Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,15,Mod(7,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(14.9194761782\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} + 9158 x^{12} + 65217 x^{11} + 61148515 x^{10} + 439019974 x^{9} + 189458968156 x^{8} + \cdots + 89\!\cdots\!84 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{81}\cdot 3^{41} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.6 | ||
Root | \(-33.2709 - 57.6269i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.15.d.a.7.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −47.8547 | + | 118.718i | −0.373865 | + | 0.927483i | ||||
\(3\) | − | 1262.67i | − | 0.577350i | ||||||
\(4\) | −11803.8 | − | 11362.4i | −0.720450 | − | 0.693507i | ||||
\(5\) | −132280. | −1.69319 | −0.846595 | − | 0.532238i | \(-0.821351\pi\) | ||||
−0.846595 | + | 0.532238i | \(0.821351\pi\) | |||||||
\(6\) | 149901. | + | 60424.5i | 0.535483 | + | 0.215851i | ||||
\(7\) | 304975.i | 0.370321i | 0.982708 | + | 0.185161i | \(0.0592805\pi\) | ||||
−0.982708 | + | 0.185161i | \(0.940719\pi\) | |||||||
\(8\) | 1.91379e6 | − | 857581.i | 0.912567 | − | 0.408927i | ||||
\(9\) | −1.59432e6 | −0.333333 | ||||||||
\(10\) | 6.33024e6 | − | 1.57040e7i | 0.633024 | − | 1.57040i | ||||
\(11\) | − | 4.87590e6i | − | 0.250211i | −0.992143 | − | 0.125105i | \(-0.960073\pi\) | ||
0.992143 | − | 0.125105i | \(-0.0399269\pi\) | |||||||
\(12\) | −1.43469e7 | + | 1.49043e7i | −0.400397 | + | 0.415952i | ||||
\(13\) | 9.89669e7 | 1.57720 | 0.788599 | − | 0.614907i | \(-0.210807\pi\) | ||||
0.788599 | + | 0.614907i | \(0.210807\pi\) | |||||||
\(14\) | −3.62060e7 | − | 1.45945e7i | −0.343467 | − | 0.138450i | ||||
\(15\) | 1.67026e8i | 0.977563i | ||||||||
\(16\) | 1.02262e7 | + | 2.68241e8i | 0.0380955 | + | 0.999274i | ||||
\(17\) | 4.23677e7 | 0.103251 | 0.0516253 | − | 0.998667i | \(-0.483560\pi\) | ||||
0.0516253 | + | 0.998667i | \(0.483560\pi\) | |||||||
\(18\) | 7.62959e7 | − | 1.89275e8i | 0.124622 | − | 0.309161i | ||||
\(19\) | 1.40872e9i | 1.57597i | 0.615693 | + | 0.787986i | \(0.288876\pi\) | ||||
−0.615693 | + | 0.787986i | \(0.711124\pi\) | |||||||
\(20\) | 1.56142e9 | + | 1.50303e9i | 1.21986 | + | 1.17424i | ||||
\(21\) | 3.85082e8 | 0.213805 | ||||||||
\(22\) | 5.78856e8 | + | 2.33335e8i | 0.232066 | + | 0.0935451i | ||||
\(23\) | − | 4.23629e9i | − | 1.24420i | −0.782937 | − | 0.622101i | \(-0.786279\pi\) | ||
0.782937 | − | 0.622101i | \(-0.213721\pi\) | |||||||
\(24\) | −1.08284e9 | − | 2.41648e9i | −0.236094 | − | 0.526871i | ||||
\(25\) | 1.13946e10 | 1.86689 | ||||||||
\(26\) | −4.73603e9 | + | 1.17491e10i | −0.589660 | + | 1.46283i | ||||
\(27\) | 2.01310e9i | 0.192450i | ||||||||
\(28\) | 3.46526e9 | − | 3.59988e9i | 0.256820 | − | 0.266798i | ||||
\(29\) | −5.57826e9 | −0.323380 | −0.161690 | − | 0.986842i | \(-0.551694\pi\) | ||||
−0.161690 | + | 0.986842i | \(0.551694\pi\) | |||||||
\(30\) | −1.98289e10 | − | 7.99298e9i | −0.906673 | − | 0.365477i | ||||
\(31\) | − | 9.56870e8i | − | 0.0347793i | −0.999849 | − | 0.0173897i | \(-0.994464\pi\) | ||
0.999849 | − | 0.0173897i | \(-0.00553558\pi\) | |||||||
\(32\) | −3.23343e10 | − | 1.16226e10i | −0.941052 | − | 0.338261i | ||||
\(33\) | −6.15663e9 | −0.144459 | ||||||||
\(34\) | −2.02750e9 | + | 5.02980e9i | −0.0386018 | + | 0.0957632i | ||||
\(35\) | − | 4.03423e10i | − | 0.627024i | ||||||
\(36\) | 1.88191e10 | + | 1.81154e10i | 0.240150 | + | 0.231169i | ||||
\(37\) | 1.19922e11 | 1.26324 | 0.631620 | − | 0.775278i | \(-0.282390\pi\) | ||||
0.631620 | + | 0.775278i | \(0.282390\pi\) | |||||||
\(38\) | −1.67240e11 | − | 6.74138e10i | −1.46169 | − | 0.589201i | ||||
\(39\) | − | 1.24962e11i | − | 0.910596i | ||||||
\(40\) | −2.53157e11 | + | 1.13441e11i | −1.54515 | + | 0.692390i | ||||
\(41\) | 2.10357e11 | 1.08012 | 0.540059 | − | 0.841627i | \(-0.318402\pi\) | ||||
0.540059 | + | 0.841627i | \(0.318402\pi\) | |||||||
\(42\) | −1.84280e10 | + | 4.57161e10i | −0.0799343 | + | 0.198301i | ||||
\(43\) | − | 3.76222e11i | − | 1.38409i | −0.721854 | − | 0.692046i | \(-0.756710\pi\) | ||
0.721854 | − | 0.692046i | \(-0.243290\pi\) | |||||||
\(44\) | −5.54020e10 | + | 5.75544e10i | −0.173523 | + | 0.180264i | ||||
\(45\) | 2.10898e11 | 0.564396 | ||||||||
\(46\) | 5.02923e11 | + | 2.02726e11i | 1.15398 | + | 0.465164i | ||||
\(47\) | 8.87229e11i | 1.75126i | 0.482982 | + | 0.875630i | \(0.339554\pi\) | ||||
−0.482982 | + | 0.875630i | \(0.660446\pi\) | |||||||
\(48\) | 3.38698e11 | − | 1.29122e10i | 0.576931 | − | 0.0219944i | ||||
\(49\) | 5.85213e11 | 0.862862 | ||||||||
\(50\) | −5.45285e11 | + | 1.35274e12i | −0.697965 | + | 1.73151i | ||||
\(51\) | − | 5.34962e10i | − | 0.0596118i | ||||||
\(52\) | −1.16819e12 | − | 1.12450e12i | −1.13629 | − | 1.09380i | ||||
\(53\) | −1.43248e11 | −0.121943 | −0.0609717 | − | 0.998139i | \(-0.519420\pi\) | ||||
−0.0609717 | + | 0.998139i | \(0.519420\pi\) | |||||||
\(54\) | −2.38990e11 | − | 9.63362e10i | −0.178494 | − | 0.0719504i | ||||
\(55\) | 6.44986e11i | 0.423654i | ||||||||
\(56\) | 2.61541e11 | + | 5.83660e11i | 0.151434 | + | 0.337943i | ||||
\(57\) | 1.77874e12 | 0.909888 | ||||||||
\(58\) | 2.66946e11 | − | 6.62239e11i | 0.120900 | − | 0.299929i | ||||
\(59\) | − | 2.40999e12i | − | 0.968391i | −0.874960 | − | 0.484195i | \(-0.839112\pi\) | ||
0.874960 | − | 0.484195i | \(-0.160888\pi\) | |||||||
\(60\) | 1.89782e12 | − | 1.97155e12i | 0.677947 | − | 0.704285i | ||||
\(61\) | −2.37831e12 | −0.756764 | −0.378382 | − | 0.925650i | \(-0.623519\pi\) | ||||
−0.378382 | + | 0.925650i | \(0.623519\pi\) | |||||||
\(62\) | 1.13598e11 | + | 4.57908e10i | 0.0322572 | + | 0.0130028i | ||||
\(63\) | − | 4.86229e11i | − | 0.123440i | ||||||
\(64\) | 2.92715e12 | − | 3.28247e12i | 0.665558 | − | 0.746346i | ||||
\(65\) | −1.30914e13 | −2.67050 | ||||||||
\(66\) | 2.94624e11 | − | 7.30901e11i | 0.0540083 | − | 0.133983i | ||||
\(67\) | − | 1.58948e12i | − | 0.262259i | −0.991365 | − | 0.131129i | \(-0.958140\pi\) | ||
0.991365 | − | 0.131129i | \(-0.0418604\pi\) | |||||||
\(68\) | −5.00102e11 | − | 4.81400e11i | −0.0743869 | − | 0.0716050i | ||||
\(69\) | −5.34901e12 | −0.718340 | ||||||||
\(70\) | 4.78935e12 | + | 1.93057e12i | 0.581554 | + | 0.234422i | ||||
\(71\) | 1.62907e13i | 1.79115i | 0.444913 | + | 0.895574i | \(0.353234\pi\) | ||||
−0.444913 | + | 0.895574i | \(0.646766\pi\) | |||||||
\(72\) | −3.05120e12 | + | 1.36726e12i | −0.304189 | + | 0.136309i | ||||
\(73\) | 8.92687e12 | 0.808052 | 0.404026 | − | 0.914747i | \(-0.367610\pi\) | ||||
0.404026 | + | 0.914747i | \(0.367610\pi\) | |||||||
\(74\) | −5.73882e12 | + | 1.42368e13i | −0.472281 | + | 1.17163i | ||||
\(75\) | − | 1.43875e13i | − | 1.07785i | ||||||
\(76\) | 1.60064e13 | − | 1.66283e13i | 1.09295 | − | 1.13541i | ||||
\(77\) | 1.48703e12 | 0.0926583 | ||||||||
\(78\) | 1.48352e13 | + | 5.98003e12i | 0.844563 | + | 0.340440i | ||||
\(79\) | 1.91983e13i | 0.999706i | 0.866110 | + | 0.499853i | \(0.166613\pi\) | ||||
−0.866110 | + | 0.499853i | \(0.833387\pi\) | |||||||
\(80\) | −1.35272e12 | − | 3.54830e13i | −0.0645028 | − | 1.69196i | ||||
\(81\) | 2.54187e12 | 0.111111 | ||||||||
\(82\) | −1.00666e13 | + | 2.49732e13i | −0.403818 | + | 1.00179i | ||||
\(83\) | − | 4.14129e11i | − | 0.0152612i | −0.999971 | − | 0.00763061i | \(-0.997571\pi\) | ||
0.999971 | − | 0.00763061i | \(-0.00242892\pi\) | |||||||
\(84\) | −4.54545e12 | − | 4.37546e12i | −0.154036 | − | 0.148275i | ||||
\(85\) | −5.60442e12 | −0.174823 | ||||||||
\(86\) | 4.46642e13 | + | 1.80040e13i | 1.28372 | + | 0.517464i | ||||
\(87\) | 7.04347e12i | 0.186703i | ||||||||
\(88\) | −4.18148e12 | − | 9.33146e12i | −0.102318 | − | 0.228334i | ||||
\(89\) | 3.16654e13 | 0.715904 | 0.357952 | − | 0.933740i | \(-0.383475\pi\) | ||||
0.357952 | + | 0.933740i | \(0.383475\pi\) | |||||||
\(90\) | −1.00925e13 | + | 2.50373e13i | −0.211008 | + | 0.523468i | ||||
\(91\) | 3.01825e13i | 0.584070i | ||||||||
\(92\) | −4.81345e13 | + | 5.00045e13i | −0.862863 | + | 0.896384i | ||||
\(93\) | −1.20821e12 | −0.0200799 | ||||||||
\(94\) | −1.05330e14 | − | 4.24581e13i | −1.62426 | − | 0.654735i | ||||
\(95\) | − | 1.86346e14i | − | 2.66842i | ||||||
\(96\) | −1.46754e13 | + | 4.08274e13i | −0.195295 | + | 0.543317i | ||||
\(97\) | 6.43443e13 | 0.796358 | 0.398179 | − | 0.917308i | \(-0.369642\pi\) | ||||
0.398179 | + | 0.917308i | \(0.369642\pi\) | |||||||
\(98\) | −2.80052e13 | + | 6.94752e13i | −0.322594 | + | 0.800290i | ||||
\(99\) | 7.77376e12i | 0.0834036i | ||||||||
\(100\) | −1.34500e14 | − | 1.29470e14i | −1.34500 | − | 1.29470i | ||||
\(101\) | 4.71110e13 | 0.439413 | 0.219706 | − | 0.975566i | \(-0.429490\pi\) | ||||
0.219706 | + | 0.975566i | \(0.429490\pi\) | |||||||
\(102\) | 6.35096e12 | + | 2.56005e12i | 0.0552889 | + | 0.0222868i | ||||
\(103\) | 6.34102e13i | 0.515583i | 0.966201 | + | 0.257791i | \(0.0829948\pi\) | ||||
−0.966201 | + | 0.257791i | \(0.917005\pi\) | |||||||
\(104\) | 1.89402e14 | − | 8.48722e13i | 1.43930 | − | 0.644959i | ||||
\(105\) | −5.09388e13 | −0.362012 | ||||||||
\(106\) | 6.85510e12 | − | 1.70061e13i | 0.0455904 | − | 0.113100i | ||||
\(107\) | − | 5.12243e13i | − | 0.318999i | −0.987198 | − | 0.159500i | \(-0.949012\pi\) | ||
0.987198 | − | 0.159500i | \(-0.0509881\pi\) | |||||||
\(108\) | 2.28736e13 | − | 2.37623e13i | 0.133466 | − | 0.138651i | ||||
\(109\) | −2.78956e13 | −0.152598 | −0.0762992 | − | 0.997085i | \(-0.524310\pi\) | ||||
−0.0762992 | + | 0.997085i | \(0.524310\pi\) | |||||||
\(110\) | −7.65713e13 | − | 3.08656e13i | −0.392932 | − | 0.158389i | ||||
\(111\) | − | 1.51421e14i | − | 0.729332i | ||||||
\(112\) | −8.18068e13 | + | 3.11873e12i | −0.370052 | + | 0.0141076i | ||||
\(113\) | 1.90871e14 | 0.811319 | 0.405659 | − | 0.914024i | \(-0.367042\pi\) | ||||
0.405659 | + | 0.914024i | \(0.367042\pi\) | |||||||
\(114\) | −8.51210e13 | + | 2.11168e14i | −0.340175 | + | 0.843906i | ||||
\(115\) | 5.60378e14i | 2.10667i | ||||||||
\(116\) | 6.58449e13 | + | 6.33825e13i | 0.232979 | + | 0.224266i | ||||
\(117\) | −1.57785e14 | −0.525733 | ||||||||
\(118\) | 2.86108e14 | + | 1.15329e14i | 0.898166 | + | 0.362048i | ||||
\(119\) | 1.29211e13i | 0.0382359i | ||||||||
\(120\) | 1.43238e14 | + | 3.19653e14i | 0.399752 | + | 0.892092i | ||||
\(121\) | 3.55975e14 | 0.937395 | ||||||||
\(122\) | 1.13814e14 | − | 2.82348e14i | 0.282928 | − | 0.701886i | ||||
\(123\) | − | 2.65611e14i | − | 0.623606i | ||||||
\(124\) | −1.08724e13 | + | 1.12948e13i | −0.0241197 | + | 0.0250568i | ||||
\(125\) | −6.99905e14 | −1.46781 | ||||||||
\(126\) | 5.77241e13 | + | 2.32684e13i | 0.114489 | + | 0.0461501i | ||||
\(127\) | 4.50531e14i | 0.845471i | 0.906253 | + | 0.422735i | \(0.138930\pi\) | ||||
−0.906253 | + | 0.422735i | \(0.861070\pi\) | |||||||
\(128\) | 2.49609e14 | + | 5.04587e14i | 0.443395 | + | 0.896327i | ||||
\(129\) | −4.75042e14 | −0.799106 | ||||||||
\(130\) | 6.26485e14 | − | 1.55418e15i | 0.998405 | − | 2.47684i | ||||
\(131\) | − | 1.94922e14i | − | 0.294417i | −0.989105 | − | 0.147208i | \(-0.952971\pi\) | ||
0.989105 | − | 0.147208i | \(-0.0470288\pi\) | |||||||
\(132\) | 7.26719e13 | + | 6.99542e13i | 0.104076 | + | 0.100184i | ||||
\(133\) | −4.29624e14 | −0.583616 | ||||||||
\(134\) | 1.88699e14 | + | 7.60640e13i | 0.243241 | + | 0.0980495i | ||||
\(135\) | − | 2.66293e14i | − | 0.325854i | ||||||
\(136\) | 8.10830e13 | − | 3.63338e13i | 0.0942231 | − | 0.0422219i | ||||
\(137\) | −1.14701e15 | −1.26626 | −0.633131 | − | 0.774044i | \(-0.718231\pi\) | ||||
−0.633131 | + | 0.774044i | \(0.718231\pi\) | |||||||
\(138\) | 2.55976e14 | − | 6.35023e14i | 0.268562 | − | 0.666248i | ||||
\(139\) | 2.30780e14i | 0.230194i | 0.993354 | + | 0.115097i | \(0.0367179\pi\) | ||||
−0.993354 | + | 0.115097i | \(0.963282\pi\) | |||||||
\(140\) | −4.58386e14 | + | 4.76194e14i | −0.434846 | + | 0.451739i | ||||
\(141\) | 1.12027e15 | 1.01109 | ||||||||
\(142\) | −1.93400e15 | − | 7.79587e14i | −1.66126 | − | 0.669648i | ||||
\(143\) | − | 4.82553e14i | − | 0.394632i | ||||||
\(144\) | −1.63038e13 | − | 4.27662e14i | −0.0126985 | − | 0.333091i | ||||
\(145\) | 7.37894e14 | 0.547543 | ||||||||
\(146\) | −4.27193e14 | + | 1.05978e15i | −0.302103 | + | 0.749455i | ||||
\(147\) | − | 7.38928e14i | − | 0.498174i | ||||||
\(148\) | −1.41554e15 | − | 1.36260e15i | −0.910101 | − | 0.876066i | ||||
\(149\) | 3.10081e14 | 0.190183 | 0.0950913 | − | 0.995469i | \(-0.469686\pi\) | ||||
0.0950913 | + | 0.995469i | \(0.469686\pi\) | |||||||
\(150\) | 1.70806e15 | + | 6.88512e14i | 0.999687 | + | 0.402970i | ||||
\(151\) | 1.66702e15i | 0.931328i | 0.884961 | + | 0.465664i | \(0.154185\pi\) | ||||
−0.884961 | + | 0.465664i | \(0.845815\pi\) | |||||||
\(152\) | 1.20809e15 | + | 2.69599e15i | 0.644457 | + | 1.43818i | ||||
\(153\) | −6.75478e13 | −0.0344169 | ||||||||
\(154\) | −7.11614e13 | + | 1.76537e14i | −0.0346417 | + | 0.0859390i | ||||
\(155\) | 1.26575e14i | 0.0588880i | ||||||||
\(156\) | −1.41987e15 | + | 1.47503e15i | −0.631505 | + | 0.656039i | ||||
\(157\) | 9.32853e14 | 0.396749 | 0.198374 | − | 0.980126i | \(-0.436434\pi\) | ||||
0.198374 | + | 0.980126i | \(0.436434\pi\) | |||||||
\(158\) | −2.27918e15 | − | 9.18728e14i | −0.927211 | − | 0.373755i | ||||
\(159\) | 1.80874e14i | 0.0704040i | ||||||||
\(160\) | 4.27720e15 | + | 1.53744e15i | 1.59338 | + | 0.572740i | ||||
\(161\) | 1.29196e15 | 0.460754 | ||||||||
\(162\) | −1.21640e14 | + | 3.01765e14i | −0.0415406 | + | 0.103054i | ||||
\(163\) | − | 4.90106e15i | − | 1.60316i | −0.597887 | − | 0.801580i | \(-0.703993\pi\) | ||
0.597887 | − | 0.801580i | \(-0.296007\pi\) | |||||||
\(164\) | −2.48303e15 | − | 2.39017e15i | −0.778170 | − | 0.749069i | ||||
\(165\) | 8.14401e14 | 0.244597 | ||||||||
\(166\) | 4.91645e13 | + | 1.98181e13i | 0.0141545 | + | 0.00570564i | ||||
\(167\) | 2.90593e15i | 0.802177i | 0.916039 | + | 0.401088i | \(0.131368\pi\) | ||||
−0.916039 | + | 0.401088i | \(0.868632\pi\) | |||||||
\(168\) | 7.36967e14 | − | 3.30239e14i | 0.195112 | − | 0.0874306i | ||||
\(169\) | 5.85707e15 | 1.48756 | ||||||||
\(170\) | 2.68198e14 | − | 6.65344e14i | 0.0653602 | − | 0.162145i | ||||
\(171\) | − | 2.24595e15i | − | 0.525324i | ||||||
\(172\) | −4.27479e15 | + | 4.44086e15i | −0.959877 | + | 0.997168i | ||||
\(173\) | 7.13782e15 | 1.53902 | 0.769508 | − | 0.638638i | \(-0.220502\pi\) | ||||
0.769508 | + | 0.638638i | \(0.220502\pi\) | |||||||
\(174\) | −8.36186e14 | − | 3.37064e14i | −0.173164 | − | 0.0698019i | ||||
\(175\) | 3.47507e15i | 0.691349i | ||||||||
\(176\) | 1.30791e15 | − | 4.98618e13i | 0.250029 | − | 0.00953189i | ||||
\(177\) | −3.04301e15 | −0.559101 | ||||||||
\(178\) | −1.51534e15 | + | 3.75925e15i | −0.267652 | + | 0.663989i | ||||
\(179\) | − | 7.67927e14i | − | 0.130421i | −0.997872 | − | 0.0652107i | \(-0.979228\pi\) | ||
0.997872 | − | 0.0652107i | \(-0.0207719\pi\) | |||||||
\(180\) | −2.48940e15 | − | 2.39631e15i | −0.406619 | − | 0.391413i | ||||
\(181\) | −1.13752e16 | −1.78735 | −0.893676 | − | 0.448713i | \(-0.851882\pi\) | ||||
−0.893676 | + | 0.448713i | \(0.851882\pi\) | |||||||
\(182\) | −3.58320e15 | − | 1.44437e15i | −0.541715 | − | 0.218364i | ||||
\(183\) | 3.00301e15i | 0.436918i | ||||||||
\(184\) | −3.63296e15 | − | 8.10738e15i | −0.508787 | − | 1.13542i | ||||
\(185\) | −1.58633e16 | −2.13890 | ||||||||
\(186\) | 5.78184e13 | − | 1.43436e14i | 0.00750716 | − | 0.0186237i | ||||
\(187\) | − | 2.06581e14i | − | 0.0258344i | ||||||
\(188\) | 1.00811e16 | − | 1.04727e16i | 1.21451 | − | 1.26170i | ||||
\(189\) | −6.13945e14 | −0.0712684 | ||||||||
\(190\) | 2.21226e16 | + | 8.91752e15i | 2.47491 | + | 0.997629i | ||||
\(191\) | − | 1.00557e16i | − | 1.08437i | −0.840259 | − | 0.542185i | \(-0.817597\pi\) | ||
0.840259 | − | 0.542185i | \(-0.182403\pi\) | |||||||
\(192\) | −4.14465e15 | − | 3.69602e15i | −0.430903 | − | 0.384260i | ||||
\(193\) | −1.56620e14 | −0.0157017 | −0.00785085 | − | 0.999969i | \(-0.502499\pi\) | ||||
−0.00785085 | + | 0.999969i | \(0.502499\pi\) | |||||||
\(194\) | −3.07918e15 | + | 7.63882e15i | −0.297730 | + | 0.738608i | ||||
\(195\) | 1.65300e16i | 1.54181i | ||||||||
\(196\) | −6.90777e15 | − | 6.64944e15i | −0.621649 | − | 0.598401i | ||||
\(197\) | 1.34099e16 | 1.16456 | 0.582281 | − | 0.812988i | \(-0.302161\pi\) | ||||
0.582281 | + | 0.812988i | \(0.302161\pi\) | |||||||
\(198\) | −9.22884e14 | − | 3.72011e14i | −0.0773554 | − | 0.0311817i | ||||
\(199\) | − | 1.95305e16i | − | 1.58031i | −0.612908 | − | 0.790154i | \(-0.710000\pi\) | ||
0.612908 | − | 0.790154i | \(-0.290000\pi\) | |||||||
\(200\) | 2.18069e16 | − | 9.77179e15i | 1.70366 | − | 0.763421i | ||||
\(201\) | −2.00698e15 | −0.151415 | ||||||||
\(202\) | −2.25448e15 | + | 5.59291e15i | −0.164281 | + | 0.407548i | ||||
\(203\) | − | 1.70123e15i | − | 0.119754i | ||||||
\(204\) | −6.07847e14 | + | 6.31461e14i | −0.0413412 | + | 0.0429473i | ||||
\(205\) | −2.78262e16 | −1.82884 | ||||||||
\(206\) | −7.52792e15 | − | 3.03448e15i | −0.478194 | − | 0.192759i | ||||
\(207\) | 6.75401e15i | 0.414734i | ||||||||
\(208\) | 1.01205e15 | + | 2.65469e16i | 0.0600841 | + | 1.57605i | ||||
\(209\) | 6.86876e15 | 0.394325 | ||||||||
\(210\) | 2.43766e15 | − | 6.04734e15i | 0.135344 | − | 0.335760i | ||||
\(211\) | 1.59797e16i | 0.858204i | 0.903256 | + | 0.429102i | \(0.141170\pi\) | ||||
−0.903256 | + | 0.429102i | \(0.858830\pi\) | |||||||
\(212\) | 1.69088e15 | + | 1.62765e15i | 0.0878540 | + | 0.0845686i | ||||
\(213\) | 2.05697e16 | 1.03412 | ||||||||
\(214\) | 6.08124e15 | + | 2.45133e15i | 0.295867 | + | 0.119263i | ||||
\(215\) | 4.97668e16i | 2.34353i | ||||||||
\(216\) | 1.72639e15 | + | 3.85265e15i | 0.0786980 | + | 0.175624i | ||||
\(217\) | 2.91822e14 | 0.0128795 | ||||||||
\(218\) | 1.33494e15 | − | 3.31170e15i | 0.0570512 | − | 0.141532i | ||||
\(219\) | − | 1.12717e16i | − | 0.466529i | ||||||
\(220\) | 7.32860e15 | − | 7.61331e15i | 0.293807 | − | 0.305221i | ||||
\(221\) | 4.19300e15 | 0.162847 | ||||||||
\(222\) | 1.79764e16 | + | 7.24621e15i | 0.676443 | + | 0.272672i | ||||
\(223\) | − | 3.22714e16i | − | 1.17675i | −0.808589 | − | 0.588374i | \(-0.799768\pi\) | ||
0.808589 | − | 0.588374i | \(-0.200232\pi\) | |||||||
\(224\) | 3.54459e15 | − | 9.86117e15i | 0.125265 | − | 0.348492i | ||||
\(225\) | −1.81667e16 | −0.622296 | ||||||||
\(226\) | −9.13409e15 | + | 2.26598e16i | −0.303324 | + | 0.752484i | ||||
\(227\) | 1.07194e16i | 0.345137i | 0.984998 | + | 0.172568i | \(0.0552066\pi\) | ||||
−0.984998 | + | 0.172568i | \(0.944793\pi\) | |||||||
\(228\) | −2.09959e16 | − | 2.02108e16i | −0.655528 | − | 0.631014i | ||||
\(229\) | 2.34325e16 | 0.709529 | 0.354764 | − | 0.934956i | \(-0.384561\pi\) | ||||
0.354764 | + | 0.934956i | \(0.384561\pi\) | |||||||
\(230\) | −6.65268e16 | − | 2.68167e16i | −1.95390 | − | 0.787610i | ||||
\(231\) | − | 1.87762e15i | − | 0.0534963i | ||||||
\(232\) | −1.06756e16 | + | 4.78381e15i | −0.295106 | + | 0.132239i | ||||
\(233\) | 2.07306e16 | 0.556060 | 0.278030 | − | 0.960572i | \(-0.410319\pi\) | ||||
0.278030 | + | 0.960572i | \(0.410319\pi\) | |||||||
\(234\) | 7.55077e15 | − | 1.87319e16i | 0.196553 | − | 0.487608i | ||||
\(235\) | − | 1.17363e17i | − | 2.96522i | ||||||
\(236\) | −2.73833e16 | + | 2.84471e16i | −0.671586 | + | 0.697677i | ||||
\(237\) | 2.42410e16 | 0.577181 | ||||||||
\(238\) | −1.53397e15 | − | 6.18337e14i | −0.0354631 | − | 0.0142951i | ||||
\(239\) | − | 2.50399e16i | − | 0.562144i | −0.959687 | − | 0.281072i | \(-0.909310\pi\) | ||
0.959687 | − | 0.281072i | \(-0.0906900\pi\) | |||||||
\(240\) | −4.48031e16 | + | 1.70803e15i | −0.976854 | + | 0.0372407i | ||||
\(241\) | 6.25474e16 | 1.32462 | 0.662308 | − | 0.749231i | \(-0.269577\pi\) | ||||
0.662308 | + | 0.749231i | \(0.269577\pi\) | |||||||
\(242\) | −1.70351e16 | + | 4.22606e16i | −0.350459 | + | 0.869418i | ||||
\(243\) | − | 3.20953e15i | − | 0.0641500i | ||||||
\(244\) | 2.80733e16 | + | 2.70234e16i | 0.545210 | + | 0.524821i | ||||
\(245\) | −7.74122e16 | −1.46099 | ||||||||
\(246\) | 3.15328e16 | + | 1.27107e16i | 0.578384 | + | 0.233145i | ||||
\(247\) | 1.39416e17i | 2.48562i | ||||||||
\(248\) | −8.20594e14 | − | 1.83125e15i | −0.0142222 | − | 0.0317385i | ||||
\(249\) | −5.22907e14 | −0.00881107 | ||||||||
\(250\) | 3.34938e16 | − | 8.30912e16i | 0.548762 | − | 1.36137i | ||||
\(251\) | − | 8.02535e16i | − | 1.27864i | −0.768941 | − | 0.639320i | \(-0.779216\pi\) | ||
0.768941 | − | 0.639320i | \(-0.220784\pi\) | |||||||
\(252\) | −5.52474e15 | + | 5.73938e15i | −0.0856068 | + | 0.0889326i | ||||
\(253\) | −2.06557e16 | −0.311312 | ||||||||
\(254\) | −5.34861e16 | − | 2.15600e16i | −0.784160 | − | 0.316092i | ||||
\(255\) | 7.07650e15i | 0.100934i | ||||||||
\(256\) | −7.18484e16 | + | 5.48615e15i | −0.997097 | + | 0.0761356i | ||||
\(257\) | −2.11552e16 | −0.285683 | −0.142842 | − | 0.989746i | \(-0.545624\pi\) | ||||
−0.142842 | + | 0.989746i | \(0.545624\pi\) | |||||||
\(258\) | 2.27330e16 | − | 5.63960e16i | 0.298758 | − | 0.741157i | ||||
\(259\) | 3.65732e16i | 0.467805i | ||||||||
\(260\) | 1.54529e17 | + | 1.48750e17i | 1.92396 | + | 1.85201i | ||||
\(261\) | 8.89355e15 | 0.107793 | ||||||||
\(262\) | 2.31408e16 | + | 9.32796e15i | 0.273067 | + | 0.110072i | ||||
\(263\) | 1.33110e17i | 1.52940i | 0.644388 | + | 0.764699i | \(0.277112\pi\) | ||||
−0.644388 | + | 0.764699i | \(0.722888\pi\) | |||||||
\(264\) | −1.17825e16 | + | 5.27981e15i | −0.131829 | + | 0.0590732i | ||||
\(265\) | 1.89489e16 | 0.206473 | ||||||||
\(266\) | 2.05596e16 | − | 5.10040e16i | 0.218194 | − | 0.541294i | ||||
\(267\) | − | 3.99828e16i | − | 0.413328i | ||||||
\(268\) | −1.80603e16 | + | 1.87619e16i | −0.181878 | + | 0.188944i | ||||
\(269\) | 9.41135e16 | 0.923391 | 0.461696 | − | 0.887038i | \(-0.347241\pi\) | ||||
0.461696 | + | 0.887038i | \(0.347241\pi\) | |||||||
\(270\) | 3.16137e16 | + | 1.27434e16i | 0.302224 | + | 0.121826i | ||||
\(271\) | 3.83327e16i | 0.357096i | 0.983931 | + | 0.178548i | \(0.0571399\pi\) | ||||
−0.983931 | + | 0.178548i | \(0.942860\pi\) | |||||||
\(272\) | 4.33260e14 | + | 1.13647e16i | 0.00393338 | + | 0.103176i | ||||
\(273\) | 3.81104e16 | 0.337213 | ||||||||
\(274\) | 5.48899e16 | − | 1.36171e17i | 0.473412 | − | 1.17444i | ||||
\(275\) | − | 5.55589e16i | − | 0.467116i | ||||||
\(276\) | 6.31389e16 | + | 6.07777e16i | 0.517528 | + | 0.498174i | ||||
\(277\) | −8.30340e16 | −0.663586 | −0.331793 | − | 0.943352i | \(-0.607654\pi\) | ||||
−0.331793 | + | 0.943352i | \(0.607654\pi\) | |||||||
\(278\) | −2.73977e16 | − | 1.10439e16i | −0.213501 | − | 0.0860616i | ||||
\(279\) | 1.52556e15i | 0.0115931i | ||||||||
\(280\) | −3.45968e16 | − | 7.72067e16i | −0.256407 | − | 0.572201i | ||||
\(281\) | −8.26427e16 | −0.597393 | −0.298697 | − | 0.954348i | \(-0.596552\pi\) | ||||
−0.298697 | + | 0.954348i | \(0.596552\pi\) | |||||||
\(282\) | −5.36104e16 | + | 1.32996e17i | −0.378012 | + | 0.937770i | ||||
\(283\) | − | 4.46688e16i | − | 0.307255i | −0.988129 | − | 0.153628i | \(-0.950904\pi\) | ||
0.988129 | − | 0.153628i | \(-0.0490956\pi\) | |||||||
\(284\) | 1.85102e17 | − | 1.92293e17i | 1.24217 | − | 1.29043i | ||||
\(285\) | −2.35292e17 | −1.54061 | ||||||||
\(286\) | 5.72876e16 | + | 2.30924e16i | 0.366015 | + | 0.147539i | ||||
\(287\) | 6.41539e16i | 0.399990i | ||||||||
\(288\) | 5.15513e16 | + | 1.85301e16i | 0.313684 | + | 0.112754i | ||||
\(289\) | −1.66583e17 | −0.989339 | ||||||||
\(290\) | −3.53117e16 | + | 8.76012e16i | −0.204707 | + | 0.507837i | ||||
\(291\) | − | 8.12454e16i | − | 0.459777i | ||||||
\(292\) | −1.05371e17 | − | 1.01431e17i | −0.582161 | − | 0.560390i | ||||
\(293\) | −1.25777e17 | −0.678463 | −0.339232 | − | 0.940703i | \(-0.610167\pi\) | ||||
−0.339232 | + | 0.940703i | \(0.610167\pi\) | |||||||
\(294\) | 8.77239e16 | + | 3.53612e16i | 0.462048 | + | 0.186250i | ||||
\(295\) | 3.18794e17i | 1.63967i | ||||||||
\(296\) | 2.29505e17 | − | 1.02843e17i | 1.15279 | − | 0.516572i | ||||
\(297\) | 9.81565e15 | 0.0481531 | ||||||||
\(298\) | −1.48388e16 | + | 3.68121e16i | −0.0711026 | + | 0.176391i | ||||
\(299\) | − | 4.19252e17i | − | 1.96235i | ||||||
\(300\) | −1.63477e17 | + | 1.69828e17i | −0.747496 | + | 0.776536i | ||||
\(301\) | 1.14738e17 | 0.512558 | ||||||||
\(302\) | −1.97905e17 | − | 7.97749e16i | −0.863791 | − | 0.348191i | ||||
\(303\) | − | 5.94854e16i | − | 0.253695i | ||||||
\(304\) | −3.77875e17 | + | 1.44058e16i | −1.57483 | + | 0.0600374i | ||||
\(305\) | 3.14604e17 | 1.28134 | ||||||||
\(306\) | 3.23248e15 | − | 8.01913e15i | 0.0128673 | − | 0.0319211i | ||||
\(307\) | 2.18013e17i | 0.848229i | 0.905609 | + | 0.424114i | \(0.139415\pi\) | ||||
−0.905609 | + | 0.424114i | \(0.860585\pi\) | |||||||
\(308\) | −1.75527e16 | − | 1.68963e16i | −0.0667557 | − | 0.0642592i | ||||
\(309\) | 8.00658e16 | 0.297672 | ||||||||
\(310\) | −1.50267e16 | − | 6.05722e15i | −0.0546176 | − | 0.0220162i | ||||
\(311\) | − | 2.54095e17i | − | 0.902971i | −0.892278 | − | 0.451486i | \(-0.850894\pi\) | ||
0.892278 | − | 0.451486i | \(-0.149106\pi\) | |||||||
\(312\) | −1.07165e17 | − | 2.39151e17i | −0.372367 | − | 0.830980i | ||||
\(313\) | 7.43667e16 | 0.252678 | 0.126339 | − | 0.991987i | \(-0.459677\pi\) | ||||
0.126339 | + | 0.991987i | \(0.459677\pi\) | |||||||
\(314\) | −4.46415e16 | + | 1.10746e17i | −0.148331 | + | 0.367978i | ||||
\(315\) | 6.43186e16i | 0.209008i | ||||||||
\(316\) | 2.18139e17 | − | 2.26613e17i | 0.693304 | − | 0.720238i | ||||
\(317\) | 1.10543e17 | 0.343651 | 0.171826 | − | 0.985127i | \(-0.445033\pi\) | ||||
0.171826 | + | 0.985127i | \(0.445033\pi\) | |||||||
\(318\) | −2.14730e16 | − | 8.65570e15i | −0.0652985 | − | 0.0263216i | ||||
\(319\) | 2.71990e16i | 0.0809130i | ||||||||
\(320\) | −3.87205e17 | + | 4.34206e17i | −1.12692 | + | 1.26371i | ||||
\(321\) | −6.46792e16 | −0.184174 | ||||||||
\(322\) | −6.18266e16 | + | 1.53379e17i | −0.172260 | + | 0.427342i | ||||
\(323\) | 5.96841e16i | 0.162720i | ||||||||
\(324\) | −3.00038e16 | − | 2.88818e16i | −0.0800500 | − | 0.0770564i | ||||
\(325\) | 1.12769e18 | 2.94446 | ||||||||
\(326\) | 5.81844e17 | + | 2.34539e17i | 1.48690 | + | 0.599366i | ||||
\(327\) | 3.52228e16i | 0.0881027i | ||||||||
\(328\) | 4.02581e17 | − | 1.80399e17i | 0.985680 | − | 0.441689i | ||||
\(329\) | −2.70583e17 | −0.648529 | ||||||||
\(330\) | −3.89730e16 | + | 9.66839e16i | −0.0914462 | + | 0.226859i | ||||
\(331\) | − | 1.45361e17i | − | 0.333927i | −0.985963 | − | 0.166964i | \(-0.946604\pi\) | ||
0.985963 | − | 0.166964i | \(-0.0533962\pi\) | |||||||
\(332\) | −4.70551e15 | + | 4.88832e15i | −0.0105838 | + | 0.0109949i | ||||
\(333\) | −1.91194e17 | −0.421080 | ||||||||
\(334\) | −3.44986e17 | − | 1.39063e17i | −0.744005 | − | 0.299906i | ||||
\(335\) | 2.10256e17i | 0.444054i | ||||||||
\(336\) | 3.93791e15 | + | 1.03295e17i | 0.00814500 | + | 0.213650i | ||||
\(337\) | −4.26108e17 | −0.863198 | −0.431599 | − | 0.902066i | \(-0.642050\pi\) | ||||
−0.431599 | + | 0.902066i | \(0.642050\pi\) | |||||||
\(338\) | −2.80289e17 | + | 6.95338e17i | −0.556145 | + | 1.37968i | ||||
\(339\) | − | 2.41006e17i | − | 0.468415i | ||||||
\(340\) | 6.61537e16 | + | 6.36798e16i | 0.125951 | + | 0.121241i | ||||
\(341\) | −4.66560e15 | −0.00870216 | ||||||||
\(342\) | 2.66634e17 | + | 1.07479e17i | 0.487229 | + | 0.196400i | ||||
\(343\) | 3.85317e17i | 0.689857i | ||||||||
\(344\) | −3.22641e17 | − | 7.20010e17i | −0.565992 | − | 1.26308i | ||||
\(345\) | 7.07570e17 | 1.21629 | ||||||||
\(346\) | −3.41579e17 | + | 8.47387e17i | −0.575384 | + | 1.42741i | ||||
\(347\) | 1.97652e17i | 0.326284i | 0.986603 | + | 0.163142i | \(0.0521628\pi\) | ||||
−0.986603 | + | 0.163142i | \(0.947837\pi\) | |||||||
\(348\) | 8.00309e16 | − | 8.31401e16i | 0.129480 | − | 0.134510i | ||||
\(349\) | −5.44653e17 | −0.863658 | −0.431829 | − | 0.901955i | \(-0.642132\pi\) | ||||
−0.431829 | + | 0.901955i | \(0.642132\pi\) | |||||||
\(350\) | −4.12553e17 | − | 1.66299e17i | −0.641214 | − | 0.258471i | ||||
\(351\) | 1.99230e17i | 0.303532i | ||||||||
\(352\) | −5.66704e16 | + | 1.57659e17i | −0.0846365 | + | 0.235461i | ||||
\(353\) | 4.38699e17 | 0.642308 | 0.321154 | − | 0.947027i | \(-0.395929\pi\) | ||||
0.321154 | + | 0.947027i | \(0.395929\pi\) | |||||||
\(354\) | 1.45622e17 | − | 3.61259e17i | 0.209028 | − | 0.518556i | ||||
\(355\) | − | 2.15494e18i | − | 3.03275i | ||||||
\(356\) | −3.73774e17 | − | 3.59796e17i | −0.515773 | − | 0.496485i | ||||
\(357\) | 1.63150e16 | 0.0220755 | ||||||||
\(358\) | 9.11666e16 | + | 3.67489e16i | 0.120964 | + | 0.0487600i | ||||
\(359\) | 1.24662e18i | 1.62208i | 0.584992 | + | 0.811039i | \(0.301098\pi\) | ||||
−0.584992 | + | 0.811039i | \(0.698902\pi\) | |||||||
\(360\) | 4.03614e17 | − | 1.80862e17i | 0.515050 | − | 0.230797i | ||||
\(361\) | −1.18548e18 | −1.48369 | ||||||||
\(362\) | 5.44358e17 | − | 1.35044e18i | 0.668228 | − | 1.65774i | ||||
\(363\) | − | 4.49478e17i | − | 0.541205i | ||||||
\(364\) | 3.42946e17 | − | 3.56269e17i | 0.405057 | − | 0.420793i | ||||
\(365\) | −1.18085e18 | −1.36819 | ||||||||
\(366\) | −3.56511e17 | − | 1.43708e17i | −0.405234 | − | 0.163348i | ||||
\(367\) | 2.63416e17i | 0.293751i | 0.989155 | + | 0.146875i | \(0.0469216\pi\) | ||||
−0.989155 | + | 0.146875i | \(0.953078\pi\) | |||||||
\(368\) | 1.13634e18 | − | 4.33210e16i | 1.24330 | − | 0.0473984i | ||||
\(369\) | −3.35378e17 | −0.360039 | ||||||||
\(370\) | 7.59134e17 | − | 1.88326e18i | 0.799662 | − | 1.98380i | ||||
\(371\) | − | 4.36872e16i | − | 0.0451582i | ||||||
\(372\) | 1.42615e16 | + | 1.37282e16i | 0.0144665 | + | 0.0139255i | ||||
\(373\) | −1.50232e17 | −0.149555 | −0.0747776 | − | 0.997200i | \(-0.523825\pi\) | ||||
−0.0747776 | + | 0.997200i | \(0.523825\pi\) | |||||||
\(374\) | 2.45248e16 | + | 9.88587e15i | 0.0239610 | + | 0.00965859i | ||||
\(375\) | 8.83746e17i | 0.847439i | ||||||||
\(376\) | 7.60871e17 | + | 1.69797e18i | 0.716137 | + | 1.59814i | ||||
\(377\) | −5.52063e17 | −0.510034 | ||||||||
\(378\) | 2.93802e16 | − | 7.28862e16i | 0.0266448 | − | 0.0661002i | ||||
\(379\) | − | 1.59400e17i | − | 0.141910i | −0.997480 | − | 0.0709549i | \(-0.977395\pi\) | ||
0.997480 | − | 0.0709549i | \(-0.0226046\pi\) | |||||||
\(380\) | −2.11734e18 | + | 2.19960e18i | −1.85057 | + | 1.92246i | ||||
\(381\) | 5.68870e17 | 0.488133 | ||||||||
\(382\) | 1.19379e18 | + | 4.81212e17i | 1.00574 | + | 0.405408i | ||||
\(383\) | 1.69592e18i | 1.40286i | 0.712738 | + | 0.701431i | \(0.247455\pi\) | ||||
−0.712738 | + | 0.701431i | \(0.752545\pi\) | |||||||
\(384\) | 6.37124e17 | − | 3.15172e17i | 0.517494 | − | 0.255994i | ||||
\(385\) | −1.96705e17 | −0.156888 | ||||||||
\(386\) | 7.49502e15 | − | 1.85936e16i | 0.00587032 | − | 0.0145631i | ||||
\(387\) | 5.99819e17i | 0.461364i | ||||||||
\(388\) | −7.59511e17 | − | 7.31108e17i | −0.573736 | − | 0.552280i | ||||
\(389\) | −1.15846e17 | −0.0859474 | −0.0429737 | − | 0.999076i | \(-0.513683\pi\) | ||||
−0.0429737 | + | 0.999076i | \(0.513683\pi\) | |||||||
\(390\) | −1.96241e18 | − | 7.91040e17i | −1.43000 | − | 0.576430i | ||||
\(391\) | − | 1.79482e17i | − | 0.128465i | ||||||
\(392\) | 1.11998e18 | − | 5.01868e17i | 0.787420 | − | 0.352847i | ||||
\(393\) | −2.46122e17 | −0.169982 | ||||||||
\(394\) | −6.41728e17 | + | 1.59200e18i | −0.435389 | + | 1.08011i | ||||
\(395\) | − | 2.53955e18i | − | 1.69269i | ||||||
\(396\) | 8.83287e16 | − | 9.17602e16i | 0.0578410 | − | 0.0600881i | ||||
\(397\) | 1.68846e18 | 1.08632 | 0.543159 | − | 0.839630i | \(-0.317228\pi\) | ||||
0.543159 | + | 0.839630i | \(0.317228\pi\) | |||||||
\(398\) | 2.31862e18 | + | 9.34627e17i | 1.46571 | + | 0.590822i | ||||
\(399\) | 5.42471e17i | 0.336951i | ||||||||
\(400\) | 1.16523e17 | + | 3.05649e18i | 0.0711200 | + | 1.86553i | ||||
\(401\) | 2.33261e18 | 1.39904 | 0.699521 | − | 0.714612i | \(-0.253397\pi\) | ||||
0.699521 | + | 0.714612i | \(0.253397\pi\) | |||||||
\(402\) | 9.60433e16 | − | 2.38264e17i | 0.0566089 | − | 0.140435i | ||||
\(403\) | − | 9.46985e16i | − | 0.0548539i | ||||||
\(404\) | −5.56091e17 | − | 5.35295e17i | −0.316575 | − | 0.304736i | ||||
\(405\) | −3.36239e17 | −0.188132 | ||||||||
\(406\) | 2.01967e17 | + | 8.14120e16i | 0.111070 | + | 0.0447720i | ||||
\(407\) | − | 5.84726e17i | − | 0.316076i | ||||||
\(408\) | −4.58774e16 | − | 1.02381e17i | −0.0243768 | − | 0.0543998i | ||||
\(409\) | 4.78215e17 | 0.249782 | 0.124891 | − | 0.992170i | \(-0.460142\pi\) | ||||
0.124891 | + | 0.992170i | \(0.460142\pi\) | |||||||
\(410\) | 1.33161e18 | − | 3.30346e18i | 0.683741 | − | 1.69622i | ||||
\(411\) | 1.44829e18i | 0.731077i | ||||||||
\(412\) | 7.20494e17 | − | 7.48484e17i | 0.357561 | − | 0.371452i | ||||
\(413\) | 7.34987e17 | 0.358616 | ||||||||
\(414\) | −8.01822e17 | − | 3.23211e17i | −0.384659 | − | 0.155055i | ||||
\(415\) | 5.47812e16i | 0.0258401i | ||||||||
\(416\) | −3.20003e18 | − | 1.15025e18i | −1.48423 | − | 0.533505i | ||||
\(417\) | 2.91398e17 | 0.132903 | ||||||||
\(418\) | −3.28703e17 | + | 8.15444e17i | −0.147424 | + | 0.365730i | ||||
\(419\) | − | 8.14966e17i | − | 0.359452i | −0.983717 | − | 0.179726i | \(-0.942479\pi\) | ||
0.983717 | − | 0.179726i | \(-0.0575212\pi\) | |||||||
\(420\) | 6.01274e17 | + | 5.78788e17i | 0.260812 | + | 0.251058i | ||||
\(421\) | −3.50746e18 | −1.49630 | −0.748149 | − | 0.663531i | \(-0.769057\pi\) | ||||
−0.748149 | + | 0.663531i | \(0.769057\pi\) | |||||||
\(422\) | −1.89707e18 | − | 7.64703e17i | −0.795970 | − | 0.320853i | ||||
\(423\) | − | 1.41453e18i | − | 0.583754i | ||||||
\(424\) | −2.74147e17 | + | 1.22847e17i | −0.111281 | + | 0.0498659i | ||||
\(425\) | 4.82763e17 | 0.192757 | ||||||||
\(426\) | −9.84358e17 | + | 2.44199e18i | −0.386621 | + | 0.959128i | ||||
\(427\) | − | 7.25327e17i | − | 0.280246i | ||||||
\(428\) | −5.82033e17 | + | 6.04644e17i | −0.221228 | + | 0.229823i | ||||
\(429\) | −6.09302e17 | −0.227841 | ||||||||
\(430\) | −5.90820e18 | − | 2.38158e18i | −2.17358 | − | 0.876164i | ||||
\(431\) | 2.91458e16i | 0.0105496i | 0.999986 | + | 0.00527478i | \(0.00167902\pi\) | ||||
−0.999986 | + | 0.00527478i | \(0.998321\pi\) | |||||||
\(432\) | −5.39994e17 | + | 2.05863e16i | −0.192310 | + | 0.00733147i | ||||
\(433\) | 4.42405e18 | 1.55026 | 0.775131 | − | 0.631800i | \(-0.217684\pi\) | ||||
0.775131 | + | 0.631800i | \(0.217684\pi\) | |||||||
\(434\) | −1.39651e16 | + | 3.46445e16i | −0.00481521 | + | 0.0119455i | ||||
\(435\) | − | 9.31713e17i | − | 0.316124i | ||||||
\(436\) | 3.29275e17 | + | 3.16961e17i | 0.109939 | + | 0.105828i | ||||
\(437\) | 5.96773e18 | 1.96083 | ||||||||
\(438\) | 1.33815e18 | + | 5.39402e17i | 0.432698 | + | 0.174419i | ||||
\(439\) | − | 2.81162e18i | − | 0.894756i | −0.894345 | − | 0.447378i | \(-0.852358\pi\) | ||
0.894345 | − | 0.447378i | \(-0.147642\pi\) | |||||||
\(440\) | 5.53128e17 | + | 1.23437e18i | 0.173243 | + | 0.386613i | ||||
\(441\) | −9.33019e17 | −0.287621 | ||||||||
\(442\) | −2.00655e17 | + | 4.97784e17i | −0.0608827 | + | 0.151038i | ||||
\(443\) | 4.60447e18i | 1.37516i | 0.726108 | + | 0.687580i | \(0.241327\pi\) | ||||
−0.726108 | + | 0.687580i | \(0.758673\pi\) | |||||||
\(444\) | −1.72051e18 | + | 1.78735e18i | −0.505797 | + | 0.525447i | ||||
\(445\) | −4.18871e18 | −1.21216 | ||||||||
\(446\) | 3.83119e18 | + | 1.54434e18i | 1.09141 | + | 0.439945i | ||||
\(447\) | − | 3.91528e17i | − | 0.109802i | ||||||
\(448\) | 1.00107e18 | + | 8.92710e17i | 0.276388 | + | 0.246470i | ||||
\(449\) | −5.52679e18 | −1.50227 | −0.751135 | − | 0.660148i | \(-0.770493\pi\) | ||||
−0.751135 | + | 0.660148i | \(0.770493\pi\) | |||||||
\(450\) | 8.69360e17 | − | 2.15671e18i | 0.232655 | − | 0.577169i | ||||
\(451\) | − | 1.02568e18i | − | 0.270257i | ||||||
\(452\) | −2.25302e18 | − | 2.16876e18i | −0.584514 | − | 0.562655i | ||||
\(453\) | 2.10489e18 | 0.537703 | ||||||||
\(454\) | −1.27259e18 | − | 5.12976e17i | −0.320109 | − | 0.129035i | ||||
\(455\) | − | 3.99255e18i | − | 0.988941i | ||||||
\(456\) | 3.40413e18 | − | 1.52541e18i | 0.830334 | − | 0.372077i | ||||
\(457\) | −1.05705e18 | −0.253912 | −0.126956 | − | 0.991908i | \(-0.540521\pi\) | ||||
−0.126956 | + | 0.991908i | \(0.540521\pi\) | |||||||
\(458\) | −1.12136e18 | + | 2.78185e18i | −0.265268 | + | 0.658076i | ||||
\(459\) | 8.52903e16i | 0.0198706i | ||||||||
\(460\) | 6.36725e18 | − | 6.61461e18i | 1.46099 | − | 1.51775i | ||||
\(461\) | −2.91154e18 | −0.657986 | −0.328993 | − | 0.944332i | \(-0.606709\pi\) | ||||
−0.328993 | + | 0.944332i | \(0.606709\pi\) | |||||||
\(462\) | 2.22907e17 | + | 8.98530e16i | 0.0496169 | + | 0.0200004i | ||||
\(463\) | 7.77165e18i | 1.70391i | 0.523616 | + | 0.851954i | \(0.324583\pi\) | ||||
−0.523616 | + | 0.851954i | \(0.675417\pi\) | |||||||
\(464\) | −5.70442e16 | − | 1.49632e18i | −0.0123193 | − | 0.323145i | ||||
\(465\) | 1.59822e17 | 0.0339990 | ||||||||
\(466\) | −9.92060e17 | + | 2.46110e18i | −0.207891 | + | 0.515736i | ||||
\(467\) | − | 1.86591e18i | − | 0.385187i | −0.981279 | − | 0.192594i | \(-0.938310\pi\) | ||
0.981279 | − | 0.192594i | \(-0.0616899\pi\) | |||||||
\(468\) | 1.86247e18 | + | 1.79282e18i | 0.378764 | + | 0.364600i | ||||
\(469\) | 4.84751e17 | 0.0971201 | ||||||||
\(470\) | 1.39331e19 | + | 5.61638e18i | 2.75019 | + | 1.10859i | ||||
\(471\) | − | 1.17788e18i | − | 0.229063i | ||||||
\(472\) | −2.06676e18 | − | 4.61222e18i | −0.396001 | − | 0.883722i | ||||
\(473\) | −1.83442e18 | −0.346314 | ||||||||
\(474\) | −1.16005e18 | + | 2.87784e18i | −0.215788 | + | 0.535325i | ||||
\(475\) | 1.60517e19i | 2.94217i | ||||||||
\(476\) | 1.46815e17 | − | 1.52519e17i | 0.0265169 | − | 0.0275470i | ||||
\(477\) | 2.28384e17 | 0.0406478 | ||||||||
\(478\) | 2.97269e18 | + | 1.19828e18i | 0.521379 | + | 0.210166i | ||||
\(479\) | − | 3.73123e18i | − | 0.644916i | −0.946584 | − | 0.322458i | \(-0.895491\pi\) | ||
0.946584 | − | 0.322458i | \(-0.104509\pi\) | |||||||
\(480\) | 1.94127e18 | − | 5.40067e18i | 0.330671 | − | 0.919938i | ||||
\(481\) | 1.18683e19 | 1.99238 | ||||||||
\(482\) | −2.99319e18 | + | 7.42550e18i | −0.495228 | + | 1.22856i | ||||
\(483\) | − | 1.63132e18i | − | 0.266017i | ||||||
\(484\) | −4.20188e18 | − | 4.04474e18i | −0.675346 | − | 0.650090i | ||||
\(485\) | −8.51150e18 | −1.34838 | ||||||||
\(486\) | 3.81028e17 | + | 1.53591e17i | 0.0594981 | + | 0.0239835i | ||||
\(487\) | − | 7.72609e18i | − | 1.18921i | −0.804019 | − | 0.594603i | \(-0.797309\pi\) | ||
0.804019 | − | 0.594603i | \(-0.202691\pi\) | |||||||
\(488\) | −4.55160e18 | + | 2.03960e18i | −0.690598 | + | 0.309461i | ||||
\(489\) | −6.18840e18 | −0.925585 | ||||||||
\(490\) | 3.70454e18 | − | 9.19021e18i | 0.546213 | − | 1.35504i | ||||
\(491\) | 6.80565e18i | 0.989234i | 0.869111 | + | 0.494617i | \(0.164692\pi\) | ||||
−0.869111 | + | 0.494617i | \(0.835308\pi\) | |||||||
\(492\) | −3.01798e18 | + | 3.13523e18i | −0.432475 | + | 0.449277i | ||||
\(493\) | −2.36338e17 | −0.0333891 | ||||||||
\(494\) | −1.65512e19 | − | 6.67173e18i | −2.30537 | − | 0.929287i | ||||
\(495\) | − | 1.02832e18i | − | 0.141218i | ||||||
\(496\) | 2.56672e17 | − | 9.78512e15i | 0.0347541 | − | 0.00132493i | ||||
\(497\) | −4.96826e18 | −0.663300 | ||||||||
\(498\) | 2.50236e16 | − | 6.20784e16i | 0.00329415 | − | 0.00817212i | ||||
\(499\) | − | 9.27270e17i | − | 0.120366i | −0.998187 | − | 0.0601828i | \(-0.980832\pi\) | ||
0.998187 | − | 0.0601828i | \(-0.0191684\pi\) | |||||||
\(500\) | 8.26157e18 | + | 7.95262e18i | 1.05748 | + | 1.01793i | ||||
\(501\) | 3.66922e18 | 0.463137 | ||||||||
\(502\) | 9.52752e18 | + | 3.84051e18i | 1.18592 | + | 0.478039i | ||||
\(503\) | 4.08155e18i | 0.501013i | 0.968115 | + | 0.250507i | \(0.0805972\pi\) | ||||
−0.968115 | + | 0.250507i | \(0.919403\pi\) | |||||||
\(504\) | −4.16981e17 | − | 9.30542e17i | −0.0504781 | − | 0.112648i | ||||
\(505\) | −6.23186e18 | −0.744009 | ||||||||
\(506\) | 9.88474e17 | − | 2.45220e18i | 0.116389 | − | 0.288737i | ||||
\(507\) | − | 7.39552e18i | − | 0.858841i | ||||||
\(508\) | 5.11912e18 | − | 5.31800e18i | 0.586340 | − | 0.609119i | ||||
\(509\) | −4.70789e18 | −0.531865 | −0.265932 | − | 0.963992i | \(-0.585680\pi\) | ||||
−0.265932 | + | 0.963992i | \(0.585680\pi\) | |||||||
\(510\) | −8.40107e17 | − | 3.38644e17i | −0.0936146 | − | 0.0377357i | ||||
\(511\) | 2.72248e18i | 0.299239i | ||||||||
\(512\) | 2.78699e18 | − | 8.79223e18i | 0.302166 | − | 0.953255i | ||||
\(513\) | −2.83588e18 | −0.303296 | ||||||||
\(514\) | 1.01238e18 | − | 2.51150e18i | 0.106807 | − | 0.264966i | ||||
\(515\) | − | 8.38793e18i | − | 0.872979i | ||||||
\(516\) | 5.60732e18 | + | 5.39763e18i | 0.575715 | + | 0.554185i | ||||
\(517\) | 4.32604e18 | 0.438184 | ||||||||
\(518\) | −4.34189e18 | − | 1.75020e18i | −0.433881 | − | 0.174896i | ||||
\(519\) | − | 9.01268e18i | − | 0.888551i | ||||||
\(520\) | −2.50542e19 | + | 1.12269e19i | −2.43701 | + | 1.09204i | ||||
\(521\) | 1.67781e19 | 1.61019 | 0.805097 | − | 0.593143i | \(-0.202113\pi\) | ||||
0.805097 | + | 0.593143i | \(0.202113\pi\) | |||||||
\(522\) | −4.25598e17 | + | 1.05582e18i | −0.0403001 | + | 0.0999764i | ||||
\(523\) | − | 1.42496e19i | − | 1.33134i | −0.746244 | − | 0.665672i | \(-0.768145\pi\) | ||
0.746244 | − | 0.665672i | \(-0.231855\pi\) | |||||||
\(524\) | −2.21479e18 | + | 2.30083e18i | −0.204180 | + | 0.212113i | ||||
\(525\) | 4.38785e18 | 0.399150 | ||||||||
\(526\) | −1.58025e19 | − | 6.36994e18i | −1.41849 | − | 0.571788i | ||||
\(527\) | − | 4.05404e16i | − | 0.00359099i | ||||||
\(528\) | −6.29587e16 | − | 1.65146e18i | −0.00550324 | − | 0.144354i | ||||
\(529\) | −6.35330e18 | −0.548037 | ||||||||
\(530\) | −9.06796e17 | + | 2.24958e18i | −0.0771931 | + | 0.191500i | ||||
\(531\) | 3.84230e18i | 0.322797i | ||||||||
\(532\) | 5.07122e18 | + | 4.88157e18i | 0.420466 | + | 0.404742i | ||||
\(533\) | 2.08184e19 | 1.70356 | ||||||||
\(534\) | 4.74667e18 | + | 1.91337e18i | 0.383354 | + | 0.154529i | ||||
\(535\) | 6.77597e18i | 0.540126i | ||||||||
\(536\) | −1.36310e18 | − | 3.04193e18i | −0.107245 | − | 0.239329i | ||||
\(537\) | −9.69635e17 | −0.0752988 | ||||||||
\(538\) | −4.50378e18 | + | 1.11729e19i | −0.345224 | + | 0.856430i | ||||
\(539\) | − | 2.85344e18i | − | 0.215897i | ||||||
\(540\) | −3.02573e18 | + | 3.14328e18i | −0.225982 | + | 0.234762i | ||||
\(541\) | 1.95653e19 | 1.44246 | 0.721232 | − | 0.692693i | \(-0.243576\pi\) | ||||
0.721232 | + | 0.692693i | \(0.243576\pi\) | |||||||
\(542\) | −4.55078e18 | − | 1.83440e18i | −0.331200 | − | 0.133506i | ||||
\(543\) | 1.43631e19i | 1.03193i | ||||||||
\(544\) | −1.36993e18 | − | 4.92421e17i | −0.0971642 | − | 0.0349256i | ||||
\(545\) | 3.69004e18 | 0.258378 | ||||||||
\(546\) | −1.82376e18 | + | 4.52438e18i | −0.126072 | + | 0.312759i | ||||
\(547\) | 2.64078e19i | 1.80227i | 0.433536 | + | 0.901136i | \(0.357266\pi\) | ||||
−0.433536 | + | 0.901136i | \(0.642734\pi\) | |||||||
\(548\) | 1.35392e19 | + | 1.30328e19i | 0.912279 | + | 0.878162i | ||||
\(549\) | 3.79180e18 | 0.252255 | ||||||||
\(550\) | 6.59583e18 | + | 2.65875e18i | 0.433242 | + | 0.174638i | ||||
\(551\) | − | 7.85819e18i | − | 0.509637i | ||||||
\(552\) | −1.02369e19 | + | 4.58721e18i | −0.655534 | + | 0.293748i | ||||
\(553\) | −5.85500e18 | −0.370212 | ||||||||
\(554\) | 3.97357e18 | − | 9.85761e18i | 0.248092 | − | 0.615465i | ||||
\(555\) | 2.00300e19i | 1.23490i | ||||||||
\(556\) | 2.62222e18 | − | 2.72409e18i | 0.159641 | − | 0.165843i | ||||
\(557\) | −5.68683e18 | −0.341888 | −0.170944 | − | 0.985281i | \(-0.554682\pi\) | ||||
−0.170944 | + | 0.985281i | \(0.554682\pi\) | |||||||
\(558\) | −1.81111e17 | − | 7.30053e16i | −0.0107524 | − | 0.00433426i | ||||
\(559\) | − | 3.72335e19i | − | 2.18299i | ||||||
\(560\) | 1.08214e19 | − | 4.12547e17i | 0.626569 | − | 0.0238868i | ||||
\(561\) | −2.60842e17 | −0.0149155 | ||||||||
\(562\) | 3.95484e18 | − | 9.81116e18i | 0.223344 | − | 0.554072i | ||||
\(563\) | 2.24264e19i | 1.25084i | 0.780289 | + | 0.625419i | \(0.215072\pi\) | ||||
−0.780289 | + | 0.625419i | \(0.784928\pi\) | |||||||
\(564\) | −1.32235e19 | − | 1.27290e19i | −0.728440 | − | 0.701199i | ||||
\(565\) | −2.52485e19 | −1.37372 | ||||||||
\(566\) | 5.30299e18 | + | 2.13761e18i | 0.284974 | + | 0.114872i | ||||
\(567\) | 7.75207e17i | 0.0411468i | ||||||||
\(568\) | 1.39706e19 | + | 3.11770e19i | 0.732448 | + | 1.63454i | ||||
\(569\) | −1.89410e18 | −0.0980881 | −0.0490441 | − | 0.998797i | \(-0.515617\pi\) | ||||
−0.0490441 | + | 0.998797i | \(0.515617\pi\) | |||||||
\(570\) | 1.12598e19 | − | 2.79334e19i | 0.575981 | − | 1.42889i | ||||
\(571\) | − | 6.41743e17i | − | 0.0324271i | −0.999869 | − | 0.0162136i | \(-0.994839\pi\) | ||
0.999869 | − | 0.0162136i | \(-0.00516116\pi\) | |||||||
\(572\) | −5.48297e18 | + | 5.69598e18i | −0.273680 | + | 0.284313i | ||||
\(573\) | −1.26970e19 | −0.626062 | ||||||||
\(574\) | −7.61621e18 | − | 3.07007e18i | −0.370984 | − | 0.149543i | ||||
\(575\) | − | 4.82708e19i | − | 2.32279i | ||||||
\(576\) | −4.66683e18 | + | 5.23331e18i | −0.221853 | + | 0.248782i | ||||
\(577\) | −1.69503e18 | −0.0796060 | −0.0398030 | − | 0.999208i | \(-0.512673\pi\) | ||||
−0.0398030 | + | 0.999208i | \(0.512673\pi\) | |||||||
\(578\) | 7.97178e18 | − | 1.97763e19i | 0.369880 | − | 0.917595i | ||||
\(579\) | 1.97759e17i | 0.00906538i | ||||||||
\(580\) | −8.70999e18 | − | 8.38427e18i | −0.394477 | − | 0.379725i | ||||
\(581\) | 1.26299e17 | 0.00565156 | ||||||||
\(582\) | 9.64527e18 | + | 3.88798e18i | 0.426436 | + | 0.171895i | ||||
\(583\) | 6.98464e17i | 0.0305115i | ||||||||
\(584\) | 1.70842e19 | − | 7.65552e18i | 0.737402 | − | 0.330434i | ||||
\(585\) | 2.08719e19 | 0.890165 | ||||||||
\(586\) | 6.01900e18 | − | 1.49319e19i | 0.253654 | − | 0.629263i | ||||
\(587\) | 2.21997e19i | 0.924444i | 0.886764 | + | 0.462222i | \(0.152948\pi\) | ||||
−0.886764 | + | 0.462222i | \(0.847052\pi\) | |||||||
\(588\) | −8.39601e18 | + | 8.72219e18i | −0.345487 | + | 0.358909i | ||||
\(589\) | 1.34796e18 | 0.0548113 | ||||||||
\(590\) | −3.78465e19 | − | 1.52558e19i | −1.52077 | − | 0.613015i | ||||
\(591\) | − | 1.69322e19i | − | 0.672360i | ||||||
\(592\) | 1.22634e18 | + | 3.21679e19i | 0.0481237 | + | 1.26232i | ||||
\(593\) | −7.48231e18 | −0.290170 | −0.145085 | − | 0.989419i | \(-0.546346\pi\) | ||||
−0.145085 | + | 0.989419i | \(0.546346\pi\) | |||||||
\(594\) | −4.69725e17 | + | 1.16529e18i | −0.0180028 | + | 0.0446612i | ||||
\(595\) | − | 1.70921e18i | − | 0.0647406i | ||||||
\(596\) | −3.66014e18 | − | 3.52327e18i | −0.137017 | − | 0.131893i | ||||
\(597\) | −2.46605e19 | −0.912392 | ||||||||
\(598\) | 4.97727e19 | + | 2.00632e19i | 1.82005 | + | 0.733655i | ||||
\(599\) | 1.41980e19i | 0.513144i | 0.966525 | + | 0.256572i | \(0.0825931\pi\) | ||||
−0.966525 | + | 0.256572i | \(0.917407\pi\) | |||||||
\(600\) | −1.23385e19 | − | 2.75348e19i | −0.440761 | − | 0.983610i | ||||
\(601\) | −5.45515e19 | −1.92613 | −0.963064 | − | 0.269271i | \(-0.913217\pi\) | ||||
−0.963064 | + | 0.269271i | \(0.913217\pi\) | |||||||
\(602\) | −5.49078e18 | + | 1.36215e19i | −0.191628 | + | 0.475389i | ||||
\(603\) | 2.53414e18i | 0.0874196i | ||||||||
\(604\) | 1.89414e19 | − | 1.96773e19i | 0.645883 | − | 0.670975i | ||||
\(605\) | −4.70886e19 | −1.58719 | ||||||||
\(606\) | 7.06198e18 | + | 2.84666e18i | 0.235298 | + | 0.0948477i | ||||
\(607\) | − | 4.27195e19i | − | 1.40704i | −0.710678 | − | 0.703518i | \(-0.751612\pi\) | ||
0.710678 | − | 0.703518i | \(-0.248388\pi\) | |||||||
\(608\) | 1.63729e19 | − | 4.55499e19i | 0.533090 | − | 1.48307i | ||||
\(609\) | −2.14809e18 | −0.0691402 | ||||||||
\(610\) | −1.50553e19 | + | 3.73491e19i | −0.479050 | + | 1.18843i | ||||
\(611\) | 8.78063e19i | 2.76209i | ||||||||
\(612\) | 7.97324e17 | + | 7.67507e17i | 0.0247956 | + | 0.0238683i | ||||
\(613\) | 2.26370e19 | 0.695979 | 0.347989 | − | 0.937498i | \(-0.386864\pi\) | ||||
0.347989 | + | 0.937498i | \(0.386864\pi\) | |||||||
\(614\) | −2.58820e19 | − | 1.04329e19i | −0.786718 | − | 0.317123i | ||||
\(615\) | 3.51351e19i | 1.05588i | ||||||||
\(616\) | 2.84587e18 | − | 1.27525e18i | 0.0845570 | − | 0.0378905i | ||||
\(617\) | 2.57332e19 | 0.755959 | 0.377980 | − | 0.925814i | \(-0.376619\pi\) | ||||
0.377980 | + | 0.925814i | \(0.376619\pi\) | |||||||
\(618\) | −3.83153e18 | + | 9.50524e18i | −0.111289 | + | 0.276086i | ||||
\(619\) | − | 5.78179e18i | − | 0.166046i | −0.996548 | − | 0.0830229i | \(-0.973543\pi\) | ||
0.996548 | − | 0.0830229i | \(-0.0264575\pi\) | |||||||
\(620\) | 1.43820e18 | − | 1.49407e18i | 0.0408392 | − | 0.0424258i | ||||
\(621\) | 8.52805e18 | 0.239447 | ||||||||
\(622\) | 3.01656e19 | + | 1.21597e19i | 0.837490 | + | 0.337589i | ||||
\(623\) | 9.65717e18i | 0.265115i | ||||||||
\(624\) | 3.35199e19 | − | 1.27788e18i | 0.909935 | − | 0.0346896i | ||||
\(625\) | 2.30367e19 | 0.618386 | ||||||||
\(626\) | −3.55880e18 | + | 8.82865e18i | −0.0944677 | + | 0.234355i | ||||
\(627\) | − | 8.67294e18i | − | 0.227664i | ||||||
\(628\) | −1.10113e19 | − | 1.05995e19i | −0.285838 | − | 0.275148i | ||||
\(629\) | 5.08081e18 | 0.130430 | ||||||||
\(630\) | −7.63577e18 | − | 3.07795e18i | −0.193851 | − | 0.0781408i | ||||
\(631\) | − | 1.55480e19i | − | 0.390363i | −0.980767 | − | 0.195181i | \(-0.937470\pi\) | ||
0.980767 | − | 0.195181i | \(-0.0625296\pi\) | |||||||
\(632\) | 1.64641e19 | + | 3.67415e19i | 0.408807 | + | 0.912299i | ||||
\(633\) | 2.01770e19 | 0.495484 | ||||||||
\(634\) | −5.29002e18 | + | 1.31235e19i | −0.128479 | + | 0.318731i | ||||
\(635\) | − | 5.95964e19i | − | 1.43154i | ||||||
\(636\) | 2.05517e18 | − | 2.13501e18i | 0.0488257 | − | 0.0507225i | ||||
\(637\) | 5.79167e19 | 1.36091 | ||||||||
\(638\) | −3.22901e18 | − | 1.30160e18i | −0.0750455 | − | 0.0302506i | ||||
\(639\) | − | 2.59726e19i | − | 0.597049i | ||||||
\(640\) | −3.30184e19 | − | 6.67470e19i | −0.750751 | − | 1.51765i | ||||
\(641\) | 5.09427e19 | 1.14571 | 0.572857 | − | 0.819655i | \(-0.305835\pi\) | ||||
0.572857 | + | 0.819655i | \(0.305835\pi\) | |||||||
\(642\) | 3.09521e18 | − | 7.67857e18i | 0.0688564 | − | 0.170819i | ||||
\(643\) | − | 9.83096e18i | − | 0.216331i | −0.994133 | − | 0.108166i | \(-0.965502\pi\) | ||
0.994133 | − | 0.108166i | \(-0.0344977\pi\) | |||||||
\(644\) | −1.52501e19 | − | 1.46798e19i | −0.331950 | − | 0.319536i | ||||
\(645\) | 6.28388e19 | 1.35304 | ||||||||
\(646\) | −7.08557e18 | − | 2.85617e18i | −0.150920 | − | 0.0608354i | ||||
\(647\) | 3.59831e19i | 0.758174i | 0.925361 | + | 0.379087i | \(0.123762\pi\) | ||||
−0.925361 | + | 0.379087i | \(0.876238\pi\) | |||||||
\(648\) | 4.86460e18 | − | 2.17986e18i | 0.101396 | − | 0.0454363i | ||||
\(649\) | −1.17509e19 | −0.242302 | ||||||||
\(650\) | −5.39652e19 | + | 1.33877e20i | −1.10083 | + | 2.73093i | ||||
\(651\) | − | 3.68473e17i | − | 0.00743600i | ||||||
\(652\) | −5.56880e19 | + | 5.78514e19i | −1.11180 | + | 1.15500i | ||||
\(653\) | −5.18011e19 | −1.02317 | −0.511584 | − | 0.859233i | \(-0.670941\pi\) | ||||
−0.511584 | + | 0.859233i | \(0.670941\pi\) | |||||||
\(654\) | −4.18157e18 | − | 1.68558e18i | −0.0817138 | − | 0.0329385i | ||||
\(655\) | 2.57844e19i | 0.498504i | ||||||||
\(656\) | 2.15115e18 | + | 5.64264e19i | 0.0411476 | + | 1.07933i | ||||
\(657\) | −1.42323e19 | −0.269351 | ||||||||
\(658\) | 1.29487e19 | − | 3.21230e19i | 0.242462 | − | 0.601500i | ||||
\(659\) | − | 6.80634e19i | − | 1.26100i | −0.776188 | − | 0.630501i | \(-0.782849\pi\) | ||
0.776188 | − | 0.630501i | \(-0.217151\pi\) | |||||||
\(660\) | −9.61307e18 | − | 9.25357e18i | −0.176220 | − | 0.169630i | ||||
\(661\) | −4.72630e19 | −0.857257 | −0.428628 | − | 0.903481i | \(-0.641003\pi\) | ||||
−0.428628 | + | 0.903481i | \(0.641003\pi\) | |||||||
\(662\) | 1.72569e19 | + | 6.95621e18i | 0.309712 | + | 0.124844i | ||||
\(663\) | − | 5.29436e18i | − | 0.0940196i | ||||||
\(664\) | −3.55150e17 | − | 7.92558e17i | −0.00624072 | − | 0.0139269i | ||||
\(665\) | 5.68309e19 | 0.988172 | ||||||||
\(666\) | 9.14954e18 | − | 2.26981e19i | 0.157427 | − | 0.390544i | ||||
\(667\) | 2.36311e19i | 0.402349i | ||||||||
\(668\) | 3.30184e19 | − | 3.43012e19i | 0.556315 | − | 0.577928i | ||||
\(669\) | −4.07479e19 | −0.679396 | ||||||||
\(670\) | −2.49612e19 | − | 1.00618e19i | −0.411853 | − | 0.166016i | ||||
\(671\) | 1.15964e19i | 0.189350i | ||||||||
\(672\) | −1.24514e19 | − | 4.47564e18i | −0.201202 | − | 0.0723219i | ||||
\(673\) | −3.15023e19 | −0.503775 | −0.251888 | − | 0.967756i | \(-0.581051\pi\) | ||||
−0.251888 | + | 0.967756i | \(0.581051\pi\) | |||||||
\(674\) | 2.03913e19 | − | 5.05866e19i | 0.322720 | − | 0.800602i | ||||
\(675\) | 2.29384e19i | 0.359283i | ||||||||
\(676\) | −6.91359e19 | − | 6.65505e19i | −1.07171 | − | 1.03163i | ||||
\(677\) | −7.30326e19 | −1.12046 | −0.560230 | − | 0.828337i | \(-0.689287\pi\) | ||||
−0.560230 | + | 0.828337i | \(0.689287\pi\) | |||||||
\(678\) | 2.86118e19 | + | 1.15333e19i | 0.434447 | + | 0.175124i | ||||
\(679\) | 1.96234e19i | 0.294908i | ||||||||
\(680\) | −1.07257e19 | + | 4.80625e18i | −0.159538 | + | 0.0714897i | ||||
\(681\) | 1.35351e19 | 0.199265 | ||||||||
\(682\) | 2.23271e17 | − | 5.53890e17i | 0.00325344 | − | 0.00807111i | ||||
\(683\) | − | 7.11794e19i | − | 1.02662i | −0.858204 | − | 0.513309i | \(-0.828419\pi\) | ||
0.858204 | − | 0.513309i | \(-0.171581\pi\) | |||||||
\(684\) | −2.55194e19 | + | 2.65109e19i | −0.364316 | + | 0.378470i | ||||
\(685\) | 1.51727e20 | 2.14402 | ||||||||
\(686\) | −4.57440e19 | − | 1.84392e19i | −0.639831 | − | 0.257914i | ||||
\(687\) | − | 2.95874e19i | − | 0.409647i | ||||||
\(688\) | 1.00918e20 | − | 3.84731e18i | 1.38309 | − | 0.0527276i | ||||
\(689\) | −1.41768e19 | −0.192329 | ||||||||
\(690\) | −3.38606e19 | + | 8.40011e19i | −0.454727 | + | 1.12808i | ||||
\(691\) | − | 4.10966e19i | − | 0.546336i | −0.961966 | − | 0.273168i | \(-0.911929\pi\) | ||
0.961966 | − | 0.273168i | \(-0.0880715\pi\) | |||||||
\(692\) | −8.42537e19 | − | 8.11029e19i | −1.10878 | − | 1.06732i | ||||
\(693\) | −2.37081e18 | −0.0308861 | ||||||||
\(694\) | −2.34648e19 | − | 9.45860e18i | −0.302623 | − | 0.121986i | ||||
\(695\) | − | 3.05277e19i | − | 0.389762i | ||||||
\(696\) | 6.04035e18 | + | 1.34797e19i | 0.0763480 | + | 0.170379i | ||||
\(697\) | 8.91237e18 | 0.111523 | ||||||||
\(698\) | 2.60642e19 | − | 6.46600e19i | 0.322892 | − | 0.801029i | ||||
\(699\) | − | 2.61759e19i | − | 0.321041i | ||||||
\(700\) | 3.94852e19 | − | 4.10192e19i | 0.479455 | − | 0.498082i | ||||
\(701\) | 7.27378e19 | 0.874448 | 0.437224 | − | 0.899353i | \(-0.355962\pi\) | ||||
0.437224 | + | 0.899353i | \(0.355962\pi\) | |||||||
\(702\) | −2.36521e19 | − | 9.53409e18i | −0.281521 | − | 0.113480i | ||||
\(703\) | 1.68936e20i | 1.99083i | ||||||||
\(704\) | −1.60050e19 | − | 1.42725e19i | −0.186744 | − | 0.166530i | ||||
\(705\) | −1.48190e20 | −1.71197 | ||||||||
\(706\) | −2.09938e19 | + | 5.20814e19i | −0.240137 | + | 0.595730i | ||||
\(707\) | 1.43677e19i | 0.162724i | ||||||||
\(708\) | 3.59192e19 | + | 3.45759e19i | 0.402804 | + | 0.387740i | ||||
\(709\) | −6.27906e19 | −0.697222 | −0.348611 | − | 0.937268i | \(-0.613347\pi\) | ||||
−0.348611 | + | 0.937268i | \(0.613347\pi\) | |||||||
\(710\) | 2.55830e20 | + | 1.03124e20i | 2.81283 | + | 1.13384i | ||||
\(711\) | − | 3.06082e19i | − | 0.333235i | ||||||
\(712\) | 6.06010e19 | − | 2.71557e19i | 0.653311 | − | 0.292752i | ||||
\(713\) | −4.05358e18 | −0.0432725 | ||||||||
\(714\) | −7.80752e17 | + | 1.93689e18i | −0.00825326 | + | 0.0204747i | ||||
\(715\) | 6.38322e19i | 0.668187i | ||||||||
\(716\) | −8.72551e18 | + | 9.06449e18i | −0.0904482 | + | 0.0939620i | ||||
\(717\) | −3.16170e19 | −0.324554 | ||||||||
\(718\) | −1.47996e20 | − | 5.96565e19i | −1.50445 | − | 0.606439i | ||||
\(719\) | 3.98180e19i | 0.400846i | 0.979709 | + | 0.200423i | \(0.0642317\pi\) | ||||
−0.979709 | + | 0.200423i | \(0.935768\pi\) | |||||||
\(720\) | 2.15668e18 | + | 5.65713e19i | 0.0215009 | + | 0.563987i | ||||
\(721\) | −1.93386e19 | −0.190931 | ||||||||
\(722\) | 5.67307e19 | − | 1.40737e20i | 0.554699 | − | 1.37610i | ||||
\(723\) | − | 7.89765e19i | − | 0.764768i | ||||||
\(724\) | 1.34271e20 | + | 1.29250e20i | 1.28770 | + | 1.23954i | ||||
\(725\) | −6.35620e19 | −0.603714 | ||||||||
\(726\) | 5.33610e19 | + | 2.15096e19i | 0.501958 | + | 0.202338i | ||||
\(727\) | 1.08316e20i | 1.00914i | 0.863371 | + | 0.504569i | \(0.168349\pi\) | ||||
−0.863371 | + | 0.504569i | \(0.831651\pi\) | |||||||
\(728\) | 2.58839e19 | + | 5.77630e19i | 0.238842 | + | 0.533003i | ||||
\(729\) | −4.05256e18 | −0.0370370 | ||||||||
\(730\) | 5.65093e19 | − | 1.40188e20i | 0.511517 | − | 1.26897i | ||||
\(731\) | − | 1.59397e19i | − | 0.142908i | ||||||
\(732\) | 3.41215e19 | − | 3.54471e19i | 0.303006 | − | 0.314777i | ||||
\(733\) | −8.71515e19 | −0.766562 | −0.383281 | − | 0.923632i | \(-0.625206\pi\) | ||||
−0.383281 | + | 0.923632i | \(0.625206\pi\) | |||||||
\(734\) | −3.12721e19 | − | 1.26057e19i | −0.272449 | − | 0.109823i | ||||
\(735\) | 9.77457e19i | 0.843502i | ||||||||
\(736\) | −4.92365e19 | + | 1.36977e20i | −0.420865 | + | 1.17086i | ||||
\(737\) | −7.75012e18 | −0.0656200 | ||||||||
\(738\) | 1.60494e19 | − | 3.98153e19i | 0.134606 | − | 0.333930i | ||||
\(739\) | 7.02462e19i | 0.583596i | 0.956480 | + | 0.291798i | \(0.0942534\pi\) | ||||
−0.956480 | + | 0.291798i | \(0.905747\pi\) | |||||||
\(740\) | 1.87248e20 | + | 1.80245e20i | 1.54097 | + | 1.48335i | ||||
\(741\) | 1.76036e20 | 1.43507 | ||||||||
\(742\) | 5.18645e18 | + | 2.09064e18i | 0.0418835 | + | 0.0168831i | ||||
\(743\) | 7.37552e19i | 0.590026i | 0.955493 | + | 0.295013i | \(0.0953240\pi\) | ||||
−0.955493 | + | 0.295013i | \(0.904676\pi\) | |||||||
\(744\) | −2.31226e18 | + | 1.03614e18i | −0.0183242 | + | 0.00821119i | ||||
\(745\) | −4.10176e19 | −0.322015 | ||||||||
\(746\) | 7.18933e18 | − | 1.78353e19i | 0.0559135 | − | 0.138710i | ||||
\(747\) | 6.60256e17i | 0.00508708i | ||||||||
\(748\) | −2.34726e18 | + | 2.43845e18i | −0.0179163 | + | 0.0186124i | ||||
\(749\) | 1.56222e19 | 0.118132 | ||||||||
\(750\) | −1.04916e20 | − | 4.22914e19i | −0.785985 | − | 0.316828i | ||||
\(751\) | − | 1.45768e20i | − | 1.08189i | −0.841059 | − | 0.540943i | \(-0.818068\pi\) | ||
0.841059 | − | 0.540943i | \(-0.181932\pi\) | |||||||
\(752\) | −2.37991e20 | + | 9.07296e18i | −1.74999 | + | 0.0667151i | ||||
\(753\) | −1.01333e20 | −0.738223 | ||||||||
\(754\) | 2.64188e19 | − | 6.55397e19i | 0.190684 | − | 0.473048i | ||||
\(755\) | − | 2.20514e20i | − | 1.57692i | ||||||
\(756\) | 7.24691e18 | + | 6.97590e18i | 0.0513453 | + | 0.0494251i | ||||
\(757\) | −1.18561e19 | −0.0832285 | −0.0416143 | − | 0.999134i | \(-0.513250\pi\) | ||||
−0.0416143 | + | 0.999134i | \(0.513250\pi\) | |||||||
\(758\) | 1.89236e19 | + | 7.62802e18i | 0.131619 | + | 0.0530552i | ||||
\(759\) | 2.60812e19i | 0.179736i | ||||||||
\(760\) | −1.59807e20 | − | 3.56627e20i | −1.09119 | − | 2.43511i | ||||
\(761\) | 1.04958e20 | 0.710103 | 0.355051 | − | 0.934847i | \(-0.384463\pi\) | ||||
0.355051 | + | 0.934847i | \(0.384463\pi\) | |||||||
\(762\) | −2.72231e19 | + | 6.75350e19i | −0.182496 | + | 0.452735i | ||||
\(763\) | − | 8.50747e18i | − | 0.0565104i | ||||||
\(764\) | −1.14257e20 | + | 1.18696e20i | −0.752019 | + | 0.781235i | ||||
\(765\) | 8.93525e18 | 0.0582743 | ||||||||
\(766\) | −2.01336e20 | − | 8.11580e19i | −1.30113 | − | 0.524481i | ||||
\(767\) | − | 2.38509e20i | − | 1.52735i | ||||||
\(768\) | 6.92717e18 | + | 9.07205e19i | 0.0439569 | + | 0.575674i | ||||
\(769\) | 2.55140e20 | 1.60433 | 0.802165 | − | 0.597102i | \(-0.203681\pi\) | ||||
0.802165 | + | 0.597102i | \(0.203681\pi\) | |||||||
\(770\) | 9.41326e18 | − | 2.33524e19i | 0.0586550 | − | 0.145511i | ||||
\(771\) | 2.67119e19i | 0.164939i | ||||||||
\(772\) | 1.84872e18 | + | 1.77959e18i | 0.0113123 | + | 0.0108892i | ||||
\(773\) | −1.49521e20 | −0.906662 | −0.453331 | − | 0.891342i | \(-0.649764\pi\) | ||||
−0.453331 | + | 0.891342i | \(0.649764\pi\) | |||||||
\(774\) | −7.12092e19 | − | 2.87042e19i | −0.427907 | − | 0.172488i | ||||
\(775\) | − | 1.09031e19i | − | 0.0649292i | ||||||
\(776\) | 1.23142e20 | − | 5.51805e19i | 0.726730 | − | 0.325652i | ||||
\(777\) | 4.61797e19 | 0.270087 | ||||||||
\(778\) | 5.54376e18 | − | 1.37529e19i | 0.0321327 | − | 0.0797147i | ||||
\(779\) | 2.96334e20i | 1.70224i | ||||||||
\(780\) | 1.87821e20 | − | 1.95118e20i | 1.06926 | − | 1.11080i | ||||
\(781\) | 7.94318e19 | 0.448164 | ||||||||
\(782\) | 2.13077e19 | + | 8.58906e18i | 0.119149 | + | 0.0480284i | ||||
\(783\) | − | 1.12296e19i | − | 0.0622344i | ||||||
\(784\) | 5.98449e18 | + | 1.56978e20i | 0.0328711 | + | 0.862236i | ||||
\(785\) | −1.23398e20 | −0.671771 | ||||||||
\(786\) | 1.17781e19 | − | 2.92190e19i | 0.0635502 | − | 0.157655i | ||||
\(787\) | − | 2.26036e20i | − | 1.20880i | −0.796681 | − | 0.604400i | \(-0.793413\pi\) | ||
0.796681 | − | 0.604400i | \(-0.206587\pi\) | |||||||
\(788\) | −1.58289e20 | − | 1.52369e20i | −0.839008 | − | 0.807632i | ||||
\(789\) | 1.68073e20 | 0.882998 | ||||||||
\(790\) | 3.01490e20 | + | 1.21530e20i | 1.56994 | + | 0.632838i | ||||
\(791\) | 5.82111e19i | 0.300449i | ||||||||
\(792\) | 6.66663e18 | + | 1.48774e19i | 0.0341059 | + | 0.0761114i | ||||
\(793\) | −2.35374e20 | −1.19357 | ||||||||
\(794\) | −8.08008e19 | + | 2.00450e20i | −0.406137 | + | 1.00754i | ||||
\(795\) | − | 2.39261e19i | − | 0.119207i | ||||||
\(796\) | −2.21914e20 | + | 2.30535e20i | −1.09596 | + | 1.13853i | ||||
\(797\) | 2.13241e20 | 1.04391 | 0.521954 | − | 0.852974i | \(-0.325203\pi\) | ||||
0.521954 | + | 0.852974i | \(0.325203\pi\) | |||||||
\(798\) | −6.44010e19 | − | 2.59598e19i | −0.312516 | − | 0.125974i | ||||
\(799\) | 3.75899e19i | 0.180819i | ||||||||
\(800\) | −3.68436e20 | − | 1.32434e20i | −1.75684 | − | 0.631496i | ||||
\(801\) | −5.04849e19 | −0.238635 | ||||||||
\(802\) | −1.11626e20 | + | 2.76922e20i | −0.523053 | + | 1.29759i | ||||
\(803\) | − | 4.35265e19i | − | 0.202183i | ||||||
\(804\) | 2.36900e19 | + | 2.28041e19i | 0.109087 | + | 0.105008i | ||||
\(805\) | −1.70902e20 | −0.780144 | ||||||||
\(806\) | 1.12424e19 | + | 4.53177e18i | 0.0508761 | + | 0.0205080i | ||||
\(807\) | − | 1.18834e20i | − | 0.533120i | ||||||
\(808\) | 9.01606e19 | − | 4.04015e19i | 0.400994 | − | 0.179688i | ||||
\(809\) | 1.21626e20 | 0.536274 | 0.268137 | − | 0.963381i | \(-0.413592\pi\) | ||||
0.268137 | + | 0.963381i | \(0.413592\pi\) | |||||||
\(810\) | 1.60906e19 | − | 3.99176e19i | 0.0703360 | − | 0.174489i | ||||
\(811\) | − | 4.05480e20i | − | 1.75721i | −0.477548 | − | 0.878605i | \(-0.658474\pi\) | ||
0.477548 | − | 0.878605i | \(-0.341526\pi\) | |||||||
\(812\) | −1.93301e19 | + | 2.00811e19i | −0.0830505 | + | 0.0862770i | ||||
\(813\) | 4.84014e19 | 0.206169 | ||||||||
\(814\) | 6.94174e19 | + | 2.79819e19i | 0.293155 | + | 0.118170i | ||||
\(815\) | 6.48315e20i | 2.71445i | ||||||||
\(816\) | 1.43499e19 | − | 5.47062e17i | 0.0595685 | − | 0.00227094i | ||||
\(817\) | 5.29990e20 | 2.18129 | ||||||||
\(818\) | −2.28849e19 | + | 5.67727e19i | −0.0933846 | + | 0.231668i | ||||
\(819\) | − | 4.81206e19i | − | 0.194690i | ||||||
\(820\) | 3.28456e20 | + | 3.16173e20i | 1.31759 | + | 1.26832i | ||||
\(821\) | 7.86083e19 | 0.312656 | 0.156328 | − | 0.987705i | \(-0.450034\pi\) | ||||
0.156328 | + | 0.987705i | \(0.450034\pi\) | |||||||
\(822\) | −1.71938e20 | − | 6.93076e19i | −0.678062 | − | 0.273324i | ||||
\(823\) | 1.32288e20i | 0.517276i | 0.965974 | + | 0.258638i | \(0.0832737\pi\) | ||||
−0.965974 | + | 0.258638i | \(0.916726\pi\) | |||||||
\(824\) | 5.43794e19 | + | 1.21354e20i | 0.210836 | + | 0.470504i | ||||
\(825\) | −7.01522e19 | −0.269689 | ||||||||
\(826\) | −3.51726e19 | + | 8.72561e19i | −0.134074 | + | 0.332610i | ||||
\(827\) | 5.83599e19i | 0.220585i | 0.993899 | + | 0.110292i | \(0.0351788\pi\) | ||||
−0.993899 | + | 0.110292i | \(0.964821\pi\) | |||||||
\(828\) | 7.67419e19 | − | 7.97233e19i | 0.287621 | − | 0.298795i | ||||
\(829\) | 2.77327e20 | 1.03065 | 0.515324 | − | 0.856995i | \(-0.327671\pi\) | ||||
0.515324 | + | 0.856995i | \(0.327671\pi\) | |||||||
\(830\) | −6.50351e18 | − | 2.62154e18i | −0.0239663 | − | 0.00966073i | ||||
\(831\) | 1.04844e20i | 0.383122i | ||||||||
\(832\) | 2.89691e20 | − | 3.24855e20i | 1.04972 | − | 1.17714i | ||||
\(833\) | 2.47941e19 | 0.0890911 | ||||||||
\(834\) | −1.39448e19 | + | 3.45941e19i | −0.0496877 | + | 0.123265i | ||||
\(835\) | − | 3.84398e20i | − | 1.35824i | ||||||
\(836\) | −8.10778e19 | − | 7.80458e19i | −0.284091 | − | 0.273467i | ||||
\(837\) | 1.92627e18 | 0.00669329 | ||||||||
\(838\) | 9.67510e19 | + | 3.90000e19i | 0.333386 | + | 0.134387i | ||||
\(839\) | 1.79936e20i | 0.614870i | 0.951569 | + | 0.307435i | \(0.0994707\pi\) | ||||
−0.951569 | + | 0.307435i | \(0.900529\pi\) | |||||||
\(840\) | −9.74862e19 | + | 4.36842e19i | −0.330361 | + | 0.148037i | ||||
\(841\) | −2.66441e20 | −0.895426 | ||||||||
\(842\) | 1.67849e20 | − | 4.16398e20i | 0.559414 | − | 1.38779i | ||||
\(843\) | 1.04350e20i | 0.344905i | ||||||||
\(844\) | 1.81568e20 | − | 1.88622e20i | 0.595171 | − | 0.618293i | ||||
\(845\) | −7.74775e20 | −2.51871 | ||||||||
\(846\) | 1.67930e20 | + | 6.76920e19i | 0.541421 | + | 0.218245i | ||||
\(847\) | 1.08564e20i | 0.347137i | ||||||||
\(848\) | −1.46488e18 | − | 3.84250e19i | −0.00464549 | − | 0.121855i | ||||
\(849\) | −5.64018e19 | −0.177394 | ||||||||
\(850\) | −2.31025e19 | + | 5.73125e19i | −0.0720653 | + | 0.178779i | ||||
\(851\) | − | 5.08023e20i | − | 1.57172i | ||||||
\(852\) | −2.42802e20 | − | 2.33722e20i | −0.745031 | − | 0.717169i | ||||
\(853\) | −5.09296e20 | −1.54998 | −0.774991 | − | 0.631972i | \(-0.782246\pi\) | ||||
−0.774991 | + | 0.631972i | \(0.782246\pi\) | |||||||
\(854\) | 8.61093e19 | + | 3.47104e19i | 0.259923 | + | 0.104774i | ||||
\(855\) | 2.97095e20i | 0.889473i | ||||||||
\(856\) | −4.39290e19 | − | 9.80327e19i | −0.130447 | − | 0.291108i | ||||
\(857\) | 3.36054e20 | 0.989790 | 0.494895 | − | 0.868953i | \(-0.335206\pi\) | ||||
0.494895 | + | 0.868953i | \(0.335206\pi\) | |||||||
\(858\) | 2.91580e19 | − | 7.23350e19i | 0.0851818 | − | 0.211319i | ||||
\(859\) | 4.59208e20i | 1.33063i | 0.746563 | + | 0.665315i | \(0.231703\pi\) | ||||
−0.746563 | + | 0.665315i | \(0.768297\pi\) | |||||||
\(860\) | 5.65471e20 | − | 5.87439e20i | 1.62525 | − | 1.68839i | ||||
\(861\) | 8.10049e19 | 0.230935 | ||||||||
\(862\) | −3.46012e18 | − | 1.39476e18i | −0.00978454 | − | 0.00394412i | ||||
\(863\) | − | 9.50106e19i | − | 0.266499i | −0.991082 | − | 0.133250i | \(-0.957459\pi\) | ||
0.991082 | − | 0.133250i | \(-0.0425412\pi\) | |||||||
\(864\) | 2.33973e19 | − | 6.50921e19i | 0.0650983 | − | 0.181106i | ||||
\(865\) | −9.44194e20 | −2.60584 | ||||||||
\(866\) | −2.11712e20 | + | 5.25214e20i | −0.579589 | + | 1.43784i | ||||
\(867\) | 2.10338e20i | 0.571195i | ||||||||
\(868\) | −3.44462e18 | − | 3.31581e18i | −0.00927905 | − | 0.00893205i | ||||
\(869\) | 9.36088e19 | 0.250137 | ||||||||
\(870\) | 1.10611e20 | + | 4.45869e19i | 0.293200 | + | 0.118188i | ||||
\(871\) | − | 1.57305e20i | − | 0.413634i | ||||||
\(872\) | −5.33863e19 | + | 2.39227e19i | −0.139256 | + | 0.0624016i | ||||
\(873\) | −1.02586e20 | −0.265453 | ||||||||
\(874\) | −2.85584e20 | + | 7.08476e20i | −0.733085 | + | 1.81863i | ||||
\(875\) | − | 2.13454e20i | − | 0.543560i | ||||||
\(876\) | −1.28073e20 | + | 1.33049e20i | −0.323541 | + | 0.336111i | ||||
\(877\) | 3.67289e20 | 0.920473 | 0.460236 | − | 0.887796i | \(-0.347765\pi\) | ||||
0.460236 | + | 0.887796i | \(0.347765\pi\) | |||||||
\(878\) | 3.33789e20 | + | 1.34549e20i | 0.829871 | + | 0.334518i | ||||
\(879\) | 1.58814e20i | 0.391711i | ||||||||
\(880\) | −1.73011e20 | + | 6.59574e18i | −0.423346 | + | 0.0161393i | ||||
\(881\) | 4.65384e20 | 1.12974 | 0.564872 | − | 0.825179i | \(-0.308926\pi\) | ||||
0.564872 | + | 0.825179i | \(0.308926\pi\) | |||||||
\(882\) | 4.46494e19 | − | 1.10766e20i | 0.107531 | − | 0.266763i | ||||
\(883\) | − | 4.03179e20i | − | 0.963325i | −0.876357 | − | 0.481662i | \(-0.840033\pi\) | ||
0.876357 | − | 0.481662i | \(-0.159967\pi\) | |||||||
\(884\) | −4.94936e19 | − | 4.76427e19i | −0.117323 | − | 0.112935i | ||||
\(885\) | 4.02530e20 | 0.946663 | ||||||||
\(886\) | −5.46632e20 | − | 2.20346e20i | −1.27544 | − | 0.514125i | ||||
\(887\) | − | 1.37724e20i | − | 0.318820i | −0.987212 | − | 0.159410i | \(-0.949041\pi\) | ||
0.987212 | − | 0.159410i | \(-0.0509592\pi\) | |||||||
\(888\) | −1.29856e20 | − | 2.89788e20i | −0.298243 | − | 0.665564i | ||||
\(889\) | −1.37401e20 | −0.313096 | ||||||||
\(890\) | 2.00450e20 | − | 4.97275e20i | 0.453185 | − | 1.12426i | ||||
\(891\) | − | 1.23939e19i | − | 0.0278012i | ||||||
\(892\) | −3.66681e20 | + | 3.80926e20i | −0.816083 | + | 0.847788i | ||||
\(893\) | −1.24985e21 | −2.75994 | ||||||||
\(894\) | 4.64814e19 | + | 1.87365e19i | 0.101839 | + | 0.0410511i | ||||
\(895\) | 1.01582e20i | 0.220828i | ||||||||
\(896\) | −1.53887e20 | + | 7.61246e19i | −0.331929 | + | 0.164198i | ||||
\(897\) | −5.29375e20 | −1.13296 | ||||||||
\(898\) | 2.64483e20 | − | 6.56128e20i | 0.561647 | − | 1.39333i | ||||
\(899\) | 5.33767e18i | 0.0112469i | ||||||||
\(900\) | 2.14436e20 | + | 2.06417e20i | 0.448333 | + | 0.431567i | ||||
\(901\) | −6.06910e18 | −0.0125907 | ||||||||
\(902\) | 1.21767e20 | + | 4.90837e19i | 0.250659 | + | 0.101040i | ||||
\(903\) | − | 1.44876e20i | − | 0.295926i | ||||||
\(904\) | 3.65288e20 | − | 1.63688e20i | 0.740383 | − | 0.331770i | ||||
\(905\) | 1.50472e21 | 3.02632 | ||||||||
\(906\) | −1.00729e20 | + | 2.49888e20i | −0.201028 | + | 0.498710i | ||||
\(907\) | 4.42250e19i | 0.0875824i | 0.999041 | + | 0.0437912i | \(0.0139436\pi\) | ||||
−0.999041 | + | 0.0437912i | \(0.986056\pi\) | |||||||
\(908\) | 1.21799e20 | − | 1.26531e20i | 0.239355 | − | 0.248654i | ||||
\(909\) | −7.51101e19 | −0.146471 | ||||||||
\(910\) | 4.73987e20 | + | 1.91062e20i | 0.917226 | + | 0.369731i | ||||
\(911\) | − | 5.50033e20i | − | 1.05623i | −0.849172 | − | 0.528117i | \(-0.822898\pi\) | ||
0.849172 | − | 0.528117i | \(-0.177102\pi\) | |||||||
\(912\) | 1.81897e19 | + | 4.77130e20i | 0.0346626 | + | 0.909227i | ||||
\(913\) | −2.01925e18 | −0.00381852 | ||||||||
\(914\) | 5.05849e19 | − | 1.25491e20i | 0.0949288 | − | 0.235499i | ||||
\(915\) | − | 3.97240e20i | − | 0.739784i | ||||||
\(916\) | −2.76594e20 | − | 2.66250e20i | −0.511180 | − | 0.492063i | ||||
\(917\) | 5.94466e19 | 0.109029 | ||||||||
\(918\) | −1.01255e19 | − | 4.08154e18i | −0.0184296 | − | 0.00742892i | ||||
\(919\) | 6.55183e19i | 0.118346i | 0.998248 | + | 0.0591730i | \(0.0188464\pi\) | ||||
−0.998248 | + | 0.0591730i | \(0.981154\pi\) | |||||||
\(920\) | 4.80570e20 | + | 1.07245e21i | 0.861473 | + | 1.92248i | ||||
\(921\) | 2.75277e20 | 0.489725 | ||||||||
\(922\) | 1.39331e20 | − | 3.45652e20i | 0.245998 | − | 0.610270i | ||||
\(923\) | 1.61224e21i | 2.82500i | ||||||||
\(924\) | −2.13343e19 | + | 2.21631e19i | −0.0371001 | + | 0.0385414i | ||||
\(925\) | 1.36646e21 | 2.35833 | ||||||||
\(926\) | −9.22633e20 | − | 3.71910e20i | −1.58035 | − | 0.637032i | ||||
\(927\) | − | 1.01096e20i | − | 0.171861i | ||||||
\(928\) | 1.80369e20 | + | 6.48336e19i | 0.304317 | + | 0.109387i | ||||
\(929\) | 3.92793e20 | 0.657739 | 0.328869 | − | 0.944375i | \(-0.393332\pi\) | ||||
0.328869 | + | 0.944375i | \(0.393332\pi\) | |||||||
\(930\) | −7.64824e18 | + | 1.89737e19i | −0.0127110 | + | 0.0315335i | ||||
\(931\) | 8.24400e20i | 1.35985i | ||||||||
\(932\) | −2.44701e20 | − | 2.35550e20i | −0.400613 | − | 0.385631i | ||||
\(933\) | −3.20837e20 | −0.521331 | ||||||||
\(934\) | 2.21516e20 | + | 8.92925e19i | 0.357255 | + | 0.144008i | ||||
\(935\) | 2.73266e19i | 0.0437425i | ||||||||
\(936\) | −3.01968e20 | + | 1.35314e20i | −0.479767 | + | 0.214986i | ||||
\(937\) | −4.24903e20 | −0.670059 | −0.335029 | − | 0.942208i | \(-0.608746\pi\) | ||||
−0.335029 | + | 0.942208i | \(0.608746\pi\) | |||||||
\(938\) | −2.31976e19 | + | 5.75486e19i | −0.0363098 | + | 0.0900772i | ||||
\(939\) | − | 9.39002e19i | − | 0.145884i | ||||||
\(940\) | −1.33353e21 | + | 1.38534e21i | −2.05640 | + | 2.13629i | ||||
\(941\) | 1.27519e20 | 0.195186 | 0.0975931 | − | 0.995226i | \(-0.468886\pi\) | ||||
0.0975931 | + | 0.995226i | \(0.468886\pi\) | |||||||
\(942\) | 1.39836e20 | + | 5.63672e19i | 0.212452 | + | 0.0856387i | ||||
\(943\) | − | 8.91135e20i | − | 1.34388i | ||||||
\(944\) | 6.46456e20 | − | 2.46449e19i | 0.967688 | − | 0.0368913i | ||||
\(945\) | 8.12129e19 | 0.120671 | ||||||||
\(946\) | 8.77857e19 | − | 2.17778e20i | 0.129475 | − | 0.321201i | ||||
\(947\) | − | 9.03455e20i | − | 1.32269i | −0.750083 | − | 0.661343i | \(-0.769987\pi\) | ||
0.750083 | − | 0.661343i | \(-0.230013\pi\) | |||||||
\(948\) | −2.86137e20 | − | 2.75436e20i | −0.415830 | − | 0.400279i | ||||
\(949\) | 8.83465e20 | 1.27446 | ||||||||
\(950\) | −1.90563e21 | − | 7.68152e20i | −2.72881 | − | 1.09997i | ||||
\(951\) | − | 1.39579e20i | − | 0.198407i | ||||||
\(952\) | 1.10809e19 | + | 2.47283e19i | 0.0156357 | + | 0.0348928i | ||||
\(953\) | −6.56931e20 | −0.920173 | −0.460087 | − | 0.887874i | \(-0.652182\pi\) | ||||
−0.460087 | + | 0.887874i | \(0.652182\pi\) | |||||||
\(954\) | −1.09293e19 | + | 2.71132e19i | −0.0151968 | + | 0.0377001i | ||||
\(955\) | 1.33017e21i | 1.83604i | ||||||||
\(956\) | −2.84514e20 | + | 2.95567e20i | −0.389851 | + | 0.404997i | ||||
\(957\) | 3.43433e19 | 0.0467152 | ||||||||
\(958\) | 4.42963e20 | + | 1.78557e20i | 0.598149 | + | 0.241112i | ||||
\(959\) | − | 3.49810e20i | − | 0.468924i | ||||||
\(960\) | 5.48256e20 | + | 4.88910e20i | 0.729601 | + | 0.650625i | ||||
\(961\) | 7.56028e20 | 0.998790 | ||||||||
\(962\) | −5.67953e20 | + | 1.40898e21i | −0.744882 | + | 1.84790i | ||||
\(963\) | 8.16681e19i | 0.106333i | ||||||||
\(964\) | −7.38300e20 | − | 7.10690e20i | −0.954320 | − | 0.918631i | ||||
\(965\) | 2.07178e19 | 0.0265859 | ||||||||
\(966\) | 1.93667e20 | + | 7.80663e19i | 0.246726 | + | 0.0994543i | ||||
\(967\) | 5.87530e20i | 0.743096i | 0.928414 | + | 0.371548i | \(0.121173\pi\) | ||||
−0.928414 | + | 0.371548i | \(0.878827\pi\) | |||||||
\(968\) | 6.81263e20 | − | 3.05278e20i | 0.855436 | − | 0.383326i | ||||
\(969\) | 7.53611e19 | 0.0939465 | ||||||||
\(970\) | 4.07315e20 | − | 1.01047e21i | 0.504114 | − | 1.25060i | ||||
\(971\) | − | 1.24174e21i | − | 1.52580i | −0.646516 | − | 0.762900i | \(-0.723775\pi\) | ||
0.646516 | − | 0.762900i | \(-0.276225\pi\) | |||||||
\(972\) | −3.64680e19 | + | 3.78847e19i | −0.0444885 | + | 0.0462169i | ||||
\(973\) | −7.03822e19 | −0.0852458 | ||||||||
\(974\) | 9.17225e20 | + | 3.69730e20i | 1.10297 | + | 0.444603i | ||||
\(975\) | − | 1.42389e21i | − | 1.69998i | ||||||
\(976\) | −2.43210e19 | − | 6.37960e20i | −0.0288293 | − | 0.756214i | ||||
\(977\) | −1.06987e21 | −1.25912 | −0.629560 | − | 0.776952i | \(-0.716765\pi\) | ||||
−0.629560 | + | 0.776952i | \(0.716765\pi\) | |||||||
\(978\) | 2.96144e20 | − | 7.34674e20i | 0.346044 | − | 0.858465i | ||||
\(979\) | − | 1.54397e20i | − | 0.179127i | ||||||
\(980\) | 9.13762e20 | + | 8.79590e20i | 1.05257 | + | 1.01321i | ||||
\(981\) | 4.44746e19 | 0.0508661 | ||||||||
\(982\) | −8.07952e20 | − | 3.25683e20i | −0.917498 | − | 0.369840i | ||||
\(983\) | − | 9.78571e20i | − | 1.10336i | −0.834055 | − | 0.551681i | \(-0.813987\pi\) | ||
0.834055 | − | 0.551681i | \(-0.186013\pi\) | |||||||
\(984\) | −2.27783e20 | − | 5.08324e20i | −0.255009 | − | 0.569083i | ||||
\(985\) | −1.77387e21 | −1.97182 | ||||||||
\(986\) | 1.13099e19 | − | 2.80575e19i | 0.0124830 | − | 0.0309679i | ||||
\(987\) | 3.41656e20i | 0.374428i | ||||||||
\(988\) | 1.58411e21 | − | 1.64565e21i | 1.72380 | − | 1.79077i | ||||
\(989\) | −1.59378e21 | −1.72209 | ||||||||
\(990\) | 1.22079e20 | + | 4.92098e19i | 0.130977 | + | 0.0527965i | ||||
\(991\) | − | 4.07431e20i | − | 0.434049i | −0.976166 | − | 0.217024i | \(-0.930365\pi\) | ||
0.976166 | − | 0.217024i | \(-0.0696351\pi\) | |||||||
\(992\) | −1.11213e19 | + | 3.09397e19i | −0.0117645 | + | 0.0327292i | ||||
\(993\) | −1.83542e20 | −0.192793 | ||||||||
\(994\) | 2.37755e20 | − | 5.89822e20i | 0.247985 | − | 0.615199i | ||||
\(995\) | 2.58350e21i | 2.67576i | ||||||||
\(996\) | 6.17231e18 | + | 5.94149e18i | 0.00634793 | + | 0.00611054i | ||||
\(997\) | 9.14631e20 | 0.934071 | 0.467036 | − | 0.884238i | \(-0.345322\pi\) | ||||
0.467036 | + | 0.884238i | \(0.345322\pi\) | |||||||
\(998\) | 1.10083e20 | + | 4.43743e19i | 0.111637 | + | 0.0450005i | ||||
\(999\) | 2.41414e20i | 0.243111i |
(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 | 12.15.d.a.7.6 | yes | 14 | |
3.2 | odd | 2 | 36.15.d.e.19.9 | 14 | |||
4.3 | odd | 2 | inner | 12.15.d.a.7.5 | ✓ | 14 | |
12.11 | even | 2 | 36.15.d.e.19.10 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.15.d.a.7.5 | ✓ | 14 | 4.3 | odd | 2 | inner | |
12.15.d.a.7.6 | yes | 14 | 1.1 | even | 1 | trivial | |
36.15.d.e.19.9 | 14 | 3.2 | odd | 2 | |||
36.15.d.e.19.10 | 14 | 12.11 | even | 2 |