Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,5,Mod(19,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.d (of order \(6\), degree \(2\), not 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: | \(10.1302563822\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.3 | ||
Root | \(-0.662827 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.19 |
Dual form | 98.5.d.c.31.3 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | − | 2.44949i | 0.353553 | − | 0.612372i | ||||
\(3\) | −13.8528 | + | 7.99789i | −1.53919 | + | 0.888654i | −0.540309 | + | 0.841467i | \(0.681693\pi\) |
−0.998886 | + | 0.0471876i | \(0.984974\pi\) | |||||||
\(4\) | −4.00000 | − | 6.92820i | −0.250000 | − | 0.433013i | ||||
\(5\) | −24.1168 | − | 13.9239i | −0.964673 | − | 0.556954i | −0.0670647 | − | 0.997749i | \(-0.521363\pi\) |
−0.897608 | + | 0.440795i | \(0.854697\pi\) | |||||||
\(6\) | 45.2429i | 1.25675i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −22.6274 | −0.353553 | ||||||||
\(9\) | 87.4325 | − | 151.438i | 1.07941 | − | 1.86960i | ||||
\(10\) | −68.2127 | + | 39.3826i | −0.682127 | + | 0.393826i | ||||
\(11\) | 69.8320 | + | 120.953i | 0.577124 | + | 0.999608i | 0.995807 | + | 0.0914757i | \(0.0291584\pi\) |
−0.418683 | + | 0.908132i | \(0.637508\pi\) | |||||||
\(12\) | 110.822 | + | 63.9831i | 0.769597 | + | 0.444327i | ||||
\(13\) | 101.931i | 0.603140i | 0.953444 | + | 0.301570i | \(0.0975106\pi\) | ||||
−0.953444 | + | 0.301570i | \(0.902489\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 445.446 | 1.97976 | ||||||||
\(16\) | −32.0000 | + | 55.4256i | −0.125000 | + | 0.216506i | ||||
\(17\) | 470.154 | − | 271.443i | 1.62683 | − | 0.939251i | 0.641799 | − | 0.766873i | \(-0.278188\pi\) |
0.985031 | − | 0.172377i | \(-0.0551448\pi\) | |||||||
\(18\) | −247.296 | − | 428.330i | −0.763261 | − | 1.32201i | ||||
\(19\) | 121.203 | + | 69.9767i | 0.335743 | + | 0.193841i | 0.658388 | − | 0.752679i | \(-0.271239\pi\) |
−0.322645 | + | 0.946520i | \(0.604572\pi\) | |||||||
\(20\) | 222.782i | 0.556954i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 395.029 | 0.816177 | ||||||||
\(23\) | −114.823 | + | 198.880i | −0.217057 | + | 0.375954i | −0.953907 | − | 0.300102i | \(-0.902979\pi\) |
0.736850 | + | 0.676057i | \(0.236313\pi\) | |||||||
\(24\) | 313.452 | − | 180.972i | 0.544188 | − | 0.314187i | ||||
\(25\) | 75.2473 | + | 130.332i | 0.120396 | + | 0.208531i | ||||
\(26\) | 249.678 | + | 144.152i | 0.369346 | + | 0.213242i | ||||
\(27\) | 1501.44i | 2.05959i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −383.113 | −0.455544 | −0.227772 | − | 0.973714i | \(-0.573144\pi\) | ||||
−0.227772 | + | 0.973714i | \(0.573144\pi\) | |||||||
\(30\) | 629.955 | − | 1091.11i | 0.699950 | − | 1.21235i | ||||
\(31\) | 344.238 | − | 198.746i | 0.358208 | − | 0.206812i | −0.310086 | − | 0.950708i | \(-0.600358\pi\) |
0.668294 | + | 0.743897i | \(0.267025\pi\) | |||||||
\(32\) | 90.5097 | + | 156.767i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −1934.73 | − | 1117.02i | −1.77661 | − | 1.02573i | ||||
\(34\) | − | 1535.52i | − | 1.32830i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1398.92 | −1.07941 | ||||||||
\(37\) | 449.456 | − | 778.480i | 0.328310 | − | 0.568649i | −0.653867 | − | 0.756610i | \(-0.726854\pi\) |
0.982177 | + | 0.187961i | \(0.0601877\pi\) | |||||||
\(38\) | 342.814 | − | 197.924i | 0.237406 | − | 0.137066i | ||||
\(39\) | −815.230 | − | 1412.02i | −0.535983 | − | 0.928349i | ||||
\(40\) | 545.701 | + | 315.061i | 0.341063 | + | 0.196913i | ||||
\(41\) | 657.862i | 0.391352i | 0.980669 | + | 0.195676i | \(0.0626900\pi\) | ||||
−0.980669 | + | 0.195676i | \(0.937310\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1155.70 | 0.625041 | 0.312521 | − | 0.949911i | \(-0.398827\pi\) | ||||
0.312521 | + | 0.949911i | \(0.398827\pi\) | |||||||
\(44\) | 558.656 | − | 967.621i | 0.288562 | − | 0.499804i | ||||
\(45\) | −4217.19 | + | 2434.79i | −2.08256 | + | 1.20237i | ||||
\(46\) | 324.770 | + | 562.517i | 0.153483 | + | 0.265840i | ||||
\(47\) | 1121.08 | + | 647.253i | 0.507504 | + | 0.293007i | 0.731807 | − | 0.681512i | \(-0.238677\pi\) |
−0.224303 | + | 0.974519i | \(0.572011\pi\) | |||||||
\(48\) | − | 1023.73i | − | 0.444327i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 425.663 | 0.170265 | ||||||||
\(51\) | −4341.95 | + | 7520.48i | −1.66934 | + | 2.89138i | ||||
\(52\) | 706.196 | − | 407.722i | 0.261167 | − | 0.150785i | ||||
\(53\) | 2584.22 | + | 4476.00i | 0.919978 | + | 1.59345i | 0.799445 | + | 0.600739i | \(0.205127\pi\) |
0.120532 | + | 0.992709i | \(0.461540\pi\) | |||||||
\(54\) | 3677.77 | + | 2123.36i | 1.26124 | + | 0.728176i | ||||
\(55\) | − | 3889.32i | − | 1.28573i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2238.66 | −0.689031 | ||||||||
\(58\) | −541.803 | + | 938.431i | −0.161059 | + | 0.278963i | ||||
\(59\) | 3598.54 | − | 2077.62i | 1.03377 | − | 0.596846i | 0.115706 | − | 0.993284i | \(-0.463087\pi\) |
0.918062 | + | 0.396438i | \(0.129754\pi\) | |||||||
\(60\) | −1781.78 | − | 3086.14i | −0.494940 | − | 0.857261i | ||||
\(61\) | −1593.56 | − | 920.043i | −0.428262 | − | 0.247257i | 0.270344 | − | 0.962764i | \(-0.412862\pi\) |
−0.698606 | + | 0.715507i | \(0.746196\pi\) | |||||||
\(62\) | − | 1124.28i | − | 0.292476i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | 1419.27 | − | 2458.24i | 0.335921 | − | 0.581832i | ||||
\(66\) | −5472.25 | + | 3159.40i | −1.25625 | + | 0.725299i | ||||
\(67\) | 3157.79 | + | 5469.45i | 0.703450 | + | 1.21841i | 0.967248 | + | 0.253833i | \(0.0816913\pi\) |
−0.263798 | + | 0.964578i | \(0.584975\pi\) | |||||||
\(68\) | −3761.23 | − | 2171.55i | −0.813415 | − | 0.469625i | ||||
\(69\) | − | 3673.38i | − | 0.771556i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1263.28 | 0.250601 | 0.125301 | − | 0.992119i | \(-0.460010\pi\) | ||||
0.125301 | + | 0.992119i | \(0.460010\pi\) | |||||||
\(72\) | −1978.37 | + | 3426.64i | −0.381630 | + | 0.661003i | ||||
\(73\) | −3460.15 | + | 1997.72i | −0.649305 | + | 0.374877i | −0.788190 | − | 0.615432i | \(-0.788982\pi\) |
0.138885 | + | 0.990309i | \(0.455648\pi\) | |||||||
\(74\) | −1271.25 | − | 2201.87i | −0.232150 | − | 0.402096i | ||||
\(75\) | −2084.76 | − | 1203.64i | −0.370625 | − | 0.213980i | ||||
\(76\) | − | 1119.63i | − | 0.193841i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4611.63 | −0.757994 | ||||||||
\(79\) | 5307.13 | − | 9192.22i | 0.850366 | − | 1.47288i | −0.0305129 | − | 0.999534i | \(-0.509714\pi\) |
0.880879 | − | 0.473342i | \(-0.156953\pi\) | |||||||
\(80\) | 1543.48 | − | 891.126i | 0.241168 | − | 0.139239i | ||||
\(81\) | −4926.35 | − | 8532.69i | −0.750854 | − | 1.30052i | ||||
\(82\) | 1611.43 | + | 930.357i | 0.239653 | + | 0.138364i | ||||
\(83\) | 5750.31i | 0.834709i | 0.908744 | + | 0.417355i | \(0.137043\pi\) | ||||
−0.908744 | + | 0.417355i | \(0.862957\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15118.2 | −2.09248 | ||||||||
\(86\) | 1634.41 | − | 2830.88i | 0.220985 | − | 0.382758i | ||||
\(87\) | 5307.17 | − | 3064.09i | 0.701171 | − | 0.404821i | ||||
\(88\) | −1580.12 | − | 2736.84i | −0.204044 | − | 0.353415i | ||||
\(89\) | −3626.09 | − | 2093.52i | −0.457782 | − | 0.264301i | 0.253329 | − | 0.967380i | \(-0.418474\pi\) |
−0.711111 | + | 0.703080i | \(0.751808\pi\) | |||||||
\(90\) | 13773.3i | 1.70040i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1837.17 | 0.217057 | ||||||||
\(93\) | −3179.10 | + | 5506.36i | −0.367568 | + | 0.636647i | ||||
\(94\) | 3170.88 | − | 1830.71i | 0.358859 | − | 0.207188i | ||||
\(95\) | −1948.69 | − | 3375.23i | −0.215921 | − | 0.373987i | ||||
\(96\) | −2507.62 | − | 1447.77i | −0.272094 | − | 0.157093i | ||||
\(97\) | − | 3814.28i | − | 0.405386i | −0.979242 | − | 0.202693i | \(-0.935031\pi\) | ||
0.979242 | − | 0.202693i | \(-0.0649694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24422.3 | 2.49182 | ||||||||
\(100\) | 601.978 | − | 1042.66i | 0.0601978 | − | 0.104266i | ||||
\(101\) | 4265.53 | − | 2462.71i | 0.418149 | − | 0.241418i | −0.276136 | − | 0.961118i | \(-0.589054\pi\) |
0.694285 | + | 0.719700i | \(0.255721\pi\) | |||||||
\(102\) | 12280.9 | + | 21271.1i | 1.18040 | + | 2.04451i | ||||
\(103\) | 16361.5 | + | 9446.32i | 1.54223 | + | 0.890407i | 0.998698 | + | 0.0510180i | \(0.0162466\pi\) |
0.543532 | + | 0.839389i | \(0.317087\pi\) | |||||||
\(104\) | − | 2306.43i | − | 0.213242i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14618.5 | 1.30104 | ||||||||
\(107\) | 4239.70 | − | 7343.37i | 0.370311 | − | 0.641398i | −0.619302 | − | 0.785153i | \(-0.712584\pi\) |
0.989613 | + | 0.143755i | \(0.0459176\pi\) | |||||||
\(108\) | 10402.3 | − | 6005.78i | 0.891830 | − | 0.514899i | ||||
\(109\) | −5838.98 | − | 10113.4i | −0.491455 | − | 0.851225i | 0.508496 | − | 0.861064i | \(-0.330202\pi\) |
−0.999952 | + | 0.00983867i | \(0.996868\pi\) | |||||||
\(110\) | −9526.85 | − | 5500.33i | −0.787343 | − | 0.454573i | ||||
\(111\) | 14378.8i | 1.16702i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19683.8 | 1.54153 | 0.770763 | − | 0.637121i | \(-0.219875\pi\) | ||||
0.770763 | + | 0.637121i | \(0.219875\pi\) | |||||||
\(114\) | −3165.95 | + | 5483.58i | −0.243609 | + | 0.421944i | ||||
\(115\) | 5538.35 | − | 3197.57i | 0.418779 | − | 0.241782i | ||||
\(116\) | 1532.45 | + | 2654.28i | 0.113886 | + | 0.197256i | ||||
\(117\) | 15436.1 | + | 8912.05i | 1.12763 | + | 0.651037i | ||||
\(118\) | − | 11752.8i | − | 0.844067i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10079.3 | −0.699950 | ||||||||
\(121\) | −2432.52 | + | 4213.24i | −0.166144 | + | 0.287770i | ||||
\(122\) | −4507.27 | + | 2602.27i | −0.302827 | + | 0.174837i | ||||
\(123\) | −5261.51 | − | 9113.20i | −0.347776 | − | 0.602366i | ||||
\(124\) | −2753.90 | − | 1589.97i | −0.179104 | − | 0.103406i | ||||
\(125\) | 13213.9i | 0.845689i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −27965.5 | −1.73386 | −0.866931 | − | 0.498428i | \(-0.833911\pi\) | ||||
−0.866931 | + | 0.498428i | \(0.833911\pi\) | |||||||
\(128\) | 724.077 | − | 1254.14i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −16009.6 | + | 9243.17i | −0.962060 | + | 0.555446i | ||||
\(130\) | −4014.29 | − | 6952.96i | −0.237532 | − | 0.411418i | ||||
\(131\) | −1013.02 | − | 584.866i | −0.0590302 | − | 0.0340811i | 0.470194 | − | 0.882563i | \(-0.344184\pi\) |
−0.529225 | + | 0.848482i | \(0.677517\pi\) | |||||||
\(132\) | 17872.3i | 1.02573i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 17863.1 | 0.994828 | ||||||||
\(135\) | 20905.9 | − | 36210.1i | 1.14710 | − | 1.98683i | ||||
\(136\) | −10638.4 | + | 6142.06i | −0.575171 | + | 0.332075i | ||||
\(137\) | 10442.3 | + | 18086.6i | 0.556359 | + | 0.963641i | 0.997796 | + | 0.0663495i | \(0.0211352\pi\) |
−0.441438 | + | 0.897292i | \(0.645531\pi\) | |||||||
\(138\) | −8997.90 | − | 5194.94i | −0.472480 | − | 0.272786i | ||||
\(139\) | − | 3499.87i | − | 0.181143i | −0.995890 | − | 0.0905716i | \(-0.971131\pi\) | ||
0.995890 | − | 0.0905716i | \(-0.0288694\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20706.6 | −1.04153 | ||||||||
\(142\) | 1786.55 | − | 3094.40i | 0.0886010 | − | 0.153461i | ||||
\(143\) | −12328.8 | + | 7118.02i | −0.602903 | + | 0.348086i | ||||
\(144\) | 5595.68 | + | 9692.00i | 0.269853 | + | 0.467400i | ||||
\(145\) | 9239.46 | + | 5334.40i | 0.439451 | + | 0.253717i | ||||
\(146\) | 11300.8i | 0.530156i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7191.29 | −0.328310 | ||||||||
\(149\) | −14766.9 | + | 25577.0i | −0.665146 | + | 1.15207i | 0.314100 | + | 0.949390i | \(0.398297\pi\) |
−0.979246 | + | 0.202677i | \(0.935036\pi\) | |||||||
\(150\) | −5896.60 | + | 3404.40i | −0.262071 | + | 0.151307i | ||||
\(151\) | −12890.4 | − | 22326.8i | −0.565344 | − | 0.979204i | −0.997018 | − | 0.0771741i | \(-0.975410\pi\) |
0.431674 | − | 0.902030i | \(-0.357923\pi\) | |||||||
\(152\) | −2742.51 | − | 1583.39i | −0.118703 | − | 0.0685332i | ||||
\(153\) | − | 94931.9i | − | 4.05536i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11069.2 | −0.460738 | ||||||||
\(156\) | −6521.84 | + | 11296.2i | −0.267991 | + | 0.464175i | ||||
\(157\) | 22195.7 | − | 12814.7i | 0.900470 | − | 0.519887i | 0.0231177 | − | 0.999733i | \(-0.492641\pi\) |
0.877353 | + | 0.479846i | \(0.159307\pi\) | |||||||
\(158\) | −15010.8 | − | 25999.5i | −0.601299 | − | 1.04148i | ||||
\(159\) | −71597.0 | − | 41336.6i | −2.83205 | − | 1.63508i | ||||
\(160\) | − | 5040.97i | − | 0.196913i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −27867.7 | −1.06187 | ||||||||
\(163\) | 3091.39 | − | 5354.45i | 0.116353 | − | 0.201530i | −0.801967 | − | 0.597369i | \(-0.796213\pi\) |
0.918320 | + | 0.395839i | \(0.129546\pi\) | |||||||
\(164\) | 4557.80 | − | 2631.45i | 0.169460 | − | 0.0978379i | ||||
\(165\) | 31106.4 | + | 53877.8i | 1.14257 | + | 1.97898i | ||||
\(166\) | 14085.3 | + | 8132.17i | 0.511153 | + | 0.295114i | ||||
\(167\) | 39270.9i | 1.40811i | 0.710144 | + | 0.704056i | \(0.248630\pi\) | ||||
−0.710144 | + | 0.704056i | \(0.751370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18171.2 | 0.636223 | ||||||||
\(170\) | −21380.3 | + | 37031.8i | −0.739803 | + | 1.28138i | ||||
\(171\) | 21194.2 | − | 12236.5i | 0.724811 | − | 0.418470i | ||||
\(172\) | −4622.80 | − | 8006.93i | −0.156260 | − | 0.270651i | ||||
\(173\) | 28497.3 | + | 16452.9i | 0.952165 | + | 0.549732i | 0.893753 | − | 0.448560i | \(-0.148063\pi\) |
0.0584119 | + | 0.998293i | \(0.481396\pi\) | |||||||
\(174\) | − | 17333.1i | − | 0.572504i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8938.50 | −0.288562 | ||||||||
\(177\) | −33233.2 | + | 57561.5i | −1.06078 | + | 1.83732i | ||||
\(178\) | −10256.1 | + | 5921.38i | −0.323701 | + | 0.186889i | ||||
\(179\) | 2383.94 | + | 4129.11i | 0.0744029 | + | 0.128870i | 0.900826 | − | 0.434179i | \(-0.142962\pi\) |
−0.826424 | + | 0.563049i | \(0.809628\pi\) | |||||||
\(180\) | 33737.5 | + | 19478.4i | 1.04128 | + | 0.601184i | ||||
\(181\) | − | 35195.4i | − | 1.07431i | −0.843484 | − | 0.537154i | \(-0.819499\pi\) | ||
0.843484 | − | 0.537154i | \(-0.180501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29433.6 | 0.878904 | ||||||||
\(184\) | 2598.16 | − | 4500.14i | 0.0767414 | − | 0.132920i | ||||
\(185\) | −21678.9 | + | 12516.3i | −0.633423 | + | 0.365707i | ||||
\(186\) | 8991.84 | + | 15574.3i | 0.259910 | + | 0.450177i | ||||
\(187\) | 65663.6 | + | 37910.9i | 1.87776 | + | 1.08413i | ||||
\(188\) | − | 10356.1i | − | 0.293007i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11023.5 | −0.305359 | ||||||||
\(191\) | −11657.5 | + | 20191.4i | −0.319551 | + | 0.553478i | −0.980394 | − | 0.197046i | \(-0.936865\pi\) |
0.660844 | + | 0.750524i | \(0.270199\pi\) | |||||||
\(192\) | −7092.61 | + | 4094.92i | −0.192399 | + | 0.111082i | ||||
\(193\) | −29591.9 | − | 51254.6i | −0.794434 | − | 1.37600i | −0.923198 | − | 0.384325i | \(-0.874434\pi\) |
0.128764 | − | 0.991675i | \(-0.458899\pi\) | |||||||
\(194\) | −9343.04 | − | 5394.21i | −0.248247 | − | 0.143326i | ||||
\(195\) | 45404.5i | 1.19407i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −60902.2 | −1.56928 | −0.784640 | − | 0.619952i | \(-0.787152\pi\) | ||||
−0.784640 | + | 0.619952i | \(0.787152\pi\) | |||||||
\(198\) | 34538.4 | − | 59822.3i | 0.880992 | − | 1.52592i | ||||
\(199\) | −34742.1 | + | 20058.4i | −0.877304 | + | 0.506512i | −0.869769 | − | 0.493460i | \(-0.835732\pi\) |
−0.00753551 | + | 0.999972i | \(0.502399\pi\) | |||||||
\(200\) | −1702.65 | − | 2949.08i | −0.0425663 | − | 0.0737270i | ||||
\(201\) | −87488.1 | − | 50511.3i | −2.16549 | − | 1.25025i | ||||
\(202\) | − | 13931.2i | − | 0.341417i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 69471.2 | 1.66934 | ||||||||
\(205\) | 9159.97 | − | 15865.5i | 0.217965 | − | 0.377526i | ||||
\(206\) | 46277.3 | − | 26718.2i | 1.09052 | − | 0.629613i | ||||
\(207\) | 20078.6 | + | 34777.1i | 0.468589 | + | 0.811621i | ||||
\(208\) | −5649.57 | − | 3261.78i | −0.130584 | − | 0.0753924i | ||||
\(209\) | 19546.4i | 0.447482i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21929.0 | 0.492554 | 0.246277 | − | 0.969200i | \(-0.420793\pi\) | ||||
0.246277 | + | 0.969200i | \(0.420793\pi\) | |||||||
\(212\) | 20673.7 | − | 35808.0i | 0.459989 | − | 0.796724i | ||||
\(213\) | −17499.9 | + | 10103.6i | −0.385724 | + | 0.222698i | ||||
\(214\) | −11991.7 | − | 20770.2i | −0.261850 | − | 0.453537i | ||||
\(215\) | −27871.8 | − | 16091.8i | −0.602960 | − | 0.348119i | ||||
\(216\) | − | 33973.8i | − | 0.728176i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −33030.3 | −0.695023 | ||||||||
\(219\) | 31955.1 | − | 55347.8i | 0.666272 | − | 1.15402i | ||||
\(220\) | −26946.0 | + | 15557.3i | −0.556736 | + | 0.321432i | ||||
\(221\) | 27668.4 | + | 47923.0i | 0.566499 | + | 0.981205i | ||||
\(222\) | 35220.7 | + | 20334.7i | 0.714648 | + | 0.412602i | ||||
\(223\) | 64358.0i | 1.29418i | 0.762416 | + | 0.647088i | \(0.224013\pi\) | ||||
−0.762416 | + | 0.647088i | \(0.775987\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26316.2 | 0.519827 | ||||||||
\(226\) | 27837.0 | − | 48215.2i | 0.545012 | − | 0.943989i | ||||
\(227\) | −37910.1 | + | 21887.4i | −0.735704 | + | 0.424759i | −0.820505 | − | 0.571639i | \(-0.806308\pi\) |
0.0848015 | + | 0.996398i | \(0.472974\pi\) | |||||||
\(228\) | 8954.65 | + | 15509.9i | 0.172258 | + | 0.298359i | ||||
\(229\) | 24687.3 | + | 14253.2i | 0.470763 | + | 0.271795i | 0.716559 | − | 0.697526i | \(-0.245716\pi\) |
−0.245796 | + | 0.969322i | \(0.579049\pi\) | |||||||
\(230\) | − | 18088.2i | − | 0.341931i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8668.85 | 0.161059 | ||||||||
\(233\) | 1097.45 | − | 1900.83i | 0.0202149 | − | 0.0350132i | −0.855741 | − | 0.517404i | \(-0.826898\pi\) |
0.875956 | + | 0.482391i | \(0.160232\pi\) | |||||||
\(234\) | 43659.9 | − | 25207.1i | 0.797354 | − | 0.460353i | ||||
\(235\) | −18024.5 | − | 31219.4i | −0.326383 | − | 0.565313i | ||||
\(236\) | −28788.3 | − | 16621.0i | −0.516884 | − | 0.298423i | ||||
\(237\) | 169783.i | 3.02273i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 80942.6 | 1.41704 | 0.708519 | − | 0.705692i | \(-0.249364\pi\) | ||||
0.708519 | + | 0.705692i | \(0.249364\pi\) | |||||||
\(240\) | −14254.3 | + | 24689.1i | −0.247470 | + | 0.428630i | ||||
\(241\) | 37253.5 | − | 21508.3i | 0.641406 | − | 0.370316i | −0.143750 | − | 0.989614i | \(-0.545916\pi\) |
0.785156 | + | 0.619298i | \(0.212583\pi\) | |||||||
\(242\) | 6880.19 | + | 11916.8i | 0.117482 | + | 0.203484i | ||||
\(243\) | 31163.7 | + | 17992.4i | 0.527760 | + | 0.304702i | ||||
\(244\) | 14720.7i | 0.247257i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −29763.6 | −0.491830 | ||||||||
\(247\) | −7132.76 | + | 12354.3i | −0.116913 | + | 0.202500i | ||||
\(248\) | −7789.22 | + | 4497.11i | −0.126646 | + | 0.0731189i | ||||
\(249\) | −45990.4 | − | 79657.6i | −0.741768 | − | 1.28478i | ||||
\(250\) | 32367.3 | + | 18687.3i | 0.517877 | + | 0.298996i | ||||
\(251\) | − | 31568.5i | − | 0.501080i | −0.968106 | − | 0.250540i | \(-0.919392\pi\) | ||
0.968106 | − | 0.250540i | \(-0.0806082\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32073.4 | −0.501076 | ||||||||
\(254\) | −39549.1 | + | 68501.1i | −0.613013 | + | 1.06177i | ||||
\(255\) | 209428. | − | 120913.i | 3.22073 | − | 1.85949i | ||||
\(256\) | −2048.00 | − | 3547.24i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −58981.4 | − | 34052.9i | −0.892995 | − | 0.515571i | −0.0180739 | − | 0.999837i | \(-0.505753\pi\) |
−0.874921 | + | 0.484266i | \(0.839087\pi\) | |||||||
\(258\) | 52287.3i | 0.785519i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −22708.3 | −0.335921 | ||||||||
\(261\) | −33496.5 | + | 58017.6i | −0.491721 | + | 0.851685i | ||||
\(262\) | −2865.25 | + | 1654.25i | −0.0417406 | + | 0.0240990i | ||||
\(263\) | 4173.78 | + | 7229.20i | 0.0603418 | + | 0.104515i | 0.894618 | − | 0.446831i | \(-0.147448\pi\) |
−0.834276 | + | 0.551346i | \(0.814114\pi\) | |||||||
\(264\) | 43778.0 | + | 25275.2i | 0.628127 | + | 0.362649i | ||||
\(265\) | − | 143929.i | − | 2.04954i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 66975.1 | 0.939488 | ||||||||
\(268\) | 25262.3 | − | 43755.6i | 0.351725 | − | 0.609205i | ||||
\(269\) | −79605.9 | + | 45960.5i | −1.10012 | + | 0.635156i | −0.936253 | − | 0.351326i | \(-0.885731\pi\) |
−0.163869 | + | 0.986482i | \(0.552397\pi\) | |||||||
\(270\) | −59130.8 | − | 102417.i | −0.811122 | − | 1.40490i | ||||
\(271\) | −4446.49 | − | 2567.18i | −0.0605450 | − | 0.0349557i | 0.469422 | − | 0.882974i | \(-0.344462\pi\) |
−0.529967 | + | 0.848018i | \(0.677796\pi\) | |||||||
\(272\) | 34744.8i | 0.469625i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 59070.5 | 0.786810 | ||||||||
\(275\) | −10509.3 | + | 18202.7i | −0.138966 | + | 0.240697i | ||||
\(276\) | −25449.9 | + | 14693.5i | −0.334094 | + | 0.192889i | ||||
\(277\) | 33127.1 | + | 57377.8i | 0.431741 | + | 0.747798i | 0.997023 | − | 0.0770996i | \(-0.0245660\pi\) |
−0.565282 | + | 0.824898i | \(0.691233\pi\) | |||||||
\(278\) | −8572.89 | − | 4949.56i | −0.110927 | − | 0.0640438i | ||||
\(279\) | − | 69507.4i | − | 0.892941i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 38156.4 | 0.483230 | 0.241615 | − | 0.970372i | \(-0.422323\pi\) | ||||
0.241615 | + | 0.970372i | \(0.422323\pi\) | |||||||
\(282\) | −29283.6 | + | 50720.7i | −0.368236 | + | 0.637804i | ||||
\(283\) | 95464.8 | − | 55116.6i | 1.19198 | − | 0.688192i | 0.233228 | − | 0.972422i | \(-0.425071\pi\) |
0.958756 | + | 0.284230i | \(0.0917379\pi\) | |||||||
\(284\) | −5053.13 | − | 8752.27i | −0.0626504 | − | 0.108514i | ||||
\(285\) | 53989.4 | + | 31170.8i | 0.664690 | + | 0.383759i | ||||
\(286\) | 40265.6i | 0.492268i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 31653.9 | 0.381630 | ||||||||
\(289\) | 105603. | − | 182909.i | 1.26438 | − | 2.18998i | ||||
\(290\) | 26133.1 | − | 15088.0i | 0.310739 | − | 0.179405i | ||||
\(291\) | 30506.2 | + | 52838.3i | 0.360248 | + | 0.623968i | ||||
\(292\) | 27681.2 | + | 15981.7i | 0.324653 | + | 0.187438i | ||||
\(293\) | − | 79011.7i | − | 0.920357i | −0.887826 | − | 0.460179i | \(-0.847785\pi\) | ||
0.887826 | − | 0.460179i | \(-0.152215\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −115714. | −1.32966 | ||||||||
\(296\) | −10170.0 | + | 17615.0i | −0.116075 | + | 0.201048i | ||||
\(297\) | −181604. | + | 104849.i | −2.05879 | + | 1.18864i | ||||
\(298\) | 41767.1 | + | 72342.8i | 0.470329 | + | 0.814634i | ||||
\(299\) | −20271.9 | − | 11704.0i | −0.226753 | − | 0.130916i | ||||
\(300\) | 19258.2i | 0.213980i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −72919.1 | −0.799517 | ||||||||
\(303\) | −39392.9 | + | 68230.6i | −0.429075 | + | 0.743179i | ||||
\(304\) | −7757.00 | + | 4478.51i | −0.0839357 | + | 0.0484603i | ||||
\(305\) | 25621.1 | + | 44377.0i | 0.275421 | + | 0.477044i | ||||
\(306\) | −232535. | − | 134254.i | −2.48339 | − | 1.43379i | ||||
\(307\) | 2801.57i | 0.0297252i | 0.999890 | + | 0.0148626i | \(0.00473109\pi\) | ||||
−0.999890 | + | 0.0148626i | \(0.995269\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −302203. | −3.16506 | ||||||||
\(310\) | −15654.3 | + | 27114.0i | −0.162896 | + | 0.282143i | ||||
\(311\) | −17891.5 | + | 10329.7i | −0.184981 | + | 0.106799i | −0.589631 | − | 0.807673i | \(-0.700727\pi\) |
0.404650 | + | 0.914472i | \(0.367393\pi\) | |||||||
\(312\) | 18446.5 | + | 31950.3i | 0.189498 | + | 0.328221i | ||||
\(313\) | −32368.6 | − | 18688.0i | −0.330397 | − | 0.190755i | 0.325620 | − | 0.945501i | \(-0.394427\pi\) |
−0.656017 | + | 0.754746i | \(0.727760\pi\) | |||||||
\(314\) | − | 72490.8i | − | 0.735231i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84914.1 | −0.850366 | ||||||||
\(317\) | 53333.0 | − | 92375.5i | 0.530735 | − | 0.919259i | −0.468622 | − | 0.883399i | \(-0.655249\pi\) |
0.999357 | − | 0.0358607i | \(-0.0114173\pi\) | |||||||
\(318\) | −202507. | + | 116917.i | −2.00256 | + | 1.15618i | ||||
\(319\) | −26753.5 | − | 46338.5i | −0.262905 | − | 0.455366i | ||||
\(320\) | −12347.8 | − | 7129.01i | −0.120584 | − | 0.0696193i | ||||
\(321\) | 135634.i | 1.31632i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 75978.8 | 0.728262 | ||||||||
\(324\) | −39410.8 | + | 68261.5i | −0.375427 | + | 0.650259i | ||||
\(325\) | −13284.8 | + | 7670.00i | −0.125773 | + | 0.0726154i | ||||
\(326\) | −8743.77 | − | 15144.7i | −0.0822742 | − | 0.142503i | ||||
\(327\) | 161772. | + | 93399.0i | 1.51289 | + | 0.873468i | ||||
\(328\) | − | 14885.7i | − | 0.138364i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 175964. | 1.61583 | ||||||||
\(331\) | −54181.4 | + | 93844.9i | −0.494532 | + | 0.856554i | −0.999980 | − | 0.00630282i | \(-0.997994\pi\) |
0.505448 | + | 0.862857i | \(0.331327\pi\) | |||||||
\(332\) | 39839.3 | − | 23001.2i | 0.361440 | − | 0.208677i | ||||
\(333\) | −78594.1 | − | 136129.i | −0.708764 | − | 1.22761i | ||||
\(334\) | 96193.6 | + | 55537.4i | 0.862289 | + | 0.497843i | ||||
\(335\) | − | 175874.i | − | 1.56716i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 186946. | 1.64610 | 0.823050 | − | 0.567968i | \(-0.192270\pi\) | ||||
0.823050 | + | 0.567968i | \(0.192270\pi\) | |||||||
\(338\) | 25697.9 | − | 44510.1i | 0.224939 | − | 0.389605i | ||||
\(339\) | −272674. | + | 157429.i | −2.37271 | + | 1.36988i | ||||
\(340\) | 60472.6 | + | 104742.i | 0.523119 | + | 0.906069i | ||||
\(341\) | 48077.7 | + | 27757.7i | 0.413461 | + | 0.238712i | ||||
\(342\) | − | 69219.9i | − | 0.591805i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −26150.5 | −0.220985 | ||||||||
\(345\) | −51147.6 | + | 88590.2i | −0.429721 | + | 0.744299i | ||||
\(346\) | 80602.6 | − | 46536.0i | 0.673282 | − | 0.388720i | ||||
\(347\) | 31613.7 | + | 54756.5i | 0.262552 | + | 0.454754i | 0.966919 | − | 0.255082i | \(-0.0821024\pi\) |
−0.704367 | + | 0.709836i | \(0.748769\pi\) | |||||||
\(348\) | −42457.3 | − | 24512.7i | −0.350586 | − | 0.202411i | ||||
\(349\) | − | 93605.0i | − | 0.768508i | −0.923227 | − | 0.384254i | \(-0.874459\pi\) | ||
0.923227 | − | 0.384254i | \(-0.125541\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −153043. | −1.24222 | ||||||||
\(352\) | −12640.9 | + | 21894.8i | −0.102022 | + | 0.176707i | ||||
\(353\) | 124059. | − | 71625.3i | 0.995583 | − | 0.574800i | 0.0886445 | − | 0.996063i | \(-0.471746\pi\) |
0.906938 | + | 0.421263i | \(0.138413\pi\) | |||||||
\(354\) | 93997.5 | + | 162809.i | 0.750084 | + | 1.29918i | ||||
\(355\) | −30466.3 | − | 17589.7i | −0.241748 | − | 0.139573i | ||||
\(356\) | 33496.4i | 0.264301i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13485.6 | 0.105222 | ||||||||
\(359\) | −51169.9 | + | 88628.9i | −0.397032 | + | 0.687680i | −0.993358 | − | 0.115062i | \(-0.963293\pi\) |
0.596326 | + | 0.802742i | \(0.296627\pi\) | |||||||
\(360\) | 95424.1 | − | 55093.1i | 0.736297 | − | 0.425101i | ||||
\(361\) | −55367.0 | − | 95898.5i | −0.424851 | − | 0.735864i | ||||
\(362\) | −86210.8 | − | 49773.9i | −0.657877 | − | 0.379826i | ||||
\(363\) | − | 77820.0i | − | 0.590579i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 111264. | 0.835156 | ||||||||
\(366\) | 41625.4 | − | 72097.3i | 0.310739 | − | 0.538216i | ||||
\(367\) | 13307.7 | − | 7683.22i | 0.0988034 | − | 0.0570442i | −0.449784 | − | 0.893137i | \(-0.648499\pi\) |
0.548588 | + | 0.836093i | \(0.315166\pi\) | |||||||
\(368\) | −7348.70 | − | 12728.3i | −0.0542644 | − | 0.0939886i | ||||
\(369\) | 99625.0 | + | 57518.5i | 0.731671 | + | 0.422430i | ||||
\(370\) | 70803.0i | 0.517187i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 50865.5 | 0.367568 | ||||||||
\(373\) | −48745.4 | + | 84429.5i | −0.350361 | + | 0.606843i | −0.986313 | − | 0.164886i | \(-0.947275\pi\) |
0.635951 | + | 0.771729i | \(0.280608\pi\) | |||||||
\(374\) | 185725. | − | 107228.i | 1.32778 | − | 0.766594i | ||||
\(375\) | −105683. | − | 183049.i | −0.751525 | − | 1.30168i | ||||
\(376\) | −25367.1 | − | 14645.7i | −0.179430 | − | 0.103594i | ||||
\(377\) | − | 39050.9i | − | 0.274757i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −66090.7 | −0.460110 | −0.230055 | − | 0.973178i | \(-0.573891\pi\) | ||||
−0.230055 | + | 0.973178i | \(0.573891\pi\) | |||||||
\(380\) | −15589.5 | + | 27001.8i | −0.107961 | + | 0.186993i | ||||
\(381\) | 387399. | − | 223665.i | 2.66875 | − | 1.54080i | ||||
\(382\) | 32972.5 | + | 57110.0i | 0.225956 | + | 0.391368i | ||||
\(383\) | 180913. | + | 104450.i | 1.23331 | + | 0.712053i | 0.967719 | − | 0.252032i | \(-0.0810990\pi\) |
0.265593 | + | 0.964085i | \(0.414432\pi\) | |||||||
\(384\) | 23164.4i | 0.157093i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −167397. | −1.12350 | ||||||||
\(387\) | 101046. | − | 175017.i | 0.674678 | − | 1.16858i | ||||
\(388\) | −26426.1 | + | 15257.1i | −0.175537 | + | 0.101347i | ||||
\(389\) | 71999.6 | + | 124707.i | 0.475807 | + | 0.824122i | 0.999616 | − | 0.0277137i | \(-0.00882267\pi\) |
−0.523809 | + | 0.851836i | \(0.675489\pi\) | |||||||
\(390\) | 111218. | + | 64211.7i | 0.731216 | + | 0.422168i | ||||
\(391\) | 124672.i | 0.815485i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18710.8 | 0.121145 | ||||||||
\(394\) | −86128.7 | + | 149179.i | −0.554824 | + | 0.960984i | ||||
\(395\) | −255982. | + | 147791.i | −1.64065 | + | 0.947229i | ||||
\(396\) | −97689.4 | − | 169203.i | −0.622955 | − | 1.07899i | ||||
\(397\) | −246451. | − | 142289.i | −1.56369 | − | 0.902796i | −0.996879 | − | 0.0789466i | \(-0.974844\pi\) |
−0.566809 | − | 0.823849i | \(-0.691822\pi\) | |||||||
\(398\) | 113467.i | 0.716316i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9631.65 | −0.0601978 | ||||||||
\(401\) | 53923.0 | − | 93397.4i | 0.335340 | − | 0.580826i | −0.648210 | − | 0.761462i | \(-0.724482\pi\) |
0.983550 | + | 0.180636i | \(0.0578155\pi\) | |||||||
\(402\) | −247454. | + | 142867.i | −1.53123 | + | 0.884059i | ||||
\(403\) | 20258.3 | + | 35088.4i | 0.124736 | + | 0.216050i | ||||
\(404\) | −34124.3 | − | 19701.7i | −0.209074 | − | 0.120709i | ||||
\(405\) | 274375.i | 1.67276i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 125546. | 0.757901 | ||||||||
\(408\) | 98247.1 | − | 170169.i | 0.590200 | − | 1.02226i | ||||
\(409\) | 73553.4 | − | 42466.1i | 0.439700 | − | 0.253861i | −0.263771 | − | 0.964585i | \(-0.584966\pi\) |
0.703470 | + | 0.710725i | \(0.251633\pi\) | |||||||
\(410\) | −25908.3 | − | 44874.5i | −0.154124 | − | 0.266951i | ||||
\(411\) | −289309. | − | 167033.i | −1.71269 | − | 0.988821i | ||||
\(412\) | − | 151141.i | − | 0.890407i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 113582. | 0.662686 | ||||||||
\(415\) | 80066.5 | − | 138679.i | 0.464895 | − | 0.805221i | ||||
\(416\) | −15979.4 | + | 9225.70i | −0.0923365 | + | 0.0533105i | ||||
\(417\) | 27991.6 | + | 48482.8i | 0.160974 | + | 0.278815i | ||||
\(418\) | 47878.8 | + | 27642.8i | 0.274025 | + | 0.158209i | ||||
\(419\) | 331905.i | 1.89054i | 0.326292 | + | 0.945269i | \(0.394201\pi\) | ||||
−0.326292 | + | 0.945269i | \(0.605799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 101490. | 0.572609 | 0.286304 | − | 0.958139i | \(-0.407573\pi\) | ||||
0.286304 | + | 0.958139i | \(0.407573\pi\) | |||||||
\(422\) | 31012.3 | − | 53714.8i | 0.174144 | − | 0.301626i | ||||
\(423\) | 196037. | − | 113182.i | 1.09561 | − | 0.632552i | ||||
\(424\) | −58474.2 | − | 101280.i | −0.325261 | − | 0.563369i | ||||
\(425\) | 70755.6 | + | 40850.7i | 0.391726 | + | 0.226163i | ||||
\(426\) | 57154.5i | 0.314943i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −67835.1 | −0.370311 | ||||||||
\(429\) | 113858. | − | 197208.i | 0.618657 | − | 1.07155i | ||||
\(430\) | −78833.4 | + | 45514.5i | −0.426357 | + | 0.246157i | ||||
\(431\) | −114899. | − | 199011.i | −0.618530 | − | 1.07133i | −0.989754 | − | 0.142782i | \(-0.954395\pi\) |
0.371224 | − | 0.928543i | \(-0.378938\pi\) | |||||||
\(432\) | −83218.5 | − | 48046.2i | −0.445915 | − | 0.257449i | ||||
\(433\) | 114264.i | 0.609442i | 0.952442 | + | 0.304721i | \(0.0985632\pi\) | ||||
−0.952442 | + | 0.304721i | \(0.901437\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −170656. | −0.901868 | ||||||||
\(436\) | −46711.8 | + | 80907.3i | −0.245728 | + | 0.425613i | ||||
\(437\) | −27833.9 | + | 16069.9i | −0.145751 | + | 0.0841493i | ||||
\(438\) | −90382.6 | − | 156547.i | −0.471125 | − | 0.816013i | ||||
\(439\) | −305134. | − | 176169.i | −1.58330 | − | 0.914116i | −0.994374 | − | 0.105926i | \(-0.966219\pi\) |
−0.588921 | − | 0.808190i | \(-0.700447\pi\) | |||||||
\(440\) | 88005.3i | 0.454573i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 156516. | 0.801151 | ||||||||
\(443\) | 98158.2 | − | 170015.i | 0.500172 | − | 0.866323i | −0.499828 | − | 0.866125i | \(-0.666604\pi\) |
1.00000 | 0.000198349i | \(-6.31363e-5\pi\) | ||||||||
\(444\) | 99619.2 | − | 57515.2i | 0.505332 | − | 0.291754i | ||||
\(445\) | 58299.9 | + | 100978.i | 0.294407 | + | 0.509927i | ||||
\(446\) | 157644. | + | 91016.0i | 0.792517 | + | 0.457560i | ||||
\(447\) | − | 472416.i | − | 2.36434i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 77520.3 | 0.384523 | 0.192262 | − | 0.981344i | \(-0.438418\pi\) | ||||
0.192262 | + | 0.981344i | \(0.438418\pi\) | |||||||
\(450\) | 37216.8 | − | 64461.3i | 0.183786 | − | 0.318328i | ||||
\(451\) | −79570.1 | + | 45939.8i | −0.391198 | + | 0.225858i | ||||
\(452\) | −78735.0 | − | 136373.i | −0.385382 | − | 0.667501i | ||||
\(453\) | 357135. | + | 206192.i | 1.74035 | + | 1.00479i | ||||
\(454\) | 123814.i | 0.600699i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 50655.2 | 0.243609 | ||||||||
\(457\) | −94936.1 | + | 164434.i | −0.454568 | + | 0.787335i | −0.998663 | − | 0.0516882i | \(-0.983540\pi\) |
0.544095 | + | 0.839024i | \(0.316873\pi\) | |||||||
\(458\) | 69826.2 | − | 40314.2i | 0.332880 | − | 0.192188i | ||||
\(459\) | 407557. | + | 705910.i | 1.93447 | + | 3.35061i | ||||
\(460\) | −44306.8 | − | 25580.5i | −0.209389 | − | 0.120891i | ||||
\(461\) | 52599.9i | 0.247505i | 0.992313 | + | 0.123752i | \(0.0394928\pi\) | ||||
−0.992313 | + | 0.123752i | \(0.960507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −244268. | −1.13947 | −0.569736 | − | 0.821828i | \(-0.692955\pi\) | ||||
−0.569736 | + | 0.821828i | \(0.692955\pi\) | |||||||
\(464\) | 12259.6 | − | 21234.3i | 0.0569430 | − | 0.0986282i | ||||
\(465\) | 153339. | − | 88530.5i | 0.709166 | − | 0.409437i | ||||
\(466\) | −3104.05 | − | 5376.36i | −0.0142941 | − | 0.0247581i | ||||
\(467\) | 257742. | + | 148807.i | 1.18182 | + | 0.682324i | 0.956435 | − | 0.291946i | \(-0.0943028\pi\) |
0.225385 | + | 0.974270i | \(0.427636\pi\) | |||||||
\(468\) | − | 142593.i | − | 0.651037i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −101962. | −0.461576 | ||||||||
\(471\) | −204981. | + | 355037.i | −0.924000 | + | 1.60041i | ||||
\(472\) | −81425.7 | + | 47011.2i | −0.365492 | + | 0.211017i | ||||
\(473\) | 80704.9 | + | 139785.i | 0.360726 | + | 0.624796i | ||||
\(474\) | 415883. | + | 240110.i | 1.85103 | + | 1.06869i | ||||
\(475\) | 21062.2i | 0.0933505i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 903778. | 3.97215 | ||||||||
\(478\) | 114470. | − | 198268.i | 0.500998 | − | 0.867755i | ||||
\(479\) | −40591.3 | + | 23435.4i | −0.176914 | + | 0.102141i | −0.585842 | − | 0.810425i | \(-0.699236\pi\) |
0.408928 | + | 0.912567i | \(0.365903\pi\) | |||||||
\(480\) | 40317.1 | + | 69831.3i | 0.174988 | + | 0.303087i | ||||
\(481\) | 79351.0 | + | 45813.3i | 0.342975 | + | 0.198016i | ||||
\(482\) | − | 121669.i | − | 0.523706i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 38920.3 | 0.166144 | ||||||||
\(485\) | −53109.5 | + | 91988.3i | −0.225782 | + | 0.391065i | ||||
\(486\) | 88144.3 | − | 50890.1i | 0.373183 | − | 0.215457i | ||||
\(487\) | −53591.9 | − | 92824.0i | −0.225965 | − | 0.391383i | 0.730643 | − | 0.682759i | \(-0.239220\pi\) |
−0.956609 | + | 0.291376i | \(0.905887\pi\) | |||||||
\(488\) | 36058.2 | + | 20818.2i | 0.151413 | + | 0.0874185i | ||||
\(489\) | 98898.4i | 0.413592i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −116367. | −0.482687 | −0.241344 | − | 0.970440i | \(-0.577588\pi\) | ||||
−0.241344 | + | 0.970440i | \(0.577588\pi\) | |||||||
\(492\) | −42092.1 | + | 72905.6i | −0.173888 | + | 0.301183i | ||||
\(493\) | −180122. | + | 103993.i | −0.741093 | + | 0.427870i | ||||
\(494\) | 20174.5 | + | 34943.3i | 0.0826702 | + | 0.143189i | ||||
\(495\) | −588989. | − | 340053.i | −2.40379 | − | 1.38783i | ||||
\(496\) | 25439.5i | 0.103406i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −260161. | −1.04902 | ||||||||
\(499\) | −221454. | + | 383569.i | −0.889369 | + | 1.54043i | −0.0487464 | + | 0.998811i | \(0.515523\pi\) |
−0.840623 | + | 0.541621i | \(0.817811\pi\) | |||||||
\(500\) | 91548.5 | − | 52855.5i | 0.366194 | − | 0.211422i | ||||
\(501\) | −314084. | − | 544009.i | −1.25133 | − | 2.16736i | ||||
\(502\) | −77326.8 | − | 44644.7i | −0.306848 | − | 0.177159i | ||||
\(503\) | 68955.1i | 0.272540i | 0.990672 | + | 0.136270i | \(0.0435115\pi\) | ||||
−0.990672 | + | 0.136270i | \(0.956489\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −137161. | −0.537835 | ||||||||
\(506\) | −45358.6 | + | 78563.4i | −0.177157 | + | 0.306845i | ||||
\(507\) | −251721. | + | 145331.i | −0.979271 | + | 0.565382i | ||||
\(508\) | 111862. | + | 193750.i | 0.433466 | + | 0.750784i | ||||
\(509\) | −80344.2 | − | 46386.8i | −0.310112 | − | 0.179044i | 0.336864 | − | 0.941553i | \(-0.390634\pi\) |
−0.646977 | + | 0.762510i | \(0.723967\pi\) | |||||||
\(510\) | − | 683989.i | − | 2.62972i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11585.2 | −0.0441942 | ||||||||
\(513\) | −105066. | + | 181980.i | −0.399234 | + | 0.691494i | ||||
\(514\) | −166825. | + | 96316.2i | −0.631443 | + | 0.364564i | ||||
\(515\) | −263058. | − | 455631.i | −0.991831 | − | 1.71790i | ||||
\(516\) | 128077. | + | 73945.4i | 0.481030 | + | 0.277723i | ||||
\(517\) | 180796.i | 0.676406i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −526355. | −1.95409 | ||||||||
\(520\) | −32114.3 | + | 55623.6i | −0.118766 | + | 0.205709i | ||||
\(521\) | 123766. | − | 71456.2i | 0.455958 | − | 0.263248i | −0.254385 | − | 0.967103i | \(-0.581873\pi\) |
0.710343 | + | 0.703855i | \(0.248540\pi\) | |||||||
\(522\) | 94742.4 | + | 164099.i | 0.347699 | + | 0.602232i | ||||
\(523\) | 19228.8 | + | 11101.8i | 0.0702990 | + | 0.0405871i | 0.534737 | − | 0.845018i | \(-0.320411\pi\) |
−0.464439 | + | 0.885605i | \(0.653744\pi\) | |||||||
\(524\) | 9357.85i | 0.0340811i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23610.5 | 0.0853361 | ||||||||
\(527\) | 107897. | − | 186882.i | 0.388496 | − | 0.672894i | ||||
\(528\) | 123823. | − | 71489.1i | 0.444153 | − | 0.256432i | ||||
\(529\) | 113552. | + | 196677.i | 0.405772 | + | 0.702818i | ||||
\(530\) | −352553. | − | 203546.i | −1.25508 | − | 0.724622i | ||||
\(531\) | − | 726606.i | − | 2.57697i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −67056.3 | −0.236040 | ||||||||
\(534\) | 94717.1 | − | 164055.i | 0.332159 | − | 0.575316i | ||||
\(535\) | −204496. | + | 118066.i | −0.714459 | + | 0.412493i | ||||
\(536\) | −71452.5 | − | 123759.i | −0.248707 | − | 0.430773i | ||||
\(537\) | −66048.3 | − | 38133.0i | −0.229041 | − | 0.132237i | ||||
\(538\) | 259992.i | 0.898246i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −334494. | −1.14710 | ||||||||
\(541\) | −105605. | + | 182912.i | −0.360818 | + | 0.624955i | −0.988096 | − | 0.153841i | \(-0.950836\pi\) |
0.627278 | + | 0.778796i | \(0.284169\pi\) | |||||||
\(542\) | −12576.6 | + | 7261.09i | −0.0428118 | + | 0.0247174i | ||||
\(543\) | 281489. | + | 487554.i | 0.954689 | + | 1.65357i | ||||
\(544\) | 85106.9 | + | 49136.5i | 0.287586 | + | 0.166038i | ||||
\(545\) | 325204.i | 1.09487i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 254227. | 0.849664 | 0.424832 | − | 0.905272i | \(-0.360333\pi\) | ||||
0.424832 | + | 0.905272i | \(0.360333\pi\) | |||||||
\(548\) | 83538.3 | − | 144693.i | 0.278179 | − | 0.481821i | ||||
\(549\) | −278658. | + | 160883.i | −0.924543 | + | 0.533785i | ||||
\(550\) | 29724.9 | + | 51485.0i | 0.0982641 | + | 0.170198i | ||||
\(551\) | −46434.5 | − | 26809.0i | −0.152946 | − | 0.0883032i | ||||
\(552\) | 83119.1i | 0.272786i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 187395. | 0.610575 | ||||||||
\(555\) | 200208. | − | 346771.i | 0.649974 | − | 1.12579i | ||||
\(556\) | −24247.8 | + | 13999.5i | −0.0784373 | + | 0.0452858i | ||||
\(557\) | −23069.6 | − | 39957.7i | −0.0743584 | − | 0.128792i | 0.826449 | − | 0.563012i | \(-0.190358\pi\) |
−0.900807 | + | 0.434220i | \(0.857024\pi\) | |||||||
\(558\) | −170258. | − | 98298.3i | −0.546812 | − | 0.315702i | ||||
\(559\) | 117801.i | 0.376987i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.21283e6 | −3.85366 | ||||||||
\(562\) | 53961.2 | − | 93463.6i | 0.170848 | − | 0.295917i | ||||
\(563\) | −302788. | + | 174814.i | −0.955259 | + | 0.551519i | −0.894711 | − | 0.446646i | \(-0.852618\pi\) |
−0.0605484 | + | 0.998165i | \(0.519285\pi\) | |||||||
\(564\) | 82826.6 | + | 143460.i | 0.260382 | + | 0.450996i | ||||
\(565\) | −474710. | − | 274074.i | −1.48707 | − | 0.858560i | ||||
\(566\) | − | 311787.i | − | 0.973251i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28584.8 | −0.0886010 | ||||||||
\(569\) | 88098.2 | − | 152591.i | 0.272109 | − | 0.471306i | −0.697293 | − | 0.716786i | \(-0.745612\pi\) |
0.969402 | + | 0.245480i | \(0.0789457\pi\) | |||||||
\(570\) | 152705. | − | 88164.4i | 0.470007 | − | 0.271358i | ||||
\(571\) | 88263.5 | + | 152877.i | 0.270713 | + | 0.468889i | 0.969045 | − | 0.246886i | \(-0.0794072\pi\) |
−0.698332 | + | 0.715774i | \(0.746074\pi\) | |||||||
\(572\) | 98630.1 | + | 56944.1i | 0.301452 | + | 0.174043i | ||||
\(573\) | − | 372943.i | − | 1.13588i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34560.6 | −0.104531 | ||||||||
\(576\) | 44765.4 | − | 77536.0i | 0.134927 | − | 0.233700i | ||||
\(577\) | 196469. | − | 113432.i | 0.590124 | − | 0.340708i | −0.175023 | − | 0.984564i | \(-0.556000\pi\) |
0.765147 | + | 0.643856i | \(0.222667\pi\) | |||||||
\(578\) | −298689. | − | 517345.i | −0.894054 | − | 1.54855i | ||||
\(579\) | 819858. | + | 473345.i | 2.44558 | + | 1.41196i | ||||
\(580\) | − | 85350.5i | − | 0.253717i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 172569. | 0.509468 | ||||||||
\(583\) | −360922. | + | 625135.i | −1.06188 | + | 1.83923i | ||||
\(584\) | 78294.2 | − | 45203.2i | 0.229564 | − | 0.132539i | ||||
\(585\) | −248180. | − | 429860.i | −0.725195 | − | 1.25608i | ||||
\(586\) | −193538. | − | 111739.i | −0.563601 | − | 0.325395i | ||||
\(587\) | − | 349659.i | − | 1.01477i | −0.861719 | − | 0.507386i | \(-0.830612\pi\) | ||
0.861719 | − | 0.507386i | \(-0.169388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 55630.3 | 0.160354 | ||||||||
\(590\) | −163644. | + | 283440.i | −0.470107 | + | 0.814249i | ||||
\(591\) | 843663. | − | 487089.i | 2.41543 | − | 1.39455i | ||||
\(592\) | 28765.2 | + | 49822.7i | 0.0820774 | + | 0.142162i | ||||
\(593\) | 119299. | + | 68877.4i | 0.339256 | + | 0.195870i | 0.659943 | − | 0.751316i | \(-0.270580\pi\) |
−0.320687 | + | 0.947185i | \(0.603914\pi\) | |||||||
\(594\) | 593115.i | 1.68099i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 236271. | 0.665146 | ||||||||
\(597\) | 320849. | − | 555727.i | 0.900228 | − | 1.55924i | ||||
\(598\) | −57337.7 | + | 33103.9i | −0.160339 | + | 0.0925715i | ||||
\(599\) | −40438.6 | − | 70041.7i | −0.112705 | − | 0.195210i | 0.804155 | − | 0.594420i | \(-0.202618\pi\) |
−0.916860 | + | 0.399209i | \(0.869285\pi\) | |||||||
\(600\) | 47172.8 | + | 27235.2i | 0.131036 | + | 0.0756534i | ||||
\(601\) | 228798.i | 0.633438i | 0.948519 | + | 0.316719i | \(0.102581\pi\) | ||||
−0.948519 | + | 0.316719i | \(0.897419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.10437e6 | 3.03725 | ||||||||
\(604\) | −103123. | + | 178615.i | −0.282672 | + | 0.489602i | ||||
\(605\) | 117329. | − | 67740.0i | 0.320549 | − | 0.185069i | ||||
\(606\) | 111420. | + | 192985.i | 0.303402 | + | 0.525507i | ||||
\(607\) | 230320. | + | 132975.i | 0.625107 | + | 0.360906i | 0.778855 | − | 0.627204i | \(-0.215801\pi\) |
−0.153748 | + | 0.988110i | \(0.549134\pi\) | |||||||
\(608\) | 25334.3i | 0.0685332i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 144935. | 0.389505 | ||||||||
\(611\) | −65974.9 | + | 114272.i | −0.176724 | + | 0.306096i | ||||
\(612\) | −657708. | + | 379728.i | −1.75602 | + | 1.01384i | ||||
\(613\) | 153261. | + | 265456.i | 0.407859 | + | 0.706433i | 0.994650 | − | 0.103306i | \(-0.0329421\pi\) |
−0.586790 | + | 0.809739i | \(0.699609\pi\) | |||||||
\(614\) | 6862.42 | + | 3962.02i | 0.0182029 | + | 0.0105095i | ||||
\(615\) | 293042.i | 0.774782i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 491906. | 1.29215 | 0.646074 | − | 0.763275i | \(-0.276410\pi\) | ||||
0.646074 | + | 0.763275i | \(0.276410\pi\) | |||||||
\(618\) | −427379. | + | 740242.i | −1.11902 | + | 1.93819i | ||||
\(619\) | 99792.1 | − | 57615.0i | 0.260444 | − | 0.150368i | −0.364093 | − | 0.931363i | \(-0.618621\pi\) |
0.624537 | + | 0.780995i | \(0.285288\pi\) | |||||||
\(620\) | 44276.9 | + | 76689.9i | 0.115185 | + | 0.199506i | ||||
\(621\) | −298607. | − | 172401.i | −0.774314 | − | 0.447050i | ||||
\(622\) | 58433.5i | 0.151036i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 104349. | 0.267991 | ||||||||
\(625\) | 231018. | − | 400134.i | 0.591405 | − | 1.02434i | ||||
\(626\) | −91552.3 | + | 52857.8i | −0.233626 | + | 0.134884i | ||||
\(627\) | −156330. | − | 270772.i | −0.397657 | − | 0.688761i | ||||
\(628\) | −177566. | − | 102518.i | −0.450235 | − | 0.259943i | ||||
\(629\) | − | 488007.i | − | 1.23346i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 72815.9 | 0.182880 | 0.0914402 | − | 0.995811i | \(-0.470853\pi\) | ||||
0.0914402 | + | 0.995811i | \(0.470853\pi\) | |||||||
\(632\) | −120087. | + | 207996.i | −0.300650 | + | 0.520741i | ||||
\(633\) | −303777. | + | 175386.i | −0.758136 | + | 0.437710i | ||||
\(634\) | −150848. | − | 261277.i | −0.375286 | − | 0.650015i | ||||
\(635\) | 674438. | + | 389387.i | 1.67261 | + | 0.965682i | ||||
\(636\) | 661385.i | 1.63508i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −151341. | −0.371805 | ||||||||
\(639\) | 110452. | − | 191308.i | 0.270503 | − | 0.468524i | ||||
\(640\) | −34924.9 | + | 20163.9i | −0.0852658 | + | 0.0492282i | ||||
\(641\) | 378897. | + | 656269.i | 0.922157 | + | 1.59722i | 0.796070 | + | 0.605204i | \(0.206908\pi\) |
0.126087 | + | 0.992019i | \(0.459758\pi\) | |||||||
\(642\) | 332235. | + | 191816.i | 0.806075 | + | 0.465388i | ||||
\(643\) | 353082.i | 0.853992i | 0.904254 | + | 0.426996i | \(0.140428\pi\) | ||||
−0.904254 | + | 0.426996i | \(0.859572\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 514802. | 1.23743 | ||||||||
\(646\) | 107450. | − | 186109.i | 0.257479 | − | 0.445967i | ||||
\(647\) | 185815. | − | 107281.i | 0.443888 | − | 0.256279i | −0.261358 | − | 0.965242i | \(-0.584170\pi\) |
0.705245 | + | 0.708963i | \(0.250837\pi\) | |||||||
\(648\) | 111471. | + | 193073.i | 0.265467 | + | 0.459802i | ||||
\(649\) | 502587. | + | 290169.i | 1.19322 | + | 0.688908i | ||||
\(650\) | 43388.1i | 0.102694i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −49462.3 | −0.116353 | ||||||||
\(653\) | 248796. | − | 430927.i | 0.583467 | − | 1.01059i | −0.411598 | − | 0.911366i | \(-0.635029\pi\) |
0.995065 | − | 0.0992289i | \(-0.0316376\pi\) | |||||||
\(654\) | 457560. | − | 264172.i | 1.06978 | − | 0.617635i | ||||
\(655\) | 16287.2 | + | 28210.2i | 0.0379632 | + | 0.0657542i | ||||
\(656\) | −36462.4 | − | 21051.6i | −0.0847301 | − | 0.0489190i | ||||
\(657\) | 698662.i | 1.61859i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −197464. | −0.454692 | −0.227346 | − | 0.973814i | \(-0.573005\pi\) | ||||
−0.227346 | + | 0.973814i | \(0.573005\pi\) | |||||||
\(660\) | 248851. | − | 431022.i | 0.571283 | − | 0.989491i | ||||
\(661\) | 578871. | − | 334211.i | 1.32489 | − | 0.764924i | 0.340383 | − | 0.940287i | \(-0.389443\pi\) |
0.984504 | + | 0.175363i | \(0.0561099\pi\) | |||||||
\(662\) | 153248. | + | 265433.i | 0.349687 | + | 0.605675i | ||||
\(663\) | −766567. | − | 442577.i | −1.74390 | − | 1.00684i | ||||
\(664\) | − | 130115.i | − | 0.295114i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −444595. | −1.00234 | ||||||||
\(667\) | 43990.3 | − | 76193.4i | 0.0988793 | − | 0.171264i | ||||
\(668\) | 272076. | − | 157083.i | 0.609731 | − | 0.352028i | ||||
\(669\) | −514729. | − | 891536.i | −1.15007 | − | 1.99199i | ||||
\(670\) | −430802. | − | 248724.i | −0.959684 | − | 0.554074i | ||||
\(671\) | − | 256994.i | − | 0.570792i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −404534. | −0.893151 | −0.446575 | − | 0.894746i | \(-0.647357\pi\) | ||||
−0.446575 | + | 0.894746i | \(0.647357\pi\) | |||||||
\(674\) | 264382. | − | 457922.i | 0.581984 | − | 1.00803i | ||||
\(675\) | −195686. | + | 112980.i | −0.429490 | + | 0.247966i | ||||
\(676\) | −72684.6 | − | 125893.i | −0.159056 | − | 0.275493i | ||||
\(677\) | −182878. | − | 105585.i | −0.399010 | − | 0.230369i | 0.287047 | − | 0.957917i | \(-0.407327\pi\) |
−0.686057 | + | 0.727548i | \(0.740660\pi\) | |||||||
\(678\) | 890550.i | 1.93731i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 342085. | 0.739803 | ||||||||
\(681\) | 350106. | − | 606401.i | 0.754927 | − | 1.30757i | ||||
\(682\) | 135984. | − | 78510.5i | 0.292361 | − | 0.168795i | ||||
\(683\) | 85054.3 | + | 147318.i | 0.182329 | + | 0.315802i | 0.942673 | − | 0.333718i | \(-0.108303\pi\) |
−0.760345 | + | 0.649520i | \(0.774970\pi\) | |||||||
\(684\) | −169554. | − | 97891.8i | −0.362405 | − | 0.209235i | ||||
\(685\) | − | 581588.i | − | 1.23946i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −455983. | −0.966128 | ||||||||
\(688\) | −36982.4 | + | 64055.4i | −0.0781301 | + | 0.135325i | ||||
\(689\) | −456241. | + | 263411.i | −0.961072 | + | 0.554875i | ||||
\(690\) | 144667. | + | 250571.i | 0.303859 | + | 0.526299i | ||||
\(691\) | −146038. | − | 84315.2i | −0.305851 | − | 0.176583i | 0.339217 | − | 0.940708i | \(-0.389838\pi\) |
−0.645068 | + | 0.764125i | \(0.723171\pi\) | |||||||
\(692\) | − | 263247.i | − | 0.549732i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 178834. | 0.371305 | ||||||||
\(695\) | −48731.6 | + | 84405.7i | −0.100888 | + | 0.174744i | ||||
\(696\) | −120087. | + | 69332.5i | −0.247901 | + | 0.143126i | ||||
\(697\) | 178572. | + | 309296.i | 0.367577 | + | 0.636662i | ||||
\(698\) | −229284. | − | 132377.i | −0.470613 | − | 0.271708i | ||||
\(699\) | 35109.0i | 0.0718562i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −487646. | −0.992359 | −0.496179 | − | 0.868220i | \(-0.665264\pi\) | ||||
−0.496179 | + | 0.868220i | \(0.665264\pi\) | |||||||
\(702\) | −216436. | + | 374877.i | −0.439192 | + | 0.760703i | ||||
\(703\) | 108951. | − | 62902.9i | 0.220455 | − | 0.127280i | ||||
\(704\) | 35754.0 | + | 61927.7i | 0.0721405 | + | 0.124951i | ||||
\(705\) | 499378. | + | 288316.i | 1.00474 | + | 0.580084i | ||||
\(706\) | − | 405174.i | − | 0.812890i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 531730. | 1.06078 | ||||||||
\(709\) | 193465. | − | 335090.i | 0.384865 | − | 0.666606i | −0.606885 | − | 0.794790i | \(-0.707581\pi\) |
0.991751 | + | 0.128183i | \(0.0409145\pi\) | |||||||
\(710\) | −86171.8 | + | 49751.3i | −0.170942 | + | 0.0986933i | ||||
\(711\) | −928032. | − | 1.60740e6i | −1.83579 | − | 3.17969i | ||||
\(712\) | 82049.1 | + | 47371.1i | 0.161850 | + | 0.0934444i | ||||
\(713\) | 91282.7i | 0.179560i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 396441. | 0.775472 | ||||||||
\(716\) | 19071.5 | − | 33032.9i | 0.0372014 | − | 0.0644348i | ||||
\(717\) | −1.12128e6 | + | 647370.i | −2.18110 | + | 1.25926i | ||||
\(718\) | 144730. | + | 250680.i | 0.280744 | + | 0.486263i | ||||
\(719\) | −163137. | − | 94187.2i | −0.315569 | − | 0.182194i | 0.333847 | − | 0.942627i | \(-0.391653\pi\) |
−0.649416 | + | 0.760433i | \(0.724987\pi\) | |||||||
\(720\) | − | 311654.i | − | 0.601184i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −313203. | −0.600830 | ||||||||
\(723\) | −344042. | + | 595899.i | −0.658166 | + | 1.13998i | ||||
\(724\) | −243841. | + | 140782.i | −0.465189 | + | 0.268577i | ||||
\(725\) | −28828.2 | − | 49931.9i | −0.0548455 | − | 0.0949952i | ||||
\(726\) | −190619. | − | 110054.i | −0.361654 | − | 0.208801i | ||||
\(727\) | 901538.i | 1.70575i | 0.522115 | + | 0.852875i | \(0.325143\pi\) | ||||
−0.522115 | + | 0.852875i | \(0.674857\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 222465. | 0.418607 | ||||||||
\(730\) | 157351. | − | 272539.i | 0.295272 | − | 0.511427i | ||||
\(731\) | 543357. | − | 313707.i | 1.01684 | − | 0.587070i | ||||
\(732\) | −117734. | − | 203922.i | −0.219726 | − | 0.380577i | ||||
\(733\) | −348560. | − | 201241.i | −0.648738 | − | 0.374549i | 0.139235 | − | 0.990259i | \(-0.455536\pi\) |
−0.787972 | + | 0.615710i | \(0.788869\pi\) | |||||||
\(734\) | − | 43462.9i | − | 0.0806726i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41570.5 | −0.0767414 | ||||||||
\(737\) | −441029. | + | 763885.i | −0.811955 | + | 1.40635i | ||||
\(738\) | 281782. | − | 162687.i | 0.517369 | − | 0.298703i | ||||
\(739\) | 18650.6 | + | 32303.7i | 0.0341510 | + | 0.0591513i | 0.882596 | − | 0.470133i | \(-0.155794\pi\) |
−0.848445 | + | 0.529284i | \(0.822461\pi\) | |||||||
\(740\) | 173431. | + | 100130.i | 0.316711 | + | 0.182853i | ||||
\(741\) | − | 228188.i | − | 0.415582i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −831221. | −1.50570 | −0.752851 | − | 0.658191i | \(-0.771322\pi\) | ||||
−0.752851 | + | 0.658191i | \(0.771322\pi\) | |||||||
\(744\) | 71934.7 | − | 124595.i | 0.129955 | − | 0.225089i | ||||
\(745\) | 712262. | − | 411224.i | 1.28330 | − | 0.740912i | ||||
\(746\) | 137873. | + | 238803.i | 0.247743 | + | 0.429103i | ||||
\(747\) | 870813. | + | 502764.i | 1.56057 | + | 0.900997i | ||||
\(748\) | − | 606574.i | − | 1.08413i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −597835. | −1.06282 | ||||||||
\(751\) | 125549. | − | 217458.i | 0.222605 | − | 0.385562i | −0.732994 | − | 0.680236i | \(-0.761877\pi\) |
0.955598 | + | 0.294673i | \(0.0952108\pi\) | |||||||
\(752\) | −71748.9 | + | 41424.2i | −0.126876 | + | 0.0732519i | ||||
\(753\) | 252482. | + | 437311.i | 0.445287 | + | 0.771260i | ||||
\(754\) | −95654.8 | − | 55226.3i | −0.168253 | − | 0.0971412i | ||||
\(755\) | 717936.i | 1.25948i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −422399. | −0.737108 | −0.368554 | − | 0.929606i | \(-0.620147\pi\) | ||||
−0.368554 | + | 0.929606i | \(0.620147\pi\) | |||||||
\(758\) | −93466.3 | + | 161888.i | −0.162673 | + | 0.281759i | ||||
\(759\) | 444305. | − | 256519.i | 0.771254 | − | 0.445284i | ||||
\(760\) | 44093.8 | + | 76372.7i | 0.0763397 | + | 0.132224i | ||||
\(761\) | −214084. | − | 123602.i | −0.369671 | − | 0.213430i | 0.303644 | − | 0.952786i | \(-0.401797\pi\) |
−0.673315 | + | 0.739356i | \(0.735130\pi\) | |||||||
\(762\) | − | 1.26524e6i | − | 2.17903i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 186520. | 0.319551 | ||||||||
\(765\) | −1.32182e6 | + | 2.28946e6i | −2.25865 | + | 3.91209i | ||||
\(766\) | 511700. | − | 295430.i | 0.872083 | − | 0.503497i | ||||
\(767\) | 211773. | + | 366802.i | 0.359981 | + | 0.623506i | ||||
\(768\) | 56740.9 | + | 32759.4i | 0.0961997 | + | 0.0555409i | ||||
\(769\) | − | 903767.i | − | 1.52828i | −0.645049 | − | 0.764141i | \(-0.723163\pi\) | ||
0.645049 | − | 0.764141i | \(-0.276837\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.08941e6 | 1.83266 | ||||||||
\(772\) | −236735. | + | 410037.i | −0.397217 | + | 0.688000i | ||||
\(773\) | −211888. | + | 122333.i | −0.354606 | + | 0.204732i | −0.666712 | − | 0.745315i | \(-0.732299\pi\) |
0.312106 | + | 0.950047i | \(0.398966\pi\) | |||||||
\(774\) | −285801. | − | 495021.i | −0.477069 | − | 0.826308i | ||||
\(775\) | 51805.9 | + | 29910.2i | 0.0862534 | + | 0.0497984i | ||||
\(776\) | 86307.3i | 0.143326i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 407291. | 0.672893 | ||||||||
\(779\) | −46035.0 | + | 79735.0i | −0.0758601 | + | 0.131393i | ||||
\(780\) | 314572. | − | 181618.i | 0.517048 | − | 0.298518i | ||||
\(781\) | 88217.5 | + | 152797.i | 0.144628 | + | 0.250503i | ||||
\(782\) | 305383. | + | 176313.i | 0.499381 | + | 0.288318i | ||||
\(783\) | − | 575222.i | − | 0.938236i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −713719. | −1.15821 | ||||||||
\(786\) | 26461.0 | − | 45831.8i | 0.0428313 | − | 0.0741860i | ||||
\(787\) | −823098. | + | 475216.i | −1.32893 | + | 0.767258i | −0.985134 | − | 0.171787i | \(-0.945046\pi\) |
−0.343795 | + | 0.939045i | \(0.611713\pi\) | |||||||
\(788\) | 243609. | + | 421943.i | 0.392320 | + | 0.679518i | ||||
\(789\) | −115637. | − | 66762.8i | −0.185755 | − | 0.107246i | ||||
\(790\) | 836035.i | 1.33958i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −552615. | −0.880992 | ||||||||
\(793\) | 93780.5 | − | 162433.i | 0.149130 | − | 0.258301i | ||||
\(794\) | −697070. | + | 402453.i | −1.10569 | + | 0.638373i | ||||
\(795\) | 1.15113e6 | + | 1.99381e6i | 1.82133 | + | 3.15464i | ||||
\(796\) | 277937. | + | 160467.i | 0.438652 | + | 0.253256i | ||||
\(797\) | − | 560412.i | − | 0.882248i | −0.897446 | − | 0.441124i | \(-0.854580\pi\) | ||
0.897446 | − | 0.441124i | \(-0.145420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 702771. | 1.10083 | ||||||||
\(800\) | −13621.2 | + | 23592.6i | −0.0212831 | + | 0.0368635i | ||||
\(801\) | −634076. | + | 366084.i | −0.988272 | + | 0.570579i | ||||
\(802\) | −152517. | − | 264168.i | −0.237121 | − | 0.410706i | ||||
\(803\) | −483258. | − | 279009.i | −0.749459 | − | 0.432701i | ||||
\(804\) | 808180.i | 1.25025i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 114598. | 0.176404 | ||||||||
\(807\) | 735174. | − | 1.27336e6i | 1.12887 | − | 1.95526i | ||||
\(808\) | −96518.0 | + | 55724.7i | −0.147838 | + | 0.0853542i | ||||
\(809\) | 25932.1 | + | 44915.7i | 0.0396224 | + | 0.0686279i | 0.885157 | − | 0.465293i | \(-0.154051\pi\) |
−0.845534 | + | 0.533921i | \(0.820718\pi\) | |||||||
\(810\) | 672079. | + | 388025.i | 1.02435 | + | 0.591412i | ||||
\(811\) | − | 978879.i | − | 1.48829i | −0.668019 | − | 0.744145i | \(-0.732857\pi\) | ||
0.668019 | − | 0.744145i | \(-0.267143\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 82128.1 | 0.124254 | ||||||||
\(814\) | 177548. | − | 307523.i | 0.267959 | − | 0.464118i | ||||
\(815\) | −149109. | + | 86088.1i | −0.224486 | + | 0.129607i | ||||
\(816\) | −277885. | − | 481311.i | −0.417335 | − | 0.722845i | ||||
\(817\) | 140075. | + | 80872.1i | 0.209853 | + | 0.121159i | ||||
\(818\) | − | 240224.i | − | 0.359013i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −146560. | −0.217965 | ||||||||
\(821\) | −74399.0 | + | 128863.i | −0.110377 | + | 0.191179i | −0.915923 | − | 0.401355i | \(-0.868539\pi\) |
0.805545 | + | 0.592535i | \(0.201873\pi\) | |||||||
\(822\) | −818289. | + | 472440.i | −1.21105 | + | 0.699202i | ||||
\(823\) | −669533. | − | 1.15966e6i | −0.988490 | − | 1.71211i | −0.625263 | − | 0.780414i | \(-0.715008\pi\) |
−0.363227 | − | 0.931701i | \(-0.618325\pi\) | |||||||
\(824\) | −370219. | − | 213746.i | −0.545260 | − | 0.314806i | ||||
\(825\) | − | 336210.i | − | 0.493972i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −127284. | −0.186108 | −0.0930538 | − | 0.995661i | \(-0.529663\pi\) | ||||
−0.0930538 | + | 0.995661i | \(0.529663\pi\) | |||||||
\(828\) | 160629. | − | 278217.i | 0.234295 | − | 0.405810i | ||||
\(829\) | −385899. | + | 222799.i | −0.561519 | + | 0.324193i | −0.753755 | − | 0.657156i | \(-0.771759\pi\) |
0.192236 | + | 0.981349i | \(0.438426\pi\) | |||||||
\(830\) | −226462. | − | 392244.i | −0.328730 | − | 0.569377i | ||||
\(831\) | −917803. | − | 529894.i | −1.32907 | − | 0.767338i | ||||
\(832\) | 52188.5i | 0.0753924i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 158344. | 0.227651 | ||||||||
\(835\) | 546802. | − | 947088.i | 0.784254 | − | 1.35837i | ||||
\(836\) | 135422. | − | 78185.8i | 0.193765 | − | 0.111870i | ||||
\(837\) | 298406. | + | 516854.i | 0.425948 | + | 0.737763i | ||||
\(838\) | 812997. | + | 469384.i | 1.15771 | + | 0.668406i | ||||
\(839\) | − | 552232.i | − | 0.784509i | −0.919857 | − | 0.392254i | \(-0.871695\pi\) | ||
0.919857 | − | 0.392254i | \(-0.128305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −560506. | −0.792479 | ||||||||
\(842\) | 143528. | − | 248598.i | 0.202448 | − | 0.350650i | ||||
\(843\) | −528571. | + | 305170.i | −0.743786 | + | 0.429425i | ||||
\(844\) | −87716.0 | − | 151928.i | −0.123138 | − | 0.213282i | ||||
\(845\) | −438230. | − | 253012.i | −0.613747 | − | 0.354347i | ||||
\(846\) | − | 640254.i | − | 0.894564i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −330780. | −0.459989 | ||||||||
\(849\) | −881634. | + | 1.52703e6i | −1.22313 | + | 2.11852i | ||||
\(850\) | 200127. | − | 115543.i | 0.276992 | − | 0.159922i | ||||
\(851\) | 103216. | + | 178775.i | 0.142524 | + | 0.246859i | ||||
\(852\) | 139999. | + | 80828.7i | 0.192862 | + | 0.111349i | ||||
\(853\) | 753308.i | 1.03532i | 0.855586 | + | 0.517660i | \(0.173197\pi\) | ||||
−0.855586 | + | 0.517660i | \(0.826803\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −681515. | −0.932274 | ||||||||
\(856\) | −95933.4 | + | 166161.i | −0.130925 | + | 0.226769i | ||||
\(857\) | 1.12685e6 | − | 650586.i | 1.53428 | − | 0.885816i | 0.535120 | − | 0.844776i | \(-0.320266\pi\) |
0.999158 | − | 0.0410399i | \(-0.0130671\pi\) | |||||||
\(858\) | −322040. | − | 557789.i | −0.437456 | − | 0.757697i | ||||
\(859\) | −850759. | − | 491186.i | −1.15298 | − | 0.665671i | −0.203366 | − | 0.979103i | \(-0.565188\pi\) |
−0.949611 | + | 0.313432i | \(0.898521\pi\) | |||||||
\(860\) | 257469.i | 0.348119i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −649966. | −0.874734 | ||||||||
\(863\) | 360718. | − | 624781.i | 0.484335 | − | 0.838893i | −0.515503 | − | 0.856888i | \(-0.672395\pi\) |
0.999838 | + | 0.0179949i | \(0.00572826\pi\) | |||||||
\(864\) | −235377. | + | 135895.i | −0.315310 | + | 0.182044i | ||||
\(865\) | −458177. | − | 793585.i | −0.612351 | − | 1.06062i | ||||
\(866\) | 279888. | + | 161593.i | 0.373205 | + | 0.215470i | ||||
\(867\) | 3.37839e6i | 4.49440i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.48243e6 | 1.96307 | ||||||||
\(870\) | −241344. | + | 418020.i | −0.318858 | + | 0.552279i | ||||
\(871\) | −557504. | + | 321875.i | −0.734872 | + | 0.424278i | ||||
\(872\) | 132121. | + | 228840.i | 0.173756 | + | 0.300954i | ||||
\(873\) | −577625. | − | 333492.i | −0.757910 | − | 0.437579i | ||||
\(874\) | 90905.2i | 0.119005i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −511281. | −0.666272 | ||||||||
\(877\) | 358504. | − | 620947.i | 0.466117 | − | 0.807338i | −0.533134 | − | 0.846031i | \(-0.678986\pi\) |
0.999251 | + | 0.0386923i | \(0.0123192\pi\) | |||||||
\(878\) | −863050. | + | 498282.i | −1.11956 | + | 0.646378i | ||||
\(879\) | 631927. | + | 1.09453e6i | 0.817879 | + | 1.41661i | ||||
\(880\) | 215568. | + | 124458.i | 0.278368 | + | 0.160716i | ||||
\(881\) | 79128.9i | 0.101949i | 0.998700 | + | 0.0509745i | \(0.0162327\pi\) | ||||
−0.998700 | + | 0.0509745i | \(0.983767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −286591. | −0.367571 | −0.183786 | − | 0.982966i | \(-0.558835\pi\) | ||||
−0.183786 | + | 0.982966i | \(0.558835\pi\) | |||||||
\(884\) | 221347. | − | 383384.i | 0.283250 | − | 0.490603i | ||||
\(885\) | 1.60296e6 | − | 925467.i | 2.04661 | − | 1.18161i | ||||
\(886\) | −277633. | − | 480875.i | −0.353675 | − | 0.612583i | ||||
\(887\) | 725266. | + | 418733.i | 0.921829 | + | 0.532218i | 0.884218 | − | 0.467074i | \(-0.154692\pi\) |
0.0376108 | + | 0.999292i | \(0.488025\pi\) | |||||||
\(888\) | − | 325355.i | − | 0.412602i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 329794. | 0.416354 | ||||||||
\(891\) | 688034. | − | 1.19171e6i | 0.866672 | − | 1.50112i | ||||
\(892\) | 445886. | − | 257432.i | 0.560394 | − | 0.323544i | ||||
\(893\) | 90585.3 | + | 156898.i | 0.113594 | + | 0.196750i | ||||
\(894\) | −1.15718e6 | − | 668098.i | −1.44786 | − | 0.835920i | ||||
\(895\) | − | 132775.i | − | 0.165756i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 374430. | 0.465356 | ||||||||
\(898\) | 109630. | − | 189885.i | 0.135950 | − | 0.235472i | ||||
\(899\) | −131882. | + | 76142.1i | −0.163180 | + | 0.0942118i | ||||
\(900\) | −105265. | − | 182324.i | −0.129957 | − | 0.225092i | ||||
\(901\) | 2.42996e6 | + | 1.40294e6i | 2.99329 | + | 1.72818i | ||||
\(902\) | 259875.i | 0.319412i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −445393. | −0.545012 | ||||||||
\(905\) | −490056. | + | 848802.i | −0.598341 | + | 1.03636i | ||||
\(906\) | 1.01013e6 | − | 583199.i | 1.23061 | − | 0.710494i | ||||
\(907\) | 423285. | + | 733150.i | 0.514538 | + | 0.891207i | 0.999858 | + | 0.0168697i | \(0.00537006\pi\) |
−0.485319 | + | 0.874337i | \(0.661297\pi\) | |||||||
\(908\) | 303281. | + | 175099.i | 0.367852 | + | 0.212379i | ||||
\(909\) | − | 861283.i | − | 1.04236i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 167017. | 0.201244 | 0.100622 | − | 0.994925i | \(-0.467917\pi\) | ||||
0.100622 | + | 0.994925i | \(0.467917\pi\) | |||||||
\(912\) | 71637.2 | − | 124079.i | 0.0861289 | − | 0.149180i | ||||
\(913\) | −695515. | + | 401556.i | −0.834382 | + | 0.481731i | ||||
\(914\) | 268520. | + | 465090.i | 0.321428 | + | 0.556730i | ||||
\(915\) | −709845. | − | 409829.i | −0.847854 | − | 0.489509i | ||||
\(916\) | − | 228051.i | − | 0.271795i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.30549e6 | 2.73576 | ||||||||
\(919\) | −561015. | + | 971707.i | −0.664268 | + | 1.15055i | 0.315215 | + | 0.949020i | \(0.397923\pi\) |
−0.979483 | + | 0.201526i | \(0.935410\pi\) | |||||||
\(920\) | −125319. | + | 72352.7i | −0.148061 | + | 0.0854829i | ||||
\(921\) | −22406.7 | − | 38809.5i | −0.0264154 | − | 0.0457529i | ||||
\(922\) | 128843. | + | 74387.5i | 0.151565 | + | 0.0875061i | ||||
\(923\) | 128767.i | 0.151148i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 135281. | 0.158108 | ||||||||
\(926\) | −345447. | + | 598331.i | −0.402864 | + | 0.697782i | ||||
\(927\) | 2.86106e6 | − | 1.65183e6i | 3.32941 | − | 1.92223i | ||||
\(928\) | −34675.4 | − | 60059.6i | −0.0402648 | − | 0.0697407i | ||||
\(929\) | −1.23549e6 | − | 713313.i | −1.43156 | − | 0.826511i | −0.434319 | − | 0.900759i | \(-0.643011\pi\) |
−0.997240 | + | 0.0742487i | \(0.976344\pi\) | |||||||
\(930\) | − | 500804.i | − | 0.579032i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17559.1 | −0.0202149 | ||||||||
\(933\) | 165231. | − | 286189.i | 0.189814 | − | 0.328768i | ||||
\(934\) | 729004. | − | 420891.i | 0.835673 | − | 0.482476i | ||||
\(935\) | −1.05573e6 | − | 1.82858e6i | −1.20762 | − | 2.09166i | ||||
\(936\) | −349279. | − | 201657.i | −0.398677 | − | 0.230176i | ||||
\(937\) | − | 265587.i | − | 0.302502i | −0.988495 | − | 0.151251i | \(-0.951670\pi\) | ||
0.988495 | − | 0.151251i | \(-0.0483301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 597860. | 0.678060 | ||||||||
\(940\) | −144196. | + | 249755.i | −0.163192 | + | 0.282656i | ||||
\(941\) | −518395. | + | 299295.i | −0.585439 | + | 0.338003i | −0.763292 | − | 0.646054i | \(-0.776418\pi\) |
0.177853 | + | 0.984057i | \(0.443085\pi\) | |||||||
\(942\) | 579774. | + | 1.00420e6i | 0.653366 | + | 1.13166i | ||||
\(943\) | −130836. | − | 75537.9i | −0.147130 | − | 0.0849458i | ||||
\(944\) | 265935.i | 0.298423i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 456536. | 0.510144 | ||||||||
\(947\) | −575427. | + | 996669.i | −0.641639 | + | 1.11135i | 0.343428 | + | 0.939179i | \(0.388412\pi\) |
−0.985067 | + | 0.172172i | \(0.944922\pi\) | |||||||
\(948\) | 1.17629e6 | − | 679134.i | 1.30888 | − | 0.755681i | ||||
\(949\) | −203629. | − | 352695.i | −0.226103 | − | 0.391622i | ||||
\(950\) | 51591.7 | + | 29786.5i | 0.0571653 | + | 0.0330044i | ||||
\(951\) | 1.70621e6i | 1.88656i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 464604. | 0.511561 | 0.255781 | − | 0.966735i | \(-0.417668\pi\) | ||||
0.255781 | + | 0.966735i | \(0.417668\pi\) | |||||||
\(954\) | 1.27814e6 | − | 2.21380e6i | 1.40437 | − | 2.43243i | ||||
\(955\) | 562285. | − | 324635.i | 0.616524 | − | 0.355950i | ||||
\(956\) | −323770. | − | 560787.i | −0.354259 | − | 0.613595i | ||||
\(957\) | 741220. | + | 427944.i | 0.809325 | + | 0.467264i | ||||
\(958\) | 132571.i | 0.144450i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 228068. | 0.247470 | ||||||||
\(961\) | −382761. | + | 662961.i | −0.414458 | + | 0.717862i | ||||
\(962\) | 224438. | − | 129580.i | 0.242520 | − | 0.140019i | ||||
\(963\) | −741374. | − | 1.28410e6i | −0.799438 | − | 1.38467i | ||||
\(964\) | −298028. | − | 172066.i | −0.320703 | − | 0.185158i | ||||
\(965\) | 1.64813e6i | 1.76985i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 101298. | 0.108330 | 0.0541648 | − | 0.998532i | \(-0.482750\pi\) | ||||
0.0541648 | + | 0.998532i | \(0.482750\pi\) | |||||||
\(968\) | 55041.6 | − | 95334.8i | 0.0587408 | − | 0.101742i | ||||
\(969\) | −1.05252e6 | + | 607670.i | −1.12094 | + | 0.647173i | ||||
\(970\) | 150216. | + | 260182.i | 0.159652 | + | 0.276525i | ||||
\(971\) | −282567. | − | 163140.i | −0.299697 | − | 0.173030i | 0.342610 | − | 0.939478i | \(-0.388689\pi\) |
−0.642307 | + | 0.766448i | \(0.722022\pi\) | |||||||
\(972\) | − | 287878.i | − | 0.304702i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −303162. | −0.319563 | ||||||||
\(975\) | 122688. | − | 212501.i | 0.129060 | − | 0.223538i | ||||
\(976\) | 101988. | − | 58882.7i | 0.107065 | − | 0.0618142i | ||||
\(977\) | −370964. | − | 642529.i | −0.388636 | − | 0.673137i | 0.603630 | − | 0.797264i | \(-0.293720\pi\) |
−0.992266 | + | 0.124127i | \(0.960387\pi\) | |||||||
\(978\) | 242251. | + | 139864.i | 0.253272 | + | 0.146227i | ||||
\(979\) | − | 584780.i | − | 0.610137i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.04207e6 | −2.12193 | ||||||||
\(982\) | −164567. | + | 285039.i | −0.170656 | + | 0.295584i | ||||
\(983\) | 506189. | − | 292248.i | 0.523849 | − | 0.302444i | −0.214659 | − | 0.976689i | \(-0.568864\pi\) |
0.738508 | + | 0.674245i | \(0.235531\pi\) | |||||||
\(984\) | 119054. | + | 206208.i | 0.122958 | + | 0.212969i | ||||
\(985\) | 1.46877e6 | + | 847993.i | 1.51384 | + | 0.874017i | ||||
\(986\) | 588276.i | 0.605100i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 114124. | 0.116913 | ||||||||
\(989\) | −132701. | + | 229846.i | −0.135670 | + | 0.234987i | ||||
\(990\) | −1.66591e6 | + | 961815.i | −1.69974 | + | 0.981344i | ||||
\(991\) | −291172. | − | 504324.i | −0.296484 | − | 0.513526i | 0.678845 | − | 0.734282i | \(-0.262481\pi\) |
−0.975329 | + | 0.220756i | \(0.929148\pi\) | |||||||
\(992\) | 62313.7 | + | 35976.9i | 0.0633229 | + | 0.0365595i | ||||
\(993\) | − | 1.73335e6i | − | 1.75787i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.11716e6 | 1.12842 | ||||||||
\(996\) | −367923. | + | 637261.i | −0.370884 | + | 0.642390i | ||||
\(997\) | −1.18588e6 | + | 684671.i | −1.19303 | + | 0.688797i | −0.958993 | − | 0.283430i | \(-0.908528\pi\) |
−0.234039 | + | 0.972227i | \(0.575194\pi\) | |||||||
\(998\) | 626366. | + | 1.08490e6i | 0.628879 | + | 1.08925i | ||||
\(999\) | 1.16884e6 | + | 674833.i | 1.17119 | + | 0.676185i |
(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 | 98.5.d.c.19.3 | 8 | ||
7.2 | even | 3 | 98.5.b.a.97.1 | ✓ | 4 | ||
7.3 | odd | 6 | inner | 98.5.d.c.31.3 | 8 | ||
7.4 | even | 3 | inner | 98.5.d.c.31.4 | 8 | ||
7.5 | odd | 6 | 98.5.b.a.97.2 | yes | 4 | ||
7.6 | odd | 2 | inner | 98.5.d.c.19.4 | 8 | ||
21.2 | odd | 6 | 882.5.c.c.685.3 | 4 | |||
21.5 | even | 6 | 882.5.c.c.685.4 | 4 | |||
28.19 | even | 6 | 784.5.c.a.97.1 | 4 | |||
28.23 | odd | 6 | 784.5.c.a.97.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.5.b.a.97.1 | ✓ | 4 | 7.2 | even | 3 | ||
98.5.b.a.97.2 | yes | 4 | 7.5 | odd | 6 | ||
98.5.d.c.19.3 | 8 | 1.1 | even | 1 | trivial | ||
98.5.d.c.19.4 | 8 | 7.6 | odd | 2 | inner | ||
98.5.d.c.31.3 | 8 | 7.3 | odd | 6 | inner | ||
98.5.d.c.31.4 | 8 | 7.4 | even | 3 | inner | ||
784.5.c.a.97.1 | 4 | 28.19 | even | 6 | |||
784.5.c.a.97.4 | 4 | 28.23 | odd | 6 | |||
882.5.c.c.685.3 | 4 | 21.2 | odd | 6 | |||
882.5.c.c.685.4 | 4 | 21.5 | even | 6 |