Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,5,Mod(2,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.f (of order \(18\), degree \(6\), 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: | \(2.79098900326\) |
Analytic rank: | \(0\) |
Dimension: | \(66\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 2.10 | ||
Character | \(\chi\) | \(=\) | 27.2 |
Dual form | 27.5.f.a.14.10 |
$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.98494 | + | 1.05531i | 1.49623 | + | 0.263826i | 0.861044 | − | 0.508530i | \(-0.169811\pi\) |
0.635189 | + | 0.772356i | \(0.280922\pi\) | |||||||
\(3\) | −1.69482 | − | 8.83898i | −0.188314 | − | 0.982109i | ||||
\(4\) | 19.6707 | + | 7.15955i | 1.22942 | + | 0.447472i | ||||
\(5\) | 10.5942 | + | 12.6257i | 0.423767 | + | 0.505026i | 0.935113 | − | 0.354349i | \(-0.115297\pi\) |
−0.511346 | + | 0.859375i | \(0.670853\pi\) | |||||||
\(6\) | −0.815584 | − | 54.6893i | −0.0226551 | − | 1.51915i | ||||
\(7\) | 7.09675 | − | 2.58301i | 0.144832 | − | 0.0527144i | −0.268587 | − | 0.963255i | \(-0.586557\pi\) |
0.413419 | + | 0.910541i | \(0.364335\pi\) | |||||||
\(8\) | 25.9633 | + | 14.9899i | 0.405677 | + | 0.234218i | ||||
\(9\) | −75.2551 | + | 29.9610i | −0.929076 | + | 0.369889i | ||||
\(10\) | 50.0816 | + | 86.7438i | 0.500816 | + | 0.867438i | ||||
\(11\) | −120.209 | + | 143.260i | −0.993463 | + | 1.18396i | −0.0105406 | + | 0.999944i | \(0.503355\pi\) |
−0.982923 | + | 0.184019i | \(0.941089\pi\) | |||||||
\(12\) | 29.9447 | − | 186.003i | 0.207950 | − | 1.29169i | ||||
\(13\) | −9.75217 | − | 55.3073i | −0.0577051 | − | 0.327262i | 0.942266 | − | 0.334865i | \(-0.108691\pi\) |
−0.999971 | + | 0.00760334i | \(0.997580\pi\) | |||||||
\(14\) | 45.1995 | − | 7.96989i | 0.230610 | − | 0.0406627i | ||||
\(15\) | 93.6426 | − | 115.040i | 0.416189 | − | 0.511289i | ||||
\(16\) | −117.001 | − | 98.1758i | −0.457037 | − | 0.383499i | ||||
\(17\) | 396.435 | − | 228.882i | 1.37175 | − | 0.791979i | 0.380599 | − | 0.924740i | \(-0.375718\pi\) |
0.991148 | + | 0.132761i | \(0.0423843\pi\) | |||||||
\(18\) | −482.015 | + | 99.8976i | −1.48770 | + | 0.308326i | ||||
\(19\) | −233.647 | + | 404.688i | −0.647221 | + | 1.12102i | 0.336562 | + | 0.941661i | \(0.390736\pi\) |
−0.983784 | + | 0.179359i | \(0.942598\pi\) | |||||||
\(20\) | 118.001 | + | 324.205i | 0.295002 | + | 0.810512i | ||||
\(21\) | −34.8589 | − | 58.3503i | −0.0790451 | − | 0.132314i | ||||
\(22\) | −870.626 | + | 730.542i | −1.79881 | + | 1.50938i | ||||
\(23\) | 177.454 | − | 487.552i | 0.335452 | − | 0.921648i | −0.651214 | − | 0.758894i | \(-0.725740\pi\) |
0.986667 | − | 0.162754i | \(-0.0520377\pi\) | |||||||
\(24\) | 88.4924 | − | 254.895i | 0.153633 | − | 0.442525i | ||||
\(25\) | 61.3597 | − | 347.988i | 0.0981755 | − | 0.556781i | ||||
\(26\) | − | 341.302i | − | 0.504885i | ||||||
\(27\) | 392.369 | + | 614.400i | 0.538229 | + | 0.842799i | ||||
\(28\) | 158.091 | 0.201647 | ||||||||
\(29\) | 1518.15 | + | 267.691i | 1.80518 | + | 0.318301i | 0.972048 | − | 0.234781i | \(-0.0754373\pi\) |
0.833127 | + | 0.553082i | \(0.186548\pi\) | |||||||
\(30\) | 681.847 | − | 589.685i | 0.757608 | − | 0.655206i | ||||
\(31\) | −719.064 | − | 261.718i | −0.748246 | − | 0.272339i | −0.0603785 | − | 0.998176i | \(-0.519231\pi\) |
−0.687867 | + | 0.725836i | \(0.741453\pi\) | |||||||
\(32\) | −904.971 | − | 1078.50i | −0.883761 | − | 1.05323i | ||||
\(33\) | 1470.00 | + | 819.726i | 1.34986 | + | 0.752733i | ||||
\(34\) | 2614.18 | − | 951.483i | 2.26140 | − | 0.823082i | ||||
\(35\) | 107.796 | + | 62.2363i | 0.0879971 | + | 0.0508051i | ||||
\(36\) | −1694.83 | + | 50.5614i | −1.30774 | + | 0.0390134i | ||||
\(37\) | −254.299 | − | 440.459i | −0.185755 | − | 0.321738i | 0.758075 | − | 0.652167i | \(-0.226140\pi\) |
−0.943831 | + | 0.330429i | \(0.892807\pi\) | |||||||
\(38\) | −1825.43 | + | 2175.46i | −1.26415 | + | 1.50655i | ||||
\(39\) | −472.332 | + | 179.935i | −0.310540 | + | 0.118301i | ||||
\(40\) | 85.8024 | + | 486.610i | 0.0536265 | + | 0.304131i | ||||
\(41\) | −562.688 | + | 99.2171i | −0.334734 | + | 0.0590227i | −0.338489 | − | 0.940970i | \(-0.609916\pi\) |
0.00375496 | + | 0.999993i | \(0.498805\pi\) | |||||||
\(42\) | −147.051 | − | 386.010i | −0.0833621 | − | 0.218826i | ||||
\(43\) | 850.976 | + | 714.053i | 0.460236 | + | 0.386183i | 0.843218 | − | 0.537572i | \(-0.180658\pi\) |
−0.382982 | + | 0.923756i | \(0.625103\pi\) | |||||||
\(44\) | −3390.27 | + | 1957.37i | −1.75117 | + | 1.01104i | ||||
\(45\) | −1175.54 | − | 632.733i | −0.580516 | − | 0.312461i | ||||
\(46\) | 1576.57 | − | 2730.70i | 0.745070 | − | 1.29050i | ||||
\(47\) | 54.5162 | + | 149.782i | 0.0246792 | + | 0.0678054i | 0.951420 | − | 0.307895i | \(-0.0996245\pi\) |
−0.926741 | + | 0.375700i | \(0.877402\pi\) | |||||||
\(48\) | −669.477 | + | 1200.56i | −0.290572 | + | 0.521078i | ||||
\(49\) | −1795.58 | + | 1506.67i | −0.747847 | + | 0.627518i | ||||
\(50\) | 734.467 | − | 2017.93i | 0.293787 | − | 0.807173i | ||||
\(51\) | −2694.97 | − | 3116.17i | −1.03613 | − | 1.19806i | ||||
\(52\) | 204.143 | − | 1157.75i | 0.0754968 | − | 0.428164i | ||||
\(53\) | − | 1535.13i | − | 0.546503i | −0.961943 | − | 0.273251i | \(-0.911901\pi\) | ||
0.961943 | − | 0.273251i | \(-0.0880991\pi\) | |||||||
\(54\) | 1699.92 | + | 4091.21i | 0.582964 | + | 1.40302i | ||||
\(55\) | −3082.26 | −1.01893 | ||||||||
\(56\) | 222.974 | + | 39.3164i | 0.0711015 | + | 0.0125371i | ||||
\(57\) | 3973.02 | + | 1379.32i | 1.22284 | + | 0.424538i | ||||
\(58\) | 8803.55 | + | 3204.23i | 2.61699 | + | 0.952506i | ||||
\(59\) | 1352.46 | + | 1611.80i | 0.388527 | + | 0.463028i | 0.924486 | − | 0.381215i | \(-0.124494\pi\) |
−0.535959 | + | 0.844244i | \(0.680050\pi\) | |||||||
\(60\) | 2665.65 | − | 1592.48i | 0.740458 | − | 0.442355i | ||||
\(61\) | −1362.35 | + | 495.855i | −0.366124 | + | 0.133258i | −0.518530 | − | 0.855060i | \(-0.673520\pi\) |
0.152405 | + | 0.988318i | \(0.451298\pi\) | |||||||
\(62\) | −4027.36 | − | 2325.20i | −1.04770 | − | 0.604890i | ||||
\(63\) | −456.678 | + | 407.011i | −0.115061 | + | 0.102547i | ||||
\(64\) | −3056.17 | − | 5293.44i | −0.746135 | − | 1.29234i | ||||
\(65\) | 594.974 | − | 709.063i | 0.140822 | − | 0.167826i | ||||
\(66\) | 7932.80 | + | 6457.31i | 1.82112 | + | 1.48239i | ||||
\(67\) | −1241.97 | − | 7043.56i | −0.276669 | − | 1.56907i | −0.733609 | − | 0.679572i | \(-0.762165\pi\) |
0.456939 | − | 0.889498i | \(-0.348946\pi\) | |||||||
\(68\) | 9436.84 | − | 1663.97i | 2.04084 | − | 0.359855i | ||||
\(69\) | −4610.21 | − | 742.201i | −0.968329 | − | 0.155892i | ||||
\(70\) | 579.476 | + | 486.238i | 0.118260 | + | 0.0992323i | ||||
\(71\) | −2436.79 | + | 1406.88i | −0.483395 | + | 0.279088i | −0.721830 | − | 0.692070i | \(-0.756699\pi\) |
0.238435 | + | 0.971158i | \(0.423365\pi\) | |||||||
\(72\) | −2402.99 | − | 350.182i | −0.463539 | − | 0.0675505i | ||||
\(73\) | −2132.26 | + | 3693.19i | −0.400125 | + | 0.693036i | −0.993741 | − | 0.111712i | \(-0.964367\pi\) |
0.593616 | + | 0.804749i | \(0.297700\pi\) | |||||||
\(74\) | −1057.14 | − | 2904.48i | −0.193051 | − | 0.530402i | ||||
\(75\) | −3179.85 | + | 47.4213i | −0.565307 | + | 0.00843045i | ||||
\(76\) | −7493.38 | + | 6287.69i | −1.29733 | + | 1.08859i | ||||
\(77\) | −483.054 | + | 1327.18i | −0.0814730 | + | 0.223845i | ||||
\(78\) | −3016.76 | + | 578.447i | −0.495852 | + | 0.0950767i | ||||
\(79\) | −992.133 | + | 5626.67i | −0.158970 | + | 0.901565i | 0.796096 | + | 0.605171i | \(0.206895\pi\) |
−0.955066 | + | 0.296394i | \(0.904216\pi\) | |||||||
\(80\) | − | 2517.31i | − | 0.393330i | ||||||
\(81\) | 4765.67 | − | 4509.44i | 0.726364 | − | 0.687310i | ||||
\(82\) | −3472.36 | −0.516412 | ||||||||
\(83\) | 4026.67 | + | 710.011i | 0.584508 | + | 0.103064i | 0.458079 | − | 0.888911i | \(-0.348538\pi\) |
0.126428 | + | 0.991976i | \(0.459649\pi\) | |||||||
\(84\) | −267.937 | − | 1397.37i | −0.0379729 | − | 0.198039i | ||||
\(85\) | 7089.69 | + | 2580.44i | 0.981272 | + | 0.357154i | ||||
\(86\) | 4339.49 | + | 5171.60i | 0.586735 | + | 0.699243i | ||||
\(87\) | −206.883 | − | 13872.6i | −0.0273329 | − | 1.83282i | ||||
\(88\) | −5268.48 | + | 1917.57i | −0.680330 | + | 0.247620i | ||||
\(89\) | 5385.27 | + | 3109.19i | 0.679873 | + | 0.392525i | 0.799807 | − | 0.600257i | \(-0.204935\pi\) |
−0.119934 | + | 0.992782i | \(0.538268\pi\) | |||||||
\(90\) | −6367.83 | − | 5027.42i | −0.786152 | − | 0.620670i | ||||
\(91\) | −212.068 | − | 367.312i | −0.0256090 | − | 0.0443560i | ||||
\(92\) | 6981.30 | − | 8319.99i | 0.824823 | − | 0.982986i | ||||
\(93\) | −1094.63 | + | 6799.36i | −0.126562 | + | 0.786144i | ||||
\(94\) | 168.210 | + | 953.968i | 0.0190369 | + | 0.107964i | ||||
\(95\) | −7584.75 | + | 1337.40i | −0.840416 | + | 0.148188i | ||||
\(96\) | −7999.10 | + | 9826.89i | −0.867957 | + | 1.06629i | ||||
\(97\) | 7112.63 | + | 5968.20i | 0.755939 | + | 0.634308i | 0.937066 | − | 0.349152i | \(-0.113530\pi\) |
−0.181127 | + | 0.983460i | \(0.557975\pi\) | |||||||
\(98\) | −12336.4 | + | 7122.44i | −1.28451 | + | 0.741612i | ||||
\(99\) | 4754.15 | − | 14382.6i | 0.485068 | − | 1.46746i | ||||
\(100\) | 3698.42 | − | 6405.86i | 0.369842 | − | 0.640586i | ||||
\(101\) | 6539.12 | + | 17966.1i | 0.641027 | + | 1.76121i | 0.648476 | + | 0.761235i | \(0.275407\pi\) |
−0.00744872 | + | 0.999972i | \(0.502371\pi\) | |||||||
\(102\) | −12840.7 | − | 21494.1i | −1.23421 | − | 2.06594i | ||||
\(103\) | −4736.32 | + | 3974.24i | −0.446443 | + | 0.374611i | −0.838114 | − | 0.545495i | \(-0.816342\pi\) |
0.391671 | + | 0.920105i | \(0.371897\pi\) | |||||||
\(104\) | 575.854 | − | 1582.15i | 0.0532409 | − | 0.146278i | ||||
\(105\) | 367.410 | − | 1058.29i | 0.0333251 | − | 0.0959900i | ||||
\(106\) | 1620.03 | − | 9187.63i | 0.144182 | − | 0.817696i | ||||
\(107\) | − | 1546.43i | − | 0.135072i | −0.997717 | − | 0.0675358i | \(-0.978486\pi\) | ||
0.997717 | − | 0.0675358i | \(-0.0215137\pi\) | |||||||
\(108\) | 3319.35 | + | 14894.9i | 0.284580 | + | 1.27699i | ||||
\(109\) | 8909.57 | 0.749901 | 0.374951 | − | 0.927045i | \(-0.377660\pi\) | ||||
0.374951 | + | 0.927045i | \(0.377660\pi\) | |||||||
\(110\) | −18447.1 | − | 3252.73i | −1.52456 | − | 0.268821i | ||||
\(111\) | −3462.22 | + | 2994.24i | −0.281001 | + | 0.243020i | ||||
\(112\) | −1083.92 | − | 394.514i | −0.0864093 | − | 0.0314504i | ||||
\(113\) | −10815.5 | − | 12889.4i | −0.847012 | − | 1.00943i | −0.999776 | − | 0.0211670i | \(-0.993262\pi\) |
0.152764 | − | 0.988263i | \(-0.451183\pi\) | |||||||
\(114\) | 22322.7 | + | 12447.9i | 1.71766 | + | 0.957827i | ||||
\(115\) | 8035.64 | − | 2924.73i | 0.607610 | − | 0.221152i | ||||
\(116\) | 27946.6 | + | 16135.0i | 2.07689 | + | 1.19909i | ||||
\(117\) | 2390.96 | + | 3869.97i | 0.174663 | + | 0.282707i | ||||
\(118\) | 6393.46 | + | 11073.8i | 0.459168 | + | 0.795302i | ||||
\(119\) | 2222.20 | − | 2648.31i | 0.156924 | − | 0.187015i | ||||
\(120\) | 4155.71 | − | 1583.12i | 0.288591 | − | 0.109939i | ||||
\(121\) | −3530.71 | − | 20023.6i | −0.241152 | − | 1.36764i | ||||
\(122\) | −8676.85 | + | 1529.96i | −0.582965 | + | 0.102792i | ||||
\(123\) | 1830.64 | + | 4805.44i | 0.121002 | + | 0.317631i | ||||
\(124\) | −12270.7 | − | 10296.4i | −0.798043 | − | 0.669638i | ||||
\(125\) | 13964.6 | − | 8062.45i | 0.893732 | − | 0.515997i | ||||
\(126\) | −3162.71 | + | 1954.00i | −0.199213 | + | 0.123079i | ||||
\(127\) | −7193.47 | + | 12459.5i | −0.445996 | + | 0.772488i | −0.998121 | − | 0.0612733i | \(-0.980484\pi\) |
0.552125 | + | 0.833762i | \(0.313817\pi\) | |||||||
\(128\) | −5000.37 | − | 13738.4i | −0.305198 | − | 0.838526i | ||||
\(129\) | 4869.25 | − | 8731.95i | 0.292606 | − | 0.524725i | ||||
\(130\) | 4309.16 | − | 3615.82i | 0.254980 | − | 0.213954i | ||||
\(131\) | −1057.26 | + | 2904.79i | −0.0616082 | + | 0.169267i | −0.966678 | − | 0.255997i | \(-0.917596\pi\) |
0.905069 | + | 0.425264i | \(0.139819\pi\) | |||||||
\(132\) | 23047.1 | + | 26649.1i | 1.32272 | + | 1.52945i | ||||
\(133\) | −612.822 | + | 3475.48i | −0.0346442 | + | 0.196477i | ||||
\(134\) | − | 43465.9i | − | 2.42069i | ||||||
\(135\) | −3600.37 | + | 11463.0i | −0.197551 | + | 0.628970i | ||||
\(136\) | 13723.7 | 0.741982 | ||||||||
\(137\) | −5162.83 | − | 910.346i | −0.275072 | − | 0.0485026i | 0.0344104 | − | 0.999408i | \(-0.489045\pi\) |
−0.309482 | + | 0.950905i | \(0.600156\pi\) | |||||||
\(138\) | −26808.6 | − | 9307.21i | −1.40772 | − | 0.488721i | ||||
\(139\) | −19913.9 | − | 7248.08i | −1.03069 | − | 0.375140i | −0.229345 | − | 0.973345i | \(-0.573659\pi\) |
−0.801343 | + | 0.598205i | \(0.795881\pi\) | |||||||
\(140\) | 1674.85 | + | 1996.01i | 0.0854514 | + | 0.101837i | ||||
\(141\) | 1231.53 | − | 735.722i | 0.0619449 | − | 0.0370063i | ||||
\(142\) | −16068.7 | + | 5848.54i | −0.796902 | + | 0.290049i | ||||
\(143\) | 9095.60 | + | 5251.35i | 0.444794 | + | 0.256802i | ||||
\(144\) | 11746.4 | + | 3882.75i | 0.566474 | + | 0.187247i | ||||
\(145\) | 12703.8 | + | 22003.6i | 0.604224 | + | 1.04655i | ||||
\(146\) | −16658.9 | + | 19853.3i | −0.781521 | + | 0.931381i | ||||
\(147\) | 16360.6 | + | 13317.6i | 0.757121 | + | 0.616297i | ||||
\(148\) | −1848.75 | − | 10484.8i | −0.0844025 | − | 0.478671i | ||||
\(149\) | −28666.8 | + | 5054.73i | −1.29124 | + | 0.227680i | −0.776745 | − | 0.629815i | \(-0.783131\pi\) |
−0.514493 | + | 0.857495i | \(0.672020\pi\) | |||||||
\(150\) | −19081.3 | − | 3071.90i | −0.848056 | − | 0.136529i | ||||
\(151\) | −27382.8 | − | 22976.9i | −1.20095 | − | 1.00771i | −0.999603 | − | 0.0281918i | \(-0.991025\pi\) |
−0.201343 | − | 0.979521i | \(-0.564530\pi\) | |||||||
\(152\) | −12132.5 | + | 7004.70i | −0.525125 | + | 0.303181i | ||||
\(153\) | −22976.2 | + | 29102.1i | −0.981513 | + | 1.24320i | ||||
\(154\) | −4291.62 | + | 7433.31i | −0.180959 | + | 0.313430i | ||||
\(155\) | −4313.54 | − | 11851.3i | −0.179544 | − | 0.493292i | ||||
\(156\) | −10579.4 | + | 157.770i | −0.434720 | + | 0.00648300i | ||||
\(157\) | 18847.0 | − | 15814.5i | 0.764616 | − | 0.641589i | −0.174708 | − | 0.984620i | \(-0.555898\pi\) |
0.939324 | + | 0.343031i | \(0.111454\pi\) | |||||||
\(158\) | −11875.7 | + | 32628.2i | −0.475713 | + | 1.30701i | ||||
\(159\) | −13569.0 | + | 2601.77i | −0.536725 | + | 0.102914i | ||||
\(160\) | 4029.37 | − | 22851.7i | 0.157397 | − | 0.892644i | ||||
\(161\) | − | 3918.40i | − | 0.151167i | ||||||
\(162\) | 33281.1 | − | 21959.5i | 1.26814 | − | 0.836743i | ||||
\(163\) | 17266.5 | 0.649875 | 0.324938 | − | 0.945735i | \(-0.394657\pi\) | ||||
0.324938 | + | 0.945735i | \(0.394657\pi\) | |||||||
\(164\) | −11778.8 | − | 2076.92i | −0.437940 | − | 0.0772206i | ||||
\(165\) | 5223.89 | + | 27244.1i | 0.191878 | + | 1.00070i | ||||
\(166\) | 23350.1 | + | 8498.74i | 0.847369 | + | 0.308417i | ||||
\(167\) | −3705.73 | − | 4416.31i | −0.132874 | − | 0.158353i | 0.695505 | − | 0.718522i | \(-0.255181\pi\) |
−0.828379 | + | 0.560168i | \(0.810736\pi\) | |||||||
\(168\) | −30.3853 | − | 2037.50i | −0.00107658 | − | 0.0721904i | ||||
\(169\) | 23874.8 | − | 8689.71i | 0.835922 | − | 0.304251i | ||||
\(170\) | 39708.2 | + | 22925.5i | 1.37399 | + | 0.793271i | ||||
\(171\) | 5458.26 | − | 37455.2i | 0.186664 | − | 1.28091i | ||||
\(172\) | 11627.0 | + | 20138.5i | 0.393016 | + | 0.680724i | ||||
\(173\) | 12635.0 | − | 15057.8i | 0.422166 | − | 0.503118i | −0.512479 | − | 0.858700i | \(-0.671273\pi\) |
0.934645 | + | 0.355582i | \(0.115717\pi\) | |||||||
\(174\) | 13401.7 | − | 83245.0i | 0.442650 | − | 2.74954i | ||||
\(175\) | −463.401 | − | 2628.08i | −0.0151315 | − | 0.0858148i | ||||
\(176\) | 28129.2 | − | 4959.95i | 0.908098 | − | 0.160122i | ||||
\(177\) | 11954.5 | − | 14686.1i | 0.381579 | − | 0.468770i | ||||
\(178\) | 28949.4 | + | 24291.4i | 0.913690 | + | 0.766677i | ||||
\(179\) | −19435.1 | + | 11220.9i | −0.606570 | + | 0.350203i | −0.771622 | − | 0.636082i | \(-0.780554\pi\) |
0.165052 | + | 0.986285i | \(0.447221\pi\) | |||||||
\(180\) | −18593.7 | − | 20862.7i | −0.573879 | − | 0.643909i | ||||
\(181\) | 13955.7 | − | 24172.0i | 0.425985 | − | 0.737828i | −0.570527 | − | 0.821279i | \(-0.693261\pi\) |
0.996512 | + | 0.0834510i | \(0.0265942\pi\) | |||||||
\(182\) | −881.586 | − | 2422.14i | −0.0266147 | − | 0.0731233i | ||||
\(183\) | 6691.79 | + | 11201.4i | 0.199821 | + | 0.334480i | ||||
\(184\) | 11915.7 | − | 9998.43i | 0.351951 | − | 0.295322i | ||||
\(185\) | 2866.99 | − | 7876.99i | 0.0837689 | − | 0.230153i | ||||
\(186\) | −13726.7 | + | 39538.6i | −0.396772 | + | 1.14287i | ||||
\(187\) | −14865.6 | + | 84306.8i | −0.425107 | + | 2.41090i | ||||
\(188\) | 3336.63i | 0.0944045i | ||||||||
\(189\) | 4371.55 | + | 3346.75i | 0.122380 | + | 0.0936915i | ||||
\(190\) | −46805.6 | −1.29655 | ||||||||
\(191\) | 52758.3 | + | 9302.72i | 1.44619 | + | 0.255002i | 0.840980 | − | 0.541067i | \(-0.181979\pi\) |
0.605207 | + | 0.796068i | \(0.293090\pi\) | |||||||
\(192\) | −41608.9 | + | 35984.8i | −1.12871 | + | 0.976152i | ||||
\(193\) | −40023.4 | − | 14567.3i | −1.07448 | − | 0.391080i | −0.256631 | − | 0.966509i | \(-0.582613\pi\) |
−0.817851 | + | 0.575430i | \(0.804835\pi\) | |||||||
\(194\) | 36270.3 | + | 43225.3i | 0.963714 | + | 1.14851i | ||||
\(195\) | −7275.77 | − | 4057.23i | −0.191342 | − | 0.106699i | ||||
\(196\) | −46107.4 | + | 16781.7i | −1.20021 | + | 0.436842i | ||||
\(197\) | −7509.39 | − | 4335.55i | −0.193496 | − | 0.111715i | 0.400122 | − | 0.916462i | \(-0.368968\pi\) |
−0.593618 | + | 0.804747i | \(0.702301\pi\) | |||||||
\(198\) | 43631.3 | − | 81061.9i | 1.11293 | − | 2.06769i | ||||
\(199\) | −31430.7 | − | 54439.5i | −0.793684 | − | 1.37470i | −0.923671 | − | 0.383185i | \(-0.874827\pi\) |
0.129987 | − | 0.991516i | \(-0.458506\pi\) | |||||||
\(200\) | 6809.42 | − | 8115.15i | 0.170235 | − | 0.202879i | ||||
\(201\) | −60152.9 | + | 22915.3i | −1.48890 | + | 0.567197i | ||||
\(202\) | 20176.5 | + | 114427.i | 0.494473 | + | 2.80430i | ||||
\(203\) | 11465.4 | − | 2021.66i | 0.278226 | − | 0.0490587i | ||||
\(204\) | −30701.6 | − | 80591.9i | −0.737735 | − | 1.93656i | ||||
\(205\) | −7213.90 | − | 6053.18i | −0.171657 | − | 0.144038i | ||||
\(206\) | −32540.6 | + | 18787.3i | −0.766816 | + | 0.442721i | ||||
\(207\) | 1253.20 | + | 42007.5i | 0.0292468 | + | 0.980361i | ||||
\(208\) | −4288.82 | + | 7428.46i | −0.0991314 | + | 0.171701i | ||||
\(209\) | −29889.0 | − | 82119.3i | −0.684256 | − | 1.87998i | ||||
\(210\) | 3315.74 | − | 5946.07i | 0.0751869 | − | 0.134831i | ||||
\(211\) | 43363.7 | − | 36386.5i | 0.974006 | − | 0.817288i | −0.00916815 | − | 0.999958i | \(-0.502918\pi\) |
0.983174 | + | 0.182670i | \(0.0584739\pi\) | |||||||
\(212\) | 10990.8 | − | 30197.0i | 0.244545 | − | 0.671881i | ||||
\(213\) | 16565.3 | + | 19154.3i | 0.365125 | + | 0.422190i | ||||
\(214\) | 1631.96 | − | 9255.31i | 0.0356354 | − | 0.202099i | ||||
\(215\) | 18308.9i | 0.396083i | ||||||||
\(216\) | 977.389 | + | 21833.5i | 0.0209488 | + | 0.467967i | ||||
\(217\) | −5779.04 | −0.122726 | ||||||||
\(218\) | 53323.2 | + | 9402.32i | 1.12203 | + | 0.197844i | ||||
\(219\) | 36257.9 | + | 12587.7i | 0.755986 | + | 0.262458i | ||||
\(220\) | −60630.2 | − | 22067.6i | −1.25269 | − | 0.455942i | ||||
\(221\) | −16524.9 | − | 19693.7i | −0.338342 | − | 0.403220i | ||||
\(222\) | −23881.0 | + | 14266.7i | −0.484558 | + | 0.289479i | ||||
\(223\) | −32580.8 | + | 11858.5i | −0.655168 | + | 0.238462i | −0.648149 | − | 0.761514i | \(-0.724456\pi\) |
−0.00701901 | + | 0.999975i | \(0.502234\pi\) | |||||||
\(224\) | −9208.14 | − | 5316.32i | −0.183517 | − | 0.105953i | ||||
\(225\) | 5808.44 | + | 28026.3i | 0.114735 | + | 0.553606i | ||||
\(226\) | −51127.8 | − | 88555.9i | −1.00101 | − | 1.73381i | ||||
\(227\) | −3339.70 | + | 3980.10i | −0.0648120 | + | 0.0772400i | −0.797476 | − | 0.603350i | \(-0.793832\pi\) |
0.732664 | + | 0.680590i | \(0.238277\pi\) | |||||||
\(228\) | 68276.8 | + | 55577.3i | 1.31342 | + | 1.06912i | ||||
\(229\) | 7561.02 | + | 42880.7i | 0.144182 | + | 0.817694i | 0.968021 | + | 0.250870i | \(0.0807168\pi\) |
−0.823839 | + | 0.566824i | \(0.808172\pi\) | |||||||
\(230\) | 51179.3 | − | 9024.29i | 0.967472 | − | 0.170591i | ||||
\(231\) | 12549.6 | + | 2020.37i | 0.235183 | + | 0.0378622i | ||||
\(232\) | 35403.6 | + | 29707.1i | 0.657766 | + | 0.551931i | ||||
\(233\) | −81822.2 | + | 47240.1i | −1.50716 | + | 0.870159i | −0.507194 | + | 0.861832i | \(0.669317\pi\) |
−0.999965 | + | 0.00832740i | \(0.997349\pi\) | |||||||
\(234\) | 10225.8 | + | 25684.7i | 0.186751 | + | 0.469076i | ||||
\(235\) | −1313.54 | + | 2275.12i | −0.0237853 | + | 0.0411973i | ||||
\(236\) | 15064.1 | + | 41388.3i | 0.270470 | + | 0.743110i | ||||
\(237\) | 51415.5 | − | 766.761i | 0.915371 | − | 0.0136510i | ||||
\(238\) | 16094.5 | − | 13504.9i | 0.284134 | − | 0.238417i | ||||
\(239\) | 6808.48 | − | 18706.1i | 0.119194 | − | 0.327483i | −0.865720 | − | 0.500529i | \(-0.833139\pi\) |
0.984914 | + | 0.173046i | \(0.0553610\pi\) | |||||||
\(240\) | −22250.5 | + | 4266.40i | −0.386293 | + | 0.0740694i | ||||
\(241\) | 5724.19 | − | 32463.5i | 0.0985554 | − | 0.558935i | −0.895044 | − | 0.445977i | \(-0.852856\pi\) |
0.993600 | − | 0.112958i | \(-0.0360326\pi\) | |||||||
\(242\) | − | 123566.i | − | 2.10993i | ||||||
\(243\) | −47935.8 | − | 34481.0i | −0.811798 | − | 0.583939i | ||||
\(244\) | −30348.5 | −0.509750 | ||||||||
\(245\) | −38045.4 | − | 6708.43i | −0.633826 | − | 0.111761i | ||||
\(246\) | 5885.03 | + | 30692.1i | 0.0972476 | + | 0.507173i | ||||
\(247\) | 24660.8 | + | 8975.79i | 0.404215 | + | 0.147122i | ||||
\(248\) | −14746.2 | − | 17573.8i | −0.239759 | − | 0.285734i | ||||
\(249\) | −548.726 | − | 36795.0i | −0.00885028 | − | 0.593459i | ||||
\(250\) | 92085.4 | − | 33516.3i | 1.47337 | − | 0.536261i | ||||
\(251\) | 36889.4 | + | 21298.1i | 0.585537 | + | 0.338060i | 0.763331 | − | 0.646008i | \(-0.223563\pi\) |
−0.177794 | + | 0.984068i | \(0.556896\pi\) | |||||||
\(252\) | −11897.2 | + | 4736.58i | −0.187345 | + | 0.0745870i | ||||
\(253\) | 48514.8 | + | 84030.2i | 0.757938 | + | 1.31279i | ||||
\(254\) | −56201.0 | + | 66977.8i | −0.871118 | + | 1.03816i | ||||
\(255\) | 10792.6 | − | 67039.0i | 0.165977 | − | 1.03097i | ||||
\(256\) | 1553.65 | + | 8811.21i | 0.0237069 | + | 0.134448i | ||||
\(257\) | −14099.5 | + | 2486.12i | −0.213470 | + | 0.0376406i | −0.279360 | − | 0.960186i | \(-0.590122\pi\) |
0.0658901 | + | 0.997827i | \(0.479011\pi\) | |||||||
\(258\) | 38357.0 | − | 47121.6i | 0.576243 | − | 0.707914i | ||||
\(259\) | −2942.41 | − | 2468.97i | −0.0438635 | − | 0.0368058i | ||||
\(260\) | 16780.1 | − | 9688.01i | 0.248227 | − | 0.143314i | ||||
\(261\) | −122269. | + | 25340.3i | −1.79488 | + | 0.371989i | ||||
\(262\) | −9393.07 | + | 16269.3i | −0.136837 | + | 0.237009i | ||||
\(263\) | 32691.1 | + | 89818.0i | 0.472626 | + | 1.29853i | 0.915634 | + | 0.402012i | \(0.131689\pi\) |
−0.443008 | + | 0.896518i | \(0.646089\pi\) | |||||||
\(264\) | 25878.5 | + | 43318.0i | 0.371305 | + | 0.621528i | ||||
\(265\) | 19382.0 | − | 16263.4i | 0.275998 | − | 0.231590i | ||||
\(266\) | −7335.40 | + | 20153.8i | −0.103672 | + | 0.284836i | ||||
\(267\) | 18355.0 | − | 52869.8i | 0.257473 | − | 0.741627i | ||||
\(268\) | 25998.3 | − | 147444.i | 0.361972 | − | 2.05285i | ||||
\(269\) | 18139.2i | 0.250677i | 0.992114 | + | 0.125338i | \(0.0400017\pi\) | ||||
−0.992114 | + | 0.125338i | \(0.959998\pi\) | |||||||
\(270\) | −33644.9 | + | 64805.7i | −0.461522 | + | 0.888967i | ||||
\(271\) | 128010. | 1.74303 | 0.871513 | − | 0.490373i | \(-0.163140\pi\) | ||||
0.871513 | + | 0.490373i | \(0.163140\pi\) | |||||||
\(272\) | −68854.1 | − | 12140.8i | −0.930662 | − | 0.164101i | ||||
\(273\) | −2887.25 | + | 2496.99i | −0.0387399 | + | 0.0335037i | ||||
\(274\) | −29938.5 | − | 10896.7i | −0.398776 | − | 0.145143i | ||||
\(275\) | 42476.6 | + | 50621.7i | 0.561674 | + | 0.669377i | ||||
\(276\) | −85372.3 | − | 47606.7i | −1.12072 | − | 0.624956i | ||||
\(277\) | 50103.9 | − | 18236.3i | 0.652998 | − | 0.237672i | 0.00578738 | − | 0.999983i | \(-0.498158\pi\) |
0.647210 | + | 0.762312i | \(0.275936\pi\) | |||||||
\(278\) | −111535. | − | 64394.6i | −1.44318 | − | 0.833220i | ||||
\(279\) | 61954.6 | − | 1848.28i | 0.795913 | − | 0.0237442i | ||||
\(280\) | 1865.84 | + | 3231.72i | 0.0237989 | + | 0.0412209i | ||||
\(281\) | 19299.9 | − | 23000.8i | 0.244424 | − | 0.291293i | −0.629859 | − | 0.776709i | \(-0.716887\pi\) |
0.874283 | + | 0.485416i | \(0.161332\pi\) | |||||||
\(282\) | 8147.02 | − | 3103.61i | 0.102447 | − | 0.0390274i | ||||
\(283\) | 449.898 | + | 2551.50i | 0.00561747 | + | 0.0318583i | 0.987488 | − | 0.157696i | \(-0.0504067\pi\) |
−0.981870 | + | 0.189555i | \(0.939296\pi\) | |||||||
\(284\) | −58006.1 | + | 10228.0i | −0.719178 | + | 0.126811i | ||||
\(285\) | 24676.0 | + | 64774.8i | 0.303798 | + | 0.797474i | ||||
\(286\) | 48894.8 | + | 41027.6i | 0.597765 | + | 0.501584i | ||||
\(287\) | −3736.98 | + | 2157.55i | −0.0453688 | + | 0.0261937i | ||||
\(288\) | 100417. | + | 54049.0i | 1.21066 | + | 0.651632i | ||||
\(289\) | 63013.3 | − | 109142.i | 0.754461 | − | 1.30676i | ||||
\(290\) | 52810.9 | + | 145097.i | 0.627953 | + | 1.72529i | ||||
\(291\) | 40698.2 | − | 72983.4i | 0.480606 | − | 0.861863i | ||||
\(292\) | −68384.7 | + | 57381.6i | −0.802035 | + | 0.672987i | ||||
\(293\) | 16296.1 | − | 44773.2i | 0.189823 | − | 0.521535i | −0.807874 | − | 0.589355i | \(-0.799382\pi\) |
0.997698 | + | 0.0678198i | \(0.0216043\pi\) | |||||||
\(294\) | 83863.2 | + | 96970.2i | 0.970235 | + | 1.12187i | ||||
\(295\) | −6021.82 | + | 34151.4i | −0.0691964 | + | 0.392432i | ||||
\(296\) | − | 15247.7i | − | 0.174029i | ||||||
\(297\) | −135185. | − | 17645.8i | −1.53255 | − | 0.200046i | ||||
\(298\) | −176903. | −1.99206 | ||||||||
\(299\) | −28695.7 | − | 5059.83i | −0.320978 | − | 0.0565970i | ||||
\(300\) | −62889.4 | − | 21833.5i | −0.698772 | − | 0.242594i | ||||
\(301\) | 7883.57 | + | 2869.38i | 0.0870141 | + | 0.0316706i | ||||
\(302\) | −139636. | − | 166412.i | −1.53103 | − | 1.82461i | ||||
\(303\) | 147719. | − | 88248.5i | 1.60898 | − | 0.961218i | ||||
\(304\) | 67067.6 | − | 24410.6i | 0.725714 | − | 0.264138i | ||||
\(305\) | −20693.5 | − | 11947.4i | −0.222451 | − | 0.128432i | ||||
\(306\) | −168223. | + | 149927.i | −1.79656 | + | 1.60117i | ||||
\(307\) | 11346.8 | + | 19653.3i | 0.120392 | + | 0.208525i | 0.919922 | − | 0.392101i | \(-0.128252\pi\) |
−0.799530 | + | 0.600626i | \(0.794918\pi\) | |||||||
\(308\) | −19004.0 | + | 22648.1i | −0.200329 | + | 0.238743i | ||||
\(309\) | 43155.5 | + | 35128.6i | 0.451980 | + | 0.367912i | ||||
\(310\) | −13309.4 | − | 75481.6i | −0.138496 | − | 0.785449i | ||||
\(311\) | −33510.1 | + | 5908.73i | −0.346461 | + | 0.0610905i | −0.344171 | − | 0.938907i | \(-0.611840\pi\) |
−0.00229010 | + | 0.999997i | \(0.500729\pi\) | |||||||
\(312\) | −14960.5 | − | 2408.50i | −0.153687 | − | 0.0247422i | ||||
\(313\) | −110952. | − | 93099.5i | −1.13252 | − | 0.950295i | −0.133349 | − | 0.991069i | \(-0.542573\pi\) |
−0.999168 | + | 0.0407737i | \(0.987018\pi\) | |||||||
\(314\) | 129487. | − | 74759.6i | 1.31331 | − | 0.758242i | ||||
\(315\) | −9976.90 | − | 1453.91i | −0.100548 | − | 0.0146527i | ||||
\(316\) | −59800.3 | + | 103577.i | −0.598866 | + | 1.03727i | ||||
\(317\) | −10091.2 | − | 27725.3i | −0.100421 | − | 0.275904i | 0.879301 | − | 0.476266i | \(-0.158010\pi\) |
−0.979722 | + | 0.200363i | \(0.935788\pi\) | |||||||
\(318\) | −83954.9 | + | 1252.02i | −0.830218 | + | 0.0123811i | ||||
\(319\) | −220845. | + | 185311.i | −2.17023 | + | 1.82104i | ||||
\(320\) | 34455.5 | − | 94665.7i | 0.336480 | − | 0.924470i | ||||
\(321\) | −13668.9 | + | 2620.93i | −0.132655 | + | 0.0254358i | ||||
\(322\) | 4135.11 | − | 23451.4i | 0.0398819 | − | 0.226181i | ||||
\(323\) | 213910.i | 2.05034i | ||||||||
\(324\) | 126030. | − | 54583.8i | 1.20056 | − | 0.519965i | ||||
\(325\) | −19844.7 | −0.187878 | ||||||||
\(326\) | 103339. | + | 18221.5i | 0.972366 | + | 0.171454i | ||||
\(327\) | −15100.2 | − | 78751.6i | −0.141217 | − | 0.736485i | ||||
\(328\) | −16096.5 | − | 5858.65i | −0.149618 | − | 0.0544565i | ||||
\(329\) | 773.777 | + | 922.151i | 0.00714865 | + | 0.00851943i | ||||
\(330\) | 2513.84 | + | 168567.i | 0.0230840 | + | 1.54790i | ||||
\(331\) | −22731.9 | + | 8273.74i | −0.207482 | + | 0.0755172i | −0.443670 | − | 0.896190i | \(-0.646324\pi\) |
0.236189 | + | 0.971707i | \(0.424102\pi\) | |||||||
\(332\) | 74124.1 | + | 42795.6i | 0.672486 | + | 0.388260i | ||||
\(333\) | 32333.9 | + | 25527.7i | 0.291588 | + | 0.230210i | ||||
\(334\) | −17518.0 | − | 30342.0i | −0.157033 | − | 0.271989i | ||||
\(335\) | 75771.8 | − | 90301.4i | 0.675178 | − | 0.804646i | ||||
\(336\) | −1650.05 | + | 10249.4i | −0.0146157 | + | 0.0907859i | ||||
\(337\) | 7201.64 | + | 40842.5i | 0.0634120 | + | 0.359627i | 0.999959 | + | 0.00908453i | \(0.00289173\pi\) |
−0.936547 | + | 0.350543i | \(0.885997\pi\) | |||||||
\(338\) | 152059. | − | 26812.1i | 1.33100 | − | 0.234692i | ||||
\(339\) | −95598.9 | + | 117443.i | −0.831866 | + | 1.02195i | ||||
\(340\) | 120984. | + | 101518.i | 1.04658 | + | 0.878183i | ||||
\(341\) | 123932. | − | 71552.0i | 1.06579 | − | 0.615337i | ||||
\(342\) | 72194.0 | − | 218407.i | 0.617232 | − | 1.86730i | ||||
\(343\) | −17917.5 | + | 31034.0i | −0.152296 | + | 0.263784i | ||||
\(344\) | 11390.5 | + | 31295.3i | 0.0962559 | + | 0.264461i | ||||
\(345\) | −39470.7 | − | 66070.0i | −0.331617 | − | 0.555093i | ||||
\(346\) | 91510.3 | − | 76786.2i | 0.764395 | − | 0.641403i | ||||
\(347\) | 36634.2 | − | 100652.i | 0.304248 | − | 0.835916i | −0.689501 | − | 0.724284i | \(-0.742170\pi\) |
0.993750 | − | 0.111631i | \(-0.0356075\pi\) | |||||||
\(348\) | 95252.1 | − | 274365.i | 0.786531 | − | 2.26553i | ||||
\(349\) | −35243.1 | + | 199874.i | −0.289350 | + | 1.64098i | 0.399970 | + | 0.916528i | \(0.369020\pi\) |
−0.689320 | + | 0.724457i | \(0.742091\pi\) | |||||||
\(350\) | − | 16217.9i | − | 0.132391i | ||||||
\(351\) | 30154.4 | − | 27692.6i | 0.244757 | − | 0.224776i | ||||
\(352\) | 263292. | 2.12496 | ||||||||
\(353\) | −24057.6 | − | 4242.00i | −0.193064 | − | 0.0340425i | 0.0762797 | − | 0.997086i | \(-0.475696\pi\) |
−0.269344 | + | 0.963044i | \(0.586807\pi\) | |||||||
\(354\) | 87045.2 | − | 75279.7i | 0.694606 | − | 0.600719i | ||||
\(355\) | −43578.6 | − | 15861.3i | −0.345794 | − | 0.125859i | ||||
\(356\) | 83671.7 | + | 99716.0i | 0.660204 | + | 0.786801i | ||||
\(357\) | −27174.6 | − | 15153.5i | −0.213220 | − | 0.118899i | ||||
\(358\) | −128159. | + | 46646.2i | −0.999963 | + | 0.363957i | ||||
\(359\) | 33774.1 | + | 19499.5i | 0.262056 | + | 0.151298i | 0.625272 | − | 0.780407i | \(-0.284988\pi\) |
−0.363216 | + | 0.931705i | \(0.618321\pi\) | |||||||
\(360\) | −21036.4 | − | 34049.2i | −0.162318 | − | 0.262725i | ||||
\(361\) | −44021.2 | − | 76247.0i | −0.337791 | − | 0.585071i | ||||
\(362\) | 109033. | − | 129940.i | 0.832032 | − | 0.991577i | ||||
\(363\) | −171005. | + | 65144.4i | −1.29776 | + | 0.494383i | ||||
\(364\) | −1541.73 | − | 8743.60i | −0.0116361 | − | 0.0659914i | ||||
\(365\) | −69218.5 | + | 12205.1i | −0.519561 | + | 0.0916127i | ||||
\(366\) | 28229.0 | + | 74101.5i | 0.210734 | + | 0.553178i | ||||
\(367\) | −107689. | − | 90361.5i | −0.799536 | − | 0.670890i | 0.148550 | − | 0.988905i | \(-0.452539\pi\) |
−0.948086 | + | 0.318015i | \(0.896984\pi\) | |||||||
\(368\) | −68628.2 | + | 39622.5i | −0.506765 | + | 0.292581i | ||||
\(369\) | 39372.5 | − | 24325.3i | 0.289162 | − | 0.178651i | ||||
\(370\) | 25471.4 | − | 44117.7i | 0.186058 | − | 0.322262i | ||||
\(371\) | −3965.24 | − | 10894.4i | −0.0288086 | − | 0.0791509i | ||||
\(372\) | −70212.6 | + | 125911.i | −0.507375 | + | 0.909868i | ||||
\(373\) | 106543. | − | 89399.9i | 0.765783 | − | 0.642568i | −0.173842 | − | 0.984774i | \(-0.555618\pi\) |
0.939625 | + | 0.342205i | \(0.111174\pi\) | |||||||
\(374\) | −177939. | + | 488883.i | −1.27212 | + | 3.49512i | ||||
\(375\) | −94931.3 | − | 109768.i | −0.675067 | − | 0.780573i | ||||
\(376\) | −829.801 | + | 4706.04i | −0.00586946 | + | 0.0332874i | ||||
\(377\) | − | 86575.5i | − | 0.609133i | ||||||
\(378\) | 22631.6 | + | 24643.4i | 0.158391 | + | 0.172472i | ||||
\(379\) | −205238. | −1.42883 | −0.714414 | − | 0.699723i | \(-0.753307\pi\) | ||||
−0.714414 | + | 0.699723i | \(0.753307\pi\) | |||||||
\(380\) | −158772. | − | 27995.9i | −1.09953 | − | 0.193877i | ||||
\(381\) | 122321. | + | 42466.4i | 0.842655 | + | 0.292547i | ||||
\(382\) | 305938. | + | 111352.i | 2.09656 | + | 0.763084i | ||||
\(383\) | 118294. | + | 140977.i | 0.806428 | + | 0.961064i | 0.999799 | − | 0.0200622i | \(-0.00638642\pi\) |
−0.193371 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(384\) | −112959. | + | 67482.4i | −0.766051 | + | 0.457644i | ||||
\(385\) | −21874.1 | + | 7961.50i | −0.147573 | + | 0.0537123i | ||||
\(386\) | −224165. | − | 129421.i | −1.50450 | − | 0.868624i | ||||
\(387\) | −85434.1 | − | 28240.1i | −0.570439 | − | 0.188558i | ||||
\(388\) | 97180.7 | + | 168322.i | 0.645530 | + | 1.11809i | ||||
\(389\) | −82339.4 | + | 98128.2i | −0.544137 | + | 0.648477i | −0.966110 | − | 0.258131i | \(-0.916893\pi\) |
0.421973 | + | 0.906608i | \(0.361338\pi\) | |||||||
\(390\) | −39263.4 | − | 31960.4i | −0.258142 | − | 0.210128i | ||||
\(391\) | −41242.6 | − | 233899.i | −0.269770 | − | 1.52994i | ||||
\(392\) | −69204.1 | + | 12202.6i | −0.450360 | + | 0.0794106i | ||||
\(393\) | 27467.3 | + | 4421.97i | 0.177840 | + | 0.0286306i | ||||
\(394\) | −40367.9 | − | 33872.7i | −0.260042 | − | 0.218201i | ||||
\(395\) | −81551.2 | + | 47083.6i | −0.522680 | + | 0.301769i | ||||
\(396\) | 196490. | − | 248878.i | 1.25300 | − | 1.58707i | ||||
\(397\) | −40759.2 | + | 70596.9i | −0.258609 | + | 0.447925i | −0.965870 | − | 0.259029i | \(-0.916598\pi\) |
0.707260 | + | 0.706953i | \(0.249931\pi\) | |||||||
\(398\) | −130660. | − | 358986.i | −0.824854 | − | 2.26627i | ||||
\(399\) | 31758.4 | − | 473.614i | 0.199486 | − | 0.00297494i | ||||
\(400\) | −41343.2 | + | 34691.0i | −0.258395 | + | 0.216819i | ||||
\(401\) | 20232.1 | − | 55587.3i | 0.125821 | − | 0.345690i | −0.860749 | − | 0.509030i | \(-0.830004\pi\) |
0.986570 | + | 0.163339i | \(0.0522266\pi\) | |||||||
\(402\) | −384194. | + | 73667.0i | −2.37738 | + | 0.455849i | ||||
\(403\) | −7462.48 | + | 42321.8i | −0.0459487 | + | 0.260588i | ||||
\(404\) | 400222.i | 2.45210i | ||||||||
\(405\) | 107423. | + | 12395.9i | 0.654919 | + | 0.0755732i | ||||
\(406\) | 70753.2 | 0.429234 | ||||||||
\(407\) | 93669.0 | + | 16516.4i | 0.565467 | + | 0.0997070i | ||||
\(408\) | −23259.2 | − | 121303.i | −0.139725 | − | 0.728707i | ||||
\(409\) | 273913. | + | 99696.1i | 1.63744 | + | 0.595980i | 0.986589 | − | 0.163225i | \(-0.0521897\pi\) |
0.650852 | + | 0.759205i | \(0.274412\pi\) | |||||||
\(410\) | −36786.8 | − | 43840.8i | −0.218839 | − | 0.260802i | ||||
\(411\) | 703.553 | + | 47177.0i | 0.00416498 | + | 0.279284i | ||||
\(412\) | −121620. | + | 44266.2i | −0.716494 | + | 0.260782i | ||||
\(413\) | 13761.4 | + | 7945.14i | 0.0806793 | + | 0.0465802i | ||||
\(414\) | −36830.4 | + | 252735.i | −0.214885 | + | 1.47457i | ||||
\(415\) | 33695.0 | + | 58361.4i | 0.195645 | + | 0.338867i | ||||
\(416\) | −50823.6 | + | 60569.2i | −0.293683 | + | 0.349998i | ||||
\(417\) | −30315.0 | + | 188303.i | −0.174335 | + | 1.08289i | ||||
\(418\) | −92222.7 | − | 523021.i | −0.527819 | − | 2.99341i | ||||
\(419\) | 121024. | − | 21339.9i | 0.689358 | − | 0.121552i | 0.182014 | − | 0.983296i | \(-0.441738\pi\) |
0.507344 | + | 0.861744i | \(0.330627\pi\) | |||||||
\(420\) | 14804.1 | − | 18186.8i | 0.0839234 | − | 0.103100i | ||||
\(421\) | −58336.5 | − | 48950.2i | −0.329137 | − | 0.276179i | 0.463211 | − | 0.886248i | \(-0.346697\pi\) |
−0.792348 | + | 0.610069i | \(0.791142\pi\) | |||||||
\(422\) | 297928. | − | 172009.i | 1.67296 | − | 0.965886i | ||||
\(423\) | −8590.25 | − | 9638.52i | −0.0480093 | − | 0.0538678i | ||||
\(424\) | 23011.4 | − | 39857.0i | 0.128001 | − | 0.221704i | ||||
\(425\) | −55323.0 | − | 151999.i | −0.306287 | − | 0.841516i | ||||
\(426\) | 78928.8 | + | 132119.i | 0.434927 | + | 0.728025i | ||||
\(427\) | −8387.46 | + | 7037.92i | −0.0460018 | + | 0.0386001i | ||||
\(428\) | 11071.8 | − | 30419.4i | 0.0604407 | − | 0.166059i | ||||
\(429\) | 31001.1 | − | 89295.9i | 0.168447 | − | 0.485196i | ||||
\(430\) | −19321.5 | + | 109578.i | −0.104497 | + | 0.592633i | ||||
\(431\) | − | 188543.i | − | 1.01497i | −0.861659 | − | 0.507487i | \(-0.830575\pi\) | ||
0.861659 | − | 0.507487i | \(-0.169425\pi\) | |||||||
\(432\) | 14411.5 | − | 110407.i | 0.0772221 | − | 0.591600i | ||||
\(433\) | 4635.55 | 0.0247244 | 0.0123622 | − | 0.999924i | \(-0.496065\pi\) | ||||
0.0123622 | + | 0.999924i | \(0.496065\pi\) | |||||||
\(434\) | −34587.2 | − | 6098.66i | −0.183627 | − | 0.0323783i | ||||
\(435\) | 172959. | − | 149581.i | 0.914039 | − | 0.790492i | ||||
\(436\) | 175258. | + | 63788.5i | 0.921942 | + | 0.335560i | ||||
\(437\) | 155845. | + | 185729.i | 0.816074 | + | 0.972559i | ||||
\(438\) | 203717. | + | 113600.i | 1.06189 | + | 0.592147i | ||||
\(439\) | 45262.1 | − | 16474.0i | 0.234858 | − | 0.0854813i | −0.221910 | − | 0.975067i | \(-0.571229\pi\) |
0.456768 | + | 0.889586i | \(0.349007\pi\) | |||||||
\(440\) | −80025.7 | − | 46202.9i | −0.413356 | − | 0.238651i | ||||
\(441\) | 89985.3 | − | 167182.i | 0.462694 | − | 0.859633i | ||||
\(442\) | −78117.9 | − | 135304.i | −0.399858 | − | 0.692574i | ||||
\(443\) | 8365.55 | − | 9969.67i | 0.0426272 | − | 0.0508011i | −0.744310 | − | 0.667835i | \(-0.767221\pi\) |
0.786937 | + | 0.617034i | \(0.211666\pi\) | |||||||
\(444\) | −89541.6 | + | 34111.0i | −0.454212 | + | 0.173033i | ||||
\(445\) | 17797.0 | + | 100932.i | 0.0898725 | + | 0.509692i | ||||
\(446\) | −207508. | + | 36589.3i | −1.04320 | + | 0.183944i | ||||
\(447\) | 93263.7 | + | 244818.i | 0.466764 | + | 1.22526i | ||||
\(448\) | −35361.9 | − | 29672.1i | −0.176189 | − | 0.147840i | ||||
\(449\) | 128969. | − | 74460.5i | 0.639726 | − | 0.369346i | −0.144783 | − | 0.989463i | \(-0.546248\pi\) |
0.784509 | + | 0.620118i | \(0.212915\pi\) | |||||||
\(450\) | 5186.87 | + | 173865.i | 0.0256142 | + | 0.858593i | ||||
\(451\) | 53426.4 | − | 92537.3i | 0.262666 | − | 0.454950i | ||||
\(452\) | −120466. | − | 330978.i | −0.589641 | − | 1.62003i | ||||
\(453\) | −156683. | + | 280977.i | −0.763529 | + | 1.36923i | ||||
\(454\) | −24188.1 | + | 20296.2i | −0.117352 | + | 0.0984699i | ||||
\(455\) | 2390.87 | − | 6568.87i | 0.0115487 | − | 0.0317298i | ||||
\(456\) | 82476.8 | + | 95367.2i | 0.396645 | + | 0.458637i | ||||
\(457\) | 3815.40 | − | 21638.2i | 0.0182687 | − | 0.103607i | −0.974310 | − | 0.225211i | \(-0.927693\pi\) |
0.992579 | + | 0.121604i | \(0.0388039\pi\) | |||||||
\(458\) | 264617.i | 1.26150i | ||||||||
\(459\) | 296174. | + | 153764.i | 1.40579 | + | 0.729841i | ||||
\(460\) | 179006. | 0.845966 | ||||||||
\(461\) | 136057. | + | 23990.6i | 0.640206 | + | 0.112886i | 0.484322 | − | 0.874890i | \(-0.339066\pi\) |
0.155884 | + | 0.987775i | \(0.450177\pi\) | |||||||
\(462\) | 72976.4 | + | 25335.4i | 0.341900 | + | 0.118698i | ||||
\(463\) | −192898. | − | 70209.0i | −0.899840 | − | 0.327515i | −0.149651 | − | 0.988739i | \(-0.547815\pi\) |
−0.750189 | + | 0.661224i | \(0.770037\pi\) | |||||||
\(464\) | −151345. | − | 180366.i | −0.702963 | − | 0.837759i | ||||
\(465\) | −97443.1 | + | 58213.2i | −0.450656 | + | 0.269225i | ||||
\(466\) | −539553. | + | 196381.i | −2.48463 | + | 0.904333i | ||||
\(467\) | −186474. | − | 107661.i | −0.855035 | − | 0.493655i | 0.00731154 | − | 0.999973i | \(-0.497673\pi\) |
−0.862346 | + | 0.506319i | \(0.831006\pi\) | |||||||
\(468\) | 19324.7 | + | 93243.3i | 0.0882308 | + | 0.425722i | ||||
\(469\) | −27007.5 | − | 46778.4i | −0.122783 | − | 0.212667i | ||||
\(470\) | −10262.4 | + | 12230.3i | −0.0464573 | + | 0.0553656i | ||||
\(471\) | −171727. | − | 139786.i | −0.774098 | − | 0.630116i | ||||
\(472\) | 10953.6 | + | 62121.0i | 0.0491670 | + | 0.278840i | ||||
\(473\) | −204590. | + | 36074.7i | −0.914454 | + | 0.161243i | ||||
\(474\) | 308527. | + | 49670.0i | 1.37321 | + | 0.221074i | ||||
\(475\) | 126490. | + | 106138.i | 0.560621 | + | 0.470417i | ||||
\(476\) | 62672.9 | − | 36184.2i | 0.276609 | − | 0.159700i | ||||
\(477\) | 45994.0 | + | 115526.i | 0.202145 | + | 0.507743i | ||||
\(478\) | 60489.0 | − | 104770.i | 0.264741 | − | 0.458544i | ||||
\(479\) | 72574.2 | + | 199396.i | 0.316309 | + | 0.869051i | 0.991347 | + | 0.131268i | \(0.0419048\pi\) |
−0.675038 | + | 0.737783i | \(0.735873\pi\) | |||||||
\(480\) | −208815. | + | 3114.06i | −0.906314 | + | 0.0135159i | ||||
\(481\) | −21880.6 | + | 18360.0i | −0.0945735 | + | 0.0793566i | ||||
\(482\) | 68517.9 | − | 188251.i | 0.294924 | − | 0.810296i | ||||
\(483\) | −34634.7 | + | 6641.00i | −0.148462 | + | 0.0284668i | ||||
\(484\) | 73908.7 | − | 419157.i | 0.315504 | − | 1.78931i | ||||
\(485\) | 153030.i | 0.650568i | ||||||||
\(486\) | −250505. | − | 256953.i | −1.06058 | − | 1.08788i | ||||
\(487\) | −5941.97 | −0.0250537 | −0.0125269 | − | 0.999922i | \(-0.503988\pi\) | ||||
−0.0125269 | + | 0.999922i | \(0.503988\pi\) | |||||||
\(488\) | −42803.9 | − | 7547.49i | −0.179740 | − | 0.0316930i | ||||
\(489\) | −29263.7 | − | 152619.i | −0.122380 | − | 0.638248i | ||||
\(490\) | −220620. | − | 80299.1i | −0.918867 | − | 0.334440i | ||||
\(491\) | −240755. | − | 286921.i | −0.998649 | − | 1.19014i | −0.981729 | − | 0.190287i | \(-0.939058\pi\) |
−0.0169206 | − | 0.999857i | \(-0.505386\pi\) | |||||||
\(492\) | 1605.13 | + | 107633.i | 0.00663103 | + | 0.444646i | ||||
\(493\) | 663118. | − | 241355.i | 2.72833 | − | 0.993032i | ||||
\(494\) | 138121. | + | 79744.2i | 0.565986 | + | 0.326772i | ||||
\(495\) | 231956. | − | 92347.7i | 0.946663 | − | 0.376891i | ||||
\(496\) | 58437.1 | + | 101216.i | 0.237534 | + | 0.411421i | ||||
\(497\) | −13659.3 | + | 16278.6i | −0.0552989 | + | 0.0659027i | ||||
\(498\) | 35545.9 | − | 220795.i | 0.143328 | − | 0.890288i | ||||
\(499\) | −13156.0 | − | 74611.3i | −0.0528351 | − | 0.299642i | 0.946927 | − | 0.321448i | \(-0.104170\pi\) |
−0.999762 | + | 0.0218057i | \(0.993058\pi\) | |||||||
\(500\) | 332416. | − | 58614.0i | 1.32967 | − | 0.234456i | ||||
\(501\) | −32755.1 | + | 40239.7i | −0.130498 | + | 0.160317i | ||||
\(502\) | 198305. | + | 166397.i | 0.786911 | + | 0.660296i | ||||
\(503\) | 88820.2 | − | 51280.3i | 0.351055 | − | 0.202682i | −0.314095 | − | 0.949392i | \(-0.601701\pi\) |
0.665150 | + | 0.746710i | \(0.268368\pi\) | |||||||
\(504\) | −17957.9 | + | 3721.78i | −0.0706961 | + | 0.0146518i | ||||
\(505\) | −157557. | + | 272896.i | −0.617809 | + | 1.07008i | ||||
\(506\) | 201681. | + | 554113.i | 0.787704 | + | 2.16420i | ||||
\(507\) | −117272. | − | 196301.i | −0.456223 | − | 0.763672i | ||||
\(508\) | −230705. | + | 193584.i | −0.893983 | + | 0.750141i | ||||
\(509\) | −117615. | + | 323146.i | −0.453972 | + | 1.24728i | 0.475934 | + | 0.879481i | \(0.342110\pi\) |
−0.929906 | + | 0.367797i | \(0.880112\pi\) | |||||||
\(510\) | 135340. | − | 389834.i | 0.520338 | − | 1.49879i | ||||
\(511\) | −5592.62 | + | 31717.3i | −0.0214177 | + | 0.121466i | ||||
\(512\) | 288296.i | 1.09976i | ||||||||
\(513\) | −340316. | + | 15234.5i | −1.29315 | + | 0.0578886i | ||||
\(514\) | −87008.2 | −0.329332 | ||||||||
\(515\) | −100355. | − | 17695.3i | −0.378376 | − | 0.0667179i | ||||
\(516\) | 158298. | − | 136902.i | 0.594534 | − | 0.514174i | ||||
\(517\) | −28011.1 | − | 10195.2i | −0.104797 | − | 0.0381430i | ||||
\(518\) | −15004.6 | − | 17881.8i | −0.0559197 | − | 0.0666425i | ||||
\(519\) | −154510. | − | 86160.2i | −0.573616 | − | 0.319869i | ||||
\(520\) | 26076.3 | − | 9491.00i | 0.0964361 | − | 0.0350999i | ||||
\(521\) | 2025.59 | + | 1169.47i | 0.00746235 | + | 0.00430839i | 0.503727 | − | 0.863863i | \(-0.331962\pi\) |
−0.496264 | + | 0.868172i | \(0.665295\pi\) | |||||||
\(522\) | −758514. | + | 22628.5i | −2.78370 | + | 0.0830454i | ||||
\(523\) | 96052.9 | + | 166369.i | 0.351162 | + | 0.608230i | 0.986453 | − | 0.164042i | \(-0.0524534\pi\) |
−0.635291 | + | 0.772272i | \(0.719120\pi\) | |||||||
\(524\) | −41594.0 | + | 49569.8i | −0.151485 | + | 0.180532i | ||||
\(525\) | −22444.1 | + | 8550.12i | −0.0814300 | + | 0.0310208i | ||||
\(526\) | 100869. | + | 572054.i | 0.364573 | + | 2.06760i | ||||
\(527\) | −344965. | + | 60826.6i | −1.24209 | + | 0.219014i | ||||
\(528\) | −91515.0 | − | 240228.i | −0.328265 | − | 0.861698i | ||||
\(529\) | 8153.95 | + | 6841.97i | 0.0291378 | + | 0.0244495i | ||||
\(530\) | 133163. | − | 76881.5i | 0.474057 | − | 0.273697i | ||||
\(531\) | −150071. | − | 80775.2i | −0.532240 | − | 0.286477i | ||||
\(532\) | −36937.5 | + | 63977.7i | −0.130510 | + | 0.226050i | ||||
\(533\) | 10974.9 | + | 30153.2i | 0.0386318 | + | 0.106140i | ||||
\(534\) | 165647. | − | 297052.i | 0.580900 | − | 1.04172i | ||||
\(535\) | 19524.7 | − | 16383.2i | 0.0682146 | − | 0.0572389i | ||||
\(536\) | 73336.8 | − | 201491.i | 0.255266 | − | 0.701336i | ||||
\(537\) | 132120. | + | 152769.i | 0.458163 | + | 0.529769i | ||||
\(538\) | −19142.4 | + | 108562.i | −0.0661352 | + | 0.375071i | ||||
\(539\) | − | 438350.i | − | 1.50884i | ||||||
\(540\) | −152892. | + | 199708.i | −0.524320 | + | 0.684869i | ||||
\(541\) | −97098.5 | −0.331755 | −0.165878 | − | 0.986146i | \(-0.553046\pi\) | ||||
−0.165878 | + | 0.986146i | \(0.553046\pi\) | |||||||
\(542\) | 766129. | + | 135089.i | 2.60797 | + | 0.459856i | ||||
\(543\) | −237308. | − | 82386.9i | −0.804846 | − | 0.279421i | ||||
\(544\) | −605612. | − | 220425.i | −2.04643 | − | 0.744839i | ||||
\(545\) | 94389.6 | + | 112489.i | 0.317783 | + | 0.378720i | ||||
\(546\) | −19915.1 | + | 11897.4i | −0.0668032 | + | 0.0399087i | ||||
\(547\) | 187642. | − | 68296.1i | 0.627127 | − | 0.228256i | −0.00885339 | − | 0.999961i | \(-0.502818\pi\) |
0.635980 | + | 0.771705i | \(0.280596\pi\) | |||||||
\(548\) | −95038.7 | − | 54870.6i | −0.316475 | − | 0.182717i | ||||
\(549\) | 87667.5 | − | 78133.0i | 0.290867 | − | 0.259233i | ||||
\(550\) | 200799. | + | 347793.i | 0.663797 | + | 1.14973i | ||||
\(551\) | −463043. | + | 551833.i | −1.52517 | + | 1.81763i | ||||
\(552\) | −108571. | − | 88376.8i | −0.356316 | − | 0.290041i | ||||
\(553\) | 7492.79 | + | 42493.7i | 0.0245015 | + | 0.138955i | ||||
\(554\) | 319113. | − | 56268.3i | 1.03974 | − | 0.183334i | ||||
\(555\) | −74483.6 | − | 11991.2i | −0.241810 | − | 0.0389292i | ||||
\(556\) | −339828. | − | 285149.i | −1.09928 | − | 0.922408i | ||||
\(557\) | 136110. | − | 78583.1i | 0.438712 | − | 0.253290i | −0.264339 | − | 0.964430i | \(-0.585154\pi\) |
0.703051 | + | 0.711139i | \(0.251821\pi\) | |||||||
\(558\) | 372745. | + | 54319.3i | 1.19714 | + | 0.174456i | ||||
\(559\) | 31193.5 | − | 54028.7i | 0.0998253 | − | 0.172902i | ||||
\(560\) | −6502.23 | − | 17864.7i | −0.0207342 | − | 0.0569666i | ||||
\(561\) | 770381. | − | 11488.7i | 2.44782 | − | 0.0365045i | ||||
\(562\) | 139782. | − | 117291.i | 0.442566 | − | 0.371357i | ||||
\(563\) | 164752. | − | 452653.i | 0.519773 | − | 1.42807i | −0.350997 | − | 0.936376i | \(-0.614157\pi\) |
0.870771 | − | 0.491689i | \(-0.163620\pi\) | |||||||
\(564\) | 29492.4 | − | 5655.00i | 0.0927155 | − | 0.0177777i | ||||
\(565\) | 48155.9 | − | 273105.i | 0.150852 | − | 0.855526i | ||||
\(566\) | 15745.3i | 0.0491495i | ||||||||
\(567\) | 22172.9 | − | 44312.2i | 0.0689694 | − | 0.137834i | ||||
\(568\) | −84356.3 | −0.261469 | ||||||||
\(569\) | −431178. | − | 76028.3i | −1.33178 | − | 0.234828i | −0.537953 | − | 0.842975i | \(-0.680802\pi\) |
−0.793825 | + | 0.608146i | \(0.791913\pi\) | |||||||
\(570\) | 79327.2 | + | 413714.i | 0.244159 | + | 1.27336i | ||||
\(571\) | 86789.3 | + | 31588.7i | 0.266191 | + | 0.0968857i | 0.471668 | − | 0.881776i | \(-0.343652\pi\) |
−0.205476 | + | 0.978662i | \(0.565874\pi\) | |||||||
\(572\) | 141320. | + | 168418.i | 0.431927 | + | 0.514750i | ||||
\(573\) | −7189.52 | − | 482096.i | −0.0218973 | − | 1.46833i | ||||
\(574\) | −24642.5 | + | 8969.12i | −0.0747929 | + | 0.0272224i | ||||
\(575\) | −158774. | − | 91668.0i | −0.480223 | − | 0.277257i | ||||
\(576\) | 388589. | + | 306793.i | 1.17124 | + | 0.924698i | ||||
\(577\) | −121423. | − | 210311.i | −0.364711 | − | 0.631699i | 0.624018 | − | 0.781410i | \(-0.285499\pi\) |
−0.988730 | + | 0.149711i | \(0.952166\pi\) | |||||||
\(578\) | 492309. | − | 586711.i | 1.47361 | − | 1.75618i | ||||
\(579\) | −60927.7 | + | 378455.i | −0.181743 | + | 1.12890i | ||||
\(580\) | 92356.6 | + | 523780.i | 0.274544 | + | 1.55702i | ||||
\(581\) | 30410.3 | − | 5362.15i | 0.0900882 | − | 0.0158850i | ||||
\(582\) | 320596. | − | 393852.i | 0.946481 | − | 1.16275i | ||||
\(583\) | 219922. | + | 184536.i | 0.647039 | + | 0.542930i | ||||
\(584\) | −110721. | + | 63925.0i | −0.324643 | + | 0.187433i | ||||
\(585\) | −23530.6 | + | 71186.7i | −0.0687578 | + | 0.208011i | ||||
\(586\) | 144781. | − | 250768.i | 0.421614 | − | 0.730258i | ||||
\(587\) | 188159. | + | 516964.i | 0.546072 | + | 1.50032i | 0.838971 | + | 0.544177i | \(0.183158\pi\) |
−0.292899 | + | 0.956144i | \(0.594620\pi\) | |||||||
\(588\) | 226477. | + | 379100.i | 0.655043 | + | 1.09648i | ||||
\(589\) | 273921. | − | 229847.i | 0.789579 | − | 0.662535i | ||||
\(590\) | −72080.4 | + | 198039.i | −0.207068 | + | 0.568915i | ||||
\(591\) | −25594.7 | + | 73723.3i | −0.0732783 | + | 0.211072i | ||||
\(592\) | −13489.1 | + | 76500.3i | −0.0384892 | + | 0.218283i | ||||
\(593\) | − | 265204.i | − | 0.754172i | −0.926178 | − | 0.377086i | \(-0.876926\pi\) | ||
0.926178 | − | 0.377086i | \(-0.123074\pi\) | |||||||
\(594\) | −790452. | − | 248271.i | −2.24028 | − | 0.703643i | ||||
\(595\) | 56979.0 | 0.160946 | ||||||||
\(596\) | −600085. | − | 105811.i | −1.68935 | − | 0.297878i | ||||
\(597\) | −427921. | + | 370081.i | −1.20064 | + | 1.03836i | ||||
\(598\) | −166402. | − | 60565.5i | −0.465326 | − | 0.169365i | ||||
\(599\) | 96884.8 | + | 115463.i | 0.270024 | + | 0.321802i | 0.883968 | − | 0.467548i | \(-0.154862\pi\) |
−0.613944 | + | 0.789350i | \(0.710418\pi\) | |||||||
\(600\) | −83270.4 | − | 46434.6i | −0.231307 | − | 0.128985i | ||||
\(601\) | −292365. | + | 106412.i | −0.809424 | + | 0.294606i | −0.713386 | − | 0.700772i | \(-0.752839\pi\) |
−0.0960378 | + | 0.995378i | \(0.530617\pi\) | |||||||
\(602\) | 44154.6 | + | 25492.7i | 0.121838 | + | 0.0703432i | ||||
\(603\) | 304497. | + | 492853.i | 0.837429 | + | 1.35545i | ||||
\(604\) | −374134. | − | 648019.i | −1.02554 | − | 1.77629i | ||||
\(605\) | 215406. | − | 256711.i | 0.588502 | − | 0.701349i | ||||
\(606\) | 977219. | − | 372272.i | 2.66101 | − | 1.01371i | ||||
\(607\) | 34423.9 | + | 195228.i | 0.0934293 | + | 0.529864i | 0.995217 | + | 0.0976852i | \(0.0311438\pi\) |
−0.901788 | + | 0.432178i | \(0.857745\pi\) | |||||||
\(608\) | 647901. | − | 114242.i | 1.75268 | − | 0.309044i | ||||
\(609\) | −37301.2 | − | 97916.1i | −0.100575 | − | 0.264009i | ||||
\(610\) | −111241. | − | 93342.2i | −0.298954 | − | 0.250852i | ||||
\(611\) | 7752.39 | − | 4475.85i | 0.0207660 | − | 0.0119893i | ||||
\(612\) | −660317. | + | 407960.i | −1.76299 | + | 1.08922i | ||||
\(613\) | −312175. | + | 540703.i | −0.830763 | + | 1.43892i | 0.0666714 | + | 0.997775i | \(0.478762\pi\) |
−0.897434 | + | 0.441148i | \(0.854571\pi\) | |||||||
\(614\) | 47169.8 | + | 129598.i | 0.125120 | + | 0.343765i | ||||
\(615\) | −41277.7 | + | 74022.6i | −0.109135 | + | 0.195711i | ||||
\(616\) | −32436.0 | + | 27217.0i | −0.0854802 | + | 0.0717264i | ||||
\(617\) | 57927.0 | − | 159153.i | 0.152164 | − | 0.418066i | −0.840066 | − | 0.542484i | \(-0.817484\pi\) |
0.992230 | + | 0.124418i | \(0.0397062\pi\) | |||||||
\(618\) | 221211. | + | 255785.i | 0.579203 | + | 0.669726i | ||||
\(619\) | 25857.6 | − | 146646.i | 0.0674850 | − | 0.382726i | −0.932294 | − | 0.361701i | \(-0.882196\pi\) |
0.999779 | − | 0.0210249i | \(-0.00669292\pi\) | |||||||
\(620\) | − | 264007.i | − | 0.686803i | ||||||
\(621\) | 369179. | − | 82272.3i | 0.957314 | − | 0.213339i | ||||
\(622\) | −206791. | −0.534504 | ||||||||
\(623\) | 46249.0 | + | 8154.95i | 0.119159 | + | 0.0210109i | ||||
\(624\) | 72928.8 | + | 25318.9i | 0.187297 | + | 0.0650243i | ||||
\(625\) | 42207.9 | + | 15362.4i | 0.108052 | + | 0.0393278i | ||||
\(626\) | −565790. | − | 674282.i | −1.44380 | − | 1.72065i | ||||
\(627\) | −675195. | + | 403366.i | −1.71749 | + | 1.02604i | ||||
\(628\) | 483959. | − | 176147.i | 1.22713 | − | 0.446638i | ||||
\(629\) | −201626. | − | 116409.i | −0.509619 | − | 0.294229i | ||||
\(630\) | −58176.8 | − | 19230.2i | −0.146578 | − | 0.0484511i | ||||
\(631\) | −298176. | − | 516456.i | −0.748883 | − | 1.29710i | −0.948359 | − | 0.317200i | \(-0.897257\pi\) |
0.199476 | − | 0.979903i | \(-0.436076\pi\) | |||||||
\(632\) | −110102. | + | 131215.i | −0.275653 | + | 0.328510i | ||||
\(633\) | −395113. | − | 321622.i | −0.986085 | − | 0.802674i | ||||
\(634\) | −31136.4 | − | 176583.i | −0.0774622 | − | 0.439310i | ||||
\(635\) | −233518. | + | 41175.5i | −0.579125 | + | 0.102115i | ||||
\(636\) | −285538. | − | 45969.0i | −0.705911 | − | 0.113645i | ||||
\(637\) | 100841. | + | 84615.4i | 0.248518 | + | 0.208531i | ||||
\(638\) | −1.51730e6 | + | 876015.i | −3.72761 | + | 2.15214i | ||||
\(639\) | 141230. | − | 178884.i | 0.345879 | − | 0.438096i | ||||
\(640\) | 120482. | − | 208680.i | 0.294144 | − | 0.509473i | ||||
\(641\) | −50133.6 | − | 137741.i | −0.122015 | − | 0.335233i | 0.863615 | − | 0.504152i | \(-0.168195\pi\) |
−0.985630 | + | 0.168918i | \(0.945973\pi\) | |||||||
\(642\) | −84573.3 | + | 1261.25i | −0.205193 | + | 0.00306006i | ||||
\(643\) | 121340. | − | 101816.i | 0.293482 | − | 0.246261i | −0.484143 | − | 0.874989i | \(-0.660869\pi\) |
0.777625 | + | 0.628728i | \(0.216424\pi\) | |||||||
\(644\) | 28054.0 | − | 77077.7i | 0.0676430 | − | 0.185848i | ||||
\(645\) | 161832. | − | 31030.4i | 0.388997 | − | 0.0745878i | ||||
\(646\) | −225741. | + | 1.28024e6i | −0.540934 | + | 3.06779i | ||||
\(647\) | 428602.i | 1.02387i | 0.859023 | + | 0.511936i | \(0.171072\pi\) | ||||
−0.859023 | + | 0.511936i | \(0.828928\pi\) | |||||||
\(648\) | 191329. | − | 45643.0i | 0.455649 | − | 0.108699i | ||||
\(649\) | −393484. | −0.934196 | ||||||||
\(650\) | −118769. | − | 20942.2i | −0.281110 | − | 0.0495673i | ||||
\(651\) | 9794.46 | + | 51080.8i | 0.0231110 | + | 0.120530i | ||||
\(652\) | 339645. | + | 123621.i | 0.798969 | + | 0.290801i | ||||
\(653\) | 472730. | + | 563377.i | 1.10863 | + | 1.32121i | 0.942159 | + | 0.335167i | \(0.108793\pi\) |
0.166470 | + | 0.986046i | \(0.446763\pi\) | |||||||
\(654\) | −7266.50 | − | 487258.i | −0.0169891 | − | 1.13921i | ||||
\(655\) | −47875.7 | + | 17425.3i | −0.111592 | + | 0.0406161i | ||||
\(656\) | 75576.0 | + | 43633.8i | 0.175621 | + | 0.101395i | ||||
\(657\) | 49812.1 | − | 341816.i | 0.115400 | − | 0.791885i | ||||
\(658\) | 3657.85 | + | 6335.59i | 0.00844840 | + | 0.0146331i | ||||
\(659\) | 318200. | − | 379216.i | 0.732706 | − | 0.873205i | −0.263093 | − | 0.964771i | \(-0.584743\pi\) |
0.995799 | + | 0.0915652i | \(0.0291870\pi\) | |||||||
\(660\) | −92297.6 | + | 573310.i | −0.211886 | + | 1.31614i | ||||
\(661\) | 102468. | + | 581125.i | 0.234523 | + | 1.33005i | 0.843616 | + | 0.536947i | \(0.180423\pi\) |
−0.609093 | + | 0.793099i | \(0.708466\pi\) | |||||||
\(662\) | −144780. | + | 25528.7i | −0.330365 | + | 0.0582522i | ||||
\(663\) | −146065. | + | 179441.i | −0.332291 | + | 0.408220i | ||||
\(664\) | 93902.8 | + | 78793.8i | 0.212982 | + | 0.178713i | ||||
\(665\) | −50372.6 | + | 29082.6i | −0.113907 | + | 0.0657643i | ||||
\(666\) | 166577. | + | 186904.i | 0.375548 | + | 0.421376i | ||||
\(667\) | 399916. | − | 692675.i | 0.898912 | − | 1.55696i | ||||
\(668\) | −41275.4 | − | 113403.i | −0.0924993 | − | 0.254140i | ||||
\(669\) | 160035. | + | 267883.i | 0.357572 | + | 0.598540i | ||||
\(670\) | 548785. | − | 460485.i | 1.22251 | − | 1.02581i | ||||
\(671\) | 92730.8 | − | 254776.i | 0.205958 | − | 0.565865i | ||||
\(672\) | −31384.7 | + | 90400.8i | −0.0694991 | + | 0.200186i | ||||
\(673\) | 148961. | − | 844798.i | 0.328883 | − | 1.86519i | −0.151968 | − | 0.988385i | \(-0.548561\pi\) |
0.480851 | − | 0.876802i | \(-0.340328\pi\) | |||||||
\(674\) | 252040.i | 0.554816i | ||||||||
\(675\) | 237879. | − | 98840.3i | 0.522095 | − | 0.216934i | ||||
\(676\) | 531848. | 1.16384 | ||||||||
\(677\) | −264276. | − | 46598.9i | −0.576607 | − | 0.101671i | −0.122263 | − | 0.992498i | \(-0.539015\pi\) |
−0.454344 | + | 0.890826i | \(0.650126\pi\) | |||||||
\(678\) | −696092. | + | 602004.i | −1.51428 | + | 1.30960i | ||||
\(679\) | 65892.5 | + | 23982.9i | 0.142921 | + | 0.0520190i | ||||
\(680\) | 145391. | + | 173271.i | 0.314427 | + | 0.374720i | ||||
\(681\) | 40840.2 | + | 22774.0i | 0.0880630 | + | 0.0491071i | ||||
\(682\) | 817232. | − | 297448.i | 1.75702 | − | 0.639503i | ||||
\(683\) | −165671. | − | 95650.1i | −0.355144 | − | 0.205043i | 0.311804 | − | 0.950146i | \(-0.399067\pi\) |
−0.666949 | + | 0.745104i | \(0.732400\pi\) | |||||||
\(684\) | 375530. | − | 697691.i | 0.802661 | − | 1.49125i | ||||
\(685\) | −43202.2 | − | 74828.4i | −0.0920714 | − | 0.159472i | ||||
\(686\) | −139985. | + | 166828.i | −0.297464 | + | 0.354504i | ||||
\(687\) | 366207. | − | 139507.i | 0.775913 | − | 0.295585i | ||||
\(688\) | −29462.5 | − | 167090.i | −0.0622434 | − | 0.353000i | ||||
\(689\) | −84903.7 | + | 14970.8i | −0.178850 | + | 0.0315360i | ||||
\(690\) | −166505. | − | 437078.i | −0.349728 | − | 0.918039i | ||||
\(691\) | 201952. | + | 169458.i | 0.422953 | + | 0.354900i | 0.829285 | − | 0.558826i | \(-0.188748\pi\) |
−0.406332 | + | 0.913725i | \(0.633192\pi\) | |||||||
\(692\) | 356346. | − | 205737.i | 0.744150 | − | 0.429635i | ||||
\(693\) | −3411.37 | − | 114350.i | −0.00710333 | − | 0.238105i | ||||
\(694\) | 325472. | − | 563734.i | 0.675763 | − | 1.17046i | ||||
\(695\) | −119460. | − | 328214.i | −0.247316 | − | 0.679496i | ||||
\(696\) | 202578. | − | 363280.i | 0.418190 | − | 0.749934i | ||||
\(697\) | −200360. | + | 168122.i | −0.412426 | + | 0.346067i | ||||
\(698\) | −421855. | + | 1.15904e6i | −0.865870 | + | 2.37896i | ||||
\(699\) | 556228. | + | 643161.i | 1.13841 | + | 1.31633i | ||||
\(700\) | 9700.43 | − | 55013.9i | 0.0197968 | − | 0.112273i | ||||
\(701\) | − | 330892.i | − | 0.673364i | −0.941618 | − | 0.336682i | \(-0.890695\pi\) | ||
0.941618 | − | 0.336682i | \(-0.109305\pi\) | |||||||
\(702\) | 209696. | − | 133916.i | 0.425516 | − | 0.271744i | ||||
\(703\) | 237665. | 0.480899 | ||||||||
\(704\) | 1.12571e6 | + | 198494.i | 2.27134 | + | 0.400499i | ||||
\(705\) | 22336.0 | + | 7754.45i | 0.0449394 | + | 0.0156017i | ||||
\(706\) | −139506. | − | 50776.2i | −0.279888 | − | 0.101871i | ||||
\(707\) | 92813.0 | + | 110610.i | 0.185682 | + | 0.221287i | ||||
\(708\) | 340299. | − | 203297.i | 0.678882 | − | 0.405569i | ||||
\(709\) | −854464. | + | 311000.i | −1.69981 | + | 0.618682i | −0.995804 | − | 0.0915085i | \(-0.970831\pi\) |
−0.704010 | + | 0.710190i | \(0.748609\pi\) | |||||||
\(710\) | −244077. | − | 140918.i | −0.484183 | − | 0.279543i | ||||
\(711\) | −93917.5 | − | 453161.i | −0.185784 | − | 0.896423i | ||||
\(712\) | 93213.0 | + | 161450.i | 0.183872 | + | 0.318476i | ||||
\(713\) | −255202. | + | 304138.i | −0.502002 | + | 0.598263i | ||||
\(714\) | −146647. | − | 119371.i | −0.287658 | − | 0.234153i | ||||
\(715\) | 30058.7 | + | 170472.i | 0.0587975 | + | 0.333457i | ||||
\(716\) | −462638. | + | 81575.6i | −0.902434 | + | 0.159123i | ||||
\(717\) | −176882. | − | 28476.4i | −0.344070 | − | 0.0553920i | ||||
\(718\) | 181558. | + | 152345.i | 0.352181 | + | 0.295515i | ||||
\(719\) | −534889. | + | 308818.i | −1.03468 | + | 0.597372i | −0.918322 | − | 0.395835i | \(-0.870455\pi\) |
−0.116358 | + | 0.993207i | \(0.537122\pi\) | |||||||
\(720\) | 75421.2 | + | 189441.i | 0.145488 | + | 0.365433i | ||||
\(721\) | −23347.0 | + | 40438.2i | −0.0449118 | + | 0.0777895i | ||||
\(722\) | −183000. | − | 502789.i | −0.351057 | − | 0.964520i | ||||
\(723\) | −296646. | + | 4423.89i | −0.567495 | + | 0.00846307i | ||||
\(724\) | 447579. | − | 375563.i | 0.853871 | − | 0.716483i | ||||
\(725\) | 186307. | − | 511873.i | 0.354448 | − | 0.973837i | ||||
\(726\) | −1.09220e6 | + | 209423.i | −2.07218 | + | 0.397329i | ||||
\(727\) | −113322. | + | 642684.i | −0.214411 | + | 1.21599i | 0.667514 | + | 0.744597i | \(0.267358\pi\) |
−0.881926 | + | 0.471389i | \(0.843753\pi\) | |||||||
\(728\) | − | 12715.5i | − | 0.0239923i | ||||||
\(729\) | −223534. | + | 482143.i | −0.420619 | + | 0.907238i | ||||
\(730\) | −427149. | −0.801555 | ||||||||
\(731\) | 500790. | + | 88302.9i | 0.937176 | + | 0.165249i | ||||
\(732\) | 51435.3 | + | 268249.i | 0.0959928 | + | 0.500630i | ||||
\(733\) | −853703. | − | 310723.i | −1.58891 | − | 0.578316i | −0.611792 | − | 0.791019i | \(-0.709551\pi\) |
−0.977117 | + | 0.212703i | \(0.931773\pi\) | |||||||
\(734\) | −549151. | − | 654452.i | −1.01929 | − | 1.21475i | ||||
\(735\) | 5184.55 | + | 347652.i | 0.00959703 | + | 0.643532i | ||||
\(736\) | −686417. | + | 249835.i | −1.26716 | + | 0.461209i | ||||
\(737\) | 1.15835e6 | + | 668775.i | 2.13258 | + | 1.23125i | ||||
\(738\) | 261313. | − | 104035.i | 0.479786 | − | 0.191015i | ||||
\(739\) | 346054. | + | 599383.i | 0.633658 | + | 1.09753i | 0.986798 | + | 0.161958i | \(0.0517808\pi\) |
−0.353139 | + | 0.935571i | \(0.614886\pi\) | |||||||
\(740\) | 112791. | − | 134420.i | 0.205974 | − | 0.245470i | ||||
\(741\) | 37541.2 | − | 233189.i | 0.0683709 | − | 0.424689i | ||||
\(742\) | −12234.8 | − | 69386.9i | −0.0222223 | − | 0.126029i | ||||
\(743\) | 868910. | − | 153212.i | 1.57397 | − | 0.277534i | 0.682595 | − | 0.730797i | \(-0.260851\pi\) |
0.891377 | + | 0.453263i | \(0.149740\pi\) | |||||||
\(744\) | −130342. | + | 160126.i | −0.235472 | + | 0.289278i | ||||
\(745\) | −367520. | − | 308386.i | −0.662169 | − | 0.555625i | ||||
\(746\) | 731995. | − | 422618.i | 1.31532 | − | 0.759399i | ||||
\(747\) | −324301. | + | 67211.3i | −0.581175 | + | 0.120448i | ||||
\(748\) | −896014. | + | 1.55194e6i | −1.60144 | + | 2.77378i | ||||
\(749\) | −3994.45 | − | 10974.7i | −0.00712022 | − | 0.0195626i | ||||
\(750\) | −452319. | − | 757137.i | −0.804122 | − | 1.34602i | ||||
\(751\) | −116154. | + | 97464.8i | −0.205946 | + | 0.172810i | −0.739927 | − | 0.672687i | \(-0.765140\pi\) |
0.533981 | + | 0.845497i | \(0.320696\pi\) | |||||||
\(752\) | 8326.51 | − | 22876.9i | 0.0147240 | − | 0.0404540i | ||||
\(753\) | 125732. | − | 362161.i | 0.221747 | − | 0.638722i | ||||
\(754\) | 91363.6 | − | 518149.i | 0.160705 | − | 0.911405i | ||||
\(755\) | − | 589146.i | − | 1.03354i | ||||||
\(756\) | 62030.1 | + | 97131.3i | 0.108532 | + | 0.169948i | ||||
\(757\) | −593090. | −1.03497 | −0.517486 | − | 0.855692i | \(-0.673132\pi\) | ||||
−0.517486 | + | 0.855692i | \(0.673132\pi\) | |||||||
\(758\) | −1.22834e6 | − | 216589.i | −2.13786 | − | 0.376963i | ||||
\(759\) | 660517. | − | 571238.i | 1.14657 | − | 0.991593i | ||||
\(760\) | −216973. | − | 78971.6i | −0.375645 | − | 0.136724i | ||||
\(761\) | 503625. | + | 600197.i | 0.869638 | + | 1.03639i | 0.998996 | + | 0.0447960i | \(0.0142638\pi\) |
−0.129358 | + | 0.991598i | \(0.541292\pi\) | |||||||
\(762\) | 687266. | + | 383244.i | 1.18363 | + | 0.660033i | ||||
\(763\) | 63229.1 | − | 23013.5i | 0.108609 | − | 0.0395306i | ||||
\(764\) | 971190. | + | 560717.i | 1.66386 | + | 0.960631i | ||||
\(765\) | −610848. | + | 18223.3i | −1.04378 | + | 0.0311389i | ||||
\(766\) | 559208. | + | 968577.i | 0.953051 | + | 1.65073i | ||||
\(767\) | 75955.0 | − | 90519.6i | 0.129112 | − | 0.153869i | ||||
\(768\) | 75248.9 | − | 28666.2i | 0.127579 | − | 0.0486012i | ||||
\(769\) | 26752.7 | + | 151722.i | 0.0452392 | + | 0.256564i | 0.999037 | − | 0.0438864i | \(-0.0139740\pi\) |
−0.953797 | + | 0.300451i | \(0.902863\pi\) | |||||||
\(770\) | −139317. | + | 24565.3i | −0.234975 | + | 0.0414324i | ||||
\(771\) | 45870.9 | + | 120412.i | 0.0771665 | + | 0.202563i | ||||
\(772\) | −682993. | − | 573099.i | −1.14599 | − | 0.961601i | ||||
\(773\) | 617858. | − | 356720.i | 1.03402 | − | 0.596992i | 0.115887 | − | 0.993262i | \(-0.463029\pi\) |
0.918134 | + | 0.396270i | \(0.129696\pi\) | |||||||
\(774\) | −481515. | − | 259174.i | −0.803763 | − | 0.432623i | ||||
\(775\) | −135196. | + | 234167.i | −0.225093 | + | 0.389872i | ||||
\(776\) | 95204.5 | + | 261572.i | 0.158101 | + | 0.434378i | ||||
\(777\) | −16836.3 | + | 30192.3i | −0.0278872 | + | 0.0500098i | ||||
\(778\) | −596351. | + | 500398.i | −0.985242 | + | 0.826716i | ||||
\(779\) | 91318.4 | − | 250895.i | 0.150482 | − | 0.413445i | ||||
\(780\) | −114072. | − | 131900.i | −0.187494 | − | 0.216798i | ||||
\(781\) | 91375.1 | − | 518214.i | 0.149805 | − | 0.849585i | ||||
\(782\) | − | 1.44339e6i | − | 2.36032i | ||||||
\(783\) | 431207. | + | 1.03779e6i | 0.703334 | + | 1.69272i | ||||
\(784\) | 358004. | 0.582446 | ||||||||
\(785\) | 399338. | + | 70414.0i | 0.648039 | + | 0.114267i | ||||
\(786\) | 159723. | + | 55451.6i | 0.258537 | + | 0.0897571i | ||||
\(787\) | 118383. | + | 43087.8i | 0.191134 | + | 0.0695672i | 0.435814 | − | 0.900037i | \(-0.356461\pi\) |
−0.244680 | + | 0.969604i | \(0.578683\pi\) | |||||||
\(788\) | −116674. | − | 139047.i | −0.187898 | − | 0.223928i | ||||
\(789\) | 738494. | − | 441182.i | 1.18630 | − | 0.708701i | ||||
\(790\) | −537766. | + | 195731.i | −0.861666 | + | 0.313621i | ||||
\(791\) | −110048. | − | 63536.4i | −0.175886 | − | 0.101548i | ||||
\(792\) | 339028. | − | 302156.i | 0.540486 | − | 0.481704i | ||||
\(793\) | 40710.2 | + | 70512.2i | 0.0647377 | + | 0.112129i | ||||
\(794\) | −318442. | + | 379505.i | −0.505114 | + | 0.601972i | ||||
\(795\) | −176601. | − | 143753.i | −0.279421 | − | 0.227449i | ||||
\(796\) | −228501. | − | 1.29589e6i | −0.360630 | − | 2.04523i | ||||
\(797\) | −989241. | + | 174430.i | −1.55735 | + | 0.274602i | −0.884985 | − | 0.465620i | \(-0.845831\pi\) |
−0.672362 | + | 0.740222i | \(0.734720\pi\) | |||||||
\(798\) | 190572. | + | 30680.2i | 0.299262 | + | 0.0481784i | ||||
\(799\) | 55894.6 | + | 46901.1i | 0.0875540 | + | 0.0734665i | ||||
\(800\) | −430835. | + | 248742.i | −0.673179 | + | 0.388660i | ||||
\(801\) | −498424. | − | 72634.1i | −0.776844 | − | 0.113208i | ||||
\(802\) | 179750. | − | 311335.i | 0.279460 | − | 0.484038i | ||||
\(803\) | −272767. | − | 749422.i | −0.423020 | − | 1.16224i | ||||
\(804\) | −1.34731e6 | + | 20092.5i | −2.08428 | + | 0.0310830i | ||||
\(805\) | 49472.4 | − | 41512.2i | 0.0763433 | − | 0.0640596i | ||||
\(806\) | −89324.9 | + | 245418.i | −0.137500 | + | 0.377778i | ||||
\(807\) | 160332. | − | 30742.8i | 0.246192 | − | 0.0472059i | ||||
\(808\) | −99533.0 | + | 564480.i | −0.152456 | + | 0.864621i | ||||
\(809\) | 583220.i | 0.891118i | 0.895253 | + | 0.445559i | \(0.146995\pi\) | ||||
−0.895253 | + | 0.445559i | \(0.853005\pi\) | |||||||
\(810\) | 629839. | + | 187553.i | 0.959973 | + | 0.285860i | ||||
\(811\) | 1.19604e6 | 1.81846 | 0.909228 | − | 0.416298i | \(-0.136673\pi\) | ||||
0.909228 | + | 0.416298i | \(0.136673\pi\) | |||||||
\(812\) | 240007. | + | 42319.6i | 0.364008 | + | 0.0641845i | ||||
\(813\) | −216954. | − | 1.13147e6i | −0.328236 | − | 1.71184i | ||||
\(814\) | 543173. | + | 197699.i | 0.819765 | + | 0.298370i | ||||
\(815\) | 182925. | + | 218001.i | 0.275396 | + | 0.328204i | ||||
\(816\) | 9382.94 | + | 629177.i | 0.0140915 | + | 0.944914i | ||||
\(817\) | −487797. | + | 177543.i | −0.730794 | + | 0.265987i | ||||
\(818\) | 1.53414e6 | + | 885736.i | 2.29276 | + | 1.32372i | ||||
\(819\) | 26964.3 | + | 21288.4i | 0.0401995 | + | 0.0317376i | ||||
\(820\) | −98564.4 | − | 170719.i | −0.146586 | − | 0.253894i | ||||
\(821\) | −590669. | + | 703931.i | −0.876310 | + | 1.04435i | 0.122345 | + | 0.992488i | \(0.460959\pi\) |
−0.998654 | + | 0.0518575i | \(0.983486\pi\) | |||||||
\(822\) | −45575.4 | + | 283094.i | −0.0674508 | + | 0.418974i | ||||
\(823\) | −141705. | − | 803651.i | −0.209212 | − | 1.18650i | −0.890672 | − | 0.454646i | \(-0.849766\pi\) |
0.681460 | − | 0.731855i | \(-0.261345\pi\) | |||||||
\(824\) | −182544. | + | 32187.5i | −0.268852 | + | 0.0474059i | ||||
\(825\) | 375454. | − | 461245.i | 0.551631 | − | 0.677678i | ||||
\(826\) | 73976.5 | + | 62073.6i | 0.108426 | + | 0.0909802i | ||||
\(827\) | −308224. | + | 177953.i | −0.450666 | + | 0.260192i | −0.708112 | − | 0.706101i | \(-0.750453\pi\) |
0.257445 | + | 0.966293i | \(0.417119\pi\) | |||||||
\(828\) | −276103. | + | 835289.i | −0.402727 | + | 1.21836i | ||||
\(829\) | −224839. | + | 389432.i | −0.327161 | + | 0.566660i | −0.981947 | − | 0.189154i | \(-0.939425\pi\) |
0.654786 | + | 0.755814i | \(0.272759\pi\) | |||||||
\(830\) | 140073. | + | 384848.i | 0.203329 | + | 0.558641i | ||||
\(831\) | −246108. | − | 411960.i | −0.356388 | − | 0.596558i | ||||
\(832\) | −262961. | + | 220651.i | −0.379879 | + | 0.318756i | ||||
\(833\) | −366981. | + | 1.00827e6i | −0.528876 | + | 1.45308i | ||||
\(834\) | −380151. | + | 1.09499e6i | −0.546542 | + | 1.57427i | ||||
\(835\) | 16499.7 | − | 93574.4i | 0.0236648 | − | 0.134210i | ||||
\(836\) | − | 1.82934e6i | − | 2.61747i | ||||||
\(837\) | −121339. | − | 544483.i | −0.173201 | − | 0.777202i | ||||
\(838\) | 746843. | 1.06351 | ||||||||
\(839\) | −167593. | − | 29551.1i | −0.238085 | − | 0.0419807i | 0.0533326 | − | 0.998577i | \(-0.483016\pi\) |
−0.291417 | + | 0.956596i | \(0.594127\pi\) | |||||||
\(840\) | 25402.9 | − | 21969.3i | 0.0360018 | − | 0.0311356i | ||||
\(841\) | 1.56850e6 | + | 570888.i | 2.21765 | + | 0.807158i | ||||
\(842\) | −297483. | − | 354526.i | −0.419602 | − | 0.500063i | ||||
\(843\) | −236013. | − | 131610.i | −0.332110 | − | 0.185196i | ||||
\(844\) | 1.11351e6 | − | 405283.i | 1.56317 | − | 0.568949i | ||||
\(845\) | 362647. | + | 209374.i | 0.507891 | + | 0.293231i | ||||
\(846\) | −41240.5 | − | 66751.2i | −0.0576214 | − | 0.0932650i | ||||
\(847\) | −76777.7 | − | 132983.i | −0.107021 | − | 0.185366i | ||||
\(848\) | −150712. | + | 179612.i | −0.209583 | + | 0.249772i | ||||
\(849\) | 21790.1 | − | 8300.98i | 0.0302304 | − | 0.0115163i | ||||
\(850\) | −170700. | − | 968085.i | −0.236262 | − | 1.33991i | ||||
\(851\) | −259873. | + | 45822.6i | −0.358841 | + | 0.0632733i | ||||
\(852\) | 188715. | + | 495380.i | 0.259973 | + | 0.682431i | ||||
\(853\) | 81021.3 | + | 67984.9i | 0.111353 | + | 0.0934360i | 0.696764 | − | 0.717300i | \(-0.254622\pi\) |
−0.585411 | + | 0.810736i | \(0.699067\pi\) | |||||||
\(854\) | −57625.6 | + | 33270.1i | −0.0790132 | + | 0.0456183i | ||||
\(855\) | 530722. | − | 327893.i | 0.725997 | − | 0.448538i | ||||
\(856\) | 23180.9 | − | 40150.6i | 0.0316361 | − | 0.0547954i | ||||
\(857\) | −143295. | − | 393699.i | −0.195105 | − | 0.536047i | 0.803106 | − | 0.595836i | \(-0.203179\pi\) |
−0.998211 | + | 0.0597895i | \(0.980957\pi\) | |||||||
\(858\) | 279774. | − | 501715.i | 0.380043 | − | 0.681526i | ||||
\(859\) | −770583. | + | 646596.i | −1.04432 | + | 0.876288i | −0.992485 | − | 0.122368i | \(-0.960951\pi\) |
−0.0518343 | + | 0.998656i | \(0.516507\pi\) | |||||||
\(860\) | −131084. | + | 360149.i | −0.177236 | + | 0.486952i | ||||
\(861\) | 25404.0 | + | 29374.4i | 0.0342686 | + | 0.0396245i | ||||
\(862\) | 198970. | − | 1.12842e6i | 0.267777 | − | 1.51864i | ||||
\(863\) | 1.38007e6i | 1.85302i | 0.376271 | + | 0.926510i | \(0.377206\pi\) | ||||
−0.376271 | + | 0.926510i | \(0.622794\pi\) | |||||||
\(864\) | 307549. | − | 979185.i | 0.411991 | − | 1.31171i | ||||
\(865\) | 323972. | 0.432988 | ||||||||
\(866\) | 27743.5 | + | 4891.92i | 0.0369935 | + | 0.00652295i | ||||
\(867\) | −1.07150e6 | − | 371997.i | −1.42546 | − | 0.494881i | ||||
\(868\) | −113678. | − | 41375.3i | −0.150882 | − | 0.0549164i | ||||
\(869\) | −686810. | − | 818509.i | −0.909489 | − | 1.08389i | ||||
\(870\) | 1.19300e6 | − | 712708.i | 1.57617 | − | 0.941614i | ||||
\(871\) | −377448. | + | 137380.i | −0.497532 | + | 0.181087i | ||||
\(872\) | 231322. | + | 133554.i | 0.304218 | + | 0.175640i | ||||
\(873\) | −714076. | − | 236036.i | −0.936948 | − | 0.309707i | ||||
\(874\) | 736721. | + | 1.27604e6i | 0.964451 | + | 1.67048i | ||||
\(875\) | 78277.7 | − | 93287.8i | 0.102240 | − | 0.121845i | ||||
\(876\) | 623095. | + | 507199.i | 0.811981 | + | 0.660953i | ||||
\(877\) | 38998.8 | + | 221173.i | 0.0507051 | + | 0.287563i | 0.999608 | − | 0.0280060i | \(-0.00891576\pi\) |
−0.948903 | + | 0.315569i | \(0.897805\pi\) | |||||||
\(878\) | 288276. | − | 50830.8i | 0.373955 | − | 0.0659383i | ||||
\(879\) | −423369. | − | 68158.4i | −0.547950 | − | 0.0882148i | ||||
\(880\) | 360629. | + | 302604.i | 0.465688 | + | 0.390759i | ||||
\(881\) | −216321. | + | 124893.i | −0.278707 | + | 0.160912i | −0.632838 | − | 0.774284i | \(-0.718110\pi\) |
0.354131 | + | 0.935196i | \(0.384777\pi\) | |||||||
\(882\) | 714984. | − | 905613.i | 0.919093 | − | 1.16414i | ||||
\(883\) | 564079. | − | 977013.i | 0.723466 | − | 1.25308i | −0.236136 | − | 0.971720i | \(-0.575881\pi\) |
0.959602 | − | 0.281361i | \(-0.0907857\pi\) | |||||||
\(884\) | −184059. | − | 505699.i | −0.235534 | − | 0.647124i | ||||
\(885\) | 312070. | − | 4653.91i | 0.398442 | − | 0.00594198i | ||||
\(886\) | 60588.3 | − | 50839.6i | 0.0771829 | − | 0.0647642i | ||||
\(887\) | 385201. | − | 1.05833e6i | 0.489598 | − | 1.34516i | −0.411447 | − | 0.911434i | \(-0.634976\pi\) |
0.901045 | − | 0.433726i | \(-0.142801\pi\) | |||||||
\(888\) | −134774. | + | 25842.2i | −0.170915 | + | 0.0327720i | ||||
\(889\) | −18867.4 | + | 107003.i | −0.0238731 | + | 0.135391i | ||||
\(890\) | 622852.i | 0.786330i | ||||||||
\(891\) | 73143.6 | + | 1.22480e6i | 0.0921342 | + | 1.54281i | ||||
\(892\) | −725789. | −0.912180 | ||||||||
\(893\) | −73352.6 | − | 12934.0i | −0.0919841 | − | 0.0162193i | ||||
\(894\) | 299819. | + | 1.56364e6i | 0.375133 | + | 1.95642i | ||||
\(895\) | −347570. | − | 126505.i | −0.433906 | − | 0.157929i | ||||
\(896\) | −70972.8 | − | 84582.1i | −0.0884048 | − | 0.105357i | ||||
\(897\) | 3910.45 | + | 262217.i | 0.00486006 | + | 0.325893i | ||||
\(898\) | 850452. | − | 309539.i | 1.05462 | − | 0.383851i | ||||
\(899\) | −1.02159e6 | − | 589815.i | −1.26403 | − | 0.729788i | ||||
\(900\) | −86399.4 | + | 592882.i | −0.106666 | + | 0.731954i | ||||
\(901\) | −351363. | − | 608578.i | −0.432819 | − | 0.749664i | ||||
\(902\) | 417409. | − | 497448.i | 0.513037 | − | 0.611413i | ||||
\(903\) | 12001.2 | − | 74545.8i | 0.0147180 | − | 0.0914214i | ||||
\(904\) | −87594.9 | − | 496775.i | −0.107187 | − | 0.607887i | ||||
\(905\) | 453036. | − | 79882.5i | 0.553141 | − | 0.0975337i | ||||
\(906\) | −1.23425e6 | + | 1.51628e6i | −1.50366 | + | 1.84724i | ||||
\(907\) | 560559. | + | 470365.i | 0.681407 | + | 0.571769i | 0.916417 | − | 0.400224i | \(-0.131068\pi\) |
−0.235010 | + | 0.971993i | \(0.575512\pi\) | |||||||
\(908\) | −94189.9 | + | 54380.6i | −0.114244 | + | 0.0659587i | ||||
\(909\) | −1.03038e6 | − | 1.15612e6i | −1.24701 | − | 1.39919i | ||||
\(910\) | 21241.4 | − | 36791.2i | 0.0256507 | − | 0.0444284i | ||||
\(911\) | 439260. | + | 1.20686e6i | 0.529279 | + | 1.45418i | 0.859922 | + | 0.510426i | \(0.170512\pi\) |
−0.330642 | + | 0.943756i | \(0.607265\pi\) | |||||||
\(912\) | −329433. | − | 551437.i | −0.396075 | − | 0.662989i | ||||
\(913\) | −585759. | + | 491510.i | −0.702712 | + | 0.589645i | ||||
\(914\) | 45669.9 | − | 125477.i | 0.0546685 | − | 0.150200i | ||||
\(915\) | −70530.8 | + | 203158.i | −0.0842436 | + | 0.242656i | ||||
\(916\) | −158276. | + | 897627.i | −0.188636 | + | 1.06981i | ||||
\(917\) | 23345.5i | 0.0277629i | ||||||||
\(918\) | 1.61031e6 | + | 1.23282e6i | 1.91084 | + | 1.46290i | ||||
\(919\) | −321358. | −0.380503 | −0.190252 | − | 0.981735i | \(-0.560930\pi\) | ||||
−0.190252 | + | 0.981735i | \(0.560930\pi\) | |||||||
\(920\) | 252474. | + | 44517.9i | 0.298291 | + | 0.0525968i | ||||
\(921\) | 154484. | − | 133603.i | 0.182123 | − | 0.157506i | ||||
\(922\) | 788976. | + | 287164.i | 0.928116 | + | 0.337807i | ||||
\(923\) | 101575. | + | 121052.i | 0.119229 | + | 0.142092i | ||||
\(924\) | 232394. | + | 129591.i | 0.272196 | + | 0.151786i | ||||
\(925\) | −168878. | + | 61466.6i | −0.197374 | + | 0.0718382i | ||||
\(926\) | −1.08039e6 | − | 623763.i | −1.25996 | − | 0.727440i | ||||
\(927\) | 237360. | − | 440987.i | 0.276215 | − | 0.513176i | ||||
\(928\) | −1.08518e6 | − | 1.87958e6i | −1.26010 | − | 2.18256i | ||||
\(929\) | 845059. | − | 1.00710e6i | 0.979164 | − | 1.16692i | −0.00680175 | − | 0.999977i | \(-0.502165\pi\) |
0.985966 | − | 0.166946i | \(-0.0533905\pi\) | |||||||
\(930\) | −644623. | + | 245570.i | −0.745316 | + | 0.283929i | ||||
\(931\) | −190200. | − | 1.07868e6i | −0.219438 | − | 1.24449i | ||||
\(932\) | −1.94772e6 | + | 343435.i | −2.24230 | + | 0.395378i | ||||
\(933\) | 109021. | + | 286181.i | 0.125241 | + | 0.328759i | ||||
\(934\) | −1.00242e6 | − | 841129.i | −1.14909 | − | 0.964204i | ||||
\(935\) | −1.22192e6 | + | 705474.i | −1.39771 | + | 0.806971i | ||||
\(936\) | 4066.73 | + | 136318.i | 0.00464188 | + | 0.155597i | ||||
\(937\) | −91197.1 | + | 157958.i | −0.103873 | + | 0.179913i | −0.913277 | − | 0.407339i | \(-0.866457\pi\) |
0.809404 | + | 0.587252i | \(0.199790\pi\) | |||||||
\(938\) | −112273. | − | 308467.i | −0.127605 | − | 0.350592i | ||||
\(939\) | −634861. | + | 1.13849e6i | −0.720025 | + | 1.29121i | ||||
\(940\) | −42127.1 | + | 35348.9i | −0.0476767 | + | 0.0400055i | ||||
\(941\) | −314314. | + | 863570.i | −0.354964 | + | 0.975255i | 0.625788 | + | 0.779994i | \(0.284778\pi\) |
−0.980751 | + | 0.195261i | \(0.937445\pi\) | |||||||
\(942\) | −880257. | − | 1.01783e6i | −0.991991 | − | 1.14703i | ||||
\(943\) | −51478.0 | + | 291946.i | −0.0578893 | + | 0.328306i | ||||
\(944\) | − | 321362.i | − | 0.360621i | ||||||
\(945\) | 4058.00 | + | 90649.7i | 0.00454410 | + | 0.101509i | ||||
\(946\) | −1.26253e6 | −1.41078 | ||||||||
\(947\) | −1.27507e6 | − | 224828.i | −1.42178 | − | 0.250698i | −0.590718 | − | 0.806878i | \(-0.701155\pi\) |
−0.831062 | + | 0.556180i | \(0.812267\pi\) | |||||||
\(948\) | 1.01687e6 | + | 353029.i | 1.13148 | + | 0.392820i | ||||
\(949\) | 225055. | + | 81913.2i | 0.249894 | + | 0.0909539i | ||||
\(950\) | 645028. | + | 768714.i | 0.714712 | + | 0.851760i | ||||
\(951\) | −227961. | + | 136185.i | −0.252057 | + | 0.150581i | ||||
\(952\) | 97393.7 | − | 35448.4i | 0.107462 | − | 0.0391131i | ||||
\(953\) | −26148.8 | − | 15097.0i | −0.0287917 | − | 0.0166229i | 0.485535 | − | 0.874217i | \(-0.338625\pi\) |
−0.514327 | + | 0.857594i | \(0.671958\pi\) | |||||||
\(954\) | 153355. | + | 739954.i | 0.168501 | + | 0.813033i | ||||
\(955\) | 441478. | + | 764663.i | 0.484064 | + | 0.838423i | ||||
\(956\) | 267855. | − | 319217.i | 0.293079 | − | 0.349278i | ||||
\(957\) | 2.01225e6 | + | 1.63798e6i | 2.19715 | + | 1.78848i | ||||
\(958\) | 223928. | + | 1.26996e6i | 0.243993 | + | 1.38375i | ||||
\(959\) | −38990.7 | + | 6875.12i | −0.0423959 | + | 0.00747555i | ||||
\(960\) | −895145. | − | 144110.i | −0.971294 | − | 0.156369i | ||||
\(961\) | −258901. | − | 217244.i | −0.280341 | − | 0.235234i | ||||
\(962\) | −150330. | + | 86792.8i | −0.162440 | + | 0.0937850i | ||||
\(963\) | 46332.7 | + | 116377.i | 0.0499615 | + | 0.125492i | ||||
\(964\) | 345023. | − | 597597.i | 0.371274 | − | 0.643065i | ||||
\(965\) | −240093. | − | 659651.i | −0.257825 | − | 0.708369i | ||||
\(966\) | −214295. | + | 3195.78i | −0.229645 | + | 0.00342470i | ||||
\(967\) | 671929. | − | 563815.i | 0.718572 | − | 0.602954i | −0.208418 | − | 0.978040i | \(-0.566831\pi\) |
0.926990 | + | 0.375086i | \(0.122387\pi\) | |||||||
\(968\) | 208484. | − | 572805.i | 0.222496 | − | 0.611302i | ||||
\(969\) | 1.89075e6 | − | 362540.i | 2.01366 | − | 0.386108i | ||||
\(970\) | −161493. | + | 915874.i | −0.171637 | + | 0.973402i | ||||
\(971\) | − | 552699.i | − | 0.586206i | −0.956081 | − | 0.293103i | \(-0.905312\pi\) | ||
0.956081 | − | 0.293103i | \(-0.0946879\pi\) | |||||||
\(972\) | −696063. | − | 1.02146e6i | −0.736743 | − | 1.08116i | ||||
\(973\) | −160046. | −0.169052 | ||||||||
\(974\) | −35562.3 | − | 6270.59i | −0.0374862 | − | 0.00660984i | ||||
\(975\) | 33633.2 | + | 175407.i | 0.0353801 | + | 0.184517i | ||||
\(976\) | 208078. | + | 75734.1i | 0.218437 | + | 0.0795045i | ||||
\(977\) | 661005. | + | 787755.i | 0.692494 | + | 0.825282i | 0.991655 | − | 0.128921i | \(-0.0411513\pi\) |
−0.299161 | + | 0.954203i | \(0.596707\pi\) | |||||||
\(978\) | −14082.3 | − | 944295.i | −0.0147230 | − | 0.987256i | ||||
\(979\) | −1.09278e6 | + | 397739.i | −1.14016 | + | 0.414986i | ||||
\(980\) | −700350. | − | 404348.i | −0.729228 | − | 0.421020i | ||||
\(981\) | −670491. | + | 266940.i | −0.696715 | + | 0.277380i | ||||
\(982\) | −1.13812e6 | − | 1.97127e6i | −1.18022 | − | 2.04420i | ||||
\(983\) | 1.15088e6 | − | 1.37157e6i | 1.19103 | − | 1.41942i | 0.307180 | − | 0.951652i | \(-0.400615\pi\) |
0.883853 | − | 0.467765i | \(-0.154941\pi\) | |||||||
\(984\) | −24503.8 | + | 152206.i | −0.0253071 | + | 0.157196i | ||||
\(985\) | −24816.7 | − | 140742.i | −0.0255783 | − | 0.145062i | ||||
\(986\) | 4.22342e6 | − | 744704.i | 4.34421 | − | 0.766002i | ||||
\(987\) | 6839.46 | − | 8402.28i | 0.00702082 | − | 0.00862508i | ||||
\(988\) | 420832. | + | 353120.i | 0.431117 | + | 0.361750i | ||||
\(989\) | 499147. | − | 288183.i | 0.510312 | − | 0.294629i | ||||
\(990\) | 1.48570e6 | − | 307911.i | 1.51586 | − | 0.314162i | ||||
\(991\) | 219634. | − | 380417.i | 0.223641 | − | 0.387358i | −0.732270 | − | 0.681015i | \(-0.761539\pi\) |
0.955911 | + | 0.293657i | \(0.0948723\pi\) | |||||||
\(992\) | 368469. | + | 1.01236e6i | 0.374436 | + | 1.02875i | ||||
\(993\) | 111658. | + | 186904.i | 0.113238 | + | 0.189549i | ||||
\(994\) | −98929.1 | + | 83011.3i | −0.100127 | + | 0.0840165i | ||||
\(995\) | 354352. | − | 973575.i | 0.357923 | − | 0.983384i | ||||
\(996\) | 252642. | − | 727713.i | 0.254675 | − | 0.733569i | ||||
\(997\) | 120978. | − | 686100.i | 0.121707 | − | 0.690235i | −0.861502 | − | 0.507754i | \(-0.830476\pi\) |
0.983209 | − | 0.182481i | \(-0.0584128\pi\) | |||||||
\(998\) | − | 460427.i | − | 0.462274i | ||||||
\(999\) | 170839. | − | 329064.i | 0.171181 | − | 0.329723i |
(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 | 27.5.f.a.2.10 | ✓ | 66 | |
3.2 | odd | 2 | 81.5.f.a.8.2 | 66 | |||
27.13 | even | 9 | 81.5.f.a.71.2 | 66 | |||
27.14 | odd | 18 | inner | 27.5.f.a.14.10 | yes | 66 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.5.f.a.2.10 | ✓ | 66 | 1.1 | even | 1 | trivial | |
27.5.f.a.14.10 | yes | 66 | 27.14 | odd | 18 | inner | |
81.5.f.a.8.2 | 66 | 3.2 | odd | 2 | |||
81.5.f.a.71.2 | 66 | 27.13 | even | 9 |