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 | 36.3 | ||
Character | \(\chi\) | \(=\) | 43.36 |
Dual form | 43.6.c.a.6.3 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.55067 | −1.51156 | −0.755779 | − | 0.654826i | \(-0.772742\pi\) | ||||
−0.755779 | + | 0.654826i | \(0.772742\pi\) | |||||||
\(3\) | −3.32584 | − | 5.76053i | −0.213353 | − | 0.369538i | 0.739409 | − | 0.673257i | \(-0.235105\pi\) |
−0.952762 | + | 0.303719i | \(0.901772\pi\) | |||||||
\(4\) | 41.1139 | 1.28481 | ||||||||
\(5\) | 8.72223 | + | 15.1073i | 0.156028 | + | 0.270248i | 0.933433 | − | 0.358752i | \(-0.116798\pi\) |
−0.777405 | + | 0.629000i | \(0.783464\pi\) | |||||||
\(6\) | 28.4382 | + | 49.2563i | 0.322495 | + | 0.558578i | ||||
\(7\) | −112.908 | + | 195.562i | −0.870922 | + | 1.50848i | −0.00987829 | + | 0.999951i | \(0.503144\pi\) |
−0.861044 | + | 0.508530i | \(0.830189\pi\) | |||||||
\(8\) | −77.9301 | −0.430507 | ||||||||
\(9\) | 99.3776 | − | 172.127i | 0.408961 | − | 0.708341i | ||||
\(10\) | −74.5809 | − | 129.178i | −0.235845 | − | 0.408496i | ||||
\(11\) | −94.8489 | −0.236347 | −0.118174 | − | 0.992993i | \(-0.537704\pi\) | ||||
−0.118174 | + | 0.992993i | \(0.537704\pi\) | |||||||
\(12\) | −136.738 | − | 236.838i | −0.274118 | − | 0.474786i | ||||
\(13\) | 387.984 | − | 672.008i | 0.636731 | − | 1.10285i | −0.349415 | − | 0.936968i | \(-0.613620\pi\) |
0.986146 | − | 0.165882i | \(-0.0530470\pi\) | |||||||
\(14\) | 965.438 | − | 1672.19i | 1.31645 | − | 2.28016i | ||||
\(15\) | 58.0175 | − | 100.489i | 0.0665780 | − | 0.115317i | ||||
\(16\) | −649.291 | −0.634073 | ||||||||
\(17\) | 407.492 | − | 705.798i | 0.341977 | − | 0.592322i | −0.642823 | − | 0.766015i | \(-0.722237\pi\) |
0.984800 | + | 0.173693i | \(0.0555701\pi\) | |||||||
\(18\) | −849.744 | + | 1471.80i | −0.618169 | + | 1.07070i | ||||
\(19\) | −1252.21 | − | 2168.89i | −0.795780 | − | 1.37833i | −0.922343 | − | 0.386373i | \(-0.873728\pi\) |
0.126562 | − | 0.991959i | \(-0.459606\pi\) | |||||||
\(20\) | 358.605 | + | 621.122i | 0.200466 | + | 0.347218i | ||||
\(21\) | 1502.06 | 0.743255 | ||||||||
\(22\) | 811.021 | 0.357253 | ||||||||
\(23\) | 1284.33 | + | 2224.53i | 0.506242 | + | 0.876837i | 0.999974 | + | 0.00722288i | \(0.00229913\pi\) |
−0.493732 | + | 0.869614i | \(0.664368\pi\) | |||||||
\(24\) | 259.183 | + | 448.918i | 0.0918499 | + | 0.159089i | ||||
\(25\) | 1410.35 | − | 2442.79i | 0.451311 | − | 0.781693i | ||||
\(26\) | −3317.52 | + | 5746.12i | −0.962456 | + | 1.66702i | ||||
\(27\) | −2938.41 | −0.775718 | ||||||||
\(28\) | −4642.09 | + | 8040.33i | −1.11897 | + | 1.93811i | ||||
\(29\) | 1154.17 | − | 1999.08i | 0.254844 | − | 0.441403i | −0.710009 | − | 0.704193i | \(-0.751309\pi\) |
0.964853 | + | 0.262790i | \(0.0846425\pi\) | |||||||
\(30\) | −496.088 | + | 859.250i | −0.100637 | + | 0.174308i | ||||
\(31\) | −550.205 | − | 952.983i | −0.102830 | − | 0.178107i | 0.810019 | − | 0.586403i | \(-0.199456\pi\) |
−0.912850 | + | 0.408296i | \(0.866123\pi\) | |||||||
\(32\) | 8045.64 | 1.38895 | ||||||||
\(33\) | 315.452 | + | 546.380i | 0.0504254 | + | 0.0873393i | ||||
\(34\) | −3484.33 | + | 6035.04i | −0.516919 | + | 0.895330i | ||||
\(35\) | −3939.24 | −0.543553 | ||||||||
\(36\) | 4085.80 | − | 7076.81i | 0.525437 | − | 0.910084i | ||||
\(37\) | −2898.78 | − | 5020.83i | −0.348105 | − | 0.602936i | 0.637808 | − | 0.770196i | \(-0.279841\pi\) |
−0.985913 | + | 0.167260i | \(0.946508\pi\) | |||||||
\(38\) | 10707.2 | + | 18545.5i | 1.20287 | + | 2.08343i | ||||
\(39\) | −5161.50 | −0.543393 | ||||||||
\(40\) | −679.724 | − | 1177.32i | −0.0671711 | − | 0.116344i | ||||
\(41\) | 4811.95 | 0.447055 | 0.223528 | − | 0.974698i | \(-0.428243\pi\) | ||||
0.223528 | + | 0.974698i | \(0.428243\pi\) | |||||||
\(42\) | −12843.6 | −1.12347 | ||||||||
\(43\) | 6825.71 | − | 10020.9i | 0.562959 | − | 0.826485i | ||||
\(44\) | −3899.61 | −0.303661 | ||||||||
\(45\) | 3467.18 | 0.255237 | ||||||||
\(46\) | −10981.9 | − | 19021.2i | −0.765215 | − | 1.32539i | ||||
\(47\) | 28586.9 | 1.88766 | 0.943828 | − | 0.330437i | \(-0.107196\pi\) | ||||
0.943828 | + | 0.330437i | \(0.107196\pi\) | |||||||
\(48\) | 2159.44 | + | 3740.26i | 0.135281 | + | 0.234314i | ||||
\(49\) | −17092.9 | − | 29605.8i | −1.01701 | − | 1.76152i | ||||
\(50\) | −12059.4 | + | 20887.5i | −0.682182 | + | 1.18157i | ||||
\(51\) | −5421.02 | −0.291847 | ||||||||
\(52\) | 15951.6 | − | 27628.9i | 0.818078 | − | 1.41695i | ||||
\(53\) | −5552.60 | − | 9617.39i | −0.271523 | − | 0.470292i | 0.697729 | − | 0.716362i | \(-0.254194\pi\) |
−0.969252 | + | 0.246070i | \(0.920861\pi\) | |||||||
\(54\) | 25125.4 | 1.17254 | ||||||||
\(55\) | −827.294 | − | 1432.91i | −0.0368768 | − | 0.0638725i | ||||
\(56\) | 8798.92 | − | 15240.2i | 0.374938 | − | 0.649412i | ||||
\(57\) | −8329.30 | + | 14426.8i | −0.339564 | + | 0.588142i | ||||
\(58\) | −9868.92 | + | 17093.5i | −0.385212 | + | 0.667207i | ||||
\(59\) | −12370.0 | −0.462637 | −0.231319 | − | 0.972878i | \(-0.574304\pi\) | ||||
−0.231319 | + | 0.972878i | \(0.574304\pi\) | |||||||
\(60\) | 2385.33 | − | 4131.51i | 0.0855401 | − | 0.148160i | ||||
\(61\) | −18367.6 | + | 31813.7i | −0.632017 | + | 1.09468i | 0.355122 | + | 0.934820i | \(0.384439\pi\) |
−0.987139 | + | 0.159865i | \(0.948894\pi\) | |||||||
\(62\) | 4704.62 | + | 8148.64i | 0.155434 | + | 0.269219i | ||||
\(63\) | 22441.0 | + | 38869.0i | 0.712347 | + | 1.23382i | ||||
\(64\) | −48018.2 | −1.46540 | ||||||||
\(65\) | 13536.3 | 0.397391 | ||||||||
\(66\) | −2697.33 | − | 4671.91i | −0.0762209 | − | 0.132018i | ||||
\(67\) | 2017.88 | + | 3495.07i | 0.0549171 | + | 0.0951192i | 0.892177 | − | 0.451686i | \(-0.149177\pi\) |
−0.837260 | + | 0.546805i | \(0.815844\pi\) | |||||||
\(68\) | 16753.6 | − | 29018.1i | 0.439376 | − | 0.761021i | ||||
\(69\) | 8542.98 | − | 14796.9i | 0.216016 | − | 0.374151i | ||||
\(70\) | 33683.1 | 0.821612 | ||||||||
\(71\) | 18927.8 | − | 32784.0i | 0.445610 | − | 0.771819i | −0.552485 | − | 0.833523i | \(-0.686320\pi\) |
0.998094 | + | 0.0617042i | \(0.0196535\pi\) | |||||||
\(72\) | −7744.50 | + | 13413.9i | −0.176061 | + | 0.304946i | ||||
\(73\) | −18456.1 | + | 31966.9i | −0.405353 | + | 0.702091i | −0.994362 | − | 0.106034i | \(-0.966185\pi\) |
0.589010 | + | 0.808126i | \(0.299518\pi\) | |||||||
\(74\) | 24786.5 | + | 42931.4i | 0.526181 | + | 0.911373i | ||||
\(75\) | −18762.3 | −0.385154 | ||||||||
\(76\) | −51483.3 | − | 89171.6i | −1.02243 | − | 1.77089i | ||||
\(77\) | 10709.2 | − | 18548.9i | 0.205840 | − | 0.356526i | ||||
\(78\) | 44134.2 | 0.821371 | ||||||||
\(79\) | 2204.87 | − | 3818.94i | 0.0397480 | − | 0.0688455i | −0.845467 | − | 0.534028i | \(-0.820678\pi\) |
0.885215 | + | 0.465182i | \(0.154011\pi\) | |||||||
\(80\) | −5663.27 | − | 9809.07i | −0.0989332 | − | 0.171357i | ||||
\(81\) | −14376.0 | − | 24900.0i | −0.243460 | − | 0.421684i | ||||
\(82\) | −41145.4 | −0.675750 | ||||||||
\(83\) | −5486.28 | − | 9502.52i | −0.0874144 | − | 0.151406i | 0.819003 | − | 0.573789i | \(-0.194527\pi\) |
−0.906418 | + | 0.422383i | \(0.861194\pi\) | |||||||
\(84\) | 61755.4 | 0.954941 | ||||||||
\(85\) | 14217.0 | 0.213432 | ||||||||
\(86\) | −58364.4 | + | 85685.3i | −0.850945 | + | 1.24928i | ||||
\(87\) | −15354.3 | −0.217487 | ||||||||
\(88\) | 7391.58 | 0.101749 | ||||||||
\(89\) | −30160.7 | − | 52239.8i | −0.403614 | − | 0.699080i | 0.590545 | − | 0.807005i | \(-0.298913\pi\) |
−0.994159 | + | 0.107925i | \(0.965579\pi\) | |||||||
\(90\) | −29646.7 | −0.385806 | ||||||||
\(91\) | 87613.0 | + | 151750.i | 1.10909 | + | 1.92099i | ||||
\(92\) | 52804.0 | + | 91459.2i | 0.650425 | + | 1.12657i | ||||
\(93\) | −3659.79 | + | 6338.94i | −0.0438782 | + | 0.0759993i | ||||
\(94\) | −244437. | −2.85330 | ||||||||
\(95\) | 21844.1 | − | 37835.1i | 0.248328 | − | 0.430117i | ||||
\(96\) | −26758.5 | − | 46347.1i | −0.296336 | − | 0.513268i | ||||
\(97\) | 53274.7 | 0.574899 | 0.287449 | − | 0.957796i | \(-0.407193\pi\) | ||||
0.287449 | + | 0.957796i | \(0.407193\pi\) | |||||||
\(98\) | 146156. | + | 253149.i | 1.53727 | + | 2.66263i | ||||
\(99\) | −9425.85 | + | 16326.1i | −0.0966569 | + | 0.167415i | ||||
\(100\) | 57984.8 | − | 100433.i | 0.579848 | − | 1.00433i | ||||
\(101\) | −22365.3 | + | 38737.9i | −0.218158 | + | 0.377861i | −0.954245 | − | 0.299026i | \(-0.903338\pi\) |
0.736087 | + | 0.676887i | \(0.236672\pi\) | |||||||
\(102\) | 46353.3 | 0.441144 | ||||||||
\(103\) | 57861.6 | − | 100219.i | 0.537399 | − | 0.930803i | −0.461644 | − | 0.887065i | \(-0.652740\pi\) |
0.999043 | − | 0.0437377i | \(-0.0139266\pi\) | |||||||
\(104\) | −30235.6 | + | 52369.7i | −0.274117 | + | 0.474784i | ||||
\(105\) | 13101.3 | + | 22692.1i | 0.115969 | + | 0.200863i | ||||
\(106\) | 47478.4 | + | 82235.1i | 0.410423 | + | 0.710874i | ||||
\(107\) | −182262. | −1.53899 | −0.769495 | − | 0.638653i | \(-0.779492\pi\) | ||||
−0.769495 | + | 0.638653i | \(0.779492\pi\) | |||||||
\(108\) | −120810. | −0.996650 | ||||||||
\(109\) | −83047.5 | − | 143842.i | −0.669515 | − | 1.15963i | −0.978040 | − | 0.208417i | \(-0.933169\pi\) |
0.308525 | − | 0.951216i | \(-0.400165\pi\) | |||||||
\(110\) | 7073.91 | + | 12252.4i | 0.0557414 | + | 0.0965470i | ||||
\(111\) | −19281.7 | + | 33397.0i | −0.148538 | + | 0.257276i | ||||
\(112\) | 73310.1 | − | 126977.i | 0.552229 | − | 0.956488i | ||||
\(113\) | 121707. | 0.896645 | 0.448323 | − | 0.893872i | \(-0.352022\pi\) | ||||
0.448323 | + | 0.893872i | \(0.352022\pi\) | |||||||
\(114\) | 71221.1 | − | 123359.i | 0.513271 | − | 0.889011i | ||||
\(115\) | −22404.5 | + | 38805.7i | −0.157976 | + | 0.273622i | ||||
\(116\) | 47452.4 | − | 82190.0i | 0.327426 | − | 0.567119i | ||||
\(117\) | −77113.8 | − | 133565.i | −0.520796 | − | 0.902045i | ||||
\(118\) | 105772. | 0.699303 | ||||||||
\(119\) | 92018.3 | + | 159380.i | 0.595671 | + | 1.03173i | ||||
\(120\) | −4521.31 | + | 7831.13i | −0.0286623 | + | 0.0496445i | ||||
\(121\) | −152055. | −0.944140 | ||||||||
\(122\) | 157055. | − | 272028.i | 0.955330 | − | 1.65468i | ||||
\(123\) | −16003.8 | − | 27719.3i | −0.0953805 | − | 0.165204i | ||||
\(124\) | −22621.1 | − | 39180.9i | −0.132117 | − | 0.228834i | ||||
\(125\) | 103719. | 0.593724 | ||||||||
\(126\) | −191886. | − | 332356.i | −1.07675 | − | 1.86499i | ||||
\(127\) | −197190. | −1.08487 | −0.542433 | − | 0.840099i | \(-0.682497\pi\) | ||||
−0.542433 | + | 0.840099i | \(0.682497\pi\) | |||||||
\(128\) | 153128. | 0.826092 | ||||||||
\(129\) | −80426.8 | − | 5991.81i | −0.425526 | − | 0.0317018i | ||||
\(130\) | −115745. | −0.600680 | ||||||||
\(131\) | −182405. | −0.928666 | −0.464333 | − | 0.885661i | \(-0.653706\pi\) | ||||
−0.464333 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(132\) | 12969.5 | + | 22463.8i | 0.0647870 | + | 0.112214i | ||||
\(133\) | 565538. | 2.77225 | ||||||||
\(134\) | −17254.2 | − | 29885.1i | −0.0830105 | − | 0.143778i | ||||
\(135\) | −25629.5 | − | 44391.6i | −0.121034 | − | 0.209636i | ||||
\(136\) | −31755.9 | + | 55002.9i | −0.147224 | + | 0.254999i | ||||
\(137\) | 191141. | 0.870065 | 0.435032 | − | 0.900415i | \(-0.356737\pi\) | ||||
0.435032 | + | 0.900415i | \(0.356737\pi\) | |||||||
\(138\) | −73048.2 | + | 126523.i | −0.326521 | + | 0.565552i | ||||
\(139\) | 24161.8 | + | 41849.4i | 0.106070 | + | 0.183718i | 0.914175 | − | 0.405320i | \(-0.132840\pi\) |
−0.808105 | + | 0.589039i | \(0.799507\pi\) | |||||||
\(140\) | −161957. | −0.698362 | ||||||||
\(141\) | −95075.6 | − | 164676.i | −0.402737 | − | 0.697561i | ||||
\(142\) | −161846. | + | 280325.i | −0.673565 | + | 1.16665i | ||||
\(143\) | −36799.9 | + | 63739.3i | −0.150490 | + | 0.260656i | ||||
\(144\) | −64525.0 | + | 111761.i | −0.259311 | + | 0.449141i | ||||
\(145\) | 40267.7 | 0.159051 | ||||||||
\(146\) | 157812. | − | 273339.i | 0.612714 | − | 1.06125i | ||||
\(147\) | −113697. | + | 196928.i | −0.433964 | + | 0.751648i | ||||
\(148\) | −119180. | − | 206426.i | −0.447249 | − | 0.774658i | ||||
\(149\) | 261173. | + | 452364.i | 0.963745 | + | 1.66925i | 0.712951 | + | 0.701214i | \(0.247358\pi\) |
0.250794 | + | 0.968041i | \(0.419308\pi\) | |||||||
\(150\) | 160431. | 0.582182 | ||||||||
\(151\) | 392778. | 1.40186 | 0.700930 | − | 0.713230i | \(-0.252768\pi\) | ||||
0.700930 | + | 0.713230i | \(0.252768\pi\) | |||||||
\(152\) | 97584.8 | + | 169022.i | 0.342589 | + | 0.593381i | ||||
\(153\) | −80991.2 | − | 140281.i | −0.279711 | − | 0.484473i | ||||
\(154\) | −91570.8 | + | 158605.i | −0.311139 | + | 0.538909i | ||||
\(155\) | 9598.03 | − | 16624.3i | 0.0320888 | − | 0.0555793i | ||||
\(156\) | −212209. | −0.698157 | ||||||||
\(157\) | −104888. | + | 181672.i | −0.339608 | + | 0.588218i | −0.984359 | − | 0.176174i | \(-0.943628\pi\) |
0.644751 | + | 0.764393i | \(0.276961\pi\) | |||||||
\(158\) | −18853.1 | + | 32654.5i | −0.0600814 | + | 0.104064i | ||||
\(159\) | −36934.1 | + | 63971.8i | −0.115860 | + | 0.200676i | ||||
\(160\) | 70175.9 | + | 121548.i | 0.216714 | + | 0.375360i | ||||
\(161\) | −580046. | −1.76359 | ||||||||
\(162\) | 122925. | + | 212912.i | 0.368003 | + | 0.637401i | ||||
\(163\) | −284044. | + | 491978.i | −0.837368 | + | 1.45036i | 0.0547203 | + | 0.998502i | \(0.482573\pi\) |
−0.892088 | + | 0.451862i | \(0.850760\pi\) | |||||||
\(164\) | 197838. | 0.574381 | ||||||||
\(165\) | −5502.90 | + | 9531.30i | −0.0157355 | + | 0.0272547i | ||||
\(166\) | 46911.4 | + | 81252.9i | 0.132132 | + | 0.228859i | ||||
\(167\) | 338891. | + | 586976.i | 0.940305 | + | 1.62866i | 0.764890 | + | 0.644161i | \(0.222793\pi\) |
0.175414 | + | 0.984495i | \(0.443873\pi\) | |||||||
\(168\) | −117055. | −0.319976 | ||||||||
\(169\) | −115417. | − | 199908.i | −0.310852 | − | 0.538411i | ||||
\(170\) | −121565. | −0.322615 | ||||||||
\(171\) | −497766. | −1.30177 | ||||||||
\(172\) | 280632. | − | 411998.i | 0.723295 | − | 1.06188i | ||||
\(173\) | −566813. | −1.43987 | −0.719937 | − | 0.694039i | \(-0.755829\pi\) | ||||
−0.719937 | + | 0.694039i | \(0.755829\pi\) | |||||||
\(174\) | 131290. | 0.328744 | ||||||||
\(175\) | 318478. | + | 551621.i | 0.786113 | + | 1.36159i | ||||
\(176\) | 61584.6 | 0.149862 | ||||||||
\(177\) | 41140.7 | + | 71257.8i | 0.0987049 | + | 0.170962i | ||||
\(178\) | 257894. | + | 446685.i | 0.610086 | + | 1.05670i | ||||
\(179\) | 291057. | − | 504125.i | 0.678962 | − | 1.17600i | −0.296332 | − | 0.955085i | \(-0.595764\pi\) |
0.975294 | − | 0.220911i | \(-0.0709031\pi\) | |||||||
\(180\) | 142549. | 0.327932 | ||||||||
\(181\) | 328534. | − | 569038.i | 0.745391 | − | 1.29106i | −0.204621 | − | 0.978841i | \(-0.565596\pi\) |
0.950012 | − | 0.312214i | \(-0.101071\pi\) | |||||||
\(182\) | −749150. | − | 1.29757e6i | −1.67645 | − | 2.90369i | ||||
\(183\) | 244351. | 0.539370 | ||||||||
\(184\) | −100088. | − | 173358.i | −0.217941 | − | 0.377484i | ||||
\(185\) | 50567.6 | − | 87585.6i | 0.108628 | − | 0.188150i | ||||
\(186\) | 31293.6 | − | 54202.2i | 0.0663245 | − | 0.114877i | ||||
\(187\) | −38650.2 | + | 66944.1i | −0.0808254 | + | 0.139994i | ||||
\(188\) | 1.17532e6 | 2.42528 | ||||||||
\(189\) | 331770. | − | 574643.i | 0.675590 | − | 1.17016i | ||||
\(190\) | −186782. | + | 323516.i | −0.375362 | + | 0.650147i | ||||
\(191\) | −482322. | − | 835406.i | −0.956651 | − | 1.65697i | −0.730543 | − | 0.682866i | \(-0.760733\pi\) |
−0.226108 | − | 0.974102i | \(-0.572600\pi\) | |||||||
\(192\) | 159701. | + | 276610.i | 0.312647 | + | 0.541521i | ||||
\(193\) | 119530. | 0.230984 | 0.115492 | − | 0.993308i | \(-0.463155\pi\) | ||||
0.115492 | + | 0.993308i | \(0.463155\pi\) | |||||||
\(194\) | −455534. | −0.868994 | ||||||||
\(195\) | −45019.7 | − | 77976.5i | −0.0847845 | − | 0.146851i | ||||
\(196\) | −702756. | − | 1.21721e6i | −1.30667 | − | 2.26321i | ||||
\(197\) | −174101. | + | 301551.i | −0.319621 | + | 0.553599i | −0.980409 | − | 0.196973i | \(-0.936889\pi\) |
0.660788 | + | 0.750572i | \(0.270222\pi\) | |||||||
\(198\) | 80597.3 | − | 139599.i | 0.146103 | − | 0.253057i | ||||
\(199\) | 53982.7 | 0.0966323 | 0.0483161 | − | 0.998832i | \(-0.484615\pi\) | ||||
0.0483161 | + | 0.998832i | \(0.484615\pi\) | |||||||
\(200\) | −109908. | + | 190367.i | −0.194292 | + | 0.336524i | ||||
\(201\) | 13422.3 | − | 23248.1i | 0.0234334 | − | 0.0405879i | ||||
\(202\) | 191238. | − | 331235.i | 0.329759 | − | 0.571159i | ||||
\(203\) | 260630. | + | 451424.i | 0.443899 | + | 0.768855i | ||||
\(204\) | −222879. | −0.374968 | ||||||||
\(205\) | 41970.9 | + | 72695.7i | 0.0697531 | + | 0.120816i | ||||
\(206\) | −494755. | + | 856941.i | −0.812311 | + | 1.40696i | ||||
\(207\) | 510536. | 0.828133 | ||||||||
\(208\) | −251915. | + | 436329.i | −0.403734 | + | 0.699288i | ||||
\(209\) | 118771. | + | 205717.i | 0.188081 | + | 0.325765i | ||||
\(210\) | −112025. | − | 194032.i | −0.175293 | − | 0.303617i | ||||
\(211\) | −272464. | −0.421312 | −0.210656 | − | 0.977560i | \(-0.567560\pi\) | ||||
−0.210656 | + | 0.977560i | \(0.567560\pi\) | |||||||
\(212\) | −228289. | − | 395408.i | −0.348856 | − | 0.604236i | ||||
\(213\) | −251804. | −0.380288 | ||||||||
\(214\) | 1.55846e6 | 2.32627 | ||||||||
\(215\) | 210924. | + | 15713.9i | 0.311194 | + | 0.0231840i | ||||
\(216\) | 228991. | 0.333952 | ||||||||
\(217\) | 248490. | 0.358228 | ||||||||
\(218\) | 710111. | + | 1.22995e6i | 1.01201 | + | 1.75285i | ||||
\(219\) | 245528. | 0.345933 | ||||||||
\(220\) | −34013.3 | − | 58912.7i | −0.0473797 | − | 0.0820640i | ||||
\(221\) | −316201. | − | 547677.i | −0.435495 | − | 0.754299i | ||||
\(222\) | 164872. | − | 285566.i | 0.224525 | − | 0.388888i | ||||
\(223\) | −364985. | −0.491488 | −0.245744 | − | 0.969335i | \(-0.579032\pi\) | ||||
−0.245744 | + | 0.969335i | \(0.579032\pi\) | |||||||
\(224\) | −908416. | + | 1.57342e6i | −1.20966 | + | 2.09520i | ||||
\(225\) | −280313. | − | 485517.i | −0.369137 | − | 0.639364i | ||||
\(226\) | −1.04068e6 | −1.35533 | ||||||||
\(227\) | −362710. | − | 628231.i | −0.467191 | − | 0.809198i | 0.532106 | − | 0.846677i | \(-0.321401\pi\) |
−0.999297 | + | 0.0374790i | \(0.988067\pi\) | |||||||
\(228\) | −342450. | + | 593141.i | −0.436275 | + | 0.755651i | ||||
\(229\) | 266349. | − | 461331.i | 0.335632 | − | 0.581331i | −0.647974 | − | 0.761662i | \(-0.724384\pi\) |
0.983606 | + | 0.180331i | \(0.0577169\pi\) | |||||||
\(230\) | 191573. | − | 331815.i | 0.238790 | − | 0.413596i | ||||
\(231\) | −142468. | −0.175666 | ||||||||
\(232\) | −89944.5 | + | 155788.i | −0.109712 | + | 0.190027i | ||||
\(233\) | 352356. | − | 610298.i | 0.425199 | − | 0.736465i | −0.571240 | − | 0.820783i | \(-0.693538\pi\) |
0.996439 | + | 0.0843173i | \(0.0268709\pi\) | |||||||
\(234\) | 659375. | + | 1.14207e6i | 0.787214 | + | 1.36349i | ||||
\(235\) | 249342. | + | 431873.i | 0.294527 | + | 0.510136i | ||||
\(236\) | −508580. | −0.594401 | ||||||||
\(237\) | −29332.2 | −0.0339214 | ||||||||
\(238\) | −786818. | − | 1.36281e6i | −0.900392 | − | 1.55952i | ||||
\(239\) | −46812.7 | − | 81081.9i | −0.0530113 | − | 0.0918183i | 0.838302 | − | 0.545206i | \(-0.183549\pi\) |
−0.891313 | + | 0.453388i | \(0.850215\pi\) | |||||||
\(240\) | −37670.3 | + | 65246.8i | −0.0422154 | + | 0.0731191i | ||||
\(241\) | 624398. | − | 1.08149e6i | 0.692499 | − | 1.19944i | −0.278518 | − | 0.960431i | \(-0.589843\pi\) |
0.971017 | − | 0.239012i | \(-0.0768236\pi\) | |||||||
\(242\) | 1.30017e6 | 1.42712 | ||||||||
\(243\) | −452642. | + | 783999.i | −0.491744 | + | 0.851726i | ||||
\(244\) | −755165. | + | 1.30798e6i | −0.812021 | + | 1.40646i | ||||
\(245\) | 298177. | − | 516457.i | 0.317364 | − | 0.549691i | ||||
\(246\) | 136843. | + | 237019.i | 0.144173 | + | 0.249715i | ||||
\(247\) | −1.94335e6 | −2.02679 | ||||||||
\(248\) | 42877.5 | + | 74266.0i | 0.0442691 | + | 0.0766763i | ||||
\(249\) | −36493.0 | + | 63207.8i | −0.0373002 | + | 0.0646059i | ||||
\(250\) | −886870. | −0.897449 | ||||||||
\(251\) | 845888. | − | 1.46512e6i | 0.847478 | − | 1.46787i | −0.0359740 | − | 0.999353i | \(-0.511453\pi\) |
0.883452 | − | 0.468522i | \(-0.155213\pi\) | |||||||
\(252\) | 922639. | + | 1.59806e6i | 0.915230 | + | 1.58523i | ||||
\(253\) | −121818. | − | 210994.i | −0.119649 | − | 0.207238i | ||||
\(254\) | 1.68611e6 | 1.63984 | ||||||||
\(255\) | −47283.4 | − | 81897.2i | −0.0455363 | − | 0.0788712i | ||||
\(256\) | 227240. | 0.216713 | ||||||||
\(257\) | 455732. | 0.430404 | 0.215202 | − | 0.976570i | \(-0.430959\pi\) | ||||
0.215202 | + | 0.976570i | \(0.430959\pi\) | |||||||
\(258\) | 687703. | + | 51234.0i | 0.643208 | + | 0.0479191i | ||||
\(259\) | 1.30918e6 | 1.21269 | ||||||||
\(260\) | 556532. | 0.510572 | ||||||||
\(261\) | −229397. | − | 397327.i | −0.208443 | − | 0.361033i | ||||
\(262\) | 1.55969e6 | 1.40373 | ||||||||
\(263\) | 587760. | + | 1.01803e6i | 0.523975 | + | 0.907551i | 0.999610 | + | 0.0279088i | \(0.00888481\pi\) |
−0.475635 | + | 0.879642i | \(0.657782\pi\) | |||||||
\(264\) | −24583.2 | − | 42579.4i | −0.0217085 | − | 0.0376002i | ||||
\(265\) | 96862.1 | − | 167770.i | 0.0847304 | − | 0.146757i | ||||
\(266\) | −4.83573e6 | −4.19042 | ||||||||
\(267\) | −200619. | + | 347483.i | −0.172224 | + | 0.298301i | ||||
\(268\) | 82962.8 | + | 143696.i | 0.0705581 | + | 0.122210i | ||||
\(269\) | −1.08503e6 | −0.914238 | −0.457119 | − | 0.889406i | \(-0.651119\pi\) | ||||
−0.457119 | + | 0.889406i | \(0.651119\pi\) | |||||||
\(270\) | 219150. | + | 379578.i | 0.182949 | + | 0.316878i | ||||
\(271\) | −1.10282e6 | + | 1.91013e6i | −0.912178 | + | 1.57994i | −0.101198 | + | 0.994866i | \(0.532268\pi\) |
−0.810981 | + | 0.585073i | \(0.801066\pi\) | |||||||
\(272\) | −264581. | + | 458268.i | −0.216839 | + | 0.375576i | ||||
\(273\) | 582774. | − | 1.00939e6i | 0.473253 | − | 0.819698i | ||||
\(274\) | −1.63438e6 | −1.31515 | ||||||||
\(275\) | −133770. | + | 231696.i | −0.106666 | + | 0.184751i | ||||
\(276\) | 351235. | − | 608358.i | 0.277540 | − | 0.480713i | ||||
\(277\) | −306493. | − | 530861.i | −0.240005 | − | 0.415701i | 0.720710 | − | 0.693236i | \(-0.243816\pi\) |
−0.960715 | + | 0.277535i | \(0.910482\pi\) | |||||||
\(278\) | −206599. | − | 357841.i | −0.160331 | − | 0.277701i | ||||
\(279\) | −218712. | −0.168214 | ||||||||
\(280\) | 306985. | 0.234003 | ||||||||
\(281\) | 166721. | + | 288770.i | 0.125958 | + | 0.218166i | 0.922107 | − | 0.386935i | \(-0.126466\pi\) |
−0.796149 | + | 0.605101i | \(0.793133\pi\) | |||||||
\(282\) | 812960. | + | 1.40809e6i | 0.608760 | + | 1.05440i | ||||
\(283\) | −30457.9 | + | 52754.6i | −0.0226065 | + | 0.0391557i | −0.877107 | − | 0.480294i | \(-0.840530\pi\) |
0.854501 | + | 0.519450i | \(0.173863\pi\) | |||||||
\(284\) | 778197. | − | 1.34788e6i | 0.572524 | − | 0.991641i | ||||
\(285\) | −290600. | −0.211926 | ||||||||
\(286\) | 314664. | − | 545013.i | 0.227474 | − | 0.393996i | ||||
\(287\) | −543307. | + | 941036.i | −0.389350 | + | 0.674375i | ||||
\(288\) | 799556. | − | 1.38487e6i | 0.568025 | − | 0.983848i | ||||
\(289\) | 377828. | + | 654418.i | 0.266103 | + | 0.460904i | ||||
\(290\) | −344316. | −0.240415 | ||||||||
\(291\) | −177183. | − | 306890.i | −0.122656 | − | 0.212447i | ||||
\(292\) | −758803. | + | 1.31429e6i | −0.520801 | + | 0.902054i | ||||
\(293\) | 2.26216e6 | 1.53941 | 0.769706 | − | 0.638399i | \(-0.220403\pi\) | ||||
0.769706 | + | 0.638399i | \(0.220403\pi\) | |||||||
\(294\) | 972182. | − | 1.68387e6i | 0.655963 | − | 1.13616i | ||||
\(295\) | −107894. | − | 186878.i | −0.0721843 | − | 0.125027i | ||||
\(296\) | 225902. | + | 391273.i | 0.149862 | + | 0.259568i | ||||
\(297\) | 278705. | 0.183339 | ||||||||
\(298\) | −2.23320e6 | − | 3.86802e6i | −1.45676 | − | 2.52318i | ||||
\(299\) | 1.99320e6 | 1.28936 | ||||||||
\(300\) | −771393. | −0.494849 | ||||||||
\(301\) | 1.18903e6 | + | 2.46629e6i | 0.756444 | + | 1.56902i | ||||
\(302\) | −3.35851e6 | −2.11899 | ||||||||
\(303\) | 297534. | 0.186179 | ||||||||
\(304\) | 813049. | + | 1.40824e6i | 0.504583 | + | 0.873964i | ||||
\(305\) | −640827. | −0.394449 | ||||||||
\(306\) | 692529. | + | 1.19950e6i | 0.422799 | + | 0.732310i | ||||
\(307\) | 557789. | + | 966119.i | 0.337772 | + | 0.585039i | 0.984013 | − | 0.178095i | \(-0.0569933\pi\) |
−0.646241 | + | 0.763133i | \(0.723660\pi\) | |||||||
\(308\) | 440297. | − | 762617.i | 0.264465 | − | 0.458068i | ||||
\(309\) | −769754. | −0.458623 | ||||||||
\(310\) | −82069.6 | + | 142149.i | −0.0485040 | + | 0.0840114i | ||||
\(311\) | −362692. | − | 628202.i | −0.212636 | − | 0.368297i | 0.739902 | − | 0.672714i | \(-0.234872\pi\) |
−0.952539 | + | 0.304417i | \(0.901538\pi\) | |||||||
\(312\) | 402236. | 0.233934 | ||||||||
\(313\) | −453648. | − | 785741.i | −0.261733 | − | 0.453334i | 0.704970 | − | 0.709237i | \(-0.250961\pi\) |
−0.966702 | + | 0.255903i | \(0.917627\pi\) | |||||||
\(314\) | 896865. | − | 1.55342e6i | 0.513338 | − | 0.889127i | ||||
\(315\) | −391472. | + | 678049.i | −0.222292 | + | 0.385021i | ||||
\(316\) | 90650.8 | − | 157012.i | 0.0510686 | − | 0.0884534i | ||||
\(317\) | −536132. | −0.299656 | −0.149828 | − | 0.988712i | \(-0.547872\pi\) | ||||
−0.149828 | + | 0.988712i | \(0.547872\pi\) | |||||||
\(318\) | 315812. | − | 547002.i | 0.175130 | − | 0.303334i | ||||
\(319\) | −109472. | + | 189611.i | −0.0602317 | + | 0.104324i | ||||
\(320\) | −418826. | − | 725428.i | −0.228643 | − | 0.396022i | ||||
\(321\) | 606173. | + | 1.04992e6i | 0.328348 | + | 0.568715i | ||||
\(322\) | 4.95978e6 | 2.66577 | ||||||||
\(323\) | −2.04106e6 | −1.08856 | ||||||||
\(324\) | −591055. | − | 1.02374e6i | −0.312799 | − | 0.541784i | ||||
\(325\) | −1.09438e6 | − | 1.89553e6i | −0.574726 | − | 0.995455i | ||||
\(326\) | 2.42876e6 | − | 4.20674e6i | 1.26573 | − | 2.19231i | ||||
\(327\) | −552405. | + | 956794.i | −0.285686 | + | 0.494822i | ||||
\(328\) | −374995. | −0.192460 | ||||||||
\(329\) | −3.22769e6 | + | 5.59053e6i | −1.64400 | + | 2.84749i | ||||
\(330\) | 47053.4 | − | 81498.9i | 0.0237852 | − | 0.0411971i | ||||
\(331\) | 15569.8 | − | 26967.6i | 0.00781110 | − | 0.0135292i | −0.862093 | − | 0.506749i | \(-0.830847\pi\) |
0.869905 | + | 0.493220i | \(0.164180\pi\) | |||||||
\(332\) | −225563. | − | 390686.i | −0.112311 | − | 0.194528i | ||||
\(333\) | −1.15229e6 | −0.569446 | ||||||||
\(334\) | −2.89774e6 | − | 5.01904e6i | −1.42133 | − | 2.46181i | ||||
\(335\) | −35200.8 | + | 60969.5i | −0.0171372 | + | 0.0296825i | ||||
\(336\) | −975272. | −0.471278 | ||||||||
\(337\) | 1.18014e6 | − | 2.04407e6i | 0.566057 | − | 0.980439i | −0.430894 | − | 0.902403i | \(-0.641802\pi\) |
0.996951 | − | 0.0780365i | \(-0.0248651\pi\) | |||||||
\(338\) | 986892. | + | 1.70935e6i | 0.469870 | + | 0.813839i | ||||
\(339\) | −404779. | − | 701098.i | −0.191302 | − | 0.331345i | ||||
\(340\) | 584515. | 0.274220 | ||||||||
\(341\) | 52186.4 | + | 90389.4i | 0.0243036 | + | 0.0420951i | ||||
\(342\) | 4.25623e6 | 1.96771 | ||||||||
\(343\) | 3.92441e6 | 1.80111 | ||||||||
\(344\) | −531928. | + | 780928.i | −0.242358 | + | 0.355807i | ||||
\(345\) | 298055. | 0.134818 | ||||||||
\(346\) | 4.84663e6 | 2.17645 | ||||||||
\(347\) | −195452. | − | 338533.i | −0.0871398 | − | 0.150931i | 0.819161 | − | 0.573563i | \(-0.194439\pi\) |
−0.906301 | + | 0.422633i | \(0.861106\pi\) | |||||||
\(348\) | −631277. | −0.279429 | ||||||||
\(349\) | −1.50441e6 | − | 2.60571e6i | −0.661153 | − | 1.14515i | −0.980313 | − | 0.197450i | \(-0.936734\pi\) |
0.319160 | − | 0.947701i | \(-0.396599\pi\) | |||||||
\(350\) | −2.72320e6 | − | 4.71673e6i | −1.18826 | − | 2.05812i | ||||
\(351\) | −1.14006e6 | + | 1.97464e6i | −0.493923 | + | 0.855500i | ||||
\(352\) | −763120. | −0.328274 | ||||||||
\(353\) | 644551. | − | 1.11640e6i | 0.275309 | − | 0.476850i | −0.694904 | − | 0.719103i | \(-0.744553\pi\) |
0.970213 | + | 0.242253i | \(0.0778864\pi\) | |||||||
\(354\) | −351781. | − | 609302.i | −0.149198 | − | 0.258419i | ||||
\(355\) | 660371. | 0.278110 | ||||||||
\(356\) | −1.24002e6 | − | 2.14778e6i | −0.518567 | − | 0.898185i | ||||
\(357\) | 612076. | − | 1.06015e6i | 0.254176 | − | 0.440246i | ||||
\(358\) | −2.48873e6 | + | 4.31061e6i | −1.02629 | + | 1.77759i | ||||
\(359\) | 461969. | − | 800153.i | 0.189181 | − | 0.327670i | −0.755797 | − | 0.654806i | \(-0.772750\pi\) |
0.944977 | + | 0.327136i | \(0.106084\pi\) | |||||||
\(360\) | −270197. | −0.109881 | ||||||||
\(361\) | −1.89801e6 | + | 3.28745e6i | −0.766532 | + | 1.32767i | ||||
\(362\) | −2.80919e6 | + | 4.86565e6i | −1.12670 | + | 1.95151i | ||||
\(363\) | 505710. | + | 875915.i | 0.201435 | + | 0.348896i | ||||
\(364\) | 3.60211e6 | + | 6.23904e6i | 1.42496 | + | 2.46811i | ||||
\(365\) | −643914. | −0.252985 | ||||||||
\(366\) | −2.08937e6 | −0.815290 | ||||||||
\(367\) | 1.75035e6 | + | 3.03170e6i | 0.678360 | + | 1.17495i | 0.975475 | + | 0.220112i | \(0.0706424\pi\) |
−0.297114 | + | 0.954842i | \(0.596024\pi\) | |||||||
\(368\) | −833907. | − | 1.44437e6i | −0.320995 | − | 0.555979i | ||||
\(369\) | 478200. | − | 828266.i | 0.182828 | − | 0.316668i | ||||
\(370\) | −432387. | + | 748916.i | −0.164198 | + | 0.284399i | ||||
\(371\) | 2.50773e6 | 0.945902 | ||||||||
\(372\) | −150468. | + | 260619.i | −0.0563751 | + | 0.0976446i | ||||
\(373\) | −1.78862e6 | + | 3.09798e6i | −0.665651 | + | 1.15294i | 0.313457 | + | 0.949602i | \(0.398513\pi\) |
−0.979108 | + | 0.203339i | \(0.934821\pi\) | |||||||
\(374\) | 330485. | − | 572417.i | 0.122172 | − | 0.211609i | ||||
\(375\) | −344954. | − | 597478.i | −0.126673 | − | 0.219404i | ||||
\(376\) | −2.22778e6 | −0.812649 | ||||||||
\(377\) | −895599. | − | 1.55122e6i | −0.324534 | − | 0.562110i | ||||
\(378\) | −2.83686e6 | + | 4.91358e6i | −1.02119 | + | 1.76876i | ||||
\(379\) | 330104. | 0.118046 | 0.0590232 | − | 0.998257i | \(-0.481201\pi\) | ||||
0.0590232 | + | 0.998257i | \(0.481201\pi\) | |||||||
\(380\) | 898097. | − | 1.55555e6i | 0.319054 | − | 0.552618i | ||||
\(381\) | 655824. | + | 1.13592e6i | 0.231459 | + | 0.400899i | ||||
\(382\) | 4.12418e6 | + | 7.14328e6i | 1.44603 | + | 2.50461i | ||||
\(383\) | −3.92370e6 | −1.36678 | −0.683390 | − | 0.730054i | \(-0.739495\pi\) | ||||
−0.683390 | + | 0.730054i | \(0.739495\pi\) | |||||||
\(384\) | −509278. | − | 882096.i | −0.176249 | − | 0.305272i | ||||
\(385\) | 373632. | 0.128467 | ||||||||
\(386\) | −1.02206e6 | −0.349147 | ||||||||
\(387\) | −1.04654e6 | − | 2.17074e6i | −0.355205 | − | 0.736767i | ||||
\(388\) | 2.19033e6 | 0.738636 | ||||||||
\(389\) | 3.78830e6 | 1.26932 | 0.634659 | − | 0.772793i | \(-0.281141\pi\) | ||||
0.634659 | + | 0.772793i | \(0.281141\pi\) | |||||||
\(390\) | 384949. | + | 666751.i | 0.128157 | + | 0.221974i | ||||
\(391\) | 2.09343e6 | 0.692493 | ||||||||
\(392\) | 1.33205e6 | + | 2.30718e6i | 0.437830 | + | 0.758344i | ||||
\(393\) | 606651. | + | 1.05075e6i | 0.198133 | + | 0.343177i | ||||
\(394\) | 1.48868e6 | − | 2.57846e6i | 0.483125 | − | 0.836798i | ||||
\(395\) | 76925.5 | 0.0248072 | ||||||||
\(396\) | −387534. | + | 671228.i | −0.124186 | + | 0.215096i | ||||
\(397\) | 1.00789e6 | + | 1.74572e6i | 0.320950 | + | 0.555903i | 0.980684 | − | 0.195597i | \(-0.0626644\pi\) |
−0.659734 | + | 0.751499i | \(0.729331\pi\) | |||||||
\(398\) | −461588. | −0.146065 | ||||||||
\(399\) | −1.88089e6 | − | 3.25780e6i | −0.591468 | − | 1.02445i | ||||
\(400\) | −915725. | + | 1.58608e6i | −0.286164 | + | 0.495651i | ||||
\(401\) | −1.71501e6 | + | 2.97049e6i | −0.532606 | + | 0.922500i | 0.466669 | + | 0.884432i | \(0.345454\pi\) |
−0.999275 | + | 0.0380685i | \(0.987879\pi\) | |||||||
\(402\) | −114769. | + | 198787.i | −0.0354210 | + | 0.0613510i | ||||
\(403\) | −853884. | −0.261900 | ||||||||
\(404\) | −919526. | + | 1.59267e6i | −0.280292 | + | 0.485480i | ||||
\(405\) | 250782. | − | 434368.i | 0.0759730 | − | 0.131589i | ||||
\(406\) | −2.22856e6 | − | 3.85998e6i | −0.670979 | − | 1.16217i | ||||
\(407\) | 274946. | + | 476220.i | 0.0822737 | + | 0.142502i | ||||
\(408\) | 422461. | 0.125642 | ||||||||
\(409\) | 927225. | 0.274080 | 0.137040 | − | 0.990566i | \(-0.456241\pi\) | ||||
0.137040 | + | 0.990566i | \(0.456241\pi\) | |||||||
\(410\) | −358879. | − | 621597.i | −0.105436 | − | 0.182620i | ||||
\(411\) | −635703. | − | 1.10107e6i | −0.185631 | − | 0.321522i | ||||
\(412\) | 2.37892e6 | − | 4.12040e6i | 0.690456 | − | 1.19591i | ||||
\(413\) | 1.39667e6 | − | 2.41911e6i | 0.402921 | − | 0.697879i | ||||
\(414\) | −4.36542e6 | −1.25177 | ||||||||
\(415\) | 95705.3 | − | 165766.i | 0.0272782 | − | 0.0472472i | ||||
\(416\) | 3.12158e6 | − | 5.40673e6i | 0.884384 | − | 1.53180i | ||||
\(417\) | 160717. | − | 278369.i | 0.0452606 | − | 0.0783937i | ||||
\(418\) | −1.01557e6 | − | 1.75902e6i | −0.284295 | − | 0.492413i | ||||
\(419\) | 226769. | 0.0631028 | 0.0315514 | − | 0.999502i | \(-0.489955\pi\) | ||||
0.0315514 | + | 0.999502i | \(0.489955\pi\) | |||||||
\(420\) | 538645. | + | 932960.i | 0.148998 | + | 0.258071i | ||||
\(421\) | 1.25571e6 | − | 2.17496e6i | 0.345291 | − | 0.598061i | −0.640116 | − | 0.768279i | \(-0.721114\pi\) |
0.985407 | + | 0.170217i | \(0.0544469\pi\) | |||||||
\(422\) | 2.32975e6 | 0.636838 | ||||||||
\(423\) | 2.84090e6 | − | 4.92058e6i | 0.771978 | − | 1.33711i | ||||
\(424\) | 432715. | + | 749484.i | 0.116893 | + | 0.202464i | ||||
\(425\) | −1.14941e6 | − | 1.99084e6i | −0.308676 | − | 0.534642i | ||||
\(426\) | 2.15309e6 | 0.574828 | ||||||||
\(427\) | −4.14770e6 | − | 7.18403e6i | −1.10087 | − | 1.90677i | ||||
\(428\) | −7.49349e6 | −1.97731 | ||||||||
\(429\) | 489562. | 0.128429 | ||||||||
\(430\) | −1.80354e6 | − | 134364.i | −0.470387 | − | 0.0350439i | ||||
\(431\) | 4.00047e6 | 1.03733 | 0.518667 | − | 0.854977i | \(-0.326429\pi\) | ||||
0.518667 | + | 0.854977i | \(0.326429\pi\) | |||||||
\(432\) | 1.90789e6 | 0.491862 | ||||||||
\(433\) | 1.61790e6 | + | 2.80229e6i | 0.414699 | + | 0.718280i | 0.995397 | − | 0.0958393i | \(-0.0305535\pi\) |
−0.580698 | + | 0.814119i | \(0.697220\pi\) | |||||||
\(434\) | −2.12476e6 | −0.541483 | ||||||||
\(435\) | −133924. | − | 231963.i | −0.0339340 | − | 0.0587755i | ||||
\(436\) | −3.41441e6 | − | 5.91393e6i | −0.860199 | − | 1.48991i | ||||
\(437\) | 3.21651e6 | − | 5.57116e6i | 0.805715 | − | 1.39554i | ||||
\(438\) | −2.09943e6 | −0.522897 | ||||||||
\(439\) | −1.47752e6 | + | 2.55914e6i | −0.365908 | + | 0.633772i | −0.988921 | − | 0.148440i | \(-0.952575\pi\) |
0.623013 | + | 0.782211i | \(0.285908\pi\) | |||||||
\(440\) | 64471.1 | + | 111667.i | 0.0158757 | + | 0.0274975i | ||||
\(441\) | −6.79461e6 | −1.66367 | ||||||||
\(442\) | 2.70373e6 | + | 4.68300e6i | 0.658276 | + | 1.14017i | ||||
\(443\) | 578945. | − | 1.00276e6i | 0.140161 | − | 0.242767i | −0.787396 | − | 0.616448i | \(-0.788571\pi\) |
0.927557 | + | 0.373681i | \(0.121905\pi\) | |||||||
\(444\) | −792748. | + | 1.37308e6i | −0.190844 | + | 0.330551i | ||||
\(445\) | 526137. | − | 911296.i | 0.125950 | − | 0.218152i | ||||
\(446\) | 3.12086e6 | 0.742912 | ||||||||
\(447\) | 1.73724e6 | − | 3.00898e6i | 0.411235 | − | 0.712280i | ||||
\(448\) | 5.42164e6 | − | 9.39056e6i | 1.27625 | − | 2.21053i | ||||
\(449\) | 3.17044e6 | + | 5.49136e6i | 0.742170 | + | 1.28548i | 0.951506 | + | 0.307632i | \(0.0995364\pi\) |
−0.209336 | + | 0.977844i | \(0.567130\pi\) | |||||||
\(450\) | 2.39687e6 | + | 4.15149e6i | 0.557972 | + | 0.966436i | ||||
\(451\) | −456408. | −0.105660 | ||||||||
\(452\) | 5.00387e6 | 1.15202 | ||||||||
\(453\) | −1.30632e6 | − | 2.26261e6i | −0.299091 | − | 0.518041i | ||||
\(454\) | 3.10141e6 | + | 5.37180e6i | 0.706187 | + | 1.22315i | ||||
\(455\) | −1.52836e6 | + | 2.64720e6i | −0.346097 | + | 0.599457i | ||||
\(456\) | 649103. | − | 1.12428e6i | 0.146185 | − | 0.253199i | ||||
\(457\) | −3.11301e6 | −0.697252 | −0.348626 | − | 0.937262i | \(-0.613352\pi\) | ||||
−0.348626 | + | 0.937262i | \(0.613352\pi\) | |||||||
\(458\) | −2.27747e6 | + | 3.94469e6i | −0.507327 | + | 0.878716i | ||||
\(459\) | −1.19738e6 | + | 2.07393e6i | −0.265278 | + | 0.459475i | ||||
\(460\) | −921137. | + | 1.59546e6i | −0.202969 | + | 0.351553i | ||||
\(461\) | 2.76471e6 | + | 4.78861e6i | 0.605894 | + | 1.04944i | 0.991910 | + | 0.126947i | \(0.0405178\pi\) |
−0.386016 | + | 0.922492i | \(0.626149\pi\) | |||||||
\(462\) | 1.21820e6 | 0.265530 | ||||||||
\(463\) | −2.62962e6 | − | 4.55464e6i | −0.570086 | − | 0.987418i | −0.996556 | − | 0.0829168i | \(-0.973576\pi\) |
0.426470 | − | 0.904502i | \(-0.359757\pi\) | |||||||
\(464\) | −749392. | + | 1.29799e6i | −0.161590 | + | 0.279882i | ||||
\(465\) | −127686. | −0.0273849 | ||||||||
\(466\) | −3.01288e6 | + | 5.21846e6i | −0.642713 | + | 1.11321i | ||||
\(467\) | 497355. | + | 861444.i | 0.105530 | + | 0.182783i | 0.913954 | − | 0.405817i | \(-0.133013\pi\) |
−0.808425 | + | 0.588599i | \(0.799680\pi\) | |||||||
\(468\) | −3.17045e6 | − | 5.49138e6i | −0.669124 | − | 1.15896i | ||||
\(469\) | −911338. | −0.191314 | ||||||||
\(470\) | −2.13204e6 | − | 3.69280e6i | −0.445195 | − | 0.771101i | ||||
\(471\) | 1.39537e6 | 0.289825 | ||||||||
\(472\) | 963997. | 0.199168 | ||||||||
\(473\) | −647411. | + | 950470.i | −0.133054 | + | 0.195337i | ||||
\(474\) | 250810. | 0.0512741 | ||||||||
\(475\) | −7.06419e6 | −1.43658 | ||||||||
\(476\) | 3.78323e6 | + | 6.55275e6i | 0.765324 | + | 1.32558i | ||||
\(477\) | −2.20722e6 | −0.444170 | ||||||||
\(478\) | 400280. | + | 693305.i | 0.0801297 | + | 0.138789i | ||||
\(479\) | 1.69502e6 | + | 2.93586e6i | 0.337548 | + | 0.584651i | 0.983971 | − | 0.178329i | \(-0.0570690\pi\) |
−0.646423 | + | 0.762980i | \(0.723736\pi\) | |||||||
\(480\) | 466788. | − | 808500.i | 0.0924733 | − | 0.160168i | ||||
\(481\) | −4.49872e6 | −0.886597 | ||||||||
\(482\) | −5.33902e6 | + | 9.24746e6i | −1.04675 | + | 1.81303i | ||||
\(483\) | 1.92914e6 | + | 3.34137e6i | 0.376267 | + | 0.651714i | ||||
\(484\) | −6.25156e6 | −1.21304 | ||||||||
\(485\) | 464674. | + | 804839.i | 0.0897003 | + | 0.155366i | ||||
\(486\) | 3.87039e6 | − | 6.70372e6i | 0.743301 | − | 1.28743i | ||||
\(487\) | 5.03830e6 | − | 8.72659e6i | 0.962635 | − | 1.66733i | 0.246796 | − | 0.969067i | \(-0.420622\pi\) |
0.715839 | − | 0.698265i | \(-0.246044\pi\) | |||||||
\(488\) | 1.43139e6 | − | 2.47924e6i | 0.272088 | − | 0.471269i | ||||
\(489\) | 3.77874e6 | 0.714619 | ||||||||
\(490\) | −2.54961e6 | + | 4.41605e6i | −0.479715 | + | 0.830891i | ||||
\(491\) | −290638. | + | 503401.i | −0.0544063 | + | 0.0942345i | −0.891946 | − | 0.452142i | \(-0.850660\pi\) |
0.837540 | + | 0.546377i | \(0.183993\pi\) | |||||||
\(492\) | −657978. | − | 1.13965e6i | −0.122546 | − | 0.212256i | ||||
\(493\) | −940631. | − | 1.62922e6i | −0.174302 | − | 0.301900i | ||||
\(494\) | 1.66169e7 | 3.06361 | ||||||||
\(495\) | −328858. | −0.0603247 | ||||||||
\(496\) | 357243. | + | 618764.i | 0.0652019 | + | 0.112933i | ||||
\(497\) | 4.27420e6 | + | 7.40314e6i | 0.776183 | + | 1.34439i | ||||
\(498\) | 312040. | − | 540469.i | 0.0563815 | − | 0.0976556i | ||||
\(499\) | 2.36539e6 | − | 4.09697e6i | 0.425257 | − | 0.736566i | −0.571188 | − | 0.820819i | \(-0.693517\pi\) |
0.996444 | + | 0.0842535i | \(0.0268505\pi\) | |||||||
\(500\) | 4.26431e6 | 0.762823 | ||||||||
\(501\) | 2.25419e6 | − | 3.90438e6i | 0.401233 | − | 0.694956i | ||||
\(502\) | −7.23290e6 | + | 1.25278e7i | −1.28101 | + | 2.21878i | ||||
\(503\) | 1.35286e6 | − | 2.34322e6i | 0.238414 | − | 0.412946i | −0.721845 | − | 0.692055i | \(-0.756706\pi\) |
0.960259 | + | 0.279109i | \(0.0900390\pi\) | |||||||
\(504\) | −1.74883e6 | − | 3.02906e6i | −0.306670 | − | 0.531168i | ||||
\(505\) | −780302. | −0.136155 | ||||||||
\(506\) | 1.04162e6 | + | 1.80414e6i | 0.180856 | + | 0.313253i | ||||
\(507\) | −767717. | + | 1.32973e6i | −0.132642 | + | 0.229743i | ||||
\(508\) | −8.10727e6 | −1.39385 | ||||||||
\(509\) | −834861. | + | 1.44602e6i | −0.142830 | + | 0.247389i | −0.928561 | − | 0.371179i | \(-0.878954\pi\) |
0.785731 | + | 0.618568i | \(0.212287\pi\) | |||||||
\(510\) | 404304. | + | 700276.i | 0.0688308 | + | 0.119219i | ||||
\(511\) | −4.16768e6 | − | 7.21864e6i | −0.706061 | − | 1.22293i | ||||
\(512\) | −6.84314e6 | −1.15367 | ||||||||
\(513\) | 3.67951e6 | + | 6.37310e6i | 0.617301 | + | 1.06920i | ||||
\(514\) | −3.89681e6 | −0.650581 | ||||||||
\(515\) | 2.01873e6 | 0.335397 | ||||||||
\(516\) | −3.30666e6 | − | 246347.i | −0.546721 | − | 0.0407308i | ||||
\(517\) | −2.71144e6 | −0.446142 | ||||||||
\(518\) | −1.11944e7 | −1.83305 | ||||||||
\(519\) | 1.88513e6 | + | 3.26514e6i | 0.307201 | + | 0.532088i | ||||
\(520\) | −1.05489e6 | −0.171080 | ||||||||
\(521\) | 5.21202e6 | + | 9.02748e6i | 0.841224 | + | 1.45704i | 0.888861 | + | 0.458178i | \(0.151498\pi\) |
−0.0476367 | + | 0.998865i | \(0.515169\pi\) | |||||||
\(522\) | 1.96150e6 | + | 3.39741e6i | 0.315073 | + | 0.545723i | ||||
\(523\) | −2.38845e6 | + | 4.13691e6i | −0.381822 | + | 0.661335i | −0.991323 | − | 0.131450i | \(-0.958037\pi\) |
0.609501 | + | 0.792786i | \(0.291370\pi\) | |||||||
\(524\) | −7.49940e6 | −1.19316 | ||||||||
\(525\) | 2.11842e6 | − | 3.66921e6i | 0.335439 | − | 0.580997i | ||||
\(526\) | −5.02574e6 | − | 8.70484e6i | −0.792019 | − | 1.37182i | ||||
\(527\) | −896818. | −0.140662 | ||||||||
\(528\) | −204820. | − | 354759.i | −0.0319734 | − | 0.0553795i | ||||
\(529\) | −80854.8 | + | 140045.i | −0.0125622 | + | 0.0217584i | ||||
\(530\) | −828236. | + | 1.43455e6i | −0.128075 | + | 0.221832i | ||||
\(531\) | −1.22930e6 | + | 2.12921e6i | −0.189201 | + | 0.327705i | ||||
\(532\) | 2.32515e7 | 3.56182 | ||||||||
\(533\) | 1.86696e6 | − | 3.23367e6i | 0.284654 | − | 0.493035i | ||||
\(534\) | 1.71543e6 | − | 2.97121e6i | 0.260327 | − | 0.450900i | ||||
\(535\) | −1.58973e6 | − | 2.75349e6i | −0.240125 | − | 0.415910i | ||||
\(536\) | −157253. | − | 272371.i | −0.0236422 | − | 0.0409495i | ||||
\(537\) | −3.87204e6 | −0.579434 | ||||||||
\(538\) | 9.27769e6 | 1.38192 | ||||||||
\(539\) | 1.62124e6 | + | 2.80808e6i | 0.240368 | + | 0.416329i | ||||
\(540\) | −1.05373e6 | − | 1.82511e6i | −0.155505 | − | 0.269343i | ||||
\(541\) | −485182. | + | 840361.i | −0.0712708 | + | 0.123445i | −0.899459 | − | 0.437006i | \(-0.856039\pi\) |
0.828188 | + | 0.560451i | \(0.189372\pi\) | |||||||
\(542\) | 9.42981e6 | − | 1.63329e7i | 1.37881 | − | 2.38817i | ||||
\(543\) | −4.37061e6 | −0.636125 | ||||||||
\(544\) | 3.27854e6 | − | 5.67859e6i | 0.474988 | − | 0.822703i | ||||
\(545\) | 1.44872e6 | − | 2.50925e6i | 0.208926 | − | 0.361871i | ||||
\(546\) | −4.98311e6 | + | 8.63099e6i | −0.715350 | + | 1.23902i | ||||
\(547\) | −3.36621e6 | − | 5.83045e6i | −0.481031 | − | 0.833170i | 0.518732 | − | 0.854937i | \(-0.326404\pi\) |
−0.999763 | + | 0.0217667i | \(0.993071\pi\) | |||||||
\(548\) | 7.85854e6 | 1.11787 | ||||||||
\(549\) | 3.65066e6 | + | 6.32313e6i | 0.516941 | + | 0.895367i | ||||
\(550\) | 1.14382e6 | − | 1.98116e6i | 0.161232 | − | 0.279262i | ||||
\(551\) | −5.78105e6 | −0.811200 | ||||||||
\(552\) | −665755. | + | 1.15312e6i | −0.0929965 | + | 0.161075i | ||||
\(553\) | 497894. | + | 862378.i | 0.0692348 | + | 0.119918i | ||||
\(554\) | 2.62072e6 | + | 4.53921e6i | 0.362782 | + | 0.628357i | ||||
\(555\) | −672719. | −0.0927046 | ||||||||
\(556\) | 993385. | + | 1.72059e6i | 0.136280 | + | 0.236043i | ||||
\(557\) | −1.39802e7 | −1.90931 | −0.954656 | − | 0.297712i | \(-0.903777\pi\) | ||||
−0.954656 | + | 0.297712i | \(0.903777\pi\) | |||||||
\(558\) | 1.87013e6 | 0.254266 | ||||||||
\(559\) | −4.08585e6 | − | 8.47488e6i | −0.553035 | − | 1.14711i | ||||
\(560\) | 2.55771e6 | 0.344652 | ||||||||
\(561\) | 514178. | 0.0689773 | ||||||||
\(562\) | −1.42558e6 | − | 2.46918e6i | −0.190393 | − | 0.329770i | ||||
\(563\) | −868060. | −0.115419 | −0.0577097 | − | 0.998333i | \(-0.518380\pi\) | ||||
−0.0577097 | + | 0.998333i | \(0.518380\pi\) | |||||||
\(564\) | −3.90893e6 | − | 6.77047e6i | −0.517440 | − | 0.896233i | ||||
\(565\) | 1.06156e6 | + | 1.83867e6i | 0.139902 | + | 0.242317i | ||||
\(566\) | 260435. | − | 451087.i | 0.0341711 | − | 0.0591861i | ||||
\(567\) | 6.49268e6 | 0.848137 | ||||||||
\(568\) | −1.47505e6 | + | 2.55486e6i | −0.191838 | + | 0.332273i | ||||
\(569\) | 1.24744e6 | + | 2.16062e6i | 0.161524 | + | 0.279768i | 0.935416 | − | 0.353550i | \(-0.115026\pi\) |
−0.773891 | + | 0.633318i | \(0.781692\pi\) | |||||||
\(570\) | 2.48483e6 | 0.320338 | ||||||||
\(571\) | 743122. | + | 1.28712e6i | 0.0953827 | + | 0.165208i | 0.909768 | − | 0.415116i | \(-0.136259\pi\) |
−0.814386 | + | 0.580324i | \(0.802926\pi\) | |||||||
\(572\) | −1.51299e6 | + | 2.62057e6i | −0.193350 | + | 0.334893i | ||||
\(573\) | −3.20825e6 | + | 5.55686e6i | −0.408209 | + | 0.707038i | ||||
\(574\) | 4.64564e6 | − | 8.04648e6i | 0.588526 | − | 1.01936i | ||||
\(575\) | 7.24542e6 | 0.913890 | ||||||||
\(576\) | −4.77193e6 | + | 8.26523e6i | −0.599292 | + | 1.03800i | ||||
\(577\) | −33546.6 | + | 58104.3i | −0.00419477 | + | 0.00726556i | −0.868115 | − | 0.496363i | \(-0.834669\pi\) |
0.863920 | + | 0.503628i | \(0.168002\pi\) | |||||||
\(578\) | −3.23068e6 | − | 5.59571e6i | −0.402230 | − | 0.696684i | ||||
\(579\) | −397537. | − | 688554.i | −0.0492812 | − | 0.0853575i | ||||
\(580\) | 1.65556e6 | 0.204351 | ||||||||
\(581\) | 2.47778e6 | 0.304525 | ||||||||
\(582\) | 1.51503e6 | + | 2.62412e6i | 0.185402 | + | 0.321126i | ||||
\(583\) | 526658. | + | 912199.i | 0.0641737 | + | 0.111152i | ||||
\(584\) | 1.43829e6 | − | 2.49118e6i | 0.174507 | − | 0.302255i | ||||
\(585\) | 1.34521e6 | − | 2.32997e6i | 0.162518 | − | 0.281489i | ||||
\(586\) | −1.93430e7 | −2.32691 | ||||||||
\(587\) | 3.92924e6 | − | 6.80564e6i | 0.470666 | − | 0.815218i | −0.528771 | − | 0.848765i | \(-0.677347\pi\) |
0.999437 | + | 0.0335466i | \(0.0106802\pi\) | |||||||
\(588\) | −4.67451e6 | + | 8.09649e6i | −0.557562 | + | 0.965725i | ||||
\(589\) | −1.37794e6 | + | 2.38667e6i | −0.163660 | + | 0.283468i | ||||
\(590\) | 922567. | + | 1.59793e6i | 0.109111 | + | 0.188986i | ||||
\(591\) | 2.31612e6 | 0.272768 | ||||||||
\(592\) | 1.88215e6 | + | 3.25998e6i | 0.220724 | + | 0.382306i | ||||
\(593\) | 533177. | − | 923489.i | 0.0622636 | − | 0.107844i | −0.833213 | − | 0.552952i | \(-0.813501\pi\) |
0.895477 | + | 0.445108i | \(0.146835\pi\) | |||||||
\(594\) | −2.38312e6 | −0.277127 | ||||||||
\(595\) | −1.60521e6 | + | 2.78030e6i | −0.185883 | + | 0.321958i | ||||
\(596\) | 1.07378e7 | + | 1.85985e7i | 1.23823 | + | 2.14467i | ||||
\(597\) | −179538. | − | 310969.i | −0.0206168 | − | 0.0357093i | ||||
\(598\) | −1.70432e7 | −1.94894 | ||||||||
\(599\) | 5.29841e6 | + | 9.17711e6i | 0.603363 | + | 1.04505i | 0.992308 | + | 0.123794i | \(0.0395061\pi\) |
−0.388945 | + | 0.921261i | \(0.627161\pi\) | |||||||
\(600\) | 1.46215e6 | 0.165811 | ||||||||
\(601\) | −1.03792e7 | −1.17214 | −0.586068 | − | 0.810262i | \(-0.699325\pi\) | ||||
−0.586068 | + | 0.810262i | \(0.699325\pi\) | |||||||
\(602\) | −1.01670e7 | − | 2.10884e7i | −1.14341 | − | 2.37166i | ||||
\(603\) | 802127. | 0.0898359 | ||||||||
\(604\) | 1.61486e7 | 1.80112 | ||||||||
\(605\) | −1.32626e6 | − | 2.29714e6i | −0.147312 | − | 0.255152i | ||||
\(606\) | −2.54411e6 | −0.281420 | ||||||||
\(607\) | 5.88121e6 | + | 1.01866e7i | 0.647880 | + | 1.12216i | 0.983628 | + | 0.180210i | \(0.0576777\pi\) |
−0.335748 | + | 0.941952i | \(0.608989\pi\) | |||||||
\(608\) | −1.00748e7 | − | 1.74501e7i | −1.10530 | − | 1.91443i | ||||
\(609\) | 1.73363e6 | − | 3.00273e6i | 0.189414 | − | 0.328075i | ||||
\(610\) | 5.47950e6 | 0.596233 | ||||||||
\(611\) | 1.10913e7 | − | 1.92107e7i | 1.20193 | − | 2.08180i | ||||
\(612\) | −3.32987e6 | − | 5.76750e6i | −0.359375 | − | 0.622456i | ||||
\(613\) | 1.53282e7 | 1.64756 | 0.823779 | − | 0.566911i | \(-0.191862\pi\) | ||||
0.823779 | + | 0.566911i | \(0.191862\pi\) | |||||||
\(614\) | −4.76947e6 | − | 8.26096e6i | −0.510563 | − | 0.884320i | ||||
\(615\) | 279177. | − | 483549.i | 0.0297641 | − | 0.0515529i | ||||
\(616\) | −834568. | + | 1.44551e6i | −0.0886156 | + | 0.153487i | ||||
\(617\) | −6.79431e6 | + | 1.17681e7i | −0.718509 | + | 1.24449i | 0.243081 | + | 0.970006i | \(0.421842\pi\) |
−0.961590 | + | 0.274489i | \(0.911491\pi\) | |||||||
\(618\) | 6.58191e6 | 0.693235 | ||||||||
\(619\) | −6.92049e6 | + | 1.19866e7i | −0.725956 | + | 1.25739i | 0.232623 | + | 0.972567i | \(0.425269\pi\) |
−0.958579 | + | 0.284826i | \(0.908064\pi\) | |||||||
\(620\) | 394613. | − | 683489.i | 0.0412279 | − | 0.0714089i | ||||
\(621\) | −3.77391e6 | − | 6.53660e6i | −0.392701 | − | 0.680178i | ||||
\(622\) | 3.10126e6 | + | 5.37154e6i | 0.321412 | + | 0.556702i | ||||
\(623\) | 1.36215e7 | 1.40607 | ||||||||
\(624\) | 3.35131e6 | 0.344551 | ||||||||
\(625\) | −3.50267e6 | − | 6.06680e6i | −0.358673 | − | 0.621240i | ||||
\(626\) | 3.87899e6 | + | 6.71861e6i | 0.395624 | + | 0.685241i | ||||
\(627\) | 790025. | − | 1.36836e6i | 0.0802550 | − | 0.139006i | ||||
\(628\) | −4.31237e6 | + | 7.46924e6i | −0.436332 | + | 0.755749i | ||||
\(629\) | −4.72492e6 | −0.476176 | ||||||||
\(630\) | 3.34734e6 | − | 5.79777e6i | 0.336007 | − | 0.581982i | ||||
\(631\) | 9.87471e6 | − | 1.71035e7i | 0.987304 | − | 1.71006i | 0.356091 | − | 0.934451i | \(-0.384109\pi\) |
0.631213 | − | 0.775609i | \(-0.282557\pi\) | |||||||
\(632\) | −171826. | + | 297611.i | −0.0171118 | + | 0.0296385i | ||||
\(633\) | 906173. | + | 1.56954e6i | 0.0898881 | + | 0.155691i | ||||
\(634\) | 4.58429e6 | 0.452948 | ||||||||
\(635\) | −1.71994e6 | − | 2.97902e6i | −0.169270 | − | 0.293183i | ||||
\(636\) | −1.51851e6 | + | 2.63013e6i | −0.148859 | + | 0.257831i | ||||
\(637\) | −2.65271e7 | −2.59025 | ||||||||
\(638\) | 936056. | − | 1.62130e6i | 0.0910438 | − | 0.157692i | ||||
\(639\) | −3.76200e6 | − | 6.51598e6i | −0.364474 | − | 0.631288i | ||||
\(640\) | 1.33561e6 | + | 2.31335e6i | 0.128894 | + | 0.223250i | ||||
\(641\) | 1.24571e7 | 1.19749 | 0.598744 | − | 0.800940i | \(-0.295667\pi\) | ||||
0.598744 | + | 0.800940i | \(0.295667\pi\) | |||||||
\(642\) | −5.18319e6 | − | 8.97754e6i | −0.496317 | − | 0.859646i | ||||
\(643\) | 8.95524e6 | 0.854181 | 0.427090 | − | 0.904209i | \(-0.359539\pi\) | ||||
0.427090 | + | 0.904209i | \(0.359539\pi\) | |||||||
\(644\) | −2.38480e7 | −2.26588 | ||||||||
\(645\) | −610981. | − | 1.26730e6i | −0.0578267 | − | 0.119944i | ||||
\(646\) | 1.74525e7 | 1.64541 | ||||||||
\(647\) | −1.87092e7 | −1.75710 | −0.878548 | − | 0.477654i | \(-0.841487\pi\) | ||||
−0.878548 | + | 0.477654i | \(0.841487\pi\) | |||||||
\(648\) | 1.12033e6 | + | 1.94046e6i | 0.104811 | + | 0.181538i | ||||
\(649\) | 1.17328e6 | 0.109343 | ||||||||
\(650\) | 9.35771e6 | + | 1.62080e7i | 0.868733 | + | 1.50469i | ||||
\(651\) | −826439. | − | 1.43143e6i | −0.0764290 | − | 0.132379i | ||||
\(652\) | −1.16782e7 | + | 2.02271e7i | −1.07586 | + | 1.86344i | ||||
\(653\) | −4.64410e6 | −0.426205 | −0.213103 | − | 0.977030i | \(-0.568357\pi\) | ||||
−0.213103 | + | 0.977030i | \(0.568357\pi\) | |||||||
\(654\) | 4.72343e6 | − | 8.18123e6i | 0.431831 | − | 0.747953i | ||||
\(655\) | −1.59098e6 | − | 2.75566e6i | −0.144898 | − | 0.250970i | ||||
\(656\) | −3.12436e6 | −0.283466 | ||||||||
\(657\) | 3.66825e6 | + | 6.35359e6i | 0.331547 | + | 0.574256i | ||||
\(658\) | 2.75989e7 | − | 4.78027e7i | 2.48501 | − | 4.30416i | ||||
\(659\) | −2.95481e6 | + | 5.11789e6i | −0.265043 | + | 0.459068i | −0.967575 | − | 0.252584i | \(-0.918720\pi\) |
0.702532 | + | 0.711652i | \(0.252053\pi\) | |||||||
\(660\) | −226246. | + | 391869.i | −0.0202172 | + | 0.0350172i | ||||
\(661\) | −1.48476e7 | −1.32176 | −0.660880 | − | 0.750492i | \(-0.729817\pi\) | ||||
−0.660880 | + | 0.750492i | \(0.729817\pi\) | |||||||
\(662\) | −133132. | + | 230591.i | −0.0118069 | + | 0.0204502i | ||||
\(663\) | −2.10327e6 | + | 3.64297e6i | −0.185828 | + | 0.321864i | ||||
\(664\) | 427547. | + | 740532.i | 0.0376325 | + | 0.0651814i | ||||
\(665\) | 4.93275e6 | + | 8.54377e6i | 0.432549 | + | 0.749196i | ||||
\(666\) | 9.85288e6 | 0.860751 | ||||||||
\(667\) | 5.92936e6 | 0.516051 | ||||||||
\(668\) | 1.39331e7 | + | 2.41329e7i | 1.20811 | + | 2.09251i | ||||
\(669\) | 1.21388e6 | + | 2.10250e6i | 0.104860 | + | 0.181623i | ||||
\(670\) | 300990. | − | 521330.i | 0.0259039 | − | 0.0448669i | ||||
\(671\) | 1.74215e6 | − | 3.01749e6i | 0.149375 | − | 0.258726i | ||||
\(672\) | 1.20850e7 | 1.03234 | ||||||||
\(673\) | 1.94361e6 | − | 3.36644e6i | 0.165414 | − | 0.286505i | −0.771388 | − | 0.636365i | \(-0.780437\pi\) |
0.936802 | + | 0.349859i | \(0.113771\pi\) | |||||||
\(674\) | −1.00910e7 | + | 1.74781e7i | −0.855628 | + | 1.48199i | ||||
\(675\) | −4.14418e6 | + | 7.17793e6i | −0.350090 | + | 0.606373i | ||||
\(676\) | −4.74525e6 | − | 8.21901e6i | −0.399385 | − | 0.691755i | ||||
\(677\) | 9.17886e6 | 0.769692 | 0.384846 | − | 0.922981i | \(-0.374254\pi\) | ||||
0.384846 | + | 0.922981i | \(0.374254\pi\) | |||||||
\(678\) | 3.46113e6 | + | 5.99486e6i | 0.289164 | + | 0.500847i | ||||
\(679\) | −6.01514e6 | + | 1.04185e7i | −0.500692 | + | 0.867225i | ||||
\(680\) | −1.10793e6 | −0.0918840 | ||||||||
\(681\) | −2.41263e6 | + | 4.17880e6i | −0.199353 | + | 0.345290i | ||||
\(682\) | −446228. | − | 772890.i | −0.0367364 | − | 0.0636292i | ||||
\(683\) | 1.13160e7 | + | 1.95999e7i | 0.928198 | + | 1.60769i | 0.786335 | + | 0.617801i | \(0.211976\pi\) |
0.141864 | + | 0.989886i | \(0.454691\pi\) | |||||||
\(684\) | −2.04651e7 | −1.67253 | ||||||||
\(685\) | 1.66717e6 | + | 2.88763e6i | 0.135754 | + | 0.235134i | ||||
\(686\) | −3.35564e7 | −2.72248 | ||||||||
\(687\) | −3.54334e6 | −0.286432 | ||||||||
\(688\) | −4.43187e6 | + | 6.50647e6i | −0.356957 | + | 0.524052i | ||||
\(689\) | −8.61729e6 | −0.691548 | ||||||||
\(690\) | −2.54857e6 | −0.203786 | ||||||||
\(691\) | 4.38633e6 | + | 7.59735e6i | 0.349467 | + | 0.605295i | 0.986155 | − | 0.165827i | \(-0.0530292\pi\) |
−0.636688 | + | 0.771122i | \(0.719696\pi\) | |||||||
\(692\) | −2.33039e7 | −1.84996 | ||||||||
\(693\) | −2.12851e6 | − | 3.68668e6i | −0.168361 | − | 0.291610i | ||||
\(694\) | 1.67125e6 | + | 2.89468e6i | 0.131717 | + | 0.228140i | ||||
\(695\) | −421489. | + | 730041.i | −0.0330997 | + | 0.0573304i | ||||
\(696\) | 1.19656e6 | 0.0936296 | ||||||||
\(697\) | 1.96083e6 | − | 3.39626e6i | 0.152883 | − | 0.264801i | ||||
\(698\) | 1.28637e7 | + | 2.22806e7i | 0.999371 | + | 1.73096i | ||||
\(699\) | −4.68752e6 | −0.362869 | ||||||||
\(700\) | 1.30939e7 | + | 2.26793e7i | 1.01001 | + | 1.74938i | ||||
\(701\) | 8.14713e6 | − | 1.41113e7i | 0.626195 | − | 1.08460i | −0.362113 | − | 0.932134i | \(-0.617945\pi\) |
0.988308 | − | 0.152468i | \(-0.0487221\pi\) | |||||||
\(702\) | 9.74826e6 | − | 1.68845e7i | 0.746594 | − | 1.29314i | ||||
\(703\) | −7.25975e6 | + | 1.25743e7i | −0.554030 | + | 0.959609i | ||||
\(704\) | 4.55448e6 | 0.346343 | ||||||||
\(705\) | 1.65854e6 | − | 2.87268e6i | 0.125676 | − | 0.217678i | ||||
\(706\) | −5.51134e6 | + | 9.54593e6i | −0.416146 | + | 0.720786i | ||||
\(707\) | −5.05044e6 | − | 8.74763e6i | −0.379998 | − | 0.658176i | ||||
\(708\) | 1.69146e6 | + | 2.92969e6i | 0.126817 | + | 0.219654i | ||||
\(709\) | 1.09142e7 | 0.815407 | 0.407704 | − | 0.913114i | \(-0.366330\pi\) | ||||
0.407704 | + | 0.913114i | \(0.366330\pi\) | |||||||
\(710\) | −5.64661e6 | −0.420380 | ||||||||
\(711\) | −438229. | − | 759035.i | −0.0325108 | − | 0.0563103i | ||||
\(712\) | 2.35042e6 | + | 4.07105e6i | 0.173759 | + | 0.300959i | ||||
\(713\) | 1.41329e6 | − | 2.44790e6i | 0.104114 | − | 0.180331i | ||||
\(714\) | −5.23366e6 | + | 9.06497e6i | −0.384202 | + | 0.665458i | ||||
\(715\) | −1.28391e6 | −0.0939223 | ||||||||
\(716\) | 1.19665e7 | − | 2.07266e7i | 0.872337 | − | 1.51093i | ||||
\(717\) | −311383. | + | 539331.i | −0.0226202 | + | 0.0391794i | ||||
\(718\) | −3.95014e6 | + | 6.84185e6i | −0.285958 | + | 0.495293i | ||||
\(719\) | 708613. | + | 1.22735e6i | 0.0511195 | + | 0.0885416i | 0.890453 | − | 0.455075i | \(-0.150388\pi\) |
−0.839333 | + | 0.543617i | \(0.817054\pi\) | |||||||
\(720\) | −2.25121e6 | −0.161839 | ||||||||
\(721\) | 1.30661e7 | + | 2.26311e7i | 0.936066 | + | 1.62131i | ||||
\(722\) | 1.62293e7 | − | 2.81099e7i | 1.15866 | − | 2.00686i | ||||
\(723\) | −8.30660e6 | −0.590986 | ||||||||
\(724\) | 1.35073e7 | − | 2.33954e7i | 0.957686 | − | 1.65876i | ||||
\(725\) | −3.25556e6 | − | 5.63879e6i | −0.230028 | − | 0.398420i | ||||
\(726\) | −4.32416e6 | − | 7.48966e6i | −0.304481 | − | 0.527376i | ||||
\(727\) | −2.41036e7 | −1.69140 | −0.845698 | − | 0.533662i | \(-0.820815\pi\) | ||||
−0.845698 | + | 0.533662i | \(0.820815\pi\) | |||||||
\(728\) | −6.82769e6 | − | 1.18259e7i | −0.477469 | − | 0.827001i | ||||
\(729\) | −965092. | −0.0672589 | ||||||||
\(730\) | 5.50589e6 | 0.382402 | ||||||||
\(731\) | −4.29129e6 | − | 8.90100e6i | −0.297026 | − | 0.616092i | ||||
\(732\) | 1.00462e7 | 0.692988 | ||||||||
\(733\) | 1.52281e7 | 1.04685 | 0.523425 | − | 0.852072i | \(-0.324654\pi\) | ||||
0.523425 | + | 0.852072i | \(0.324654\pi\) | |||||||
\(734\) | −1.49667e7 | − | 2.59231e7i | −1.02538 | − | 1.77601i | ||||
\(735\) | −3.96675e6 | −0.270842 | ||||||||
\(736\) | 1.03333e7 | + | 1.78978e7i | 0.703143 | + | 1.21788i | ||||
\(737\) | −191393. | − | 331503.i | −0.0129795 | − | 0.0224812i | ||||
\(738\) | −4.08893e6 | + | 7.08223e6i | −0.276356 | + | 0.478662i | ||||
\(739\) | −5.93028e6 | −0.399452 | −0.199726 | − | 0.979852i | \(-0.564005\pi\) | ||||
−0.199726 | + | 0.979852i | \(0.564005\pi\) | |||||||
\(740\) | 2.07903e6 | − | 3.60099e6i | 0.139567 | − | 0.241737i | ||||
\(741\) | 6.46328e6 | + | 1.11947e7i | 0.432421 | + | 0.748976i | ||||
\(742\) | −2.14428e7 | −1.42979 | ||||||||
\(743\) | 7.31882e6 | + | 1.26766e7i | 0.486373 | + | 0.842422i | 0.999877 | − | 0.0156648i | \(-0.00498647\pi\) |
−0.513505 | + | 0.858087i | \(0.671653\pi\) | |||||||
\(744\) | 285208. | − | 493994.i | 0.0188899 | − | 0.0327182i | ||||
\(745\) | −4.55601e6 | + | 7.89125e6i | −0.300742 | + | 0.520901i | ||||
\(746\) | 1.52939e7 | − | 2.64898e7i | 1.00617 | − | 1.74274i | ||||
\(747\) | −2.18085e6 | −0.142996 | ||||||||
\(748\) | −1.58906e6 | + | 2.75234e6i | −0.103845 | + | 0.179865i | ||||
\(749\) | 2.05788e7 | − | 3.56435e7i | 1.34034 | − | 2.32154i | ||||
\(750\) | 2.94959e6 | + | 5.10884e6i | 0.191473 | + | 0.331641i | ||||
\(751\) | −4.87420e6 | − | 8.44236e6i | −0.315358 | − | 0.546216i | 0.664156 | − | 0.747594i | \(-0.268791\pi\) |
−0.979513 | + | 0.201379i | \(0.935458\pi\) | |||||||
\(752\) | −1.85612e7 | −1.19691 | ||||||||
\(753\) | −1.12532e7 | −0.723247 | ||||||||
\(754\) | 7.65797e6 | + | 1.32640e7i | 0.490552 | + | 0.849662i | ||||
\(755\) | 3.42590e6 | + | 5.93383e6i | 0.218729 | + | 0.378850i | ||||
\(756\) | 1.36404e7 | − | 2.36258e7i | 0.868005 | − | 1.50343i | ||||
\(757\) | 1.38728e7 | − | 2.40284e7i | 0.879884 | − | 1.52400i | 0.0284158 | − | 0.999596i | \(-0.490954\pi\) |
0.851468 | − | 0.524407i | \(-0.175713\pi\) | |||||||
\(758\) | −2.82261e6 | −0.178434 | ||||||||
\(759\) | −810292. | + | 1.40347e6i | −0.0510549 | + | 0.0884297i | ||||
\(760\) | −1.70231e6 | + | 2.94849e6i | −0.106907 | + | 0.185168i | ||||
\(761\) | −1.19538e7 | + | 2.07045e7i | −0.748243 | + | 1.29600i | 0.200421 | + | 0.979710i | \(0.435769\pi\) |
−0.948664 | + | 0.316285i | \(0.897564\pi\) | |||||||
\(762\) | −5.60773e6 | − | 9.71288e6i | −0.349864 | − | 0.605983i | ||||
\(763\) | 3.75069e7 | 2.33238 | ||||||||
\(764\) | −1.98301e7 | − | 3.43468e7i | −1.22912 | − | 2.12889i | ||||
\(765\) | 1.41285e6 | − | 2.44712e6i | 0.0872854 | − | 0.151183i | ||||
\(766\) | 3.35502e7 | 2.06597 | ||||||||
\(767\) | −4.79937e6 | + | 8.31276e6i | −0.294575 | + | 0.510219i | ||||
\(768\) | −755764. | − | 1.30902e6i | −0.0462363 | − | 0.0800837i | ||||
\(769\) | −8.58602e6 | − | 1.48714e7i | −0.523572 | − | 0.906853i | −0.999624 | − | 0.0274355i | \(-0.991266\pi\) |
0.476052 | − | 0.879417i | \(-0.342067\pi\) | |||||||
\(770\) | −3.19480e6 | −0.194186 | ||||||||
\(771\) | −1.51569e6 | − | 2.62526e6i | −0.0918280 | − | 0.159051i | ||||
\(772\) | 4.91434e6 | 0.296771 | ||||||||
\(773\) | 1.30619e7 | 0.786246 | 0.393123 | − | 0.919486i | \(-0.371395\pi\) | ||||
0.393123 | + | 0.919486i | \(0.371395\pi\) | |||||||
\(774\) | 8.94863e6 | + | 1.85613e7i | 0.536914 | + | 1.11367i | ||||
\(775\) | −3.10392e6 | −0.185633 | ||||||||
\(776\) | −4.15170e6 | −0.247498 | ||||||||
\(777\) | −4.35412e6 | − | 7.54156e6i | −0.258731 | − | 0.448135i | ||||
\(778\) | −3.23925e7 | −1.91865 | ||||||||
\(779\) | −6.02557e6 | − | 1.04366e7i | −0.355758 | − | 0.616191i | ||||
\(780\) | −1.85094e6 | − | 3.20592e6i | −0.108932 | − | 0.188676i | ||||
\(781\) | −1.79528e6 | + | 3.10952e6i | −0.105319 | + | 0.182417i | ||||
\(782\) | −1.79002e7 | −1.04674 | ||||||||
\(783\) | −3.39143e6 | + | 5.87413e6i | −0.197687 | + | 0.342404i | ||||
\(784\) | 1.10983e7 | + | 1.92228e7i | 0.644860 | + | 1.11693i | ||||
\(785\) | −3.65944e6 | −0.211953 | ||||||||
\(786\) | −5.18727e6 | − | 8.98462e6i | −0.299490 | − | 0.518732i | ||||
\(787\) | 3.10053e6 | − | 5.37028e6i | 0.178443 | − | 0.309072i | −0.762904 | − | 0.646511i | \(-0.776227\pi\) |
0.941347 | + | 0.337439i | \(0.109561\pi\) | |||||||
\(788\) | −7.15796e6 | + | 1.23979e7i | −0.410652 | + | 0.711270i | ||||
\(789\) | 3.90959e6 | − | 6.77161e6i | 0.223583 | − | 0.387257i | ||||
\(790\) | −657764. | −0.0374975 | ||||||||
\(791\) | −1.37417e7 | + | 2.38014e7i | −0.780909 | + | 1.35257i | ||||
\(792\) | 734557. | − | 1.27229e6i | 0.0416114 | − | 0.0720731i | ||||
\(793\) | 1.42527e7 | + | 2.46864e7i | 0.804849 | + | 1.39404i | ||||
\(794\) | −8.61816e6 | − | 1.49271e7i | −0.485136 | − | 0.840279i | ||||
\(795\) | −1.28859e6 | −0.0723099 | ||||||||
\(796\) | 2.21944e6 | 0.124154 | ||||||||
\(797\) | −2.86062e6 | − | 4.95474e6i | −0.159520 | − | 0.276296i | 0.775176 | − | 0.631745i | \(-0.217661\pi\) |
−0.934696 | + | 0.355449i | \(0.884328\pi\) | |||||||
\(798\) | 1.60829e7 | + | 2.78563e7i | 0.894038 | + | 1.54852i | ||||
\(799\) | 1.16490e7 | − | 2.01766e7i | 0.645536 | − | 1.11810i | ||||
\(800\) | 1.13471e7 | − | 1.96538e7i | 0.626846 | − | 1.08573i | ||||
\(801\) | −1.19892e7 | −0.660250 | ||||||||
\(802\) | 1.46645e7 | − | 2.53996e7i | 0.805065 | − | 1.39441i | ||||
\(803\) | 1.75054e6 | − | 3.03203e6i | 0.0958040 | − | 0.165937i | ||||
\(804\) | 551842. | − | 955819.i | 0.0301075 | − | 0.0521478i | ||||
\(805\) | −5.05929e6 | − | 8.76295e6i | −0.275169 | − | 0.476607i | ||||
\(806\) | 7.30127e6 | 0.395878 | ||||||||
\(807\) | 3.60862e6 | + | 6.25032e6i | 0.195055 | + | 0.337845i | ||||
\(808\) | 1.74293e6 | − | 3.01884e6i | 0.0939186 | − | 0.162672i | ||||
\(809\) | −1.44351e7 | −0.775443 | −0.387722 | − | 0.921777i | \(-0.626738\pi\) | ||||
−0.387722 | + | 0.921777i | \(0.626738\pi\) | |||||||
\(810\) | −2.14436e6 | + | 3.71413e6i | −0.114838 | + | 0.198905i | ||||
\(811\) | −3.98944e6 | − | 6.90991e6i | −0.212990 | − | 0.368910i | 0.739659 | − | 0.672982i | \(-0.234987\pi\) |
−0.952649 | + | 0.304072i | \(0.901654\pi\) | |||||||
\(812\) | 1.07155e7 | + | 1.85598e7i | 0.570326 | + | 0.987833i | ||||
\(813\) | 1.46712e7 | 0.778463 | ||||||||
\(814\) | −2.35097e6 | − | 4.07200e6i | −0.124362 | − | 0.215400i | ||||
\(815\) | −9.90998e6 | −0.522611 | ||||||||
\(816\) | 3.51982e6 | 0.185053 | ||||||||
\(817\) | −3.02814e7 | − | 2.25597e6i | −1.58716 | − | 0.118244i | ||||
\(818\) | −7.92839e6 | −0.414287 | ||||||||
\(819\) | 3.48271e7 | 1.81429 | ||||||||
\(820\) | 1.72559e6 | + | 2.98881e6i | 0.0896195 | + | 0.155226i | ||||
\(821\) | 5.98464e6 | 0.309870 | 0.154935 | − | 0.987925i | \(-0.450483\pi\) | ||||
0.154935 | + | 0.987925i | \(0.450483\pi\) | |||||||
\(822\) | 5.43569e6 | + | 9.41489e6i | 0.280592 | + | 0.485999i | ||||
\(823\) | 6.67346e6 | + | 1.15588e7i | 0.343440 | + | 0.594856i | 0.985069 | − | 0.172159i | \(-0.0550743\pi\) |
−0.641629 | + | 0.767015i | \(0.721741\pi\) | |||||||
\(824\) | −4.50916e6 | + | 7.81009e6i | −0.231354 | + | 0.400717i | ||||
\(825\) | 1.77959e6 | 0.0910300 | ||||||||
\(826\) | −1.19425e7 | + | 2.06850e7i | −0.609039 | + | 1.05489i | ||||
\(827\) | 476273. | + | 824930.i | 0.0242154 | + | 0.0419424i | 0.877879 | − | 0.478882i | \(-0.158958\pi\) |
−0.853664 | + | 0.520825i | \(0.825625\pi\) | |||||||
\(828\) | 2.09901e7 | 1.06399 | ||||||||
\(829\) | −1.17498e7 | − | 2.03513e7i | −0.593806 | − | 1.02850i | −0.993714 | − | 0.111947i | \(-0.964291\pi\) |
0.399908 | − | 0.916555i | \(-0.369042\pi\) | |||||||
\(830\) | −818344. | + | 1.41741e6i | −0.0412326 | + | 0.0714169i | ||||
\(831\) | −2.03869e6 | + | 3.53112e6i | −0.102412 | + | 0.177382i | ||||
\(832\) | −1.86303e7 | + | 3.22687e7i | −0.933065 | + | 1.61612i | ||||
\(833\) | −2.78609e7 | −1.39118 | ||||||||
\(834\) | −1.37423e6 | + | 2.38024e6i | −0.0684141 | + | 0.118497i | ||||
\(835\) | −5.91177e6 | + | 1.02395e7i | −0.293428 | + | 0.508232i | ||||
\(836\) | 4.88313e6 | + | 8.45783e6i | 0.241648 | + | 0.418546i | ||||
\(837\) | 1.61673e6 | + | 2.80026e6i | 0.0797672 | + | 0.138161i | ||||
\(838\) | −1.93903e6 | −0.0953836 | ||||||||
\(839\) | −2.92562e7 | −1.43487 | −0.717435 | − | 0.696626i | \(-0.754684\pi\) | ||||
−0.717435 | + | 0.696626i | \(0.754684\pi\) | |||||||
\(840\) | −1.02098e6 | − | 1.76839e6i | −0.0499253 | − | 0.0864731i | ||||
\(841\) | 7.59136e6 | + | 1.31486e7i | 0.370109 | + | 0.641047i | ||||
\(842\) | −1.07372e7 | + | 1.85973e7i | −0.521927 | + | 0.904005i | ||||
\(843\) | 1.10898e6 | − | 1.92081e6i | 0.0537470 | − | 0.0930925i | ||||
\(844\) | −1.12021e7 | −0.541306 | ||||||||
\(845\) | 2.01339e6 | − | 3.48729e6i | 0.0970031 | − | 0.168014i | ||||
\(846\) | −2.42916e7 | + | 4.20743e7i | −1.16689 | + | 2.02111i | ||||
\(847\) | 1.71682e7 | − | 2.97362e7i | 0.822273 | − | 1.42422i | ||||
\(848\) | 3.60525e6 | + | 6.24448e6i | 0.172166 | + | 0.298200i | ||||
\(849\) | 405193. | 0.0192927 | ||||||||
\(850\) | 9.82823e6 | + | 1.70230e7i | 0.466582 | + | 0.808143i | ||||
\(851\) | 7.44599e6 | − | 1.28968e7i | 0.352451 | − | 0.610463i | ||||
\(852\) | −1.03526e7 | −0.488598 | ||||||||
\(853\) | −1.37979e6 | + | 2.38986e6i | −0.0649291 | + | 0.112461i | −0.896663 | − | 0.442715i | \(-0.854015\pi\) |
0.831733 | + | 0.555175i | \(0.187349\pi\) | |||||||
\(854\) | 3.54656e7 | + | 6.14283e7i | 1.66404 | + | 2.88220i | ||||
\(855\) | −4.34163e6 | − | 7.51993e6i | −0.203113 | − | 0.351802i | ||||
\(856\) | 1.42037e7 | 0.662546 | ||||||||
\(857\) | 1.68086e7 | + | 2.91133e7i | 0.781770 | + | 1.35406i | 0.930910 | + | 0.365249i | \(0.119016\pi\) |
−0.149140 | + | 0.988816i | \(0.547651\pi\) | |||||||
\(858\) | −4.18608e6 | −0.194129 | ||||||||
\(859\) | 3.26569e7 | 1.51005 | 0.755027 | − | 0.655694i | \(-0.227624\pi\) | ||||
0.755027 | + | 0.655694i | \(0.227624\pi\) | |||||||
\(860\) | 8.67193e6 | + | 646060.i | 0.399825 | + | 0.0297870i | ||||
\(861\) | 7.22781e6 | 0.332276 | ||||||||
\(862\) | −3.42067e7 | −1.56799 | ||||||||
\(863\) | 932357. | + | 1.61489e6i | 0.0426143 | + | 0.0738101i | 0.886546 | − | 0.462641i | \(-0.153098\pi\) |
−0.843932 | + | 0.536451i | \(0.819765\pi\) | |||||||
\(864\) | −2.36414e7 | −1.07743 | ||||||||
\(865\) | −4.94387e6 | − | 8.56304e6i | −0.224661 | − | 0.389124i | ||||
\(866\) | −1.38342e7 | − | 2.39615e7i | −0.626842 | − | 1.08572i | ||||
\(867\) | 2.51319e6 | − | 4.35298e6i | 0.113548 | − | 0.196670i | ||||
\(868\) | 1.02164e7 | 0.460255 | ||||||||
\(869\) | −209129. | + | 362223.i | −0.00939433 | + | 0.0162715i | ||||
\(870\) | 1.14514e6 | + | 1.98344e6i | 0.0512933 | + | 0.0888426i | ||||
\(871\) | 3.13162e6 | 0.139870 | ||||||||
\(872\) | 6.47189e6 | + | 1.12096e7i | 0.288231 | + | 0.499230i | ||||
\(873\) | 5.29431e6 | − | 9.17001e6i | 0.235111 | − | 0.407225i | ||||
\(874\) | −2.75033e7 | + | 4.76371e7i | −1.21789 | + | 2.10944i | ||||
\(875\) | −1.17107e7 | + | 2.02836e7i | −0.517088 | + | 0.895622i | ||||
\(876\) | 1.00946e7 | 0.444458 | ||||||||
\(877\) | 1.35888e7 | − | 2.35365e7i | 0.596598 | − | 1.03334i | −0.396721 | − | 0.917939i | \(-0.629852\pi\) |
0.993319 | − | 0.115400i | \(-0.0368148\pi\) | |||||||
\(878\) | 1.26338e7 | − | 2.18824e7i | 0.553092 | − | 0.957983i | ||||
\(879\) | −7.52359e6 | − | 1.30312e7i | −0.328438 | − | 0.568871i | ||||
\(880\) | 537155. | + | 930379.i | 0.0233826 | + | 0.0404998i | ||||
\(881\) | 2.11121e7 | 0.916413 | 0.458207 | − | 0.888846i | \(-0.348492\pi\) | ||||
0.458207 | + | 0.888846i | \(0.348492\pi\) | |||||||
\(882\) | 5.80984e7 | 2.51474 | ||||||||
\(883\) | 4.30707e6 | + | 7.46006e6i | 0.185900 | + | 0.321989i | 0.943879 | − | 0.330290i | \(-0.107147\pi\) |
−0.757979 | + | 0.652279i | \(0.773813\pi\) | |||||||
\(884\) | −1.30003e7 | − | 2.25171e7i | −0.559528 | − | 0.969131i | ||||
\(885\) | −717678. | + | 1.24305e6i | −0.0308015 | + | 0.0533497i | ||||
\(886\) | −4.95037e6 | + | 8.57429e6i | −0.211862 | + | 0.366956i | ||||
\(887\) | −1.14097e7 | −0.486929 | −0.243464 | − | 0.969910i | \(-0.578284\pi\) | ||||
−0.243464 | + | 0.969910i | \(0.578284\pi\) | |||||||
\(888\) | 1.50263e6 | − | 2.60263e6i | 0.0639468 | − | 0.110759i | ||||
\(889\) | 2.22644e7 | − | 3.85630e7i | 0.944835 | − | 1.63650i | ||||
\(890\) | −4.49882e6 | + | 7.79219e6i | −0.190381 | + | 0.329750i | ||||
\(891\) | 1.36355e6 | + | 2.36174e6i | 0.0575410 | + | 0.0996640i | ||||
\(892\) | −1.50060e7 | −0.631468 | ||||||||
\(893\) | −3.57968e7 | − | 6.20019e7i | −1.50216 | − | 2.60182i | ||||
\(894\) | −1.48545e7 | + | 2.57288e7i | −0.621606 | + | 1.07665i | ||||
\(895\) | 1.01547e7 | 0.423748 | ||||||||
\(896\) | −1.72893e7 | + | 2.99460e7i | −0.719462 | + | 1.24615i | ||||
\(897\) | −6.62908e6 | − | 1.14819e7i | −0.275088 | − | 0.476467i | ||||
\(898\) | −2.71093e7 | − | 4.69548e7i | −1.12183 | − | 1.94307i | ||||
\(899\) | −2.54012e6 | −0.104823 | ||||||||
\(900\) | −1.15248e7 | − | 1.99615e7i | −0.474271 | − | 0.821461i | ||||
\(901\) | −9.05057e6 | −0.371419 | ||||||||
\(902\) | 3.90259e6 | 0.159712 | ||||||||
\(903\) | 1.02526e7 | − | 1.50519e7i | 0.418422 | − | 0.614289i | ||||
\(904\) | −9.48466e6 | −0.386012 | ||||||||
\(905\) | 1.14622e7 | 0.465207 | ||||||||
\(906\) | 1.11699e7 | + | 1.93468e7i | 0.452093 | + | 0.783049i | ||||
\(907\) | −1.32088e7 | −0.533146 | −0.266573 | − | 0.963815i | \(-0.585891\pi\) | ||||
−0.266573 | + | 0.963815i | \(0.585891\pi\) | |||||||
\(908\) | −1.49124e7 | − | 2.58291e7i | −0.600252 | − | 1.03967i | ||||
\(909\) | 4.44522e6 | + | 7.69935e6i | 0.178437 | + | 0.309061i | ||||
\(910\) | 1.30685e7 | − | 2.26353e7i | 0.523146 | − | 0.906115i | ||||
\(911\) | 2.85541e7 | 1.13991 | 0.569957 | − | 0.821675i | \(-0.306960\pi\) | ||||
0.569957 | + | 0.821675i | \(0.306960\pi\) | |||||||
\(912\) | 5.40814e6 | − | 9.36718e6i | 0.215308 | − | 0.372925i | ||||
\(913\) | 520368. | + | 901304.i | 0.0206602 | + | 0.0357845i | ||||
\(914\) | 2.66183e7 | 1.05394 | ||||||||
\(915\) | 2.13129e6 | + | 3.69150e6i | 0.0841568 | + | 0.145764i | ||||
\(916\) | 1.09507e7 | − | 1.89671e7i | 0.431223 | − | 0.746900i | ||||
\(917\) | 2.05950e7 | − | 3.56716e7i | 0.808796 | − | 1.40088i | ||||
\(918\) | 1.02384e7 | − | 1.77335e7i | 0.400983 | − | 0.694523i | ||||
\(919\) | −2.26646e7 | −0.885236 | −0.442618 | − | 0.896710i | \(-0.645950\pi\) | ||||
−0.442618 | + | 0.896710i | \(0.645950\pi\) | |||||||
\(920\) | 1.74598e6 | − | 3.02413e6i | 0.0680097 | − | 0.117796i | ||||
\(921\) | 3.71023e6 | − | 6.42632e6i | 0.144129 | − | 0.249639i | ||||
\(922\) | −2.36401e7 | − | 4.09458e7i | −0.915844 | − | 1.58629i | ||||
\(923\) | −1.46874e7 | − | 2.54393e7i | −0.567467 | − | 0.982881i | ||||
\(924\) | −5.85743e6 | −0.225698 | ||||||||
\(925\) | −1.63531e7 | −0.628414 | ||||||||
\(926\) | 2.24850e7 | + | 3.89452e7i | 0.861719 | + | 1.49254i | ||||
\(927\) | −1.15003e7 | − | 1.99191e7i | −0.439551 | − | 0.761325i | ||||
\(928\) | 9.28603e6 | − | 1.60839e7i | 0.353965 | − | 0.613085i | ||||
\(929\) | −1.35278e7 | + | 2.34308e7i | −0.514266 | + | 0.890734i | 0.485597 | + | 0.874183i | \(0.338602\pi\) |
−0.999863 | + | 0.0165516i | \(0.994731\pi\) | |||||||
\(930\) | 1.09180e6 | 0.0413939 | ||||||||
\(931\) | −4.28078e7 | + | 7.41453e7i | −1.61863 | + | 2.80356i | ||||
\(932\) | 1.44867e7 | − | 2.50918e7i | 0.546299 | − | 0.946218i | ||||
\(933\) | −2.41251e6 | + | 4.17860e6i | −0.0907331 | + | 0.157154i | ||||
\(934\) | −4.25271e6 | − | 7.36592e6i | −0.159514 | − | 0.276287i | ||||
\(935\) | −1.34846e6 | −0.0504441 | ||||||||
\(936\) | 6.00949e6 | + | 1.04087e7i | 0.224206 | + | 0.388337i | ||||
\(937\) | −2.49303e7 | + | 4.31805e7i | −0.927637 | + | 1.60671i | −0.140373 | + | 0.990099i | \(0.544830\pi\) |
−0.787264 | + | 0.616616i | \(0.788503\pi\) | |||||||
\(938\) | 7.79254e6 | 0.289183 | ||||||||
\(939\) | −3.01752e6 | + | 5.22650e6i | −0.111683 | + | 0.193440i | ||||
\(940\) | 1.02514e7 | + | 1.77560e7i | 0.378411 | + | 0.655428i | ||||
\(941\) | 3.17666e6 | + | 5.50214e6i | 0.116949 | + | 0.202562i | 0.918557 | − | 0.395288i | \(-0.129355\pi\) |
−0.801608 | + | 0.597850i | \(0.796022\pi\) | |||||||
\(942\) | −1.19313e7 | −0.438088 | ||||||||
\(943\) | 6.18015e6 | + | 1.07043e7i | 0.226318 | + | 0.391995i | ||||
\(944\) | 8.03175e6 | 0.293346 | ||||||||
\(945\) | 1.15751e7 | 0.421644 | ||||||||
\(946\) | 5.53580e6 | − | 8.12715e6i | 0.201119 | − | 0.295264i | ||||
\(947\) | −8.27044e6 | −0.299677 | −0.149839 | − | 0.988710i | \(-0.547875\pi\) | ||||
−0.149839 | + | 0.988710i | \(0.547875\pi\) | |||||||
\(948\) | −1.20596e6 | −0.0435825 | ||||||||
\(949\) | 1.43214e7 | + | 2.48053e7i | 0.516201 | + | 0.894086i | ||||
\(950\) | 6.04036e7 | 2.17147 | ||||||||
\(951\) | 1.78309e6 | + | 3.08840e6i | 0.0639325 | + | 0.110734i | ||||
\(952\) | −7.17099e6 | − | 1.24205e7i | −0.256441 | − | 0.444168i | ||||
\(953\) | 4.93718e6 | − | 8.55145e6i | 0.176095 | − | 0.305005i | −0.764445 | − | 0.644689i | \(-0.776987\pi\) |
0.940540 | + | 0.339684i | \(0.110320\pi\) | |||||||
\(954\) | 1.88732e7 | 0.671388 | ||||||||
\(955\) | 8.41385e6 | − | 1.45732e7i | 0.298529 | − | 0.517067i | ||||
\(956\) | −1.92465e6 | − | 3.33360e6i | −0.0681095 | − | 0.117969i | ||||
\(957\) | 1.45634e6 | 0.0514024 | ||||||||
\(958\) | −1.44936e7 | − | 2.51036e7i | −0.510224 | − | 0.883734i | ||||
\(959\) | −2.15813e7 | + | 3.73799e7i | −0.757759 | + | 1.31248i | ||||
\(960\) | −2.78590e6 | + | 4.82532e6i | −0.0975634 | + | 0.168985i | ||||
\(961\) | 1.37091e7 | − | 2.37449e7i | 0.478852 | − | 0.829396i | ||||
\(962\) | 3.84670e7 | 1.34014 | ||||||||
\(963\) | −1.81127e7 | + | 3.13721e7i | −0.629387 | + | 1.09013i | ||||
\(964\) | 2.56715e7 | − | 4.44643e7i | 0.889729 | − | 1.54106i | ||||
\(965\) | 1.04257e6 | + | 1.80578e6i | 0.0360400 | + | 0.0624232i | ||||
\(966\) | −1.64954e7 | − | 2.85709e7i | −0.568750 | − | 0.985103i | ||||
\(967\) | 1.48445e7 | 0.510504 | 0.255252 | − | 0.966875i | \(-0.417842\pi\) | ||||
0.255252 | + | 0.966875i | \(0.417842\pi\) | |||||||
\(968\) | 1.18496e7 | 0.406459 | ||||||||
\(969\) | 6.78826e6 | + | 1.17576e7i | 0.232246 | + | 0.402262i | ||||
\(970\) | −3.97327e6 | − | 6.88191e6i | −0.135587 | − | 0.234844i | ||||
\(971\) | 5.25576e6 | − | 9.10324e6i | 0.178890 | − | 0.309847i | −0.762610 | − | 0.646858i | \(-0.776083\pi\) |
0.941501 | + | 0.337011i | \(0.109416\pi\) | |||||||
\(972\) | −1.86099e7 | + | 3.22333e7i | −0.631798 | + | 1.09431i | ||||
\(973\) | −1.09122e7 | −0.369514 | ||||||||
\(974\) | −4.30808e7 | + | 7.46182e7i | −1.45508 | + | 2.52027i | ||||
\(975\) | −7.27949e6 | + | 1.26085e7i | −0.245239 | + | 0.424766i | ||||
\(976\) | 1.19259e7 | − | 2.06563e7i | 0.400745 | − | 0.694111i | ||||
\(977\) | 1.52382e7 | + | 2.63933e7i | 0.510737 | + | 0.884622i | 0.999923 | + | 0.0124425i | \(0.00396068\pi\) |
−0.489186 | + | 0.872180i | \(0.662706\pi\) | |||||||
\(978\) | −3.23107e7 | −1.08019 | ||||||||
\(979\) | 2.86071e6 | + | 4.95489e6i | 0.0953931 | + | 0.165226i | ||||
\(980\) | 1.22592e7 | − | 2.12336e7i | 0.407753 | − | 0.706249i | ||||
\(981\) | −3.30122e7 | −1.09522 | ||||||||
\(982\) | 2.48515e6 | − | 4.30441e6i | 0.0822384 | − | 0.142441i | ||||
\(983\) | 3.99325e6 | + | 6.91650e6i | 0.131808 | + | 0.228298i | 0.924374 | − | 0.381488i | \(-0.124588\pi\) |
−0.792565 | + | 0.609787i | \(0.791255\pi\) | |||||||
\(984\) | 1.24718e6 | + | 2.16017e6i | 0.0410620 | + | 0.0711214i | ||||
\(985\) | −6.07418e6 | −0.199479 | ||||||||
\(986\) | 8.04302e6 | + | 1.39309e7i | 0.263467 | + | 0.456339i | ||||
\(987\) | 4.29392e7 | 1.40301 | ||||||||
\(988\) | −7.98988e7 | −2.60404 | ||||||||
\(989\) | 3.10583e7 | + | 2.31385e6i | 1.00969 | + | 0.0752218i | ||||
\(990\) | 2.81195e6 | 0.0911843 | ||||||||
\(991\) | 3.20123e7 | 1.03546 | 0.517729 | − | 0.855545i | \(-0.326778\pi\) | ||||
0.517729 | + | 0.855545i | \(0.326778\pi\) | |||||||
\(992\) | −4.42675e6 | − | 7.66736e6i | −0.142826 | − | 0.247381i | ||||
\(993\) | −207130. | −0.00666608 | ||||||||
\(994\) | −3.65473e7 | − | 6.33018e7i | −1.17325 | − | 2.03212i | ||||
\(995\) | 470850. | + | 815536.i | 0.0150773 | + | 0.0261147i | ||||
\(996\) | −1.50037e6 | + | 2.59872e6i | −0.0479237 | + | 0.0830063i | ||||
\(997\) | −2.48126e7 | −0.790558 | −0.395279 | − | 0.918561i | \(-0.629352\pi\) | ||||
−0.395279 | + | 0.918561i | \(0.629352\pi\) | |||||||
\(998\) | −2.02256e7 | + | 3.50318e7i | −0.642800 | + | 1.11336i | ||||
\(999\) | 8.51781e6 | + | 1.47533e7i | 0.270031 | + | 0.467708i |
(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.36.3 | yes | 34 | |
43.6 | even | 3 | inner | 43.6.c.a.6.3 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.3 | ✓ | 34 | 43.6 | even | 3 | inner | |
43.6.c.a.36.3 | yes | 34 | 1.1 | even | 1 | trivial |