Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,6,Mod(4,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.4");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.e (of order \(3\), degree \(2\), 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: | \(3.36806021607\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-83})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 20x^{2} - 21x + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.1 | ||
Root | \(4.19493 - 1.84460i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.16 |
Dual form | 21.6.e.b.4.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.19493 | + | 5.53379i | −0.564790 | + | 0.978245i | 0.432279 | + | 0.901740i | \(0.357709\pi\) |
−0.997069 | + | 0.0765049i | \(0.975624\pi\) | |||||||
\(3\) | 4.50000 | + | 7.79423i | 0.288675 | + | 0.500000i | ||||
\(4\) | −4.41520 | − | 7.64735i | −0.137975 | − | 0.238980i | ||||
\(5\) | −19.3645 | + | 33.5404i | −0.346403 | + | 0.599988i | −0.985608 | − | 0.169049i | \(-0.945930\pi\) |
0.639204 | + | 0.769037i | \(0.279264\pi\) | |||||||
\(6\) | −57.5088 | −0.652163 | ||||||||
\(7\) | −87.5000 | − | 95.6596i | −0.674937 | − | 0.737876i | ||||
\(8\) | −148.051 | −0.817872 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | −123.737 | − | 214.318i | −0.391290 | − | 0.677734i | ||||
\(11\) | 288.195 | + | 499.168i | 0.718133 | + | 1.24384i | 0.961739 | + | 0.273968i | \(0.0883362\pi\) |
−0.243606 | + | 0.969874i | \(0.578330\pi\) | |||||||
\(12\) | 39.7368 | − | 68.8262i | 0.0796599 | − | 0.137975i | ||||
\(13\) | 391.491 | 0.642486 | 0.321243 | − | 0.946997i | \(-0.395899\pi\) | ||||
0.321243 | + | 0.946997i | \(0.395899\pi\) | |||||||
\(14\) | 808.916 | − | 178.580i | 1.10302 | − | 0.243508i | ||||
\(15\) | −348.562 | −0.399992 | ||||||||
\(16\) | 614.298 | − | 1064.00i | 0.599901 | − | 1.03906i | ||||
\(17\) | 664.850 | + | 1151.55i | 0.557958 | + | 0.966412i | 0.997667 | + | 0.0682711i | \(0.0217483\pi\) |
−0.439709 | + | 0.898140i | \(0.644918\pi\) | |||||||
\(18\) | −258.790 | − | 448.237i | −0.188263 | − | 0.326082i | ||||
\(19\) | −471.237 | + | 816.206i | −0.299471 | + | 0.518699i | −0.976015 | − | 0.217703i | \(-0.930144\pi\) |
0.676544 | + | 0.736402i | \(0.263477\pi\) | |||||||
\(20\) | 341.993 | 0.191180 | ||||||||
\(21\) | 351.842 | − | 1112.46i | 0.174100 | − | 0.550475i | ||||
\(22\) | −3683.05 | −1.62238 | ||||||||
\(23\) | 816.040 | − | 1413.42i | 0.321656 | − | 0.557124i | −0.659174 | − | 0.751991i | \(-0.729094\pi\) |
0.980830 | + | 0.194866i | \(0.0624272\pi\) | |||||||
\(24\) | −666.228 | − | 1153.94i | −0.236099 | − | 0.408936i | ||||
\(25\) | 812.530 | + | 1407.34i | 0.260009 | + | 0.450350i | ||||
\(26\) | −1250.79 | + | 2166.43i | −0.362869 | + | 0.628508i | ||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −345.212 | + | 1091.50i | −0.0832130 | + | 0.263105i | ||||
\(29\) | −1463.54 | −0.323155 | −0.161577 | − | 0.986860i | \(-0.551658\pi\) | ||||
−0.161577 | + | 0.986860i | \(0.551658\pi\) | |||||||
\(30\) | 1113.63 | − | 1928.87i | 0.225911 | − | 0.391290i | ||||
\(31\) | 1956.21 | + | 3388.25i | 0.365604 | + | 0.633245i | 0.988873 | − | 0.148763i | \(-0.0475291\pi\) |
−0.623269 | + | 0.782008i | \(0.714196\pi\) | |||||||
\(32\) | 1556.47 | + | 2695.89i | 0.268700 | + | 0.465401i | ||||
\(33\) | −2593.75 | + | 4492.51i | −0.414614 | + | 0.718133i | ||||
\(34\) | −8496.61 | −1.26052 | ||||||||
\(35\) | 4902.85 | − | 1082.38i | 0.676517 | − | 0.149351i | ||||
\(36\) | 715.262 | 0.0919833 | ||||||||
\(37\) | 8150.17 | − | 14116.5i | 0.978729 | − | 1.69521i | 0.311691 | − | 0.950184i | \(-0.399105\pi\) |
0.667038 | − | 0.745024i | \(-0.267562\pi\) | |||||||
\(38\) | −3011.14 | − | 5215.45i | −0.338277 | − | 0.585912i | ||||
\(39\) | 1761.71 | + | 3051.37i | 0.185470 | + | 0.321243i | ||||
\(40\) | 2866.93 | − | 4965.67i | 0.283314 | − | 0.490714i | ||||
\(41\) | −13103.8 | −1.21741 | −0.608707 | − | 0.793395i | \(-0.708312\pi\) | ||||
−0.608707 | + | 0.793395i | \(0.708312\pi\) | |||||||
\(42\) | 5032.02 | + | 5501.27i | 0.440169 | + | 0.481215i | ||||
\(43\) | 14733.5 | 1.21516 | 0.607582 | − | 0.794257i | \(-0.292140\pi\) | ||||
0.607582 | + | 0.794257i | \(0.292140\pi\) | |||||||
\(44\) | 2544.88 | − | 4407.86i | 0.198169 | − | 0.343238i | ||||
\(45\) | −1568.53 | − | 2716.77i | −0.115468 | − | 0.199996i | ||||
\(46\) | 5214.38 | + | 9031.58i | 0.363336 | + | 0.629316i | ||||
\(47\) | 3407.26 | − | 5901.55i | 0.224989 | − | 0.389692i | −0.731327 | − | 0.682027i | \(-0.761099\pi\) |
0.956316 | + | 0.292335i | \(0.0944322\pi\) | |||||||
\(48\) | 11057.4 | 0.692706 | ||||||||
\(49\) | −1494.50 | + | 16740.4i | −0.0889213 | + | 0.996039i | ||||
\(50\) | −10383.9 | −0.587403 | ||||||||
\(51\) | −5983.65 | + | 10364.0i | −0.322137 | + | 0.557958i | ||||
\(52\) | −1728.51 | − | 2993.87i | −0.0886470 | − | 0.153541i | ||||
\(53\) | 1005.67 | + | 1741.87i | 0.0491775 | + | 0.0851779i | 0.889566 | − | 0.456806i | \(-0.151007\pi\) |
−0.840389 | + | 0.541984i | \(0.817673\pi\) | |||||||
\(54\) | 2329.11 | − | 4034.13i | 0.108694 | − | 0.188263i | ||||
\(55\) | −22323.0 | −0.995054 | ||||||||
\(56\) | 12954.4 | + | 14162.5i | 0.552012 | + | 0.603488i | ||||
\(57\) | −8482.26 | −0.345800 | ||||||||
\(58\) | 4675.93 | − | 8098.94i | 0.182515 | − | 0.316125i | ||||
\(59\) | −25726.6 | − | 44559.7i | −0.962170 | − | 1.66653i | −0.717035 | − | 0.697037i | \(-0.754501\pi\) |
−0.245135 | − | 0.969489i | \(-0.578832\pi\) | |||||||
\(60\) | 1538.97 | + | 2665.57i | 0.0551889 | + | 0.0955900i | ||||
\(61\) | −20548.9 | + | 35591.8i | −0.707073 | + | 1.22469i | 0.258865 | + | 0.965913i | \(0.416651\pi\) |
−0.965938 | + | 0.258773i | \(0.916682\pi\) | |||||||
\(62\) | −24999.8 | −0.825958 | ||||||||
\(63\) | 10254.1 | − | 2263.74i | 0.325496 | − | 0.0718581i | ||||
\(64\) | 19423.8 | 0.592766 | ||||||||
\(65\) | −7581.04 | + | 13130.8i | −0.222559 | + | 0.385484i | ||||
\(66\) | −16573.7 | − | 28706.6i | −0.468340 | − | 0.811188i | ||||
\(67\) | −25289.1 | − | 43802.0i | −0.688250 | − | 1.19208i | −0.972404 | − | 0.233305i | \(-0.925046\pi\) |
0.284153 | − | 0.958779i | \(-0.408288\pi\) | |||||||
\(68\) | 5870.89 | − | 10168.7i | 0.153968 | − | 0.266681i | ||||
\(69\) | 14688.7 | 0.371416 | ||||||||
\(70\) | −9674.63 | + | 30589.5i | −0.235988 | + | 0.746151i | ||||
\(71\) | 39970.6 | 0.941012 | 0.470506 | − | 0.882397i | \(-0.344071\pi\) | ||||
0.470506 | + | 0.882397i | \(0.344071\pi\) | |||||||
\(72\) | 5996.05 | − | 10385.5i | 0.136312 | − | 0.236099i | ||||
\(73\) | 27843.3 | + | 48226.0i | 0.611524 | + | 1.05919i | 0.990984 | + | 0.133983i | \(0.0427767\pi\) |
−0.379459 | + | 0.925208i | \(0.623890\pi\) | |||||||
\(74\) | 52078.5 | + | 90202.6i | 1.10555 | + | 1.91487i | ||||
\(75\) | −7312.77 | + | 12666.1i | −0.150117 | + | 0.260009i | ||||
\(76\) | 8322.42 | 0.165278 | ||||||||
\(77\) | 22533.2 | − | 71245.8i | 0.433107 | − | 1.36941i | ||||
\(78\) | −22514.2 | −0.419006 | ||||||||
\(79\) | 31575.7 | − | 54690.7i | 0.569226 | − | 0.985929i | −0.427416 | − | 0.904055i | \(-0.640576\pi\) |
0.996643 | − | 0.0818739i | \(-0.0260905\pi\) | |||||||
\(80\) | 23791.2 | + | 41207.6i | 0.415615 | + | 0.719867i | ||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 41865.9 | − | 72513.8i | 0.687583 | − | 1.19093i | ||||
\(83\) | 45572.4 | 0.726116 | 0.363058 | − | 0.931766i | \(-0.381733\pi\) | ||||
0.363058 | + | 0.931766i | \(0.381733\pi\) | |||||||
\(84\) | −10060.8 | + | 2221.08i | −0.155574 | + | 0.0343453i | ||||
\(85\) | −51498.1 | −0.773114 | ||||||||
\(86\) | −47072.5 | + | 81532.0i | −0.686312 | + | 1.18873i | ||||
\(87\) | −6585.95 | − | 11407.2i | −0.0932868 | − | 0.161577i | ||||
\(88\) | −42667.5 | − | 73902.2i | −0.587341 | − | 1.01730i | ||||
\(89\) | −7843.34 | + | 13585.1i | −0.104961 | + | 0.181797i | −0.913722 | − | 0.406340i | \(-0.866805\pi\) |
0.808762 | + | 0.588137i | \(0.200138\pi\) | |||||||
\(90\) | 20045.4 | 0.260860 | ||||||||
\(91\) | −34255.5 | − | 37449.9i | −0.433637 | − | 0.474075i | ||||
\(92\) | −14411.9 | −0.177522 | ||||||||
\(93\) | −17605.9 | + | 30494.3i | −0.211082 | + | 0.365604i | ||||
\(94\) | 21771.9 | + | 37710.1i | 0.254143 | + | 0.440188i | ||||
\(95\) | −18250.6 | − | 31610.9i | −0.207476 | − | 0.359358i | ||||
\(96\) | −14008.3 | + | 24263.0i | −0.155134 | + | 0.268700i | ||||
\(97\) | 3128.49 | 0.0337603 | 0.0168801 | − | 0.999858i | \(-0.494627\pi\) | ||||
0.0168801 | + | 0.999858i | \(0.494627\pi\) | |||||||
\(98\) | −87863.1 | − | 61754.8i | −0.924148 | − | 0.649539i | ||||
\(99\) | −46687.6 | −0.478755 | ||||||||
\(100\) | 7174.96 | − | 12427.4i | 0.0717496 | − | 0.124274i | ||||
\(101\) | 84505.5 | + | 146368.i | 0.824292 | + | 1.42772i | 0.902459 | + | 0.430776i | \(0.141760\pi\) |
−0.0781663 | + | 0.996940i | \(0.524907\pi\) | |||||||
\(102\) | −38234.7 | − | 66224.5i | −0.363880 | − | 0.630258i | ||||
\(103\) | −56410.1 | + | 97705.1i | −0.523918 | + | 0.907453i | 0.475694 | + | 0.879611i | \(0.342197\pi\) |
−0.999612 | + | 0.0278422i | \(0.991136\pi\) | |||||||
\(104\) | −57960.5 | −0.525471 | ||||||||
\(105\) | 30499.1 | + | 33343.2i | 0.269969 | + | 0.295144i | ||||
\(106\) | −12852.2 | −0.111100 | ||||||||
\(107\) | 11154.7 | − | 19320.6i | 0.0941890 | − | 0.163140i | −0.815081 | − | 0.579347i | \(-0.803308\pi\) |
0.909270 | + | 0.416207i | \(0.136641\pi\) | |||||||
\(108\) | 3218.68 | + | 5574.92i | 0.0265533 | + | 0.0459917i | ||||
\(109\) | 41909.8 | + | 72589.8i | 0.337869 | + | 0.585207i | 0.984032 | − | 0.177993i | \(-0.0569604\pi\) |
−0.646162 | + | 0.763200i | \(0.723627\pi\) | |||||||
\(110\) | 71320.6 | − | 123531.i | 0.561996 | − | 0.973406i | ||||
\(111\) | 146703. | 1.13014 | ||||||||
\(112\) | −155532. | + | 34336.1i | −1.17159 | + | 0.258646i | ||||
\(113\) | −40928.4 | −0.301529 | −0.150764 | − | 0.988570i | \(-0.548174\pi\) | ||||
−0.150764 | + | 0.988570i | \(0.548174\pi\) | |||||||
\(114\) | 27100.3 | − | 46939.0i | 0.195304 | − | 0.338277i | ||||
\(115\) | 31604.4 | + | 54740.5i | 0.222845 | + | 0.385980i | ||||
\(116\) | 6461.84 | + | 11192.2i | 0.0445873 | + | 0.0772275i | ||||
\(117\) | −15855.4 | + | 27462.3i | −0.107081 | + | 0.185470i | ||||
\(118\) | 328779. | 2.17369 | ||||||||
\(119\) | 51982.8 | − | 164360.i | 0.336505 | − | 1.06397i | ||||
\(120\) | 51604.8 | 0.327142 | ||||||||
\(121\) | −85587.1 | + | 148241.i | −0.531429 | + | 0.920462i | ||||
\(122\) | −131305. | − | 227427.i | −0.798695 | − | 1.38338i | ||||
\(123\) | −58967.2 | − | 102134.i | −0.351437 | − | 0.608707i | ||||
\(124\) | 17274.1 | − | 29919.6i | 0.100888 | − | 0.174744i | ||||
\(125\) | −183965. | −1.05308 | ||||||||
\(126\) | −20234.0 | + | 63976.4i | −0.113542 | + | 0.358999i | ||||
\(127\) | 83270.1 | 0.458120 | 0.229060 | − | 0.973412i | \(-0.426435\pi\) | ||||
0.229060 | + | 0.973412i | \(0.426435\pi\) | |||||||
\(128\) | −111865. | + | 193756.i | −0.603488 | + | 1.04527i | ||||
\(129\) | 66300.7 | + | 114836.i | 0.350788 | + | 0.607582i | ||||
\(130\) | −48441.9 | − | 83903.8i | −0.251398 | − | 0.435435i | ||||
\(131\) | 83437.4 | − | 144518.i | 0.424798 | − | 0.735772i | −0.571603 | − | 0.820530i | \(-0.693678\pi\) |
0.996402 | + | 0.0847580i | \(0.0270117\pi\) | |||||||
\(132\) | 45807.8 | 0.228825 | ||||||||
\(133\) | 119311. | − | 26339.7i | 0.584860 | − | 0.129117i | ||||
\(134\) | 323188. | 1.55487 | ||||||||
\(135\) | 14116.7 | − | 24450.9i | 0.0666653 | − | 0.115468i | ||||
\(136\) | −98431.5 | − | 170488.i | −0.456338 | − | 0.790401i | ||||
\(137\) | −19111.9 | − | 33102.9i | −0.0869969 | − | 0.150683i | 0.819244 | − | 0.573446i | \(-0.194394\pi\) |
−0.906240 | + | 0.422763i | \(0.861060\pi\) | |||||||
\(138\) | −46929.5 | + | 81284.2i | −0.209772 | + | 0.363336i | ||||
\(139\) | 106263. | 0.466492 | 0.233246 | − | 0.972418i | \(-0.425065\pi\) | ||||
0.233246 | + | 0.972418i | \(0.425065\pi\) | |||||||
\(140\) | −29924.4 | − | 32714.9i | −0.129034 | − | 0.141067i | ||||
\(141\) | 61330.7 | 0.259795 | ||||||||
\(142\) | −127703. | + | 221189.i | −0.531474 | + | 0.920540i | ||||
\(143\) | 112826. | + | 195420.i | 0.461390 | + | 0.799151i | ||||
\(144\) | 49758.2 | + | 86183.7i | 0.199967 | + | 0.346353i | ||||
\(145\) | 28340.8 | − | 49087.8i | 0.111942 | − | 0.193889i | ||||
\(146\) | −355830. | −1.38153 | ||||||||
\(147\) | −137204. | + | 63683.4i | −0.523689 | + | 0.243071i | ||||
\(148\) | −143938. | −0.540160 | ||||||||
\(149\) | −96277.8 | + | 166758.i | −0.355271 | + | 0.615348i | −0.987164 | − | 0.159708i | \(-0.948945\pi\) |
0.631893 | + | 0.775056i | \(0.282278\pi\) | |||||||
\(150\) | −46727.6 | − | 80934.6i | −0.169569 | − | 0.293701i | ||||
\(151\) | −70849.3 | − | 122715.i | −0.252868 | − | 0.437980i | 0.711447 | − | 0.702740i | \(-0.248040\pi\) |
−0.964314 | + | 0.264761i | \(0.914707\pi\) | |||||||
\(152\) | 69766.9 | − | 120840.i | 0.244929 | − | 0.424230i | ||||
\(153\) | −107706. | −0.371972 | ||||||||
\(154\) | 322267. | + | 352319.i | 1.09500 | + | 1.19711i | ||||
\(155\) | −151524. | −0.506586 | ||||||||
\(156\) | 15556.6 | − | 26944.8i | 0.0511804 | − | 0.0886470i | ||||
\(157\) | −282885. | − | 489972.i | −0.915928 | − | 1.58643i | −0.805536 | − | 0.592546i | \(-0.798123\pi\) |
−0.110392 | − | 0.993888i | \(-0.535211\pi\) | |||||||
\(158\) | 201764. | + | 349466.i | 0.642986 | + | 1.11368i | ||||
\(159\) | −9051.04 | + | 15676.9i | −0.0283926 | + | 0.0491775i | ||||
\(160\) | −120562. | −0.372314 | ||||||||
\(161\) | −206611. | + | 45612.4i | −0.628186 | + | 0.138682i | ||||
\(162\) | 41923.9 | 0.125509 | ||||||||
\(163\) | 215101. | − | 372565.i | 0.634121 | − | 1.09833i | −0.352579 | − | 0.935782i | \(-0.614695\pi\) |
0.986701 | − | 0.162549i | \(-0.0519714\pi\) | |||||||
\(164\) | 57856.0 | + | 100210.i | 0.167973 | + | 0.290937i | ||||
\(165\) | −100454. | − | 173991.i | −0.287247 | − | 0.497527i | ||||
\(166\) | −145601. | + | 252188.i | −0.410103 | + | 0.710319i | ||||
\(167\) | −240265. | −0.666653 | −0.333327 | − | 0.942811i | \(-0.608171\pi\) | ||||
−0.333327 | + | 0.942811i | \(0.608171\pi\) | |||||||
\(168\) | −52090.5 | + | 164701.i | −0.142392 | + | 0.450218i | ||||
\(169\) | −218028. | −0.587212 | ||||||||
\(170\) | 164533. | − | 284979.i | 0.436647 | − | 0.756295i | ||||
\(171\) | −38170.2 | − | 66112.7i | −0.0998238 | − | 0.172900i | ||||
\(172\) | −65051.3 | − | 112672.i | −0.167662 | − | 0.290399i | ||||
\(173\) | 89650.1 | − | 155279.i | 0.227738 | − | 0.394454i | −0.729399 | − | 0.684088i | \(-0.760200\pi\) |
0.957137 | + | 0.289634i | \(0.0935337\pi\) | |||||||
\(174\) | 84166.7 | 0.210750 | ||||||||
\(175\) | 63529.4 | − | 200869.i | 0.156812 | − | 0.495812i | ||||
\(176\) | 708151. | 1.72323 | ||||||||
\(177\) | 231539. | − | 401037.i | 0.555509 | − | 0.962170i | ||||
\(178\) | −50117.9 | − | 86806.8i | −0.118561 | − | 0.205354i | ||||
\(179\) | 287780. | + | 498449.i | 0.671317 | + | 1.16275i | 0.977531 | + | 0.210792i | \(0.0676043\pi\) |
−0.306214 | + | 0.951963i | \(0.599062\pi\) | |||||||
\(180\) | −13850.7 | + | 23990.2i | −0.0318633 | + | 0.0551889i | ||||
\(181\) | 581006. | 1.31821 | 0.659105 | − | 0.752051i | \(-0.270935\pi\) | ||||
0.659105 | + | 0.752051i | \(0.270935\pi\) | |||||||
\(182\) | 316684. | − | 69912.7i | 0.708675 | − | 0.156451i | ||||
\(183\) | −369880. | −0.816458 | ||||||||
\(184\) | −120815. | + | 209258.i | −0.263073 | + | 0.455657i | ||||
\(185\) | 315648. | + | 546719.i | 0.678070 | + | 1.17445i | ||||
\(186\) | −112499. | − | 194854.i | −0.238433 | − | 0.412979i | ||||
\(187\) | −383213. | + | 663744.i | −0.801376 | + | 1.38802i | ||||
\(188\) | −60174.9 | −0.124171 | ||||||||
\(189\) | 63787.5 | + | 69735.8i | 0.129892 | + | 0.142004i | ||||
\(190\) | 233237. | 0.468721 | ||||||||
\(191\) | 330280. | − | 572062.i | 0.655087 | − | 1.13464i | −0.326785 | − | 0.945099i | \(-0.605965\pi\) |
0.981872 | − | 0.189545i | \(-0.0607013\pi\) | |||||||
\(192\) | 87407.0 | + | 151393.i | 0.171117 | + | 0.296383i | ||||
\(193\) | 278655. | + | 482645.i | 0.538485 | + | 0.932684i | 0.998986 | + | 0.0450243i | \(0.0143365\pi\) |
−0.460501 | + | 0.887659i | \(0.652330\pi\) | |||||||
\(194\) | −9995.33 | + | 17312.4i | −0.0190675 | + | 0.0330258i | ||||
\(195\) | −136459. | −0.256989 | ||||||||
\(196\) | 134618. | − | 62483.3i | 0.250302 | − | 0.116178i | ||||
\(197\) | −761400. | −1.39781 | −0.698904 | − | 0.715216i | \(-0.746328\pi\) | ||||
−0.698904 | + | 0.715216i | \(0.746328\pi\) | |||||||
\(198\) | 149164. | − | 258359.i | 0.270396 | − | 0.468340i | ||||
\(199\) | 67929.9 | + | 117658.i | 0.121598 | + | 0.210615i | 0.920398 | − | 0.390982i | \(-0.127865\pi\) |
−0.798800 | + | 0.601597i | \(0.794531\pi\) | |||||||
\(200\) | −120296. | − | 208358.i | −0.212655 | − | 0.368328i | ||||
\(201\) | 227602. | − | 394218.i | 0.397361 | − | 0.688250i | ||||
\(202\) | −1.07996e6 | −1.86221 | ||||||||
\(203\) | 128060. | + | 140002.i | 0.218109 | + | 0.238448i | ||||
\(204\) | 105676. | 0.177787 | ||||||||
\(205\) | 253750. | − | 439507.i | 0.421716 | − | 0.730434i | ||||
\(206\) | −360453. | − | 624323.i | −0.591807 | − | 1.02504i | ||||
\(207\) | 66099.2 | + | 114487.i | 0.107219 | + | 0.185708i | ||||
\(208\) | 240492. | − | 416545.i | 0.385428 | − | 0.667581i | ||||
\(209\) | −543232. | −0.860240 | ||||||||
\(210\) | −281957. | + | 62246.3i | −0.441199 | + | 0.0974014i | ||||
\(211\) | −991157. | −1.53263 | −0.766313 | − | 0.642467i | \(-0.777911\pi\) | ||||
−0.766313 | + | 0.642467i | \(0.777911\pi\) | |||||||
\(212\) | 8880.48 | − | 15381.4i | 0.0135705 | − | 0.0235048i | ||||
\(213\) | 179868. | + | 311540.i | 0.271647 | + | 0.470506i | ||||
\(214\) | 71277.3 | + | 123456.i | 0.106394 | + | 0.184280i | ||||
\(215\) | −285307. | + | 494167.i | −0.420937 | + | 0.729084i | ||||
\(216\) | 107929. | 0.157400 | ||||||||
\(217\) | 152951. | − | 483602.i | 0.220496 | − | 0.697170i | ||||
\(218\) | −535596. | −0.763301 | ||||||||
\(219\) | −250590. | + | 434034.i | −0.353064 | + | 0.611524i | ||||
\(220\) | 98560.7 | + | 170712.i | 0.137293 | + | 0.237798i | ||||
\(221\) | 260283. | + | 450823.i | 0.358480 | + | 0.620906i | ||||
\(222\) | −468706. | + | 811823.i | −0.638291 | + | 1.10555i | ||||
\(223\) | 543344. | 0.731666 | 0.365833 | − | 0.930681i | \(-0.380784\pi\) | ||||
0.365833 | + | 0.930681i | \(0.380784\pi\) | |||||||
\(224\) | 121696. | − | 384782.i | 0.162053 | − | 0.512383i | ||||
\(225\) | −131630. | −0.173340 | ||||||||
\(226\) | 130764. | − | 226489.i | 0.170300 | − | 0.294969i | ||||
\(227\) | −8.16704 | − | 14.1457i | −1.05196e−5 | − | 1.82205e-5i | 0.866020 | − | 0.500009i | \(-0.166670\pi\) |
−0.866031 | + | 0.499991i | \(0.833337\pi\) | |||||||
\(228\) | 37450.9 | + | 64866.8i | 0.0477117 | + | 0.0826391i | ||||
\(229\) | 38689.5 | − | 67012.2i | 0.0487534 | − | 0.0844433i | −0.840619 | − | 0.541627i | \(-0.817808\pi\) |
0.889372 | + | 0.457184i | \(0.151142\pi\) | |||||||
\(230\) | −403896. | −0.503443 | ||||||||
\(231\) | 656705. | − | 144978.i | 0.809731 | − | 0.178760i | ||||
\(232\) | 216679. | 0.264299 | ||||||||
\(233\) | 51828.6 | − | 89769.9i | 0.0625432 | − | 0.108328i | −0.833058 | − | 0.553185i | \(-0.813412\pi\) |
0.895602 | + | 0.444857i | \(0.146746\pi\) | |||||||
\(234\) | −101314. | − | 175481.i | −0.120956 | − | 0.209503i | ||||
\(235\) | 131960. | + | 228561.i | 0.155874 | + | 0.269981i | ||||
\(236\) | −227176. | + | 393480.i | −0.265511 | + | 0.459878i | ||||
\(237\) | 568362. | 0.657286 | ||||||||
\(238\) | 743453. | + | 812782.i | 0.850768 | + | 0.930104i | ||||
\(239\) | 689109. | 0.780356 | 0.390178 | − | 0.920739i | \(-0.372413\pi\) | ||||
0.390178 | + | 0.920739i | \(0.372413\pi\) | |||||||
\(240\) | −214121. | + | 370868.i | −0.239956 | + | 0.415615i | ||||
\(241\) | −110148. | − | 190782.i | −0.122161 | − | 0.211590i | 0.798458 | − | 0.602050i | \(-0.205649\pi\) |
−0.920620 | + | 0.390460i | \(0.872316\pi\) | |||||||
\(242\) | −546890. | − | 947242.i | −0.600291 | − | 1.03973i | ||||
\(243\) | 29524.5 | − | 51137.9i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 362910. | 0.390234 | ||||||||
\(245\) | −532539. | − | 374297.i | −0.566809 | − | 0.398383i | ||||
\(246\) | 753585. | 0.793953 | ||||||||
\(247\) | −184485. | + | 319537.i | −0.192406 | + | 0.333257i | ||||
\(248\) | −289618. | − | 501633.i | −0.299017 | − | 0.517913i | ||||
\(249\) | 205076. | + | 355201.i | 0.209612 | + | 0.363058i | ||||
\(250\) | 587757. | − | 1.01803e6i | 0.594768 | − | 1.03017i | ||||
\(251\) | 1.43641e6 | 1.43912 | 0.719558 | − | 0.694433i | \(-0.244345\pi\) | ||||
0.719558 | + | 0.694433i | \(0.244345\pi\) | |||||||
\(252\) | −62585.5 | − | 68421.7i | −0.0620829 | − | 0.0678723i | ||||
\(253\) | 940714. | 0.923966 | ||||||||
\(254\) | −266042. | + | 460799.i | −0.258742 | + | 0.448154i | ||||
\(255\) | −231741. | − | 401388.i | −0.223179 | − | 0.386557i | ||||
\(256\) | −404021. | − | 699785.i | −0.385305 | − | 0.667367i | ||||
\(257\) | 454598. | − | 787388.i | 0.429334 | − | 0.743628i | −0.567480 | − | 0.823387i | \(-0.692082\pi\) |
0.996814 | + | 0.0797589i | \(0.0254151\pi\) | |||||||
\(258\) | −847306. | −0.792485 | ||||||||
\(259\) | −2.06352e6 | + | 455553.i | −1.91143 | + | 0.421977i | ||||
\(260\) | 133887. | 0.122830 | ||||||||
\(261\) | 59273.5 | − | 102665.i | 0.0538592 | − | 0.0932868i | ||||
\(262\) | 533154. | + | 923450.i | 0.479843 | + | 0.831113i | ||||
\(263\) | −374528. | − | 648702.i | −0.333884 | − | 0.578304i | 0.649386 | − | 0.760459i | \(-0.275026\pi\) |
−0.983270 | + | 0.182155i | \(0.941693\pi\) | |||||||
\(264\) | 384007. | − | 665120.i | 0.339101 | − | 0.587341i | ||||
\(265\) | −77897.4 | −0.0681410 | ||||||||
\(266\) | −235433. | + | 744396.i | −0.204015 | + | 0.645060i | ||||
\(267\) | −141180. | −0.121198 | ||||||||
\(268\) | −223313. | + | 386789.i | −0.189923 | + | 0.328956i | ||||
\(269\) | −334972. | − | 580189.i | −0.282246 | − | 0.488865i | 0.689691 | − | 0.724104i | \(-0.257746\pi\) |
−0.971938 | + | 0.235238i | \(0.924413\pi\) | |||||||
\(270\) | 90204.1 | + | 156238.i | 0.0753038 | + | 0.130430i | ||||
\(271\) | −270330. | + | 468225.i | −0.223599 | + | 0.387285i | −0.955898 | − | 0.293698i | \(-0.905114\pi\) |
0.732299 | + | 0.680983i | \(0.238447\pi\) | |||||||
\(272\) | 1.63367e6 | 1.33888 | ||||||||
\(273\) | 137743. | − | 435519.i | 0.111857 | − | 0.353672i | ||||
\(274\) | 244246. | 0.196540 | ||||||||
\(275\) | −468334. | + | 811178.i | −0.373443 | + | 0.646821i | ||||
\(276\) | −64853.6 | − | 112330.i | −0.0512462 | − | 0.0887610i | ||||
\(277\) | 200955. | + | 348064.i | 0.157362 | + | 0.272558i | 0.933916 | − | 0.357491i | \(-0.116368\pi\) |
−0.776555 | + | 0.630050i | \(0.783035\pi\) | |||||||
\(278\) | −339502. | + | 588035.i | −0.263470 | + | 0.456343i | ||||
\(279\) | −316906. | −0.243736 | ||||||||
\(280\) | −725871. | + | 160247.i | −0.553304 | + | 0.122150i | ||||
\(281\) | −429139. | −0.324214 | −0.162107 | − | 0.986773i | \(-0.551829\pi\) | ||||
−0.162107 | + | 0.986773i | \(0.551829\pi\) | |||||||
\(282\) | −195947. | + | 339391.i | −0.146729 | + | 0.254143i | ||||
\(283\) | 170463. | + | 295251.i | 0.126522 | + | 0.219142i | 0.922327 | − | 0.386411i | \(-0.126285\pi\) |
−0.795805 | + | 0.605553i | \(0.792952\pi\) | |||||||
\(284\) | −176478. | − | 305669.i | −0.129836 | − | 0.224883i | ||||
\(285\) | 164255. | − | 284498.i | 0.119786 | − | 0.207476i | ||||
\(286\) | −1.44188e6 | −1.04235 | ||||||||
\(287\) | 1.14658e6 | + | 1.25351e6i | 0.821678 | + | 0.898301i | ||||
\(288\) | −252149. | −0.179133 | ||||||||
\(289\) | −174123. | + | 301590.i | −0.122634 | + | 0.212409i | ||||
\(290\) | 181094. | + | 313664.i | 0.126447 | + | 0.219013i | ||||
\(291\) | 14078.2 | + | 24384.2i | 0.00974575 | + | 0.0168801i | ||||
\(292\) | 245868. | − | 425855.i | 0.168750 | − | 0.292284i | ||||
\(293\) | −388847. | −0.264612 | −0.132306 | − | 0.991209i | \(-0.542238\pi\) | ||||
−0.132306 | + | 0.991209i | \(0.542238\pi\) | |||||||
\(294\) | 85946.9 | − | 962722.i | 0.0579912 | − | 0.649580i | ||||
\(295\) | 1.99273e6 | 1.33319 | ||||||||
\(296\) | −1.20664e6 | + | 2.08996e6i | −0.800475 | + | 1.38646i | ||||
\(297\) | −210094. | − | 363894.i | −0.138205 | − | 0.239378i | ||||
\(298\) | −615202. | − | 1.06556e6i | −0.401307 | − | 0.695085i | ||||
\(299\) | 319472. | − | 553342.i | 0.206659 | − | 0.357945i | ||||
\(300\) | 129149. | 0.0828493 | ||||||||
\(301\) | −1.28918e6 | − | 1.40940e6i | −0.820158 | − | 0.896640i | ||||
\(302\) | 905435. | 0.571268 | ||||||||
\(303\) | −760549. | + | 1.31731e6i | −0.475905 | + | 0.824292i | ||||
\(304\) | 578960. | + | 1.00279e6i | 0.359306 | + | 0.622336i | ||||
\(305\) | −795840. | − | 1.37844e6i | −0.489865 | − | 0.848471i | ||||
\(306\) | 344113. | − | 596021.i | 0.210086 | − | 0.363880i | ||||
\(307\) | −2.35747e6 | −1.42758 | −0.713789 | − | 0.700361i | \(-0.753022\pi\) | ||||
−0.713789 | + | 0.700361i | \(0.753022\pi\) | |||||||
\(308\) | −644330. | + | 142246.i | −0.387018 | + | 0.0854402i | ||||
\(309\) | −1.01538e6 | −0.604969 | ||||||||
\(310\) | 484110. | − | 838503.i | 0.286114 | − | 0.495565i | ||||
\(311\) | 718314. | + | 1.24416e6i | 0.421127 | + | 0.729414i | 0.996050 | − | 0.0887939i | \(-0.0283013\pi\) |
−0.574923 | + | 0.818208i | \(0.694968\pi\) | |||||||
\(312\) | −260822. | − | 451758.i | −0.151691 | − | 0.262736i | ||||
\(313\) | 411400. | − | 712566.i | 0.237358 | − | 0.411116i | −0.722598 | − | 0.691269i | \(-0.757052\pi\) |
0.959955 | + | 0.280153i | \(0.0903853\pi\) | |||||||
\(314\) | 3.61520e6 | 2.06923 | ||||||||
\(315\) | −122639. | + | 387762.i | −0.0696388 | + | 0.220186i | ||||
\(316\) | −557652. | −0.314156 | ||||||||
\(317\) | 883467. | − | 1.53021e6i | 0.493790 | − | 0.855269i | −0.506184 | − | 0.862425i | \(-0.668944\pi\) |
0.999974 | + | 0.00715584i | \(0.00227779\pi\) | |||||||
\(318\) | −57835.0 | − | 100173.i | −0.0320718 | − | 0.0555499i | ||||
\(319\) | −421786. | − | 730555.i | −0.232068 | − | 0.401954i | ||||
\(320\) | −376132. | + | 651480.i | −0.205336 | + | 0.355653i | ||||
\(321\) | 200785. | 0.108760 | ||||||||
\(322\) | 407698. | − | 1.28907e6i | 0.219129 | − | 0.692845i | ||||
\(323\) | −1.25321e6 | −0.668370 | ||||||||
\(324\) | −28968.1 | + | 50174.3i | −0.0153306 | + | 0.0265533i | ||||
\(325\) | 318098. | + | 550962.i | 0.167052 | + | 0.289343i | ||||
\(326\) | 1.37446e6 | + | 2.38064e6i | 0.716291 | + | 1.24065i | ||||
\(327\) | −377188. | + | 653309.i | −0.195069 | + | 0.337869i | ||||
\(328\) | 1.94003e6 | 0.995689 | ||||||||
\(329\) | −862675. | + | 190448.i | −0.439397 | + | 0.0970036i | ||||
\(330\) | 1.28377e6 | 0.648937 | ||||||||
\(331\) | 1526.14 | − | 2643.35i | 0.000765638 | − | 0.00132612i | −0.865642 | − | 0.500663i | \(-0.833090\pi\) |
0.866408 | + | 0.499337i | \(0.166423\pi\) | |||||||
\(332\) | −201211. | − | 348508.i | −0.100186 | − | 0.173527i | ||||
\(333\) | 660164. | + | 1.14344e6i | 0.326243 | + | 0.565069i | ||||
\(334\) | 767632. | − | 1.32958e6i | 0.376519 | − | 0.652150i | ||||
\(335\) | 1.95885e6 | 0.953649 | ||||||||
\(336\) | −967520. | − | 1.05774e6i | −0.467532 | − | 0.511131i | ||||
\(337\) | 2.02939e6 | 0.973398 | 0.486699 | − | 0.873570i | \(-0.338201\pi\) | ||||
0.486699 | + | 0.873570i | \(0.338201\pi\) | |||||||
\(338\) | 696584. | − | 1.20652e6i | 0.331651 | − | 0.574437i | ||||
\(339\) | −184178. | − | 319006.i | −0.0870439 | − | 0.150764i | ||||
\(340\) | 227374. | + | 393824.i | 0.106670 | + | 0.184759i | ||||
\(341\) | −1.12754e6 | + | 1.95295e6i | −0.525104 | + | 0.909507i | ||||
\(342\) | 487805. | 0.225518 | ||||||||
\(343\) | 1.73215e6 | − | 1.32182e6i | 0.794969 | − | 0.606650i | ||||
\(344\) | −2.18130e6 | −0.993848 | ||||||||
\(345\) | −284440. | + | 492665.i | −0.128660 | + | 0.222845i | ||||
\(346\) | 572852. | + | 992209.i | 0.257248 | + | 0.445567i | ||||
\(347\) | −1.89109e6 | − | 3.27547e6i | −0.843119 | − | 1.46033i | −0.887245 | − | 0.461299i | \(-0.847383\pi\) |
0.0441252 | − | 0.999026i | \(-0.485950\pi\) | |||||||
\(348\) | −58156.6 | + | 100730.i | −0.0257425 | + | 0.0445873i | ||||
\(349\) | 291147. | 0.127953 | 0.0639763 | − | 0.997951i | \(-0.479622\pi\) | ||||
0.0639763 | + | 0.997951i | \(0.479622\pi\) | |||||||
\(350\) | 908592. | + | 993320.i | 0.396460 | + | 0.433430i | ||||
\(351\) | −285397. | −0.123646 | ||||||||
\(352\) | −897136. | + | 1.55389e6i | −0.385924 | + | 0.668440i | ||||
\(353\) | −192538. | − | 333486.i | −0.0822394 | − | 0.142443i | 0.821972 | − | 0.569528i | \(-0.192874\pi\) |
−0.904212 | + | 0.427085i | \(0.859541\pi\) | |||||||
\(354\) | 1.47950e6 | + | 2.56257e6i | 0.627491 | + | 1.08685i | ||||
\(355\) | −774013. | + | 1.34063e6i | −0.325970 | + | 0.564596i | ||||
\(356\) | 138520. | 0.0579277 | ||||||||
\(357\) | 1.51498e6 | − | 334456.i | 0.629126 | − | 0.138889i | ||||
\(358\) | −3.67775e6 | −1.51661 | ||||||||
\(359\) | 1.61507e6 | − | 2.79738e6i | 0.661385 | − | 1.14555i | −0.318866 | − | 0.947800i | \(-0.603302\pi\) |
0.980252 | − | 0.197753i | \(-0.0633645\pi\) | |||||||
\(360\) | 232222. | + | 402219.i | 0.0944379 | + | 0.163571i | ||||
\(361\) | 793921. | + | 1.37511e6i | 0.320634 | + | 0.555354i | ||||
\(362\) | −1.85628e6 | + | 3.21517e6i | −0.744511 | + | 1.28953i | ||||
\(363\) | −1.54057e6 | −0.613641 | ||||||||
\(364\) | −135148. | + | 427312.i | −0.0534632 | + | 0.169041i | ||||
\(365\) | −2.15669e6 | −0.847336 | ||||||||
\(366\) | 1.18174e6 | − | 2.04684e6i | 0.461127 | − | 0.798695i | ||||
\(367\) | 239779. | + | 415310.i | 0.0929280 | + | 0.160956i | 0.908742 | − | 0.417358i | \(-0.137044\pi\) |
−0.815814 | + | 0.578314i | \(0.803711\pi\) | |||||||
\(368\) | −1.00258e6 | − | 1.73653e6i | −0.385923 | − | 0.668439i | ||||
\(369\) | 530705. | − | 919208.i | 0.202902 | − | 0.351437i | ||||
\(370\) | −4.03390e6 | −1.53187 | ||||||||
\(371\) | 78630.6 | − | 248616.i | 0.0296590 | − | 0.0937766i | ||||
\(372\) | 310934. | 0.116496 | ||||||||
\(373\) | −436333. | + | 755751.i | −0.162385 | + | 0.281259i | −0.935724 | − | 0.352734i | \(-0.885252\pi\) |
0.773339 | + | 0.633993i | \(0.218585\pi\) | |||||||
\(374\) | −2.44868e6 | − | 4.24124e6i | −0.905217 | − | 1.56788i | ||||
\(375\) | −827844. | − | 1.43387e6i | −0.303998 | − | 0.526540i | ||||
\(376\) | −504447. | + | 873728.i | −0.184012 | + | 0.318718i | ||||
\(377\) | −572965. | −0.207622 | ||||||||
\(378\) | −589700. | + | 130185.i | −0.212276 | + | 0.0468632i | ||||
\(379\) | −2.43493e6 | −0.870742 | −0.435371 | − | 0.900251i | \(-0.643383\pi\) | ||||
−0.435371 | + | 0.900251i | \(0.643383\pi\) | |||||||
\(380\) | −161160. | + | 279137.i | −0.0572529 | + | 0.0991650i | ||||
\(381\) | 374715. | + | 649026.i | 0.132248 | + | 0.229060i | ||||
\(382\) | 2.11044e6 | + | 3.65540e6i | 0.739973 | + | 1.28167i | ||||
\(383\) | 1.80584e6 | − | 3.12781e6i | 0.629047 | − | 1.08954i | −0.358696 | − | 0.933454i | \(-0.616778\pi\) |
0.987743 | − | 0.156087i | \(-0.0498882\pi\) | |||||||
\(384\) | −2.01357e6 | −0.696848 | ||||||||
\(385\) | 1.95327e6 | + | 2.13541e6i | 0.671598 | + | 0.734226i | ||||
\(386\) | −3.56114e6 | −1.21652 | ||||||||
\(387\) | −596707. | + | 1.03353e6i | −0.202527 | + | 0.350788i | ||||
\(388\) | −13812.9 | − | 23924.7i | −0.00465807 | − | 0.00806802i | ||||
\(389\) | 87616.2 | + | 151756.i | 0.0293569 | + | 0.0508477i | 0.880331 | − | 0.474361i | \(-0.157321\pi\) |
−0.850974 | + | 0.525208i | \(0.823987\pi\) | |||||||
\(390\) | 435977. | − | 755134.i | 0.145145 | − | 0.251398i | ||||
\(391\) | 2.17018e6 | 0.717882 | ||||||||
\(392\) | 221262. | − | 2.47843e6i | 0.0727262 | − | 0.814632i | ||||
\(393\) | 1.50187e6 | 0.490515 | ||||||||
\(394\) | 2.43262e6 | − | 4.21343e6i | 0.789467 | − | 1.36740i | ||||
\(395\) | 1.22290e6 | + | 2.11812e6i | 0.394364 | + | 0.683058i | ||||
\(396\) | 206135. | + | 357036.i | 0.0660562 | + | 0.114413i | ||||
\(397\) | −942577. | + | 1.63259e6i | −0.300152 | + | 0.519878i | −0.976170 | − | 0.217007i | \(-0.930371\pi\) |
0.676019 | + | 0.736885i | \(0.263704\pi\) | |||||||
\(398\) | −868126. | −0.274710 | ||||||||
\(399\) | 742198. | + | 811409.i | 0.233393 | + | 0.255157i | ||||
\(400\) | 1.99654e6 | 0.623920 | ||||||||
\(401\) | −669915. | + | 1.16033e6i | −0.208046 | + | 0.360346i | −0.951099 | − | 0.308887i | \(-0.900044\pi\) |
0.743053 | + | 0.669232i | \(0.233377\pi\) | |||||||
\(402\) | 1.45435e6 | + | 2.51900e6i | 0.448851 | + | 0.777433i | ||||
\(403\) | 765839. | + | 1.32647e6i | 0.234895 | + | 0.406851i | ||||
\(404\) | 746217. | − | 1.29249e6i | 0.227463 | − | 0.393978i | ||||
\(405\) | 254101. | 0.0769785 | ||||||||
\(406\) | −1.18388e6 | + | 261360.i | −0.356446 | + | 0.0786909i | ||||
\(407\) | 9.39535e6 | 2.81143 | ||||||||
\(408\) | 885884. | − | 1.53440e6i | 0.263467 | − | 0.456338i | ||||
\(409\) | −3.29314e6 | − | 5.70388e6i | −0.973423 | − | 1.68602i | −0.685043 | − | 0.728503i | \(-0.740217\pi\) |
−0.288381 | − | 0.957516i | \(-0.593117\pi\) | |||||||
\(410\) | 1.62143e6 | + | 2.80839e6i | 0.476362 | + | 0.825084i | ||||
\(411\) | 172008. | − | 297926.i | 0.0502277 | − | 0.0869969i | ||||
\(412\) | 996247. | 0.289150 | ||||||||
\(413\) | −2.01149e6 | + | 6.35996e6i | −0.580286 | + | 1.83476i | ||||
\(414\) | −844730. | −0.242224 | ||||||||
\(415\) | −882487. | + | 1.52851e6i | −0.251529 | + | 0.435661i | ||||
\(416\) | 609346. | + | 1.05542e6i | 0.172636 | + | 0.299014i | ||||
\(417\) | 478182. | + | 828236.i | 0.134665 | + | 0.233246i | ||||
\(418\) | 1.73559e6 | − | 3.00613e6i | 0.485855 | − | 0.841525i | ||||
\(419\) | −6.96869e6 | −1.93917 | −0.969585 | − | 0.244754i | \(-0.921293\pi\) | ||||
−0.969585 | + | 0.244754i | \(0.921293\pi\) | |||||||
\(420\) | 120328. | − | 380455.i | 0.0332845 | − | 0.105240i | ||||
\(421\) | 3.84041e6 | 1.05602 | 0.528010 | − | 0.849238i | \(-0.322938\pi\) | ||||
0.528010 | + | 0.849238i | \(0.322938\pi\) | |||||||
\(422\) | 3.16668e6 | − | 5.48485e6i | 0.865612 | − | 1.49928i | ||||
\(423\) | 275988. | + | 478025.i | 0.0749962 | + | 0.129897i | ||||
\(424\) | −148890. | − | 257886.i | −0.0402209 | − | 0.0696647i | ||||
\(425\) | −1.08042e6 | + | 1.87134e6i | −0.290149 | + | 0.502552i | ||||
\(426\) | −2.29866e6 | −0.613693 | ||||||||
\(427\) | 5.20272e6 | − | 1.14858e6i | 1.38090 | − | 0.304854i | ||||
\(428\) | −197002. | −0.0519829 | ||||||||
\(429\) | −1.01543e6 | + | 1.75878e6i | −0.266384 | + | 0.461390i | ||||
\(430\) | −1.82308e6 | − | 3.15766e6i | −0.475481 | − | 0.823558i | ||||
\(431\) | −1.51818e6 | − | 2.62957e6i | −0.393668 | − | 0.681854i | 0.599262 | − | 0.800553i | \(-0.295461\pi\) |
−0.992930 | + | 0.118699i | \(0.962128\pi\) | |||||||
\(432\) | −447824. | + | 775653.i | −0.115451 | + | 0.199967i | ||||
\(433\) | −941529. | −0.241332 | −0.120666 | − | 0.992693i | \(-0.538503\pi\) | ||||
−0.120666 | + | 0.992693i | \(0.538503\pi\) | |||||||
\(434\) | 2.18749e6 | + | 2.39147e6i | 0.557469 | + | 0.609454i | ||||
\(435\) | 510135. | 0.129259 | ||||||||
\(436\) | 370080. | − | 640997.i | 0.0932351 | − | 0.161488i | ||||
\(437\) | 769096. | + | 1.33211e6i | 0.192653 | + | 0.333686i | ||||
\(438\) | −1.60124e6 | − | 2.77342e6i | −0.398814 | − | 0.690765i | ||||
\(439\) | −670546. | + | 1.16142e6i | −0.166061 | + | 0.287626i | −0.937031 | − | 0.349245i | \(-0.886438\pi\) |
0.770971 | + | 0.636871i | \(0.219771\pi\) | |||||||
\(440\) | 3.30494e6 | 0.813827 | ||||||||
\(441\) | −1.11378e6 | − | 782823.i | −0.272711 | − | 0.191676i | ||||
\(442\) | −3.32635e6 | −0.809864 | ||||||||
\(443\) | 386171. | − | 668867.i | 0.0934910 | − | 0.161931i | −0.815487 | − | 0.578776i | \(-0.803531\pi\) |
0.908978 | + | 0.416844i | \(0.136864\pi\) | |||||||
\(444\) | −647723. | − | 1.12189e6i | −0.155931 | − | 0.270080i | ||||
\(445\) | −303765. | − | 526137.i | −0.0727174 | − | 0.125950i | ||||
\(446\) | −1.73595e6 | + | 3.00675e6i | −0.413238 | + | 0.715748i | ||||
\(447\) | −1.73300e6 | −0.410232 | ||||||||
\(448\) | −1.69958e6 | − | 1.85807e6i | −0.400080 | − | 0.437388i | ||||
\(449\) | 2.25684e6 | 0.528304 | 0.264152 | − | 0.964481i | \(-0.414908\pi\) | ||||
0.264152 | + | 0.964481i | \(0.414908\pi\) | |||||||
\(450\) | 420548. | − | 728411.i | 0.0979005 | − | 0.169569i | ||||
\(451\) | −3.77646e6 | − | 6.54101e6i | −0.874265 | − | 1.51427i | ||||
\(452\) | 180707. | + | 312994.i | 0.0416034 | + | 0.0720593i | ||||
\(453\) | 637644. | − | 1.10443e6i | 0.145993 | − | 0.252868i | ||||
\(454\) | 104.373 | 2.37655e−5 | ||||||||
\(455\) | 1.91942e6 | − | 423742.i | 0.434653 | − | 0.0959561i | ||||
\(456\) | 1.25580e6 | 0.282820 | ||||||||
\(457\) | −2.14235e6 | + | 3.71066e6i | −0.479844 | + | 0.831114i | −0.999733 | − | 0.0231196i | \(-0.992640\pi\) |
0.519889 | + | 0.854234i | \(0.325973\pi\) | |||||||
\(458\) | 247221. | + | 428199.i | 0.0550708 | + | 0.0953854i | ||||
\(459\) | −484676. | − | 839483.i | −0.107379 | − | 0.185986i | ||||
\(460\) | 279080. | − | 483381.i | 0.0614942 | − | 0.106511i | ||||
\(461\) | −3.10462e6 | −0.680387 | −0.340193 | − | 0.940355i | \(-0.610493\pi\) | ||||
−0.340193 | + | 0.940355i | \(0.610493\pi\) | |||||||
\(462\) | −1.29585e6 | + | 4.09726e6i | −0.282456 | + | 0.893077i | ||||
\(463\) | −3.53386e6 | −0.766121 | −0.383060 | − | 0.923723i | \(-0.625130\pi\) | ||||
−0.383060 | + | 0.923723i | \(0.625130\pi\) | |||||||
\(464\) | −899053. | + | 1.55721e6i | −0.193861 | + | 0.335777i | ||||
\(465\) | −681859. | − | 1.18102e6i | −0.146239 | − | 0.253293i | ||||
\(466\) | 331178. | + | 573617.i | 0.0706475 | + | 0.122365i | ||||
\(467\) | −1.36230e6 | + | 2.35957e6i | −0.289054 | + | 0.500657i | −0.973584 | − | 0.228328i | \(-0.926674\pi\) |
0.684530 | + | 0.728985i | \(0.260007\pi\) | |||||||
\(468\) | 280019. | 0.0590980 | ||||||||
\(469\) | −1.97728e6 | + | 6.25182e6i | −0.415085 | + | 1.31242i | ||||
\(470\) | −1.68641e6 | −0.352143 | ||||||||
\(471\) | 2.54597e6 | − | 4.40975e6i | 0.528812 | − | 0.915928i | ||||
\(472\) | 3.80883e6 | + | 6.59709e6i | 0.786932 | + | 1.36301i | ||||
\(473\) | 4.24612e6 | + | 7.35449e6i | 0.872649 | + | 1.51147i | ||||
\(474\) | −1.81588e6 | + | 3.14520e6i | −0.371228 | + | 0.642986i | ||||
\(475\) | −1.53158e6 | −0.311461 | ||||||||
\(476\) | −1.48643e6 | + | 328153.i | −0.300697 | + | 0.0663833i | ||||
\(477\) | −162919. | −0.0327850 | ||||||||
\(478\) | −2.20166e6 | + | 3.81338e6i | −0.440737 | + | 0.763379i | ||||
\(479\) | −489342. | − | 847566.i | −0.0974482 | − | 0.168785i | 0.813180 | − | 0.582013i | \(-0.197735\pi\) |
−0.910628 | + | 0.413228i | \(0.864401\pi\) | |||||||
\(480\) | −542527. | − | 939685.i | −0.107478 | − | 0.186157i | ||||
\(481\) | 3.19072e6 | − | 5.52649e6i | 0.628819 | − | 1.08915i | ||||
\(482\) | 1.40766e6 | 0.275982 | ||||||||
\(483\) | −1.28526e6 | − | 1.40512e6i | −0.250682 | − | 0.274059i | ||||
\(484\) | 1.51154e6 | 0.293296 | ||||||||
\(485\) | −60581.8 | + | 104931.i | −0.0116947 | + | 0.0202558i | ||||
\(486\) | 188658. | + | 326765.i | 0.0362313 | + | 0.0627544i | ||||
\(487\) | −1.96372e6 | − | 3.40126e6i | −0.375195 | − | 0.649857i | 0.615161 | − | 0.788401i | \(-0.289091\pi\) |
−0.990356 | + | 0.138544i | \(0.955758\pi\) | |||||||
\(488\) | 3.04228e6 | − | 5.26938e6i | 0.578295 | − | 1.00164i | ||||
\(489\) | 3.87181e6 | 0.732220 | ||||||||
\(490\) | 3.77271e6 | − | 1.75111e6i | 0.709844 | − | 0.329475i | ||||
\(491\) | 2.63241e6 | 0.492777 | 0.246388 | − | 0.969171i | \(-0.420756\pi\) | ||||
0.246388 | + | 0.969171i | \(0.420756\pi\) | |||||||
\(492\) | −520704. | + | 901886.i | −0.0969791 | + | 0.167973i | ||||
\(493\) | −973037. | − | 1.68535e6i | −0.180307 | − | 0.312301i | ||||
\(494\) | −1.17883e6 | − | 2.04180e6i | −0.217338 | − | 0.376440i | ||||
\(495\) | 904083. | − | 1.56592e6i | 0.165842 | − | 0.287247i | ||||
\(496\) | 4.80678e6 | 0.877305 | ||||||||
\(497\) | −3.49743e6 | − | 3.82357e6i | −0.635123 | − | 0.694350i | ||||
\(498\) | −2.62081e6 | −0.473546 | ||||||||
\(499\) | −1.06272e6 | + | 1.84069e6i | −0.191059 | + | 0.330924i | −0.945601 | − | 0.325327i | \(-0.894526\pi\) |
0.754542 | + | 0.656251i | \(0.227859\pi\) | |||||||
\(500\) | 812244. | + | 1.40685e6i | 0.145299 | + | 0.251665i | ||||
\(501\) | −1.08119e6 | − | 1.87268e6i | −0.192446 | − | 0.333327i | ||||
\(502\) | −4.58925e6 | + | 7.94881e6i | −0.812798 | + | 1.40781i | ||||
\(503\) | 2.60929e6 | 0.459835 | 0.229917 | − | 0.973210i | \(-0.426154\pi\) | ||||
0.229917 | + | 0.973210i | \(0.426154\pi\) | |||||||
\(504\) | −1.51812e6 | + | 335149.i | −0.266214 | + | 0.0587707i | ||||
\(505\) | −6.54564e6 | −1.14215 | ||||||||
\(506\) | −3.00552e6 | + | 5.20571e6i | −0.521847 | + | 0.903865i | ||||
\(507\) | −981124. | − | 1.69936e6i | −0.169513 | − | 0.293606i | ||||
\(508\) | −367654. | − | 636795.i | −0.0632092 | − | 0.109481i | ||||
\(509\) | 5.00911e6 | − | 8.67603e6i | 0.856970 | − | 1.48432i | −0.0178348 | − | 0.999841i | \(-0.505677\pi\) |
0.874805 | − | 0.484475i | \(-0.160989\pi\) | |||||||
\(510\) | 2.96159e6 | 0.504196 | ||||||||
\(511\) | 2.17699e6 | − | 6.88326e6i | 0.368811 | − | 1.16612i | ||||
\(512\) | −1.99607e6 | −0.336512 | ||||||||
\(513\) | 343532. | − | 595014.i | 0.0576333 | − | 0.0998238i | ||||
\(514\) | 2.90482e6 | + | 5.03130e6i | 0.484967 | + | 0.839987i | ||||
\(515\) | −2.18471e6 | − | 3.78403e6i | −0.362974 | − | 0.628689i | ||||
\(516\) | 585462. | − | 1.01405e6i | 0.0967998 | − | 0.167662i | ||||
\(517\) | 3.92782e6 | 0.646287 | ||||||||
\(518\) | 4.07187e6 | − | 1.28745e7i | 0.666760 | − | 2.10818i | ||||
\(519\) | 1.61370e6 | 0.262969 | ||||||||
\(520\) | 1.12238e6 | − | 1.94402e6i | 0.182025 | − | 0.315277i | ||||
\(521\) | 2.08970e6 | + | 3.61947e6i | 0.337280 | + | 0.584186i | 0.983920 | − | 0.178609i | \(-0.0571598\pi\) |
−0.646640 | + | 0.762795i | \(0.723826\pi\) | |||||||
\(522\) | 378750. | + | 656014.i | 0.0608382 | + | 0.105375i | ||||
\(523\) | −1.80263e6 | + | 3.12224e6i | −0.288172 | + | 0.499128i | −0.973373 | − | 0.229225i | \(-0.926381\pi\) |
0.685202 | + | 0.728353i | \(0.259714\pi\) | |||||||
\(524\) | −1.47357e6 | −0.234446 | ||||||||
\(525\) | 1.85150e6 | − | 408746.i | 0.293174 | − | 0.0647225i | ||||
\(526\) | 4.78637e6 | 0.754297 | ||||||||
\(527\) | −2.60117e6 | + | 4.50536e6i | −0.407983 | + | 0.706648i | ||||
\(528\) | 3.18668e6 | + | 5.51949e6i | 0.497455 | + | 0.861617i | ||||
\(529\) | 1.88633e6 | + | 3.26722e6i | 0.293075 | + | 0.507621i | ||||
\(530\) | 248877. | − | 431068.i | 0.0384853 | − | 0.0666586i | ||||
\(531\) | 4.16770e6 | 0.641446 | ||||||||
\(532\) | −728212. | − | 796119.i | −0.111552 | − | 0.121955i | ||||
\(533\) | −5.13003e6 | −0.782172 | ||||||||
\(534\) | 451061. | − | 781261.i | 0.0684514 | − | 0.118561i | ||||
\(535\) | 432013. | + | 748268.i | 0.0652547 | + | 0.113025i | ||||
\(536\) | 3.74407e6 | + | 6.48492e6i | 0.562901 | + | 0.974972i | ||||
\(537\) | −2.59002e6 | + | 4.48604e6i | −0.387585 | + | 0.671317i | ||||
\(538\) | 4.28086e6 | 0.637640 | ||||||||
\(539\) | −8.78699e6 | + | 4.07850e6i | −1.30277 | + | 0.604684i | ||||
\(540\) | −249313. | −0.0367926 | ||||||||
\(541\) | 3.34083e6 | − | 5.78648e6i | 0.490751 | − | 0.850005i | −0.509193 | − | 0.860653i | \(-0.670056\pi\) |
0.999943 | + | 0.0106475i | \(0.00338926\pi\) | |||||||
\(542\) | −1.72737e6 | − | 2.99189e6i | −0.252573 | − | 0.437470i | ||||
\(543\) | 2.61453e6 | + | 4.52850e6i | 0.380534 | + | 0.659105i | ||||
\(544\) | −2.06964e6 | + | 3.58473e6i | −0.299846 | + | 0.519349i | ||||
\(545\) | −3.24625e6 | −0.468156 | ||||||||
\(546\) | 1.96999e6 | + | 2.15370e6i | 0.282802 | + | 0.309174i | ||||
\(547\) | 8.69076e6 | 1.24191 | 0.620954 | − | 0.783847i | \(-0.286745\pi\) | ||||
0.620954 | + | 0.783847i | \(0.286745\pi\) | |||||||
\(548\) | −168766. | + | 292312.i | −0.0240068 | + | 0.0415810i | ||||
\(549\) | −1.66446e6 | − | 2.88293e6i | −0.235691 | − | 0.408229i | ||||
\(550\) | −2.99259e6 | − | 5.18332e6i | −0.421833 | − | 0.730636i | ||||
\(551\) | 689676. | − | 1.19455e6i | 0.0967756 | − | 0.167620i | ||||
\(552\) | −2.17467e6 | −0.303771 | ||||||||
\(553\) | −7.99456e6 | + | 1.76492e6i | −1.11168 | + | 0.245421i | ||||
\(554\) | −2.56815e6 | −0.355505 | ||||||||
\(555\) | −2.84084e6 | + | 4.92047e6i | −0.391484 | + | 0.678070i | ||||
\(556\) | −469171. | − | 812628.i | −0.0643642 | − | 0.111482i | ||||
\(557\) | −3.12371e6 | − | 5.41042e6i | −0.426612 | − | 0.738913i | 0.569958 | − | 0.821674i | \(-0.306960\pi\) |
−0.996569 | + | 0.0827611i | \(0.973626\pi\) | |||||||
\(558\) | 1.01249e6 | − | 1.75369e6i | 0.137660 | − | 0.238433i | ||||
\(559\) | 5.76803e6 | 0.780725 | ||||||||
\(560\) | 1.86017e6 | − | 5.88152e6i | 0.250658 | − | 0.792537i | ||||
\(561\) | −6.89783e6 | −0.925349 | ||||||||
\(562\) | 1.37107e6 | − | 2.37476e6i | 0.183113 | − | 0.317161i | ||||
\(563\) | 5.95223e6 | + | 1.03096e7i | 0.791423 | + | 1.37078i | 0.925086 | + | 0.379758i | \(0.123993\pi\) |
−0.133663 | + | 0.991027i | \(0.542674\pi\) | |||||||
\(564\) | −270787. | − | 469017.i | −0.0358451 | − | 0.0620856i | ||||
\(565\) | 792560. | − | 1.37275e6i | 0.104451 | − | 0.180914i | ||||
\(566\) | −2.17848e6 | −0.285833 | ||||||||
\(567\) | −256493. | + | 810986.i | −0.0335057 | + | 0.105939i | ||||
\(568\) | −5.91768e6 | −0.769627 | ||||||||
\(569\) | −10707.2 | + | 18545.4i | −0.00138642 | + | 0.00240135i | −0.866718 | − | 0.498799i | \(-0.833775\pi\) |
0.865331 | + | 0.501200i | \(0.167108\pi\) | |||||||
\(570\) | 1.04957e6 | + | 1.81791e6i | 0.135308 | + | 0.234360i | ||||
\(571\) | −3.55823e6 | − | 6.16304e6i | −0.456714 | − | 0.791051i | 0.542071 | − | 0.840333i | \(-0.317640\pi\) |
−0.998785 | + | 0.0492811i | \(0.984307\pi\) | |||||||
\(572\) | 996297. | − | 1.72564e6i | 0.127321 | − | 0.220526i | ||||
\(573\) | 5.94504e6 | 0.756429 | ||||||||
\(574\) | −1.05999e7 | + | 2.34009e6i | −1.34283 | + | 0.296451i | ||||
\(575\) | 2.65223e6 | 0.334534 | ||||||||
\(576\) | −786663. | + | 1.36254e6i | −0.0987944 | + | 0.171117i | ||||
\(577\) | 5.33259e6 | + | 9.23632e6i | 0.666805 | + | 1.15494i | 0.978793 | + | 0.204854i | \(0.0656719\pi\) |
−0.311988 | + | 0.950086i | \(0.600995\pi\) | |||||||
\(578\) | −1.11262e6 | − | 1.92712e6i | −0.138525 | − | 0.239932i | ||||
\(579\) | −2.50790e6 | + | 4.34380e6i | −0.310895 | + | 0.538485i | ||||
\(580\) | −500522. | −0.0617808 | ||||||||
\(581\) | −3.98758e6 | − | 4.35943e6i | −0.490083 | − | 0.535784i | ||||
\(582\) | −179916. | −0.0220172 | ||||||||
\(583\) | −579659. | + | 1.00400e6i | −0.0706319 | + | 0.122338i | ||||
\(584\) | −4.12222e6 | − | 7.13990e6i | −0.500149 | − | 0.866283i | ||||
\(585\) | −614065. | − | 1.06359e6i | −0.0741864 | − | 0.128495i | ||||
\(586\) | 1.24234e6 | − | 2.15180e6i | 0.149450 | − | 0.258856i | ||||
\(587\) | −1.30101e7 | −1.55843 | −0.779213 | − | 0.626759i | \(-0.784381\pi\) | ||||
−0.779213 | + | 0.626759i | \(0.784381\pi\) | |||||||
\(588\) | 1.09279e6 | + | 768071.i | 0.130345 | + | 0.0916132i | ||||
\(589\) | −3.68735e6 | −0.437952 | ||||||||
\(590\) | −6.36664e6 | + | 1.10273e7i | −0.752975 | + | 1.30419i | ||||
\(591\) | −3.42630e6 | − | 5.93453e6i | −0.403512 | − | 0.698904i | ||||
\(592\) | −1.00133e7 | − | 1.73435e7i | −1.17428 | − | 2.03391i | ||||
\(593\) | −2.13043e6 | + | 3.69002e6i | −0.248789 | + | 0.430915i | −0.963190 | − | 0.268821i | \(-0.913366\pi\) |
0.714401 | + | 0.699736i | \(0.246699\pi\) | |||||||
\(594\) | 2.68495e6 | 0.312226 | ||||||||
\(595\) | 4.50608e6 | + | 4.92628e6i | 0.521803 | + | 0.570462i | ||||
\(596\) | 1.70034e6 | 0.196074 | ||||||||
\(597\) | −611369. | + | 1.05892e6i | −0.0702049 | + | 0.121598i | ||||
\(598\) | 2.04139e6 | + | 3.53578e6i | 0.233438 | + | 0.404327i | ||||
\(599\) | 6.89790e6 | + | 1.19475e7i | 0.785507 | + | 1.36054i | 0.928696 | + | 0.370842i | \(0.120931\pi\) |
−0.143189 | + | 0.989695i | \(0.545736\pi\) | |||||||
\(600\) | 1.08266e6 | − | 1.87522e6i | 0.122776 | − | 0.212655i | ||||
\(601\) | 4.99695e6 | 0.564311 | 0.282155 | − | 0.959369i | \(-0.408951\pi\) | ||||
0.282155 | + | 0.959369i | \(0.408951\pi\) | |||||||
\(602\) | 1.19182e7 | − | 2.63111e6i | 1.34035 | − | 0.295902i | ||||
\(603\) | 4.09683e6 | 0.458833 | ||||||||
\(604\) | −625628. | + | 1.08362e6i | −0.0697788 | + | 0.120860i | ||||
\(605\) | −3.31471e6 | − | 5.74125e6i | −0.368177 | − | 0.637702i | ||||
\(606\) | −4.85981e6 | − | 8.41743e6i | −0.537573 | − | 0.931104i | ||||
\(607\) | 1.52473e6 | − | 2.64091e6i | 0.167966 | − | 0.290926i | −0.769739 | − | 0.638359i | \(-0.779613\pi\) |
0.937705 | + | 0.347434i | \(0.112947\pi\) | |||||||
\(608\) | −2.93387e6 | −0.321871 | ||||||||
\(609\) | −514937. | + | 1.62814e6i | −0.0562614 | + | 0.177889i | ||||
\(610\) | 1.01706e7 | 1.10668 | ||||||||
\(611\) | 1.33391e6 | − | 2.31040e6i | 0.144552 | − | 0.250372i | ||||
\(612\) | 475542. | + | 823663.i | 0.0513228 | + | 0.0888937i | ||||
\(613\) | 3.51813e6 | + | 6.09357e6i | 0.378147 | + | 0.654969i | 0.990793 | − | 0.135388i | \(-0.0432282\pi\) |
−0.612646 | + | 0.790357i | \(0.709895\pi\) | |||||||
\(614\) | 7.53195e6 | − | 1.30457e7i | 0.806281 | − | 1.39652i | ||||
\(615\) | 4.56749e6 | 0.486956 | ||||||||
\(616\) | −3.33605e6 | + | 1.05480e7i | −0.354226 | + | 1.12000i | ||||
\(617\) | 1.00066e7 | 1.05822 | 0.529108 | − | 0.848554i | \(-0.322527\pi\) | ||||
0.529108 | + | 0.848554i | \(0.322527\pi\) | |||||||
\(618\) | 3.24408e6 | − | 5.61890e6i | 0.341680 | − | 0.591807i | ||||
\(619\) | 3.27533e6 | + | 5.67304e6i | 0.343581 | + | 0.595099i | 0.985095 | − | 0.172012i | \(-0.0550268\pi\) |
−0.641514 | + | 0.767111i | \(0.721693\pi\) | |||||||
\(620\) | 669010. | + | 1.15876e6i | 0.0698962 | + | 0.121064i | ||||
\(621\) | −594893. | + | 1.03038e6i | −0.0619027 | + | 0.107219i | ||||
\(622\) | −9.17986e6 | −0.951393 | ||||||||
\(623\) | 1.98583e6 | − | 438403.i | 0.204985 | − | 0.0452536i | ||||
\(624\) | 4.32886e6 | 0.445054 | ||||||||
\(625\) | 1.02325e6 | − | 1.77232e6i | 0.104781 | − | 0.181485i | ||||
\(626\) | 2.62879e6 | + | 4.55320e6i | 0.268114 | + | 0.464388i | ||||
\(627\) | −2.44455e6 | − | 4.23408e6i | −0.248330 | − | 0.430120i | ||||
\(628\) | −2.49799e6 | + | 4.32665e6i | −0.252750 | + | 0.437777i | ||||
\(629\) | 2.16746e7 | 2.18436 | ||||||||
\(630\) | −1.75397e6 | − | 1.91753e6i | −0.176064 | − | 0.192482i | ||||
\(631\) | 2.22672e6 | 0.222635 | 0.111317 | − | 0.993785i | \(-0.464493\pi\) | ||||
0.111317 | + | 0.993785i | \(0.464493\pi\) | |||||||
\(632\) | −4.67480e6 | + | 8.09699e6i | −0.465554 | + | 0.806364i | ||||
\(633\) | −4.46021e6 | − | 7.72531e6i | −0.442431 | − | 0.766313i | ||||
\(634\) | 5.64524e6 | + | 9.77784e6i | 0.557775 | + | 0.966095i | ||||
\(635\) | −1.61249e6 | + | 2.79291e6i | −0.158694 | + | 0.274867i | ||||
\(636\) | 159849. | 0.0156699 | ||||||||
\(637\) | −585084. | + | 6.55373e6i | −0.0571307 | + | 0.639941i | ||||
\(638\) | 5.39031e6 | 0.524279 | ||||||||
\(639\) | −1.61881e6 | + | 2.80386e6i | −0.156835 | + | 0.271647i | ||||
\(640\) | −4.33242e6 | − | 7.50397e6i | −0.418101 | − | 0.724171i | ||||
\(641\) | 7.96698e6 | + | 1.37992e7i | 0.765859 | + | 1.32651i | 0.939791 | + | 0.341749i | \(0.111019\pi\) |
−0.173932 | + | 0.984758i | \(0.555647\pi\) | |||||||
\(642\) | −641496. | + | 1.11110e6i | −0.0614266 | + | 0.106394i | ||||
\(643\) | −1.49933e7 | −1.43011 | −0.715056 | − | 0.699067i | \(-0.753599\pi\) | ||||
−0.715056 | + | 0.699067i | \(0.753599\pi\) | |||||||
\(644\) | 1.26104e6 | + | 1.37864e6i | 0.119816 | + | 0.130989i | ||||
\(645\) | −5.13553e6 | −0.486056 | ||||||||
\(646\) | 4.00391e6 | − | 6.93498e6i | 0.377488 | − | 0.653829i | ||||
\(647\) | −6.49027e6 | − | 1.12415e7i | −0.609540 | − | 1.05575i | −0.991316 | − | 0.131500i | \(-0.958021\pi\) |
0.381776 | − | 0.924255i | \(-0.375313\pi\) | |||||||
\(648\) | 485680. | + | 841223.i | 0.0454373 | + | 0.0786998i | ||||
\(649\) | 1.48285e7 | − | 2.56838e7i | 1.38193 | − | 2.39357i | ||||
\(650\) | −4.06521e6 | −0.377398 | ||||||||
\(651\) | 4.45758e6 | − | 984079.i | 0.412237 | − | 0.0910075i | ||||
\(652\) | −3.79885e6 | −0.349972 | ||||||||
\(653\) | 8.27460e6 | − | 1.43320e7i | 0.759389 | − | 1.31530i | −0.183774 | − | 0.982969i | \(-0.558831\pi\) |
0.943163 | − | 0.332332i | \(-0.107835\pi\) | |||||||
\(654\) | −2.41018e6 | − | 4.17455e6i | −0.220346 | − | 0.381650i | ||||
\(655\) | 3.23145e6 | + | 5.59704e6i | 0.294303 | + | 0.509748i | ||||
\(656\) | −8.04966e6 | + | 1.39424e7i | −0.730328 | + | 1.26497i | ||||
\(657\) | −4.51062e6 | −0.407683 | ||||||||
\(658\) | 1.70229e6 | − | 5.38233e6i | 0.153274 | − | 0.484625i | ||||
\(659\) | 5.86879e6 | 0.526423 | 0.263212 | − | 0.964738i | \(-0.415218\pi\) | ||||
0.263212 | + | 0.964738i | \(0.415218\pi\) | |||||||
\(660\) | −887046. | + | 1.53641e6i | −0.0792659 | + | 0.137293i | ||||
\(661\) | −3.63843e6 | − | 6.30195e6i | −0.323900 | − | 0.561011i | 0.657389 | − | 0.753551i | \(-0.271661\pi\) |
−0.981289 | + | 0.192540i | \(0.938327\pi\) | |||||||
\(662\) | 9751.81 | + | 16890.6i | 0.000864849 | + | 0.00149796i | ||||
\(663\) | −2.34255e6 | + | 4.05741e6i | −0.206969 | + | 0.358480i | ||||
\(664\) | −6.74702e6 | −0.593870 | ||||||||
\(665\) | −1.42696e6 | + | 4.51179e6i | −0.125129 | + | 0.395635i | ||||
\(666\) | −8.43672e6 | −0.737035 | ||||||||
\(667\) | −1.19431e6 | + | 2.06861e6i | −0.103945 | + | 0.180038i | ||||
\(668\) | 1.06082e6 | + | 1.83739e6i | 0.0919815 | + | 0.159317i | ||||
\(669\) | 2.44505e6 | + | 4.23495e6i | 0.211214 | + | 0.365833i | ||||
\(670\) | −6.25838e6 | + | 1.08398e7i | −0.538611 | + | 0.932902i | ||||
\(671\) | −2.36884e7 | −2.03109 | ||||||||
\(672\) | 3.54671e6 | − | 782991.i | 0.302972 | − | 0.0668857i | ||||
\(673\) | −1.82417e7 | −1.55248 | −0.776241 | − | 0.630437i | \(-0.782876\pi\) | ||||
−0.776241 | + | 0.630437i | \(0.782876\pi\) | |||||||
\(674\) | −6.48376e6 | + | 1.12302e7i | −0.549765 | + | 0.952222i | ||||
\(675\) | −592334. | − | 1.02595e6i | −0.0500388 | − | 0.0866698i | ||||
\(676\) | 962636. | + | 1.66733e6i | 0.0810205 | + | 0.140332i | ||||
\(677\) | 3.88203e6 | − | 6.72387e6i | 0.325527 | − | 0.563829i | −0.656092 | − | 0.754681i | \(-0.727792\pi\) |
0.981619 | + | 0.190852i | \(0.0611250\pi\) | |||||||
\(678\) | 2.35374e6 | 0.196646 | ||||||||
\(679\) | −273743. | − | 299270.i | −0.0227860 | − | 0.0249109i | ||||
\(680\) | 7.62432e6 | 0.632308 | ||||||||
\(681\) | 73.5034 | − | 127.312i | 6.07351e−6 | − | 1.05196e-5i | ||||
\(682\) | −7.20482e6 | − | 1.24791e7i | −0.593147 | − | 1.02736i | ||||
\(683\) | −4.28162e6 | − | 7.41598e6i | −0.351201 | − | 0.608299i | 0.635259 | − | 0.772299i | \(-0.280893\pi\) |
−0.986460 | + | 0.164001i | \(0.947560\pi\) | |||||||
\(684\) | −337058. | + | 583801.i | −0.0275464 | + | 0.0477117i | ||||
\(685\) | 1.48038e6 | 0.120544 | ||||||||
\(686\) | 1.78059e6 | + | 1.38085e7i | 0.144462 | + | 1.12030i | ||||
\(687\) | 696411. | 0.0562955 | ||||||||
\(688\) | 9.05076e6 | − | 1.56764e7i | 0.728978 | − | 1.26263i | ||||
\(689\) | 393712. | + | 681928.i | 0.0315959 | + | 0.0547256i | ||||
\(690\) | −1.81753e6 | − | 3.14806e6i | −0.145332 | − | 0.251722i | ||||
\(691\) | −8.22547e6 | + | 1.42469e7i | −0.655338 | + | 1.13508i | 0.326471 | + | 0.945207i | \(0.394140\pi\) |
−0.981809 | + | 0.189872i | \(0.939193\pi\) | |||||||
\(692\) | −1.58329e6 | −0.125689 | ||||||||
\(693\) | 4.08516e6 | + | 4.46611e6i | 0.323129 | + | 0.353262i | ||||
\(694\) | 2.41677e7 | 1.90474 | ||||||||
\(695\) | −2.05773e6 | + | 3.56409e6i | −0.161594 | + | 0.279890i | ||||
\(696\) | 975054. | + | 1.68884e6i | 0.0762967 | + | 0.132150i | ||||
\(697\) | −8.71208e6 | − | 1.50898e7i | −0.679266 | − | 1.17652i | ||||
\(698\) | −930197. | + | 1.61115e6i | −0.0722664 | + | 0.125169i | ||||
\(699\) | 932916. | 0.0722187 | ||||||||
\(700\) | −1.81661e6 | + | 401044.i | −0.140125 | + | 0.0309347i | ||||
\(701\) | −1.66928e7 | −1.28302 | −0.641512 | − | 0.767113i | \(-0.721693\pi\) | ||||
−0.641512 | + | 0.767113i | \(0.721693\pi\) | |||||||
\(702\) | 911825. | − | 1.57933e6i | 0.0698343 | − | 0.120956i | ||||
\(703\) | 7.68132e6 | + | 1.33044e7i | 0.586202 | + | 1.01533i | ||||
\(704\) | 5.59783e6 | + | 9.69573e6i | 0.425685 | + | 0.737308i | ||||
\(705\) | −1.18764e6 | + | 2.05705e6i | −0.0899937 | + | 0.155874i | ||||
\(706\) | 2.46059e6 | 0.185792 | ||||||||
\(707\) | 6.60725e6 | − | 2.08909e7i | 0.497132 | − | 1.57184i | ||||
\(708\) | −4.08916e6 | −0.306585 | ||||||||
\(709\) | −2.80890e6 | + | 4.86515e6i | −0.209855 | + | 0.363480i | −0.951669 | − | 0.307126i | \(-0.900633\pi\) |
0.741813 | + | 0.670606i | \(0.233966\pi\) | |||||||
\(710\) | −4.94584e6 | − | 8.56644e6i | −0.368209 | − | 0.637756i | ||||
\(711\) | 2.55763e6 | + | 4.42994e6i | 0.189742 | + | 0.328643i | ||||
\(712\) | 1.16121e6 | − | 2.01128e6i | 0.0858443 | − | 0.148687i | ||||
\(713\) | 6.38537e6 | 0.470395 | ||||||||
\(714\) | −2.98947e6 | + | 9.45216e6i | −0.219456 | + | 0.693882i | ||||
\(715\) | −8.73927e6 | −0.639308 | ||||||||
\(716\) | 2.54121e6 | − | 4.40150e6i | 0.185250 | − | 0.320862i | ||||
\(717\) | 3.10099e6 | + | 5.37107e6i | 0.225269 | + | 0.390178i | ||||
\(718\) | 1.03201e7 | + | 1.78749e7i | 0.747087 | + | 1.29399i | ||||
\(719\) | −5.18592e6 | + | 8.98227e6i | −0.374113 | + | 0.647983i | −0.990194 | − | 0.139700i | \(-0.955386\pi\) |
0.616081 | + | 0.787683i | \(0.288720\pi\) | |||||||
\(720\) | −3.85418e6 | −0.277077 | ||||||||
\(721\) | 1.42823e7 | − | 3.15303e6i | 1.02320 | − | 0.225887i | ||||
\(722\) | −1.01461e7 | −0.724363 | ||||||||
\(723\) | 991332. | − | 1.71704e6i | 0.0705299 | − | 0.122161i | ||||
\(724\) | −2.56526e6 | − | 4.44316e6i | −0.181880 | − | 0.315025i | ||||
\(725\) | −1.18917e6 | − | 2.05971e6i | −0.0840233 | − | 0.145533i | ||||
\(726\) | 4.92201e6 | − | 8.52518e6i | 0.346578 | − | 0.600291i | ||||
\(727\) | 1.15369e7 | 0.809565 | 0.404783 | − | 0.914413i | \(-0.367347\pi\) | ||||
0.404783 | + | 0.914413i | \(0.367347\pi\) | |||||||
\(728\) | 5.07155e6 | + | 5.54448e6i | 0.354660 | + | 0.387733i | ||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 6.89049e6 | − | 1.19347e7i | 0.478567 | − | 0.828902i | ||||
\(731\) | 9.79557e6 | + | 1.69664e7i | 0.678010 | + | 1.17435i | ||||
\(732\) | 1.63310e6 | + | 2.82860e6i | 0.112651 | + | 0.195117i | ||||
\(733\) | −7.47349e6 | + | 1.29445e7i | −0.513764 | + | 0.889865i | 0.486109 | + | 0.873898i | \(0.338416\pi\) |
−0.999873 | + | 0.0159667i | \(0.994917\pi\) | |||||||
\(734\) | −3.06432e6 | −0.209939 | ||||||||
\(735\) | 520925. | − | 5.83507e6i | 0.0355678 | − | 0.398408i | ||||
\(736\) | 5.08058e6 | 0.345715 | ||||||||
\(737\) | 1.45764e7 | − | 2.52470e7i | 0.988510 | − | 1.71215i | ||||
\(738\) | 3.39113e6 | + | 5.87362e6i | 0.229194 | + | 0.396976i | ||||
\(739\) | −4.50682e6 | − | 7.80604e6i | −0.303570 | − | 0.525799i | 0.673372 | − | 0.739304i | \(-0.264845\pi\) |
−0.976942 | + | 0.213505i | \(0.931512\pi\) | |||||||
\(740\) | 2.78730e6 | − | 4.82775e6i | 0.187113 | − | 0.324090i | ||||
\(741\) | −3.32073e6 | −0.222171 | ||||||||
\(742\) | 1.12457e6 | + | 1.22944e6i | 0.0749853 | + | 0.0819779i | ||||
\(743\) | −2.10239e7 | −1.39714 | −0.698571 | − | 0.715541i | \(-0.746180\pi\) | ||||
−0.698571 | + | 0.715541i | \(0.746180\pi\) | |||||||
\(744\) | 2.60656e6 | − | 4.51470e6i | 0.172638 | − | 0.299017i | ||||
\(745\) | −3.72875e6 | − | 6.45838e6i | −0.246134 | − | 0.426317i | ||||
\(746\) | −2.78811e6 | − | 4.82915e6i | −0.183427 | − | 0.317705i | ||||
\(747\) | −1.84568e6 | + | 3.19681e6i | −0.121019 | + | 0.209612i | ||||
\(748\) | 6.76785e6 | 0.442279 | ||||||||
\(749\) | −2.82424e6 | + | 623493.i | −0.183949 | + | 0.0406094i | ||||
\(750\) | 1.05796e7 | 0.686779 | ||||||||
\(751\) | −2.02110e6 | + | 3.50064e6i | −0.130764 | + | 0.226489i | −0.923971 | − | 0.382462i | \(-0.875076\pi\) |
0.793207 | + | 0.608952i | \(0.208410\pi\) | |||||||
\(752\) | −4.18615e6 | − | 7.25062e6i | −0.269942 | − | 0.467553i | ||||
\(753\) | 6.46387e6 | + | 1.11957e7i | 0.415437 | + | 0.719558i | ||||
\(754\) | 1.83058e6 | − | 3.17066e6i | 0.117263 | − | 0.203106i | ||||
\(755\) | 5.48786e6 | 0.350377 | ||||||||
\(756\) | 251660. | − | 795703.i | 0.0160143 | − | 0.0506345i | ||||
\(757\) | −1.82059e7 | −1.15471 | −0.577353 | − | 0.816495i | \(-0.695914\pi\) | ||||
−0.577353 | + | 0.816495i | \(0.695914\pi\) | |||||||
\(758\) | 7.77945e6 | − | 1.34744e7i | 0.491786 | − | 0.851798i | ||||
\(759\) | 4.23321e6 | + | 7.33214e6i | 0.266726 | + | 0.461983i | ||||
\(760\) | 2.70201e6 | + | 4.68001e6i | 0.169689 | + | 0.293909i | ||||
\(761\) | 9.45999e6 | − | 1.63852e7i | 0.592146 | − | 1.02563i | −0.401797 | − | 0.915729i | \(-0.631614\pi\) |
0.993943 | − | 0.109898i | \(-0.0350526\pi\) | |||||||
\(762\) | −4.78876e6 | −0.298769 | ||||||||
\(763\) | 3.27681e6 | − | 1.03607e7i | 0.203770 | − | 0.644283i | ||||
\(764\) | −5.83301e6 | −0.361542 | ||||||||
\(765\) | 2.08567e6 | − | 3.61249e6i | 0.128852 | − | 0.223179i | ||||
\(766\) | 1.15391e7 | + | 1.99863e7i | 0.710559 | + | 1.23072i | ||||
\(767\) | −1.00717e7 | − | 1.74447e7i | −0.618180 | − | 1.07072i | ||||
\(768\) | 3.63619e6 | − | 6.29807e6i | 0.222456 | − | 0.385305i | ||||
\(769\) | −1.12831e7 | −0.688037 | −0.344019 | − | 0.938963i | \(-0.611788\pi\) | ||||
−0.344019 | + | 0.938963i | \(0.611788\pi\) | |||||||
\(770\) | −1.80575e7 | + | 3.98646e6i | −1.09756 | + | 0.242304i | ||||
\(771\) | 8.18277e6 | 0.495752 | ||||||||
\(772\) | 2.46064e6 | − | 4.26195e6i | 0.148595 | − | 0.257374i | ||||
\(773\) | 1.84282e6 | + | 3.19186e6i | 0.110926 | + | 0.192130i | 0.916144 | − | 0.400849i | \(-0.131285\pi\) |
−0.805218 | + | 0.592979i | \(0.797952\pi\) | |||||||
\(774\) | −3.81288e6 | − | 6.60410e6i | −0.228771 | − | 0.396242i | ||||
\(775\) | −3.17896e6 | + | 5.50611e6i | −0.190121 | + | 0.329299i | ||||
\(776\) | −463176. | −0.0276116 | ||||||||
\(777\) | −1.28365e7 | − | 1.40335e7i | −0.762772 | − | 0.833902i | ||||
\(778\) | −1.11971e6 | −0.0663219 | ||||||||
\(779\) | 6.17501e6 | − | 1.06954e7i | 0.364581 | − | 0.631472i | ||||
\(780\) | 602493. | + | 1.04355e6i | 0.0354581 | + | 0.0614152i | ||||
\(781\) | 1.15193e7 | + | 1.99521e7i | 0.675771 | + | 1.17047i | ||||
\(782\) | −6.93357e6 | + | 1.20093e7i | −0.405452 | + | 0.702264i | ||||
\(783\) | 1.06692e6 | 0.0621912 | ||||||||
\(784\) | 1.68937e7 | + | 1.18738e7i | 0.981599 | + | 0.689919i | ||||
\(785\) | 2.19118e7 | 1.26912 | ||||||||
\(786\) | −4.79839e6 | + | 8.31105e6i | −0.277038 | + | 0.479843i | ||||
\(787\) | 7.03741e6 | + | 1.21891e7i | 0.405019 | + | 0.701514i | 0.994324 | − | 0.106397i | \(-0.0339314\pi\) |
−0.589304 | + | 0.807911i | \(0.700598\pi\) | |||||||
\(788\) | 3.36173e6 | + | 5.82269e6i | 0.192862 | + | 0.334048i | ||||
\(789\) | 3.37076e6 | − | 5.83832e6i | 0.192768 | − | 0.333884i | ||||
\(790\) | −1.56283e7 | −0.890930 | ||||||||
\(791\) | 3.58124e6 | + | 3.91519e6i | 0.203513 | + | 0.222491i | ||||
\(792\) | 6.91213e6 | 0.391560 | ||||||||
\(793\) | −8.04472e6 | + | 1.39339e7i | −0.454284 | + | 0.786844i | ||||
\(794\) | −6.02294e6 | − | 1.04320e7i | −0.339045 | − | 0.587243i | ||||
\(795\) | −350538. | − | 607150.i | −0.0196706 | − | 0.0340705i | ||||
\(796\) | 599848. | − | 1.03897e6i | 0.0335551 | − | 0.0581191i | ||||
\(797\) | −1.75191e7 | −0.976937 | −0.488469 | − | 0.872582i | \(-0.662444\pi\) | ||||
−0.488469 | + | 0.872582i | \(0.662444\pi\) | |||||||
\(798\) | −6.86144e6 | + | 1.51477e6i | −0.381424 | + | 0.0842051i | ||||
\(799\) | 9.06127e6 | 0.502137 | ||||||||
\(800\) | −2.52936e6 | + | 4.38099e6i | −0.139729 | + | 0.242018i | ||||
\(801\) | −635311. | − | 1.10039e6i | −0.0349869 | − | 0.0605990i | ||||
\(802\) | −4.28067e6 | − | 7.41433e6i | −0.235004 | − | 0.407039i | ||||
\(803\) | −1.60486e7 | + | 2.77970e7i | −0.878311 | + | 1.52128i | ||||
\(804\) | −4.01963e6 | −0.219304 | ||||||||
\(805\) | 2.47106e6 | − | 7.81306e6i | 0.134398 | − | 0.424944i | ||||
\(806\) | −9.78721e6 | −0.530666 | ||||||||
\(807\) | 3.01475e6 | − | 5.22170e6i | 0.162955 | − | 0.282246i | ||||
\(808\) | −1.25111e7 | − | 2.16698e7i | −0.674166 | − | 1.16769i | ||||
\(809\) | −407261. | − | 705396.i | −0.0218777 | − | 0.0378932i | 0.854879 | − | 0.518827i | \(-0.173631\pi\) |
−0.876757 | + | 0.480934i | \(0.840298\pi\) | |||||||
\(810\) | −811837. | + | 1.40614e6i | −0.0434767 | + | 0.0753038i | ||||
\(811\) | 1.26533e7 | 0.675540 | 0.337770 | − | 0.941229i | \(-0.390327\pi\) | ||||
0.337770 | + | 0.941229i | \(0.390327\pi\) | |||||||
\(812\) | 505233. | − | 1.59746e6i | 0.0268907 | − | 0.0850235i | ||||
\(813\) | −4.86593e6 | −0.258190 | ||||||||
\(814\) | −3.00175e7 | + | 5.19919e7i | −1.58787 | + | 2.75026i | ||||
\(815\) | 8.33064e6 | + | 1.44291e7i | 0.439324 | + | 0.760931i | ||||
\(816\) | 7.35150e6 | + | 1.27332e7i | 0.386501 | + | 0.669439i | ||||
\(817\) | −6.94297e6 | + | 1.20256e7i | −0.363907 | + | 0.630305i | ||||
\(818\) | 4.20854e7 | 2.19912 | ||||||||
\(819\) | 4.01438e6 | − | 886236.i | 0.209126 | − | 0.0461678i | ||||
\(820\) | −4.48142e6 | −0.232745 | ||||||||
\(821\) | −2.13697e6 | + | 3.70133e6i | −0.110647 | + | 0.191646i | −0.916031 | − | 0.401107i | \(-0.868626\pi\) |
0.805384 | + | 0.592753i | \(0.201959\pi\) | |||||||
\(822\) | 1.09911e6 | + | 1.90371e6i | 0.0567361 | + | 0.0982699i | ||||
\(823\) | −8.52317e6 | − | 1.47626e7i | −0.438633 | − | 0.759735i | 0.558951 | − | 0.829201i | \(-0.311204\pi\) |
−0.997584 | + | 0.0694656i | \(0.977871\pi\) | |||||||
\(824\) | 8.35155e6 | − | 1.44653e7i | 0.428498 | − | 0.742180i | ||||
\(825\) | −8.43001e6 | −0.431214 | ||||||||
\(826\) | −2.87681e7 | − | 3.14508e7i | −1.46711 | − | 1.60392i | ||||
\(827\) | 2.60828e6 | 0.132614 | 0.0663071 | − | 0.997799i | \(-0.478878\pi\) | ||||
0.0663071 | + | 0.997799i | \(0.478878\pi\) | |||||||
\(828\) | 583682. | − | 1.01097e6i | 0.0295870 | − | 0.0512462i | ||||
\(829\) | −1.06932e7 | − | 1.85212e7i | −0.540409 | − | 0.936016i | −0.998880 | − | 0.0473066i | \(-0.984936\pi\) |
0.458471 | − | 0.888709i | \(-0.348397\pi\) | |||||||
\(830\) | −5.63898e6 | − | 9.76700e6i | −0.284122 | − | 0.492114i | ||||
\(831\) | −1.80859e6 | + | 3.13257e6i | −0.0908528 | + | 0.157362i | ||||
\(832\) | 7.60423e6 | 0.380844 | ||||||||
\(833\) | −2.02711e7 | + | 9.40887e6i | −1.01220 | + | 0.469813i | ||||
\(834\) | −6.11104e6 | −0.304229 | ||||||||
\(835\) | 4.65263e6 | − | 8.05859e6i | 0.230931 | − | 0.399984i | ||||
\(836\) | 2.39848e6 | + | 4.15429e6i | 0.118692 | + | 0.205580i | ||||
\(837\) | −1.42608e6 | − | 2.47004e6i | −0.0703605 | − | 0.121868i | ||||
\(838\) | 2.22645e7 | − | 3.85632e7i | 1.09522 | − | 1.89698i | ||||
\(839\) | 771393. | 0.0378330 | 0.0189165 | − | 0.999821i | \(-0.493978\pi\) | ||||
0.0189165 | + | 0.999821i | \(0.493978\pi\) | |||||||
\(840\) | −4.51542e6 | − | 4.93649e6i | −0.220800 | − | 0.241390i | ||||
\(841\) | −1.83692e7 | −0.895571 | ||||||||
\(842\) | −1.22699e7 | + | 2.12520e7i | −0.596430 | + | 1.03305i | ||||
\(843\) | −1.93112e6 | − | 3.34480e6i | −0.0935925 | − | 0.162107i | ||||
\(844\) | 4.37616e6 | + | 7.57973e6i | 0.211464 | + | 0.366267i | ||||
\(845\) | 4.22200e6 | − | 7.31272e6i | 0.203412 | − | 0.352320i | ||||
\(846\) | −3.52705e6 | −0.169428 | ||||||||
\(847\) | 2.16696e7 | − | 4.78388e6i | 1.03787 | − | 0.229125i | ||||
\(848\) | 2.47113e6 | 0.118006 | ||||||||
\(849\) | −1.53417e6 | + | 2.65726e6i | −0.0730474 | + | 0.126522i | ||||
\(850\) | −6.90375e6 | − | 1.19576e7i | −0.327746 | − | 0.567673i | ||||
\(851\) | −1.33017e7 | − | 2.30393e7i | −0.629628 | − | 1.09055i | ||||
\(852\) | 1.58830e6 | − | 2.75102e6i | 0.0749609 | − | 0.129836i | ||||
\(853\) | 2.94032e7 | 1.38364 | 0.691818 | − | 0.722072i | \(-0.256810\pi\) | ||||
0.691818 | + | 0.722072i | \(0.256810\pi\) | |||||||
\(854\) | −1.02664e7 | + | 3.24604e7i | −0.481694 | + | 1.52303i | ||||
\(855\) | 2.95659e6 | 0.138317 | ||||||||
\(856\) | −1.65147e6 | + | 2.86042e6i | −0.0770345 | + | 0.133428i | ||||
\(857\) | 1.32505e7 | + | 2.29505e7i | 0.616283 | + | 1.06743i | 0.990158 | + | 0.139954i | \(0.0446955\pi\) |
−0.373875 | + | 0.927479i | \(0.621971\pi\) | |||||||
\(858\) | −6.48848e6 | − | 1.12384e7i | −0.300902 | − | 0.521177i | ||||
\(859\) | 1.83759e7 | − | 3.18281e7i | 0.849702 | − | 1.47173i | −0.0317727 | − | 0.999495i | \(-0.510115\pi\) |
0.881475 | − | 0.472232i | \(-0.156551\pi\) | |||||||
\(860\) | 5.03876e6 | 0.232315 | ||||||||
\(861\) | −4.61048e6 | + | 1.45775e7i | −0.211952 | + | 0.670156i | ||||
\(862\) | 1.94020e7 | 0.889360 | ||||||||
\(863\) | −5.90946e6 | + | 1.02355e7i | −0.270098 | + | 0.467823i | −0.968887 | − | 0.247505i | \(-0.920389\pi\) |
0.698789 | + | 0.715328i | \(0.253723\pi\) | |||||||
\(864\) | −1.13467e6 | − | 1.96531e6i | −0.0517113 | − | 0.0895665i | ||||
\(865\) | 3.47207e6 | + | 6.01379e6i | 0.157778 | + | 0.273280i | ||||
\(866\) | 3.00812e6 | − | 5.21022e6i | 0.136302 | − | 0.236081i | ||||
\(867\) | −3.13421e6 | −0.141606 | ||||||||
\(868\) | −4.37358e6 | + | 965534.i | −0.197033 | + | 0.0434979i | ||||
\(869\) | 3.63998e7 | 1.63512 | ||||||||
\(870\) | −1.62985e6 | + | 2.82298e6i | −0.0730044 | + | 0.126447i | ||||
\(871\) | −9.90046e6 | − | 1.71481e7i | −0.442191 | − | 0.765897i | ||||
\(872\) | −6.20477e6 | − | 1.07470e7i | −0.276334 | − | 0.478625i | ||||
\(873\) | −126704. | + | 219458.i | −0.00562671 | + | 0.00974575i | ||||
\(874\) | −9.82884e6 | −0.435235 | ||||||||
\(875\) | 1.60970e7 | + | 1.75980e7i | 0.710762 | + | 0.777042i | ||||
\(876\) | 4.42562e6 | 0.194856 | ||||||||
\(877\) | −3.96754e6 | + | 6.87199e6i | −0.174190 | + | 0.301706i | −0.939881 | − | 0.341503i | \(-0.889064\pi\) |
0.765691 | + | 0.643209i | \(0.222397\pi\) | |||||||
\(878\) | −4.28470e6 | − | 7.42131e6i | −0.187579 | − | 0.324896i | ||||
\(879\) | −1.74981e6 | − | 3.03077e6i | −0.0763870 | − | 0.132306i | ||||
\(880\) | −1.37130e7 | + | 2.37516e7i | −0.596934 | + | 1.03392i | ||||
\(881\) | 4.20152e7 | 1.82375 | 0.911877 | − | 0.410464i | \(-0.134633\pi\) | ||||
0.911877 | + | 0.410464i | \(0.134633\pi\) | |||||||
\(882\) | 7.89043e6 | − | 3.66236e6i | 0.341530 | − | 0.158522i | ||||
\(883\) | 2.12461e7 | 0.917016 | 0.458508 | − | 0.888690i | \(-0.348384\pi\) | ||||
0.458508 | + | 0.888690i | \(0.348384\pi\) | |||||||
\(884\) | 2.29840e6 | − | 3.98095e6i | 0.0989226 | − | 0.171339i | ||||
\(885\) | 8.96729e6 | + | 1.55318e7i | 0.384860 | + | 0.666597i | ||||
\(886\) | 2.46758e6 | + | 4.27397e6i | 0.105606 | + | 0.182914i | ||||
\(887\) | −9.42452e6 | + | 1.63238e7i | −0.402208 | + | 0.696644i | −0.993992 | − | 0.109452i | \(-0.965090\pi\) |
0.591784 | + | 0.806096i | \(0.298424\pi\) | |||||||
\(888\) | −2.17195e7 | −0.924309 | ||||||||
\(889\) | −7.28613e6 | − | 7.96558e6i | −0.309202 | − | 0.338036i | ||||
\(890\) | 3.88204e6 | 0.164280 | ||||||||
\(891\) | 1.89085e6 | − | 3.27504e6i | 0.0797925 | − | 0.138205i | ||||
\(892\) | −2.39897e6 | − | 4.15514e6i | −0.100952 | − | 0.174853i | ||||
\(893\) | 3.21125e6 | + | 5.56205e6i | 0.134755 | + | 0.233403i | ||||
\(894\) | 5.53682e6 | − | 9.59005e6i | 0.231695 | − | 0.401307i | ||||
\(895\) | −2.22909e7 | −0.930186 | ||||||||
\(896\) | 2.83227e7 | − | 6.25267e6i | 1.17860 | − | 0.260193i | ||||
\(897\) | 5.75050e6 | 0.238630 | ||||||||
\(898\) | −7.21044e6 | + | 1.24889e7i | −0.298381 | + | 0.516811i | ||||
\(899\) | −2.86300e6 | − | 4.95886e6i | −0.118147 | − | 0.204636i | ||||
\(900\) | 581172. | + | 1.00662e6i | 0.0239165 | + | 0.0414247i | ||||
\(901\) | −1.33724e6 | + | 2.31617e6i | −0.0548780 | + | 0.0950514i | ||||
\(902\) | 4.82621e7 | 1.97510 | ||||||||
\(903\) | 5.18387e6 | − | 1.63905e7i | 0.211561 | − | 0.668917i | ||||
\(904\) | 6.05948e6 | 0.246612 | ||||||||
\(905\) | −1.12509e7 | + | 1.94872e7i | −0.456632 | + | 0.790910i | ||||
\(906\) | 4.07446e6 | + | 7.05717e6i | 0.164911 | + | 0.285634i | ||||
\(907\) | 3.09723e6 | + | 5.36456e6i | 0.125013 | + | 0.216529i | 0.921738 | − | 0.387813i | \(-0.126769\pi\) |
−0.796725 | + | 0.604342i | \(0.793436\pi\) | |||||||
\(908\) | −72.1183 | + | 124.912i | −2.90289e−6 | + | 5.02795e-6i | ||||
\(909\) | −1.36899e7 | −0.549528 | ||||||||
\(910\) | −3.78753e6 | + | 1.19755e7i | −0.151619 | + | 0.479392i | ||||
\(911\) | −2.50171e7 | −0.998712 | −0.499356 | − | 0.866397i | \(-0.666430\pi\) | ||||
−0.499356 | + | 0.866397i | \(0.666430\pi\) | |||||||
\(912\) | −5.21064e6 | + | 9.02509e6i | −0.207445 | + | 0.359306i | ||||
\(913\) | 1.31337e7 | + | 2.27483e7i | 0.521448 | + | 0.903174i | ||||
\(914\) | −1.36893e7 | − | 2.37106e7i | −0.542022 | − | 0.938810i | ||||
\(915\) | 7.16256e6 | − | 1.24059e7i | 0.282824 | − | 0.489865i | ||||
\(916\) | −683288. | −0.0269070 | ||||||||
\(917\) | −2.11253e7 | + | 4.66373e6i | −0.829620 | + | 0.183151i | ||||
\(918\) | 6.19403e6 | 0.242586 | ||||||||
\(919\) | −7.74961e6 | + | 1.34227e7i | −0.302685 | + | 0.524266i | −0.976743 | − | 0.214412i | \(-0.931216\pi\) |
0.674058 | + | 0.738678i | \(0.264550\pi\) | |||||||
\(920\) | −4.67906e6 | − | 8.10437e6i | −0.182259 | − | 0.315682i | ||||
\(921\) | −1.06086e7 | − | 1.83746e7i | −0.412106 | − | 0.713789i | ||||
\(922\) | 9.91905e6 | − | 1.71803e7i | 0.384276 | − | 0.665585i | ||||
\(923\) | 1.56481e7 | 0.604587 | ||||||||
\(924\) | −4.00818e6 | − | 4.38195e6i | −0.154443 | − | 0.168845i | ||||
\(925\) | 2.64890e7 | 1.01791 | ||||||||
\(926\) | 1.12905e7 | − | 1.95556e7i | 0.432697 | − | 0.749453i | ||||
\(927\) | −4.56921e6 | − | 7.91411e6i | −0.174639 | − | 0.302484i | ||||
\(928\) | −2.27797e6 | − | 3.94556e6i | −0.0868316 | − | 0.150397i | ||||
\(929\) | −1.87643e7 | + | 3.25007e7i | −0.713333 | + | 1.23553i | 0.250266 | + | 0.968177i | \(0.419482\pi\) |
−0.963599 | + | 0.267352i | \(0.913852\pi\) | |||||||
\(930\) | 8.71398e6 | 0.330377 | ||||||||
\(931\) | −1.29594e7 | − | 9.10852e6i | −0.490015 | − | 0.344408i | ||||
\(932\) | −915335. | −0.0345176 | ||||||||
\(933\) | −6.46483e6 | + | 1.11974e7i | −0.243138 | + | 0.421127i | ||||
\(934\) | −8.70489e6 | − | 1.50773e7i | −0.326510 | − | 0.565532i | ||||
\(935\) | −1.48415e7 | − | 2.57062e7i | −0.555198 | − | 0.961632i | ||||
\(936\) | 2.34740e6 | − | 4.06582e6i | 0.0875786 | − | 0.151691i | ||||
\(937\) | −1.08298e7 | −0.402969 | −0.201485 | − | 0.979492i | \(-0.564577\pi\) | ||||
−0.201485 | + | 0.979492i | \(0.564577\pi\) | |||||||
\(938\) | −2.82789e7 | − | 3.09160e7i | −1.04944 | − | 1.14730i | ||||
\(939\) | 7.40520e6 | 0.274077 | ||||||||
\(940\) | 1.16526e6 | − | 2.01829e6i | 0.0430133 | − | 0.0745013i | ||||
\(941\) | −1.62295e7 | − | 2.81104e7i | −0.597492 | − | 1.03489i | −0.993190 | − | 0.116505i | \(-0.962831\pi\) |
0.395699 | − | 0.918380i | \(-0.370503\pi\) | |||||||
\(942\) | 1.62684e7 | + | 2.81777e7i | 0.597335 | + | 1.03461i | ||||
\(943\) | −1.06932e7 | + | 1.85212e7i | −0.391589 | + | 0.678251i | ||||
\(944\) | −6.32151e7 | −2.30883 | ||||||||
\(945\) | −3.57418e6 | + | 789054.i | −0.130196 | + | 0.0287427i | ||||
\(946\) | −5.42643e7 | −1.97145 | ||||||||
\(947\) | −3.76939e6 | + | 6.52877e6i | −0.136583 | + | 0.236568i | −0.926201 | − | 0.377030i | \(-0.876945\pi\) |
0.789618 | + | 0.613598i | \(0.210279\pi\) | |||||||
\(948\) | −2.50943e6 | − | 4.34646e6i | −0.0906890 | − | 0.157078i | ||||
\(949\) | 1.09004e7 | + | 1.88801e7i | 0.392896 | + | 0.680516i | ||||
\(950\) | 4.89328e6 | − | 8.47541e6i | 0.175910 | − | 0.304686i | ||||
\(951\) | 1.59024e7 | 0.570180 | ||||||||
\(952\) | −7.69608e6 | + | 2.43336e7i | −0.275218 | + | 0.870191i | ||||
\(953\) | −3.01356e7 | −1.07485 | −0.537424 | − | 0.843312i | \(-0.680602\pi\) | ||||
−0.537424 | + | 0.843312i | \(0.680602\pi\) | |||||||
\(954\) | 520515. | − | 901558.i | 0.0185166 | − | 0.0320718i | ||||
\(955\) | 1.27914e7 | + | 2.21554e7i | 0.453848 | + | 0.786089i | ||||
\(956\) | −3.04255e6 | − | 5.26986e6i | −0.107670 | − | 0.186489i | ||||
\(957\) | 3.79607e6 | − | 6.57499e6i | 0.133985 | − | 0.232068i | ||||
\(958\) | 6.25366e6 | 0.220151 | ||||||||
\(959\) | −1.49431e6 | + | 4.72474e6i | −0.0524680 | + | 0.165894i | ||||
\(960\) | −6.77038e6 | −0.237102 | ||||||||
\(961\) | 6.66107e6 | − | 1.15373e7i | 0.232667 | − | 0.402992i | ||||
\(962\) | 2.03883e7 | + | 3.53135e7i | 0.710301 | + | 1.23028i | ||||
\(963\) | 903534. | + | 1.56497e6i | 0.0313963 | + | 0.0543800i | ||||
\(964\) | −972650. | + | 1.68468e6i | −0.0337104 | + | 0.0583882i | ||||
\(965\) | −2.15841e7 | −0.746132 | ||||||||
\(966\) | 1.18819e7 | − | 2.62312e6i | 0.409680 | − | 0.0904430i | ||||
\(967\) | 2.88021e6 | 0.0990509 | 0.0495255 | − | 0.998773i | \(-0.484229\pi\) | ||||
0.0495255 | + | 0.998773i | \(0.484229\pi\) | |||||||
\(968\) | 1.26712e7 | − | 2.19472e7i | 0.434641 | − | 0.752820i | ||||
\(969\) | −5.63943e6 | − | 9.76779e6i | −0.192942 | − | 0.334185i | ||||
\(970\) | −387110. | − | 670494.i | −0.0132101 | − | 0.0228805i | ||||
\(971\) | 1.37245e7 | − | 2.37715e7i | 0.467142 | − | 0.809113i | −0.532154 | − | 0.846648i | \(-0.678617\pi\) |
0.999295 | + | 0.0375347i | \(0.0119505\pi\) | |||||||
\(972\) | −521426. | −0.0177022 | ||||||||
\(973\) | −9.29799e6 | − | 1.01650e7i | −0.314852 | − | 0.344213i | ||||
\(974\) | 2.50958e7 | 0.847626 | ||||||||
\(975\) | −2.86288e6 | + | 4.95866e6i | −0.0964478 | + | 0.167052i | ||||
\(976\) | 2.52463e7 | + | 4.37279e7i | 0.848347 | + | 1.46938i | ||||
\(977\) | 2.94262e7 | + | 5.09676e7i | 0.986274 | + | 1.70828i | 0.636133 | + | 0.771579i | \(0.280533\pi\) |
0.350141 | + | 0.936697i | \(0.386134\pi\) | |||||||
\(978\) | −1.23702e7 | + | 2.14258e7i | −0.413551 | + | 0.716291i | ||||
\(979\) | −9.04164e6 | −0.301502 | ||||||||
\(980\) | −511109. | + | 5.72511e6i | −0.0170000 | + | 0.190423i | ||||
\(981\) | −6.78938e6 | −0.225246 | ||||||||
\(982\) | −8.41039e6 | + | 1.45672e7i | −0.278315 | + | 0.482056i | ||||
\(983\) | −9.30384e6 | − | 1.61147e7i | −0.307099 | − | 0.531911i | 0.670627 | − | 0.741794i | \(-0.266025\pi\) |
−0.977726 | + | 0.209883i | \(0.932692\pi\) | |||||||
\(984\) | 8.73014e6 | + | 1.51210e7i | 0.287431 | + | 0.497845i | ||||
\(985\) | 1.47442e7 | − | 2.55376e7i | 0.484205 | − | 0.838668i | ||||
\(986\) | 1.24352e7 | 0.407342 | ||||||||
\(987\) | −5.36643e6 | − | 5.86687e6i | −0.175345 | − | 0.191696i | ||||
\(988\) | 3.25815e6 | 0.106189 | ||||||||
\(989\) | 1.20231e7 | − | 2.08246e7i | 0.390865 | − | 0.676997i | ||||
\(990\) | 5.77697e6 | + | 1.00060e7i | 0.187332 | + | 0.324469i | ||||
\(991\) | −1.23577e7 | − | 2.14041e7i | −0.399718 | − | 0.692331i | 0.593973 | − | 0.804485i | \(-0.297558\pi\) |
−0.993691 | + | 0.112154i | \(0.964225\pi\) | |||||||
\(992\) | −6.08958e6 | + | 1.05475e7i | −0.196475 | + | 0.340305i | ||||
\(993\) | 27470.5 | 0.000884083 | ||||||||
\(994\) | 3.23329e7 | − | 7.13797e6i | 1.03796 | − | 0.229144i | ||||
\(995\) | −5.26172e6 | −0.168488 | ||||||||
\(996\) | 1.81090e6 | − | 3.13657e6i | 0.0578424 | − | 0.100186i | ||||
\(997\) | 8.97906e6 | + | 1.55522e7i | 0.286084 | + | 0.495511i | 0.972871 | − | 0.231347i | \(-0.0743131\pi\) |
−0.686788 | + | 0.726858i | \(0.740980\pi\) | |||||||
\(998\) | −6.79064e6 | − | 1.17617e7i | −0.215816 | − | 0.373805i | ||||
\(999\) | −5.94147e6 | + | 1.02909e7i | −0.188356 | + | 0.326243i |
(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 | 21.6.e.b.16.1 | yes | 4 | |
3.2 | odd | 2 | 63.6.e.c.37.2 | 4 | |||
4.3 | odd | 2 | 336.6.q.e.289.1 | 4 | |||
7.2 | even | 3 | 147.6.a.i.1.2 | 2 | |||
7.3 | odd | 6 | 147.6.e.l.67.1 | 4 | |||
7.4 | even | 3 | inner | 21.6.e.b.4.1 | ✓ | 4 | |
7.5 | odd | 6 | 147.6.a.k.1.2 | 2 | |||
7.6 | odd | 2 | 147.6.e.l.79.1 | 4 | |||
21.2 | odd | 6 | 441.6.a.t.1.1 | 2 | |||
21.5 | even | 6 | 441.6.a.s.1.1 | 2 | |||
21.11 | odd | 6 | 63.6.e.c.46.2 | 4 | |||
28.11 | odd | 6 | 336.6.q.e.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.b.4.1 | ✓ | 4 | 7.4 | even | 3 | inner | |
21.6.e.b.16.1 | yes | 4 | 1.1 | even | 1 | trivial | |
63.6.e.c.37.2 | 4 | 3.2 | odd | 2 | |||
63.6.e.c.46.2 | 4 | 21.11 | odd | 6 | |||
147.6.a.i.1.2 | 2 | 7.2 | even | 3 | |||
147.6.a.k.1.2 | 2 | 7.5 | odd | 6 | |||
147.6.e.l.67.1 | 4 | 7.3 | odd | 6 | |||
147.6.e.l.79.1 | 4 | 7.6 | odd | 2 | |||
336.6.q.e.193.1 | 4 | 28.11 | odd | 6 | |||
336.6.q.e.289.1 | 4 | 4.3 | odd | 2 | |||
441.6.a.s.1.1 | 2 | 21.5 | even | 6 | |||
441.6.a.t.1.1 | 2 | 21.2 | odd | 6 |