Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,5,Mod(7,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
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("15.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.f (of order \(4\), 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: | \(1.55054944626\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 60x^{5} + 1973x^{4} - 3300x^{3} + 1800x^{2} + 31560x + 276676 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.3 | ||
Root | \(3.30519 + 3.30519i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.7 |
Dual form | 15.5.f.a.13.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.30519 | + | 3.30519i | 0.826298 | + | 0.826298i | 0.987003 | − | 0.160705i | \(-0.0513767\pi\) |
−0.160705 | + | 0.987003i | \(0.551377\pi\) | |||||||
\(3\) | 3.67423 | − | 3.67423i | 0.408248 | − | 0.408248i | ||||
\(4\) | 5.84858i | 0.365537i | ||||||||
\(5\) | −16.2403 | + | 19.0066i | −0.649613 | + | 0.760265i | ||||
\(6\) | 24.2881 | 0.674669 | ||||||||
\(7\) | −33.1649 | − | 33.1649i | −0.676834 | − | 0.676834i | 0.282448 | − | 0.959283i | \(-0.408853\pi\) |
−0.959283 | + | 0.282448i | \(0.908853\pi\) | |||||||
\(8\) | 33.5524 | − | 33.5524i | 0.524256 | − | 0.524256i | ||||
\(9\) | − | 27.0000i | − | 0.333333i | ||||||
\(10\) | −116.498 | + | 9.14312i | −1.16498 | + | 0.0914312i | ||||
\(11\) | 55.3118 | 0.457122 | 0.228561 | − | 0.973530i | \(-0.426598\pi\) | ||||
0.228561 | + | 0.973530i | \(0.426598\pi\) | |||||||
\(12\) | 21.4891 | + | 21.4891i | 0.149230 | + | 0.149230i | ||||
\(13\) | −161.918 | + | 161.918i | −0.958095 | + | 0.958095i | −0.999157 | − | 0.0410619i | \(-0.986926\pi\) |
0.0410619 | + | 0.999157i | \(0.486926\pi\) | |||||||
\(14\) | − | 219.233i | − | 1.11853i | ||||||
\(15\) | 10.1640 | + | 129.506i | 0.0451733 | + | 0.575580i | ||||
\(16\) | 315.371 | 1.23192 | ||||||||
\(17\) | 278.961 | + | 278.961i | 0.965264 | + | 0.965264i | 0.999417 | − | 0.0341531i | \(-0.0108734\pi\) |
−0.0341531 | + | 0.999417i | \(0.510873\pi\) | |||||||
\(18\) | 89.2402 | − | 89.2402i | 0.275433 | − | 0.275433i | ||||
\(19\) | − | 179.871i | − | 0.498258i | −0.968470 | − | 0.249129i | \(-0.919856\pi\) | ||
0.968470 | − | 0.249129i | \(-0.0801443\pi\) | |||||||
\(20\) | −111.162 | − | 94.9829i | −0.277905 | − | 0.237457i | ||||
\(21\) | −243.711 | −0.552633 | ||||||||
\(22\) | 182.816 | + | 182.816i | 0.377719 | + | 0.377719i | ||||
\(23\) | −398.080 | + | 398.080i | −0.752514 | + | 0.752514i | −0.974948 | − | 0.222434i | \(-0.928600\pi\) |
0.222434 | + | 0.974948i | \(0.428600\pi\) | |||||||
\(24\) | − | 246.559i | − | 0.428053i | ||||||
\(25\) | −97.5033 | − | 617.348i | −0.156005 | − | 0.987756i | ||||
\(26\) | −1070.34 | −1.58334 | ||||||||
\(27\) | −99.2043 | − | 99.2043i | −0.136083 | − | 0.136083i | ||||
\(28\) | 193.968 | − | 193.968i | 0.247408 | − | 0.247408i | ||||
\(29\) | − | 547.472i | − | 0.650977i | −0.945546 | − | 0.325488i | \(-0.894471\pi\) | ||
0.945546 | − | 0.325488i | \(-0.105529\pi\) | |||||||
\(30\) | −394.447 | + | 461.635i | −0.438274 | + | 0.512927i | ||||
\(31\) | 1538.11 | 1.60053 | 0.800263 | − | 0.599649i | \(-0.204693\pi\) | ||||
0.800263 | + | 0.599649i | \(0.204693\pi\) | |||||||
\(32\) | 505.525 | + | 505.525i | 0.493677 | + | 0.493677i | ||||
\(33\) | 203.229 | − | 203.229i | 0.186619 | − | 0.186619i | ||||
\(34\) | 1844.04i | 1.59519i | ||||||||
\(35\) | 1168.96 | − | 91.7437i | 0.954254 | − | 0.0748928i | ||||
\(36\) | 157.912 | 0.121846 | ||||||||
\(37\) | −1660.74 | − | 1660.74i | −1.21311 | − | 1.21311i | −0.969999 | − | 0.243109i | \(-0.921833\pi\) |
−0.243109 | − | 0.969999i | \(-0.578167\pi\) | |||||||
\(38\) | 594.509 | − | 594.509i | 0.411710 | − | 0.411710i | ||||
\(39\) | 1189.85i | 0.782281i | ||||||||
\(40\) | 92.8156 | + | 1182.62i | 0.0580097 | + | 0.739137i | ||||
\(41\) | −307.601 | −0.182987 | −0.0914933 | − | 0.995806i | \(-0.529164\pi\) | ||||
−0.0914933 | + | 0.995806i | \(0.529164\pi\) | |||||||
\(42\) | −805.512 | − | 805.512i | −0.456640 | − | 0.456640i | ||||
\(43\) | 104.254 | − | 104.254i | 0.0563841 | − | 0.0563841i | −0.678353 | − | 0.734737i | \(-0.737306\pi\) |
0.734737 | + | 0.678353i | \(0.237306\pi\) | |||||||
\(44\) | 323.496i | 0.167095i | ||||||||
\(45\) | 513.179 | + | 438.489i | 0.253422 | + | 0.216538i | ||||
\(46\) | −2631.46 | −1.24360 | ||||||||
\(47\) | −346.159 | − | 346.159i | −0.156704 | − | 0.156704i | 0.624400 | − | 0.781104i | \(-0.285343\pi\) |
−0.781104 | + | 0.624400i | \(0.785343\pi\) | |||||||
\(48\) | 1158.75 | − | 1158.75i | 0.502929 | − | 0.502929i | ||||
\(49\) | − | 201.180i | − | 0.0837903i | ||||||
\(50\) | 1718.19 | − | 2362.72i | 0.687274 | − | 0.945088i | ||||
\(51\) | 2049.94 | 0.788134 | ||||||||
\(52\) | −946.991 | − | 946.991i | −0.350219 | − | 0.350219i | ||||
\(53\) | −2025.02 | + | 2025.02i | −0.720906 | + | 0.720906i | −0.968790 | − | 0.247884i | \(-0.920265\pi\) |
0.247884 | + | 0.968790i | \(0.420265\pi\) | |||||||
\(54\) | − | 655.779i | − | 0.224890i | ||||||
\(55\) | −898.282 | + | 1051.29i | −0.296953 | + | 0.347534i | ||||
\(56\) | −2225.52 | −0.709669 | ||||||||
\(57\) | −660.889 | − | 660.889i | −0.203413 | − | 0.203413i | ||||
\(58\) | 1809.50 | − | 1809.50i | 0.537901 | − | 0.537901i | ||||
\(59\) | 2854.49i | 0.820020i | 0.912081 | + | 0.410010i | \(0.134475\pi\) | ||||
−0.912081 | + | 0.410010i | \(0.865525\pi\) | |||||||
\(60\) | −757.424 | + | 59.4450i | −0.210396 | + | 0.0165125i | ||||
\(61\) | −1057.37 | −0.284163 | −0.142082 | − | 0.989855i | \(-0.545380\pi\) | ||||
−0.142082 | + | 0.989855i | \(0.545380\pi\) | |||||||
\(62\) | 5083.73 | + | 5083.73i | 1.32251 | + | 1.32251i | ||||
\(63\) | −895.452 | + | 895.452i | −0.225611 | + | 0.225611i | ||||
\(64\) | − | 1704.23i | − | 0.416071i | ||||||
\(65\) | −447.912 | − | 5707.12i | −0.106015 | − | 1.35080i | ||||
\(66\) | 1343.42 | 0.308406 | ||||||||
\(67\) | 3756.53 | + | 3756.53i | 0.836830 | + | 0.836830i | 0.988440 | − | 0.151611i | \(-0.0484460\pi\) |
−0.151611 | + | 0.988440i | \(0.548446\pi\) | |||||||
\(68\) | −1631.53 | + | 1631.53i | −0.352839 | + | 0.352839i | ||||
\(69\) | 2925.28i | 0.614425i | ||||||||
\(70\) | 4166.87 | + | 3560.41i | 0.850382 | + | 0.726614i | ||||
\(71\) | 1429.24 | 0.283523 | 0.141761 | − | 0.989901i | \(-0.454723\pi\) | ||||
0.141761 | + | 0.989901i | \(0.454723\pi\) | |||||||
\(72\) | −905.914 | − | 905.914i | −0.174752 | − | 0.174752i | ||||
\(73\) | 813.690 | − | 813.690i | 0.152691 | − | 0.152691i | −0.626628 | − | 0.779319i | \(-0.715565\pi\) |
0.779319 | + | 0.626628i | \(0.215565\pi\) | |||||||
\(74\) | − | 10978.2i | − | 2.00478i | ||||||
\(75\) | −2626.53 | − | 1910.03i | −0.466939 | − | 0.339561i | ||||
\(76\) | 1051.99 | 0.182132 | ||||||||
\(77\) | −1834.41 | − | 1834.41i | −0.309396 | − | 0.309396i | ||||
\(78\) | −3932.68 | + | 3932.68i | −0.646397 | + | 0.646397i | ||||
\(79\) | − | 4854.69i | − | 0.777871i | −0.921265 | − | 0.388936i | \(-0.872843\pi\) | ||
0.921265 | − | 0.388936i | \(-0.127157\pi\) | |||||||
\(80\) | −5121.74 | + | 5994.14i | −0.800271 | + | 0.936585i | ||||
\(81\) | −729.000 | −0.111111 | ||||||||
\(82\) | −1016.68 | − | 1016.68i | −0.151201 | − | 0.151201i | ||||
\(83\) | −1316.57 | + | 1316.57i | −0.191111 | + | 0.191111i | −0.796176 | − | 0.605065i | \(-0.793147\pi\) |
0.605065 | + | 0.796176i | \(0.293147\pi\) | |||||||
\(84\) | − | 1425.37i | − | 0.202008i | ||||||
\(85\) | −9832.53 | + | 771.687i | −1.36090 | + | 0.106808i | ||||
\(86\) | 689.160 | 0.0931801 | ||||||||
\(87\) | −2011.54 | − | 2011.54i | −0.265760 | − | 0.265760i | ||||
\(88\) | 1855.84 | − | 1855.84i | 0.239649 | − | 0.239649i | ||||
\(89\) | 5185.49i | 0.654651i | 0.944912 | + | 0.327326i | \(0.106147\pi\) | ||||
−0.944912 | + | 0.327326i | \(0.893853\pi\) | |||||||
\(90\) | 246.864 | + | 3145.44i | 0.0304771 | + | 0.388326i | ||||
\(91\) | 10740.0 | 1.29694 | ||||||||
\(92\) | −2328.20 | − | 2328.20i | −0.275071 | − | 0.275071i | ||||
\(93\) | 5651.36 | − | 5651.36i | 0.653412 | − | 0.653412i | ||||
\(94\) | − | 2288.24i | − | 0.258968i | ||||||
\(95\) | 3418.74 | + | 2921.17i | 0.378808 | + | 0.323675i | ||||
\(96\) | 3714.83 | 0.403085 | ||||||||
\(97\) | 3495.32 | + | 3495.32i | 0.371487 | + | 0.371487i | 0.868018 | − | 0.496532i | \(-0.165393\pi\) |
−0.496532 | + | 0.868018i | \(0.665393\pi\) | |||||||
\(98\) | 664.940 | − | 664.940i | 0.0692357 | − | 0.0692357i | ||||
\(99\) | − | 1493.42i | − | 0.152374i | ||||||
\(100\) | 3610.61 | − | 570.256i | 0.361061 | − | 0.0570256i | ||||
\(101\) | 7708.86 | 0.755697 | 0.377848 | − | 0.925867i | \(-0.376664\pi\) | ||||
0.377848 | + | 0.925867i | \(0.376664\pi\) | |||||||
\(102\) | 6775.44 | + | 6775.44i | 0.651234 | + | 0.651234i | ||||
\(103\) | −5098.51 | + | 5098.51i | −0.480583 | + | 0.480583i | −0.905318 | − | 0.424735i | \(-0.860367\pi\) |
0.424735 | + | 0.905318i | \(0.360367\pi\) | |||||||
\(104\) | 10865.5i | 1.00457i | ||||||||
\(105\) | 3957.95 | − | 4632.13i | 0.358998 | − | 0.420147i | ||||
\(106\) | −13386.2 | −1.19137 | ||||||||
\(107\) | −2041.19 | − | 2041.19i | −0.178285 | − | 0.178285i | 0.612323 | − | 0.790608i | \(-0.290235\pi\) |
−0.790608 | + | 0.612323i | \(0.790235\pi\) | |||||||
\(108\) | 580.205 | − | 580.205i | 0.0497432 | − | 0.0497432i | ||||
\(109\) | 11999.0i | 1.00993i | 0.863139 | + | 0.504966i | \(0.168495\pi\) | ||||
−0.863139 | + | 0.504966i | \(0.831505\pi\) | |||||||
\(110\) | −6443.71 | + | 505.722i | −0.532538 | + | 0.0417952i | ||||
\(111\) | −12203.9 | −0.990498 | ||||||||
\(112\) | −10459.3 | − | 10459.3i | −0.833806 | − | 0.833806i | ||||
\(113\) | 8953.64 | − | 8953.64i | 0.701202 | − | 0.701202i | −0.263467 | − | 0.964668i | \(-0.584866\pi\) |
0.964668 | + | 0.263467i | \(0.0848659\pi\) | |||||||
\(114\) | − | 4368.73i | − | 0.336160i | ||||||
\(115\) | −1101.20 | − | 14031.1i | −0.0832669 | − | 1.06095i | ||||
\(116\) | 3201.93 | 0.237956 | ||||||||
\(117\) | 4371.79 | + | 4371.79i | 0.319365 | + | 0.319365i | ||||
\(118\) | −9434.64 | + | 9434.64i | −0.677581 | + | 0.677581i | ||||
\(119\) | − | 18503.4i | − | 1.30665i | ||||||
\(120\) | 4686.25 | + | 4004.19i | 0.325434 | + | 0.278069i | ||||
\(121\) | −11581.6 | −0.791039 | ||||||||
\(122\) | −3494.82 | − | 3494.82i | −0.234804 | − | 0.234804i | ||||
\(123\) | −1130.20 | + | 1130.20i | −0.0747040 | + | 0.0747040i | ||||
\(124\) | 8995.74i | 0.585051i | ||||||||
\(125\) | 13317.2 | + | 8172.72i | 0.852299 | + | 0.523054i | ||||
\(126\) | −5919.28 | −0.372845 | ||||||||
\(127\) | 6051.36 | + | 6051.36i | 0.375185 | + | 0.375185i | 0.869361 | − | 0.494177i | \(-0.164530\pi\) |
−0.494177 | + | 0.869361i | \(0.664530\pi\) | |||||||
\(128\) | 13721.2 | − | 13721.2i | 0.837476 | − | 0.837476i | ||||
\(129\) | − | 766.109i | − | 0.0460374i | ||||||
\(130\) | 17382.7 | − | 20343.5i | 1.02856 | − | 1.20376i | ||||
\(131\) | −22015.7 | −1.28289 | −0.641446 | − | 0.767168i | \(-0.721665\pi\) | ||||
−0.641446 | + | 0.767168i | \(0.721665\pi\) | |||||||
\(132\) | 1188.60 | + | 1188.60i | 0.0682162 | + | 0.0682162i | ||||
\(133\) | −5965.41 | + | 5965.41i | −0.337238 | + | 0.337238i | ||||
\(134\) | 24832.1i | 1.38294i | ||||||||
\(135\) | 3496.65 | − | 274.428i | 0.191860 | − | 0.0150578i | ||||
\(136\) | 18719.6 | 1.01209 | ||||||||
\(137\) | −11424.0 | − | 11424.0i | −0.608661 | − | 0.608661i | 0.333935 | − | 0.942596i | \(-0.391623\pi\) |
−0.942596 | + | 0.333935i | \(0.891623\pi\) | |||||||
\(138\) | −9668.61 | + | 9668.61i | −0.507698 | + | 0.507698i | ||||
\(139\) | 432.165i | 0.0223676i | 0.999937 | + | 0.0111838i | \(0.00356000\pi\) | ||||
−0.999937 | + | 0.0111838i | \(0.996440\pi\) | |||||||
\(140\) | 536.571 | + | 6836.77i | 0.0273761 | + | 0.348815i | ||||
\(141\) | −2543.74 | −0.127948 | ||||||||
\(142\) | 4723.90 | + | 4723.90i | 0.234274 | + | 0.234274i | ||||
\(143\) | −8955.98 | + | 8955.98i | −0.437967 | + | 0.437967i | ||||
\(144\) | − | 8515.03i | − | 0.410640i | ||||||
\(145\) | 10405.6 | + | 8891.12i | 0.494915 | + | 0.422883i | ||||
\(146\) | 5378.81 | 0.252337 | ||||||||
\(147\) | −739.184 | − | 739.184i | −0.0342072 | − | 0.0342072i | ||||
\(148\) | 9713.00 | − | 9713.00i | 0.443435 | − | 0.443435i | ||||
\(149\) | 17370.9i | 0.782438i | 0.920298 | + | 0.391219i | \(0.127947\pi\) | ||||
−0.920298 | + | 0.391219i | \(0.872053\pi\) | |||||||
\(150\) | −2368.17 | − | 14994.2i | −0.105252 | − | 0.666409i | ||||
\(151\) | 20493.6 | 0.898805 | 0.449402 | − | 0.893329i | \(-0.351637\pi\) | ||||
0.449402 | + | 0.893329i | \(0.351637\pi\) | |||||||
\(152\) | −6035.10 | − | 6035.10i | −0.261215 | − | 0.261215i | ||||
\(153\) | 7531.95 | − | 7531.95i | 0.321755 | − | 0.321755i | ||||
\(154\) | − | 12126.2i | − | 0.511307i | ||||||
\(155\) | −24979.3 | + | 29234.2i | −1.03972 | + | 1.21682i | ||||
\(156\) | −6958.94 | −0.285952 | ||||||||
\(157\) | 2340.31 | + | 2340.31i | 0.0949456 | + | 0.0949456i | 0.752984 | − | 0.658039i | \(-0.228614\pi\) |
−0.658039 | + | 0.752984i | \(0.728614\pi\) | |||||||
\(158\) | 16045.7 | − | 16045.7i | 0.642753 | − | 0.642753i | ||||
\(159\) | 14880.8i | 0.588617i | ||||||||
\(160\) | −17818.2 | + | 1398.43i | −0.696024 | + | 0.0546261i | ||||
\(161\) | 26404.6 | 1.01866 | ||||||||
\(162\) | −2409.48 | − | 2409.48i | −0.0918109 | − | 0.0918109i | ||||
\(163\) | 15303.1 | − | 15303.1i | 0.575977 | − | 0.575977i | −0.357815 | − | 0.933792i | \(-0.616478\pi\) |
0.933792 | + | 0.357815i | \(0.116478\pi\) | |||||||
\(164\) | − | 1799.03i | − | 0.0668883i | ||||||
\(165\) | 562.189 | + | 7163.19i | 0.0206497 | + | 0.263111i | ||||
\(166\) | −8703.01 | −0.315830 | ||||||||
\(167\) | −23457.8 | − | 23457.8i | −0.841113 | − | 0.841113i | 0.147891 | − | 0.989004i | \(-0.452752\pi\) |
−0.989004 | + | 0.147891i | \(0.952752\pi\) | |||||||
\(168\) | −8177.09 | + | 8177.09i | −0.289721 | + | 0.289721i | ||||
\(169\) | − | 23873.9i | − | 0.835891i | ||||||
\(170\) | −35049.0 | − | 29947.8i | −1.21277 | − | 1.03626i | ||||
\(171\) | −4856.52 | −0.166086 | ||||||||
\(172\) | 609.739 | + | 609.739i | 0.0206104 | + | 0.0206104i | ||||
\(173\) | −20512.3 | + | 20512.3i | −0.685366 | + | 0.685366i | −0.961204 | − | 0.275838i | \(-0.911045\pi\) |
0.275838 | + | 0.961204i | \(0.411045\pi\) | |||||||
\(174\) | − | 13297.0i | − | 0.439194i | ||||||
\(175\) | −17240.6 | + | 23708.0i | −0.562958 | + | 0.774137i | ||||
\(176\) | 17443.8 | 0.563138 | ||||||||
\(177\) | 10488.1 | + | 10488.1i | 0.334772 | + | 0.334772i | ||||
\(178\) | −17139.0 | + | 17139.0i | −0.540937 | + | 0.540937i | ||||
\(179\) | − | 52460.9i | − | 1.63731i | −0.574288 | − | 0.818653i | \(-0.694721\pi\) | ||
0.574288 | − | 0.818653i | \(-0.305279\pi\) | |||||||
\(180\) | −2564.54 | + | 3001.37i | −0.0791525 | + | 0.0926349i | ||||
\(181\) | −60242.8 | −1.83886 | −0.919428 | − | 0.393258i | \(-0.871348\pi\) | ||||
−0.919428 | + | 0.393258i | \(0.871348\pi\) | |||||||
\(182\) | 35497.7 | + | 35497.7i | 1.07166 | + | 1.07166i | ||||
\(183\) | −3885.03 | + | 3885.03i | −0.116009 | + | 0.116009i | ||||
\(184\) | 26713.1i | 0.789020i | ||||||||
\(185\) | 58536.2 | − | 4594.10i | 1.71033 | − | 0.134232i | ||||
\(186\) | 37357.7 | 1.07983 | ||||||||
\(187\) | 15429.8 | + | 15429.8i | 0.441244 | + | 0.441244i | ||||
\(188\) | 2024.54 | − | 2024.54i | 0.0572810 | − | 0.0572810i | ||||
\(189\) | 6580.20i | 0.184211i | ||||||||
\(190\) | 1644.58 | + | 20954.6i | 0.0455563 | + | 0.580460i | ||||
\(191\) | 44243.4 | 1.21278 | 0.606390 | − | 0.795167i | \(-0.292617\pi\) | ||||
0.606390 | + | 0.795167i | \(0.292617\pi\) | |||||||
\(192\) | −6261.74 | − | 6261.74i | −0.169860 | − | 0.169860i | ||||
\(193\) | 18449.5 | − | 18449.5i | 0.495303 | − | 0.495303i | −0.414669 | − | 0.909972i | \(-0.636103\pi\) |
0.909972 | + | 0.414669i | \(0.136103\pi\) | |||||||
\(194\) | 23105.4i | 0.613917i | ||||||||
\(195\) | −22615.0 | − | 19323.5i | −0.594741 | − | 0.508180i | ||||
\(196\) | 1176.62 | 0.0306284 | ||||||||
\(197\) | 18454.6 | + | 18454.6i | 0.475524 | + | 0.475524i | 0.903697 | − | 0.428173i | \(-0.140843\pi\) |
−0.428173 | + | 0.903697i | \(0.640843\pi\) | |||||||
\(198\) | 4936.04 | − | 4936.04i | 0.125906 | − | 0.125906i | ||||
\(199\) | − | 69350.3i | − | 1.75123i | −0.483013 | − | 0.875613i | \(-0.660458\pi\) | ||
0.483013 | − | 0.875613i | \(-0.339542\pi\) | |||||||
\(200\) | −23984.9 | − | 17442.0i | −0.599624 | − | 0.436050i | ||||
\(201\) | 27604.7 | 0.683269 | ||||||||
\(202\) | 25479.3 | + | 25479.3i | 0.624431 | + | 0.624431i | ||||
\(203\) | −18156.8 | + | 18156.8i | −0.440604 | + | 0.440604i | ||||
\(204\) | 11989.2i | 0.288092i | ||||||||
\(205\) | 4995.53 | − | 5846.45i | 0.118871 | − | 0.139118i | ||||
\(206\) | −33703.1 | −0.794210 | ||||||||
\(207\) | 10748.2 | + | 10748.2i | 0.250838 | + | 0.250838i | ||||
\(208\) | −51064.3 | + | 51064.3i | −1.18030 | + | 1.18030i | ||||
\(209\) | − | 9949.00i | − | 0.227765i | ||||||
\(210\) | 28391.8 | − | 2228.28i | 0.643806 | − | 0.0505279i | ||||
\(211\) | −19458.0 | −0.437052 | −0.218526 | − | 0.975831i | \(-0.570125\pi\) | ||||
−0.218526 | + | 0.975831i | \(0.570125\pi\) | |||||||
\(212\) | −11843.5 | − | 11843.5i | −0.263517 | − | 0.263517i | ||||
\(213\) | 5251.35 | − | 5251.35i | 0.115748 | − | 0.115748i | ||||
\(214\) | − | 13493.0i | − | 0.294633i | ||||||
\(215\) | 288.397 | + | 3674.64i | 0.00623899 | + | 0.0794947i | ||||
\(216\) | −6657.08 | −0.142684 | ||||||||
\(217\) | −51011.1 | − | 51011.1i | −1.08329 | − | 1.08329i | ||||
\(218\) | −39659.0 | + | 39659.0i | −0.834505 | + | 0.834505i | ||||
\(219\) | − | 5979.38i | − | 0.124672i | ||||||
\(220\) | −6148.56 | − | 5253.68i | −0.127036 | − | 0.108547i | ||||
\(221\) | −90337.7 | −1.84963 | ||||||||
\(222\) | −40336.3 | − | 40336.3i | −0.818447 | − | 0.818447i | ||||
\(223\) | 52732.0 | − | 52732.0i | 1.06039 | − | 1.06039i | 0.0623311 | − | 0.998056i | \(-0.480147\pi\) |
0.998056 | − | 0.0623311i | \(-0.0198535\pi\) | |||||||
\(224\) | − | 33531.4i | − | 0.668275i | ||||||
\(225\) | −16668.4 | + | 2632.59i | −0.329252 | + | 0.0520018i | ||||
\(226\) | 59187.0 | 1.15880 | ||||||||
\(227\) | 61436.6 | + | 61436.6i | 1.19227 | + | 1.19227i | 0.976428 | + | 0.215844i | \(0.0692503\pi\) |
0.215844 | + | 0.976428i | \(0.430750\pi\) | |||||||
\(228\) | 3865.26 | − | 3865.26i | 0.0743549 | − | 0.0743549i | ||||
\(229\) | 98741.9i | 1.88292i | 0.337132 | + | 0.941458i | \(0.390543\pi\) | ||||
−0.337132 | + | 0.941458i | \(0.609457\pi\) | |||||||
\(230\) | 42735.8 | − | 50015.2i | 0.807860 | − | 0.945467i | ||||
\(231\) | −13480.1 | −0.252621 | ||||||||
\(232\) | −18369.0 | − | 18369.0i | −0.341278 | − | 0.341278i | ||||
\(233\) | 26861.4 | − | 26861.4i | 0.494785 | − | 0.494785i | −0.415025 | − | 0.909810i | \(-0.636227\pi\) |
0.909810 | + | 0.415025i | \(0.136227\pi\) | |||||||
\(234\) | 28899.2i | 0.527781i | ||||||||
\(235\) | 12201.1 | − | 957.576i | 0.220934 | − | 0.0173395i | ||||
\(236\) | −16694.7 | −0.299747 | ||||||||
\(237\) | −17837.3 | − | 17837.3i | −0.317565 | − | 0.317565i | ||||
\(238\) | 61157.4 | − | 61157.4i | 1.07968 | − | 1.07968i | ||||
\(239\) | 64860.8i | 1.13550i | 0.823202 | + | 0.567749i | \(0.192186\pi\) | ||||
−0.823202 | + | 0.567749i | \(0.807814\pi\) | |||||||
\(240\) | 3205.43 | + | 40842.4i | 0.0556499 | + | 0.709069i | ||||
\(241\) | 11766.6 | 0.202590 | 0.101295 | − | 0.994856i | \(-0.467701\pi\) | ||||
0.101295 | + | 0.994856i | \(0.467701\pi\) | |||||||
\(242\) | −38279.4 | − | 38279.4i | −0.653634 | − | 0.653634i | ||||
\(243\) | −2678.52 | + | 2678.52i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 6184.13i | − | 0.103872i | ||||||
\(245\) | 3823.76 | + | 3267.24i | 0.0637028 | + | 0.0544313i | ||||
\(246\) | −7471.03 | −0.123455 | ||||||||
\(247\) | 29124.4 | + | 29124.4i | 0.477378 | + | 0.477378i | ||||
\(248\) | 51607.1 | − | 51607.1i | 0.839085 | − | 0.839085i | ||||
\(249\) | 9674.75i | 0.156042i | ||||||||
\(250\) | 17003.4 | + | 71028.2i | 0.272055 | + | 1.13645i | ||||
\(251\) | 14659.6 | 0.232688 | 0.116344 | − | 0.993209i | \(-0.462882\pi\) | ||||
0.116344 | + | 0.993209i | \(0.462882\pi\) | |||||||
\(252\) | −5237.13 | − | 5237.13i | −0.0824692 | − | 0.0824692i | ||||
\(253\) | −22018.5 | + | 22018.5i | −0.343991 | + | 0.343991i | ||||
\(254\) | 40001.8i | 0.620029i | ||||||||
\(255\) | −33291.7 | + | 38962.4i | −0.511983 | + | 0.599191i | ||||
\(256\) | 63434.7 | 0.967937 | ||||||||
\(257\) | −47816.3 | − | 47816.3i | −0.723951 | − | 0.723951i | 0.245456 | − | 0.969408i | \(-0.421062\pi\) |
−0.969408 | + | 0.245456i | \(0.921062\pi\) | |||||||
\(258\) | 2532.14 | − | 2532.14i | 0.0380406 | − | 0.0380406i | ||||
\(259\) | 110157.i | 1.64215i | ||||||||
\(260\) | 33378.6 | − | 2619.65i | 0.493766 | − | 0.0387522i | ||||
\(261\) | −14781.7 | −0.216992 | ||||||||
\(262\) | −72766.2 | − | 72766.2i | −1.06005 | − | 1.06005i | ||||
\(263\) | −45872.6 | + | 45872.6i | −0.663197 | + | 0.663197i | −0.956132 | − | 0.292936i | \(-0.905368\pi\) |
0.292936 | + | 0.956132i | \(0.405368\pi\) | |||||||
\(264\) | − | 13637.6i | − | 0.195673i | ||||||
\(265\) | −5601.80 | − | 71375.9i | −0.0797694 | − | 1.01639i | ||||
\(266\) | −39433.6 | −0.557319 | ||||||||
\(267\) | 19052.7 | + | 19052.7i | 0.267260 | + | 0.267260i | ||||
\(268\) | −21970.4 | + | 21970.4i | −0.305892 | + | 0.305892i | ||||
\(269\) | − | 80295.1i | − | 1.10965i | −0.831968 | − | 0.554823i | \(-0.812786\pi\) | ||
0.831968 | − | 0.554823i | \(-0.187214\pi\) | |||||||
\(270\) | 12464.1 | + | 10650.1i | 0.170976 | + | 0.146091i | ||||
\(271\) | 40047.7 | 0.545304 | 0.272652 | − | 0.962113i | \(-0.412099\pi\) | ||||
0.272652 | + | 0.962113i | \(0.412099\pi\) | |||||||
\(272\) | 87976.4 | + | 87976.4i | 1.18913 | + | 1.18913i | ||||
\(273\) | 39461.2 | − | 39461.2i | 0.529475 | − | 0.529475i | ||||
\(274\) | − | 75516.8i | − | 1.00587i | ||||||
\(275\) | −5393.08 | − | 34146.6i | −0.0713135 | − | 0.451525i | ||||
\(276\) | −17108.7 | −0.224595 | ||||||||
\(277\) | −49870.0 | − | 49870.0i | −0.649950 | − | 0.649950i | 0.303031 | − | 0.952981i | \(-0.402001\pi\) |
−0.952981 | + | 0.303031i | \(0.902001\pi\) | |||||||
\(278\) | −1428.39 | + | 1428.39i | −0.0184823 | + | 0.0184823i | ||||
\(279\) | − | 41528.9i | − | 0.533509i | ||||||
\(280\) | 36143.2 | − | 42299.6i | 0.461010 | − | 0.539536i | ||||
\(281\) | −12842.2 | −0.162639 | −0.0813196 | − | 0.996688i | \(-0.525913\pi\) | ||||
−0.0813196 | + | 0.996688i | \(0.525913\pi\) | |||||||
\(282\) | −8407.55 | − | 8407.55i | −0.105723 | − | 0.105723i | ||||
\(283\) | −35925.4 | + | 35925.4i | −0.448568 | + | 0.448568i | −0.894878 | − | 0.446310i | \(-0.852738\pi\) |
0.446310 | + | 0.894878i | \(0.352738\pi\) | |||||||
\(284\) | 8359.02i | 0.103638i | ||||||||
\(285\) | 23294.3 | − | 1828.21i | 0.286788 | − | 0.0225080i | ||||
\(286\) | −59202.4 | −0.723782 | ||||||||
\(287\) | 10201.5 | + | 10201.5i | 0.123852 | + | 0.123852i | ||||
\(288\) | 13649.2 | − | 13649.2i | 0.164559 | − | 0.164559i | ||||
\(289\) | 72117.7i | 0.863467i | ||||||||
\(290\) | 5005.60 | + | 63779.3i | 0.0595196 | + | 0.758375i | ||||
\(291\) | 25685.2 | 0.303318 | ||||||||
\(292\) | 4758.94 | + | 4758.94i | 0.0558141 | + | 0.0558141i | ||||
\(293\) | −50366.0 | + | 50366.0i | −0.586681 | + | 0.586681i | −0.936731 | − | 0.350050i | \(-0.886165\pi\) |
0.350050 | + | 0.936731i | \(0.386165\pi\) | |||||||
\(294\) | − | 4886.29i | − | 0.0565307i | ||||||
\(295\) | −54254.2 | − | 46357.9i | −0.623432 | − | 0.532696i | ||||
\(296\) | −111444. | −1.27196 | ||||||||
\(297\) | −5487.17 | − | 5487.17i | −0.0622065 | − | 0.0622065i | ||||
\(298\) | −57414.2 | + | 57414.2i | −0.646527 | + | 0.646527i | ||||
\(299\) | − | 128913.i | − | 1.44196i | ||||||
\(300\) | 11171.0 | − | 15361.5i | 0.124122 | − | 0.170683i | ||||
\(301\) | −6915.16 | −0.0763254 | ||||||||
\(302\) | 67735.4 | + | 67735.4i | 0.742680 | + | 0.742680i | ||||
\(303\) | 28324.2 | − | 28324.2i | 0.308512 | − | 0.308512i | ||||
\(304\) | − | 56726.2i | − | 0.613814i | ||||||
\(305\) | 17172.1 | − | 20097.1i | 0.184596 | − | 0.216039i | ||||
\(306\) | 49789.1 | 0.531730 | ||||||||
\(307\) | 75581.6 | + | 75581.6i | 0.801936 | + | 0.801936i | 0.983398 | − | 0.181462i | \(-0.0580830\pi\) |
−0.181462 | + | 0.983398i | \(0.558083\pi\) | |||||||
\(308\) | 10728.7 | − | 10728.7i | 0.113096 | − | 0.113096i | ||||
\(309\) | 37466.2i | 0.392395i | ||||||||
\(310\) | −179186. | + | 14063.1i | −1.86458 | + | 0.146338i | ||||
\(311\) | 107241. | 1.10877 | 0.554384 | − | 0.832261i | \(-0.312954\pi\) | ||||
0.554384 | + | 0.832261i | \(0.312954\pi\) | |||||||
\(312\) | 39922.3 | + | 39922.3i | 0.410115 | + | 0.410115i | ||||
\(313\) | 24848.0 | − | 24848.0i | 0.253631 | − | 0.253631i | −0.568826 | − | 0.822458i | \(-0.692602\pi\) |
0.822458 | + | 0.568826i | \(0.192602\pi\) | |||||||
\(314\) | 15470.4i | 0.156907i | ||||||||
\(315\) | −2477.08 | − | 31562.0i | −0.0249643 | − | 0.318085i | ||||
\(316\) | 28393.1 | 0.284340 | ||||||||
\(317\) | −7619.16 | − | 7619.16i | −0.0758209 | − | 0.0758209i | 0.668179 | − | 0.744000i | \(-0.267074\pi\) |
−0.744000 | + | 0.668179i | \(0.767074\pi\) | |||||||
\(318\) | −49184.0 | + | 49184.0i | −0.486373 | + | 0.486373i | ||||
\(319\) | − | 30281.6i | − | 0.297576i | ||||||
\(320\) | 32391.6 | + | 27677.2i | 0.316324 | + | 0.270286i | ||||
\(321\) | −14999.6 | −0.145569 | ||||||||
\(322\) | 87272.1 | + | 87272.1i | 0.841713 | + | 0.841713i | ||||
\(323\) | 50177.1 | − | 50177.1i | 0.480950 | − | 0.480950i | ||||
\(324\) | − | 4263.62i | − | 0.0406152i | ||||||
\(325\) | 115747. | + | 84172.2i | 1.09583 | + | 0.796896i | ||||
\(326\) | 101160. | 0.951857 | ||||||||
\(327\) | 44087.2 | + | 44087.2i | 0.412303 | + | 0.412303i | ||||
\(328\) | −10320.7 | + | 10320.7i | −0.0959318 | + | 0.0959318i | ||||
\(329\) | 22960.7i | 0.212125i | ||||||||
\(330\) | −21817.6 | + | 25533.8i | −0.200345 | + | 0.234471i | ||||
\(331\) | 28518.2 | 0.260295 | 0.130148 | − | 0.991495i | \(-0.458455\pi\) | ||||
0.130148 | + | 0.991495i | \(0.458455\pi\) | |||||||
\(332\) | −7700.05 | − | 7700.05i | −0.0698582 | − | 0.0698582i | ||||
\(333\) | −44840.1 | + | 44840.1i | −0.404369 | + | 0.404369i | ||||
\(334\) | − | 155065.i | − | 1.39002i | ||||||
\(335\) | −132406. | + | 10391.6i | −1.17983 | + | 0.0925965i | ||||
\(336\) | −76859.5 | −0.680799 | ||||||||
\(337\) | −22519.8 | − | 22519.8i | −0.198292 | − | 0.198292i | 0.600976 | − | 0.799267i | \(-0.294779\pi\) |
−0.799267 | + | 0.600976i | \(0.794779\pi\) | |||||||
\(338\) | 78907.8 | − | 78907.8i | 0.690695 | − | 0.690695i | ||||
\(339\) | − | 65795.6i | − | 0.572529i | ||||||
\(340\) | −4513.28 | − | 57506.4i | −0.0390422 | − | 0.497460i | ||||
\(341\) | 85075.4 | 0.731636 | ||||||||
\(342\) | −16051.7 | − | 16051.7i | −0.137237 | − | 0.137237i | ||||
\(343\) | −86301.0 | + | 86301.0i | −0.733547 | + | 0.733547i | ||||
\(344\) | − | 6995.95i | − | 0.0591194i | ||||||
\(345\) | −55599.7 | − | 47507.5i | −0.467126 | − | 0.399139i | ||||
\(346\) | −135594. | −1.13263 | ||||||||
\(347\) | −123818. | − | 123818.i | −1.02831 | − | 1.02831i | −0.999587 | − | 0.0287203i | \(-0.990857\pi\) |
−0.0287203 | − | 0.999587i | \(-0.509143\pi\) | |||||||
\(348\) | 11764.7 | − | 11764.7i | 0.0971451 | − | 0.0971451i | ||||
\(349\) | 53357.0i | 0.438067i | 0.975717 | + | 0.219034i | \(0.0702905\pi\) | ||||
−0.975717 | + | 0.219034i | \(0.929710\pi\) | |||||||
\(350\) | −135343. | + | 21375.9i | −1.10484 | + | 0.174497i | ||||
\(351\) | 32125.9 | 0.260760 | ||||||||
\(352\) | 27961.5 | + | 27961.5i | 0.225671 | + | 0.225671i | ||||
\(353\) | −48279.2 | + | 48279.2i | −0.387445 | + | 0.387445i | −0.873775 | − | 0.486330i | \(-0.838335\pi\) |
0.486330 | + | 0.873775i | \(0.338335\pi\) | |||||||
\(354\) | 69330.1i | 0.553242i | ||||||||
\(355\) | −23211.3 | + | 27165.0i | −0.184180 | + | 0.215552i | ||||
\(356\) | −30327.8 | −0.239299 | ||||||||
\(357\) | −67985.9 | − | 67985.9i | −0.533436 | − | 0.533436i | ||||
\(358\) | 173393. | − | 173393.i | 1.35290 | − | 1.35290i | ||||
\(359\) | 91012.9i | 0.706178i | 0.935590 | + | 0.353089i | \(0.114869\pi\) | ||||
−0.935590 | + | 0.353089i | \(0.885131\pi\) | |||||||
\(360\) | 31930.7 | − | 2506.02i | 0.246379 | − | 0.0193366i | ||||
\(361\) | 97967.4 | 0.751739 | ||||||||
\(362\) | −199114. | − | 199114.i | −1.51944 | − | 1.51944i | ||||
\(363\) | −42553.5 | + | 42553.5i | −0.322940 | + | 0.322940i | ||||
\(364\) | 62813.7i | 0.474080i | ||||||||
\(365\) | 2250.90 | + | 28680.1i | 0.0168955 | + | 0.215276i | ||||
\(366\) | −25681.6 | −0.191716 | ||||||||
\(367\) | −94731.0 | − | 94731.0i | −0.703331 | − | 0.703331i | 0.261793 | − | 0.965124i | \(-0.415686\pi\) |
−0.965124 | + | 0.261793i | \(0.915686\pi\) | |||||||
\(368\) | −125543. | + | 125543.i | −0.927037 | + | 0.927037i | ||||
\(369\) | 8305.21i | 0.0609955i | ||||||||
\(370\) | 208658. | + | 178289.i | 1.52416 | + | 1.30233i | ||||
\(371\) | 134319. | 0.975868 | ||||||||
\(372\) | 33052.5 | + | 33052.5i | 0.238846 | + | 0.238846i | ||||
\(373\) | 174691. | − | 174691.i | 1.25560 | − | 1.25560i | 0.302430 | − | 0.953172i | \(-0.402202\pi\) |
0.953172 | − | 0.302430i | \(-0.0977978\pi\) | |||||||
\(374\) | 101997.i | 0.729197i | ||||||||
\(375\) | 78958.9 | − | 18901.9i | 0.561486 | − | 0.134414i | ||||
\(376\) | −23228.9 | −0.164306 | ||||||||
\(377\) | 88645.5 | + | 88645.5i | 0.623697 | + | 0.623697i | ||||
\(378\) | −21748.8 | + | 21748.8i | −0.152213 | + | 0.152213i | ||||
\(379\) | − | 216082.i | − | 1.50432i | −0.658981 | − | 0.752159i | \(-0.729012\pi\) | ||
0.658981 | − | 0.752159i | \(-0.270988\pi\) | |||||||
\(380\) | −17084.7 | + | 19994.8i | −0.118315 | + | 0.138468i | ||||
\(381\) | 44468.2 | 0.306337 | ||||||||
\(382\) | 146233. | + | 146233.i | 1.00212 | + | 1.00212i | ||||
\(383\) | −6943.25 | + | 6943.25i | −0.0473331 | + | 0.0473331i | −0.730377 | − | 0.683044i | \(-0.760656\pi\) |
0.683044 | + | 0.730377i | \(0.260656\pi\) | |||||||
\(384\) | − | 100830.i | − | 0.683796i | ||||||
\(385\) | 64657.4 | − | 5074.51i | 0.436211 | − | 0.0342352i | ||||
\(386\) | 121959. | 0.818536 | ||||||||
\(387\) | −2814.86 | − | 2814.86i | −0.0187947 | − | 0.0187947i | ||||
\(388\) | −20442.7 | + | 20442.7i | −0.135792 | + | 0.135792i | ||||
\(389\) | 171993.i | 1.13661i | 0.822817 | + | 0.568306i | \(0.192401\pi\) | ||||
−0.822817 | + | 0.568306i | \(0.807599\pi\) | |||||||
\(390\) | −10878.9 | − | 138615.i | −0.0715249 | − | 0.911341i | ||||
\(391\) | −222098. | −1.45275 | ||||||||
\(392\) | −6750.08 | − | 6750.08i | −0.0439275 | − | 0.0439275i | ||||
\(393\) | −80890.9 | + | 80890.9i | −0.523739 | + | 0.523739i | ||||
\(394\) | 121992.i | 0.785849i | ||||||||
\(395\) | 92271.3 | + | 78841.8i | 0.591388 | + | 0.505315i | ||||
\(396\) | 8734.39 | 0.0556983 | ||||||||
\(397\) | 47564.4 | + | 47564.4i | 0.301787 | + | 0.301787i | 0.841713 | − | 0.539925i | \(-0.181548\pi\) |
−0.539925 | + | 0.841713i | \(0.681548\pi\) | |||||||
\(398\) | 229216. | − | 229216.i | 1.44703 | − | 1.44703i | ||||
\(399\) | 43836.6i | 0.275354i | ||||||||
\(400\) | −30749.7 | − | 194694.i | −0.192186 | − | 1.21684i | ||||
\(401\) | −193768. | −1.20502 | −0.602508 | − | 0.798113i | \(-0.705832\pi\) | ||||
−0.602508 | + | 0.798113i | \(0.705832\pi\) | |||||||
\(402\) | 91238.9 | + | 91238.9i | 0.564583 | + | 0.564583i | ||||
\(403\) | −249047. | + | 249047.i | −1.53346 | + | 1.53346i | ||||
\(404\) | 45085.9i | 0.276235i | ||||||||
\(405\) | 11839.2 | − | 13855.8i | 0.0721792 | − | 0.0844739i | ||||
\(406\) | −120024. | −0.728140 | ||||||||
\(407\) | −91858.8 | − | 91858.8i | −0.554539 | − | 0.554539i | ||||
\(408\) | 68780.3 | − | 68780.3i | 0.413184 | − | 0.413184i | ||||
\(409\) | − | 265.258i | − | 0.00158570i | −1.00000 | 0.000792852i | \(-0.999748\pi\) | |||
1.00000 | 0.000792852i | \(-0.000252373\pi\) | ||||||||
\(410\) | 35834.8 | − | 2812.43i | 0.213176 | − | 0.0167307i | ||||
\(411\) | −83948.6 | −0.496970 | ||||||||
\(412\) | −29819.0 | − | 29819.0i | −0.175671 | − | 0.175671i | ||||
\(413\) | 94668.8 | − | 94668.8i | 0.555018 | − | 0.555018i | ||||
\(414\) | 71049.5i | 0.414534i | ||||||||
\(415\) | −3642.00 | − | 46405.0i | −0.0211468 | − | 0.269444i | ||||
\(416\) | −163707. | −0.945978 | ||||||||
\(417\) | 1587.88 | + | 1587.88i | 0.00913155 | + | 0.00913155i | ||||
\(418\) | 32883.3 | − | 32883.3i | 0.188202 | − | 0.188202i | ||||
\(419\) | 30926.0i | 0.176155i | 0.996114 | + | 0.0880775i | \(0.0280723\pi\) | ||||
−0.996114 | + | 0.0880775i | \(0.971928\pi\) | |||||||
\(420\) | 27091.4 | + | 23148.4i | 0.153579 | + | 0.131227i | ||||
\(421\) | −62470.0 | −0.352458 | −0.176229 | − | 0.984349i | \(-0.556390\pi\) | ||||
−0.176229 | + | 0.984349i | \(0.556390\pi\) | |||||||
\(422\) | −64312.3 | − | 64312.3i | −0.361135 | − | 0.361135i | ||||
\(423\) | −9346.30 | + | 9346.30i | −0.0522347 | + | 0.0522347i | ||||
\(424\) | 135889.i | 0.755878i | ||||||||
\(425\) | 145016. | − | 199416.i | 0.802859 | − | 1.10403i | ||||
\(426\) | 34713.5 | 0.191284 | ||||||||
\(427\) | 35067.6 | + | 35067.6i | 0.192332 | + | 0.192332i | ||||
\(428\) | 11938.1 | − | 11938.1i | 0.0651698 | − | 0.0651698i | ||||
\(429\) | 65812.7i | 0.357598i | ||||||||
\(430\) | −11192.2 | + | 13098.6i | −0.0605310 | + | 0.0708416i | ||||
\(431\) | 69270.8 | 0.372903 | 0.186451 | − | 0.982464i | \(-0.440301\pi\) | ||||
0.186451 | + | 0.982464i | \(0.440301\pi\) | |||||||
\(432\) | −31286.2 | − | 31286.2i | −0.167643 | − | 0.167643i | ||||
\(433\) | −110961. | + | 110961.i | −0.591829 | + | 0.591829i | −0.938125 | − | 0.346296i | \(-0.887439\pi\) |
0.346296 | + | 0.938125i | \(0.387439\pi\) | |||||||
\(434\) | − | 337203.i | − | 1.79024i | ||||||
\(435\) | 70900.6 | − | 5564.50i | 0.374689 | − | 0.0294068i | ||||
\(436\) | −70177.2 | −0.369167 | ||||||||
\(437\) | 71603.1 | + | 71603.1i | 0.374946 | + | 0.374946i | ||||
\(438\) | 19763.0 | − | 19763.0i | 0.103016 | − | 0.103016i | ||||
\(439\) | − | 167998.i | − | 0.871716i | −0.900016 | − | 0.435858i | \(-0.856445\pi\) | ||
0.900016 | − | 0.435858i | \(-0.143555\pi\) | |||||||
\(440\) | 5133.80 | + | 65412.8i | 0.0265176 | + | 0.337876i | ||||
\(441\) | −5431.87 | −0.0279301 | ||||||||
\(442\) | −298583. | − | 298583.i | −1.52834 | − | 1.52834i | ||||
\(443\) | 66278.3 | − | 66278.3i | 0.337726 | − | 0.337726i | −0.517785 | − | 0.855511i | \(-0.673243\pi\) |
0.855511 | + | 0.517785i | \(0.173243\pi\) | |||||||
\(444\) | − | 71375.7i | − | 0.362063i | ||||||
\(445\) | −98558.7 | − | 84214.1i | −0.497708 | − | 0.425270i | ||||
\(446\) | 348579. | 1.75239 | ||||||||
\(447\) | 63824.8 | + | 63824.8i | 0.319429 | + | 0.319429i | ||||
\(448\) | −56520.6 | + | 56520.6i | −0.281611 | + | 0.281611i | ||||
\(449\) | 212689.i | 1.05500i | 0.849556 | + | 0.527499i | \(0.176870\pi\) | ||||
−0.849556 | + | 0.527499i | \(0.823130\pi\) | |||||||
\(450\) | −63793.4 | − | 46391.0i | −0.315029 | − | 0.229091i | ||||
\(451\) | −17013.9 | −0.0836473 | ||||||||
\(452\) | 52366.1 | + | 52366.1i | 0.256315 | + | 0.256315i | ||||
\(453\) | 75298.5 | − | 75298.5i | 0.366935 | − | 0.366935i | ||||
\(454\) | 406119.i | 1.97034i | ||||||||
\(455\) | −174421. | + | 204131.i | −0.842511 | + | 0.986020i | ||||
\(456\) | −44348.8 | −0.213281 | ||||||||
\(457\) | 188980. | + | 188980.i | 0.904864 | + | 0.904864i | 0.995852 | − | 0.0909883i | \(-0.0290026\pi\) |
−0.0909883 | + | 0.995852i | \(0.529003\pi\) | |||||||
\(458\) | −326361. | + | 326361.i | −1.55585 | + | 1.55585i | ||||
\(459\) | − | 55348.3i | − | 0.262711i | ||||||
\(460\) | 82062.1 | − | 6440.49i | 0.387817 | − | 0.0304371i | ||||
\(461\) | −203463. | −0.957379 | −0.478690 | − | 0.877984i | \(-0.658888\pi\) | ||||
−0.478690 | + | 0.877984i | \(0.658888\pi\) | |||||||
\(462\) | −44554.3 | − | 44554.3i | −0.208740 | − | 0.208740i | ||||
\(463\) | 280217. | − | 280217.i | 1.30717 | − | 1.30717i | 0.383724 | − | 0.923448i | \(-0.374641\pi\) |
0.923448 | − | 0.383724i | \(-0.125359\pi\) | |||||||
\(464\) | − | 172657.i | − | 0.801951i | ||||||
\(465\) | 15633.3 | + | 199193.i | 0.0723011 | + | 0.921231i | ||||
\(466\) | 177564. | 0.817679 | ||||||||
\(467\) | 25143.8 | + | 25143.8i | 0.115291 | + | 0.115291i | 0.762399 | − | 0.647107i | \(-0.224021\pi\) |
−0.647107 | + | 0.762399i | \(0.724021\pi\) | |||||||
\(468\) | −25568.8 | + | 25568.8i | −0.116740 | + | 0.116740i | ||||
\(469\) | − | 249170.i | − | 1.13279i | ||||||
\(470\) | 43491.8 | + | 37161.8i | 0.196885 | + | 0.168229i | ||||
\(471\) | 17197.7 | 0.0775227 | ||||||||
\(472\) | 95774.9 | + | 95774.9i | 0.429900 | + | 0.429900i | ||||
\(473\) | 5766.49 | − | 5766.49i | 0.0257744 | − | 0.0257744i | ||||
\(474\) | − | 117911.i | − | 0.524806i | ||||||
\(475\) | −111043. | + | 17538.0i | −0.492158 | + | 0.0777309i | ||||
\(476\) | 108219. | 0.477627 | ||||||||
\(477\) | 54675.7 | + | 54675.7i | 0.240302 | + | 0.240302i | ||||
\(478\) | −214377. | + | 214377.i | −0.938260 | + | 0.938260i | ||||
\(479\) | − | 17282.5i | − | 0.0753246i | −0.999291 | − | 0.0376623i | \(-0.988009\pi\) | ||
0.999291 | − | 0.0376623i | \(-0.0119911\pi\) | |||||||
\(480\) | −60330.1 | + | 70606.5i | −0.261850 | + | 0.306452i | ||||
\(481\) | 537809. | 2.32454 | ||||||||
\(482\) | 38891.0 | + | 38891.0i | 0.167400 | + | 0.167400i | ||||
\(483\) | 97016.5 | − | 97016.5i | 0.415864 | − | 0.415864i | ||||
\(484\) | − | 67736.0i | − | 0.289154i | ||||||
\(485\) | −123199. | + | 9669.06i | −0.523751 | + | 0.0411056i | ||||
\(486\) | −17706.0 | −0.0749633 | ||||||||
\(487\) | −250914. | − | 250914.i | −1.05795 | − | 1.05795i | −0.998214 | − | 0.0597410i | \(-0.980973\pi\) |
−0.0597410 | − | 0.998214i | \(-0.519027\pi\) | |||||||
\(488\) | −35477.4 | + | 35477.4i | −0.148974 | + | 0.148974i | ||||
\(489\) | − | 112455.i | − | 0.470283i | ||||||
\(490\) | 1839.42 | + | 23437.1i | 0.00766104 | + | 0.0976139i | ||||
\(491\) | −175178. | −0.726634 | −0.363317 | − | 0.931666i | \(-0.618356\pi\) | ||||
−0.363317 | + | 0.931666i | \(0.618356\pi\) | |||||||
\(492\) | −6610.05 | − | 6610.05i | −0.0273070 | − | 0.0273070i | ||||
\(493\) | 152723. | − | 152723.i | 0.628364 | − | 0.628364i | ||||
\(494\) | 192523.i | 0.788914i | ||||||||
\(495\) | 28384.8 | + | 24253.6i | 0.115845 | + | 0.0989842i | ||||
\(496\) | 485075. | 1.97172 | ||||||||
\(497\) | −47400.5 | − | 47400.5i | −0.191898 | − | 0.191898i | ||||
\(498\) | −31976.9 | + | 31976.9i | −0.128937 | + | 0.128937i | ||||
\(499\) | 219732.i | 0.882454i | 0.897396 | + | 0.441227i | \(0.145457\pi\) | ||||
−0.897396 | + | 0.441227i | \(0.854543\pi\) | |||||||
\(500\) | −47798.9 | + | 77886.6i | −0.191195 | + | 0.311547i | ||||
\(501\) | −172379. | −0.686766 | ||||||||
\(502\) | 48452.8 | + | 48452.8i | 0.192270 | + | 0.192270i | ||||
\(503\) | 298149. | − | 298149.i | 1.17841 | − | 1.17841i | 0.198266 | − | 0.980148i | \(-0.436469\pi\) |
0.980148 | − | 0.198266i | \(-0.0635311\pi\) | |||||||
\(504\) | 60089.1i | 0.236556i | ||||||||
\(505\) | −125194. | + | 146519.i | −0.490911 | + | 0.574530i | ||||
\(506\) | −145551. | −0.568478 | ||||||||
\(507\) | −87718.2 | − | 87718.2i | −0.341251 | − | 0.341251i | ||||
\(508\) | −35391.9 | + | 35391.9i | −0.137144 | + | 0.137144i | ||||
\(509\) | − | 476403.i | − | 1.83882i | −0.393303 | − | 0.919409i | \(-0.628668\pi\) | ||
0.393303 | − | 0.919409i | \(-0.371332\pi\) | |||||||
\(510\) | −238813. | + | 18742.8i | −0.918160 | + | 0.0720601i | ||||
\(511\) | −53971.9 | −0.206693 | ||||||||
\(512\) | −9875.23 | − | 9875.23i | −0.0376710 | − | 0.0376710i | ||||
\(513\) | −17844.0 | + | 17844.0i | −0.0678043 | + | 0.0678043i | ||||
\(514\) | − | 316084.i | − | 1.19640i | ||||||
\(515\) | −14103.9 | − | 179707.i | −0.0531773 | − | 0.677564i | ||||
\(516\) | 4480.65 | 0.0168284 | ||||||||
\(517\) | −19146.7 | − | 19146.7i | −0.0716329 | − | 0.0716329i | ||||
\(518\) | −364089. | + | 364089.i | −1.35690 | + | 1.35690i | ||||
\(519\) | 150734.i | 0.559599i | ||||||||
\(520\) | −206516. | − | 176459.i | −0.763742 | − | 0.652584i | ||||
\(521\) | −366162. | −1.34896 | −0.674479 | − | 0.738294i | \(-0.735632\pi\) | ||||
−0.674479 | + | 0.738294i | \(0.735632\pi\) | |||||||
\(522\) | −48856.5 | − | 48856.5i | −0.179300 | − | 0.179300i | ||||
\(523\) | −236853. | + | 236853.i | −0.865916 | + | 0.865916i | −0.992017 | − | 0.126101i | \(-0.959754\pi\) |
0.126101 | + | 0.992017i | \(0.459754\pi\) | |||||||
\(524\) | − | 128761.i | − | 0.468944i | ||||||
\(525\) | 23762.6 | + | 150455.i | 0.0862137 | + | 0.545867i | ||||
\(526\) | −303236. | −1.09600 | ||||||||
\(527\) | 429072. | + | 429072.i | 1.54493 | + | 1.54493i | ||||
\(528\) | 64092.5 | − | 64092.5i | 0.229900 | − | 0.229900i | ||||
\(529\) | − | 37094.3i | − | 0.132555i | ||||||
\(530\) | 217396. | − | 254426.i | 0.773927 | − | 0.905754i | ||||
\(531\) | 77071.2 | 0.273340 | ||||||||
\(532\) | −34889.2 | − | 34889.2i | −0.123273 | − | 0.123273i | ||||
\(533\) | 49806.1 | − | 49806.1i | 0.175319 | − | 0.175319i | ||||
\(534\) | 125946.i | 0.441673i | ||||||||
\(535\) | 71945.6 | − | 5646.52i | 0.251360 | − | 0.0197275i | ||||
\(536\) | 252081. | 0.877426 | ||||||||
\(537\) | −192754. | − | 192754.i | −0.668428 | − | 0.668428i | ||||
\(538\) | 265391. | − | 265391.i | 0.916898 | − | 0.916898i | ||||
\(539\) | − | 11127.7i | − | 0.0383024i | ||||||
\(540\) | 1605.01 | + | 20450.5i | 0.00550417 | + | 0.0701319i | ||||
\(541\) | 70441.7 | 0.240678 | 0.120339 | − | 0.992733i | \(-0.461602\pi\) | ||||
0.120339 | + | 0.992733i | \(0.461602\pi\) | |||||||
\(542\) | 132365. | + | 132365.i | 0.450584 | + | 0.450584i | ||||
\(543\) | −221346. | + | 221346.i | −0.750710 | + | 0.750710i | ||||
\(544\) | 282044.i | 0.953056i | ||||||||
\(545\) | −228061. | − | 194868.i | −0.767816 | − | 0.656065i | ||||
\(546\) | 260854. | 0.875008 | ||||||||
\(547\) | 347520. | + | 347520.i | 1.16146 | + | 1.16146i | 0.984155 | + | 0.177308i | \(0.0567387\pi\) |
0.177308 | + | 0.984155i | \(0.443261\pi\) | |||||||
\(548\) | 66814.0 | − | 66814.0i | 0.222488 | − | 0.222488i | ||||
\(549\) | 28549.1i | 0.0947212i | ||||||||
\(550\) | 95035.9 | − | 130686.i | 0.314168 | − | 0.432021i | ||||
\(551\) | −98474.3 | −0.324354 | ||||||||
\(552\) | 98150.0 | + | 98150.0i | 0.322116 | + | 0.322116i | ||||
\(553\) | −161005. | + | 161005.i | −0.526490 | + | 0.526490i | ||||
\(554\) | − | 329660.i | − | 1.07410i | ||||||
\(555\) | 198196. | − | 231955.i | 0.643441 | − | 0.753041i | ||||
\(556\) | −2527.56 | −0.00817619 | ||||||||
\(557\) | 254820. | + | 254820.i | 0.821340 | + | 0.821340i | 0.986300 | − | 0.164960i | \(-0.0527495\pi\) |
−0.164960 | + | 0.986300i | \(0.552749\pi\) | |||||||
\(558\) | 137261. | − | 137261.i | 0.440837 | − | 0.440837i | ||||
\(559\) | 33761.3i | 0.108043i | ||||||||
\(560\) | 368657. | − | 28933.3i | 1.17556 | − | 0.0922619i | ||||
\(561\) | 113386. | 0.360274 | ||||||||
\(562\) | −42445.8 | − | 42445.8i | −0.134389 | − | 0.134389i | ||||
\(563\) | 31884.1 | − | 31884.1i | 0.100591 | − | 0.100591i | −0.655021 | − | 0.755611i | \(-0.727340\pi\) |
0.755611 | + | 0.655021i | \(0.227340\pi\) | |||||||
\(564\) | − | 14877.3i | − | 0.0467698i | ||||||
\(565\) | 24768.4 | + | 315589.i | 0.0775891 | + | 0.988609i | ||||
\(566\) | −237480. | −0.741302 | ||||||||
\(567\) | 24177.2 | + | 24177.2i | 0.0752038 | + | 0.0752038i | ||||
\(568\) | 47954.3 | − | 47954.3i | 0.148638 | − | 0.148638i | ||||
\(569\) | 609312.i | 1.88198i | 0.338431 | + | 0.940991i | \(0.390104\pi\) | ||||
−0.338431 | + | 0.940991i | \(0.609896\pi\) | |||||||
\(570\) | 83034.8 | + | 70949.6i | 0.255570 | + | 0.218374i | ||||
\(571\) | −233321. | −0.715618 | −0.357809 | − | 0.933795i | \(-0.616476\pi\) | ||||
−0.357809 | + | 0.933795i | \(0.616476\pi\) | |||||||
\(572\) | −52379.8 | − | 52379.8i | −0.160093 | − | 0.160093i | ||||
\(573\) | 162561. | − | 162561.i | 0.495115 | − | 0.495115i | ||||
\(574\) | 67436.1i | 0.204677i | ||||||||
\(575\) | 284568. | + | 206940.i | 0.860697 | + | 0.625904i | ||||
\(576\) | −46014.2 | −0.138690 | ||||||||
\(577\) | −324793. | − | 324793.i | −0.975562 | − | 0.975562i | 0.0241466 | − | 0.999708i | \(-0.492313\pi\) |
−0.999708 | + | 0.0241466i | \(0.992313\pi\) | |||||||
\(578\) | −238363. | + | 238363.i | −0.713481 | + | 0.713481i | ||||
\(579\) | − | 135576.i | − | 0.404413i | ||||||
\(580\) | −52000.5 | + | 60857.9i | −0.154579 | + | 0.180909i | ||||
\(581\) | 87327.6 | 0.258702 | ||||||||
\(582\) | 84894.6 | + | 84894.6i | 0.250631 | + | 0.250631i | ||||
\(583\) | −112008. | + | 112008.i | −0.329542 | + | 0.329542i | ||||
\(584\) | − | 54602.5i | − | 0.160098i | ||||||
\(585\) | −154092. | + | 12093.6i | −0.450266 | + | 0.0353382i | ||||
\(586\) | −332939. | −0.969547 | ||||||||
\(587\) | −369440. | − | 369440.i | −1.07218 | − | 1.07218i | −0.997184 | − | 0.0749961i | \(-0.976106\pi\) |
−0.0749961 | − | 0.997184i | \(-0.523894\pi\) | |||||||
\(588\) | 4323.18 | − | 4323.18i | 0.0125040 | − | 0.0125040i | ||||
\(589\) | − | 276661.i | − | 0.797475i | ||||||
\(590\) | −26098.9 | − | 332542.i | −0.0749754 | − | 0.955306i | ||||
\(591\) | 135613. | 0.388263 | ||||||||
\(592\) | −523751. | − | 523751.i | −1.49445 | − | 1.49445i | ||||
\(593\) | −263575. | + | 263575.i | −0.749541 | + | 0.749541i | −0.974393 | − | 0.224852i | \(-0.927810\pi\) |
0.224852 | + | 0.974393i | \(0.427810\pi\) | |||||||
\(594\) | − | 36272.3i | − | 0.102802i | ||||||
\(595\) | 351688. | + | 300502.i | 0.993398 | + | 0.848815i | ||||
\(596\) | −101595. | −0.286010 | ||||||||
\(597\) | −254809. | − | 254809.i | −0.714935 | − | 0.714935i | ||||
\(598\) | 426081. | − | 426081.i | 1.19149 | − | 1.19149i | ||||
\(599\) | 319604.i | 0.890756i | 0.895343 | + | 0.445378i | \(0.146931\pi\) | ||||
−0.895343 | + | 0.445378i | \(0.853069\pi\) | |||||||
\(600\) | −152212. | + | 24040.3i | −0.422812 | + | 0.0667785i | ||||
\(601\) | −558724. | −1.54685 | −0.773425 | − | 0.633887i | \(-0.781458\pi\) | ||||
−0.773425 | + | 0.633887i | \(0.781458\pi\) | |||||||
\(602\) | −22855.9 | − | 22855.9i | −0.0630675 | − | 0.0630675i | ||||
\(603\) | 101426. | − | 101426.i | 0.278943 | − | 0.278943i | ||||
\(604\) | 119859.i | 0.328546i | ||||||||
\(605\) | 188089. | − | 220127.i | 0.513870 | − | 0.601399i | ||||
\(606\) | 187234. | 0.509845 | ||||||||
\(607\) | 31979.5 | + | 31979.5i | 0.0867950 | + | 0.0867950i | 0.749171 | − | 0.662376i | \(-0.230452\pi\) |
−0.662376 | + | 0.749171i | \(0.730452\pi\) | |||||||
\(608\) | 90929.4 | − | 90929.4i | 0.245978 | − | 0.245978i | ||||
\(609\) | 133425.i | 0.359751i | ||||||||
\(610\) | 123182. | − | 9667.68i | 0.331045 | − | 0.0259814i | ||||
\(611\) | 112099. | 0.300275 | ||||||||
\(612\) | 44051.3 | + | 44051.3i | 0.117613 | + | 0.117613i | ||||
\(613\) | 181360. | − | 181360.i | 0.482636 | − | 0.482636i | −0.423336 | − | 0.905973i | \(-0.639141\pi\) |
0.905973 | + | 0.423336i | \(0.139141\pi\) | |||||||
\(614\) | 499624.i | 1.32528i | ||||||||
\(615\) | −3126.45 | − | 39836.0i | −0.00826611 | − | 0.105323i | ||||
\(616\) | −123098. | −0.324405 | ||||||||
\(617\) | 58514.8 | + | 58514.8i | 0.153708 | + | 0.153708i | 0.779772 | − | 0.626064i | \(-0.215335\pi\) |
−0.626064 | + | 0.779772i | \(0.715335\pi\) | |||||||
\(618\) | −123833. | + | 123833.i | −0.324235 | + | 0.324235i | ||||
\(619\) | 193773.i | 0.505722i | 0.967503 | + | 0.252861i | \(0.0813716\pi\) | ||||
−0.967503 | + | 0.252861i | \(0.918628\pi\) | |||||||
\(620\) | −170979. | − | 146094.i | −0.444794 | − | 0.380057i | ||||
\(621\) | 78982.5 | 0.204808 | ||||||||
\(622\) | 354452. | + | 354452.i | 0.916172 | + | 0.916172i | ||||
\(623\) | 171976. | − | 171976.i | 0.443090 | − | 0.443090i | ||||
\(624\) | 375245.i | 0.963707i | ||||||||
\(625\) | −371611. | + | 120387.i | −0.951325 | + | 0.308190i | ||||
\(626\) | 164255. | 0.419150 | ||||||||
\(627\) | −36555.0 | − | 36555.0i | −0.0929846 | − | 0.0929846i | ||||
\(628\) | −13687.5 | + | 13687.5i | −0.0347061 | + | 0.0347061i | ||||
\(629\) | − | 926566.i | − | 2.34194i | ||||||
\(630\) | 96131.1 | − | 112506.i | 0.242205 | − | 0.283461i | ||||
\(631\) | 276166. | 0.693604 | 0.346802 | − | 0.937938i | \(-0.387268\pi\) | ||||
0.346802 | + | 0.937938i | \(0.387268\pi\) | |||||||
\(632\) | −162886. | − | 162886.i | −0.407803 | − | 0.407803i | ||||
\(633\) | −71493.2 | + | 71493.2i | −0.178426 | + | 0.178426i | ||||
\(634\) | − | 50365.6i | − | 0.125301i | ||||||
\(635\) | −213292. | + | 16739.8i | −0.528965 | + | 0.0415148i | ||||
\(636\) | −87031.8 | −0.215161 | ||||||||
\(637\) | 32574.7 | + | 32574.7i | 0.0802790 | + | 0.0802790i | ||||
\(638\) | 100087. | − | 100087.i | 0.245886 | − | 0.245886i | ||||
\(639\) | − | 38589.4i | − | 0.0945075i | ||||||
\(640\) | 37956.8 | + | 483631.i | 0.0926680 | + | 1.18074i | ||||
\(641\) | 556595. | 1.35464 | 0.677319 | − | 0.735689i | \(-0.263142\pi\) | ||||
0.677319 | + | 0.735689i | \(0.263142\pi\) | |||||||
\(642\) | −49576.6 | − | 49576.6i | −0.120284 | − | 0.120284i | ||||
\(643\) | 288950. | − | 288950.i | 0.698878 | − | 0.698878i | −0.265291 | − | 0.964169i | \(-0.585468\pi\) |
0.964169 | + | 0.265291i | \(0.0854679\pi\) | |||||||
\(644\) | 154429.i | 0.372356i | ||||||||
\(645\) | 14561.1 | + | 12441.9i | 0.0350006 | + | 0.0299065i | ||||
\(646\) | 331690. | 0.794817 | ||||||||
\(647\) | −435693. | − | 435693.i | −1.04081 | − | 1.04081i | −0.999131 | − | 0.0416796i | \(-0.986729\pi\) |
−0.0416796 | − | 0.999131i | \(-0.513271\pi\) | |||||||
\(648\) | −24459.7 | + | 24459.7i | −0.0582507 | + | 0.0582507i | ||||
\(649\) | 157887.i | 0.374849i | ||||||||
\(650\) | 104362. | + | 660772.i | 0.247010 | + | 1.56396i | ||||
\(651\) | −374854. | −0.884504 | ||||||||
\(652\) | 89501.7 | + | 89501.7i | 0.210541 | + | 0.210541i | ||||
\(653\) | −96648.2 | + | 96648.2i | −0.226656 | + | 0.226656i | −0.811294 | − | 0.584638i | \(-0.801237\pi\) |
0.584638 | + | 0.811294i | \(0.301237\pi\) | |||||||
\(654\) | 291433.i | 0.681370i | ||||||||
\(655\) | 357543. | − | 418444.i | 0.833384 | − | 0.975338i | ||||
\(656\) | −97008.4 | −0.225425 | ||||||||
\(657\) | −21969.6 | − | 21969.6i | −0.0508970 | − | 0.0508970i | ||||
\(658\) | −75889.4 | + | 75889.4i | −0.175279 | + | 0.175279i | ||||
\(659\) | 693374.i | 1.59660i | 0.602259 | + | 0.798301i | \(0.294267\pi\) | ||||
−0.602259 | + | 0.798301i | \(0.705733\pi\) | |||||||
\(660\) | −41894.5 | + | 3288.01i | −0.0961765 | + | 0.00754823i | ||||
\(661\) | 102052. | 0.233572 | 0.116786 | − | 0.993157i | \(-0.462741\pi\) | ||||
0.116786 | + | 0.993157i | \(0.462741\pi\) | |||||||
\(662\) | 94258.1 | + | 94258.1i | 0.215081 | + | 0.215081i | ||||
\(663\) | −331922. | + | 331922.i | −0.755107 | + | 0.755107i | ||||
\(664\) | 88347.9i | 0.200383i | ||||||||
\(665\) | −16502.0 | − | 210262.i | −0.0373159 | − | 0.475465i | ||||
\(666\) | −296410. | −0.668259 | ||||||||
\(667\) | 217937. | + | 217937.i | 0.489869 | + | 0.489869i | ||||
\(668\) | 137195. | − | 137195.i | 0.307457 | − | 0.307457i | ||||
\(669\) | − | 387499.i | − | 0.865802i | ||||||
\(670\) | −471974. | − | 403281.i | −1.05140 | − | 0.898377i | ||||
\(671\) | −58485.2 | −0.129897 | ||||||||
\(672\) | −123202. | − | 123202.i | −0.272822 | − | 0.272822i | ||||
\(673\) | −222583. | + | 222583.i | −0.491431 | + | 0.491431i | −0.908757 | − | 0.417326i | \(-0.862967\pi\) |
0.417326 | + | 0.908757i | \(0.362967\pi\) | |||||||
\(674\) | − | 148865.i | − | 0.327696i | ||||||
\(675\) | −51570.8 | + | 70916.3i | −0.113187 | + | 0.155646i | ||||
\(676\) | 139628. | 0.305549 | ||||||||
\(677\) | 423786. | + | 423786.i | 0.924633 | + | 0.924633i | 0.997352 | − | 0.0727193i | \(-0.0231677\pi\) |
−0.0727193 | + | 0.997352i | \(0.523168\pi\) | |||||||
\(678\) | 217467. | − | 217467.i | 0.473079 | − | 0.473079i | ||||
\(679\) | − | 231844.i | − | 0.502870i | ||||||
\(680\) | −304013. | + | 355797.i | −0.657467 | + | 0.769457i | ||||
\(681\) | 451465. | 0.973486 | ||||||||
\(682\) | 281191. | + | 281191.i | 0.604550 | + | 0.604550i | ||||
\(683\) | 215197. | − | 215197.i | 0.461313 | − | 0.461313i | −0.437773 | − | 0.899086i | \(-0.644233\pi\) |
0.899086 | + | 0.437773i | \(0.144233\pi\) | |||||||
\(684\) | − | 28403.8i | − | 0.0607105i | ||||||
\(685\) | 402660. | − | 31602.0i | 0.858138 | − | 0.0673493i | ||||
\(686\) | −570483. | −1.21226 | ||||||||
\(687\) | 362801. | + | 362801.i | 0.768697 | + | 0.768697i | ||||
\(688\) | 32878.8 | − | 32878.8i | 0.0694607 | − | 0.0694607i | ||||
\(689\) | − | 655776.i | − | 1.38139i | ||||||
\(690\) | −26746.2 | − | 340789.i | −0.0561776 | − | 0.715793i | ||||
\(691\) | 322148. | 0.674683 | 0.337341 | − | 0.941382i | \(-0.390472\pi\) | ||||
0.337341 | + | 0.941382i | \(0.390472\pi\) | |||||||
\(692\) | −119968. | − | 119968.i | −0.250526 | − | 0.250526i | ||||
\(693\) | −49529.1 | + | 49529.1i | −0.103132 | + | 0.103132i | ||||
\(694\) | − | 818481.i | − | 1.69938i | ||||||
\(695\) | −8214.00 | − | 7018.51i | −0.0170053 | − | 0.0145303i | ||||
\(696\) | −134984. | −0.278653 | ||||||||
\(697\) | −85808.6 | − | 85808.6i | −0.176630 | − | 0.176630i | ||||
\(698\) | −176355. | + | 176355.i | −0.361974 | + | 0.361974i | ||||
\(699\) | − | 197390.i | − | 0.403990i | ||||||
\(700\) | −138658. | − | 100833.i | −0.282975 | − | 0.205782i | ||||
\(701\) | −324568. | −0.660495 | −0.330248 | − | 0.943894i | \(-0.607132\pi\) | ||||
−0.330248 | + | 0.943894i | \(0.607132\pi\) | |||||||
\(702\) | 106182. | + | 106182.i | 0.215466 | + | 0.215466i | ||||
\(703\) | −298720. | + | 298720.i | −0.604441 | + | 0.604441i | ||||
\(704\) | − | 94264.0i | − | 0.190196i | ||||||
\(705\) | 41311.2 | − | 48347.9i | 0.0831169 | − | 0.0972746i | ||||
\(706\) | −319144. | −0.640291 | ||||||||
\(707\) | −255664. | − | 255664.i | −0.511482 | − | 0.511482i | ||||
\(708\) | −61340.3 | + | 61340.3i | −0.122371 | + | 0.122371i | ||||
\(709\) | − | 248026.i | − | 0.493406i | −0.969091 | − | 0.246703i | \(-0.920653\pi\) | ||
0.969091 | − | 0.246703i | \(-0.0793472\pi\) | |||||||
\(710\) | −166503. | + | 13067.7i | −0.330298 | + | 0.0259228i | ||||
\(711\) | −131077. | −0.259290 | ||||||||
\(712\) | 173986. | + | 173986.i | 0.343205 | + | 0.343205i | ||||
\(713\) | −612289. | + | 612289.i | −1.20442 | + | 1.20442i | ||||
\(714\) | − | 449413.i | − | 0.881555i | ||||||
\(715\) | −24774.8 | − | 315671.i | −0.0484617 | − | 0.617479i | ||||
\(716\) | 306822. | 0.598495 | ||||||||
\(717\) | 238314. | + | 238314.i | 0.463565 | + | 0.463565i | ||||
\(718\) | −300815. | + | 300815.i | −0.583514 | + | 0.583514i | ||||
\(719\) | 406907.i | 0.787113i | 0.919300 | + | 0.393557i | \(0.128756\pi\) | ||||
−0.919300 | + | 0.393557i | \(0.871244\pi\) | |||||||
\(720\) | 161842. | + | 138287.i | 0.312195 | + | 0.266757i | ||||
\(721\) | 338183. | 0.650550 | ||||||||
\(722\) | 323801. | + | 323801.i | 0.621160 | + | 0.621160i | ||||
\(723\) | 43233.4 | − | 43233.4i | 0.0827070 | − | 0.0827070i | ||||
\(724\) | − | 352335.i | − | 0.672169i | ||||||
\(725\) | −337980. | + | 53380.3i | −0.643006 | + | 0.101556i | ||||
\(726\) | −281295. | −0.533690 | ||||||||
\(727\) | −465457. | − | 465457.i | −0.880664 | − | 0.880664i | 0.112938 | − | 0.993602i | \(-0.463974\pi\) |
−0.993602 | + | 0.112938i | \(0.963974\pi\) | |||||||
\(728\) | 360352. | − | 360352.i | 0.679930 | − | 0.679930i | ||||
\(729\) | 19683.0i | 0.0370370i | ||||||||
\(730\) | −87353.6 | + | 102233.i | −0.163921 | + | 0.191843i | ||||
\(731\) | 58165.7 | 0.108851 | ||||||||
\(732\) | −22721.9 | − | 22721.9i | −0.0424056 | − | 0.0424056i | ||||
\(733\) | −596415. | + | 596415.i | −1.11004 | + | 1.11004i | −0.116901 | + | 0.993144i | \(0.537296\pi\) |
−0.993144 | + | 0.116901i | \(0.962704\pi\) | |||||||
\(734\) | − | 626208.i | − | 1.16232i | ||||||
\(735\) | 26054.0 | − | 2044.80i | 0.0482280 | − | 0.00378508i | ||||
\(736\) | −402479. | −0.742997 | ||||||||
\(737\) | 207780. | + | 207780.i | 0.382534 | + | 0.382534i | ||||
\(738\) | −27450.3 | + | 27450.3i | −0.0504005 | + | 0.0504005i | ||||
\(739\) | 672211.i | 1.23088i | 0.788182 | + | 0.615442i | \(0.211022\pi\) | ||||
−0.788182 | + | 0.615442i | \(0.788978\pi\) | |||||||
\(740\) | 26869.0 | + | 342354.i | 0.0490668 | + | 0.625190i | ||||
\(741\) | 214020. | 0.389778 | ||||||||
\(742\) | 443951. | + | 443951.i | 0.806358 | + | 0.806358i | ||||
\(743\) | 251951. | − | 251951.i | 0.456393 | − | 0.456393i | −0.441076 | − | 0.897470i | \(-0.645403\pi\) |
0.897470 | + | 0.441076i | \(0.145403\pi\) | |||||||
\(744\) | − | 379233.i | − | 0.685110i | ||||||
\(745\) | −330162. | − | 282109.i | −0.594860 | − | 0.508282i | ||||
\(746\) | 1.15477e6 | 2.07500 | ||||||||
\(747\) | 35547.3 | + | 35547.3i | 0.0637038 | + | 0.0637038i | ||||
\(748\) | −90242.8 | + | 90242.8i | −0.161291 | + | 0.161291i | ||||
\(749\) | 135392.i | 0.241339i | ||||||||
\(750\) | 323449. | + | 198500.i | 0.575020 | + | 0.352889i | ||||
\(751\) | −37245.9 | −0.0660387 | −0.0330194 | − | 0.999455i | \(-0.510512\pi\) | ||||
−0.0330194 | + | 0.999455i | \(0.510512\pi\) | |||||||
\(752\) | −109169. | − | 109169.i | −0.193047 | − | 0.193047i | ||||
\(753\) | 53862.8 | − | 53862.8i | 0.0949946 | − | 0.0949946i | ||||
\(754\) | 585981.i | 1.03072i | ||||||||
\(755\) | −332824. | + | 389515.i | −0.583875 | + | 0.683330i | ||||
\(756\) | −38484.9 | −0.0673359 | ||||||||
\(757\) | −133738. | − | 133738.i | −0.233380 | − | 0.233380i | 0.580722 | − | 0.814102i | \(-0.302770\pi\) |
−0.814102 | + | 0.580722i | \(0.802770\pi\) | |||||||
\(758\) | 714192. | − | 714192.i | 1.24302 | − | 1.24302i | ||||
\(759\) | 161802.i | 0.280868i | ||||||||
\(760\) | 212719. | − | 16694.8i | 0.368281 | − | 0.0289038i | ||||
\(761\) | 969173. | 1.67352 | 0.836762 | − | 0.547567i | \(-0.184446\pi\) | ||||
0.836762 | + | 0.547567i | \(0.184446\pi\) | |||||||
\(762\) | 146976. | + | 146976.i | 0.253126 | + | 0.253126i | ||||
\(763\) | 397946. | − | 397946.i | 0.683557 | − | 0.683557i | ||||
\(764\) | 258761.i | 0.443315i | ||||||||
\(765\) | 20835.6 | + | 265478.i | 0.0356026 | + | 0.453635i | ||||
\(766\) | −45897.5 | −0.0782225 | ||||||||
\(767\) | −462193. | − | 462193.i | −0.785657 | − | 0.785657i | ||||
\(768\) | 233074. | − | 233074.i | 0.395159 | − | 0.395159i | ||||
\(769\) | 572412.i | 0.967956i | 0.875080 | + | 0.483978i | \(0.160809\pi\) | ||||
−0.875080 | + | 0.483978i | \(0.839191\pi\) | |||||||
\(770\) | 230477. | + | 196933.i | 0.388729 | + | 0.332152i | ||||
\(771\) | −351376. | −0.591104 | ||||||||
\(772\) | 107904. | + | 107904.i | 0.181051 | + | 0.181051i | ||||
\(773\) | 345426. | − | 345426.i | 0.578090 | − | 0.578090i | −0.356287 | − | 0.934377i | \(-0.615957\pi\) |
0.934377 | + | 0.356287i | \(0.115957\pi\) | |||||||
\(774\) | − | 18607.3i | − | 0.0310600i | ||||||
\(775\) | −149970. | − | 949546.i | −0.249691 | − | 1.58093i | ||||
\(776\) | 234552. | 0.389508 | ||||||||
\(777\) | 404742. | + | 404742.i | 0.670403 | + | 0.670403i | ||||
\(778\) | −568471. | + | 568471.i | −0.939180 | + | 0.939180i | ||||
\(779\) | 55328.5i | 0.0911746i | ||||||||
\(780\) | 113015. | − | 132266.i | 0.185758 | − | 0.217399i | ||||
\(781\) | 79053.7 | 0.129605 | ||||||||
\(782\) | −734076. | − | 734076.i | −1.20040 | − | 1.20040i | ||||
\(783\) | −54311.5 | + | 54311.5i | −0.0885867 | + | 0.0885867i | ||||
\(784\) | − | 63446.5i | − | 0.103223i | ||||||
\(785\) | −82488.9 | + | 6473.99i | −0.133862 | + | 0.0105059i | ||||
\(786\) | −534720. | −0.865528 | ||||||||
\(787\) | −172088. | − | 172088.i | −0.277843 | − | 0.277843i | 0.554404 | − | 0.832248i | \(-0.312946\pi\) |
−0.832248 | + | 0.554404i | \(0.812946\pi\) | |||||||
\(788\) | −107933. | + | 107933.i | −0.173821 | + | 0.173821i | ||||
\(789\) | 337094.i | 0.541498i | ||||||||
\(790\) | 44387.0 | + | 565562.i | 0.0711217 | + | 0.906204i | ||||
\(791\) | −593893. | −0.949195 | ||||||||
\(792\) | −50107.7 | − | 50107.7i | −0.0798830 | − | 0.0798830i | ||||
\(793\) | 171208. | − | 171208.i | 0.272256 | − | 0.272256i | ||||
\(794\) | 314419.i | 0.498733i | ||||||||
\(795\) | −282834. | − | 241670.i | −0.447505 | − | 0.382374i | ||||
\(796\) | 405601. | 0.640137 | ||||||||
\(797\) | 296648. | + | 296648.i | 0.467009 | + | 0.467009i | 0.900944 | − | 0.433935i | \(-0.142875\pi\) |
−0.433935 | + | 0.900944i | \(0.642875\pi\) | |||||||
\(798\) | −144888. | + | 144888.i | −0.227524 | + | 0.227524i | ||||
\(799\) | − | 193130.i | − | 0.302521i | ||||||
\(800\) | 262794. | − | 361375.i | 0.410616 | − | 0.564648i | ||||
\(801\) | 140008. | 0.218217 | ||||||||
\(802\) | −640440. | − | 640440.i | −0.995703 | − | 0.995703i | ||||
\(803\) | 45006.7 | − | 45006.7i | 0.0697985 | − | 0.0697985i | ||||
\(804\) | 161449.i | 0.249760i | ||||||||
\(805\) | −428819. | + | 501861.i | −0.661732 | + | 0.774448i | ||||
\(806\) | −1.64630e6 | −2.53418 | ||||||||
\(807\) | −295023. | − | 295023.i | −0.453011 | − | 0.453011i | ||||
\(808\) | 258651. | − | 258651.i | 0.396178 | − | 0.396178i | ||||
\(809\) | 286471.i | 0.437707i | 0.975758 | + | 0.218854i | \(0.0702317\pi\) | ||||
−0.975758 | + | 0.218854i | \(0.929768\pi\) | |||||||
\(810\) | 84927.0 | − | 6665.33i | 0.129442 | − | 0.0101590i | ||||
\(811\) | −672778. | −1.02289 | −0.511447 | − | 0.859315i | \(-0.670890\pi\) | ||||
−0.511447 | + | 0.859315i | \(0.670890\pi\) | |||||||
\(812\) | −106192. | − | 106192.i | −0.161057 | − | 0.161057i | ||||
\(813\) | 147145. | − | 147145.i | 0.222619 | − | 0.222619i | ||||
\(814\) | − | 607222.i | − | 0.916428i | ||||||
\(815\) | 42332.9 | + | 539389.i | 0.0637328 | + | 0.812058i | ||||
\(816\) | 646492. | 0.970918 | ||||||||
\(817\) | −18752.3 | − | 18752.3i | −0.0280938 | − | 0.0280938i | ||||
\(818\) | 876.729 | − | 876.729i | 0.00131026 | − | 0.00131026i | ||||
\(819\) | − | 289980.i | − | 0.432314i | ||||||
\(820\) | 34193.4 | + | 29216.8i | 0.0508528 | + | 0.0434515i | ||||
\(821\) | −270459. | −0.401251 | −0.200625 | − | 0.979668i | \(-0.564297\pi\) | ||||
−0.200625 | + | 0.979668i | \(0.564297\pi\) | |||||||
\(822\) | −277466. | − | 277466.i | −0.410645 | − | 0.410645i | ||||
\(823\) | 445888. | − | 445888.i | 0.658304 | − | 0.658304i | −0.296675 | − | 0.954979i | \(-0.595878\pi\) |
0.954979 | + | 0.296675i | \(0.0958777\pi\) | |||||||
\(824\) | 342134.i | 0.503897i | ||||||||
\(825\) | −145278. | − | 105647.i | −0.213448 | − | 0.155221i | ||||
\(826\) | 625797. | 0.917220 | ||||||||
\(827\) | −505149. | − | 505149.i | −0.738599 | − | 0.738599i | 0.233708 | − | 0.972307i | \(-0.424914\pi\) |
−0.972307 | + | 0.233708i | \(0.924914\pi\) | |||||||
\(828\) | −62861.5 | + | 62861.5i | −0.0916905 | + | 0.0916905i | ||||
\(829\) | 176611.i | 0.256986i | 0.991710 | + | 0.128493i | \(0.0410139\pi\) | ||||
−0.991710 | + | 0.128493i | \(0.958986\pi\) | |||||||
\(830\) | 141340. | − | 165415.i | 0.205167 | − | 0.240114i | ||||
\(831\) | −366468. | −0.530682 | ||||||||
\(832\) | 275945. | + | 275945.i | 0.398636 | + | 0.398636i | ||||
\(833\) | 56121.5 | − | 56121.5i | 0.0808797 | − | 0.0808797i | ||||
\(834\) | 10496.5i | 0.0150908i | ||||||||
\(835\) | 826816. | − | 64891.1i | 1.18587 | − | 0.0930705i | ||||
\(836\) | 58187.6 | 0.0832564 | ||||||||
\(837\) | −152587. | − | 152587.i | −0.217804 | − | 0.217804i | ||||
\(838\) | −102216. | + | 102216.i | −0.145557 | + | 0.145557i | ||||
\(839\) | 153954.i | 0.218709i | 0.994003 | + | 0.109354i | \(0.0348783\pi\) | ||||
−0.994003 | + | 0.109354i | \(0.965122\pi\) | |||||||
\(840\) | −22620.2 | − | 288217.i | −0.0320581 | − | 0.408471i | ||||
\(841\) | 407556. | 0.576229 | ||||||||
\(842\) | −206475. | − | 206475.i | −0.291235 | − | 0.291235i | ||||
\(843\) | −47185.1 | + | 47185.1i | −0.0663972 | + | 0.0663972i | ||||
\(844\) | − | 113802.i | − | 0.159758i | ||||||
\(845\) | 453762. | + | 387720.i | 0.635498 | + | 0.543006i | ||||
\(846\) | −61782.6 | −0.0863228 | ||||||||
\(847\) | 384103. | + | 384103.i | 0.535403 | + | 0.535403i | ||||
\(848\) | −638635. | + | 638635.i | −0.888098 | + | 0.888098i | ||||
\(849\) | 263996.i | 0.366254i | ||||||||
\(850\) | 1.13841e6 | − | 179800.i | 1.57566 | − | 0.248858i | ||||
\(851\) | 1.32222e6 | 1.82576 | ||||||||
\(852\) | 30713.0 | + | 30713.0i | 0.0423100 | + | 0.0423100i | ||||
\(853\) | 601023. | − | 601023.i | 0.826025 | − | 0.826025i | −0.160940 | − | 0.986964i | \(-0.551452\pi\) |
0.986964 | + | 0.160940i | \(0.0514524\pi\) | |||||||
\(854\) | 231811.i | 0.317846i | ||||||||
\(855\) | 78871.5 | − | 92306.1i | 0.107892 | − | 0.126269i | ||||
\(856\) | −136973. | −0.186934 | ||||||||
\(857\) | 479752. | + | 479752.i | 0.653214 | + | 0.653214i | 0.953766 | − | 0.300552i | \(-0.0971708\pi\) |
−0.300552 | + | 0.953766i | \(0.597171\pi\) | |||||||
\(858\) | −217524. | + | 217524.i | −0.295483 | + | 0.295483i | ||||
\(859\) | 925363.i | 1.25408i | 0.778987 | + | 0.627041i | \(0.215734\pi\) | ||||
−0.778987 | + | 0.627041i | \(0.784266\pi\) | |||||||
\(860\) | −21491.5 | + | 1686.72i | −0.0290582 | + | 0.00228058i | ||||
\(861\) | 74965.7 | 0.101124 | ||||||||
\(862\) | 228953. | + | 228953.i | 0.308129 | + | 0.308129i | ||||
\(863\) | −882185. | + | 882185.i | −1.18451 | + | 1.18451i | −0.205944 | + | 0.978564i | \(0.566026\pi\) |
−0.978564 | + | 0.205944i | \(0.933974\pi\) | |||||||
\(864\) | − | 100301.i | − | 0.134362i | ||||||
\(865\) | −56743.0 | − | 722997.i | −0.0758368 | − | 0.966282i | ||||
\(866\) | −733498. | −0.978054 | ||||||||
\(867\) | 264977. | + | 264977.i | 0.352509 | + | 0.352509i | ||||
\(868\) | 298343. | − | 298343.i | 0.395983 | − | 0.395983i | ||||
\(869\) | − | 268522.i | − | 0.355582i | ||||||
\(870\) | 252732. | + | 215948.i | 0.333904 | + | 0.285306i | ||||
\(871\) | −1.21650e6 | −1.60352 | ||||||||
\(872\) | 402595. | + | 402595.i | 0.529463 | + | 0.529463i | ||||
\(873\) | 94373.6 | − | 94373.6i | 0.123829 | − | 0.123829i | ||||
\(874\) | 473324.i | 0.619635i | ||||||||
\(875\) | −170615. | − | 712710.i | −0.222844 | − | 0.930887i | ||||
\(876\) | 34970.9 | 0.0455721 | ||||||||
\(877\) | −272599. | − | 272599.i | −0.354426 | − | 0.354426i | 0.507328 | − | 0.861753i | \(-0.330633\pi\) |
−0.861753 | + | 0.507328i | \(0.830633\pi\) | |||||||
\(878\) | 555265. | − | 555265.i | 0.720297 | − | 0.720297i | ||||
\(879\) | 370113.i | 0.479023i | ||||||||
\(880\) | −283292. | + | 331547.i | −0.365822 | + | 0.428134i | ||||
\(881\) | −557598. | −0.718405 | −0.359202 | − | 0.933260i | \(-0.616951\pi\) | ||||
−0.359202 | + | 0.933260i | \(0.616951\pi\) | |||||||
\(882\) | −17953.4 | − | 17953.4i | −0.0230786 | − | 0.0230786i | ||||
\(883\) | 180236. | − | 180236.i | 0.231164 | − | 0.231164i | −0.582014 | − | 0.813179i | \(-0.697735\pi\) |
0.813179 | + | 0.582014i | \(0.197735\pi\) | |||||||
\(884\) | − | 528347.i | − | 0.676107i | ||||||
\(885\) | −369672. | + | 29013.0i | −0.471987 | + | 0.0370430i | ||||
\(886\) | 438125. | 0.558124 | ||||||||
\(887\) | 170589. | + | 170589.i | 0.216822 | + | 0.216822i | 0.807158 | − | 0.590336i | \(-0.201005\pi\) |
−0.590336 | + | 0.807158i | \(0.701005\pi\) | |||||||
\(888\) | −409471. | + | 409471.i | −0.519274 | + | 0.519274i | ||||
\(889\) | − | 401385.i | − | 0.507876i | ||||||
\(890\) | −47411.6 | − | 604099.i | −0.0598555 | − | 0.762655i | ||||
\(891\) | −40322.3 | −0.0507914 | ||||||||
\(892\) | 308407. | + | 308407.i | 0.387610 | + | 0.387610i | ||||
\(893\) | −62264.0 | + | 62264.0i | −0.0780790 | + | 0.0780790i | ||||
\(894\) | 421907.i | 0.527887i | ||||||||
\(895\) | 997105. | + | 851983.i | 1.24479 | + | 1.06362i | ||||
\(896\) | −910124. | −1.13366 | ||||||||
\(897\) | −473655. | − | 473655.i | −0.588678 | − | 0.588678i | ||||
\(898\) | −702977. | + | 702977.i | −0.871743 | + | 0.871743i | ||||
\(899\) | − | 842069.i | − | 1.04191i | ||||||
\(900\) | −15396.9 | − | 97486.5i | −0.0190085 | − | 0.120354i | ||||
\(901\) | −1.12981e6 | −1.39173 | ||||||||
\(902\) | −56234.3 | − | 56234.3i | −0.0691176 | − | 0.0691176i | ||||
\(903\) | −25407.9 | + | 25407.9i | −0.0311597 | + | 0.0311597i | ||||
\(904\) | − | 600832.i | − | 0.735218i | ||||||
\(905\) | 978362. | − | 1.14501e6i | 1.19455 | − | 1.39802i | ||||
\(906\) | 497752. | 0.606396 | ||||||||
\(907\) | 399726. | + | 399726.i | 0.485901 | + | 0.485901i | 0.907010 | − | 0.421109i | \(-0.138359\pi\) |
−0.421109 | + | 0.907010i | \(0.638359\pi\) | |||||||
\(908\) | −359317. | + | 359317.i | −0.435819 | + | 0.435819i | ||||
\(909\) | − | 208139.i | − | 0.251899i | ||||||
\(910\) | −1.25119e6 | + | 98196.9i | −1.51091 | + | 0.118581i | ||||
\(911\) | 1.58194e6 | 1.90614 | 0.953068 | − | 0.302757i | \(-0.0979071\pi\) | ||||
0.953068 | + | 0.302757i | \(0.0979071\pi\) | |||||||
\(912\) | −208425. | − | 208425.i | −0.250588 | − | 0.250588i | ||||
\(913\) | −72821.7 | + | 72821.7i | −0.0873613 | + | 0.0873613i | ||||
\(914\) | 1.24923e6i | 1.49537i | ||||||||
\(915\) | −10747.1 | − | 136936.i | −0.0128366 | − | 0.163559i | ||||
\(916\) | −577501. | −0.688274 | ||||||||
\(917\) | 730149. | + | 730149.i | 0.868306 | + | 0.868306i | ||||
\(918\) | 182937. | − | 182937.i | 0.217078 | − | 0.217078i | ||||
\(919\) | − | 1.60006e6i | − | 1.89455i | −0.320420 | − | 0.947276i | \(-0.603824\pi\) | ||
0.320420 | − | 0.947276i | \(-0.396176\pi\) | |||||||
\(920\) | −507725. | − | 433829.i | −0.599864 | − | 0.512558i | ||||
\(921\) | 555409. | 0.654778 | ||||||||
\(922\) | −672485. | − | 672485.i | −0.791081 | − | 0.791081i | ||||
\(923\) | −231419. | + | 231419.i | −0.271641 | + | 0.271641i | ||||
\(924\) | − | 78839.5i | − | 0.0923422i | ||||||
\(925\) | −863329. | + | 1.18718e6i | −1.00900 | + | 1.38751i | ||||
\(926\) | 1.85234e6 | 2.16023 | ||||||||
\(927\) | 137660. | + | 137660.i | 0.160194 | + | 0.160194i | ||||
\(928\) | 276761. | − | 276761.i | 0.321372 | − | 0.321372i | ||||
\(929\) | − | 1.50251e6i | − | 1.74095i | −0.492209 | − | 0.870477i | \(-0.663811\pi\) | ||
0.492209 | − | 0.870477i | \(-0.336189\pi\) | |||||||
\(930\) | −606701. | + | 710043.i | −0.701469 | + | 0.820954i | ||||
\(931\) | −36186.6 | −0.0417492 | ||||||||
\(932\) | 157101. | + | 157101.i | 0.180862 | + | 0.180862i | ||||
\(933\) | 394029. | − | 394029.i | 0.452652 | − | 0.452652i | ||||
\(934\) | 166210.i | 0.190530i | ||||||||
\(935\) | −543855. | + | 42683.4i | −0.622100 | + | 0.0488243i | ||||
\(936\) | 293368. | 0.334858 | ||||||||
\(937\) | 45116.6 | + | 45116.6i | 0.0513874 | + | 0.0513874i | 0.732334 | − | 0.680946i | \(-0.238431\pi\) |
−0.680946 | + | 0.732334i | \(0.738431\pi\) | |||||||
\(938\) | 823554. | − | 823554.i | 0.936022 | − | 0.936022i | ||||
\(939\) | − | 182595.i | − | 0.207089i | ||||||
\(940\) | 5600.47 | + | 71358.9i | 0.00633824 | + | 0.0807593i | ||||
\(941\) | −1.62275e6 | −1.83262 | −0.916312 | − | 0.400466i | \(-0.868848\pi\) | ||||
−0.916312 | + | 0.400466i | \(0.868848\pi\) | |||||||
\(942\) | 56841.8 | + | 56841.8i | 0.0640569 | + | 0.0640569i | ||||
\(943\) | 122450. | − | 122450.i | 0.137700 | − | 0.137700i | ||||
\(944\) | 900224.i | 1.01020i | ||||||||
\(945\) | −125067. | − | 106865.i | −0.140049 | − | 0.119666i | ||||
\(946\) | 38118.7 | 0.0425947 | ||||||||
\(947\) | −868195. | − | 868195.i | −0.968094 | − | 0.968094i | 0.0314128 | − | 0.999506i | \(-0.489999\pi\) |
−0.999506 | + | 0.0314128i | \(0.989999\pi\) | |||||||
\(948\) | 104323. | − | 104323.i | 0.116081 | − | 0.116081i | ||||
\(949\) | 263502.i | 0.292585i | ||||||||
\(950\) | −424985. | − | 309052.i | −0.470898 | − | 0.342440i | ||||
\(951\) | −55989.2 | −0.0619075 | ||||||||
\(952\) | −620834. | − | 620834.i | −0.685017 | − | 0.685017i | ||||
\(953\) | −221674. | + | 221674.i | −0.244078 | + | 0.244078i | −0.818535 | − | 0.574457i | \(-0.805213\pi\) |
0.574457 | + | 0.818535i | \(0.305213\pi\) | |||||||
\(954\) | 361427.i | 0.397122i | ||||||||
\(955\) | −718528. | + | 840918.i | −0.787838 | + | 0.922034i | ||||
\(956\) | −379344. | −0.415066 | ||||||||
\(957\) | −111262. | − | 111262.i | −0.121485 | − | 0.121485i | ||||
\(958\) | 57122.1 | − | 57122.1i | 0.0622406 | − | 0.0622406i | ||||
\(959\) | 757749.i | 0.823926i | ||||||||
\(960\) | 220707. | − | 17321.8i | 0.239483 | − | 0.0187953i | ||||
\(961\) | 1.44225e6 | 1.56168 | ||||||||
\(962\) | 1.77756e6 | + | 1.77756e6i | 1.92077 | + | 1.92077i | ||||
\(963\) | −55112.1 | + | 55112.1i | −0.0594284 | + | 0.0594284i | ||||
\(964\) | 68818.1i | 0.0740540i | ||||||||
\(965\) | 51036.8 | + | 650290.i | 0.0548061 | + | 0.698317i | ||||
\(966\) | 641316. | 0.687255 | ||||||||
\(967\) | 310704. | + | 310704.i | 0.332272 | + | 0.332272i | 0.853449 | − | 0.521176i | \(-0.174507\pi\) |
−0.521176 | + | 0.853449i | \(0.674507\pi\) | |||||||
\(968\) | −388590. | + | 388590.i | −0.414707 | + | 0.414707i | ||||
\(969\) | − | 368725.i | − | 0.392694i | ||||||
\(970\) | −439155. | − | 375239.i | −0.466740 | − | 0.398809i | ||||
\(971\) | −993419. | −1.05364 | −0.526822 | − | 0.849976i | \(-0.676617\pi\) | ||||
−0.526822 | + | 0.849976i | \(0.676617\pi\) | |||||||
\(972\) | −15665.5 | − | 15665.5i | −0.0165811 | − | 0.0165811i | ||||
\(973\) | 14332.7 | − | 14332.7i | 0.0151392 | − | 0.0151392i | ||||
\(974\) | − | 1.65864e6i | − | 1.74837i | ||||||
\(975\) | 734551. | − | 116014.i | 0.772703 | − | 0.122040i | ||||
\(976\) | −333465. | −0.350067 | ||||||||
\(977\) | −575998. | − | 575998.i | −0.603437 | − | 0.603437i | 0.337786 | − | 0.941223i | \(-0.390322\pi\) |
−0.941223 | + | 0.337786i | \(0.890322\pi\) | |||||||
\(978\) | 371684. | − | 371684.i | 0.388594 | − | 0.388594i | ||||
\(979\) | 286819.i | 0.299256i | ||||||||
\(980\) | −19108.7 | + | 22363.6i | −0.0198966 | + | 0.0232857i | ||||
\(981\) | 323973. | 0.336644 | ||||||||
\(982\) | −578996. | − | 578996.i | −0.600416 | − | 0.600416i | ||||
\(983\) | −164785. | + | 164785.i | −0.170533 | + | 0.170533i | −0.787214 | − | 0.616680i | \(-0.788477\pi\) |
0.616680 | + | 0.787214i | \(0.288477\pi\) | |||||||
\(984\) | 75841.5i | 0.0783280i | ||||||||
\(985\) | −650468. | + | 51050.8i | −0.670430 | + | 0.0526175i | ||||
\(986\) | 1.00956e6 | 1.03843 | ||||||||
\(987\) | 84362.8 | + | 84362.8i | 0.0865998 | + | 0.0865998i | ||||
\(988\) | −170336. | + | 170336.i | −0.174499 | + | 0.174499i | ||||
\(989\) | 83003.0i | 0.0848596i | ||||||||
\(990\) | 13654.5 | + | 173980.i | 0.0139317 | + | 0.177513i | ||||
\(991\) | 1.06880e6 | 1.08830 | 0.544148 | − | 0.838989i | \(-0.316853\pi\) | ||||
0.544148 | + | 0.838989i | \(0.316853\pi\) | |||||||
\(992\) | 777551. | + | 777551.i | 0.790143 | + | 0.790143i | ||||
\(993\) | 104782. | − | 104782.i | 0.106265 | − | 0.106265i | ||||
\(994\) | − | 313335.i | − | 0.317130i | ||||||
\(995\) | 1.31811e6 | + | 1.12627e6i | 1.33140 | + | 1.13762i | ||||
\(996\) | −56583.6 | −0.0570390 | ||||||||
\(997\) | 205698. | + | 205698.i | 0.206938 | + | 0.206938i | 0.802965 | − | 0.596027i | \(-0.203255\pi\) |
−0.596027 | + | 0.802965i | \(0.703255\pi\) | |||||||
\(998\) | −726256. | + | 726256.i | −0.729170 | + | 0.729170i | ||||
\(999\) | 329506.i | 0.330166i |
(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 | 15.5.f.a.7.3 | ✓ | 8 | |
3.2 | odd | 2 | 45.5.g.e.37.2 | 8 | |||
4.3 | odd | 2 | 240.5.bg.c.97.1 | 8 | |||
5.2 | odd | 4 | 75.5.f.e.43.2 | 8 | |||
5.3 | odd | 4 | inner | 15.5.f.a.13.3 | yes | 8 | |
5.4 | even | 2 | 75.5.f.e.7.2 | 8 | |||
15.2 | even | 4 | 225.5.g.m.118.3 | 8 | |||
15.8 | even | 4 | 45.5.g.e.28.2 | 8 | |||
15.14 | odd | 2 | 225.5.g.m.82.3 | 8 | |||
20.3 | even | 4 | 240.5.bg.c.193.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.5.f.a.7.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
15.5.f.a.13.3 | yes | 8 | 5.3 | odd | 4 | inner | |
45.5.g.e.28.2 | 8 | 15.8 | even | 4 | |||
45.5.g.e.37.2 | 8 | 3.2 | odd | 2 | |||
75.5.f.e.7.2 | 8 | 5.4 | even | 2 | |||
75.5.f.e.43.2 | 8 | 5.2 | odd | 4 | |||
225.5.g.m.82.3 | 8 | 15.14 | odd | 2 | |||
225.5.g.m.118.3 | 8 | 15.2 | even | 4 | |||
240.5.bg.c.97.1 | 8 | 4.3 | odd | 2 | |||
240.5.bg.c.193.1 | 8 | 20.3 | even | 4 |