Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (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: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 6.10 | ||
Character | \(\chi\) | \(=\) | 43.6 |
Dual form | 43.6.c.a.36.10 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.74361 | 0.308230 | 0.154115 | − | 0.988053i | \(-0.450747\pi\) | ||||
0.154115 | + | 0.988053i | \(0.450747\pi\) | |||||||
\(3\) | 7.37567 | − | 12.7750i | 0.473150 | − | 0.819519i | −0.526378 | − | 0.850251i | \(-0.676450\pi\) |
0.999528 | + | 0.0307315i | \(0.00978368\pi\) | |||||||
\(4\) | −28.9598 | −0.904994 | ||||||||
\(5\) | −8.29752 | + | 14.3717i | −0.148430 | + | 0.257089i | −0.930648 | − | 0.365917i | \(-0.880755\pi\) |
0.782217 | + | 0.623006i | \(0.214089\pi\) | |||||||
\(6\) | 12.8603 | − | 22.2747i | 0.145839 | − | 0.252600i | ||||
\(7\) | −98.7307 | − | 171.007i | −0.761565 | − | 1.31907i | −0.942044 | − | 0.335490i | \(-0.891098\pi\) |
0.180479 | − | 0.983579i | \(-0.442235\pi\) | |||||||
\(8\) | −106.290 | −0.587177 | ||||||||
\(9\) | 12.6989 | + | 21.9952i | 0.0522589 | + | 0.0905151i | ||||
\(10\) | −14.4677 | + | 25.0587i | −0.0457507 | + | 0.0792426i | ||||
\(11\) | −376.577 | −0.938365 | −0.469182 | − | 0.883101i | \(-0.655451\pi\) | ||||
−0.469182 | + | 0.883101i | \(0.655451\pi\) | |||||||
\(12\) | −213.598 | + | 369.963i | −0.428198 | + | 0.741660i | ||||
\(13\) | −55.5603 | − | 96.2332i | −0.0911813 | − | 0.157931i | 0.816827 | − | 0.576882i | \(-0.195731\pi\) |
−0.908008 | + | 0.418952i | \(0.862398\pi\) | |||||||
\(14\) | −172.148 | − | 298.169i | −0.234737 | − | 0.406577i | ||||
\(15\) | 122.400 | + | 212.002i | 0.140460 | + | 0.243283i | ||||
\(16\) | 741.385 | 0.724009 | ||||||||
\(17\) | −786.400 | − | 1362.08i | −0.659965 | − | 1.14309i | −0.980624 | − | 0.195899i | \(-0.937238\pi\) |
0.320659 | − | 0.947195i | \(-0.396096\pi\) | |||||||
\(18\) | 22.1420 | + | 38.3511i | 0.0161078 | + | 0.0278995i | ||||
\(19\) | 444.429 | − | 769.773i | 0.282435 | − | 0.489191i | −0.689549 | − | 0.724239i | \(-0.742191\pi\) |
0.971984 | + | 0.235048i | \(0.0755246\pi\) | |||||||
\(20\) | 240.295 | − | 416.202i | 0.134329 | − | 0.232664i | ||||
\(21\) | −2912.82 | −1.44134 | ||||||||
\(22\) | −656.604 | −0.289232 | ||||||||
\(23\) | 428.153 | − | 741.583i | 0.168764 | − | 0.292308i | −0.769222 | − | 0.638982i | \(-0.779356\pi\) |
0.937986 | + | 0.346674i | \(0.112689\pi\) | |||||||
\(24\) | −783.963 | + | 1357.86i | −0.277822 | + | 0.481202i | ||||
\(25\) | 1424.80 | + | 2467.83i | 0.455937 | + | 0.789706i | ||||
\(26\) | −96.8756 | − | 167.793i | −0.0281048 | − | 0.0486790i | ||||
\(27\) | 3959.23 | 1.04520 | ||||||||
\(28\) | 2859.22 | + | 4952.32i | 0.689212 | + | 1.19375i | ||||
\(29\) | 12.2237 | + | 21.1721i | 0.00269903 | + | 0.00467486i | 0.867372 | − | 0.497661i | \(-0.165808\pi\) |
−0.864673 | + | 0.502336i | \(0.832474\pi\) | |||||||
\(30\) | 213.417 | + | 369.650i | 0.0432939 | + | 0.0749872i | ||||
\(31\) | 2222.35 | − | 3849.23i | 0.415345 | − | 0.719399i | −0.580119 | − | 0.814531i | \(-0.696994\pi\) |
0.995465 | + | 0.0951325i | \(0.0303275\pi\) | |||||||
\(32\) | 4693.98 | 0.810338 | ||||||||
\(33\) | −2777.51 | + | 4810.78i | −0.443987 | + | 0.769008i | ||||
\(34\) | −1371.18 | − | 2374.95i | −0.203421 | − | 0.352336i | ||||
\(35\) | 3276.88 | 0.452158 | ||||||||
\(36\) | −367.758 | − | 636.976i | −0.0472940 | − | 0.0819157i | ||||
\(37\) | −3154.45 | + | 5463.66i | −0.378808 | + | 0.656114i | −0.990889 | − | 0.134681i | \(-0.956999\pi\) |
0.612081 | + | 0.790795i | \(0.290332\pi\) | |||||||
\(38\) | 774.912 | − | 1342.19i | 0.0870549 | − | 0.150784i | ||||
\(39\) | −1639.18 | −0.172570 | ||||||||
\(40\) | 881.946 | − | 1527.57i | 0.0871549 | − | 0.150957i | ||||
\(41\) | 5203.64 | 0.483446 | 0.241723 | − | 0.970345i | \(-0.422287\pi\) | ||||
0.241723 | + | 0.970345i | \(0.422287\pi\) | |||||||
\(42\) | −5078.83 | −0.444263 | ||||||||
\(43\) | 3986.93 | − | 11450.5i | 0.328827 | − | 0.944390i | ||||
\(44\) | 10905.6 | 0.849215 | ||||||||
\(45\) | −421.478 | −0.0310273 | ||||||||
\(46\) | 746.533 | − | 1293.03i | 0.0520181 | − | 0.0900980i | ||||
\(47\) | −13328.9 | −0.880139 | −0.440069 | − | 0.897964i | \(-0.645046\pi\) | ||||
−0.440069 | + | 0.897964i | \(0.645046\pi\) | |||||||
\(48\) | 5468.21 | − | 9471.22i | 0.342564 | − | 0.593339i | ||||
\(49\) | −11092.0 | + | 19211.9i | −0.659963 | + | 1.14309i | ||||
\(50\) | 2484.30 | + | 4302.94i | 0.140533 | + | 0.243411i | ||||
\(51\) | −23200.9 | −1.24905 | ||||||||
\(52\) | 1609.01 | + | 2786.90i | 0.0825186 | + | 0.142926i | ||||
\(53\) | 2126.84 | − | 3683.80i | 0.104003 | − | 0.180138i | −0.809327 | − | 0.587358i | \(-0.800168\pi\) |
0.913330 | + | 0.407219i | \(0.133502\pi\) | |||||||
\(54\) | 6903.36 | 0.322163 | ||||||||
\(55\) | 3124.65 | − | 5412.05i | 0.139282 | − | 0.241243i | ||||
\(56\) | 10494.1 | + | 18176.3i | 0.447173 | + | 0.774527i | ||||
\(57\) | −6555.92 | − | 11355.2i | −0.267268 | − | 0.462921i | ||||
\(58\) | 21.3134 | + | 36.9159i | 0.000831922 | + | 0.00144093i | ||||
\(59\) | −49458.5 | −1.84974 | −0.924871 | − | 0.380281i | \(-0.875827\pi\) | ||||
−0.924871 | + | 0.380281i | \(0.875827\pi\) | |||||||
\(60\) | −3544.67 | − | 6139.54i | −0.127115 | − | 0.220170i | ||||
\(61\) | −17027.7 | − | 29492.8i | −0.585910 | − | 1.01483i | −0.994761 | − | 0.102225i | \(-0.967404\pi\) |
0.408851 | − | 0.912601i | \(-0.365930\pi\) | |||||||
\(62\) | 3874.93 | − | 6711.57i | 0.128022 | − | 0.221740i | ||||
\(63\) | 2507.55 | − | 4343.20i | 0.0795972 | − | 0.137866i | ||||
\(64\) | −15539.8 | −0.474238 | ||||||||
\(65\) | 1844.05 | 0.0541363 | ||||||||
\(66\) | −4842.90 | + | 8388.14i | −0.136850 | + | 0.237031i | ||||
\(67\) | 21053.3 | − | 36465.4i | 0.572972 | − | 0.992416i | −0.423287 | − | 0.905996i | \(-0.639124\pi\) |
0.996259 | − | 0.0864206i | \(-0.0275429\pi\) | |||||||
\(68\) | 22774.0 | + | 39445.7i | 0.597265 | + | 1.03449i | ||||
\(69\) | −6315.84 | − | 10939.3i | −0.159701 | − | 0.276611i | ||||
\(70\) | 5713.61 | 0.139369 | ||||||||
\(71\) | −19431.3 | − | 33656.0i | −0.457463 | − | 0.792349i | 0.541363 | − | 0.840789i | \(-0.317908\pi\) |
−0.998826 | + | 0.0484399i | \(0.984575\pi\) | |||||||
\(72\) | −1349.77 | − | 2337.87i | −0.0306852 | − | 0.0531484i | ||||
\(73\) | −12721.3 | − | 22034.0i | −0.279400 | − | 0.483934i | 0.691836 | − | 0.722055i | \(-0.256802\pi\) |
−0.971236 | + | 0.238120i | \(0.923469\pi\) | |||||||
\(74\) | −5500.13 | + | 9526.51i | −0.116760 | + | 0.202234i | ||||
\(75\) | 42035.5 | 0.862905 | ||||||||
\(76\) | −12870.6 | + | 22292.5i | −0.255602 | + | 0.442715i | ||||
\(77\) | 37179.7 | + | 64397.1i | 0.714626 | + | 1.23777i | ||||
\(78\) | −2858.09 | −0.0531912 | ||||||||
\(79\) | 47886.5 | + | 82941.8i | 0.863267 | + | 1.49522i | 0.868758 | + | 0.495237i | \(0.164919\pi\) |
−0.00549153 | + | 0.999985i | \(0.501748\pi\) | |||||||
\(80\) | −6151.65 | + | 10655.0i | −0.107465 | + | 0.186135i | ||||
\(81\) | 26116.1 | − | 45234.5i | 0.442279 | − | 0.766050i | ||||
\(82\) | 9073.14 | 0.149013 | ||||||||
\(83\) | −1039.08 | + | 1799.74i | −0.0165560 | + | 0.0286758i | −0.874185 | − | 0.485594i | \(-0.838604\pi\) |
0.857629 | + | 0.514269i | \(0.171937\pi\) | |||||||
\(84\) | 84354.7 | 1.30440 | ||||||||
\(85\) | 26100.7 | 0.391836 | ||||||||
\(86\) | 6951.65 | − | 19965.2i | 0.101354 | − | 0.291090i | ||||
\(87\) | 360.632 | 0.00510818 | ||||||||
\(88\) | 40026.5 | 0.550986 | ||||||||
\(89\) | −73066.1 | + | 126554.i | −0.977780 | + | 1.69356i | −0.307342 | + | 0.951599i | \(0.599440\pi\) |
−0.670438 | + | 0.741966i | \(0.733894\pi\) | |||||||
\(90\) | −734.895 | −0.00956354 | ||||||||
\(91\) | −10971.0 | + | 19002.3i | −0.138881 | + | 0.240549i | ||||
\(92\) | −12399.2 | + | 21476.1i | −0.152730 | + | 0.264537i | ||||
\(93\) | −32782.7 | − | 56781.3i | −0.393041 | − | 0.680767i | ||||
\(94\) | −23240.5 | −0.271285 | ||||||||
\(95\) | 7375.31 | + | 12774.4i | 0.0838439 | + | 0.145222i | ||||
\(96\) | 34621.2 | − | 59965.8i | 0.383411 | − | 0.664087i | ||||
\(97\) | 18998.2 | 0.205014 | 0.102507 | − | 0.994732i | \(-0.467314\pi\) | ||||
0.102507 | + | 0.994732i | \(0.467314\pi\) | |||||||
\(98\) | −19340.1 | + | 33498.1i | −0.203420 | + | 0.352334i | ||||
\(99\) | −4782.12 | − | 8282.87i | −0.0490379 | − | 0.0849362i | ||||
\(100\) | −41262.0 | − | 71467.9i | −0.412620 | − | 0.714679i | ||||
\(101\) | 19393.1 | + | 33589.9i | 0.189167 | + | 0.327646i | 0.944973 | − | 0.327149i | \(-0.106088\pi\) |
−0.755806 | + | 0.654796i | \(0.772755\pi\) | |||||||
\(102\) | −40453.4 | −0.384995 | ||||||||
\(103\) | −86224.2 | − | 149345.i | −0.800823 | − | 1.38707i | −0.919075 | − | 0.394082i | \(-0.871063\pi\) |
0.118253 | − | 0.992984i | \(-0.462271\pi\) | |||||||
\(104\) | 5905.52 | + | 10228.7i | 0.0535395 | + | 0.0927332i | ||||
\(105\) | 24169.2 | − | 41862.2i | 0.213938 | − | 0.370552i | ||||
\(106\) | 3708.39 | − | 6423.12i | 0.0320568 | − | 0.0555241i | ||||
\(107\) | 215412. | 1.81891 | 0.909453 | − | 0.415806i | \(-0.136500\pi\) | ||||
0.909453 | + | 0.415806i | \(0.136500\pi\) | |||||||
\(108\) | −114659. | −0.945904 | ||||||||
\(109\) | −7192.91 | + | 12458.5i | −0.0579880 | + | 0.100438i | −0.893562 | − | 0.448940i | \(-0.851802\pi\) |
0.835574 | + | 0.549378i | \(0.185135\pi\) | |||||||
\(110\) | 5448.18 | − | 9436.53i | 0.0429309 | − | 0.0743585i | ||||
\(111\) | 46532.3 | + | 80596.3i | 0.358465 | + | 0.620880i | ||||
\(112\) | −73197.4 | − | 126782.i | −0.551380 | − | 0.955018i | ||||
\(113\) | −10848.6 | −0.0799242 | −0.0399621 | − | 0.999201i | \(-0.512724\pi\) | ||||
−0.0399621 | + | 0.999201i | \(0.512724\pi\) | |||||||
\(114\) | −11431.0 | − | 19799.1i | −0.0823800 | − | 0.142686i | ||||
\(115\) | 7105.22 | + | 12306.6i | 0.0500994 | + | 0.0867747i | ||||
\(116\) | −353.996 | − | 613.139i | −0.00244261 | − | 0.00423072i | ||||
\(117\) | 1411.11 | − | 2444.12i | 0.00953008 | − | 0.0165066i | ||||
\(118\) | −86236.5 | −0.570146 | ||||||||
\(119\) | −155284. | + | 268959.i | −1.00521 | + | 1.74108i | ||||
\(120\) | −13009.9 | − | 22533.8i | −0.0824746 | − | 0.142850i | ||||
\(121\) | −19241.0 | −0.119472 | ||||||||
\(122\) | −29689.7 | − | 51424.1i | −0.180595 | − | 0.312800i | ||||
\(123\) | 38380.4 | − | 66476.8i | 0.228742 | − | 0.396193i | ||||
\(124\) | −64359.0 | + | 111473.i | −0.375885 | + | 0.651052i | ||||
\(125\) | −99148.8 | −0.567561 | ||||||||
\(126\) | 4372.19 | − | 7572.86i | 0.0245342 | − | 0.0424946i | ||||
\(127\) | 159848. | 0.879424 | 0.439712 | − | 0.898139i | \(-0.355080\pi\) | ||||
0.439712 | + | 0.898139i | \(0.355080\pi\) | |||||||
\(128\) | −177303. | −0.956512 | ||||||||
\(129\) | −116874. | − | 135388.i | −0.618362 | − | 0.716318i | ||||
\(130\) | 3215.31 | 0.0166865 | ||||||||
\(131\) | 103109. | 0.524952 | 0.262476 | − | 0.964938i | \(-0.415461\pi\) | ||||
0.262476 | + | 0.964938i | \(0.415461\pi\) | |||||||
\(132\) | 80436.1 | − | 139319.i | 0.401806 | − | 0.695948i | ||||
\(133\) | −175515. | −0.860370 | ||||||||
\(134\) | 36708.8 | − | 63581.5i | 0.176607 | − | 0.305893i | ||||
\(135\) | −32851.8 | + | 56900.9i | −0.155140 | + | 0.268711i | ||||
\(136\) | 83586.7 | + | 144776.i | 0.387516 | + | 0.671198i | ||||
\(137\) | 260707. | 1.18673 | 0.593363 | − | 0.804935i | \(-0.297800\pi\) | ||||
0.593363 | + | 0.804935i | \(0.297800\pi\) | |||||||
\(138\) | −11012.4 | − | 19074.0i | −0.0492247 | − | 0.0852597i | ||||
\(139\) | 156477. | − | 271026.i | 0.686932 | − | 1.18980i | −0.285894 | − | 0.958261i | \(-0.592290\pi\) |
0.972826 | − | 0.231539i | \(-0.0743762\pi\) | |||||||
\(140\) | −94897.8 | −0.409200 | ||||||||
\(141\) | −98309.9 | + | 170278.i | −0.416437 | + | 0.721290i | ||||
\(142\) | −33880.7 | − | 58683.0i | −0.141004 | − | 0.244226i | ||||
\(143\) | 20922.7 | + | 36239.2i | 0.0855613 | + | 0.148197i | ||||
\(144\) | 9414.79 | + | 16306.9i | 0.0378359 | + | 0.0655337i | ||||
\(145\) | −405.705 | −0.00160247 | ||||||||
\(146\) | −22181.1 | − | 38418.8i | −0.0861194 | − | 0.149163i | ||||
\(147\) | 163622. | + | 283401.i | 0.624522 | + | 1.08170i | ||||
\(148\) | 91352.2 | − | 158227.i | 0.342819 | − | 0.593780i | ||||
\(149\) | −16523.6 | + | 28619.7i | −0.0609732 | + | 0.105609i | −0.894901 | − | 0.446265i | \(-0.852754\pi\) |
0.833928 | + | 0.551874i | \(0.186087\pi\) | |||||||
\(150\) | 73293.6 | 0.265973 | ||||||||
\(151\) | 171625. | 0.612547 | 0.306273 | − | 0.951944i | \(-0.400918\pi\) | ||||
0.306273 | + | 0.951944i | \(0.400918\pi\) | |||||||
\(152\) | −47238.5 | + | 81819.5i | −0.165839 | + | 0.287242i | ||||
\(153\) | 19972.9 | − | 34594.0i | 0.0689782 | − | 0.119474i | ||||
\(154\) | 64827.0 | + | 112284.i | 0.220269 | + | 0.381517i | ||||
\(155\) | 36880.0 | + | 63878.1i | 0.123300 | + | 0.213561i | ||||
\(156\) | 47470.3 | 0.156174 | ||||||||
\(157\) | −133583. | − | 231373.i | −0.432517 | − | 0.749142i | 0.564572 | − | 0.825384i | \(-0.309041\pi\) |
−0.997089 | + | 0.0762420i | \(0.975708\pi\) | |||||||
\(158\) | 83495.4 | + | 144618.i | 0.266085 | + | 0.460872i | ||||
\(159\) | −31373.8 | − | 54341.0i | −0.0984179 | − | 0.170465i | ||||
\(160\) | −38948.4 | + | 67460.5i | −0.120279 | + | 0.208329i | ||||
\(161\) | −169087. | −0.514099 | ||||||||
\(162\) | 45536.4 | − | 78871.4i | 0.136324 | − | 0.236120i | ||||
\(163\) | 152556. | + | 264235.i | 0.449740 | + | 0.778972i | 0.998369 | − | 0.0570939i | \(-0.0181835\pi\) |
−0.548629 | + | 0.836066i | \(0.684850\pi\) | |||||||
\(164\) | −150697. | −0.437516 | ||||||||
\(165\) | −46092.8 | − | 79835.1i | −0.131802 | − | 0.228288i | ||||
\(166\) | −1811.76 | + | 3138.05i | −0.00510305 | + | 0.00883874i | ||||
\(167\) | −80139.4 | + | 138805.i | −0.222359 | + | 0.385137i | −0.955524 | − | 0.294914i | \(-0.904709\pi\) |
0.733165 | + | 0.680051i | \(0.238042\pi\) | |||||||
\(168\) | 309605. | 0.846319 | ||||||||
\(169\) | 179473. | − | 310856.i | 0.483372 | − | 0.837225i | ||||
\(170\) | 45509.5 | 0.120776 | ||||||||
\(171\) | 22575.1 | 0.0590390 | ||||||||
\(172\) | −115461. | + | 331603.i | −0.297586 | + | 0.854668i | ||||
\(173\) | 654616. | 1.66292 | 0.831460 | − | 0.555585i | \(-0.187506\pi\) | ||||
0.831460 | + | 0.555585i | \(0.187506\pi\) | |||||||
\(174\) | 628.802 | 0.00157449 | ||||||||
\(175\) | 281343. | − | 487301.i | 0.694451 | − | 1.20282i | ||||
\(176\) | −279188. | −0.679384 | ||||||||
\(177\) | −364790. | + | 631835.i | −0.875205 | + | 1.51590i | ||||
\(178\) | −127399. | + | 220662.i | −0.301381 | + | 0.522008i | ||||
\(179\) | 374942. | + | 649418.i | 0.874643 | + | 1.51493i | 0.857142 | + | 0.515080i | \(0.172238\pi\) |
0.0175011 | + | 0.999847i | \(0.494429\pi\) | |||||||
\(180\) | 12205.9 | 0.0280795 | ||||||||
\(181\) | −401046. | − | 694632.i | −0.909908 | − | 1.57601i | −0.814190 | − | 0.580598i | \(-0.802819\pi\) |
−0.0957176 | − | 0.995409i | \(-0.530515\pi\) | |||||||
\(182\) | −19129.2 | + | 33132.7i | −0.0428073 | + | 0.0741444i | ||||
\(183\) | −502363. | −1.10889 | ||||||||
\(184\) | −45508.5 | + | 78823.1i | −0.0990942 | + | 0.171636i | ||||
\(185\) | −52348.1 | − | 90669.6i | −0.112453 | − | 0.194775i | ||||
\(186\) | −57160.4 | − | 99004.7i | −0.121147 | − | 0.209833i | ||||
\(187\) | 296140. | + | 512929.i | 0.619288 | + | 1.07264i | ||||
\(188\) | 386004. | 0.796520 | ||||||||
\(189\) | −390897. | − | 677054.i | −0.795991 | − | 1.37870i | ||||
\(190\) | 12859.7 | + | 22273.6i | 0.0258432 | + | 0.0447617i | ||||
\(191\) | 34284.6 | − | 59382.7i | 0.0680011 | − | 0.117781i | −0.830020 | − | 0.557733i | \(-0.811671\pi\) |
0.898021 | + | 0.439952i | \(0.145005\pi\) | |||||||
\(192\) | −114617. | + | 198522.i | −0.224386 | + | 0.388647i | ||||
\(193\) | 352076. | 0.680367 | 0.340184 | − | 0.940359i | \(-0.389511\pi\) | ||||
0.340184 | + | 0.940359i | \(0.389511\pi\) | |||||||
\(194\) | 33125.5 | 0.0631914 | ||||||||
\(195\) | 13601.1 | − | 23557.8i | 0.0256146 | − | 0.0443658i | ||||
\(196\) | 321222. | − | 556373.i | 0.597262 | − | 1.03449i | ||||
\(197\) | −171254. | − | 296621.i | −0.314395 | − | 0.544548i | 0.664914 | − | 0.746920i | \(-0.268468\pi\) |
−0.979309 | + | 0.202372i | \(0.935135\pi\) | |||||||
\(198\) | −8338.16 | − | 14442.1i | −0.0151150 | − | 0.0261799i | ||||
\(199\) | −703078. | −1.25855 | −0.629275 | − | 0.777183i | \(-0.716648\pi\) | ||||
−0.629275 | + | 0.777183i | \(0.716648\pi\) | |||||||
\(200\) | −151443. | − | 262306.i | −0.267715 | − | 0.463697i | ||||
\(201\) | −310565. | − | 537914.i | −0.542203 | − | 0.939123i | ||||
\(202\) | 33814.1 | + | 58567.8i | 0.0583069 | + | 0.100990i | ||||
\(203\) | 2413.71 | − | 4180.66i | 0.00411097 | − | 0.00712041i | ||||
\(204\) | 671894. | 1.13038 | ||||||||
\(205\) | −43177.3 | + | 74785.3i | −0.0717581 | + | 0.124289i | ||||
\(206\) | −150342. | − | 260399.i | −0.246838 | − | 0.427535i | ||||
\(207\) | 21748.3 | 0.0352777 | ||||||||
\(208\) | −41191.5 | − | 71345.8i | −0.0660161 | − | 0.114343i | ||||
\(209\) | −167362. | + | 289879.i | −0.265027 | + | 0.459040i | ||||
\(210\) | 42141.7 | − | 72991.5i | 0.0659422 | − | 0.114215i | ||||
\(211\) | −668712. | −1.03403 | −0.517015 | − | 0.855977i | \(-0.672957\pi\) | ||||
−0.517015 | + | 0.855977i | \(0.672957\pi\) | |||||||
\(212\) | −61593.0 | + | 106682.i | −0.0941221 | + | 0.163024i | ||||
\(213\) | −573275. | −0.865793 | ||||||||
\(214\) | 375595. | 0.560642 | ||||||||
\(215\) | 131481. | + | 152309.i | 0.193985 | + | 0.224714i | ||||
\(216\) | −420828. | −0.613720 | ||||||||
\(217\) | −877658. | −1.26525 | ||||||||
\(218\) | −12541.7 | + | 21722.8i | −0.0178737 | + | 0.0309581i | ||||
\(219\) | −375314. | −0.528791 | ||||||||
\(220\) | −90489.3 | + | 156732.i | −0.126049 | + | 0.218324i | ||||
\(221\) | −87385.2 | + | 151356.i | −0.120353 | + | 0.208458i | ||||
\(222\) | 81134.4 | + | 140529.i | 0.110490 | + | 0.191374i | ||||
\(223\) | 441945. | 0.595122 | 0.297561 | − | 0.954703i | \(-0.403827\pi\) | ||||
0.297561 | + | 0.954703i | \(0.403827\pi\) | |||||||
\(224\) | −463440. | − | 802701.i | −0.617125 | − | 1.06889i | ||||
\(225\) | −36186.9 | + | 62677.6i | −0.0476535 | + | 0.0825384i | ||||
\(226\) | −18915.8 | −0.0246350 | ||||||||
\(227\) | −458549. | + | 794230.i | −0.590638 | + | 1.02301i | 0.403509 | + | 0.914976i | \(0.367790\pi\) |
−0.994147 | + | 0.108039i | \(0.965543\pi\) | |||||||
\(228\) | 189858. | + | 328844.i | 0.241876 | + | 0.418941i | ||||
\(229\) | 113484. | + | 196560.i | 0.143003 | + | 0.247689i | 0.928626 | − | 0.371017i | \(-0.120991\pi\) |
−0.785623 | + | 0.618705i | \(0.787657\pi\) | |||||||
\(230\) | 12388.7 | + | 21457.9i | 0.0154422 | + | 0.0267466i | ||||
\(231\) | 1.09690e6 | 1.35250 | ||||||||
\(232\) | −1299.26 | − | 2250.39i | −0.00158481 | − | 0.00274497i | ||||
\(233\) | −184877. | − | 320217.i | −0.223097 | − | 0.386415i | 0.732650 | − | 0.680606i | \(-0.238283\pi\) |
−0.955747 | + | 0.294190i | \(0.904950\pi\) | |||||||
\(234\) | 2460.43 | − | 4261.59i | 0.00293746 | − | 0.00508782i | ||||
\(235\) | 110597. | − | 191560.i | 0.130639 | − | 0.226274i | ||||
\(236\) | 1.43231e6 | 1.67401 | ||||||||
\(237\) | 1.41278e6 | 1.63382 | ||||||||
\(238\) | −270754. | + | 468961.i | −0.309837 | + | 0.536653i | ||||
\(239\) | 326490. | − | 565496.i | 0.369721 | − | 0.640376i | −0.619801 | − | 0.784759i | \(-0.712786\pi\) |
0.989522 | + | 0.144383i | \(0.0461198\pi\) | |||||||
\(240\) | 90745.1 | + | 157175.i | 0.101694 | + | 0.176139i | ||||
\(241\) | 76516.8 | + | 132531.i | 0.0848622 | + | 0.146986i | 0.905332 | − | 0.424704i | \(-0.139622\pi\) |
−0.820470 | + | 0.571689i | \(0.806288\pi\) | |||||||
\(242\) | −33548.9 | −0.0368247 | ||||||||
\(243\) | 95798.2 | + | 165927.i | 0.104074 | + | 0.180261i | ||||
\(244\) | 493119. | + | 854107.i | 0.530245 | + | 0.918412i | ||||
\(245\) | −184072. | − | 318822.i | −0.195917 | − | 0.339338i | ||||
\(246\) | 66920.5 | − | 115910.i | 0.0705053 | − | 0.122119i | ||||
\(247\) | −98770.3 | −0.103011 | ||||||||
\(248\) | −236215. | + | 409136.i | −0.243881 | + | 0.422414i | ||||
\(249\) | 15327.9 | + | 26548.6i | 0.0156669 | + | 0.0271359i | ||||
\(250\) | −172877. | −0.174939 | ||||||||
\(251\) | −321024. | − | 556031.i | −0.321628 | − | 0.557076i | 0.659196 | − | 0.751971i | \(-0.270897\pi\) |
−0.980824 | + | 0.194895i | \(0.937563\pi\) | |||||||
\(252\) | −72618.1 | + | 125778.i | −0.0720350 | + | 0.124768i | ||||
\(253\) | −161233. | + | 279263.i | −0.158362 | + | 0.274291i | ||||
\(254\) | 278713. | 0.271065 | ||||||||
\(255\) | 192510. | − | 333437.i | 0.185397 | − | 0.321117i | ||||
\(256\) | 188127. | 0.179412 | ||||||||
\(257\) | −1.22989e6 | −1.16154 | −0.580771 | − | 0.814067i | \(-0.697249\pi\) | ||||
−0.580771 | + | 0.814067i | \(0.697249\pi\) | |||||||
\(258\) | −203783. | − | 236064.i | −0.190598 | − | 0.220791i | ||||
\(259\) | 1.24576e6 | 1.15395 | ||||||||
\(260\) | −53403.3 | −0.0489931 | ||||||||
\(261\) | −310.455 | + | 537.725i | −0.000282097 | + | 0.000488606i | ||||
\(262\) | 179783. | 0.161806 | ||||||||
\(263\) | 768545. | − | 1.33116e6i | 0.685141 | − | 1.18670i | −0.288251 | − | 0.957555i | \(-0.593074\pi\) |
0.973392 | − | 0.229145i | \(-0.0735929\pi\) | |||||||
\(264\) | 295222. | − | 511340.i | 0.260699 | − | 0.451543i | ||||
\(265\) | 35295.0 | + | 61132.8i | 0.0308744 | + | 0.0534760i | ||||
\(266\) | −306030. | −0.265192 | ||||||||
\(267\) | 1.07782e6 | + | 1.86685e6i | 0.925272 | + | 1.60262i | ||||
\(268\) | −609700. | + | 1.05603e6i | −0.518536 | + | 0.898131i | ||||
\(269\) | −211417. | −0.178139 | −0.0890694 | − | 0.996025i | \(-0.528389\pi\) | ||||
−0.0890694 | + | 0.996025i | \(0.528389\pi\) | |||||||
\(270\) | −57280.8 | + | 99213.2i | −0.0478189 | + | 0.0828247i | ||||
\(271\) | 371455. | + | 643378.i | 0.307243 | + | 0.532161i | 0.977758 | − | 0.209735i | \(-0.0672601\pi\) |
−0.670515 | + | 0.741896i | \(0.733927\pi\) | |||||||
\(272\) | −583025. | − | 1.00983e6i | −0.477821 | − | 0.827610i | ||||
\(273\) | 161837. | + | 280310.i | 0.131423 | + | 0.227631i | ||||
\(274\) | 454572. | 0.365785 | ||||||||
\(275\) | −536547. | − | 929327.i | −0.427835 | − | 0.741032i | ||||
\(276\) | 182905. | + | 316801.i | 0.144529 | + | 0.250331i | ||||
\(277\) | −399396. | + | 691774.i | −0.312755 | + | 0.541707i | −0.978958 | − | 0.204063i | \(-0.934585\pi\) |
0.666203 | + | 0.745771i | \(0.267919\pi\) | |||||||
\(278\) | 272835. | − | 472565.i | 0.211733 | − | 0.366732i | ||||
\(279\) | 112886. | 0.0868220 | ||||||||
\(280\) | −348300. | −0.265497 | ||||||||
\(281\) | 584582. | − | 1.01252e6i | 0.441651 | − | 0.764962i | −0.556161 | − | 0.831074i | \(-0.687726\pi\) |
0.997812 | + | 0.0661124i | \(0.0210596\pi\) | |||||||
\(282\) | −171414. | + | 296899.i | −0.128358 | + | 0.222323i | ||||
\(283\) | 345423. | + | 598291.i | 0.256381 | + | 0.444065i | 0.965270 | − | 0.261256i | \(-0.0841365\pi\) |
−0.708889 | + | 0.705320i | \(0.750803\pi\) | |||||||
\(284\) | 562727. | + | 974671.i | 0.414001 | + | 0.717071i | ||||
\(285\) | 217591. | 0.158683 | ||||||||
\(286\) | 36481.1 | + | 63187.1i | 0.0263726 | + | 0.0456787i | ||||
\(287\) | −513759. | − | 889857.i | −0.368176 | − | 0.637699i | ||||
\(288\) | 59608.5 | + | 103245.i | 0.0423474 | + | 0.0733478i | ||||
\(289\) | −526921. | + | 912655.i | −0.371109 | + | 0.642779i | ||||
\(290\) | −707.393 | −0.000493930 | ||||||||
\(291\) | 140124. | − | 242702.i | 0.0970021 | − | 0.168013i | ||||
\(292\) | 368408. | + | 638101.i | 0.252855 | + | 0.437958i | ||||
\(293\) | −1.22064e6 | −0.830652 | −0.415326 | − | 0.909673i | \(-0.636332\pi\) | ||||
−0.415326 | + | 0.909673i | \(0.636332\pi\) | |||||||
\(294\) | 285293. | + | 494142.i | 0.192497 | + | 0.333414i | ||||
\(295\) | 410383. | − | 710804.i | 0.274558 | − | 0.475549i | ||||
\(296\) | 335287. | − | 580734.i | 0.222427 | − | 0.385255i | ||||
\(297\) | −1.49095e6 | −0.980783 | ||||||||
\(298\) | −28810.7 | + | 49901.7i | −0.0187938 | + | 0.0325518i | ||||
\(299\) | −95153.2 | −0.0615525 | ||||||||
\(300\) | −1.21734e6 | −0.780924 | ||||||||
\(301\) | −2.35173e6 | + | 448721.i | −1.49614 | + | 0.285470i | ||||
\(302\) | 299248. | 0.188805 | ||||||||
\(303\) | 572150. | 0.358017 | ||||||||
\(304\) | 329493. | − | 570698.i | 0.204485 | − | 0.354179i | ||||
\(305\) | 565150. | 0.347868 | ||||||||
\(306\) | 34824.9 | − | 60318.6i | 0.0212612 | − | 0.0368254i | ||||
\(307\) | −1.42690e6 | + | 2.47146e6i | −0.864065 | + | 1.49660i | 0.00390831 | + | 0.999992i | \(0.498756\pi\) |
−0.867973 | + | 0.496611i | \(0.834577\pi\) | |||||||
\(308\) | −1.07672e6 | − | 1.86493e6i | −0.646732 | − | 1.12017i | ||||
\(309\) | −2.54385e6 | −1.51564 | ||||||||
\(310\) | 64304.5 | + | 111379.i | 0.0380047 | + | 0.0658261i | ||||
\(311\) | 1.29700e6 | − | 2.24646e6i | 0.760392 | − | 1.31704i | −0.182256 | − | 0.983251i | \(-0.558340\pi\) |
0.942648 | − | 0.333787i | \(-0.108327\pi\) | |||||||
\(312\) | 174229. | 0.101329 | ||||||||
\(313\) | 1.14805e6 | − | 1.98848e6i | 0.662370 | − | 1.14726i | −0.317622 | − | 0.948218i | \(-0.602884\pi\) |
0.979991 | − | 0.199040i | \(-0.0637825\pi\) | |||||||
\(314\) | −232918. | − | 403425.i | −0.133315 | − | 0.230908i | ||||
\(315\) | 41612.8 | + | 72075.5i | 0.0236293 | + | 0.0409271i | ||||
\(316\) | −1.38678e6 | − | 2.40198e6i | −0.781251 | − | 1.35317i | ||||
\(317\) | 1.00744e6 | 0.563083 | 0.281542 | − | 0.959549i | \(-0.409154\pi\) | ||||
0.281542 | + | 0.959549i | \(0.409154\pi\) | |||||||
\(318\) | −54703.7 | − | 94749.6i | −0.0303354 | − | 0.0525424i | ||||
\(319\) | −4603.16 | − | 7972.90i | −0.00253267 | − | 0.00438672i | ||||
\(320\) | 128942. | − | 223334.i | 0.0703914 | − | 0.121921i | ||||
\(321\) | 1.58881e6 | − | 2.75190e6i | 0.860615 | − | 1.49063i | ||||
\(322\) | −294823. | −0.158461 | ||||||||
\(323\) | −1.39800e6 | −0.745589 | ||||||||
\(324\) | −756318. | + | 1.30998e6i | −0.400260 | + | 0.693271i | ||||
\(325\) | 158325. | − | 274227.i | 0.0831458 | − | 0.144013i | ||||
\(326\) | 265999. | + | 460724.i | 0.138623 | + | 0.240103i | ||||
\(327\) | 106105. | + | 183779.i | 0.0548740 | + | 0.0950446i | ||||
\(328\) | −553097. | −0.283868 | ||||||||
\(329\) | 1.31598e6 | + | 2.27934e6i | 0.670283 | + | 1.16096i | ||||
\(330\) | −80368.0 | − | 139201.i | −0.0406255 | − | 0.0703654i | ||||
\(331\) | −798717. | − | 1.38342e6i | −0.400703 | − | 0.694038i | 0.593108 | − | 0.805123i | \(-0.297901\pi\) |
−0.993811 | + | 0.111085i | \(0.964568\pi\) | |||||||
\(332\) | 30091.6 | − | 52120.2i | 0.0149831 | − | 0.0259514i | ||||
\(333\) | −160232. | −0.0791844 | ||||||||
\(334\) | −139732. | + | 242023.i | −0.0685378 | + | 0.118711i | ||||
\(335\) | 349380. | + | 605144.i | 0.170093 | + | 0.294610i | ||||
\(336\) | −2.15952e6 | −1.04354 | ||||||||
\(337\) | 1.84240e6 | + | 3.19112e6i | 0.883707 | + | 1.53063i | 0.847189 | + | 0.531292i | \(0.178293\pi\) |
0.0365180 | + | 0.999333i | \(0.488373\pi\) | |||||||
\(338\) | 312931. | − | 542012.i | 0.148990 | − | 0.258058i | ||||
\(339\) | −80015.8 | + | 138591.i | −0.0378161 | + | 0.0654994i | ||||
\(340\) | −755870. | −0.354609 | ||||||||
\(341\) | −836887. | + | 1.44953e6i | −0.389745 | + | 0.675059i | ||||
\(342\) | 39362.2 | 0.0181976 | ||||||||
\(343\) | 1.06175e6 | 0.487288 | ||||||||
\(344\) | −423772. | + | 1.21707e6i | −0.193079 | + | 0.554524i | ||||
\(345\) | 209623. | 0.0948181 | ||||||||
\(346\) | 1.14140e6 | 0.512562 | ||||||||
\(347\) | −1.11833e6 | + | 1.93700e6i | −0.498591 | + | 0.863585i | −0.999999 | − | 0.00162608i | \(-0.999482\pi\) |
0.501408 | + | 0.865211i | \(0.332816\pi\) | |||||||
\(348\) | −10443.8 | −0.00462287 | ||||||||
\(349\) | 2.02855e6 | − | 3.51354e6i | 0.891500 | − | 1.54412i | 0.0534215 | − | 0.998572i | \(-0.482987\pi\) |
0.838078 | − | 0.545550i | \(-0.183679\pi\) | |||||||
\(350\) | 490554. | − | 849664.i | 0.214051 | − | 0.370747i | ||||
\(351\) | −219976. | − | 381009.i | −0.0953031 | − | 0.165070i | ||||
\(352\) | −1.76764e6 | −0.760393 | ||||||||
\(353\) | 1.48821e6 | + | 2.57765e6i | 0.635663 | + | 1.10100i | 0.986374 | + | 0.164517i | \(0.0526064\pi\) |
−0.350712 | + | 0.936484i | \(0.614060\pi\) | |||||||
\(354\) | −636052. | + | 1.10168e6i | −0.269764 | + | 0.467246i | ||||
\(355\) | 644926. | 0.271606 | ||||||||
\(356\) | 2.11598e6 | − | 3.66499e6i | 0.884885 | − | 1.53267i | ||||
\(357\) | 2.29064e6 | + | 3.96751e6i | 0.951232 | + | 1.64758i | ||||
\(358\) | 653753. | + | 1.13233e6i | 0.269591 | + | 0.466946i | ||||
\(359\) | 1.35299e6 | + | 2.34344e6i | 0.554060 | + | 0.959660i | 0.997976 | + | 0.0635919i | \(0.0202556\pi\) |
−0.443916 | + | 0.896069i | \(0.646411\pi\) | |||||||
\(360\) | 44799.0 | 0.0182185 | ||||||||
\(361\) | 843016. | + | 1.46015e6i | 0.340461 | + | 0.589696i | ||||
\(362\) | −699268. | − | 1.21117e6i | −0.280461 | − | 0.485773i | ||||
\(363\) | −141915. | + | 245805.i | −0.0565279 | + | 0.0979092i | ||||
\(364\) | 317718. | − | 550304.i | 0.125687 | − | 0.217695i | ||||
\(365\) | 422222. | 0.165886 | ||||||||
\(366\) | −875926. | −0.341794 | ||||||||
\(367\) | 1.67727e6 | − | 2.90511e6i | 0.650035 | − | 1.12589i | −0.333078 | − | 0.942899i | \(-0.608087\pi\) |
0.983114 | − | 0.182995i | \(-0.0585793\pi\) | |||||||
\(368\) | 317426. | − | 549798.i | 0.122187 | − | 0.211633i | ||||
\(369\) | 66080.7 | + | 114455.i | 0.0252644 | + | 0.0437592i | ||||
\(370\) | −91274.9 | − | 158093.i | −0.0346615 | − | 0.0600354i | ||||
\(371\) | −839938. | −0.316820 | ||||||||
\(372\) | 949382. | + | 1.64438e6i | 0.355700 | + | 0.616090i | ||||
\(373\) | −1.43111e6 | − | 2.47875e6i | −0.532599 | − | 0.922489i | −0.999275 | − | 0.0380608i | \(-0.987882\pi\) |
0.466676 | − | 0.884428i | \(-0.345451\pi\) | |||||||
\(374\) | 516353. | + | 894350.i | 0.190883 | + | 0.330620i | ||||
\(375\) | −731289. | + | 1.26663e6i | −0.268541 | + | 0.465127i | ||||
\(376\) | 1.41674e6 | 0.516797 | ||||||||
\(377\) | 1358.30 | − | 2352.65i | 0.000492202 | − | 0.000852519i | ||||
\(378\) | −681574. | − | 1.18052e6i | −0.245348 | − | 0.424956i | ||||
\(379\) | 1.41370e6 | 0.505545 | 0.252773 | − | 0.967526i | \(-0.418658\pi\) | ||||
0.252773 | + | 0.967526i | \(0.418658\pi\) | |||||||
\(380\) | −213588. | − | 369945.i | −0.0758782 | − | 0.131425i | ||||
\(381\) | 1.17899e6 | − | 2.04207e6i | 0.416099 | − | 0.720705i | ||||
\(382\) | 59779.2 | − | 103541.i | 0.0209600 | − | 0.0363038i | ||||
\(383\) | −1.02683e6 | −0.357685 | −0.178843 | − | 0.983878i | \(-0.557235\pi\) | ||||
−0.178843 | + | 0.983878i | \(0.557235\pi\) | |||||||
\(384\) | −1.30773e6 | + | 2.26505e6i | −0.452573 | + | 0.783880i | ||||
\(385\) | −1.23400e6 | −0.424289 | ||||||||
\(386\) | 613885. | 0.209710 | ||||||||
\(387\) | 302484. | − | 57715.3i | 0.102666 | − | 0.0195891i | ||||
\(388\) | −550184. | −0.185536 | ||||||||
\(389\) | −2.18252e6 | −0.731282 | −0.365641 | − | 0.930756i | \(-0.619150\pi\) | ||||
−0.365641 | + | 0.930756i | \(0.619150\pi\) | |||||||
\(390\) | 23715.0 | − | 41075.7i | 0.00789519 | − | 0.0136749i | ||||
\(391\) | −1.34680e6 | −0.445513 | ||||||||
\(392\) | 1.17897e6 | − | 2.04204e6i | 0.387515 | − | 0.671195i | ||||
\(393\) | 760501. | − | 1.31723e6i | 0.248381 | − | 0.430208i | ||||
\(394\) | −298601. | − | 517192.i | −0.0969060 | − | 0.167846i | ||||
\(395\) | −1.58935e6 | −0.512540 | ||||||||
\(396\) | 138489. | + | 239870.i | 0.0443791 | + | 0.0768668i | ||||
\(397\) | −262158. | + | 454071.i | −0.0834808 | + | 0.144593i | −0.904743 | − | 0.425958i | \(-0.859937\pi\) |
0.821262 | + | 0.570551i | \(0.193270\pi\) | |||||||
\(398\) | −1.22590e6 | −0.387923 | ||||||||
\(399\) | −1.29454e6 | + | 2.24221e6i | −0.407084 | + | 0.705090i | ||||
\(400\) | 1.05633e6 | + | 1.82961e6i | 0.330102 | + | 0.571754i | ||||
\(401\) | −439508. | − | 761250.i | −0.136492 | − | 0.236410i | 0.789675 | − | 0.613526i | \(-0.210249\pi\) |
−0.926166 | + | 0.377115i | \(0.876916\pi\) | |||||||
\(402\) | −541504. | − | 937913.i | −0.167123 | − | 0.289466i | ||||
\(403\) | −493898. | −0.151487 | ||||||||
\(404\) | −561622. | − | 972757.i | −0.171195 | − | 0.296518i | ||||
\(405\) | 433398. | + | 750668.i | 0.131295 | + | 0.227410i | ||||
\(406\) | 4208.57 | − | 7289.46i | 0.00126713 | − | 0.00219473i | ||||
\(407\) | 1.18789e6 | − | 2.05749e6i | 0.355460 | − | 0.615674i | ||||
\(408\) | 2.46603e6 | 0.733413 | ||||||||
\(409\) | 4.28678e6 | 1.26714 | 0.633568 | − | 0.773687i | \(-0.281590\pi\) | ||||
0.633568 | + | 0.773687i | \(0.281590\pi\) | |||||||
\(410\) | −75284.5 | + | 130397.i | −0.0221180 | + | 0.0383095i | ||||
\(411\) | 1.92289e6 | − | 3.33054e6i | 0.561499 | − | 0.972545i | ||||
\(412\) | 2.49704e6 | + | 4.32500e6i | 0.724740 | + | 1.25529i | ||||
\(413\) | 4.88307e6 | + | 8.45773e6i | 1.40870 | + | 2.43994i | ||||
\(414\) | 37920.7 | 0.0108736 | ||||||||
\(415\) | −17243.6 | − | 29866.8i | −0.00491482 | − | 0.00851272i | ||||
\(416\) | −260799. | − | 451717.i | −0.0738877 | − | 0.127977i | ||||
\(417\) | −2.30825e6 | − | 3.99800e6i | −0.650043 | − | 1.12591i | ||||
\(418\) | −291814. | + | 505436.i | −0.0816893 | + | 0.141490i | ||||
\(419\) | 1.98522e6 | 0.552424 | 0.276212 | − | 0.961097i | \(-0.410921\pi\) | ||||
0.276212 | + | 0.961097i | \(0.410921\pi\) | |||||||
\(420\) | −699935. | + | 1.21232e6i | −0.193613 | + | 0.335347i | ||||
\(421\) | −3.21855e6 | − | 5.57469e6i | −0.885024 | − | 1.53291i | −0.845687 | − | 0.533680i | \(-0.820809\pi\) |
−0.0393371 | − | 0.999226i | \(-0.512525\pi\) | |||||||
\(422\) | −1.16597e6 | −0.318719 | ||||||||
\(423\) | −169263. | − | 293172.i | −0.0459951 | − | 0.0796659i | ||||
\(424\) | −226063. | + | 391552.i | −0.0610681 | + | 0.105773i | ||||
\(425\) | 2.24093e6 | − | 3.88140e6i | 0.601805 | − | 1.04236i | ||||
\(426\) | −999570. | −0.266864 | ||||||||
\(427\) | −3.36231e6 | + | 5.82369e6i | −0.892418 | + | 1.54571i | ||||
\(428\) | −6.23829e6 | −1.64610 | ||||||||
\(429\) | 617276. | 0.161933 | ||||||||
\(430\) | 229252. | + | 265568.i | 0.0597919 | + | 0.0692636i | ||||
\(431\) | −6.75585e6 | −1.75181 | −0.875905 | − | 0.482483i | \(-0.839735\pi\) | ||||
−0.875905 | + | 0.482483i | \(0.839735\pi\) | |||||||
\(432\) | 2.93531e6 | 0.756737 | ||||||||
\(433\) | 163731. | − | 283591.i | 0.0419673 | − | 0.0726896i | −0.844279 | − | 0.535904i | \(-0.819971\pi\) |
0.886246 | + | 0.463215i | \(0.153304\pi\) | |||||||
\(434\) | −1.53030e6 | −0.389988 | ||||||||
\(435\) | −2992.35 | + | 5182.90i | −0.000758209 | + | 0.00131326i | ||||
\(436\) | 208305. | − | 360795.i | 0.0524788 | − | 0.0908960i | ||||
\(437\) | −380567. | − | 659162.i | −0.0953296 | − | 0.165116i | ||||
\(438\) | −654402. | −0.162989 | ||||||||
\(439\) | −2.10457e6 | − | 3.64523e6i | −0.521198 | − | 0.902742i | −0.999696 | − | 0.0246529i | \(-0.992152\pi\) |
0.478498 | − | 0.878089i | \(-0.341181\pi\) | |||||||
\(440\) | −332120. | + | 575249.i | −0.0817831 | + | 0.141652i | ||||
\(441\) | −563425. | −0.137956 | ||||||||
\(442\) | −152366. | + | 263906.i | −0.0370964 | + | 0.0642529i | ||||
\(443\) | 1.94880e6 | + | 3.37542e6i | 0.471800 | + | 0.817182i | 0.999479 | − | 0.0322618i | \(-0.0102710\pi\) |
−0.527679 | + | 0.849444i | \(0.676938\pi\) | |||||||
\(444\) | −1.34757e6 | − | 2.33406e6i | −0.324409 | − | 0.561893i | ||||
\(445\) | −1.21253e6 | − | 2.10017e6i | −0.290265 | − | 0.502753i | ||||
\(446\) | 770581. | 0.183435 | ||||||||
\(447\) | 243745. | + | 422179.i | 0.0576988 | + | 0.0999373i | ||||
\(448\) | 1.53426e6 | + | 2.65741e6i | 0.361163 | + | 0.625553i | ||||
\(449\) | −2.93163e6 | + | 5.07773e6i | −0.686268 | + | 1.18865i | 0.286769 | + | 0.958000i | \(0.407419\pi\) |
−0.973037 | + | 0.230651i | \(0.925915\pi\) | |||||||
\(450\) | −63096.0 | + | 109285.i | −0.0146883 | + | 0.0254408i | ||||
\(451\) | −1.95957e6 | −0.453649 | ||||||||
\(452\) | 314174. | 0.0723309 | ||||||||
\(453\) | 1.26585e6 | − | 2.19252e6i | 0.289826 | − | 0.501994i | ||||
\(454\) | −799532. | + | 1.38483e6i | −0.182052 | + | 0.315324i | ||||
\(455\) | −182064. | − | 315344.i | −0.0412283 | − | 0.0714096i | ||||
\(456\) | 696831. | + | 1.20695e6i | 0.156933 | + | 0.271817i | ||||
\(457\) | −3.91502e6 | −0.876887 | −0.438443 | − | 0.898759i | \(-0.644470\pi\) | ||||
−0.438443 | + | 0.898759i | \(0.644470\pi\) | |||||||
\(458\) | 197872. | + | 342724.i | 0.0440779 | + | 0.0763451i | ||||
\(459\) | −3.11354e6 | − | 5.39281e6i | −0.689799 | − | 1.19477i | ||||
\(460\) | −205766. | − | 356397.i | −0.0453397 | − | 0.0785306i | ||||
\(461\) | 2.05874e6 | − | 3.56585e6i | 0.451180 | − | 0.781466i | −0.547280 | − | 0.836950i | \(-0.684337\pi\) |
0.998460 | + | 0.0554833i | \(0.0176699\pi\) | |||||||
\(462\) | 1.91257e6 | 0.416881 | ||||||||
\(463\) | 2.75528e6 | − | 4.77229e6i | 0.597330 | − | 1.03461i | −0.395884 | − | 0.918301i | \(-0.629562\pi\) |
0.993214 | − | 0.116305i | \(-0.0371049\pi\) | |||||||
\(464\) | 9062.46 | + | 15696.6i | 0.00195412 | + | 0.00338464i | ||||
\(465\) | 1.08806e6 | 0.233357 | ||||||||
\(466\) | −322354. | − | 558334.i | −0.0687652 | − | 0.119105i | ||||
\(467\) | 4.17217e6 | − | 7.22640e6i | 0.885257 | − | 1.53331i | 0.0398381 | − | 0.999206i | \(-0.487316\pi\) |
0.845419 | − | 0.534104i | \(-0.179351\pi\) | |||||||
\(468\) | −40865.5 | + | 70781.1i | −0.00862466 | + | 0.0149384i | ||||
\(469\) | −8.31443e6 | −1.74542 | ||||||||
\(470\) | 192839. | − | 334006.i | 0.0402670 | − | 0.0697445i | ||||
\(471\) | −3.94107e6 | −0.818581 | ||||||||
\(472\) | 5.25696e6 | 1.08613 | ||||||||
\(473\) | −1.50138e6 | + | 4.31197e6i | −0.308559 | + | 0.886183i | ||||
\(474\) | 2.46334e6 | 0.503592 | ||||||||
\(475\) | 2.53289e6 | 0.515090 | ||||||||
\(476\) | 4.49698e6 | − | 7.78900e6i | 0.909712 | − | 1.57567i | ||||
\(477\) | 108034. | 0.0217403 | ||||||||
\(478\) | 569271. | − | 986007.i | 0.113959 | − | 0.197383i | ||||
\(479\) | −4.26690e6 | + | 7.39050e6i | −0.849717 | + | 1.47175i | 0.0317445 | + | 0.999496i | \(0.489894\pi\) |
−0.881461 | + | 0.472257i | \(0.843440\pi\) | |||||||
\(480\) | 574541. | + | 995134.i | 0.113820 | + | 0.197142i | ||||
\(481\) | 701047. | 0.138161 | ||||||||
\(482\) | 133416. | + | 231083.i | 0.0261571 | + | 0.0453054i | ||||
\(483\) | −1.24713e6 | + | 2.16010e6i | −0.243246 | + | 0.421314i | ||||
\(484\) | 557216. | 0.108121 | ||||||||
\(485\) | −157638. | + | 273036.i | −0.0304303 | + | 0.0527068i | ||||
\(486\) | 167035. | + | 289313.i | 0.0320787 | + | 0.0555619i | ||||
\(487\) | −2.37754e6 | − | 4.11802e6i | −0.454261 | − | 0.786803i | 0.544384 | − | 0.838836i | \(-0.316763\pi\) |
−0.998645 | + | 0.0520328i | \(0.983430\pi\) | |||||||
\(488\) | 1.80988e6 | + | 3.13480e6i | 0.344033 | + | 0.595882i | ||||
\(489\) | 4.50082e6 | 0.851176 | ||||||||
\(490\) | −320950. | − | 555902.i | −0.0603876 | − | 0.104594i | ||||
\(491\) | 2.51600e6 | + | 4.35785e6i | 0.470986 | + | 0.815771i | 0.999449 | − | 0.0331848i | \(-0.0105650\pi\) |
−0.528464 | + | 0.848956i | \(0.677232\pi\) | |||||||
\(492\) | −1.11149e6 | + | 1.92515e6i | −0.207010 | + | 0.358553i | ||||
\(493\) | 19225.4 | − | 33299.4i | 0.00356253 | − | 0.00617049i | ||||
\(494\) | −172217. | −0.0317511 | ||||||||
\(495\) | 158719. | 0.0291149 | ||||||||
\(496\) | 1.64762e6 | − | 2.85376e6i | 0.300714 | − | 0.520851i | ||||
\(497\) | −3.83693e6 | + | 6.64576e6i | −0.696775 | + | 1.20685i | ||||
\(498\) | 26725.8 | + | 46290.5i | 0.00482901 | + | 0.00836409i | ||||
\(499\) | 1.89043e6 | + | 3.27431e6i | 0.339866 | + | 0.588666i | 0.984407 | − | 0.175904i | \(-0.0562848\pi\) |
−0.644541 | + | 0.764570i | \(0.722951\pi\) | |||||||
\(500\) | 2.87133e6 | 0.513639 | ||||||||
\(501\) | 1.18216e6 | + | 2.04757e6i | 0.210418 | + | 0.364455i | ||||
\(502\) | −559742. | − | 969502.i | −0.0991354 | − | 0.171708i | ||||
\(503\) | 5.17226e6 | + | 8.95861e6i | 0.911507 | + | 1.57878i | 0.811936 | + | 0.583746i | \(0.198414\pi\) |
0.0995708 | + | 0.995030i | \(0.468253\pi\) | |||||||
\(504\) | −266528. | + | 461640.i | −0.0467376 | + | 0.0809519i | ||||
\(505\) | −643659. | −0.112312 | ||||||||
\(506\) | −281127. | + | 486926.i | −0.0488120 | + | 0.0845448i | ||||
\(507\) | −2.64746e6 | − | 4.58554e6i | −0.457414 | − | 0.792265i | ||||
\(508\) | −4.62917e6 | −0.795874 | ||||||||
\(509\) | 2.03678e6 | + | 3.52780e6i | 0.348457 | + | 0.603545i | 0.985976 | − | 0.166890i | \(-0.0533724\pi\) |
−0.637519 | + | 0.770435i | \(0.720039\pi\) | |||||||
\(510\) | 335663. | − | 581385.i | 0.0571449 | − | 0.0989779i | ||||
\(511\) | −2.51197e6 | + | 4.35086e6i | −0.425562 | + | 0.737095i | ||||
\(512\) | 6.00171e6 | 1.01181 | ||||||||
\(513\) | 1.75960e6 | − | 3.04771e6i | 0.295202 | − | 0.511305i | ||||
\(514\) | −2.14446e6 | −0.358022 | ||||||||
\(515\) | 2.86179e6 | 0.475466 | ||||||||
\(516\) | 3.38464e6 | + | 3.92081e6i | 0.559614 | + | 0.648263i | ||||
\(517\) | 5.01937e6 | 0.825891 | ||||||||
\(518\) | 2.17213e6 | 0.355681 | ||||||||
\(519\) | 4.82823e6 | − | 8.36274e6i | 0.786810 | − | 1.36279i | ||||
\(520\) | −196005. | −0.0317876 | ||||||||
\(521\) | −848912. | + | 1.47036e6i | −0.137015 | + | 0.237317i | −0.926365 | − | 0.376626i | \(-0.877084\pi\) |
0.789350 | + | 0.613943i | \(0.210418\pi\) | |||||||
\(522\) | −541.314 | + | 937.584i | −8.69507e−5 | + | 0.000150603i | ||||
\(523\) | 522177. | + | 904436.i | 0.0834763 | + | 0.144585i | 0.904741 | − | 0.425962i | \(-0.140064\pi\) |
−0.821265 | + | 0.570547i | \(0.806731\pi\) | |||||||
\(524\) | −2.98603e6 | −0.475079 | ||||||||
\(525\) | −4.15019e6 | − | 7.18835e6i | −0.657158 | − | 1.13823i | ||||
\(526\) | 1.34005e6 | − | 2.32103e6i | 0.211181 | − | 0.365777i | ||||
\(527\) | −6.99064e6 | −1.09645 | ||||||||
\(528\) | −2.05920e6 | + | 3.56664e6i | −0.321450 | + | 0.556768i | ||||
\(529\) | 2.85154e6 | + | 4.93901e6i | 0.443037 | + | 0.767363i | ||||
\(530\) | 61540.8 | + | 106592.i | 0.00951642 | + | 0.0164829i | ||||
\(531\) | −628070. | − | 1.08785e6i | −0.0966656 | − | 0.167430i | ||||
\(532\) | 5.08288e6 | 0.778630 | ||||||||
\(533\) | −289116. | − | 500763.i | −0.0440812 | − | 0.0763510i | ||||
\(534\) | 1.87931e6 | + | 3.25506e6i | 0.285197 | + | 0.493975i | ||||
\(535\) | −1.78738e6 | + | 3.09584e6i | −0.269981 | + | 0.467621i | ||||
\(536\) | −2.23776e6 | + | 3.87592e6i | −0.336436 | + | 0.582724i | ||||
\(537\) | 1.10618e7 | 1.65535 | ||||||||
\(538\) | −368629. | −0.0549077 | ||||||||
\(539\) | 4.17699e6 | − | 7.23475e6i | 0.619286 | − | 1.07263i | ||||
\(540\) | 951381. | − | 1.64784e6i | 0.140401 | − | 0.243182i | ||||
\(541\) | 3.42182e6 | + | 5.92676e6i | 0.502648 | + | 0.870611i | 0.999995 | + | 0.00305985i | \(0.000973981\pi\) |
−0.497348 | + | 0.867551i | \(0.665693\pi\) | |||||||
\(542\) | 647673. | + | 1.12180e6i | 0.0947017 | + | 0.164028i | ||||
\(543\) | −1.18319e7 | −1.72209 | ||||||||
\(544\) | −3.69134e6 | − | 6.39360e6i | −0.534795 | − | 0.926292i | ||||
\(545\) | −119367. | − | 206749.i | −0.0172144 | − | 0.0298162i | ||||
\(546\) | 282181. | + | 488752.i | 0.0405085 | + | 0.0701628i | ||||
\(547\) | 1.04409e6 | − | 1.80841e6i | 0.149200 | − | 0.258422i | −0.781732 | − | 0.623615i | \(-0.785664\pi\) |
0.930932 | + | 0.365193i | \(0.118997\pi\) | |||||||
\(548\) | −7.55002e6 | −1.07398 | ||||||||
\(549\) | 432467. | − | 749054.i | 0.0612381 | − | 0.106068i | ||||
\(550\) | −935531. | − | 1.62039e6i | −0.131872 | − | 0.228408i | ||||
\(551\) | 21730.2 | 0.00304920 | ||||||||
\(552\) | 671312. | + | 1.16275e6i | 0.0937728 | + | 0.162419i | ||||
\(553\) | 9.45572e6 | − | 1.63778e7i | 1.31487 | − | 2.27742i | ||||
\(554\) | −696392. | + | 1.20619e6i | −0.0964005 | + | 0.166971i | ||||
\(555\) | −1.54441e6 | −0.212829 | ||||||||
\(556\) | −4.53155e6 | + | 7.84887e6i | −0.621669 | + | 1.07676i | ||||
\(557\) | −5.78663e6 | −0.790292 | −0.395146 | − | 0.918618i | \(-0.629306\pi\) | ||||
−0.395146 | + | 0.918618i | \(0.629306\pi\) | |||||||
\(558\) | 196830. | 0.0267612 | ||||||||
\(559\) | −1.32343e6 | + | 252516.i | −0.179131 | + | 0.0341789i | ||||
\(560\) | 2.42943e6 | 0.327366 | ||||||||
\(561\) | 8.73692e6 | 1.17206 | ||||||||
\(562\) | 1.01928e6 | − | 1.76545e6i | 0.136130 | − | 0.235784i | ||||
\(563\) | −1.23011e7 | −1.63559 | −0.817794 | − | 0.575511i | \(-0.804803\pi\) | ||||
−0.817794 | + | 0.575511i | \(0.804803\pi\) | |||||||
\(564\) | 2.84704e6 | − | 4.93121e6i | 0.376873 | − | 0.652764i | ||||
\(565\) | 90016.5 | − | 155913.i | 0.0118632 | − | 0.0205476i | ||||
\(566\) | 602285. | + | 1.04319e6i | 0.0790243 | + | 0.136874i | ||||
\(567\) | −1.03139e7 | −1.34730 | ||||||||
\(568\) | 2.06536e6 | + | 3.57731e6i | 0.268611 | + | 0.465249i | ||||
\(569\) | 228430. | − | 395652.i | 0.0295782 | − | 0.0512310i | −0.850857 | − | 0.525397i | \(-0.823917\pi\) |
0.880436 | + | 0.474166i | \(0.157250\pi\) | |||||||
\(570\) | 379395. | 0.0489108 | ||||||||
\(571\) | 552741. | − | 957376.i | 0.0709466 | − | 0.122883i | −0.828370 | − | 0.560182i | \(-0.810731\pi\) |
0.899316 | + | 0.437298i | \(0.144065\pi\) | |||||||
\(572\) | −605917. | − | 1.04948e6i | −0.0774325 | − | 0.134117i | ||||
\(573\) | −505745. | − | 875975.i | −0.0643494 | − | 0.111456i | ||||
\(574\) | −895797. | − | 1.55157e6i | −0.113483 | − | 0.196558i | ||||
\(575\) | 2.44013e6 | 0.307783 | ||||||||
\(576\) | −197339. | − | 341801.i | −0.0247832 | − | 0.0429257i | ||||
\(577\) | 5.82894e6 | + | 1.00960e7i | 0.728870 | + | 1.26244i | 0.957361 | + | 0.288894i | \(0.0932877\pi\) |
−0.228491 | + | 0.973546i | \(0.573379\pi\) | |||||||
\(578\) | −918747. | + | 1.59132e6i | −0.114387 | + | 0.198124i | ||||
\(579\) | 2.59680e6 | − | 4.49779e6i | 0.321915 | − | 0.557574i | ||||
\(580\) | 11749.1 | 0.00145023 | ||||||||
\(581\) | 410357. | 0.0504338 | ||||||||
\(582\) | 244323. | − | 423179.i | 0.0298990 | − | 0.0517865i | ||||
\(583\) | −800919. | + | 1.38723e6i | −0.0975927 | + | 0.169036i | ||||
\(584\) | 1.35216e6 | + | 2.34200e6i | 0.164057 | + | 0.284155i | ||||
\(585\) | 23417.4 | + | 40560.2i | 0.00282911 | + | 0.00490016i | ||||
\(586\) | −2.12833e6 | −0.256032 | ||||||||
\(587\) | −4.19450e6 | − | 7.26509e6i | −0.502441 | − | 0.870254i | −0.999996 | − | 0.00282121i | \(-0.999102\pi\) |
0.497555 | − | 0.867433i | \(-0.334231\pi\) | |||||||
\(588\) | −4.73846e6 | − | 8.20725e6i | −0.565189 | − | 0.978936i | ||||
\(589\) | −1.97536e6 | − | 3.42142e6i | −0.234616 | − | 0.406367i | ||||
\(590\) | 715549. | − | 1.23937e6i | 0.0846271 | − | 0.146578i | ||||
\(591\) | −5.05246e6 | −0.595023 | ||||||||
\(592\) | −2.33866e6 | + | 4.05068e6i | −0.274260 | + | 0.475032i | ||||
\(593\) | −3.65226e6 | − | 6.32590e6i | −0.426506 | − | 0.738730i | 0.570054 | − | 0.821607i | \(-0.306922\pi\) |
−0.996560 | + | 0.0828774i | \(0.973589\pi\) | |||||||
\(594\) | −2.59965e6 | −0.302307 | ||||||||
\(595\) | −2.57694e6 | − | 4.46338e6i | −0.298409 | − | 0.516859i | ||||
\(596\) | 478520. | − | 828821.i | 0.0551803 | − | 0.0955752i | ||||
\(597\) | −5.18567e6 | + | 8.98185e6i | −0.595483 | + | 1.03141i | ||||
\(598\) | −165910. | −0.0189723 | ||||||||
\(599\) | −7.26051e6 | + | 1.25756e7i | −0.826799 | + | 1.43206i | 0.0737373 | + | 0.997278i | \(0.476507\pi\) |
−0.900536 | + | 0.434780i | \(0.856826\pi\) | |||||||
\(600\) | −4.46797e6 | −0.506678 | ||||||||
\(601\) | 3.76875e6 | 0.425609 | 0.212804 | − | 0.977095i | \(-0.431740\pi\) | ||||
0.212804 | + | 0.977095i | \(0.431740\pi\) | |||||||
\(602\) | −4.10051e6 | + | 782395.i | −0.461155 | + | 0.0879903i | ||||
\(603\) | 1.06942e6 | 0.119772 | ||||||||
\(604\) | −4.97024e6 | −0.554351 | ||||||||
\(605\) | 159653. | − | 276526.i | 0.0177332 | − | 0.0307148i | ||||
\(606\) | 997608. | 0.110351 | ||||||||
\(607\) | 3.15728e6 | − | 5.46857e6i | 0.347810 | − | 0.602424i | −0.638050 | − | 0.769995i | \(-0.720259\pi\) |
0.985860 | + | 0.167570i | \(0.0535922\pi\) | |||||||
\(608\) | 2.08614e6 | − | 3.61330e6i | 0.228868 | − | 0.396410i | ||||
\(609\) | −35605.4 | − | 61670.4i | −0.00389021 | − | 0.00673804i | ||||
\(610\) | 985403. | 0.107223 | ||||||||
\(611\) | 740559. | + | 1.28269e6i | 0.0802522 | + | 0.139001i | ||||
\(612\) | −578410. | + | 1.00184e6i | −0.0624249 | + | 0.108123i | ||||
\(613\) | −1.43635e7 | −1.54387 | −0.771934 | − | 0.635703i | \(-0.780710\pi\) | ||||
−0.771934 | + | 0.635703i | \(0.780710\pi\) | |||||||
\(614\) | −2.48795e6 | + | 4.30926e6i | −0.266331 | + | 0.461298i | ||||
\(615\) | 636924. | + | 1.10318e6i | 0.0679047 | + | 0.117614i | ||||
\(616\) | −3.95184e6 | − | 6.84479e6i | −0.419612 | − | 0.726789i | ||||
\(617\) | 9.08559e6 | + | 1.57367e7i | 0.960816 | + | 1.66418i | 0.720459 | + | 0.693497i | \(0.243931\pi\) |
0.240357 | + | 0.970685i | \(0.422736\pi\) | |||||||
\(618\) | −4.43548e6 | −0.467165 | ||||||||
\(619\) | −7.21390e6 | − | 1.24948e7i | −0.756734 | − | 1.31070i | −0.944508 | − | 0.328489i | \(-0.893460\pi\) |
0.187774 | − | 0.982212i | \(-0.439873\pi\) | |||||||
\(620\) | −1.06804e6 | − | 1.84990e6i | −0.111586 | − | 0.193272i | ||||
\(621\) | 1.69516e6 | − | 2.93610e6i | 0.176393 | − | 0.305521i | ||||
\(622\) | 2.26146e6 | − | 3.91696e6i | 0.234376 | − | 0.405951i | ||||
\(623\) | 2.88555e7 | 2.97857 | ||||||||
\(624\) | −1.21526e6 | −0.124942 | ||||||||
\(625\) | −3.62982e6 | + | 6.28703e6i | −0.371693 | + | 0.643792i | ||||
\(626\) | 2.00176e6 | − | 3.46715e6i | 0.204162 | − | 0.353619i | ||||
\(627\) | 2.46881e6 | + | 4.27610e6i | 0.250795 | + | 0.434389i | ||||
\(628\) | 3.86855e6 | + | 6.70053e6i | 0.391426 | + | 0.677969i | ||||
\(629\) | 9.92263e6 | 1.00000 | ||||||||
\(630\) | 72556.6 | + | 125672.i | 0.00728326 | + | 0.0126150i | ||||
\(631\) | −2.42729e6 | − | 4.20419e6i | −0.242688 | − | 0.420348i | 0.718791 | − | 0.695226i | \(-0.244696\pi\) |
−0.961479 | + | 0.274878i | \(0.911363\pi\) | |||||||
\(632\) | −5.08987e6 | − | 8.81591e6i | −0.506890 | − | 0.877959i | ||||
\(633\) | −4.93220e6 | + | 8.54282e6i | −0.489250 | + | 0.847407i | ||||
\(634\) | 1.75659e6 | 0.173559 | ||||||||
\(635\) | −1.32634e6 | + | 2.29729e6i | −0.130533 | + | 0.226090i | ||||
\(636\) | 908579. | + | 1.57370e6i | 0.0890676 | + | 0.154270i | ||||
\(637\) | 2.46510e6 | 0.240705 | ||||||||
\(638\) | −8026.13 | − | 13901.7i | −0.000780646 | − | 0.00135212i | ||||
\(639\) | 493513. | − | 854789.i | 0.0478130 | − | 0.0828146i | ||||
\(640\) | 1.47117e6 | − | 2.54815e6i | 0.141976 | − | 0.245909i | ||||
\(641\) | 4.66681e6 | 0.448617 | 0.224308 | − | 0.974518i | \(-0.427988\pi\) | ||||
0.224308 | + | 0.974518i | \(0.427988\pi\) | |||||||
\(642\) | 2.77027e6 | − | 4.79824e6i | 0.265268 | − | 0.459457i | ||||
\(643\) | 1.78877e7 | 1.70619 | 0.853094 | − | 0.521757i | \(-0.174723\pi\) | ||||
0.853094 | + | 0.521757i | \(0.174723\pi\) | |||||||
\(644\) | 4.89674e6 | 0.465256 | ||||||||
\(645\) | 2.91552e6 | − | 556293.i | 0.275941 | − | 0.0526507i | ||||
\(646\) | −2.43756e6 | −0.229813 | ||||||||
\(647\) | 9.98853e6 | 0.938082 | 0.469041 | − | 0.883176i | \(-0.344600\pi\) | ||||
0.469041 | + | 0.883176i | \(0.344600\pi\) | |||||||
\(648\) | −2.77589e6 | + | 4.80799e6i | −0.259696 | + | 0.449807i | ||||
\(649\) | 1.86249e7 | 1.73573 | ||||||||
\(650\) | 276057. | − | 478145.i | 0.0256281 | − | 0.0443891i | ||||
\(651\) | −6.47332e6 | + | 1.12121e7i | −0.598652 | + | 1.03690i | ||||
\(652\) | −4.41800e6 | − | 7.65220e6i | −0.407012 | − | 0.704965i | ||||
\(653\) | −2.12539e7 | −1.95055 | −0.975273 | − | 0.221004i | \(-0.929067\pi\) | ||||
−0.975273 | + | 0.221004i | \(0.929067\pi\) | |||||||
\(654\) | 185006. | + | 320440.i | 0.0169138 | + | 0.0292956i | ||||
\(655\) | −855551. | + | 1.48186e6i | −0.0779189 | + | 0.134960i | ||||
\(656\) | 3.85790e6 | 0.350019 | ||||||||
\(657\) | 323095. | − | 559616.i | 0.0292022 | − | 0.0505798i | ||||
\(658\) | 2.29455e6 | + | 3.97428e6i | 0.206601 | + | 0.357844i | ||||
\(659\) | −8.03176e6 | − | 1.39114e7i | −0.720439 | − | 1.24784i | −0.960824 | − | 0.277159i | \(-0.910607\pi\) |
0.240385 | − | 0.970678i | \(-0.422726\pi\) | |||||||
\(660\) | 1.33484e6 | + | 2.31201e6i | 0.119280 | + | 0.206600i | ||||
\(661\) | −837223. | −0.0745311 | −0.0372656 | − | 0.999305i | \(-0.511865\pi\) | ||||
−0.0372656 | + | 0.999305i | \(0.511865\pi\) | |||||||
\(662\) | −1.39265e6 | − | 2.41215e6i | −0.123509 | − | 0.213924i | ||||
\(663\) | 1.28905e6 | + | 2.23270e6i | 0.113890 | + | 0.197263i | ||||
\(664\) | 110444. | − | 191295.i | 0.00972128 | − | 0.0168377i | ||||
\(665\) | 1.45634e6 | − | 2.52245e6i | 0.127705 | − | 0.221192i | ||||
\(666\) | −279383. | −0.0244070 | ||||||||
\(667\) | 20934.5 | 0.00182199 | ||||||||
\(668\) | 2.32082e6 | − | 4.01978e6i | 0.201234 | − | 0.348547i | ||||
\(669\) | 3.25964e6 | − | 5.64587e6i | 0.281582 | − | 0.487714i | ||||
\(670\) | 609184. | + | 1.05514e6i | 0.0524278 | + | 0.0908076i | ||||
\(671\) | 6.41223e6 | + | 1.11063e7i | 0.549798 | + | 0.952277i | ||||
\(672\) | −1.36727e7 | −1.16797 | ||||||||
\(673\) | 6.52897e6 | + | 1.13085e7i | 0.555657 | + | 0.962427i | 0.997852 | + | 0.0655076i | \(0.0208667\pi\) |
−0.442195 | + | 0.896919i | \(0.645800\pi\) | |||||||
\(674\) | 3.21243e6 | + | 5.56408e6i | 0.272385 | + | 0.471785i | ||||
\(675\) | 5.64112e6 | + | 9.77071e6i | 0.476547 | + | 0.825404i | ||||
\(676\) | −5.19749e6 | + | 9.00232e6i | −0.437449 | + | 0.757684i | ||||
\(677\) | 1.92168e6 | 0.161142 | 0.0805709 | − | 0.996749i | \(-0.474326\pi\) | ||||
0.0805709 | + | 0.996749i | \(0.474326\pi\) | |||||||
\(678\) | −139517. | + | 241650.i | −0.0116561 | + | 0.0201889i | ||||
\(679\) | −1.87570e6 | − | 3.24881e6i | −0.156131 | − | 0.270427i | ||||
\(680\) | −2.77425e6 | −0.230077 | ||||||||
\(681\) | 6.76421e6 | + | 1.17160e7i | 0.558920 | + | 0.968078i | ||||
\(682\) | −1.45921e6 | + | 2.52742e6i | −0.120131 | + | 0.208073i | ||||
\(683\) | 9.92777e6 | − | 1.71954e7i | 0.814329 | − | 1.41046i | −0.0954799 | − | 0.995431i | \(-0.530439\pi\) |
0.909809 | − | 0.415028i | \(-0.136228\pi\) | |||||||
\(684\) | −653770. | −0.0534299 | ||||||||
\(685\) | −2.16322e6 | + | 3.74680e6i | −0.176146 | + | 0.305095i | ||||
\(686\) | 1.85127e6 | 0.150197 | ||||||||
\(687\) | 3.34808e6 | 0.270647 | ||||||||
\(688\) | 2.95585e6 | − | 8.48919e6i | 0.238073 | − | 0.683747i | ||||
\(689\) | −472672. | −0.0379325 | ||||||||
\(690\) | 365501. | 0.0292258 | ||||||||
\(691\) | 85129.2 | − | 147448.i | 0.00678240 | − | 0.0117475i | −0.862614 | − | 0.505862i | \(-0.831174\pi\) |
0.869397 | + | 0.494115i | \(0.164508\pi\) | |||||||
\(692\) | −1.89576e7 | −1.50493 | ||||||||
\(693\) | −944283. | + | 1.63555e6i | −0.0746912 | + | 0.129369i | ||||
\(694\) | −1.94993e6 | + | 3.37737e6i | −0.153681 | + | 0.266183i | ||||
\(695\) | 2.59674e6 | + | 4.49769e6i | 0.203923 | + | 0.353205i | ||||
\(696\) | −38331.7 | −0.00299940 | ||||||||
\(697\) | −4.09215e6 | − | 7.08780e6i | −0.319058 | − | 0.552624i | ||||
\(698\) | 3.53700e6 | − | 6.12626e6i | 0.274787 | − | 0.475945i | ||||
\(699\) | −5.45438e6 | −0.422233 | ||||||||
\(700\) | −8.14765e6 | + | 1.41121e7i | −0.628474 | + | 1.08855i | ||||
\(701\) | 4.44955e6 | + | 7.70684e6i | 0.341996 | + | 0.592354i | 0.984803 | − | 0.173674i | \(-0.0555638\pi\) |
−0.642807 | + | 0.766028i | \(0.722230\pi\) | |||||||
\(702\) | −383553. | − | 664333.i | −0.0293753 | − | 0.0508795i | ||||
\(703\) | 2.80385e6 | + | 4.85642e6i | 0.213977 | + | 0.370619i | ||||
\(704\) | 5.85194e6 | 0.445008 | ||||||||
\(705\) | −1.63146e6 | − | 2.82576e6i | −0.123624 | − | 0.214123i | ||||
\(706\) | 2.59486e6 | + | 4.49443e6i | 0.195930 | + | 0.339361i | ||||
\(707\) | 3.82940e6 | − | 6.63271e6i | 0.288125 | − | 0.499048i | ||||
\(708\) | 1.05642e7 | − | 1.82978e7i | 0.792055 | − | 1.37188i | ||||
\(709\) | 4.71951e6 | 0.352599 | 0.176300 | − | 0.984337i | \(-0.443587\pi\) | ||||
0.176300 | + | 0.984337i | \(0.443587\pi\) | |||||||
\(710\) | 1.12450e6 | 0.0837171 | ||||||||
\(711\) | −1.21621e6 | + | 2.10654e6i | −0.0902268 | + | 0.156277i | ||||
\(712\) | 7.76622e6 | − | 1.34515e7i | 0.574130 | − | 0.994422i | ||||
\(713\) | −1.90302e6 | − | 3.29612e6i | −0.140191 | − | 0.242817i | ||||
\(714\) | 3.99399e6 | + | 6.91780e6i | 0.293199 | + | 0.507835i | ||||
\(715\) | −694426. | −0.0507996 | ||||||||
\(716\) | −1.08582e7 | − | 1.88070e7i | −0.791547 | − | 1.37100i | ||||
\(717\) | −4.81616e6 | − | 8.34183e6i | −0.349867 | − | 0.605987i | ||||
\(718\) | 2.35908e6 | + | 4.08605e6i | 0.170778 | + | 0.295796i | ||||
\(719\) | 2.28570e6 | − | 3.95896e6i | 0.164891 | − | 0.285600i | −0.771725 | − | 0.635956i | \(-0.780606\pi\) |
0.936617 | + | 0.350356i | \(0.113939\pi\) | |||||||
\(720\) | −312477. | −0.0224640 | ||||||||
\(721\) | −1.70260e7 | + | 2.94898e7i | −1.21976 | + | 2.11268i | ||||
\(722\) | 1.46989e6 | + | 2.54593e6i | 0.104940 | + | 0.181762i | ||||
\(723\) | 2.25745e6 | 0.160610 | ||||||||
\(724\) | 1.16142e7 | + | 2.01164e7i | 0.823461 | + | 1.42628i | ||||
\(725\) | −34832.7 | + | 60332.0i | −0.00246117 | + | 0.00426288i | ||||
\(726\) | −247446. | + | 428588.i | −0.0174236 | + | 0.0301786i | ||||
\(727\) | −2.14070e7 | −1.50217 | −0.751087 | − | 0.660204i | \(-0.770470\pi\) | ||||
−0.751087 | + | 0.660204i | \(0.770470\pi\) | |||||||
\(728\) | 1.16611e6 | − | 2.01976e6i | 0.0815477 | − | 0.141245i | ||||
\(729\) | 1.55187e7 | 1.08153 | ||||||||
\(730\) | 736192. | 0.0511309 | ||||||||
\(731\) | −1.87318e7 | + | 3.57411e6i | −1.29654 | + | 0.247385i | ||||
\(732\) | 1.45483e7 | 1.00354 | ||||||||
\(733\) | 2.49500e6 | 0.171518 | 0.0857591 | − | 0.996316i | \(-0.472668\pi\) | ||||
0.0857591 | + | 0.996316i | \(0.472668\pi\) | |||||||
\(734\) | 2.92450e6 | − | 5.06539e6i | 0.200360 | − | 0.347035i | ||||
\(735\) | −5.43062e6 | −0.370792 | ||||||||
\(736\) | 2.00974e6 | − | 3.48098e6i | 0.136756 | − | 0.236868i | ||||
\(737\) | −7.92818e6 | + | 1.37320e7i | −0.537657 | + | 0.931248i | ||||
\(738\) | 115219. | + | 199565.i | 0.00778724 | + | 0.0134879i | ||||
\(739\) | −1.42343e7 | −0.958796 | −0.479398 | − | 0.877598i | \(-0.659145\pi\) | ||||
−0.479398 | + | 0.877598i | \(0.659145\pi\) | |||||||
\(740\) | 1.51599e6 | + | 2.62578e6i | 0.101770 | + | 0.176270i | ||||
\(741\) | −728497. | + | 1.26179e6i | −0.0487397 | + | 0.0844196i | ||||
\(742\) | −1.46453e6 | −0.0976535 | ||||||||
\(743\) | 1.12676e7 | − | 1.95161e7i | 0.748791 | − | 1.29694i | −0.199612 | − | 0.979875i | \(-0.563968\pi\) |
0.948403 | − | 0.317069i | \(-0.102699\pi\) | |||||||
\(744\) | 3.48449e6 | + | 6.03531e6i | 0.230784 | + | 0.399730i | ||||
\(745\) | −274209. | − | 474945.i | −0.0181005 | − | 0.0313511i | ||||
\(746\) | −2.49530e6 | − | 4.32199e6i | −0.164163 | − | 0.284339i | ||||
\(747\) | −52780.9 | −0.00346079 | ||||||||
\(748\) | −8.57616e6 | − | 1.48543e7i | −0.560452 | − | 0.970732i | ||||
\(749\) | −2.12678e7 | − | 3.68369e7i | −1.38522 | − | 2.39926i | ||||
\(750\) | −1.27508e6 | + | 2.20851e6i | −0.0827725 | + | 0.143366i | ||||
\(751\) | 9.68188e6 | − | 1.67695e7i | 0.626412 | − | 1.08498i | −0.361854 | − | 0.932235i | \(-0.617856\pi\) |
0.988266 | − | 0.152742i | \(-0.0488104\pi\) | |||||||
\(752\) | −9.88188e6 | −0.637228 | ||||||||
\(753\) | −9.47108e6 | −0.608712 | ||||||||
\(754\) | 2368.36 | − | 4102.11i | 0.000151711 | − | 0.000262772i | ||||
\(755\) | −1.42407e6 | + | 2.46655e6i | −0.0909206 | + | 0.157479i | ||||
\(756\) | 1.13203e7 | + | 1.96074e7i | 0.720367 | + | 1.24771i | ||||
\(757\) | −6.66046e6 | − | 1.15362e7i | −0.422439 | − | 0.731686i | 0.573738 | − | 0.819039i | \(-0.305493\pi\) |
−0.996177 | + | 0.0873524i | \(0.972159\pi\) | |||||||
\(758\) | 2.46495e6 | 0.155824 | ||||||||
\(759\) | 2.37840e6 | + | 4.11950e6i | 0.149858 | + | 0.259562i | ||||
\(760\) | −783924. | − | 1.35780e6i | −0.0492312 | − | 0.0852709i | ||||
\(761\) | −8.36937e6 | − | 1.44962e7i | −0.523879 | − | 0.907385i | −0.999614 | − | 0.0277960i | \(-0.991151\pi\) |
0.475735 | − | 0.879589i | \(-0.342182\pi\) | |||||||
\(762\) | 2.05570e6 | − | 3.56057e6i | 0.128254 | − | 0.222143i | ||||
\(763\) | 2.84064e6 | 0.176647 | ||||||||
\(764\) | −992877. | + | 1.71971e6i | −0.0615406 | + | 0.106592i | ||||
\(765\) | 331450. | + | 574089.i | 0.0204769 | + | 0.0354671i | ||||
\(766\) | −1.79039e6 | −0.110249 | ||||||||
\(767\) | 2.74793e6 | + | 4.75955e6i | 0.168662 | + | 0.292131i | ||||
\(768\) | 1.38757e6 | − | 2.40333e6i | 0.0848888 | − | 0.147032i | ||||
\(769\) | 5.74320e6 | − | 9.94752e6i | 0.350218 | − | 0.606595i | −0.636070 | − | 0.771632i | \(-0.719441\pi\) |
0.986287 | + | 0.165037i | \(0.0527742\pi\) | |||||||
\(770\) | −2.15161e6 | −0.130779 | ||||||||
\(771\) | −9.07130e6 | + | 1.57119e7i | −0.549583 | + | 0.951906i | ||||
\(772\) | −1.01961e7 | −0.615728 | ||||||||
\(773\) | −2.87417e7 | −1.73007 | −0.865036 | − | 0.501710i | \(-0.832705\pi\) | ||||
−0.865036 | + | 0.501710i | \(0.832705\pi\) | |||||||
\(774\) | 527416. | − | 100633.i | 0.0316447 | − | 0.00603794i | ||||
\(775\) | 1.26657e7 | 0.757485 | ||||||||
\(776\) | −2.01932e6 | −0.120379 | ||||||||
\(777\) | 9.18834e6 | − | 1.59147e7i | 0.545989 | − | 0.945682i | ||||
\(778\) | −3.80548e6 | −0.225403 | ||||||||
\(779\) | 2.31265e6 | − | 4.00563e6i | 0.136542 | − | 0.236498i | ||||
\(780\) | −393885. | + | 682229.i | −0.0231811 | + | 0.0401508i | ||||
\(781\) | 7.31737e6 | + | 1.26741e7i | 0.429267 | + | 0.743512i | ||||
\(782\) | −2.34830e6 | −0.137321 | ||||||||
\(783\) | 48396.4 | + | 83825.0i | 0.00282104 | + | 0.00488618i | ||||
\(784\) | −8.22343e6 | + | 1.42434e7i | −0.477819 | + | 0.827606i | ||||
\(785\) | 4.43364e6 | 0.256795 | ||||||||
\(786\) | 1.32602e6 | − | 2.29673e6i | 0.0765585 | − | 0.132603i | ||||
\(787\) | −1.29048e6 | − | 2.23518e6i | −0.0742703 | − | 0.128640i | 0.826498 | − | 0.562939i | \(-0.190329\pi\) |
−0.900769 | + | 0.434299i | \(0.856996\pi\) | |||||||
\(788\) | 4.95949e6 | + | 8.59008e6i | 0.284526 | + | 0.492813i | ||||
\(789\) | −1.13371e7 | − | 1.96364e7i | −0.648349 | − | 1.12297i | ||||
\(790\) | −2.77122e6 | −0.157980 | ||||||||
\(791\) | 1.07109e6 | + | 1.85518e6i | 0.0608674 | + | 0.105426i | ||||
\(792\) | 508293. | + | 880389.i | 0.0287939 | + | 0.0498726i | ||||
\(793\) | −1.89213e6 | + | 3.27726e6i | −0.106848 | + | 0.185066i | ||||
\(794\) | −457102. | + | 791723.i | −0.0257313 | + | 0.0445679i | ||||
\(795\) | 1.04130e6 | 0.0584329 | ||||||||
\(796\) | 2.03610e7 | 1.13898 | ||||||||
\(797\) | −843320. | + | 1.46067e6i | −0.0470269 | + | 0.0814531i | −0.888581 | − | 0.458720i | \(-0.848308\pi\) |
0.841554 | + | 0.540173i | \(0.181641\pi\) | |||||||
\(798\) | −2.25718e6 | + | 3.90955e6i | −0.125475 | + | 0.217330i | ||||
\(799\) | 1.04819e7 | + | 1.81551e7i | 0.580861 | + | 1.00608i | ||||
\(800\) | 6.68799e6 | + | 1.15839e7i | 0.369463 | + | 0.639928i | ||||
\(801\) | −3.71144e6 | −0.204391 | ||||||||
\(802\) | −766332. | − | 1.32733e6i | −0.0420708 | − | 0.0728688i | ||||
\(803\) | 4.79056e6 | + | 8.29749e6i | 0.262179 | + | 0.454107i | ||||
\(804\) | 8.99389e6 | + | 1.55779e7i | 0.490690 | + | 0.849901i | ||||
\(805\) | 1.40301e6 | − | 2.43008e6i | 0.0763079 | − | 0.132169i | ||||
\(806\) | −861168. | −0.0466928 | ||||||||
\(807\) | −1.55934e6 | + | 2.70086e6i | −0.0842863 | + | 0.145988i | ||||
\(808\) | −2.06130e6 | − | 3.57028e6i | −0.111074 | − | 0.192386i | ||||
\(809\) | −1.96253e7 | −1.05425 | −0.527126 | − | 0.849787i | \(-0.676730\pi\) | ||||
−0.527126 | + | 0.849787i | \(0.676730\pi\) | |||||||
\(810\) | 755679. | + | 1.30887e6i | 0.0404692 | + | 0.0700947i | ||||
\(811\) | −3.13921e6 | + | 5.43726e6i | −0.167598 | + | 0.290288i | −0.937575 | − | 0.347784i | \(-0.886934\pi\) |
0.769977 | + | 0.638072i | \(0.220268\pi\) | |||||||
\(812\) | −69900.5 | + | 121071.i | −0.00372041 | + | 0.00644393i | ||||
\(813\) | 1.09589e7 | 0.581488 | ||||||||
\(814\) | 2.07122e6 | − | 3.58746e6i | 0.109563 | − | 0.189769i | ||||
\(815\) | −5.06335e6 | −0.267020 | ||||||||
\(816\) | −1.72008e7 | −0.904323 | ||||||||
\(817\) | −7.04235e6 | − | 8.15794e6i | −0.369116 | − | 0.427588i | ||||
\(818\) | 7.47449e6 | 0.390570 | ||||||||
\(819\) | −557280. | −0.0290311 | ||||||||
\(820\) | 1.25041e6 | − | 2.16577e6i | 0.0649407 | − | 0.112481i | ||||
\(821\) | 3.77563e6 | 0.195493 | 0.0977465 | − | 0.995211i | \(-0.468837\pi\) | ||||
0.0977465 | + | 0.995211i | \(0.468837\pi\) | |||||||
\(822\) | 3.35277e6 | − | 5.80717e6i | 0.173071 | − | 0.299768i | ||||
\(823\) | −1.83420e6 | + | 3.17692e6i | −0.0943945 | + | 0.163496i | −0.909356 | − | 0.416019i | \(-0.863425\pi\) |
0.814961 | + | 0.579515i | \(0.196758\pi\) | |||||||
\(824\) | 9.16480e6 | + | 1.58739e7i | 0.470224 | + | 0.814452i | ||||
\(825\) | −1.58296e7 | −0.809720 | ||||||||
\(826\) | 8.51419e6 | + | 1.47470e7i | 0.434203 | + | 0.752062i | ||||
\(827\) | 7.97868e6 | − | 1.38195e7i | 0.405665 | − | 0.702632i | −0.588734 | − | 0.808327i | \(-0.700373\pi\) |
0.994399 | + | 0.105695i | \(0.0337068\pi\) | |||||||
\(828\) | −629828. | −0.0319261 | ||||||||
\(829\) | −8.62565e6 | + | 1.49401e7i | −0.435919 | + | 0.755033i | −0.997370 | − | 0.0724763i | \(-0.976910\pi\) |
0.561451 | + | 0.827510i | \(0.310243\pi\) | |||||||
\(830\) | −30066.2 | − | 52076.1i | −0.00151490 | − | 0.00262388i | ||||
\(831\) | 5.89163e6 | + | 1.02046e7i | 0.295960 | + | 0.512617i | ||||
\(832\) | 863397. | + | 1.49545e6i | 0.0432417 | + | 0.0748967i | ||||
\(833\) | 3.48910e7 | 1.74221 | ||||||||
\(834\) | −4.02469e6 | − | 6.97096e6i | −0.200363 | − | 0.347039i | ||||
\(835\) | −1.32992e6 | − | 2.30348e6i | −0.0660097 | − | 0.114332i | ||||
\(836\) | 4.84676e6 | − | 8.39483e6i | 0.239848 | − | 0.415429i | ||||
\(837\) | 8.79881e6 | − | 1.52400e7i | 0.434121 | − | 0.751919i | ||||
\(838\) | 3.46145e6 | 0.170274 | ||||||||
\(839\) | 8.69080e6 | 0.426241 | 0.213120 | − | 0.977026i | \(-0.431637\pi\) | ||||
0.213120 | + | 0.977026i | \(0.431637\pi\) | |||||||
\(840\) | −2.56895e6 | + | 4.44955e6i | −0.125620 | + | 0.217579i | ||||
\(841\) | 1.02553e7 | − | 1.77627e7i | 0.499985 | − | 0.866000i | ||||
\(842\) | −5.61190e6 | − | 9.72010e6i | −0.272791 | − | 0.472488i | ||||
\(843\) | −8.62336e6 | − | 1.49361e7i | −0.417934 | − | 0.723883i | ||||
\(844\) | 1.93658e7 | 0.935790 | ||||||||
\(845\) | 2.97835e6 | + | 5.15866e6i | 0.143494 | + | 0.248539i | ||||
\(846\) | −295129. | − | 511179.i | −0.0141771 | − | 0.0245554i | ||||
\(847\) | 1.89968e6 | + | 3.29034e6i | 0.0909854 | + | 0.157591i | ||||
\(848\) | 1.57681e6 | − | 2.73111e6i | 0.0752990 | − | 0.130422i | ||||
\(849\) | 1.01909e7 | 0.485226 | ||||||||
\(850\) | 3.90731e6 | − | 6.76767e6i | 0.185494 | − | 0.321286i | ||||
\(851\) | 2.70117e6 | + | 4.67857e6i | 0.127858 | + | 0.221457i | ||||
\(852\) | 1.66019e7 | 0.783538 | ||||||||
\(853\) | −1.27111e7 | − | 2.20163e7i | −0.598151 | − | 1.03603i | −0.993094 | − | 0.117322i | \(-0.962569\pi\) |
0.394943 | − | 0.918706i | \(-0.370764\pi\) | |||||||
\(854\) | −5.86257e6 | + | 1.01543e7i | −0.275070 | + | 0.476435i | ||||
\(855\) | −187317. | + | 324443.i | −0.00876318 | + | 0.0151783i | ||||
\(856\) | −2.28962e7 | −1.06802 | ||||||||
\(857\) | −2.64869e6 | + | 4.58766e6i | −0.123191 | + | 0.213373i | −0.921024 | − | 0.389505i | \(-0.872646\pi\) |
0.797833 | + | 0.602878i | \(0.205979\pi\) | |||||||
\(858\) | 1.07629e6 | 0.0499127 | ||||||||
\(859\) | 8.47249e6 | 0.391767 | 0.195884 | − | 0.980627i | \(-0.437243\pi\) | ||||
0.195884 | + | 0.980627i | \(0.437243\pi\) | |||||||
\(860\) | −3.80767e6 | − | 4.41085e6i | −0.175555 | − | 0.203365i | ||||
\(861\) | −1.51573e7 | −0.696809 | ||||||||
\(862\) | −1.17796e7 | −0.539961 | ||||||||
\(863\) | −7.36333e6 | + | 1.27537e7i | −0.336548 | + | 0.582919i | −0.983781 | − | 0.179374i | \(-0.942593\pi\) |
0.647233 | + | 0.762293i | \(0.275926\pi\) | |||||||
\(864\) | 1.85845e7 | 0.846969 | ||||||||
\(865\) | −5.43169e6 | + | 9.40796e6i | −0.246828 | + | 0.427519i | ||||
\(866\) | 285484. | − | 494472.i | 0.0129356 | − | 0.0224051i | ||||
\(867\) | 7.77280e6 | + | 1.34629e7i | 0.351180 | + | 0.608261i | ||||
\(868\) | 2.54168e7 | 1.14504 | ||||||||
\(869\) | −1.80329e7 | − | 3.12339e7i | −0.810059 | − | 1.40306i | ||||
\(870\) | −5217.50 | + | 9036.97i | −0.000233703 | + | 0.000404785i | ||||
\(871\) | −4.67891e6 | −0.208977 | ||||||||
\(872\) | 764537. | − | 1.32422e6i | 0.0340492 | − | 0.0589750i | ||||
\(873\) | 241256. | + | 417868.i | 0.0107138 | + | 0.0185568i | ||||
\(874\) | −663562. | − | 1.14932e6i | −0.0293835 | − | 0.0508936i | ||||
\(875\) | 9.78902e6 | + | 1.69551e7i | 0.432234 | + | 0.748652i | ||||
\(876\) | 1.08690e7 | 0.478553 | ||||||||
\(877\) | 6.22489e6 | + | 1.07818e7i | 0.273295 | + | 0.473362i | 0.969704 | − | 0.244284i | \(-0.0785530\pi\) |
−0.696408 | + | 0.717646i | \(0.745220\pi\) | |||||||
\(878\) | −3.66956e6 | − | 6.35587e6i | −0.160649 | − | 0.278252i | ||||
\(879\) | −9.00305e6 | + | 1.55937e7i | −0.393023 | + | 0.680735i | ||||
\(880\) | 2.31657e6 | − | 4.01241e6i | 0.100841 | − | 0.174662i | ||||
\(881\) | 3.02396e7 | 1.31261 | 0.656307 | − | 0.754494i | \(-0.272118\pi\) | ||||
0.656307 | + | 0.754494i | \(0.272118\pi\) | |||||||
\(882\) | −982396. | −0.0425221 | ||||||||
\(883\) | −1.88332e7 | + | 3.26200e7i | −0.812871 | + | 1.40793i | 0.0979755 | + | 0.995189i | \(0.468763\pi\) |
−0.910847 | + | 0.412745i | \(0.864570\pi\) | |||||||
\(884\) | 2.53066e6 | − | 4.38323e6i | 0.108919 | − | 0.188653i | ||||
\(885\) | −6.05370e6 | − | 1.04853e7i | −0.259814 | − | 0.450011i | ||||
\(886\) | 3.39795e6 | + | 5.88543e6i | 0.145423 | + | 0.251880i | ||||
\(887\) | 1.65492e7 | 0.706265 | 0.353133 | − | 0.935573i | \(-0.385116\pi\) | ||||
0.353133 | + | 0.935573i | \(0.385116\pi\) | |||||||
\(888\) | −4.94594e6 | − | 8.56661e6i | −0.210483 | − | 0.364566i | ||||
\(889\) | −1.57819e7 | − | 2.73351e7i | −0.669739 | − | 1.16002i | ||||
\(890\) | −2.11419e6 | − | 3.66189e6i | −0.0894683 | − | 0.154964i | ||||
\(891\) | −9.83473e6 | + | 1.70342e7i | −0.415019 | + | 0.718834i | ||||
\(892\) | −1.27986e7 | −0.538582 | ||||||||
\(893\) | −5.92377e6 | + | 1.02603e7i | −0.248582 | + | 0.430556i | ||||
\(894\) | 424997. | + | 736117.i | 0.0177845 | + | 0.0308037i | ||||
\(895\) | −1.24443e7 | −0.519295 | ||||||||
\(896\) | 1.75052e7 | + | 3.03199e7i | 0.728446 | + | 1.26171i | ||||
\(897\) | −701819. | + | 1.21559e6i | −0.0291235 | + | 0.0504434i | ||||
\(898\) | −5.11163e6 | + | 8.85360e6i | −0.211528 | + | 0.366378i | ||||
\(899\) | 108662. | 0.00448411 | ||||||||
\(900\) | 1.04797e6 | − | 1.81513e6i | 0.0431262 | − | 0.0746967i | ||||
\(901\) | −6.69019e6 | −0.274553 | ||||||||
\(902\) | −3.41673e6 | −0.139828 | ||||||||
\(903\) | −1.16132e7 | + | 3.33531e7i | −0.473950 | + | 1.36118i | ||||
\(904\) | 1.15310e6 | 0.0469296 | ||||||||
\(905\) | 1.33107e7 | 0.540232 | ||||||||
\(906\) | 2.20716e6 | − | 3.82291e6i | 0.0893332 | − | 0.154730i | ||||
\(907\) | 3.27281e7 | 1.32100 | 0.660499 | − | 0.750827i | \(-0.270345\pi\) | ||||
0.660499 | + | 0.750827i | \(0.270345\pi\) | |||||||
\(908\) | 1.32795e7 | − | 2.30008e7i | 0.534524 | − | 0.925822i | ||||
\(909\) | −492544. | + | 853111.i | −0.0197713 | + | 0.0342449i | ||||
\(910\) | −317449. | − | 549838.i | −0.0127078 | − | 0.0220106i | ||||
\(911\) | 3.14907e7 | 1.25715 | 0.628573 | − | 0.777751i | \(-0.283639\pi\) | ||||
0.628573 | + | 0.777751i | \(0.283639\pi\) | |||||||
\(912\) | −4.86046e6 | − | 8.41857e6i | −0.193504 | − | 0.335159i | ||||
\(913\) | 391294. | − | 677741.i | 0.0155355 | − | 0.0269083i | ||||
\(914\) | −6.82628e6 | −0.270283 | ||||||||
\(915\) | 4.16836e6 | − | 7.21982e6i | 0.164594 | − | 0.285084i | ||||
\(916\) | −3.28647e6 | − | 5.69233e6i | −0.129417 | − | 0.224157i | ||||
\(917\) | −1.01801e7 | − | 1.76324e7i | −0.399785 | − | 0.692448i | ||||
\(918\) | −5.42880e6 | − | 9.40297e6i | −0.212617 | − | 0.368263i | ||||
\(919\) | 2.90075e7 | 1.13298 | 0.566489 | − | 0.824069i | \(-0.308301\pi\) | ||||
0.566489 | + | 0.824069i | \(0.308301\pi\) | |||||||
\(920\) | −755216. | − | 1.30807e6i | −0.0294172 | − | 0.0509521i | ||||
\(921\) | 2.10486e7 | + | 3.64573e7i | 0.817664 | + | 1.41623i | ||||
\(922\) | 3.58965e6 | − | 6.21746e6i | 0.139067 | − | 0.240872i | ||||
\(923\) | −2.15922e6 | + | 3.73987e6i | −0.0834241 | + | 0.144495i | ||||
\(924\) | −3.17660e7 | −1.22400 | ||||||||
\(925\) | −1.79779e7 | −0.690850 | ||||||||
\(926\) | 4.80415e6 | − | 8.32103e6i | 0.184115 | − | 0.318897i | ||||
\(927\) | 2.18991e6 | − | 3.79303e6i | 0.0837003 | − | 0.144973i | ||||
\(928\) | 57377.8 | + | 99381.2i | 0.00218713 | + | 0.00378821i | ||||
\(929\) | 7.25370e6 | + | 1.25638e7i | 0.275753 | + | 0.477618i | 0.970325 | − | 0.241805i | \(-0.0777395\pi\) |
−0.694572 | + | 0.719423i | \(0.744406\pi\) | |||||||
\(930\) | 1.89716e6 | 0.0719276 | ||||||||
\(931\) | 9.85920e6 | + | 1.70766e7i | 0.372793 | + | 0.645696i | ||||
\(932\) | 5.35401e6 | + | 9.27342e6i | 0.201902 | + | 0.349704i | ||||
\(933\) | −1.91324e7 | − | 3.31384e7i | −0.719559 | − | 1.24631i | ||||
\(934\) | 7.27464e6 | − | 1.26000e7i | 0.272863 | − | 0.472612i | ||||
\(935\) | −9.82890e6 | −0.367685 | ||||||||
\(936\) | −149987. | + | 259786.i | −0.00559584 | + | 0.00969228i | ||||
\(937\) | −1.73638e6 | − | 3.00749e6i | −0.0646093 | − | 0.111907i | 0.831911 | − | 0.554909i | \(-0.187247\pi\) |
−0.896521 | + | 0.443002i | \(0.853913\pi\) | |||||||
\(938\) | −1.44971e7 | −0.537991 | ||||||||
\(939\) | −1.69353e7 | − | 2.93328e7i | −0.626800 | − | 1.08565i | ||||
\(940\) | −3.20287e6 | + | 5.54754e6i | −0.118228 | + | 0.204777i | ||||
\(941\) | −1.00308e7 | + | 1.73739e7i | −0.369285 | + | 0.639621i | −0.989454 | − | 0.144848i | \(-0.953731\pi\) |
0.620169 | + | 0.784468i | \(0.287064\pi\) | |||||||
\(942\) | −6.87170e6 | −0.252311 | ||||||||
\(943\) | 2.22796e6 | − | 3.85893e6i | 0.0815882 | − | 0.141315i | ||||
\(944\) | −3.66678e7 | −1.33923 | ||||||||
\(945\) | 1.29739e7 | 0.472597 | ||||||||
\(946\) | −2.61783e6 | + | 7.51841e6i | −0.0951073 | + | 0.273148i | ||||
\(947\) | −3.95996e7 | −1.43488 | −0.717440 | − | 0.696620i | \(-0.754686\pi\) | ||||
−0.717440 | + | 0.696620i | \(0.754686\pi\) | |||||||
\(948\) | −4.09138e7 | −1.47859 | ||||||||
\(949\) | −1.41360e6 | + | 2.44843e6i | −0.0509520 | + | 0.0882515i | ||||
\(950\) | 4.41639e6 | 0.158766 | ||||||||
\(951\) | 7.43057e6 | − | 1.28701e7i | 0.266423 | − | 0.461457i | ||||
\(952\) | 1.65051e7 | − | 2.85877e7i | 0.590238 | − | 1.02232i | ||||
\(953\) | −5.80349e6 | − | 1.00519e7i | −0.206994 | − | 0.358523i | 0.743773 | − | 0.668433i | \(-0.233035\pi\) |
−0.950766 | + | 0.309909i | \(0.899701\pi\) | |||||||
\(954\) | 188370. | 0.00670103 | ||||||||
\(955\) | 568955. | + | 985459.i | 0.0201869 | + | 0.0349647i | ||||
\(956\) | −9.45508e6 | + | 1.63767e7i | −0.334596 | + | 0.579537i | ||||
\(957\) | −135806. | −0.00479333 | ||||||||
\(958\) | −7.43983e6 | + | 1.28862e7i | −0.261908 | + | 0.453638i | ||||
\(959\) | −2.57397e7 | − | 4.45826e7i | −0.903770 | − | 1.56538i | ||||
\(960\) | −1.90207e6 | − | 3.29448e6i | −0.0666113 | − | 0.115374i | ||||
\(961\) | 4.43685e6 | + | 7.68485e6i | 0.154977 | + | 0.268428i | ||||
\(962\) | 1.22236e6 | 0.0425853 | ||||||||
\(963\) | 2.73550e6 | + | 4.73803e6i | 0.0950541 | + | 0.164639i | ||||
\(964\) | −2.21591e6 | − | 3.83807e6i | −0.0767998 | − | 0.133021i | ||||
\(965\) | −2.92136e6 | + | 5.05994e6i | −0.100987 | + | 0.174915i | ||||
\(966\) | −2.17452e6 | + | 3.76638e6i | −0.0749756 | + | 0.129862i | ||||
\(967\) | 3.18850e7 | 1.09653 | 0.548264 | − | 0.836305i | \(-0.315289\pi\) | ||||
0.548264 | + | 0.836305i | \(0.315289\pi\) | |||||||
\(968\) | 2.04513e6 | 0.0701509 | ||||||||
\(969\) | −1.03112e7 | + | 1.78594e7i | −0.352775 | + | 0.611024i | ||||
\(970\) | −274859. | + | 476070.i | −0.00937952 | + | 0.0162458i | ||||
\(971\) | −1.84696e7 | − | 3.19902e7i | −0.628650 | − | 1.08885i | −0.987823 | − | 0.155583i | \(-0.950275\pi\) |
0.359173 | − | 0.933271i | \(-0.383059\pi\) | |||||||
\(972\) | −2.77430e6 | − | 4.80522e6i | −0.0941862 | − | 0.163135i | ||||
\(973\) | −6.17963e7 | −2.09257 | ||||||||
\(974\) | −4.14551e6 | − | 7.18023e6i | −0.140017 | − | 0.242516i | ||||
\(975\) | −2.33550e6 | − | 4.04521e6i | −0.0786808 | − | 0.136279i | ||||
\(976\) | −1.26241e7 | − | 2.18655e7i | −0.424204 | − | 0.734743i | ||||
\(977\) | 1.15353e7 | − | 1.99797e7i | 0.386627 | − | 0.669658i | −0.605366 | − | 0.795947i | \(-0.706973\pi\) |
0.991993 | + | 0.126289i | \(0.0403067\pi\) | |||||||
\(978\) | 7.84769e6 | 0.262358 | ||||||||
\(979\) | 2.75150e7 | − | 4.76574e7i | 0.917514 | − | 1.58918i | ||||
\(980\) | 5.33069e6 | + | 9.23302e6i | 0.177304 | + | 0.307099i | ||||
\(981\) | −365369. | −0.0121216 | ||||||||
\(982\) | 4.38694e6 | + | 7.59840e6i | 0.145172 | + | 0.251445i | ||||
\(983\) | 5.57125e6 | − | 9.64969e6i | 0.183895 | − | 0.318515i | −0.759309 | − | 0.650730i | \(-0.774463\pi\) |
0.943203 | + | 0.332216i | \(0.107796\pi\) | |||||||
\(984\) | −4.07946e6 | + | 7.06584e6i | −0.134312 | + | 0.232635i | ||||
\(985\) | 5.68394e6 | 0.186663 | ||||||||
\(986\) | 33521.7 | − | 58061.3i | 0.00109808 | − | 0.00190193i | ||||
\(987\) | 3.88248e7 | 1.26858 | ||||||||
\(988\) | 2.86037e6 | 0.0932245 | ||||||||
\(989\) | −6.78445e6 | − | 7.85918e6i | −0.220558 | − | 0.255498i | ||||
\(990\) | 276744. | 0.00897409 | ||||||||
\(991\) | −4.05356e7 | −1.31115 | −0.655575 | − | 0.755130i | \(-0.727574\pi\) | ||||
−0.655575 | + | 0.755130i | \(0.727574\pi\) | |||||||
\(992\) | 1.04317e7 | − | 1.80682e7i | 0.336570 | − | 0.582956i | ||||
\(993\) | −2.35643e7 | −0.758370 | ||||||||
\(994\) | −6.69012e6 | + | 1.15876e7i | −0.214767 | + | 0.371988i | ||||
\(995\) | 5.83380e6 | − | 1.01044e7i | 0.186807 | − | 0.323560i | ||||
\(996\) | −443892. | − | 768843.i | −0.0141785 | − | 0.0245578i | ||||
\(997\) | 7.50635e6 | 0.239161 | 0.119581 | − | 0.992824i | \(-0.461845\pi\) | ||||
0.119581 | + | 0.992824i | \(0.461845\pi\) | |||||||
\(998\) | 3.29617e6 | + | 5.70913e6i | 0.104757 | + | 0.181445i | ||||
\(999\) | −1.24892e7 | + | 2.16319e7i | −0.395931 | + | 0.685773i |
(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 | 43.6.c.a.6.10 | ✓ | 34 | |
43.36 | even | 3 | inner | 43.6.c.a.36.10 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.10 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.6.c.a.36.10 | yes | 34 | 43.36 | even | 3 | inner |