Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,5,Mod(19,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.96175822802\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.16 | ||
Character | \(\chi\) | \(=\) | 48.43 |
Dual form | 48.5.l.a.19.16 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.90016 | − | 0.888110i | 0.975040 | − | 0.222027i | ||||
\(3\) | 3.67423 | + | 3.67423i | 0.408248 | + | 0.408248i | ||||
\(4\) | 14.4225 | − | 6.92754i | 0.901408 | − | 0.432971i | ||||
\(5\) | −17.3646 | − | 17.3646i | −0.694586 | − | 0.694586i | 0.268652 | − | 0.963237i | \(-0.413422\pi\) |
−0.963237 | + | 0.268652i | \(0.913422\pi\) | |||||||
\(6\) | 17.5932 | + | 11.0670i | 0.488701 | + | 0.307416i | ||||
\(7\) | 89.8255 | 1.83317 | 0.916587 | − | 0.399836i | \(-0.130933\pi\) | ||||
0.916587 | + | 0.399836i | \(0.130933\pi\) | |||||||
\(8\) | 50.0978 | − | 39.8273i | 0.782777 | − | 0.622302i | ||||
\(9\) | 27.0000i | 0.333333i | ||||||||
\(10\) | −83.1466 | − | 52.3032i | −0.831466 | − | 0.523032i | ||||
\(11\) | −94.2659 | + | 94.2659i | −0.779057 | + | 0.779057i | −0.979670 | − | 0.200613i | \(-0.935706\pi\) |
0.200613 | + | 0.979670i | \(0.435706\pi\) | |||||||
\(12\) | 78.4451 | + | 27.5383i | 0.544758 | + | 0.191238i | ||||
\(13\) | −100.821 | + | 100.821i | −0.596573 | + | 0.596573i | −0.939399 | − | 0.342826i | \(-0.888616\pi\) |
0.342826 | + | 0.939399i | \(0.388616\pi\) | |||||||
\(14\) | 350.334 | − | 79.7749i | 1.78742 | − | 0.407015i | ||||
\(15\) | − | 127.604i | − | 0.567127i | ||||||
\(16\) | 160.018 | − | 199.825i | 0.625072 | − | 0.780567i | ||||
\(17\) | −66.1361 | −0.228845 | −0.114422 | − | 0.993432i | \(-0.536502\pi\) | ||||
−0.114422 | + | 0.993432i | \(0.536502\pi\) | |||||||
\(18\) | 23.9790 | + | 105.304i | 0.0740091 | + | 0.325013i | ||||
\(19\) | −324.678 | − | 324.678i | −0.899384 | − | 0.899384i | 0.0959975 | − | 0.995382i | \(-0.469396\pi\) |
−0.995382 | + | 0.0959975i | \(0.969396\pi\) | |||||||
\(20\) | −370.736 | − | 130.148i | −0.926841 | − | 0.325369i | ||||
\(21\) | 330.040 | + | 330.040i | 0.748390 | + | 0.748390i | ||||
\(22\) | −283.934 | + | 451.371i | −0.586640 | + | 0.932584i | ||||
\(23\) | −467.308 | −0.883381 | −0.441690 | − | 0.897168i | \(-0.645621\pi\) | ||||
−0.441690 | + | 0.897168i | \(0.645621\pi\) | |||||||
\(24\) | 330.406 | + | 37.7360i | 0.573621 | + | 0.0655139i | ||||
\(25\) | − | 21.9384i | − | 0.0351015i | ||||||
\(26\) | −303.678 | + | 482.757i | −0.449227 | + | 0.714138i | ||||
\(27\) | −99.2043 | + | 99.2043i | −0.136083 | + | 0.136083i | ||||
\(28\) | 1295.51 | − | 622.270i | 1.65244 | − | 0.793712i | ||||
\(29\) | −321.838 | + | 321.838i | −0.382685 | + | 0.382685i | −0.872069 | − | 0.489384i | \(-0.837222\pi\) |
0.489384 | + | 0.872069i | \(0.337222\pi\) | |||||||
\(30\) | −113.326 | − | 497.674i | −0.125918 | − | 0.552972i | ||||
\(31\) | 1587.33i | 1.65175i | 0.563852 | + | 0.825876i | \(0.309319\pi\) | ||||
−0.563852 | + | 0.825876i | \(0.690681\pi\) | |||||||
\(32\) | 446.631 | − | 921.465i | 0.436163 | − | 0.899868i | ||||
\(33\) | −692.710 | −0.636097 | ||||||||
\(34\) | −257.942 | + | 58.7361i | −0.223133 | + | 0.0508098i | ||||
\(35\) | −1559.79 | − | 1559.79i | −1.27330 | − | 1.27330i | ||||
\(36\) | 187.044 | + | 389.408i | 0.144324 | + | 0.300469i | ||||
\(37\) | 982.813 | + | 982.813i | 0.717906 | + | 0.717906i | 0.968176 | − | 0.250270i | \(-0.0805195\pi\) |
−0.250270 | + | 0.968176i | \(0.580520\pi\) | |||||||
\(38\) | −1554.64 | − | 977.946i | −1.07662 | − | 0.677248i | ||||
\(39\) | −740.879 | −0.487100 | ||||||||
\(40\) | −1561.52 | − | 178.343i | −0.975948 | − | 0.111464i | ||||
\(41\) | 1217.57i | 0.724314i | 0.932117 | + | 0.362157i | \(0.117960\pi\) | ||||
−0.932117 | + | 0.362157i | \(0.882040\pi\) | |||||||
\(42\) | 1580.32 | + | 994.098i | 0.895874 | + | 0.563547i | ||||
\(43\) | 1303.65 | − | 1303.65i | 0.705056 | − | 0.705056i | −0.260435 | − | 0.965491i | \(-0.583866\pi\) |
0.965491 | + | 0.260435i | \(0.0838661\pi\) | |||||||
\(44\) | −706.521 | + | 2012.58i | −0.364939 | + | 1.03956i | ||||
\(45\) | 468.845 | − | 468.845i | 0.231529 | − | 0.231529i | ||||
\(46\) | −1822.58 | + | 415.021i | −0.861332 | + | 0.196135i | ||||
\(47\) | − | 3979.92i | − | 1.80168i | −0.434147 | − | 0.900842i | \(-0.642950\pi\) | ||
0.434147 | − | 0.900842i | \(-0.357050\pi\) | |||||||
\(48\) | 1322.15 | − | 146.260i | 0.573850 | − | 0.0634809i | ||||
\(49\) | 5667.62 | 2.36053 | ||||||||
\(50\) | −19.4837 | − | 85.5634i | −0.00779349 | − | 0.0342254i | ||||
\(51\) | −243.000 | − | 243.000i | −0.0934255 | − | 0.0934255i | ||||
\(52\) | −755.650 | + | 2152.53i | −0.279456 | + | 0.796054i | ||||
\(53\) | 672.674 | + | 672.674i | 0.239471 | + | 0.239471i | 0.816631 | − | 0.577160i | \(-0.195839\pi\) |
−0.577160 | + | 0.816631i | \(0.695839\pi\) | |||||||
\(54\) | −298.809 | + | 475.017i | −0.102472 | + | 0.162900i | ||||
\(55\) | 3273.79 | 1.08224 | ||||||||
\(56\) | 4500.06 | − | 3577.51i | 1.43497 | − | 1.14079i | ||||
\(57\) | − | 2385.88i | − | 0.734344i | ||||||
\(58\) | −969.392 | + | 1541.05i | −0.288167 | + | 0.458100i | ||||
\(59\) | −1188.14 | + | 1188.14i | −0.341323 | + | 0.341323i | −0.856864 | − | 0.515542i | \(-0.827591\pi\) |
0.515542 | + | 0.856864i | \(0.327591\pi\) | |||||||
\(60\) | −883.979 | − | 1840.36i | −0.245550 | − | 0.511212i | ||||
\(61\) | −979.221 | + | 979.221i | −0.263161 | + | 0.263161i | −0.826337 | − | 0.563176i | \(-0.809579\pi\) |
0.563176 | + | 0.826337i | \(0.309579\pi\) | |||||||
\(62\) | 1409.73 | + | 6190.86i | 0.366734 | + | 1.61052i | ||||
\(63\) | 2425.29i | 0.611058i | ||||||||
\(64\) | 923.570 | − | 3990.52i | 0.225481 | − | 0.974248i | ||||
\(65\) | 3501.43 | 0.828742 | ||||||||
\(66\) | −2701.68 | + | 615.202i | −0.620221 | + | 0.141231i | ||||
\(67\) | −2267.04 | − | 2267.04i | −0.505021 | − | 0.505021i | 0.407973 | − | 0.912994i | \(-0.366236\pi\) |
−0.912994 | + | 0.407973i | \(0.866236\pi\) | |||||||
\(68\) | −953.850 | + | 458.161i | −0.206282 | + | 0.0990832i | ||||
\(69\) | −1717.00 | − | 1717.00i | −0.360639 | − | 0.360639i | ||||
\(70\) | −7468.69 | − | 4698.16i | −1.52422 | − | 0.958809i | ||||
\(71\) | 5875.26 | 1.16550 | 0.582748 | − | 0.812653i | \(-0.301978\pi\) | ||||
0.582748 | + | 0.812653i | \(0.301978\pi\) | |||||||
\(72\) | 1075.34 | + | 1352.64i | 0.207434 | + | 0.260926i | ||||
\(73\) | − | 3661.25i | − | 0.687043i | −0.939145 | − | 0.343521i | \(-0.888380\pi\) | ||
0.939145 | − | 0.343521i | \(-0.111620\pi\) | |||||||
\(74\) | 4705.97 | + | 2960.28i | 0.859382 | + | 0.540592i | ||||
\(75\) | 80.6069 | − | 80.6069i | 0.0143301 | − | 0.0143301i | ||||
\(76\) | −6931.89 | − | 2433.45i | −1.20012 | − | 0.421304i | ||||
\(77\) | −8467.48 | + | 8467.48i | −1.42815 | + | 1.42815i | ||||
\(78\) | −2889.55 | + | 657.981i | −0.474942 | + | 0.108149i | ||||
\(79\) | 539.165i | 0.0863908i | 0.999067 | + | 0.0431954i | \(0.0137538\pi\) | ||||
−0.999067 | + | 0.0431954i | \(0.986246\pi\) | |||||||
\(80\) | −6248.56 | + | 691.233i | −0.976337 | + | 0.108005i | ||||
\(81\) | −729.000 | −0.111111 | ||||||||
\(82\) | 1081.34 | + | 4748.73i | 0.160818 | + | 0.706235i | ||||
\(83\) | −3607.17 | − | 3607.17i | −0.523612 | − | 0.523612i | 0.395048 | − | 0.918660i | \(-0.370728\pi\) |
−0.918660 | + | 0.395048i | \(0.870728\pi\) | |||||||
\(84\) | 7046.38 | + | 2473.64i | 0.998636 | + | 0.350573i | ||||
\(85\) | 1148.43 | + | 1148.43i | 0.158952 | + | 0.158952i | ||||
\(86\) | 3926.66 | − | 6242.22i | 0.530916 | − | 0.844000i | ||||
\(87\) | −2365.02 | −0.312461 | ||||||||
\(88\) | −968.153 | + | 8476.87i | −0.125020 | + | 1.09464i | ||||
\(89\) | − | 7549.35i | − | 0.953081i | −0.879153 | − | 0.476540i | \(-0.841891\pi\) | ||
0.879153 | − | 0.476540i | \(-0.158109\pi\) | |||||||
\(90\) | 1412.19 | − | 2244.96i | 0.174344 | − | 0.277155i | ||||
\(91\) | −9056.28 | + | 9056.28i | −1.09362 | + | 1.09362i | ||||
\(92\) | −6739.77 | + | 3237.30i | −0.796286 | + | 0.382479i | ||||
\(93\) | −5832.23 | + | 5832.23i | −0.674325 | + | 0.674325i | ||||
\(94\) | −3534.60 | − | 15522.3i | −0.400023 | − | 1.75671i | ||||
\(95\) | 11275.8i | 1.24940i | ||||||||
\(96\) | 5026.70 | − | 1744.65i | 0.545432 | − | 0.189307i | ||||
\(97\) | −9595.79 | −1.01985 | −0.509926 | − | 0.860218i | \(-0.670327\pi\) | ||||
−0.509926 | + | 0.860218i | \(0.670327\pi\) | |||||||
\(98\) | 22104.6 | − | 5033.47i | 2.30161 | − | 0.524101i | ||||
\(99\) | −2545.18 | − | 2545.18i | −0.259686 | − | 0.259686i | ||||
\(100\) | −151.979 | − | 316.408i | −0.0151979 | − | 0.0316408i | ||||
\(101\) | 2342.75 | + | 2342.75i | 0.229659 | + | 0.229659i | 0.812550 | − | 0.582891i | \(-0.198079\pi\) |
−0.582891 | + | 0.812550i | \(0.698079\pi\) | |||||||
\(102\) | −1163.55 | − | 731.928i | −0.111837 | − | 0.0703506i | ||||
\(103\) | 13654.1 | 1.28703 | 0.643513 | − | 0.765435i | \(-0.277476\pi\) | ||||
0.643513 | + | 0.765435i | \(0.277476\pi\) | |||||||
\(104\) | −1035.47 | + | 9066.32i | −0.0957354 | + | 0.838232i | ||||
\(105\) | − | 11462.1i | − | 1.03964i | ||||||
\(106\) | 3220.94 | + | 2026.13i | 0.286663 | + | 0.180325i | ||||
\(107\) | 10621.9 | − | 10621.9i | 0.927761 | − | 0.927761i | −0.0698004 | − | 0.997561i | \(-0.522236\pi\) |
0.997561 | + | 0.0698004i | \(0.0222362\pi\) | |||||||
\(108\) | −743.535 | + | 2118.02i | −0.0637461 | + | 0.181586i | ||||
\(109\) | 6098.45 | − | 6098.45i | 0.513294 | − | 0.513294i | −0.402240 | − | 0.915534i | \(-0.631768\pi\) |
0.915534 | + | 0.402240i | \(0.131768\pi\) | |||||||
\(110\) | 12768.3 | − | 2907.48i | 1.05523 | − | 0.240288i | ||||
\(111\) | 7222.17i | 0.586168i | ||||||||
\(112\) | 14373.7 | − | 17949.4i | 1.14586 | − | 1.43092i | ||||
\(113\) | 2094.31 | 0.164015 | 0.0820075 | − | 0.996632i | \(-0.473867\pi\) | ||||
0.0820075 | + | 0.996632i | \(0.473867\pi\) | |||||||
\(114\) | −2118.93 | − | 9305.33i | −0.163044 | − | 0.716015i | ||||
\(115\) | 8114.64 | + | 8114.64i | 0.613584 | + | 0.613584i | ||||
\(116\) | −2412.17 | + | 6871.26i | −0.179263 | + | 0.510646i | ||||
\(117\) | −2722.16 | − | 2722.16i | −0.198858 | − | 0.198858i | ||||
\(118\) | −3578.75 | + | 5689.16i | −0.257020 | + | 0.408586i | ||||
\(119\) | −5940.71 | −0.419512 | ||||||||
\(120\) | −5082.11 | − | 6392.65i | −0.352924 | − | 0.443934i | ||||
\(121\) | − | 3131.12i | − | 0.213860i | ||||||
\(122\) | −2949.47 | + | 4688.78i | −0.198164 | + | 0.315021i | ||||
\(123\) | −4473.64 | + | 4473.64i | −0.295700 | + | 0.295700i | ||||
\(124\) | 10996.3 | + | 22893.4i | 0.715161 | + | 1.48890i | ||||
\(125\) | −11233.9 | + | 11233.9i | −0.718967 | + | 0.718967i | ||||
\(126\) | 2153.92 | + | 9459.02i | 0.135672 | + | 0.595806i | ||||
\(127\) | 14529.4i | 0.900823i | 0.892821 | + | 0.450412i | \(0.148723\pi\) | ||||
−0.892821 | + | 0.450412i | \(0.851277\pi\) | |||||||
\(128\) | 58.0571 | − | 16383.9i | 0.00354352 | − | 0.999994i | ||||
\(129\) | 9579.82 | 0.575676 | ||||||||
\(130\) | 13656.2 | − | 3109.66i | 0.808057 | − | 0.184003i | ||||
\(131\) | −11099.9 | − | 11099.9i | −0.646812 | − | 0.646812i | 0.305409 | − | 0.952221i | \(-0.401207\pi\) |
−0.952221 | + | 0.305409i | \(0.901207\pi\) | |||||||
\(132\) | −9990.63 | + | 4798.78i | −0.573383 | + | 0.275412i | ||||
\(133\) | −29164.3 | − | 29164.3i | −1.64873 | − | 1.64873i | ||||
\(134\) | −10855.2 | − | 6828.44i | −0.604544 | − | 0.380287i | ||||
\(135\) | 3445.30 | 0.189042 | ||||||||
\(136\) | −3313.27 | + | 2634.02i | −0.179135 | + | 0.142410i | ||||
\(137\) | 18444.8i | 0.982728i | 0.870954 | + | 0.491364i | \(0.163502\pi\) | ||||
−0.870954 | + | 0.491364i | \(0.836498\pi\) | |||||||
\(138\) | −8221.47 | − | 5171.70i | −0.431709 | − | 0.271566i | ||||
\(139\) | −14540.4 | + | 14540.4i | −0.752570 | + | 0.752570i | −0.974958 | − | 0.222388i | \(-0.928615\pi\) |
0.222388 | + | 0.974958i | \(0.428615\pi\) | |||||||
\(140\) | −33301.6 | − | 11690.6i | −1.69906 | − | 0.596458i | ||||
\(141\) | 14623.2 | − | 14623.2i | 0.735534 | − | 0.735534i | ||||
\(142\) | 22914.5 | − | 5217.88i | 1.13641 | − | 0.258772i | ||||
\(143\) | − | 19007.9i | − | 0.929528i | ||||||
\(144\) | 5395.28 | + | 4320.50i | 0.260189 | + | 0.208357i | ||||
\(145\) | 11177.2 | 0.531615 | ||||||||
\(146\) | −3251.59 | − | 14279.5i | −0.152542 | − | 0.669895i | ||||
\(147\) | 20824.2 | + | 20824.2i | 0.963681 | + | 0.963681i | ||||
\(148\) | 20983.1 | + | 7366.16i | 0.957958 | + | 0.336293i | ||||
\(149\) | 19098.8 | + | 19098.8i | 0.860266 | + | 0.860266i | 0.991369 | − | 0.131103i | \(-0.0418518\pi\) |
−0.131103 | + | 0.991369i | \(0.541852\pi\) | |||||||
\(150\) | 242.792 | − | 385.968i | 0.0107908 | − | 0.0171541i | ||||
\(151\) | 19549.9 | 0.857415 | 0.428707 | − | 0.903443i | \(-0.358969\pi\) | ||||
0.428707 | + | 0.903443i | \(0.358969\pi\) | |||||||
\(152\) | −29196.7 | − | 3334.58i | −1.26371 | − | 0.144329i | ||||
\(153\) | − | 1785.68i | − | 0.0762816i | ||||||
\(154\) | −25504.5 | + | 40544.6i | −1.07541 | + | 1.70959i | ||||
\(155\) | 27563.5 | − | 27563.5i | 1.14728 | − | 1.14728i | ||||
\(156\) | −10685.3 | + | 5132.47i | −0.439075 | + | 0.210900i | ||||
\(157\) | 1667.24 | − | 1667.24i | 0.0676393 | − | 0.0676393i | −0.672478 | − | 0.740117i | \(-0.734770\pi\) |
0.740117 | + | 0.672478i | \(0.234770\pi\) | |||||||
\(158\) | 478.837 | + | 2102.83i | 0.0191811 | + | 0.0842345i | ||||
\(159\) | 4943.12i | 0.195527i | ||||||||
\(160\) | −23756.5 | + | 8245.32i | −0.927988 | + | 0.322083i | ||||
\(161\) | −41976.2 | −1.61939 | ||||||||
\(162\) | −2843.22 | + | 647.432i | −0.108338 | + | 0.0246697i | ||||
\(163\) | −25019.4 | − | 25019.4i | −0.941676 | − | 0.941676i | 0.0567142 | − | 0.998390i | \(-0.481938\pi\) |
−0.998390 | + | 0.0567142i | \(0.981938\pi\) | |||||||
\(164\) | 8434.78 | + | 17560.5i | 0.313607 | + | 0.652902i | ||||
\(165\) | 12028.7 | + | 12028.7i | 0.441824 | + | 0.441824i | ||||
\(166\) | −17272.1 | − | 10865.0i | −0.626799 | − | 0.394287i | ||||
\(167\) | −8048.66 | −0.288596 | −0.144298 | − | 0.989534i | \(-0.546092\pi\) | ||||
−0.144298 | + | 0.989534i | \(0.546092\pi\) | |||||||
\(168\) | 29678.9 | + | 3389.66i | 1.05155 | + | 0.120098i | ||||
\(169\) | 8231.33i | 0.288202i | ||||||||
\(170\) | 5499.00 | + | 3459.13i | 0.190277 | + | 0.119693i | ||||
\(171\) | 8766.30 | − | 8766.30i | 0.299795 | − | 0.299795i | ||||
\(172\) | 9770.82 | − | 27833.0i | 0.330274 | − | 0.940812i | ||||
\(173\) | 14994.1 | − | 14994.1i | 0.500990 | − | 0.500990i | −0.410755 | − | 0.911746i | \(-0.634735\pi\) |
0.911746 | + | 0.410755i | \(0.134735\pi\) | |||||||
\(174\) | −9223.94 | + | 2100.39i | −0.304662 | + | 0.0693748i | ||||
\(175\) | − | 1970.63i | − | 0.0643471i | ||||||
\(176\) | 3752.43 | + | 33921.0i | 0.121140 | + | 1.09507i | ||||
\(177\) | −8731.04 | −0.278689 | ||||||||
\(178\) | −6704.65 | − | 29443.7i | −0.211610 | − | 0.929292i | ||||
\(179\) | 22215.1 | + | 22215.1i | 0.693333 | + | 0.693333i | 0.962964 | − | 0.269631i | \(-0.0869016\pi\) |
−0.269631 | + | 0.962964i | \(0.586902\pi\) | |||||||
\(180\) | 3513.99 | − | 10009.9i | 0.108456 | − | 0.308947i | ||||
\(181\) | −7611.92 | − | 7611.92i | −0.232347 | − | 0.232347i | 0.581325 | − | 0.813672i | \(-0.302535\pi\) |
−0.813672 | + | 0.581325i | \(0.802535\pi\) | |||||||
\(182\) | −27278.0 | + | 43363.9i | −0.823511 | + | 1.30914i | ||||
\(183\) | −7195.78 | −0.214870 | ||||||||
\(184\) | −23411.1 | + | 18611.6i | −0.691491 | + | 0.549729i | ||||
\(185\) | − | 34132.4i | − | 0.997294i | ||||||
\(186\) | −17567.0 | + | 27926.3i | −0.507775 | + | 0.807212i | ||||
\(187\) | 6234.38 | − | 6234.38i | 0.178283 | − | 0.178283i | ||||
\(188\) | −27571.1 | − | 57400.5i | −0.780078 | − | 1.62405i | ||||
\(189\) | −8911.08 | + | 8911.08i | −0.249463 | + | 0.249463i | ||||
\(190\) | 10014.2 | + | 43977.5i | 0.277401 | + | 1.21821i | ||||
\(191\) | − | 31974.8i | − | 0.876479i | −0.898858 | − | 0.438239i | \(-0.855602\pi\) | ||
0.898858 | − | 0.438239i | \(-0.144398\pi\) | |||||||
\(192\) | 18055.5 | − | 11268.7i | 0.489787 | − | 0.305683i | ||||
\(193\) | 17517.2 | 0.470272 | 0.235136 | − | 0.971962i | \(-0.424446\pi\) | ||||
0.235136 | + | 0.971962i | \(0.424446\pi\) | |||||||
\(194\) | −37425.1 | + | 8522.11i | −0.994397 | + | 0.226435i | ||||
\(195\) | 12865.1 | + | 12865.1i | 0.338332 | + | 0.338332i | ||||
\(196\) | 81741.4 | − | 39262.7i | 2.12780 | − | 1.02204i | ||||
\(197\) | 46651.3 | + | 46651.3i | 1.20207 | + | 1.20207i | 0.973535 | + | 0.228540i | \(0.0733951\pi\) |
0.228540 | + | 0.973535i | \(0.426605\pi\) | |||||||
\(198\) | −12187.0 | − | 7666.21i | −0.310861 | − | 0.195547i | ||||
\(199\) | −48575.7 | −1.22663 | −0.613314 | − | 0.789839i | \(-0.710164\pi\) | ||||
−0.613314 | + | 0.789839i | \(0.710164\pi\) | |||||||
\(200\) | −873.749 | − | 1099.07i | −0.0218437 | − | 0.0274767i | ||||
\(201\) | − | 16659.3i | − | 0.412348i | ||||||
\(202\) | 11217.7 | + | 7056.48i | 0.274917 | + | 0.172936i | ||||
\(203\) | −28909.2 | + | 28909.2i | −0.701527 | + | 0.701527i | ||||
\(204\) | −5188.06 | − | 1821.28i | −0.124665 | − | 0.0437639i | ||||
\(205\) | 21142.7 | − | 21142.7i | 0.503098 | − | 0.503098i | ||||
\(206\) | 53253.0 | − | 12126.3i | 1.25490 | − | 0.285755i | ||||
\(207\) | − | 12617.3i | − | 0.294460i | ||||||
\(208\) | 4013.37 | + | 36279.7i | 0.0927645 | + | 0.838566i | ||||
\(209\) | 61212.1 | 1.40134 | ||||||||
\(210\) | −10179.6 | − | 44703.9i | −0.230829 | − | 1.01369i | ||||
\(211\) | −43450.3 | − | 43450.3i | −0.975950 | − | 0.975950i | 0.0237673 | − | 0.999718i | \(-0.492434\pi\) |
−0.999718 | + | 0.0237673i | \(0.992434\pi\) | |||||||
\(212\) | 14361.6 | + | 5041.68i | 0.319545 | + | 0.112177i | ||||
\(213\) | 21587.1 | + | 21587.1i | 0.475811 | + | 0.475811i | ||||
\(214\) | 31993.8 | − | 50860.7i | 0.698616 | − | 1.11059i | ||||
\(215\) | −45274.8 | −0.979444 | ||||||||
\(216\) | −1018.87 | + | 8920.96i | −0.0218380 | + | 0.191207i | ||||
\(217\) | 142583.i | 3.02795i | ||||||||
\(218\) | 18368.8 | − | 29201.0i | 0.386517 | − | 0.614448i | ||||
\(219\) | 13452.3 | − | 13452.3i | 0.280484 | − | 0.280484i | ||||
\(220\) | 47216.3 | − | 22679.3i | 0.975543 | − | 0.468580i | ||||
\(221\) | 6667.90 | − | 6667.90i | 0.136523 | − | 0.136523i | ||||
\(222\) | 6414.08 | + | 28167.6i | 0.130145 | + | 0.571537i | ||||
\(223\) | − | 76389.5i | − | 1.53612i | −0.640380 | − | 0.768058i | \(-0.721223\pi\) | ||
0.640380 | − | 0.768058i | \(-0.278777\pi\) | |||||||
\(224\) | 40118.8 | − | 82771.0i | 0.799562 | − | 1.64961i | ||||
\(225\) | 592.338 | 0.0117005 | ||||||||
\(226\) | 8168.14 | − | 1859.97i | 0.159921 | − | 0.0364158i | ||||
\(227\) | 41467.0 | + | 41467.0i | 0.804731 | + | 0.804731i | 0.983831 | − | 0.179100i | \(-0.0573185\pi\) |
−0.179100 | + | 0.983831i | \(0.557318\pi\) | |||||||
\(228\) | −16528.3 | − | 34410.5i | −0.317950 | − | 0.661943i | ||||
\(229\) | −26777.4 | − | 26777.4i | −0.510620 | − | 0.510620i | 0.404096 | − | 0.914716i | \(-0.367586\pi\) |
−0.914716 | + | 0.404096i | \(0.867586\pi\) | |||||||
\(230\) | 38855.1 | + | 24441.7i | 0.734501 | + | 0.462036i | ||||
\(231\) | −62223.0 | −1.16608 | ||||||||
\(232\) | −3305.42 | + | 28941.3i | −0.0614116 | + | 0.537702i | ||||
\(233\) | 98378.0i | 1.81212i | 0.423153 | + | 0.906058i | \(0.360923\pi\) | ||||
−0.423153 | + | 0.906058i | \(0.639077\pi\) | |||||||
\(234\) | −13034.4 | − | 8199.29i | −0.238046 | − | 0.149742i | ||||
\(235\) | −69109.9 | + | 69109.9i | −1.25142 | + | 1.25142i | ||||
\(236\) | −8905.12 | + | 25367.0i | −0.159888 | + | 0.455454i | ||||
\(237\) | −1981.02 | + | 1981.02i | −0.0352689 | + | 0.0352689i | ||||
\(238\) | −23169.7 | + | 5276.00i | −0.409041 | + | 0.0931432i | ||||
\(239\) | − | 27673.0i | − | 0.484463i | −0.970218 | − | 0.242232i | \(-0.922121\pi\) | ||
0.970218 | − | 0.242232i | \(-0.0778794\pi\) | |||||||
\(240\) | −25498.4 | − | 20418.9i | −0.442681 | − | 0.354495i | ||||
\(241\) | −46490.2 | −0.800438 | −0.400219 | − | 0.916419i | \(-0.631066\pi\) | ||||
−0.400219 | + | 0.916419i | \(0.631066\pi\) | |||||||
\(242\) | −2780.78 | − | 12211.9i | −0.0474827 | − | 0.208522i | ||||
\(243\) | −2678.52 | − | 2678.52i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −7339.25 | + | 20906.4i | −0.123274 | + | 0.351156i | ||||
\(245\) | −98416.2 | − | 98416.2i | −1.63959 | − | 1.63959i | ||||
\(246\) | −13474.8 | + | 21421.0i | −0.222666 | + | 0.353973i | ||||
\(247\) | 65468.5 | 1.07310 | ||||||||
\(248\) | 63219.2 | + | 79521.8i | 1.02789 | + | 1.29295i | ||||
\(249\) | − | 26507.1i | − | 0.427528i | ||||||
\(250\) | −33837.0 | + | 53790.7i | −0.541391 | + | 0.860652i | ||||
\(251\) | 26522.0 | − | 26522.0i | 0.420978 | − | 0.420978i | −0.464563 | − | 0.885540i | \(-0.653788\pi\) |
0.885540 | + | 0.464563i | \(0.153788\pi\) | |||||||
\(252\) | 16801.3 | + | 34978.8i | 0.264571 | + | 0.550812i | ||||
\(253\) | 44051.2 | − | 44051.2i | 0.688204 | − | 0.688204i | ||||
\(254\) | 12903.7 | + | 56666.9i | 0.200007 | + | 0.878339i | ||||
\(255\) | 8439.20i | 0.129784i | ||||||||
\(256\) | −14324.3 | − | 63951.4i | −0.218571 | − | 0.975821i | ||||
\(257\) | −31183.5 | −0.472127 | −0.236064 | − | 0.971738i | \(-0.575857\pi\) | ||||
−0.236064 | + | 0.971738i | \(0.575857\pi\) | |||||||
\(258\) | 37362.9 | − | 8507.93i | 0.561307 | − | 0.127816i | ||||
\(259\) | 88281.7 | + | 88281.7i | 1.31605 | + | 1.31605i | ||||
\(260\) | 50499.5 | − | 24256.3i | 0.747034 | − | 0.358821i | ||||
\(261\) | −8689.62 | − | 8689.62i | −0.127562 | − | 0.127562i | ||||
\(262\) | −53149.5 | − | 33433.6i | −0.774278 | − | 0.487058i | ||||
\(263\) | −87530.3 | −1.26546 | −0.632728 | − | 0.774374i | \(-0.718065\pi\) | ||||
−0.632728 | + | 0.774374i | \(0.718065\pi\) | |||||||
\(264\) | −34703.2 | + | 27588.8i | −0.497923 | + | 0.395845i | ||||
\(265\) | − | 23361.5i | − | 0.332666i | ||||||
\(266\) | −139647. | − | 87844.5i | −1.97364 | − | 1.24151i | ||||
\(267\) | 27738.1 | − | 27738.1i | 0.389094 | − | 0.389094i | ||||
\(268\) | −48401.4 | − | 16991.4i | −0.673889 | − | 0.236570i | ||||
\(269\) | −38179.9 | + | 38179.9i | −0.527631 | + | 0.527631i | −0.919865 | − | 0.392234i | \(-0.871702\pi\) |
0.392234 | + | 0.919865i | \(0.371702\pi\) | |||||||
\(270\) | 13437.2 | − | 3059.80i | 0.184324 | − | 0.0419726i | ||||
\(271\) | 19976.0i | 0.272001i | 0.990709 | + | 0.136000i | \(0.0434249\pi\) | ||||
−0.990709 | + | 0.136000i | \(0.956575\pi\) | |||||||
\(272\) | −10583.0 | + | 13215.7i | −0.143044 | + | 0.178629i | ||||
\(273\) | −66549.8 | −0.892938 | ||||||||
\(274\) | 16381.0 | + | 71937.8i | 0.218193 | + | 0.958200i | ||||
\(275\) | 2068.05 | + | 2068.05i | 0.0273461 | + | 0.0273461i | ||||
\(276\) | −36658.1 | − | 12868.9i | −0.481229 | − | 0.168936i | ||||
\(277\) | 8347.44 | + | 8347.44i | 0.108791 | + | 0.108791i | 0.759407 | − | 0.650616i | \(-0.225489\pi\) |
−0.650616 | + | 0.759407i | \(0.725489\pi\) | |||||||
\(278\) | −43796.5 | + | 69623.4i | −0.566695 | + | 0.900877i | ||||
\(279\) | −42858.0 | −0.550584 | ||||||||
\(280\) | −140264. | − | 16019.7i | −1.78908 | − | 0.204333i | ||||
\(281\) | − | 42474.9i | − | 0.537922i | −0.963151 | − | 0.268961i | \(-0.913320\pi\) | ||
0.963151 | − | 0.268961i | \(-0.0866803\pi\) | |||||||
\(282\) | 44045.7 | − | 70019.7i | 0.553867 | − | 0.880485i | ||||
\(283\) | 35828.8 | − | 35828.8i | 0.447362 | − | 0.447362i | −0.447115 | − | 0.894477i | \(-0.647548\pi\) |
0.894477 | + | 0.447115i | \(0.147548\pi\) | |||||||
\(284\) | 84736.1 | − | 40701.1i | 1.05059 | − | 0.504626i | ||||
\(285\) | −41430.0 | + | 41430.0i | −0.510065 | + | 0.510065i | ||||
\(286\) | −16881.1 | − | 74134.0i | −0.206381 | − | 0.906328i | ||||
\(287\) | 109369.i | 1.32779i | ||||||||
\(288\) | 24879.5 | + | 12059.0i | 0.299956 | + | 0.145388i | ||||
\(289\) | −79147.0 | −0.947630 | ||||||||
\(290\) | 43592.9 | − | 9926.57i | 0.518346 | − | 0.118033i | ||||
\(291\) | −35257.2 | − | 35257.2i | −0.416353 | − | 0.416353i | ||||
\(292\) | −25363.5 | − | 52804.5i | −0.297470 | − | 0.619306i | ||||
\(293\) | 90088.6 | + | 90088.6i | 1.04938 | + | 1.04938i | 0.998716 | + | 0.0506689i | \(0.0161353\pi\) |
0.0506689 | + | 0.998716i | \(0.483865\pi\) | |||||||
\(294\) | 99711.8 | + | 62723.5i | 1.15359 | + | 0.725664i | ||||
\(295\) | 41263.4 | 0.474156 | ||||||||
\(296\) | 88379.5 | + | 10093.9i | 1.00871 | + | 0.115206i | ||||
\(297\) | − | 18703.2i | − | 0.212032i | ||||||
\(298\) | 91450.1 | + | 57526.5i | 1.02980 | + | 0.647791i | ||||
\(299\) | 47114.4 | − | 47114.4i | 0.527001 | − | 0.527001i | ||||
\(300\) | 604.148 | − | 1720.96i | 0.00671275 | − | 0.0191218i | ||||
\(301\) | 117101. | − | 117101.i | 1.29249 | − | 1.29249i | ||||
\(302\) | 76247.8 | − | 17362.5i | 0.836014 | − | 0.190370i | ||||
\(303\) | 17215.6i | 0.187516i | ||||||||
\(304\) | −116833. | + | 12924.4i | −1.26421 | + | 0.139850i | ||||
\(305\) | 34007.7 | 0.365575 | ||||||||
\(306\) | −1585.88 | − | 6964.42i | −0.0169366 | − | 0.0743776i | ||||
\(307\) | 8380.03 | + | 8380.03i | 0.0889137 | + | 0.0889137i | 0.750165 | − | 0.661251i | \(-0.229974\pi\) |
−0.661251 | + | 0.750165i | \(0.729974\pi\) | |||||||
\(308\) | −63463.6 | + | 180781.i | −0.668996 | + | 1.90569i | ||||
\(309\) | 50168.2 | + | 50168.2i | 0.525426 | + | 0.525426i | ||||
\(310\) | 83022.6 | − | 131981.i | 0.863919 | − | 1.37338i | ||||
\(311\) | 111760. | 1.15549 | 0.577743 | − | 0.816219i | \(-0.303933\pi\) | ||||
0.577743 | + | 0.816219i | \(0.303933\pi\) | |||||||
\(312\) | −37116.4 | + | 29507.2i | −0.381291 | + | 0.303123i | ||||
\(313\) | 84467.1i | 0.862182i | 0.902308 | + | 0.431091i | \(0.141871\pi\) | ||||
−0.902308 | + | 0.431091i | \(0.858129\pi\) | |||||||
\(314\) | 5021.81 | − | 7983.20i | 0.0509332 | − | 0.0809688i | ||||
\(315\) | 42114.3 | − | 42114.3i | 0.424432 | − | 0.424432i | ||||
\(316\) | 3735.09 | + | 7776.12i | 0.0374047 | + | 0.0778733i | ||||
\(317\) | 105937. | − | 105937.i | 1.05422 | − | 1.05422i | 0.0557723 | − | 0.998444i | \(-0.482238\pi\) |
0.998444 | − | 0.0557723i | \(-0.0177621\pi\) | |||||||
\(318\) | 4390.03 | + | 19279.0i | 0.0434124 | + | 0.190647i | ||||
\(319\) | − | 60676.7i | − | 0.596266i | ||||||
\(320\) | −85331.4 | + | 53256.4i | −0.833314 | + | 0.520082i | ||||
\(321\) | 78054.9 | 0.757513 | ||||||||
\(322\) | −163714. | + | 37279.5i | −1.57897 | + | 0.359549i | ||||
\(323\) | 21472.9 | + | 21472.9i | 0.205819 | + | 0.205819i | ||||
\(324\) | −10514.0 | + | 5050.18i | −0.100156 | + | 0.0481079i | ||||
\(325\) | 2211.85 | + | 2211.85i | 0.0209406 | + | 0.0209406i | ||||
\(326\) | −119800. | − | 75359.7i | −1.12725 | − | 0.709095i | ||||
\(327\) | 44814.2 | 0.419103 | ||||||||
\(328\) | 48492.6 | + | 60997.6i | 0.450742 | + | 0.566977i | ||||
\(329\) | − | 357498.i | − | 3.30280i | ||||||
\(330\) | 57596.5 | + | 36231.0i | 0.528893 | + | 0.332699i | ||||
\(331\) | −22373.4 | + | 22373.4i | −0.204209 | + | 0.204209i | −0.801801 | − | 0.597592i | \(-0.796124\pi\) |
0.597592 | + | 0.801801i | \(0.296124\pi\) | |||||||
\(332\) | −77013.2 | − | 27035.6i | −0.698697 | − | 0.245279i | ||||
\(333\) | −26535.9 | + | 26535.9i | −0.239302 | + | 0.239302i | ||||
\(334\) | −31391.1 | + | 7148.09i | −0.281393 | + | 0.0640762i | ||||
\(335\) | 78732.6i | 0.701560i | ||||||||
\(336\) | 118763. | − | 13137.9i | 1.05197 | − | 0.116371i | ||||
\(337\) | 124397. | 1.09534 | 0.547671 | − | 0.836694i | \(-0.315515\pi\) | ||||
0.547671 | + | 0.836694i | \(0.315515\pi\) | |||||||
\(338\) | 7310.32 | + | 32103.5i | 0.0639887 | + | 0.281008i | ||||
\(339\) | 7694.98 | + | 7694.98i | 0.0669588 | + | 0.0669588i | ||||
\(340\) | 24519.1 | + | 8607.46i | 0.212103 | + | 0.0744590i | ||||
\(341\) | −149631. | − | 149631.i | −1.28681 | − | 1.28681i | ||||
\(342\) | 26404.5 | − | 41975.4i | 0.225749 | − | 0.358875i | ||||
\(343\) | 293426. | 2.49408 | ||||||||
\(344\) | 13389.0 | − | 117231.i | 0.113144 | − | 0.990659i | ||||
\(345\) | 59630.2i | 0.500989i | ||||||||
\(346\) | 45163.1 | − | 71796.0i | 0.377252 | − | 0.599719i | ||||
\(347\) | −163054. | + | 163054.i | −1.35417 | + | 1.35417i | −0.473232 | + | 0.880938i | \(0.656913\pi\) |
−0.880938 | + | 0.473232i | \(0.843087\pi\) | |||||||
\(348\) | −34109.5 | + | 16383.7i | −0.281655 | + | 0.135287i | ||||
\(349\) | −122260. | + | 122260.i | −1.00377 | + | 1.00377i | −0.00377908 | + | 0.999993i | \(0.501203\pi\) |
−0.999993 | + | 0.00377908i | \(0.998797\pi\) | |||||||
\(350\) | −1750.14 | − | 7685.78i | −0.0142868 | − | 0.0627410i | ||||
\(351\) | − | 20003.7i | − | 0.162367i | ||||||
\(352\) | 44760.6 | + | 128965.i | 0.361253 | + | 1.04084i | ||||
\(353\) | −216947. | −1.74102 | −0.870511 | − | 0.492150i | \(-0.836211\pi\) | ||||
−0.870511 | + | 0.492150i | \(0.836211\pi\) | |||||||
\(354\) | −34052.5 | + | 7754.12i | −0.271733 | + | 0.0618765i | ||||
\(355\) | −102022. | − | 102022.i | −0.809536 | − | 0.809536i | ||||
\(356\) | −52298.4 | − | 108881.i | −0.412657 | − | 0.859114i | ||||
\(357\) | −21827.6 | − | 21827.6i | −0.171265 | − | 0.171265i | ||||
\(358\) | 106372. | + | 66913.0i | 0.829967 | + | 0.522089i | ||||
\(359\) | −63960.0 | −0.496271 | −0.248136 | − | 0.968725i | \(-0.579818\pi\) | ||||
−0.248136 | + | 0.968725i | \(0.579818\pi\) | |||||||
\(360\) | 4815.25 | − | 42160.9i | 0.0371547 | − | 0.325316i | ||||
\(361\) | 80510.1i | 0.617783i | ||||||||
\(362\) | −36448.0 | − | 22927.5i | −0.278135 | − | 0.174960i | ||||
\(363\) | 11504.5 | − | 11504.5i | 0.0873078 | − | 0.0873078i | ||||
\(364\) | −67876.7 | + | 193352.i | −0.512292 | + | 1.45931i | ||||
\(365\) | −63576.3 | + | 63576.3i | −0.477210 | + | 0.477210i | ||||
\(366\) | −28064.7 | + | 6390.64i | −0.209507 | + | 0.0477070i | ||||
\(367\) | 71673.9i | 0.532144i | 0.963953 | + | 0.266072i | \(0.0857258\pi\) | ||||
−0.963953 | + | 0.266072i | \(0.914274\pi\) | |||||||
\(368\) | −74777.9 | + | 93380.0i | −0.552176 | + | 0.689538i | ||||
\(369\) | −32874.4 | −0.241438 | ||||||||
\(370\) | −30313.3 | − | 133122.i | −0.221427 | − | 0.972402i | ||||
\(371\) | 60423.3 | + | 60423.3i | 0.438992 | + | 0.438992i | ||||
\(372\) | −43712.5 | + | 124519.i | −0.315878 | + | 0.899805i | ||||
\(373\) | −62867.7 | − | 62867.7i | −0.451866 | − | 0.451866i | 0.444108 | − | 0.895973i | \(-0.353521\pi\) |
−0.895973 | + | 0.444108i | \(0.853521\pi\) | |||||||
\(374\) | 18778.3 | − | 29851.9i | 0.134250 | − | 0.213417i | ||||
\(375\) | −82551.6 | −0.587034 | ||||||||
\(376\) | −158510. | − | 199385.i | −1.12119 | − | 1.41032i | ||||
\(377\) | − | 64895.9i | − | 0.456599i | ||||||
\(378\) | −26840.6 | + | 42668.7i | −0.187849 | + | 0.298625i | ||||
\(379\) | 23713.9 | − | 23713.9i | 0.165092 | − | 0.165092i | −0.619726 | − | 0.784818i | \(-0.712756\pi\) |
0.784818 | + | 0.619726i | \(0.212756\pi\) | |||||||
\(380\) | 78113.7 | + | 162626.i | 0.540954 | + | 1.12622i | ||||
\(381\) | −53384.3 | + | 53384.3i | −0.367759 | + | 0.367759i | ||||
\(382\) | −28397.1 | − | 124707.i | −0.194602 | − | 0.854602i | ||||
\(383\) | 121708.i | 0.829701i | 0.909890 | + | 0.414850i | \(0.136166\pi\) | ||||
−0.909890 | + | 0.414850i | \(0.863834\pi\) | |||||||
\(384\) | 60411.6 | − | 59985.0i | 0.409692 | − | 0.406799i | ||||
\(385\) | 294070. | 1.98394 | ||||||||
\(386\) | 68319.8 | − | 15557.2i | 0.458534 | − | 0.104413i | ||||
\(387\) | 35198.5 | + | 35198.5i | 0.235019 | + | 0.235019i | ||||
\(388\) | −138396. | + | 66475.2i | −0.919303 | + | 0.441567i | ||||
\(389\) | 40074.9 | + | 40074.9i | 0.264834 | + | 0.264834i | 0.827014 | − | 0.562181i | \(-0.190037\pi\) |
−0.562181 | + | 0.827014i | \(0.690037\pi\) | |||||||
\(390\) | 61601.5 | + | 38750.3i | 0.405007 | + | 0.254769i | ||||
\(391\) | 30906.0 | 0.202157 | ||||||||
\(392\) | 283935. | − | 225726.i | 1.84777 | − | 1.46896i | ||||
\(393\) | − | 81567.6i | − | 0.528120i | ||||||
\(394\) | 223379. | + | 140516.i | 1.43896 | + | 0.905178i | ||||
\(395\) | 9362.41 | − | 9362.41i | 0.0600058 | − | 0.0600058i | ||||
\(396\) | −54339.7 | − | 19076.1i | −0.346519 | − | 0.121646i | ||||
\(397\) | −118458. | + | 118458.i | −0.751595 | + | 0.751595i | −0.974777 | − | 0.223182i | \(-0.928356\pi\) |
0.223182 | + | 0.974777i | \(0.428356\pi\) | |||||||
\(398\) | −189453. | + | 43140.5i | −1.19601 | + | 0.272345i | ||||
\(399\) | − | 214313.i | − | 1.34618i | ||||||
\(400\) | −4383.85 | − | 3510.55i | −0.0273991 | − | 0.0219409i | ||||
\(401\) | 45116.3 | 0.280572 | 0.140286 | − | 0.990111i | \(-0.455198\pi\) | ||||
0.140286 | + | 0.990111i | \(0.455198\pi\) | |||||||
\(402\) | −14795.2 | − | 64973.8i | −0.0915525 | − | 0.402056i | ||||
\(403\) | −160036. | − | 160036.i | −0.985390 | − | 0.985390i | ||||
\(404\) | 50017.8 | + | 17558.9i | 0.306452 | + | 0.107580i | ||||
\(405\) | 12658.8 | + | 12658.8i | 0.0771762 | + | 0.0771762i | ||||
\(406\) | −87076.2 | + | 138425.i | −0.528259 | + | 0.839776i | ||||
\(407\) | −185291. | −1.11858 | ||||||||
\(408\) | −21851.8 | − | 2495.71i | −0.131270 | − | 0.0149925i | ||||
\(409\) | 93624.9i | 0.559687i | 0.960046 | + | 0.279843i | \(0.0902825\pi\) | ||||
−0.960046 | + | 0.279843i | \(0.909718\pi\) | |||||||
\(410\) | 63682.9 | − | 101237.i | 0.378839 | − | 0.602242i | ||||
\(411\) | −67770.6 | + | 67770.6i | −0.401197 | + | 0.401197i | ||||
\(412\) | 196926. | − | 94589.1i | 1.16014 | − | 0.557245i | ||||
\(413\) | −106726. | + | 106726.i | −0.625704 | + | 0.625704i | ||||
\(414\) | −11205.6 | − | 49209.6i | −0.0653782 | − | 0.287111i | ||||
\(415\) | 125274.i | 0.727387i | ||||||||
\(416\) | 47873.1 | + | 137932.i | 0.276634 | + | 0.797040i | ||||
\(417\) | −106850. | −0.614471 | ||||||||
\(418\) | 238737. | − | 54363.0i | 1.36637 | − | 0.311136i | ||||
\(419\) | −122699. | − | 122699.i | −0.698895 | − | 0.698895i | 0.265277 | − | 0.964172i | \(-0.414537\pi\) |
−0.964172 | + | 0.265277i | \(0.914537\pi\) | |||||||
\(420\) | −79403.8 | − | 165312.i | −0.450135 | − | 0.937141i | ||||
\(421\) | 48594.3 | + | 48594.3i | 0.274171 | + | 0.274171i | 0.830777 | − | 0.556606i | \(-0.187897\pi\) |
−0.556606 | + | 0.830777i | \(0.687897\pi\) | |||||||
\(422\) | −208052. | − | 130875.i | −1.16828 | − | 0.734903i | ||||
\(423\) | 107458. | 0.600561 | ||||||||
\(424\) | 60490.2 | + | 6908.66i | 0.336476 | + | 0.0384293i | ||||
\(425\) | 1450.92i | 0.00803279i | ||||||||
\(426\) | 103365. | + | 65021.4i | 0.569579 | + | 0.358292i | ||||
\(427\) | −87959.1 | + | 87959.1i | −0.482419 | + | 0.482419i | ||||
\(428\) | 79611.2 | − | 226779.i | 0.434597 | − | 1.23798i | ||||
\(429\) | 69839.6 | − | 69839.6i | 0.379478 | − | 0.379478i | ||||
\(430\) | −176579. | + | 40209.0i | −0.954997 | + | 0.217463i | ||||
\(431\) | 32150.5i | 0.173075i | 0.996249 | + | 0.0865374i | \(0.0275802\pi\) | ||||
−0.996249 | + | 0.0865374i | \(0.972420\pi\) | |||||||
\(432\) | 3949.02 | + | 35698.0i | 0.0211603 | + | 0.191283i | ||||
\(433\) | −91093.8 | −0.485862 | −0.242931 | − | 0.970044i | \(-0.578109\pi\) | ||||
−0.242931 | + | 0.970044i | \(0.578109\pi\) | |||||||
\(434\) | 126629. | + | 556097.i | 0.672287 | + | 2.95237i | ||||
\(435\) | 41067.6 | + | 41067.6i | 0.217031 | + | 0.217031i | ||||
\(436\) | 45707.7 | − | 130202.i | 0.240446 | − | 0.684929i | ||||
\(437\) | 151725. | + | 151725.i | 0.794499 | + | 0.794499i | ||||
\(438\) | 40519.0 | − | 64413.2i | 0.211208 | − | 0.335758i | ||||
\(439\) | −267216. | −1.38655 | −0.693273 | − | 0.720675i | \(-0.743832\pi\) | ||||
−0.693273 | + | 0.720675i | \(0.743832\pi\) | |||||||
\(440\) | 164009. | − | 130386.i | 0.847156 | − | 0.673482i | ||||
\(441\) | 153026.i | 0.786842i | ||||||||
\(442\) | 20084.1 | − | 31927.7i | 0.102803 | − | 0.163427i | ||||
\(443\) | 167381. | − | 167381.i | 0.852900 | − | 0.852900i | −0.137589 | − | 0.990489i | \(-0.543935\pi\) |
0.990489 | + | 0.137589i | \(0.0439353\pi\) | |||||||
\(444\) | 50031.9 | + | 104162.i | 0.253794 | + | 0.528376i | ||||
\(445\) | −131092. | + | 131092.i | −0.661996 | + | 0.661996i | ||||
\(446\) | −67842.3 | − | 297932.i | −0.341060 | − | 1.49778i | ||||
\(447\) | 140347.i | 0.702404i | ||||||||
\(448\) | 82960.2 | − | 358450.i | 0.413346 | − | 1.78596i | ||||
\(449\) | 175788. | 0.871960 | 0.435980 | − | 0.899956i | \(-0.356402\pi\) | ||||
0.435980 | + | 0.899956i | \(0.356402\pi\) | |||||||
\(450\) | 2310.21 | − | 526.061i | 0.0114085 | − | 0.00259783i | ||||
\(451\) | −114775. | − | 114775.i | −0.564282 | − | 0.564282i | ||||
\(452\) | 30205.2 | − | 14508.4i | 0.147844 | − | 0.0710138i | ||||
\(453\) | 71831.0 | + | 71831.0i | 0.350038 | + | 0.350038i | ||||
\(454\) | 198555. | + | 124901.i | 0.963318 | + | 0.605973i | ||||
\(455\) | 314518. | 1.51923 | ||||||||
\(456\) | −95023.3 | − | 119527.i | −0.456984 | − | 0.574828i | ||||
\(457\) | − | 393478.i | − | 1.88403i | −0.335570 | − | 0.942015i | \(-0.608929\pi\) | ||
0.335570 | − | 0.942015i | \(-0.391071\pi\) | |||||||
\(458\) | −128218. | − | 80655.0i | −0.611247 | − | 0.384504i | ||||
\(459\) | 6560.99 | − | 6560.99i | 0.0311418 | − | 0.0311418i | ||||
\(460\) | 173248. | + | 60819.1i | 0.818753 | + | 0.287425i | ||||
\(461\) | 85882.9 | − | 85882.9i | 0.404115 | − | 0.404115i | −0.475565 | − | 0.879680i | \(-0.657756\pi\) |
0.879680 | + | 0.475565i | \(0.157756\pi\) | |||||||
\(462\) | −242680. | + | 55260.9i | −1.13697 | + | 0.258901i | ||||
\(463\) | − | 112113.i | − | 0.522992i | −0.965205 | − | 0.261496i | \(-0.915784\pi\) | ||
0.965205 | − | 0.261496i | \(-0.0842159\pi\) | |||||||
\(464\) | 12811.4 | + | 115811.i | 0.0595058 | + | 0.537917i | ||||
\(465\) | 202549. | 0.936753 | ||||||||
\(466\) | 87370.4 | + | 383690.i | 0.402339 | + | 1.76689i | ||||
\(467\) | 40803.5 | + | 40803.5i | 0.187096 | + | 0.187096i | 0.794439 | − | 0.607344i | \(-0.207765\pi\) |
−0.607344 | + | 0.794439i | \(0.707765\pi\) | |||||||
\(468\) | −58118.3 | − | 20402.6i | −0.265351 | − | 0.0931521i | ||||
\(469\) | −203638. | − | 203638.i | −0.925791 | − | 0.925791i | ||||
\(470\) | −208163. | + | 330917.i | −0.942339 | + | 1.49804i | ||||
\(471\) | 12251.7 | 0.0552272 | ||||||||
\(472\) | −12202.8 | + | 106844.i | −0.0547740 | + | 0.479585i | ||||
\(473\) | 245779.i | 1.09856i | ||||||||
\(474\) | −5966.93 | + | 9485.65i | −0.0265579 | + | 0.0422193i | ||||
\(475\) | −7122.92 | + | 7122.92i | −0.0315697 | + | 0.0315697i | ||||
\(476\) | −85680.1 | + | 41154.5i | −0.378152 | + | 0.181637i | ||||
\(477\) | −18162.2 | + | 18162.2i | −0.0798236 | + | 0.0798236i | ||||
\(478\) | −24576.7 | − | 107929.i | −0.107564 | − | 0.472371i | ||||
\(479\) | − | 111665.i | − | 0.486683i | −0.969941 | − | 0.243341i | \(-0.921757\pi\) | ||
0.969941 | − | 0.243341i | \(-0.0782435\pi\) | |||||||
\(480\) | −117582. | − | 56991.7i | −0.510339 | − | 0.247360i | ||||
\(481\) | −198176. | −0.856566 | ||||||||
\(482\) | −181319. | + | 41288.4i | −0.780460 | + | 0.177719i | ||||
\(483\) | −154230. | − | 154230.i | −0.661113 | − | 0.661113i | ||||
\(484\) | −21690.9 | − | 45158.6i | −0.0925951 | − | 0.192775i | ||||
\(485\) | 166627. | + | 166627.i | 0.708375 | + | 0.708375i | ||||
\(486\) | −12825.5 | − | 8067.83i | −0.0543001 | − | 0.0341574i | ||||
\(487\) | 63810.7 | 0.269052 | 0.134526 | − | 0.990910i | \(-0.457049\pi\) | ||||
0.134526 | + | 0.990910i | \(0.457049\pi\) | |||||||
\(488\) | −10057.0 | + | 88056.5i | −0.0422309 | + | 0.369762i | ||||
\(489\) | − | 183854.i | − | 0.768875i | ||||||
\(490\) | −471244. | − | 296435.i | −1.96270 | − | 1.23463i | ||||
\(491\) | 100954. | − | 100954.i | 0.418758 | − | 0.418758i | −0.466018 | − | 0.884775i | \(-0.654312\pi\) |
0.884775 | + | 0.466018i | \(0.154312\pi\) | |||||||
\(492\) | −33529.9 | + | 95512.6i | −0.138517 | + | 0.394576i | ||||
\(493\) | 21285.1 | − | 21285.1i | 0.0875754 | − | 0.0875754i | ||||
\(494\) | 255338. | − | 58143.2i | 1.04631 | − | 0.238257i | ||||
\(495\) | 88392.2i | 0.360748i | ||||||||
\(496\) | 317189. | + | 254002.i | 1.28930 | + | 1.03246i | ||||
\(497\) | 527748. | 2.13656 | ||||||||
\(498\) | −23541.2 | − | 103382.i | −0.0949229 | − | 0.416857i | ||||
\(499\) | 3018.09 | + | 3018.09i | 0.0121208 | + | 0.0121208i | 0.713141 | − | 0.701020i | \(-0.247272\pi\) |
−0.701020 | + | 0.713141i | \(0.747272\pi\) | |||||||
\(500\) | −84197.5 | + | 239844.i | −0.336790 | + | 0.959374i | ||||
\(501\) | −29572.7 | − | 29572.7i | −0.117819 | − | 0.117819i | ||||
\(502\) | 79885.7 | − | 126995.i | 0.317002 | − | 0.503939i | ||||
\(503\) | 139696. | 0.552140 | 0.276070 | − | 0.961138i | \(-0.410968\pi\) | ||||
0.276070 | + | 0.961138i | \(0.410968\pi\) | |||||||
\(504\) | 96592.7 | + | 121502.i | 0.380262 | + | 0.478322i | ||||
\(505\) | − | 81362.0i | − | 0.319035i | ||||||
\(506\) | 132685. | − | 210929.i | 0.518227 | − | 0.823827i | ||||
\(507\) | −30243.8 | + | 30243.8i | −0.117658 | + | 0.117658i | ||||
\(508\) | 100653. | + | 209550.i | 0.390031 | + | 0.812009i | ||||
\(509\) | −98475.6 | + | 98475.6i | −0.380096 | + | 0.380096i | −0.871137 | − | 0.491041i | \(-0.836617\pi\) |
0.491041 | + | 0.871137i | \(0.336617\pi\) | |||||||
\(510\) | 7494.94 | + | 32914.3i | 0.0288156 | + | 0.126545i | ||||
\(511\) | − | 328874.i | − | 1.25947i | ||||||
\(512\) | −112663. | − | 236699.i | −0.429774 | − | 0.902936i | ||||
\(513\) | 64418.9 | 0.244781 | ||||||||
\(514\) | −121621. | + | 27694.4i | −0.460343 | + | 0.104825i | ||||
\(515\) | −237098. | − | 237098.i | −0.893950 | − | 0.893950i | ||||
\(516\) | 138165. | − | 66364.6i | 0.518919 | − | 0.249251i | ||||
\(517\) | 375171. | + | 375171.i | 1.40361 | + | 1.40361i | ||||
\(518\) | 422717. | + | 265909.i | 1.57540 | + | 0.991000i | ||||
\(519\) | 110184. | 0.409057 | ||||||||
\(520\) | 175414. | − | 139453.i | 0.648720 | − | 0.515728i | ||||
\(521\) | 122222.i | 0.450271i | 0.974327 | + | 0.225136i | \(0.0722825\pi\) | ||||
−0.974327 | + | 0.225136i | \(0.927718\pi\) | |||||||
\(522\) | −41608.3 | − | 26173.6i | −0.152700 | − | 0.0960555i | ||||
\(523\) | 50532.0 | − | 50532.0i | 0.184741 | − | 0.184741i | −0.608677 | − | 0.793418i | \(-0.708300\pi\) |
0.793418 | + | 0.608677i | \(0.208300\pi\) | |||||||
\(524\) | −236984. | − | 83193.8i | −0.863092 | − | 0.302990i | ||||
\(525\) | 7240.56 | − | 7240.56i | 0.0262696 | − | 0.0262696i | ||||
\(526\) | −341382. | + | 77736.5i | −1.23387 | + | 0.280966i | ||||
\(527\) | − | 104980.i | − | 0.377995i | ||||||
\(528\) | −110846. | + | 138421.i | −0.397606 | + | 0.496517i | ||||
\(529\) | −61463.8 | −0.219638 | ||||||||
\(530\) | −20747.6 | − | 91113.5i | −0.0738610 | − | 0.324363i | ||||
\(531\) | −32079.9 | − | 32079.9i | −0.113774 | − | 0.113774i | ||||
\(532\) | −622660. | − | 218586.i | −2.20003 | − | 0.772324i | ||||
\(533\) | −122757. | − | 122757.i | −0.432106 | − | 0.432106i | ||||
\(534\) | 83548.6 | − | 132817.i | 0.292993 | − | 0.465771i | ||||
\(535\) | −368892. | −1.28882 | ||||||||
\(536\) | −203864. | − | 23283.5i | −0.709594 | − | 0.0810436i | ||||
\(537\) | 163247.i | 0.566104i | ||||||||
\(538\) | −115000. | + | 182816.i | −0.397313 | + | 0.631610i | ||||
\(539\) | −534263. | + | 534263.i | −1.83898 | + | 1.83898i | ||||
\(540\) | 49689.9 | − | 23867.4i | 0.170404 | − | 0.0818499i | ||||
\(541\) | 72575.2 | − | 72575.2i | 0.247967 | − | 0.247967i | −0.572169 | − | 0.820136i | \(-0.693898\pi\) |
0.820136 | + | 0.572169i | \(0.193898\pi\) | |||||||
\(542\) | 17740.9 | + | 77909.7i | 0.0603916 | + | 0.265212i | ||||
\(543\) | − | 55936.0i | − | 0.189711i | ||||||
\(544\) | −29538.4 | + | 60942.1i | −0.0998136 | + | 0.205930i | ||||
\(545\) | −211795. | −0.713053 | ||||||||
\(546\) | −259555. | + | 59103.5i | −0.870651 | + | 0.198257i | ||||
\(547\) | 312820. | + | 312820.i | 1.04549 | + | 1.04549i | 0.998915 | + | 0.0465736i | \(0.0148302\pi\) |
0.0465736 | + | 0.998915i | \(0.485170\pi\) | |||||||
\(548\) | 127777. | + | 266021.i | 0.425493 | + | 0.885839i | ||||
\(549\) | −26439.0 | − | 26439.0i | −0.0877203 | − | 0.0877203i | ||||
\(550\) | 9902.36 | + | 6229.06i | 0.0327351 | + | 0.0205919i | ||||
\(551\) | 208987. | 0.688361 | ||||||||
\(552\) | −154401. | − | 17634.4i | −0.506726 | − | 0.0578737i | ||||
\(553\) | 48430.8i | 0.158369i | ||||||||
\(554\) | 39969.8 | + | 25142.9i | 0.130230 | + | 0.0819212i | ||||
\(555\) | 125410. | − | 125410.i | 0.407144 | − | 0.407144i | ||||
\(556\) | −108980. | + | 310439.i | −0.352531 | + | 1.00421i | ||||
\(557\) | 127859. | − | 127859.i | 0.412118 | − | 0.412118i | −0.470358 | − | 0.882476i | \(-0.655875\pi\) |
0.882476 | + | 0.470358i | \(0.155875\pi\) | |||||||
\(558\) | −167153. | + | 38062.6i | −0.536842 | + | 0.122245i | ||||
\(559\) | 262870.i | 0.841234i | ||||||||
\(560\) | −561280. | + | 62090.3i | −1.78979 | + | 0.197992i | ||||
\(561\) | 45813.2 | 0.145568 | ||||||||
\(562\) | −37722.3 | − | 165659.i | −0.119433 | − | 0.524496i | ||||
\(563\) | −16640.0 | − | 16640.0i | −0.0524972 | − | 0.0524972i | 0.680371 | − | 0.732868i | \(-0.261819\pi\) |
−0.732868 | + | 0.680371i | \(0.761819\pi\) | |||||||
\(564\) | 109600. | − | 312205.i | 0.344551 | − | 0.981482i | ||||
\(565\) | −36366.9 | − | 36366.9i | −0.113922 | − | 0.113922i | ||||
\(566\) | 107918. | − | 171558.i | 0.336870 | − | 0.535523i | ||||
\(567\) | −65482.8 | −0.203686 | ||||||||
\(568\) | 294337. | − | 233996.i | 0.912323 | − | 0.725290i | ||||
\(569\) | 2582.50i | 0.00797655i | 0.999992 | + | 0.00398828i | \(0.00126951\pi\) | ||||
−0.999992 | + | 0.00398828i | \(0.998730\pi\) | |||||||
\(570\) | −124789. | + | 198378.i | −0.384085 | + | 0.610582i | ||||
\(571\) | 57323.0 | − | 57323.0i | 0.175815 | − | 0.175815i | −0.613713 | − | 0.789529i | \(-0.710325\pi\) |
0.789529 | + | 0.613713i | \(0.210325\pi\) | |||||||
\(572\) | −131678. | − | 274142.i | −0.402459 | − | 0.837884i | ||||
\(573\) | 117483. | − | 117483.i | 0.357821 | − | 0.357821i | ||||
\(574\) | 97131.6 | + | 426557.i | 0.294806 | + | 1.29465i | ||||
\(575\) | 10252.0i | 0.0310080i | ||||||||
\(576\) | 107744. | + | 24936.4i | 0.324749 | + | 0.0751604i | ||||
\(577\) | −572563. | −1.71978 | −0.859888 | − | 0.510484i | \(-0.829466\pi\) | ||||
−0.859888 | + | 0.510484i | \(0.829466\pi\) | |||||||
\(578\) | −308686. | + | 70291.2i | −0.923978 | + | 0.210400i | ||||
\(579\) | 64362.2 | + | 64362.2i | 0.191988 | + | 0.191988i | ||||
\(580\) | 161203. | − | 77430.5i | 0.479201 | − | 0.230174i | ||||
\(581\) | −324015. | − | 324015.i | −0.959872 | − | 0.959872i | ||||
\(582\) | −168821. | − | 106196.i | −0.498403 | − | 0.313519i | ||||
\(583\) | −126820. | −0.373123 | ||||||||
\(584\) | −145818. | − | 183420.i | −0.427548 | − | 0.537802i | ||||
\(585\) | 94538.7i | 0.276247i | ||||||||
\(586\) | 431369. | + | 271352.i | 1.25618 | + | 0.790200i | ||||
\(587\) | 374560. | − | 374560.i | 1.08704 | − | 1.08704i | 0.0912058 | − | 0.995832i | \(-0.470928\pi\) |
0.995832 | − | 0.0912058i | \(-0.0290721\pi\) | |||||||
\(588\) | 444597. | + | 156077.i | 1.28592 | + | 0.451423i | ||||
\(589\) | 515372. | − | 515372.i | 1.48556 | − | 1.48556i | ||||
\(590\) | 160934. | − | 36646.4i | 0.462321 | − | 0.105276i | ||||
\(591\) | 342816.i | 0.981490i | ||||||||
\(592\) | 353659. | − | 39122.7i | 1.00912 | − | 0.111631i | ||||
\(593\) | −335988. | −0.955464 | −0.477732 | − | 0.878506i | \(-0.658541\pi\) | ||||
−0.477732 | + | 0.878506i | \(0.658541\pi\) | |||||||
\(594\) | −16610.5 | − | 72945.4i | −0.0470770 | − | 0.206740i | ||||
\(595\) | 103158. | + | 103158.i | 0.291387 | + | 0.291387i | ||||
\(596\) | 407760. | + | 143145.i | 1.14792 | + | 0.402980i | ||||
\(597\) | −178478. | − | 178478.i | −0.500768 | − | 0.500768i | ||||
\(598\) | 141911. | − | 225597.i | 0.396839 | − | 0.630856i | ||||
\(599\) | −210952. | −0.587936 | −0.293968 | − | 0.955815i | \(-0.594976\pi\) | ||||
−0.293968 | + | 0.955815i | \(0.594976\pi\) | |||||||
\(600\) | 827.869 | − | 7248.58i | 0.00229964 | − | 0.0201350i | ||||
\(601\) | − | 237359.i | − | 0.657139i | −0.944480 | − | 0.328569i | \(-0.893433\pi\) | ||
0.944480 | − | 0.328569i | \(-0.106567\pi\) | |||||||
\(602\) | 352714. | − | 560711.i | 0.973262 | − | 1.54720i | ||||
\(603\) | 61210.0 | − | 61210.0i | 0.168340 | − | 0.168340i | ||||
\(604\) | 281959. | − | 135433.i | 0.772880 | − | 0.371236i | ||||
\(605\) | −54370.7 | + | 54370.7i | −0.148544 | + | 0.148544i | ||||
\(606\) | 15289.3 | + | 67143.7i | 0.0416336 | + | 0.182835i | ||||
\(607\) | 354704.i | 0.962695i | 0.876530 | + | 0.481348i | \(0.159852\pi\) | ||||
−0.876530 | + | 0.481348i | \(0.840148\pi\) | |||||||
\(608\) | −444190. | + | 154168.i | −1.20160 | + | 0.417049i | ||||
\(609\) | −212439. | −0.572795 | ||||||||
\(610\) | 132635. | − | 30202.5i | 0.356451 | − | 0.0811678i | ||||
\(611\) | 401259. | + | 401259.i | 1.07484 | + | 1.07484i | ||||
\(612\) | −12370.3 | − | 25753.9i | −0.0330277 | − | 0.0687608i | ||||
\(613\) | 194911. | + | 194911.i | 0.518699 | + | 0.518699i | 0.917178 | − | 0.398478i | \(-0.130462\pi\) |
−0.398478 | + | 0.917178i | \(0.630462\pi\) | |||||||
\(614\) | 40125.9 | + | 25241.1i | 0.106436 | + | 0.0669532i | ||||
\(615\) | 155366. | 0.410778 | ||||||||
\(616\) | −86964.8 | + | 761439.i | −0.229183 | + | 2.00666i | ||||
\(617\) | 443656.i | 1.16540i | 0.812687 | + | 0.582701i | \(0.198004\pi\) | ||||
−0.812687 | + | 0.582701i | \(0.801996\pi\) | |||||||
\(618\) | 240219. | + | 151109.i | 0.628971 | + | 0.395653i | ||||
\(619\) | 304378. | − | 304378.i | 0.794388 | − | 0.794388i | −0.187816 | − | 0.982204i | \(-0.560141\pi\) |
0.982204 | + | 0.187816i | \(0.0601410\pi\) | |||||||
\(620\) | 206588. | − | 588482.i | 0.537429 | − | 1.53091i | ||||
\(621\) | 46359.0 | − | 46359.0i | 0.120213 | − | 0.120213i | ||||
\(622\) | 435881. | − | 99255.0i | 1.12665 | − | 0.256550i | ||||
\(623\) | − | 678124.i | − | 1.74716i | ||||||
\(624\) | −118554. | + | 148046.i | −0.304472 | + | 0.380214i | ||||
\(625\) | 376432. | 0.963666 | ||||||||
\(626\) | 75016.1 | + | 329435.i | 0.191428 | + | 0.840663i | ||||
\(627\) | 224907. | + | 224907.i | 0.572096 | + | 0.572096i | ||||
\(628\) | 12495.9 | − | 35595.7i | 0.0316847 | − | 0.0902564i | ||||
\(629\) | −64999.4 | − | 64999.4i | −0.164289 | − | 0.164289i | ||||
\(630\) | 126850. | − | 201655.i | 0.319603 | − | 0.508074i | ||||
\(631\) | −182483. | −0.458315 | −0.229157 | − | 0.973389i | \(-0.573597\pi\) | ||||
−0.229157 | + | 0.973389i | \(0.573597\pi\) | |||||||
\(632\) | 21473.5 | + | 27011.0i | 0.0537611 | + | 0.0676248i | ||||
\(633\) | − | 319293.i | − | 0.796860i | ||||||
\(634\) | 319088. | − | 507256.i | 0.793838 | − | 1.26197i | ||||
\(635\) | 252297. | − | 252297.i | 0.625699 | − | 0.625699i | ||||
\(636\) | 34243.7 | + | 71292.3i | 0.0846577 | + | 0.176250i | ||||
\(637\) | −571414. | + | 571414.i | −1.40823 | + | 1.40823i | ||||
\(638\) | −53887.5 | − | 236649.i | −0.132387 | − | 0.581384i | ||||
\(639\) | 158632.i | 0.388498i | ||||||||
\(640\) | −285509. | + | 283492.i | −0.697043 | + | 0.692120i | ||||
\(641\) | −469986. | −1.14385 | −0.571925 | − | 0.820306i | \(-0.693803\pi\) | ||||
−0.571925 | + | 0.820306i | \(0.693803\pi\) | |||||||
\(642\) | 304427. | − | 69321.3i | 0.738606 | − | 0.168189i | ||||
\(643\) | 536836. | + | 536836.i | 1.29843 | + | 1.29843i | 0.929427 | + | 0.369006i | \(0.120302\pi\) |
0.369006 | + | 0.929427i | \(0.379698\pi\) | |||||||
\(644\) | −605403. | + | 290792.i | −1.45973 | + | 0.701150i | ||||
\(645\) | −166350. | − | 166350.i | −0.399856 | − | 0.399856i | ||||
\(646\) | 102818. | + | 64677.6i | 0.246380 | + | 0.154985i | ||||
\(647\) | −359725. | −0.859333 | −0.429667 | − | 0.902988i | \(-0.641369\pi\) | ||||
−0.429667 | + | 0.902988i | \(0.641369\pi\) | |||||||
\(648\) | −36521.3 | + | 29034.1i | −0.0869753 | + | 0.0691446i | ||||
\(649\) | − | 224003.i | − | 0.531820i | ||||||
\(650\) | 10590.9 | + | 6662.21i | 0.0250673 | + | 0.0157685i | ||||
\(651\) | −523883. | + | 523883.i | −1.23615 | + | 1.23615i | ||||
\(652\) | −534166. | − | 187520.i | −1.25655 | − | 0.441115i | ||||
\(653\) | 149383. | − | 149383.i | 0.350328 | − | 0.350328i | −0.509904 | − | 0.860232i | \(-0.670319\pi\) |
0.860232 | + | 0.509904i | \(0.170319\pi\) | |||||||
\(654\) | 174783. | − | 39800.0i | 0.408642 | − | 0.0930523i | ||||
\(655\) | 385493.i | 0.898533i | ||||||||
\(656\) | 243302. | + | 194834.i | 0.565376 | + | 0.452748i | ||||
\(657\) | 98853.8 | 0.229014 | ||||||||
\(658\) | −317498. | − | 1.39430e6i | −0.733312 | − | 3.22036i | ||||
\(659\) | −381578. | − | 381578.i | −0.878644 | − | 0.878644i | 0.114750 | − | 0.993394i | \(-0.463393\pi\) |
−0.993394 | + | 0.114750i | \(0.963393\pi\) | |||||||
\(660\) | 256813. | + | 90154.6i | 0.589561 | + | 0.206966i | ||||
\(661\) | −124940. | − | 124940.i | −0.285955 | − | 0.285955i | 0.549523 | − | 0.835479i | \(-0.314809\pi\) |
−0.835479 | + | 0.549523i | \(0.814809\pi\) | |||||||
\(662\) | −67389.7 | + | 107130.i | −0.153772 | + | 0.244452i | ||||
\(663\) | 48998.8 | 0.111470 | ||||||||
\(664\) | −324375. | − | 37047.2i | −0.735717 | − | 0.0840271i | ||||
\(665\) | 1.01286e6i | 2.29036i | ||||||||
\(666\) | −79927.7 | + | 127061.i | −0.180197 | + | 0.286461i | ||||
\(667\) | 150398. | − | 150398.i | 0.338056 | − | 0.338056i | ||||
\(668\) | −116082. | + | 55757.4i | −0.260143 | + | 0.124954i | ||||
\(669\) | 280673. | − | 280673.i | 0.627117 | − | 0.627117i | ||||
\(670\) | 69923.2 | + | 307070.i | 0.155766 | + | 0.684050i | ||||
\(671\) | − | 184614.i | − | 0.410034i | ||||||
\(672\) | 451526. | − | 156714.i | 0.999872 | − | 0.347032i | ||||
\(673\) | −428903. | −0.946955 | −0.473478 | − | 0.880806i | \(-0.657002\pi\) | ||||
−0.473478 | + | 0.880806i | \(0.657002\pi\) | |||||||
\(674\) | 485168. | − | 110478.i | 1.06800 | − | 0.243196i | ||||
\(675\) | 2176.39 | + | 2176.39i | 0.00477671 | + | 0.00477671i | ||||
\(676\) | 57022.9 | + | 118717.i | 0.124783 | + | 0.259787i | ||||
\(677\) | −104764. | − | 104764.i | −0.228579 | − | 0.228579i | 0.583520 | − | 0.812099i | \(-0.301675\pi\) |
−0.812099 | + | 0.583520i | \(0.801675\pi\) | |||||||
\(678\) | 36845.6 | + | 23177.7i | 0.0801543 | + | 0.0504209i | ||||
\(679\) | −861947. | −1.86957 | ||||||||
\(680\) | 103273. | + | 11794.9i | 0.223341 | + | 0.0255080i | ||||
\(681\) | 304719.i | 0.657060i | ||||||||
\(682\) | −716476. | − | 450698.i | −1.54040 | − | 0.968984i | ||||
\(683\) | −463952. | + | 463952.i | −0.994561 | + | 0.994561i | −0.999985 | − | 0.00542469i | \(-0.998273\pi\) |
0.00542469 | + | 0.999985i | \(0.498273\pi\) | |||||||
\(684\) | 65703.2 | − | 187161.i | 0.140435 | − | 0.400040i | ||||
\(685\) | 320288. | − | 320288.i | 0.682589 | − | 0.682589i | ||||
\(686\) | 1.14441e6 | − | 260594.i | 2.43183 | − | 0.553754i | ||||
\(687\) | − | 196773.i | − | 0.416920i | ||||||
\(688\) | −51894.2 | − | 469110.i | −0.109633 | − | 0.991054i | ||||
\(689\) | −135639. | −0.285724 | ||||||||
\(690\) | 52958.2 | + | 232567.i | 0.111233 | + | 0.488484i | ||||
\(691\) | 515030. | + | 515030.i | 1.07864 | + | 1.07864i | 0.996632 | + | 0.0820090i | \(0.0261336\pi\) |
0.0820090 | + | 0.996632i | \(0.473866\pi\) | |||||||
\(692\) | 112381. | − | 320126.i | 0.234682 | − | 0.668511i | ||||
\(693\) | −228622. | − | 228622.i | −0.476049 | − | 0.476049i | ||||
\(694\) | −491128. | + | 780748.i | −1.01971 | + | 1.62103i | ||||
\(695\) | 504978. | 1.04545 | ||||||||
\(696\) | −118482. | + | 94192.2i | −0.244587 | + | 0.194445i | ||||
\(697\) | − | 80525.5i | − | 0.165755i | ||||||
\(698\) | −368255. | + | 585416.i | −0.755853 | + | 1.20158i | ||||
\(699\) | −361464. | + | 361464.i | −0.739793 | + | 0.739793i | ||||
\(700\) | −13651.6 | − | 28421.5i | −0.0278605 | − | 0.0580030i | ||||
\(701\) | −468514. | + | 468514.i | −0.953424 | + | 0.953424i | −0.998963 | − | 0.0455384i | \(-0.985500\pi\) |
0.0455384 | + | 0.998963i | \(0.485500\pi\) | |||||||
\(702\) | −17765.5 | − | 78017.8i | −0.0360498 | − | 0.158314i | ||||
\(703\) | − | 638195.i | − | 1.29135i | ||||||
\(704\) | 289109. | + | 463231.i | 0.583332 | + | 0.934657i | ||||
\(705\) | −507852. | −1.02178 | ||||||||
\(706\) | −846128. | + | 192673.i | −1.69757 | + | 0.386554i | ||||
\(707\) | 210439. | + | 210439.i | 0.421004 | + | 0.421004i | ||||
\(708\) | −125924. | + | 60484.7i | −0.251212 | + | 0.120664i | ||||
\(709\) | −177649. | − | 177649.i | −0.353403 | − | 0.353403i | 0.507971 | − | 0.861374i | \(-0.330396\pi\) |
−0.861374 | + | 0.507971i | \(0.830396\pi\) | |||||||
\(710\) | −488508. | − | 307295.i | −0.969070 | − | 0.609591i | ||||
\(711\) | −14557.5 | −0.0287969 | ||||||||
\(712\) | −300670. | − | 378206.i | −0.593104 | − | 0.746050i | ||||
\(713\) | − | 741774.i | − | 1.45913i | ||||||
\(714\) | −104516. | − | 65745.8i | −0.205016 | − | 0.128965i | ||||
\(715\) | −330066. | + | 330066.i | −0.645637 | + | 0.645637i | ||||
\(716\) | 474294. | + | 166502.i | 0.925169 | + | 0.324783i | ||||
\(717\) | 101677. | − | 101677.i | 0.197781 | − | 0.197781i | ||||
\(718\) | −249454. | + | 56803.4i | −0.483885 | + | 0.110186i | ||||
\(719\) | − | 23226.4i | − | 0.0449287i | −0.999748 | − | 0.0224644i | \(-0.992849\pi\) | ||
0.999748 | − | 0.0224644i | \(-0.00715123\pi\) | |||||||
\(720\) | −18663.3 | − | 168711.i | −0.0360017 | − | 0.325446i | ||||
\(721\) | 1.22648e6 | 2.35934 | ||||||||
\(722\) | 71501.8 | + | 314003.i | 0.137165 | + | 0.602364i | ||||
\(723\) | −170816. | − | 170816.i | −0.326778 | − | 0.326778i | ||||
\(724\) | −162515. | − | 57051.2i | −0.310039 | − | 0.108840i | ||||
\(725\) | 7060.62 | + | 7060.62i | 0.0134328 | + | 0.0134328i | ||||
\(726\) | 34652.0 | − | 55086.5i | 0.0657439 | − | 0.104513i | ||||
\(727\) | 845037. | 1.59885 | 0.799423 | − | 0.600768i | \(-0.205138\pi\) | ||||
0.799423 | + | 0.600768i | \(0.205138\pi\) | |||||||
\(728\) | −93012.0 | + | 814387.i | −0.175500 | + | 1.53663i | ||||
\(729\) | − | 19683.0i | − | 0.0370370i | ||||||
\(730\) | −191495. | + | 304421.i | −0.359345 | + | 0.571253i | ||||
\(731\) | −86218.3 | + | 86218.3i | −0.161348 | + | 0.161348i | ||||
\(732\) | −103781. | + | 49849.0i | −0.193685 | + | 0.0930325i | ||||
\(733\) | −179935. | + | 179935.i | −0.334895 | + | 0.334895i | −0.854442 | − | 0.519547i | \(-0.826101\pi\) |
0.519547 | + | 0.854442i | \(0.326101\pi\) | |||||||
\(734\) | 63654.3 | + | 279540.i | 0.118150 | + | 0.518862i | ||||
\(735\) | − | 723209.i | − | 1.33872i | ||||||
\(736\) | −208714. | + | 430608.i | −0.385298 | + | 0.794926i | ||||
\(737\) | 427409. | 0.786880 | ||||||||
\(738\) | −128216. | + | 29196.1i | −0.235412 | + | 0.0536058i | ||||
\(739\) | −151733. | − | 151733.i | −0.277837 | − | 0.277837i | 0.554408 | − | 0.832245i | \(-0.312945\pi\) |
−0.832245 | + | 0.554408i | \(0.812945\pi\) | |||||||
\(740\) | −236454. | − | 492275.i | −0.431800 | − | 0.898968i | ||||
\(741\) | 240547. | + | 240547.i | 0.438090 | + | 0.438090i | ||||
\(742\) | 289323. | + | 181998.i | 0.525503 | + | 0.330567i | ||||
\(743\) | −576375. | −1.04406 | −0.522032 | − | 0.852926i | \(-0.674826\pi\) | ||||
−0.522032 | + | 0.852926i | \(0.674826\pi\) | |||||||
\(744\) | −59899.6 | + | 524464.i | −0.108213 | + | 0.947480i | ||||
\(745\) | − | 663286.i | − | 1.19506i | ||||||
\(746\) | −301027. | − | 189361.i | −0.540914 | − | 0.340261i | ||||
\(747\) | 97393.5 | − | 97393.5i | 0.174537 | − | 0.174537i | ||||
\(748\) | 46726.6 | − | 133104.i | 0.0835143 | − | 0.237897i | ||||
\(749\) | 954120. | − | 954120.i | 1.70075 | − | 1.70075i | ||||
\(750\) | −321965. | + | 73314.9i | −0.572382 | + | 0.130338i | ||||
\(751\) | 316650.i | 0.561435i | 0.959790 | + | 0.280718i | \(0.0905725\pi\) | ||||
−0.959790 | + | 0.280718i | \(0.909428\pi\) | |||||||
\(752\) | −795289. | − | 636860.i | −1.40634 | − | 1.12618i | ||||
\(753\) | 194896. | 0.343727 | ||||||||
\(754\) | −57634.7 | − | 253105.i | −0.101377 | − | 0.445202i | ||||
\(755\) | −339477. | − | 339477.i | −0.595548 | − | 0.595548i | ||||
\(756\) | −66788.4 | + | 190252.i | −0.116858 | + | 0.332879i | ||||
\(757\) | 370431. | + | 370431.i | 0.646420 | + | 0.646420i | 0.952126 | − | 0.305706i | \(-0.0988923\pi\) |
−0.305706 | + | 0.952126i | \(0.598892\pi\) | |||||||
\(758\) | 71427.6 | − | 113549.i | 0.124316 | − | 0.197626i | ||||
\(759\) | 323709. | 0.561916 | ||||||||
\(760\) | 449086. | + | 564893.i | 0.777503 | + | 0.978001i | ||||
\(761\) | 1.11708e6i | 1.92893i | 0.264218 | + | 0.964463i | \(0.414886\pi\) | ||||
−0.264218 | + | 0.964463i | \(0.585114\pi\) | |||||||
\(762\) | −160796. | + | 255619.i | −0.276928 | + | 0.440233i | ||||
\(763\) | 547796. | − | 547796.i | 0.940957 | − | 0.940957i | ||||
\(764\) | −221507. | − | 461158.i | −0.379490 | − | 0.790065i | ||||
\(765\) | −31007.6 | + | 31007.6i | −0.0529841 | + | 0.0529841i | ||||
\(766\) | 108090. | + | 474681.i | 0.184216 | + | 0.808992i | ||||
\(767\) | − | 239579.i | − | 0.407248i | ||||||
\(768\) | 182342. | − | 287603.i | 0.309146 | − | 0.487608i | ||||
\(769\) | 214105. | 0.362055 | 0.181028 | − | 0.983478i | \(-0.442058\pi\) | ||||
0.181028 | + | 0.983478i | \(0.442058\pi\) | |||||||
\(770\) | 1.14692e6 | − | 261166.i | 1.93442 | − | 0.440489i | ||||
\(771\) | −114576. | − | 114576.i | −0.192745 | − | 0.192745i | ||||
\(772\) | 252642. | − | 121351.i | 0.423907 | − | 0.203614i | ||||
\(773\) | 503106. | + | 503106.i | 0.841978 | + | 0.841978i | 0.989116 | − | 0.147138i | \(-0.0470061\pi\) |
−0.147138 | + | 0.989116i | \(0.547006\pi\) | |||||||
\(774\) | 168540. | + | 106020.i | 0.281333 | + | 0.176972i | ||||
\(775\) | 34823.6 | 0.0579789 | ||||||||
\(776\) | −480728. | + | 382175.i | −0.798317 | + | 0.634656i | ||||
\(777\) | 648735.i | 1.07455i | ||||||||
\(778\) | 191890. | + | 120708.i | 0.317024 | + | 0.199423i | ||||
\(779\) | 395318. | − | 395318.i | 0.651436 | − | 0.651436i | ||||
\(780\) | 274671. | + | 96423.6i | 0.451464 | + | 0.158487i | ||||
\(781\) | −553837. | + | 553837.i | −0.907987 | + | 0.907987i | ||||
\(782\) | 120538. | − | 27447.9i | 0.197111 | − | 0.0448844i | ||||
\(783\) | − | 63855.4i | − | 0.104154i | ||||||
\(784\) | 906923. | − | 1.13253e6i | 1.47550 | − | 1.84255i | ||||
\(785\) | −57902.1 | −0.0939625 | ||||||||
\(786\) | −72440.9 | − | 318127.i | −0.117257 | − | 0.514938i | ||||
\(787\) | −437192. | − | 437192.i | −0.705868 | − | 0.705868i | 0.259796 | − | 0.965664i | \(-0.416345\pi\) |
−0.965664 | + | 0.259796i | \(0.916345\pi\) | |||||||
\(788\) | 996008. | + | 349651.i | 1.60402 | + | 0.563095i | ||||
\(789\) | −321607. | − | 321607.i | −0.516620 | − | 0.516620i | ||||
\(790\) | 28200.1 | − | 44829.7i | 0.0451852 | − | 0.0718310i | ||||
\(791\) | 188122. | 0.300668 | ||||||||
\(792\) | −228875. | − | 26140.1i | −0.364879 | − | 0.0416732i | ||||
\(793\) | − | 197452.i | − | 0.313989i | ||||||
\(794\) | −356802. | + | 567210.i | −0.565961 | + | 0.899710i | ||||
\(795\) | 85835.6 | − | 85835.6i | 0.135810 | − | 0.135810i | ||||
\(796\) | −700584. | + | 336510.i | −1.10569 | + | 0.531094i | ||||
\(797\) | −37761.0 | + | 37761.0i | −0.0594466 | + | 0.0594466i | −0.736205 | − | 0.676759i | \(-0.763384\pi\) |
0.676759 | + | 0.736205i | \(0.263384\pi\) | |||||||
\(798\) | −190334. | − | 835856.i | −0.298889 | − | 1.31258i | ||||
\(799\) | 263217.i | 0.412306i | ||||||||
\(800\) | −20215.5 | − | 9798.38i | −0.0315867 | − | 0.0153100i | ||||
\(801\) | 203832. | 0.317694 | ||||||||
\(802\) | 175961. | − | 40068.2i | 0.273569 | − | 0.0622947i | ||||
\(803\) | 345131. | + | 345131.i | 0.535245 | + | 0.535245i | ||||
\(804\) | −115408. | − | 240269.i | −0.178535 | − | 0.371693i | ||||
\(805\) | 728902. | + | 728902.i | 1.12481 | + | 1.12481i | ||||
\(806\) | −766297. | − | 482037.i | −1.17958 | − | 0.742012i | ||||
\(807\) | −280564. | −0.430809 | ||||||||
\(808\) | 210672. | + | 24061.1i | 0.322689 | + | 0.0368546i | ||||
\(809\) | − | 1.19381e6i | − | 1.82406i | −0.410120 | − | 0.912032i | \(-0.634513\pi\) | ||
0.410120 | − | 0.912032i | \(-0.365487\pi\) | |||||||
\(810\) | 60613.9 | + | 38129.0i | 0.0923851 | + | 0.0581147i | ||||
\(811\) | 660081. | − | 660081.i | 1.00359 | − | 1.00359i | 0.00359390 | − | 0.999994i | \(-0.498856\pi\) |
0.999994 | − | 0.00359390i | \(-0.00114398\pi\) | |||||||
\(812\) | −216674. | + | 617214.i | −0.328621 | + | 0.936104i | ||||
\(813\) | −73396.6 | + | 73396.6i | −0.111044 | + | 0.111044i | ||||
\(814\) | −722667. | + | 164559.i | −1.09066 | + | 0.248355i | ||||
\(815\) | 868906.i | 1.30815i | ||||||||
\(816\) | −87441.9 | + | 9673.07i | −0.131323 | + | 0.0145273i | ||||
\(817\) | −846531. | −1.26823 | ||||||||
\(818\) | 83149.2 | + | 365152.i | 0.124266 | + | 0.545717i | ||||
\(819\) | −244520. | − | 244520.i | −0.364541 | − | 0.364541i | ||||
\(820\) | 158464. | − | 451398.i | 0.235669 | − | 0.671323i | ||||
\(821\) | 344916. | + | 344916.i | 0.511714 | + | 0.511714i | 0.915051 | − | 0.403337i | \(-0.132150\pi\) |
−0.403337 | + | 0.915051i | \(0.632150\pi\) | |||||||
\(822\) | −204129. | + | 324504.i | −0.302107 | + | 0.480260i | ||||
\(823\) | −1.06287e6 | −1.56921 | −0.784603 | − | 0.619999i | \(-0.787133\pi\) | ||||
−0.784603 | + | 0.619999i | \(0.787133\pi\) | |||||||
\(824\) | 684038. | − | 543804.i | 1.00745 | − | 0.800919i | ||||
\(825\) | 15197.0i | 0.0223280i | ||||||||
\(826\) | −321463. | + | 511031.i | −0.471163 | + | 0.749010i | ||||
\(827\) | 514170. | − | 514170.i | 0.751789 | − | 0.751789i | −0.223024 | − | 0.974813i | \(-0.571593\pi\) |
0.974813 | + | 0.223024i | \(0.0715928\pi\) | |||||||
\(828\) | −87407.1 | − | 181974.i | −0.127493 | − | 0.265429i | ||||
\(829\) | 613712. | − | 613712.i | 0.893009 | − | 0.893009i | −0.101796 | − | 0.994805i | \(-0.532459\pi\) |
0.994805 | + | 0.101796i | \(0.0324589\pi\) | |||||||
\(830\) | 111257. | + | 488590.i | 0.161500 | + | 0.709232i | ||||
\(831\) | 61340.9i | 0.0888277i | ||||||||
\(832\) | 309212. | + | 495442.i | 0.446694 | + | 0.715726i | ||||
\(833\) | −374835. | −0.540194 | ||||||||
\(834\) | −416731. | + | 94894.3i | −0.599134 | + | 0.136429i | ||||
\(835\) | 139762. | + | 139762.i | 0.200455 | + | 0.200455i | ||||
\(836\) | 882832. | − | 424049.i | 1.26318 | − | 0.606741i | ||||
\(837\) | −157470. | − | 157470.i | −0.224775 | − | 0.224775i | ||||
\(838\) | −587515. | − | 369575.i | −0.836625 | − | 0.526277i | ||||
\(839\) | 840032. | 1.19336 | 0.596680 | − | 0.802479i | \(-0.296486\pi\) | ||||
0.596680 | + | 0.802479i | \(0.296486\pi\) | |||||||
\(840\) | −456503. | − | 574223.i | −0.646971 | − | 0.813808i | ||||
\(841\) | 500122.i | 0.707105i | ||||||||
\(842\) | 232683. | + | 146369.i | 0.328201 | + | 0.206454i | ||||
\(843\) | 156063. | − | 156063.i | 0.219606 | − | 0.219606i | ||||
\(844\) | −927666. | − | 325659.i | −1.30229 | − | 0.457171i | ||||
\(845\) | 142934. | − | 142934.i | 0.200181 | − | 0.200181i | ||||
\(846\) | 419103. | − | 95434.3i | 0.585572 | − | 0.133341i | ||||
\(847\) | − | 281254.i | − | 0.392042i | ||||||
\(848\) | 242057. | − | 26777.1i | 0.336610 | − | 0.0372367i | ||||
\(849\) | 263287. | 0.365270 | ||||||||
\(850\) | 1288.58 | + | 5658.83i | 0.00178350 | + | 0.00783230i | ||||
\(851\) | −459277. | − | 459277.i | −0.634184 | − | 0.634184i | ||||
\(852\) | 460886. | + | 161795.i | 0.634913 | + | 0.222887i | ||||
\(853\) | −268667. | − | 268667.i | −0.369246 | − | 0.369246i | 0.497956 | − | 0.867202i | \(-0.334084\pi\) |
−0.867202 | + | 0.497956i | \(0.834084\pi\) | |||||||
\(854\) | −264937. | + | 421172.i | −0.363268 | + | 0.577489i | ||||
\(855\) | −304447. | −0.416466 | ||||||||
\(856\) | 109092. | − | 955178.i | 0.148883 | − | 1.30358i | ||||
\(857\) | − | 178340.i | − | 0.242821i | −0.992602 | − | 0.121411i | \(-0.961258\pi\) | ||
0.992602 | − | 0.121411i | \(-0.0387418\pi\) | |||||||
\(858\) | 210360. | − | 334411.i | 0.285752 | − | 0.454261i | ||||
\(859\) | −449410. | + | 449410.i | −0.609055 | + | 0.609055i | −0.942699 | − | 0.333644i | \(-0.891722\pi\) |
0.333644 | + | 0.942699i | \(0.391722\pi\) | |||||||
\(860\) | −652977. | + | 313643.i | −0.882878 | + | 0.424071i | ||||
\(861\) | −401847. | + | 401847.i | −0.542069 | + | 0.542069i | ||||
\(862\) | 28553.2 | + | 125392.i | 0.0384273 | + | 0.168755i | ||||
\(863\) | 278925.i | 0.374512i | 0.982311 | + | 0.187256i | \(0.0599594\pi\) | ||||
−0.982311 | + | 0.187256i | \(0.940041\pi\) | |||||||
\(864\) | 47105.6 | + | 135721.i | 0.0631023 | + | 0.181811i | ||||
\(865\) | −520735. | −0.695961 | ||||||||
\(866\) | −355280. | + | 80901.2i | −0.473735 | + | 0.107875i | ||||
\(867\) | −290805. | − | 290805.i | −0.386868 | − | 0.386868i | ||||
\(868\) | 987750. | + | 2.05641e6i | 1.31101 | + | 2.72942i | ||||
\(869\) | −50824.9 | − | 50824.9i | −0.0673033 | − | 0.0673033i | ||||
\(870\) | 196643. | + | 123698.i | 0.259801 | + | 0.163427i | ||||
\(871\) | 457129. | 0.602563 | ||||||||
\(872\) | 62633.8 | − | 548403.i | 0.0823712 | − | 0.721219i | ||||
\(873\) | − | 259086.i | − | 0.339951i | ||||||
\(874\) | 726498. | + | 457002.i | 0.951069 | + | 0.598268i | ||||
\(875\) | −1.00909e6 | + | 1.00909e6i | −1.31799 | + | 1.31799i | ||||
\(876\) | 100825. | − | 287207.i | 0.131389 | − | 0.374272i | ||||
\(877\) | −391918. | + | 391918.i | −0.509560 | + | 0.509560i | −0.914392 | − | 0.404831i | \(-0.867330\pi\) |
0.404831 | + | 0.914392i | \(0.367330\pi\) | |||||||
\(878\) | −1.04219e6 | + | 237317.i | −1.35194 | + | 0.307851i | ||||
\(879\) | 662013.i | 0.856819i | ||||||||
\(880\) | 523866. | − | 654185.i | 0.676480 | − | 0.844764i | ||||
\(881\) | 971511. | 1.25169 | 0.625844 | − | 0.779949i | \(-0.284755\pi\) | ||||
0.625844 | + | 0.779949i | \(0.284755\pi\) | |||||||
\(882\) | 135904. | + | 596825.i | 0.174700 | + | 0.767203i | ||||
\(883\) | 86997.4 | + | 86997.4i | 0.111580 | + | 0.111580i | 0.760692 | − | 0.649113i | \(-0.224860\pi\) |
−0.649113 | + | 0.760692i | \(0.724860\pi\) | |||||||
\(884\) | 49975.8 | − | 142360.i | 0.0639521 | − | 0.182173i | ||||
\(885\) | 151611. | + | 151611.i | 0.193573 | + | 0.193573i | ||||
\(886\) | 504160. | − | 801465.i | 0.642245 | − | 1.02098i | ||||
\(887\) | −266811. | −0.339123 | −0.169561 | − | 0.985520i | \(-0.554235\pi\) | ||||
−0.169561 | + | 0.985520i | \(0.554235\pi\) | |||||||
\(888\) | 287640. | + | 361815.i | 0.364773 | + | 0.458839i | ||||
\(889\) | 1.30511e6i | 1.65137i | ||||||||
\(890\) | −394855. | + | 627703.i | −0.498492 | + | 0.792454i | ||||
\(891\) | 68719.8 | − | 68719.8i | 0.0865619 | − | 0.0865619i | ||||
\(892\) | −529192. | − | 1.10173e6i | −0.665094 | − | 1.38467i | ||||
\(893\) | −1.29219e6 | + | 1.29219e6i | −1.62041 | + | 1.62041i | ||||
\(894\) | 124643. | + | 547375.i | 0.155953 | + | 0.684872i | ||||
\(895\) | − | 771514.i | − | 0.963159i | ||||||
\(896\) | 5215.01 | − | 1.47169e6i | 0.00649590 | − | 1.83316i | ||||
\(897\) | 346219. | 0.430294 | ||||||||
\(898\) | 685602. | − | 156119.i | 0.850196 | − | 0.193599i | ||||
\(899\) | −510864. | − | 510864.i | −0.632100 | − | 0.632100i | ||||
\(900\) | 8543.00 | − | 4103.44i | 0.0105469 | − | 0.00506598i | ||||
\(901\) | −44488.0 | − | 44488.0i | −0.0548017 | − | 0.0548017i | ||||
\(902\) | −549576. | − | 345710.i | −0.675484 | − | 0.424912i | ||||
\(903\) | 860512. | 1.05531 | ||||||||
\(904\) | 104920. | − | 83410.6i | 0.128387 | − | 0.102067i | ||||
\(905\) | 264357.i | 0.322770i | ||||||||
\(906\) | 343946. | + | 216359.i | 0.419019 | + | 0.263583i | ||||
\(907\) | −544293. | + | 544293.i | −0.661634 | + | 0.661634i | −0.955765 | − | 0.294131i | \(-0.904970\pi\) |
0.294131 | + | 0.955765i | \(0.404970\pi\) | |||||||
\(908\) | 885323. | + | 310794.i | 1.07382 | + | 0.376965i | ||||
\(909\) | −63254.2 | + | 63254.2i | −0.0765529 | + | 0.0765529i | ||||
\(910\) | 1.22667e6 | − | 279327.i | 1.48131 | − | 0.337310i | ||||
\(911\) | − | 234819.i | − | 0.282941i | −0.989942 | − | 0.141470i | \(-0.954817\pi\) | ||
0.989942 | − | 0.141470i | \(-0.0451830\pi\) | |||||||
\(912\) | −476760. | − | 381785.i | −0.573205 | − | 0.459018i | ||||
\(913\) | 680065. | 0.815848 | ||||||||
\(914\) | −349451. | − | 1.53463e6i | −0.418306 | − | 1.83701i | ||||
\(915\) | 124952. | + | 124952.i | 0.149246 | + | 0.149246i | ||||
\(916\) | −571700. | − | 200696.i | −0.681361 | − | 0.239193i | ||||
\(917\) | −997058. | − | 997058.i | −1.18572 | − | 1.18572i | ||||
\(918\) | 19762.0 | − | 31415.8i | 0.0234502 | − | 0.0372789i | ||||
\(919\) | −1.14238e6 | −1.35263 | −0.676317 | − | 0.736610i | \(-0.736425\pi\) | ||||
−0.676317 | + | 0.736610i | \(0.736425\pi\) | |||||||
\(920\) | 729710. | + | 83341.0i | 0.862134 | + | 0.0984653i | ||||
\(921\) | 61580.4i | 0.0725978i | ||||||||
\(922\) | 258684. | − | 411231.i | 0.304304 | − | 0.483753i | ||||
\(923\) | −592349. | + | 592349.i | −0.695303 | + | 0.695303i | ||||
\(924\) | −897413. | + | 431053.i | −1.05111 | + | 0.504878i | ||||
\(925\) | 21561.4 | − | 21561.4i | 0.0251996 | − | 0.0251996i | ||||
\(926\) | −99568.9 | − | 437260.i | −0.116119 | − | 0.509939i | ||||
\(927\) | 368660.i | 0.429009i | ||||||||
\(928\) | 152820. | + | 440305.i | 0.177453 | + | 0.511278i | ||||
\(929\) | 832146. | 0.964202 | 0.482101 | − | 0.876116i | \(-0.339874\pi\) | ||||
0.482101 | + | 0.876116i | \(0.339874\pi\) | |||||||
\(930\) | 789975. | − | 179886.i | 0.913372 | − | 0.207985i | ||||
\(931\) | −1.84015e6 | − | 1.84015e6i | −2.12302 | − | 2.12302i | ||||
\(932\) | 681518. | + | 1.41886e6i | 0.784594 | + | 1.63346i | ||||
\(933\) | 410632. | + | 410632.i | 0.471725 | + | 0.471725i | ||||
\(934\) | 195378. | + | 122902.i | 0.223966 | + | 0.140886i | ||||
\(935\) | −216516. | −0.247666 | ||||||||
\(936\) | −244791. | − | 27957.8i | −0.279411 | − | 0.0319118i | ||||
\(937\) | − | 1.26470e6i | − | 1.44048i | −0.693723 | − | 0.720242i | \(-0.744031\pi\) | ||
0.693723 | − | 0.720242i | \(-0.255969\pi\) | |||||||
\(938\) | −975073. | − | 613368.i | −1.10823 | − | 0.697133i | ||||
\(939\) | −310352. | + | 310352.i | −0.351984 | + | 0.351984i | ||||
\(940\) | −517977. | + | 1.47550e6i | −0.586212 | + | 1.66987i | ||||
\(941\) | 596498. | − | 596498.i | 0.673643 | − | 0.673643i | −0.284911 | − | 0.958554i | \(-0.591964\pi\) |
0.958554 | + | 0.284911i | \(0.0919639\pi\) | |||||||
\(942\) | 47783.5 | − | 10880.8i | 0.0538488 | − | 0.0122620i | ||||
\(943\) | − | 568981.i | − | 0.639845i | ||||||
\(944\) | 47296.4 | + | 427546.i | 0.0530742 | + | 0.479777i | ||||
\(945\) | 309475. | 0.346547 | ||||||||
\(946\) | 218279. | + | 958579.i | 0.243910 | + | 1.07114i | ||||
\(947\) | −428200. | − | 428200.i | −0.477471 | − | 0.477471i | 0.426851 | − | 0.904322i | \(-0.359623\pi\) |
−0.904322 | + | 0.426851i | \(0.859623\pi\) | |||||||
\(948\) | −14847.7 | + | 42294.9i | −0.0165212 | + | 0.0470621i | ||||
\(949\) | 369130. | + | 369130.i | 0.409871 | + | 0.409871i | ||||
\(950\) | −21454.6 | + | 34106.5i | −0.0237724 | + | 0.0377911i | ||||
\(951\) | 778475. | 0.860764 | ||||||||
\(952\) | −297616. | + | 236603.i | −0.328385 | + | 0.261063i | ||||
\(953\) | − | 273921.i | − | 0.301606i | −0.988564 | − | 0.150803i | \(-0.951814\pi\) | ||
0.988564 | − | 0.150803i | \(-0.0481859\pi\) | |||||||
\(954\) | −54705.5 | + | 86965.5i | −0.0601082 | + | 0.0955543i | ||||
\(955\) | −555231. | + | 555231.i | −0.608790 | + | 0.608790i | ||||
\(956\) | −191706. | − | 399115.i | −0.209759 | − | 0.436699i | ||||
\(957\) | 222940. | − | 222940.i | 0.243425 | − | 0.243425i | ||||
\(958\) | −99170.7 | − | 435511.i | −0.108057 | − | 0.474535i | ||||
\(959\) | 1.65682e6i | 1.80151i | ||||||||
\(960\) | −509204. | − | 117851.i | −0.552522 | − | 0.127876i | ||||
\(961\) | −1.59611e6 | −1.72828 | ||||||||
\(962\) | −772918. | + | 176002.i | −0.835187 | + | 0.190181i | ||||
\(963\) | 286792. | + | 286792.i | 0.309254 | + | 0.309254i | ||||
\(964\) | −670507. | + | 322063.i | −0.721521 | + | 0.346567i | ||||
\(965\) | −304179. | − | 304179.i | −0.326644 | − | 0.326644i | ||||
\(966\) | −738497. | − | 464550.i | −0.791397 | − | 0.497827i | ||||
\(967\) | 715792. | 0.765480 | 0.382740 | − | 0.923856i | \(-0.374981\pi\) | ||||
0.382740 | + | 0.923856i | \(0.374981\pi\) | |||||||
\(968\) | −124704. | − | 156862.i | −0.133085 | − | 0.167404i | ||||
\(969\) | 157793.i | 0.168051i | ||||||||
\(970\) | 797858. | + | 501891.i | 0.847973 | + | 0.533416i | ||||
\(971\) | 332443. | − | 332443.i | 0.352597 | − | 0.352597i | −0.508478 | − | 0.861075i | \(-0.669792\pi\) |
0.861075 | + | 0.508478i | \(0.169792\pi\) | |||||||
\(972\) | −57186.5 | − | 20075.4i | −0.0605287 | − | 0.0212487i | ||||
\(973\) | −1.30610e6 | + | 1.30610e6i | −1.37959 | + | 1.37959i | ||||
\(974\) | 248872. | − | 56670.9i | 0.262336 | − | 0.0597368i | ||||
\(975\) | 16253.7i | 0.0170979i | ||||||||
\(976\) | 38979.8 | + | 352366.i | 0.0409204 | + | 0.369909i | ||||
\(977\) | −174170. | −0.182467 | −0.0912333 | − | 0.995830i | \(-0.529081\pi\) | ||||
−0.0912333 | + | 0.995830i | \(0.529081\pi\) | |||||||
\(978\) | −163283. | − | 717061.i | −0.170711 | − | 0.749685i | ||||
\(979\) | 711646. | + | 711646.i | 0.742504 | + | 0.742504i | ||||
\(980\) | −2.10119e6 | − | 737628.i | −2.18783 | − | 0.768042i | ||||
\(981\) | 164658. | + | 164658.i | 0.171098 | + | 0.171098i | ||||
\(982\) | 304080. | − | 483397.i | 0.315330 | − | 0.501281i | ||||
\(983\) | 1.62409e6 | 1.68075 | 0.840376 | − | 0.542004i | \(-0.182334\pi\) | ||||
0.840376 | + | 0.542004i | \(0.182334\pi\) | |||||||
\(984\) | −45946.3 | + | 402293.i | −0.0474526 | + | 0.415482i | ||||
\(985\) | − | 1.62017e6i | − | 1.66989i | ||||||
\(986\) | 64111.9 | − | 101919.i | 0.0659454 | − | 0.104834i | ||||
\(987\) | 1.31353e6 | − | 1.31353e6i | 1.34836 | − | 1.34836i | ||||
\(988\) | 944221. | − | 453536.i | 0.967297 | − | 0.464620i | ||||
\(989\) | −609206. | + | 609206.i | −0.622833 | + | 0.622833i | ||||
\(990\) | 78502.0 | + | 344744.i | 0.0800959 | + | 0.351744i | ||||
\(991\) | 931514.i | 0.948510i | 0.880387 | + | 0.474255i | \(0.157283\pi\) | ||||
−0.880387 | + | 0.474255i | \(0.842717\pi\) | |||||||
\(992\) | 1.46267e6 | + | 708952.i | 1.48636 | + | 0.720433i | ||||
\(993\) | −164410. | −0.166736 | ||||||||
\(994\) | 2.05830e6 | − | 468698.i | 2.08323 | − | 0.474374i | ||||
\(995\) | 843499. | + | 843499.i | 0.851998 | + | 0.851998i | ||||
\(996\) | −183629. | − | 382300.i | −0.185107 | − | 0.385377i | ||||
\(997\) | 226779. | + | 226779.i | 0.228145 | + | 0.228145i | 0.811918 | − | 0.583772i | \(-0.198424\pi\) |
−0.583772 | + | 0.811918i | \(0.698424\pi\) | |||||||
\(998\) | 14451.4 | + | 9090.63i | 0.0145094 | + | 0.00912711i | ||||
\(999\) | −194999. | −0.195389 |
(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 | 48.5.l.a.43.16 | yes | 32 | |
3.2 | odd | 2 | 144.5.m.c.91.1 | 32 | |||
4.3 | odd | 2 | 192.5.l.a.79.2 | 32 | |||
8.3 | odd | 2 | 384.5.l.a.31.15 | 32 | |||
8.5 | even | 2 | 384.5.l.b.31.2 | 32 | |||
12.11 | even | 2 | 576.5.m.b.271.13 | 32 | |||
16.3 | odd | 4 | inner | 48.5.l.a.19.16 | ✓ | 32 | |
16.5 | even | 4 | 384.5.l.a.223.15 | 32 | |||
16.11 | odd | 4 | 384.5.l.b.223.2 | 32 | |||
16.13 | even | 4 | 192.5.l.a.175.2 | 32 | |||
48.29 | odd | 4 | 576.5.m.b.559.13 | 32 | |||
48.35 | even | 4 | 144.5.m.c.19.1 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.5.l.a.19.16 | ✓ | 32 | 16.3 | odd | 4 | inner | |
48.5.l.a.43.16 | yes | 32 | 1.1 | even | 1 | trivial | |
144.5.m.c.19.1 | 32 | 48.35 | even | 4 | |||
144.5.m.c.91.1 | 32 | 3.2 | odd | 2 | |||
192.5.l.a.79.2 | 32 | 4.3 | odd | 2 | |||
192.5.l.a.175.2 | 32 | 16.13 | even | 4 | |||
384.5.l.a.31.15 | 32 | 8.3 | odd | 2 | |||
384.5.l.a.223.15 | 32 | 16.5 | even | 4 | |||
384.5.l.b.31.2 | 32 | 8.5 | even | 2 | |||
384.5.l.b.223.2 | 32 | 16.11 | odd | 4 | |||
576.5.m.b.271.13 | 32 | 12.11 | even | 2 | |||
576.5.m.b.559.13 | 32 | 48.29 | odd | 4 |