Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(19,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.9 | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.7.f.a.19.10 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.26743 | − | 6.02115i | −0.658429 | − | 0.752643i | ||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | −8.50840 | + | 63.4319i | −0.132944 | + | 0.991124i | ||||
\(5\) | −13.2381 | − | 124.297i | −0.105905 | − | 0.994376i | ||||
\(6\) | 82.1111 | + | 93.8604i | 0.380144 | + | 0.434539i | ||||
\(7\) | 380.004 | 1.10788 | 0.553941 | − | 0.832556i | \(-0.313123\pi\) | ||||
0.553941 | + | 0.832556i | \(0.313123\pi\) | |||||||
\(8\) | 426.750 | − | 282.893i | 0.833496 | − | 0.552525i | ||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | −678.680 | + | 734.434i | −0.678680 | + | 0.734434i | ||||
\(11\) | − | 847.255i | − | 0.636555i | −0.947998 | − | 0.318278i | \(-0.896896\pi\) | ||
0.947998 | − | 0.318278i | \(-0.103104\pi\) | |||||||
\(12\) | 132.633 | − | 988.806i | 0.0767551 | − | 0.572225i | ||||
\(13\) | − | 311.394i | − | 0.141736i | −0.997486 | − | 0.0708679i | \(-0.977423\pi\) | ||
0.997486 | − | 0.0708679i | \(-0.0225769\pi\) | |||||||
\(14\) | −2001.64 | − | 2288.06i | −0.729461 | − | 0.833840i | ||||
\(15\) | 206.362 | + | 1937.60i | 0.0611444 | + | 0.574103i | ||||
\(16\) | −3951.21 | − | 1079.41i | −0.964652 | − | 0.263527i | ||||
\(17\) | − | 4506.17i | − | 0.917192i | −0.888645 | − | 0.458596i | \(-0.848352\pi\) | ||
0.888645 | − | 0.458596i | \(-0.151648\pi\) | |||||||
\(18\) | −1279.99 | − | 1463.14i | −0.219476 | − | 0.250881i | ||||
\(19\) | 5561.11i | 0.810775i | 0.914145 | + | 0.405387i | \(0.132863\pi\) | ||||
−0.914145 | + | 0.405387i | \(0.867137\pi\) | |||||||
\(20\) | 7997.03 | + | 217.848i | 0.999629 | + | 0.0272310i | ||||
\(21\) | −5923.67 | −0.639636 | ||||||||
\(22\) | −5101.45 | + | 4462.86i | −0.479099 | + | 0.419126i | ||||
\(23\) | −15489.8 | −1.27310 | −0.636551 | − | 0.771235i | \(-0.719640\pi\) | ||||
−0.636551 | + | 0.771235i | \(0.719640\pi\) | |||||||
\(24\) | −6652.38 | + | 4409.86i | −0.481219 | + | 0.319000i | ||||
\(25\) | −15274.5 | + | 3290.92i | −0.977568 | + | 0.210619i | ||||
\(26\) | −1874.95 | + | 1640.24i | −0.106677 | + | 0.0933229i | ||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | −3233.22 | + | 24104.4i | −0.147286 | + | 1.09805i | ||||
\(29\) | −18883.3 | −0.774253 | −0.387127 | − | 0.922027i | \(-0.626532\pi\) | ||||
−0.387127 | + | 0.922027i | \(0.626532\pi\) | |||||||
\(30\) | 10579.6 | − | 11448.7i | 0.391836 | − | 0.424026i | ||||
\(31\) | − | 460.340i | − | 0.0154523i | −0.999970 | − | 0.00772616i | \(-0.997541\pi\) | ||
0.999970 | − | 0.00772616i | \(-0.00245934\pi\) | |||||||
\(32\) | 14313.5 | + | 29476.5i | 0.436812 | + | 0.899553i | ||||
\(33\) | 13207.4i | 0.367515i | ||||||||
\(34\) | −27132.3 | + | 23735.9i | −0.690319 | + | 0.603906i | ||||
\(35\) | −5030.54 | − | 47233.3i | −0.117330 | − | 1.10165i | ||||
\(36\) | −2067.54 | + | 15414.0i | −0.0443146 | + | 0.330375i | ||||
\(37\) | − | 98574.7i | − | 1.94608i | −0.230640 | − | 0.973039i | \(-0.574082\pi\) | ||
0.230640 | − | 0.973039i | \(-0.425918\pi\) | |||||||
\(38\) | 33484.2 | − | 29292.7i | 0.610224 | − | 0.533837i | ||||
\(39\) | 4854.15i | 0.0818312i | ||||||||
\(40\) | −40812.1 | − | 49298.8i | −0.637689 | − | 0.770294i | ||||
\(41\) | 69606.4 | 1.00995 | 0.504973 | − | 0.863135i | \(-0.331503\pi\) | ||||
0.504973 | + | 0.863135i | \(0.331503\pi\) | |||||||
\(42\) | 31202.5 | + | 35667.3i | 0.421155 | + | 0.481418i | ||||
\(43\) | −145883. | −1.83485 | −0.917425 | − | 0.397910i | \(-0.869736\pi\) | ||||
−0.917425 | + | 0.397910i | \(0.869736\pi\) | |||||||
\(44\) | 53743.0 | + | 7208.79i | 0.630905 | + | 0.0846261i | ||||
\(45\) | −3216.87 | − | 30204.2i | −0.0353017 | − | 0.331459i | ||||
\(46\) | 81591.6 | + | 93266.5i | 0.838247 | + | 0.958192i | ||||
\(47\) | 33666.1 | 0.324264 | 0.162132 | − | 0.986769i | \(-0.448163\pi\) | ||||
0.162132 | + | 0.986769i | \(0.448163\pi\) | |||||||
\(48\) | 61593.3 | + | 16826.3i | 0.556942 | + | 0.152148i | ||||
\(49\) | 26753.8 | 0.227403 | ||||||||
\(50\) | 100272. | + | 74635.3i | 0.802180 | + | 0.597082i | ||||
\(51\) | 70244.2i | 0.529541i | ||||||||
\(52\) | 19752.3 | + | 2649.46i | 0.140478 | + | 0.0188429i | ||||
\(53\) | − | 128136.i | − | 0.860681i | −0.902667 | − | 0.430341i | \(-0.858393\pi\) | ||
0.902667 | − | 0.430341i | \(-0.141607\pi\) | |||||||
\(54\) | 19953.0 | + | 22808.1i | 0.126715 | + | 0.144846i | ||||
\(55\) | −105311. | + | 11216.1i | −0.632976 | + | 0.0674145i | ||||
\(56\) | 162167. | − | 107500.i | 0.923416 | − | 0.612133i | ||||
\(57\) | − | 86689.1i | − | 0.468101i | ||||||
\(58\) | 99466.2 | + | 113699.i | 0.509790 | + | 0.582737i | ||||
\(59\) | − | 114967.i | − | 0.559781i | −0.960032 | − | 0.279891i | \(-0.909702\pi\) | ||
0.960032 | − | 0.279891i | \(-0.0902982\pi\) | |||||||
\(60\) | −124661. | − | 3395.91i | −0.577136 | − | 0.0157218i | ||||
\(61\) | 254794. | 1.12253 | 0.561266 | − | 0.827635i | \(-0.310314\pi\) | ||||
0.561266 | + | 0.827635i | \(0.310314\pi\) | |||||||
\(62\) | −2771.78 | + | 2424.81i | −0.0116301 | + | 0.0101743i | ||||
\(63\) | 92340.9 | 0.369294 | ||||||||
\(64\) | 102087. | − | 241449.i | 0.389433 | − | 0.921055i | ||||
\(65\) | −38705.3 | + | 4122.27i | −0.140939 | + | 0.0150106i | ||||
\(66\) | 79523.7 | − | 69569.0i | 0.276608 | − | 0.241983i | ||||
\(67\) | −523410. | −1.74028 | −0.870138 | − | 0.492809i | \(-0.835970\pi\) | ||||
−0.870138 | + | 0.492809i | \(0.835970\pi\) | |||||||
\(68\) | 285835. | + | 38340.3i | 0.909051 | + | 0.121935i | ||||
\(69\) | 241463. | 0.735026 | ||||||||
\(70\) | −257901. | + | 279088.i | −0.751897 | + | 0.813667i | ||||
\(71\) | 165291.i | 0.461822i | 0.972975 | + | 0.230911i | \(0.0741706\pi\) | ||||
−0.972975 | + | 0.230911i | \(0.925829\pi\) | |||||||
\(72\) | 103700. | − | 68742.9i | 0.277832 | − | 0.184175i | ||||
\(73\) | 508290.i | 1.30660i | 0.757098 | + | 0.653301i | \(0.226616\pi\) | ||||
−0.757098 | + | 0.653301i | \(0.773384\pi\) | |||||||
\(74\) | −593533. | + | 519235.i | −1.46470 | + | 1.28135i | ||||
\(75\) | 238106. | − | 51300.4i | 0.564399 | − | 0.121601i | ||||
\(76\) | −352752. | − | 47316.1i | −0.803578 | − | 0.107787i | ||||
\(77\) | − | 321960.i | − | 0.705229i | ||||||
\(78\) | 29227.5 | − | 25568.9i | 0.0615897 | − | 0.0538800i | ||||
\(79\) | − | 101497.i | − | 0.205859i | −0.994689 | − | 0.102930i | \(-0.967178\pi\) | ||
0.994689 | − | 0.102930i | \(-0.0328216\pi\) | |||||||
\(80\) | −81860.5 | + | 505414.i | −0.159884 | + | 0.987136i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −366647. | − | 419110.i | −0.664977 | − | 0.760128i | ||||
\(83\) | −38887.4 | −0.0680103 | −0.0340051 | − | 0.999422i | \(-0.510826\pi\) | ||||
−0.0340051 | + | 0.999422i | \(0.510826\pi\) | |||||||
\(84\) | 50401.0 | − | 375750.i | 0.0850356 | − | 0.633959i | ||||
\(85\) | −560103. | + | 59653.3i | −0.912034 | + | 0.0971354i | ||||
\(86\) | 768430. | + | 878385.i | 1.20812 | + | 1.38099i | ||||
\(87\) | 294361. | 0.447015 | ||||||||
\(88\) | −239682. | − | 361566.i | −0.351713 | − | 0.530567i | ||||
\(89\) | −1.05953e6 | −1.50295 | −0.751475 | − | 0.659761i | \(-0.770657\pi\) | ||||
−0.751475 | + | 0.659761i | \(0.770657\pi\) | |||||||
\(90\) | −164919. | + | 178468.i | −0.226227 | + | 0.244811i | ||||
\(91\) | − | 118331.i | − | 0.157027i | ||||||
\(92\) | 131794. | − | 982550.i | 0.169251 | − | 1.26180i | ||||
\(93\) | 7176.00i | 0.00892141i | ||||||||
\(94\) | −177334. | − | 202708.i | −0.213505 | − | 0.244055i | ||||
\(95\) | 691229. | − | 73618.7i | 0.806215 | − | 0.0858652i | ||||
\(96\) | −223125. | − | 459494.i | −0.252194 | − | 0.519357i | ||||
\(97\) | − | 631894.i | − | 0.692355i | −0.938169 | − | 0.346178i | \(-0.887479\pi\) | ||
0.938169 | − | 0.346178i | \(-0.112521\pi\) | |||||||
\(98\) | −140924. | − | 161088.i | −0.149729 | − | 0.171154i | ||||
\(99\) | − | 205883.i | − | 0.212185i | ||||||
\(100\) | −78788.0 | − | 996891.i | −0.0787880 | − | 0.996891i | ||||
\(101\) | −1.49061e6 | −1.44677 | −0.723385 | − | 0.690445i | \(-0.757415\pi\) | ||||
−0.723385 | + | 0.690445i | \(0.757415\pi\) | |||||||
\(102\) | 422950. | − | 370006.i | 0.398556 | − | 0.348665i | ||||
\(103\) | 498876. | 0.456543 | 0.228271 | − | 0.973598i | \(-0.426693\pi\) | ||||
0.228271 | + | 0.973598i | \(0.426693\pi\) | |||||||
\(104\) | −88091.0 | − | 132887.i | −0.0783126 | − | 0.118136i | ||||
\(105\) | 78418.4 | + | 736295.i | 0.0677408 | + | 0.636039i | ||||
\(106\) | −771523. | + | 674945.i | −0.647786 | + | 0.566697i | ||||
\(107\) | 1.17394e6 | 0.958286 | 0.479143 | − | 0.877737i | \(-0.340948\pi\) | ||||
0.479143 | + | 0.877737i | \(0.340948\pi\) | |||||||
\(108\) | 32229.8 | − | 240280.i | 0.0255850 | − | 0.190742i | ||||
\(109\) | 1.24446e6 | 0.960953 | 0.480476 | − | 0.877008i | \(-0.340464\pi\) | ||||
0.480476 | + | 0.877008i | \(0.340464\pi\) | |||||||
\(110\) | 622253. | + | 575015.i | 0.467508 | + | 0.432017i | ||||
\(111\) | 1.53663e6i | 1.12357i | ||||||||
\(112\) | −1.50148e6 | − | 410179.i | −1.06872 | − | 0.291957i | ||||
\(113\) | 2.28429e6i | 1.58313i | 0.611087 | + | 0.791564i | \(0.290733\pi\) | ||||
−0.611087 | + | 0.791564i | \(0.709267\pi\) | |||||||
\(114\) | −521967. | + | 456628.i | −0.352313 | + | 0.308211i | ||||
\(115\) | 205057. | + | 1.92534e6i | 0.134828 | + | 1.26594i | ||||
\(116\) | 160666. | − | 1.19780e6i | 0.102932 | − | 0.767381i | ||||
\(117\) | − | 75668.7i | − | 0.0472453i | ||||||
\(118\) | −692235. | + | 605582.i | −0.421316 | + | 0.368576i | ||||
\(119\) | − | 1.71236e6i | − | 1.01614i | ||||||
\(120\) | 636198. | + | 768492.i | 0.368170 | + | 0.444729i | ||||
\(121\) | 1.05372e6 | 0.594797 | ||||||||
\(122\) | −1.34211e6 | − | 1.53415e6i | −0.739108 | − | 0.844867i | ||||
\(123\) | −1.08506e6 | −0.583092 | ||||||||
\(124\) | 29200.3 | + | 3916.76i | 0.0153152 | + | 0.00205429i | ||||
\(125\) | 611258. | + | 1.85501e6i | 0.312964 | + | 0.949765i | ||||
\(126\) | −486399. | − | 555998.i | −0.243154 | − | 0.277947i | ||||
\(127\) | 1.33841e6 | 0.653396 | 0.326698 | − | 0.945129i | \(-0.394064\pi\) | ||||
0.326698 | + | 0.945129i | \(0.394064\pi\) | |||||||
\(128\) | −1.99154e6 | + | 657132.i | −0.949639 | + | 0.313345i | ||||
\(129\) | 2.27410e6 | 1.05935 | ||||||||
\(130\) | 228698. | + | 211337.i | 0.104096 | + | 0.0961932i | ||||
\(131\) | − | 3.50060e6i | − | 1.55714i | −0.627556 | − | 0.778572i | \(-0.715945\pi\) | ||
0.627556 | − | 0.778572i | \(-0.284055\pi\) | |||||||
\(132\) | −837771. | − | 112374.i | −0.364253 | − | 0.0488589i | ||||
\(133\) | 2.11324e6i | 0.898243i | ||||||||
\(134\) | 2.75703e6 | + | 3.15153e6i | 1.14585 | + | 1.30981i | ||||
\(135\) | 50146.0 | + | 470837.i | 0.0203815 | + | 0.191368i | ||||
\(136\) | −1.27476e6 | − | 1.92301e6i | −0.506772 | − | 0.764476i | ||||
\(137\) | − | 3.77105e6i | − | 1.46656i | −0.679926 | − | 0.733281i | \(-0.737988\pi\) | ||
0.679926 | − | 0.733281i | \(-0.262012\pi\) | |||||||
\(138\) | −1.27189e6 | − | 1.45388e6i | −0.483962 | − | 0.553212i | ||||
\(139\) | 593087.i | 0.220838i | 0.993885 | + | 0.110419i | \(0.0352193\pi\) | ||||
−0.993885 | + | 0.110419i | \(0.964781\pi\) | |||||||
\(140\) | 3.03890e6 | + | 82783.0i | 1.10747 | + | 0.0301687i | ||||
\(141\) | −524802. | −0.187214 | ||||||||
\(142\) | 995242. | − | 870659.i | 0.347587 | − | 0.304077i | ||||
\(143\) | −263830. | −0.0902227 | ||||||||
\(144\) | −960145. | − | 262296.i | −0.321551 | − | 0.0878424i | ||||
\(145\) | 249979. | + | 2.34713e6i | 0.0819974 | + | 0.769899i | ||||
\(146\) | 3.06049e6 | − | 2.67738e6i | 0.983405 | − | 0.860304i | ||||
\(147\) | −417050. | −0.131291 | ||||||||
\(148\) | 6.25278e6 | + | 838713.i | 1.92880 | + | 0.258719i | ||||
\(149\) | 1.48276e6 | 0.448240 | 0.224120 | − | 0.974562i | \(-0.428049\pi\) | ||||
0.224120 | + | 0.974562i | \(0.428049\pi\) | |||||||
\(150\) | −1.56309e6 | − | 1.16345e6i | −0.463139 | − | 0.344726i | ||||
\(151\) | 1.46213e6i | 0.424672i | 0.977197 | + | 0.212336i | \(0.0681072\pi\) | ||||
−0.977197 | + | 0.212336i | \(0.931893\pi\) | |||||||
\(152\) | 1.57320e6 | + | 2.37320e6i | 0.447973 | + | 0.675778i | ||||
\(153\) | − | 1.09500e6i | − | 0.305731i | ||||||
\(154\) | −1.93857e6 | + | 1.69590e6i | −0.530786 | + | 0.464343i | ||||
\(155\) | −57218.9 | + | 6094.05i | −0.0153654 | + | 0.00163648i | ||||
\(156\) | −307908. | − | 41301.0i | −0.0811049 | − | 0.0108789i | ||||
\(157\) | − | 4.68323e6i | − | 1.21017i | −0.796161 | − | 0.605085i | \(-0.793139\pi\) | ||
0.796161 | − | 0.605085i | \(-0.206861\pi\) | |||||||
\(158\) | −611126. | + | 534626.i | −0.154939 | + | 0.135544i | ||||
\(159\) | 1.99744e6i | 0.496915i | ||||||||
\(160\) | 3.47436e6 | − | 2.16934e6i | 0.848233 | − | 0.529623i | ||||
\(161\) | −5.88619e6 | −1.41045 | ||||||||
\(162\) | −311036. | − | 355543.i | −0.0731587 | − | 0.0836270i | ||||
\(163\) | 6.78005e6 | 1.56556 | 0.782781 | − | 0.622298i | \(-0.213801\pi\) | ||||
0.782781 | + | 0.622298i | \(0.213801\pi\) | |||||||
\(164\) | −592239. | + | 4.41527e6i | −0.134266 | + | 1.00098i | ||||
\(165\) | 1.64164e6 | − | 174841.i | 0.365449 | − | 0.0389218i | ||||
\(166\) | 204837. | + | 234147.i | 0.0447799 | + | 0.0511875i | ||||
\(167\) | −6.63886e6 | −1.42542 | −0.712712 | − | 0.701457i | \(-0.752533\pi\) | ||||
−0.712712 | + | 0.701457i | \(0.752533\pi\) | |||||||
\(168\) | −2.52793e6 | + | 1.67576e6i | −0.533134 | + | 0.353415i | ||||
\(169\) | 4.72984e6 | 0.979911 | ||||||||
\(170\) | 3.30948e6 | + | 3.05824e6i | 0.673618 | + | 0.622480i | ||||
\(171\) | 1.35135e6i | 0.270258i | ||||||||
\(172\) | 1.24123e6 | − | 9.25366e6i | 0.243932 | − | 1.81856i | ||||
\(173\) | − | 8.64108e6i | − | 1.66890i | −0.551085 | − | 0.834449i | \(-0.685786\pi\) | ||
0.551085 | − | 0.834449i | \(-0.314214\pi\) | |||||||
\(174\) | −1.55053e6 | − | 1.77239e6i | −0.294328 | − | 0.336443i | ||||
\(175\) | −5.80437e6 | + | 1.25056e6i | −1.08303 | + | 0.233341i | ||||
\(176\) | −914534. | + | 3.34769e6i | −0.167750 | + | 0.614054i | ||||
\(177\) | 1.79216e6i | 0.323190i | ||||||||
\(178\) | 5.58102e6 | + | 6.37961e6i | 0.989586 | + | 1.13119i | ||||
\(179\) | − | 9.09605e6i | − | 1.58596i | −0.609244 | − | 0.792982i | \(-0.708527\pi\) | ||
0.609244 | − | 0.792982i | \(-0.291473\pi\) | |||||||
\(180\) | 1.94328e6 | + | 52937.0i | 0.333210 | + | 0.00907700i | ||||
\(181\) | −3.61021e6 | −0.608831 | −0.304416 | − | 0.952539i | \(-0.598461\pi\) | ||||
−0.304416 | + | 0.952539i | \(0.598461\pi\) | |||||||
\(182\) | −712487. | + | 623299.i | −0.118185 | + | 0.103391i | ||||
\(183\) | −3.97184e6 | −0.648095 | ||||||||
\(184\) | −6.61029e6 | + | 4.38196e6i | −1.06113 | + | 0.703421i | ||||
\(185\) | −1.22525e7 | + | 1.30495e6i | −1.93513 | + | 0.206100i | ||||
\(186\) | 43207.7 | − | 37799.0i | 0.00671464 | − | 0.00587411i | ||||
\(187\) | −3.81787e6 | −0.583844 | ||||||||
\(188\) | −286444. | + | 2.13550e6i | −0.0431089 | + | 0.321386i | ||||
\(189\) | −1.43945e6 | −0.213212 | ||||||||
\(190\) | −4.08427e6 | − | 3.77421e6i | −0.595461 | − | 0.550256i | ||||
\(191\) | − | 770722.i | − | 0.110611i | −0.998469 | − | 0.0553054i | \(-0.982387\pi\) | ||
0.998469 | − | 0.0553054i | \(-0.0176133\pi\) | |||||||
\(192\) | −1.59139e6 | + | 3.76382e6i | −0.224839 | + | 0.531771i | ||||
\(193\) | − | 856832.i | − | 0.119186i | −0.998223 | − | 0.0595928i | \(-0.981020\pi\) | ||
0.998223 | − | 0.0595928i | \(-0.0189802\pi\) | |||||||
\(194\) | −3.80473e6 | + | 3.32846e6i | −0.521096 | + | 0.455866i | ||||
\(195\) | 603356. | − | 64259.9i | 0.0813710 | − | 0.00866635i | ||||
\(196\) | −227632. | + | 1.69704e6i | −0.0302319 | + | 0.225385i | ||||
\(197\) | 6.40644e6i | 0.837950i | 0.907998 | + | 0.418975i | \(0.137610\pi\) | ||||
−0.907998 | + | 0.418975i | \(0.862390\pi\) | |||||||
\(198\) | −1.23965e6 | + | 1.08447e6i | −0.159700 | + | 0.139709i | ||||
\(199\) | − | 7.76623e6i | − | 0.985487i | −0.870175 | − | 0.492743i | \(-0.835994\pi\) | ||
0.870175 | − | 0.492743i | \(-0.164006\pi\) | |||||||
\(200\) | −5.58742e6 | + | 5.72545e6i | −0.698427 | + | 0.715681i | ||||
\(201\) | 8.15916e6 | 1.00475 | ||||||||
\(202\) | 7.85168e6 | + | 8.97517e6i | 0.952595 | + | 1.08890i | ||||
\(203\) | −7.17571e6 | −0.857782 | ||||||||
\(204\) | −4.45572e6 | − | 597665.i | −0.524841 | − | 0.0703992i | ||||
\(205\) | −921460. | − | 8.65187e6i | −0.106958 | − | 1.00427i | ||||
\(206\) | −2.62780e6 | − | 3.00381e6i | −0.300601 | − | 0.343614i | ||||
\(207\) | −3.76403e6 | −0.424367 | ||||||||
\(208\) | −336121. | + | 1.23038e6i | −0.0373513 | + | 0.136726i | ||||
\(209\) | 4.71168e6 | 0.516103 | ||||||||
\(210\) | 4.02027e6 | − | 4.35055e6i | 0.434108 | − | 0.469771i | ||||
\(211\) | 1.37248e7i | 1.46103i | 0.682898 | + | 0.730514i | \(0.260719\pi\) | ||||
−0.682898 | + | 0.730514i | \(0.739281\pi\) | |||||||
\(212\) | 8.12789e6 | + | 1.09023e6i | 0.853041 | + | 0.114422i | ||||
\(213\) | − | 2.57663e6i | − | 0.266633i | ||||||
\(214\) | −6.18365e6 | − | 7.06847e6i | −0.630963 | − | 0.721247i | ||||
\(215\) | 1.93122e6 | + | 1.81329e7i | 0.194320 | + | 1.82453i | ||||
\(216\) | −1.61653e6 | + | 1.07160e6i | −0.160406 | + | 0.106333i | ||||
\(217\) | − | 174931.i | − | 0.0171194i | ||||||
\(218\) | −6.55511e6 | − | 7.49309e6i | −0.632719 | − | 0.723255i | ||||
\(219\) | − | 7.92346e6i | − | 0.754367i | ||||||
\(220\) | 184573. | − | 6.77553e6i | 0.0173340 | − | 0.636319i | ||||
\(221\) | −1.40319e6 | −0.129999 | ||||||||
\(222\) | 9.25226e6 | − | 8.09408e6i | 0.845647 | − | 0.739790i | ||||
\(223\) | 6.24824e6 | 0.563434 | 0.281717 | − | 0.959498i | \(-0.409096\pi\) | ||||
0.281717 | + | 0.959498i | \(0.409096\pi\) | |||||||
\(224\) | 5.43917e6 | + | 1.12012e7i | 0.483937 | + | 0.996599i | ||||
\(225\) | −3.71170e6 | + | 799695.i | −0.325856 | + | 0.0702064i | ||||
\(226\) | 1.37540e7 | − | 1.20323e7i | 1.19153 | − | 1.04238i | ||||
\(227\) | 9.00061e6 | 0.769475 | 0.384738 | − | 0.923026i | \(-0.374292\pi\) | ||||
0.384738 | + | 0.923026i | \(0.374292\pi\) | |||||||
\(228\) | 5.49885e6 | + | 737585.i | 0.463946 | + | 0.0622311i | ||||
\(229\) | 7.98446e6 | 0.664873 | 0.332437 | − | 0.943126i | \(-0.392129\pi\) | ||||
0.332437 | + | 0.943126i | \(0.392129\pi\) | |||||||
\(230\) | 1.05126e7 | − | 1.13763e7i | 0.864028 | − | 0.935010i | ||||
\(231\) | 5.01886e6i | 0.407164i | ||||||||
\(232\) | −8.05844e6 | + | 5.34194e6i | −0.645337 | + | 0.427794i | ||||
\(233\) | − | 5.18086e6i | − | 0.409575i | −0.978806 | − | 0.204788i | \(-0.934350\pi\) | ||
0.978806 | − | 0.204788i | \(-0.0656504\pi\) | |||||||
\(234\) | −455612. | + | 398579.i | −0.0355588 | + | 0.0311076i | ||||
\(235\) | −445676. | − | 4.18459e6i | −0.0343412 | − | 0.322440i | ||||
\(236\) | 7.29260e6 | + | 978188.i | 0.554812 | + | 0.0744194i | ||||
\(237\) | 1.58218e6i | 0.118853i | ||||||||
\(238\) | −1.03104e7 | + | 9.01973e6i | −0.764792 | + | 0.669056i | ||||
\(239\) | − | 2.14971e6i | − | 0.157466i | −0.996896 | − | 0.0787330i | \(-0.974913\pi\) | ||
0.996896 | − | 0.0787330i | \(-0.0250874\pi\) | |||||||
\(240\) | 1.27608e6 | − | 7.87862e6i | 0.0923089 | − | 0.569923i | ||||
\(241\) | 9.40539e6 | 0.671933 | 0.335966 | − | 0.941874i | \(-0.390937\pi\) | ||||
0.335966 | + | 0.941874i | \(0.390937\pi\) | |||||||
\(242\) | −5.55039e6 | − | 6.34460e6i | −0.391631 | − | 0.447670i | ||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | −2.16789e6 | + | 1.61620e7i | −0.149234 | + | 1.11257i | ||||
\(245\) | −354170. | − | 3.32542e6i | −0.0240832 | − | 0.226125i | ||||
\(246\) | 5.71546e6 | + | 6.53329e6i | 0.383924 | + | 0.438860i | ||||
\(247\) | 1.73169e6 | 0.114916 | ||||||||
\(248\) | −130227. | − | 196450.i | −0.00853780 | − | 0.0128795i | ||||
\(249\) | 606195. | 0.0392658 | ||||||||
\(250\) | 7.94953e6 | − | 1.34516e7i | 0.508770 | − | 0.860903i | ||||
\(251\) | − | 1.65833e7i | − | 1.04870i | −0.851504 | − | 0.524349i | \(-0.824309\pi\) | ||
0.851504 | − | 0.524349i | \(-0.175691\pi\) | |||||||
\(252\) | −785673. | + | 5.85736e6i | −0.0490953 | + | 0.366016i | ||||
\(253\) | 1.31238e7i | 0.810400i | ||||||||
\(254\) | −7.04995e6 | − | 8.05873e6i | −0.430215 | − | 0.491774i | ||||
\(255\) | 8.73114e6 | − | 929902.i | 0.526563 | − | 0.0560811i | ||||
\(256\) | 1.44470e7 | + | 8.52994e6i | 0.861107 | + | 0.508424i | ||||
\(257\) | 1.55714e7i | 0.917335i | 0.888608 | + | 0.458667i | \(0.151673\pi\) | ||||
−0.888608 | + | 0.458667i | \(0.848327\pi\) | |||||||
\(258\) | −1.19786e7 | − | 1.36927e7i | −0.697507 | − | 0.797313i | ||||
\(259\) | − | 3.74588e7i | − | 2.15603i | ||||||
\(260\) | 67836.5 | − | 2.49023e6i | 0.00385961 | − | 0.141683i | ||||
\(261\) | −4.58863e6 | −0.258084 | ||||||||
\(262\) | −2.10776e7 | + | 1.84392e7i | −1.17197 | + | 1.02527i | ||||
\(263\) | 6.62596e6 | 0.364235 | 0.182117 | − | 0.983277i | \(-0.441705\pi\) | ||||
0.182117 | + | 0.983277i | \(0.441705\pi\) | |||||||
\(264\) | 3.73628e6 | + | 5.63626e6i | 0.203061 | + | 0.306323i | ||||
\(265\) | −1.59269e7 | + | 1.69628e6i | −0.855841 | + | 0.0911506i | ||||
\(266\) | 1.27241e7 | − | 1.11313e7i | 0.676057 | − | 0.591429i | ||||
\(267\) | 1.65165e7 | 0.867729 | ||||||||
\(268\) | 4.45339e6 | − | 3.32009e7i | 0.231359 | − | 1.72483i | ||||
\(269\) | 3.17423e7 | 1.63073 | 0.815363 | − | 0.578950i | \(-0.196538\pi\) | ||||
0.815363 | + | 0.578950i | \(0.196538\pi\) | |||||||
\(270\) | 2.57083e6 | − | 2.78203e6i | 0.130612 | − | 0.141342i | ||||
\(271\) | 3.46140e7i | 1.73918i | 0.493778 | + | 0.869588i | \(0.335616\pi\) | ||||
−0.493778 | + | 0.869588i | \(0.664384\pi\) | |||||||
\(272\) | −4.86399e6 | + | 1.78048e7i | −0.241705 | + | 0.884771i | ||||
\(273\) | 1.84459e6i | 0.0906594i | ||||||||
\(274\) | −2.27060e7 | + | 1.98637e7i | −1.10380 | + | 0.965626i | ||||
\(275\) | 2.78825e6 | + | 1.29414e7i | 0.134071 | + | 0.622276i | ||||
\(276\) | −2.05446e6 | + | 1.53164e7i | −0.0977171 | + | 0.728501i | ||||
\(277\) | 2.60617e7i | 1.22620i | 0.790004 | + | 0.613102i | \(0.210079\pi\) | ||||
−0.790004 | + | 0.613102i | \(0.789921\pi\) | |||||||
\(278\) | 3.57107e6 | − | 3.12405e6i | 0.166212 | − | 0.145406i | ||||
\(279\) | − | 111863.i | − | 0.00515078i | ||||||
\(280\) | −1.55087e7 | − | 1.87337e7i | −0.706485 | − | 0.853395i | ||||
\(281\) | 1.09611e7 | 0.494008 | 0.247004 | − | 0.969014i | \(-0.420554\pi\) | ||||
0.247004 | + | 0.969014i | \(0.420554\pi\) | |||||||
\(282\) | 2.76436e6 | + | 3.15991e6i | 0.123267 | + | 0.140905i | ||||
\(283\) | −1.99923e7 | −0.882071 | −0.441035 | − | 0.897490i | \(-0.645389\pi\) | ||||
−0.441035 | + | 0.897490i | \(0.645389\pi\) | |||||||
\(284\) | −1.04847e7 | − | 1.40636e6i | −0.457722 | − | 0.0613963i | ||||
\(285\) | −1.07752e7 | + | 1.14760e6i | −0.465469 | + | 0.0495743i | ||||
\(286\) | 1.38971e6 | + | 1.58856e6i | 0.0594052 | + | 0.0679055i | ||||
\(287\) | 2.64507e7 | 1.11890 | ||||||||
\(288\) | 3.47817e6 | + | 7.16280e6i | 0.145604 | + | 0.299851i | ||||
\(289\) | 3.83204e6 | 0.158758 | ||||||||
\(290\) | 1.28157e7 | − | 1.38685e7i | 0.525470 | − | 0.568638i | ||||
\(291\) | 9.85025e6i | 0.399731i | ||||||||
\(292\) | −3.22418e7 | − | 4.32474e6i | −1.29500 | − | 0.173705i | ||||
\(293\) | 2.67017e7i | 1.06154i | 0.847516 | + | 0.530770i | \(0.178097\pi\) | ||||
−0.847516 | + | 0.530770i | \(0.821903\pi\) | |||||||
\(294\) | 2.19678e6 | + | 2.51112e6i | 0.0864460 | + | 0.0988156i | ||||
\(295\) | −1.42901e7 | + | 1.52195e6i | −0.556633 | + | 0.0592837i | ||||
\(296\) | −2.78861e7 | − | 4.20668e7i | −1.07526 | − | 1.62205i | ||||
\(297\) | 3.20940e6i | 0.122505i | ||||||||
\(298\) | −7.81031e6 | − | 8.92789e6i | −0.295134 | − | 0.337365i | ||||
\(299\) | 4.82344e6i | 0.180444i | ||||||||
\(300\) | 1.22818e6 | + | 1.55400e7i | 0.0454883 | + | 0.575556i | ||||
\(301\) | −5.54362e7 | −2.03280 | ||||||||
\(302\) | 8.80368e6 | − | 7.70165e6i | 0.319627 | − | 0.279616i | ||||
\(303\) | 2.32363e7 | 0.835293 | ||||||||
\(304\) | 6.00270e6 | − | 2.19731e7i | 0.213661 | − | 0.782116i | ||||
\(305\) | −3.37299e6 | − | 3.16701e7i | −0.118882 | − | 1.11622i | ||||
\(306\) | −6.59314e6 | + | 5.76782e6i | −0.230106 | + | 0.201302i | ||||
\(307\) | 2.87808e6 | 0.0994689 | 0.0497344 | − | 0.998762i | \(-0.484163\pi\) | ||||
0.0497344 | + | 0.998762i | \(0.484163\pi\) | |||||||
\(308\) | 2.04225e7 | + | 2.73936e6i | 0.698969 | + | 0.0937557i | ||||
\(309\) | −7.77671e6 | −0.263585 | ||||||||
\(310\) | 338090. | + | 312424.i | 0.0113487 | + | 0.0104872i | ||||
\(311\) | 3.85699e6i | 0.128223i | 0.997943 | + | 0.0641117i | \(0.0204214\pi\) | ||||
−0.997943 | + | 0.0641117i | \(0.979579\pi\) | |||||||
\(312\) | 1.37320e6 | + | 2.07151e6i | 0.0452138 | + | 0.0682060i | ||||
\(313\) | − | 1.83655e7i | − | 0.598922i | −0.954109 | − | 0.299461i | \(-0.903193\pi\) | ||
0.954109 | − | 0.299461i | \(-0.0968068\pi\) | |||||||
\(314\) | −2.81984e7 | + | 2.46686e7i | −0.910826 | + | 0.796811i | ||||
\(315\) | −1.22242e6 | − | 1.14777e7i | −0.0391102 | − | 0.367217i | ||||
\(316\) | 6.43812e6 | + | 863574.i | 0.204032 | + | 0.0273677i | ||||
\(317\) | 1.47905e7i | 0.464305i | 0.972679 | + | 0.232153i | \(0.0745769\pi\) | ||||
−0.972679 | + | 0.232153i | \(0.925423\pi\) | |||||||
\(318\) | 1.20269e7 | − | 1.05214e7i | 0.373999 | − | 0.327183i | ||||
\(319\) | 1.59989e7i | 0.492855i | ||||||||
\(320\) | −3.13628e7 | − | 9.49283e6i | −0.957118 | − | 0.289698i | ||||
\(321\) | −1.82999e7 | −0.553267 | ||||||||
\(322\) | 3.10051e7 | + | 3.54416e7i | 0.928679 | + | 1.06156i | ||||
\(323\) | 2.50593e7 | 0.743637 | ||||||||
\(324\) | −502412. | + | 3.74559e6i | −0.0147715 | + | 0.110125i | ||||
\(325\) | 1.02477e6 | + | 4.75638e6i | 0.0298523 | + | 0.138556i | ||||
\(326\) | −3.57134e7 | − | 4.08237e7i | −1.03081 | − | 1.17831i | ||||
\(327\) | −1.93992e7 | −0.554806 | ||||||||
\(328\) | 2.97046e7 | − | 1.96912e7i | 0.841786 | − | 0.558020i | ||||
\(329\) | 1.27932e7 | 0.359246 | ||||||||
\(330\) | −9.69997e6 | − | 8.96359e6i | −0.269916 | − | 0.249425i | ||||
\(331\) | − | 5.72550e7i | − | 1.57881i | −0.613873 | − | 0.789404i | \(-0.710390\pi\) | ||
0.613873 | − | 0.789404i | \(-0.289610\pi\) | |||||||
\(332\) | 330869. | − | 2.46670e6i | 0.00904154 | − | 0.0674066i | ||||
\(333\) | − | 2.39537e7i | − | 0.648693i | ||||||
\(334\) | 3.49697e7 | + | 3.99735e7i | 0.938540 | + | 1.07284i | ||||
\(335\) | 6.92898e6 | + | 6.50584e7i | 0.184304 | + | 1.73049i | ||||
\(336\) | 2.34057e7 | + | 6.39406e6i | 0.617026 | + | 0.168562i | ||||
\(337\) | − | 1.73651e7i | − | 0.453719i | −0.973928 | − | 0.226859i | \(-0.927154\pi\) | ||
0.973928 | − | 0.226859i | \(-0.0728458\pi\) | |||||||
\(338\) | −2.49141e7 | − | 2.84791e7i | −0.645201 | − | 0.737523i | ||||
\(339\) | − | 3.56085e7i | − | 0.914019i | ||||||
\(340\) | 981659. | − | 3.60360e7i | 0.0249761 | − | 0.916852i | ||||
\(341\) | −390026. | −0.00983626 | ||||||||
\(342\) | 8.13667e6 | − | 7.11813e6i | 0.203408 | − | 0.177946i | ||||
\(343\) | −3.45405e7 | −0.855946 | ||||||||
\(344\) | −6.22557e7 | + | 4.12693e7i | −1.52934 | + | 1.01380i | ||||
\(345\) | −3.19652e6 | − | 3.00131e7i | −0.0778430 | − | 0.730892i | ||||
\(346\) | −5.20292e7 | + | 4.55163e7i | −1.25608 | + | 1.09885i | ||||
\(347\) | −6.56313e7 | −1.57081 | −0.785403 | − | 0.618985i | \(-0.787544\pi\) | ||||
−0.785403 | + | 0.618985i | \(0.787544\pi\) | |||||||
\(348\) | −2.50454e6 | + | 1.86719e7i | −0.0594279 | + | 0.443047i | ||||
\(349\) | 1.61690e7 | 0.380370 | 0.190185 | − | 0.981748i | \(-0.439091\pi\) | ||||
0.190185 | + | 0.981748i | \(0.439091\pi\) | |||||||
\(350\) | 3.81039e7 | + | 2.83617e7i | 0.888721 | + | 0.661497i | ||||
\(351\) | 1.17956e6i | 0.0272771i | ||||||||
\(352\) | 2.49742e7 | − | 1.21272e7i | 0.572615 | − | 0.278055i | ||||
\(353\) | − | 2.08055e7i | − | 0.472993i | −0.971632 | − | 0.236497i | \(-0.924001\pi\) | ||
0.971632 | − | 0.236497i | \(-0.0759992\pi\) | |||||||
\(354\) | 1.07909e7 | − | 9.44009e6i | 0.243247 | − | 0.212797i | ||||
\(355\) | 2.05452e7 | − | 2.18815e6i | 0.459225 | − | 0.0489093i | ||||
\(356\) | 9.01493e6 | − | 6.72082e7i | 0.199808 | − | 1.48961i | ||||
\(357\) | 2.66930e7i | 0.586669i | ||||||||
\(358\) | −5.47686e7 | + | 4.79128e7i | −1.19367 | + | 1.04424i | ||||
\(359\) | 6.24674e7i | 1.35011i | 0.737766 | + | 0.675057i | \(0.235881\pi\) | ||||
−0.737766 | + | 0.675057i | \(0.764119\pi\) | |||||||
\(360\) | −9.91734e6 | − | 1.19796e7i | −0.212563 | − | 0.256765i | ||||
\(361\) | 1.61200e7 | 0.342644 | ||||||||
\(362\) | 1.90165e7 | + | 2.17376e7i | 0.400872 | + | 0.458233i | ||||
\(363\) | −1.64259e7 | −0.343406 | ||||||||
\(364\) | 7.50594e6 | + | 1.00681e6i | 0.155633 | + | 0.0208757i | ||||
\(365\) | 6.31790e7 | − | 6.72882e6i | 1.29925 | − | 0.138376i | ||||
\(366\) | 2.09214e7 | + | 2.39150e7i | 0.426724 | + | 0.487784i | ||||
\(367\) | 4.84042e7 | 0.979230 | 0.489615 | − | 0.871939i | \(-0.337137\pi\) | ||||
0.489615 | + | 0.871939i | \(0.337137\pi\) | |||||||
\(368\) | 6.12037e7 | + | 1.67198e7i | 1.22810 | + | 0.335497i | ||||
\(369\) | 1.69144e7 | 0.336648 | ||||||||
\(370\) | 7.23967e7 | + | 6.69006e7i | 1.42927 | + | 1.32076i | ||||
\(371\) | − | 4.86920e7i | − | 0.953534i | ||||||
\(372\) | −455187. | − | 61056.2i | −0.00884222 | − | 0.00118604i | ||||
\(373\) | 591779.i | 0.0114034i | 0.999984 | + | 0.00570168i | \(0.00181491\pi\) | ||||
−0.999984 | + | 0.00570168i | \(0.998185\pi\) | |||||||
\(374\) | 2.01104e7 | + | 2.29880e7i | 0.384419 | + | 0.439426i | ||||
\(375\) | −9.52857e6 | − | 2.89167e7i | −0.180690 | − | 0.548347i | ||||
\(376\) | 1.43670e7 | − | 9.52388e6i | 0.270273 | − | 0.179164i | ||||
\(377\) | 5.88013e6i | 0.109739i | ||||||||
\(378\) | 7.58221e6 | + | 8.66715e6i | 0.140385 | + | 0.160473i | ||||
\(379\) | − | 8.70799e7i | − | 1.59956i | −0.600294 | − | 0.799779i | \(-0.704950\pi\) | ||
0.600294 | − | 0.799779i | \(-0.295050\pi\) | |||||||
\(380\) | −1.21148e6 | + | 4.44723e7i | −0.0220782 | + | 0.810474i | ||||
\(381\) | −2.08637e7 | −0.377238 | ||||||||
\(382\) | −4.64063e6 | + | 4.05972e6i | −0.0832505 | + | 0.0728293i | ||||
\(383\) | −7.55854e7 | −1.34537 | −0.672685 | − | 0.739929i | \(-0.734859\pi\) | ||||
−0.672685 | + | 0.739929i | \(0.734859\pi\) | |||||||
\(384\) | 3.10450e7 | − | 1.02437e7i | 0.548275 | − | 0.180910i | ||||
\(385\) | −4.00187e7 | + | 4.26215e6i | −0.701263 | + | 0.0746873i | ||||
\(386\) | −5.15911e6 | + | 4.51330e6i | −0.0897043 | + | 0.0784752i | ||||
\(387\) | −3.54497e7 | −0.611616 | ||||||||
\(388\) | 4.00822e7 | + | 5.37641e6i | 0.686210 | + | 0.0920443i | ||||
\(389\) | −3.84170e6 | −0.0652641 | −0.0326320 | − | 0.999467i | \(-0.510389\pi\) | ||||
−0.0326320 | + | 0.999467i | \(0.510389\pi\) | |||||||
\(390\) | −3.56505e6 | − | 3.29441e6i | −0.0600997 | − | 0.0555372i | ||||
\(391\) | 6.97998e7i | 1.16768i | ||||||||
\(392\) | 1.14172e7 | − | 7.56845e6i | 0.189540 | − | 0.125646i | ||||
\(393\) | 5.45689e7i | 0.899017i | ||||||||
\(394\) | 3.85741e7 | − | 3.37454e7i | 0.630677 | − | 0.551730i | ||||
\(395\) | −1.26157e7 | + | 1.34363e6i | −0.204701 | + | 0.0218015i | ||||
\(396\) | 1.30596e7 | + | 1.75173e6i | 0.210302 | + | 0.0282087i | ||||
\(397\) | − | 1.13247e8i | − | 1.80990i | −0.425521 | − | 0.904949i | \(-0.639909\pi\) | ||
0.425521 | − | 0.904949i | \(-0.360091\pi\) | |||||||
\(398\) | −4.67616e7 | + | 4.09080e7i | −0.741720 | + | 0.648873i | ||||
\(399\) | − | 3.29422e7i | − | 0.518601i | ||||||
\(400\) | 6.39051e7 | + | 3.48427e6i | 0.998517 | + | 0.0544418i | ||||
\(401\) | 5.79807e6 | 0.0899188 | 0.0449594 | − | 0.998989i | \(-0.485684\pi\) | ||||
0.0449594 | + | 0.998989i | \(0.485684\pi\) | |||||||
\(402\) | −4.29778e7 | − | 4.91275e7i | −0.661555 | − | 0.756217i | ||||
\(403\) | −143347. | −0.00219015 | ||||||||
\(404\) | 1.26827e7 | − | 9.45522e7i | 0.192339 | − | 1.43393i | ||||
\(405\) | −781699. | − | 7.33962e6i | −0.0117672 | − | 0.110486i | ||||
\(406\) | 3.77975e7 | + | 4.32060e7i | 0.564788 | + | 0.645604i | ||||
\(407\) | −8.35179e7 | −1.23879 | ||||||||
\(408\) | 1.98716e7 | + | 2.99767e7i | 0.292585 | + | 0.441371i | ||||
\(409\) | 384767. | 0.00562378 | 0.00281189 | − | 0.999996i | \(-0.499105\pi\) | ||||
0.00281189 | + | 0.999996i | \(0.499105\pi\) | |||||||
\(410\) | −4.72405e7 | + | 5.11214e7i | −0.685429 | + | 0.741739i | ||||
\(411\) | 5.87848e7i | 0.846720i | ||||||||
\(412\) | −4.24464e6 | + | 3.16447e7i | −0.0606945 | + | 0.452490i | ||||
\(413\) | − | 4.36880e7i | − | 0.620172i | ||||||
\(414\) | 1.98268e7 | + | 2.26638e7i | 0.279416 | + | 0.319397i | ||||
\(415\) | 514797. | + | 4.83359e6i | 0.00720264 | + | 0.0676278i | ||||
\(416\) | 9.17881e6 | − | 4.45712e6i | 0.127499 | − | 0.0619120i | ||||
\(417\) | − | 9.24532e6i | − | 0.127501i | ||||||
\(418\) | −2.48184e7 | − | 2.83697e7i | −0.339817 | − | 0.388442i | ||||
\(419\) | 1.49355e7i | 0.203039i | 0.994834 | + | 0.101519i | \(0.0323704\pi\) | ||||
−0.994834 | + | 0.101519i | \(0.967630\pi\) | |||||||
\(420\) | −4.73718e7 | − | 1.29046e6i | −0.639399 | − | 0.0174179i | ||||
\(421\) | 9.49221e7 | 1.27210 | 0.636049 | − | 0.771648i | \(-0.280567\pi\) | ||||
0.636049 | + | 0.771648i | \(0.280567\pi\) | |||||||
\(422\) | 8.26390e7 | − | 7.22944e7i | 1.09963 | − | 0.961982i | ||||
\(423\) | 8.18085e6 | 0.108088 | ||||||||
\(424\) | −3.62486e7 | − | 5.46819e7i | −0.475548 | − | 0.717375i | ||||
\(425\) | 1.48294e7 | + | 6.88294e7i | 0.193178 | + | 0.896618i | ||||
\(426\) | −1.55143e7 | + | 1.35722e7i | −0.200679 | + | 0.175559i | ||||
\(427\) | 9.68225e7 | 1.24363 | ||||||||
\(428\) | −9.98836e6 | + | 7.44653e7i | −0.127398 | + | 0.949780i | ||||
\(429\) | 4.11270e6 | 0.0520901 | ||||||||
\(430\) | 9.90080e7 | − | 1.07142e8i | 1.24527 | − | 1.34758i | ||||
\(431\) | − | 1.79875e7i | − | 0.224667i | −0.993671 | − | 0.112333i | \(-0.964168\pi\) | ||
0.993671 | − | 0.112333i | \(-0.0358325\pi\) | |||||||
\(432\) | 1.49672e7 | + | 4.08879e6i | 0.185647 | + | 0.0507159i | ||||
\(433\) | − | 2.17575e7i | − | 0.268006i | −0.990981 | − | 0.134003i | \(-0.957217\pi\) | ||
0.990981 | − | 0.134003i | \(-0.0427833\pi\) | |||||||
\(434\) | −1.05329e6 | + | 921436.i | −0.0128848 | + | 0.0112719i | ||||
\(435\) | −3.89679e6 | − | 3.65882e7i | −0.0473412 | − | 0.444501i | ||||
\(436\) | −1.05884e7 | + | 7.89386e7i | −0.127753 | + | 0.952423i | ||||
\(437\) | − | 8.61406e7i | − | 1.03220i | ||||||
\(438\) | −4.77083e7 | + | 4.17363e7i | −0.567769 | + | 0.496697i | ||||
\(439\) | 9.99238e7i | 1.18107i | 0.807012 | + | 0.590534i | \(0.201083\pi\) | ||||
−0.807012 | + | 0.590534i | \(0.798917\pi\) | |||||||
\(440\) | −4.17687e7 | + | 3.45783e7i | −0.490335 | + | 0.405924i | ||||
\(441\) | 6.50117e6 | 0.0758011 | ||||||||
\(442\) | 7.39121e6 | + | 8.44882e6i | 0.0855951 | + | 0.0978429i | ||||
\(443\) | 1.05070e8 | 1.20856 | 0.604278 | − | 0.796773i | \(-0.293462\pi\) | ||||
0.604278 | + | 0.796773i | \(0.293462\pi\) | |||||||
\(444\) | −9.74712e7 | − | 1.30742e7i | −1.11360 | − | 0.149371i | ||||
\(445\) | 1.40263e7 | + | 1.31697e8i | 0.159170 | + | 1.49450i | ||||
\(446\) | −3.29122e7 | − | 3.76216e7i | −0.370981 | − | 0.424065i | ||||
\(447\) | −2.31139e7 | −0.258792 | ||||||||
\(448\) | 3.87936e7 | − | 9.17515e7i | 0.431446 | − | 1.02042i | ||||
\(449\) | 1.88095e7 | 0.207796 | 0.103898 | − | 0.994588i | \(-0.466868\pi\) | ||||
0.103898 | + | 0.994588i | \(0.466868\pi\) | |||||||
\(450\) | 2.43662e7 | + | 1.81364e7i | 0.267393 | + | 0.199027i | ||||
\(451\) | − | 5.89744e7i | − | 0.642886i | ||||||
\(452\) | −1.44897e8 | − | 1.94356e7i | −1.56907 | − | 0.210467i | ||||
\(453\) | − | 2.27923e7i | − | 0.245185i | ||||||
\(454\) | −4.74101e7 | − | 5.41940e7i | −0.506644 | − | 0.579140i | ||||
\(455\) | −1.47082e7 | + | 1.56648e6i | −0.156144 | + | 0.0166299i | ||||
\(456\) | −2.45237e7 | − | 3.69946e7i | −0.258638 | − | 0.390161i | ||||
\(457\) | − | 3.09010e7i | − | 0.323761i | −0.986810 | − | 0.161880i | \(-0.948244\pi\) | ||
0.986810 | − | 0.161880i | \(-0.0517559\pi\) | |||||||
\(458\) | −4.20576e7 | − | 4.80756e7i | −0.437772 | − | 0.500412i | ||||
\(459\) | 1.70693e7i | 0.176514i | ||||||||
\(460\) | −1.23873e8 | − | 3.37443e6i | −1.27263 | − | 0.0346678i | ||||
\(461\) | −3.31900e7 | −0.338769 | −0.169385 | − | 0.985550i | \(-0.554178\pi\) | ||||
−0.169385 | + | 0.985550i | \(0.554178\pi\) | |||||||
\(462\) | 3.02193e7 | − | 2.64365e7i | 0.306449 | − | 0.268088i | ||||
\(463\) | −1.33317e7 | −0.134321 | −0.0671603 | − | 0.997742i | \(-0.521394\pi\) | ||||
−0.0671603 | + | 0.997742i | \(0.521394\pi\) | |||||||
\(464\) | 7.46118e7 | + | 2.03827e7i | 0.746885 | + | 0.204037i | ||||
\(465\) | 891955. | − | 94996.9i | 0.00887123 | − | 0.000944823i | ||||
\(466\) | −3.11947e7 | + | 2.72898e7i | −0.308264 | + | 0.269676i | ||||
\(467\) | 8.54793e7 | 0.839287 | 0.419643 | − | 0.907689i | \(-0.362155\pi\) | ||||
0.419643 | + | 0.907689i | \(0.362155\pi\) | |||||||
\(468\) | 4.79981e6 | + | 643819.i | 0.0468259 | + | 0.00628096i | ||||
\(469\) | −1.98898e8 | −1.92802 | ||||||||
\(470\) | −2.28485e7 | + | 2.47255e7i | −0.220071 | + | 0.238151i | ||||
\(471\) | 7.30043e7i | 0.698692i | ||||||||
\(472\) | −3.25234e7 | − | 4.90623e7i | −0.309293 | − | 0.466576i | ||||
\(473\) | 1.23600e8i | 1.16798i | ||||||||
\(474\) | 9.52651e6 | − | 8.33400e6i | 0.0894538 | − | 0.0782561i | ||||
\(475\) | −1.83012e7 | − | 8.49431e7i | −0.170765 | − | 0.792588i | ||||
\(476\) | 1.08618e8 | + | 1.45694e7i | 1.00712 | + | 0.135090i | ||||
\(477\) | − | 3.11370e7i | − | 0.286894i | ||||||
\(478\) | −1.29437e7 | + | 1.13235e7i | −0.118516 | + | 0.103680i | ||||
\(479\) | 1.27765e7i | 0.116254i | 0.998309 | + | 0.0581268i | \(0.0185128\pi\) | ||||
−0.998309 | + | 0.0581268i | \(0.981487\pi\) | |||||||
\(480\) | −5.41600e7 | + | 3.38166e7i | −0.489728 | + | 0.305778i | ||||
\(481\) | −3.06955e7 | −0.275829 | ||||||||
\(482\) | −4.95422e7 | − | 5.66312e7i | −0.442420 | − | 0.505725i | ||||
\(483\) | 9.17567e7 | 0.814322 | ||||||||
\(484\) | −8.96547e6 | + | 6.68394e7i | −0.0790746 | + | 0.589518i | ||||
\(485\) | −7.85425e7 | + | 8.36510e6i | −0.688462 | + | 0.0733240i | ||||
\(486\) | 4.84858e6 | + | 5.54236e6i | 0.0422382 | + | 0.0482821i | ||||
\(487\) | 3.20267e7 | 0.277285 | 0.138642 | − | 0.990343i | \(-0.455726\pi\) | ||||
0.138642 | + | 0.990343i | \(0.455726\pi\) | |||||||
\(488\) | 1.08733e8 | − | 7.20793e7i | 0.935627 | − | 0.620227i | ||||
\(489\) | −1.05691e8 | −0.903877 | ||||||||
\(490\) | −1.81572e7 | + | 1.96489e7i | −0.154334 | + | 0.167013i | ||||
\(491\) | − | 1.89567e8i | − | 1.60147i | −0.599022 | − | 0.800733i | \(-0.704444\pi\) | ||
0.599022 | − | 0.800733i | \(-0.295556\pi\) | |||||||
\(492\) | 9.23210e6 | − | 6.88272e7i | 0.0775184 | − | 0.577916i | ||||
\(493\) | 8.50911e7i | 0.710139i | ||||||||
\(494\) | −9.12157e6 | − | 1.04268e7i | −0.0756639 | − | 0.0864907i | ||||
\(495\) | −2.55906e7 | + | 2.72551e6i | −0.210992 | + | 0.0224715i | ||||
\(496\) | −496895. | + | 1.81890e6i | −0.00407211 | + | 0.0149061i | ||||
\(497\) | 6.28112e7i | 0.511644i | ||||||||
\(498\) | −3.19309e6 | − | 3.64999e6i | −0.0258537 | − | 0.0295531i | ||||
\(499\) | 1.21997e8i | 0.981855i | 0.871200 | + | 0.490928i | \(0.163342\pi\) | ||||
−0.871200 | + | 0.490928i | \(0.836658\pi\) | |||||||
\(500\) | −1.22868e8 | + | 2.29901e7i | −0.982941 | + | 0.183921i | ||||
\(501\) | 1.03490e8 | 0.822969 | ||||||||
\(502\) | −9.98505e7 | + | 8.73514e7i | −0.789295 | + | 0.690492i | ||||
\(503\) | 1.54905e8 | 1.21720 | 0.608599 | − | 0.793478i | \(-0.291732\pi\) | ||||
0.608599 | + | 0.793478i | \(0.291732\pi\) | |||||||
\(504\) | 3.94065e7 | − | 2.61226e7i | 0.307805 | − | 0.204044i | ||||
\(505\) | 1.97329e7 | + | 1.85278e8i | 0.153220 | + | 1.43863i | ||||
\(506\) | 7.90206e7 | − | 6.91289e7i | 0.609942 | − | 0.533591i | ||||
\(507\) | −7.37310e7 | −0.565752 | ||||||||
\(508\) | −1.13877e7 | + | 8.48976e7i | −0.0868649 | + | 0.647596i | ||||
\(509\) | −2.04699e8 | −1.55225 | −0.776127 | − | 0.630576i | \(-0.782819\pi\) | ||||
−0.776127 | + | 0.630576i | \(0.782819\pi\) | |||||||
\(510\) | −5.15897e7 | − | 4.76733e7i | −0.388913 | − | 0.359389i | ||||
\(511\) | 1.93152e8i | 1.44756i | ||||||||
\(512\) | −2.47384e7 | − | 1.31918e8i | −0.184315 | − | 0.982867i | ||||
\(513\) | − | 2.10654e7i | − | 0.156034i | ||||||
\(514\) | 9.37576e7 | − | 8.20212e7i | 0.690426 | − | 0.604000i | ||||
\(515\) | −6.60420e6 | − | 6.20089e7i | −0.0483502 | − | 0.453975i | ||||
\(516\) | −1.93489e7 | + | 1.44250e8i | −0.140834 | + | 1.04995i | ||||
\(517\) | − | 2.85237e7i | − | 0.206412i | ||||||
\(518\) | −2.25545e8 | + | 1.97311e8i | −1.62272 | + | 1.41959i | ||||
\(519\) | 1.34701e8i | 0.963539i | ||||||||
\(520\) | −1.53513e7 | + | 1.27086e7i | −0.109178 | + | 0.0903834i | ||||
\(521\) | −1.10279e6 | −0.00779792 | −0.00389896 | − | 0.999992i | \(-0.501241\pi\) | ||||
−0.00389896 | + | 0.999992i | \(0.501241\pi\) | |||||||
\(522\) | 2.41703e7 | + | 2.76288e7i | 0.169930 | + | 0.194246i | ||||
\(523\) | −7.01848e7 | −0.490612 | −0.245306 | − | 0.969446i | \(-0.578888\pi\) | ||||
−0.245306 | + | 0.969446i | \(0.578888\pi\) | |||||||
\(524\) | 2.22050e8 | + | 2.97845e7i | 1.54332 | + | 0.207012i | ||||
\(525\) | 9.04811e7 | − | 1.94944e7i | 0.625288 | − | 0.134720i | ||||
\(526\) | −3.49018e7 | − | 3.98959e7i | −0.239823 | − | 0.274139i | ||||
\(527\) | −2.07437e6 | −0.0141728 | ||||||||
\(528\) | 1.42562e7 | − | 5.21853e7i | 0.0968504 | − | 0.354524i | ||||
\(529\) | 9.18990e7 | 0.620789 | ||||||||
\(530\) | 9.41072e7 | + | 8.69630e7i | 0.632114 | + | 0.584127i | ||||
\(531\) | − | 2.79371e7i | − | 0.186594i | ||||||
\(532\) | −1.34047e8 | − | 1.79803e7i | −0.890270 | − | 0.119416i | ||||
\(533\) | − | 2.16750e7i | − | 0.143145i | ||||||
\(534\) | −8.69994e7 | − | 9.94482e7i | −0.571337 | − | 0.653090i | ||||
\(535\) | −1.55408e7 | − | 1.45917e8i | −0.101487 | − | 0.952897i | ||||
\(536\) | −2.23366e8 | + | 1.48069e8i | −1.45051 | + | 0.961545i | ||||
\(537\) | 1.41793e8i | 0.915657i | ||||||||
\(538\) | −1.67200e8 | − | 1.91125e8i | −1.07372 | − | 1.22735i | ||||
\(539\) | − | 2.26673e7i | − | 0.144755i | ||||||
\(540\) | −3.02927e7 | − | 825207.i | −0.192379 | − | 0.00524061i | ||||
\(541\) | 1.96474e8 | 1.24083 | 0.620417 | − | 0.784272i | \(-0.286963\pi\) | ||||
0.620417 | + | 0.784272i | \(0.286963\pi\) | |||||||
\(542\) | 2.08416e8 | − | 1.82327e8i | 1.30898 | − | 1.14512i | ||||
\(543\) | 5.62776e7 | 0.351509 | ||||||||
\(544\) | 1.32826e8 | − | 6.44988e7i | 0.825063 | − | 0.400641i | ||||
\(545\) | −1.64744e7 | − | 1.54683e8i | −0.101770 | − | 0.955549i | ||||
\(546\) | 1.11066e7 | − | 9.71626e6i | 0.0682342 | − | 0.0596927i | ||||
\(547\) | 4.61576e7 | 0.282021 | 0.141010 | − | 0.990008i | \(-0.454965\pi\) | ||||
0.141010 | + | 0.990008i | \(0.454965\pi\) | |||||||
\(548\) | 2.39205e8 | + | 3.20856e7i | 1.45354 | + | 0.194970i | ||||
\(549\) | 6.19148e7 | 0.374178 | ||||||||
\(550\) | 6.32352e7 | − | 8.49564e7i | 0.380076 | − | 0.510632i | ||||
\(551\) | − | 1.05012e8i | − | 0.627745i | ||||||
\(552\) | 1.03044e8 | − | 6.83080e7i | 0.612641 | − | 0.406120i | ||||
\(553\) | − | 3.85691e7i | − | 0.228068i | ||||||
\(554\) | 1.56921e8 | − | 1.37278e8i | 0.922894 | − | 0.807368i | ||||
\(555\) | 1.90998e8 | − | 2.03421e7i | 1.11725 | − | 0.118992i | ||||
\(556\) | −3.76207e7 | − | 5.04622e6i | −0.218878 | − | 0.0293591i | ||||
\(557\) | 9.17119e7i | 0.530714i | 0.964150 | + | 0.265357i | \(0.0854898\pi\) | ||||
−0.964150 | + | 0.265357i | \(0.914510\pi\) | |||||||
\(558\) | −673542. | + | 589229.i | −0.00387670 | + | 0.00339142i | ||||
\(559\) | 4.54271e7i | 0.260064i | ||||||||
\(560\) | −3.11073e7 | + | 1.92059e8i | −0.177132 | + | 1.09363i | ||||
\(561\) | 5.95147e7 | 0.337082 | ||||||||
\(562\) | −5.77367e7 | − | 6.59983e7i | −0.325269 | − | 0.371812i | ||||
\(563\) | −2.08056e7 | −0.116588 | −0.0582941 | − | 0.998299i | \(-0.518566\pi\) | ||||
−0.0582941 | + | 0.998299i | \(0.518566\pi\) | |||||||
\(564\) | 4.46522e6 | − | 3.32892e7i | 0.0248889 | − | 0.185552i | ||||
\(565\) | 2.83930e8 | − | 3.02398e7i | 1.57422 | − | 0.167661i | ||||
\(566\) | 1.05308e8 | + | 1.20377e8i | 0.580780 | + | 0.663885i | ||||
\(567\) | 2.24388e7 | 0.123098 | ||||||||
\(568\) | 4.67596e7 | + | 7.05380e7i | 0.255168 | + | 0.384927i | ||||
\(569\) | 2.96314e7 | 0.160848 | 0.0804239 | − | 0.996761i | \(-0.474373\pi\) | ||||
0.0804239 | + | 0.996761i | \(0.474373\pi\) | |||||||
\(570\) | 6.36674e7 | + | 5.88341e7i | 0.343790 | + | 0.317691i | ||||
\(571\) | − | 8.21130e7i | − | 0.441066i | −0.975380 | − | 0.220533i | \(-0.929220\pi\) | ||
0.975380 | − | 0.220533i | \(-0.0707797\pi\) | |||||||
\(572\) | 2.24477e6 | − | 1.67352e7i | 0.0119945 | − | 0.0894219i | ||||
\(573\) | 1.20144e7i | 0.0638612i | ||||||||
\(574\) | −1.39327e8 | − | 1.59264e8i | −0.736716 | − | 0.842133i | ||||
\(575\) | 2.36600e8 | − | 5.09759e7i | 1.24454 | − | 0.268140i | ||||
\(576\) | 2.48072e7 | − | 5.86721e7i | 0.129811 | − | 0.307018i | ||||
\(577\) | − | 3.79151e8i | − | 1.97372i | −0.161582 | − | 0.986859i | \(-0.551660\pi\) | ||
0.161582 | − | 0.986859i | \(-0.448340\pi\) | |||||||
\(578\) | −2.01850e7 | − | 2.30733e7i | −0.104531 | − | 0.119488i | ||||
\(579\) | 1.33567e7i | 0.0688119i | ||||||||
\(580\) | −1.51010e8 | − | 4.11368e6i | −0.773966 | − | 0.0210837i | ||||
\(581\) | −1.47774e7 | −0.0753474 | ||||||||
\(582\) | 5.93098e7 | − | 5.18855e7i | 0.300855 | − | 0.263195i | ||||
\(583\) | −1.08564e8 | −0.547871 | ||||||||
\(584\) | 1.43792e8 | + | 2.16913e8i | 0.721930 | + | 1.08905i | ||||
\(585\) | −9.40539e6 | + | 1.00171e6i | −0.0469796 | + | 0.00500352i | ||||
\(586\) | 1.60775e8 | − | 1.40649e8i | 0.798961 | − | 0.698948i | ||||
\(587\) | −2.59598e8 | −1.28347 | −0.641737 | − | 0.766925i | \(-0.721786\pi\) | ||||
−0.641737 | + | 0.766925i | \(0.721786\pi\) | |||||||
\(588\) | 3.54843e6 | − | 2.64543e7i | 0.0174544 | − | 0.130126i | ||||
\(589\) | 2.56000e6 | 0.0125284 | ||||||||
\(590\) | 8.44359e7 | + | 7.80260e7i | 0.411123 | + | 0.379912i | ||||
\(591\) | − | 9.98665e7i | − | 0.483790i | ||||||
\(592\) | −1.06402e8 | + | 3.89490e8i | −0.512845 | + | 1.87729i | ||||
\(593\) | − | 7.63709e7i | − | 0.366238i | −0.983091 | − | 0.183119i | \(-0.941381\pi\) | ||
0.983091 | − | 0.183119i | \(-0.0586194\pi\) | |||||||
\(594\) | 1.93243e7 | − | 1.69053e7i | 0.0922027 | − | 0.0806609i | ||||
\(595\) | −2.12841e8 | + | 2.26685e7i | −1.01043 | + | 0.107615i | ||||
\(596\) | −1.26159e7 | + | 9.40541e7i | −0.0595907 | + | 0.444262i | ||||
\(597\) | 1.21063e8i | 0.568971i | ||||||||
\(598\) | 2.90426e7 | − | 2.54071e7i | 0.135810 | − | 0.118810i | ||||
\(599\) | 3.48124e8i | 1.61977i | 0.586587 | + | 0.809886i | \(0.300471\pi\) | ||||
−0.586587 | + | 0.809886i | \(0.699529\pi\) | |||||||
\(600\) | 8.70992e7 | − | 8.92509e7i | 0.403237 | − | 0.413199i | ||||
\(601\) | −2.40011e8 | −1.10562 | −0.552811 | − | 0.833306i | \(-0.686445\pi\) | ||||
−0.552811 | + | 0.833306i | \(0.686445\pi\) | |||||||
\(602\) | 2.92006e8 | + | 3.33789e8i | 1.33845 | + | 1.52997i | ||||
\(603\) | −1.27189e8 | −0.580092 | ||||||||
\(604\) | −9.27455e7 | − | 1.24404e7i | −0.420903 | − | 0.0564575i | ||||
\(605\) | −1.39493e7 | − | 1.30974e8i | −0.0629921 | − | 0.591452i | ||||
\(606\) | −1.22396e8 | − | 1.39909e8i | −0.549981 | − | 0.628678i | ||||
\(607\) | −9.26126e6 | −0.0414099 | −0.0207049 | − | 0.999786i | \(-0.506591\pi\) | ||||
−0.0207049 | + | 0.999786i | \(0.506591\pi\) | |||||||
\(608\) | −1.63922e8 | + | 7.95987e7i | −0.729335 | + | 0.354156i | ||||
\(609\) | 1.11858e8 | 0.495240 | ||||||||
\(610\) | −1.72923e8 | + | 1.87129e8i | −0.761840 | + | 0.824427i | ||||
\(611\) | − | 1.04834e7i | − | 0.0459598i | ||||||
\(612\) | 6.94578e7 | + | 9.31668e6i | 0.303017 | + | 0.0406450i | ||||
\(613\) | 3.01920e8i | 1.31072i | 0.755316 | + | 0.655361i | \(0.227483\pi\) | ||||
−0.755316 | + | 0.655361i | \(0.772517\pi\) | |||||||
\(614\) | −1.51601e7 | − | 1.73293e7i | −0.0654931 | − | 0.0748646i | ||||
\(615\) | 1.43641e7 | + | 1.34869e8i | 0.0617525 | + | 0.579813i | ||||
\(616\) | −9.10802e7 | − | 1.37397e8i | −0.389656 | − | 0.587805i | ||||
\(617\) | 1.47492e8i | 0.627933i | 0.949434 | + | 0.313966i | \(0.101658\pi\) | ||||
−0.949434 | + | 0.313966i | \(0.898342\pi\) | |||||||
\(618\) | 4.09633e7 | + | 4.68247e7i | 0.173552 | + | 0.198385i | ||||
\(619\) | 1.93464e8i | 0.815697i | 0.913050 | + | 0.407849i | \(0.133721\pi\) | ||||
−0.913050 | + | 0.407849i | \(0.866279\pi\) | |||||||
\(620\) | 100284. | − | 3.68136e6i | 0.000420782 | − | 0.0154466i | ||||
\(621\) | 5.86754e7 | 0.245009 | ||||||||
\(622\) | 2.32235e7 | − | 2.03164e7i | 0.0965065 | − | 0.0844260i | ||||
\(623\) | −4.02627e8 | −1.66509 | ||||||||
\(624\) | 5.23960e6 | − | 1.91798e7i | 0.0215648 | − | 0.0789387i | ||||
\(625\) | 2.22480e8 | − | 1.00534e8i | 0.911279 | − | 0.411789i | ||||
\(626\) | −1.10581e8 | + | 9.67390e7i | −0.450774 | + | 0.394347i | ||||
\(627\) | −7.34478e7 | −0.297972 | ||||||||
\(628\) | 2.97066e8 | + | 3.98468e7i | 1.19943 | + | 0.160885i | ||||
\(629\) | −4.44194e8 | −1.78493 | ||||||||
\(630\) | −6.26699e7 | + | 6.78183e7i | −0.250632 | + | 0.271222i | ||||
\(631\) | − | 1.92567e8i | − | 0.766468i | −0.923651 | − | 0.383234i | \(-0.874810\pi\) | ||
0.923651 | − | 0.383234i | \(-0.125190\pi\) | |||||||
\(632\) | −2.87127e7 | − | 4.33137e7i | −0.113742 | − | 0.171583i | ||||
\(633\) | − | 2.13948e8i | − | 0.843525i | ||||||
\(634\) | 8.90555e7 | − | 7.79077e7i | 0.349456 | − | 0.305712i | ||||
\(635\) | −1.77180e7 | − | 1.66360e8i | −0.0691980 | − | 0.649722i | ||||
\(636\) | −1.26701e8 | − | 1.69950e7i | −0.492504 | − | 0.0660617i | ||||
\(637\) | − | 8.33096e6i | − | 0.0322312i | ||||||
\(638\) | 9.63320e7 | − | 8.42733e7i | 0.370944 | − | 0.324510i | ||||
\(639\) | 4.01657e7i | 0.153941i | ||||||||
\(640\) | 1.08044e8 | + | 2.38843e8i | 0.412155 | + | 0.911114i | ||||
\(641\) | −2.82910e8 | −1.07417 | −0.537086 | − | 0.843528i | \(-0.680475\pi\) | ||||
−0.537086 | + | 0.843528i | \(0.680475\pi\) | |||||||
\(642\) | 9.63936e7 | + | 1.10187e8i | 0.364287 | + | 0.416412i | ||||
\(643\) | −3.08979e8 | −1.16224 | −0.581120 | − | 0.813818i | \(-0.697385\pi\) | ||||
−0.581120 | + | 0.813818i | \(0.697385\pi\) | |||||||
\(644\) | 5.00821e7 | − | 3.73372e8i | 0.187510 | − | 1.39793i | ||||
\(645\) | −3.01048e7 | − | 2.82663e8i | −0.112191 | − | 1.05339i | ||||
\(646\) | −1.31998e8 | − | 1.50885e8i | −0.489632 | − | 0.559693i | ||||
\(647\) | 3.15317e8 | 1.16422 | 0.582109 | − | 0.813111i | \(-0.302228\pi\) | ||||
0.582109 | + | 0.813111i | \(0.302228\pi\) | |||||||
\(648\) | 2.51992e7 | − | 1.67045e7i | 0.0926107 | − | 0.0613916i | ||||
\(649\) | −9.74066e7 | −0.356332 | ||||||||
\(650\) | 2.32410e7 | − | 3.12242e7i | 0.0846280 | − | 0.113698i | ||||
\(651\) | 2.72690e6i | 0.00988387i | ||||||||
\(652\) | −5.76874e7 | + | 4.30072e8i | −0.208132 | + | 1.55166i | ||||
\(653\) | − | 3.98350e8i | − | 1.43062i | −0.698805 | − | 0.715312i | \(-0.746284\pi\) | ||
0.698805 | − | 0.715312i | \(-0.253716\pi\) | |||||||
\(654\) | 1.02184e8 | + | 1.16806e8i | 0.365300 | + | 0.417571i | ||||
\(655\) | −4.35114e8 | + | 4.63414e7i | −1.54839 | + | 0.164909i | ||||
\(656\) | −2.75030e8 | − | 7.51337e7i | −0.974246 | − | 0.266148i | ||||
\(657\) | 1.23515e8i | 0.435534i | ||||||||
\(658\) | −6.73874e7 | − | 7.70299e7i | −0.236538 | − | 0.270384i | ||||
\(659\) | − | 2.49936e8i | − | 0.873317i | −0.899627 | − | 0.436659i | \(-0.856162\pi\) | ||
0.899627 | − | 0.436659i | \(-0.143838\pi\) | |||||||
\(660\) | −2.87721e6 | + | 1.05620e8i | −0.0100078 | + | 0.367379i | ||||
\(661\) | −8.36472e7 | −0.289632 | −0.144816 | − | 0.989459i | \(-0.546259\pi\) | ||||
−0.144816 | + | 0.989459i | \(0.546259\pi\) | |||||||
\(662\) | −3.44741e8 | + | 3.01587e8i | −1.18828 | + | 1.03953i | ||||
\(663\) | 2.18736e7 | 0.0750550 | ||||||||
\(664\) | −1.65952e7 | + | 1.10010e7i | −0.0566863 | + | 0.0375774i | ||||
\(665\) | 2.62670e8 | − | 2.79754e7i | 0.893192 | − | 0.0951286i | ||||
\(666\) | −1.44228e8 | + | 1.26174e8i | −0.488234 | + | 0.427118i | ||||
\(667\) | 2.92499e8 | 0.985704 | ||||||||
\(668\) | 5.64861e7 | − | 4.21116e8i | 0.189501 | − | 1.41277i | ||||
\(669\) | −9.74004e7 | −0.325299 | ||||||||
\(670\) | 3.55228e8 | − | 3.84411e8i | 1.18109 | − | 1.27812i | ||||
\(671\) | − | 2.15875e8i | − | 0.714554i | ||||||
\(672\) | −8.47883e7 | − | 1.74609e8i | −0.279401 | − | 0.575386i | ||||
\(673\) | 1.44164e8i | 0.472945i | 0.971638 | + | 0.236473i | \(0.0759913\pi\) | ||||
−0.971638 | + | 0.236473i | \(0.924009\pi\) | |||||||
\(674\) | −1.04558e8 | + | 9.14693e7i | −0.341488 | + | 0.298741i | ||||
\(675\) | 5.78597e7 | − | 1.24660e7i | 0.188133 | − | 0.0405337i | ||||
\(676\) | −4.02434e7 | + | 3.00023e8i | −0.130273 | + | 0.971213i | ||||
\(677\) | 9.93179e7i | 0.320082i | 0.987110 | + | 0.160041i | \(0.0511627\pi\) | ||||
−0.987110 | + | 0.160041i | \(0.948837\pi\) | |||||||
\(678\) | −2.14404e8 | + | 1.87565e8i | −0.687930 | + | 0.601816i | ||||
\(679\) | − | 2.40122e8i | − | 0.767048i | ||||||
\(680\) | −2.22149e8 | + | 1.83906e8i | −0.706508 | + | 0.584884i | ||||
\(681\) | −1.40306e8 | −0.444257 | ||||||||
\(682\) | 2.05443e6 | + | 2.34840e6i | 0.00647648 | + | 0.00740320i | ||||
\(683\) | 3.90996e8 | 1.22719 | 0.613593 | − | 0.789623i | \(-0.289724\pi\) | ||||
0.613593 | + | 0.789623i | \(0.289724\pi\) | |||||||
\(684\) | −8.57186e7 | − | 1.14978e7i | −0.267859 | − | 0.0359291i | ||||
\(685\) | −4.68730e8 | + | 4.99217e7i | −1.45831 | + | 0.155316i | ||||
\(686\) | 1.81940e8 | + | 2.07973e8i | 0.563579 | + | 0.644222i | ||||
\(687\) | −1.24465e8 | −0.383865 | ||||||||
\(688\) | 5.76416e8 | + | 1.57468e8i | 1.76999 | + | 0.483533i | ||||
\(689\) | −3.99006e7 | −0.121989 | ||||||||
\(690\) | −1.63876e8 | + | 1.77338e8i | −0.498847 | + | 0.539828i | ||||
\(691\) | 3.51198e8i | 1.06443i | 0.846608 | + | 0.532217i | \(0.178641\pi\) | ||||
−0.846608 | + | 0.532217i | \(0.821359\pi\) | |||||||
\(692\) | 5.48120e8 | + | 7.35218e7i | 1.65408 | + | 0.221870i | ||||
\(693\) | − | 7.82363e7i | − | 0.235076i | ||||||
\(694\) | 3.45708e8 | + | 3.95176e8i | 1.03426 | + | 1.18226i | ||||
\(695\) | 7.37190e7 | − | 7.85138e6i | 0.219596 | − | 0.0233879i | ||||
\(696\) | 1.25619e8 | − | 8.32726e7i | 0.372586 | − | 0.246987i | ||||
\(697\) | − | 3.13658e8i | − | 0.926314i | ||||||
\(698\) | −8.51690e7 | − | 9.73559e7i | −0.250447 | − | 0.286283i | ||||
\(699\) | 8.07616e7i | 0.236469i | ||||||||
\(700\) | −2.99397e7 | − | 3.78822e8i | −0.0872879 | − | 1.10444i | ||||
\(701\) | 3.99331e8 | 1.15925 | 0.579627 | − | 0.814882i | \(-0.303198\pi\) | ||||
0.579627 | + | 0.814882i | \(0.303198\pi\) | |||||||
\(702\) | 7.10229e6 | − | 6.21324e6i | 0.0205299 | − | 0.0179600i | ||||
\(703\) | 5.48184e8 | 1.57783 | ||||||||
\(704\) | −2.04569e8 | − | 8.64941e7i | −0.586303 | − | 0.247895i | ||||
\(705\) | 6.94740e6 | + | 6.52313e7i | 0.0198269 | + | 0.186161i | ||||
\(706\) | −1.25273e8 | + | 1.09592e8i | −0.355995 | + | 0.311432i | ||||
\(707\) | −5.66437e8 | −1.60285 | ||||||||
\(708\) | −1.13680e8 | − | 1.52484e7i | −0.320321 | − | 0.0429661i | ||||
\(709\) | 9.18319e6 | 0.0257665 | 0.0128832 | − | 0.999917i | \(-0.495899\pi\) | ||||
0.0128832 | + | 0.999917i | \(0.495899\pi\) | |||||||
\(710\) | −1.21395e8 | − | 1.12180e8i | −0.339178 | − | 0.313429i | ||||
\(711\) | − | 2.46637e7i | − | 0.0686197i | ||||||
\(712\) | −4.52156e8 | + | 2.99734e8i | −1.25270 | + | 0.830418i | ||||
\(713\) | 7.13059e6i | 0.0196724i | ||||||||
\(714\) | 1.60723e8 | − | 1.40604e8i | 0.441553 | − | 0.386280i | ||||
\(715\) | 3.49262e6 | + | 3.27933e7i | 0.00955505 | + | 0.0897153i | ||||
\(716\) | 5.76980e8 | + | 7.73928e7i | 1.57189 | + | 0.210844i | ||||
\(717\) | 3.35107e7i | 0.0909130i | ||||||||
\(718\) | 3.76126e8 | − | 3.29043e8i | 1.01615 | − | 0.888953i | ||||
\(719\) | − | 2.20660e8i | − | 0.593658i | −0.954931 | − | 0.296829i | \(-0.904071\pi\) | ||
0.954931 | − | 0.296829i | \(-0.0959292\pi\) | |||||||
\(720\) | −1.98921e7 | + | 1.22815e8i | −0.0532946 | + | 0.329045i | ||||
\(721\) | 1.89575e8 | 0.505796 | ||||||||
\(722\) | −8.49109e7 | − | 9.70608e7i | −0.225607 | − | 0.257889i | ||||
\(723\) | −1.46616e8 | −0.387940 | ||||||||
\(724\) | 3.07171e7 | − | 2.29003e8i | 0.0809403 | − | 0.603427i | ||||
\(725\) | 2.88432e8 | − | 6.21434e7i | 0.756885 | − | 0.163073i | ||||
\(726\) | 8.65220e7 | + | 9.89025e7i | 0.226109 | + | 0.258462i | ||||
\(727\) | 4.38080e8 | 1.14012 | 0.570059 | − | 0.821604i | \(-0.306920\pi\) | ||||
0.570059 | + | 0.821604i | \(0.306920\pi\) | |||||||
\(728\) | −3.34749e7 | − | 5.04977e7i | −0.0867611 | − | 0.130881i | ||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | −3.73306e8 | − | 3.44966e8i | −0.959614 | − | 0.886764i | ||||
\(731\) | 6.57375e8i | 1.68291i | ||||||||
\(732\) | 3.37940e7 | − | 2.51941e8i | 0.0861601 | − | 0.642342i | ||||
\(733\) | 3.17227e7i | 0.0805487i | 0.999189 | + | 0.0402744i | \(0.0128232\pi\) | ||||
−0.999189 | + | 0.0402744i | \(0.987177\pi\) | |||||||
\(734\) | −2.54966e8 | − | 2.91449e8i | −0.644753 | − | 0.737011i | ||||
\(735\) | 5.52097e6 | + | 5.18381e7i | 0.0139044 | + | 0.130553i | ||||
\(736\) | −2.21713e8 | − | 4.56587e8i | −0.556107 | − | 1.14522i | ||||
\(737\) | 4.43462e8i | 1.10778i | ||||||||
\(738\) | −8.90952e7 | − | 1.01844e8i | −0.221659 | − | 0.253376i | ||||
\(739\) | 4.13892e8i | 1.02554i | 0.858526 | + | 0.512771i | \(0.171381\pi\) | ||||
−0.858526 | + | 0.512771i | \(0.828619\pi\) | |||||||
\(740\) | 2.14743e7 | − | 7.88305e8i | 0.0529936 | − | 1.94536i | ||||
\(741\) | −2.69944e7 | −0.0663467 | ||||||||
\(742\) | −2.93182e8 | + | 2.56482e8i | −0.717671 | + | 0.627834i | ||||
\(743\) | −4.45636e8 | −1.08646 | −0.543230 | − | 0.839584i | \(-0.682799\pi\) | ||||
−0.543230 | + | 0.839584i | \(0.682799\pi\) | |||||||
\(744\) | 2.03004e6 | + | 3.06236e6i | 0.00492930 | + | 0.00743596i | ||||
\(745\) | −1.96289e7 | − | 1.84302e8i | −0.0474710 | − | 0.445720i | ||||
\(746\) | 3.56319e6 | − | 3.11715e6i | 0.00858266 | − | 0.00750830i | ||||
\(747\) | −9.44964e6 | −0.0226701 | ||||||||
\(748\) | 3.24840e7 | − | 2.42175e8i | 0.0776184 | − | 0.578661i | ||||
\(749\) | 4.46102e8 | 1.06167 | ||||||||
\(750\) | −1.23921e8 | + | 2.09690e8i | −0.293738 | + | 0.497042i | ||||
\(751\) | − | 5.33301e8i | − | 1.25908i | −0.776969 | − | 0.629539i | \(-0.783244\pi\) | ||
0.776969 | − | 0.629539i | \(-0.216756\pi\) | |||||||
\(752\) | −1.33022e8 | − | 3.63394e7i | −0.312802 | − | 0.0854524i | ||||
\(753\) | 2.58508e8i | 0.605466i | ||||||||
\(754\) | 3.54051e7 | − | 3.09732e7i | 0.0825947 | − | 0.0722556i | ||||
\(755\) | 1.81738e8 | − | 1.93558e7i | 0.422284 | − | 0.0449750i | ||||
\(756\) | 1.22474e7 | − | 9.13072e7i | 0.0283452 | − | 0.211320i | ||||
\(757\) | 4.21379e8i | 0.971371i | 0.874134 | + | 0.485685i | \(0.161430\pi\) | ||||
−0.874134 | + | 0.485685i | \(0.838570\pi\) | |||||||
\(758\) | −5.24321e8 | + | 4.58687e8i | −1.20390 | + | 1.05320i | ||||
\(759\) | − | 2.04580e8i | − | 0.467885i | ||||||
\(760\) | 2.74156e8 | − | 2.26960e8i | 0.624535 | − | 0.517022i | ||||
\(761\) | 3.86731e8 | 0.877517 | 0.438758 | − | 0.898605i | \(-0.355418\pi\) | ||||
0.438758 | + | 0.898605i | \(0.355418\pi\) | |||||||
\(762\) | 1.09898e8 | + | 1.25623e8i | 0.248385 | + | 0.283926i | ||||
\(763\) | 4.72900e8 | 1.06462 | ||||||||
\(764\) | 4.88884e7 | + | 6.55761e6i | 0.109629 | + | 0.0147050i | ||||
\(765\) | −1.36105e8 | + | 1.44957e7i | −0.304011 | + | 0.0323785i | ||||
\(766\) | 3.98141e8 | + | 4.55111e8i | 0.885830 | + | 1.01258i | ||||
\(767\) | −3.58001e7 | −0.0793411 | ||||||||
\(768\) | −2.25206e8 | − | 1.32969e8i | −0.497160 | − | 0.293539i | ||||
\(769\) | 2.56434e8 | 0.563894 | 0.281947 | − | 0.959430i | \(-0.409020\pi\) | ||||
0.281947 | + | 0.959430i | \(0.409020\pi\) | |||||||
\(770\) | 2.36459e8 | + | 2.18508e8i | 0.517944 | + | 0.478624i | ||||
\(771\) | − | 2.42734e8i | − | 0.529624i | ||||||
\(772\) | 5.43505e7 | + | 7.29027e6i | 0.118128 | + | 0.0158450i | ||||
\(773\) | 1.49302e8i | 0.323241i | 0.986853 | + | 0.161620i | \(0.0516720\pi\) | ||||
−0.986853 | + | 0.161620i | \(0.948328\pi\) | |||||||
\(774\) | 1.86729e8 | + | 2.13448e8i | 0.402706 | + | 0.460329i | ||||
\(775\) | 1.51494e6 | + | 7.03147e6i | 0.00325456 | + | 0.0151057i | ||||
\(776\) | −1.78758e8 | − | 2.69661e8i | −0.382543 | − | 0.577076i | ||||
\(777\) | 5.83924e8i | 1.24478i | ||||||||
\(778\) | 2.02359e7 | + | 2.31314e7i | 0.0429717 | + | 0.0491206i | ||||
\(779\) | 3.87089e8i | 0.818838i | ||||||||
\(780\) | −1.05747e6 | + | 3.88188e7i | −0.00222835 | + | 0.0818009i | ||||
\(781\) | 1.40044e8 | 0.293975 | ||||||||
\(782\) | 4.20275e8 | − | 3.67665e8i | 0.878846 | − | 0.768833i | ||||
\(783\) | 7.15297e7 | 0.149005 | ||||||||
\(784\) | −1.05710e8 | − | 2.88782e7i | −0.219365 | − | 0.0599270i | ||||
\(785\) | −5.82111e8 | + | 6.19973e7i | −1.20336 | + | 0.128163i | ||||
\(786\) | 3.28568e8 | − | 2.87438e8i | 0.676639 | − | 0.591938i | ||||
\(787\) | 5.82854e8 | 1.19574 | 0.597869 | − | 0.801594i | \(-0.296014\pi\) | ||||
0.597869 | + | 0.801594i | \(0.296014\pi\) | |||||||
\(788\) | −4.06373e8 | − | 5.45085e7i | −0.830512 | − | 0.111400i | ||||
\(789\) | −1.03288e8 | −0.210291 | ||||||||
\(790\) | 7.45426e7 | + | 6.88837e7i | 0.151190 | + | 0.139712i | ||||
\(791\) | 8.68038e8i | 1.75392i | ||||||||
\(792\) | −5.82428e7 | − | 8.78606e7i | −0.117238 | − | 0.176856i | ||||
\(793\) | − | 7.93411e7i | − | 0.159103i | ||||||
\(794\) | −6.81875e8 | + | 5.96519e8i | −1.36221 | + | 1.19169i | ||||
\(795\) | 2.48275e8 | − | 2.64424e7i | 0.494120 | − | 0.0526258i | ||||
\(796\) | 4.92627e8 | + | 6.60782e7i | 0.976739 | + | 0.131014i | ||||
\(797\) | 7.32923e8i | 1.44772i | 0.689949 | + | 0.723858i | \(0.257633\pi\) | ||||
−0.689949 | + | 0.723858i | \(0.742367\pi\) | |||||||
\(798\) | −1.98350e8 | + | 1.73520e8i | −0.390322 | + | 0.341462i | ||||
\(799\) | − | 1.51705e8i | − | 0.297412i | ||||||
\(800\) | −3.15636e8 | − | 4.03135e8i | −0.616477 | − | 0.787373i | ||||
\(801\) | −2.57467e8 | −0.500984 | ||||||||
\(802\) | −3.05409e7 | − | 3.49110e7i | −0.0592051 | − | 0.0676767i | ||||
\(803\) | 4.30652e8 | 0.831725 | ||||||||
\(804\) | −6.94214e7 | + | 5.17551e8i | −0.133575 | + | 0.995830i | ||||
\(805\) | 7.79223e7 | + | 7.31636e8i | 0.149374 | + | 1.40252i | ||||
\(806\) | 755070. | + | 863113.i | 0.00144206 | + | 0.00164840i | ||||
\(807\) | −4.94813e8 | −0.941500 | ||||||||
\(808\) | −6.36118e8 | + | 4.21682e8i | −1.20588 | + | 0.799377i | ||||
\(809\) | 3.74521e8 | 0.707343 | 0.353672 | − | 0.935370i | \(-0.384933\pi\) | ||||
0.353672 | + | 0.935370i | \(0.384933\pi\) | |||||||
\(810\) | −4.00754e7 | + | 4.33676e7i | −0.0754088 | + | 0.0816038i | ||||
\(811\) | − | 7.54657e8i | − | 1.41477i | −0.706826 | − | 0.707387i | \(-0.749874\pi\) | ||
0.706826 | − | 0.707387i | \(-0.250126\pi\) | |||||||
\(812\) | 6.10538e7 | − | 4.55169e8i | 0.114037 | − | 0.850168i | ||||
\(813\) | − | 5.39579e8i | − | 1.00411i | ||||||
\(814\) | 4.39925e8 | + | 5.02874e8i | 0.815653 | + | 0.932365i | ||||
\(815\) | −8.97553e7 | − | 8.42740e8i | −0.165801 | − | 1.55676i | ||||
\(816\) | 7.58221e7 | − | 2.77550e8i | 0.139549 | − | 0.510823i | ||||
\(817\) | − | 8.11273e8i | − | 1.48765i | ||||||
\(818\) | −2.02673e6 | − | 2.31674e6i | −0.00370286 | − | 0.00423270i | ||||
\(819\) | − | 2.87544e7i | − | 0.0523422i | ||||||
\(820\) | 5.56645e8 | + | 1.51636e7i | 1.00957 | + | 0.0275018i | ||||
\(821\) | 4.19834e8 | 0.758661 | 0.379330 | − | 0.925261i | \(-0.376154\pi\) | ||||
0.379330 | + | 0.925261i | \(0.376154\pi\) | |||||||
\(822\) | 3.53952e8 | − | 3.09645e8i | 0.637278 | − | 0.557504i | ||||
\(823\) | 5.49205e7 | 0.0985224 | 0.0492612 | − | 0.998786i | \(-0.484313\pi\) | ||||
0.0492612 | + | 0.998786i | \(0.484313\pi\) | |||||||
\(824\) | 2.12896e8 | − | 1.41129e8i | 0.380527 | − | 0.252251i | ||||
\(825\) | −4.34646e7 | − | 2.01737e8i | −0.0774058 | − | 0.359271i | ||||
\(826\) | −2.63052e8 | + | 2.30123e8i | −0.466768 | + | 0.408339i | ||||
\(827\) | 1.20010e8 | 0.212178 | 0.106089 | − | 0.994357i | \(-0.466167\pi\) | ||||
0.106089 | + | 0.994357i | \(0.466167\pi\) | |||||||
\(828\) | 3.20259e7 | − | 2.38760e8i | 0.0564170 | − | 0.420601i | ||||
\(829\) | −5.25236e8 | −0.921915 | −0.460957 | − | 0.887422i | \(-0.652494\pi\) | ||||
−0.460957 | + | 0.887422i | \(0.652494\pi\) | |||||||
\(830\) | 2.63921e7 | − | 2.85602e7i | 0.0461572 | − | 0.0499491i | ||||
\(831\) | − | 4.06261e8i | − | 0.707949i | ||||||
\(832\) | −7.51857e7 | − | 3.17894e7i | −0.130547 | − | 0.0551966i | ||||
\(833\) | − | 1.20557e8i | − | 0.208573i | ||||||
\(834\) | −5.56674e7 | + | 4.86990e7i | −0.0959628 | + | 0.0839503i | ||||
\(835\) | 8.78862e7 | + | 8.25191e8i | 0.150960 | + | 1.41741i | ||||
\(836\) | −4.00888e7 | + | 2.98871e8i | −0.0686127 | + | 0.511522i | ||||
\(837\) | 1.74377e6i | 0.00297380i | ||||||||
\(838\) | 8.99290e7 | − | 7.86719e7i | 0.152816 | − | 0.133686i | ||||
\(839\) | − | 5.84293e8i | − | 0.989338i | −0.869081 | − | 0.494669i | \(-0.835289\pi\) | ||
0.869081 | − | 0.494669i | \(-0.164711\pi\) | |||||||
\(840\) | 2.41757e8 | + | 2.92030e8i | 0.407889 | + | 0.492708i | ||||
\(841\) | −2.38246e8 | −0.400532 | ||||||||
\(842\) | −4.99995e8 | − | 5.71540e8i | −0.837586 | − | 0.957437i | ||||
\(843\) | −1.70866e8 | −0.285216 | ||||||||
\(844\) | −8.70590e8 | − | 1.16776e8i | −1.44806 | − | 0.194234i | ||||
\(845\) | −6.26143e7 | − | 5.87905e8i | −0.103778 | − | 0.974400i | ||||
\(846\) | −4.30921e7 | − | 4.92581e7i | −0.0711682 | − | 0.0813517i | ||||
\(847\) | 4.00417e8 | 0.658965 | ||||||||
\(848\) | −1.38311e8 | + | 5.06291e8i | −0.226813 | + | 0.830258i | ||||
\(849\) | 3.11649e8 | 0.509264 | ||||||||
\(850\) | 3.36319e8 | − | 4.51844e8i | 0.547639 | − | 0.735753i | ||||
\(851\) | 1.52691e9i | 2.47756i | ||||||||
\(852\) | 1.63441e8 | + | 2.19230e7i | 0.264266 | + | 0.0354472i | ||||
\(853\) | 4.23065e8i | 0.681647i | 0.940127 | + | 0.340824i | \(0.110706\pi\) | ||||
−0.940127 | + | 0.340824i | \(0.889294\pi\) | |||||||
\(854\) | −5.10006e8 | − | 5.82982e8i | −0.818844 | − | 0.936013i | ||||
\(855\) | 1.67969e8 | − | 1.78893e7i | 0.268738 | − | 0.0286217i | ||||
\(856\) | 5.00980e8 | − | 3.32099e8i | 0.798728 | − | 0.529477i | ||||
\(857\) | − | 5.82340e6i | − | 0.00925197i | −0.999989 | − | 0.00462599i | \(-0.998527\pi\) | ||
0.999989 | − | 0.00462599i | \(-0.00147250\pi\) | |||||||
\(858\) | −2.16634e7 | − | 2.47632e7i | −0.0342976 | − | 0.0392053i | ||||
\(859\) | − | 7.80303e8i | − | 1.23107i | −0.788108 | − | 0.615537i | \(-0.788939\pi\) | ||
0.788108 | − | 0.615537i | \(-0.211061\pi\) | |||||||
\(860\) | −1.16663e9 | − | 3.17804e7i | −1.83417 | − | 0.0499648i | ||||
\(861\) | −4.12326e8 | −0.645997 | ||||||||
\(862\) | −1.08305e8 | + | 9.47479e7i | −0.169094 | + | 0.147927i | ||||
\(863\) | 1.24930e8 | 0.194373 | 0.0971863 | − | 0.995266i | \(-0.469016\pi\) | ||||
0.0971863 | + | 0.995266i | \(0.469016\pi\) | |||||||
\(864\) | −5.42193e7 | − | 1.11657e8i | −0.0840646 | − | 0.173119i | ||||
\(865\) | −1.07406e9 | + | 1.14392e8i | −1.65951 | + | 0.176745i | ||||
\(866\) | −1.31005e8 | + | 1.14606e8i | −0.201713 | + | 0.176463i | ||||
\(867\) | −5.97356e7 | −0.0916591 | ||||||||
\(868\) | 1.10962e7 | + | 1.48838e6i | 0.0169674 | + | 0.00227591i | ||||
\(869\) | −8.59935e7 | −0.131041 | ||||||||
\(870\) | −1.99777e8 | + | 2.16189e8i | −0.303380 | + | 0.328303i | ||||
\(871\) | 1.62987e8i | 0.246659i | ||||||||
\(872\) | 5.31074e8 | − | 3.52049e8i | 0.800951 | − | 0.530950i | ||||
\(873\) | − | 1.53550e8i | − | 0.230785i | ||||||
\(874\) | −5.18665e8 | + | 4.53739e8i | −0.776878 | + | 0.679629i | ||||
\(875\) | 2.32280e8 | + | 7.04910e8i | 0.346727 | + | 1.05223i | ||||
\(876\) | 5.02600e8 | + | 6.74160e7i | 0.747671 | + | 0.100288i | ||||
\(877\) | − | 7.92920e8i | − | 1.17552i | −0.809035 | − | 0.587761i | \(-0.800010\pi\) | ||
0.809035 | − | 0.587761i | \(-0.199990\pi\) | |||||||
\(878\) | 6.01656e8 | − | 5.26341e8i | 0.888924 | − | 0.777649i | ||||
\(879\) | − | 4.16239e8i | − | 0.612880i | ||||||
\(880\) | 4.28214e8 | + | 6.93567e7i | 0.628367 | + | 0.101775i | ||||
\(881\) | −7.45465e8 | −1.09018 | −0.545092 | − | 0.838377i | \(-0.683505\pi\) | ||||
−0.545092 | + | 0.838377i | \(0.683505\pi\) | |||||||
\(882\) | −3.42444e7 | − | 3.91445e7i | −0.0499096 | − | 0.0570512i | ||||
\(883\) | −9.67235e8 | −1.40492 | −0.702458 | − | 0.711726i | \(-0.747914\pi\) | ||||
−0.702458 | + | 0.711726i | \(0.747914\pi\) | |||||||
\(884\) | 1.19389e7 | − | 8.90071e7i | 0.0172826 | − | 0.128845i | ||||
\(885\) | 2.22761e8 | − | 2.37249e7i | 0.321372 | − | 0.0342275i | ||||
\(886\) | −5.53448e8 | − | 6.32641e8i | −0.795748 | − | 0.909612i | ||||
\(887\) | −2.50813e8 | −0.359400 | −0.179700 | − | 0.983721i | \(-0.557513\pi\) | ||||
−0.179700 | + | 0.983721i | \(0.557513\pi\) | |||||||
\(888\) | 4.34701e8 | + | 6.55756e8i | 0.620800 | + | 0.936491i | ||||
\(889\) | 5.08599e8 | 0.723886 | ||||||||
\(890\) | 7.19084e8 | − | 7.78158e8i | 1.02002 | − | 1.10382i | ||||
\(891\) | − | 5.00296e7i | − | 0.0707284i | ||||||
\(892\) | −5.31625e7 | + | 3.96338e8i | −0.0749050 | + | 0.558433i | ||||
\(893\) | 1.87221e8i | 0.262905i | ||||||||
\(894\) | 1.21751e8 | + | 1.39172e8i | 0.170396 | + | 0.194778i | ||||
\(895\) | −1.13061e9 | + | 1.20415e8i | −1.57705 | + | 0.167962i | ||||
\(896\) | −7.56792e8 | + | 2.49713e8i | −1.05209 | + | 0.347149i | ||||
\(897\) | − | 7.51899e7i | − | 0.104180i | ||||||
\(898\) | −9.90777e7 | − | 1.13255e8i | −0.136819 | − | 0.156397i | ||||
\(899\) | 8.69273e6i | 0.0119640i | ||||||||
\(900\) | −1.91455e7 | − | 2.42245e8i | −0.0262627 | − | 0.332297i | ||||
\(901\) | −5.77400e8 | −0.789410 | ||||||||
\(902\) | −3.55094e8 | + | 3.10643e8i | −0.483864 | + | 0.423295i | ||||
\(903\) | 8.64165e8 | 1.17364 | ||||||||
\(904\) | 6.46209e8 | + | 9.74821e8i | 0.874717 | + | 1.31953i | ||||
\(905\) | 4.77925e7 | + | 4.48738e8i | 0.0644783 | + | 0.605407i | ||||
\(906\) | −1.37236e8 | + | 1.20057e8i | −0.184537 | + | 0.161437i | ||||
\(907\) | −1.03612e9 | −1.38863 | −0.694315 | − | 0.719672i | \(-0.744292\pi\) | ||||
−0.694315 | + | 0.719672i | \(0.744292\pi\) | |||||||
\(908\) | −7.65808e7 | + | 5.70926e8i | −0.102297 | + | 0.762645i | ||||
\(909\) | −3.62218e8 | −0.482257 | ||||||||
\(910\) | 8.69062e7 | + | 8.03087e7i | 0.115326 | + | 0.106571i | ||||
\(911\) | 2.02292e8i | 0.267562i | 0.991011 | + | 0.133781i | \(0.0427118\pi\) | ||||
−0.991011 | + | 0.133781i | \(0.957288\pi\) | |||||||
\(912\) | −9.35729e7 | + | 3.42527e8i | −0.123357 | + | 0.451555i | ||||
\(913\) | 3.29476e7i | 0.0432923i | ||||||||
\(914\) | −1.86060e8 | + | 1.62769e8i | −0.243676 | + | 0.213173i | ||||
\(915\) | 5.25798e7 | + | 4.93688e8i | 0.0686366 | + | 0.644450i | ||||
\(916\) | −6.79349e7 | + | 5.06469e8i | −0.0883908 | + | 0.658972i | ||||
\(917\) | − | 1.33024e9i | − | 1.72513i | ||||||
\(918\) | 1.02777e8 | − | 8.99115e7i | 0.132852 | − | 0.116222i | ||||
\(919\) | − | 8.53644e8i | − | 1.09984i | −0.835217 | − | 0.549921i | \(-0.814658\pi\) | ||
0.835217 | − | 0.549921i | \(-0.185342\pi\) | |||||||
\(920\) | 6.32173e8 | + | 7.63630e8i | 0.811843 | + | 0.980663i | ||||
\(921\) | −4.48648e7 | −0.0574284 | ||||||||
\(922\) | 1.74826e8 | + | 1.99842e8i | 0.223055 | + | 0.254972i | ||||
\(923\) | 5.14706e7 | 0.0654567 | ||||||||
\(924\) | −3.18356e8 | − | 4.27025e7i | −0.403550 | − | 0.0541299i | ||||
\(925\) | 3.24402e8 | + | 1.50568e9i | 0.409881 | + | 1.90242i | ||||
\(926\) | 7.02238e7 | + | 8.02721e7i | 0.0884405 | + | 0.101096i | ||||
\(927\) | 1.21227e8 | 0.152181 | ||||||||
\(928\) | −2.70285e8 | − | 5.56613e8i | −0.338203 | − | 0.696482i | ||||
\(929\) | 1.26523e9 | 1.57805 | 0.789027 | − | 0.614358i | \(-0.210585\pi\) | ||||
0.789027 | + | 0.614358i | \(0.210585\pi\) | |||||||
\(930\) | −5.27030e6 | − | 4.87020e6i | −0.00655219 | − | 0.00605478i | ||||
\(931\) | 1.48781e8i | 0.184373i | ||||||||
\(932\) | 3.28632e8 | + | 4.40808e7i | 0.405940 | + | 0.0544505i | ||||
\(933\) | − | 6.01246e7i | − | 0.0740299i | ||||||
\(934\) | −4.50256e8 | − | 5.14683e8i | −0.552610 | − | 0.631683i | ||||
\(935\) | 5.05415e7 | + | 4.74550e8i | 0.0618321 | + | 0.580560i | ||||
\(936\) | −2.14061e7 | − | 3.22916e7i | −0.0261042 | − | 0.0393788i | ||||
\(937\) | − | 1.48128e9i | − | 1.80060i | −0.435265 | − | 0.900302i | \(-0.643345\pi\) | ||
0.435265 | − | 0.900302i | \(-0.356655\pi\) | |||||||
\(938\) | 1.04768e9 | + | 1.19759e9i | 1.26946 | + | 1.45111i | ||||
\(939\) | 2.86290e8i | 0.345788i | ||||||||
\(940\) | 2.69229e8 | + | 7.33408e6i | 0.324144 | + | 0.00883003i | ||||
\(941\) | −5.87649e7 | −0.0705259 | −0.0352630 | − | 0.999378i | \(-0.511227\pi\) | ||||
−0.0352630 | + | 0.999378i | \(0.511227\pi\) | |||||||
\(942\) | 4.39570e8 | − | 3.84545e8i | 0.525866 | − | 0.460039i | ||||
\(943\) | −1.07819e9 | −1.28576 | ||||||||
\(944\) | −1.24097e8 | + | 4.54260e8i | −0.147518 | + | 0.539994i | ||||
\(945\) | 1.90557e7 | + | 1.78920e8i | 0.0225803 | + | 0.212013i | ||||
\(946\) | 7.44216e8 | − | 6.51056e8i | 0.879075 | − | 0.769033i | ||||
\(947\) | −8.51061e8 | −1.00210 | −0.501050 | − | 0.865419i | \(-0.667053\pi\) | ||||
−0.501050 | + | 0.865419i | \(0.667053\pi\) | |||||||
\(948\) | −1.00360e8 | − | 1.34618e7i | −0.117798 | − | 0.0158007i | ||||
\(949\) | 1.58278e8 | 0.185192 | ||||||||
\(950\) | −4.15055e8 | + | 5.57626e8i | −0.484099 | + | 0.650387i | ||||
\(951\) | − | 2.30560e8i | − | 0.268067i | ||||||
\(952\) | −4.84414e8 | − | 7.30750e8i | −0.561443 | − | 0.846950i | ||||
\(953\) | − | 4.68464e8i | − | 0.541250i | −0.962685 | − | 0.270625i | \(-0.912770\pi\) | ||
0.962685 | − | 0.270625i | \(-0.0872303\pi\) | |||||||
\(954\) | −1.87480e8 | + | 1.64012e8i | −0.215929 | + | 0.188899i | ||||
\(955\) | −9.57985e7 | + | 1.02029e7i | −0.109989 | + | 0.0117143i | ||||
\(956\) | 1.36360e8 | + | 1.82906e7i | 0.156068 | + | 0.0209341i | ||||
\(957\) | − | 2.49399e8i | − | 0.284550i | ||||||
\(958\) | 7.69294e7 | − | 6.72995e7i | 0.0874975 | − | 0.0765447i | ||||
\(959\) | − | 1.43301e9i | − | 1.62478i | ||||||
\(960\) | 4.88898e8 | + | 1.47979e8i | 0.552592 | + | 0.167257i | ||||
\(961\) | 8.87292e8 | 0.999761 | ||||||||
\(962\) | 1.61687e8 | + | 1.84822e8i | 0.181614 | + | 0.207601i | ||||
\(963\) | 2.85268e8 | 0.319429 | ||||||||
\(964\) | −8.00248e7 | + | 5.96602e8i | −0.0893292 | + | 0.665968i | ||||
\(965\) | −1.06502e8 | + | 1.13429e7i | −0.118515 | + | 0.0126224i | ||||
\(966\) | −4.83322e8 | − | 5.52480e8i | −0.536173 | − | 0.612894i | ||||
\(967\) | 5.93383e8 | 0.656229 | 0.328114 | − | 0.944638i | \(-0.393587\pi\) | ||||
0.328114 | + | 0.944638i | \(0.393587\pi\) | |||||||
\(968\) | 4.49675e8 | − | 2.98090e8i | 0.495761 | − | 0.328640i | ||||
\(969\) | −3.90635e8 | −0.429339 | ||||||||
\(970\) | 4.64085e8 | + | 4.28853e8i | 0.508490 | + | 0.469887i | ||||
\(971\) | − | 4.83882e8i | − | 0.528544i | −0.964448 | − | 0.264272i | \(-0.914868\pi\) | ||
0.964448 | − | 0.264272i | \(-0.0851317\pi\) | |||||||
\(972\) | 7.83183e6 | − | 5.83880e7i | 0.00852834 | − | 0.0635806i | ||||
\(973\) | 2.25375e8i | 0.244663i | ||||||||
\(974\) | −1.68699e8 | − | 1.92838e8i | −0.182572 | − | 0.208696i | ||||
\(975\) | −1.59746e7 | − | 7.41447e7i | −0.0172352 | − | 0.0799956i | ||||
\(976\) | −1.00674e9 | − | 2.75026e8i | −1.08285 | − | 0.295818i | ||||
\(977\) | 2.25662e8i | 0.241977i | 0.992654 | + | 0.120989i | \(0.0386064\pi\) | ||||
−0.992654 | + | 0.120989i | \(0.961394\pi\) | |||||||
\(978\) | 5.56717e8 | + | 6.36378e8i | 0.595139 | + | 0.680297i | ||||
\(979\) | 8.97695e8i | 0.956711i | ||||||||
\(980\) | 2.13951e8 | + | 5.82826e6i | 0.227319 | + | 0.00619242i | ||||
\(981\) | 3.02404e8 | 0.320318 | ||||||||
\(982\) | −1.14141e9 | + | 9.98529e8i | −1.20533 | + | 1.05445i | ||||
\(983\) | 2.00052e8 | 0.210611 | 0.105306 | − | 0.994440i | \(-0.466418\pi\) | ||||
0.105306 | + | 0.994440i | \(0.466418\pi\) | |||||||
\(984\) | −4.63048e8 | + | 3.06955e8i | −0.486005 | + | 0.322173i | ||||
\(985\) | 7.96301e8 | − | 8.48093e7i | 0.833237 | − | 0.0887432i | ||||
\(986\) | 5.12346e8 | − | 4.48211e8i | 0.534481 | − | 0.467576i | ||||
\(987\) | −1.99427e8 | −0.207411 | ||||||||
\(988\) | −1.47339e7 | + | 1.09845e8i | −0.0152773 | + | 0.113896i | ||||
\(989\) | 2.25971e9 | 2.33595 | ||||||||
\(990\) | 1.51208e8 | + | 1.39729e8i | 0.155836 | + | 0.144006i | ||||
\(991\) | − | 9.52073e8i | − | 0.978249i | −0.872214 | − | 0.489125i | \(-0.837316\pi\) | ||
0.872214 | − | 0.489125i | \(-0.162684\pi\) | |||||||
\(992\) | 1.35692e7 | − | 6.58906e6i | 0.0139002 | − | 0.00674977i | ||||
\(993\) | 8.92517e8i | 0.911526i | ||||||||
\(994\) | 3.78196e8 | − | 3.30854e8i | 0.385086 | − | 0.336881i | ||||
\(995\) | −9.65319e8 | + | 1.02810e8i | −0.979945 | + | 0.104368i | ||||
\(996\) | −5.15775e6 | + | 3.84521e7i | −0.00522014 | + | 0.0389172i | ||||
\(997\) | − | 2.94735e8i | − | 0.297404i | −0.988882 | − | 0.148702i | \(-0.952491\pi\) | ||
0.988882 | − | 0.148702i | \(-0.0475094\pi\) | |||||||
\(998\) | 7.34561e8 | − | 6.42610e8i | 0.738987 | − | 0.646481i | ||||
\(999\) | 3.73401e8i | 0.374523i |
(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 | 60.7.f.a.19.9 | ✓ | 36 | |
3.2 | odd | 2 | 180.7.f.g.19.28 | 36 | |||
4.3 | odd | 2 | inner | 60.7.f.a.19.27 | yes | 36 | |
5.4 | even | 2 | inner | 60.7.f.a.19.28 | yes | 36 | |
12.11 | even | 2 | 180.7.f.g.19.10 | 36 | |||
15.14 | odd | 2 | 180.7.f.g.19.9 | 36 | |||
20.19 | odd | 2 | inner | 60.7.f.a.19.10 | yes | 36 | |
60.59 | even | 2 | 180.7.f.g.19.27 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.f.a.19.9 | ✓ | 36 | 1.1 | even | 1 | trivial | |
60.7.f.a.19.10 | yes | 36 | 20.19 | odd | 2 | inner | |
60.7.f.a.19.27 | yes | 36 | 4.3 | odd | 2 | inner | |
60.7.f.a.19.28 | yes | 36 | 5.4 | even | 2 | inner | |
180.7.f.g.19.9 | 36 | 15.14 | odd | 2 | |||
180.7.f.g.19.10 | 36 | 12.11 | even | 2 | |||
180.7.f.g.19.27 | 36 | 60.59 | even | 2 | |||
180.7.f.g.19.28 | 36 | 3.2 | odd | 2 |