Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,14,Mod(1,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.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: | \(35.3862065541\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 33.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 140.000 | 1.54680 | 0.773398 | − | 0.633921i | \(-0.218555\pi\) | ||||
0.773398 | + | 0.633921i | \(0.218555\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 11408.0 | 1.39258 | ||||||||
\(5\) | 48740.0 | 1.39502 | 0.697510 | − | 0.716575i | \(-0.254291\pi\) | ||||
0.697510 | + | 0.716575i | \(0.254291\pi\) | |||||||
\(6\) | 102060. | 0.893043 | ||||||||
\(7\) | 487486. | 1.56612 | 0.783060 | − | 0.621947i | \(-0.213658\pi\) | ||||
0.783060 | + | 0.621947i | \(0.213658\pi\) | |||||||
\(8\) | 450240. | 0.607238 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 6.82360e6 | 2.15781 | ||||||||
\(11\) | −1.77156e6 | −0.301511 | ||||||||
\(12\) | 8.31643e6 | 0.804005 | ||||||||
\(13\) | −1.83883e7 | −1.05660 | −0.528299 | − | 0.849058i | \(-0.677170\pi\) | ||||
−0.528299 | + | 0.849058i | \(0.677170\pi\) | |||||||
\(14\) | 6.82480e7 | 2.42247 | ||||||||
\(15\) | 3.55315e7 | 0.805415 | ||||||||
\(16\) | −3.04207e7 | −0.453304 | ||||||||
\(17\) | −9.62333e7 | −0.966957 | −0.483479 | − | 0.875356i | \(-0.660627\pi\) | ||||
−0.483479 | + | 0.875356i | \(0.660627\pi\) | |||||||
\(18\) | 7.44017e7 | 0.515599 | ||||||||
\(19\) | −1.49547e7 | −0.0729252 | −0.0364626 | − | 0.999335i | \(-0.511609\pi\) | ||||
−0.0364626 | + | 0.999335i | \(0.511609\pi\) | |||||||
\(20\) | 5.56026e8 | 1.94267 | ||||||||
\(21\) | 3.55377e8 | 0.904199 | ||||||||
\(22\) | −2.48019e8 | −0.466377 | ||||||||
\(23\) | 1.53804e8 | 0.216640 | 0.108320 | − | 0.994116i | \(-0.465453\pi\) | ||||
0.108320 | + | 0.994116i | \(0.465453\pi\) | |||||||
\(24\) | 3.28225e8 | 0.350589 | ||||||||
\(25\) | 1.15488e9 | 0.946081 | ||||||||
\(26\) | −2.57436e9 | −1.63434 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 5.56124e9 | 2.18094 | ||||||||
\(29\) | 5.21901e9 | 1.62930 | 0.814650 | − | 0.579953i | \(-0.196929\pi\) | ||||
0.814650 | + | 0.579953i | \(0.196929\pi\) | |||||||
\(30\) | 4.97440e9 | 1.24581 | ||||||||
\(31\) | 1.18381e9 | 0.239570 | 0.119785 | − | 0.992800i | \(-0.461780\pi\) | ||||
0.119785 | + | 0.992800i | \(0.461780\pi\) | |||||||
\(32\) | −7.94727e9 | −1.30841 | ||||||||
\(33\) | −1.29147e9 | −0.174078 | ||||||||
\(34\) | −1.34727e10 | −1.49569 | ||||||||
\(35\) | 2.37601e10 | 2.18477 | ||||||||
\(36\) | 6.06268e9 | 0.464193 | ||||||||
\(37\) | −1.76722e10 | −1.13235 | −0.566173 | − | 0.824286i | \(-0.691577\pi\) | ||||
−0.566173 | + | 0.824286i | \(0.691577\pi\) | |||||||
\(38\) | −2.09365e9 | −0.112800 | ||||||||
\(39\) | −1.34051e10 | −0.610027 | ||||||||
\(40\) | 2.19447e10 | 0.847110 | ||||||||
\(41\) | −1.94617e10 | −0.639862 | −0.319931 | − | 0.947441i | \(-0.603660\pi\) | ||||
−0.319931 | + | 0.947441i | \(0.603660\pi\) | |||||||
\(42\) | 4.97528e10 | 1.39861 | ||||||||
\(43\) | −3.41230e9 | −0.0823195 | −0.0411598 | − | 0.999153i | \(-0.513105\pi\) | ||||
−0.0411598 | + | 0.999153i | \(0.513105\pi\) | |||||||
\(44\) | −2.02100e10 | −0.419878 | ||||||||
\(45\) | 2.59024e10 | 0.465007 | ||||||||
\(46\) | 2.15326e10 | 0.335097 | ||||||||
\(47\) | −1.00328e11 | −1.35764 | −0.678820 | − | 0.734304i | \(-0.737509\pi\) | ||||
−0.678820 | + | 0.734304i | \(0.737509\pi\) | |||||||
\(48\) | −2.21767e10 | −0.261715 | ||||||||
\(49\) | 1.40754e11 | 1.45273 | ||||||||
\(50\) | 1.61684e11 | 1.46339 | ||||||||
\(51\) | −7.01540e10 | −0.558273 | ||||||||
\(52\) | −2.09774e11 | −1.47140 | ||||||||
\(53\) | 2.75469e11 | 1.70718 | 0.853591 | − | 0.520944i | \(-0.174420\pi\) | ||||
0.853591 | + | 0.520944i | \(0.174420\pi\) | |||||||
\(54\) | 5.42389e10 | 0.297681 | ||||||||
\(55\) | −8.63459e10 | −0.420614 | ||||||||
\(56\) | 2.19486e11 | 0.951008 | ||||||||
\(57\) | −1.09019e10 | −0.0421034 | ||||||||
\(58\) | 7.30661e11 | 2.52020 | ||||||||
\(59\) | −2.67677e11 | −0.826176 | −0.413088 | − | 0.910691i | \(-0.635550\pi\) | ||||
−0.413088 | + | 0.910691i | \(0.635550\pi\) | |||||||
\(60\) | 4.05343e11 | 1.12160 | ||||||||
\(61\) | 5.63487e11 | 1.40036 | 0.700180 | − | 0.713966i | \(-0.253103\pi\) | ||||
0.700180 | + | 0.713966i | \(0.253103\pi\) | |||||||
\(62\) | 1.65734e11 | 0.370565 | ||||||||
\(63\) | 2.59070e11 | 0.522040 | ||||||||
\(64\) | −8.63411e11 | −1.57054 | ||||||||
\(65\) | −8.96246e11 | −1.47398 | ||||||||
\(66\) | −1.80806e11 | −0.269263 | ||||||||
\(67\) | 1.08084e12 | 1.45974 | 0.729871 | − | 0.683585i | \(-0.239580\pi\) | ||||
0.729871 | + | 0.683585i | \(0.239580\pi\) | |||||||
\(68\) | −1.09783e12 | −1.34656 | ||||||||
\(69\) | 1.12123e11 | 0.125077 | ||||||||
\(70\) | 3.32641e12 | 3.37939 | ||||||||
\(71\) | −1.15056e12 | −1.06594 | −0.532968 | − | 0.846136i | \(-0.678923\pi\) | ||||
−0.532968 | + | 0.846136i | \(0.678923\pi\) | |||||||
\(72\) | 2.39276e11 | 0.202413 | ||||||||
\(73\) | −3.45915e11 | −0.267529 | −0.133764 | − | 0.991013i | \(-0.542707\pi\) | ||||
−0.133764 | + | 0.991013i | \(0.542707\pi\) | |||||||
\(74\) | −2.47411e12 | −1.75151 | ||||||||
\(75\) | 8.41911e11 | 0.546220 | ||||||||
\(76\) | −1.70603e11 | −0.101554 | ||||||||
\(77\) | −8.63611e11 | −0.472203 | ||||||||
\(78\) | −1.87671e12 | −0.943588 | ||||||||
\(79\) | −2.00408e12 | −0.927554 | −0.463777 | − | 0.885952i | \(-0.653506\pi\) | ||||
−0.463777 | + | 0.885952i | \(0.653506\pi\) | |||||||
\(80\) | −1.48271e12 | −0.632369 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −2.72464e12 | −0.989737 | ||||||||
\(83\) | −3.33673e12 | −1.12025 | −0.560123 | − | 0.828409i | \(-0.689246\pi\) | ||||
−0.560123 | + | 0.828409i | \(0.689246\pi\) | |||||||
\(84\) | 4.05414e12 | 1.25917 | ||||||||
\(85\) | −4.69041e12 | −1.34892 | ||||||||
\(86\) | −4.77723e11 | −0.127332 | ||||||||
\(87\) | 3.80466e12 | 0.940677 | ||||||||
\(88\) | −7.97628e11 | −0.183089 | ||||||||
\(89\) | −5.69624e12 | −1.21494 | −0.607468 | − | 0.794344i | \(-0.707815\pi\) | ||||
−0.607468 | + | 0.794344i | \(0.707815\pi\) | |||||||
\(90\) | 3.62634e12 | 0.719271 | ||||||||
\(91\) | −8.96404e12 | −1.65476 | ||||||||
\(92\) | 1.75460e12 | 0.301688 | ||||||||
\(93\) | 8.62999e11 | 0.138316 | ||||||||
\(94\) | −1.40459e13 | −2.09999 | ||||||||
\(95\) | −7.28890e11 | −0.101732 | ||||||||
\(96\) | −5.79356e12 | −0.755409 | ||||||||
\(97\) | −6.55011e12 | −0.798422 | −0.399211 | − | 0.916859i | \(-0.630716\pi\) | ||||
−0.399211 | + | 0.916859i | \(0.630716\pi\) | |||||||
\(98\) | 1.97055e13 | 2.24708 | ||||||||
\(99\) | −9.41480e11 | −0.100504 | ||||||||
\(100\) | 1.31749e13 | 1.31749 | ||||||||
\(101\) | 2.00225e13 | 1.87685 | 0.938424 | − | 0.345487i | \(-0.112286\pi\) | ||||
0.938424 | + | 0.345487i | \(0.112286\pi\) | |||||||
\(102\) | −9.82157e12 | −0.863534 | ||||||||
\(103\) | 8.50230e12 | 0.701608 | 0.350804 | − | 0.936449i | \(-0.385908\pi\) | ||||
0.350804 | + | 0.936449i | \(0.385908\pi\) | |||||||
\(104\) | −8.27915e12 | −0.641607 | ||||||||
\(105\) | 1.73211e13 | 1.26138 | ||||||||
\(106\) | 3.85657e13 | 2.64066 | ||||||||
\(107\) | 2.60740e13 | 1.67963 | 0.839814 | − | 0.542875i | \(-0.182664\pi\) | ||||
0.839814 | + | 0.542875i | \(0.182664\pi\) | |||||||
\(108\) | 4.41969e12 | 0.268002 | ||||||||
\(109\) | −2.65871e12 | −0.151844 | −0.0759222 | − | 0.997114i | \(-0.524190\pi\) | ||||
−0.0759222 | + | 0.997114i | \(0.524190\pi\) | |||||||
\(110\) | −1.20884e13 | −0.650605 | ||||||||
\(111\) | −1.28830e13 | −0.653761 | ||||||||
\(112\) | −1.48297e13 | −0.709929 | ||||||||
\(113\) | −3.76049e13 | −1.69916 | −0.849580 | − | 0.527460i | \(-0.823144\pi\) | ||||
−0.849580 | + | 0.527460i | \(0.823144\pi\) | |||||||
\(114\) | −1.52627e12 | −0.0651254 | ||||||||
\(115\) | 7.49643e12 | 0.302217 | ||||||||
\(116\) | 5.95385e13 | 2.26893 | ||||||||
\(117\) | −9.77230e12 | −0.352199 | ||||||||
\(118\) | −3.74748e13 | −1.27793 | ||||||||
\(119\) | −4.69124e13 | −1.51437 | ||||||||
\(120\) | 1.59977e13 | 0.489079 | ||||||||
\(121\) | 3.13843e12 | 0.0909091 | ||||||||
\(122\) | 7.88881e13 | 2.16607 | ||||||||
\(123\) | −1.41876e13 | −0.369425 | ||||||||
\(124\) | 1.35049e13 | 0.333619 | ||||||||
\(125\) | −3.20800e12 | −0.0752176 | ||||||||
\(126\) | 3.62698e13 | 0.807489 | ||||||||
\(127\) | −6.93279e13 | −1.46617 | −0.733084 | − | 0.680138i | \(-0.761920\pi\) | ||||
−0.733084 | + | 0.680138i | \(0.761920\pi\) | |||||||
\(128\) | −5.57735e13 | −1.12089 | ||||||||
\(129\) | −2.48757e12 | −0.0475272 | ||||||||
\(130\) | −1.25474e14 | −2.27994 | ||||||||
\(131\) | −5.31970e13 | −0.919653 | −0.459827 | − | 0.888009i | \(-0.652088\pi\) | ||||
−0.459827 | + | 0.888009i | \(0.652088\pi\) | |||||||
\(132\) | −1.47331e13 | −0.242417 | ||||||||
\(133\) | −7.29018e12 | −0.114210 | ||||||||
\(134\) | 1.51318e14 | 2.25792 | ||||||||
\(135\) | 1.88829e13 | 0.268472 | ||||||||
\(136\) | −4.33281e13 | −0.587173 | ||||||||
\(137\) | 1.21037e14 | 1.56399 | 0.781994 | − | 0.623286i | \(-0.214203\pi\) | ||||
0.781994 | + | 0.623286i | \(0.214203\pi\) | |||||||
\(138\) | 1.56973e13 | 0.193468 | ||||||||
\(139\) | 1.03707e14 | 1.21958 | 0.609791 | − | 0.792562i | \(-0.291253\pi\) | ||||
0.609791 | + | 0.792562i | \(0.291253\pi\) | |||||||
\(140\) | 2.71055e14 | 3.04246 | ||||||||
\(141\) | −7.31389e13 | −0.783834 | ||||||||
\(142\) | −1.61079e14 | −1.64878 | ||||||||
\(143\) | 3.25760e13 | 0.318576 | ||||||||
\(144\) | −1.61668e13 | −0.151101 | ||||||||
\(145\) | 2.54375e14 | 2.27291 | ||||||||
\(146\) | −4.84280e13 | −0.413812 | ||||||||
\(147\) | 1.02609e14 | 0.838734 | ||||||||
\(148\) | −2.01604e14 | −1.57688 | ||||||||
\(149\) | −2.94068e13 | −0.220159 | −0.110080 | − | 0.993923i | \(-0.535111\pi\) | ||||
−0.110080 | + | 0.993923i | \(0.535111\pi\) | |||||||
\(150\) | 1.17868e14 | 0.844891 | ||||||||
\(151\) | −4.86579e13 | −0.334043 | −0.167022 | − | 0.985953i | \(-0.553415\pi\) | ||||
−0.167022 | + | 0.985953i | \(0.553415\pi\) | |||||||
\(152\) | −6.73318e12 | −0.0442830 | ||||||||
\(153\) | −5.11423e13 | −0.322319 | ||||||||
\(154\) | −1.20906e14 | −0.730401 | ||||||||
\(155\) | 5.76990e13 | 0.334204 | ||||||||
\(156\) | −1.52925e14 | −0.849511 | ||||||||
\(157\) | −2.31548e14 | −1.23394 | −0.616969 | − | 0.786988i | \(-0.711640\pi\) | ||||
−0.616969 | + | 0.786988i | \(0.711640\pi\) | |||||||
\(158\) | −2.80571e14 | −1.43474 | ||||||||
\(159\) | 2.00817e14 | 0.985642 | ||||||||
\(160\) | −3.87350e14 | −1.82526 | ||||||||
\(161\) | 7.49775e13 | 0.339283 | ||||||||
\(162\) | 3.95401e13 | 0.171866 | ||||||||
\(163\) | 1.44315e14 | 0.602688 | 0.301344 | − | 0.953516i | \(-0.402565\pi\) | ||||
0.301344 | + | 0.953516i | \(0.402565\pi\) | |||||||
\(164\) | −2.22020e14 | −0.891058 | ||||||||
\(165\) | −6.29461e13 | −0.242842 | ||||||||
\(166\) | −4.67143e14 | −1.73279 | ||||||||
\(167\) | 4.17920e14 | 1.49086 | 0.745429 | − | 0.666585i | \(-0.232244\pi\) | ||||
0.745429 | + | 0.666585i | \(0.232244\pi\) | |||||||
\(168\) | 1.60005e14 | 0.549065 | ||||||||
\(169\) | 3.52546e13 | 0.116400 | ||||||||
\(170\) | −6.56657e14 | −2.08651 | ||||||||
\(171\) | −7.94752e12 | −0.0243084 | ||||||||
\(172\) | −3.89276e13 | −0.114636 | ||||||||
\(173\) | 4.17435e14 | 1.18383 | 0.591914 | − | 0.806001i | \(-0.298372\pi\) | ||||
0.591914 | + | 0.806001i | \(0.298372\pi\) | |||||||
\(174\) | 5.32652e14 | 1.45504 | ||||||||
\(175\) | 5.62990e14 | 1.48168 | ||||||||
\(176\) | 5.38922e13 | 0.136676 | ||||||||
\(177\) | −1.95136e14 | −0.476993 | ||||||||
\(178\) | −7.97473e14 | −1.87926 | ||||||||
\(179\) | 4.89549e14 | 1.11238 | 0.556188 | − | 0.831056i | \(-0.312263\pi\) | ||||
0.556188 | + | 0.831056i | \(0.312263\pi\) | |||||||
\(180\) | 2.95495e14 | 0.647558 | ||||||||
\(181\) | 3.82069e14 | 0.807664 | 0.403832 | − | 0.914833i | \(-0.367678\pi\) | ||||
0.403832 | + | 0.914833i | \(0.367678\pi\) | |||||||
\(182\) | −1.25497e15 | −2.55957 | ||||||||
\(183\) | 4.10782e14 | 0.808498 | ||||||||
\(184\) | 6.92489e13 | 0.131552 | ||||||||
\(185\) | −8.61343e14 | −1.57965 | ||||||||
\(186\) | 1.20820e14 | 0.213946 | ||||||||
\(187\) | 1.70483e14 | 0.291549 | ||||||||
\(188\) | −1.14454e15 | −1.89062 | ||||||||
\(189\) | 1.88862e14 | 0.301400 | ||||||||
\(190\) | −1.02045e14 | −0.157359 | ||||||||
\(191\) | 2.81803e14 | 0.419980 | 0.209990 | − | 0.977704i | \(-0.432657\pi\) | ||||
0.209990 | + | 0.977704i | \(0.432657\pi\) | |||||||
\(192\) | −6.29427e14 | −0.906749 | ||||||||
\(193\) | 6.26551e14 | 0.872638 | 0.436319 | − | 0.899792i | \(-0.356282\pi\) | ||||
0.436319 | + | 0.899792i | \(0.356282\pi\) | |||||||
\(194\) | −9.17016e14 | −1.23500 | ||||||||
\(195\) | −6.53363e14 | −0.851000 | ||||||||
\(196\) | 1.60572e15 | 2.02304 | ||||||||
\(197\) | −6.60082e14 | −0.804576 | −0.402288 | − | 0.915513i | \(-0.631785\pi\) | ||||
−0.402288 | + | 0.915513i | \(0.631785\pi\) | |||||||
\(198\) | −1.31807e14 | −0.155459 | ||||||||
\(199\) | −1.45047e15 | −1.65564 | −0.827818 | − | 0.560996i | \(-0.810418\pi\) | ||||
−0.827818 | + | 0.560996i | \(0.810418\pi\) | |||||||
\(200\) | 5.19975e14 | 0.574497 | ||||||||
\(201\) | 7.87934e14 | 0.842783 | ||||||||
\(202\) | 2.80315e15 | 2.90310 | ||||||||
\(203\) | 2.54419e15 | 2.55168 | ||||||||
\(204\) | −8.00317e14 | −0.777439 | ||||||||
\(205\) | −9.48565e14 | −0.892621 | ||||||||
\(206\) | 1.19032e15 | 1.08524 | ||||||||
\(207\) | 8.17380e13 | 0.0722132 | ||||||||
\(208\) | 5.59386e14 | 0.478961 | ||||||||
\(209\) | 2.64931e13 | 0.0219878 | ||||||||
\(210\) | 2.42495e15 | 1.95109 | ||||||||
\(211\) | −1.86139e15 | −1.45212 | −0.726059 | − | 0.687633i | \(-0.758650\pi\) | ||||
−0.726059 | + | 0.687633i | \(0.758650\pi\) | |||||||
\(212\) | 3.14255e15 | 2.37738 | ||||||||
\(213\) | −8.38760e14 | −0.615418 | ||||||||
\(214\) | 3.65036e15 | 2.59804 | ||||||||
\(215\) | −1.66316e14 | −0.114837 | ||||||||
\(216\) | 1.74432e14 | 0.116863 | ||||||||
\(217\) | 5.77092e14 | 0.375195 | ||||||||
\(218\) | −3.72219e14 | −0.234872 | ||||||||
\(219\) | −2.52172e14 | −0.154458 | ||||||||
\(220\) | −9.85034e14 | −0.585738 | ||||||||
\(221\) | 1.76957e15 | 1.02169 | ||||||||
\(222\) | −1.80362e15 | −1.01123 | ||||||||
\(223\) | 2.64472e15 | 1.44012 | 0.720059 | − | 0.693913i | \(-0.244115\pi\) | ||||
0.720059 | + | 0.693913i | \(0.244115\pi\) | |||||||
\(224\) | −3.87418e15 | −2.04912 | ||||||||
\(225\) | 6.13753e14 | 0.315360 | ||||||||
\(226\) | −5.26468e15 | −2.62825 | ||||||||
\(227\) | 3.07427e15 | 1.49133 | 0.745666 | − | 0.666319i | \(-0.232131\pi\) | ||||
0.745666 | + | 0.666319i | \(0.232131\pi\) | |||||||
\(228\) | −1.24369e14 | −0.0586323 | ||||||||
\(229\) | −2.98623e15 | −1.36834 | −0.684168 | − | 0.729324i | \(-0.739835\pi\) | ||||
−0.684168 | + | 0.729324i | \(0.739835\pi\) | |||||||
\(230\) | 1.04950e15 | 0.467467 | ||||||||
\(231\) | −6.29573e14 | −0.272626 | ||||||||
\(232\) | 2.34981e15 | 0.989374 | ||||||||
\(233\) | −1.86637e15 | −0.764159 | −0.382079 | − | 0.924130i | \(-0.624792\pi\) | ||||
−0.382079 | + | 0.924130i | \(0.624792\pi\) | |||||||
\(234\) | −1.36812e15 | −0.544781 | ||||||||
\(235\) | −4.88997e15 | −1.89394 | ||||||||
\(236\) | −3.05366e15 | −1.15052 | ||||||||
\(237\) | −1.46098e15 | −0.535524 | ||||||||
\(238\) | −6.56773e15 | −2.34242 | ||||||||
\(239\) | −3.11970e14 | −0.108275 | −0.0541373 | − | 0.998534i | \(-0.517241\pi\) | ||||
−0.0541373 | + | 0.998534i | \(0.517241\pi\) | |||||||
\(240\) | −1.08089e15 | −0.365098 | ||||||||
\(241\) | 5.25176e15 | 1.72661 | 0.863305 | − | 0.504683i | \(-0.168391\pi\) | ||||
0.863305 | + | 0.504683i | \(0.168391\pi\) | |||||||
\(242\) | 4.39380e14 | 0.140618 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 6.42826e15 | 1.95011 | ||||||||
\(245\) | 6.86033e15 | 2.02659 | ||||||||
\(246\) | −1.98627e15 | −0.571425 | ||||||||
\(247\) | 2.74991e14 | 0.0770527 | ||||||||
\(248\) | 5.32999e14 | 0.145476 | ||||||||
\(249\) | −2.43248e15 | −0.646775 | ||||||||
\(250\) | −4.49120e14 | −0.116346 | ||||||||
\(251\) | −2.46350e15 | −0.621833 | −0.310916 | − | 0.950437i | \(-0.600636\pi\) | ||||
−0.310916 | + | 0.950437i | \(0.600636\pi\) | |||||||
\(252\) | 2.95547e15 | 0.726981 | ||||||||
\(253\) | −2.72474e14 | −0.0653193 | ||||||||
\(254\) | −9.70590e15 | −2.26786 | ||||||||
\(255\) | −3.41931e15 | −0.778802 | ||||||||
\(256\) | −7.35229e14 | −0.163254 | ||||||||
\(257\) | 2.41514e15 | 0.522851 | 0.261425 | − | 0.965224i | \(-0.415808\pi\) | ||||
0.261425 | + | 0.965224i | \(0.415808\pi\) | |||||||
\(258\) | −3.48260e14 | −0.0735149 | ||||||||
\(259\) | −8.61495e15 | −1.77339 | ||||||||
\(260\) | −1.02244e16 | −2.05263 | ||||||||
\(261\) | 2.77360e15 | 0.543100 | ||||||||
\(262\) | −7.44759e15 | −1.42252 | ||||||||
\(263\) | −1.68025e15 | −0.313084 | −0.156542 | − | 0.987671i | \(-0.550035\pi\) | ||||
−0.156542 | + | 0.987671i | \(0.550035\pi\) | |||||||
\(264\) | −5.81471e14 | −0.105707 | ||||||||
\(265\) | 1.34264e16 | 2.38155 | ||||||||
\(266\) | −1.02063e15 | −0.176659 | ||||||||
\(267\) | −4.15256e15 | −0.701443 | ||||||||
\(268\) | 1.23303e16 | 2.03281 | ||||||||
\(269\) | −5.87926e14 | −0.0946091 | −0.0473046 | − | 0.998881i | \(-0.515063\pi\) | ||||
−0.0473046 | + | 0.998881i | \(0.515063\pi\) | |||||||
\(270\) | 2.64360e15 | 0.415271 | ||||||||
\(271\) | 3.69154e14 | 0.0566119 | 0.0283059 | − | 0.999599i | \(-0.490989\pi\) | ||||
0.0283059 | + | 0.999599i | \(0.490989\pi\) | |||||||
\(272\) | 2.92749e15 | 0.438326 | ||||||||
\(273\) | −6.53479e15 | −0.955376 | ||||||||
\(274\) | 1.69451e16 | 2.41917 | ||||||||
\(275\) | −2.04595e15 | −0.285254 | ||||||||
\(276\) | 1.27910e15 | 0.174179 | ||||||||
\(277\) | 3.44319e15 | 0.457976 | 0.228988 | − | 0.973429i | \(-0.426458\pi\) | ||||
0.228988 | + | 0.973429i | \(0.426458\pi\) | |||||||
\(278\) | 1.45190e16 | 1.88645 | ||||||||
\(279\) | 6.29126e14 | 0.0798565 | ||||||||
\(280\) | 1.06977e16 | 1.32667 | ||||||||
\(281\) | 1.73559e15 | 0.210309 | 0.105154 | − | 0.994456i | \(-0.466466\pi\) | ||||
0.105154 | + | 0.994456i | \(0.466466\pi\) | |||||||
\(282\) | −1.02394e16 | −1.21243 | ||||||||
\(283\) | 1.72244e15 | 0.199311 | 0.0996556 | − | 0.995022i | \(-0.468226\pi\) | ||||
0.0996556 | + | 0.995022i | \(0.468226\pi\) | |||||||
\(284\) | −1.31256e16 | −1.48440 | ||||||||
\(285\) | −5.31361e14 | −0.0587351 | ||||||||
\(286\) | 4.56064e15 | 0.492773 | ||||||||
\(287\) | −9.48733e15 | −1.00210 | ||||||||
\(288\) | −4.22350e15 | −0.436136 | ||||||||
\(289\) | −6.43739e14 | −0.0649941 | ||||||||
\(290\) | 3.56124e16 | 3.51572 | ||||||||
\(291\) | −4.77503e15 | −0.460969 | ||||||||
\(292\) | −3.94619e15 | −0.372554 | ||||||||
\(293\) | −9.32911e15 | −0.861392 | −0.430696 | − | 0.902497i | \(-0.641732\pi\) | ||||
−0.430696 | + | 0.902497i | \(0.641732\pi\) | |||||||
\(294\) | 1.43653e16 | 1.29735 | ||||||||
\(295\) | −1.30466e16 | −1.15253 | ||||||||
\(296\) | −7.95673e15 | −0.687604 | ||||||||
\(297\) | −6.86339e14 | −0.0580259 | ||||||||
\(298\) | −4.11695e15 | −0.340541 | ||||||||
\(299\) | −2.82820e15 | −0.228901 | ||||||||
\(300\) | 9.60452e15 | 0.760654 | ||||||||
\(301\) | −1.66345e15 | −0.128922 | ||||||||
\(302\) | −6.81210e15 | −0.516697 | ||||||||
\(303\) | 1.45964e16 | 1.08360 | ||||||||
\(304\) | 4.54932e14 | 0.0330573 | ||||||||
\(305\) | 2.74643e16 | 1.95353 | ||||||||
\(306\) | −7.15992e15 | −0.498562 | ||||||||
\(307\) | −1.85795e16 | −1.26658 | −0.633292 | − | 0.773913i | \(-0.718297\pi\) | ||||
−0.633292 | + | 0.773913i | \(0.718297\pi\) | |||||||
\(308\) | −9.85208e15 | −0.657579 | ||||||||
\(309\) | 6.19818e15 | 0.405074 | ||||||||
\(310\) | 8.07786e15 | 0.516946 | ||||||||
\(311\) | 1.10219e16 | 0.690739 | 0.345369 | − | 0.938467i | \(-0.387754\pi\) | ||||
0.345369 | + | 0.938467i | \(0.387754\pi\) | |||||||
\(312\) | −6.03550e15 | −0.370432 | ||||||||
\(313\) | 2.44634e16 | 1.47055 | 0.735273 | − | 0.677771i | \(-0.237054\pi\) | ||||
0.735273 | + | 0.677771i | \(0.237054\pi\) | |||||||
\(314\) | −3.24167e16 | −1.90865 | ||||||||
\(315\) | 1.26271e16 | 0.728256 | ||||||||
\(316\) | −2.28626e16 | −1.29169 | ||||||||
\(317\) | 7.28014e15 | 0.402953 | 0.201477 | − | 0.979493i | \(-0.435426\pi\) | ||||
0.201477 | + | 0.979493i | \(0.435426\pi\) | |||||||
\(318\) | 2.81144e16 | 1.52459 | ||||||||
\(319\) | −9.24580e15 | −0.491253 | ||||||||
\(320\) | −4.20827e16 | −2.19093 | ||||||||
\(321\) | 1.90079e16 | 0.969733 | ||||||||
\(322\) | 1.04968e16 | 0.524802 | ||||||||
\(323\) | 1.43913e15 | 0.0705156 | ||||||||
\(324\) | 3.22196e15 | 0.154731 | ||||||||
\(325\) | −2.12364e16 | −0.999628 | ||||||||
\(326\) | 2.02041e16 | 0.932235 | ||||||||
\(327\) | −1.93820e15 | −0.0876674 | ||||||||
\(328\) | −8.76245e15 | −0.388549 | ||||||||
\(329\) | −4.89084e16 | −2.12623 | ||||||||
\(330\) | −8.81246e15 | −0.375627 | ||||||||
\(331\) | 4.91941e15 | 0.205604 | 0.102802 | − | 0.994702i | \(-0.467219\pi\) | ||||
0.102802 | + | 0.994702i | \(0.467219\pi\) | |||||||
\(332\) | −3.80654e16 | −1.56003 | ||||||||
\(333\) | −9.39173e15 | −0.377449 | ||||||||
\(334\) | 5.85089e16 | 2.30605 | ||||||||
\(335\) | 5.26803e16 | 2.03637 | ||||||||
\(336\) | −1.08108e16 | −0.409878 | ||||||||
\(337\) | −3.61707e15 | −0.134512 | −0.0672562 | − | 0.997736i | \(-0.521424\pi\) | ||||
−0.0672562 | + | 0.997736i | \(0.521424\pi\) | |||||||
\(338\) | 4.93565e15 | 0.180047 | ||||||||
\(339\) | −2.74139e16 | −0.981010 | ||||||||
\(340\) | −5.35082e16 | −1.87848 | ||||||||
\(341\) | −2.09719e15 | −0.0722329 | ||||||||
\(342\) | −1.11265e15 | −0.0376002 | ||||||||
\(343\) | 2.13834e16 | 0.709030 | ||||||||
\(344\) | −1.53636e15 | −0.0499876 | ||||||||
\(345\) | 5.46489e15 | 0.174485 | ||||||||
\(346\) | 5.84408e16 | 1.83114 | ||||||||
\(347\) | 2.03135e16 | 0.624660 | 0.312330 | − | 0.949974i | \(-0.398890\pi\) | ||||
0.312330 | + | 0.949974i | \(0.398890\pi\) | |||||||
\(348\) | 4.34035e16 | 1.30997 | ||||||||
\(349\) | −1.16091e16 | −0.343902 | −0.171951 | − | 0.985106i | \(-0.555007\pi\) | ||||
−0.171951 | + | 0.985106i | \(0.555007\pi\) | |||||||
\(350\) | 7.88186e16 | 2.29185 | ||||||||
\(351\) | −7.12401e15 | −0.203342 | ||||||||
\(352\) | 1.40791e16 | 0.394500 | ||||||||
\(353\) | 1.93894e16 | 0.533370 | 0.266685 | − | 0.963784i | \(-0.414072\pi\) | ||||
0.266685 | + | 0.963784i | \(0.414072\pi\) | |||||||
\(354\) | −2.73191e16 | −0.737811 | ||||||||
\(355\) | −5.60784e16 | −1.48700 | ||||||||
\(356\) | −6.49827e16 | −1.69189 | ||||||||
\(357\) | −3.41991e16 | −0.874322 | ||||||||
\(358\) | 6.85369e16 | 1.72062 | ||||||||
\(359\) | −1.45895e16 | −0.359689 | −0.179844 | − | 0.983695i | \(-0.557559\pi\) | ||||
−0.179844 | + | 0.983695i | \(0.557559\pi\) | |||||||
\(360\) | 1.16623e16 | 0.282370 | ||||||||
\(361\) | −4.18293e16 | −0.994682 | ||||||||
\(362\) | 5.34896e16 | 1.24929 | ||||||||
\(363\) | 2.28791e15 | 0.0524864 | ||||||||
\(364\) | −1.02262e17 | −2.30438 | ||||||||
\(365\) | −1.68599e16 | −0.373208 | ||||||||
\(366\) | 5.75094e16 | 1.25058 | ||||||||
\(367\) | −5.04342e16 | −1.07745 | −0.538724 | − | 0.842482i | \(-0.681093\pi\) | ||||
−0.538724 | + | 0.842482i | \(0.681093\pi\) | |||||||
\(368\) | −4.67884e15 | −0.0982037 | ||||||||
\(369\) | −1.03428e16 | −0.213287 | ||||||||
\(370\) | −1.20588e17 | −2.44339 | ||||||||
\(371\) | 1.34287e17 | 2.67365 | ||||||||
\(372\) | 9.84509e15 | 0.192615 | ||||||||
\(373\) | 6.41403e15 | 0.123317 | 0.0616586 | − | 0.998097i | \(-0.480361\pi\) | ||||
0.0616586 | + | 0.998097i | \(0.480361\pi\) | |||||||
\(374\) | 2.38676e16 | 0.450966 | ||||||||
\(375\) | −2.33863e15 | −0.0434269 | ||||||||
\(376\) | −4.51716e16 | −0.824411 | ||||||||
\(377\) | −9.59688e16 | −1.72152 | ||||||||
\(378\) | 2.64407e16 | 0.466204 | ||||||||
\(379\) | 6.85830e15 | 0.118867 | 0.0594335 | − | 0.998232i | \(-0.481071\pi\) | ||||
0.0594335 | + | 0.998232i | \(0.481071\pi\) | |||||||
\(380\) | −8.31517e15 | −0.141670 | ||||||||
\(381\) | −5.05400e16 | −0.846492 | ||||||||
\(382\) | 3.94524e16 | 0.649623 | ||||||||
\(383\) | 5.27865e16 | 0.854537 | 0.427268 | − | 0.904125i | \(-0.359476\pi\) | ||||
0.427268 | + | 0.904125i | \(0.359476\pi\) | |||||||
\(384\) | −4.06589e16 | −0.647146 | ||||||||
\(385\) | −4.20924e16 | −0.658732 | ||||||||
\(386\) | 8.77171e16 | 1.34979 | ||||||||
\(387\) | −1.81344e15 | −0.0274398 | ||||||||
\(388\) | −7.47237e16 | −1.11187 | ||||||||
\(389\) | 6.57216e16 | 0.961692 | 0.480846 | − | 0.876805i | \(-0.340330\pi\) | ||||
0.480846 | + | 0.876805i | \(0.340330\pi\) | |||||||
\(390\) | −9.14709e16 | −1.31632 | ||||||||
\(391\) | −1.48011e16 | −0.209481 | ||||||||
\(392\) | 6.33729e16 | 0.882153 | ||||||||
\(393\) | −3.87806e16 | −0.530962 | ||||||||
\(394\) | −9.24114e16 | −1.24452 | ||||||||
\(395\) | −9.76789e16 | −1.29396 | ||||||||
\(396\) | −1.07404e16 | −0.139959 | ||||||||
\(397\) | −1.04942e17 | −1.34528 | −0.672639 | − | 0.739971i | \(-0.734839\pi\) | ||||
−0.672639 | + | 0.739971i | \(0.734839\pi\) | |||||||
\(398\) | −2.03066e17 | −2.56093 | ||||||||
\(399\) | −5.31454e15 | −0.0659390 | ||||||||
\(400\) | −3.51324e16 | −0.428863 | ||||||||
\(401\) | 2.14759e16 | 0.257936 | 0.128968 | − | 0.991649i | \(-0.458834\pi\) | ||||
0.128968 | + | 0.991649i | \(0.458834\pi\) | |||||||
\(402\) | 1.10311e17 | 1.30361 | ||||||||
\(403\) | −2.17683e16 | −0.253129 | ||||||||
\(404\) | 2.28416e17 | 2.61366 | ||||||||
\(405\) | 1.37656e16 | 0.155002 | ||||||||
\(406\) | 3.56187e17 | 3.94693 | ||||||||
\(407\) | 3.13074e16 | 0.341415 | ||||||||
\(408\) | −3.15862e16 | −0.339005 | ||||||||
\(409\) | 1.57661e17 | 1.66542 | 0.832708 | − | 0.553713i | \(-0.186790\pi\) | ||||
0.832708 | + | 0.553713i | \(0.186790\pi\) | |||||||
\(410\) | −1.32799e17 | −1.38070 | ||||||||
\(411\) | 8.82358e16 | 0.902969 | ||||||||
\(412\) | 9.69943e16 | 0.977044 | ||||||||
\(413\) | −1.30489e17 | −1.29389 | ||||||||
\(414\) | 1.14433e16 | 0.111699 | ||||||||
\(415\) | −1.62632e17 | −1.56277 | ||||||||
\(416\) | 1.46137e17 | 1.38246 | ||||||||
\(417\) | 7.56023e16 | 0.704126 | ||||||||
\(418\) | 3.70903e15 | 0.0340106 | ||||||||
\(419\) | 8.20257e16 | 0.740558 | 0.370279 | − | 0.928921i | \(-0.379262\pi\) | ||||
0.370279 | + | 0.928921i | \(0.379262\pi\) | |||||||
\(420\) | 1.97599e17 | 1.75657 | ||||||||
\(421\) | −5.59695e16 | −0.489912 | −0.244956 | − | 0.969534i | \(-0.578774\pi\) | ||||
−0.244956 | + | 0.969534i | \(0.578774\pi\) | |||||||
\(422\) | −2.60595e17 | −2.24613 | ||||||||
\(423\) | −5.33183e16 | −0.452547 | ||||||||
\(424\) | 1.24027e17 | 1.03667 | ||||||||
\(425\) | −1.11138e17 | −0.914820 | ||||||||
\(426\) | −1.17426e17 | −0.951926 | ||||||||
\(427\) | 2.74692e17 | 2.19313 | ||||||||
\(428\) | 2.97452e17 | 2.33901 | ||||||||
\(429\) | 2.37479e16 | 0.183930 | ||||||||
\(430\) | −2.32842e16 | −0.177630 | ||||||||
\(431\) | 1.77267e17 | 1.33207 | 0.666034 | − | 0.745921i | \(-0.267991\pi\) | ||||
0.666034 | + | 0.745921i | \(0.267991\pi\) | |||||||
\(432\) | −1.17856e16 | −0.0872385 | ||||||||
\(433\) | −5.06598e16 | −0.369396 | −0.184698 | − | 0.982795i | \(-0.559131\pi\) | ||||
−0.184698 | + | 0.982795i | \(0.559131\pi\) | |||||||
\(434\) | 8.07928e16 | 0.580349 | ||||||||
\(435\) | 1.85439e17 | 1.31226 | ||||||||
\(436\) | −3.03306e16 | −0.211455 | ||||||||
\(437\) | −2.30009e15 | −0.0157985 | ||||||||
\(438\) | −3.53040e16 | −0.238915 | ||||||||
\(439\) | −6.76669e16 | −0.451187 | −0.225594 | − | 0.974221i | \(-0.572432\pi\) | ||||
−0.225594 | + | 0.974221i | \(0.572432\pi\) | |||||||
\(440\) | −3.88764e16 | −0.255413 | ||||||||
\(441\) | 7.48022e16 | 0.484243 | ||||||||
\(442\) | 2.47739e17 | 1.58034 | ||||||||
\(443\) | 1.70873e17 | 1.07411 | 0.537057 | − | 0.843546i | \(-0.319536\pi\) | ||||
0.537057 | + | 0.843546i | \(0.319536\pi\) | |||||||
\(444\) | −1.46970e17 | −0.910413 | ||||||||
\(445\) | −2.77635e17 | −1.69486 | ||||||||
\(446\) | 3.70261e17 | 2.22757 | ||||||||
\(447\) | −2.14376e16 | −0.127109 | ||||||||
\(448\) | −4.20901e17 | −2.45965 | ||||||||
\(449\) | 2.13667e14 | 0.00123066 | 0.000615329 | − | 1.00000i | \(-0.499804\pi\) | ||||
0.000615329 | 1.00000i | \(0.499804\pi\) | ||||||||
\(450\) | 8.59254e16 | 0.487798 | ||||||||
\(451\) | 3.44777e16 | 0.192926 | ||||||||
\(452\) | −4.28996e17 | −2.36621 | ||||||||
\(453\) | −3.54716e16 | −0.192860 | ||||||||
\(454\) | 4.30398e17 | 2.30679 | ||||||||
\(455\) | −4.36907e17 | −2.30842 | ||||||||
\(456\) | −4.90849e15 | −0.0255668 | ||||||||
\(457\) | 3.31395e17 | 1.70173 | 0.850864 | − | 0.525386i | \(-0.176079\pi\) | ||||
0.850864 | + | 0.525386i | \(0.176079\pi\) | |||||||
\(458\) | −4.18073e17 | −2.11654 | ||||||||
\(459\) | −3.72827e16 | −0.186091 | ||||||||
\(460\) | 8.55192e16 | 0.420860 | ||||||||
\(461\) | −2.65757e17 | −1.28952 | −0.644761 | − | 0.764384i | \(-0.723043\pi\) | ||||
−0.644761 | + | 0.764384i | \(0.723043\pi\) | |||||||
\(462\) | −8.81402e16 | −0.421697 | ||||||||
\(463\) | −4.27497e15 | −0.0201677 | −0.0100839 | − | 0.999949i | \(-0.503210\pi\) | ||||
−0.0100839 | + | 0.999949i | \(0.503210\pi\) | |||||||
\(464\) | −1.58766e17 | −0.738569 | ||||||||
\(465\) | 4.20626e16 | 0.192953 | ||||||||
\(466\) | −2.61291e17 | −1.18200 | ||||||||
\(467\) | −2.56398e16 | −0.114381 | −0.0571907 | − | 0.998363i | \(-0.518214\pi\) | ||||
−0.0571907 | + | 0.998363i | \(0.518214\pi\) | |||||||
\(468\) | −1.11482e17 | −0.490465 | ||||||||
\(469\) | 5.26896e17 | 2.28613 | ||||||||
\(470\) | −6.84596e17 | −2.92953 | ||||||||
\(471\) | −1.68798e17 | −0.712414 | ||||||||
\(472\) | −1.20519e17 | −0.501686 | ||||||||
\(473\) | 6.04511e15 | 0.0248203 | ||||||||
\(474\) | −2.04537e17 | −0.828346 | ||||||||
\(475\) | −1.72709e16 | −0.0689932 | ||||||||
\(476\) | −5.35176e17 | −2.10888 | ||||||||
\(477\) | 1.46396e17 | 0.569061 | ||||||||
\(478\) | −4.36758e16 | −0.167479 | ||||||||
\(479\) | 3.69707e17 | 1.39855 | 0.699274 | − | 0.714854i | \(-0.253507\pi\) | ||||
0.699274 | + | 0.714854i | \(0.253507\pi\) | |||||||
\(480\) | −2.82378e17 | −1.05381 | ||||||||
\(481\) | 3.24962e17 | 1.19644 | ||||||||
\(482\) | 7.35246e17 | 2.67071 | ||||||||
\(483\) | 5.46586e16 | 0.195885 | ||||||||
\(484\) | 3.58032e16 | 0.126598 | ||||||||
\(485\) | −3.19253e17 | −1.11382 | ||||||||
\(486\) | 2.88248e16 | 0.0992270 | ||||||||
\(487\) | −5.17795e17 | −1.75881 | −0.879406 | − | 0.476073i | \(-0.842060\pi\) | ||||
−0.879406 | + | 0.476073i | \(0.842060\pi\) | |||||||
\(488\) | 2.53704e17 | 0.850352 | ||||||||
\(489\) | 1.05206e17 | 0.347962 | ||||||||
\(490\) | 9.60446e17 | 3.13472 | ||||||||
\(491\) | 1.72056e17 | 0.554165 | 0.277082 | − | 0.960846i | \(-0.410632\pi\) | ||||
0.277082 | + | 0.960846i | \(0.410632\pi\) | |||||||
\(492\) | −1.61852e17 | −0.514453 | ||||||||
\(493\) | −5.02242e17 | −1.57546 | ||||||||
\(494\) | 3.84987e16 | 0.119185 | ||||||||
\(495\) | −4.58877e16 | −0.140205 | ||||||||
\(496\) | −3.60124e16 | −0.108598 | ||||||||
\(497\) | −5.60883e17 | −1.66938 | ||||||||
\(498\) | −3.40547e17 | −1.00043 | ||||||||
\(499\) | 1.31941e17 | 0.382584 | 0.191292 | − | 0.981533i | \(-0.438732\pi\) | ||||
0.191292 | + | 0.981533i | \(0.438732\pi\) | |||||||
\(500\) | −3.65969e16 | −0.104746 | ||||||||
\(501\) | 3.04664e17 | 0.860748 | ||||||||
\(502\) | −3.44890e17 | −0.961848 | ||||||||
\(503\) | 2.26740e17 | 0.624218 | 0.312109 | − | 0.950046i | \(-0.398965\pi\) | ||||
0.312109 | + | 0.950046i | \(0.398965\pi\) | |||||||
\(504\) | 1.16644e17 | 0.317003 | ||||||||
\(505\) | 9.75896e17 | 2.61824 | ||||||||
\(506\) | −3.81463e16 | −0.101036 | ||||||||
\(507\) | 2.57006e16 | 0.0672035 | ||||||||
\(508\) | −7.90892e17 | −2.04175 | ||||||||
\(509\) | −8.67070e16 | −0.220998 | −0.110499 | − | 0.993876i | \(-0.535245\pi\) | ||||
−0.110499 | + | 0.993876i | \(0.535245\pi\) | |||||||
\(510\) | −4.78703e17 | −1.20465 | ||||||||
\(511\) | −1.68628e17 | −0.418982 | ||||||||
\(512\) | 3.53965e17 | 0.868371 | ||||||||
\(513\) | −5.79374e15 | −0.0140345 | ||||||||
\(514\) | 3.38120e17 | 0.808743 | ||||||||
\(515\) | 4.14402e17 | 0.978758 | ||||||||
\(516\) | −2.83782e16 | −0.0661853 | ||||||||
\(517\) | 1.77737e17 | 0.409344 | ||||||||
\(518\) | −1.20609e18 | −2.74307 | ||||||||
\(519\) | 3.04310e17 | 0.683484 | ||||||||
\(520\) | −4.03526e17 | −0.895055 | ||||||||
\(521\) | 5.57568e17 | 1.22138 | 0.610692 | − | 0.791868i | \(-0.290891\pi\) | ||||
0.610692 | + | 0.791868i | \(0.290891\pi\) | |||||||
\(522\) | 3.88303e17 | 0.840065 | ||||||||
\(523\) | −4.80021e17 | −1.02565 | −0.512826 | − | 0.858493i | \(-0.671401\pi\) | ||||
−0.512826 | + | 0.858493i | \(0.671401\pi\) | |||||||
\(524\) | −6.06872e17 | −1.28069 | ||||||||
\(525\) | 4.10420e17 | 0.855446 | ||||||||
\(526\) | −2.35235e17 | −0.484277 | ||||||||
\(527\) | −1.13922e17 | −0.231653 | ||||||||
\(528\) | 3.92874e16 | 0.0789101 | ||||||||
\(529\) | −4.80381e17 | −0.953067 | ||||||||
\(530\) | 1.87969e18 | 3.68378 | ||||||||
\(531\) | −1.42254e17 | −0.275392 | ||||||||
\(532\) | −8.31664e16 | −0.159046 | ||||||||
\(533\) | 3.57868e17 | 0.676077 | ||||||||
\(534\) | −5.81358e17 | −1.08499 | ||||||||
\(535\) | 1.27085e18 | 2.34311 | ||||||||
\(536\) | 4.86639e17 | 0.886412 | ||||||||
\(537\) | 3.56881e17 | 0.642231 | ||||||||
\(538\) | −8.23097e16 | −0.146341 | ||||||||
\(539\) | −2.49354e17 | −0.438015 | ||||||||
\(540\) | 2.15416e17 | 0.373868 | ||||||||
\(541\) | −3.07367e17 | −0.527078 | −0.263539 | − | 0.964649i | \(-0.584890\pi\) | ||||
−0.263539 | + | 0.964649i | \(0.584890\pi\) | |||||||
\(542\) | 5.16816e16 | 0.0875670 | ||||||||
\(543\) | 2.78528e17 | 0.466305 | ||||||||
\(544\) | 7.64792e17 | 1.26517 | ||||||||
\(545\) | −1.29585e17 | −0.211826 | ||||||||
\(546\) | −9.14870e17 | −1.47777 | ||||||||
\(547\) | 6.25426e17 | 0.998294 | 0.499147 | − | 0.866517i | \(-0.333647\pi\) | ||||
0.499147 | + | 0.866517i | \(0.333647\pi\) | |||||||
\(548\) | 1.38079e18 | 2.17798 | ||||||||
\(549\) | 2.99460e17 | 0.466787 | ||||||||
\(550\) | −2.86433e17 | −0.441230 | ||||||||
\(551\) | −7.80485e16 | −0.118817 | ||||||||
\(552\) | 5.04824e16 | 0.0759515 | ||||||||
\(553\) | −9.76961e17 | −1.45266 | ||||||||
\(554\) | 4.82047e17 | 0.708396 | ||||||||
\(555\) | −6.27919e17 | −0.912009 | ||||||||
\(556\) | 1.18309e18 | 1.69836 | ||||||||
\(557\) | 5.97923e17 | 0.848372 | 0.424186 | − | 0.905575i | \(-0.360560\pi\) | ||||
0.424186 | + | 0.905575i | \(0.360560\pi\) | |||||||
\(558\) | 8.80777e16 | 0.123522 | ||||||||
\(559\) | 6.27465e16 | 0.0869787 | ||||||||
\(560\) | −7.22799e17 | −0.990365 | ||||||||
\(561\) | 1.24282e17 | 0.168326 | ||||||||
\(562\) | 2.42983e17 | 0.325305 | ||||||||
\(563\) | −9.48274e16 | −0.125496 | −0.0627479 | − | 0.998029i | \(-0.519986\pi\) | ||||
−0.0627479 | + | 0.998029i | \(0.519986\pi\) | |||||||
\(564\) | −8.34369e17 | −1.09155 | ||||||||
\(565\) | −1.83286e18 | −2.37036 | ||||||||
\(566\) | 2.41141e17 | 0.308294 | ||||||||
\(567\) | 1.37680e17 | 0.174013 | ||||||||
\(568\) | −5.18029e17 | −0.647277 | ||||||||
\(569\) | 7.42364e17 | 0.917038 | 0.458519 | − | 0.888685i | \(-0.348380\pi\) | ||||
0.458519 | + | 0.888685i | \(0.348380\pi\) | |||||||
\(570\) | −7.43905e16 | −0.0908512 | ||||||||
\(571\) | 9.72970e17 | 1.17480 | 0.587401 | − | 0.809296i | \(-0.300151\pi\) | ||||
0.587401 | + | 0.809296i | \(0.300151\pi\) | |||||||
\(572\) | 3.71627e17 | 0.443642 | ||||||||
\(573\) | 2.05434e17 | 0.242475 | ||||||||
\(574\) | −1.32823e18 | −1.55005 | ||||||||
\(575\) | 1.77626e17 | 0.204959 | ||||||||
\(576\) | −4.58852e17 | −0.523512 | ||||||||
\(577\) | −4.88742e17 | −0.551362 | −0.275681 | − | 0.961249i | \(-0.588903\pi\) | ||||
−0.275681 | + | 0.961249i | \(0.588903\pi\) | |||||||
\(578\) | −9.01234e16 | −0.100533 | ||||||||
\(579\) | 4.56756e17 | 0.503817 | ||||||||
\(580\) | 2.90191e18 | 3.16520 | ||||||||
\(581\) | −1.62661e18 | −1.75444 | ||||||||
\(582\) | −6.68505e17 | −0.713025 | ||||||||
\(583\) | −4.88010e17 | −0.514735 | ||||||||
\(584\) | −1.55745e17 | −0.162454 | ||||||||
\(585\) | −4.76302e17 | −0.491325 | ||||||||
\(586\) | −1.30608e18 | −1.33240 | ||||||||
\(587\) | 1.09582e18 | 1.10558 | 0.552792 | − | 0.833320i | \(-0.313563\pi\) | ||||
0.552792 | + | 0.833320i | \(0.313563\pi\) | |||||||
\(588\) | 1.17057e18 | 1.16800 | ||||||||
\(589\) | −1.77035e16 | −0.0174707 | ||||||||
\(590\) | −1.82652e18 | −1.78273 | ||||||||
\(591\) | −4.81199e17 | −0.464522 | ||||||||
\(592\) | 5.37601e17 | 0.513298 | ||||||||
\(593\) | −1.82087e18 | −1.71959 | −0.859794 | − | 0.510641i | \(-0.829408\pi\) | ||||
−0.859794 | + | 0.510641i | \(0.829408\pi\) | |||||||
\(594\) | −9.60875e16 | −0.0897542 | ||||||||
\(595\) | −2.28651e18 | −2.11258 | ||||||||
\(596\) | −3.35473e17 | −0.306589 | ||||||||
\(597\) | −1.05740e18 | −0.955882 | ||||||||
\(598\) | −3.95948e17 | −0.354063 | ||||||||
\(599\) | 5.79052e17 | 0.512204 | 0.256102 | − | 0.966650i | \(-0.417562\pi\) | ||||
0.256102 | + | 0.966650i | \(0.417562\pi\) | |||||||
\(600\) | 3.79062e17 | 0.331686 | ||||||||
\(601\) | −1.68040e18 | −1.45455 | −0.727273 | − | 0.686348i | \(-0.759213\pi\) | ||||
−0.727273 | + | 0.686348i | \(0.759213\pi\) | |||||||
\(602\) | −2.32883e17 | −0.199416 | ||||||||
\(603\) | 5.74404e17 | 0.486581 | ||||||||
\(604\) | −5.55089e17 | −0.465182 | ||||||||
\(605\) | 1.52967e17 | 0.126820 | ||||||||
\(606\) | 2.04349e18 | 1.67611 | ||||||||
\(607\) | −2.18412e17 | −0.177235 | −0.0886176 | − | 0.996066i | \(-0.528245\pi\) | ||||
−0.0886176 | + | 0.996066i | \(0.528245\pi\) | |||||||
\(608\) | 1.18849e17 | 0.0954159 | ||||||||
\(609\) | 1.85472e18 | 1.47321 | ||||||||
\(610\) | 3.84501e18 | 3.02171 | ||||||||
\(611\) | 1.84486e18 | 1.43448 | ||||||||
\(612\) | −5.83431e17 | −0.448854 | ||||||||
\(613\) | −8.91819e16 | −0.0678865 | −0.0339433 | − | 0.999424i | \(-0.510807\pi\) | ||||
−0.0339433 | + | 0.999424i | \(0.510807\pi\) | |||||||
\(614\) | −2.60113e18 | −1.95915 | ||||||||
\(615\) | −6.91504e17 | −0.515355 | ||||||||
\(616\) | −3.88832e17 | −0.286740 | ||||||||
\(617\) | 1.19832e18 | 0.874419 | 0.437210 | − | 0.899360i | \(-0.355967\pi\) | ||||
0.437210 | + | 0.899360i | \(0.355967\pi\) | |||||||
\(618\) | 8.67745e17 | 0.626566 | ||||||||
\(619\) | 2.57248e18 | 1.83807 | 0.919037 | − | 0.394170i | \(-0.128968\pi\) | ||||
0.919037 | + | 0.394170i | \(0.128968\pi\) | |||||||
\(620\) | 6.58230e17 | 0.465406 | ||||||||
\(621\) | 5.95870e16 | 0.0416923 | ||||||||
\(622\) | 1.54307e18 | 1.06843 | ||||||||
\(623\) | −2.77684e18 | −1.90273 | ||||||||
\(624\) | 4.07792e17 | 0.276528 | ||||||||
\(625\) | −1.56613e18 | −1.05101 | ||||||||
\(626\) | 3.42488e18 | 2.27463 | ||||||||
\(627\) | 1.93135e16 | 0.0126947 | ||||||||
\(628\) | −2.64150e18 | −1.71835 | ||||||||
\(629\) | 1.70065e18 | 1.09493 | ||||||||
\(630\) | 1.76779e18 | 1.12646 | ||||||||
\(631\) | 1.23798e18 | 0.780767 | 0.390383 | − | 0.920652i | \(-0.372342\pi\) | ||||
0.390383 | + | 0.920652i | \(0.372342\pi\) | |||||||
\(632\) | −9.02317e17 | −0.563246 | ||||||||
\(633\) | −1.35695e18 | −0.838380 | ||||||||
\(634\) | 1.01922e18 | 0.623286 | ||||||||
\(635\) | −3.37904e18 | −2.04533 | ||||||||
\(636\) | 2.29092e18 | 1.37258 | ||||||||
\(637\) | −2.58822e18 | −1.53495 | ||||||||
\(638\) | −1.29441e18 | −0.759868 | ||||||||
\(639\) | −6.11456e17 | −0.355312 | ||||||||
\(640\) | −2.71840e18 | −1.56366 | ||||||||
\(641\) | −3.15860e17 | −0.179853 | −0.0899264 | − | 0.995948i | \(-0.528663\pi\) | ||||
−0.0899264 | + | 0.995948i | \(0.528663\pi\) | |||||||
\(642\) | 2.66111e18 | 1.49998 | ||||||||
\(643\) | 1.62866e18 | 0.908782 | 0.454391 | − | 0.890802i | \(-0.349857\pi\) | ||||
0.454391 | + | 0.890802i | \(0.349857\pi\) | |||||||
\(644\) | 8.55343e17 | 0.472479 | ||||||||
\(645\) | −1.21244e17 | −0.0663014 | ||||||||
\(646\) | 2.01479e17 | 0.109073 | ||||||||
\(647\) | −1.20409e18 | −0.645327 | −0.322664 | − | 0.946514i | \(-0.604578\pi\) | ||||
−0.322664 | + | 0.946514i | \(0.604578\pi\) | |||||||
\(648\) | 1.27161e17 | 0.0674709 | ||||||||
\(649\) | 4.74206e17 | 0.249102 | ||||||||
\(650\) | −2.97309e18 | −1.54622 | ||||||||
\(651\) | 4.20700e17 | 0.216619 | ||||||||
\(652\) | 1.64635e18 | 0.839290 | ||||||||
\(653\) | −2.58301e18 | −1.30374 | −0.651869 | − | 0.758332i | \(-0.726015\pi\) | ||||
−0.651869 | + | 0.758332i | \(0.726015\pi\) | |||||||
\(654\) | −2.71348e17 | −0.135604 | ||||||||
\(655\) | −2.59282e18 | −1.28293 | ||||||||
\(656\) | 5.92040e17 | 0.290052 | ||||||||
\(657\) | −1.83833e17 | −0.0891762 | ||||||||
\(658\) | −6.84717e18 | −3.28884 | ||||||||
\(659\) | 2.90720e18 | 1.38267 | 0.691337 | − | 0.722532i | \(-0.257022\pi\) | ||||
0.691337 | + | 0.722532i | \(0.257022\pi\) | |||||||
\(660\) | −7.18090e17 | −0.338176 | ||||||||
\(661\) | −3.29270e18 | −1.53547 | −0.767737 | − | 0.640765i | \(-0.778617\pi\) | ||||
−0.767737 | + | 0.640765i | \(0.778617\pi\) | |||||||
\(662\) | 6.88717e17 | 0.318027 | ||||||||
\(663\) | 1.29001e18 | 0.589870 | ||||||||
\(664\) | −1.50233e18 | −0.680257 | ||||||||
\(665\) | −3.55324e17 | −0.159325 | ||||||||
\(666\) | −1.31484e18 | −0.583836 | ||||||||
\(667\) | 8.02707e17 | 0.352971 | ||||||||
\(668\) | 4.76764e18 | 2.07614 | ||||||||
\(669\) | 1.92800e18 | 0.831453 | ||||||||
\(670\) | 7.37524e18 | 3.14985 | ||||||||
\(671\) | −9.98251e17 | −0.422224 | ||||||||
\(672\) | −2.82428e18 | −1.18306 | ||||||||
\(673\) | −2.98149e18 | −1.23690 | −0.618451 | − | 0.785823i | \(-0.712240\pi\) | ||||
−0.618451 | + | 0.785823i | \(0.712240\pi\) | |||||||
\(674\) | −5.06390e17 | −0.208063 | ||||||||
\(675\) | 4.47426e17 | 0.182073 | ||||||||
\(676\) | 4.02185e17 | 0.162096 | ||||||||
\(677\) | −6.19017e17 | −0.247102 | −0.123551 | − | 0.992338i | \(-0.539428\pi\) | ||||
−0.123551 | + | 0.992338i | \(0.539428\pi\) | |||||||
\(678\) | −3.83795e18 | −1.51742 | ||||||||
\(679\) | −3.19309e18 | −1.25042 | ||||||||
\(680\) | −2.11181e18 | −0.819119 | ||||||||
\(681\) | 2.24115e18 | 0.861021 | ||||||||
\(682\) | −2.93607e17 | −0.111730 | ||||||||
\(683\) | 1.07700e18 | 0.405960 | 0.202980 | − | 0.979183i | \(-0.434937\pi\) | ||||
0.202980 | + | 0.979183i | \(0.434937\pi\) | |||||||
\(684\) | −9.06653e16 | −0.0338514 | ||||||||
\(685\) | 5.89933e18 | 2.18180 | ||||||||
\(686\) | 2.99367e18 | 1.09672 | ||||||||
\(687\) | −2.17696e18 | −0.790010 | ||||||||
\(688\) | 1.03805e17 | 0.0373158 | ||||||||
\(689\) | −5.06541e18 | −1.80381 | ||||||||
\(690\) | 7.65085e17 | 0.269892 | ||||||||
\(691\) | −4.77336e17 | −0.166808 | −0.0834039 | − | 0.996516i | \(-0.526579\pi\) | ||||
−0.0834039 | + | 0.996516i | \(0.526579\pi\) | |||||||
\(692\) | 4.76209e18 | 1.64857 | ||||||||
\(693\) | −4.58958e17 | −0.157401 | ||||||||
\(694\) | 2.84390e18 | 0.966222 | ||||||||
\(695\) | 5.05467e18 | 1.70134 | ||||||||
\(696\) | 1.71301e18 | 0.571215 | ||||||||
\(697\) | 1.87287e18 | 0.618719 | ||||||||
\(698\) | −1.62528e18 | −0.531946 | ||||||||
\(699\) | −1.36058e18 | −0.441187 | ||||||||
\(700\) | 6.42259e18 | 2.06335 | ||||||||
\(701\) | 4.37219e18 | 1.39166 | 0.695828 | − | 0.718208i | \(-0.255038\pi\) | ||||
0.695828 | + | 0.718208i | \(0.255038\pi\) | |||||||
\(702\) | −9.97361e17 | −0.314529 | ||||||||
\(703\) | 2.64282e17 | 0.0825767 | ||||||||
\(704\) | 1.52959e18 | 0.473534 | ||||||||
\(705\) | −3.56479e18 | −1.09346 | ||||||||
\(706\) | 2.71451e18 | 0.825014 | ||||||||
\(707\) | 9.76068e18 | 2.93937 | ||||||||
\(708\) | −2.22612e18 | −0.664250 | ||||||||
\(709\) | −2.41723e18 | −0.714689 | −0.357344 | − | 0.933973i | \(-0.616318\pi\) | ||||
−0.357344 | + | 0.933973i | \(0.616318\pi\) | |||||||
\(710\) | −7.85098e18 | −2.30009 | ||||||||
\(711\) | −1.06505e18 | −0.309185 | ||||||||
\(712\) | −2.56467e18 | −0.737755 | ||||||||
\(713\) | 1.82075e17 | 0.0519002 | ||||||||
\(714\) | −4.78788e18 | −1.35240 | ||||||||
\(715\) | 1.58775e18 | 0.444420 | ||||||||
\(716\) | 5.58478e18 | 1.54907 | ||||||||
\(717\) | −2.27426e17 | −0.0625123 | ||||||||
\(718\) | −2.04253e18 | −0.556365 | ||||||||
\(719\) | −1.88829e18 | −0.509719 | −0.254860 | − | 0.966978i | \(-0.582029\pi\) | ||||
−0.254860 | + | 0.966978i | \(0.582029\pi\) | |||||||
\(720\) | −7.87971e17 | −0.210790 | ||||||||
\(721\) | 4.14475e18 | 1.09880 | ||||||||
\(722\) | −5.85611e18 | −1.53857 | ||||||||
\(723\) | 3.82853e18 | 0.996858 | ||||||||
\(724\) | 4.35864e18 | 1.12474 | ||||||||
\(725\) | 6.02735e18 | 1.54145 | ||||||||
\(726\) | 3.20308e17 | 0.0811857 | ||||||||
\(727\) | −5.58551e17 | −0.140310 | −0.0701551 | − | 0.997536i | \(-0.522349\pi\) | ||||
−0.0701551 | + | 0.997536i | \(0.522349\pi\) | |||||||
\(728\) | −4.03597e18 | −1.00483 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −2.36038e18 | −0.577276 | ||||||||
\(731\) | 3.28377e17 | 0.0795994 | ||||||||
\(732\) | 4.68620e18 | 1.12590 | ||||||||
\(733\) | −1.54585e18 | −0.368122 | −0.184061 | − | 0.982915i | \(-0.558924\pi\) | ||||
−0.184061 | + | 0.982915i | \(0.558924\pi\) | |||||||
\(734\) | −7.06079e18 | −1.66659 | ||||||||
\(735\) | 5.00118e18 | 1.17005 | ||||||||
\(736\) | −1.22232e18 | −0.283453 | ||||||||
\(737\) | −1.91478e18 | −0.440129 | ||||||||
\(738\) | −1.44799e18 | −0.329912 | ||||||||
\(739\) | −6.42538e18 | −1.45114 | −0.725571 | − | 0.688147i | \(-0.758424\pi\) | ||||
−0.725571 | + | 0.688147i | \(0.758424\pi\) | |||||||
\(740\) | −9.82620e18 | −2.19978 | ||||||||
\(741\) | 2.00468e17 | 0.0444864 | ||||||||
\(742\) | 1.88002e19 | 4.13559 | ||||||||
\(743\) | 4.38566e18 | 0.956330 | 0.478165 | − | 0.878270i | \(-0.341302\pi\) | ||||
0.478165 | + | 0.878270i | \(0.341302\pi\) | |||||||
\(744\) | 3.88557e17 | 0.0839905 | ||||||||
\(745\) | −1.43329e18 | −0.307127 | ||||||||
\(746\) | 8.97965e17 | 0.190747 | ||||||||
\(747\) | −1.77328e18 | −0.373416 | ||||||||
\(748\) | 1.94487e18 | 0.406004 | ||||||||
\(749\) | 1.27107e19 | 2.63050 | ||||||||
\(750\) | −3.27409e17 | −0.0671726 | ||||||||
\(751\) | 1.75685e18 | 0.357334 | 0.178667 | − | 0.983910i | \(-0.442821\pi\) | ||||
0.178667 | + | 0.983910i | \(0.442821\pi\) | |||||||
\(752\) | 3.05204e18 | 0.615424 | ||||||||
\(753\) | −1.79589e18 | −0.359015 | ||||||||
\(754\) | −1.34356e19 | −2.66283 | ||||||||
\(755\) | −2.37158e18 | −0.465997 | ||||||||
\(756\) | 2.15454e18 | 0.419723 | ||||||||
\(757\) | −1.97367e18 | −0.381199 | −0.190600 | − | 0.981668i | \(-0.561043\pi\) | ||||
−0.190600 | + | 0.981668i | \(0.561043\pi\) | |||||||
\(758\) | 9.60161e17 | 0.183863 | ||||||||
\(759\) | −1.98633e17 | −0.0377121 | ||||||||
\(760\) | −3.28175e17 | −0.0617757 | ||||||||
\(761\) | 1.91433e18 | 0.357286 | 0.178643 | − | 0.983914i | \(-0.442829\pi\) | ||||
0.178643 | + | 0.983914i | \(0.442829\pi\) | |||||||
\(762\) | −7.07560e18 | −1.30935 | ||||||||
\(763\) | −1.29608e18 | −0.237806 | ||||||||
\(764\) | 3.21481e18 | 0.584855 | ||||||||
\(765\) | −2.49268e18 | −0.449642 | ||||||||
\(766\) | 7.39011e18 | 1.32179 | ||||||||
\(767\) | 4.92212e18 | 0.872936 | ||||||||
\(768\) | −5.35982e17 | −0.0942545 | ||||||||
\(769\) | −9.69949e18 | −1.69133 | −0.845664 | − | 0.533716i | \(-0.820795\pi\) | ||||
−0.845664 | + | 0.533716i | \(0.820795\pi\) | |||||||
\(770\) | −5.89294e18 | −1.01892 | ||||||||
\(771\) | 1.76064e18 | 0.301868 | ||||||||
\(772\) | 7.14769e18 | 1.21522 | ||||||||
\(773\) | −1.83115e18 | −0.308714 | −0.154357 | − | 0.988015i | \(-0.549331\pi\) | ||||
−0.154357 | + | 0.988015i | \(0.549331\pi\) | |||||||
\(774\) | −2.53881e17 | −0.0424438 | ||||||||
\(775\) | 1.36717e18 | 0.226652 | ||||||||
\(776\) | −2.94912e18 | −0.484833 | ||||||||
\(777\) | −6.28030e18 | −1.02387 | ||||||||
\(778\) | 9.20103e18 | 1.48754 | ||||||||
\(779\) | 2.91044e17 | 0.0466621 | ||||||||
\(780\) | −7.45357e18 | −1.18508 | ||||||||
\(781\) | 2.03829e18 | 0.321392 | ||||||||
\(782\) | −2.07215e18 | −0.324025 | ||||||||
\(783\) | 2.02195e18 | 0.313559 | ||||||||
\(784\) | −4.28183e18 | −0.658529 | ||||||||
\(785\) | −1.12856e19 | −1.72137 | ||||||||
\(786\) | −5.42929e18 | −0.821290 | ||||||||
\(787\) | 4.83945e17 | 0.0726039 | 0.0363019 | − | 0.999341i | \(-0.488442\pi\) | ||||
0.0363019 | + | 0.999341i | \(0.488442\pi\) | |||||||
\(788\) | −7.53021e18 | −1.12044 | ||||||||
\(789\) | −1.22490e18 | −0.180759 | ||||||||
\(790\) | −1.36750e19 | −2.00149 | ||||||||
\(791\) | −1.83318e19 | −2.66109 | ||||||||
\(792\) | −4.23892e17 | −0.0610297 | ||||||||
\(793\) | −1.03616e19 | −1.47962 | ||||||||
\(794\) | −1.46919e19 | −2.08087 | ||||||||
\(795\) | 9.78782e18 | 1.37499 | ||||||||
\(796\) | −1.65470e19 | −2.30560 | ||||||||
\(797\) | −1.28612e19 | −1.77747 | −0.888734 | − | 0.458423i | \(-0.848415\pi\) | ||||
−0.888734 | + | 0.458423i | \(0.848415\pi\) | |||||||
\(798\) | −7.44036e17 | −0.101994 | ||||||||
\(799\) | 9.65486e18 | 1.31278 | ||||||||
\(800\) | −9.17818e18 | −1.23786 | ||||||||
\(801\) | −3.02721e18 | −0.404978 | ||||||||
\(802\) | 3.00662e18 | 0.398975 | ||||||||
\(803\) | 6.12809e17 | 0.0806629 | ||||||||
\(804\) | 8.98876e18 | 1.17364 | ||||||||
\(805\) | 3.65440e18 | 0.473307 | ||||||||
\(806\) | −3.04756e18 | −0.391539 | ||||||||
\(807\) | −4.28598e17 | −0.0546226 | ||||||||
\(808\) | 9.01492e18 | 1.13969 | ||||||||
\(809\) | 6.97044e18 | 0.874168 | 0.437084 | − | 0.899421i | \(-0.356011\pi\) | ||||
0.437084 | + | 0.899421i | \(0.356011\pi\) | |||||||
\(810\) | 1.92719e18 | 0.239757 | ||||||||
\(811\) | 1.21111e19 | 1.49468 | 0.747338 | − | 0.664444i | \(-0.231332\pi\) | ||||
0.747338 | + | 0.664444i | \(0.231332\pi\) | |||||||
\(812\) | 2.90242e19 | 3.55341 | ||||||||
\(813\) | 2.69113e17 | 0.0326849 | ||||||||
\(814\) | 4.38303e18 | 0.528100 | ||||||||
\(815\) | 7.03392e18 | 0.840762 | ||||||||
\(816\) | 2.13414e18 | 0.253068 | ||||||||
\(817\) | 5.10298e16 | 0.00600317 | ||||||||
\(818\) | 2.20725e19 | 2.57606 | ||||||||
\(819\) | −4.76386e18 | −0.551586 | ||||||||
\(820\) | −1.08212e19 | −1.24304 | ||||||||
\(821\) | 1.13387e19 | 1.29220 | 0.646102 | − | 0.763251i | \(-0.276398\pi\) | ||||
0.646102 | + | 0.763251i | \(0.276398\pi\) | |||||||
\(822\) | 1.23530e19 | 1.39671 | ||||||||
\(823\) | −4.21754e17 | −0.0473108 | −0.0236554 | − | 0.999720i | \(-0.507530\pi\) | ||||
−0.0236554 | + | 0.999720i | \(0.507530\pi\) | |||||||
\(824\) | 3.82808e18 | 0.426043 | ||||||||
\(825\) | −1.49150e18 | −0.164692 | ||||||||
\(826\) | −1.82684e19 | −2.00139 | ||||||||
\(827\) | 9.62297e18 | 1.04598 | 0.522990 | − | 0.852339i | \(-0.324817\pi\) | ||||
0.522990 | + | 0.852339i | \(0.324817\pi\) | |||||||
\(828\) | 9.32467e17 | 0.100563 | ||||||||
\(829\) | −1.01074e19 | −1.08152 | −0.540759 | − | 0.841178i | \(-0.681863\pi\) | ||||
−0.540759 | + | 0.841178i | \(0.681863\pi\) | |||||||
\(830\) | −2.27685e19 | −2.41728 | ||||||||
\(831\) | 2.51009e18 | 0.264413 | ||||||||
\(832\) | 1.58767e19 | 1.65943 | ||||||||
\(833\) | −1.35452e19 | −1.40473 | ||||||||
\(834\) | 1.05843e19 | 1.08914 | ||||||||
\(835\) | 2.03694e19 | 2.07978 | ||||||||
\(836\) | 3.02233e17 | 0.0306197 | ||||||||
\(837\) | 4.58633e17 | 0.0461052 | ||||||||
\(838\) | 1.14836e19 | 1.14549 | ||||||||
\(839\) | −9.83113e17 | −0.0973085 | −0.0486543 | − | 0.998816i | \(-0.515493\pi\) | ||||
−0.0486543 | + | 0.998816i | \(0.515493\pi\) | |||||||
\(840\) | 7.79865e18 | 0.765956 | ||||||||
\(841\) | 1.69774e19 | 1.65462 | ||||||||
\(842\) | −7.83573e18 | −0.757794 | ||||||||
\(843\) | 1.26525e18 | 0.121422 | ||||||||
\(844\) | −2.12348e19 | −2.02219 | ||||||||
\(845\) | 1.71831e18 | 0.162380 | ||||||||
\(846\) | −7.46456e18 | −0.699998 | ||||||||
\(847\) | 1.52994e18 | 0.142374 | ||||||||
\(848\) | −8.37997e18 | −0.773873 | ||||||||
\(849\) | 1.25566e18 | 0.115072 | ||||||||
\(850\) | −1.55594e19 | −1.41504 | ||||||||
\(851\) | −2.71806e18 | −0.245311 | ||||||||
\(852\) | −9.56857e18 | −0.857018 | ||||||||
\(853\) | 1.20347e19 | 1.06971 | 0.534854 | − | 0.844944i | \(-0.320367\pi\) | ||||
0.534854 | + | 0.844944i | \(0.320367\pi\) | |||||||
\(854\) | 3.84569e19 | 3.39233 | ||||||||
\(855\) | −3.87362e17 | −0.0339107 | ||||||||
\(856\) | 1.17396e19 | 1.01993 | ||||||||
\(857\) | −5.60320e18 | −0.483127 | −0.241563 | − | 0.970385i | \(-0.577660\pi\) | ||||
−0.241563 | + | 0.970385i | \(0.577660\pi\) | |||||||
\(858\) | 3.32471e18 | 0.284502 | ||||||||
\(859\) | 1.16060e17 | 0.00985656 | 0.00492828 | − | 0.999988i | \(-0.498431\pi\) | ||||
0.00492828 | + | 0.999988i | \(0.498431\pi\) | |||||||
\(860\) | −1.89733e18 | −0.159920 | ||||||||
\(861\) | −6.91626e18 | −0.578563 | ||||||||
\(862\) | 2.48174e19 | 2.06044 | ||||||||
\(863\) | −1.14438e18 | −0.0942978 | −0.0471489 | − | 0.998888i | \(-0.515014\pi\) | ||||
−0.0471489 | + | 0.998888i | \(0.515014\pi\) | |||||||
\(864\) | −3.07893e18 | −0.251803 | ||||||||
\(865\) | 2.03458e19 | 1.65146 | ||||||||
\(866\) | −7.09237e18 | −0.571380 | ||||||||
\(867\) | −4.69286e17 | −0.0375243 | ||||||||
\(868\) | 6.58346e18 | 0.522488 | ||||||||
\(869\) | 3.55035e18 | 0.279668 | ||||||||
\(870\) | 2.59615e19 | 2.02980 | ||||||||
\(871\) | −1.98749e19 | −1.54236 | ||||||||
\(872\) | −1.19706e18 | −0.0922057 | ||||||||
\(873\) | −3.48100e18 | −0.266141 | ||||||||
\(874\) | −3.22013e17 | −0.0244371 | ||||||||
\(875\) | −1.56386e18 | −0.117800 | ||||||||
\(876\) | −2.87677e18 | −0.215094 | ||||||||
\(877\) | 5.25918e17 | 0.0390320 | 0.0195160 | − | 0.999810i | \(-0.493787\pi\) | ||||
0.0195160 | + | 0.999810i | \(0.493787\pi\) | |||||||
\(878\) | −9.47337e18 | −0.697895 | ||||||||
\(879\) | −6.80092e18 | −0.497325 | ||||||||
\(880\) | 2.62671e18 | 0.190666 | ||||||||
\(881\) | −1.02154e19 | −0.736056 | −0.368028 | − | 0.929815i | \(-0.619967\pi\) | ||||
−0.368028 | + | 0.929815i | \(0.619967\pi\) | |||||||
\(882\) | 1.04723e19 | 0.749026 | ||||||||
\(883\) | −1.67904e19 | −1.19211 | −0.596055 | − | 0.802943i | \(-0.703266\pi\) | ||||
−0.596055 | + | 0.802943i | \(0.703266\pi\) | |||||||
\(884\) | 2.01872e19 | 1.42278 | ||||||||
\(885\) | −9.51095e18 | −0.665415 | ||||||||
\(886\) | 2.39223e19 | 1.66143 | ||||||||
\(887\) | −9.98165e18 | −0.688175 | −0.344087 | − | 0.938938i | \(-0.611812\pi\) | ||||
−0.344087 | + | 0.938938i | \(0.611812\pi\) | |||||||
\(888\) | −5.80046e18 | −0.396989 | ||||||||
\(889\) | −3.37964e19 | −2.29619 | ||||||||
\(890\) | −3.88688e19 | −2.62160 | ||||||||
\(891\) | −5.00341e17 | −0.0335013 | ||||||||
\(892\) | 3.01710e19 | 2.00548 | ||||||||
\(893\) | 1.50037e18 | 0.0990063 | ||||||||
\(894\) | −3.00126e18 | −0.196612 | ||||||||
\(895\) | 2.38606e19 | 1.55179 | ||||||||
\(896\) | −2.71888e19 | −1.75545 | ||||||||
\(897\) | −2.06176e18 | −0.132156 | ||||||||
\(898\) | 2.99134e16 | 0.00190358 | ||||||||
\(899\) | 6.17833e18 | 0.390331 | ||||||||
\(900\) | 7.00169e18 | 0.439164 | ||||||||
\(901\) | −2.65093e19 | −1.65077 | ||||||||
\(902\) | 4.82687e18 | 0.298417 | ||||||||
\(903\) | −1.21266e18 | −0.0744333 | ||||||||
\(904\) | −1.69312e19 | −1.03179 | ||||||||
\(905\) | 1.86220e19 | 1.12671 | ||||||||
\(906\) | −4.96602e18 | −0.298315 | ||||||||
\(907\) | −1.90931e19 | −1.13875 | −0.569377 | − | 0.822076i | \(-0.692816\pi\) | ||||
−0.569377 | + | 0.822076i | \(0.692816\pi\) | |||||||
\(908\) | 3.50713e19 | 2.07680 | ||||||||
\(909\) | 1.06408e19 | 0.625616 | ||||||||
\(910\) | −6.11670e19 | −3.57066 | ||||||||
\(911\) | 2.12403e19 | 1.23109 | 0.615547 | − | 0.788100i | \(-0.288935\pi\) | ||||
0.615547 | + | 0.788100i | \(0.288935\pi\) | |||||||
\(912\) | 3.31645e17 | 0.0190857 | ||||||||
\(913\) | 5.91122e18 | 0.337767 | ||||||||
\(914\) | 4.63953e19 | 2.63223 | ||||||||
\(915\) | 2.00215e19 | 1.12787 | ||||||||
\(916\) | −3.40669e19 | −1.90552 | ||||||||
\(917\) | −2.59328e19 | −1.44029 | ||||||||
\(918\) | −5.21958e18 | −0.287845 | ||||||||
\(919\) | 2.14539e19 | 1.17478 | 0.587388 | − | 0.809305i | \(-0.300156\pi\) | ||||
0.587388 | + | 0.809305i | \(0.300156\pi\) | |||||||
\(920\) | 3.37519e18 | 0.183517 | ||||||||
\(921\) | −1.35444e19 | −0.731263 | ||||||||
\(922\) | −3.72060e19 | −1.99463 | ||||||||
\(923\) | 2.11569e19 | 1.12627 | ||||||||
\(924\) | −7.18216e18 | −0.379654 | ||||||||
\(925\) | −2.04093e19 | −1.07129 | ||||||||
\(926\) | −5.98496e17 | −0.0311953 | ||||||||
\(927\) | 4.51847e18 | 0.233869 | ||||||||
\(928\) | −4.14769e19 | −2.13179 | ||||||||
\(929\) | 6.27434e17 | 0.0320233 | 0.0160116 | − | 0.999872i | \(-0.494903\pi\) | ||||
0.0160116 | + | 0.999872i | \(0.494903\pi\) | |||||||
\(930\) | 5.88876e18 | 0.298459 | ||||||||
\(931\) | −2.10492e18 | −0.105941 | ||||||||
\(932\) | −2.12915e19 | −1.06415 | ||||||||
\(933\) | 8.03496e18 | 0.398798 | ||||||||
\(934\) | −3.58957e18 | −0.176925 | ||||||||
\(935\) | 8.30935e18 | 0.406716 | ||||||||
\(936\) | −4.39988e18 | −0.213869 | ||||||||
\(937\) | 1.14580e19 | 0.553098 | 0.276549 | − | 0.961000i | \(-0.410809\pi\) | ||||
0.276549 | + | 0.961000i | \(0.410809\pi\) | |||||||
\(938\) | 7.37654e19 | 3.53618 | ||||||||
\(939\) | 1.78338e19 | 0.849020 | ||||||||
\(940\) | −5.57848e19 | −2.63745 | ||||||||
\(941\) | 8.37033e18 | 0.393016 | 0.196508 | − | 0.980502i | \(-0.437040\pi\) | ||||
0.196508 | + | 0.980502i | \(0.437040\pi\) | |||||||
\(942\) | −2.36318e19 | −1.10196 | ||||||||
\(943\) | −2.99330e18 | −0.138620 | ||||||||
\(944\) | 8.14293e18 | 0.374509 | ||||||||
\(945\) | 9.20514e18 | 0.420459 | ||||||||
\(946\) | 8.46315e17 | 0.0383919 | ||||||||
\(947\) | −1.66309e19 | −0.749275 | −0.374637 | − | 0.927171i | \(-0.622233\pi\) | ||||
−0.374637 | + | 0.927171i | \(0.622233\pi\) | |||||||
\(948\) | −1.66668e19 | −0.745758 | ||||||||
\(949\) | 6.36078e18 | 0.282670 | ||||||||
\(950\) | −2.41793e18 | −0.106718 | ||||||||
\(951\) | 5.30722e18 | 0.232645 | ||||||||
\(952\) | −2.11218e19 | −0.919584 | ||||||||
\(953\) | −2.54297e19 | −1.09961 | −0.549803 | − | 0.835294i | \(-0.685297\pi\) | ||||
−0.549803 | + | 0.835294i | \(0.685297\pi\) | |||||||
\(954\) | 2.04954e19 | 0.880221 | ||||||||
\(955\) | 1.37351e19 | 0.585880 | ||||||||
\(956\) | −3.55895e18 | −0.150781 | ||||||||
\(957\) | −6.74018e18 | −0.283625 | ||||||||
\(958\) | 5.17590e19 | 2.16327 | ||||||||
\(959\) | 5.90037e19 | 2.44939 | ||||||||
\(960\) | −3.06783e19 | −1.26493 | ||||||||
\(961\) | −2.30161e19 | −0.942606 | ||||||||
\(962\) | 4.54947e19 | 1.85064 | ||||||||
\(963\) | 1.38568e19 | 0.559876 | ||||||||
\(964\) | 5.99121e19 | 2.40444 | ||||||||
\(965\) | 3.05381e19 | 1.21735 | ||||||||
\(966\) | 7.65220e18 | 0.302995 | ||||||||
\(967\) | 5.78322e18 | 0.227456 | 0.113728 | − | 0.993512i | \(-0.463721\pi\) | ||||
0.113728 | + | 0.993512i | \(0.463721\pi\) | |||||||
\(968\) | 1.41305e18 | 0.0552035 | ||||||||
\(969\) | 1.04913e18 | 0.0407122 | ||||||||
\(970\) | −4.46954e19 | −1.72284 | ||||||||
\(971\) | −4.12182e19 | −1.57821 | −0.789104 | − | 0.614259i | \(-0.789455\pi\) | ||||
−0.789104 | + | 0.614259i | \(0.789455\pi\) | |||||||
\(972\) | 2.34881e18 | 0.0893339 | ||||||||
\(973\) | 5.05556e19 | 1.91001 | ||||||||
\(974\) | −7.24912e19 | −2.72052 | ||||||||
\(975\) | −1.54813e19 | −0.577135 | ||||||||
\(976\) | −1.71417e19 | −0.634789 | ||||||||
\(977\) | −4.33217e19 | −1.59364 | −0.796822 | − | 0.604215i | \(-0.793487\pi\) | ||||
−0.796822 | + | 0.604215i | \(0.793487\pi\) | |||||||
\(978\) | 1.47288e19 | 0.538226 | ||||||||
\(979\) | 1.00912e19 | 0.366317 | ||||||||
\(980\) | 7.82626e19 | 2.82218 | ||||||||
\(981\) | −1.41295e18 | −0.0506148 | ||||||||
\(982\) | 2.40878e19 | 0.857180 | ||||||||
\(983\) | −2.52492e19 | −0.892584 | −0.446292 | − | 0.894887i | \(-0.647256\pi\) | ||||
−0.446292 | + | 0.894887i | \(0.647256\pi\) | |||||||
\(984\) | −6.38783e18 | −0.224329 | ||||||||
\(985\) | −3.21724e19 | −1.12240 | ||||||||
\(986\) | −7.03139e19 | −2.43692 | ||||||||
\(987\) | −3.56542e19 | −1.22758 | ||||||||
\(988\) | 3.13709e18 | 0.107302 | ||||||||
\(989\) | −5.24827e17 | −0.0178337 | ||||||||
\(990\) | −6.42428e18 | −0.216868 | ||||||||
\(991\) | 1.90400e19 | 0.638539 | 0.319269 | − | 0.947664i | \(-0.396562\pi\) | ||||
0.319269 | + | 0.947664i | \(0.396562\pi\) | |||||||
\(992\) | −9.40807e18 | −0.313455 | ||||||||
\(993\) | 3.58625e18 | 0.118705 | ||||||||
\(994\) | −7.85236e19 | −2.58219 | ||||||||
\(995\) | −7.06961e19 | −2.30965 | ||||||||
\(996\) | −2.77497e19 | −0.900685 | ||||||||
\(997\) | 3.63643e19 | 1.17262 | 0.586309 | − | 0.810087i | \(-0.300580\pi\) | ||||
0.586309 | + | 0.810087i | \(0.300580\pi\) | |||||||
\(998\) | 1.84717e19 | 0.591779 | ||||||||
\(999\) | −6.84657e18 | −0.217920 |
(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 | 33.14.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 99.14.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.14.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
99.14.a.a.1.1 | 1 | 3.2 | odd | 2 |