Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(211.244930035\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −172.035 | −1.90074 | −0.950369 | − | 0.311124i | \(-0.899295\pi\) | ||||
−0.950369 | + | 0.311124i | \(0.899295\pi\) | |||||||
\(3\) | −63.8588 | −0.0505746 | −0.0252873 | − | 0.999680i | \(-0.508050\pi\) | ||||
−0.0252873 | + | 0.999680i | \(0.508050\pi\) | |||||||
\(4\) | 21404.1 | 2.61281 | ||||||||
\(5\) | −26311.4 | −0.753077 | −0.376539 | − | 0.926401i | \(-0.622886\pi\) | ||||
−0.376539 | + | 0.926401i | \(0.622886\pi\) | |||||||
\(6\) | 10986.0 | 0.0961291 | ||||||||
\(7\) | −168215. | −0.540414 | −0.270207 | − | 0.962802i | \(-0.587092\pi\) | ||||
−0.270207 | + | 0.962802i | \(0.587092\pi\) | |||||||
\(8\) | −2.27295e6 | −3.06553 | ||||||||
\(9\) | −1.59025e6 | −0.997442 | ||||||||
\(10\) | 4.52650e6 | 1.43140 | ||||||||
\(11\) | 7.08307e6 | 1.20551 | 0.602753 | − | 0.797928i | \(-0.294070\pi\) | ||||
0.602753 | + | 0.797928i | \(0.294070\pi\) | |||||||
\(12\) | −1.36684e6 | −0.132142 | ||||||||
\(13\) | −1.35177e7 | −0.776732 | −0.388366 | − | 0.921505i | \(-0.626960\pi\) | ||||
−0.388366 | + | 0.921505i | \(0.626960\pi\) | |||||||
\(14\) | 2.89389e7 | 1.02719 | ||||||||
\(15\) | 1.68022e6 | 0.0380866 | ||||||||
\(16\) | 2.15685e8 | 3.21396 | ||||||||
\(17\) | 1.48916e8 | 1.49632 | 0.748160 | − | 0.663518i | \(-0.230938\pi\) | ||||
0.748160 | + | 0.663518i | \(0.230938\pi\) | |||||||
\(18\) | 2.73578e8 | 1.89588 | ||||||||
\(19\) | 3.64027e8 | 1.77515 | 0.887574 | − | 0.460664i | \(-0.152389\pi\) | ||||
0.887574 | + | 0.460664i | \(0.152389\pi\) | |||||||
\(20\) | −5.63173e8 | −1.96765 | ||||||||
\(21\) | 1.07420e7 | 0.0273312 | ||||||||
\(22\) | −1.21854e9 | −2.29135 | ||||||||
\(23\) | 6.00850e8 | 0.846320 | 0.423160 | − | 0.906055i | \(-0.360921\pi\) | ||||
0.423160 | + | 0.906055i | \(0.360921\pi\) | |||||||
\(24\) | 1.45148e8 | 0.155038 | ||||||||
\(25\) | −5.28411e8 | −0.432874 | ||||||||
\(26\) | 2.32552e9 | 1.47636 | ||||||||
\(27\) | 2.03363e8 | 0.101020 | ||||||||
\(28\) | −3.60049e9 | −1.41200 | ||||||||
\(29\) | 3.66758e9 | 1.14496 | 0.572482 | − | 0.819917i | \(-0.305981\pi\) | ||||
0.572482 | + | 0.819917i | \(0.305981\pi\) | |||||||
\(30\) | −2.89056e8 | −0.0723926 | ||||||||
\(31\) | −3.03901e9 | −0.615009 | −0.307504 | − | 0.951547i | \(-0.599494\pi\) | ||||
−0.307504 | + | 0.951547i | \(0.599494\pi\) | |||||||
\(32\) | −1.84854e10 | −3.04337 | ||||||||
\(33\) | −4.52316e8 | −0.0609680 | ||||||||
\(34\) | −2.56189e10 | −2.84411 | ||||||||
\(35\) | 4.42597e9 | 0.406974 | ||||||||
\(36\) | −3.40378e10 | −2.60613 | ||||||||
\(37\) | 1.64898e10 | 1.05659 | 0.528293 | − | 0.849062i | \(-0.322832\pi\) | ||||
0.528293 | + | 0.849062i | \(0.322832\pi\) | |||||||
\(38\) | −6.26254e10 | −3.37409 | ||||||||
\(39\) | 8.63224e8 | 0.0392829 | ||||||||
\(40\) | 5.98046e10 | 2.30858 | ||||||||
\(41\) | 2.85360e9 | 0.0938207 | 0.0469104 | − | 0.998899i | \(-0.485062\pi\) | ||||
0.0469104 | + | 0.998899i | \(0.485062\pi\) | |||||||
\(42\) | −1.84800e9 | −0.0519495 | ||||||||
\(43\) | 4.65537e10 | 1.12308 | 0.561539 | − | 0.827451i | \(-0.310210\pi\) | ||||
0.561539 | + | 0.827451i | \(0.310210\pi\) | |||||||
\(44\) | 1.51607e11 | 3.14976 | ||||||||
\(45\) | 4.18416e10 | 0.751151 | ||||||||
\(46\) | −1.03367e11 | −1.60863 | ||||||||
\(47\) | −5.12739e10 | −0.693841 | −0.346920 | − | 0.937895i | \(-0.612773\pi\) | ||||
−0.346920 | + | 0.937895i | \(0.612773\pi\) | |||||||
\(48\) | −1.37734e10 | −0.162545 | ||||||||
\(49\) | −6.85928e10 | −0.707952 | ||||||||
\(50\) | 9.09053e10 | 0.822781 | ||||||||
\(51\) | −9.50961e9 | −0.0756757 | ||||||||
\(52\) | −2.89335e11 | −2.02945 | ||||||||
\(53\) | 2.79882e10 | 0.173453 | 0.0867264 | − | 0.996232i | \(-0.472359\pi\) | ||||
0.0867264 | + | 0.996232i | \(0.472359\pi\) | |||||||
\(54\) | −3.49855e10 | −0.192012 | ||||||||
\(55\) | −1.86366e11 | −0.907839 | ||||||||
\(56\) | 3.82344e11 | 1.65666 | ||||||||
\(57\) | −2.32463e10 | −0.0897774 | ||||||||
\(58\) | −6.30952e11 | −2.17628 | ||||||||
\(59\) | 3.35418e11 | 1.03526 | 0.517628 | − | 0.855606i | \(-0.326815\pi\) | ||||
0.517628 | + | 0.855606i | \(0.326815\pi\) | |||||||
\(60\) | 3.59636e10 | 0.0995129 | ||||||||
\(61\) | 5.64009e10 | 0.140166 | 0.0700829 | − | 0.997541i | \(-0.477674\pi\) | ||||
0.0700829 | + | 0.997541i | \(0.477674\pi\) | |||||||
\(62\) | 5.22817e11 | 1.16897 | ||||||||
\(63\) | 2.67503e11 | 0.539032 | ||||||||
\(64\) | 1.41325e12 | 2.57069 | ||||||||
\(65\) | 3.55670e11 | 0.584939 | ||||||||
\(66\) | 7.78143e10 | 0.115884 | ||||||||
\(67\) | 7.15230e10 | 0.0965961 | 0.0482981 | − | 0.998833i | \(-0.484620\pi\) | ||||
0.0482981 | + | 0.998833i | \(0.484620\pi\) | |||||||
\(68\) | 3.18742e12 | 3.90960 | ||||||||
\(69\) | −3.83695e10 | −0.0428023 | ||||||||
\(70\) | −7.61424e11 | −0.773551 | ||||||||
\(71\) | −8.56849e11 | −0.793825 | −0.396913 | − | 0.917856i | \(-0.629918\pi\) | ||||
−0.396913 | + | 0.917856i | \(0.629918\pi\) | |||||||
\(72\) | 3.61455e12 | 3.05769 | ||||||||
\(73\) | 2.39608e12 | 1.85312 | 0.926558 | − | 0.376151i | \(-0.122753\pi\) | ||||
0.926558 | + | 0.376151i | \(0.122753\pi\) | |||||||
\(74\) | −2.83683e12 | −2.00830 | ||||||||
\(75\) | 3.37437e10 | 0.0218924 | ||||||||
\(76\) | 7.79167e12 | 4.63812 | ||||||||
\(77\) | −1.19148e12 | −0.651473 | ||||||||
\(78\) | −1.48505e11 | −0.0746665 | ||||||||
\(79\) | 1.85526e12 | 0.858673 | 0.429337 | − | 0.903144i | \(-0.358747\pi\) | ||||
0.429337 | + | 0.903144i | \(0.358747\pi\) | |||||||
\(80\) | −5.67499e12 | −2.42036 | ||||||||
\(81\) | 2.52238e12 | 0.992333 | ||||||||
\(82\) | −4.90921e11 | −0.178329 | ||||||||
\(83\) | 3.36851e12 | 1.13092 | 0.565458 | − | 0.824777i | \(-0.308699\pi\) | ||||
0.565458 | + | 0.824777i | \(0.308699\pi\) | |||||||
\(84\) | 2.29923e11 | 0.0714113 | ||||||||
\(85\) | −3.91820e12 | −1.12684 | ||||||||
\(86\) | −8.00888e12 | −2.13468 | ||||||||
\(87\) | −2.34207e11 | −0.0579061 | ||||||||
\(88\) | −1.60995e13 | −3.69551 | ||||||||
\(89\) | −8.44395e12 | −1.80099 | −0.900493 | − | 0.434870i | \(-0.856794\pi\) | ||||
−0.900493 | + | 0.434870i | \(0.856794\pi\) | |||||||
\(90\) | −7.19824e12 | −1.42774 | ||||||||
\(91\) | 2.27388e12 | 0.419757 | ||||||||
\(92\) | 1.28607e13 | 2.21127 | ||||||||
\(93\) | 1.94067e11 | 0.0311038 | ||||||||
\(94\) | 8.82091e12 | 1.31881 | ||||||||
\(95\) | −9.57807e12 | −1.33682 | ||||||||
\(96\) | 1.18046e12 | 0.153917 | ||||||||
\(97\) | −7.81335e12 | −0.952404 | −0.476202 | − | 0.879336i | \(-0.657987\pi\) | ||||
−0.476202 | + | 0.879336i | \(0.657987\pi\) | |||||||
\(98\) | 1.18004e13 | 1.34563 | ||||||||
\(99\) | −1.12638e13 | −1.20242 | ||||||||
\(100\) | −1.13102e13 | −1.13102 | ||||||||
\(101\) | −1.52078e13 | −1.42553 | −0.712765 | − | 0.701403i | \(-0.752557\pi\) | ||||
−0.712765 | + | 0.701403i | \(0.752557\pi\) | |||||||
\(102\) | 1.63599e12 | 0.143840 | ||||||||
\(103\) | 1.30991e13 | 1.08093 | 0.540467 | − | 0.841365i | \(-0.318248\pi\) | ||||
0.540467 | + | 0.841365i | \(0.318248\pi\) | |||||||
\(104\) | 3.07251e13 | 2.38109 | ||||||||
\(105\) | −2.82637e11 | −0.0205825 | ||||||||
\(106\) | −4.81495e12 | −0.329688 | ||||||||
\(107\) | −1.28498e13 | −0.827753 | −0.413876 | − | 0.910333i | \(-0.635825\pi\) | ||||
−0.413876 | + | 0.910333i | \(0.635825\pi\) | |||||||
\(108\) | 4.35280e12 | 0.263945 | ||||||||
\(109\) | −1.26119e13 | −0.720290 | −0.360145 | − | 0.932896i | \(-0.617273\pi\) | ||||
−0.360145 | + | 0.932896i | \(0.617273\pi\) | |||||||
\(110\) | 3.20615e13 | 1.72557 | ||||||||
\(111\) | −1.05302e12 | −0.0534364 | ||||||||
\(112\) | −3.62814e13 | −1.73687 | ||||||||
\(113\) | −1.11804e13 | −0.505182 | −0.252591 | − | 0.967573i | \(-0.581283\pi\) | ||||
−0.252591 | + | 0.967573i | \(0.581283\pi\) | |||||||
\(114\) | 3.99918e12 | 0.170643 | ||||||||
\(115\) | −1.58092e13 | −0.637345 | ||||||||
\(116\) | 7.85012e13 | 2.99157 | ||||||||
\(117\) | 2.14965e13 | 0.774745 | ||||||||
\(118\) | −5.77037e13 | −1.96775 | ||||||||
\(119\) | −2.50499e13 | −0.808633 | ||||||||
\(120\) | −3.81905e12 | −0.116755 | ||||||||
\(121\) | 1.56472e13 | 0.453244 | ||||||||
\(122\) | −9.70294e12 | −0.266419 | ||||||||
\(123\) | −1.82228e11 | −0.00474494 | ||||||||
\(124\) | −6.50474e13 | −1.60690 | ||||||||
\(125\) | 4.60217e13 | 1.07907 | ||||||||
\(126\) | −4.60199e13 | −1.02456 | ||||||||
\(127\) | 3.75142e13 | 0.793362 | 0.396681 | − | 0.917957i | \(-0.370162\pi\) | ||||
0.396681 | + | 0.917957i | \(0.370162\pi\) | |||||||
\(128\) | −9.16967e13 | −1.84285 | ||||||||
\(129\) | −2.97286e12 | −0.0567992 | ||||||||
\(130\) | −6.11878e13 | −1.11182 | ||||||||
\(131\) | −6.86287e13 | −1.18643 | −0.593215 | − | 0.805044i | \(-0.702142\pi\) | ||||
−0.593215 | + | 0.805044i | \(0.702142\pi\) | |||||||
\(132\) | −9.68144e12 | −0.159298 | ||||||||
\(133\) | −6.12347e13 | −0.959316 | ||||||||
\(134\) | −1.23045e13 | −0.183604 | ||||||||
\(135\) | −5.35076e12 | −0.0760757 | ||||||||
\(136\) | −3.38480e14 | −4.58701 | ||||||||
\(137\) | 5.99220e13 | 0.774288 | 0.387144 | − | 0.922019i | \(-0.373462\pi\) | ||||
0.387144 | + | 0.922019i | \(0.373462\pi\) | |||||||
\(138\) | 6.60091e12 | 0.0813560 | ||||||||
\(139\) | 9.78581e13 | 1.15080 | 0.575401 | − | 0.817871i | \(-0.304846\pi\) | ||||
0.575401 | + | 0.817871i | \(0.304846\pi\) | |||||||
\(140\) | 9.47341e13 | 1.06334 | ||||||||
\(141\) | 3.27428e12 | 0.0350907 | ||||||||
\(142\) | 1.47408e14 | 1.50885 | ||||||||
\(143\) | −9.57469e13 | −0.936355 | ||||||||
\(144\) | −3.42992e14 | −3.20574 | ||||||||
\(145\) | −9.64992e13 | −0.862247 | ||||||||
\(146\) | −4.12210e14 | −3.52229 | ||||||||
\(147\) | 4.38025e12 | 0.0358044 | ||||||||
\(148\) | 3.52951e14 | 2.76066 | ||||||||
\(149\) | −7.83903e13 | −0.586883 | −0.293442 | − | 0.955977i | \(-0.594801\pi\) | ||||
−0.293442 | + | 0.955977i | \(0.594801\pi\) | |||||||
\(150\) | −5.80510e12 | −0.0416118 | ||||||||
\(151\) | −3.08346e13 | −0.211684 | −0.105842 | − | 0.994383i | \(-0.533754\pi\) | ||||
−0.105842 | + | 0.994383i | \(0.533754\pi\) | |||||||
\(152\) | −8.27415e14 | −5.44177 | ||||||||
\(153\) | −2.36814e14 | −1.49249 | ||||||||
\(154\) | 2.04976e14 | 1.23828 | ||||||||
\(155\) | 7.99608e13 | 0.463149 | ||||||||
\(156\) | 1.84765e13 | 0.102639 | ||||||||
\(157\) | 2.70280e14 | 1.44034 | 0.720172 | − | 0.693795i | \(-0.244063\pi\) | ||||
0.720172 | + | 0.693795i | \(0.244063\pi\) | |||||||
\(158\) | −3.19170e14 | −1.63211 | ||||||||
\(159\) | −1.78729e12 | −0.00877230 | ||||||||
\(160\) | 4.86379e14 | 2.29189 | ||||||||
\(161\) | −1.01072e14 | −0.457364 | ||||||||
\(162\) | −4.33938e14 | −1.88617 | ||||||||
\(163\) | −1.75321e14 | −0.732173 | −0.366086 | − | 0.930581i | \(-0.619303\pi\) | ||||
−0.366086 | + | 0.930581i | \(0.619303\pi\) | |||||||
\(164\) | 6.10789e13 | 0.245136 | ||||||||
\(165\) | 1.19011e13 | 0.0459136 | ||||||||
\(166\) | −5.79503e14 | −2.14958 | ||||||||
\(167\) | 3.60391e14 | 1.28563 | 0.642816 | − | 0.766020i | \(-0.277766\pi\) | ||||
0.642816 | + | 0.766020i | \(0.277766\pi\) | |||||||
\(168\) | −2.44160e13 | −0.0837847 | ||||||||
\(169\) | −1.20147e14 | −0.396688 | ||||||||
\(170\) | 6.74069e14 | 2.14184 | ||||||||
\(171\) | −5.78892e14 | −1.77061 | ||||||||
\(172\) | 9.96442e14 | 2.93439 | ||||||||
\(173\) | −3.27747e14 | −0.929479 | −0.464739 | − | 0.885447i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885447i | \(0.653852\pi\) | |||||||
\(174\) | 4.02918e13 | 0.110064 | ||||||||
\(175\) | 8.88866e13 | 0.233932 | ||||||||
\(176\) | 1.52771e15 | 3.87445 | ||||||||
\(177\) | −2.14194e13 | −0.0523577 | ||||||||
\(178\) | 1.45266e15 | 3.42320 | ||||||||
\(179\) | 4.61583e13 | 0.104883 | 0.0524415 | − | 0.998624i | \(-0.483300\pi\) | ||||
0.0524415 | + | 0.998624i | \(0.483300\pi\) | |||||||
\(180\) | 8.95584e14 | 1.96261 | ||||||||
\(181\) | 1.40907e14 | 0.297866 | 0.148933 | − | 0.988847i | \(-0.452416\pi\) | ||||
0.148933 | + | 0.988847i | \(0.452416\pi\) | |||||||
\(182\) | −3.91187e14 | −0.797849 | ||||||||
\(183\) | −3.60169e12 | −0.00708882 | ||||||||
\(184\) | −1.36570e15 | −2.59442 | ||||||||
\(185\) | −4.33871e14 | −0.795692 | ||||||||
\(186\) | −3.33864e13 | −0.0591202 | ||||||||
\(187\) | 1.05479e15 | 1.80382 | ||||||||
\(188\) | −1.09747e15 | −1.81287 | ||||||||
\(189\) | −3.42086e13 | −0.0545926 | ||||||||
\(190\) | 1.64777e15 | 2.54095 | ||||||||
\(191\) | −8.93595e14 | −1.33175 | −0.665877 | − | 0.746062i | \(-0.731942\pi\) | ||||
−0.665877 | + | 0.746062i | \(0.731942\pi\) | |||||||
\(192\) | −9.02486e13 | −0.130012 | ||||||||
\(193\) | 7.79283e14 | 1.08536 | 0.542679 | − | 0.839940i | \(-0.317410\pi\) | ||||
0.542679 | + | 0.839940i | \(0.317410\pi\) | |||||||
\(194\) | 1.34417e15 | 1.81027 | ||||||||
\(195\) | −2.27127e13 | −0.0295831 | ||||||||
\(196\) | −1.46817e15 | −1.84974 | ||||||||
\(197\) | 5.84517e13 | 0.0712470 | ||||||||
\(198\) | 1.93777e15 | 2.28549 | ||||||||
\(199\) | −9.47463e14 | −1.08148 | −0.540738 | − | 0.841191i | \(-0.681855\pi\) | ||||
−0.540738 | + | 0.841191i | \(0.681855\pi\) | |||||||
\(200\) | 1.20105e15 | 1.32699 | ||||||||
\(201\) | −4.56737e12 | −0.00488531 | ||||||||
\(202\) | 2.61627e15 | 2.70956 | ||||||||
\(203\) | −6.16940e14 | −0.618755 | ||||||||
\(204\) | −2.03545e14 | −0.197726 | ||||||||
\(205\) | −7.50825e13 | −0.0706543 | ||||||||
\(206\) | −2.25351e15 | −2.05457 | ||||||||
\(207\) | −9.55498e14 | −0.844156 | ||||||||
\(208\) | −2.91557e15 | −2.49638 | ||||||||
\(209\) | 2.57843e15 | 2.13995 | ||||||||
\(210\) | 4.86236e13 | 0.0391220 | ||||||||
\(211\) | 1.38881e15 | 1.08345 | 0.541724 | − | 0.840557i | \(-0.317772\pi\) | ||||
0.541724 | + | 0.840557i | \(0.317772\pi\) | |||||||
\(212\) | 5.99062e14 | 0.453199 | ||||||||
\(213\) | 5.47173e13 | 0.0401474 | ||||||||
\(214\) | 2.21061e15 | 1.57334 | ||||||||
\(215\) | −1.22490e15 | −0.845764 | ||||||||
\(216\) | −4.62233e14 | −0.309679 | ||||||||
\(217\) | 5.11207e14 | 0.332360 | ||||||||
\(218\) | 2.16969e15 | 1.36908 | ||||||||
\(219\) | −1.53011e14 | −0.0937206 | ||||||||
\(220\) | −3.98900e15 | −2.37201 | ||||||||
\(221\) | −2.01301e15 | −1.16224 | ||||||||
\(222\) | 1.81157e14 | 0.101569 | ||||||||
\(223\) | −1.18057e15 | −0.642851 | −0.321426 | − | 0.946935i | \(-0.604162\pi\) | ||||
−0.321426 | + | 0.946935i | \(0.604162\pi\) | |||||||
\(224\) | 3.10952e15 | 1.64468 | ||||||||
\(225\) | 8.40303e14 | 0.431767 | ||||||||
\(226\) | 1.92342e15 | 0.960219 | ||||||||
\(227\) | −8.98384e14 | −0.435807 | −0.217903 | − | 0.975970i | \(-0.569922\pi\) | ||||
−0.217903 | + | 0.975970i | \(0.569922\pi\) | |||||||
\(228\) | −4.97567e14 | −0.234571 | ||||||||
\(229\) | 2.00568e13 | 0.00919032 | 0.00459516 | − | 0.999989i | \(-0.498537\pi\) | ||||
0.00459516 | + | 0.999989i | \(0.498537\pi\) | |||||||
\(230\) | 2.71974e15 | 1.21143 | ||||||||
\(231\) | 7.60863e13 | 0.0329480 | ||||||||
\(232\) | −8.33622e15 | −3.50992 | ||||||||
\(233\) | −2.49792e15 | −1.02274 | −0.511369 | − | 0.859361i | \(-0.670862\pi\) | ||||
−0.511369 | + | 0.859361i | \(0.670862\pi\) | |||||||
\(234\) | −3.69815e15 | −1.47259 | ||||||||
\(235\) | 1.34909e15 | 0.522516 | ||||||||
\(236\) | 7.17932e15 | 2.70493 | ||||||||
\(237\) | −1.18474e14 | −0.0434271 | ||||||||
\(238\) | 4.30947e15 | 1.53700 | ||||||||
\(239\) | −7.52534e14 | −0.261180 | −0.130590 | − | 0.991436i | \(-0.541687\pi\) | ||||
−0.130590 | + | 0.991436i | \(0.541687\pi\) | |||||||
\(240\) | 3.62398e14 | 0.122409 | ||||||||
\(241\) | 5.34556e15 | 1.75745 | 0.878723 | − | 0.477331i | \(-0.158396\pi\) | ||||
0.878723 | + | 0.477331i | \(0.158396\pi\) | |||||||
\(242\) | −2.69187e15 | −0.861499 | ||||||||
\(243\) | −4.85301e14 | −0.151207 | ||||||||
\(244\) | 1.20721e15 | 0.366226 | ||||||||
\(245\) | 1.80478e15 | 0.533143 | ||||||||
\(246\) | 3.13496e13 | 0.00901890 | ||||||||
\(247\) | −4.92080e15 | −1.37881 | ||||||||
\(248\) | 6.90753e15 | 1.88533 | ||||||||
\(249\) | −2.15109e14 | −0.0571956 | ||||||||
\(250\) | −7.91736e15 | −2.05102 | ||||||||
\(251\) | 1.16407e15 | 0.293832 | 0.146916 | − | 0.989149i | \(-0.453065\pi\) | ||||
0.146916 | + | 0.989149i | \(0.453065\pi\) | |||||||
\(252\) | 5.72566e15 | 1.40839 | ||||||||
\(253\) | 4.25586e15 | 1.02024 | ||||||||
\(254\) | −6.45376e15 | −1.50797 | ||||||||
\(255\) | 2.50212e14 | 0.0569897 | ||||||||
\(256\) | 4.19770e15 | 0.932076 | ||||||||
\(257\) | −9.44364e14 | −0.204444 | −0.102222 | − | 0.994762i | \(-0.532595\pi\) | ||||
−0.102222 | + | 0.994762i | \(0.532595\pi\) | |||||||
\(258\) | 5.11437e14 | 0.107960 | ||||||||
\(259\) | −2.77383e15 | −0.570995 | ||||||||
\(260\) | 7.61281e15 | 1.52833 | ||||||||
\(261\) | −5.83234e15 | −1.14204 | ||||||||
\(262\) | 1.18066e16 | 2.25509 | ||||||||
\(263\) | 4.27412e15 | 0.796405 | 0.398202 | − | 0.917298i | \(-0.369634\pi\) | ||||
0.398202 | + | 0.917298i | \(0.369634\pi\) | |||||||
\(264\) | 1.02809e15 | 0.186899 | ||||||||
\(265\) | −7.36409e14 | −0.130623 | ||||||||
\(266\) | 1.05345e16 | 1.82341 | ||||||||
\(267\) | 5.39220e14 | 0.0910841 | ||||||||
\(268\) | 1.53089e15 | 0.252387 | ||||||||
\(269\) | −6.63891e15 | −1.06833 | −0.534167 | − | 0.845379i | \(-0.679375\pi\) | ||||
−0.534167 | + | 0.845379i | \(0.679375\pi\) | |||||||
\(270\) | 9.20520e14 | 0.144600 | ||||||||
\(271\) | 7.41915e14 | 0.113777 | 0.0568884 | − | 0.998381i | \(-0.481882\pi\) | ||||
0.0568884 | + | 0.998381i | \(0.481882\pi\) | |||||||
\(272\) | 3.21191e16 | 4.80911 | ||||||||
\(273\) | −1.45207e14 | −0.0212290 | ||||||||
\(274\) | −1.03087e16 | −1.47172 | ||||||||
\(275\) | −3.74277e15 | −0.521833 | ||||||||
\(276\) | −8.21266e14 | −0.111834 | ||||||||
\(277\) | 4.98961e15 | 0.663664 | 0.331832 | − | 0.943339i | \(-0.392333\pi\) | ||||
0.331832 | + | 0.943339i | \(0.392333\pi\) | |||||||
\(278\) | −1.68350e16 | −2.18737 | ||||||||
\(279\) | 4.83277e15 | 0.613436 | ||||||||
\(280\) | −1.00600e16 | −1.24759 | ||||||||
\(281\) | 9.37190e15 | 1.13563 | 0.567815 | − | 0.823156i | \(-0.307789\pi\) | ||||
0.567815 | + | 0.823156i | \(0.307789\pi\) | |||||||
\(282\) | −5.63292e14 | −0.0666983 | ||||||||
\(283\) | 5.30685e15 | 0.614080 | 0.307040 | − | 0.951697i | \(-0.400661\pi\) | ||||
0.307040 | + | 0.951697i | \(0.400661\pi\) | |||||||
\(284\) | −1.83401e16 | −2.07411 | ||||||||
\(285\) | 6.11643e14 | 0.0676093 | ||||||||
\(286\) | 1.64718e16 | 1.77977 | ||||||||
\(287\) | −4.80019e14 | −0.0507021 | ||||||||
\(288\) | 2.93964e16 | 3.03559 | ||||||||
\(289\) | 1.22715e16 | 1.23897 | ||||||||
\(290\) | 1.66013e16 | 1.63891 | ||||||||
\(291\) | 4.98951e14 | 0.0481674 | ||||||||
\(292\) | 5.12860e16 | 4.84184 | ||||||||
\(293\) | 3.77760e15 | 0.348800 | 0.174400 | − | 0.984675i | \(-0.444202\pi\) | ||||
0.174400 | + | 0.984675i | \(0.444202\pi\) | |||||||
\(294\) | −7.53557e14 | −0.0680548 | ||||||||
\(295\) | −8.82533e15 | −0.779628 | ||||||||
\(296\) | −3.74806e16 | −3.23900 | ||||||||
\(297\) | 1.44043e15 | 0.121780 | ||||||||
\(298\) | 1.34859e16 | 1.11551 | ||||||||
\(299\) | −8.12210e15 | −0.657364 | ||||||||
\(300\) | 7.22254e14 | 0.0572008 | ||||||||
\(301\) | −7.83103e15 | −0.606927 | ||||||||
\(302\) | 5.30463e15 | 0.402356 | ||||||||
\(303\) | 9.71149e14 | 0.0720956 | ||||||||
\(304\) | 7.85152e16 | 5.70526 | ||||||||
\(305\) | −1.48399e15 | −0.105556 | ||||||||
\(306\) | 4.07403e16 | 2.83684 | ||||||||
\(307\) | −2.77133e16 | −1.88925 | −0.944624 | − | 0.328156i | \(-0.893573\pi\) | ||||
−0.944624 | + | 0.328156i | \(0.893573\pi\) | |||||||
\(308\) | −2.55025e16 | −1.70217 | ||||||||
\(309\) | −8.36492e14 | −0.0546678 | ||||||||
\(310\) | −1.37561e16 | −0.880326 | ||||||||
\(311\) | −2.22649e16 | −1.39533 | −0.697666 | − | 0.716424i | \(-0.745778\pi\) | ||||
−0.697666 | + | 0.716424i | \(0.745778\pi\) | |||||||
\(312\) | −1.96207e15 | −0.120423 | ||||||||
\(313\) | −2.18947e16 | −1.31613 | −0.658067 | − | 0.752959i | \(-0.728626\pi\) | ||||
−0.658067 | + | 0.752959i | \(0.728626\pi\) | |||||||
\(314\) | −4.64977e16 | −2.73772 | ||||||||
\(315\) | −7.03838e15 | −0.405933 | ||||||||
\(316\) | 3.97102e16 | 2.24355 | ||||||||
\(317\) | 5.02815e15 | 0.278306 | 0.139153 | − | 0.990271i | \(-0.455562\pi\) | ||||
0.139153 | + | 0.990271i | \(0.455562\pi\) | |||||||
\(318\) | 3.07477e14 | 0.0166739 | ||||||||
\(319\) | 2.59777e16 | 1.38026 | ||||||||
\(320\) | −3.71847e16 | −1.93593 | ||||||||
\(321\) | 8.20570e14 | 0.0418632 | ||||||||
\(322\) | 1.73879e16 | 0.869329 | ||||||||
\(323\) | 5.42095e16 | 2.65619 | ||||||||
\(324\) | 5.39893e16 | 2.59278 | ||||||||
\(325\) | 7.14290e15 | 0.336227 | ||||||||
\(326\) | 3.01613e16 | 1.39167 | ||||||||
\(327\) | 8.05378e14 | 0.0364283 | ||||||||
\(328\) | −6.48610e15 | −0.287610 | ||||||||
\(329\) | 8.62502e15 | 0.374962 | ||||||||
\(330\) | −2.04741e15 | −0.0872698 | ||||||||
\(331\) | −4.07285e16 | −1.70222 | −0.851111 | − | 0.524985i | \(-0.824071\pi\) | ||||
−0.851111 | + | 0.524985i | \(0.824071\pi\) | |||||||
\(332\) | 7.21001e16 | 2.95487 | ||||||||
\(333\) | −2.62229e16 | −1.05388 | ||||||||
\(334\) | −6.20000e16 | −2.44365 | ||||||||
\(335\) | −1.88187e15 | −0.0727444 | ||||||||
\(336\) | 2.31689e15 | 0.0878415 | ||||||||
\(337\) | 4.09748e16 | 1.52378 | 0.761890 | − | 0.647707i | \(-0.224272\pi\) | ||||
0.761890 | + | 0.647707i | \(0.224272\pi\) | |||||||
\(338\) | 2.06695e16 | 0.754000 | ||||||||
\(339\) | 7.13967e14 | 0.0255494 | ||||||||
\(340\) | −8.38657e16 | −2.94423 | ||||||||
\(341\) | −2.15255e16 | −0.741397 | ||||||||
\(342\) | 9.95898e16 | 3.36546 | ||||||||
\(343\) | 2.78365e16 | 0.923002 | ||||||||
\(344\) | −1.05814e17 | −3.44282 | ||||||||
\(345\) | 1.00956e15 | 0.0322334 | ||||||||
\(346\) | 5.63841e16 | 1.76670 | ||||||||
\(347\) | −1.30655e16 | −0.401776 | −0.200888 | − | 0.979614i | \(-0.564383\pi\) | ||||
−0.200888 | + | 0.979614i | \(0.564383\pi\) | |||||||
\(348\) | −5.01299e15 | −0.151298 | ||||||||
\(349\) | −7.64906e15 | −0.226591 | −0.113296 | − | 0.993561i | \(-0.536141\pi\) | ||||
−0.113296 | + | 0.993561i | \(0.536141\pi\) | |||||||
\(350\) | −1.52916e16 | −0.444643 | ||||||||
\(351\) | −2.74899e15 | −0.0784653 | ||||||||
\(352\) | −1.30934e17 | −3.66880 | ||||||||
\(353\) | 2.31293e16 | 0.636248 | 0.318124 | − | 0.948049i | \(-0.396947\pi\) | ||||
0.318124 | + | 0.948049i | \(0.396947\pi\) | |||||||
\(354\) | 3.68489e15 | 0.0995183 | ||||||||
\(355\) | 2.25449e16 | 0.597812 | ||||||||
\(356\) | −1.80735e17 | −4.70563 | ||||||||
\(357\) | 1.59966e15 | 0.0408963 | ||||||||
\(358\) | −7.94086e15 | −0.199355 | ||||||||
\(359\) | −6.06805e16 | −1.49601 | −0.748007 | − | 0.663691i | \(-0.768989\pi\) | ||||
−0.748007 | + | 0.663691i | \(0.768989\pi\) | |||||||
\(360\) | −9.51040e16 | −2.30268 | ||||||||
\(361\) | 9.04624e16 | 2.15115 | ||||||||
\(362\) | −2.42409e16 | −0.566166 | ||||||||
\(363\) | −9.99212e14 | −0.0229226 | ||||||||
\(364\) | 4.86704e16 | 1.09674 | ||||||||
\(365\) | −6.30443e16 | −1.39554 | ||||||||
\(366\) | 6.19618e14 | 0.0134740 | ||||||||
\(367\) | −2.38532e16 | −0.509585 | −0.254792 | − | 0.966996i | \(-0.582007\pi\) | ||||
−0.254792 | + | 0.966996i | \(0.582007\pi\) | |||||||
\(368\) | 1.29594e17 | 2.72004 | ||||||||
\(369\) | −4.53793e15 | −0.0935807 | ||||||||
\(370\) | 7.46412e16 | 1.51240 | ||||||||
\(371\) | −4.70802e15 | −0.0937364 | ||||||||
\(372\) | 4.15384e15 | 0.0812683 | ||||||||
\(373\) | 4.49041e16 | 0.863333 | 0.431666 | − | 0.902033i | \(-0.357926\pi\) | ||||
0.431666 | + | 0.902033i | \(0.357926\pi\) | |||||||
\(374\) | −1.81460e17 | −3.42860 | ||||||||
\(375\) | −2.93889e15 | −0.0545733 | ||||||||
\(376\) | 1.16543e17 | 2.12699 | ||||||||
\(377\) | −4.95772e16 | −0.889330 | ||||||||
\(378\) | 5.88508e15 | 0.103766 | ||||||||
\(379\) | −2.06523e16 | −0.357942 | −0.178971 | − | 0.983854i | \(-0.557277\pi\) | ||||
−0.178971 | + | 0.983854i | \(0.557277\pi\) | |||||||
\(380\) | −2.05010e17 | −3.49287 | ||||||||
\(381\) | −2.39561e15 | −0.0401240 | ||||||||
\(382\) | 1.53730e17 | 2.53132 | ||||||||
\(383\) | 6.19958e16 | 1.00362 | 0.501811 | − | 0.864977i | \(-0.332667\pi\) | ||||
0.501811 | + | 0.864977i | \(0.332667\pi\) | |||||||
\(384\) | 5.85564e15 | 0.0932012 | ||||||||
\(385\) | 3.13495e16 | 0.490609 | ||||||||
\(386\) | −1.34064e17 | −2.06298 | ||||||||
\(387\) | −7.40318e16 | −1.12020 | ||||||||
\(388\) | −1.67238e17 | −2.48845 | ||||||||
\(389\) | 1.66800e16 | 0.244075 | 0.122037 | − | 0.992525i | \(-0.461057\pi\) | ||||
0.122037 | + | 0.992525i | \(0.461057\pi\) | |||||||
\(390\) | 3.90738e15 | 0.0562297 | ||||||||
\(391\) | 8.94763e16 | 1.26637 | ||||||||
\(392\) | 1.55908e17 | 2.17025 | ||||||||
\(393\) | 4.38254e15 | 0.0600032 | ||||||||
\(394\) | −1.00558e16 | −0.135422 | ||||||||
\(395\) | −4.88145e16 | −0.646648 | ||||||||
\(396\) | −2.41092e17 | −3.14170 | ||||||||
\(397\) | −9.05295e16 | −1.16052 | −0.580259 | − | 0.814432i | \(-0.697049\pi\) | ||||
−0.580259 | + | 0.814432i | \(0.697049\pi\) | |||||||
\(398\) | 1.62997e17 | 2.05560 | ||||||||
\(399\) | 3.91037e15 | 0.0485170 | ||||||||
\(400\) | −1.13970e17 | −1.39124 | ||||||||
\(401\) | −5.44307e16 | −0.653740 | −0.326870 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326870 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(402\) | 7.85749e14 | 0.00928570 | ||||||||
\(403\) | 4.10804e16 | 0.477697 | ||||||||
\(404\) | −3.25509e17 | −3.72464 | ||||||||
\(405\) | −6.63674e16 | −0.747304 | ||||||||
\(406\) | 1.06136e17 | 1.17609 | ||||||||
\(407\) | 1.16799e17 | 1.27372 | ||||||||
\(408\) | 2.16149e16 | 0.231986 | ||||||||
\(409\) | −3.72472e15 | −0.0393452 | −0.0196726 | − | 0.999806i | \(-0.506262\pi\) | ||||
−0.0196726 | + | 0.999806i | \(0.506262\pi\) | |||||||
\(410\) | 1.29168e16 | 0.134295 | ||||||||
\(411\) | −3.82655e15 | −0.0391593 | ||||||||
\(412\) | 2.80375e17 | 2.82427 | ||||||||
\(413\) | −5.64222e16 | −0.559468 | ||||||||
\(414\) | 1.64379e17 | 1.60452 | ||||||||
\(415\) | −8.86304e16 | −0.851668 | ||||||||
\(416\) | 2.49881e17 | 2.36388 | ||||||||
\(417\) | −6.24910e15 | −0.0582013 | ||||||||
\(418\) | −4.43580e17 | −4.06749 | ||||||||
\(419\) | 3.64682e16 | 0.329248 | 0.164624 | − | 0.986356i | \(-0.447359\pi\) | ||||
0.164624 | + | 0.986356i | \(0.447359\pi\) | |||||||
\(420\) | −6.04960e15 | −0.0537782 | ||||||||
\(421\) | 1.52315e17 | 1.33324 | 0.666619 | − | 0.745399i | \(-0.267741\pi\) | ||||
0.666619 | + | 0.745399i | \(0.267741\pi\) | |||||||
\(422\) | −2.38925e17 | −2.05935 | ||||||||
\(423\) | 8.15380e16 | 0.692066 | ||||||||
\(424\) | −6.36157e16 | −0.531724 | ||||||||
\(425\) | −7.86891e16 | −0.647718 | ||||||||
\(426\) | −9.41330e15 | −0.0763097 | ||||||||
\(427\) | −9.48746e15 | −0.0757476 | ||||||||
\(428\) | −2.75038e17 | −2.16276 | ||||||||
\(429\) | 6.11428e15 | 0.0473557 | ||||||||
\(430\) | 2.10725e17 | 1.60758 | ||||||||
\(431\) | 4.15615e16 | 0.312312 | 0.156156 | − | 0.987732i | \(-0.450090\pi\) | ||||
0.156156 | + | 0.987732i | \(0.450090\pi\) | |||||||
\(432\) | 4.38623e16 | 0.324674 | ||||||||
\(433\) | 1.11089e17 | 0.810026 | 0.405013 | − | 0.914311i | \(-0.367267\pi\) | ||||
0.405013 | + | 0.914311i | \(0.367267\pi\) | |||||||
\(434\) | −8.79456e16 | −0.631729 | ||||||||
\(435\) | 6.16232e15 | 0.0436078 | ||||||||
\(436\) | −2.69946e17 | −1.88198 | ||||||||
\(437\) | 2.18725e17 | 1.50234 | ||||||||
\(438\) | 2.63232e16 | 0.178138 | ||||||||
\(439\) | 1.52657e17 | 1.01788 | 0.508942 | − | 0.860801i | \(-0.330037\pi\) | ||||
0.508942 | + | 0.860801i | \(0.330037\pi\) | |||||||
\(440\) | 4.23601e17 | 2.78301 | ||||||||
\(441\) | 1.09079e17 | 0.706141 | ||||||||
\(442\) | 3.46308e17 | 2.20911 | ||||||||
\(443\) | −1.84693e17 | −1.16098 | −0.580491 | − | 0.814267i | \(-0.697139\pi\) | ||||
−0.580491 | + | 0.814267i | \(0.697139\pi\) | |||||||
\(444\) | −2.25390e16 | −0.139619 | ||||||||
\(445\) | 2.22172e17 | 1.35628 | ||||||||
\(446\) | 2.03100e17 | 1.22189 | ||||||||
\(447\) | 5.00591e15 | 0.0296814 | ||||||||
\(448\) | −2.37730e17 | −1.38924 | ||||||||
\(449\) | 3.14842e17 | 1.81339 | 0.906695 | − | 0.421787i | \(-0.138597\pi\) | ||||
0.906695 | + | 0.421787i | \(0.138597\pi\) | |||||||
\(450\) | −1.44562e17 | −0.820677 | ||||||||
\(451\) | 2.02123e16 | 0.113101 | ||||||||
\(452\) | −2.39307e17 | −1.31994 | ||||||||
\(453\) | 1.96906e15 | 0.0107058 | ||||||||
\(454\) | 1.54554e17 | 0.828355 | ||||||||
\(455\) | −5.98290e16 | −0.316110 | ||||||||
\(456\) | 5.28377e16 | 0.275215 | ||||||||
\(457\) | 2.69381e17 | 1.38329 | 0.691644 | − | 0.722239i | \(-0.256887\pi\) | ||||
0.691644 | + | 0.722239i | \(0.256887\pi\) | |||||||
\(458\) | −3.45047e15 | −0.0174684 | ||||||||
\(459\) | 3.02840e16 | 0.151158 | ||||||||
\(460\) | −3.38383e17 | −1.66526 | ||||||||
\(461\) | 3.66421e17 | 1.77797 | 0.888986 | − | 0.457935i | \(-0.151411\pi\) | ||||
0.888986 | + | 0.457935i | \(0.151411\pi\) | |||||||
\(462\) | −1.30895e16 | −0.0626255 | ||||||||
\(463\) | 3.66603e17 | 1.72950 | 0.864749 | − | 0.502204i | \(-0.167478\pi\) | ||||
0.864749 | + | 0.502204i | \(0.167478\pi\) | |||||||
\(464\) | 7.91042e17 | 3.67987 | ||||||||
\(465\) | −5.10620e15 | −0.0234236 | ||||||||
\(466\) | 4.29730e17 | 1.94396 | ||||||||
\(467\) | −6.94235e16 | −0.309704 | −0.154852 | − | 0.987938i | \(-0.549490\pi\) | ||||
−0.154852 | + | 0.987938i | \(0.549490\pi\) | |||||||
\(468\) | 4.60113e17 | 2.02426 | ||||||||
\(469\) | −1.20312e16 | −0.0522020 | ||||||||
\(470\) | −2.32091e17 | −0.993166 | ||||||||
\(471\) | −1.72598e16 | −0.0728448 | ||||||||
\(472\) | −7.62388e17 | −3.17361 | ||||||||
\(473\) | 3.29744e17 | 1.35388 | ||||||||
\(474\) | 2.03818e16 | 0.0825435 | ||||||||
\(475\) | −1.92356e17 | −0.768416 | ||||||||
\(476\) | −5.36172e17 | −2.11280 | ||||||||
\(477\) | −4.45080e16 | −0.173009 | ||||||||
\(478\) | 1.29462e17 | 0.496435 | ||||||||
\(479\) | 3.67023e17 | 1.38839 | 0.694196 | − | 0.719786i | \(-0.255760\pi\) | ||||
0.694196 | + | 0.719786i | \(0.255760\pi\) | |||||||
\(480\) | −3.10595e16 | −0.115912 | ||||||||
\(481\) | −2.22905e17 | −0.820684 | ||||||||
\(482\) | −9.19624e17 | −3.34045 | ||||||||
\(483\) | 6.45432e15 | 0.0231310 | ||||||||
\(484\) | 3.34915e17 | 1.18424 | ||||||||
\(485\) | 2.05581e17 | 0.717234 | ||||||||
\(486\) | 8.34890e16 | 0.287404 | ||||||||
\(487\) | −2.68060e17 | −0.910528 | −0.455264 | − | 0.890357i | \(-0.650455\pi\) | ||||
−0.455264 | + | 0.890357i | \(0.650455\pi\) | |||||||
\(488\) | −1.28196e17 | −0.429682 | ||||||||
\(489\) | 1.11958e16 | 0.0370293 | ||||||||
\(490\) | −3.10485e17 | −1.01337 | ||||||||
\(491\) | −5.16026e17 | −1.66204 | −0.831021 | − | 0.556240i | \(-0.812243\pi\) | ||||
−0.831021 | + | 0.556240i | \(0.812243\pi\) | |||||||
\(492\) | −3.90042e15 | −0.0123976 | ||||||||
\(493\) | 5.46162e17 | 1.71323 | ||||||||
\(494\) | 8.46552e17 | 2.62077 | ||||||||
\(495\) | 2.96367e17 | 0.905517 | ||||||||
\(496\) | −6.55470e17 | −1.97661 | ||||||||
\(497\) | 1.44135e17 | 0.428995 | ||||||||
\(498\) | 3.70063e16 | 0.108714 | ||||||||
\(499\) | −4.94534e17 | −1.43398 | −0.716989 | − | 0.697085i | \(-0.754480\pi\) | ||||
−0.716989 | + | 0.697085i | \(0.754480\pi\) | |||||||
\(500\) | 9.85055e17 | 2.81939 | ||||||||
\(501\) | −2.30141e16 | −0.0650203 | ||||||||
\(502\) | −2.00261e17 | −0.558498 | ||||||||
\(503\) | −7.50547e16 | −0.206626 | −0.103313 | − | 0.994649i | \(-0.532944\pi\) | ||||
−0.103313 | + | 0.994649i | \(0.532944\pi\) | |||||||
\(504\) | −6.08021e17 | −1.65242 | ||||||||
\(505\) | 4.00138e17 | 1.07353 | ||||||||
\(506\) | −7.32158e17 | −1.93922 | ||||||||
\(507\) | 7.67243e15 | 0.0200623 | ||||||||
\(508\) | 8.02959e17 | 2.07290 | ||||||||
\(509\) | −6.81044e17 | −1.73584 | −0.867920 | − | 0.496704i | \(-0.834543\pi\) | ||||
−0.867920 | + | 0.496704i | \(0.834543\pi\) | |||||||
\(510\) | −4.30452e16 | −0.108323 | ||||||||
\(511\) | −4.03056e17 | −1.00145 | ||||||||
\(512\) | 2.90276e16 | 0.0712126 | ||||||||
\(513\) | 7.40294e16 | 0.179325 | ||||||||
\(514\) | 1.62464e17 | 0.388595 | ||||||||
\(515\) | −3.44656e17 | −0.814027 | ||||||||
\(516\) | −6.36316e16 | −0.148405 | ||||||||
\(517\) | −3.63176e17 | −0.836429 | ||||||||
\(518\) | 4.77197e17 | 1.08531 | ||||||||
\(519\) | 2.09295e16 | 0.0470080 | ||||||||
\(520\) | −8.08421e17 | −1.79315 | ||||||||
\(521\) | 1.06572e17 | 0.233452 | 0.116726 | − | 0.993164i | \(-0.462760\pi\) | ||||
0.116726 | + | 0.993164i | \(0.462760\pi\) | |||||||
\(522\) | 1.00337e18 | 2.17071 | ||||||||
\(523\) | −1.69125e17 | −0.361365 | −0.180683 | − | 0.983541i | \(-0.557831\pi\) | ||||
−0.180683 | + | 0.983541i | \(0.557831\pi\) | |||||||
\(524\) | −1.46894e18 | −3.09992 | ||||||||
\(525\) | −5.67619e15 | −0.0118310 | ||||||||
\(526\) | −7.35299e17 | −1.51376 | ||||||||
\(527\) | −4.52559e17 | −0.920250 | ||||||||
\(528\) | −9.75579e16 | −0.195949 | ||||||||
\(529\) | −1.43016e17 | −0.283742 | ||||||||
\(530\) | 1.26688e17 | 0.248281 | ||||||||
\(531\) | −5.33396e17 | −1.03261 | ||||||||
\(532\) | −1.31067e18 | −2.50651 | ||||||||
\(533\) | −3.85742e16 | −0.0728735 | ||||||||
\(534\) | −9.27648e16 | −0.173127 | ||||||||
\(535\) | 3.38096e17 | 0.623362 | ||||||||
\(536\) | −1.62568e17 | −0.296118 | ||||||||
\(537\) | −2.94761e15 | −0.00530441 | ||||||||
\(538\) | 1.14213e18 | 2.03062 | ||||||||
\(539\) | −4.85848e17 | −0.853441 | ||||||||
\(540\) | −1.14528e17 | −0.198771 | ||||||||
\(541\) | 4.94957e17 | 0.848761 | 0.424380 | − | 0.905484i | \(-0.360492\pi\) | ||||
0.424380 | + | 0.905484i | \(0.360492\pi\) | |||||||
\(542\) | −1.27636e17 | −0.216260 | ||||||||
\(543\) | −8.99813e15 | −0.0150645 | ||||||||
\(544\) | −2.75278e18 | −4.55386 | ||||||||
\(545\) | 3.31836e17 | 0.542434 | ||||||||
\(546\) | 2.49807e16 | 0.0403509 | ||||||||
\(547\) | 6.84775e17 | 1.09303 | 0.546513 | − | 0.837451i | \(-0.315955\pi\) | ||||
0.546513 | + | 0.837451i | \(0.315955\pi\) | |||||||
\(548\) | 1.28258e18 | 2.02307 | ||||||||
\(549\) | −8.96912e16 | −0.139807 | ||||||||
\(550\) | 6.43889e17 | 0.991868 | ||||||||
\(551\) | 1.33510e18 | 2.03248 | ||||||||
\(552\) | 8.72120e16 | 0.131212 | ||||||||
\(553\) | −3.12082e17 | −0.464040 | ||||||||
\(554\) | −8.58389e17 | −1.26145 | ||||||||
\(555\) | 2.77065e16 | 0.0402418 | ||||||||
\(556\) | 2.09457e18 | 3.00682 | ||||||||
\(557\) | −4.24245e17 | −0.601947 | −0.300974 | − | 0.953632i | \(-0.597312\pi\) | ||||
−0.300974 | + | 0.953632i | \(0.597312\pi\) | |||||||
\(558\) | −8.31407e17 | −1.16598 | ||||||||
\(559\) | −6.29300e17 | −0.872330 | ||||||||
\(560\) | 9.54617e17 | 1.30800 | ||||||||
\(561\) | −6.73573e16 | −0.0912276 | ||||||||
\(562\) | −1.61230e18 | −2.15853 | ||||||||
\(563\) | 1.08909e18 | 1.44131 | 0.720657 | − | 0.693292i | \(-0.243840\pi\) | ||||
0.720657 | + | 0.693292i | \(0.243840\pi\) | |||||||
\(564\) | 7.00832e16 | 0.0916853 | ||||||||
\(565\) | 2.94173e17 | 0.380441 | ||||||||
\(566\) | −9.12966e17 | −1.16721 | ||||||||
\(567\) | −4.24301e17 | −0.536271 | ||||||||
\(568\) | 1.94758e18 | 2.43349 | ||||||||
\(569\) | 1.51324e18 | 1.86930 | 0.934649 | − | 0.355572i | \(-0.115714\pi\) | ||||
0.934649 | + | 0.355572i | \(0.115714\pi\) | |||||||
\(570\) | −1.05224e17 | −0.128508 | ||||||||
\(571\) | 1.41235e18 | 1.70533 | 0.852666 | − | 0.522456i | \(-0.174984\pi\) | ||||
0.852666 | + | 0.522456i | \(0.174984\pi\) | |||||||
\(572\) | −2.04938e18 | −2.44652 | ||||||||
\(573\) | 5.70639e16 | 0.0673529 | ||||||||
\(574\) | 8.25801e16 | 0.0963714 | ||||||||
\(575\) | −3.17496e17 | −0.366350 | ||||||||
\(576\) | −2.24742e18 | −2.56412 | ||||||||
\(577\) | 1.34945e17 | 0.152235 | 0.0761174 | − | 0.997099i | \(-0.475748\pi\) | ||||
0.0761174 | + | 0.997099i | \(0.475748\pi\) | |||||||
\(578\) | −2.11113e18 | −2.35496 | ||||||||
\(579\) | −4.97640e16 | −0.0548915 | ||||||||
\(580\) | −2.06548e18 | −2.25289 | ||||||||
\(581\) | −5.66634e17 | −0.611164 | ||||||||
\(582\) | −8.58372e16 | −0.0915537 | ||||||||
\(583\) | 1.98242e17 | 0.209098 | ||||||||
\(584\) | −5.44617e18 | −5.68078 | ||||||||
\(585\) | −5.65603e17 | −0.583443 | ||||||||
\(586\) | −6.49880e17 | −0.662977 | ||||||||
\(587\) | 1.91612e17 | 0.193319 | 0.0966595 | − | 0.995318i | \(-0.469184\pi\) | ||||
0.0966595 | + | 0.995318i | \(0.469184\pi\) | |||||||
\(588\) | 9.37554e16 | 0.0935500 | ||||||||
\(589\) | −1.10628e18 | −1.09173 | ||||||||
\(590\) | 1.51827e18 | 1.48187 | ||||||||
\(591\) | −3.73265e15 | −0.00360329 | ||||||||
\(592\) | 3.55661e18 | 3.39583 | ||||||||
\(593\) | 1.86646e18 | 1.76264 | 0.881319 | − | 0.472521i | \(-0.156656\pi\) | ||||
0.881319 | + | 0.472521i | \(0.156656\pi\) | |||||||
\(594\) | −2.47805e17 | −0.231472 | ||||||||
\(595\) | 6.59100e17 | 0.608963 | ||||||||
\(596\) | −1.67788e18 | −1.53341 | ||||||||
\(597\) | 6.05038e16 | 0.0546952 | ||||||||
\(598\) | 1.39729e18 | 1.24948 | ||||||||
\(599\) | −1.06545e18 | −0.942452 | −0.471226 | − | 0.882013i | \(-0.656188\pi\) | ||||
−0.471226 | + | 0.882013i | \(0.656188\pi\) | |||||||
\(600\) | −7.66977e16 | −0.0671119 | ||||||||
\(601\) | 1.83640e18 | 1.58959 | 0.794793 | − | 0.606881i | \(-0.207580\pi\) | ||||
0.794793 | + | 0.606881i | \(0.207580\pi\) | |||||||
\(602\) | 1.34721e18 | 1.15361 | ||||||||
\(603\) | −1.13739e17 | −0.0963491 | ||||||||
\(604\) | −6.59987e17 | −0.553089 | ||||||||
\(605\) | −4.11701e17 | −0.341328 | ||||||||
\(606\) | −1.67072e17 | −0.137035 | ||||||||
\(607\) | 8.60353e17 | 0.698152 | 0.349076 | − | 0.937094i | \(-0.386495\pi\) | ||||
0.349076 | + | 0.937094i | \(0.386495\pi\) | |||||||
\(608\) | −6.72919e18 | −5.40244 | ||||||||
\(609\) | 3.93971e16 | 0.0312933 | ||||||||
\(610\) | 2.55298e17 | 0.200634 | ||||||||
\(611\) | 6.93105e17 | 0.538928 | ||||||||
\(612\) | −5.06879e18 | −3.89960 | ||||||||
\(613\) | 1.19125e18 | 0.906795 | 0.453398 | − | 0.891308i | \(-0.350212\pi\) | ||||
0.453398 | + | 0.891308i | \(0.350212\pi\) | |||||||
\(614\) | 4.76766e18 | 3.59097 | ||||||||
\(615\) | 4.79467e15 | 0.00357331 | ||||||||
\(616\) | 2.70817e18 | 1.99711 | ||||||||
\(617\) | 9.56470e17 | 0.697940 | 0.348970 | − | 0.937134i | \(-0.386532\pi\) | ||||
0.348970 | + | 0.937134i | \(0.386532\pi\) | |||||||
\(618\) | 1.43906e17 | 0.103909 | ||||||||
\(619\) | 8.06377e17 | 0.576168 | 0.288084 | − | 0.957605i | \(-0.406982\pi\) | ||||
0.288084 | + | 0.957605i | \(0.406982\pi\) | |||||||
\(620\) | 1.71149e18 | 1.21012 | ||||||||
\(621\) | 1.22190e17 | 0.0854951 | ||||||||
\(622\) | 3.83034e18 | 2.65216 | ||||||||
\(623\) | 1.42040e18 | 0.973279 | ||||||||
\(624\) | 1.86185e17 | 0.126254 | ||||||||
\(625\) | −5.65865e17 | −0.379745 | ||||||||
\(626\) | 3.76665e18 | 2.50163 | ||||||||
\(627\) | −1.64655e17 | −0.108227 | ||||||||
\(628\) | 5.78511e18 | 3.76334 | ||||||||
\(629\) | 2.45561e18 | 1.58099 | ||||||||
\(630\) | 1.21085e18 | 0.771573 | ||||||||
\(631\) | −1.28671e16 | −0.00811502 | −0.00405751 | − | 0.999992i | \(-0.501292\pi\) | ||||
−0.00405751 | + | 0.999992i | \(0.501292\pi\) | |||||||
\(632\) | −4.21691e18 | −2.63229 | ||||||||
\(633\) | −8.86878e16 | −0.0547949 | ||||||||
\(634\) | −8.65020e17 | −0.528988 | ||||||||
\(635\) | −9.87053e17 | −0.597463 | ||||||||
\(636\) | −3.82554e16 | −0.0229203 | ||||||||
\(637\) | 9.27217e17 | 0.549889 | ||||||||
\(638\) | −4.46908e18 | −2.62352 | ||||||||
\(639\) | 1.36260e18 | 0.791795 | ||||||||
\(640\) | 2.41267e18 | 1.38781 | ||||||||
\(641\) | −1.98043e18 | −1.12767 | −0.563835 | − | 0.825888i | \(-0.690674\pi\) | ||||
−0.563835 | + | 0.825888i | \(0.690674\pi\) | |||||||
\(642\) | −1.41167e17 | −0.0795711 | ||||||||
\(643\) | −8.02979e17 | −0.448056 | −0.224028 | − | 0.974583i | \(-0.571921\pi\) | ||||
−0.224028 | + | 0.974583i | \(0.571921\pi\) | |||||||
\(644\) | −2.16335e18 | −1.19500 | ||||||||
\(645\) | 7.82203e16 | 0.0427742 | ||||||||
\(646\) | −9.32595e18 | −5.04872 | ||||||||
\(647\) | −2.75749e18 | −1.47787 | −0.738936 | − | 0.673776i | \(-0.764671\pi\) | ||||
−0.738936 | + | 0.673776i | \(0.764671\pi\) | |||||||
\(648\) | −5.73324e18 | −3.04203 | ||||||||
\(649\) | 2.37579e18 | 1.24801 | ||||||||
\(650\) | −1.22883e18 | −0.639080 | ||||||||
\(651\) | −3.26450e16 | −0.0168089 | ||||||||
\(652\) | −3.75258e18 | −1.91303 | ||||||||
\(653\) | 3.49617e18 | 1.76464 | 0.882320 | − | 0.470649i | \(-0.155980\pi\) | ||||
0.882320 | + | 0.470649i | \(0.155980\pi\) | |||||||
\(654\) | −1.38553e17 | −0.0692408 | ||||||||
\(655\) | 1.80572e18 | 0.893474 | ||||||||
\(656\) | 6.15480e17 | 0.301536 | ||||||||
\(657\) | −3.81035e18 | −1.84838 | ||||||||
\(658\) | −1.48381e18 | −0.712704 | ||||||||
\(659\) | 2.57366e18 | 1.22404 | 0.612020 | − | 0.790843i | \(-0.290357\pi\) | ||||
0.612020 | + | 0.790843i | \(0.290357\pi\) | |||||||
\(660\) | 2.54733e17 | 0.119963 | ||||||||
\(661\) | −1.58831e18 | −0.740673 | −0.370336 | − | 0.928898i | \(-0.620758\pi\) | ||||
−0.370336 | + | 0.928898i | \(0.620758\pi\) | |||||||
\(662\) | 7.00674e18 | 3.23548 | ||||||||
\(663\) | 1.28548e17 | 0.0587798 | ||||||||
\(664\) | −7.65647e18 | −3.46686 | ||||||||
\(665\) | 1.61117e18 | 0.722439 | ||||||||
\(666\) | 4.51126e18 | 2.00316 | ||||||||
\(667\) | 2.20366e18 | 0.969007 | ||||||||
\(668\) | 7.71385e18 | 3.35911 | ||||||||
\(669\) | 7.53898e16 | 0.0325119 | ||||||||
\(670\) | 3.23749e17 | 0.138268 | ||||||||
\(671\) | 3.99492e17 | 0.168971 | ||||||||
\(672\) | −1.98570e17 | −0.0831791 | ||||||||
\(673\) | −4.61407e18 | −1.91419 | −0.957097 | − | 0.289768i | \(-0.906422\pi\) | ||||
−0.957097 | + | 0.289768i | \(0.906422\pi\) | |||||||
\(674\) | −7.04910e18 | −2.89631 | ||||||||
\(675\) | −1.07459e17 | −0.0437289 | ||||||||
\(676\) | −2.57164e18 | −1.03647 | ||||||||
\(677\) | −2.72951e18 | −1.08958 | −0.544790 | − | 0.838573i | \(-0.683391\pi\) | ||||
−0.544790 | + | 0.838573i | \(0.683391\pi\) | |||||||
\(678\) | −1.22828e17 | −0.0485627 | ||||||||
\(679\) | 1.31432e18 | 0.514693 | ||||||||
\(680\) | 8.90589e18 | 3.45437 | ||||||||
\(681\) | 5.73697e16 | 0.0220407 | ||||||||
\(682\) | 3.70315e18 | 1.40920 | ||||||||
\(683\) | −2.16774e18 | −0.817095 | −0.408548 | − | 0.912737i | \(-0.633965\pi\) | ||||
−0.408548 | + | 0.912737i | \(0.633965\pi\) | |||||||
\(684\) | −1.23907e19 | −4.62626 | ||||||||
\(685\) | −1.57663e18 | −0.583099 | ||||||||
\(686\) | −4.78886e18 | −1.75439 | ||||||||
\(687\) | −1.28080e15 | −0.000464797 0 | ||||||||
\(688\) | 1.00410e19 | 3.60952 | ||||||||
\(689\) | −3.78336e17 | −0.134726 | ||||||||
\(690\) | −1.73679e17 | −0.0612674 | ||||||||
\(691\) | 1.57881e18 | 0.551725 | 0.275863 | − | 0.961197i | \(-0.411037\pi\) | ||||
0.275863 | + | 0.961197i | \(0.411037\pi\) | |||||||
\(692\) | −7.01515e18 | −2.42855 | ||||||||
\(693\) | 1.89474e18 | 0.649806 | ||||||||
\(694\) | 2.24773e18 | 0.763672 | ||||||||
\(695\) | −2.57479e18 | −0.866643 | ||||||||
\(696\) | 5.32341e17 | 0.177513 | ||||||||
\(697\) | 4.24948e17 | 0.140386 | ||||||||
\(698\) | 1.31591e18 | 0.430691 | ||||||||
\(699\) | 1.59514e17 | 0.0517246 | ||||||||
\(700\) | 1.90254e18 | 0.611218 | ||||||||
\(701\) | 8.34232e17 | 0.265534 | 0.132767 | − | 0.991147i | \(-0.457614\pi\) | ||||
0.132767 | + | 0.991147i | \(0.457614\pi\) | |||||||
\(702\) | 4.72924e17 | 0.149142 | ||||||||
\(703\) | 6.00274e18 | 1.87560 | ||||||||
\(704\) | 1.00102e19 | 3.09899 | ||||||||
\(705\) | −8.61511e16 | −0.0264260 | ||||||||
\(706\) | −3.97905e18 | −1.20934 | ||||||||
\(707\) | 2.55817e18 | 0.770377 | ||||||||
\(708\) | −4.58463e17 | −0.136801 | ||||||||
\(709\) | 4.44918e18 | 1.31546 | 0.657732 | − | 0.753252i | \(-0.271516\pi\) | ||||
0.657732 | + | 0.753252i | \(0.271516\pi\) | |||||||
\(710\) | −3.87852e18 | −1.13628 | ||||||||
\(711\) | −2.95031e18 | −0.856477 | ||||||||
\(712\) | 1.91927e19 | 5.52097 | ||||||||
\(713\) | −1.82599e18 | −0.520494 | ||||||||
\(714\) | −2.75198e17 | −0.0777331 | ||||||||
\(715\) | 2.51924e18 | 0.705148 | ||||||||
\(716\) | 9.87978e17 | 0.274039 | ||||||||
\(717\) | 4.80559e16 | 0.0132091 | ||||||||
\(718\) | 1.04392e19 | 2.84353 | ||||||||
\(719\) | 5.55360e18 | 1.49912 | 0.749561 | − | 0.661936i | \(-0.230265\pi\) | ||||
0.749561 | + | 0.661936i | \(0.230265\pi\) | |||||||
\(720\) | 9.02462e18 | 2.41417 | ||||||||
\(721\) | −2.20346e18 | −0.584152 | ||||||||
\(722\) | −1.55627e19 | −4.08878 | ||||||||
\(723\) | −3.41361e17 | −0.0888821 | ||||||||
\(724\) | 3.01599e18 | 0.778267 | ||||||||
\(725\) | −1.93799e18 | −0.495626 | ||||||||
\(726\) | 1.71900e17 | 0.0435700 | ||||||||
\(727\) | 6.78768e18 | 1.70509 | 0.852545 | − | 0.522653i | \(-0.175058\pi\) | ||||
0.852545 | + | 0.522653i | \(0.175058\pi\) | |||||||
\(728\) | −5.16841e18 | −1.28678 | ||||||||
\(729\) | −3.99049e18 | −0.984686 | ||||||||
\(730\) | 1.08458e19 | 2.65256 | ||||||||
\(731\) | 6.93261e18 | 1.68048 | ||||||||
\(732\) | −7.70910e16 | −0.0185217 | ||||||||
\(733\) | −6.28285e18 | −1.49617 | −0.748085 | − | 0.663603i | \(-0.769026\pi\) | ||||
−0.748085 | + | 0.663603i | \(0.769026\pi\) | |||||||
\(734\) | 4.10358e18 | 0.968588 | ||||||||
\(735\) | −1.15251e17 | −0.0269635 | ||||||||
\(736\) | −1.11070e19 | −2.57567 | ||||||||
\(737\) | 5.06603e17 | 0.116447 | ||||||||
\(738\) | 7.80684e17 | 0.177873 | ||||||||
\(739\) | −3.01382e18 | −0.680658 | −0.340329 | − | 0.940307i | \(-0.610538\pi\) | ||||
−0.340329 | + | 0.940307i | \(0.610538\pi\) | |||||||
\(740\) | −9.28664e18 | −2.07899 | ||||||||
\(741\) | 3.14236e17 | 0.0697330 | ||||||||
\(742\) | 8.09946e17 | 0.178168 | ||||||||
\(743\) | −1.90536e18 | −0.415479 | −0.207739 | − | 0.978184i | \(-0.566611\pi\) | ||||
−0.207739 | + | 0.978184i | \(0.566611\pi\) | |||||||
\(744\) | −4.41106e17 | −0.0953496 | ||||||||
\(745\) | 2.06256e18 | 0.441969 | ||||||||
\(746\) | −7.72508e18 | −1.64097 | ||||||||
\(747\) | −5.35676e18 | −1.12802 | ||||||||
\(748\) | 2.25768e19 | 4.71304 | ||||||||
\(749\) | 2.16152e18 | 0.447329 | ||||||||
\(750\) | 5.05593e17 | 0.103730 | ||||||||
\(751\) | −5.17090e18 | −1.05174 | −0.525868 | − | 0.850566i | \(-0.676260\pi\) | ||||
−0.525868 | + | 0.850566i | \(0.676260\pi\) | |||||||
\(752\) | −1.10590e19 | −2.22998 | ||||||||
\(753\) | −7.43359e16 | −0.0148604 | ||||||||
\(754\) | 8.52902e18 | 1.69038 | ||||||||
\(755\) | 8.11302e17 | 0.159414 | ||||||||
\(756\) | −7.32205e17 | −0.142640 | ||||||||
\(757\) | −8.59437e18 | −1.65993 | −0.829967 | − | 0.557813i | \(-0.811641\pi\) | ||||
−0.829967 | + | 0.557813i | \(0.811641\pi\) | |||||||
\(758\) | 3.55292e18 | 0.680354 | ||||||||
\(759\) | −2.71774e17 | −0.0515984 | ||||||||
\(760\) | 2.17705e19 | 4.09807 | ||||||||
\(761\) | −4.75000e18 | −0.886529 | −0.443265 | − | 0.896391i | \(-0.646180\pi\) | ||||
−0.443265 | + | 0.896391i | \(0.646180\pi\) | |||||||
\(762\) | 4.12129e17 | 0.0762652 | ||||||||
\(763\) | 2.12150e18 | 0.389255 | ||||||||
\(764\) | −1.91266e19 | −3.47962 | ||||||||
\(765\) | 6.23091e18 | 1.12396 | ||||||||
\(766\) | −1.06655e19 | −1.90762 | ||||||||
\(767\) | −4.53408e18 | −0.804117 | ||||||||
\(768\) | −2.68060e17 | −0.0471394 | ||||||||
\(769\) | 6.03880e18 | 1.05300 | 0.526501 | − | 0.850174i | \(-0.323503\pi\) | ||||
0.526501 | + | 0.850174i | \(0.323503\pi\) | |||||||
\(770\) | −5.39322e18 | −0.932521 | ||||||||
\(771\) | 6.03059e16 | 0.0103397 | ||||||||
\(772\) | 1.66799e19 | 2.83583 | ||||||||
\(773\) | 4.42542e18 | 0.746085 | 0.373042 | − | 0.927814i | \(-0.378315\pi\) | ||||
0.373042 | + | 0.927814i | \(0.378315\pi\) | |||||||
\(774\) | 1.27361e19 | 2.12922 | ||||||||
\(775\) | 1.60585e18 | 0.266222 | ||||||||
\(776\) | 1.77594e19 | 2.91962 | ||||||||
\(777\) | 1.77134e17 | 0.0288778 | ||||||||
\(778\) | −2.86955e18 | −0.463923 | ||||||||
\(779\) | 1.03879e18 | 0.166546 | ||||||||
\(780\) | −4.86145e17 | −0.0772949 | ||||||||
\(781\) | −6.06912e18 | −0.956961 | ||||||||
\(782\) | −1.53931e19 | −2.40703 | ||||||||
\(783\) | 7.45847e17 | 0.115664 | ||||||||
\(784\) | −1.47944e19 | −2.27533 | ||||||||
\(785\) | −7.11146e18 | −1.08469 | ||||||||
\(786\) | −7.53952e17 | −0.114050 | ||||||||
\(787\) | 2.40013e18 | 0.360080 | 0.180040 | − | 0.983659i | \(-0.442377\pi\) | ||||
0.180040 | + | 0.983659i | \(0.442377\pi\) | |||||||
\(788\) | 1.25111e18 | 0.186155 | ||||||||
\(789\) | −2.72940e17 | −0.0402778 | ||||||||
\(790\) | 8.39781e18 | 1.22911 | ||||||||
\(791\) | 1.88071e18 | 0.273008 | ||||||||
\(792\) | 2.56021e19 | 3.68606 | ||||||||
\(793\) | −7.62410e17 | −0.108871 | ||||||||
\(794\) | 1.55743e19 | 2.20584 | ||||||||
\(795\) | 4.70262e16 | 0.00660622 | ||||||||
\(796\) | −2.02796e19 | −2.82569 | ||||||||
\(797\) | −8.80632e17 | −0.121707 | −0.0608535 | − | 0.998147i | \(-0.519382\pi\) | ||||
−0.0608535 | + | 0.998147i | \(0.519382\pi\) | |||||||
\(798\) | −6.72721e17 | −0.0922182 | ||||||||
\(799\) | −7.63552e18 | −1.03821 | ||||||||
\(800\) | 9.76791e18 | 1.31740 | ||||||||
\(801\) | 1.34279e19 | 1.79638 | ||||||||
\(802\) | 9.36400e18 | 1.24259 | ||||||||
\(803\) | 1.69716e19 | 2.23394 | ||||||||
\(804\) | −9.77606e16 | −0.0127644 | ||||||||
\(805\) | 2.65934e18 | 0.344430 | ||||||||
\(806\) | −7.06729e18 | −0.907977 | ||||||||
\(807\) | 4.23952e17 | 0.0540305 | ||||||||
\(808\) | 3.45665e19 | 4.37000 | ||||||||
\(809\) | 6.40994e18 | 0.803875 | 0.401937 | − | 0.915667i | \(-0.368337\pi\) | ||||
0.401937 | + | 0.915667i | \(0.368337\pi\) | |||||||
\(810\) | 1.14175e19 | 1.42043 | ||||||||
\(811\) | −1.26952e19 | −1.56677 | −0.783385 | − | 0.621537i | \(-0.786509\pi\) | ||||
−0.783385 | + | 0.621537i | \(0.786509\pi\) | |||||||
\(812\) | −1.32051e19 | −1.61669 | ||||||||
\(813\) | −4.73778e16 | −0.00575422 | ||||||||
\(814\) | −2.00935e19 | −2.42101 | ||||||||
\(815\) | 4.61294e18 | 0.551383 | ||||||||
\(816\) | −2.05108e18 | −0.243219 | ||||||||
\(817\) | 1.69468e19 | 1.99363 | ||||||||
\(818\) | 6.40783e17 | 0.0747850 | ||||||||
\(819\) | −3.61602e18 | −0.418683 | ||||||||
\(820\) | −1.60707e18 | −0.184606 | ||||||||
\(821\) | −1.01610e19 | −1.15799 | −0.578996 | − | 0.815331i | \(-0.696555\pi\) | ||||
−0.578996 | + | 0.815331i | \(0.696555\pi\) | |||||||
\(822\) | 6.58301e17 | 0.0744316 | ||||||||
\(823\) | −5.57992e18 | −0.625934 | −0.312967 | − | 0.949764i | \(-0.601323\pi\) | ||||
−0.312967 | + | 0.949764i | \(0.601323\pi\) | |||||||
\(824\) | −2.97736e19 | −3.31363 | ||||||||
\(825\) | 2.39009e17 | 0.0263915 | ||||||||
\(826\) | 9.70661e18 | 1.06340 | ||||||||
\(827\) | −4.02076e17 | −0.0437041 | −0.0218521 | − | 0.999761i | \(-0.506956\pi\) | ||||
−0.0218521 | + | 0.999761i | \(0.506956\pi\) | |||||||
\(828\) | −2.04516e19 | −2.20562 | ||||||||
\(829\) | −8.10479e18 | −0.867236 | −0.433618 | − | 0.901097i | \(-0.642763\pi\) | ||||
−0.433618 | + | 0.901097i | \(0.642763\pi\) | |||||||
\(830\) | 1.52476e19 | 1.61880 | ||||||||
\(831\) | −3.18630e17 | −0.0335645 | ||||||||
\(832\) | −1.91039e19 | −1.99674 | ||||||||
\(833\) | −1.02146e19 | −1.05932 | ||||||||
\(834\) | 1.07506e18 | 0.110626 | ||||||||
\(835\) | −9.48241e18 | −0.968181 | ||||||||
\(836\) | 5.51890e19 | 5.59129 | ||||||||
\(837\) | −6.18021e17 | −0.0621281 | ||||||||
\(838\) | −6.27381e18 | −0.625814 | ||||||||
\(839\) | 1.47569e19 | 1.46064 | 0.730320 | − | 0.683105i | \(-0.239371\pi\) | ||||
0.730320 | + | 0.683105i | \(0.239371\pi\) | |||||||
\(840\) | 6.42421e17 | 0.0630963 | ||||||||
\(841\) | 3.19048e18 | 0.310944 | ||||||||
\(842\) | −2.62035e19 | −2.53414 | ||||||||
\(843\) | −5.98478e17 | −0.0574340 | ||||||||
\(844\) | 2.97263e19 | 2.83084 | ||||||||
\(845\) | 3.16124e18 | 0.298737 | ||||||||
\(846\) | −1.40274e19 | −1.31544 | ||||||||
\(847\) | −2.63210e18 | −0.244940 | ||||||||
\(848\) | 6.03663e18 | 0.557470 | ||||||||
\(849\) | −3.38889e17 | −0.0310569 | ||||||||
\(850\) | 1.35373e19 | 1.23114 | ||||||||
\(851\) | 9.90791e18 | 0.894211 | ||||||||
\(852\) | 1.17118e18 | 0.104897 | ||||||||
\(853\) | 2.75384e18 | 0.244777 | 0.122388 | − | 0.992482i | \(-0.460945\pi\) | ||||
0.122388 | + | 0.992482i | \(0.460945\pi\) | |||||||
\(854\) | 1.63218e18 | 0.143976 | ||||||||
\(855\) | 1.52315e19 | 1.33341 | ||||||||
\(856\) | 2.92069e19 | 2.53750 | ||||||||
\(857\) | −4.04490e18 | −0.348765 | −0.174382 | − | 0.984678i | \(-0.555793\pi\) | ||||
−0.174382 | + | 0.984678i | \(0.555793\pi\) | |||||||
\(858\) | −1.05187e18 | −0.0900109 | ||||||||
\(859\) | −8.44802e18 | −0.717463 | −0.358732 | − | 0.933441i | \(-0.616791\pi\) | ||||
−0.358732 | + | 0.933441i | \(0.616791\pi\) | |||||||
\(860\) | −2.62178e19 | −2.20982 | ||||||||
\(861\) | 3.06534e16 | 0.00256424 | ||||||||
\(862\) | −7.15005e18 | −0.593624 | ||||||||
\(863\) | 1.25169e19 | 1.03140 | 0.515700 | − | 0.856769i | \(-0.327532\pi\) | ||||
0.515700 | + | 0.856769i | \(0.327532\pi\) | |||||||
\(864\) | −3.75925e18 | −0.307441 | ||||||||
\(865\) | 8.62351e18 | 0.699970 | ||||||||
\(866\) | −1.91112e19 | −1.53965 | ||||||||
\(867\) | −7.83643e17 | −0.0626605 | ||||||||
\(868\) | 1.09419e19 | 0.868392 | ||||||||
\(869\) | 1.31409e19 | 1.03514 | ||||||||
\(870\) | −1.06014e18 | −0.0828870 | ||||||||
\(871\) | −9.66827e17 | −0.0750293 | ||||||||
\(872\) | 2.86662e19 | 2.20807 | ||||||||
\(873\) | 1.24251e19 | 0.949968 | ||||||||
\(874\) | −3.76285e19 | −2.85557 | ||||||||
\(875\) | −7.74153e18 | −0.583143 | ||||||||
\(876\) | −3.27506e18 | −0.244874 | ||||||||
\(877\) | −1.36834e17 | −0.0101554 | −0.00507770 | − | 0.999987i | \(-0.501616\pi\) | ||||
−0.00507770 | + | 0.999987i | \(0.501616\pi\) | |||||||
\(878\) | −2.62624e19 | −1.93473 | ||||||||
\(879\) | −2.41233e17 | −0.0176404 | ||||||||
\(880\) | −4.01964e19 | −2.91776 | ||||||||
\(881\) | 1.43457e19 | 1.03366 | 0.516830 | − | 0.856088i | \(-0.327112\pi\) | ||||
0.516830 | + | 0.856088i | \(0.327112\pi\) | |||||||
\(882\) | −1.87655e19 | −1.34219 | ||||||||
\(883\) | 1.93837e18 | 0.137624 | 0.0688118 | − | 0.997630i | \(-0.478079\pi\) | ||||
0.0688118 | + | 0.997630i | \(0.478079\pi\) | |||||||
\(884\) | −4.30867e19 | −3.03671 | ||||||||
\(885\) | 5.63574e17 | 0.0394294 | ||||||||
\(886\) | 3.17736e19 | 2.20672 | ||||||||
\(887\) | −1.02952e19 | −0.709791 | −0.354895 | − | 0.934906i | \(-0.615483\pi\) | ||||
−0.354895 | + | 0.934906i | \(0.615483\pi\) | |||||||
\(888\) | 2.39346e18 | 0.163811 | ||||||||
\(889\) | −6.31044e18 | −0.428744 | ||||||||
\(890\) | −3.82215e19 | −2.57794 | ||||||||
\(891\) | 1.78662e19 | 1.19626 | ||||||||
\(892\) | −2.52691e19 | −1.67965 | ||||||||
\(893\) | −1.86650e19 | −1.23167 | ||||||||
\(894\) | −8.61193e17 | −0.0564166 | ||||||||
\(895\) | −1.21449e18 | −0.0789850 | ||||||||
\(896\) | 1.54247e19 | 0.995901 | ||||||||
\(897\) | 5.18668e17 | 0.0332459 | ||||||||
\(898\) | −5.41639e19 | −3.44678 | ||||||||
\(899\) | −1.11458e19 | −0.704163 | ||||||||
\(900\) | 1.79860e19 | 1.12812 | ||||||||
\(901\) | 4.16790e18 | 0.259541 | ||||||||
\(902\) | −3.47723e18 | −0.214976 | ||||||||
\(903\) | 5.00080e17 | 0.0306951 | ||||||||
\(904\) | 2.54125e19 | 1.54865 | ||||||||
\(905\) | −3.70746e18 | −0.224316 | ||||||||
\(906\) | −3.38747e17 | −0.0203490 | ||||||||
\(907\) | 1.38977e19 | 0.828890 | 0.414445 | − | 0.910074i | \(-0.363976\pi\) | ||||
0.414445 | + | 0.910074i | \(0.363976\pi\) | |||||||
\(908\) | −1.92291e19 | −1.13868 | ||||||||
\(909\) | 2.41841e19 | 1.42188 | ||||||||
\(910\) | 1.02927e19 | 0.600842 | ||||||||
\(911\) | −7.03802e18 | −0.407926 | −0.203963 | − | 0.978979i | \(-0.565382\pi\) | ||||
−0.203963 | + | 0.978979i | \(0.565382\pi\) | |||||||
\(912\) | −5.01388e18 | −0.288541 | ||||||||
\(913\) | 2.38594e19 | 1.36333 | ||||||||
\(914\) | −4.63431e19 | −2.62927 | ||||||||
\(915\) | 9.47657e16 | 0.00533843 | ||||||||
\(916\) | 4.29298e17 | 0.0240125 | ||||||||
\(917\) | 1.15444e19 | 0.641164 | ||||||||
\(918\) | −5.20992e18 | −0.287312 | ||||||||
\(919\) | −6.39596e18 | −0.350231 | −0.175116 | − | 0.984548i | \(-0.556030\pi\) | ||||
−0.175116 | + | 0.984548i | \(0.556030\pi\) | |||||||
\(920\) | 3.59336e19 | 1.95380 | ||||||||
\(921\) | 1.76974e18 | 0.0955479 | ||||||||
\(922\) | −6.30374e19 | −3.37946 | ||||||||
\(923\) | 1.15826e19 | 0.616589 | ||||||||
\(924\) | 1.62856e18 | 0.0860867 | ||||||||
\(925\) | −8.71341e18 | −0.457369 | ||||||||
\(926\) | −6.30687e19 | −3.28732 | ||||||||
\(927\) | −2.08308e19 | −1.07817 | ||||||||
\(928\) | −6.77967e19 | −3.48455 | ||||||||
\(929\) | −8.05207e18 | −0.410966 | −0.205483 | − | 0.978661i | \(-0.565876\pi\) | ||||
−0.205483 | + | 0.978661i | \(0.565876\pi\) | |||||||
\(930\) | 8.78446e17 | 0.0445221 | ||||||||
\(931\) | −2.49696e19 | −1.25672 | ||||||||
\(932\) | −5.34658e19 | −2.67222 | ||||||||
\(933\) | 1.42181e18 | 0.0705683 | ||||||||
\(934\) | 1.19433e19 | 0.588667 | ||||||||
\(935\) | −2.77529e19 | −1.35842 | ||||||||
\(936\) | −4.88604e19 | −2.37500 | ||||||||
\(937\) | 1.55596e19 | 0.751087 | 0.375544 | − | 0.926805i | \(-0.377456\pi\) | ||||
0.375544 | + | 0.926805i | \(0.377456\pi\) | |||||||
\(938\) | 2.06980e18 | 0.0992223 | ||||||||
\(939\) | 1.39817e18 | 0.0665629 | ||||||||
\(940\) | 2.88761e19 | 1.36523 | ||||||||
\(941\) | −1.57748e19 | −0.740681 | −0.370340 | − | 0.928896i | \(-0.620759\pi\) | ||||
−0.370340 | + | 0.928896i | \(0.620759\pi\) | |||||||
\(942\) | 2.96929e18 | 0.138459 | ||||||||
\(943\) | 1.71459e18 | 0.0794024 | ||||||||
\(944\) | 7.23446e19 | 3.32727 | ||||||||
\(945\) | 9.00077e17 | 0.0411124 | ||||||||
\(946\) | −5.67275e19 | −2.57336 | ||||||||
\(947\) | −2.78601e19 | −1.25518 | −0.627592 | − | 0.778542i | \(-0.715960\pi\) | ||||
−0.627592 | + | 0.778542i | \(0.715960\pi\) | |||||||
\(948\) | −2.53584e18 | −0.113467 | ||||||||
\(949\) | −3.23895e19 | −1.43937 | ||||||||
\(950\) | 3.30920e19 | 1.46056 | ||||||||
\(951\) | −3.21092e17 | −0.0140752 | ||||||||
\(952\) | 5.69373e19 | 2.47889 | ||||||||
\(953\) | −3.74684e19 | −1.62017 | −0.810086 | − | 0.586311i | \(-0.800580\pi\) | ||||
−0.810086 | + | 0.586311i | \(0.800580\pi\) | |||||||
\(954\) | 7.65695e18 | 0.328845 | ||||||||
\(955\) | 2.35118e19 | 1.00291 | ||||||||
\(956\) | −1.61073e19 | −0.682413 | ||||||||
\(957\) | −1.65890e18 | −0.0698061 | ||||||||
\(958\) | −6.31408e19 | −2.63897 | ||||||||
\(959\) | −1.00798e19 | −0.418437 | ||||||||
\(960\) | 2.37457e18 | 0.0979089 | ||||||||
\(961\) | −1.51820e19 | −0.621764 | ||||||||
\(962\) | 3.83475e19 | 1.55991 | ||||||||
\(963\) | 2.04343e19 | 0.825635 | ||||||||
\(964\) | 1.14417e20 | 4.59187 | ||||||||
\(965\) | −2.05041e19 | −0.817358 | ||||||||
\(966\) | −1.11037e18 | −0.0439660 | ||||||||
\(967\) | −4.43213e19 | −1.74317 | −0.871586 | − | 0.490243i | \(-0.836908\pi\) | ||||
−0.871586 | + | 0.490243i | \(0.836908\pi\) | |||||||
\(968\) | −3.55654e19 | −1.38943 | ||||||||
\(969\) | −3.46175e18 | −0.134336 | ||||||||
\(970\) | −3.53671e19 | −1.36327 | ||||||||
\(971\) | 7.78932e18 | 0.298246 | 0.149123 | − | 0.988819i | \(-0.452355\pi\) | ||||
0.149123 | + | 0.988819i | \(0.452355\pi\) | |||||||
\(972\) | −1.03875e19 | −0.395074 | ||||||||
\(973\) | −1.64612e19 | −0.621910 | ||||||||
\(974\) | 4.61157e19 | 1.73068 | ||||||||
\(975\) | −4.56137e17 | −0.0170046 | ||||||||
\(976\) | 1.21648e19 | 0.450487 | ||||||||
\(977\) | 1.51495e19 | 0.557292 | 0.278646 | − | 0.960394i | \(-0.410114\pi\) | ||||
0.278646 | + | 0.960394i | \(0.410114\pi\) | |||||||
\(978\) | −1.92606e18 | −0.0703831 | ||||||||
\(979\) | −5.98091e19 | −2.17110 | ||||||||
\(980\) | 3.86296e19 | 1.39300 | ||||||||
\(981\) | 2.00560e19 | 0.718447 | ||||||||
\(982\) | 8.87747e19 | 3.15911 | ||||||||
\(983\) | −2.28813e19 | −0.808879 | −0.404440 | − | 0.914565i | \(-0.632533\pi\) | ||||
−0.404440 | + | 0.914565i | \(0.632533\pi\) | |||||||
\(984\) | 4.14195e17 | 0.0145458 | ||||||||
\(985\) | −1.53795e18 | −0.0536545 | ||||||||
\(986\) | −9.39591e19 | −3.25641 | ||||||||
\(987\) | −5.50783e17 | −0.0189635 | ||||||||
\(988\) | −1.05326e20 | −3.60258 | ||||||||
\(989\) | 2.79718e19 | 0.950483 | ||||||||
\(990\) | −5.09857e19 | −1.72115 | ||||||||
\(991\) | −6.43960e18 | −0.215964 | −0.107982 | − | 0.994153i | \(-0.534439\pi\) | ||||
−0.107982 | + | 0.994153i | \(0.534439\pi\) | |||||||
\(992\) | 5.61774e19 | 1.87170 | ||||||||
\(993\) | 2.60087e18 | 0.0860892 | ||||||||
\(994\) | −2.47962e19 | −0.815407 | ||||||||
\(995\) | 2.49291e19 | 0.814436 | ||||||||
\(996\) | −4.60422e18 | −0.149441 | ||||||||
\(997\) | 2.43126e19 | 0.783994 | 0.391997 | − | 0.919966i | \(-0.371784\pi\) | ||||
0.391997 | + | 0.919966i | \(0.371784\pi\) | |||||||
\(998\) | 8.50773e19 | 2.72562 | ||||||||
\(999\) | 3.35341e18 | 0.106736 |
(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 | 197.14.a.b.1.5 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.b.1.5 | ✓ | 109 | 1.1 | even | 1 | trivial |