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 | 6.17 | ||
Character | \(\chi\) | \(=\) | 43.6 |
Dual form | 43.6.c.a.36.17 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.96731 | 1.76199 | 0.880994 | − | 0.473128i | \(-0.156875\pi\) | ||||
0.880994 | + | 0.473128i | \(0.156875\pi\) | |||||||
\(3\) | −9.83333 | + | 17.0318i | −0.630809 | + | 1.09259i | 0.356578 | + | 0.934265i | \(0.383943\pi\) |
−0.987387 | + | 0.158327i | \(0.949390\pi\) | |||||||
\(4\) | 67.3472 | 2.10460 | ||||||||
\(5\) | 6.65929 | − | 11.5342i | 0.119125 | − | 0.206330i | −0.800296 | − | 0.599605i | \(-0.795324\pi\) |
0.919421 | + | 0.393274i | \(0.128658\pi\) | |||||||
\(6\) | −98.0118 | + | 169.761i | −1.11148 | + | 1.92513i | ||||
\(7\) | 61.0081 | + | 105.669i | 0.470590 | + | 0.815085i | 0.999434 | − | 0.0336333i | \(-0.0107078\pi\) |
−0.528844 | + | 0.848719i | \(0.677375\pi\) | |||||||
\(8\) | 352.316 | 1.94629 | ||||||||
\(9\) | −71.8888 | − | 124.515i | −0.295839 | − | 0.512408i | ||||
\(10\) | 66.3751 | − | 114.965i | 0.209897 | − | 0.363552i | ||||
\(11\) | −64.2046 | −0.159987 | −0.0799935 | − | 0.996795i | \(-0.525490\pi\) | ||||
−0.0799935 | + | 0.996795i | \(0.525490\pi\) | |||||||
\(12\) | −662.247 | + | 1147.05i | −1.32760 | + | 2.29947i | ||||
\(13\) | 38.2202 | + | 66.1993i | 0.0627241 | + | 0.108641i | 0.895682 | − | 0.444695i | \(-0.146688\pi\) |
−0.832958 | + | 0.553336i | \(0.813355\pi\) | |||||||
\(14\) | 608.087 | + | 1053.24i | 0.829173 | + | 1.43617i | ||||
\(15\) | 130.966 | + | 226.840i | 0.150290 | + | 0.260310i | ||||
\(16\) | 1356.53 | 1.32474 | ||||||||
\(17\) | −984.059 | − | 1704.44i | −0.825846 | − | 1.43041i | −0.901271 | − | 0.433255i | \(-0.857365\pi\) |
0.0754258 | − | 0.997151i | \(-0.475968\pi\) | |||||||
\(18\) | −716.538 | − | 1241.08i | −0.521264 | − | 0.902856i | ||||
\(19\) | 1244.22 | − | 2155.06i | 0.790705 | − | 1.36954i | −0.134826 | − | 0.990869i | \(-0.543048\pi\) |
0.925531 | − | 0.378672i | \(-0.123619\pi\) | |||||||
\(20\) | 448.484 | − | 776.797i | 0.250710 | − | 0.434243i | ||||
\(21\) | −2399.65 | −1.18741 | ||||||||
\(22\) | −639.947 | −0.281895 | ||||||||
\(23\) | 2292.28 | − | 3970.35i | 0.903543 | − | 1.56498i | 0.0806819 | − | 0.996740i | \(-0.474290\pi\) |
0.822861 | − | 0.568243i | \(-0.192376\pi\) | |||||||
\(24\) | −3464.44 | + | 6000.59i | −1.22774 | + | 2.12650i | ||||
\(25\) | 1473.81 | + | 2552.71i | 0.471619 | + | 0.816867i | ||||
\(26\) | 380.952 | + | 659.828i | 0.110519 | + | 0.191425i | ||||
\(27\) | −1951.37 | −0.515146 | ||||||||
\(28\) | 4108.72 | + | 7116.52i | 0.990403 | + | 1.71543i | ||||
\(29\) | 887.712 | + | 1537.56i | 0.196010 | + | 0.339499i | 0.947231 | − | 0.320552i | \(-0.103868\pi\) |
−0.751221 | + | 0.660050i | \(0.770535\pi\) | |||||||
\(30\) | 1305.38 | + | 2260.98i | 0.264809 | + | 0.458663i | ||||
\(31\) | −721.458 | + | 1249.60i | −0.134836 | + | 0.233543i | −0.925535 | − | 0.378662i | \(-0.876384\pi\) |
0.790699 | + | 0.612206i | \(0.209718\pi\) | |||||||
\(32\) | 2246.86 | 0.387883 | ||||||||
\(33\) | 631.345 | − | 1093.52i | 0.100921 | − | 0.174801i | ||||
\(34\) | −9808.42 | − | 16988.7i | −1.45513 | − | 2.52036i | ||||
\(35\) | 1625.08 | 0.224236 | ||||||||
\(36\) | −4841.51 | − | 8385.74i | −0.622622 | − | 1.07841i | ||||
\(37\) | −4283.83 | + | 7419.81i | −0.514432 | + | 0.891022i | 0.485428 | + | 0.874277i | \(0.338664\pi\) |
−0.999860 | + | 0.0167456i | \(0.994669\pi\) | |||||||
\(38\) | 12401.6 | − | 21480.1i | 1.39321 | − | 2.41311i | ||||
\(39\) | −1503.33 | −0.158267 | ||||||||
\(40\) | 2346.17 | − | 4063.69i | 0.231852 | − | 0.401579i | ||||
\(41\) | −4836.07 | −0.449296 | −0.224648 | − | 0.974440i | \(-0.572123\pi\) | ||||
−0.224648 | + | 0.974440i | \(0.572123\pi\) | |||||||
\(42\) | −23918.1 | −2.09220 | ||||||||
\(43\) | 2285.74 | + | 11907.3i | 0.188519 | + | 0.982070i | ||||
\(44\) | −4324.00 | −0.336708 | ||||||||
\(45\) | −1914.91 | −0.140967 | ||||||||
\(46\) | 22847.9 | − | 39573.7i | 1.59203 | − | 2.75748i | ||||
\(47\) | −9504.55 | −0.627606 | −0.313803 | − | 0.949488i | \(-0.601603\pi\) | ||||
−0.313803 | + | 0.949488i | \(0.601603\pi\) | |||||||
\(48\) | −13339.2 | + | 23104.2i | −0.835656 | + | 1.44740i | ||||
\(49\) | 959.520 | − | 1661.94i | 0.0570905 | − | 0.0988836i | ||||
\(50\) | 14689.9 | + | 25443.6i | 0.830986 | + | 1.43931i | ||||
\(51\) | 38706.3 | 2.08380 | ||||||||
\(52\) | 2574.02 | + | 4458.33i | 0.132009 | + | 0.228646i | ||||
\(53\) | −10269.9 | + | 17787.9i | −0.502198 | + | 0.869832i | 0.497799 | + | 0.867292i | \(0.334142\pi\) |
−0.999997 | + | 0.00253957i | \(0.999192\pi\) | |||||||
\(54\) | −19449.9 | −0.907681 | ||||||||
\(55\) | −427.557 | + | 740.550i | −0.0190584 | + | 0.0330102i | ||||
\(56\) | 21494.1 | + | 37228.9i | 0.915904 | + | 1.58639i | ||||
\(57\) | 24469.7 | + | 42382.8i | 0.997567 | + | 1.72784i | ||||
\(58\) | 8848.10 | + | 15325.4i | 0.345366 | + | 0.598192i | ||||
\(59\) | −12309.9 | −0.460388 | −0.230194 | − | 0.973145i | \(-0.573936\pi\) | ||||
−0.230194 | + | 0.973145i | \(0.573936\pi\) | |||||||
\(60\) | 8820.19 | + | 15277.0i | 0.316300 | + | 0.547848i | ||||
\(61\) | −9716.67 | − | 16829.8i | −0.334343 | − | 0.579100i | 0.649015 | − | 0.760776i | \(-0.275181\pi\) |
−0.983358 | + | 0.181676i | \(0.941848\pi\) | |||||||
\(62\) | −7190.99 | + | 12455.2i | −0.237580 | + | 0.411500i | ||||
\(63\) | 8771.60 | − | 15192.9i | 0.278437 | − | 0.482268i | ||||
\(64\) | −21013.9 | −0.641294 | ||||||||
\(65\) | 1018.08 | 0.0298880 | ||||||||
\(66\) | 6292.81 | − | 10899.5i | 0.177822 | − | 0.307996i | ||||
\(67\) | 34280.7 | − | 59375.9i | 0.932959 | − | 1.61593i | 0.154725 | − | 0.987958i | \(-0.450551\pi\) |
0.778234 | − | 0.627974i | \(-0.216116\pi\) | |||||||
\(68\) | −66273.6 | − | 114789.i | −1.73807 | − | 3.01043i | ||||
\(69\) | 45081.6 | + | 78083.6i | 1.13993 | + | 1.97441i | ||||
\(70\) | 16197.7 | 0.395101 | ||||||||
\(71\) | 21742.0 | + | 37658.3i | 0.511864 | + | 0.886574i | 0.999905 | + | 0.0137540i | \(0.00437817\pi\) |
−0.488041 | + | 0.872820i | \(0.662289\pi\) | |||||||
\(72\) | −25327.6 | − | 43868.7i | −0.575788 | − | 0.997294i | ||||
\(73\) | 27405.2 | + | 47467.3i | 0.601903 | + | 1.04253i | 0.992533 | + | 0.121978i | \(0.0389238\pi\) |
−0.390630 | + | 0.920548i | \(0.627743\pi\) | |||||||
\(74\) | −42698.2 | + | 73955.5i | −0.906423 | + | 1.56997i | ||||
\(75\) | −57969.8 | −1.19000 | ||||||||
\(76\) | 83795.0 | − | 145137.i | 1.66412 | − | 2.88234i | ||||
\(77\) | −3917.00 | − | 6784.45i | −0.0752882 | − | 0.130403i | ||||
\(78\) | −14984.1 | −0.278865 | ||||||||
\(79\) | −14291.6 | − | 24753.9i | −0.257641 | − | 0.446247i | 0.707969 | − | 0.706244i | \(-0.249612\pi\) |
−0.965609 | + | 0.259997i | \(0.916278\pi\) | |||||||
\(80\) | 9033.54 | − | 15646.5i | 0.157809 | − | 0.273334i | ||||
\(81\) | 36657.5 | − | 63492.6i | 0.620798 | − | 1.07525i | ||||
\(82\) | −48202.6 | −0.791655 | ||||||||
\(83\) | −3057.73 | + | 5296.14i | −0.0487196 | + | 0.0843848i | −0.889357 | − | 0.457214i | \(-0.848847\pi\) |
0.840637 | + | 0.541599i | \(0.182181\pi\) | |||||||
\(84\) | −161610. | −2.49902 | ||||||||
\(85\) | −26212.5 | −0.393515 | ||||||||
\(86\) | 22782.7 | + | 118684.i | 0.332168 | + | 1.73039i | ||||
\(87\) | −34916.7 | −0.494578 | ||||||||
\(88\) | −22620.3 | −0.311381 | ||||||||
\(89\) | −37106.7 | + | 64270.7i | −0.496567 | + | 0.860078i | −0.999992 | − | 0.00396011i | \(-0.998739\pi\) |
0.503426 | + | 0.864039i | \(0.332073\pi\) | |||||||
\(90\) | −19086.5 | −0.248382 | ||||||||
\(91\) | −4663.48 | + | 8077.38i | −0.0590346 | + | 0.102251i | ||||
\(92\) | 154379. | − | 267392.i | 1.90160 | − | 3.29366i | ||||
\(93\) | −14188.7 | − | 24575.5i | −0.170112 | − | 0.294642i | ||||
\(94\) | −94734.7 | −1.10583 | ||||||||
\(95\) | −16571.3 | − | 28702.3i | −0.188385 | − | 0.326293i | ||||
\(96\) | −22094.1 | + | 38268.1i | −0.244680 | + | 0.423798i | ||||
\(97\) | 65857.2 | 0.710680 | 0.355340 | − | 0.934737i | \(-0.384365\pi\) | ||||
0.355340 | + | 0.934737i | \(0.384365\pi\) | |||||||
\(98\) | 9563.82 | − | 16565.0i | 0.100593 | − | 0.174232i | ||||
\(99\) | 4615.60 | + | 7994.45i | 0.0473304 | + | 0.0819786i | ||||
\(100\) | 99256.8 | + | 171918.i | 0.992568 | + | 1.71918i | ||||
\(101\) | −99361.1 | − | 172098.i | −0.969199 | − | 1.67870i | −0.697885 | − | 0.716210i | \(-0.745875\pi\) |
−0.271314 | − | 0.962491i | \(-0.587458\pi\) | |||||||
\(102\) | 385798. | 3.67163 | ||||||||
\(103\) | −12190.9 | − | 21115.3i | −0.113225 | − | 0.196112i | 0.803844 | − | 0.594841i | \(-0.202785\pi\) |
−0.917069 | + | 0.398729i | \(0.869451\pi\) | |||||||
\(104\) | 13465.6 | + | 23323.1i | 0.122079 | + | 0.211447i | ||||
\(105\) | −15980.0 | + | 27678.1i | −0.141450 | + | 0.244998i | ||||
\(106\) | −102363. | + | 177298.i | −0.884866 | + | 1.53263i | ||||
\(107\) | 184018. | 1.55382 | 0.776912 | − | 0.629609i | \(-0.216785\pi\) | ||||
0.776912 | + | 0.629609i | \(0.216785\pi\) | |||||||
\(108\) | −131419. | −1.08418 | ||||||||
\(109\) | −104049. | + | 180219.i | −0.838828 | + | 1.45289i | 0.0520468 | + | 0.998645i | \(0.483425\pi\) |
−0.890875 | + | 0.454248i | \(0.849908\pi\) | |||||||
\(110\) | −4261.59 | + | 7381.29i | −0.0335807 | + | 0.0581635i | ||||
\(111\) | −84248.7 | − | 145923.i | −0.649016 | − | 1.12413i | ||||
\(112\) | 82759.5 | + | 143344.i | 0.623409 | + | 1.07978i | ||||
\(113\) | 40753.9 | 0.300243 | 0.150122 | − | 0.988668i | \(-0.452033\pi\) | ||||
0.150122 | + | 0.988668i | \(0.452033\pi\) | |||||||
\(114\) | 243897. | + | 422442.i | 1.75770 | + | 3.04443i | ||||
\(115\) | −30529.9 | − | 52879.4i | −0.215269 | − | 0.372857i | ||||
\(116\) | 59784.9 | + | 103551.i | 0.412522 | + | 0.714508i | ||||
\(117\) | 5495.21 | − | 9517.98i | 0.0371124 | − | 0.0642806i | ||||
\(118\) | −122696. | −0.811198 | ||||||||
\(119\) | 120071. | − | 207969.i | 0.777269 | − | 1.34627i | ||||
\(120\) | 46141.4 | + | 79919.3i | 0.292508 | + | 0.506639i | ||||
\(121\) | −156929. | −0.974404 | ||||||||
\(122\) | −96849.0 | − | 167747.i | −0.589109 | − | 1.02037i | ||||
\(123\) | 47554.7 | − | 82367.1i | 0.283420 | − | 0.490898i | ||||
\(124\) | −48588.2 | + | 84157.2i | −0.283776 | + | 0.491515i | ||||
\(125\) | 80878.6 | 0.462976 | ||||||||
\(126\) | 87429.3 | − | 151432.i | 0.490603 | − | 0.849750i | ||||
\(127\) | −248512. | −1.36722 | −0.683608 | − | 0.729849i | \(-0.739590\pi\) | ||||
−0.683608 | + | 0.729849i | \(0.739590\pi\) | |||||||
\(128\) | −281352. | −1.51783 | ||||||||
\(129\) | −225280. | − | 78158.1i | −1.19192 | − | 0.413523i | ||||
\(130\) | 10147.5 | 0.0526623 | ||||||||
\(131\) | −254368. | −1.29504 | −0.647522 | − | 0.762047i | \(-0.724195\pi\) | ||||
−0.647522 | + | 0.762047i | \(0.724195\pi\) | |||||||
\(132\) | 42519.3 | − | 73645.6i | 0.212399 | − | 0.367885i | ||||
\(133\) | 303631. | 1.48839 | ||||||||
\(134\) | 341686. | − | 591818.i | 1.64386 | − | 2.84725i | ||||
\(135\) | −12994.7 | + | 22507.6i | −0.0613668 | + | 0.106290i | ||||
\(136\) | −346700. | − | 600502.i | −1.60733 | − | 2.78399i | ||||
\(137\) | −89866.3 | −0.409068 | −0.204534 | − | 0.978859i | \(-0.565568\pi\) | ||||
−0.204534 | + | 0.978859i | \(0.565568\pi\) | |||||||
\(138\) | 449342. | + | 778283.i | 2.00853 | + | 3.47888i | ||||
\(139\) | −155524. | + | 269376.i | −0.682748 | + | 1.18255i | 0.291390 | + | 0.956604i | \(0.405882\pi\) |
−0.974139 | + | 0.225951i | \(0.927451\pi\) | |||||||
\(140\) | 109445. | 0.471927 | ||||||||
\(141\) | 93461.4 | − | 161880.i | 0.395899 | − | 0.685717i | ||||
\(142\) | 216710. | + | 375352.i | 0.901898 | + | 1.56213i | ||||
\(143\) | −2453.91 | − | 4250.30i | −0.0100350 | − | 0.0173812i | ||||
\(144\) | −97519.5 | − | 168909.i | −0.391909 | − | 0.678807i | ||||
\(145\) | 23646.1 | 0.0933985 | ||||||||
\(146\) | 273156. | + | 473121.i | 1.06054 | + | 1.83692i | ||||
\(147\) | 18870.5 | + | 32684.7i | 0.0720263 | + | 0.124753i | ||||
\(148\) | −288504. | + | 499703.i | −1.08267 | + | 1.87525i | ||||
\(149\) | 67505.9 | − | 116924.i | 0.249101 | − | 0.431456i | −0.714175 | − | 0.699967i | \(-0.753198\pi\) |
0.963277 | + | 0.268511i | \(0.0865314\pi\) | |||||||
\(150\) | −577802. | −2.09677 | ||||||||
\(151\) | 233223. | 0.832393 | 0.416197 | − | 0.909275i | \(-0.363363\pi\) | ||||
0.416197 | + | 0.909275i | \(0.363363\pi\) | |||||||
\(152\) | 438360. | − | 759262.i | 1.53894 | − | 2.66552i | ||||
\(153\) | −141486. | + | 245060.i | −0.488634 | + | 0.846340i | ||||
\(154\) | −39042.0 | − | 67622.7i | −0.132657 | − | 0.229769i | ||||
\(155\) | 9608.79 | + | 16642.9i | 0.0321247 | + | 0.0556417i | ||||
\(156\) | −101245. | −0.333090 | ||||||||
\(157\) | 171445. | + | 296952.i | 0.555107 | + | 0.961473i | 0.997895 | + | 0.0648469i | \(0.0206559\pi\) |
−0.442789 | + | 0.896626i | \(0.646011\pi\) | |||||||
\(158\) | −142449. | − | 246729.i | −0.453960 | − | 0.786281i | ||||
\(159\) | −201974. | − | 349829.i | −0.633581 | − | 1.09739i | ||||
\(160\) | 14962.5 | − | 25915.8i | 0.0462065 | − | 0.0800321i | ||||
\(161\) | 559392. | 1.70079 | ||||||||
\(162\) | 365376. | − | 632850.i | 1.09384 | − | 1.89458i | ||||
\(163\) | 28679.6 | + | 49674.5i | 0.0845481 | + | 0.146442i | 0.905199 | − | 0.424989i | \(-0.139722\pi\) |
−0.820650 | + | 0.571431i | \(0.806389\pi\) | |||||||
\(164\) | −325696. | −0.945589 | ||||||||
\(165\) | −8408.62 | − | 14564.2i | −0.0240444 | − | 0.0416462i | ||||
\(166\) | −30477.3 | + | 52788.2i | −0.0858432 | + | 0.148685i | ||||
\(167\) | 66256.0 | − | 114759.i | 0.183838 | − | 0.318416i | −0.759347 | − | 0.650686i | \(-0.774481\pi\) |
0.943184 | + | 0.332270i | \(0.107815\pi\) | |||||||
\(168\) | −845436. | −2.31104 | ||||||||
\(169\) | 182725. | − | 316489.i | 0.492131 | − | 0.852397i | ||||
\(170\) | −261268. | −0.693369 | ||||||||
\(171\) | −357783. | −0.935685 | ||||||||
\(172\) | 153938. | + | 801923.i | 0.396757 | + | 2.06686i | ||||
\(173\) | 159660. | 0.405585 | 0.202792 | − | 0.979222i | \(-0.434998\pi\) | ||||
0.202792 | + | 0.979222i | \(0.434998\pi\) | |||||||
\(174\) | −348025. | −0.871440 | ||||||||
\(175\) | −179828. | + | 311472.i | −0.443878 | + | 0.768819i | ||||
\(176\) | −87095.7 | −0.211941 | ||||||||
\(177\) | 121047. | − | 209660.i | 0.290417 | − | 0.503016i | ||||
\(178\) | −369854. | + | 640606.i | −0.874944 | + | 1.51545i | ||||
\(179\) | −41797.1 | − | 72394.7i | −0.0975020 | − | 0.168878i | 0.813148 | − | 0.582057i | \(-0.197752\pi\) |
−0.910650 | + | 0.413178i | \(0.864419\pi\) | |||||||
\(180\) | −128964. | −0.296679 | ||||||||
\(181\) | 155097. | + | 268635.i | 0.351889 | + | 0.609490i | 0.986580 | − | 0.163276i | \(-0.0522060\pi\) |
−0.634691 | + | 0.772766i | \(0.718873\pi\) | |||||||
\(182\) | −46482.3 | + | 80509.8i | −0.104018 | + | 0.180165i | ||||
\(183\) | 382189. | 0.843627 | ||||||||
\(184\) | 807609. | − | 1.39882e6i | 1.75856 | − | 3.04591i | ||||
\(185\) | 57054.5 | + | 98821.3i | 0.122563 | + | 0.212286i | ||||
\(186\) | −141423. | − | 244952.i | −0.299735 | − | 0.519156i | ||||
\(187\) | 63181.1 | + | 109433.i | 0.132125 | + | 0.228846i | ||||
\(188\) | −640104. | −1.32086 | ||||||||
\(189\) | −119050. | − | 206200.i | −0.242423 | − | 0.419888i | ||||
\(190\) | −165171. | − | 286085.i | −0.331933 | − | 0.574924i | ||||
\(191\) | 116587. | − | 201934.i | 0.231241 | − | 0.400521i | −0.726932 | − | 0.686709i | \(-0.759055\pi\) |
0.958174 | + | 0.286187i | \(0.0923880\pi\) | |||||||
\(192\) | 206637. | − | 357905.i | 0.404534 | − | 0.700673i | ||||
\(193\) | −304008. | −0.587478 | −0.293739 | − | 0.955886i | \(-0.594900\pi\) | ||||
−0.293739 | + | 0.955886i | \(0.594900\pi\) | |||||||
\(194\) | 656419. | 1.25221 | ||||||||
\(195\) | −10011.1 | + | 17339.7i | −0.0188536 | + | 0.0326554i | ||||
\(196\) | 64620.9 | − | 111927.i | 0.120153 | − | 0.208110i | ||||
\(197\) | 378642. | + | 655827.i | 0.695126 | + | 1.20399i | 0.970138 | + | 0.242552i | \(0.0779846\pi\) |
−0.275013 | + | 0.961441i | \(0.588682\pi\) | |||||||
\(198\) | 46005.1 | + | 79683.1i | 0.0833955 | + | 0.144445i | ||||
\(199\) | −615727. | −1.10219 | −0.551094 | − | 0.834443i | \(-0.685789\pi\) | ||||
−0.551094 | + | 0.834443i | \(0.685789\pi\) | |||||||
\(200\) | 519246. | + | 899361.i | 0.917906 | + | 1.58986i | ||||
\(201\) | 674187. | + | 1.16773e6i | 1.17704 | + | 2.03869i | ||||
\(202\) | −990362. | − | 1.71536e6i | −1.70772 | − | 2.95785i | ||||
\(203\) | −108315. | + | 187608.i | −0.184480 | + | 0.319529i | ||||
\(204\) | 2.60676e6 | 4.38557 | ||||||||
\(205\) | −32204.8 | + | 55780.3i | −0.0535224 | + | 0.0927035i | ||||
\(206\) | −121511. | − | 210462.i | −0.199501 | − | 0.345547i | ||||
\(207\) | −659159. | −1.06921 | ||||||||
\(208\) | 51846.9 | + | 89801.4i | 0.0830930 | + | 0.143921i | ||||
\(209\) | −79884.9 | + | 138365.i | −0.126502 | + | 0.219109i | ||||
\(210\) | −159277. | + | 275876.i | −0.249233 | + | 0.431684i | ||||
\(211\) | 511196. | 0.790463 | 0.395232 | − | 0.918581i | \(-0.370664\pi\) | ||||
0.395232 | + | 0.918581i | \(0.370664\pi\) | |||||||
\(212\) | −691646. | + | 1.19797e6i | −1.05692 | + | 1.83065i | ||||
\(213\) | −855187. | −1.29155 | ||||||||
\(214\) | 1.83417e6 | 2.73782 | ||||||||
\(215\) | 152563. | + | 52929.9i | 0.225088 | + | 0.0780917i | ||||
\(216\) | −687500. | −1.00262 | ||||||||
\(217\) | −176059. | −0.253810 | ||||||||
\(218\) | −1.03709e6 | + | 1.79630e6i | −1.47800 | + | 2.55998i | ||||
\(219\) | −1.07794e6 | −1.51874 | ||||||||
\(220\) | −28794.8 | + | 49874.0i | −0.0401104 | + | 0.0694732i | ||||
\(221\) | 75221.8 | − | 130288.i | 0.103601 | − | 0.179442i | ||||
\(222\) | −839732. | − | 1.45446e6i | −1.14356 | − | 1.98070i | ||||
\(223\) | 256944. | 0.346000 | 0.173000 | − | 0.984922i | \(-0.444654\pi\) | ||||
0.173000 | + | 0.984922i | \(0.444654\pi\) | |||||||
\(224\) | 137077. | + | 237424.i | 0.182534 | + | 0.316158i | ||||
\(225\) | 211901. | − | 367023.i | 0.279046 | − | 0.483322i | ||||
\(226\) | 406207. | 0.529025 | ||||||||
\(227\) | 220739. | − | 382330.i | 0.284324 | − | 0.492464i | −0.688121 | − | 0.725596i | \(-0.741564\pi\) |
0.972445 | + | 0.233132i | \(0.0748975\pi\) | |||||||
\(228\) | 1.64797e6 | + | 2.85436e6i | 2.09948 | + | 3.63640i | ||||
\(229\) | 238261. | + | 412680.i | 0.300237 | + | 0.520025i | 0.976189 | − | 0.216920i | \(-0.0696010\pi\) |
−0.675953 | + | 0.736945i | \(0.736268\pi\) | |||||||
\(230\) | −304301. | − | 527065.i | −0.379301 | − | 0.656969i | ||||
\(231\) | 154069. | 0.189970 | ||||||||
\(232\) | 312755. | + | 541708.i | 0.381491 | + | 0.660762i | ||||
\(233\) | 18109.0 | + | 31365.7i | 0.0218527 | + | 0.0378500i | 0.876745 | − | 0.480956i | \(-0.159710\pi\) |
−0.854892 | + | 0.518806i | \(0.826377\pi\) | |||||||
\(234\) | 54772.4 | − | 94868.6i | 0.0653916 | − | 0.113262i | ||||
\(235\) | −63293.5 | + | 109628.i | −0.0747635 | + | 0.129494i | ||||
\(236\) | −829036. | −0.968932 | ||||||||
\(237\) | 562138. | 0.650088 | ||||||||
\(238\) | 1.19679e6 | − | 2.07289e6i | 1.36954 | − | 2.37211i | ||||
\(239\) | 333746. | − | 578066.i | 0.377939 | − | 0.654610i | −0.612823 | − | 0.790220i | \(-0.709966\pi\) |
0.990762 | + | 0.135611i | \(0.0432996\pi\) | |||||||
\(240\) | 177660. | + | 307715.i | 0.199095 | + | 0.344843i | ||||
\(241\) | −109771. | − | 190128.i | −0.121743 | − | 0.210865i | 0.798712 | − | 0.601713i | \(-0.205515\pi\) |
−0.920455 | + | 0.390848i | \(0.872182\pi\) | |||||||
\(242\) | −1.56416e6 | −1.71689 | ||||||||
\(243\) | 483839. | + | 838033.i | 0.525636 | + | 0.910428i | ||||
\(244\) | −654390. | − | 1.13344e6i | −0.703659 | − | 1.21877i | ||||
\(245\) | −12779.4 | − | 22134.6i | −0.0136018 | − | 0.0235590i | ||||
\(246\) | 473992. | − | 820978.i | 0.499382 | − | 0.864956i | ||||
\(247\) | 190218. | 0.198385 | ||||||||
\(248\) | −254181. | + | 440255.i | −0.262430 | + | 0.454543i | ||||
\(249\) | −60135.3 | − | 104157.i | −0.0614654 | − | 0.106461i | ||||
\(250\) | 806141. | 0.815758 | ||||||||
\(251\) | −685995. | − | 1.18818e6i | −0.687285 | − | 1.19041i | −0.972713 | − | 0.232012i | \(-0.925469\pi\) |
0.285428 | − | 0.958400i | \(-0.407864\pi\) | |||||||
\(252\) | 590743. | − | 1.02320e6i | 0.585999 | − | 1.01498i | ||||
\(253\) | −147175. | + | 254915.i | −0.144555 | + | 0.250377i | ||||
\(254\) | −2.47699e6 | −2.40902 | ||||||||
\(255\) | 257756. | − | 446447.i | 0.248233 | − | 0.429952i | ||||
\(256\) | −2.13187e6 | −2.03311 | ||||||||
\(257\) | 794811. | 0.750639 | 0.375320 | − | 0.926895i | \(-0.377533\pi\) | ||||
0.375320 | + | 0.926895i | \(0.377533\pi\) | |||||||
\(258\) | −2.24543e6 | − | 779026.i | −2.10015 | − | 0.728623i | ||||
\(259\) | −1.04539e6 | −0.968346 | ||||||||
\(260\) | 68564.5 | 0.0629022 | ||||||||
\(261\) | 127633. | − | 221067.i | 0.115974 | − | 0.200874i | ||||
\(262\) | −2.53537e6 | −2.28185 | ||||||||
\(263\) | 731593. | − | 1.26716e6i | 0.652199 | − | 1.12964i | −0.330389 | − | 0.943845i | \(-0.607180\pi\) |
0.982588 | − | 0.185797i | \(-0.0594868\pi\) | |||||||
\(264\) | 222433. | − | 385265.i | 0.196422 | − | 0.340213i | ||||
\(265\) | 136780. | + | 236910.i | 0.119649 | + | 0.207237i | ||||
\(266\) | 3.02638e6 | 2.62253 | ||||||||
\(267\) | −729765. | − | 1.26399e6i | −0.626477 | − | 1.08509i | ||||
\(268\) | 2.30871e6 | − | 3.99880e6i | 1.96350 | − | 3.40089i | ||||
\(269\) | 107923. | 0.0909357 | 0.0454679 | − | 0.998966i | \(-0.485522\pi\) | ||||
0.0454679 | + | 0.998966i | \(0.485522\pi\) | |||||||
\(270\) | −129523. | + | 224340.i | −0.108127 | + | 0.187282i | ||||
\(271\) | −730659. | − | 1.26554e6i | −0.604354 | − | 1.04677i | −0.992153 | − | 0.125028i | \(-0.960098\pi\) |
0.387799 | − | 0.921744i | \(-0.373235\pi\) | |||||||
\(272\) | −1.33491e6 | − | 2.31213e6i | −1.09403 | − | 1.89491i | ||||
\(273\) | −91715.1 | − | 158855.i | −0.0744791 | − | 0.129002i | ||||
\(274\) | −895725. | −0.720772 | ||||||||
\(275\) | −94625.3 | − | 163896.i | −0.0754528 | − | 0.130688i | ||||
\(276\) | 3.03612e6 | + | 5.25871e6i | 2.39909 | + | 4.15534i | ||||
\(277\) | −363438. | + | 629492.i | −0.284597 | + | 0.492937i | −0.972511 | − | 0.232855i | \(-0.925193\pi\) |
0.687914 | + | 0.725792i | \(0.258526\pi\) | |||||||
\(278\) | −1.55016e6 | + | 2.68495e6i | −1.20299 | + | 2.08365i | ||||
\(279\) | 207459. | 0.159559 | ||||||||
\(280\) | 572543. | 0.436428 | ||||||||
\(281\) | −395912. | + | 685739.i | −0.299111 | + | 0.518076i | −0.975933 | − | 0.218071i | \(-0.930023\pi\) |
0.676822 | + | 0.736147i | \(0.263357\pi\) | |||||||
\(282\) | 931558. | − | 1.61351e6i | 0.697569 | − | 1.20822i | ||||
\(283\) | 1.28066e6 | + | 2.21818e6i | 0.950538 | + | 1.64638i | 0.744265 | + | 0.667885i | \(0.232800\pi\) |
0.206273 | + | 0.978494i | \(0.433866\pi\) | |||||||
\(284\) | 1.46427e6 | + | 2.53618e6i | 1.07727 | + | 1.86588i | ||||
\(285\) | 651804. | 0.475340 | ||||||||
\(286\) | −24458.9 | − | 42364.0i | −0.0176816 | − | 0.0306254i | ||||
\(287\) | −295040. | − | 511023.i | −0.211434 | − | 0.366215i | ||||
\(288\) | −161524. | − | 279768.i | −0.114751 | − | 0.198754i | ||||
\(289\) | −1.22682e6 | + | 2.12491e6i | −0.864042 | + | 1.49656i | ||||
\(290\) | 235688. | 0.164567 | ||||||||
\(291\) | −647596. | + | 1.12167e6i | −0.448303 | + | 0.776484i | ||||
\(292\) | 1.84566e6 | + | 3.19679e6i | 1.26676 | + | 2.19410i | ||||
\(293\) | −42451.1 | −0.0288881 | −0.0144441 | − | 0.999896i | \(-0.504598\pi\) | ||||
−0.0144441 | + | 0.999896i | \(0.504598\pi\) | |||||||
\(294\) | 188089. | + | 325779.i | 0.126909 | + | 0.219814i | ||||
\(295\) | −81975.1 | + | 141985.i | −0.0548437 | + | 0.0949921i | ||||
\(296\) | −1.50926e6 | + | 2.61412e6i | −1.00123 | + | 1.73419i | ||||
\(297\) | 125287. | 0.0824167 | ||||||||
\(298\) | 672852. | − | 1.16541e6i | 0.438914 | − | 0.760221i | ||||
\(299\) | 350446. | 0.226696 | ||||||||
\(300\) | −3.90410e6 | −2.50448 | ||||||||
\(301\) | −1.11879e6 | + | 967974.i | −0.711755 | + | 0.615811i | ||||
\(302\) | 2.32460e6 | 1.46667 | ||||||||
\(303\) | 3.90820e6 | 2.44551 | ||||||||
\(304\) | 1.68783e6 | − | 2.92341e6i | 1.04748 | − | 1.81428i | ||||
\(305\) | −258824. | −0.159315 | ||||||||
\(306\) | −1.41023e6 | + | 2.44259e6i | −0.860968 | + | 1.49124i | ||||
\(307\) | −82279.4 | + | 142512.i | −0.0498248 | + | 0.0862990i | −0.889862 | − | 0.456229i | \(-0.849200\pi\) |
0.840037 | + | 0.542529i | \(0.182533\pi\) | |||||||
\(308\) | −263799. | − | 456913.i | −0.158452 | − | 0.274446i | ||||
\(309\) | 479509. | 0.285694 | ||||||||
\(310\) | 95773.7 | + | 165885.i | 0.0566034 | + | 0.0980399i | ||||
\(311\) | 1.49086e6 | − | 2.58225e6i | 0.874049 | − | 1.51390i | 0.0162774 | − | 0.999868i | \(-0.494819\pi\) |
0.857772 | − | 0.514030i | \(-0.171848\pi\) | |||||||
\(312\) | −529646. | −0.308034 | ||||||||
\(313\) | 498808. | − | 863960.i | 0.287788 | − | 0.498463i | −0.685494 | − | 0.728079i | \(-0.740414\pi\) |
0.973281 | + | 0.229616i | \(0.0737469\pi\) | |||||||
\(314\) | 1.70885e6 | + | 2.95981e6i | 0.978091 | + | 1.69410i | ||||
\(315\) | −116825. | − | 202347.i | −0.0663377 | − | 0.114900i | ||||
\(316\) | −962502. | − | 1.66710e6i | −0.542231 | − | 0.939171i | ||||
\(317\) | 2.04824e6 | 1.14481 | 0.572403 | − | 0.819972i | \(-0.306011\pi\) | ||||
0.572403 | + | 0.819972i | \(0.306011\pi\) | |||||||
\(318\) | −2.01313e6 | − | 3.48685e6i | −1.11636 | − | 1.93360i | ||||
\(319\) | −56995.2 | − | 98718.6i | −0.0313590 | − | 0.0543153i | ||||
\(320\) | −139938. | + | 242379.i | −0.0763941 | + | 0.132318i | ||||
\(321\) | −1.80951e6 | + | 3.13417e6i | −0.980165 | + | 1.69770i | ||||
\(322\) | 5.57563e6 | 2.99677 | ||||||||
\(323\) | −4.89756e6 | −2.61200 | ||||||||
\(324\) | 2.46878e6 | − | 4.27605e6i | 1.30653 | − | 2.26298i | ||||
\(325\) | −112658. | + | 195130.i | −0.0591637 | + | 0.102474i | ||||
\(326\) | 285858. | + | 495121.i | 0.148973 | + | 0.258028i | ||||
\(327\) | −2.04630e6 | − | 3.54430e6i | −1.05828 | − | 1.83299i | ||||
\(328\) | −1.70383e6 | −0.874461 | ||||||||
\(329\) | −579855. | − | 1.00434e6i | −0.295345 | − | 0.511552i | ||||
\(330\) | −83811.3 | − | 145165.i | −0.0423660 | − | 0.0733801i | ||||
\(331\) | 1.76103e6 | + | 3.05019e6i | 0.883480 | + | 1.53023i | 0.847446 | + | 0.530882i | \(0.178139\pi\) |
0.0360345 | + | 0.999351i | \(0.488527\pi\) | |||||||
\(332\) | −205929. | + | 356680.i | −0.102535 | + | 0.177596i | ||||
\(333\) | 1.23184e6 | 0.608756 | ||||||||
\(334\) | 660394. | − | 1.14384e6i | 0.323919 | − | 0.561045i | ||||
\(335\) | −456570. | − | 790802.i | −0.222277 | − | 0.384996i | ||||
\(336\) | −3.25521e6 | −1.57301 | ||||||||
\(337\) | −1.59018e6 | − | 2.75427e6i | −0.762729 | − | 1.32109i | −0.941439 | − | 0.337184i | \(-0.890526\pi\) |
0.178710 | − | 0.983902i | \(-0.442808\pi\) | |||||||
\(338\) | 1.82128e6 | − | 3.15454e6i | 0.867129 | − | 1.50191i | ||||
\(339\) | −400747. | + | 694114.i | −0.189396 | + | 0.328044i | ||||
\(340\) | −1.76534e6 | −0.828192 | ||||||||
\(341\) | 46320.9 | − | 80230.2i | 0.0215720 | − | 0.0373639i | ||||
\(342\) | −3.56613e6 | −1.64867 | ||||||||
\(343\) | 2.28488e6 | 1.04864 | ||||||||
\(344\) | 805303. | + | 4.19513e6i | 0.366913 | + | 1.91139i | ||||
\(345\) | 1.20084e6 | 0.543174 | ||||||||
\(346\) | 1.59138e6 | 0.714635 | ||||||||
\(347\) | −806594. | + | 1.39706e6i | −0.359609 | + | 0.622862i | −0.987896 | − | 0.155121i | \(-0.950423\pi\) |
0.628286 | + | 0.777982i | \(0.283757\pi\) | |||||||
\(348\) | −2.35154e6 | −1.04089 | ||||||||
\(349\) | −1.30042e6 | + | 2.25239e6i | −0.571504 | + | 0.989874i | 0.424908 | + | 0.905237i | \(0.360307\pi\) |
−0.996412 | + | 0.0846375i | \(0.973027\pi\) | |||||||
\(350\) | −1.79241e6 | + | 3.10454e6i | −0.782107 | + | 1.35465i | ||||
\(351\) | −74581.8 | − | 129179.i | −0.0323121 | − | 0.0559662i | ||||
\(352\) | −144259. | −0.0620562 | ||||||||
\(353\) | −557211. | − | 965117.i | −0.238003 | − | 0.412234i | 0.722138 | − | 0.691749i | \(-0.243160\pi\) |
−0.960141 | + | 0.279515i | \(0.909826\pi\) | |||||||
\(354\) | 1.20651e6 | − | 2.08974e6i | 0.511711 | − | 0.886309i | ||||
\(355\) | 579146. | 0.243903 | ||||||||
\(356\) | −2.49903e6 | + | 4.32845e6i | −1.04507 | + | 1.81012i | ||||
\(357\) | 2.36140e6 | + | 4.09006e6i | 0.980616 | + | 1.69848i | ||||
\(358\) | −416604. | − | 721580.i | −0.171797 | − | 0.297561i | ||||
\(359\) | 661665. | + | 1.14604e6i | 0.270958 | + | 0.469313i | 0.969107 | − | 0.246639i | \(-0.0793262\pi\) |
−0.698149 | + | 0.715952i | \(0.745993\pi\) | |||||||
\(360\) | −674655. | −0.274363 | ||||||||
\(361\) | −1.85814e6 | − | 3.21839e6i | −0.750429 | − | 1.29978i | ||||
\(362\) | 1.54590e6 | + | 2.67757e6i | 0.620025 | + | 1.07391i | ||||
\(363\) | 1.54313e6 | − | 2.67278e6i | 0.614662 | − | 1.06463i | ||||
\(364\) | −314072. | + | 543989.i | −0.124244 | + | 0.215197i | ||||
\(365\) | 729997. | 0.286806 | ||||||||
\(366\) | 3.80939e6 | 1.48646 | ||||||||
\(367\) | 811350. | − | 1.40530e6i | 0.314444 | − | 0.544633i | −0.664875 | − | 0.746954i | \(-0.731515\pi\) |
0.979319 | + | 0.202322i | \(0.0648487\pi\) | |||||||
\(368\) | 3.10956e6 | − | 5.38591e6i | 1.19696 | − | 2.07319i | ||||
\(369\) | 347659. | + | 602164.i | 0.132919 | + | 0.230223i | ||||
\(370\) | 568680. | + | 984982.i | 0.215955 | + | 0.374045i | ||||
\(371\) | −2.50618e6 | −0.945316 | ||||||||
\(372\) | −955567. | − | 1.65509e6i | −0.358017 | − | 0.620104i | ||||
\(373\) | −543097. | − | 940671.i | −0.202118 | − | 0.350079i | 0.747093 | − | 0.664720i | \(-0.231449\pi\) |
−0.949211 | + | 0.314641i | \(0.898116\pi\) | |||||||
\(374\) | 629746. | + | 1.09075e6i | 0.232802 | + | 0.403224i | ||||
\(375\) | −795306. | + | 1.37751e6i | −0.292049 | + | 0.505844i | ||||
\(376\) | −3.34860e6 | −1.22150 | ||||||||
\(377\) | −67857.0 | + | 117532.i | −0.0245890 | + | 0.0425894i | ||||
\(378\) | −1.18660e6 | − | 2.05526e6i | −0.427146 | − | 0.739838i | ||||
\(379\) | −3.16873e6 | −1.13315 | −0.566575 | − | 0.824010i | \(-0.691732\pi\) | ||||
−0.566575 | + | 0.824010i | \(0.691732\pi\) | |||||||
\(380\) | −1.11603e6 | − | 1.93302e6i | −0.396476 | − | 0.686716i | ||||
\(381\) | 2.44370e6 | − | 4.23261e6i | 0.862452 | − | 1.49381i | ||||
\(382\) | 1.16205e6 | − | 2.01274e6i | 0.407444 | − | 0.705714i | ||||
\(383\) | 5.07150e6 | 1.76661 | 0.883303 | − | 0.468802i | \(-0.155314\pi\) | ||||
0.883303 | + | 0.468802i | \(0.155314\pi\) | |||||||
\(384\) | 2.76662e6 | − | 4.79193e6i | 0.957463 | − | 1.65837i | ||||
\(385\) | −104338. | −0.0358748 | ||||||||
\(386\) | −3.03014e6 | −1.03513 | ||||||||
\(387\) | 1.31832e6 | − | 1.14061e6i | 0.447449 | − | 0.387133i | ||||
\(388\) | 4.43530e6 | 1.49570 | ||||||||
\(389\) | −4.34521e6 | −1.45592 | −0.727959 | − | 0.685621i | \(-0.759531\pi\) | ||||
−0.727959 | + | 0.685621i | \(0.759531\pi\) | |||||||
\(390\) | −99783.5 | + | 172830.i | −0.0332198 | + | 0.0575384i | ||||
\(391\) | −9.02297e6 | −2.98475 | ||||||||
\(392\) | 338054. | − | 585527.i | 0.111115 | − | 0.192456i | ||||
\(393\) | 2.50129e6 | − | 4.33236e6i | 0.816925 | − | 1.41496i | ||||
\(394\) | 3.77404e6 | + | 6.53683e6i | 1.22480 | + | 2.12142i | ||||
\(395\) | −380689. | −0.122766 | ||||||||
\(396\) | 310847. | + | 538403.i | 0.0996114 | + | 0.172532i | ||||
\(397\) | −2.37845e6 | + | 4.11960e6i | −0.757387 | + | 1.31183i | 0.186792 | + | 0.982400i | \(0.440191\pi\) |
−0.944179 | + | 0.329433i | \(0.893142\pi\) | |||||||
\(398\) | −6.13714e6 | −1.94204 | ||||||||
\(399\) | −2.98570e6 | + | 5.17139e6i | −0.938890 | + | 1.62620i | ||||
\(400\) | 1.99927e6 | + | 3.46283e6i | 0.624771 | + | 1.08214i | ||||
\(401\) | 1.74745e6 | + | 3.02667e6i | 0.542680 | + | 0.939949i | 0.998749 | + | 0.0500049i | \(0.0159237\pi\) |
−0.456069 | + | 0.889944i | \(0.650743\pi\) | |||||||
\(402\) | 6.71982e6 | + | 1.16391e7i | 2.07392 | + | 3.59214i | ||||
\(403\) | −110297. | −0.0338299 | ||||||||
\(404\) | −6.69169e6 | − | 1.15903e7i | −2.03977 | − | 3.53299i | ||||
\(405\) | −488225. | − | 845631.i | −0.147905 | − | 0.256179i | ||||
\(406\) | −1.07961e6 | + | 1.86994e6i | −0.325052 | + | 0.563006i | ||||
\(407\) | 275042. | − | 476386.i | 0.0823024 | − | 0.142552i | ||||
\(408\) | 1.36369e7 | 4.05568 | ||||||||
\(409\) | 2.15155e6 | 0.635981 | 0.317990 | − | 0.948094i | \(-0.396992\pi\) | ||||
0.317990 | + | 0.948094i | \(0.396992\pi\) | |||||||
\(410\) | −320995. | + | 555979.i | −0.0943058 | + | 0.163342i | ||||
\(411\) | 883685. | − | 1.53059e6i | 0.258043 | − | 0.446944i | ||||
\(412\) | −821024. | − | 1.42205e6i | −0.238294 | − | 0.412737i | ||||
\(413\) | −751003. | − | 1.30078e6i | −0.216654 | − | 0.375256i | ||||
\(414\) | −6.57003e6 | −1.88394 | ||||||||
\(415\) | 40724.5 | + | 70537.0i | 0.0116074 | + | 0.0201047i | ||||
\(416\) | 85875.3 | + | 148740.i | 0.0243296 | + | 0.0421401i | ||||
\(417\) | −3.05864e6 | − | 5.29772e6i | −0.861367 | − | 1.49193i | ||||
\(418\) | −796237. | + | 1.37912e6i | −0.222896 | + | 0.386067i | ||||
\(419\) | 5.86423e6 | 1.63183 | 0.815917 | − | 0.578168i | \(-0.196232\pi\) | ||||
0.815917 | + | 0.578168i | \(0.196232\pi\) | |||||||
\(420\) | −1.07621e6 | + | 1.86404e6i | −0.297695 | + | 0.515624i | ||||
\(421\) | −381550. | − | 660864.i | −0.104917 | − | 0.181722i | 0.808787 | − | 0.588101i | \(-0.200124\pi\) |
−0.913704 | + | 0.406380i | \(0.866791\pi\) | |||||||
\(422\) | 5.09525e6 | 1.39279 | ||||||||
\(423\) | 683271. | + | 1.18346e6i | 0.185670 | + | 0.321590i | ||||
\(424\) | −3.61824e6 | + | 6.26697e6i | −0.977422 | + | 1.69295i | ||||
\(425\) | 2.90063e6 | − | 5.02403e6i | 0.778968 | − | 1.34921i | ||||
\(426\) | −8.52391e6 | −2.27570 | ||||||||
\(427\) | 1.18559e6 | − | 2.05350e6i | 0.314677 | − | 0.545037i | ||||
\(428\) | 1.23931e7 | 3.27018 | ||||||||
\(429\) | 96520.5 | 0.0253207 | ||||||||
\(430\) | 1.52064e6 | + | 527569.i | 0.396602 | + | 0.137597i | ||||
\(431\) | 4.90960e6 | 1.27307 | 0.636536 | − | 0.771247i | \(-0.280367\pi\) | ||||
0.636536 | + | 0.771247i | \(0.280367\pi\) | |||||||
\(432\) | −2.64710e6 | −0.682434 | ||||||||
\(433\) | −757783. | + | 1.31252e6i | −0.194234 | + | 0.336423i | −0.946649 | − | 0.322266i | \(-0.895555\pi\) |
0.752415 | + | 0.658689i | \(0.228889\pi\) | |||||||
\(434\) | −1.75484e6 | −0.447211 | ||||||||
\(435\) | −232520. | + | 402737.i | −0.0589166 | + | 0.102046i | ||||
\(436\) | −7.00743e6 | + | 1.21372e7i | −1.76540 | + | 3.05776i | ||||
\(437\) | −5.70423e6 | − | 9.88001e6i | −1.42887 | − | 2.47488i | ||||
\(438\) | −1.07441e7 | −2.67600 | ||||||||
\(439\) | 1.13980e6 | + | 1.97420e6i | 0.282273 | + | 0.488911i | 0.971944 | − | 0.235212i | \(-0.0755784\pi\) |
−0.689671 | + | 0.724122i | \(0.742245\pi\) | |||||||
\(440\) | −150635. | + | 260908.i | −0.0370932 | + | 0.0642474i | ||||
\(441\) | −275915. | −0.0675583 | ||||||||
\(442\) | 749759. | − | 1.29862e6i | 0.182543 | − | 0.316174i | ||||
\(443\) | −1.45095e6 | − | 2.51312e6i | −0.351271 | − | 0.608420i | 0.635201 | − | 0.772347i | \(-0.280917\pi\) |
−0.986472 | + | 0.163927i | \(0.947584\pi\) | |||||||
\(444\) | −5.67391e6 | − | 9.82750e6i | −1.36592 | − | 2.36584i | ||||
\(445\) | 494208. | + | 855994.i | 0.118307 | + | 0.204914i | ||||
\(446\) | 2.56104e6 | 0.609648 | ||||||||
\(447\) | 1.32762e6 | + | 2.29950e6i | 0.314271 | + | 0.544333i | ||||
\(448\) | −1.28202e6 | − | 2.22052e6i | −0.301786 | − | 0.522709i | ||||
\(449\) | 186135. | − | 322396.i | 0.0435726 | − | 0.0754699i | −0.843417 | − | 0.537260i | \(-0.819459\pi\) |
0.886989 | + | 0.461790i | \(0.152793\pi\) | |||||||
\(450\) | 2.11208e6 | − | 3.65823e6i | 0.491676 | − | 0.851607i | ||||
\(451\) | 310498. | 0.0718816 | ||||||||
\(452\) | 2.74466e6 | 0.631892 | ||||||||
\(453\) | −2.29336e6 | + | 3.97221e6i | −0.525081 | + | 0.909466i | ||||
\(454\) | 2.20017e6 | − | 3.81080e6i | 0.500975 | − | 0.867715i | ||||
\(455\) | 62110.9 | + | 107579.i | 0.0140650 | + | 0.0243613i | ||||
\(456\) | 8.62108e6 | + | 1.49321e7i | 1.94155 | + | 3.36287i | ||||
\(457\) | 3.73465e6 | 0.836487 | 0.418244 | − | 0.908335i | \(-0.362646\pi\) | ||||
0.418244 | + | 0.908335i | \(0.362646\pi\) | |||||||
\(458\) | 2.37482e6 | + | 4.11330e6i | 0.529013 | + | 0.916278i | ||||
\(459\) | 1.92027e6 | + | 3.32600e6i | 0.425431 | + | 0.736869i | ||||
\(460\) | −2.05611e6 | − | 3.56128e6i | −0.453055 | − | 0.784714i | ||||
\(461\) | −2.49556e6 | + | 4.32244e6i | −0.546910 | + | 0.947276i | 0.451574 | + | 0.892234i | \(0.350863\pi\) |
−0.998484 | + | 0.0550424i | \(0.982471\pi\) | |||||||
\(462\) | 1.53565e6 | 0.334724 | ||||||||
\(463\) | −165773. | + | 287127.i | −0.0359385 | + | 0.0622474i | −0.883435 | − | 0.468553i | \(-0.844775\pi\) |
0.847497 | + | 0.530801i | \(0.178109\pi\) | |||||||
\(464\) | 1.20421e6 | + | 2.08575e6i | 0.259661 | + | 0.449747i | ||||
\(465\) | −377946. | −0.0810582 | ||||||||
\(466\) | 180498. | + | 312632.i | 0.0385042 | + | 0.0666912i | ||||
\(467\) | −2.18649e6 | + | 3.78710e6i | −0.463932 | + | 0.803554i | −0.999153 | − | 0.0411584i | \(-0.986895\pi\) |
0.535221 | + | 0.844712i | \(0.320228\pi\) | |||||||
\(468\) | 370087. | − | 641009.i | 0.0781068 | − | 0.135285i | ||||
\(469\) | 8.36560e6 | 1.75616 | ||||||||
\(470\) | −630866. | + | 1.09269e6i | −0.131732 | + | 0.228167i | ||||
\(471\) | −6.74351e6 | −1.40066 | ||||||||
\(472\) | −4.33697e6 | −0.896049 | ||||||||
\(473\) | −146755. | − | 764504.i | −0.0301606 | − | 0.157118i | ||||
\(474\) | 5.60300e6 | 1.14545 | ||||||||
\(475\) | 7.33499e6 | 1.49164 | ||||||||
\(476\) | 8.08645e6 | − | 1.40061e7i | 1.63584 | − | 2.83336i | ||||
\(477\) | 2.95315e6 | 0.594278 | ||||||||
\(478\) | 3.32655e6 | − | 5.76176e6i | 0.665924 | − | 1.15341i | ||||
\(479\) | −1.21317e6 | + | 2.10127e6i | −0.241592 | + | 0.418449i | −0.961168 | − | 0.275965i | \(-0.911003\pi\) |
0.719576 | + | 0.694413i | \(0.244336\pi\) | |||||||
\(480\) | 294262. | + | 509676.i | 0.0582949 | + | 0.100970i | ||||
\(481\) | −654915. | −0.129069 | ||||||||
\(482\) | −1.09412e6 | − | 1.89507e6i | −0.214509 | − | 0.371541i | ||||
\(483\) | −5.50068e6 | + | 9.52746e6i | −1.07287 | + | 1.85827i | ||||
\(484\) | −1.05687e7 | −2.05073 | ||||||||
\(485\) | 438562. | − | 759612.i | 0.0846597 | − | 0.146635i | ||||
\(486\) | 4.82257e6 | + | 8.35293e6i | 0.926163 | + | 1.60416i | ||||
\(487\) | −78130.6 | − | 135326.i | −0.0149279 | − | 0.0258559i | 0.858465 | − | 0.512872i | \(-0.171419\pi\) |
−0.873393 | + | 0.487016i | \(0.838085\pi\) | |||||||
\(488\) | −3.42334e6 | − | 5.92940e6i | −0.650729 | − | 1.12710i | ||||
\(489\) | −1.12806e6 | −0.213335 | ||||||||
\(490\) | −127376. | − | 220623.i | −0.0239662 | − | 0.0415107i | ||||
\(491\) | 2.49338e6 | + | 4.31866e6i | 0.466750 | + | 0.808435i | 0.999279 | − | 0.0379773i | \(-0.0120915\pi\) |
−0.532529 | + | 0.846412i | \(0.678758\pi\) | |||||||
\(492\) | 3.20267e6 | − | 5.54719e6i | 0.596486 | − | 1.03314i | ||||
\(493\) | 1.74712e6 | − | 3.02610e6i | 0.323747 | − | 0.560747i | ||||
\(494\) | 1.89596e6 | 0.349552 | ||||||||
\(495\) | 122946. | 0.0225529 | ||||||||
\(496\) | −978681. | + | 1.69513e6i | −0.178623 | + | 0.309384i | ||||
\(497\) | −2.65288e6 | + | 4.59493e6i | −0.481756 | + | 0.834426i | ||||
\(498\) | −599387. | − | 1.03817e6i | −0.108301 | − | 0.187583i | ||||
\(499\) | 1.11429e6 | + | 1.93001e6i | 0.200331 | + | 0.346983i | 0.948635 | − | 0.316372i | \(-0.102465\pi\) |
−0.748304 | + | 0.663356i | \(0.769132\pi\) | |||||||
\(500\) | 5.44694e6 | 0.974379 | ||||||||
\(501\) | 1.30303e6 | + | 2.25692e6i | 0.231933 | + | 0.401719i | ||||
\(502\) | −6.83752e6 | − | 1.18429e7i | −1.21099 | − | 2.09749i | ||||
\(503\) | 2.13628e6 | + | 3.70015e6i | 0.376477 | + | 0.652078i | 0.990547 | − | 0.137174i | \(-0.0438020\pi\) |
−0.614070 | + | 0.789252i | \(0.710469\pi\) | |||||||
\(504\) | 3.09038e6 | − | 5.35269e6i | 0.541920 | − | 0.938633i | ||||
\(505\) | −2.64669e6 | −0.461823 | ||||||||
\(506\) | −1.46694e6 | + | 2.54082e6i | −0.254704 | + | 0.441161i | ||||
\(507\) | 3.59359e6 | + | 6.22428e6i | 0.620881 | + | 1.07540i | ||||
\(508\) | −1.67366e7 | −2.87744 | ||||||||
\(509\) | 1.97221e6 | + | 3.41596e6i | 0.337410 | + | 0.584411i | 0.983945 | − | 0.178473i | \(-0.0571159\pi\) |
−0.646535 | + | 0.762884i | \(0.723783\pi\) | |||||||
\(510\) | 2.56914e6 | − | 4.44988e6i | 0.437383 | − | 0.757569i | ||||
\(511\) | −3.34388e6 | + | 5.79178e6i | −0.566499 | + | 0.981204i | ||||
\(512\) | −1.22458e7 | −2.06448 | ||||||||
\(513\) | −2.42794e6 | + | 4.20532e6i | −0.407329 | + | 0.705514i | ||||
\(514\) | 7.92213e6 | 1.32262 | ||||||||
\(515\) | −324731. | −0.0539518 | ||||||||
\(516\) | −1.51719e7 | − | 5.26373e6i | −2.50852 | − | 0.870301i | ||||
\(517\) | 610236. | 0.100409 | ||||||||
\(518\) | −1.04198e7 | −1.70621 | ||||||||
\(519\) | −1.56999e6 | + | 2.71931e6i | −0.255846 | + | 0.443139i | ||||
\(520\) | 358685. | 0.0581707 | ||||||||
\(521\) | 4.25817e6 | − | 7.37536e6i | 0.687271 | − | 1.19039i | −0.285446 | − | 0.958395i | \(-0.592142\pi\) |
0.972717 | − | 0.231994i | \(-0.0745250\pi\) | |||||||
\(522\) | 1.27216e6 | − | 2.20344e6i | 0.204346 | − | 0.353937i | ||||
\(523\) | 1.33171e6 | + | 2.30660e6i | 0.212891 | + | 0.368738i | 0.952618 | − | 0.304169i | \(-0.0983788\pi\) |
−0.739727 | + | 0.672907i | \(0.765045\pi\) | |||||||
\(524\) | −1.71310e7 | −2.72555 | ||||||||
\(525\) | −3.53663e6 | − | 6.12562e6i | −0.560004 | − | 0.969955i | ||||
\(526\) | 7.29201e6 | − | 1.26301e7i | 1.14917 | − | 1.99042i | ||||
\(527\) | 2.83983e6 | 0.445416 | ||||||||
\(528\) | 856440. | − | 1.48340e6i | 0.133694 | − | 0.231565i | ||||
\(529\) | −7.29096e6 | − | 1.26283e7i | −1.13278 | − | 1.96203i | ||||
\(530\) | 1.36333e6 | + | 2.36135e6i | 0.210819 | + | 0.365150i | ||||
\(531\) | 884943. | + | 1.53277e6i | 0.136201 | + | 0.235906i | ||||
\(532\) | 2.04487e7 | 3.13247 | ||||||||
\(533\) | −184835. | − | 320144.i | −0.0281817 | − | 0.0488121i | ||||
\(534\) | −7.27379e6 | − | 1.25986e7i | −1.10384 | − | 1.91191i | ||||
\(535\) | 1.22543e6 | − | 2.12251e6i | 0.185099 | − | 0.320601i | ||||
\(536\) | 1.20776e7 | − | 2.09191e7i | 1.81581 | − | 3.14507i | ||||
\(537\) | 1.64402e6 | 0.246020 | ||||||||
\(538\) | 1.07570e6 | 0.160228 | ||||||||
\(539\) | −61605.6 | + | 106704.i | −0.00913373 | + | 0.0158201i | ||||
\(540\) | −875159. | + | 1.51582e6i | −0.129152 | + | 0.223699i | ||||
\(541\) | 4.65356e6 | + | 8.06020e6i | 0.683584 | + | 1.18400i | 0.973880 | + | 0.227065i | \(0.0729130\pi\) |
−0.290296 | + | 0.956937i | \(0.593754\pi\) | |||||||
\(542\) | −7.28270e6 | − | 1.26140e7i | −1.06486 | − | 1.84440i | ||||
\(543\) | −6.10047e6 | −0.887899 | ||||||||
\(544\) | −2.21104e6 | − | 3.82963e6i | −0.320331 | − | 0.554830i | ||||
\(545\) | 1.38579e6 | + | 2.40026e6i | 0.199851 | + | 0.346152i | ||||
\(546\) | −914152. | − | 1.58336e6i | −0.131231 | − | 0.227299i | ||||
\(547\) | 3.05092e6 | − | 5.28435e6i | 0.435976 | − | 0.755132i | −0.561399 | − | 0.827545i | \(-0.689737\pi\) |
0.997375 | + | 0.0724130i | \(0.0230700\pi\) | |||||||
\(548\) | −6.05224e6 | −0.860924 | ||||||||
\(549\) | −1.39704e6 | + | 2.41974e6i | −0.197824 | + | 0.342640i | ||||
\(550\) | −943159. | − | 1.63360e6i | −0.132947 | − | 0.230271i | ||||
\(551\) | 4.41805e6 | 0.619943 | ||||||||
\(552\) | 1.58830e7 | + | 2.75101e7i | 2.21863 | + | 3.84277i | ||||
\(553\) | 1.74381e6 | − | 3.02037e6i | 0.242486 | − | 0.419998i | ||||
\(554\) | −3.62249e6 | + | 6.27434e6i | −0.501456 | + | 0.868548i | ||||
\(555\) | −2.24414e6 | −0.309256 | ||||||||
\(556\) | −1.04741e7 | + | 1.81417e7i | −1.43691 | + | 2.48880i | ||||
\(557\) | −5.98575e6 | −0.817486 | −0.408743 | − | 0.912650i | \(-0.634033\pi\) | ||||
−0.408743 | + | 0.912650i | \(0.634033\pi\) | |||||||
\(558\) | 2.06781e6 | 0.281141 | ||||||||
\(559\) | −700893. | + | 606413.i | −0.0948686 | + | 0.0820803i | ||||
\(560\) | 2.20448e6 | 0.297054 | ||||||||
\(561\) | −2.48512e6 | −0.333381 | ||||||||
\(562\) | −3.94617e6 | + | 6.83497e6i | −0.527030 | + | 0.912843i | ||||
\(563\) | 3.57765e6 | 0.475694 | 0.237847 | − | 0.971303i | \(-0.423558\pi\) | ||||
0.237847 | + | 0.971303i | \(0.423558\pi\) | |||||||
\(564\) | 6.29436e6 | − | 1.09022e7i | 0.833209 | − | 1.44316i | ||||
\(565\) | 271392. | − | 470065.i | 0.0357665 | − | 0.0619494i | ||||
\(566\) | 1.27648e7 | + | 2.21092e7i | 1.67484 | + | 2.90090i | ||||
\(567\) | 8.94561e6 | 1.16856 | ||||||||
\(568\) | 7.66007e6 | + | 1.32676e7i | 0.996236 | + | 1.72553i | ||||
\(569\) | −555792. | + | 962661.i | −0.0719668 | + | 0.124650i | −0.899763 | − | 0.436378i | \(-0.856261\pi\) |
0.827796 | + | 0.561029i | \(0.189594\pi\) | |||||||
\(570\) | 6.49673e6 | 0.837544 | ||||||||
\(571\) | 7.27086e6 | − | 1.25935e7i | 0.933245 | − | 1.61643i | 0.155511 | − | 0.987834i | \(-0.450298\pi\) |
0.777734 | − | 0.628594i | \(-0.216369\pi\) | |||||||
\(572\) | −165264. | − | 286246.i | −0.0211197 | − | 0.0365804i | ||||
\(573\) | 2.29287e6 | + | 3.97137e6i | 0.291738 | + | 0.505305i | ||||
\(574\) | −2.94075e6 | − | 5.09353e6i | −0.372545 | − | 0.645266i | ||||
\(575\) | 1.35135e7 | 1.70451 | ||||||||
\(576\) | 1.51067e6 | + | 2.61655e6i | 0.189720 | + | 0.328604i | ||||
\(577\) | −3.12595e6 | − | 5.41430e6i | −0.390879 | − | 0.677022i | 0.601687 | − | 0.798732i | \(-0.294495\pi\) |
−0.992566 | + | 0.121710i | \(0.961162\pi\) | |||||||
\(578\) | −1.22280e7 | + | 2.11796e7i | −1.52243 | + | 2.63693i | ||||
\(579\) | 2.98941e6 | − | 5.17782e6i | 0.370586 | − | 0.641875i | ||||
\(580\) | 1.59250e6 | 0.196566 | ||||||||
\(581\) | −746184. | −0.0917077 | ||||||||
\(582\) | −6.45479e6 | + | 1.11800e7i | −0.789904 | + | 1.36815i | ||||
\(583\) | 659372. | − | 1.14207e6i | 0.0803451 | − | 0.139162i | ||||
\(584\) | 9.65530e6 | + | 1.67235e7i | 1.17148 | + | 2.02906i | ||||
\(585\) | −73188.3 | − | 126766.i | −0.00884203 | − | 0.0153148i | ||||
\(586\) | −423123. | −0.0509005 | ||||||||
\(587\) | −2.75602e6 | − | 4.77357e6i | −0.330132 | − | 0.571805i | 0.652406 | − | 0.757870i | \(-0.273760\pi\) |
−0.982537 | + | 0.186065i | \(0.940426\pi\) | |||||||
\(588\) | 1.27088e6 | + | 2.20123e6i | 0.151587 | + | 0.262556i | ||||
\(589\) | 1.79531e6 | + | 3.10957e6i | 0.213231 | + | 0.369328i | ||||
\(590\) | −817070. | + | 1.41521e6i | −0.0966339 | + | 0.167375i | ||||
\(591\) | −1.48933e7 | −1.75396 | ||||||||
\(592\) | −5.81116e6 | + | 1.00652e7i | −0.681488 | + | 1.18037i | ||||
\(593\) | −5.03378e6 | − | 8.71876e6i | −0.587837 | − | 1.01816i | −0.994515 | − | 0.104592i | \(-0.966646\pi\) |
0.406678 | − | 0.913572i | \(-0.366687\pi\) | |||||||
\(594\) | 1.24877e6 | 0.145217 | ||||||||
\(595\) | −1.59918e6 | − | 2.76985e6i | −0.185184 | − | 0.320748i | ||||
\(596\) | 4.54633e6 | − | 7.87448e6i | 0.524259 | − | 0.908043i | ||||
\(597\) | 6.05465e6 | − | 1.04870e7i | 0.695269 | − | 1.20424i | ||||
\(598\) | 3.49300e6 | 0.399435 | ||||||||
\(599\) | −4.08485e6 | + | 7.07516e6i | −0.465167 | + | 0.805692i | −0.999209 | − | 0.0397654i | \(-0.987339\pi\) |
0.534042 | + | 0.845458i | \(0.320672\pi\) | |||||||
\(600\) | −2.04237e7 | −2.31609 | ||||||||
\(601\) | −1.13683e7 | −1.28383 | −0.641916 | − | 0.766775i | \(-0.721860\pi\) | ||||
−0.641916 | + | 0.766775i | \(0.721860\pi\) | |||||||
\(602\) | −1.11513e7 | + | 9.64809e6i | −1.25410 | + | 1.08505i | ||||
\(603\) | −9.85759e6 | −1.10402 | ||||||||
\(604\) | 1.57069e7 | 1.75185 | ||||||||
\(605\) | −1.04503e6 | + | 1.81005e6i | −0.116076 | + | 0.201049i | ||||
\(606\) | 3.89542e7 | 4.30897 | ||||||||
\(607\) | 3.99736e6 | − | 6.92364e6i | 0.440354 | − | 0.762716i | −0.557362 | − | 0.830270i | \(-0.688186\pi\) |
0.997716 | + | 0.0675543i | \(0.0215196\pi\) | |||||||
\(608\) | 2.79559e6 | − | 4.84211e6i | 0.306701 | − | 0.531222i | ||||
\(609\) | −2.13020e6 | − | 3.68962e6i | −0.232743 | − | 0.403123i | ||||
\(610\) | −2.57978e6 | −0.280710 | ||||||||
\(611\) | −363265. | − | 629194.i | −0.0393660 | − | 0.0681839i | ||||
\(612\) | −9.52866e6 | + | 1.65041e7i | −1.02838 | + | 1.78121i | ||||
\(613\) | 6.94295e6 | 0.746265 | 0.373132 | − | 0.927778i | \(-0.378284\pi\) | ||||
0.373132 | + | 0.927778i | \(0.378284\pi\) | |||||||
\(614\) | −820104. | + | 1.42046e6i | −0.0877906 | + | 0.152058i | ||||
\(615\) | −633360. | − | 1.09701e6i | −0.0675248 | − | 0.116956i | ||||
\(616\) | −1.38002e6 | − | 2.39027e6i | −0.146533 | − | 0.253802i | ||||
\(617\) | −8.84860e6 | − | 1.53262e7i | −0.935754 | − | 1.62077i | −0.773283 | − | 0.634061i | \(-0.781387\pi\) |
−0.162471 | − | 0.986713i | \(-0.551946\pi\) | |||||||
\(618\) | 4.77941e6 | 0.503389 | ||||||||
\(619\) | 3.44611e6 | + | 5.96884e6i | 0.361496 | + | 0.626129i | 0.988207 | − | 0.153123i | \(-0.0489329\pi\) |
−0.626712 | + | 0.779251i | \(0.715600\pi\) | |||||||
\(620\) | 647125. | + | 1.12085e6i | 0.0676097 | + | 0.117103i | ||||
\(621\) | −4.47310e6 | + | 7.74764e6i | −0.465457 | + | 0.806195i | ||||
\(622\) | 1.48599e7 | − | 2.57380e7i | 1.54006 | − | 2.66747i | ||||
\(623\) | −9.05524e6 | −0.934717 | ||||||||
\(624\) | −2.03931e6 | −0.209663 | ||||||||
\(625\) | −4.06706e6 | + | 7.04435e6i | −0.416467 | + | 0.721341i | ||||
\(626\) | 4.97177e6 | − | 8.61136e6i | 0.507078 | − | 0.878285i | ||||
\(627\) | −1.57107e6 | − | 2.72117e6i | −0.159598 | − | 0.276431i | ||||
\(628\) | 1.15464e7 | + | 1.99989e7i | 1.16828 | + | 2.02352i | ||||
\(629\) | 1.68622e7 | 1.69937 | ||||||||
\(630\) | −1.16443e6 | − | 2.01686e6i | −0.116886 | − | 0.202453i | ||||
\(631\) | −5.65192e6 | − | 9.78941e6i | −0.565096 | − | 0.978776i | −0.997041 | − | 0.0768754i | \(-0.975506\pi\) |
0.431944 | − | 0.901900i | \(-0.357828\pi\) | |||||||
\(632\) | −5.03518e6 | − | 8.72118e6i | −0.501444 | − | 0.868526i | ||||
\(633\) | −5.02676e6 | + | 8.70661e6i | −0.498631 | + | 0.863654i | ||||
\(634\) | 2.04154e7 | 2.01713 | ||||||||
\(635\) | −1.65491e6 | + | 2.86639e6i | −0.162870 | + | 0.282098i | ||||
\(636\) | −1.36024e7 | − | 2.35600e7i | −1.33343 | − | 2.30958i | ||||
\(637\) | 146692. | 0.0143238 | ||||||||
\(638\) | −568089. | − | 983959.i | −0.0552541 | − | 0.0957029i | ||||
\(639\) | 3.12602e6 | − | 5.41443e6i | 0.302858 | − | 0.524566i | ||||
\(640\) | −1.87360e6 | + | 3.24517e6i | −0.180812 | + | 0.313175i | ||||
\(641\) | −1.40110e7 | −1.34687 | −0.673433 | − | 0.739248i | \(-0.735181\pi\) | ||||
−0.673433 | + | 0.739248i | \(0.735181\pi\) | |||||||
\(642\) | −1.80360e7 | + | 3.12392e7i | −1.72704 | + | 2.99132i | ||||
\(643\) | −4.27504e6 | −0.407767 | −0.203884 | − | 0.978995i | \(-0.565356\pi\) | ||||
−0.203884 | + | 0.978995i | \(0.565356\pi\) | |||||||
\(644\) | 3.76735e7 | 3.57949 | ||||||||
\(645\) | −2.40169e6 | + | 2.07795e6i | −0.227310 | + | 0.196669i | ||||
\(646\) | −4.88155e7 | −4.60231 | ||||||||
\(647\) | −7.88684e6 | −0.740700 | −0.370350 | − | 0.928892i | \(-0.620762\pi\) | ||||
−0.370350 | + | 0.928892i | \(0.620762\pi\) | |||||||
\(648\) | 1.29150e7 | − | 2.23695e7i | 1.20825 | − | 2.09275i | ||||
\(649\) | 790352. | 0.0736561 | ||||||||
\(650\) | −1.12290e6 | + | 1.94492e6i | −0.104246 | + | 0.180559i | ||||
\(651\) | 1.73125e6 | − | 2.99861e6i | 0.160106 | − | 0.277311i | ||||
\(652\) | 1.93149e6 | + | 3.34544e6i | 0.177940 | + | 0.308201i | ||||
\(653\) | 1.39028e7 | 1.27591 | 0.637954 | − | 0.770075i | \(-0.279781\pi\) | ||||
0.637954 | + | 0.770075i | \(0.279781\pi\) | |||||||
\(654\) | −2.03961e7 | − | 3.53271e7i | −1.86468 | − | 3.22971i | ||||
\(655\) | −1.69391e6 | + | 2.93394e6i | −0.154272 | + | 0.267207i | ||||
\(656\) | −6.56029e6 | −0.595200 | ||||||||
\(657\) | 3.94026e6 | − | 6.82473e6i | 0.356132 | − | 0.616839i | ||||
\(658\) | −5.77959e6 | − | 1.00105e7i | −0.520394 | − | 0.901348i | ||||
\(659\) | −755746. | − | 1.30899e6i | −0.0677895 | − | 0.117415i | 0.830138 | − | 0.557557i | \(-0.188261\pi\) |
−0.897928 | + | 0.440142i | \(0.854928\pi\) | |||||||
\(660\) | −566297. | − | 980855.i | −0.0506039 | − | 0.0876486i | ||||
\(661\) | 670631. | 0.0597008 | 0.0298504 | − | 0.999554i | \(-0.490497\pi\) | ||||
0.0298504 | + | 0.999554i | \(0.490497\pi\) | |||||||
\(662\) | 1.75527e7 | + | 3.04022e7i | 1.55668 | + | 2.69625i | ||||
\(663\) | 1.47936e6 | + | 2.56233e6i | 0.130704 | + | 0.226387i | ||||
\(664\) | −1.07729e6 | + | 1.86591e6i | −0.0948224 | + | 0.164237i | ||||
\(665\) | 2.02197e6 | − | 3.50215e6i | 0.177304 | − | 0.307100i | ||||
\(666\) | 1.22781e7 | 1.07262 | ||||||||
\(667\) | 8.13955e6 | 0.708412 | ||||||||
\(668\) | 4.46216e6 | − | 7.72868e6i | 0.386904 | − | 0.670138i | ||||
\(669\) | −2.52662e6 | + | 4.37623e6i | −0.218260 | + | 0.378037i | ||||
\(670\) | −4.55077e6 | − | 7.88216e6i | −0.391650 | − | 0.678357i | ||||
\(671\) | 623855. | + | 1.08055e6i | 0.0534906 | + | 0.0926484i | ||||
\(672\) | −5.39168e6 | −0.460575 | ||||||||
\(673\) | −5.24651e6 | − | 9.08723e6i | −0.446512 | − | 0.773381i | 0.551644 | − | 0.834080i | \(-0.314001\pi\) |
−0.998156 | + | 0.0606981i | \(0.980667\pi\) | |||||||
\(674\) | −1.58498e7 | − | 2.74526e7i | −1.34392 | − | 2.32774i | ||||
\(675\) | −2.87595e6 | − | 4.98129e6i | −0.242953 | − | 0.420806i | ||||
\(676\) | 1.23060e7 | − | 2.13146e7i | 1.03574 | − | 1.79395i | ||||
\(677\) | −1.21425e7 | −1.01821 | −0.509103 | − | 0.860706i | \(-0.670023\pi\) | ||||
−0.509103 | + | 0.860706i | \(0.670023\pi\) | |||||||
\(678\) | −3.99437e6 | + | 6.91845e6i | −0.333714 | + | 0.578009i | ||||
\(679\) | 4.01783e6 | + | 6.95908e6i | 0.334439 | + | 0.579265i | ||||
\(680\) | −9.23509e6 | −0.765895 | ||||||||
\(681\) | 4.34119e6 | + | 7.51916e6i | 0.358708 | + | 0.621301i | ||||
\(682\) | 461695. | − | 799679.i | 0.0380097 | − | 0.0658347i | ||||
\(683\) | 8.82663e6 | − | 1.52882e7i | 0.724008 | − | 1.25402i | −0.235374 | − | 0.971905i | \(-0.575631\pi\) |
0.959381 | − | 0.282113i | \(-0.0910353\pi\) | |||||||
\(684\) | −2.40957e7 | −1.96924 | ||||||||
\(685\) | −598445. | + | 1.03654e6i | −0.0487302 | + | 0.0844031i | ||||
\(686\) | 2.27741e7 | 1.84770 | ||||||||
\(687\) | −9.37159e6 | −0.757567 | ||||||||
\(688\) | 3.10068e6 | + | 1.61526e7i | 0.249739 | + | 1.30099i | ||||
\(689\) | −1.57006e6 | −0.126000 | ||||||||
\(690\) | 1.19692e7 | 0.957066 | ||||||||
\(691\) | 5.81354e6 | − | 1.00693e7i | 0.463175 | − | 0.802243i | −0.535942 | − | 0.844255i | \(-0.680043\pi\) |
0.999117 | + | 0.0420116i | \(0.0133766\pi\) | |||||||
\(692\) | 1.07527e7 | 0.853593 | ||||||||
\(693\) | −563178. | + | 975452.i | −0.0445464 | + | 0.0771566i | ||||
\(694\) | −8.03957e6 | + | 1.39249e7i | −0.633627 | + | 1.09747i | ||||
\(695\) | 2.07136e6 | + | 3.58770e6i | 0.162665 | + | 0.281744i | ||||
\(696\) | −1.23017e7 | −0.962592 | ||||||||
\(697\) | 4.75898e6 | + | 8.24279e6i | 0.371049 | + | 0.642676i | ||||
\(698\) | −1.29617e7 | + | 2.24503e7i | −1.00698 | + | 1.74415i | ||||
\(699\) | −712288. | −0.0551395 | ||||||||
\(700\) | −1.21109e7 | + | 2.09768e7i | −0.934185 | + | 1.61806i | ||||
\(701\) | 2.87557e6 | + | 4.98064e6i | 0.221019 | + | 0.382816i | 0.955118 | − | 0.296227i | \(-0.0957284\pi\) |
−0.734099 | + | 0.679043i | \(0.762395\pi\) | |||||||
\(702\) | −743379. | − | 1.28757e6i | −0.0569335 | − | 0.0986117i | ||||
\(703\) | 1.06601e7 | + | 1.84638e7i | 0.813528 | + | 1.40907i | ||||
\(704\) | 1.34919e6 | 0.102599 | ||||||||
\(705\) | −1.24477e6 | − | 2.15601e6i | −0.0943229 | − | 0.163372i | ||||
\(706\) | −5.55389e6 | − | 9.61962e6i | −0.419358 | − | 0.726350i | ||||
\(707\) | 1.21237e7 | − | 2.09988e7i | 0.912190 | − | 1.57996i | ||||
\(708\) | 8.15219e6 | − | 1.41200e7i | 0.611211 | − | 1.05865i | ||||
\(709\) | −2.30040e7 | −1.71865 | −0.859326 | − | 0.511428i | \(-0.829117\pi\) | ||||
−0.859326 | + | 0.511428i | \(0.829117\pi\) | |||||||
\(710\) | 5.77253e6 | 0.429754 | ||||||||
\(711\) | −2.05482e6 | + | 3.55905e6i | −0.152440 | + | 0.264034i | ||||
\(712\) | −1.30733e7 | + | 2.26436e7i | −0.966462 | + | 1.67396i | ||||
\(713\) | 3.30757e6 | + | 5.72888e6i | 0.243661 | + | 0.422033i | ||||
\(714\) | 2.35368e7 | + | 4.07669e7i | 1.72783 | + | 2.99269i | ||||
\(715\) | −65365.2 | −0.00478169 | ||||||||
\(716\) | −2.81491e6 | − | 4.87558e6i | −0.205203 | − | 0.355421i | ||||
\(717\) | 6.56368e6 | + | 1.13686e7i | 0.476814 | + | 0.825867i | ||||
\(718\) | 6.59502e6 | + | 1.14229e7i | 0.477425 | + | 0.826924i | ||||
\(719\) | −1.26494e7 | + | 2.19095e7i | −0.912533 | + | 1.58055i | −0.102061 | + | 0.994778i | \(0.532544\pi\) |
−0.810473 | + | 0.585776i | \(0.800790\pi\) | |||||||
\(720\) | −2.59764e6 | −0.186745 | ||||||||
\(721\) | 1.48749e6 | − | 2.57641e6i | 0.106565 | − | 0.184576i | ||||
\(722\) | −1.85206e7 | − | 3.20786e7i | −1.32225 | − | 2.29020i | ||||
\(723\) | 4.31764e6 | 0.307186 | ||||||||
\(724\) | 1.04453e7 | + | 1.80918e7i | 0.740586 | + | 1.28273i | ||||
\(725\) | −2.61663e6 | + | 4.53214e6i | −0.184883 | + | 0.320228i | ||||
\(726\) | 1.53809e7 | − | 2.66405e7i | 1.08303 | − | 1.87586i | ||||
\(727\) | 2.19269e7 | 1.53865 | 0.769326 | − | 0.638856i | \(-0.220592\pi\) | ||||
0.769326 | + | 0.638856i | \(0.220592\pi\) | |||||||
\(728\) | −1.64302e6 | + | 2.84579e6i | −0.114898 | + | 0.199010i | ||||
\(729\) | −1.21545e6 | −0.0847066 | ||||||||
\(730\) | 7.27610e6 | 0.505349 | ||||||||
\(731\) | 1.80460e7 | − | 1.56134e7i | 1.24907 | − | 1.08070i | ||||
\(732\) | 2.57393e7 | 1.77550 | ||||||||
\(733\) | −1.44070e7 | −0.990406 | −0.495203 | − | 0.868777i | \(-0.664906\pi\) | ||||
−0.495203 | + | 0.868777i | \(0.664906\pi\) | |||||||
\(734\) | 8.08697e6 | − | 1.40070e7i | 0.554046 | − | 0.959636i | ||||
\(735\) | 502658. | 0.0343205 | ||||||||
\(736\) | 5.15044e6 | − | 8.92082e6i | 0.350469 | − | 0.607030i | ||||
\(737\) | −2.20098e6 | + | 3.81221e6i | −0.149261 | + | 0.258528i | ||||
\(738\) | 3.46523e6 | + | 6.00195e6i | 0.234202 | + | 0.405650i | ||||
\(739\) | −7.09096e6 | −0.477633 | −0.238816 | − | 0.971065i | \(-0.576759\pi\) | ||||
−0.238816 | + | 0.971065i | \(0.576759\pi\) | |||||||
\(740\) | 3.84246e6 | + | 6.65534e6i | 0.257947 | + | 0.446777i | ||||
\(741\) | −1.87047e6 | + | 3.23976e6i | −0.125143 | + | 0.216754i | ||||
\(742\) | −2.49798e7 | −1.66564 | ||||||||
\(743\) | −7.74297e6 | + | 1.34112e7i | −0.514559 | + | 0.891243i | 0.485298 | + | 0.874349i | \(0.338711\pi\) |
−0.999857 | + | 0.0168942i | \(0.994622\pi\) | |||||||
\(744\) | −4.99890e6 | − | 8.65834e6i | −0.331087 | − | 0.573459i | ||||
\(745\) | −899082. | − | 1.55726e6i | −0.0593484 | − | 0.102794i | ||||
\(746\) | −5.41321e6 | − | 9.37596e6i | −0.356130 | − | 0.616834i | ||||
\(747\) | 879265. | 0.0576526 | ||||||||
\(748\) | 4.25507e6 | + | 7.37000e6i | 0.278069 | + | 0.481630i | ||||
\(749\) | 1.12266e7 | + | 1.94451e7i | 0.731214 | + | 1.26650i | ||||
\(750\) | −7.92706e6 | + | 1.37301e7i | −0.514587 | + | 0.891291i | ||||
\(751\) | 6.94541e6 | − | 1.20298e7i | 0.449364 | − | 0.778321i | −0.548981 | − | 0.835835i | \(-0.684984\pi\) |
0.998345 | + | 0.0575139i | \(0.0183174\pi\) | |||||||
\(752\) | −1.28932e7 | −0.831413 | ||||||||
\(753\) | 2.69825e7 | 1.73418 | ||||||||
\(754\) | −676352. | + | 1.17148e6i | −0.0433256 | + | 0.0750421i | ||||
\(755\) | 1.55310e6 | − | 2.69004e6i | 0.0991588 | − | 0.171748i | ||||
\(756\) | −8.01765e6 | − | 1.38870e7i | −0.510203 | − | 0.883697i | ||||
\(757\) | 590046. | + | 1.02199e6i | 0.0374237 | + | 0.0648197i | 0.884131 | − | 0.467240i | \(-0.154752\pi\) |
−0.846707 | + | 0.532060i | \(0.821418\pi\) | |||||||
\(758\) | −3.15837e7 | −1.99660 | ||||||||
\(759\) | −2.89445e6 | − | 5.01333e6i | −0.182373 | − | 0.315880i | ||||
\(760\) | −5.83833e6 | − | 1.01123e7i | −0.366653 | − | 0.635061i | ||||
\(761\) | −1.39544e7 | − | 2.41698e7i | −0.873475 | − | 1.51290i | −0.858378 | − | 0.513018i | \(-0.828528\pi\) |
−0.0150972 | − | 0.999886i | \(-0.504806\pi\) | |||||||
\(762\) | 2.43571e7 | − | 4.21877e7i | 1.51963 | − | 2.63208i | ||||
\(763\) | −2.53914e7 | −1.57898 | ||||||||
\(764\) | 7.85178e6 | − | 1.35997e7i | 0.486670 | − | 0.842937i | ||||
\(765\) | 1.88439e6 | + | 3.26386e6i | 0.116417 | + | 0.201640i | ||||
\(766\) | 5.05492e7 | 3.11274 | ||||||||
\(767\) | −470486. | − | 814905.i | −0.0288774 | − | 0.0500171i | ||||
\(768\) | 2.09634e7 | − | 3.63097e7i | 1.28250 | − | 2.22136i | ||||
\(769\) | −1.09877e7 | + | 1.90313e7i | −0.670027 | + | 1.16052i | 0.307869 | + | 0.951429i | \(0.400384\pi\) |
−0.977896 | + | 0.209092i | \(0.932949\pi\) | |||||||
\(770\) | −1.03997e6 | −0.0632110 | ||||||||
\(771\) | −7.81565e6 | + | 1.35371e7i | −0.473510 | + | 0.820143i | ||||
\(772\) | −2.04741e7 | −1.23641 | ||||||||
\(773\) | 3.40639e6 | 0.205043 | 0.102522 | − | 0.994731i | \(-0.467309\pi\) | ||||
0.102522 | + | 0.994731i | \(0.467309\pi\) | |||||||
\(774\) | 1.31401e7 | − | 1.13688e7i | 0.788399 | − | 0.682123i | ||||
\(775\) | −4.25316e6 | −0.254365 | ||||||||
\(776\) | 2.32026e7 | 1.38319 | ||||||||
\(777\) | 1.02797e7 | − | 1.78050e7i | 0.610841 | − | 1.05801i | ||||
\(778\) | −4.33100e7 | −2.56531 | ||||||||
\(779\) | −6.01715e6 | + | 1.04220e7i | −0.355261 | + | 0.615330i | ||||
\(780\) | −674218. | + | 1.16778e6i | −0.0396793 | + | 0.0687265i | ||||
\(781\) | −1.39594e6 | − | 2.41784e6i | −0.0818916 | − | 0.141840i | ||||
\(782\) | −8.99347e7 | −5.25909 | ||||||||
\(783\) | −1.73226e6 | − | 3.00036e6i | −0.100974 | − | 0.174891i | ||||
\(784\) | 1.30162e6 | − | 2.25447e6i | 0.0756300 | − | 0.130995i | ||||
\(785\) | 4.56681e6 | 0.264508 | ||||||||
\(786\) | 2.49311e7 | − | 4.31819e7i | 1.43941 | − | 2.49313i | ||||
\(787\) | 8.48650e6 | + | 1.46990e7i | 0.488418 | + | 0.845965i | 0.999911 | − | 0.0133224i | \(-0.00424077\pi\) |
−0.511493 | + | 0.859287i | \(0.670907\pi\) | |||||||
\(788\) | 2.55005e7 | + | 4.41681e7i | 1.46296 | + | 2.53392i | ||||
\(789\) | 1.43880e7 | + | 2.49207e7i | 0.822826 | + | 1.42518i | ||||
\(790\) | −3.79444e6 | −0.216312 | ||||||||
\(791\) | 2.48632e6 | + | 4.30643e6i | 0.141291 | + | 0.244724i | ||||
\(792\) | 1.62615e6 | + | 2.81657e6i | 0.0921186 | + | 0.159554i | ||||
\(793\) | 742745. | − | 1.28647e6i | 0.0419428 | − | 0.0726470i | ||||
\(794\) | −2.37067e7 | + | 4.10613e7i | −1.33451 | + | 2.31143i | ||||
\(795\) | −5.38001e6 | −0.301901 | ||||||||
\(796\) | −4.14675e7 | −2.31966 | ||||||||
\(797\) | 1.28751e7 | − | 2.23003e7i | 0.717967 | − | 1.24355i | −0.243837 | − | 0.969816i | \(-0.578406\pi\) |
0.961804 | − | 0.273739i | \(-0.0882603\pi\) | |||||||
\(798\) | −2.97594e7 | + | 5.15448e7i | −1.65431 | + | 2.86535i | ||||
\(799\) | 9.35304e6 | + | 1.61999e7i | 0.518305 | + | 0.897731i | ||||
\(800\) | 3.31144e6 | + | 5.73558e6i | 0.182933 | + | 0.316849i | ||||
\(801\) | 1.06702e7 | 0.587615 | ||||||||
\(802\) | 1.74174e7 | + | 3.01678e7i | 0.956195 | + | 1.65618i | ||||
\(803\) | −1.75954e6 | − | 3.04762e6i | −0.0962966 | − | 0.166791i | ||||
\(804\) | 4.54046e7 | + | 7.86430e7i | 2.47719 | + | 4.29062i | ||||
\(805\) | 3.72515e6 | − | 6.45215e6i | 0.202607 | − | 0.350925i | ||||
\(806\) | −1.09936e6 | −0.0596079 | ||||||||
\(807\) | −1.06125e6 | + | 1.83813e6i | −0.0573630 | + | 0.0993557i | ||||
\(808\) | −3.50065e7 | − | 6.06330e7i | −1.88634 | − | 3.26724i | ||||
\(809\) | −7.51409e6 | −0.403650 | −0.201825 | − | 0.979422i | \(-0.564687\pi\) | ||||
−0.201825 | + | 0.979422i | \(0.564687\pi\) | |||||||
\(810\) | −4.86629e6 | − | 8.42866e6i | −0.260607 | − | 0.451384i | ||||
\(811\) | 1.59404e6 | − | 2.76095e6i | 0.0851032 | − | 0.147403i | −0.820332 | − | 0.571888i | \(-0.806211\pi\) |
0.905435 | + | 0.424484i | \(0.139545\pi\) | |||||||
\(812\) | −7.29473e6 | + | 1.26348e7i | −0.388257 | + | 0.672481i | ||||
\(813\) | 2.87392e7 | 1.52493 | ||||||||
\(814\) | 2.74143e6 | − | 4.74829e6i | 0.145016 | − | 0.251175i | ||||
\(815\) | 763942. | 0.0402871 | ||||||||
\(816\) | 5.25064e7 | 2.76049 | ||||||||
\(817\) | 2.85049e7 | + | 9.88945e6i | 1.49405 | + | 0.518343i | ||||
\(818\) | 2.14452e7 | 1.12059 | ||||||||
\(819\) | 1.34101e6 | 0.0698589 | ||||||||
\(820\) | −2.16890e6 | + | 3.75665e6i | −0.112643 | + | 0.195104i | ||||
\(821\) | 1.23540e7 | 0.639662 | 0.319831 | − | 0.947475i | \(-0.396374\pi\) | ||||
0.319831 | + | 0.947475i | \(0.396374\pi\) | |||||||
\(822\) | 8.80796e6 | − | 1.52558e7i | 0.454669 | − | 0.787510i | ||||
\(823\) | 8.40509e6 | − | 1.45580e7i | 0.432557 | − | 0.749210i | −0.564536 | − | 0.825408i | \(-0.690945\pi\) |
0.997093 | + | 0.0761985i | \(0.0242783\pi\) | |||||||
\(824\) | −4.29506e6 | − | 7.43925e6i | −0.220369 | − | 0.381690i | ||||
\(825\) | 3.72193e6 | 0.190385 | ||||||||
\(826\) | −7.48548e6 | − | 1.29652e7i | −0.381741 | − | 0.661196i | ||||
\(827\) | −1.26785e7 | + | 2.19598e7i | −0.644621 | + | 1.11652i | 0.339768 | + | 0.940509i | \(0.389652\pi\) |
−0.984389 | + | 0.176007i | \(0.943682\pi\) | |||||||
\(828\) | −4.43925e7 | −2.25026 | ||||||||
\(829\) | −6.43498e6 | + | 1.11457e7i | −0.325207 | + | 0.563276i | −0.981554 | − | 0.191183i | \(-0.938767\pi\) |
0.656347 | + | 0.754459i | \(0.272101\pi\) | |||||||
\(830\) | 405914. | + | 703064.i | 0.0204521 | + | 0.0354241i | ||||
\(831\) | −7.14760e6 | − | 1.23800e7i | −0.359052 | − | 0.621897i | ||||
\(832\) | −803155. | − | 1.39111e6i | −0.0402246 | − | 0.0696710i | ||||
\(833\) | −3.77690e6 | −0.188592 | ||||||||
\(834\) | −3.04864e7 | − | 5.28040e7i | −1.51772 | − | 2.62876i | ||||
\(835\) | −882436. | − | 1.52842e6i | −0.0437993 | − | 0.0758626i | ||||
\(836\) | −5.38002e6 | + | 9.31847e6i | −0.266237 | + | 0.461136i | ||||
\(837\) | 1.40783e6 | − | 2.43844e6i | 0.0694604 | − | 0.120309i | ||||
\(838\) | 5.84506e7 | 2.87527 | ||||||||
\(839\) | −2.64776e7 | −1.29859 | −0.649296 | − | 0.760536i | \(-0.724937\pi\) | ||||
−0.649296 | + | 0.760536i | \(0.724937\pi\) | |||||||
\(840\) | −5.63000e6 | + | 9.75145e6i | −0.275303 | + | 0.476838i | ||||
\(841\) | 8.67951e6 | − | 1.50333e7i | 0.423161 | − | 0.732936i | ||||
\(842\) | −3.80303e6 | − | 6.58703e6i | −0.184863 | − | 0.320191i | ||||
\(843\) | −7.78626e6 | − | 1.34862e7i | −0.377364 | − | 0.653613i | ||||
\(844\) | 3.44276e7 | 1.66361 | ||||||||
\(845\) | −2.43364e6 | − | 4.21518e6i | −0.117250 | − | 0.203083i | ||||
\(846\) | 6.81037e6 | + | 1.17959e7i | 0.327148 | + | 0.566638i | ||||
\(847\) | −9.57393e6 | − | 1.65825e7i | −0.458545 | − | 0.794223i | ||||
\(848\) | −1.39314e7 | + | 2.41299e7i | −0.665281 | + | 1.15230i | ||||
\(849\) | −5.03728e7 | −2.39843 | ||||||||
\(850\) | 2.89114e7 | − | 5.00761e7i | 1.37253 | − | 2.37729i | ||||
\(851\) | 1.96395e7 | + | 3.40166e7i | 0.929623 | + | 1.61015i | ||||
\(852\) | −5.75944e7 | −2.71820 | ||||||||
\(853\) | 1.38697e6 | + | 2.40229e6i | 0.0652669 | + | 0.113046i | 0.896812 | − | 0.442411i | \(-0.145877\pi\) |
−0.831545 | + | 0.555457i | \(0.812543\pi\) | |||||||
\(854\) | 1.18172e7 | − | 2.04679e7i | 0.554457 | − | 0.960348i | ||||
\(855\) | −2.38258e6 | + | 4.12675e6i | −0.111463 | + | 0.193060i | ||||
\(856\) | 6.48326e7 | 3.02419 | ||||||||
\(857\) | −3.36540e6 | + | 5.82904e6i | −0.156525 | + | 0.271110i | −0.933613 | − | 0.358282i | \(-0.883363\pi\) |
0.777088 | + | 0.629392i | \(0.216696\pi\) | |||||||
\(858\) | 962049. | 0.0446148 | ||||||||
\(859\) | −2.90254e7 | −1.34213 | −0.671066 | − | 0.741397i | \(-0.734163\pi\) | ||||
−0.671066 | + | 0.741397i | \(0.734163\pi\) | |||||||
\(860\) | 1.02747e7 | + | 3.56468e6i | 0.473720 | + | 0.164352i | ||||
\(861\) | 1.16049e7 | 0.533498 | ||||||||
\(862\) | 4.89355e7 | 2.24314 | ||||||||
\(863\) | 6.23289e6 | − | 1.07957e7i | 0.284880 | − | 0.493427i | −0.687700 | − | 0.725995i | \(-0.741379\pi\) |
0.972580 | + | 0.232568i | \(0.0747128\pi\) | |||||||
\(864\) | −4.38446e6 | −0.199817 | ||||||||
\(865\) | 1.06322e6 | − | 1.84156e6i | 0.0483153 | − | 0.0836845i | ||||
\(866\) | −7.55306e6 | + | 1.30823e7i | −0.342238 | + | 0.592773i | ||||
\(867\) | −2.41274e7 | − | 4.17898e7i | −1.09009 | − | 1.88809i | ||||
\(868\) | −1.18571e7 | −0.534169 | ||||||||
\(869\) | 917590. | + | 1.58931e6i | 0.0412192 | + | 0.0713937i | ||||
\(870\) | −2.31760e6 | + | 4.01420e6i | −0.103810 | + | 0.179805i | ||||
\(871\) | 5.24085e6 | 0.234076 | ||||||||
\(872\) | −3.66583e7 | + | 6.34940e7i | −1.63260 | + | 2.82775i | ||||
\(873\) | −4.73440e6 | − | 8.20022e6i | −0.210247 | − | 0.364158i | ||||
\(874\) | −5.68558e7 | − | 9.84771e7i | −2.51765 | − | 4.36071i | ||||
\(875\) | 4.93425e6 | + | 8.54637e6i | 0.217872 | + | 0.377365i | ||||
\(876\) | −7.25961e7 | −3.19634 | ||||||||
\(877\) | 6.68062e6 | + | 1.15712e7i | 0.293304 | + | 0.508017i | 0.974589 | − | 0.224001i | \(-0.0719119\pi\) |
−0.681285 | + | 0.732018i | \(0.738579\pi\) | |||||||
\(878\) | 1.13608e7 | + | 1.96774e7i | 0.497361 | + | 0.861454i | ||||
\(879\) | 417435. | − | 723019.i | 0.0182229 | − | 0.0315630i | ||||
\(880\) | −579995. | + | 1.00458e6i | −0.0252474 | + | 0.0437299i | ||||
\(881\) | 2.97673e7 | 1.29211 | 0.646056 | − | 0.763290i | \(-0.276417\pi\) | ||||
0.646056 | + | 0.763290i | \(0.276417\pi\) | |||||||
\(882\) | −2.75013e6 | −0.119037 | ||||||||
\(883\) | 1.06356e6 | − | 1.84215e6i | 0.0459052 | − | 0.0795101i | −0.842160 | − | 0.539228i | \(-0.818716\pi\) |
0.888065 | + | 0.459718i | \(0.152049\pi\) | |||||||
\(884\) | 5.06597e6 | − | 8.77453e6i | 0.218038 | − | 0.377653i | ||||
\(885\) | −1.61218e6 | − | 2.79237e6i | −0.0691917 | − | 0.119844i | ||||
\(886\) | −1.44620e7 | − | 2.50490e7i | −0.618936 | − | 1.07203i | ||||
\(887\) | 2.35571e7 | 1.00534 | 0.502670 | − | 0.864478i | \(-0.332351\pi\) | ||||
0.502670 | + | 0.864478i | \(0.332351\pi\) | |||||||
\(888\) | −2.96822e7 | − | 5.14110e7i | −1.26317 | − | 2.18788i | ||||
\(889\) | −1.51612e7 | − | 2.62600e7i | −0.643398 | − | 1.11440i | ||||
\(890\) | 4.92593e6 | + | 8.53195e6i | 0.208455 | + | 0.361055i | ||||
\(891\) | −2.35358e6 | + | 4.07652e6i | −0.0993195 | + | 0.172026i | ||||
\(892\) | 1.73045e7 | 0.728192 | ||||||||
\(893\) | −1.18258e7 | + | 2.04829e7i | −0.496251 | + | 0.859532i | ||||
\(894\) | 1.32328e7 | + | 2.29198e7i | 0.553741 | + | 0.959107i | ||||
\(895\) | −1.11335e6 | −0.0464597 | ||||||||
\(896\) | −1.71647e7 | − | 2.97302e7i | −0.714277 | − | 1.23716i | ||||
\(897\) | −3.44605e6 | + | 5.96873e6i | −0.143001 | + | 0.247686i | ||||
\(898\) | 1.85527e6 | − | 3.21342e6i | 0.0767743 | − | 0.132977i | ||||
\(899\) | −2.56179e6 | −0.105717 | ||||||||
\(900\) | 1.42709e7 | − | 2.47179e7i | 0.587280 | − | 1.01720i | ||||
\(901\) | 4.04246e7 | 1.65895 | ||||||||
\(902\) | 3.09483e6 | 0.126654 | ||||||||
\(903\) | −5.48498e6 | − | 2.85734e7i | −0.223849 | − | 1.16612i | ||||
\(904\) | 1.43583e7 | 0.584361 | ||||||||
\(905\) | 4.13133e6 | 0.167675 | ||||||||
\(906\) | −2.28586e7 | + | 3.95922e7i | −0.925185 | + | 1.60247i | ||||
\(907\) | −1.56908e7 | −0.633327 | −0.316663 | − | 0.948538i | \(-0.602563\pi\) | ||||
−0.316663 | + | 0.948538i | \(0.602563\pi\) | |||||||
\(908\) | 1.48661e7 | − | 2.57489e7i | 0.598388 | − | 1.03644i | ||||
\(909\) | −1.42859e7 | + | 2.47439e7i | −0.573453 | + | 0.993250i | ||||
\(910\) | 619078. | + | 1.07227e6i | 0.0247823 | + | 0.0429242i | ||||
\(911\) | −2.53728e7 | −1.01291 | −0.506457 | − | 0.862265i | \(-0.669045\pi\) | ||||
−0.506457 | + | 0.862265i | \(0.669045\pi\) | |||||||
\(912\) | 3.31940e7 | + | 5.74937e7i | 1.32152 | + | 2.28893i | ||||
\(913\) | 196320. | − | 340036.i | 0.00779449 | − | 0.0135005i | ||||
\(914\) | 3.72244e7 | 1.47388 | ||||||||
\(915\) | 2.54511e6 | − | 4.40825e6i | 0.100497 | − | 0.174066i | ||||
\(916\) | 1.60462e7 | + | 2.77928e7i | 0.631878 | + | 1.09444i | ||||
\(917\) | −1.55185e7 | − | 2.68789e7i | −0.609435 | − | 1.05557i | ||||
\(918\) | 1.91399e7 | + | 3.31512e7i | 0.749605 | + | 1.29835i | ||||
\(919\) | 8.85863e6 | 0.346002 | 0.173001 | − | 0.984922i | \(-0.444654\pi\) | ||||
0.173001 | + | 0.984922i | \(0.444654\pi\) | |||||||
\(920\) | −1.07562e7 | − | 1.86303e7i | −0.418976 | − | 0.725687i | ||||
\(921\) | −1.61816e6 | − | 2.80274e6i | −0.0628598 | − | 0.108876i | ||||
\(922\) | −2.48740e7 | + | 4.30831e7i | −0.963649 | + | 1.66909i | ||||
\(923\) | −1.66197e6 | + | 2.87862e6i | −0.0642124 | + | 0.111219i | ||||
\(924\) | 1.03761e7 | 0.399810 | ||||||||
\(925\) | −2.52542e7 | −0.970463 | ||||||||
\(926\) | −1.65231e6 | + | 2.86188e6i | −0.0633232 | + | 0.109679i | ||||
\(927\) | −1.75278e6 | + | 3.03591e6i | −0.0669928 | + | 0.116035i | ||||
\(928\) | 1.99456e6 | + | 3.45469e6i | 0.0760288 | + | 0.131686i | ||||
\(929\) | −8.50638e6 | − | 1.47335e7i | −0.323374 | − | 0.560101i | 0.657808 | − | 0.753186i | \(-0.271484\pi\) |
−0.981182 | + | 0.193085i | \(0.938151\pi\) | |||||||
\(930\) | −3.76710e6 | −0.142824 | ||||||||
\(931\) | −2.38771e6 | − | 4.13564e6i | −0.0902834 | − | 0.156376i | ||||
\(932\) | 1.21959e6 | + | 2.11239e6i | 0.0459912 | + | 0.0796591i | ||||
\(933\) | 2.93202e7 | + | 5.07842e7i | 1.10272 | + | 1.90996i | ||||
\(934\) | −2.17934e7 | + | 3.77472e7i | −0.817442 | + | 1.41585i | ||||
\(935\) | 1.68297e6 | 0.0629573 | ||||||||
\(936\) | 1.93605e6 | − | 3.35334e6i | 0.0722315 | − | 0.125109i | ||||
\(937\) | 8.52950e6 | + | 1.47735e7i | 0.317376 | + | 0.549712i | 0.979940 | − | 0.199294i | \(-0.0638649\pi\) |
−0.662564 | + | 0.749006i | \(0.730532\pi\) | |||||||
\(938\) | 8.33825e7 | 3.09434 | ||||||||
\(939\) | 9.80988e6 | + | 1.69912e7i | 0.363078 | + | 0.628869i | ||||
\(940\) | −4.26264e6 | + | 7.38311e6i | −0.157347 | + | 0.272533i | ||||
\(941\) | −1.27842e7 | + | 2.21429e7i | −0.470652 | + | 0.815193i | −0.999437 | − | 0.0335630i | \(-0.989315\pi\) |
0.528785 | + | 0.848756i | \(0.322648\pi\) | |||||||
\(942\) | −6.72147e7 | −2.46795 | ||||||||
\(943\) | −1.10856e7 | + | 1.92009e7i | −0.405959 | + | 0.703141i | ||||
\(944\) | −1.66988e7 | −0.609894 | ||||||||
\(945\) | −3.17114e6 | −0.115514 | ||||||||
\(946\) | −1.46275e6 | − | 7.62004e6i | −0.0531426 | − | 0.276840i | ||||
\(947\) | −7.75549e6 | −0.281018 | −0.140509 | − | 0.990079i | \(-0.544874\pi\) | ||||
−0.140509 | + | 0.990079i | \(0.544874\pi\) | |||||||
\(948\) | 3.78584e7 | 1.36817 | ||||||||
\(949\) | −2.09486e6 | + | 3.62841e6i | −0.0755076 | + | 0.130783i | ||||
\(950\) | 7.31101e7 | 2.62826 | ||||||||
\(951\) | −2.01410e7 | + | 3.48852e7i | −0.722154 | + | 1.25081i | ||||
\(952\) | 4.23030e7 | − | 7.32710e7i | 1.51279 | − | 2.62023i | ||||
\(953\) | −5.60800e6 | − | 9.71334e6i | −0.200021 | − | 0.346447i | 0.748514 | − | 0.663119i | \(-0.230768\pi\) |
−0.948535 | + | 0.316672i | \(0.897434\pi\) | |||||||
\(954\) | 2.94350e7 | 1.04711 | ||||||||
\(955\) | −1.55277e6 | − | 2.68947e6i | −0.0550932 | − | 0.0954242i | ||||
\(956\) | 2.24769e7 | − | 3.89311e7i | 0.795410 | − | 1.37769i | ||||
\(957\) | 2.24181e6 | 0.0791260 | ||||||||
\(958\) | −1.20920e7 | + | 2.09440e7i | −0.425681 | + | 0.737302i | ||||
\(959\) | −5.48257e6 | − | 9.49609e6i | −0.192503 | − | 0.333425i | ||||
\(960\) | −2.75211e6 | − | 4.76679e6i | −0.0963801 | − | 0.166935i | ||||
\(961\) | 1.32736e7 | + | 2.29905e7i | 0.463638 | + | 0.803045i | ||||
\(962\) | −6.52774e6 | −0.227418 | ||||||||
\(963\) | −1.32289e7 | − | 2.29131e7i | −0.459681 | − | 0.796191i | ||||
\(964\) | −7.39274e6 | − | 1.28046e7i | −0.256220 | − | 0.443786i | ||||
\(965\) | −2.02448e6 | + | 3.50650e6i | −0.0699833 | + | 0.121215i | ||||
\(966\) | −5.48270e7 | + | 9.49632e7i | −1.89039 | + | 3.27425i | ||||
\(967\) | 1.79514e7 | 0.617352 | 0.308676 | − | 0.951167i | \(-0.400114\pi\) | ||||
0.308676 | + | 0.951167i | \(0.400114\pi\) | |||||||
\(968\) | −5.52885e7 | −1.89647 | ||||||||
\(969\) | 4.81593e7 | − | 8.34144e7i | 1.64767 | − | 2.85385i | ||||
\(970\) | 4.37128e6 | − | 7.57128e6i | 0.149169 | − | 0.258369i | ||||
\(971\) | −1.86247e7 | − | 3.22589e7i | −0.633930 | − | 1.09800i | −0.986741 | − | 0.162304i | \(-0.948108\pi\) |
0.352811 | − | 0.935694i | \(-0.385226\pi\) | |||||||
\(972\) | 3.25852e7 | + | 5.64392e7i | 1.10625 | + | 1.91609i | ||||
\(973\) | −3.79529e7 | −1.28518 | ||||||||
\(974\) | −778751. | − | 1.34884e6i | −0.0263028 | − | 0.0455577i | ||||
\(975\) | −2.21561e6 | − | 3.83756e6i | −0.0746419 | − | 0.129284i | ||||
\(976\) | −1.31810e7 | − | 2.28301e7i | −0.442918 | − | 0.767156i | ||||
\(977\) | −1.56405e7 | + | 2.70902e7i | −0.524221 | + | 0.907978i | 0.475381 | + | 0.879780i | \(0.342310\pi\) |
−0.999602 | + | 0.0281977i | \(0.991023\pi\) | |||||||
\(978\) | −1.12438e7 | −0.375893 | ||||||||
\(979\) | 2.38242e6 | − | 4.12648e6i | 0.0794442 | − | 0.137601i | ||||
\(980\) | −860659. | − | 1.49070e6i | −0.0286263 | − | 0.0495823i | ||||
\(981\) | 2.99199e7 | 0.992632 | ||||||||
\(982\) | 2.48523e7 | + | 4.30454e7i | 0.822408 | + | 1.42445i | ||||
\(983\) | 2.80313e7 | − | 4.85516e7i | 0.925249 | − | 1.60258i | 0.134089 | − | 0.990969i | \(-0.457189\pi\) |
0.791160 | − | 0.611609i | \(-0.209478\pi\) | |||||||
\(984\) | 1.67543e7 | − | 2.90193e7i | 0.551617 | − | 0.955429i | ||||
\(985\) | 1.00859e7 | 0.331227 | ||||||||
\(986\) | 1.74141e7 | − | 3.01621e7i | 0.570439 | − | 0.988028i | ||||
\(987\) | 2.28076e7 | 0.745224 | ||||||||
\(988\) | 1.28106e7 | 0.417521 | ||||||||
\(989\) | 5.25157e7 | + | 1.82197e7i | 1.70726 | + | 0.592313i | ||||
\(990\) | 1.22544e6 | 0.0397379 | ||||||||
\(991\) | −3.57931e7 | −1.15775 | −0.578875 | − | 0.815416i | \(-0.696508\pi\) | ||||
−0.578875 | + | 0.815416i | \(0.696508\pi\) | |||||||
\(992\) | −1.62101e6 | + | 2.80768e6i | −0.0523007 | + | 0.0905875i | ||||
\(993\) | −6.92672e7 | −2.22923 | ||||||||
\(994\) | −2.64421e7 | + | 4.57990e7i | −0.848848 | + | 1.47025i | ||||
\(995\) | −4.10030e6 | + | 7.10193e6i | −0.131298 | + | 0.227415i | ||||
\(996\) | −4.04994e6 | − | 7.01470e6i | −0.129360 | − | 0.224058i | ||||
\(997\) | 4.54026e7 | 1.44658 | 0.723291 | − | 0.690543i | \(-0.242629\pi\) | ||||
0.723291 | + | 0.690543i | \(0.242629\pi\) | |||||||
\(998\) | 1.11065e7 | + | 1.92370e7i | 0.352981 | + | 0.611380i | ||||
\(999\) | 8.35935e6 | − | 1.44788e7i | 0.265008 | − | 0.459007i |
(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.6.17 | ✓ | 34 | |
43.36 | even | 3 | inner | 43.6.c.a.36.17 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.17 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.6.c.a.36.17 | yes | 34 | 43.36 | even | 3 | inner |