Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,21,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, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.7");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
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: | \(30.4216518123\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 1800529 x^{18} + 10471600 x^{17} + 1401323871170 x^{16} - 8255926364216 x^{15} + \cdots + 17\!\cdots\!88 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{174}\cdot 3^{82}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 7.16 | ||
Root | \(-144.957 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.7 |
Dual form | 12.21.d.a.7.15 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 734.722 | + | 713.274i | 0.717502 | + | 0.696556i | ||||
\(3\) | 34092.0i | 0.577350i | ||||||||
\(4\) | 31057.2 | + | 1.04812e6i | 0.0296185 | + | 0.999561i | ||||
\(5\) | 6.80556e6 | 0.696889 | 0.348445 | − | 0.937329i | \(-0.386710\pi\) | ||||
0.348445 | + | 0.937329i | \(0.386710\pi\) | |||||||
\(6\) | −2.43169e7 | + | 2.50481e7i | −0.402157 | + | 0.414250i | ||||
\(7\) | 4.46066e7i | 0.157913i | 0.996878 | + | 0.0789567i | \(0.0251589\pi\) | ||||
−0.996878 | + | 0.0789567i | \(0.974841\pi\) | |||||||
\(8\) | −7.24775e8 | + | 7.92226e8i | −0.674999 | + | 0.737818i | ||||
\(9\) | −1.16226e9 | −0.333333 | ||||||||
\(10\) | 5.00020e9 | + | 4.85423e9i | 0.500020 | + | 0.485423i | ||||
\(11\) | 3.23666e10i | 1.24787i | 0.781475 | + | 0.623936i | \(0.214468\pi\) | ||||
−0.781475 | + | 0.623936i | \(0.785532\pi\) | |||||||
\(12\) | −3.57323e10 | + | 1.05880e9i | −0.577097 | + | 0.0171002i | ||||
\(13\) | 7.05819e10 | 0.511988 | 0.255994 | − | 0.966678i | \(-0.417597\pi\) | ||||
0.255994 | + | 0.966678i | \(0.417597\pi\) | |||||||
\(14\) | −3.18167e10 | + | 3.27735e10i | −0.109996 | + | 0.113303i | ||||
\(15\) | 2.32015e11i | 0.402349i | ||||||||
\(16\) | −1.09758e12 | + | 6.51032e10i | −0.998245 | + | 0.0592110i | ||||
\(17\) | −1.15701e12 | −0.573917 | −0.286958 | − | 0.957943i | \(-0.592644\pi\) | ||||
−0.286958 | + | 0.957943i | \(0.592644\pi\) | |||||||
\(18\) | −8.53939e11 | − | 8.29011e11i | −0.239167 | − | 0.232185i | ||||
\(19\) | 4.69812e12i | 0.766282i | 0.923690 | + | 0.383141i | \(0.125158\pi\) | ||||
−0.923690 | + | 0.383141i | \(0.874842\pi\) | |||||||
\(20\) | 2.11362e11 | + | 7.13302e12i | 0.0206408 | + | 0.696584i | ||||
\(21\) | −1.52073e12 | −0.0911714 | ||||||||
\(22\) | −2.30862e13 | + | 2.37805e13i | −0.869214 | + | 0.895351i | ||||
\(23\) | − | 3.62713e13i | − | 0.875558i | −0.899083 | − | 0.437779i | \(-0.855765\pi\) | ||
0.899083 | − | 0.437779i | \(-0.144235\pi\) | |||||||
\(24\) | −2.70085e13 | − | 2.47090e13i | −0.425980 | − | 0.389711i | ||||
\(25\) | −4.90518e13 | −0.514345 | ||||||||
\(26\) | 5.18581e13 | + | 5.03442e13i | 0.367352 | + | 0.356628i | ||||
\(27\) | − | 3.96238e13i | − | 0.192450i | ||||||
\(28\) | −4.67529e13 | + | 1.38536e12i | −0.157844 | + | 0.00467716i | ||||
\(29\) | 3.47780e14 | 0.826655 | 0.413327 | − | 0.910583i | \(-0.364367\pi\) | ||||
0.413327 | + | 0.910583i | \(0.364367\pi\) | |||||||
\(30\) | −1.65490e14 | + | 1.70466e14i | −0.280259 | + | 0.288686i | ||||
\(31\) | − | 3.23494e14i | − | 0.394684i | −0.980335 | − | 0.197342i | \(-0.936769\pi\) | ||
0.980335 | − | 0.197342i | \(-0.0632310\pi\) | |||||||
\(32\) | −8.52855e14 | − | 7.35044e14i | −0.757487 | − | 0.652850i | ||||
\(33\) | −1.10344e15 | −0.720460 | ||||||||
\(34\) | −8.50083e14 | − | 8.25267e14i | −0.411786 | − | 0.399765i | ||||
\(35\) | 3.03573e14i | 0.110048i | ||||||||
\(36\) | −3.60966e13 | − | 1.21818e15i | −0.00987283 | − | 0.333187i | ||||
\(37\) | −6.74908e15 | −1.40355 | −0.701774 | − | 0.712400i | \(-0.747608\pi\) | ||||
−0.701774 | + | 0.712400i | \(0.747608\pi\) | |||||||
\(38\) | −3.35105e15 | + | 3.45181e15i | −0.533758 | + | 0.549809i | ||||
\(39\) | 2.40627e15i | 0.295596i | ||||||||
\(40\) | −4.93250e15 | + | 5.39154e15i | −0.470400 | + | 0.514178i | ||||
\(41\) | −2.06196e16 | −1.53618 | −0.768089 | − | 0.640343i | \(-0.778792\pi\) | ||||
−0.768089 | + | 0.640343i | \(0.778792\pi\) | |||||||
\(42\) | −1.11731e15 | − | 1.08470e15i | −0.0654157 | − | 0.0635060i | ||||
\(43\) | 2.47203e16i | 1.14385i | 0.820306 | + | 0.571925i | \(0.193803\pi\) | ||||
−0.820306 | + | 0.571925i | \(0.806197\pi\) | |||||||
\(44\) | −3.39240e16 | + | 1.00522e15i | −1.24733 | + | 0.0369601i | ||||
\(45\) | −7.90984e15 | −0.232296 | ||||||||
\(46\) | 2.58714e16 | − | 2.66493e16i | 0.609875 | − | 0.628215i | ||||
\(47\) | − | 4.97745e16i | − | 0.946299i | −0.880982 | − | 0.473149i | \(-0.843117\pi\) | ||
0.880982 | − | 0.473149i | \(-0.156883\pi\) | |||||||
\(48\) | −2.21949e15 | − | 3.74187e16i | −0.0341855 | − | 0.576337i | ||||
\(49\) | 7.78025e16 | 0.975063 | ||||||||
\(50\) | −3.60394e16 | − | 3.49873e16i | −0.369044 | − | 0.358270i | ||||
\(51\) | − | 3.94448e16i | − | 0.331351i | ||||||
\(52\) | 2.19208e15 | + | 7.39780e16i | 0.0151643 | + | 0.511763i | ||||
\(53\) | 2.42735e17 | 1.38795 | 0.693974 | − | 0.720000i | \(-0.255858\pi\) | ||||
0.693974 | + | 0.720000i | \(0.255858\pi\) | |||||||
\(54\) | 2.82626e16 | − | 2.91125e16i | 0.134052 | − | 0.138083i | ||||
\(55\) | 2.20273e17i | 0.869629i | ||||||||
\(56\) | −3.53386e16 | − | 3.23298e16i | −0.116511 | − | 0.106591i | ||||
\(57\) | −1.60168e17 | −0.442413 | ||||||||
\(58\) | 2.55521e17 | + | 2.48062e17i | 0.593126 | + | 0.575812i | ||||
\(59\) | 2.94263e17i | 0.575726i | 0.957672 | + | 0.287863i | \(0.0929447\pi\) | ||||
−0.957672 | + | 0.287863i | \(0.907055\pi\) | |||||||
\(60\) | −2.43179e17 | + | 7.20574e15i | −0.402173 | + | 0.0119170i | ||||
\(61\) | 1.13045e18 | 1.58472 | 0.792360 | − | 0.610053i | \(-0.208852\pi\) | ||||
0.792360 | + | 0.610053i | \(0.208852\pi\) | |||||||
\(62\) | 2.30740e17 | − | 2.37678e17i | 0.274920 | − | 0.283187i | ||||
\(63\) | − | 5.18446e16i | − | 0.0526378i | ||||||
\(64\) | −1.02324e17 | − | 1.14837e18i | −0.0887515 | − | 0.996054i | ||||
\(65\) | 4.80349e17 | 0.356799 | ||||||||
\(66\) | −8.10722e17 | − | 7.87055e17i | −0.516931 | − | 0.501841i | ||||
\(67\) | 2.38409e18i | 1.30790i | 0.756537 | + | 0.653951i | \(0.226890\pi\) | ||||
−0.756537 | + | 0.653951i | \(0.773110\pi\) | |||||||
\(68\) | −3.59336e16 | − | 1.21268e18i | −0.0169985 | − | 0.573665i | ||||
\(69\) | 1.23656e18 | 0.505504 | ||||||||
\(70\) | −2.16531e17 | + | 2.23042e17i | −0.0766548 | + | 0.0789598i | ||||
\(71\) | 3.37689e18i | 1.03737i | 0.854966 | + | 0.518685i | \(0.173578\pi\) | ||||
−0.854966 | + | 0.518685i | \(0.826422\pi\) | |||||||
\(72\) | 8.42378e17 | − | 9.20774e17i | 0.225000 | − | 0.245939i | ||||
\(73\) | 3.65986e18 | 0.851601 | 0.425801 | − | 0.904817i | \(-0.359993\pi\) | ||||
0.425801 | + | 0.904817i | \(0.359993\pi\) | |||||||
\(74\) | −4.95870e18 | − | 4.81394e18i | −1.00705 | − | 0.977650i | ||||
\(75\) | − | 1.67227e18i | − | 0.296957i | ||||||
\(76\) | −4.92418e18 | + | 1.45911e17i | −0.765945 | + | 0.0226961i | ||||
\(77\) | −1.44377e18 | −0.197056 | ||||||||
\(78\) | −1.71633e18 | + | 1.76794e18i | −0.205900 | + | 0.212091i | ||||
\(79\) | − | 1.94374e18i | − | 0.205290i | −0.994718 | − | 0.102645i | \(-0.967269\pi\) | ||
0.994718 | − | 0.102645i | \(-0.0327306\pi\) | |||||||
\(80\) | −7.46967e18 | + | 4.43064e17i | −0.695667 | + | 0.0412635i | ||||
\(81\) | 1.35085e18 | 0.111111 | ||||||||
\(82\) | −1.51497e19 | − | 1.47074e19i | −1.10221 | − | 1.07003i | ||||
\(83\) | 2.58303e19i | 1.66475i | 0.554213 | + | 0.832375i | \(0.313019\pi\) | ||||
−0.554213 | + | 0.832375i | \(0.686981\pi\) | |||||||
\(84\) | −4.72296e16 | − | 1.59390e18i | −0.00270036 | − | 0.0911314i | ||||
\(85\) | −7.87412e18 | −0.399956 | ||||||||
\(86\) | −1.76323e19 | + | 1.81625e19i | −0.796755 | + | 0.820714i | ||||
\(87\) | 1.18565e19i | 0.477269i | ||||||||
\(88\) | −2.56417e19 | − | 2.34585e19i | −0.920703 | − | 0.842313i | ||||
\(89\) | 4.32814e19 | 1.38804 | 0.694020 | − | 0.719956i | \(-0.255838\pi\) | ||||
0.694020 | + | 0.719956i | \(0.255838\pi\) | |||||||
\(90\) | −5.81154e18 | − | 5.64188e18i | −0.166673 | − | 0.161808i | ||||
\(91\) | 3.14842e18i | 0.0808498i | ||||||||
\(92\) | 3.80165e19 | − | 1.12649e18i | 0.875174 | − | 0.0259327i | ||||
\(93\) | 1.10286e19 | 0.227871 | ||||||||
\(94\) | 3.55028e19 | − | 3.65704e19i | 0.659150 | − | 0.678971i | ||||
\(95\) | 3.19734e19i | 0.534014i | ||||||||
\(96\) | 2.50591e19 | − | 2.90755e19i | 0.376923 | − | 0.437335i | ||||
\(97\) | 2.46901e19 | 0.334815 | 0.167408 | − | 0.985888i | \(-0.446460\pi\) | ||||
0.167408 | + | 0.985888i | \(0.446460\pi\) | |||||||
\(98\) | 5.71632e19 | + | 5.54945e19i | 0.699610 | + | 0.679187i | ||||
\(99\) | − | 3.76185e19i | − | 0.415958i | ||||||
\(100\) | −1.52341e18 | − | 5.14119e19i | −0.0152341 | − | 0.514119i | ||||
\(101\) | 5.44781e19 | 0.493183 | 0.246592 | − | 0.969119i | \(-0.420689\pi\) | ||||
0.246592 | + | 0.969119i | \(0.420689\pi\) | |||||||
\(102\) | 2.81350e19 | − | 2.89810e19i | 0.230805 | − | 0.237745i | ||||
\(103\) | − | 1.28800e20i | − | 0.958393i | −0.877708 | − | 0.479196i | \(-0.840928\pi\) | ||
0.877708 | − | 0.479196i | \(-0.159072\pi\) | |||||||
\(104\) | −5.11560e19 | + | 5.59168e19i | −0.345592 | + | 0.377754i | ||||
\(105\) | −1.03494e19 | −0.0635364 | ||||||||
\(106\) | 1.78343e20 | + | 1.73136e20i | 0.995856 | + | 0.966784i | ||||
\(107\) | 1.89241e20i | 0.962004i | 0.876719 | + | 0.481002i | \(0.159727\pi\) | ||||
−0.876719 | + | 0.481002i | \(0.840273\pi\) | |||||||
\(108\) | 4.15303e19 | − | 1.23060e18i | 0.192366 | − | 0.00570008i | ||||
\(109\) | −1.36179e18 | −0.00575235 | −0.00287618 | − | 0.999996i | \(-0.500916\pi\) | ||||
−0.00287618 | + | 0.999996i | \(0.500916\pi\) | |||||||
\(110\) | −1.57115e20 | + | 1.61839e20i | −0.605746 | + | 0.623961i | ||||
\(111\) | − | 2.30089e20i | − | 0.810339i | ||||||
\(112\) | −2.90403e18 | − | 4.89595e19i | −0.00935021 | − | 0.157636i | ||||
\(113\) | −5.55681e20 | −1.63697 | −0.818485 | − | 0.574528i | \(-0.805186\pi\) | ||||
−0.818485 | + | 0.574528i | \(0.805186\pi\) | |||||||
\(114\) | −1.17679e20 | − | 1.14244e20i | −0.317432 | − | 0.308165i | ||||
\(115\) | − | 2.46847e20i | − | 0.610167i | ||||||
\(116\) | 1.08011e19 | + | 3.64513e20i | 0.0244843 | + | 0.826292i | ||||
\(117\) | −8.20346e19 | −0.170663 | ||||||||
\(118\) | −2.09890e20 | + | 2.16202e20i | −0.401025 | + | 0.413084i | ||||
\(119\) | − | 5.16104e19i | − | 0.0906292i | ||||||
\(120\) | −1.83808e20 | − | 1.68159e20i | −0.296861 | − | 0.271586i | ||||
\(121\) | −3.74847e20 | −0.557186 | ||||||||
\(122\) | 8.30566e20 | + | 8.06320e20i | 1.13704 | + | 1.10385i | ||||
\(123\) | − | 7.02962e20i | − | 0.886913i | ||||||
\(124\) | 3.39060e20 | − | 1.00468e19i | 0.394511 | − | 0.0116899i | ||||
\(125\) | −9.82854e20 | −1.05533 | ||||||||
\(126\) | 3.69794e19 | − | 3.80914e19i | 0.0366652 | − | 0.0377677i | ||||
\(127\) | − | 1.22633e21i | − | 1.12349i | −0.827309 | − | 0.561747i | \(-0.810129\pi\) | ||
0.827309 | − | 0.561747i | \(-0.189871\pi\) | |||||||
\(128\) | 7.43924e20 | − | 9.16719e20i | 0.630128 | − | 0.776491i | ||||
\(129\) | −8.42762e20 | −0.660402 | ||||||||
\(130\) | 3.52923e20 | + | 3.42621e20i | 0.256004 | + | 0.248531i | ||||
\(131\) | 1.17661e21i | 0.790535i | 0.918566 | + | 0.395267i | \(0.129348\pi\) | ||||
−0.918566 | + | 0.395267i | \(0.870652\pi\) | |||||||
\(132\) | −3.42698e19 | − | 1.15653e21i | −0.0213389 | − | 0.720144i | ||||
\(133\) | −2.09567e20 | −0.121006 | ||||||||
\(134\) | −1.70051e21 | + | 1.75165e21i | −0.911028 | + | 0.938423i | ||||
\(135\) | − | 2.69662e20i | − | 0.134116i | ||||||
\(136\) | 8.38574e20 | − | 9.16616e20i | 0.387393 | − | 0.423446i | ||||
\(137\) | 1.78135e21 | 0.764792 | 0.382396 | − | 0.923999i | \(-0.375099\pi\) | ||||
0.382396 | + | 0.923999i | \(0.375099\pi\) | |||||||
\(138\) | 9.08528e20 | + | 8.82006e20i | 0.362700 | + | 0.352112i | ||||
\(139\) | 1.12261e21i | 0.416947i | 0.978028 | + | 0.208474i | \(0.0668495\pi\) | ||||
−0.978028 | + | 0.208474i | \(0.933150\pi\) | |||||||
\(140\) | −3.18180e20 | + | 9.42814e18i | −0.110000 | + | 0.00325946i | ||||
\(141\) | 1.69691e21 | 0.546346 | ||||||||
\(142\) | −2.40865e21 | + | 2.48108e21i | −0.722586 | + | 0.744315i | ||||
\(143\) | 2.28450e21i | 0.638896i | ||||||||
\(144\) | 1.27568e21 | − | 7.56669e19i | 0.332748 | − | 0.0197370i | ||||
\(145\) | 2.36684e21 | 0.576087 | ||||||||
\(146\) | 2.68898e21 | + | 2.61048e21i | 0.611026 | + | 0.593188i | ||||
\(147\) | 2.65244e21i | 0.562953i | ||||||||
\(148\) | −2.09608e20 | − | 7.07382e21i | −0.0415710 | − | 1.40293i | ||||
\(149\) | 4.00639e21 | 0.742831 | 0.371416 | − | 0.928467i | \(-0.378872\pi\) | ||||
0.371416 | + | 0.928467i | \(0.378872\pi\) | |||||||
\(150\) | 1.19279e21 | − | 1.22865e21i | 0.206847 | − | 0.213067i | ||||
\(151\) | − | 7.29464e21i | − | 1.18368i | −0.806055 | − | 0.591840i | \(-0.798402\pi\) | ||
0.806055 | − | 0.591840i | \(-0.201598\pi\) | |||||||
\(152\) | −3.72198e21 | − | 3.40508e21i | −0.565377 | − | 0.517240i | ||||
\(153\) | 1.34475e21 | 0.191306 | ||||||||
\(154\) | −1.06077e21 | − | 1.02980e21i | −0.141388 | − | 0.137261i | ||||
\(155\) | − | 2.20156e21i | − | 0.275051i | ||||||
\(156\) | −2.52205e21 | + | 7.47322e19i | −0.295467 | + | 0.00875512i | ||||
\(157\) | 8.81074e21 | 0.968313 | 0.484156 | − | 0.874981i | \(-0.339127\pi\) | ||||
0.484156 | + | 0.874981i | \(0.339127\pi\) | |||||||
\(158\) | 1.38642e21 | − | 1.42811e21i | 0.142996 | − | 0.147296i | ||||
\(159\) | 8.27530e21i | 0.801332i | ||||||||
\(160\) | −5.80415e21 | − | 5.00239e21i | −0.527885 | − | 0.454964i | ||||
\(161\) | 1.61794e21 | 0.138262 | ||||||||
\(162\) | 9.92501e20 | + | 9.63527e20i | 0.0797225 | + | 0.0773952i | ||||
\(163\) | 1.97253e22i | 1.48987i | 0.667140 | + | 0.744933i | \(0.267518\pi\) | ||||
−0.667140 | + | 0.744933i | \(0.732482\pi\) | |||||||
\(164\) | −6.40387e20 | − | 2.16117e22i | −0.0454993 | − | 1.53550i | ||||
\(165\) | −7.50953e21 | −0.502081 | ||||||||
\(166\) | −1.84241e22 | + | 1.89781e22i | −1.15959 | + | 1.19446i | ||||
\(167\) | 1.68957e22i | 1.00141i | 0.865619 | + | 0.500704i | \(0.166925\pi\) | ||||
−0.865619 | + | 0.500704i | \(0.833075\pi\) | |||||||
\(168\) | 1.10219e21 | − | 1.20476e21i | 0.0615406 | − | 0.0672679i | ||||
\(169\) | −1.40232e22 | −0.737868 | ||||||||
\(170\) | −5.78529e21 | − | 5.61640e21i | −0.286970 | − | 0.278592i | ||||
\(171\) | − | 5.46045e21i | − | 0.255427i | ||||||
\(172\) | −2.59097e22 | + | 7.67743e20i | −1.14335 | + | 0.0338791i | ||||
\(173\) | −1.66335e22 | −0.692664 | −0.346332 | − | 0.938112i | \(-0.612573\pi\) | ||||
−0.346332 | + | 0.938112i | \(0.612573\pi\) | |||||||
\(174\) | −8.45692e21 | + | 8.71122e21i | −0.332445 | + | 0.342442i | ||||
\(175\) | − | 2.18803e21i | − | 0.0812220i | ||||||
\(176\) | −2.10717e21 | − | 3.55250e22i | −0.0738878 | − | 1.24568i | ||||
\(177\) | −1.00320e22 | −0.332395 | ||||||||
\(178\) | 3.17998e22 | + | 3.08715e22i | 0.995921 | + | 0.966847i | ||||
\(179\) | − | 4.84099e22i | − | 1.43352i | −0.697320 | − | 0.716759i | \(-0.745625\pi\) | ||
0.697320 | − | 0.716759i | \(-0.254375\pi\) | |||||||
\(180\) | −2.45658e20 | − | 8.29043e21i | −0.00688027 | − | 0.232195i | ||||
\(181\) | 6.45669e22 | 1.71090 | 0.855449 | − | 0.517887i | \(-0.173281\pi\) | ||||
0.855449 | + | 0.517887i | \(0.173281\pi\) | |||||||
\(182\) | −2.24569e21 | + | 2.31321e21i | −0.0563164 | + | 0.0580099i | ||||
\(183\) | 3.85392e22i | 0.914939i | ||||||||
\(184\) | 2.87351e22 | + | 2.62885e22i | 0.646003 | + | 0.591001i | ||||
\(185\) | −4.59313e22 | −0.978118 | ||||||||
\(186\) | 8.10292e21 | + | 7.86638e21i | 0.163498 | + | 0.158725i | ||||
\(187\) | − | 3.74486e22i | − | 0.716175i | ||||||
\(188\) | 5.21694e22 | − | 1.54586e21i | 0.945884 | − | 0.0280279i | ||||
\(189\) | 1.76748e21 | 0.0303905 | ||||||||
\(190\) | −2.28058e22 | + | 2.34915e22i | −0.371971 | + | 0.383156i | ||||
\(191\) | − | 6.09764e22i | − | 0.943688i | −0.881682 | − | 0.471844i | \(-0.843589\pi\) | ||
0.881682 | − | 0.471844i | \(-0.156411\pi\) | |||||||
\(192\) | 3.91502e22 | − | 3.48841e21i | 0.575072 | − | 0.0512407i | ||||
\(193\) | 6.71512e22 | 0.936441 | 0.468221 | − | 0.883612i | \(-0.344895\pi\) | ||||
0.468221 | + | 0.883612i | \(0.344895\pi\) | |||||||
\(194\) | 1.81403e22 | + | 1.76108e22i | 0.240230 | + | 0.233218i | ||||
\(195\) | 1.63760e22i | 0.205998i | ||||||||
\(196\) | 2.41633e21 | + | 8.15461e22i | 0.0288799 | + | 0.974636i | ||||
\(197\) | 4.80894e22 | 0.546245 | 0.273122 | − | 0.961979i | \(-0.411944\pi\) | ||||
0.273122 | + | 0.961979i | \(0.411944\pi\) | |||||||
\(198\) | 2.68323e22 | − | 2.76391e22i | 0.289738 | − | 0.298450i | ||||
\(199\) | − | 5.44705e22i | − | 0.559282i | −0.960105 | − | 0.279641i | \(-0.909785\pi\) | ||
0.960105 | − | 0.279641i | \(-0.0902155\pi\) | |||||||
\(200\) | 3.55515e22 | − | 3.88601e22i | 0.347183 | − | 0.379493i | ||||
\(201\) | −8.12784e22 | −0.755118 | ||||||||
\(202\) | 4.00263e22 | + | 3.88578e22i | 0.353860 | + | 0.343530i | ||||
\(203\) | 1.55133e22i | 0.130540i | ||||||||
\(204\) | 4.13427e22 | − | 1.22505e21i | 0.331206 | − | 0.00981411i | ||||
\(205\) | −1.40328e23 | −1.07055 | ||||||||
\(206\) | 9.18696e22 | − | 9.46322e22i | 0.667574 | − | 0.687649i | ||||
\(207\) | 4.21567e22i | 0.291853i | ||||||||
\(208\) | −7.74694e22 | + | 4.59510e21i | −0.511090 | + | 0.0303153i | ||||
\(209\) | −1.52062e23 | −0.956222 | ||||||||
\(210\) | −7.60394e21 | − | 7.38196e21i | −0.0455875 | − | 0.0442567i | ||||
\(211\) | − | 2.08170e23i | − | 1.19013i | −0.803679 | − | 0.595063i | \(-0.797127\pi\) | ||
0.803679 | − | 0.595063i | \(-0.202873\pi\) | |||||||
\(212\) | 7.53867e21 | + | 2.54414e23i | 0.0411089 | + | 1.38734i | ||||
\(213\) | −1.15125e23 | −0.598926 | ||||||||
\(214\) | −1.34981e23 | + | 1.39039e23i | −0.670090 | + | 0.690240i | ||||
\(215\) | 1.68235e23i | 0.797136i | ||||||||
\(216\) | 3.13910e22 | + | 2.87183e22i | 0.141993 | + | 0.129904i | ||||
\(217\) | 1.44300e22 | 0.0623259 | ||||||||
\(218\) | −1.00054e21 | − | 9.71330e20i | −0.00412732 | − | 0.00400684i | ||||
\(219\) | 1.24772e23i | 0.491672i | ||||||||
\(220\) | −2.30872e23 | + | 6.84107e21i | −0.869248 | + | 0.0257571i | ||||
\(221\) | −8.16641e22 | −0.293838 | ||||||||
\(222\) | 1.64117e23 | − | 1.69052e23i | 0.564447 | − | 0.581420i | ||||
\(223\) | − | 4.56842e23i | − | 1.50216i | −0.660209 | − | 0.751082i | \(-0.729532\pi\) | ||
0.660209 | − | 0.751082i | \(-0.270468\pi\) | |||||||
\(224\) | 3.27878e22 | − | 3.80430e22i | 0.103094 | − | 0.119617i | ||||
\(225\) | 5.70110e22 | 0.171448 | ||||||||
\(226\) | −4.08271e23 | − | 3.96352e23i | −1.17453 | − | 1.14024i | ||||
\(227\) | 4.29781e23i | 1.18301i | 0.806301 | + | 0.591505i | \(0.201466\pi\) | ||||
−0.806301 | + | 0.591505i | \(0.798534\pi\) | |||||||
\(228\) | −4.97438e21 | − | 1.67875e23i | −0.0131036 | − | 0.442219i | ||||
\(229\) | 7.90228e23 | 1.99250 | 0.996248 | − | 0.0865428i | \(-0.0275819\pi\) | ||||
0.996248 | + | 0.0865428i | \(0.0275819\pi\) | |||||||
\(230\) | 1.76069e23 | − | 1.81364e23i | 0.425016 | − | 0.437796i | ||||
\(231\) | − | 4.92208e22i | − | 0.113770i | ||||||
\(232\) | −2.52062e23 | + | 2.75520e23i | −0.557991 | + | 0.609921i | ||||
\(233\) | −3.95801e23 | −0.839302 | −0.419651 | − | 0.907686i | \(-0.637847\pi\) | ||||
−0.419651 | + | 0.907686i | \(0.637847\pi\) | |||||||
\(234\) | −6.02726e22 | − | 5.85131e22i | −0.122451 | − | 0.118876i | ||||
\(235\) | − | 3.38743e23i | − | 0.659466i | ||||||
\(236\) | −3.08422e23 | + | 9.13900e21i | −0.575473 | + | 0.0170521i | ||||
\(237\) | 6.62660e22 | 0.118524 | ||||||||
\(238\) | 3.68124e22 | − | 3.79193e22i | 0.0631283 | − | 0.0650266i | ||||
\(239\) | 9.99178e23i | 1.64310i | 0.570137 | + | 0.821550i | \(0.306890\pi\) | ||||
−0.570137 | + | 0.821550i | \(0.693110\pi\) | |||||||
\(240\) | −1.51049e22 | − | 2.54655e23i | −0.0238235 | − | 0.401643i | ||||
\(241\) | 7.12027e23 | 1.07727 | 0.538637 | − | 0.842538i | \(-0.318939\pi\) | ||||
0.538637 | + | 0.842538i | \(0.318939\pi\) | |||||||
\(242\) | −2.75408e23 | − | 2.67368e23i | −0.399782 | − | 0.388111i | ||||
\(243\) | 4.60532e22i | 0.0641500i | ||||||||
\(244\) | 3.51086e22 | + | 1.18484e24i | 0.0469370 | + | 1.58403i | ||||
\(245\) | 5.29490e23 | 0.679511 | ||||||||
\(246\) | 5.01404e23 | − | 5.16482e23i | 0.617785 | − | 0.636362i | ||||
\(247\) | 3.31602e23i | 0.392327i | ||||||||
\(248\) | 2.56281e23 | + | 2.34461e23i | 0.291205 | + | 0.266412i | ||||
\(249\) | −8.80607e23 | −0.961144 | ||||||||
\(250\) | −7.22124e23 | − | 7.01044e23i | −0.757202 | − | 0.735098i | ||||
\(251\) | 1.17581e24i | 1.18468i | 0.805689 | + | 0.592339i | \(0.201795\pi\) | ||||
−0.805689 | + | 0.592339i | \(0.798205\pi\) | |||||||
\(252\) | 5.43391e22 | − | 1.61015e21i | 0.0526147 | − | 0.00155905i | ||||
\(253\) | 1.17398e24 | 1.09258 | ||||||||
\(254\) | 8.74710e23 | − | 9.01013e23i | 0.782577 | − | 0.806109i | ||||
\(255\) | − | 2.68444e23i | − | 0.230915i | ||||||
\(256\) | 1.20045e24 | − | 1.42912e23i | 0.992988 | − | 0.118214i | ||||
\(257\) | 4.64222e23 | 0.369313 | 0.184656 | − | 0.982803i | \(-0.440883\pi\) | ||||
0.184656 | + | 0.982803i | \(0.440883\pi\) | |||||||
\(258\) | −6.19196e23 | − | 6.01120e23i | −0.473839 | − | 0.460007i | ||||
\(259\) | − | 3.01054e23i | − | 0.221639i | ||||||
\(260\) | 1.49183e22 | + | 5.03462e23i | 0.0105678 | + | 0.356642i | ||||
\(261\) | −4.04211e23 | −0.275552 | ||||||||
\(262\) | −8.39247e23 | + | 8.64484e23i | −0.550652 | + | 0.567210i | ||||
\(263\) | − | 1.09646e24i | − | 0.692522i | −0.938138 | − | 0.346261i | \(-0.887451\pi\) | ||
0.938138 | − | 0.346261i | \(-0.112549\pi\) | |||||||
\(264\) | 7.99746e23 | − | 8.74175e23i | 0.486310 | − | 0.531568i | ||||
\(265\) | 1.65195e24 | 0.967247 | ||||||||
\(266\) | −1.53974e23 | − | 1.49479e23i | −0.0868222 | − | 0.0842876i | ||||
\(267\) | 1.47555e24i | 0.801385i | ||||||||
\(268\) | −2.49881e24 | + | 7.40433e22i | −1.30733 | + | 0.0387381i | ||||
\(269\) | −1.35487e24 | −0.682929 | −0.341464 | − | 0.939895i | \(-0.610923\pi\) | ||||
−0.341464 | + | 0.939895i | \(0.610923\pi\) | |||||||
\(270\) | 1.92343e23 | − | 1.98127e23i | 0.0934197 | − | 0.0962288i | ||||
\(271\) | − | 1.97275e24i | − | 0.923378i | −0.887042 | − | 0.461689i | \(-0.847244\pi\) | ||
0.887042 | − | 0.461689i | \(-0.152756\pi\) | |||||||
\(272\) | 1.26992e24 | − | 7.53252e22i | 0.572910 | − | 0.0339822i | ||||
\(273\) | −1.07336e23 | −0.0466786 | ||||||||
\(274\) | 1.30880e24 | + | 1.27059e24i | 0.548740 | + | 0.532720i | ||||
\(275\) | − | 1.58764e24i | − | 0.641837i | ||||||
\(276\) | 3.84041e22 | + | 1.29606e24i | 0.0149723 | + | 0.505282i | ||||
\(277\) | −3.29424e24 | −1.23867 | −0.619337 | − | 0.785125i | \(-0.712599\pi\) | ||||
−0.619337 | + | 0.785125i | \(0.712599\pi\) | |||||||
\(278\) | −8.00728e23 | + | 8.24806e23i | −0.290427 | + | 0.299160i | ||||
\(279\) | 3.75985e23i | 0.131561i | ||||||||
\(280\) | −2.40499e23 | − | 2.20022e23i | −0.0811956 | − | 0.0742825i | ||||
\(281\) | −3.12153e24 | −1.01696 | −0.508481 | − | 0.861073i | \(-0.669793\pi\) | ||||
−0.508481 | + | 0.861073i | \(0.669793\pi\) | |||||||
\(282\) | 1.24676e24 | + | 1.21036e24i | 0.392004 | + | 0.380561i | ||||
\(283\) | − | 2.96270e24i | − | 0.899133i | −0.893247 | − | 0.449567i | \(-0.851578\pi\) | ||
0.893247 | − | 0.449567i | \(-0.148422\pi\) | |||||||
\(284\) | −3.53937e24 | + | 1.04877e23i | −1.03691 | + | 0.0307253i | ||||
\(285\) | −1.09003e24 | −0.308313 | ||||||||
\(286\) | −1.62947e24 | + | 1.67847e24i | −0.445027 | + | 0.458409i | ||||
\(287\) | − | 9.19771e23i | − | 0.242583i | ||||||
\(288\) | 9.91240e23 | + | 8.54313e23i | 0.252496 | + | 0.217617i | ||||
\(289\) | −2.72555e24 | −0.670620 | ||||||||
\(290\) | 1.73897e24 | + | 1.68820e24i | 0.413344 | + | 0.401277i | ||||
\(291\) | 8.41733e23i | 0.193306i | ||||||||
\(292\) | 1.13665e23 | + | 3.83596e24i | 0.0252231 | + | 0.851228i | ||||
\(293\) | −3.37322e24 | −0.723383 | −0.361692 | − | 0.932298i | \(-0.617801\pi\) | ||||
−0.361692 | + | 0.932298i | \(0.617801\pi\) | |||||||
\(294\) | −1.89192e24 | + | 1.94881e24i | −0.392129 | + | 0.403920i | ||||
\(295\) | 2.00263e24i | 0.401217i | ||||||||
\(296\) | 4.89157e24 | − | 5.34680e24i | 0.947394 | − | 1.03556i | ||||
\(297\) | 1.28249e24 | 0.240153 | ||||||||
\(298\) | 2.94358e24 | + | 2.85765e24i | 0.532983 | + | 0.517424i | ||||
\(299\) | − | 2.56010e24i | − | 0.448275i | ||||||
\(300\) | 1.75273e24 | − | 5.19361e22i | 0.296827 | − | 0.00879542i | ||||
\(301\) | −1.10269e24 | −0.180629 | ||||||||
\(302\) | 5.20308e24 | − | 5.35954e24i | 0.824500 | − | 0.849293i | ||||
\(303\) | 1.85727e24i | 0.284740i | ||||||||
\(304\) | −3.05863e23 | − | 5.15658e24i | −0.0453723 | − | 0.764937i | ||||
\(305\) | 7.69334e24 | 1.10438 | ||||||||
\(306\) | 9.88018e23 | + | 9.59176e23i | 0.137262 | + | 0.133255i | ||||
\(307\) | − | 1.98725e24i | − | 0.267220i | −0.991034 | − | 0.133610i | \(-0.957343\pi\) | ||
0.991034 | − | 0.133610i | \(-0.0426570\pi\) | |||||||
\(308\) | −4.48394e22 | − | 1.51323e24i | −0.00583650 | − | 0.196969i | ||||
\(309\) | 4.39104e24 | 0.553328 | ||||||||
\(310\) | 1.57031e24 | − | 1.61753e24i | 0.191589 | − | 0.197350i | ||||
\(311\) | − | 6.19352e24i | − | 0.731701i | −0.930674 | − | 0.365851i | \(-0.880778\pi\) | ||
0.930674 | − | 0.365851i | \(-0.119222\pi\) | |||||||
\(312\) | −1.90631e24 | − | 1.74401e24i | −0.218096 | − | 0.199527i | ||||
\(313\) | 7.98735e24 | 0.885033 | 0.442516 | − | 0.896760i | \(-0.354086\pi\) | ||||
0.442516 | + | 0.896760i | \(0.354086\pi\) | |||||||
\(314\) | 6.47344e24 | + | 6.28447e24i | 0.694767 | + | 0.674484i | ||||
\(315\) | − | 3.52831e23i | − | 0.0366827i | ||||||
\(316\) | 2.03727e24 | − | 6.03672e22i | 0.205200 | − | 0.00608038i | ||||
\(317\) | 5.13715e24 | 0.501337 | 0.250668 | − | 0.968073i | \(-0.419350\pi\) | ||||
0.250668 | + | 0.968073i | \(0.419350\pi\) | |||||||
\(318\) | −5.90256e24 | + | 6.08005e24i | −0.558173 | + | 0.574958i | ||||
\(319\) | 1.12564e25i | 1.03156i | ||||||||
\(320\) | −6.96369e23 | − | 7.81532e24i | −0.0618500 | − | 0.694139i | ||||
\(321\) | −6.45159e24 | −0.555414 | ||||||||
\(322\) | 1.18874e24 | + | 1.15404e24i | 0.0992036 | + | 0.0963075i | ||||
\(323\) | − | 5.43579e24i | − | 0.439782i | ||||||
\(324\) | 4.19537e22 | + | 1.41585e24i | 0.00329094 | + | 0.111062i | ||||
\(325\) | −3.46217e24 | −0.263338 | ||||||||
\(326\) | −1.40695e25 | + | 1.44926e25i | −1.03777 | + | 1.06898i | ||||
\(327\) | − | 4.64261e22i | − | 0.00332112i | ||||||
\(328\) | 1.49446e25 | − | 1.63354e25i | 1.03692 | − | 1.13342i | ||||
\(329\) | 2.22027e24 | 0.149433 | ||||||||
\(330\) | −5.51742e24 | − | 5.35635e24i | −0.360244 | − | 0.349728i | ||||
\(331\) | 2.60799e25i | 1.65206i | 0.563624 | + | 0.826032i | \(0.309407\pi\) | ||||
−0.563624 | + | 0.826032i | \(0.690593\pi\) | |||||||
\(332\) | −2.70732e25 | + | 8.02219e23i | −1.66402 | + | 0.0493074i | ||||
\(333\) | 7.84420e24 | 0.467849 | ||||||||
\(334\) | −1.20512e25 | + | 1.24136e25i | −0.697537 | + | 0.718512i | ||||
\(335\) | 1.62251e25i | 0.911463i | ||||||||
\(336\) | 1.66912e24 | − | 9.90042e22i | 0.0910114 | − | 0.00539835i | ||||
\(337\) | −1.20056e24 | −0.0635454 | −0.0317727 | − | 0.999495i | \(-0.510115\pi\) | ||||
−0.0317727 | + | 0.999495i | \(0.510115\pi\) | |||||||
\(338\) | −1.03031e25 | − | 1.00024e25i | −0.529422 | − | 0.513967i | ||||
\(339\) | − | 1.89442e25i | − | 0.945105i | ||||||
\(340\) | −2.44548e23 | − | 8.25299e24i | −0.0118461 | − | 0.399781i | ||||
\(341\) | 1.04704e25 | 0.492516 | ||||||||
\(342\) | 3.89479e24 | − | 4.01191e24i | 0.177919 | − | 0.183270i | ||||
\(343\) | 7.02977e24i | 0.311889i | ||||||||
\(344\) | −1.95841e25 | − | 1.79166e25i | −0.843953 | − | 0.772097i | ||||
\(345\) | 8.41548e24 | 0.352280 | ||||||||
\(346\) | −1.22210e25 | − | 1.18642e25i | −0.496988 | − | 0.482479i | ||||
\(347\) | − | 9.80143e24i | − | 0.387253i | −0.981075 | − | 0.193627i | \(-0.937975\pi\) | ||
0.981075 | − | 0.193627i | \(-0.0620250\pi\) | |||||||
\(348\) | −1.24270e25 | + | 3.68230e23i | −0.477060 | + | 0.0141360i | ||||
\(349\) | −3.29545e25 | −1.22931 | −0.614653 | − | 0.788797i | \(-0.710704\pi\) | ||||
−0.614653 | + | 0.788797i | \(0.710704\pi\) | |||||||
\(350\) | 1.56067e24 | − | 1.60760e24i | 0.0565757 | − | 0.0582770i | ||||
\(351\) | − | 2.79672e24i | − | 0.0985321i | ||||||
\(352\) | 2.37909e25 | − | 2.76040e25i | 0.814674 | − | 0.945247i | ||||
\(353\) | −8.82040e24 | −0.293590 | −0.146795 | − | 0.989167i | \(-0.546896\pi\) | ||||
−0.146795 | + | 0.989167i | \(0.546896\pi\) | |||||||
\(354\) | −7.37073e24 | − | 7.15556e24i | −0.238494 | − | 0.231532i | ||||
\(355\) | 2.29816e25i | 0.722932i | ||||||||
\(356\) | 1.34420e24 | + | 4.53640e25i | 0.0411116 | + | 1.38743i | ||||
\(357\) | 1.75950e24 | 0.0523248 | ||||||||
\(358\) | 3.45295e25 | − | 3.55678e25i | 0.998527 | − | 1.02855i | ||||
\(359\) | 3.05618e25i | 0.859478i | 0.902953 | + | 0.429739i | \(0.141394\pi\) | ||||
−0.902953 | + | 0.429739i | \(0.858606\pi\) | |||||||
\(360\) | 5.73286e24 | − | 6.26638e24i | 0.156800 | − | 0.171393i | ||||
\(361\) | 1.55176e25 | 0.412813 | ||||||||
\(362\) | 4.74387e25 | + | 4.60539e25i | 1.22757 | + | 1.19174i | ||||
\(363\) | − | 1.27793e25i | − | 0.321692i | ||||||
\(364\) | −3.29991e24 | + | 9.77812e22i | −0.0808143 | + | 0.00239465i | ||||
\(365\) | 2.49074e25 | 0.593472 | ||||||||
\(366\) | −2.74890e25 | + | 2.83156e25i | −0.637306 | + | 0.656471i | ||||
\(367\) | − | 4.75297e25i | − | 1.07227i | −0.844132 | − | 0.536135i | \(-0.819884\pi\) | ||
0.844132 | − | 0.536135i | \(-0.180116\pi\) | |||||||
\(368\) | 2.36138e24 | + | 3.98108e25i | 0.0518426 | + | 0.874022i | ||||
\(369\) | 2.39654e25 | 0.512059 | ||||||||
\(370\) | −3.37467e25 | − | 3.27616e25i | −0.701802 | − | 0.681314i | ||||
\(371\) | 1.08276e25i | 0.219176i | ||||||||
\(372\) | 3.42516e23 | + | 1.15592e25i | 0.00674919 | + | 0.227771i | ||||
\(373\) | −1.01643e26 | −1.94979 | −0.974893 | − | 0.222673i | \(-0.928522\pi\) | ||||
−0.974893 | + | 0.222673i | \(0.928522\pi\) | |||||||
\(374\) | 2.67111e25 | − | 2.75143e25i | 0.498856 | − | 0.513857i | ||||
\(375\) | − | 3.35074e25i | − | 0.609296i | ||||||
\(376\) | 3.94327e25 | + | 3.60753e25i | 0.698197 | + | 0.638751i | ||||
\(377\) | 2.45469e25 | 0.423237 | ||||||||
\(378\) | 1.29861e24 | + | 1.26070e24i | 0.0218052 | + | 0.0211687i | ||||
\(379\) | − | 3.14986e25i | − | 0.515109i | −0.966264 | − | 0.257555i | \(-0.917083\pi\) | ||
0.966264 | − | 0.257555i | \(-0.0829167\pi\) | |||||||
\(380\) | −3.35118e25 | + | 9.93004e23i | −0.533779 | + | 0.0158167i | ||||
\(381\) | 4.18081e25 | 0.648650 | ||||||||
\(382\) | 4.34929e25 | − | 4.48007e25i | 0.657332 | − | 0.677098i | ||||
\(383\) | − | 1.38501e25i | − | 0.203922i | −0.994788 | − | 0.101961i | \(-0.967488\pi\) | ||
0.994788 | − | 0.101961i | \(-0.0325117\pi\) | |||||||
\(384\) | 3.12527e25 | + | 2.53618e25i | 0.448307 | + | 0.363805i | ||||
\(385\) | −9.82563e24 | −0.137326 | ||||||||
\(386\) | 4.93375e25 | + | 4.78972e25i | 0.671899 | + | 0.652284i | ||||
\(387\) | − | 2.87314e25i | − | 0.381283i | ||||||
\(388\) | 7.66805e23 | + | 2.58781e25i | 0.00991671 | + | 0.334668i | ||||
\(389\) | 2.02805e25 | 0.255613 | 0.127807 | − | 0.991799i | \(-0.459206\pi\) | ||||
0.127807 | + | 0.991799i | \(0.459206\pi\) | |||||||
\(390\) | −1.16806e25 | + | 1.20318e25i | −0.143489 | + | 0.147804i | ||||
\(391\) | 4.19664e25i | 0.502497i | ||||||||
\(392\) | −5.63893e25 | + | 6.16372e25i | −0.658167 | + | 0.719420i | ||||
\(393\) | −4.01131e25 | −0.456415 | ||||||||
\(394\) | 3.53324e25 | + | 3.43009e25i | 0.391932 | + | 0.380490i | ||||
\(395\) | − | 1.32283e25i | − | 0.143064i | ||||||
\(396\) | 3.94285e25 | − | 1.16832e24i | 0.415775 | − | 0.0123200i | ||||
\(397\) | 6.26890e25 | 0.644594 | 0.322297 | − | 0.946639i | \(-0.395545\pi\) | ||||
0.322297 | + | 0.946639i | \(0.395545\pi\) | |||||||
\(398\) | 3.88524e25 | − | 4.00207e25i | 0.389571 | − | 0.401286i | ||||
\(399\) | − | 7.14457e24i | − | 0.0698629i | ||||||
\(400\) | 5.38384e25 | − | 3.19342e24i | 0.513443 | − | 0.0304549i | ||||
\(401\) | −1.44421e26 | −1.34334 | −0.671672 | − | 0.740849i | \(-0.734423\pi\) | ||||
−0.671672 | + | 0.740849i | \(0.734423\pi\) | |||||||
\(402\) | −5.97171e25 | − | 5.79738e25i | −0.541799 | − | 0.525982i | ||||
\(403\) | − | 2.28328e25i | − | 0.202074i | ||||||
\(404\) | 1.69194e24 | + | 5.70994e25i | 0.0146073 | + | 0.492967i | ||||
\(405\) | 9.19330e24 | 0.0774322 | ||||||||
\(406\) | −1.10652e25 | + | 1.13980e25i | −0.0909284 | + | 0.0936626i | ||||
\(407\) | − | 2.18445e26i | − | 1.75145i | ||||||
\(408\) | 3.12492e25 | + | 2.85886e25i | 0.244477 | + | 0.223662i | ||||
\(409\) | −1.74636e26 | −1.33322 | −0.666609 | − | 0.745408i | \(-0.732255\pi\) | ||||
−0.666609 | + | 0.745408i | \(0.732255\pi\) | |||||||
\(410\) | −1.03102e26 | − | 1.00092e26i | −0.768119 | − | 0.745696i | ||||
\(411\) | 6.07296e25i | 0.441553i | ||||||||
\(412\) | 1.34997e26 | − | 4.00017e24i | 0.957972 | − | 0.0283861i | ||||
\(413\) | −1.31261e25 | −0.0909148 | ||||||||
\(414\) | −3.00693e25 | + | 3.09735e25i | −0.203292 | + | 0.209405i | ||||
\(415\) | 1.75790e26i | 1.16015i | ||||||||
\(416\) | −6.01961e25 | − | 5.18808e25i | −0.387824 | − | 0.334251i | ||||
\(417\) | −3.82720e25 | −0.240725 | ||||||||
\(418\) | −1.11724e26 | − | 1.08462e26i | −0.686091 | − | 0.666062i | ||||
\(419\) | − | 5.60940e25i | − | 0.336338i | −0.985758 | − | 0.168169i | \(-0.946215\pi\) | ||
0.985758 | − | 0.168169i | \(-0.0537855\pi\) | |||||||
\(420\) | −3.21424e23 | − | 1.08474e25i | −0.00188185 | − | 0.0635085i | ||||
\(421\) | 3.18608e25 | 0.182153 | 0.0910763 | − | 0.995844i | \(-0.470969\pi\) | ||||
0.0910763 | + | 0.995844i | \(0.470969\pi\) | |||||||
\(422\) | 1.48482e26 | − | 1.52947e26i | 0.828989 | − | 0.853917i | ||||
\(423\) | 5.78510e25i | 0.315433i | ||||||||
\(424\) | −1.75928e26 | + | 1.92301e26i | −0.936865 | + | 1.02405i | ||||
\(425\) | 5.67535e25 | 0.295191 | ||||||||
\(426\) | −8.45847e25 | − | 8.21155e25i | −0.429730 | − | 0.417185i | ||||
\(427\) | 5.04255e25i | 0.250249i | ||||||||
\(428\) | −1.98346e26 | + | 5.87730e24i | −0.961582 | + | 0.0284931i | ||||
\(429\) | −7.78829e25 | −0.368867 | ||||||||
\(430\) | −1.19998e26 | + | 1.23606e26i | −0.555250 | + | 0.571947i | ||||
\(431\) | 2.27471e26i | 1.02838i | 0.857677 | + | 0.514189i | \(0.171907\pi\) | ||||
−0.857677 | + | 0.514189i | \(0.828093\pi\) | |||||||
\(432\) | 2.57963e24 | + | 4.34904e25i | 0.0113952 | + | 0.192112i | ||||
\(433\) | 2.82108e26 | 1.21769 | 0.608845 | − | 0.793289i | \(-0.291633\pi\) | ||||
0.608845 | + | 0.793289i | \(0.291633\pi\) | |||||||
\(434\) | 1.06020e25 | + | 1.02925e25i | 0.0447190 | + | 0.0434135i | ||||
\(435\) | 8.06900e25i | 0.332604i | ||||||||
\(436\) | −4.22935e22 | − | 1.42731e24i | −0.000170376 | − | 0.00574983i | ||||
\(437\) | 1.70407e26 | 0.670924 | ||||||||
\(438\) | −8.89965e25 | + | 9.16727e25i | −0.342477 | + | 0.352776i | ||||
\(439\) | 2.29649e26i | 0.863814i | 0.901918 | + | 0.431907i | \(0.142159\pi\) | ||||
−0.901918 | + | 0.431907i | \(0.857841\pi\) | |||||||
\(440\) | −1.74506e26 | − | 1.59648e26i | −0.641628 | − | 0.586999i | ||||
\(441\) | −9.04269e25 | −0.325021 | ||||||||
\(442\) | −6.00004e25 | − | 5.82489e25i | −0.210830 | − | 0.204675i | ||||
\(443\) | − | 5.36533e25i | − | 0.184314i | −0.995744 | − | 0.0921571i | \(-0.970624\pi\) | ||
0.995744 | − | 0.0921571i | \(-0.0293762\pi\) | |||||||
\(444\) | 2.41160e26 | − | 7.14594e24i | 0.809983 | − | 0.0240010i | ||||
\(445\) | 2.94555e26 | 0.967310 | ||||||||
\(446\) | 3.25853e26 | − | 3.35652e26i | 1.04634 | − | 1.07781i | ||||
\(447\) | 1.36586e26i | 0.428874i | ||||||||
\(448\) | 5.12250e25 | − | 4.56431e24i | 0.157290 | − | 0.0140151i | ||||
\(449\) | 2.39589e26 | 0.719454 | 0.359727 | − | 0.933058i | \(-0.382870\pi\) | ||||
0.359727 | + | 0.933058i | \(0.382870\pi\) | |||||||
\(450\) | 4.18872e25 | + | 4.06644e25i | 0.123015 | + | 0.119423i | ||||
\(451\) | − | 6.67386e26i | − | 1.91695i | ||||||
\(452\) | −1.72579e25 | − | 5.82418e26i | −0.0484846 | − | 1.63625i | ||||
\(453\) | 2.48689e26 | 0.683398 | ||||||||
\(454\) | −3.06551e26 | + | 3.15770e26i | −0.824034 | + | 0.848813i | ||||
\(455\) | 2.14268e25i | 0.0563434i | ||||||||
\(456\) | 1.16086e26 | − | 1.26889e26i | 0.298628 | − | 0.326420i | ||||
\(457\) | 5.24638e26 | 1.32038 | 0.660188 | − | 0.751100i | \(-0.270476\pi\) | ||||
0.660188 | + | 0.751100i | \(0.270476\pi\) | |||||||
\(458\) | 5.80598e26 | + | 5.63649e26i | 1.42962 | + | 1.38789i | ||||
\(459\) | 4.58452e25i | 0.110450i | ||||||||
\(460\) | 2.58724e26 | − | 7.66637e24i | 0.609899 | − | 0.0180722i | ||||
\(461\) | −2.71648e26 | −0.626610 | −0.313305 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313305 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(462\) | 3.51079e25 | − | 3.61636e25i | 0.0792474 | − | 0.0816304i | ||||
\(463\) | 1.40917e26i | 0.311282i | 0.987814 | + | 0.155641i | \(0.0497442\pi\) | ||||
−0.987814 | + | 0.155641i | \(0.950256\pi\) | |||||||
\(464\) | −3.81717e26 | + | 2.26415e25i | −0.825204 | + | 0.0489470i | ||||
\(465\) | 7.50555e25 | 0.158801 | ||||||||
\(466\) | −2.90804e26 | − | 2.82315e26i | −0.602201 | − | 0.584621i | ||||
\(467\) | 1.67552e26i | 0.339610i | 0.985478 | + | 0.169805i | \(0.0543137\pi\) | ||||
−0.985478 | + | 0.169805i | \(0.945686\pi\) | |||||||
\(468\) | −2.54777e24 | − | 8.59818e25i | −0.00505477 | − | 0.170588i | ||||
\(469\) | −1.06346e26 | −0.206535 | ||||||||
\(470\) | 2.41617e26 | − | 2.48882e26i | 0.459355 | − | 0.473168i | ||||
\(471\) | 3.00375e26i | 0.559056i | ||||||||
\(472\) | −2.33123e26 | − | 2.13275e26i | −0.424781 | − | 0.388615i | ||||
\(473\) | −8.00111e26 | −1.42738 | ||||||||
\(474\) | 4.86871e25 | + | 4.72658e25i | 0.0850414 | + | 0.0825588i | ||||
\(475\) | − | 2.30451e26i | − | 0.394133i | ||||||
\(476\) | 5.40937e25 | − | 1.60288e24i | 0.0905894 | − | 0.00268430i | ||||
\(477\) | −2.82121e26 | −0.462650 | ||||||||
\(478\) | −7.12687e26 | + | 7.34118e26i | −1.14451 | + | 1.17893i | ||||
\(479\) | 1.04506e27i | 1.64356i | 0.569802 | + | 0.821782i | \(0.307020\pi\) | ||||
−0.569802 | + | 0.821782i | \(0.692980\pi\) | |||||||
\(480\) | 1.70541e26 | − | 1.97875e26i | 0.262674 | − | 0.304774i | ||||
\(481\) | −4.76363e26 | −0.718600 | ||||||||
\(482\) | 5.23142e26 | + | 5.07870e26i | 0.772946 | + | 0.750382i | ||||
\(483\) | 5.51588e25i | 0.0798258i | ||||||||
\(484\) | −1.16417e25 | − | 3.92883e26i | −0.0165030 | − | 0.556942i | ||||
\(485\) | 1.68030e26 | 0.233329 | ||||||||
\(486\) | −3.28485e25 | + | 3.38363e25i | −0.0446841 | + | 0.0460278i | ||||
\(487\) | − | 1.19020e27i | − | 1.58610i | −0.609155 | − | 0.793051i | \(-0.708491\pi\) | ||
0.609155 | − | 0.793051i | \(-0.291509\pi\) | |||||||
\(488\) | −8.19321e26 | + | 8.95572e26i | −1.06969 | + | 1.16924i | ||||
\(489\) | −6.72473e26 | −0.860174 | ||||||||
\(490\) | 3.89028e26 | + | 3.77671e26i | 0.487551 | + | 0.473318i | ||||
\(491\) | − | 8.00412e26i | − | 0.982875i | −0.870913 | − | 0.491438i | \(-0.836472\pi\) | ||
0.870913 | − | 0.491438i | \(-0.163528\pi\) | |||||||
\(492\) | 7.36786e26 | − | 2.18321e25i | 0.886524 | − | 0.0262690i | ||||
\(493\) | −4.02385e26 | −0.474431 | ||||||||
\(494\) | −2.36523e26 | + | 2.43636e26i | −0.273278 | + | 0.281495i | ||||
\(495\) | − | 2.56015e26i | − | 0.289876i | ||||||
\(496\) | 2.10605e25 | + | 3.55062e26i | 0.0233696 | + | 0.393992i | ||||
\(497\) | −1.50632e26 | −0.163815 | ||||||||
\(498\) | −6.47001e26 | − | 6.28114e26i | −0.689623 | − | 0.669491i | ||||
\(499\) | − | 1.31447e27i | − | 1.37324i | −0.727017 | − | 0.686620i | \(-0.759094\pi\) | ||
0.727017 | − | 0.686620i | \(-0.240906\pi\) | |||||||
\(500\) | −3.05247e25 | − | 1.03014e27i | −0.0312573 | − | 1.05487i | ||||
\(501\) | −5.76007e26 | −0.578163 | ||||||||
\(502\) | −8.38676e26 | + | 8.63895e26i | −0.825195 | + | 0.850009i | ||||
\(503\) | 6.91567e26i | 0.667044i | 0.942742 | + | 0.333522i | \(0.108237\pi\) | ||||
−0.942742 | + | 0.333522i | \(0.891763\pi\) | |||||||
\(504\) | 4.10726e25 | + | 3.75757e25i | 0.0388371 | + | 0.0355305i | ||||
\(505\) | 3.70754e26 | 0.343694 | ||||||||
\(506\) | 8.62548e26 | + | 8.37368e26i | 0.783932 | + | 0.761047i | ||||
\(507\) | − | 4.78077e26i | − | 0.426008i | ||||||
\(508\) | 1.28534e27 | − | 3.80865e25i | 1.12300 | − | 0.0332762i | ||||
\(509\) | −1.04999e27 | −0.899509 | −0.449755 | − | 0.893152i | \(-0.648489\pi\) | ||||
−0.449755 | + | 0.893152i | \(0.648489\pi\) | |||||||
\(510\) | 1.91474e26 | − | 1.97232e26i | 0.160845 | − | 0.165682i | ||||
\(511\) | 1.63254e26i | 0.134479i | ||||||||
\(512\) | 9.83932e26 | + | 7.51248e26i | 0.794814 | + | 0.606853i | ||||
\(513\) | 1.86157e26 | 0.147471 | ||||||||
\(514\) | 3.41074e26 | + | 3.31117e26i | 0.264983 | + | 0.257247i | ||||
\(515\) | − | 8.76556e26i | − | 0.667894i | ||||||
\(516\) | −2.61739e25 | − | 8.83313e26i | −0.0195601 | − | 0.660112i | ||||
\(517\) | 1.61103e27 | 1.18086 | ||||||||
\(518\) | 2.14734e26 | − | 2.21191e26i | 0.154384 | − | 0.159027i | ||||
\(519\) | − | 5.67068e26i | − | 0.399910i | ||||||
\(520\) | −3.48145e26 | + | 3.80545e26i | −0.240839 | + | 0.263253i | ||||
\(521\) | 1.08094e27 | 0.733541 | 0.366771 | − | 0.930311i | \(-0.380463\pi\) | ||||
0.366771 | + | 0.930311i | \(0.380463\pi\) | |||||||
\(522\) | −2.96983e26 | − | 2.88313e26i | −0.197709 | − | 0.191937i | ||||
\(523\) | 1.08490e27i | 0.708556i | 0.935140 | + | 0.354278i | \(0.115273\pi\) | ||||
−0.935140 | + | 0.354278i | \(0.884727\pi\) | |||||||
\(524\) | −1.23323e27 | + | 3.65424e25i | −0.790188 | + | 0.0234144i | ||||
\(525\) | 7.45944e25 | 0.0468935 | ||||||||
\(526\) | 7.82073e26 | − | 8.05590e26i | 0.482381 | − | 0.496886i | ||||
\(527\) | 3.74287e26i | 0.226516i | ||||||||
\(528\) | 1.21112e27 | − | 7.18375e25i | 0.719196 | − | 0.0426591i | ||||
\(529\) | 4.00548e26 | 0.233398 | ||||||||
\(530\) | 1.21372e27 | + | 1.17829e27i | 0.694002 | + | 0.673742i | ||||
\(531\) | − | 3.42011e26i | − | 0.191909i | ||||||
\(532\) | −6.50859e24 | − | 2.19651e26i | −0.00358402 | − | 0.120953i | ||||
\(533\) | −1.45537e27 | −0.786505 | ||||||||
\(534\) | −1.05247e27 | + | 1.08412e27i | −0.558210 | + | 0.574995i | ||||
\(535\) | 1.28789e27i | 0.670411i | ||||||||
\(536\) | −1.88874e27 | − | 1.72793e27i | −0.964994 | − | 0.882833i | ||||
\(537\) | 1.65039e27 | 0.827643 | ||||||||
\(538\) | −9.95454e26 | − | 9.66394e26i | −0.490003 | − | 0.475698i | ||||
\(539\) | 2.51820e27i | 1.21675i | ||||||||
\(540\) | 2.82637e26 | − | 8.37495e24i | 0.134058 | − | 0.00397233i | ||||
\(541\) | 4.24156e26 | 0.197494 | 0.0987469 | − | 0.995113i | \(-0.468517\pi\) | ||||
0.0987469 | + | 0.995113i | \(0.468517\pi\) | |||||||
\(542\) | 1.40711e27 | − | 1.44942e27i | 0.643185 | − | 0.662525i | ||||
\(543\) | 2.20121e27i | 0.987788i | ||||||||
\(544\) | 9.86763e26 | + | 8.50455e26i | 0.434734 | + | 0.374682i | ||||
\(545\) | −9.26775e24 | −0.00400875 | ||||||||
\(546\) | −7.88620e25 | − | 7.65598e25i | −0.0334920 | − | 0.0325143i | ||||
\(547\) | − | 1.75220e27i | − | 0.730654i | −0.930879 | − | 0.365327i | \(-0.880957\pi\) | ||
0.930879 | − | 0.365327i | \(-0.119043\pi\) | |||||||
\(548\) | 5.53237e25 | + | 1.86706e27i | 0.0226520 | + | 0.764456i | ||||
\(549\) | −1.31388e27 | −0.528240 | ||||||||
\(550\) | 1.13242e27 | − | 1.16647e27i | 0.447076 | − | 0.460519i | ||||
\(551\) | 1.63391e27i | 0.633450i | ||||||||
\(552\) | −8.96228e26 | + | 9.79635e26i | −0.341215 | + | 0.372970i | ||||
\(553\) | 8.67038e25 | 0.0324180 | ||||||||
\(554\) | −2.42035e27 | − | 2.34969e27i | −0.888751 | − | 0.862806i | ||||
\(555\) | − | 1.56589e27i | − | 0.564717i | ||||||
\(556\) | −1.17663e27 | + | 3.48652e25i | −0.416764 | + | 0.0123493i | ||||
\(557\) | 3.78069e27 | 1.31528 | 0.657642 | − | 0.753331i | \(-0.271554\pi\) | ||||
0.657642 | + | 0.753331i | \(0.271554\pi\) | |||||||
\(558\) | −2.68180e26 | + | 2.76244e26i | −0.0916399 | + | 0.0943956i | ||||
\(559\) | 1.74480e27i | 0.585637i | ||||||||
\(560\) | −1.97636e25 | − | 3.33197e26i | −0.00651606 | − | 0.109855i | ||||
\(561\) | 1.27669e27 | 0.413484 | ||||||||
\(562\) | −2.29346e27 | − | 2.22651e27i | −0.729673 | − | 0.708372i | ||||
\(563\) | − | 5.51625e27i | − | 1.72409i | −0.506831 | − | 0.862045i | \(-0.669183\pi\) | ||
0.506831 | − | 0.862045i | \(-0.330817\pi\) | |||||||
\(564\) | 5.27013e25 | + | 1.77856e27i | 0.0161819 | + | 0.546106i | ||||
\(565\) | −3.78172e27 | −1.14079 | ||||||||
\(566\) | 2.11322e27 | − | 2.17676e27i | 0.626297 | − | 0.645130i | ||||
\(567\) | 6.02570e25i | 0.0175459i | ||||||||
\(568\) | −2.67526e27 | − | 2.44749e27i | −0.765390 | − | 0.700224i | ||||
\(569\) | 4.63358e27 | 1.30255 | 0.651275 | − | 0.758842i | \(-0.274235\pi\) | ||||
0.651275 | + | 0.758842i | \(0.274235\pi\) | |||||||
\(570\) | −8.00873e26 | − | 7.77493e26i | −0.221215 | − | 0.214757i | ||||
\(571\) | 2.14483e27i | 0.582145i | 0.956701 | + | 0.291073i | \(0.0940121\pi\) | ||||
−0.956701 | + | 0.291073i | \(0.905988\pi\) | |||||||
\(572\) | −2.39442e27 | + | 7.09501e25i | −0.638615 | + | 0.0189231i | ||||
\(573\) | 2.07881e27 | 0.544838 | ||||||||
\(574\) | 6.56048e26 | − | 6.75776e26i | 0.168973 | − | 0.174054i | ||||
\(575\) | 1.77917e27i | 0.450339i | ||||||||
\(576\) | 1.18927e26 | + | 1.33471e27i | 0.0295838 | + | 0.332018i | ||||
\(577\) | −4.73352e27 | −1.15725 | −0.578623 | − | 0.815595i | \(-0.696410\pi\) | ||||
−0.578623 | + | 0.815595i | \(0.696410\pi\) | |||||||
\(578\) | −2.00252e27 | − | 1.94407e27i | −0.481171 | − | 0.467124i | ||||
\(579\) | 2.28932e27i | 0.540655i | ||||||||
\(580\) | 7.35074e25 | + | 2.48072e27i | 0.0170628 | + | 0.575834i | ||||
\(581\) | −1.15220e27 | −0.262886 | ||||||||
\(582\) | −6.00386e26 | + | 6.18440e26i | −0.134648 | + | 0.138697i | ||||
\(583\) | 7.85650e27i | 1.73198i | ||||||||
\(584\) | −2.65258e27 | + | 2.89944e27i | −0.574830 | + | 0.628327i | ||||
\(585\) | −5.58292e26 | −0.118933 | ||||||||
\(586\) | −2.47838e27 | − | 2.40603e27i | −0.519029 | − | 0.503877i | ||||
\(587\) | − | 8.80412e27i | − | 1.81261i | −0.422622 | − | 0.906306i | \(-0.638890\pi\) | ||
0.422622 | − | 0.906306i | \(-0.361110\pi\) | |||||||
\(588\) | −2.78006e27 | + | 8.23774e25i | −0.562706 | + | 0.0166738i | ||||
\(589\) | 1.51982e27 | 0.302439 | ||||||||
\(590\) | −1.42842e27 | + | 1.47137e27i | −0.279470 | + | 0.287874i | ||||
\(591\) | 1.63946e27i | 0.315375i | ||||||||
\(592\) | 7.40767e27 | − | 4.39386e26i | 1.40109 | − | 0.0831055i | ||||
\(593\) | −3.10069e27 | −0.576648 | −0.288324 | − | 0.957533i | \(-0.593098\pi\) | ||||
−0.288324 | + | 0.957533i | \(0.593098\pi\) | |||||||
\(594\) | 9.42271e26 | + | 9.14764e26i | 0.172310 | + | 0.167280i | ||||
\(595\) | − | 3.51238e26i | − | 0.0631585i | ||||||
\(596\) | 1.24427e26 | + | 4.19916e27i | 0.0220015 | + | 0.742506i | ||||
\(597\) | 1.85701e27 | 0.322902 | ||||||||
\(598\) | 1.82605e27 | − | 1.88096e27i | 0.312249 | − | 0.321638i | ||||
\(599\) | − | 1.85197e27i | − | 0.311434i | −0.987802 | − | 0.155717i | \(-0.950231\pi\) | ||
0.987802 | − | 0.155717i | \(-0.0497689\pi\) | |||||||
\(600\) | 1.32482e27 | + | 1.21202e27i | 0.219100 | + | 0.200446i | ||||
\(601\) | −5.45089e27 | −0.886590 | −0.443295 | − | 0.896376i | \(-0.646191\pi\) | ||||
−0.443295 | + | 0.896376i | \(0.646191\pi\) | |||||||
\(602\) | −8.10170e26 | − | 7.86519e26i | −0.129602 | − | 0.125818i | ||||
\(603\) | − | 2.77094e27i | − | 0.435967i | ||||||
\(604\) | 7.64563e27 | − | 2.26551e26i | 1.18316 | − | 0.0350588i | ||||
\(605\) | −2.55104e27 | −0.388297 | ||||||||
\(606\) | −1.32474e27 | + | 1.36457e27i | −0.198337 | + | 0.204301i | ||||
\(607\) | 3.53803e27i | 0.521045i | 0.965468 | + | 0.260522i | \(0.0838948\pi\) | ||||
−0.965468 | + | 0.260522i | \(0.916105\pi\) | |||||||
\(608\) | 3.45333e27 | − | 4.00682e27i | 0.500267 | − | 0.580448i | ||||
\(609\) | −5.28878e26 | −0.0753672 | ||||||||
\(610\) | 5.65247e27 | + | 5.48746e27i | 0.792391 | + | 0.769259i | ||||
\(611\) | − | 3.51318e27i | − | 0.484494i | ||||||
\(612\) | 4.17642e25 | + | 1.40946e27i | 0.00566618 | + | 0.191222i | ||||
\(613\) | 5.25248e26 | 0.0701067 | 0.0350534 | − | 0.999385i | \(-0.488840\pi\) | ||||
0.0350534 | + | 0.999385i | \(0.488840\pi\) | |||||||
\(614\) | 1.41745e27 | − | 1.46008e27i | 0.186134 | − | 0.191731i | ||||
\(615\) | − | 4.78405e27i | − | 0.618080i | ||||||
\(616\) | 1.04641e27 | − | 1.14379e27i | 0.133013 | − | 0.145391i | ||||
\(617\) | 3.18164e27 | 0.397924 | 0.198962 | − | 0.980007i | \(-0.436243\pi\) | ||||
0.198962 | + | 0.980007i | \(0.436243\pi\) | |||||||
\(618\) | 3.22620e27 | + | 3.13201e27i | 0.397014 | + | 0.385424i | ||||
\(619\) | − | 7.66961e27i | − | 0.928681i | −0.885657 | − | 0.464340i | \(-0.846291\pi\) | ||
0.885657 | − | 0.464340i | \(-0.153709\pi\) | |||||||
\(620\) | 2.30749e27 | − | 6.83744e25i | 0.274931 | − | 0.00814660i | ||||
\(621\) | −1.43721e27 | −0.168501 | ||||||||
\(622\) | 4.41768e27 | − | 4.55052e27i | 0.509671 | − | 0.524997i | ||||
\(623\) | 1.93064e27i | 0.219190i | ||||||||
\(624\) | −1.56656e26 | − | 2.64108e27i | −0.0175026 | − | 0.295078i | ||||
\(625\) | −2.01093e27 | −0.221104 | ||||||||
\(626\) | 5.86848e27 | + | 5.69717e27i | 0.635013 | + | 0.616475i | ||||
\(627\) | − | 5.18410e27i | − | 0.552075i | ||||||
\(628\) | 2.73637e26 | + | 9.23467e27i | 0.0286800 | + | 0.967888i | ||||
\(629\) | 7.80877e27 | 0.805520 | ||||||||
\(630\) | 2.51665e26 | − | 2.59233e26i | 0.0255516 | − | 0.0263199i | ||||
\(631\) | 1.65860e28i | 1.65748i | 0.559632 | + | 0.828741i | \(0.310943\pi\) | ||||
−0.559632 | + | 0.828741i | \(0.689057\pi\) | |||||||
\(632\) | 1.53988e27 | + | 1.40878e27i | 0.151467 | + | 0.138571i | ||||
\(633\) | 7.09691e27 | 0.687119 | ||||||||
\(634\) | 3.77438e27 | + | 3.66419e27i | 0.359710 | + | 0.349209i | ||||
\(635\) | − | 8.34588e27i | − | 0.782951i | ||||||
\(636\) | −8.67348e27 | + | 2.57008e26i | −0.800981 | + | 0.0237343i | ||||
\(637\) | 5.49145e27 | 0.499221 | ||||||||
\(638\) | −8.02893e27 | + | 8.27036e27i | −0.718539 | + | 0.740146i | ||||
\(639\) | − | 3.92483e27i | − | 0.345790i | ||||||
\(640\) | 5.06282e27 | − | 6.23879e27i | 0.439130 | − | 0.541128i | ||||
\(641\) | −6.63028e27 | −0.566176 | −0.283088 | − | 0.959094i | \(-0.591359\pi\) | ||||
−0.283088 | + | 0.959094i | \(0.591359\pi\) | |||||||
\(642\) | −4.74013e27 | − | 4.60175e27i | −0.398510 | − | 0.386877i | ||||
\(643\) | − | 2.19500e28i | − | 1.81687i | −0.418022 | − | 0.908437i | \(-0.637277\pi\) | ||
0.418022 | − | 0.908437i | \(-0.362723\pi\) | |||||||
\(644\) | 5.02488e25 | + | 1.69579e27i | 0.00409512 | + | 0.138202i | ||||
\(645\) | −5.73547e27 | −0.460227 | ||||||||
\(646\) | 3.87720e27 | − | 3.99379e27i | 0.306333 | − | 0.315544i | ||||
\(647\) | 8.47014e27i | 0.658943i | 0.944166 | + | 0.329471i | \(0.106871\pi\) | ||||
−0.944166 | + | 0.329471i | \(0.893129\pi\) | |||||||
\(648\) | −9.79064e26 | + | 1.07018e27i | −0.0749999 | + | 0.0819798i | ||||
\(649\) | −9.52429e27 | −0.718432 | ||||||||
\(650\) | −2.54373e27 | − | 2.46947e27i | −0.188946 | − | 0.183430i | ||||
\(651\) | 4.91947e26i | 0.0359839i | ||||||||
\(652\) | −2.06744e28 | + | 6.12612e26i | −1.48921 | + | 0.0441275i | ||||
\(653\) | −1.27267e28 | −0.902783 | −0.451391 | − | 0.892326i | \(-0.649072\pi\) | ||||
−0.451391 | + | 0.892326i | \(0.649072\pi\) | |||||||
\(654\) | 3.31145e25 | − | 3.41103e25i | 0.00231335 | − | 0.00238291i | ||||
\(655\) | 8.00752e27i | 0.550915i | ||||||||
\(656\) | 2.26317e28 | − | 1.34240e27i | 1.53348 | − | 0.0909586i | ||||
\(657\) | −4.25372e27 | −0.283867 | ||||||||
\(658\) | 1.63128e27 | + | 1.58366e27i | 0.107219 | + | 0.104089i | ||||
\(659\) | 7.25771e27i | 0.469835i | 0.972015 | + | 0.234917i | \(0.0754820\pi\) | ||||
−0.972015 | + | 0.234917i | \(0.924518\pi\) | |||||||
\(660\) | −2.33225e26 | − | 7.87086e27i | −0.0148709 | − | 0.501860i | ||||
\(661\) | −1.61821e28 | −1.01630 | −0.508148 | − | 0.861270i | \(-0.669670\pi\) | ||||
−0.508148 | + | 0.861270i | \(0.669670\pi\) | |||||||
\(662\) | −1.86021e28 | + | 1.91615e28i | −1.15076 | + | 1.18536i | ||||
\(663\) | − | 2.78409e27i | − | 0.169648i | ||||||
\(664\) | −2.04635e28 | − | 1.87212e28i | −1.22828 | − | 1.12371i | ||||
\(665\) | −1.42622e27 | −0.0843279 | ||||||||
\(666\) | 5.76330e27 | + | 5.59506e27i | 0.335683 | + | 0.325883i | ||||
\(667\) | − | 1.26144e28i | − | 0.723784i | ||||||
\(668\) | −1.77086e28 | + | 5.24733e26i | −1.00097 | + | 0.0296602i | ||||
\(669\) | 1.55746e28 | 0.867275 | ||||||||
\(670\) | −1.15729e28 | + | 1.19209e28i | −0.634886 | + | 0.653977i | ||||
\(671\) | 3.65888e28i | 1.97753i | ||||||||
\(672\) | 1.29696e27 | + | 1.11780e27i | 0.0690611 | + | 0.0595213i | ||||
\(673\) | 1.29113e28 | 0.677362 | 0.338681 | − | 0.940901i | \(-0.390019\pi\) | ||||
0.338681 | + | 0.940901i | \(0.390019\pi\) | |||||||
\(674\) | −8.82077e26 | − | 8.56327e26i | −0.0455940 | − | 0.0442630i | ||||
\(675\) | 1.94362e27i | 0.0989858i | ||||||||
\(676\) | −4.35521e26 | − | 1.46979e28i | −0.0218545 | − | 0.737545i | ||||
\(677\) | 8.50196e27 | 0.420371 | 0.210185 | − | 0.977662i | \(-0.432593\pi\) | ||||
0.210185 | + | 0.977662i | \(0.432593\pi\) | |||||||
\(678\) | 1.35124e28 | − | 1.39187e28i | 0.658319 | − | 0.678115i | ||||
\(679\) | 1.10134e27i | 0.0528718i | ||||||||
\(680\) | 5.70697e27 | − | 6.23808e27i | 0.269970 | − | 0.295095i | ||||
\(681\) | −1.46521e28 | −0.683011 | ||||||||
\(682\) | 7.69284e27 | + | 7.46827e27i | 0.353381 | + | 0.343065i | ||||
\(683\) | 2.84927e27i | 0.128981i | 0.997918 | + | 0.0644906i | \(0.0205423\pi\) | ||||
−0.997918 | + | 0.0644906i | \(0.979458\pi\) | |||||||
\(684\) | 5.72318e27 | − | 1.69586e26i | 0.255315 | − | 0.00756537i | ||||
\(685\) | 1.21231e28 | 0.532975 | ||||||||
\(686\) | −5.01415e27 | + | 5.16493e27i | −0.217248 | + | 0.223781i | ||||
\(687\) | 2.69404e28i | 1.15037i | ||||||||
\(688\) | −1.60937e27 | − | 2.71325e28i | −0.0677284 | − | 1.14184i | ||||
\(689\) | 1.71327e28 | 0.710613 | ||||||||
\(690\) | 6.18304e27 | + | 6.00254e27i | 0.252762 | + | 0.245383i | ||||
\(691\) | 7.52148e26i | 0.0303056i | 0.999885 | + | 0.0151528i | \(0.00482347\pi\) | ||||
−0.999885 | + | 0.0151528i | \(0.995177\pi\) | |||||||
\(692\) | −5.16590e26 | − | 1.74338e28i | −0.0205157 | − | 0.692360i | ||||
\(693\) | 1.67803e27 | 0.0656853 | ||||||||
\(694\) | 6.99111e27 | − | 7.20133e27i | 0.269744 | − | 0.277855i | ||||
\(695\) | 7.63999e27i | 0.290566i | ||||||||
\(696\) | −9.39302e27 | − | 8.59329e27i | −0.352138 | − | 0.322157i | ||||
\(697\) | 2.38571e28 | 0.881638 | ||||||||
\(698\) | −2.42124e28 | − | 2.35056e28i | −0.882030 | − | 0.856281i | ||||
\(699\) | − | 1.34936e28i | − | 0.484571i | ||||||
\(700\) | 2.29331e27 | − | 6.79543e25i | 0.0811864 | − | 0.00240567i | ||||
\(701\) | 2.49892e28 | 0.872111 | 0.436055 | − | 0.899920i | \(-0.356375\pi\) | ||||
0.436055 | + | 0.899920i | \(0.356375\pi\) | |||||||
\(702\) | 1.99483e27 | − | 2.05481e27i | 0.0686332 | − | 0.0706970i | ||||
\(703\) | − | 3.17080e28i | − | 1.07551i | ||||||
\(704\) | 3.71689e28 | − | 3.31186e27i | 1.24295 | − | 0.110751i | ||||
\(705\) | 1.15484e28 | 0.380743 | ||||||||
\(706\) | −6.48054e27 | − | 6.29136e27i | −0.210651 | − | 0.204502i | ||||
\(707\) | 2.43009e27i | 0.0778803i | ||||||||
\(708\) | −3.11566e26 | − | 1.05147e28i | −0.00984505 | − | 0.332250i | ||||
\(709\) | 4.53449e28 | 1.41275 | 0.706376 | − | 0.707837i | \(-0.250329\pi\) | ||||
0.706376 | + | 0.707837i | \(0.250329\pi\) | |||||||
\(710\) | −1.63922e28 | + | 1.68851e28i | −0.503563 | + | 0.518705i | ||||
\(711\) | 2.25914e27i | 0.0684300i | ||||||||
\(712\) | −3.13693e28 | + | 3.42887e28i | −0.936926 | + | 1.02412i | ||||
\(713\) | −1.17336e28 | −0.345569 | ||||||||
\(714\) | 1.29274e27 | + | 1.25501e27i | 0.0375431 | + | 0.0364472i | ||||
\(715\) | 1.55473e28i | 0.445240i | ||||||||
\(716\) | 5.07391e28 | − | 1.50348e27i | 1.43289 | − | 0.0424587i | ||||
\(717\) | −3.40639e28 | −0.948644 | ||||||||
\(718\) | −2.17989e28 | + | 2.24544e28i | −0.598675 | + | 0.616677i | ||||
\(719\) | − | 2.03741e28i | − | 0.551811i | −0.961185 | − | 0.275905i | \(-0.911022\pi\) | ||
0.961185 | − | 0.275905i | \(-0.0889777\pi\) | |||||||
\(720\) | 8.68170e27 | − | 5.14956e26i | 0.231889 | − | 0.0137545i | ||||
\(721\) | 5.74533e27 | 0.151343 | ||||||||
\(722\) | 1.14011e28 | + | 1.10683e28i | 0.296194 | + | 0.287547i | ||||
\(723\) | 2.42744e28i | 0.621964i | ||||||||
\(724\) | 2.00527e27 | + | 6.76736e28i | 0.0506742 | + | 1.71015i | ||||
\(725\) | −1.70592e28 | −0.425186 | ||||||||
\(726\) | 9.11511e27 | − | 9.38921e27i | 0.224076 | − | 0.230814i | ||||
\(727\) | 3.71664e28i | 0.901169i | 0.892734 | + | 0.450585i | \(0.148784\pi\) | ||||
−0.892734 | + | 0.450585i | \(0.851216\pi\) | |||||||
\(728\) | −2.49426e27 | − | 2.28190e27i | −0.0596524 | − | 0.0545736i | ||||
\(729\) | −1.57004e27 | −0.0370370 | ||||||||
\(730\) | 1.83000e28 | + | 1.77658e28i | 0.425817 | + | 0.413387i | ||||
\(731\) | − | 2.86017e28i | − | 0.656474i | ||||||
\(732\) | −4.03936e28 | + | 1.19692e27i | −0.914537 | + | 0.0270991i | ||||
\(733\) | −6.98760e27 | −0.156059 | −0.0780294 | − | 0.996951i | \(-0.524863\pi\) | ||||
−0.0780294 | + | 0.996951i | \(0.524863\pi\) | |||||||
\(734\) | 3.39017e28 | − | 3.49211e28i | 0.746897 | − | 0.769356i | ||||
\(735\) | 1.80513e28i | 0.392316i | ||||||||
\(736\) | −2.66610e28 | + | 3.09342e28i | −0.571608 | + | 0.663224i | ||||
\(737\) | −7.71650e28 | −1.63210 | ||||||||
\(738\) | 1.76079e28 | + | 1.70939e28i | 0.367404 | + | 0.356678i | ||||
\(739\) | − | 4.71283e28i | − | 0.970148i | −0.874473 | − | 0.485074i | \(-0.838793\pi\) | ||
0.874473 | − | 0.485074i | \(-0.161207\pi\) | |||||||
\(740\) | −1.42650e27 | − | 4.81413e28i | −0.0289704 | − | 0.977689i | ||||
\(741\) | −1.13050e28 | −0.226510 | ||||||||
\(742\) | −7.72303e27 | + | 7.95527e27i | −0.152668 | + | 0.157259i | ||||
\(743\) | 8.89929e27i | 0.173567i | 0.996227 | + | 0.0867835i | \(0.0276588\pi\) | ||||
−0.996227 | + | 0.0867835i | \(0.972341\pi\) | |||||||
\(744\) | −7.99322e27 | + | 8.73711e27i | −0.153813 | + | 0.168127i | ||||
\(745\) | 2.72657e28 | 0.517671 | ||||||||
\(746\) | −7.46790e28 | − | 7.24989e28i | −1.39898 | − | 1.35814i | ||||
\(747\) | − | 3.00216e28i | − | 0.554917i | ||||||
\(748\) | 3.92504e28 | − | 1.16305e27i | 0.715861 | − | 0.0212120i | ||||
\(749\) | −8.44140e27 | −0.151913 | ||||||||
\(750\) | 2.39000e28 | − | 2.46186e28i | 0.424409 | − | 0.437171i | ||||
\(751\) | − | 6.86746e28i | − | 1.20336i | −0.798736 | − | 0.601682i | \(-0.794497\pi\) | ||
0.798736 | − | 0.601682i | \(-0.205503\pi\) | |||||||
\(752\) | 3.24048e27 | + | 5.46316e28i | 0.0560313 | + | 0.944639i | ||||
\(753\) | −4.00857e28 | −0.683975 | ||||||||
\(754\) | 1.80352e28 | + | 1.75087e28i | 0.303674 | + | 0.294809i | ||||
\(755\) | − | 4.96441e28i | − | 0.824895i | ||||||
\(756\) | 5.48931e25 | + | 1.85253e27i | 0.000900119 | + | 0.0303771i | ||||
\(757\) | −5.91786e28 | −0.957648 | −0.478824 | − | 0.877911i | \(-0.658937\pi\) | ||||
−0.478824 | + | 0.877911i | \(0.658937\pi\) | |||||||
\(758\) | 2.24671e28 | − | 2.31427e28i | 0.358803 | − | 0.369592i | ||||
\(759\) | 4.00232e28i | 0.630804i | ||||||||
\(760\) | −2.53301e28 | − | 2.31735e28i | −0.394005 | − | 0.360459i | ||||
\(761\) | −1.70853e26 | −0.00262287 | −0.00131143 | − | 0.999999i | \(-0.500417\pi\) | ||||
−0.00131143 | + | 0.999999i | \(0.500417\pi\) | |||||||
\(762\) | 3.07173e28 | + | 2.98206e28i | 0.465407 | + | 0.451821i | ||||
\(763\) | − | 6.07449e25i | − | 0.000908374i | ||||||
\(764\) | 6.39104e28 | − | 1.89376e27i | 0.943274 | − | 0.0279506i | ||||
\(765\) | 9.15179e27 | 0.133319 | ||||||||
\(766\) | 9.87890e27 | − | 1.01760e28i | 0.142043 | − | 0.146315i | ||||
\(767\) | 2.07696e28i | 0.294765i | ||||||||
\(768\) | 4.87216e27 | + | 4.09257e28i | 0.0682510 | + | 0.573302i | ||||
\(769\) | 5.09126e28 | 0.703982 | 0.351991 | − | 0.936003i | \(-0.385505\pi\) | ||||
0.351991 | + | 0.936003i | \(0.385505\pi\) | |||||||
\(770\) | −7.21911e27 | − | 7.00837e27i | −0.0985318 | − | 0.0956554i | ||||
\(771\) | 1.58262e28i | 0.213223i | ||||||||
\(772\) | 2.08553e27 | + | 7.03822e28i | 0.0277360 | + | 0.936031i | ||||
\(773\) | −1.48178e29 | −1.94532 | −0.972658 | − | 0.232243i | \(-0.925394\pi\) | ||||
−0.972658 | + | 0.232243i | \(0.925394\pi\) | |||||||
\(774\) | 2.04934e28 | − | 2.11096e28i | 0.265585 | − | 0.273571i | ||||
\(775\) | 1.58680e28i | 0.203004i | ||||||||
\(776\) | −1.78947e28 | + | 1.95601e28i | −0.226000 | + | 0.247033i | ||||
\(777\) | 1.02635e28 | 0.127963 | ||||||||
\(778\) | 1.49006e28 | + | 1.44656e28i | 0.183403 | + | 0.178049i | ||||
\(779\) | − | 9.68734e28i | − | 1.17714i | ||||||
\(780\) | −1.71640e28 | + | 5.08595e26i | −0.205908 | + | 0.00610135i | ||||
\(781\) | −1.09298e29 | −1.29450 | ||||||||
\(782\) | −2.99335e28 | + | 3.08336e28i | −0.350018 | + | 0.360543i | ||||
\(783\) | − | 1.37803e28i | − | 0.159090i | ||||||
\(784\) | −8.53947e28 | + | 5.06519e27i | −0.973353 | + | 0.0577345i | ||||
\(785\) | 5.99620e28 | 0.674807 | ||||||||
\(786\) | −2.94719e28 | − | 2.86116e28i | −0.327479 | − | 0.317919i | ||||
\(787\) | − | 3.62601e27i | − | 0.0397815i | −0.999802 | − | 0.0198908i | \(-0.993668\pi\) | ||
0.999802 | − | 0.0198908i | \(-0.00633184\pi\) | |||||||
\(788\) | 1.49352e27 | + | 5.04033e28i | 0.0161789 | + | 0.546005i | ||||
\(789\) | 3.73803e28 | 0.399828 | ||||||||
\(790\) | 9.43537e27 | − | 9.71909e27i | 0.0996524 | − | 0.102649i | ||||
\(791\) | − | 2.47870e28i | − | 0.258500i | ||||||
\(792\) | 2.98023e28 | + | 2.72649e28i | 0.306901 | + | 0.280771i | ||||
\(793\) | 7.97892e28 | 0.811358 | ||||||||
\(794\) | 4.60590e28 | + | 4.47144e28i | 0.462497 | + | 0.448996i | ||||
\(795\) | 5.63181e28i | 0.558440i | ||||||||
\(796\) | 5.70914e28 | − | 1.69170e27i | 0.559037 | − | 0.0165651i | ||||
\(797\) | 1.79945e29 | 1.74003 | 0.870015 | − | 0.493026i | \(-0.164109\pi\) | ||||
0.870015 | + | 0.493026i | \(0.164109\pi\) | |||||||
\(798\) | 5.09603e27 | − | 5.24927e27i | 0.0486635 | − | 0.0501268i | ||||
\(799\) | 5.75897e28i | 0.543097i | ||||||||
\(800\) | 4.18340e28 | + | 3.60552e28i | 0.389610 | + | 0.335790i | ||||
\(801\) | −5.03044e28 | −0.462680 | ||||||||
\(802\) | −1.06109e29 | − | 1.03012e29i | −0.963852 | − | 0.935714i | ||||
\(803\) | 1.18457e29i | 1.06269i | ||||||||
\(804\) | −2.52428e27 | − | 8.51892e28i | −0.0223654 | − | 0.754786i | ||||
\(805\) | 1.10110e28 | 0.0963536 | ||||||||
\(806\) | 1.62861e28 | − | 1.67758e28i | 0.140756 | − | 0.144988i | ||||
\(807\) | − | 4.61902e28i | − | 0.394289i | ||||||
\(808\) | −3.94844e28 | + | 4.31590e28i | −0.332898 | + | 0.363880i | ||||
\(809\) | 1.65606e29 | 1.37909 | 0.689543 | − | 0.724245i | \(-0.257811\pi\) | ||||
0.689543 | + | 0.724245i | \(0.257811\pi\) | |||||||
\(810\) | 6.75452e27 | + | 6.55734e27i | 0.0555577 | + | 0.0539359i | ||||
\(811\) | − | 9.73666e28i | − | 0.791045i | −0.918456 | − | 0.395523i | \(-0.870564\pi\) | ||
0.918456 | − | 0.395523i | \(-0.129436\pi\) | |||||||
\(812\) | −1.62597e28 | + | 4.81800e26i | −0.130483 | + | 0.00386639i | ||||
\(813\) | 6.72549e28 | 0.533112 | ||||||||
\(814\) | 1.55811e29 | − | 1.60496e29i | 1.21998 | − | 1.25667i | ||||
\(815\) | 1.34242e29i | 1.03827i | ||||||||
\(816\) | 2.56798e27 | + | 4.32939e28i | 0.0196196 | + | 0.330770i | ||||
\(817\) | −1.16139e29 | −0.876510 | ||||||||
\(818\) | −1.28309e29 | − | 1.24563e29i | −0.956586 | − | 0.928661i | ||||
\(819\) | − | 3.65929e27i | − | 0.0269499i | ||||||
\(820\) | −4.35820e27 | − | 1.47080e29i | −0.0317080 | − | 1.07008i | ||||
\(821\) | 7.58552e28 | 0.545197 | 0.272599 | − | 0.962128i | \(-0.412117\pi\) | ||||
0.272599 | + | 0.962128i | \(0.412117\pi\) | |||||||
\(822\) | −4.33169e28 | + | 4.46194e28i | −0.307566 | + | 0.316815i | ||||
\(823\) | 7.89044e28i | 0.553481i | 0.960945 | + | 0.276740i | \(0.0892542\pi\) | ||||
−0.960945 | + | 0.276740i | \(0.910746\pi\) | |||||||
\(824\) | 1.02039e29 | + | 9.33510e28i | 0.707119 | + | 0.646914i | ||||
\(825\) | 5.41257e28 | 0.370565 | ||||||||
\(826\) | −9.64403e27 | − | 9.36249e27i | −0.0652316 | − | 0.0633273i | ||||
\(827\) | 7.12169e28i | 0.475914i | 0.971276 | + | 0.237957i | \(0.0764777\pi\) | ||||
−0.971276 | + | 0.237957i | \(0.923522\pi\) | |||||||
\(828\) | −4.41852e28 | + | 1.30927e27i | −0.291725 | + | 0.00864423i | ||||
\(829\) | 1.95023e29 | 1.27216 | 0.636079 | − | 0.771624i | \(-0.280555\pi\) | ||||
0.636079 | + | 0.771624i | \(0.280555\pi\) | |||||||
\(830\) | −1.25386e29 | + | 1.29157e29i | −0.808108 | + | 0.832408i | ||||
\(831\) | − | 1.12307e29i | − | 0.715149i | ||||||
\(832\) | −7.22219e27 | − | 8.10543e28i | −0.0454397 | − | 0.509968i | ||||
\(833\) | −9.00185e28 | −0.559605 | ||||||||
\(834\) | −2.81193e28 | − | 2.72984e28i | −0.172720 | − | 0.167678i | ||||
\(835\) | 1.14985e29i | 0.697870i | ||||||||
\(836\) | −4.72263e27 | − | 1.59379e29i | −0.0283218 | − | 0.955802i | ||||
\(837\) | −1.28181e28 | −0.0759570 | ||||||||
\(838\) | 4.00104e28 | − | 4.12135e28i | 0.234279 | − | 0.241323i | ||||
\(839\) | 2.01853e28i | 0.116793i | 0.998293 | + | 0.0583963i | \(0.0185987\pi\) | ||||
−0.998293 | + | 0.0583963i | \(0.981401\pi\) | |||||||
\(840\) | 7.50099e27 | − | 8.19907e27i | 0.0428870 | − | 0.0468783i | ||||
\(841\) | −5.60439e28 | −0.316642 | ||||||||
\(842\) | 2.34088e28 | + | 2.27254e28i | 0.130695 | + | 0.126880i | ||||
\(843\) | − | 1.06419e29i | − | 0.587144i | ||||||
\(844\) | 2.18186e29 | − | 6.46517e27i | 1.18960 | − | 0.0352497i | ||||
\(845\) | −9.54355e28 | −0.514213 | ||||||||
\(846\) | −4.12636e28 | + | 4.25044e28i | −0.219717 | + | 0.226324i | ||||
\(847\) | − | 1.67207e28i | − | 0.0879872i | ||||||
\(848\) | −2.66421e29 | + | 1.58028e28i | −1.38551 | + | 0.0821818i | ||||
\(849\) | 1.01004e29 | 0.519115 | ||||||||
\(850\) | 4.16981e28 | + | 4.04808e28i | 0.211800 | + | 0.205617i | ||||
\(851\) | 2.44798e29i | 1.22889i | ||||||||
\(852\) | −3.57546e27 | − | 1.20664e29i | −0.0177393 | − | 0.598663i | ||||
\(853\) | −2.38026e29 | −1.16717 | −0.583586 | − | 0.812051i | \(-0.698351\pi\) | ||||
−0.583586 | + | 0.812051i | \(0.698351\pi\) | |||||||
\(854\) | −3.59672e28 | + | 3.70488e28i | −0.174312 | + | 0.179554i | ||||
\(855\) | − | 3.71614e28i | − | 0.178005i | ||||||
\(856\) | −1.49922e29 | − | 1.37157e29i | −0.709784 | − | 0.649352i | ||||
\(857\) | −2.28117e29 | −1.06745 | −0.533727 | − | 0.845657i | \(-0.679209\pi\) | ||||
−0.533727 | + | 0.845657i | \(0.679209\pi\) | |||||||
\(858\) | −5.72223e28 | − | 5.55518e28i | −0.264663 | − | 0.256936i | ||||
\(859\) | 3.10756e29i | 1.42065i | 0.703872 | + | 0.710327i | \(0.251453\pi\) | ||||
−0.703872 | + | 0.710327i | \(0.748547\pi\) | |||||||
\(860\) | −1.76330e29 | + | 5.22492e27i | −0.796787 | + | 0.0236100i | ||||
\(861\) | 3.13568e28 | 0.140055 | ||||||||
\(862\) | −1.62249e29 | + | 1.67128e29i | −0.716324 | + | 0.737864i | ||||
\(863\) | − | 3.18530e29i | − | 1.39009i | −0.718968 | − | 0.695043i | \(-0.755385\pi\) | ||
0.718968 | − | 0.695043i | \(-0.244615\pi\) | |||||||
\(864\) | −2.91252e28 | + | 3.37933e28i | −0.125641 | + | 0.145778i | ||||
\(865\) | −1.13200e29 | −0.482710 | ||||||||
\(866\) | 2.07271e29 | + | 2.01220e29i | 0.873695 | + | 0.848190i | ||||
\(867\) | − | 9.29195e28i | − | 0.387182i | ||||||
\(868\) | 4.48156e26 | + | 1.51243e28i | 0.00184600 | + | 0.0622986i | ||||
\(869\) | 6.29123e28 | 0.256176 | ||||||||
\(870\) | −5.75541e28 | + | 5.92848e28i | −0.231677 | + | 0.238644i | ||||
\(871\) | 1.68274e29i | 0.669630i | ||||||||
\(872\) | 9.86992e26 | − | 1.07885e27i | 0.00388283 | − | 0.00424419i | ||||
\(873\) | −2.86963e28 | −0.111605 | ||||||||
\(874\) | 1.25202e29 | + | 1.21547e29i | 0.481389 | + | 0.467336i | ||||
\(875\) | − | 4.38418e28i | − | 0.166651i | ||||||
\(876\) | −1.30775e29 | + | 3.87507e27i | −0.491456 | + | 0.0145626i | ||||
\(877\) | 7.71724e28 | 0.286725 | 0.143363 | − | 0.989670i | \(-0.454208\pi\) | ||||
0.143363 | + | 0.989670i | \(0.454208\pi\) | |||||||
\(878\) | −1.63803e29 | + | 1.68728e29i | −0.601695 | + | 0.619788i | ||||
\(879\) | − | 1.15000e29i | − | 0.417646i | ||||||
\(880\) | −1.43405e28 | − | 2.41768e29i | −0.0514916 | − | 0.868104i | ||||
\(881\) | 4.67747e28 | 0.166055 | 0.0830275 | − | 0.996547i | \(-0.473541\pi\) | ||||
0.0830275 | + | 0.996547i | \(0.473541\pi\) | |||||||
\(882\) | −6.64386e28 | − | 6.44991e28i | −0.233203 | − | 0.226396i | ||||
\(883\) | − | 1.45636e29i | − | 0.505430i | −0.967541 | − | 0.252715i | \(-0.918676\pi\) | ||
0.967541 | − | 0.252715i | \(-0.0813235\pi\) | |||||||
\(884\) | −2.53626e27 | − | 8.55935e28i | −0.00870305 | − | 0.293710i | ||||
\(885\) | −6.82734e28 | −0.231643 | ||||||||
\(886\) | 3.82695e28 | − | 3.94202e28i | 0.128385 | − | 0.132246i | ||||
\(887\) | − | 2.59212e29i | − | 0.859841i | −0.902867 | − | 0.429921i | \(-0.858542\pi\) | ||
0.902867 | − | 0.429921i | \(-0.141458\pi\) | |||||||
\(888\) | 1.82283e29 | + | 1.66763e29i | 0.597883 | + | 0.546978i | ||||
\(889\) | 5.47025e28 | 0.177415 | ||||||||
\(890\) | 2.16416e29 | + | 2.10098e29i | 0.694047 | + | 0.673786i | ||||
\(891\) | 4.37225e28i | 0.138653i | ||||||||
\(892\) | 4.78823e29 | − | 1.41882e28i | 1.50151 | − | 0.0444918i | ||||
\(893\) | 2.33847e29 | 0.725131 | ||||||||
\(894\) | −9.74229e28 | + | 1.00352e29i | −0.298735 | + | 0.307718i | ||||
\(895\) | − | 3.29456e29i | − | 0.999004i | ||||||
\(896\) | 4.08918e28 | + | 3.31840e28i | 0.122618 | + | 0.0995057i | ||||
\(897\) | 8.72787e28 | 0.258812 | ||||||||
\(898\) | 1.76031e29 | + | 1.70892e29i | 0.516210 | + | 0.501140i | ||||
\(899\) | − | 1.12505e29i | − | 0.326267i | ||||||
\(900\) | 1.77060e27 | + | 5.97541e28i | 0.00507804 | + | 0.171373i | ||||
\(901\) | −2.80847e29 | −0.796567 | ||||||||
\(902\) | 4.76029e29 | − | 4.90343e29i | 1.33527 | − | 1.37542i | ||||
\(903\) | − | 3.75928e28i | − | 0.104286i | ||||||
\(904\) | 4.02743e29 | − | 4.40225e29i | 1.10495 | − | 1.20779i | ||||
\(905\) | 4.39414e29 | 1.19231 | ||||||||
\(906\) | 1.82717e29 | + | 1.77383e29i | 0.490340 | + | 0.476026i | ||||
\(907\) | 4.96477e29i | 1.31773i | 0.752262 | + | 0.658864i | \(0.228963\pi\) | ||||
−0.752262 | + | 0.658864i | \(0.771037\pi\) | |||||||
\(908\) | −4.50460e29 | + | 1.33478e28i | −1.18249 | + | 0.0350390i | ||||
\(909\) | −6.33178e28 | −0.164394 | ||||||||
\(910\) | −1.52832e28 | + | 1.57427e28i | −0.0392463 | + | 0.0404265i | ||||
\(911\) | − | 4.77893e29i | − | 1.21380i | −0.794778 | − | 0.606900i | \(-0.792413\pi\) | ||
0.794778 | − | 0.606900i | \(-0.207587\pi\) | |||||||
\(912\) | 1.75798e29 | − | 1.04275e28i | 0.441637 | − | 0.0261957i | ||||
\(913\) | −8.36040e29 | −2.07740 | ||||||||
\(914\) | 3.85463e29 | + | 3.74211e29i | 0.947373 | + | 0.919717i | ||||
\(915\) | 2.62281e29i | 0.637611i | ||||||||
\(916\) | 2.45423e28 | + | 8.28250e29i | 0.0590147 | + | 1.99162i | ||||
\(917\) | −5.24848e28 | −0.124836 | ||||||||
\(918\) | −3.27002e28 | + | 3.36835e28i | −0.0769349 | + | 0.0792483i | ||||
\(919\) | − | 7.74788e29i | − | 1.80313i | −0.432640 | − | 0.901567i | \(-0.642418\pi\) | ||
0.432640 | − | 0.901567i | \(-0.357582\pi\) | |||||||
\(920\) | 1.95558e29 | + | 1.78908e29i | 0.450192 | + | 0.411862i | ||||
\(921\) | 6.77493e28 | 0.154280 | ||||||||
\(922\) | −1.99586e29 | − | 1.93759e29i | −0.449594 | − | 0.436469i | ||||
\(923\) | 2.38347e29i | 0.531121i | ||||||||
\(924\) | 5.15891e28 | − | 1.52866e27i | 0.113720 | − | 0.00336970i | ||||
\(925\) | 3.31054e29 | 0.721908 | ||||||||
\(926\) | −1.00512e29 | + | 1.03535e29i | −0.216825 | + | 0.223345i | ||||
\(927\) | 1.49699e29i | 0.319464i | ||||||||
\(928\) | −2.96605e29 | − | 2.55633e29i | −0.626180 | − | 0.539682i | ||||
\(929\) | −2.23342e29 | −0.466458 | −0.233229 | − | 0.972422i | \(-0.574929\pi\) | ||||
−0.233229 | + | 0.972422i | \(0.574929\pi\) | |||||||
\(930\) | 5.51449e28 | + | 5.35351e28i | 0.113940 | + | 0.110614i | ||||
\(931\) | 3.65526e29i | 0.747173i | ||||||||
\(932\) | −1.22925e28 | − | 4.14846e29i | −0.0248588 | − | 0.838933i | ||||
\(933\) | 2.11149e29 | 0.422448 | ||||||||
\(934\) | −1.19510e29 | + | 1.23104e29i | −0.236557 | + | 0.243671i | ||||
\(935\) | − | 2.54858e29i | − | 0.499095i | ||||||
\(936\) | 5.94566e28 | − | 6.49900e28i | 0.115197 | − | 0.125918i | ||||
\(937\) | 1.49570e29 | 0.286714 | 0.143357 | − | 0.989671i | \(-0.454210\pi\) | ||||
0.143357 | + | 0.989671i | \(0.454210\pi\) | |||||||
\(938\) | −7.81351e28 | − | 7.58541e28i | −0.148190 | − | 0.143864i | ||||
\(939\) | 2.72304e29i | 0.510974i | ||||||||
\(940\) | 3.55042e29 | − | 1.05204e28i | 0.659176 | − | 0.0195324i | ||||
\(941\) | −5.48715e29 | −1.00798 | −0.503989 | − | 0.863710i | \(-0.668135\pi\) | ||||
−0.503989 | + | 0.863710i | \(0.668135\pi\) | |||||||
\(942\) | −2.14250e29 | + | 2.20692e29i | −0.389414 | + | 0.401124i | ||||
\(943\) | 7.47900e29i | 1.34501i | ||||||||
\(944\) | −1.91575e28 | − | 3.22978e29i | −0.0340893 | − | 0.574716i | ||||
\(945\) | 1.20287e28 | 0.0211788 | ||||||||
\(946\) | −5.87859e29 | − | 5.70698e29i | −1.02415 | − | 0.994249i | ||||
\(947\) | − | 2.71697e29i | − | 0.468366i | −0.972193 | − | 0.234183i | \(-0.924758\pi\) | ||
0.972193 | − | 0.234183i | \(-0.0752415\pi\) | |||||||
\(948\) | 2.05804e27 | + | 6.94544e28i | 0.00351051 | + | 0.118472i | ||||
\(949\) | 2.58320e29 | 0.436010 | ||||||||
\(950\) | 1.64375e29 | − | 1.69318e29i | 0.274536 | − | 0.282791i | ||||
\(951\) | 1.75135e29i | 0.289447i | ||||||||
\(952\) | 4.08872e28 | + | 3.74060e28i | 0.0668679 | + | 0.0611746i | ||||
\(953\) | −5.38208e29 | −0.871006 | −0.435503 | − | 0.900187i | \(-0.643429\pi\) | ||||
−0.435503 | + | 0.900187i | \(0.643429\pi\) | |||||||
\(954\) | −2.07281e29 | − | 2.01230e29i | −0.331952 | − | 0.322261i | ||||
\(955\) | − | 4.14979e29i | − | 0.657646i | ||||||
\(956\) | −1.04725e30 | + | 3.10317e28i | −1.64238 | + | 0.0486661i | ||||
\(957\) | −3.83754e29 | −0.595571 | ||||||||
\(958\) | −7.45415e29 | + | 7.67829e29i | −1.14483 | + | 1.17926i | ||||
\(959\) | 7.94600e28i | 0.120771i | ||||||||
\(960\) | 2.66439e29 | − | 2.37406e28i | 0.400762 | − | 0.0357091i | ||||
\(961\) | 5.67142e29 | 0.844224 | ||||||||
\(962\) | −3.49994e29 | − | 3.39777e29i | −0.515597 | − | 0.500545i | ||||
\(963\) | − | 2.19947e29i | − | 0.320668i | ||||||
\(964\) | 2.21136e28 | + | 7.46287e29i | 0.0319072 | + | 1.07680i | ||||
\(965\) | 4.57002e29 | 0.652596 | ||||||||
\(966\) | −3.93433e28 | + | 4.05264e28i | −0.0556032 | + | 0.0572752i | ||||
\(967\) | − | 9.17171e29i | − | 1.28288i | −0.767174 | − | 0.641439i | \(-0.778338\pi\) | ||
0.767174 | − | 0.641439i | \(-0.221662\pi\) | |||||||
\(968\) | 2.71680e29 | − | 2.96964e29i | 0.376100 | − | 0.411102i | ||||
\(969\) | 1.85317e29 | 0.253908 | ||||||||
\(970\) | 1.23455e29 | + | 1.19851e29i | 0.167414 | + | 0.162527i | ||||
\(971\) | 9.27236e29i | 1.24451i | 0.782815 | + | 0.622254i | \(0.213783\pi\) | ||||
−0.782815 | + | 0.622254i | \(0.786217\pi\) | |||||||
\(972\) | −4.82691e28 | + | 1.43028e27i | −0.0641219 | + | 0.00190003i | ||||
\(973\) | −5.00759e28 | −0.0658416 | ||||||||
\(974\) | 8.48940e29 | − | 8.74468e29i | 1.10481 | − | 1.13803i | ||||
\(975\) | − | 1.18032e29i | − | 0.152039i | ||||||
\(976\) | −1.24076e30 | + | 7.35958e28i | −1.58194 | + | 0.0938329i | ||||
\(977\) | 1.46598e29 | 0.185005 | 0.0925024 | − | 0.995712i | \(-0.470513\pi\) | ||||
0.0925024 | + | 0.995712i | \(0.470513\pi\) | |||||||
\(978\) | −4.94081e29 | − | 4.79657e29i | −0.617177 | − | 0.599160i | ||||
\(979\) | 1.40087e30i | 1.73210i | ||||||||
\(980\) | 1.64445e28 | + | 5.54967e29i | 0.0201261 | + | 0.679213i | ||||
\(981\) | 1.58276e27 | 0.00191745 | ||||||||
\(982\) | 5.70913e29 | − | 5.88080e29i | 0.684628 | − | 0.705215i | ||||
\(983\) | 3.74401e29i | 0.444429i | 0.974998 | + | 0.222214i | \(0.0713285\pi\) | ||||
−0.974998 | + | 0.222214i | \(0.928672\pi\) | |||||||
\(984\) | 5.56905e29 | + | 5.09490e29i | 0.654380 | + | 0.598666i | ||||
\(985\) | 3.27276e29 | 0.380672 | ||||||||
\(986\) | −2.95641e29 | − | 2.87011e29i | −0.340405 | − | 0.330468i | ||||
\(987\) | 7.56935e28i | 0.0862754i | ||||||||
\(988\) | −3.47558e29 | + | 1.02987e28i | −0.392155 | + | 0.0116201i | ||||
\(989\) | 8.96637e29 | 1.00151 | ||||||||
\(990\) | 1.82609e29 | − | 1.88100e29i | 0.201915 | − | 0.207987i | ||||
\(991\) | − | 9.45710e29i | − | 1.03519i | −0.855625 | − | 0.517597i | \(-0.826827\pi\) | ||
0.855625 | − | 0.517597i | \(-0.173173\pi\) | |||||||
\(992\) | −2.37783e29 | + | 2.75894e29i | −0.257670 | + | 0.298968i | ||||
\(993\) | −8.89116e29 | −0.953819 | ||||||||
\(994\) | −1.10672e29 | − | 1.07442e29i | −0.117537 | − | 0.114106i | ||||
\(995\) | − | 3.70703e29i | − | 0.389758i | ||||||
\(996\) | −2.73492e28 | − | 9.22978e29i | −0.0284676 | − | 0.960722i | ||||
\(997\) | 1.11720e30 | 1.15128 | 0.575638 | − | 0.817704i | \(-0.304754\pi\) | ||||
0.575638 | + | 0.817704i | \(0.304754\pi\) | |||||||
\(998\) | 9.37579e29 | − | 9.65772e29i | 0.956538 | − | 0.985302i | ||||
\(999\) | 2.67424e29i | 0.270113i |
(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 | 12.21.d.a.7.16 | yes | 20 | |
3.2 | odd | 2 | 36.21.d.c.19.5 | 20 | |||
4.3 | odd | 2 | inner | 12.21.d.a.7.15 | ✓ | 20 | |
12.11 | even | 2 | 36.21.d.c.19.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.21.d.a.7.15 | ✓ | 20 | 4.3 | odd | 2 | inner | |
12.21.d.a.7.16 | yes | 20 | 1.1 | even | 1 | trivial | |
36.21.d.c.19.5 | 20 | 3.2 | odd | 2 | |||
36.21.d.c.19.6 | 20 | 12.11 | even | 2 |