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 | 61.2 | ||
Character | \(\chi\) | \(=\) | 80.61 |
Dual form | 80.6.l.a.21.2 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.65514 | − | 0.139396i | −0.999696 | − | 0.0246420i | ||||
\(3\) | 19.6483 | + | 19.6483i | 1.26044 | + | 1.26044i | 0.950881 | + | 0.309556i | \(0.100180\pi\) |
0.309556 | + | 0.950881i | \(0.399820\pi\) | |||||||
\(4\) | 31.9611 | + | 1.57661i | 0.998786 | + | 0.0492690i | ||||
\(5\) | −17.6777 | + | 17.6777i | −0.316228 | + | 0.316228i | ||||
\(6\) | −108.375 | − | 113.853i | −1.22899 | − | 1.29111i | ||||
\(7\) | 152.043i | 1.17279i | 0.810024 | + | 0.586397i | \(0.199454\pi\) | ||||
−0.810024 | + | 0.586397i | \(0.800546\pi\) | |||||||
\(8\) | −180.525 | − | 13.3712i | −0.997268 | − | 0.0738660i | ||||
\(9\) | 529.109i | 2.17740i | ||||||||
\(10\) | 102.434 | − | 97.5054i | 0.323924 | − | 0.308339i | ||||
\(11\) | −11.6148 | + | 11.6148i | −0.0289422 | + | 0.0289422i | −0.721430 | − | 0.692488i | \(-0.756515\pi\) |
0.692488 | + | 0.721430i | \(0.256515\pi\) | |||||||
\(12\) | 597.003 | + | 658.959i | 1.19681 | + | 1.32101i | ||||
\(13\) | −337.401 | − | 337.401i | −0.553717 | − | 0.553717i | 0.373795 | − | 0.927511i | \(-0.378056\pi\) |
−0.927511 | + | 0.373795i | \(0.878056\pi\) | |||||||
\(14\) | 21.1942 | − | 859.825i | 0.0289000 | − | 1.17244i | ||||
\(15\) | −694.671 | −0.797170 | ||||||||
\(16\) | 1019.03 | + | 100.780i | 0.995145 | + | 0.0984182i | ||||
\(17\) | 1971.39 | 1.65443 | 0.827217 | − | 0.561882i | \(-0.189922\pi\) | ||||
0.827217 | + | 0.561882i | \(0.189922\pi\) | |||||||
\(18\) | 73.7557 | − | 2992.18i | 0.0536555 | − | 2.17674i | ||||
\(19\) | −1675.04 | − | 1675.04i | −1.06449 | − | 1.06449i | −0.997772 | − | 0.0667196i | \(-0.978747\pi\) |
−0.0667196 | − | 0.997772i | \(-0.521253\pi\) | |||||||
\(20\) | −592.869 | + | 537.128i | −0.331424 | + | 0.300264i | ||||
\(21\) | −2987.39 | + | 2987.39i | −1.47823 | + | 1.47823i | ||||
\(22\) | 67.3025 | − | 64.0644i | 0.0296466 | − | 0.0282202i | ||||
\(23\) | 2713.65i | 1.06963i | 0.844968 | + | 0.534816i | \(0.179619\pi\) | ||||
−0.844968 | + | 0.534816i | \(0.820381\pi\) | |||||||
\(24\) | −3284.28 | − | 3809.72i | −1.16389 | − | 1.35010i | ||||
\(25\) | − | 625.000i | − | 0.200000i | ||||||
\(26\) | 1861.01 | + | 1955.08i | 0.539904 | + | 0.567193i | ||||
\(27\) | −5621.55 | + | 5621.55i | −1.48404 | + | 1.48404i | ||||
\(28\) | −239.712 | + | 4859.47i | −0.0577824 | + | 1.17137i | ||||
\(29\) | 2271.81 | + | 2271.81i | 0.501622 | + | 0.501622i | 0.911942 | − | 0.410320i | \(-0.134583\pi\) |
−0.410320 | + | 0.911942i | \(0.634583\pi\) | |||||||
\(30\) | 3928.46 | + | 96.8344i | 0.796928 | + | 0.0196438i | ||||
\(31\) | −9252.07 | −1.72916 | −0.864579 | − | 0.502497i | \(-0.832415\pi\) | ||||
−0.864579 | + | 0.502497i | \(0.832415\pi\) | |||||||
\(32\) | −5748.70 | − | 711.975i | −0.992418 | − | 0.122911i | ||||
\(33\) | −456.423 | −0.0729596 | ||||||||
\(34\) | −11148.5 | − | 274.804i | −1.65393 | − | 0.0407685i | ||||
\(35\) | −2687.77 | − | 2687.77i | −0.370870 | − | 0.370870i | ||||
\(36\) | −834.197 | + | 16910.9i | −0.107278 | + | 2.17476i | ||||
\(37\) | 2728.98 | − | 2728.98i | 0.327715 | − | 0.327715i | −0.524002 | − | 0.851717i | \(-0.675562\pi\) |
0.851717 | + | 0.524002i | \(0.175562\pi\) | |||||||
\(38\) | 9239.11 | + | 9706.10i | 1.03794 | + | 1.09040i | ||||
\(39\) | − | 13258.7i | − | 1.39585i | ||||||
\(40\) | 3427.63 | − | 2954.89i | 0.338722 | − | 0.292005i | ||||
\(41\) | 9698.90i | 0.901079i | 0.892757 | + | 0.450539i | \(0.148768\pi\) | ||||
−0.892757 | + | 0.450539i | \(0.851232\pi\) | |||||||
\(42\) | 17310.5 | − | 16477.6i | 1.51421 | − | 1.44136i | ||||
\(43\) | 7983.39 | − | 7983.39i | 0.658440 | − | 0.658440i | −0.296571 | − | 0.955011i | \(-0.595843\pi\) |
0.955011 | + | 0.296571i | \(0.0958432\pi\) | |||||||
\(44\) | −389.535 | + | 352.911i | −0.0303330 | + | 0.0274811i | ||||
\(45\) | −9353.41 | − | 9353.41i | −0.688555 | − | 0.688555i | ||||
\(46\) | 378.272 | − | 15346.1i | 0.0263578 | − | 1.06931i | ||||
\(47\) | −12393.3 | −0.818359 | −0.409179 | − | 0.912454i | \(-0.634185\pi\) | ||||
−0.409179 | + | 0.912454i | \(0.634185\pi\) | |||||||
\(48\) | 18042.0 | + | 22002.3i | 1.13027 | + | 1.37837i | ||||
\(49\) | −6310.14 | −0.375447 | ||||||||
\(50\) | −87.1225 | + | 3534.46i | −0.00492839 | + | 0.199939i | ||||
\(51\) | 38734.4 | + | 38734.4i | 2.08531 | + | 2.08531i | ||||
\(52\) | −10251.8 | − | 11315.7i | −0.525763 | − | 0.580325i | ||||
\(53\) | 779.013 | − | 779.013i | 0.0380939 | − | 0.0380939i | −0.687803 | − | 0.725897i | \(-0.741425\pi\) |
0.725897 | + | 0.687803i | \(0.241425\pi\) | |||||||
\(54\) | 32574.2 | − | 31007.0i | 1.52016 | − | 1.44702i | ||||
\(55\) | − | 410.646i | − | 0.0183046i | ||||||
\(56\) | 2033.00 | − | 27447.6i | 0.0866297 | − | 1.16959i | ||||
\(57\) | − | 65823.4i | − | 2.68345i | ||||||
\(58\) | −12530.7 | − | 13164.1i | −0.489109 | − | 0.513831i | ||||
\(59\) | −2779.17 | + | 2779.17i | −0.103940 | + | 0.103940i | −0.757165 | − | 0.653224i | \(-0.773416\pi\) |
0.653224 | + | 0.757165i | \(0.273416\pi\) | |||||||
\(60\) | −22202.5 | − | 1095.22i | −0.796202 | − | 0.0392758i | ||||
\(61\) | 16149.2 | + | 16149.2i | 0.555682 | + | 0.555682i | 0.928075 | − | 0.372393i | \(-0.121463\pi\) |
−0.372393 | + | 0.928075i | \(0.621463\pi\) | |||||||
\(62\) | 52321.7 | + | 1289.70i | 1.72863 | + | 0.0426098i | ||||
\(63\) | −80447.4 | −2.55365 | ||||||||
\(64\) | 32410.4 | + | 4827.66i | 0.989088 | + | 0.147328i | ||||
\(65\) | 11928.9 | 0.350201 | ||||||||
\(66\) | 2581.13 | + | 63.6235i | 0.0729375 | + | 0.00179787i | ||||
\(67\) | 27196.6 | + | 27196.6i | 0.740164 | + | 0.740164i | 0.972609 | − | 0.232445i | \(-0.0746727\pi\) |
−0.232445 | + | 0.972609i | \(0.574673\pi\) | |||||||
\(68\) | 63007.8 | + | 3108.10i | 1.65243 | + | 0.0815123i | ||||
\(69\) | −53318.6 | + | 53318.6i | −1.34820 | + | 1.34820i | ||||
\(70\) | 14825.0 | + | 15574.4i | 0.361619 | + | 0.379897i | ||||
\(71\) | 61737.5i | 1.45346i | 0.686923 | + | 0.726730i | \(0.258961\pi\) | ||||
−0.686923 | + | 0.726730i | \(0.741039\pi\) | |||||||
\(72\) | 7074.81 | − | 95517.3i | 0.160836 | − | 2.17146i | ||||
\(73\) | − | 18521.1i | − | 0.406780i | −0.979098 | − | 0.203390i | \(-0.934804\pi\) | ||
0.979098 | − | 0.203390i | \(-0.0651960\pi\) | |||||||
\(74\) | −15813.2 | + | 15052.4i | −0.335691 | + | 0.319540i | ||||
\(75\) | 12280.2 | − | 12280.2i | 0.252087 | − | 0.252087i | ||||
\(76\) | −50895.4 | − | 56177.2i | −1.01075 | − | 1.11564i | ||||
\(77\) | −1765.96 | − | 1765.96i | −0.0339432 | − | 0.0339432i | ||||
\(78\) | −1848.21 | + | 74979.6i | −0.0343965 | + | 1.39543i | ||||
\(79\) | 54765.8 | 0.987284 | 0.493642 | − | 0.869665i | \(-0.335665\pi\) | ||||
0.493642 | + | 0.869665i | \(0.335665\pi\) | |||||||
\(80\) | −19795.6 | + | 16232.5i | −0.345815 | + | 0.283570i | ||||
\(81\) | −92333.9 | −1.56368 | ||||||||
\(82\) | 1351.99 | − | 54848.6i | 0.0222043 | − | 0.900805i | ||||
\(83\) | 76036.0 | + | 76036.0i | 1.21150 | + | 1.21150i | 0.970533 | + | 0.240969i | \(0.0774653\pi\) |
0.240969 | + | 0.970533i | \(0.422535\pi\) | |||||||
\(84\) | −100190. | + | 90770.3i | −1.54927 | + | 1.40361i | ||||
\(85\) | −34849.5 | + | 34849.5i | −0.523178 | + | 0.523178i | ||||
\(86\) | −46260.0 | + | 44034.3i | −0.674465 | + | 0.642015i | ||||
\(87\) | 89274.2i | 1.26453i | ||||||||
\(88\) | 2252.07 | − | 1941.46i | 0.0310010 | − | 0.0267253i | ||||
\(89\) | − | 60590.0i | − | 0.810823i | −0.914134 | − | 0.405412i | \(-0.867128\pi\) | ||
0.914134 | − | 0.405412i | \(-0.132872\pi\) | |||||||
\(90\) | 51591.0 | + | 54198.7i | 0.671379 | + | 0.705314i | ||||
\(91\) | 51299.5 | − | 51299.5i | 0.649396 | − | 0.649396i | ||||
\(92\) | −4278.36 | + | 86731.4i | −0.0526997 | + | 1.06833i | ||||
\(93\) | −181787. | − | 181787.i | −2.17949 | − | 2.17949i | ||||
\(94\) | 70086.0 | + | 1727.58i | 0.818110 | + | 0.0201660i | ||||
\(95\) | 59221.7 | 0.673243 | ||||||||
\(96\) | −98962.9 | − | 126941.i | −1.09596 | − | 1.40580i | ||||
\(97\) | 80405.2 | 0.867670 | 0.433835 | − | 0.900992i | \(-0.357160\pi\) | ||||
0.433835 | + | 0.900992i | \(0.357160\pi\) | |||||||
\(98\) | 35684.7 | + | 879.608i | 0.375333 | + | 0.00925175i | ||||
\(99\) | −6145.52 | − | 6145.52i | −0.0630188 | − | 0.0630188i | ||||
\(100\) | 985.379 | − | 19975.7i | 0.00985379 | − | 0.199757i | ||||
\(101\) | −19812.4 | + | 19812.4i | −0.193256 | + | 0.193256i | −0.797102 | − | 0.603845i | \(-0.793634\pi\) |
0.603845 | + | 0.797102i | \(0.293634\pi\) | |||||||
\(102\) | −213649. | − | 224447.i | −2.03329 | − | 2.13606i | ||||
\(103\) | − | 130085.i | − | 1.20819i | −0.796912 | − | 0.604095i | \(-0.793535\pi\) | ||
0.796912 | − | 0.604095i | \(-0.206465\pi\) | |||||||
\(104\) | 56397.7 | + | 65420.6i | 0.511303 | + | 0.593105i | ||||
\(105\) | − | 105620.i | − | 0.934917i | ||||||
\(106\) | −4514.02 | + | 4296.83i | −0.0390210 | + | 0.0371436i | ||||
\(107\) | 141881. | − | 141881.i | 1.19802 | − | 1.19802i | 0.223260 | − | 0.974759i | \(-0.428330\pi\) |
0.974759 | − | 0.223260i | \(-0.0716700\pi\) | |||||||
\(108\) | −188534. | + | 170808.i | −1.55536 | + | 1.40912i | ||||
\(109\) | 9250.02 | + | 9250.02i | 0.0745721 | + | 0.0745721i | 0.743409 | − | 0.668837i | \(-0.233208\pi\) |
−0.668837 | + | 0.743409i | \(0.733208\pi\) | |||||||
\(110\) | −57.2425 | + | 2322.26i | −0.000451062 | + | 0.0182991i | ||||
\(111\) | 107240. | 0.826128 | ||||||||
\(112\) | −15323.0 | + | 154936.i | −0.115424 | + | 1.16710i | ||||
\(113\) | 46485.0 | 0.342466 | 0.171233 | − | 0.985231i | \(-0.445225\pi\) | ||||
0.171233 | + | 0.985231i | \(0.445225\pi\) | |||||||
\(114\) | −9175.52 | + | 372240.i | −0.0661254 | + | 2.68263i | ||||
\(115\) | −47971.0 | − | 47971.0i | −0.338247 | − | 0.338247i | ||||
\(116\) | 69027.8 | + | 76191.3i | 0.476298 | + | 0.525727i | ||||
\(117\) | 178522. | − | 178522.i | 1.20566 | − | 1.20566i | ||||
\(118\) | 16104.0 | − | 15329.2i | 0.106470 | − | 0.101348i | ||||
\(119\) | 299736.i | 1.94031i | ||||||||
\(120\) | 125405. | + | 9288.57i | 0.794993 | + | 0.0588838i | ||||
\(121\) | 160781.i | 0.998325i | ||||||||
\(122\) | −89074.7 | − | 93577.0i | −0.541820 | − | 0.569206i | ||||
\(123\) | −190567. | + | 190567.i | −1.13575 | + | 1.13575i | ||||
\(124\) | −295707. | − | 14586.9i | −1.72706 | − | 0.0851938i | ||||
\(125\) | 11048.5 | + | 11048.5i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 454941. | + | 11214.1i | 2.55287 | + | 0.0629269i | ||||
\(127\) | −286357. | −1.57543 | −0.787714 | − | 0.616041i | \(-0.788736\pi\) | ||||
−0.787714 | + | 0.616041i | \(0.788736\pi\) | |||||||
\(128\) | −182612. | − | 31819.0i | −0.985157 | − | 0.171657i | ||||
\(129\) | 313719. | 1.65984 | ||||||||
\(130\) | −67459.6 | − | 1662.84i | −0.350095 | − | 0.00862964i | ||||
\(131\) | 117828. | + | 117828.i | 0.599887 | + | 0.599887i | 0.940282 | − | 0.340396i | \(-0.110561\pi\) |
−0.340396 | + | 0.940282i | \(0.610561\pi\) | |||||||
\(132\) | −14587.8 | − | 719.599i | −0.0728710 | − | 0.00359464i | ||||
\(133\) | 254679. | − | 254679.i | 1.24843 | − | 1.24843i | ||||
\(134\) | −150010. | − | 157592.i | −0.721700 | − | 0.758178i | ||||
\(135\) | − | 198752.i | − | 0.938591i | ||||||
\(136\) | −355884. | − | 26359.8i | −1.64992 | − | 0.122207i | ||||
\(137\) | 82337.9i | 0.374799i | 0.982284 | + | 0.187400i | \(0.0600059\pi\) | ||||
−0.982284 | + | 0.187400i | \(0.939994\pi\) | |||||||
\(138\) | 308956. | − | 294091.i | 1.38102 | − | 1.31457i | ||||
\(139\) | −214865. | + | 214865.i | −0.943255 | + | 0.943255i | −0.998474 | − | 0.0552189i | \(-0.982414\pi\) |
0.0552189 | + | 0.998474i | \(0.482414\pi\) | |||||||
\(140\) | −81666.6 | − | 90141.7i | −0.352147 | − | 0.388692i | ||||
\(141\) | −243508. | − | 243508.i | −1.03149 | − | 1.03149i | ||||
\(142\) | 8605.96 | − | 349134.i | 0.0358161 | − | 1.45302i | ||||
\(143\) | 7837.71 | 0.0320515 | ||||||||
\(144\) | −53323.8 | + | 539177.i | −0.214296 | + | 2.16683i | ||||
\(145\) | −80320.5 | −0.317254 | ||||||||
\(146\) | −2581.77 | + | 104739.i | −0.0100239 | + | 0.406657i | ||||
\(147\) | −123983. | − | 123983.i | −0.473227 | − | 0.473227i | ||||
\(148\) | 91523.9 | − | 82918.8i | 0.343463 | − | 0.311171i | ||||
\(149\) | 359536. | − | 359536.i | 1.32671 | − | 1.32671i | 0.418494 | − | 0.908220i | \(-0.362558\pi\) |
0.908220 | − | 0.418494i | \(-0.137442\pi\) | |||||||
\(150\) | −71157.8 | + | 67734.2i | −0.258223 | + | 0.245799i | ||||
\(151\) | 89139.5i | 0.318147i | 0.987267 | + | 0.159073i | \(0.0508507\pi\) | ||||
−0.987267 | + | 0.159073i | \(0.949149\pi\) | |||||||
\(152\) | 279990. | + | 324784.i | 0.982954 | + | 1.14021i | ||||
\(153\) | 1.04308e6i | 3.60237i | ||||||||
\(154\) | 9740.56 | + | 10232.9i | 0.0330965 | + | 0.0347694i | ||||
\(155\) | 163555. | − | 163555.i | 0.546808 | − | 0.546808i | ||||
\(156\) | 20903.7 | − | 423762.i | 0.0687721 | − | 1.39415i | ||||
\(157\) | 41880.8 | + | 41880.8i | 0.135602 | + | 0.135602i | 0.771650 | − | 0.636048i | \(-0.219432\pi\) |
−0.636048 | + | 0.771650i | \(0.719432\pi\) | |||||||
\(158\) | −309708. | − | 7634.14i | −0.986984 | − | 0.0243286i | ||||
\(159\) | 30612.5 | 0.0960298 | ||||||||
\(160\) | 114210. | − | 89037.5i | 0.352698 | − | 0.274962i | ||||
\(161\) | −412592. | −1.25446 | ||||||||
\(162\) | 522161. | + | 12871.0i | 1.56321 | + | 0.0385322i | ||||
\(163\) | 119285. | + | 119285.i | 0.351654 | + | 0.351654i | 0.860725 | − | 0.509070i | \(-0.170011\pi\) |
−0.509070 | + | 0.860725i | \(0.670011\pi\) | |||||||
\(164\) | −15291.3 | + | 309988.i | −0.0443952 | + | 0.899984i | ||||
\(165\) | 8068.49 | − | 8068.49i | 0.0230719 | − | 0.0230719i | ||||
\(166\) | −419395. | − | 440593.i | −1.18128 | − | 1.24099i | ||||
\(167\) | 121470.i | 0.337036i | 0.985699 | + | 0.168518i | \(0.0538982\pi\) | ||||
−0.985699 | + | 0.168518i | \(0.946102\pi\) | |||||||
\(168\) | 579242. | − | 499352.i | 1.58339 | − | 1.36500i | ||||
\(169\) | − | 143615.i | − | 0.386796i | ||||||
\(170\) | 201937. | − | 192221.i | 0.535912 | − | 0.510127i | ||||
\(171\) | 886281. | − | 886281.i | 2.31783 | − | 2.31783i | ||||
\(172\) | 267745. | − | 242571.i | 0.690081 | − | 0.625199i | ||||
\(173\) | 219318. | + | 219318.i | 0.557134 | + | 0.557134i | 0.928490 | − | 0.371356i | \(-0.121107\pi\) |
−0.371356 | + | 0.928490i | \(0.621107\pi\) | |||||||
\(174\) | 12444.5 | − | 504858.i | 0.0311604 | − | 1.26414i | ||||
\(175\) | 95027.0 | 0.234559 | ||||||||
\(176\) | −13006.4 | + | 10665.3i | −0.0316501 | + | 0.0259532i | ||||
\(177\) | −109212. | −0.262021 | ||||||||
\(178\) | −8446.01 | + | 342645.i | −0.0199803 | + | 0.810577i | ||||
\(179\) | −481512. | − | 481512.i | −1.12325 | − | 1.12325i | −0.991250 | − | 0.131996i | \(-0.957862\pi\) |
−0.131996 | − | 0.991250i | \(-0.542138\pi\) | |||||||
\(180\) | −284199. | − | 313692.i | −0.653795 | − | 0.721644i | ||||
\(181\) | −185016. | + | 185016.i | −0.419772 | + | 0.419772i | −0.885125 | − | 0.465353i | \(-0.845927\pi\) |
0.465353 | + | 0.885125i | \(0.345927\pi\) | |||||||
\(182\) | −297256. | + | 282955.i | −0.665201 | + | 0.633196i | ||||
\(183\) | 634607.i | 1.40080i | ||||||||
\(184\) | 36284.7 | − | 489881.i | 0.0790095 | − | 1.06671i | ||||
\(185\) | 96484.1i | 0.207265i | ||||||||
\(186\) | 1.00269e6 | + | 1.05337e6i | 2.12513 | + | 2.23254i | ||||
\(187\) | −22897.3 | + | 22897.3i | −0.0478830 | + | 0.0478830i | ||||
\(188\) | −396105. | − | 19539.4i | −0.817365 | − | 0.0403197i | ||||
\(189\) | −854718. | − | 854718.i | −1.74048 | − | 1.74048i | ||||
\(190\) | −334907. | − | 8255.27i | −0.673039 | − | 0.0165900i | ||||
\(191\) | 144475. | 0.286556 | 0.143278 | − | 0.989682i | \(-0.454236\pi\) | ||||
0.143278 | + | 0.989682i | \(0.454236\pi\) | |||||||
\(192\) | 541954. | + | 731664.i | 1.06098 | + | 1.43238i | ||||
\(193\) | 573446. | 1.10815 | 0.554076 | − | 0.832466i | \(-0.313072\pi\) | ||||
0.554076 | + | 0.832466i | \(0.313072\pi\) | |||||||
\(194\) | −454702. | − | 11208.2i | −0.867407 | − | 0.0213811i | ||||
\(195\) | 234383. | + | 234383.i | 0.441406 | + | 0.441406i | ||||
\(196\) | −201679. | − | 9948.61i | −0.374991 | − | 0.0184979i | ||||
\(197\) | 228983. | − | 228983.i | 0.420376 | − | 0.420376i | −0.464957 | − | 0.885333i | \(-0.653930\pi\) |
0.885333 | + | 0.464957i | \(0.153930\pi\) | |||||||
\(198\) | 33897.1 | + | 35610.4i | 0.0614468 | + | 0.0645526i | ||||
\(199\) | − | 455416.i | − | 0.815221i | −0.913156 | − | 0.407611i | \(-0.866362\pi\) | ||
0.913156 | − | 0.407611i | \(-0.133638\pi\) | |||||||
\(200\) | −8356.99 | + | 112828.i | −0.0147732 | + | 0.199454i | ||||
\(201\) | 1.06873e6i | 1.86586i | ||||||||
\(202\) | 114804. | − | 109280.i | 0.197960 | − | 0.188435i | ||||
\(203\) | −345413. | + | 345413.i | −0.588300 | + | 0.588300i | ||||
\(204\) | 1.17693e6 | + | 1.29906e6i | 1.98004 | + | 2.18552i | ||||
\(205\) | −171454. | − | 171454.i | −0.284946 | − | 0.284946i | ||||
\(206\) | −18133.4 | + | 735651.i | −0.0297722 | + | 1.20782i | ||||
\(207\) | −1.43582e6 | −2.32902 | ||||||||
\(208\) | −309818. | − | 377824.i | −0.496533 | − | 0.605524i | ||||
\(209\) | 38910.7 | 0.0616174 | ||||||||
\(210\) | −14723.0 | + | 597296.i | −0.0230382 | + | 0.934633i | ||||
\(211\) | −375836. | − | 375836.i | −0.581156 | − | 0.581156i | 0.354065 | − | 0.935221i | \(-0.384799\pi\) |
−0.935221 | + | 0.354065i | \(0.884799\pi\) | |||||||
\(212\) | 26126.3 | − | 23669.9i | 0.0399244 | − | 0.0361708i | ||||
\(213\) | −1.21304e6 | + | 1.21304e6i | −1.83200 | + | 1.83200i | ||||
\(214\) | −822132. | + | 782577.i | −1.22718 | + | 1.16813i | ||||
\(215\) | 282255.i | 0.416434i | ||||||||
\(216\) | 1.09000e6 | − | 939662.i | 1.58961 | − | 1.37037i | ||||
\(217\) | − | 1.40671e6i | − | 2.02795i | ||||||
\(218\) | −51020.7 | − | 53599.5i | −0.0727119 | − | 0.0763871i | ||||
\(219\) | 363908. | − | 363908.i | 0.512721 | − | 0.512721i | ||||
\(220\) | 647.428 | − | 13124.7i | 0.000901851 | − | 0.0182824i | ||||
\(221\) | −665147. | − | 665147.i | −0.916088 | − | 0.916088i | ||||
\(222\) | −606454. | − | 14948.8i | −0.825877 | − | 0.0203574i | ||||
\(223\) | −372759. | −0.501956 | −0.250978 | − | 0.967993i | \(-0.580752\pi\) | ||||
−0.250978 | + | 0.967993i | \(0.580752\pi\) | |||||||
\(224\) | 108251. | − | 874050.i | 0.144149 | − | 1.16390i | ||||
\(225\) | 330693. | 0.435481 | ||||||||
\(226\) | −262879. | − | 6479.83i | −0.342362 | − | 0.00843902i | ||||
\(227\) | 603192. | + | 603192.i | 0.776946 | + | 0.776946i | 0.979310 | − | 0.202365i | \(-0.0648626\pi\) |
−0.202365 | + | 0.979310i | \(0.564863\pi\) | |||||||
\(228\) | 103778. | − | 2.10379e6i | 0.132211 | − | 2.68019i | ||||
\(229\) | 578307. | − | 578307.i | 0.728736 | − | 0.728736i | −0.241632 | − | 0.970368i | \(-0.577683\pi\) |
0.970368 | + | 0.241632i | \(0.0776828\pi\) | |||||||
\(230\) | 264596. | + | 277970.i | 0.329810 | + | 0.346480i | ||||
\(231\) | − | 69396.0i | − | 0.0855666i | ||||||
\(232\) | −379741. | − | 440494.i | −0.463199 | − | 0.537304i | ||||
\(233\) | 815767.i | 0.984410i | 0.870479 | + | 0.492205i | \(0.163809\pi\) | ||||
−0.870479 | + | 0.492205i | \(0.836191\pi\) | |||||||
\(234\) | −1.03445e6 | + | 984679.i | −1.23501 | + | 1.17559i | ||||
\(235\) | 219085. | − | 219085.i | 0.258788 | − | 0.258788i | ||||
\(236\) | −93207.0 | + | 84443.7i | −0.108935 | + | 0.0986931i | ||||
\(237\) | 1.07605e6 | + | 1.07605e6i | 1.24441 | + | 1.24441i | ||||
\(238\) | 41782.0 | − | 1.69505e6i | 0.0478131 | − | 1.93972i | ||||
\(239\) | 255220. | 0.289015 | 0.144507 | − | 0.989504i | \(-0.453840\pi\) | ||||
0.144507 | + | 0.989504i | \(0.453840\pi\) | |||||||
\(240\) | −707890. | − | 70009.2i | −0.793300 | − | 0.0784561i | ||||
\(241\) | −1.21711e6 | −1.34986 | −0.674928 | − | 0.737883i | \(-0.735825\pi\) | ||||
−0.674928 | + | 0.737883i | \(0.735825\pi\) | |||||||
\(242\) | 22412.3 | − | 909240.i | 0.0246007 | − | 0.998022i | ||||
\(243\) | −448165. | − | 448165.i | −0.486880 | − | 0.486880i | ||||
\(244\) | 490686. | + | 541607.i | 0.527629 | + | 0.582385i | ||||
\(245\) | 111549. | − | 111549.i | 0.118727 | − | 0.118727i | ||||
\(246\) | 1.10424e6 | − | 1.05112e6i | 1.16340 | − | 1.10742i | ||||
\(247\) | 1.13032e6i | 1.17885i | ||||||||
\(248\) | 1.67023e6 | + | 123711.i | 1.72443 | + | 0.127726i | ||||
\(249\) | 2.98795e6i | 3.05404i | ||||||||
\(250\) | −60940.9 | − | 64021.1i | −0.0616679 | − | 0.0647848i | ||||
\(251\) | −711568. | + | 711568.i | −0.712906 | + | 0.712906i | −0.967142 | − | 0.254236i | \(-0.918176\pi\) |
0.254236 | + | 0.967142i | \(0.418176\pi\) | |||||||
\(252\) | −2.57119e6 | − | 126834.i | −2.55055 | − | 0.125816i | ||||
\(253\) | −31518.6 | − | 31518.6i | −0.0309575 | − | 0.0309575i | ||||
\(254\) | 1.61939e6 | + | 39917.0i | 1.57495 | + | 0.0388217i | ||||
\(255\) | −1.36947e6 | −1.31887 | ||||||||
\(256\) | 1.02826e6 | + | 205396.i | 0.980628 | + | 0.195881i | ||||
\(257\) | −394842. | −0.372899 | −0.186449 | − | 0.982465i | \(-0.559698\pi\) | ||||
−0.186449 | + | 0.982465i | \(0.559698\pi\) | |||||||
\(258\) | −1.77413e6 | − | 43731.2i | −1.65934 | − | 0.0409018i | ||||
\(259\) | 414923. | + | 414923.i | 0.384342 | + | 0.384342i | ||||
\(260\) | 381262. | + | 18807.2i | 0.349776 | + | 0.0172540i | ||||
\(261\) | −1.20203e6 | + | 1.20203e6i | −1.09223 | + | 1.09223i | ||||
\(262\) | −649907. | − | 682757.i | −0.584922 | − | 0.614487i | ||||
\(263\) | − | 446751.i | − | 0.398269i | −0.979972 | − | 0.199134i | \(-0.936187\pi\) | ||
0.979972 | − | 0.199134i | \(-0.0638130\pi\) | |||||||
\(264\) | 82395.7 | + | 6102.91i | 0.0727603 | + | 0.00538924i | ||||
\(265\) | 27542.3i | 0.0240927i | ||||||||
\(266\) | −1.47575e6 | + | 1.40474e6i | −1.27881 | + | 1.21729i | ||||
\(267\) | 1.19049e6 | − | 1.19049e6i | 1.02199 | − | 1.02199i | ||||
\(268\) | 826357. | + | 912113.i | 0.702798 | + | 0.775732i | ||||
\(269\) | −616974. | − | 616974.i | −0.519860 | − | 0.519860i | 0.397669 | − | 0.917529i | \(-0.369819\pi\) |
−0.917529 | + | 0.397669i | \(0.869819\pi\) | |||||||
\(270\) | −27705.2 | + | 1.12397e6i | −0.0231287 | + | 0.938306i | ||||
\(271\) | −302965. | −0.250593 | −0.125297 | − | 0.992119i | \(-0.539988\pi\) | ||||
−0.125297 | + | 0.992119i | \(0.539988\pi\) | |||||||
\(272\) | 2.00890e6 | + | 198677.i | 1.64640 | + | 0.162827i | ||||
\(273\) | 2.01589e6 | 1.63705 | ||||||||
\(274\) | 11477.6 | − | 465632.i | 0.00923579 | − | 0.374685i | ||||
\(275\) | 7259.27 | + | 7259.27i | 0.00578844 | + | 0.00578844i | ||||
\(276\) | −1.78818e6 | + | 1.62006e6i | −1.41299 | + | 1.28014i | ||||
\(277\) | −754020. | + | 754020.i | −0.590450 | + | 0.590450i | −0.937753 | − | 0.347303i | \(-0.887098\pi\) |
0.347303 | + | 0.937753i | \(0.387098\pi\) | |||||||
\(278\) | 1.24504e6 | − | 1.18514e6i | 0.966213 | − | 0.919725i | ||||
\(279\) | − | 4.89535e6i | − | 3.76507i | ||||||
\(280\) | 449270. | + | 521148.i | 0.342462 | + | 0.397252i | ||||
\(281\) | − | 1.82778e6i | − | 1.38088i | −0.723388 | − | 0.690442i | \(-0.757416\pi\) | ||
0.723388 | − | 0.690442i | \(-0.242584\pi\) | |||||||
\(282\) | 1.34312e6 | + | 1.41101e6i | 1.00576 | + | 1.05659i | ||||
\(283\) | 112611. | − | 112611.i | 0.0835825 | − | 0.0835825i | −0.664079 | − | 0.747662i | \(-0.731176\pi\) |
0.747662 | + | 0.664079i | \(0.231176\pi\) | |||||||
\(284\) | −97335.8 | + | 1.97320e6i | −0.0716105 | + | 1.45170i | ||||
\(285\) | 1.16360e6 | + | 1.16360e6i | 0.848581 | + | 0.848581i | ||||
\(286\) | −44323.3 | − | 1092.54i | −0.0320418 | − | 0.000789813i | ||||
\(287\) | −1.47465e6 | −1.05678 | ||||||||
\(288\) | 376712. | − | 3.04169e6i | 0.267626 | − | 2.16089i | ||||
\(289\) | 2.46651e6 | 1.73716 | ||||||||
\(290\) | 454224. | + | 11196.4i | 0.317157 | + | 0.00781775i | ||||
\(291\) | 1.57982e6 | + | 1.57982e6i | 1.09364 | + | 1.09364i | ||||
\(292\) | 29200.5 | − | 591956.i | 0.0200416 | − | 0.406286i | ||||
\(293\) | 1.02302e6 | − | 1.02302e6i | 0.696168 | − | 0.696168i | −0.267414 | − | 0.963582i | \(-0.586169\pi\) |
0.963582 | + | 0.267414i | \(0.0861691\pi\) | |||||||
\(294\) | 683860. | + | 718425.i | 0.461422 | + | 0.484745i | ||||
\(295\) | − | 98258.4i | − | 0.0657377i | ||||||
\(296\) | −529139. | + | 456159.i | −0.351027 | + | 0.302613i | ||||
\(297\) | − | 130587.i | − | 0.0859029i | ||||||
\(298\) | −2.08334e6 | + | 1.98311e6i | −1.35900 | + | 1.29362i | ||||
\(299\) | 915588. | − | 915588.i | 0.592273 | − | 0.592273i | ||||
\(300\) | 411849. | − | 373127.i | 0.264201 | − | 0.239361i | ||||
\(301\) | 1.21382e6 | + | 1.21382e6i | 0.772215 | + | 0.772215i | ||||
\(302\) | 12425.7 | − | 504096.i | 0.00783977 | − | 0.318050i | ||||
\(303\) | −778559. | −0.487175 | ||||||||
\(304\) | −1.53811e6 | − | 1.87573e6i | −0.954558 | − | 1.16409i | ||||
\(305\) | −570960. | −0.351444 | ||||||||
\(306\) | 145401. | − | 5.89875e6i | 0.0887695 | − | 3.60128i | ||||
\(307\) | 712045. | + | 712045.i | 0.431183 | + | 0.431183i | 0.889031 | − | 0.457848i | \(-0.151379\pi\) |
−0.457848 | + | 0.889031i | \(0.651379\pi\) | |||||||
\(308\) | −53657.8 | − | 59226.2i | −0.0322297 | − | 0.0355744i | ||||
\(309\) | 2.55595e6 | − | 2.55595e6i | 1.52285 | − | 1.52285i | ||||
\(310\) | −947725. | + | 902127.i | −0.560116 | + | 0.533167i | ||||
\(311\) | 459793.i | 0.269564i | 0.990875 | + | 0.134782i | \(0.0430334\pi\) | ||||
−0.990875 | + | 0.134782i | \(0.956967\pi\) | |||||||
\(312\) | −177284. | + | 2.39352e6i | −0.103106 | + | 1.39204i | ||||
\(313\) | − | 2.11774e6i | − | 1.22183i | −0.791696 | − | 0.610915i | \(-0.790802\pi\) | ||
0.791696 | − | 0.610915i | \(-0.209198\pi\) | |||||||
\(314\) | −231004. | − | 242680.i | −0.132219 | − | 0.138902i | ||||
\(315\) | 1.42212e6 | − | 1.42212e6i | 0.807534 | − | 0.807534i | ||||
\(316\) | 1.75038e6 | + | 86344.2i | 0.986085 | + | 0.0486424i | ||||
\(317\) | 818417. | + | 818417.i | 0.457432 | + | 0.457432i | 0.897812 | − | 0.440380i | \(-0.145156\pi\) |
−0.440380 | + | 0.897812i | \(0.645156\pi\) | |||||||
\(318\) | −173118. | − | 4267.26i | −0.0960007 | − | 0.00236636i | ||||
\(319\) | −52773.3 | −0.0290361 | ||||||||
\(320\) | −658283. | + | 487599.i | −0.359366 | + | 0.266188i | ||||
\(321\) | 5.57542e6 | 3.02006 | ||||||||
\(322\) | 2.33327e6 | + | 57513.7i | 1.25408 | + | 0.0309123i | ||||
\(323\) | −3.30216e6 | − | 3.30216e6i | −1.76113 | − | 1.76113i | ||||
\(324\) | −2.95110e6 | − | 145574.i | −1.56178 | − | 0.0770410i | ||||
\(325\) | −210875. | + | 210875.i | −0.110743 | + | 0.110743i | ||||
\(326\) | −657944. | − | 691199.i | −0.342882 | − | 0.360213i | ||||
\(327\) | 363494.i | 0.187987i | ||||||||
\(328\) | 129686. | − | 1.75089e6i | 0.0665591 | − | 0.898617i | ||||
\(329\) | − | 1.88432e6i | − | 0.959766i | ||||||
\(330\) | −46753.1 | + | 44503.7i | −0.0236334 | + | 0.0224963i | ||||
\(331\) | −930448. | + | 930448.i | −0.466790 | + | 0.466790i | −0.900873 | − | 0.434083i | \(-0.857073\pi\) |
0.434083 | + | 0.900873i | \(0.357073\pi\) | |||||||
\(332\) | 2.31032e6 | + | 2.55008e6i | 1.15034 | + | 1.26972i | ||||
\(333\) | 1.44393e6 | + | 1.44393e6i | 0.713568 | + | 0.713568i | ||||
\(334\) | 16932.4 | − | 686928.i | 0.00830524 | − | 0.336934i | ||||
\(335\) | −961546. | −0.468121 | ||||||||
\(336\) | −3.34530e6 | + | 2.74316e6i | −1.61654 | + | 1.32557i | ||||
\(337\) | −1.66985e6 | −0.800946 | −0.400473 | − | 0.916308i | \(-0.631154\pi\) | ||||
−0.400473 | + | 0.916308i | \(0.631154\pi\) | |||||||
\(338\) | −20019.3 | + | 812160.i | −0.00953141 | + | 0.386679i | ||||
\(339\) | 913350. | + | 913350.i | 0.431656 | + | 0.431656i | ||||
\(340\) | −1.16877e6 | + | 1.05889e6i | −0.548319 | + | 0.496766i | ||||
\(341\) | 107461. | − | 107461.i | 0.0500456 | − | 0.0500456i | ||||
\(342\) | −5.13558e6 | + | 4.88849e6i | −2.37424 | + | 2.26001i | ||||
\(343\) | 1.59598e6i | 0.732472i | ||||||||
\(344\) | −1.54795e6 | + | 1.33445e6i | −0.705277 | + | 0.608005i | ||||
\(345\) | − | 1.88510e6i | − | 0.852679i | ||||||
\(346\) | −1.20970e6 | − | 1.27085e6i | −0.543236 | − | 0.570694i | ||||
\(347\) | 2.96486e6 | − | 2.96486e6i | 1.32185 | − | 1.32185i | 0.409565 | − | 0.912281i | \(-0.365680\pi\) |
0.912281 | − | 0.409565i | \(-0.134320\pi\) | |||||||
\(348\) | −140750. | + | 2.85330e6i | −0.0623019 | + | 1.26299i | ||||
\(349\) | −2.89685e6 | − | 2.89685e6i | −1.27310 | − | 1.27310i | −0.944452 | − | 0.328650i | \(-0.893406\pi\) |
−0.328650 | − | 0.944452i | \(-0.606594\pi\) | |||||||
\(350\) | −537391. | − | 13246.4i | −0.234488 | − | 0.00577999i | ||||
\(351\) | 3.79343e6 | 1.64348 | ||||||||
\(352\) | 75039.7 | − | 58500.7i | 0.0322800 | − | 0.0251654i | ||||
\(353\) | −2.14860e6 | −0.917740 | −0.458870 | − | 0.888503i | \(-0.651746\pi\) | ||||
−0.458870 | + | 0.888503i | \(0.651746\pi\) | |||||||
\(354\) | 617607. | + | 15223.7i | 0.261941 | + | 0.00645670i | ||||
\(355\) | −1.09138e6 | − | 1.09138e6i | −0.459625 | − | 0.459625i | ||||
\(356\) | 95526.7 | − | 1.93653e6i | 0.0399484 | − | 0.809839i | ||||
\(357\) | −5.88930e6 | + | 5.88930e6i | −2.44564 | + | 2.44564i | ||||
\(358\) | 2.65590e6 | + | 2.79014e6i | 1.09523 | + | 1.15058i | ||||
\(359\) | 2.61006e6i | 1.06884i | 0.845218 | + | 0.534421i | \(0.179470\pi\) | ||||
−0.845218 | + | 0.534421i | \(0.820530\pi\) | |||||||
\(360\) | 1.56346e6 | + | 1.81359e6i | 0.635814 | + | 0.737535i | ||||
\(361\) | 3.13544e6i | 1.26628i | ||||||||
\(362\) | 1.07208e6 | − | 1.02050e6i | 0.429988 | − | 0.409300i | ||||
\(363\) | −3.15907e6 | + | 3.15907e6i | −1.25833 | + | 1.25833i | ||||
\(364\) | 1.72047e6 | − | 1.55871e6i | 0.680602 | − | 0.616612i | ||||
\(365\) | 327410. | + | 327410.i | 0.128635 | + | 0.128635i | ||||
\(366\) | 88461.7 | − | 3.58879e6i | 0.0345186 | − | 1.40038i | ||||
\(367\) | −7255.03 | −0.00281173 | −0.00140587 | − | 0.999999i | \(-0.500448\pi\) | ||||
−0.00140587 | + | 0.999999i | \(0.500448\pi\) | |||||||
\(368\) | −273483. | + | 2.76529e6i | −0.105271 | + | 1.06444i | ||||
\(369\) | −5.13177e6 | −1.96201 | ||||||||
\(370\) | 13449.5 | − | 545631.i | 0.00510742 | − | 0.207202i | ||||
\(371\) | 118444. | + | 118444.i | 0.0446763 | + | 0.0446763i | ||||
\(372\) | −5.52352e6 | − | 6.09673e6i | −2.06947 | − | 2.28423i | ||||
\(373\) | 3.28076e6 | − | 3.28076e6i | 1.22096 | − | 1.22096i | 0.253675 | − | 0.967290i | \(-0.418361\pi\) |
0.967290 | − | 0.253675i | \(-0.0816393\pi\) | |||||||
\(374\) | 132679. | − | 126296.i | 0.0490484 | − | 0.0466885i | ||||
\(375\) | 434170.i | 0.159434i | ||||||||
\(376\) | 2.23730e6 | + | 165714.i | 0.816123 | + | 0.0604489i | ||||
\(377\) | − | 1.53302e6i | − | 0.555513i | ||||||
\(378\) | 4.71440e6 | + | 4.95269e6i | 1.69706 | + | 1.78284i | ||||
\(379\) | −1.97719e6 | + | 1.97719e6i | −0.707051 | + | 0.707051i | −0.965914 | − | 0.258863i | \(-0.916652\pi\) |
0.258863 | + | 0.965914i | \(0.416652\pi\) | |||||||
\(380\) | 1.89279e6 | + | 93369.4i | 0.672426 | + | 0.0331700i | ||||
\(381\) | −5.62642e6 | − | 5.62642e6i | −1.98573 | − | 1.98573i | ||||
\(382\) | −817027. | − | 20139.3i | −0.286469 | − | 0.00706130i | ||||
\(383\) | 925457. | 0.322374 | 0.161187 | − | 0.986924i | \(-0.448468\pi\) | ||||
0.161187 | + | 0.986924i | \(0.448468\pi\) | |||||||
\(384\) | −2.96283e6 | − | 4.21321e6i | −1.02537 | − | 1.45809i | ||||
\(385\) | 62436.0 | 0.0214676 | ||||||||
\(386\) | −3.24291e6 | − | 79936.1i | −1.10781 | − | 0.0273070i | ||||
\(387\) | 4.22408e6 | + | 4.22408e6i | 1.43369 | + | 1.43369i | ||||
\(388\) | 2.56984e6 | + | 126767.i | 0.866617 | + | 0.0427492i | ||||
\(389\) | −1.44312e6 | + | 1.44312e6i | −0.483536 | + | 0.483536i | −0.906259 | − | 0.422723i | \(-0.861074\pi\) |
0.422723 | + | 0.906259i | \(0.361074\pi\) | |||||||
\(390\) | −1.29279e6 | − | 1.35814e6i | −0.430395 | − | 0.452150i | ||||
\(391\) | 5.34966e6i | 1.76964i | ||||||||
\(392\) | 1.13914e6 | + | 84374.0i | 0.374421 | + | 0.0277328i | ||||
\(393\) | 4.63022e6i | 1.51224i | ||||||||
\(394\) | −1.32685e6 | + | 1.26301e6i | −0.430607 | + | 0.409889i | ||||
\(395\) | −968132. | + | 968132.i | −0.312207 | + | 0.312207i | ||||
\(396\) | −186729. | − | 206107.i | −0.0598374 | − | 0.0660472i | ||||
\(397\) | 2.24787e6 | + | 2.24787e6i | 0.715807 | + | 0.715807i | 0.967744 | − | 0.251937i | \(-0.0810676\pi\) |
−0.251937 | + | 0.967744i | \(0.581068\pi\) | |||||||
\(398\) | −63483.2 | + | 2.57544e6i | −0.0200887 | + | 0.814974i | ||||
\(399\) | 1.00080e7 | 3.14713 | ||||||||
\(400\) | 62987.7 | − | 636893.i | 0.0196836 | − | 0.199029i | ||||
\(401\) | −2.69259e6 | −0.836200 | −0.418100 | − | 0.908401i | \(-0.637304\pi\) | ||||
−0.418100 | + | 0.908401i | \(0.637304\pi\) | |||||||
\(402\) | 148977. | − | 6.04383e6i | 0.0459785 | − | 1.86529i | ||||
\(403\) | 3.12165e6 | + | 3.12165e6i | 0.957463 | + | 0.957463i | ||||
\(404\) | −664463. | + | 601990.i | −0.202543 | + | 0.183500i | ||||
\(405\) | 1.63225e6 | − | 1.63225e6i | 0.494480 | − | 0.494480i | ||||
\(406\) | 2.00151e6 | − | 1.90521e6i | 0.602618 | − | 0.573624i | ||||
\(407\) | 63393.3i | 0.0189696i | ||||||||
\(408\) | −6.47459e6 | − | 7.51044e6i | −1.92558 | − | 2.23365i | ||||
\(409\) | − | 625505.i | − | 0.184894i | −0.995718 | − | 0.0924470i | \(-0.970531\pi\) | ||
0.995718 | − | 0.0924470i | \(-0.0294689\pi\) | |||||||
\(410\) | 945695. | + | 993495.i | 0.277838 | + | 0.291881i | ||||
\(411\) | −1.61780e6 | + | 1.61780e6i | −0.472411 | + | 0.472411i | ||||
\(412\) | 205093. | − | 4.15768e6i | 0.0595263 | − | 1.20672i | ||||
\(413\) | −422553. | − | 422553.i | −0.121901 | − | 0.121901i | ||||
\(414\) | 8.11974e6 | + | 200147.i | 2.32831 | + | 0.0573916i | ||||
\(415\) | −2.68828e6 | −0.766221 | ||||||||
\(416\) | 1.69939e6 | + | 2.17983e6i | 0.481460 | + | 0.617576i | ||||
\(417\) | −8.44346e6 | −2.37783 | ||||||||
\(418\) | −220045. | − | 5424.00i | −0.0615987 | − | 0.00151837i | ||||
\(419\) | −3.97089e6 | − | 3.97089e6i | −1.10497 | − | 1.10497i | −0.993801 | − | 0.111174i | \(-0.964539\pi\) |
−0.111174 | − | 0.993801i | \(-0.535461\pi\) | |||||||
\(420\) | 166521. | − | 3.37574e6i | 0.0460624 | − | 0.933782i | ||||
\(421\) | 4.47822e6 | − | 4.47822e6i | 1.23140 | − | 1.23140i | 0.267979 | − | 0.963425i | \(-0.413644\pi\) |
0.963425 | − | 0.267979i | \(-0.0863558\pi\) | |||||||
\(422\) | 2.07301e6 | + | 2.17779e6i | 0.566658 | + | 0.595300i | ||||
\(423\) | − | 6.55743e6i | − | 1.78190i | ||||||
\(424\) | −151048. | + | 130215.i | −0.0408036 | + | 0.0351760i | ||||
\(425\) | − | 1.23212e6i | − | 0.330887i | ||||||
\(426\) | 7.02897e6 | − | 6.69079e6i | 1.87658 | − | 1.78630i | ||||
\(427\) | −2.45537e6 | + | 2.45537e6i | −0.651701 | + | 0.651701i | ||||
\(428\) | 4.75836e6 | − | 4.31098e6i | 1.25559 | − | 1.13754i | ||||
\(429\) | 153997. | + | 153997.i | 0.0403989 | + | 0.0403989i | ||||
\(430\) | 39345.3 | − | 1.59619e6i | 0.0102617 | − | 0.416307i | ||||
\(431\) | −3.93764e6 | −1.02104 | −0.510521 | − | 0.859865i | \(-0.670547\pi\) | ||||
−0.510521 | + | 0.859865i | \(0.670547\pi\) | |||||||
\(432\) | −6.29506e6 | + | 5.16198e6i | −1.62290 | + | 1.33078i | ||||
\(433\) | −3.83172e6 | −0.982141 | −0.491071 | − | 0.871120i | \(-0.663394\pi\) | ||||
−0.491071 | + | 0.871120i | \(0.663394\pi\) | |||||||
\(434\) | −196090. | + | 7.95516e6i | −0.0499726 | + | 2.02733i | ||||
\(435\) | −1.57816e6 | − | 1.57816e6i | −0.399878 | − | 0.399878i | ||||
\(436\) | 281058. | + | 310225.i | 0.0708075 | + | 0.0781556i | ||||
\(437\) | 4.54548e6 | − | 4.54548e6i | 1.13861 | − | 1.13861i | ||||
\(438\) | −2.10868e6 | + | 2.00722e6i | −0.525200 | + | 0.499931i | ||||
\(439\) | − | 1.34172e6i | − | 0.332278i | −0.986102 | − | 0.166139i | \(-0.946870\pi\) | ||
0.986102 | − | 0.166139i | \(-0.0531301\pi\) | |||||||
\(440\) | −5490.83 | + | 74131.9i | −0.00135209 | + | 0.0182546i | ||||
\(441\) | − | 3.33875e6i | − | 0.817500i | ||||||
\(442\) | 3.66878e6 | + | 3.85422e6i | 0.893236 | + | 0.938384i | ||||
\(443\) | −655716. | + | 655716.i | −0.158747 | + | 0.158747i | −0.782011 | − | 0.623264i | \(-0.785806\pi\) |
0.623264 | + | 0.782011i | \(0.285806\pi\) | |||||||
\(444\) | 3.42750e6 | + | 169075.i | 0.825125 | + | 0.0407025i | ||||
\(445\) | 1.07109e6 | + | 1.07109e6i | 0.256405 | + | 0.256405i | ||||
\(446\) | 2.10800e6 | + | 51961.1i | 0.501804 | + | 0.0123692i | ||||
\(447\) | 1.41285e7 | 3.34448 | ||||||||
\(448\) | −734013. | + | 4.92778e6i | −0.172786 | + | 1.16000i | ||||
\(449\) | 3.17602e6 | 0.743476 | 0.371738 | − | 0.928338i | \(-0.378762\pi\) | ||||
0.371738 | + | 0.928338i | \(0.378762\pi\) | |||||||
\(450\) | −1.87011e6 | − | 46097.3i | −0.435348 | − | 0.0107311i | ||||
\(451\) | −112651. | − | 112651.i | −0.0260792 | − | 0.0260792i | ||||
\(452\) | 1.48571e6 | + | 73288.6i | 0.342050 | + | 0.0168729i | ||||
\(453\) | −1.75144e6 | + | 1.75144e6i | −0.401004 | + | 0.401004i | ||||
\(454\) | −3.32705e6 | − | 3.49521e6i | −0.757564 | − | 0.795855i | ||||
\(455\) | 1.81371e6i | 0.410714i | ||||||||
\(456\) | −880137. | + | 1.18828e7i | −0.198216 | + | 2.67612i | ||||
\(457\) | − | 4.41310e6i | − | 0.988447i | −0.869335 | − | 0.494224i | \(-0.835452\pi\) | ||
0.869335 | − | 0.494224i | \(-0.164548\pi\) | |||||||
\(458\) | −3.35102e6 | + | 3.18979e6i | −0.746472 | + | 0.710557i | ||||
\(459\) | −1.10822e7 | + | 1.10822e7i | −2.45525 | + | 2.45525i | ||||
\(460\) | −1.45758e6 | − | 1.60884e6i | −0.321172 | − | 0.354502i | ||||
\(461\) | −2.80445e6 | − | 2.80445e6i | −0.614604 | − | 0.614604i | 0.329539 | − | 0.944142i | \(-0.393107\pi\) |
−0.944142 | + | 0.329539i | \(0.893107\pi\) | |||||||
\(462\) | −9673.52 | + | 392444.i | −0.00210853 | + | 0.0855407i | ||||
\(463\) | −2.47795e6 | −0.537205 | −0.268603 | − | 0.963251i | \(-0.586562\pi\) | ||||
−0.268603 | + | 0.963251i | \(0.586562\pi\) | |||||||
\(464\) | 2.08608e6 | + | 2.54399e6i | 0.449818 | + | 0.548555i | ||||
\(465\) | 6.42714e6 | 1.37843 | ||||||||
\(466\) | 113715. | − | 4.61327e6i | 0.0242578 | − | 0.984111i | ||||
\(467\) | −1.18173e6 | − | 1.18173e6i | −0.250742 | − | 0.250742i | 0.570533 | − | 0.821275i | \(-0.306737\pi\) |
−0.821275 | + | 0.570533i | \(0.806737\pi\) | |||||||
\(468\) | 5.98722e6 | − | 5.42430e6i | 1.26360 | − | 1.14480i | ||||
\(469\) | −4.13506e6 | + | 4.13506e6i | −0.868060 | + | 0.868060i | ||||
\(470\) | −1.26950e6 | + | 1.20842e6i | −0.265086 | + | 0.252332i | ||||
\(471\) | 1.64577e6i | 0.341835i | ||||||||
\(472\) | 538869. | − | 464548.i | 0.111334 | − | 0.0959788i | ||||
\(473\) | 185451.i | 0.0381134i | ||||||||
\(474\) | −5.93523e6 | − | 6.23523e6i | −1.21337 | − | 1.27470i | ||||
\(475\) | −1.04690e6 | + | 1.04690e6i | −0.212898 | + | 0.212898i | ||||
\(476\) | −472566. | + | 9.57991e6i | −0.0955972 | + | 1.93796i | ||||
\(477\) | 412183. | + | 412183.i | 0.0829457 | + | 0.0829457i | ||||
\(478\) | −1.44330e6 | − | 35576.6i | −0.288927 | − | 0.00712189i | ||||
\(479\) | 9.82296e6 | 1.95616 | 0.978078 | − | 0.208240i | \(-0.0667734\pi\) | ||||
0.978078 | + | 0.208240i | \(0.0667734\pi\) | |||||||
\(480\) | 3.99345e6 | + | 494588.i | 0.791126 | + | 0.0979808i | ||||
\(481\) | −1.84152e6 | −0.362922 | ||||||||
\(482\) | 6.88293e6 | + | 169660.i | 1.34945 | + | 0.0332631i | ||||
\(483\) | −8.10672e6 | − | 8.10672e6i | −1.58117 | − | 1.58117i | ||||
\(484\) | −253489. | + | 5.13875e6i | −0.0491864 | + | 0.997112i | ||||
\(485\) | −1.42138e6 | + | 1.42138e6i | −0.274381 | + | 0.274381i | ||||
\(486\) | 2.47196e6 | + | 2.59691e6i | 0.474735 | + | 0.498730i | ||||
\(487\) | − | 2.05462e6i | − | 0.392562i | −0.980548 | − | 0.196281i | \(-0.937114\pi\) | ||
0.980548 | − | 0.196281i | \(-0.0628865\pi\) | |||||||
\(488\) | −2.69940e6 | − | 3.13126e6i | −0.513118 | − | 0.595210i | ||||
\(489\) | 4.68748e6i | 0.886476i | ||||||||
\(490\) | −646372. | + | 615273.i | −0.121616 | + | 0.115765i | ||||
\(491\) | 4.27455e6 | − | 4.27455e6i | 0.800178 | − | 0.800178i | −0.182945 | − | 0.983123i | \(-0.558563\pi\) |
0.983123 | + | 0.182945i | \(0.0585631\pi\) | |||||||
\(492\) | −6.39117e6 | + | 5.79028e6i | −1.19033 | + | 1.07842i | ||||
\(493\) | 4.47861e6 | + | 4.47861e6i | 0.829901 | + | 0.829901i | ||||
\(494\) | 157562. | − | 6.39212e6i | 0.0290492 | − | 1.17849i | ||||
\(495\) | 217277. | 0.0398566 | ||||||||
\(496\) | −9.42812e6 | − | 932426.i | −1.72076 | − | 0.170181i | ||||
\(497\) | −9.38677e6 | −1.70461 | ||||||||
\(498\) | 416509. | − | 1.68973e7i | 0.0752576 | − | 3.05312i | ||||
\(499\) | −2.64763e6 | − | 2.64763e6i | −0.475999 | − | 0.475999i | 0.427850 | − | 0.903850i | \(-0.359271\pi\) |
−0.903850 | + | 0.427850i | \(0.859271\pi\) | |||||||
\(500\) | 335705. | + | 370543.i | 0.0600527 | + | 0.0662848i | ||||
\(501\) | −2.38667e6 | + | 2.38667e6i | −0.424813 | + | 0.424813i | ||||
\(502\) | 4.12320e6 | − | 3.92483e6i | 0.730257 | − | 0.695122i | ||||
\(503\) | − | 475460.i | − | 0.0837904i | −0.999122 | − | 0.0418952i | \(-0.986660\pi\) | ||
0.999122 | − | 0.0418952i | \(-0.0133396\pi\) | |||||||
\(504\) | 1.45228e7 | + | 1.07568e6i | 2.54667 | + | 0.188628i | ||||
\(505\) | − | 700474.i | − | 0.122226i | ||||||
\(506\) | 173849. | + | 182636.i | 0.0301852 | + | 0.0317110i | ||||
\(507\) | 2.82178e6 | − | 2.82178e6i | 0.487532 | − | 0.487532i | ||||
\(508\) | −9.15230e6 | − | 451473.i | −1.57352 | − | 0.0776197i | ||||
\(509\) | 2.26623e6 | + | 2.26623e6i | 0.387712 | + | 0.387712i | 0.873870 | − | 0.486159i | \(-0.161602\pi\) |
−0.486159 | + | 0.873870i | \(0.661602\pi\) | |||||||
\(510\) | 7.74452e6 | + | 190898.i | 1.31847 | + | 0.0324995i | ||||
\(511\) | 2.81601e6 | 0.477070 | ||||||||
\(512\) | −5.78633e6 | − | 1.30488e6i | −0.975503 | − | 0.219986i | ||||
\(513\) | 1.88327e7 | 3.15950 | ||||||||
\(514\) | 2.23289e6 | + | 55039.4i | 0.372785 | + | 0.00918895i | ||||
\(515\) | 2.29961e6 | + | 2.29961e6i | 0.382063 | + | 0.382063i | ||||
\(516\) | 1.00268e7 | + | 494612.i | 1.65783 | + | 0.0817788i | ||||
\(517\) | 143947. | − | 143947.i | 0.0236851 | − | 0.0236851i | ||||
\(518\) | −2.28861e6 | − | 2.40429e6i | −0.374755 | − | 0.393697i | ||||
\(519\) | 8.61845e6i | 1.40447i | ||||||||
\(520\) | −2.15346e6 | − | 159504.i | −0.349244 | − | 0.0258680i | ||||
\(521\) | − | 5.50679e6i | − | 0.888801i | −0.895828 | − | 0.444401i | \(-0.853417\pi\) | ||
0.895828 | − | 0.444401i | \(-0.146583\pi\) | |||||||
\(522\) | 6.96522e6 | − | 6.63011e6i | 1.11882 | − | 1.06499i | ||||
\(523\) | 4.02488e6 | − | 4.02488e6i | 0.643426 | − | 0.643426i | −0.307970 | − | 0.951396i | \(-0.599650\pi\) |
0.951396 | + | 0.307970i | \(0.0996496\pi\) | |||||||
\(524\) | 3.58014e6 | + | 3.95168e6i | 0.569602 | + | 0.628714i | ||||
\(525\) | 1.86712e6 | + | 1.86712e6i | 0.295647 | + | 0.295647i | ||||
\(526\) | −62275.3 | + | 2.52644e6i | −0.00981412 | + | 0.398148i | ||||
\(527\) | −1.82394e7 | −2.86078 | ||||||||
\(528\) | −465108. | − | 45998.4i | −0.0726054 | − | 0.00718056i | ||||
\(529\) | −927561. | −0.144113 | ||||||||
\(530\) | 3839.28 | − | 155755.i | 0.000593691 | − | 0.0240854i | ||||
\(531\) | −1.47048e6 | − | 1.47048e6i | −0.226320 | − | 0.226320i | ||||
\(532\) | 8.54136e6 | − | 7.73830e6i | 1.30842 | − | 1.18540i | ||||
\(533\) | 3.27241e6 | − | 3.27241e6i | 0.498942 | − | 0.498942i | ||||
\(534\) | −6.89833e6 | + | 6.56643e6i | −1.04687 | + | 0.996497i | ||||
\(535\) | 5.01624e6i | 0.757694i | ||||||||
\(536\) | −4.54601e6 | − | 5.27332e6i | −0.683469 | − | 0.792815i | ||||
\(537\) | − | 1.89218e7i | − | 2.83156i | ||||||
\(538\) | 3.40307e6 | + | 3.57508e6i | 0.506892 | + | 0.532513i | ||||
\(539\) | 73291.2 | − | 73291.2i | 0.0108663 | − | 0.0108663i | ||||
\(540\) | 313353. | − | 6.35233e6i | 0.0462434 | − | 0.937451i | ||||
\(541\) | 7.20318e6 | + | 7.20318e6i | 1.05811 | + | 1.05811i | 0.998204 | + | 0.0599075i | \(0.0190806\pi\) |
0.0599075 | + | 0.998204i | \(0.480919\pi\) | |||||||
\(542\) | 1.71331e6 | + | 42232.1i | 0.250517 | + | 0.00617511i | ||||
\(543\) | −7.27049e6 | −1.05819 | ||||||||
\(544\) | −1.13329e7 | − | 1.40358e6i | −1.64189 | − | 0.203348i | ||||
\(545\) | −327038. | −0.0471635 | ||||||||
\(546\) | −1.14001e7 | − | 281007.i | −1.63655 | − | 0.0403400i | ||||
\(547\) | 579264. | + | 579264.i | 0.0827767 | + | 0.0827767i | 0.747283 | − | 0.664506i | \(-0.231358\pi\) |
−0.664506 | + | 0.747283i | \(0.731358\pi\) | |||||||
\(548\) | −129815. | + | 2.63161e6i | −0.0184660 | + | 0.374344i | ||||
\(549\) | −8.54468e6 | + | 8.54468e6i | −1.20994 | + | 1.20994i | ||||
\(550\) | −40040.3 | − | 42064.1i | −0.00564404 | − | 0.00592932i | ||||
\(551\) | − | 7.61075e6i | − | 1.06794i | ||||||
\(552\) | 1.03383e7 | − | 8.91239e6i | 1.44411 | − | 1.24493i | ||||
\(553\) | 8.32677e6i | 1.15788i | ||||||||
\(554\) | 4.36919e6 | − | 4.15898e6i | 0.604821 | − | 0.575721i | ||||
\(555\) | −1.89574e6 | + | 1.89574e6i | −0.261245 | + | 0.261245i | ||||
\(556\) | −7.20610e6 | + | 6.52858e6i | −0.988583 | + | 0.895637i | ||||
\(557\) | 1.06112e6 | + | 1.06112e6i | 0.144920 | + | 0.144920i | 0.775844 | − | 0.630925i | \(-0.217324\pi\) |
−0.630925 | + | 0.775844i | \(0.717324\pi\) | |||||||
\(558\) | −682392. | + | 2.76839e7i | −0.0927788 | + | 3.76393i | ||||
\(559\) | −5.38720e6 | −0.729178 | ||||||||
\(560\) | −2.46804e6 | − | 3.00979e6i | −0.332569 | − | 0.405570i | ||||
\(561\) | −899786. | −0.120707 | ||||||||
\(562\) | −254785. | + | 1.03363e7i | −0.0340277 | + | 1.38046i | ||||
\(563\) | 5.65144e6 | + | 5.65144e6i | 0.751429 | + | 0.751429i | 0.974746 | − | 0.223317i | \(-0.0716885\pi\) |
−0.223317 | + | 0.974746i | \(0.571688\pi\) | |||||||
\(564\) | −7.39887e6 | − | 8.16670e6i | −0.979416 | − | 1.08106i | ||||
\(565\) | −821747. | + | 821747.i | −0.108297 | + | 0.108297i | ||||
\(566\) | −652529. | + | 621134.i | −0.0856168 | + | 0.0814975i | ||||
\(567\) | − | 1.40387e7i | − | 1.83388i | ||||||
\(568\) | 825504. | − | 1.11452e7i | 0.107361 | − | 1.44949i | ||||
\(569\) | − | 5.69200e6i | − | 0.737028i | −0.929622 | − | 0.368514i | \(-0.879867\pi\) | ||
0.929622 | − | 0.368514i | \(-0.120133\pi\) | |||||||
\(570\) | −6.41814e6 | − | 6.74255e6i | −0.827413 | − | 0.869234i | ||||
\(571\) | −500996. | + | 500996.i | −0.0643049 | + | 0.0643049i | −0.738528 | − | 0.674223i | \(-0.764479\pi\) |
0.674223 | + | 0.738528i | \(0.264479\pi\) | |||||||
\(572\) | 250502. | + | 12357.0i | 0.0320126 | + | 0.00157915i | ||||
\(573\) | 2.83869e6 | + | 2.83869e6i | 0.361186 | + | 0.361186i | ||||
\(574\) | 8.33936e6 | + | 205561.i | 1.05646 | + | 0.0260411i | ||||
\(575\) | 1.69603e6 | 0.213926 | ||||||||
\(576\) | −2.55436e6 | + | 1.71486e7i | −0.320794 | + | 2.15364i | ||||
\(577\) | 4.96081e6 | 0.620316 | 0.310158 | − | 0.950685i | \(-0.399618\pi\) | ||||
0.310158 | + | 0.950685i | \(0.399618\pi\) | |||||||
\(578\) | −1.39485e7 | − | 343822.i | −1.73663 | − | 0.0428069i | ||||
\(579\) | 1.12672e7 | + | 1.12672e7i | 1.39676 | + | 1.39676i | ||||
\(580\) | −2.56714e6 | − | 126634.i | −0.316868 | − | 0.0156308i | ||||
\(581\) | −1.15608e7 | + | 1.15608e7i | −1.42084 | + | 1.42084i | ||||
\(582\) | −8.71389e6 | − | 9.15434e6i | −1.06636 | − | 1.12026i | ||||
\(583\) | 18096.2i | 0.00220504i | ||||||||
\(584\) | −247649. | + | 3.34352e6i | −0.0300473 | + | 0.405669i | ||||
\(585\) | 6.31170e6i | 0.762529i | ||||||||
\(586\) | −5.92791e6 | + | 5.64270e6i | −0.713111 | + | 0.678802i | ||||
\(587\) | −2.22699e6 | + | 2.22699e6i | −0.266761 | + | 0.266761i | −0.827794 | − | 0.561032i | \(-0.810404\pi\) |
0.561032 | + | 0.827794i | \(0.310404\pi\) | |||||||
\(588\) | −3.76717e6 | − | 4.15812e6i | −0.449337 | − | 0.495968i | ||||
\(589\) | 1.54976e7 | + | 1.54976e7i | 1.84067 | + | 1.84067i | ||||
\(590\) | −13696.8 | + | 555664.i | −0.00161991 | + | 0.0657177i | ||||
\(591\) | 8.99824e6 | 1.05971 | ||||||||
\(592\) | 3.05594e6 | − | 2.50588e6i | 0.358377 | − | 0.293871i | ||||
\(593\) | −749550. | −0.0875314 | −0.0437657 | − | 0.999042i | \(-0.513936\pi\) | ||||
−0.0437657 | + | 0.999042i | \(0.513936\pi\) | |||||||
\(594\) | −18203.3 | + | 738486.i | −0.00211682 | + | 0.0858768i | ||||
\(595\) | −5.29864e6 | − | 5.29864e6i | −0.613581 | − | 0.613581i | ||||
\(596\) | 1.20580e7 | − | 1.09243e7i | 1.39047 | − | 1.25974i | ||||
\(597\) | 8.94814e6 | − | 8.94814e6i | 1.02754 | − | 1.02754i | ||||
\(598\) | −5.30540e6 | + | 5.05014e6i | −0.606688 | + | 0.577498i | ||||
\(599\) | − | 1.24336e7i | − | 1.41589i | −0.706267 | − | 0.707946i | \(-0.749622\pi\) | ||
0.706267 | − | 0.707946i | \(-0.250378\pi\) | |||||||
\(600\) | −2.38108e6 | + | 2.05267e6i | −0.270019 | + | 0.232778i | ||||
\(601\) | − | 1.06573e7i | − | 1.20354i | −0.798668 | − | 0.601772i | \(-0.794462\pi\) | ||
0.798668 | − | 0.601772i | \(-0.205538\pi\) | |||||||
\(602\) | −6.69511e6 | − | 7.03352e6i | −0.752951 | − | 0.791009i | ||||
\(603\) | −1.43900e7 | + | 1.43900e7i | −1.61164 | + | 1.61164i | ||||
\(604\) | −140538. | + | 2.84900e6i | −0.0156748 | + | 0.317761i | ||||
\(605\) | −2.84224e6 | − | 2.84224e6i | −0.315698 | − | 0.315698i | ||||
\(606\) | 4.40286e6 | + | 108528.i | 0.487027 | + | 0.0120049i | ||||
\(607\) | 1.21466e7 | 1.33808 | 0.669039 | − | 0.743228i | \(-0.266706\pi\) | ||||
0.669039 | + | 0.743228i | \(0.266706\pi\) | |||||||
\(608\) | 8.43673e6 | + | 1.08219e7i | 0.925583 | + | 1.18726i | ||||
\(609\) | −1.35735e7 | −1.48303 | ||||||||
\(610\) | 3.22886e6 | + | 79589.5i | 0.351337 | + | 0.00866027i | ||||
\(611\) | 4.18152e6 | + | 4.18152e6i | 0.453139 | + | 0.453139i | ||||
\(612\) | −1.64453e6 | + | 3.33380e7i | −0.177485 | + | 3.59800i | ||||
\(613\) | 189949. | − | 189949.i | 0.0204168 | − | 0.0204168i | −0.696825 | − | 0.717241i | \(-0.745404\pi\) |
0.717241 | + | 0.696825i | \(0.245404\pi\) | |||||||
\(614\) | −3.92746e6 | − | 4.12597e6i | −0.420427 | − | 0.441677i | ||||
\(615\) | − | 6.73755e6i | − | 0.718313i | ||||||
\(616\) | 295186. | + | 342412.i | 0.0313433 | + | 0.0363578i | ||||
\(617\) | 1.08751e7i | 1.15006i | 0.818133 | + | 0.575028i | \(0.195009\pi\) | ||||
−0.818133 | + | 0.575028i | \(0.804991\pi\) | |||||||
\(618\) | −1.48106e7 | + | 1.40980e7i | −1.55991 | + | 1.48486i | ||||
\(619\) | 1.32235e7 | − | 1.32235e7i | 1.38714 | − | 1.38714i | 0.555859 | − | 0.831277i | \(-0.312389\pi\) |
0.831277 | − | 0.555859i | \(-0.187611\pi\) | |||||||
\(620\) | 5.48527e6 | − | 4.96954e6i | 0.573084 | − | 0.519203i | ||||
\(621\) | −1.52549e7 | − | 1.52549e7i | −1.58738 | − | 1.58738i | ||||
\(622\) | 64093.3 | − | 2.60019e6i | 0.00664258 | − | 0.269482i | ||||
\(623\) | 9.21230e6 | 0.950929 | ||||||||
\(624\) | 1.33621e6 | − | 1.35110e7i | 0.137377 | − | 1.38907i | ||||
\(625\) | −390625. | −0.0400000 | ||||||||
\(626\) | −295204. | + | 1.19761e7i | −0.0301083 | + | 1.22146i | ||||
\(627\) | 764528. | + | 764528.i | 0.0776649 | + | 0.0776649i | ||||
\(628\) | 1.27253e6 | + | 1.40459e6i | 0.128756 | + | 0.142118i | ||||
\(629\) | 5.37988e6 | − | 5.37988e6i | 0.542183 | − | 0.542183i | ||||
\(630\) | −8.24054e6 | + | 7.84406e6i | −0.827188 | + | 0.787390i | ||||
\(631\) | 1.12988e7i | 1.12969i | 0.825197 | + | 0.564845i | \(0.191064\pi\) | ||||
−0.825197 | + | 0.564845i | \(0.808936\pi\) | |||||||
\(632\) | −9.88659e6 | − | 732284.i | −0.984587 | − | 0.0729267i | ||||
\(633\) | − | 1.47691e7i | − | 1.46502i | ||||||
\(634\) | −4.51418e6 | − | 4.74235e6i | −0.446021 | − | 0.468565i | ||||
\(635\) | 5.06213e6 | − | 5.06213e6i | 0.498194 | − | 0.498194i | ||||
\(636\) | 978411. | + | 48263.9i | 0.0959132 | + | 0.00473129i | ||||
\(637\) | 2.12904e6 | + | 2.12904e6i | 0.207891 | + | 0.207891i | ||||
\(638\) | 298440. | + | 7356.39i | 0.0290273 | + | 0.000715506i | ||||
\(639\) | −3.26659e7 | −3.16477 | ||||||||
\(640\) | 3.79065e6 | − | 2.66568e6i | 0.365817 | − | 0.257251i | ||||
\(641\) | −1.29242e7 | −1.24239 | −0.621195 | − | 0.783656i | \(-0.713352\pi\) | ||||
−0.621195 | + | 0.783656i | \(0.713352\pi\) | |||||||
\(642\) | −3.15298e7 | − | 777191.i | −3.01914 | − | 0.0744201i | ||||
\(643\) | −816087. | − | 816087.i | −0.0778411 | − | 0.0778411i | 0.667114 | − | 0.744955i | \(-0.267529\pi\) |
−0.744955 | + | 0.667114i | \(0.767529\pi\) | |||||||
\(644\) | −1.31869e7 | − | 650496.i | −1.25294 | − | 0.0618059i | ||||
\(645\) | −5.54583e6 | + | 5.54583e6i | −0.524889 | + | 0.524889i | ||||
\(646\) | 1.82139e7 | + | 1.91345e7i | 1.71720 | + | 1.80399i | ||||
\(647\) | − | 1.14750e7i | − | 1.07769i | −0.842406 | − | 0.538844i | \(-0.818861\pi\) | ||
0.842406 | − | 0.538844i | \(-0.181139\pi\) | |||||||
\(648\) | 1.66686e7 | + | 1.23461e6i | 1.55941 | + | 0.115503i | ||||
\(649\) | − | 64559.1i | − | 0.00601653i | ||||||
\(650\) | 1.22192e6 | − | 1.16313e6i | 0.113439 | − | 0.107981i | ||||
\(651\) | 2.76395e7 | − | 2.76395e7i | 2.55610 | − | 2.55610i | ||||
\(652\) | 3.62441e6 | + | 4.00054e6i | 0.333902 | + | 0.368553i | ||||
\(653\) | 5.60167e6 | + | 5.60167e6i | 0.514084 | + | 0.514084i | 0.915775 | − | 0.401691i | \(-0.131577\pi\) |
−0.401691 | + | 0.915775i | \(0.631577\pi\) | |||||||
\(654\) | 50669.6 | − | 2.05561e6i | 0.00463237 | − | 0.187930i | ||||
\(655\) | −4.16584e6 | −0.379402 | ||||||||
\(656\) | −977458. | + | 9.88346e6i | −0.0886826 | + | 0.896704i | ||||
\(657\) | 9.79969e6 | 0.885725 | ||||||||
\(658\) | −262667. | + | 1.06561e7i | −0.0236505 | + | 0.959475i | ||||
\(659\) | 3.61020e6 | + | 3.61020e6i | 0.323831 | + | 0.323831i | 0.850235 | − | 0.526404i | \(-0.176460\pi\) |
−0.526404 | + | 0.850235i | \(0.676460\pi\) | |||||||
\(660\) | 270599. | − | 245157.i | 0.0241806 | − | 0.0219071i | ||||
\(661\) | 4.16305e6 | − | 4.16305e6i | 0.370602 | − | 0.370602i | −0.497094 | − | 0.867696i | \(-0.665600\pi\) |
0.867696 | + | 0.497094i | \(0.165600\pi\) | |||||||
\(662\) | 5.39151e6 | − | 5.13211e6i | 0.478151 | − | 0.455146i | ||||
\(663\) | − | 2.61380e7i | − | 2.30934i | ||||||
\(664\) | −1.27097e7 | − | 1.47431e7i | −1.11870 | − | 1.29768i | ||||
\(665\) | 9.00426e6i | 0.789576i | ||||||||
\(666\) | −7.96434e6 | − | 8.36689e6i | −0.695767 | − | 0.730935i | ||||
\(667\) | −6.16489e6 | + | 6.16489e6i | −0.536551 | + | 0.536551i | ||||
\(668\) | −191510. | + | 3.88231e6i | −0.0166054 | + | 0.336627i | ||||
\(669\) | −7.32406e6 | − | 7.32406e6i | −0.632684 | − | 0.632684i | ||||
\(670\) | 5.43767e6 | + | 134036.i | 0.467979 | + | 0.0115354i | ||||
\(671\) | −375140. | −0.0321653 | ||||||||
\(672\) | 1.93005e7 | − | 1.50466e7i | 1.64872 | − | 1.28533i | ||||
\(673\) | 2.21199e7 | 1.88255 | 0.941273 | − | 0.337645i | \(-0.109630\pi\) | ||||
0.941273 | + | 0.337645i | \(0.109630\pi\) | |||||||
\(674\) | 9.44324e6 | + | 232771.i | 0.800703 | + | 0.0197369i | ||||
\(675\) | 3.51347e6 | + | 3.51347e6i | 0.296809 | + | 0.296809i | ||||
\(676\) | 226424. | − | 4.59009e6i | 0.0190570 | − | 0.386326i | ||||
\(677\) | −5.09252e6 | + | 5.09252e6i | −0.427033 | + | 0.427033i | −0.887616 | − | 0.460584i | \(-0.847640\pi\) |
0.460584 | + | 0.887616i | \(0.347640\pi\) | |||||||
\(678\) | −5.03780e6 | − | 5.29244e6i | −0.420888 | − | 0.442162i | ||||
\(679\) | 1.22251e7i | 1.01760i | ||||||||
\(680\) | 6.75719e6 | − | 5.82523e6i | 0.560394 | − | 0.483104i | ||||
\(681\) | 2.37033e7i | 1.95858i | ||||||||
\(682\) | −622688. | + | 592728.i | −0.0512636 | + | 0.0487972i | ||||
\(683\) | 5.69497e6 | − | 5.69497e6i | 0.467132 | − | 0.467132i | −0.433852 | − | 0.900984i | \(-0.642846\pi\) |
0.900984 | + | 0.433852i | \(0.142846\pi\) | |||||||
\(684\) | 2.97239e7 | − | 2.69292e7i | 2.42921 | − | 2.20082i | ||||
\(685\) | −1.45554e6 | − | 1.45554e6i | −0.118522 | − | 0.118522i | ||||
\(686\) | 222473. | − | 9.02546e6i | 0.0180496 | − | 0.732250i | ||||
\(687\) | 2.27255e7 | 1.83705 | ||||||||
\(688\) | 8.93987e6 | − | 7.33073e6i | 0.720046 | − | 0.590441i | ||||
\(689\) | −525679. | −0.0421864 | ||||||||
\(690\) | −262775. | + | 1.06605e7i | −0.0210117 | + | 0.852420i | ||||
\(691\) | −2.98475e6 | − | 2.98475e6i | −0.237801 | − | 0.237801i | 0.578138 | − | 0.815939i | \(-0.303779\pi\) |
−0.815939 | + | 0.578138i | \(0.803779\pi\) | |||||||
\(692\) | 6.66389e6 | + | 7.35544e6i | 0.529008 | + | 0.583907i | ||||
\(693\) | 934384. | − | 934384.i | 0.0739081 | − | 0.0739081i | ||||
\(694\) | −1.71800e7 | + | 1.63534e7i | −1.35402 | + | 1.28887i | ||||
\(695\) | − | 7.59664e6i | − | 0.596567i | ||||||
\(696\) | 1.19370e6 | − | 1.61162e7i | 0.0934055 | − | 1.26107i | ||||
\(697\) | 1.91203e7i | 1.49078i | ||||||||
\(698\) | 1.59783e7 | + | 1.67859e7i | 1.24134 | + | 1.30409i | ||||
\(699\) | −1.60284e7 | + | 1.60284e7i | −1.24079 | + | 1.24079i | ||||
\(700\) | 3.03717e6 | + | 149820.i | 0.234274 | + | 0.0115565i | ||||
\(701\) | −9.70805e6 | − | 9.70805e6i | −0.746169 | − | 0.746169i | 0.227589 | − | 0.973757i | \(-0.426916\pi\) |
−0.973757 | + | 0.227589i | \(0.926916\pi\) | |||||||
\(702\) | −2.14524e7 | − | 528789.i | −1.64298 | − | 0.0404985i | ||||
\(703\) | −9.14233e6 | −0.697699 | ||||||||
\(704\) | −432514. | + | 320369.i | −0.0328904 | + | 0.0243624i | ||||
\(705\) | 8.60929e6 | 0.652371 | ||||||||
\(706\) | 1.21506e7 | + | 299507.i | 0.917461 | + | 0.0226149i | ||||
\(707\) | −3.01234e6 | − | 3.01234e6i | −0.226650 | − | 0.226650i | ||||
\(708\) | −3.49053e6 | − | 172184.i | −0.261702 | − | 0.0129095i | ||||
\(709\) | 1.00421e7 | − | 1.00421e7i | 0.750256 | − | 0.750256i | −0.224270 | − | 0.974527i | \(-0.572000\pi\) |
0.974527 | + | 0.224270i | \(0.0719999\pi\) | |||||||
\(710\) | 6.01974e6 | + | 6.32401e6i | 0.448159 | + | 0.470811i | ||||
\(711\) | 2.89771e7i | 2.14972i | ||||||||
\(712\) | −810160. | + | 1.09380e7i | −0.0598923 | + | 0.808608i | ||||
\(713\) | − | 2.51069e7i | − | 1.84956i | ||||||
\(714\) | 3.41257e7 | − | 3.24838e7i | 2.50516 | − | 2.38463i | ||||
\(715\) | −138552. | + | 138552.i | −0.0101356 | + | 0.0101356i | ||||
\(716\) | −1.46305e7 | − | 1.61488e7i | −1.06654 | − | 1.17722i | ||||
\(717\) | 5.01463e6 | + | 5.01463e6i | 0.364285 | + | 0.364285i | ||||
\(718\) | 363831. | − | 1.47602e7i | 0.0263384 | − | 1.06852i | ||||
\(719\) | −3.73707e6 | −0.269593 | −0.134796 | − | 0.990873i | \(-0.543038\pi\) | ||||
−0.134796 | + | 0.990873i | \(0.543038\pi\) | |||||||
\(720\) | −8.58876e6 | − | 1.04740e7i | −0.617446 | − | 0.752979i | ||||
\(721\) | 1.97786e7 | 1.41696 | ||||||||
\(722\) | 437068. | − | 1.77314e7i | 0.0312037 | − | 1.26590i | ||||
\(723\) | −2.39141e7 | − | 2.39141e7i | −1.70141 | − | 1.70141i | ||||
\(724\) | −6.20502e6 | + | 5.62163e6i | −0.439943 | + | 0.398580i | ||||
\(725\) | 1.41988e6 | − | 1.41988e6i | 0.100324 | − | 0.100324i | ||||
\(726\) | 1.83053e7 | − | 1.74246e7i | 1.28895 | − | 1.22694i | ||||
\(727\) | 2.73870e7i | 1.92180i | 0.276894 | + | 0.960900i | \(0.410695\pi\) | ||||
−0.276894 | + | 0.960900i | \(0.589305\pi\) | |||||||
\(728\) | −9.94676e6 | + | 8.57489e6i | −0.695590 | + | 0.599653i | ||||
\(729\) | 4.82580e6i | 0.336318i | ||||||||
\(730\) | −1.80591e6 | − | 1.89719e6i | −0.125426 | − | 0.131766i | ||||
\(731\) | 1.57383e7 | − | 1.57383e7i | 1.08935 | − | 1.08935i | ||||
\(732\) | −1.00053e6 | + | 2.02828e7i | −0.0690161 | + | 1.39910i | ||||
\(733\) | −1.05278e6 | − | 1.05278e6i | −0.0723728 | − | 0.0723728i | 0.669994 | − | 0.742367i | \(-0.266297\pi\) |
−0.742367 | + | 0.669994i | \(0.766297\pi\) | |||||||
\(734\) | 41028.2 | + | 1011.32i | 0.00281088 | + | 6.92866e-5i | ||||
\(735\) | 4.38347e6 | 0.299295 | ||||||||
\(736\) | 1.93205e6 | − | 1.56000e7i | 0.131469 | − | 1.06152i | ||||
\(737\) | −631769. | −0.0428439 | ||||||||
\(738\) | 2.90209e7 | + | 715349.i | 1.96142 | + | 0.0483478i | ||||
\(739\) | −1.09564e6 | − | 1.09564e6i | −0.0737998 | − | 0.0737998i | 0.669243 | − | 0.743043i | \(-0.266618\pi\) |
−0.743043 | + | 0.669243i | \(0.766618\pi\) | |||||||
\(740\) | −152117. | + | 3.08374e6i | −0.0102117 | + | 0.207013i | ||||
\(741\) | −2.22089e7 | + | 2.22089e7i | −1.48587 | + | 1.48587i | ||||
\(742\) | −653304. | − | 686326.i | −0.0435618 | − | 0.0457636i | ||||
\(743\) | 4.23113e6i | 0.281180i | 0.990068 | + | 0.140590i | \(0.0448999\pi\) | ||||
−0.990068 | + | 0.140590i | \(0.955100\pi\) | |||||||
\(744\) | 3.03864e7 | + | 3.52478e7i | 2.01255 | + | 2.33453i | ||||
\(745\) | 1.27115e7i | 0.839087i | ||||||||
\(746\) | −1.90105e7 | + | 1.80958e7i | −1.25068 | + | 1.19051i | ||||
\(747\) | −4.02313e7 | + | 4.02313e7i | −2.63793 | + | 2.63793i | ||||
\(748\) | −767925. | + | 695725.i | −0.0501840 | + | 0.0454657i | ||||
\(749\) | 2.15720e7 | + | 2.15720e7i | 1.40503 | + | 1.40503i | ||||
\(750\) | 60521.5 | − | 2.45529e6i | 0.00392877 | − | 0.159386i | ||||
\(751\) | 1.15236e7 | 0.745568 | 0.372784 | − | 0.927918i | \(-0.378403\pi\) | ||||
0.372784 | + | 0.927918i | \(0.378403\pi\) | |||||||
\(752\) | −1.26292e7 | − | 1.24900e6i | −0.814386 | − | 0.0805414i | ||||
\(753\) | −2.79622e7 | −1.79715 | ||||||||
\(754\) | −213697. | + | 8.66943e6i | −0.0136889 | + | 0.555344i | ||||
\(755\) | −1.57578e6 | − | 1.57578e6i | −0.100607 | − | 0.100607i | ||||
\(756\) | −2.59702e7 | − | 2.86653e7i | −1.65261 | − | 1.82412i | ||||
\(757\) | −3.45229e6 | + | 3.45229e6i | −0.218962 | + | 0.218962i | −0.808061 | − | 0.589099i | \(-0.799483\pi\) |
0.589099 | + | 0.808061i | \(0.299483\pi\) | |||||||
\(758\) | 1.14569e7 | − | 1.09057e7i | 0.724260 | − | 0.689414i | ||||
\(759\) | − | 1.23857e6i | − | 0.0780400i | ||||||
\(760\) | −1.06910e7 | − | 791865.i | −0.671404 | − | 0.0497298i | ||||
\(761\) | 1.60302e7i | 1.00341i | 0.865040 | + | 0.501703i | \(0.167293\pi\) | ||||
−0.865040 | + | 0.501703i | \(0.832707\pi\) | |||||||
\(762\) | 3.10339e7 | + | 3.26025e7i | 1.93619 | + | 2.03406i | ||||
\(763\) | −1.40640e6 | + | 1.40640e6i | −0.0874578 | + | 0.0874578i | ||||
\(764\) | 4.61759e6 | + | 227780.i | 0.286208 | + | 0.0141183i | ||||
\(765\) | −1.84392e7 | − | 1.84392e7i | −1.13917 | − | 1.13917i | ||||
\(766\) | −5.23359e6 | − | 129005.i | −0.322276 | − | 0.00794392i | ||||
\(767\) | 1.87538e6 | 0.115107 | ||||||||
\(768\) | 1.61679e7 | + | 2.42393e7i | 0.989124 | + | 1.48292i | ||||
\(769\) | −1.30895e7 | −0.798189 | −0.399095 | − | 0.916910i | \(-0.630675\pi\) | ||||
−0.399095 | + | 0.916910i | \(0.630675\pi\) | |||||||
\(770\) | −353084. | − | 8703.33i | −0.0214611 | − | 0.000529004i | ||||
\(771\) | −7.75797e6 | − | 7.75797e6i | −0.470015 | − | 0.470015i | ||||
\(772\) | 1.83280e7 | + | 904099.i | 1.10681 | + | 0.0545975i | ||||
\(773\) | 4.93181e6 | − | 4.93181e6i | 0.296864 | − | 0.296864i | −0.542920 | − | 0.839784i | \(-0.682681\pi\) |
0.839784 | + | 0.542920i | \(0.182681\pi\) | |||||||
\(774\) | −2.32989e7 | − | 2.44766e7i | −1.39792 | − | 1.46858i | ||||
\(775\) | 5.78254e6i | 0.345831i | ||||||||
\(776\) | −1.45151e7 | − | 1.07511e6i | −0.865300 | − | 0.0640914i | ||||
\(777\) | 1.63050e7i | 0.968879i | ||||||||
\(778\) | 8.36222e6 | − | 7.95989e6i | 0.495305 | − | 0.471474i | ||||
\(779\) | 1.62461e7 | − | 1.62461e7i | 0.959191 | − | 0.959191i | ||||
\(780\) | 7.12160e6 | + | 7.86066e6i | 0.419123 | + | 0.462618i | ||||
\(781\) | −717071. | − | 717071.i | −0.0420663 | − | 0.0420663i | ||||
\(782\) | 745721. | − | 3.02530e7i | 0.0436073 | − | 1.76910i | ||||
\(783\) | −2.55422e7 | −1.48886 | ||||||||
\(784\) | −6.43021e6 | − | 635938.i | −0.373624 | − | 0.0369508i | ||||
\(785\) | −1.48071e6 | −0.0857622 | ||||||||
\(786\) | 645434. | − | 2.61845e7i | 0.0372645 | − | 1.51178i | ||||
\(787\) | −2.31058e7 | − | 2.31058e7i | −1.32979 | − | 1.32979i | −0.905549 | − | 0.424242i | \(-0.860540\pi\) |
−0.424242 | − | 0.905549i | \(-0.639460\pi\) | |||||||
\(788\) | 7.67957e6 | − | 6.95754e6i | 0.440577 | − | 0.399154i | ||||
\(789\) | 8.77788e6 | − | 8.77788e6i | 0.501993 | − | 0.501993i | ||||
\(790\) | 5.60987e6 | − | 5.33997e6i | 0.319805 | − | 0.304418i | ||||
\(791\) | 7.06773e6i | 0.401642i | ||||||||
\(792\) | 1.02725e6 | + | 1.19159e6i | 0.0581917 | + | 0.0675016i | ||||
\(793\) | − | 1.08975e7i | − | 0.615380i | ||||||
\(794\) | −1.23987e7 | − | 1.30254e7i | −0.697950 | − | 0.733228i | ||||
\(795\) | −541158. | + | 541158.i | −0.0303673 | + | 0.0303673i | ||||
\(796\) | 718012. | − | 1.45556e7i | 0.0401651 | − | 0.814231i | ||||
\(797\) | −9.91730e6 | − | 9.91730e6i | −0.553029 | − | 0.553029i | 0.374285 | − | 0.927314i | \(-0.377888\pi\) |
−0.927314 | + | 0.374285i | \(0.877888\pi\) | |||||||
\(798\) | −5.65966e7 | − | 1.39508e6i | −3.14618 | − | 0.0775516i | ||||
\(799\) | −2.44321e7 | −1.35392 | ||||||||
\(800\) | −444984. | + | 3.59294e6i | −0.0245821 | + | 0.198484i | ||||
\(801\) | 3.20587e7 | 1.76549 | ||||||||
\(802\) | 1.52270e7 | + | 375337.i | 0.835946 | + | 0.0206056i | ||||
\(803\) | 215120. | + | 215120.i | 0.0117731 | + | 0.0117731i | ||||
\(804\) | −1.68497e6 | + | 3.41579e7i | −0.0919290 | + | 1.86359i | ||||
\(805\) | 7.29367e6 | − | 7.29367e6i | 0.396695 | − | 0.396695i | ||||
\(806\) | −1.72182e7 | − | 1.80885e7i | −0.933579 | − | 0.980766i | ||||
\(807\) | − | 2.42450e7i | − | 1.31050i | ||||||
\(808\) | 3.84154e6 | − | 3.31171e6i | 0.207003 | − | 0.178453i | ||||
\(809\) | 1.84026e7i | 0.988569i | 0.869300 | + | 0.494284i | \(0.164570\pi\) | ||||
−0.869300 | + | 0.494284i | \(0.835430\pi\) | |||||||
\(810\) | −9.45811e6 | + | 9.00306e6i | −0.506515 | + | 0.482145i | ||||
\(811\) | 6.67819e6 | − | 6.67819e6i | 0.356539 | − | 0.356539i | −0.505997 | − | 0.862535i | \(-0.668875\pi\) |
0.862535 | + | 0.505997i | \(0.168875\pi\) | |||||||
\(812\) | −1.15844e7 | + | 1.04952e7i | −0.616570 | + | 0.558600i | ||||
\(813\) | −5.95274e6 | − | 5.95274e6i | −0.315857 | − | 0.315857i | ||||
\(814\) | 8836.78 | − | 358498.i | 0.000467448 | − | 0.0189638i | ||||
\(815\) | −4.21735e6 | −0.222406 | ||||||||
\(816\) | 3.55678e7 | + | 4.33751e7i | 1.86995 | + | 2.28042i | ||||
\(817\) | −2.67450e7 | −1.40181 | ||||||||
\(818\) | −87192.9 | + | 3.53732e6i | −0.00455615 | + | 0.184838i | ||||
\(819\) | 2.71430e7 | + | 2.71430e7i | 1.41400 | + | 1.41400i | ||||
\(820\) | −5.20955e6 | − | 5.75018e6i | −0.270561 | − | 0.298639i | ||||
\(821\) | 4.76725e6 | − | 4.76725e6i | 0.246837 | − | 0.246837i | −0.572834 | − | 0.819671i | \(-0.694156\pi\) |
0.819671 | + | 0.572834i | \(0.194156\pi\) | |||||||
\(822\) | 9.37438e6 | − | 8.92336e6i | 0.483908 | − | 0.460626i | ||||
\(823\) | 1.24864e7i | 0.642593i | 0.946979 | + | 0.321297i | \(0.104119\pi\) | ||||
−0.946979 | + | 0.321297i | \(0.895881\pi\) | |||||||
\(824\) | −1.73940e6 | + | 2.34836e7i | −0.0892443 | + | 1.20489i | ||||
\(825\) | 285264.i | 0.0145919i | ||||||||
\(826\) | 2.33069e6 | + | 2.44850e6i | 0.118860 | + | 0.124868i | ||||
\(827\) | −1.97584e7 | + | 1.97584e7i | −1.00459 | + | 1.00459i | −0.00459995 | + | 0.999989i | \(0.501464\pi\) |
−0.999989 | + | 0.00459995i | \(0.998536\pi\) | |||||||
\(828\) | −4.58904e7 | − | 2.26372e6i | −2.32619 | − | 0.114748i | ||||
\(829\) | −1.04021e7 | − | 1.04021e7i | −0.525695 | − | 0.525695i | 0.393591 | − | 0.919286i | \(-0.371233\pi\) |
−0.919286 | + | 0.393591i | \(0.871233\pi\) | |||||||
\(830\) | 1.52026e7 | + | 374735.i | 0.765988 | + | 0.0188812i | ||||
\(831\) | −2.96304e7 | −1.48845 | ||||||||
\(832\) | −9.30644e6 | − | 1.25642e7i | −0.466096 | − | 0.629252i | ||||
\(833\) | −1.24397e7 | −0.621153 | ||||||||
\(834\) | 4.77489e7 | + | 1.17698e6i | 2.37711 | + | 0.0585944i | ||||
\(835\) | −2.14730e6 | − | 2.14730e6i | −0.106580 | − | 0.106580i | ||||
\(836\) | 1.24363e6 | + | 61346.9i | 0.0615426 | + | 0.00303583i | ||||
\(837\) | 5.20109e7 | − | 5.20109e7i | 2.56614 | − | 2.56614i | ||||
\(838\) | 2.19024e7 | + | 2.30094e7i | 1.07741 | + | 1.13187i | ||||
\(839\) | 5.97699e6i | 0.293142i | 0.989200 | + | 0.146571i | \(0.0468237\pi\) | ||||
−0.989200 | + | 0.146571i | \(0.953176\pi\) | |||||||
\(840\) | −1.41226e6 | + | 1.90670e7i | −0.0690586 | + | 0.932363i | ||||
\(841\) | − | 1.01889e7i | − | 0.496751i | ||||||
\(842\) | −2.59492e7 | + | 2.47007e7i | −1.26137 | + | 1.20069i | ||||
\(843\) | 3.59126e7 | − | 3.59126e7i | 1.74052 | − | 1.74052i | ||||
\(844\) | −1.14196e7 | − | 1.26047e7i | −0.551817 | − | 0.609083i | ||||
\(845\) | 2.53877e6 | + | 2.53877e6i | 0.122316 | + | 0.122316i | ||||
\(846\) | −914079. | + | 3.70831e7i | −0.0439094 | + | 1.78136i | ||||
\(847\) | −2.44457e7 | −1.17083 | ||||||||
\(848\) | 872346. | − | 715327.i | 0.0416581 | − | 0.0341598i | ||||
\(849\) | 4.42523e6 | 0.210701 | ||||||||
\(850\) | −171752. | + | 6.96779e6i | −0.00815370 | + | 0.330787i | ||||
\(851\) | 7.40550e6 | + | 7.40550e6i | 0.350534 | + | 0.350534i | ||||
\(852\) | −4.06825e7 | + | 3.68575e7i | −1.92003 | + | 1.73951i | ||||
\(853\) | 17875.4 | − | 17875.4i | 0.000841170 | − | 0.000841170i | −0.706686 | − | 0.707527i | \(-0.749811\pi\) |
0.707527 | + | 0.706686i | \(0.249811\pi\) | |||||||
\(854\) | 1.42277e7 | − | 1.35432e7i | 0.667562 | − | 0.635443i | ||||
\(855\) | 3.13348e7i | 1.46592i | ||||||||
\(856\) | −2.75101e7 | + | 2.37159e7i | −1.28324 | + | 1.10625i | ||||
\(857\) | 1.76443e7i | 0.820640i | 0.911942 | + | 0.410320i | \(0.134583\pi\) | ||||
−0.911942 | + | 0.410320i | \(0.865417\pi\) | |||||||
\(858\) | −849410. | − | 892343.i | −0.0393912 | − | 0.0413822i | ||||
\(859\) | 920994. | − | 920994.i | 0.0425867 | − | 0.0425867i | −0.685493 | − | 0.728079i | \(-0.740413\pi\) |
0.728079 | + | 0.685493i | \(0.240413\pi\) | |||||||
\(860\) | −445006. | + | 9.02120e6i | −0.0205173 | + | 0.415928i | ||||
\(861\) | −2.89744e7 | − | 2.89744e7i | −1.33201 | − | 1.33201i | ||||
\(862\) | 2.22679e7 | + | 548892.i | 1.02073 | + | 0.0251605i | ||||
\(863\) | 1.98421e7 | 0.906901 | 0.453450 | − | 0.891281i | \(-0.350193\pi\) | ||||
0.453450 | + | 0.891281i | \(0.350193\pi\) | |||||||
\(864\) | 3.63190e7 | − | 2.83142e7i | 1.65520 | − | 1.29039i | ||||
\(865\) | −7.75408e6 | −0.352363 | ||||||||
\(866\) | 2.16689e7 | + | 534126.i | 0.981843 | + | 0.0242019i | ||||
\(867\) | 4.84627e7 | + | 4.84627e7i | 2.18957 | + | 2.18957i | ||||
\(868\) | 2.21783e6 | − | 4.49602e7i | 0.0999148 | − | 2.02548i | ||||
\(869\) | −636096. | + | 636096.i | −0.0285742 | + | 0.0285742i | ||||
\(870\) | 8.70472e6 | + | 9.14470e6i | 0.389903 | + | 0.409611i | ||||
\(871\) | − | 1.83523e7i | − | 0.819682i | ||||||
\(872\) | −1.54617e6 | − | 1.79354e6i | −0.0688600 | − | 0.0798767i | ||||
\(873\) | 4.25431e7i | 1.88927i | ||||||||
\(874\) | −2.63390e7 | + | 2.50717e7i | −1.16633 | + | 1.11021i | ||||
\(875\) | −1.67986e6 | + | 1.67986e6i | −0.0741740 | + | 0.0741740i | ||||
\(876\) | 1.22046e7 | − | 1.10572e7i | 0.537360 | − | 0.486837i | ||||
\(877\) | −2.55034e7 | − | 2.55034e7i | −1.11969 | − | 1.11969i | −0.991786 | − | 0.127905i | \(-0.959175\pi\) |
−0.127905 | − | 0.991786i | \(-0.540825\pi\) | |||||||
\(878\) | −187031. | + | 7.58763e6i | −0.00818799 | + | 0.332177i | ||||
\(879\) | 4.02010e7 | 1.75495 | ||||||||
\(880\) | 41385.1 | − | 418461.i | 0.00180151 | − | 0.0182158i | ||||
\(881\) | −3.12202e7 | −1.35518 | −0.677588 | − | 0.735442i | \(-0.736975\pi\) | ||||
−0.677588 | + | 0.735442i | \(0.736975\pi\) | |||||||
\(882\) | −465409. | + | 1.88811e7i | −0.0201448 | + | 0.817252i | ||||
\(883\) | −751066. | − | 751066.i | −0.0324173 | − | 0.0324173i | 0.690712 | − | 0.723130i | \(-0.257297\pi\) |
−0.723130 | + | 0.690712i | \(0.757297\pi\) | |||||||
\(884\) | −2.02102e7 | − | 2.23075e7i | −0.869841 | − | 0.960110i | ||||
\(885\) | 1.93061e6 | − | 1.93061e6i | 0.0828582 | − | 0.0828582i | ||||
\(886\) | 3.79957e6 | − | 3.61676e6i | 0.162611 | − | 0.154787i | ||||
\(887\) | − | 1.33534e6i | − | 0.0569878i | −0.999594 | − | 0.0284939i | \(-0.990929\pi\) | ||
0.999594 | − | 0.0284939i | \(-0.00907112\pi\) | |||||||
\(888\) | −1.93594e7 | − | 1.43392e6i | −0.823871 | − | 0.0610228i | ||||
\(889\) | − | 4.35387e7i | − | 1.84765i | ||||||
\(890\) | −5.90786e6 | − | 6.20647e6i | −0.250009 | − | 0.262645i | ||||
\(891\) | 1.07244e6 | − | 1.07244e6i | 0.0452564 | − | 0.0452564i | ||||
\(892\) | −1.19138e7 | − | 587694.i | −0.501346 | − | 0.0247309i | ||||
\(893\) | 2.07594e7 | + | 2.07594e7i | 0.871136 | + | 0.871136i | ||||
\(894\) | −7.98988e7 | − | 1.96946e6i | −3.34346 | − | 0.0824145i | ||||
\(895\) | 1.70240e7 | 0.710403 | ||||||||
\(896\) | 4.83786e6 | − | 2.77650e7i | 0.201318 | − | 1.15539i | ||||
\(897\) | 3.59794e7 | 1.49305 | ||||||||
\(898\) | −1.79608e7 | − | 442724.i | −0.743250 | − | 0.0183207i | ||||
\(899\) | −2.10189e7 | − | 2.10189e7i | −0.867383 | − | 0.867383i | ||||
\(900\) | 1.05693e7 | + | 521373.i | 0.434952 | + | 0.0214557i | ||||
\(901\) | 1.53574e6 | − | 1.53574e6i | 0.0630238 | − | 0.0630238i | ||||
\(902\) | 621354. | + | 652761.i | 0.0254286 | + | 0.0267139i | ||||
\(903\) | 4.76989e7i | 1.94666i | ||||||||
\(904\) | −8.39170e6 | − | 621560.i | −0.341530 | − | 0.0252966i | ||||
\(905\) | − | 6.54131e6i | − | 0.265487i | ||||||
\(906\) | 1.01488e7 | − | 9.66047e6i | 0.410764 | − | 0.391001i | ||||
\(907\) | −1.98474e7 | + | 1.98474e7i | −0.801098 | + | 0.801098i | −0.983267 | − | 0.182169i | \(-0.941688\pi\) |
0.182169 | + | 0.983267i | \(0.441688\pi\) | |||||||
\(908\) | 1.83277e7 | + | 2.02297e7i | 0.737723 | + | 0.814281i | ||||
\(909\) | −1.04829e7 | − | 1.04829e7i | −0.420797 | − | 0.420797i | ||||
\(910\) | 252824. | − | 1.02568e7i | 0.0101208 | − | 0.410589i | ||||
\(911\) | 1.80547e7 | 0.720767 | 0.360383 | − | 0.932804i | \(-0.382646\pi\) | ||||
0.360383 | + | 0.932804i | \(0.382646\pi\) | |||||||
\(912\) | 6.63370e6 | − | 6.70760e7i | 0.264100 | − | 2.67042i | ||||
\(913\) | −1.76629e6 | −0.0701270 | ||||||||
\(914\) | −615169. | + | 2.49567e7i | −0.0243573 | + | 0.988147i | ||||
\(915\) | −1.12184e7 | − | 1.12184e7i | −0.442973 | − | 0.442973i | ||||
\(916\) | 1.93951e7 | − | 1.75716e7i | 0.763755 | − | 0.691947i | ||||
\(917\) | −1.79149e7 | + | 1.79149e7i | −0.703544 | + | 0.703544i | ||||
\(918\) | 6.42165e7 | − | 6.11268e7i | 2.51501 | − | 2.39400i | ||||
\(919\) | − | 2.96410e7i | − | 1.15772i | −0.815426 | − | 0.578861i | \(-0.803497\pi\) | ||
0.815426 | − | 0.578861i | \(-0.196503\pi\) | |||||||
\(920\) | 8.01853e6 | + | 9.30139e6i | 0.312338 | + | 0.362308i | ||||
\(921\) | 2.79809e7i | 1.08696i | ||||||||
\(922\) | 1.54686e7 | + | 1.62505e7i | 0.599272 | + | 0.629562i | ||||
\(923\) | 2.08303e7 | − | 2.08303e7i | 0.804805 | − | 0.804805i | ||||
\(924\) | 109410. | − | 2.21798e6i | 0.00421578 | − | 0.0854627i | ||||
\(925\) | −1.70561e6 | − | 1.70561e6i | −0.0655430 | − | 0.0655430i | ||||
\(926\) | 1.40131e7 | + | 345416.i | 0.537042 | + | 0.0132378i | ||||
\(927\) | 6.88294e7 | 2.63072 | ||||||||
\(928\) | −1.14425e7 | − | 1.46774e7i | −0.436164 | − | 0.559473i | ||||
\(929\) | −8.63963e6 | −0.328440 | −0.164220 | − | 0.986424i | \(-0.552511\pi\) | ||||
−0.164220 | + | 0.986424i | \(0.552511\pi\) | |||||||
\(930\) | −3.63464e7 | − | 895918.i | −1.37801 | − | 0.0339673i | ||||
\(931\) | 1.05698e7 | + | 1.05698e7i | 0.399660 | + | 0.399660i | ||||
\(932\) | −1.28614e6 | + | 2.60728e7i | −0.0485009 | + | 0.983215i | ||||
\(933\) | −9.03414e6 | + | 9.03414e6i | −0.339768 | + | 0.339768i | ||||
\(934\) | 6.51813e6 | + | 6.84759e6i | 0.244487 | + | 0.256845i | ||||
\(935\) | − | 809543.i | − | 0.0302838i | ||||||
\(936\) | −3.46146e7 | + | 2.98406e7i | −1.29143 | + | 1.11331i | ||||
\(937\) | − | 1.12375e7i | − | 0.418138i | −0.977901 | − | 0.209069i | \(-0.932957\pi\) | ||
0.977901 | − | 0.209069i | \(-0.0670434\pi\) | |||||||
\(938\) | 2.39608e7 | − | 2.28079e7i | 0.889188 | − | 0.846406i | ||||
\(939\) | 4.16098e7 | − | 4.16098e7i | 1.54004 | − | 1.54004i | ||||
\(940\) | 7.34763e6 | − | 6.65680e6i | 0.271224 | − | 0.245723i | ||||
\(941\) | −2.30935e7 | − | 2.30935e7i | −0.850190 | − | 0.850190i | 0.139966 | − | 0.990156i | \(-0.455301\pi\) |
−0.990156 | + | 0.139966i | \(0.955301\pi\) | |||||||
\(942\) | 229414. | − | 9.30706e6i | 0.00842349 | − | 0.341732i | ||||
\(943\) | −2.63194e7 | −0.963823 | ||||||||
\(944\) | −3.11213e6 | + | 2.55196e6i | −0.113665 | + | 0.0932062i | ||||
\(945\) | 3.02189e7 | 1.10077 | ||||||||
\(946\) | 25851.2 | − | 1.04875e6i | 0.000939188 | − | 0.0381018i | ||||
\(947\) | 1.68224e7 | + | 1.68224e7i | 0.609557 | + | 0.609557i | 0.942830 | − | 0.333274i | \(-0.108153\pi\) |
−0.333274 | + | 0.942830i | \(0.608153\pi\) | |||||||
\(948\) | 3.26954e7 | + | 3.60884e7i | 1.18159 | + | 1.30421i | ||||
\(949\) | −6.24904e6 | + | 6.24904e6i | −0.225241 | + | 0.225241i | ||||
\(950\) | 6.06631e6 | − | 5.77444e6i | 0.218080 | − | 0.207587i | ||||
\(951\) | 3.21610e7i | 1.15313i | ||||||||
\(952\) | 4.00783e6 | − | 5.41098e7i | 0.143323 | − | 1.93501i | ||||
\(953\) | 2.32202e7i | 0.828199i | 0.910232 | + | 0.414099i | \(0.135903\pi\) | ||||
−0.910232 | + | 0.414099i | \(0.864097\pi\) | |||||||
\(954\) | −2.27349e6 | − | 2.38841e6i | −0.0808766 | − | 0.0849645i | ||||
\(955\) | −2.55398e6 | + | 2.55398e6i | −0.0906170 | + | 0.0906170i | ||||
\(956\) | 8.15712e6 | + | 402382.i | 0.288664 | + | 0.0142395i | ||||
\(957\) | −1.03691e6 | − | 1.03691e6i | −0.0365981 | − | 0.0365981i | ||||
\(958\) | −5.55502e7 | − | 1.36928e6i | −1.95556 | − | 0.0482035i | ||||
\(959\) | −1.25189e7 | −0.439562 | ||||||||
\(960\) | −2.25146e7 | − | 3.35364e6i | −0.788471 | − | 0.117446i | ||||
\(961\) | 5.69716e7 | 1.98999 | ||||||||
\(962\) | 1.04140e7 | + | 256701.i | 0.362812 | + | 0.00894312i | ||||
\(963\) | 7.50703e7 | + | 7.50703e7i | 2.60857 | + | 2.60857i | ||||
\(964\) | −3.89003e7 | − | 1.91891e6i | −1.34822 | − | 0.0665060i | ||||
\(965\) | −1.01372e7 | + | 1.01372e7i | −0.350428 | + | 0.350428i | ||||
\(966\) | 4.47146e7 | + | 4.69747e7i | 1.54172 | + | 1.61965i | ||||
\(967\) | − | 4.77137e7i | − | 1.64088i | −0.571731 | − | 0.820441i | \(-0.693728\pi\) | ||
0.571731 | − | 0.820441i | \(-0.306272\pi\) | |||||||
\(968\) | 2.14983e6 | − | 2.90250e7i | 0.0737423 | − | 0.995597i | ||||
\(969\) | − | 1.29763e8i | − | 4.43959i | ||||||
\(970\) | 8.23621e6 | − | 7.83994e6i | 0.281059 | − | 0.267537i | ||||
\(971\) | −2.29107e7 | + | 2.29107e7i | −0.779813 | + | 0.779813i | −0.979799 | − | 0.199986i | \(-0.935910\pi\) |
0.199986 | + | 0.979799i | \(0.435910\pi\) | |||||||
\(972\) | −1.36173e7 | − | 1.50304e7i | −0.462301 | − | 0.510277i | ||||
\(973\) | −3.26688e7 | − | 3.26688e7i | −1.10624 | − | 1.10624i | ||||
\(974\) | −286405. | + | 1.16191e7i | −0.00967349 | + | 0.392443i | ||||
\(975\) | −8.28667e6 | −0.279170 | ||||||||
\(976\) | 1.48290e7 | + | 1.80840e7i | 0.498295 | + | 0.607673i | ||||
\(977\) | −5.07357e7 | −1.70050 | −0.850251 | − | 0.526377i | \(-0.823550\pi\) | ||||
−0.850251 | + | 0.526377i | \(0.823550\pi\) | |||||||
\(978\) | 653416. | − | 2.65083e7i | 0.0218445 | − | 0.886207i | ||||
\(979\) | 703743. | + | 703743.i | 0.0234670 | + | 0.0234670i | ||||
\(980\) | 3.74109e6 | − | 3.38935e6i | 0.124432 | − | 0.112733i | ||||
\(981\) | −4.89427e6 | + | 4.89427e6i | −0.162374 | + | 0.162374i | ||||
\(982\) | −2.47690e7 | + | 2.35773e7i | −0.819653 | + | 0.780217i | ||||
\(983\) | 6.51198e6i | 0.214946i | 0.994208 | + | 0.107473i | \(0.0342759\pi\) | ||||
−0.994208 | + | 0.107473i | \(0.965724\pi\) | |||||||
\(984\) | 3.69501e7 | − | 3.18539e7i | 1.21654 | − | 1.04876i | ||||
\(985\) | 8.09577e6i | 0.265869i | ||||||||
\(986\) | −2.47029e7 | − | 2.59515e7i | −0.809199 | − | 0.850099i | ||||
\(987\) | 3.70237e7 | − | 3.70237e7i | 1.20973 | − | 1.20973i | ||||
\(988\) | −1.78207e6 | + | 3.61264e7i | −0.0580809 | + | 1.17742i | ||||
\(989\) | 2.16641e7 | + | 2.16641e7i | 0.704288 | + | 0.704288i | ||||
\(990\) | −1.22873e6 | − | 30287.5i | −0.0398445 | − | 0.000982145i | ||||
\(991\) | −5.04162e7 | −1.63074 | −0.815372 | − | 0.578938i | \(-0.803467\pi\) | ||||
−0.815372 | + | 0.578938i | \(0.803467\pi\) | |||||||
\(992\) | 5.31873e7 | + | 6.58724e6i | 1.71605 | + | 0.212532i | ||||
\(993\) | −3.65634e7 | −1.17672 | ||||||||
\(994\) | 5.30835e7 | + | 1.30848e6i | 1.70409 | + | 0.0420050i | ||||
\(995\) | 8.05069e6 | + | 8.05069e6i | 0.257796 | + | 0.257796i | ||||
\(996\) | −4.71083e6 | + | 9.54984e7i | −0.150470 | + | 3.05034i | ||||
\(997\) | 1.83995e7 | − | 1.83995e7i | 0.586229 | − | 0.586229i | −0.350379 | − | 0.936608i | \(-0.613947\pi\) |
0.936608 | + | 0.350379i | \(0.113947\pi\) | |||||||
\(998\) | 1.46037e7 | + | 1.53418e7i | 0.464125 | + | 0.487584i | ||||
\(999\) | 3.06822e7i | 0.972686i |
(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.61.2 | yes | 80 | |
4.3 | odd | 2 | 320.6.l.a.81.3 | 80 | |||
16.5 | even | 4 | inner | 80.6.l.a.21.2 | ✓ | 80 | |
16.11 | odd | 4 | 320.6.l.a.241.3 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.l.a.21.2 | ✓ | 80 | 16.5 | even | 4 | inner | |
80.6.l.a.61.2 | yes | 80 | 1.1 | even | 1 | trivial | |
320.6.l.a.81.3 | 80 | 4.3 | odd | 2 | |||
320.6.l.a.241.3 | 80 | 16.11 | odd | 4 |