Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,5,Mod(5,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.h (of order \(10\), degree \(4\), 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: | \(3.41120878177\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 5.13 | ||
Character | \(\chi\) | \(=\) | 33.5 |
Dual form | 33.5.h.a.20.13 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.11716 | − | 1.98759i | 1.52929 | − | 0.496896i | 0.580892 | − | 0.813980i | \(-0.302704\pi\) |
0.948397 | + | 0.317084i | \(0.102704\pi\) | |||||||
\(3\) | 8.27649 | + | 3.53550i | 0.919610 | + | 0.392834i | ||||
\(4\) | 20.5249 | − | 14.9122i | 1.28280 | − | 0.932012i | ||||
\(5\) | −26.2596 | − | 8.53227i | −1.05039 | − | 0.341291i | −0.267566 | − | 0.963540i | \(-0.586219\pi\) |
−0.782820 | + | 0.622249i | \(0.786219\pi\) | |||||||
\(6\) | 57.6557 | + | 5.17701i | 1.60155 | + | 0.143806i | ||||
\(7\) | −49.1578 | + | 35.7152i | −1.00322 | + | 0.728882i | −0.962776 | − | 0.270300i | \(-0.912877\pi\) |
−0.0404437 | + | 0.999182i | \(0.512877\pi\) | |||||||
\(8\) | 35.4248 | − | 48.7581i | 0.553513 | − | 0.761845i | ||||
\(9\) | 56.0004 | + | 58.5231i | 0.691363 | + | 0.722507i | ||||
\(10\) | −177.593 | −1.77593 | ||||||||
\(11\) | 63.8969 | − | 102.753i | 0.528074 | − | 0.849198i | ||||
\(12\) | 222.596 | − | 50.8548i | 1.54580 | − | 0.353158i | ||||
\(13\) | −47.0040 | − | 144.663i | −0.278130 | − | 0.855997i | −0.988374 | − | 0.152041i | \(-0.951415\pi\) |
0.710244 | − | 0.703956i | \(-0.248585\pi\) | |||||||
\(14\) | −229.719 | + | 316.181i | −1.17204 | + | 1.61317i | ||||
\(15\) | −187.172 | − | 163.458i | −0.831874 | − | 0.726481i | ||||
\(16\) | −5.64836 | + | 17.3839i | −0.0220639 | + | 0.0679057i | ||||
\(17\) | 38.7120 | + | 12.5783i | 0.133952 | + | 0.0435235i | 0.375226 | − | 0.926934i | \(-0.377565\pi\) |
−0.241274 | + | 0.970457i | \(0.577565\pi\) | |||||||
\(18\) | 458.883 | + | 246.689i | 1.41631 | + | 0.761387i | ||||
\(19\) | 377.439 | + | 274.225i | 1.04554 | + | 0.759627i | 0.971359 | − | 0.237618i | \(-0.0763667\pi\) |
0.0741779 | + | 0.997245i | \(0.476367\pi\) | |||||||
\(20\) | −666.211 | + | 216.465i | −1.66553 | + | 0.541162i | ||||
\(21\) | −533.125 | + | 121.799i | −1.20890 | + | 0.276188i | ||||
\(22\) | 186.637 | − | 755.557i | 0.385614 | − | 1.56107i | ||||
\(23\) | 179.292i | 0.338926i | 0.985537 | + | 0.169463i | \(0.0542033\pi\) | ||||
−0.985537 | + | 0.169463i | \(0.945797\pi\) | |||||||
\(24\) | 465.578 | − | 278.301i | 0.808295 | − | 0.483162i | ||||
\(25\) | 111.133 | + | 80.7431i | 0.177813 | + | 0.129189i | ||||
\(26\) | −575.062 | − | 791.505i | −0.850683 | − | 1.17087i | ||||
\(27\) | 256.578 | + | 682.355i | 0.351959 | + | 0.936015i | ||||
\(28\) | −476.365 | + | 1466.10i | −0.607608 | + | 1.87003i | ||||
\(29\) | −800.506 | − | 1101.80i | −0.951850 | − | 1.31011i | −0.950701 | − | 0.310110i | \(-0.899634\pi\) |
−0.00114925 | − | 0.999999i | \(-0.500366\pi\) | |||||||
\(30\) | −1469.85 | − | 627.881i | −1.63316 | − | 0.697645i | ||||
\(31\) | −9.57512 | − | 29.4692i | −0.00996370 | − | 0.0306651i | 0.945951 | − | 0.324309i | \(-0.105132\pi\) |
−0.955915 | + | 0.293644i | \(0.905132\pi\) | |||||||
\(32\) | 1081.86i | 1.05650i | ||||||||
\(33\) | 892.126 | − | 624.526i | 0.819216 | − | 0.573486i | ||||
\(34\) | 261.808 | 0.226478 | ||||||||
\(35\) | 1595.60 | − | 518.441i | 1.30253 | − | 0.423217i | ||||
\(36\) | 2022.11 | + | 366.089i | 1.56027 | + | 0.282476i | ||||
\(37\) | 2141.57 | − | 1555.94i | 1.56433 | − | 1.13655i | 0.631985 | − | 0.774981i | \(-0.282240\pi\) |
0.932344 | − | 0.361571i | \(-0.117760\pi\) | |||||||
\(38\) | 2853.90 | + | 927.288i | 1.97638 | + | 0.642166i | ||||
\(39\) | 122.430 | − | 1363.49i | 0.0804931 | − | 0.896442i | ||||
\(40\) | −1346.26 | + | 978.116i | −0.841413 | + | 0.611322i | ||||
\(41\) | −1213.82 | + | 1670.68i | −0.722083 | + | 0.993863i | 0.277369 | + | 0.960764i | \(0.410538\pi\) |
−0.999452 | + | 0.0330990i | \(0.989462\pi\) | |||||||
\(42\) | −3019.12 | + | 1804.70i | −1.71152 | + | 1.02307i | ||||
\(43\) | 720.538 | 0.389691 | 0.194845 | − | 0.980834i | \(-0.437580\pi\) | ||||
0.194845 | + | 0.980834i | \(0.437580\pi\) | |||||||
\(44\) | −220.796 | − | 3061.84i | −0.114047 | − | 1.58153i | ||||
\(45\) | −971.216 | − | 2014.61i | −0.479613 | − | 0.994867i | ||||
\(46\) | 356.358 | + | 1096.76i | 0.168411 | + | 0.518316i | ||||
\(47\) | −328.274 | + | 451.831i | −0.148608 | + | 0.204541i | −0.876831 | − | 0.480799i | \(-0.840347\pi\) |
0.728223 | + | 0.685340i | \(0.240347\pi\) | |||||||
\(48\) | −108.209 | + | 123.907i | −0.0469658 | + | 0.0537793i | ||||
\(49\) | 398.960 | − | 1227.87i | 0.166164 | − | 0.511401i | ||||
\(50\) | 840.304 | + | 273.031i | 0.336122 | + | 0.109213i | ||||
\(51\) | 275.929 | + | 240.971i | 0.106086 | + | 0.0926454i | ||||
\(52\) | −3122.00 | − | 2268.27i | −1.15459 | − | 0.838856i | ||||
\(53\) | 99.2928 | − | 32.2622i | 0.0353481 | − | 0.0114853i | −0.291290 | − | 0.956635i | \(-0.594084\pi\) |
0.326638 | + | 0.945150i | \(0.394084\pi\) | |||||||
\(54\) | 2925.77 | + | 3664.10i | 1.00335 | + | 1.25655i | ||||
\(55\) | −2554.63 | + | 2153.07i | −0.844505 | + | 0.711759i | ||||
\(56\) | 3662.05i | 1.16774i | ||||||||
\(57\) | 2154.34 | + | 3604.06i | 0.663078 | + | 1.10928i | ||||
\(58\) | −7086.75 | − | 5148.82i | −2.10664 | − | 1.53057i | ||||
\(59\) | −2197.67 | − | 3024.83i | −0.631333 | − | 0.868956i | 0.366783 | − | 0.930306i | \(-0.380459\pi\) |
−0.998116 | + | 0.0613509i | \(0.980459\pi\) | |||||||
\(60\) | −6279.19 | − | 563.820i | −1.74422 | − | 0.156617i | ||||
\(61\) | −319.475 | + | 983.242i | −0.0858572 | + | 0.264241i | −0.984763 | − | 0.173900i | \(-0.944363\pi\) |
0.898906 | + | 0.438141i | \(0.144363\pi\) | |||||||
\(62\) | −117.145 | − | 161.236i | −0.0304748 | − | 0.0419449i | ||||
\(63\) | −4843.02 | − | 876.796i | −1.22021 | − | 0.220911i | ||||
\(64\) | 2059.92 | + | 6339.77i | 0.502909 | + | 1.54779i | ||||
\(65\) | 4199.86i | 0.994050i | ||||||||
\(66\) | 4215.98 | − | 5593.50i | 0.967855 | − | 1.28409i | ||||
\(67\) | 3713.07 | 0.827148 | 0.413574 | − | 0.910471i | \(-0.364280\pi\) | ||||
0.413574 | + | 0.910471i | \(0.364280\pi\) | |||||||
\(68\) | 982.129 | − | 319.113i | 0.212398 | − | 0.0690124i | ||||
\(69\) | −633.887 | + | 1483.91i | −0.133141 | + | 0.311679i | ||||
\(70\) | 8730.08 | − | 6342.77i | 1.78165 | − | 1.29444i | ||||
\(71\) | 1810.99 | + | 588.426i | 0.359252 | + | 0.116728i | 0.483081 | − | 0.875576i | \(-0.339518\pi\) |
−0.123829 | + | 0.992304i | \(0.539518\pi\) | |||||||
\(72\) | 4837.28 | − | 657.305i | 0.933118 | − | 0.126795i | ||||
\(73\) | −4996.81 | + | 3630.39i | −0.937663 | + | 0.681252i | −0.947857 | − | 0.318696i | \(-0.896755\pi\) |
0.0101937 | + | 0.999948i | \(0.496755\pi\) | |||||||
\(74\) | 10007.7 | − | 13774.5i | 1.82756 | − | 2.51543i | ||||
\(75\) | 634.326 | + | 1061.18i | 0.112769 | + | 0.188654i | ||||
\(76\) | 11836.2 | 2.04920 | ||||||||
\(77\) | 528.814 | + | 7333.20i | 0.0891911 | + | 1.23684i | ||||
\(78\) | −1961.12 | − | 8584.01i | −0.322341 | − | 1.41092i | ||||
\(79\) | −1722.61 | − | 5301.64i | −0.276014 | − | 0.849485i | −0.988949 | − | 0.148255i | \(-0.952634\pi\) |
0.712935 | − | 0.701230i | \(-0.247366\pi\) | |||||||
\(80\) | 296.648 | − | 408.300i | 0.0463512 | − | 0.0637969i | ||||
\(81\) | −288.901 | + | 6554.64i | −0.0440331 | + | 0.999030i | ||||
\(82\) | −4104.52 | + | 12632.4i | −0.610428 | + | 1.87870i | ||||
\(83\) | −5406.90 | − | 1756.81i | −0.784860 | − | 0.255016i | −0.110946 | − | 0.993826i | \(-0.535388\pi\) |
−0.673914 | + | 0.738810i | \(0.735388\pi\) | |||||||
\(84\) | −9126.03 | + | 10450.0i | −1.29337 | + | 1.48100i | ||||
\(85\) | −909.242 | − | 660.603i | −0.125847 | − | 0.0914330i | ||||
\(86\) | 4407.65 | − | 1432.13i | 0.595950 | − | 0.193636i | ||||
\(87\) | −2729.95 | − | 11949.2i | −0.360675 | − | 1.57871i | ||||
\(88\) | −2746.50 | − | 6755.50i | −0.354662 | − | 0.872353i | ||||
\(89\) | 12094.8i | 1.52693i | 0.645848 | + | 0.763466i | \(0.276504\pi\) | ||||
−0.645848 | + | 0.763466i | \(0.723496\pi\) | |||||||
\(90\) | −9945.29 | − | 10393.3i | −1.22781 | − | 1.28312i | ||||
\(91\) | 7477.30 | + | 5432.57i | 0.902946 | + | 0.656029i | ||||
\(92\) | 2673.63 | + | 3679.94i | 0.315883 | + | 0.434776i | ||||
\(93\) | 24.9401 | − | 277.754i | 0.00288358 | − | 0.0321140i | ||||
\(94\) | −1110.05 | + | 3416.39i | −0.125629 | + | 0.386645i | ||||
\(95\) | −7571.64 | − | 10421.5i | −0.838963 | − | 1.15473i | ||||
\(96\) | −3824.92 | + | 8954.00i | −0.415030 | + | 0.971571i | ||||
\(97\) | −1750.09 | − | 5386.21i | −0.186001 | − | 0.572453i | 0.813963 | − | 0.580917i | \(-0.197306\pi\) |
−0.999964 | + | 0.00846375i | \(0.997306\pi\) | |||||||
\(98\) | − | 8304.07i | − | 0.864647i | ||||||
\(99\) | 9591.68 | − | 2014.77i | 0.978643 | − | 0.205568i | ||||
\(100\) | 3485.05 | 0.348505 | ||||||||
\(101\) | −10552.6 | + | 3428.76i | −1.03447 | + | 0.336120i | −0.776556 | − | 0.630048i | \(-0.783035\pi\) |
−0.257914 | + | 0.966168i | \(0.583035\pi\) | |||||||
\(102\) | 2166.85 | + | 925.623i | 0.208271 | + | 0.0889680i | ||||
\(103\) | −4038.05 | + | 2933.82i | −0.380625 | + | 0.276540i | −0.761603 | − | 0.648044i | \(-0.775587\pi\) |
0.380978 | + | 0.924584i | \(0.375587\pi\) | |||||||
\(104\) | −8718.62 | − | 2832.85i | −0.806086 | − | 0.261913i | ||||
\(105\) | 15038.9 | + | 1350.37i | 1.36407 | + | 0.122482i | ||||
\(106\) | 543.266 | − | 394.706i | 0.0483505 | − | 0.0351287i | ||||
\(107\) | −3310.40 | + | 4556.37i | −0.289143 | + | 0.397971i | −0.928735 | − | 0.370743i | \(-0.879103\pi\) |
0.639593 | + | 0.768714i | \(0.279103\pi\) | |||||||
\(108\) | 15441.6 | + | 10179.1i | 1.32387 | + | 0.872694i | ||||
\(109\) | 1350.21 | 0.113644 | 0.0568222 | − | 0.998384i | \(-0.481903\pi\) | ||||
0.0568222 | + | 0.998384i | \(0.481903\pi\) | |||||||
\(110\) | −11347.7 | + | 18248.2i | −0.937822 | + | 1.50812i | ||||
\(111\) | 23225.7 | − | 5306.20i | 1.88505 | − | 0.430663i | ||||
\(112\) | −343.207 | − | 1056.28i | −0.0273603 | − | 0.0842063i | ||||
\(113\) | 7467.91 | − | 10278.7i | 0.584847 | − | 0.804973i | −0.409369 | − | 0.912369i | \(-0.634251\pi\) |
0.994216 | + | 0.107396i | \(0.0342512\pi\) | |||||||
\(114\) | 20341.8 | + | 17764.7i | 1.56524 | + | 1.36693i | ||||
\(115\) | 1529.77 | − | 4708.14i | 0.115672 | − | 0.356003i | ||||
\(116\) | −32860.6 | − | 10677.0i | −2.44207 | − | 0.793478i | ||||
\(117\) | 5833.90 | − | 10852.0i | 0.426175 | − | 0.792756i | ||||
\(118\) | −19455.6 | − | 14135.3i | −1.39727 | − | 1.01518i | ||||
\(119\) | −2352.23 | + | 764.287i | −0.166106 | + | 0.0539713i | ||||
\(120\) | −14600.4 | + | 3335.65i | −1.01392 | + | 0.231643i | ||||
\(121\) | −6475.36 | − | 13131.2i | −0.442276 | − | 0.896879i | ||||
\(122\) | 6649.63i | 0.446764i | ||||||||
\(123\) | −15952.9 | + | 9535.91i | −1.05446 | + | 0.630307i | ||||
\(124\) | −635.978 | − | 462.065i | −0.0413617 | − | 0.0300511i | ||||
\(125\) | 7913.94 | + | 10892.6i | 0.506492 | + | 0.697127i | ||||
\(126\) | −31368.2 | + | 4262.42i | −1.97583 | + | 0.268482i | ||||
\(127\) | −1996.19 | + | 6143.63i | −0.123764 | + | 0.380906i | −0.993674 | − | 0.112305i | \(-0.964177\pi\) |
0.869910 | + | 0.493210i | \(0.164177\pi\) | |||||||
\(128\) | 15027.2 | + | 20683.2i | 0.917190 | + | 1.26240i | ||||
\(129\) | 5963.52 | + | 2547.46i | 0.358363 | + | 0.153084i | ||||
\(130\) | 8347.58 | + | 25691.2i | 0.493940 | + | 1.52019i | ||||
\(131\) | − | 25297.5i | − | 1.47413i | −0.675824 | − | 0.737063i | \(-0.736212\pi\) | ||
0.675824 | − | 0.737063i | \(-0.263788\pi\) | |||||||
\(132\) | 8997.71 | − | 26121.9i | 0.516398 | − | 1.49919i | ||||
\(133\) | −28348.1 | −1.60258 | ||||||||
\(134\) | 22713.4 | − | 7380.04i | 1.26495 | − | 0.411007i | ||||
\(135\) | −915.615 | − | 20107.6i | −0.0502395 | − | 1.10330i | ||||
\(136\) | 1984.66 | − | 1441.94i | 0.107302 | − | 0.0779596i | ||||
\(137\) | 34755.6 | + | 11292.8i | 1.85176 | + | 0.601672i | 0.996512 | + | 0.0834478i | \(0.0265932\pi\) |
0.855245 | + | 0.518224i | \(0.173407\pi\) | |||||||
\(138\) | −928.195 | + | 10337.2i | −0.0487395 | + | 0.542806i | ||||
\(139\) | −1876.63 | + | 1363.45i | −0.0971291 | + | 0.0705684i | −0.635290 | − | 0.772274i | \(-0.719119\pi\) |
0.538161 | + | 0.842842i | \(0.319119\pi\) | |||||||
\(140\) | 25018.3 | − | 34434.8i | 1.27645 | − | 1.75688i | ||||
\(141\) | −4314.41 | + | 2578.96i | −0.217012 | + | 0.129720i | ||||
\(142\) | 12247.6 | 0.607402 | ||||||||
\(143\) | −17868.0 | − | 4413.75i | −0.873784 | − | 0.215842i | ||||
\(144\) | −1333.67 | + | 642.944i | −0.0643165 | + | 0.0310062i | ||||
\(145\) | 11620.1 | + | 35763.1i | 0.552681 | + | 1.70098i | ||||
\(146\) | −23350.6 | + | 32139.3i | −1.09545 | + | 1.50775i | ||||
\(147\) | 7643.14 | − | 8751.96i | 0.353702 | − | 0.405014i | ||||
\(148\) | 20752.9 | − | 63870.9i | 0.947449 | − | 2.91595i | ||||
\(149\) | −8020.66 | − | 2606.07i | −0.361275 | − | 0.117385i | 0.122755 | − | 0.992437i | \(-0.460827\pi\) |
−0.484029 | + | 0.875052i | \(0.660827\pi\) | |||||||
\(150\) | 5989.46 | + | 5230.64i | 0.266198 | + | 0.232473i | ||||
\(151\) | −3726.37 | − | 2707.37i | −0.163430 | − | 0.118739i | 0.503064 | − | 0.864249i | \(-0.332206\pi\) |
−0.666494 | + | 0.745510i | \(0.732206\pi\) | |||||||
\(152\) | 26741.4 | − | 8688.81i | 1.15744 | − | 0.376074i | ||||
\(153\) | 1431.77 | + | 2969.94i | 0.0611632 | + | 0.126872i | ||||
\(154\) | 17810.2 | + | 43807.3i | 0.750978 | + | 1.84716i | ||||
\(155\) | 855.548i | 0.0356107i | ||||||||
\(156\) | −17819.7 | − | 29811.1i | −0.732237 | − | 1.22498i | ||||
\(157\) | 21905.6 | + | 15915.3i | 0.888701 | + | 0.645679i | 0.935539 | − | 0.353224i | \(-0.114915\pi\) |
−0.0468383 | + | 0.998902i | \(0.514915\pi\) | |||||||
\(158\) | −21074.9 | − | 29007.1i | −0.844212 | − | 1.16196i | ||||
\(159\) | 935.858 | + | 84.0324i | 0.0370183 | + | 0.00332394i | ||||
\(160\) | 9230.72 | − | 28409.2i | 0.360575 | − | 1.10974i | ||||
\(161\) | −6403.44 | − | 8813.58i | −0.247037 | − | 0.340017i | ||||
\(162\) | 11260.6 | + | 40670.0i | 0.429075 | + | 1.54969i | ||||
\(163\) | −4211.61 | − | 12962.0i | −0.158516 | − | 0.487862i | 0.839984 | − | 0.542611i | \(-0.182564\pi\) |
−0.998500 | + | 0.0547487i | \(0.982564\pi\) | |||||||
\(164\) | 52391.3i | 1.94792i | ||||||||
\(165\) | −28755.5 | + | 8787.97i | −1.05622 | + | 0.322790i | ||||
\(166\) | −36566.7 | −1.32700 | ||||||||
\(167\) | 23640.9 | − | 7681.38i | 0.847677 | − | 0.275427i | 0.147204 | − | 0.989106i | \(-0.452973\pi\) |
0.700473 | + | 0.713679i | \(0.252973\pi\) | |||||||
\(168\) | −12947.2 | + | 30308.9i | −0.458729 | + | 1.07387i | ||||
\(169\) | 4388.20 | − | 3188.22i | 0.153643 | − | 0.111628i | ||||
\(170\) | −6874.99 | − | 2233.82i | −0.237889 | − | 0.0772948i | ||||
\(171\) | 5088.23 | + | 37445.6i | 0.174010 | + | 1.28059i | ||||
\(172\) | 14788.9 | − | 10744.8i | 0.499897 | − | 0.363196i | ||||
\(173\) | −7566.35 | + | 10414.2i | −0.252810 | + | 0.347963i | −0.916493 | − | 0.400051i | \(-0.868992\pi\) |
0.663683 | + | 0.748014i | \(0.268992\pi\) | |||||||
\(174\) | −40449.7 | − | 67669.4i | −1.33603 | − | 2.23508i | ||||
\(175\) | −8346.83 | −0.272549 | ||||||||
\(176\) | 1425.33 | + | 1691.16i | 0.0460140 | + | 0.0545958i | ||||
\(177\) | −7494.68 | − | 32804.9i | −0.239225 | − | 1.04711i | ||||
\(178\) | 24039.5 | + | 73986.0i | 0.758727 | + | 2.33512i | ||||
\(179\) | 20527.7 | − | 28254.0i | 0.640670 | − | 0.881807i | −0.357981 | − | 0.933729i | \(-0.616535\pi\) |
0.998651 | + | 0.0519217i | \(0.0165346\pi\) | |||||||
\(180\) | −49976.3 | − | 26866.6i | −1.54248 | − | 0.829215i | ||||
\(181\) | −1076.55 | + | 3313.29i | −0.0328608 | + | 0.101135i | −0.966142 | − | 0.258012i | \(-0.916933\pi\) |
0.933281 | + | 0.359147i | \(0.116933\pi\) | |||||||
\(182\) | 56537.5 | + | 18370.2i | 1.70684 | + | 0.554587i | ||||
\(183\) | −6120.38 | + | 7008.29i | −0.182758 | + | 0.209271i | ||||
\(184\) | 8741.93 | + | 6351.38i | 0.258209 | + | 0.187600i | ||||
\(185\) | −69512.5 | + | 22586.0i | −2.03104 | + | 0.659926i | ||||
\(186\) | −399.498 | − | 1748.64i | −0.0115475 | − | 0.0505445i | ||||
\(187\) | 3766.04 | − | 3174.06i | 0.107696 | − | 0.0907679i | ||||
\(188\) | 14169.1i | 0.400890i | ||||||||
\(189\) | −36983.3 | − | 24379.3i | −1.03534 | − | 0.682492i | ||||
\(190\) | −67030.5 | − | 48700.5i | −1.85680 | − | 1.34904i | ||||
\(191\) | −16506.9 | − | 22719.9i | −0.452481 | − | 0.622786i | 0.520448 | − | 0.853894i | \(-0.325765\pi\) |
−0.972928 | + | 0.231107i | \(0.925765\pi\) | |||||||
\(192\) | −5365.40 | + | 59753.8i | −0.145546 | + | 1.62093i | ||||
\(193\) | 3990.81 | − | 12282.4i | 0.107139 | − | 0.329739i | −0.883088 | − | 0.469208i | \(-0.844540\pi\) |
0.990226 | + | 0.139469i | \(0.0445395\pi\) | |||||||
\(194\) | −21411.1 | − | 29469.9i | −0.568900 | − | 0.783023i | ||||
\(195\) | −14848.6 | + | 34760.1i | −0.390496 | + | 0.914138i | ||||
\(196\) | −10121.7 | − | 31151.3i | −0.263476 | − | 0.810895i | ||||
\(197\) | 26731.0i | 0.688783i | 0.938826 | + | 0.344391i | \(0.111915\pi\) | ||||
−0.938826 | + | 0.344391i | \(0.888085\pi\) | |||||||
\(198\) | 54669.3 | − | 31388.9i | 1.39448 | − | 0.800657i | ||||
\(199\) | 25985.0 | 0.656169 | 0.328085 | − | 0.944648i | \(-0.393597\pi\) | ||||
0.328085 | + | 0.944648i | \(0.393597\pi\) | |||||||
\(200\) | 7873.76 | − | 2558.34i | 0.196844 | − | 0.0639585i | ||||
\(201\) | 30731.1 | + | 13127.6i | 0.760653 | + | 0.324931i | ||||
\(202\) | −57737.2 | + | 41948.5i | −1.41499 | + | 1.02805i | ||||
\(203\) | 78702.2 | + | 25571.9i | 1.90983 | + | 0.620541i | ||||
\(204\) | 9256.80 | + | 831.185i | 0.222434 | + | 0.0199727i | ||||
\(205\) | 46129.3 | − | 33514.9i | 1.09766 | − | 0.797498i | ||||
\(206\) | −18870.2 | + | 25972.6i | −0.444674 | + | 0.612042i | ||||
\(207\) | −10492.7 | + | 10040.4i | −0.244876 | + | 0.234321i | ||||
\(208\) | 2780.30 | 0.0642637 | ||||||||
\(209\) | 52294.6 | − | 21260.8i | 1.19719 | − | 0.486729i | ||||
\(210\) | 94679.3 | − | 21630.7i | 2.14692 | − | 0.490491i | ||||
\(211\) | −16810.5 | − | 51737.4i | −0.377586 | − | 1.16209i | −0.941717 | − | 0.336405i | \(-0.890789\pi\) |
0.564132 | − | 0.825685i | \(-0.309211\pi\) | |||||||
\(212\) | 1556.87 | − | 2142.85i | 0.0346403 | − | 0.0476782i | ||||
\(213\) | 12908.2 | + | 11272.8i | 0.284517 | + | 0.248470i | ||||
\(214\) | −11194.0 | + | 34451.7i | −0.244433 | + | 0.752287i | ||||
\(215\) | −18921.1 | − | 6147.83i | −0.409325 | − | 0.132998i | ||||
\(216\) | 42359.6 | + | 11662.0i | 0.907913 | + | 0.249958i | ||||
\(217\) | 1523.19 | + | 1106.66i | 0.0323470 | + | 0.0235015i | ||||
\(218\) | 8259.44 | − | 2683.65i | 0.173795 | − | 0.0564694i | ||||
\(219\) | −54191.3 | + | 12380.7i | −1.12990 | + | 0.258140i | ||||
\(220\) | −20326.4 | + | 82286.6i | −0.419967 | + | 1.70014i | ||||
\(221\) | − | 6191.44i | − | 0.126767i | ||||||
\(222\) | 131529. | − | 78621.9i | 2.66879 | − | 1.59528i | ||||
\(223\) | 28902.8 | + | 20999.1i | 0.581207 | + | 0.422272i | 0.839159 | − | 0.543886i | \(-0.183048\pi\) |
−0.257952 | + | 0.966158i | \(0.583048\pi\) | |||||||
\(224\) | −38638.9 | − | 53181.8i | −0.770066 | − | 1.05991i | ||||
\(225\) | 1498.18 | + | 11025.5i | 0.0295937 | + | 0.217788i | ||||
\(226\) | 25252.6 | − | 77719.6i | 0.494413 | − | 1.52165i | ||||
\(227\) | −3974.33 | − | 5470.20i | −0.0771281 | − | 0.106158i | 0.768710 | − | 0.639598i | \(-0.220899\pi\) |
−0.845838 | + | 0.533440i | \(0.820899\pi\) | |||||||
\(228\) | 97962.0 | + | 41846.8i | 1.88446 | + | 0.804995i | ||||
\(229\) | −128.942 | − | 396.843i | −0.00245881 | − | 0.00756743i | 0.949820 | − | 0.312798i | \(-0.101266\pi\) |
−0.952278 | + | 0.305231i | \(0.901266\pi\) | |||||||
\(230\) | − | 31841.0i | − | 0.601909i | ||||||
\(231\) | −21549.8 | + | 62562.8i | −0.403850 | + | 1.17244i | ||||
\(232\) | −82079.6 | −1.52496 | ||||||||
\(233\) | 12779.8 | − | 4152.40i | 0.235403 | − | 0.0764870i | −0.188940 | − | 0.981989i | \(-0.560505\pi\) |
0.424343 | + | 0.905502i | \(0.360505\pi\) | |||||||
\(234\) | 14117.6 | − | 77979.0i | 0.257827 | − | 1.42412i | ||||
\(235\) | 12475.5 | − | 9063.99i | 0.225903 | − | 0.164128i | ||||
\(236\) | −90213.8 | − | 29312.2i | −1.61975 | − | 0.526290i | ||||
\(237\) | 4486.82 | − | 49969.2i | 0.0798808 | − | 0.889622i | ||||
\(238\) | −12869.9 | + | 9350.53i | −0.227207 | + | 0.165075i | ||||
\(239\) | −47060.4 | + | 64773.1i | −0.823872 | + | 1.13396i | 0.165160 | + | 0.986267i | \(0.447186\pi\) |
−0.989033 | + | 0.147696i | \(0.952814\pi\) | |||||||
\(240\) | 3898.75 | − | 2330.49i | 0.0676866 | − | 0.0404600i | ||||
\(241\) | −68717.9 | −1.18314 | −0.591570 | − | 0.806254i | \(-0.701492\pi\) | ||||
−0.591570 | + | 0.806254i | \(0.701492\pi\) | |||||||
\(242\) | −65710.2 | − | 67455.3i | −1.12202 | − | 1.15182i | ||||
\(243\) | −25565.0 | + | 53227.9i | −0.432946 | + | 0.901420i | ||||
\(244\) | 8105.12 | + | 24945.0i | 0.136138 | + | 0.418990i | ||||
\(245\) | −20953.1 | + | 28839.5i | −0.349073 | + | 0.480458i | ||||
\(246\) | −78632.9 | + | 90040.4i | −1.29937 | + | 1.48788i | ||||
\(247\) | 21929.2 | − | 67491.3i | 0.359443 | − | 1.10625i | ||||
\(248\) | −1776.06 | − | 577.077i | −0.0288771 | − | 0.00938275i | ||||
\(249\) | −38538.9 | − | 33656.3i | −0.621586 | − | 0.542835i | ||||
\(250\) | 70060.9 | + | 50902.2i | 1.12097 | + | 0.814435i | ||||
\(251\) | 76509.2 | − | 24859.3i | 1.21441 | − | 0.394586i | 0.369368 | − | 0.929283i | \(-0.379574\pi\) |
0.845044 | + | 0.534697i | \(0.179574\pi\) | |||||||
\(252\) | −112477. | + | 54223.9i | −1.77118 | + | 0.853866i | ||||
\(253\) | 18422.8 | + | 11456.2i | 0.287815 | + | 0.178978i | ||||
\(254\) | 41549.1i | 0.644013i | ||||||||
\(255\) | −5189.77 | − | 8682.10i | −0.0798119 | − | 0.133519i | ||||
\(256\) | 46746.8 | + | 33963.6i | 0.713300 | + | 0.518243i | ||||
\(257\) | 10279.4 | + | 14148.4i | 0.155633 | + | 0.214210i | 0.879712 | − | 0.475506i | \(-0.157735\pi\) |
−0.724079 | + | 0.689717i | \(0.757735\pi\) | |||||||
\(258\) | 41543.1 | + | 3730.23i | 0.624108 | + | 0.0560398i | ||||
\(259\) | −49704.0 | + | 152973.i | −0.740954 | + | 2.28042i | ||||
\(260\) | 62629.1 | + | 86201.6i | 0.926466 | + | 1.27517i | ||||
\(261\) | 19652.1 | − | 108549.i | 0.288489 | − | 1.59348i | ||||
\(262\) | −50280.9 | − | 154749.i | −0.732488 | − | 2.25437i | ||||
\(263\) | 13984.5i | 0.202178i | 0.994877 | + | 0.101089i | \(0.0322327\pi\) | ||||
−0.994877 | + | 0.101089i | \(0.967767\pi\) | |||||||
\(264\) | 1152.70 | − | 65622.1i | 0.0165390 | − | 0.941548i | ||||
\(265\) | −2882.66 | −0.0410490 | ||||||||
\(266\) | −173410. | + | 56344.2i | −2.45081 | + | 0.796317i | ||||
\(267\) | −42761.3 | + | 100103.i | −0.599830 | + | 1.40418i | ||||
\(268\) | 76210.2 | − | 55370.0i | 1.06107 | − | 0.770912i | ||||
\(269\) | −54052.5 | − | 17562.7i | −0.746984 | − | 0.242710i | −0.0893010 | − | 0.996005i | \(-0.528463\pi\) |
−0.657683 | + | 0.753295i | \(0.728463\pi\) | |||||||
\(270\) | −45566.5 | − | 121182.i | −0.625055 | − | 1.66230i | ||||
\(271\) | 50902.4 | − | 36982.7i | 0.693105 | − | 0.503571i | −0.184574 | − | 0.982819i | \(-0.559091\pi\) |
0.877680 | + | 0.479248i | \(0.159091\pi\) | |||||||
\(272\) | −437.319 | + | 601.917i | −0.00591099 | + | 0.00813578i | ||||
\(273\) | 42678.9 | + | 71398.6i | 0.572648 | + | 0.957998i | ||||
\(274\) | 235051. | 3.13084 | ||||||||
\(275\) | 15397.7 | − | 6260.05i | 0.203606 | − | 0.0827775i | ||||
\(276\) | 9117.85 | + | 39909.6i | 0.119695 | + | 0.523913i | ||||
\(277\) | 28126.7 | + | 86565.0i | 0.366572 | + | 1.12819i | 0.948991 | + | 0.315303i | \(0.102106\pi\) |
−0.582419 | + | 0.812889i | \(0.697894\pi\) | |||||||
\(278\) | −8769.67 | + | 12070.4i | −0.113473 | + | 0.156183i | ||||
\(279\) | 1188.42 | − | 2210.65i | 0.0152672 | − | 0.0283996i | ||||
\(280\) | 31245.6 | − | 96164.0i | 0.398541 | − | 1.22658i | ||||
\(281\) | 4131.65 | + | 1342.46i | 0.0523252 | + | 0.0170015i | 0.335063 | − | 0.942196i | \(-0.391243\pi\) |
−0.282737 | + | 0.959197i | \(0.591243\pi\) | |||||||
\(282\) | −21266.0 | + | 24351.1i | −0.267416 | + | 0.306211i | ||||
\(283\) | −33963.7 | − | 24676.1i | −0.424075 | − | 0.308108i | 0.355200 | − | 0.934790i | \(-0.384413\pi\) |
−0.779275 | + | 0.626682i | \(0.784413\pi\) | |||||||
\(284\) | 45945.0 | − | 14928.4i | 0.569642 | − | 0.185088i | ||||
\(285\) | −25821.4 | − | 113023.i | −0.317900 | − | 1.39148i | ||||
\(286\) | −118074. | + | 8514.60i | −1.44352 | + | 0.104096i | ||||
\(287\) | − | 125479.i | − | 1.52338i | ||||||
\(288\) | −63313.8 | + | 60584.6i | −0.763331 | + | 0.730428i | ||||
\(289\) | −66229.5 | − | 48118.5i | −0.792968 | − | 0.576125i | ||||
\(290\) | 142164. | + | 195672.i | 1.69042 | + | 2.32666i | ||||
\(291\) | 4558.40 | − | 50766.3i | 0.0538303 | − | 0.599501i | ||||
\(292\) | −48421.7 | + | 149027.i | −0.567903 | + | 1.74783i | ||||
\(293\) | −14990.8 | − | 20633.1i | −0.174619 | − | 0.240342i | 0.712733 | − | 0.701436i | \(-0.247457\pi\) |
−0.887351 | + | 0.461094i | \(0.847457\pi\) | |||||||
\(294\) | 29359.1 | − | 68728.5i | 0.339662 | − | 0.795137i | ||||
\(295\) | 31901.3 | + | 98182.2i | 0.366577 | + | 1.12821i | ||||
\(296\) | − | 159538.i | − | 1.82087i | ||||||
\(297\) | 86508.6 | + | 17236.2i | 0.980723 | + | 0.195402i | ||||
\(298\) | −54243.4 | −0.610822 | ||||||||
\(299\) | 25937.0 | − | 8427.43i | 0.290119 | − | 0.0942655i | ||||
\(300\) | 28844.0 | + | 12321.4i | 0.320489 | + | 0.136905i | ||||
\(301\) | −35420.0 | + | 25734.2i | −0.390945 | + | 0.284038i | ||||
\(302\) | −28175.9 | − | 9154.91i | −0.308933 | − | 0.100378i | ||||
\(303\) | −99461.1 | − | 8930.79i | −1.08335 | − | 0.0972758i | ||||
\(304\) | −6899.00 | + | 5012.42i | −0.0746516 | + | 0.0542375i | ||||
\(305\) | 16778.6 | − | 23093.7i | 0.180366 | − | 0.248253i | ||||
\(306\) | 14661.4 | + | 15321.8i | 0.156578 | + | 0.163632i | ||||
\(307\) | 39375.3 | 0.417780 | 0.208890 | − | 0.977939i | \(-0.433015\pi\) | ||||
0.208890 | + | 0.977939i | \(0.433015\pi\) | |||||||
\(308\) | 120208. | + | 142627.i | 1.26716 | + | 1.50349i | ||||
\(309\) | −43793.4 | + | 10005.2i | −0.458661 | + | 0.104787i | ||||
\(310\) | 1700.47 | + | 5233.52i | 0.0176948 | + | 0.0544591i | ||||
\(311\) | 47661.9 | − | 65600.9i | 0.492777 | − | 0.678249i | −0.488120 | − | 0.872776i | \(-0.662317\pi\) |
0.980897 | + | 0.194527i | \(0.0623173\pi\) | |||||||
\(312\) | −62144.0 | − | 54270.8i | −0.638396 | − | 0.557516i | ||||
\(313\) | 28678.5 | − | 88263.3i | 0.292730 | − | 0.900931i | −0.691244 | − | 0.722621i | \(-0.742937\pi\) |
0.983974 | − | 0.178310i | \(-0.0570629\pi\) | |||||||
\(314\) | 165633. | + | 53817.4i | 1.67992 | + | 0.545838i | ||||
\(315\) | 119695. | + | 64346.3i | 1.20630 | + | 0.648489i | ||||
\(316\) | −114415. | − | 83127.6i | −1.14580 | − | 0.832474i | ||||
\(317\) | −24247.0 | + | 7878.34i | −0.241291 | + | 0.0784001i | −0.427166 | − | 0.904173i | \(-0.640488\pi\) |
0.185875 | + | 0.982573i | \(0.440488\pi\) | |||||||
\(318\) | 5891.82 | − | 1346.06i | 0.0582633 | − | 0.0133110i | ||||
\(319\) | −164363. | + | 11852.6i | −1.61519 | + | 0.116475i | ||||
\(320\) | − | 184056.i | − | 1.79742i | ||||||
\(321\) | −43507.5 | + | 26006.8i | −0.422235 | + | 0.252393i | ||||
\(322\) | −56688.6 | − | 41186.7i | −0.546744 | − | 0.397233i | ||||
\(323\) | 11162.1 | + | 15363.4i | 0.106990 | + | 0.147259i | ||||
\(324\) | 91814.3 | + | 138841.i | 0.874622 | + | 1.32260i | ||||
\(325\) | 6456.86 | − | 19872.2i | 0.0611301 | − | 0.188139i | ||||
\(326\) | −51526.2 | − | 70919.8i | −0.484834 | − | 0.667317i | ||||
\(327\) | 11175.0 | + | 4773.66i | 0.104508 | + | 0.0446433i | ||||
\(328\) | 38459.9 | + | 118367.i | 0.357487 | + | 1.10023i | ||||
\(329\) | − | 33935.4i | − | 0.313517i | ||||||
\(330\) | −158435. | + | 110911.i | −1.45487 | + | 1.01847i | ||||
\(331\) | −82268.6 | −0.750893 | −0.375446 | − | 0.926844i | \(-0.622511\pi\) | ||||
−0.375446 | + | 0.926844i | \(0.622511\pi\) | |||||||
\(332\) | −137174. | + | 44570.5i | −1.24450 | + | 0.404363i | ||||
\(333\) | 210987. | + | 38197.8i | 1.90269 | + | 0.344469i | ||||
\(334\) | 129347. | − | 93976.4i | 1.15948 | − | 0.842415i | ||||
\(335\) | −97503.8 | − | 31680.9i | −0.868824 | − | 0.282298i | ||||
\(336\) | 893.943 | − | 9955.73i | 0.00791829 | − | 0.0881850i | ||||
\(337\) | 92414.9 | − | 67143.4i | 0.813734 | − | 0.591212i | −0.101177 | − | 0.994868i | \(-0.532261\pi\) |
0.914911 | + | 0.403656i | \(0.132261\pi\) | |||||||
\(338\) | 20506.5 | − | 28224.8i | 0.179497 | − | 0.247057i | ||||
\(339\) | 98148.4 | − | 58668.7i | 0.854051 | − | 0.510513i | ||||
\(340\) | −28513.1 | −0.246653 | ||||||||
\(341\) | −3639.87 | − | 899.119i | −0.0313024 | − | 0.00773229i | ||||
\(342\) | 105552. | + | 218947.i | 0.902430 | + | 1.87192i | ||||
\(343\) | −20840.8 | − | 64141.5i | −0.177144 | − | 0.545194i | ||||
\(344\) | 25524.9 | − | 35132.1i | 0.215699 | − | 0.296884i | ||||
\(345\) | 29306.7 | − | 33558.3i | 0.246223 | − | 0.281944i | ||||
\(346\) | −25585.5 | + | 78744.0i | −0.213718 | + | 0.657757i | ||||
\(347\) | 69401.7 | + | 22550.0i | 0.576383 | + | 0.187278i | 0.582679 | − | 0.812702i | \(-0.302004\pi\) |
−0.00629670 | + | 0.999980i | \(0.502004\pi\) | |||||||
\(348\) | −234221. | − | 204547.i | −1.93405 | − | 1.68902i | ||||
\(349\) | 67237.4 | + | 48850.8i | 0.552027 | + | 0.401071i | 0.828532 | − | 0.559942i | \(-0.189176\pi\) |
−0.276506 | + | 0.961012i | \(0.589176\pi\) | |||||||
\(350\) | −51058.9 | + | 16590.0i | −0.416807 | + | 0.135429i | ||||
\(351\) | 86651.6 | − | 69190.9i | 0.703335 | − | 0.561610i | ||||
\(352\) | 111164. | + | 69127.5i | 0.897181 | + | 0.557912i | ||||
\(353\) | 41091.9i | 0.329767i | 0.986313 | + | 0.164884i | \(0.0527248\pi\) | ||||
−0.986313 | + | 0.164884i | \(0.947275\pi\) | |||||||
\(354\) | −111049. | − | 185776.i | −0.886149 | − | 1.48246i | ||||
\(355\) | −42535.3 | − | 30903.7i | −0.337515 | − | 0.245219i | ||||
\(356\) | 180360. | + | 248245.i | 1.42312 | + | 1.95876i | ||||
\(357\) | −22170.4 | − | 1990.72i | −0.173955 | − | 0.0156197i | ||||
\(358\) | 69414.1 | − | 213635.i | 0.541604 | − | 1.66689i | ||||
\(359\) | 128858. | + | 177357.i | 0.999819 | + | 1.37613i | 0.925436 | + | 0.378903i | \(0.123699\pi\) |
0.0743825 | + | 0.997230i | \(0.476301\pi\) | |||||||
\(360\) | −132634. | − | 24012.4i | −1.02341 | − | 0.185281i | ||||
\(361\) | 26989.1 | + | 83063.8i | 0.207097 | + | 0.637379i | ||||
\(362\) | 22407.7i | 0.170994i | ||||||||
\(363\) | −7167.81 | − | 131574.i | −0.0543968 | − | 0.998519i | ||||
\(364\) | 234482. | 1.76973 | ||||||||
\(365\) | 162190. | − | 52698.7i | 1.21741 | − | 0.395562i | ||||
\(366\) | −23509.8 | + | 55035.6i | −0.175504 | + | 0.410848i | ||||
\(367\) | 126891. | − | 92192.0i | 0.942107 | − | 0.684480i | −0.00682026 | − | 0.999977i | \(-0.502171\pi\) |
0.948927 | + | 0.315496i | \(0.102171\pi\) | |||||||
\(368\) | −3116.78 | − | 1012.70i | −0.0230150 | − | 0.00747802i | ||||
\(369\) | −165748. | + | 22522.4i | −1.21729 | + | 0.165410i | ||||
\(370\) | −380327. | + | 276324.i | −2.77814 | + | 2.01844i | ||||
\(371\) | −3728.76 | + | 5132.20i | −0.0270905 | + | 0.0372869i | ||||
\(372\) | −3630.03 | − | 6072.78i | −0.0262316 | − | 0.0438835i | ||||
\(373\) | −229002. | −1.64597 | −0.822983 | − | 0.568066i | \(-0.807692\pi\) | ||||
−0.822983 | + | 0.568066i | \(0.807692\pi\) | |||||||
\(374\) | 16728.7 | − | 26901.6i | 0.119597 | − | 0.192324i | ||||
\(375\) | 26988.8 | + | 118132.i | 0.191920 | + | 0.840052i | ||||
\(376\) | 10401.4 | + | 32012.1i | 0.0735723 | + | 0.226432i | ||||
\(377\) | −121763. | + | 167593.i | −0.856711 | + | 1.17916i | ||||
\(378\) | −274689. | − | 75624.7i | −1.92246 | − | 0.529273i | ||||
\(379\) | −49247.6 | + | 151569.i | −0.342852 | + | 1.05519i | 0.619871 | + | 0.784704i | \(0.287185\pi\) |
−0.962724 | + | 0.270487i | \(0.912815\pi\) | |||||||
\(380\) | −310814. | − | 100990.i | −2.15245 | − | 0.699373i | ||||
\(381\) | −38242.2 | + | 43790.1i | −0.263447 | + | 0.301666i | ||||
\(382\) | −146133. | − | 106172.i | −1.00143 | − | 0.727585i | ||||
\(383\) | −174098. | + | 56567.9i | −1.18685 | + | 0.385631i | −0.834908 | − | 0.550390i | \(-0.814479\pi\) |
−0.351944 | + | 0.936021i | \(0.614479\pi\) | |||||||
\(384\) | 51247.2 | + | 224313.i | 0.347542 | + | 1.52122i | ||||
\(385\) | 48682.4 | − | 197079.i | 0.328436 | − | 1.32960i | ||||
\(386\) | − | 83065.7i | − | 0.557503i | ||||||
\(387\) | 40350.4 | + | 42168.1i | 0.269418 | + | 0.281554i | ||||
\(388\) | −116241. | − | 84453.7i | −0.772136 | − | 0.560990i | ||||
\(389\) | −104943. | − | 144442.i | −0.693515 | − | 0.954542i | −0.999996 | − | 0.00266505i | \(-0.999152\pi\) |
0.306481 | − | 0.951877i | \(-0.400848\pi\) | |||||||
\(390\) | −21742.7 | + | 242146.i | −0.142950 | + | 1.59202i | ||||
\(391\) | −2255.19 | + | 6940.75i | −0.0147512 | + | 0.0453997i | ||||
\(392\) | −45735.7 | − | 62949.8i | −0.297634 | − | 0.409659i | ||||
\(393\) | 89439.3 | − | 209374.i | 0.579087 | − | 1.35562i | ||||
\(394\) | 53130.1 | + | 163518.i | 0.342254 | + | 1.05335i | ||||
\(395\) | 153917.i | 0.986488i | ||||||||
\(396\) | 166823. | − | 184386.i | 1.06382 | − | 1.17581i | ||||
\(397\) | 95760.8 | 0.607585 | 0.303792 | − | 0.952738i | \(-0.401747\pi\) | ||||
0.303792 | + | 0.952738i | \(0.401747\pi\) | |||||||
\(398\) | 158954. | − | 51647.3i | 1.00347 | − | 0.326048i | ||||
\(399\) | −234622. | − | 100225.i | −1.47375 | − | 0.629548i | ||||
\(400\) | −2031.35 | + | 1475.86i | −0.0126959 | + | 0.00922413i | ||||
\(401\) | −218674. | − | 71051.4i | −1.35990 | − | 0.441859i | −0.463893 | − | 0.885891i | \(-0.653548\pi\) |
−0.896011 | + | 0.444032i | \(0.853548\pi\) | |||||||
\(402\) | 214079. | + | 19222.6i | 1.32472 | + | 0.118949i | ||||
\(403\) | −3813.05 | + | 2770.34i | −0.0234780 | + | 0.0170578i | ||||
\(404\) | −165461. | + | 227738.i | −1.01376 | + | 1.39532i | ||||
\(405\) | 63512.4 | − | 169657.i | 0.387212 | − | 1.03434i | ||||
\(406\) | 532260. | 3.22903 | ||||||||
\(407\) | −23037.9 | − | 319472.i | −0.139076 | − | 1.92861i | ||||
\(408\) | 21524.0 | − | 4917.43i | 0.129301 | − | 0.0295405i | ||||
\(409\) | 12329.8 | + | 37947.3i | 0.0737072 | + | 0.226847i | 0.981122 | − | 0.193388i | \(-0.0619475\pi\) |
−0.907415 | + | 0.420235i | \(0.861948\pi\) | |||||||
\(410\) | 215566. | − | 296702.i | 1.28237 | − | 1.76503i | ||||
\(411\) | 247729. | + | 216343.i | 1.46654 | + | 1.28074i | ||||
\(412\) | −39130.9 | + | 120432.i | −0.230529 | + | 0.709495i | ||||
\(413\) | 216065. | + | 70203.8i | 1.26673 | + | 0.411586i | ||||
\(414\) | −44229.4 | + | 82274.0i | −0.258054 | + | 0.480023i | ||||
\(415\) | 126994. | + | 92266.3i | 0.737371 | + | 0.535731i | ||||
\(416\) | 156506. | − | 50851.7i | 0.904364 | − | 0.293846i | ||||
\(417\) | −20352.4 | + | 4649.76i | −0.117043 | + | 0.0267398i | ||||
\(418\) | 277637. | − | 233996.i | 1.58900 | − | 1.33923i | ||||
\(419\) | 125731.i | 0.716166i | 0.933690 | + | 0.358083i | \(0.116569\pi\) | ||||
−0.933690 | + | 0.358083i | \(0.883431\pi\) | |||||||
\(420\) | 328808. | − | 196547.i | 1.86399 | − | 1.11421i | ||||
\(421\) | 214700. | + | 155989.i | 1.21135 | + | 0.880094i | 0.995352 | − | 0.0963010i | \(-0.0307011\pi\) |
0.215993 | + | 0.976395i | \(0.430701\pi\) | |||||||
\(422\) | −205665. | − | 283074.i | −1.15488 | − | 1.58955i | ||||
\(423\) | −44826.0 | + | 6091.10i | −0.250524 | + | 0.0340420i | ||||
\(424\) | 1944.39 | − | 5984.21i | 0.0108156 | − | 0.0332870i | ||||
\(425\) | 3286.59 | + | 4523.60i | 0.0181956 | + | 0.0250441i | ||||
\(426\) | 101367. | + | 43301.6i | 0.558572 | + | 0.238608i | ||||
\(427\) | −19412.0 | − | 59744.1i | −0.106467 | − | 0.327672i | ||||
\(428\) | 142884.i | 0.780004i | ||||||||
\(429\) | −132280. | − | 99702.7i | −0.718750 | − | 0.541742i | ||||
\(430\) | −127963. | −0.692063 | ||||||||
\(431\) | −37316.6 | + | 12124.9i | −0.200885 | + | 0.0652716i | −0.407731 | − | 0.913102i | \(-0.633680\pi\) |
0.206846 | + | 0.978373i | \(0.433680\pi\) | |||||||
\(432\) | −13311.2 | + | 606.136i | −0.0713263 | + | 0.00324790i | ||||
\(433\) | −255610. | + | 185711.i | −1.36333 | + | 0.990519i | −0.365107 | + | 0.930966i | \(0.618968\pi\) |
−0.998225 | + | 0.0595531i | \(0.981032\pi\) | |||||||
\(434\) | 11517.2 | + | 3742.16i | 0.0611458 | + | 0.0198675i | ||||
\(435\) | −30266.6 | + | 337075.i | −0.159950 | + | 1.78135i | ||||
\(436\) | 27712.8 | − | 20134.6i | 0.145783 | − | 0.105918i | ||||
\(437\) | −49166.3 | + | 67671.7i | −0.257457 | + | 0.354359i | ||||
\(438\) | −306889. | + | 183444.i | −1.59968 | + | 0.956216i | ||||
\(439\) | −172376. | −0.894430 | −0.447215 | − | 0.894426i | \(-0.647584\pi\) | ||||
−0.447215 | + | 0.894426i | \(0.647584\pi\) | |||||||
\(440\) | 14482.4 | + | 200831.i | 0.0748057 | + | 1.03735i | ||||
\(441\) | 94200.9 | − | 45413.1i | 0.484371 | − | 0.233509i | ||||
\(442\) | −12306.0 | − | 37874.1i | −0.0629902 | − | 0.193864i | ||||
\(443\) | −90332.6 | + | 124332.i | −0.460296 | + | 0.633543i | −0.974570 | − | 0.224083i | \(-0.928061\pi\) |
0.514274 | + | 0.857626i | \(0.328061\pi\) | |||||||
\(444\) | 397577. | − | 455255.i | 2.01677 | − | 2.30934i | ||||
\(445\) | 103196. | − | 317606.i | 0.521128 | − | 1.60387i | ||||
\(446\) | 218541. | + | 71008.2i | 1.09866 | + | 0.356976i | ||||
\(447\) | −57169.1 | − | 49926.1i | −0.286119 | − | 0.249869i | ||||
\(448\) | −327687. | − | 238079.i | −1.63269 | − | 1.18622i | ||||
\(449\) | −204970. | + | 66598.9i | −1.01671 | + | 0.330350i | −0.769524 | − | 0.638617i | \(-0.779507\pi\) |
−0.247189 | + | 0.968967i | \(0.579507\pi\) | |||||||
\(450\) | 31078.8 | + | 64467.1i | 0.153475 | + | 0.318356i | ||||
\(451\) | 94108.2 | + | 231475.i | 0.462673 | + | 1.13802i | ||||
\(452\) | − | 322332.i | − | 1.57771i | ||||||
\(453\) | −21269.3 | − | 35582.1i | −0.103647 | − | 0.173394i | ||||
\(454\) | −35184.1 | − | 25562.8i | −0.170701 | − | 0.124021i | ||||
\(455\) | −149999. | − | 206456.i | −0.724545 | − | 0.997251i | ||||
\(456\) | 252044. | + | 22631.5i | 1.21212 | + | 0.108839i | ||||
\(457\) | 7958.14 | − | 24492.6i | 0.0381047 | − | 0.117274i | −0.930195 | − | 0.367066i | \(-0.880362\pi\) |
0.968300 | + | 0.249792i | \(0.0803622\pi\) | |||||||
\(458\) | −1577.52 | − | 2171.27i | −0.00752045 | − | 0.0103510i | ||||
\(459\) | 1349.80 | + | 29642.7i | 0.00640685 | + | 0.140699i | ||||
\(460\) | −38810.4 | − | 119446.i | −0.183414 | − | 0.564490i | ||||
\(461\) | 365316.i | 1.71897i | 0.511164 | + | 0.859483i | \(0.329214\pi\) | ||||
−0.511164 | + | 0.859483i | \(0.670786\pi\) | |||||||
\(462\) | −7474.92 | + | 425539.i | −0.0350205 | + | 1.99368i | ||||
\(463\) | −214032. | −0.998430 | −0.499215 | − | 0.866478i | \(-0.666378\pi\) | ||||
−0.499215 | + | 0.866478i | \(0.666378\pi\) | |||||||
\(464\) | 23675.1 | − | 7692.51i | 0.109965 | − | 0.0357299i | ||||
\(465\) | −3024.79 | + | 7080.93i | −0.0139891 | + | 0.0327480i | ||||
\(466\) | 69922.7 | − | 50801.8i | 0.321993 | − | 0.233941i | ||||
\(467\) | 347983. | + | 113066.i | 1.59560 | + | 0.518442i | 0.966014 | − | 0.258490i | \(-0.0832249\pi\) |
0.629585 | + | 0.776932i | \(0.283225\pi\) | |||||||
\(468\) | −42087.5 | − | 309733.i | −0.192159 | − | 1.41415i | ||||
\(469\) | −182526. | + | 132613.i | −0.829811 | + | 0.602893i | ||||
\(470\) | 58299.2 | − | 80242.0i | 0.263917 | − | 0.363250i | ||||
\(471\) | 125033. | + | 209170.i | 0.563613 | + | 0.942884i | ||||
\(472\) | −225337. | −1.01146 | ||||||||
\(473\) | 46040.2 | − | 74037.5i | 0.205785 | − | 0.330925i | ||||
\(474\) | −71871.4 | − | 314587.i | −0.319889 | − | 1.40018i | ||||
\(475\) | 19804.2 | + | 60951.1i | 0.0877750 | + | 0.270144i | ||||
\(476\) | −36882.1 | + | 50763.8i | −0.162780 | + | 0.224048i | ||||
\(477\) | 7448.52 | + | 4004.22i | 0.0327366 | + | 0.0175987i | ||||
\(478\) | −159134. | + | 489764.i | −0.696478 | + | 2.14354i | ||||
\(479\) | −247762. | − | 80502.7i | −1.07985 | − | 0.350864i | −0.285533 | − | 0.958369i | \(-0.592171\pi\) |
−0.794316 | + | 0.607504i | \(0.792171\pi\) | |||||||
\(480\) | 176839. | − | 202494.i | 0.767530 | − | 0.878878i | ||||
\(481\) | −325750. | − | 236671.i | −1.40797 | − | 1.02295i | ||||
\(482\) | −420358. | + | 136583.i | −1.80936 | + | 0.587898i | ||||
\(483\) | −21837.6 | − | 95584.9i | −0.0936073 | − | 0.409727i | ||||
\(484\) | −328721. | − | 172954.i | −1.40326 | − | 0.738314i | ||||
\(485\) | 156372.i | 0.664777i | ||||||||
\(486\) | −50590.2 | + | 376416.i | −0.214187 | + | 1.59366i | ||||
\(487\) | 146203. | + | 106223.i | 0.616452 | + | 0.447878i | 0.851680 | − | 0.524062i | \(-0.175584\pi\) |
−0.235229 | + | 0.971940i | \(0.575584\pi\) | |||||||
\(488\) | 36623.7 | + | 50408.2i | 0.153788 | + | 0.211671i | ||||
\(489\) | 10969.9 | − | 122170.i | 0.0458758 | − | 0.510913i | ||||
\(490\) | −70852.6 | + | 218062.i | −0.295096 | + | 0.908213i | ||||
\(491\) | 6936.11 | + | 9546.74i | 0.0287709 | + | 0.0395997i | 0.823160 | − | 0.567809i | \(-0.192209\pi\) |
−0.794389 | + | 0.607409i | \(0.792209\pi\) | |||||||
\(492\) | −185230. | + | 433616.i | −0.765209 | + | 1.79133i | ||||
\(493\) | −17130.4 | − | 52722.0i | −0.0704813 | − | 0.216919i | ||||
\(494\) | − | 456441.i | − | 1.87038i | ||||||
\(495\) | −269065. | − | 28931.8i | −1.09811 | − | 0.118077i | ||||
\(496\) | 566.372 | 0.00230217 | ||||||||
\(497\) | −110040. | + | 35754.1i | −0.445489 | + | 0.144748i | ||||
\(498\) | −302644. | − | 129282.i | −1.22032 | − | 0.521288i | ||||
\(499\) | 375761. | − | 273007.i | 1.50908 | − | 1.09641i | 0.542490 | − | 0.840062i | \(-0.317482\pi\) |
0.966585 | − | 0.256345i | \(-0.0825183\pi\) | |||||||
\(500\) | 324865. | + | 105555.i | 1.29946 | + | 0.422221i | ||||
\(501\) | 222821. | + | 20007.5i | 0.887729 | + | 0.0797107i | ||||
\(502\) | 418609. | − | 304137.i | 1.66112 | − | 1.20687i | ||||
\(503\) | 234925. | − | 323347.i | 0.928525 | − | 1.27800i | −0.0319077 | − | 0.999491i | \(-0.510158\pi\) |
0.960432 | − | 0.278514i | \(-0.0898417\pi\) | |||||||
\(504\) | −214314. | + | 205076.i | −0.843704 | + | 0.807336i | ||||
\(505\) | 306364. | 1.20131 | ||||||||
\(506\) | 135465. | + | 33462.6i | 0.529086 | + | 0.130695i | ||||
\(507\) | 47590.8 | − | 10872.7i | 0.185143 | − | 0.0422982i | ||||
\(508\) | 50643.5 | + | 155865.i | 0.196244 | + | 0.603977i | ||||
\(509\) | −199400. | + | 274451.i | −0.769645 | + | 1.05932i | 0.226705 | + | 0.973963i | \(0.427205\pi\) |
−0.996350 | + | 0.0853615i | \(0.972795\pi\) | |||||||
\(510\) | −49003.1 | − | 42794.7i | −0.188401 | − | 0.164532i | ||||
\(511\) | 115972. | − | 356924.i | 0.444130 | − | 1.36689i | ||||
\(512\) | −35570.0 | − | 11557.4i | −0.135689 | − | 0.0440880i | ||||
\(513\) | −90276.4 | + | 327908.i | −0.343036 | + | 1.24600i | ||||
\(514\) | 91001.9 | + | 66116.7i | 0.344448 | + | 0.250256i | ||||
\(515\) | 131070. | − | 42587.2i | 0.494184 | − | 0.160570i | ||||
\(516\) | 160389. | − | 36642.8i | 0.602386 | − | 0.137623i | ||||
\(517\) | 25451.2 | + | 62601.8i | 0.0952199 | + | 0.234210i | ||||
\(518\) | 1.03455e6i | 3.85560i | ||||||||
\(519\) | −99442.2 | + | 59442.0i | −0.369178 | + | 0.220678i | ||||
\(520\) | 204777. | + | 148779.i | 0.757312 | + | 0.550220i | ||||
\(521\) | −58336.8 | − | 80293.8i | −0.214915 | − | 0.295806i | 0.687925 | − | 0.725782i | \(-0.258522\pi\) |
−0.902840 | + | 0.429976i | \(0.858522\pi\) | |||||||
\(522\) | −95536.0 | − | 703075.i | −0.350611 | − | 2.58024i | ||||
\(523\) | 104148. | − | 320535.i | 0.380757 | − | 1.17185i | −0.558755 | − | 0.829333i | \(-0.688721\pi\) |
0.939512 | − | 0.342516i | \(-0.111279\pi\) | |||||||
\(524\) | −377241. | − | 519228.i | −1.37390 | − | 1.89102i | ||||
\(525\) | −69082.4 | − | 29510.2i | −0.250639 | − | 0.107067i | ||||
\(526\) | 27795.3 | + | 85545.1i | 0.100462 | + | 0.309189i | ||||
\(527\) | − | 1261.25i | − | 0.00454130i | ||||||
\(528\) | 5817.62 | + | 19036.1i | 0.0208679 | + | 0.0682827i | ||||
\(529\) | 247695. | 0.885129 | ||||||||
\(530\) | −17633.7 | + | 5729.54i | −0.0627757 | + | 0.0203971i | ||||
\(531\) | 53952.1 | − | 298007.i | 0.191346 | − | 1.05691i | ||||
\(532\) | −581840. | + | 422732.i | −2.05580 | + | 1.49362i | ||||
\(533\) | 298741. | + | 97066.9i | 1.05158 | + | 0.341678i | ||||
\(534\) | −62615.0 | + | 697336.i | −0.219582 | + | 2.44545i | ||||
\(535\) | 125806. | − | 91403.4i | 0.439535 | − | 0.319341i | ||||
\(536\) | 131535. | − | 181042.i | 0.457837 | − | 0.630159i | ||||
\(537\) | 269789. | − | 161268.i | 0.935570 | − | 0.559241i | ||||
\(538\) | −365555. | −1.26296 | ||||||||
\(539\) | −100675. | − | 119452.i | −0.346534 | − | 0.411164i | ||||
\(540\) | −318641. | − | 399052.i | −1.09273 | − | 1.36849i | ||||
\(541\) | 35946.3 | + | 110631.i | 0.122817 | + | 0.377993i | 0.993497 | − | 0.113858i | \(-0.0363208\pi\) |
−0.870680 | + | 0.491850i | \(0.836321\pi\) | |||||||
\(542\) | 237872. | − | 327402.i | 0.809737 | − | 1.11451i | ||||
\(543\) | −20624.2 | + | 23616.3i | −0.0699485 | + | 0.0800961i | ||||
\(544\) | −13608.0 | + | 41881.0i | −0.0459828 | + | 0.141520i | ||||
\(545\) | −35456.0 | − | 11520.3i | −0.119370 | − | 0.0387858i | ||||
\(546\) | 402984. | + | 351929.i | 1.35177 | + | 1.18051i | ||||
\(547\) | 372669. | + | 270760.i | 1.24551 | + | 0.904919i | 0.997953 | − | 0.0639537i | \(-0.0203710\pi\) |
0.247561 | + | 0.968872i | \(0.420371\pi\) | |||||||
\(548\) | 881755. | − | 286500.i | 2.93621 | − | 0.954032i | ||||
\(549\) | −75433.1 | + | 36365.4i | −0.250275 | + | 0.120654i | ||||
\(550\) | 81747.7 | − | 68897.9i | 0.270240 | − | 0.227762i | ||||
\(551\) | − | 635382.i | − | 2.09282i | ||||||
\(552\) | 49897.1 | + | 83474.2i | 0.163756 | + | 0.273952i | ||||
\(553\) | 274029. | + | 199093.i | 0.896077 | + | 0.651038i | ||||
\(554\) | 344111. | + | 473628.i | 1.12119 | + | 1.54318i | ||||
\(555\) | −655172. | − | 58829.1i | −2.12701 | − | 0.190988i | ||||
\(556\) | −18185.6 | + | 55969.4i | −0.0588270 | + | 0.181051i | ||||
\(557\) | 134977. | + | 185779.i | 0.435059 | + | 0.598807i | 0.969105 | − | 0.246648i | \(-0.0793292\pi\) |
−0.534046 | + | 0.845455i | \(0.679329\pi\) | |||||||
\(558\) | 2875.87 | − | 15885.0i | 0.00923637 | − | 0.0510175i | ||||
\(559\) | −33868.2 | − | 104236.i | −0.108385 | − | 0.333574i | ||||
\(560\) | 30666.0i | 0.0977869i | ||||||||
\(561\) | 42391.5 | − | 12955.2i | 0.134695 | − | 0.0411642i | ||||
\(562\) | 27942.2 | 0.0884685 | ||||||||
\(563\) | 251720. | − | 81788.9i | 0.794148 | − | 0.258034i | 0.116278 | − | 0.993217i | \(-0.462904\pi\) |
0.677869 | + | 0.735182i | \(0.262904\pi\) | |||||||
\(564\) | −50094.7 | + | 117270.i | −0.157483 | + | 0.368662i | ||||
\(565\) | −283805. | + | 206197.i | −0.889045 | + | 0.645929i | ||||
\(566\) | −256807. | − | 83441.8i | −0.801631 | − | 0.260466i | ||||
\(567\) | −219898. | − | 332529.i | −0.684000 | − | 1.03434i | ||||
\(568\) | 92844.5 | − | 67455.5i | 0.287779 | − | 0.209084i | ||||
\(569\) | 71966.6 | − | 99053.5i | 0.222283 | − | 0.305946i | −0.683281 | − | 0.730155i | \(-0.739448\pi\) |
0.905564 | + | 0.424209i | \(0.139448\pi\) | |||||||
\(570\) | −382596. | − | 640055.i | −1.17758 | − | 1.97001i | ||||
\(571\) | −641906. | −1.96879 | −0.984395 | − | 0.175973i | \(-0.943693\pi\) | ||||
−0.984395 | + | 0.175973i | \(0.943693\pi\) | |||||||
\(572\) | −432557. | + | 175860.i | −1.32206 | + | 0.537494i | ||||
\(573\) | −56293.4 | − | 246401.i | −0.171454 | − | 0.750470i | ||||
\(574\) | −249400. | − | 767575.i | −0.756960 | − | 2.32968i | ||||
\(575\) | −14476.6 | + | 19925.3i | −0.0437855 | + | 0.0602655i | ||||
\(576\) | −255667. | + | 475582.i | −0.770600 | + | 1.43344i | ||||
\(577\) | −109128. | + | 335861.i | −0.327781 | + | 1.00881i | 0.642389 | + | 0.766379i | \(0.277943\pi\) |
−0.970170 | + | 0.242427i | \(0.922057\pi\) | |||||||
\(578\) | −500776. | − | 162712.i | −1.49895 | − | 0.487039i | ||||
\(579\) | 76454.5 | − | 87546.0i | 0.228058 | − | 0.261143i | ||||
\(580\) | 771807. | + | 560751.i | 2.29431 | + | 1.66692i | ||||
\(581\) | 328536. | − | 106748.i | 0.973264 | − | 0.316233i | ||||
\(582\) | −73018.0 | − | 319606.i | −0.215568 | − | 0.943559i | ||||
\(583\) | 3029.47 | − | 12264.1i | 0.00891312 | − | 0.0360826i | ||||
\(584\) | 372241.i | 1.09144i | ||||||||
\(585\) | −245789. | + | 235194.i | −0.718208 | + | 0.687250i | ||||
\(586\) | −132711. | − | 96420.5i | −0.386468 | − | 0.280785i | ||||
\(587\) | 31515.3 | + | 43377.1i | 0.0914630 | + | 0.125888i | 0.852296 | − | 0.523059i | \(-0.175209\pi\) |
−0.760833 | + | 0.648948i | \(0.775209\pi\) | |||||||
\(588\) | 26363.7 | − | 293609.i | 0.0762520 | − | 0.849208i | ||||
\(589\) | 4467.18 | − | 13748.6i | 0.0128766 | − | 0.0396302i | ||||
\(590\) | 390291. | + | 537189.i | 1.12120 | + | 1.54320i | ||||
\(591\) | −94507.4 | + | 221238.i | −0.270577 | + | 0.633411i | ||||
\(592\) | 14951.9 | + | 46017.2i | 0.0426631 | + | 0.131304i | ||||
\(593\) | − | 339988.i | − | 0.966840i | −0.875388 | − | 0.483420i | \(-0.839394\pi\) | ||
0.875388 | − | 0.483420i | \(-0.160606\pi\) | |||||||
\(594\) | 563445. | − | 66506.6i | 1.59690 | − | 0.188492i | ||||
\(595\) | 68289.9 | 0.192896 | ||||||||
\(596\) | −203485. | + | 66116.3i | −0.572849 | + | 0.186130i | ||||
\(597\) | 215064. | + | 91869.9i | 0.603419 | + | 0.257765i | ||||
\(598\) | 141910. | − | 103104.i | 0.396836 | − | 0.288319i | ||||
\(599\) | −282410. | − | 91760.4i | −0.787092 | − | 0.255742i | −0.112227 | − | 0.993683i | \(-0.535798\pi\) |
−0.674865 | + | 0.737941i | \(0.735798\pi\) | |||||||
\(600\) | 74212.1 | + | 6663.64i | 0.206145 | + | 0.0185101i | ||||
\(601\) | −85302.8 | + | 61976.1i | −0.236164 | + | 0.171583i | −0.699573 | − | 0.714561i | \(-0.746626\pi\) |
0.463408 | + | 0.886145i | \(0.346626\pi\) | |||||||
\(602\) | −165521. | + | 227820.i | −0.456731 | + | 0.628636i | ||||
\(603\) | 207933. | + | 217300.i | 0.571860 | + | 0.597620i | ||||
\(604\) | −116856. | −0.320315 | ||||||||
\(605\) | 58001.6 | + | 400070.i | 0.158463 | + | 1.09301i | ||||
\(606\) | −626170. | + | 143056.i | −1.70509 | + | 0.389549i | ||||
\(607\) | −151534. | − | 466375.i | −0.411276 | − | 1.26578i | −0.915539 | − | 0.402228i | \(-0.868236\pi\) |
0.504263 | − | 0.863550i | \(-0.331764\pi\) | |||||||
\(608\) | −296673. | + | 408336.i | −0.802549 | + | 1.10461i | ||||
\(609\) | 560968. | + | 489897.i | 1.51253 | + | 1.32090i | ||||
\(610\) | 56736.5 | − | 174617.i | 0.152476 | − | 0.469274i | ||||
\(611\) | 80793.6 | + | 26251.4i | 0.216419 | + | 0.0703186i | ||||
\(612\) | 73675.2 | + | 39606.8i | 0.196706 | + | 0.105747i | ||||
\(613\) | 241543. | + | 175491.i | 0.642797 | + | 0.467019i | 0.860810 | − | 0.508927i | \(-0.169958\pi\) |
−0.218013 | + | 0.975946i | \(0.569958\pi\) | |||||||
\(614\) | 240865. | − | 78261.9i | 0.638907 | − | 0.207593i | ||||
\(615\) | 500280. | − | 114295.i | 1.32270 | − | 0.302188i | ||||
\(616\) | 376286. | + | 233994.i | 0.991647 | + | 0.616655i | ||||
\(617\) | 429132.i | 1.12725i | 0.826031 | + | 0.563625i | \(0.190594\pi\) | ||||
−0.826031 | + | 0.563625i | \(0.809406\pi\) | |||||||
\(618\) | −248005. | + | 148246.i | −0.649357 | + | 0.388156i | ||||
\(619\) | −361989. | − | 263001.i | −0.944745 | − | 0.686397i | 0.00481327 | − | 0.999988i | \(-0.498468\pi\) |
−0.949558 | + | 0.313591i | \(0.898468\pi\) | |||||||
\(620\) | 12758.1 | + | 17560.0i | 0.0331896 | + | 0.0456816i | ||||
\(621\) | −122341. | + | 46002.4i | −0.317240 | + | 0.119288i | ||||
\(622\) | 161168. | − | 496023.i | 0.416579 | − | 1.28210i | ||||
\(623\) | −431969. | − | 594555.i | −1.11295 | − | 1.53185i | ||||
\(624\) | 23011.1 | + | 9829.77i | 0.0590975 | + | 0.0252449i | ||||
\(625\) | −141409. | − | 435213.i | −0.362008 | − | 1.11415i | ||||
\(626\) | − | 596922.i | − | 1.52324i | ||||||
\(627\) | 507984. | + | 8923.13i | 1.29215 | + | 0.0226977i | ||||
\(628\) | 686942. | 1.74181 | ||||||||
\(629\) | 102475. | − | 33296.3i | 0.259011 | − | 0.0841579i | ||||
\(630\) | 860087. | + | 155713.i | 2.16701 | + | 0.392323i | ||||
\(631\) | −337626. | + | 245300.i | −0.847963 | + | 0.616081i | −0.924584 | − | 0.380979i | \(-0.875587\pi\) |
0.0766203 | + | 0.997060i | \(0.475587\pi\) | |||||||
\(632\) | −319521. | − | 103819.i | −0.799954 | − | 0.259921i | ||||
\(633\) | 43785.8 | − | 487637.i | 0.109276 | − | 1.21700i | ||||
\(634\) | −132664. | + | 96386.2i | −0.330047 | + | 0.239793i | ||||
\(635\) | 104838. | − | 144297.i | 0.259999 | − | 0.357858i | ||||
\(636\) | 20461.5 | − | 12230.9i | 0.0505851 | − | 0.0302375i | ||||
\(637\) | −196381. | −0.483973 | ||||||||
\(638\) | −981879. | + | 399190.i | −2.41222 | + | 0.980706i | ||||
\(639\) | 66979.6 | + | 138937.i | 0.164037 | + | 0.340263i | ||||
\(640\) | −218135. | − | 671350.i | −0.532556 | − | 1.63904i | ||||
\(641\) | −14998.0 | + | 20642.9i | −0.0365020 | + | 0.0502407i | −0.826878 | − | 0.562381i | \(-0.809885\pi\) |
0.790376 | + | 0.612622i | \(0.209885\pi\) | |||||||
\(642\) | −214452. | + | 245563.i | −0.520307 | + | 0.595789i | ||||
\(643\) | −215189. | + | 662282.i | −0.520472 | + | 1.60185i | 0.252628 | + | 0.967563i | \(0.418705\pi\) |
−0.773100 | + | 0.634284i | \(0.781295\pi\) | |||||||
\(644\) | −262860. | − | 85408.3i | −0.633800 | − | 0.205934i | ||||
\(645\) | −134864. | − | 117778.i | −0.324174 | − | 0.283103i | ||||
\(646\) | 98816.5 | + | 71794.4i | 0.236791 | + | 0.172038i | ||||
\(647\) | −349651. | + | 113608.i | −0.835268 | + | 0.271395i | −0.695263 | − | 0.718756i | \(-0.744712\pi\) |
−0.140005 | + | 0.990151i | \(0.544712\pi\) | |||||||
\(648\) | 309357. | + | 246283.i | 0.736734 | + | 0.586523i | ||||
\(649\) | −451235. | + | 32539.6i | −1.07131 | + | 0.0772543i | ||||
\(650\) | − | 134395.i | − | 0.318094i | ||||||
\(651\) | 8694.05 | + | 14544.5i | 0.0205145 | + | 0.0343192i | ||||
\(652\) | −279735. | − | 203239.i | −0.658039 | − | 0.478093i | ||||
\(653\) | −400213. | − | 550846.i | −0.938565 | − | 1.29182i | −0.956423 | − | 0.291984i | \(-0.905685\pi\) |
0.0178578 | − | 0.999841i | \(-0.494315\pi\) | |||||||
\(654\) | 77847.2 | + | 6990.04i | 0.182007 | + | 0.0163427i | ||||
\(655\) | −215845. | + | 664303.i | −0.503106 | + | 1.54840i | ||||
\(656\) | −22186.8 | − | 30537.5i | −0.0515569 | − | 0.0709620i | ||||
\(657\) | −492285. | − | 89124.9i | −1.14048 | − | 0.206475i | ||||
\(658\) | −67449.5 | − | 207588.i | −0.155785 | − | 0.479458i | ||||
\(659\) | 322970.i | 0.743690i | 0.928295 | + | 0.371845i | \(0.121275\pi\) | ||||
−0.928295 | + | 0.371845i | \(0.878725\pi\) | |||||||
\(660\) | −459156. | + | 609180.i | −1.05408 | + | 1.39848i | ||||
\(661\) | 35506.6 | 0.0812656 | 0.0406328 | − | 0.999174i | \(-0.487063\pi\) | ||||
0.0406328 | + | 0.999174i | \(0.487063\pi\) | |||||||
\(662\) | −503250. | + | 163516.i | −1.14833 | + | 0.373116i | ||||
\(663\) | 21889.9 | − | 51243.4i | 0.0497985 | − | 0.116576i | ||||
\(664\) | −277197. | + | 201396.i | −0.628713 | + | 0.456787i | ||||
\(665\) | 744410. | + | 241873.i | 1.68333 | + | 0.546946i | ||||
\(666\) | 1.36656e6 | − | 185693.i | 3.08093 | − | 0.418646i | ||||
\(667\) | 197544. | − | 143524.i | 0.444030 | − | 0.322607i | ||||
\(668\) | 370679. | − | 510196.i | 0.830702 | − | 1.14336i | ||||
\(669\) | 164971. | + | 275985.i | 0.368601 | + | 0.616643i | ||||
\(670\) | −659415. | −1.46896 | ||||||||
\(671\) | 80617.6 | + | 95653.2i | 0.179054 | + | 0.212449i | ||||
\(672\) | −131769. | − | 576766.i | −0.291794 | − | 1.27721i | ||||
\(673\) | 211497. | + | 650922.i | 0.466955 | + | 1.43714i | 0.856508 | + | 0.516134i | \(0.172629\pi\) |
−0.389553 | + | 0.921004i | \(0.627371\pi\) | |||||||
\(674\) | 431864. | − | 594409.i | 0.950663 | − | 1.30848i | ||||
\(675\) | −26581.1 | + | 96549.3i | −0.0583398 | + | 0.211905i | ||||
\(676\) | 42524.0 | − | 130875.i | 0.0930552 | − | 0.286395i | ||||
\(677\) | 18781.9 | + | 6102.62i | 0.0409792 | + | 0.0133149i | 0.329435 | − | 0.944178i | \(-0.393142\pi\) |
−0.288456 | + | 0.957493i | \(0.593142\pi\) | |||||||
\(678\) | 483781. | − | 553964.i | 1.05242 | − | 1.20510i | ||||
\(679\) | 278400. | + | 202269.i | 0.603851 | + | 0.438723i | ||||
\(680\) | −64419.5 | + | 20931.2i | −0.139316 | + | 0.0452664i | ||||
\(681\) | −13553.6 | − | 59325.3i | −0.0292254 | − | 0.127922i | ||||
\(682\) | −24052.7 | + | 1734.50i | −0.0517125 | + | 0.00372911i | ||||
\(683\) | 462733.i | 0.991948i | 0.868337 | + | 0.495974i | \(0.165189\pi\) | ||||
−0.868337 | + | 0.495974i | \(0.834811\pi\) | |||||||
\(684\) | 662831. | + | 692690.i | 1.41674 | + | 1.48056i | ||||
\(685\) | −816317. | − | 593089.i | −1.73971 | − | 1.26398i | ||||
\(686\) | −254973. | − | 350941.i | −0.541810 | − | 0.745737i | ||||
\(687\) | 335.852 | − | 3740.35i | 0.000711598 | − | 0.00792498i | ||||
\(688\) | −4069.86 | + | 12525.7i | −0.00859809 | + | 0.0264622i | ||||
\(689\) | −9334.32 | − | 12847.6i | −0.0196627 | − | 0.0270634i | ||||
\(690\) | 112574. | − | 263531.i | 0.236450 | − | 0.553521i | ||||
\(691\) | −90314.4 | − | 277959.i | −0.189148 | − | 0.582136i | 0.810848 | − | 0.585257i | \(-0.199007\pi\) |
−0.999995 | + | 0.00312105i | \(0.999007\pi\) | |||||||
\(692\) | 326581.i | 0.681991i | ||||||||
\(693\) | −399548. | + | 441610.i | −0.831960 | + | 0.919545i | ||||
\(694\) | 469361. | 0.974514 | ||||||||
\(695\) | 60913.0 | − | 19791.8i | 0.126107 | − | 0.0409748i | ||||
\(696\) | −679330. | − | 290193.i | −1.40237 | − | 0.599056i | ||||
\(697\) | −68003.9 | + | 49407.7i | −0.139981 | + | 0.101702i | ||||
\(698\) | 508397. | + | 165188.i | 1.04350 | + | 0.339053i | ||||
\(699\) | 120452. | + | 10815.6i | 0.246525 | + | 0.0221359i | ||||
\(700\) | −171317. | + | 124469.i | −0.349628 | + | 0.254019i | ||||
\(701\) | −536392. | + | 738281.i | −1.09156 | + | 1.50240i | −0.245434 | + | 0.969413i | \(0.578930\pi\) |
−0.846124 | + | 0.532987i | \(0.821070\pi\) | |||||||
\(702\) | 392539. | − | 595479.i | 0.796542 | − | 1.20835i | ||||
\(703\) | 1.23499e6 | 2.49892 | ||||||||
\(704\) | 783052. | + | 193429.i | 1.57996 | + | 0.390281i | ||||
\(705\) | 135299. | − | 30910.8i | 0.272218 | − | 0.0621916i | ||||
\(706\) | 81673.7 | + | 251366.i | 0.163860 | + | 0.504309i | ||||
\(707\) | 396285. | − | 545440.i | 0.792810 | − | 1.09121i | ||||
\(708\) | −643020. | − | 561554.i | −1.28280 | − | 1.12028i | ||||
\(709\) | 183839. | − | 565797.i | 0.365716 | − | 1.12556i | −0.583815 | − | 0.811886i | \(-0.698441\pi\) |
0.949531 | − | 0.313672i | \(-0.101559\pi\) | |||||||
\(710\) | −321619. | − | 104500.i | −0.638006 | − | 0.207301i | ||||
\(711\) | 213801. | − | 397706.i | 0.422933 | − | 0.786725i | ||||
\(712\) | 589721. | + | 428457.i | 1.16329 | + | 0.845177i | ||||
\(713\) | 5283.58 | − | 1716.74i | 0.0103932 | − | 0.00337696i | ||||
\(714\) | −139576. | + | 31888.0i | −0.273789 | + | 0.0625504i | ||||
\(715\) | 431548. | + | 268358.i | 0.844146 | + | 0.524932i | ||||
\(716\) | − | 886023.i | − | 1.72830i | ||||||
\(717\) | −618500. | + | 369711.i | −1.20310 | + | 0.719159i | ||||
\(718\) | 1.14076e6 | + | 828808.i | 2.21281 | + | 1.60770i | ||||
\(719\) | 210955. | + | 290354.i | 0.408067 | + | 0.561656i | 0.962746 | − | 0.270408i | \(-0.0871587\pi\) |
−0.554678 | + | 0.832065i | \(0.687159\pi\) | |||||||
\(720\) | 40507.4 | − | 5504.27i | 0.0781393 | − | 0.0106178i | ||||
\(721\) | 93719.8 | − | 288440.i | 0.180285 | − | 0.554862i | ||||
\(722\) | 330193. | + | 454471.i | 0.633422 | + | 0.871831i | ||||
\(723\) | −568743. | − | 242952.i | −1.08803 | − | 0.464777i | ||||
\(724\) | 27312.3 | + | 84058.6i | 0.0521052 | + | 0.160363i | ||||
\(725\) | − | 187082.i | − | 0.355923i | ||||||
\(726\) | −305361. | − | 790612.i | −0.579349 | − | 1.50000i | ||||
\(727\) | −717511. | −1.35756 | −0.678781 | − | 0.734341i | \(-0.737491\pi\) | ||||
−0.678781 | + | 0.734341i | \(0.737491\pi\) | |||||||
\(728\) | 529764. | − | 172131.i | 0.999585 | − | 0.324785i | ||||
\(729\) | −399776. | + | 350155.i | −0.752249 | + | 0.658879i | ||||
\(730\) | 887398. | − | 644733.i | 1.66522 | − | 1.20986i | ||||
\(731\) | 27893.5 | + | 9063.14i | 0.0521997 | + | 0.0169607i | ||||
\(732\) | −21111.2 | + | 235113.i | −0.0393995 | + | 0.438787i | ||||
\(733\) | 343734. | − | 249737.i | 0.639757 | − | 0.464810i | −0.220010 | − | 0.975498i | \(-0.570609\pi\) |
0.859767 | + | 0.510687i | \(0.170609\pi\) | |||||||
\(734\) | 592975. | − | 816161.i | 1.10064 | − | 1.51490i | ||||
\(735\) | −275380. | + | 164610.i | −0.509751 | + | 0.304706i | ||||
\(736\) | −193969. | −0.358076 | ||||||||
\(737\) | 237254. | − | 381529.i | 0.436795 | − | 0.702413i | ||||
\(738\) | −969142. | + | 467211.i | −1.77941 | + | 0.857829i | ||||
\(739\) | −185981. | − | 572390.i | −0.340548 | − | 1.04810i | −0.963924 | − | 0.266178i | \(-0.914239\pi\) |
0.623375 | − | 0.781923i | \(-0.285761\pi\) | |||||||
\(740\) | −1.08993e6 | + | 1.50016e6i | −1.99037 | + | 2.73951i | ||||
\(741\) | 420113. | − | 481060.i | 0.765119 | − | 0.876118i | ||||
\(742\) | −12608.7 | + | 38805.7i | −0.0229015 | + | 0.0704836i | ||||
\(743\) | 482664. | + | 156827.i | 0.874313 | + | 0.284081i | 0.711594 | − | 0.702591i | \(-0.247974\pi\) |
0.162719 | + | 0.986672i | \(0.447974\pi\) | |||||||
\(744\) | −12659.3 | − | 11055.4i | −0.0228698 | − | 0.0199724i | ||||
\(745\) | 188384. | + | 136869.i | 0.339415 | + | 0.246599i | ||||
\(746\) | −1.40084e6 | + | 455160.i | −2.51716 | + | 0.817874i | ||||
\(747\) | −199975. | − | 414810.i | −0.358372 | − | 0.743376i | ||||
\(748\) | 29965.2 | − | 121307.i | 0.0535568 | − | 0.216812i | ||||
\(749\) | − | 342213.i | − | 0.610003i | ||||||
\(750\) | 399893. | + | 668992.i | 0.710921 | + | 1.18932i | ||||
\(751\) | 103107. | + | 74911.8i | 0.182814 | + | 0.132822i | 0.675428 | − | 0.737426i | \(-0.263959\pi\) |
−0.492615 | + | 0.870248i | \(0.663959\pi\) | |||||||
\(752\) | −6000.35 | − | 8258.77i | −0.0106106 | − | 0.0146043i | ||||
\(753\) | 721117. | + | 64750.4i | 1.27179 | + | 0.114196i | ||||
\(754\) | −411741. | + | 1.26721e6i | −0.724238 | + | 2.22898i | ||||
\(755\) | 74753.1 | + | 102889.i | 0.131140 | + | 0.180499i | ||||
\(756\) | −1.12263e6 | + | 51119.6i | −1.96423 | + | 0.0894425i | ||||
\(757\) | −206354. | − | 635092.i | −0.360098 | − | 1.10827i | −0.952994 | − | 0.302989i | \(-0.902015\pi\) |
0.592896 | − | 0.805279i | \(-0.297985\pi\) | |||||||
\(758\) | 1.02505e6i | 1.78405i | ||||||||
\(759\) | 111972. | + | 159951.i | 0.194369 | + | 0.277653i | ||||
\(760\) | −776355. | −1.34411 | ||||||||
\(761\) | 611810. | − | 198789.i | 1.05645 | − | 0.343260i | 0.271250 | − | 0.962509i | \(-0.412563\pi\) |
0.785195 | + | 0.619249i | \(0.212563\pi\) | |||||||
\(762\) | −146897. | + | 343881.i | −0.252990 | + | 0.592240i | ||||
\(763\) | −66373.2 | + | 48223.0i | −0.114010 | + | 0.0828333i | ||||
\(764\) | −677606. | − | 220167.i | −1.16089 | − | 0.377195i | ||||
\(765\) | −12257.4 | − | 90205.7i | −0.0209448 | − | 0.154139i | ||||
\(766\) | −952552. | + | 692069.i | −1.62342 | + | 1.17948i | ||||
\(767\) | −334284. | + | 460102.i | −0.568230 | + | 0.782102i | ||||
\(768\) | 266821. | + | 446373.i | 0.452374 | + | 0.756789i | ||||
\(769\) | 518839. | 0.877364 | 0.438682 | − | 0.898642i | \(-0.355445\pi\) | ||||
0.438682 | + | 0.898642i | \(0.355445\pi\) | |||||||
\(770\) | −93913.6 | − | 1.30233e6i | −0.158397 | − | 2.19653i | ||||
\(771\) | 35055.7 | + | 153442.i | 0.0589725 | + | 0.258128i | ||||
\(772\) | −101247. | − | 311607.i | −0.169883 | − | 0.522845i | ||||
\(773\) | 646621. | − | 889997.i | 1.08216 | − | 1.48946i | 0.225035 | − | 0.974351i | \(-0.427751\pi\) |
0.857123 | − | 0.515112i | \(-0.172249\pi\) | |||||||
\(774\) | 330643. | + | 177749.i | 0.551921 | + | 0.296705i | ||||
\(775\) | 1315.32 | − | 4048.13i | 0.00218992 | − | 0.00673987i | ||||
\(776\) | −324618. | − | 105475.i | −0.539075 | − | 0.175156i | ||||
\(777\) | −952211. | + | 1.09035e6i | −1.57722 | + | 1.80603i | ||||
\(778\) | −929047. | − | 674992.i | −1.53489 | − | 1.11517i | ||||
\(779\) | −916287. | + | 297720.i | −1.50993 | + | 0.490606i | ||||
\(780\) | 213583. | + | 934872.i | 0.351057 | + | 1.53661i | ||||
\(781\) | 176179. | − | 148486.i | 0.288837 | − | 0.243435i | ||||
\(782\) | 46940.0i | 0.0767591i | ||||||||
\(783\) | 546428. | − | 828928.i | 0.891270 | − | 1.35205i | ||||
\(784\) | 19091.7 | + | 13870.9i | 0.0310608 | + | 0.0225670i | ||||
\(785\) | −439439. | − | 604835.i | −0.713114 | − | 0.981517i | ||||
\(786\) | 130965. | − | 1.45854e6i | 0.211988 | − | 2.36088i | ||||
\(787\) | −95897.6 | + | 295142.i | −0.154831 | + | 0.476521i | −0.998144 | − | 0.0609021i | \(-0.980602\pi\) |
0.843313 | + | 0.537423i | \(0.180602\pi\) | |||||||
\(788\) | 398617. | + | 548650.i | 0.641954 | + | 0.883573i | ||||
\(789\) | −49442.1 | + | 115742.i | −0.0794223 | + | 0.185925i | ||||
\(790\) | 305923. | + | 941534.i | 0.490182 | + | 1.50863i | ||||
\(791\) | 771996.i | 1.23385i | ||||||||
\(792\) | 241547. | − | 539045.i | 0.385081 | − | 0.859359i | ||||
\(793\) | 157256. | 0.250069 | ||||||||
\(794\) | 585784. | − | 190333.i | 0.929173 | − | 0.301907i | ||||
\(795\) | −23858.3 | − | 10191.7i | −0.0377490 | − | 0.0161254i | ||||
\(796\) | 533338. | − | 387493.i | 0.841736 | − | 0.611557i | ||||
\(797\) | −797684. | − | 259183.i | −1.25578 | − | 0.408028i | −0.395792 | − | 0.918340i | \(-0.629530\pi\) |
−0.859989 | + | 0.510312i | \(0.829530\pi\) | |||||||
\(798\) | −1.63443e6 | − | 146758.i | −2.56661 | − | 0.230460i | ||||
\(799\) | −18391.4 | + | 13362.2i | −0.0288086 | + | 0.0209307i | ||||
\(800\) | −87352.7 | + | 120231.i | −0.136489 | + | 0.187860i | ||||
\(801\) | −707827. | + | 677316.i | −1.10322 | + | 1.05567i | ||||
\(802\) | −1.47888e6 | −2.29925 | ||||||||
\(803\) | 53753.1 | + | 745408.i | 0.0833628 | + | 1.15601i | ||||
\(804\) | 826513. | − | 188827.i | 1.27861 | − | 0.292114i | ||||
\(805\) | 92952.2 | + | 286077.i | 0.143439 | + | 0.441461i | ||||
\(806\) | −17818.7 | + | 24525.4i | −0.0274288 | + | 0.0377525i | ||||
\(807\) | −385272. | − | 336460.i | −0.591589 | − | 0.516639i | ||||
\(808\) | −206646. | + | 635990.i | −0.316522 | + | 0.974154i | ||||
\(809\) | 272461. | + | 88528.0i | 0.416301 | + | 0.135264i | 0.509676 | − | 0.860367i | \(-0.329765\pi\) |
−0.0933745 | + | 0.995631i | \(0.529765\pi\) | |||||||
\(810\) | 51306.8 | − | 1.16406e6i | 0.0781997 | − | 1.77421i | ||||
\(811\) | −412877. | − | 299972.i | −0.627738 | − | 0.456079i | 0.227878 | − | 0.973690i | \(-0.426821\pi\) |
−0.855616 | + | 0.517611i | \(0.826821\pi\) | |||||||
\(812\) | 1.99668e6 | − | 648762.i | 3.02829 | − | 0.983951i | ||||
\(813\) | 552045. | − | 126122.i | 0.835206 | − | 0.190813i | ||||
\(814\) | −775905. | − | 1.90847e6i | −1.17101 | − | 2.88030i | ||||
\(815\) | 376313.i | 0.566544i | ||||||||
\(816\) | −5747.54 | + | 3435.62i | −0.00863181 | + | 0.00515970i | ||||
\(817\) | 271959. | + | 197590.i | 0.407436 | + | 0.296019i | ||||
\(818\) | 150847. | + | 207623.i | 0.225439 | + | 0.310291i | ||||
\(819\) | 100801. | + | 741821.i | 0.150279 | + | 1.10594i | ||||
\(820\) | 447017. | − | 1.37578e6i | 0.664808 | − | 2.04607i | ||||
\(821\) | −283072. | − | 389615.i | −0.419962 | − | 0.578029i | 0.545650 | − | 0.838013i | \(-0.316283\pi\) |
−0.965613 | + | 0.259984i | \(0.916283\pi\) | |||||||
\(822\) | 1.94540e6 | + | 831024.i | 2.87915 | + | 1.22990i | ||||
\(823\) | 148801. | + | 457963.i | 0.219688 | + | 0.676132i | 0.998787 | + | 0.0492306i | \(0.0156769\pi\) |
−0.779099 | + | 0.626901i | \(0.784323\pi\) | |||||||
\(824\) | 300818.i | 0.443046i | ||||||||
\(825\) | 149571. | + | 2627.33i | 0.219755 | + | 0.00386018i | ||||
\(826\) | 1.46124e6 | 2.14172 | ||||||||
\(827\) | 30456.9 | − | 9896.04i | 0.0445322 | − | 0.0144694i | −0.286666 | − | 0.958031i | \(-0.592547\pi\) |
0.331198 | + | 0.943561i | \(0.392547\pi\) | |||||||
\(828\) | −65636.8 | + | 362548.i | −0.0957385 | + | 0.528816i | ||||
\(829\) | −494515. | + | 359286.i | −0.719566 | + | 0.522795i | −0.886245 | − | 0.463216i | \(-0.846695\pi\) |
0.166680 | + | 0.986011i | \(0.446695\pi\) | |||||||
\(830\) | 960228. | + | 311997.i | 1.39386 | + | 0.452891i | ||||
\(831\) | −73260.8 | + | 815896.i | −0.106089 | + | 1.18150i | ||||
\(832\) | 820308. | − | 595989.i | 1.18503 | − | 0.860977i | ||||
\(833\) | 30889.1 | − | 42515.2i | 0.0445160 | − | 0.0612710i | ||||
\(834\) | −115257. | + | 68895.5i | −0.165705 | + | 0.0990509i | ||||
\(835\) | −686340. | −0.984388 | ||||||||
\(836\) | 756296. | − | 1.21620e6i | 1.08213 | − | 1.74018i | ||||
\(837\) | 17651.7 | − | 14094.8i | 0.0251962 | − | 0.0201191i | ||||
\(838\) | 249901. | + | 769115.i | 0.355860 | + | 1.09523i | ||||
\(839\) | 16352.9 | − | 22507.8i | 0.0232311 | − | 0.0319749i | −0.797243 | − | 0.603658i | \(-0.793709\pi\) |
0.820475 | + | 0.571683i | \(0.193709\pi\) | |||||||
\(840\) | 598592. | − | 685431.i | 0.848344 | − | 0.971416i | ||||
\(841\) | −354596. | + | 1.09133e6i | −0.501351 | + | 1.54300i | ||||
\(842\) | 1.62340e6 | + | 527473.i | 2.28981 | + | 0.744006i | ||||
\(843\) | 29449.3 | + | 25718.3i | 0.0414400 | + | 0.0361899i | ||||
\(844\) | −1.11655e6 | − | 811222.i | −1.56745 | − | 1.13882i | ||||
\(845\) | −142435. | + | 46280.0i | −0.199482 | + | 0.0648157i | ||||
\(846\) | −262101. | + | 126356.i | −0.366209 | + | 0.176545i | ||||
\(847\) | 787298. | + | 414232.i | 1.09742 | + | 0.577400i | ||||
\(848\) | 1908.32i | 0.00265375i | ||||||||
\(849\) | −193858. | − | 324310.i | −0.268948 | − | 0.449930i | ||||
\(850\) | 29095.6 | + | 21139.2i | 0.0402707 | + | 0.0292584i | ||||
\(851\) | 278967. | + | 383965.i | 0.385207 | + | 0.530192i | ||||
\(852\) | 433043. | + | 38883.7i | 0.596556 | + | 0.0535659i | ||||
\(853\) | 261048. | − | 803425.i | 0.358776 | − | 1.10420i | −0.595012 | − | 0.803717i | \(-0.702853\pi\) |
0.953788 | − | 0.300481i | \(-0.0971473\pi\) | |||||||
\(854\) | −237493. | − | 326881.i | −0.325638 | − | 0.448202i | ||||
\(855\) | 185881. | − | 1.02672e6i | 0.254275 | − | 1.40450i | ||||
\(856\) | 104890. | + | 322817.i | 0.143148 | + | 0.440564i | ||||
\(857\) | − | 884737.i | − | 1.20463i | −0.798260 | − | 0.602313i | \(-0.794246\pi\) | ||
0.798260 | − | 0.602313i | \(-0.205754\pi\) | |||||||
\(858\) | −1.00734e6 | − | 346981.i | −1.36837 | − | 0.471336i | ||||
\(859\) | 182995. | 0.248001 | 0.124000 | − | 0.992282i | \(-0.460428\pi\) | ||||
0.124000 | + | 0.992282i | \(0.460428\pi\) | |||||||
\(860\) | −480030. | + | 155971.i | −0.649040 | + | 0.210886i | ||||
\(861\) | 443631. | − | 1.03852e6i | 0.598433 | − | 1.40091i | ||||
\(862\) | −204173. | + | 148340.i | −0.274779 | + | 0.199638i | ||||
\(863\) | 1.28770e6 | + | 418398.i | 1.72899 | + | 0.561783i | 0.993303 | − | 0.115539i | \(-0.0368596\pi\) |
0.735687 | + | 0.677322i | \(0.236860\pi\) | |||||||
\(864\) | −738213. | + | 277582.i | −0.988904 | + | 0.371846i | ||||
\(865\) | 287546. | − | 208915.i | 0.384305 | − | 0.279214i | ||||
\(866\) | −1.19449e6 | + | 1.64407e6i | −1.59274 | + | 2.19222i | ||||
\(867\) | −378024. | − | 632407.i | −0.502900 | − | 0.841315i | ||||
\(868\) | 47766.0 | 0.0633986 | ||||||||
\(869\) | −654828. | − | 161755.i | −0.867137 | − | 0.214200i | ||||
\(870\) | 484820. | + | 2.12210e6i | 0.640534 | + | 2.80367i | ||||
\(871\) | −174529. | − | 537145.i | −0.230055 | − | 0.708036i | ||||
\(872\) | 47830.9 | − | 65833.6i | 0.0629036 | − | 0.0865794i | ||||
\(873\) | 217212. | − | 404051.i | 0.285007 | − | 0.530160i | ||||
\(874\) | −166255. | + | 511681.i | −0.217647 | + | 0.669848i | ||||
\(875\) | −778064. | − | 252808.i | −1.01625 | − | 0.330199i | ||||
\(876\) | −927646. | + | 1.06222e6i | −1.20885 | + | 1.38423i | ||||
\(877\) | 392807. | + | 285391.i | 0.510716 | + | 0.371057i | 0.813095 | − | 0.582131i | \(-0.197781\pi\) |
−0.302379 | + | 0.953188i | \(0.597781\pi\) | |||||||
\(878\) | −1.05445e6 | + | 342611.i | −1.36784 | + | 0.444439i | ||||
\(879\) | −51123.0 | − | 223770.i | −0.0661666 | − | 0.289617i | ||||
\(880\) | −22999.2 | − | 56570.6i | −0.0296994 | − | 0.0730509i | ||||
\(881\) | − | 1.19197e6i | − | 1.53572i | −0.640615 | − | 0.767862i | \(-0.721320\pi\) | ||
0.640615 | − | 0.767862i | \(-0.278680\pi\) | |||||||
\(882\) | 485980. | − | 465031.i | 0.624713 | − | 0.597785i | ||||
\(883\) | 179194. | + | 130192.i | 0.229828 | + | 0.166980i | 0.696740 | − | 0.717324i | \(-0.254633\pi\) |
−0.466911 | + | 0.884304i | \(0.654633\pi\) | |||||||
\(884\) | −92328.0 | − | 127079.i | −0.118149 | − | 0.162618i | ||||
\(885\) | −83092.5 | + | 925391.i | −0.106090 | + | 1.18151i | ||||
\(886\) | −305458. | + | 940103.i | −0.389120 | + | 1.19759i | ||||
\(887\) | 28798.8 | + | 39638.1i | 0.0366038 | + | 0.0503809i | 0.826927 | − | 0.562310i | \(-0.190087\pi\) |
−0.790323 | + | 0.612691i | \(0.790087\pi\) | |||||||
\(888\) | 564046. | − | 1.32041e6i | 0.715300 | − | 1.67449i | ||||
\(889\) | −121293. | − | 373301.i | −0.153473 | − | 0.472341i | ||||
\(890\) | − | 2.14796e6i | − | 2.71173i | ||||||
\(891\) | 655049. | + | 448507.i | 0.825122 | + | 0.564955i | ||||
\(892\) | 906370. | 1.13914 | ||||||||
\(893\) | −247807. | + | 80517.3i | −0.310749 | + | 0.100969i | ||||
\(894\) | −448945. | − | 191778.i | −0.561717 | − | 0.239951i | ||||
\(895\) | −780121. | + | 566791.i | −0.973904 | + | 0.707583i | ||||
\(896\) | −1.47741e6 | − | 480040.i | −1.84029 | − | 0.597945i | ||||
\(897\) | 244462. | + | 21950.7i | 0.303827 | + | 0.0272812i | ||||
\(898\) | −1.12147e6 | + | 814792.i | −1.39070 | + | 1.01040i | ||||
\(899\) | −24804.3 | + | 34140.1i | −0.0306907 | + | 0.0422421i | ||||
\(900\) | 195165. | + | 203956.i | 0.240944 | + | 0.251798i | ||||
\(901\) | 4249.63 | 0.00523482 | ||||||||
\(902\) | 1.03575e6 | + | 1.22892e6i | 1.27304 | + | 1.51047i | ||||
\(903\) | −384137. | + | 87760.8i | −0.471097 | + | 0.107628i | ||||
\(904\) | −236620. | − | 728243.i | −0.289544 | − | 0.891126i | ||||
\(905\) | 56539.8 | − | 77820.4i | 0.0690331 | − | 0.0950159i | ||||
\(906\) | −200830. | − | 175387.i | −0.244666 | − | 0.213668i | ||||
\(907\) | 12445.2 | − | 38302.4i | 0.0151282 | − | 0.0465599i | −0.943207 | − | 0.332204i | \(-0.892208\pi\) |
0.958336 | + | 0.285644i | \(0.0922076\pi\) | |||||||
\(908\) | −163145. | − | 53009.1i | −0.197881 | − | 0.0642953i | ||||
\(909\) | −791614. | − | 425561.i | −0.958044 | − | 0.515031i | ||||
\(910\) | −1.32792e6 | − | 964787.i | −1.60357 | − | 1.16506i | ||||
\(911\) | 120836. | − | 39262.1i | 0.145600 | − | 0.0473083i | −0.235310 | − | 0.971920i | \(-0.575611\pi\) |
0.380910 | + | 0.924612i | \(0.375611\pi\) | |||||||
\(912\) | −74820.9 | + | 17093.8i | −0.0899566 | + | 0.0205517i | ||||
\(913\) | −526002. | + | 443321.i | −0.631024 | + | 0.531834i | ||||
\(914\) | − | 165643.i | − | 0.198281i | ||||||
\(915\) | 220516. | − | 131814.i | 0.263389 | − | 0.157442i | ||||
\(916\) | −8564.33 | − | 6222.35i | −0.0102071 | − | 0.00741589i | ||||
\(917\) | 903505. | + | 1.24357e6i | 1.07446 | + | 1.47887i | ||||
\(918\) | 67174.3 | + | 178646.i | 0.0797109 | + | 0.211986i | ||||
\(919\) | 424987. | − | 1.30797e6i | 0.503204 | − | 1.54870i | −0.300565 | − | 0.953761i | \(-0.597175\pi\) |
0.803769 | − | 0.594942i | \(-0.202825\pi\) | |||||||
\(920\) | −175368. | − | 241374.i | −0.207193 | − | 0.285177i | ||||
\(921\) | 325889. | + | 139212.i | 0.384194 | + | 0.164118i | ||||
\(922\) | 726098. | + | 2.23470e6i | 0.854148 | + | 2.62880i | ||||
\(923\) | − | 289642.i | − | 0.339984i | ||||||
\(924\) | 490640. | + | 1.60545e6i | 0.574671 | + | 1.88041i | ||||
\(925\) | 363631. | 0.424989 | ||||||||
\(926\) | −1.30927e6 | + | 425408.i | −1.52689 | + | 0.496116i | ||||
\(927\) | −397829. | − | 72024.2i | −0.462953 | − | 0.0838145i | ||||
\(928\) | 1.19200e6 | − | 866035.i | 1.38414 | − | 1.00563i | ||||
\(929\) | −706572. | − | 229579.i | −0.818700 | − | 0.266012i | −0.130422 | − | 0.991459i | \(-0.541633\pi\) |
−0.688278 | + | 0.725447i | \(0.741633\pi\) | |||||||
\(930\) | −4429.18 | + | 49327.2i | −0.00512103 | + | 0.0570323i | ||||
\(931\) | 487297. | − | 354042.i | 0.562205 | − | 0.408466i | ||||
\(932\) | 200382. | − | 275802.i | 0.230689 | − | 0.317516i | ||||
\(933\) | 626405. | − | 374437.i | 0.719601 | − | 0.430145i | ||||
\(934\) | 2.35339e6 | 2.69775 | ||||||||
\(935\) | −125977. | + | 51216.9i | −0.144101 | + | 0.0585854i | ||||
\(936\) | −322460. | − | 668882.i | −0.368064 | − | 0.763480i | ||||
\(937\) | −83969.2 | − | 258431.i | −0.0956403 | − | 0.294350i | 0.891780 | − | 0.452470i | \(-0.149457\pi\) |
−0.987420 | + | 0.158119i | \(0.949457\pi\) | |||||||
\(938\) | −852962. | + | 1.17400e6i | −0.969446 | + | 1.33433i | ||||
\(939\) | 549412. | − | 629117.i | 0.623113 | − | 0.713510i | ||||
\(940\) | 120894. | − | 372074.i | 0.136820 | − | 0.421089i | ||||
\(941\) | 1.02694e6 | + | 333672.i | 1.15975 | + | 0.376825i | 0.824807 | − | 0.565414i | \(-0.191284\pi\) |
0.334941 | + | 0.942239i | \(0.391284\pi\) | |||||||
\(942\) | 1.18059e6 | + | 1.03102e6i | 1.33044 | + | 1.16189i | ||||
\(943\) | −299540. | − | 217628.i | −0.336846 | − | 0.244733i | ||||
\(944\) | 64996.5 | − | 21118.6i | 0.0729367 | − | 0.0236986i | ||||
\(945\) | 763157. | + | 955743.i | 0.854575 | + | 1.07023i | ||||
\(946\) | 134479. | − | 544408.i | 0.150270 | − | 0.608334i | ||||
\(947\) | − | 1.39524e6i | − | 1.55578i | −0.628402 | − | 0.777889i | \(-0.716291\pi\) | ||
0.628402 | − | 0.777889i | \(-0.283709\pi\) | |||||||
\(948\) | −653059. | − | 1.09252e6i | −0.726667 | − | 1.21566i | ||||
\(949\) | 760055. | + | 552212.i | 0.843942 | + | 0.613160i | ||||
\(950\) | 242291. | + | 333485.i | 0.268467 | + | 0.369513i | ||||
\(951\) | −228534. | − | 20520.5i | −0.252691 | − | 0.0226896i | ||||
\(952\) | −46062.3 | + | 141765.i | −0.0508244 | + | 0.156421i | ||||
\(953\) | −594506. | − | 818267.i | −0.654591 | − | 0.900968i | 0.344696 | − | 0.938714i | \(-0.387982\pi\) |
−0.999287 | + | 0.0377466i | \(0.987982\pi\) | |||||||
\(954\) | 53522.5 | + | 9689.90i | 0.0588085 | + | 0.0106469i | ||||
\(955\) | 239614. | + | 737457.i | 0.262728 | + | 0.808593i | ||||
\(956\) | 2.03123e6i | 2.22251i | ||||||||
\(957\) | −1.40226e6 | − | 483009.i | −1.53110 | − | 0.527389i | ||||
\(958\) | −1.67560e6 | −1.82575 | ||||||||
\(959\) | −2.11183e6 | + | 686176.i | −2.29627 | + | 0.746102i | ||||
\(960\) | 650730. | − | 1.52333e6i | 0.706087 | − | 1.65292i | ||||
\(961\) | 746367. | − | 542268.i | 0.808176 | − | 0.587174i | ||||
\(962\) | −2.46307e6 | − | 800299.i | −2.66150 | − | 0.864773i | ||||
\(963\) | −452037. | + | 61424.1i | −0.487440 | + | 0.0662349i | ||||
\(964\) | −1.41043e6 | + | 1.02473e6i | −1.51774 | + | 1.10270i | ||||
\(965\) | −209594. | + | 288482.i | −0.225074 | + | 0.309788i | ||||
\(966\) | −323567. | − | 541304.i | −0.346745 | − | 0.580079i | ||||
\(967\) | 1.37559e6 | 1.47107 | 0.735537 | − | 0.677484i | \(-0.236930\pi\) | ||||
0.735537 | + | 0.677484i | \(0.236930\pi\) | |||||||
\(968\) | −869641. | − | 149445.i | −0.928089 | − | 0.159489i | ||||
\(969\) | 38066.0 | + | 166618.i | 0.0405406 | + | 0.177450i | ||||
\(970\) | 310803. | + | 956554.i | 0.330325 | + | 1.01664i | ||||
\(971\) | −379800. | + | 522749.i | −0.402825 | + | 0.554441i | −0.961450 | − | 0.274979i | \(-0.911329\pi\) |
0.558625 | + | 0.829420i | \(0.311329\pi\) | |||||||
\(972\) | 269027. | + | 1.47373e6i | 0.284749 | + | 1.55986i | ||||
\(973\) | 43555.0 | − | 134049.i | 0.0460058 | − | 0.141591i | ||||
\(974\) | 1.10548e6 | + | 359191.i | 1.16528 | + | 0.378623i | ||||
\(975\) | 123698. | − | 141644.i | 0.130123 | − | 0.149000i | ||||
\(976\) | −15288.0 | − | 11107.4i | −0.0160491 | − | 0.0116604i | ||||
\(977\) | 504563. | − | 163943.i | 0.528599 | − | 0.171752i | −0.0325450 | − | 0.999470i | \(-0.510361\pi\) |
0.561144 | + | 0.827718i | \(0.310361\pi\) | |||||||
\(978\) | −175719. | − | 769138.i | −0.183714 | − | 0.804130i | ||||
\(979\) | 1.24278e6 | + | 772823.i | 1.29667 | + | 0.806333i | ||||
\(980\) | 904383.i | 0.941674i | ||||||||
\(981\) | 75612.2 | + | 79018.3i | 0.0785695 | + | 0.0821088i | ||||
\(982\) | 61404.3 | + | 44612.8i | 0.0636760 | + | 0.0462633i | ||||
\(983\) | 634704. | + | 873595.i | 0.656847 | + | 0.904072i | 0.999372 | − | 0.0354365i | \(-0.0112821\pi\) |
−0.342525 | + | 0.939509i | \(0.611282\pi\) | |||||||
\(984\) | −100175. | + | 1.11564e6i | −0.103460 | + | 1.15222i | ||||
\(985\) | 228076. | − | 701946.i | 0.235075 | − | 0.723487i | ||||
\(986\) | −209579. | − | 288461.i | −0.215573 | − | 0.296710i | ||||
\(987\) | 119979. | − | 280866.i | 0.123160 | − | 0.288313i | ||||
\(988\) | −556348. | − | 1.71226e6i | −0.569944 | − | 1.75411i | ||||
\(989\) | 129187.i | 0.132076i | ||||||||
\(990\) | −1.70342e6 | + | 357809.i | −1.73800 | + | 0.365074i | ||||
\(991\) | −1.74237e6 | −1.77416 | −0.887080 | − | 0.461615i | \(-0.847270\pi\) | ||||
−0.887080 | + | 0.461615i | \(0.847270\pi\) | |||||||
\(992\) | 31881.5 | − | 10358.9i | 0.0323978 | − | 0.0105267i | ||||
\(993\) | −680895. | − | 290861.i | −0.690528 | − | 0.294976i | ||||
\(994\) | −602067. | + | 437427.i | −0.609357 | + | 0.442724i | ||||
\(995\) | −682355. | − | 221711.i | −0.689231 | − | 0.223945i | ||||
\(996\) | −1.29290e6 | − | 116091.i | −1.30330 | − | 0.117026i | ||||
\(997\) | −1.00990e6 | + | 733734.i | −1.01599 | + | 0.738157i | −0.965456 | − | 0.260566i | \(-0.916091\pi\) |
−0.0505294 | + | 0.998723i | \(0.516091\pi\) | |||||||
\(998\) | 1.75597e6 | − | 2.41688e6i | 1.76301 | − | 2.42658i | ||||
\(999\) | 1.61118e6 | + | 1.06209e6i | 1.61441 | + | 1.06422i |
(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 | 33.5.h.a.5.13 | yes | 56 | |
3.2 | odd | 2 | inner | 33.5.h.a.5.2 | ✓ | 56 | |
11.9 | even | 5 | inner | 33.5.h.a.20.2 | yes | 56 | |
33.20 | odd | 10 | inner | 33.5.h.a.20.13 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.5.h.a.5.2 | ✓ | 56 | 3.2 | odd | 2 | inner | |
33.5.h.a.5.13 | yes | 56 | 1.1 | even | 1 | trivial | |
33.5.h.a.20.2 | yes | 56 | 11.9 | even | 5 | inner | |
33.5.h.a.20.13 | yes | 56 | 33.20 | odd | 10 | inner |