Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 6.16 | ||
Character | \(\chi\) | \(=\) | 43.6 |
Dual form | 43.6.c.a.36.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.70119 | 1.71494 | 0.857472 | − | 0.514530i | \(-0.172034\pi\) | ||||
0.857472 | + | 0.514530i | \(0.172034\pi\) | |||||||
\(3\) | 7.50728 | − | 13.0030i | 0.481592 | − | 0.834142i | −0.518184 | − | 0.855269i | \(-0.673392\pi\) |
0.999777 | + | 0.0211264i | \(0.00672525\pi\) | |||||||
\(4\) | 62.1131 | 1.94104 | ||||||||
\(5\) | −9.53861 | + | 16.5214i | −0.170632 | + | 0.295543i | −0.938641 | − | 0.344896i | \(-0.887914\pi\) |
0.768009 | + | 0.640439i | \(0.221248\pi\) | |||||||
\(6\) | 72.8296 | − | 126.145i | 0.825904 | − | 1.43051i | ||||
\(7\) | −13.4501 | − | 23.2962i | −0.103748 | − | 0.179697i | 0.809478 | − | 0.587150i | \(-0.199750\pi\) |
−0.913226 | + | 0.407453i | \(0.866417\pi\) | |||||||
\(8\) | 292.133 | 1.61382 | ||||||||
\(9\) | 8.78143 | + | 15.2099i | 0.0361376 | + | 0.0625921i | ||||
\(10\) | −92.5359 | + | 160.277i | −0.292624 | + | 0.506840i | ||||
\(11\) | −218.352 | −0.544096 | −0.272048 | − | 0.962284i | \(-0.587701\pi\) | ||||
−0.272048 | + | 0.962284i | \(0.587701\pi\) | |||||||
\(12\) | 466.301 | − | 807.657i | 0.934788 | − | 1.61910i | ||||
\(13\) | −136.773 | − | 236.897i | −0.224461 | − | 0.388778i | 0.731696 | − | 0.681631i | \(-0.238729\pi\) |
−0.956158 | + | 0.292852i | \(0.905396\pi\) | |||||||
\(14\) | −130.482 | − | 226.001i | −0.177922 | − | 0.308170i | ||||
\(15\) | 143.218 | + | 248.061i | 0.164350 | + | 0.284662i | ||||
\(16\) | 846.420 | 0.826582 | ||||||||
\(17\) | 386.269 | + | 669.037i | 0.324166 | + | 0.561471i | 0.981343 | − | 0.192264i | \(-0.0615831\pi\) |
−0.657177 | + | 0.753736i | \(0.728250\pi\) | |||||||
\(18\) | 85.1903 | + | 147.554i | 0.0619739 | + | 0.107342i | ||||
\(19\) | −605.204 | + | 1048.24i | −0.384607 | + | 0.666160i | −0.991715 | − | 0.128460i | \(-0.958996\pi\) |
0.607107 | + | 0.794620i | \(0.292330\pi\) | |||||||
\(20\) | −592.473 | + | 1026.19i | −0.331202 | + | 0.573659i | ||||
\(21\) | −403.895 | −0.199857 | ||||||||
\(22\) | −2118.27 | −0.933094 | ||||||||
\(23\) | −422.115 | + | 731.124i | −0.166384 | + | 0.288185i | −0.937146 | − | 0.348938i | \(-0.886542\pi\) |
0.770762 | + | 0.637123i | \(0.219876\pi\) | |||||||
\(24\) | 2193.13 | − | 3798.61i | 0.777205 | − | 1.34616i | ||||
\(25\) | 1380.53 | + | 2391.15i | 0.441770 | + | 0.765167i | ||||
\(26\) | −1326.86 | − | 2298.19i | −0.384939 | − | 0.666733i | ||||
\(27\) | 3912.24 | 1.03280 | ||||||||
\(28\) | −835.427 | − | 1447.00i | −0.201379 | − | 0.348798i | ||||
\(29\) | −3608.91 | − | 6250.81i | −0.796857 | − | 1.38020i | −0.921653 | − | 0.388015i | \(-0.873161\pi\) |
0.124796 | − | 0.992182i | \(-0.460172\pi\) | |||||||
\(30\) | 1389.39 | + | 2406.49i | 0.281851 | + | 0.488180i | ||||
\(31\) | −100.481 | + | 174.038i | −0.0187793 | + | 0.0325268i | −0.875262 | − | 0.483648i | \(-0.839311\pi\) |
0.856483 | + | 0.516175i | \(0.172645\pi\) | |||||||
\(32\) | −1136.98 | −0.196280 | ||||||||
\(33\) | −1639.23 | + | 2839.23i | −0.262032 | + | 0.453853i | ||||
\(34\) | 3747.27 | + | 6490.45i | 0.555926 | + | 0.962892i | ||||
\(35\) | 513.181 | 0.0708109 | ||||||||
\(36\) | 545.442 | + | 944.733i | 0.0701443 | + | 0.121493i | ||||
\(37\) | 1834.25 | − | 3177.02i | 0.220270 | − | 0.381519i | −0.734620 | − | 0.678479i | \(-0.762640\pi\) |
0.954890 | + | 0.296960i | \(0.0959728\pi\) | |||||||
\(38\) | −5871.20 | + | 10169.2i | −0.659580 | + | 1.14243i | ||||
\(39\) | −4107.17 | −0.432395 | ||||||||
\(40\) | −2786.54 | + | 4826.44i | −0.275370 | + | 0.476954i | ||||
\(41\) | −14604.4 | −1.35683 | −0.678414 | − | 0.734680i | \(-0.737332\pi\) | ||||
−0.678414 | + | 0.734680i | \(0.737332\pi\) | |||||||
\(42\) | −3918.26 | −0.342744 | ||||||||
\(43\) | −11825.4 | + | 2677.49i | −0.975312 | + | 0.220830i | ||||
\(44\) | −13562.5 | −1.05611 | ||||||||
\(45\) | −335.050 | −0.0246649 | ||||||||
\(46\) | −4095.02 | + | 7092.78i | −0.285339 | + | 0.494222i | ||||
\(47\) | 23450.9 | 1.54851 | 0.774255 | − | 0.632873i | \(-0.218125\pi\) | ||||
0.774255 | + | 0.632873i | \(0.218125\pi\) | |||||||
\(48\) | 6354.31 | − | 11006.0i | 0.398076 | − | 0.689487i | ||||
\(49\) | 8041.69 | − | 13928.6i | 0.478473 | − | 0.828739i | ||||
\(50\) | 13392.8 | + | 23197.0i | 0.757610 | + | 1.31222i | ||||
\(51\) | 11599.3 | 0.624463 | ||||||||
\(52\) | −8495.39 | − | 14714.4i | −0.435687 | − | 0.754632i | ||||
\(53\) | 15577.4 | − | 26980.8i | 0.761736 | − | 1.31937i | −0.180219 | − | 0.983626i | \(-0.557681\pi\) |
0.941955 | − | 0.335739i | \(-0.108986\pi\) | |||||||
\(54\) | 37953.4 | 1.77119 | ||||||||
\(55\) | 2082.77 | − | 3607.47i | 0.0928400 | − | 0.160804i | ||||
\(56\) | −3929.22 | − | 6805.61i | −0.167431 | − | 0.289999i | ||||
\(57\) | 9086.87 | + | 15738.9i | 0.370448 | + | 0.641635i | ||||
\(58\) | −35010.7 | − | 60640.3i | −1.36657 | − | 2.36696i | ||||
\(59\) | 34542.5 | 1.29189 | 0.645943 | − | 0.763386i | \(-0.276464\pi\) | ||||
0.645943 | + | 0.763386i | \(0.276464\pi\) | |||||||
\(60\) | 8895.72 | + | 15407.8i | 0.319009 | + | 0.552540i | ||||
\(61\) | 2226.37 | + | 3856.19i | 0.0766078 | + | 0.132689i | 0.901784 | − | 0.432186i | \(-0.142258\pi\) |
−0.825177 | + | 0.564875i | \(0.808924\pi\) | |||||||
\(62\) | −974.787 | + | 1688.38i | −0.0322055 | + | 0.0557816i | ||||
\(63\) | 236.222 | − | 409.149i | 0.00749841 | − | 0.0129876i | ||||
\(64\) | −38115.5 | −1.16319 | ||||||||
\(65\) | 5218.49 | 0.153201 | ||||||||
\(66\) | −15902.5 | + | 27543.9i | −0.449371 | + | 0.778333i | ||||
\(67\) | 18556.3 | − | 32140.4i | 0.505014 | − | 0.874710i | −0.494969 | − | 0.868911i | \(-0.664821\pi\) |
0.999983 | − | 0.00579951i | \(-0.00184605\pi\) | |||||||
\(68\) | 23992.3 | + | 41556.0i | 0.629217 | + | 1.08984i | ||||
\(69\) | 6337.87 | + | 10977.5i | 0.160258 | + | 0.277576i | ||||
\(70\) | 4978.46 | 0.121437 | ||||||||
\(71\) | 4558.20 | + | 7895.03i | 0.107312 | + | 0.185869i | 0.914680 | − | 0.404178i | \(-0.132442\pi\) |
−0.807369 | + | 0.590047i | \(0.799109\pi\) | |||||||
\(72\) | 2565.35 | + | 4443.31i | 0.0583196 | + | 0.101013i | ||||
\(73\) | −15744.3 | − | 27270.0i | −0.345793 | − | 0.598932i | 0.639704 | − | 0.768621i | \(-0.279057\pi\) |
−0.985498 | + | 0.169690i | \(0.945724\pi\) | |||||||
\(74\) | 17794.5 | − | 30820.9i | 0.377751 | − | 0.654284i | ||||
\(75\) | 41456.1 | 0.851011 | ||||||||
\(76\) | −37591.1 | + | 65109.7i | −0.746536 | + | 1.29304i | ||||
\(77\) | 2936.85 | + | 5086.78i | 0.0564489 | + | 0.0977724i | ||||
\(78\) | −39844.4 | −0.741534 | ||||||||
\(79\) | 17569.3 | + | 30431.0i | 0.316729 | + | 0.548590i | 0.979803 | − | 0.199963i | \(-0.0640822\pi\) |
−0.663075 | + | 0.748553i | \(0.730749\pi\) | |||||||
\(80\) | −8073.67 | + | 13984.0i | −0.141041 | + | 0.244291i | ||||
\(81\) | 27236.4 | − | 47174.8i | 0.461251 | − | 0.798909i | ||||
\(82\) | −141680. | −2.32688 | ||||||||
\(83\) | −16623.8 | + | 28793.3i | −0.264872 | + | 0.458771i | −0.967530 | − | 0.252756i | \(-0.918663\pi\) |
0.702658 | + | 0.711527i | \(0.251996\pi\) | |||||||
\(84\) | −25087.2 | −0.387930 | ||||||||
\(85\) | −14737.9 | −0.221252 | ||||||||
\(86\) | −114720. | + | 25974.9i | −1.67261 | + | 0.378710i | ||||
\(87\) | −108372. | −1.53504 | ||||||||
\(88\) | −63787.8 | −0.878074 | ||||||||
\(89\) | 2143.02 | − | 3711.82i | 0.0286781 | − | 0.0496720i | −0.851330 | − | 0.524630i | \(-0.824204\pi\) |
0.880008 | + | 0.474958i | \(0.157537\pi\) | |||||||
\(90\) | −3250.39 | −0.0422989 | ||||||||
\(91\) | −3679.22 | + | 6372.59i | −0.0465749 | + | 0.0806701i | ||||
\(92\) | −26218.9 | + | 45412.4i | −0.322957 | + | 0.559378i | ||||
\(93\) | 1508.68 | + | 2613.11i | 0.0180880 | + | 0.0313293i | ||||
\(94\) | 227501. | 2.65561 | ||||||||
\(95\) | −11545.6 | − | 19997.6i | −0.131252 | − | 0.227336i | ||||
\(96\) | −8535.62 | + | 14784.1i | −0.0945272 | + | 0.163726i | ||||
\(97\) | −4932.36 | −0.0532262 | −0.0266131 | − | 0.999646i | \(-0.508472\pi\) | ||||
−0.0266131 | + | 0.999646i | \(0.508472\pi\) | |||||||
\(98\) | 78014.0 | − | 135124.i | 0.820554 | − | 1.42124i | ||||
\(99\) | −1917.44 | − | 3321.11i | −0.0196623 | − | 0.0340561i | ||||
\(100\) | 85749.0 | + | 148522.i | 0.857490 | + | 1.48522i | ||||
\(101\) | 2725.57 | + | 4720.83i | 0.0265861 | + | 0.0460484i | 0.879012 | − | 0.476799i | \(-0.158203\pi\) |
−0.852426 | + | 0.522847i | \(0.824870\pi\) | |||||||
\(102\) | 112527. | 1.07092 | ||||||||
\(103\) | 76854.6 | + | 133116.i | 0.713801 | + | 1.23634i | 0.963420 | + | 0.267995i | \(0.0863611\pi\) |
−0.249620 | + | 0.968344i | \(0.580306\pi\) | |||||||
\(104\) | −39955.9 | − | 69205.6i | −0.362241 | − | 0.627419i | ||||
\(105\) | 3852.59 | − | 6672.89i | 0.0341020 | − | 0.0590664i | ||||
\(106\) | 151119. | − | 261746.i | 1.30633 | − | 2.26264i | ||||
\(107\) | −170219. | −1.43730 | −0.718652 | − | 0.695370i | \(-0.755241\pi\) | ||||
−0.718652 | + | 0.695370i | \(0.755241\pi\) | |||||||
\(108\) | 243001. | 2.00470 | ||||||||
\(109\) | −18065.7 | + | 31290.7i | −0.145642 | + | 0.252260i | −0.929612 | − | 0.368539i | \(-0.879858\pi\) |
0.783970 | + | 0.620799i | \(0.213192\pi\) | |||||||
\(110\) | 20205.4 | − | 34996.7i | 0.159215 | − | 0.275769i | ||||
\(111\) | −27540.5 | − | 47701.6i | −0.212161 | − | 0.367473i | ||||
\(112\) | −11384.4 | − | 19718.4i | −0.0857563 | − | 0.148534i | ||||
\(113\) | −12789.5 | −0.0942235 | −0.0471117 | − | 0.998890i | \(-0.515002\pi\) | ||||
−0.0471117 | + | 0.998890i | \(0.515002\pi\) | |||||||
\(114\) | 88153.5 | + | 152686.i | 0.635298 | + | 1.10037i | ||||
\(115\) | −8052.78 | − | 13947.8i | −0.0567807 | − | 0.0983471i | ||||
\(116\) | −224160. | − | 388257.i | −1.54673 | − | 2.67901i | ||||
\(117\) | 2402.12 | − | 4160.60i | 0.0162230 | − | 0.0280990i | ||||
\(118\) | 335104. | 2.21551 | ||||||||
\(119\) | 10390.7 | − | 17997.2i | 0.0672632 | − | 0.116503i | ||||
\(120\) | 41838.7 | + | 72466.8i | 0.265232 | + | 0.459395i | ||||
\(121\) | −113373. | −0.703960 | ||||||||
\(122\) | 21598.4 | + | 37409.6i | 0.131378 | + | 0.227554i | ||||
\(123\) | −109640. | + | 189901.i | −0.653438 | + | 1.13179i | ||||
\(124\) | −6241.20 | + | 10810.1i | −0.0364514 | + | 0.0631356i | ||||
\(125\) | −112290. | −0.642783 | ||||||||
\(126\) | 2291.64 | − | 3969.23i | 0.0128594 | − | 0.0222731i | ||||
\(127\) | −48266.3 | −0.265543 | −0.132771 | − | 0.991147i | \(-0.542388\pi\) | ||||
−0.132771 | + | 0.991147i | \(0.542388\pi\) | |||||||
\(128\) | −333382. | −1.79853 | ||||||||
\(129\) | −53961.0 | + | 173866.i | −0.285500 | + | 0.919899i | ||||
\(130\) | 50625.6 | 0.262731 | ||||||||
\(131\) | −295377. | −1.50383 | −0.751915 | − | 0.659260i | \(-0.770870\pi\) | ||||
−0.751915 | + | 0.659260i | \(0.770870\pi\) | |||||||
\(132\) | −101818. | + | 176353.i | −0.508614 | + | 0.880945i | ||||
\(133\) | 32560.2 | 0.159609 | ||||||||
\(134\) | 180018. | − | 311800.i | 0.866071 | − | 1.50008i | ||||
\(135\) | −37317.3 | + | 64635.5i | −0.176228 | + | 0.305236i | ||||
\(136\) | 112842. | + | 195448.i | 0.523146 | + | 0.906116i | ||||
\(137\) | 42056.8 | 0.191441 | 0.0957205 | − | 0.995408i | \(-0.469485\pi\) | ||||
0.0957205 | + | 0.995408i | \(0.469485\pi\) | |||||||
\(138\) | 61484.9 | + | 106495.i | 0.274834 | + | 0.476027i | ||||
\(139\) | −32118.9 | + | 55631.5i | −0.141001 | + | 0.244221i | −0.927874 | − | 0.372894i | \(-0.878366\pi\) |
0.786873 | + | 0.617115i | \(0.211699\pi\) | |||||||
\(140\) | 31875.3 | 0.137446 | ||||||||
\(141\) | 176052. | − | 304931.i | 0.745751 | − | 1.29168i | ||||
\(142\) | 44220.0 | + | 76591.2i | 0.184034 | + | 0.318756i | ||||
\(143\) | 29864.6 | + | 51727.0i | 0.122128 | + | 0.211533i | ||||
\(144\) | 7432.78 | + | 12873.9i | 0.0298707 | + | 0.0517375i | ||||
\(145\) | 137696. | 0.543877 | ||||||||
\(146\) | −152739. | − | 264551.i | −0.593016 | − | 1.02713i | ||||
\(147\) | −120742. | − | 209132.i | −0.460858 | − | 0.798229i | ||||
\(148\) | 113931. | − | 197335.i | 0.427552 | − | 0.740541i | ||||
\(149\) | 87550.4 | − | 151642.i | 0.323067 | − | 0.559568i | −0.658052 | − | 0.752972i | \(-0.728619\pi\) |
0.981119 | + | 0.193404i | \(0.0619528\pi\) | |||||||
\(150\) | 402174. | 1.45944 | ||||||||
\(151\) | 199671. | 0.712642 | 0.356321 | − | 0.934364i | \(-0.384031\pi\) | ||||
0.356321 | + | 0.934364i | \(0.384031\pi\) | |||||||
\(152\) | −176800. | + | 306227.i | −0.620688 | + | 1.07506i | ||||
\(153\) | −6783.98 | + | 11750.2i | −0.0234291 | + | 0.0405804i | ||||
\(154\) | 28491.0 | + | 49347.8i | 0.0968068 | + | 0.167674i | ||||
\(155\) | −1916.90 | − | 3320.17i | −0.00640871 | − | 0.0111002i | ||||
\(156\) | −255109. | −0.839295 | ||||||||
\(157\) | 300483. | + | 520452.i | 0.972905 | + | 1.68512i | 0.686681 | + | 0.726959i | \(0.259067\pi\) |
0.286224 | + | 0.958163i | \(0.407600\pi\) | |||||||
\(158\) | 170443. | + | 295217.i | 0.543172 | + | 0.940801i | ||||
\(159\) | −233887. | − | 405105.i | −0.733692 | − | 1.27079i | ||||
\(160\) | 10845.2 | − | 18784.4i | 0.0334917 | − | 0.0580093i | ||||
\(161\) | 22709.9 | 0.0690480 | ||||||||
\(162\) | 264225. | − | 457652.i | 0.791019 | − | 1.37009i | ||||
\(163\) | 211370. | + | 366103.i | 0.623123 | + | 1.07928i | 0.988901 | + | 0.148579i | \(0.0474698\pi\) |
−0.365777 | + | 0.930702i | \(0.619197\pi\) | |||||||
\(164\) | −907126. | −2.63365 | ||||||||
\(165\) | −31271.9 | − | 54164.6i | −0.0894221 | − | 0.154884i | ||||
\(166\) | −161271. | + | 279329.i | −0.454240 | + | 0.786767i | ||||
\(167\) | −177087. | + | 306724.i | −0.491355 | + | 0.851052i | −0.999950 | − | 0.00995388i | \(-0.996832\pi\) |
0.508596 | + | 0.861006i | \(0.330165\pi\) | |||||||
\(168\) | −117991. | −0.322534 | ||||||||
\(169\) | 148233. | − | 256747.i | 0.399234 | − | 0.691494i | ||||
\(170\) | −142975. | −0.379435 | ||||||||
\(171\) | −21258.2 | −0.0555951 | ||||||||
\(172\) | −734511. | + | 166307.i | −1.89312 | + | 0.428638i | ||||
\(173\) | 535409. | 1.36010 | 0.680050 | − | 0.733166i | \(-0.261958\pi\) | ||||
0.680050 | + | 0.733166i | \(0.261958\pi\) | |||||||
\(174\) | −1.05134e6 | −2.63251 | ||||||||
\(175\) | 37136.5 | − | 64322.3i | 0.0916655 | − | 0.158769i | ||||
\(176\) | −184817. | −0.449740 | ||||||||
\(177\) | 259321. | − | 449156.i | 0.622163 | − | 1.07762i | ||||
\(178\) | 20789.8 | − | 36009.1i | 0.0491814 | − | 0.0851847i | ||||
\(179\) | −237346. | − | 411095.i | −0.553667 | − | 0.958980i | −0.998006 | − | 0.0631211i | \(-0.979895\pi\) |
0.444338 | − | 0.895859i | \(-0.353439\pi\) | |||||||
\(180\) | −20811.0 | −0.0478754 | ||||||||
\(181\) | 343639. | + | 595199.i | 0.779660 | + | 1.35041i | 0.932138 | + | 0.362104i | \(0.117942\pi\) |
−0.152477 | + | 0.988307i | \(0.548725\pi\) | |||||||
\(182\) | −35692.8 | + | 61821.7i | −0.0798733 | + | 0.138345i | ||||
\(183\) | 66856.0 | 0.147575 | ||||||||
\(184\) | −123314. | + | 213586.i | −0.268514 | + | 0.465080i | ||||
\(185\) | 34992.5 | + | 60608.7i | 0.0751701 | + | 0.130198i | ||||
\(186\) | 14636.0 | + | 25350.3i | 0.0310199 | + | 0.0537280i | ||||
\(187\) | −84342.5 | − | 146085.i | −0.176377 | − | 0.305494i | ||||
\(188\) | 1.45661e6 | 3.00571 | ||||||||
\(189\) | −52620.0 | − | 91140.5i | −0.107151 | − | 0.185591i | ||||
\(190\) | −112006. | − | 194000.i | −0.225091 | − | 0.389869i | ||||
\(191\) | −398997. | + | 691083.i | −0.791382 | + | 1.37071i | 0.133730 | + | 0.991018i | \(0.457305\pi\) |
−0.925112 | + | 0.379695i | \(0.876029\pi\) | |||||||
\(192\) | −286144. | + | 495615.i | −0.560185 | + | 0.970268i | ||||
\(193\) | 408554. | 0.789506 | 0.394753 | − | 0.918787i | \(-0.370830\pi\) | ||||
0.394753 | + | 0.918787i | \(0.370830\pi\) | |||||||
\(194\) | −47849.8 | −0.0912800 | ||||||||
\(195\) | 39176.7 | − | 67856.0i | 0.0737804 | − | 0.127791i | ||||
\(196\) | 499494. | − | 865150.i | 0.928732 | − | 1.60861i | ||||
\(197\) | −322760. | − | 559036.i | −0.592535 | − | 1.02630i | −0.993890 | − | 0.110378i | \(-0.964794\pi\) |
0.401355 | − | 0.915923i | \(-0.368539\pi\) | |||||||
\(198\) | −18601.5 | − | 32218.7i | −0.0337197 | − | 0.0584043i | ||||
\(199\) | 289218. | 0.517717 | 0.258858 | − | 0.965915i | \(-0.416654\pi\) | ||||
0.258858 | + | 0.965915i | \(0.416654\pi\) | |||||||
\(200\) | 403299. | + | 698534.i | 0.712938 | + | 1.23484i | ||||
\(201\) | −278614. | − | 482574.i | −0.486422 | − | 0.842507i | ||||
\(202\) | 26441.3 | + | 45797.6i | 0.0455936 | + | 0.0789704i | ||||
\(203\) | −97080.2 | + | 168148.i | −0.165345 | + | 0.286386i | ||||
\(204\) | 720469. | 1.21210 | ||||||||
\(205\) | 139306. | − | 241285.i | 0.231518 | − | 0.401001i | ||||
\(206\) | 745581. | + | 1.29138e6i | 1.22413 | + | 2.12025i | ||||
\(207\) | −14827.1 | −0.0240508 | ||||||||
\(208\) | −115767. | − | 200515.i | −0.185536 | − | 0.321357i | ||||
\(209\) | 132147. | − | 228886.i | 0.209263 | − | 0.362455i | ||||
\(210\) | 37374.7 | − | 64734.9i | 0.0584830 | − | 0.101296i | ||||
\(211\) | −675422. | −1.04441 | −0.522203 | − | 0.852821i | \(-0.674890\pi\) | ||||
−0.522203 | + | 0.852821i | \(0.674890\pi\) | |||||||
\(212\) | 967559. | − | 1.67586e6i | 1.47856 | − | 2.56093i | ||||
\(213\) | 136879. | 0.206722 | ||||||||
\(214\) | −1.65133e6 | −2.46490 | ||||||||
\(215\) | 68561.8 | − | 220911.i | 0.101155 | − | 0.325927i | ||||
\(216\) | 1.14289e6 | 1.66675 | ||||||||
\(217\) | 5405.92 | 0.00779329 | ||||||||
\(218\) | −175259. | + | 303557.i | −0.249769 | + | 0.432612i | ||||
\(219\) | −472788. | −0.666126 | ||||||||
\(220\) | 129368. | − | 224071.i | 0.180206 | − | 0.312126i | ||||
\(221\) | 105662. | − | 183012.i | 0.145525 | − | 0.252057i | ||||
\(222\) | −267176. | − | 462762.i | −0.363844 | − | 0.630196i | ||||
\(223\) | −4792.23 | −0.00645320 | −0.00322660 | − | 0.999995i | \(-0.501027\pi\) | ||||
−0.00322660 | + | 0.999995i | \(0.501027\pi\) | |||||||
\(224\) | 15292.5 | + | 26487.3i | 0.0203637 | + | 0.0352710i | ||||
\(225\) | −24246.0 | + | 41995.4i | −0.0319290 | + | 0.0553026i | ||||
\(226\) | −124074. | −0.161588 | ||||||||
\(227\) | −146116. | + | 253080.i | −0.188206 | + | 0.325982i | −0.944652 | − | 0.328074i | \(-0.893601\pi\) |
0.756446 | + | 0.654056i | \(0.226934\pi\) | |||||||
\(228\) | 564414. | + | 977594.i | 0.719053 | + | 1.24544i | ||||
\(229\) | −116174. | − | 201219.i | −0.146393 | − | 0.253560i | 0.783499 | − | 0.621393i | \(-0.213433\pi\) |
−0.929892 | + | 0.367833i | \(0.880100\pi\) | |||||||
\(230\) | −78121.5 | − | 135310.i | −0.0973758 | − | 0.168660i | ||||
\(231\) | 88191.2 | 0.108741 | ||||||||
\(232\) | −1.05428e6 | − | 1.82607e6i | −1.28599 | − | 2.22739i | ||||
\(233\) | 473517. | + | 820156.i | 0.571408 | + | 0.989707i | 0.996422 | + | 0.0845204i | \(0.0269358\pi\) |
−0.425014 | + | 0.905187i | \(0.639731\pi\) | |||||||
\(234\) | 23303.4 | − | 40362.7i | 0.0278215 | − | 0.0481882i | ||||
\(235\) | −223689. | + | 387440.i | −0.264225 | + | 0.457651i | ||||
\(236\) | 2.14554e6 | 2.50760 | ||||||||
\(237\) | 527591. | 0.610136 | ||||||||
\(238\) | 100802. | − | 174594.i | 0.115353 | − | 0.199797i | ||||
\(239\) | 432126. | − | 748465.i | 0.489346 | − | 0.847572i | −0.510579 | − | 0.859831i | \(-0.670569\pi\) |
0.999925 | + | 0.0122588i | \(0.00390220\pi\) | |||||||
\(240\) | 121223. | + | 209964.i | 0.135849 | + | 0.235297i | ||||
\(241\) | 166478. | + | 288348.i | 0.184635 | + | 0.319797i | 0.943453 | − | 0.331505i | \(-0.107556\pi\) |
−0.758818 | + | 0.651302i | \(0.774223\pi\) | |||||||
\(242\) | −1.09986e6 | −1.20725 | ||||||||
\(243\) | 66394.4 | + | 114999.i | 0.0721300 | + | 0.124933i | ||||
\(244\) | 138287. | + | 239520.i | 0.148698 | + | 0.257553i | ||||
\(245\) | 153413. | + | 265719.i | 0.163285 | + | 0.282818i | ||||
\(246\) | −1.06363e6 | + | 1.84227e6i | −1.12061 | + | 1.94095i | ||||
\(247\) | 331102. | 0.345318 | ||||||||
\(248\) | −29353.9 | + | 50842.4i | −0.0303065 | + | 0.0524925i | ||||
\(249\) | 249599. | + | 432319.i | 0.255120 | + | 0.441882i | ||||
\(250\) | −1.08934e6 | −1.10234 | ||||||||
\(251\) | −614278. | − | 1.06396e6i | −0.615433 | − | 1.06596i | −0.990308 | − | 0.138886i | \(-0.955648\pi\) |
0.374876 | − | 0.927075i | \(-0.377685\pi\) | |||||||
\(252\) | 14672.5 | − | 25413.5i | 0.0145547 | − | 0.0252094i | ||||
\(253\) | 92169.6 | − | 159642.i | 0.0905287 | − | 0.156800i | ||||
\(254\) | −468240. | −0.455391 | ||||||||
\(255\) | −110641. | + | 191636.i | −0.106553 | + | 0.184556i | ||||
\(256\) | −2.01451e6 | −1.92119 | ||||||||
\(257\) | −1.76419e6 | −1.66614 | −0.833070 | − | 0.553168i | \(-0.813419\pi\) | ||||
−0.833070 | + | 0.553168i | \(0.813419\pi\) | |||||||
\(258\) | −523486. | + | 1.68671e6i | −0.489616 | + | 1.57758i | ||||
\(259\) | −98683.6 | −0.0914104 | ||||||||
\(260\) | 324137. | 0.297368 | ||||||||
\(261\) | 63382.7 | − | 109782.i | 0.0575930 | − | 0.0997539i | ||||
\(262\) | −2.86551e6 | −2.57899 | ||||||||
\(263\) | −1.03465e6 | + | 1.79206e6i | −0.922363 | + | 1.59758i | −0.126616 | + | 0.991952i | \(0.540412\pi\) |
−0.795748 | + | 0.605628i | \(0.792922\pi\) | |||||||
\(264\) | −478873. | + | 829433.i | −0.422874 | + | 0.732439i | ||||
\(265\) | 297173. | + | 514718.i | 0.259953 | + | 0.450251i | ||||
\(266\) | 315873. | 0.273721 | ||||||||
\(267\) | −32176.5 | − | 55731.3i | −0.0276223 | − | 0.0478433i | ||||
\(268\) | 1.15259e6 | − | 1.99634e6i | 0.980250 | − | 1.69784i | ||||
\(269\) | −216488. | −0.182412 | −0.0912059 | − | 0.995832i | \(-0.529072\pi\) | ||||
−0.0912059 | + | 0.995832i | \(0.529072\pi\) | |||||||
\(270\) | −362022. | + | 627041.i | −0.302222 | + | 0.523464i | ||||
\(271\) | 1.03032e6 | + | 1.78457e6i | 0.852216 | + | 1.47608i | 0.879204 | + | 0.476446i | \(0.158075\pi\) |
−0.0269875 | + | 0.999636i | \(0.508591\pi\) | |||||||
\(272\) | 326945. | + | 566286.i | 0.267950 | + | 0.464102i | ||||
\(273\) | 55241.8 | + | 95681.6i | 0.0448602 | + | 0.0777002i | ||||
\(274\) | 408001. | 0.328311 | ||||||||
\(275\) | −301441. | − | 522112.i | −0.240365 | − | 0.416324i | ||||
\(276\) | 393665. | + | 681848.i | 0.311067 | + | 0.538784i | ||||
\(277\) | 1.16701e6 | − | 2.02132e6i | 0.913852 | − | 1.58284i | 0.105280 | − | 0.994443i | \(-0.466426\pi\) |
0.808573 | − | 0.588396i | \(-0.200240\pi\) | |||||||
\(278\) | −311591. | + | 539692.i | −0.241809 | + | 0.418826i | ||||
\(279\) | −3529.47 | −0.00271456 | ||||||||
\(280\) | 149917. | 0.114276 | ||||||||
\(281\) | 961404. | − | 1.66520e6i | 0.726340 | − | 1.25806i | −0.232080 | − | 0.972697i | \(-0.574553\pi\) |
0.958420 | − | 0.285361i | \(-0.0921135\pi\) | |||||||
\(282\) | 1.70792e6 | − | 2.95820e6i | 1.27892 | − | 2.21516i | ||||
\(283\) | 1397.26 | + | 2420.12i | 0.00103708 | + | 0.00179627i | 0.866543 | − | 0.499102i | \(-0.166337\pi\) |
−0.865506 | + | 0.500898i | \(0.833003\pi\) | |||||||
\(284\) | 283124. | + | 490385.i | 0.208296 | + | 0.360779i | ||||
\(285\) | −346704. | −0.252841 | ||||||||
\(286\) | 289722. | + | 501814.i | 0.209443 | + | 0.362767i | ||||
\(287\) | 196431. | + | 340228.i | 0.140768 | + | 0.243818i | ||||
\(288\) | −9984.29 | − | 17293.3i | −0.00709310 | − | 0.0122856i | ||||
\(289\) | 411522. | − | 712777.i | 0.289833 | − | 0.502006i | ||||
\(290\) | 1.33581e6 | 0.932718 | ||||||||
\(291\) | −37028.6 | + | 64135.5i | −0.0256333 | + | 0.0443982i | ||||
\(292\) | −977929. | − | 1.69382e6i | −0.671197 | − | 1.16255i | ||||
\(293\) | 333287. | 0.226803 | 0.113402 | − | 0.993549i | \(-0.463825\pi\) | ||||
0.113402 | + | 0.993549i | \(0.463825\pi\) | |||||||
\(294\) | −1.17135e6 | − | 2.02883e6i | −0.790345 | − | 1.36892i | ||||
\(295\) | −329488. | + | 570689.i | −0.220437 | + | 0.381808i | ||||
\(296\) | 535847. | − | 928113.i | 0.355477 | − | 0.615704i | ||||
\(297\) | −854245. | −0.561942 | ||||||||
\(298\) | 849343. | − | 1.47111e6i | 0.554042 | − | 0.959629i | ||||
\(299\) | 230935. | 0.149387 | ||||||||
\(300\) | 2.57497e6 | 1.65184 | ||||||||
\(301\) | 221428. | + | 239474.i | 0.140869 | + | 0.152350i | ||||
\(302\) | 1.93704e6 | 1.22214 | ||||||||
\(303\) | 81846.5 | 0.0512146 | ||||||||
\(304\) | −512257. | + | 887255.i | −0.317910 | + | 0.550636i | ||||
\(305\) | −84945.9 | −0.0522869 | ||||||||
\(306\) | −65812.7 | + | 113991.i | −0.0401796 | + | 0.0695932i | ||||
\(307\) | −523370. | + | 906504.i | −0.316930 | + | 0.548939i | −0.979846 | − | 0.199755i | \(-0.935985\pi\) |
0.662916 | + | 0.748694i | \(0.269319\pi\) | |||||||
\(308\) | 182417. | + | 315956.i | 0.109569 | + | 0.189780i | ||||
\(309\) | 2.30788e6 | 1.37504 | ||||||||
\(310\) | −18596.2 | − | 32209.6i | −0.0109906 | − | 0.0190362i | ||||
\(311\) | 1.41589e6 | − | 2.45240e6i | 0.830099 | − | 1.43777i | −0.0678598 | − | 0.997695i | \(-0.521617\pi\) |
0.897959 | − | 0.440079i | \(-0.145050\pi\) | |||||||
\(312\) | −1.19984e6 | −0.697810 | ||||||||
\(313\) | 632268. | − | 1.09512e6i | 0.364788 | − | 0.631831i | −0.623954 | − | 0.781461i | \(-0.714475\pi\) |
0.988742 | + | 0.149630i | \(0.0478082\pi\) | |||||||
\(314\) | 2.91504e6 | + | 5.04900e6i | 1.66848 | + | 2.88989i | ||||
\(315\) | 4506.46 | + | 7805.42i | 0.00255893 | + | 0.00443220i | ||||
\(316\) | 1.09129e6 | + | 1.89016e6i | 0.614781 | + | 1.06483i | ||||
\(317\) | −3.22703e6 | −1.80366 | −0.901831 | − | 0.432089i | \(-0.857776\pi\) | ||||
−0.901831 | + | 0.432089i | \(0.857776\pi\) | |||||||
\(318\) | −2.26899e6 | − | 3.93000e6i | −1.25824 | − | 2.17934i | ||||
\(319\) | 788011. | + | 1.36488e6i | 0.433567 | + | 0.750959i | ||||
\(320\) | 363569. | − | 629719.i | 0.198478 | − | 0.343773i | ||||
\(321\) | −1.27788e6 | + | 2.21336e6i | −0.692195 | + | 1.19892i | ||||
\(322\) | 220314. | 0.118414 | ||||||||
\(323\) | −935085. | −0.498706 | ||||||||
\(324\) | 1.69174e6 | − | 2.93017e6i | 0.895304 | − | 1.55071i | ||||
\(325\) | 377638. | − | 654088.i | 0.198320 | − | 0.343501i | ||||
\(326\) | 2.05054e6 | + | 3.55164e6i | 1.06862 | + | 1.85091i | ||||
\(327\) | 271248. | + | 469816.i | 0.140281 | + | 0.242973i | ||||
\(328\) | −4.26644e6 | −2.18968 | ||||||||
\(329\) | −315416. | − | 546317.i | −0.160655 | − | 0.278263i | ||||
\(330\) | −303375. | − | 525461.i | −0.153354 | − | 0.265617i | ||||
\(331\) | −749788. | − | 1.29867e6i | −0.376156 | − | 0.651522i | 0.614343 | − | 0.789039i | \(-0.289421\pi\) |
−0.990499 | + | 0.137517i | \(0.956088\pi\) | |||||||
\(332\) | −1.03256e6 | + | 1.78844e6i | −0.514125 | + | 0.890491i | ||||
\(333\) | 64429.5 | 0.0318401 | ||||||||
\(334\) | −1.71795e6 | + | 2.97558e6i | −0.842646 | + | 1.45951i | ||||
\(335\) | 354002. | + | 613149.i | 0.172343 | + | 0.298507i | ||||
\(336\) | −341865. | −0.165198 | ||||||||
\(337\) | 438472. | + | 759456.i | 0.210313 | + | 0.364274i | 0.951813 | − | 0.306680i | \(-0.0992182\pi\) |
−0.741499 | + | 0.670954i | \(0.765885\pi\) | |||||||
\(338\) | 1.43804e6 | − | 2.49075e6i | 0.684665 | − | 1.18587i | ||||
\(339\) | −96014.8 | + | 166302.i | −0.0453773 | + | 0.0785958i | ||||
\(340\) | −915414. | −0.429458 | ||||||||
\(341\) | 21940.3 | − | 38001.6i | 0.0102178 | − | 0.0176977i | ||||
\(342\) | −206230. | −0.0953425 | ||||||||
\(343\) | −884757. | −0.406059 | ||||||||
\(344\) | −3.45458e6 | + | 782185.i | −1.57398 | + | 0.356380i | ||||
\(345\) | −241818. | −0.109381 | ||||||||
\(346\) | 5.19411e6 | 2.33250 | ||||||||
\(347\) | 864304. | − | 1.49702e6i | 0.385339 | − | 0.667426i | −0.606477 | − | 0.795101i | \(-0.707418\pi\) |
0.991816 | + | 0.127674i | \(0.0407512\pi\) | |||||||
\(348\) | −6.73134e6 | −2.97957 | ||||||||
\(349\) | −1.44102e6 | + | 2.49592e6i | −0.633294 | + | 1.09690i | 0.353579 | + | 0.935404i | \(0.384964\pi\) |
−0.986874 | + | 0.161493i | \(0.948369\pi\) | |||||||
\(350\) | 360268. | − | 624003.i | 0.157201 | − | 0.272281i | ||||
\(351\) | −535088. | − | 926799.i | −0.231823 | − | 0.401530i | ||||
\(352\) | 248261. | 0.106795 | ||||||||
\(353\) | −1.10269e6 | − | 1.90992e6i | −0.470997 | − | 0.815792i | 0.528452 | − | 0.848963i | \(-0.322773\pi\) |
−0.999450 | + | 0.0331715i | \(0.989439\pi\) | |||||||
\(354\) | 2.51572e6 | − | 4.35735e6i | 1.06697 | − | 1.84805i | ||||
\(355\) | −173915. | −0.0732432 | ||||||||
\(356\) | 133110. | − | 230553.i | 0.0556653 | − | 0.0964151i | ||||
\(357\) | −156012. | − | 270220.i | −0.0647869 | − | 0.112214i | ||||
\(358\) | −2.30254e6 | − | 3.98811e6i | −0.949509 | − | 1.64460i | ||||
\(359\) | 1.28587e6 | + | 2.22718e6i | 0.526574 | + | 0.912053i | 0.999521 | + | 0.0309619i | \(0.00985707\pi\) |
−0.472946 | + | 0.881091i | \(0.656810\pi\) | |||||||
\(360\) | −97879.3 | −0.0398047 | ||||||||
\(361\) | 505506. | + | 875562.i | 0.204154 | + | 0.353606i | ||||
\(362\) | 3.33370e6 | + | 5.77414e6i | 1.33707 | + | 2.31588i | ||||
\(363\) | −851126. | + | 1.47419e6i | −0.339022 | + | 0.587203i | ||||
\(364\) | −228528. | + | 395821.i | −0.0904035 | + | 0.156583i | ||||
\(365\) | 600715. | 0.236013 | ||||||||
\(366\) | 648583. | 0.253083 | ||||||||
\(367\) | 1.52376e6 | − | 2.63922e6i | 0.590541 | − | 1.02285i | −0.403619 | − | 0.914927i | \(-0.632248\pi\) |
0.994160 | − | 0.107920i | \(-0.0344189\pi\) | |||||||
\(368\) | −357287. | + | 618838.i | −0.137530 | + | 0.238209i | ||||
\(369\) | −128248. | − | 222131.i | −0.0490324 | − | 0.0849267i | ||||
\(370\) | 339469. | + | 587977.i | 0.128913 | + | 0.223283i | ||||
\(371\) | −838068. | −0.316115 | ||||||||
\(372\) | 93708.9 | + | 162309.i | 0.0351094 | + | 0.0608113i | ||||
\(373\) | −1.02592e6 | − | 1.77695e6i | −0.381805 | − | 0.661306i | 0.609515 | − | 0.792774i | \(-0.291364\pi\) |
−0.991320 | + | 0.131469i | \(0.958031\pi\) | |||||||
\(374\) | −818223. | − | 1.41720e6i | −0.302477 | − | 0.523906i | ||||
\(375\) | −842990. | + | 1.46010e6i | −0.309560 | + | 0.536173i | ||||
\(376\) | 6.85078e6 | 2.49902 | ||||||||
\(377\) | −987200. | + | 1.70988e6i | −0.357727 | + | 0.619602i | ||||
\(378\) | −510476. | − | 884171.i | −0.183758 | − | 0.318278i | ||||
\(379\) | 2.08546e6 | 0.745769 | 0.372884 | − | 0.927878i | \(-0.378369\pi\) | ||||
0.372884 | + | 0.927878i | \(0.378369\pi\) | |||||||
\(380\) | −717133. | − | 1.24211e6i | −0.254766 | − | 0.441267i | ||||
\(381\) | −362349. | + | 627606.i | −0.127883 | + | 0.221501i | ||||
\(382\) | −3.87074e6 | + | 6.70433e6i | −1.35718 | + | 2.35070i | ||||
\(383\) | −1.53676e6 | −0.535314 | −0.267657 | − | 0.963514i | \(-0.586249\pi\) | ||||
−0.267657 | + | 0.963514i | \(0.586249\pi\) | |||||||
\(384\) | −2.50280e6 | + | 4.33497e6i | −0.866158 | + | 1.50023i | ||||
\(385\) | −112054. | −0.0385279 | ||||||||
\(386\) | 3.96346e6 | 1.35396 | ||||||||
\(387\) | −144568. | − | 156350.i | −0.0490676 | − | 0.0530666i | ||||
\(388\) | −306364. | −0.103314 | ||||||||
\(389\) | −581673. | −0.194897 | −0.0974484 | − | 0.995241i | \(-0.531068\pi\) | ||||
−0.0974484 | + | 0.995241i | \(0.531068\pi\) | |||||||
\(390\) | 380060. | − | 658284.i | 0.126529 | − | 0.219155i | ||||
\(391\) | −652199. | −0.215744 | ||||||||
\(392\) | 2.34924e6 | − | 4.06901e6i | 0.772170 | − | 1.33744i | ||||
\(393\) | −2.21748e6 | + | 3.84079e6i | −0.724233 | + | 1.25441i | ||||
\(394\) | −3.13116e6 | − | 5.42332e6i | −1.01616 | − | 1.76005i | ||||
\(395\) | −670347. | −0.216176 | ||||||||
\(396\) | −119098. | − | 206284.i | −0.0381652 | − | 0.0661041i | ||||
\(397\) | 369051. | − | 639215.i | 0.117520 | − | 0.203550i | −0.801265 | − | 0.598310i | \(-0.795839\pi\) |
0.918784 | + | 0.394760i | \(0.129172\pi\) | |||||||
\(398\) | 2.80576e6 | 0.887856 | ||||||||
\(399\) | 244439. | − | 423380.i | 0.0768666 | − | 0.133137i | ||||
\(400\) | 1.16851e6 | + | 2.02392e6i | 0.365159 | + | 0.632474i | ||||
\(401\) | −3.04184e6 | − | 5.26862e6i | −0.944659 | − | 1.63620i | −0.756433 | − | 0.654072i | \(-0.773060\pi\) |
−0.188226 | − | 0.982126i | \(-0.560274\pi\) | |||||||
\(402\) | −2.70289e6 | − | 4.68154e6i | −0.834187 | − | 1.44485i | ||||
\(403\) | 54972.4 | 0.0168609 | ||||||||
\(404\) | 169294. | + | 293225.i | 0.0516045 | + | 0.0893815i | ||||
\(405\) | 519594. | + | 899964.i | 0.157408 | + | 0.272639i | ||||
\(406\) | −941794. | + | 1.63124e6i | −0.283557 | + | 0.491136i | ||||
\(407\) | −400513. | + | 693709.i | −0.119848 | + | 0.207583i | ||||
\(408\) | 3.38854e6 | 1.00777 | ||||||||
\(409\) | 4.27147e6 | 1.26261 | 0.631304 | − | 0.775535i | \(-0.282520\pi\) | ||||
0.631304 | + | 0.775535i | \(0.282520\pi\) | |||||||
\(410\) | 1.35143e6 | − | 2.34075e6i | 0.397040 | − | 0.687694i | ||||
\(411\) | 315732. | − | 546864.i | 0.0921965 | − | 0.159689i | ||||
\(412\) | 4.77368e6 | + | 8.26826e6i | 1.38551 | + | 2.39978i | ||||
\(413\) | −464600. | − | 804712.i | −0.134031 | − | 0.232148i | ||||
\(414\) | −143840. | −0.0412458 | ||||||||
\(415\) | −317136. | − | 549296.i | −0.0903911 | − | 0.156562i | ||||
\(416\) | 155508. | + | 269347.i | 0.0440574 | + | 0.0763096i | ||||
\(417\) | 482251. | + | 835283.i | 0.135810 | + | 0.235230i | ||||
\(418\) | 1.28199e6 | − | 2.22047e6i | 0.358875 | − | 0.621589i | ||||
\(419\) | −1.43550e6 | −0.399456 | −0.199728 | − | 0.979851i | \(-0.564006\pi\) | ||||
−0.199728 | + | 0.979851i | \(0.564006\pi\) | |||||||
\(420\) | 239297. | − | 414474.i | 0.0661932 | − | 0.114650i | ||||
\(421\) | 2.74777e6 | + | 4.75929e6i | 0.755572 | + | 1.30869i | 0.945089 | + | 0.326812i | \(0.105974\pi\) |
−0.189517 | + | 0.981877i | \(0.560692\pi\) | |||||||
\(422\) | −6.55240e6 | −1.79110 | ||||||||
\(423\) | 205932. | + | 356685.i | 0.0559594 | + | 0.0969245i | ||||
\(424\) | 4.55067e6 | − | 7.88199e6i | 1.22931 | − | 2.12922i | ||||
\(425\) | −1.06651e6 | + | 1.84725e6i | −0.286413 | + | 0.496082i | ||||
\(426\) | 1.32789e6 | 0.354517 | ||||||||
\(427\) | 59889.8 | − | 103732.i | 0.0158958 | − | 0.0275324i | ||||
\(428\) | −1.05728e7 | −2.78986 | ||||||||
\(429\) | 896808. | 0.235264 | ||||||||
\(430\) | 665131. | − | 2.14310e6i | 0.173475 | − | 0.558947i | ||||
\(431\) | −1.71842e6 | −0.445591 | −0.222795 | − | 0.974865i | \(-0.571518\pi\) | ||||
−0.222795 | + | 0.974865i | \(0.571518\pi\) | |||||||
\(432\) | 3.31140e6 | 0.853693 | ||||||||
\(433\) | −3.37501e6 | + | 5.84569e6i | −0.865078 | + | 1.49836i | 0.00189188 | + | 0.999998i | \(0.499398\pi\) |
−0.866970 | + | 0.498361i | \(0.833936\pi\) | |||||||
\(434\) | 52443.9 | 0.0133651 | ||||||||
\(435\) | 1.03372e6 | − | 1.79046e6i | 0.261927 | − | 0.453671i | ||||
\(436\) | −1.12212e6 | + | 1.94356e6i | −0.282697 | + | 0.489646i | ||||
\(437\) | −510931. | − | 884959.i | −0.127985 | − | 0.221676i | ||||
\(438\) | −4.58661e6 | −1.14237 | ||||||||
\(439\) | 1.03603e6 | + | 1.79446e6i | 0.256574 | + | 0.444399i | 0.965322 | − | 0.261063i | \(-0.0840730\pi\) |
−0.708748 | + | 0.705462i | \(0.750740\pi\) | |||||||
\(440\) | 608447. | − | 1.05386e6i | 0.149827 | − | 0.259509i | ||||
\(441\) | 282470. | 0.0691633 | ||||||||
\(442\) | 1.02505e6 | − | 1.77544e6i | 0.249568 | − | 0.432264i | ||||
\(443\) | 687784. | + | 1.19128e6i | 0.166511 | + | 0.288406i | 0.937191 | − | 0.348817i | \(-0.113417\pi\) |
−0.770680 | + | 0.637223i | \(0.780083\pi\) | |||||||
\(444\) | −1.71063e6 | − | 2.96290e6i | −0.411811 | − | 0.713278i | ||||
\(445\) | 40882.8 | + | 70811.1i | 0.00978681 | + | 0.0169512i | ||||
\(446\) | −46490.3 | −0.0110669 | ||||||||
\(447\) | −1.31453e6 | − | 2.27683e6i | −0.311173 | − | 0.538968i | ||||
\(448\) | 512657. | + | 887948.i | 0.120679 | + | 0.209022i | ||||
\(449\) | −534198. | + | 925258.i | −0.125051 | + | 0.216594i | −0.921753 | − | 0.387778i | \(-0.873243\pi\) |
0.796702 | + | 0.604372i | \(0.206576\pi\) | |||||||
\(450\) | −235216. | + | 407405.i | −0.0547564 | + | 0.0948408i | ||||
\(451\) | 3.18890e6 | 0.738244 | ||||||||
\(452\) | −794399. | −0.182891 | ||||||||
\(453\) | 1.49898e6 | − | 2.59631e6i | 0.343203 | − | 0.594445i | ||||
\(454\) | −1.41750e6 | + | 2.45518e6i | −0.322763 | + | 0.559041i | ||||
\(455\) | −70189.2 | − | 121571.i | −0.0158943 | − | 0.0275298i | ||||
\(456\) | 2.65458e6 | + | 4.59786e6i | 0.597838 | + | 1.03548i | ||||
\(457\) | −3.15223e6 | −0.706036 | −0.353018 | − | 0.935616i | \(-0.614845\pi\) | ||||
−0.353018 | + | 0.935616i | \(0.614845\pi\) | |||||||
\(458\) | −1.12702e6 | − | 1.95206e6i | −0.251056 | − | 0.434841i | ||||
\(459\) | 1.51117e6 | + | 2.61743e6i | 0.334798 | + | 0.579887i | ||||
\(460\) | −500183. | − | 866343.i | −0.110213 | − | 0.190895i | ||||
\(461\) | 2.41406e6 | − | 4.18128e6i | 0.529050 | − | 0.916341i | −0.470377 | − | 0.882466i | \(-0.655882\pi\) |
0.999426 | − | 0.0338749i | \(-0.0107848\pi\) | |||||||
\(462\) | 855559. | 0.186486 | ||||||||
\(463\) | 2.68183e6 | − | 4.64507e6i | 0.581406 | − | 1.00702i | −0.413907 | − | 0.910319i | \(-0.635836\pi\) |
0.995313 | − | 0.0967054i | \(-0.0308305\pi\) | |||||||
\(464\) | −3.05465e6 | − | 5.29081e6i | −0.658668 | − | 1.14085i | ||||
\(465\) | −57562.9 | −0.0123455 | ||||||||
\(466\) | 4.59368e6 | + | 7.95649e6i | 0.979933 | + | 1.69729i | ||||
\(467\) | 2.84727e6 | − | 4.93162e6i | 0.604138 | − | 1.04640i | −0.388049 | − | 0.921639i | \(-0.626851\pi\) |
0.992187 | − | 0.124759i | \(-0.0398159\pi\) | |||||||
\(468\) | 149203. | − | 258428.i | 0.0314893 | − | 0.0545412i | ||||
\(469\) | −998334. | −0.209577 | ||||||||
\(470\) | −2.17005e6 | + | 3.75863e6i | −0.453132 | + | 0.784847i | ||||
\(471\) | 9.02324e6 | 1.87417 | ||||||||
\(472\) | 1.00910e7 | 2.08488 | ||||||||
\(473\) | 2.58209e6 | − | 584636.i | 0.530663 | − | 0.120152i | ||||
\(474\) | 5.11826e6 | 1.04635 | ||||||||
\(475\) | −3.34201e6 | −0.679631 | ||||||||
\(476\) | 645399. | − | 1.11786e6i | 0.130560 | − | 0.226137i | ||||
\(477\) | 547166. | 0.110109 | ||||||||
\(478\) | 4.19214e6 | − | 7.26100e6i | 0.839201 | − | 1.45354i | ||||
\(479\) | −1.04650e6 | + | 1.81259e6i | −0.208401 | + | 0.360961i | −0.951211 | − | 0.308541i | \(-0.900159\pi\) |
0.742810 | + | 0.669502i | \(0.233493\pi\) | |||||||
\(480\) | −162836. | − | 282040.i | −0.0322587 | − | 0.0558737i | ||||
\(481\) | −1.00350e6 | −0.197768 | ||||||||
\(482\) | 1.61503e6 | + | 2.79732e6i | 0.316639 | + | 0.548435i | ||||
\(483\) | 170490. | − | 295297.i | 0.0332530 | − | 0.0575959i | ||||
\(484\) | −7.04198e6 | −1.36641 | ||||||||
\(485\) | 47047.9 | − | 81489.3i | 0.00908208 | − | 0.0157306i | ||||
\(486\) | 644105. | + | 1.11562e6i | 0.123699 | + | 0.214253i | ||||
\(487\) | −2.05270e6 | − | 3.55538e6i | −0.392196 | − | 0.679304i | 0.600543 | − | 0.799593i | \(-0.294951\pi\) |
−0.992739 | + | 0.120289i | \(0.961618\pi\) | |||||||
\(488\) | 650397. | + | 1.12652e6i | 0.123631 | + | 0.214136i | ||||
\(489\) | 6.34725e6 | 1.20037 | ||||||||
\(490\) | 1.48829e6 | + | 2.57779e6i | 0.280025 | + | 0.485018i | ||||
\(491\) | 786609. | + | 1.36245e6i | 0.147250 | + | 0.255044i | 0.930210 | − | 0.367027i | \(-0.119624\pi\) |
−0.782960 | + | 0.622072i | \(0.786291\pi\) | |||||||
\(492\) | −6.81005e6 | + | 1.17954e7i | −1.26835 | + | 2.19684i | ||||
\(493\) | 2.78801e6 | − | 4.82898e6i | 0.516628 | − | 0.894825i | ||||
\(494\) | 3.21208e6 | 0.592201 | ||||||||
\(495\) | 73158.9 | 0.0134200 | ||||||||
\(496\) | −85049.3 | + | 147310.i | −0.0155227 | + | 0.0268861i | ||||
\(497\) | 122616. | − | 212378.i | 0.0222668 | − | 0.0385672i | ||||
\(498\) | 2.42141e6 | + | 4.19401e6i | 0.437517 | + | 0.757802i | ||||
\(499\) | −2.03361e6 | − | 3.52231e6i | −0.365608 | − | 0.633252i | 0.623266 | − | 0.782010i | \(-0.285806\pi\) |
−0.988874 | + | 0.148759i | \(0.952472\pi\) | |||||||
\(500\) | −6.97466e6 | −1.24766 | ||||||||
\(501\) | 2.65888e6 | + | 4.60532e6i | 0.473266 | + | 0.819720i | ||||
\(502\) | −5.95923e6 | − | 1.03217e7i | −1.05543 | − | 1.82806i | ||||
\(503\) | −2.51936e6 | − | 4.36365e6i | −0.443986 | − | 0.769007i | 0.553995 | − | 0.832520i | \(-0.313103\pi\) |
−0.997981 | + | 0.0635134i | \(0.979769\pi\) | |||||||
\(504\) | 69008.3 | − | 119526.i | 0.0121011 | − | 0.0209597i | ||||
\(505\) | −103993. | −0.0181457 | ||||||||
\(506\) | 894155. | − | 1.54872e6i | 0.155252 | − | 0.268904i | ||||
\(507\) | −2.22565e6 | − | 3.85494e6i | −0.384536 | − | 0.666036i | ||||
\(508\) | −2.99797e6 | −0.515428 | ||||||||
\(509\) | −1.04539e6 | − | 1.81068e6i | −0.178849 | − | 0.309775i | 0.762638 | − | 0.646826i | \(-0.223904\pi\) |
−0.941486 | + | 0.337051i | \(0.890571\pi\) | |||||||
\(510\) | −1.07335e6 | + | 1.85910e6i | −0.182733 | + | 0.316503i | ||||
\(511\) | −423525. | + | 733567.i | −0.0717508 | + | 0.124276i | ||||
\(512\) | −8.87492e6 | −1.49620 | ||||||||
\(513\) | −2.36770e6 | + | 4.10098e6i | −0.397222 | + | 0.688009i | ||||
\(514\) | −1.71147e7 | −2.85734 | ||||||||
\(515\) | −2.93234e6 | −0.487188 | ||||||||
\(516\) | −3.35169e6 | + | 1.07994e7i | −0.554165 | + | 1.78556i | ||||
\(517\) | −5.12054e6 | −0.842538 | ||||||||
\(518\) | −957348. | −0.156764 | ||||||||
\(519\) | 4.01947e6 | − | 6.96192e6i | 0.655014 | − | 1.13452i | ||||
\(520\) | 1.52449e6 | 0.247239 | ||||||||
\(521\) | −506310. | + | 876954.i | −0.0817188 | + | 0.141541i | −0.903988 | − | 0.427557i | \(-0.859374\pi\) |
0.822270 | + | 0.569098i | \(0.192708\pi\) | |||||||
\(522\) | 614888. | − | 1.06502e6i | 0.0987687 | − | 0.171072i | ||||
\(523\) | 1.31129e6 | + | 2.27122e6i | 0.209626 | + | 0.363082i | 0.951597 | − | 0.307350i | \(-0.0994421\pi\) |
−0.741971 | + | 0.670432i | \(0.766109\pi\) | |||||||
\(524\) | −1.83468e7 | −2.91899 | ||||||||
\(525\) | −557589. | − | 965772.i | −0.0882908 | − | 0.152924i | ||||
\(526\) | −1.00373e7 | + | 1.73851e7i | −1.58180 | + | 2.73976i | ||||
\(527\) | −155251. | −0.0243505 | ||||||||
\(528\) | −1.38748e6 | + | 2.40318e6i | −0.216591 | + | 0.375147i | ||||
\(529\) | 2.86181e6 | + | 4.95680e6i | 0.444633 | + | 0.770127i | ||||
\(530\) | 2.88293e6 | + | 4.99338e6i | 0.445805 | + | 0.772156i | ||||
\(531\) | 303333. | + | 525388.i | 0.0466856 | + | 0.0808619i | ||||
\(532\) | 2.02242e6 | 0.309807 | ||||||||
\(533\) | 1.99749e6 | + | 3.45975e6i | 0.304555 | + | 0.527505i | ||||
\(534\) | −312150. | − | 540660.i | −0.0473708 | − | 0.0820486i | ||||
\(535\) | 1.62365e6 | − | 2.81225e6i | 0.245250 | − | 0.424785i | ||||
\(536\) | 5.42090e6 | − | 9.38927e6i | 0.815003 | − | 1.41163i | ||||
\(537\) | −7.12729e6 | −1.06657 | ||||||||
\(538\) | −2.10019e6 | −0.312826 | ||||||||
\(539\) | −1.75592e6 | + | 3.04134e6i | −0.260335 | + | 0.450913i | ||||
\(540\) | −2.31789e6 | + | 4.01471e6i | −0.342065 | + | 0.592475i | ||||
\(541\) | −3.00801e6 | − | 5.21003e6i | −0.441862 | − | 0.765328i | 0.555966 | − | 0.831205i | \(-0.312349\pi\) |
−0.997828 | + | 0.0658777i | \(0.979015\pi\) | |||||||
\(542\) | 9.99535e6 | + | 1.73125e7i | 1.46150 | + | 2.53140i | ||||
\(543\) | 1.03192e7 | 1.50191 | ||||||||
\(544\) | −439179. | − | 760680.i | −0.0636274 | − | 0.110206i | ||||
\(545\) | −344643. | − | 596939.i | −0.0497024 | − | 0.0860872i | ||||
\(546\) | 535911. | + | 928226.i | 0.0769328 | + | 0.133251i | ||||
\(547\) | −28069.5 | + | 48617.8i | −0.00401113 | + | 0.00694747i | −0.868024 | − | 0.496522i | \(-0.834610\pi\) |
0.864013 | + | 0.503470i | \(0.167943\pi\) | |||||||
\(548\) | 2.61228e6 | 0.371594 | ||||||||
\(549\) | −39101.4 | + | 67725.6i | −0.00553684 | + | 0.00959008i | ||||
\(550\) | −2.92434e6 | − | 5.06511e6i | −0.412213 | − | 0.713973i | ||||
\(551\) | 8.73649e6 | 1.22591 | ||||||||
\(552\) | 1.85150e6 | + | 3.20690e6i | 0.258629 | + | 0.447958i | ||||
\(553\) | 472618. | − | 818598.i | 0.0657200 | − | 0.113830i | ||||
\(554\) | 1.13214e7 | − | 1.96093e7i | 1.56721 | − | 2.71448i | ||||
\(555\) | 1.05079e6 | 0.144805 | ||||||||
\(556\) | −1.99500e6 | + | 3.45545e6i | −0.273688 | + | 0.474042i | ||||
\(557\) | 3.39535e6 | 0.463710 | 0.231855 | − | 0.972750i | \(-0.425520\pi\) | ||||
0.231855 | + | 0.972750i | \(0.425520\pi\) | |||||||
\(558\) | −34240.1 | −0.00465532 | ||||||||
\(559\) | 2.25168e6 | + | 2.43519e6i | 0.304774 | + | 0.329613i | ||||
\(560\) | 434366. | 0.0585310 | ||||||||
\(561\) | −2.53273e6 | −0.339768 | ||||||||
\(562\) | 9.32676e6 | − | 1.61544e7i | 1.24563 | − | 2.15750i | ||||
\(563\) | 1.14249e7 | 1.51908 | 0.759542 | − | 0.650458i | \(-0.225423\pi\) | ||||
0.759542 | + | 0.650458i | \(0.225423\pi\) | |||||||
\(564\) | 1.09352e7 | − | 1.89402e7i | 1.44753 | − | 2.50719i | ||||
\(565\) | 121994. | − | 211301.i | 0.0160775 | − | 0.0278471i | ||||
\(566\) | 13555.1 | + | 23478.1i | 0.00177853 | + | 0.00308050i | ||||
\(567\) | −1.46533e6 | −0.191416 | ||||||||
\(568\) | 1.33160e6 | + | 2.30640e6i | 0.173182 | + | 0.299960i | ||||
\(569\) | −6.93642e6 | + | 1.20142e7i | −0.898162 | + | 1.55566i | −0.0683210 | + | 0.997663i | \(0.521764\pi\) |
−0.829841 | + | 0.557999i | \(0.811569\pi\) | |||||||
\(570\) | −3.36345e6 | −0.433608 | ||||||||
\(571\) | 3.46572e6 | − | 6.00280e6i | 0.444839 | − | 0.770484i | −0.553202 | − | 0.833047i | \(-0.686594\pi\) |
0.998041 | + | 0.0625632i | \(0.0199275\pi\) | |||||||
\(572\) | 1.85498e6 | + | 3.21293e6i | 0.237056 | + | 0.410592i | ||||
\(573\) | 5.99076e6 | + | 1.03763e7i | 0.762247 | + | 1.32025i | ||||
\(574\) | 1.90561e6 | + | 3.30062e6i | 0.241410 | + | 0.418134i | ||||
\(575\) | −2.33097e6 | −0.294013 | ||||||||
\(576\) | −334708. | − | 579732.i | −0.0420349 | − | 0.0728066i | ||||
\(577\) | −6.03914e6 | − | 1.04601e7i | −0.755154 | − | 1.30797i | −0.945298 | − | 0.326209i | \(-0.894229\pi\) |
0.190144 | − | 0.981756i | \(-0.439105\pi\) | |||||||
\(578\) | 3.99225e6 | − | 6.91478e6i | 0.497048 | − | 0.860912i | ||||
\(579\) | 3.06713e6 | − | 5.31242e6i | 0.380220 | − | 0.658561i | ||||
\(580\) | 8.55271e6 | 1.05568 | ||||||||
\(581\) | 894368. | 0.109920 | ||||||||
\(582\) | −359222. | + | 622190.i | −0.0439598 | + | 0.0761405i | ||||
\(583\) | −3.40135e6 | + | 5.89131e6i | −0.414457 | + | 0.717861i | ||||
\(584\) | −4.59944e6 | − | 7.96646e6i | −0.558049 | − | 0.966570i | ||||
\(585\) | 45825.8 | + | 79372.6i | 0.00553631 | + | 0.00958917i | ||||
\(586\) | 3.23328e6 | 0.388955 | ||||||||
\(587\) | 6.81822e6 | + | 1.18095e7i | 0.816725 | + | 1.41461i | 0.908082 | + | 0.418791i | \(0.137546\pi\) |
−0.0913572 | + | 0.995818i | \(0.529121\pi\) | |||||||
\(588\) | −7.49969e6 | − | 1.29898e7i | −0.894541 | − | 1.54939i | ||||
\(589\) | −121623. | − | 210657.i | −0.0144453 | − | 0.0250201i | ||||
\(590\) | −3.19642e6 | + | 5.53637e6i | −0.378037 | + | 0.654779i | ||||
\(591\) | −9.69220e6 | −1.14144 | ||||||||
\(592\) | 1.55255e6 | − | 2.68910e6i | 0.182071 | − | 0.315357i | ||||
\(593\) | −3.42044e6 | − | 5.92438e6i | −0.399435 | − | 0.691841i | 0.594222 | − | 0.804301i | \(-0.297460\pi\) |
−0.993656 | + | 0.112460i | \(0.964127\pi\) | |||||||
\(594\) | −8.28719e6 | −0.963699 | ||||||||
\(595\) | 198226. | + | 343337.i | 0.0229545 | + | 0.0397583i | ||||
\(596\) | 5.43803e6 | − | 9.41894e6i | 0.627084 | − | 1.08614i | ||||
\(597\) | 2.17124e6 | − | 3.76070e6i | 0.249328 | − | 0.431850i | ||||
\(598\) | 2.24035e6 | 0.256190 | ||||||||
\(599\) | −3.74140e6 | + | 6.48029e6i | −0.426056 | + | 0.737951i | −0.996518 | − | 0.0833728i | \(-0.973431\pi\) |
0.570462 | + | 0.821324i | \(0.306764\pi\) | |||||||
\(600\) | 1.21107e7 | 1.37338 | ||||||||
\(601\) | −1.61098e7 | −1.81930 | −0.909652 | − | 0.415372i | \(-0.863651\pi\) | ||||
−0.909652 | + | 0.415372i | \(0.863651\pi\) | |||||||
\(602\) | 2.14812e6 | + | 2.32319e6i | 0.241583 | + | 0.261272i | ||||
\(603\) | 651802. | 0.0729999 | ||||||||
\(604\) | 1.24022e7 | 1.38326 | ||||||||
\(605\) | 1.08142e6 | − | 1.87308e6i | 0.120118 | − | 0.208050i | ||||
\(606\) | 794008. | 0.0878301 | ||||||||
\(607\) | −5.39955e6 | + | 9.35230e6i | −0.594821 | + | 1.03026i | 0.398752 | + | 0.917059i | \(0.369444\pi\) |
−0.993572 | + | 0.113200i | \(0.963890\pi\) | |||||||
\(608\) | 688103. | − | 1.19183e6i | 0.0754909 | − | 0.130754i | ||||
\(609\) | 1.45762e6 | + | 2.52467e6i | 0.159258 | + | 0.275842i | ||||
\(610\) | −824076. | −0.0896691 | ||||||||
\(611\) | −3.20744e6 | − | 5.55545e6i | −0.347581 | − | 0.602028i | ||||
\(612\) | −421374. | + | 729841.i | −0.0454767 | + | 0.0787680i | ||||
\(613\) | −4.53519e6 | −0.487466 | −0.243733 | − | 0.969842i | \(-0.578372\pi\) | ||||
−0.243733 | + | 0.969842i | \(0.578372\pi\) | |||||||
\(614\) | −5.07732e6 | + | 8.79417e6i | −0.543517 | + | 0.941399i | ||||
\(615\) | −2.09162e6 | − | 3.62279e6i | −0.222995 | − | 0.386238i | ||||
\(616\) | 857953. | + | 1.48602e6i | 0.0910986 | + | 0.157787i | ||||
\(617\) | −501748. | − | 869053.i | −0.0530607 | − | 0.0919038i | 0.838275 | − | 0.545248i | \(-0.183564\pi\) |
−0.891336 | + | 0.453344i | \(0.850231\pi\) | |||||||
\(618\) | 2.23892e7 | 2.35812 | ||||||||
\(619\) | 5.73770e6 | + | 9.93798e6i | 0.601881 | + | 1.04249i | 0.992536 | + | 0.121952i | \(0.0389153\pi\) |
−0.390655 | + | 0.920537i | \(0.627751\pi\) | |||||||
\(620\) | −119065. | − | 206226.i | −0.0124395 | − | 0.0215459i | ||||
\(621\) | −1.65141e6 | + | 2.86033e6i | −0.171841 | + | 0.297637i | ||||
\(622\) | 1.37359e7 | − | 2.37912e7i | 1.42357 | − | 2.46570i | ||||
\(623\) | −115295. | −0.0119012 | ||||||||
\(624\) | −3.47639e6 | −0.357410 | ||||||||
\(625\) | −3.24307e6 | + | 5.61716e6i | −0.332090 | + | 0.575197i | ||||
\(626\) | 6.13375e6 | − | 1.06240e7i | 0.625591 | − | 1.08356i | ||||
\(627\) | −1.98414e6 | − | 3.43662e6i | −0.201559 | − | 0.349111i | ||||
\(628\) | 1.86639e7 | + | 3.23269e7i | 1.88844 | + | 3.27088i | ||||
\(629\) | 2.83406e6 | 0.285616 | ||||||||
\(630\) | 43718.0 | + | 75721.8i | 0.00438843 | + | 0.00760098i | ||||
\(631\) | −5.97711e6 | − | 1.03526e7i | −0.597610 | − | 1.03509i | −0.993173 | − | 0.116651i | \(-0.962784\pi\) |
0.395563 | − | 0.918439i | \(-0.370549\pi\) | |||||||
\(632\) | 5.13258e6 | + | 8.88989e6i | 0.511144 | + | 0.885327i | ||||
\(633\) | −5.07058e6 | + | 8.78251e6i | −0.502978 | + | 0.871183i | ||||
\(634\) | −3.13061e7 | −3.09318 | ||||||||
\(635\) | 460393. | − | 797424.i | 0.0453100 | − | 0.0784793i | ||||
\(636\) | −1.45275e7 | − | 2.51623e7i | −1.42412 | − | 2.46665i | ||||
\(637\) | −4.39954e6 | −0.429594 | ||||||||
\(638\) | 7.64465e6 | + | 1.32409e7i | 0.743543 | + | 1.28785i | ||||
\(639\) | −80055.0 | + | 138659.i | −0.00775597 | + | 0.0134337i | ||||
\(640\) | 3.18000e6 | − | 5.50793e6i | 0.306886 | − | 0.531543i | ||||
\(641\) | −7.44664e6 | −0.715839 | −0.357919 | − | 0.933753i | \(-0.616514\pi\) | ||||
−0.357919 | + | 0.933753i | \(0.616514\pi\) | |||||||
\(642\) | −1.23970e7 | + | 2.14722e7i | −1.18708 | + | 2.05608i | ||||
\(643\) | −1.01638e7 | −0.969460 | −0.484730 | − | 0.874664i | \(-0.661082\pi\) | ||||
−0.484730 | + | 0.874664i | \(0.661082\pi\) | |||||||
\(644\) | 1.41059e6 | 0.134025 | ||||||||
\(645\) | −2.35779e6 | − | 2.54995e6i | −0.223154 | − | 0.241341i | ||||
\(646\) | −9.07144e6 | −0.855253 | ||||||||
\(647\) | −9.18915e6 | −0.863008 | −0.431504 | − | 0.902111i | \(-0.642017\pi\) | ||||
−0.431504 | + | 0.902111i | \(0.642017\pi\) | |||||||
\(648\) | 7.95665e6 | − | 1.37813e7i | 0.744377 | − | 1.28930i | ||||
\(649\) | −7.54243e6 | −0.702910 | ||||||||
\(650\) | 3.66354e6 | − | 6.34543e6i | 0.340108 | − | 0.589085i | ||||
\(651\) | 40583.8 | − | 70293.2i | 0.00375319 | − | 0.00650071i | ||||
\(652\) | 1.31288e7 | + | 2.27398e7i | 1.20950 | + | 2.09492i | ||||
\(653\) | −1.14604e7 | −1.05176 | −0.525879 | − | 0.850559i | \(-0.676264\pi\) | ||||
−0.525879 | + | 0.850559i | \(0.676264\pi\) | |||||||
\(654\) | 2.63143e6 | + | 4.55777e6i | 0.240573 | + | 0.416685i | ||||
\(655\) | 2.81749e6 | − | 4.88003e6i | 0.256601 | − | 0.444447i | ||||
\(656\) | −1.23615e7 | −1.12153 | ||||||||
\(657\) | 276515. | − | 478938.i | 0.0249923 | − | 0.0432879i | ||||
\(658\) | −3.05992e6 | − | 5.29993e6i | −0.275515 | − | 0.477205i | ||||
\(659\) | 7.75611e6 | + | 1.34340e7i | 0.695714 | + | 1.20501i | 0.969939 | + | 0.243346i | \(0.0782451\pi\) |
−0.274226 | + | 0.961665i | \(0.588422\pi\) | |||||||
\(660\) | −1.94240e6 | − | 3.36433e6i | −0.173571 | − | 0.300635i | ||||
\(661\) | 1.90205e7 | 1.69324 | 0.846619 | − | 0.532200i | \(-0.178635\pi\) | ||||
0.846619 | + | 0.532200i | \(0.178635\pi\) | |||||||
\(662\) | −7.27384e6 | − | 1.25987e7i | −0.645087 | − | 1.11732i | ||||
\(663\) | −1.58647e6 | − | 2.74785e6i | −0.140168 | − | 0.242778i | ||||
\(664\) | −4.85637e6 | + | 8.41148e6i | −0.427456 | + | 0.740376i | ||||
\(665\) | −310579. | + | 537938.i | −0.0272344 | + | 0.0471714i | ||||
\(666\) | 625043. | 0.0546040 | ||||||||
\(667\) | 6.09349e6 | 0.530337 | ||||||||
\(668\) | −1.09994e7 | + | 1.90516e7i | −0.953737 | + | 1.65192i | ||||
\(669\) | −35976.6 | + | 62313.3i | −0.00310781 | + | 0.00538289i | ||||
\(670\) | 3.43424e6 | + | 5.94828e6i | 0.295559 | + | 0.511922i | ||||
\(671\) | −486132. | − | 842006.i | −0.0416820 | − | 0.0721953i | ||||
\(672\) | 459219. | 0.0392281 | ||||||||
\(673\) | 407802. | + | 706334.i | 0.0347066 | + | 0.0601136i | 0.882857 | − | 0.469642i | \(-0.155617\pi\) |
−0.848150 | + | 0.529756i | \(0.822284\pi\) | |||||||
\(674\) | 4.25370e6 | + | 7.36763e6i | 0.360676 | + | 0.624709i | ||||
\(675\) | 5.40096e6 | + | 9.35474e6i | 0.456259 | + | 0.790264i | ||||
\(676\) | 9.20721e6 | − | 1.59474e7i | 0.774928 | − | 1.34221i | ||||
\(677\) | −1.04057e7 | −0.872567 | −0.436284 | − | 0.899809i | \(-0.643706\pi\) | ||||
−0.436284 | + | 0.899809i | \(0.643706\pi\) | |||||||
\(678\) | −931458. | + | 1.61333e6i | −0.0778196 | + | 0.134787i | ||||
\(679\) | 66340.7 | + | 114906.i | 0.00552212 | + | 0.00956459i | ||||
\(680\) | −4.30542e6 | −0.357061 | ||||||||
\(681\) | 2.19387e6 | + | 3.79989e6i | 0.181277 | + | 0.313981i | ||||
\(682\) | 212847. | − | 368661.i | 0.0175229 | − | 0.0303505i | ||||
\(683\) | 6.68197e6 | − | 1.15735e7i | 0.548091 | − | 0.949322i | −0.450314 | − | 0.892870i | \(-0.648688\pi\) |
0.998405 | − | 0.0564516i | \(-0.0179787\pi\) | |||||||
\(684\) | −1.32041e6 | −0.107912 | ||||||||
\(685\) | −401163. | + | 694835.i | −0.0326659 | + | 0.0565790i | ||||
\(686\) | −8.58320e6 | −0.696368 | ||||||||
\(687\) | −3.48860e6 | −0.282007 | ||||||||
\(688\) | −1.00092e7 | + | 2.26628e6i | −0.806176 | + | 0.182534i | ||||
\(689\) | −8.52224e6 | −0.683921 | ||||||||
\(690\) | −2.34592e6 | −0.187582 | ||||||||
\(691\) | −7.97022e6 | + | 1.38048e7i | −0.635002 | + | 1.09986i | 0.351512 | + | 0.936183i | \(0.385668\pi\) |
−0.986515 | + | 0.163673i | \(0.947666\pi\) | |||||||
\(692\) | 3.32559e7 | 2.64000 | ||||||||
\(693\) | −51579.5 | + | 89338.4i | −0.00407985 | + | 0.00706651i | ||||
\(694\) | 8.38478e6 | − | 1.45229e7i | 0.660835 | − | 1.14460i | ||||
\(695\) | −612738. | − | 1.06129e6i | −0.0481186 | − | 0.0833439i | ||||
\(696\) | −3.16591e7 | −2.47729 | ||||||||
\(697\) | −5.64123e6 | − | 9.77089e6i | −0.439837 | − | 0.761820i | ||||
\(698\) | −1.39796e7 | + | 2.42134e7i | −1.08606 | + | 1.88112i | ||||
\(699\) | 1.42193e7 | 1.10074 | ||||||||
\(700\) | 2.30667e6 | − | 3.99526e6i | 0.177926 | − | 0.308177i | ||||
\(701\) | −5.52424e6 | − | 9.56827e6i | −0.424598 | − | 0.735425i | 0.571785 | − | 0.820404i | \(-0.306251\pi\) |
−0.996383 | + | 0.0849785i | \(0.972918\pi\) | |||||||
\(702\) | −5.19099e6 | − | 8.99106e6i | −0.397564 | − | 0.688602i | ||||
\(703\) | 2.22020e6 | + | 3.84549e6i | 0.169435 | + | 0.293470i | ||||
\(704\) | 8.32259e6 | 0.632888 | ||||||||
\(705\) | 3.35859e6 | + | 5.81724e6i | 0.254498 | + | 0.440803i | ||||
\(706\) | −1.06975e7 | − | 1.85285e7i | −0.807735 | − | 1.39904i | ||||
\(707\) | 73318.3 | − | 126991.i | 0.00551651 | − | 0.00955487i | ||||
\(708\) | 1.61072e7 | − | 2.78985e7i | 1.20764 | − | 2.09169i | ||||
\(709\) | 1.51125e7 | 1.12907 | 0.564536 | − | 0.825408i | \(-0.309055\pi\) | ||||
0.564536 | + | 0.825408i | \(0.309055\pi\) | |||||||
\(710\) | −1.68719e6 | −0.125608 | ||||||||
\(711\) | −308567. | + | 534454.i | −0.0228916 | + | 0.0396494i | ||||
\(712\) | 626047. | − | 1.08435e6i | 0.0462814 | − | 0.0801618i | ||||
\(713\) | −84829.2 | − | 146928.i | −0.00624916 | − | 0.0108239i | ||||
\(714\) | −1.51350e6 | − | 2.62146e6i | −0.111106 | − | 0.192441i | ||||
\(715\) | −1.13947e6 | −0.0833560 | ||||||||
\(716\) | −1.47423e7 | − | 2.55344e7i | −1.07469 | − | 1.86141i | ||||
\(717\) | −6.48819e6 | − | 1.12379e7i | −0.471331 | − | 0.816369i | ||||
\(718\) | 1.24744e7 | + | 2.16063e7i | 0.903045 | + | 1.56412i | ||||
\(719\) | −932291. | + | 1.61478e6i | −0.0672557 | + | 0.116490i | −0.897692 | − | 0.440623i | \(-0.854758\pi\) |
0.830437 | + | 0.557113i | \(0.188091\pi\) | |||||||
\(720\) | −283593. | −0.0203875 | ||||||||
\(721\) | 2.06740e6 | − | 3.58085e6i | 0.148111 | − | 0.256536i | ||||
\(722\) | 4.90401e6 | + | 8.49400e6i | 0.350113 | + | 0.606414i | ||||
\(723\) | 4.99919e6 | 0.355675 | ||||||||
\(724\) | 2.13445e7 | + | 3.69697e7i | 1.51335 | + | 2.62120i | ||||
\(725\) | 9.96440e6 | − | 1.72589e7i | 0.704055 | − | 1.21946i | ||||
\(726\) | −8.25694e6 | + | 1.43014e7i | −0.581403 | + | 1.00702i | ||||
\(727\) | 4.41487e6 | 0.309801 | 0.154900 | − | 0.987930i | \(-0.450494\pi\) | ||||
0.154900 | + | 0.987930i | \(0.450494\pi\) | |||||||
\(728\) | −1.07482e6 | + | 1.86164e6i | −0.0751636 | + | 0.130187i | ||||
\(729\) | 1.52307e7 | 1.06145 | ||||||||
\(730\) | 5.82765e6 | 0.404750 | ||||||||
\(731\) | −6.35911e6 | − | 6.87738e6i | −0.440152 | − | 0.476025i | ||||
\(732\) | 4.15263e6 | 0.286448 | ||||||||
\(733\) | 2.75979e7 | 1.89721 | 0.948605 | − | 0.316462i | \(-0.102495\pi\) | ||||
0.948605 | + | 0.316462i | \(0.102495\pi\) | |||||||
\(734\) | 1.47822e7 | − | 2.56036e7i | 1.01275 | − | 1.75413i | ||||
\(735\) | 4.60686e6 | 0.314548 | ||||||||
\(736\) | 479935. | − | 831272.i | 0.0326579 | − | 0.0565651i | ||||
\(737\) | −4.05180e6 | + | 7.01792e6i | −0.274776 | + | 0.475926i | ||||
\(738\) | −1.24416e6 | − | 2.15494e6i | −0.0840879 | − | 0.145645i | ||||
\(739\) | 9.00737e6 | 0.606718 | 0.303359 | − | 0.952876i | \(-0.401892\pi\) | ||||
0.303359 | + | 0.952876i | \(0.401892\pi\) | |||||||
\(740\) | 2.17349e6 | + | 3.76460e6i | 0.145908 | + | 0.252720i | ||||
\(741\) | 2.48567e6 | − | 4.30531e6i | 0.166302 | − | 0.288044i | ||||
\(742\) | −8.13026e6 | −0.542119 | ||||||||
\(743\) | 29536.9 | − | 51159.4i | 0.00196288 | − | 0.00339980i | −0.865042 | − | 0.501699i | \(-0.832709\pi\) |
0.867005 | + | 0.498299i | \(0.166042\pi\) | |||||||
\(744\) | 440736. | + | 763377.i | 0.0291908 | + | 0.0505599i | ||||
\(745\) | 1.67022e6 | + | 2.89290e6i | 0.110251 | + | 0.190960i | ||||
\(746\) | −9.95265e6 | − | 1.72385e7i | −0.654774 | − | 1.13410i | ||||
\(747\) | −583924. | −0.0382873 | ||||||||
\(748\) | −5.23877e6 | − | 9.07382e6i | −0.342354 | − | 0.592975i | ||||
\(749\) | 2.28946e6 | + | 3.96547e6i | 0.149118 | + | 0.258279i | ||||
\(750\) | −8.17801e6 | + | 1.41647e7i | −0.530877 | + | 0.919507i | ||||
\(751\) | 1.72832e6 | − | 2.99353e6i | 0.111821 | − | 0.193680i | −0.804684 | − | 0.593704i | \(-0.797665\pi\) |
0.916504 | + | 0.400024i | \(0.130998\pi\) | |||||||
\(752\) | 1.98493e7 | 1.27997 | ||||||||
\(753\) | −1.84462e7 | −1.18555 | ||||||||
\(754\) | −9.57702e6 | + | 1.65879e7i | −0.613482 | + | 1.06258i | ||||
\(755\) | −1.90458e6 | + | 3.29883e6i | −0.121599 | + | 0.210616i | ||||
\(756\) | −3.26839e6 | − | 5.66102e6i | −0.207984 | − | 0.360238i | ||||
\(757\) | −1.34214e6 | − | 2.32466e6i | −0.0851254 | − | 0.147441i | 0.820319 | − | 0.571906i | \(-0.193796\pi\) |
−0.905445 | + | 0.424464i | \(0.860462\pi\) | |||||||
\(758\) | 2.02315e7 | 1.27895 | ||||||||
\(759\) | −1.38389e6 | − | 2.39696e6i | −0.0871959 | − | 0.151028i | ||||
\(760\) | −3.37285e6 | − | 5.84195e6i | −0.211818 | − | 0.366880i | ||||
\(761\) | −1.49439e6 | − | 2.58836e6i | −0.0935411 | − | 0.162018i | 0.815458 | − | 0.578817i | \(-0.196485\pi\) |
−0.908999 | + | 0.416799i | \(0.863152\pi\) | |||||||
\(762\) | −3.51521e6 | + | 6.08853e6i | −0.219313 | + | 0.379861i | ||||
\(763\) | 971940. | 0.0604405 | ||||||||
\(764\) | −2.47829e7 | + | 4.29253e7i | −1.53610 | + | 2.66060i | ||||
\(765\) | −129419. | − | 224161.i | −0.00799550 | − | 0.0138486i | ||||
\(766\) | −1.49084e7 | −0.918033 | ||||||||
\(767\) | −4.72448e6 | − | 8.18304e6i | −0.289978 | − | 0.502257i | ||||
\(768\) | −1.51235e7 | + | 2.61947e7i | −0.925229 | + | 1.60254i | ||||
\(769\) | −2.96623e6 | + | 5.13767e6i | −0.180880 | + | 0.313293i | −0.942180 | − | 0.335106i | \(-0.891228\pi\) |
0.761301 | + | 0.648399i | \(0.224561\pi\) | |||||||
\(770\) | −1.08706e6 | −0.0660732 | ||||||||
\(771\) | −1.32442e7 | + | 2.29397e7i | −0.802400 | + | 1.38980i | ||||
\(772\) | 2.53765e7 | 1.53246 | ||||||||
\(773\) | 1.41823e7 | 0.853687 | 0.426844 | − | 0.904325i | \(-0.359625\pi\) | ||||
0.426844 | + | 0.904325i | \(0.359625\pi\) | |||||||
\(774\) | −1.40248e6 | − | 1.51678e6i | −0.0841482 | − | 0.0910063i | ||||
\(775\) | −554869. | −0.0331846 | ||||||||
\(776\) | −1.44091e6 | −0.0858977 | ||||||||
\(777\) | −740846. | + | 1.28318e6i | −0.0440225 | + | 0.0762493i | ||||
\(778\) | −5.64292e6 | −0.334237 | ||||||||
\(779\) | 8.83865e6 | − | 1.53090e7i | 0.521846 | − | 0.903864i | ||||
\(780\) | 2.43339e6 | − | 4.21475e6i | 0.143210 | − | 0.248048i | ||||
\(781\) | −995291. | − | 1.72390e6i | −0.0583879 | − | 0.101131i | ||||
\(782\) | −6.32711e6 | −0.369989 | ||||||||
\(783\) | −1.41189e7 | − | 2.44546e7i | −0.822993 | − | 1.42547i | ||||
\(784\) | 6.80665e6 | − | 1.17895e7i | 0.395497 | − | 0.685021i | ||||
\(785\) | −1.14648e7 | −0.664034 | ||||||||
\(786\) | −2.15122e7 | + | 3.72602e7i | −1.24202 | + | 2.15124i | ||||
\(787\) | −1.02103e7 | − | 1.76848e7i | −0.587629 | − | 1.01780i | −0.994542 | − | 0.104336i | \(-0.966728\pi\) |
0.406913 | − | 0.913467i | \(-0.366605\pi\) | |||||||
\(788\) | −2.00476e7 | − | 3.47235e7i | −1.15013 | − | 1.99209i | ||||
\(789\) | 1.55347e7 | + | 2.69070e7i | 0.888406 | + | 1.53876i | ||||
\(790\) | −6.50317e6 | −0.370730 | ||||||||
\(791\) | 172021. | + | 297949.i | 0.00977551 | + | 0.0169317i | ||||
\(792\) | −560148. | − | 970205.i | −0.0317315 | − | 0.0549605i | ||||
\(793\) | 609014. | − | 1.05484e6i | 0.0343910 | − | 0.0595669i | ||||
\(794\) | 3.58023e6 | − | 6.20115e6i | 0.201540 | − | 0.349077i | ||||
\(795\) | 8.92384e6 | 0.500765 | ||||||||
\(796\) | 1.79642e7 | 1.00491 | ||||||||
\(797\) | 6.51515e6 | − | 1.12846e7i | 0.363311 | − | 0.629273i | −0.625193 | − | 0.780471i | \(-0.714980\pi\) |
0.988504 | + | 0.151197i | \(0.0483129\pi\) | |||||||
\(798\) | 2.37135e6 | − | 4.10729e6i | 0.131822 | − | 0.228322i | ||||
\(799\) | 9.05833e6 | + | 1.56895e7i | 0.501974 | + | 0.869445i | ||||
\(800\) | −1.56963e6 | − | 2.71868e6i | −0.0867108 | − | 0.150187i | ||||
\(801\) | 75275.1 | 0.00414543 | ||||||||
\(802\) | −2.95094e7 | − | 5.11119e7i | −1.62004 | − | 2.80599i | ||||
\(803\) | 3.43780e6 | + | 5.95445e6i | 0.188145 | + | 0.325876i | ||||
\(804\) | −1.73056e7 | − | 2.99742e7i | −0.944162 | − | 1.63534i | ||||
\(805\) | −216621. | + | 375199.i | −0.0117818 | + | 0.0204067i | ||||
\(806\) | 533298. | 0.0289156 | ||||||||
\(807\) | −1.62524e6 | + | 2.81499e6i | −0.0878482 | + | 0.152157i | ||||
\(808\) | 796229. | + | 1.37911e6i | 0.0429052 | + | 0.0743140i | ||||
\(809\) | 3.31770e7 | 1.78224 | 0.891119 | − | 0.453770i | \(-0.149921\pi\) | ||||
0.891119 | + | 0.453770i | \(0.149921\pi\) | |||||||
\(810\) | 5.04068e6 | + | 8.73072e6i | 0.269946 | + | 0.467560i | ||||
\(811\) | 8.53077e6 | − | 1.47757e7i | 0.455445 | − | 0.788854i | −0.543268 | − | 0.839559i | \(-0.682813\pi\) |
0.998714 | + | 0.0507048i | \(0.0161468\pi\) | |||||||
\(812\) | −6.02996e6 | + | 1.04442e7i | −0.320940 | + | 0.555885i | ||||
\(813\) | 3.09397e7 | 1.64168 | ||||||||
\(814\) | −3.88545e6 | + | 6.72980e6i | −0.205533 | + | 0.355993i | ||||
\(815\) | −8.06469e6 | −0.425298 | ||||||||
\(816\) | 9.81789e6 | 0.516170 | ||||||||
\(817\) | 4.35010e6 | − | 1.40163e7i | 0.228005 | − | 0.734646i | ||||
\(818\) | 4.14383e7 | 2.16530 | ||||||||
\(819\) | −129235. | −0.00673241 | ||||||||
\(820\) | 8.65272e6 | − | 1.49870e7i | 0.449384 | − | 0.778357i | ||||
\(821\) | 2.68197e7 | 1.38866 | 0.694330 | − | 0.719657i | \(-0.255701\pi\) | ||||
0.694330 | + | 0.719657i | \(0.255701\pi\) | |||||||
\(822\) | 3.06298e6 | − | 5.30524e6i | 0.158112 | − | 0.273858i | ||||
\(823\) | −1.77702e7 | + | 3.07788e7i | −0.914518 | + | 1.58399i | −0.106912 | + | 0.994269i | \(0.534096\pi\) |
−0.807606 | + | 0.589722i | \(0.799237\pi\) | |||||||
\(824\) | 2.24518e7 | + | 3.88876e7i | 1.15195 | + | 1.99523i | ||||
\(825\) | −9.05202e6 | −0.463032 | ||||||||
\(826\) | −4.50718e6 | − | 7.80666e6i | −0.229855 | − | 0.398121i | ||||
\(827\) | −1.70824e7 | + | 2.95876e7i | −0.868532 | + | 1.50434i | −0.00503531 | + | 0.999987i | \(0.501603\pi\) |
−0.863497 | + | 0.504354i | \(0.831731\pi\) | |||||||
\(828\) | −920957. | −0.0466835 | ||||||||
\(829\) | 1.08028e7 | − | 1.87110e7i | 0.545946 | − | 0.945606i | −0.452601 | − | 0.891713i | \(-0.649504\pi\) |
0.998547 | − | 0.0538925i | \(-0.0171628\pi\) | |||||||
\(830\) | −3.07660e6 | − | 5.32883e6i | −0.155016 | − | 0.268495i | ||||
\(831\) | −1.75222e7 | − | 3.03493e7i | −0.880209 | − | 1.52457i | ||||
\(832\) | 5.21316e6 | + | 9.02946e6i | 0.261092 | + | 0.452224i | ||||
\(833\) | 1.24250e7 | 0.620418 | ||||||||
\(834\) | 4.67841e6 | + | 8.10324e6i | 0.232907 | + | 0.403407i | ||||
\(835\) | −3.37833e6 | − | 5.85143e6i | −0.167682 | − | 0.290433i | ||||
\(836\) | 8.20809e6 | − | 1.42168e7i | 0.406187 | − | 0.703537i | ||||
\(837\) | −393106. | + | 680880.i | −0.0193953 | + | 0.0335936i | ||||
\(838\) | −1.39261e7 | −0.685045 | ||||||||
\(839\) | 1.67006e7 | 0.819081 | 0.409540 | − | 0.912292i | \(-0.365689\pi\) | ||||
0.409540 | + | 0.912292i | \(0.365689\pi\) | |||||||
\(840\) | 1.12547e6 | − | 1.94937e6i | 0.0550346 | − | 0.0953227i | ||||
\(841\) | −1.57928e7 | + | 2.73540e7i | −0.769963 | + | 1.33361i | ||||
\(842\) | 2.66567e7 | + | 4.61707e7i | 1.29576 | + | 2.24433i | ||||
\(843\) | −1.44351e7 | − | 2.50022e7i | −0.699600 | − | 1.21174i | ||||
\(844\) | −4.19526e7 | −2.02723 | ||||||||
\(845\) | 2.82787e6 | + | 4.89802e6i | 0.136244 | + | 0.235982i | ||||
\(846\) | 1.99779e6 | + | 3.46027e6i | 0.0959673 | + | 0.166220i | ||||
\(847\) | 1.52488e6 | + | 2.64118e6i | 0.0730345 | + | 0.126499i | ||||
\(848\) | 1.31850e7 | − | 2.28371e7i | 0.629637 | − | 1.09056i | ||||
\(849\) | 41958.5 | 0.00199779 | ||||||||
\(850\) | −1.03464e7 | + | 1.79205e7i | −0.491183 | + | 0.850753i | ||||
\(851\) | 1.54853e6 | + | 2.68214e6i | 0.0732987 | + | 0.126957i | ||||
\(852\) | 8.50196e6 | 0.401255 | ||||||||
\(853\) | −7.49511e6 | − | 1.29819e7i | −0.352700 | − | 0.610894i | 0.634022 | − | 0.773315i | \(-0.281403\pi\) |
−0.986722 | + | 0.162421i | \(0.948070\pi\) | |||||||
\(854\) | 581002. | − | 1.00633e6i | 0.0272605 | − | 0.0472165i | ||||
\(855\) | 202774. | − | 351214.i | 0.00948629 | − | 0.0164307i | ||||
\(856\) | −4.97266e7 | −2.31955 | ||||||||
\(857\) | 1.76802e6 | − | 3.06231e6i | 0.0822311 | − | 0.142428i | −0.821977 | − | 0.569521i | \(-0.807129\pi\) |
0.904208 | + | 0.427092i | \(0.140462\pi\) | |||||||
\(858\) | 8.70011e6 | 0.403466 | ||||||||
\(859\) | 7.76090e6 | 0.358863 | 0.179432 | − | 0.983770i | \(-0.442574\pi\) | ||||
0.179432 | + | 0.983770i | \(0.442574\pi\) | |||||||
\(860\) | 4.25859e6 | − | 1.37215e7i | 0.196345 | − | 0.632636i | ||||
\(861\) | 5.89865e6 | 0.271172 | ||||||||
\(862\) | −1.66707e7 | −0.764164 | ||||||||
\(863\) | −1.94627e7 | + | 3.37104e7i | −0.889561 | + | 1.54077i | −0.0491669 | + | 0.998791i | \(0.515657\pi\) |
−0.840395 | + | 0.541975i | \(0.817677\pi\) | |||||||
\(864\) | −4.44813e6 | −0.202718 | ||||||||
\(865\) | −5.10706e6 | + | 8.84569e6i | −0.232076 | + | 0.401968i | ||||
\(866\) | −3.27416e7 | + | 5.67101e7i | −1.48356 | + | 2.56960i | ||||
\(867\) | −6.17882e6 | − | 1.07020e7i | −0.279163 | − | 0.483524i | ||||
\(868\) | 335779. | 0.0151270 | ||||||||
\(869\) | −3.83629e6 | − | 6.64466e6i | −0.172331 | − | 0.298485i | ||||
\(870\) | 1.00283e7 | − | 1.73696e7i | 0.449190 | − | 0.778020i | ||||
\(871\) | −1.01520e7 | −0.453424 | ||||||||
\(872\) | −5.27758e6 | + | 9.14104e6i | −0.235041 | + | 0.407103i | ||||
\(873\) | −43313.2 | − | 75020.6i | −0.00192347 | − | 0.00333154i | ||||
\(874\) | −4.95664e6 | − | 8.58515e6i | −0.219487 | − | 0.380163i | ||||
\(875\) | 1.51031e6 | + | 2.61593e6i | 0.0666876 | + | 0.115506i | ||||
\(876\) | −2.93663e7 | −1.29297 | ||||||||
\(877\) | −1.24863e7 | − | 2.16270e7i | −0.548197 | − | 0.949505i | −0.998398 | − | 0.0565777i | \(-0.981981\pi\) |
0.450201 | − | 0.892927i | \(-0.351352\pi\) | |||||||
\(878\) | 1.00508e7 | + | 1.74084e7i | 0.440010 | + | 0.762120i | ||||
\(879\) | 2.50208e6 | − | 4.33373e6i | 0.109227 | − | 0.189186i | ||||
\(880\) | 1.76290e6 | − | 3.05343e6i | 0.0767399 | − | 0.132917i | ||||
\(881\) | 3.41908e6 | 0.148412 | 0.0742061 | − | 0.997243i | \(-0.476358\pi\) | ||||
0.0742061 | + | 0.997243i | \(0.476358\pi\) | |||||||
\(882\) | 2.74030e6 | 0.118611 | ||||||||
\(883\) | −8.84755e6 | + | 1.53244e7i | −0.381875 | + | 0.661427i | −0.991330 | − | 0.131393i | \(-0.958055\pi\) |
0.609455 | + | 0.792821i | \(0.291388\pi\) | |||||||
\(884\) | 6.56300e6 | − | 1.13675e7i | 0.282470 | − | 0.489252i | ||||
\(885\) | 4.94711e6 | + | 8.56865e6i | 0.212321 | + | 0.367751i | ||||
\(886\) | 6.67233e6 | + | 1.15568e7i | 0.285557 | + | 0.494599i | ||||
\(887\) | 3.81040e6 | 0.162616 | 0.0813078 | − | 0.996689i | \(-0.474090\pi\) | ||||
0.0813078 | + | 0.996689i | \(0.474090\pi\) | |||||||
\(888\) | −8.04550e6 | − | 1.39352e7i | −0.342390 | − | 0.593036i | ||||
\(889\) | 649186. | + | 1.12442e6i | 0.0275496 | + | 0.0477173i | ||||
\(890\) | 396612. | + | 686952.i | 0.0167838 | + | 0.0290704i | ||||
\(891\) | −5.94712e6 | + | 1.03007e7i | −0.250964 | + | 0.434683i | ||||
\(892\) | −297660. | −0.0125259 | ||||||||
\(893\) | −1.41926e7 | + | 2.45822e7i | −0.595569 | + | 1.03156i | ||||
\(894\) | −1.27525e7 | − | 2.20880e7i | −0.533645 | − | 0.924300i | ||||
\(895\) | 9.05579e6 | 0.377893 | ||||||||
\(896\) | 4.48402e6 | + | 7.76656e6i | 0.186594 | + | 0.323190i | ||||
\(897\) | 1.73370e6 | − | 3.00285e6i | 0.0719436 | − | 0.124610i | ||||
\(898\) | −5.18236e6 | + | 8.97610e6i | −0.214455 | + | 0.371447i | ||||
\(899\) | 1.45051e6 | 0.0598578 | ||||||||
\(900\) | −1.50600e6 | + | 2.60846e6i | −0.0619752 | + | 0.107344i | ||||
\(901\) | 2.40682e7 | 0.987715 | ||||||||
\(902\) | 3.09362e7 | 1.26605 | ||||||||
\(903\) | 4.77621e6 | − | 1.08143e6i | 0.194923 | − | 0.0441344i | ||||
\(904\) | −3.73625e6 | −0.152060 | ||||||||
\(905\) | −1.31113e7 | −0.532139 | ||||||||
\(906\) | 1.45419e7 | − | 2.51873e7i | 0.588574 | − | 1.01944i | ||||
\(907\) | −4.40691e7 | −1.77876 | −0.889378 | − | 0.457173i | \(-0.848862\pi\) | ||||
−0.889378 | + | 0.457173i | \(0.848862\pi\) | |||||||
\(908\) | −9.07572e6 | + | 1.57196e7i | −0.365314 | + | 0.632743i | ||||
\(909\) | −47868.8 | + | 82911.2i | −0.00192151 | + | 0.00332815i | ||||
\(910\) | −680919. | − | 1.17939e6i | −0.0272579 | − | 0.0472120i | ||||
\(911\) | −1.89199e7 | −0.755308 | −0.377654 | − | 0.925947i | \(-0.623269\pi\) | ||||
−0.377654 | + | 0.925947i | \(0.623269\pi\) | |||||||
\(912\) | 7.69131e6 | + | 1.33217e7i | 0.306206 | + | 0.530364i | ||||
\(913\) | 3.62984e6 | − | 6.28707e6i | 0.144116 | − | 0.249615i | ||||
\(914\) | −3.05804e7 | −1.21081 | ||||||||
\(915\) | −637713. | + | 1.10455e6i | −0.0251810 | + | 0.0436147i | ||||
\(916\) | −7.21592e6 | − | 1.24983e7i | −0.284154 | − | 0.492168i | ||||
\(917\) | 3.97285e6 | + | 6.88118e6i | 0.156020 | + | 0.270234i | ||||
\(918\) | 1.46602e7 | + | 2.53922e7i | 0.574160 | + | 0.994474i | ||||
\(919\) | −2.52471e7 | −0.986102 | −0.493051 | − | 0.870000i | \(-0.664118\pi\) | ||||
−0.493051 | + | 0.870000i | \(0.664118\pi\) | |||||||
\(920\) | −2.35248e6 | − | 4.07462e6i | −0.0916341 | − | 0.158715i | ||||
\(921\) | 7.85818e6 | + | 1.36108e7i | 0.305262 | + | 0.528729i | ||||
\(922\) | 2.34193e7 | − | 4.05634e7i | 0.907291 | − | 1.57147i | ||||
\(923\) | 1.24688e6 | − | 2.15965e6i | 0.0481747 | − | 0.0834410i | ||||
\(924\) | 5.47783e6 | 0.211071 | ||||||||
\(925\) | 1.01290e7 | 0.389234 | ||||||||
\(926\) | 2.60170e7 | − | 4.50627e7i | 0.997079 | − | 1.72699i | ||||
\(927\) | −1.34979e6 | + | 2.33790e6i | −0.0515900 | + | 0.0893566i | ||||
\(928\) | 4.10325e6 | + | 7.10703e6i | 0.156408 | + | 0.270906i | ||||
\(929\) | −2.20283e7 | − | 3.81542e7i | −0.837418 | − | 1.45045i | −0.892046 | − | 0.451944i | \(-0.850731\pi\) |
0.0546285 | − | 0.998507i | \(-0.482603\pi\) | |||||||
\(930\) | −558428. | −0.0211719 | ||||||||
\(931\) | 9.73372e6 | + | 1.68593e7i | 0.368048 | + | 0.637478i | ||||
\(932\) | 2.94116e7 | + | 5.09425e7i | 1.10912 | + | 1.92106i | ||||
\(933\) | −2.12590e7 | − | 3.68217e7i | −0.799539 | − | 1.38484i | ||||
\(934\) | 2.76219e7 | − | 4.78426e7i | 1.03606 | − | 1.79452i | ||||
\(935\) | 3.21804e6 | 0.120382 | ||||||||
\(936\) | 701739. | − | 1.21545e6i | 0.0261810 | − | 0.0453468i | ||||
\(937\) | 3.20035e6 | + | 5.54316e6i | 0.119083 | + | 0.206257i | 0.919404 | − | 0.393314i | \(-0.128671\pi\) |
−0.800322 | + | 0.599571i | \(0.795338\pi\) | |||||||
\(938\) | −9.68503e6 | −0.359413 | ||||||||
\(939\) | −9.49323e6 | − | 1.64428e7i | −0.351358 | − | 0.608570i | ||||
\(940\) | −1.38940e7 | + | 2.40651e7i | −0.512870 | + | 0.888318i | ||||
\(941\) | 1.14783e7 | − | 1.98810e7i | 0.422575 | − | 0.731921i | −0.573616 | − | 0.819125i | \(-0.694460\pi\) |
0.996191 | + | 0.0872034i | \(0.0277930\pi\) | |||||||
\(942\) | 8.75362e7 | 3.21411 | ||||||||
\(943\) | 6.16474e6 | − | 1.06776e7i | 0.225754 | − | 0.391018i | ||||
\(944\) | 2.92375e7 | 1.06785 | ||||||||
\(945\) | 2.00768e6 | 0.0731334 | ||||||||
\(946\) | 2.50494e7 | − | 5.67166e6i | 0.910058 | − | 0.206055i | ||||
\(947\) | −1.54669e7 | −0.560437 | −0.280219 | − | 0.959936i | \(-0.590407\pi\) | ||||
−0.280219 | + | 0.959936i | \(0.590407\pi\) | |||||||
\(948\) | 3.27703e7 | 1.18430 | ||||||||
\(949\) | −4.30679e6 | + | 7.45958e6i | −0.155234 | + | 0.268874i | ||||
\(950\) | −3.24215e7 | −1.16553 | ||||||||
\(951\) | −2.42262e7 | + | 4.19611e7i | −0.868630 | + | 1.50451i | ||||
\(952\) | 3.03547e6 | − | 5.25758e6i | 0.108551 | − | 0.188016i | ||||
\(953\) | −4.39274e6 | − | 7.60845e6i | −0.156676 | − | 0.271371i | 0.776992 | − | 0.629511i | \(-0.216745\pi\) |
−0.933668 | + | 0.358139i | \(0.883411\pi\) | |||||||
\(954\) | 5.30816e6 | 0.188831 | ||||||||
\(955\) | −7.61175e6 | − | 1.31839e7i | −0.270070 | − | 0.467775i | ||||
\(956\) | 2.68407e7 | − | 4.64895e7i | 0.949838 | − | 1.64517i | ||||
\(957\) | 2.36633e7 | 0.835209 | ||||||||
\(958\) | −1.01523e7 | + | 1.75843e7i | −0.357396 | + | 0.619028i | ||||
\(959\) | −565668. | − | 979766.i | −0.0198616 | − | 0.0344014i | ||||
\(960\) | −5.45882e6 | − | 9.45496e6i | −0.191171 | − | 0.331117i | ||||
\(961\) | 1.42944e7 | + | 2.47586e7i | 0.499295 | + | 0.864804i | ||||
\(962\) | −9.73519e6 | −0.339162 | ||||||||
\(963\) | −1.49477e6 | − | 2.58901e6i | −0.0519407 | − | 0.0899639i | ||||
\(964\) | 1.03405e7 | + | 1.79102e7i | 0.358383 | + | 0.620738i | ||||
\(965\) | −3.89703e6 | + | 6.74986e6i | −0.134715 | + | 0.233333i | ||||
\(966\) | 1.65396e6 | − | 2.86474e6i | 0.0570271 | − | 0.0987738i | ||||
\(967\) | 9.97371e6 | 0.342997 | 0.171499 | − | 0.985184i | \(-0.445139\pi\) | ||||
0.171499 | + | 0.985184i | \(0.445139\pi\) | |||||||
\(968\) | −3.31201e7 | −1.13607 | ||||||||
\(969\) | −7.01995e6 | + | 1.21589e7i | −0.240173 | + | 0.415992i | ||||
\(970\) | 456420. | − | 790543.i | 0.0155753 | − | 0.0269772i | ||||
\(971\) | 82862.1 | + | 143521.i | 0.00282038 | + | 0.00488504i | 0.867432 | − | 0.497555i | \(-0.165769\pi\) |
−0.864612 | + | 0.502441i | \(0.832436\pi\) | |||||||
\(972\) | 4.12396e6 | + | 7.14292e6i | 0.140007 | + | 0.242499i | ||||
\(973\) | 1.72801e6 | 0.0585145 | ||||||||
\(974\) | −1.99137e7 | − | 3.44915e7i | −0.672595 | − | 1.16497i | ||||
\(975\) | −5.67007e6 | − | 9.82085e6i | −0.191019 | − | 0.330855i | ||||
\(976\) | 1.88444e6 | + | 3.26395e6i | 0.0633226 | + | 0.109678i | ||||
\(977\) | −1.81566e7 | + | 3.14482e7i | −0.608554 | + | 1.05405i | 0.382925 | + | 0.923779i | \(0.374917\pi\) |
−0.991479 | + | 0.130267i | \(0.958417\pi\) | |||||||
\(978\) | 6.15759e7 | 2.05856 | ||||||||
\(979\) | −467932. | + | 810483.i | −0.0156037 | + | 0.0270263i | ||||
\(980\) | 9.52896e6 | + | 1.65046e7i | 0.316942 | + | 0.548960i | ||||
\(981\) | −634569. | −0.0210526 | ||||||||
\(982\) | 7.63105e6 | + | 1.32174e7i | 0.252526 | + | 0.437387i | ||||
\(983\) | 2.72724e7 | − | 4.72371e7i | 0.900200 | − | 1.55919i | 0.0729656 | − | 0.997334i | \(-0.476754\pi\) |
0.827234 | − | 0.561857i | \(-0.189913\pi\) | |||||||
\(984\) | −3.20293e7 | + | 5.54764e7i | −1.05453 | + | 1.82650i | ||||
\(985\) | 1.23147e7 | 0.404421 | ||||||||
\(986\) | 2.70471e7 | − | 4.68469e7i | 0.885988 | − | 1.53458i | ||||
\(987\) | −9.47168e6 | −0.309481 | ||||||||
\(988\) | 2.05658e7 | 0.670274 | ||||||||
\(989\) | 3.03409e6 | − | 9.77603e6i | 0.0986364 | − | 0.317813i | ||||
\(990\) | 709728. | 0.0230146 | ||||||||
\(991\) | 4.88358e7 | 1.57963 | 0.789813 | − | 0.613348i | \(-0.210178\pi\) | ||||
0.789813 | + | 0.613348i | \(0.210178\pi\) | |||||||
\(992\) | 114245. | − | 197878.i | 0.00368602 | − | 0.00638437i | ||||
\(993\) | −2.25155e7 | −0.724616 | ||||||||
\(994\) | 1.18953e6 | − | 2.06032e6i | 0.0381863 | − | 0.0661406i | ||||
\(995\) | −2.75873e6 | + | 4.77827e6i | −0.0883389 | + | 0.153008i | ||||
\(996\) | 1.55034e7 | + | 2.68527e7i | 0.495198 | + | 0.857708i | ||||
\(997\) | 5.74163e7 | 1.82935 | 0.914676 | − | 0.404187i | \(-0.132445\pi\) | ||||
0.914676 | + | 0.404187i | \(0.132445\pi\) | |||||||
\(998\) | −1.97284e7 | − | 3.41706e7i | −0.626997 | − | 1.08599i | ||||
\(999\) | 7.17604e6 | − | 1.24293e7i | 0.227495 | − | 0.394032i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 43.6.c.a.6.16 | ✓ | 34 | |
43.36 | even | 3 | inner | 43.6.c.a.36.16 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.16 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.6.c.a.36.16 | yes | 34 | 43.36 | even | 3 | inner |