Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,18,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(53.1344053299\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −237.844 | −0.656958 | −0.328479 | − | 0.944511i | \(-0.606536\pi\) | ||||
−0.328479 | + | 0.944511i | \(0.606536\pi\) | |||||||
\(3\) | −14184.6 | −1.24821 | −0.624104 | − | 0.781341i | \(-0.714536\pi\) | ||||
−0.624104 | + | 0.781341i | \(0.714536\pi\) | |||||||
\(4\) | −74502.2 | −0.568406 | ||||||||
\(5\) | 1.22166e6 | 1.39864 | 0.699322 | − | 0.714807i | \(-0.253485\pi\) | ||||
0.699322 | + | 0.714807i | \(0.253485\pi\) | |||||||
\(6\) | 3.37373e6 | 0.820020 | ||||||||
\(7\) | 1.05564e7 | 0.692120 | 0.346060 | − | 0.938212i | \(-0.387519\pi\) | ||||
0.346060 | + | 0.938212i | \(0.387519\pi\) | |||||||
\(8\) | 4.88946e7 | 1.03038 | ||||||||
\(9\) | 7.20633e7 | 0.558024 | ||||||||
\(10\) | −2.90566e8 | −0.918850 | ||||||||
\(11\) | 9.82200e8 | 1.38154 | 0.690768 | − | 0.723076i | \(-0.257273\pi\) | ||||
0.690768 | + | 0.723076i | \(0.257273\pi\) | |||||||
\(12\) | 1.05678e9 | 0.709490 | ||||||||
\(13\) | 5.20942e9 | 1.77121 | 0.885607 | − | 0.464435i | \(-0.153743\pi\) | ||||
0.885607 | + | 0.464435i | \(0.153743\pi\) | |||||||
\(14\) | −2.51077e9 | −0.454694 | ||||||||
\(15\) | −1.73289e10 | −1.74580 | ||||||||
\(16\) | −1.86415e9 | −0.108508 | ||||||||
\(17\) | −2.48405e10 | −0.863663 | −0.431831 | − | 0.901954i | \(-0.642132\pi\) | ||||
−0.431831 | + | 0.901954i | \(0.642132\pi\) | |||||||
\(18\) | −1.71398e10 | −0.366598 | ||||||||
\(19\) | 7.35139e10 | 0.993034 | 0.496517 | − | 0.868027i | \(-0.334612\pi\) | ||||
0.496517 | + | 0.868027i | \(0.334612\pi\) | |||||||
\(20\) | −9.10167e10 | −0.794998 | ||||||||
\(21\) | −1.49738e11 | −0.863910 | ||||||||
\(22\) | −2.33611e11 | −0.907611 | ||||||||
\(23\) | −4.63391e11 | −1.23385 | −0.616923 | − | 0.787023i | \(-0.711621\pi\) | ||||
−0.616923 | + | 0.787023i | \(0.711621\pi\) | |||||||
\(24\) | −6.93552e11 | −1.28613 | ||||||||
\(25\) | 7.29526e11 | 0.956204 | ||||||||
\(26\) | −1.23903e12 | −1.16361 | ||||||||
\(27\) | 8.09613e11 | 0.551678 | ||||||||
\(28\) | −7.86473e11 | −0.393406 | ||||||||
\(29\) | 5.00246e11 | 0.185695 | ||||||||
\(30\) | 4.12157e12 | 1.14692 | ||||||||
\(31\) | 4.00808e12 | 0.844038 | 0.422019 | − | 0.906587i | \(-0.361322\pi\) | ||||
0.422019 | + | 0.906587i | \(0.361322\pi\) | |||||||
\(32\) | −5.96534e12 | −0.959092 | ||||||||
\(33\) | −1.39321e13 | −1.72444 | ||||||||
\(34\) | 5.90816e12 | 0.567390 | ||||||||
\(35\) | 1.28964e13 | 0.968030 | ||||||||
\(36\) | −5.36887e12 | −0.317184 | ||||||||
\(37\) | 9.74612e12 | 0.456160 | 0.228080 | − | 0.973642i | \(-0.426755\pi\) | ||||
0.228080 | + | 0.973642i | \(0.426755\pi\) | |||||||
\(38\) | −1.74849e13 | −0.652381 | ||||||||
\(39\) | −7.38937e13 | −2.21084 | ||||||||
\(40\) | 5.97328e13 | 1.44113 | ||||||||
\(41\) | 5.79656e13 | 1.13372 | 0.566862 | − | 0.823813i | \(-0.308157\pi\) | ||||
0.566862 | + | 0.823813i | \(0.308157\pi\) | |||||||
\(42\) | 3.56144e13 | 0.567553 | ||||||||
\(43\) | −8.74679e13 | −1.14121 | −0.570607 | − | 0.821223i | \(-0.693292\pi\) | ||||
−0.570607 | + | 0.821223i | \(0.693292\pi\) | |||||||
\(44\) | −7.31760e13 | −0.785274 | ||||||||
\(45\) | 8.80372e13 | 0.780477 | ||||||||
\(46\) | 1.10215e14 | 0.810585 | ||||||||
\(47\) | 8.94917e13 | 0.548215 | 0.274107 | − | 0.961699i | \(-0.411618\pi\) | ||||
0.274107 | + | 0.961699i | \(0.411618\pi\) | |||||||
\(48\) | 2.64423e13 | 0.135440 | ||||||||
\(49\) | −1.21193e14 | −0.520970 | ||||||||
\(50\) | −1.73513e14 | −0.628186 | ||||||||
\(51\) | 3.52353e14 | 1.07803 | ||||||||
\(52\) | −3.88113e14 | −1.00677 | ||||||||
\(53\) | 6.03303e14 | 1.33104 | 0.665519 | − | 0.746381i | \(-0.268210\pi\) | ||||
0.665519 | + | 0.746381i | \(0.268210\pi\) | |||||||
\(54\) | −1.92562e14 | −0.362429 | ||||||||
\(55\) | 1.19992e15 | 1.93228 | ||||||||
\(56\) | 5.16150e14 | 0.713145 | ||||||||
\(57\) | −1.04277e15 | −1.23951 | ||||||||
\(58\) | −1.18981e14 | −0.121994 | ||||||||
\(59\) | 9.08899e14 | 0.805886 | 0.402943 | − | 0.915225i | \(-0.367987\pi\) | ||||
0.402943 | + | 0.915225i | \(0.367987\pi\) | |||||||
\(60\) | 1.29104e15 | 0.992323 | ||||||||
\(61\) | −2.23542e15 | −1.49298 | −0.746492 | − | 0.665395i | \(-0.768263\pi\) | ||||
−0.746492 | + | 0.665395i | \(0.768263\pi\) | |||||||
\(62\) | −9.53298e14 | −0.554497 | ||||||||
\(63\) | 7.60728e14 | 0.386220 | ||||||||
\(64\) | 1.66316e15 | 0.738591 | ||||||||
\(65\) | 6.36417e15 | 2.47730 | ||||||||
\(66\) | 3.31368e15 | 1.13289 | ||||||||
\(67\) | 1.04268e15 | 0.313702 | 0.156851 | − | 0.987622i | \(-0.449866\pi\) | ||||
0.156851 | + | 0.987622i | \(0.449866\pi\) | |||||||
\(68\) | 1.85067e15 | 0.490911 | ||||||||
\(69\) | 6.57303e15 | 1.54010 | ||||||||
\(70\) | −3.06732e15 | −0.635955 | ||||||||
\(71\) | 2.03035e15 | 0.373143 | 0.186571 | − | 0.982441i | \(-0.440262\pi\) | ||||
0.186571 | + | 0.982441i | \(0.440262\pi\) | |||||||
\(72\) | 3.52351e15 | 0.574975 | ||||||||
\(73\) | −3.65531e15 | −0.530493 | −0.265246 | − | 0.964181i | \(-0.585453\pi\) | ||||
−0.265246 | + | 0.964181i | \(0.585453\pi\) | |||||||
\(74\) | −2.31806e15 | −0.299678 | ||||||||
\(75\) | −1.03480e16 | −1.19354 | ||||||||
\(76\) | −5.47695e15 | −0.564447 | ||||||||
\(77\) | 1.03685e16 | 0.956189 | ||||||||
\(78\) | 1.75752e16 | 1.45243 | ||||||||
\(79\) | 6.95275e15 | 0.515616 | 0.257808 | − | 0.966196i | \(-0.417000\pi\) | ||||
0.257808 | + | 0.966196i | \(0.417000\pi\) | |||||||
\(80\) | −2.27737e15 | −0.151764 | ||||||||
\(81\) | −2.07903e16 | −1.24663 | ||||||||
\(82\) | −1.37868e16 | −0.744809 | ||||||||
\(83\) | −1.05156e16 | −0.512470 | −0.256235 | − | 0.966615i | \(-0.582482\pi\) | ||||
−0.256235 | + | 0.966615i | \(0.582482\pi\) | |||||||
\(84\) | 1.11558e16 | 0.491052 | ||||||||
\(85\) | −3.03467e16 | −1.20796 | ||||||||
\(86\) | 2.08037e16 | 0.749729 | ||||||||
\(87\) | −7.09581e15 | −0.231786 | ||||||||
\(88\) | 4.80243e16 | 1.42350 | ||||||||
\(89\) | −3.63273e16 | −0.978179 | −0.489089 | − | 0.872234i | \(-0.662671\pi\) | ||||
−0.489089 | + | 0.872234i | \(0.662671\pi\) | |||||||
\(90\) | −2.09391e16 | −0.512740 | ||||||||
\(91\) | 5.49926e16 | 1.22589 | ||||||||
\(92\) | 3.45236e16 | 0.701326 | ||||||||
\(93\) | −5.68531e16 | −1.05354 | ||||||||
\(94\) | −2.12851e16 | −0.360154 | ||||||||
\(95\) | 8.98094e16 | 1.38890 | ||||||||
\(96\) | 8.46160e16 | 1.19715 | ||||||||
\(97\) | 1.37559e17 | 1.78209 | 0.891043 | − | 0.453919i | \(-0.149975\pi\) | ||||
0.891043 | + | 0.453919i | \(0.149975\pi\) | |||||||
\(98\) | 2.88251e16 | 0.342255 | ||||||||
\(99\) | 7.07806e16 | 0.770930 | ||||||||
\(100\) | −5.43512e16 | −0.543512 | ||||||||
\(101\) | −2.04386e17 | −1.87810 | −0.939050 | − | 0.343781i | \(-0.888292\pi\) | ||||
−0.939050 | + | 0.343781i | \(0.888292\pi\) | |||||||
\(102\) | −8.38050e16 | −0.708221 | ||||||||
\(103\) | −1.18180e16 | −0.0919234 | −0.0459617 | − | 0.998943i | \(-0.514635\pi\) | ||||
−0.0459617 | + | 0.998943i | \(0.514635\pi\) | |||||||
\(104\) | 2.54713e17 | 1.82502 | ||||||||
\(105\) | −1.82930e17 | −1.20830 | ||||||||
\(106\) | −1.43492e17 | −0.874436 | ||||||||
\(107\) | −2.47034e17 | −1.38994 | −0.694969 | − | 0.719040i | \(-0.744582\pi\) | ||||
−0.694969 | + | 0.719040i | \(0.744582\pi\) | |||||||
\(108\) | −6.03179e16 | −0.313577 | ||||||||
\(109\) | −5.51412e15 | −0.0265064 | −0.0132532 | − | 0.999912i | \(-0.504219\pi\) | ||||
−0.0132532 | + | 0.999912i | \(0.504219\pi\) | |||||||
\(110\) | −2.85394e17 | −1.26942 | ||||||||
\(111\) | −1.38245e17 | −0.569383 | ||||||||
\(112\) | −1.96787e16 | −0.0751005 | ||||||||
\(113\) | 2.51475e16 | 0.0889872 | 0.0444936 | − | 0.999010i | \(-0.485833\pi\) | ||||
0.0444936 | + | 0.999010i | \(0.485833\pi\) | |||||||
\(114\) | 2.48016e17 | 0.814308 | ||||||||
\(115\) | −5.66109e17 | −1.72571 | ||||||||
\(116\) | −3.72694e16 | −0.105550 | ||||||||
\(117\) | 3.75408e17 | 0.988380 | ||||||||
\(118\) | −2.16176e17 | −0.529433 | ||||||||
\(119\) | −2.62225e17 | −0.597758 | ||||||||
\(120\) | −8.47288e17 | −1.79883 | ||||||||
\(121\) | 4.59270e17 | 0.908642 | ||||||||
\(122\) | 5.31681e17 | 0.980827 | ||||||||
\(123\) | −8.22220e17 | −1.41512 | ||||||||
\(124\) | −2.98611e17 | −0.479757 | ||||||||
\(125\) | −4.08205e16 | −0.0612552 | ||||||||
\(126\) | −1.80935e17 | −0.253730 | ||||||||
\(127\) | −4.74031e17 | −0.621549 | −0.310774 | − | 0.950484i | \(-0.600588\pi\) | ||||
−0.310774 | + | 0.950484i | \(0.600588\pi\) | |||||||
\(128\) | 3.86316e17 | 0.473869 | ||||||||
\(129\) | 1.24070e18 | 1.42447 | ||||||||
\(130\) | −1.51368e18 | −1.62748 | ||||||||
\(131\) | 1.16841e18 | 1.17703 | 0.588517 | − | 0.808485i | \(-0.299712\pi\) | ||||
0.588517 | + | 0.808485i | \(0.299712\pi\) | |||||||
\(132\) | 1.03797e18 | 0.980185 | ||||||||
\(133\) | 7.76041e17 | 0.687299 | ||||||||
\(134\) | −2.47996e17 | −0.206089 | ||||||||
\(135\) | 9.89076e17 | 0.771601 | ||||||||
\(136\) | −1.21457e18 | −0.889898 | ||||||||
\(137\) | 2.80722e18 | 1.93264 | 0.966322 | − | 0.257335i | \(-0.0828443\pi\) | ||||
0.966322 | + | 0.257335i | \(0.0828443\pi\) | |||||||
\(138\) | −1.56336e18 | −1.01178 | ||||||||
\(139\) | −2.89479e17 | −0.176194 | −0.0880971 | − | 0.996112i | \(-0.528079\pi\) | ||||
−0.0880971 | + | 0.996112i | \(0.528079\pi\) | |||||||
\(140\) | −9.60806e17 | −0.550234 | ||||||||
\(141\) | −1.26941e18 | −0.684286 | ||||||||
\(142\) | −4.82907e17 | −0.245139 | ||||||||
\(143\) | 5.11670e18 | 2.44700 | ||||||||
\(144\) | −1.34337e17 | −0.0605500 | ||||||||
\(145\) | 6.11133e17 | 0.259722 | ||||||||
\(146\) | 8.69394e17 | 0.348512 | ||||||||
\(147\) | 1.71908e18 | 0.650278 | ||||||||
\(148\) | −7.26107e17 | −0.259284 | ||||||||
\(149\) | −9.75114e17 | −0.328830 | −0.164415 | − | 0.986391i | \(-0.552574\pi\) | ||||
−0.164415 | + | 0.986391i | \(0.552574\pi\) | |||||||
\(150\) | 2.46122e18 | 0.784107 | ||||||||
\(151\) | −1.42811e18 | −0.429988 | −0.214994 | − | 0.976615i | \(-0.568973\pi\) | ||||
−0.214994 | + | 0.976615i | \(0.568973\pi\) | |||||||
\(152\) | 3.59444e18 | 1.02320 | ||||||||
\(153\) | −1.79009e18 | −0.481945 | ||||||||
\(154\) | −2.46608e18 | −0.628176 | ||||||||
\(155\) | 4.89653e18 | 1.18051 | ||||||||
\(156\) | 5.50524e18 | 1.25666 | ||||||||
\(157\) | 8.21807e18 | 1.77673 | 0.888367 | − | 0.459134i | \(-0.151840\pi\) | ||||
0.888367 | + | 0.459134i | \(0.151840\pi\) | |||||||
\(158\) | −1.65367e18 | −0.338738 | ||||||||
\(159\) | −8.55762e18 | −1.66141 | ||||||||
\(160\) | −7.28764e18 | −1.34143 | ||||||||
\(161\) | −4.89173e18 | −0.853970 | ||||||||
\(162\) | 4.94486e18 | 0.818986 | ||||||||
\(163\) | 7.38540e18 | 1.16086 | 0.580429 | − | 0.814311i | \(-0.302885\pi\) | ||||
0.580429 | + | 0.814311i | \(0.302885\pi\) | |||||||
\(164\) | −4.31856e18 | −0.644416 | ||||||||
\(165\) | −1.70204e19 | −2.41188 | ||||||||
\(166\) | 2.50106e18 | 0.336671 | ||||||||
\(167\) | −3.96033e17 | −0.0506572 | −0.0253286 | − | 0.999679i | \(-0.508063\pi\) | ||||
−0.0253286 | + | 0.999679i | \(0.508063\pi\) | |||||||
\(168\) | −7.32139e18 | −0.890153 | ||||||||
\(169\) | 1.84877e19 | 2.13720 | ||||||||
\(170\) | 7.21779e18 | 0.793576 | ||||||||
\(171\) | 5.29766e18 | 0.554137 | ||||||||
\(172\) | 6.51655e18 | 0.648673 | ||||||||
\(173\) | −1.63389e19 | −1.54821 | −0.774106 | − | 0.633056i | \(-0.781800\pi\) | ||||
−0.774106 | + | 0.633056i | \(0.781800\pi\) | |||||||
\(174\) | 1.68770e18 | 0.152274 | ||||||||
\(175\) | 7.70115e18 | 0.661808 | ||||||||
\(176\) | −1.83097e18 | −0.149908 | ||||||||
\(177\) | −1.28924e19 | −1.00591 | ||||||||
\(178\) | 8.64024e18 | 0.642622 | ||||||||
\(179\) | 2.73924e19 | 1.94258 | 0.971289 | − | 0.237901i | \(-0.0764595\pi\) | ||||
0.971289 | + | 0.237901i | \(0.0764595\pi\) | |||||||
\(180\) | −6.55896e18 | −0.443628 | ||||||||
\(181\) | −8.93353e18 | −0.576441 | −0.288221 | − | 0.957564i | \(-0.593064\pi\) | ||||
−0.288221 | + | 0.957564i | \(0.593064\pi\) | |||||||
\(182\) | −1.30797e19 | −0.805360 | ||||||||
\(183\) | 3.17085e19 | 1.86355 | ||||||||
\(184\) | −2.26573e19 | −1.27133 | ||||||||
\(185\) | 1.19065e19 | 0.638005 | ||||||||
\(186\) | 1.35222e19 | 0.692128 | ||||||||
\(187\) | −2.43983e19 | −1.19318 | ||||||||
\(188\) | −6.66732e18 | −0.311609 | ||||||||
\(189\) | 8.54659e18 | 0.381828 | ||||||||
\(190\) | −2.13606e19 | −0.912449 | ||||||||
\(191\) | 7.52613e18 | 0.307460 | 0.153730 | − | 0.988113i | \(-0.450871\pi\) | ||||
0.153730 | + | 0.988113i | \(0.450871\pi\) | |||||||
\(192\) | −2.35913e19 | −0.921915 | ||||||||
\(193\) | −4.31029e19 | −1.61165 | −0.805823 | − | 0.592156i | \(-0.798277\pi\) | ||||
−0.805823 | + | 0.592156i | \(0.798277\pi\) | |||||||
\(194\) | −3.27175e19 | −1.17076 | ||||||||
\(195\) | −9.02733e19 | −3.09218 | ||||||||
\(196\) | 9.02917e18 | 0.296122 | ||||||||
\(197\) | −1.81537e19 | −0.570167 | −0.285083 | − | 0.958503i | \(-0.592021\pi\) | ||||
−0.285083 | + | 0.958503i | \(0.592021\pi\) | |||||||
\(198\) | −1.68348e19 | −0.506469 | ||||||||
\(199\) | 2.25070e19 | 0.648733 | 0.324367 | − | 0.945931i | \(-0.394849\pi\) | ||||
0.324367 | + | 0.945931i | \(0.394849\pi\) | |||||||
\(200\) | 3.56699e19 | 0.985250 | ||||||||
\(201\) | −1.47901e19 | −0.391565 | ||||||||
\(202\) | 4.86119e19 | 1.23383 | ||||||||
\(203\) | 5.28079e18 | 0.128524 | ||||||||
\(204\) | −2.62510e19 | −0.612760 | ||||||||
\(205\) | 7.08145e19 | 1.58568 | ||||||||
\(206\) | 2.81083e18 | 0.0603898 | ||||||||
\(207\) | −3.33935e19 | −0.688516 | ||||||||
\(208\) | −9.71115e18 | −0.192191 | ||||||||
\(209\) | 7.22054e19 | 1.37191 | ||||||||
\(210\) | 4.35088e19 | 0.793804 | ||||||||
\(211\) | 7.39746e19 | 1.29623 | 0.648115 | − | 0.761543i | \(-0.275558\pi\) | ||||
0.648115 | + | 0.761543i | \(0.275558\pi\) | |||||||
\(212\) | −4.49474e19 | −0.756570 | ||||||||
\(213\) | −2.87997e19 | −0.465760 | ||||||||
\(214\) | 5.87557e19 | 0.913131 | ||||||||
\(215\) | −1.06856e20 | −1.59615 | ||||||||
\(216\) | 3.95857e19 | 0.568436 | ||||||||
\(217\) | 4.23108e19 | 0.584176 | ||||||||
\(218\) | 1.31150e18 | 0.0174136 | ||||||||
\(219\) | 5.18492e19 | 0.662166 | ||||||||
\(220\) | −8.93966e19 | −1.09832 | ||||||||
\(221\) | −1.29405e20 | −1.52973 | ||||||||
\(222\) | 3.28808e19 | 0.374061 | ||||||||
\(223\) | 5.06723e19 | 0.554854 | 0.277427 | − | 0.960747i | \(-0.410518\pi\) | ||||
0.277427 | + | 0.960747i | \(0.410518\pi\) | |||||||
\(224\) | −6.29724e19 | −0.663807 | ||||||||
\(225\) | 5.25720e19 | 0.533585 | ||||||||
\(226\) | −5.98118e18 | −0.0584608 | ||||||||
\(227\) | 6.30244e19 | 0.593320 | 0.296660 | − | 0.954983i | \(-0.404127\pi\) | ||||
0.296660 | + | 0.954983i | \(0.404127\pi\) | |||||||
\(228\) | 7.76884e19 | 0.704547 | ||||||||
\(229\) | −1.57688e20 | −1.37784 | −0.688918 | − | 0.724840i | \(-0.741914\pi\) | ||||
−0.688918 | + | 0.724840i | \(0.741914\pi\) | |||||||
\(230\) | 1.34646e20 | 1.13372 | ||||||||
\(231\) | −1.47073e20 | −1.19352 | ||||||||
\(232\) | 2.44594e19 | 0.191336 | ||||||||
\(233\) | 3.00771e19 | 0.226836 | 0.113418 | − | 0.993547i | \(-0.463820\pi\) | ||||
0.113418 | + | 0.993547i | \(0.463820\pi\) | |||||||
\(234\) | −8.92887e19 | −0.649324 | ||||||||
\(235\) | 1.09329e20 | 0.766757 | ||||||||
\(236\) | −6.77150e19 | −0.458071 | ||||||||
\(237\) | −9.86221e19 | −0.643596 | ||||||||
\(238\) | 6.23688e19 | 0.392702 | ||||||||
\(239\) | −1.38253e20 | −0.840026 | −0.420013 | − | 0.907518i | \(-0.637974\pi\) | ||||
−0.420013 | + | 0.907518i | \(0.637974\pi\) | |||||||
\(240\) | 3.23036e19 | 0.189433 | ||||||||
\(241\) | 1.57658e20 | 0.892422 | 0.446211 | − | 0.894928i | \(-0.352773\pi\) | ||||
0.446211 | + | 0.894928i | \(0.352773\pi\) | |||||||
\(242\) | −1.09235e20 | −0.596939 | ||||||||
\(243\) | 1.90349e20 | 1.00438 | ||||||||
\(244\) | 1.66543e20 | 0.848621 | ||||||||
\(245\) | −1.48058e20 | −0.728651 | ||||||||
\(246\) | 1.95560e20 | 0.929677 | ||||||||
\(247\) | 3.82965e20 | 1.75888 | ||||||||
\(248\) | 1.95974e20 | 0.869677 | ||||||||
\(249\) | 1.49159e20 | 0.639669 | ||||||||
\(250\) | 9.70891e18 | 0.0402421 | ||||||||
\(251\) | 2.64777e19 | 0.106085 | 0.0530424 | − | 0.998592i | \(-0.483108\pi\) | ||||
0.0530424 | + | 0.998592i | \(0.483108\pi\) | |||||||
\(252\) | −5.66758e19 | −0.219530 | ||||||||
\(253\) | −4.55143e20 | −1.70460 | ||||||||
\(254\) | 1.12746e20 | 0.408331 | ||||||||
\(255\) | 4.30457e20 | 1.50778 | ||||||||
\(256\) | −3.09877e20 | −1.04990 | ||||||||
\(257\) | 2.73778e19 | 0.0897360 | 0.0448680 | − | 0.998993i | \(-0.485713\pi\) | ||||
0.0448680 | + | 0.998993i | \(0.485713\pi\) | |||||||
\(258\) | −2.95093e20 | −0.935818 | ||||||||
\(259\) | 1.02884e20 | 0.315718 | ||||||||
\(260\) | −4.74144e20 | −1.40811 | ||||||||
\(261\) | 3.60494e19 | 0.103622 | ||||||||
\(262\) | −2.77899e20 | −0.773261 | ||||||||
\(263\) | 6.19094e20 | 1.66776 | 0.833878 | − | 0.551949i | \(-0.186116\pi\) | ||||
0.833878 | + | 0.551949i | \(0.186116\pi\) | |||||||
\(264\) | −6.81207e20 | −1.77683 | ||||||||
\(265\) | 7.37034e20 | 1.86165 | ||||||||
\(266\) | −1.84577e20 | −0.451526 | ||||||||
\(267\) | 5.15289e20 | 1.22097 | ||||||||
\(268\) | −7.76822e19 | −0.178310 | ||||||||
\(269\) | 4.77375e20 | 1.06161 | 0.530805 | − | 0.847494i | \(-0.321890\pi\) | ||||
0.530805 | + | 0.847494i | \(0.321890\pi\) | |||||||
\(270\) | −2.35246e20 | −0.506909 | ||||||||
\(271\) | 8.30074e20 | 1.73332 | 0.866658 | − | 0.498903i | \(-0.166264\pi\) | ||||
0.866658 | + | 0.498903i | \(0.166264\pi\) | |||||||
\(272\) | 4.63064e19 | 0.0937142 | ||||||||
\(273\) | −7.80050e20 | −1.53017 | ||||||||
\(274\) | −6.67681e20 | −1.26967 | ||||||||
\(275\) | 7.16540e20 | 1.32103 | ||||||||
\(276\) | −4.89705e20 | −0.875401 | ||||||||
\(277\) | −2.63424e20 | −0.456644 | −0.228322 | − | 0.973586i | \(-0.573324\pi\) | ||||
−0.228322 | + | 0.973586i | \(0.573324\pi\) | |||||||
\(278\) | 6.88510e19 | 0.115752 | ||||||||
\(279\) | 2.88836e20 | 0.470994 | ||||||||
\(280\) | 6.30562e20 | 0.997435 | ||||||||
\(281\) | 6.96762e20 | 1.06925 | 0.534627 | − | 0.845088i | \(-0.320452\pi\) | ||||
0.534627 | + | 0.845088i | \(0.320452\pi\) | |||||||
\(282\) | 3.01921e20 | 0.449547 | ||||||||
\(283\) | −9.79407e20 | −1.41507 | −0.707536 | − | 0.706678i | \(-0.750193\pi\) | ||||
−0.707536 | + | 0.706678i | \(0.750193\pi\) | |||||||
\(284\) | −1.51265e20 | −0.212097 | ||||||||
\(285\) | −1.27391e21 | −1.73364 | ||||||||
\(286\) | −1.21698e21 | −1.60757 | ||||||||
\(287\) | 6.11907e20 | 0.784674 | ||||||||
\(288\) | −4.29882e20 | −0.535196 | ||||||||
\(289\) | −2.10191e20 | −0.254087 | ||||||||
\(290\) | −1.45355e20 | −0.170626 | ||||||||
\(291\) | −1.95122e21 | −2.22441 | ||||||||
\(292\) | 2.72328e20 | 0.301536 | ||||||||
\(293\) | −7.92943e20 | −0.852839 | −0.426420 | − | 0.904525i | \(-0.640225\pi\) | ||||
−0.426420 | + | 0.904525i | \(0.640225\pi\) | |||||||
\(294\) | −4.08874e20 | −0.427206 | ||||||||
\(295\) | 1.11037e21 | 1.12715 | ||||||||
\(296\) | 4.76533e20 | 0.470017 | ||||||||
\(297\) | 7.95203e20 | 0.762163 | ||||||||
\(298\) | 2.31925e20 | 0.216028 | ||||||||
\(299\) | −2.41400e21 | −2.18541 | ||||||||
\(300\) | 7.70952e20 | 0.678417 | ||||||||
\(301\) | −9.23344e20 | −0.789857 | ||||||||
\(302\) | 3.39667e20 | 0.282484 | ||||||||
\(303\) | 2.89913e21 | 2.34426 | ||||||||
\(304\) | −1.37041e20 | −0.107752 | ||||||||
\(305\) | −2.73093e21 | −2.08815 | ||||||||
\(306\) | 4.25762e20 | 0.316617 | ||||||||
\(307\) | 6.85552e20 | 0.495866 | 0.247933 | − | 0.968777i | \(-0.420249\pi\) | ||||
0.247933 | + | 0.968777i | \(0.420249\pi\) | |||||||
\(308\) | −7.72474e20 | −0.543504 | ||||||||
\(309\) | 1.67633e20 | 0.114740 | ||||||||
\(310\) | −1.16461e21 | −0.775544 | ||||||||
\(311\) | 6.30454e20 | 0.408498 | 0.204249 | − | 0.978919i | \(-0.434525\pi\) | ||||
0.204249 | + | 0.978919i | \(0.434525\pi\) | |||||||
\(312\) | −3.61300e21 | −2.27800 | ||||||||
\(313\) | −1.36573e21 | −0.837988 | −0.418994 | − | 0.907989i | \(-0.637617\pi\) | ||||
−0.418994 | + | 0.907989i | \(0.637617\pi\) | |||||||
\(314\) | −1.95462e21 | −1.16724 | ||||||||
\(315\) | 9.29354e20 | 0.540184 | ||||||||
\(316\) | −5.17994e20 | −0.293079 | ||||||||
\(317\) | −1.46033e21 | −0.804352 | −0.402176 | − | 0.915562i | \(-0.631746\pi\) | ||||
−0.402176 | + | 0.915562i | \(0.631746\pi\) | |||||||
\(318\) | 2.03538e21 | 1.09148 | ||||||||
\(319\) | 4.91342e20 | 0.256545 | ||||||||
\(320\) | 2.03182e21 | 1.03303 | ||||||||
\(321\) | 3.50409e21 | 1.73493 | ||||||||
\(322\) | 1.16347e21 | 0.561023 | ||||||||
\(323\) | −1.82612e21 | −0.857646 | ||||||||
\(324\) | 1.54892e21 | 0.708594 | ||||||||
\(325\) | 3.80041e21 | 1.69364 | ||||||||
\(326\) | −1.75657e21 | −0.762635 | ||||||||
\(327\) | 7.82157e19 | 0.0330855 | ||||||||
\(328\) | 2.83421e21 | 1.16816 | ||||||||
\(329\) | 9.44708e20 | 0.379431 | ||||||||
\(330\) | 4.04820e21 | 1.58451 | ||||||||
\(331\) | 1.56688e21 | 0.597721 | 0.298860 | − | 0.954297i | \(-0.403394\pi\) | ||||
0.298860 | + | 0.954297i | \(0.403394\pi\) | |||||||
\(332\) | 7.83432e20 | 0.291291 | ||||||||
\(333\) | 7.02338e20 | 0.254548 | ||||||||
\(334\) | 9.41941e19 | 0.0332796 | ||||||||
\(335\) | 1.27381e21 | 0.438757 | ||||||||
\(336\) | 2.79135e20 | 0.0937411 | ||||||||
\(337\) | 2.53384e21 | 0.829708 | 0.414854 | − | 0.909888i | \(-0.363833\pi\) | ||||
0.414854 | + | 0.909888i | \(0.363833\pi\) | |||||||
\(338\) | −4.39718e21 | −1.40405 | ||||||||
\(339\) | −3.56707e20 | −0.111075 | ||||||||
\(340\) | 2.26090e21 | 0.686610 | ||||||||
\(341\) | 3.93674e21 | 1.16607 | ||||||||
\(342\) | −1.26002e21 | −0.364045 | ||||||||
\(343\) | −3.73510e21 | −1.05269 | ||||||||
\(344\) | −4.27671e21 | −1.17588 | ||||||||
\(345\) | 8.03004e21 | 2.15405 | ||||||||
\(346\) | 3.88611e21 | 1.01711 | ||||||||
\(347\) | −3.01289e21 | −0.769453 | −0.384727 | − | 0.923031i | \(-0.625704\pi\) | ||||
−0.384727 | + | 0.923031i | \(0.625704\pi\) | |||||||
\(348\) | 5.28653e20 | 0.131749 | ||||||||
\(349\) | −1.08133e21 | −0.262992 | −0.131496 | − | 0.991317i | \(-0.541978\pi\) | ||||
−0.131496 | + | 0.991317i | \(0.541978\pi\) | |||||||
\(350\) | −1.83167e21 | −0.434780 | ||||||||
\(351\) | 4.21762e21 | 0.977140 | ||||||||
\(352\) | −5.85916e21 | −1.32502 | ||||||||
\(353\) | −6.80308e21 | −1.50183 | −0.750915 | − | 0.660399i | \(-0.770387\pi\) | ||||
−0.750915 | + | 0.660399i | \(0.770387\pi\) | |||||||
\(354\) | 3.06638e21 | 0.660843 | ||||||||
\(355\) | 2.48041e21 | 0.521894 | ||||||||
\(356\) | 2.70646e21 | 0.556003 | ||||||||
\(357\) | 3.71957e21 | 0.746127 | ||||||||
\(358\) | −6.51511e21 | −1.27619 | ||||||||
\(359\) | −6.03010e21 | −1.15351 | −0.576755 | − | 0.816917i | \(-0.695681\pi\) | ||||
−0.576755 | + | 0.816917i | \(0.695681\pi\) | |||||||
\(360\) | 4.30455e21 | 0.804185 | ||||||||
\(361\) | −7.60878e19 | −0.0138837 | ||||||||
\(362\) | 2.12479e21 | 0.378698 | ||||||||
\(363\) | −6.51458e21 | −1.13417 | ||||||||
\(364\) | −4.09707e21 | −0.696806 | ||||||||
\(365\) | −4.46556e21 | −0.741971 | ||||||||
\(366\) | −7.54169e21 | −1.22428 | ||||||||
\(367\) | −5.73509e21 | −0.909658 | −0.454829 | − | 0.890579i | \(-0.650300\pi\) | ||||
−0.454829 | + | 0.890579i | \(0.650300\pi\) | |||||||
\(368\) | 8.63831e20 | 0.133882 | ||||||||
\(369\) | 4.17719e21 | 0.632646 | ||||||||
\(370\) | −2.83189e21 | −0.419143 | ||||||||
\(371\) | 6.36869e21 | 0.921238 | ||||||||
\(372\) | 4.23568e21 | 0.598836 | ||||||||
\(373\) | −6.10804e21 | −0.844067 | −0.422033 | − | 0.906580i | \(-0.638684\pi\) | ||||
−0.422033 | + | 0.906580i | \(0.638684\pi\) | |||||||
\(374\) | 5.80300e21 | 0.783870 | ||||||||
\(375\) | 5.79023e20 | 0.0764592 | ||||||||
\(376\) | 4.37566e21 | 0.564868 | ||||||||
\(377\) | 2.60600e21 | 0.328906 | ||||||||
\(378\) | −2.03276e21 | −0.250845 | ||||||||
\(379\) | 5.55696e21 | 0.670508 | 0.335254 | − | 0.942128i | \(-0.391178\pi\) | ||||
0.335254 | + | 0.942128i | \(0.391178\pi\) | |||||||
\(380\) | −6.69099e21 | −0.789460 | ||||||||
\(381\) | 6.72395e21 | 0.775822 | ||||||||
\(382\) | −1.79005e21 | −0.201988 | ||||||||
\(383\) | 4.05111e21 | 0.447079 | 0.223540 | − | 0.974695i | \(-0.428239\pi\) | ||||
0.223540 | + | 0.974695i | \(0.428239\pi\) | |||||||
\(384\) | −5.47975e21 | −0.591487 | ||||||||
\(385\) | 1.26668e22 | 1.33737 | ||||||||
\(386\) | 1.02518e22 | 1.05878 | ||||||||
\(387\) | −6.30323e21 | −0.636825 | ||||||||
\(388\) | −1.02484e22 | −1.01295 | ||||||||
\(389\) | −1.55408e22 | −1.50280 | −0.751399 | − | 0.659848i | \(-0.770621\pi\) | ||||
−0.751399 | + | 0.659848i | \(0.770621\pi\) | |||||||
\(390\) | 2.14710e22 | 2.03143 | ||||||||
\(391\) | 1.15109e22 | 1.06563 | ||||||||
\(392\) | −5.92570e21 | −0.536795 | ||||||||
\(393\) | −1.65734e22 | −1.46918 | ||||||||
\(394\) | 4.31775e21 | 0.374575 | ||||||||
\(395\) | 8.49392e21 | 0.721162 | ||||||||
\(396\) | −5.27331e21 | −0.438202 | ||||||||
\(397\) | −1.02208e22 | −0.831314 | −0.415657 | − | 0.909521i | \(-0.636448\pi\) | ||||
−0.415657 | + | 0.909521i | \(0.636448\pi\) | |||||||
\(398\) | −5.35316e21 | −0.426191 | ||||||||
\(399\) | −1.10078e22 | −0.857892 | ||||||||
\(400\) | −1.35995e21 | −0.103756 | ||||||||
\(401\) | −8.17444e21 | −0.610563 | −0.305282 | − | 0.952262i | \(-0.598751\pi\) | ||||
−0.305282 | + | 0.952262i | \(0.598751\pi\) | |||||||
\(402\) | 3.51773e21 | 0.257242 | ||||||||
\(403\) | 2.08798e22 | 1.49497 | ||||||||
\(404\) | 1.52272e22 | 1.06752 | ||||||||
\(405\) | −2.53988e22 | −1.74360 | ||||||||
\(406\) | −1.25601e21 | −0.0844345 | ||||||||
\(407\) | 9.57265e21 | 0.630202 | ||||||||
\(408\) | 1.72282e22 | 1.11078 | ||||||||
\(409\) | −1.63861e22 | −1.03473 | −0.517364 | − | 0.855765i | \(-0.673087\pi\) | ||||
−0.517364 | + | 0.855765i | \(0.673087\pi\) | |||||||
\(410\) | −1.68428e22 | −1.04172 | ||||||||
\(411\) | −3.98194e22 | −2.41234 | ||||||||
\(412\) | 8.80463e20 | 0.0522498 | ||||||||
\(413\) | 9.59468e21 | 0.557770 | ||||||||
\(414\) | 7.94245e21 | 0.452326 | ||||||||
\(415\) | −1.28465e22 | −0.716763 | ||||||||
\(416\) | −3.10760e22 | −1.69876 | ||||||||
\(417\) | 4.10615e21 | 0.219927 | ||||||||
\(418\) | −1.71736e22 | −0.901288 | ||||||||
\(419\) | 2.91601e22 | 1.49958 | 0.749789 | − | 0.661677i | \(-0.230155\pi\) | ||||
0.749789 | + | 0.661677i | \(0.230155\pi\) | |||||||
\(420\) | 1.36287e22 | 0.686807 | ||||||||
\(421\) | 1.82872e22 | 0.903128 | 0.451564 | − | 0.892239i | \(-0.350866\pi\) | ||||
0.451564 | + | 0.892239i | \(0.350866\pi\) | |||||||
\(422\) | −1.75944e22 | −0.851568 | ||||||||
\(423\) | 6.44907e21 | 0.305917 | ||||||||
\(424\) | 2.94983e22 | 1.37147 | ||||||||
\(425\) | −1.81218e22 | −0.825838 | ||||||||
\(426\) | 6.84985e21 | 0.305985 | ||||||||
\(427\) | −2.35979e22 | −1.03332 | ||||||||
\(428\) | 1.84046e22 | 0.790050 | ||||||||
\(429\) | −7.25784e22 | −3.05436 | ||||||||
\(430\) | 2.54152e22 | 1.04860 | ||||||||
\(431\) | −1.56184e21 | −0.0631801 | −0.0315900 | − | 0.999501i | \(-0.510057\pi\) | ||||
−0.0315900 | + | 0.999501i | \(0.510057\pi\) | |||||||
\(432\) | −1.50924e21 | −0.0598614 | ||||||||
\(433\) | 4.19456e22 | 1.63132 | 0.815660 | − | 0.578532i | \(-0.196374\pi\) | ||||
0.815660 | + | 0.578532i | \(0.196374\pi\) | |||||||
\(434\) | −1.00634e22 | −0.383779 | ||||||||
\(435\) | −8.66870e21 | −0.324187 | ||||||||
\(436\) | 4.10814e20 | 0.0150664 | ||||||||
\(437\) | −3.40657e22 | −1.22525 | ||||||||
\(438\) | −1.23320e22 | −0.435015 | ||||||||
\(439\) | 1.98023e22 | 0.685121 | 0.342561 | − | 0.939496i | \(-0.388706\pi\) | ||||
0.342561 | + | 0.939496i | \(0.388706\pi\) | |||||||
\(440\) | 5.86696e22 | 1.99097 | ||||||||
\(441\) | −8.73360e21 | −0.290714 | ||||||||
\(442\) | 3.07781e22 | 1.00497 | ||||||||
\(443\) | 1.66103e22 | 0.532043 | 0.266021 | − | 0.963967i | \(-0.414291\pi\) | ||||
0.266021 | + | 0.963967i | \(0.414291\pi\) | |||||||
\(444\) | 1.02996e22 | 0.323641 | ||||||||
\(445\) | −4.43798e22 | −1.36812 | ||||||||
\(446\) | −1.20521e22 | −0.364516 | ||||||||
\(447\) | 1.38316e22 | 0.410449 | ||||||||
\(448\) | 1.75569e22 | 0.511194 | ||||||||
\(449\) | 5.25193e22 | 1.50046 | 0.750231 | − | 0.661176i | \(-0.229942\pi\) | ||||
0.750231 | + | 0.661176i | \(0.229942\pi\) | |||||||
\(450\) | −1.25040e22 | −0.350543 | ||||||||
\(451\) | 5.69338e22 | 1.56628 | ||||||||
\(452\) | −1.87354e21 | −0.0505809 | ||||||||
\(453\) | 2.02572e22 | 0.536715 | ||||||||
\(454\) | −1.49900e22 | −0.389786 | ||||||||
\(455\) | 6.71826e22 | 1.71459 | ||||||||
\(456\) | −5.09857e22 | −1.27717 | ||||||||
\(457\) | −3.05676e22 | −0.751577 | −0.375788 | − | 0.926706i | \(-0.622628\pi\) | ||||
−0.375788 | + | 0.926706i | \(0.622628\pi\) | |||||||
\(458\) | 3.75052e22 | 0.905180 | ||||||||
\(459\) | −2.01112e22 | −0.476464 | ||||||||
\(460\) | 4.21763e22 | 0.980906 | ||||||||
\(461\) | 5.88809e21 | 0.134436 | 0.0672182 | − | 0.997738i | \(-0.478588\pi\) | ||||
0.0672182 | + | 0.997738i | \(0.478588\pi\) | |||||||
\(462\) | 3.49804e22 | 0.784095 | ||||||||
\(463\) | −3.11045e22 | −0.684517 | −0.342259 | − | 0.939606i | \(-0.611192\pi\) | ||||
−0.342259 | + | 0.939606i | \(0.611192\pi\) | |||||||
\(464\) | −9.32535e20 | −0.0201494 | ||||||||
\(465\) | −6.94554e22 | −1.47352 | ||||||||
\(466\) | −7.15367e21 | −0.149021 | ||||||||
\(467\) | 3.18998e22 | 0.652522 | 0.326261 | − | 0.945280i | \(-0.394211\pi\) | ||||
0.326261 | + | 0.945280i | \(0.394211\pi\) | |||||||
\(468\) | −2.79687e22 | −0.561802 | ||||||||
\(469\) | 1.10070e22 | 0.217119 | ||||||||
\(470\) | −2.60032e22 | −0.503727 | ||||||||
\(471\) | −1.16570e23 | −2.21773 | ||||||||
\(472\) | 4.44403e22 | 0.830366 | ||||||||
\(473\) | −8.59110e22 | −1.57663 | ||||||||
\(474\) | 2.34567e22 | 0.422815 | ||||||||
\(475\) | 5.36303e22 | 0.949543 | ||||||||
\(476\) | 1.95364e22 | 0.339770 | ||||||||
\(477\) | 4.34760e22 | 0.742751 | ||||||||
\(478\) | 3.28827e22 | 0.551862 | ||||||||
\(479\) | −6.35415e22 | −1.04762 | −0.523812 | − | 0.851834i | \(-0.675491\pi\) | ||||
−0.523812 | + | 0.851834i | \(0.675491\pi\) | |||||||
\(480\) | 1.03372e23 | 1.67438 | ||||||||
\(481\) | 5.07717e22 | 0.807957 | ||||||||
\(482\) | −3.74979e22 | −0.586283 | ||||||||
\(483\) | 6.93874e22 | 1.06593 | ||||||||
\(484\) | −3.42166e22 | −0.516478 | ||||||||
\(485\) | 1.68051e23 | 2.49250 | ||||||||
\(486\) | −4.52735e22 | −0.659835 | ||||||||
\(487\) | 1.72595e22 | 0.247191 | 0.123596 | − | 0.992333i | \(-0.460557\pi\) | ||||
0.123596 | + | 0.992333i | \(0.460557\pi\) | |||||||
\(488\) | −1.09300e23 | −1.53834 | ||||||||
\(489\) | −1.04759e23 | −1.44899 | ||||||||
\(490\) | 3.52147e22 | 0.478693 | ||||||||
\(491\) | 3.48189e22 | 0.465181 | 0.232591 | − | 0.972575i | \(-0.425280\pi\) | ||||
0.232591 | + | 0.972575i | \(0.425280\pi\) | |||||||
\(492\) | 6.12572e22 | 0.804366 | ||||||||
\(493\) | −1.24264e22 | −0.160378 | ||||||||
\(494\) | −9.10860e22 | −1.15551 | ||||||||
\(495\) | 8.64702e22 | 1.07826 | ||||||||
\(496\) | −7.47167e21 | −0.0915848 | ||||||||
\(497\) | 2.14331e22 | 0.258260 | ||||||||
\(498\) | −3.54766e22 | −0.420236 | ||||||||
\(499\) | 5.70356e22 | 0.664189 | 0.332094 | − | 0.943246i | \(-0.392245\pi\) | ||||
0.332094 | + | 0.943246i | \(0.392245\pi\) | |||||||
\(500\) | 3.04121e21 | 0.0348178 | ||||||||
\(501\) | 5.61757e21 | 0.0632307 | ||||||||
\(502\) | −6.29756e21 | −0.0696933 | ||||||||
\(503\) | −1.92954e22 | −0.209955 | −0.104977 | − | 0.994475i | \(-0.533477\pi\) | ||||
−0.104977 | + | 0.994475i | \(0.533477\pi\) | |||||||
\(504\) | 3.71955e22 | 0.397952 | ||||||||
\(505\) | −2.49691e23 | −2.62679 | ||||||||
\(506\) | 1.08253e23 | 1.11985 | ||||||||
\(507\) | −2.62241e23 | −2.66767 | ||||||||
\(508\) | 3.53163e22 | 0.353292 | ||||||||
\(509\) | −1.21292e23 | −1.19325 | −0.596627 | − | 0.802519i | \(-0.703493\pi\) | ||||
−0.596627 | + | 0.802519i | \(0.703493\pi\) | |||||||
\(510\) | −1.02382e23 | −0.990549 | ||||||||
\(511\) | −3.85868e22 | −0.367165 | ||||||||
\(512\) | 2.30671e22 | 0.215873 | ||||||||
\(513\) | 5.95179e22 | 0.547835 | ||||||||
\(514\) | −6.51165e21 | −0.0589528 | ||||||||
\(515\) | −1.44376e22 | −0.128568 | ||||||||
\(516\) | −9.24348e22 | −0.809679 | ||||||||
\(517\) | 8.78987e22 | 0.757379 | ||||||||
\(518\) | −2.44703e22 | −0.207413 | ||||||||
\(519\) | 2.31761e23 | 1.93249 | ||||||||
\(520\) | 3.11174e23 | 2.55255 | ||||||||
\(521\) | 2.27742e23 | 1.83790 | 0.918951 | − | 0.394371i | \(-0.129038\pi\) | ||||
0.918951 | + | 0.394371i | \(0.129038\pi\) | |||||||
\(522\) | −8.57414e21 | −0.0680756 | ||||||||
\(523\) | −1.00048e23 | −0.781525 | −0.390763 | − | 0.920492i | \(-0.627789\pi\) | ||||
−0.390763 | + | 0.920492i | \(0.627789\pi\) | |||||||
\(524\) | −8.70490e22 | −0.669033 | ||||||||
\(525\) | −1.09238e23 | −0.826074 | ||||||||
\(526\) | −1.47248e23 | −1.09565 | ||||||||
\(527\) | −9.95626e22 | −0.728964 | ||||||||
\(528\) | 2.59716e22 | 0.187116 | ||||||||
\(529\) | 7.36814e22 | 0.522378 | ||||||||
\(530\) | −1.75299e23 | −1.22302 | ||||||||
\(531\) | 6.54983e22 | 0.449704 | ||||||||
\(532\) | −5.78167e22 | −0.390665 | ||||||||
\(533\) | 3.01967e23 | 2.00807 | ||||||||
\(534\) | −1.22559e23 | −0.802126 | ||||||||
\(535\) | −3.01793e23 | −1.94403 | ||||||||
\(536\) | 5.09816e22 | 0.323231 | ||||||||
\(537\) | −3.88550e23 | −2.42474 | ||||||||
\(538\) | −1.13541e23 | −0.697433 | ||||||||
\(539\) | −1.19036e23 | −0.719738 | ||||||||
\(540\) | −7.36883e22 | −0.438583 | ||||||||
\(541\) | 1.99451e23 | 1.16858 | 0.584292 | − | 0.811543i | \(-0.301372\pi\) | ||||
0.584292 | + | 0.811543i | \(0.301372\pi\) | |||||||
\(542\) | −1.97428e23 | −1.13872 | ||||||||
\(543\) | 1.26719e23 | 0.719519 | ||||||||
\(544\) | 1.48182e23 | 0.828332 | ||||||||
\(545\) | −6.73641e21 | −0.0370730 | ||||||||
\(546\) | 1.85530e23 | 1.00526 | ||||||||
\(547\) | 3.31665e23 | 1.76932 | 0.884662 | − | 0.466232i | \(-0.154389\pi\) | ||||
0.884662 | + | 0.466232i | \(0.154389\pi\) | |||||||
\(548\) | −2.09144e23 | −1.09853 | ||||||||
\(549\) | −1.61092e23 | −0.833121 | ||||||||
\(550\) | −1.70425e23 | −0.867861 | ||||||||
\(551\) | 3.67751e22 | 0.184402 | ||||||||
\(552\) | 3.21386e23 | 1.58688 | ||||||||
\(553\) | 7.33958e22 | 0.356868 | ||||||||
\(554\) | 6.26540e22 | 0.299996 | ||||||||
\(555\) | −1.68889e23 | −0.796364 | ||||||||
\(556\) | 2.15668e22 | 0.100150 | ||||||||
\(557\) | 1.81484e23 | 0.829982 | 0.414991 | − | 0.909825i | \(-0.363785\pi\) | ||||
0.414991 | + | 0.909825i | \(0.363785\pi\) | |||||||
\(558\) | −6.86979e22 | −0.309423 | ||||||||
\(559\) | −4.55657e23 | −2.02133 | ||||||||
\(560\) | −2.40408e22 | −0.105039 | ||||||||
\(561\) | 3.46081e23 | 1.48934 | ||||||||
\(562\) | −1.65721e23 | −0.702455 | ||||||||
\(563\) | −4.35433e23 | −1.81802 | −0.909012 | − | 0.416770i | \(-0.863162\pi\) | ||||
−0.909012 | + | 0.416770i | \(0.863162\pi\) | |||||||
\(564\) | 9.45734e22 | 0.388953 | ||||||||
\(565\) | 3.07218e22 | 0.124461 | ||||||||
\(566\) | 2.32946e23 | 0.929642 | ||||||||
\(567\) | −2.19471e23 | −0.862820 | ||||||||
\(568\) | 9.92732e22 | 0.384478 | ||||||||
\(569\) | −1.29059e23 | −0.492417 | −0.246208 | − | 0.969217i | \(-0.579185\pi\) | ||||
−0.246208 | + | 0.969217i | \(0.579185\pi\) | |||||||
\(570\) | 3.02993e23 | 1.13893 | ||||||||
\(571\) | 4.64417e23 | 1.71989 | 0.859946 | − | 0.510386i | \(-0.170497\pi\) | ||||
0.859946 | + | 0.510386i | \(0.170497\pi\) | |||||||
\(572\) | −3.81205e23 | −1.39089 | ||||||||
\(573\) | −1.06755e23 | −0.383774 | ||||||||
\(574\) | −1.45538e23 | −0.515498 | ||||||||
\(575\) | −3.38056e23 | −1.17981 | ||||||||
\(576\) | 1.19853e23 | 0.412151 | ||||||||
\(577\) | −6.87036e22 | −0.232801 | −0.116400 | − | 0.993202i | \(-0.537136\pi\) | ||||
−0.116400 | + | 0.993202i | \(0.537136\pi\) | |||||||
\(578\) | 4.99927e22 | 0.166924 | ||||||||
\(579\) | 6.11399e23 | 2.01167 | ||||||||
\(580\) | −4.55308e22 | −0.147627 | ||||||||
\(581\) | −1.11006e23 | −0.354691 | ||||||||
\(582\) | 4.64086e23 | 1.46135 | ||||||||
\(583\) | 5.92564e23 | 1.83888 | ||||||||
\(584\) | −1.78725e23 | −0.546608 | ||||||||
\(585\) | 4.58623e23 | 1.38239 | ||||||||
\(586\) | 1.88597e23 | 0.560279 | ||||||||
\(587\) | 3.83769e23 | 1.12369 | 0.561844 | − | 0.827243i | \(-0.310092\pi\) | ||||
0.561844 | + | 0.827243i | \(0.310092\pi\) | |||||||
\(588\) | −1.28075e23 | −0.369622 | ||||||||
\(589\) | 2.94650e23 | 0.838158 | ||||||||
\(590\) | −2.64095e23 | −0.740488 | ||||||||
\(591\) | 2.57503e23 | 0.711687 | ||||||||
\(592\) | −1.81682e22 | −0.0494970 | ||||||||
\(593\) | 4.18329e22 | 0.112345 | 0.0561724 | − | 0.998421i | \(-0.482110\pi\) | ||||
0.0561724 | + | 0.998421i | \(0.482110\pi\) | |||||||
\(594\) | −1.89134e23 | −0.500709 | ||||||||
\(595\) | −3.20352e23 | −0.836051 | ||||||||
\(596\) | 7.26481e22 | 0.186909 | ||||||||
\(597\) | −3.19253e23 | −0.809754 | ||||||||
\(598\) | 5.74156e23 | 1.43572 | ||||||||
\(599\) | 6.00244e23 | 1.47979 | 0.739894 | − | 0.672723i | \(-0.234876\pi\) | ||||
0.739894 | + | 0.672723i | \(0.234876\pi\) | |||||||
\(600\) | −5.05964e23 | −1.22980 | ||||||||
\(601\) | 7.80759e23 | 1.87104 | 0.935522 | − | 0.353267i | \(-0.114929\pi\) | ||||
0.935522 | + | 0.353267i | \(0.114929\pi\) | |||||||
\(602\) | 2.19612e23 | 0.518903 | ||||||||
\(603\) | 7.51392e22 | 0.175053 | ||||||||
\(604\) | 1.06397e23 | 0.244408 | ||||||||
\(605\) | 5.61074e23 | 1.27087 | ||||||||
\(606\) | −6.89542e23 | −1.54008 | ||||||||
\(607\) | −1.52608e23 | −0.336103 | −0.168051 | − | 0.985778i | \(-0.553747\pi\) | ||||
−0.168051 | + | 0.985778i | \(0.553747\pi\) | |||||||
\(608\) | −4.38535e23 | −0.952411 | ||||||||
\(609\) | −7.49060e22 | −0.160424 | ||||||||
\(610\) | 6.49536e23 | 1.37183 | ||||||||
\(611\) | 4.66200e23 | 0.971006 | ||||||||
\(612\) | 1.33365e23 | 0.273940 | ||||||||
\(613\) | 1.75688e23 | 0.355899 | 0.177950 | − | 0.984040i | \(-0.443054\pi\) | ||||
0.177950 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(614\) | −1.63054e23 | −0.325763 | ||||||||
\(615\) | −1.00448e24 | −1.97925 | ||||||||
\(616\) | 5.06963e23 | 0.985235 | ||||||||
\(617\) | 1.85521e23 | 0.355606 | 0.177803 | − | 0.984066i | \(-0.443101\pi\) | ||||
0.177803 | + | 0.984066i | \(0.443101\pi\) | |||||||
\(618\) | −3.98706e22 | −0.0753791 | ||||||||
\(619\) | −6.46969e23 | −1.20646 | −0.603230 | − | 0.797567i | \(-0.706120\pi\) | ||||
−0.603230 | + | 0.797567i | \(0.706120\pi\) | |||||||
\(620\) | −3.64802e23 | −0.671008 | ||||||||
\(621\) | −3.75168e23 | −0.680686 | ||||||||
\(622\) | −1.49950e23 | −0.268366 | ||||||||
\(623\) | −3.83485e23 | −0.677017 | ||||||||
\(624\) | 1.37749e23 | 0.239894 | ||||||||
\(625\) | −6.06453e23 | −1.04188 | ||||||||
\(626\) | 3.24831e23 | 0.550523 | ||||||||
\(627\) | −1.02421e24 | −1.71243 | ||||||||
\(628\) | −6.12264e23 | −1.00991 | ||||||||
\(629\) | −2.42098e23 | −0.393968 | ||||||||
\(630\) | −2.21041e23 | −0.354878 | ||||||||
\(631\) | 5.43759e23 | 0.861305 | 0.430653 | − | 0.902518i | \(-0.358283\pi\) | ||||
0.430653 | + | 0.902518i | \(0.358283\pi\) | |||||||
\(632\) | 3.39952e23 | 0.531278 | ||||||||
\(633\) | −1.04930e24 | −1.61796 | ||||||||
\(634\) | 3.47330e23 | 0.528425 | ||||||||
\(635\) | −5.79107e23 | −0.869325 | ||||||||
\(636\) | 6.37561e23 | 0.944357 | ||||||||
\(637\) | −6.31348e23 | −0.922749 | ||||||||
\(638\) | −1.16863e23 | −0.168539 | ||||||||
\(639\) | 1.46314e23 | 0.208223 | ||||||||
\(640\) | 4.71949e23 | 0.662773 | ||||||||
\(641\) | −2.60005e23 | −0.360321 | −0.180160 | − | 0.983637i | \(-0.557662\pi\) | ||||
−0.180160 | + | 0.983637i | \(0.557662\pi\) | |||||||
\(642\) | −8.33427e23 | −1.13978 | ||||||||
\(643\) | −3.09562e23 | −0.417787 | −0.208893 | − | 0.977938i | \(-0.566986\pi\) | ||||
−0.208893 | + | 0.977938i | \(0.566986\pi\) | |||||||
\(644\) | 3.64445e23 | 0.485402 | ||||||||
\(645\) | 1.51572e24 | 1.99233 | ||||||||
\(646\) | 4.34332e23 | 0.563437 | ||||||||
\(647\) | −1.34080e24 | −1.71664 | −0.858319 | − | 0.513116i | \(-0.828491\pi\) | ||||
−0.858319 | + | 0.513116i | \(0.828491\pi\) | |||||||
\(648\) | −1.01654e24 | −1.28450 | ||||||||
\(649\) | 8.92721e23 | 1.11336 | ||||||||
\(650\) | −9.03905e23 | −1.11265 | ||||||||
\(651\) | −6.00163e23 | −0.729173 | ||||||||
\(652\) | −5.50228e23 | −0.659840 | ||||||||
\(653\) | 6.55237e23 | 0.775597 | 0.387798 | − | 0.921744i | \(-0.373236\pi\) | ||||
0.387798 | + | 0.921744i | \(0.373236\pi\) | |||||||
\(654\) | −1.86032e22 | −0.0217358 | ||||||||
\(655\) | 1.42740e24 | 1.64625 | ||||||||
\(656\) | −1.08057e23 | −0.123018 | ||||||||
\(657\) | −2.63414e23 | −0.296028 | ||||||||
\(658\) | −2.24693e23 | −0.249270 | ||||||||
\(659\) | −2.46802e23 | −0.270286 | −0.135143 | − | 0.990826i | \(-0.543149\pi\) | ||||
−0.135143 | + | 0.990826i | \(0.543149\pi\) | |||||||
\(660\) | 1.26806e24 | 1.37093 | ||||||||
\(661\) | 1.79192e24 | 1.91252 | 0.956261 | − | 0.292516i | \(-0.0944925\pi\) | ||||
0.956261 | + | 0.292516i | \(0.0944925\pi\) | |||||||
\(662\) | −3.72674e23 | −0.392677 | ||||||||
\(663\) | 1.83555e24 | 1.90942 | ||||||||
\(664\) | −5.14154e23 | −0.528037 | ||||||||
\(665\) | 9.48062e23 | 0.961286 | ||||||||
\(666\) | −1.67047e23 | −0.167228 | ||||||||
\(667\) | −2.31810e23 | −0.229120 | ||||||||
\(668\) | 2.95053e22 | 0.0287939 | ||||||||
\(669\) | −7.18767e23 | −0.692574 | ||||||||
\(670\) | −3.02968e23 | −0.288245 | ||||||||
\(671\) | −2.19563e24 | −2.06261 | ||||||||
\(672\) | 8.93239e23 | 0.828569 | ||||||||
\(673\) | −1.61280e24 | −1.47725 | −0.738623 | − | 0.674119i | \(-0.764524\pi\) | ||||
−0.738623 | + | 0.674119i | \(0.764524\pi\) | |||||||
\(674\) | −6.02659e23 | −0.545083 | ||||||||
\(675\) | 5.90634e23 | 0.527517 | ||||||||
\(676\) | −1.37737e24 | −1.21480 | ||||||||
\(677\) | −5.39428e23 | −0.469818 | −0.234909 | − | 0.972017i | \(-0.575479\pi\) | ||||
−0.234909 | + | 0.972017i | \(0.575479\pi\) | |||||||
\(678\) | 8.48407e22 | 0.0729713 | ||||||||
\(679\) | 1.45212e24 | 1.23342 | ||||||||
\(680\) | −1.48379e24 | −1.24465 | ||||||||
\(681\) | −8.93977e23 | −0.740587 | ||||||||
\(682\) | −9.36330e23 | −0.766058 | ||||||||
\(683\) | −1.34863e24 | −1.08973 | −0.544863 | − | 0.838525i | \(-0.683418\pi\) | ||||
−0.544863 | + | 0.838525i | \(0.683418\pi\) | |||||||
\(684\) | −3.94687e23 | −0.314975 | ||||||||
\(685\) | 3.42949e24 | 2.70308 | ||||||||
\(686\) | 8.88371e23 | 0.691576 | ||||||||
\(687\) | 2.23675e24 | 1.71983 | ||||||||
\(688\) | 1.63053e23 | 0.123831 | ||||||||
\(689\) | 3.14286e24 | 2.35755 | ||||||||
\(690\) | −1.90990e24 | −1.41512 | ||||||||
\(691\) | −1.23627e24 | −0.904792 | −0.452396 | − | 0.891817i | \(-0.649431\pi\) | ||||
−0.452396 | + | 0.891817i | \(0.649431\pi\) | |||||||
\(692\) | 1.21728e24 | 0.880013 | ||||||||
\(693\) | 7.47187e23 | 0.533577 | ||||||||
\(694\) | 7.16597e23 | 0.505498 | ||||||||
\(695\) | −3.53647e23 | −0.246433 | ||||||||
\(696\) | −3.46947e23 | −0.238827 | ||||||||
\(697\) | −1.43989e24 | −0.979156 | ||||||||
\(698\) | 2.57188e23 | 0.172775 | ||||||||
\(699\) | −4.26633e23 | −0.283138 | ||||||||
\(700\) | −5.73752e23 | −0.376176 | ||||||||
\(701\) | −1.61438e24 | −1.04569 | −0.522846 | − | 0.852427i | \(-0.675130\pi\) | ||||
−0.522846 | + | 0.852427i | \(0.675130\pi\) | |||||||
\(702\) | −1.00314e24 | −0.641940 | ||||||||
\(703\) | 7.16476e23 | 0.452982 | ||||||||
\(704\) | 1.63355e24 | 1.02039 | ||||||||
\(705\) | −1.55079e24 | −0.957073 | ||||||||
\(706\) | 1.61807e24 | 0.986639 | ||||||||
\(707\) | −2.15757e24 | −1.29987 | ||||||||
\(708\) | 9.60511e23 | 0.571768 | ||||||||
\(709\) | 6.23711e23 | 0.366852 | 0.183426 | − | 0.983034i | \(-0.441281\pi\) | ||||
0.183426 | + | 0.983034i | \(0.441281\pi\) | |||||||
\(710\) | −5.89950e23 | −0.342862 | ||||||||
\(711\) | 5.01038e23 | 0.287726 | ||||||||
\(712\) | −1.77621e24 | −1.00789 | ||||||||
\(713\) | −1.85731e24 | −1.04141 | ||||||||
\(714\) | −8.84678e23 | −0.490174 | ||||||||
\(715\) | 6.25089e24 | 3.42248 | ||||||||
\(716\) | −2.04079e24 | −1.10417 | ||||||||
\(717\) | 1.96107e24 | 1.04853 | ||||||||
\(718\) | 1.43422e24 | 0.757808 | ||||||||
\(719\) | −1.75531e24 | −0.916557 | −0.458278 | − | 0.888809i | \(-0.651534\pi\) | ||||
−0.458278 | + | 0.888809i | \(0.651534\pi\) | |||||||
\(720\) | −1.64115e23 | −0.0846879 | ||||||||
\(721\) | −1.24755e23 | −0.0636221 | ||||||||
\(722\) | 1.80970e22 | 0.00912098 | ||||||||
\(723\) | −2.23631e24 | −1.11393 | ||||||||
\(724\) | 6.65567e23 | 0.327653 | ||||||||
\(725\) | 3.64943e23 | 0.177563 | ||||||||
\(726\) | 1.54945e24 | 0.745105 | ||||||||
\(727\) | 1.18905e24 | 0.565142 | 0.282571 | − | 0.959246i | \(-0.408813\pi\) | ||||
0.282571 | + | 0.959246i | \(0.408813\pi\) | |||||||
\(728\) | 2.68884e24 | 1.26313 | ||||||||
\(729\) | −1.51667e22 | −0.00704217 | ||||||||
\(730\) | 1.06211e24 | 0.487443 | ||||||||
\(731\) | 2.17274e24 | 0.985623 | ||||||||
\(732\) | −2.36235e24 | −1.05926 | ||||||||
\(733\) | −1.24090e24 | −0.549986 | −0.274993 | − | 0.961446i | \(-0.588675\pi\) | ||||
−0.274993 | + | 0.961446i | \(0.588675\pi\) | |||||||
\(734\) | 1.36406e24 | 0.597607 | ||||||||
\(735\) | 2.10014e24 | 0.909508 | ||||||||
\(736\) | 2.76429e24 | 1.18337 | ||||||||
\(737\) | 1.02412e24 | 0.433390 | ||||||||
\(738\) | −9.93521e23 | −0.415622 | ||||||||
\(739\) | 2.80759e24 | 1.16106 | 0.580532 | − | 0.814237i | \(-0.302845\pi\) | ||||
0.580532 | + | 0.814237i | \(0.302845\pi\) | |||||||
\(740\) | −8.87060e23 | −0.362646 | ||||||||
\(741\) | −5.43222e24 | −2.19544 | ||||||||
\(742\) | −1.51476e24 | −0.605215 | ||||||||
\(743\) | −3.17587e24 | −1.25446 | −0.627231 | − | 0.778833i | \(-0.715812\pi\) | ||||
−0.627231 | + | 0.778833i | \(0.715812\pi\) | |||||||
\(744\) | −2.77981e24 | −1.08554 | ||||||||
\(745\) | −1.19126e24 | −0.459917 | ||||||||
\(746\) | 1.45276e24 | 0.554516 | ||||||||
\(747\) | −7.57786e23 | −0.285971 | ||||||||
\(748\) | 1.81773e24 | 0.678212 | ||||||||
\(749\) | −2.60779e24 | −0.962004 | ||||||||
\(750\) | −1.37717e23 | −0.0502305 | ||||||||
\(751\) | 2.22510e24 | 0.802435 | 0.401217 | − | 0.915983i | \(-0.368587\pi\) | ||||
0.401217 | + | 0.915983i | \(0.368587\pi\) | |||||||
\(752\) | −1.66826e23 | −0.0594856 | ||||||||
\(753\) | −3.75576e23 | −0.132416 | ||||||||
\(754\) | −6.19821e23 | −0.216078 | ||||||||
\(755\) | −1.74467e24 | −0.601400 | ||||||||
\(756\) | −6.36739e23 | −0.217033 | ||||||||
\(757\) | 2.90700e24 | 0.979783 | 0.489892 | − | 0.871783i | \(-0.337036\pi\) | ||||
0.489892 | + | 0.871783i | \(0.337036\pi\) | |||||||
\(758\) | −1.32169e24 | −0.440496 | ||||||||
\(759\) | 6.45603e24 | 2.12770 | ||||||||
\(760\) | 4.39120e24 | 1.43109 | ||||||||
\(761\) | −5.65138e24 | −1.82131 | −0.910657 | − | 0.413164i | \(-0.864424\pi\) | ||||
−0.910657 | + | 0.413164i | \(0.864424\pi\) | |||||||
\(762\) | −1.59925e24 | −0.509683 | ||||||||
\(763\) | −5.82092e22 | −0.0183456 | ||||||||
\(764\) | −5.60713e23 | −0.174762 | ||||||||
\(765\) | −2.18689e24 | −0.674069 | ||||||||
\(766\) | −9.63533e23 | −0.293712 | ||||||||
\(767\) | 4.73484e24 | 1.42740 | ||||||||
\(768\) | 4.39548e24 | 1.31050 | ||||||||
\(769\) | −1.93750e24 | −0.571306 | −0.285653 | − | 0.958333i | \(-0.592210\pi\) | ||||
−0.285653 | + | 0.958333i | \(0.592210\pi\) | |||||||
\(770\) | −3.01273e24 | −0.878594 | ||||||||
\(771\) | −3.88344e23 | −0.112009 | ||||||||
\(772\) | 3.21126e24 | 0.916070 | ||||||||
\(773\) | −1.33043e24 | −0.375377 | −0.187688 | − | 0.982229i | \(-0.560099\pi\) | ||||
−0.187688 | + | 0.982229i | \(0.560099\pi\) | |||||||
\(774\) | 1.49919e24 | 0.418367 | ||||||||
\(775\) | 2.92400e24 | 0.807072 | ||||||||
\(776\) | 6.72588e24 | 1.83622 | ||||||||
\(777\) | −1.45937e24 | −0.394081 | ||||||||
\(778\) | 3.69628e24 | 0.987275 | ||||||||
\(779\) | 4.26128e24 | 1.12583 | ||||||||
\(780\) | 6.72556e24 | 1.75762 | ||||||||
\(781\) | 1.99421e24 | 0.515510 | ||||||||
\(782\) | −2.73779e24 | −0.700072 | ||||||||
\(783\) | 4.05006e23 | 0.102444 | ||||||||
\(784\) | 2.25923e23 | 0.0565293 | ||||||||
\(785\) | 1.00397e25 | 2.48502 | ||||||||
\(786\) | 3.94189e24 | 0.965191 | ||||||||
\(787\) | −3.58217e24 | −0.867683 | −0.433842 | − | 0.900989i | \(-0.642842\pi\) | ||||
−0.433842 | + | 0.900989i | \(0.642842\pi\) | |||||||
\(788\) | 1.35249e24 | 0.324086 | ||||||||
\(789\) | −8.78161e24 | −2.08171 | ||||||||
\(790\) | −2.02023e24 | −0.473773 | ||||||||
\(791\) | 2.65466e23 | 0.0615898 | ||||||||
\(792\) | 3.46079e24 | 0.794349 | ||||||||
\(793\) | −1.16452e25 | −2.64439 | ||||||||
\(794\) | 2.43095e24 | 0.546138 | ||||||||
\(795\) | −1.04545e25 | −2.32372 | ||||||||
\(796\) | −1.67682e24 | −0.368744 | ||||||||
\(797\) | −4.17640e24 | −0.908670 | −0.454335 | − | 0.890831i | \(-0.650123\pi\) | ||||
−0.454335 | + | 0.890831i | \(0.650123\pi\) | |||||||
\(798\) | 2.61815e24 | 0.563599 | ||||||||
\(799\) | −2.22302e24 | −0.473473 | ||||||||
\(800\) | −4.35187e24 | −0.917087 | ||||||||
\(801\) | −2.61787e24 | −0.545847 | ||||||||
\(802\) | 1.94424e24 | 0.401114 | ||||||||
\(803\) | −3.59024e24 | −0.732895 | ||||||||
\(804\) | 1.10189e24 | 0.222568 | ||||||||
\(805\) | −5.97606e24 | −1.19440 | ||||||||
\(806\) | −4.96613e24 | −0.982134 | ||||||||
\(807\) | −6.77138e24 | −1.32511 | ||||||||
\(808\) | −9.99336e24 | −1.93515 | ||||||||
\(809\) | −1.19044e24 | −0.228111 | −0.114055 | − | 0.993474i | \(-0.536384\pi\) | ||||
−0.114055 | + | 0.993474i | \(0.536384\pi\) | |||||||
\(810\) | 6.04096e24 | 1.14547 | ||||||||
\(811\) | 1.26895e24 | 0.238105 | 0.119052 | − | 0.992888i | \(-0.462014\pi\) | ||||
0.119052 | + | 0.992888i | \(0.462014\pi\) | |||||||
\(812\) | −3.93430e23 | −0.0730536 | ||||||||
\(813\) | −1.17743e25 | −2.16354 | ||||||||
\(814\) | −2.27680e24 | −0.414016 | ||||||||
\(815\) | 9.02248e24 | 1.62363 | ||||||||
\(816\) | −6.56839e23 | −0.116975 | ||||||||
\(817\) | −6.43011e24 | −1.13326 | ||||||||
\(818\) | 3.89733e24 | 0.679773 | ||||||||
\(819\) | 3.96295e24 | 0.684078 | ||||||||
\(820\) | −5.27584e24 | −0.901309 | ||||||||
\(821\) | 2.08061e24 | 0.351782 | 0.175891 | − | 0.984410i | \(-0.443719\pi\) | ||||
0.175891 | + | 0.984410i | \(0.443719\pi\) | |||||||
\(822\) | 9.47081e24 | 1.58481 | ||||||||
\(823\) | 2.64902e24 | 0.438720 | 0.219360 | − | 0.975644i | \(-0.429603\pi\) | ||||
0.219360 | + | 0.975644i | \(0.429603\pi\) | |||||||
\(824\) | −5.77835e23 | −0.0947157 | ||||||||
\(825\) | −1.01639e25 | −1.64892 | ||||||||
\(826\) | −2.28204e24 | −0.366431 | ||||||||
\(827\) | −6.65948e24 | −1.05838 | −0.529192 | − | 0.848502i | \(-0.677505\pi\) | ||||
−0.529192 | + | 0.848502i | \(0.677505\pi\) | |||||||
\(828\) | 2.48789e24 | 0.391357 | ||||||||
\(829\) | 9.74066e23 | 0.151661 | 0.0758306 | − | 0.997121i | \(-0.475839\pi\) | ||||
0.0758306 | + | 0.997121i | \(0.475839\pi\) | |||||||
\(830\) | 3.05546e24 | 0.470883 | ||||||||
\(831\) | 3.73658e24 | 0.569987 | ||||||||
\(832\) | 8.66410e24 | 1.30820 | ||||||||
\(833\) | 3.01050e24 | 0.449942 | ||||||||
\(834\) | −9.76625e23 | −0.144483 | ||||||||
\(835\) | −4.83819e23 | −0.0708514 | ||||||||
\(836\) | −5.37946e24 | −0.779804 | ||||||||
\(837\) | 3.24500e24 | 0.465637 | ||||||||
\(838\) | −6.93555e24 | −0.985160 | ||||||||
\(839\) | 3.43808e24 | 0.483436 | 0.241718 | − | 0.970347i | \(-0.422289\pi\) | ||||
0.241718 | + | 0.970347i | \(0.422289\pi\) | |||||||
\(840\) | −8.94429e24 | −1.24501 | ||||||||
\(841\) | 2.50246e23 | 0.0344828 | ||||||||
\(842\) | −4.34950e24 | −0.593317 | ||||||||
\(843\) | −9.88331e24 | −1.33465 | ||||||||
\(844\) | −5.51127e24 | −0.736785 | ||||||||
\(845\) | 2.25857e25 | 2.98918 | ||||||||
\(846\) | −1.53387e24 | −0.200975 | ||||||||
\(847\) | 4.84823e24 | 0.628889 | ||||||||
\(848\) | −1.12465e24 | −0.144428 | ||||||||
\(849\) | 1.38925e25 | 1.76630 | ||||||||
\(850\) | 4.31016e24 | 0.542540 | ||||||||
\(851\) | −4.51627e24 | −0.562832 | ||||||||
\(852\) | 2.14564e24 | 0.264741 | ||||||||
\(853\) | 8.21174e24 | 1.00316 | 0.501578 | − | 0.865112i | \(-0.332753\pi\) | ||||
0.501578 | + | 0.865112i | \(0.332753\pi\) | |||||||
\(854\) | 5.61262e24 | 0.678850 | ||||||||
\(855\) | 6.47196e24 | 0.775040 | ||||||||
\(856\) | −1.20787e25 | −1.43216 | ||||||||
\(857\) | 1.49858e24 | 0.175931 | 0.0879656 | − | 0.996124i | \(-0.471963\pi\) | ||||
0.0879656 | + | 0.996124i | \(0.471963\pi\) | |||||||
\(858\) | 1.72623e25 | 2.00659 | ||||||||
\(859\) | −5.73359e24 | −0.659911 | −0.329955 | − | 0.943997i | \(-0.607034\pi\) | ||||
−0.329955 | + | 0.943997i | \(0.607034\pi\) | |||||||
\(860\) | 7.96104e24 | 0.907262 | ||||||||
\(861\) | −8.67967e24 | −0.979436 | ||||||||
\(862\) | 3.71475e23 | 0.0415067 | ||||||||
\(863\) | 9.31180e23 | 0.103025 | 0.0515124 | − | 0.998672i | \(-0.483596\pi\) | ||||
0.0515124 | + | 0.998672i | \(0.483596\pi\) | |||||||
\(864\) | −4.82962e24 | −0.529110 | ||||||||
\(865\) | −1.99606e25 | −2.16540 | ||||||||
\(866\) | −9.97651e24 | −1.07171 | ||||||||
\(867\) | 2.98148e24 | 0.317153 | ||||||||
\(868\) | −3.15225e24 | −0.332049 | ||||||||
\(869\) | 6.82899e24 | 0.712342 | ||||||||
\(870\) | 2.06180e24 | 0.212977 | ||||||||
\(871\) | 5.43178e24 | 0.555633 | ||||||||
\(872\) | −2.69611e23 | −0.0273116 | ||||||||
\(873\) | 9.91294e24 | 0.994447 | ||||||||
\(874\) | 8.10233e24 | 0.804939 | ||||||||
\(875\) | −4.30916e23 | −0.0423959 | ||||||||
\(876\) | −3.86287e24 | −0.376379 | ||||||||
\(877\) | 1.12860e25 | 1.08904 | 0.544518 | − | 0.838749i | \(-0.316712\pi\) | ||||
0.544518 | + | 0.838749i | \(0.316712\pi\) | |||||||
\(878\) | −4.70986e24 | −0.450096 | ||||||||
\(879\) | 1.12476e25 | 1.06452 | ||||||||
\(880\) | −2.23683e24 | −0.209667 | ||||||||
\(881\) | −1.33735e25 | −1.24151 | −0.620756 | − | 0.784004i | \(-0.713174\pi\) | ||||
−0.620756 | + | 0.784004i | \(0.713174\pi\) | |||||||
\(882\) | 2.07724e24 | 0.190987 | ||||||||
\(883\) | 1.98397e25 | 1.80663 | 0.903316 | − | 0.428976i | \(-0.141126\pi\) | ||||
0.903316 | + | 0.428976i | \(0.141126\pi\) | |||||||
\(884\) | 9.64092e24 | 0.869509 | ||||||||
\(885\) | −1.57502e25 | −1.40691 | ||||||||
\(886\) | −3.95067e24 | −0.349530 | ||||||||
\(887\) | −2.20564e24 | −0.193279 | −0.0966395 | − | 0.995319i | \(-0.530809\pi\) | ||||
−0.0966395 | + | 0.995319i | \(0.530809\pi\) | |||||||
\(888\) | −6.75944e24 | −0.586679 | ||||||||
\(889\) | −5.00405e24 | −0.430186 | ||||||||
\(890\) | 1.05555e25 | 0.898799 | ||||||||
\(891\) | −2.04203e25 | −1.72227 | ||||||||
\(892\) | −3.77519e24 | −0.315383 | ||||||||
\(893\) | 6.57889e24 | 0.544396 | ||||||||
\(894\) | −3.28977e24 | −0.269648 | ||||||||
\(895\) | 3.34643e25 | 2.71698 | ||||||||
\(896\) | 4.07810e24 | 0.327974 | ||||||||
\(897\) | 3.42417e25 | 2.72784 | ||||||||
\(898\) | −1.24914e25 | −0.985740 | ||||||||
\(899\) | 2.00503e24 | 0.156734 | ||||||||
\(900\) | −3.91673e24 | −0.303293 | ||||||||
\(901\) | −1.49863e25 | −1.14957 | ||||||||
\(902\) | −1.35414e25 | −1.02898 | ||||||||
\(903\) | 1.30973e25 | 0.985906 | ||||||||
\(904\) | 1.22958e24 | 0.0916903 | ||||||||
\(905\) | −1.09138e25 | −0.806236 | ||||||||
\(906\) | −4.81805e24 | −0.352599 | ||||||||
\(907\) | 3.48076e24 | 0.252355 | 0.126177 | − | 0.992008i | \(-0.459729\pi\) | ||||
0.126177 | + | 0.992008i | \(0.459729\pi\) | |||||||
\(908\) | −4.69545e24 | −0.337247 | ||||||||
\(909\) | −1.47287e25 | −1.04802 | ||||||||
\(910\) | −1.59790e25 | −1.12641 | ||||||||
\(911\) | 2.83850e24 | 0.198236 | 0.0991181 | − | 0.995076i | \(-0.468398\pi\) | ||||
0.0991181 | + | 0.995076i | \(0.468398\pi\) | |||||||
\(912\) | 1.94388e24 | 0.134497 | ||||||||
\(913\) | −1.03284e25 | −0.707996 | ||||||||
\(914\) | 7.27032e24 | 0.493754 | ||||||||
\(915\) | 3.87372e25 | 2.60645 | ||||||||
\(916\) | 1.17481e25 | 0.783170 | ||||||||
\(917\) | 1.23342e25 | 0.814649 | ||||||||
\(918\) | 4.78333e24 | 0.313017 | ||||||||
\(919\) | −1.30046e25 | −0.843173 | −0.421587 | − | 0.906788i | \(-0.638527\pi\) | ||||
−0.421587 | + | 0.906788i | \(0.638527\pi\) | |||||||
\(920\) | −2.76797e25 | −1.77813 | ||||||||
\(921\) | −9.72429e24 | −0.618943 | ||||||||
\(922\) | −1.40045e24 | −0.0883190 | ||||||||
\(923\) | 1.05770e25 | 0.660916 | ||||||||
\(924\) | 1.09572e25 | 0.678406 | ||||||||
\(925\) | 7.11005e24 | 0.436182 | ||||||||
\(926\) | 7.39802e24 | 0.449699 | ||||||||
\(927\) | −8.51641e23 | −0.0512955 | ||||||||
\(928\) | −2.98414e24 | −0.178099 | ||||||||
\(929\) | 1.92619e25 | 1.13911 | 0.569555 | − | 0.821954i | \(-0.307116\pi\) | ||||
0.569555 | + | 0.821954i | \(0.307116\pi\) | |||||||
\(930\) | 1.65196e25 | 0.968041 | ||||||||
\(931\) | −8.90940e24 | −0.517340 | ||||||||
\(932\) | −2.24081e24 | −0.128935 | ||||||||
\(933\) | −8.94274e24 | −0.509890 | ||||||||
\(934\) | −7.58719e24 | −0.428679 | ||||||||
\(935\) | −2.98066e25 | −1.66884 | ||||||||
\(936\) | 1.83554e25 | 1.01840 | ||||||||
\(937\) | 3.06535e25 | 1.68536 | 0.842681 | − | 0.538413i | \(-0.180976\pi\) | ||||
0.842681 | + | 0.538413i | \(0.180976\pi\) | |||||||
\(938\) | −2.61794e24 | −0.142638 | ||||||||
\(939\) | 1.93724e25 | 1.04598 | ||||||||
\(940\) | −8.14523e24 | −0.435830 | ||||||||
\(941\) | −5.57666e23 | −0.0295708 | −0.0147854 | − | 0.999891i | \(-0.504707\pi\) | ||||
−0.0147854 | + | 0.999891i | \(0.504707\pi\) | |||||||
\(942\) | 2.77255e25 | 1.45696 | ||||||||
\(943\) | −2.68608e25 | −1.39884 | ||||||||
\(944\) | −1.69433e24 | −0.0874450 | ||||||||
\(945\) | 1.04411e25 | 0.534041 | ||||||||
\(946\) | 2.04334e25 | 1.03578 | ||||||||
\(947\) | −2.97873e25 | −1.49643 | −0.748215 | − | 0.663456i | \(-0.769089\pi\) | ||||
−0.748215 | + | 0.663456i | \(0.769089\pi\) | |||||||
\(948\) | 7.34756e24 | 0.365824 | ||||||||
\(949\) | −1.90420e25 | −0.939617 | ||||||||
\(950\) | −1.27557e25 | −0.623810 | ||||||||
\(951\) | 2.07142e25 | 1.00400 | ||||||||
\(952\) | −1.28214e25 | −0.615916 | ||||||||
\(953\) | −2.28962e25 | −1.09012 | −0.545059 | − | 0.838398i | \(-0.683493\pi\) | ||||
−0.545059 | + | 0.838398i | \(0.683493\pi\) | |||||||
\(954\) | −1.03405e25 | −0.487956 | ||||||||
\(955\) | 9.19441e24 | 0.430027 | ||||||||
\(956\) | 1.03002e25 | 0.477476 | ||||||||
\(957\) | −6.96950e24 | −0.320221 | ||||||||
\(958\) | 1.51130e25 | 0.688245 | ||||||||
\(959\) | 2.96341e25 | 1.33762 | ||||||||
\(960\) | −2.88206e25 | −1.28943 | ||||||||
\(961\) | −6.48541e24 | −0.287600 | ||||||||
\(962\) | −1.20757e25 | −0.530794 | ||||||||
\(963\) | −1.78021e25 | −0.775619 | ||||||||
\(964\) | −1.17458e25 | −0.507258 | ||||||||
\(965\) | −5.26573e25 | −2.25412 | ||||||||
\(966\) | −1.65034e25 | −0.700273 | ||||||||
\(967\) | 3.33756e25 | 1.40380 | 0.701898 | − | 0.712278i | \(-0.252336\pi\) | ||||
0.701898 | + | 0.712278i | \(0.252336\pi\) | |||||||
\(968\) | 2.24558e25 | 0.936244 | ||||||||
\(969\) | 2.59028e25 | 1.07052 | ||||||||
\(970\) | −3.99699e25 | −1.63747 | ||||||||
\(971\) | 3.17068e25 | 1.28762 | 0.643812 | − | 0.765184i | \(-0.277352\pi\) | ||||
0.643812 | + | 0.765184i | \(0.277352\pi\) | |||||||
\(972\) | −1.41814e25 | −0.570896 | ||||||||
\(973\) | −3.05585e24 | −0.121948 | ||||||||
\(974\) | −4.10508e24 | −0.162394 | ||||||||
\(975\) | −5.39073e25 | −2.11402 | ||||||||
\(976\) | 4.16716e24 | 0.162000 | ||||||||
\(977\) | −2.62945e25 | −1.01335 | −0.506676 | − | 0.862136i | \(-0.669126\pi\) | ||||
−0.506676 | + | 0.862136i | \(0.669126\pi\) | |||||||
\(978\) | 2.49163e25 | 0.951928 | ||||||||
\(979\) | −3.56807e25 | −1.35139 | ||||||||
\(980\) | 1.10306e25 | 0.414170 | ||||||||
\(981\) | −3.97366e23 | −0.0147912 | ||||||||
\(982\) | −8.28147e24 | −0.305604 | ||||||||
\(983\) | 1.91222e25 | 0.699572 | 0.349786 | − | 0.936830i | \(-0.386254\pi\) | ||||
0.349786 | + | 0.936830i | \(0.386254\pi\) | |||||||
\(984\) | −4.02021e25 | −1.45811 | ||||||||
\(985\) | −2.21777e25 | −0.797460 | ||||||||
\(986\) | 2.95554e24 | 0.105362 | ||||||||
\(987\) | −1.34003e25 | −0.473609 | ||||||||
\(988\) | −2.85317e25 | −0.999756 | ||||||||
\(989\) | 4.05319e25 | 1.40808 | ||||||||
\(990\) | −2.05664e25 | −0.708369 | ||||||||
\(991\) | −1.64728e24 | −0.0562524 | −0.0281262 | − | 0.999604i | \(-0.508954\pi\) | ||||
−0.0281262 | + | 0.999604i | \(0.508954\pi\) | |||||||
\(992\) | −2.39095e25 | −0.809510 | ||||||||
\(993\) | −2.22256e25 | −0.746080 | ||||||||
\(994\) | −5.09775e24 | −0.169666 | ||||||||
\(995\) | 2.74960e25 | 0.907347 | ||||||||
\(996\) | −1.11127e25 | −0.363592 | ||||||||
\(997\) | −9.66652e24 | −0.313589 | −0.156795 | − | 0.987631i | \(-0.550116\pi\) | ||||
−0.156795 | + | 0.987631i | \(0.550116\pi\) | |||||||
\(998\) | −1.35656e25 | −0.436344 | ||||||||
\(999\) | 7.89059e24 | 0.251654 |
(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 | 29.18.a.b.1.8 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.18.a.b.1.8 | ✓ | 21 | 1.1 | even | 1 | trivial |