Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(21,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.21");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.l (of order \(4\), 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: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 21.16 | ||
Character | \(\chi\) | \(=\) | 80.21 |
Dual form | 80.6.l.a.61.16 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24441 | + | 5.19255i | −0.396759 | + | 0.917923i | ||||
\(3\) | 1.65480 | − | 1.65480i | 0.106156 | − | 0.106156i | −0.652034 | − | 0.758190i | \(-0.726084\pi\) |
0.758190 | + | 0.652034i | \(0.226084\pi\) | |||||||
\(4\) | −21.9252 | − | 23.3084i | −0.685164 | − | 0.728389i | ||||
\(5\) | −17.6777 | − | 17.6777i | −0.316228 | − | 0.316228i | ||||
\(6\) | 4.87860 | + | 12.3067i | 0.0553245 | + | 0.139561i | ||||
\(7\) | − | 111.270i | − | 0.858286i | −0.903237 | − | 0.429143i | \(-0.858816\pi\) | ||
0.903237 | − | 0.429143i | \(-0.141184\pi\) | |||||||
\(8\) | 170.240 | − | 61.5343i | 0.940450 | − | 0.339932i | ||||
\(9\) | 237.523i | 0.977462i | ||||||||
\(10\) | 131.468 | − | 52.1163i | 0.415739 | − | 0.164806i | ||||
\(11\) | 263.604 | + | 263.604i | 0.656856 | + | 0.656856i | 0.954635 | − | 0.297779i | \(-0.0962458\pi\) |
−0.297779 | + | 0.954635i | \(0.596246\pi\) | |||||||
\(12\) | −74.8529 | − | 2.28894i | −0.150057 | − | 0.00458860i | ||||
\(13\) | −480.266 | + | 480.266i | −0.788176 | + | 0.788176i | −0.981195 | − | 0.193019i | \(-0.938172\pi\) |
0.193019 | + | 0.981195i | \(0.438172\pi\) | |||||||
\(14\) | 577.774 | + | 249.735i | 0.787840 | + | 0.340533i | ||||
\(15\) | −58.5062 | −0.0671388 | ||||||||
\(16\) | −62.5675 | + | 1022.09i | −0.0611011 | + | 0.998132i | ||||
\(17\) | 1411.28 | 1.18438 | 0.592189 | − | 0.805799i | \(-0.298264\pi\) | ||||
0.592189 | + | 0.805799i | \(0.298264\pi\) | |||||||
\(18\) | −1233.35 | − | 533.100i | −0.897234 | − | 0.387817i | ||||
\(19\) | 555.890 | − | 555.890i | 0.353269 | − | 0.353269i | −0.508056 | − | 0.861324i | \(-0.669636\pi\) |
0.861324 | + | 0.508056i | \(0.169636\pi\) | |||||||
\(20\) | −24.4519 | + | 799.626i | −0.0136690 | + | 0.447005i | ||||
\(21\) | −184.130 | − | 184.130i | −0.0911120 | − | 0.0911120i | ||||
\(22\) | −1960.41 | + | 777.142i | −0.863557 | + | 0.342329i | ||||
\(23\) | 3849.49i | 1.51734i | 0.651474 | + | 0.758671i | \(0.274151\pi\) | ||||
−0.651474 | + | 0.758671i | \(0.725849\pi\) | |||||||
\(24\) | 179.886 | − | 383.541i | 0.0637484 | − | 0.135920i | ||||
\(25\) | 625.000i | 0.200000i | ||||||||
\(26\) | −1415.89 | − | 3571.72i | −0.410768 | − | 1.03620i | ||||
\(27\) | 795.172 | + | 795.172i | 0.209919 | + | 0.209919i | ||||
\(28\) | −2593.53 | + | 2439.62i | −0.625166 | + | 0.588066i | ||||
\(29\) | −2779.61 | + | 2779.61i | −0.613747 | + | 0.613747i | −0.943920 | − | 0.330174i | \(-0.892893\pi\) |
0.330174 | + | 0.943920i | \(0.392893\pi\) | |||||||
\(30\) | 131.312 | − | 303.797i | 0.0266380 | − | 0.0616282i | ||||
\(31\) | −5160.34 | −0.964437 | −0.482219 | − | 0.876051i | \(-0.660169\pi\) | ||||
−0.482219 | + | 0.876051i | \(0.660169\pi\) | |||||||
\(32\) | −5166.81 | − | 2618.87i | −0.891965 | − | 0.452104i | ||||
\(33\) | 872.426 | 0.139458 | ||||||||
\(34\) | −3167.49 | + | 7328.14i | −0.469913 | + | 1.08717i | ||||
\(35\) | −1966.99 | + | 1966.99i | −0.271414 | + | 0.271414i | ||||
\(36\) | 5536.30 | − | 5207.75i | 0.711973 | − | 0.669722i | ||||
\(37\) | 7576.66 | + | 7576.66i | 0.909858 | + | 0.909858i | 0.996260 | − | 0.0864025i | \(-0.0275371\pi\) |
−0.0864025 | + | 0.996260i | \(0.527537\pi\) | |||||||
\(38\) | 1638.84 | + | 4134.14i | 0.184111 | + | 0.464436i | ||||
\(39\) | 1589.49i | 0.167339i | ||||||||
\(40\) | −4097.22 | − | 1921.66i | −0.404892 | − | 0.189900i | ||||
\(41\) | − | 3026.02i | − | 0.281134i | −0.990071 | − | 0.140567i | \(-0.955108\pi\) | ||
0.990071 | − | 0.140567i | \(-0.0448925\pi\) | |||||||
\(42\) | 1369.37 | − | 542.841i | 0.119783 | − | 0.0474842i | ||||
\(43\) | 10147.2 | + | 10147.2i | 0.836900 | + | 0.836900i | 0.988450 | − | 0.151549i | \(-0.0484263\pi\) |
−0.151549 | + | 0.988450i | \(0.548426\pi\) | |||||||
\(44\) | 364.619 | − | 11923.8i | 0.0283927 | − | 0.928501i | ||||
\(45\) | 4198.86 | − | 4198.86i | 0.309101 | − | 0.309101i | ||||
\(46\) | −19988.7 | − | 8639.83i | −1.39280 | − | 0.602020i | ||||
\(47\) | 25138.6 | 1.65995 | 0.829977 | − | 0.557798i | \(-0.188353\pi\) | ||||
0.829977 | + | 0.557798i | \(0.188353\pi\) | |||||||
\(48\) | 1587.82 | + | 1794.89i | 0.0994712 | + | 0.112444i | ||||
\(49\) | 4426.04 | 0.263345 | ||||||||
\(50\) | −3245.35 | − | 1402.76i | −0.183585 | − | 0.0793519i | ||||
\(51\) | 2335.39 | − | 2335.39i | 0.125729 | − | 0.125729i | ||||
\(52\) | 21724.2 | + | 664.307i | 1.11413 | + | 0.0340691i | ||||
\(53\) | −21380.6 | − | 21380.6i | −1.04552 | − | 1.04552i | −0.998914 | − | 0.0466020i | \(-0.985161\pi\) |
−0.0466020 | − | 0.998914i | \(-0.514839\pi\) | |||||||
\(54\) | −5913.67 | + | 2344.28i | −0.275977 | + | 0.109402i | ||||
\(55\) | − | 9319.81i | − | 0.415432i | ||||||
\(56\) | −6846.90 | − | 18942.5i | −0.291759 | − | 0.807175i | ||||
\(57\) | − | 1839.78i | − | 0.0750030i | ||||||
\(58\) | −8194.69 | − | 20671.9i | −0.319862 | − | 0.806882i | ||||
\(59\) | 24893.6 | + | 24893.6i | 0.931016 | + | 0.931016i | 0.997769 | − | 0.0667538i | \(-0.0212642\pi\) |
−0.0667538 | + | 0.997769i | \(0.521264\pi\) | |||||||
\(60\) | 1282.76 | + | 1363.69i | 0.0460011 | + | 0.0489032i | ||||
\(61\) | 5605.68 | − | 5605.68i | 0.192887 | − | 0.192887i | −0.604055 | − | 0.796943i | \(-0.706449\pi\) |
0.796943 | + | 0.604055i | \(0.206449\pi\) | |||||||
\(62\) | 11581.9 | − | 26795.3i | 0.382650 | − | 0.885279i | ||||
\(63\) | 26429.2 | 0.838942 | ||||||||
\(64\) | 25195.1 | − | 20951.1i | 0.768892 | − | 0.639378i | ||||
\(65\) | 16980.0 | 0.498486 | ||||||||
\(66\) | −1958.08 | + | 4530.12i | −0.0553313 | + | 0.128012i | ||||
\(67\) | −19174.5 | + | 19174.5i | −0.521841 | + | 0.521841i | −0.918127 | − | 0.396286i | \(-0.870299\pi\) |
0.396286 | + | 0.918127i | \(0.370299\pi\) | |||||||
\(68\) | −30942.6 | − | 32894.7i | −0.811493 | − | 0.862688i | ||||
\(69\) | 6370.15 | + | 6370.15i | 0.161075 | + | 0.161075i | ||||
\(70\) | −5798.97 | − | 14628.4i | −0.141451 | − | 0.356823i | ||||
\(71\) | 17973.8i | 0.423151i | 0.977362 | + | 0.211575i | \(0.0678594\pi\) | ||||
−0.977362 | + | 0.211575i | \(0.932141\pi\) | |||||||
\(72\) | 14615.8 | + | 40435.9i | 0.332271 | + | 0.919254i | ||||
\(73\) | 14533.0i | 0.319189i | 0.987183 | + | 0.159595i | \(0.0510187\pi\) | ||||
−0.987183 | + | 0.159595i | \(0.948981\pi\) | |||||||
\(74\) | −56347.4 | + | 22337.1i | −1.19617 | + | 0.474184i | ||||
\(75\) | 1034.25 | + | 1034.25i | 0.0212312 | + | 0.0212312i | ||||
\(76\) | −25145.0 | − | 768.911i | −0.499364 | − | 0.0152701i | ||||
\(77\) | 29331.1 | − | 29331.1i | 0.563770 | − | 0.563770i | ||||
\(78\) | −8253.53 | − | 3567.47i | −0.153604 | − | 0.0663933i | ||||
\(79\) | −56320.7 | −1.01531 | −0.507657 | − | 0.861559i | \(-0.669488\pi\) | ||||
−0.507657 | + | 0.861559i | \(0.669488\pi\) | |||||||
\(80\) | 19174.2 | − | 16962.1i | 0.334959 | − | 0.296315i | ||||
\(81\) | −55086.4 | −0.932894 | ||||||||
\(82\) | 15712.8 | + | 6791.64i | 0.258059 | + | 0.111542i | ||||
\(83\) | −5922.95 | + | 5922.95i | −0.0943720 | + | 0.0943720i | −0.752717 | − | 0.658345i | \(-0.771257\pi\) |
0.658345 | + | 0.752717i | \(0.271257\pi\) | |||||||
\(84\) | −254.689 | + | 8328.87i | −0.00393833 | + | 0.128792i | ||||
\(85\) | −24948.1 | − | 24948.1i | −0.374533 | − | 0.374533i | ||||
\(86\) | −75464.1 | + | 29915.3i | −1.10026 | + | 0.436162i | ||||
\(87\) | 9199.43i | 0.130305i | ||||||||
\(88\) | 61096.5 | + | 28655.2i | 0.841027 | + | 0.394454i | ||||
\(89\) | − | 124737.i | − | 1.66924i | −0.550827 | − | 0.834620i | \(-0.685687\pi\) | ||
0.550827 | − | 0.834620i | \(-0.314313\pi\) | |||||||
\(90\) | 12378.8 | + | 31226.8i | 0.161092 | + | 0.406369i | ||||
\(91\) | 53439.1 | + | 53439.1i | 0.676481 | + | 0.676481i | ||||
\(92\) | 89725.6 | − | 84400.9i | 1.10521 | − | 1.03963i | ||||
\(93\) | −8539.35 | + | 8539.35i | −0.102381 | + | 0.102381i | ||||
\(94\) | −56421.3 | + | 130533.i | −0.658603 | + | 1.52371i | ||||
\(95\) | −19653.7 | −0.223427 | ||||||||
\(96\) | −12883.8 | + | 4216.35i | −0.142681 | + | 0.0466938i | ||||
\(97\) | 50538.0 | 0.545367 | 0.272684 | − | 0.962104i | \(-0.412089\pi\) | ||||
0.272684 | + | 0.962104i | \(0.412089\pi\) | |||||||
\(98\) | −9933.86 | + | 22982.5i | −0.104485 | + | 0.241731i | ||||
\(99\) | −62612.1 | + | 62612.1i | −0.642052 | + | 0.642052i | ||||
\(100\) | 14567.8 | − | 13703.3i | 0.145678 | − | 0.137033i | ||||
\(101\) | −73443.7 | − | 73443.7i | −0.716392 | − | 0.716392i | 0.251472 | − | 0.967865i | \(-0.419085\pi\) |
−0.967865 | + | 0.251472i | \(0.919085\pi\) | |||||||
\(102\) | 6885.07 | + | 17368.2i | 0.0655251 | + | 0.165293i | ||||
\(103\) | 100092.i | 0.929617i | 0.885411 | + | 0.464809i | \(0.153877\pi\) | ||||
−0.885411 | + | 0.464809i | \(0.846123\pi\) | |||||||
\(104\) | −52207.5 | + | 111313.i | −0.473314 | + | 1.00917i | ||||
\(105\) | 6509.97i | 0.0576243i | ||||||||
\(106\) | 159007. | − | 63033.1i | 1.37452 | − | 0.544884i | ||||
\(107\) | 43501.2 | + | 43501.2i | 0.367318 | + | 0.367318i | 0.866498 | − | 0.499180i | \(-0.166365\pi\) |
−0.499180 | + | 0.866498i | \(0.666365\pi\) | |||||||
\(108\) | 1099.89 | − | 35968.6i | 0.00907379 | − | 0.296732i | ||||
\(109\) | −118270. | + | 118270.i | −0.953475 | + | 0.953475i | −0.998965 | − | 0.0454893i | \(-0.985515\pi\) |
0.0454893 | + | 0.998965i | \(0.485515\pi\) | |||||||
\(110\) | 48393.6 | + | 20917.5i | 0.381335 | + | 0.164827i | ||||
\(111\) | 25075.8 | 0.193173 | ||||||||
\(112\) | 113727. | + | 6961.87i | 0.856682 | + | 0.0524422i | ||||
\(113\) | −33752.4 | −0.248661 | −0.124331 | − | 0.992241i | \(-0.539678\pi\) | ||||
−0.124331 | + | 0.992241i | \(0.539678\pi\) | |||||||
\(114\) | 9553.16 | + | 4129.22i | 0.0688470 | + | 0.0297582i | ||||
\(115\) | 68050.0 | − | 68050.0i | 0.479826 | − | 0.479826i | ||||
\(116\) | 125732. | + | 3844.78i | 0.867563 | + | 0.0265293i | ||||
\(117\) | −114074. | − | 114074.i | −0.770412 | − | 0.770412i | ||||
\(118\) | −185133. | + | 73389.8i | −1.22399 | + | 0.485211i | ||||
\(119\) | − | 157033.i | − | 1.01654i | ||||||
\(120\) | −9960.07 | + | 3600.14i | −0.0631407 | + | 0.0228226i | ||||
\(121\) | − | 22077.0i | − | 0.137081i | ||||||
\(122\) | 16526.4 | + | 41689.3i | 0.100526 | + | 0.253586i | ||||
\(123\) | −5007.48 | − | 5007.48i | −0.0298440 | − | 0.0298440i | ||||
\(124\) | 113142. | + | 120279.i | 0.660797 | + | 0.702485i | ||||
\(125\) | 11048.5 | − | 11048.5i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | −59317.9 | + | 137235.i | −0.332858 | + | 0.770084i | ||||
\(127\) | 254716. | 1.40135 | 0.700675 | − | 0.713481i | \(-0.252883\pi\) | ||||
0.700675 | + | 0.713481i | \(0.252883\pi\) | |||||||
\(128\) | 52241.9 | + | 177850.i | 0.281834 | + | 0.959463i | ||||
\(129\) | 33583.2 | 0.177684 | ||||||||
\(130\) | −38110.0 | + | 88169.4i | −0.197779 | + | 0.457572i | ||||
\(131\) | −241006. | + | 241006.i | −1.22701 | + | 1.22701i | −0.261926 | + | 0.965088i | \(0.584358\pi\) |
−0.965088 | + | 0.261926i | \(0.915642\pi\) | |||||||
\(132\) | −19128.2 | − | 20334.9i | −0.0955517 | − | 0.101580i | ||||
\(133\) | −61853.8 | − | 61853.8i | −0.303206 | − | 0.303206i | ||||
\(134\) | −56529.3 | − | 142600.i | −0.271964 | − | 0.686055i | ||||
\(135\) | − | 28113.6i | − | 0.132764i | ||||||
\(136\) | 240256. | − | 86842.0i | 1.11385 | − | 0.402608i | ||||
\(137\) | − | 293678.i | − | 1.33681i | −0.743798 | − | 0.668405i | \(-0.766977\pi\) | ||
0.743798 | − | 0.668405i | \(-0.233023\pi\) | |||||||
\(138\) | −47374.6 | + | 18780.1i | −0.211762 | + | 0.0839461i | ||||
\(139\) | −30954.7 | − | 30954.7i | −0.135891 | − | 0.135891i | 0.635890 | − | 0.771780i | \(-0.280633\pi\) |
−0.771780 | + | 0.635890i | \(0.780633\pi\) | |||||||
\(140\) | 88974.2 | + | 2720.75i | 0.383658 | + | 0.0117319i | ||||
\(141\) | 41599.4 | − | 41599.4i | 0.176214 | − | 0.176214i | ||||
\(142\) | −93330.2 | − | 40340.7i | −0.388420 | − | 0.167889i | ||||
\(143\) | −253200. | −1.03544 | ||||||||
\(144\) | −242769. | − | 14861.2i | −0.975636 | − | 0.0597240i | ||||
\(145\) | 98274.1 | 0.388167 | ||||||||
\(146\) | −75463.4 | − | 32618.0i | −0.292991 | − | 0.126641i | ||||
\(147\) | 7324.24 | − | 7324.24i | 0.0279556 | − | 0.0279556i | ||||
\(148\) | 10480.1 | − | 342720.i | 0.0393288 | − | 1.28613i | ||||
\(149\) | −382188. | − | 382188.i | −1.41030 | − | 1.41030i | −0.757724 | − | 0.652575i | \(-0.773689\pi\) |
−0.652575 | − | 0.757724i | \(-0.726311\pi\) | |||||||
\(150\) | −7691.70 | + | 3049.13i | −0.0279122 | + | 0.0110649i | ||||
\(151\) | − | 135907.i | − | 0.485064i | −0.970143 | − | 0.242532i | \(-0.922022\pi\) | ||
0.970143 | − | 0.242532i | \(-0.0779779\pi\) | |||||||
\(152\) | 60428.3 | − | 128841.i | 0.212144 | − | 0.452319i | ||||
\(153\) | 335212.i | 1.15769i | ||||||||
\(154\) | 86472.4 | + | 218135.i | 0.293816 | + | 0.741179i | ||||
\(155\) | 91222.7 | + | 91222.7i | 0.304982 | + | 0.304982i | ||||
\(156\) | 37048.6 | − | 34850.0i | 0.121888 | − | 0.114655i | ||||
\(157\) | −100753. | + | 100753.i | −0.326219 | + | 0.326219i | −0.851147 | − | 0.524928i | \(-0.824092\pi\) |
0.524928 | + | 0.851147i | \(0.324092\pi\) | |||||||
\(158\) | 126407. | − | 292448.i | 0.402835 | − | 0.931979i | ||||
\(159\) | −70761.5 | −0.221975 | ||||||||
\(160\) | 45041.8 | + | 137633.i | 0.139096 | + | 0.425032i | ||||
\(161\) | 428332. | 1.30231 | ||||||||
\(162\) | 123637. | − | 286039.i | 0.370134 | − | 0.856324i | ||||
\(163\) | −16864.2 | + | 16864.2i | −0.0497161 | + | 0.0497161i | −0.731528 | − | 0.681812i | \(-0.761192\pi\) |
0.681812 | + | 0.731528i | \(0.261192\pi\) | |||||||
\(164\) | −70531.9 | + | 66346.3i | −0.204775 | + | 0.192623i | ||||
\(165\) | −15422.5 | − | 15422.5i | −0.0441005 | − | 0.0441005i | ||||
\(166\) | −17461.7 | − | 44048.8i | −0.0491832 | − | 0.124069i | ||||
\(167\) | − | 538886.i | − | 1.49522i | −0.664136 | − | 0.747612i | \(-0.731201\pi\) | ||
0.664136 | − | 0.747612i | \(-0.268799\pi\) | |||||||
\(168\) | −42676.5 | − | 20015.9i | −0.116658 | − | 0.0547144i | ||||
\(169\) | − | 90017.5i | − | 0.242443i | ||||||
\(170\) | 185538. | − | 73550.7i | 0.492392 | − | 0.195193i | ||||
\(171\) | 132037. | + | 132037.i | 0.345307 | + | 0.345307i | ||||
\(172\) | 14035.6 | − | 458994.i | 0.0361752 | − | 1.18300i | ||||
\(173\) | −329401. | + | 329401.i | −0.836776 | + | 0.836776i | −0.988433 | − | 0.151657i | \(-0.951539\pi\) |
0.151657 | + | 0.988433i | \(0.451539\pi\) | |||||||
\(174\) | −47768.5 | − | 20647.3i | −0.119610 | − | 0.0516999i | ||||
\(175\) | 69543.6 | 0.171657 | ||||||||
\(176\) | −285919. | + | 252933.i | −0.695763 | + | 0.615494i | ||||
\(177\) | 82388.0 | 0.197665 | ||||||||
\(178\) | 647701. | + | 279960.i | 1.53223 | + | 0.662287i | ||||
\(179\) | −229.262 | + | 229.262i | −0.000534809 | + | 0.000534809i | −0.707374 | − | 0.706839i | \(-0.750120\pi\) |
0.706839 | + | 0.707374i | \(0.250120\pi\) | |||||||
\(180\) | −189930. | − | 5807.89i | −0.436930 | − | 0.0133609i | ||||
\(181\) | 326773. | + | 326773.i | 0.741395 | + | 0.741395i | 0.972846 | − | 0.231451i | \(-0.0743474\pi\) |
−0.231451 | + | 0.972846i | \(0.574347\pi\) | |||||||
\(182\) | −397424. | + | 157546.i | −0.889357 | + | 0.352557i | ||||
\(183\) | − | 18552.6i | − | 0.0409522i | ||||||
\(184\) | 236875. | + | 655335.i | 0.515793 | + | 1.42698i | ||||
\(185\) | − | 267875.i | − | 0.575445i | ||||||
\(186\) | −25175.2 | − | 63506.9i | −0.0533570 | − | 0.134598i | ||||
\(187\) | 372019. | + | 372019.i | 0.777966 | + | 0.777966i | ||||
\(188\) | −551169. | − | 585941.i | −1.13734 | − | 1.20909i | ||||
\(189\) | 88478.6 | − | 88478.6i | 0.180171 | − | 0.180171i | ||||
\(190\) | 44111.0 | − | 102053.i | 0.0886467 | − | 0.205088i | ||||
\(191\) | 262656. | 0.520960 | 0.260480 | − | 0.965479i | \(-0.416119\pi\) | ||||
0.260480 | + | 0.965479i | \(0.416119\pi\) | |||||||
\(192\) | 7022.85 | − | 76363.0i | 0.0137487 | − | 0.149496i | ||||
\(193\) | 741418. | 1.43275 | 0.716374 | − | 0.697717i | \(-0.245801\pi\) | ||||
0.716374 | + | 0.697717i | \(0.245801\pi\) | |||||||
\(194\) | −113428. | + | 262421.i | −0.216380 | + | 0.500605i | ||||
\(195\) | 28098.5 | − | 28098.5i | 0.0529172 | − | 0.0529172i | ||||
\(196\) | −97042.1 | − | 103164.i | −0.180435 | − | 0.191818i | ||||
\(197\) | 443287. | + | 443287.i | 0.813803 | + | 0.813803i | 0.985202 | − | 0.171399i | \(-0.0548286\pi\) |
−0.171399 | + | 0.985202i | \(0.554829\pi\) | |||||||
\(198\) | −184589. | − | 465644.i | −0.334614 | − | 0.844094i | ||||
\(199\) | − | 578894.i | − | 1.03625i | −0.855303 | − | 0.518127i | \(-0.826629\pi\) | ||
0.855303 | − | 0.518127i | \(-0.173371\pi\) | |||||||
\(200\) | 38458.9 | + | 106400.i | 0.0679864 | + | 0.188090i | ||||
\(201\) | 63460.3i | 0.110793i | ||||||||
\(202\) | 546198. | − | 216523.i | 0.941828 | − | 0.373357i | ||||
\(203\) | 309287. | + | 309287.i | 0.526770 | + | 0.526770i | ||||
\(204\) | −105638. | − | 3230.33i | −0.177724 | − | 0.00543465i | ||||
\(205\) | −53493.1 | + | 53493.1i | −0.0889023 | + | 0.0889023i | ||||
\(206\) | −519731. | − | 224646.i | −0.853317 | − | 0.368835i | ||||
\(207\) | −914343. | −1.48314 | ||||||||
\(208\) | −460824. | − | 520922.i | −0.738545 | − | 0.834862i | ||||
\(209\) | 293070. | 0.464093 | ||||||||
\(210\) | −33803.4 | − | 14611.0i | −0.0528946 | − | 0.0228630i | ||||
\(211\) | −525264. | + | 525264.i | −0.812215 | + | 0.812215i | −0.984966 | − | 0.172750i | \(-0.944735\pi\) |
0.172750 | + | 0.984966i | \(0.444735\pi\) | |||||||
\(212\) | −29573.8 | + | 967124.i | −0.0451926 | + | 1.47789i | ||||
\(213\) | 29743.2 | + | 29743.2i | 0.0449199 | + | 0.0449199i | ||||
\(214\) | −323517. | + | 128248.i | −0.482906 | + | 0.191433i | ||||
\(215\) | − | 358757.i | − | 0.529302i | ||||||
\(216\) | 184300. | + | 86439.5i | 0.268777 | + | 0.126060i | ||||
\(217\) | 574189.i | 0.827763i | ||||||||
\(218\) | −348678. | − | 879572.i | −0.496916 | − | 1.25352i | ||||
\(219\) | 24049.3 | + | 24049.3i | 0.0338838 | + | 0.0338838i | ||||
\(220\) | −217230. | + | 204339.i | −0.302596 | + | 0.284639i | ||||
\(221\) | −677789. | + | 677789.i | −0.933499 | + | 0.933499i | ||||
\(222\) | −56280.4 | + | 130207.i | −0.0766434 | + | 0.177318i | ||||
\(223\) | 571278. | 0.769282 | 0.384641 | − | 0.923066i | \(-0.374325\pi\) | ||||
0.384641 | + | 0.923066i | \(0.374325\pi\) | |||||||
\(224\) | −291401. | + | 574910.i | −0.388035 | + | 0.765561i | ||||
\(225\) | −148452. | −0.195492 | ||||||||
\(226\) | 75754.1 | − | 175261.i | 0.0986587 | − | 0.228252i | ||||
\(227\) | −263502. | + | 263502.i | −0.339406 | + | 0.339406i | −0.856144 | − | 0.516738i | \(-0.827146\pi\) |
0.516738 | + | 0.856144i | \(0.327146\pi\) | |||||||
\(228\) | −42882.4 | + | 40337.6i | −0.0546314 | + | 0.0513894i | ||||
\(229\) | −92037.0 | − | 92037.0i | −0.115978 | − | 0.115978i | 0.646736 | − | 0.762714i | \(-0.276133\pi\) |
−0.762714 | + | 0.646736i | \(0.776133\pi\) | |||||||
\(230\) | 200621. | + | 506085.i | 0.250067 | + | 0.630818i | ||||
\(231\) | − | 97074.6i | − | 0.119695i | ||||||
\(232\) | −302159. | + | 644241.i | −0.368566 | + | 0.785830i | ||||
\(233\) | 1.40826e6i | 1.69939i | 0.527271 | + | 0.849697i | \(0.323215\pi\) | ||||
−0.527271 | + | 0.849697i | \(0.676785\pi\) | |||||||
\(234\) | 848367. | − | 336307.i | 1.01285 | − | 0.401510i | ||||
\(235\) | −444391. | − | 444391.i | −0.524924 | − | 0.524924i | ||||
\(236\) | 34432.9 | − | 1.12603e6i | 0.0402433 | − | 1.31604i | ||||
\(237\) | −93199.7 | + | 93199.7i | −0.107781 | + | 0.107781i | ||||
\(238\) | 815401. | + | 352446.i | 0.933101 | + | 0.403320i | ||||
\(239\) | 731934. | 0.828852 | 0.414426 | − | 0.910083i | \(-0.363982\pi\) | ||||
0.414426 | + | 0.910083i | \(0.363982\pi\) | |||||||
\(240\) | 3660.59 | − | 59798.4i | 0.00410226 | − | 0.0670134i | ||||
\(241\) | 528564. | 0.586212 | 0.293106 | − | 0.956080i | \(-0.405311\pi\) | ||||
0.293106 | + | 0.956080i | \(0.405311\pi\) | |||||||
\(242\) | 114636. | + | 49549.8i | 0.125829 | + | 0.0543880i | ||||
\(243\) | −284384. | + | 284384.i | −0.308951 | + | 0.308951i | ||||
\(244\) | −253566. | − | 7753.82i | −0.272657 | − | 0.00833760i | ||||
\(245\) | −78242.1 | − | 78242.1i | −0.0832771 | − | 0.0832771i | ||||
\(246\) | 37240.5 | − | 14762.8i | 0.0392353 | − | 0.0155536i | ||||
\(247\) | 533950.i | 0.556876i | ||||||||
\(248\) | −878494. | + | 317538.i | −0.907005 | + | 0.327843i | ||||
\(249\) | 19602.7i | 0.0200363i | ||||||||
\(250\) | 32572.7 | + | 82167.6i | 0.0329612 | + | 0.0831478i | ||||
\(251\) | −59639.9 | − | 59639.9i | −0.0597520 | − | 0.0597520i | 0.676599 | − | 0.736351i | \(-0.263453\pi\) |
−0.736351 | + | 0.676599i | \(0.763453\pi\) | |||||||
\(252\) | −579466. | − | 616022.i | −0.574813 | − | 0.611076i | ||||
\(253\) | −1.01474e6 | + | 1.01474e6i | −0.996675 | + | 0.996675i | ||||
\(254\) | −571687. | + | 1.32262e6i | −0.555999 | + | 1.28633i | ||||
\(255\) | −82568.6 | −0.0795178 | ||||||||
\(256\) | −1.04075e6 | − | 127899.i | −0.992533 | − | 0.121974i | ||||
\(257\) | 1.13847e6 | 1.07520 | 0.537600 | − | 0.843200i | \(-0.319331\pi\) | ||||
0.537600 | + | 0.843200i | \(0.319331\pi\) | |||||||
\(258\) | −75374.4 | + | 174382.i | −0.0704977 | + | 0.163100i | ||||
\(259\) | 843053. | − | 843053.i | 0.780918 | − | 0.780918i | ||||
\(260\) | −372290. | − | 395777.i | −0.341545 | − | 0.363092i | ||||
\(261\) | −660222. | − | 660222.i | −0.599914 | − | 0.599914i | ||||
\(262\) | −710520. | − | 1.79235e6i | −0.639474 | − | 1.61313i | ||||
\(263\) | − | 1.24414e6i | − | 1.10912i | −0.832143 | − | 0.554562i | \(-0.812886\pi\) | ||
0.832143 | − | 0.554562i | \(-0.187114\pi\) | |||||||
\(264\) | 148521. | − | 53684.1i | 0.131153 | − | 0.0474063i | ||||
\(265\) | 755919.i | 0.661242i | ||||||||
\(266\) | 460004. | − | 182354.i | 0.398619 | − | 0.158020i | ||||
\(267\) | −206415. | − | 206415.i | −0.177199 | − | 0.177199i | ||||
\(268\) | 867335. | + | 26522.3i | 0.737649 | + | 0.0225567i | ||||
\(269\) | 989230. | − | 989230.i | 0.833521 | − | 0.833521i | −0.154476 | − | 0.987997i | \(-0.549369\pi\) |
0.987997 | + | 0.154476i | \(0.0493688\pi\) | |||||||
\(270\) | 145981. | + | 63098.4i | 0.121867 | + | 0.0526756i | ||||
\(271\) | −803591. | −0.664679 | −0.332339 | − | 0.943160i | \(-0.607838\pi\) | ||||
−0.332339 | + | 0.943160i | \(0.607838\pi\) | |||||||
\(272\) | −88300.2 | + | 1.44245e6i | −0.0723668 | + | 1.18217i | ||||
\(273\) | 176862. | 0.143625 | ||||||||
\(274\) | 1.52494e6 | + | 659133.i | 1.22709 | + | 0.530392i | ||||
\(275\) | −164752. | + | 164752.i | −0.131371 | + | 0.131371i | ||||
\(276\) | 8811.23 | − | 288145.i | 0.00696248 | − | 0.227687i | ||||
\(277\) | −728210. | − | 728210.i | −0.570239 | − | 0.570239i | 0.361956 | − | 0.932195i | \(-0.382109\pi\) |
−0.932195 | + | 0.361956i | \(0.882109\pi\) | |||||||
\(278\) | 230209. | − | 91258.9i | 0.178653 | − | 0.0708212i | ||||
\(279\) | − | 1.22570e6i | − | 0.942700i | ||||||
\(280\) | −213822. | + | 455897.i | −0.162989 | + | 0.347513i | ||||
\(281\) | − | 942622.i | − | 0.712151i | −0.934457 | − | 0.356075i | \(-0.884115\pi\) | ||
0.934457 | − | 0.356075i | \(-0.115885\pi\) | |||||||
\(282\) | 122641. | + | 309374.i | 0.0918361 | + | 0.231665i | ||||
\(283\) | 433822. | + | 433822.i | 0.321992 | + | 0.321992i | 0.849531 | − | 0.527539i | \(-0.176885\pi\) |
−0.527539 | + | 0.849531i | \(0.676885\pi\) | |||||||
\(284\) | 418942. | − | 394081.i | 0.308218 | − | 0.289928i | ||||
\(285\) | −32523.0 | + | 32523.0i | −0.0237180 | + | 0.0237180i | ||||
\(286\) | 568285. | − | 1.31475e6i | 0.410819 | − | 0.950451i | ||||
\(287\) | −336705. | −0.241293 | ||||||||
\(288\) | 622042. | − | 1.22724e6i | 0.441915 | − | 0.871862i | ||||
\(289\) | 571851. | 0.402753 | ||||||||
\(290\) | −220567. | + | 510294.i | −0.154009 | + | 0.356308i | ||||
\(291\) | 83630.6 | − | 83630.6i | 0.0578939 | − | 0.0578939i | ||||
\(292\) | 338742. | − | 318640.i | 0.232494 | − | 0.218697i | ||||
\(293\) | 1.25809e6 | + | 1.25809e6i | 0.856138 | + | 0.856138i | 0.990881 | − | 0.134742i | \(-0.0430207\pi\) |
−0.134742 | + | 0.990881i | \(0.543021\pi\) | |||||||
\(294\) | 21592.9 | + | 54470.1i | 0.0145694 | + | 0.0367528i | ||||
\(295\) | − | 880120.i | − | 0.588826i | ||||||
\(296\) | 1.75607e6 | + | 823624.i | 1.16497 | + | 0.546386i | ||||
\(297\) | 419221.i | 0.275773i | ||||||||
\(298\) | 2.84232e6 | − | 1.12674e6i | 1.85410 | − | 0.734996i | ||||
\(299\) | −1.84878e6 | − | 1.84878e6i | −1.19593 | − | 1.19593i | ||||
\(300\) | 1430.59 | − | 46783.1i | 0.000917721 | − | 0.0300114i | ||||
\(301\) | 1.12907e6 | − | 1.12907e6i | 0.718300 | − | 0.718300i | ||||
\(302\) | 705703. | + | 305031.i | 0.445251 | + | 0.192454i | ||||
\(303\) | −243070. | −0.152098 | ||||||||
\(304\) | 533387. | + | 602949.i | 0.331024 | + | 0.374194i | ||||
\(305\) | −198191. | −0.121993 | ||||||||
\(306\) | −1.74060e6 | − | 752352.i | −1.06267 | − | 0.459323i | ||||
\(307\) | −256109. | + | 256109.i | −0.155088 | + | 0.155088i | −0.780386 | − | 0.625298i | \(-0.784977\pi\) |
0.625298 | + | 0.780386i | \(0.284977\pi\) | |||||||
\(308\) | −1.32676e6 | − | 40571.0i | −0.796919 | − | 0.0243691i | ||||
\(309\) | 165632. | + | 165632.i | 0.0986843 | + | 0.0986843i | ||||
\(310\) | −678420. | + | 268938.i | −0.400954 | + | 0.158945i | ||||
\(311\) | 320420.i | 0.187853i | 0.995579 | + | 0.0939265i | \(0.0299419\pi\) | ||||
−0.995579 | + | 0.0939265i | \(0.970058\pi\) | |||||||
\(312\) | 97808.3 | + | 270595.i | 0.0568839 | + | 0.157374i | ||||
\(313\) | − | 554361.i | − | 0.319839i | −0.987130 | − | 0.159920i | \(-0.948876\pi\) | ||
0.987130 | − | 0.159920i | \(-0.0511235\pi\) | |||||||
\(314\) | −297034. | − | 749296.i | −0.170013 | − | 0.428874i | ||||
\(315\) | −467206. | − | 467206.i | −0.265297 | − | 0.265297i | ||||
\(316\) | 1.23484e6 | + | 1.31275e6i | 0.695656 | + | 0.739543i | ||||
\(317\) | −185206. | + | 185206.i | −0.103516 | + | 0.103516i | −0.756968 | − | 0.653452i | \(-0.773320\pi\) |
0.653452 | + | 0.756968i | \(0.273320\pi\) | |||||||
\(318\) | 158818. | − | 367433.i | 0.0880707 | − | 0.203756i | ||||
\(319\) | −1.46543e6 | −0.806286 | ||||||||
\(320\) | −815757. | − | 75022.6i | −0.445334 | − | 0.0409559i | ||||
\(321\) | 143972. | 0.0779859 | ||||||||
\(322\) | −961352. | + | 2.22413e6i | −0.516705 | + | 1.19542i | ||||
\(323\) | 784516. | − | 784516.i | 0.418404 | − | 0.418404i | ||||
\(324\) | 1.20778e6 | + | 1.28398e6i | 0.639185 | + | 0.679509i | ||||
\(325\) | −300166. | − | 300166.i | −0.157635 | − | 0.157635i | ||||
\(326\) | −49718.1 | − | 125418.i | −0.0259102 | − | 0.0653608i | ||||
\(327\) | 391429.i | 0.202434i | ||||||||
\(328\) | −186204. | − | 515149.i | −0.0955663 | − | 0.264392i | ||||
\(329\) | − | 2.79716e6i | − | 1.42472i | ||||||
\(330\) | 114696. | − | 45467.6i | 0.0579782 | − | 0.0229836i | ||||
\(331\) | 1.69283e6 | + | 1.69283e6i | 0.849265 | + | 0.849265i | 0.990041 | − | 0.140777i | \(-0.0449599\pi\) |
−0.140777 | + | 0.990041i | \(0.544960\pi\) | |||||||
\(332\) | 267917. | + | 8192.67i | 0.133400 | + | 0.00407925i | ||||
\(333\) | −1.79963e6 | + | 1.79963e6i | −0.889351 | + | 0.889351i | ||||
\(334\) | 2.79820e6 | + | 1.20948e6i | 1.37250 | + | 0.593244i | ||||
\(335\) | 677922. | 0.330041 | ||||||||
\(336\) | 199717. | − | 176676.i | 0.0965088 | − | 0.0853747i | ||||
\(337\) | −3.80713e6 | −1.82609 | −0.913047 | − | 0.407855i | \(-0.866277\pi\) | ||||
−0.913047 | + | 0.407855i | \(0.866277\pi\) | |||||||
\(338\) | 467421. | + | 202036.i | 0.222544 | + | 0.0961917i | ||||
\(339\) | −55853.6 | + | 55853.6i | −0.0263968 | + | 0.0263968i | ||||
\(340\) | −34508.4 | + | 1.12850e6i | −0.0161893 | + | 0.529423i | ||||
\(341\) | −1.36029e6 | − | 1.36029e6i | −0.633496 | − | 0.633496i | ||||
\(342\) | −981954. | + | 389264.i | −0.453969 | + | 0.179961i | ||||
\(343\) | − | 2.36260e6i | − | 1.08431i | ||||||
\(344\) | 2.35185e6 | + | 1.10305e6i | 1.07155 | + | 0.502574i | ||||
\(345\) | − | 225219.i | − | 0.101873i | ||||||
\(346\) | −971121. | − | 2.44974e6i | −0.436097 | − | 1.10009i | ||||
\(347\) | 278710. | + | 278710.i | 0.124259 | + | 0.124259i | 0.766502 | − | 0.642242i | \(-0.221996\pi\) |
−0.642242 | + | 0.766502i | \(0.721996\pi\) | |||||||
\(348\) | 214424. | − | 201700.i | 0.0949131 | − | 0.0892806i | ||||
\(349\) | 177239. | − | 177239.i | 0.0778926 | − | 0.0778926i | −0.667087 | − | 0.744980i | \(-0.732459\pi\) |
0.744980 | + | 0.667087i | \(0.232459\pi\) | |||||||
\(350\) | −156084. | + | 361109.i | −0.0681066 | + | 0.157568i | ||||
\(351\) | −763788. | −0.330906 | ||||||||
\(352\) | −671649. | − | 2.05234e6i | −0.288925 | − | 0.882860i | ||||
\(353\) | −2.64544e6 | −1.12996 | −0.564978 | − | 0.825106i | \(-0.691115\pi\) | ||||
−0.564978 | + | 0.825106i | \(0.691115\pi\) | |||||||
\(354\) | −184912. | + | 427804.i | −0.0784256 | + | 0.181442i | ||||
\(355\) | 317736. | − | 317736.i | 0.133812 | − | 0.133812i | ||||
\(356\) | −2.90741e6 | + | 2.73488e6i | −1.21586 | + | 1.14370i | ||||
\(357\) | −259858. | − | 259858.i | −0.107911 | − | 0.107911i | ||||
\(358\) | −675.896 | − | 1705.01i | −0.000278723 | − | 0.000703104i | ||||
\(359\) | 976508.i | 0.399889i | 0.979807 | + | 0.199945i | \(0.0640762\pi\) | ||||
−0.979807 | + | 0.199945i | \(0.935924\pi\) | |||||||
\(360\) | 456438. | − | 973186.i | 0.185620 | − | 0.395767i | ||||
\(361\) | 1.85807e6i | 0.750402i | ||||||||
\(362\) | −2.43020e6 | + | 963374.i | −0.974699 | + | 0.386388i | ||||
\(363\) | −36533.1 | − | 36533.1i | −0.0145519 | − | 0.0145519i | ||||
\(364\) | 73917.2 | − | 2.41725e6i | 0.0292410 | − | 0.956241i | ||||
\(365\) | 256910. | − | 256910.i | 0.100937 | − | 0.100937i | ||||
\(366\) | 96335.5 | + | 41639.7i | 0.0375910 | + | 0.0162482i | ||||
\(367\) | 535830. | 0.207664 | 0.103832 | − | 0.994595i | \(-0.466889\pi\) | ||||
0.103832 | + | 0.994595i | \(0.466889\pi\) | |||||||
\(368\) | −3.93451e6 | − | 240853.i | −1.51451 | − | 0.0927112i | ||||
\(369\) | 718751. | 0.274797 | ||||||||
\(370\) | 1.39096e6 | + | 601222.i | 0.528214 | + | 0.228313i | ||||
\(371\) | −2.37902e6 | + | 2.37902e6i | −0.897351 | + | 0.897351i | ||||
\(372\) | 386266. | + | 11811.7i | 0.144720 | + | 0.00442542i | ||||
\(373\) | 1.70833e6 | + | 1.70833e6i | 0.635770 | + | 0.635770i | 0.949509 | − | 0.313739i | \(-0.101582\pi\) |
−0.313739 | + | 0.949509i | \(0.601582\pi\) | |||||||
\(374\) | −2.76669e6 | + | 1.09676e6i | −1.02278 | + | 0.405447i | ||||
\(375\) | − | 36566.4i | − | 0.0134278i | ||||||
\(376\) | 4.27958e6 | − | 1.54688e6i | 1.56110 | − | 0.564272i | ||||
\(377\) | − | 2.66990e6i | − | 0.967481i | ||||||
\(378\) | 260848. | + | 658012.i | 0.0938982 | + | 0.236867i | ||||
\(379\) | 1.64313e6 | + | 1.64313e6i | 0.587591 | + | 0.587591i | 0.936978 | − | 0.349388i | \(-0.113610\pi\) |
−0.349388 | + | 0.936978i | \(0.613610\pi\) | |||||||
\(380\) | 430912. | + | 458097.i | 0.153084 | + | 0.162742i | ||||
\(381\) | 421505. | − | 421505.i | 0.148761 | − | 0.148761i | ||||
\(382\) | −589509. | + | 1.36386e6i | −0.206696 | + | 0.478201i | ||||
\(383\) | 2.24417e6 | 0.781732 | 0.390866 | − | 0.920448i | \(-0.372176\pi\) | ||||
0.390866 | + | 0.920448i | \(0.372176\pi\) | |||||||
\(384\) | 380757. | + | 207856.i | 0.131771 | + | 0.0719342i | ||||
\(385\) | −1.03701e6 | −0.356560 | ||||||||
\(386\) | −1.66405e6 | + | 3.84985e6i | −0.568456 | + | 1.31515i | ||||
\(387\) | −2.41019e6 | + | 2.41019e6i | −0.818038 | + | 0.818038i | ||||
\(388\) | −1.10806e6 | − | 1.17796e6i | −0.373666 | − | 0.397239i | ||||
\(389\) | −917079. | − | 917079.i | −0.307279 | − | 0.307279i | 0.536574 | − | 0.843853i | \(-0.319718\pi\) |
−0.843853 | + | 0.536574i | \(0.819718\pi\) | |||||||
\(390\) | 82838.5 | + | 208968.i | 0.0275785 | + | 0.0695693i | ||||
\(391\) | 5.43270e6i | 1.79711i | ||||||||
\(392\) | 753488. | − | 272353.i | 0.247663 | − | 0.0895195i | ||||
\(393\) | 797635.i | 0.260509i | ||||||||
\(394\) | −3.29671e6 | + | 1.30687e6i | −1.06989 | + | 0.424124i | ||||
\(395\) | 995618. | + | 995618.i | 0.321070 | + | 0.321070i | ||||
\(396\) | 2.83217e6 | + | 86605.4i | 0.907574 | + | 0.0277528i | ||||
\(397\) | 903998. | − | 903998.i | 0.287867 | − | 0.287867i | −0.548370 | − | 0.836236i | \(-0.684751\pi\) |
0.836236 | + | 0.548370i | \(0.184751\pi\) | |||||||
\(398\) | 3.00594e6 | + | 1.29928e6i | 0.951202 | + | 0.411144i | ||||
\(399\) | −204712. | −0.0643740 | ||||||||
\(400\) | −638804. | − | 39104.7i | −0.199626 | − | 0.0122202i | ||||
\(401\) | 4.99527e6 | 1.55131 | 0.775654 | − | 0.631158i | \(-0.217420\pi\) | ||||
0.775654 | + | 0.631158i | \(0.217420\pi\) | |||||||
\(402\) | −329521. | − | 142431.i | −0.101699 | − | 0.0439581i | ||||
\(403\) | 2.47833e6 | − | 2.47833e6i | 0.760146 | − | 0.760146i | ||||
\(404\) | −101588. | + | 3.32213e6i | −0.0309662 | + | 1.01266i | ||||
\(405\) | 973800. | + | 973800.i | 0.295007 | + | 0.295007i | ||||
\(406\) | −2.30015e6 | + | 911822.i | −0.692535 | + | 0.274533i | ||||
\(407\) | 3.99447e6i | 1.19529i | ||||||||
\(408\) | 253870. | − | 541283.i | 0.0755023 | − | 0.160981i | ||||
\(409\) | − | 447165.i | − | 0.132178i | −0.997814 | − | 0.0660891i | \(-0.978948\pi\) | ||
0.997814 | − | 0.0660891i | \(-0.0210522\pi\) | |||||||
\(410\) | −157705. | − | 397826.i | −0.0463326 | − | 0.116878i | ||||
\(411\) | −485979. | − | 485979.i | −0.141910 | − | 0.141910i | ||||
\(412\) | 2.33298e6 | − | 2.19453e6i | 0.677123 | − | 0.636940i | ||||
\(413\) | 2.76990e6 | − | 2.76990e6i | 0.799078 | − | 0.799078i | ||||
\(414\) | 2.05216e6 | − | 4.74777e6i | 0.588451 | − | 1.36141i | ||||
\(415\) | 209408. | 0.0596861 | ||||||||
\(416\) | 3.73920e6 | − | 1.22369e6i | 1.05936 | − | 0.346688i | ||||
\(417\) | −102448. | −0.0288511 | ||||||||
\(418\) | −657769. | + | 1.52178e6i | −0.184133 | + | 0.426002i | ||||
\(419\) | 2.95570e6 | − | 2.95570e6i | 0.822481 | − | 0.822481i | −0.163982 | − | 0.986463i | \(-0.552434\pi\) |
0.986463 | + | 0.163982i | \(0.0524340\pi\) | |||||||
\(420\) | 151737. | − | 142733.i | 0.0419729 | − | 0.0394821i | ||||
\(421\) | −2.32051e6 | − | 2.32051e6i | −0.638084 | − | 0.638084i | 0.311998 | − | 0.950083i | \(-0.399002\pi\) |
−0.950083 | + | 0.311998i | \(0.899002\pi\) | |||||||
\(422\) | −1.54855e6 | − | 3.90637e6i | −0.423297 | − | 1.06781i | ||||
\(423\) | 5.97100e6i | 1.62254i | ||||||||
\(424\) | −4.95547e6 | − | 2.32419e6i | −1.33866 | − | 0.627851i | ||||
\(425\) | 882049.i | 0.236876i | ||||||||
\(426\) | −221199. | + | 87687.2i | −0.0590554 | + | 0.0234106i | ||||
\(427\) | −623743. | − | 623743.i | −0.165553 | − | 0.165553i | ||||
\(428\) | 60171.2 | − | 1.96772e6i | 0.0158774 | − | 0.519223i | ||||
\(429\) | −418996. | + | 418996.i | −0.109918 | + | 0.109918i | ||||
\(430\) | 1.86286e6 | + | 805197.i | 0.485858 | + | 0.210006i | ||||
\(431\) | 2.57689e6 | 0.668195 | 0.334098 | − | 0.942538i | \(-0.391568\pi\) | ||||
0.334098 | + | 0.942538i | \(0.391568\pi\) | |||||||
\(432\) | −862487. | + | 762983.i | −0.222353 | + | 0.196701i | ||||
\(433\) | −3.68386e6 | −0.944242 | −0.472121 | − | 0.881534i | \(-0.656511\pi\) | ||||
−0.472121 | + | 0.881534i | \(0.656511\pi\) | |||||||
\(434\) | −2.98151e6 | − | 1.28872e6i | −0.759822 | − | 0.328423i | ||||
\(435\) | 162624. | − | 162624.i | 0.0412062 | − | 0.0412062i | ||||
\(436\) | 5.34980e6 | + | 163592.i | 1.34779 | + | 0.0412142i | ||||
\(437\) | 2.13989e6 | + | 2.13989e6i | 0.536029 | + | 0.536029i | ||||
\(438\) | −178854. | + | 70900.8i | −0.0445464 | + | 0.0176590i | ||||
\(439\) | 6.45899e6i | 1.59957i | 0.600287 | + | 0.799785i | \(0.295053\pi\) | ||||
−0.600287 | + | 0.799785i | \(0.704947\pi\) | |||||||
\(440\) | −573488. | − | 1.58660e6i | −0.141219 | − | 0.390693i | ||||
\(441\) | 1.05129e6i | 0.257410i | ||||||||
\(442\) | −1.99822e6 | − | 5.04069e6i | −0.486505 | − | 1.22725i | ||||
\(443\) | −4.16997e6 | − | 4.16997e6i | −1.00954 | − | 1.00954i | −0.999954 | − | 0.00958598i | \(-0.996949\pi\) |
−0.00958598 | − | 0.999954i | \(-0.503051\pi\) | |||||||
\(444\) | −549793. | − | 584478.i | −0.132355 | − | 0.140705i | ||||
\(445\) | −2.20505e6 | + | 2.20505e6i | −0.527860 | + | 0.527860i | ||||
\(446\) | −1.28218e6 | + | 2.96639e6i | −0.305220 | + | 0.706142i | ||||
\(447\) | −1.26489e6 | −0.299423 | ||||||||
\(448\) | −2.33123e6 | − | 2.80345e6i | −0.548769 | − | 0.659929i | ||||
\(449\) | −3.47801e6 | −0.814169 | −0.407085 | − | 0.913390i | \(-0.633455\pi\) | ||||
−0.407085 | + | 0.913390i | \(0.633455\pi\) | |||||||
\(450\) | 333187. | − | 770845.i | 0.0775635 | − | 0.179447i | ||||
\(451\) | 797672. | − | 797672.i | 0.184664 | − | 0.184664i | ||||
\(452\) | 740029. | + | 786715.i | 0.170374 | + | 0.181122i | ||||
\(453\) | −224899. | − | 224899.i | −0.0514923 | − | 0.0514923i | ||||
\(454\) | −776841. | − | 1.95965e6i | −0.176886 | − | 0.446211i | ||||
\(455\) | − | 1.88936e6i | − | 0.427844i | ||||||
\(456\) | −113210. | − | 313203.i | −0.0254959 | − | 0.0705366i | ||||
\(457\) | − | 6.53808e6i | − | 1.46440i | −0.681089 | − | 0.732200i | \(-0.738494\pi\) | ||
0.681089 | − | 0.732200i | \(-0.261506\pi\) | |||||||
\(458\) | 684476. | − | 271338.i | 0.152474 | − | 0.0604432i | ||||
\(459\) | 1.12221e6 | + | 1.12221e6i | 0.248624 | + | 0.248624i | ||||
\(460\) | −3.07815e6 | − | 94127.1i | −0.678259 | − | 0.0207406i | ||||
\(461\) | 5.79897e6 | − | 5.79897e6i | 1.27086 | − | 1.27086i | 0.325225 | − | 0.945637i | \(-0.394560\pi\) |
0.945637 | − | 0.325225i | \(-0.105440\pi\) | |||||||
\(462\) | 504065. | + | 217875.i | 0.109871 | + | 0.0474901i | ||||
\(463\) | 2.33971e6 | 0.507235 | 0.253618 | − | 0.967305i | \(-0.418379\pi\) | ||||
0.253618 | + | 0.967305i | \(0.418379\pi\) | |||||||
\(464\) | −2.66709e6 | − | 3.01492e6i | −0.575099 | − | 0.650100i | ||||
\(465\) | 301912. | 0.0647512 | ||||||||
\(466\) | −7.31249e6 | − | 3.16072e6i | −1.55991 | − | 0.674251i | ||||
\(467\) | 5.60644e6 | − | 5.60644e6i | 1.18958 | − | 1.18958i | 0.212402 | − | 0.977182i | \(-0.431871\pi\) |
0.977182 | − | 0.212402i | \(-0.0681285\pi\) | |||||||
\(468\) | −157788. | + | 5.16000e6i | −0.0333012 | + | 1.08902i | ||||
\(469\) | 2.13355e6 | + | 2.13355e6i | 0.447889 | + | 0.447889i | ||||
\(470\) | 3.30492e6 | − | 1.31013e6i | 0.690108 | − | 0.273571i | ||||
\(471\) | 333453.i | 0.0692600i | ||||||||
\(472\) | 5.76968e6 | + | 2.70606e6i | 1.19206 | + | 0.559092i | ||||
\(473\) | 5.34967e6i | 1.09945i | ||||||||
\(474\) | −274766. | − | 693123.i | −0.0561717 | − | 0.141698i | ||||
\(475\) | 347431. | + | 347431.i | 0.0706537 | + | 0.0706537i | ||||
\(476\) | −3.66019e6 | + | 3.44298e6i | −0.740433 | + | 0.696493i | ||||
\(477\) | 5.07839e6 | − | 5.07839e6i | 1.02195 | − | 1.02195i | ||||
\(478\) | −1.64276e6 | + | 3.80061e6i | −0.328855 | + | 0.760822i | ||||
\(479\) | 3.58644e6 | 0.714207 | 0.357104 | − | 0.934065i | \(-0.383764\pi\) | ||||
0.357104 | + | 0.934065i | \(0.383764\pi\) | |||||||
\(480\) | 302291. | + | 153220.i | 0.0598855 | + | 0.0303537i | ||||
\(481\) | −7.27762e6 | −1.43426 | ||||||||
\(482\) | −1.18631e6 | + | 2.74460e6i | −0.232585 | + | 0.538097i | ||||
\(483\) | 708805. | − | 708805.i | 0.138248 | − | 0.138248i | ||||
\(484\) | −514580. | + | 484043.i | −0.0998480 | + | 0.0939226i | ||||
\(485\) | −893395. | − | 893395.i | −0.172460 | − | 0.172460i | ||||
\(486\) | −838405. | − | 2.11495e6i | −0.161014 | − | 0.406172i | ||||
\(487\) | 4.95472e6i | 0.946666i | 0.880884 | + | 0.473333i | \(0.156949\pi\) | ||||
−0.880884 | + | 0.473333i | \(0.843051\pi\) | |||||||
\(488\) | 609368. | − | 1.29925e6i | 0.115832 | − | 0.246970i | ||||
\(489\) | 55813.9i | 0.0105553i | ||||||||
\(490\) | 581884. | − | 230669.i | 0.109483 | − | 0.0434009i | ||||
\(491\) | 1.50044e6 | + | 1.50044e6i | 0.280876 | + | 0.280876i | 0.833458 | − | 0.552582i | \(-0.186357\pi\) |
−0.552582 | + | 0.833458i | \(0.686357\pi\) | |||||||
\(492\) | −6926.38 | + | 226507.i | −0.00129001 | + | 0.0421860i | ||||
\(493\) | −3.92281e6 | + | 3.92281e6i | −0.726908 | + | 0.726908i | ||||
\(494\) | −2.77257e6 | − | 1.19840e6i | −0.511169 | − | 0.220946i | ||||
\(495\) | 2.21367e6 | 0.406069 | ||||||||
\(496\) | 322870. | − | 5.27431e6i | 0.0589282 | − | 0.962635i | ||||
\(497\) | 1.99995e6 | 0.363184 | ||||||||
\(498\) | −101788. | − | 43996.4i | −0.0183917 | − | 0.00794958i | ||||
\(499\) | −6.54048e6 | + | 6.54048e6i | −1.17587 | + | 1.17587i | −0.195081 | + | 0.980787i | \(0.562497\pi\) |
−0.980787 | + | 0.195081i | \(0.937503\pi\) | |||||||
\(500\) | −499766. | − | 15282.4i | −0.0894009 | − | 0.00273380i | ||||
\(501\) | −891752. | − | 891752.i | −0.158727 | − | 0.158727i | ||||
\(502\) | 443539. | − | 175827.i | 0.0785548 | − | 0.0311405i | ||||
\(503\) | − | 7.17695e6i | − | 1.26479i | −0.774645 | − | 0.632397i | \(-0.782071\pi\) | ||
0.774645 | − | 0.632397i | \(-0.217929\pi\) | |||||||
\(504\) | 4.49929e6 | − | 1.62630e6i | 0.788983 | − | 0.285183i | ||||
\(505\) | 2.59663e6i | 0.453086i | ||||||||
\(506\) | −2.99160e6 | − | 7.54659e6i | −0.519430 | − | 1.31031i | ||||
\(507\) | −148961. | − | 148961.i | −0.0257368 | − | 0.0257368i | ||||
\(508\) | −5.58470e6 | − | 5.93703e6i | −0.960154 | − | 1.02073i | ||||
\(509\) | −902441. | + | 902441.i | −0.154392 | + | 0.154392i | −0.780076 | − | 0.625684i | \(-0.784820\pi\) |
0.625684 | + | 0.780076i | \(0.284820\pi\) | |||||||
\(510\) | 185318. | − | 428742.i | 0.0315494 | − | 0.0729912i | ||||
\(511\) | 1.61708e6 | 0.273956 | ||||||||
\(512\) | 2.99998e6 | − | 5.11708e6i | 0.505760 | − | 0.862674i | ||||
\(513\) | 884057. | 0.148316 | ||||||||
\(514\) | −2.55520e6 | + | 5.91157e6i | −0.426596 | + | 0.986950i | ||||
\(515\) | 1.76939e6 | − | 1.76939e6i | 0.293971 | − | 0.293971i | ||||
\(516\) | −736319. | − | 782771.i | −0.121742 | − | 0.129423i | ||||
\(517\) | 6.62663e6 | + | 6.62663e6i | 1.09035 | + | 1.09035i | ||||
\(518\) | 2.48544e6 | + | 6.26976e6i | 0.406986 | + | 1.02666i | ||||
\(519\) | 1.09019e6i | 0.177657i | ||||||||
\(520\) | 2.89066e6 | − | 1.04485e6i | 0.468802 | − | 0.169452i | ||||
\(521\) | − | 1.16790e7i | − | 1.88501i | −0.334196 | − | 0.942504i | \(-0.608465\pi\) | ||
0.334196 | − | 0.942504i | \(-0.391535\pi\) | |||||||
\(522\) | 4.91005e6 | − | 1.94643e6i | 0.788696 | − | 0.312653i | ||||
\(523\) | −3.92307e6 | − | 3.92307e6i | −0.627151 | − | 0.627151i | 0.320199 | − | 0.947350i | \(-0.396250\pi\) |
−0.947350 | + | 0.320199i | \(0.896250\pi\) | |||||||
\(524\) | 1.09016e7 | + | 333361.i | 1.73445 | + | 0.0530379i | ||||
\(525\) | 115081. | − | 115081.i | 0.0182224 | − | 0.0182224i | ||||
\(526\) | 6.46026e6 | + | 2.79236e6i | 1.01809 | + | 0.440055i | ||||
\(527\) | −7.28268e6 | −1.14226 | ||||||||
\(528\) | −54585.5 | + | 891695.i | −0.00852104 | + | 0.139198i | ||||
\(529\) | −8.38221e6 | −1.30233 | ||||||||
\(530\) | −3.92515e6 | − | 1.69659e6i | −0.606969 | − | 0.262354i | ||||
\(531\) | −5.91280e6 | + | 5.91280e6i | −0.910032 | + | 0.910032i | ||||
\(532\) | −85556.5 | + | 2.79787e6i | −0.0131061 | + | 0.428597i | ||||
\(533\) | 1.45330e6 | + | 1.45330e6i | 0.221583 | + | 0.221583i | ||||
\(534\) | 1.53510e6 | − | 608540.i | 0.232961 | − | 0.0923498i | ||||
\(535\) | − | 1.53800e6i | − | 0.232312i | ||||||
\(536\) | −2.08438e6 | + | 4.44416e6i | −0.313375 | + | 0.668156i | ||||
\(537\) | 758.767i | 0.000113546i | ||||||||
\(538\) | 2.91639e6 | + | 7.35687e6i | 0.434400 | + | 1.09582i | ||||
\(539\) | 1.16672e6 | + | 1.16672e6i | 0.172980 | + | 0.172980i | ||||
\(540\) | −655284. | + | 616397.i | −0.0967042 | + | 0.0909654i | ||||
\(541\) | 2.41552e6 | − | 2.41552e6i | 0.354827 | − | 0.354827i | −0.507075 | − | 0.861902i | \(-0.669273\pi\) |
0.861902 | + | 0.507075i | \(0.169273\pi\) | |||||||
\(542\) | 1.80359e6 | − | 4.17269e6i | 0.263718 | − | 0.610124i | ||||
\(543\) | 1.08149e6 | 0.157407 | ||||||||
\(544\) | −7.29182e6 | − | 3.69595e6i | −1.05642 | − | 0.535463i | ||||
\(545\) | 4.18149e6 | 0.603031 | ||||||||
\(546\) | −396952. | + | 918368.i | −0.0569844 | + | 0.131836i | ||||
\(547\) | 6.54146e6 | − | 6.54146e6i | 0.934773 | − | 0.934773i | −0.0632263 | − | 0.997999i | \(-0.520139\pi\) |
0.997999 | + | 0.0632263i | \(0.0201390\pi\) | |||||||
\(548\) | −6.84517e6 | + | 6.43895e6i | −0.973717 | + | 0.915933i | ||||
\(549\) | 1.33148e6 | + | 1.33148e6i | 0.188540 | + | 0.188540i | ||||
\(550\) | −485714. | − | 1.22526e6i | −0.0684658 | − | 0.172711i | ||||
\(551\) | 3.09032e6i | 0.433635i | ||||||||
\(552\) | 1.47643e6 | + | 692469.i | 0.206237 | + | 0.0967282i | ||||
\(553\) | 6.26679e6i | 0.871429i | ||||||||
\(554\) | 5.41567e6 | − | 2.14687e6i | 0.749684 | − | 0.297188i | ||||
\(555\) | −443282. | − | 443282.i | −0.0610868 | − | 0.0610868i | ||||
\(556\) | −42816.7 | + | 1.40019e6i | −0.00587390 | + | 0.192089i | ||||
\(557\) | 3.16244e6 | − | 3.16244e6i | 0.431901 | − | 0.431901i | −0.457373 | − | 0.889275i | \(-0.651210\pi\) |
0.889275 | + | 0.457373i | \(0.151210\pi\) | |||||||
\(558\) | 6.36451e6 | + | 2.75097e6i | 0.865326 | + | 0.374025i | ||||
\(559\) | −9.74668e6 | −1.31925 | ||||||||
\(560\) | −1.88736e6 | − | 2.13350e6i | −0.254323 | − | 0.287490i | ||||
\(561\) | 1.23124e6 | 0.165171 | ||||||||
\(562\) | 4.89462e6 | + | 2.11563e6i | 0.653699 | + | 0.282553i | ||||
\(563\) | 9.31793e6 | − | 9.31793e6i | 1.23893 | − | 1.23893i | 0.278498 | − | 0.960437i | \(-0.410164\pi\) |
0.960437 | − | 0.278498i | \(-0.0898365\pi\) | |||||||
\(564\) | −1.88170e6 | − | 57540.6i | −0.249087 | − | 0.00761687i | ||||
\(565\) | 596663. | + | 596663.i | 0.0786336 | + | 0.0786336i | ||||
\(566\) | −3.22632e6 | + | 1.27897e6i | −0.423318 | + | 0.167811i | ||||
\(567\) | 6.12945e6i | 0.800690i | ||||||||
\(568\) | 1.10601e6 | + | 3.05986e6i | 0.143843 | + | 0.397952i | ||||
\(569\) | 4.94714e6i | 0.640580i | 0.947320 | + | 0.320290i | \(0.103780\pi\) | ||||
−0.947320 | + | 0.320290i | \(0.896220\pi\) | |||||||
\(570\) | −95882.6 | − | 241873.i | −0.0123610 | − | 0.0311817i | ||||
\(571\) | −8.93540e6 | − | 8.93540e6i | −1.14690 | − | 1.14690i | −0.987160 | − | 0.159735i | \(-0.948936\pi\) |
−0.159735 | − | 0.987160i | \(-0.551064\pi\) | |||||||
\(572\) | 5.55147e6 | + | 5.90170e6i | 0.709444 | + | 0.754201i | ||||
\(573\) | 434645. | − | 434645.i | 0.0553029 | − | 0.0553029i | ||||
\(574\) | 755704. | − | 1.74836e6i | 0.0957353 | − | 0.221488i | ||||
\(575\) | −2.40593e6 | −0.303468 | ||||||||
\(576\) | 4.97638e6 | + | 5.98441e6i | 0.624968 | + | 0.751563i | ||||
\(577\) | −6.71522e6 | −0.839694 | −0.419847 | − | 0.907595i | \(-0.637916\pi\) | ||||
−0.419847 | + | 0.907595i | \(0.637916\pi\) | |||||||
\(578\) | −1.28347e6 | + | 2.96937e6i | −0.159796 | + | 0.369696i | ||||
\(579\) | 1.22690e6 | − | 1.22690e6i | 0.152094 | − | 0.152094i | ||||
\(580\) | −2.15468e6 | − | 2.29062e6i | −0.265958 | − | 0.282737i | ||||
\(581\) | 659045. | + | 659045.i | 0.0809981 | + | 0.0809981i | ||||
\(582\) | 246555. | + | 621958.i | 0.0301722 | + | 0.0761120i | ||||
\(583\) | − | 1.12720e7i | − | 1.37351i | ||||||
\(584\) | 894278. | + | 2.47409e6i | 0.108503 | + | 0.300182i | ||||
\(585\) | 4.03314e6i | 0.487251i | ||||||||
\(586\) | −9.35640e6 | + | 3.70904e6i | −1.12555 | + | 0.446188i | ||||
\(587\) | 6.17039e6 | + | 6.17039e6i | 0.739124 | + | 0.739124i | 0.972408 | − | 0.233285i | \(-0.0749474\pi\) |
−0.233285 | + | 0.972408i | \(0.574947\pi\) | |||||||
\(588\) | −331302. | − | 10130.9i | −0.0395167 | − | 0.00120839i | ||||
\(589\) | −2.86858e6 | + | 2.86858e6i | −0.340705 | + | 0.340705i | ||||
\(590\) | 4.57007e6 | + | 1.97535e6i | 0.540497 | + | 0.233622i | ||||
\(591\) | 1.46711e6 | 0.172780 | ||||||||
\(592\) | −8.21806e6 | + | 7.26995e6i | −0.963751 | + | 0.852564i | ||||
\(593\) | −1.25869e7 | −1.46988 | −0.734941 | − | 0.678131i | \(-0.762790\pi\) | ||||
−0.734941 | + | 0.678131i | \(0.762790\pi\) | |||||||
\(594\) | −2.17683e6 | − | 940904.i | −0.253138 | − | 0.109416i | ||||
\(595\) | −2.77597e6 | + | 2.77597e6i | −0.321457 | + | 0.321457i | ||||
\(596\) | −528645. | + | 1.72878e7i | −0.0609605 | + | 1.99353i | ||||
\(597\) | −957957. | − | 957957.i | −0.110004 | − | 0.110004i | ||||
\(598\) | 1.37493e7 | − | 5.45046e6i | 1.57227 | − | 0.623276i | ||||
\(599\) | 1.23633e7i | 1.40789i | 0.710255 | + | 0.703945i | \(0.248580\pi\) | ||||
−0.710255 | + | 0.703945i | \(0.751420\pi\) | |||||||
\(600\) | 239713. | + | 112429.i | 0.0271840 | + | 0.0127497i | ||||
\(601\) | − | 112472.i | − | 0.0127016i | −0.999980 | − | 0.00635082i | \(-0.997978\pi\) | ||
0.999980 | − | 0.00635082i | \(-0.00202154\pi\) | |||||||
\(602\) | 3.32867e6 | + | 8.39687e6i | 0.374351 | + | 0.944336i | ||||
\(603\) | −4.55440e6 | − | 4.55440e6i | −0.510079 | − | 0.510079i | ||||
\(604\) | −3.16778e6 | + | 2.97979e6i | −0.353315 | + | 0.332348i | ||||
\(605\) | −390269. | + | 390269.i | −0.0433487 | + | 0.0433487i | ||||
\(606\) | 545549. | − | 1.26215e6i | 0.0603465 | − | 0.139615i | ||||
\(607\) | 4.40422e6 | 0.485174 | 0.242587 | − | 0.970130i | \(-0.422004\pi\) | ||||
0.242587 | + | 0.970130i | \(0.422004\pi\) | |||||||
\(608\) | −4.32799e6 | + | 1.41638e6i | −0.474818 | + | 0.155389i | ||||
\(609\) | 1.02362e6 | 0.111839 | ||||||||
\(610\) | 444822. | − | 1.02912e6i | 0.0484018 | − | 0.111980i | ||||
\(611\) | −1.20732e7 | + | 1.20732e7i | −1.30834 | + | 1.30834i | ||||
\(612\) | 7.81326e6 | − | 7.34959e6i | 0.843245 | − | 0.793204i | ||||
\(613\) | −7.03209e6 | − | 7.03209e6i | −0.755846 | − | 0.755846i | 0.219717 | − | 0.975564i | \(-0.429486\pi\) |
−0.975564 | + | 0.219717i | \(0.929486\pi\) | |||||||
\(614\) | −755046. | − | 1.90467e6i | −0.0808263 | − | 0.203892i | ||||
\(615\) | 177041.i | 0.0188750i | ||||||||
\(616\) | 3.18845e6 | − | 6.79819e6i | 0.338554 | − | 0.721841i | ||||
\(617\) | − | 3.79732e6i | − | 0.401572i | −0.979635 | − | 0.200786i | \(-0.935650\pi\) | ||
0.979635 | − | 0.200786i | \(-0.0643497\pi\) | |||||||
\(618\) | −1.23180e6 | + | 488307.i | −0.129738 | + | 0.0514306i | ||||
\(619\) | −3.72415e6 | − | 3.72415e6i | −0.390661 | − | 0.390661i | 0.484262 | − | 0.874923i | \(-0.339088\pi\) |
−0.874923 | + | 0.484262i | \(0.839088\pi\) | |||||||
\(620\) | 126180. | − | 4.12634e6i | 0.0131829 | − | 0.431108i | ||||
\(621\) | −3.06101e6 | + | 3.06101e6i | −0.318519 | + | 0.318519i | ||||
\(622\) | −1.66380e6 | − | 719153.i | −0.172435 | − | 0.0745325i | ||||
\(623\) | −1.38794e7 | −1.43268 | ||||||||
\(624\) | −1.62460e6 | − | 99450.6i | −0.167026 | − | 0.0102246i | ||||
\(625\) | −390625. | −0.0400000 | ||||||||
\(626\) | 2.87855e6 | + | 1.24421e6i | 0.293588 | + | 0.126899i | ||||
\(627\) | 484973. | − | 484973.i | 0.0492662 | − | 0.0492662i | ||||
\(628\) | 4.55743e6 | + | 139362.i | 0.461127 | + | 0.0141009i | ||||
\(629\) | 1.06928e7 | + | 1.06928e7i | 1.07762 | + | 1.07762i | ||||
\(630\) | 3.47459e6 | − | 1.37739e6i | 0.348781 | − | 0.138263i | ||||
\(631\) | − | 1.65548e7i | − | 1.65520i | −0.561315 | − | 0.827602i | \(-0.689704\pi\) | ||
0.561315 | − | 0.827602i | \(-0.310296\pi\) | |||||||
\(632\) | −9.58801e6 | + | 3.46565e6i | −0.954852 | + | 0.345138i | ||||
\(633\) | 1.73842e6i | 0.172443i | ||||||||
\(634\) | −546014. | − | 1.37737e6i | −0.0539486 | − | 0.136090i | ||||
\(635\) | −4.50278e6 | − | 4.50278e6i | −0.443145 | − | 0.443145i | ||||
\(636\) | 1.55146e6 | + | 1.64934e6i | 0.152089 | + | 0.161684i | ||||
\(637\) | −2.12568e6 | + | 2.12568e6i | −0.207562 | + | 0.207562i | ||||
\(638\) | 3.28903e6 | − | 7.60934e6i | 0.319902 | − | 0.740108i | ||||
\(639\) | −4.26921e6 | −0.413614 | ||||||||
\(640\) | 2.22045e6 | − | 4.06748e6i | 0.214285 | − | 0.392533i | ||||
\(641\) | 1.37252e7 | 1.31939 | 0.659695 | − | 0.751534i | \(-0.270686\pi\) | ||||
0.659695 | + | 0.751534i | \(0.270686\pi\) | |||||||
\(642\) | −323133. | + | 747583.i | −0.0309416 | + | 0.0715850i | ||||
\(643\) | 1.06645e7 | − | 1.06645e7i | 1.01722 | − | 1.01722i | 0.0173689 | − | 0.999849i | \(-0.494471\pi\) |
0.999849 | − | 0.0173689i | \(-0.00552896\pi\) | |||||||
\(644\) | −9.39127e6 | − | 9.98374e6i | −0.892298 | − | 0.948590i | ||||
\(645\) | −593672. | − | 593672.i | −0.0561885 | − | 0.0561885i | ||||
\(646\) | 2.31287e6 | + | 5.83442e6i | 0.218057 | + | 0.550068i | ||||
\(647\) | − | 1.48483e7i | − | 1.39449i | −0.716832 | − | 0.697246i | \(-0.754408\pi\) | ||
0.716832 | − | 0.697246i | \(-0.245592\pi\) | |||||||
\(648\) | −9.37789e6 | + | 3.38970e6i | −0.877340 | + | 0.317121i | ||||
\(649\) | 1.31241e7i | 1.22309i | ||||||||
\(650\) | 2.23233e6 | − | 884933.i | 0.207240 | − | 0.0821537i | ||||
\(651\) | 950171. | + | 950171.i | 0.0878718 | + | 0.0878718i | ||||
\(652\) | 762830. | + | 23326.7i | 0.0702763 | + | 0.00214899i | ||||
\(653\) | −2.85059e6 | + | 2.85059e6i | −0.261609 | + | 0.261609i | −0.825707 | − | 0.564099i | \(-0.809224\pi\) |
0.564099 | + | 0.825707i | \(0.309224\pi\) | |||||||
\(654\) | −2.03251e6 | − | 878527.i | −0.185819 | − | 0.0803176i | ||||
\(655\) | 8.52084e6 | 0.776032 | ||||||||
\(656\) | 3.09286e6 | + | 189331.i | 0.280608 | + | 0.0171776i | ||||
\(657\) | −3.45193e6 | −0.311995 | ||||||||
\(658\) | 1.45244e7 | + | 6.27798e6i | 1.30778 | + | 0.565269i | ||||
\(659\) | 7.02539e6 | − | 7.02539e6i | 0.630169 | − | 0.630169i | −0.317941 | − | 0.948110i | \(-0.602991\pi\) |
0.948110 | + | 0.317941i | \(0.102991\pi\) | |||||||
\(660\) | −21332.4 | + | 697615.i | −0.00190625 | + | 0.0623384i | ||||
\(661\) | −1.40520e7 | − | 1.40520e7i | −1.25093 | − | 1.25093i | −0.955303 | − | 0.295629i | \(-0.904471\pi\) |
−0.295629 | − | 0.955303i | \(-0.595529\pi\) | |||||||
\(662\) | −1.25895e7 | + | 4.99070e6i | −1.11651 | + | 0.442606i | ||||
\(663\) | 2.24322e6i | 0.198193i | ||||||||
\(664\) | −643857. | + | 1.37279e6i | −0.0566721 | + | 0.120832i | ||||
\(665\) | 2.18686e6i | 0.191764i | ||||||||
\(666\) | −5.30558e6 | − | 1.33838e7i | −0.463497 | − | 1.16921i | ||||
\(667\) | −1.07001e7 | − | 1.07001e7i | −0.931263 | − | 0.931263i | ||||
\(668\) | −1.25606e7 | + | 1.18152e7i | −1.08910 | + | 1.02447i | ||||
\(669\) | 945354. | − | 945354.i | 0.0816638 | − | 0.0816638i | ||||
\(670\) | −1.52154e6 | + | 3.52015e6i | −0.130947 | + | 0.302952i | ||||
\(671\) | 2.95536e6 | 0.253399 | ||||||||
\(672\) | 469153. | + | 1.43358e6i | 0.0400766 | + | 0.122461i | ||||
\(673\) | 1.61346e7 | 1.37316 | 0.686578 | − | 0.727056i | \(-0.259112\pi\) | ||||
0.686578 | + | 0.727056i | \(0.259112\pi\) | |||||||
\(674\) | 8.54476e6 | − | 1.97687e7i | 0.724520 | − | 1.67621i | ||||
\(675\) | −496983. | + | 496983.i | −0.0419838 | + | 0.0419838i | ||||
\(676\) | −2.09817e6 | + | 1.97366e6i | −0.176593 | + | 0.166113i | ||||
\(677\) | 3.14851e6 | + | 3.14851e6i | 0.264018 | + | 0.264018i | 0.826684 | − | 0.562666i | \(-0.190224\pi\) |
−0.562666 | + | 0.826684i | \(0.690224\pi\) | |||||||
\(678\) | −164664. | − | 415381.i | −0.0137570 | − | 0.0347034i | ||||
\(679\) | − | 5.62335e6i | − | 0.468081i | ||||||
\(680\) | −5.78232e6 | − | 2.71199e6i | −0.479546 | − | 0.224914i | ||||
\(681\) | 872088.i | 0.0720597i | ||||||||
\(682\) | 1.01164e7 | − | 4.01032e6i | 0.832846 | − | 0.330155i | ||||
\(683\) | 1.64501e6 | + | 1.64501e6i | 0.134932 | + | 0.134932i | 0.771347 | − | 0.636415i | \(-0.219583\pi\) |
−0.636415 | + | 0.771347i | \(0.719583\pi\) | |||||||
\(684\) | 182634. | − | 5.97252e6i | 0.0149259 | − | 0.488109i | ||||
\(685\) | −5.19154e6 | + | 5.19154e6i | −0.422736 | + | 0.422736i | ||||
\(686\) | 1.22679e7 | + | 5.30263e6i | 0.995314 | + | 0.430211i | ||||
\(687\) | −304607. | −0.0246234 | ||||||||
\(688\) | −1.10062e7 | + | 9.73640e6i | −0.886472 | + | 0.784201i | ||||
\(689\) | 2.05368e7 | 1.64810 | ||||||||
\(690\) | 1.16946e6 | + | 505484.i | 0.0935111 | + | 0.0404189i | ||||
\(691\) | −6.96341e6 | + | 6.96341e6i | −0.554788 | + | 0.554788i | −0.927819 | − | 0.373031i | \(-0.878319\pi\) |
0.373031 | + | 0.927819i | \(0.378319\pi\) | |||||||
\(692\) | 1.49000e7 | + | 455629.i | 1.18283 | + | 0.0361698i | ||||
\(693\) | 6.96683e6 | + | 6.96683e6i | 0.551064 | + | 0.551064i | ||||
\(694\) | −2.07275e6 | + | 821676.i | −0.163361 | + | 0.0647593i | ||||
\(695\) | 1.09441e6i | 0.0859448i | ||||||||
\(696\) | 566080. | + | 1.56611e6i | 0.0442950 | + | 0.122546i | ||||
\(697\) | − | 4.27056e6i | − | 0.332969i | ||||||
\(698\) | 522527. | + | 1.31812e6i | 0.0405948 | + | 0.102404i | ||||
\(699\) | 2.33040e6 | + | 2.33040e6i | 0.180401 | + | 0.180401i | ||||
\(700\) | −1.52476e6 | − | 1.62095e6i | −0.117613 | − | 0.125033i | ||||
\(701\) | 6.11701e6 | − | 6.11701e6i | 0.470158 | − | 0.470158i | −0.431808 | − | 0.901966i | \(-0.642124\pi\) |
0.901966 | + | 0.431808i | \(0.142124\pi\) | |||||||
\(702\) | 1.71425e6 | − | 3.96601e6i | 0.131290 | − | 0.303746i | ||||
\(703\) | 8.42359e6 | 0.642849 | ||||||||
\(704\) | 1.21643e7 | + | 1.11871e6i | 0.925031 | + | 0.0850721i | ||||
\(705\) | −1.47076e6 | −0.111447 | ||||||||
\(706\) | 5.93746e6 | − | 1.37366e7i | 0.448320 | − | 1.03721i | ||||
\(707\) | −8.17206e6 | + | 8.17206e6i | −0.614870 | + | 0.614870i | ||||
\(708\) | −1.80638e6 | − | 1.92034e6i | −0.135433 | − | 0.143977i | ||||
\(709\) | 6.88103e6 | + | 6.88103e6i | 0.514089 | + | 0.514089i | 0.915777 | − | 0.401688i | \(-0.131576\pi\) |
−0.401688 | + | 0.915777i | \(0.631576\pi\) | |||||||
\(710\) | 936730. | + | 2.36299e6i | 0.0697379 | + | 0.175920i | ||||
\(711\) | − | 1.33775e7i | − | 0.992430i | ||||||
\(712\) | −7.67557e6 | − | 2.12351e7i | −0.567428 | − | 1.56984i | ||||
\(713\) | − | 1.98647e7i | − | 1.46338i | ||||||
\(714\) | 1.93256e6 | − | 766100.i | 0.141869 | − | 0.0562393i | ||||
\(715\) | 4.47598e6 | + | 4.47598e6i | 0.327434 | + | 0.327434i | ||||
\(716\) | 10370.3 | + | 317.116i | 0.000755981 | + | 2.31172e-5i | ||||
\(717\) | 1.21121e6 | − | 1.21121e6i | 0.0879874 | − | 0.0879874i | ||||
\(718\) | −5.07057e6 | − | 2.19168e6i | −0.367067 | − | 0.158660i | ||||
\(719\) | −8.72879e6 | −0.629697 | −0.314849 | − | 0.949142i | \(-0.601954\pi\) | ||||
−0.314849 | + | 0.949142i | \(0.601954\pi\) | |||||||
\(720\) | 4.02888e6 | + | 4.55431e6i | 0.289637 | + | 0.327409i | ||||
\(721\) | 1.11372e7 | 0.797878 | ||||||||
\(722\) | −9.64813e6 | − | 4.17027e6i | −0.688811 | − | 0.297729i | ||||
\(723\) | 874670. | − | 874670.i | 0.0622298 | − | 0.0622298i | ||||
\(724\) | 451994. | − | 1.47811e7i | 0.0320469 | − | 1.04800i | ||||
\(725\) | −1.73726e6 | − | 1.73726e6i | −0.122749 | − | 0.122749i | ||||
\(726\) | 271695. | − | 107705.i | 0.0191311 | − | 0.00758391i | ||||
\(727\) | 2.42302e7i | 1.70028i | 0.526556 | + | 0.850140i | \(0.323483\pi\) | ||||
−0.526556 | + | 0.850140i | \(0.676517\pi\) | |||||||
\(728\) | 1.23858e7 | + | 5.80911e6i | 0.866154 | + | 0.406239i | ||||
\(729\) | − | 1.24448e7i | − | 0.867300i | ||||||
\(730\) | 757407. | + | 1.91063e6i | 0.0526044 | + | 0.132699i | ||||
\(731\) | 1.43205e7 | + | 1.43205e7i | 0.991207 | + | 0.991207i | ||||
\(732\) | −432433. | + | 406771.i | −0.0298292 | + | 0.0280590i | ||||
\(733\) | −7.88120e6 | + | 7.88120e6i | −0.541792 | + | 0.541792i | −0.924054 | − | 0.382262i | \(-0.875145\pi\) |
0.382262 | + | 0.924054i | \(0.375145\pi\) | |||||||
\(734\) | −1.20262e6 | + | 2.78233e6i | −0.0823928 | + | 0.190620i | ||||
\(735\) | −258951. | −0.0176807 | ||||||||
\(736\) | 1.00813e7 | − | 1.98896e7i | 0.685997 | − | 1.35342i | ||||
\(737\) | −1.01090e7 | −0.685548 | ||||||||
\(738\) | −1.61317e6 | + | 3.73215e6i | −0.109028 | + | 0.252243i | ||||
\(739\) | 236806. | − | 236806.i | 0.0159507 | − | 0.0159507i | −0.699086 | − | 0.715037i | \(-0.746410\pi\) |
0.715037 | + | 0.699086i | \(0.246410\pi\) | |||||||
\(740\) | −6.24376e6 | + | 5.87323e6i | −0.419148 | + | 0.394274i | ||||
\(741\) | 883584. | + | 883584.i | 0.0591156 | + | 0.0591156i | ||||
\(742\) | −7.01368e6 | − | 1.76927e7i | −0.467666 | − | 1.17973i | ||||
\(743\) | − | 1.34350e7i | − | 0.892821i | −0.894828 | − | 0.446410i | \(-0.852702\pi\) | ||
0.894828 | − | 0.446410i | \(-0.147298\pi\) | |||||||
\(744\) | −928273. | + | 1.97920e6i | −0.0614814 | + | 0.131086i | ||||
\(745\) | 1.35124e7i | 0.891951i | ||||||||
\(746\) | −1.27048e7 | + | 5.03640e6i | −0.835835 | + | 0.331340i | ||||
\(747\) | −1.40684e6 | − | 1.40684e6i | −0.0922450 | − | 0.0922450i | ||||
\(748\) | 514579. | − | 1.68278e7i | 0.0336277 | − | 1.09970i | ||||
\(749\) | 4.84037e6 | − | 4.84037e6i | 0.315264 | − | 0.315264i | ||||
\(750\) | 189873. | + | 82069.9i | 0.0123256 | + | 0.00532759i | ||||
\(751\) | 1.81960e7 | 1.17727 | 0.588635 | − | 0.808399i | \(-0.299666\pi\) | ||||
0.588635 | + | 0.808399i | \(0.299666\pi\) | |||||||
\(752\) | −1.57286e6 | + | 2.56938e7i | −0.101425 | + | 1.65685i | ||||
\(753\) | −197385. | −0.0126860 | ||||||||
\(754\) | 1.38636e7 | + | 5.99236e6i | 0.888073 | + | 0.383857i | ||||
\(755\) | −2.40251e6 | + | 2.40251e6i | −0.153391 | + | 0.153391i | ||||
\(756\) | −4.00221e6 | − | 122384.i | −0.254681 | − | 0.00778791i | ||||
\(757\) | 2.57560e6 | + | 2.57560e6i | 0.163358 | + | 0.163358i | 0.784052 | − | 0.620695i | \(-0.213149\pi\) |
−0.620695 | + | 0.784052i | \(0.713149\pi\) | |||||||
\(758\) | −1.22199e7 | + | 4.84420e6i | −0.772495 | + | 0.306231i | ||||
\(759\) | 3.35839e6i | 0.211606i | ||||||||
\(760\) | −3.34584e6 | + | 1.20938e6i | −0.210122 | + | 0.0759499i | ||||
\(761\) | 2.94832e7i | 1.84550i | 0.385404 | + | 0.922748i | \(0.374062\pi\) | ||||
−0.385404 | + | 0.922748i | \(0.625938\pi\) | |||||||
\(762\) | 1.24266e6 | + | 3.13472e6i | 0.0775289 | + | 0.195574i | ||||
\(763\) | 1.31599e7 | + | 1.31599e7i | 0.818355 | + | 0.818355i | ||||
\(764\) | −5.75880e6 | − | 6.12211e6i | −0.356943 | − | 0.379462i | ||||
\(765\) | 5.92576e6 | − | 5.92576e6i | 0.366092 | − | 0.366092i | ||||
\(766\) | −5.03683e6 | + | 1.16529e7i | −0.310160 | + | 0.717569i | ||||
\(767\) | −2.39111e7 | −1.46761 | ||||||||
\(768\) | −1.93388e6 | + | 1.51058e6i | −0.118311 | + | 0.0924149i | ||||
\(769\) | −2.91405e7 | −1.77697 | −0.888487 | − | 0.458902i | \(-0.848243\pi\) | ||||
−0.888487 | + | 0.458902i | \(0.848243\pi\) | |||||||
\(770\) | 2.32748e6 | − | 5.38474e6i | 0.141468 | − | 0.327294i | ||||
\(771\) | 1.88395e6 | − | 1.88395e6i | 0.114139 | − | 0.114139i | ||||
\(772\) | −1.62558e7 | − | 1.72813e7i | −0.981667 | − | 1.04360i | ||||
\(773\) | 5.49279e6 | + | 5.49279e6i | 0.330631 | + | 0.330631i | 0.852826 | − | 0.522195i | \(-0.174887\pi\) |
−0.522195 | + | 0.852826i | \(0.674887\pi\) | |||||||
\(774\) | −7.10558e6 | − | 1.79245e7i | −0.426331 | − | 1.07546i | ||||
\(775\) | − | 3.22521e6i | − | 0.192887i | ||||||
\(776\) | 8.60358e6 | − | 3.10982e6i | 0.512891 | − | 0.185388i | ||||
\(777\) | − | 2.79018e6i | − | 0.165798i | ||||||
\(778\) | 6.82028e6 | − | 2.70368e6i | 0.403974 | − | 0.160142i | ||||
\(779\) | −1.68214e6 | − | 1.68214e6i | −0.0993157 | − | 0.0993157i | ||||
\(780\) | −1.27100e6 | − | 38866.1i | −0.0748013 | − | 0.00228736i | ||||
\(781\) | −4.73798e6 | + | 4.73798e6i | −0.277949 | + | 0.277949i | ||||
\(782\) | −2.82096e7 | − | 1.21932e7i | −1.64961 | − | 0.713019i | ||||
\(783\) | −4.42054e6 | −0.257674 | ||||||||
\(784\) | −276927. | + | 4.52380e6i | −0.0160907 | + | 0.262853i | ||||
\(785\) | 3.56216e6 | 0.206319 | ||||||||
\(786\) | −4.14177e6 | − | 1.79022e6i | −0.239127 | − | 0.103359i | ||||
\(787\) | 1.15963e7 | − | 1.15963e7i | 0.667396 | − | 0.667396i | −0.289716 | − | 0.957113i | \(-0.593561\pi\) |
0.957113 | + | 0.289716i | \(0.0935610\pi\) | |||||||
\(788\) | 613157. | − | 2.00515e7i | 0.0351768 | − | 1.15035i | ||||
\(789\) | −2.05881e6 | − | 2.05881e6i | −0.117740 | − | 0.117740i | ||||
\(790\) | −7.40438e6 | + | 2.93523e6i | −0.422105 | + | 0.167330i | ||||
\(791\) | 3.75562e6i | 0.213422i | ||||||||
\(792\) | −6.80627e6 | + | 1.45118e7i | −0.385563 | + | 0.822071i | ||||
\(793\) | 5.38444e6i | 0.304059i | ||||||||
\(794\) | 2.66512e6 | + | 6.72300e6i | 0.150025 | + | 0.378453i | ||||
\(795\) | 1.25090e6 | + | 1.25090e6i | 0.0701947 | + | 0.0701947i | ||||
\(796\) | −1.34931e7 | + | 1.26924e7i | −0.754797 | + | 0.710004i | ||||
\(797\) | −1.90085e7 | + | 1.90085e7i | −1.05999 | + | 1.05999i | −0.0619067 | + | 0.998082i | \(0.519718\pi\) |
−0.998082 | + | 0.0619067i | \(0.980282\pi\) | |||||||
\(798\) | 459457. | − | 1.06298e6i | 0.0255410 | − | 0.0590904i | ||||
\(799\) | 3.54775e7 | 1.96601 | ||||||||
\(800\) | 1.63679e6 | − | 3.22926e6i | 0.0904209 | − | 0.178393i | ||||
\(801\) | 2.96278e7 | 1.63162 | ||||||||
\(802\) | −1.12114e7 | + | 2.59382e7i | −0.615496 | + | 1.42398i | ||||
\(803\) | −3.83096e6 | + | 3.83096e6i | −0.209661 | + | 0.209661i | ||||
\(804\) | 1.47916e6 | − | 1.39138e6i | 0.0807003 | − | 0.0759112i | ||||
\(805\) | −7.57190e6 | − | 7.57190e6i | −0.411827 | − | 0.411827i | ||||
\(806\) | 7.30648e6 | + | 1.84313e7i | 0.396160 | + | 0.999351i | ||||
\(807\) | − | 3.27397e6i | − | 0.176966i | ||||||
\(808\) | −1.70223e7 | − | 7.98372e6i | −0.917256 | − | 0.430206i | ||||
\(809\) | − | 7.55662e6i | − | 0.405935i | −0.979186 | − | 0.202967i | \(-0.934941\pi\) | ||
0.979186 | − | 0.202967i | \(-0.0650585\pi\) | |||||||
\(810\) | −7.24212e6 | + | 2.87090e6i | −0.387840 | + | 0.153747i | ||||
\(811\) | 1.05702e7 | + | 1.05702e7i | 0.564327 | + | 0.564327i | 0.930534 | − | 0.366206i | \(-0.119344\pi\) |
−0.366206 | + | 0.930534i | \(0.619344\pi\) | |||||||
\(812\) | 427807. | − | 1.39902e7i | 0.0227697 | − | 0.744617i | ||||
\(813\) | −1.32979e6 | + | 1.32979e6i | −0.0705595 | + | 0.0705595i | ||||
\(814\) | −2.07415e7 | − | 8.96524e6i | −1.09718 | − | 0.474243i | ||||
\(815\) | 596239. | 0.0314432 | ||||||||
\(816\) | 2.24085e6 | + | 2.53309e6i | 0.117812 | + | 0.133176i | ||||
\(817\) | 1.12814e7 | 0.591301 | ||||||||
\(818\) | 2.32193e6 | + | 1.00362e6i | 0.121329 | + | 0.0524429i | ||||
\(819\) | −1.26930e7 | + | 1.26930e7i | −0.661234 | + | 0.661234i | ||||
\(820\) | 2.41969e6 | + | 73991.9i | 0.125668 | + | 0.00384282i | ||||
\(821\) | −2.13595e7 | − | 2.13595e7i | −1.10594 | − | 1.10594i | −0.993679 | − | 0.112263i | \(-0.964190\pi\) |
−0.112263 | − | 0.993679i | \(-0.535810\pi\) | |||||||
\(822\) | 3.61421e6 | − | 1.43274e6i | 0.186567 | − | 0.0739583i | ||||
\(823\) | − | 7.38656e6i | − | 0.380139i | −0.981771 | − | 0.190070i | \(-0.939129\pi\) | ||
0.981771 | − | 0.190070i | \(-0.0608714\pi\) | |||||||
\(824\) | 6.15906e6 | + | 1.70395e7i | 0.316007 | + | 0.874259i | ||||
\(825\) | 545266.i | 0.0278916i | ||||||||
\(826\) | 8.16606e6 | + | 2.05997e7i | 0.416450 | + | 1.05053i | ||||
\(827\) | 5.91263e6 | + | 5.91263e6i | 0.300619 | + | 0.300619i | 0.841256 | − | 0.540637i | \(-0.181817\pi\) |
−0.540637 | + | 0.841256i | \(0.681817\pi\) | |||||||
\(828\) | 2.00472e7 | + | 2.13119e7i | 1.01620 | + | 1.08031i | ||||
\(829\) | −6.79928e6 | + | 6.79928e6i | −0.343619 | + | 0.343619i | −0.857726 | − | 0.514107i | \(-0.828123\pi\) |
0.514107 | + | 0.857726i | \(0.328123\pi\) | |||||||
\(830\) | −469998. | + | 1.08736e6i | −0.0236810 | + | 0.0547872i | ||||
\(831\) | −2.41009e6 | −0.121068 | ||||||||
\(832\) | −2.03821e6 | + | 2.21624e7i | −0.102080 | + | 1.10997i | ||||
\(833\) | 6.24638e6 | 0.311900 | ||||||||
\(834\) | 229935. | − | 531966.i | 0.0114470 | − | 0.0264831i | ||||
\(835\) | −9.52625e6 | + | 9.52625e6i | −0.472831 | + | 0.472831i | ||||
\(836\) | −6.42562e6 | − | 6.83100e6i | −0.317980 | − | 0.338040i | ||||
\(837\) | −4.10336e6 | − | 4.10336e6i | −0.202454 | − | 0.202454i | ||||
\(838\) | 8.71384e6 | + | 2.19815e7i | 0.428647 | + | 1.08130i | ||||
\(839\) | 5.39057e6i | 0.264381i | 0.991224 | + | 0.132190i | \(0.0422010\pi\) | ||||
−0.991224 | + | 0.132190i | \(0.957799\pi\) | |||||||
\(840\) | 400586. | + | 1.10825e6i | 0.0195883 | + | 0.0541928i | ||||
\(841\) | 5.05867e6i | 0.246630i | ||||||||
\(842\) | 1.72575e7 | − | 6.84119e6i | 0.838878 | − | 0.332546i | ||||
\(843\) | −1.55986e6 | − | 1.55986e6i | −0.0755989 | − | 0.0755989i | ||||
\(844\) | 2.37596e7 | + | 726548.i | 1.14811 | + | 0.0351082i | ||||
\(845\) | −1.59130e6 | + | 1.59130e6i | −0.0766673 | + | 0.0766673i | ||||
\(846\) | −3.10047e7 | − | 1.34014e7i | −1.48937 | − | 0.643759i | ||||
\(847\) | −2.45650e6 | −0.117654 | ||||||||
\(848\) | 2.31906e7 | − | 2.05151e7i | 1.10744 | − | 0.979680i | ||||
\(849\) | 1.43578e6 | 0.0683627 | ||||||||
\(850\) | −4.58009e6 | − | 1.97968e6i | −0.217434 | − | 0.0939827i | ||||
\(851\) | −2.91663e7 | + | 2.91663e7i | −1.38057 | + | 1.38057i | ||||
\(852\) | 41141.0 | − | 1.34539e6i | 0.00194167 | − | 0.0634967i | ||||
\(853\) | −7.01452e6 | − | 7.01452e6i | −0.330085 | − | 0.330085i | 0.522534 | − | 0.852619i | \(-0.324987\pi\) |
−0.852619 | + | 0.522534i | \(0.824987\pi\) | |||||||
\(854\) | 4.63876e6 | − | 1.83888e6i | 0.217649 | − | 0.0862799i | ||||
\(855\) | − | 4.66821e6i | − | 0.218391i | ||||||
\(856\) | 1.00825e7 | + | 4.72882e6i | 0.470307 | + | 0.220581i | ||||
\(857\) | − | 1.69469e7i | − | 0.788202i | −0.919067 | − | 0.394101i | \(-0.871056\pi\) | ||
0.919067 | − | 0.394101i | \(-0.128944\pi\) | |||||||
\(858\) | −1.23526e6 | − | 3.11606e6i | −0.0572850 | − | 0.144507i | ||||
\(859\) | 2.68324e7 | + | 2.68324e7i | 1.24073 | + | 1.24073i | 0.959699 | + | 0.281032i | \(0.0906766\pi\) |
0.281032 | + | 0.959699i | \(0.409323\pi\) | |||||||
\(860\) | −8.36206e6 | + | 7.86582e6i | −0.385538 | + | 0.362659i | ||||
\(861\) | −557181. | + | 557181.i | −0.0256146 | + | 0.0256146i | ||||
\(862\) | −5.78361e6 | + | 1.33807e7i | −0.265113 | + | 0.613351i | ||||
\(863\) | 1.43927e7 | 0.657834 | 0.328917 | − | 0.944359i | \(-0.393316\pi\) | ||||
0.328917 | + | 0.944359i | \(0.393316\pi\) | |||||||
\(864\) | −2.02606e6 | − | 6.19096e6i | −0.0923352 | − | 0.282146i | ||||
\(865\) | 1.16461e7 | 0.529224 | ||||||||
\(866\) | 8.26809e6 | − | 1.91286e7i | 0.374637 | − | 0.866741i | ||||
\(867\) | 946302. | − | 946302.i | 0.0427545 | − | 0.0427545i | ||||
\(868\) | 1.33835e7 | − | 1.25892e7i | 0.602933 | − | 0.567153i | ||||
\(869\) | −1.48464e7 | − | 1.48464e7i | −0.666915 | − | 0.666915i | ||||
\(870\) | 479440. | + | 1.20943e6i | 0.0214752 | + | 0.0541731i | ||||
\(871\) | − | 1.84178e7i | − | 0.822605i | ||||||
\(872\) | −1.28566e7 | + | 2.74120e7i | −0.572579 | + | 1.22081i | ||||
\(873\) | 1.20040e7i | 0.533076i | ||||||||
\(874\) | −1.59143e7 | + | 6.30871e6i | −0.704708 | + | 0.279359i | ||||
\(875\) | −1.22937e6 | − | 1.22937e6i | −0.0542828 | − | 0.0542828i | ||||
\(876\) | 33265.1 | − | 1.08784e6i | 0.00146463 | − | 0.0478965i | ||||
\(877\) | −4.01089e6 | + | 4.01089e6i | −0.176093 | + | 0.176093i | −0.789650 | − | 0.613557i | \(-0.789738\pi\) |
0.613557 | + | 0.789650i | \(0.289738\pi\) | |||||||
\(878\) | −3.35386e7 | − | 1.44966e7i | −1.46828 | − | 0.634644i | ||||
\(879\) | 4.16380e6 | 0.181768 | ||||||||
\(880\) | 9.52565e6 | + | 583117.i | 0.414656 | + | 0.0253834i | ||||
\(881\) | 9.44035e6 | 0.409778 | 0.204889 | − | 0.978785i | \(-0.434317\pi\) | ||||
0.204889 | + | 0.978785i | \(0.434317\pi\) | |||||||
\(882\) | −5.45887e6 | − | 2.35952e6i | −0.236282 | − | 0.102130i | ||||
\(883\) | −2.75650e7 | + | 2.75650e7i | −1.18975 | + | 1.18975i | −0.212617 | + | 0.977136i | \(0.568199\pi\) |
−0.977136 | + | 0.212617i | \(0.931801\pi\) | |||||||
\(884\) | 3.06589e7 | + | 937522.i | 1.31955 | + | 0.0403507i | ||||
\(885\) | −1.45643e6 | − | 1.45643e6i | −0.0625073 | − | 0.0625073i | ||||
\(886\) | 3.10119e7 | − | 1.22937e7i | 1.32722 | − | 0.526135i | ||||
\(887\) | 3.10886e7i | 1.32676i | 0.748282 | + | 0.663380i | \(0.230879\pi\) | ||||
−0.748282 | + | 0.663380i | \(0.769121\pi\) | |||||||
\(888\) | 4.26889e6 | − | 1.54302e6i | 0.181670 | − | 0.0656658i | ||||
\(889\) | − | 2.83421e7i | − | 1.20276i | ||||||
\(890\) | −6.50081e6 | − | 1.63989e7i | −0.275101 | − | 0.693968i | ||||
\(891\) | −1.45210e7 | − | 1.45210e7i | −0.612777 | − | 0.612777i | ||||
\(892\) | −1.25254e7 | − | 1.33156e7i | −0.527084 | − | 0.560337i | ||||
\(893\) | 1.39743e7 | − | 1.39743e7i | 0.586410 | − | 0.586410i | ||||
\(894\) | 2.83894e6 | − | 6.56802e6i | 0.118799 | − | 0.274847i | ||||
\(895\) | 8105.62 | 0.000338243 | ||||||||
\(896\) | 1.97893e7 | − | 5.81294e6i | 0.823494 | − | 0.241895i | ||||
\(897\) | −6.11873e6 | −0.253910 | ||||||||
\(898\) | 7.80608e6 | − | 1.80597e7i | 0.323029 | − | 0.747345i | ||||
\(899\) | 1.43437e7 | − | 1.43437e7i | 0.591920 | − | 0.591920i | ||||
\(900\) | 3.25485e6 | + | 3.46019e6i | 0.133944 | + | 0.142395i | ||||
\(901\) | −3.01740e7 | − | 3.01740e7i | −1.23829 | − | 1.23829i | ||||
\(902\) | 2.35165e6 | + | 5.93226e6i | 0.0962402 | + | 0.242775i | ||||
\(903\) | − | 3.73679e6i | − | 0.152503i | ||||||
\(904\) | −5.74599e6 | + | 2.07693e6i | −0.233853 | + | 0.0845279i | ||||
\(905\) | − | 1.15532e7i | − | 0.468899i | ||||||
\(906\) | 1.67257e6 | − | 663035.i | 0.0676960 | − | 0.0268359i | ||||
\(907\) | 1.45941e7 | + | 1.45941e7i | 0.589059 | + | 0.589059i | 0.937377 | − | 0.348318i | \(-0.113247\pi\) |
−0.348318 | + | 0.937377i | \(0.613247\pi\) | |||||||
\(908\) | 1.19192e7 | + | 364477.i | 0.479768 | + | 0.0146709i | ||||
\(909\) | 1.74446e7 | − | 1.74446e7i | 0.700246 | − | 0.700246i | ||||
\(910\) | 9.81058e6 | + | 4.24049e6i | 0.392728 | + | 0.169751i | ||||
\(911\) | −1.29136e7 | −0.515525 | −0.257762 | − | 0.966208i | \(-0.582985\pi\) | ||||
−0.257762 | + | 0.966208i | \(0.582985\pi\) | |||||||
\(912\) | 1.88041e6 | + | 115110.i | 0.0748629 | + | 0.00458277i | ||||
\(913\) | −3.12263e6 | −0.123978 | ||||||||
\(914\) | 3.39493e7 | + | 1.46741e7i | 1.34421 | + | 0.581015i | ||||
\(915\) | −327967. | + | 327967.i | −0.0129502 | + | 0.0129502i | ||||
\(916\) | −127306. | + | 4.16318e6i | −0.00501315 | + | 0.163940i | ||||
\(917\) | 2.68167e7 | + | 2.68167e7i | 1.05313 | + | 1.05313i | ||||
\(918\) | −8.34584e6 | + | 3.30844e6i | −0.326861 | + | 0.129573i | ||||
\(919\) | − | 3.83716e7i | − | 1.49872i | −0.662161 | − | 0.749362i | \(-0.730360\pi\) | ||
0.662161 | − | 0.749362i | \(-0.269640\pi\) | |||||||
\(920\) | 7.39740e6 | − | 1.57722e7i | 0.288144 | − | 0.614360i | ||||
\(921\) | 847621.i | 0.0329270i | ||||||||
\(922\) | 1.70962e7 | + | 4.31267e7i | 0.662326 | + | 1.67078i | ||||
\(923\) | −8.63222e6 | − | 8.63222e6i | −0.333517 | − | 0.333517i | ||||
\(924\) | −2.26266e6 | + | 2.12838e6i | −0.0871845 | + | 0.0820106i | ||||
\(925\) | −4.73541e6 | + | 4.73541e6i | −0.181972 | + | 0.181972i | ||||
\(926\) | −5.25127e6 | + | 1.21491e7i | −0.201250 | + | 0.465603i | ||||
\(927\) | −2.37741e7 | −0.908666 | ||||||||
\(928\) | 2.16412e7 | − | 7.08230e6i | 0.824918 | − | 0.269963i | ||||
\(929\) | 1.22760e7 | 0.466680 | 0.233340 | − | 0.972395i | \(-0.425034\pi\) | ||||
0.233340 | + | 0.972395i | \(0.425034\pi\) | |||||||
\(930\) | −677614. | + | 1.56769e6i | −0.0256906 | + | 0.0594365i | ||||
\(931\) | 2.46039e6 | − | 2.46039e6i | 0.0930316 | − | 0.0930316i | ||||
\(932\) | 3.28244e7 | − | 3.08765e7i | 1.23782 | − | 1.16436i | ||||
\(933\) | 530232. | + | 530232.i | 0.0199417 | + | 0.0199417i | ||||
\(934\) | 1.65286e7 | + | 4.16949e7i | 0.619967 | + | 1.56392i | ||||
\(935\) | − | 1.31528e7i | − | 0.492029i | ||||||
\(936\) | −2.64394e7 | − | 1.24005e7i | −0.986422 | − | 0.462646i | ||||
\(937\) | − | 2.42972e7i | − | 0.904081i | −0.891997 | − | 0.452040i | \(-0.850696\pi\) | ||
0.891997 | − | 0.452040i | \(-0.149304\pi\) | |||||||
\(938\) | −1.58671e7 | + | 6.29000e6i | −0.588831 | + | 0.233423i | ||||
\(939\) | −917359. | − | 917359.i | −0.0339528 | − | 0.0339528i | ||||
\(940\) | −614685. | + | 2.01015e7i | −0.0226899 | + | 0.742007i | ||||
\(941\) | −6.55983e6 | + | 6.55983e6i | −0.241501 | + | 0.241501i | −0.817471 | − | 0.575970i | \(-0.804625\pi\) |
0.575970 | + | 0.817471i | \(0.304625\pi\) | |||||||
\(942\) | −1.73147e6 | − | 748405.i | −0.0635753 | − | 0.0274796i | ||||
\(943\) | 1.16486e7 | 0.426576 | ||||||||
\(944\) | −2.70009e7 | + | 2.38858e7i | −0.986162 | + | 0.872390i | ||||
\(945\) | −3.12819e6 | −0.113950 | ||||||||
\(946\) | −2.77784e7 | − | 1.20068e7i | −1.00921 | − | 0.436216i | ||||
\(947\) | 2.49052e7 | − | 2.49052e7i | 0.902431 | − | 0.902431i | −0.0932146 | − | 0.995646i | \(-0.529714\pi\) |
0.995646 | + | 0.0932146i | \(0.0297143\pi\) | |||||||
\(948\) | 4.21577e6 | + | 128914.i | 0.152355 | + | 0.00465887i | ||||
\(949\) | −6.97971e6 | − | 6.97971e6i | −0.251577 | − | 0.251577i | ||||
\(950\) | −2.58384e6 | + | 1.02428e6i | −0.0928872 | + | 0.0368221i | ||||
\(951\) | 612959.i | 0.0219776i | ||||||||
\(952\) | −9.66289e6 | − | 2.67332e7i | −0.345553 | − | 0.956001i | ||||
\(953\) | − | 4.45703e7i | − | 1.58969i | −0.606810 | − | 0.794847i | \(-0.707551\pi\) | ||
0.606810 | − | 0.794847i | \(-0.292449\pi\) | |||||||
\(954\) | 1.49718e7 | + | 3.77678e7i | 0.532603 | + | 1.34354i | ||||
\(955\) | −4.64315e6 | − | 4.64315e6i | −0.164742 | − | 0.164742i | ||||
\(956\) | −1.60478e7 | − | 1.70602e7i | −0.567899 | − | 0.603727i | ||||
\(957\) | −2.42501e6 | + | 2.42501e6i | −0.0855919 | + | 0.0855919i | ||||
\(958\) | −8.04943e6 | + | 1.86228e7i | −0.283368 | + | 0.655587i | ||||
\(959\) | −3.26774e7 | −1.14736 | ||||||||
\(960\) | −1.47407e6 | + | 1.22577e6i | −0.0516225 | + | 0.0429271i | ||||
\(961\) | −2.00007e6 | −0.0698612 | ||||||||
\(962\) | 1.63340e7 | − | 3.77895e7i | 0.569055 | − | 1.31654i | ||||
\(963\) | −1.03326e7 | + | 1.03326e7i | −0.359039 | + | 0.359039i | ||||
\(964\) | −1.15889e7 | − | 1.23200e7i | −0.401651 | − | 0.426990i | ||||
\(965\) | −1.31065e7 | − | 1.31065e7i | −0.453074 | − | 0.453074i | ||||
\(966\) | 2.08966e6 | + | 5.27136e6i | 0.0720498 | + | 0.181752i | ||||
\(967\) | − | 7.28077e6i | − | 0.250387i | −0.992132 | − | 0.125193i | \(-0.960045\pi\) | ||
0.992132 | − | 0.125193i | \(-0.0399551\pi\) | |||||||
\(968\) | −1.35849e6 | − | 3.75837e6i | −0.0465981 | − | 0.128917i | ||||
\(969\) | − | 2.59644e6i | − | 0.0888320i | ||||||
\(970\) | 6.64414e6 | − | 2.63386e6i | 0.226730 | − | 0.0898799i | ||||
\(971\) | 1.58454e7 | + | 1.58454e7i | 0.539330 | + | 0.539330i | 0.923332 | − | 0.384002i | \(-0.125454\pi\) |
−0.384002 | + | 0.923332i | \(0.625454\pi\) | |||||||
\(972\) | 1.28637e7 | + | 393362.i | 0.436719 | + | 0.0133545i | ||||
\(973\) | −3.44432e6 | + | 3.44432e6i | −0.116633 | + | 0.116633i | ||||
\(974\) | −2.57276e7 | − | 1.11204e7i | −0.868966 | − | 0.375599i | ||||
\(975\) | −993433. | −0.0334678 | ||||||||
\(976\) | 5.37876e6 | + | 6.08023e6i | 0.180741 | + | 0.204313i | ||||
\(977\) | −2.60033e7 | −0.871549 | −0.435774 | − | 0.900056i | \(-0.643525\pi\) | ||||
−0.435774 | + | 0.900056i | \(0.643525\pi\) | |||||||
\(978\) | −289817. | − | 125269.i | −0.00968894 | − | 0.00418791i | ||||
\(979\) | 3.28810e7 | − | 3.28810e7i | 1.09645 | − | 1.09645i | ||||
\(980\) | −108225. | + | 3.53918e6i | −0.00359967 | + | 0.117717i | ||||
\(981\) | −2.80919e7 | − | 2.80919e7i | −0.931986 | − | 0.931986i | ||||
\(982\) | −1.11587e7 | + | 4.42352e6i | −0.369263 | + | 0.146382i | ||||
\(983\) | 4.67075e7i | 1.54171i | 0.637010 | + | 0.770855i | \(0.280171\pi\) | ||||
−0.637010 | + | 0.770855i | \(0.719829\pi\) | |||||||
\(984\) | −1.16060e6 | − | 544340.i | −0.0382117 | − | 0.0179218i | ||||
\(985\) | − | 1.56726e7i | − | 0.514694i | ||||||
\(986\) | −1.15650e7 | − | 2.91738e7i | −0.378838 | − | 0.955653i | ||||
\(987\) | −4.62876e6 | − | 4.62876e6i | −0.151242 | − | 0.151242i | ||||
\(988\) | 1.24456e7 | − | 1.17070e7i | 0.405622 | − | 0.381551i | ||||
\(989\) | −3.90614e7 | + | 3.90614e7i | −1.26986 | + | 1.26986i | ||||
\(990\) | −4.96839e6 | + | 1.14946e7i | −0.161112 | + | 0.372740i | ||||
\(991\) | 4.72379e7 | 1.52794 | 0.763969 | − | 0.645252i | \(-0.223248\pi\) | ||||
0.763969 | + | 0.645252i | \(0.223248\pi\) | |||||||
\(992\) | 2.66625e7 | + | 1.35142e7i | 0.860244 | + | 0.436026i | ||||
\(993\) | 5.60260e6 | 0.180309 | ||||||||
\(994\) | −4.48870e6 | + | 1.03848e7i | −0.144097 | + | 0.333375i | ||||
\(995\) | −1.02335e7 | + | 1.02335e7i | −0.327693 | + | 0.327693i | ||||
\(996\) | 456908. | − | 429793.i | 0.0145942 | − | 0.0137281i | ||||
\(997\) | 5.04466e6 | + | 5.04466e6i | 0.160729 | + | 0.160729i | 0.782890 | − | 0.622161i | \(-0.213745\pi\) |
−0.622161 | + | 0.782890i | \(0.713745\pi\) | |||||||
\(998\) | −1.92823e7 | − | 4.86414e7i | −0.612819 | − | 1.54589i | ||||
\(999\) | 1.20495e7i | 0.381993i |
(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 | 80.6.l.a.21.16 | ✓ | 80 | |
4.3 | odd | 2 | 320.6.l.a.241.21 | 80 | |||
16.3 | odd | 4 | 320.6.l.a.81.21 | 80 | |||
16.13 | even | 4 | inner | 80.6.l.a.61.16 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.l.a.21.16 | ✓ | 80 | 1.1 | even | 1 | trivial | |
80.6.l.a.61.16 | yes | 80 | 16.13 | even | 4 | inner | |
320.6.l.a.81.21 | 80 | 16.3 | odd | 4 | |||
320.6.l.a.241.21 | 80 | 4.3 | odd | 2 |