Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,5,Mod(10,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.10");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(2.17076922476\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.19 |
Dual form | 21.5.f.b.10.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.50000 | − | 4.33013i | 0.625000 | − | 1.08253i | −0.363541 | − | 0.931578i | \(-0.618432\pi\) |
0.988541 | − | 0.150954i | \(-0.0482344\pi\) | |||||||
\(3\) | 4.50000 | − | 2.59808i | 0.500000 | − | 0.288675i | ||||
\(4\) | −4.50000 | − | 7.79423i | −0.281250 | − | 0.487139i | ||||
\(5\) | −1.50000 | − | 0.866025i | −0.0600000 | − | 0.0346410i | 0.469700 | − | 0.882826i | \(-0.344362\pi\) |
−0.529700 | + | 0.848185i | \(0.677695\pi\) | |||||||
\(6\) | − | 25.9808i | − | 0.721688i | ||||||
\(7\) | −45.5000 | + | 18.1865i | −0.928571 | + | 0.371154i | ||||
\(8\) | 35.0000 | 0.546875 | ||||||||
\(9\) | 13.5000 | − | 23.3827i | 0.166667 | − | 0.288675i | ||||
\(10\) | −7.50000 | + | 4.33013i | −0.0750000 | + | 0.0433013i | ||||
\(11\) | 74.5000 | + | 129.038i | 0.615702 | + | 1.06643i | 0.990261 | + | 0.139225i | \(0.0444610\pi\) |
−0.374558 | + | 0.927203i | \(0.622206\pi\) | |||||||
\(12\) | −40.5000 | − | 23.3827i | −0.281250 | − | 0.162380i | ||||
\(13\) | 41.5692i | 0.245972i | 0.992408 | + | 0.122986i | \(0.0392470\pi\) | ||||
−0.992408 | + | 0.122986i | \(0.960753\pi\) | |||||||
\(14\) | −35.0000 | + | 242.487i | −0.178571 | + | 1.23718i | ||||
\(15\) | −9.00000 | −0.0400000 | ||||||||
\(16\) | 159.500 | − | 276.262i | 0.623047 | − | 1.07915i | ||||
\(17\) | −231.000 | + | 133.368i | −0.799308 | + | 0.461481i | −0.843229 | − | 0.537554i | \(-0.819348\pi\) |
0.0439212 | + | 0.999035i | \(0.486015\pi\) | |||||||
\(18\) | −67.5000 | − | 116.913i | −0.208333 | − | 0.360844i | ||||
\(19\) | −309.000 | − | 178.401i | −0.855956 | − | 0.494186i | 0.00670019 | − | 0.999978i | \(-0.497867\pi\) |
−0.862656 | + | 0.505791i | \(0.831201\pi\) | |||||||
\(20\) | 15.5885i | 0.0389711i | ||||||||
\(21\) | −157.500 | + | 200.052i | −0.357143 | + | 0.453632i | ||||
\(22\) | 745.000 | 1.53926 | ||||||||
\(23\) | 280.000 | − | 484.974i | 0.529301 | − | 0.916775i | −0.470115 | − | 0.882605i | \(-0.655788\pi\) |
0.999416 | − | 0.0341705i | \(-0.0108789\pi\) | |||||||
\(24\) | 157.500 | − | 90.9327i | 0.273438 | − | 0.157869i | ||||
\(25\) | −311.000 | − | 538.668i | −0.497600 | − | 0.861868i | ||||
\(26\) | 180.000 | + | 103.923i | 0.266272 | + | 0.153732i | ||||
\(27\) | − | 140.296i | − | 0.192450i | ||||||
\(28\) | 346.500 | + | 272.798i | 0.441964 | + | 0.347957i | ||||
\(29\) | 235.000 | 0.279429 | 0.139715 | − | 0.990192i | \(-0.455381\pi\) | ||||
0.139715 | + | 0.990192i | \(0.455381\pi\) | |||||||
\(30\) | −22.5000 | + | 38.9711i | −0.0250000 | + | 0.0433013i | ||||
\(31\) | −1114.50 | + | 643.457i | −1.15973 | + | 0.669570i | −0.951239 | − | 0.308454i | \(-0.900188\pi\) |
−0.208490 | + | 0.978024i | \(0.566855\pi\) | |||||||
\(32\) | −517.500 | − | 896.336i | −0.505371 | − | 0.875328i | ||||
\(33\) | 670.500 | + | 387.113i | 0.615702 | + | 0.355476i | ||||
\(34\) | 1333.68i | 1.15370i | ||||||||
\(35\) | 84.0000 | + | 12.1244i | 0.0685714 | + | 0.00989743i | ||||
\(36\) | −243.000 | −0.187500 | ||||||||
\(37\) | −985.000 | + | 1706.07i | −0.719503 | + | 1.24622i | 0.241694 | + | 0.970353i | \(0.422297\pi\) |
−0.961197 | + | 0.275864i | \(0.911036\pi\) | |||||||
\(38\) | −1545.00 | + | 892.006i | −1.06994 | + | 0.617733i | ||||
\(39\) | 108.000 | + | 187.061i | 0.0710059 | + | 0.122986i | ||||
\(40\) | −52.5000 | − | 30.3109i | −0.0328125 | − | 0.0189443i | ||||
\(41\) | − | 2816.31i | − | 1.67538i | −0.546146 | − | 0.837690i | \(-0.683905\pi\) | ||
0.546146 | − | 0.837690i | \(-0.316095\pi\) | |||||||
\(42\) | 472.500 | + | 1182.12i | 0.267857 | + | 0.670139i | ||||
\(43\) | 2798.00 | 1.51325 | 0.756625 | − | 0.653849i | \(-0.226847\pi\) | ||||
0.756625 | + | 0.653849i | \(0.226847\pi\) | |||||||
\(44\) | 670.500 | − | 1161.34i | 0.346333 | − | 0.599866i | ||||
\(45\) | −40.5000 | + | 23.3827i | −0.0200000 | + | 0.0115470i | ||||
\(46\) | −1400.00 | − | 2424.87i | −0.661626 | − | 1.14597i | ||||
\(47\) | 3576.00 | + | 2064.60i | 1.61883 | + | 0.934633i | 0.987223 | + | 0.159346i | \(0.0509386\pi\) |
0.631609 | + | 0.775287i | \(0.282395\pi\) | |||||||
\(48\) | − | 1657.57i | − | 0.719433i | ||||||
\(49\) | 1739.50 | − | 1654.97i | 0.724490 | − | 0.689286i | ||||
\(50\) | −3110.00 | −1.24400 | ||||||||
\(51\) | −693.000 | + | 1200.31i | −0.266436 | + | 0.461481i | ||||
\(52\) | 324.000 | − | 187.061i | 0.119822 | − | 0.0691795i | ||||
\(53\) | −450.500 | − | 780.289i | −0.160377 | − | 0.277782i | 0.774627 | − | 0.632419i | \(-0.217938\pi\) |
−0.935004 | + | 0.354637i | \(0.884604\pi\) | |||||||
\(54\) | −607.500 | − | 350.740i | −0.208333 | − | 0.120281i | ||||
\(55\) | − | 258.076i | − | 0.0853142i | ||||||
\(56\) | −1592.50 | + | 636.529i | −0.507812 | + | 0.202975i | ||||
\(57\) | −1854.00 | −0.570637 | ||||||||
\(58\) | 587.500 | − | 1017.58i | 0.174643 | − | 0.302491i | ||||
\(59\) | 1195.50 | − | 690.222i | 0.343436 | − | 0.198283i | −0.318355 | − | 0.947972i | \(-0.603130\pi\) |
0.661790 | + | 0.749689i | \(0.269797\pi\) | |||||||
\(60\) | 40.5000 | + | 70.1481i | 0.0112500 | + | 0.0194856i | ||||
\(61\) | −3090.00 | − | 1784.01i | −0.830422 | − | 0.479444i | 0.0235752 | − | 0.999722i | \(-0.492495\pi\) |
−0.853997 | + | 0.520278i | \(0.825828\pi\) | |||||||
\(62\) | 6434.57i | 1.67393i | ||||||||
\(63\) | −189.000 | + | 1309.43i | −0.0476190 | + | 0.329914i | ||||
\(64\) | −71.0000 | −0.0173340 | ||||||||
\(65\) | 36.0000 | − | 62.3538i | 0.00852071 | − | 0.0147583i | ||||
\(66\) | 3352.50 | − | 1935.57i | 0.769628 | − | 0.444345i | ||||
\(67\) | 2078.00 | + | 3599.20i | 0.462909 | + | 0.801782i | 0.999104 | − | 0.0423116i | \(-0.0134722\pi\) |
−0.536195 | + | 0.844094i | \(0.680139\pi\) | |||||||
\(68\) | 2079.00 | + | 1200.31i | 0.449611 | + | 0.259583i | ||||
\(69\) | − | 2909.85i | − | 0.611184i | ||||||
\(70\) | 262.500 | − | 333.420i | 0.0535714 | − | 0.0680449i | ||||
\(71\) | 484.000 | 0.0960127 | 0.0480063 | − | 0.998847i | \(-0.484713\pi\) | ||||
0.0480063 | + | 0.998847i | \(0.484713\pi\) | |||||||
\(72\) | 472.500 | − | 818.394i | 0.0911458 | − | 0.157869i | ||||
\(73\) | −822.000 | + | 474.582i | −0.154250 | + | 0.0890565i | −0.575138 | − | 0.818056i | \(-0.695052\pi\) |
0.420888 | + | 0.907113i | \(0.361718\pi\) | |||||||
\(74\) | 4925.00 | + | 8530.35i | 0.899379 | + | 1.55777i | ||||
\(75\) | −2799.00 | − | 1616.00i | −0.497600 | − | 0.287289i | ||||
\(76\) | 3211.22i | 0.555960i | ||||||||
\(77\) | −5736.50 | − | 4516.32i | −0.967532 | − | 0.761734i | ||||
\(78\) | 1080.00 | 0.177515 | ||||||||
\(79\) | −2162.50 | + | 3745.56i | −0.346499 | + | 0.600154i | −0.985625 | − | 0.168948i | \(-0.945963\pi\) |
0.639126 | + | 0.769102i | \(0.279296\pi\) | |||||||
\(80\) | −478.500 | + | 276.262i | −0.0747656 | + | 0.0431660i | ||||
\(81\) | −364.500 | − | 631.333i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −12195.0 | − | 7040.79i | −1.81365 | − | 1.04711i | ||||
\(83\) | 1304.23i | 0.189321i | 0.995510 | + | 0.0946606i | \(0.0301766\pi\) | ||||
−0.995510 | + | 0.0946606i | \(0.969823\pi\) | |||||||
\(84\) | 2268.00 | + | 327.358i | 0.321429 | + | 0.0463942i | ||||
\(85\) | 462.000 | 0.0639446 | ||||||||
\(86\) | 6995.00 | − | 12115.7i | 0.945782 | − | 1.63814i | ||||
\(87\) | 1057.50 | − | 610.548i | 0.139715 | − | 0.0806643i | ||||
\(88\) | 2607.50 | + | 4516.32i | 0.336712 | + | 0.583203i | ||||
\(89\) | 1713.00 | + | 989.001i | 0.216261 | + | 0.124858i | 0.604218 | − | 0.796819i | \(-0.293486\pi\) |
−0.387957 | + | 0.921677i | \(0.626819\pi\) | |||||||
\(90\) | 233.827i | 0.0288675i | ||||||||
\(91\) | −756.000 | − | 1891.40i | −0.0912933 | − | 0.228402i | ||||
\(92\) | −5040.00 | −0.595463 | ||||||||
\(93\) | −3343.50 | + | 5791.11i | −0.386576 | + | 0.669570i | ||||
\(94\) | 17880.0 | − | 10323.0i | 2.02354 | − | 1.16829i | ||||
\(95\) | 309.000 | + | 535.204i | 0.0342382 | + | 0.0593023i | ||||
\(96\) | −4657.50 | − | 2689.01i | −0.505371 | − | 0.291776i | ||||
\(97\) | − | 5450.76i | − | 0.579314i | −0.957131 | − | 0.289657i | \(-0.906459\pi\) | ||
0.957131 | − | 0.289657i | \(-0.0935412\pi\) | |||||||
\(98\) | −2817.50 | − | 11669.7i | −0.293367 | − | 1.21509i | ||||
\(99\) | 4023.00 | 0.410468 | ||||||||
\(100\) | −2799.00 | + | 4848.01i | −0.279900 | + | 0.484801i | ||||
\(101\) | −3750.00 | + | 2165.06i | −0.367611 | + | 0.212240i | −0.672414 | − | 0.740175i | \(-0.734743\pi\) |
0.304803 | + | 0.952415i | \(0.401409\pi\) | |||||||
\(102\) | 3465.00 | + | 6001.56i | 0.333045 | + | 0.576851i | ||||
\(103\) | 12516.0 | + | 7226.12i | 1.17975 | + | 0.681131i | 0.955957 | − | 0.293505i | \(-0.0948219\pi\) |
0.223796 | + | 0.974636i | \(0.428155\pi\) | |||||||
\(104\) | 1454.92i | 0.134516i | ||||||||
\(105\) | 409.500 | − | 163.679i | 0.0371429 | − | 0.0148461i | ||||
\(106\) | −4505.00 | −0.400943 | ||||||||
\(107\) | −2232.50 | + | 3866.80i | −0.194995 | + | 0.337742i | −0.946899 | − | 0.321531i | \(-0.895802\pi\) |
0.751904 | + | 0.659273i | \(0.229136\pi\) | |||||||
\(108\) | −1093.50 | + | 631.333i | −0.0937500 | + | 0.0541266i | ||||
\(109\) | −1660.00 | − | 2875.20i | −0.139719 | − | 0.242000i | 0.787671 | − | 0.616096i | \(-0.211287\pi\) |
−0.927390 | + | 0.374096i | \(0.877953\pi\) | |||||||
\(110\) | −1117.50 | − | 645.189i | −0.0923554 | − | 0.0533214i | ||||
\(111\) | 10236.4i | 0.830811i | ||||||||
\(112\) | −2233.00 | + | 15470.7i | −0.178013 | + | 1.23331i | ||||
\(113\) | −9734.00 | −0.762315 | −0.381157 | − | 0.924510i | \(-0.624474\pi\) | ||||
−0.381157 | + | 0.924510i | \(0.624474\pi\) | |||||||
\(114\) | −4635.00 | + | 8028.06i | −0.356648 | + | 0.617733i | ||||
\(115\) | −840.000 | + | 484.974i | −0.0635161 | + | 0.0366710i | ||||
\(116\) | −1057.50 | − | 1831.64i | −0.0785895 | − | 0.136121i | ||||
\(117\) | 972.000 | + | 561.184i | 0.0710059 | + | 0.0409953i | ||||
\(118\) | − | 6902.22i | − | 0.495707i | ||||||
\(119\) | 8085.00 | − | 10269.3i | 0.570934 | − | 0.725184i | ||||
\(120\) | −315.000 | −0.0218750 | ||||||||
\(121\) | −3780.00 | + | 6547.15i | −0.258179 | + | 0.447179i | ||||
\(122\) | −15450.0 | + | 8920.06i | −1.03803 | + | 0.599305i | ||||
\(123\) | −7317.00 | − | 12673.4i | −0.483641 | − | 0.837690i | ||||
\(124\) | 10030.5 | + | 5791.11i | 0.652348 | + | 0.376633i | ||||
\(125\) | 2159.87i | 0.138232i | ||||||||
\(126\) | 5197.50 | + | 4091.97i | 0.327381 | + | 0.257746i | ||||
\(127\) | −29149.0 | −1.80724 | −0.903621 | − | 0.428333i | \(-0.859101\pi\) | ||||
−0.903621 | + | 0.428333i | \(0.859101\pi\) | |||||||
\(128\) | 8102.50 | − | 14033.9i | 0.494537 | − | 0.856564i | ||||
\(129\) | 12591.0 | − | 7269.42i | 0.756625 | − | 0.436838i | ||||
\(130\) | −180.000 | − | 311.769i | −0.0106509 | − | 0.0184479i | ||||
\(131\) | 23866.5 | + | 13779.3i | 1.39074 | + | 0.802944i | 0.993397 | − | 0.114726i | \(-0.0365989\pi\) |
0.397343 | + | 0.917670i | \(0.369932\pi\) | |||||||
\(132\) | − | 6968.04i | − | 0.399910i | ||||||
\(133\) | 17304.0 | + | 2497.62i | 0.978235 | + | 0.141196i | ||||
\(134\) | 20780.0 | 1.15727 | ||||||||
\(135\) | −121.500 | + | 210.444i | −0.00666667 | + | 0.0115470i | ||||
\(136\) | −8085.00 | + | 4667.88i | −0.437122 | + | 0.252372i | ||||
\(137\) | −8912.00 | − | 15436.0i | −0.474826 | − | 0.822422i | 0.524759 | − | 0.851251i | \(-0.324155\pi\) |
−0.999584 | + | 0.0288290i | \(0.990822\pi\) | |||||||
\(138\) | −12600.0 | − | 7274.61i | −0.661626 | − | 0.381990i | ||||
\(139\) | − | 27986.5i | − | 1.44850i | −0.689537 | − | 0.724250i | \(-0.742186\pi\) | ||
0.689537 | − | 0.724250i | \(-0.257814\pi\) | |||||||
\(140\) | −283.500 | − | 709.275i | −0.0144643 | − | 0.0361875i | ||||
\(141\) | 21456.0 | 1.07922 | ||||||||
\(142\) | 1210.00 | − | 2095.78i | 0.0600079 | − | 0.103937i | ||||
\(143\) | −5364.00 | + | 3096.91i | −0.262311 | + | 0.151445i | ||||
\(144\) | −4306.50 | − | 7459.08i | −0.207682 | − | 0.359716i | ||||
\(145\) | −352.500 | − | 203.516i | −0.0167658 | − | 0.00967971i | ||||
\(146\) | 4745.82i | 0.222641i | ||||||||
\(147\) | 3528.00 | − | 11966.7i | 0.163265 | − | 0.553785i | ||||
\(148\) | 17730.0 | 0.809441 | ||||||||
\(149\) | −4607.00 | + | 7979.56i | −0.207513 | + | 0.359423i | −0.950931 | − | 0.309404i | \(-0.899870\pi\) |
0.743417 | + | 0.668828i | \(0.233204\pi\) | |||||||
\(150\) | −13995.0 | + | 8080.02i | −0.622000 | + | 0.359112i | ||||
\(151\) | −5987.50 | − | 10370.7i | −0.262598 | − | 0.454833i | 0.704333 | − | 0.709869i | \(-0.251246\pi\) |
−0.966932 | + | 0.255036i | \(0.917913\pi\) | |||||||
\(152\) | −10815.0 | − | 6244.04i | −0.468101 | − | 0.270258i | ||||
\(153\) | 7201.87i | 0.307654i | ||||||||
\(154\) | −33897.5 | + | 13549.0i | −1.42931 | + | 0.571301i | ||||
\(155\) | 2229.00 | 0.0927784 | ||||||||
\(156\) | 972.000 | − | 1683.55i | 0.0399408 | − | 0.0691795i | ||||
\(157\) | −1722.00 | + | 994.197i | −0.0698608 | + | 0.0403342i | −0.534524 | − | 0.845154i | \(-0.679509\pi\) |
0.464663 | + | 0.885488i | \(0.346176\pi\) | |||||||
\(158\) | 10812.5 | + | 18727.8i | 0.433124 | + | 0.750192i | ||||
\(159\) | −4054.50 | − | 2340.87i | −0.160377 | − | 0.0925939i | ||||
\(160\) | 1792.67i | 0.0700263i | ||||||||
\(161\) | −3920.00 | + | 27158.6i | −0.151229 | + | 1.04774i | ||||
\(162\) | −3645.00 | −0.138889 | ||||||||
\(163\) | 10400.0 | − | 18013.3i | 0.391434 | − | 0.677983i | −0.601205 | − | 0.799095i | \(-0.705313\pi\) |
0.992639 | + | 0.121112i | \(0.0386459\pi\) | |||||||
\(164\) | −21951.0 | + | 12673.4i | −0.816144 | + | 0.471201i | ||||
\(165\) | −670.500 | − | 1161.34i | −0.0246281 | − | 0.0426571i | ||||
\(166\) | 5647.50 | + | 3260.59i | 0.204946 | + | 0.118326i | ||||
\(167\) | 42483.7i | 1.52332i | 0.647980 | + | 0.761658i | \(0.275614\pi\) | ||||
−0.647980 | + | 0.761658i | \(0.724386\pi\) | |||||||
\(168\) | −5512.50 | + | 7001.82i | −0.195312 | + | 0.248080i | ||||
\(169\) | 26833.0 | 0.939498 | ||||||||
\(170\) | 1155.00 | − | 2000.52i | 0.0399654 | − | 0.0692221i | ||||
\(171\) | −8343.00 | + | 4816.83i | −0.285319 | + | 0.164729i | ||||
\(172\) | −12591.0 | − | 21808.3i | −0.425602 | − | 0.737164i | ||||
\(173\) | −2094.00 | − | 1208.97i | −0.0699656 | − | 0.0403946i | 0.464609 | − | 0.885516i | \(-0.346195\pi\) |
−0.534575 | + | 0.845121i | \(0.679528\pi\) | |||||||
\(174\) | − | 6105.48i | − | 0.201661i | ||||||
\(175\) | 23947.0 | + | 18853.4i | 0.781943 | + | 0.615620i | ||||
\(176\) | 47531.0 | 1.53445 | ||||||||
\(177\) | 3586.50 | − | 6212.00i | 0.114479 | − | 0.198283i | ||||
\(178\) | 8565.00 | − | 4945.01i | 0.270326 | − | 0.156073i | ||||
\(179\) | −9689.00 | − | 16781.8i | −0.302394 | − | 0.523761i | 0.674284 | − | 0.738472i | \(-0.264452\pi\) |
−0.976678 | + | 0.214711i | \(0.931119\pi\) | |||||||
\(180\) | 364.500 | + | 210.444i | 0.0112500 | + | 0.00649519i | ||||
\(181\) | 7451.28i | 0.227444i | 0.993513 | + | 0.113722i | \(0.0362773\pi\) | ||||
−0.993513 | + | 0.113722i | \(0.963723\pi\) | |||||||
\(182\) | −10080.0 | − | 1454.92i | −0.304311 | − | 0.0439235i | ||||
\(183\) | −18540.0 | −0.553615 | ||||||||
\(184\) | 9800.00 | − | 16974.1i | 0.289461 | − | 0.501362i | ||||
\(185\) | 2955.00 | − | 1706.07i | 0.0863404 | − | 0.0498486i | ||||
\(186\) | 16717.5 | + | 28955.6i | 0.483221 | + | 0.836963i | ||||
\(187\) | −34419.0 | − | 19871.8i | −0.984272 | − | 0.568270i | ||||
\(188\) | − | 37162.9i | − | 1.05146i | ||||||
\(189\) | 2551.50 | + | 6383.47i | 0.0714286 | + | 0.178704i | ||||
\(190\) | 3090.00 | 0.0855956 | ||||||||
\(191\) | 14380.0 | − | 24906.9i | 0.394178 | − | 0.682736i | −0.598818 | − | 0.800885i | \(-0.704363\pi\) |
0.992996 | + | 0.118149i | \(0.0376961\pi\) | |||||||
\(192\) | −319.500 | + | 184.463i | −0.00866699 | + | 0.00500389i | ||||
\(193\) | 22044.5 | + | 38182.2i | 0.591815 | + | 1.02505i | 0.993988 | + | 0.109489i | \(0.0349216\pi\) |
−0.402173 | + | 0.915564i | \(0.631745\pi\) | |||||||
\(194\) | −23602.5 | − | 13626.9i | −0.627126 | − | 0.362071i | ||||
\(195\) | − | 374.123i | − | 0.00983887i | ||||||
\(196\) | −20727.0 | − | 6110.68i | −0.539541 | − | 0.159066i | ||||
\(197\) | −46478.0 | −1.19761 | −0.598804 | − | 0.800895i | \(-0.704357\pi\) | ||||
−0.598804 | + | 0.800895i | \(0.704357\pi\) | |||||||
\(198\) | 10057.5 | − | 17420.1i | 0.256543 | − | 0.444345i | ||||
\(199\) | −33978.0 | + | 19617.2i | −0.858009 | + | 0.495372i | −0.863345 | − | 0.504614i | \(-0.831635\pi\) |
0.00533629 | + | 0.999986i | \(0.498301\pi\) | |||||||
\(200\) | −10885.0 | − | 18853.4i | −0.272125 | − | 0.471334i | ||||
\(201\) | 18702.0 | + | 10797.6i | 0.462909 | + | 0.267261i | ||||
\(202\) | 21650.6i | 0.530601i | ||||||||
\(203\) | −10692.5 | + | 4273.84i | −0.259470 | + | 0.103711i | ||||
\(204\) | 12474.0 | 0.299740 | ||||||||
\(205\) | −2439.00 | + | 4224.47i | −0.0580369 | + | 0.100523i | ||||
\(206\) | 62580.0 | − | 36130.6i | 1.47469 | − | 0.851413i | ||||
\(207\) | −7560.00 | − | 13094.3i | −0.176434 | − | 0.305592i | ||||
\(208\) | 11484.0 | + | 6630.29i | 0.265440 | + | 0.153252i | ||||
\(209\) | − | 53163.6i | − | 1.21709i | ||||||
\(210\) | 315.000 | − | 2182.38i | 0.00714286 | − | 0.0494872i | ||||
\(211\) | −27688.0 | −0.621909 | −0.310954 | − | 0.950425i | \(-0.600649\pi\) | ||||
−0.310954 | + | 0.950425i | \(0.600649\pi\) | |||||||
\(212\) | −4054.50 | + | 7022.60i | −0.0902123 | + | 0.156252i | ||||
\(213\) | 2178.00 | − | 1257.47i | 0.0480063 | − | 0.0277165i | ||||
\(214\) | 11162.5 | + | 19334.0i | 0.243744 | + | 0.422177i | ||||
\(215\) | −4197.00 | − | 2423.14i | −0.0907950 | − | 0.0524205i | ||||
\(216\) | − | 4910.36i | − | 0.105246i | ||||||
\(217\) | 39007.5 | − | 49546.2i | 0.828378 | − | 1.05218i | ||||
\(218\) | −16600.0 | −0.349297 | ||||||||
\(219\) | −2466.00 | + | 4271.24i | −0.0514168 | + | 0.0890565i | ||||
\(220\) | −2011.50 | + | 1161.34i | −0.0415599 | + | 0.0239946i | ||||
\(221\) | −5544.00 | − | 9602.49i | −0.113511 | − | 0.196607i | ||||
\(222\) | 44325.0 | + | 25591.1i | 0.899379 | + | 0.519257i | ||||
\(223\) | 49077.7i | 0.986902i | 0.869774 | + | 0.493451i | \(0.164265\pi\) | ||||
−0.869774 | + | 0.493451i | \(0.835735\pi\) | |||||||
\(224\) | 39847.5 | + | 31371.8i | 0.794155 | + | 0.625235i | ||||
\(225\) | −16794.0 | −0.331733 | ||||||||
\(226\) | −24335.0 | + | 42149.5i | −0.476447 | + | 0.825230i | ||||
\(227\) | 64141.5 | − | 37032.1i | 1.24477 | − | 0.718665i | 0.274705 | − | 0.961529i | \(-0.411420\pi\) |
0.970061 | + | 0.242863i | \(0.0780866\pi\) | |||||||
\(228\) | 8343.00 | + | 14450.5i | 0.160492 | + | 0.277980i | ||||
\(229\) | 20697.0 | + | 11949.4i | 0.394672 | + | 0.227864i | 0.684183 | − | 0.729311i | \(-0.260159\pi\) |
−0.289510 | + | 0.957175i | \(0.593492\pi\) | |||||||
\(230\) | 4849.74i | 0.0916775i | ||||||||
\(231\) | −37548.0 | − | 5419.59i | −0.703660 | − | 0.101565i | ||||
\(232\) | 8225.00 | 0.152813 | ||||||||
\(233\) | −48191.0 | + | 83469.3i | −0.887675 | + | 1.53750i | −0.0450588 | + | 0.998984i | \(0.514348\pi\) |
−0.842616 | + | 0.538514i | \(0.818986\pi\) | |||||||
\(234\) | 4860.00 | − | 2805.92i | 0.0887574 | − | 0.0512441i | ||||
\(235\) | −3576.00 | − | 6193.81i | −0.0647533 | − | 0.112156i | ||||
\(236\) | −10759.5 | − | 6212.00i | −0.193183 | − | 0.111534i | ||||
\(237\) | 22473.4i | 0.400103i | ||||||||
\(238\) | −24255.0 | − | 60682.4i | −0.428201 | − | 1.07129i | ||||
\(239\) | −44276.0 | −0.775126 | −0.387563 | − | 0.921843i | \(-0.626683\pi\) | ||||
−0.387563 | + | 0.921843i | \(0.626683\pi\) | |||||||
\(240\) | −1435.50 | + | 2486.36i | −0.0249219 | + | 0.0431660i | ||||
\(241\) | −49318.5 | + | 28474.0i | −0.849133 | + | 0.490247i | −0.860358 | − | 0.509690i | \(-0.829760\pi\) |
0.0112252 | + | 0.999937i | \(0.496427\pi\) | |||||||
\(242\) | 18900.0 | + | 32735.8i | 0.322724 | + | 0.558974i | ||||
\(243\) | −3280.50 | − | 1894.00i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 32112.2i | 0.539375i | ||||||||
\(245\) | −4042.50 | + | 976.011i | −0.0673469 | + | 0.0162601i | ||||
\(246\) | −73170.0 | −1.20910 | ||||||||
\(247\) | 7416.00 | − | 12844.9i | 0.121556 | − | 0.210541i | ||||
\(248\) | −39007.5 | + | 22521.0i | −0.634227 | + | 0.366171i | ||||
\(249\) | 3388.50 | + | 5869.05i | 0.0546523 | + | 0.0946606i | ||||
\(250\) | 9352.50 | + | 5399.67i | 0.149640 | + | 0.0863947i | ||||
\(251\) | − | 74715.5i | − | 1.18594i | −0.805224 | − | 0.592971i | \(-0.797955\pi\) | ||
0.805224 | − | 0.592971i | \(-0.202045\pi\) | |||||||
\(252\) | 11056.5 | − | 4419.33i | 0.174107 | − | 0.0695913i | ||||
\(253\) | 83440.0 | 1.30357 | ||||||||
\(254\) | −72872.5 | + | 126219.i | −1.12953 | + | 1.95640i | ||||
\(255\) | 2079.00 | − | 1200.31i | 0.0319723 | − | 0.0184592i | ||||
\(256\) | −41080.5 | − | 71153.5i | −0.626839 | − | 1.08572i | ||||
\(257\) | 25419.0 | + | 14675.7i | 0.384851 | + | 0.222194i | 0.679927 | − | 0.733280i | \(-0.262012\pi\) |
−0.295076 | + | 0.955474i | \(0.595345\pi\) | |||||||
\(258\) | − | 72694.2i | − | 1.09209i | ||||||
\(259\) | 13790.0 | − | 95539.9i | 0.205572 | − | 1.42425i | ||||
\(260\) | −648.000 | −0.00958580 | ||||||||
\(261\) | 3172.50 | − | 5494.93i | 0.0465715 | − | 0.0806643i | ||||
\(262\) | 119332. | − | 68896.7i | 1.73843 | − | 1.00368i | ||||
\(263\) | 44539.0 | + | 77143.8i | 0.643916 | + | 1.11529i | 0.984551 | + | 0.175099i | \(0.0560246\pi\) |
−0.340635 | + | 0.940196i | \(0.610642\pi\) | |||||||
\(264\) | 23467.5 | + | 13549.0i | 0.336712 | + | 0.194401i | ||||
\(265\) | 1560.58i | 0.0222225i | ||||||||
\(266\) | 54075.0 | − | 68684.5i | 0.764246 | − | 0.970723i | ||||
\(267\) | 10278.0 | 0.144174 | ||||||||
\(268\) | 18702.0 | − | 32392.8i | 0.260387 | − | 0.451003i | ||||
\(269\) | 61693.5 | − | 35618.8i | 0.852579 | − | 0.492237i | −0.00894091 | − | 0.999960i | \(-0.502846\pi\) |
0.861520 | + | 0.507723i | \(0.169513\pi\) | |||||||
\(270\) | 607.500 | + | 1052.22i | 0.00833333 | + | 0.0144338i | ||||
\(271\) | −36664.5 | − | 21168.3i | −0.499237 | − | 0.288235i | 0.229161 | − | 0.973389i | \(-0.426402\pi\) |
−0.728399 | + | 0.685154i | \(0.759735\pi\) | |||||||
\(272\) | 85088.7i | 1.15010i | ||||||||
\(273\) | −8316.00 | − | 6547.15i | −0.111581 | − | 0.0878470i | ||||
\(274\) | −89120.0 | −1.18706 | ||||||||
\(275\) | 46339.0 | − | 80261.5i | 0.612747 | − | 1.06131i | ||||
\(276\) | −22680.0 | + | 13094.3i | −0.297732 | + | 0.171895i | ||||
\(277\) | 23258.0 | + | 40284.0i | 0.303119 | + | 0.525017i | 0.976841 | − | 0.213968i | \(-0.0686388\pi\) |
−0.673722 | + | 0.738985i | \(0.735305\pi\) | |||||||
\(278\) | −121185. | − | 69966.2i | −1.56805 | − | 0.905313i | ||||
\(279\) | 34746.7i | 0.446380i | ||||||||
\(280\) | 2940.00 | + | 424.352i | 0.0375000 | + | 0.00541266i | ||||
\(281\) | 50284.0 | 0.636821 | 0.318410 | − | 0.947953i | \(-0.396851\pi\) | ||||
0.318410 | + | 0.947953i | \(0.396851\pi\) | |||||||
\(282\) | 53640.0 | − | 92907.2i | 0.674513 | − | 1.16829i | ||||
\(283\) | −32043.0 | + | 18500.0i | −0.400092 | + | 0.230993i | −0.686524 | − | 0.727107i | \(-0.740864\pi\) |
0.286431 | + | 0.958101i | \(0.407531\pi\) | |||||||
\(284\) | −2178.00 | − | 3772.41i | −0.0270036 | − | 0.0467716i | ||||
\(285\) | 2781.00 | + | 1605.61i | 0.0342382 | + | 0.0197674i | ||||
\(286\) | 30969.1i | 0.378613i | ||||||||
\(287\) | 51219.0 | + | 128142.i | 0.621824 | + | 1.55571i | ||||
\(288\) | −27945.0 | −0.336914 | ||||||||
\(289\) | −6186.50 | + | 10715.3i | −0.0740712 | + | 0.128295i | ||||
\(290\) | −1762.50 | + | 1017.58i | −0.0209572 | + | 0.0120996i | ||||
\(291\) | −14161.5 | − | 24528.4i | −0.167233 | − | 0.289657i | ||||
\(292\) | 7398.00 | + | 4271.24i | 0.0867658 | + | 0.0500943i | ||||
\(293\) | − | 66994.0i | − | 0.780370i | −0.920736 | − | 0.390185i | \(-0.872411\pi\) | ||
0.920736 | − | 0.390185i | \(-0.127589\pi\) | |||||||
\(294\) | −42997.5 | − | 45193.5i | −0.497449 | − | 0.522855i | ||||
\(295\) | −2391.00 | −0.0274749 | ||||||||
\(296\) | −34475.0 | + | 59712.5i | −0.393478 | + | 0.681525i | ||||
\(297\) | 18103.5 | − | 10452.1i | 0.205234 | − | 0.118492i | ||||
\(298\) | 23035.0 | + | 39897.8i | 0.259391 | + | 0.449279i | ||||
\(299\) | 20160.0 | + | 11639.4i | 0.225501 | + | 0.130193i | ||||
\(300\) | 29088.1i | 0.323201i | ||||||||
\(301\) | −127309. | + | 50885.9i | −1.40516 | + | 0.561649i | ||||
\(302\) | −59875.0 | −0.656495 | ||||||||
\(303\) | −11250.0 | + | 19485.6i | −0.122537 | + | 0.212240i | ||||
\(304\) | −98571.0 | + | 56910.0i | −1.06660 | + | 0.615802i | ||||
\(305\) | 3090.00 | + | 5352.04i | 0.0332169 | + | 0.0575333i | ||||
\(306\) | 31185.0 | + | 18004.7i | 0.333045 | + | 0.192284i | ||||
\(307\) | 76258.7i | 0.809120i | 0.914511 | + | 0.404560i | \(0.132575\pi\) | ||||
−0.914511 | + | 0.404560i | \(0.867425\pi\) | |||||||
\(308\) | −9387.00 | + | 65035.0i | −0.0989522 | + | 0.685561i | ||||
\(309\) | 75096.0 | 0.786502 | ||||||||
\(310\) | 5572.50 | − | 9651.85i | 0.0579865 | − | 0.100436i | ||||
\(311\) | 45543.0 | − | 26294.3i | 0.470870 | − | 0.271857i | −0.245734 | − | 0.969337i | \(-0.579029\pi\) |
0.716604 | + | 0.697480i | \(0.245696\pi\) | |||||||
\(312\) | 3780.00 | + | 6547.15i | 0.0388314 | + | 0.0672579i | ||||
\(313\) | −80404.5 | − | 46421.6i | −0.820714 | − | 0.473839i | 0.0299488 | − | 0.999551i | \(-0.490466\pi\) |
−0.850663 | + | 0.525712i | \(0.823799\pi\) | |||||||
\(314\) | 9941.97i | 0.100835i | ||||||||
\(315\) | 1417.50 | − | 1800.47i | 0.0142857 | − | 0.0181453i | ||||
\(316\) | 38925.0 | 0.389811 | ||||||||
\(317\) | 30791.5 | − | 53332.4i | 0.306417 | − | 0.530729i | −0.671159 | − | 0.741313i | \(-0.734203\pi\) |
0.977576 | + | 0.210584i | \(0.0675366\pi\) | |||||||
\(318\) | −20272.5 | + | 11704.3i | −0.200472 | + | 0.115742i | ||||
\(319\) | 17507.5 | + | 30323.9i | 0.172045 | + | 0.297991i | ||||
\(320\) | 106.500 | + | 61.4878i | 0.00104004 | + | 0.000600467i | ||||
\(321\) | 23200.8i | 0.225161i | ||||||||
\(322\) | 107800. | + | 84870.5i | 1.03970 | + | 0.818550i | ||||
\(323\) | 95172.0 | 0.912230 | ||||||||
\(324\) | −3280.50 | + | 5681.99i | −0.0312500 | + | 0.0541266i | ||||
\(325\) | 22392.0 | − | 12928.0i | 0.211995 | − | 0.122396i | ||||
\(326\) | −52000.0 | − | 90066.6i | −0.489292 | − | 0.847479i | ||||
\(327\) | −14940.0 | − | 8625.61i | −0.139719 | − | 0.0806667i | ||||
\(328\) | − | 98571.0i | − | 0.916224i | ||||||
\(329\) | −200256. | − | 28904.5i | −1.85009 | − | 0.267038i | ||||
\(330\) | −6705.00 | −0.0615702 | ||||||||
\(331\) | 45740.0 | − | 79224.0i | 0.417484 | − | 0.723104i | −0.578201 | − | 0.815894i | \(-0.696245\pi\) |
0.995686 | + | 0.0927900i | \(0.0295785\pi\) | |||||||
\(332\) | 10165.5 | − | 5869.05i | 0.0922258 | − | 0.0532466i | ||||
\(333\) | 26595.0 | + | 46063.9i | 0.239834 | + | 0.415405i | ||||
\(334\) | 183960. | + | 106209.i | 1.64904 | + | 0.952072i | ||||
\(335\) | − | 7198.40i | − | 0.0641426i | ||||||
\(336\) | 30145.5 | + | 75419.6i | 0.267020 | + | 0.668045i | ||||
\(337\) | 9995.00 | 0.0880082 | 0.0440041 | − | 0.999031i | \(-0.485989\pi\) | ||||
0.0440041 | + | 0.999031i | \(0.485989\pi\) | |||||||
\(338\) | 67082.5 | − | 116190.i | 0.587186 | − | 1.01704i | ||||
\(339\) | −43803.0 | + | 25289.7i | −0.381157 | + | 0.220061i | ||||
\(340\) | −2079.00 | − | 3600.93i | −0.0179844 | − | 0.0311499i | ||||
\(341\) | −166060. | − | 95875.1i | −1.42810 | − | 0.824512i | ||||
\(342\) | 48168.3i | 0.411822i | ||||||||
\(343\) | −49049.0 | + | 106937.i | −0.416910 | + | 0.908948i | ||||
\(344\) | 97930.0 | 0.827559 | ||||||||
\(345\) | −2520.00 | + | 4364.77i | −0.0211720 | + | 0.0366710i | ||||
\(346\) | −10470.0 | + | 6044.86i | −0.0874570 | + | 0.0504933i | ||||
\(347\) | −31229.0 | − | 54090.2i | −0.259358 | − | 0.449221i | 0.706712 | − | 0.707501i | \(-0.250178\pi\) |
−0.966070 | + | 0.258280i | \(0.916844\pi\) | |||||||
\(348\) | −9517.50 | − | 5494.93i | −0.0785895 | − | 0.0453737i | ||||
\(349\) | − | 233370.i | − | 1.91599i | −0.286784 | − | 0.957995i | \(-0.592586\pi\) | ||
0.286784 | − | 0.957995i | \(-0.407414\pi\) | |||||||
\(350\) | 141505. | − | 56560.1i | 1.15514 | − | 0.461715i | ||||
\(351\) | 5832.00 | 0.0473373 | ||||||||
\(352\) | 77107.5 | − | 133554.i | 0.622316 | − | 1.07788i | ||||
\(353\) | −71898.0 | + | 41510.3i | −0.576989 | + | 0.333125i | −0.759936 | − | 0.649998i | \(-0.774770\pi\) |
0.182947 | + | 0.983123i | \(0.441436\pi\) | |||||||
\(354\) | −17932.5 | − | 31060.0i | −0.143098 | − | 0.247853i | ||||
\(355\) | −726.000 | − | 419.156i | −0.00576076 | − | 0.00332598i | ||||
\(356\) | − | 17802.0i | − | 0.140465i | ||||||
\(357\) | 9702.00 | − | 67217.4i | 0.0761246 | − | 0.527406i | ||||
\(358\) | −96890.0 | −0.755985 | ||||||||
\(359\) | −82022.0 | + | 142066.i | −0.636417 | + | 1.10231i | 0.349797 | + | 0.936826i | \(0.386251\pi\) |
−0.986213 | + | 0.165480i | \(0.947083\pi\) | |||||||
\(360\) | −1417.50 | + | 818.394i | −0.0109375 | + | 0.00631477i | ||||
\(361\) | −1506.50 | − | 2609.33i | −0.0115599 | − | 0.0200224i | ||||
\(362\) | 32265.0 | + | 18628.2i | 0.246215 | + | 0.142152i | ||||
\(363\) | 39282.9i | 0.298120i | ||||||||
\(364\) | −11340.0 | + | 14403.7i | −0.0855875 | + | 0.108711i | ||||
\(365\) | 1644.00 | 0.0123400 | ||||||||
\(366\) | −46350.0 | + | 80280.6i | −0.346009 | + | 0.599305i | ||||
\(367\) | −3715.50 | + | 2145.14i | −0.0275858 | + | 0.0159267i | −0.513729 | − | 0.857952i | \(-0.671736\pi\) |
0.486144 | + | 0.873879i | \(0.338403\pi\) | |||||||
\(368\) | −89320.0 | − | 154707.i | −0.659558 | − | 1.14239i | ||||
\(369\) | −65853.0 | − | 38020.2i | −0.483641 | − | 0.279230i | ||||
\(370\) | − | 17060.7i | − | 0.124622i | ||||||
\(371\) | 34688.5 | + | 27310.1i | 0.252022 | + | 0.198416i | ||||
\(372\) | 60183.0 | 0.434899 | ||||||||
\(373\) | −39313.0 | + | 68092.1i | −0.282565 | + | 0.489417i | −0.972016 | − | 0.234916i | \(-0.924519\pi\) |
0.689451 | + | 0.724333i | \(0.257852\pi\) | |||||||
\(374\) | −172095. | + | 99359.1i | −1.23034 | + | 0.710337i | ||||
\(375\) | 5611.50 | + | 9719.40i | 0.0399040 | + | 0.0691158i | ||||
\(376\) | 125160. | + | 72261.2i | 0.885299 | + | 0.511127i | ||||
\(377\) | 9768.77i | 0.0687317i | ||||||||
\(378\) | 34020.0 | + | 4910.36i | 0.238095 | + | 0.0343661i | ||||
\(379\) | 56234.0 | 0.391490 | 0.195745 | − | 0.980655i | \(-0.437288\pi\) | ||||
0.195745 | + | 0.980655i | \(0.437288\pi\) | |||||||
\(380\) | 2781.00 | − | 4816.83i | 0.0192590 | − | 0.0333576i | ||||
\(381\) | −131170. | + | 75731.3i | −0.903621 | + | 0.521706i | ||||
\(382\) | −71900.0 | − | 124534.i | −0.492722 | − | 0.853420i | ||||
\(383\) | 189957. | + | 109672.i | 1.29496 | + | 0.747648i | 0.979530 | − | 0.201299i | \(-0.0645164\pi\) |
0.315434 | + | 0.948947i | \(0.397850\pi\) | |||||||
\(384\) | − | 84203.7i | − | 0.571043i | ||||||
\(385\) | 4693.50 | + | 11742.4i | 0.0316647 | + | 0.0792204i | ||||
\(386\) | 220445. | 1.47954 | ||||||||
\(387\) | 37773.0 | − | 65424.8i | 0.252208 | − | 0.436838i | ||||
\(388\) | −42484.5 | + | 24528.4i | −0.282207 | + | 0.162932i | ||||
\(389\) | 2131.00 | + | 3691.00i | 0.0140826 | + | 0.0243919i | 0.872981 | − | 0.487754i | \(-0.162184\pi\) |
−0.858898 | + | 0.512146i | \(0.828851\pi\) | |||||||
\(390\) | −1620.00 | − | 935.307i | −0.0106509 | − | 0.00614929i | ||||
\(391\) | 149372.i | 0.977048i | ||||||||
\(392\) | 60882.5 | − | 57924.1i | 0.396205 | − | 0.376953i | ||||
\(393\) | 143199. | 0.927160 | ||||||||
\(394\) | −116195. | + | 201256.i | −0.748506 | + | 1.29645i | ||||
\(395\) | 6487.50 | − | 3745.56i | 0.0415799 | − | 0.0240062i | ||||
\(396\) | −18103.5 | − | 31356.2i | −0.115444 | − | 0.199955i | ||||
\(397\) | 126618. | + | 73102.9i | 0.803368 | + | 0.463825i | 0.844647 | − | 0.535323i | \(-0.179810\pi\) |
−0.0412796 | + | 0.999148i | \(0.513143\pi\) | |||||||
\(398\) | 196172.i | 1.23843i | ||||||||
\(399\) | 84357.0 | − | 33717.8i | 0.529877 | − | 0.211794i | ||||
\(400\) | −198418. | −1.24011 | ||||||||
\(401\) | 45406.0 | − | 78645.5i | 0.282374 | − | 0.489086i | −0.689595 | − | 0.724195i | \(-0.742211\pi\) |
0.971969 | + | 0.235109i | \(0.0755448\pi\) | |||||||
\(402\) | 93510.0 | − | 53988.0i | 0.578637 | − | 0.334076i | ||||
\(403\) | −26748.0 | − | 46328.9i | −0.164695 | − | 0.285261i | ||||
\(404\) | 33750.0 | + | 19485.6i | 0.206781 | + | 0.119385i | ||||
\(405\) | 1262.67i | 0.00769800i | ||||||||
\(406\) | −8225.00 | + | 56984.5i | −0.0498981 | + | 0.345704i | ||||
\(407\) | −293530. | −1.77200 | ||||||||
\(408\) | −24255.0 | + | 42010.9i | −0.145707 | + | 0.252372i | ||||
\(409\) | 39250.5 | − | 22661.3i | 0.234638 | − | 0.135468i | −0.378072 | − | 0.925776i | \(-0.623413\pi\) |
0.612710 | + | 0.790308i | \(0.290079\pi\) | |||||||
\(410\) | 12195.0 | + | 21122.4i | 0.0725461 | + | 0.125654i | ||||
\(411\) | −80208.0 | − | 46308.1i | −0.474826 | − | 0.274141i | ||||
\(412\) | − | 130070.i | − | 0.766272i | ||||||
\(413\) | −41842.5 | + | 53147.1i | −0.245311 | + | 0.311587i | ||||
\(414\) | −75600.0 | −0.441084 | ||||||||
\(415\) | 1129.50 | − | 1956.35i | 0.00655828 | − | 0.0113593i | ||||
\(416\) | 37260.0 | − | 21512.1i | 0.215306 | − | 0.124307i | ||||
\(417\) | −72711.0 | − | 125939.i | −0.418146 | − | 0.724250i | ||||
\(418\) | −230205. | − | 132909.i | −1.31754 | − | 0.760679i | ||||
\(419\) | 148922.i | 0.848262i | 0.905601 | + | 0.424131i | \(0.139420\pi\) | ||||
−0.905601 | + | 0.424131i | \(0.860580\pi\) | |||||||
\(420\) | −3118.50 | − | 2455.18i | −0.0176786 | − | 0.0139183i | ||||
\(421\) | 4256.00 | 0.0240125 | 0.0120063 | − | 0.999928i | \(-0.496178\pi\) | ||||
0.0120063 | + | 0.999928i | \(0.496178\pi\) | |||||||
\(422\) | −69220.0 | + | 119893.i | −0.388693 | + | 0.673236i | ||||
\(423\) | 96552.0 | − | 55744.3i | 0.539611 | − | 0.311544i | ||||
\(424\) | −15767.5 | − | 27310.1i | −0.0877064 | − | 0.151912i | ||||
\(425\) | 143682. | + | 82954.8i | 0.795471 | + | 0.459266i | ||||
\(426\) | − | 12574.7i | − | 0.0692912i | ||||||
\(427\) | 173040. | + | 24976.2i | 0.949054 | + | 0.136984i | ||||
\(428\) | 40185.0 | 0.219370 | ||||||||
\(429\) | −16092.0 | + | 27872.2i | −0.0874370 | + | 0.151445i | ||||
\(430\) | −20985.0 | + | 12115.7i | −0.113494 | + | 0.0655257i | ||||
\(431\) | 73831.0 | + | 127879.i | 0.397452 | + | 0.688406i | 0.993411 | − | 0.114608i | \(-0.0365613\pi\) |
−0.595959 | + | 0.803015i | \(0.703228\pi\) | |||||||
\(432\) | −38758.5 | − | 22377.2i | −0.207682 | − | 0.119905i | ||||
\(433\) | − | 58799.7i | − | 0.313617i | −0.987629 | − | 0.156808i | \(-0.949880\pi\) | ||
0.987629 | − | 0.156808i | \(-0.0501205\pi\) | |||||||
\(434\) | −117022. | − | 292773.i | −0.621284 | − | 1.55436i | ||||
\(435\) | −2115.00 | −0.0111772 | ||||||||
\(436\) | −14940.0 | + | 25876.8i | −0.0785919 | + | 0.136125i | ||||
\(437\) | −173040. | + | 99904.7i | −0.906116 | + | 0.523146i | ||||
\(438\) | 12330.0 | + | 21356.2i | 0.0642710 | + | 0.111321i | ||||
\(439\) | −88882.5 | − | 51316.3i | −0.461198 | − | 0.266273i | 0.251350 | − | 0.967896i | \(-0.419125\pi\) |
−0.712548 | + | 0.701624i | \(0.752459\pi\) | |||||||
\(440\) | − | 9032.64i | − | 0.0466562i | ||||||
\(441\) | −15214.5 | − | 63016.3i | −0.0782313 | − | 0.324023i | ||||
\(442\) | −55440.0 | −0.283778 | ||||||||
\(443\) | 146990. | − | 254595.i | 0.749000 | − | 1.29731i | −0.199302 | − | 0.979938i | \(-0.563868\pi\) |
0.948302 | − | 0.317368i | \(-0.102799\pi\) | |||||||
\(444\) | 79785.0 | − | 46063.9i | 0.404721 | − | 0.233666i | ||||
\(445\) | −1713.00 | − | 2967.00i | −0.00865042 | − | 0.0149830i | ||||
\(446\) | 212512. | + | 122694.i | 1.06835 | + | 0.616814i | ||||
\(447\) | 47877.3i | 0.239616i | ||||||||
\(448\) | 3230.50 | − | 1291.24i | 0.0160958 | − | 0.00643357i | ||||
\(449\) | 21220.0 | 0.105257 | 0.0526287 | − | 0.998614i | \(-0.483240\pi\) | ||||
0.0526287 | + | 0.998614i | \(0.483240\pi\) | |||||||
\(450\) | −41985.0 | + | 72720.2i | −0.207333 | + | 0.359112i | ||||
\(451\) | 363411. | − | 209815.i | 1.78667 | − | 1.03154i | ||||
\(452\) | 43803.0 | + | 75869.0i | 0.214401 | + | 0.371354i | ||||
\(453\) | −53887.5 | − | 31112.0i | −0.262598 | − | 0.151611i | ||||
\(454\) | − | 370321.i | − | 1.79666i | ||||||
\(455\) | −504.000 | + | 3491.81i | −0.00243449 | + | 0.0168666i | ||||
\(456\) | −64890.0 | −0.312067 | ||||||||
\(457\) | 88233.5 | − | 152825.i | 0.422475 | − | 0.731748i | −0.573706 | − | 0.819061i | \(-0.694495\pi\) |
0.996181 | + | 0.0873131i | \(0.0278281\pi\) | |||||||
\(458\) | 103485. | − | 59747.1i | 0.493340 | − | 0.284830i | ||||
\(459\) | 18711.0 | + | 32408.4i | 0.0888120 | + | 0.153827i | ||||
\(460\) | 7560.00 | + | 4364.77i | 0.0357278 | + | 0.0206274i | ||||
\(461\) | − | 222063.i | − | 1.04490i | −0.852671 | − | 0.522449i | \(-0.825019\pi\) | ||
0.852671 | − | 0.522449i | \(-0.174981\pi\) | |||||||
\(462\) | −117337. | + | 149039.i | −0.549734 | + | 0.698256i | ||||
\(463\) | 142286. | 0.663743 | 0.331872 | − | 0.943325i | \(-0.392320\pi\) | ||||
0.331872 | + | 0.943325i | \(0.392320\pi\) | |||||||
\(464\) | 37482.5 | − | 64921.6i | 0.174098 | − | 0.301546i | ||||
\(465\) | 10030.5 | − | 5791.11i | 0.0463892 | − | 0.0267828i | ||||
\(466\) | 240955. | + | 417346.i | 1.10959 | + | 1.92187i | ||||
\(467\) | −338190. | − | 195254.i | −1.55070 | − | 0.895295i | −0.998085 | − | 0.0618569i | \(-0.980298\pi\) |
−0.552612 | − | 0.833439i | \(-0.686369\pi\) | |||||||
\(468\) | − | 10101.3i | − | 0.0461197i | ||||||
\(469\) | −160006. | − | 125972.i | −0.727429 | − | 0.572702i | ||||
\(470\) | −35760.0 | −0.161883 | ||||||||
\(471\) | −5166.00 | + | 8947.77i | −0.0232869 | + | 0.0403342i | ||||
\(472\) | 41842.5 | − | 24157.8i | 0.187816 | − | 0.108436i | ||||
\(473\) | 208451. | + | 361048.i | 0.931712 | + | 1.61377i | ||||
\(474\) | 97312.5 | + | 56183.4i | 0.433124 | + | 0.250064i | ||||
\(475\) | 221931.i | 0.983628i | ||||||||
\(476\) | −116424. | − | 16804.4i | −0.513841 | − | 0.0741665i | ||||
\(477\) | −24327.0 | −0.106918 | ||||||||
\(478\) | −110690. | + | 191721.i | −0.484454 | + | 0.839099i | ||||
\(479\) | −131271. | + | 75789.3i | −0.572134 | + | 0.330322i | −0.758001 | − | 0.652253i | \(-0.773824\pi\) |
0.185867 | + | 0.982575i | \(0.440491\pi\) | |||||||
\(480\) | 4657.50 | + | 8067.03i | 0.0202148 | + | 0.0350131i | ||||
\(481\) | −70920.0 | − | 40945.7i | −0.306534 | − | 0.176977i | ||||
\(482\) | 284740.i | 1.22562i | ||||||||
\(483\) | 52920.0 | + | 132398.i | 0.226843 | + | 0.567528i | ||||
\(484\) | 68040.0 | 0.290451 | ||||||||
\(485\) | −4720.50 | + | 8176.15i | −0.0200680 | + | 0.0347588i | ||||
\(486\) | −16402.5 | + | 9469.99i | −0.0694444 | + | 0.0400938i | ||||
\(487\) | −103014. | − | 178425.i | −0.434346 | − | 0.752310i | 0.562896 | − | 0.826528i | \(-0.309687\pi\) |
−0.997242 | + | 0.0742179i | \(0.976354\pi\) | |||||||
\(488\) | −108150. | − | 62440.4i | −0.454137 | − | 0.262196i | ||||
\(489\) | − | 108080.i | − | 0.451989i | ||||||
\(490\) | −5880.00 | + | 19944.6i | −0.0244898 | + | 0.0830677i | ||||
\(491\) | −477113. | −1.97906 | −0.989528 | − | 0.144338i | \(-0.953895\pi\) | ||||
−0.989528 | + | 0.144338i | \(0.953895\pi\) | |||||||
\(492\) | −65853.0 | + | 114061.i | −0.272048 | + | 0.471201i | ||||
\(493\) | −54285.0 | + | 31341.5i | −0.223350 | + | 0.128951i | ||||
\(494\) | −37080.0 | − | 64224.4i | −0.151945 | − | 0.263176i | ||||
\(495\) | −6034.50 | − | 3484.02i | −0.0246281 | − | 0.0142190i | ||||
\(496\) | 410525.i | 1.66869i | ||||||||
\(497\) | −22022.0 | + | 8802.28i | −0.0891546 | + | 0.0356355i | ||||
\(498\) | 33885.0 | 0.136631 | ||||||||
\(499\) | −82405.0 | + | 142730.i | −0.330942 | + | 0.573209i | −0.982697 | − | 0.185221i | \(-0.940700\pi\) |
0.651754 | + | 0.758430i | \(0.274033\pi\) | |||||||
\(500\) | 16834.5 | − | 9719.40i | 0.0673380 | − | 0.0388776i | ||||
\(501\) | 110376. | + | 191177.i | 0.439743 | + | 0.761658i | ||||
\(502\) | −323528. | − | 186789.i | −1.28382 | − | 0.741213i | ||||
\(503\) | − | 203616.i | − | 0.804779i | −0.915468 | − | 0.402390i | \(-0.868180\pi\) | ||
0.915468 | − | 0.402390i | \(-0.131820\pi\) | |||||||
\(504\) | −6615.00 | + | 45830.1i | −0.0260417 | + | 0.180422i | ||||
\(505\) | 7500.00 | 0.0294089 | ||||||||
\(506\) | 208600. | − | 361306.i | 0.814729 | − | 1.41115i | ||||
\(507\) | 120748. | − | 69714.2i | 0.469749 | − | 0.271210i | ||||
\(508\) | 131170. | + | 227194.i | 0.508287 | + | 0.880378i | ||||
\(509\) | 408536. | + | 235868.i | 1.57686 | + | 0.910403i | 0.995293 | + | 0.0969069i | \(0.0308949\pi\) |
0.581571 | + | 0.813496i | \(0.302438\pi\) | |||||||
\(510\) | − | 12003.1i | − | 0.0461481i | ||||||
\(511\) | 28770.0 | − | 36542.8i | 0.110179 | − | 0.139946i | ||||
\(512\) | −151525. | −0.578022 | ||||||||
\(513\) | −25029.0 | + | 43351.5i | −0.0951062 | + | 0.164729i | ||||
\(514\) | 127095. | − | 73378.3i | 0.481063 | − | 0.277742i | ||||
\(515\) | −12516.0 | − | 21678.3i | −0.0471901 | − | 0.0817357i | ||||
\(516\) | −113319. | − | 65424.8i | −0.425602 | − | 0.245721i | ||||
\(517\) | 615252.i | 2.30182i | ||||||||
\(518\) | −379225. | − | 298562.i | −1.41331 | − | 1.11269i | ||||
\(519\) | −12564.0 | −0.0466437 | ||||||||
\(520\) | 1260.00 | − | 2182.38i | 0.00465976 | − | 0.00807095i | ||||
\(521\) | 363081. | − | 209625.i | 1.33761 | − | 0.772267i | 0.351154 | − | 0.936318i | \(-0.385789\pi\) |
0.986452 | + | 0.164051i | \(0.0524561\pi\) | |||||||
\(522\) | −15862.5 | − | 27474.7i | −0.0582144 | − | 0.100830i | ||||
\(523\) | −259374. | − | 149750.i | −0.948250 | − | 0.547473i | −0.0557134 | − | 0.998447i | \(-0.517743\pi\) |
−0.892537 | + | 0.450974i | \(0.851077\pi\) | |||||||
\(524\) | − | 248028.i | − | 0.903313i | ||||||
\(525\) | 156744. | + | 22624.0i | 0.568686 | + | 0.0820827i | ||||
\(526\) | 445390. | 1.60979 | ||||||||
\(527\) | 171633. | − | 297277.i | 0.617987 | − | 1.07039i | ||||
\(528\) | 213890. | − | 123489.i | 0.767223 | − | 0.442956i | ||||
\(529\) | −16879.5 | − | 29236.2i | −0.0603182 | − | 0.104474i | ||||
\(530\) | 6757.50 | + | 3901.44i | 0.0240566 | + | 0.0138891i | ||||
\(531\) | − | 37272.0i | − | 0.132188i | ||||||
\(532\) | −58401.0 | − | 146111.i | −0.206346 | − | 0.516248i | ||||
\(533\) | 117072. | 0.412096 | ||||||||
\(534\) | 25695.0 | − | 44505.0i | 0.0901086 | − | 0.156073i | ||||
\(535\) | 6697.50 | − | 3866.80i | 0.0233994 | − | 0.0135097i | ||||
\(536\) | 72730.0 | + | 125972.i | 0.253154 | + | 0.438475i | ||||
\(537\) | −87201.0 | − | 50345.5i | −0.302394 | − | 0.174587i | ||||
\(538\) | − | 356188.i | − | 1.23059i | ||||||
\(539\) | 343147. | + | 101166.i | 1.18114 | + | 0.348221i | ||||
\(540\) | 2187.00 | 0.00750000 | ||||||||
\(541\) | −152545. | + | 264216.i | −0.521199 | + | 0.902743i | 0.478497 | + | 0.878089i | \(0.341182\pi\) |
−0.999696 | + | 0.0246538i | \(0.992152\pi\) | |||||||
\(542\) | −183322. | + | 105841.i | −0.624047 | + | 0.360294i | ||||
\(543\) | 19359.0 | + | 33530.8i | 0.0656573 | + | 0.113722i | ||||
\(544\) | 239085. | + | 138036.i | 0.807894 | + | 0.466438i | ||||
\(545\) | 5750.41i | 0.0193600i | ||||||||
\(546\) | −49140.0 | + | 19641.5i | −0.164835 | + | 0.0658853i | ||||
\(547\) | −260974. | −0.872213 | −0.436107 | − | 0.899895i | \(-0.643643\pi\) | ||||
−0.436107 | + | 0.899895i | \(0.643643\pi\) | |||||||
\(548\) | −80208.0 | + | 138924.i | −0.267089 | + | 0.462612i | ||||
\(549\) | −83430.0 | + | 48168.3i | −0.276807 | + | 0.159815i | ||||
\(550\) | −231695. | − | 401308.i | −0.765934 | − | 1.32664i | ||||
\(551\) | −72615.0 | − | 41924.3i | −0.239179 | − | 0.138090i | ||||
\(552\) | − | 101845.i | − | 0.334241i | ||||||
\(553\) | 30275.0 | − | 209751.i | 0.0989997 | − | 0.685890i | ||||
\(554\) | 232580. | 0.757797 | ||||||||
\(555\) | 8865.00 | − | 15354.6i | 0.0287801 | − | 0.0498486i | ||||
\(556\) | −218133. | + | 125939.i | −0.705621 | + | 0.407391i | ||||
\(557\) | −125632. | − | 217600.i | −0.404938 | − | 0.701373i | 0.589377 | − | 0.807858i | \(-0.299373\pi\) |
−0.994314 | + | 0.106486i | \(0.966040\pi\) | |||||||
\(558\) | 150458. | + | 86866.7i | 0.483221 | + | 0.278988i | ||||
\(559\) | 116311.i | 0.372217i | ||||||||
\(560\) | 16747.5 | − | 21272.2i | 0.0534040 | − | 0.0678322i | ||||
\(561\) | −206514. | −0.656181 | ||||||||
\(562\) | 125710. | − | 217736.i | 0.398013 | − | 0.689379i | ||||
\(563\) | −179111. | + | 103409.i | −0.565073 | + | 0.326245i | −0.755179 | − | 0.655519i | \(-0.772450\pi\) |
0.190106 | + | 0.981764i | \(0.439117\pi\) | |||||||
\(564\) | −96552.0 | − | 167233.i | −0.303531 | − | 0.525731i | ||||
\(565\) | 14601.0 | + | 8429.89i | 0.0457389 | + | 0.0264074i | ||||
\(566\) | 185000.i | 0.577484i | ||||||||
\(567\) | 28066.5 | + | 22096.6i | 0.0873016 | + | 0.0687322i | ||||
\(568\) | 16940.0 | 0.0525069 | ||||||||
\(569\) | −255431. | + | 442419.i | −0.788949 | + | 1.36650i | 0.137662 | + | 0.990479i | \(0.456041\pi\) |
−0.926611 | + | 0.376021i | \(0.877292\pi\) | |||||||
\(570\) | 13905.0 | − | 8028.06i | 0.0427978 | − | 0.0247093i | ||||
\(571\) | −187300. | − | 324413.i | −0.574468 | − | 0.995007i | −0.996099 | − | 0.0882399i | \(-0.971876\pi\) |
0.421632 | − | 0.906767i | \(-0.361458\pi\) | |||||||
\(572\) | 48276.0 | + | 27872.2i | 0.147550 | + | 0.0851880i | ||||
\(573\) | − | 149441.i | − | 0.455157i | ||||||
\(574\) | 682920. | + | 98571.0i | 2.07275 | + | 0.299175i | ||||
\(575\) | −348320. | −1.05352 | ||||||||
\(576\) | −958.500 | + | 1660.17i | −0.00288900 | + | 0.00500389i | ||||
\(577\) | −339416. | + | 195962.i | −1.01948 | + | 0.588599i | −0.913954 | − | 0.405817i | \(-0.866987\pi\) |
−0.105529 | + | 0.994416i | \(0.533654\pi\) | |||||||
\(578\) | 30932.5 | + | 53576.7i | 0.0925890 | + | 0.160369i | ||||
\(579\) | 198400. | + | 114547.i | 0.591815 | + | 0.341684i | ||||
\(580\) | 3663.29i | 0.0108897i | ||||||||
\(581\) | −23719.5 | − | 59342.7i | −0.0702673 | − | 0.175798i | ||||
\(582\) | −141615. | −0.418084 | ||||||||
\(583\) | 67124.5 | − | 116263.i | 0.197489 | − | 0.342062i | ||||
\(584\) | −28770.0 | + | 16610.4i | −0.0843556 | + | 0.0487028i | ||||
\(585\) | −972.000 | − | 1683.55i | −0.00284024 | − | 0.00491943i | ||||
\(586\) | −290092. | − | 167485.i | −0.844775 | − | 0.487731i | ||||
\(587\) | 202645.i | 0.588111i | 0.955788 | + | 0.294055i | \(0.0950050\pi\) | ||||
−0.955788 | + | 0.294055i | \(0.904995\pi\) | |||||||
\(588\) | −109148. | + | 26352.3i | −0.315689 | + | 0.0762191i | ||||
\(589\) | 459174. | 1.32357 | ||||||||
\(590\) | −5977.50 | + | 10353.3i | −0.0171718 | + | 0.0297424i | ||||
\(591\) | −209151. | + | 120753.i | −0.598804 | + | 0.345720i | ||||
\(592\) | 314215. | + | 544236.i | 0.896569 | + | 1.55290i | ||||
\(593\) | 554700. | + | 320256.i | 1.57743 | + | 0.910727i | 0.995217 | + | 0.0976870i | \(0.0311444\pi\) |
0.582208 | + | 0.813040i | \(0.302189\pi\) | |||||||
\(594\) | − | 104521.i | − | 0.296230i | ||||||
\(595\) | −21021.0 | + | 8402.18i | −0.0593772 | + | 0.0237333i | ||||
\(596\) | 82926.0 | 0.233452 | ||||||||
\(597\) | −101934. | + | 176555.i | −0.286003 | + | 0.495372i | ||||
\(598\) | 100800. | − | 58196.9i | 0.281876 | − | 0.162741i | ||||
\(599\) | −230642. | − | 399484.i | −0.642813 | − | 1.11339i | −0.984802 | − | 0.173681i | \(-0.944434\pi\) |
0.341989 | − | 0.939704i | \(-0.388900\pi\) | |||||||
\(600\) | −97965.0 | − | 56560.1i | −0.272125 | − | 0.157111i | ||||
\(601\) | − | 603767.i | − | 1.67155i | −0.549069 | − | 0.835777i | \(-0.685018\pi\) | ||
0.549069 | − | 0.835777i | \(-0.314982\pi\) | |||||||
\(602\) | −97930.0 | + | 678479.i | −0.270223 | + | 1.87216i | ||||
\(603\) | 112212. | 0.308606 | ||||||||
\(604\) | −53887.5 | + | 93335.9i | −0.147711 | + | 0.255844i | ||||
\(605\) | 11340.0 | − | 6547.15i | 0.0309815 | − | 0.0178872i | ||||
\(606\) | 56250.0 | + | 97427.9i | 0.153171 | + | 0.265300i | ||||
\(607\) | 340958. | + | 196852.i | 0.925386 | + | 0.534272i | 0.885349 | − | 0.464926i | \(-0.153919\pi\) |
0.0400366 | + | 0.999198i | \(0.487253\pi\) | |||||||
\(608\) | 369291.i | 0.998990i | ||||||||
\(609\) | −37012.5 | + | 47012.2i | −0.0997962 | + | 0.126758i | ||||
\(610\) | 30900.0 | 0.0830422 | ||||||||
\(611\) | −85824.0 | + | 148652.i | −0.229893 | + | 0.398187i | ||||
\(612\) | 56133.0 | − | 32408.4i | 0.149870 | − | 0.0865276i | ||||
\(613\) | −202450. | − | 350654.i | −0.538762 | − | 0.933163i | −0.998971 | − | 0.0453524i | \(-0.985559\pi\) |
0.460209 | − | 0.887811i | \(-0.347774\pi\) | |||||||
\(614\) | 330210. | + | 190647.i | 0.875898 | + | 0.505700i | ||||
\(615\) | 25346.8i | 0.0670152i | ||||||||
\(616\) | −200778. | − | 158071.i | −0.529119 | − | 0.416573i | ||||
\(617\) | 258952. | 0.680219 | 0.340110 | − | 0.940386i | \(-0.389536\pi\) | ||||
0.340110 | + | 0.940386i | \(0.389536\pi\) | |||||||
\(618\) | 187740. | − | 325175.i | 0.491564 | − | 0.851413i | ||||
\(619\) | −110244. | + | 63649.4i | −0.287722 | + | 0.166117i | −0.636914 | − | 0.770935i | \(-0.719789\pi\) |
0.349192 | + | 0.937051i | \(0.386456\pi\) | |||||||
\(620\) | −10030.5 | − | 17373.3i | −0.0260939 | − | 0.0451960i | ||||
\(621\) | −68040.0 | − | 39282.9i | −0.176434 | − | 0.101864i | ||||
\(622\) | − | 262943.i | − | 0.679642i | ||||||
\(623\) | −95928.0 | − | 13846.0i | −0.247155 | − | 0.0356737i | ||||
\(624\) | 68904.0 | 0.176960 | ||||||||
\(625\) | −192504. | + | 333428.i | −0.492812 | + | 0.853575i | ||||
\(626\) | −402022. | + | 232108.i | −1.02589 | + | 0.592299i | ||||
\(627\) | −138123. | − | 239236.i | −0.351343 | − | 0.608543i | ||||
\(628\) | 15498.0 | + | 8947.77i | 0.0392967 | + | 0.0226880i | ||||
\(629\) | − | 525470.i | − | 1.32815i | ||||||
\(630\) | −4252.50 | − | 10639.1i | −0.0107143 | − | 0.0268055i | ||||
\(631\) | −211021. | −0.529989 | −0.264995 | − | 0.964250i | \(-0.585370\pi\) | ||||
−0.264995 | + | 0.964250i | \(0.585370\pi\) | |||||||
\(632\) | −75687.5 | + | 131095.i | −0.189492 | + | 0.328209i | ||||
\(633\) | −124596. | + | 71935.5i | −0.310954 | + | 0.179530i | ||||
\(634\) | −153958. | − | 266662.i | −0.383021 | − | 0.663411i | ||||
\(635\) | 43723.5 | + | 25243.8i | 0.108434 | + | 0.0626047i | ||||
\(636\) | 42135.6i | 0.104168i | ||||||||
\(637\) | 68796.0 | + | 72309.7i | 0.169545 | + | 0.178204i | ||||
\(638\) | 175075. | 0.430113 | ||||||||
\(639\) | 6534.00 | − | 11317.2i | 0.0160021 | − | 0.0277165i | ||||
\(640\) | −24307.5 | + | 14033.9i | −0.0593445 | + | 0.0342626i | ||||
\(641\) | 80584.0 | + | 139576.i | 0.196125 | + | 0.339698i | 0.947269 | − | 0.320440i | \(-0.103831\pi\) |
−0.751144 | + | 0.660139i | \(0.770498\pi\) | |||||||
\(642\) | 100462. | + | 58002.1i | 0.243744 | + | 0.140726i | ||||
\(643\) | 427976.i | 1.03514i | 0.855642 | + | 0.517568i | \(0.173163\pi\) | ||||
−0.855642 | + | 0.517568i | \(0.826837\pi\) | |||||||
\(644\) | 229320. | − | 91660.1i | 0.552930 | − | 0.221008i | ||||
\(645\) | −25182.0 | −0.0605300 | ||||||||
\(646\) | 237930. | − | 412107.i | 0.570143 | − | 0.987517i | ||||
\(647\) | 276222. | − | 159477.i | 0.659857 | − | 0.380969i | −0.132366 | − | 0.991201i | \(-0.542257\pi\) |
0.792222 | + | 0.610232i | \(0.208924\pi\) | |||||||
\(648\) | −12757.5 | − | 22096.6i | −0.0303819 | − | 0.0526231i | ||||
\(649\) | 178130. | + | 102843.i | 0.422909 | + | 0.244166i | ||||
\(650\) | − | 129280.i | − | 0.305989i | ||||||
\(651\) | 46809.0 | − | 324302.i | 0.110450 | − | 0.765223i | ||||
\(652\) | −187200. | −0.440363 | ||||||||
\(653\) | 233024. | − | 403610.i | 0.546481 | − | 0.946533i | −0.452031 | − | 0.892002i | \(-0.649300\pi\) |
0.998512 | − | 0.0545309i | \(-0.0173663\pi\) | |||||||
\(654\) | −74700.0 | + | 43128.1i | −0.174649 | + | 0.100833i | ||||
\(655\) | −23866.5 | − | 41338.0i | −0.0556296 | − | 0.0963533i | ||||
\(656\) | −778041. | − | 449202.i | −1.80798 | − | 1.04384i | ||||
\(657\) | 25627.4i | 0.0593710i | ||||||||
\(658\) | −625800. | + | 794873.i | −1.44539 | + | 1.83589i | ||||
\(659\) | 103258. | 0.237768 | 0.118884 | − | 0.992908i | \(-0.462068\pi\) | ||||
0.118884 | + | 0.992908i | \(0.462068\pi\) | |||||||
\(660\) | −6034.50 | + | 10452.1i | −0.0138533 | + | 0.0239946i | ||||
\(661\) | 173265. | − | 100035.i | 0.396559 | − | 0.228954i | −0.288439 | − | 0.957498i | \(-0.593136\pi\) |
0.684998 | + | 0.728545i | \(0.259803\pi\) | |||||||
\(662\) | −228700. | − | 396120.i | −0.521855 | − | 0.903880i | ||||
\(663\) | −49896.0 | − | 28807.5i | −0.113511 | − | 0.0655357i | ||||
\(664\) | 45648.2i | 0.103535i | ||||||||
\(665\) | −23793.0 | − | 18732.1i | −0.0538029 | − | 0.0423588i | ||||
\(666\) | 265950. | 0.599586 | ||||||||
\(667\) | 65800.0 | − | 113969.i | 0.147902 | − | 0.256174i | ||||
\(668\) | 331128. | − | 191177.i | 0.742067 | − | 0.428432i | ||||
\(669\) | 127508. | + | 220849.i | 0.284894 | + | 0.493451i | ||||
\(670\) | −31170.0 | − | 17996.0i | −0.0694364 | − | 0.0400891i | ||||
\(671\) | − | 531636.i | − | 1.18078i | ||||||
\(672\) | 260820. | + | 37646.1i | 0.577567 | + | 0.0833646i | ||||
\(673\) | 160973. | 0.355404 | 0.177702 | − | 0.984084i | \(-0.443134\pi\) | ||||
0.177702 | + | 0.984084i | \(0.443134\pi\) | |||||||
\(674\) | 24987.5 | − | 43279.6i | 0.0550051 | − | 0.0952716i | ||||
\(675\) | −75573.0 | + | 43632.1i | −0.165867 | + | 0.0957632i | ||||
\(676\) | −120748. | − | 209143.i | −0.264234 | − | 0.457666i | ||||
\(677\) | −186356. | − | 107592.i | −0.406598 | − | 0.234749i | 0.282729 | − | 0.959200i | \(-0.408760\pi\) |
−0.689327 | + | 0.724451i | \(0.742094\pi\) | |||||||
\(678\) | 252897.i | 0.550153i | ||||||||
\(679\) | 99130.5 | + | 248010.i | 0.215014 | + | 0.537934i | ||||
\(680\) | 16170.0 | 0.0349697 | ||||||||
\(681\) | 192424. | − | 333289.i | 0.414922 | − | 0.718665i | ||||
\(682\) | −830302. | + | 479375.i | −1.78512 | + | 1.03064i | ||||
\(683\) | 72998.5 | + | 126437.i | 0.156485 | + | 0.271040i | 0.933599 | − | 0.358320i | \(-0.116650\pi\) |
−0.777114 | + | 0.629360i | \(0.783317\pi\) | |||||||
\(684\) | 75087.0 | + | 43351.5i | 0.160492 | + | 0.0926599i | ||||
\(685\) | 30872.1i | 0.0657938i | ||||||||
\(686\) | 340428. | + | 479730.i | 0.723397 | + | 1.01941i | ||||
\(687\) | 124182. | 0.263115 | ||||||||
\(688\) | 446281. | − | 772981.i | 0.942826 | − | 1.63302i | ||||
\(689\) | 32436.0 | − | 18726.9i | 0.0683264 | − | 0.0394483i | ||||
\(690\) | 12600.0 | + | 21823.8i | 0.0264650 | + | 0.0458388i | ||||
\(691\) | 537693. | + | 310437.i | 1.12610 | + | 0.650156i | 0.942952 | − | 0.332929i | \(-0.108037\pi\) |
0.183151 | + | 0.983085i | \(0.441370\pi\) | |||||||
\(692\) | 21761.5i | 0.0454440i | ||||||||
\(693\) | −183046. | + | 73164.4i | −0.381149 | + | 0.152347i | ||||
\(694\) | −312290. | −0.648394 | ||||||||
\(695\) | −24237.0 | + | 41979.7i | −0.0501775 | + | 0.0869100i | ||||
\(696\) | 37012.5 | − | 21369.2i | 0.0764064 | − | 0.0441133i | ||||
\(697\) | 375606. | + | 650569.i | 0.773156 | + | 1.33914i | ||||
\(698\) | −1.01052e6 | − | 583424.i | −2.07412 | − | 1.19749i | ||||
\(699\) | 500816.i | 1.02500i | ||||||||
\(700\) | 39186.0 | − | 271489.i | 0.0799714 | − | 0.554058i | ||||
\(701\) | 626353. | 1.27463 | 0.637314 | − | 0.770605i | \(-0.280046\pi\) | ||||
0.637314 | + | 0.770605i | \(0.280046\pi\) | |||||||
\(702\) | 14580.0 | − | 25253.3i | 0.0295858 | − | 0.0512441i | ||||
\(703\) | 608730. | − | 351450.i | 1.23173 | − | 0.711137i | ||||
\(704\) | −5289.50 | − | 9161.68i | −0.0106726 | − | 0.0184854i | ||||
\(705\) | −32184.0 | − | 18581.4i | −0.0647533 | − | 0.0373853i | ||||
\(706\) | 415103.i | 0.832812i | ||||||||
\(707\) | 131250. | − | 166710.i | 0.262579 | − | 0.333521i | ||||
\(708\) | −64557.0 | −0.128788 | ||||||||
\(709\) | −155149. | + | 268726.i | −0.308643 | + | 0.534585i | −0.978066 | − | 0.208296i | \(-0.933208\pi\) |
0.669423 | + | 0.742882i | \(0.266542\pi\) | |||||||
\(710\) | −3630.00 | + | 2095.78i | −0.00720095 | + | 0.00415747i | ||||
\(711\) | 58387.5 | + | 101130.i | 0.115500 | + | 0.200051i | ||||
\(712\) | 59955.0 | + | 34615.0i | 0.118268 | + | 0.0682818i | ||||
\(713\) | 720672.i | 1.41762i | ||||||||
\(714\) | −266805. | − | 210054.i | −0.523356 | − | 0.412036i | ||||
\(715\) | 10728.0 | 0.0209849 | ||||||||
\(716\) | −87201.0 | + | 151037.i | −0.170097 | + | 0.294616i | ||||
\(717\) | −199242. | + | 115032.i | −0.387563 | + | 0.223760i | ||||
\(718\) | 410110. | + | 710331.i | 0.795521 | + | 1.37788i | ||||
\(719\) | −507615. | − | 293072.i | −0.981921 | − | 0.566913i | −0.0790716 | − | 0.996869i | \(-0.525196\pi\) |
−0.902850 | + | 0.429956i | \(0.858529\pi\) | |||||||
\(720\) | 14918.2i | 0.0287773i | ||||||||
\(721\) | −700896. | − | 101166.i | −1.34829 | − | 0.194609i | ||||
\(722\) | −15065.0 | −0.0288998 | ||||||||
\(723\) | −147956. | + | 256266.i | −0.283044 | + | 0.490247i | ||||
\(724\) | 58077.0 | − | 33530.8i | 0.110797 | − | 0.0639685i | ||||
\(725\) | −73085.0 | − | 126587.i | −0.139044 | − | 0.240831i | ||||
\(726\) | 170100. | + | 98207.3i | 0.322724 | + | 0.186325i | ||||
\(727\) | − | 756846.i | − | 1.43198i | −0.698108 | − | 0.715992i | \(-0.745974\pi\) | ||
0.698108 | − | 0.715992i | \(-0.254026\pi\) | |||||||
\(728\) | −26460.0 | − | 66199.0i | −0.0499260 | − | 0.124908i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 4110.00 | − | 7118.73i | 0.00771252 | − | 0.0133585i | ||||
\(731\) | −646338. | + | 373163.i | −1.20955 | + | 0.698336i | ||||
\(732\) | 83430.0 | + | 144505.i | 0.155704 | + | 0.269687i | ||||
\(733\) | −95619.0 | − | 55205.7i | −0.177966 | − | 0.102749i | 0.408371 | − | 0.912816i | \(-0.366097\pi\) |
−0.586337 | + | 0.810068i | \(0.699430\pi\) | |||||||
\(734\) | 21451.4i | 0.0398166i | ||||||||
\(735\) | −15655.5 | + | 14894.8i | −0.0289796 | + | 0.0275714i | ||||
\(736\) | −579600. | −1.06997 | ||||||||
\(737\) | −309622. | + | 536281.i | −0.570029 | + | 0.987319i | ||||
\(738\) | −329265. | + | 190101.i | −0.604551 | + | 0.349038i | ||||
\(739\) | −53581.0 | − | 92805.0i | −0.0981120 | − | 0.169935i | 0.812791 | − | 0.582555i | \(-0.197947\pi\) |
−0.910903 | + | 0.412620i | \(0.864614\pi\) | |||||||
\(740\) | −26595.0 | − | 15354.6i | −0.0485665 | − | 0.0280399i | ||||
\(741\) | − | 77069.3i | − | 0.140361i | ||||||
\(742\) | 204978. | − | 81930.3i | 0.372305 | − | 0.148812i | ||||
\(743\) | 90580.0 | 0.164080 | 0.0820398 | − | 0.996629i | \(-0.473857\pi\) | ||||
0.0820398 | + | 0.996629i | \(0.473857\pi\) | |||||||
\(744\) | −117022. | + | 202689.i | −0.211409 | + | 0.366171i | ||||
\(745\) | 13821.0 | − | 7979.56i | 0.0249016 | − | 0.0143769i | ||||
\(746\) | 196565. | + | 340461.i | 0.353206 | + | 0.611771i | ||||
\(747\) | 30496.5 | + | 17607.2i | 0.0546523 | + | 0.0315535i | ||||
\(748\) | 357693.i | 0.639303i | ||||||||
\(749\) | 31255.0 | − | 216541.i | 0.0557129 | − | 0.385990i | ||||
\(750\) | 56115.0 | 0.0997600 | ||||||||
\(751\) | 62139.5 | − | 107629.i | 0.110176 | − | 0.190831i | −0.805665 | − | 0.592371i | \(-0.798192\pi\) |
0.915841 | + | 0.401541i | \(0.131525\pi\) | |||||||
\(752\) | 1.14074e6 | − | 658609.i | 2.01722 | − | 1.16464i | ||||
\(753\) | −194116. | − | 336220.i | −0.342352 | − | 0.592971i | ||||
\(754\) | 42300.0 | + | 24421.9i | 0.0744042 | + | 0.0429573i | ||||
\(755\) | 20741.3i | 0.0363867i | ||||||||
\(756\) | 38272.5 | − | 48612.6i | 0.0669643 | − | 0.0850561i | ||||
\(757\) | −147904. | −0.258100 | −0.129050 | − | 0.991638i | \(-0.541193\pi\) | ||||
−0.129050 | + | 0.991638i | \(0.541193\pi\) | |||||||
\(758\) | 140585. | − | 243500.i | 0.244681 | − | 0.423800i | ||||
\(759\) | 375480. | − | 216783.i | 0.651783 | − | 0.376307i | ||||
\(760\) | 10815.0 | + | 18732.1i | 0.0187240 | + | 0.0324310i | ||||
\(761\) | −345318. | − | 199369.i | −0.596280 | − | 0.344262i | 0.171297 | − | 0.985219i | \(-0.445204\pi\) |
−0.767577 | + | 0.640957i | \(0.778538\pi\) | |||||||
\(762\) | 757313.i | 1.30426i | ||||||||
\(763\) | 127820. | + | 100632.i | 0.219558 | + | 0.172857i | ||||
\(764\) | −258840. | −0.443450 | ||||||||
\(765\) | 6237.00 | − | 10802.8i | 0.0106574 | − | 0.0184592i | ||||
\(766\) | 949785. | − | 548359.i | 1.61871 | − | 0.934560i | ||||
\(767\) | 28692.0 | + | 49696.0i | 0.0487719 | + | 0.0844755i | ||||
\(768\) | −369724. | − | 213461.i | −0.626839 | − | 0.361905i | ||||
\(769\) | − | 1.07770e6i | − | 1.82240i | −0.411962 | − | 0.911201i | \(-0.635156\pi\) | ||
0.411962 | − | 0.911201i | \(-0.364844\pi\) | |||||||
\(770\) | 62580.0 | + | 9032.64i | 0.105549 | + | 0.0152347i | ||||
\(771\) | 152514. | 0.256567 | ||||||||
\(772\) | 198400. | − | 343640.i | 0.332896 | − | 0.576592i | ||||
\(773\) | 33762.0 | − | 19492.5i | 0.0565027 | − | 0.0326218i | −0.471483 | − | 0.881875i | \(-0.656281\pi\) |
0.527985 | + | 0.849254i | \(0.322948\pi\) | |||||||
\(774\) | −188865. | − | 327124.i | −0.315261 | − | 0.546047i | ||||
\(775\) | 693219. | + | 400230.i | 1.15416 | + | 0.666356i | ||||
\(776\) | − | 190777.i | − | 0.316812i | ||||||
\(777\) | −186165. | − | 465757.i | −0.308359 | − | 0.771467i | ||||
\(778\) | 21310.0 | 0.0352066 | ||||||||
\(779\) | −502434. | + | 870241.i | −0.827950 | + | 1.43405i | ||||
\(780\) | −2916.00 | + | 1683.55i | −0.00479290 | + | 0.00276718i | ||||
\(781\) | 36058.0 | + | 62454.3i | 0.0591153 | + | 0.102391i | ||||
\(782\) | 646800. | + | 373430.i | 1.05769 | + | 0.610655i | ||||
\(783\) | − | 32969.6i | − | 0.0537762i | ||||||
\(784\) | −179756. | − | 744526.i | −0.292451 | − | 1.21129i | ||||
\(785\) | 3444.00 | 0.00558887 | ||||||||
\(786\) | 357998. | − | 620070.i | 0.579475 | − | 1.00368i | ||||
\(787\) | −393276. | + | 227058.i | −0.634962 | + | 0.366596i | −0.782671 | − | 0.622435i | \(-0.786143\pi\) |
0.147709 | + | 0.989031i | \(0.452810\pi\) | |||||||
\(788\) | 209151. | + | 362260.i | 0.336827 | + | 0.583402i | ||||
\(789\) | 400851. | + | 231431.i | 0.643916 | + | 0.371765i | ||||
\(790\) | − | 37455.6i | − | 0.0600154i | ||||||
\(791\) | 442897. | − | 177028.i | 0.707864 | − | 0.282936i | ||||
\(792\) | 140805. | 0.224475 | ||||||||
\(793\) | 74160.0 | − | 128449.i | 0.117930 | − | 0.204260i | ||||
\(794\) | 633090. | − | 365515.i | 1.00421 | − | 0.579781i | ||||
\(795\) | 4054.50 | + | 7022.60i | 0.00641509 | + | 0.0111113i | ||||
\(796\) | 305802. | + | 176555.i | 0.482630 | + | 0.278646i | ||||
\(797\) | − | 639589.i | − | 1.00690i | −0.864026 | − | 0.503448i | \(-0.832065\pi\) | ||
0.864026 | − | 0.503448i | \(-0.167935\pi\) | |||||||
\(798\) | 64890.0 | − | 449571.i | 0.101899 | − | 0.705980i | ||||
\(799\) | −1.10141e6 | −1.72526 | ||||||||
\(800\) | −321885. | + | 557521.i | −0.502945 | + | 0.871127i | ||||
\(801\) | 46251.0 | − | 26703.0i | 0.0720869 | − | 0.0416194i | ||||
\(802\) | −227030. | − | 393227.i | −0.352967 | − | 0.611357i | ||||
\(803\) | −122478. | − | 70712.7i | −0.189945 | − | 0.109665i | ||||
\(804\) | − | 194357.i | − | 0.300668i | ||||||
\(805\) | 29400.0 | − | 37343.0i | 0.0453686 | − | 0.0576259i | ||||
\(806\) | −267480. | −0.411738 | ||||||||
\(807\) | 185080. | − | 320569.i | 0.284193 | − | 0.492237i | ||||
\(808\) | −131250. | + | 75777.2i | −0.201037 | + | 0.116069i | ||||
\(809\) | −152636. | − | 264373.i | −0.233217 | − | 0.403943i | 0.725536 | − | 0.688184i | \(-0.241592\pi\) |
−0.958753 | + | 0.284241i | \(0.908259\pi\) | |||||||
\(810\) | 5467.50 | + | 3156.66i | 0.00833333 | + | 0.00481125i | ||||
\(811\) | 644552.i | 0.979977i | 0.871729 | + | 0.489989i | \(0.162999\pi\) | ||||
−0.871729 | + | 0.489989i | \(0.837001\pi\) | |||||||
\(812\) | 81427.5 | + | 64107.5i | 0.123498 | + | 0.0972293i | ||||
\(813\) | −219987. | −0.332825 | ||||||||
\(814\) | −733825. | + | 1.27102e6i | −1.10750 | + | 1.91825i | ||||
\(815\) | −31200.0 | + | 18013.3i | −0.0469720 | + | 0.0271193i | ||||
\(816\) | 221067. | + | 382899.i | 0.332004 | + | 0.575048i | ||||
\(817\) | −864582. | − | 499167.i | −1.29528 | − | 0.747828i | ||||
\(818\) | − | 226613.i | − | 0.338671i | ||||||
\(819\) | −54432.0 | − | 7856.58i | −0.0811496 | − | 0.0117129i | ||||
\(820\) | 43902.0 | 0.0652915 | ||||||||
\(821\) | −459960. | + | 796675.i | −0.682392 | + | 1.18194i | 0.291856 | + | 0.956462i | \(0.405727\pi\) |
−0.974249 | + | 0.225476i | \(0.927606\pi\) | |||||||
\(822\) | −401040. | + | 231541.i | −0.593532 | + | 0.342676i | ||||
\(823\) | 107009. | + | 185345.i | 0.157987 | + | 0.273641i | 0.934143 | − | 0.356900i | \(-0.116166\pi\) |
−0.776156 | + | 0.630541i | \(0.782833\pi\) | |||||||
\(824\) | 438060. | + | 252914.i | 0.645177 | + | 0.372493i | ||||
\(825\) | − | 481569.i | − | 0.707539i | ||||||
\(826\) | 125528. | + | 314051.i | 0.183983 | + | 0.460299i | ||||
\(827\) | 129841. | 0.189846 | 0.0949229 | − | 0.995485i | \(-0.469740\pi\) | ||||
0.0949229 | + | 0.995485i | \(0.469740\pi\) | |||||||
\(828\) | −68040.0 | + | 117849.i | −0.0992439 | + | 0.171895i | ||||
\(829\) | −528375. | + | 305057.i | −0.768835 | + | 0.443887i | −0.832459 | − | 0.554087i | \(-0.813068\pi\) |
0.0636238 | + | 0.997974i | \(0.479734\pi\) | |||||||
\(830\) | −5647.50 | − | 9781.76i | −0.00819785 | − | 0.0141991i | ||||
\(831\) | 209322. | + | 120852.i | 0.303119 | + | 0.175006i | ||||
\(832\) | − | 2951.41i | − | 0.00426367i | ||||||
\(833\) | −181104. | + | 614293.i | −0.260999 | + | 0.885289i | ||||
\(834\) | −727110. | −1.04537 | ||||||||
\(835\) | 36792.0 | − | 63725.6i | 0.0527692 | − | 0.0913989i | ||||
\(836\) | −414369. | + | 239236.i | −0.592891 | + | 0.342306i | ||||
\(837\) | 90274.5 | + | 156360.i | 0.128859 | + | 0.223190i | ||||
\(838\) | 644850. | + | 372304.i | 0.918271 | + | 0.530164i | ||||
\(839\) | 903206.i | 1.28311i | 0.767079 | + | 0.641553i | \(0.221710\pi\) | ||||
−0.767079 | + | 0.641553i | \(0.778290\pi\) | |||||||
\(840\) | 14332.5 | − | 5728.76i | 0.0203125 | − | 0.00811899i | ||||
\(841\) | −652056. | −0.921919 | ||||||||
\(842\) | 10640.0 | − | 18429.0i | 0.0150078 | − | 0.0259943i | ||||
\(843\) | 226278. | − | 130642.i | 0.318410 | − | 0.183834i | ||||
\(844\) | 124596. | + | 215807.i | 0.174912 | + | 0.302956i | ||||
\(845\) | −40249.5 | − | 23238.1i | −0.0563699 | − | 0.0325452i | ||||
\(846\) | − | 557443.i | − | 0.778861i | ||||||
\(847\) | 52920.0 | − | 366641.i | 0.0737655 | − | 0.511062i | ||||
\(848\) | −287419. | −0.399690 | ||||||||
\(849\) | −96129.0 | + | 166500.i | −0.133364 | + | 0.230993i | ||||
\(850\) | 718410. | − | 414774.i | 0.994339 | − | 0.574082i | ||||
\(851\) | 551600. | + | 955399.i | 0.761667 | + | 1.31925i | ||||
\(852\) | −19602.0 | − | 11317.2i | −0.0270036 | − | 0.0155905i | ||||
\(853\) | − | 266542.i | − | 0.366326i | −0.983083 | − | 0.183163i | \(-0.941366\pi\) | ||
0.983083 | − | 0.183163i | \(-0.0586336\pi\) | |||||||
\(854\) | 540750. | − | 686845.i | 0.741448 | − | 0.941766i | ||||
\(855\) | 16686.0 | 0.0228255 | ||||||||
\(856\) | −78137.5 | + | 135338.i | −0.106638 | + | 0.184702i | ||||
\(857\) | 993954. | − | 573860.i | 1.35333 | − | 0.781347i | 0.364618 | − | 0.931157i | \(-0.381200\pi\) |
0.988715 | + | 0.149810i | \(0.0478662\pi\) | |||||||
\(858\) | 80460.0 | + | 139361.i | 0.109296 | + | 0.189307i | ||||
\(859\) | −229917. | − | 132743.i | −0.311591 | − | 0.179897i | 0.336047 | − | 0.941845i | \(-0.390910\pi\) |
−0.647638 | + | 0.761948i | \(0.724243\pi\) | |||||||
\(860\) | 43616.5i | 0.0589731i | ||||||||
\(861\) | 563409. | + | 443570.i | 0.760007 | + | 0.598350i | ||||
\(862\) | 738310. | 0.993629 | ||||||||
\(863\) | 528331. | − | 915096.i | 0.709389 | − | 1.22870i | −0.255695 | − | 0.966758i | \(-0.582304\pi\) |
0.965084 | − | 0.261940i | \(-0.0843624\pi\) | |||||||
\(864\) | −125752. | + | 72603.2i | −0.168457 | + | 0.0972587i | ||||
\(865\) | 2094.00 | + | 3626.91i | 0.00279862 | + | 0.00484736i | ||||
\(866\) | −254610. | − | 146999.i | −0.339500 | − | 0.196010i | ||||
\(867\) | 64292.0i | 0.0855300i | ||||||||
\(868\) | −561708. | − | 81075.6i | −0.745540 | − | 0.107609i | ||||
\(869\) | −644425. | −0.853361 | ||||||||
\(870\) | −5287.50 | + | 9158.22i | −0.00698573 | + | 0.0120996i | ||||
\(871\) | −149616. | + | 86380.8i | −0.197216 | + | 0.113863i | ||||
\(872\) | −58100.0 | − | 100632.i | −0.0764088 | − | 0.132344i | ||||
\(873\) | −127454. | − | 73585.3i | −0.167233 | − | 0.0965523i | ||||
\(874\) | 999047.i | 1.30787i | ||||||||
\(875\) | −39280.5 | − | 98274.0i | −0.0513051 | − | 0.128358i | ||||
\(876\) | 44388.0 | 0.0578439 | ||||||||
\(877\) | 261728. | − | 453326.i | 0.340291 | − | 0.589402i | −0.644195 | − | 0.764861i | \(-0.722808\pi\) |
0.984487 | + | 0.175459i | \(0.0561409\pi\) | |||||||
\(878\) | −444412. | + | 256582.i | −0.576497 | + | 0.332841i | ||||
\(879\) | −174056. | − | 301473.i | −0.225273 | − | 0.390185i | ||||
\(880\) | −71296.5 | − | 41163.1i | −0.0920668 | − | 0.0531548i | ||||
\(881\) | 1.20087e6i | 1.54719i | 0.633677 | + | 0.773597i | \(0.281545\pi\) | ||||
−0.633677 | + | 0.773597i | \(0.718455\pi\) | |||||||
\(882\) | −310905. | − | 91660.1i | −0.399660 | − | 0.117827i | ||||
\(883\) | 872138. | 1.11857 | 0.559286 | − | 0.828975i | \(-0.311075\pi\) | ||||
0.559286 | + | 0.828975i | \(0.311075\pi\) | |||||||
\(884\) | −49896.0 | + | 86422.4i | −0.0638500 | + | 0.110592i | ||||
\(885\) | −10759.5 | + | 6212.00i | −0.0137374 | + | 0.00793131i | ||||
\(886\) | −734952. | − | 1.27298e6i | −0.936250 | − | 1.62163i | ||||
\(887\) | 367212. | + | 212010.i | 0.466734 | + | 0.269469i | 0.714872 | − | 0.699256i | \(-0.246485\pi\) |
−0.248137 | + | 0.968725i | \(0.579818\pi\) | |||||||
\(888\) | 358275.i | 0.454350i | ||||||||
\(889\) | 1.32628e6 | − | 530119.i | 1.67815 | − | 0.670764i | ||||
\(890\) | −17130.0 | −0.0216261 | ||||||||
\(891\) | 54310.5 | − | 94068.5i | 0.0684114 | − | 0.118492i | ||||
\(892\) | 382522. | − | 220849.i | 0.480759 | − | 0.277566i | ||||
\(893\) | −736656. | − | 1.27593e6i | −0.923766 | − | 1.60001i | ||||
\(894\) | 207315. | + | 119693.i | 0.259391 | + | 0.149760i | ||||
\(895\) | 33563.7i | 0.0419009i | ||||||||
\(896\) | −113435. | + | 785901.i | −0.141296 | + | 0.978930i | ||||
\(897\) | 120960. | 0.150334 | ||||||||
\(898\) | 53050.0 | − | 91885.3i | 0.0657859 | − | 0.113944i | ||||
\(899\) | −261908. | + | 151212.i | −0.324062 | + | 0.187097i | ||||
\(900\) | 75573.0 | + | 130896.i | 0.0933000 | + | 0.161600i | ||||
\(901\) | 208131. | + | 120164.i | 0.256382 | + | 0.148022i | ||||
\(902\) | − | 2.09815e6i | − | 2.57884i | ||||||
\(903\) | −440685. | + | 559745.i | −0.540447 | + | 0.686459i | ||||
\(904\) | −340690. | −0.416891 | ||||||||
\(905\) | 6453.00 | − | 11176.9i | 0.00787888 | − | 0.0136466i | ||||
\(906\) | −269438. | + | 155560.i | −0.328248 | + | 0.189514i | ||||
\(907\) | 778646. | + | 1.34865e6i | 0.946511 | + | 1.63940i | 0.752698 | + | 0.658366i | \(0.228752\pi\) |
0.193813 | + | 0.981039i | \(0.437915\pi\) | |||||||
\(908\) | −577274. | − | 333289.i | −0.700180 | − | 0.404249i | ||||
\(909\) | 116913.i | 0.141494i | ||||||||
\(910\) | 13860.0 | + | 10911.9i | 0.0167371 | + | 0.0131771i | ||||
\(911\) | 491572. | 0.592312 | 0.296156 | − | 0.955140i | \(-0.404295\pi\) | ||||
0.296156 | + | 0.955140i | \(0.404295\pi\) | |||||||
\(912\) | −295713. | + | 512190.i | −0.355534 | + | 0.615802i | ||||
\(913\) | −168296. | + | 97165.5i | −0.201898 | + | 0.116566i | ||||
\(914\) | −441168. | − | 764125.i | −0.528094 | − | 0.914685i | ||||
\(915\) | 27810.0 | + | 16056.1i | 0.0332169 | + | 0.0191778i | ||||
\(916\) | − | 215090.i | − | 0.256347i | ||||||
\(917\) | −1.33652e6 | − | 192911.i | −1.58942 | − | 0.229413i | ||||
\(918\) | 187110. | 0.222030 | ||||||||
\(919\) | 516515. | − | 894630.i | 0.611578 | − | 1.05928i | −0.379396 | − | 0.925234i | \(-0.623868\pi\) |
0.990975 | − | 0.134050i | \(-0.0427983\pi\) | |||||||
\(920\) | −29400.0 | + | 16974.1i | −0.0347353 | + | 0.0200545i | ||||
\(921\) | 198126. | + | 343164.i | 0.233573 | + | 0.404560i | ||||
\(922\) | −961560. | − | 555157.i | −1.13114 | − | 0.653061i | ||||
\(923\) | 20119.5i | 0.0236164i | ||||||||
\(924\) | 126724. | + | 317046.i | 0.148428 | + | 0.371345i | ||||
\(925\) | 1.22534e6 | 1.43210 | ||||||||
\(926\) | 355715. | − | 616116.i | 0.414840 | − | 0.718523i | ||||
\(927\) | 337932. | − | 195105.i | 0.393251 | − | 0.227044i | ||||
\(928\) | −121612. | − | 210639.i | −0.141215 | − | 0.244592i | ||||
\(929\) | −553623. | − | 319634.i | −0.641479 | − | 0.370358i | 0.143705 | − | 0.989621i | \(-0.454098\pi\) |
−0.785184 | + | 0.619262i | \(0.787432\pi\) | |||||||
\(930\) | − | 57911.1i | − | 0.0669570i | ||||||
\(931\) | −832755. | + | 201058.i | −0.960767 | + | 0.231965i | ||||
\(932\) | 867438. | 0.998635 | ||||||||
\(933\) | 136629. | − | 236648.i | 0.156957 | − | 0.271857i | ||||
\(934\) | −1.69095e6 | + | 976270.i | −1.93837 | + | 1.11912i | ||||
\(935\) | 34419.0 | + | 59615.5i | 0.0393709 | + | 0.0681923i | ||||
\(936\) | 34020.0 | + | 19641.5i | 0.0388314 | + | 0.0224193i | ||||
\(937\) | 656103.i | 0.747296i | 0.927571 | + | 0.373648i | \(0.121893\pi\) | ||||
−0.927571 | + | 0.373648i | \(0.878107\pi\) | |||||||
\(938\) | −945490. | + | 377916.i | −1.07461 | + | 0.429526i | ||||
\(939\) | −482427. | −0.547142 | ||||||||
\(940\) | −32184.0 | + | 55744.3i | −0.0364237 | + | 0.0630877i | ||||
\(941\) | 429820. | − | 248157.i | 0.485409 | − | 0.280251i | −0.237259 | − | 0.971446i | \(-0.576249\pi\) |
0.722668 | + | 0.691195i | \(0.242916\pi\) | |||||||
\(942\) | 25830.0 | + | 44738.9i | 0.0291087 | + | 0.0504177i | ||||
\(943\) | −1.36584e6 | − | 788568.i | −1.53595 | − | 0.886780i | ||||
\(944\) | − | 440362.i | − | 0.494158i | ||||||
\(945\) | 1701.00 | − | 11784.9i | 0.00190476 | − | 0.0131966i | ||||
\(946\) | 2.08451e6 | 2.32928 | ||||||||
\(947\) | 595411. | − | 1.03128e6i | 0.663922 | − | 1.14995i | −0.315655 | − | 0.948874i | \(-0.602224\pi\) |
0.979576 | − | 0.201072i | \(-0.0644425\pi\) | |||||||
\(948\) | 175162. | − | 101130.i | 0.194906 | − | 0.112529i | ||||
\(949\) | −19728.0 | − | 34169.9i | −0.0219054 | − | 0.0379412i | ||||
\(950\) | 960990. | + | 554828.i | 1.06481 | + | 0.614768i | ||||
\(951\) | − | 319995.i | − | 0.353819i | ||||||
\(952\) | 282975. | − | 359427.i | 0.312230 | − | 0.396585i | ||||
\(953\) | 255670. | 0.281510 | 0.140755 | − | 0.990044i | \(-0.455047\pi\) | ||||
0.140755 | + | 0.990044i | \(0.455047\pi\) | |||||||
\(954\) | −60817.5 | + | 105339.i | −0.0668239 | + | 0.115742i | ||||
\(955\) | −43140.0 | + | 24906.9i | −0.0473013 | + | 0.0273094i | ||||
\(956\) | 199242. | + | 345097.i | 0.218004 | + | 0.377595i | ||||
\(957\) | 157568. | + | 90971.6i | 0.172045 | + | 0.0993304i | ||||
\(958\) | 757893.i | 0.825804i | ||||||||
\(959\) | 686224. | + | 540261.i | 0.746154 | + | 0.587444i | ||||
\(960\) | 639.000 | 0.000693359 | ||||||||
\(961\) | 366313. | − | 634473.i | 0.396648 | − | 0.687015i | ||||
\(962\) | −354600. | + | 204728.i | −0.383167 | + | 0.221222i | ||||
\(963\) | 60277.5 | + | 104404.i | 0.0649984 | + | 0.112581i | ||||
\(964\) | 443866. | + | 256266.i | 0.477637 | + | 0.275764i | ||||
\(965\) | − | 76364.4i | − | 0.0820042i | ||||||
\(966\) | 705600. | + | 101845.i | 0.756144 | + | 0.109140i | ||||
\(967\) | 417065. | 0.446016 | 0.223008 | − | 0.974817i | \(-0.428412\pi\) | ||||
0.223008 | + | 0.974817i | \(0.428412\pi\) | |||||||
\(968\) | −132300. | + | 229150.i | −0.141192 | + | 0.244551i | ||||
\(969\) | 428274. | − | 247264.i | 0.456115 | − | 0.263338i | ||||
\(970\) | 23602.5 | + | 40880.7i | 0.0250850 | + | 0.0434485i | ||||
\(971\) | 143530. | + | 82867.4i | 0.152232 | + | 0.0878911i | 0.574181 | − | 0.818728i | \(-0.305321\pi\) |
−0.421949 | + | 0.906620i | \(0.638654\pi\) | |||||||
\(972\) | 34092.0i | 0.0360844i | ||||||||
\(973\) | 508977. | + | 1.27338e6i | 0.537616 | + | 1.34504i | ||||
\(974\) | −1.03014e6 | −1.08587 | ||||||||
\(975\) | 67176.0 | − | 116352.i | 0.0706651 | − | 0.122396i | ||||
\(976\) | −985710. | + | 569100.i | −1.03478 | + | 0.597433i | ||||
\(977\) | 176185. | + | 305161.i | 0.184578 | + | 0.319698i | 0.943434 | − | 0.331560i | \(-0.107575\pi\) |
−0.758856 | + | 0.651258i | \(0.774242\pi\) | |||||||
\(978\) | −468000. | − | 270200.i | −0.489292 | − | 0.282493i | ||||
\(979\) | 294722.i | 0.307502i | ||||||||
\(980\) | 25798.5 | + | 27116.1i | 0.0268622 | + | 0.0282342i | ||||
\(981\) | −89640.0 | −0.0931459 | ||||||||
\(982\) | −1.19278e6 | + | 2.06596e6i | −1.23691 | + | 2.14239i | ||||
\(983\) | −480759. | + | 277566.i | −0.497531 | + | 0.287250i | −0.727693 | − | 0.685902i | \(-0.759408\pi\) |
0.230162 | + | 0.973152i | \(0.426074\pi\) | |||||||
\(984\) | −256095. | − | 443570.i | −0.264491 | − | 0.458112i | ||||
\(985\) | 69717.0 | + | 40251.1i | 0.0718565 | + | 0.0414864i | ||||
\(986\) | 313415.i | 0.322378i | ||||||||
\(987\) | −976248. | + | 390210.i | −1.00213 | + | 0.400557i | ||||
\(988\) | −133488. | −0.136750 | ||||||||
\(989\) | 783440. | − | 1.35696e6i | 0.800964 | − | 1.38731i | ||||
\(990\) | −30172.5 | + | 17420.1i | −0.0307851 | + | 0.0177738i | ||||
\(991\) | −418896. | − | 725548.i | −0.426539 | − | 0.738787i | 0.570024 | − | 0.821628i | \(-0.306934\pi\) |
−0.996563 | + | 0.0828414i | \(0.973601\pi\) | |||||||
\(992\) | 1.15351e6 | + | 665978.i | 1.17219 | + | 0.676763i | ||||
\(993\) | − | 475344.i | − | 0.482069i | ||||||
\(994\) | −16940.0 | + | 117364.i | −0.0171451 | + | 0.118785i | ||||
\(995\) | 67956.0 | 0.0686407 | ||||||||
\(996\) | 30496.5 | − | 52821.5i | 0.0307419 | − | 0.0532466i | ||||
\(997\) | −876990. | + | 506330.i | −0.882276 | + | 0.509382i | −0.871408 | − | 0.490559i | \(-0.836793\pi\) |
−0.0108676 | + | 0.999941i | \(0.503459\pi\) | |||||||
\(998\) | 412025. | + | 713648.i | 0.413678 | + | 0.716511i | ||||
\(999\) | 239355. | + | 138192.i | 0.239834 | + | 0.138468i |
(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 | 21.5.f.b.19.1 | yes | 2 | |
3.2 | odd | 2 | 63.5.m.a.19.1 | 2 | |||
4.3 | odd | 2 | 336.5.bh.a.145.1 | 2 | |||
7.2 | even | 3 | 147.5.d.a.97.2 | 2 | |||
7.3 | odd | 6 | inner | 21.5.f.b.10.1 | ✓ | 2 | |
7.4 | even | 3 | 147.5.f.b.31.1 | 2 | |||
7.5 | odd | 6 | 147.5.d.a.97.1 | 2 | |||
7.6 | odd | 2 | 147.5.f.b.19.1 | 2 | |||
21.2 | odd | 6 | 441.5.d.c.244.1 | 2 | |||
21.5 | even | 6 | 441.5.d.c.244.2 | 2 | |||
21.17 | even | 6 | 63.5.m.a.10.1 | 2 | |||
28.3 | even | 6 | 336.5.bh.a.241.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.5.f.b.10.1 | ✓ | 2 | 7.3 | odd | 6 | inner | |
21.5.f.b.19.1 | yes | 2 | 1.1 | even | 1 | trivial | |
63.5.m.a.10.1 | 2 | 21.17 | even | 6 | |||
63.5.m.a.19.1 | 2 | 3.2 | odd | 2 | |||
147.5.d.a.97.1 | 2 | 7.5 | odd | 6 | |||
147.5.d.a.97.2 | 2 | 7.2 | even | 3 | |||
147.5.f.b.19.1 | 2 | 7.6 | odd | 2 | |||
147.5.f.b.31.1 | 2 | 7.4 | even | 3 | |||
336.5.bh.a.145.1 | 2 | 4.3 | odd | 2 | |||
336.5.bh.a.241.1 | 2 | 28.3 | even | 6 | |||
441.5.d.c.244.1 | 2 | 21.2 | odd | 6 | |||
441.5.d.c.244.2 | 2 | 21.5 | even | 6 |