4.19668e147 | −0.0207116 | ||||||||
\(550\) | −3.25434e148 | −0.145444 | ||||||||
\(551\) | 1.88808e149 | 0.764291 | ||||||||
\(552\) | 4.50552e148 | 0.165221 | ||||||||
\(553\) | 5.39770e149 | 1.79345 | ||||||||
\(554\) | −4.89967e148 | −0.147531 | ||||||||
\(555\) | −1.06092e150 | −2.89543 | ||||||||
\(556\) | −3.28126e149 | −0.811829 | ||||||||
\(557\) | −3.51708e149 | −0.788994 | −0.394497 | − | 0.918897i | \(-0.629081\pi\) | ||||
−0.394497 | + | 0.918897i | \(0.629081\pi\) | |||||||
\(558\) | −3.98399e145 | −8.10503e−5 0 | ||||||||
\(559\) | −1.29529e149 | −0.239015 | ||||||||
\(560\) | 1.30412e150 | 2.18308 | ||||||||
\(561\) | −7.84650e149 | −1.19179 | ||||||||
\(562\) | 2.62394e148 | 0.0361680 | ||||||||
\(563\) | −4.35628e148 | −0.0545014 | −0.0272507 | − | 0.999629i | \(-0.508675\pi\) | ||||
−0.0272507 | + | 0.999629i | \(0.508675\pi\) | |||||||
\(564\) | 7.49261e149 | 0.850985 | ||||||||
\(565\) | −1.08903e150 | −1.12305 | ||||||||
\(566\) | 3.06744e147 | 0.00287264 | ||||||||
\(567\) | 1.48100e150 | 1.25973 | ||||||||
\(568\) | −3.88910e148 | −0.0300514 | ||||||||
\(569\) | 3.28942e149 | 0.230941 | 0.115470 | − | 0.993311i | \(-0.463162\pi\) | ||||
0.115470 | + | 0.993311i | \(0.463162\pi\) | |||||||
\(570\) | 1.99346e149 | 0.127183 | ||||||||
\(571\) | 3.01006e149 | 0.174545 | 0.0872725 | − | 0.996184i | \(-0.472185\pi\) | ||||
0.0872725 | + | 0.996184i | \(0.472185\pi\) | |||||||
\(572\) | 1.17206e150 | 0.617828 | ||||||||
\(573\) | 3.19479e150 | 1.53114 | ||||||||
\(574\) | 1.60587e149 | 0.0699860 | ||||||||
\(575\) | −5.27020e150 | −2.08896 | ||||||||
\(576\) | 5.75990e148 | 0.0207677 | ||||||||
\(577\) | 1.14168e150 | 0.374511 | 0.187255 | − | 0.982311i | \(-0.440041\pi\) | ||||
0.187255 | + | 0.982311i | \(0.440041\pi\) | |||||||
\(578\) | −1.89710e149 | −0.0566268 | ||||||||
\(579\) | −1.81966e150 | −0.494320 | ||||||||
\(580\) | −5.67337e150 | −1.40286 | ||||||||
\(581\) | −1.70363e150 | −0.383508 | ||||||||
\(582\) | 4.82095e149 | 0.0988167 | ||||||||
\(583\) | 7.32127e150 | 1.36663 | ||||||||
\(584\) | −1.24308e150 | −0.211348 | ||||||||
\(585\) | −1.62526e149 | −0.0251726 | ||||||||
\(586\) | −4.99102e149 | −0.0704318 | ||||||||
\(587\) | −7.65183e150 | −0.983986 | −0.491993 | − | 0.870599i | \(-0.663731\pi\) | ||||
−0.491993 | + | 0.870599i | \(0.663731\pi\) | |||||||
\(588\) | 5.52895e150 | 0.648005 | ||||||||
\(589\) | 4.13033e149 | 0.0441266 | ||||||||
\(590\) | 9.14545e149 | 0.0890779 | ||||||||
\(591\) | −6.92368e150 | −0.614921 | ||||||||
\(592\) | −2.05233e151 | −1.66232 | ||||||||
\(593\) | 9.96267e150 | 0.736029 | 0.368014 | − | 0.929820i | \(-0.380038\pi\) | ||||
0.368014 | + | 0.929820i | \(0.380038\pi\) | |||||||
\(594\) | −1.09896e150 | −0.0740660 | ||||||||
\(595\) | 4.73424e151 | 2.91122 | ||||||||
\(596\) | 1.90630e151 | 1.06972 | ||||||||
\(597\) | 3.74527e149 | 0.0191815 | ||||||||
\(598\) | −1.20989e150 | −0.0565628 | ||||||||
\(599\) | −4.15148e150 | −0.177191 | −0.0885955 | − | 0.996068i | \(-0.528238\pi\) | ||||
−0.0885955 | + | 0.996068i | \(0.528238\pi\) | |||||||
\(600\) | −7.99110e150 | −0.311432 | ||||||||
\(601\) | −5.13527e150 | −0.182770 | −0.0913848 | − | 0.995816i | \(-0.529129\pi\) | ||||
−0.0913848 | + | 0.995816i | \(0.529129\pi\) | |||||||
\(602\) | 1.11648e150 | 0.0362946 | ||||||||
\(603\) | 4.79883e149 | 0.0142509 | ||||||||
\(604\) | −6.14733e151 | −1.66791 | ||||||||
\(605\) | 1.05774e151 | 0.262248 | ||||||||
\(606\) | 3.62178e150 | 0.0820661 | ||||||||
\(607\) | −4.21841e150 | −0.0873705 | −0.0436853 | − | 0.999045i | \(-0.513910\pi\) | ||||
−0.0436853 | + | 0.999045i | \(0.513910\pi\) | |||||||
\(608\) | 1.16932e151 | 0.221405 | ||||||||
\(609\) | −6.01474e151 | −1.04130 | ||||||||
\(610\) | 8.33340e150 | 0.131931 | ||||||||
\(611\) | −4.03687e151 | −0.584519 | ||||||||
\(612\) | 2.11841e150 | 0.0280580 | ||||||||
\(613\) | 7.73237e150 | 0.0936951 | 0.0468475 | − | 0.998902i | \(-0.485083\pi\) | ||||
0.0468475 | + | 0.998902i | \(0.485083\pi\) | |||||||
\(614\) | −5.48443e149 | −0.00608073 | ||||||||
\(615\) | 1.14972e152 | 1.16654 | ||||||||
\(616\) | −2.02696e151 | −0.188233 | ||||||||
\(617\) | −2.11130e151 | −0.179477 | −0.0897385 | − | 0.995965i | \(-0.528603\pi\) | ||||
−0.0897385 | + | 0.995965i | \(0.528603\pi\) | |||||||
\(618\) | −7.61432e150 | −0.0592597 | ||||||||
\(619\) | 9.83927e151 | 0.701169 | 0.350584 | − | 0.936531i | \(-0.385983\pi\) | ||||
0.350584 | + | 0.936531i | \(0.385983\pi\) | |||||||
\(620\) | −1.24109e151 | −0.0809949 | ||||||||
\(621\) | −1.77969e152 | −1.06378 | ||||||||
\(622\) | 2.57078e151 | 0.140763 | ||||||||
\(623\) | 1.14478e152 | 0.574279 | ||||||||
\(624\) | 1.42524e152 | 0.655130 | ||||||||
\(625\) | 2.26287e152 | 0.953232 | ||||||||
\(626\) | 6.52981e149 | 0.00252115 | ||||||||
\(627\) | 2.40712e152 | 0.851955 | ||||||||
\(628\) | 4.23015e152 | 1.37264 | ||||||||
\(629\) | −7.45040e152 | −2.21676 | ||||||||
\(630\) | 1.40089e150 | 0.00382248 | ||||||||
\(631\) | −3.94557e152 | −0.987439 | −0.493719 | − | 0.869621i | \(-0.664363\pi\) | ||||
−0.493719 | + | 0.869621i | \(0.664363\pi\) | |||||||
\(632\) | −9.62270e151 | −0.220910 | ||||||||
\(633\) | −3.61675e152 | −0.761756 | ||||||||
\(634\) | −3.25850e151 | −0.0629729 | ||||||||
\(635\) | −8.38962e152 | −1.48790 | ||||||||
\(636\) | 8.96020e152 | 1.45849 | ||||||||
\(637\) | −2.97889e152 | −0.445097 | ||||||||
\(638\) | 4.36678e151 | 0.0599011 | ||||||||
\(639\) | 3.24563e150 | 0.00408792 | ||||||||
\(640\) | −4.67974e152 | −0.541269 | ||||||||
\(641\) | 1.84989e153 | 1.96510 | 0.982549 | − | 0.186004i | \(-0.0595536\pi\) | ||||
0.982549 | + | 0.186004i | \(0.0595536\pi\) | |||||||
\(642\) | 4.56613e151 | 0.0445543 | ||||||||
\(643\) | −5.38862e152 | −0.483036 | −0.241518 | − | 0.970396i | \(-0.577645\pi\) | ||||
−0.241518 | + | 0.970396i | \(0.577645\pi\) | |||||||
\(644\) | −1.63605e153 | −1.34746 | ||||||||
\(645\) | 7.99346e152 | 0.604965 | ||||||||
\(646\) | 1.39993e152 | 0.0973719 | ||||||||
\(647\) | 7.98584e152 | 0.510549 | 0.255275 | − | 0.966869i | \(-0.417834\pi\) | ||||
0.255275 | + | 0.966869i | \(0.417834\pi\) | |||||||
\(648\) | −2.64024e152 | −0.155169 | ||||||||
\(649\) | 1.10432e153 | 0.596704 | ||||||||
\(650\) | 2.14589e152 | 0.106618 | ||||||||
\(651\) | −1.31577e152 | −0.0601197 | ||||||||
\(652\) | 2.57235e153 | 1.08103 | ||||||||
\(653\) | 2.62517e153 | 1.01482 | 0.507409 | − | 0.861705i | \(-0.330603\pi\) | ||||
0.507409 | + | 0.861705i | \(0.330603\pi\) | |||||||
\(654\) | 9.40331e151 | 0.0334421 | ||||||||
\(655\) | −5.45947e153 | −1.78649 | ||||||||
\(656\) | 2.22413e153 | 0.669732 | ||||||||
\(657\) | 1.03740e152 | 0.0287498 | ||||||||
\(658\) | 3.47958e152 | 0.0887598 | ||||||||
\(659\) | −7.70190e153 | −1.80860 | −0.904300 | − | 0.426897i | \(-0.859607\pi\) | ||||
−0.904300 | + | 0.426897i | \(0.859607\pi\) | |||||||
\(660\) | −7.23299e153 | −1.56377 | ||||||||
\(661\) | 9.26631e153 | 1.84471 | 0.922353 | − | 0.386348i | \(-0.126264\pi\) | ||||
0.922353 | + | 0.386348i | \(0.126264\pi\) | |||||||
\(662\) | −4.89868e152 | −0.0898087 | ||||||||
\(663\) | 5.17392e153 | 0.873639 | ||||||||
\(664\) | 3.03712e152 | 0.0472391 | ||||||||
\(665\) | −1.45235e154 | −2.08109 | ||||||||
\(666\) | −2.20463e151 | −0.00291065 | ||||||||
\(667\) | 7.07172e153 | 0.860334 | ||||||||
\(668\) | −1.37037e154 | −1.53646 | ||||||||
\(669\) | −1.69140e153 | −0.174793 | ||||||||
\(670\) | −9.52910e152 | −0.0907768 | ||||||||
\(671\) | 1.00626e154 | 0.883761 | ||||||||
\(672\) | −3.72501e153 | −0.301649 | ||||||||
\(673\) | 2.43592e154 | 1.81904 | 0.909520 | − | 0.415660i | \(-0.136449\pi\) | ||||
0.909520 | + | 0.415660i | \(0.136449\pi\) | |||||||
\(674\) | 1.96287e153 | 0.135184 | ||||||||
\(675\) | 3.15649e154 | 2.00516 | ||||||||
\(676\) | 9.22799e153 | 0.540769 | ||||||||
\(677\) | −1.82490e154 | −0.986634 | −0.493317 | − | 0.869850i | \(-0.664216\pi\) | ||||
−0.493317 | + | 0.869850i | \(0.664216\pi\) | |||||||
\(678\) | 1.02586e153 | 0.0511766 | ||||||||
\(679\) | −3.51234e154 | −1.61694 | ||||||||
\(680\) | −8.43991e153 | −0.358593 | ||||||||
\(681\) | 2.62710e153 | 0.103029 | ||||||||
\(682\) | 9.55268e151 | 0.00345841 | ||||||||
\(683\) | 3.13386e154 | 1.04749 | 0.523747 | − | 0.851874i | \(-0.324534\pi\) | ||||
0.523747 | + | 0.851874i | \(0.324534\pi\) | |||||||
\(684\) | −6.49876e152 | −0.0200573 | ||||||||
\(685\) | −3.97425e154 | −1.13271 | ||||||||
\(686\) | −1.32693e153 | −0.0349287 | ||||||||
\(687\) | 5.93097e154 | 1.44206 | ||||||||
\(688\) | 1.54633e154 | 0.347321 | ||||||||
\(689\) | −4.82758e154 | −1.00180 | ||||||||
\(690\) | 7.46641e153 | 0.143165 | ||||||||
\(691\) | −8.30513e154 | −1.47161 | −0.735805 | − | 0.677193i | \(-0.763196\pi\) | ||||
−0.735805 | + | 0.677193i | \(0.763196\pi\) | |||||||
\(692\) | −2.18536e154 | −0.357883 | ||||||||
\(693\) | 1.69159e153 | 0.0256055 | ||||||||
\(694\) | 2.00011e153 | 0.0279875 | ||||||||
\(695\) | −1.09099e155 | −1.41139 | ||||||||
\(696\) | 1.07227e154 | 0.128263 | ||||||||
\(697\) | 8.07406e154 | 0.893112 | ||||||||
\(698\) | −3.53581e153 | −0.0361716 | ||||||||
\(699\) | −5.25770e154 | −0.497497 | ||||||||
\(700\) | 2.90174e155 | 2.53989 | ||||||||
\(701\) | −9.99671e154 | −0.809516 | −0.404758 | − | 0.914424i | \(-0.632644\pi\) | ||||
−0.404758 | + | 0.914424i | \(0.632644\pi\) | |||||||
\(702\) | 7.24642e153 | 0.0542939 | ||||||||
\(703\) | 2.28560e155 | 1.58466 | ||||||||
\(704\) | −1.38109e155 | −0.886159 | ||||||||
\(705\) | 2.49122e155 | 1.47947 | ||||||||
\(706\) | −1.19595e153 | −0.00657443 | ||||||||
\(707\) | −2.63867e155 | −1.34285 | ||||||||
\(708\) | 1.35153e155 | 0.636816 | ||||||||
\(709\) | −1.82497e155 | −0.796227 | −0.398113 | − | 0.917336i | \(-0.630335\pi\) | ||||
−0.398113 | + | 0.917336i | \(0.630335\pi\) | |||||||
\(710\) | −6.44489e153 | −0.0260397 | ||||||||
\(711\) | 8.03058e153 | 0.0300506 | ||||||||
\(712\) | −2.04084e154 | −0.0707375 | ||||||||
\(713\) | 1.54700e154 | 0.0496718 | ||||||||
\(714\) | −4.45966e154 | −0.132663 | ||||||||
\(715\) | 3.89699e155 | 1.07411 | ||||||||
\(716\) | −1.89014e155 | −0.482763 | ||||||||
\(717\) | −5.98143e155 | −1.41583 | ||||||||
\(718\) | 2.03841e154 | 0.0447207 | ||||||||
\(719\) | −5.62215e155 | −1.14335 | −0.571673 | − | 0.820481i | \(-0.693706\pi\) | ||||
−0.571673 | + | 0.820481i | \(0.693706\pi\) | |||||||
\(720\) | 1.94024e154 | 0.0365792 | ||||||||
\(721\) | 5.54747e155 | 0.969668 | ||||||||
\(722\) | 6.15712e153 | 0.00997930 | ||||||||
\(723\) | 6.07604e155 | 0.913237 | ||||||||
\(724\) | −3.73341e155 | −0.520420 | ||||||||
\(725\) | −1.25426e156 | −1.62168 | ||||||||
\(726\) | −9.96397e153 | −0.0119505 | ||||||||
\(727\) | −1.84945e154 | −0.0205787 | −0.0102893 | − | 0.999947i | \(-0.503275\pi\) | ||||
−0.0102893 | + | 0.999947i | \(0.503275\pi\) | |||||||
\(728\) | 1.33656e155 | 0.137984 | ||||||||
\(729\) | 1.06543e156 | 1.02064 | ||||||||
\(730\) | −2.05999e155 | −0.183134 | ||||||||
\(731\) | 5.61349e155 | 0.463165 | ||||||||
\(732\) | 1.23153e156 | 0.943169 | ||||||||
\(733\) | 8.12603e155 | 0.577713 | 0.288856 | − | 0.957372i | \(-0.406725\pi\) | ||||
0.288856 | + | 0.957372i | \(0.406725\pi\) | |||||||
\(734\) | 1.31313e155 | 0.0866707 | ||||||||
\(735\) | 1.83832e156 | 1.12658 | ||||||||
\(736\) | 4.37962e155 | 0.249227 | ||||||||
\(737\) | −1.15065e156 | −0.608084 | ||||||||
\(738\) | 2.38917e153 | 0.00117267 | ||||||||
\(739\) | 1.31041e156 | 0.597426 | 0.298713 | − | 0.954343i | \(-0.403443\pi\) | ||||
0.298713 | + | 0.954343i | \(0.403443\pi\) | |||||||
\(740\) | −6.86785e156 | −2.90866 | ||||||||
\(741\) | −1.58723e156 | −0.624523 | ||||||||
\(742\) | 4.16113e155 | 0.152124 | ||||||||
\(743\) | −6.49975e155 | −0.220804 | −0.110402 | − | 0.993887i | \(-0.535214\pi\) | ||||
−0.110402 | + | 0.993887i | \(0.535214\pi\) | |||||||
\(744\) | 2.34568e154 | 0.00740532 | ||||||||
\(745\) | 6.33827e156 | 1.85975 | ||||||||
\(746\) | −9.79149e154 | −0.0267044 | ||||||||
\(747\) | −2.53462e154 | −0.00642598 | ||||||||
\(748\) | −5.07944e156 | −1.19723 | ||||||||
\(749\) | −3.32669e156 | −0.729043 | ||||||||
\(750\) | −6.56901e155 | −0.133863 | ||||||||
\(751\) | −4.15514e156 | −0.787425 | −0.393713 | − | 0.919234i | \(-0.628809\pi\) | ||||
−0.393713 | + | 0.919234i | \(0.628809\pi\) | |||||||
\(752\) | 4.81923e156 | 0.849387 | ||||||||
\(753\) | 6.06049e156 | 0.993532 | ||||||||
\(754\) | −2.87942e155 | −0.0439103 | ||||||||
\(755\) | −2.04393e157 | −2.89972 | ||||||||
\(756\) | 9.79885e156 | 1.29341 | ||||||||
\(757\) | 1.53128e157 | 1.88074 | 0.940370 | − | 0.340154i | \(-0.110479\pi\) | ||||
0.940370 | + | 0.340154i | \(0.110479\pi\) | |||||||
\(758\) | −9.96469e155 | −0.113892 | ||||||||
\(759\) | 9.01575e156 | 0.959015 | ||||||||
\(760\) | 2.58916e156 | 0.256341 | ||||||||
\(761\) | −9.88537e156 | −0.911022 | −0.455511 | − | 0.890230i | \(-0.650543\pi\) | ||||
−0.455511 | + | 0.890230i | \(0.650543\pi\) | |||||||
\(762\) | 7.90305e155 | 0.0678029 | ||||||||
\(763\) | −6.85085e156 | −0.547214 | ||||||||
\(764\) | 2.06815e157 | 1.53813 | ||||||||
\(765\) | 7.04349e155 | 0.0487798 | ||||||||
\(766\) | −8.32977e155 | −0.0537236 | ||||||||
\(767\) | −7.28179e156 | −0.437412 | ||||||||
\(768\) | −1.65695e157 | −0.927091 | ||||||||
\(769\) | 2.54160e157 | 1.32471 | 0.662356 | − | 0.749190i | \(-0.269557\pi\) | ||||
0.662356 | + | 0.749190i | \(0.269557\pi\) | |||||||
\(770\) | −3.35902e156 | −0.163105 | ||||||||
\(771\) | 2.63036e157 | 1.19001 | ||||||||
\(772\) | −1.17796e157 | −0.496577 | ||||||||
\(773\) | −4.34579e157 | −1.70721 | −0.853604 | − | 0.520922i | \(-0.825588\pi\) | ||||
−0.853604 | + | 0.520922i | \(0.825588\pi\) | |||||||
\(774\) | 1.66107e154 | 0.000608143 0 | ||||||||
\(775\) | −2.74379e156 | −0.0936284 | ||||||||
\(776\) | 6.26159e156 | 0.199169 | ||||||||
\(777\) | −7.28110e157 | −2.15899 | ||||||||
\(778\) | 1.41863e156 | 0.0392177 | ||||||||
\(779\) | −2.47693e157 | −0.638443 | ||||||||
\(780\) | 4.76937e157 | 1.14632 | ||||||||
\(781\) | −7.78226e156 | −0.174431 | ||||||||
\(782\) | 5.24337e156 | 0.109608 | ||||||||
\(783\) | −4.23549e157 | −0.825823 | ||||||||
\(784\) | 3.55621e157 | 0.646788 | ||||||||
\(785\) | 1.40648e158 | 2.38637 | ||||||||
\(786\) | 5.14283e156 | 0.0814092 | ||||||||
\(787\) | 8.49250e157 | 1.25433 | 0.627166 | − | 0.778886i | \(-0.284215\pi\) | ||||
0.627166 | + | 0.778886i | \(0.284215\pi\) | |||||||
\(788\) | −4.48205e157 | −0.617729 | ||||||||
\(789\) | −6.96406e157 | −0.895707 | ||||||||
\(790\) | −1.59464e157 | −0.191420 | ||||||||
\(791\) | −7.47401e157 | −0.837405 | ||||||||
\(792\) | −3.01567e155 | −0.00315399 | ||||||||
\(793\) | −6.63522e157 | −0.647838 | ||||||||
\(794\) | 1.47233e157 | 0.134211 | ||||||||
\(795\) | 2.97918e158 | 2.53564 | ||||||||
\(796\) | 2.42450e156 | 0.0192691 | ||||||||
\(797\) | −4.32541e157 | −0.321032 | −0.160516 | − | 0.987033i | \(-0.551316\pi\) | ||||
−0.160516 | + | 0.987033i | \(0.551316\pi\) | |||||||
\(798\) | 1.36812e157 | 0.0948343 | ||||||||
\(799\) | 1.74948e158 | 1.13269 | ||||||||
\(800\) | −7.76779e157 | −0.469778 | ||||||||
\(801\) | 1.70317e156 | 0.00962248 | ||||||||
\(802\) | −2.79269e157 | −0.147407 | ||||||||
\(803\) | −2.48745e158 | −1.22675 | ||||||||
\(804\) | −1.40823e158 | −0.648961 | ||||||||
\(805\) | −5.43971e158 | −2.34261 | ||||||||
\(806\) | −6.29895e155 | −0.00253518 | ||||||||
\(807\) | 6.88675e157 | 0.259064 | ||||||||
\(808\) | 4.70407e157 | 0.165407 | ||||||||
\(809\) | 4.42811e158 | 1.45554 | 0.727769 | − | 0.685822i | \(-0.240557\pi\) | ||||
0.727769 | + | 0.685822i | \(0.240557\pi\) | |||||||
\(810\) | −4.37531e157 | −0.134455 | ||||||||
\(811\) | −3.12561e158 | −0.898046 | −0.449023 | − | 0.893520i | \(-0.648228\pi\) | ||||
−0.449023 | + | 0.893520i | \(0.648228\pi\) | |||||||
\(812\) | −3.89365e158 | −1.04605 | ||||||||
\(813\) | 7.02915e158 | 1.76591 | ||||||||
\(814\) | 5.28618e157 | 0.124197 | ||||||||
\(815\) | 8.55281e158 | 1.87940 | ||||||||
\(816\) | −6.17664e158 | −1.26952 | ||||||||
\(817\) | −1.72208e158 | −0.331095 | ||||||||
\(818\) | −1.63957e157 | −0.0294900 | ||||||||
\(819\) | −1.11542e157 | −0.0187701 | ||||||||
\(820\) | 7.44275e158 | 1.17187 | ||||||||
\(821\) | 5.69745e158 | 0.839418 | 0.419709 | − | 0.907659i | \(-0.362132\pi\) | ||||
0.419709 | + | 0.907659i | \(0.362132\pi\) | |||||||
\(822\) | 3.74376e157 | 0.0516171 | ||||||||
\(823\) | −4.03382e157 | −0.0520505 | −0.0260253 | − | 0.999661i | \(-0.508285\pi\) | ||||
−0.0260253 | + | 0.999661i | \(0.508285\pi\) | |||||||
\(824\) | −9.88969e157 | −0.119440 | ||||||||
\(825\) | −1.59905e159 | −1.80769 | ||||||||
\(826\) | 6.27654e157 | 0.0664214 | ||||||||
\(827\) | 9.76894e158 | 0.967825 | 0.483913 | − | 0.875116i | \(-0.339215\pi\) | ||||
0.483913 | + | 0.875116i | \(0.339215\pi\) | |||||||
\(828\) | −2.43408e157 | −0.0225778 | ||||||||
\(829\) | 1.04176e159 | 0.904786 | 0.452393 | − | 0.891819i | \(-0.350570\pi\) | ||||
0.452393 | + | 0.891819i | \(0.350570\pi\) | |||||||
\(830\) | 5.03302e157 | 0.0409329 | ||||||||
\(831\) | −2.40750e159 | −1.83363 | ||||||||
\(832\) | 9.10677e158 | 0.649596 | ||||||||
\(833\) | 1.29098e159 | 0.862515 | ||||||||
\(834\) | 1.02771e158 | 0.0643164 | ||||||||
\(835\) | −4.55634e159 | −2.67118 | ||||||||
\(836\) | 1.55825e159 | 0.855845 | ||||||||
\(837\) | −9.26546e157 | −0.0476793 | ||||||||
\(838\) | 2.09458e158 | 0.100995 | ||||||||
\(839\) | −1.51200e159 | −0.683164 | −0.341582 | − | 0.939852i | \(-0.610963\pi\) | ||||
−0.341582 | + | 0.939852i | \(0.610963\pi\) | |||||||
\(840\) | −8.24813e158 | −0.349248 | ||||||||
\(841\) | −8.36890e158 | −0.332113 | ||||||||
\(842\) | 3.48799e157 | 0.0129738 | ||||||||
\(843\) | 1.28930e159 | 0.449522 | ||||||||
\(844\) | −2.34130e159 | −0.765235 | ||||||||
\(845\) | 3.06821e159 | 0.940145 | ||||||||
\(846\) | 5.17685e156 | 0.00148724 | ||||||||
\(847\) | 7.25932e158 | 0.195547 | ||||||||
\(848\) | 5.76318e159 | 1.45576 | ||||||||
\(849\) | 1.50722e158 | 0.0357032 | ||||||||
\(850\) | −9.29975e158 | −0.206605 | ||||||||
\(851\) | 8.56062e159 | 1.78379 | ||||||||
\(852\) | −9.52439e158 | −0.186157 | ||||||||
\(853\) | −3.07144e159 | −0.563144 | −0.281572 | − | 0.959540i | \(-0.590856\pi\) | ||||
−0.281572 | + | 0.959540i | \(0.590856\pi\) | |||||||
\(854\) | 5.71923e158 | 0.0983748 | ||||||||
\(855\) | −2.16077e158 | −0.0348703 | ||||||||
\(856\) | 5.93062e158 | 0.0898007 | ||||||||
\(857\) | −8.89973e159 | −1.26451 | −0.632255 | − | 0.774761i | \(-0.717870\pi\) | ||||
−0.632255 | + | 0.774761i | \(0.717870\pi\) | |||||||
\(858\) | −3.67098e158 | −0.0489468 | ||||||||
\(859\) | −4.57533e159 | −0.572525 | −0.286263 | − | 0.958151i | \(-0.592413\pi\) | ||||
−0.286263 | + | 0.958151i | \(0.592413\pi\) | |||||||
\(860\) | 5.17457e159 | 0.607728 | ||||||||
\(861\) | 7.89059e159 | 0.869837 | ||||||||
\(862\) | 6.68844e158 | 0.0692116 | ||||||||
\(863\) | −4.25641e159 | −0.413481 | −0.206740 | − | 0.978396i | \(-0.566286\pi\) | ||||
−0.206740 | + | 0.978396i | \(0.566286\pi\) | |||||||
\(864\) | −2.62310e159 | −0.239230 | ||||||||
\(865\) | −7.26610e159 | −0.622191 | ||||||||
\(866\) | 7.18227e158 | 0.0577480 | ||||||||
\(867\) | −9.32157e159 | −0.703798 | ||||||||
\(868\) | −8.51766e158 | −0.0603942 | ||||||||
\(869\) | −1.92554e160 | −1.28226 | ||||||||
\(870\) | 1.77693e159 | 0.111140 | ||||||||
\(871\) | 7.58726e159 | 0.445754 | ||||||||
\(872\) | 1.22133e159 | 0.0674037 | ||||||||
\(873\) | −5.22558e158 | −0.0270931 | ||||||||
\(874\) | −1.60854e159 | −0.0783535 | ||||||||
\(875\) | 4.78590e160 | 2.19041 | ||||||||
\(876\) | −3.04429e160 | −1.30922 | ||||||||
\(877\) | 4.15823e160 | 1.68047 | 0.840235 | − | 0.542222i | \(-0.182417\pi\) | ||||
0.840235 | + | 0.542222i | \(0.182417\pi\) | |||||||
\(878\) | −2.68483e158 | −0.0101968 | ||||||||
\(879\) | −2.45239e160 | −0.875377 | ||||||||
\(880\) | −4.65224e160 | −1.56083 | ||||||||
\(881\) | 2.49774e160 | 0.787698 | 0.393849 | − | 0.919175i | \(-0.371143\pi\) | ||||
0.393849 | + | 0.919175i | \(0.371143\pi\) | |||||||
\(882\) | 3.82010e157 | 0.00113250 | ||||||||
\(883\) | 6.64721e159 | 0.185260 | 0.0926299 | − | 0.995701i | \(-0.470473\pi\) | ||||
0.0926299 | + | 0.995701i | \(0.470473\pi\) | |||||||
\(884\) | 3.34934e160 | 0.877628 | ||||||||
\(885\) | 4.49371e160 | 1.10712 | ||||||||
\(886\) | 5.05717e157 | 0.00117157 | ||||||||
\(887\) | 6.17454e160 | 1.34514 | 0.672570 | − | 0.740033i | \(-0.265190\pi\) | ||||
0.672570 | + | 0.740033i | \(0.265190\pi\) | |||||||
\(888\) | 1.29803e160 | 0.265937 | ||||||||
\(889\) | −5.75782e160 | −1.10946 | ||||||||
\(890\) | −3.38202e159 | −0.0612944 | ||||||||
\(891\) | −5.28323e160 | −0.900667 | ||||||||
\(892\) | −1.09493e160 | −0.175591 | ||||||||
\(893\) | −5.36700e160 | −0.809705 | ||||||||
\(894\) | −5.97066e159 | −0.0847477 | ||||||||
\(895\) | −6.28452e160 | −0.839300 | ||||||||
\(896\) | −3.21172e160 | −0.403600 | ||||||||
\(897\) | −5.94491e160 | −0.703003 | ||||||||
\(898\) | −1.01836e160 | −0.113329 | ||||||||
\(899\) | 3.68170e159 | 0.0385607 | ||||||||
\(900\) | 4.31714e159 | 0.0425578 | ||||||||
\(901\) | 2.09216e161 | 1.94130 | ||||||||
\(902\) | −5.72868e159 | −0.0500378 | ||||||||
\(903\) | 5.48593e160 | 0.451095 | ||||||||
\(904\) | 1.33242e160 | 0.103148 | ||||||||
\(905\) | −1.24132e161 | −0.904766 | ||||||||
\(906\) | 1.92538e160 | 0.132139 | ||||||||
\(907\) | −3.57082e160 | −0.230765 | −0.115383 | − | 0.993321i | \(-0.536809\pi\) | ||||
−0.115383 | + | 0.993321i | \(0.536809\pi\) | |||||||
\(908\) | 1.70065e160 | 0.103499 | ||||||||
\(909\) | −3.92576e159 | −0.0225005 | ||||||||
\(910\) | 2.21490e160 | 0.119564 | ||||||||
\(911\) | −2.92874e161 | −1.48912 | −0.744559 | − | 0.667556i | \(-0.767340\pi\) | ||||
−0.744559 | + | 0.667556i | \(0.767340\pi\) | |||||||
\(912\) | 1.89484e161 | 0.907517 | ||||||||
\(913\) | 6.07741e160 | 0.274196 | ||||||||
\(914\) | −5.00944e159 | −0.0212923 | ||||||||
\(915\) | 4.09470e161 | 1.63973 | ||||||||
\(916\) | 3.83942e161 | 1.44865 | ||||||||
\(917\) | −3.74685e161 | −1.33210 | ||||||||
\(918\) | −3.14042e160 | −0.105211 | ||||||||
\(919\) | 4.40405e161 | 1.39046 | 0.695228 | − | 0.718789i | \(-0.255303\pi\) | ||||
0.695228 | + | 0.718789i | \(0.255303\pi\) | |||||||
\(920\) | 9.69759e160 | 0.288554 | ||||||||
\(921\) | −2.69483e160 | −0.0755756 | ||||||||
\(922\) | −1.83925e160 | −0.0486190 | ||||||||
\(923\) | 5.13155e160 | 0.127866 | ||||||||
\(924\) | −4.96402e161 | −1.16603 | ||||||||
\(925\) | −1.51833e162 | −3.36234 | ||||||||
\(926\) | 4.44672e159 | 0.00928412 | ||||||||
\(927\) | 8.25340e159 | 0.0162475 | ||||||||
\(928\) | 1.04231e161 | 0.193478 | ||||||||
\(929\) | 6.33862e161 | 1.10953 | 0.554764 | − | 0.832008i | \(-0.312809\pi\) | ||||
0.554764 | + | 0.832008i | \(0.312809\pi\) | |||||||
\(930\) | 3.88719e159 | 0.00641674 | ||||||||
\(931\) | −3.96041e161 | −0.616571 | ||||||||
\(932\) | −3.40358e161 | −0.499768 | ||||||||
\(933\) | 1.26318e162 | 1.74951 | ||||||||
\(934\) | −1.57197e160 | −0.0205372 | ||||||||
\(935\) | −1.68886e162 | −2.08143 | ||||||||
\(936\) | 1.98850e159 | 0.00231203 | ||||||||
\(937\) | 1.10322e162 | 1.21019 | 0.605095 | − | 0.796153i | \(-0.293135\pi\) | ||||
0.605095 | + | 0.796153i | \(0.293135\pi\) | |||||||
\(938\) | −6.53984e160 | −0.0676882 | ||||||||
\(939\) | 3.20849e160 | 0.0313347 | ||||||||
\(940\) | 1.61269e162 | 1.48622 | ||||||||
\(941\) | −8.53090e161 | −0.741925 | −0.370963 | − | 0.928648i | \(-0.620972\pi\) | ||||
−0.370963 | + | 0.928648i | \(0.620972\pi\) | |||||||
\(942\) | −1.32491e161 | −0.108746 | ||||||||
\(943\) | −9.27722e161 | −0.718672 | ||||||||
\(944\) | 8.69303e161 | 0.635620 | ||||||||
\(945\) | 3.25802e162 | 2.24864 | ||||||||
\(946\) | −3.98286e160 | −0.0259495 | ||||||||
\(947\) | −5.35159e161 | −0.329162 | −0.164581 | − | 0.986364i | \(-0.552627\pi\) | ||||
−0.164581 | + | 0.986364i | \(0.552627\pi\) | |||||||
\(948\) | −2.35659e162 | −1.36846 | ||||||||
\(949\) | 1.64020e162 | 0.899268 | ||||||||
\(950\) | 2.85294e161 | 0.147692 | ||||||||
\(951\) | −1.60110e162 | −0.782672 | ||||||||
\(952\) | −5.79233e161 | −0.267387 | ||||||||
\(953\) | −1.03103e162 | −0.449477 | −0.224739 | − | 0.974419i | \(-0.572153\pi\) | ||||
−0.224739 | + | 0.974419i | \(0.572153\pi\) | |||||||
\(954\) | 6.19084e159 | 0.00254896 | ||||||||
\(955\) | 6.87639e162 | 2.67409 | ||||||||
\(956\) | −3.87209e162 | −1.42230 | ||||||||
\(957\) | 2.14566e162 | 0.744493 | ||||||||
\(958\) | 2.53283e161 | 0.0830205 | ||||||||
\(959\) | −2.72754e162 | −0.844612 | ||||||||
\(960\) | −5.61994e162 | −1.64418 | ||||||||
\(961\) | −3.60958e162 | −0.997774 | ||||||||
\(962\) | −3.48566e161 | −0.0910423 | ||||||||
\(963\) | −4.94937e160 | −0.0122157 | ||||||||
\(964\) | 3.93333e162 | 0.917407 | ||||||||
\(965\) | −3.91659e162 | −0.863315 | ||||||||
\(966\) | 5.12422e161 | 0.106752 | ||||||||
\(967\) | −3.03077e162 | −0.596774 | −0.298387 | − | 0.954445i | \(-0.596449\pi\) | ||||
−0.298387 | + | 0.954445i | \(0.596449\pi\) | |||||||
\(968\) | −1.29415e161 | −0.0240867 | ||||||||
\(969\) | 6.87869e162 | 1.21021 | ||||||||
\(970\) | 1.03765e162 | 0.172580 | ||||||||
\(971\) | 6.89509e162 | 1.08416 | 0.542078 | − | 0.840328i | \(-0.317638\pi\) | ||||
0.542078 | + | 0.840328i | \(0.317638\pi\) | |||||||
\(972\) | 2.88490e161 | 0.0428864 | ||||||||
\(973\) | −7.48747e162 | −1.05241 | ||||||||
\(974\) | −4.98248e161 | −0.0662189 | ||||||||
\(975\) | 1.05440e163 | 1.32512 | ||||||||
\(976\) | 7.92115e162 | 0.941398 | ||||||||
\(977\) | −6.84252e162 | −0.769064 | −0.384532 | − | 0.923112i | \(-0.625637\pi\) | ||||
−0.384532 | + | 0.923112i | \(0.625637\pi\) | |||||||
\(978\) | −8.05677e161 | −0.0856433 | ||||||||
\(979\) | −4.08381e162 | −0.410591 | ||||||||
\(980\) | 1.19004e163 | 1.13172 | ||||||||
\(981\) | −1.01925e161 | −0.00916899 | ||||||||
\(982\) | −4.43078e161 | −0.0377055 | ||||||||
\(983\) | 2.23686e162 | 0.180083 | 0.0900415 | − | 0.995938i | \(-0.471300\pi\) | ||||
0.0900415 | + | 0.995938i | \(0.471300\pi\) | |||||||
\(984\) | −1.40669e162 | −0.107143 | ||||||||
\(985\) | −1.49024e163 | −1.07394 | ||||||||
\(986\) | 1.24787e162 | 0.0850899 | ||||||||
\(987\) | 1.70973e163 | 1.10317 | ||||||||
\(988\) | −1.02750e163 | −0.627375 | ||||||||
\(989\) | −6.44999e162 | −0.372701 | ||||||||
\(990\) | −4.99747e160 | −0.00273295 | ||||||||
\(991\) | −9.24985e162 | −0.478763 | −0.239382 | − | 0.970926i | \(-0.576945\pi\) | ||||
−0.239382 | + | 0.970926i | \(0.576945\pi\) | |||||||
\(992\) | 2.28013e161 | 0.0111705 | ||||||||
\(993\) | −2.40702e163 | −1.11621 | ||||||||
\(994\) | −4.42315e161 | −0.0194166 | ||||||||
\(995\) | 8.06124e161 | 0.0334999 | ||||||||
\(996\) | 7.43790e162 | 0.292628 | ||||||||
\(997\) | 1.90575e163 | 0.709873 | 0.354937 | − | 0.934890i | \(-0.384502\pi\) | ||||
0.354937 | + | 0.934890i | \(0.384502\pi\) | |||||||
\(998\) | −2.96488e162 | −0.104566 | ||||||||
\(999\) | −5.12724e163 | −1.71224 |
(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 | 1.110.a.a.1.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.110.a.a.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial |