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 | 21.4 | ||
Character | \(\chi\) | \(=\) | 80.21 |
Dual form | 80.6.l.a.61.4 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.55875 | + | 1.04896i | −0.982657 | + | 0.185432i | ||||
\(3\) | 9.77316 | − | 9.77316i | 0.626948 | − | 0.626948i | −0.320351 | − | 0.947299i | \(-0.603801\pi\) |
0.947299 | + | 0.320351i | \(0.103801\pi\) | |||||||
\(4\) | 29.7994 | − | 11.6618i | 0.931230 | − | 0.364432i | ||||
\(5\) | 17.6777 | + | 17.6777i | 0.316228 | + | 0.316228i | ||||
\(6\) | −44.0749 | + | 64.5782i | −0.499819 | + | 0.732332i | ||||
\(7\) | 103.649i | 0.799504i | 0.916623 | + | 0.399752i | \(0.130904\pi\) | ||||
−0.916623 | + | 0.399752i | \(0.869096\pi\) | |||||||
\(8\) | −153.414 | + | 96.0835i | −0.847503 | + | 0.530791i | ||||
\(9\) | 51.9707i | 0.213871i | ||||||||
\(10\) | −116.809 | − | 79.7225i | −0.369382 | − | 0.252105i | ||||
\(11\) | 1.18069 | + | 1.18069i | 0.00294208 | + | 0.00294208i | 0.708576 | − | 0.705634i | \(-0.249338\pi\) |
−0.705634 | + | 0.708576i | \(0.749338\pi\) | |||||||
\(12\) | 177.261 | − | 405.207i | 0.355353 | − | 0.812313i | ||||
\(13\) | −196.412 | + | 196.412i | −0.322337 | + | 0.322337i | −0.849663 | − | 0.527326i | \(-0.823195\pi\) |
0.527326 | + | 0.849663i | \(0.323195\pi\) | |||||||
\(14\) | −108.724 | − | 576.159i | −0.148253 | − | 0.785638i | ||||
\(15\) | 345.533 | 0.396517 | ||||||||
\(16\) | 752.004 | − | 695.029i | 0.734379 | − | 0.678740i | ||||
\(17\) | 274.760 | 0.230585 | 0.115292 | − | 0.993332i | \(-0.463219\pi\) | ||||
0.115292 | + | 0.993332i | \(0.463219\pi\) | |||||||
\(18\) | −54.5152 | − | 288.892i | −0.0396585 | − | 0.210162i | ||||
\(19\) | −464.105 | + | 464.105i | −0.294939 | + | 0.294939i | −0.839028 | − | 0.544089i | \(-0.816876\pi\) |
0.544089 | + | 0.839028i | \(0.316876\pi\) | |||||||
\(20\) | 732.937 | + | 320.630i | 0.409724 | + | 0.179237i | ||||
\(21\) | 1012.98 | + | 1012.98i | 0.501248 | + | 0.501248i | ||||
\(22\) | −7.80165 | − | 5.32466i | −0.00343661 | − | 0.00234550i | ||||
\(23\) | 3172.08i | 1.25033i | 0.780493 | + | 0.625164i | \(0.214968\pi\) | ||||
−0.780493 | + | 0.625164i | \(0.785032\pi\) | |||||||
\(24\) | −560.304 | + | 2438.38i | −0.198562 | + | 0.864119i | ||||
\(25\) | 625.000i | 0.200000i | ||||||||
\(26\) | 885.777 | − | 1297.83i | 0.256975 | − | 0.376518i | ||||
\(27\) | 2882.80 | + | 2882.80i | 0.761035 | + | 0.761035i | ||||
\(28\) | 1208.74 | + | 3088.68i | 0.291365 | + | 0.744522i | ||||
\(29\) | −3615.12 | + | 3615.12i | −0.798229 | + | 0.798229i | −0.982816 | − | 0.184587i | \(-0.940905\pi\) |
0.184587 | + | 0.982816i | \(0.440905\pi\) | |||||||
\(30\) | −1920.73 | + | 362.451i | −0.389640 | + | 0.0735269i | ||||
\(31\) | 8594.55 | 1.60627 | 0.803135 | − | 0.595797i | \(-0.203164\pi\) | ||||
0.803135 | + | 0.595797i | \(0.203164\pi\) | |||||||
\(32\) | −3451.14 | + | 4652.32i | −0.595783 | + | 0.803146i | ||||
\(33\) | 23.0781 | 0.00368906 | ||||||||
\(34\) | −1527.32 | + | 288.212i | −0.226586 | + | 0.0427578i | ||||
\(35\) | −1832.27 | + | 1832.27i | −0.252825 | + | 0.252825i | ||||
\(36\) | 606.073 | + | 1548.69i | 0.0779415 | + | 0.199163i | ||||
\(37\) | 5380.92 | + | 5380.92i | 0.646178 | + | 0.646178i | 0.952067 | − | 0.305889i | \(-0.0989538\pi\) |
−0.305889 | + | 0.952067i | \(0.598954\pi\) | |||||||
\(38\) | 2093.02 | − | 3066.67i | 0.235133 | − | 0.344515i | ||||
\(39\) | 3839.13i | 0.404177i | ||||||||
\(40\) | −4410.54 | − | 1013.48i | −0.435855 | − | 0.100153i | ||||
\(41\) | − | 12794.9i | − | 1.18871i | −0.804203 | − | 0.594355i | \(-0.797407\pi\) | ||
0.804203 | − | 0.594355i | \(-0.202593\pi\) | |||||||
\(42\) | −6693.47 | − | 4568.32i | −0.585502 | − | 0.399607i | ||||
\(43\) | 2059.02 | + | 2059.02i | 0.169820 | + | 0.169820i | 0.786900 | − | 0.617080i | \(-0.211685\pi\) |
−0.617080 | + | 0.786900i | \(0.711685\pi\) | |||||||
\(44\) | 48.9528 | + | 21.4148i | 0.00381194 | + | 0.00166756i | ||||
\(45\) | −918.721 | + | 918.721i | −0.0676320 | + | 0.0676320i | ||||
\(46\) | −3327.38 | − | 17632.8i | −0.231851 | − | 1.22864i | ||||
\(47\) | −19.2201 | −0.00126914 | −0.000634572 | − | 1.00000i | \(-0.500202\pi\) | ||||
−0.000634572 | 1.00000i | \(0.500202\pi\) | ||||||||
\(48\) | 556.822 | − | 14142.1i | 0.0348830 | − | 0.885953i | ||||
\(49\) | 6063.86 | 0.360794 | ||||||||
\(50\) | −655.600 | − | 3474.22i | −0.0370864 | − | 0.196531i | ||||
\(51\) | 2685.27 | − | 2685.27i | 0.144565 | − | 0.144565i | ||||
\(52\) | −3562.43 | + | 8143.48i | −0.182700 | + | 0.417639i | ||||
\(53\) | 2845.02 | + | 2845.02i | 0.139122 | + | 0.139122i | 0.773238 | − | 0.634116i | \(-0.218636\pi\) |
−0.634116 | + | 0.773238i | \(0.718636\pi\) | |||||||
\(54\) | −19048.7 | − | 13000.8i | −0.888956 | − | 0.606716i | ||||
\(55\) | 41.7437i | 0.00186073i | ||||||||
\(56\) | −9958.97 | − | 15901.3i | −0.424370 | − | 0.677582i | ||||
\(57\) | 9071.55i | 0.369823i | ||||||||
\(58\) | 16303.4 | − | 23887.7i | 0.636369 | − | 0.932403i | ||||
\(59\) | −16076.8 | − | 16076.8i | −0.601268 | − | 0.601268i | 0.339381 | − | 0.940649i | \(-0.389782\pi\) |
−0.940649 | + | 0.339381i | \(0.889782\pi\) | |||||||
\(60\) | 10296.7 | − | 4029.55i | 0.369249 | − | 0.144503i | ||||
\(61\) | 28235.3 | − | 28235.3i | 0.971557 | − | 0.971557i | −0.0280491 | − | 0.999607i | \(-0.508929\pi\) |
0.999607 | + | 0.0280491i | \(0.00892948\pi\) | |||||||
\(62\) | −47774.9 | + | 9015.34i | −1.57841 | + | 0.297854i | ||||
\(63\) | −5386.72 | −0.170991 | ||||||||
\(64\) | 14303.9 | − | 29481.2i | 0.436521 | − | 0.899694i | ||||
\(65\) | −6944.22 | −0.203864 | ||||||||
\(66\) | −128.286 | + | 24.2081i | −0.00362508 | + | 0.000684069i | ||||
\(67\) | −41683.6 | + | 41683.6i | −1.13443 | + | 1.13443i | −0.145000 | + | 0.989432i | \(0.546318\pi\) |
−0.989432 | + | 0.145000i | \(0.953682\pi\) | |||||||
\(68\) | 8187.66 | − | 3204.20i | 0.214727 | − | 0.0840324i | ||||
\(69\) | 31001.2 | + | 31001.2i | 0.783891 | + | 0.783891i | ||||
\(70\) | 8263.17 | − | 12107.1i | 0.201559 | − | 0.295322i | ||||
\(71\) | 25386.5i | 0.597663i | 0.954306 | + | 0.298832i | \(0.0965969\pi\) | ||||
−0.954306 | + | 0.298832i | \(0.903403\pi\) | |||||||
\(72\) | −4993.52 | − | 7973.05i | −0.113521 | − | 0.181256i | ||||
\(73\) | − | 24731.7i | − | 0.543184i | −0.962412 | − | 0.271592i | \(-0.912450\pi\) | ||
0.962412 | − | 0.271592i | \(-0.0875502\pi\) | |||||||
\(74\) | −35555.5 | − | 24266.8i | −0.754793 | − | 0.515149i | ||||
\(75\) | 6108.22 | + | 6108.22i | 0.125390 | + | 0.125390i | ||||
\(76\) | −8417.73 | + | 19242.4i | −0.167171 | + | 0.382142i | ||||
\(77\) | −122.377 | + | 122.377i | −0.00235220 | + | 0.00235220i | ||||
\(78\) | −4027.10 | − | 21340.8i | −0.0749473 | − | 0.397167i | ||||
\(79\) | 8180.40 | 0.147471 | 0.0737355 | − | 0.997278i | \(-0.476508\pi\) | ||||
0.0737355 | + | 0.997278i | \(0.476508\pi\) | |||||||
\(80\) | 25580.2 | + | 1007.18i | 0.446867 | + | 0.0175947i | ||||
\(81\) | 43719.2 | 0.740388 | ||||||||
\(82\) | 13421.3 | + | 71123.4i | 0.220425 | + | 1.16809i | ||||
\(83\) | −73736.2 | + | 73736.2i | −1.17486 | + | 1.17486i | −0.193822 | + | 0.981037i | \(0.562088\pi\) |
−0.981037 | + | 0.193822i | \(0.937912\pi\) | |||||||
\(84\) | 41999.3 | + | 18373.0i | 0.649448 | + | 0.284106i | ||||
\(85\) | 4857.11 | + | 4857.11i | 0.0729173 | + | 0.0729173i | ||||
\(86\) | −13605.4 | − | 9285.75i | −0.198365 | − | 0.135385i | ||||
\(87\) | 70662.3i | 1.00090i | ||||||||
\(88\) | −294.579 | − | 67.6900i | −0.00405505 | − | 0.000931789i | ||||
\(89\) | − | 31074.5i | − | 0.415842i | −0.978146 | − | 0.207921i | \(-0.933330\pi\) | ||
0.978146 | − | 0.207921i | \(-0.0666698\pi\) | |||||||
\(90\) | 4143.24 | − | 6070.64i | 0.0539179 | − | 0.0790002i | ||||
\(91\) | −20357.9 | − | 20357.9i | −0.257709 | − | 0.257709i | ||||
\(92\) | 36992.2 | + | 94525.8i | 0.455659 | + | 1.16434i | ||||
\(93\) | 83995.9 | − | 83995.9i | 1.00705 | − | 1.00705i | ||||
\(94\) | 106.840 | − | 20.1611i | 0.00124713 | − | 0.000235340i | ||||
\(95\) | −16408.6 | −0.186536 | ||||||||
\(96\) | 11739.3 | + | 79196.4i | 0.130006 | + | 0.877056i | ||||
\(97\) | 48319.6 | 0.521427 | 0.260714 | − | 0.965416i | \(-0.416042\pi\) | ||||
0.260714 | + | 0.965416i | \(0.416042\pi\) | |||||||
\(98\) | −33707.5 | + | 6360.75i | −0.354536 | + | 0.0669026i | ||||
\(99\) | −61.3613 | + | 61.3613i | −0.000629225 | + | 0.000629225i | ||||
\(100\) | 7288.64 | + | 18624.6i | 0.0728864 | + | 0.186246i | ||||
\(101\) | −83227.2 | − | 83227.2i | −0.811824 | − | 0.811824i | 0.173083 | − | 0.984907i | \(-0.444627\pi\) |
−0.984907 | + | 0.173083i | \(0.944627\pi\) | |||||||
\(102\) | −12110.0 | + | 17743.5i | −0.115251 | + | 0.168865i | ||||
\(103\) | − | 24932.4i | − | 0.231564i | −0.993275 | − | 0.115782i | \(-0.963063\pi\) | ||
0.993275 | − | 0.115782i | \(-0.0369374\pi\) | |||||||
\(104\) | 11260.5 | − | 49004.4i | 0.102088 | − | 0.444275i | ||||
\(105\) | 35814.2i | 0.317017i | ||||||||
\(106\) | −18799.1 | − | 12830.4i | −0.162507 | − | 0.110912i | ||||
\(107\) | −86761.1 | − | 86761.1i | −0.732598 | − | 0.732598i | 0.238536 | − | 0.971134i | \(-0.423332\pi\) |
−0.971134 | + | 0.238536i | \(0.923332\pi\) | |||||||
\(108\) | 119524. | + | 52286.8i | 0.986044 | + | 0.431353i | ||||
\(109\) | 108586. | − | 108586.i | 0.875399 | − | 0.875399i | −0.117656 | − | 0.993054i | \(-0.537538\pi\) |
0.993054 | + | 0.117656i | \(0.0375379\pi\) | |||||||
\(110\) | −43.7875 | − | 232.043i | −0.000345039 | − | 0.00182846i | ||||
\(111\) | 105177. | 0.810240 | ||||||||
\(112\) | 72039.2 | + | 77944.6i | 0.542655 | + | 0.587139i | ||||
\(113\) | −96237.1 | −0.709000 | −0.354500 | − | 0.935056i | \(-0.615349\pi\) | ||||
−0.354500 | + | 0.935056i | \(0.615349\pi\) | |||||||
\(114\) | −9515.70 | − | 50426.5i | −0.0685770 | − | 0.363410i | ||||
\(115\) | −56074.9 | + | 56074.9i | −0.395388 | + | 0.395388i | ||||
\(116\) | −65569.4 | + | 149887.i | −0.452435 | + | 1.03424i | ||||
\(117\) | −10207.7 | − | 10207.7i | −0.0689385 | − | 0.0689385i | ||||
\(118\) | 106230. | + | 72502.7i | 0.702335 | + | 0.479346i | ||||
\(119\) | 28478.6i | 0.184353i | ||||||||
\(120\) | −53009.8 | + | 33200.0i | −0.336049 | + | 0.210468i | ||||
\(121\) | − | 161048.i | − | 0.999983i | ||||||
\(122\) | −127335. | + | 186571.i | −0.774550 | + | 1.13487i | ||||
\(123\) | −125046. | − | 125046.i | −0.745260 | − | 0.745260i | ||||
\(124\) | 256112. | − | 100228.i | 1.49581 | − | 0.585376i | ||||
\(125\) | −11048.5 | + | 11048.5i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 29943.4 | − | 5650.45i | 0.168025 | − | 0.0317071i | ||||
\(127\) | −83496.0 | −0.459363 | −0.229682 | − | 0.973266i | \(-0.573768\pi\) | ||||
−0.229682 | + | 0.973266i | \(0.573768\pi\) | |||||||
\(128\) | −48587.4 | + | 178883.i | −0.262119 | + | 0.965036i | ||||
\(129\) | 40246.3 | 0.212937 | ||||||||
\(130\) | 38601.1 | − | 7284.21i | 0.200328 | − | 0.0378028i | ||||
\(131\) | 4990.15 | − | 4990.15i | 0.0254059 | − | 0.0254059i | −0.694290 | − | 0.719696i | \(-0.744281\pi\) |
0.719696 | + | 0.694290i | \(0.244281\pi\) | |||||||
\(132\) | 687.714 | − | 269.133i | 0.00343536 | − | 0.00134441i | ||||
\(133\) | −48104.1 | − | 48104.1i | −0.235805 | − | 0.235805i | ||||
\(134\) | 187984. | − | 275433.i | 0.904398 | − | 1.32512i | ||||
\(135\) | 101922.i | 0.481321i | ||||||||
\(136\) | −42152.1 | + | 26399.9i | −0.195421 | + | 0.122392i | ||||
\(137\) | 319403.i | 1.45391i | 0.686686 | + | 0.726954i | \(0.259065\pi\) | ||||
−0.686686 | + | 0.726954i | \(0.740935\pi\) | |||||||
\(138\) | −204847. | − | 139809.i | −0.915655 | − | 0.624938i | ||||
\(139\) | −126010. | − | 126010.i | −0.553182 | − | 0.553182i | 0.374176 | − | 0.927358i | \(-0.377926\pi\) |
−0.927358 | + | 0.374176i | \(0.877926\pi\) | |||||||
\(140\) | −33233.0 | + | 75968.3i | −0.143301 | + | 0.327576i | ||||
\(141\) | −187.841 | + | 187.841i | −0.000795689 | + | 0.000795689i | ||||
\(142\) | −26629.4 | − | 141117.i | −0.110826 | − | 0.587298i | ||||
\(143\) | −463.803 | −0.00189668 | ||||||||
\(144\) | 36121.2 | + | 39082.2i | 0.145163 | + | 0.157062i | ||||
\(145\) | −127814. | −0.504845 | ||||||||
\(146\) | 25942.6 | + | 137477.i | 0.100724 | + | 0.533764i | ||||
\(147\) | 59263.1 | − | 59263.1i | 0.226199 | − | 0.226199i | ||||
\(148\) | 223099. | + | 97596.6i | 0.837228 | + | 0.366252i | ||||
\(149\) | −127764. | − | 127764.i | −0.471456 | − | 0.471456i | 0.430929 | − | 0.902386i | \(-0.358186\pi\) |
−0.902386 | + | 0.430929i | \(0.858186\pi\) | |||||||
\(150\) | −40361.4 | − | 27546.8i | −0.146466 | − | 0.0999638i | ||||
\(151\) | 313476.i | 1.11882i | 0.828890 | + | 0.559412i | \(0.188973\pi\) | ||||
−0.828890 | + | 0.559412i | \(0.811027\pi\) | |||||||
\(152\) | 26607.6 | − | 115793.i | 0.0934106 | − | 0.406513i | ||||
\(153\) | 14279.5i | 0.0493154i | ||||||||
\(154\) | 551.896 | − | 808.634i | 0.00187523 | − | 0.00274758i | ||||
\(155\) | 151932. | + | 151932.i | 0.507947 | + | 0.507947i | ||||
\(156\) | 44771.3 | + | 114404.i | 0.147295 | + | 0.376382i | ||||
\(157\) | 252249. | − | 252249.i | 0.816734 | − | 0.816734i | −0.168899 | − | 0.985633i | \(-0.554021\pi\) |
0.985633 | + | 0.168899i | \(0.0540212\pi\) | |||||||
\(158\) | −45472.8 | + | 8580.91i | −0.144913 | + | 0.0273458i | ||||
\(159\) | 55609.7 | 0.174445 | ||||||||
\(160\) | −143250. | + | 21234.0i | −0.442380 | + | 0.0655739i | ||||
\(161\) | −328783. | −0.999642 | ||||||||
\(162\) | −243024. | + | 45859.7i | −0.727547 | + | 0.137291i | ||||
\(163\) | 282574. | − | 282574.i | 0.833035 | − | 0.833035i | −0.154896 | − | 0.987931i | \(-0.549504\pi\) |
0.987931 | + | 0.154896i | \(0.0495041\pi\) | |||||||
\(164\) | −149211. | − | 381279.i | −0.433204 | − | 1.10696i | ||||
\(165\) | 407.968 | + | 407.968i | 0.00116658 | + | 0.00116658i | ||||
\(166\) | 332535. | − | 487228.i | 0.936627 | − | 1.37234i | ||||
\(167\) | − | 52609.2i | − | 0.145972i | −0.997333 | − | 0.0729861i | \(-0.976747\pi\) | ||
0.997333 | − | 0.0729861i | \(-0.0232529\pi\) | |||||||
\(168\) | −252736. | − | 58075.0i | −0.690867 | − | 0.158751i | ||||
\(169\) | 294138.i | 0.792198i | ||||||||
\(170\) | −32094.4 | − | 21904.5i | −0.0851739 | − | 0.0581315i | ||||
\(171\) | −24119.9 | − | 24119.9i | −0.0630790 | − | 0.0630790i | ||||
\(172\) | 85369.4 | + | 37345.6i | 0.220030 | + | 0.0962539i | ||||
\(173\) | 538675. | − | 538675.i | 1.36839 | − | 1.36839i | 0.505663 | − | 0.862731i | \(-0.331248\pi\) |
0.862731 | − | 0.505663i | \(-0.168752\pi\) | |||||||
\(174\) | −74122.0 | − | 392794.i | −0.185598 | − | 0.983539i | ||||
\(175\) | −64780.7 | −0.159901 | ||||||||
\(176\) | 1708.50 | + | 67.2693i | 0.00415750 | + | 0.000163695i | ||||
\(177\) | −314241. | −0.753928 | ||||||||
\(178\) | 32595.9 | + | 172735.i | 0.0771104 | + | 0.408631i | ||||
\(179\) | −194994. | + | 194994.i | −0.454871 | + | 0.454871i | −0.896967 | − | 0.442097i | \(-0.854235\pi\) |
0.442097 | + | 0.896967i | \(0.354235\pi\) | |||||||
\(180\) | −16663.3 | + | 38091.2i | −0.0383337 | + | 0.0876282i | ||||
\(181\) | −417889. | − | 417889.i | −0.948123 | − | 0.948123i | 0.0505962 | − | 0.998719i | \(-0.483888\pi\) |
−0.998719 | + | 0.0505962i | \(0.983888\pi\) | |||||||
\(182\) | 134519. | + | 91810.0i | 0.301028 | + | 0.205452i | ||||
\(183\) | − | 551897.i | − | 1.21823i | ||||||
\(184\) | −304784. | − | 486642.i | −0.663663 | − | 1.05966i | ||||
\(185\) | 190244.i | 0.408679i | ||||||||
\(186\) | −378803. | + | 555020.i | −0.802845 | + | 1.17632i | ||||
\(187\) | 324.406 | + | 324.406i | 0.000678398 | + | 0.000678398i | ||||
\(188\) | −572.747 | + | 224.141i | −0.00118187 | + | 0.000462517i | ||||
\(189\) | −298799. | + | 298799.i | −0.608450 | + | 0.608450i | ||||
\(190\) | 91211.3 | − | 17212.0i | 0.183301 | − | 0.0345897i | ||||
\(191\) | 497076. | 0.985915 | 0.492957 | − | 0.870053i | \(-0.335916\pi\) | ||||
0.492957 | + | 0.870053i | \(0.335916\pi\) | |||||||
\(192\) | −148330. | − | 427919.i | −0.290385 | − | 0.837738i | ||||
\(193\) | 462532. | 0.893817 | 0.446908 | − | 0.894580i | \(-0.352525\pi\) | ||||
0.446908 | + | 0.894580i | \(0.352525\pi\) | |||||||
\(194\) | −268596. | + | 50685.4i | −0.512384 | + | 0.0966892i | ||||
\(195\) | −67866.9 | + | 67866.9i | −0.127812 | + | 0.127812i | ||||
\(196\) | 180699. | − | 70715.6i | 0.335982 | − | 0.131485i | ||||
\(197\) | 286303. | + | 286303.i | 0.525606 | + | 0.525606i | 0.919259 | − | 0.393653i | \(-0.128789\pi\) |
−0.393653 | + | 0.919259i | \(0.628789\pi\) | |||||||
\(198\) | 276.726 | − | 405.457i | 0.000501634 | − | 0.000734991i | ||||
\(199\) | 1.00987e6i | 1.80772i | 0.427828 | + | 0.903860i | \(0.359279\pi\) | ||||
−0.427828 | + | 0.903860i | \(0.640721\pi\) | |||||||
\(200\) | −60052.2 | − | 95884.0i | −0.106158 | − | 0.169501i | ||||
\(201\) | 814761.i | 1.42246i | ||||||||
\(202\) | 549941. | + | 375337.i | 0.948283 | + | 0.647207i | ||||
\(203\) | −374704. | − | 374704.i | −0.638187 | − | 0.638187i | ||||
\(204\) | 48704.2 | − | 111334.i | 0.0819391 | − | 0.187307i | ||||
\(205\) | 226183. | − | 226183.i | 0.375903 | − | 0.375903i | ||||
\(206\) | 26153.1 | + | 138593.i | 0.0429393 | + | 0.227548i | ||||
\(207\) | −164855. | −0.267409 | ||||||||
\(208\) | −11190.5 | + | 284215.i | −0.0179346 | + | 0.455500i | ||||
\(209\) | −1095.93 | −0.00173547 | ||||||||
\(210\) | −37567.7 | − | 199082.i | −0.0587850 | − | 0.311519i | ||||
\(211\) | 277285. | − | 277285.i | 0.428765 | − | 0.428765i | −0.459442 | − | 0.888208i | \(-0.651951\pi\) |
0.888208 | + | 0.459442i | \(0.151951\pi\) | |||||||
\(212\) | 117958. | + | 51601.7i | 0.180255 | + | 0.0788541i | ||||
\(213\) | 248106. | + | 248106.i | 0.374704 | + | 0.374704i | ||||
\(214\) | 573292. | + | 391274.i | 0.855739 | + | 0.584045i | ||||
\(215\) | 72797.4i | 0.107404i | ||||||||
\(216\) | −719251. | − | 165273.i | −1.04893 | − | 0.241028i | ||||
\(217\) | 890817.i | 1.28422i | ||||||||
\(218\) | −489698. | + | 717502.i | −0.697890 | + | 1.02254i | ||||
\(219\) | −241707. | − | 241707.i | −0.340549 | − | 0.340549i | ||||
\(220\) | 486.807 | + | 1243.93i | 0.000678110 | + | 0.00173277i | ||||
\(221\) | −53966.1 | + | 53966.1i | −0.0743259 | + | 0.0743259i | ||||
\(222\) | −584653. | + | 110327.i | −0.796188 | + | 0.150244i | ||||
\(223\) | 912396. | 1.22863 | 0.614315 | − | 0.789061i | \(-0.289432\pi\) | ||||
0.614315 | + | 0.789061i | \(0.289432\pi\) | |||||||
\(224\) | −482208. | − | 357708.i | −0.642118 | − | 0.476331i | ||||
\(225\) | −32481.7 | −0.0427742 | ||||||||
\(226\) | 534958. | − | 100949.i | 0.696704 | − | 0.131471i | ||||
\(227\) | 173993. | − | 173993.i | 0.224113 | − | 0.224113i | −0.586115 | − | 0.810228i | \(-0.699343\pi\) |
0.810228 | + | 0.586115i | \(0.199343\pi\) | |||||||
\(228\) | 105791. | + | 270326.i | 0.134775 | + | 0.344391i | ||||
\(229\) | 845428. | + | 845428.i | 1.06534 | + | 1.06534i | 0.997711 | + | 0.0676288i | \(0.0215434\pi\) |
0.0676288 | + | 0.997711i | \(0.478457\pi\) | |||||||
\(230\) | 252886. | − | 370527.i | 0.315214 | − | 0.461849i | ||||
\(231\) | 2392.03i | 0.00294942i | ||||||||
\(232\) | 207258. | − | 901965.i | 0.252808 | − | 1.10019i | ||||
\(233\) | 33744.0i | 0.0407199i | 0.999793 | + | 0.0203599i | \(0.00648122\pi\) | ||||
−0.999793 | + | 0.0203599i | \(0.993519\pi\) | |||||||
\(234\) | 67449.3 | + | 46034.4i | 0.0805263 | + | 0.0549595i | ||||
\(235\) | −339.767 | − | 339.767i | −0.000401339 | − | 0.000401339i | ||||
\(236\) | −666561. | − | 291593.i | −0.779040 | − | 0.340798i | ||||
\(237\) | 79948.3 | − | 79948.3i | 0.0924567 | − | 0.0924567i | ||||
\(238\) | −29872.9 | − | 158305.i | −0.0341850 | − | 0.181156i | ||||
\(239\) | 1.42903e6 | 1.61825 | 0.809125 | − | 0.587637i | \(-0.199942\pi\) | ||||
0.809125 | + | 0.587637i | \(0.199942\pi\) | |||||||
\(240\) | 259843. | − | 240156.i | 0.291194 | − | 0.269132i | ||||
\(241\) | −387370. | −0.429619 | −0.214809 | − | 0.976656i | \(-0.568913\pi\) | ||||
−0.214809 | + | 0.976656i | \(0.568913\pi\) | |||||||
\(242\) | 168933. | + | 895226.i | 0.185429 | + | 0.982640i | ||||
\(243\) | −273245. | + | 273245.i | −0.296850 | + | 0.296850i | ||||
\(244\) | 512120. | − | 1.17067e6i | 0.550677 | − | 1.25881i | ||||
\(245\) | 107195. | + | 107195.i | 0.114093 | + | 0.114093i | ||||
\(246\) | 826269. | + | 563932.i | 0.870530 | + | 0.594140i | ||||
\(247\) | − | 182312.i | − | 0.190140i | ||||||
\(248\) | −1.31853e6 | + | 825794.i | −1.36132 | + | 0.852594i | ||||
\(249\) | 1.44127e6i | 1.47315i | ||||||||
\(250\) | 49826.6 | − | 73005.6i | 0.0504210 | − | 0.0738764i | ||||
\(251\) | −151092. | − | 151092.i | −0.151376 | − | 0.151376i | 0.627356 | − | 0.778732i | \(-0.284137\pi\) |
−0.778732 | + | 0.627356i | \(0.784137\pi\) | |||||||
\(252\) | −160521. | + | 62818.9i | −0.159232 | + | 0.0623145i | ||||
\(253\) | −3745.24 | + | 3745.24i | −0.00367856 | + | 0.00367856i | ||||
\(254\) | 464133. | − | 87584.0i | 0.451396 | − | 0.0851805i | ||||
\(255\) | 94938.6 | 0.0914308 | ||||||||
\(256\) | 82444.2 | − | 1.04533e6i | 0.0786249 | − | 0.996904i | ||||
\(257\) | −1.10772e6 | −1.04616 | −0.523081 | − | 0.852283i | \(-0.675218\pi\) | ||||
−0.523081 | + | 0.852283i | \(0.675218\pi\) | |||||||
\(258\) | −223719. | + | 42216.8i | −0.209244 | + | 0.0394853i | ||||
\(259\) | −557727. | + | 557727.i | −0.516621 | + | 0.516621i | ||||
\(260\) | −206933. | + | 80982.2i | −0.189844 | + | 0.0742944i | ||||
\(261\) | −187880. | − | 187880.i | −0.170718 | − | 0.170718i | ||||
\(262\) | −22504.5 | + | 32973.5i | −0.0202543 | + | 0.0296764i | ||||
\(263\) | 166218.i | 0.148179i | 0.997252 | + | 0.0740897i | \(0.0236051\pi\) | ||||
−0.997252 | + | 0.0740897i | \(0.976395\pi\) | |||||||
\(264\) | −3540.52 | + | 2217.43i | −0.00312649 | + | 0.00195812i | ||||
\(265\) | 100587.i | 0.0879884i | ||||||||
\(266\) | 317858. | + | 216939.i | 0.275441 | + | 0.187990i | ||||
\(267\) | −303696. | − | 303696.i | −0.260712 | − | 0.260712i | ||||
\(268\) | −756038. | + | 1.72825e6i | −0.642994 | + | 1.46984i | ||||
\(269\) | −1.20947e6 | + | 1.20947e6i | −1.01910 | + | 1.01910i | −0.0192827 | + | 0.999814i | \(0.506138\pi\) |
−0.999814 | + | 0.0192827i | \(0.993862\pi\) | |||||||
\(270\) | −106912. | − | 566560.i | −0.0892522 | − | 0.472973i | ||||
\(271\) | 1.78497e6 | 1.47641 | 0.738207 | − | 0.674574i | \(-0.235673\pi\) | ||||
0.738207 | + | 0.674574i | \(0.235673\pi\) | |||||||
\(272\) | 206620. | − | 190966.i | 0.169337 | − | 0.156507i | ||||
\(273\) | −397923. | −0.323141 | ||||||||
\(274\) | −335041. | − | 1.77548e6i | −0.269601 | − | 1.42869i | ||||
\(275\) | −737.931 | + | 737.931i | −0.000588415 | + | 0.000588415i | ||||
\(276\) | 1.28535e6 | + | 562286.i | 1.01566 | + | 0.444308i | ||||
\(277\) | −1.21139e6 | − | 1.21139e6i | −0.948602 | − | 0.948602i | 0.0501403 | − | 0.998742i | \(-0.484033\pi\) |
−0.998742 | + | 0.0501403i | \(0.984033\pi\) | |||||||
\(278\) | 832638. | + | 568279.i | 0.646166 | + | 0.441011i | ||||
\(279\) | 446665.i | 0.343535i | ||||||||
\(280\) | 105046. | − | 457149.i | 0.0800727 | − | 0.348468i | ||||
\(281\) | − | 2.33417e6i | − | 1.76347i | −0.471748 | − | 0.881734i | \(-0.656377\pi\) | ||
0.471748 | − | 0.881734i | \(-0.343623\pi\) | |||||||
\(282\) | 847.124 | − | 1241.20i | 0.000634343 | − | 0.000929435i | ||||
\(283\) | −1.45993e6 | − | 1.45993e6i | −1.08359 | − | 1.08359i | −0.996171 | − | 0.0874233i | \(-0.972137\pi\) |
−0.0874233 | − | 0.996171i | \(-0.527863\pi\) | |||||||
\(284\) | 296052. | + | 756501.i | 0.217807 | + | 0.556562i | ||||
\(285\) | −160364. | + | 160364.i | −0.116948 | + | 0.116948i | ||||
\(286\) | 2578.17 | − | 486.511i | 0.00186378 | − | 0.000351705i | ||||
\(287\) | 1.32618e6 | 0.950378 | ||||||||
\(288\) | −241784. | − | 179358.i | −0.171770 | − | 0.127421i | ||||
\(289\) | −1.34436e6 | −0.946831 | ||||||||
\(290\) | 710485. | − | 134072.i | 0.496089 | − | 0.0936142i | ||||
\(291\) | 472235. | − | 472235.i | 0.326908 | − | 0.326908i | ||||
\(292\) | −288417. | − | 736990.i | −0.197954 | − | 0.505830i | ||||
\(293\) | −268466. | − | 268466.i | −0.182692 | − | 0.182692i | 0.609836 | − | 0.792528i | \(-0.291235\pi\) |
−0.792528 | + | 0.609836i | \(0.791235\pi\) | |||||||
\(294\) | −267264. | + | 391593.i | −0.180332 | + | 0.264221i | ||||
\(295\) | − | 568399.i | − | 0.380275i | ||||||
\(296\) | −1.34253e6 | − | 308493.i | −0.890622 | − | 0.204652i | ||||
\(297\) | 6807.37i | 0.00447804i | ||||||||
\(298\) | 844225. | + | 576187.i | 0.550703 | + | 0.375857i | ||||
\(299\) | −623034. | − | 623034.i | −0.403027 | − | 0.403027i | ||||
\(300\) | 253254. | + | 110788.i | 0.162463 | + | 0.0710707i | ||||
\(301\) | −213416. | + | 213416.i | −0.135772 | + | 0.135772i | ||||
\(302\) | −328824. | − | 1.74253e6i | −0.207466 | − | 1.09942i | ||||
\(303\) | −1.62679e6 | −1.01794 | ||||||||
\(304\) | −26442.2 | + | 671576.i | −0.0164102 | + | 0.416784i | ||||
\(305\) | 998270. | 0.614467 | ||||||||
\(306\) | −14978.6 | − | 79375.9i | −0.00914465 | − | 0.0484602i | ||||
\(307\) | 1.30877e6 | − | 1.30877e6i | 0.792534 | − | 0.792534i | −0.189372 | − | 0.981905i | \(-0.560645\pi\) |
0.981905 | + | 0.189372i | \(0.0606452\pi\) | |||||||
\(308\) | −2219.63 | + | 5073.91i | −0.00133322 | + | 0.00304766i | ||||
\(309\) | −243668. | − | 243668.i | −0.145179 | − | 0.145179i | ||||
\(310\) | −1.00392e6 | − | 685179.i | −0.593328 | − | 0.404948i | ||||
\(311\) | − | 3.06774e6i | − | 1.79853i | −0.437406 | − | 0.899264i | \(-0.644103\pi\) | ||
0.437406 | − | 0.899264i | \(-0.355897\pi\) | |||||||
\(312\) | −368877. | − | 588978.i | −0.214534 | − | 0.342541i | ||||
\(313\) | − | 2.27439e6i | − | 1.31221i | −0.754669 | − | 0.656105i | \(-0.772203\pi\) | ||
0.754669 | − | 0.656105i | \(-0.227797\pi\) | |||||||
\(314\) | −1.13759e6 | + | 1.66679e6i | −0.651121 | + | 0.954018i | ||||
\(315\) | −95224.6 | − | 95224.6i | −0.0540720 | − | 0.0540720i | ||||
\(316\) | 243771. | − | 95398.3i | 0.137329 | − | 0.0537431i | ||||
\(317\) | 2.44805e6 | − | 2.44805e6i | 1.36827 | − | 1.36827i | 0.505360 | − | 0.862909i | \(-0.331360\pi\) |
0.862909 | − | 0.505360i | \(-0.168640\pi\) | |||||||
\(318\) | −309120. | + | 58332.3i | −0.171419 | + | 0.0323476i | ||||
\(319\) | −8536.67 | −0.00469690 | ||||||||
\(320\) | 774019. | − | 268298.i | 0.422548 | − | 0.146468i | ||||
\(321\) | −1.69586e6 | −0.918602 | ||||||||
\(322\) | 1.82762e6 | − | 344880.i | 0.982305 | − | 0.185365i | ||||
\(323\) | −127517. | + | 127517.i | −0.0680085 | + | 0.0680085i | ||||
\(324\) | 1.30280e6 | − | 509845.i | 0.689472 | − | 0.269821i | ||||
\(325\) | −122758. | − | 122758.i | −0.0644673 | − | 0.0644673i | ||||
\(326\) | −1.27435e6 | + | 1.86717e6i | −0.664117 | + | 0.973059i | ||||
\(327\) | − | 2.12245e6i | − | 1.09766i | ||||||
\(328\) | 1.22937e6 | + | 1.96292e6i | 0.630957 | + | 1.00743i | ||||
\(329\) | − | 1992.15i | − | 0.00101469i | ||||||
\(330\) | −2695.73 | − | 1839.85i | −0.00136267 | − | 0.000930030i | ||||
\(331\) | 786844. | + | 786844.i | 0.394747 | + | 0.394747i | 0.876376 | − | 0.481628i | \(-0.159955\pi\) |
−0.481628 | + | 0.876376i | \(0.659955\pi\) | |||||||
\(332\) | −1.33739e6 | + | 3.05719e6i | −0.665908 | + | 1.52222i | ||||
\(333\) | −279650. | + | 279650.i | −0.138199 | + | 0.138199i | ||||
\(334\) | 55185.0 | + | 292441.i | 0.0270679 | + | 0.143441i | ||||
\(335\) | −1.47374e6 | −0.717478 | ||||||||
\(336\) | 1.46582e6 | + | 57714.1i | 0.708322 | + | 0.0278891i | ||||
\(337\) | −1.52615e6 | −0.732021 | −0.366010 | − | 0.930611i | \(-0.619276\pi\) | ||||
−0.366010 | + | 0.930611i | \(0.619276\pi\) | |||||||
\(338\) | −308539. | − | 1.63504e6i | −0.146899 | − | 0.778459i | ||||
\(339\) | −940541. | + | 940541.i | −0.444507 | + | 0.444507i | ||||
\(340\) | 201382. | + | 88096.1i | 0.0944762 | + | 0.0413294i | ||||
\(341\) | 10147.5 | + | 10147.5i | 0.00472577 | + | 0.00472577i | ||||
\(342\) | 159377. | + | 108776.i | 0.0736819 | + | 0.0502882i | ||||
\(343\) | 2.37054e6i | 1.08796i | ||||||||
\(344\) | −513721. | − | 118046.i | −0.234062 | − | 0.0537840i | ||||
\(345\) | 1.09606e6i | 0.495776i | ||||||||
\(346\) | −2.42931e6 | + | 3.55940e6i | −1.09092 | + | 1.59841i | ||||
\(347\) | 2.37371e6 | + | 2.37371e6i | 1.05829 | + | 1.05829i | 0.998193 | + | 0.0600956i | \(0.0191405\pi\) |
0.0600956 | + | 0.998193i | \(0.480859\pi\) | |||||||
\(348\) | 824051. | + | 2.10569e6i | 0.364759 | + | 0.932066i | ||||
\(349\) | −1.11045e6 | + | 1.11045e6i | −0.488017 | + | 0.488017i | −0.907680 | − | 0.419663i | \(-0.862148\pi\) |
0.419663 | + | 0.907680i | \(0.362148\pi\) | |||||||
\(350\) | 360100. | − | 67952.4i | 0.157128 | − | 0.0296507i | ||||
\(351\) | −1.13243e6 | −0.490619 | ||||||||
\(352\) | −9567.67 | + | 1418.21i | −0.00411575 | + | 0.000610077i | ||||
\(353\) | 4.02943e6 | 1.72110 | 0.860551 | − | 0.509365i | \(-0.170120\pi\) | ||||
0.860551 | + | 0.509365i | \(0.170120\pi\) | |||||||
\(354\) | 1.74679e6 | − | 329627.i | 0.740853 | − | 0.139802i | ||||
\(355\) | −448774. | + | 448774.i | −0.188998 | + | 0.188998i | ||||
\(356\) | −362385. | − | 926000.i | −0.151546 | − | 0.387245i | ||||
\(357\) | 278326. | + | 278326.i | 0.115580 | + | 0.115580i | ||||
\(358\) | 879380. | − | 1.28846e6i | 0.362634 | − | 0.531329i | ||||
\(359\) | 2.88668e6i | 1.18212i | 0.806626 | + | 0.591062i | \(0.201291\pi\) | ||||
−0.806626 | + | 0.591062i | \(0.798709\pi\) | |||||||
\(360\) | 52671.1 | − | 229219.i | 0.0214198 | − | 0.0932168i | ||||
\(361\) | 2.04531e6i | 0.826022i | ||||||||
\(362\) | 2.76129e6 | + | 1.88459e6i | 1.10749 | + | 0.755868i | ||||
\(363\) | −1.57395e6 | − | 1.57395e6i | −0.626938 | − | 0.626938i | ||||
\(364\) | −844064. | − | 369243.i | −0.333904 | − | 0.146069i | ||||
\(365\) | 437199. | − | 437199.i | 0.171770 | − | 0.171770i | ||||
\(366\) | 578918. | + | 3.06786e6i | 0.225899 | + | 1.19711i | ||||
\(367\) | −1.53810e6 | −0.596100 | −0.298050 | − | 0.954550i | \(-0.596336\pi\) | ||||
−0.298050 | + | 0.954550i | \(0.596336\pi\) | |||||||
\(368\) | 2.20469e6 | + | 2.38541e6i | 0.848647 | + | 0.918214i | ||||
\(369\) | 664958. | 0.254231 | ||||||||
\(370\) | −199559. | − | 1.05752e6i | −0.0757820 | − | 0.401591i | ||||
\(371\) | −294884. | + | 294884.i | −0.111228 | + | 0.111228i | ||||
\(372\) | 1.52348e6 | − | 3.48257e6i | 0.570794 | − | 1.30479i | ||||
\(373\) | 665688. | + | 665688.i | 0.247741 | + | 0.247741i | 0.820043 | − | 0.572302i | \(-0.193949\pi\) |
−0.572302 | + | 0.820043i | \(0.693949\pi\) | |||||||
\(374\) | −2143.58 | − | 1463.00i | −0.000792429 | − | 0.000540836i | ||||
\(375\) | 215958.i | 0.0793034i | ||||||||
\(376\) | 2948.64 | − | 1846.73i | 0.00107560 | − | 0.000673651i | ||||
\(377\) | − | 1.42011e6i | − | 0.514597i | ||||||
\(378\) | 1.34752e6 | − | 1.97438e6i | 0.485072 | − | 0.710724i | ||||
\(379\) | 733269. | + | 733269.i | 0.262220 | + | 0.262220i | 0.825955 | − | 0.563736i | \(-0.190636\pi\) |
−0.563736 | + | 0.825955i | \(0.690636\pi\) | |||||||
\(380\) | −488966. | + | 191354.i | −0.173708 | + | 0.0679796i | ||||
\(381\) | −816019. | + | 816019.i | −0.287997 | + | 0.287997i | ||||
\(382\) | −2.76312e6 | + | 521413.i | −0.968816 | + | 0.182820i | ||||
\(383\) | −2.45123e6 | −0.853863 | −0.426931 | − | 0.904284i | \(-0.640405\pi\) | ||||
−0.426931 | + | 0.904284i | \(0.640405\pi\) | |||||||
\(384\) | 1.27340e6 | + | 2.22310e6i | 0.440692 | + | 0.769363i | ||||
\(385\) | −4326.70 | −0.00148766 | ||||||||
\(386\) | −2.57110e6 | + | 485178.i | −0.878315 | + | 0.165742i | ||||
\(387\) | −107009. | + | 107009.i | −0.0363197 | + | 0.0363197i | ||||
\(388\) | 1.43989e6 | − | 563494.i | 0.485569 | − | 0.190025i | ||||
\(389\) | 1.54868e6 | + | 1.54868e6i | 0.518906 | + | 0.518906i | 0.917240 | − | 0.398334i | \(-0.130412\pi\) |
−0.398334 | + | 0.917240i | \(0.630412\pi\) | |||||||
\(390\) | 306065. | − | 448445.i | 0.101895 | − | 0.149296i | ||||
\(391\) | 871558.i | 0.288307i | ||||||||
\(392\) | −930283. | + | 582637.i | −0.305774 | + | 0.191506i | ||||
\(393\) | − | 97539.1i | − | 0.0318564i | ||||||
\(394\) | −1.89181e6 | − | 1.29117e6i | −0.613955 | − | 0.419026i | ||||
\(395\) | 144610. | + | 144610.i | 0.0466344 | + | 0.0466344i | ||||
\(396\) | −1112.94 | + | 2544.11i | −0.000356644 | + | 0.000815263i | ||||
\(397\) | 552320. | − | 552320.i | 0.175879 | − | 0.175879i | −0.613678 | − | 0.789557i | \(-0.710311\pi\) |
0.789557 | + | 0.613678i | \(0.210311\pi\) | |||||||
\(398\) | −1.05931e6 | − | 5.61359e6i | −0.335209 | − | 1.77637i | ||||
\(399\) | −940258. | −0.295675 | ||||||||
\(400\) | 434393. | + | 470003.i | 0.135748 | + | 0.146876i | ||||
\(401\) | 4.92193e6 | 1.52853 | 0.764266 | − | 0.644901i | \(-0.223101\pi\) | ||||
0.764266 | + | 0.644901i | \(0.223101\pi\) | |||||||
\(402\) | −854652. | − | 4.52905e6i | −0.263769 | − | 1.39779i | ||||
\(403\) | −1.68807e6 | + | 1.68807e6i | −0.517760 | + | 0.517760i | ||||
\(404\) | −3.45070e6 | − | 1.50954e6i | −1.05185 | − | 0.460141i | ||||
\(405\) | 772853. | + | 772853.i | 0.234131 | + | 0.234131i | ||||
\(406\) | 2.47593e6 | + | 1.68984e6i | 0.745460 | + | 0.508779i | ||||
\(407\) | 12706.4i | 0.00380221i | ||||||||
\(408\) | −153949. | + | 669969.i | −0.0457853 | + | 0.199253i | ||||
\(409\) | − | 5.16304e6i | − | 1.52615i | −0.646311 | − | 0.763074i | \(-0.723689\pi\) | ||
0.646311 | − | 0.763074i | \(-0.276311\pi\) | |||||||
\(410\) | −1.02004e6 | + | 1.49455e6i | −0.299679 | + | 0.439088i | ||||
\(411\) | 3.12157e6 | + | 3.12157e6i | 0.911526 | + | 0.911526i | ||||
\(412\) | −290757. | − | 742970.i | −0.0843893 | − | 0.215639i | ||||
\(413\) | 1.66634e6 | − | 1.66634e6i | 0.480716 | − | 0.480716i | ||||
\(414\) | 916387. | − | 172926.i | 0.262771 | − | 0.0495862i | ||||
\(415\) | −2.60697e6 | −0.743046 | ||||||||
\(416\) | −235925. | − | 1.59162e6i | −0.0668406 | − | 0.450926i | ||||
\(417\) | −2.46303e6 | −0.693633 | ||||||||
\(418\) | 6091.99 | − | 1149.59i | 0.00170537 | − | 0.000321811i | ||||
\(419\) | 1.56043e6 | − | 1.56043e6i | 0.434219 | − | 0.434219i | −0.455842 | − | 0.890061i | \(-0.650662\pi\) |
0.890061 | + | 0.455842i | \(0.150662\pi\) | |||||||
\(420\) | 417659. | + | 1.06724e6i | 0.115531 | + | 0.295216i | ||||
\(421\) | −905154. | − | 905154.i | −0.248896 | − | 0.248896i | 0.571622 | − | 0.820517i | \(-0.306315\pi\) |
−0.820517 | + | 0.571622i | \(0.806315\pi\) | |||||||
\(422\) | −1.25050e6 | + | 1.83222e6i | −0.341823 | + | 0.500836i | ||||
\(423\) | − | 998.883i | − | 0.000271434i | ||||||
\(424\) | −709826. | − | 163108.i | −0.191751 | − | 0.0440615i | ||||
\(425\) | 171725.i | 0.0461170i | ||||||||
\(426\) | −1.63941e6 | − | 1.11891e6i | −0.437688 | − | 0.298724i | ||||
\(427\) | 2.92657e6 | + | 2.92657e6i | 0.776764 | + | 0.776764i | ||||
\(428\) | −3.59722e6 | − | 1.57363e6i | −0.949199 | − | 0.415235i | ||||
\(429\) | −4532.82 | + | 4532.82i | −0.00118912 | + | 0.00118912i | ||||
\(430\) | −76361.6 | − | 404662.i | −0.0199161 | − | 0.105541i | ||||
\(431\) | −1.58952e6 | −0.412168 | −0.206084 | − | 0.978534i | \(-0.566072\pi\) | ||||
−0.206084 | + | 0.978534i | \(0.566072\pi\) | |||||||
\(432\) | 4.17150e6 | + | 164246.i | 1.07543 | + | 0.0423434i | ||||
\(433\) | 6.53092e6 | 1.67400 | 0.836998 | − | 0.547205i | \(-0.184308\pi\) | ||||
0.836998 | + | 0.547205i | \(0.184308\pi\) | |||||||
\(434\) | −934432. | − | 4.95183e6i | −0.238135 | − | 1.26195i | ||||
\(435\) | −1.24914e6 | + | 1.24914e6i | −0.316512 | + | 0.316512i | ||||
\(436\) | 1.96948e6 | − | 4.50209e6i | 0.496175 | − | 1.13422i | ||||
\(437\) | −1.47218e6 | − | 1.47218e6i | −0.368771 | − | 0.368771i | ||||
\(438\) | 1.59713e6 | + | 1.09005e6i | 0.397791 | + | 0.271494i | ||||
\(439\) | 2.38268e6i | 0.590071i | 0.955486 | + | 0.295036i | \(0.0953315\pi\) | ||||
−0.955486 | + | 0.295036i | \(0.904669\pi\) | |||||||
\(440\) | −4010.88 | − | 6404.08i | −0.000987660 | − | 0.00157698i | ||||
\(441\) | 315143.i | 0.0771634i | ||||||||
\(442\) | 243376. | − | 356592.i | 0.0592545 | − | 0.0868193i | ||||
\(443\) | −32077.4 | − | 32077.4i | −0.00776586 | − | 0.00776586i | 0.703213 | − | 0.710979i | \(-0.251748\pi\) |
−0.710979 | + | 0.703213i | \(0.751748\pi\) | |||||||
\(444\) | 3.13421e6 | − | 1.22656e6i | 0.754520 | − | 0.295277i | ||||
\(445\) | 549324. | − | 549324.i | 0.131501 | − | 0.131501i | ||||
\(446\) | −5.07178e6 | + | 957067.i | −1.20732 | + | 0.227827i | ||||
\(447\) | −2.49731e6 | −0.591158 | ||||||||
\(448\) | 3.05570e6 | + | 1.48259e6i | 0.719309 | + | 0.349001i | ||||
\(449\) | 4.51574e6 | 1.05709 | 0.528547 | − | 0.848904i | \(-0.322737\pi\) | ||||
0.528547 | + | 0.848904i | \(0.322737\pi\) | |||||||
\(450\) | 180558. | − | 34072.0i | 0.0420324 | − | 0.00793170i | ||||
\(451\) | 15106.8 | − | 15106.8i | 0.00349728 | − | 0.00349728i | ||||
\(452\) | −2.86780e6 | + | 1.12230e6i | −0.660243 | + | 0.258382i | ||||
\(453\) | 3.06365e6 | + | 3.06365e6i | 0.701445 | + | 0.701445i | ||||
\(454\) | −784671. | + | 1.14969e6i | −0.178669 | + | 0.261784i | ||||
\(455\) | − | 719762.i | − | 0.162990i | ||||||
\(456\) | −871626. | − | 1.39171e6i | −0.196299 | − | 0.313426i | ||||
\(457\) | 1.27748e6i | 0.286131i | 0.989713 | + | 0.143065i | \(0.0456959\pi\) | ||||
−0.989713 | + | 0.143065i | \(0.954304\pi\) | |||||||
\(458\) | −5.58634e6 | − | 3.81270e6i | −1.24441 | − | 0.849316i | ||||
\(459\) | 792076. | + | 792076.i | 0.175483 | + | 0.175483i | ||||
\(460\) | −1.01706e6 | + | 2.32493e6i | −0.224105 | + | 0.512290i | ||||
\(461\) | −4.40915e6 | + | 4.40915e6i | −0.966279 | + | 0.966279i | −0.999450 | − | 0.0331708i | \(-0.989439\pi\) |
0.0331708 | + | 0.999450i | \(0.489439\pi\) | |||||||
\(462\) | −2509.14 | − | 13296.7i | −0.000546916 | − | 0.00289827i | ||||
\(463\) | −4.01094e6 | −0.869548 | −0.434774 | − | 0.900540i | \(-0.643172\pi\) | ||||
−0.434774 | + | 0.900540i | \(0.643172\pi\) | |||||||
\(464\) | −205970. | + | 5.23120e6i | −0.0444129 | + | 1.12799i | ||||
\(465\) | 2.96970e6 | 0.636914 | ||||||||
\(466\) | −35396.1 | − | 187574.i | −0.00755076 | − | 0.0400137i | ||||
\(467\) | 2.22576e6 | − | 2.22576e6i | 0.472266 | − | 0.472266i | −0.430381 | − | 0.902647i | \(-0.641621\pi\) |
0.902647 | + | 0.430381i | \(0.141621\pi\) | |||||||
\(468\) | −423222. | − | 185142.i | −0.0893210 | − | 0.0390742i | ||||
\(469\) | −4.32047e6 | − | 4.32047e6i | −0.906982 | − | 0.906982i | ||||
\(470\) | 2245.08 | + | 1532.28i | 0.000468800 | + | 0.000319958i | ||||
\(471\) | − | 4.93054e6i | − | 1.02410i | ||||||
\(472\) | 4.01111e6 | + | 921695.i | 0.828724 | + | 0.190429i | ||||
\(473\) | 4862.13i | 0.000999249i | ||||||||
\(474\) | −360550. | + | 528275.i | −0.0737088 | + | 0.107998i | ||||
\(475\) | −290066. | − | 290066.i | −0.0589878 | − | 0.0589878i | ||||
\(476\) | 332112. | + | 848644.i | 0.0671842 | + | 0.171675i | ||||
\(477\) | −147858. | + | 147858.i | −0.0297542 | + | 0.0297542i | ||||
\(478\) | −7.94360e6 | + | 1.49899e6i | −1.59018 | + | 0.300075i | ||||
\(479\) | 2.87342e6 | 0.572216 | 0.286108 | − | 0.958197i | \(-0.407638\pi\) | ||||
0.286108 | + | 0.958197i | \(0.407638\pi\) | |||||||
\(480\) | −1.19248e6 | + | 1.60753e6i | −0.236238 | + | 0.318461i | ||||
\(481\) | −2.11375e6 | −0.416574 | ||||||||
\(482\) | 2.15329e6 | − | 406336.i | 0.422168 | − | 0.0796650i | ||||
\(483\) | −3.21325e6 | + | 3.21325e6i | −0.626724 | + | 0.626724i | ||||
\(484\) | −1.87811e6 | − | 4.79913e6i | −0.364425 | − | 0.931214i | ||||
\(485\) | 854178. | + | 854178.i | 0.164890 | + | 0.164890i | ||||
\(486\) | 1.23228e6 | − | 1.80552e6i | 0.236656 | − | 0.346747i | ||||
\(487\) | 9.71226e6i | 1.85566i | 0.373007 | + | 0.927829i | \(0.378327\pi\) | ||||
−0.373007 | + | 0.927829i | \(0.621673\pi\) | |||||||
\(488\) | −1.61876e6 | + | 7.04466e6i | −0.307703 | + | 1.33909i | ||||
\(489\) | − | 5.52328e6i | − | 1.04454i | ||||||
\(490\) | −708313. | − | 483426.i | −0.133271 | − | 0.0909578i | ||||
\(491\) | 941766. | + | 941766.i | 0.176295 | + | 0.176295i | 0.789738 | − | 0.613444i | \(-0.210216\pi\) |
−0.613444 | + | 0.789738i | \(0.710216\pi\) | |||||||
\(492\) | −5.18456e6 | − | 2.26803e6i | −0.965605 | − | 0.422412i | ||||
\(493\) | −993289. | + | 993289.i | −0.184060 | + | 0.184060i | ||||
\(494\) | 191238. | + | 1.01343e6i | 0.0352579 | + | 0.186842i | ||||
\(495\) | −2169.45 | −0.000397957 | ||||||||
\(496\) | 6.46313e6 | − | 5.97346e6i | 1.17961 | − | 1.09024i | ||||
\(497\) | −2.63129e6 | −0.477834 | ||||||||
\(498\) | −1.51184e6 | − | 8.01167e6i | −0.273169 | − | 1.44760i | ||||
\(499\) | 1.63368e6 | − | 1.63368e6i | 0.293708 | − | 0.293708i | −0.544835 | − | 0.838543i | \(-0.683408\pi\) |
0.838543 | + | 0.544835i | \(0.183408\pi\) | |||||||
\(500\) | −200393. | + | 458086.i | −0.0358475 | + | 0.0819449i | ||||
\(501\) | −514158. | − | 514158.i | −0.0915171 | − | 0.0915171i | ||||
\(502\) | 998374. | + | 681394.i | 0.176821 | + | 0.120681i | ||||
\(503\) | − | 3.45939e6i | − | 0.609649i | −0.952409 | − | 0.304825i | \(-0.901402\pi\) | ||
0.952409 | − | 0.304825i | \(-0.0985978\pi\) | |||||||
\(504\) | 826400. | − | 517574.i | 0.144915 | − | 0.0907604i | ||||
\(505\) | − | 2.94253e6i | − | 0.513443i | ||||||
\(506\) | 16890.2 | − | 24747.4i | 0.00293264 | − | 0.00429689i | ||||
\(507\) | 2.87465e6 | + | 2.87465e6i | 0.496667 | + | 0.496667i | ||||
\(508\) | −2.48813e6 | + | 973714.i | −0.427773 | + | 0.167407i | ||||
\(509\) | 4.00462e6 | − | 4.00462e6i | 0.685120 | − | 0.685120i | −0.276029 | − | 0.961149i | \(-0.589019\pi\) |
0.961149 | + | 0.276029i | \(0.0890186\pi\) | |||||||
\(510\) | −527740. | + | 99586.9i | −0.0898451 | + | 0.0169542i | ||||
\(511\) | 2.56342e6 | 0.434278 | ||||||||
\(512\) | 638223. | + | 5.89721e6i | 0.107596 | + | 0.994195i | ||||
\(513\) | −2.67584e6 | −0.448918 | ||||||||
\(514\) | 6.15756e6 | − | 1.16196e6i | 1.02802 | − | 0.193992i | ||||
\(515\) | 440747. | − | 440747.i | 0.0732270 | − | 0.0732270i | ||||
\(516\) | 1.19931e6 | − | 469345.i | 0.198293 | − | 0.0776011i | ||||
\(517\) | −22.6930 | − | 22.6930i | −3.73392e−6 | − | 3.73392e-6i | ||||
\(518\) | 2.51523e6 | − | 3.68530e6i | 0.411864 | − | 0.603460i | ||||
\(519\) | − | 1.05291e7i | − | 1.71583i | ||||||
\(520\) | 1.06534e6 | − | 667224.i | 0.172775 | − | 0.108209i | ||||
\(521\) | − | 3.26819e6i | − | 0.527489i | −0.964593 | − | 0.263744i | \(-0.915042\pi\) | ||
0.964593 | − | 0.263744i | \(-0.0849575\pi\) | |||||||
\(522\) | 1.24146e6 | + | 847300.i | 0.199414 | + | 0.136101i | ||||
\(523\) | 2.30613e6 | + | 2.30613e6i | 0.368662 | + | 0.368662i | 0.866989 | − | 0.498327i | \(-0.166052\pi\) |
−0.498327 | + | 0.866989i | \(0.666052\pi\) | |||||||
\(524\) | 90509.1 | − | 206898.i | 0.0144000 | − | 0.0329175i | ||||
\(525\) | −633112. | + | 633112.i | −0.100250 | + | 0.100250i | ||||
\(526\) | −174356. | − | 923962.i | −0.0274772 | − | 0.145610i | ||||
\(527\) | 2.36143e6 | 0.370382 | ||||||||
\(528\) | 17354.9 | − | 16040.0i | 0.00270917 | − | 0.00250391i | ||||
\(529\) | −3.62572e6 | −0.563320 | ||||||||
\(530\) | −105511. | − | 559136.i | −0.0163159 | − | 0.0864624i | ||||
\(531\) | 835520. | − | 835520.i | 0.128594 | − | 0.128594i | ||||
\(532\) | −1.99445e6 | − | 872491.i | −0.305524 | − | 0.133654i | ||||
\(533\) | 2.51306e6 | + | 2.51306e6i | 0.383165 | + | 0.383165i | ||||
\(534\) | 2.00673e6 | + | 1.36960e6i | 0.304535 | + | 0.207846i | ||||
\(535\) | − | 3.06747e6i | − | 0.463335i | ||||||
\(536\) | 2.38976e6 | − | 1.04000e7i | 0.359288 | − | 1.56358i | ||||
\(537\) | 3.81141e6i | 0.570361i | ||||||||
\(538\) | 5.45447e6 | − | 7.99184e6i | 0.812450 | − | 1.19040i | ||||
\(539\) | 7159.53 | + | 7159.53i | 0.00106148 | + | 0.00106148i | ||||
\(540\) | 1.18860e6 | + | 3.03722e6i | 0.175409 | + | 0.448220i | ||||
\(541\) | −8.57389e6 | + | 8.57389e6i | −1.25946 | + | 1.25946i | −0.308111 | + | 0.951350i | \(0.599697\pi\) |
−0.951350 | + | 0.308111i | \(0.900303\pi\) | |||||||
\(542\) | −9.92221e6 | + | 1.87237e6i | −1.45081 | + | 0.273774i | ||||
\(543\) | −8.16820e6 | −1.18885 | ||||||||
\(544\) | −948235. | + | 1.27827e6i | −0.137378 | + | 0.185193i | ||||
\(545\) | 3.83908e6 | 0.553651 | ||||||||
\(546\) | 2.21195e6 | − | 417405.i | 0.317537 | − | 0.0599206i | ||||
\(547\) | −552021. | + | 552021.i | −0.0788837 | + | 0.0788837i | −0.745448 | − | 0.666564i | \(-0.767764\pi\) |
0.666564 | + | 0.745448i | \(0.267764\pi\) | |||||||
\(548\) | 3.72481e6 | + | 9.51799e6i | 0.529850 | + | 1.35392i | ||||
\(549\) | 1.46741e6 | + | 1.46741e6i | 0.207788 | + | 0.207788i | ||||
\(550\) | 3327.91 | − | 4876.03i | 0.000469100 | − | 0.000687321i | ||||
\(551\) | − | 3.35559e6i | − | 0.470858i | ||||||
\(552\) | −7.73473e6 | − | 1.77733e6i | −1.08043 | − | 0.248267i | ||||
\(553\) | 847891.i | 0.117904i | ||||||||
\(554\) | 8.00450e6 | + | 5.46310e6i | 1.10805 | + | 0.756249i | ||||
\(555\) | 1.85929e6 | + | 1.85929e6i | 0.256220 | + | 0.256220i | ||||
\(556\) | −5.22453e6 | − | 2.28551e6i | −0.716737 | − | 0.313543i | ||||
\(557\) | −8.78654e6 | + | 8.78654e6i | −1.20000 | + | 1.20000i | −0.225829 | + | 0.974167i | \(0.572509\pi\) |
−0.974167 | + | 0.225829i | \(0.927491\pi\) | |||||||
\(558\) | −468534. | − | 2.48290e6i | −0.0637023 | − | 0.337577i | ||||
\(559\) | −808833. | −0.109479 | ||||||||
\(560\) | −104393. | + | 2.65136e6i | −0.0140670 | + | 0.357272i | ||||
\(561\) | 6340.94 | 0.000850641 | ||||||||
\(562\) | 2.44846e6 | + | 1.29751e7i | 0.327003 | + | 1.73288i | ||||
\(563\) | 971504. | − | 971504.i | 0.129174 | − | 0.129174i | −0.639564 | − | 0.768738i | \(-0.720885\pi\) |
0.768738 | + | 0.639564i | \(0.220885\pi\) | |||||||
\(564\) | −3406.98 | + | 7788.12i | −0.000450995 | + | 0.00103094i | ||||
\(565\) | −1.70125e6 | − | 1.70125e6i | −0.224206 | − | 0.224206i | ||||
\(566\) | 9.64681e6 | + | 6.58399e6i | 1.26573 | + | 0.863869i | ||||
\(567\) | 4.53145e6i | 0.591943i | ||||||||
\(568\) | −2.43922e6 | − | 3.89465e6i | −0.317234 | − | 0.506521i | ||||
\(569\) | − | 2.27634e6i | − | 0.294752i | −0.989081 | − | 0.147376i | \(-0.952917\pi\) | ||
0.989081 | − | 0.147376i | \(-0.0470828\pi\) | |||||||
\(570\) | 723207. | − | 1.05964e6i | 0.0932343 | − | 0.136606i | ||||
\(571\) | 8.52439e6 | + | 8.52439e6i | 1.09414 | + | 1.09414i | 0.995082 | + | 0.0990592i | \(0.0315833\pi\) |
0.0990592 | + | 0.995082i | \(0.468417\pi\) | |||||||
\(572\) | −13821.0 | + | 5408.79i | −0.00176624 | + | 0.000691210i | ||||
\(573\) | 4.85800e6 | − | 4.85800e6i | 0.618118 | − | 0.618118i | ||||
\(574\) | −7.37188e6 | + | 1.39111e6i | −0.933896 | + | 0.176230i | ||||
\(575\) | −1.98255e6 | −0.250066 | ||||||||
\(576\) | 1.53216e6 | + | 743386.i | 0.192419 | + | 0.0933594i | ||||
\(577\) | −1.05005e7 | −1.31301 | −0.656506 | − | 0.754321i | \(-0.727966\pi\) | ||||
−0.656506 | + | 0.754321i | \(0.727966\pi\) | |||||||
\(578\) | 7.47298e6 | − | 1.41019e6i | 0.930410 | − | 0.175573i | ||||
\(579\) | 4.52040e6 | − | 4.52040e6i | 0.560377 | − | 0.560377i | ||||
\(580\) | −3.80877e6 | + | 1.49054e6i | −0.470126 | + | 0.183981i | ||||
\(581\) | −7.64270e6 | − | 7.64270e6i | −0.939304 | − | 0.939304i | ||||
\(582\) | −2.12968e6 | + | 3.12039e6i | −0.260619 | + | 0.381858i | ||||
\(583\) | 6718.17i | 0.000818615i | ||||||||
\(584\) | 2.37631e6 | + | 3.79420e6i | 0.288317 | + | 0.460350i | ||||
\(585\) | − | 360896.i | − | 0.0436006i | ||||||
\(586\) | 1.77395e6 | + | 1.21073e6i | 0.213401 | + | 0.145647i | ||||
\(587\) | −8.30426e6 | − | 8.30426e6i | −0.994731 | − | 0.994731i | 0.00525489 | − | 0.999986i | \(-0.498327\pi\) |
−0.999986 | + | 0.00525489i | \(0.998327\pi\) | |||||||
\(588\) | 1.07489e6 | − | 2.45712e6i | 0.128209 | − | 0.293077i | ||||
\(589\) | −3.98877e6 | + | 3.98877e6i | −0.473752 | + | 0.473752i | ||||
\(590\) | 596228. | + | 3.15959e6i | 0.0705152 | + | 0.373680i | ||||
\(591\) | 5.59617e6 | 0.659056 | ||||||||
\(592\) | 7.78636e6 | + | 306576.i | 0.913126 | + | 0.0359529i | ||||
\(593\) | 1.25153e7 | 1.46152 | 0.730759 | − | 0.682635i | \(-0.239166\pi\) | ||||
0.730759 | + | 0.682635i | \(0.239166\pi\) | |||||||
\(594\) | −7140.67 | − | 37840.5i | −0.000830372 | − | 0.00440038i | ||||
\(595\) | −503435. | + | 503435.i | −0.0582977 | + | 0.0582977i | ||||
\(596\) | −5.29723e6 | − | 2.31732e6i | −0.610848 | − | 0.267221i | ||||
\(597\) | 9.86958e6 | + | 9.86958e6i | 1.13335 | + | 1.13335i | ||||
\(598\) | 4.11683e6 | + | 2.80975e6i | 0.470771 | + | 0.321303i | ||||
\(599\) | − | 6.70362e6i | − | 0.763383i | −0.924290 | − | 0.381691i | \(-0.875342\pi\) | ||
0.924290 | − | 0.381691i | \(-0.124658\pi\) | |||||||
\(600\) | −1.52399e6 | − | 350190.i | −0.172824 | − | 0.0397124i | ||||
\(601\) | − | 5.33668e6i | − | 0.602677i | −0.953517 | − | 0.301339i | \(-0.902567\pi\) | ||
0.953517 | − | 0.301339i | \(-0.0974335\pi\) | |||||||
\(602\) | 962460. | − | 1.41019e6i | 0.108241 | − | 0.158594i | ||||
\(603\) | −2.16633e6 | − | 2.16633e6i | −0.242622 | − | 0.242622i | ||||
\(604\) | 3.65570e6 | + | 9.34138e6i | 0.407735 | + | 1.04188i | ||||
\(605\) | 2.84696e6 | − | 2.84696e6i | 0.316222 | − | 0.316222i | ||||
\(606\) | 9.04289e6 | − | 1.70643e6i | 1.00029 | − | 0.188759i | ||||
\(607\) | 871941. | 0.0960540 | 0.0480270 | − | 0.998846i | \(-0.484707\pi\) | ||||
0.0480270 | + | 0.998846i | \(0.484707\pi\) | |||||||
\(608\) | −557471. | − | 3.76086e6i | −0.0611594 | − | 0.412599i | ||||
\(609\) | −7.32408e6 | −0.800221 | ||||||||
\(610\) | −5.54913e6 | + | 1.04715e6i | −0.603810 | + | 0.113942i | ||||
\(611\) | 3775.06 | − | 3775.06i | 0.000409092 | − | 0.000409092i | ||||
\(612\) | 166524. | + | 425519.i | 0.0179721 | + | 0.0459240i | ||||
\(613\) | 7.72342e6 | + | 7.72342e6i | 0.830154 | + | 0.830154i | 0.987537 | − | 0.157384i | \(-0.0503060\pi\) |
−0.157384 | + | 0.987537i | \(0.550306\pi\) | |||||||
\(614\) | −5.90228e6 | + | 8.64798e6i | −0.631828 | + | 0.925750i | ||||
\(615\) | − | 4.42105e6i | − | 0.471344i | ||||||
\(616\) | 7016.01 | − | 30532.9i | 0.000744969 | − | 0.00324202i | ||||
\(617\) | − | 644309.i | − | 0.0681367i | −0.999420 | − | 0.0340684i | \(-0.989154\pi\) | ||
0.999420 | − | 0.0340684i | \(-0.0108464\pi\) | |||||||
\(618\) | 1.61009e6 | + | 1.09889e6i | 0.169582 | + | 0.115740i | ||||
\(619\) | −1.08770e7 | − | 1.08770e7i | −1.14099 | − | 1.14099i | −0.988269 | − | 0.152725i | \(-0.951195\pi\) |
−0.152725 | − | 0.988269i | \(-0.548805\pi\) | |||||||
\(620\) | 6.29926e6 | + | 2.75567e6i | 0.658128 | + | 0.287904i | ||||
\(621\) | −9.14445e6 | + | 9.14445e6i | −0.951543 | + | 0.951543i | ||||
\(622\) | 3.21794e6 | + | 1.70528e7i | 0.333504 | + | 1.76734i | ||||
\(623\) | 3.22084e6 | 0.332468 | ||||||||
\(624\) | 2.66831e6 | + | 2.88704e6i | 0.274331 | + | 0.296819i | ||||
\(625\) | −390625. | −0.0400000 | ||||||||
\(626\) | 2.38574e6 | + | 1.26427e7i | 0.243326 | + | 1.28945i | ||||
\(627\) | −10710.7 | + | 10710.7i | −0.00108805 | + | 0.00108805i | ||||
\(628\) | 4.57518e6 | − | 1.04586e7i | 0.462924 | − | 1.05821i | ||||
\(629\) | 1.47846e6 | + | 1.47846e6i | 0.148999 | + | 0.148999i | ||||
\(630\) | 629216. | + | 429443.i | 0.0631610 | + | 0.0431076i | ||||
\(631\) | − | 1.93042e6i | − | 0.193010i | −0.995333 | − | 0.0965048i | \(-0.969234\pi\) | ||
0.995333 | − | 0.0965048i | \(-0.0307663\pi\) | |||||||
\(632\) | −1.25499e6 | + | 786001.i | −0.124982 | + | 0.0782763i | ||||
\(633\) | − | 5.41990e6i | − | 0.537628i | ||||||
\(634\) | −1.10402e7 | + | 1.61760e7i | −1.09082 | + | 1.59826i | ||||
\(635\) | −1.47601e6 | − | 1.47601e6i | −0.145263 | − | 0.145263i | ||||
\(636\) | 1.65713e6 | − | 648510.i | 0.162448 | − | 0.0635731i | ||||
\(637\) | −1.19102e6 | + | 1.19102e6i | −0.116297 | + | 0.116297i | ||||
\(638\) | 47453.2 | − | 8954.63i | 0.00461545 | − | 0.000870955i | ||||
\(639\) | −1.31935e6 | −0.127823 | ||||||||
\(640\) | −4.02114e6 | + | 2.30332e6i | −0.388060 | + | 0.222282i | ||||
\(641\) | 4.63206e6 | 0.445275 | 0.222638 | − | 0.974901i | \(-0.428533\pi\) | ||||
0.222638 | + | 0.974901i | \(0.428533\pi\) | |||||||
\(642\) | 9.42686e6 | − | 1.77889e6i | 0.902671 | − | 0.170338i | ||||
\(643\) | −8.05489e6 | + | 8.05489e6i | −0.768303 | + | 0.768303i | −0.977808 | − | 0.209505i | \(-0.932815\pi\) |
0.209505 | + | 0.977808i | \(0.432815\pi\) | |||||||
\(644\) | −9.79752e6 | + | 3.83421e6i | −0.930897 | + | 0.364301i | ||||
\(645\) | 711460. | + | 711460.i | 0.0673366 | + | 0.0673366i | ||||
\(646\) | 575076. | − | 842598.i | 0.0542181 | − | 0.0794400i | ||||
\(647\) | − | 5.33268e6i | − | 0.500824i | −0.968139 | − | 0.250412i | \(-0.919434\pi\) | ||
0.968139 | − | 0.250412i | \(-0.0805660\pi\) | |||||||
\(648\) | −6.70715e6 | + | 4.20069e6i | −0.627481 | + | 0.392991i | ||||
\(649\) | − | 37963.3i | − | 0.00353795i | ||||||
\(650\) | 811146. | + | 553610.i | 0.0753036 | + | 0.0513950i | ||||
\(651\) | 8.70610e6 | + | 8.70610e6i | 0.805139 | + | 0.805139i | ||||
\(652\) | 5.12520e6 | − | 1.17159e7i | 0.472163 | − | 1.07933i | ||||
\(653\) | 316713. | − | 316713.i | 0.0290659 | − | 0.0290659i | −0.692424 | − | 0.721490i | \(-0.743457\pi\) |
0.721490 | + | 0.692424i | \(0.243457\pi\) | |||||||
\(654\) | 2.22637e6 | + | 1.17982e7i | 0.203541 | + | 1.07862i | ||||
\(655\) | 176428. | 0.0160681 | ||||||||
\(656\) | −8.89280e6 | − | 9.62179e6i | −0.806825 | − | 0.872963i | ||||
\(657\) | 1.28532e6 | 0.116171 | ||||||||
\(658\) | 2089.68 | + | 11073.8i | 0.000188155 | + | 0.000997089i | ||||
\(659\) | 1.13480e7 | − | 1.13480e7i | 1.01790 | − | 1.01790i | 0.0180657 | − | 0.999837i | \(-0.494249\pi\) |
0.999837 | − | 0.0180657i | \(-0.00575081\pi\) | |||||||
\(660\) | 16914.8 | + | 7399.53i | 0.00151150 | + | 0.000661218i | ||||
\(661\) | −8.40738e6 | − | 8.40738e6i | −0.748440 | − | 0.748440i | 0.225746 | − | 0.974186i | \(-0.427518\pi\) |
−0.974186 | + | 0.225746i | \(0.927518\pi\) | |||||||
\(662\) | −5.19924e6 | − | 3.54850e6i | −0.461100 | − | 0.314702i | ||||
\(663\) | 1.05484e6i | 0.0931971i | ||||||||
\(664\) | 4.22736e6 | − | 1.83970e7i | 0.372091 | − | 1.61930i | ||||
\(665\) | − | 1.70074e6i | − | 0.149136i | ||||||
\(666\) | 1.26116e6 | − | 1.84785e6i | 0.110176 | − | 0.161428i | ||||
\(667\) | −1.14674e7 | − | 1.14674e7i | −0.998048 | − | 0.998048i | ||||
\(668\) | −613519. | − | 1.56772e6i | −0.0531969 | − | 0.135934i | ||||
\(669\) | 8.91699e6 | − | 8.91699e6i | 0.770288 | − | 0.770288i | ||||
\(670\) | 8.19214e6 | − | 1.54589e6i | 0.705034 | − | 0.133043i | ||||
\(671\) | 66674.3 | 0.00571679 | ||||||||
\(672\) | −8.20864e6 | + | 1.21676e6i | −0.701210 | + | 0.103940i | ||||
\(673\) | −1.83364e7 | −1.56054 | −0.780272 | − | 0.625440i | \(-0.784920\pi\) | ||||
−0.780272 | + | 0.625440i | \(0.784920\pi\) | |||||||
\(674\) | 8.48350e6 | − | 1.60087e6i | 0.719325 | − | 0.135740i | ||||
\(675\) | −1.80175e6 | + | 1.80175e6i | −0.152207 | + | 0.152207i | ||||
\(676\) | 3.43018e6 | + | 8.76511e6i | 0.288702 | + | 0.737719i | ||||
\(677\) | −1.19331e6 | − | 1.19331e6i | −0.100065 | − | 0.100065i | 0.655302 | − | 0.755367i | \(-0.272541\pi\) |
−0.755367 | + | 0.655302i | \(0.772541\pi\) | |||||||
\(678\) | 4.24164e6 | − | 6.21482e6i | 0.354372 | − | 0.519223i | ||||
\(679\) | 5.00828e6i | 0.416883i | ||||||||
\(680\) | −1.21184e6 | − | 278463.i | −0.100501 | − | 0.0230938i | ||||
\(681\) | − | 3.40092e6i | − | 0.281015i | ||||||
\(682\) | −67051.7 | − | 45763.0i | −0.00552012 | − | 0.00376750i | ||||
\(683\) | −2.57827e6 | − | 2.57827e6i | −0.211483 | − | 0.211483i | 0.593414 | − | 0.804897i | \(-0.297780\pi\) |
−0.804897 | + | 0.593414i | \(0.797780\pi\) | |||||||
\(684\) | −1.00004e6 | − | 437475.i | −0.0817291 | − | 0.0357531i | ||||
\(685\) | −5.64629e6 | + | 5.64629e6i | −0.459766 | + | 0.459766i | ||||
\(686\) | −2.48661e6 | − | 1.31773e7i | −0.201742 | − | 1.06909i | ||||
\(687\) | 1.65250e7 | 1.33583 | ||||||||
\(688\) | 2.97947e6 | + | 117312.i | 0.239976 | + | 0.00944868i | ||||
\(689\) | −1.11759e6 | −0.0896882 | ||||||||
\(690\) | −1.14972e6 | − | 6.09271e6i | −0.0919327 | − | 0.487178i | ||||
\(691\) | 2.88279e6 | − | 2.88279e6i | 0.229678 | − | 0.229678i | −0.582880 | − | 0.812558i | \(-0.698074\pi\) |
0.812558 | + | 0.582880i | \(0.198074\pi\) | |||||||
\(692\) | 9.77023e6 | − | 2.23341e7i | 0.775603 | − | 1.77298i | ||||
\(693\) | −6360.04 | − | 6360.04i | −0.000503068 | − | 0.000503068i | ||||
\(694\) | −1.56848e7 | − | 1.07049e7i | −1.23617 | − | 0.843694i | ||||
\(695\) | − | 4.45513e6i | − | 0.349863i | ||||||
\(696\) | −6.78948e6 | − | 1.08406e7i | −0.531267 | − | 0.848263i | ||||
\(697\) | − | 3.51551e6i | − | 0.274098i | ||||||
\(698\) | 5.00789e6 | − | 7.33752e6i | 0.389060 | − | 0.570047i | ||||
\(699\) | 329785. | + | 329785.i | 0.0255293 | + | 0.0255293i | ||||
\(700\) | −1.93042e6 | + | 755461.i | −0.148904 | + | 0.0582729i | ||||
\(701\) | −5.60275e6 | + | 5.60275e6i | −0.430632 | + | 0.430632i | −0.888843 | − | 0.458211i | \(-0.848490\pi\) |
0.458211 | + | 0.888843i | \(0.348490\pi\) | |||||||
\(702\) | 6.29490e6 | − | 1.18788e6i | 0.482110 | − | 0.0909763i | ||||
\(703\) | −4.99462e6 | −0.381166 | ||||||||
\(704\) | 51696.6 | − | 17919.6i | 0.00393125 | − | 0.00136269i | ||||
\(705\) | −6641.19 | −0.000503238 | ||||||||
\(706\) | −2.23986e7 | + | 4.22671e6i | −1.69125 | + | 0.319147i | ||||
\(707\) | 8.62643e6 | − | 8.62643e6i | 0.649056 | − | 0.649056i | ||||
\(708\) | −9.36419e6 | + | 3.66462e6i | −0.702081 | + | 0.274755i | ||||
\(709\) | −1.35415e6 | − | 1.35415e6i | −0.101170 | − | 0.101170i | 0.654710 | − | 0.755880i | \(-0.272791\pi\) |
−0.755880 | + | 0.654710i | \(0.772791\pi\) | |||||||
\(710\) | 2.02387e6 | − | 2.96537e6i | 0.150674 | − | 0.220766i | ||||
\(711\) | 425141.i | 0.0315398i | ||||||||
\(712\) | 2.98574e6 | + | 4.76727e6i | 0.220725 | + | 0.352428i | ||||
\(713\) | 2.72625e7i | 2.00836i | ||||||||
\(714\) | −1.83910e6 | − | 1.25519e6i | −0.135008 | − | 0.0921434i | ||||
\(715\) | −8198.96 | − | 8198.96i | −0.000599782 | − | 0.000599782i | ||||
\(716\) | −3.53671e6 | + | 8.08467e6i | −0.257820 | + | 0.589359i | ||||
\(717\) | 1.39661e7 | − | 1.39661e7i | 1.01456 | − | 1.01456i | ||||
\(718\) | −3.02802e6 | − | 1.60463e7i | −0.219203 | − | 1.16162i | ||||
\(719\) | 2.32962e6 | 0.168059 | 0.0840297 | − | 0.996463i | \(-0.473221\pi\) | ||||
0.0840297 | + | 0.996463i | \(0.473221\pi\) | |||||||
\(720\) | −52343.8 | + | 1.32942e6i | −0.00376300 | + | 0.0955720i | ||||
\(721\) | 2.58422e6 | 0.185136 | ||||||||
\(722\) | −2.14545e6 | − | 1.13694e7i | −0.153171 | − | 0.811696i | ||||
\(723\) | −3.78583e6 | + | 3.78583e6i | −0.269349 | + | 0.269349i | ||||
\(724\) | −1.73262e7 | − | 7.57948e6i | −1.22845 | − | 0.537395i | ||||
\(725\) | −2.25945e6 | − | 2.25945e6i | −0.159646 | − | 0.159646i | ||||
\(726\) | 1.04002e7 | + | 7.09818e6i | 0.732319 | + | 0.499811i | ||||
\(727\) | 7.09851e6i | 0.498117i | 0.968488 | + | 0.249058i | \(0.0801211\pi\) | ||||
−0.968488 | + | 0.249058i | \(0.919879\pi\) | |||||||
\(728\) | 5.07926e6 | + | 1.16714e6i | 0.355199 | + | 0.0816195i | ||||
\(729\) | 1.59647e7i | 1.11261i | ||||||||
\(730\) | −1.97168e6 | + | 2.88889e6i | −0.136939 | + | 0.200643i | ||||
\(731\) | 565736. | + | 565736.i | 0.0391580 | + | 0.0391580i | ||||
\(732\) | −6.43612e6 | − | 1.64462e7i | −0.443963 | − | 1.13446i | ||||
\(733\) | −4.97014e6 | + | 4.97014e6i | −0.341672 | + | 0.341672i | −0.856995 | − | 0.515324i | \(-0.827672\pi\) |
0.515324 | + | 0.856995i | \(0.327672\pi\) | |||||||
\(734\) | 8.54990e6 | − | 1.61340e6i | 0.585762 | − | 0.110536i | ||||
\(735\) | 2.09527e6 | 0.143061 | ||||||||
\(736\) | −1.47575e7 | − | 1.09473e7i | −1.00420 | − | 0.744924i | ||||
\(737\) | −98430.8 | −0.00667517 | ||||||||
\(738\) | −3.69633e6 | + | 697515.i | −0.249822 | + | 0.0471425i | ||||
\(739\) | −3.33606e6 | + | 3.33606e6i | −0.224710 | + | 0.224710i | −0.810478 | − | 0.585768i | \(-0.800793\pi\) |
0.585768 | + | 0.810478i | \(0.300793\pi\) | |||||||
\(740\) | 2.21859e6 | + | 5.66915e6i | 0.148935 | + | 0.380574i | ||||
\(741\) | −1.78176e6 | − | 1.78176e6i | −0.119208 | − | 0.119208i | ||||
\(742\) | 1.32986e6 | − | 1.94851e6i | 0.0886742 | − | 0.129925i | ||||
\(743\) | 1.56473e7i | 1.03985i | 0.854213 | + | 0.519923i | \(0.174039\pi\) | ||||
−0.854213 | + | 0.519923i | \(0.825961\pi\) | |||||||
\(744\) | −4.81556e6 | + | 2.09568e7i | −0.318944 | + | 1.38801i | ||||
\(745\) | − | 4.51713e6i | − | 0.298175i | ||||||
\(746\) | −4.39867e6 | − | 3.00211e6i | −0.289384 | − | 0.197506i | ||||
\(747\) | −3.83212e6 | − | 3.83212e6i | −0.251268 | − | 0.251268i | ||||
\(748\) | 13450.2 | + | 5883.93i | 0.000878975 | + | 0.000384515i | ||||
\(749\) | 8.99271e6 | − | 8.99271e6i | 0.585714 | − | 0.585714i | ||||
\(750\) | −226532. | − | 1.20046e6i | −0.0147054 | − | 0.0779281i | ||||
\(751\) | 2.63215e7 | 1.70298 | 0.851491 | − | 0.524369i | \(-0.175699\pi\) | ||||
0.851491 | + | 0.524369i | \(0.175699\pi\) | |||||||
\(752\) | −14453.6 | + | 13358.5i | −0.000932033 | + | 0.000861419i | ||||
\(753\) | −2.95330e6 | −0.189810 | ||||||||
\(754\) | 1.48964e6 | + | 7.89401e6i | 0.0954227 | + | 0.505673i | ||||
\(755\) | −5.54152e6 | + | 5.54152e6i | −0.353803 | + | 0.353803i | ||||
\(756\) | −5.41949e6 | + | 1.23886e7i | −0.344869 | + | 0.788346i | ||||
\(757\) | −6.68400e6 | − | 6.68400e6i | −0.423932 | − | 0.423932i | 0.462623 | − | 0.886555i | \(-0.346908\pi\) |
−0.886555 | + | 0.462623i | \(0.846908\pi\) | |||||||
\(758\) | −4.84523e6 | − | 3.30689e6i | −0.306296 | − | 0.209048i | ||||
\(759\) | 73205.6i | 0.00461254i | ||||||||
\(760\) | 2.51732e6 | − | 1.57660e6i | 0.158090 | − | 0.0990116i | ||||
\(761\) | 2.40574e7i | 1.50587i | 0.658096 | + | 0.752934i | \(0.271362\pi\) | ||||
−0.658096 | + | 0.752934i | \(0.728638\pi\) | |||||||
\(762\) | 3.68007e6 | − | 5.39202e6i | 0.229599 | − | 0.336406i | ||||
\(763\) | 1.12548e7 | + | 1.12548e7i | 0.699885 | + | 0.699885i | ||||
\(764\) | 1.48125e7 | − | 5.79681e6i | 0.918113 | − | 0.359299i | ||||
\(765\) | −252427. | + | 252427.i | −0.0155949 | + | 0.0155949i | ||||
\(766\) | 1.36258e7 | − | 2.57125e6i | 0.839054 | − | 0.158333i | ||||
\(767\) | 6.31534e6 | 0.387622 | ||||||||
\(768\) | −9.41044e6 | − | 1.10219e7i | −0.575714 | − | 0.674301i | ||||
\(769\) | −4.66056e6 | −0.284199 | −0.142099 | − | 0.989852i | \(-0.545385\pi\) | ||||
−0.142099 | + | 0.989852i | \(0.545385\pi\) | |||||||
\(770\) | 24051.0 | − | 4538.53i | 0.00146186 | − | 0.000275860i | ||||
\(771\) | −1.08260e7 | + | 1.08260e7i | −0.655890 | + | 0.655890i | ||||
\(772\) | 1.37832e7 | − | 5.39396e6i | 0.832349 | − | 0.325735i | ||||
\(773\) | 5.41580e6 | + | 5.41580e6i | 0.325997 | + | 0.325997i | 0.851062 | − | 0.525065i | \(-0.175959\pi\) |
−0.525065 | + | 0.851062i | \(0.675959\pi\) | |||||||
\(774\) | 482587. | − | 707083.i | 0.0289550 | − | 0.0424246i | ||||
\(775\) | 5.37159e6i | 0.321254i | ||||||||
\(776\) | −7.41292e6 | + | 4.64271e6i | −0.441911 | + | 0.276769i | ||||
\(777\) | 1.09015e7i | 0.647790i | ||||||||
\(778\) | −1.02333e7 | − | 6.98423e6i | −0.606128 | − | 0.413685i | ||||
\(779\) | 5.93816e6 | + | 5.93816e6i | 0.350597 | + | 0.350597i | ||||
\(780\) | −1.23094e6 | + | 2.81384e6i | −0.0724436 | + | 0.165601i | ||||
\(781\) | −29973.5 | + | 29973.5i | −0.00175837 | + | 0.00175837i | ||||
\(782\) | −914230. | − | 4.84477e6i | −0.0534612 | − | 0.283307i | ||||
\(783\) | −2.08433e7 | −1.21496 | ||||||||
\(784\) | 4.56005e6 | − | 4.21456e6i | 0.264959 | − | 0.244885i | ||||
\(785\) | 8.91836e6 | 0.516548 | ||||||||
\(786\) | 102315. | + | 542195.i | 0.00590720 | + | 0.0313040i | ||||
\(787\) | 1.95136e7 | − | 1.95136e7i | 1.12306 | − | 1.12306i | 0.131777 | − | 0.991279i | \(-0.457932\pi\) |
0.991279 | − | 0.131777i | \(-0.0420681\pi\) | |||||||
\(788\) | 1.18705e7 | + | 5.19283e6i | 0.681008 | + | 0.297913i | ||||
\(789\) | 1.62447e6 | + | 1.62447e6i | 0.0929009 | + | 0.0929009i | ||||
\(790\) | −955543. | − | 652162.i | −0.0544732 | − | 0.0371781i | ||||
\(791\) | − | 9.97489e6i | − | 0.566849i | ||||||
\(792\) | 3517.90 | − | 15309.5i | 0.000199283 | − | 0.000867257i | ||||
\(793\) | 1.10915e7i | 0.626337i | ||||||||
\(794\) | −2.49084e6 | + | 3.64957e6i | −0.140215 | + | 0.205442i | ||||
\(795\) | 983049. | + | 983049.i | 0.0551642 | + | 0.0551642i | ||||
\(796\) | 1.17769e7 | + | 3.00934e7i | 0.658791 | + | 1.68340i | ||||
\(797\) | 4.44673e6 | − | 4.44673e6i | 0.247968 | − | 0.247968i | −0.572168 | − | 0.820136i | \(-0.693898\pi\) |
0.820136 | + | 0.572168i | \(0.193898\pi\) | |||||||
\(798\) | 5.22666e6 | − | 986294.i | 0.290547 | − | 0.0548276i | ||||
\(799\) | −5280.91 | −0.000292646 | ||||||||
\(800\) | −2.90770e6 | − | 2.15696e6i | −0.160629 | − | 0.119157i | ||||
\(801\) | 1.61496e6 | 0.0889367 | ||||||||
\(802\) | −2.73598e7 | + | 5.16291e6i | −1.50202 | + | 0.283438i | ||||
\(803\) | 29200.5 | − | 29200.5i | 0.00159809 | − | 0.00159809i | ||||
\(804\) | 9.50160e6 | + | 2.42794e7i | 0.518390 | + | 1.32464i | ||||
\(805\) | −5.81211e6 | − | 5.81211e6i | −0.316115 | − | 0.316115i | ||||
\(806\) | 7.61285e6 | − | 1.11543e7i | 0.412771 | − | 0.604790i | ||||
\(807\) | 2.36407e7i | 1.27784i | ||||||||
\(808\) | 2.07650e7 | + | 4.77149e6i | 1.11893 | + | 0.257114i | ||||
\(809\) | 2.99189e7i | 1.60722i | 0.595158 | + | 0.803609i | \(0.297090\pi\) | ||||
−0.595158 | + | 0.803609i | \(0.702910\pi\) | |||||||
\(810\) | −5.10679e6 | − | 3.48540e6i | −0.273486 | − | 0.186655i | ||||
\(811\) | 2.42789e7 | + | 2.42789e7i | 1.29622 | + | 1.29622i | 0.930873 | + | 0.365343i | \(0.119048\pi\) |
0.365343 | + | 0.930873i | \(0.380952\pi\) | |||||||
\(812\) | −1.55357e7 | − | 6.79621e6i | −0.826875 | − | 0.361724i | ||||
\(813\) | 1.74448e7 | − | 1.74448e7i | 0.925636 | − | 0.925636i | ||||
\(814\) | −13328.5 | − | 70631.6i | −0.000705050 | − | 0.00373627i | ||||
\(815\) | 9.99050e6 | 0.526858 | ||||||||
\(816\) | 152992. | − | 3.88568e6i | 0.00804348 | − | 0.204287i | ||||
\(817\) | −1.91121e6 | −0.100173 | ||||||||
\(818\) | 5.41582e6 | + | 2.87000e7i | 0.282997 | + | 1.49968i | ||||
\(819\) | 1.05802e6 | − | 1.05802e6i | 0.0551166 | − | 0.0551166i | ||||
\(820\) | 4.10241e6 | − | 9.37783e6i | 0.213061 | − | 0.487043i | ||||
\(821\) | −1.14896e7 | − | 1.14896e7i | −0.594906 | − | 0.594906i | 0.344047 | − | 0.938953i | \(-0.388202\pi\) |
−0.938953 | + | 0.344047i | \(0.888202\pi\) | |||||||
\(822\) | −2.06264e7 | − | 1.40776e7i | −1.06474 | − | 0.726691i | ||||
\(823\) | 7.71299e6i | 0.396938i | 0.980107 | + | 0.198469i | \(0.0635970\pi\) | ||||
−0.980107 | + | 0.198469i | \(0.936403\pi\) | |||||||
\(824\) | 2.39559e6 | + | 3.82499e6i | 0.122912 | + | 0.196251i | ||||
\(825\) | 14423.8i | 0.000737812i | ||||||||
\(826\) | −7.51484e6 | + | 1.10107e7i | −0.383239 | + | 0.561519i | ||||
\(827\) | −2.71359e7 | − | 2.71359e7i | −1.37969 | − | 1.37969i | −0.845138 | − | 0.534549i | \(-0.820482\pi\) |
−0.534549 | − | 0.845138i | \(-0.679518\pi\) | |||||||
\(828\) | −4.91257e6 | + | 1.92251e6i | −0.249019 | + | 0.0974524i | ||||
\(829\) | 2.12728e7 | − | 2.12728e7i | 1.07507 | − | 1.07507i | 0.0781283 | − | 0.996943i | \(-0.475106\pi\) |
0.996943 | − | 0.0781283i | \(-0.0248944\pi\) | |||||||
\(830\) | 1.44915e7 | − | 2.73461e6i | 0.730159 | − | 0.137784i | ||||
\(831\) | −2.36782e7 | −1.18945 | ||||||||
\(832\) | 2.98099e6 | + | 8.59992e6i | 0.149297 | + | 0.430711i | ||||
\(833\) | 1.66610e6 | 0.0831935 | ||||||||
\(834\) | 1.36914e7 | − | 2.58362e6i | 0.681604 | − | 0.128622i | ||||
\(835\) | 930008. | − | 930008.i | 0.0461605 | − | 0.0461605i | ||||
\(836\) | −32658.0 | + | 12780.5i | −0.00161612 | + | 0.000632460i | ||||
\(837\) | 2.47763e7 | + | 2.47763e7i | 1.22243 | + | 1.22243i | ||||
\(838\) | −7.03721e6 | + | 1.03109e7i | −0.346171 | + | 0.507207i | ||||
\(839\) | 1.96910e7i | 0.965745i | 0.875691 | + | 0.482873i | \(0.160407\pi\) | ||||
−0.875691 | + | 0.482873i | \(0.839593\pi\) | |||||||
\(840\) | −3.44116e6 | − | 5.49442e6i | −0.168270 | − | 0.268673i | ||||
\(841\) | − | 5.62703e6i | − | 0.274340i | ||||||
\(842\) | 5.98100e6 | + | 4.08205e6i | 0.290732 | + | 0.198426i | ||||
\(843\) | −2.28123e7 | − | 2.28123e7i | −1.10560 | − | 1.10560i | ||||
\(844\) | 5.02926e6 | − | 1.14966e7i | 0.243024 | − | 0.555535i | ||||
\(845\) | −5.19967e6 | + | 5.19967e6i | −0.250515 | + | 0.250515i | ||||
\(846\) | 1047.79 | + | 5552.54i | 5.03324e−5 | + | 0.000266726i | ||||
\(847\) | 1.66925e7 | 0.799490 | ||||||||
\(848\) | 4.11684e6 | + | 162094.i | 0.196596 | + | 0.00774064i | ||||
\(849\) | −2.85363e7 | −1.35872 | ||||||||
\(850\) | −180133. | − | 954575.i | −0.00855155 | − | 0.0453172i | ||||
\(851\) | −1.70687e7 | + | 1.70687e7i | −0.807934 | + | 0.807934i | ||||
\(852\) | 1.02868e7 | + | 4.50004e6i | 0.485490 | + | 0.212382i | ||||
\(853\) | −9.12953e6 | − | 9.12953e6i | −0.429612 | − | 0.429612i | 0.458884 | − | 0.888496i | \(-0.348249\pi\) |
−0.888496 | + | 0.458884i | \(0.848249\pi\) | |||||||
\(854\) | −1.93379e7 | − | 1.31982e7i | −0.907329 | − | 0.619256i | ||||
\(855\) | − | 852766.i | − | 0.0398947i | ||||||
\(856\) | 2.16467e7 | + | 4.97409e6i | 1.00973 | + | 0.232022i | ||||
\(857\) | − | 2.16457e7i | − | 1.00674i | −0.864070 | − | 0.503372i | \(-0.832093\pi\) | ||
0.864070 | − | 0.503372i | \(-0.167907\pi\) | |||||||
\(858\) | 20442.1 | − | 29951.6i | 0.000947996 | − | 0.00138900i | ||||
\(859\) | 7.40375e6 | + | 7.40375e6i | 0.342349 | + | 0.342349i | 0.857250 | − | 0.514901i | \(-0.172171\pi\) |
−0.514901 | + | 0.857250i | \(0.672171\pi\) | |||||||
\(860\) | 848950. | + | 2.16932e6i | 0.0391414 | + | 0.100018i | ||||
\(861\) | 1.29609e7 | − | 1.29609e7i | 0.595838 | − | 0.595838i | ||||
\(862\) | 8.83577e6 | − | 1.66735e6i | 0.405020 | − | 0.0764290i | ||||
\(863\) | 1.53905e7 | 0.703438 | 0.351719 | − | 0.936106i | \(-0.385597\pi\) | ||||
0.351719 | + | 0.936106i | \(0.385597\pi\) | |||||||
\(864\) | −2.33606e7 | + | 3.46274e6i | −1.06463 | + | 0.157810i | ||||
\(865\) | 1.90450e7 | 0.865448 | ||||||||
\(866\) | −3.63037e7 | + | 6.85068e6i | −1.64496 | + | 0.310412i | ||||
\(867\) | −1.31387e7 | + | 1.31387e7i | −0.593614 | + | 0.593614i | ||||
\(868\) | 1.03885e7 | + | 2.65458e7i | 0.468010 | + | 1.19590i | ||||
\(869\) | 9658.51 | + | 9658.51i | 0.000433871 | + | 0.000433871i | ||||
\(870\) | 5.63338e6 | − | 8.25398e6i | 0.252331 | − | 0.369714i | ||||
\(871\) | − | 1.63743e7i | − | 0.731338i | ||||||
\(872\) | −6.22531e6 | + | 2.70919e7i | −0.277249 | + | 1.20656i | ||||
\(873\) | 2.51120e6i | 0.111518i | ||||||||
\(874\) | 9.72772e6 | + | 6.63921e6i | 0.430757 | + | 0.293993i | ||||
\(875\) | −1.14517e6 | − | 1.14517e6i | −0.0505651 | − | 0.0505651i | ||||
\(876\) | −1.00215e7 | − | 4.38397e6i | −0.441236 | − | 0.193022i | ||||
\(877\) | 2.65611e7 | − | 2.65611e7i | 1.16613 | − | 1.16613i | 0.183023 | − | 0.983109i | \(-0.441412\pi\) |
0.983109 | − | 0.183023i | \(-0.0585882\pi\) | |||||||
\(878\) | −2.49934e6 | − | 1.32447e7i | −0.109418 | − | 0.579838i | ||||
\(879\) | −5.24752e6 | −0.229077 | ||||||||
\(880\) | 29013.1 | + | 31391.4i | 0.00126295 | + | 0.00136648i | ||||
\(881\) | 1.79339e7 | 0.778457 | 0.389229 | − | 0.921141i | \(-0.372742\pi\) | ||||
0.389229 | + | 0.921141i | \(0.372742\pi\) | |||||||
\(882\) | −330573. | − | 1.75180e6i | −0.0143085 | − | 0.0758251i | ||||
\(883\) | 1.62943e7 | − | 1.62943e7i | 0.703287 | − | 0.703287i | −0.261827 | − | 0.965115i | \(-0.584325\pi\) |
0.965115 | + | 0.261827i | \(0.0843251\pi\) | |||||||
\(884\) | −978813. | + | 2.23750e6i | −0.0421278 | + | 0.0963013i | ||||
\(885\) | −5.55505e6 | − | 5.55505e6i | −0.238413 | − | 0.238413i | ||||
\(886\) | 211958. | + | 144662.i | 0.00907121 | + | 0.00619114i | ||||
\(887\) | 2.41655e7i | 1.03131i | 0.856798 | + | 0.515653i | \(0.172451\pi\) | ||||
−0.856798 | + | 0.515653i | \(0.827549\pi\) | |||||||
\(888\) | −1.61357e7 | + | 1.01058e7i | −0.686681 | + | 0.430068i | ||||
\(889\) | − | 8.65428e6i | − | 0.367263i | ||||||
\(890\) | −2.47734e6 | + | 3.62978e6i | −0.104836 | + | 0.153605i | ||||
\(891\) | 51618.8 | + | 51618.8i | 0.00217828 | + | 0.00217828i | ||||
\(892\) | 2.71888e7 | − | 1.06402e7i | 1.14414 | − | 0.447752i | ||||
\(893\) | 8920.16 | − | 8920.16i | 0.000374321 | − | 0.000374321i | ||||
\(894\) | 1.38819e7 | − | 2.61958e6i | 0.580905 | − | 0.109619i | ||||
\(895\) | −6.89407e6 | −0.287685 | ||||||||
\(896\) | −1.85410e7 | − | 5.03604e6i | −0.771550 | − | 0.209565i | ||||
\(897\) | −1.21780e7 | −0.505354 | ||||||||
\(898\) | −2.51019e7 | + | 4.73684e6i | −1.03876 | + | 0.196019i | ||||
\(899\) | −3.10703e7 | + | 3.10703e7i | −1.28217 | + | 1.28217i | ||||
\(900\) | −967934. | + | 378795.i | −0.0398327 | + | 0.0155883i | ||||
\(901\) | 781696. | + | 781696.i | 0.0320794 | + | 0.0320794i | ||||
\(902\) | −68128.3 | + | 99821.0i | −0.00278812 | + | 0.00408513i | ||||
\(903\) | 4.17149e6i | 0.170244i | ||||||||
\(904\) | 1.47642e7 | − | 9.24680e6i | 0.600880 | − | 0.376331i | ||||
\(905\) | − | 1.47746e7i | − | 0.599646i | ||||||
\(906\) | −2.02437e7 | − | 1.38164e7i | −0.819350 | − | 0.559210i | ||||
\(907\) | −2.80535e7 | − | 2.80535e7i | −1.13232 | − | 1.13232i | −0.989791 | − | 0.142530i | \(-0.954476\pi\) |
−0.142530 | − | 0.989791i | \(-0.545524\pi\) | |||||||
\(908\) | 3.15581e6 | − | 7.21395e6i | 0.127027 | − | 0.290375i | ||||
\(909\) | 4.32538e6 | − | 4.32538e6i | 0.173626 | − | 0.173626i | ||||
\(910\) | 755002. | + | 4.00097e6i | 0.0302235 | + | 0.160163i | ||||
\(911\) | −3.79892e7 | −1.51658 | −0.758288 | − | 0.651920i | \(-0.773964\pi\) | ||||
−0.758288 | + | 0.651920i | \(0.773964\pi\) | |||||||
\(912\) | 6.30500e6 | + | 6.82184e6i | 0.251014 | + | 0.271591i | ||||
\(913\) | −174119. | −0.00691305 | ||||||||
\(914\) | −1.34003e6 | − | 7.10121e6i | −0.0530578 | − | 0.281169i | ||||
\(915\) | 9.75625e6 | − | 9.75625e6i | 0.385239 | − | 0.385239i | ||||
\(916\) | 3.50524e7 | + | 1.53340e7i | 1.38032 | + | 0.603833i | ||||
\(917\) | 517225. | + | 517225.i | 0.0203122 | + | 0.0203122i | ||||
\(918\) | −5.23381e6 | − | 3.57209e6i | −0.204980 | − | 0.139900i | ||||
\(919\) | 2.68420e7i | 1.04840i | 0.851595 | + | 0.524200i | \(0.175635\pi\) | ||||
−0.851595 | + | 0.524200i | \(0.824365\pi\) | |||||||
\(920\) | 3.21482e6 | − | 1.39906e7i | 0.125224 | − | 0.544961i | ||||
\(921\) | − | 2.55817e7i | − | 0.993755i | ||||||
\(922\) | 1.98843e7 | − | 2.91344e7i | 0.770342 | − | 1.12870i | ||||
\(923\) | −4.98621e6 | − | 4.98621e6i | −0.192649 | − | 0.192649i | ||||
\(924\) | 27895.4 | + | 71280.9i | 0.00107486 | + | 0.00274659i | ||||
\(925\) | −3.36307e6 | + | 3.36307e6i | −0.129236 | + | 0.129236i | ||||
\(926\) | 2.22958e7 | − | 4.20732e6i | 0.854467 | − | 0.161242i | ||||
\(927\) | 1.29575e6 | 0.0495249 | ||||||||
\(928\) | −4.34239e6 | − | 2.92950e7i | −0.165523 | − | 1.11667i | ||||
\(929\) | 3.48868e6 | 0.132624 | 0.0663120 | − | 0.997799i | \(-0.478877\pi\) | ||||
0.0663120 | + | 0.997799i | \(0.478877\pi\) | |||||||
\(930\) | −1.65078e7 | + | 3.11510e6i | −0.625868 | + | 0.118104i | ||||
\(931\) | −2.81427e6 | + | 2.81427e6i | −0.106412 | + | 0.106412i | ||||
\(932\) | 393516. | + | 1.00555e6i | 0.0148396 | + | 0.0379196i | ||||
\(933\) | −2.99815e7 | − | 2.99815e7i | −1.12758 | − | 1.12758i | ||||
\(934\) | −1.00377e7 | + | 1.47072e7i | −0.376502 | + | 0.551649i | ||||
\(935\) | 11469.5i | 0.000429057i | ||||||||
\(936\) | 2.54679e6 | + | 585215.i | 0.0950176 | + | 0.0218336i | ||||
\(937\) | − | 3.53133e6i | − | 0.131398i | −0.997839 | − | 0.0656990i | \(-0.979072\pi\) | ||
0.997839 | − | 0.0656990i | \(-0.0209277\pi\) | |||||||
\(938\) | 2.85484e7 | + | 1.94844e7i | 1.05944 | + | 0.723069i | ||||
\(939\) | −2.22279e7 | − | 2.22279e7i | −0.822688 | − | 0.822688i | ||||
\(940\) | −14087.1 | − | 6162.54i | −0.000519999 | − | 0.000227478i | ||||
\(941\) | −8.19988e6 | + | 8.19988e6i | −0.301879 | + | 0.301879i | −0.841749 | − | 0.539870i | \(-0.818474\pi\) |
0.539870 | + | 0.841749i | \(0.318474\pi\) | |||||||
\(942\) | 5.17195e6 | + | 2.74077e7i | 0.189901 | + | 1.00634i | ||||
\(943\) | 4.05863e7 | 1.48628 | ||||||||
\(944\) | −2.32636e7 | − | 915967.i | −0.849663 | − | 0.0334541i | ||||
\(945\) | −1.05641e7 | −0.384818 | ||||||||
\(946\) | −5100.18 | − | 27027.3i | −0.000185292 | − | 0.000981919i | ||||
\(947\) | −1.46571e7 | + | 1.46571e7i | −0.531096 | + | 0.531096i | −0.920898 | − | 0.389803i | \(-0.872543\pi\) |
0.389803 | + | 0.920898i | \(0.372543\pi\) | |||||||
\(948\) | 1.45007e6 | − | 3.31475e6i | 0.0524043 | − | 0.119793i | ||||
\(949\) | 4.85761e6 | + | 4.85761e6i | 0.175088 | + | 0.175088i | ||||
\(950\) | 1.91667e6 | + | 1.30814e6i | 0.0689031 | + | 0.0470266i | ||||
\(951\) | − | 4.78503e7i | − | 1.71567i | ||||||
\(952\) | −2.73632e6 | − | 4.36903e6i | −0.0978532 | − | 0.156240i | ||||
\(953\) | − | 2.06766e7i | − | 0.737474i | −0.929534 | − | 0.368737i | \(-0.879790\pi\) | ||
0.929534 | − | 0.368737i | \(-0.120210\pi\) | |||||||
\(954\) | 666806. | − | 977000.i | 0.0237208 | − | 0.0347555i | ||||
\(955\) | 8.78714e6 | + | 8.78714e6i | 0.311774 | + | 0.311774i | ||||
\(956\) | 4.25841e7 | − | 1.66650e7i | 1.50696 | − | 0.589742i | ||||
\(957\) | −83430.2 | + | 83430.2i | −0.00294472 | + | 0.00294472i | ||||
\(958\) | −1.59726e7 | + | 3.01410e6i | −0.562292 | + | 0.106107i | ||||
\(959\) | −3.31058e7 | −1.16241 | ||||||||
\(960\) | 4.94249e6 | − | 1.01867e7i | 0.173088 | − | 0.356744i | ||||
\(961\) | 4.52371e7 | 1.58010 | ||||||||
\(962\) | 1.17498e7 | − | 2.21724e6i | 0.409349 | − | 0.0772460i | ||||
\(963\) | 4.50903e6 | − | 4.50903e6i | 0.156681 | − | 0.156681i | ||||
\(964\) | −1.15434e7 | + | 4.51744e6i | −0.400074 | + | 0.156567i | ||||
\(965\) | 8.17649e6 | + | 8.17649e6i | 0.282650 | + | 0.282650i | ||||
\(966\) | 1.44911e7 | − | 2.12322e7i | 0.499640 | − | 0.732069i | ||||
\(967\) | 2.80312e7i | 0.963998i | 0.876172 | + | 0.481999i | \(0.160089\pi\) | ||||
−0.876172 | + | 0.481999i | \(0.839911\pi\) | |||||||
\(968\) | 1.54741e7 | + | 2.47071e7i | 0.530782 | + | 0.847488i | ||||
\(969\) | 2.49250e6i | 0.0852757i | ||||||||
\(970\) | −5.64416e6 | − | 3.85216e6i | −0.192606 | − | 0.131454i | ||||
\(971\) | −2.48615e7 | − | 2.48615e7i | −0.846214 | − | 0.846214i | 0.143445 | − | 0.989658i | \(-0.454182\pi\) |
−0.989658 | + | 0.143445i | \(0.954182\pi\) | |||||||
\(972\) | −4.95599e6 | + | 1.13291e7i | −0.168254 | + | 0.384617i | ||||
\(973\) | 1.30608e7 | − | 1.30608e7i | 0.442271 | − | 0.442271i | ||||
\(974\) | −1.01878e7 | − | 5.39880e7i | −0.344098 | − | 1.82347i | ||||
\(975\) | −2.39946e6 | −0.0808354 | ||||||||
\(976\) | 1.60870e6 | − | 4.08575e7i | 0.0540568 | − | 1.37293i | ||||
\(977\) | −4.94994e7 | −1.65906 | −0.829532 | − | 0.558459i | \(-0.811393\pi\) | ||||
−0.829532 | + | 0.558459i | \(0.811393\pi\) | |||||||
\(978\) | 5.79371e6 | + | 3.07025e7i | 0.193691 | + | 1.02643i | ||||
\(979\) | 36689.3 | − | 36689.3i | 0.00122344 | − | 0.00122344i | ||||
\(980\) | 4.44443e6 | + | 1.94425e6i | 0.147826 | + | 0.0646677i | ||||
\(981\) | 5.64327e6 | + | 5.64327e6i | 0.187223 | + | 0.187223i | ||||
\(982\) | −6.22291e6 | − | 4.24716e6i | −0.205928 | − | 0.140547i | ||||
\(983\) | − | 3.48169e7i | − | 1.14923i | −0.818424 | − | 0.574615i | \(-0.805152\pi\) | ||
0.818424 | − | 0.574615i | \(-0.194848\pi\) | |||||||
\(984\) | 3.11988e7 | + | 7.16901e6i | 1.02719 | + | 0.236032i | ||||
\(985\) | 1.01223e7i | 0.332422i | ||||||||
\(986\) | 4.47952e6 | − | 6.56336e6i | 0.146737 | − | 0.214998i | ||||
\(987\) | −19469.6 | − | 19469.6i | −0.000636156 | − | 0.000636156i | ||||
\(988\) | −2.12609e6 | − | 5.43277e6i | −0.0692929 | − | 0.177064i | ||||
\(989\) | −6.53137e6 | + | 6.53137e6i | −0.212331 | + | 0.212331i | ||||
\(990\) | 12059.4 | − | 2275.67i | 0.000391055 | − | 7.37939e-5i | ||||
\(991\) | 1.18705e7 | 0.383959 | 0.191979 | − | 0.981399i | \(-0.438509\pi\) | ||||
0.191979 | + | 0.981399i | \(0.438509\pi\) | |||||||
\(992\) | −2.96610e7 | + | 3.99845e7i | −0.956988 | + | 1.29007i | ||||
\(993\) | 1.53799e7 | 0.494972 | ||||||||
\(994\) | 1.46267e7 | − | 2.76012e6i | 0.469547 | − | 0.0886056i | ||||
\(995\) | −1.78521e7 | + | 1.78521e7i | −0.571651 | + | 0.571651i | ||||
\(996\) | 1.68078e7 | + | 4.29490e7i | 0.536863 | + | 1.37184i | ||||
\(997\) | −8.43454e6 | − | 8.43454e6i | −0.268735 | − | 0.268735i | 0.559856 | − | 0.828590i | \(-0.310857\pi\) |
−0.828590 | + | 0.559856i | \(0.810857\pi\) | |||||||
\(998\) | −7.36754e6 | + | 1.07949e7i | −0.234151 | + | 0.343077i | ||||
\(999\) | 3.10242e7i | 0.983527i |
(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.21.4 | ✓ | 80 | |
4.3 | odd | 2 | 320.6.l.a.241.12 | 80 | |||
16.3 | odd | 4 | 320.6.l.a.81.12 | 80 | |||
16.13 | even | 4 | inner | 80.6.l.a.61.4 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.l.a.21.4 | ✓ | 80 | 1.1 | even | 1 | trivial | |
80.6.l.a.61.4 | yes | 80 | 16.13 | even | 4 | inner | |
320.6.l.a.81.12 | 80 | 16.3 | odd | 4 | |||
320.6.l.a.241.12 | 80 | 4.3 | odd | 2 |