Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,11,Mod(19,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.19");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.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: | \(12.7071450535\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.6 | ||
Character | \(\chi\) | \(=\) | 20.19 |
Dual form | 20.11.d.d.19.5 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −23.9223 | + | 21.2538i | −0.747571 | + | 0.664182i | ||||
\(3\) | 94.4407 | 0.388645 | 0.194323 | − | 0.980938i | \(-0.437749\pi\) | ||||
0.194323 | + | 0.980938i | \(0.437749\pi\) | |||||||
\(4\) | 120.549 | − | 1016.88i | 0.117724 | − | 0.993046i | ||||
\(5\) | 3107.65 | − | 328.861i | 0.994447 | − | 0.105236i | ||||
\(6\) | −2259.24 | + | 2007.23i | −0.290540 | + | 0.258131i | ||||
\(7\) | −20081.9 | −1.19485 | −0.597426 | − | 0.801924i | \(-0.703810\pi\) | ||||
−0.597426 | + | 0.801924i | \(0.703810\pi\) | |||||||
\(8\) | 18728.8 | + | 26888.2i | 0.571557 | + | 0.820562i | ||||
\(9\) | −50129.9 | −0.848955 | ||||||||
\(10\) | −67352.4 | + | 73916.5i | −0.673524 | + | 0.739165i | ||||
\(11\) | − | 198980.i | − | 1.23551i | −0.786370 | − | 0.617756i | \(-0.788042\pi\) | ||
0.786370 | − | 0.617756i | \(-0.211958\pi\) | |||||||
\(12\) | 11384.7 | − | 96034.9i | 0.0457527 | − | 0.385943i | ||||
\(13\) | 352944.i | 0.950580i | 0.879829 | + | 0.475290i | \(0.157657\pi\) | ||||
−0.879829 | + | 0.475290i | \(0.842343\pi\) | |||||||
\(14\) | 480404. | − | 426817.i | 0.893236 | − | 0.793600i | ||||
\(15\) | 293489. | − | 31057.9i | 0.386487 | − | 0.0408993i | ||||
\(16\) | −1.01951e6 | − | 245167.i | −0.972282 | − | 0.233810i | ||||
\(17\) | − | 1.97539e6i | − | 1.39126i | −0.718401 | − | 0.695630i | \(-0.755126\pi\) | ||
0.718401 | − | 0.695630i | \(-0.244874\pi\) | |||||||
\(18\) | 1.19922e6 | − | 1.06545e6i | 0.634654 | − | 0.563861i | ||||
\(19\) | − | 3.78502e6i | − | 1.52862i | −0.644847 | − | 0.764312i | \(-0.723079\pi\) | ||
0.644847 | − | 0.764312i | \(-0.276921\pi\) | |||||||
\(20\) | 40211.3 | − | 3.19975e6i | 0.0125660 | − | 0.999921i | ||||
\(21\) | −1.89655e6 | −0.464373 | ||||||||
\(22\) | 4.22910e6 | + | 4.76006e6i | 0.820605 | + | 0.923633i | ||||
\(23\) | −4.41929e6 | −0.686615 | −0.343307 | − | 0.939223i | \(-0.611547\pi\) | ||||
−0.343307 | + | 0.939223i | \(0.611547\pi\) | |||||||
\(24\) | 1.76876e6 | + | 2.53934e6i | 0.222133 | + | 0.318907i | ||||
\(25\) | 9.54933e6 | − | 2.04397e6i | 0.977851 | − | 0.209303i | ||||
\(26\) | −7.50141e6 | − | 8.44321e6i | −0.631358 | − | 0.710626i | ||||
\(27\) | −1.03109e7 | −0.718587 | ||||||||
\(28\) | −2.42085e6 | + | 2.04209e7i | −0.140662 | + | 1.18654i | ||||
\(29\) | −1.04937e7 | −0.511609 | −0.255804 | − | 0.966729i | \(-0.582340\pi\) | ||||
−0.255804 | + | 0.966729i | \(0.582340\pi\) | |||||||
\(30\) | −6.36081e6 | + | 6.98073e6i | −0.261762 | + | 0.287273i | ||||
\(31\) | 1.45342e7i | 0.507671i | 0.967247 | + | 0.253835i | \(0.0816922\pi\) | ||||
−0.967247 | + | 0.253835i | \(0.918308\pi\) | |||||||
\(32\) | 2.95998e7 | − | 1.58036e7i | 0.882142 | − | 0.470983i | ||||
\(33\) | − | 1.87919e7i | − | 0.480176i | ||||||
\(34\) | 4.19846e7 | + | 4.72558e7i | 0.924050 | + | 1.04006i | ||||
\(35\) | −6.24074e7 | + | 6.60416e6i | −1.18822 | + | 0.125741i | ||||
\(36\) | −6.04311e6 | + | 5.09761e7i | −0.0999420 | + | 0.843052i | ||||
\(37\) | − | 1.27275e8i | − | 1.83542i | −0.397250 | − | 0.917710i | \(-0.630035\pi\) | ||
0.397250 | − | 0.917710i | \(-0.369965\pi\) | |||||||
\(38\) | 8.04463e7 | + | 9.05463e7i | 1.01529 | + | 1.14275i | ||||
\(39\) | 3.33323e7i | 0.369438i | ||||||||
\(40\) | 6.70450e7 | + | 7.73998e7i | 0.654736 | + | 0.755858i | ||||
\(41\) | 9.37194e7 | 0.808929 | 0.404464 | − | 0.914554i | \(-0.367458\pi\) | ||||
0.404464 | + | 0.914554i | \(0.367458\pi\) | |||||||
\(42\) | 4.53697e7 | − | 4.03089e7i | 0.347152 | − | 0.308429i | ||||
\(43\) | −2.01807e8 | −1.37276 | −0.686380 | − | 0.727243i | \(-0.740801\pi\) | ||||
−0.686380 | + | 0.727243i | \(0.740801\pi\) | |||||||
\(44\) | −2.02339e8 | − | 2.39869e7i | −1.22692 | − | 0.145449i | ||||
\(45\) | −1.55786e8 | + | 1.64858e7i | −0.844241 | + | 0.0893403i | ||||
\(46\) | 1.05719e8 | − | 9.39268e7i | 0.513293 | − | 0.456038i | ||||
\(47\) | 6.61391e7 | 0.288383 | 0.144191 | − | 0.989550i | \(-0.453942\pi\) | ||||
0.144191 | + | 0.989550i | \(0.453942\pi\) | |||||||
\(48\) | −9.62835e7 | − | 2.31538e7i | −0.377873 | − | 0.0908691i | ||||
\(49\) | 1.20807e8 | 0.427672 | ||||||||
\(50\) | −1.84999e8 | + | 2.51856e8i | −0.591998 | + | 0.805940i | ||||
\(51\) | − | 1.86557e8i | − | 0.540706i | ||||||
\(52\) | 3.58901e8 | + | 4.25470e7i | 0.943970 | + | 0.111906i | ||||
\(53\) | 8.60363e7i | 0.205732i | 0.994695 | + | 0.102866i | \(0.0328013\pi\) | ||||
−0.994695 | + | 0.102866i | \(0.967199\pi\) | |||||||
\(54\) | 2.46661e8 | − | 2.19147e8i | 0.537195 | − | 0.477273i | ||||
\(55\) | −6.54370e7 | − | 6.18361e8i | −0.130020 | − | 1.22865i | ||||
\(56\) | −3.76109e8 | − | 5.39965e8i | −0.682926 | − | 0.980451i | ||||
\(57\) | − | 3.57460e8i | − | 0.594092i | ||||||
\(58\) | 2.51033e8 | − | 2.23031e8i | 0.382464 | − | 0.339802i | ||||
\(59\) | 5.09233e8i | 0.712290i | 0.934431 | + | 0.356145i | \(0.115909\pi\) | ||||
−0.934431 | + | 0.356145i | \(0.884091\pi\) | |||||||
\(60\) | 3.79758e6 | − | 3.02187e8i | 0.00488372 | − | 0.388614i | ||||
\(61\) | −2.18265e8 | −0.258425 | −0.129212 | − | 0.991617i | \(-0.541245\pi\) | ||||
−0.129212 | + | 0.991617i | \(0.541245\pi\) | |||||||
\(62\) | −3.08907e8 | − | 3.47691e8i | −0.337186 | − | 0.379520i | ||||
\(63\) | 1.00670e9 | 1.01438 | ||||||||
\(64\) | −3.72207e8 | + | 1.00717e9i | −0.346645 | + | 0.937997i | ||||
\(65\) | 1.16070e8 | + | 1.09682e9i | 0.100035 | + | 0.945302i | ||||
\(66\) | 3.99399e8 | + | 4.49544e8i | 0.318924 | + | 0.358965i | ||||
\(67\) | 7.20783e8 | 0.533864 | 0.266932 | − | 0.963715i | \(-0.413990\pi\) | ||||
0.266932 | + | 0.963715i | \(0.413990\pi\) | |||||||
\(68\) | −2.00873e9 | − | 2.38131e8i | −1.38158 | − | 0.163784i | ||||
\(69\) | −4.17361e8 | −0.266849 | ||||||||
\(70\) | 1.35256e9 | − | 1.48438e9i | 0.804762 | − | 0.883194i | ||||
\(71\) | 1.16390e9i | 0.645098i | 0.946553 | + | 0.322549i | \(0.104540\pi\) | ||||
−0.946553 | + | 0.322549i | \(0.895460\pi\) | |||||||
\(72\) | −9.38873e8 | − | 1.34790e9i | −0.485226 | − | 0.696620i | ||||
\(73\) | 1.07283e9i | 0.517506i | 0.965943 | + | 0.258753i | \(0.0833116\pi\) | ||||
−0.965943 | + | 0.258753i | \(0.916688\pi\) | |||||||
\(74\) | 2.70509e9 | + | 3.04471e9i | 1.21905 | + | 1.37211i | ||||
\(75\) | 9.01845e8 | − | 1.93034e8i | 0.380037 | − | 0.0813444i | ||||
\(76\) | −3.84891e9 | − | 4.56281e8i | −1.51799 | − | 0.179955i | ||||
\(77\) | 3.99590e9i | 1.47625i | ||||||||
\(78\) | −7.08438e8 | − | 7.97383e8i | −0.245374 | − | 0.276181i | ||||
\(79\) | 3.63818e9i | 1.18236i | 0.806541 | + | 0.591179i | \(0.201337\pi\) | ||||
−0.806541 | + | 0.591179i | \(0.798663\pi\) | |||||||
\(80\) | −3.24891e9 | − | 4.26616e8i | −0.991489 | − | 0.130193i | ||||
\(81\) | 1.98635e9 | 0.569680 | ||||||||
\(82\) | −2.24198e9 | + | 1.99190e9i | −0.604731 | + | 0.537276i | ||||
\(83\) | 1.43526e9 | 0.364367 | 0.182183 | − | 0.983265i | \(-0.441684\pi\) | ||||
0.182183 | + | 0.983265i | \(0.441684\pi\) | |||||||
\(84\) | −2.28627e8 | + | 1.92856e9i | −0.0546677 | + | 0.461144i | ||||
\(85\) | −6.49629e8 | − | 6.13881e9i | −0.146410 | − | 1.38353i | ||||
\(86\) | 4.82769e9 | − | 4.28918e9i | 1.02623 | − | 0.911763i | ||||
\(87\) | −9.91032e8 | −0.198834 | ||||||||
\(88\) | 5.35022e9 | − | 3.72666e9i | 1.01381 | − | 0.706166i | ||||
\(89\) | −9.94640e8 | −0.178121 | −0.0890606 | − | 0.996026i | \(-0.528386\pi\) | ||||
−0.0890606 | + | 0.996026i | \(0.528386\pi\) | |||||||
\(90\) | 3.37637e9 | − | 3.70543e9i | 0.571792 | − | 0.627518i | ||||
\(91\) | − | 7.08777e9i | − | 1.13580i | ||||||
\(92\) | −5.32741e8 | + | 4.49388e9i | −0.0808308 | + | 0.681840i | ||||
\(93\) | 1.37262e9i | 0.197304i | ||||||||
\(94\) | −1.58220e9 | + | 1.40571e9i | −0.215586 | + | 0.191539i | ||||
\(95\) | −1.24475e9 | − | 1.17625e10i | −0.160866 | − | 1.52014i | ||||
\(96\) | 2.79542e9 | − | 1.49250e9i | 0.342840 | − | 0.183045i | ||||
\(97\) | − | 4.59239e9i | − | 0.534786i | −0.963588 | − | 0.267393i | \(-0.913838\pi\) | ||
0.963588 | − | 0.267393i | \(-0.0861622\pi\) | |||||||
\(98\) | −2.88997e9 | + | 2.56761e9i | −0.319715 | + | 0.284052i | ||||
\(99\) | 9.97488e9i | 1.04889i | ||||||||
\(100\) | −9.27311e8 | − | 9.95691e9i | −0.0927311 | − | 0.995691i | ||||
\(101\) | −4.05319e9 | −0.385647 | −0.192824 | − | 0.981233i | \(-0.561764\pi\) | ||||
−0.192824 | + | 0.981233i | \(0.561764\pi\) | |||||||
\(102\) | 3.96506e9 | + | 4.46287e9i | 0.359127 | + | 0.404216i | ||||
\(103\) | 6.33329e8 | 0.0546315 | 0.0273158 | − | 0.999627i | \(-0.491304\pi\) | ||||
0.0273158 | + | 0.999627i | \(0.491304\pi\) | |||||||
\(104\) | −9.49001e9 | + | 6.61021e9i | −0.780010 | + | 0.543311i | ||||
\(105\) | −5.89380e9 | + | 6.23701e8i | −0.461795 | + | 0.0488686i | ||||
\(106\) | −1.82860e9 | − | 2.05818e9i | −0.136644 | − | 0.153799i | ||||
\(107\) | −2.41225e10 | −1.71990 | −0.859949 | − | 0.510380i | \(-0.829505\pi\) | ||||
−0.859949 | + | 0.510380i | \(0.829505\pi\) | |||||||
\(108\) | −1.24297e9 | + | 1.04850e10i | −0.0845946 | + | 0.713590i | ||||
\(109\) | 1.71612e10 | 1.11536 | 0.557680 | − | 0.830056i | \(-0.311692\pi\) | ||||
0.557680 | + | 0.830056i | \(0.311692\pi\) | |||||||
\(110\) | 1.47079e10 | + | 1.34018e10i | 0.913248 | + | 0.832147i | ||||
\(111\) | − | 1.20200e10i | − | 0.713327i | ||||||
\(112\) | 2.04737e10 | + | 4.92342e9i | 1.16173 | + | 0.279368i | ||||
\(113\) | − | 1.15376e10i | − | 0.626216i | −0.949717 | − | 0.313108i | \(-0.898630\pi\) | ||
0.949717 | − | 0.313108i | \(-0.101370\pi\) | |||||||
\(114\) | 7.59741e9 | + | 8.55126e9i | 0.394585 | + | 0.444126i | ||||
\(115\) | −1.37336e10 | + | 1.45333e9i | −0.682802 | + | 0.0722564i | ||||
\(116\) | −1.26500e9 | + | 1.06708e10i | −0.0602284 | + | 0.508051i | ||||
\(117\) | − | 1.76930e10i | − | 0.807000i | ||||||
\(118\) | −1.08232e10 | − | 1.21820e10i | −0.473090 | − | 0.532487i | ||||
\(119\) | 3.96695e10i | 1.66235i | ||||||||
\(120\) | 6.33178e9 | + | 7.30970e9i | 0.254460 | + | 0.293760i | ||||
\(121\) | −1.36558e10 | −0.526490 | ||||||||
\(122\) | 5.22139e9 | − | 4.63896e9i | 0.193191 | − | 0.171641i | ||||
\(123\) | 8.85093e9 | 0.314386 | ||||||||
\(124\) | 1.47795e10 | + | 1.75208e9i | 0.504141 | + | 0.0597648i | ||||
\(125\) | 2.90038e10 | − | 9.49234e9i | 0.950395 | − | 0.311045i | ||||
\(126\) | −2.40826e10 | + | 2.13963e10i | −0.758318 | + | 0.673731i | ||||
\(127\) | 3.87619e10 | 1.17324 | 0.586619 | − | 0.809863i | \(-0.300459\pi\) | ||||
0.586619 | + | 0.809863i | \(0.300459\pi\) | |||||||
\(128\) | −1.25021e10 | − | 3.20045e10i | −0.363859 | − | 0.931454i | ||||
\(129\) | −1.90588e10 | −0.533516 | ||||||||
\(130\) | −2.60884e10 | − | 2.37716e10i | −0.702636 | − | 0.640238i | ||||
\(131\) | 2.60443e10i | 0.675081i | 0.941311 | + | 0.337540i | \(0.109595\pi\) | ||||
−0.941311 | + | 0.337540i | \(0.890405\pi\) | |||||||
\(132\) | −1.91091e10 | − | 2.26534e9i | −0.476837 | − | 0.0565280i | ||||
\(133\) | 7.60104e10i | 1.82648i | ||||||||
\(134\) | −1.72428e10 | + | 1.53194e10i | −0.399101 | + | 0.354583i | ||||
\(135\) | −3.20428e10 | + | 3.39087e9i | −0.714597 | + | 0.0756210i | ||||
\(136\) | 5.31146e10 | − | 3.69966e10i | 1.14161 | − | 0.795184i | ||||
\(137\) | − | 2.02285e9i | − | 0.0419142i | −0.999780 | − | 0.0209571i | \(-0.993329\pi\) | ||
0.999780 | − | 0.0209571i | \(-0.00667134\pi\) | |||||||
\(138\) | 9.98422e9 | − | 8.87052e9i | 0.199489 | − | 0.177237i | ||||
\(139\) | − | 9.04079e10i | − | 1.74234i | −0.490983 | − | 0.871169i | \(-0.663362\pi\) | ||
0.490983 | − | 0.871169i | \(-0.336638\pi\) | |||||||
\(140\) | −8.07518e8 | + | 6.42570e10i | −0.0150145 | + | 1.19476i | ||||
\(141\) | 6.24623e9 | 0.112078 | ||||||||
\(142\) | −2.47374e10 | − | 2.78432e10i | −0.428463 | − | 0.482256i | ||||
\(143\) | 7.02289e10 | 1.17445 | ||||||||
\(144\) | 5.11081e10 | + | 1.22902e10i | 0.825424 | + | 0.198494i | ||||
\(145\) | −3.26107e10 | + | 3.45097e9i | −0.508768 | + | 0.0538395i | ||||
\(146\) | −2.28017e10 | − | 2.56645e10i | −0.343719 | − | 0.386873i | ||||
\(147\) | 1.14091e10 | 0.166213 | ||||||||
\(148\) | −1.29424e11 | − | 1.53429e10i | −1.82266 | − | 0.216072i | ||||
\(149\) | −2.65310e10 | −0.361262 | −0.180631 | − | 0.983551i | \(-0.557814\pi\) | ||||
−0.180631 | + | 0.983551i | \(0.557814\pi\) | |||||||
\(150\) | −1.74715e10 | + | 2.37855e10i | −0.230077 | + | 0.313224i | ||||
\(151\) | − | 6.12549e10i | − | 0.780291i | −0.920753 | − | 0.390145i | \(-0.872425\pi\) | ||
0.920753 | − | 0.390145i | \(-0.127575\pi\) | |||||||
\(152\) | 1.01772e11 | − | 7.08889e10i | 1.25433 | − | 0.873696i | ||||
\(153\) | 9.90261e10i | 1.18112i | ||||||||
\(154\) | −8.49283e10 | − | 9.55910e10i | −0.980502 | − | 1.10360i | ||||
\(155\) | 4.77973e9 | + | 4.51671e10i | 0.0534251 | + | 0.504852i | ||||
\(156\) | 3.38949e10 | + | 4.01817e9i | 0.366869 | + | 0.0434916i | ||||
\(157\) | − | 4.55319e10i | − | 0.477329i | −0.971102 | − | 0.238664i | \(-0.923290\pi\) | ||
0.971102 | − | 0.238664i | \(-0.0767095\pi\) | |||||||
\(158\) | −7.73253e10 | − | 8.70335e10i | −0.785301 | − | 0.883896i | ||||
\(159\) | 8.12533e9i | 0.0799568i | ||||||||
\(160\) | 8.67885e10 | − | 5.88462e10i | 0.827680 | − | 0.561201i | ||||
\(161\) | 8.87476e10 | 0.820403 | ||||||||
\(162\) | −4.75180e10 | + | 4.22176e10i | −0.425876 | + | 0.378371i | ||||
\(163\) | 2.22540e11 | 1.93406 | 0.967032 | − | 0.254656i | \(-0.0819623\pi\) | ||||
0.967032 | + | 0.254656i | \(0.0819623\pi\) | |||||||
\(164\) | 1.12978e10 | − | 9.53014e10i | 0.0952300 | − | 0.803304i | ||||
\(165\) | −6.17992e9 | − | 5.83985e10i | −0.0505316 | − | 0.477509i | ||||
\(166\) | −3.43346e10 | + | 3.05047e10i | −0.272390 | + | 0.242006i | ||||
\(167\) | −1.03405e11 | −0.796086 | −0.398043 | − | 0.917367i | \(-0.630310\pi\) | ||||
−0.398043 | + | 0.917367i | \(0.630310\pi\) | |||||||
\(168\) | −3.55200e10 | − | 5.09947e10i | −0.265416 | − | 0.381047i | ||||
\(169\) | 1.32893e10 | 0.0963980 | ||||||||
\(170\) | 1.46014e11 | + | 1.33047e11i | 1.02837 | + | 0.937046i | ||||
\(171\) | 1.89743e11i | 1.29773i | ||||||||
\(172\) | −2.43277e10 | + | 2.05214e11i | −0.161606 | + | 1.36321i | ||||
\(173\) | 7.83241e10i | 0.505435i | 0.967540 | + | 0.252717i | \(0.0813243\pi\) | ||||
−0.967540 | + | 0.252717i | \(0.918676\pi\) | |||||||
\(174\) | 2.37077e10 | − | 2.10632e10i | 0.148643 | − | 0.132062i | ||||
\(175\) | −1.91768e11 | + | 4.10468e10i | −1.16839 | + | 0.250086i | ||||
\(176\) | −4.87835e10 | + | 2.02863e11i | −0.288875 | + | 1.20127i | ||||
\(177\) | 4.80924e10i | 0.276828i | ||||||||
\(178\) | 2.37940e10 | − | 2.11399e10i | 0.133158 | − | 0.118305i | ||||
\(179\) | − | 1.37989e11i | − | 0.750898i | −0.926843 | − | 0.375449i | \(-0.877489\pi\) | ||
0.926843 | − | 0.375449i | \(-0.122511\pi\) | |||||||
\(180\) | −2.01579e9 | + | 1.60403e11i | −0.0106680 | + | 0.848888i | ||||
\(181\) | −1.50269e11 | −0.773527 | −0.386764 | − | 0.922179i | \(-0.626407\pi\) | ||||
−0.386764 | + | 0.922179i | \(0.626407\pi\) | |||||||
\(182\) | 1.50642e11 | + | 1.69556e11i | 0.754380 | + | 0.849093i | ||||
\(183\) | −2.06131e10 | −0.100436 | ||||||||
\(184\) | −8.27679e10 | − | 1.18827e11i | −0.392440 | − | 0.563410i | ||||
\(185\) | −4.18559e10 | − | 3.95527e11i | −0.193152 | − | 1.82523i | ||||
\(186\) | −2.91734e10 | − | 3.28362e10i | −0.131046 | − | 0.147498i | ||||
\(187\) | −3.93064e11 | −1.71892 | ||||||||
\(188\) | 7.97300e9 | − | 6.72555e10i | 0.0339494 | − | 0.286377i | ||||
\(189\) | 2.07063e11 | 0.858606 | ||||||||
\(190\) | 2.79776e11 | + | 2.54930e11i | 1.12991 | + | 1.02956i | ||||
\(191\) | 1.81401e11i | 0.713629i | 0.934175 | + | 0.356814i | \(0.116137\pi\) | ||||
−0.934175 | + | 0.356814i | \(0.883863\pi\) | |||||||
\(192\) | −3.51515e10 | + | 9.51175e10i | −0.134722 | + | 0.364548i | ||||
\(193\) | 6.88155e10i | 0.256980i | 0.991711 | + | 0.128490i | \(0.0410130\pi\) | ||||
−0.991711 | + | 0.128490i | \(0.958987\pi\) | |||||||
\(194\) | 9.76059e10 | + | 1.09860e11i | 0.355195 | + | 0.399790i | ||||
\(195\) | 1.09617e10 | + | 1.03585e11i | 0.0388781 | + | 0.367387i | ||||
\(196\) | 1.45631e10 | − | 1.22846e11i | 0.0503471 | − | 0.424698i | ||||
\(197\) | − | 1.58831e11i | − | 0.535309i | −0.963515 | − | 0.267654i | \(-0.913751\pi\) | ||
0.963515 | − | 0.267654i | \(-0.0862485\pi\) | |||||||
\(198\) | −2.12004e11 | − | 2.38622e11i | −0.696657 | − | 0.784123i | ||||
\(199\) | − | 4.21020e11i | − | 1.34908i | −0.738239 | − | 0.674539i | \(-0.764342\pi\) | ||
0.738239 | − | 0.674539i | \(-0.235658\pi\) | |||||||
\(200\) | 2.33806e11 | + | 2.18483e11i | 0.730644 | + | 0.682759i | ||||
\(201\) | 6.80713e10 | 0.207484 | ||||||||
\(202\) | 9.69614e10 | − | 8.61458e10i | 0.288298 | − | 0.256140i | ||||
\(203\) | 2.10733e11 | 0.611297 | ||||||||
\(204\) | −1.89706e11 | − | 2.24893e10i | −0.536946 | − | 0.0636538i | ||||
\(205\) | 2.91247e11 | − | 3.08207e10i | 0.804437 | − | 0.0851281i | ||||
\(206\) | −1.51507e10 | + | 1.34607e10i | −0.0408409 | + | 0.0362853i | ||||
\(207\) | 2.21539e11 | 0.582905 | ||||||||
\(208\) | 8.65303e10 | − | 3.59830e11i | 0.222255 | − | 0.924232i | ||||
\(209\) | −7.53146e11 | −1.88863 | ||||||||
\(210\) | 1.27737e11 | − | 1.40186e11i | 0.312767 | − | 0.343249i | ||||
\(211\) | − | 4.83255e11i | − | 1.15548i | −0.816219 | − | 0.577742i | \(-0.803934\pi\) | ||
0.816219 | − | 0.577742i | \(-0.196066\pi\) | |||||||
\(212\) | 8.74886e10 | + | 1.03716e10i | 0.204302 | + | 0.0242195i | ||||
\(213\) | 1.09920e11i | 0.250714i | ||||||||
\(214\) | 5.77064e11 | − | 5.12695e11i | 1.28575 | − | 1.14233i | ||||
\(215\) | −6.27146e11 | + | 6.63666e10i | −1.36514 | + | 0.144463i | ||||
\(216\) | −1.93111e11 | − | 2.77242e11i | −0.410714 | − | 0.589645i | ||||
\(217\) | − | 2.91874e11i | − | 0.606592i | ||||||
\(218\) | −4.10534e11 | + | 3.64741e11i | −0.833810 | + | 0.740802i | ||||
\(219\) | 1.01319e11i | 0.201126i | ||||||||
\(220\) | −6.36687e11 | − | 8.00125e9i | −1.23541 | − | 0.0155255i | ||||
\(221\) | 6.97201e11 | 1.32250 | ||||||||
\(222\) | 2.55471e11 | + | 2.87545e11i | 0.473779 | + | 0.533262i | ||||
\(223\) | 7.41346e11 | 1.34430 | 0.672151 | − | 0.740414i | \(-0.265371\pi\) | ||||
0.672151 | + | 0.740414i | \(0.265371\pi\) | |||||||
\(224\) | −5.94419e11 | + | 3.17366e11i | −1.05403 | + | 0.562756i | ||||
\(225\) | −4.78707e11 | + | 1.02464e11i | −0.830151 | + | 0.177688i | ||||
\(226\) | 2.45219e11 | + | 2.76006e11i | 0.415922 | + | 0.468141i | ||||
\(227\) | −4.66330e11 | −0.773685 | −0.386843 | − | 0.922146i | \(-0.626434\pi\) | ||||
−0.386843 | + | 0.922146i | \(0.626434\pi\) | |||||||
\(228\) | −3.63494e11 | − | 4.30915e10i | −0.589961 | − | 0.0699386i | ||||
\(229\) | 6.80666e11 | 1.08083 | 0.540414 | − | 0.841399i | \(-0.318267\pi\) | ||||
0.540414 | + | 0.841399i | \(0.318267\pi\) | |||||||
\(230\) | 2.97650e11 | − | 3.26659e11i | 0.462452 | − | 0.507522i | ||||
\(231\) | 3.77376e11i | 0.573739i | ||||||||
\(232\) | −1.96534e11 | − | 2.82156e11i | −0.292414 | − | 0.419807i | ||||
\(233\) | 1.14942e12i | 1.67378i | 0.547369 | + | 0.836892i | \(0.315630\pi\) | ||||
−0.547369 | + | 0.836892i | \(0.684370\pi\) | |||||||
\(234\) | 3.76045e11 | + | 4.23258e11i | 0.535995 | + | 0.603289i | ||||
\(235\) | 2.05537e11 | − | 2.17506e10i | 0.286781 | − | 0.0303481i | ||||
\(236\) | 5.17829e11 | + | 6.13875e10i | 0.707337 | + | 0.0838533i | ||||
\(237\) | 3.43592e11i | 0.459517i | ||||||||
\(238\) | −8.43130e11 | − | 9.48985e11i | −1.10410 | − | 1.24272i | ||||
\(239\) | 5.70858e11i | 0.732047i | 0.930606 | + | 0.366023i | \(0.119281\pi\) | ||||
−0.930606 | + | 0.366023i | \(0.880719\pi\) | |||||||
\(240\) | −3.06829e11 | − | 4.02899e10i | −0.385337 | − | 0.0505988i | ||||
\(241\) | −1.57187e12 | −1.93344 | −0.966719 | − | 0.255840i | \(-0.917648\pi\) | ||||
−0.966719 | + | 0.255840i | \(0.917648\pi\) | |||||||
\(242\) | 3.26678e11 | − | 2.90238e11i | 0.393589 | − | 0.349686i | ||||
\(243\) | 7.96443e11 | 0.939990 | ||||||||
\(244\) | −2.63116e10 | + | 2.21949e11i | −0.0304227 | + | 0.256628i | ||||
\(245\) | 3.75425e11 | − | 3.97287e10i | 0.425297 | − | 0.0450063i | ||||
\(246\) | −2.11734e11 | + | 1.88116e11i | −0.235026 | + | 0.208810i | ||||
\(247\) | 1.33590e12 | 1.45308 | ||||||||
\(248\) | −3.90798e11 | + | 2.72208e11i | −0.416576 | + | 0.290163i | ||||
\(249\) | 1.35547e11 | 0.141609 | ||||||||
\(250\) | −4.92087e11 | + | 8.43519e11i | −0.503897 | + | 0.863764i | ||||
\(251\) | − | 3.37622e11i | − | 0.338893i | −0.985539 | − | 0.169446i | \(-0.945802\pi\) | ||
0.985539 | − | 0.169446i | \(-0.0541979\pi\) | |||||||
\(252\) | 1.21357e11 | − | 1.02370e12i | 0.119416 | − | 1.00732i | ||||
\(253\) | 8.79352e11i | 0.848321i | ||||||||
\(254\) | −9.27271e11 | + | 8.23838e11i | −0.877078 | + | 0.779244i | ||||
\(255\) | −6.13515e10 | − | 5.79754e11i | −0.0569015 | − | 0.537704i | ||||
\(256\) | 9.79297e11 | + | 4.99902e11i | 0.890666 | + | 0.454659i | ||||
\(257\) | − | 1.58528e12i | − | 1.41397i | −0.707230 | − | 0.706983i | \(-0.750056\pi\) | ||
0.707230 | − | 0.706983i | \(-0.249944\pi\) | |||||||
\(258\) | 4.55930e11 | − | 4.05073e11i | 0.398841 | − | 0.354352i | ||||
\(259\) | 2.55593e12i | 2.19306i | ||||||||
\(260\) | 1.12933e12 | + | 1.41923e10i | 0.950505 | + | 0.0119450i | ||||
\(261\) | 5.26048e11 | 0.434333 | ||||||||
\(262\) | −5.53540e11 | − | 6.23038e11i | −0.448377 | − | 0.504670i | ||||
\(263\) | −1.08215e12 | −0.860017 | −0.430008 | − | 0.902825i | \(-0.641489\pi\) | ||||
−0.430008 | + | 0.902825i | \(0.641489\pi\) | |||||||
\(264\) | 5.05279e11 | − | 3.51949e11i | 0.394014 | − | 0.274448i | ||||
\(265\) | 2.82940e10 | + | 2.67371e11i | 0.0216504 | + | 0.204590i | ||||
\(266\) | −1.61551e12 | − | 1.81834e12i | −1.21312 | − | 1.36542i | ||||
\(267\) | −9.39345e10 | −0.0692260 | ||||||||
\(268\) | 8.68897e10 | − | 7.32950e11i | 0.0628484 | − | 0.530152i | ||||
\(269\) | 1.04444e12 | 0.741517 | 0.370758 | − | 0.928729i | \(-0.379098\pi\) | ||||
0.370758 | + | 0.928729i | \(0.379098\pi\) | |||||||
\(270\) | 6.94467e11 | − | 7.62149e11i | 0.483986 | − | 0.531155i | ||||
\(271\) | − | 1.29600e12i | − | 0.886662i | −0.896358 | − | 0.443331i | \(-0.853797\pi\) | ||
0.896358 | − | 0.443331i | \(-0.146203\pi\) | |||||||
\(272\) | −4.84301e11 | + | 2.01393e12i | −0.325290 | + | 1.35270i | ||||
\(273\) | − | 6.69375e11i | − | 0.441424i | ||||||
\(274\) | 4.29933e10 | + | 4.83912e10i | 0.0278387 | + | 0.0313338i | ||||
\(275\) | −4.06710e11 | − | 1.90013e12i | −0.258596 | − | 1.20815i | ||||
\(276\) | −5.03124e10 | + | 4.24406e11i | −0.0314145 | + | 0.264994i | ||||
\(277\) | 1.69663e12i | 1.04037i | 0.854054 | + | 0.520184i | \(0.174137\pi\) | ||||
−0.854054 | + | 0.520184i | \(0.825863\pi\) | |||||||
\(278\) | 1.92152e12 | + | 2.16276e12i | 1.15723 | + | 1.30252i | ||||
\(279\) | − | 7.28598e11i | − | 0.430990i | ||||||
\(280\) | −1.34639e12 | − | 1.55433e12i | −0.782313 | − | 0.903138i | ||||
\(281\) | −1.13457e12 | −0.647592 | −0.323796 | − | 0.946127i | \(-0.604959\pi\) | ||||
−0.323796 | + | 0.946127i | \(0.604959\pi\) | |||||||
\(282\) | −1.49424e11 | + | 1.32756e11i | −0.0837866 | + | 0.0744406i | ||||
\(283\) | −1.25948e11 | −0.0693837 | −0.0346919 | − | 0.999398i | \(-0.511045\pi\) | ||||
−0.0346919 | + | 0.999398i | \(0.511045\pi\) | |||||||
\(284\) | 1.18355e12 | + | 1.40307e11i | 0.640612 | + | 0.0759432i | ||||
\(285\) | −1.17555e11 | − | 1.11086e12i | −0.0625197 | − | 0.590793i | ||||
\(286\) | −1.68003e12 | + | 1.49263e12i | −0.877987 | + | 0.780051i | ||||
\(287\) | −1.88206e12 | −0.966551 | ||||||||
\(288\) | −1.48384e12 | + | 7.92233e11i | −0.748899 | + | 0.399844i | ||||
\(289\) | −1.88617e12 | −0.935602 | ||||||||
\(290\) | 7.06775e11 | − | 7.75657e11i | 0.344581 | − | 0.378164i | ||||
\(291\) | − | 4.33709e11i | − | 0.207842i | ||||||
\(292\) | 1.09094e12 | + | 1.29328e11i | 0.513908 | + | 0.0609227i | ||||
\(293\) | − | 3.67054e12i | − | 1.69978i | −0.526964 | − | 0.849888i | \(-0.676670\pi\) | ||
0.526964 | − | 0.849888i | \(-0.323330\pi\) | |||||||
\(294\) | −2.72931e11 | + | 2.42487e11i | −0.124256 | + | 0.110395i | ||||
\(295\) | 1.67467e11 | + | 1.58252e12i | 0.0749583 | + | 0.708335i | ||||
\(296\) | 3.42220e12 | − | 2.38371e12i | 1.50608 | − | 1.04905i | ||||
\(297\) | 2.05168e12i | 0.887823i | ||||||||
\(298\) | 6.34682e11 | − | 5.63886e11i | 0.270069 | − | 0.239944i | ||||
\(299\) | − | 1.55976e12i | − | 0.652682i | ||||||
\(300\) | −8.75759e10 | − | 9.40338e11i | −0.0360395 | − | 0.386970i | ||||
\(301\) | 4.05267e12 | 1.64025 | ||||||||
\(302\) | 1.30190e12 | + | 1.46536e12i | 0.518255 | + | 0.583322i | ||||
\(303\) | −3.82786e11 | −0.149880 | ||||||||
\(304\) | −9.27965e11 | + | 3.85888e12i | −0.357407 | + | 1.48625i | ||||
\(305\) | −6.78290e11 | + | 7.17789e10i | −0.256990 | + | 0.0271955i | ||||
\(306\) | −2.10469e12 | − | 2.36893e12i | −0.784477 | − | 0.882968i | ||||
\(307\) | −1.65876e12 | −0.608262 | −0.304131 | − | 0.952630i | \(-0.598366\pi\) | ||||
−0.304131 | + | 0.952630i | \(0.598366\pi\) | |||||||
\(308\) | 4.06335e12 | + | 4.81702e11i | 1.46599 | + | 0.173790i | ||||
\(309\) | 5.98121e10 | 0.0212323 | ||||||||
\(310\) | −1.07432e12 | − | 9.78912e11i | −0.375253 | − | 0.341928i | ||||
\(311\) | 1.47617e12i | 0.507381i | 0.967285 | + | 0.253691i | \(0.0816445\pi\) | ||||
−0.967285 | + | 0.253691i | \(0.918355\pi\) | |||||||
\(312\) | −8.96244e11 | + | 6.24273e11i | −0.303147 | + | 0.211155i | ||||
\(313\) | − | 4.13023e12i | − | 1.37484i | −0.726259 | − | 0.687421i | \(-0.758743\pi\) | ||
0.726259 | − | 0.687421i | \(-0.241257\pi\) | |||||||
\(314\) | 9.67727e11 | + | 1.08923e12i | 0.317033 | + | 0.356837i | ||||
\(315\) | 3.12848e12 | − | 3.31066e11i | 1.00874 | − | 0.106748i | ||||
\(316\) | 3.69959e12 | + | 4.38579e11i | 1.17414 | + | 0.139191i | ||||
\(317\) | − | 4.04562e12i | − | 1.26383i | −0.775037 | − | 0.631916i | \(-0.782269\pi\) | ||
0.775037 | − | 0.631916i | \(-0.217731\pi\) | |||||||
\(318\) | −1.72694e11 | − | 1.94376e11i | −0.0531059 | − | 0.0597734i | ||||
\(319\) | 2.08804e12i | 0.632099i | ||||||||
\(320\) | −8.25470e11 | + | 3.25232e12i | −0.246009 | + | 0.969267i | ||||
\(321\) | −2.27814e12 | −0.668430 | ||||||||
\(322\) | −2.12304e12 | + | 1.88623e12i | −0.613309 | + | 0.544897i | ||||
\(323\) | −7.47690e12 | −2.12671 | ||||||||
\(324\) | 2.39452e11 | − | 2.01988e12i | 0.0670647 | − | 0.565718i | ||||
\(325\) | 7.21406e11 | + | 3.37037e12i | 0.198959 | + | 0.929525i | ||||
\(326\) | −5.32367e12 | + | 4.72984e12i | −1.44585 | + | 1.28457i | ||||
\(327\) | 1.62071e12 | 0.433479 | ||||||||
\(328\) | 1.75525e12 | + | 2.51994e12i | 0.462349 | + | 0.663776i | ||||
\(329\) | −1.32820e12 | −0.344575 | ||||||||
\(330\) | 1.38903e12 | + | 1.26568e12i | 0.354929 | + | 0.323410i | ||||
\(331\) | 4.40361e12i | 1.10833i | 0.832407 | + | 0.554164i | \(0.186962\pi\) | ||||
−0.832407 | + | 0.554164i | \(0.813038\pi\) | |||||||
\(332\) | 1.73019e11 | − | 1.45948e12i | 0.0428946 | − | 0.361833i | ||||
\(333\) | 6.38031e12i | 1.55819i | ||||||||
\(334\) | 2.47369e12 | − | 2.19776e12i | 0.595130 | − | 0.528746i | ||||
\(335\) | 2.23994e12 | − | 2.37038e11i | 0.530900 | − | 0.0561815i | ||||
\(336\) | 1.93355e12 | + | 4.64972e11i | 0.451502 | + | 0.108575i | ||||
\(337\) | 5.34596e12i | 1.22992i | 0.788559 | + | 0.614959i | \(0.210828\pi\) | ||||
−0.788559 | + | 0.614959i | \(0.789172\pi\) | |||||||
\(338\) | −3.17910e11 | + | 2.82448e11i | −0.0720643 | + | 0.0640258i | ||||
\(339\) | − | 1.08962e12i | − | 0.243376i | ||||||
\(340\) | −6.32075e12 | − | 7.94329e10i | −1.39115 | − | 0.0174826i | ||||
\(341\) | 2.89202e12 | 0.627234 | ||||||||
\(342\) | −4.03277e12 | − | 4.53908e12i | −0.861931 | − | 0.970147i | ||||
\(343\) | 3.24661e12 | 0.683847 | ||||||||
\(344\) | −3.77961e12 | − | 5.42623e12i | −0.784611 | − | 1.12643i | ||||
\(345\) | −1.29701e12 | + | 1.37254e11i | −0.265368 | + | 0.0280821i | ||||
\(346\) | −1.66469e12 | − | 1.87369e12i | −0.335701 | − | 0.377848i | ||||
\(347\) | 7.04996e12 | 1.40133 | 0.700664 | − | 0.713492i | \(-0.252887\pi\) | ||||
0.700664 | + | 0.713492i | \(0.252887\pi\) | |||||||
\(348\) | −1.19468e11 | + | 1.00776e12i | −0.0234075 | + | 0.197452i | ||||
\(349\) | 5.35614e12 | 1.03449 | 0.517243 | − | 0.855838i | \(-0.326958\pi\) | ||||
0.517243 | + | 0.855838i | \(0.326958\pi\) | |||||||
\(350\) | 3.71513e12 | − | 5.05775e12i | 0.707350 | − | 0.962979i | ||||
\(351\) | − | 3.63918e12i | − | 0.683074i | ||||||
\(352\) | −3.14460e12 | − | 5.88978e12i | −0.581906 | − | 1.08990i | ||||
\(353\) | − | 5.32913e12i | − | 0.972261i | −0.873886 | − | 0.486130i | \(-0.838408\pi\) | ||
0.873886 | − | 0.486130i | \(-0.161592\pi\) | |||||||
\(354\) | −1.02215e12 | − | 1.15048e12i | −0.183864 | − | 0.206948i | ||||
\(355\) | 3.82763e11 | + | 3.61700e12i | 0.0678873 | + | 0.641516i | ||||
\(356\) | −1.19903e11 | + | 1.01143e12i | −0.0209691 | + | 0.176883i | ||||
\(357\) | 3.74642e12i | 0.646064i | ||||||||
\(358\) | 2.93281e12 | + | 3.30102e12i | 0.498733 | + | 0.561349i | ||||
\(359\) | − | 5.94891e12i | − | 0.997621i | −0.866711 | − | 0.498810i | \(-0.833770\pi\) | ||
0.866711 | − | 0.498810i | \(-0.166230\pi\) | |||||||
\(360\) | −3.36096e12 | − | 3.88005e12i | −0.555841 | − | 0.641689i | ||||
\(361\) | −8.19534e12 | −1.33669 | ||||||||
\(362\) | 3.59477e12 | − | 3.19379e12i | 0.578266 | − | 0.513763i | ||||
\(363\) | −1.28966e12 | −0.204618 | ||||||||
\(364\) | −7.20741e12 | − | 8.54423e11i | −1.12790 | − | 0.133711i | ||||
\(365\) | 3.52812e11 | + | 3.33397e12i | 0.0544601 | + | 0.514633i | ||||
\(366\) | 4.93112e11 | − | 4.38107e11i | 0.0750827 | − | 0.0667075i | ||||
\(367\) | 4.30747e12 | 0.646982 | 0.323491 | − | 0.946231i | \(-0.395143\pi\) | ||||
0.323491 | + | 0.946231i | \(0.395143\pi\) | |||||||
\(368\) | 4.50552e12 | + | 1.08347e12i | 0.667584 | + | 0.160537i | ||||
\(369\) | −4.69815e12 | −0.686744 | ||||||||
\(370\) | 9.40775e12 | + | 8.57230e12i | 1.35668 | + | 1.23620i | ||||
\(371\) | − | 1.72777e12i | − | 0.245820i | ||||||
\(372\) | 1.39579e12 | + | 1.65468e11i | 0.195932 | + | 0.0232273i | ||||
\(373\) | − | 6.18537e12i | − | 0.856686i | −0.903616 | − | 0.428343i | \(-0.859097\pi\) | ||
0.903616 | − | 0.428343i | \(-0.140903\pi\) | |||||||
\(374\) | 9.40298e12 | − | 8.35412e12i | 1.28501 | − | 1.14167i | ||||
\(375\) | 2.73914e12 | − | 8.96464e11i | 0.369366 | − | 0.120886i | ||||
\(376\) | 1.23871e12 | + | 1.77836e12i | 0.164827 | + | 0.236636i | ||||
\(377\) | − | 3.70368e12i | − | 0.486325i | ||||||
\(378\) | −4.95342e12 | + | 4.40089e12i | −0.641868 | + | 0.570271i | ||||
\(379\) | − | 1.18170e13i | − | 1.51116i | −0.655055 | − | 0.755581i | \(-0.727355\pi\) | ||
0.655055 | − | 0.755581i | \(-0.272645\pi\) | |||||||
\(380\) | −1.21111e13 | − | 1.52201e11i | −1.52850 | − | 0.0192087i | ||||
\(381\) | 3.66070e12 | 0.455973 | ||||||||
\(382\) | −3.85546e12 | − | 4.33952e12i | −0.473980 | − | 0.533488i | ||||
\(383\) | −1.08823e13 | −1.32046 | −0.660231 | − | 0.751063i | \(-0.729542\pi\) | ||||
−0.660231 | + | 0.751063i | \(0.729542\pi\) | |||||||
\(384\) | −1.18071e12 | − | 3.02253e12i | −0.141412 | − | 0.362005i | ||||
\(385\) | 1.31410e12 | + | 1.24179e13i | 0.155355 | + | 1.46806i | ||||
\(386\) | −1.46259e12 | − | 1.64622e12i | −0.170682 | − | 0.192111i | ||||
\(387\) | 1.01166e13 | 1.16541 | ||||||||
\(388\) | −4.66991e12 | − | 5.53608e11i | −0.531067 | − | 0.0629569i | ||||
\(389\) | 2.39414e12 | 0.268783 | 0.134391 | − | 0.990928i | \(-0.457092\pi\) | ||||
0.134391 | + | 0.990928i | \(0.457092\pi\) | |||||||
\(390\) | −2.46381e12 | − | 2.24501e12i | −0.273076 | − | 0.248825i | ||||
\(391\) | 8.72982e12i | 0.955259i | ||||||||
\(392\) | 2.26256e12 | + | 3.24827e12i | 0.244439 | + | 0.350932i | ||||
\(393\) | 2.45964e12i | 0.262367i | ||||||||
\(394\) | 3.37577e12 | + | 3.79960e12i | 0.355543 | + | 0.400181i | ||||
\(395\) | 1.19646e12 | + | 1.13062e13i | 0.124426 | + | 1.17579i | ||||
\(396\) | 1.01433e13 | + | 1.20246e12i | 1.04160 | + | 0.123480i | ||||
\(397\) | − | 2.29424e12i | − | 0.232641i | −0.993212 | − | 0.116321i | \(-0.962890\pi\) | ||
0.993212 | − | 0.116321i | \(-0.0371101\pi\) | |||||||
\(398\) | 8.94828e12 | + | 1.00717e13i | 0.896034 | + | 1.00853i | ||||
\(399\) | 7.17848e12i | 0.709852i | ||||||||
\(400\) | −1.02368e13 | − | 2.57332e11i | −0.999684 | − | 0.0251300i | ||||
\(401\) | 3.17790e12 | 0.306492 | 0.153246 | − | 0.988188i | \(-0.451027\pi\) | ||||
0.153246 | + | 0.988188i | \(0.451027\pi\) | |||||||
\(402\) | −1.62842e12 | + | 1.44678e12i | −0.155109 | + | 0.137807i | ||||
\(403\) | −5.12975e12 | −0.482582 | ||||||||
\(404\) | −4.88608e11 | + | 4.12161e12i | −0.0453997 | + | 0.382965i | ||||
\(405\) | 6.17288e12 | − | 6.53234e11i | 0.566516 | − | 0.0599506i | ||||
\(406\) | −5.04121e12 | + | 4.47888e12i | −0.456988 | + | 0.406013i | ||||
\(407\) | −2.53253e13 | −2.26768 | ||||||||
\(408\) | 5.01618e12 | − | 3.49399e12i | 0.443683 | − | 0.309044i | ||||
\(409\) | −1.17989e13 | −1.03092 | −0.515458 | − | 0.856915i | \(-0.672378\pi\) | ||||
−0.515458 | + | 0.856915i | \(0.672378\pi\) | |||||||
\(410\) | −6.31223e12 | + | 6.92742e12i | −0.544833 | + | 0.597932i | ||||
\(411\) | − | 1.91040e11i | − | 0.0162897i | ||||||
\(412\) | 7.63471e10 | − | 6.44019e11i | 0.00643142 | − | 0.0542516i | ||||
\(413\) | − | 1.02264e13i | − | 0.851081i | ||||||
\(414\) | −5.29971e12 | + | 4.70855e12i | −0.435763 | + | 0.387155i | ||||
\(415\) | 4.46027e12 | − | 4.72000e11i | 0.362344 | − | 0.0383444i | ||||
\(416\) | 5.57777e12 | + | 1.04471e13i | 0.447707 | + | 0.838547i | ||||
\(417\) | − | 8.53819e12i | − | 0.677151i | ||||||
\(418\) | 1.80170e13 | − | 1.60072e13i | 1.41189 | − | 1.25440i | ||||
\(419\) | 1.20017e12i | 0.0929338i | 0.998920 | + | 0.0464669i | \(0.0147962\pi\) | ||||
−0.998920 | + | 0.0464669i | \(0.985204\pi\) | |||||||
\(420\) | −7.62626e10 | + | 6.06847e12i | −0.00583532 | + | 0.464337i | ||||
\(421\) | 6.28498e12 | 0.475219 | 0.237609 | − | 0.971361i | \(-0.423636\pi\) | ||||
0.237609 | + | 0.971361i | \(0.423636\pi\) | |||||||
\(422\) | 1.02710e13 | + | 1.15606e13i | 0.767452 | + | 0.863806i | ||||
\(423\) | −3.31555e12 | −0.244824 | ||||||||
\(424\) | −2.31336e12 | + | 1.61136e12i | −0.168816 | + | 0.117588i | ||||
\(425\) | −4.03764e12 | − | 1.88636e13i | −0.291194 | − | 1.36044i | ||||
\(426\) | −2.33622e12 | − | 2.62953e12i | −0.166520 | − | 0.187426i | ||||
\(427\) | 4.38317e12 | 0.308780 | ||||||||
\(428\) | −2.90794e12 | + | 2.45296e13i | −0.202473 | + | 1.70794i | ||||
\(429\) | 6.63247e12 | 0.456445 | ||||||||
\(430\) | 1.35922e13 | − | 1.49169e13i | 0.924587 | − | 1.01470i | ||||
\(431\) | − | 5.24267e12i | − | 0.352506i | −0.984345 | − | 0.176253i | \(-0.943602\pi\) | ||
0.984345 | − | 0.176253i | \(-0.0563977\pi\) | |||||||
\(432\) | 1.05121e13 | + | 2.52791e12i | 0.698670 | + | 0.168013i | ||||
\(433\) | − | 1.01639e13i | − | 0.667759i | −0.942616 | − | 0.333880i | \(-0.891642\pi\) | ||
0.942616 | − | 0.333880i | \(-0.108358\pi\) | |||||||
\(434\) | 6.20344e12 | + | 6.98228e12i | 0.402887 | + | 0.453470i | ||||
\(435\) | −3.07978e12 | + | 3.25912e11i | −0.197730 | + | 0.0209245i | ||||
\(436\) | 2.06876e12 | − | 1.74509e13i | 0.131304 | − | 1.10760i | ||||
\(437\) | 1.67271e13i | 1.04958i | ||||||||
\(438\) | −2.15341e12 | − | 2.42377e12i | −0.133585 | − | 0.150356i | ||||
\(439\) | − | 2.59322e11i | − | 0.0159044i | −0.999968 | − | 0.00795219i | \(-0.997469\pi\) | ||
0.999968 | − | 0.00795219i | \(-0.00253129\pi\) | |||||||
\(440\) | 1.54011e13 | − | 1.33406e13i | 0.933871 | − | 0.808934i | ||||
\(441\) | −6.05604e12 | −0.363074 | ||||||||
\(442\) | −1.66786e13 | + | 1.48182e13i | −0.988664 | + | 0.878383i | ||||
\(443\) | −1.16943e13 | −0.685417 | −0.342709 | − | 0.939442i | \(-0.611344\pi\) | ||||
−0.342709 | + | 0.939442i | \(0.611344\pi\) | |||||||
\(444\) | −1.22229e13 | − | 1.44900e12i | −0.708367 | − | 0.0839754i | ||||
\(445\) | −3.09099e12 | + | 3.27099e11i | −0.177132 | + | 0.0187447i | ||||
\(446\) | −1.77347e13 | + | 1.57565e13i | −1.00496 | + | 0.892862i | ||||
\(447\) | −2.50561e12 | −0.140403 | ||||||||
\(448\) | 7.47461e12 | − | 2.02258e13i | 0.414189 | − | 1.12077i | ||||
\(449\) | 1.97779e13 | 1.08380 | 0.541899 | − | 0.840444i | \(-0.317706\pi\) | ||||
0.541899 | + | 0.840444i | \(0.317706\pi\) | |||||||
\(450\) | 9.27400e12 | − | 1.26255e13i | 0.502579 | − | 0.684207i | ||||
\(451\) | − | 1.86483e13i | − | 0.999442i | ||||||
\(452\) | −1.17324e13 | − | 1.39085e12i | −0.621862 | − | 0.0737204i | ||||
\(453\) | − | 5.78496e12i | − | 0.303256i | ||||||
\(454\) | 1.11557e13 | − | 9.91131e12i | 0.578384 | − | 0.513868i | ||||
\(455\) | −2.33089e12 | − | 2.20263e13i | −0.119527 | − | 1.12950i | ||||
\(456\) | 9.61146e12 | − | 6.69480e12i | 0.487489 | − | 0.339558i | ||||
\(457\) | 1.37176e13i | 0.688171i | 0.938938 | + | 0.344086i | \(0.111811\pi\) | ||||
−0.938938 | + | 0.344086i | \(0.888189\pi\) | |||||||
\(458\) | −1.62831e13 | + | 1.44668e13i | −0.807996 | + | 0.717867i | ||||
\(459\) | 2.03681e13i | 0.999741i | ||||||||
\(460\) | −1.77705e11 | + | 1.41406e13i | −0.00862801 | + | 0.686561i | ||||
\(461\) | −3.74685e13 | −1.79954 | −0.899770 | − | 0.436365i | \(-0.856266\pi\) | ||||
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(462\) | −8.02069e12 | − | 9.02769e12i | −0.381067 | − | 0.428910i | ||||
\(463\) | 4.08483e13 | 1.91986 | 0.959929 | − | 0.280244i | \(-0.0904153\pi\) | ||||
0.959929 | + | 0.280244i | \(0.0904153\pi\) | |||||||
\(464\) | 1.06984e13 | + | 2.57271e12i | 0.497428 | + | 0.119619i | ||||
\(465\) | 4.51401e11 | + | 4.26562e12i | 0.0207634 | + | 0.196208i | ||||
\(466\) | −2.44296e13 | − | 2.74967e13i | −1.11170 | − | 1.25127i | ||||
\(467\) | 8.08702e11 | 0.0364086 | 0.0182043 | − | 0.999834i | \(-0.494205\pi\) | ||||
0.0182043 | + | 0.999834i | \(0.494205\pi\) | |||||||
\(468\) | −1.79917e13 | − | 2.13288e12i | −0.801388 | − | 0.0950029i | ||||
\(469\) | −1.44747e13 | −0.637889 | ||||||||
\(470\) | −4.45463e12 | + | 4.88878e12i | −0.194233 | + | 0.213163i | ||||
\(471\) | − | 4.30007e12i | − | 0.185511i | ||||||
\(472\) | −1.36924e13 | + | 9.53732e12i | −0.584478 | + | 0.407114i | ||||
\(473\) | 4.01557e13i | 1.69606i | ||||||||
\(474\) | −7.30266e12 | − | 8.21951e12i | −0.305203 | − | 0.343522i | ||||
\(475\) | −7.73648e12 | − | 3.61444e13i | −0.319945 | − | 1.49477i | ||||
\(476\) | 4.03391e13 | + | 4.78212e12i | 1.65079 | + | 0.195698i | ||||
\(477\) | − | 4.31300e12i | − | 0.174657i | ||||||
\(478\) | −1.21329e13 | − | 1.36562e13i | −0.486212 | − | 0.547256i | ||||
\(479\) | 1.53920e13i | 0.610403i | 0.952288 | + | 0.305202i | \(0.0987239\pi\) | ||||
−0.952288 | + | 0.305202i | \(0.901276\pi\) | |||||||
\(480\) | 8.19637e12 | − | 5.55748e12i | 0.321674 | − | 0.218108i | ||||
\(481\) | 4.49210e13 | 1.74471 | ||||||||
\(482\) | 3.76026e13 | − | 3.34082e13i | 1.44538 | − | 1.28416i | ||||
\(483\) | 8.38139e12 | 0.318846 | ||||||||
\(484\) | −1.64619e12 | + | 1.38863e13i | −0.0619803 | + | 0.522829i | ||||
\(485\) | −1.51026e12 | − | 1.42715e13i | −0.0562785 | − | 0.531816i | ||||
\(486\) | −1.90527e13 | + | 1.69275e13i | −0.702709 | + | 0.624325i | ||||
\(487\) | 1.35284e12 | 0.0493858 | 0.0246929 | − | 0.999695i | \(-0.492139\pi\) | ||||
0.0246929 | + | 0.999695i | \(0.492139\pi\) | |||||||
\(488\) | −4.08783e12 | − | 5.86874e12i | −0.147705 | − | 0.212054i | ||||
\(489\) | 2.10169e13 | 0.751664 | ||||||||
\(490\) | −8.13662e12 | + | 8.92962e12i | −0.288047 | + | 0.316120i | ||||
\(491\) | 3.98512e13i | 1.39648i | 0.715865 | + | 0.698239i | \(0.246033\pi\) | ||||
−0.715865 | + | 0.698239i | \(0.753967\pi\) | |||||||
\(492\) | 1.06697e12 | − | 9.00033e12i | 0.0370107 | − | 0.312200i | ||||
\(493\) | 2.07291e13i | 0.711781i | ||||||||
\(494\) | −3.19577e13 | + | 2.83930e13i | −1.08628 | + | 0.965109i | ||||
\(495\) | 3.28035e12 | + | 3.09984e13i | 0.110381 | + | 1.04307i | ||||
\(496\) | 3.56331e12 | − | 1.48178e13i | 0.118698 | − | 0.493599i | ||||
\(497\) | − | 2.33734e13i | − | 0.770796i | ||||||
\(498\) | −3.24258e12 | + | 2.88089e12i | −0.105863 | + | 0.0940545i | ||||
\(499\) | 2.28789e13i | 0.739492i | 0.929133 | + | 0.369746i | \(0.120555\pi\) | ||||
−0.929133 | + | 0.369746i | \(0.879445\pi\) | |||||||
\(500\) | −6.15620e12 | − | 3.06376e13i | −0.196998 | − | 0.980404i | ||||
\(501\) | −9.76566e12 | −0.309395 | ||||||||
\(502\) | 7.17576e12 | + | 8.07668e12i | 0.225087 | + | 0.253346i | ||||
\(503\) | 4.14427e13 | 1.28709 | 0.643544 | − | 0.765409i | \(-0.277464\pi\) | ||||
0.643544 | + | 0.765409i | \(0.277464\pi\) | |||||||
\(504\) | 1.88543e13 | + | 2.70684e13i | 0.579774 | + | 0.832359i | ||||
\(505\) | −1.25959e13 | + | 1.33294e12i | −0.383506 | + | 0.0405838i | ||||
\(506\) | −1.86896e13 | − | 2.10361e13i | −0.563440 | − | 0.634180i | ||||
\(507\) | 1.25505e12 | 0.0374646 | ||||||||
\(508\) | 4.67270e12 | − | 3.94161e13i | 0.138118 | − | 1.16508i | ||||
\(509\) | −3.35157e13 | −0.980978 | −0.490489 | − | 0.871447i | \(-0.663182\pi\) | ||||
−0.490489 | + | 0.871447i | \(0.663182\pi\) | |||||||
\(510\) | 1.37897e13 | + | 1.25651e13i | 0.399671 | + | 0.364178i | ||||
\(511\) | − | 2.15444e13i | − | 0.618344i | ||||||
\(512\) | −3.40518e13 | + | 8.85503e12i | −0.967812 | + | 0.251675i | ||||
\(513\) | 3.90272e13i | 1.09845i | ||||||||
\(514\) | 3.36932e13 | + | 3.79234e13i | 0.939132 | + | 1.05704i | ||||
\(515\) | 1.96816e12 | − | 2.08277e11i | 0.0543282 | − | 0.00574918i | ||||
\(516\) | −2.29752e12 | + | 1.93805e13i | −0.0628074 | + | 0.529806i | ||||
\(517\) | − | 1.31604e13i | − | 0.356300i | ||||||
\(518\) | −5.43233e13 | − | 6.11436e13i | −1.45659 | − | 1.63946i | ||||
\(519\) | 7.39699e12i | 0.196435i | ||||||||
\(520\) | −2.73178e13 | + | 2.36631e13i | −0.718503 | + | 0.622379i | ||||
\(521\) | 4.91504e13 | 1.28038 | 0.640189 | − | 0.768218i | \(-0.278856\pi\) | ||||
0.640189 | + | 0.768218i | \(0.278856\pi\) | |||||||
\(522\) | −1.25843e13 | + | 1.11805e13i | −0.324695 | + | 0.288476i | ||||
\(523\) | −2.33806e12 | −0.0597512 | −0.0298756 | − | 0.999554i | \(-0.509511\pi\) | ||||
−0.0298756 | + | 0.999554i | \(0.509511\pi\) | |||||||
\(524\) | 2.64839e13 | + | 3.13961e12i | 0.670386 | + | 0.0794729i | ||||
\(525\) | −1.81108e13 | + | 3.87649e12i | −0.454088 | + | 0.0971946i | ||||
\(526\) | 2.58874e13 | − | 2.29997e13i | 0.642923 | − | 0.571208i | ||||
\(527\) | 2.87107e13 | 0.706302 | ||||||||
\(528\) | −4.60715e12 | + | 1.91585e13i | −0.112270 | + | 0.466866i | ||||
\(529\) | −2.18964e13 | −0.528560 | ||||||||
\(530\) | −6.35951e12 | − | 5.79475e12i | −0.152070 | − | 0.138566i | ||||
\(531\) | − | 2.55278e13i | − | 0.604702i | ||||||
\(532\) | 7.72934e13 | + | 9.16297e12i | 1.81378 | + | 0.215020i | ||||
\(533\) | 3.30777e13i | 0.768951i | ||||||||
\(534\) | 2.24713e12 | − | 1.99647e12i | 0.0517513 | − | 0.0459787i | ||||
\(535\) | −7.49641e13 | + | 7.93294e12i | −1.71035 | + | 0.180995i | ||||
\(536\) | 1.34994e13 | + | 1.93806e13i | 0.305134 | + | 0.438069i | ||||
\(537\) | − | 1.30318e13i | − | 0.291833i | ||||||
\(538\) | −2.49853e13 | + | 2.21983e13i | −0.554336 | + | 0.492502i | ||||
\(539\) | − | 2.40382e13i | − | 0.528394i | ||||||
\(540\) | −4.14616e11 | + | 3.29924e13i | −0.00902978 | + | 0.718530i | ||||
\(541\) | −2.96527e13 | −0.639850 | −0.319925 | − | 0.947443i | \(-0.603658\pi\) | ||||
−0.319925 | + | 0.947443i | \(0.603658\pi\) | |||||||
\(542\) | 2.75450e13 | + | 3.10032e13i | 0.588906 | + | 0.662843i | ||||
\(543\) | −1.41915e13 | −0.300627 | ||||||||
\(544\) | −3.12182e13 | − | 5.84711e13i | −0.655260 | − | 1.22729i | ||||
\(545\) | 5.33309e13 | − | 5.64365e12i | 1.10917 | − | 0.117376i | ||||
\(546\) | 1.42268e13 | + | 1.60130e13i | 0.293186 | + | 0.329996i | ||||
\(547\) | −5.51686e13 | −1.12656 | −0.563281 | − | 0.826266i | \(-0.690461\pi\) | ||||
−0.563281 | + | 0.826266i | \(0.690461\pi\) | |||||||
\(548\) | −2.05700e12 | − | 2.43852e11i | −0.0416227 | − | 0.00493429i | ||||
\(549\) | 1.09416e13 | 0.219391 | ||||||||
\(550\) | 5.01145e13 | + | 3.68112e13i | 0.995748 | + | 0.731420i | ||||
\(551\) | 3.97189e13i | 0.782058i | ||||||||
\(552\) | −7.81666e12 | − | 1.12221e13i | −0.152520 | − | 0.218967i | ||||
\(553\) | − | 7.30615e13i | − | 1.41274i | ||||||
\(554\) | −3.60598e13 | − | 4.05871e13i | −0.690995 | − | 0.777749i | ||||
\(555\) | −3.95291e12 | − | 3.73539e13i | −0.0750674 | − | 0.709366i | ||||
\(556\) | −9.19340e13 | − | 1.08986e13i | −1.73022 | − | 0.205114i | ||||
\(557\) | − | 5.24747e13i | − | 0.978756i | −0.872072 | − | 0.489378i | \(-0.837224\pi\) | ||
0.872072 | − | 0.489378i | \(-0.162776\pi\) | |||||||
\(558\) | 1.54855e13 | + | 1.74297e13i | 0.286256 | + | 0.322195i | ||||
\(559\) | − | 7.12266e13i | − | 1.30492i | ||||||
\(560\) | 6.52442e13 | + | 8.56725e12i | 1.18468 | + | 0.155561i | ||||
\(561\) | −3.71212e13 | −0.668049 | ||||||||
\(562\) | 2.71416e13 | − | 2.41140e13i | 0.484120 | − | 0.430119i | ||||
\(563\) | 6.04415e13 | 1.06855 | 0.534273 | − | 0.845312i | \(-0.320586\pi\) | ||||
0.534273 | + | 0.845312i | \(0.320586\pi\) | |||||||
\(564\) | 7.52976e11 | − | 6.35166e12i | 0.0131943 | − | 0.111299i | ||||
\(565\) | −3.79428e12 | − | 3.58549e13i | −0.0659003 | − | 0.622739i | ||||
\(566\) | 3.01295e12 | − | 2.67687e12i | 0.0518692 | − | 0.0460834i | ||||
\(567\) | −3.98897e13 | −0.680683 | ||||||||
\(568\) | −3.12953e13 | + | 2.17985e13i | −0.529343 | + | 0.368710i | ||||
\(569\) | 3.91402e13 | 0.656238 | 0.328119 | − | 0.944636i | \(-0.393585\pi\) | ||||
0.328119 | + | 0.944636i | \(0.393585\pi\) | |||||||
\(570\) | 2.64222e13 | + | 2.40758e13i | 0.439132 | + | 0.400135i | ||||
\(571\) | − | 1.76561e13i | − | 0.290881i | −0.989367 | − | 0.145441i | \(-0.953540\pi\) | ||
0.989367 | − | 0.145441i | \(-0.0464599\pi\) | |||||||
\(572\) | 8.46602e12 | − | 7.14143e13i | 0.138261 | − | 1.16629i | ||||
\(573\) | 1.71316e13i | 0.277348i | ||||||||
\(574\) | 4.50232e13 | − | 4.00010e13i | 0.722565 | − | 0.641966i | ||||
\(575\) | −4.22012e13 | + | 9.03290e12i | −0.671407 | + | 0.143710i | ||||
\(576\) | 1.86587e13 | − | 5.04892e13i | 0.294286 | − | 0.796317i | ||||
\(577\) | 1.79666e13i | 0.280922i | 0.990086 | + | 0.140461i | \(0.0448585\pi\) | ||||
−0.990086 | + | 0.140461i | \(0.955142\pi\) | |||||||
\(578\) | 4.51214e13 | − | 4.00883e13i | 0.699429 | − | 0.621410i | ||||
\(579\) | 6.49898e12i | 0.0998740i | ||||||||
\(580\) | −4.21964e11 | + | 3.35771e13i | −0.00642889 | + | 0.511569i | ||||
\(581\) | −2.88226e13 | −0.435365 | ||||||||
\(582\) | 9.21797e12 | + | 1.03753e13i | 0.138045 | + | 0.155376i | ||||
\(583\) | 1.71195e13 | 0.254185 | ||||||||
\(584\) | −2.88464e13 | + | 2.00928e13i | −0.424646 | + | 0.295785i | ||||
\(585\) | −5.81856e12 | − | 5.49838e13i | −0.0849251 | − | 0.802519i | ||||
\(586\) | 7.80130e13 | + | 8.78075e13i | 1.12896 | + | 1.27070i | ||||
\(587\) | 8.72417e11 | 0.0125180 | 0.00625898 | − | 0.999980i | \(-0.498008\pi\) | ||||
0.00625898 | + | 0.999980i | \(0.498008\pi\) | |||||||
\(588\) | 1.37535e12 | − | 1.16017e13i | 0.0195671 | − | 0.165057i | ||||
\(589\) | 5.50122e13 | 0.776038 | ||||||||
\(590\) | −3.76408e13 | − | 3.42981e13i | −0.526500 | − | 0.479744i | ||||
\(591\) | − | 1.50001e13i | − | 0.208045i | ||||||
\(592\) | −3.12038e13 | + | 1.29759e14i | −0.429140 | + | 1.78455i | ||||
\(593\) | 5.87343e13i | 0.800974i | 0.916302 | + | 0.400487i | \(0.131159\pi\) | ||||
−0.916302 | + | 0.400487i | \(0.868841\pi\) | |||||||
\(594\) | −4.36060e13 | − | 4.90807e13i | −0.589677 | − | 0.663711i | ||||
\(595\) | 1.30458e13 | + | 1.23279e14i | 0.174938 | + | 1.65312i | ||||
\(596\) | −3.19829e12 | + | 2.69789e13i | −0.0425291 | + | 0.358750i | ||||
\(597\) | − | 3.97614e13i | − | 0.524312i | ||||||
\(598\) | 3.31509e13 | + | 3.73130e13i | 0.433500 | + | 0.487926i | ||||
\(599\) | − | 2.16425e13i | − | 0.280655i | −0.990105 | − | 0.140328i | \(-0.955184\pi\) | ||
0.990105 | − | 0.140328i | \(-0.0448156\pi\) | |||||||
\(600\) | 2.20808e13 | + | 2.06337e13i | 0.283961 | + | 0.265351i | ||||
\(601\) | −1.16404e13 | −0.148456 | −0.0742278 | − | 0.997241i | \(-0.523649\pi\) | ||||
−0.0742278 | + | 0.997241i | \(0.523649\pi\) | |||||||
\(602\) | −9.69490e13 | + | 8.61348e13i | −1.22620 | + | 1.08942i | ||||
\(603\) | −3.61328e13 | −0.453227 | ||||||||
\(604\) | −6.22889e13 | − | 7.38422e12i | −0.774865 | − | 0.0918586i | ||||
\(605\) | −4.24374e13 | + | 4.49087e12i | −0.523567 | + | 0.0554056i | ||||
\(606\) | 9.15711e12 | − | 8.13568e12i | 0.112046 | − | 0.0995475i | ||||
\(607\) | −1.55538e13 | −0.188752 | −0.0943760 | − | 0.995537i | \(-0.530086\pi\) | ||||
−0.0943760 | + | 0.995537i | \(0.530086\pi\) | |||||||
\(608\) | −5.98169e13 | − | 1.12036e14i | −0.719956 | − | 1.34846i | ||||
\(609\) | 1.99018e13 | 0.237578 | ||||||||
\(610\) | 1.47007e13 | − | 1.61334e13i | 0.174055 | − | 0.191019i | ||||
\(611\) | 2.33434e13i | 0.274131i | ||||||||
\(612\) | 1.00698e14 | + | 1.19375e13i | 1.17290 | + | 0.139045i | ||||
\(613\) | 6.09416e13i | 0.704062i | 0.935988 | + | 0.352031i | \(0.114509\pi\) | ||||
−0.935988 | + | 0.352031i | \(0.885491\pi\) | |||||||
\(614\) | 3.96812e13 | − | 3.52549e13i | 0.454719 | − | 0.403997i | ||||
\(615\) | 2.75056e13 | − | 2.91073e12i | 0.312640 | − | 0.0330846i | ||||
\(616\) | −1.07443e14 | + | 7.48384e13i | −1.21136 | + | 0.843764i | ||||
\(617\) | 1.35014e14i | 1.50991i | 0.655775 | + | 0.754957i | \(0.272342\pi\) | ||||
−0.655775 | + | 0.754957i | \(0.727658\pi\) | |||||||
\(618\) | −1.43084e12 | + | 1.27124e12i | −0.0158726 | + | 0.0141021i | ||||
\(619\) | 3.76014e13i | 0.413762i | 0.978366 | + | 0.206881i | \(0.0663314\pi\) | ||||
−0.978366 | + | 0.206881i | \(0.933669\pi\) | |||||||
\(620\) | 4.65057e13 | + | 5.84438e11i | 0.507631 | + | 0.00637940i | ||||
\(621\) | 4.55670e13 | 0.493393 | ||||||||
\(622\) | −3.13743e13 | − | 3.53133e13i | −0.336994 | − | 0.379303i | ||||
\(623\) | 1.99742e13 | 0.212829 | ||||||||
\(624\) | 8.17199e12 | − | 3.39826e13i | 0.0863783 | − | 0.359198i | ||||
\(625\) | 8.70118e13 | − | 3.90371e13i | 0.912385 | − | 0.409333i | ||||
\(626\) | 8.77833e13 | + | 9.88045e13i | 0.913146 | + | 1.02779i | ||||
\(627\) | −7.11277e13 | −0.734008 | ||||||||
\(628\) | −4.63004e13 | − | 5.48882e12i | −0.474009 | − | 0.0561928i | ||||
\(629\) | −2.51418e14 | −2.55355 | ||||||||
\(630\) | −6.78039e13 | + | 7.44121e13i | −0.683206 | + | 0.749792i | ||||
\(631\) | 7.54478e13i | 0.754223i | 0.926168 | + | 0.377111i | \(0.123083\pi\) | ||||
−0.926168 | + | 0.377111i | \(0.876917\pi\) | |||||||
\(632\) | −9.78241e13 | + | 6.81387e13i | −0.970198 | + | 0.675785i | ||||
\(633\) | − | 4.56390e13i | − | 0.449073i | ||||||
\(634\) | 8.59850e13 | + | 9.67804e13i | 0.839414 | + | 0.944803i | ||||
\(635\) | 1.20458e14 | − | 1.27473e13i | 1.16672 | − | 0.123466i | ||||
\(636\) | 8.26248e12 | + | 9.79500e11i | 0.0794008 | + | 0.00941280i | ||||
\(637\) | 4.26380e13i | 0.406536i | ||||||||
\(638\) | −4.43788e13 | − | 4.99506e13i | −0.419829 | − | 0.472539i | ||||
\(639\) | − | 5.83465e13i | − | 0.547659i | ||||||
\(640\) | −4.93772e13 | − | 9.53473e13i | −0.459861 | − | 0.887991i | ||||
\(641\) | 1.39673e14 | 1.29069 | 0.645346 | − | 0.763890i | \(-0.276713\pi\) | ||||
0.645346 | + | 0.763890i | \(0.276713\pi\) | |||||||
\(642\) | 5.44983e13 | − | 4.84193e13i | 0.499698 | − | 0.443959i | ||||
\(643\) | 7.36940e13 | 0.670467 | 0.335233 | − | 0.942135i | \(-0.391185\pi\) | ||||
0.335233 | + | 0.942135i | \(0.391185\pi\) | |||||||
\(644\) | 1.06984e13 | − | 9.02457e13i | 0.0965808 | − | 0.814699i | ||||
\(645\) | −5.92281e13 | + | 6.26771e12i | −0.530554 | + | 0.0561449i | ||||
\(646\) | 1.78864e14 | − | 1.58913e14i | 1.58987 | − | 1.41252i | ||||
\(647\) | 1.49570e14 | 1.31924 | 0.659618 | − | 0.751601i | \(-0.270718\pi\) | ||||
0.659618 | + | 0.751601i | \(0.270718\pi\) | |||||||
\(648\) | 3.72019e13 | + | 5.34093e13i | 0.325605 | + | 0.467458i | ||||
\(649\) | 1.01327e14 | 0.880043 | ||||||||
\(650\) | −8.88910e13 | − | 6.52943e13i | −0.766110 | − | 0.562741i | ||||
\(651\) | − | 2.75648e13i | − | 0.235749i | ||||||
\(652\) | 2.68270e13 | − | 2.26297e14i | 0.227685 | − | 1.92061i | ||||
\(653\) | − | 4.17133e13i | − | 0.351325i | −0.984450 | − | 0.175662i | \(-0.943793\pi\) | ||
0.984450 | − | 0.175662i | \(-0.0562067\pi\) | |||||||
\(654\) | −3.87712e13 | + | 3.44464e13i | −0.324056 | + | 0.287909i | ||||
\(655\) | 8.56495e12 | + | 8.09364e13i | 0.0710425 | + | 0.671332i | ||||
\(656\) | −9.55481e13 | − | 2.29770e13i | −0.786507 | − | 0.189136i | ||||
\(657\) | − | 5.37808e13i | − | 0.439340i | ||||||
\(658\) | 3.17735e13 | − | 2.82293e13i | 0.257594 | − | 0.228860i | ||||
\(659\) | − | 2.32341e14i | − | 1.86938i | −0.355458 | − | 0.934692i | \(-0.615675\pi\) | ||
0.355458 | − | 0.934692i | \(-0.384325\pi\) | |||||||
\(660\) | −6.01292e13 | − | 7.55644e11i | −0.480138 | − | 0.00603390i | ||||
\(661\) | −1.40637e14 | −1.11453 | −0.557266 | − | 0.830334i | \(-0.688150\pi\) | ||||
−0.557266 | + | 0.830334i | \(0.688150\pi\) | |||||||
\(662\) | −9.35935e13 | − | 1.05344e14i | −0.736132 | − | 0.828554i | ||||
\(663\) | 6.58442e13 | 0.513984 | ||||||||
\(664\) | 2.68806e13 | + | 3.85914e13i | 0.208257 | + | 0.298986i | ||||
\(665\) | 2.49969e13 | + | 2.36214e14i | 0.192211 | + | 1.81634i | ||||
\(666\) | −1.35606e14 | − | 1.52631e14i | −1.03492 | − | 1.16486i | ||||
\(667\) | 4.63746e13 | 0.351278 | ||||||||
\(668\) | −1.24654e13 | + | 1.05151e14i | −0.0937181 | + | 0.790550i | ||||
\(669\) | 7.00133e13 | 0.522456 | ||||||||
\(670\) | −4.85465e13 | + | 5.32778e13i | −0.359570 | + | 0.394614i | ||||
\(671\) | 4.34304e13i | 0.319287i | ||||||||
\(672\) | −5.61374e13 | + | 2.99722e13i | −0.409643 | + | 0.218712i | ||||
\(673\) | 2.06777e13i | 0.149771i | 0.997192 | + | 0.0748853i | \(0.0238591\pi\) | ||||
−0.997192 | + | 0.0748853i | \(0.976141\pi\) | |||||||
\(674\) | −1.13622e14 | − | 1.27888e14i | −0.816890 | − | 0.919451i | ||||
\(675\) | −9.84625e13 | + | 2.10753e13i | −0.702671 | + | 0.150402i | ||||
\(676\) | 1.60201e12 | − | 1.35136e13i | 0.0113483 | − | 0.0957276i | ||||
\(677\) | 1.35666e14i | 0.953957i | 0.878915 | + | 0.476979i | \(0.158268\pi\) | ||||
−0.878915 | + | 0.476979i | \(0.841732\pi\) | |||||||
\(678\) | 2.31587e13 | + | 2.60662e13i | 0.161646 | + | 0.181941i | ||||
\(679\) | 9.22238e13i | 0.638990i | ||||||||
\(680\) | 1.52895e14 | − | 1.32440e14i | 1.05159 | − | 0.910907i | ||||
\(681\) | −4.40406e13 | −0.300689 | ||||||||
\(682\) | −6.91836e13 | + | 6.14665e13i | −0.468901 | + | 0.416597i | ||||
\(683\) | −9.63487e13 | −0.648250 | −0.324125 | − | 0.946014i | \(-0.605070\pi\) | ||||
−0.324125 | + | 0.946014i | \(0.605070\pi\) | |||||||
\(684\) | 1.92946e14 | + | 2.28733e13i | 1.28871 | + | 0.152774i | ||||
\(685\) | −6.65237e11 | − | 6.28631e12i | −0.00441087 | − | 0.0416814i | ||||
\(686\) | −7.76662e13 | + | 6.90029e13i | −0.511224 | + | 0.454199i | ||||
\(687\) | 6.42826e13 | 0.420059 | ||||||||
\(688\) | 2.05745e14 | + | 4.94766e13i | 1.33471 | + | 0.320965i | ||||
\(689\) | −3.03660e13 | −0.195565 | ||||||||
\(690\) | 2.81103e13 | − | 3.08499e13i | 0.179729 | − | 0.197246i | ||||
\(691\) | − | 7.79765e13i | − | 0.494964i | −0.968892 | − | 0.247482i | \(-0.920397\pi\) | ||
0.968892 | − | 0.247482i | \(-0.0796031\pi\) | |||||||
\(692\) | 7.96462e13 | + | 9.44189e12i | 0.501920 | + | 0.0595016i | ||||
\(693\) | − | 2.00314e14i | − | 1.25327i | ||||||
\(694\) | −1.68651e14 | + | 1.49839e14i | −1.04759 | + | 0.930737i | ||||
\(695\) | −2.97317e13 | − | 2.80956e14i | −0.183356 | − | 1.73266i | ||||
\(696\) | −1.85608e13 | − | 2.66470e13i | −0.113645 | − | 0.163156i | ||||
\(697\) | − | 1.85132e14i | − | 1.12543i | ||||||
\(698\) | −1.28131e14 | + | 1.13839e14i | −0.773352 | + | 0.687088i | ||||
\(699\) | 1.08552e14i | 0.650507i | ||||||||
\(700\) | 1.86221e13 | + | 1.99954e14i | 0.110800 | + | 1.18970i | ||||
\(701\) | 6.84476e13 | 0.404360 | 0.202180 | − | 0.979348i | \(-0.435197\pi\) | ||||
0.202180 | + | 0.979348i | \(0.435197\pi\) | |||||||
\(702\) | 7.73466e13 | + | 8.70574e13i | 0.453686 | + | 0.510646i | ||||
\(703\) | −4.81740e14 | −2.80567 | ||||||||
\(704\) | 2.00406e14 | + | 7.40619e13i | 1.15891 | + | 0.428284i | ||||
\(705\) | 1.94111e13 | − | 2.05414e12i | 0.111456 | − | 0.0117947i | ||||
\(706\) | 1.13264e14 | + | 1.27485e14i | 0.645759 | + | 0.726834i | ||||
\(707\) | 8.13957e13 | 0.460791 | ||||||||
\(708\) | 4.89041e13 | + | 5.79748e12i | 0.274903 | + | 0.0325892i | ||||
\(709\) | −2.02898e13 | −0.113252 | −0.0566261 | − | 0.998395i | \(-0.518034\pi\) | ||||
−0.0566261 | + | 0.998395i | \(0.518034\pi\) | |||||||
\(710\) | −8.60318e13 | − | 7.83917e13i | −0.476834 | − | 0.434489i | ||||
\(711\) | − | 1.82382e14i | − | 1.00377i | ||||||
\(712\) | −1.86284e13 | − | 2.67441e13i | −0.101807 | − | 0.146160i | ||||
\(713\) | − | 6.42308e13i | − | 0.348574i | ||||||
\(714\) | −7.96258e13 | − | 8.96228e13i | −0.429104 | − | 0.482978i | ||||
\(715\) | 2.18247e14 | − | 2.30956e13i | 1.16793 | − | 0.123594i | ||||
\(716\) | −1.40319e14 | − | 1.66345e13i | −0.745676 | − | 0.0883984i | ||||
\(717\) | 5.39123e13i | 0.284506i | ||||||||
\(718\) | 1.26437e14 | + | 1.42311e14i | 0.662602 | + | 0.745792i | ||||
\(719\) | 3.35545e14i | 1.74625i | 0.487498 | + | 0.873124i | \(0.337910\pi\) | ||||
−0.487498 | + | 0.873124i | \(0.662090\pi\) | |||||||
\(720\) | 1.62868e14 | + | 2.13862e13i | 0.841729 | + | 0.110528i | ||||
\(721\) | −1.27184e13 | −0.0652766 | ||||||||
\(722\) | 1.96051e14 | − | 1.74182e14i | 0.999271 | − | 0.887807i | ||||
\(723\) | −1.48448e14 | −0.751421 | ||||||||
\(724\) | −1.81147e13 | + | 1.52805e14i | −0.0910624 | + | 0.768148i | ||||
\(725\) | −1.00208e14 | + | 2.14488e13i | −0.500277 | + | 0.107081i | ||||
\(726\) | 3.08517e13 | − | 2.74103e13i | 0.152966 | − | 0.135904i | ||||
\(727\) | −6.92547e13 | −0.341018 | −0.170509 | − | 0.985356i | \(-0.554541\pi\) | ||||
−0.170509 | + | 0.985356i | \(0.554541\pi\) | |||||||
\(728\) | 1.90577e14 | − | 1.32745e14i | 0.931997 | − | 0.649176i | ||||
\(729\) | −4.20753e13 | −0.204357 | ||||||||
\(730\) | −7.92997e13 | − | 7.22575e13i | −0.382523 | − | 0.348553i | ||||
\(731\) | 3.98648e14i | 1.90986i | ||||||||
\(732\) | −2.48489e12 | + | 2.09610e13i | −0.0118236 | + | 0.0997372i | ||||
\(733\) | − | 1.71681e14i | − | 0.811337i | −0.914020 | − | 0.405669i | \(-0.867039\pi\) | ||
0.914020 | − | 0.405669i | \(-0.132961\pi\) | |||||||
\(734\) | −1.03044e14 | + | 9.15503e13i | −0.483665 | + | 0.429714i | ||||
\(735\) | 3.54554e13 | − | 3.75201e12i | 0.165290 | − | 0.0174915i | ||||
\(736\) | −1.30810e14 | + | 6.98406e13i | −0.605692 | + | 0.323384i | ||||
\(737\) | − | 1.43422e14i | − | 0.659596i | ||||||
\(738\) | 1.12390e14 | − | 9.98537e13i | 0.513390 | − | 0.456123i | ||||
\(739\) | 2.12086e14i | 0.962254i | 0.876651 | + | 0.481127i | \(0.159772\pi\) | ||||
−0.876651 | + | 0.481127i | \(0.840228\pi\) | |||||||
\(740\) | −4.07249e14 | − | 5.11790e12i | −1.83528 | − | 0.0230639i | ||||
\(741\) | 1.26163e14 | 0.564732 | ||||||||
\(742\) | 3.67218e13 | + | 4.13322e13i | 0.163269 | + | 0.183768i | ||||
\(743\) | 1.30199e14 | 0.574996 | 0.287498 | − | 0.957781i | \(-0.407177\pi\) | ||||
0.287498 | + | 0.957781i | \(0.407177\pi\) | |||||||
\(744\) | −3.69072e13 | + | 2.57075e13i | −0.161900 | + | 0.112770i | ||||
\(745\) | −8.24491e13 | + | 8.72503e12i | −0.359256 | + | 0.0380177i | ||||
\(746\) | 1.31463e14 | + | 1.47968e14i | 0.568996 | + | 0.640433i | ||||
\(747\) | −7.19493e13 | −0.309331 | ||||||||
\(748\) | −4.73834e13 | + | 3.99699e14i | −0.202357 | + | 1.70697i | ||||
\(749\) | 4.84424e14 | 2.05502 | ||||||||
\(750\) | −4.64730e13 | + | 7.96626e13i | −0.195837 | + | 0.335698i | ||||
\(751\) | − | 3.16975e14i | − | 1.32686i | −0.748238 | − | 0.663431i | \(-0.769100\pi\) | ||
0.748238 | − | 0.663431i | \(-0.230900\pi\) | |||||||
\(752\) | −6.74296e13 | − | 1.62152e13i | −0.280389 | − | 0.0674267i | ||||
\(753\) | − | 3.18853e13i | − | 0.131709i | ||||||
\(754\) | 7.87174e13 | + | 8.86004e13i | 0.323009 | + | 0.363562i | ||||
\(755\) | −2.01444e13 | − | 1.90359e14i | −0.0821144 | − | 0.775958i | ||||
\(756\) | 2.49612e13 | − | 2.10558e14i | 0.101078 | − | 0.852635i | ||||
\(757\) | − | 2.04193e14i | − | 0.821413i | −0.911768 | − | 0.410706i | \(-0.865282\pi\) | ||
0.911768 | − | 0.410706i | \(-0.134718\pi\) | |||||||
\(758\) | 2.51157e14 | + | 2.82689e14i | 1.00369 | + | 1.12970i | ||||
\(759\) | 8.30467e13i | 0.329696i | ||||||||
\(760\) | 2.92960e14 | − | 2.53767e14i | 1.15542 | − | 1.00084i | ||||
\(761\) | −2.25073e14 | −0.881862 | −0.440931 | − | 0.897541i | \(-0.645352\pi\) | ||||
−0.440931 | + | 0.897541i | \(0.645352\pi\) | |||||||
\(762\) | −8.75722e13 | + | 7.78039e13i | −0.340872 | + | 0.302849i | ||||
\(763\) | −3.44629e14 | −1.33269 | ||||||||
\(764\) | 1.84463e14 | + | 2.18677e13i | 0.708666 | + | 0.0840109i | ||||
\(765\) | 3.25659e13 | + | 3.07738e14i | 0.124296 | + | 1.17456i | ||||
\(766\) | 2.60329e14 | − | 2.31290e14i | 0.987138 | − | 0.877027i | ||||
\(767\) | −1.79731e14 | −0.677088 | ||||||||
\(768\) | 9.24856e13 | + | 4.72111e13i | 0.346153 | + | 0.176701i | ||||
\(769\) | −3.21415e14 | −1.19518 | −0.597592 | − | 0.801800i | \(-0.703876\pi\) | ||||
−0.597592 | + | 0.801800i | \(0.703876\pi\) | |||||||
\(770\) | −2.95363e14 | − | 2.69134e14i | −1.09120 | − | 0.994293i | ||||
\(771\) | − | 1.49715e14i | − | 0.549531i | ||||||
\(772\) | 6.99770e13 | + | 8.29563e12i | 0.255193 | + | 0.0302526i | ||||
\(773\) | − | 5.70492e13i | − | 0.206706i | −0.994645 | − | 0.103353i | \(-0.967043\pi\) | ||
0.994645 | − | 0.103353i | \(-0.0329571\pi\) | |||||||
\(774\) | −2.42012e14 | + | 2.15016e14i | −0.871227 | + | 0.774046i | ||||
\(775\) | 2.97074e13 | + | 1.38792e14i | 0.106257 | + | 0.496426i | ||||
\(776\) | 1.23481e14 | − | 8.60099e13i | 0.438825 | − | 0.305661i | ||||
\(777\) | 2.41384e14i | 0.852321i | ||||||||
\(778\) | −5.72733e13 | + | 5.08847e13i | −0.200934 | + | 0.178521i | ||||
\(779\) | − | 3.54730e14i | − | 1.23655i | ||||||
\(780\) | 1.06655e14 | + | 1.34033e12i | 0.369409 | + | 0.00464237i | ||||
\(781\) | 2.31594e14 | 0.797026 | ||||||||
\(782\) | −1.85542e14 | − | 2.08837e14i | −0.634466 | − | 0.714124i | ||||
\(783\) | 1.08200e14 | 0.367636 | ||||||||
\(784\) | −1.23164e14 | − | 2.96179e13i | −0.415818 | − | 0.0999940i | ||||
\(785\) | −1.49737e13 | − | 1.41497e14i | −0.0502320 | − | 0.474678i | ||||
\(786\) | −5.22768e13 | − | 5.88401e13i | −0.174259 | − | 0.196138i | ||||
\(787\) | 3.38595e14 | 1.12152 | 0.560759 | − | 0.827979i | \(-0.310509\pi\) | ||||
0.560759 | + | 0.827979i | \(0.310509\pi\) | |||||||
\(788\) | −1.61512e14 | − | 1.91469e13i | −0.531586 | − | 0.0630185i | ||||
\(789\) | −1.02199e14 | −0.334241 | ||||||||
\(790\) | −2.68922e14 | − | 2.45040e14i | −0.873958 | − | 0.796346i | ||||
\(791\) | 2.31697e14i | 0.748236i | ||||||||
\(792\) | −2.68206e14 | + | 1.86817e14i | −0.860683 | + | 0.599503i | ||||
\(793\) | − | 7.70352e13i | − | 0.245654i | ||||||
\(794\) | 4.87615e13 | + | 5.48835e13i | 0.154516 | + | 0.173916i | ||||
\(795\) | 2.67211e12 | + | 2.52507e13i | 0.00841431 | + | 0.0795129i | ||||
\(796\) | −4.28126e14 | − | 5.07535e13i | −1.33970 | − | 0.158818i | ||||
\(797\) | 4.36562e14i | 1.35754i | 0.734349 | + | 0.678772i | \(0.237487\pi\) | ||||
−0.734349 | + | 0.678772i | \(0.762513\pi\) | |||||||
\(798\) | −1.52570e14 | − | 1.71725e14i | −0.471471 | − | 0.530665i | ||||
\(799\) | − | 1.30651e14i | − | 0.401215i | ||||||
\(800\) | 2.50356e14 | − | 2.11415e14i | 0.764025 | − | 0.645186i | ||||
\(801\) | 4.98612e13 | 0.151217 | ||||||||
\(802\) | −7.60226e13 | + | 6.75426e13i | −0.229124 | + | 0.203566i | ||||
\(803\) | 2.13472e14 | 0.639386 | ||||||||
\(804\) | 8.20592e12 | − | 6.92203e13i | 0.0244257 | − | 0.206041i | ||||
\(805\) | 2.75796e14 | − | 2.91857e13i | 0.815848 | − | 0.0863357i | ||||
\(806\) | 1.22715e14 | − | 1.09027e14i | 0.360764 | − | 0.320522i | ||||
\(807\) | 9.86374e13 | 0.288187 | ||||||||
\(808\) | −7.59113e13 | − | 1.08983e14i | −0.220419 | − | 0.316447i | ||||
\(809\) | −4.65090e14 | −1.34213 | −0.671065 | − | 0.741399i | \(-0.734163\pi\) | ||||
−0.671065 | + | 0.741399i | \(0.734163\pi\) | |||||||
\(810\) | −1.33785e14 | + | 1.46824e14i | −0.383693 | + | 0.421088i | ||||
\(811\) | − | 5.09101e14i | − | 1.45111i | −0.688166 | − | 0.725554i | \(-0.741584\pi\) | ||
0.688166 | − | 0.725554i | \(-0.258416\pi\) | |||||||
\(812\) | 2.54036e13 | − | 2.14290e14i | 0.0719641 | − | 0.607046i | ||||
\(813\) | − | 1.22395e14i | − | 0.344597i | ||||||
\(814\) | 6.05839e14 | − | 5.38260e14i | 1.69525 | − | 1.50616i | ||||
\(815\) | 6.91577e14 | − | 7.31849e13i | 1.92332 | − | 0.203532i | ||||
\(816\) | −4.57378e13 | + | 1.90197e14i | −0.126422 | + | 0.525719i | ||||
\(817\) | 7.63845e14i | 2.09843i | ||||||||
\(818\) | 2.82255e14 | − | 2.50771e14i | 0.770683 | − | 0.684717i | ||||
\(819\) | 3.55310e14i | 0.964245i | ||||||||
\(820\) | 3.76858e12 | − | 2.99878e14i | 0.0101650 | − | 0.808865i | ||||
\(821\) | −2.27891e14 | −0.610957 | −0.305479 | − | 0.952199i | \(-0.598816\pi\) | ||||
−0.305479 | + | 0.952199i | \(0.598816\pi\) | |||||||
\(822\) | 4.06032e12 | + | 4.57010e12i | 0.0108194 | + | 0.0121777i | ||||
\(823\) | 1.27232e14 | 0.336975 | 0.168487 | − | 0.985704i | \(-0.446112\pi\) | ||||
0.168487 | + | 0.985704i | \(0.446112\pi\) | |||||||
\(824\) | 1.18615e13 | + | 1.70291e13i | 0.0312250 | + | 0.0448286i | ||||
\(825\) | −3.84100e13 | − | 1.79450e14i | −0.100502 | − | 0.469540i | ||||
\(826\) | 2.17349e14 | + | 2.44638e14i | 0.565273 | + | 0.636243i | ||||
\(827\) | −1.07724e13 | −0.0278473 | −0.0139237 | − | 0.999903i | \(-0.504432\pi\) | ||||
−0.0139237 | + | 0.999903i | \(0.504432\pi\) | |||||||
\(828\) | 2.67063e13 | − | 2.25278e14i | 0.0686217 | − | 0.578852i | ||||
\(829\) | 4.90888e14 | 1.25375 | 0.626873 | − | 0.779121i | \(-0.284334\pi\) | ||||
0.626873 | + | 0.779121i | \(0.284334\pi\) | |||||||
\(830\) | −9.66679e13 | + | 1.06089e14i | −0.245410 | + | 0.269327i | ||||
\(831\) | 1.60231e14i | 0.404334i | ||||||||
\(832\) | −3.55473e14 | − | 1.31368e14i | −0.891641 | − | 0.329513i | ||||
\(833\) | − | 2.38640e14i | − | 0.595003i | ||||||
\(834\) | 1.81469e14 | + | 2.04253e14i | 0.449752 | + | 0.506218i | ||||
\(835\) | −3.21347e14 | + | 3.40060e13i | −0.791665 | + | 0.0837766i | ||||
\(836\) | −9.07909e13 | + | 7.65859e14i | −0.222337 | + | 1.87550i | ||||
\(837\) | − | 1.49861e14i | − | 0.364806i | ||||||
\(838\) | −2.55083e13 | − | 2.87108e13i | −0.0617250 | − | 0.0694746i | ||||
\(839\) | − | 3.31532e14i | − | 0.797473i | −0.917065 | − | 0.398737i | \(-0.869449\pi\) | ||
0.917065 | − | 0.398737i | \(-0.130551\pi\) | |||||||
\(840\) | −1.27154e14 | − | 1.46792e14i | −0.304042 | − | 0.351000i | ||||
\(841\) | −3.10590e14 | −0.738256 | ||||||||
\(842\) | −1.50351e14 | + | 1.33580e14i | −0.355260 | + | 0.315632i | ||||
\(843\) | −1.07150e14 | −0.251683 | ||||||||
\(844\) | −4.91412e14 | − | 5.82559e13i | −1.14745 | − | 0.136028i | ||||
\(845\) | 4.12984e13 | − | 4.37033e12i | 0.0958627 | − | 0.0101445i | ||||
\(846\) | 7.93155e13 | − | 7.04682e13i | 0.183023 | − | 0.162608i | ||||
\(847\) | 2.74234e14 | 0.629078 | ||||||||
\(848\) | 2.10933e13 | − | 8.77150e13i | 0.0481022 | − | 0.200030i | ||||
\(849\) | −1.18946e13 | −0.0269656 | ||||||||
\(850\) | 4.97514e14 | + | 3.65445e14i | 1.12127 | + | 0.823622i | ||||
\(851\) | 5.62466e14i | 1.26023i | ||||||||
\(852\) | 1.11775e14 | + | 1.32507e13i | 0.248971 | + | 0.0295149i | ||||
\(853\) | 8.22258e14i | 1.82080i | 0.413727 | + | 0.910401i | \(0.364227\pi\) | ||||
−0.413727 | + | 0.910401i | \(0.635773\pi\) | |||||||
\(854\) | −1.04855e14 | + | 9.31591e13i | −0.230835 | + | 0.205086i | ||||
\(855\) | 6.23992e13 | + | 5.89655e14i | 0.136568 | + | 1.29053i | ||||
\(856\) | −4.51784e14 | − | 6.48609e14i | −0.983020 | − | 1.41128i | ||||
\(857\) | − | 6.80976e14i | − | 1.47308i | −0.676392 | − | 0.736542i | \(-0.736457\pi\) | ||
0.676392 | − | 0.736542i | \(-0.263543\pi\) | |||||||
\(858\) | −1.58664e14 | + | 1.40965e14i | −0.341225 | + | 0.303163i | ||||
\(859\) | 1.37051e14i | 0.293033i | 0.989208 | + | 0.146517i | \(0.0468062\pi\) | ||||
−0.989208 | + | 0.146517i | \(0.953194\pi\) | |||||||
\(860\) | −8.11492e12 | + | 6.45732e14i | −0.0172501 | + | 1.37265i | ||||
\(861\) | −1.77743e14 | −0.375645 | ||||||||
\(862\) | 1.11427e14 | + | 1.25417e14i | 0.234128 | + | 0.263523i | ||||
\(863\) | −3.18751e14 | −0.665882 | −0.332941 | − | 0.942948i | \(-0.608041\pi\) | ||||
−0.332941 | + | 0.942948i | \(0.608041\pi\) | |||||||
\(864\) | −3.05202e14 | + | 1.62950e14i | −0.633896 | + | 0.338443i | ||||
\(865\) | 2.57578e13 | + | 2.43404e14i | 0.0531897 | + | 0.502628i | ||||
\(866\) | 2.16021e14 | + | 2.43143e14i | 0.443514 | + | 0.499197i | ||||
\(867\) | −1.78131e14 | −0.363617 | ||||||||
\(868\) | −2.96800e14 | − | 3.51851e13i | −0.602374 | − | 0.0714101i | ||||
\(869\) | 7.23927e14 | 1.46082 | ||||||||
\(870\) | 6.67483e13 | − | 7.32536e13i | 0.133920 | − | 0.146971i | ||||
\(871\) | 2.54396e14i | 0.507480i | ||||||||
\(872\) | 3.21408e14 | + | 4.61433e14i | 0.637492 | + | 0.915222i | ||||
\(873\) | 2.30216e14i | 0.454009i | ||||||||
\(874\) | −3.55515e14 | − | 4.00150e14i | −0.697110 | − | 0.784632i | ||||
\(875\) | −5.82450e14 | + | 1.90624e14i | −1.13558 | + | 0.371653i | ||||
\(876\) | 1.03029e14 | + | 1.22139e13i | 0.199728 | + | 0.0236773i | ||||
\(877\) | − | 3.95684e14i | − | 0.762694i | −0.924432 | − | 0.381347i | \(-0.875460\pi\) | ||
0.924432 | − | 0.381347i | \(-0.124540\pi\) | |||||||
\(878\) | 5.51159e12 | + | 6.20357e12i | 0.0105634 | + | 0.0118896i | ||||
\(879\) | − | 3.46648e14i | − | 0.660609i | ||||||
\(880\) | −8.48883e13 | + | 6.46470e14i | −0.160855 | + | 1.22500i | ||||
\(881\) | 4.64098e14 | 0.874440 | 0.437220 | − | 0.899355i | \(-0.355963\pi\) | ||||
0.437220 | + | 0.899355i | \(0.355963\pi\) | |||||||
\(882\) | 1.44874e14 | − | 1.28714e14i | 0.271424 | − | 0.241148i | ||||
\(883\) | 7.09767e14 | 1.32225 | 0.661123 | − | 0.750278i | \(-0.270080\pi\) | ||||
0.661123 | + | 0.750278i | \(0.270080\pi\) | |||||||
\(884\) | 8.40468e13 | − | 7.08969e14i | 0.155690 | − | 1.31331i | ||||
\(885\) | 1.58157e13 | + | 1.49454e14i | 0.0291322 | + | 0.275291i | ||||
\(886\) | 2.79754e14 | − | 2.48548e14i | 0.512398 | − | 0.455242i | ||||
\(887\) | −1.00628e15 | −1.83274 | −0.916368 | − | 0.400337i | \(-0.868893\pi\) | ||||
−0.916368 | + | 0.400337i | \(0.868893\pi\) | |||||||
\(888\) | 3.23195e14 | − | 2.25120e14i | 0.585329 | − | 0.407707i | ||||
\(889\) | −7.78411e14 | −1.40185 | ||||||||
\(890\) | 6.69914e13 | − | 7.35203e13i | 0.119969 | − | 0.131661i | ||||
\(891\) | − | 3.95245e14i | − | 0.703846i | ||||||
\(892\) | 8.93685e13 | − | 7.53860e14i | 0.158256 | − | 1.33495i | ||||
\(893\) | − | 2.50338e14i | − | 0.440829i | ||||||
\(894\) | 5.99399e13 | − | 5.32538e13i | 0.104961 | − | 0.0932531i | ||||
\(895\) | −4.53794e13 | − | 4.28823e14i | −0.0790212 | − | 0.746728i | ||||
\(896\) | 2.51066e14 | + | 6.42711e14i | 0.434758 | + | 1.11295i | ||||
\(897\) | − | 1.47305e14i | − | 0.253662i | ||||||
\(898\) | −4.73132e14 | + | 4.20356e14i | −0.810215 | + | 0.719839i | ||||
\(899\) | − | 1.52517e14i | − | 0.259729i | ||||||
\(900\) | 4.64860e13 | + | 4.99139e14i | 0.0787245 | + | 0.845297i | ||||
\(901\) | 1.69955e14 | 0.286227 | ||||||||
\(902\) | 3.96349e14 | + | 4.46110e14i | 0.663811 | + | 0.747153i | ||||
\(903\) | 3.82737e14 | 0.637473 | ||||||||
\(904\) | 3.10226e14 | − | 2.16086e14i | 0.513849 | − | 0.357918i | ||||
\(905\) | −4.66982e14 | + | 4.94176e13i | −0.769232 | + | 0.0814026i | ||||
\(906\) | 1.22953e14 | + | 1.38389e14i | 0.201417 | + | 0.226705i | ||||
\(907\) | 4.79149e14 | 0.780610 | 0.390305 | − | 0.920686i | \(-0.372370\pi\) | ||||
0.390305 | + | 0.920686i | \(0.372370\pi\) | |||||||
\(908\) | −5.62156e13 | + | 4.74202e14i | −0.0910810 | + | 0.768305i | ||||
\(909\) | 2.03186e14 | 0.327397 | ||||||||
\(910\) | 5.23904e14 | + | 4.77378e14i | 0.839546 | + | 0.764990i | ||||
\(911\) | 3.79171e14i | 0.604287i | 0.953262 | + | 0.302144i | \(0.0977022\pi\) | ||||
−0.953262 | + | 0.302144i | \(0.902298\pi\) | |||||||
\(912\) | −8.76377e13 | + | 3.64435e14i | −0.138905 | + | 0.577625i | ||||
\(913\) | − | 2.85588e14i | − | 0.450180i | ||||||
\(914\) | −2.91551e14 | − | 3.28155e14i | −0.457071 | − | 0.514456i | ||||
\(915\) | −6.40582e13 | + | 6.77885e12i | −0.0998779 | + | 0.0105694i | ||||
\(916\) | 8.20536e13 | − | 6.92156e14i | 0.127239 | − | 1.07331i | ||||
\(917\) | − | 5.23018e14i | − | 0.806622i | ||||||
\(918\) | −4.32901e14 | − | 4.87251e14i | −0.664010 | − | 0.747377i | ||||
\(919\) | − | 8.93753e14i | − | 1.36345i | −0.731608 | − | 0.681726i | \(-0.761230\pi\) | ||
0.731608 | − | 0.681726i | \(-0.238770\pi\) | |||||||
\(920\) | −2.96291e14 | − | 3.42052e14i | −0.449551 | − | 0.518983i | ||||
\(921\) | −1.56654e14 | −0.236398 | ||||||||
\(922\) | 8.96331e14 | − | 7.96349e14i | 1.34528 | − | 1.19522i | ||||
\(923\) | −4.10793e14 | −0.613217 | ||||||||
\(924\) | 3.83746e14 | + | 4.54923e13i | 0.569749 | + | 0.0675426i | ||||
\(925\) | −2.60147e14 | − | 1.21539e15i | −0.384158 | − | 1.79477i | ||||
\(926\) | −9.77184e14 | + | 8.68183e14i | −1.43523 | + | 1.27514i | ||||
\(927\) | −3.17487e13 | −0.0463797 | ||||||||
\(928\) | −3.10611e14 | + | 1.65838e14i | −0.451312 | + | 0.240959i | ||||
\(929\) | −2.76125e14 | −0.399049 | −0.199525 | − | 0.979893i | \(-0.563940\pi\) | ||||
−0.199525 | + | 0.979893i | \(0.563940\pi\) | |||||||
\(930\) | −1.01459e14 | − | 9.24492e13i | −0.145840 | − | 0.132889i | ||||
\(931\) | − | 4.57256e14i | − | 0.653750i | ||||||
\(932\) | 1.16882e15 | + | 1.38561e14i | 1.66214 | + | 0.197044i | ||||
\(933\) | 1.39411e14i | 0.197191i | ||||||||
\(934\) | −1.93460e13 | + | 1.71880e13i | −0.0272180 | + | 0.0241819i | ||||
\(935\) | −1.22150e15 | + | 1.29264e14i | −1.70937 | + | 0.180891i | ||||
\(936\) | 4.75734e14 | − | 3.31369e14i | 0.662193 | − | 0.461246i | ||||
\(937\) | − | 2.96955e14i | − | 0.411143i | −0.978642 | − | 0.205572i | \(-0.934095\pi\) | ||
0.978642 | − | 0.205572i | \(-0.0659054\pi\) | |||||||
\(938\) | 3.46267e14 | − | 3.07643e14i | 0.476867 | − | 0.423674i | ||||
\(939\) | − | 3.90062e14i | − | 0.534326i | ||||||
\(940\) | 2.65954e12 | − | 2.11628e14i | 0.00362382 | − | 0.288360i | ||||
\(941\) | 7.21500e14 | 0.977886 | 0.488943 | − | 0.872316i | \(-0.337383\pi\) | ||||
0.488943 | + | 0.872316i | \(0.337383\pi\) | |||||||
\(942\) | 9.13929e13 | + | 1.02867e14i | 0.123213 | + | 0.138683i | ||||
\(943\) | −4.14173e14 | −0.555423 | ||||||||
\(944\) | 1.24847e14 | − | 5.19169e14i | 0.166540 | − | 0.692547i | ||||
\(945\) | 6.43479e14 | − | 6.80951e13i | 0.853838 | − | 0.0903559i | ||||
\(946\) | −8.53463e14 | − | 9.60615e14i | −1.12649 | − | 1.26793i | ||||
\(947\) | −1.64992e14 | −0.216627 | −0.108314 | − | 0.994117i | \(-0.534545\pi\) | ||||
−0.108314 | + | 0.994117i | \(0.534545\pi\) | |||||||
\(948\) | 3.49392e14 | + | 4.14197e13i | 0.456322 | + | 0.0540960i | ||||
\(949\) | −3.78648e14 | −0.491931 | ||||||||
\(950\) | 9.53282e14 | + | 7.00226e14i | 1.23198 | + | 0.904941i | ||||
\(951\) | − | 3.82072e14i | − | 0.491182i | ||||||
\(952\) | −1.06664e15 | + | 7.42962e14i | −1.36406 | + | 0.950128i | ||||
\(953\) | 8.63297e14i | 1.09824i | 0.835745 | + | 0.549118i | \(0.185036\pi\) | ||||
−0.835745 | + | 0.549118i | \(0.814964\pi\) | |||||||
\(954\) | 9.16677e13 | + | 1.03177e14i | 0.116004 | + | 0.130569i | ||||
\(955\) | 5.96557e13 | + | 5.63730e14i | 0.0750992 | + | 0.709666i | ||||
\(956\) | 5.80494e14 | + | 6.88163e13i | 0.726956 | + | 0.0861791i | ||||
\(957\) | 1.97196e14i | 0.245662i | ||||||||
\(958\) | −3.27139e14 | − | 3.68211e14i | −0.405419 | − | 0.456320i | ||||
\(959\) | 4.06226e13i | 0.0500813i | ||||||||
\(960\) | −7.79580e13 | + | 3.07152e14i | −0.0956102 | + | 0.376701i | ||||
\(961\) | 6.08386e14 | 0.742270 | ||||||||
\(962\) | −1.07461e15 | + | 9.54744e14i | −1.30430 | + | 1.15881i | ||||
\(963\) | 1.20926e15 | 1.46012 | ||||||||
\(964\) | −1.89487e14 | + | 1.59840e15i | −0.227611 | + | 1.91999i | ||||
\(965\) | 2.26307e13 | + | 2.13854e14i | 0.0270435 | + | 0.255553i | ||||
\(966\) | −2.00502e14 | + | 1.78137e14i | −0.238360 | + | 0.211772i | ||||
\(967\) | 1.77491e13 | 0.0209915 | 0.0104958 | − | 0.999945i | \(-0.496659\pi\) | ||||
0.0104958 | + | 0.999945i | \(0.496659\pi\) | |||||||
\(968\) | −2.55757e14 | − | 3.67180e14i | −0.300919 | − | 0.432018i | ||||
\(969\) | −7.06124e14 | −0.826536 | ||||||||
\(970\) | 3.39453e14 | + | 3.09308e14i | 0.395295 | + | 0.360191i | ||||
\(971\) | 8.66070e14i | 1.00336i | 0.865053 | + | 0.501680i | \(0.167284\pi\) | ||||
−0.865053 | + | 0.501680i | \(0.832716\pi\) | |||||||
\(972\) | 9.60104e13 | − | 8.09887e14i | 0.110659 | − | 0.933454i | ||||
\(973\) | 1.81556e15i | 2.08184i | ||||||||
\(974\) | −3.23630e13 | + | 2.87531e13i | −0.0369194 | + | 0.0328012i | ||||
\(975\) | 6.81302e13 | + | 3.18301e14i | 0.0773244 | + | 0.361255i | ||||
\(976\) | 2.22524e14 | + | 5.35114e13i | 0.251262 | + | 0.0604223i | ||||
\(977\) | − | 4.90063e14i | − | 0.550528i | −0.961369 | − | 0.275264i | \(-0.911235\pi\) | ||
0.961369 | − | 0.275264i | \(-0.0887652\pi\) | |||||||
\(978\) | −5.02771e14 | + | 4.46689e14i | −0.561922 | + | 0.499242i | ||||
\(979\) | 1.97914e14i | 0.220071i | ||||||||
\(980\) | 4.85779e12 | − | 3.86551e14i | 0.00537413 | − | 0.427638i | ||||
\(981\) | −8.60289e14 | −0.946890 | ||||||||
\(982\) | −8.46991e14 | − | 9.53330e14i | −0.927515 | − | 1.04397i | ||||
\(983\) | 7.44254e14 | 0.810874 | 0.405437 | − | 0.914123i | \(-0.367119\pi\) | ||||
0.405437 | + | 0.914123i | \(0.367119\pi\) | |||||||
\(984\) | 1.65767e14 | + | 2.37985e14i | 0.179690 | + | 0.257973i | ||||
\(985\) | −5.22334e13 | − | 4.93591e14i | −0.0563336 | − | 0.532336i | ||||
\(986\) | −4.40573e14 | − | 4.95887e14i | −0.472752 | − | 0.532106i | ||||
\(987\) | −1.25436e14 | −0.133917 | ||||||||
\(988\) | 1.61041e14 | − | 1.35845e15i | 0.171062 | − | 1.44297i | ||||
\(989\) | 8.91845e14 | 0.942557 | ||||||||
\(990\) | −7.37309e14 | − | 6.71832e14i | −0.775306 | − | 0.706455i | ||||
\(991\) | 9.81943e14i | 1.02735i | 0.857985 | + | 0.513674i | \(0.171716\pi\) | ||||
−0.857985 | + | 0.513674i | \(0.828284\pi\) | |||||||
\(992\) | 2.29692e14 | + | 4.30209e14i | 0.239105 | + | 0.447838i | ||||
\(993\) | 4.15880e14i | 0.430746i | ||||||||
\(994\) | 4.96774e14 | + | 5.59144e14i | 0.511949 | + | 0.576225i | ||||
\(995\) | −1.38457e14 | − | 1.30838e15i | −0.141971 | − | 1.34159i | ||||
\(996\) | 1.63400e13 | − | 1.37835e14i | 0.0166708 | − | 0.140625i | ||||
\(997\) | 9.31888e14i | 0.945993i | 0.881064 | + | 0.472997i | \(0.156828\pi\) | ||||
−0.881064 | + | 0.472997i | \(0.843172\pi\) | |||||||
\(998\) | −4.86265e14 | − | 5.47316e14i | −0.491157 | − | 0.552822i | ||||
\(999\) | 1.31233e15i | 1.31891i |
(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 | 20.11.d.d.19.6 | yes | 24 | |
4.3 | odd | 2 | inner | 20.11.d.d.19.20 | yes | 24 | |
5.2 | odd | 4 | 100.11.b.h.51.7 | 24 | |||
5.3 | odd | 4 | 100.11.b.h.51.18 | 24 | |||
5.4 | even | 2 | inner | 20.11.d.d.19.19 | yes | 24 | |
20.3 | even | 4 | 100.11.b.h.51.17 | 24 | |||
20.7 | even | 4 | 100.11.b.h.51.8 | 24 | |||
20.19 | odd | 2 | inner | 20.11.d.d.19.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.11.d.d.19.5 | ✓ | 24 | 20.19 | odd | 2 | inner | |
20.11.d.d.19.6 | yes | 24 | 1.1 | even | 1 | trivial | |
20.11.d.d.19.19 | yes | 24 | 5.4 | even | 2 | inner | |
20.11.d.d.19.20 | yes | 24 | 4.3 | odd | 2 | inner | |
100.11.b.h.51.7 | 24 | 5.2 | odd | 4 | |||
100.11.b.h.51.8 | 24 | 20.7 | even | 4 | |||
100.11.b.h.51.17 | 24 | 20.3 | even | 4 | |||
100.11.b.h.51.18 | 24 | 5.3 | odd | 4 |