Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,7,Mod(8,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.8");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.b (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: | \(4.83113575602\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 642x^{10} + 155265x^{8} + 17813036x^{6} + 1003321428x^{4} + 26369892864x^{2} + 256461520896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{8}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 8.6 | ||
Root | \(-5.05795i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.8 |
Dual form | 21.7.b.a.8.7 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.05795i | − | 0.632244i | −0.948719 | − | 0.316122i | \(-0.897619\pi\) | ||
0.948719 | − | 0.316122i | \(-0.102381\pi\) | |||||||
\(3\) | 10.0378 | − | 25.0648i | 0.371771 | − | 0.928325i | ||||
\(4\) | 38.4172 | 0.600268 | ||||||||
\(5\) | − | 24.8176i | − | 0.198540i | −0.995061 | − | 0.0992702i | \(-0.968349\pi\) | ||
0.995061 | − | 0.0992702i | \(-0.0316508\pi\) | |||||||
\(6\) | −126.776 | − | 50.7707i | −0.586927 | − | 0.235050i | ||||
\(7\) | −129.642 | −0.377964 | ||||||||
\(8\) | − | 518.021i | − | 1.01176i | ||||||
\(9\) | −527.485 | − | 503.190i | −0.723573 | − | 0.690248i | ||||
\(10\) | −125.526 | −0.125526 | ||||||||
\(11\) | 230.584i | 0.173241i | 0.996241 | + | 0.0866207i | \(0.0276068\pi\) | ||||
−0.996241 | + | 0.0866207i | \(0.972393\pi\) | |||||||
\(12\) | 385.624 | − | 962.917i | 0.223162 | − | 0.557244i | ||||
\(13\) | 690.732 | 0.314398 | 0.157199 | − | 0.987567i | \(-0.449754\pi\) | ||||
0.157199 | + | 0.987567i | \(0.449754\pi\) | |||||||
\(14\) | 655.722i | 0.238966i | ||||||||
\(15\) | −622.046 | − | 249.114i | −0.184310 | − | 0.0738115i | ||||
\(16\) | −161.424 | −0.0394101 | ||||||||
\(17\) | 4808.07i | 0.978642i | 0.872104 | + | 0.489321i | \(0.162755\pi\) | ||||
−0.872104 | + | 0.489321i | \(0.837245\pi\) | |||||||
\(18\) | −2545.11 | + | 2667.99i | −0.436405 | + | 0.457475i | ||||
\(19\) | 11105.9 | 1.61917 | 0.809587 | − | 0.587000i | \(-0.199691\pi\) | ||||
0.809587 | + | 0.587000i | \(0.199691\pi\) | |||||||
\(20\) | − | 953.420i | − | 0.119177i | ||||||
\(21\) | −1301.32 | + | 3249.44i | −0.140516 | + | 0.350874i | ||||
\(22\) | 1166.28 | 0.109531 | ||||||||
\(23\) | 8678.68i | 0.713297i | 0.934239 | + | 0.356648i | \(0.116081\pi\) | ||||
−0.934239 | + | 0.356648i | \(0.883919\pi\) | |||||||
\(24\) | −12984.1 | − | 5199.79i | −0.939241 | − | 0.376142i | ||||
\(25\) | 15009.1 | 0.960582 | ||||||||
\(26\) | − | 3493.69i | − | 0.198776i | ||||||
\(27\) | −17907.1 | + | 8170.36i | −0.909777 | + | 0.415097i | ||||
\(28\) | −4980.47 | −0.226880 | ||||||||
\(29\) | − | 24282.0i | − | 0.995612i | −0.867288 | − | 0.497806i | \(-0.834139\pi\) | ||
0.867288 | − | 0.497806i | \(-0.165861\pi\) | |||||||
\(30\) | −1260.00 | + | 3146.28i | −0.0466668 | + | 0.116529i | ||||
\(31\) | −7150.68 | −0.240028 | −0.120014 | − | 0.992772i | \(-0.538294\pi\) | ||||
−0.120014 | + | 0.992772i | \(0.538294\pi\) | |||||||
\(32\) | − | 32336.9i | − | 0.986842i | ||||||
\(33\) | 5779.54 | + | 2314.56i | 0.160824 | + | 0.0644061i | ||||
\(34\) | 24319.0 | 0.618740 | ||||||||
\(35\) | 3217.39i | 0.0750412i | ||||||||
\(36\) | −20264.5 | − | 19331.1i | −0.434338 | − | 0.414334i | ||||
\(37\) | 29502.1 | 0.582435 | 0.291218 | − | 0.956657i | \(-0.405940\pi\) | ||||
0.291218 | + | 0.956657i | \(0.405940\pi\) | |||||||
\(38\) | − | 56173.1i | − | 1.02371i | ||||||
\(39\) | 6933.44 | − | 17313.0i | 0.116884 | − | 0.291863i | ||||
\(40\) | −12856.0 | −0.200875 | ||||||||
\(41\) | 102478.i | 1.48690i | 0.668794 | + | 0.743448i | \(0.266811\pi\) | ||||
−0.668794 | + | 0.743448i | \(0.733189\pi\) | |||||||
\(42\) | 16435.5 | + | 6582.01i | 0.221838 | + | 0.0888404i | ||||
\(43\) | −108429. | −1.36377 | −0.681886 | − | 0.731458i | \(-0.738840\pi\) | ||||
−0.681886 | + | 0.731458i | \(0.738840\pi\) | |||||||
\(44\) | 8858.39i | 0.103991i | ||||||||
\(45\) | −12488.0 | + | 13090.9i | −0.137042 | + | 0.143659i | ||||
\(46\) | 43896.3 | 0.450977 | ||||||||
\(47\) | 203296.i | 1.95810i | 0.203613 | + | 0.979051i | \(0.434732\pi\) | ||||
−0.203613 | + | 0.979051i | \(0.565268\pi\) | |||||||
\(48\) | −1620.34 | + | 4046.05i | −0.0146515 | + | 0.0365854i | ||||
\(49\) | 16807.0 | 0.142857 | ||||||||
\(50\) | − | 75915.2i | − | 0.607322i | ||||||
\(51\) | 120513. | + | 48262.4i | 0.908497 | + | 0.363830i | ||||
\(52\) | 26536.0 | 0.188723 | ||||||||
\(53\) | − | 35192.0i | − | 0.236383i | −0.992991 | − | 0.118192i | \(-0.962290\pi\) | ||
0.992991 | − | 0.118192i | \(-0.0377097\pi\) | |||||||
\(54\) | 41325.3 | + | 90573.4i | 0.262443 | + | 0.575201i | ||||
\(55\) | 5722.54 | 0.0343954 | ||||||||
\(56\) | 67157.1i | 0.382409i | ||||||||
\(57\) | 111479. | − | 278367.i | 0.601961 | − | 1.50312i | ||||
\(58\) | −122817. | −0.629469 | ||||||||
\(59\) | − | 224755.i | − | 1.09434i | −0.837021 | − | 0.547170i | \(-0.815705\pi\) | ||
0.837021 | − | 0.547170i | \(-0.184295\pi\) | |||||||
\(60\) | −23897.2 | − | 9570.24i | −0.110635 | − | 0.0443067i | ||||
\(61\) | −35470.3 | −0.156270 | −0.0781350 | − | 0.996943i | \(-0.524897\pi\) | ||||
−0.0781350 | + | 0.996943i | \(0.524897\pi\) | |||||||
\(62\) | 36167.8i | 0.151756i | ||||||||
\(63\) | 68384.1 | + | 65234.5i | 0.273485 | + | 0.260889i | ||||
\(64\) | −173889. | −0.663335 | ||||||||
\(65\) | − | 17142.3i | − | 0.0624207i | ||||||
\(66\) | 11706.9 | − | 29232.6i | 0.0407203 | − | 0.101680i | ||||
\(67\) | −523102. | −1.73925 | −0.869624 | − | 0.493714i | \(-0.835639\pi\) | ||||
−0.869624 | + | 0.493714i | \(0.835639\pi\) | |||||||
\(68\) | 184712.i | 0.587447i | ||||||||
\(69\) | 217529. | + | 87114.9i | 0.662171 | + | 0.265183i | ||||
\(70\) | 16273.4 | 0.0474443 | ||||||||
\(71\) | − | 622802.i | − | 1.74010i | −0.492961 | − | 0.870052i | \(-0.664085\pi\) | ||
0.492961 | − | 0.870052i | \(-0.335915\pi\) | |||||||
\(72\) | −260663. | + | 273248.i | −0.698364 | + | 0.732082i | ||||
\(73\) | −99977.5 | −0.257000 | −0.128500 | − | 0.991709i | \(-0.541016\pi\) | ||||
−0.128500 | + | 0.991709i | \(0.541016\pi\) | |||||||
\(74\) | − | 149220.i | − | 0.368241i | ||||||
\(75\) | 150658. | − | 376199.i | 0.357116 | − | 0.891732i | ||||
\(76\) | 426658. | 0.971938 | ||||||||
\(77\) | − | 29893.4i | − | 0.0654791i | ||||||
\(78\) | −87568.5 | − | 35069.0i | −0.184529 | − | 0.0738991i | ||||
\(79\) | 275833. | 0.559454 | 0.279727 | − | 0.960080i | \(-0.409756\pi\) | ||||
0.279727 | + | 0.960080i | \(0.409756\pi\) | |||||||
\(80\) | 4006.14i | 0.00782450i | ||||||||
\(81\) | 25039.8 | + | 530851.i | 0.0471167 | + | 0.998889i | ||||
\(82\) | 518330. | 0.940080 | ||||||||
\(83\) | 375630.i | 0.656940i | 0.944514 | + | 0.328470i | \(0.106533\pi\) | ||||
−0.944514 | + | 0.328470i | \(0.893467\pi\) | |||||||
\(84\) | −49993.0 | + | 124834.i | −0.0843473 | + | 0.210618i | ||||
\(85\) | 119324. | 0.194300 | ||||||||
\(86\) | 548431.i | 0.862237i | ||||||||
\(87\) | −608622. | − | 243738.i | −0.924251 | − | 0.370139i | ||||
\(88\) | 119447. | 0.175279 | ||||||||
\(89\) | 617008.i | 0.875227i | 0.899163 | + | 0.437614i | \(0.144176\pi\) | ||||
−0.899163 | + | 0.437614i | \(0.855824\pi\) | |||||||
\(90\) | 66213.0 | + | 63163.4i | 0.0908272 | + | 0.0866439i | ||||
\(91\) | −89547.8 | −0.118831 | ||||||||
\(92\) | 333410.i | 0.428169i | ||||||||
\(93\) | −71777.1 | + | 179230.i | −0.0892354 | + | 0.222824i | ||||
\(94\) | 1.02826e6 | 1.23800 | ||||||||
\(95\) | − | 275622.i | − | 0.321471i | ||||||
\(96\) | −810516. | − | 324591.i | −0.916110 | − | 0.366879i | ||||
\(97\) | −1.14802e6 | −1.25787 | −0.628933 | − | 0.777460i | \(-0.716508\pi\) | ||||
−0.628933 | + | 0.777460i | \(0.716508\pi\) | |||||||
\(98\) | − | 85008.9i | − | 0.0903205i | ||||||
\(99\) | 116028. | − | 121630.i | 0.119579 | − | 0.125353i | ||||
\(100\) | 576607. | 0.576607 | ||||||||
\(101\) | 106534.i | 0.103401i | 0.998663 | + | 0.0517004i | \(0.0164641\pi\) | ||||
−0.998663 | + | 0.0517004i | \(0.983536\pi\) | |||||||
\(102\) | 244109. | − | 609549.i | 0.230029 | − | 0.574391i | ||||
\(103\) | 21323.9 | 0.0195144 | 0.00975719 | − | 0.999952i | \(-0.496894\pi\) | ||||
0.00975719 | + | 0.999952i | \(0.496894\pi\) | |||||||
\(104\) | − | 357814.i | − | 0.318095i | ||||||
\(105\) | 80643.2 | + | 32295.6i | 0.0696626 | + | 0.0278981i | ||||
\(106\) | −178000. | −0.149452 | ||||||||
\(107\) | − | 1.89640e6i | − | 1.54803i | −0.633168 | − | 0.774014i | \(-0.718246\pi\) | ||
0.633168 | − | 0.774014i | \(-0.281754\pi\) | |||||||
\(108\) | −687941. | + | 313882.i | −0.546110 | + | 0.249170i | ||||
\(109\) | 551935. | 0.426195 | 0.213097 | − | 0.977031i | \(-0.431645\pi\) | ||||
0.213097 | + | 0.977031i | \(0.431645\pi\) | |||||||
\(110\) | − | 28944.3i | − | 0.0217463i | ||||||
\(111\) | 296136. | − | 739463.i | 0.216532 | − | 0.540689i | ||||
\(112\) | 20927.3 | 0.0148956 | ||||||||
\(113\) | 2.03418e6i | 1.40979i | 0.709314 | + | 0.704893i | \(0.249005\pi\) | ||||
−0.709314 | + | 0.704893i | \(0.750995\pi\) | |||||||
\(114\) | −1.40797e6 | − | 563855.i | −0.950337 | − | 0.380586i | ||||
\(115\) | 215384. | 0.141618 | ||||||||
\(116\) | − | 932845.i | − | 0.597634i | ||||||
\(117\) | −364351. | − | 347570.i | −0.227490 | − | 0.217012i | ||||
\(118\) | −1.13680e6 | −0.691890 | ||||||||
\(119\) | − | 623326.i | − | 0.369892i | ||||||
\(120\) | −129046. | + | 322233.i | −0.0746794 | + | 0.186477i | ||||
\(121\) | 1.71839e6 | 0.969987 | ||||||||
\(122\) | 179407.i | 0.0988006i | ||||||||
\(123\) | 2.56859e6 | + | 1.02866e6i | 1.38032 | + | 0.552784i | ||||
\(124\) | −274709. | −0.144081 | ||||||||
\(125\) | − | 760263.i | − | 0.389255i | ||||||
\(126\) | 329953. | − | 345883.i | 0.164945 | − | 0.172909i | ||||
\(127\) | −1.27146e6 | −0.620715 | −0.310357 | − | 0.950620i | \(-0.600449\pi\) | ||||
−0.310357 | + | 0.950620i | \(0.600449\pi\) | |||||||
\(128\) | − | 1.19004e6i | − | 0.567453i | ||||||
\(129\) | −1.08839e6 | + | 2.71776e6i | −0.507011 | + | 1.26602i | ||||
\(130\) | −86704.8 | −0.0394651 | ||||||||
\(131\) | − | 719484.i | − | 0.320042i | −0.987114 | − | 0.160021i | \(-0.948844\pi\) | ||
0.987114 | − | 0.160021i | \(-0.0511562\pi\) | |||||||
\(132\) | 222034. | + | 88918.8i | 0.0965377 | + | 0.0386609i | ||||
\(133\) | −1.43979e6 | −0.611990 | ||||||||
\(134\) | 2.64582e6i | 1.09963i | ||||||||
\(135\) | 202768. | + | 444411.i | 0.0824136 | + | 0.180628i | ||||
\(136\) | 2.49068e6 | 0.990150 | ||||||||
\(137\) | 2.85051e6i | 1.10856i | 0.832329 | + | 0.554282i | \(0.187007\pi\) | ||||
−0.832329 | + | 0.554282i | \(0.812993\pi\) | |||||||
\(138\) | 440623. | − | 1.10025e6i | 0.167660 | − | 0.418653i | ||||
\(139\) | −973777. | −0.362589 | −0.181295 | − | 0.983429i | \(-0.558029\pi\) | ||||
−0.181295 | + | 0.983429i | \(0.558029\pi\) | |||||||
\(140\) | 123603.i | 0.0450449i | ||||||||
\(141\) | 5.09557e6 | + | 2.04065e6i | 1.81776 | + | 0.727965i | ||||
\(142\) | −3.15010e6 | −1.10017 | ||||||||
\(143\) | 159272.i | 0.0544668i | ||||||||
\(144\) | 85148.6 | + | 81226.9i | 0.0285161 | + | 0.0272027i | ||||
\(145\) | −602620. | −0.197669 | ||||||||
\(146\) | 505681.i | 0.162487i | ||||||||
\(147\) | 168705. | − | 421264.i | 0.0531101 | − | 0.132618i | ||||
\(148\) | 1.13339e6 | 0.349617 | ||||||||
\(149\) | 2.91215e6i | 0.880350i | 0.897912 | + | 0.440175i | \(0.145084\pi\) | ||||
−0.897912 | + | 0.440175i | \(0.854916\pi\) | |||||||
\(150\) | −1.90280e6 | − | 762022.i | −0.563792 | − | 0.225784i | ||||
\(151\) | −5.49247e6 | −1.59528 | −0.797640 | − | 0.603133i | \(-0.793919\pi\) | ||||
−0.797640 | + | 0.603133i | \(0.793919\pi\) | |||||||
\(152\) | − | 5.75309e6i | − | 1.63821i | ||||||
\(153\) | 2.41937e6 | − | 2.53618e6i | 0.675505 | − | 0.708119i | ||||
\(154\) | −151199. | −0.0413987 | ||||||||
\(155\) | 177462.i | 0.0476553i | ||||||||
\(156\) | 266363. | − | 665118.i | 0.0701617 | − | 0.175196i | ||||
\(157\) | 4.14432e6 | 1.07091 | 0.535457 | − | 0.844562i | \(-0.320139\pi\) | ||||
0.535457 | + | 0.844562i | \(0.320139\pi\) | |||||||
\(158\) | − | 1.39515e6i | − | 0.353711i | ||||||
\(159\) | −882080. | − | 353251.i | −0.219441 | − | 0.0878804i | ||||
\(160\) | −802521. | −0.195928 | ||||||||
\(161\) | − | 1.12512e6i | − | 0.269601i | ||||||
\(162\) | 2.68502e6 | − | 126650.i | 0.631541 | − | 0.0297893i | ||||
\(163\) | 1.41248e6 | 0.326151 | 0.163076 | − | 0.986614i | \(-0.447859\pi\) | ||||
0.163076 | + | 0.986614i | \(0.447859\pi\) | |||||||
\(164\) | 3.93692e6i | 0.892536i | ||||||||
\(165\) | 57441.7 | − | 143434.i | 0.0127872 | − | 0.0319301i | ||||
\(166\) | 1.89992e6 | 0.415346 | ||||||||
\(167\) | − | 7.57450e6i | − | 1.62631i | −0.582045 | − | 0.813157i | \(-0.697747\pi\) | ||
0.582045 | − | 0.813157i | \(-0.302253\pi\) | |||||||
\(168\) | 1.68328e6 | + | 674110.i | 0.355000 | + | 0.142168i | ||||
\(169\) | −4.34970e6 | −0.901154 | ||||||||
\(170\) | − | 603537.i | − | 0.122845i | ||||||
\(171\) | −5.85820e6 | − | 5.58839e6i | −1.17159 | − | 1.11763i | ||||
\(172\) | −4.16555e6 | −0.818629 | ||||||||
\(173\) | 955257.i | 0.184494i | 0.995736 | + | 0.0922469i | \(0.0294049\pi\) | ||||
−0.995736 | + | 0.0922469i | \(0.970595\pi\) | |||||||
\(174\) | −1.23281e6 | + | 3.07838e6i | −0.234018 | + | 0.584352i | ||||
\(175\) | −1.94581e6 | −0.363066 | ||||||||
\(176\) | − | 37221.8i | − | 0.00682746i | ||||||
\(177\) | −5.63342e6 | − | 2.25604e6i | −1.01590 | − | 0.406844i | ||||
\(178\) | 3.12080e6 | 0.553357 | ||||||||
\(179\) | 6.09170e6i | 1.06214i | 0.847329 | + | 0.531068i | \(0.178209\pi\) | ||||
−0.847329 | + | 0.531068i | \(0.821791\pi\) | |||||||
\(180\) | −479752. | + | 502915.i | −0.0822620 | + | 0.0862336i | ||||
\(181\) | 3.91245e6 | 0.659802 | 0.329901 | − | 0.944016i | \(-0.392985\pi\) | ||||
0.329901 | + | 0.944016i | \(0.392985\pi\) | |||||||
\(182\) | 452928.i | 0.0751303i | ||||||||
\(183\) | −356044. | + | 889055.i | −0.0580966 | + | 0.145069i | ||||
\(184\) | 4.49574e6 | 0.721684 | ||||||||
\(185\) | − | 732169.i | − | 0.115637i | ||||||
\(186\) | 906536. | + | 363045.i | 0.140879 | + | 0.0564185i | ||||
\(187\) | −1.10866e6 | −0.169541 | ||||||||
\(188\) | 7.81006e6i | 1.17539i | ||||||||
\(189\) | 2.32151e6 | − | 1.05922e6i | 0.343863 | − | 0.156892i | ||||
\(190\) | −1.39408e6 | −0.203248 | ||||||||
\(191\) | 1.02097e6i | 0.146525i | 0.997313 | + | 0.0732627i | \(0.0233411\pi\) | ||||
−0.997313 | + | 0.0732627i | \(0.976659\pi\) | |||||||
\(192\) | −1.74547e6 | + | 4.35849e6i | −0.246608 | + | 0.615790i | ||||
\(193\) | 8.60150e6 | 1.19647 | 0.598236 | − | 0.801320i | \(-0.295869\pi\) | ||||
0.598236 | + | 0.801320i | \(0.295869\pi\) | |||||||
\(194\) | 5.80663e6i | 0.795278i | ||||||||
\(195\) | −429667. | − | 172071.i | −0.0579467 | − | 0.0232062i | ||||
\(196\) | 645677. | 0.0857526 | ||||||||
\(197\) | − | 1.15308e7i | − | 1.50821i | −0.656753 | − | 0.754106i | \(-0.728071\pi\) | ||
0.656753 | − | 0.754106i | \(-0.271929\pi\) | |||||||
\(198\) | −615197. | − | 586863.i | −0.0792535 | − | 0.0756033i | ||||
\(199\) | 1.31963e7 | 1.67452 | 0.837262 | − | 0.546802i | \(-0.184155\pi\) | ||||
0.837262 | + | 0.546802i | \(0.184155\pi\) | |||||||
\(200\) | − | 7.77502e6i | − | 0.971877i | ||||||
\(201\) | −5.25079e6 | + | 1.31114e7i | −0.646601 | + | 1.61459i | ||||
\(202\) | 538844. | 0.0653745 | ||||||||
\(203\) | 3.14796e6i | 0.376306i | ||||||||
\(204\) | 4.62977e6 | + | 1.85411e6i | 0.545342 | + | 0.218396i | ||||
\(205\) | 2.54326e6 | 0.295209 | ||||||||
\(206\) | − | 107855.i | − | 0.0123378i | ||||||
\(207\) | 4.36703e6 | − | 4.57787e6i | 0.492351 | − | 0.516122i | ||||
\(208\) | −111501. | −0.0123905 | ||||||||
\(209\) | 2.56085e6i | 0.280508i | ||||||||
\(210\) | 163349. | − | 407889.i | 0.0176384 | − | 0.0440437i | ||||
\(211\) | −7.77953e6 | −0.828144 | −0.414072 | − | 0.910244i | \(-0.635894\pi\) | ||||
−0.414072 | + | 0.910244i | \(0.635894\pi\) | |||||||
\(212\) | − | 1.35198e6i | − | 0.141893i | ||||||
\(213\) | −1.56104e7 | − | 6.25156e6i | −1.61538 | − | 0.646919i | ||||
\(214\) | −9.59190e6 | −0.978731 | ||||||||
\(215\) | 2.69095e6i | 0.270764i | ||||||||
\(216\) | 4.23242e6 | + | 9.27627e6i | 0.419978 | + | 0.920475i | ||||
\(217\) | 927027. | 0.0907221 | ||||||||
\(218\) | − | 2.79166e6i | − | 0.269459i | ||||||
\(219\) | −1.00355e6 | + | 2.50591e6i | −0.0955452 | + | 0.238580i | ||||
\(220\) | 219844. | 0.0206465 | ||||||||
\(221\) | 3.32109e6i | 0.307683i | ||||||||
\(222\) | −3.74016e6 | − | 1.49784e6i | −0.341847 | − | 0.136901i | ||||
\(223\) | −1.23203e7 | −1.11098 | −0.555492 | − | 0.831522i | \(-0.687470\pi\) | ||||
−0.555492 | + | 0.831522i | \(0.687470\pi\) | |||||||
\(224\) | 4.19221e6i | 0.372991i | ||||||||
\(225\) | −7.91707e6 | − | 7.55243e6i | −0.695051 | − | 0.663039i | ||||
\(226\) | 1.02888e7 | 0.891328 | ||||||||
\(227\) | − | 1.68616e7i | − | 1.44152i | −0.693182 | − | 0.720762i | \(-0.743792\pi\) | ||
0.693182 | − | 0.720762i | \(-0.256208\pi\) | |||||||
\(228\) | 4.28271e6 | − | 1.06941e7i | 0.361338 | − | 0.902274i | ||||
\(229\) | 1.88076e7 | 1.56613 | 0.783064 | − | 0.621941i | \(-0.213656\pi\) | ||||
0.783064 | + | 0.621941i | \(0.213656\pi\) | |||||||
\(230\) | − | 1.08940e6i | − | 0.0895372i | ||||||
\(231\) | −749270. | − | 300064.i | −0.0607859 | − | 0.0243432i | ||||
\(232\) | −1.25786e7 | −1.00732 | ||||||||
\(233\) | 1.08234e7i | 0.855647i | 0.903862 | + | 0.427824i | \(0.140720\pi\) | ||||
−0.903862 | + | 0.427824i | \(0.859280\pi\) | |||||||
\(234\) | −1.75799e6 | + | 1.84287e6i | −0.137205 | + | 0.143829i | ||||
\(235\) | 5.04531e6 | 0.388763 | ||||||||
\(236\) | − | 8.63443e6i | − | 0.656898i | ||||||
\(237\) | 2.76876e6 | − | 6.91369e6i | 0.207989 | − | 0.519355i | ||||
\(238\) | −3.15275e6 | −0.233862 | ||||||||
\(239\) | − | 9.41829e6i | − | 0.689888i | −0.938623 | − | 0.344944i | \(-0.887898\pi\) | ||
0.938623 | − | 0.344944i | \(-0.112102\pi\) | |||||||
\(240\) | 100413. | + | 40212.9i | 0.00726368 | + | 0.00290892i | ||||
\(241\) | −1.15621e7 | −0.826010 | −0.413005 | − | 0.910729i | \(-0.635521\pi\) | ||||
−0.413005 | + | 0.910729i | \(0.635521\pi\) | |||||||
\(242\) | − | 8.69154e6i | − | 0.613268i | ||||||
\(243\) | 1.35570e7 | + | 4.70096e6i | 0.944810 | + | 0.327618i | ||||
\(244\) | −1.36267e6 | −0.0938038 | ||||||||
\(245\) | − | 417109.i | − | 0.0283629i | ||||||
\(246\) | 5.20289e6 | − | 1.29918e7i | 0.349494 | − | 0.872699i | ||||
\(247\) | 7.67121e6 | 0.509065 | ||||||||
\(248\) | 3.70420e6i | 0.242851i | ||||||||
\(249\) | 9.41507e6 | + | 3.77050e6i | 0.609853 | + | 0.244231i | ||||
\(250\) | −3.84537e6 | −0.246104 | ||||||||
\(251\) | 1.73215e7i | 1.09538i | 0.836682 | + | 0.547689i | \(0.184492\pi\) | ||||
−0.836682 | + | 0.547689i | \(0.815508\pi\) | |||||||
\(252\) | 2.62712e6 | + | 2.50612e6i | 0.164164 | + | 0.156603i | ||||
\(253\) | −2.00117e6 | −0.123573 | ||||||||
\(254\) | 6.43099e6i | 0.392443i | ||||||||
\(255\) | 1.19776e6 | − | 2.99084e6i | 0.0722350 | − | 0.180373i | ||||
\(256\) | −1.71481e7 | −1.02210 | ||||||||
\(257\) | 1.19973e6i | 0.0706779i | 0.999375 | + | 0.0353390i | \(0.0112511\pi\) | ||||
−0.999375 | + | 0.0353390i | \(0.988749\pi\) | |||||||
\(258\) | 1.37463e7 | + | 5.50504e6i | 0.800435 | + | 0.320554i | ||||
\(259\) | −3.82470e6 | −0.220140 | ||||||||
\(260\) | − | 658558.i | − | 0.0374692i | ||||||
\(261\) | −1.22185e7 | + | 1.28084e7i | −0.687219 | + | 0.720399i | ||||
\(262\) | −3.63911e6 | −0.202345 | ||||||||
\(263\) | 2.34931e7i | 1.29144i | 0.763575 | + | 0.645719i | \(0.223442\pi\) | ||||
−0.763575 | + | 0.645719i | \(0.776558\pi\) | |||||||
\(264\) | 1.19899e6 | − | 2.99392e6i | 0.0651634 | − | 0.162715i | ||||
\(265\) | −873381. | −0.0469317 | ||||||||
\(266\) | 7.28239e6i | 0.386927i | ||||||||
\(267\) | 1.54652e7 | + | 6.19341e6i | 0.812495 | + | 0.325384i | ||||
\(268\) | −2.00961e7 | −1.04402 | ||||||||
\(269\) | 1.36239e7i | 0.699912i | 0.936766 | + | 0.349956i | \(0.113804\pi\) | ||||
−0.936766 | + | 0.349956i | \(0.886196\pi\) | |||||||
\(270\) | 2.24781e6 | − | 1.02559e6i | 0.114201 | − | 0.0521055i | ||||
\(271\) | 1.38490e6 | 0.0695843 | 0.0347922 | − | 0.999395i | \(-0.488923\pi\) | ||||
0.0347922 | + | 0.999395i | \(0.488923\pi\) | |||||||
\(272\) | − | 776137.i | − | 0.0385684i | ||||||
\(273\) | −898863. | + | 2.24449e6i | −0.0441780 | + | 0.110314i | ||||
\(274\) | 1.44177e7 | 0.700883 | ||||||||
\(275\) | 3.46086e6i | 0.166413i | ||||||||
\(276\) | 8.35685e6 | + | 3.34671e6i | 0.397480 | + | 0.159181i | ||||
\(277\) | −9.21086e6 | −0.433372 | −0.216686 | − | 0.976241i | \(-0.569525\pi\) | ||||
−0.216686 | + | 0.976241i | \(0.569525\pi\) | |||||||
\(278\) | 4.92531e6i | 0.229245i | ||||||||
\(279\) | 3.77188e6 | + | 3.59815e6i | 0.173678 | + | 0.165679i | ||||
\(280\) | 1.66668e6 | 0.0759236 | ||||||||
\(281\) | − | 1.91243e7i | − | 0.861921i | −0.902371 | − | 0.430961i | \(-0.858175\pi\) | ||
0.902371 | − | 0.430961i | \(-0.141825\pi\) | |||||||
\(282\) | 1.03215e7 | − | 2.57731e7i | 0.460251 | − | 1.14926i | ||||
\(283\) | 1.59127e7 | 0.702076 | 0.351038 | − | 0.936361i | \(-0.385829\pi\) | ||||
0.351038 | + | 0.936361i | \(0.385829\pi\) | |||||||
\(284\) | − | 2.39263e7i | − | 1.04453i | ||||||
\(285\) | −6.90839e6 | − | 2.76664e6i | −0.298430 | − | 0.119514i | ||||
\(286\) | 805590. | 0.0344363 | ||||||||
\(287\) | − | 1.32855e7i | − | 0.561994i | ||||||
\(288\) | −1.62716e7 | + | 1.70572e7i | −0.681166 | + | 0.714053i | ||||
\(289\) | 1.02007e6 | 0.0422605 | ||||||||
\(290\) | 3.04802e6i | 0.124975i | ||||||||
\(291\) | −1.15236e7 | + | 2.87749e7i | −0.467638 | + | 1.16771i | ||||
\(292\) | −3.84085e6 | −0.154269 | ||||||||
\(293\) | − | 2.62096e7i | − | 1.04198i | −0.853564 | − | 0.520988i | \(-0.825564\pi\) | ||
0.853564 | − | 0.520988i | \(-0.174436\pi\) | |||||||
\(294\) | −2.13073e6 | − | 853303.i | −0.0838468 | − | 0.0335785i | ||||
\(295\) | −5.57786e6 | −0.217271 | ||||||||
\(296\) | − | 1.52827e7i | − | 0.589284i | ||||||
\(297\) | −1.88396e6 | − | 4.12911e6i | −0.0719120 | − | 0.157611i | ||||
\(298\) | 1.47295e7 | 0.556596 | ||||||||
\(299\) | 5.99465e6i | 0.224259i | ||||||||
\(300\) | 5.78786e6 | − | 1.44525e7i | 0.214365 | − | 0.535278i | ||||
\(301\) | 1.40570e7 | 0.515458 | ||||||||
\(302\) | 2.77806e7i | 1.00861i | ||||||||
\(303\) | 2.67025e6 | + | 1.06937e6i | 0.0959896 | + | 0.0384414i | ||||
\(304\) | −1.79276e6 | −0.0638118 | ||||||||
\(305\) | 880286.i | 0.0310259i | ||||||||
\(306\) | −1.28279e7 | − | 1.22371e7i | −0.447704 | − | 0.427084i | ||||
\(307\) | −1.56647e7 | −0.541384 | −0.270692 | − | 0.962666i | \(-0.587253\pi\) | ||||
−0.270692 | + | 0.962666i | \(0.587253\pi\) | |||||||
\(308\) | − | 1.14842e6i | − | 0.0393050i | ||||||
\(309\) | 214045. | − | 534478.i | 0.00725487 | − | 0.0181157i | ||||
\(310\) | 897595. | 0.0301297 | ||||||||
\(311\) | − | 1.54014e7i | − | 0.512011i | −0.966675 | − | 0.256006i | \(-0.917593\pi\) | ||
0.966675 | − | 0.256006i | \(-0.0824065\pi\) | |||||||
\(312\) | −8.96852e6 | − | 3.59166e6i | −0.295296 | − | 0.118258i | ||||
\(313\) | −1.75634e7 | −0.572763 | −0.286382 | − | 0.958116i | \(-0.592453\pi\) | ||||
−0.286382 | + | 0.958116i | \(0.592453\pi\) | |||||||
\(314\) | − | 2.09618e7i | − | 0.677079i | ||||||
\(315\) | 1.61896e6 | − | 1.69713e6i | 0.0517970 | − | 0.0542978i | ||||
\(316\) | 1.05967e7 | 0.335823 | ||||||||
\(317\) | − | 3.77721e7i | − | 1.18575i | −0.805294 | − | 0.592876i | \(-0.797992\pi\) | ||
0.805294 | − | 0.592876i | \(-0.202008\pi\) | |||||||
\(318\) | −1.78672e6 | + | 4.46152e6i | −0.0555618 | + | 0.138740i | ||||
\(319\) | 5.59905e6 | 0.172481 | ||||||||
\(320\) | 4.31551e6i | 0.131699i | ||||||||
\(321\) | −4.75329e7 | − | 1.90357e7i | −1.43707 | − | 0.575511i | ||||
\(322\) | −5.69080e6 | −0.170453 | ||||||||
\(323\) | 5.33980e7i | 1.58459i | ||||||||
\(324\) | 961957. | + | 2.03938e7i | 0.0282827 | + | 0.599601i | ||||
\(325\) | 1.03673e7 | 0.302005 | ||||||||
\(326\) | − | 7.14424e6i | − | 0.206207i | ||||||
\(327\) | 5.54021e6 | − | 1.38341e7i | 0.158447 | − | 0.395647i | ||||
\(328\) | 5.30859e7 | 1.50438 | ||||||||
\(329\) | − | 2.63557e7i | − | 0.740093i | ||||||
\(330\) | −725482. | − | 290537.i | −0.0201876 | − | 0.00808463i | ||||
\(331\) | −3.53421e6 | −0.0974559 | −0.0487279 | − | 0.998812i | \(-0.515517\pi\) | ||||
−0.0487279 | + | 0.998812i | \(0.515517\pi\) | |||||||
\(332\) | 1.44306e7i | 0.394340i | ||||||||
\(333\) | −1.55619e7 | − | 1.48452e7i | −0.421434 | − | 0.402024i | ||||
\(334\) | −3.83114e7 | −1.02823 | ||||||||
\(335\) | 1.29821e7i | 0.345311i | ||||||||
\(336\) | 210064. | − | 524537.i | 0.00553775 | − | 0.0138280i | ||||
\(337\) | 4.61131e7 | 1.20485 | 0.602427 | − | 0.798174i | \(-0.294201\pi\) | ||||
0.602427 | + | 0.798174i | \(0.294201\pi\) | |||||||
\(338\) | 2.20005e7i | 0.569749i | ||||||||
\(339\) | 5.09862e7 | + | 2.04187e7i | 1.30874 | + | 0.524117i | ||||
\(340\) | 4.58411e6 | 0.116632 | ||||||||
\(341\) | − | 1.64883e6i | − | 0.0415828i | ||||||
\(342\) | −2.82658e7 | + | 2.96305e7i | −0.706615 | + | 0.740731i | ||||
\(343\) | −2.17889e6 | −0.0539949 | ||||||||
\(344\) | 5.61687e7i | 1.37981i | ||||||||
\(345\) | 2.16198e6 | − | 5.39854e6i | 0.0526495 | − | 0.131468i | ||||
\(346\) | 4.83164e6 | 0.116645 | ||||||||
\(347\) | 2.66807e7i | 0.638571i | 0.947659 | + | 0.319285i | \(0.103443\pi\) | ||||
−0.947659 | + | 0.319285i | \(0.896557\pi\) | |||||||
\(348\) | −2.33815e7 | − | 9.36372e6i | −0.554799 | − | 0.222183i | ||||
\(349\) | 1.06810e7 | 0.251268 | 0.125634 | − | 0.992077i | \(-0.459904\pi\) | ||||
0.125634 | + | 0.992077i | \(0.459904\pi\) | |||||||
\(350\) | 9.84178e6i | 0.229546i | ||||||||
\(351\) | −1.23690e7 | + | 5.64353e6i | −0.286032 | + | 0.130506i | ||||
\(352\) | 7.45637e6 | 0.170962 | ||||||||
\(353\) | 6.31242e6i | 0.143506i | 0.997422 | + | 0.0717532i | \(0.0228594\pi\) | ||||
−0.997422 | + | 0.0717532i | \(0.977141\pi\) | |||||||
\(354\) | −1.14109e7 | + | 2.84936e7i | −0.257224 | + | 0.642298i | ||||
\(355\) | −1.54564e7 | −0.345481 | ||||||||
\(356\) | 2.37037e7i | 0.525371i | ||||||||
\(357\) | −1.56235e7 | − | 6.25683e6i | −0.343380 | − | 0.137515i | ||||
\(358\) | 3.08115e7 | 0.671528 | ||||||||
\(359\) | − | 2.70408e7i | − | 0.584436i | −0.956352 | − | 0.292218i | \(-0.905607\pi\) | ||
0.956352 | − | 0.292218i | \(-0.0943933\pi\) | |||||||
\(360\) | 6.78135e6 | + | 6.46902e6i | 0.145348 | + | 0.138654i | ||||
\(361\) | 7.62954e7 | 1.62172 | ||||||||
\(362\) | − | 1.97890e7i | − | 0.417155i | ||||||
\(363\) | 1.72489e7 | − | 4.30711e7i | 0.360613 | − | 0.900463i | ||||
\(364\) | −3.44017e6 | −0.0713306 | ||||||||
\(365\) | 2.48120e6i | 0.0510250i | ||||||||
\(366\) | 4.49679e6 | + | 1.80085e6i | 0.0917191 | + | 0.0367312i | ||||
\(367\) | −7.63777e7 | −1.54514 | −0.772571 | − | 0.634928i | \(-0.781030\pi\) | ||||
−0.772571 | + | 0.634928i | \(0.781030\pi\) | |||||||
\(368\) | − | 1.40095e6i | − | 0.0281111i | ||||||
\(369\) | 5.15661e7 | − | 5.40558e7i | 1.02633 | − | 1.07588i | ||||
\(370\) | −3.70328e6 | −0.0731107 | ||||||||
\(371\) | 4.56236e6i | 0.0893445i | ||||||||
\(372\) | −2.75747e6 | + | 6.88551e6i | −0.0535652 | + | 0.133754i | ||||
\(373\) | −5.76666e7 | −1.11121 | −0.555607 | − | 0.831445i | \(-0.687514\pi\) | ||||
−0.555607 | + | 0.831445i | \(0.687514\pi\) | |||||||
\(374\) | 5.60757e6i | 0.107191i | ||||||||
\(375\) | −1.90558e7 | − | 7.63137e6i | −0.361355 | − | 0.144713i | ||||
\(376\) | 1.05312e8 | 1.98113 | ||||||||
\(377\) | − | 1.67724e7i | − | 0.313019i | ||||||
\(378\) | −5.35748e6 | − | 1.17421e7i | −0.0991940 | − | 0.217405i | ||||
\(379\) | −3.28161e7 | −0.602795 | −0.301397 | − | 0.953499i | \(-0.597453\pi\) | ||||
−0.301397 | + | 0.953499i | \(0.597453\pi\) | |||||||
\(380\) | − | 1.05886e7i | − | 0.192969i | ||||||
\(381\) | −1.27627e7 | + | 3.18689e7i | −0.230764 | + | 0.576225i | ||||
\(382\) | 5.16401e6 | 0.0926397 | ||||||||
\(383\) | − | 3.06896e7i | − | 0.546254i | −0.961978 | − | 0.273127i | \(-0.911942\pi\) | ||
0.961978 | − | 0.273127i | \(-0.0880579\pi\) | |||||||
\(384\) | −2.98280e7 | − | 1.19453e7i | −0.526781 | − | 0.210962i | ||||
\(385\) | −741880. | −0.0130002 | ||||||||
\(386\) | − | 4.35060e7i | − | 0.756461i | ||||||
\(387\) | 5.71949e7 | + | 5.45607e7i | 0.986790 | + | 0.941341i | ||||
\(388\) | −4.41037e7 | −0.755057 | ||||||||
\(389\) | − | 8.48450e6i | − | 0.144138i | −0.997400 | − | 0.0720688i | \(-0.977040\pi\) | ||
0.997400 | − | 0.0720688i | \(-0.0229601\pi\) | |||||||
\(390\) | −870326. | + | 2.17324e6i | −0.0146720 | + | 0.0366364i | ||||
\(391\) | −4.17277e7 | −0.698062 | ||||||||
\(392\) | − | 8.70637e6i | − | 0.144537i | ||||||
\(393\) | −1.80337e7 | − | 7.22204e6i | −0.297103 | − | 0.118982i | ||||
\(394\) | −5.83224e7 | −0.953557 | ||||||||
\(395\) | − | 6.84550e6i | − | 0.111074i | ||||||
\(396\) | 4.45746e6 | − | 4.67267e6i | 0.0717797 | − | 0.0752453i | ||||
\(397\) | −7.06433e7 | −1.12902 | −0.564508 | − | 0.825428i | \(-0.690934\pi\) | ||||
−0.564508 | + | 0.825428i | \(0.690934\pi\) | |||||||
\(398\) | − | 6.67460e7i | − | 1.05871i | ||||||
\(399\) | −1.44523e7 | + | 3.60880e7i | −0.227520 | + | 0.568125i | ||||
\(400\) | −2.42282e6 | −0.0378566 | ||||||||
\(401\) | − | 3.52542e7i | − | 0.546736i | −0.961910 | − | 0.273368i | \(-0.911862\pi\) | ||
0.961910 | − | 0.273368i | \(-0.0881376\pi\) | |||||||
\(402\) | 6.63169e7 | + | 2.65582e7i | 1.02081 | + | 0.408809i | ||||
\(403\) | −4.93921e6 | −0.0754644 | ||||||||
\(404\) | 4.09273e6i | 0.0620682i | ||||||||
\(405\) | 1.31744e7 | − | 621426.i | 0.198320 | − | 0.00935458i | ||||
\(406\) | 1.59222e7 | 0.237917 | ||||||||
\(407\) | 6.80272e6i | 0.100902i | ||||||||
\(408\) | 2.50009e7 | − | 6.24283e7i | 0.368108 | − | 0.919180i | ||||
\(409\) | −8.93055e7 | −1.30529 | −0.652647 | − | 0.757662i | \(-0.726341\pi\) | ||||
−0.652647 | + | 0.757662i | \(0.726341\pi\) | |||||||
\(410\) | − | 1.28637e7i | − | 0.186644i | ||||||
\(411\) | 7.14474e7 | + | 2.86129e7i | 1.02911 | + | 0.412132i | ||||
\(412\) | 819204. | 0.0117139 | ||||||||
\(413\) | 2.91376e7i | 0.413622i | ||||||||
\(414\) | −2.31546e7 | − | 2.20882e7i | −0.326315 | − | 0.311286i | ||||
\(415\) | 9.32221e6 | 0.130429 | ||||||||
\(416\) | − | 2.23361e7i | − | 0.310261i | ||||||
\(417\) | −9.77458e6 | + | 2.44075e7i | −0.134800 | + | 0.336601i | ||||
\(418\) | 1.29526e7 | 0.177349 | ||||||||
\(419\) | 8.05066e7i | 1.09443i | 0.836991 | + | 0.547217i | \(0.184313\pi\) | ||||
−0.836991 | + | 0.547217i | \(0.815687\pi\) | |||||||
\(420\) | 3.09808e6 | + | 1.24070e6i | 0.0418162 | + | 0.0167463i | ||||
\(421\) | 6.22934e7 | 0.834825 | 0.417413 | − | 0.908717i | \(-0.362937\pi\) | ||||
0.417413 | + | 0.908717i | \(0.362937\pi\) | |||||||
\(422\) | 3.93484e7i | 0.523589i | ||||||||
\(423\) | 1.02297e8 | − | 1.07236e8i | 1.35158 | − | 1.41683i | ||||
\(424\) | −1.82302e7 | −0.239163 | ||||||||
\(425\) | 7.21647e7i | 0.940065i | ||||||||
\(426\) | −3.16201e7 | + | 7.89565e7i | −0.409010 | + | 1.02131i | ||||
\(427\) | 4.59843e6 | 0.0590645 | ||||||||
\(428\) | − | 7.28544e7i | − | 0.929232i | ||||||
\(429\) | 3.99212e6 | + | 1.59874e6i | 0.0505628 | + | 0.0202491i | ||||
\(430\) | 1.36107e7 | 0.171189 | ||||||||
\(431\) | − | 6.89532e7i | − | 0.861237i | −0.902534 | − | 0.430619i | \(-0.858295\pi\) | ||
0.902534 | − | 0.430619i | \(-0.141705\pi\) | |||||||
\(432\) | 2.89064e6 | − | 1.31889e6i | 0.0358544 | − | 0.0163590i | ||||
\(433\) | 7.87562e7 | 0.970110 | 0.485055 | − | 0.874484i | \(-0.338800\pi\) | ||||
0.485055 | + | 0.874484i | \(0.338800\pi\) | |||||||
\(434\) | − | 4.68885e6i | − | 0.0573585i | ||||||
\(435\) | −6.04898e6 | + | 1.51045e7i | −0.0734876 | + | 0.183501i | ||||
\(436\) | 2.12038e7 | 0.255831 | ||||||||
\(437\) | 9.63846e7i | 1.15495i | ||||||||
\(438\) | 1.26748e7 | + | 5.07593e6i | 0.150841 | + | 0.0604078i | ||||
\(439\) | −7.00109e7 | −0.827508 | −0.413754 | − | 0.910389i | \(-0.635783\pi\) | ||||
−0.413754 | + | 0.910389i | \(0.635783\pi\) | |||||||
\(440\) | − | 2.96439e6i | − | 0.0347999i | ||||||
\(441\) | −8.86544e6 | − | 8.45712e6i | −0.103368 | − | 0.0986068i | ||||
\(442\) | 1.67979e7 | 0.194531 | ||||||||
\(443\) | 1.12349e8i | 1.29229i | 0.763216 | + | 0.646143i | \(0.223619\pi\) | ||||
−0.763216 | + | 0.646143i | \(0.776381\pi\) | |||||||
\(444\) | 1.13767e7 | − | 2.84081e7i | 0.129977 | − | 0.324558i | ||||
\(445\) | 1.53126e7 | 0.173768 | ||||||||
\(446\) | 6.23156e7i | 0.702413i | ||||||||
\(447\) | 7.29924e7 | + | 2.92316e7i | 0.817251 | + | 0.327288i | ||||
\(448\) | 2.25433e7 | 0.250717 | ||||||||
\(449\) | − | 5.57815e7i | − | 0.616242i | −0.951347 | − | 0.308121i | \(-0.900300\pi\) | ||
0.951347 | − | 0.308121i | \(-0.0997002\pi\) | |||||||
\(450\) | −3.81998e7 | + | 4.00441e7i | −0.419202 | + | 0.439442i | ||||
\(451\) | −2.36299e7 | −0.257592 | ||||||||
\(452\) | 7.81473e7i | 0.846250i | ||||||||
\(453\) | −5.51324e7 | + | 1.37668e8i | −0.593078 | + | 1.48094i | ||||
\(454\) | −8.52853e7 | −0.911395 | ||||||||
\(455\) | 2.22236e6i | 0.0235928i | ||||||||
\(456\) | −1.44200e8 | − | 5.77484e7i | −1.52079 | − | 0.609040i | ||||
\(457\) | 7.88955e7 | 0.826616 | 0.413308 | − | 0.910591i | \(-0.364373\pi\) | ||||
0.413308 | + | 0.910591i | \(0.364373\pi\) | |||||||
\(458\) | − | 9.51280e7i | − | 0.990175i | ||||||
\(459\) | −3.92836e7 | − | 8.60987e7i | −0.406231 | − | 0.890346i | ||||
\(460\) | 8.27443e6 | 0.0850089 | ||||||||
\(461\) | 8.57691e7i | 0.875444i | 0.899110 | + | 0.437722i | \(0.144215\pi\) | ||||
−0.899110 | + | 0.437722i | \(0.855785\pi\) | |||||||
\(462\) | −1.51771e6 | + | 3.78977e6i | −0.0153908 | + | 0.0384315i | ||||
\(463\) | −8.76401e7 | −0.882998 | −0.441499 | − | 0.897262i | \(-0.645553\pi\) | ||||
−0.441499 | + | 0.897262i | \(0.645553\pi\) | |||||||
\(464\) | 3.91969e6i | 0.0392372i | ||||||||
\(465\) | 4.44805e6 | + | 1.78133e6i | 0.0442396 | + | 0.0177168i | ||||
\(466\) | 5.47441e7 | 0.540978 | ||||||||
\(467\) | − | 6.79717e6i | − | 0.0667387i | −0.999443 | − | 0.0333694i | \(-0.989376\pi\) | ||
0.999443 | − | 0.0333694i | \(-0.0106238\pi\) | |||||||
\(468\) | −1.39973e7 | − | 1.33526e7i | −0.136555 | − | 0.130266i | ||||
\(469\) | 6.78158e7 | 0.657374 | ||||||||
\(470\) | − | 2.55189e7i | − | 0.245793i | ||||||
\(471\) | 4.15999e7 | − | 1.03877e8i | 0.398134 | − | 0.994156i | ||||
\(472\) | −1.16428e8 | −1.10721 | ||||||||
\(473\) | − | 2.50021e7i | − | 0.236262i | ||||||
\(474\) | −3.49691e7 | − | 1.40042e7i | −0.328359 | − | 0.131499i | ||||
\(475\) | 1.66690e8 | 1.55535 | ||||||||
\(476\) | − | 2.39464e7i | − | 0.222034i | ||||||
\(477\) | −1.77083e7 | + | 1.85633e7i | −0.163163 | + | 0.171041i | ||||
\(478\) | −4.76372e7 | −0.436177 | ||||||||
\(479\) | − | 1.44663e8i | − | 1.31629i | −0.752891 | − | 0.658145i | \(-0.771341\pi\) | ||
0.752891 | − | 0.658145i | \(-0.228659\pi\) | |||||||
\(480\) | −8.05555e6 | + | 2.01150e7i | −0.0728403 | + | 0.181885i | ||||
\(481\) | 2.03780e7 | 0.183116 | ||||||||
\(482\) | 5.84804e7i | 0.522239i | ||||||||
\(483\) | −2.82009e7 | − | 1.12937e7i | −0.250277 | − | 0.100230i | ||||
\(484\) | 6.60157e7 | 0.582252 | ||||||||
\(485\) | 2.84911e7i | 0.249737i | ||||||||
\(486\) | 2.37772e7 | − | 6.85706e7i | 0.207134 | − | 0.597350i | ||||
\(487\) | −6.06863e7 | −0.525416 | −0.262708 | − | 0.964875i | \(-0.584616\pi\) | ||||
−0.262708 | + | 0.964875i | \(0.584616\pi\) | |||||||
\(488\) | 1.83744e7i | 0.158108i | ||||||||
\(489\) | 1.41782e7 | − | 3.54034e7i | 0.121253 | − | 0.302774i | ||||
\(490\) | −2.10971e6 | −0.0179323 | ||||||||
\(491\) | − | 1.76370e8i | − | 1.48998i | −0.667074 | − | 0.744991i | \(-0.732454\pi\) | ||
0.667074 | − | 0.744991i | \(-0.267546\pi\) | |||||||
\(492\) | 9.86781e7 | + | 3.95181e7i | 0.828563 | + | 0.331818i | ||||
\(493\) | 1.16749e8 | 0.974348 | ||||||||
\(494\) | − | 3.88006e7i | − | 0.321853i | ||||||
\(495\) | −3.01855e6 | − | 2.87953e6i | −0.0248876 | − | 0.0237414i | ||||
\(496\) | 1.15429e6 | 0.00945954 | ||||||||
\(497\) | 8.07412e7i | 0.657697i | ||||||||
\(498\) | 1.90710e7 | − | 4.76209e7i | 0.154413 | − | 0.385576i | ||||
\(499\) | −2.02073e7 | −0.162632 | −0.0813161 | − | 0.996688i | \(-0.525912\pi\) | ||||
−0.0813161 | + | 0.996688i | \(0.525912\pi\) | |||||||
\(500\) | − | 2.92071e7i | − | 0.233657i | ||||||
\(501\) | −1.89853e8 | − | 7.60313e7i | −1.50975 | − | 0.604615i | ||||
\(502\) | 8.76112e7 | 0.692546 | ||||||||
\(503\) | − | 8.81635e7i | − | 0.692763i | −0.938094 | − | 0.346382i | \(-0.887410\pi\) | ||
0.938094 | − | 0.346382i | \(-0.112590\pi\) | |||||||
\(504\) | 3.37928e7 | − | 3.54244e7i | 0.263957 | − | 0.276701i | ||||
\(505\) | 2.64391e6 | 0.0205293 | ||||||||
\(506\) | 1.01218e7i | 0.0781279i | ||||||||
\(507\) | −4.36614e7 | + | 1.09024e8i | −0.335022 | + | 0.836563i | ||||
\(508\) | −4.88460e7 | −0.372595 | ||||||||
\(509\) | − | 8.14242e7i | − | 0.617448i | −0.951152 | − | 0.308724i | \(-0.900098\pi\) | ||
0.951152 | − | 0.308724i | \(-0.0999019\pi\) | |||||||
\(510\) | −1.51275e7 | − | 6.05819e6i | −0.114040 | − | 0.0456701i | ||||
\(511\) | 1.29613e7 | 0.0971370 | ||||||||
\(512\) | 1.05717e7i | 0.0787651i | ||||||||
\(513\) | −1.98875e8 | + | 9.07393e7i | −1.47309 | + | 0.672115i | ||||
\(514\) | 6.06817e6 | 0.0446857 | ||||||||
\(515\) | − | 529207.i | − | 0.00387439i | ||||||
\(516\) | −4.18130e7 | + | 1.04409e8i | −0.304342 | + | 0.759954i | ||||
\(517\) | −4.68769e7 | −0.339225 | ||||||||
\(518\) | 1.93452e7i | 0.139182i | ||||||||
\(519\) | 2.39433e7 | + | 9.58868e6i | 0.171270 | + | 0.0685894i | ||||
\(520\) | −8.88006e6 | −0.0631547 | ||||||||
\(521\) | 1.28904e8i | 0.911491i | 0.890110 | + | 0.455745i | \(0.150627\pi\) | ||||
−0.890110 | + | 0.455745i | \(0.849373\pi\) | |||||||
\(522\) | 6.47841e7 | + | 6.18004e7i | 0.455467 | + | 0.434490i | ||||
\(523\) | −9.04202e7 | −0.632063 | −0.316032 | − | 0.948749i | \(-0.602351\pi\) | ||||
−0.316032 | + | 0.948749i | \(0.602351\pi\) | |||||||
\(524\) | − | 2.76405e7i | − | 0.192111i | ||||||
\(525\) | −1.95316e7 | + | 4.87712e7i | −0.134977 | + | 0.337043i | ||||
\(526\) | 1.18827e8 | 0.816503 | ||||||||
\(527\) | − | 3.43809e7i | − | 0.234902i | ||||||
\(528\) | −932956. | − | 373625.i | −0.00633810 | − | 0.00253825i | ||||
\(529\) | 7.27164e7 | 0.491208 | ||||||||
\(530\) | 4.41751e6i | 0.0296722i | ||||||||
\(531\) | −1.13094e8 | + | 1.18555e8i | −0.755366 | + | 0.791836i | ||||
\(532\) | −5.53127e7 | −0.367358 | ||||||||
\(533\) | 7.07851e7i | 0.467477i | ||||||||
\(534\) | 3.13259e7 | − | 7.82220e7i | 0.205722 | − | 0.513695i | ||||
\(535\) | −4.70640e7 | −0.307346 | ||||||||
\(536\) | 2.70977e8i | 1.75970i | ||||||||
\(537\) | 1.52687e8 | + | 6.11473e7i | 0.986006 | + | 0.394871i | ||||
\(538\) | 6.89088e7 | 0.442515 | ||||||||
\(539\) | 3.87543e6i | 0.0247488i | ||||||||
\(540\) | 7.78978e6 | + | 1.70730e7i | 0.0494702 | + | 0.108425i | ||||
\(541\) | 6.32413e7 | 0.399401 | 0.199700 | − | 0.979857i | \(-0.436003\pi\) | ||||
0.199700 | + | 0.979857i | \(0.436003\pi\) | |||||||
\(542\) | − | 7.00477e6i | − | 0.0439943i | ||||||
\(543\) | 3.92724e7 | − | 9.80647e7i | 0.245295 | − | 0.612510i | ||||
\(544\) | 1.55478e8 | 0.965765 | ||||||||
\(545\) | − | 1.36977e7i | − | 0.0846169i | ||||||
\(546\) | 1.13525e7 | + | 4.54640e6i | 0.0697453 | + | 0.0279312i | ||||
\(547\) | 5.93163e7 | 0.362420 | 0.181210 | − | 0.983444i | \(-0.441999\pi\) | ||||
0.181210 | + | 0.983444i | \(0.441999\pi\) | |||||||
\(548\) | 1.09509e8i | 0.665436i | ||||||||
\(549\) | 1.87101e7 | + | 1.78483e7i | 0.113073 | + | 0.107865i | ||||
\(550\) | 1.75049e7 | 0.105213 | ||||||||
\(551\) | − | 2.69674e8i | − | 1.61207i | ||||||
\(552\) | 4.51273e7 | − | 1.12685e8i | 0.268301 | − | 0.669957i | ||||
\(553\) | −3.57595e7 | −0.211454 | ||||||||
\(554\) | 4.65880e7i | 0.273997i | ||||||||
\(555\) | −1.83517e7 | − | 7.34937e6i | −0.107349 | − | 0.0429904i | ||||
\(556\) | −3.74097e7 | −0.217651 | ||||||||
\(557\) | 1.44815e7i | 0.0838005i | 0.999122 | + | 0.0419003i | \(0.0133412\pi\) | ||||
−0.999122 | + | 0.0419003i | \(0.986659\pi\) | |||||||
\(558\) | 1.81993e7 | − | 1.90779e7i | 0.104749 | − | 0.109807i | ||||
\(559\) | −7.48958e7 | −0.428767 | ||||||||
\(560\) | − | 519364.i | − | 0.00295738i | ||||||
\(561\) | −1.11286e7 | + | 2.77884e7i | −0.0630304 | + | 0.157389i | ||||
\(562\) | −9.67300e7 | −0.544944 | ||||||||
\(563\) | 1.93149e8i | 1.08235i | 0.840910 | + | 0.541175i | \(0.182020\pi\) | ||||
−0.840910 | + | 0.541175i | \(0.817980\pi\) | |||||||
\(564\) | 1.95757e8 | + | 7.83958e7i | 1.09114 | + | 0.436974i | ||||
\(565\) | 5.04833e7 | 0.279900 | ||||||||
\(566\) | − | 8.04855e7i | − | 0.443883i | ||||||
\(567\) | −3.24620e6 | − | 6.88205e7i | −0.0178085 | − | 0.377545i | ||||
\(568\) | −3.22624e8 | −1.76057 | ||||||||
\(569\) | − | 2.61758e8i | − | 1.42090i | −0.703749 | − | 0.710449i | \(-0.748492\pi\) | ||
0.703749 | − | 0.710449i | \(-0.251508\pi\) | |||||||
\(570\) | −1.39935e7 | + | 3.49423e7i | −0.0755617 | + | 0.188680i | ||||
\(571\) | −3.71956e7 | −0.199794 | −0.0998971 | − | 0.994998i | \(-0.531851\pi\) | ||||
−0.0998971 | + | 0.994998i | \(0.531851\pi\) | |||||||
\(572\) | 6.11878e6i | 0.0326947i | ||||||||
\(573\) | 2.55904e7 | + | 1.02483e7i | 0.136023 | + | 0.0544738i | ||||
\(574\) | −6.71972e7 | −0.355317 | ||||||||
\(575\) | 1.30259e8i | 0.685180i | ||||||||
\(576\) | 9.17240e7 | + | 8.74994e7i | 0.479971 | + | 0.457865i | ||||
\(577\) | 1.22705e8 | 0.638754 | 0.319377 | − | 0.947628i | \(-0.396526\pi\) | ||||
0.319377 | + | 0.947628i | \(0.396526\pi\) | |||||||
\(578\) | − | 5.15944e6i | − | 0.0267189i | ||||||
\(579\) | 8.63402e7 | − | 2.15595e8i | 0.444813 | − | 1.11071i | ||||
\(580\) | −2.31509e7 | −0.118655 | ||||||||
\(581\) | − | 4.86973e7i | − | 0.248300i | ||||||
\(582\) | 1.45542e8 | + | 5.82858e7i | 0.738276 | + | 0.295661i | ||||
\(583\) | 8.11474e6 | 0.0409514 | ||||||||
\(584\) | 5.17904e7i | 0.260022i | ||||||||
\(585\) | −8.62584e6 | + | 9.04230e6i | −0.0430857 | + | 0.0451660i | ||||
\(586\) | −1.32567e8 | −0.658783 | ||||||||
\(587\) | 1.30022e8i | 0.642840i | 0.946937 | + | 0.321420i | \(0.104160\pi\) | ||||
−0.946937 | + | 0.321420i | \(0.895840\pi\) | |||||||
\(588\) | 6.48118e6 | − | 1.61837e7i | 0.0318803 | − | 0.0796062i | ||||
\(589\) | −7.94148e7 | −0.388647 | ||||||||
\(590\) | 2.82125e7i | 0.137368i | ||||||||
\(591\) | −2.89018e8 | − | 1.15744e8i | −1.40011 | − | 0.560709i | ||||
\(592\) | −4.76234e6 | −0.0229538 | ||||||||
\(593\) | 499581.i | 0.00239575i | 0.999999 | + | 0.00119788i | \(0.000381296\pi\) | ||||
−0.999999 | + | 0.00119788i | \(0.999619\pi\) | |||||||
\(594\) | −2.08848e7 | + | 9.52896e6i | −0.0996486 | + | 0.0454659i | ||||
\(595\) | −1.54694e7 | −0.0734385 | ||||||||
\(596\) | 1.11877e8i | 0.528446i | ||||||||
\(597\) | 1.32461e8 | − | 3.30761e8i | 0.622539 | − | 1.55450i | ||||
\(598\) | 3.03206e7 | 0.141786 | ||||||||
\(599\) | − | 3.74144e8i | − | 1.74084i | −0.492312 | − | 0.870419i | \(-0.663848\pi\) | ||
0.492312 | − | 0.870419i | \(-0.336152\pi\) | |||||||
\(600\) | −1.94879e8 | − | 7.80441e7i | −0.902218 | − | 0.361315i | ||||
\(601\) | −1.80986e8 | −0.833722 | −0.416861 | − | 0.908970i | \(-0.636870\pi\) | ||||
−0.416861 | + | 0.908970i | \(0.636870\pi\) | |||||||
\(602\) | − | 7.10996e7i | − | 0.325895i | ||||||
\(603\) | 2.75928e8 | + | 2.63220e8i | 1.25847 | + | 1.20051i | ||||
\(604\) | −2.11005e8 | −0.957596 | ||||||||
\(605\) | − | 4.26463e7i | − | 0.192582i | ||||||
\(606\) | 5.40881e6 | − | 1.35060e7i | 0.0243043 | − | 0.0606888i | ||||
\(607\) | −3.74919e8 | −1.67637 | −0.838187 | − | 0.545383i | \(-0.816384\pi\) | ||||
−0.838187 | + | 0.545383i | \(0.816384\pi\) | |||||||
\(608\) | − | 3.59130e8i | − | 1.59787i | ||||||
\(609\) | 7.89029e7 | + | 3.15986e7i | 0.349334 | + | 0.139900i | ||||
\(610\) | 4.45244e6 | 0.0196159 | ||||||||
\(611\) | 1.40423e8i | 0.615624i | ||||||||
\(612\) | 9.29454e7 | − | 9.74329e7i | 0.405484 | − | 0.425061i | ||||
\(613\) | 1.88911e8 | 0.820118 | 0.410059 | − | 0.912059i | \(-0.365508\pi\) | ||||
0.410059 | + | 0.912059i | \(0.365508\pi\) | |||||||
\(614\) | 7.92310e7i | 0.342287i | ||||||||
\(615\) | 2.55288e7 | − | 6.37462e7i | 0.109750 | − | 0.274050i | ||||
\(616\) | −1.54854e7 | −0.0662491 | ||||||||
\(617\) | 1.92575e8i | 0.819867i | 0.912115 | + | 0.409933i | \(0.134448\pi\) | ||||
−0.912115 | + | 0.409933i | \(0.865552\pi\) | |||||||
\(618\) | −2.70336e6 | − | 1.08263e6i | −0.0114535 | − | 0.00458685i | ||||
\(619\) | 2.47431e8 | 1.04324 | 0.521618 | − | 0.853179i | \(-0.325328\pi\) | ||||
0.521618 | + | 0.853179i | \(0.325328\pi\) | |||||||
\(620\) | 6.81760e6i | 0.0286059i | ||||||||
\(621\) | −7.09079e7 | − | 1.55410e8i | −0.296087 | − | 0.648941i | ||||
\(622\) | −7.78996e7 | −0.323716 | ||||||||
\(623\) | − | 7.99900e7i | − | 0.330805i | ||||||
\(624\) | −1.11922e6 | + | 2.79474e6i | −0.00460641 | + | 0.0115024i | ||||
\(625\) | 2.15649e8 | 0.883299 | ||||||||
\(626\) | 8.88347e7i | 0.362126i | ||||||||
\(627\) | 6.41871e7 | + | 2.57053e7i | 0.260402 | + | 0.104285i | ||||
\(628\) | 1.59213e8 | 0.642836 | ||||||||
\(629\) | 1.41848e8i | 0.569995i | ||||||||
\(630\) | −8.58398e6 | − | 8.18862e6i | −0.0343295 | − | 0.0327483i | ||||
\(631\) | 1.43118e8 | 0.569649 | 0.284825 | − | 0.958580i | \(-0.408065\pi\) | ||||
0.284825 | + | 0.958580i | \(0.408065\pi\) | |||||||
\(632\) | − | 1.42887e8i | − | 0.566033i | ||||||
\(633\) | −7.80894e7 | + | 1.94992e8i | −0.307879 | + | 0.768786i | ||||
\(634\) | −1.91050e8 | −0.749684 | ||||||||
\(635\) | 3.15546e7i | 0.123237i | ||||||||
\(636\) | −3.38870e7 | − | 1.35709e7i | −0.131723 | − | 0.0527518i | ||||
\(637\) | 1.16091e7 | 0.0449140 | ||||||||
\(638\) | − | 2.83197e7i | − | 0.109050i | ||||||
\(639\) | −3.13388e8 | + | 3.28519e8i | −1.20110 | + | 1.25909i | ||||
\(640\) | −2.95338e7 | −0.112662 | ||||||||
\(641\) | 1.77654e8i | 0.674530i | 0.941410 | + | 0.337265i | \(0.109502\pi\) | ||||
−0.941410 | + | 0.337265i | \(0.890498\pi\) | |||||||
\(642\) | −9.62816e7 | + | 2.40419e8i | −0.363863 | + | 0.908580i | ||||
\(643\) | −1.61496e8 | −0.607477 | −0.303739 | − | 0.952755i | \(-0.598235\pi\) | ||||
−0.303739 | + | 0.952755i | \(0.598235\pi\) | |||||||
\(644\) | − | 4.32239e7i | − | 0.161833i | ||||||
\(645\) | 6.74481e7 | + | 2.70113e7i | 0.251357 | + | 0.100662i | ||||
\(646\) | 2.70084e8 | 1.00185 | ||||||||
\(647\) | 1.19839e8i | 0.442472i | 0.975220 | + | 0.221236i | \(0.0710092\pi\) | ||||
−0.975220 | + | 0.221236i | \(0.928991\pi\) | |||||||
\(648\) | 2.74992e8 | − | 1.29711e7i | 1.01064 | − | 0.0476708i | ||||
\(649\) | 5.18249e7 | 0.189585 | ||||||||
\(650\) | − | 5.24371e7i | − | 0.190941i | ||||||
\(651\) | 9.30531e6 | − | 2.32357e7i | 0.0337278 | − | 0.0842196i | ||||
\(652\) | 5.42634e7 | 0.195778 | ||||||||
\(653\) | − | 1.07660e8i | − | 0.386647i | −0.981135 | − | 0.193324i | \(-0.938073\pi\) | ||
0.981135 | − | 0.193324i | \(-0.0619268\pi\) | |||||||
\(654\) | −6.99722e7 | − | 2.80221e7i | −0.250145 | − | 0.100177i | ||||
\(655\) | −1.78558e7 | −0.0635413 | ||||||||
\(656\) | − | 1.65424e7i | − | 0.0585987i | ||||||
\(657\) | 5.27366e7 | + | 5.03077e7i | 0.185959 | + | 0.177394i | ||||
\(658\) | −1.33306e8 | −0.467919 | ||||||||
\(659\) | 4.17916e8i | 1.46027i | 0.683303 | + | 0.730135i | \(0.260543\pi\) | ||||
−0.683303 | + | 0.730135i | \(0.739457\pi\) | |||||||
\(660\) | 2.20675e6 | − | 5.51033e6i | 0.00767575 | − | 0.0191666i | ||||
\(661\) | 4.82007e8 | 1.66897 | 0.834486 | − | 0.551028i | \(-0.185764\pi\) | ||||
0.834486 | + | 0.551028i | \(0.185764\pi\) | |||||||
\(662\) | 1.78758e7i | 0.0616159i | ||||||||
\(663\) | 8.32423e7 | + | 3.33364e7i | 0.285630 | + | 0.114387i | ||||
\(664\) | 1.94584e8 | 0.664665 | ||||||||
\(665\) | 3.57321e7i | 0.121505i | ||||||||
\(666\) | −7.50861e7 | + | 7.87113e7i | −0.254177 | + | 0.266449i | ||||
\(667\) | 2.10736e8 | 0.710167 | ||||||||
\(668\) | − | 2.90991e8i | − | 0.976224i | ||||||
\(669\) | −1.23669e8 | + | 3.08806e8i | −0.413031 | + | 1.03135i | ||||
\(670\) | 6.56628e7 | 0.218321 | ||||||||
\(671\) | − | 8.17890e6i | − | 0.0270724i | ||||||
\(672\) | 1.05077e8 | + | 4.20806e7i | 0.346257 | + | 0.138667i | ||||
\(673\) | −3.60190e8 | −1.18164 | −0.590822 | − | 0.806802i | \(-0.701196\pi\) | ||||
−0.590822 | + | 0.806802i | \(0.701196\pi\) | |||||||
\(674\) | − | 2.33238e8i | − | 0.761761i | ||||||
\(675\) | −2.68770e8 | + | 1.22630e8i | −0.873915 | + | 0.398735i | ||||
\(676\) | −1.67103e8 | −0.540934 | ||||||||
\(677\) | 6.06843e7i | 0.195574i | 0.995207 | + | 0.0977869i | \(0.0311763\pi\) | ||||
−0.995207 | + | 0.0977869i | \(0.968824\pi\) | |||||||
\(678\) | 1.03277e8 | − | 2.57885e8i | 0.331370 | − | 0.827442i | ||||
\(679\) | 1.48831e8 | 0.475429 | ||||||||
\(680\) | − | 6.18125e7i | − | 0.196585i | ||||||
\(681\) | −4.22633e8 | − | 1.69254e8i | −1.33820 | − | 0.535916i | ||||
\(682\) | −8.33972e6 | −0.0262905 | ||||||||
\(683\) | 1.72870e8i | 0.542573i | 0.962499 | + | 0.271287i | \(0.0874492\pi\) | ||||
−0.962499 | + | 0.271287i | \(0.912551\pi\) | |||||||
\(684\) | −2.25055e8 | − | 2.14690e8i | −0.703269 | − | 0.670878i | ||||
\(685\) | 7.07427e7 | 0.220095 | ||||||||
\(686\) | 1.10207e7i | 0.0341379i | ||||||||
\(687\) | 1.88787e8 | − | 4.71409e8i | 0.582240 | − | 1.45388i | ||||
\(688\) | 1.75031e7 | 0.0537464 | ||||||||
\(689\) | − | 2.43083e7i | − | 0.0743185i | ||||||
\(690\) | −2.73055e7 | − | 1.09352e7i | −0.0831196 | − | 0.0332873i | ||||
\(691\) | 1.06853e8 | 0.323856 | 0.161928 | − | 0.986803i | \(-0.448229\pi\) | ||||
0.161928 | + | 0.986803i | \(0.448229\pi\) | |||||||
\(692\) | 3.66983e7i | 0.110746i | ||||||||
\(693\) | −1.50421e7 | + | 1.57683e7i | −0.0451968 | + | 0.0473789i | ||||
\(694\) | 1.34950e8 | 0.403732 | ||||||||
\(695\) | 2.41668e7i | 0.0719886i | ||||||||
\(696\) | −1.26261e8 | + | 3.15279e8i | −0.374492 | + | 0.935120i | ||||
\(697\) | −4.92722e8 | −1.45514 | ||||||||
\(698\) | − | 5.40241e7i | − | 0.158862i | ||||||
\(699\) | 2.71285e8 | + | 1.08643e8i | 0.794319 | + | 0.318104i | ||||
\(700\) | −7.47523e7 | −0.217937 | ||||||||
\(701\) | − | 2.10475e8i | − | 0.611007i | −0.952191 | − | 0.305503i | \(-0.901175\pi\) | ||
0.952191 | − | 0.305503i | \(-0.0988247\pi\) | |||||||
\(702\) | 2.85447e7 | + | 6.25620e7i | 0.0825114 | + | 0.180842i | ||||
\(703\) | 3.27647e8 | 0.943063 | ||||||||
\(704\) | − | 4.00961e7i | − | 0.114917i | ||||||
\(705\) | 5.06439e7 | − | 1.26460e8i | 0.144530 | − | 0.360898i | ||||
\(706\) | 3.19279e7 | 0.0907310 | ||||||||
\(707\) | − | 1.38113e7i | − | 0.0390819i | ||||||
\(708\) | −2.16420e8 | − | 8.66707e7i | −0.609814 | − | 0.244215i | ||||
\(709\) | −4.24747e8 | −1.19177 | −0.595884 | − | 0.803070i | \(-0.703198\pi\) | ||||
−0.595884 | + | 0.803070i | \(0.703198\pi\) | |||||||
\(710\) | 7.81778e7i | 0.218428i | ||||||||
\(711\) | −1.45498e8 | − | 1.38796e8i | −0.404806 | − | 0.386162i | ||||
\(712\) | 3.19623e8 | 0.885519 | ||||||||
\(713\) | − | 6.20584e7i | − | 0.171211i | ||||||
\(714\) | −3.16467e7 | + | 7.90230e7i | −0.0869429 | + | 0.217100i | ||||
\(715\) | 3.95274e6 | 0.0108139 | ||||||||
\(716\) | 2.34026e8i | 0.637566i | ||||||||
\(717\) | −2.36067e8 | − | 9.45389e7i | −0.640440 | − | 0.256480i | ||||
\(718\) | −1.36771e8 | −0.369506 | ||||||||
\(719\) | 2.09831e8i | 0.564526i | 0.959337 | + | 0.282263i | \(0.0910851\pi\) | ||||
−0.959337 | + | 0.282263i | \(0.908915\pi\) | |||||||
\(720\) | 2.01585e6 | − | 2.11318e6i | 0.00540084 | − | 0.00566160i | ||||
\(721\) | −2.76447e6 | −0.00737574 | ||||||||
\(722\) | − | 3.85898e8i | − | 1.02532i | ||||||
\(723\) | −1.16058e8 | + | 2.89801e8i | −0.307086 | + | 0.766805i | ||||
\(724\) | 1.50305e8 | 0.396058 | ||||||||
\(725\) | − | 3.64451e8i | − | 0.956367i | ||||||
\(726\) | −2.17851e8 | − | 8.72440e7i | −0.569312 | − | 0.227995i | ||||
\(727\) | −6.02308e7 | −0.156753 | −0.0783765 | − | 0.996924i | \(-0.524974\pi\) | ||||
−0.0783765 | + | 0.996924i | \(0.524974\pi\) | |||||||
\(728\) | 4.63876e7i | 0.120229i | ||||||||
\(729\) | 2.53911e8 | − | 2.92616e8i | 0.655388 | − | 0.755292i | ||||
\(730\) | 1.25498e7 | 0.0322602 | ||||||||
\(731\) | − | 5.21336e8i | − | 1.33464i | ||||||
\(732\) | −1.36782e7 | + | 3.41550e7i | −0.0348735 | + | 0.0870804i | ||||
\(733\) | 2.24031e8 | 0.568847 | 0.284423 | − | 0.958699i | \(-0.408198\pi\) | ||||
0.284423 | + | 0.958699i | \(0.408198\pi\) | |||||||
\(734\) | 3.86314e8i | 0.976906i | ||||||||
\(735\) | −1.04547e7 | − | 4.18685e6i | −0.0263300 | − | 0.0105445i | ||||
\(736\) | 2.80641e8 | 0.703911 | ||||||||
\(737\) | − | 1.20619e8i | − | 0.301310i | ||||||
\(738\) | −2.73411e8 | − | 2.60819e8i | −0.680217 | − | 0.648888i | ||||
\(739\) | 1.32642e8 | 0.328660 | 0.164330 | − | 0.986405i | \(-0.447454\pi\) | ||||
0.164330 | + | 0.986405i | \(0.447454\pi\) | |||||||
\(740\) | − | 2.81279e7i | − | 0.0694131i | ||||||
\(741\) | 7.70021e7 | − | 1.92277e8i | 0.189255 | − | 0.472578i | ||||
\(742\) | 2.30762e7 | 0.0564875 | ||||||||
\(743\) | − | 3.18777e8i | − | 0.777178i | −0.921411 | − | 0.388589i | \(-0.872963\pi\) | ||
0.921411 | − | 0.388589i | \(-0.127037\pi\) | |||||||
\(744\) | 9.28449e7 | + | 3.71820e7i | 0.225444 | + | 0.0902847i | ||||
\(745\) | 7.22725e7 | 0.174785 | ||||||||
\(746\) | 2.91675e8i | 0.702558i | ||||||||
\(747\) | 1.89013e8 | − | 1.98139e8i | 0.453451 | − | 0.475344i | ||||
\(748\) | −4.25918e7 | −0.101770 | ||||||||
\(749\) | 2.45853e8i | 0.585100i | ||||||||
\(750\) | −3.85991e7 | + | 9.63833e7i | −0.0914941 | + | 0.228464i | ||||
\(751\) | 5.79013e8 | 1.36700 | 0.683500 | − | 0.729951i | \(-0.260457\pi\) | ||||
0.683500 | + | 0.729951i | \(0.260457\pi\) | |||||||
\(752\) | − | 3.28168e7i | − | 0.0771691i | ||||||
\(753\) | 4.34159e8 | + | 1.73870e8i | 1.01687 | + | 0.407229i | ||||
\(754\) | −8.48337e7 | −0.197904 | ||||||||
\(755\) | 1.36310e8i | 0.316728i | ||||||||
\(756\) | 8.91860e7 | − | 4.06922e7i | 0.206410 | − | 0.0941773i | ||||
\(757\) | −5.93337e8 | −1.36777 | −0.683886 | − | 0.729589i | \(-0.739712\pi\) | ||||
−0.683886 | + | 0.729589i | \(0.739712\pi\) | |||||||
\(758\) | 1.65982e8i | 0.381113i | ||||||||
\(759\) | −2.00873e7 | + | 5.01588e7i | −0.0459406 | + | 0.114715i | ||||
\(760\) | −1.42778e8 | −0.325252 | ||||||||
\(761\) | 5.95666e8i | 1.35160i | 0.737084 | + | 0.675801i | \(0.236202\pi\) | ||||
−0.737084 | + | 0.675801i | \(0.763798\pi\) | |||||||
\(762\) | 1.61191e8 | + | 6.45530e7i | 0.364315 | + | 0.145899i | ||||
\(763\) | −7.15538e7 | −0.161086 | ||||||||
\(764\) | 3.92227e7i | 0.0879545i | ||||||||
\(765\) | −6.29418e7 | − | 6.00429e7i | −0.140590 | − | 0.134115i | ||||
\(766\) | −1.55226e8 | −0.345365 | ||||||||
\(767\) | − | 1.55245e8i | − | 0.344059i | ||||||
\(768\) | −1.72129e8 | + | 4.29812e8i | −0.379988 | + | 0.948844i | ||||
\(769\) | −6.24679e8 | −1.37366 | −0.686828 | − | 0.726820i | \(-0.740997\pi\) | ||||
−0.686828 | + | 0.726820i | \(0.740997\pi\) | |||||||
\(770\) | 3.75239e6i | 0.00821932i | ||||||||
\(771\) | 3.00709e7 | + | 1.20426e7i | 0.0656121 | + | 0.0262760i | ||||
\(772\) | 3.30445e8 | 0.718204 | ||||||||
\(773\) | − | 1.23150e8i | − | 0.266623i | −0.991074 | − | 0.133311i | \(-0.957439\pi\) | ||
0.991074 | − | 0.133311i | \(-0.0425610\pi\) | |||||||
\(774\) | 2.75965e8 | − | 2.89289e8i | 0.595157 | − | 0.623891i | ||||
\(775\) | −1.07325e8 | −0.230567 | ||||||||
\(776\) | 5.94698e8i | 1.27266i | ||||||||
\(777\) | −3.83916e7 | + | 9.58653e7i | −0.0818415 | + | 0.204361i | ||||
\(778\) | −4.29142e7 | −0.0911301 | ||||||||
\(779\) | 1.13811e9i | 2.40754i | ||||||||
\(780\) | −1.65066e7 | − | 6.61048e6i | −0.0347835 | − | 0.0139299i | ||||
\(781\) | 1.43608e8 | 0.301458 | ||||||||
\(782\) | 2.11056e8i | 0.441345i | ||||||||
\(783\) | 1.98393e8 | + | 4.34821e8i | 0.413276 | + | 0.905785i | ||||
\(784\) | −2.71305e6 | −0.00563002 | ||||||||
\(785\) | − | 1.02852e8i | − | 0.212620i | ||||||
\(786\) | −3.65287e7 | + | 9.12136e7i | −0.0752258 | + | 0.187842i | ||||
\(787\) | −7.93771e8 | −1.62844 | −0.814219 | − | 0.580558i | \(-0.802834\pi\) | ||||
−0.814219 | + | 0.580558i | \(0.802834\pi\) | |||||||
\(788\) | − | 4.42982e8i | − | 0.905331i | ||||||
\(789\) | 5.88849e8 | + | 2.35819e8i | 1.19887 | + | 0.480118i | ||||
\(790\) | −3.46242e7 | −0.0702260 | ||||||||
\(791\) | − | 2.63714e8i | − | 0.532849i | ||||||
\(792\) | −6.30067e7 | − | 6.01048e7i | −0.126827 | − | 0.120986i | ||||
\(793\) | −2.45005e7 | −0.0491310 | ||||||||
\(794\) | 3.57310e8i | 0.713813i | ||||||||
\(795\) | −8.76682e6 | + | 2.18911e7i | −0.0174478 | + | 0.0435678i | ||||
\(796\) | 5.06963e8 | 1.00516 | ||||||||
\(797\) | − | 8.56808e8i | − | 1.69242i | −0.532848 | − | 0.846211i | \(-0.678878\pi\) | ||
0.532848 | − | 0.846211i | \(-0.321122\pi\) | |||||||
\(798\) | 1.82531e8 | + | 7.30992e7i | 0.359194 | + | 0.143848i | ||||
\(799\) | −9.77461e8 | −1.91628 | ||||||||
\(800\) | − | 4.85347e8i | − | 0.947943i | ||||||
\(801\) | 3.10473e8 | − | 3.25462e8i | 0.604123 | − | 0.633291i | ||||
\(802\) | −1.78314e8 | −0.345670 | ||||||||
\(803\) | − | 2.30532e7i | − | 0.0445231i | ||||||
\(804\) | −2.01720e8 | + | 5.03703e8i | −0.388134 | + | 0.969185i | ||||
\(805\) | −2.79227e7 | −0.0535267 | ||||||||
\(806\) | 2.49822e7i | 0.0477119i | ||||||||
\(807\) | 3.41479e8 | + | 1.36754e8i | 0.649746 | + | 0.260207i | ||||
\(808\) | 5.51868e7 | 0.104617 | ||||||||
\(809\) | − | 3.69671e8i | − | 0.698184i | −0.937088 | − | 0.349092i | \(-0.886490\pi\) | ||
0.937088 | − | 0.349092i | \(-0.113510\pi\) | |||||||
\(810\) | −3.14314e6 | − | 6.66355e7i | −0.00591437 | − | 0.125386i | ||||
\(811\) | 7.57101e8 | 1.41936 | 0.709678 | − | 0.704526i | \(-0.248840\pi\) | ||||
0.709678 | + | 0.704526i | \(0.248840\pi\) | |||||||
\(812\) | 1.20936e8i | 0.225885i | ||||||||
\(813\) | 1.39014e7 | − | 3.47123e7i | 0.0258694 | − | 0.0645969i | ||||
\(814\) | 3.44078e7 | 0.0637946 | ||||||||
\(815\) | − | 3.50543e7i | − | 0.0647542i | ||||||
\(816\) | −1.94537e7 | − | 7.79071e6i | −0.0358040 | − | 0.0143386i | ||||
\(817\) | −1.20421e9 | −2.20818 | ||||||||
\(818\) | 4.51702e8i | 0.825263i | ||||||||
\(819\) | 4.72351e7 | + | 4.50596e7i | 0.0859831 | + | 0.0820230i | ||||
\(820\) | 9.77048e7 | 0.177204 | ||||||||
\(821\) | − | 9.58875e8i | − | 1.73274i | −0.499406 | − | 0.866368i | \(-0.666448\pi\) | ||
0.499406 | − | 0.866368i | \(-0.333552\pi\) | |||||||
\(822\) | 1.44722e8 | − | 3.61377e8i | 0.260568 | − | 0.650647i | ||||
\(823\) | 8.30255e8 | 1.48940 | 0.744701 | − | 0.667398i | \(-0.232592\pi\) | ||||
0.744701 | + | 0.667398i | \(0.232592\pi\) | |||||||
\(824\) | − | 1.10462e7i | − | 0.0197439i | ||||||
\(825\) | 8.67457e7 | + | 3.47394e7i | 0.154485 | + | 0.0618673i | ||||
\(826\) | 1.47376e8 | 0.261510 | ||||||||
\(827\) | − | 7.38927e8i | − | 1.30643i | −0.757174 | − | 0.653213i | \(-0.773420\pi\) | ||
0.757174 | − | 0.653213i | \(-0.226580\pi\) | |||||||
\(828\) | 1.67769e8 | − | 1.75869e8i | 0.295543 | − | 0.309812i | ||||
\(829\) | 4.57605e8 | 0.803207 | 0.401603 | − | 0.915814i | \(-0.368453\pi\) | ||||
0.401603 | + | 0.915814i | \(0.368453\pi\) | |||||||
\(830\) | − | 4.71512e7i | − | 0.0824630i | ||||||
\(831\) | −9.24568e7 | + | 2.30868e8i | −0.161115 | + | 0.402310i | ||||
\(832\) | −1.20111e8 | −0.208551 | ||||||||
\(833\) | 8.08092e7i | 0.139806i | ||||||||
\(834\) | 1.23452e8 | + | 4.94393e7i | 0.212814 | + | 0.0852264i | ||||
\(835\) | −1.87980e8 | −0.322889 | ||||||||
\(836\) | 9.83805e7i | 0.168380i | ||||||||
\(837\) | 1.28048e8 | − | 5.84236e7i | 0.218372 | − | 0.0996350i | ||||
\(838\) | 4.07198e8 | 0.691949 | ||||||||
\(839\) | 2.73528e8i | 0.463143i | 0.972818 | + | 0.231572i | \(0.0743867\pi\) | ||||
−0.972818 | + | 0.231572i | \(0.925613\pi\) | |||||||
\(840\) | 1.67298e7 | − | 4.17748e7i | 0.0282262 | − | 0.0704818i | ||||
\(841\) | 5.20830e6 | 0.00875605 | ||||||||
\(842\) | − | 3.15077e8i | − | 0.527813i | ||||||
\(843\) | −4.79347e8 | − | 1.91966e8i | −0.800143 | − | 0.320437i | ||||
\(844\) | −2.98867e8 | −0.497108 | ||||||||
\(845\) | 1.07949e8i | 0.178915i | ||||||||
\(846\) | −5.42392e8 | − | 5.17411e8i | −0.895782 | − | 0.854525i | ||||
\(847\) | −2.22775e8 | −0.366621 | ||||||||
\(848\) | 5.68084e6i | 0.00931590i | ||||||||
\(849\) | 1.59728e8 | − | 3.98848e8i | 0.261011 | − | 0.651754i | ||||
\(850\) | 3.65005e8 | 0.594350 | ||||||||
\(851\) | 2.56039e8i | 0.415449i | ||||||||
\(852\) | −5.99707e8 | − | 2.40167e8i | −0.969661 | − | 0.388325i | ||||
\(853\) | −6.33977e8 | −1.02147 | −0.510736 | − | 0.859738i | \(-0.670627\pi\) | ||||
−0.510736 | + | 0.859738i | \(0.670627\pi\) | |||||||
\(854\) | − | 2.32586e7i | − | 0.0373431i | ||||||
\(855\) | −1.38690e8 | + | 1.45386e8i | −0.221895 | + | 0.232608i | ||||
\(856\) | −9.82375e8 | −1.56623 | ||||||||
\(857\) | − | 3.02812e8i | − | 0.481095i | −0.970637 | − | 0.240548i | \(-0.922673\pi\) | ||
0.970637 | − | 0.240548i | \(-0.0773270\pi\) | |||||||
\(858\) | 8.08635e6 | − | 2.01919e7i | 0.0128024 | − | 0.0319680i | ||||
\(859\) | 9.67375e7 | 0.152621 | 0.0763107 | − | 0.997084i | \(-0.475686\pi\) | ||||
0.0763107 | + | 0.997084i | \(0.475686\pi\) | |||||||
\(860\) | 1.03379e8i | 0.162531i | ||||||||
\(861\) | −3.32997e8 | − | 1.33357e8i | −0.521712 | − | 0.208933i | ||||
\(862\) | −3.48762e8 | −0.544512 | ||||||||
\(863\) | 8.09109e8i | 1.25885i | 0.777061 | + | 0.629426i | \(0.216710\pi\) | ||||
−0.777061 | + | 0.629426i | \(0.783290\pi\) | |||||||
\(864\) | 2.64204e8 | + | 5.79061e8i | 0.409636 | + | 0.897807i | ||||
\(865\) | 2.37071e7 | 0.0366295 | ||||||||
\(866\) | − | 3.98345e8i | − | 0.613346i | ||||||
\(867\) | 1.02392e7 | − | 2.55677e7i | 0.0157112 | − | 0.0392315i | ||||
\(868\) | 3.56137e7 | 0.0544576 | ||||||||
\(869\) | 6.36027e7i | 0.0969207i | ||||||||
\(870\) | 7.63979e7 | + | 3.05954e7i | 0.116017 | + | 0.0464621i | ||||
\(871\) | −3.61323e8 | −0.546816 | ||||||||
\(872\) | − | 2.85914e8i | − | 0.431206i | ||||||
\(873\) | 6.05563e8 | + | 5.77673e8i | 0.910158 | + | 0.868239i | ||||
\(874\) | 4.87509e8 | 0.730210 | ||||||||
\(875\) | 9.85619e7i | 0.147124i | ||||||||
\(876\) | −3.85537e7 | + | 9.62700e7i | −0.0573527 | + | 0.143212i | ||||
\(877\) | 3.70800e8 | 0.549719 | 0.274860 | − | 0.961484i | \(-0.411369\pi\) | ||||
0.274860 | + | 0.961484i | \(0.411369\pi\) | |||||||
\(878\) | 3.54112e8i | 0.523187i | ||||||||
\(879\) | −6.56938e8 | − | 2.63087e8i | −0.967292 | − | 0.387376i | ||||
\(880\) | −923754. | −0.00135553 | ||||||||
\(881\) | − | 1.00505e9i | − | 1.46980i | −0.678175 | − | 0.734900i | \(-0.737229\pi\) | ||
0.678175 | − | 0.734900i | \(-0.262771\pi\) | |||||||
\(882\) | −4.27757e7 | + | 4.48409e7i | −0.0623435 | + | 0.0653535i | ||||
\(883\) | 9.82183e8 | 1.42663 | 0.713313 | − | 0.700846i | \(-0.247194\pi\) | ||||
0.713313 | + | 0.700846i | \(0.247194\pi\) | |||||||
\(884\) | 1.27587e8i | 0.184692i | ||||||||
\(885\) | −5.59895e7 | + | 1.39808e8i | −0.0807749 | + | 0.201698i | ||||
\(886\) | 5.68256e8 | 0.817039 | ||||||||
\(887\) | − | 1.55330e8i | − | 0.222579i | −0.993788 | − | 0.111290i | \(-0.964502\pi\) | ||
0.993788 | − | 0.111290i | \(-0.0354981\pi\) | |||||||
\(888\) | −3.83057e8 | − | 1.53405e8i | −0.547047 | − | 0.219078i | ||||
\(889\) | 1.64835e8 | 0.234608 | ||||||||
\(890\) | − | 7.74505e7i | − | 0.109864i | ||||||
\(891\) | −1.22406e8 | + | 5.77378e6i | −0.173049 | + | 0.00816257i | ||||
\(892\) | −4.73312e8 | −0.666889 | ||||||||
\(893\) | 2.25779e9i | 3.17051i | ||||||||
\(894\) | 1.47852e8 | − | 3.69192e8i | 0.206926 | − | 0.516702i | ||||
\(895\) | 1.51181e8 | 0.210877 | ||||||||
\(896\) | 1.54278e8i | 0.214477i | ||||||||
\(897\) | 1.50254e8 | + | 6.01731e7i | 0.208185 | + | 0.0833729i | ||||
\(898\) | −2.82140e8 | −0.389615 | ||||||||
\(899\) | 1.73633e8i | 0.238975i | ||||||||
\(900\) | −3.04151e8 | − | 2.90143e8i | −0.417217 | − | 0.398001i | ||||
\(901\) | 1.69206e8 | 0.231335 | ||||||||
\(902\) | 1.19519e8i | 0.162861i | ||||||||
\(903\) | 1.41101e8 | − | 3.52335e8i | 0.191632 | − | 0.478512i | ||||
\(904\) | 1.05375e9 | 1.42636 | ||||||||
\(905\) | − | 9.70975e7i | − | 0.130997i | ||||||
\(906\) | 6.96315e8 | + | 2.78857e8i | 0.936314 | + | 0.374970i | ||||
\(907\) | −2.18956e7 | −0.0293451 | −0.0146725 | − | 0.999892i | \(-0.504671\pi\) | ||||
−0.0146725 | + | 0.999892i | \(0.504671\pi\) | |||||||
\(908\) | − | 6.47776e8i | − | 0.865301i | ||||||
\(909\) | 5.36069e7 | − | 5.61951e7i | 0.0713722 | − | 0.0748181i | ||||
\(910\) | 1.12406e7 | 0.0149164 | ||||||||
\(911\) | 1.45755e9i | 1.92783i | 0.266207 | + | 0.963916i | \(0.414229\pi\) | ||||
−0.266207 | + | 0.963916i | \(0.585771\pi\) | |||||||
\(912\) | −1.79954e7 | + | 4.49351e7i | −0.0237234 | + | 0.0592381i | ||||
\(913\) | −8.66143e7 | −0.113809 | ||||||||
\(914\) | − | 3.99049e8i | − | 0.522622i | ||||||
\(915\) | 2.20642e7 | + | 8.83614e6i | 0.0288021 | + | 0.0115345i | ||||
\(916\) | 7.22535e8 | 0.940097 | ||||||||
\(917\) | 9.32752e7i | 0.120965i | ||||||||
\(918\) | −4.35483e8 | + | 1.98695e8i | −0.562915 | + | 0.256837i | ||||
\(919\) | 2.19853e8 | 0.283260 | 0.141630 | − | 0.989920i | \(-0.454766\pi\) | ||||
0.141630 | + | 0.989920i | \(0.454766\pi\) | |||||||
\(920\) | − | 1.11573e8i | − | 0.143284i | ||||||
\(921\) | −1.57239e8 | + | 3.92631e8i | −0.201271 | + | 0.502580i | ||||
\(922\) | 4.33816e8 | 0.553494 | ||||||||
\(923\) | − | 4.30190e8i | − | 0.547085i | ||||||
\(924\) | −2.87848e7 | − | 1.15276e7i | −0.0364878 | − | 0.0146124i | ||||
\(925\) | 4.42799e8 | 0.559476 | ||||||||
\(926\) | 4.43279e8i | 0.558270i | ||||||||
\(927\) | −1.12480e7 | − | 1.07300e7i | −0.0141201 | − | 0.0134698i | ||||
\(928\) | −7.85203e8 | −0.982512 | ||||||||
\(929\) | − | 7.14835e8i | − | 0.891576i | −0.895138 | − | 0.445788i | \(-0.852923\pi\) | ||
0.895138 | − | 0.445788i | \(-0.147077\pi\) | |||||||
\(930\) | 9.00989e6 | − | 2.24980e7i | 0.0112014 | − | 0.0279702i | ||||
\(931\) | 1.86657e8 | 0.231311 | ||||||||
\(932\) | 4.15803e8i | 0.513618i | ||||||||
\(933\) | −3.86033e8 | − | 1.54596e8i | −0.475313 | − | 0.190351i | ||||
\(934\) | −3.43798e7 | −0.0421951 | ||||||||
\(935\) | 2.75143e7i | 0.0336608i | ||||||||
\(936\) | −1.80048e8 | + | 1.88741e8i | −0.219564 | + | 0.230165i | ||||
\(937\) | 1.23168e9 | 1.49719 | 0.748597 | − | 0.663025i | \(-0.230728\pi\) | ||||
0.748597 | + | 0.663025i | \(0.230728\pi\) | |||||||
\(938\) | − | 3.43009e8i | − | 0.415621i | ||||||
\(939\) | −1.76298e8 | + | 4.40222e8i | −0.212937 | + | 0.531710i | ||||
\(940\) | 1.93827e8 | 0.233362 | ||||||||
\(941\) | 1.03258e9i | 1.23924i | 0.784904 | + | 0.619618i | \(0.212712\pi\) | ||||
−0.784904 | + | 0.619618i | \(0.787288\pi\) | |||||||
\(942\) | −5.25402e8 | − | 2.10410e8i | −0.628549 | − | 0.251718i | ||||
\(943\) | −8.89376e8 | −1.06060 | ||||||||
\(944\) | 3.62807e7i | 0.0431281i | ||||||||
\(945\) | −2.62873e7 | − | 5.76143e7i | −0.0311494 | − | 0.0682708i | ||||
\(946\) | −1.26460e8 | −0.149375 | ||||||||
\(947\) | 5.32292e8i | 0.626758i | 0.949628 | + | 0.313379i | \(0.101461\pi\) | ||||
−0.949628 | + | 0.313379i | \(0.898539\pi\) | |||||||
\(948\) | 1.06368e8 | − | 2.65604e8i | 0.124849 | − | 0.311752i | ||||
\(949\) | −6.90577e7 | −0.0808004 | ||||||||
\(950\) | − | 8.43107e8i | − | 0.983359i | ||||||
\(951\) | −9.46750e8 | − | 3.79149e8i | −1.10076 | − | 0.440828i | ||||
\(952\) | −3.22896e8 | −0.374241 | ||||||||
\(953\) | 5.77302e7i | 0.0666998i | 0.999444 | + | 0.0333499i | \(0.0106176\pi\) | ||||
−0.999444 | + | 0.0333499i | \(0.989382\pi\) | |||||||
\(954\) | 9.38921e7 | + | 8.95677e7i | 0.108139 | + | 0.103159i | ||||
\(955\) | 2.53380e7 | 0.0290912 | ||||||||
\(956\) | − | 3.61824e8i | − | 0.414117i | ||||||
\(957\) | 5.62021e7 | − | 1.40339e8i | 0.0641235 | − | 0.160119i | ||||
\(958\) | −7.31699e8 | −0.832216 | ||||||||
\(959\) | − | 3.69545e8i | − | 0.418998i | ||||||
\(960\) | 1.08167e8 | + | 4.33182e7i | 0.122259 | + | 0.0489617i | ||||
\(961\) | −8.36371e8 | −0.942386 | ||||||||
\(962\) | − | 1.03071e8i | − | 0.115774i | ||||||
\(963\) | −9.54251e8 | + | 1.00032e9i | −1.06852 | + | 1.12011i | ||||
\(964\) | −4.44182e8 | −0.495827 | ||||||||
\(965\) | − | 2.13468e8i | − | 0.237548i | ||||||
\(966\) | −5.71231e7 | + | 1.42639e8i | −0.0633695 | + | 0.158236i | ||||
\(967\) | 1.16749e9 | 1.29114 | 0.645572 | − | 0.763699i | \(-0.276619\pi\) | ||||
0.645572 | + | 0.763699i | \(0.276619\pi\) | |||||||
\(968\) | − | 8.90163e8i | − | 0.981394i | ||||||
\(969\) | 1.33841e9 | + | 5.35998e8i | 1.47101 | + | 0.589104i | ||||
\(970\) | 1.44106e8 | 0.157895 | ||||||||
\(971\) | − | 1.00383e9i | − | 1.09648i | −0.836320 | − | 0.548242i | \(-0.815297\pi\) | ||
0.836320 | − | 0.548242i | \(-0.184703\pi\) | |||||||
\(972\) | 5.20821e8 | + | 1.80598e8i | 0.567139 | + | 0.196659i | ||||
\(973\) | 1.26242e8 | 0.137046 | ||||||||
\(974\) | 3.06948e8i | 0.332191i | ||||||||
\(975\) | 1.04065e8 | − | 2.59853e8i | 0.112277 | − | 0.280359i | ||||
\(976\) | 5.72575e6 | 0.00615862 | ||||||||
\(977\) | 7.81614e8i | 0.838125i | 0.907957 | + | 0.419062i | \(0.137641\pi\) | ||||
−0.907957 | + | 0.419062i | \(0.862359\pi\) | |||||||
\(978\) | −1.79069e8 | − | 7.17125e7i | −0.191427 | − | 0.0766617i | ||||
\(979\) | −1.42272e8 | −0.151626 | ||||||||
\(980\) | − | 1.60241e7i | − | 0.0170254i | ||||||
\(981\) | −2.91137e8 | − | 2.77728e8i | −0.308383 | − | 0.294180i | ||||
\(982\) | −8.92073e8 | −0.942032 | ||||||||
\(983\) | − | 1.54179e9i | − | 1.62317i | −0.584235 | − | 0.811585i | \(-0.698605\pi\) | ||
0.584235 | − | 0.811585i | \(-0.301395\pi\) | |||||||
\(984\) | 5.32866e8 | − | 1.33059e9i | 0.559284 | − | 1.39655i | ||||
\(985\) | −2.86167e8 | −0.299441 | ||||||||
\(986\) | − | 5.90513e8i | − | 0.616025i | ||||||
\(987\) | −6.60599e8 | − | 2.64553e8i | −0.687047 | − | 0.275145i | ||||
\(988\) | 2.94706e8 | 0.305575 | ||||||||
\(989\) | − | 9.41025e8i | − | 0.972774i | ||||||
\(990\) | −1.45645e7 | + | 1.52677e7i | −0.0150103 | + | 0.0157350i | ||||
\(991\) | 1.59156e9 | 1.63532 | 0.817661 | − | 0.575701i | \(-0.195271\pi\) | ||||
0.817661 | + | 0.575701i | \(0.195271\pi\) | |||||||
\(992\) | 2.31230e8i | 0.236870i | ||||||||
\(993\) | −3.54757e7 | + | 8.85841e7i | −0.0362312 | + | 0.0904707i | ||||
\(994\) | 4.08385e8 | 0.415825 | ||||||||
\(995\) | − | 3.27499e8i | − | 0.332461i | ||||||
\(996\) | 3.61700e8 | + | 1.44852e8i | 0.366076 | + | 0.146604i | ||||
\(997\) | −1.16332e9 | −1.17385 | −0.586927 | − | 0.809640i | \(-0.699662\pi\) | ||||
−0.586927 | + | 0.809640i | \(0.699662\pi\) | |||||||
\(998\) | 1.02208e8i | 0.102823i | ||||||||
\(999\) | −5.28298e8 | + | 2.41043e8i | −0.529886 | + | 0.241767i |
(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 | 21.7.b.a.8.6 | ✓ | 12 | |
3.2 | odd | 2 | inner | 21.7.b.a.8.7 | yes | 12 | |
4.3 | odd | 2 | 336.7.d.a.113.6 | 12 | |||
7.6 | odd | 2 | 147.7.b.b.50.6 | 12 | |||
12.11 | even | 2 | 336.7.d.a.113.5 | 12 | |||
21.20 | even | 2 | 147.7.b.b.50.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.7.b.a.8.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
21.7.b.a.8.7 | yes | 12 | 3.2 | odd | 2 | inner | |
147.7.b.b.50.6 | 12 | 7.6 | odd | 2 | |||
147.7.b.b.50.7 | 12 | 21.20 | even | 2 | |||
336.7.d.a.113.5 | 12 | 12.11 | even | 2 | |||
336.7.d.a.113.6 | 12 | 4.3 | odd | 2 |