Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(21,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.21");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 21.7 | ||
Character | \(\chi\) | \(=\) | 80.21 |
Dual form | 80.6.l.a.61.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.61831 | − | 3.26668i | −0.816410 | − | 0.577473i | ||||
\(3\) | −15.8638 | + | 15.8638i | −1.01767 | + | 1.01767i | −0.0178243 | + | 0.999841i | \(0.505674\pi\) |
−0.999841 | + | 0.0178243i | \(0.994326\pi\) | |||||||
\(4\) | 10.6576 | + | 30.1731i | 0.333049 | + | 0.942909i | ||||
\(5\) | −17.6777 | − | 17.6777i | −0.316228 | − | 0.316228i | ||||
\(6\) | 125.086 | − | 21.4420i | 1.41851 | − | 0.243157i | ||||
\(7\) | − | 207.627i | − | 1.60155i | −0.598968 | − | 0.800773i | \(-0.704422\pi\) | ||
0.598968 | − | 0.800773i | \(-0.295578\pi\) | |||||||
\(8\) | 49.3459 | − | 174.164i | 0.272600 | − | 0.962127i | ||||
\(9\) | − | 260.322i | − | 1.07129i | ||||||
\(10\) | 23.8936 | + | 139.388i | 0.0755584 | + | 0.440784i | ||||
\(11\) | 105.997 | + | 105.997i | 0.264127 | + | 0.264127i | 0.826728 | − | 0.562601i | \(-0.190199\pi\) |
−0.562601 | + | 0.826728i | \(0.690199\pi\) | |||||||
\(12\) | −647.731 | − | 309.591i | −1.29850 | − | 0.620633i | ||||
\(13\) | −218.980 | + | 218.980i | −0.359373 | + | 0.359373i | −0.863582 | − | 0.504209i | \(-0.831784\pi\) |
0.504209 | + | 0.863582i | \(0.331784\pi\) | |||||||
\(14\) | −678.253 | + | 958.888i | −0.924850 | + | 1.30752i | ||||
\(15\) | 560.871 | 0.643628 | ||||||||
\(16\) | −796.832 | + | 643.145i | −0.778156 | + | 0.628071i | ||||
\(17\) | 790.765 | 0.663628 | 0.331814 | − | 0.943345i | \(-0.392339\pi\) | ||||
0.331814 | + | 0.943345i | \(0.392339\pi\) | |||||||
\(18\) | −850.391 | + | 1202.25i | −0.618639 | + | 0.874608i | ||||
\(19\) | −557.116 | + | 557.116i | −0.354048 | + | 0.354048i | −0.861613 | − | 0.507565i | \(-0.830546\pi\) |
0.507565 | + | 0.861613i | \(0.330546\pi\) | |||||||
\(20\) | 344.989 | − | 721.791i | 0.192855 | − | 0.403494i | ||||
\(21\) | 3293.77 | + | 3293.77i | 1.62984 | + | 1.62984i | ||||
\(22\) | −143.269 | − | 835.788i | −0.0631097 | − | 0.368163i | ||||
\(23\) | − | 725.182i | − | 0.285843i | −0.989734 | − | 0.142921i | \(-0.954350\pi\) | ||
0.989734 | − | 0.142921i | \(-0.0456496\pi\) | |||||||
\(24\) | 1980.09 | + | 3545.72i | 0.701708 | + | 1.25654i | ||||
\(25\) | 625.000i | 0.200000i | ||||||||
\(26\) | 1726.65 | − | 295.979i | 0.500924 | − | 0.0858674i | ||||
\(27\) | 274.800 | + | 274.800i | 0.0725451 | + | 0.0725451i | ||||
\(28\) | 6264.76 | − | 2212.81i | 1.51011 | − | 0.533394i | ||||
\(29\) | −5557.94 | + | 5557.94i | −1.22721 | + | 1.22721i | −0.262195 | + | 0.965015i | \(0.584446\pi\) |
−0.965015 | + | 0.262195i | \(0.915554\pi\) | |||||||
\(30\) | −2590.28 | − | 1832.19i | −0.525464 | − | 0.371678i | ||||
\(31\) | 5937.84 | 1.10975 | 0.554874 | − | 0.831934i | \(-0.312766\pi\) | ||||
0.554874 | + | 0.831934i | \(0.312766\pi\) | |||||||
\(32\) | 5780.97 | − | 367.246i | 0.997988 | − | 0.0633989i | ||||
\(33\) | −3363.05 | −0.537587 | ||||||||
\(34\) | −3652.00 | − | 2583.18i | −0.541793 | − | 0.383228i | ||||
\(35\) | −3670.37 | + | 3670.37i | −0.506453 | + | 0.506453i | ||||
\(36\) | 7854.73 | − | 2774.41i | 1.01013 | − | 0.356791i | ||||
\(37\) | 11244.1 | + | 11244.1i | 1.35027 | + | 1.35027i | 0.885360 | + | 0.464905i | \(0.153912\pi\) |
0.464905 | + | 0.885360i | \(0.346088\pi\) | |||||||
\(38\) | 4392.86 | − | 753.014i | 0.493501 | − | 0.0845949i | ||||
\(39\) | − | 6947.72i | − | 0.731443i | ||||||
\(40\) | −3951.13 | + | 2206.49i | −0.390455 | + | 0.218048i | ||||
\(41\) | 15399.5i | 1.43069i | 0.698771 | + | 0.715345i | \(0.253731\pi\) | ||||
−0.698771 | + | 0.715345i | \(0.746269\pi\) | |||||||
\(42\) | −4451.95 | − | 25971.3i | −0.389428 | − | 2.27180i | ||||
\(43\) | −9696.97 | − | 9696.97i | −0.799769 | − | 0.799769i | 0.183290 | − | 0.983059i | \(-0.441325\pi\) |
−0.983059 | + | 0.183290i | \(0.941325\pi\) | |||||||
\(44\) | −2068.59 | + | 4327.94i | −0.161081 | + | 0.337016i | ||||
\(45\) | −4601.89 | + | 4601.89i | −0.338770 | + | 0.338770i | ||||
\(46\) | −2368.94 | + | 3349.12i | −0.165067 | + | 0.233365i | ||||
\(47\) | −10271.7 | −0.678264 | −0.339132 | − | 0.940739i | \(-0.610133\pi\) | ||||
−0.339132 | + | 0.940739i | \(0.610133\pi\) | |||||||
\(48\) | 2438.07 | − | 22843.5i | 0.152736 | − | 1.43107i | ||||
\(49\) | −26302.1 | −1.56495 | ||||||||
\(50\) | 2041.68 | − | 2886.44i | 0.115495 | − | 0.163282i | ||||
\(51\) | −12544.6 | + | 12544.6i | −0.675352 | + | 0.675352i | ||||
\(52\) | −8941.09 | − | 4273.50i | −0.458545 | − | 0.219167i | ||||
\(53\) | 22621.4 | + | 22621.4i | 1.10619 | + | 1.10619i | 0.993647 | + | 0.112541i | \(0.0358991\pi\) |
0.112541 | + | 0.993647i | \(0.464101\pi\) | |||||||
\(54\) | −371.428 | − | 2166.80i | −0.0173337 | − | 0.101119i | ||||
\(55\) | − | 3747.57i | − | 0.167049i | ||||||
\(56\) | −36161.1 | − | 10245.6i | −1.54089 | − | 0.436582i | ||||
\(57\) | − | 17676.0i | − | 0.720604i | ||||||
\(58\) | 43824.3 | − | 7512.27i | 1.71059 | − | 0.293225i | ||||
\(59\) | 15232.3 | + | 15232.3i | 0.569686 | + | 0.569686i | 0.932040 | − | 0.362354i | \(-0.118027\pi\) |
−0.362354 | + | 0.932040i | \(0.618027\pi\) | |||||||
\(60\) | 5977.53 | + | 16923.2i | 0.214360 | + | 0.606883i | ||||
\(61\) | 29775.5 | − | 29775.5i | 1.02455 | − | 1.02455i | 0.0248633 | − | 0.999691i | \(-0.492085\pi\) |
0.999691 | − | 0.0248633i | \(-0.00791503\pi\) | |||||||
\(62\) | −27422.8 | − | 19397.0i | −0.906009 | − | 0.640850i | ||||
\(63\) | −54050.1 | −1.71571 | ||||||||
\(64\) | −27898.0 | − | 17188.5i | −0.851378 | − | 0.524552i | ||||
\(65\) | 7742.11 | 0.227288 | ||||||||
\(66\) | 15531.6 | + | 10986.0i | 0.438891 | + | 0.310442i | ||||
\(67\) | 8220.39 | − | 8220.39i | 0.223720 | − | 0.223720i | −0.586343 | − | 0.810063i | \(-0.699433\pi\) |
0.810063 | + | 0.586343i | \(0.199433\pi\) | |||||||
\(68\) | 8427.64 | + | 23859.8i | 0.221021 | + | 0.625741i | ||||
\(69\) | 11504.2 | + | 11504.2i | 0.290892 | + | 0.290892i | ||||
\(70\) | 28940.8 | − | 4960.98i | 0.705937 | − | 0.121010i | ||||
\(71\) | 23239.8i | 0.547124i | 0.961854 | + | 0.273562i | \(0.0882019\pi\) | ||||
−0.961854 | + | 0.273562i | \(0.911798\pi\) | |||||||
\(72\) | −45338.7 | − | 12845.8i | −1.03071 | − | 0.292033i | ||||
\(73\) | − | 39178.1i | − | 0.860472i | −0.902716 | − | 0.430236i | \(-0.858430\pi\) | ||
0.902716 | − | 0.430236i | \(-0.141570\pi\) | |||||||
\(74\) | −15197.8 | − | 88659.4i | −0.322628 | − | 1.88211i | ||||
\(75\) | −9914.90 | − | 9914.90i | −0.203533 | − | 0.203533i | ||||
\(76\) | −22747.4 | − | 10872.4i | −0.451750 | − | 0.215919i | ||||
\(77\) | 22008.0 | − | 22008.0i | 0.423012 | − | 0.423012i | ||||
\(78\) | −22696.0 | + | 32086.7i | −0.422389 | + | 0.597157i | ||||
\(79\) | 60064.3 | 1.08280 | 0.541401 | − | 0.840765i | \(-0.317894\pi\) | ||||
0.541401 | + | 0.840765i | \(0.317894\pi\) | |||||||
\(80\) | 25455.4 | + | 2716.83i | 0.444688 | + | 0.0474611i | ||||
\(81\) | 54539.6 | 0.923633 | ||||||||
\(82\) | 50305.1 | − | 71119.5i | 0.826186 | − | 1.16803i | ||||
\(83\) | −49937.5 | + | 49937.5i | −0.795668 | + | 0.795668i | −0.982409 | − | 0.186741i | \(-0.940207\pi\) |
0.186741 | + | 0.982409i | \(0.440207\pi\) | |||||||
\(84\) | −64279.6 | + | 134487.i | −0.993973 | + | 2.07961i | ||||
\(85\) | −13978.9 | − | 13978.9i | −0.209858 | − | 0.209858i | ||||
\(86\) | 13106.7 | + | 76460.5i | 0.191094 | + | 1.11478i | ||||
\(87\) | − | 176340.i | − | 2.49778i | ||||||
\(88\) | 23691.4 | − | 13230.4i | 0.326125 | − | 0.182123i | ||||
\(89\) | 80470.0i | 1.07686i | 0.842670 | + | 0.538430i | \(0.180982\pi\) | ||||
−0.842670 | + | 0.538430i | \(0.819018\pi\) | |||||||
\(90\) | 36285.9 | − | 6220.05i | 0.472206 | − | 0.0809446i | ||||
\(91\) | 45466.2 | + | 45466.2i | 0.575553 | + | 0.575553i | ||||
\(92\) | 21881.0 | − | 7728.69i | 0.269524 | − | 0.0951998i | ||||
\(93\) | −94196.9 | + | 94196.9i | −1.12935 | + | 1.12935i | ||||
\(94\) | 47438.0 | + | 33554.4i | 0.553741 | + | 0.391679i | ||||
\(95\) | 19697.0 | 0.223919 | ||||||||
\(96\) | −85882.3 | + | 97534.2i | −0.951099 | + | 1.08014i | ||||
\(97\) | −25522.0 | −0.275413 | −0.137707 | − | 0.990473i | \(-0.543973\pi\) | ||||
−0.137707 | + | 0.990473i | \(0.543973\pi\) | |||||||
\(98\) | 121471. | + | 85920.7i | 1.27764 | + | 0.903717i | ||||
\(99\) | 27593.5 | − | 27593.5i | 0.282956 | − | 0.282956i | ||||
\(100\) | −18858.2 | + | 6660.99i | −0.188582 | + | 0.0666099i | ||||
\(101\) | 139868. | + | 139868.i | 1.36432 | + | 1.36432i | 0.868327 | + | 0.495992i | \(0.165196\pi\) |
0.495992 | + | 0.868327i | \(0.334804\pi\) | |||||||
\(102\) | 98913.7 | − | 16955.6i | 0.941361 | − | 0.161366i | ||||
\(103\) | 115209.i | 1.07003i | 0.844844 | + | 0.535013i | \(0.179693\pi\) | ||||
−0.844844 | + | 0.535013i | \(0.820307\pi\) | |||||||
\(104\) | 27332.6 | + | 48944.1i | 0.247798 | + | 0.443728i | ||||
\(105\) | − | 116452.i | − | 1.03080i | ||||||
\(106\) | −30575.7 | − | 178369.i | −0.264309 | − | 1.54190i | ||||
\(107\) | −26851.6 | − | 26851.6i | −0.226731 | − | 0.226731i | 0.584595 | − | 0.811325i | \(-0.301254\pi\) |
−0.811325 | + | 0.584595i | \(0.801254\pi\) | |||||||
\(108\) | −5362.87 | + | 11220.3i | −0.0442423 | + | 0.0925645i | ||||
\(109\) | −3142.11 | + | 3142.11i | −0.0253311 | + | 0.0253311i | −0.719659 | − | 0.694328i | \(-0.755702\pi\) |
0.694328 | + | 0.719659i | \(0.255702\pi\) | |||||||
\(110\) | −12242.1 | + | 17307.5i | −0.0964662 | + | 0.136380i | ||||
\(111\) | −356748. | −2.74824 | ||||||||
\(112\) | 133534. | + | 165444.i | 1.00588 | + | 1.24625i | ||||
\(113\) | −80743.8 | −0.594858 | −0.297429 | − | 0.954744i | \(-0.596129\pi\) | ||||
−0.297429 | + | 0.954744i | \(0.596129\pi\) | |||||||
\(114\) | −57741.9 | + | 81633.2i | −0.416130 | + | 0.588308i | ||||
\(115\) | −12819.5 | + | 12819.5i | −0.0903915 | + | 0.0903915i | ||||
\(116\) | −226934. | − | 108466.i | −1.56587 | − | 0.748426i | ||||
\(117\) | 57005.4 | + | 57005.4i | 0.384991 | + | 0.384991i | ||||
\(118\) | −20588.4 | − | 120107.i | −0.136119 | − | 0.794076i | ||||
\(119\) | − | 164184.i | − | 1.06283i | ||||||
\(120\) | 27676.7 | − | 97683.4i | 0.175453 | − | 0.619252i | ||||
\(121\) | − | 138580.i | − | 0.860473i | ||||||
\(122\) | −234780. | + | 40245.5i | −1.42811 | + | 0.244803i | ||||
\(123\) | −244294. | − | 244294.i | −1.45596 | − | 1.45596i | ||||
\(124\) | 63283.1 | + | 179163.i | 0.369601 | + | 1.04639i | ||||
\(125\) | 11048.5 | − | 11048.5i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 249620. | + | 176564.i | 1.40073 | + | 0.990779i | ||||
\(127\) | 133944. | 0.736907 | 0.368453 | − | 0.929646i | \(-0.379887\pi\) | ||||
0.368453 | + | 0.929646i | \(0.379887\pi\) | |||||||
\(128\) | 72692.1 | + | 170516.i | 0.392159 | + | 0.919897i | ||||
\(129\) | 307662. | 1.62779 | ||||||||
\(130\) | −35755.4 | − | 25291.0i | −0.185560 | − | 0.131252i | ||||
\(131\) | 109479. | − | 109479.i | 0.557382 | − | 0.557382i | −0.371179 | − | 0.928561i | \(-0.621047\pi\) |
0.928561 | + | 0.371179i | \(0.121047\pi\) | |||||||
\(132\) | −35842.0 | − | 101474.i | −0.179043 | − | 0.506895i | ||||
\(133\) | 115673. | + | 115673.i | 0.567024 | + | 0.567024i | ||||
\(134\) | −64817.7 | + | 11110.9i | −0.311840 | + | 0.0534549i | ||||
\(135\) | − | 9715.66i | − | 0.0458815i | ||||||
\(136\) | 39021.0 | − | 137722.i | 0.180905 | − | 0.638495i | ||||
\(137\) | 84564.2i | 0.384933i | 0.981304 | + | 0.192467i | \(0.0616487\pi\) | ||||
−0.981304 | + | 0.192467i | \(0.938351\pi\) | |||||||
\(138\) | −15549.4 | − | 90710.3i | −0.0695048 | − | 0.405470i | ||||
\(139\) | 49908.2 | + | 49908.2i | 0.219096 | + | 0.219096i | 0.808118 | − | 0.589021i | \(-0.200487\pi\) |
−0.589021 | + | 0.808118i | \(0.700487\pi\) | |||||||
\(140\) | −149864. | − | 71629.1i | −0.646214 | − | 0.308866i | ||||
\(141\) | 162949. | − | 162949.i | 0.690246 | − | 0.690246i | ||||
\(142\) | 75916.9 | − | 107328.i | 0.315949 | − | 0.446677i | ||||
\(143\) | −46422.6 | −0.189841 | ||||||||
\(144\) | 167425. | + | 207433.i | 0.672843 | + | 0.833628i | ||||
\(145\) | 196503. | 0.776156 | ||||||||
\(146\) | −127983. | + | 180937.i | −0.496899 | + | 0.702498i | ||||
\(147\) | 417253. | − | 417253.i | 1.59260 | − | 1.59260i | ||||
\(148\) | −219434. | + | 459103.i | −0.823473 | + | 1.72288i | ||||
\(149\) | −31361.2 | − | 31361.2i | −0.115725 | − | 0.115725i | 0.646873 | − | 0.762598i | \(-0.276076\pi\) |
−0.762598 | + | 0.646873i | \(0.776076\pi\) | |||||||
\(150\) | 13401.3 | + | 78178.9i | 0.0486315 | + | 0.283701i | ||||
\(151\) | 27122.5i | 0.0968028i | 0.998828 | + | 0.0484014i | \(0.0154127\pi\) | ||||
−0.998828 | + | 0.0484014i | \(0.984587\pi\) | |||||||
\(152\) | 69538.0 | + | 124521.i | 0.244126 | + | 0.437152i | ||||
\(153\) | − | 205854.i | − | 0.710936i | ||||||
\(154\) | −173533. | + | 29746.6i | −0.589629 | + | 0.101073i | ||||
\(155\) | −104967. | − | 104967.i | −0.350933 | − | 0.350933i | ||||
\(156\) | 209634. | − | 74045.9i | 0.689685 | − | 0.243607i | ||||
\(157\) | −285267. | + | 285267.i | −0.923640 | + | 0.923640i | −0.997285 | − | 0.0736442i | \(-0.976537\pi\) |
0.0736442 | + | 0.997285i | \(0.476537\pi\) | |||||||
\(158\) | −277396. | − | 196211.i | −0.884010 | − | 0.625289i | ||||
\(159\) | −717723. | −2.25146 | ||||||||
\(160\) | −108686. | − | 95701.9i | −0.335640 | − | 0.295543i | ||||
\(161\) | −150568. | −0.457791 | ||||||||
\(162\) | −251881. | − | 178163.i | −0.754063 | − | 0.533373i | ||||
\(163\) | 370586. | − | 370586.i | 1.09250 | − | 1.09250i | 0.0972352 | − | 0.995261i | \(-0.469000\pi\) |
0.995261 | − | 0.0972352i | \(-0.0309999\pi\) | |||||||
\(164\) | −464649. | + | 164121.i | −1.34901 | + | 0.476491i | ||||
\(165\) | 59450.9 | + | 59450.9i | 0.170000 | + | 0.170000i | ||||
\(166\) | 393757. | − | 67497.0i | 1.10907 | − | 0.190114i | ||||
\(167\) | 11117.4i | 0.0308470i | 0.999881 | + | 0.0154235i | \(0.00490964\pi\) | ||||
−0.999881 | + | 0.0154235i | \(0.995090\pi\) | |||||||
\(168\) | 736188. | − | 411121.i | 2.01241 | − | 1.12382i | ||||
\(169\) | 275389.i | 0.741702i | ||||||||
\(170\) | 18894.3 | + | 110223.i | 0.0501427 | + | 0.292517i | ||||
\(171\) | 145030. | + | 145030.i | 0.379286 | + | 0.379286i | ||||
\(172\) | 189241. | − | 395934.i | 0.487747 | − | 1.02047i | ||||
\(173\) | −415152. | + | 415152.i | −1.05461 | + | 1.05461i | −0.0561909 | + | 0.998420i | \(0.517896\pi\) |
−0.998420 | + | 0.0561909i | \(0.982104\pi\) | |||||||
\(174\) | −576048. | + | 814395.i | −1.44240 | + | 2.03921i | ||||
\(175\) | 129767. | 0.320309 | ||||||||
\(176\) | −152634. | − | 16290.4i | −0.371423 | − | 0.0396416i | ||||
\(177\) | −483286. | −1.15950 | ||||||||
\(178\) | 262870. | − | 371636.i | 0.621858 | − | 0.879159i | ||||
\(179\) | 482106. | − | 482106.i | 1.12463 | − | 1.12463i | 0.133595 | − | 0.991036i | \(-0.457348\pi\) |
0.991036 | − | 0.133595i | \(-0.0426520\pi\) | |||||||
\(180\) | −187898. | − | 89808.3i | −0.432257 | − | 0.206602i | ||||
\(181\) | −530714. | − | 530714.i | −1.20410 | − | 1.20410i | −0.972907 | − | 0.231197i | \(-0.925736\pi\) |
−0.231197 | − | 0.972907i | \(-0.574264\pi\) | |||||||
\(182\) | −61453.4 | − | 358501.i | −0.137521 | − | 0.802253i | ||||
\(183\) | 944708.i | 2.08531i | ||||||||
\(184\) | −126300. | − | 35784.7i | −0.275017 | − | 0.0779208i | ||||
\(185\) | − | 397538.i | − | 0.853983i | ||||||
\(186\) | 742742. | − | 127319.i | 1.57418 | − | 0.269843i | ||||
\(187\) | 83819.0 | + | 83819.0i | 0.175282 | + | 0.175282i | ||||
\(188\) | −109472. | − | 309930.i | −0.225895 | − | 0.639541i | ||||
\(189\) | 57056.1 | − | 57056.1i | 0.116184 | − | 0.116184i | ||||
\(190\) | −90967.0 | − | 64343.9i | −0.182810 | − | 0.129307i | ||||
\(191\) | −988041. | −1.95971 | −0.979854 | − | 0.199713i | \(-0.935999\pi\) | ||||
−0.979854 | + | 0.199713i | \(0.935999\pi\) | |||||||
\(192\) | 715245. | − | 169893.i | 1.40024 | − | 0.332600i | ||||
\(193\) | 274345. | 0.530156 | 0.265078 | − | 0.964227i | \(-0.414602\pi\) | ||||
0.265078 | + | 0.964227i | \(0.414602\pi\) | |||||||
\(194\) | 117868. | + | 83372.1i | 0.224850 | + | 0.159044i | ||||
\(195\) | −122819. | + | 122819.i | −0.231303 | + | 0.231303i | ||||
\(196\) | −280317. | − | 793617.i | −0.521206 | − | 1.47561i | ||||
\(197\) | 452496. | + | 452496.i | 0.830709 | + | 0.830709i | 0.987614 | − | 0.156905i | \(-0.0501516\pi\) |
−0.156905 | + | 0.987614i | \(0.550152\pi\) | |||||||
\(198\) | −217574. | + | 37296.2i | −0.394407 | + | 0.0676085i | ||||
\(199\) | 504657.i | 0.903365i | 0.892179 | + | 0.451683i | \(0.149176\pi\) | ||||
−0.892179 | + | 0.451683i | \(0.850824\pi\) | |||||||
\(200\) | 108852. | + | 30841.2i | 0.192425 | + | 0.0545200i | ||||
\(201\) | 260814.i | 0.455345i | ||||||||
\(202\) | −189050. | − | 1.10286e6i | −0.325986 | − | 1.90170i | ||||
\(203\) | 1.15398e6 | + | 1.15398e6i | 1.96543 | + | 1.96543i | ||||
\(204\) | −512203. | − | 244814.i | −0.861721 | − | 0.411870i | ||||
\(205\) | 272227. | − | 272227.i | 0.452424 | − | 0.452424i | ||||
\(206\) | 376352. | − | 532073.i | 0.617912 | − | 0.873580i | ||||
\(207\) | −188781. | −0.306219 | ||||||||
\(208\) | 33654.4 | − | 315326.i | 0.0539366 | − | 0.505360i | ||||
\(209\) | −118106. | −0.187027 | ||||||||
\(210\) | −380412. | + | 537813.i | −0.595260 | + | 0.841555i | ||||
\(211\) | −556380. | + | 556380.i | −0.860331 | + | 0.860331i | −0.991376 | − | 0.131046i | \(-0.958167\pi\) |
0.131046 | + | 0.991376i | \(0.458167\pi\) | |||||||
\(212\) | −441468. | + | 923646.i | −0.674620 | + | 1.41145i | ||||
\(213\) | −368672. | − | 368672.i | −0.556789 | − | 0.556789i | ||||
\(214\) | 36293.4 | + | 211725.i | 0.0541743 | + | 0.316036i | ||||
\(215\) | 342839.i | 0.505818i | ||||||||
\(216\) | 61420.5 | − | 34300.0i | 0.0895734 | − | 0.0500218i | ||||
\(217\) | − | 1.23286e6i | − | 1.77731i | ||||||
\(218\) | 24775.5 | − | 4246.96i | 0.0353086 | − | 0.00605253i | ||||
\(219\) | 621516. | + | 621516.i | 0.875673 | + | 0.875673i | ||||
\(220\) | 113076. | − | 39940.1i | 0.157512 | − | 0.0556355i | ||||
\(221\) | −173161. | + | 173161.i | −0.238490 | + | 0.238490i | ||||
\(222\) | 1.64757e6 | + | 1.16538e6i | 2.24369 | + | 1.58703i | ||||
\(223\) | 135203. | 0.182063 | 0.0910317 | − | 0.995848i | \(-0.470984\pi\) | ||||
0.0910317 | + | 0.995848i | \(0.470984\pi\) | |||||||
\(224\) | −76250.3 | − | 1.20029e6i | −0.101536 | − | 1.59832i | ||||
\(225\) | 162702. | 0.214257 | ||||||||
\(226\) | 372900. | + | 263764.i | 0.485648 | + | 0.343515i | ||||
\(227\) | −555431. | + | 555431.i | −0.715428 | + | 0.715428i | −0.967665 | − | 0.252237i | \(-0.918834\pi\) |
0.252237 | + | 0.967665i | \(0.418834\pi\) | |||||||
\(228\) | 533340. | − | 188383.i | 0.679464 | − | 0.239997i | ||||
\(229\) | 212624. | + | 212624.i | 0.267931 | + | 0.267931i | 0.828266 | − | 0.560335i | \(-0.189328\pi\) |
−0.560335 | + | 0.828266i | \(0.689328\pi\) | |||||||
\(230\) | 101082. | − | 17327.2i | 0.125995 | − | 0.0215978i | ||||
\(231\) | 698261.i | 0.860970i | ||||||||
\(232\) | 693730. | + | 1.24225e6i | 0.846195 | + | 1.51527i | ||||
\(233\) | − | 5580.59i | − | 0.00673426i | −0.999994 | − | 0.00336713i | \(-0.998928\pi\) | ||
0.999994 | − | 0.00336713i | \(-0.00107179\pi\) | |||||||
\(234\) | −77050.1 | − | 449487.i | −0.0919885 | − | 0.536633i | ||||
\(235\) | 181580. | + | 181580.i | 0.214486 | + | 0.214486i | ||||
\(236\) | −297266. | + | 621946.i | −0.347429 | + | 0.726896i | ||||
\(237\) | −952851. | + | 952851.i | −1.10193 | + | 1.10193i | ||||
\(238\) | −536338. | + | 758255.i | −0.613757 | + | 0.867706i | ||||
\(239\) | 956719. | 1.08340 | 0.541701 | − | 0.840571i | \(-0.317781\pi\) | ||||
0.541701 | + | 0.840571i | \(0.317781\pi\) | |||||||
\(240\) | −446920. | + | 360721.i | −0.500843 | + | 0.404244i | ||||
\(241\) | −380557. | −0.422063 | −0.211031 | − | 0.977479i | \(-0.567682\pi\) | ||||
−0.211031 | + | 0.977479i | \(0.567682\pi\) | |||||||
\(242\) | −452697. | + | 640006.i | −0.496900 | + | 0.702499i | ||||
\(243\) | −931983. | + | 931983.i | −1.01249 | + | 1.01249i | ||||
\(244\) | 1.21576e6 | + | 581085.i | 1.30729 | + | 0.624834i | ||||
\(245\) | 464960. | + | 464960.i | 0.494881 | + | 0.494881i | ||||
\(246\) | 330195. | + | 1.92626e6i | 0.347883 | + | 2.02944i | ||||
\(247\) | − | 243994.i | − | 0.254471i | ||||||
\(248\) | 293008. | − | 1.03416e6i | 0.302517 | − | 1.06772i | ||||
\(249\) | − | 1.58440e6i | − | 1.61945i | ||||||
\(250\) | −87117.7 | + | 14933.5i | −0.0881569 | + | 0.0151117i | ||||
\(251\) | 520698. | + | 520698.i | 0.521676 | + | 0.521676i | 0.918077 | − | 0.396401i | \(-0.129741\pi\) |
−0.396401 | + | 0.918077i | \(0.629741\pi\) | |||||||
\(252\) | −576043. | − | 1.63086e6i | −0.571418 | − | 1.61776i | ||||
\(253\) | 76867.4 | − | 76867.4i | 0.0754989 | − | 0.0754989i | ||||
\(254\) | −618593. | − | 437551.i | −0.601618 | − | 0.425544i | ||||
\(255\) | 443517. | 0.427130 | ||||||||
\(256\) | 221306. | − | 1.02496e6i | 0.211054 | − | 0.977474i | ||||
\(257\) | −1.17674e6 | −1.11135 | −0.555673 | − | 0.831401i | \(-0.687539\pi\) | ||||
−0.555673 | + | 0.831401i | \(0.687539\pi\) | |||||||
\(258\) | −1.42088e6 | − | 1.00503e6i | −1.32895 | − | 0.940008i | ||||
\(259\) | 2.33458e6 | − | 2.33458e6i | 2.16251 | − | 2.16251i | ||||
\(260\) | 82512.1 | + | 233603.i | 0.0756980 | + | 0.214312i | ||||
\(261\) | 1.44686e6 | + | 1.44686e6i | 1.31469 | + | 1.31469i | ||||
\(262\) | −863241. | + | 147975.i | −0.776925 | + | 0.133179i | ||||
\(263\) | − | 634969.i | − | 0.566061i | −0.959111 | − | 0.283030i | \(-0.908660\pi\) | ||
0.959111 | − | 0.283030i | \(-0.0913397\pi\) | |||||||
\(264\) | −165953. | + | 585721.i | −0.146546 | + | 0.517227i | ||||
\(265\) | − | 799786.i | − | 0.699615i | ||||||
\(266\) | −156346. | − | 912077.i | −0.135483 | − | 0.790365i | ||||
\(267\) | −1.27656e6 | − | 1.27656e6i | −1.09588 | − | 1.09588i | ||||
\(268\) | 335644. | + | 160425.i | 0.285458 | + | 0.136438i | ||||
\(269\) | 1.21819e6 | − | 1.21819e6i | 1.02644 | − | 1.02644i | 0.0267968 | − | 0.999641i | \(-0.491469\pi\) |
0.999641 | − | 0.0267968i | \(-0.00853069\pi\) | |||||||
\(270\) | −31738.0 | + | 44869.9i | −0.0264954 | + | 0.0374581i | ||||
\(271\) | 602236. | 0.498131 | 0.249065 | − | 0.968487i | \(-0.419877\pi\) | ||||
0.249065 | + | 0.968487i | \(0.419877\pi\) | |||||||
\(272\) | −630106. | + | 508576.i | −0.516406 | + | 0.416806i | ||||
\(273\) | −1.44254e6 | −1.17144 | ||||||||
\(274\) | 276244. | − | 390544.i | 0.222289 | − | 0.314263i | ||||
\(275\) | −66248.4 | + | 66248.4i | −0.0528255 | + | 0.0528255i | ||||
\(276\) | −224510. | + | 469723.i | −0.177404 | + | 0.371167i | ||||
\(277\) | 886773. | + | 886773.i | 0.694406 | + | 0.694406i | 0.963198 | − | 0.268792i | \(-0.0866246\pi\) |
−0.268792 | + | 0.963198i | \(0.586625\pi\) | |||||||
\(278\) | −67457.4 | − | 393526.i | −0.0523501 | − | 0.305395i | ||||
\(279\) | − | 1.54575e6i | − | 1.18886i | ||||||
\(280\) | 458127. | + | 820362.i | 0.349214 | + | 0.625332i | ||||
\(281\) | − | 891843.i | − | 0.673787i | −0.941543 | − | 0.336893i | \(-0.890624\pi\) | ||
0.941543 | − | 0.336893i | \(-0.109376\pi\) | |||||||
\(282\) | −1.28485e6 | + | 220246.i | −0.962122 | + | 0.164925i | ||||
\(283\) | −215112. | − | 215112.i | −0.159661 | − | 0.159661i | 0.622756 | − | 0.782416i | \(-0.286013\pi\) |
−0.782416 | + | 0.622756i | \(0.786013\pi\) | |||||||
\(284\) | −701216. | + | 247680.i | −0.515888 | + | 0.182219i | ||||
\(285\) | −312470. | + | 312470.i | −0.227875 | + | 0.227875i | ||||
\(286\) | 214394. | + | 151648.i | 0.154988 | + | 0.109628i | ||||
\(287\) | 3.19735e6 | 2.29132 | ||||||||
\(288\) | −95602.3 | − | 1.50492e6i | −0.0679184 | − | 1.06913i | ||||
\(289\) | −794548. | −0.559597 | ||||||||
\(290\) | −907511. | − | 641912.i | −0.633661 | − | 0.448209i | ||||
\(291\) | 404876. | − | 404876.i | 0.280279 | − | 0.280279i | ||||
\(292\) | 1.18213e6 | − | 417544.i | 0.811347 | − | 0.286580i | ||||
\(293\) | −967135. | − | 967135.i | −0.658140 | − | 0.658140i | 0.296800 | − | 0.954940i | \(-0.404080\pi\) |
−0.954940 | + | 0.296800i | \(0.904080\pi\) | |||||||
\(294\) | −3.29003e6 | + | 563971.i | −2.21989 | + | 0.380529i | ||||
\(295\) | − | 538544.i | − | 0.360301i | ||||||
\(296\) | 2.51316e6 | − | 1.40346e6i | 1.66721 | − | 0.931045i | ||||
\(297\) | 58256.2i | 0.0383223i | ||||||||
\(298\) | 42388.6 | + | 247282.i | 0.0276509 | + | 0.161307i | ||||
\(299\) | 158800. | + | 158800.i | 0.102724 | + | 0.102724i | ||||
\(300\) | 193494. | − | 404832.i | 0.124127 | − | 0.259700i | ||||
\(301\) | −2.01336e6 | + | 2.01336e6i | −1.28087 | + | 1.28087i | ||||
\(302\) | 88600.7 | − | 125260.i | 0.0559010 | − | 0.0790308i | ||||
\(303\) | −4.43770e6 | −2.77684 | ||||||||
\(304\) | 85621.6 | − | 802234.i | 0.0531373 | − | 0.497871i | ||||
\(305\) | −1.05272e6 | −0.647985 | ||||||||
\(306\) | −672459. | + | 950697.i | −0.410546 | + | 0.580415i | ||||
\(307\) | −2.10116e6 | + | 2.10116e6i | −1.27237 | + | 1.27237i | −0.327528 | + | 0.944842i | \(0.606216\pi\) |
−0.944842 | + | 0.327528i | \(0.893784\pi\) | |||||||
\(308\) | 898600. | + | 429497.i | 0.539746 | + | 0.257978i | ||||
\(309\) | −1.82766e6 | − | 1.82766e6i | −1.08893 | − | 1.08893i | ||||
\(310\) | 141877. | + | 827666.i | 0.0838507 | + | 0.489160i | ||||
\(311\) | − | 2.92143e6i | − | 1.71275i | −0.516351 | − | 0.856377i | \(-0.672710\pi\) | ||
0.516351 | − | 0.856377i | \(-0.327290\pi\) | |||||||
\(312\) | −1.21004e6 | − | 342841.i | −0.703742 | − | 0.199391i | ||||
\(313\) | − | 329253.i | − | 0.189963i | −0.995479 | − | 0.0949814i | \(-0.969721\pi\) | ||
0.995479 | − | 0.0949814i | \(-0.0302792\pi\) | |||||||
\(314\) | 2.24933e6 | − | 385576.i | 1.28745 | − | 0.220691i | ||||
\(315\) | 955479. | + | 955479.i | 0.542556 | + | 0.542556i | ||||
\(316\) | 640141. | + | 1.81233e6i | 0.360627 | + | 1.02098i | ||||
\(317\) | −165590. | + | 165590.i | −0.0925519 | + | 0.0925519i | −0.751867 | − | 0.659315i | \(-0.770846\pi\) |
0.659315 | + | 0.751867i | \(0.270846\pi\) | |||||||
\(318\) | 3.31467e6 | + | 2.34457e6i | 1.83811 | + | 1.30016i | ||||
\(319\) | −1.17825e6 | −0.648279 | ||||||||
\(320\) | 189318. | + | 797024.i | 0.103352 | + | 0.435107i | ||||
\(321\) | 851938. | 0.461472 | ||||||||
\(322\) | 695368. | + | 491857.i | 0.373745 | + | 0.264362i | ||||
\(323\) | −440548. | + | 440548.i | −0.234956 | + | 0.234956i | ||||
\(324\) | 581260. | + | 1.64563e6i | 0.307615 | + | 0.870902i | ||||
\(325\) | −136862. | − | 136862.i | −0.0718746 | − | 0.0718746i | ||||
\(326\) | −2.92207e6 | + | 500895.i | −1.52281 | + | 0.261037i | ||||
\(327\) | − | 99691.7i | − | 0.0515572i | ||||||
\(328\) | 2.68203e6 | + | 759900.i | 1.37651 | + | 0.390006i | ||||
\(329\) | 2.13269e6i | 1.08627i | ||||||||
\(330\) | −80355.5 | − | 468770.i | −0.0406192 | − | 0.236960i | ||||
\(331\) | −1.93413e6 | − | 1.93413e6i | −0.970320 | − | 0.970320i | 0.0292523 | − | 0.999572i | \(-0.490687\pi\) |
−0.999572 | + | 0.0292523i | \(0.990687\pi\) | |||||||
\(332\) | −2.03898e6 | − | 974557.i | −1.01524 | − | 0.485246i | ||||
\(333\) | 2.92708e6 | − | 2.92708e6i | 1.44652 | − | 1.44652i | ||||
\(334\) | 36317.0 | − | 51343.7i | 0.0178133 | − | 0.0251838i | ||||
\(335\) | −290635. | −0.141493 | ||||||||
\(336\) | −4.74295e6 | − | 506210.i | −2.29192 | − | 0.244615i | ||||
\(337\) | 2.32458e6 | 1.11499 | 0.557493 | − | 0.830181i | \(-0.311763\pi\) | ||||
0.557493 | + | 0.830181i | \(0.311763\pi\) | |||||||
\(338\) | 899607. | − | 1.27183e6i | 0.428313 | − | 0.605533i | ||||
\(339\) | 1.28091e6 | − | 1.28091e6i | 0.605366 | − | 0.605366i | ||||
\(340\) | 272805. | − | 570767.i | 0.127984 | − | 0.267770i | ||||
\(341\) | 629396. | + | 629396.i | 0.293115 | + | 0.293115i | ||||
\(342\) | −196027. | − | 1.14356e6i | −0.0906253 | − | 0.528681i | ||||
\(343\) | 1.97145e6i | 0.904796i | ||||||||
\(344\) | −2.16736e6 | + | 1.21035e6i | −0.987497 | + | 0.551463i | ||||
\(345\) | − | 406734.i | − | 0.183977i | ||||||
\(346\) | 3.27347e6 | − | 561132.i | 1.47000 | − | 0.251985i | ||||
\(347\) | 491869. | + | 491869.i | 0.219293 | + | 0.219293i | 0.808201 | − | 0.588907i | \(-0.200442\pi\) |
−0.588907 | + | 0.808201i | \(0.700442\pi\) | |||||||
\(348\) | 5.32074e6 | − | 1.87936e6i | 2.35518 | − | 0.831884i | ||||
\(349\) | 2.24702e6 | − | 2.24702e6i | 0.987514 | − | 0.987514i | −0.0124086 | − | 0.999923i | \(-0.503950\pi\) |
0.999923 | + | 0.0124086i | \(0.00394988\pi\) | |||||||
\(350\) | −599305. | − | 423908.i | −0.261504 | − | 0.184970i | ||||
\(351\) | −120351. | −0.0521415 | ||||||||
\(352\) | 651694. | + | 573840.i | 0.280341 | + | 0.246851i | ||||
\(353\) | −735511. | −0.314161 | −0.157080 | − | 0.987586i | \(-0.550208\pi\) | ||||
−0.157080 | + | 0.987586i | \(0.550208\pi\) | |||||||
\(354\) | 2.23196e6 | + | 1.57874e6i | 0.946627 | + | 0.669580i | ||||
\(355\) | 410825. | − | 410825.i | 0.173016 | − | 0.173016i | ||||
\(356\) | −2.42803e6 | + | 857616.i | −1.01538 | + | 0.358648i | ||||
\(357\) | 2.60459e6 | + | 2.60459e6i | 1.08161 | + | 1.08161i | ||||
\(358\) | −3.80140e6 | + | 651628.i | −1.56760 | + | 0.268715i | ||||
\(359\) | 777474.i | 0.318383i | 0.987248 | + | 0.159191i | \(0.0508887\pi\) | ||||
−0.987248 | + | 0.159191i | \(0.949111\pi\) | |||||||
\(360\) | 574398. | + | 1.02857e6i | 0.233591 | + | 0.418289i | ||||
\(361\) | 1.85534e6i | 0.749300i | ||||||||
\(362\) | 717328. | + | 4.18467e6i | 0.287704 | + | 1.67838i | ||||
\(363\) | 2.19841e6 | + | 2.19841e6i | 0.875674 | + | 0.875674i | ||||
\(364\) | −887296. | + | 1.85642e6i | −0.351007 | + | 0.734382i | ||||
\(365\) | −692578. | + | 692578.i | −0.272105 | + | 0.272105i | ||||
\(366\) | 3.08606e6 | − | 4.36296e6i | 1.20421 | − | 1.70246i | ||||
\(367\) | 1.55035e6 | 0.600850 | 0.300425 | − | 0.953805i | \(-0.402872\pi\) | ||||
0.300425 | + | 0.953805i | \(0.402872\pi\) | |||||||
\(368\) | 466397. | + | 577848.i | 0.179530 | + | 0.222430i | ||||
\(369\) | 4.00882e6 | 1.53268 | ||||||||
\(370\) | −1.29863e6 | + | 1.83595e6i | −0.493152 | + | 0.697200i | ||||
\(371\) | 4.69681e6 | − | 4.69681e6i | 1.77161 | − | 1.77161i | ||||
\(372\) | −3.84613e6 | − | 1.83830e6i | −1.44101 | − | 0.688747i | ||||
\(373\) | −3.16935e6 | − | 3.16935e6i | −1.17950 | − | 1.17950i | −0.979871 | − | 0.199630i | \(-0.936026\pi\) |
−0.199630 | − | 0.979871i | \(-0.563974\pi\) | |||||||
\(374\) | −113292. | − | 660912.i | −0.0418814 | − | 0.244323i | ||||
\(375\) | 350545.i | 0.128726i | ||||||||
\(376\) | −506867. | + | 1.78896e6i | −0.184895 | + | 0.652576i | ||||
\(377\) | − | 2.43415e6i | − | 0.882053i | ||||||
\(378\) | −449887. | + | 77118.6i | −0.161947 | + | 0.0277607i | ||||
\(379\) | −1.07742e6 | − | 1.07742e6i | −0.385289 | − | 0.385289i | 0.487715 | − | 0.873003i | \(-0.337831\pi\) |
−0.873003 | + | 0.487715i | \(0.837831\pi\) | |||||||
\(380\) | 209923. | + | 594320.i | 0.0745762 | + | 0.211136i | ||||
\(381\) | −2.12486e6 | + | 2.12486e6i | −0.749924 | + | 0.749924i | ||||
\(382\) | 4.56308e6 | + | 3.22762e6i | 1.59993 | + | 1.13168i | ||||
\(383\) | 417931. | 0.145582 | 0.0727910 | − | 0.997347i | \(-0.476809\pi\) | ||||
0.0727910 | + | 0.997347i | \(0.476809\pi\) | |||||||
\(384\) | −3.85821e6 | − | 1.55186e6i | −1.33523 | − | 0.537061i | ||||
\(385\) | −778099. | −0.267536 | ||||||||
\(386\) | −1.26701e6 | − | 896197.i | −0.432824 | − | 0.306151i | ||||
\(387\) | −2.52434e6 | + | 2.52434e6i | −0.856781 | + | 0.856781i | ||||
\(388\) | −272002. | − | 770077.i | −0.0917262 | − | 0.259690i | ||||
\(389\) | 307997. | + | 307997.i | 0.103198 | + | 0.103198i | 0.756821 | − | 0.653622i | \(-0.226752\pi\) |
−0.653622 | + | 0.756821i | \(0.726752\pi\) | |||||||
\(390\) | 968431. | − | 166006.i | 0.322409 | − | 0.0552667i | ||||
\(391\) | − | 573448.i | − | 0.189693i | ||||||
\(392\) | −1.29790e6 | + | 4.58088e6i | −0.426606 | + | 1.50568i | ||||
\(393\) | 3.47351e6i | 1.13446i | ||||||||
\(394\) | −611606. | − | 3.56793e6i | −0.198487 | − | 1.15791i | ||||
\(395\) | −1.06180e6 | − | 1.06180e6i | −0.342412 | − | 0.342412i | ||||
\(396\) | 1.12666e6 | + | 538501.i | 0.361040 | + | 0.172563i | ||||
\(397\) | −1.38664e6 | + | 1.38664e6i | −0.441559 | + | 0.441559i | −0.892536 | − | 0.450977i | \(-0.851076\pi\) |
0.450977 | + | 0.892536i | \(0.351076\pi\) | |||||||
\(398\) | 1.64855e6 | − | 2.33066e6i | 0.521669 | − | 0.737516i | ||||
\(399\) | −3.67002e6 | −1.15408 | ||||||||
\(400\) | −401965. | − | 498020.i | −0.125614 | − | 0.155631i | ||||
\(401\) | 4.12677e6 | 1.28159 | 0.640795 | − | 0.767712i | \(-0.278605\pi\) | ||||
0.640795 | + | 0.767712i | \(0.278605\pi\) | |||||||
\(402\) | 851995. | − | 1.20452e6i | 0.262949 | − | 0.371748i | ||||
\(403\) | −1.30027e6 | + | 1.30027e6i | −0.398814 | + | 0.398814i | ||||
\(404\) | −2.72960e6 | + | 5.71092e6i | −0.832044 | + | 1.74082i | ||||
\(405\) | −964133. | − | 964133.i | −0.292078 | − | 0.292078i | ||||
\(406\) | −1.55975e6 | − | 9.09913e6i | −0.469614 | − | 2.73958i | ||||
\(407\) | 2.38368e6i | 0.713284i | ||||||||
\(408\) | 1.56578e6 | + | 2.80383e6i | 0.465673 | + | 0.833875i | ||||
\(409\) | 3.82776e6i | 1.13145i | 0.824593 | + | 0.565727i | \(0.191404\pi\) | ||||
−0.824593 | + | 0.565727i | \(0.808596\pi\) | |||||||
\(410\) | −2.14650e6 | + | 367949.i | −0.630626 | + | 0.108101i | ||||
\(411\) | −1.34151e6 | − | 1.34151e6i | −0.391733 | − | 0.391733i | ||||
\(412\) | −3.47622e6 | + | 1.22785e6i | −1.00894 | + | 0.356372i | ||||
\(413\) | 3.16264e6 | − | 3.16264e6i | 0.912379 | − | 0.912379i | ||||
\(414\) | 871850. | + | 616688.i | 0.250000 | + | 0.176833i | ||||
\(415\) | 1.76556e6 | 0.503225 | ||||||||
\(416\) | −1.18550e6 | + | 1.34633e6i | −0.335866 | + | 0.381434i | ||||
\(417\) | −1.58347e6 | −0.445934 | ||||||||
\(418\) | 545449. | + | 385814.i | 0.152691 | + | 0.108003i | ||||
\(419\) | −2.93291e6 | + | 2.93291e6i | −0.816139 | + | 0.816139i | −0.985546 | − | 0.169407i | \(-0.945815\pi\) |
0.169407 | + | 0.985546i | \(0.445815\pi\) | |||||||
\(420\) | 3.51372e6 | − | 1.24110e6i | 0.971951 | − | 0.343308i | ||||
\(421\) | −663610. | − | 663610.i | −0.182477 | − | 0.182477i | 0.609957 | − | 0.792434i | \(-0.291187\pi\) |
−0.792434 | + | 0.609957i | \(0.791187\pi\) | |||||||
\(422\) | 4.38705e6 | − | 752019.i | 1.19920 | − | 0.205564i | ||||
\(423\) | 2.67396e6i | 0.726614i | ||||||||
\(424\) | 5.05609e6 | − | 2.82355e6i | 1.36584 | − | 0.762747i | ||||
\(425\) | 494228.i | 0.132726i | ||||||||
\(426\) | 498307. | + | 2.90697e6i | 0.133037 | + | 0.776099i | ||||
\(427\) | −6.18222e6 | − | 6.18222e6i | −1.64087 | − | 1.64087i | ||||
\(428\) | 524022. | − | 1.09637e6i | 0.138274 | − | 0.289299i | ||||
\(429\) | 736440. | − | 736440.i | 0.193194 | − | 0.193194i | ||||
\(430\) | 1.11995e6 | − | 1.58334e6i | 0.292097 | − | 0.412955i | ||||
\(431\) | 5.51305e6 | 1.42955 | 0.714774 | − | 0.699355i | \(-0.246529\pi\) | ||||
0.714774 | + | 0.699355i | \(0.246529\pi\) | |||||||
\(432\) | −395706. | − | 42233.3i | −0.102015 | − | 0.0108879i | ||||
\(433\) | 1.36860e6 | 0.350797 | 0.175398 | − | 0.984498i | \(-0.443879\pi\) | ||||
0.175398 | + | 0.984498i | \(0.443879\pi\) | |||||||
\(434\) | −4.02736e6 | + | 5.69372e6i | −1.02635 | + | 1.45102i | ||||
\(435\) | −3.11729e6 | + | 3.11729e6i | −0.789867 | + | 0.789867i | ||||
\(436\) | −128294. | − | 61319.8i | −0.0323215 | − | 0.0154484i | ||||
\(437\) | 404011. | + | 404011.i | 0.101202 | + | 0.101202i | ||||
\(438\) | −840058. | − | 4.90065e6i | −0.209230 | − | 1.22058i | ||||
\(439\) | 5.68148e6i | 1.40702i | 0.710686 | + | 0.703510i | \(0.248385\pi\) | ||||
−0.710686 | + | 0.703510i | \(0.751615\pi\) | |||||||
\(440\) | −652691. | − | 184927.i | −0.160722 | − | 0.0455375i | ||||
\(441\) | 6.84704e6i | 1.67651i | ||||||||
\(442\) | 1.36538e6 | − | 234050.i | 0.332427 | − | 0.0569840i | ||||
\(443\) | 306470. | + | 306470.i | 0.0741957 | + | 0.0741957i | 0.743231 | − | 0.669035i | \(-0.233292\pi\) |
−0.669035 | + | 0.743231i | \(0.733292\pi\) | |||||||
\(444\) | −3.80207e6 | − | 1.07642e7i | −0.915299 | − | 2.59134i | ||||
\(445\) | 1.42252e6 | − | 1.42252e6i | 0.340533 | − | 0.340533i | ||||
\(446\) | −624407. | − | 441664.i | −0.148638 | − | 0.105137i | ||||
\(447\) | 995016. | 0.235538 | ||||||||
\(448\) | −3.56881e6 | + | 5.79238e6i | −0.840094 | + | 1.36352i | ||||
\(449\) | 1.77337e6 | 0.415130 | 0.207565 | − | 0.978221i | \(-0.433446\pi\) | ||||
0.207565 | + | 0.978221i | \(0.433446\pi\) | |||||||
\(450\) | −751406. | − | 531494.i | −0.174922 | − | 0.123728i | ||||
\(451\) | −1.63230e6 | + | 1.63230e6i | −0.377885 | + | 0.377885i | ||||
\(452\) | −860534. | − | 2.43629e6i | −0.198117 | − | 0.560897i | ||||
\(453\) | −430268. | − | 430268.i | −0.0985129 | − | 0.0985129i | ||||
\(454\) | 4.37957e6 | − | 750737.i | 0.997223 | − | 0.170942i | ||||
\(455\) | − | 1.60747e6i | − | 0.364012i | ||||||
\(456\) | −3.07852e6 | − | 872238.i | −0.693313 | − | 0.196437i | ||||
\(457\) | 131715.i | 0.0295016i | 0.999891 | + | 0.0147508i | \(0.00469549\pi\) | ||||
−0.999891 | + | 0.0147508i | \(0.995305\pi\) | |||||||
\(458\) | −287388. | − | 1.67654e6i | −0.0640185 | − | 0.373464i | ||||
\(459\) | 217302. | + | 217302.i | 0.0481430 | + | 0.0481430i | ||||
\(460\) | −523430. | − | 250180.i | −0.115336 | − | 0.0551261i | ||||
\(461\) | −5.97163e6 | + | 5.97163e6i | −1.30870 | + | 1.30870i | −0.386348 | + | 0.922353i | \(0.626264\pi\) |
−0.922353 | + | 0.386348i | \(0.873736\pi\) | |||||||
\(462\) | 2.28100e6 | − | 3.22479e6i | 0.497187 | − | 0.702904i | ||||
\(463\) | −1.48252e6 | −0.321401 | −0.160700 | − | 0.987003i | \(-0.551375\pi\) | ||||
−0.160700 | + | 0.987003i | \(0.551375\pi\) | |||||||
\(464\) | 854184. | − | 8.00330e6i | 0.184186 | − | 1.72574i | ||||
\(465\) | 3.33037e6 | 0.714265 | ||||||||
\(466\) | −18230.0 | + | 25772.9i | −0.00388886 | + | 0.00549792i | ||||
\(467\) | 539353. | − | 539353.i | 0.114441 | − | 0.114441i | −0.647567 | − | 0.762008i | \(-0.724214\pi\) |
0.762008 | + | 0.647567i | \(0.224214\pi\) | |||||||
\(468\) | −1.11249e6 | + | 2.32757e6i | −0.234791 | + | 0.491233i | ||||
\(469\) | −1.70678e6 | − | 1.70678e6i | −0.358298 | − | 0.358298i | ||||
\(470\) | −245429. | − | 1.43176e6i | −0.0512485 | − | 0.298968i | ||||
\(471\) | − | 9.05087e6i | − | 1.87991i | ||||||
\(472\) | 3.40457e6 | − | 1.90126e6i | 0.703407 | − | 0.392814i | ||||
\(473\) | − | 2.05571e6i | − | 0.422482i | ||||||
\(474\) | 7.51322e6 | − | 1.28790e6i | 1.53596 | − | 0.263291i | ||||
\(475\) | −348198. | − | 348198.i | −0.0708095 | − | 0.0708095i | ||||
\(476\) | 4.95395e6 | − | 1.74981e6i | 1.00215 | − | 0.353976i | ||||
\(477\) | 5.88885e6 | − | 5.88885e6i | 1.18504 | − | 1.18504i | ||||
\(478\) | −4.41843e6 | − | 3.12530e6i | −0.884500 | − | 0.625636i | ||||
\(479\) | 817685. | 0.162835 | 0.0814174 | − | 0.996680i | \(-0.474055\pi\) | ||||
0.0814174 | + | 0.996680i | \(0.474055\pi\) | |||||||
\(480\) | 3.24238e6 | − | 205978.i | 0.642333 | − | 0.0408053i | ||||
\(481\) | −4.92445e6 | −0.970499 | ||||||||
\(482\) | 1.75753e6 | + | 1.24316e6i | 0.344576 | + | 0.243730i | ||||
\(483\) | 2.38858e6 | − | 2.38858e6i | 0.465878 | − | 0.465878i | ||||
\(484\) | 4.18139e6 | − | 1.47693e6i | 0.811348 | − | 0.286580i | ||||
\(485\) | 451169. | + | 451169.i | 0.0870933 | + | 0.0870933i | ||||
\(486\) | 7.34868e6 | − | 1.25970e6i | 1.41130 | − | 0.241922i | ||||
\(487\) | − | 2.31590e6i | − | 0.442483i | −0.975219 | − | 0.221242i | \(-0.928989\pi\) | ||
0.975219 | − | 0.221242i | \(-0.0710110\pi\) | |||||||
\(488\) | −3.71652e6 | − | 6.65512e6i | −0.706458 | − | 1.26505i | ||||
\(489\) | 1.17578e7i | 2.22359i | ||||||||
\(490\) | −628454. | − | 3.66621e6i | −0.118245 | − | 0.689806i | ||||
\(491\) | −826277. | − | 826277.i | −0.154676 | − | 0.154676i | 0.625527 | − | 0.780203i | \(-0.284884\pi\) |
−0.780203 | + | 0.625527i | \(0.784884\pi\) | |||||||
\(492\) | 4.76753e6 | − | 9.97471e6i | 0.887934 | − | 1.85775i | ||||
\(493\) | −4.39502e6 | + | 4.39502e6i | −0.814411 | + | 0.814411i | ||||
\(494\) | −797052. | + | 1.12684e6i | −0.146950 | + | 0.207752i | ||||
\(495\) | −975577. | −0.178957 | ||||||||
\(496\) | −4.73146e6 | + | 3.81889e6i | −0.863557 | + | 0.697001i | ||||
\(497\) | 4.82521e6 | 0.876245 | ||||||||
\(498\) | −5.17574e6 | + | 7.31726e6i | −0.935188 | + | 1.32213i | ||||
\(499\) | −5.05925e6 | + | 5.05925e6i | −0.909567 | + | 0.909567i | −0.996237 | − | 0.0866697i | \(-0.972378\pi\) |
0.0866697 | + | 0.996237i | \(0.472378\pi\) | |||||||
\(500\) | 451120. | + | 215618.i | 0.0806987 | + | 0.0385709i | ||||
\(501\) | −176365. | − | 176365.i | −0.0313919 | − | 0.0313919i | ||||
\(502\) | −703790. | − | 4.10570e6i | −0.124648 | − | 0.727156i | ||||
\(503\) | 6.85970e6i | 1.20888i | 0.796649 | + | 0.604442i | \(0.206604\pi\) | ||||
−0.796649 | + | 0.604442i | \(0.793396\pi\) | |||||||
\(504\) | −2.66715e6 | + | 9.41356e6i | −0.467704 | + | 1.65074i | ||||
\(505\) | − | 4.94509e6i | − | 0.862871i | ||||||
\(506\) | −606099. | + | 103896.i | −0.105237 | + | 0.0180394i | ||||
\(507\) | −4.36872e6 | − | 4.36872e6i | −0.754804 | − | 0.754804i | ||||
\(508\) | 1.42751e6 | + | 4.04149e6i | 0.245426 | + | 0.694836i | ||||
\(509\) | −2.44299e6 | + | 2.44299e6i | −0.417952 | + | 0.417952i | −0.884497 | − | 0.466545i | \(-0.845499\pi\) |
0.466545 | + | 0.884497i | \(0.345499\pi\) | |||||||
\(510\) | −2.04830e6 | − | 1.44883e6i | −0.348713 | − | 0.246656i | ||||
\(511\) | −8.13446e6 | −1.37809 | ||||||||
\(512\) | −4.37027e6 | + | 4.01063e6i | −0.736772 | + | 0.676142i | ||||
\(513\) | −306191. | −0.0513688 | ||||||||
\(514\) | 5.43457e6 | + | 3.84405e6i | 0.907313 | + | 0.641772i | ||||
\(515\) | 2.03663e6 | − | 2.03663e6i | 0.338372 | − | 0.338372i | ||||
\(516\) | 3.27893e6 | + | 9.28312e6i | 0.542136 | + | 1.53486i | ||||
\(517\) | −1.08878e6 | − | 1.08878e6i | −0.179148 | − | 0.179148i | ||||
\(518\) | −1.84081e7 | + | 3.15548e6i | −3.01429 | + | 0.516703i | ||||
\(519\) | − | 1.31718e7i | − | 2.14648i | ||||||
\(520\) | 382041. | − | 1.34839e6i | 0.0619586 | − | 0.218680i | ||||
\(521\) | 6.94705e6i | 1.12126i | 0.828066 | + | 0.560630i | \(0.189441\pi\) | ||||
−0.828066 | + | 0.560630i | \(0.810559\pi\) | |||||||
\(522\) | −1.95561e6 | − | 1.14084e7i | −0.314128 | − | 1.83253i | ||||
\(523\) | 3.42284e6 | + | 3.42284e6i | 0.547182 | + | 0.547182i | 0.925625 | − | 0.378442i | \(-0.123540\pi\) |
−0.378442 | + | 0.925625i | \(0.623540\pi\) | |||||||
\(524\) | 4.47010e6 | + | 2.13654e6i | 0.711196 | + | 0.339925i | ||||
\(525\) | −2.05860e6 | + | 2.05860e6i | −0.325968 | + | 0.325968i | ||||
\(526\) | −2.07424e6 | + | 2.93248e6i | −0.326885 | + | 0.462138i | ||||
\(527\) | 4.69544e6 | 0.736460 | ||||||||
\(528\) | 2.67978e6 | − | 2.16293e6i | 0.418326 | − | 0.337642i | ||||
\(529\) | 5.91045e6 | 0.918294 | ||||||||
\(530\) | −2.61265e6 | + | 3.69366e6i | −0.404009 | + | 0.571172i | ||||
\(531\) | 3.96531e6 | − | 3.96531e6i | 0.610297 | − | 0.610297i | ||||
\(532\) | −2.25741e6 | + | 4.72299e6i | −0.345805 | + | 0.723499i | ||||
\(533\) | −3.37217e6 | − | 3.37217e6i | −0.514152 | − | 0.514152i | ||||
\(534\) | 1.72544e6 | + | 1.00657e7i | 0.261846 | + | 1.52753i | ||||
\(535\) | 949347.i | 0.143397i | ||||||||
\(536\) | −1.02605e6 | − | 1.83733e6i | −0.154261 | − | 0.276233i | ||||
\(537\) | 1.52961e7i | 2.28900i | ||||||||
\(538\) | −9.60538e6 | + | 1.64653e6i | −1.43073 | + | 0.245253i | ||||
\(539\) | −2.78796e6 | − | 2.78796e6i | −0.413346 | − | 0.413346i | ||||
\(540\) | 293152. | − | 103545.i | 0.0432621 | − | 0.0152808i | ||||
\(541\) | 3.55529e6 | − | 3.55529e6i | 0.522255 | − | 0.522255i | −0.395997 | − | 0.918252i | \(-0.629601\pi\) |
0.918252 | + | 0.395997i | \(0.129601\pi\) | |||||||
\(542\) | −2.78131e6 | − | 1.96731e6i | −0.406679 | − | 0.287657i | ||||
\(543\) | 1.68383e7 | 2.45075 | ||||||||
\(544\) | 4.57138e6 | − | 290405.i | 0.662293 | − | 0.0420733i | ||||
\(545\) | 111090. | 0.0160208 | ||||||||
\(546\) | 6.66208e6 | + | 4.71231e6i | 0.956375 | + | 0.676475i | ||||
\(547\) | −841266. | + | 841266.i | −0.120217 | + | 0.120217i | −0.764656 | − | 0.644439i | \(-0.777091\pi\) |
0.644439 | + | 0.764656i | \(0.277091\pi\) | |||||||
\(548\) | −2.55156e6 | + | 901250.i | −0.362957 | + | 0.128202i | ||||
\(549\) | −7.75124e6 | − | 7.75124e6i | −1.09759 | − | 1.09759i | ||||
\(550\) | 522368. | − | 89543.2i | 0.0736325 | − | 0.0126219i | ||||
\(551\) | − | 6.19284e6i | − | 0.868981i | ||||||
\(552\) | 2.57129e6 | − | 1.43592e6i | 0.359173 | − | 0.200578i | ||||
\(553\) | − | 1.24710e7i | − | 1.73416i | ||||||
\(554\) | −1.19859e6 | − | 6.99220e6i | −0.165919 | − | 0.967920i | ||||
\(555\) | 6.30648e6 | + | 6.30648e6i | 0.869069 | + | 0.869069i | ||||
\(556\) | −973985. | + | 2.03779e6i | −0.133618 | + | 0.279558i | ||||
\(557\) | 5.27270e6 | − | 5.27270e6i | 0.720104 | − | 0.720104i | −0.248522 | − | 0.968626i | \(-0.579945\pi\) |
0.968626 | + | 0.248522i | \(0.0799449\pi\) | |||||||
\(558\) | −5.04949e6 | + | 7.13877e6i | −0.686533 | + | 0.970595i | ||||
\(559\) | 4.24688e6 | 0.574831 | ||||||||
\(560\) | 564089. | − | 5.28524e6i | 0.0760111 | − | 0.712189i | ||||
\(561\) | −2.65938e6 | −0.356758 | ||||||||
\(562\) | −2.91337e6 | + | 4.11881e6i | −0.389094 | + | 0.550086i | ||||
\(563\) | −2.72831e6 | + | 2.72831e6i | −0.362763 | + | 0.362763i | −0.864829 | − | 0.502066i | \(-0.832573\pi\) |
0.502066 | + | 0.864829i | \(0.332573\pi\) | |||||||
\(564\) | 6.65332e6 | + | 3.18003e6i | 0.880725 | + | 0.420953i | ||||
\(565\) | 1.42736e6 | + | 1.42736e6i | 0.188111 | + | 0.188111i | ||||
\(566\) | 290752. | + | 1.69616e6i | 0.0381488 | + | 0.222549i | ||||
\(567\) | − | 1.13239e7i | − | 1.47924i | ||||||
\(568\) | 4.04752e6 | + | 1.14679e6i | 0.526403 | + | 0.149146i | ||||
\(569\) | − | 2.27113e6i | − | 0.294077i | −0.989131 | − | 0.147039i | \(-0.953026\pi\) | ||
0.989131 | − | 0.147039i | \(-0.0469741\pi\) | |||||||
\(570\) | 2.46383e6 | − | 422344.i | 0.317631 | − | 0.0544477i | ||||
\(571\) | 4.09926e6 | + | 4.09926e6i | 0.526157 | + | 0.526157i | 0.919424 | − | 0.393267i | \(-0.128655\pi\) |
−0.393267 | + | 0.919424i | \(0.628655\pi\) | |||||||
\(572\) | −494752. | − | 1.40071e6i | −0.0632263 | − | 0.179002i | ||||
\(573\) | 1.56741e7 | − | 1.56741e7i | 1.99433 | − | 1.99433i | ||||
\(574\) | −1.47664e7 | − | 1.04447e7i | −1.87065 | − | 1.32317i | ||||
\(575\) | 453239. | 0.0571686 | ||||||||
\(576\) | −4.47456e6 | + | 7.26247e6i | −0.561945 | + | 0.912070i | ||||
\(577\) | −1.13593e7 | −1.42040 | −0.710200 | − | 0.703999i | \(-0.751396\pi\) | ||||
−0.710200 | + | 0.703999i | \(0.751396\pi\) | |||||||
\(578\) | 3.66947e6 | + | 2.59554e6i | 0.456861 | + | 0.323153i | ||||
\(579\) | −4.35216e6 | + | 4.35216e6i | −0.539521 | + | 0.539521i | ||||
\(580\) | 2.09425e6 | + | 5.92910e6i | 0.258498 | + | 0.731844i | ||||
\(581\) | 1.03684e7 | + | 1.03684e7i | 1.27430 | + | 1.27430i | ||||
\(582\) | −3.19245e6 | + | 547242.i | −0.390675 | + | 0.0669688i | ||||
\(583\) | 4.79561e6i | 0.584349i | ||||||||
\(584\) | −6.82341e6 | − | 1.93328e6i | −0.827884 | − | 0.234565i | ||||
\(585\) | − | 2.01544e6i | − | 0.243490i | ||||||
\(586\) | 1.30721e6 | + | 7.62585e6i | 0.157254 | + | 0.917369i | ||||
\(587\) | −2.60566e6 | − | 2.60566e6i | −0.312120 | − | 0.312120i | 0.533610 | − | 0.845731i | \(-0.320835\pi\) |
−0.845731 | + | 0.533610i | \(0.820835\pi\) | |||||||
\(588\) | 1.70367e7 | + | 8.14290e6i | 2.03209 | + | 0.971261i | ||||
\(589\) | −3.30807e6 | + | 3.30807e6i | −0.392904 | + | 0.392904i | ||||
\(590\) | −1.75925e6 | + | 2.48716e6i | −0.208064 | + | 0.294153i | ||||
\(591\) | −1.43566e7 | −1.69077 | ||||||||
\(592\) | −1.61912e7 | − | 1.72807e6i | −1.89878 | − | 0.202655i | ||||
\(593\) | 1.03991e7 | 1.21440 | 0.607198 | − | 0.794551i | \(-0.292293\pi\) | ||||
0.607198 | + | 0.794551i | \(0.292293\pi\) | |||||||
\(594\) | 190305. | − | 269045.i | 0.0221301 | − | 0.0312867i | ||||
\(595\) | −2.90240e6 | + | 2.90240e6i | −0.336097 | + | 0.336097i | ||||
\(596\) | 612029. | − | 1.28050e6i | 0.0705759 | − | 0.147660i | ||||
\(597\) | −8.00579e6 | − | 8.00579e6i | −0.919324 | − | 0.919324i | ||||
\(598\) | −214639. | − | 1.25214e6i | −0.0245446 | − | 0.143186i | ||||
\(599\) | 1.71039e7i | 1.94772i | 0.227143 | + | 0.973861i | \(0.427061\pi\) | ||||
−0.227143 | + | 0.973861i | \(0.572939\pi\) | |||||||
\(600\) | −2.21607e6 | + | 1.23756e6i | −0.251308 | + | 0.140342i | ||||
\(601\) | − | 1.36618e7i | − | 1.54284i | −0.636325 | − | 0.771421i | \(-0.719546\pi\) | ||
0.636325 | − | 0.771421i | \(-0.280454\pi\) | |||||||
\(602\) | 1.58753e7 | − | 2.72131e6i | 1.78538 | − | 0.306046i | ||||
\(603\) | −2.13995e6 | − | 2.13995e6i | −0.239668 | − | 0.239668i | ||||
\(604\) | −818371. | + | 289061.i | −0.0912763 | + | 0.0322401i | ||||
\(605\) | −2.44977e6 | + | 2.44977e6i | −0.272106 | + | 0.272106i | ||||
\(606\) | 2.04947e7 | + | 1.44965e7i | 2.26704 | + | 1.60355i | ||||
\(607\) | 1.13901e7 | 1.25475 | 0.627375 | − | 0.778717i | \(-0.284129\pi\) | ||||
0.627375 | + | 0.778717i | \(0.284129\pi\) | |||||||
\(608\) | −3.01607e6 | + | 3.42527e6i | −0.330889 | + | 0.375782i | ||||
\(609\) | −3.66131e7 | −4.00031 | ||||||||
\(610\) | 4.86181e6 | + | 3.43891e6i | 0.529021 | + | 0.374194i | ||||
\(611\) | 2.24930e6 | − | 2.24930e6i | 0.243750 | − | 0.243750i | ||||
\(612\) | 6.21125e6 | − | 2.19390e6i | 0.670348 | − | 0.236777i | ||||
\(613\) | 4.60658e6 | + | 4.60658e6i | 0.495139 | + | 0.495139i | 0.909921 | − | 0.414782i | \(-0.136142\pi\) |
−0.414782 | + | 0.909921i | \(0.636142\pi\) | |||||||
\(614\) | 1.65676e7 | − | 2.83999e6i | 1.77353 | − | 0.304015i | ||||
\(615\) | 8.63711e6i | 0.920833i | ||||||||
\(616\) | −2.74698e6 | − | 4.91899e6i | −0.291679 | − | 0.522305i | ||||
\(617\) | − | 4.57951e6i | − | 0.484291i | −0.970240 | − | 0.242145i | \(-0.922149\pi\) | ||
0.970240 | − | 0.242145i | \(-0.0778511\pi\) | |||||||
\(618\) | 2.47032e6 | + | 1.44111e7i | 0.260185 | + | 1.51784i | ||||
\(619\) | −1.45301e6 | − | 1.45301e6i | −0.152419 | − | 0.152419i | 0.626778 | − | 0.779198i | \(-0.284373\pi\) |
−0.779198 | + | 0.626778i | \(0.784373\pi\) | |||||||
\(620\) | 2.04849e6 | − | 4.28588e6i | 0.214020 | − | 0.447776i | ||||
\(621\) | 199280. | − | 199280.i | 0.0207365 | − | 0.0207365i | ||||
\(622\) | −9.54339e6 | + | 1.34921e7i | −0.989069 | + | 1.39831i | ||||
\(623\) | 1.67078e7 | 1.72464 | ||||||||
\(624\) | 4.46839e6 | + | 5.53616e6i | 0.459398 | + | 0.569177i | ||||
\(625\) | −390625. | −0.0400000 | ||||||||
\(626\) | −1.07556e6 | + | 1.52059e6i | −0.109698 | + | 0.155087i | ||||
\(627\) | 1.87361e6 | − | 1.87361e6i | 0.190331 | − | 0.190331i | ||||
\(628\) | −1.16477e7 | − | 5.56714e6i | −1.17853 | − | 0.563291i | ||||
\(629\) | 8.89141e6 | + | 8.89141e6i | 0.896075 | + | 0.896075i | ||||
\(630\) | −1.29145e6 | − | 7.53395e6i | −0.129637 | − | 0.756260i | ||||
\(631\) | − | 3.58456e6i | − | 0.358396i | −0.983813 | − | 0.179198i | \(-0.942650\pi\) | ||
0.983813 | − | 0.179198i | \(-0.0573502\pi\) | |||||||
\(632\) | 2.96393e6 | − | 1.04610e7i | 0.295172 | − | 1.04179i | ||||
\(633\) | − | 1.76526e7i | − | 1.75106i | ||||||
\(634\) | 1.30567e6 | − | 223816.i | 0.129006 | − | 0.0221140i | ||||
\(635\) | −2.36781e6 | − | 2.36781e6i | −0.233030 | − | 0.233030i | ||||
\(636\) | −7.64919e6 | − | 2.16559e7i | −0.749847 | − | 2.12292i | ||||
\(637\) | 5.75964e6 | − | 5.75964e6i | 0.562402 | − | 0.562402i | ||||
\(638\) | 5.44154e6 | + | 3.84898e6i | 0.529261 | + | 0.374364i | ||||
\(639\) | 6.04983e6 | 0.586126 | ||||||||
\(640\) | 1.72929e6 | − | 4.29935e6i | 0.166886 | − | 0.414909i | ||||
\(641\) | 1.01972e7 | 0.980245 | 0.490123 | − | 0.871654i | \(-0.336952\pi\) | ||||
0.490123 | + | 0.871654i | \(0.336952\pi\) | |||||||
\(642\) | −3.93451e6 | − | 2.78301e6i | −0.376750 | − | 0.266488i | ||||
\(643\) | −1.32210e7 | + | 1.32210e7i | −1.26107 | + | 1.26107i | −0.310490 | + | 0.950577i | \(0.600493\pi\) |
−0.950577 | + | 0.310490i | \(0.899507\pi\) | |||||||
\(644\) | −1.60469e6 | − | 4.54309e6i | −0.152467 | − | 0.431655i | ||||
\(645\) | −5.43875e6 | − | 5.43875e6i | −0.514754 | − | 0.514754i | ||||
\(646\) | 3.47372e6 | − | 595457.i | 0.327501 | − | 0.0561396i | ||||
\(647\) | 6.81276e6i | 0.639827i | 0.947447 | + | 0.319914i | \(0.103654\pi\) | ||||
−0.947447 | + | 0.319914i | \(0.896346\pi\) | |||||||
\(648\) | 2.69130e6 | − | 9.49881e6i | 0.251782 | − | 0.888652i | ||||
\(649\) | 3.22917e6i | 0.300939i | ||||||||
\(650\) | 184987. | + | 1.07916e6i | 0.0171735 | + | 0.100185i | ||||
\(651\) | 1.95579e7 | + | 1.95579e7i | 1.80871 | + | 1.80871i | ||||
\(652\) | 1.51313e7 | + | 7.23218e6i | 1.39398 | + | 0.666270i | ||||
\(653\) | −8.83712e6 | + | 8.83712e6i | −0.811013 | + | 0.811013i | −0.984786 | − | 0.173773i | \(-0.944404\pi\) |
0.173773 | + | 0.984786i | \(0.444404\pi\) | |||||||
\(654\) | −325661. | + | 460407.i | −0.0297729 | + | 0.0420918i | ||||
\(655\) | −3.87067e6 | −0.352519 | ||||||||
\(656\) | −9.90408e6 | − | 1.22708e7i | −0.898575 | − | 1.11330i | ||||
\(657\) | −1.01990e7 | −0.921811 | ||||||||
\(658\) | 6.96682e6 | − | 9.84943e6i | 0.627292 | − | 0.886842i | ||||
\(659\) | −147564. | + | 147564.i | −0.0132363 | + | 0.0132363i | −0.713694 | − | 0.700458i | \(-0.752979\pi\) |
0.700458 | + | 0.713694i | \(0.252979\pi\) | |||||||
\(660\) | −1.16021e6 | + | 2.42742e6i | −0.103676 | + | 0.216913i | ||||
\(661\) | −7.72470e6 | − | 7.72470e6i | −0.687667 | − | 0.687667i | 0.274049 | − | 0.961716i | \(-0.411637\pi\) |
−0.961716 | + | 0.274049i | \(0.911637\pi\) | |||||||
\(662\) | 2.61422e6 | + | 1.52506e7i | 0.231845 | + | 1.35251i | ||||
\(663\) | − | 5.49401e6i | − | 0.485407i | ||||||
\(664\) | 6.23309e6 | + | 1.11615e7i | 0.548635 | + | 0.982433i | ||||
\(665\) | − | 4.08964e6i | − | 0.358617i | ||||||
\(666\) | −2.30800e7 | + | 3.95633e6i | −2.01628 | + | 0.345627i | ||||
\(667\) | 4.03052e6 | + | 4.03052e6i | 0.350789 | + | 0.350789i | ||||
\(668\) | −335447. | + | 118485.i | −0.0290859 | + | 0.0102736i | ||||
\(669\) | −2.14483e6 | + | 2.14483e6i | −0.185280 | + | 0.185280i | ||||
\(670\) | 1.34224e6 | + | 949410.i | 0.115516 | + | 0.0817085i | ||||
\(671\) | 6.31226e6 | 0.541226 | ||||||||
\(672\) | 2.02508e7 | + | 1.78315e7i | 1.72989 | + | 1.52323i | ||||
\(673\) | 6.85944e6 | 0.583782 | 0.291891 | − | 0.956452i | \(-0.405715\pi\) | ||||
0.291891 | + | 0.956452i | \(0.405715\pi\) | |||||||
\(674\) | −1.07356e7 | − | 7.59366e6i | −0.910286 | − | 0.643875i | ||||
\(675\) | −171750. | + | 171750.i | −0.0145090 | + | 0.0145090i | ||||
\(676\) | −8.30933e6 | + | 2.93498e6i | −0.699358 | + | 0.247023i | ||||
\(677\) | −5.18225e6 | − | 5.18225e6i | −0.434557 | − | 0.434557i | 0.455618 | − | 0.890175i | \(-0.349418\pi\) |
−0.890175 | + | 0.455618i | \(0.849418\pi\) | |||||||
\(678\) | −1.00999e7 | + | 1.73131e6i | −0.843810 | + | 0.144644i | ||||
\(679\) | 5.29906e6i | 0.441087i | ||||||||
\(680\) | −3.12441e6 | + | 1.74481e6i | −0.259117 | + | 0.144703i | ||||
\(681\) | − | 1.76225e7i | − | 1.45613i | ||||||
\(682\) | −850709. | − | 4.96278e6i | −0.0700358 | − | 0.408568i | ||||
\(683\) | −7.44176e6 | − | 7.44176e6i | −0.610413 | − | 0.610413i | 0.332641 | − | 0.943054i | \(-0.392060\pi\) |
−0.943054 | + | 0.332641i | \(0.892060\pi\) | |||||||
\(684\) | −2.83033e6 | + | 5.92167e6i | −0.231311 | + | 0.483954i | ||||
\(685\) | 1.49490e6 | − | 1.49490e6i | 0.121727 | − | 0.121727i | ||||
\(686\) | 6.44010e6 | − | 9.10477e6i | 0.522495 | − | 0.738684i | ||||
\(687\) | −6.74605e6 | −0.545328 | ||||||||
\(688\) | 1.39634e7 | + | 1.49030e6i | 1.12466 | + | 0.120033i | ||||
\(689\) | −9.90724e6 | −0.795069 | ||||||||
\(690\) | −1.32867e6 | + | 1.87842e6i | −0.106242 | + | 0.150200i | ||||
\(691\) | −1.57551e7 | + | 1.57551e7i | −1.25524 | + | 1.25524i | −0.301900 | + | 0.953340i | \(0.597621\pi\) |
−0.953340 | + | 0.301900i | \(0.902379\pi\) | |||||||
\(692\) | −1.69510e7 | − | 8.10191e6i | −1.34564 | − | 0.643165i | ||||
\(693\) | −5.72917e6 | − | 5.72917e6i | −0.453167 | − | 0.453167i | ||||
\(694\) | −664824. | − | 3.87838e6i | −0.0523972 | − | 0.305669i | ||||
\(695\) | − | 1.76452e6i | − | 0.138569i | ||||||
\(696\) | −3.07121e7 | − | 8.70167e6i | −2.40318 | − | 0.680894i | ||||
\(697\) | 1.21773e7i | 0.949447i | ||||||||
\(698\) | −1.77177e7 | + | 3.03714e6i | −1.37648 | + | 0.235953i | ||||
\(699\) | 88529.5 | + | 88529.5i | 0.00685323 | + | 0.00685323i | ||||
\(700\) | 1.38300e6 | + | 3.91548e6i | 0.106679 | + | 0.302023i | ||||
\(701\) | 719226. | − | 719226.i | 0.0552803 | − | 0.0552803i | −0.678926 | − | 0.734206i | \(-0.737554\pi\) |
0.734206 | + | 0.678926i | \(0.237554\pi\) | |||||||
\(702\) | 555820. | + | 393150.i | 0.0425688 | + | 0.0301103i | ||||
\(703\) | −1.25285e7 | −0.956117 | ||||||||
\(704\) | −1.13517e6 | − | 4.77905e6i | −0.0863238 | − | 0.363421i | ||||
\(705\) | −5.76111e6 | −0.436550 | ||||||||
\(706\) | 3.39682e6 | + | 2.40268e6i | 0.256484 | + | 0.181419i | ||||
\(707\) | 2.90405e7 | − | 2.90405e7i | 2.18502 | − | 2.18502i | ||||
\(708\) | −5.15066e6 | − | 1.45822e7i | −0.386171 | − | 1.09330i | ||||
\(709\) | 8.53872e6 | + | 8.53872e6i | 0.637936 | + | 0.637936i | 0.950046 | − | 0.312110i | \(-0.101036\pi\) |
−0.312110 | + | 0.950046i | \(0.601036\pi\) | |||||||
\(710\) | −3.23935e6 | + | 555283.i | −0.241164 | + | 0.0413398i | ||||
\(711\) | − | 1.56361e7i | − | 1.15999i | ||||||
\(712\) | 1.40150e7 | + | 3.97086e6i | 1.03608 | + | 0.293552i | ||||
\(713\) | − | 4.30602e6i | − | 0.317214i | ||||||
\(714\) | −3.52044e6 | − | 2.05372e7i | −0.258435 | − | 1.50763i | ||||
\(715\) | 820643. | + | 820643.i | 0.0600329 | + | 0.0600329i | ||||
\(716\) | 1.96847e7 | + | 9.40855e6i | 1.43498 | + | 0.685867i | ||||
\(717\) | −1.51772e7 | + | 1.51772e7i | −1.10254 | + | 1.10254i | ||||
\(718\) | 2.53976e6 | − | 3.59062e6i | 0.183858 | − | 0.259931i | ||||
\(719\) | 8.24173e6 | 0.594560 | 0.297280 | − | 0.954790i | \(-0.403920\pi\) | ||||
0.297280 | + | 0.954790i | \(0.403920\pi\) | |||||||
\(720\) | 707252. | − | 6.62662e6i | 0.0508444 | − | 0.476388i | ||||
\(721\) | 2.39206e7 | 1.71370 | ||||||||
\(722\) | 6.06081e6 | − | 8.56855e6i | 0.432701 | − | 0.611736i | ||||
\(723\) | 6.03709e6 | − | 6.03709e6i | 0.429519 | − | 0.429519i | ||||
\(724\) | 1.03572e7 | − | 2.16694e7i | 0.734335 | − | 1.53639i | ||||
\(725\) | −3.47371e6 | − | 3.47371e6i | −0.245442 | − | 0.245442i | ||||
\(726\) | −2.97144e6 | − | 1.73345e7i | −0.209231 | − | 1.22059i | ||||
\(727\) | − | 1.76538e6i | − | 0.123880i | −0.998080 | − | 0.0619401i | \(-0.980271\pi\) | ||
0.998080 | − | 0.0619401i | \(-0.0197288\pi\) | |||||||
\(728\) | 1.01621e7 | − | 5.67499e6i | 0.710651 | − | 0.396859i | ||||
\(729\) | − | 1.63165e7i | − | 1.13713i | ||||||
\(730\) | 5.46097e6 | − | 936109.i | 0.379283 | − | 0.0650158i | ||||
\(731\) | −7.66802e6 | − | 7.66802e6i | −0.530750 | − | 0.530750i | ||||
\(732\) | −2.85048e7 | + | 1.00683e7i | −1.96626 | + | 0.694510i | ||||
\(733\) | 1.08345e6 | − | 1.08345e6i | 0.0744816 | − | 0.0744816i | −0.668885 | − | 0.743366i | \(-0.733228\pi\) |
0.743366 | + | 0.668885i | \(0.233228\pi\) | |||||||
\(734\) | −7.16002e6 | − | 5.06451e6i | −0.490539 | − | 0.346975i | ||||
\(735\) | −1.47521e7 | −1.00725 | ||||||||
\(736\) | −266320. | − | 4.19225e6i | −0.0181221 | − | 0.285268i | ||||
\(737\) | 1.74268e6 | 0.118181 | ||||||||
\(738\) | −1.85140e7 | − | 1.30956e7i | −1.25129 | − | 0.885081i | ||||
\(739\) | 6.95031e6 | − | 6.95031e6i | 0.468159 | − | 0.468159i | −0.433159 | − | 0.901318i | \(-0.642601\pi\) |
0.901318 | + | 0.433159i | \(0.142601\pi\) | |||||||
\(740\) | 1.19950e7 | − | 4.23679e6i | 0.805229 | − | 0.284419i | ||||
\(741\) | 3.87069e6 | + | 3.87069e6i | 0.258966 | + | 0.258966i | ||||
\(742\) | −3.70343e7 | + | 6.34835e6i | −2.46942 | + | 0.423303i | ||||
\(743\) | 279867.i | 0.0185986i | 0.999957 | + | 0.00929929i | \(0.00296010\pi\) | ||||
−0.999957 | + | 0.00929929i | \(0.997040\pi\) | |||||||
\(744\) | 1.17575e7 | + | 2.10539e7i | 0.778719 | + | 1.39444i | ||||
\(745\) | 1.10878e6i | 0.0731908i | ||||||||
\(746\) | 4.28379e6 | + | 2.49903e7i | 0.281826 | + | 1.64409i | ||||
\(747\) | 1.29999e7 | + | 1.29999e7i | 0.852388 | + | 0.852388i | ||||
\(748\) | −1.63577e6 | + | 3.42239e6i | −0.106898 | + | 0.223653i | ||||
\(749\) | −5.57512e6 | + | 5.57512e6i | −0.363120 | + | 0.363120i | ||||
\(750\) | 1.14512e6 | − | 1.61892e6i | 0.0743356 | − | 0.105093i | ||||
\(751\) | −1.44307e7 | −0.933659 | −0.466829 | − | 0.884347i | \(-0.654604\pi\) | ||||
−0.466829 | + | 0.884347i | \(0.654604\pi\) | |||||||
\(752\) | 8.18484e6 | − | 6.60620e6i | 0.527795 | − | 0.425998i | ||||
\(753\) | −1.65205e7 | −1.06178 | ||||||||
\(754\) | −7.95160e6 | + | 1.12417e7i | −0.509362 | + | 0.720116i | ||||
\(755\) | 479463. | − | 479463.i | 0.0306117 | − | 0.0306117i | ||||
\(756\) | 2.32964e6 | + | 1.11348e6i | 0.148246 | + | 0.0708561i | ||||
\(757\) | 7.09593e6 | + | 7.09593e6i | 0.450059 | + | 0.450059i | 0.895374 | − | 0.445315i | \(-0.146908\pi\) |
−0.445315 | + | 0.895374i | \(0.646908\pi\) | |||||||
\(758\) | 1.45627e6 | + | 8.49543e6i | 0.0920595 | + | 0.537047i | ||||
\(759\) | 2.43882e6i | 0.153665i | ||||||||
\(760\) | 971967. | − | 3.43051e6i | 0.0610404 | − | 0.215439i | ||||
\(761\) | 8.79439e6i | 0.550483i | 0.961375 | + | 0.275242i | \(0.0887578\pi\) | ||||
−0.961375 | + | 0.275242i | \(0.911242\pi\) | |||||||
\(762\) | 1.67545e7 | − | 2.87202e6i | 1.04531 | − | 0.179184i | ||||
\(763\) | 652387. | + | 652387.i | 0.0405690 | + | 0.0405690i | ||||
\(764\) | −1.05301e7 | − | 2.98123e7i | −0.652680 | − | 1.84783i | ||||
\(765\) | −3.63901e6 | + | 3.63901e6i | −0.224818 | + | 0.224818i | ||||
\(766\) | −1.93014e6 | − | 1.36525e6i | −0.118855 | − | 0.0840697i | ||||
\(767\) | −6.67114e6 | −0.409460 | ||||||||
\(768\) | 1.27490e7 | + | 1.97705e7i | 0.779960 | + | 1.20952i | ||||
\(769\) | 2.36196e7 | 1.44031 | 0.720157 | − | 0.693812i | \(-0.244070\pi\) | ||||
0.720157 | + | 0.693812i | \(0.244070\pi\) | |||||||
\(770\) | 3.59350e6 | + | 2.54180e6i | 0.218419 | + | 0.154495i | ||||
\(771\) | 1.86677e7 | − | 1.86677e7i | 1.13098 | − | 1.13098i | ||||
\(772\) | 2.92385e6 | + | 8.27783e6i | 0.176568 | + | 0.499889i | ||||
\(773\) | −3.99930e6 | − | 3.99930e6i | −0.240733 | − | 0.240733i | 0.576420 | − | 0.817153i | \(-0.304449\pi\) |
−0.817153 | + | 0.576420i | \(0.804449\pi\) | |||||||
\(774\) | 1.99044e7 | − | 3.41197e6i | 1.19425 | − | 0.204716i | ||||
\(775\) | 3.71115e6i | 0.221950i | ||||||||
\(776\) | −1.25940e6 | + | 4.44500e6i | −0.0750777 | + | 0.264983i | ||||
\(777\) | 7.40707e7i | 4.40143i | ||||||||
\(778\) | −416298. | − | 2.42856e6i | −0.0246579 | − | 0.143846i | ||||
\(779\) | −8.57929e6 | − | 8.57929e6i | −0.506533 | − | 0.506533i | ||||
\(780\) | −5.01480e6 | − | 2.39689e6i | −0.295133 | − | 0.141062i | ||||
\(781\) | −2.46335e6 | + | 2.46335e6i | −0.144510 | + | 0.144510i | ||||
\(782\) | −1.87327e6 | + | 2.64836e6i | −0.109543 | + | 0.154868i | ||||
\(783\) | −3.05465e6 | −0.178056 | ||||||||
\(784\) | 2.09584e7 | − | 1.69161e7i | 1.21778 | − | 0.982900i | ||||
\(785\) | 1.00857e7 | 0.584161 | ||||||||
\(786\) | 1.13469e7 | − | 1.60418e7i | 0.655118 | − | 0.926181i | ||||
\(787\) | −1.07443e7 | + | 1.07443e7i | −0.618358 | + | 0.618358i | −0.945110 | − | 0.326752i | \(-0.894046\pi\) |
0.326752 | + | 0.945110i | \(0.394046\pi\) | |||||||
\(788\) | −8.83069e6 | + | 1.84757e7i | −0.506616 | + | 1.05995i | ||||
\(789\) | 1.00730e7 | + | 1.00730e7i | 0.576061 | + | 0.576061i | ||||
\(790\) | 1.43516e6 | + | 8.37227e6i | 0.0818147 | + | 0.477282i | ||||
\(791\) | 1.67646e7i | 0.952693i | ||||||||
\(792\) | −3.44416e6 | − | 6.16741e6i | −0.195106 | − | 0.349373i | ||||
\(793\) | 1.30405e7i | 0.736395i | ||||||||
\(794\) | 1.09337e7 | − | 1.87423e6i | 0.615481 | − | 0.105504i | ||||
\(795\) | 1.26877e7 | + | 1.26877e7i | 0.711974 | + | 0.711974i | ||||
\(796\) | −1.52271e7 | + | 5.37842e6i | −0.851792 | + | 0.300865i | ||||
\(797\) | 7.46849e6 | − | 7.46849e6i | 0.416473 | − | 0.416473i | −0.467513 | − | 0.883986i | \(-0.654850\pi\) |
0.883986 | + | 0.467513i | \(0.154850\pi\) | |||||||
\(798\) | 1.69493e7 | + | 1.19888e7i | 0.942203 | + | 0.666451i | ||||
\(799\) | −8.12252e6 | −0.450115 | ||||||||
\(800\) | 229529. | + | 3.61310e6i | 0.0126798 | + | 0.199598i | ||||
\(801\) | 2.09482e7 | 1.15362 | ||||||||
\(802\) | −1.90587e7 | − | 1.34808e7i | −1.04630 | − | 0.740084i | ||||
\(803\) | 4.15278e6 | − | 4.15278e6i | 0.227274 | − | 0.227274i | ||||
\(804\) | −7.86956e6 | + | 2.77964e6i | −0.429349 | + | 0.151652i | ||||
\(805\) | 2.66168e6 | + | 2.66168e6i | 0.144766 | + | 0.144766i | ||||
\(806\) | 1.02526e7 | − | 1.75748e6i | 0.555900 | − | 0.0952912i | ||||
\(807\) | 3.86502e7i | 2.08914i | ||||||||
\(808\) | 3.12619e7 | − | 1.74581e7i | 1.68456 | − | 0.940736i | ||||
\(809\) | − | 3.16263e6i | − | 0.169894i | −0.996385 | − | 0.0849469i | \(-0.972928\pi\) | ||
0.996385 | − | 0.0849469i | \(-0.0270721\pi\) | |||||||
\(810\) | 1.30315e6 | + | 7.60218e6i | 0.0697882 | + | 0.407123i | ||||
\(811\) | 9.00235e6 | + | 9.00235e6i | 0.480622 | + | 0.480622i | 0.905330 | − | 0.424708i | \(-0.139623\pi\) |
−0.424708 | + | 0.905330i | \(0.639623\pi\) | |||||||
\(812\) | −2.25205e7 | + | 4.71178e7i | −1.19864 | + | 2.50781i | ||||
\(813\) | −9.55377e6 | + | 9.55377e6i | −0.506930 | + | 0.506930i | ||||
\(814\) | 7.78674e6 | − | 1.10086e7i | 0.411903 | − | 0.582332i | ||||
\(815\) | −1.31022e7 | −0.690956 | ||||||||
\(816\) | 1.92794e6 | − | 1.80639e7i | 0.101360 | − | 0.949698i | ||||
\(817\) | 1.08047e7 | 0.566313 | ||||||||
\(818\) | 1.25041e7 | − | 1.76778e7i | 0.653384 | − | 0.923730i | ||||
\(819\) | 1.18359e7 | − | 1.18359e7i | 0.616582 | − | 0.616582i | ||||
\(820\) | 1.11152e7 | + | 5.31264e6i | 0.577275 | + | 0.275915i | ||||
\(821\) | 8.43706e6 | + | 8.43706e6i | 0.436851 | + | 0.436851i | 0.890951 | − | 0.454100i | \(-0.150039\pi\) |
−0.454100 | + | 0.890951i | \(0.650039\pi\) | |||||||
\(822\) | 1.81323e6 | + | 1.05778e7i | 0.0935993 | + | 0.546030i | ||||
\(823\) | 2.43280e7i | 1.25201i | 0.779820 | + | 0.626004i | \(0.215311\pi\) | ||||
−0.779820 | + | 0.626004i | \(0.784689\pi\) | |||||||
\(824\) | 2.00653e7 | + | 5.68511e6i | 1.02950 | + | 0.291689i | ||||
\(825\) | − | 2.10191e6i | − | 0.107517i | ||||||
\(826\) | −2.49374e7 | + | 4.27472e6i | −1.27175 | + | 0.218001i | ||||
\(827\) | −1.04991e7 | − | 1.04991e7i | −0.533811 | − | 0.533811i | 0.387893 | − | 0.921704i | \(-0.373203\pi\) |
−0.921704 | + | 0.387893i | \(0.873203\pi\) | |||||||
\(828\) | −2.01195e6 | − | 5.69611e6i | −0.101986 | − | 0.288737i | ||||
\(829\) | −5.20448e6 | + | 5.20448e6i | −0.263021 | + | 0.263021i | −0.826280 | − | 0.563259i | \(-0.809547\pi\) |
0.563259 | + | 0.826280i | \(0.309547\pi\) | |||||||
\(830\) | −8.15390e6 | − | 5.76752e6i | −0.410837 | − | 0.290599i | ||||
\(831\) | −2.81353e7 | −1.41335 | ||||||||
\(832\) | 9.87303e6 | − | 2.34515e6i | 0.494473 | − | 0.117453i | ||||
\(833\) | −2.07988e7 | −1.03855 | ||||||||
\(834\) | 7.31296e6 | + | 5.17270e6i | 0.364064 | + | 0.257515i | ||||
\(835\) | 196530. | − | 196530.i | 0.00975467 | − | 0.00975467i | ||||
\(836\) | −1.25872e6 | − | 3.56362e6i | −0.0622894 | − | 0.176350i | ||||
\(837\) | 1.63172e6 | + | 1.63172e6i | 0.0805068 | + | 0.0805068i | ||||
\(838\) | 2.31260e7 | − | 3.96421e6i | 1.13760 | − | 0.195005i | ||||
\(839\) | − | 2.67714e7i | − | 1.31301i | −0.754323 | − | 0.656503i | \(-0.772035\pi\) | ||
0.754323 | − | 0.656503i | \(-0.227965\pi\) | |||||||
\(840\) | −2.02817e7 | − | 5.74644e6i | −0.991761 | − | 0.280996i | ||||
\(841\) | − | 4.12702e7i | − | 2.01209i | ||||||
\(842\) | 896955. | + | 5.23256e6i | 0.0436004 | + | 0.254351i | ||||
\(843\) | 1.41480e7 | + | 1.41480e7i | 0.685689 | + | 0.685689i | ||||
\(844\) | −2.27174e7 | − | 1.08580e7i | −1.09775 | − | 0.524681i | ||||
\(845\) | 4.86823e6 | − | 4.86823e6i | 0.234547 | − | 0.234547i | ||||
\(846\) | 8.73498e6 | − | 1.23492e7i | 0.419600 | − | 0.593215i | ||||
\(847\) | −2.87730e7 | −1.37809 | ||||||||
\(848\) | −3.25742e7 | − | 3.47661e6i | −1.55555 | − | 0.166022i | ||||
\(849\) | 6.82500e6 | 0.324963 | ||||||||
\(850\) | 1.61449e6 | − | 2.28250e6i | 0.0766455 | − | 0.108359i | ||||
\(851\) | 8.15400e6 | − | 8.15400e6i | 0.385964 | − | 0.385964i | ||||
\(852\) | 7.19482e6 | − | 1.50531e7i | 0.339563 | − | 0.710440i | ||||
\(853\) | −6.00949e6 | − | 6.00949e6i | −0.282791 | − | 0.282791i | 0.551430 | − | 0.834221i | \(-0.314082\pi\) |
−0.834221 | + | 0.551430i | \(0.814082\pi\) | |||||||
\(854\) | 8.35606e6 | + | 4.87467e7i | 0.392064 | + | 2.28718i | ||||
\(855\) | − | 5.12758e6i | − | 0.239882i | ||||||
\(856\) | −6.00159e6 | + | 3.35156e6i | −0.279951 | + | 0.156337i | ||||
\(857\) | 1.56237e6i | 0.0726661i | 0.999340 | + | 0.0363330i | \(0.0115677\pi\) | ||||
−0.999340 | + | 0.0363330i | \(0.988432\pi\) | |||||||
\(858\) | −5.80682e6 | + | 995393.i | −0.269290 | + | 0.0461611i | ||||
\(859\) | −2.74479e7 | − | 2.74479e7i | −1.26919 | − | 1.26919i | −0.946508 | − | 0.322681i | \(-0.895416\pi\) |
−0.322681 | − | 0.946508i | \(-0.604584\pi\) | |||||||
\(860\) | −1.03445e7 | + | 3.65384e6i | −0.476941 | + | 0.168463i | ||||
\(861\) | −5.07222e7 | + | 5.07222e7i | −2.33179 | + | 2.33179i | ||||
\(862\) | −2.54610e7 | − | 1.80094e7i | −1.16710 | − | 0.825526i | ||||
\(863\) | −2.06982e7 | −0.946030 | −0.473015 | − | 0.881054i | \(-0.656834\pi\) | ||||
−0.473015 | + | 0.881054i | \(0.656834\pi\) | |||||||
\(864\) | 1.68953e6 | + | 1.48769e6i | 0.0769984 | + | 0.0677998i | ||||
\(865\) | 1.46779e7 | 0.666995 | ||||||||
\(866\) | −6.32060e6 | − | 4.47076e6i | −0.286394 | − | 0.202576i | ||||
\(867\) | 1.26046e7 | − | 1.26046e7i | 0.569483 | − | 0.569483i | ||||
\(868\) | 3.71992e7 | − | 1.31393e7i | 1.67585 | − | 0.591933i | ||||
\(869\) | 6.36666e6 | + | 6.36666e6i | 0.285998 | + | 0.285998i | ||||
\(870\) | 2.45798e7 | − | 4.21342e6i | 1.10098 | − | 0.188728i | ||||
\(871\) | 3.60020e6i | 0.160798i | ||||||||
\(872\) | 392191. | + | 702291.i | 0.0174665 | + | 0.0312771i | ||||
\(873\) | 6.64394e6i | 0.295046i | ||||||||
\(874\) | −546072. | − | 3.18562e6i | −0.0241809 | − | 0.141064i | ||||
\(875\) | −2.29398e6 | − | 2.29398e6i | −0.101291 | − | 0.101291i | ||||
\(876\) | −1.21292e7 | + | 2.53769e7i | −0.534038 | + | 1.11732i | ||||
\(877\) | 3.10711e7 | − | 3.10711e7i | 1.36414 | − | 1.36414i | 0.495565 | − | 0.868571i | \(-0.334961\pi\) |
0.868571 | − | 0.495565i | \(-0.165039\pi\) | |||||||
\(878\) | 1.85596e7 | − | 2.62388e7i | 0.812516 | − | 1.14870i | ||||
\(879\) | 3.06849e7 | 1.33953 | ||||||||
\(880\) | 2.41023e6 | + | 2.98619e6i | 0.104918 | + | 0.129990i | ||||
\(881\) | −1.66776e7 | −0.723925 | −0.361962 | − | 0.932193i | \(-0.617893\pi\) | ||||
−0.361962 | + | 0.932193i | \(0.617893\pi\) | |||||||
\(882\) | 2.23671e7 | − | 3.16217e7i | 0.968139 | − | 1.36872i | ||||
\(883\) | 1.68084e7 | − | 1.68084e7i | 0.725477 | − | 0.725477i | −0.244238 | − | 0.969715i | \(-0.578538\pi\) |
0.969715 | + | 0.244238i | \(0.0785378\pi\) | |||||||
\(884\) | −7.07030e6 | − | 3.37934e6i | −0.304304 | − | 0.145446i | ||||
\(885\) | 8.54336e6 | + | 8.54336e6i | 0.366666 | + | 0.366666i | ||||
\(886\) | −414234. | − | 2.41652e6i | −0.0177281 | − | 0.103420i | ||||
\(887\) | 2.64495e7i | 1.12878i | 0.825509 | + | 0.564390i | \(0.190888\pi\) | ||||
−0.825509 | + | 0.564390i | \(0.809112\pi\) | |||||||
\(888\) | −1.76040e7 | + | 6.21326e7i | −0.749170 | + | 2.64415i | ||||
\(889\) | − | 2.78103e7i | − | 1.18019i | ||||||
\(890\) | −1.12166e7 | + | 1.92272e6i | −0.474663 | + | 0.0813657i | ||||
\(891\) | 5.78105e6 | + | 5.78105e6i | 0.243957 | + | 0.243957i | ||||
\(892\) | 1.44093e6 | + | 4.07948e6i | 0.0606361 | + | 0.171669i | ||||
\(893\) | 5.72254e6 | − | 5.72254e6i | 0.240138 | − | 0.240138i | ||||
\(894\) | −4.59529e6 | − | 3.25040e6i | −0.192296 | − | 0.136017i | ||||
\(895\) | −1.70450e7 | −0.711279 | ||||||||
\(896\) | 3.54037e7 | − | 1.50929e7i | 1.47326 | − | 0.628061i | ||||
\(897\) | −5.03836e6 | −0.209078 | ||||||||
\(898\) | −8.18998e6 | − | 5.79304e6i | −0.338916 | − | 0.239726i | ||||
\(899\) | −3.30022e7 | + | 3.30022e7i | −1.36189 | + | 1.36189i | ||||
\(900\) | 1.73401e6 | + | 4.90921e6i | 0.0713582 | + | 0.202025i | ||||
\(901\) | 1.78882e7 | + | 1.78882e7i | 0.734098 | + | 0.734098i | ||||
\(902\) | 1.28707e7 | − | 2.20627e6i | 0.526727 | − | 0.0902904i | ||||
\(903\) | − | 6.38791e7i | − | 2.60699i | ||||||
\(904\) | −3.98438e6 | + | 1.40626e7i | −0.162158 | + | 0.572329i | ||||
\(905\) | 1.87636e7i | 0.761542i | ||||||||
\(906\) | 581562. | + | 3.39266e6i | 0.0235383 | + | 0.137315i | ||||
\(907\) | −2.24504e7 | − | 2.24504e7i | −0.906161 | − | 0.906161i | 0.0897985 | − | 0.995960i | \(-0.471378\pi\) |
−0.995960 | + | 0.0897985i | \(0.971378\pi\) | |||||||
\(908\) | −2.26786e7 | − | 1.08395e7i | −0.912857 | − | 0.436311i | ||||
\(909\) | 3.64109e7 | − | 3.64109e7i | 1.46158 | − | 1.46158i | ||||
\(910\) | −5.25110e6 | + | 7.42381e6i | −0.210207 | + | 0.297183i | ||||
\(911\) | −1.55193e7 | −0.619551 | −0.309776 | − | 0.950810i | \(-0.600254\pi\) | ||||
−0.309776 | + | 0.950810i | \(0.600254\pi\) | |||||||
\(912\) | 1.13682e7 | + | 1.40848e7i | 0.452591 | + | 0.560743i | ||||
\(913\) | −1.05865e7 | −0.420315 | ||||||||
\(914\) | 430271. | − | 608301.i | 0.0170364 | − | 0.0240854i | ||||
\(915\) | 1.67002e7 | − | 1.67002e7i | 0.659432 | − | 0.659432i | ||||
\(916\) | −4.14946e6 | + | 8.68157e6i | −0.163400 | + | 0.341869i | ||||
\(917\) | −2.27308e7 | − | 2.27308e7i | −0.892673 | − | 0.892673i | ||||
\(918\) | −293712. | − | 1.71343e6i | −0.0115031 | − | 0.0671056i | ||||
\(919\) | 2.14907e6i | 0.0839387i | 0.999119 | + | 0.0419693i | \(0.0133632\pi\) | ||||
−0.999119 | + | 0.0419693i | \(0.986637\pi\) | |||||||
\(920\) | 1.60011e6 | + | 2.86529e6i | 0.0623274 | + | 0.111609i | ||||
\(921\) | − | 6.66649e7i | − | 2.58969i | ||||||
\(922\) | 4.70862e7 | − | 8.07143e6i | 1.82418 | − | 0.312696i | ||||
\(923\) | −5.08904e6 | − | 5.08904e6i | −0.196622 | − | 0.196622i | ||||
\(924\) | −2.10687e7 | + | 7.44178e6i | −0.811816 | + | 0.286746i | ||||
\(925\) | −7.02754e6 | + | 7.02754e6i | −0.270053 | + | 0.270053i | ||||
\(926\) | 6.84672e6 | + | 4.84291e6i | 0.262395 | + | 0.185600i | ||||
\(927\) | 2.99916e7 | 1.14630 | ||||||||
\(928\) | −3.00891e7 | + | 3.41714e7i | −1.14694 | + | 1.30254i | ||||
\(929\) | −2.75055e7 | −1.04564 | −0.522818 | − | 0.852444i | \(-0.675119\pi\) | ||||
−0.522818 | + | 0.852444i | \(0.675119\pi\) | |||||||
\(930\) | −1.53807e7 | − | 1.08792e7i | −0.583133 | − | 0.412469i | ||||
\(931\) | 1.46533e7 | − | 1.46533e7i | 0.554067 | − | 0.554067i | ||||
\(932\) | 168384. | − | 59475.6i | 0.00634980 | − | 0.00224284i | ||||
\(933\) | 4.63451e7 | + | 4.63451e7i | 1.74301 | + | 1.74301i | ||||
\(934\) | −4.25279e6 | + | 729005.i | −0.159517 | + | 0.0273441i | ||||
\(935\) | − | 2.96345e6i | − | 0.110858i | ||||||
\(936\) | 1.27412e7 | − | 7.11528e6i | 0.475359 | − | 0.265462i | ||||
\(937\) | − | 4.80616e7i | − | 1.78834i | −0.447731 | − | 0.894168i | \(-0.647768\pi\) | ||
0.447731 | − | 0.894168i | \(-0.352232\pi\) | |||||||
\(938\) | 2.30693e6 | + | 1.34579e7i | 0.0856105 | + | 0.499426i | ||||
\(939\) | 5.22321e6 | + | 5.22321e6i | 0.193319 | + | 0.193319i | ||||
\(940\) | −3.54363e6 | + | 7.41404e6i | −0.130806 | + | 0.273675i | ||||
\(941\) | −2.42321e7 | + | 2.42321e7i | −0.892109 | + | 0.892109i | −0.994721 | − | 0.102613i | \(-0.967280\pi\) |
0.102613 | + | 0.994721i | \(0.467280\pi\) | |||||||
\(942\) | −2.95663e7 | + | 4.17997e7i | −1.08560 | + | 1.53478i | ||||
\(943\) | 1.11674e7 | 0.408953 | ||||||||
\(944\) | −2.19342e7 | − | 2.34101e6i | −0.801108 | − | 0.0855014i | ||||
\(945\) | −2.01724e6 | −0.0734814 | ||||||||
\(946\) | −6.71534e6 | + | 9.49389e6i | −0.243972 | + | 0.344918i | ||||
\(947\) | −1.53606e7 | + | 1.53606e7i | −0.556585 | + | 0.556585i | −0.928334 | − | 0.371748i | \(-0.878758\pi\) |
0.371748 | + | 0.928334i | \(0.378758\pi\) | |||||||
\(948\) | −3.89056e7 | − | 1.85954e7i | −1.40602 | − | 0.672023i | ||||
\(949\) | 8.57922e6 | + | 8.57922e6i | 0.309231 | + | 0.309231i | ||||
\(950\) | 470634. | + | 2.74554e6i | 0.0169190 | + | 0.0987002i | ||||
\(951\) | − | 5.25377e6i | − | 0.188374i | ||||||
\(952\) | −2.85950e7 | − | 8.10182e6i | −1.02258 | − | 0.289728i | ||||
\(953\) | 2.08505e6i | 0.0743678i | 0.999308 | + | 0.0371839i | \(0.0118387\pi\) | ||||
−0.999308 | + | 0.0371839i | \(0.988161\pi\) | |||||||
\(954\) | −4.64335e7 | + | 7.95954e6i | −1.65181 | + | 0.283150i | ||||
\(955\) | 1.74663e7 | + | 1.74663e7i | 0.619714 | + | 0.619714i | ||||
\(956\) | 1.01963e7 | + | 2.88672e7i | 0.360826 | + | 1.02155i | ||||
\(957\) | 1.86916e7 | − | 1.86916e7i | 0.659731 | − | 0.659731i | ||||
\(958\) | −3.77632e6 | − | 2.67112e6i | −0.132940 | − | 0.0940327i | ||||
\(959\) | 1.75579e7 | 0.616488 | ||||||||
\(960\) | −1.56472e7 | − | 9.64055e6i | −0.547971 | − | 0.337616i | ||||
\(961\) | 6.62882e6 | 0.231541 | ||||||||
\(962\) | 2.27426e7 | + | 1.60866e7i | 0.792324 | + | 0.560437i | ||||
\(963\) | −6.99007e6 | + | 6.99007e6i | −0.242893 | + | 0.242893i | ||||
\(964\) | −4.05582e6 | − | 1.14826e7i | −0.140568 | − | 0.397967i | ||||
\(965\) | −4.84978e6 | − | 4.84978e6i | −0.167650 | − | 0.167650i | ||||
\(966\) | −1.88339e7 | + | 3.22847e6i | −0.649379 | + | 0.111315i | ||||
\(967\) | − | 4.89482e7i | − | 1.68334i | −0.539995 | − | 0.841668i | \(-0.681574\pi\) | ||
0.539995 | − | 0.841668i | \(-0.318426\pi\) | |||||||
\(968\) | −2.41356e7 | − | 6.83836e6i | −0.827885 | − | 0.234565i | ||||
\(969\) | − | 1.39776e7i | − | 0.478213i | ||||||
\(970\) | −609813. | − | 3.55746e6i | −0.0208098 | − | 0.121398i | ||||
\(971\) | 2.47021e7 | + | 2.47021e7i | 0.840785 | + | 0.840785i | 0.988961 | − | 0.148176i | \(-0.0473401\pi\) |
−0.148176 | + | 0.988961i | \(0.547340\pi\) | |||||||
\(972\) | −3.80535e7 | − | 1.81881e7i | −1.29190 | − | 0.617479i | ||||
\(973\) | 1.03623e7 | − | 1.03623e7i | 0.350893 | − | 0.350893i | ||||
\(974\) | −7.56530e6 | + | 1.06955e7i | −0.255522 | + | 0.361248i | ||||
\(975\) | 4.34232e6 | 0.146289 | ||||||||
\(976\) | −4.57612e6 | + | 4.28761e7i | −0.153770 | + | 1.44076i | ||||
\(977\) | −4.10791e7 | −1.37684 | −0.688421 | − | 0.725311i | \(-0.741696\pi\) | ||||
−0.688421 | + | 0.725311i | \(0.741696\pi\) | |||||||
\(978\) | 3.84091e7 | − | 5.43013e7i | 1.28406 | − | 1.81536i | ||||
\(979\) | −8.52961e6 | + | 8.52961e6i | −0.284428 | + | 0.284428i | ||||
\(980\) | −9.07394e6 | + | 1.89847e7i | −0.301808 | + | 0.631448i | ||||
\(981\) | 817961. | + | 817961.i | 0.0271369 | + | 0.0271369i | ||||
\(982\) | 1.11682e6 | + | 6.51519e6i | 0.0369577 | + | 0.215600i | ||||
\(983\) | − | 4.98960e6i | − | 0.164696i | −0.996604 | − | 0.0823478i | \(-0.973758\pi\) | ||
0.996604 | − | 0.0823478i | \(-0.0262418\pi\) | |||||||
\(984\) | −5.46021e7 | + | 3.04923e7i | −1.79772 | + | 1.00393i | ||||
\(985\) | − | 1.59981e7i | − | 0.525386i | ||||||
\(986\) | 3.46547e7 | − | 5.94044e6i | 1.13519 | − | 0.194593i | ||||
\(987\) | −3.38327e7 | − | 3.38327e7i | −1.10546 | − | 1.10546i | ||||
\(988\) | 7.36207e6 | − | 2.60039e6i | 0.239943 | − | 0.0847513i | ||||
\(989\) | −7.03206e6 | + | 7.03206e6i | −0.228608 | + | 0.228608i | ||||
\(990\) | 4.50552e6 | + | 3.18690e6i | 0.146102 | + | 0.103343i | ||||
\(991\) | 1.24838e7 | 0.403795 | 0.201898 | − | 0.979407i | \(-0.435289\pi\) | ||||
0.201898 | + | 0.979407i | \(0.435289\pi\) | |||||||
\(992\) | 3.43265e7 | − | 2.18065e6i | 1.10752 | − | 0.0703568i | ||||
\(993\) | 6.13653e7 | 1.97492 | ||||||||
\(994\) | −2.22843e7 | − | 1.57624e7i | −0.715375 | − | 0.506008i | ||||
\(995\) | 8.92116e6 | − | 8.92116e6i | 0.285669 | − | 0.285669i | ||||
\(996\) | 4.78063e7 | − | 1.68859e7i | 1.52699 | − | 0.539356i | ||||
\(997\) | −2.60064e6 | − | 2.60064e6i | −0.0828595 | − | 0.0828595i | 0.664462 | − | 0.747322i | \(-0.268661\pi\) |
−0.747322 | + | 0.664462i | \(0.768661\pi\) | |||||||
\(998\) | 3.98922e7 | − | 6.83823e6i | 1.26783 | − | 0.217329i | ||||
\(999\) | 6.17975e6i | 0.195910i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 80.6.l.a.21.7 | ✓ | 80 | |
4.3 | odd | 2 | 320.6.l.a.241.35 | 80 | |||
16.3 | odd | 4 | 320.6.l.a.81.35 | 80 | |||
16.13 | even | 4 | inner | 80.6.l.a.61.7 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.l.a.21.7 | ✓ | 80 | 1.1 | even | 1 | trivial | |
80.6.l.a.61.7 | yes | 80 | 16.13 | even | 4 | inner | |
320.6.l.a.81.35 | 80 | 16.3 | odd | 4 | |||
320.6.l.a.241.35 | 80 | 4.3 | odd | 2 |