Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [36,5,Mod(7,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("36.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.72131867102\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.11 | ||
Character | \(\chi\) | \(=\) | 36.31 |
Dual form | 36.5.f.a.7.11 |
$q$-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 \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.485844 | + | 3.97038i | −0.121461 | + | 0.992596i | ||||
\(3\) | −4.25251 | + | 7.93197i | −0.472501 | + | 0.881330i | ||||
\(4\) | −15.5279 | − | 3.85798i | −0.970494 | − | 0.241124i | ||||
\(5\) | 1.01545 | − | 1.75881i | 0.0406181 | − | 0.0703525i | −0.845002 | − | 0.534764i | \(-0.820401\pi\) |
0.885620 | + | 0.464411i | \(0.153734\pi\) | |||||||
\(6\) | −29.4269 | − | 20.7378i | −0.817415 | − | 0.576050i | ||||
\(7\) | −20.0352 | + | 11.5673i | −0.408882 | + | 0.236068i | −0.690309 | − | 0.723514i | \(-0.742526\pi\) |
0.281427 | + | 0.959583i | \(0.409192\pi\) | |||||||
\(8\) | 22.8618 | − | 59.7774i | 0.357216 | − | 0.934022i | ||||
\(9\) | −44.8324 | − | 67.4615i | −0.553486 | − | 0.832859i | ||||
\(10\) | 6.48981 | + | 4.88624i | 0.0648981 | + | 0.0488624i | ||||
\(11\) | −4.32958 | + | 2.49968i | −0.0357816 | + | 0.0206585i | −0.517784 | − | 0.855511i | \(-0.673243\pi\) |
0.482002 | + | 0.876170i | \(0.339910\pi\) | |||||||
\(12\) | 96.6339 | − | 106.761i | 0.671069 | − | 0.741395i | ||||
\(13\) | −137.824 | + | 238.718i | −0.815527 | + | 1.41253i | 0.0934218 | + | 0.995627i | \(0.470219\pi\) |
−0.908949 | + | 0.416908i | \(0.863114\pi\) | |||||||
\(14\) | −36.1928 | − | 85.1675i | −0.184657 | − | 0.434528i | ||||
\(15\) | 9.63264 | + | 15.5339i | 0.0428117 | + | 0.0690395i | ||||
\(16\) | 226.232 | + | 119.813i | 0.883719 | + | 0.468018i | ||||
\(17\) | −266.009 | −0.920447 | −0.460224 | − | 0.887803i | \(-0.652231\pi\) | ||||
−0.460224 | + | 0.887803i | \(0.652231\pi\) | |||||||
\(18\) | 289.630 | − | 145.226i | 0.893919 | − | 0.448228i | ||||
\(19\) | 367.194i | 1.01716i | 0.861015 | + | 0.508579i | \(0.169829\pi\) | ||||
−0.861015 | + | 0.508579i | \(0.830171\pi\) | |||||||
\(20\) | −22.5533 | + | 23.3931i | −0.0563832 | + | 0.0584828i | ||||
\(21\) | −6.55189 | − | 208.109i | −0.0148569 | − | 0.471902i | ||||
\(22\) | −7.82120 | − | 18.4045i | −0.0161595 | − | 0.0380259i | ||||
\(23\) | 544.473 | + | 314.352i | 1.02925 | + | 0.594238i | 0.916770 | − | 0.399416i | \(-0.130787\pi\) |
0.112481 | + | 0.993654i | \(0.464120\pi\) | |||||||
\(24\) | 376.933 | + | 435.543i | 0.654397 | + | 0.756151i | ||||
\(25\) | 310.438 | + | 537.694i | 0.496700 | + | 0.860310i | ||||
\(26\) | −880.842 | − | 663.194i | −1.30302 | − | 0.981057i | ||||
\(27\) | 725.753 | − | 68.7283i | 0.995546 | − | 0.0942775i | ||||
\(28\) | 355.732 | − | 102.321i | 0.453739 | − | 0.130512i | ||||
\(29\) | −319.481 | − | 553.357i | −0.379882 | − | 0.657975i | 0.611163 | − | 0.791505i | \(-0.290702\pi\) |
−0.991045 | + | 0.133530i | \(0.957369\pi\) | |||||||
\(30\) | −66.3555 | + | 30.6982i | −0.0737284 | + | 0.0341092i | ||||
\(31\) | −1191.19 | − | 687.735i | −1.23953 | − | 0.715645i | −0.270535 | − | 0.962710i | \(-0.587201\pi\) |
−0.968999 | + | 0.247065i | \(0.920534\pi\) | |||||||
\(32\) | −585.616 | + | 840.018i | −0.571891 | + | 0.820330i | ||||
\(33\) | −1.41585 | − | 44.9720i | −0.00130014 | − | 0.0412966i | ||||
\(34\) | 129.239 | − | 1056.16i | 0.111799 | − | 0.913633i | ||||
\(35\) | 46.9843i | 0.0383545i | ||||||||
\(36\) | 435.888 | + | 1220.50i | 0.336333 | + | 0.941743i | ||||
\(37\) | 1466.19 | 1.07099 | 0.535496 | − | 0.844538i | \(-0.320125\pi\) | ||||
0.535496 | + | 0.844538i | \(0.320125\pi\) | |||||||
\(38\) | −1457.90 | − | 178.399i | −1.00963 | − | 0.123545i | ||||
\(39\) | −1307.41 | − | 2108.37i | −0.859572 | − | 1.38617i | ||||
\(40\) | −81.9222 | − | 100.911i | −0.0512014 | − | 0.0630692i | ||||
\(41\) | 593.019 | − | 1027.14i | 0.352777 | − | 0.611028i | −0.633958 | − | 0.773368i | \(-0.718571\pi\) |
0.986735 | + | 0.162339i | \(0.0519040\pi\) | |||||||
\(42\) | 829.456 | + | 75.0950i | 0.470213 | + | 0.0425709i | ||||
\(43\) | −1430.33 | + | 825.804i | −0.773572 | + | 0.446622i | −0.834147 | − | 0.551542i | \(-0.814040\pi\) |
0.0605755 | + | 0.998164i | \(0.480706\pi\) | |||||||
\(44\) | 76.8730 | − | 22.1114i | 0.0397071 | − | 0.0114212i | ||||
\(45\) | −164.177 | + | 10.3478i | −0.0810752 | + | 0.00511004i | ||||
\(46\) | −1512.63 | + | 2009.04i | −0.714852 | + | 0.949453i | ||||
\(47\) | −307.864 | + | 177.745i | −0.139368 | + | 0.0804642i | −0.568063 | − | 0.822985i | \(-0.692307\pi\) |
0.428695 | + | 0.903449i | \(0.358974\pi\) | |||||||
\(48\) | −1912.40 | + | 1284.96i | −0.830036 | + | 0.557709i | ||||
\(49\) | −932.893 | + | 1615.82i | −0.388544 | + | 0.672977i | ||||
\(50\) | −2285.68 | + | 971.322i | −0.914270 | + | 0.388529i | ||||
\(51\) | 1131.21 | − | 2109.98i | 0.434912 | − | 0.811218i | ||||
\(52\) | 3061.09 | − | 3175.07i | 1.13206 | − | 1.17421i | ||||
\(53\) | 5297.49 | 1.88590 | 0.942950 | − | 0.332934i | \(-0.108039\pi\) | ||||
0.942950 | + | 0.332934i | \(0.108039\pi\) | |||||||
\(54\) | −79.7250 | + | 2914.91i | −0.0273405 | + | 0.999626i | ||||
\(55\) | 10.1532i | 0.00335644i | ||||||||
\(56\) | 233.424 | + | 1462.10i | 0.0744338 | + | 0.466232i | ||||
\(57\) | −2912.57 | − | 1561.50i | −0.896452 | − | 0.480608i | ||||
\(58\) | 2352.26 | − | 999.617i | 0.699245 | − | 0.297151i | ||||
\(59\) | 5223.32 | + | 3015.68i | 1.50052 | + | 0.866327i | 1.00000 | 0.000603027i | \(0.000191950\pi\) | |
0.500522 | + | 0.865724i | \(0.333141\pi\) | |||||||
\(60\) | −89.6454 | − | 278.371i | −0.0249015 | − | 0.0773254i | ||||
\(61\) | −833.364 | − | 1443.43i | −0.223962 | − | 0.387914i | 0.732045 | − | 0.681256i | \(-0.238566\pi\) |
−0.956008 | + | 0.293342i | \(0.905233\pi\) | |||||||
\(62\) | 3309.31 | − | 4395.36i | 0.860902 | − | 1.14343i | ||||
\(63\) | 1678.58 | + | 833.016i | 0.422922 | + | 0.209880i | ||||
\(64\) | −3050.68 | − | 2733.24i | −0.744794 | − | 0.667295i | ||||
\(65\) | 279.907 | + | 484.814i | 0.0662502 | + | 0.114749i | ||||
\(66\) | 179.244 | + | 16.2279i | 0.0411488 | + | 0.00372541i | ||||
\(67\) | 1908.36 | + | 1101.79i | 0.425119 | + | 0.245443i | 0.697265 | − | 0.716813i | \(-0.254400\pi\) |
−0.272146 | + | 0.962256i | \(0.587733\pi\) | |||||||
\(68\) | 4130.57 | + | 1026.26i | 0.893289 | + | 0.221942i | ||||
\(69\) | −4808.81 | + | 2981.96i | −1.01004 | + | 0.626332i | ||||
\(70\) | −186.546 | − | 22.8270i | −0.0380705 | − | 0.00465858i | ||||
\(71\) | − | 524.299i | − | 0.104007i | −0.998647 | − | 0.0520035i | \(-0.983439\pi\) | ||
0.998647 | − | 0.0520035i | \(-0.0165607\pi\) | |||||||
\(72\) | −5057.62 | + | 1137.67i | −0.975622 | + | 0.219458i | ||||
\(73\) | −1492.29 | −0.280032 | −0.140016 | − | 0.990149i | \(-0.544715\pi\) | ||||
−0.140016 | + | 0.990149i | \(0.544715\pi\) | |||||||
\(74\) | −712.338 | + | 5821.33i | −0.130084 | + | 1.06306i | ||||
\(75\) | −5585.11 | + | 175.836i | −0.992909 | + | 0.0312597i | ||||
\(76\) | 1416.63 | − | 5701.76i | 0.245261 | − | 0.987146i | ||||
\(77\) | 57.8293 | − | 100.163i | 0.00975364 | − | 0.0168938i | ||||
\(78\) | 9006.23 | − | 4166.58i | 1.48031 | − | 0.684842i | ||||
\(79\) | −4448.35 | + | 2568.25i | −0.712762 | + | 0.411513i | −0.812083 | − | 0.583542i | \(-0.801666\pi\) |
0.0993209 | + | 0.995055i | \(0.468333\pi\) | |||||||
\(80\) | 440.456 | − | 276.236i | 0.0688212 | − | 0.0431619i | ||||
\(81\) | −2541.12 | + | 6048.92i | −0.387307 | + | 0.921951i | ||||
\(82\) | 3790.02 | + | 2853.54i | 0.563656 | + | 0.424382i | ||||
\(83\) | −6918.39 | + | 3994.33i | −1.00427 | + | 0.579813i | −0.909508 | − | 0.415687i | \(-0.863541\pi\) |
−0.0947580 | + | 0.995500i | \(0.530208\pi\) | |||||||
\(84\) | −701.143 | + | 3256.78i | −0.0993683 | + | 0.461561i | ||||
\(85\) | −270.120 | + | 467.861i | −0.0373868 | + | 0.0647558i | ||||
\(86\) | −2583.84 | − | 6080.19i | −0.349356 | − | 0.822092i | ||||
\(87\) | 5747.81 | − | 180.958i | 0.759388 | − | 0.0239078i | ||||
\(88\) | 50.4426 | + | 315.958i | 0.00651376 | + | 0.0408004i | ||||
\(89\) | −8860.17 | −1.11857 | −0.559283 | − | 0.828977i | \(-0.688924\pi\) | ||||
−0.559283 | + | 0.828977i | \(0.688924\pi\) | |||||||
\(90\) | 38.6797 | − | 656.875i | 0.00477527 | − | 0.0810956i | ||||
\(91\) | − | 6377.03i | − | 0.770080i | ||||||
\(92\) | −7241.77 | − | 6981.79i | −0.855597 | − | 0.824881i | ||||
\(93\) | 10520.7 | − | 6523.91i | 1.21640 | − | 0.754296i | ||||
\(94\) | −556.144 | − | 1308.70i | −0.0629407 | − | 0.148110i | ||||
\(95\) | 645.826 | + | 372.868i | 0.0715596 | + | 0.0413150i | ||||
\(96\) | −4172.66 | − | 8217.27i | −0.452763 | − | 0.891631i | ||||
\(97\) | −3409.33 | − | 5905.14i | −0.362348 | − | 0.627606i | 0.625999 | − | 0.779824i | \(-0.284692\pi\) |
−0.988347 | + | 0.152219i | \(0.951358\pi\) | |||||||
\(98\) | −5962.18 | − | 4488.98i | −0.620802 | − | 0.467408i | ||||
\(99\) | 362.737 | + | 180.013i | 0.0370103 | + | 0.0183668i | ||||
\(100\) | −2746.04 | − | 9546.92i | −0.274604 | − | 0.954692i | ||||
\(101\) | −1545.53 | − | 2676.93i | −0.151507 | − | 0.262418i | 0.780274 | − | 0.625437i | \(-0.215079\pi\) |
−0.931782 | + | 0.363019i | \(0.881746\pi\) | |||||||
\(102\) | 7827.84 | + | 5516.45i | 0.752387 | + | 0.530224i | ||||
\(103\) | 9409.35 | + | 5432.49i | 0.886922 | + | 0.512065i | 0.872934 | − | 0.487838i | \(-0.162214\pi\) |
0.0139875 | + | 0.999902i | \(0.495547\pi\) | |||||||
\(104\) | 11119.1 | + | 13696.3i | 1.02802 | + | 1.26630i | ||||
\(105\) | −372.678 | − | 199.801i | −0.0338030 | − | 0.0181225i | ||||
\(106\) | −2573.76 | + | 21033.1i | −0.229063 | + | 1.87194i | ||||
\(107\) | − | 14106.5i | − | 1.23212i | −0.787699 | − | 0.616060i | \(-0.788728\pi\) | ||
0.787699 | − | 0.616060i | \(-0.211272\pi\) | |||||||
\(108\) | −11534.6 | − | 1732.73i | −0.988904 | − | 0.148554i | ||||
\(109\) | 16328.3 | 1.37432 | 0.687160 | − | 0.726506i | \(-0.258857\pi\) | ||||
0.687160 | + | 0.726506i | \(0.258857\pi\) | |||||||
\(110\) | −40.3122 | − | 4.93288i | −0.00333159 | − | 0.000407676i | ||||
\(111\) | −6234.97 | + | 11629.8i | −0.506044 | + | 0.943897i | ||||
\(112\) | −5918.52 | + | 216.430i | −0.471821 | + | 0.0172536i | ||||
\(113\) | −5911.44 | + | 10238.9i | −0.462952 | + | 0.801857i | −0.999107 | − | 0.0422631i | \(-0.986543\pi\) |
0.536154 | + | 0.844120i | \(0.319877\pi\) | |||||||
\(114\) | 7614.79 | − | 10805.4i | 0.585934 | − | 0.831440i | ||||
\(115\) | 1105.77 | − | 638.418i | 0.0836123 | − | 0.0482736i | ||||
\(116\) | 2826.03 | + | 9825.03i | 0.210020 | + | 0.730160i | ||||
\(117\) | 22283.3 | − | 1404.48i | 1.62782 | − | 0.102599i | ||||
\(118\) | −14511.1 | + | 19273.4i | −1.04217 | + | 1.38419i | ||||
\(119\) | 5329.56 | − | 3077.02i | 0.376354 | − | 0.217288i | ||||
\(120\) | 1148.80 | − | 220.682i | 0.0797775 | − | 0.0153251i | ||||
\(121\) | −7308.00 | + | 12657.8i | −0.499146 | + | 0.864547i | ||||
\(122\) | 6135.85 | − | 2607.49i | 0.412245 | − | 0.175188i | ||||
\(123\) | 5625.42 | + | 9071.72i | 0.371830 | + | 0.599625i | ||||
\(124\) | 15843.5 | + | 15274.7i | 1.03040 | + | 0.993411i | ||||
\(125\) | 2530.25 | 0.161936 | ||||||||
\(126\) | −4122.92 | + | 6259.88i | −0.259695 | + | 0.394298i | ||||
\(127\) | − | 20979.9i | − | 1.30076i | −0.759609 | − | 0.650379i | \(-0.774610\pi\) | ||
0.759609 | − | 0.650379i | \(-0.225390\pi\) | |||||||
\(128\) | 12334.2 | − | 10784.4i | 0.752817 | − | 0.658229i | ||||
\(129\) | −467.746 | − | 14857.1i | −0.0281081 | − | 0.892802i | ||||
\(130\) | −2060.89 | + | 875.796i | −0.121946 | + | 0.0518222i | ||||
\(131\) | −24723.9 | − | 14274.3i | −1.44070 | − | 0.831789i | −0.442804 | − | 0.896618i | \(-0.646016\pi\) |
−0.997896 | + | 0.0648298i | \(0.979350\pi\) | |||||||
\(132\) | −151.516 | + | 703.783i | −0.00869580 | + | 0.0403916i | ||||
\(133\) | −4247.46 | − | 7356.81i | −0.240119 | − | 0.415898i | ||||
\(134\) | −5301.70 | + | 7041.62i | −0.295261 | + | 0.392160i | ||||
\(135\) | 616.087 | − | 1346.25i | 0.0338045 | − | 0.0738685i | ||||
\(136\) | −6081.45 | + | 15901.3i | −0.328798 | + | 0.859718i | ||||
\(137\) | 309.436 | + | 535.959i | 0.0164866 | + | 0.0285556i | 0.874151 | − | 0.485654i | \(-0.161419\pi\) |
−0.857664 | + | 0.514210i | \(0.828085\pi\) | |||||||
\(138\) | −9503.22 | − | 20541.6i | −0.499014 | − | 1.07864i | ||||
\(139\) | 16819.9 | + | 9710.99i | 0.870552 | + | 0.502613i | 0.867532 | − | 0.497382i | \(-0.165705\pi\) |
0.00302027 | + | 0.999995i | \(0.499039\pi\) | |||||||
\(140\) | 181.264 | − | 729.568i | 0.00924818 | − | 0.0372228i | ||||
\(141\) | −100.677 | − | 3197.83i | −0.00506400 | − | 0.160849i | ||||
\(142\) | 2081.67 | + | 254.728i | 0.103237 | + | 0.0126328i | ||||
\(143\) | − | 1378.07i | − | 0.0673903i | ||||||
\(144\) | −2059.77 | − | 20633.4i | −0.0993330 | − | 0.995054i | ||||
\(145\) | −1297.67 | −0.0617203 | ||||||||
\(146\) | 725.022 | − | 5924.98i | 0.0340130 | − | 0.277959i | ||||
\(147\) | −8849.49 | − | 14271.0i | −0.409528 | − | 0.660418i | ||||
\(148\) | −22766.8 | − | 5656.52i | −1.03939 | − | 0.258241i | ||||
\(149\) | −309.641 | + | 536.313i | −0.0139471 | + | 0.0241572i | −0.872915 | − | 0.487873i | \(-0.837773\pi\) |
0.858968 | + | 0.512030i | \(0.171106\pi\) | |||||||
\(150\) | 2015.36 | − | 22260.5i | 0.0895715 | − | 0.989354i | ||||
\(151\) | 3758.08 | − | 2169.73i | 0.164821 | − | 0.0951593i | −0.415321 | − | 0.909675i | \(-0.636331\pi\) |
0.580141 | + | 0.814516i | \(0.302997\pi\) | |||||||
\(152\) | 21949.9 | + | 8394.72i | 0.950048 | + | 0.363345i | ||||
\(153\) | 11925.8 | + | 17945.4i | 0.509455 | + | 0.766603i | ||||
\(154\) | 369.591 | + | 278.268i | 0.0155840 | + | 0.0117334i | ||||
\(155\) | −2419.20 | + | 1396.72i | −0.100695 | + | 0.0581362i | ||||
\(156\) | 12167.3 | + | 37782.5i | 0.499971 | + | 1.55254i | ||||
\(157\) | 3103.88 | − | 5376.08i | 0.125923 | − | 0.218105i | −0.796170 | − | 0.605073i | \(-0.793144\pi\) |
0.922093 | + | 0.386967i | \(0.126477\pi\) | |||||||
\(158\) | −8035.75 | − | 18909.4i | −0.321894 | − | 0.757468i | ||||
\(159\) | −22527.6 | + | 42019.6i | −0.891090 | + | 1.66210i | ||||
\(160\) | 882.770 | + | 1882.99i | 0.0344832 | + | 0.0735541i | ||||
\(161\) | −14544.9 | −0.561123 | ||||||||
\(162\) | −22782.0 | − | 13028.1i | −0.868082 | − | 0.496420i | ||||
\(163\) | 15857.0i | 0.596824i | 0.954437 | + | 0.298412i | \(0.0964569\pi\) | ||||
−0.954437 | + | 0.298412i | \(0.903543\pi\) | |||||||
\(164\) | −13171.0 | + | 13661.5i | −0.489702 | + | 0.507937i | ||||
\(165\) | −80.5351 | − | 43.1766i | −0.00295813 | − | 0.00158592i | ||||
\(166\) | −12497.8 | − | 29409.3i | −0.453541 | − | 1.06725i | ||||
\(167\) | 362.861 | + | 209.498i | 0.0130109 | + | 0.00751186i | 0.506491 | − | 0.862245i | \(-0.330942\pi\) |
−0.493480 | + | 0.869757i | \(0.664276\pi\) | |||||||
\(168\) | −12590.0 | − | 4366.09i | −0.446074 | − | 0.154694i | ||||
\(169\) | −23710.4 | − | 41067.7i | −0.830169 | − | 1.43789i | ||||
\(170\) | −1726.35 | − | 1299.79i | −0.0597353 | − | 0.0449753i | ||||
\(171\) | 24771.5 | − | 16462.2i | 0.847149 | − | 0.562983i | ||||
\(172\) | 25396.0 | − | 7304.81i | 0.858438 | − | 0.246918i | ||||
\(173\) | 9600.40 | + | 16628.4i | 0.320772 | + | 0.555594i | 0.980648 | − | 0.195781i | \(-0.0627242\pi\) |
−0.659875 | + | 0.751375i | \(0.729391\pi\) | |||||||
\(174\) | −2074.07 | + | 22908.9i | −0.0685053 | + | 0.756670i | ||||
\(175\) | −12439.4 | − | 7181.88i | −0.406184 | − | 0.234510i | ||||
\(176\) | −1278.98 | + | 46.7701i | −0.0412895 | + | 0.00150988i | ||||
\(177\) | −46132.5 | + | 28607.0i | −1.47252 | + | 0.913115i | ||||
\(178\) | 4304.66 | − | 35178.3i | 0.135862 | − | 1.11028i | ||||
\(179\) | 49821.7i | 1.55494i | 0.628922 | + | 0.777468i | \(0.283496\pi\) | ||||
−0.628922 | + | 0.777468i | \(0.716504\pi\) | |||||||
\(180\) | 2589.25 | + | 472.712i | 0.0799152 | + | 0.0145899i | ||||
\(181\) | 13970.7 | 0.426443 | 0.213222 | − | 0.977004i | \(-0.431604\pi\) | ||||
0.213222 | + | 0.977004i | \(0.431604\pi\) | |||||||
\(182\) | 25319.3 | + | 3098.24i | 0.764378 | + | 0.0935347i | ||||
\(183\) | 14993.1 | − | 472.028i | 0.447703 | − | 0.0140950i | ||||
\(184\) | 31238.8 | − | 25360.6i | 0.922696 | − | 0.749071i | ||||
\(185\) | 1488.84 | − | 2578.75i | 0.0435016 | − | 0.0753469i | ||||
\(186\) | 20791.0 | + | 44940.6i | 0.600966 | + | 1.29901i | ||||
\(187\) | 1151.71 | − | 664.939i | 0.0329351 | − | 0.0190151i | ||||
\(188\) | 5466.22 | − | 1572.28i | 0.154658 | − | 0.0444851i | ||||
\(189\) | −13745.6 | + | 9772.02i | −0.384805 | + | 0.273565i | ||||
\(190\) | −1794.20 | + | 2383.02i | −0.0497008 | + | 0.0660117i | ||||
\(191\) | 26994.8 | − | 15585.5i | 0.739969 | − | 0.427221i | −0.0820893 | − | 0.996625i | \(-0.526159\pi\) |
0.822058 | + | 0.569404i | \(0.192826\pi\) | |||||||
\(192\) | 34653.0 | − | 12574.8i | 0.940023 | − | 0.341112i | ||||
\(193\) | −13498.2 | + | 23379.5i | −0.362377 | + | 0.627655i | −0.988351 | − | 0.152189i | \(-0.951368\pi\) |
0.625975 | + | 0.779843i | \(0.284701\pi\) | |||||||
\(194\) | 25102.1 | − | 10667.4i | 0.666970 | − | 0.283436i | ||||
\(195\) | −5035.84 | + | 158.543i | −0.132435 | + | 0.00416944i | ||||
\(196\) | 20719.7 | − | 21491.2i | 0.539350 | − | 0.559434i | ||||
\(197\) | 10416.4 | 0.268402 | 0.134201 | − | 0.990954i | \(-0.457153\pi\) | ||||
0.134201 | + | 0.990954i | \(0.457153\pi\) | |||||||
\(198\) | −890.956 | + | 1352.75i | −0.0227261 | + | 0.0345054i | ||||
\(199\) | − | 8438.68i | − | 0.213093i | −0.994308 | − | 0.106546i | \(-0.966021\pi\) | ||
0.994308 | − | 0.106546i | \(-0.0339793\pi\) | |||||||
\(200\) | 39239.1 | − | 6264.51i | 0.980978 | − | 0.156613i | ||||
\(201\) | −16854.7 | + | 10451.7i | −0.417185 | + | 0.258699i | ||||
\(202\) | 11379.3 | − | 4835.76i | 0.278878 | − | 0.118512i | ||||
\(203\) | 12801.7 | + | 7391.09i | 0.310654 | + | 0.179356i | ||||
\(204\) | −25705.5 | + | 28399.4i | −0.617684 | + | 0.682415i | ||||
\(205\) | −1204.36 | − | 2086.02i | −0.0286583 | − | 0.0496376i | ||||
\(206\) | −26140.6 | + | 34719.4i | −0.616000 | + | 0.818159i | ||||
\(207\) | −3203.37 | − | 50824.2i | −0.0747594 | − | 1.18612i | ||||
\(208\) | −59781.7 | + | 37492.7i | −1.38179 | + | 0.866602i | ||||
\(209\) | −917.868 | − | 1589.79i | −0.0210130 | − | 0.0363956i | ||||
\(210\) | 974.350 | − | 1382.60i | 0.0220941 | − | 0.0313515i | ||||
\(211\) | 19871.6 | + | 11472.8i | 0.446341 | + | 0.257695i | 0.706284 | − | 0.707929i | \(-0.250370\pi\) |
−0.259943 | + | 0.965624i | \(0.583704\pi\) | |||||||
\(212\) | −82259.0 | − | 20437.6i | −1.83026 | − | 0.454735i | ||||
\(213\) | 4158.73 | + | 2229.59i | 0.0916645 | + | 0.0491434i | ||||
\(214\) | 56008.4 | + | 6853.58i | 1.22300 | + | 0.149655i | ||||
\(215\) | 3354.25i | 0.0725637i | ||||||||
\(216\) | 12483.6 | − | 44954.9i | 0.267567 | − | 0.963539i | ||||
\(217\) | 31821.1 | 0.675764 | ||||||||
\(218\) | −7933.01 | + | 64829.6i | −0.166926 | + | 1.36414i | ||||
\(219\) | 6345.99 | − | 11836.8i | 0.132316 | − | 0.246801i | ||||
\(220\) | 39.1709 | − | 157.658i | 0.000809316 | − | 0.00325740i | ||||
\(221\) | 36662.5 | − | 63501.3i | 0.750650 | − | 1.30016i | ||||
\(222\) | −43145.4 | − | 30405.5i | −0.875444 | − | 0.616944i | ||||
\(223\) | −55651.0 | + | 32130.1i | −1.11909 | + | 0.646105i | −0.941167 | − | 0.337941i | \(-0.890270\pi\) |
−0.177919 | + | 0.984045i | \(0.556936\pi\) | |||||||
\(224\) | 2016.17 | − | 23604.0i | 0.0401820 | − | 0.470423i | ||||
\(225\) | 22356.0 | − | 45048.7i | 0.441600 | − | 0.889851i | ||||
\(226\) | −37780.4 | − | 28445.2i | −0.739690 | − | 0.556919i | ||||
\(227\) | −5807.02 | + | 3352.69i | −0.112694 | + | 0.0650641i | −0.555288 | − | 0.831658i | \(-0.687392\pi\) |
0.442593 | + | 0.896722i | \(0.354059\pi\) | |||||||
\(228\) | 39202.0 | + | 35483.4i | 0.754116 | + | 0.682583i | ||||
\(229\) | −17775.1 | + | 30787.4i | −0.338955 | + | 0.587087i | −0.984236 | − | 0.176858i | \(-0.943407\pi\) |
0.645281 | + | 0.763945i | \(0.276740\pi\) | |||||||
\(230\) | 1997.53 | + | 4700.51i | 0.0377605 | + | 0.0888566i | ||||
\(231\) | 548.573 | + | 884.646i | 0.0102804 | + | 0.0165785i | ||||
\(232\) | −40382.2 | + | 6447.00i | −0.750263 | + | 0.119779i | ||||
\(233\) | 62439.9 | 1.15014 | 0.575070 | − | 0.818105i | \(-0.304975\pi\) | ||||
0.575070 | + | 0.818105i | \(0.304975\pi\) | |||||||
\(234\) | −5249.88 | + | 89155.6i | −0.0958777 | + | 1.62823i | ||||
\(235\) | 721.967i | 0.0130732i | ||||||||
\(236\) | −69472.8 | − | 66978.7i | −1.24736 | − | 1.20258i | ||||
\(237\) | −1454.69 | − | 46205.7i | −0.0258985 | − | 0.822619i | ||||
\(238\) | 9627.62 | + | 22655.3i | 0.169967 | + | 0.399960i | ||||
\(239\) | 3250.59 | + | 1876.73i | 0.0569070 | + | 0.0328553i | 0.528184 | − | 0.849130i | \(-0.322873\pi\) |
−0.471277 | + | 0.881985i | \(0.656207\pi\) | |||||||
\(240\) | 318.055 | + | 4668.38i | 0.00552178 | + | 0.0810482i | ||||
\(241\) | 44832.6 | + | 77652.3i | 0.771898 | + | 1.33697i | 0.936522 | + | 0.350610i | \(0.114026\pi\) |
−0.164624 | + | 0.986356i | \(0.552641\pi\) | |||||||
\(242\) | −46705.9 | − | 35165.3i | −0.797519 | − | 0.600460i | ||||
\(243\) | −37173.7 | − | 45879.2i | −0.629541 | − | 0.776968i | ||||
\(244\) | 7371.68 | + | 25628.5i | 0.123819 | + | 0.430471i | ||||
\(245\) | 1894.62 | + | 3281.57i | 0.0315638 | + | 0.0546701i | ||||
\(246\) | −38751.3 | + | 17927.6i | −0.640348 | + | 0.296246i | ||||
\(247\) | −87655.9 | − | 50608.2i | −1.43677 | − | 0.829520i | ||||
\(248\) | −68343.8 | + | 55483.5i | −1.11121 | + | 0.902112i | ||||
\(249\) | −2262.44 | − | 71862.4i | −0.0364904 | − | 1.15905i | ||||
\(250\) | −1229.31 | + | 10046.1i | −0.0196689 | + | 0.160737i | ||||
\(251\) | 9246.49i | 0.146767i | 0.997304 | + | 0.0733836i | \(0.0233798\pi\) | ||||
−0.997304 | + | 0.0733836i | \(0.976620\pi\) | |||||||
\(252\) | −22851.0 | − | 19410.9i | −0.359836 | − | 0.305664i | ||||
\(253\) | −3143.12 | −0.0491043 | ||||||||
\(254\) | 83298.4 | + | 10193.0i | 1.29113 | + | 0.157992i | ||||
\(255\) | −2562.37 | − | 4132.16i | −0.0394060 | − | 0.0635473i | ||||
\(256\) | 36825.9 | + | 54210.9i | 0.561918 | + | 0.827193i | ||||
\(257\) | −7624.85 | + | 13206.6i | −0.115442 | + | 0.199952i | −0.917956 | − | 0.396681i | \(-0.870162\pi\) |
0.802514 | + | 0.596633i | \(0.203495\pi\) | |||||||
\(258\) | 59215.7 | + | 5361.11i | 0.889605 | + | 0.0805407i | ||||
\(259\) | −29375.4 | + | 16959.9i | −0.437909 | + | 0.252827i | ||||
\(260\) | −2475.97 | − | 8608.02i | −0.0366268 | − | 0.127338i | ||||
\(261\) | −23007.2 | + | 46361.0i | −0.337741 | + | 0.680568i | ||||
\(262\) | 68686.5 | − | 91228.1i | 1.00062 | − | 1.32900i | ||||
\(263\) | 89478.0 | − | 51660.2i | 1.29361 | − | 0.746869i | 0.314322 | − | 0.949317i | \(-0.398223\pi\) |
0.979293 | + | 0.202448i | \(0.0648896\pi\) | |||||||
\(264\) | −2720.68 | − | 943.505i | −0.0390364 | − | 0.0135374i | ||||
\(265\) | 5379.35 | − | 9317.30i | 0.0766016 | − | 0.132678i | ||||
\(266\) | 31273.0 | − | 13289.8i | 0.441983 | − | 0.187825i | ||||
\(267\) | 37677.9 | − | 70278.6i | 0.528524 | − | 0.985826i | ||||
\(268\) | −25382.2 | − | 24470.9i | −0.353394 | − | 0.340707i | ||||
\(269\) | −86017.8 | −1.18873 | −0.594366 | − | 0.804195i | \(-0.702597\pi\) | ||||
−0.594366 | + | 0.804195i | \(0.702597\pi\) | |||||||
\(270\) | 5045.83 | + | 3100.17i | 0.0692157 | + | 0.0425263i | ||||
\(271\) | − | 15629.0i | − | 0.212810i | −0.994323 | − | 0.106405i | \(-0.966066\pi\) | ||
0.994323 | − | 0.106405i | \(-0.0339340\pi\) | |||||||
\(272\) | −60179.8 | − | 31871.3i | −0.813417 | − | 0.430786i | ||||
\(273\) | 50582.4 | + | 27118.4i | 0.678695 | + | 0.363863i | ||||
\(274\) | −2278.30 | + | 968.188i | −0.0303466 | + | 0.0128961i | ||||
\(275\) | −2688.13 | − | 1551.99i | −0.0355455 | − | 0.0205222i | ||||
\(276\) | 86175.1 | − | 27751.4i | 1.13126 | − | 0.364306i | ||||
\(277\) | 28307.3 | + | 49029.7i | 0.368926 | + | 0.638998i | 0.989398 | − | 0.145231i | \(-0.0463924\pi\) |
−0.620472 | + | 0.784228i | \(0.713059\pi\) | |||||||
\(278\) | −46728.2 | + | 62063.6i | −0.604630 | + | 0.803059i | ||||
\(279\) | 7008.29 | + | 111192.i | 0.0900334 | + | 1.42846i | ||||
\(280\) | 2808.60 | + | 1074.15i | 0.0358240 | + | 0.0137008i | ||||
\(281\) | −55533.5 | − | 96186.8i | −0.703303 | − | 1.21816i | −0.967301 | − | 0.253633i | \(-0.918374\pi\) |
0.263998 | − | 0.964523i | \(-0.414959\pi\) | |||||||
\(282\) | 12745.5 | + | 1153.92i | 0.160273 | + | 0.0145104i | ||||
\(283\) | 78979.6 | + | 45598.9i | 0.986148 | + | 0.569353i | 0.904121 | − | 0.427278i | \(-0.140527\pi\) |
0.0820271 | + | 0.996630i | \(0.473861\pi\) | |||||||
\(284\) | −2022.73 | + | 8141.27i | −0.0250785 | + | 0.100938i | ||||
\(285\) | −5703.95 | + | 3537.05i | −0.0702241 | + | 0.0435463i | ||||
\(286\) | 5471.45 | + | 669.525i | 0.0668914 | + | 0.00818530i | ||||
\(287\) | 27438.6i | 0.333118i | ||||||||
\(288\) | 82923.4 | + | 1846.57i | 0.999752 | + | 0.0222628i | ||||
\(289\) | −12760.0 | −0.152776 | ||||||||
\(290\) | 630.465 | − | 5152.25i | 0.00749661 | − | 0.0612633i | ||||
\(291\) | 61337.6 | − | 1931.09i | 0.724338 | − | 0.0228043i | ||||
\(292\) | 23172.2 | + | 5757.23i | 0.271770 | + | 0.0675224i | ||||
\(293\) | −41507.5 | + | 71893.1i | −0.483494 | + | 0.837436i | −0.999820 | − | 0.0189556i | \(-0.993966\pi\) |
0.516326 | + | 0.856392i | \(0.327299\pi\) | |||||||
\(294\) | 60960.7 | − | 28202.4i | 0.705270 | − | 0.326281i | ||||
\(295\) | 10608.0 | − | 6124.56i | 0.121897 | − | 0.0703770i | ||||
\(296\) | 33519.7 | − | 87644.8i | 0.382575 | − | 1.00033i | ||||
\(297\) | −2970.40 | + | 2111.72i | −0.0336746 | + | 0.0239399i | ||||
\(298\) | −1978.93 | − | 1489.96i | −0.0222843 | − | 0.0167780i | ||||
\(299\) | −150083. | + | 86650.5i | −1.67876 | + | 0.969234i | ||||
\(300\) | 87403.5 | + | 18816.9i | 0.971150 | + | 0.209076i | ||||
\(301\) | 19104.7 | − | 33090.3i | 0.210866 | − | 0.365231i | ||||
\(302\) | 6788.81 | + | 15975.2i | 0.0744355 | + | 0.175159i | ||||
\(303\) | 27805.7 | − | 875.407i | 0.302865 | − | 0.00953508i | ||||
\(304\) | −43994.5 | + | 83071.0i | −0.476048 | + | 0.898882i | ||||
\(305\) | −3384.96 | −0.0363876 | ||||||||
\(306\) | −77044.2 | + | 38631.4i | −0.822806 | + | 0.412570i | ||||
\(307\) | 65201.8i | 0.691803i | 0.938271 | + | 0.345902i | \(0.112427\pi\) | ||||
−0.938271 | + | 0.345902i | \(0.887573\pi\) | |||||||
\(308\) | −1284.40 | + | 1332.22i | −0.0135393 | + | 0.0140435i | ||||
\(309\) | −83103.7 | + | 51533.0i | −0.870369 | + | 0.539720i | ||||
\(310\) | −4370.18 | − | 10283.7i | −0.0454753 | − | 0.107011i | ||||
\(311\) | 115786. | + | 66849.3i | 1.19712 | + | 0.691156i | 0.959911 | − | 0.280303i | \(-0.0904350\pi\) |
0.237206 | + | 0.971459i | \(0.423768\pi\) | |||||||
\(312\) | −155922. | + | 29952.4i | −1.60177 | + | 0.307697i | ||||
\(313\) | −5620.04 | − | 9734.19i | −0.0573655 | − | 0.0993599i | 0.835917 | − | 0.548857i | \(-0.184937\pi\) |
−0.893282 | + | 0.449497i | \(0.851603\pi\) | |||||||
\(314\) | 19837.1 | + | 14935.5i | 0.201196 | + | 0.151482i | ||||
\(315\) | 3169.63 | − | 2106.42i | 0.0319439 | − | 0.0212287i | ||||
\(316\) | 78981.8 | − | 22718.0i | 0.790957 | − | 0.227508i | ||||
\(317\) | 19603.1 | + | 33953.5i | 0.195077 | + | 0.337883i | 0.946926 | − | 0.321452i | \(-0.104171\pi\) |
−0.751849 | + | 0.659336i | \(0.770838\pi\) | |||||||
\(318\) | −155889. | − | 109858.i | −1.54156 | − | 1.08637i | ||||
\(319\) | 2766.43 | + | 1597.20i | 0.0271856 | + | 0.0156956i | ||||
\(320\) | −7905.07 | + | 2590.10i | −0.0771979 | + | 0.0252939i | ||||
\(321\) | 111893. | + | 59988.2i | 1.08590 | + | 0.582178i | ||||
\(322\) | 7066.54 | − | 57748.7i | 0.0681546 | − | 0.556968i | ||||
\(323\) | − | 97677.0i | − | 0.936240i | ||||||
\(324\) | 62794.9 | − | 84123.5i | 0.598183 | − | 0.801359i | ||||
\(325\) | −171143. | −1.62029 | ||||||||
\(326\) | −62958.4 | − | 7704.04i | −0.592405 | − | 0.0724908i | ||||
\(327\) | −69436.2 | + | 129516.i | −0.649367 | + | 1.21123i | ||||
\(328\) | −47842.2 | − | 58931.4i | −0.444696 | − | 0.547771i | ||||
\(329\) | 4112.08 | − | 7122.34i | 0.0379901 | − | 0.0658007i | ||||
\(330\) | 210.555 | − | 298.778i | 0.00193347 | − | 0.00274360i | ||||
\(331\) | 64736.6 | − | 37375.7i | 0.590873 | − | 0.341141i | −0.174570 | − | 0.984645i | \(-0.555853\pi\) |
0.765443 | + | 0.643504i | \(0.222520\pi\) | |||||||
\(332\) | 122838. | − | 35332.7i | 1.11444 | − | 0.320553i | ||||
\(333\) | −65732.6 | − | 98911.2i | −0.592779 | − | 0.891984i | ||||
\(334\) | −1008.08 | + | 1338.92i | −0.00903656 | + | 0.0120022i | ||||
\(335\) | 3875.69 | − | 2237.63i | 0.0345350 | − | 0.0199388i | ||||
\(336\) | 23451.8 | − | 47865.9i | 0.207730 | − | 0.423982i | ||||
\(337\) | 70909.1 | − | 122818.i | 0.624370 | − | 1.08144i | −0.364293 | − | 0.931285i | \(-0.618689\pi\) |
0.988662 | − | 0.150156i | \(-0.0479775\pi\) | |||||||
\(338\) | 174574. | − | 74187.1i | 1.52808 | − | 0.649374i | ||||
\(339\) | −56076.3 | − | 90430.4i | −0.487955 | − | 0.786892i | ||||
\(340\) | 5999.39 | − | 6222.78i | 0.0518978 | − | 0.0538303i | ||||
\(341\) | 6876.48 | 0.0591367 | ||||||||
\(342\) | 53326.1 | + | 106350.i | 0.455919 | + | 0.909257i | ||||
\(343\) | − | 98710.7i | − | 0.839027i | ||||||
\(344\) | 16664.4 | + | 104381.i | 0.140823 | + | 0.882073i | ||||
\(345\) | 361.608 | + | 11485.8i | 0.00303809 | + | 0.0964994i | ||||
\(346\) | −70685.3 | + | 30038.5i | −0.590442 | + | 0.250914i | ||||
\(347\) | −158508. | − | 91514.6i | −1.31641 | − | 0.760032i | −0.333264 | − | 0.942834i | \(-0.608150\pi\) |
−0.983150 | + | 0.182802i | \(0.941483\pi\) | |||||||
\(348\) | −89949.6 | − | 19365.0i | −0.742747 | − | 0.159904i | ||||
\(349\) | −67279.0 | − | 116531.i | −0.552368 | − | 0.956729i | −0.998103 | − | 0.0615644i | \(-0.980391\pi\) |
0.445735 | − | 0.895165i | \(-0.352942\pi\) | |||||||
\(350\) | 34558.4 | − | 45899.8i | 0.282110 | − | 0.374693i | ||||
\(351\) | −83619.5 | + | 182723.i | −0.678724 | + | 1.48313i | ||||
\(352\) | 435.691 | − | 5100.77i | 0.00351636 | − | 0.0411671i | ||||
\(353\) | 100139. | + | 173446.i | 0.803626 | + | 1.39192i | 0.917215 | + | 0.398393i | \(0.130432\pi\) |
−0.113589 | + | 0.993528i | \(0.536235\pi\) | |||||||
\(354\) | −91167.5 | − | 197062.i | −0.727501 | − | 1.57252i | ||||
\(355\) | −922.144 | − | 532.400i | −0.00731715 | − | 0.00422456i | ||||
\(356\) | 137580. | + | 34182.3i | 1.08556 | + | 0.269713i | ||||
\(357\) | 1742.86 | + | 55358.9i | 0.0136750 | + | 0.434361i | ||||
\(358\) | −197811. | − | 24205.6i | −1.54342 | − | 0.188864i | ||||
\(359\) | − | 161179.i | − | 1.25060i | −0.780385 | − | 0.625300i | \(-0.784977\pi\) | ||
0.780385 | − | 0.625300i | \(-0.215023\pi\) | |||||||
\(360\) | −3134.82 | + | 10050.7i | −0.0241884 | + | 0.0775514i | ||||
\(361\) | −4510.46 | −0.0346104 | ||||||||
\(362\) | −6787.59 | + | 55469.1i | −0.0517962 | + | 0.423286i | ||||
\(363\) | −69324.2 | − | 111794.i | −0.526104 | − | 0.848412i | ||||
\(364\) | −24602.4 | + | 99022.0i | −0.185684 | + | 0.747358i | ||||
\(365\) | −1515.35 | + | 2624.66i | −0.0113744 | + | 0.0197010i | ||||
\(366\) | −5410.19 | + | 59757.8i | −0.0403878 | + | 0.446100i | ||||
\(367\) | 172828. | − | 99782.5i | 1.28317 | − | 0.740836i | 0.305740 | − | 0.952115i | \(-0.401096\pi\) |
0.977426 | + | 0.211279i | \(0.0677627\pi\) | |||||||
\(368\) | 85514.0 | + | 136351.i | 0.631454 | + | 1.00685i | ||||
\(369\) | −95878.8 | + | 6043.09i | −0.704158 | + | 0.0443820i | ||||
\(370\) | 9515.28 | + | 7164.14i | 0.0695053 | + | 0.0523312i | ||||
\(371\) | −106136. | + | 61277.9i | −0.771111 | + | 0.445201i | ||||
\(372\) | −188533. | + | 60714.2i | −1.36239 | + | 0.438737i | ||||
\(373\) | 2894.35 | − | 5013.15i | 0.0208033 | − | 0.0360324i | −0.855436 | − | 0.517908i | \(-0.826711\pi\) |
0.876240 | + | 0.481876i | \(0.160044\pi\) | |||||||
\(374\) | 2080.51 | + | 4895.78i | 0.0148740 | + | 0.0350008i | ||||
\(375\) | −10759.9 | + | 20069.9i | −0.0765149 | + | 0.142719i | ||||
\(376\) | 3586.83 | + | 22466.9i | 0.0253709 | + | 0.158916i | ||||
\(377\) | 176129. | 1.23922 | ||||||||
\(378\) | −32120.4 | − | 59323.1i | −0.224801 | − | 0.415183i | ||||
\(379\) | 217930.i | 1.51719i | 0.651565 | + | 0.758593i | \(0.274113\pi\) | ||||
−0.651565 | + | 0.758593i | \(0.725887\pi\) | |||||||
\(380\) | −8589.81 | − | 8281.44i | −0.0594862 | − | 0.0573507i | ||||
\(381\) | 166412. | + | 89217.4i | 1.14640 | + | 0.614610i | ||||
\(382\) | 48765.0 | + | 114752.i | 0.334181 | + | 0.786381i | ||||
\(383\) | 60187.2 | + | 34749.1i | 0.410305 | + | 0.236890i | 0.690921 | − | 0.722930i | \(-0.257205\pi\) |
−0.280616 | + | 0.959820i | \(0.590539\pi\) | |||||||
\(384\) | 33090.7 | + | 143695.i | 0.224411 | + | 0.974495i | ||||
\(385\) | −117.446 | − | 203.422i | −0.000792348 | − | 0.00137239i | ||||
\(386\) | −86267.6 | − | 64951.7i | −0.578993 | − | 0.435929i | ||||
\(387\) | 119835. | + | 59469.8i | 0.800134 | + | 0.397077i | ||||
\(388\) | 30157.9 | + | 104848.i | 0.200326 | + | 0.696458i | ||||
\(389\) | −28733.0 | − | 49767.0i | −0.189881 | − | 0.328884i | 0.755329 | − | 0.655345i | \(-0.227477\pi\) |
−0.945210 | + | 0.326462i | \(0.894144\pi\) | |||||||
\(390\) | 1817.15 | − | 20071.2i | 0.0119471 | − | 0.131961i | ||||
\(391\) | −144835. | − | 83620.5i | −0.947371 | − | 0.546965i | ||||
\(392\) | 75261.8 | + | 92706.5i | 0.489782 | + | 0.603306i | ||||
\(393\) | 218362. | − | 135407.i | 1.41381 | − | 0.876712i | ||||
\(394\) | −5060.76 | + | 41357.2i | −0.0326004 | + | 0.266415i | ||||
\(395\) | 10431.7i | 0.0668595i | ||||||||
\(396\) | −4938.07 | − | 4194.66i | −0.0314896 | − | 0.0267489i | ||||
\(397\) | 13255.8 | 0.0841056 | 0.0420528 | − | 0.999115i | \(-0.486610\pi\) | ||||
0.0420528 | + | 0.999115i | \(0.486610\pi\) | |||||||
\(398\) | 33504.8 | + | 4099.89i | 0.211515 | + | 0.0258825i | ||||
\(399\) | 76416.4 | − | 2405.82i | 0.479999 | − | 0.0151118i | ||||
\(400\) | 5808.42 | + | 158838.i | 0.0363026 | + | 0.992737i | ||||
\(401\) | 2687.66 | − | 4655.16i | 0.0167142 | − | 0.0289498i | −0.857547 | − | 0.514405i | \(-0.828013\pi\) |
0.874262 | + | 0.485455i | \(0.161346\pi\) | |||||||
\(402\) | −33308.4 | − | 71997.5i | −0.206111 | − | 0.445518i | ||||
\(403\) | 328350. | − | 189573.i | 2.02175 | − | 1.16726i | ||||
\(404\) | 13671.3 | + | 47529.7i | 0.0837618 | + | 0.291208i | ||||
\(405\) | 8058.54 | + | 10611.7i | 0.0491299 | + | 0.0646959i | ||||
\(406\) | −35565.1 | + | 47236.9i | −0.215761 | + | 0.286569i | ||||
\(407\) | −6347.97 | + | 3665.00i | −0.0383218 | + | 0.0221251i | ||||
\(408\) | −100268. | − | 115859.i | −0.602338 | − | 0.695997i | ||||
\(409\) | 120347. | − | 208446.i | 0.719427 | − | 1.24608i | −0.241800 | − | 0.970326i | \(-0.577738\pi\) |
0.961227 | − | 0.275758i | \(-0.0889289\pi\) | |||||||
\(410\) | 8867.43 | − | 3768.31i | 0.0527509 | − | 0.0224170i | ||||
\(411\) | −5567.10 | + | 175.269i | −0.0329568 | + | 0.00103758i | ||||
\(412\) | −125149. | − | 120656.i | −0.737282 | − | 0.710814i | ||||
\(413\) | −139534. | −0.818049 | ||||||||
\(414\) | 203348. | + | 11974.0i | 1.18642 | + | 0.0698618i | ||||
\(415\) | 16224.2i | 0.0942035i | ||||||||
\(416\) | −119816. | − | 255572.i | −0.692352 | − | 1.47682i | ||||
\(417\) | −148554. | + | 92119.2i | −0.854305 | + | 0.529758i | ||||
\(418\) | 6758.04 | − | 2871.90i | 0.0386784 | − | 0.0164368i | ||||
\(419\) | −30669.6 | − | 17707.1i | −0.174695 | − | 0.100860i | 0.410103 | − | 0.912039i | \(-0.365493\pi\) |
−0.584798 | + | 0.811179i | \(0.698826\pi\) | |||||||
\(420\) | 5016.08 | + | 4540.28i | 0.0284358 | + | 0.0257385i | ||||
\(421\) | 82548.0 | + | 142977.i | 0.465739 | + | 0.806683i | 0.999235 | − | 0.0391198i | \(-0.0124554\pi\) |
−0.533496 | + | 0.845803i | \(0.679122\pi\) | |||||||
\(422\) | −55206.1 | + | 73323.7i | −0.310000 | + | 0.411737i | ||||
\(423\) | 25793.3 | + | 12800.2i | 0.144154 | + | 0.0715381i | ||||
\(424\) | 121110. | − | 316670.i | 0.673673 | − | 1.76147i | ||||
\(425\) | −82579.3 | − | 143032.i | −0.457187 | − | 0.791870i | ||||
\(426\) | −10872.8 | + | 15428.5i | −0.0599132 | + | 0.0850168i | ||||
\(427\) | 33393.2 | + | 19279.6i | 0.183148 | + | 0.105741i | ||||
\(428\) | −54422.7 | + | 219045.i | −0.297093 | + | 1.19577i | ||||
\(429\) | 10930.8 | + | 5860.23i | 0.0593931 | + | 0.0318420i | ||||
\(430\) | −13317.7 | − | 1629.65i | −0.0720264 | − | 0.00881366i | ||||
\(431\) | − | 161673.i | − | 0.870327i | −0.900351 | − | 0.435163i | \(-0.856691\pi\) | ||
0.900351 | − | 0.435163i | \(-0.143309\pi\) | |||||||
\(432\) | 172423. | + | 71405.8i | 0.923906 | + | 0.382619i | ||||
\(433\) | −61835.3 | −0.329808 | −0.164904 | − | 0.986310i | \(-0.552731\pi\) | ||||
−0.164904 | + | 0.986310i | \(0.552731\pi\) | |||||||
\(434\) | −15460.1 | + | 126342.i | −0.0820791 | + | 0.670761i | ||||
\(435\) | 5518.35 | − | 10293.1i | 0.0291629 | − | 0.0543960i | ||||
\(436\) | −253544. | − | 62994.2i | −1.33377 | − | 0.331381i | ||||
\(437\) | −115428. | + | 199927.i | −0.604434 | + | 1.04691i | ||||
\(438\) | 43913.6 | + | 30946.9i | 0.228903 | + | 0.161313i | ||||
\(439\) | −268021. | + | 154742.i | −1.39072 | + | 0.802933i | −0.993395 | − | 0.114744i | \(-0.963395\pi\) |
−0.397326 | + | 0.917677i | \(0.630062\pi\) | |||||||
\(440\) | 606.933 | + | 232.121i | 0.00313499 | + | 0.00119897i | ||||
\(441\) | 150829. | − | 9506.54i | 0.775548 | − | 0.0488816i | ||||
\(442\) | 234312. | + | 176416.i | 1.19936 | + | 0.903011i | ||||
\(443\) | 40615.5 | − | 23449.4i | 0.206959 | − | 0.119488i | −0.392938 | − | 0.919565i | \(-0.628541\pi\) |
0.599897 | + | 0.800077i | \(0.295208\pi\) | |||||||
\(444\) | 141683. | − | 156531.i | 0.718709 | − | 0.794027i | ||||
\(445\) | −8997.07 | + | 15583.4i | −0.0454340 | + | 0.0786940i | ||||
\(446\) | −100531. | − | 236566.i | −0.505396 | − | 1.18928i | ||||
\(447\) | −2937.27 | − | 4736.74i | −0.0147004 | − | 0.0237063i | ||||
\(448\) | 92737.3 | + | 19472.8i | 0.462060 | + | 0.0970226i | ||||
\(449\) | −124857. | −0.619328 | −0.309664 | − | 0.950846i | \(-0.600217\pi\) | ||||
−0.309664 | + | 0.950846i | \(0.600217\pi\) | |||||||
\(450\) | 167999. | + | 110649.i | 0.829625 | + | 0.546413i | ||||
\(451\) | 5929.43i | 0.0291514i | ||||||||
\(452\) | 131294. | − | 136183.i | 0.642639 | − | 0.666569i | ||||
\(453\) | 1228.96 | + | 39035.8i | 0.00598883 | + | 0.190224i | ||||
\(454\) | −10490.1 | − | 24685.0i | −0.0508944 | − | 0.119763i | ||||
\(455\) | −11216.0 | − | 6475.56i | −0.0541771 | − | 0.0312791i | ||||
\(456\) | −159929. | + | 138407.i | −0.769125 | + | 0.665625i | ||||
\(457\) | 62748.5 | + | 108684.i | 0.300449 | + | 0.520393i | 0.976238 | − | 0.216703i | \(-0.0695302\pi\) |
−0.675789 | + | 0.737095i | \(0.736197\pi\) | |||||||
\(458\) | −113602. | − | 85532.1i | −0.541571 | − | 0.407754i | ||||
\(459\) | −193057. | + | 18282.4i | −0.916348 | + | 0.0867775i | ||||
\(460\) | −19633.3 | + | 5647.25i | −0.0927852 | + | 0.0266883i | ||||
\(461\) | −51647.4 | − | 89455.9i | −0.243022 | − | 0.420927i | 0.718551 | − | 0.695474i | \(-0.244806\pi\) |
−0.961574 | + | 0.274547i | \(0.911472\pi\) | |||||||
\(462\) | −3778.91 | + | 1748.25i | −0.0177044 | + | 0.00819066i | ||||
\(463\) | −277564. | − | 160252.i | −1.29480 | − | 0.747552i | −0.315297 | − | 0.948993i | \(-0.602104\pi\) |
−0.979501 | + | 0.201442i | \(0.935437\pi\) | |||||||
\(464\) | −5977.62 | − | 163465.i | −0.0277646 | − | 0.759257i | ||||
\(465\) | −791.122 | − | 25128.6i | −0.00365879 | − | 0.116215i | ||||
\(466\) | −30336.1 | + | 247910.i | −0.139697 | + | 1.14162i | ||||
\(467\) | 427381.i | 1.95967i | 0.199820 | + | 0.979833i | \(0.435964\pi\) | ||||
−0.199820 | + | 0.979833i | \(0.564036\pi\) | |||||||
\(468\) | −351431. | − | 64159.8i | −1.60453 | − | 0.292935i | ||||
\(469\) | −50979.2 | −0.231765 | ||||||||
\(470\) | −2866.49 | − | 350.764i | −0.0129764 | − | 0.00158788i | ||||
\(471\) | 29443.6 | + | 47481.7i | 0.132724 | + | 0.214035i | ||||
\(472\) | 299684. | − | 243292.i | 1.34518 | − | 1.09205i | ||||
\(473\) | 4128.49 | − | 7150.76i | 0.0184531 | − | 0.0319617i | ||||
\(474\) | 184161. | + | 16673.1i | 0.819674 | + | 0.0742094i | ||||
\(475\) | −197438. | + | 113991.i | −0.875071 | + | 0.505223i | ||||
\(476\) | −94627.9 | + | 27218.4i | −0.417643 | + | 0.120129i | ||||
\(477\) | −237499. | − | 357377.i | −1.04382 | − | 1.57069i | ||||
\(478\) | −9030.61 | + | 11994.3i | −0.0395240 | + | 0.0524951i | ||||
\(479\) | 166330. | − | 96030.5i | 0.724935 | − | 0.418541i | −0.0916316 | − | 0.995793i | \(-0.529208\pi\) |
0.816566 | + | 0.577252i | \(0.195875\pi\) | |||||||
\(480\) | −18689.8 | − | 1005.30i | −0.0811188 | − | 0.00436330i | ||||
\(481\) | −202076. | + | 350006.i | −0.873422 | + | 1.51281i | ||||
\(482\) | −330091. | + | 140276.i | −1.42082 | + | 0.603793i | ||||
\(483\) | 61852.1 | − | 115369.i | 0.265131 | − | 0.494534i | ||||
\(484\) | 162312. | − | 168356.i | 0.692882 | − | 0.718682i | ||||
\(485\) | −13848.1 | −0.0588715 | ||||||||
\(486\) | 200219. | − | 125304.i | 0.847680 | − | 0.530508i | ||||
\(487\) | 52885.1i | 0.222985i | 0.993765 | + | 0.111492i | \(0.0355631\pi\) | ||||
−0.993765 | + | 0.111492i | \(0.964437\pi\) | |||||||
\(488\) | −105337. | + | 16816.9i | −0.442323 | + | 0.0706167i | ||||
\(489\) | −125777. | − | 67432.0i | −0.525999 | − | 0.282000i | ||||
\(490\) | −13949.6 | + | 5928.02i | −0.0580991 | + | 0.0246898i | ||||
\(491\) | −6368.89 | − | 3677.08i | −0.0264180 | − | 0.0152525i | 0.486733 | − | 0.873551i | \(-0.338189\pi\) |
−0.513151 | + | 0.858298i | \(0.671522\pi\) | |||||||
\(492\) | −52352.5 | − | 162568.i | −0.216275 | − | 0.671590i | ||||
\(493\) | 84984.9 | + | 147198.i | 0.349662 | + | 0.605632i | ||||
\(494\) | 243521. | − | 323440.i | 0.997890 | − | 1.32538i | ||||
\(495\) | 684.952 | − | 455.193i | 0.00279544 | − | 0.00185774i | ||||
\(496\) | −187086. | − | 298308.i | −0.760465 | − | 1.21255i | ||||
\(497\) | 6064.75 | + | 10504.4i | 0.0245527 | + | 0.0425266i | ||||
\(498\) | 286420. | + | 25931.2i | 1.15490 | + | 0.104559i | ||||
\(499\) | 359442. | + | 207524.i | 1.44354 | + | 0.833426i | 0.998084 | − | 0.0618804i | \(-0.0197097\pi\) |
0.445452 | + | 0.895306i | \(0.353043\pi\) | |||||||
\(500\) | −39289.5 | − | 9761.65i | −0.157158 | − | 0.0390466i | ||||
\(501\) | −3204.80 | + | 1987.31i | −0.0127681 | + | 0.00791756i | ||||
\(502\) | −36712.1 | − | 4492.35i | −0.145681 | − | 0.0178265i | ||||
\(503\) | 53242.3i | 0.210436i | 0.994449 | + | 0.105218i | \(0.0335541\pi\) | ||||
−0.994449 | + | 0.105218i | \(0.966446\pi\) | |||||||
\(504\) | 88170.8 | − | 81296.7i | 0.347107 | − | 0.320046i | ||||
\(505\) | −6277.63 | −0.0246157 | ||||||||
\(506\) | 1527.07 | − | 12479.4i | 0.00596426 | − | 0.0487408i | ||||
\(507\) | 426577. | − | 13429.9i | 1.65952 | − | 0.0522465i | ||||
\(508\) | −80940.1 | + | 325775.i | −0.313644 | + | 1.26238i | ||||
\(509\) | 248630. | − | 430640.i | 0.959662 | − | 1.66218i | 0.236344 | − | 0.971669i | \(-0.424051\pi\) |
0.723319 | − | 0.690515i | \(-0.242616\pi\) | |||||||
\(510\) | 17651.2 | − | 8166.02i | 0.0678631 | − | 0.0313957i | ||||
\(511\) | 29898.4 | − | 17261.9i | 0.114500 | − | 0.0661068i | ||||
\(512\) | −233130. | + | 119875.i | −0.889320 | + | 0.457286i | ||||
\(513\) | 25236.6 | + | 266492.i | 0.0958952 | + | 1.01263i | ||||
\(514\) | −48730.9 | − | 36689.9i | −0.184450 | − | 0.138874i | ||||
\(515\) | 19109.5 | − | 11032.9i | 0.0720501 | − | 0.0415981i | ||||
\(516\) | −50055.3 | + | 232504.i | −0.187997 | + | 0.873236i | ||||
\(517\) | 888.614 | − | 1539.12i | 0.00332454 | − | 0.00575828i | ||||
\(518\) | −53065.4 | − | 124871.i | −0.197766 | − | 0.465375i | ||||
\(519\) | −172722. | + | 5437.79i | −0.641227 | + | 0.0201877i | ||||
\(520\) | 35380.1 | − | 5648.42i | 0.130843 | − | 0.0208891i | ||||
\(521\) | −58965.8 | −0.217233 | −0.108616 | − | 0.994084i | \(-0.534642\pi\) | ||||
−0.108616 | + | 0.994084i | \(0.534642\pi\) | |||||||
\(522\) | −172893. | − | 113872.i | −0.634507 | − | 0.417903i | ||||
\(523\) | 117488.i | 0.429527i | 0.976666 | + | 0.214763i | \(0.0688980\pi\) | ||||
−0.976666 | + | 0.214763i | \(0.931102\pi\) | |||||||
\(524\) | 328840. | + | 317035.i | 1.19763 | + | 1.15463i | ||||
\(525\) | 109865. | − | 68127.8i | 0.398603 | − | 0.247176i | ||||
\(526\) | 161638. | + | 380361.i | 0.584215 | + | 1.37475i | ||||
\(527\) | 316868. | + | 182944.i | 1.14093 | + | 0.658714i | ||||
\(528\) | 5067.90 | − | 10343.7i | 0.0181786 | − | 0.0371031i | ||||
\(529\) | 57713.8 | + | 99963.2i | 0.206238 | + | 0.357214i | ||||
\(530\) | 34379.8 | + | 25884.8i | 0.122391 | + | 0.0921497i | ||||
\(531\) | −30731.0 | − | 487573.i | −0.108990 | − | 1.72922i | ||||
\(532\) | 37571.7 | + | 130623.i | 0.132751 | + | 0.461525i | ||||
\(533\) | 163465. | + | 283129.i | 0.575399 | + | 0.996620i | ||||
\(534\) | 260727. | + | 183740.i | 0.914333 | + | 0.644350i | ||||
\(535\) | −24810.8 | − | 14324.5i | −0.0866828 | − | 0.0500463i | ||||
\(536\) | 109491. | − | 88887.9i | 0.381108 | − | 0.309395i | ||||
\(537\) | −395185. | − | 211867.i | −1.37041 | − | 0.734709i | ||||
\(538\) | 41791.3 | − | 341524.i | 0.144385 | − | 1.17993i | ||||
\(539\) | − | 9327.75i | − | 0.0321070i | ||||||
\(540\) | −14760.4 | + | 18527.7i | −0.0506185 | + | 0.0635380i | ||||
\(541\) | −16461.8 | −0.0562448 | −0.0281224 | − | 0.999604i | \(-0.508953\pi\) | ||||
−0.0281224 | + | 0.999604i | \(0.508953\pi\) | |||||||
\(542\) | 62053.1 | + | 7593.26i | 0.211235 | + | 0.0258482i | ||||
\(543\) | −59410.5 | + | 110815.i | −0.201495 | + | 0.375837i | ||||
\(544\) | 155779. | − | 223453.i | 0.526395 | − | 0.755071i | ||||
\(545\) | 16580.6 | − | 28718.4i | 0.0558222 | − | 0.0966869i | ||||
\(546\) | −132246. | + | 187656.i | −0.443604 | + | 0.629474i | ||||
\(547\) | −337391. | + | 194793.i | −1.12761 | + | 0.651026i | −0.943333 | − | 0.331848i | \(-0.892328\pi\) |
−0.184277 | + | 0.982874i | \(0.558994\pi\) | |||||||
\(548\) | −2737.18 | − | 9516.13i | −0.00911470 | − | 0.0316883i | ||||
\(549\) | −60014.2 | + | 120932.i | −0.199118 | + | 0.401234i | ||||
\(550\) | 7468.01 | − | 9918.87i | 0.0246876 | − | 0.0327897i | ||||
\(551\) | 203189. | − | 117312.i | 0.669265 | − | 0.386400i | ||||
\(552\) | 68316.1 | + | 355631.i | 0.224205 | + | 1.16714i | ||||
\(553\) | 59415.7 | − | 102911.i | 0.194290 | − | 0.336521i | ||||
\(554\) | −208420. | + | 88570.1i | −0.679077 | + | 0.288581i | ||||
\(555\) | 14123.3 | + | 22775.6i | 0.0458510 | + | 0.0739407i | ||||
\(556\) | −223714. | − | 215682.i | −0.723674 | − | 0.697694i | ||||
\(557\) | 434133. | 1.39931 | 0.699653 | − | 0.714483i | \(-0.253338\pi\) | ||||
0.699653 | + | 0.714483i | \(0.253338\pi\) | |||||||
\(558\) | −444882. | − | 26196.6i | −1.42882 | − | 0.0841350i | ||||
\(559\) | − | 455263.i | − | 1.45693i | ||||||
\(560\) | −5629.31 | + | 10629.3i | −0.0179506 | + | 0.0338946i | ||||
\(561\) | 376.630 | + | 11963.0i | 0.00119671 | + | 0.0380113i | ||||
\(562\) | 408879. | − | 173758.i | 1.29456 | − | 0.550137i | ||||
\(563\) | −192477. | − | 111127.i | −0.607244 | − | 0.350592i | 0.164642 | − | 0.986353i | \(-0.447353\pi\) |
−0.771886 | + | 0.635761i | \(0.780686\pi\) | |||||||
\(564\) | −10773.9 | + | 50044.1i | −0.0338698 | + | 0.157324i | ||||
\(565\) | 12005.6 | + | 20794.2i | 0.0376084 | + | 0.0651397i | ||||
\(566\) | −219417. | + | 291425.i | −0.684916 | + | 0.909692i | ||||
\(567\) | −19058.0 | − | 150585.i | −0.0592805 | − | 0.468400i | ||||
\(568\) | −31341.2 | − | 11986.4i | −0.0971448 | − | 0.0371529i | ||||
\(569\) | −1962.56 | − | 3399.25i | −0.00606175 | − | 0.0104993i | 0.862979 | − | 0.505240i | \(-0.168596\pi\) |
−0.869040 | + | 0.494741i | \(0.835263\pi\) | |||||||
\(570\) | −11272.2 | − | 24365.3i | −0.0346944 | − | 0.0749934i | ||||
\(571\) | −331554. | − | 191423.i | −1.01691 | − | 0.587112i | −0.103702 | − | 0.994608i | \(-0.533069\pi\) |
−0.913207 | + | 0.407496i | \(0.866402\pi\) | |||||||
\(572\) | −5316.54 | + | 21398.5i | −0.0162494 | + | 0.0654020i | ||||
\(573\) | 8827.80 | + | 280399.i | 0.0268871 | + | 0.854019i | ||||
\(574\) | −108942. | − | 13330.9i | −0.330652 | − | 0.0404609i | ||||
\(575\) | 390347.i | 1.18063i | ||||||||
\(576\) | −47619.5 | + | 328341.i | −0.143529 | + | 0.989646i | ||||
\(577\) | 18219.2 | 0.0547239 | 0.0273620 | − | 0.999626i | \(-0.491289\pi\) | ||||
0.0273620 | + | 0.999626i | \(0.491289\pi\) | |||||||
\(578\) | 6199.39 | − | 50662.3i | 0.0185564 | − | 0.151645i | ||||
\(579\) | −128045. | − | 206489.i | −0.381948 | − | 0.615941i | ||||
\(580\) | 20150.1 | + | 5006.38i | 0.0598992 | + | 0.0148822i | ||||
\(581\) | 92407.6 | − | 160055.i | 0.273751 | − | 0.474150i | ||||
\(582\) | −22133.4 | + | 244472.i | −0.0653433 | + | 0.721745i | ||||
\(583\) | −22935.9 | + | 13242.0i | −0.0674806 | + | 0.0389599i | ||||
\(584\) | −34116.5 | + | 89205.4i | −0.100032 | + | 0.261556i | ||||
\(585\) | 20157.4 | − | 40618.3i | 0.0589009 | − | 0.118689i | ||||
\(586\) | −265277. | − | 199730.i | −0.772510 | − | 0.581630i | ||||
\(587\) | −45835.0 | + | 26462.8i | −0.133021 | + | 0.0767998i | −0.565034 | − | 0.825068i | \(-0.691137\pi\) |
0.432013 | + | 0.901868i | \(0.357804\pi\) | |||||||
\(588\) | 82357.1 | + | 255739.i | 0.238202 | + | 0.739678i | ||||
\(589\) | 252532. | − | 437399.i | 0.727924 | − | 1.26080i | ||||
\(590\) | 19163.0 | + | 45093.6i | 0.0550503 | + | 0.129542i | ||||
\(591\) | −44295.9 | + | 82622.8i | −0.126820 | + | 0.236551i | ||||
\(592\) | 331698. | + | 175668.i | 0.946455 | + | 0.501243i | ||||
\(593\) | 216280. | 0.615046 | 0.307523 | − | 0.951541i | \(-0.400500\pi\) | ||||
0.307523 | + | 0.951541i | \(0.400500\pi\) | |||||||
\(594\) | −6941.17 | − | 12819.6i | −0.0196725 | − | 0.0363331i | ||||
\(595\) | − | 12498.3i | − | 0.0353033i | ||||||
\(596\) | 6877.16 | − | 7133.24i | 0.0193605 | − | 0.0200814i | ||||
\(597\) | 66935.4 | + | 35885.6i | 0.187805 | + | 0.100686i | ||||
\(598\) | −271119. | − | 637986.i | −0.758154 | − | 1.78406i | ||||
\(599\) | −260151. | − | 150198.i | −0.725057 | − | 0.418612i | 0.0915543 | − | 0.995800i | \(-0.470816\pi\) |
−0.816611 | + | 0.577188i | \(0.804150\pi\) | |||||||
\(600\) | −117175. | + | 337883.i | −0.325485 | + | 0.938565i | ||||
\(601\) | −255485. | − | 442514.i | −0.707322 | − | 1.22512i | −0.965847 | − | 0.259113i | \(-0.916570\pi\) |
0.258525 | − | 0.966005i | \(-0.416764\pi\) | |||||||
\(602\) | 122099. | + | 91929.8i | 0.336915 | + | 0.253667i | ||||
\(603\) | −11227.7 | − | 178137.i | −0.0308785 | − | 0.489913i | ||||
\(604\) | −66725.9 | + | 19192.8i | −0.182903 | + | 0.0526094i | ||||
\(605\) | 14841.8 | + | 25706.8i | 0.0405487 | + | 0.0702324i | ||||
\(606\) | −10033.5 | + | 110825.i | −0.0273218 | + | 0.301780i | ||||
\(607\) | 154217. | + | 89037.5i | 0.418558 | + | 0.241655i | 0.694460 | − | 0.719531i | \(-0.255643\pi\) |
−0.275902 | + | 0.961186i | \(0.588976\pi\) | |||||||
\(608\) | −308450. | − | 215035.i | −0.834405 | − | 0.581703i | ||||
\(609\) | −113065. | + | 70112.4i | −0.304856 | + | 0.189043i | ||||
\(610\) | 1644.56 | − | 13439.6i | 0.00441968 | − | 0.0361182i | ||||
\(611\) | − | 97990.4i | − | 0.262483i | ||||||
\(612\) | −115950. | − | 324664.i | −0.309577 | − | 0.866825i | ||||
\(613\) | 570495. | 1.51821 | 0.759103 | − | 0.650970i | \(-0.225638\pi\) | ||||
0.759103 | + | 0.650970i | \(0.225638\pi\) | |||||||
\(614\) | −258876. | − | 31677.9i | −0.686681 | − | 0.0840272i | ||||
\(615\) | 21667.8 | − | 682.167i | 0.0572881 | − | 0.00180360i | ||||
\(616\) | −4665.42 | − | 5746.80i | −0.0122950 | − | 0.0151448i | ||||
\(617\) | −107951. | + | 186976.i | −0.283567 | + | 0.491153i | −0.972261 | − | 0.233900i | \(-0.924851\pi\) |
0.688694 | + | 0.725052i | \(0.258185\pi\) | |||||||
\(618\) | −164230. | − | 354991.i | −0.430008 | − | 0.929480i | ||||
\(619\) | 158318. | − | 91404.9i | 0.413189 | − | 0.238555i | −0.278970 | − | 0.960300i | \(-0.589993\pi\) |
0.692159 | + | 0.721745i | \(0.256660\pi\) | |||||||
\(620\) | 42953.6 | − | 12355.0i | 0.111742 | − | 0.0321410i | ||||
\(621\) | 416758. | + | 190721.i | 1.08069 | + | 0.494556i | ||||
\(622\) | −321672. | + | 427238.i | −0.831442 | + | 1.10431i | ||||
\(623\) | 177515. | − | 102489.i | 0.457362 | − | 0.264058i | ||||
\(624\) | −43168.6 | − | 633624.i | −0.110866 | − | 1.62728i | ||||
\(625\) | −191454. | + | 331608.i | −0.490123 | + | 0.848918i | ||||
\(626\) | 41378.9 | − | 17584.4i | 0.105592 | − | 0.0448724i | ||||
\(627\) | 16513.4 | − | 519.893i | 0.0420052 | − | 0.00132245i | ||||
\(628\) | −68937.6 | + | 71504.6i | −0.174798 | + | 0.181307i | ||||
\(629\) | −390019. | −0.985791 | ||||||||
\(630\) | 6823.34 | + | 13608.0i | 0.0171916 | + | 0.0342858i | ||||
\(631\) | 153307.i | 0.385037i | 0.981293 | + | 0.192518i | \(0.0616655\pi\) | ||||
−0.981293 | + | 0.192518i | \(0.938335\pi\) | |||||||
\(632\) | 51826.4 | + | 324626.i | 0.129753 | + | 0.812734i | ||||
\(633\) | −175506. | + | 108832.i | −0.438011 | + | 0.271613i | ||||
\(634\) | −144333. | + | 61335.7i | −0.359076 | + | 0.152593i | ||||
\(635\) | −36899.8 | − | 21304.1i | −0.0915117 | − | 0.0528343i | ||||
\(636\) | 511918. | − | 565565.i | 1.26557 | − | 1.39820i | ||||
\(637\) | −257150. | − | 445397.i | −0.633736 | − | 1.09766i | ||||
\(638\) | −7685.56 | + | 10207.8i | −0.0188814 | + | 0.0250779i | ||||
\(639\) | −35370.0 | + | 23505.6i | −0.0866231 | + | 0.0575664i | ||||
\(640\) | −6443.06 | − | 32644.5i | −0.0157301 | − | 0.0796986i | ||||
\(641\) | −196626. | − | 340566.i | −0.478547 | − | 0.828869i | 0.521150 | − | 0.853465i | \(-0.325503\pi\) |
−0.999697 | + | 0.0245966i | \(0.992170\pi\) | |||||||
\(642\) | −292539. | + | 415112.i | −0.709763 | + | 1.00715i | ||||
\(643\) | 384971. | + | 222263.i | 0.931120 | + | 0.537583i | 0.887166 | − | 0.461451i | \(-0.152671\pi\) |
0.0439545 | + | 0.999034i | \(0.486004\pi\) | |||||||
\(644\) | 225851. | + | 56113.7i | 0.544566 | + | 0.135300i | ||||
\(645\) | −26605.9 | − | 14264.0i | −0.0639525 | − | 0.0342864i | ||||
\(646\) | 387815. | + | 47455.8i | 0.929309 | + | 0.113717i | ||||
\(647\) | 152505.i | 0.364314i | 0.983269 | + | 0.182157i | \(0.0583079\pi\) | ||||
−0.983269 | + | 0.182157i | \(0.941692\pi\) | |||||||
\(648\) | 303494. | + | 290191.i | 0.722770 | + | 0.691088i | ||||
\(649\) | −30153.0 | −0.0715881 | ||||||||
\(650\) | 83148.9 | − | 679504.i | 0.196802 | − | 1.60829i | ||||
\(651\) | −135319. | + | 252404.i | −0.319299 | + | 0.595572i | ||||
\(652\) | 61176.0 | − | 246226.i | 0.143908 | − | 0.579214i | ||||
\(653\) | 149617. | − | 259144.i | 0.350876 | − | 0.607736i | −0.635527 | − | 0.772079i | \(-0.719217\pi\) |
0.986403 | + | 0.164343i | \(0.0525504\pi\) | |||||||
\(654\) | −480492. | − | 338613.i | −1.12339 | − | 0.791677i | ||||
\(655\) | −50211.7 | + | 28989.8i | −0.117037 | + | 0.0675713i | ||||
\(656\) | 257224. | − | 161321.i | 0.597728 | − | 0.374871i | ||||
\(657\) | 66903.0 | + | 100672.i | 0.154994 | + | 0.233227i | ||||
\(658\) | 26280.6 | + | 19786.9i | 0.0606992 | + | 0.0457010i | ||||
\(659\) | −361192. | + | 208535.i | −0.831702 | + | 0.480183i | −0.854435 | − | 0.519558i | \(-0.826097\pi\) |
0.0227330 | + | 0.999742i | \(0.492763\pi\) | |||||||
\(660\) | 1083.97 | + | 981.145i | 0.00248844 | + | 0.00225240i | ||||
\(661\) | −379775. | + | 657790.i | −0.869208 | + | 1.50551i | −0.00639999 | + | 0.999980i | \(0.502037\pi\) |
−0.862808 | + | 0.505532i | \(0.831296\pi\) | |||||||
\(662\) | 116944. | + | 275188.i | 0.266847 | + | 0.627933i | ||||
\(663\) | 347783. | + | 560846.i | 0.791191 | + | 1.27590i | ||||
\(664\) | 80604.0 | + | 504881.i | 0.182819 | + | 1.14512i | ||||
\(665\) | −17252.3 | −0.0390126 | ||||||||
\(666\) | 424651. | − | 212928.i | 0.957380 | − | 0.480048i | ||||
\(667\) | − | 401718.i | − | 0.902962i | ||||||
\(668\) | −4826.24 | − | 4652.98i | −0.0108157 | − | 0.0104275i | ||||
\(669\) | −18198.9 | − | 578056.i | −0.0406625 | − | 1.29157i | ||||
\(670\) | 7001.28 | + | 16475.1i | 0.0155965 | + | 0.0367011i | ||||
\(671\) | 7216.22 | + | 4166.29i | 0.0160275 | + | 0.00925346i | ||||
\(672\) | 178652. | + | 116368.i | 0.395612 | + | 0.257689i | ||||
\(673\) | 18836.0 | + | 32624.9i | 0.0415871 | + | 0.0720309i | 0.886070 | − | 0.463552i | \(-0.153425\pi\) |
−0.844483 | + | 0.535583i | \(0.820092\pi\) | |||||||
\(674\) | 453184. | + | 341207.i | 0.997597 | + | 0.751100i | ||||
\(675\) | 262256. | + | 368897.i | 0.575596 | + | 0.809651i | ||||
\(676\) | 209735. | + | 729170.i | 0.458964 | + | 1.59564i | ||||
\(677\) | 347010. | + | 601039.i | 0.757120 | + | 1.31137i | 0.944313 | + | 0.329047i | \(0.106728\pi\) |
−0.187193 | + | 0.982323i | \(0.559939\pi\) | |||||||
\(678\) | 386288. | − | 178710.i | 0.840334 | − | 0.388766i | ||||
\(679\) | 136614. | + | 78873.9i | 0.296315 | + | 0.171078i | ||||
\(680\) | 21792.1 | + | 26843.2i | 0.0471282 | + | 0.0580519i | ||||
\(681\) | −1899.01 | − | 60318.5i | −0.00409479 | − | 0.130064i | ||||
\(682\) | −3340.90 | + | 27302.3i | −0.00718281 | + | 0.0586989i | ||||
\(683\) | − | 357197.i | − | 0.765714i | −0.923808 | − | 0.382857i | \(-0.874940\pi\) | ||
0.923808 | − | 0.382857i | \(-0.125060\pi\) | |||||||
\(684\) | −448160. | + | 160055.i | −0.957901 | + | 0.342104i | ||||
\(685\) | 1256.87 | 0.00267861 | ||||||||
\(686\) | 391920. | + | 47958.0i | 0.832815 | + | 0.101909i | ||||
\(687\) | −168616. | − | 271916.i | −0.357261 | − | 0.576131i | ||||
\(688\) | −422529. | + | 15451.1i | −0.892647 | + | 0.0326425i | ||||
\(689\) | −730122. | + | 1.26461e6i | −1.53800 | + | 2.66390i | ||||
\(690\) | −45778.9 | − | 4144.60i | −0.0961539 | − | 0.00870532i | ||||
\(691\) | 384473. | − | 221976.i | 0.805212 | − | 0.464889i | −0.0400786 | − | 0.999197i | \(-0.512761\pi\) |
0.845290 | + | 0.534307i | \(0.179427\pi\) | |||||||
\(692\) | −84922.2 | − | 295242.i | −0.177341 | − | 0.616547i | ||||
\(693\) | −9349.80 | + | 589.303i | −0.0194686 | + | 0.00122708i | ||||
\(694\) | 440359. | − | 584876.i | 0.914297 | − | 1.21435i | ||||
\(695\) | 34159.6 | − | 19722.1i | 0.0707202 | − | 0.0408304i | ||||
\(696\) | 120588. | − | 347726.i | 0.248935 | − | 0.717826i | ||||
\(697\) | −157749. | + | 273228.i | −0.324713 | + | 0.562420i | ||||
\(698\) | 495358. | − | 210508.i | 1.01674 | − | 0.432073i | ||||
\(699\) | −265526. | + | 495272.i | −0.543442 | + | 1.01365i | ||||
\(700\) | 165450. | + | 159510.i | 0.337653 | + | 0.325531i | ||||
\(701\) | −483771. | −0.984474 | −0.492237 | − | 0.870461i | \(-0.663821\pi\) | ||||
−0.492237 | + | 0.870461i | \(0.663821\pi\) | |||||||
\(702\) | −684854. | − | 420777.i | −1.38971 | − | 0.853842i | ||||
\(703\) | 538375.i | 1.08937i | ||||||||
\(704\) | 20040.4 | + | 4208.04i | 0.0404353 | + | 0.00849053i | ||||
\(705\) | −5726.62 | − | 3070.17i | −0.0115218 | − | 0.00617710i | ||||
\(706\) | −737299. | + | 313323.i | −1.47922 | + | 0.628612i | ||||
\(707\) | 61929.9 | + | 35755.3i | 0.123897 | + | 0.0715321i | ||||
\(708\) | 826707. | − | 266229.i | 1.64924 | − | 0.531114i | ||||
\(709\) | −79169.5 | − | 137126.i | −0.157494 | − | 0.272788i | 0.776470 | − | 0.630154i | \(-0.217008\pi\) |
−0.933965 | + | 0.357366i | \(0.883675\pi\) | |||||||
\(710\) | 2561.85 | − | 3402.60i | 0.00508203 | − | 0.00674986i | ||||
\(711\) | 372688. | + | 184951.i | 0.737236 | + | 0.365863i | ||||
\(712\) | −202559. | + | 529638.i | −0.399569 | + | 1.04477i | ||||
\(713\) | −432382. | − | 748907.i | −0.850527 | − | 1.47316i | ||||
\(714\) | −220643. | − | 19976.0i | −0.432807 | − | 0.0391843i | ||||
\(715\) | −2423.76 | − | 1399.36i | −0.00474108 | − | 0.00273726i | ||||
\(716\) | 192211. | − | 773627.i | 0.374932 | − | 1.50906i | ||||
\(717\) | −28709.3 | + | 17802.8i | −0.0558450 | + | 0.0346297i | ||||
\(718\) | 639941. | + | 78307.7i | 1.24134 | + | 0.151899i | ||||
\(719\) | − | 781622.i | − | 1.51196i | −0.654597 | − | 0.755978i | \(-0.727162\pi\) | ||
0.654597 | − | 0.755978i | \(-0.272838\pi\) | |||||||
\(720\) | −38382.0 | − | 17329.5i | −0.0740393 | − | 0.0334288i | ||||
\(721\) | −251358. | −0.483529 | ||||||||
\(722\) | 2191.38 | − | 17908.3i | 0.00420381 | − | 0.0343541i | ||||
\(723\) | −806587. | + | 25393.8i | −1.54303 | + | 0.0485792i | ||||
\(724\) | −216936. | − | 53898.7i | −0.413861 | − | 0.102826i | ||||
\(725\) | 198358. | − | 343566.i | 0.377375 | − | 0.653633i | ||||
\(726\) | 477548. | − | 220929.i | 0.906032 | − | 0.419160i | ||||
\(727\) | 51590.1 | − | 29785.6i | 0.0976107 | − | 0.0563556i | −0.450400 | − | 0.892827i | \(-0.648719\pi\) |
0.548011 | + | 0.836471i | \(0.315385\pi\) | |||||||
\(728\) | −381202. | − | 145790.i | −0.719271 | − | 0.275085i | ||||
\(729\) | 521994. | − | 99759.6i | 0.982223 | − | 0.187715i | ||||
\(730\) | −9684.71 | − | 7291.71i | −0.0181736 | − | 0.0136831i | ||||
\(731\) | 380482. | − | 219672.i | 0.712032 | − | 0.411092i | ||||
\(732\) | −234633. | − | 50513.5i | −0.437892 | − | 0.0942726i | ||||
\(733\) | 106923. | − | 185196.i | 0.199004 | − | 0.344685i | −0.749202 | − | 0.662342i | \(-0.769563\pi\) |
0.948206 | + | 0.317657i | \(0.102896\pi\) | |||||||
\(734\) | 312207. | + | 734674.i | 0.579497 | + | 1.36365i | ||||
\(735\) | −34086.2 | + | 1073.13i | −0.0630963 | + | 0.00198646i | ||||
\(736\) | −582914. | + | 273278.i | −1.07609 | + | 0.504486i | ||||
\(737\) | −11016.5 | −0.0202819 | ||||||||
\(738\) | 22588.8 | − | 383612.i | 0.0414744 | − | 0.704335i | ||||
\(739\) | − | 218903.i | − | 0.400832i | −0.979711 | − | 0.200416i | \(-0.935771\pi\) | ||
0.979711 | − | 0.200416i | \(-0.0642294\pi\) | |||||||
\(740\) | −33067.3 | + | 34298.7i | −0.0603860 | + | 0.0626345i | ||||
\(741\) | 774180. | − | 480073.i | 1.40996 | − | 0.874320i | ||||
\(742\) | −191731. | − | 451174.i | −0.348245 | − | 0.819476i | ||||
\(743\) | −431487. | − | 249119.i | −0.781610 | − | 0.451263i | 0.0553907 | − | 0.998465i | \(-0.482360\pi\) |
−0.837001 | + | 0.547202i | \(0.815693\pi\) | |||||||
\(744\) | −149461. | − | 778045.i | −0.270012 | − | 1.40559i | ||||
\(745\) | 628.850 | + | 1089.20i | 0.00113301 | + | 0.00196243i | ||||
\(746\) | 18497.9 | + | 13927.3i | 0.0332388 | + | 0.0250258i | ||||
\(747\) | 579631. | + | 287650.i | 1.03875 | + | 0.515493i | ||||
\(748\) | −20448.9 | + | 5881.85i | −0.0365483 | + | 0.0105126i | ||||
\(749\) | 163175. | + | 282628.i | 0.290864 | + | 0.503792i | ||||
\(750\) | −74457.5 | − | 52471.8i | −0.132369 | − | 0.0932833i | ||||
\(751\) | 534346. | + | 308505.i | 0.947421 | + | 0.546994i | 0.892279 | − | 0.451485i | \(-0.149106\pi\) |
0.0551419 | + | 0.998479i | \(0.482439\pi\) | |||||||
\(752\) | −90944.9 | + | 3325.69i | −0.160821 | + | 0.00588093i | ||||
\(753\) | −73342.9 | − | 39320.8i | −0.129350 | − | 0.0693477i | ||||
\(754\) | −85571.1 | + | 699299.i | −0.150517 | + | 1.23004i | ||||
\(755\) | − | 8813.01i | − | 0.0154607i | ||||||
\(756\) | 251141. | − | 98708.7i | 0.439414 | − | 0.172708i | ||||
\(757\) | 483106. | 0.843045 | 0.421523 | − | 0.906818i | \(-0.361496\pi\) | ||||
0.421523 | + | 0.906818i | \(0.361496\pi\) | |||||||
\(758\) | −865266. | − | 105880.i | −1.50595 | − | 0.184279i | ||||
\(759\) | 13366.1 | − | 24931.1i | 0.0232018 | − | 0.0432771i | ||||
\(760\) | 37053.8 | − | 30081.4i | 0.0641513 | − | 0.0520799i | ||||
\(761\) | 68847.3 | − | 119247.i | 0.118882 | − | 0.205910i | −0.800443 | − | 0.599409i | \(-0.795402\pi\) |
0.919325 | + | 0.393499i | \(0.128736\pi\) | |||||||
\(762\) | −435078. | + | 617375.i | −0.749302 | + | 1.06326i | ||||
\(763\) | −327141. | + | 188875.i | −0.561935 | + | 0.324433i | ||||
\(764\) | −479301. | + | 137864.i | −0.821148 | + | 0.236192i | ||||
\(765\) | 43672.7 | − | 2752.62i | 0.0746255 | − | 0.00470353i | ||||
\(766\) | −167209. | + | 222084.i | −0.284972 | + | 0.378494i | ||||
\(767\) | −1.43980e6 | + | 831268.i | −2.44743 | + | 1.41303i | ||||
\(768\) | −586602. | + | 61569.3i | −0.994537 | + | 0.104386i | ||||
\(769\) | 173385. | − | 300311.i | 0.293196 | − | 0.507830i | −0.681368 | − | 0.731941i | \(-0.738614\pi\) |
0.974564 | + | 0.224111i | \(0.0719478\pi\) | |||||||
\(770\) | 864.724 | − | 367.473i | 0.00145847 | − | 0.000619790i | ||||
\(771\) | −72329.9 | − | 116641.i | −0.121677 | − | 0.196220i | ||||
\(772\) | 299796. | − | 310959.i | 0.503027 | − | 0.521758i | ||||
\(773\) | −456941. | −0.764717 | −0.382358 | − | 0.924014i | \(-0.624888\pi\) | ||||
−0.382358 | + | 0.924014i | \(0.624888\pi\) | |||||||
\(774\) | −294339. | + | 446899.i | −0.491322 | + | 0.745981i | ||||
\(775\) | − | 853996.i | − | 1.42185i | ||||||
\(776\) | −430938. | + | 68799.0i | −0.715634 | + | 0.114251i | ||||
\(777\) | −9606.30 | − | 305127.i | −0.0159116 | − | 0.505403i | ||||
\(778\) | 211554. | − | 89902.1i | 0.349512 | − | 0.148529i | ||||
\(779\) | 377159. | + | 217753.i | 0.621512 | + | 0.358830i | ||||
\(780\) | 78807.7 | + | 16966.3i | 0.129533 | + | 0.0278867i | ||||
\(781\) | 1310.58 | + | 2269.99i | 0.00214863 | + | 0.00372154i | ||||
\(782\) | 402373. | − | 534424.i | 0.657984 | − | 0.873922i | ||||
\(783\) | −269896. | − | 379643.i | −0.440223 | − | 0.619230i | ||||
\(784\) | −404646. | + | 253777.i | −0.658329 | + | 0.412877i | ||||
\(785\) | −6303.68 | − | 10918.3i | −0.0102295 | − | 0.0177180i | ||||
\(786\) | 431529. | + | 932768.i | 0.698498 | + | 1.50983i | ||||
\(787\) | −602982. | − | 348132.i | −0.973543 | − | 0.562075i | −0.0732283 | − | 0.997315i | \(-0.523330\pi\) |
−0.900314 | + | 0.435240i | \(0.856663\pi\) | |||||||
\(788\) | −161745. | − | 40186.4i | −0.260483 | − | 0.0647182i | ||||
\(789\) | 29261.0 | + | 929423.i | 0.0470040 | + | 1.49300i | ||||
\(790\) | −41418.1 | − | 5068.21i | −0.0663645 | − | 0.00812082i | ||||
\(791\) | − | 273518.i | − | 0.437153i | ||||||
\(792\) | 19053.6 | − | 17568.1i | 0.0303757 | − | 0.0280075i | ||||
\(793\) | 459430. | 0.730589 | ||||||||
\(794\) | −6440.25 | + | 52630.6i | −0.0102156 | + | 0.0834829i | ||||
\(795\) | 51028.9 | + | 82290.7i | 0.0807387 | + | 0.130202i | ||||
\(796\) | −32556.3 | + | 131035.i | −0.0513817 | + | 0.206805i | ||||
\(797\) | −65680.3 | + | 113762.i | −0.103399 | + | 0.179093i | −0.913083 | − | 0.407773i | \(-0.866305\pi\) |
0.809684 | + | 0.586867i | \(0.199639\pi\) | |||||||
\(798\) | −27574.4 | + | 304571.i | −0.0433013 | + | 0.478281i | ||||
\(799\) | 81894.7 | − | 47281.9i | 0.128281 | − | 0.0740631i | ||||
\(800\) | −633470. | − | 54108.9i | −0.989796 | − | 0.0845451i | ||||
\(801\) | 397222. | + | 597720.i | 0.619111 | + | 0.931608i | ||||
\(802\) | 17177.0 | + | 12932.7i | 0.0267053 | + | 0.0201067i | ||||
\(803\) | 6461.00 | − | 3730.26i | 0.0100200 | − | 0.00578506i | ||||
\(804\) | 302041. | − | 97267.7i | 0.467254 | − | 0.150472i | ||||
\(805\) | −14769.6 | + | 25581.7i | −0.0227917 | + | 0.0394764i | ||||
\(806\) | 593151. | + | 1.39578e6i | 0.913051 | + | 2.14855i | ||||
\(807\) | 365791. | − | 682291.i | 0.561677 | − | 1.04767i | ||||
\(808\) | −195353. | + | 31188.1i | −0.299225 | + | 0.0477712i | ||||
\(809\) | 796199. | 1.21653 | 0.608267 | − | 0.793732i | \(-0.291865\pi\) | ||||
0.608267 | + | 0.793732i | \(0.291865\pi\) | |||||||
\(810\) | −46047.9 | + | 26839.8i | −0.0701842 | + | 0.0409082i | ||||
\(811\) | 116976.i | 0.177851i | 0.996038 | + | 0.0889253i | \(0.0283432\pi\) | ||||
−0.996038 | + | 0.0889253i | \(0.971657\pi\) | |||||||
\(812\) | −170270. | − | 164157.i | −0.258241 | − | 0.248970i | ||||
\(813\) | 123969. | + | 66462.4i | 0.187556 | + | 0.100553i | ||||
\(814\) | −11467.3 | − | 26984.5i | −0.0173067 | − | 0.0407254i | ||||
\(815\) | 27889.5 | + | 16102.0i | 0.0419881 | + | 0.0242418i | ||||
\(816\) | 508717. | − | 341812.i | 0.764005 | − | 0.513342i | ||||
\(817\) | −303230. | − | 525210.i | −0.454285 | − | 0.786845i | ||||
\(818\) | 769142. | + | 579094.i | 1.14948 | + | 0.865451i | ||||
\(819\) | −430204. | + | 285897.i | −0.641368 | + | 0.426228i | ||||
\(820\) | 10653.4 | + | 37037.9i | 0.0158439 | + | 0.0550832i | ||||
\(821\) | −146773. | − | 254219.i | −0.217751 | − | 0.377157i | 0.736369 | − | 0.676580i | \(-0.236539\pi\) |
−0.954120 | + | 0.299424i | \(0.903206\pi\) | |||||||
\(822\) | 2008.86 | − | 22188.7i | 0.00297307 | − | 0.0328388i | ||||
\(823\) | 198711. | + | 114726.i | 0.293375 | + | 0.169380i | 0.639463 | − | 0.768822i | \(-0.279157\pi\) |
−0.346088 | + | 0.938202i | \(0.612490\pi\) | |||||||
\(824\) | 539855. | − | 438270.i | 0.795102 | − | 0.645487i | ||||
\(825\) | 23741.6 | − | 14722.3i | 0.0348821 | − | 0.0216306i | ||||
\(826\) | 67791.7 | − | 554003.i | 0.0993611 | − | 0.811992i | ||||
\(827\) | − | 673431.i | − | 0.984651i | −0.870411 | − | 0.492326i | \(-0.836147\pi\) | ||
0.870411 | − | 0.492326i | \(-0.163853\pi\) | |||||||
\(828\) | −146337. | + | 801552.i | −0.213448 | + | 1.16915i | ||||
\(829\) | 268282. | 0.390375 | 0.195188 | − | 0.980766i | \(-0.437468\pi\) | ||||
0.195188 | + | 0.980766i | \(0.437468\pi\) | |||||||
\(830\) | −64416.3 | − | 7882.43i | −0.0935060 | − | 0.0114421i | ||||
\(831\) | −509279. | + | 16033.6i | −0.737486 | + | 0.0232183i | ||||
\(832\) | 1.07293e6 | − | 351546.i | 1.54998 | − | 0.507850i | ||||
\(833\) | 248158. | − | 429823.i | 0.357634 | − | 0.619440i | ||||
\(834\) | −293574. | − | 634573.i | −0.422071 | − | 0.912325i | ||||
\(835\) | 736.936 | − | 425.470i | 0.00105696 | − | 0.000610234i | ||||
\(836\) | 8119.18 | + | 28227.3i | 0.0116172 | + | 0.0403884i | ||||
\(837\) | −911778. | − | 417257.i | −1.30148 | − | 0.595598i | ||||
\(838\) | 85204.7 | − | 113167.i | 0.121332 | − | 0.161151i | ||||
\(839\) | 867924. | − | 501096.i | 1.23299 | − | 0.711865i | 0.265334 | − | 0.964156i | \(-0.414518\pi\) |
0.967651 | + | 0.252292i | \(0.0811843\pi\) | |||||||
\(840\) | −20463.7 | + | 17709.9i | −0.0290018 | + | 0.0250991i | ||||
\(841\) | 149504. | − | 258949.i | 0.211379 | − | 0.366119i | ||||
\(842\) | −607780. | + | 258283.i | −0.857279 | + | 0.364310i | ||||
\(843\) | 999108. | − | 31454.9i | 1.40591 | − | 0.0442622i | ||||
\(844\) | −264302. | − | 254813.i | −0.371035 | − | 0.357715i | ||||
\(845\) | −96307.2 | −0.134879 | ||||||||
\(846\) | −63353.4 | + | 96190.2i | −0.0885175 | + | 0.134397i | ||||
\(847\) | − | 338137.i | − | 0.471330i | ||||||
\(848\) | 1.19846e6 | + | 634707.i | 1.66661 | + | 0.882636i | ||||
\(849\) | −697550. | + | 432554.i | −0.967743 | + | 0.600102i | ||||
\(850\) | 608011. | − | 258381.i | 0.841538 | − | 0.357620i | ||||
\(851\) | 798300. | + | 460899.i | 1.10232 | + | 0.636424i | ||||
\(852\) | −55974.6 | − | 50665.1i | −0.0771102 | − | 0.0697958i | ||||
\(853\) | −205795. | − | 356448.i | −0.282837 | − | 0.489889i | 0.689245 | − | 0.724528i | \(-0.257942\pi\) |
−0.972082 | + | 0.234640i | \(0.924609\pi\) | |||||||
\(854\) | −92771.3 | + | 123217.i | −0.127203 | + | 0.168949i | ||||
\(855\) | −3799.67 | − | 60284.9i | −0.00519772 | − | 0.0824663i | ||||
\(856\) | −843253. | − | 322501.i | −1.15083 | − | 0.440133i | ||||
\(857\) | 460403. | + | 797442.i | 0.626869 | + | 1.08577i | 0.988176 | + | 0.153322i | \(0.0489972\pi\) |
−0.361307 | + | 0.932447i | \(0.617669\pi\) | |||||||
\(858\) | −28578.0 | + | 40552.2i | −0.0388202 | + | 0.0550859i | ||||
\(859\) | 520799. | + | 300684.i | 0.705804 | + | 0.407496i | 0.809505 | − | 0.587112i | \(-0.199735\pi\) |
−0.103702 | + | 0.994608i | \(0.533069\pi\) | |||||||
\(860\) | 12940.6 | − | 52084.6i | 0.0174968 | − | 0.0704226i | ||||
\(861\) | −217642. | − | 116683.i | −0.293587 | − | 0.157399i | ||||
\(862\) | 641903. | + | 78547.8i | 0.863883 | + | 0.105711i | ||||
\(863\) | 1.01872e6i | 1.36783i | 0.729560 | + | 0.683917i | \(0.239725\pi\) | ||||
−0.729560 | + | 0.683917i | \(0.760275\pi\) | |||||||
\(864\) | −367279. | + | 649894.i | −0.492005 | + | 0.870593i | ||||
\(865\) | 38994.9 | 0.0521166 | ||||||||
\(866\) | 30042.3 | − | 245510.i | 0.0400588 | − | 0.327366i | ||||
\(867\) | 54262.2 | − | 101212.i | 0.0721870 | − | 0.134647i | ||||
\(868\) | −494115. | − | 122765.i | −0.655826 | − | 0.162943i | ||||
\(869\) | 12839.6 | − | 22238.9i | 0.0170025 | − | 0.0294492i | ||||
\(870\) | 38186.4 | + | 26910.8i | 0.0504511 | + | 0.0355540i | ||||
\(871\) | −526036. | + | 303707.i | −0.693392 | + | 0.400330i | ||||
\(872\) | 373294. | − | 976063.i | 0.490929 | − | 1.28365i | ||||
\(873\) | −245521. | + | 494740.i | −0.322152 | + | 0.649156i | ||||
\(874\) | −737709. | − | 555428.i | −0.965744 | − | 0.727118i | ||||
\(875\) | −50694.1 | + | 29268.3i | −0.0662128 | + | 0.0382280i | ||||
\(876\) | −144206. | + | 159319.i | −0.187921 | + | 0.207615i | ||||
\(877\) | −432672. | + | 749411.i | −0.562549 | + | 0.974363i | 0.434724 | + | 0.900564i | \(0.356846\pi\) |
−0.997273 | + | 0.0737993i | \(0.976488\pi\) | |||||||
\(878\) | −484169. | − | 1.13933e6i | −0.628070 | − | 1.47795i | ||||
\(879\) | −393743. | − | 634962.i | −0.509607 | − | 0.821807i | ||||
\(880\) | −1216.48 | + | 2296.98i | −0.00157087 | + | 0.00296615i | ||||
\(881\) | 1.46275e6 | 1.88459 | 0.942296 | − | 0.334780i | \(-0.108662\pi\) | ||||
0.942296 | + | 0.334780i | \(0.108662\pi\) | |||||||
\(882\) | −35535.0 | + | 603470.i | −0.0456792 | + | 0.775744i | ||||
\(883\) | − | 162909.i | − | 0.208941i | −0.994528 | − | 0.104470i | \(-0.966685\pi\) | ||
0.994528 | − | 0.104470i | \(-0.0333148\pi\) | |||||||
\(884\) | −814278. | + | 844599.i | −1.04200 | + | 1.08080i | ||||
\(885\) | 3469.03 | + | 110187.i | 0.00442916 | + | 0.140684i | ||||
\(886\) | 73370.2 | + | 172652.i | 0.0934657 | + | 0.219940i | ||||
\(887\) | 192525. | + | 111154.i | 0.244703 | + | 0.141280i | 0.617337 | − | 0.786699i | \(-0.288212\pi\) |
−0.372633 | + | 0.927979i | \(0.621545\pi\) | |||||||
\(888\) | 552654. | + | 638587.i | 0.700853 | + | 0.809831i | ||||
\(889\) | 242682. | + | 420338.i | 0.307068 | + | 0.531857i | ||||
\(890\) | −57500.8 | − | 43292.9i | −0.0725929 | − | 0.0546559i | ||||
\(891\) | −4118.41 | − | 32541.2i | −0.00518769 | − | 0.0409901i | ||||
\(892\) | 988102. | − | 284213.i | 1.24186 | − | 0.357203i | ||||
\(893\) | −65267.1 | − | 113046.i | −0.0818448 | − | 0.141759i | ||||
\(894\) | 20233.7 | − | 9360.79i | 0.0253163 | − | 0.0117122i | ||||
\(895\) | 87627.1 | + | 50591.5i | 0.109394 | + | 0.0631585i | ||||
\(896\) | −122370. | + | 358742.i | −0.152427 | + | 0.446854i | ||||
\(897\) | −49080.0 | − | 1.55894e6i | −0.0609986 | − | 1.93751i | ||||
\(898\) | 60661.2 | − | 495731.i | 0.0752243 | − | 0.614743i | ||||
\(899\) | 878873.i | 1.08744i | ||||||||
\(900\) | −520939. | + | 613263.i | −0.643134 | + | 0.757115i | ||||
\(901\) | −1.40918e6 | −1.73587 | ||||||||
\(902\) | −23542.1 | − | 2880.78i | −0.0289356 | − | 0.00354077i | ||||
\(903\) | 181229. | + | 292255.i | 0.222255 | + | 0.358415i | ||||
\(904\) | 476909. | + | 587450.i | 0.583578 | + | 0.718844i | ||||
\(905\) | 14186.6 | − | 24571.9i | 0.0173213 | − | 0.0300014i | ||||
\(906\) | −155584. | − | 14085.8i | −0.189543 | − | 0.0171604i | ||||
\(907\) | −1.03664e6 | + | 598505.i | −1.26013 | + | 0.727534i | −0.973099 | − | 0.230388i | \(-0.926001\pi\) |
−0.287028 | + | 0.957922i | \(0.592667\pi\) | |||||||
\(908\) | 103106. | − | 29656.8i | 0.125058 | − | 0.0359711i | ||||
\(909\) | −111300. | + | 224277.i | −0.134700 | + | 0.271429i | ||||
\(910\) | 31159.7 | − | 41385.7i | 0.0376280 | − | 0.0499767i | ||||
\(911\) | −806036. | + | 465365.i | −0.971220 | + | 0.560734i | −0.899608 | − | 0.436698i | \(-0.856148\pi\) |
−0.0716123 | + | 0.997433i | \(0.522814\pi\) | |||||||
\(912\) | −471830. | − | 702223.i | −0.567278 | − | 0.844278i | ||||
\(913\) | 19969.1 | − | 34587.5i | 0.0239562 | − | 0.0414933i | ||||
\(914\) | −462001. | + | 196332.i | −0.553033 | + | 0.235017i | ||||
\(915\) | 14394.6 | − | 26849.4i | 0.0171932 | − | 0.0320695i | ||||
\(916\) | 394788. | − | 409489.i | 0.470515 | − | 0.488035i | ||||
\(917\) | 660464. | 0.785435 | ||||||||
\(918\) | 21207.6 | − | 775393.i | 0.0251655 | − | 0.920103i | ||||
\(919\) | 1.46503e6i | 1.73467i | 0.497725 | + | 0.867335i | \(0.334169\pi\) | ||||
−0.497725 | + | 0.867335i | \(0.665831\pi\) | |||||||
\(920\) | −12883.0 | − | 80695.6i | −0.0152210 | − | 0.0953398i | ||||
\(921\) | −517178. | − | 277271.i | −0.609707 | − | 0.326878i | ||||
\(922\) | 380267. | − | 161598.i | 0.447329 | − | 0.190097i | ||||
\(923\) | 125160. | + | 72261.0i | 0.146913 | + | 0.0848205i | ||||
\(924\) | −5105.25 | − | 15853.1i | −0.00597961 | − | 0.0185682i | ||||
\(925\) | 455160. | + | 788360.i | 0.531962 | + | 0.921385i | ||||
\(926\) | 771115. | − | 1.02418e6i | 0.899284 | − | 1.19441i | ||||
\(927\) | −55359.2 | − | 878321.i | −0.0644214 | − | 1.02210i | ||||
\(928\) | 651923. | + | 55685.1i | 0.757008 | + | 0.0646611i | ||||
\(929\) | −493591. | − | 854925.i | −0.571921 | − | 0.990596i | −0.996369 | − | 0.0851437i | \(-0.972865\pi\) |
0.424448 | − | 0.905452i | \(-0.360468\pi\) | |||||||
\(930\) | 100154. | + | 9067.51i | 0.115799 | + | 0.0104839i | ||||
\(931\) | −593319. | − | 342553.i | −0.684524 | − | 0.395210i | ||||
\(932\) | −969561. | − | 240892.i | −1.11620 | − | 0.277326i | ||||
\(933\) | −1.02263e6 | + | 634137.i | −1.17478 | + | 0.728484i | ||||
\(934\) | −1.69687e6 | − | 207641.i | −1.94516 | − | 0.238023i | ||||
\(935\) | − | 2700.85i | − | 0.00308942i | ||||||
\(936\) | 425480. | − | 1.36415e6i | 0.485654 | − | 1.55707i | ||||
\(937\) | −287243. | −0.327167 | −0.163584 | − | 0.986529i | \(-0.552305\pi\) | ||||
−0.163584 | + | 0.986529i | \(0.552305\pi\) | |||||||
\(938\) | 24768.0 | − | 202407.i | 0.0281504 | − | 0.230049i | ||||
\(939\) | 101111. | − | 3183.26i | 0.114674 | − | 0.00361028i | ||||
\(940\) | 2785.33 | − | 11210.6i | 0.00315226 | − | 0.0126875i | ||||
\(941\) | 149097. | − | 258244.i | 0.168380 | − | 0.291643i | −0.769470 | − | 0.638683i | \(-0.779480\pi\) |
0.937850 | + | 0.347040i | \(0.112813\pi\) | |||||||
\(942\) | −202826. | + | 93833.8i | −0.228571 | + | 0.105744i | ||||
\(943\) | 645766. | − | 372833.i | 0.726193 | − | 0.419267i | ||||
\(944\) | 820364. | + | 1.30806e6i | 0.920583 | + | 1.46786i | ||||
\(945\) | 3229.15 | + | 34099.0i | 0.00361597 | + | 0.0381837i | ||||
\(946\) | 26385.5 | + | 19865.9i | 0.0294837 | + | 0.0221986i | ||||
\(947\) | 904210. | − | 522046.i | 1.00825 | − | 0.582115i | 0.0975732 | − | 0.995228i | \(-0.468892\pi\) |
0.910680 | + | 0.413113i | \(0.135559\pi\) | |||||||
\(948\) | −155672. | + | 723090.i | −0.173219 | + | 0.804592i | ||||
\(949\) | 205674. | − | 356238.i | 0.228374 | − | 0.395555i | ||||
\(950\) | −356664. | − | 839287.i | −0.395195 | − | 0.929957i | ||||
\(951\) | −352681. | + | 11103.4i | −0.389961 | + | 0.0122771i | ||||
\(952\) | −62093.0 | − | 388933.i | −0.0685124 | − | 0.429142i | ||||
\(953\) | −1.38691e6 | −1.52708 | −0.763539 | − | 0.645762i | \(-0.776540\pi\) | ||||
−0.763539 | + | 0.645762i | \(0.776540\pi\) | |||||||
\(954\) | 1.53431e6 | − | 769334.i | 1.68584 | − | 0.845314i | ||||
\(955\) | − | 63305.1i | − | 0.0694115i | ||||||
\(956\) | −43234.4 | − | 41682.3i | −0.0473058 | − | 0.0456075i | ||||
\(957\) | −24433.2 | + | 15151.2i | −0.0266782 | + | 0.0165433i | ||||
\(958\) | 300468. | + | 707049.i | 0.327391 | + | 0.770404i | ||||
\(959\) | −12399.2 | − | 7158.71i | −0.0134821 | − | 0.00778391i | ||||
\(960\) | 13071.8 | − | 73717.2i | 0.0141838 | − | 0.0799883i | ||||
\(961\) | 484199. | + | 838657.i | 0.524297 | + | 0.908109i | ||||
\(962\) | −1.29148e6 | − | 972367.i | −1.39552 | − | 1.05070i | ||||
\(963\) | −951649. | + | 632430.i | −1.02618 | + | 0.681961i | ||||
\(964\) | −396576. | − | 1.37874e6i | −0.426748 | − | 1.48364i | ||||
\(965\) | 27413.5 | + | 47481.5i | 0.0294381 | + | 0.0509882i | ||||
\(966\) | 428011. | + | 301628.i | 0.458670 | + | 0.323235i | ||||
\(967\) | −697159. | − | 402505.i | −0.745554 | − | 0.430446i | 0.0785311 | − | 0.996912i | \(-0.474977\pi\) |
−0.824085 | + | 0.566466i | \(0.808310\pi\) | |||||||
\(968\) | 589578. | + | 726234.i | 0.629203 | + | 0.775043i | ||||
\(969\) | 774772. | + | 415372.i | 0.825137 | + | 0.442374i | ||||
\(970\) | 6728.00 | − | 54982.1i | 0.00715060 | − | 0.0584356i | ||||
\(971\) | − | 643421.i | − | 0.682428i | −0.939986 | − | 0.341214i | \(-0.889162\pi\) | ||
0.939986 | − | 0.341214i | \(-0.110838\pi\) | |||||||
\(972\) | 400230. | + | 855823.i | 0.423620 | + | 0.905840i | ||||
\(973\) | −449321. | −0.474604 | ||||||||
\(974\) | −209974. | − | 25693.9i | −0.221334 | − | 0.0270840i | ||||
\(975\) | 727788. | − | 1.35750e6i | 0.765588 | − | 1.42801i | ||||
\(976\) | −15592.6 | − | 426397.i | −0.0163688 | − | 0.447625i | ||||
\(977\) | 63505.8 | − | 109995.i | 0.0665311 | − | 0.115235i | −0.830841 | − | 0.556510i | \(-0.812140\pi\) |
0.897372 | + | 0.441275i | \(0.145474\pi\) | |||||||
\(978\) | 328839. | − | 466623.i | 0.343800 | − | 0.487852i | ||||
\(979\) | 38360.8 | − | 22147.6i | 0.0400241 | − | 0.0231079i | ||||
\(980\) | −16759.2 | − | 58265.3i | −0.0174502 | − | 0.0606678i | ||||
\(981\) | −732036. | − | 1.10153e6i | −0.760667 | − | 1.14461i | ||||
\(982\) | 17693.7 | − | 23500.5i | 0.0183483 | − | 0.0243699i | ||||
\(983\) | −158662. | + | 91603.6i | −0.164197 | + | 0.0947994i | −0.579847 | − | 0.814725i | \(-0.696888\pi\) |
0.415650 | + | 0.909525i | \(0.363554\pi\) | |||||||
\(984\) | 670891. | − | 128877.i | 0.692886 | − | 0.133102i | ||||
\(985\) | 10577.4 | − | 18320.6i | 0.0109020 | − | 0.0188828i | ||||
\(986\) | −625723. | + | 265907.i | −0.643618 | + | 0.273512i | ||||
\(987\) | 39007.5 | + | 62904.7i | 0.0400418 | + | 0.0645727i | ||||
\(988\) | 1.16587e6 | + | 1.12401e6i | 1.19436 | + | 1.15148i | ||||
\(989\) | −1.03837e6 | −1.06160 | ||||||||
\(990\) | 1474.51 | + | 2940.68i | 0.00150445 | + | 0.00300038i | ||||
\(991\) | 684255.i | 0.696740i | 0.937357 | + | 0.348370i | \(0.113265\pi\) | ||||
−0.937357 | + | 0.348370i | \(0.886735\pi\) | |||||||
\(992\) | 1.27529e6 | − | 597874.i | 1.29594 | − | 0.607556i | ||||
\(993\) | 21170.1 | + | 672429.i | 0.0214696 | + | 0.681943i | ||||
\(994\) | −44653.2 | + | 18975.8i | −0.0451939 | + | 0.0192056i | ||||
\(995\) | −14842.1 | − | 8569.07i | −0.0149916 | − | 0.00865541i | ||||
\(996\) | −242112. | + | 1.12460e6i | −0.244061 | + | 1.13365i | ||||
\(997\) | 271816. | + | 470800.i | 0.273455 | + | 0.473637i | 0.969744 | − | 0.244124i | \(-0.0785003\pi\) |
−0.696289 | + | 0.717761i | \(0.745167\pi\) | |||||||
\(998\) | −998582. | + | 1.32630e6i | −1.00259 | + | 1.33162i | ||||
\(999\) | 1.06409e6 | − | 100769.i | 1.06622 | − | 0.100970i |
(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 | 36.5.f.a.31.11 | yes | 44 | |
3.2 | odd | 2 | 108.5.f.a.91.12 | 44 | |||
4.3 | odd | 2 | inner | 36.5.f.a.31.20 | yes | 44 | |
9.2 | odd | 6 | 108.5.f.a.19.3 | 44 | |||
9.4 | even | 3 | 324.5.d.f.163.5 | 22 | |||
9.5 | odd | 6 | 324.5.d.e.163.18 | 22 | |||
9.7 | even | 3 | inner | 36.5.f.a.7.20 | yes | 44 | |
12.11 | even | 2 | 108.5.f.a.91.3 | 44 | |||
36.7 | odd | 6 | inner | 36.5.f.a.7.11 | ✓ | 44 | |
36.11 | even | 6 | 108.5.f.a.19.12 | 44 | |||
36.23 | even | 6 | 324.5.d.e.163.17 | 22 | |||
36.31 | odd | 6 | 324.5.d.f.163.6 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.11 | ✓ | 44 | 36.7 | odd | 6 | inner | |
36.5.f.a.7.20 | yes | 44 | 9.7 | even | 3 | inner | |
36.5.f.a.31.11 | yes | 44 | 1.1 | even | 1 | trivial | |
36.5.f.a.31.20 | yes | 44 | 4.3 | odd | 2 | inner | |
108.5.f.a.19.3 | 44 | 9.2 | odd | 6 | |||
108.5.f.a.19.12 | 44 | 36.11 | even | 6 | |||
108.5.f.a.91.3 | 44 | 12.11 | even | 2 | |||
108.5.f.a.91.12 | 44 | 3.2 | odd | 2 | |||
324.5.d.e.163.17 | 22 | 36.23 | even | 6 | |||
324.5.d.e.163.18 | 22 | 9.5 | odd | 6 | |||
324.5.d.f.163.5 | 22 | 9.4 | even | 3 | |||
324.5.d.f.163.6 | 22 | 36.31 | odd | 6 |