Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,5,Mod(5,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.i (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: | \(4.96175822802\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(30\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 5.12 | ||
Character | \(\chi\) | \(=\) | 48.5 |
Dual form | 48.5.i.a.29.12 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96807 | + | 3.48234i | −0.492017 | + | 0.870586i | ||||
\(3\) | 8.97524 | − | 0.667113i | 0.997249 | − | 0.0741236i | ||||
\(4\) | −8.25342 | − | 13.7070i | −0.515838 | − | 0.856686i | ||||
\(5\) | −17.7419 | + | 17.7419i | −0.709677 | + | 0.709677i | −0.966467 | − | 0.256790i | \(-0.917335\pi\) |
0.256790 | + | 0.966467i | \(0.417335\pi\) | |||||||
\(6\) | −15.3408 | + | 32.5678i | −0.426133 | + | 0.904661i | ||||
\(7\) | 66.4694i | 1.35652i | 0.734823 | + | 0.678259i | \(0.237265\pi\) | ||||
−0.734823 | + | 0.678259i | \(0.762735\pi\) | |||||||
\(8\) | 63.9757 | − | 1.76496i | 0.999620 | − | 0.0275775i | ||||
\(9\) | 80.1099 | − | 11.9750i | 0.989011 | − | 0.147839i | ||||
\(10\) | −26.8661 | − | 96.7008i | −0.268661 | − | 0.967008i | ||||
\(11\) | −124.446 | + | 124.446i | −1.02848 | + | 1.02848i | −0.0288939 | + | 0.999582i | \(0.509198\pi\) |
−0.999582 | + | 0.0288939i | \(0.990802\pi\) | |||||||
\(12\) | −83.2205 | − | 117.517i | −0.577920 | − | 0.816093i | ||||
\(13\) | −64.0011 | + | 64.0011i | −0.378705 | + | 0.378705i | −0.870635 | − | 0.491930i | \(-0.836292\pi\) |
0.491930 | + | 0.870635i | \(0.336292\pi\) | |||||||
\(14\) | −231.469 | − | 130.816i | −1.18097 | − | 0.667430i | ||||
\(15\) | −147.402 | + | 171.074i | −0.655121 | + | 0.760329i | ||||
\(16\) | −119.762 | + | 226.259i | −0.467821 | + | 0.883823i | ||||
\(17\) | − | 74.1965i | − | 0.256735i | −0.991727 | − | 0.128368i | \(-0.959026\pi\) | ||
0.991727 | − | 0.128368i | \(-0.0409738\pi\) | |||||||
\(18\) | −115.961 | + | 302.538i | −0.357904 | + | 0.933759i | ||||
\(19\) | 442.958 | − | 442.958i | 1.22703 | − | 1.22703i | 0.261947 | − | 0.965082i | \(-0.415635\pi\) |
0.965082 | − | 0.261947i | \(-0.0843646\pi\) | |||||||
\(20\) | 389.620 | + | 96.7566i | 0.974049 | + | 0.241892i | ||||
\(21\) | 44.3426 | + | 596.579i | 0.100550 | + | 1.35279i | ||||
\(22\) | −188.445 | − | 678.280i | −0.389349 | − | 1.40140i | ||||
\(23\) | −181.796 | −0.343660 | −0.171830 | − | 0.985127i | \(-0.554968\pi\) | ||||
−0.171830 | + | 0.985127i | \(0.554968\pi\) | |||||||
\(24\) | 573.020 | − | 58.5199i | 0.994826 | − | 0.101597i | ||||
\(25\) | − | 4.55190i | − | 0.00728304i | ||||||
\(26\) | −96.9153 | − | 348.832i | −0.143366 | − | 0.516024i | ||||
\(27\) | 711.017 | − | 160.921i | 0.975332 | − | 0.220742i | ||||
\(28\) | 911.095 | − | 548.600i | 1.16211 | − | 0.699745i | ||||
\(29\) | 320.985 | + | 320.985i | 0.381671 | + | 0.381671i | 0.871704 | − | 0.490033i | \(-0.163015\pi\) |
−0.490033 | + | 0.871704i | \(0.663015\pi\) | |||||||
\(30\) | −305.640 | − | 849.990i | −0.339600 | − | 0.944433i | ||||
\(31\) | 1493.03 | 1.55362 | 0.776811 | − | 0.629734i | \(-0.216836\pi\) | ||||
0.776811 | + | 0.629734i | \(0.216836\pi\) | |||||||
\(32\) | −552.210 | − | 862.346i | −0.539268 | − | 0.842134i | ||||
\(33\) | −1033.91 | + | 1199.95i | −0.949413 | + | 1.10188i | ||||
\(34\) | 258.378 | + | 146.024i | 0.223510 | + | 0.126318i | ||||
\(35\) | −1179.30 | − | 1179.30i | −0.962690 | − | 0.962690i | ||||
\(36\) | −825.321 | − | 999.230i | −0.636822 | − | 0.771011i | ||||
\(37\) | 490.065 | + | 490.065i | 0.357973 | + | 0.357973i | 0.863065 | − | 0.505092i | \(-0.168542\pi\) |
−0.505092 | + | 0.863065i | \(0.668542\pi\) | |||||||
\(38\) | 670.759 | + | 2414.30i | 0.464515 | + | 1.67195i | ||||
\(39\) | −531.730 | + | 617.122i | −0.349592 | + | 0.405734i | ||||
\(40\) | −1103.74 | + | 1166.37i | −0.689836 | + | 0.728978i | ||||
\(41\) | 1104.51 | 0.657054 | 0.328527 | − | 0.944495i | \(-0.393448\pi\) | ||||
0.328527 | + | 0.944495i | \(0.393448\pi\) | |||||||
\(42\) | −2164.76 | − | 1019.69i | −1.22719 | − | 0.578057i | ||||
\(43\) | −1274.62 | − | 1274.62i | −0.689359 | − | 0.689359i | 0.272732 | − | 0.962090i | \(-0.412073\pi\) |
−0.962090 | + | 0.272732i | \(0.912073\pi\) | |||||||
\(44\) | 2732.87 | + | 678.672i | 1.41161 | + | 0.350553i | ||||
\(45\) | −1208.84 | + | 1633.76i | −0.596960 | + | 0.806797i | ||||
\(46\) | 357.788 | − | 633.077i | 0.169087 | − | 0.299186i | ||||
\(47\) | − | 2133.60i | − | 0.965868i | −0.875657 | − | 0.482934i | \(-0.839571\pi\) | ||
0.875657 | − | 0.482934i | \(-0.160429\pi\) | |||||||
\(48\) | −923.955 | + | 2110.62i | −0.401022 | + | 0.916068i | ||||
\(49\) | −2017.18 | −0.840144 | ||||||||
\(50\) | 15.8513 | + | 8.95844i | 0.00634051 | + | 0.00358338i | ||||
\(51\) | −49.4975 | − | 665.932i | −0.0190302 | − | 0.256029i | ||||
\(52\) | 1405.49 | + | 349.034i | 0.519782 | + | 0.129081i | ||||
\(53\) | −707.634 | + | 707.634i | −0.251917 | + | 0.251917i | −0.821756 | − | 0.569839i | \(-0.807005\pi\) |
0.569839 | + | 0.821756i | \(0.307005\pi\) | |||||||
\(54\) | −838.949 | + | 2792.71i | −0.287705 | + | 0.957719i | ||||
\(55\) | − | 4415.81i | − | 1.45977i | ||||||
\(56\) | 117.316 | + | 4252.43i | 0.0374094 | + | 1.35600i | ||||
\(57\) | 3680.15 | − | 4271.15i | 1.13270 | − | 1.31461i | ||||
\(58\) | −1749.50 | + | 486.060i | −0.520066 | + | 0.144489i | ||||
\(59\) | 2258.64 | − | 2258.64i | 0.648848 | − | 0.648848i | −0.303867 | − | 0.952715i | \(-0.598278\pi\) |
0.952715 | + | 0.303867i | \(0.0982777\pi\) | |||||||
\(60\) | 3561.48 | + | 608.494i | 0.989299 | + | 0.169026i | ||||
\(61\) | −2631.71 | + | 2631.71i | −0.707258 | + | 0.707258i | −0.965958 | − | 0.258700i | \(-0.916706\pi\) |
0.258700 | + | 0.965958i | \(0.416706\pi\) | |||||||
\(62\) | −2938.39 | + | 5199.24i | −0.764409 | + | 1.35256i | ||||
\(63\) | 795.971 | + | 5324.86i | 0.200547 | + | 1.34161i | ||||
\(64\) | 4089.77 | − | 225.829i | 0.998479 | − | 0.0551340i | ||||
\(65\) | − | 2271.01i | − | 0.537516i | ||||||
\(66\) | −2143.83 | − | 5962.01i | −0.492155 | − | 1.36869i | ||||
\(67\) | −3764.72 | + | 3764.72i | −0.838654 | + | 0.838654i | −0.988682 | − | 0.150028i | \(-0.952064\pi\) |
0.150028 | + | 0.988682i | \(0.452064\pi\) | |||||||
\(68\) | −1017.01 | + | 612.375i | −0.219942 | + | 0.132434i | ||||
\(69\) | −1631.67 | + | 121.279i | −0.342715 | + | 0.0254734i | ||||
\(70\) | 6427.65 | − | 1785.78i | 1.31176 | − | 0.364444i | ||||
\(71\) | 900.771 | 0.178689 | 0.0893444 | − | 0.996001i | \(-0.471523\pi\) | ||||
0.0893444 | + | 0.996001i | \(0.471523\pi\) | |||||||
\(72\) | 5103.95 | − | 907.499i | 0.984558 | − | 0.175058i | ||||
\(73\) | 3774.93i | 0.708374i | 0.935175 | + | 0.354187i | \(0.115242\pi\) | ||||
−0.935175 | + | 0.354187i | \(0.884758\pi\) | |||||||
\(74\) | −2671.05 | + | 742.092i | −0.487775 | + | 0.135517i | ||||
\(75\) | −3.03663 | − | 40.8544i | −0.000539845 | − | 0.00726300i | ||||
\(76\) | −9727.52 | − | 2415.69i | −1.68413 | − | 0.418230i | ||||
\(77\) | −8271.83 | − | 8271.83i | −1.39515 | − | 1.39515i | ||||
\(78\) | −1102.55 | − | 3066.20i | −0.181221 | − | 0.503978i | ||||
\(79\) | 8699.16 | 1.39387 | 0.696936 | − | 0.717133i | \(-0.254546\pi\) | ||||
0.696936 | + | 0.717133i | \(0.254546\pi\) | |||||||
\(80\) | −1889.45 | − | 6139.08i | −0.295227 | − | 0.959231i | ||||
\(81\) | 6274.20 | − | 1918.63i | 0.956287 | − | 0.292430i | ||||
\(82\) | −2173.75 | + | 3846.27i | −0.323282 | + | 0.572022i | ||||
\(83\) | −7189.71 | − | 7189.71i | −1.04365 | − | 1.04365i | −0.999003 | − | 0.0446487i | \(-0.985783\pi\) |
−0.0446487 | − | 0.999003i | \(-0.514217\pi\) | |||||||
\(84\) | 7811.32 | − | 5531.62i | 1.10705 | − | 0.783960i | ||||
\(85\) | 1316.39 | + | 1316.39i | 0.182199 | + | 0.182199i | ||||
\(86\) | 6947.22 | − | 1930.13i | 0.939322 | − | 0.260969i | ||||
\(87\) | 3095.05 | + | 2666.79i | 0.408912 | + | 0.352330i | ||||
\(88\) | −7741.85 | + | 8181.13i | −0.999722 | + | 1.05645i | ||||
\(89\) | 9551.25 | 1.20581 | 0.602907 | − | 0.797811i | \(-0.294009\pi\) | ||||
0.602907 | + | 0.797811i | \(0.294009\pi\) | |||||||
\(90\) | −3310.24 | − | 7424.97i | −0.408671 | − | 0.916663i | ||||
\(91\) | −4254.12 | − | 4254.12i | −0.513720 | − | 0.513720i | ||||
\(92\) | 1500.44 | + | 2491.88i | 0.177273 | + | 0.294409i | ||||
\(93\) | 13400.3 | − | 996.020i | 1.54935 | − | 0.115160i | ||||
\(94\) | 7429.93 | + | 4199.08i | 0.840871 | + | 0.475224i | ||||
\(95\) | 15717.8i | 1.74159i | ||||||||
\(96\) | −5531.50 | − | 7371.37i | −0.600206 | − | 0.799845i | ||||
\(97\) | 6553.25 | 0.696488 | 0.348244 | − | 0.937404i | \(-0.386778\pi\) | ||||
0.348244 | + | 0.937404i | \(0.386778\pi\) | |||||||
\(98\) | 3969.96 | − | 7024.53i | 0.413365 | − | 0.731417i | ||||
\(99\) | −8479.09 | + | 11459.6i | −0.865125 | + | 1.16922i | ||||
\(100\) | −62.3927 | + | 37.5687i | −0.00623927 | + | 0.00375687i | ||||
\(101\) | −7694.15 | + | 7694.15i | −0.754255 | + | 0.754255i | −0.975270 | − | 0.221016i | \(-0.929063\pi\) |
0.221016 | + | 0.975270i | \(0.429063\pi\) | |||||||
\(102\) | 2416.42 | + | 1138.23i | 0.232258 | + | 0.109403i | ||||
\(103\) | 2266.82i | 0.213669i | 0.994277 | + | 0.106835i | \(0.0340715\pi\) | ||||
−0.994277 | + | 0.106835i | \(0.965928\pi\) | |||||||
\(104\) | −3981.56 | + | 4207.47i | −0.368117 | + | 0.389005i | ||||
\(105\) | −11371.2 | − | 9797.74i | −1.03140 | − | 0.888684i | ||||
\(106\) | −1071.55 | − | 3856.90i | −0.0953677 | − | 0.343262i | ||||
\(107\) | 1220.58 | − | 1220.58i | 0.106610 | − | 0.106610i | −0.651790 | − | 0.758400i | \(-0.725981\pi\) |
0.758400 | + | 0.651790i | \(0.225981\pi\) | |||||||
\(108\) | −8074.06 | − | 8417.75i | −0.692220 | − | 0.721686i | ||||
\(109\) | −7683.11 | + | 7683.11i | −0.646672 | + | 0.646672i | −0.952187 | − | 0.305515i | \(-0.901171\pi\) |
0.305515 | + | 0.952187i | \(0.401171\pi\) | |||||||
\(110\) | 15377.4 | + | 8690.62i | 1.27086 | + | 0.718233i | ||||
\(111\) | 4725.38 | + | 4071.52i | 0.383522 | + | 0.330454i | ||||
\(112\) | −15039.3 | − | 7960.53i | −1.19892 | − | 0.634608i | ||||
\(113\) | 8741.53i | 0.684590i | 0.939592 | + | 0.342295i | \(0.111204\pi\) | ||||
−0.939592 | + | 0.342295i | \(0.888796\pi\) | |||||||
\(114\) | 7630.84 | + | 21221.5i | 0.587168 | + | 1.63292i | ||||
\(115\) | 3225.42 | − | 3225.42i | 0.243888 | − | 0.243888i | ||||
\(116\) | 1750.51 | − | 7048.96i | 0.130092 | − | 0.523853i | ||||
\(117\) | −4360.71 | + | 5893.54i | −0.318556 | + | 0.430531i | ||||
\(118\) | 3420.20 | + | 12310.5i | 0.245633 | + | 0.884122i | ||||
\(119\) | 4931.80 | 0.348266 | ||||||||
\(120\) | −9128.21 | + | 11204.7i | −0.633904 | + | 0.778106i | ||||
\(121\) | − | 16332.4i | − | 1.11553i | ||||||
\(122\) | −3985.13 | − | 14343.9i | −0.267746 | − | 0.963711i | ||||
\(123\) | 9913.22 | − | 736.831i | 0.655246 | − | 0.0487032i | ||||
\(124\) | −12322.6 | − | 20464.9i | −0.801418 | − | 1.33097i | ||||
\(125\) | −11007.9 | − | 11007.9i | −0.704508 | − | 0.704508i | ||||
\(126\) | −20109.5 | − | 7707.84i | −1.26666 | − | 0.485503i | ||||
\(127\) | −17352.2 | −1.07584 | −0.537918 | − | 0.842997i | \(-0.680789\pi\) | ||||
−0.537918 | + | 0.842997i | \(0.680789\pi\) | |||||||
\(128\) | −7262.53 | + | 14686.4i | −0.443270 | + | 0.896388i | ||||
\(129\) | −12290.4 | − | 10589.7i | −0.738560 | − | 0.636364i | ||||
\(130\) | 7908.42 | + | 4469.50i | 0.467954 | + | 0.264467i | ||||
\(131\) | 18962.2 | + | 18962.2i | 1.10496 | + | 1.10496i | 0.993803 | + | 0.111156i | \(0.0354555\pi\) |
0.111156 | + | 0.993803i | \(0.464545\pi\) | |||||||
\(132\) | 24981.0 | + | 4268.11i | 1.43371 | + | 0.244956i | ||||
\(133\) | 29443.1 | + | 29443.1i | 1.66449 | + | 1.66449i | ||||
\(134\) | −5700.82 | − | 20519.3i | −0.317488 | − | 1.14275i | ||||
\(135\) | −9759.77 | + | 15469.9i | −0.535515 | + | 0.848826i | ||||
\(136\) | −130.954 | − | 4746.77i | −0.00708012 | − | 0.256638i | ||||
\(137\) | 13867.7 | 0.738863 | 0.369431 | − | 0.929258i | \(-0.379552\pi\) | ||||
0.369431 | + | 0.929258i | \(0.379552\pi\) | |||||||
\(138\) | 2788.90 | − | 5920.71i | 0.146445 | − | 0.310896i | ||||
\(139\) | −6584.96 | − | 6584.96i | −0.340819 | − | 0.340819i | 0.515856 | − | 0.856675i | \(-0.327474\pi\) |
−0.856675 | + | 0.515856i | \(0.827474\pi\) | |||||||
\(140\) | −6431.36 | + | 25897.8i | −0.328130 | + | 1.32132i | ||||
\(141\) | −1423.35 | − | 19149.6i | −0.0715937 | − | 0.963211i | ||||
\(142\) | −1772.78 | + | 3136.79i | −0.0879180 | + | 0.155564i | ||||
\(143\) | − | 15929.3i | − | 0.778978i | ||||||
\(144\) | −6884.70 | + | 19559.7i | −0.332017 | + | 0.943274i | ||||
\(145\) | −11389.8 | −0.541726 | ||||||||
\(146\) | −13145.6 | − | 7429.31i | −0.616700 | − | 0.348532i | ||||
\(147\) | −18104.7 | + | 1345.69i | −0.837832 | + | 0.0622745i | ||||
\(148\) | 2672.60 | − | 10762.0i | 0.122014 | − | 0.491326i | ||||
\(149\) | 12299.5 | − | 12299.5i | 0.554006 | − | 0.554006i | −0.373589 | − | 0.927594i | \(-0.621873\pi\) |
0.927594 | + | 0.373589i | \(0.121873\pi\) | |||||||
\(150\) | 148.245 | + | 69.8296i | 0.00658868 | + | 0.00310354i | ||||
\(151\) | − | 14588.5i | − | 0.639820i | −0.947448 | − | 0.319910i | \(-0.896347\pi\) | ||
0.947448 | − | 0.319910i | \(-0.103653\pi\) | |||||||
\(152\) | 27556.7 | − | 29120.3i | 1.19272 | − | 1.26040i | ||||
\(153\) | −888.503 | − | 5943.88i | −0.0379556 | − | 0.253914i | ||||
\(154\) | 45084.9 | − | 12525.8i | 1.90103 | − | 0.528159i | ||||
\(155\) | −26489.2 | + | 26489.2i | −1.10257 | + | 1.10257i | ||||
\(156\) | 12847.5 | + | 2195.04i | 0.527920 | + | 0.0901974i | ||||
\(157\) | 5811.82 | − | 5811.82i | 0.235783 | − | 0.235783i | −0.579318 | − | 0.815101i | \(-0.696681\pi\) |
0.815101 | + | 0.579318i | \(0.196681\pi\) | |||||||
\(158\) | −17120.5 | + | 30293.4i | −0.685809 | + | 1.21348i | ||||
\(159\) | −5879.11 | + | 6823.26i | −0.232551 | + | 0.269897i | ||||
\(160\) | 25096.9 | + | 5502.41i | 0.980349 | + | 0.214938i | ||||
\(161\) | − | 12083.9i | − | 0.466182i | ||||||
\(162\) | −5666.72 | + | 25624.9i | −0.215924 | + | 0.976410i | ||||
\(163\) | 26298.0 | − | 26298.0i | 0.989801 | − | 0.989801i | −0.0101471 | − | 0.999949i | \(-0.503230\pi\) |
0.999949 | + | 0.0101471i | \(0.00322999\pi\) | |||||||
\(164\) | −9115.96 | − | 15139.5i | −0.338934 | − | 0.562889i | ||||
\(165\) | −2945.84 | − | 39633.0i | −0.108204 | − | 1.45576i | ||||
\(166\) | 39186.9 | − | 10887.2i | 1.42208 | − | 0.395094i | ||||
\(167\) | 16926.2 | 0.606914 | 0.303457 | − | 0.952845i | \(-0.401859\pi\) | ||||
0.303457 | + | 0.952845i | \(0.401859\pi\) | |||||||
\(168\) | 3889.79 | + | 38088.3i | 0.137818 | + | 1.34950i | ||||
\(169\) | 20368.7i | 0.713165i | ||||||||
\(170\) | −7174.86 | + | 1993.37i | −0.248265 | + | 0.0689749i | ||||
\(171\) | 30180.9 | − | 40789.7i | 1.03214 | − | 1.39495i | ||||
\(172\) | −6951.24 | + | 27991.2i | −0.234966 | + | 0.946161i | ||||
\(173\) | 18944.8 | + | 18944.8i | 0.632993 | + | 0.632993i | 0.948818 | − | 0.315825i | \(-0.102281\pi\) |
−0.315825 | + | 0.948818i | \(0.602281\pi\) | |||||||
\(174\) | −15377.9 | + | 5529.62i | −0.507925 | + | 0.182640i | ||||
\(175\) | 302.562 | 0.00987958 | ||||||||
\(176\) | −13253.0 | − | 43060.8i | −0.427848 | − | 1.39013i | ||||
\(177\) | 18765.1 | − | 21778.6i | 0.598968 | − | 0.695158i | ||||
\(178\) | −18797.5 | + | 33260.7i | −0.593281 | + | 1.04976i | ||||
\(179\) | −13650.2 | − | 13650.2i | −0.426023 | − | 0.426023i | 0.461248 | − | 0.887271i | \(-0.347402\pi\) |
−0.887271 | + | 0.461248i | \(0.847402\pi\) | |||||||
\(180\) | 32371.1 | + | 3085.47i | 0.999107 | + | 0.0952306i | ||||
\(181\) | −40429.6 | − | 40429.6i | −1.23408 | − | 1.23408i | −0.962384 | − | 0.271694i | \(-0.912416\pi\) |
−0.271694 | − | 0.962384i | \(-0.587584\pi\) | |||||||
\(182\) | 23186.7 | − | 6441.90i | 0.699997 | − | 0.194478i | ||||
\(183\) | −21864.6 | + | 25375.8i | −0.652888 | + | 0.757737i | ||||
\(184\) | −11630.5 | + | 320.863i | −0.343530 | + | 0.00947730i | ||||
\(185\) | −17389.4 | −0.508090 | ||||||||
\(186\) | −22904.2 | + | 48624.7i | −0.662049 | + | 1.40550i | ||||
\(187\) | 9233.44 | + | 9233.44i | 0.264046 | + | 0.264046i | ||||
\(188\) | −29245.2 | + | 17609.5i | −0.827446 | + | 0.498232i | ||||
\(189\) | 10696.3 | + | 47260.9i | 0.299441 | + | 1.32306i | ||||
\(190\) | −54734.9 | − | 30933.8i | −1.51620 | − | 0.856891i | ||||
\(191\) | − | 42146.2i | − | 1.15529i | −0.816287 | − | 0.577647i | \(-0.803971\pi\) | ||
0.816287 | − | 0.577647i | \(-0.196029\pi\) | |||||||
\(192\) | 36556.0 | − | 4755.21i | 0.991645 | − | 0.128993i | ||||
\(193\) | −8055.74 | −0.216267 | −0.108134 | − | 0.994136i | \(-0.534487\pi\) | ||||
−0.108134 | + | 0.994136i | \(0.534487\pi\) | |||||||
\(194\) | −12897.2 | + | 22820.7i | −0.342684 | + | 0.606352i | ||||
\(195\) | −1515.02 | − | 20382.8i | −0.0398427 | − | 0.536038i | ||||
\(196\) | 16648.7 | + | 27649.5i | 0.433378 | + | 0.719739i | ||||
\(197\) | −21035.2 | + | 21035.2i | −0.542019 | + | 0.542019i | −0.924120 | − | 0.382102i | \(-0.875200\pi\) |
0.382102 | + | 0.924120i | \(0.375200\pi\) | |||||||
\(198\) | −23218.7 | − | 52080.3i | −0.592253 | − | 1.32844i | ||||
\(199\) | − | 39040.7i | − | 0.985851i | −0.870072 | − | 0.492925i | \(-0.835928\pi\) | ||
0.870072 | − | 0.492925i | \(-0.164072\pi\) | |||||||
\(200\) | −8.03392 | − | 291.211i | −0.000200848 | − | 0.00728027i | ||||
\(201\) | −31277.8 | + | 36300.8i | −0.774183 | + | 0.898511i | ||||
\(202\) | −11651.1 | − | 41936.3i | −0.285537 | − | 1.02775i | ||||
\(203\) | −21335.7 | + | 21335.7i | −0.517744 | + | 0.517744i | ||||
\(204\) | −8719.39 | + | 6174.67i | −0.209520 | + | 0.148373i | ||||
\(205\) | −19596.1 | + | 19596.1i | −0.466296 | + | 0.466296i | ||||
\(206\) | −7893.83 | − | 4461.25i | −0.186017 | − | 0.105129i | ||||
\(207\) | −14563.7 | + | 2177.01i | −0.339884 | + | 0.0508066i | ||||
\(208\) | −6815.89 | − | 22145.7i | −0.157542 | − | 0.511874i | ||||
\(209\) | 110248.i | 2.52394i | ||||||||
\(210\) | 56498.4 | − | 20315.7i | 1.28114 | − | 0.460674i | ||||
\(211\) | 5761.30 | − | 5761.30i | 0.129406 | − | 0.129406i | −0.639437 | − | 0.768843i | \(-0.720833\pi\) |
0.768843 | + | 0.639437i | \(0.220833\pi\) | |||||||
\(212\) | 15539.9 | + | 3859.12i | 0.345762 | + | 0.0858651i | ||||
\(213\) | 8084.63 | − | 600.916i | 0.178197 | − | 0.0132451i | ||||
\(214\) | 1848.30 | + | 6652.67i | 0.0403593 | + | 0.145268i | ||||
\(215\) | 45228.6 | 0.978444 | ||||||||
\(216\) | 45203.8 | − | 11549.9i | 0.968874 | − | 0.247555i | ||||
\(217\) | 99240.9i | 2.10752i | ||||||||
\(218\) | −11634.3 | − | 41876.1i | −0.244810 | − | 0.881157i | ||||
\(219\) | 2518.30 | + | 33880.9i | 0.0525073 | + | 0.706425i | ||||
\(220\) | −60527.4 | + | 36445.5i | −1.25057 | + | 0.753007i | ||||
\(221\) | 4748.66 | + | 4748.66i | 0.0972270 | + | 0.0972270i | ||||
\(222\) | −23478.3 | + | 8442.35i | −0.476388 | + | 0.171300i | ||||
\(223\) | 34855.2 | 0.700902 | 0.350451 | − | 0.936581i | \(-0.386028\pi\) | ||||
0.350451 | + | 0.936581i | \(0.386028\pi\) | |||||||
\(224\) | 57319.6 | − | 36705.1i | 1.14237 | − | 0.731527i | ||||
\(225\) | −54.5090 | − | 364.652i | −0.00107672 | − | 0.00720301i | ||||
\(226\) | −30441.0 | − | 17203.9i | −0.595994 | − | 0.336830i | ||||
\(227\) | 42809.5 | + | 42809.5i | 0.830784 | + | 0.830784i | 0.987624 | − | 0.156840i | \(-0.0501307\pi\) |
−0.156840 | + | 0.987624i | \(0.550131\pi\) | |||||||
\(228\) | −88918.4 | − | 15192.1i | −1.71050 | − | 0.292246i | ||||
\(229\) | −16253.5 | − | 16253.5i | −0.309939 | − | 0.309939i | 0.534946 | − | 0.844886i | \(-0.320332\pi\) |
−0.844886 | + | 0.534946i | \(0.820332\pi\) | |||||||
\(230\) | 4884.17 | + | 17579.9i | 0.0923283 | + | 0.332322i | ||||
\(231\) | −79759.9 | − | 68723.4i | −1.49472 | − | 1.28790i | ||||
\(232\) | 21101.8 | + | 19968.7i | 0.392051 | + | 0.371000i | ||||
\(233\) | 35313.9 | 0.650480 | 0.325240 | − | 0.945631i | \(-0.394555\pi\) | ||||
0.325240 | + | 0.945631i | \(0.394555\pi\) | |||||||
\(234\) | −11941.1 | − | 26784.4i | −0.218079 | − | 0.489159i | ||||
\(235\) | 37854.2 | + | 37854.2i | 0.685454 | + | 0.685454i | ||||
\(236\) | −49600.6 | − | 12317.6i | −0.890560 | − | 0.221158i | ||||
\(237\) | 78077.0 | − | 5803.32i | 1.39004 | − | 0.103319i | ||||
\(238\) | −9706.12 | + | 17174.2i | −0.171353 | + | 0.303196i | ||||
\(239\) | − | 110450.i | − | 1.93362i | −0.255497 | − | 0.966810i | \(-0.582239\pi\) | ||
0.255497 | − | 0.966810i | \(-0.417761\pi\) | |||||||
\(240\) | −21053.7 | − | 53839.2i | −0.365516 | − | 0.934709i | ||||
\(241\) | 13880.4 | 0.238983 | 0.119492 | − | 0.992835i | \(-0.461873\pi\) | ||||
0.119492 | + | 0.992835i | \(0.461873\pi\) | |||||||
\(242\) | 56875.1 | + | 32143.3i | 0.971162 | + | 0.548858i | ||||
\(243\) | 55032.5 | − | 21405.8i | 0.931980 | − | 0.362509i | ||||
\(244\) | 57793.3 | + | 14352.2i | 0.970729 | + | 0.241067i | ||||
\(245\) | 35788.7 | − | 35788.7i | 0.596231 | − | 0.596231i | ||||
\(246\) | −16944.0 | + | 35971.4i | −0.279992 | + | 0.594411i | ||||
\(247\) | 56699.6i | 0.929364i | ||||||||
\(248\) | 95517.6 | − | 2635.14i | 1.55303 | − | 0.0428450i | ||||
\(249\) | −69325.8 | − | 59733.1i | −1.11814 | − | 0.963421i | ||||
\(250\) | 59997.8 | − | 16669.0i | 0.959965 | − | 0.266705i | ||||
\(251\) | −65760.8 | + | 65760.8i | −1.04381 | + | 1.04381i | −0.0448096 | + | 0.998996i | \(0.514268\pi\) |
−0.998996 | + | 0.0448096i | \(0.985732\pi\) | |||||||
\(252\) | 66418.2 | − | 54858.6i | 1.04589 | − | 0.863861i | ||||
\(253\) | 22623.8 | − | 22623.8i | 0.353447 | − | 0.353447i | ||||
\(254\) | 34150.2 | − | 60426.2i | 0.529330 | − | 0.936607i | ||||
\(255\) | 12693.1 | + | 10936.7i | 0.195203 | + | 0.168193i | ||||
\(256\) | −36850.0 | − | 54194.5i | −0.562286 | − | 0.826943i | ||||
\(257\) | − | 15669.1i | − | 0.237234i | −0.992940 | − | 0.118617i | \(-0.962154\pi\) | ||
0.992940 | − | 0.118617i | \(-0.0378461\pi\) | |||||||
\(258\) | 61065.4 | − | 21958.0i | 0.917394 | − | 0.329878i | ||||
\(259\) | −32574.3 | + | 32574.3i | −0.485597 | + | 0.485597i | ||||
\(260\) | −31128.6 | + | 18743.6i | −0.460483 | + | 0.277272i | ||||
\(261\) | 29557.9 | + | 21870.3i | 0.433903 | + | 0.321051i | ||||
\(262\) | −103352. | + | 28714.0i | −1.50562 | + | 0.418303i | ||||
\(263\) | −84189.2 | −1.21715 | −0.608576 | − | 0.793495i | \(-0.708259\pi\) | ||||
−0.608576 | + | 0.793495i | \(0.708259\pi\) | |||||||
\(264\) | −64027.2 | + | 78592.3i | −0.918664 | + | 1.12764i | ||||
\(265\) | − | 25109.6i | − | 0.357559i | ||||||
\(266\) | −160477. | + | 44585.0i | −2.26804 | + | 0.630123i | ||||
\(267\) | 85724.8 | − | 6371.76i | 1.20250 | − | 0.0893793i | ||||
\(268\) | 82674.7 | + | 20531.1i | 1.15107 | + | 0.285853i | ||||
\(269\) | −70429.7 | − | 70429.7i | −0.973310 | − | 0.973310i | 0.0263433 | − | 0.999653i | \(-0.491614\pi\) |
−0.999653 | + | 0.0263433i | \(0.991614\pi\) | |||||||
\(270\) | −34663.5 | − | 64432.6i | −0.475493 | − | 0.883849i | ||||
\(271\) | −64568.0 | −0.879182 | −0.439591 | − | 0.898198i | \(-0.644877\pi\) | ||||
−0.439591 | + | 0.898198i | \(0.644877\pi\) | |||||||
\(272\) | 16787.6 | + | 8885.94i | 0.226909 | + | 0.120106i | ||||
\(273\) | −41019.7 | − | 35343.8i | −0.550386 | − | 0.474228i | ||||
\(274\) | −27292.6 | + | 48292.1i | −0.363533 | + | 0.643243i | ||||
\(275\) | 566.464 | + | 566.464i | 0.00749043 | + | 0.00749043i | ||||
\(276\) | 15129.2 | + | 21364.2i | 0.198608 | + | 0.280459i | ||||
\(277\) | −18877.3 | − | 18877.3i | −0.246025 | − | 0.246025i | 0.573312 | − | 0.819337i | \(-0.305658\pi\) |
−0.819337 | + | 0.573312i | \(0.805658\pi\) | |||||||
\(278\) | 35890.7 | − | 9971.43i | 0.464400 | − | 0.129023i | ||||
\(279\) | 119607. | − | 17879.0i | 1.53655 | − | 0.229687i | ||||
\(280\) | −77527.6 | − | 73364.8i | −0.988873 | − | 0.935776i | ||||
\(281\) | −27140.7 | −0.343723 | −0.171862 | − | 0.985121i | \(-0.554978\pi\) | ||||
−0.171862 | + | 0.985121i | \(0.554978\pi\) | |||||||
\(282\) | 69486.7 | + | 32731.1i | 0.873783 | + | 0.411588i | ||||
\(283\) | −64645.3 | − | 64645.3i | −0.807168 | − | 0.807168i | 0.177036 | − | 0.984204i | \(-0.443349\pi\) |
−0.984204 | + | 0.177036i | \(0.943349\pi\) | |||||||
\(284\) | −7434.43 | − | 12346.8i | −0.0921746 | − | 0.153080i | ||||
\(285\) | 10485.6 | + | 141071.i | 0.129093 | + | 1.73680i | ||||
\(286\) | 55471.4 | + | 31350.0i | 0.678167 | + | 0.383271i | ||||
\(287\) | 73416.0i | 0.891306i | ||||||||
\(288\) | −54564.1 | − | 62469.7i | −0.657842 | − | 0.753156i | ||||
\(289\) | 78015.9 | 0.934087 | ||||||||
\(290\) | 22415.9 | − | 39663.2i | 0.266539 | − | 0.471619i | ||||
\(291\) | 58817.0 | − | 4371.76i | 0.694572 | − | 0.0516262i | ||||
\(292\) | 51742.8 | − | 31156.0i | 0.606854 | − | 0.365407i | ||||
\(293\) | 75450.3 | − | 75450.3i | 0.878872 | − | 0.878872i | −0.114546 | − | 0.993418i | \(-0.536541\pi\) |
0.993418 | + | 0.114546i | \(0.0365412\pi\) | |||||||
\(294\) | 30945.2 | − | 65695.2i | 0.358013 | − | 0.760045i | ||||
\(295\) | 80145.2i | 0.920945i | ||||||||
\(296\) | 32217.2 | + | 30487.3i | 0.367709 | + | 0.347965i | ||||
\(297\) | −68457.1 | + | 108509.i | −0.776078 | + | 1.23013i | ||||
\(298\) | 18624.8 | + | 67037.2i | 0.209729 | + | 0.754890i | ||||
\(299\) | 11635.2 | − | 11635.2i | 0.130146 | − | 0.130146i | ||||
\(300\) | −534.927 | + | 378.811i | −0.00594364 | + | 0.00420901i | ||||
\(301\) | 84723.5 | − | 84723.5i | 0.935128 | − | 0.935128i | ||||
\(302\) | 50802.3 | + | 28711.2i | 0.557018 | + | 0.314802i | ||||
\(303\) | −63924.0 | + | 74189.7i | −0.696272 | + | 0.808088i | ||||
\(304\) | 47173.4 | + | 153273.i | 0.510446 | + | 1.65851i | ||||
\(305\) | − | 93383.1i | − | 1.00385i | ||||||
\(306\) | 22447.3 | + | 8603.89i | 0.239729 | + | 0.0918865i | ||||
\(307\) | −14104.3 | + | 14104.3i | −0.149649 | + | 0.149649i | −0.777961 | − | 0.628312i | \(-0.783746\pi\) |
0.628312 | + | 0.777961i | \(0.283746\pi\) | |||||||
\(308\) | −45110.9 | + | 181653.i | −0.475532 | + | 1.91487i | ||||
\(309\) | 1512.22 | + | 20345.2i | 0.0158379 | + | 0.213081i | ||||
\(310\) | −40112.0 | − | 144377.i | −0.417398 | − | 1.50236i | ||||
\(311\) | 80409.1 | 0.831351 | 0.415676 | − | 0.909513i | \(-0.363545\pi\) | ||||
0.415676 | + | 0.909513i | \(0.363545\pi\) | |||||||
\(312\) | −32928.6 | + | 40419.2i | −0.338270 | + | 0.415221i | ||||
\(313\) | − | 99621.6i | − | 1.01687i | −0.861101 | − | 0.508434i | \(-0.830224\pi\) | ||
0.861101 | − | 0.508434i | \(-0.169776\pi\) | |||||||
\(314\) | 8800.69 | + | 31676.8i | 0.0892601 | + | 0.321279i | ||||
\(315\) | −108595. | − | 80351.2i | −1.09444 | − | 0.809788i | ||||
\(316\) | −71797.7 | − | 119239.i | −0.719013 | − | 1.19411i | ||||
\(317\) | −111446. | − | 111446.i | −1.10903 | − | 1.10903i | −0.993278 | − | 0.115756i | \(-0.963071\pi\) |
−0.115756 | − | 0.993278i | \(-0.536929\pi\) | |||||||
\(318\) | −12190.4 | − | 33901.7i | −0.120549 | − | 0.335249i | ||||
\(319\) | −79890.5 | −0.785079 | ||||||||
\(320\) | −68553.8 | + | 76567.0i | −0.669470 | + | 0.747725i | ||||
\(321\) | 10140.8 | − | 11769.3i | 0.0984147 | − | 0.114219i | ||||
\(322\) | 42080.3 | + | 23781.9i | 0.405851 | + | 0.229369i | ||||
\(323\) | −32865.9 | − | 32865.9i | −0.315022 | − | 0.315022i | ||||
\(324\) | −78082.2 | − | 70165.0i | −0.743810 | − | 0.668391i | ||||
\(325\) | 291.327 | + | 291.327i | 0.00275812 | + | 0.00275812i | ||||
\(326\) | 39822.4 | + | 143335.i | 0.374708 | + | 1.34871i | ||||
\(327\) | −63832.3 | + | 74083.3i | −0.596959 | + | 0.692827i | ||||
\(328\) | 70661.6 | − | 1949.41i | 0.656804 | − | 0.0181199i | ||||
\(329\) | 141819. | 1.31022 | ||||||||
\(330\) | 143813. | + | 67741.9i | 1.32060 | + | 0.622056i | ||||
\(331\) | 59142.9 | + | 59142.9i | 0.539817 | + | 0.539817i | 0.923475 | − | 0.383658i | \(-0.125336\pi\) |
−0.383658 | + | 0.923475i | \(0.625336\pi\) | |||||||
\(332\) | −39209.5 | + | 157889.i | −0.355726 | + | 1.43244i | ||||
\(333\) | 45127.6 | + | 33390.5i | 0.406962 | + | 0.301117i | ||||
\(334\) | −33312.0 | + | 58942.9i | −0.298612 | + | 0.528371i | ||||
\(335\) | − | 133587.i | − | 1.19035i | ||||||
\(336\) | −140292. | − | 61414.8i | −1.24266 | − | 0.543994i | ||||
\(337\) | −205625. | −1.81058 | −0.905289 | − | 0.424797i | \(-0.860346\pi\) | ||||
−0.905289 | + | 0.424797i | \(0.860346\pi\) | |||||||
\(338\) | −70930.8 | − | 40087.0i | −0.620871 | − | 0.350889i | ||||
\(339\) | 5831.59 | + | 78457.4i | 0.0507443 | + | 0.682707i | ||||
\(340\) | 7179.01 | − | 28908.4i | 0.0621021 | − | 0.250073i | ||||
\(341\) | −185801. | + | 185801.i | −1.59786 | + | 1.59786i | ||||
\(342\) | 82645.7 | + | 185377.i | 0.706591 | + | 1.58491i | ||||
\(343\) | 25512.0i | 0.216848i | ||||||||
\(344\) | −83794.6 | − | 79295.2i | −0.708107 | − | 0.670086i | ||||
\(345\) | 26797.2 | − | 31100.6i | 0.225139 | − | 0.261295i | ||||
\(346\) | −103257. | + | 28687.7i | −0.862518 | + | 0.239631i | ||||
\(347\) | 62131.0 | − | 62131.0i | 0.516000 | − | 0.516000i | −0.400359 | − | 0.916359i | \(-0.631114\pi\) |
0.916359 | + | 0.400359i | \(0.131114\pi\) | |||||||
\(348\) | 11008.8 | − | 64433.9i | 0.0909038 | − | 0.532055i | ||||
\(349\) | 38159.1 | − | 38159.1i | 0.313290 | − | 0.313290i | −0.532893 | − | 0.846183i | \(-0.678895\pi\) |
0.846183 | + | 0.532893i | \(0.178895\pi\) | |||||||
\(350\) | −595.463 | + | 1053.62i | −0.00486092 | + | 0.00860102i | ||||
\(351\) | −35206.8 | + | 55805.0i | −0.285767 | + | 0.452959i | ||||
\(352\) | 176035. | + | 38595.0i | 1.42074 | + | 0.311491i | ||||
\(353\) | 44381.3i | 0.356165i | 0.984016 | + | 0.178082i | \(0.0569893\pi\) | ||||
−0.984016 | + | 0.178082i | \(0.943011\pi\) | |||||||
\(354\) | 38909.6 | + | 108208.i | 0.310492 | + | 0.863482i | ||||
\(355\) | −15981.4 | + | 15981.4i | −0.126811 | + | 0.126811i | ||||
\(356\) | −78830.5 | − | 130919.i | −0.622005 | − | 1.03300i | ||||
\(357\) | 44264.1 | − | 3290.07i | 0.347308 | − | 0.0258148i | ||||
\(358\) | 74399.3 | − | 20670.2i | 0.580501 | − | 0.161279i | ||||
\(359\) | 157807. | 1.22444 | 0.612218 | − | 0.790689i | \(-0.290277\pi\) | ||||
0.612218 | + | 0.790689i | \(0.290277\pi\) | |||||||
\(360\) | −74453.1 | + | 106655.i | −0.574484 | + | 0.822953i | ||||
\(361\) | − | 262102.i | − | 2.01120i | ||||||
\(362\) | 220358. | − | 61221.5i | 1.68156 | − | 0.467183i | ||||
\(363\) | −10895.6 | − | 146588.i | −0.0826869 | − | 1.11246i | ||||
\(364\) | −23200.1 | + | 93422.1i | −0.175100 | + | 0.705094i | ||||
\(365\) | −66974.5 | − | 66974.5i | −0.502717 | − | 0.502717i | ||||
\(366\) | −45336.4 | − | 126081.i | −0.338443 | − | 0.941214i | ||||
\(367\) | 33574.3 | 0.249273 | 0.124636 | − | 0.992202i | \(-0.460224\pi\) | ||||
0.124636 | + | 0.992202i | \(0.460224\pi\) | |||||||
\(368\) | 21772.3 | − | 41133.0i | 0.160772 | − | 0.303735i | ||||
\(369\) | 88482.0 | − | 13226.5i | 0.649834 | − | 0.0971385i | ||||
\(370\) | 34223.5 | − | 60555.8i | 0.249989 | − | 0.442336i | ||||
\(371\) | −47036.0 | − | 47036.0i | −0.341730 | − | 0.341730i | ||||
\(372\) | −124251. | − | 175457.i | −0.897869 | − | 1.26790i | ||||
\(373\) | 45698.6 | + | 45698.6i | 0.328462 | + | 0.328462i | 0.852001 | − | 0.523539i | \(-0.175389\pi\) |
−0.523539 | + | 0.852001i | \(0.675389\pi\) | |||||||
\(374\) | −50326.0 | + | 13982.0i | −0.359790 | + | 0.0999596i | ||||
\(375\) | −106143. | − | 91455.4i | −0.754791 | − | 0.650350i | ||||
\(376\) | −3765.72 | − | 136499.i | −0.0266362 | − | 0.965501i | ||||
\(377\) | −41086.9 | −0.289081 | ||||||||
\(378\) | −185630. | − | 55764.5i | −1.29916 | − | 0.390278i | ||||
\(379\) | 109150. | + | 109150.i | 0.759880 | + | 0.759880i | 0.976300 | − | 0.216420i | \(-0.0694381\pi\) |
−0.216420 | + | 0.976300i | \(0.569438\pi\) | |||||||
\(380\) | 215444. | − | 129726.i | 1.49199 | − | 0.898379i | ||||
\(381\) | −155740. | + | 11575.8i | −1.07288 | + | 0.0797449i | ||||
\(382\) | 146768. | + | 82946.7i | 1.00578 | + | 0.568424i | ||||
\(383\) | 34088.1i | 0.232384i | 0.993227 | + | 0.116192i | \(0.0370687\pi\) | ||||
−0.993227 | + | 0.116192i | \(0.962931\pi\) | |||||||
\(384\) | −55385.5 | + | 136659.i | −0.375607 | + | 0.926779i | ||||
\(385\) | 293516. | 1.98021 | ||||||||
\(386\) | 15854.2 | − | 28052.8i | 0.106407 | − | 0.188279i | ||||
\(387\) | −117374. | − | 86846.4i | −0.783698 | − | 0.579869i | ||||
\(388\) | −54086.7 | − | 89825.3i | −0.359275 | − | 0.596671i | ||||
\(389\) | 93777.5 | − | 93777.5i | 0.619726 | − | 0.619726i | −0.325735 | − | 0.945461i | \(-0.605612\pi\) |
0.945461 | + | 0.325735i | \(0.105612\pi\) | |||||||
\(390\) | 73961.7 | + | 34839.0i | 0.486270 | + | 0.229053i | ||||
\(391\) | 13488.7i | 0.0882298i | ||||||||
\(392\) | −129051. | + | 3560.25i | −0.839824 | + | 0.0231691i | ||||
\(393\) | 182840. | + | 157540.i | 1.18382 | + | 1.02002i | ||||
\(394\) | −31853.1 | − | 114651.i | −0.205191 | − | 0.738556i | ||||
\(395\) | −154340. | + | 154340.i | −0.989199 | + | 0.989199i | ||||
\(396\) | 227057. | + | 21642.2i | 1.44792 | + | 0.138010i | ||||
\(397\) | −64452.0 | + | 64452.0i | −0.408936 | + | 0.408936i | −0.881367 | − | 0.472431i | \(-0.843376\pi\) |
0.472431 | + | 0.881367i | \(0.343376\pi\) | |||||||
\(398\) | 135953. | + | 76834.7i | 0.858267 | + | 0.485055i | ||||
\(399\) | 283901. | + | 244617.i | 1.78329 | + | 1.53653i | ||||
\(400\) | 1029.91 | + | 545.145i | 0.00643691 | + | 0.00340716i | ||||
\(401\) | 26294.9i | 0.163524i | 0.996652 | + | 0.0817622i | \(0.0260548\pi\) | ||||
−0.996652 | + | 0.0817622i | \(0.973945\pi\) | |||||||
\(402\) | −64854.9 | − | 180362.i | −0.401320 | − | 1.11608i | ||||
\(403\) | −95555.7 | + | 95555.7i | −0.588364 | + | 0.588364i | ||||
\(404\) | 168967. | + | 41960.5i | 1.03523 | + | 0.257086i | ||||
\(405\) | −77276.1 | + | 145357.i | −0.471124 | + | 0.886186i | ||||
\(406\) | −32308.1 | − | 116288.i | −0.196002 | − | 0.705479i | ||||
\(407\) | −121973. | −0.736333 | ||||||||
\(408\) | −4341.98 | − | 42516.1i | −0.0260836 | − | 0.255407i | ||||
\(409\) | − | 47775.7i | − | 0.285601i | −0.989751 | − | 0.142801i | \(-0.954389\pi\) | ||
0.989751 | − | 0.142801i | \(-0.0456108\pi\) | |||||||
\(410\) | −29673.9 | − | 106807.i | −0.176525 | − | 0.635376i | ||||
\(411\) | 124466. | − | 9251.33i | 0.736830 | − | 0.0547672i | ||||
\(412\) | 31071.2 | − | 18709.0i | 0.183047 | − | 0.110219i | ||||
\(413\) | 150130. | + | 150130.i | 0.880174 | + | 0.880174i | ||||
\(414\) | 21081.2 | − | 55000.3i | 0.122997 | − | 0.320896i | ||||
\(415\) | 255119. | 1.48131 | ||||||||
\(416\) | 90533.2 | + | 19849.0i | 0.523144 | + | 0.114697i | ||||
\(417\) | −63494.5 | − | 54708.7i | −0.365144 | − | 0.314618i | ||||
\(418\) | −383922. | − | 216976.i | −2.19731 | − | 1.24182i | ||||
\(419\) | 100811. | + | 100811.i | 0.574222 | + | 0.574222i | 0.933305 | − | 0.359084i | \(-0.116911\pi\) |
−0.359084 | + | 0.933305i | \(0.616911\pi\) | |||||||
\(420\) | −40446.2 | + | 236729.i | −0.229287 | + | 1.34200i | ||||
\(421\) | 118705. | + | 118705.i | 0.669736 | + | 0.669736i | 0.957655 | − | 0.287919i | \(-0.0929633\pi\) |
−0.287919 | + | 0.957655i | \(0.592963\pi\) | |||||||
\(422\) | 8724.19 | + | 31401.5i | 0.0489892 | + | 0.176329i | ||||
\(423\) | −25549.9 | − | 170923.i | −0.142793 | − | 0.955254i | ||||
\(424\) | −44022.4 | + | 46520.3i | −0.244874 | + | 0.258768i | ||||
\(425\) | −337.735 | −0.00186981 | ||||||||
\(426\) | −13818.5 | + | 29336.1i | −0.0761451 | + | 0.161653i | ||||
\(427\) | −174928. | − | 174928.i | −0.959409 | − | 0.959409i | ||||
\(428\) | −26804.5 | − | 6656.51i | −0.146325 | − | 0.0363379i | ||||
\(429\) | −10626.7 | − | 142970.i | −0.0577407 | − | 0.776835i | ||||
\(430\) | −89012.9 | + | 157501.i | −0.481411 | + | 0.851819i | ||||
\(431\) | 210900.i | 1.13533i | 0.823261 | + | 0.567664i | \(0.192153\pi\) | ||||
−0.823261 | + | 0.567664i | \(0.807847\pi\) | |||||||
\(432\) | −48743.3 | + | 180146.i | −0.261184 | + | 0.965289i | ||||
\(433\) | −108894. | −0.580800 | −0.290400 | − | 0.956905i | \(-0.593788\pi\) | ||||
−0.290400 | + | 0.956905i | \(0.593788\pi\) | |||||||
\(434\) | −345591. | − | 195313.i | −1.83477 | − | 1.03693i | ||||
\(435\) | −102226. | + | 7598.28i | −0.540236 | + | 0.0401547i | ||||
\(436\) | 168724. | + | 41900.3i | 0.887573 | + | 0.220416i | ||||
\(437\) | −80528.1 | + | 80528.1i | −0.421681 | + | 0.421681i | ||||
\(438\) | −122941. | − | 57910.3i | −0.640838 | − | 0.301861i | ||||
\(439\) | − | 89145.0i | − | 0.462560i | −0.972887 | − | 0.231280i | \(-0.925709\pi\) | ||
0.972887 | − | 0.231280i | \(-0.0742913\pi\) | |||||||
\(440\) | −7793.73 | − | 282504.i | −0.0402569 | − | 1.45922i | ||||
\(441\) | −161597. | + | 24155.8i | −0.830912 | + | 0.124206i | ||||
\(442\) | −25882.2 | + | 7190.78i | −0.132482 | + | 0.0368071i | ||||
\(443\) | 60710.4 | − | 60710.4i | 0.309354 | − | 0.309354i | −0.535305 | − | 0.844659i | \(-0.679803\pi\) |
0.844659 | + | 0.535305i | \(0.179803\pi\) | |||||||
\(444\) | 16807.7 | − | 98374.6i | 0.0852595 | − | 0.499019i | ||||
\(445\) | −169458. | + | 169458.i | −0.855739 | + | 0.855739i | ||||
\(446\) | −68597.3 | + | 121378.i | −0.344856 | + | 0.610195i | ||||
\(447\) | 102186. | − | 118596.i | 0.511417 | − | 0.593547i | ||||
\(448\) | 15010.7 | + | 271845.i | 0.0747904 | + | 1.35446i | ||||
\(449\) | 104982.i | 0.520741i | 0.965509 | + | 0.260370i | \(0.0838447\pi\) | ||||
−0.965509 | + | 0.260370i | \(0.916155\pi\) | |||||||
\(450\) | 1377.12 | + | 527.841i | 0.00680060 | + | 0.00260662i | ||||
\(451\) | −137451. | + | 137451.i | −0.675764 | + | 0.675764i | ||||
\(452\) | 119820. | − | 72147.5i | 0.586479 | − | 0.353138i | ||||
\(453\) | −9732.20 | − | 130936.i | −0.0474258 | − | 0.638060i | ||||
\(454\) | −233329. | + | 64825.3i | −1.13203 | + | 0.314509i | ||||
\(455\) | 150953. | 0.729151 | ||||||||
\(456\) | 227902. | − | 279745.i | 1.09602 | − | 1.34534i | ||||
\(457\) | 267352.i | 1.28012i | 0.768324 | + | 0.640061i | \(0.221091\pi\) | ||||
−0.768324 | + | 0.640061i | \(0.778909\pi\) | |||||||
\(458\) | 88588.4 | − | 24612.3i | 0.422324 | − | 0.117333i | ||||
\(459\) | −11939.8 | − | 52755.0i | −0.0566723 | − | 0.250402i | ||||
\(460\) | −70831.4 | − | 17590.0i | −0.334742 | − | 0.0831286i | ||||
\(461\) | −39986.2 | − | 39986.2i | −0.188152 | − | 0.188152i | 0.606745 | − | 0.794897i | \(-0.292475\pi\) |
−0.794897 | + | 0.606745i | \(0.792475\pi\) | |||||||
\(462\) | 396291. | − | 142499.i | 1.85665 | − | 0.667617i | ||||
\(463\) | 76575.3 | 0.357213 | 0.178606 | − | 0.983921i | \(-0.442841\pi\) | ||||
0.178606 | + | 0.983921i | \(0.442841\pi\) | |||||||
\(464\) | −111068. | + | 34183.8i | −0.515884 | + | 0.158776i | ||||
\(465\) | −220076. | + | 255419.i | −1.01781 | + | 1.18126i | ||||
\(466\) | −69500.2 | + | 122975.i | −0.320047 | + | 0.566299i | ||||
\(467\) | −253478. | − | 253478.i | −1.16227 | − | 1.16227i | −0.983978 | − | 0.178292i | \(-0.942943\pi\) |
−0.178292 | − | 0.983978i | \(-0.557057\pi\) | |||||||
\(468\) | 116773. | + | 11130.3i | 0.533153 | + | 0.0508179i | ||||
\(469\) | −250239. | − | 250239.i | −1.13765 | − | 1.13765i | ||||
\(470\) | −206321. | + | 57321.7i | −0.934002 | + | 0.259491i | ||||
\(471\) | 48285.3 | − | 56039.6i | 0.217657 | − | 0.252612i | ||||
\(472\) | 140512. | − | 148484.i | 0.630708 | − | 0.666495i | ||||
\(473\) | 317243. | 1.41798 | ||||||||
\(474\) | −133452. | + | 283312.i | −0.593974 | + | 1.26098i | ||||
\(475\) | −2016.30 | − | 2016.30i | −0.00893650 | − | 0.00893650i | ||||
\(476\) | −40704.2 | − | 67600.1i | −0.179649 | − | 0.298355i | ||||
\(477\) | −48214.6 | + | 65162.4i | −0.211905 | + | 0.286392i | ||||
\(478\) | 384626. | + | 217374.i | 1.68338 | + | 0.951374i | ||||
\(479\) | 162232.i | 0.707075i | 0.935420 | + | 0.353538i | \(0.115021\pi\) | ||||
−0.935420 | + | 0.353538i | \(0.884979\pi\) | |||||||
\(480\) | 228922. | + | 32642.9i | 0.993584 | + | 0.141679i | ||||
\(481\) | −62729.4 | −0.271132 | ||||||||
\(482\) | −27317.6 | + | 48336.3i | −0.117584 | + | 0.208056i | ||||
\(483\) | −8061.32 | − | 108456.i | −0.0345551 | − | 0.464899i | ||||
\(484\) | −223868. | + | 134798.i | −0.955656 | + | 0.575432i | ||||
\(485\) | −116267. | + | 116267.i | −0.494281 | + | 0.494281i | ||||
\(486\) | −33765.5 | + | 233770.i | −0.142955 | + | 0.989729i | ||||
\(487\) | 16868.0i | 0.0711224i | 0.999368 | + | 0.0355612i | \(0.0113219\pi\) | ||||
−0.999368 | + | 0.0355612i | \(0.988678\pi\) | |||||||
\(488\) | −163720. | + | 173010.i | −0.687484 | + | 0.726493i | ||||
\(489\) | 218487. | − | 253575.i | 0.913711 | − | 1.06045i | ||||
\(490\) | 54194.0 | + | 195063.i | 0.225714 | + | 0.812425i | ||||
\(491\) | 127595. | − | 127595.i | 0.529263 | − | 0.529263i | −0.391089 | − | 0.920353i | \(-0.627902\pi\) |
0.920353 | + | 0.391089i | \(0.127902\pi\) | |||||||
\(492\) | −91917.7 | − | 129799.i | −0.379725 | − | 0.536217i | ||||
\(493\) | 23816.0 | − | 23816.0i | 0.0979885 | − | 0.0979885i | ||||
\(494\) | −197447. | − | 111589.i | −0.809091 | − | 0.457263i | ||||
\(495\) | −52879.3 | − | 353750.i | −0.215812 | − | 1.44373i | ||||
\(496\) | −178809. | + | 337811.i | −0.726818 | + | 1.37313i | ||||
\(497\) | 59873.7i | 0.242395i | ||||||||
\(498\) | 344449. | − | 123857.i | 1.38888 | − | 0.499417i | ||||
\(499\) | 293361. | − | 293361.i | 1.17815 | − | 1.17815i | 0.197936 | − | 0.980215i | \(-0.436576\pi\) |
0.980215 | − | 0.197936i | \(-0.0634238\pi\) | |||||||
\(500\) | −60032.5 | + | 241739.i | −0.240130 | + | 0.966955i | ||||
\(501\) | 151917. | − | 11291.7i | 0.605245 | − | 0.0449867i | ||||
\(502\) | −99579.8 | − | 358423.i | −0.395152 | − | 1.42229i | ||||
\(503\) | −446767. | −1.76582 | −0.882908 | − | 0.469546i | \(-0.844418\pi\) | ||||
−0.882908 | + | 0.469546i | \(0.844418\pi\) | |||||||
\(504\) | 60320.9 | + | 339257.i | 0.237469 | + | 1.33557i | ||||
\(505\) | − | 273018.i | − | 1.07055i | ||||||
\(506\) | 34258.6 | + | 123309.i | 0.133804 | + | 0.481607i | ||||
\(507\) | 13588.2 | + | 182814.i | 0.0528624 | + | 0.711203i | ||||
\(508\) | 143215. | + | 237846.i | 0.554958 | + | 0.921654i | ||||
\(509\) | 207666. | + | 207666.i | 0.801548 | + | 0.801548i | 0.983338 | − | 0.181789i | \(-0.0581889\pi\) |
−0.181789 | + | 0.983338i | \(0.558189\pi\) | |||||||
\(510\) | −63066.3 | + | 22677.5i | −0.242470 | + | 0.0871875i | ||||
\(511\) | −250917. | −0.960923 | ||||||||
\(512\) | 261247. | − | 21665.8i | 0.996579 | − | 0.0826486i | ||||
\(513\) | 243669. | − | 386232.i | 0.925905 | − | 1.46762i | ||||
\(514\) | 54565.1 | + | 30837.8i | 0.206533 | + | 0.116723i | ||||
\(515\) | −40217.7 | − | 40217.7i | −0.151636 | − | 0.151636i | ||||
\(516\) | −43715.7 | + | 255865.i | −0.164187 | + | 0.960975i | ||||
\(517\) | 265518. | + | 265518.i | 0.993372 | + | 0.993372i | ||||
\(518\) | −49326.5 | − | 177543.i | −0.183832 | − | 0.661676i | ||||
\(519\) | 182673. | + | 157396.i | 0.678171 | + | 0.584332i | ||||
\(520\) | −4008.24 | − | 145289.i | −0.0148234 | − | 0.537312i | ||||
\(521\) | 157196. | 0.579118 | 0.289559 | − | 0.957160i | \(-0.406491\pi\) | ||||
0.289559 | + | 0.957160i | \(0.406491\pi\) | |||||||
\(522\) | −134332. | + | 59888.5i | −0.492990 | + | 0.219787i | ||||
\(523\) | 5618.21 | + | 5618.21i | 0.0205397 | + | 0.0205397i | 0.717302 | − | 0.696762i | \(-0.245377\pi\) |
−0.696762 | + | 0.717302i | \(0.745377\pi\) | |||||||
\(524\) | 103412. | − | 416417.i | 0.376623 | − | 1.51658i | ||||
\(525\) | 2715.57 | − | 201.843i | 0.00985240 | − | 0.000732310i | ||||
\(526\) | 165690. | − | 293176.i | 0.598860 | − | 1.05964i | ||||
\(527\) | − | 110778.i | − | 0.398870i | ||||||
\(528\) | −147675. | − | 377640.i | −0.529713 | − | 1.35460i | ||||
\(529\) | −246791. | −0.881898 | ||||||||
\(530\) | 87440.1 | + | 49417.4i | 0.311286 | + | 0.175925i | ||||
\(531\) | 153892. | − | 207987.i | 0.545793 | − | 0.737643i | ||||
\(532\) | 160570. | − | 646583.i | 0.567337 | − | 2.28455i | ||||
\(533\) | −70689.7 | + | 70689.7i | −0.248830 | + | 0.248830i | ||||
\(534\) | −146524. | + | 311063.i | −0.513837 | + | 1.09085i | ||||
\(535\) | 43310.9i | 0.151318i | ||||||||
\(536\) | −234206. | + | 247495.i | −0.815207 | + | 0.861463i | ||||
\(537\) | −131620. | − | 113408.i | −0.456430 | − | 0.393273i | ||||
\(538\) | 383871. | − | 106650.i | 1.32623 | − | 0.368464i | ||||
\(539\) | 251030. | − | 251030.i | 0.864068 | − | 0.864068i | ||||
\(540\) | 292596. | + | 6097.71i | 1.00342 | + | 0.0209112i | ||||
\(541\) | −309554. | + | 309554.i | −1.05765 | + | 1.05765i | −0.0594167 | + | 0.998233i | \(0.518924\pi\) |
−0.998233 | + | 0.0594167i | \(0.981076\pi\) | |||||||
\(542\) | 127074. | − | 224848.i | 0.432572 | − | 0.765403i | ||||
\(543\) | −389837. | − | 335894.i | −1.32216 | − | 1.13921i | ||||
\(544\) | −63983.1 | + | 40972.1i | −0.216206 | + | 0.138449i | ||||
\(545\) | − | 272626.i | − | 0.917857i | ||||||
\(546\) | 203809. | − | 73285.8i | 0.683656 | − | 0.245830i | ||||
\(547\) | 83309.8 | − | 83309.8i | 0.278434 | − | 0.278434i | −0.554050 | − | 0.832483i | \(-0.686918\pi\) |
0.832483 | + | 0.554050i | \(0.186918\pi\) | |||||||
\(548\) | −114456. | − | 190084.i | −0.381134 | − | 0.632973i | ||||
\(549\) | −179311. | + | 242340.i | −0.594925 | + | 0.804047i | ||||
\(550\) | −3087.46 | + | 857.781i | −0.0102065 | + | 0.00283564i | ||||
\(551\) | 284366. | 0.936643 | ||||||||
\(552\) | −104173. | + | 10638.7i | −0.341882 | + | 0.0349149i | ||||
\(553\) | 578228.i | 1.89081i | ||||||||
\(554\) | 102889. | − | 28585.4i | 0.335235 | − | 0.0931375i | ||||
\(555\) | −156074. | + | 11600.7i | −0.506692 | + | 0.0376615i | ||||
\(556\) | −35911.5 | + | 144608.i | −0.116167 | + | 0.467782i | ||||
\(557\) | −132736. | − | 132736.i | −0.427836 | − | 0.427836i | 0.460055 | − | 0.887891i | \(-0.347830\pi\) |
−0.887891 | + | 0.460055i | \(0.847830\pi\) | |||||||
\(558\) | −173133. | + | 451698.i | −0.556047 | + | 1.45071i | ||||
\(559\) | 163155. | 0.522127 | ||||||||
\(560\) | 408061. | − | 125591.i | 1.30121 | − | 0.400481i | ||||
\(561\) | 89032.1 | + | 76712.6i | 0.282892 | + | 0.243748i | ||||
\(562\) | 53414.8 | − | 94513.3i | 0.169118 | − | 0.299240i | ||||
\(563\) | 347273. | + | 347273.i | 1.09560 | + | 1.09560i | 0.994918 | + | 0.100687i | \(0.0321040\pi\) |
0.100687 | + | 0.994918i | \(0.467896\pi\) | |||||||
\(564\) | −250736. | + | 177559.i | −0.788238 | + | 0.558195i | ||||
\(565\) | −155092. | − | 155092.i | −0.485838 | − | 0.485838i | ||||
\(566\) | 352343. | − | 97890.7i | 1.09985 | − | 0.305568i | ||||
\(567\) | 127530. | + | 417042.i | 0.396687 | + | 1.29722i | ||||
\(568\) | 57627.4 | − | 1589.82i | 0.178621 | − | 0.00492779i | ||||
\(569\) | −571037. | −1.76376 | −0.881880 | − | 0.471474i | \(-0.843722\pi\) | ||||
−0.881880 | + | 0.471474i | \(0.843722\pi\) | |||||||
\(570\) | −511895. | − | 241124.i | −1.57555 | − | 0.742148i | ||||
\(571\) | −52056.7 | − | 52056.7i | −0.159663 | − | 0.159663i | 0.622754 | − | 0.782417i | \(-0.286014\pi\) |
−0.782417 | + | 0.622754i | \(0.786014\pi\) | |||||||
\(572\) | −218343. | + | 131471.i | −0.667340 | + | 0.401827i | ||||
\(573\) | −28116.3 | − | 378273.i | −0.0856345 | − | 1.15211i | ||||
\(574\) | −255660. | − | 144488.i | −0.775958 | − | 0.438538i | ||||
\(575\) | 827.518i | 0.00250289i | ||||||||
\(576\) | 324927. | − | 67066.1i | 0.979356 | − | 0.202143i | ||||
\(577\) | −130477. | −0.391905 | −0.195953 | − | 0.980613i | \(-0.562780\pi\) | ||||
−0.195953 | + | 0.980613i | \(0.562780\pi\) | |||||||
\(578\) | −153541. | + | 271678.i | −0.459587 | + | 0.813203i | ||||
\(579\) | −72302.2 | + | 5374.09i | −0.215672 | + | 0.0160305i | ||||
\(580\) | 94004.7 | + | 156120.i | 0.279443 | + | 0.464089i | ||||
\(581\) | 477896. | − | 477896.i | 1.41573 | − | 1.41573i | ||||
\(582\) | −100532. | + | 213425.i | −0.296796 | + | 0.630085i | ||||
\(583\) | − | 176124.i | − | 0.518181i | ||||||
\(584\) | 6662.60 | + | 241503.i | 0.0195352 | + | 0.708105i | ||||
\(585\) | −27195.3 | − | 181930.i | −0.0794661 | − | 0.531610i | ||||
\(586\) | 114252. | + | 411235.i | 0.332713 | + | 1.19755i | ||||
\(587\) | −293596. | + | 293596.i | −0.852066 | + | 0.852066i | −0.990387 | − | 0.138321i | \(-0.955829\pi\) |
0.138321 | + | 0.990387i | \(0.455829\pi\) | |||||||
\(588\) | 167871. | + | 237054.i | 0.485536 | + | 0.685636i | ||||
\(589\) | 661349. | − | 661349.i | 1.90634 | − | 1.90634i | ||||
\(590\) | −279093. | − | 157731.i | −0.801761 | − | 0.453121i | ||||
\(591\) | −174763. | + | 202829.i | −0.500351 | + | 0.580704i | ||||
\(592\) | −169573. | + | 52190.2i | −0.483852 | + | 0.148917i | ||||
\(593\) | 281113.i | 0.799415i | 0.916643 | + | 0.399707i | \(0.130888\pi\) | ||||
−0.916643 | + | 0.399707i | \(0.869112\pi\) | |||||||
\(594\) | −243137. | − | 451944.i | −0.689093 | − | 1.28089i | ||||
\(595\) | −87499.7 | + | 87499.7i | −0.247157 | + | 0.247157i | ||||
\(596\) | −270101. | − | 67075.9i | −0.760386 | − | 0.188831i | ||||
\(597\) | −26044.5 | − | 350399.i | −0.0730748 | − | 0.983139i | ||||
\(598\) | 17618.8 | + | 63416.5i | 0.0492691 | + | 0.177337i | ||||
\(599\) | −155311. | −0.432861 | −0.216430 | − | 0.976298i | \(-0.569441\pi\) | ||||
−0.216430 | + | 0.976298i | \(0.569441\pi\) | |||||||
\(600\) | −266.377 | − | 2608.33i | −0.000739935 | − | 0.00724535i | ||||
\(601\) | − | 116278.i | − | 0.321921i | −0.986961 | − | 0.160960i | \(-0.948541\pi\) | ||
0.986961 | − | 0.160960i | \(-0.0514591\pi\) | |||||||
\(602\) | 128295. | + | 461778.i | 0.354010 | + | 1.27421i | ||||
\(603\) | −256509. | + | 346674.i | −0.705452 | + | 0.953425i | ||||
\(604\) | −199965. | + | 120405.i | −0.548125 | + | 0.330044i | ||||
\(605\) | 289769. | + | 289769.i | 0.791664 | + | 0.791664i | ||||
\(606\) | −132547. | − | 368616.i | −0.360932 | − | 1.00376i | ||||
\(607\) | 37914.6 | 0.102903 | 0.0514516 | − | 0.998675i | \(-0.483615\pi\) | ||||
0.0514516 | + | 0.998675i | \(0.483615\pi\) | |||||||
\(608\) | −626588. | − | 137377.i | −1.69502 | − | 0.371627i | ||||
\(609\) | −177260. | + | 205726.i | −0.477943 | + | 0.554697i | ||||
\(610\) | 325192. | + | 183784.i | 0.873937 | + | 0.493911i | ||||
\(611\) | 136553. | + | 136553.i | 0.365779 | + | 0.365779i | ||||
\(612\) | −74139.4 | + | 61236.0i | −0.197946 | + | 0.163495i | ||||
\(613\) | 154607. | + | 154607.i | 0.411442 | + | 0.411442i | 0.882241 | − | 0.470799i | \(-0.156034\pi\) |
−0.470799 | + | 0.882241i | \(0.656034\pi\) | |||||||
\(614\) | −21357.8 | − | 76874.1i | −0.0566525 | − | 0.203912i | ||||
\(615\) | −162807. | + | 188952.i | −0.430450 | + | 0.499577i | ||||
\(616\) | −543795. | − | 514596.i | −1.43309 | − | 1.35614i | ||||
\(617\) | −313295. | −0.822967 | −0.411484 | − | 0.911417i | \(-0.634989\pi\) | ||||
−0.411484 | + | 0.911417i | \(0.634989\pi\) | |||||||
\(618\) | −73825.2 | − | 34774.7i | −0.193298 | − | 0.0910514i | ||||
\(619\) | 5042.52 | + | 5042.52i | 0.0131603 | + | 0.0131603i | 0.713656 | − | 0.700496i | \(-0.247038\pi\) |
−0.700496 | + | 0.713656i | \(0.747038\pi\) | |||||||
\(620\) | 581714. | + | 144461.i | 1.51330 | + | 0.375808i | ||||
\(621\) | −129260. | + | 29254.8i | −0.335183 | + | 0.0758603i | ||||
\(622\) | −158251. | + | 280012.i | −0.409039 | + | 0.723762i | ||||
\(623\) | 634866.i | 1.63571i | ||||||||
\(624\) | −75948.0 | − | 194216.i | −0.195051 | − | 0.498789i | ||||
\(625\) | 393449. | 1.00723 | ||||||||
\(626\) | 346917. | + | 196062.i | 0.885271 | + | 0.500317i | ||||
\(627\) | 73548.0 | + | 989505.i | 0.187084 | + | 2.51700i | ||||
\(628\) | −127630. | − | 31695.1i | −0.323618 | − | 0.0803661i | ||||
\(629\) | 36361.1 | − | 36361.1i | 0.0919043 | − | 0.0919043i | ||||
\(630\) | 493533. | − | 220029.i | 1.24347 | − | 0.554370i | ||||
\(631\) | − | 512563.i | − | 1.28733i | −0.765309 | − | 0.643663i | \(-0.777414\pi\) | ||
0.765309 | − | 0.643663i | \(-0.222586\pi\) | |||||||
\(632\) | 556534. | − | 15353.7i | 1.39334 | − | 0.0384395i | ||||
\(633\) | 47865.6 | − | 55552.5i | 0.119458 | − | 0.138642i | ||||
\(634\) | 607425. | − | 168759.i | 1.51117 | − | 0.419845i | ||||
\(635\) | 307861. | − | 307861.i | 0.763496 | − | 0.763496i | ||||
\(636\) | 142049. | + | 24269.7i | 0.351175 | + | 0.0599998i | ||||
\(637\) | 129102. | − | 129102.i | 0.318167 | − | 0.318167i | ||||
\(638\) | 157230. | − | 278206.i | 0.386272 | − | 0.683479i | ||||
\(639\) | 72160.7 | − | 10786.7i | 0.176725 | − | 0.0264173i | ||||
\(640\) | −131714. | − | 389417.i | −0.321568 | − | 0.950725i | ||||
\(641\) | − | 533175.i | − | 1.29764i | −0.760943 | − | 0.648819i | \(-0.775263\pi\) | ||
0.760943 | − | 0.648819i | \(-0.224737\pi\) | |||||||
\(642\) | 21027.0 | + | 58476.3i | 0.0510161 | + | 0.141876i | ||||
\(643\) | 36204.0 | − | 36204.0i | 0.0875659 | − | 0.0875659i | −0.661967 | − | 0.749533i | \(-0.730278\pi\) |
0.749533 | + | 0.661967i | \(0.230278\pi\) | |||||||
\(644\) | −165634. | + | 99733.5i | −0.399371 | + | 0.240475i | ||||
\(645\) | 405937. | − | 30172.6i | 0.975752 | − | 0.0725258i | ||||
\(646\) | 179133. | − | 49768.0i | 0.429250 | − | 0.119257i | ||||
\(647\) | −365116. | −0.872213 | −0.436107 | − | 0.899895i | \(-0.643643\pi\) | ||||
−0.436107 | + | 0.899895i | \(0.643643\pi\) | |||||||
\(648\) | 398010. | − | 133819.i | 0.947859 | − | 0.318691i | ||||
\(649\) | 562156.i | 1.33465i | ||||||||
\(650\) | −1587.85 | + | 441.148i | −0.00375822 | + | 0.00104414i | ||||
\(651\) | 66204.9 | + | 890711.i | 0.156217 | + | 2.10172i | ||||
\(652\) | −577515. | − | 143418.i | −1.35853 | − | 0.337371i | ||||
\(653\) | 33696.0 | + | 33696.0i | 0.0790228 | + | 0.0790228i | 0.745513 | − | 0.666491i | \(-0.232204\pi\) |
−0.666491 | + | 0.745513i | \(0.732204\pi\) | |||||||
\(654\) | −132357. | − | 368087.i | −0.309451 | − | 0.860587i | ||||
\(655\) | −672852. | −1.56833 | ||||||||
\(656\) | −132278. | + | 249904.i | −0.307384 | + | 0.580719i | ||||
\(657\) | 45204.7 | + | 302409.i | 0.104726 | + | 0.700590i | ||||
\(658\) | −279110. | + | 493863.i | −0.644650 | + | 1.14066i | ||||
\(659\) | 156573. | + | 156573.i | 0.360533 | + | 0.360533i | 0.864009 | − | 0.503476i | \(-0.167946\pi\) |
−0.503476 | + | 0.864009i | \(0.667946\pi\) | |||||||
\(660\) | −518935. | + | 367486.i | −1.19131 | + | 0.843632i | ||||
\(661\) | −65482.1 | − | 65482.1i | −0.149872 | − | 0.149872i | 0.628189 | − | 0.778061i | \(-0.283796\pi\) |
−0.778061 | + | 0.628189i | \(0.783796\pi\) | |||||||
\(662\) | −322353. | + | 89558.6i | −0.735556 | + | 0.204358i | ||||
\(663\) | 45788.3 | + | 39452.5i | 0.104166 | + | 0.0897527i | ||||
\(664\) | −472656. | − | 447277.i | −1.07204 | − | 1.01447i | ||||
\(665\) | −1.04476e6 | −2.36250 | ||||||||
\(666\) | −205091. | + | 91434.8i | −0.462380 | + | 0.206140i | ||||
\(667\) | −58354.0 | − | 58354.0i | −0.131165 | − | 0.131165i | ||||
\(668\) | −139699. | − | 232007.i | −0.313070 | − | 0.519935i | ||||
\(669\) | 312834. | − | 23252.3i | 0.698974 | − | 0.0519534i | ||||
\(670\) | 465195. | + | 262908.i | 1.03630 | + | 0.585671i | ||||
\(671\) | − | 655009.i | − | 1.45480i | ||||||
\(672\) | 489971. | − | 367676.i | 1.08501 | − | 0.814191i | ||||
\(673\) | 812214. | 1.79325 | 0.896624 | − | 0.442793i | \(-0.146012\pi\) | ||||
0.896624 | + | 0.442793i | \(0.146012\pi\) | |||||||
\(674\) | 404685. | − | 716058.i | 0.890835 | − | 1.57626i | ||||
\(675\) | −732.495 | − | 3236.48i | −0.00160767 | − | 0.00710338i | ||||
\(676\) | 279193. | − | 168111.i | 0.610958 | − | 0.367878i | ||||
\(677\) | −190499. | + | 190499.i | −0.415639 | + | 0.415639i | −0.883697 | − | 0.468059i | \(-0.844954\pi\) |
0.468059 | + | 0.883697i | \(0.344954\pi\) | |||||||
\(678\) | −284692. | − | 134102.i | −0.619322 | − | 0.291726i | ||||
\(679\) | 435591.i | 0.944799i | ||||||||
\(680\) | 86540.3 | + | 81893.5i | 0.187155 | + | 0.177105i | ||||
\(681\) | 412784. | + | 355667.i | 0.890079 | + | 0.766918i | ||||
\(682\) | −281354. | − | 1.01269e6i | −0.604901 | − | 2.17725i | ||||
\(683\) | −57211.2 | + | 57211.2i | −0.122642 | + | 0.122642i | −0.765764 | − | 0.643122i | \(-0.777639\pi\) |
0.643122 | + | 0.765764i | \(0.277639\pi\) | |||||||
\(684\) | −808199. | − | 77034.1i | −1.72745 | − | 0.164653i | ||||
\(685\) | −246040. | + | 246040.i | −0.524354 | + | 0.524354i | ||||
\(686\) | −88841.5 | − | 50209.3i | −0.188785 | − | 0.106693i | ||||
\(687\) | −156722. | − | 135036.i | −0.332061 | − | 0.286113i | ||||
\(688\) | 441047. | − | 135743.i | 0.931768 | − | 0.286774i | ||||
\(689\) | − | 90578.7i | − | 0.190804i | ||||||
\(690\) | 55564.3 | + | 154525.i | 0.116707 | + | 0.324564i | ||||
\(691\) | 180385. | − | 180385.i | 0.377785 | − | 0.377785i | −0.492518 | − | 0.870303i | \(-0.663923\pi\) |
0.870303 | + | 0.492518i | \(0.163923\pi\) | |||||||
\(692\) | 103317. | − | 416036.i | 0.215754 | − | 0.868798i | ||||
\(693\) | −761711. | − | 563601.i | −1.58607 | − | 1.17356i | ||||
\(694\) | 94083.4 | + | 338640.i | 0.195341 | + | 0.703103i | ||||
\(695\) | 233660. | 0.483742 | ||||||||
\(696\) | 202715. | + | 165147.i | 0.418473 | + | 0.340919i | ||||
\(697\) | − | 81950.6i | − | 0.168689i | ||||||
\(698\) | 57783.3 | + | 207983.i | 0.118602 | + | 0.426890i | ||||
\(699\) | 316951. | − | 23558.4i | 0.648691 | − | 0.0482160i | ||||
\(700\) | −2497.17 | − | 4147.21i | −0.00509627 | − | 0.00846369i | ||||
\(701\) | 220677. | + | 220677.i | 0.449077 | + | 0.449077i | 0.895048 | − | 0.445971i | \(-0.147141\pi\) |
−0.445971 | + | 0.895048i | \(0.647141\pi\) | |||||||
\(702\) | −125043. | − | 232430.i | −0.253737 | − | 0.471648i | ||||
\(703\) | 434156. | 0.878486 | ||||||||
\(704\) | −480851. | + | 537057.i | −0.970208 | + | 1.08362i | ||||
\(705\) | 365004. | + | 314498.i | 0.734377 | + | 0.632760i | ||||
\(706\) | −154551. | − | 87345.5i | −0.310072 | − | 0.175239i | ||||
\(707\) | −511426. | − | 511426.i | −1.02316 | − | 1.02316i | ||||
\(708\) | −453395. | − | 77464.4i | −0.904503 | − | 0.154538i | ||||
\(709\) | −280640. | − | 280640.i | −0.558286 | − | 0.558286i | 0.370533 | − | 0.928819i | \(-0.379175\pi\) |
−0.928819 | + | 0.370533i | \(0.879175\pi\) | |||||||
\(710\) | −24200.2 | − | 87105.2i | −0.0480068 | − | 0.172794i | ||||
\(711\) | 696889. | − | 104172.i | 1.37856 | − | 0.206069i | ||||
\(712\) | 611048. | − | 16857.6i | 1.20536 | − | 0.0332534i | ||||
\(713\) | −271428. | −0.533918 | ||||||||
\(714\) | −75657.6 | + | 160618.i | −0.148408 | + | 0.315063i | ||||
\(715\) | 282617. | + | 282617.i | 0.552823 | + | 0.552823i | ||||
\(716\) | −74442.2 | + | 299764.i | −0.145209 | + | 0.584728i | ||||
\(717\) | −73682.8 | − | 991318.i | −0.143327 | − | 1.92830i | ||||
\(718\) | −310574. | + | 549536.i | −0.602443 | + | 1.06598i | ||||
\(719\) | − | 679245.i | − | 1.31392i | −0.753926 | − | 0.656959i | \(-0.771842\pi\) | ||
0.753926 | − | 0.656959i | \(-0.228158\pi\) | |||||||
\(720\) | −224879. | − | 469175.i | −0.433795 | − | 0.905044i | ||||
\(721\) | −150674. | −0.289846 | ||||||||
\(722\) | 912728. | + | 515834.i | 1.75092 | + | 0.989546i | ||||
\(723\) | 124580. | − | 9259.79i | 0.238326 | − | 0.0177143i | ||||
\(724\) | −220485. | + | 887850.i | −0.420632 | + | 1.69380i | ||||
\(725\) | 1461.09 | − | 1461.09i | 0.00277972 | − | 0.00277972i | ||||
\(726\) | 531911. | + | 250552.i | 1.00917 | + | 0.475363i | ||||
\(727\) | − | 65636.2i | − | 0.124187i | −0.998070 | − | 0.0620933i | \(-0.980222\pi\) | ||
0.998070 | − | 0.0620933i | \(-0.0197776\pi\) | |||||||
\(728\) | −279668. | − | 264652.i | −0.527692 | − | 0.499358i | ||||
\(729\) | 479650. | − | 228835.i | 0.902546 | − | 0.430593i | ||||
\(730\) | 365038. | − | 101418.i | 0.685003 | − | 0.190313i | ||||
\(731\) | −94572.7 | + | 94572.7i | −0.176983 | + | 0.176983i | ||||
\(732\) | 528283. | + | 90259.5i | 0.985927 | + | 0.168450i | ||||
\(733\) | −468743. | + | 468743.i | −0.872423 | + | 0.872423i | −0.992736 | − | 0.120313i | \(-0.961610\pi\) |
0.120313 | + | 0.992736i | \(0.461610\pi\) | |||||||
\(734\) | −66076.5 | + | 116917.i | −0.122647 | + | 0.217013i | ||||
\(735\) | 297337. | − | 345088.i | 0.550396 | − | 0.638785i | ||||
\(736\) | 100390. | + | 156771.i | 0.185325 | + | 0.289408i | ||||
\(737\) | − | 937006.i | − | 1.72507i | ||||||
\(738\) | −128079. | + | 334155.i | −0.235162 | + | 0.613530i | ||||
\(739\) | 495095. | − | 495095.i | 0.906566 | − | 0.906566i | −0.0894270 | − | 0.995993i | \(-0.528504\pi\) |
0.995993 | + | 0.0894270i | \(0.0285036\pi\) | |||||||
\(740\) | 143522. | + | 238356.i | 0.262092 | + | 0.435274i | ||||
\(741\) | 37825.0 | + | 508892.i | 0.0688879 | + | 0.926808i | ||||
\(742\) | 256366. | − | 71225.4i | 0.465642 | − | 0.129368i | ||||
\(743\) | −89831.8 | −0.162724 | −0.0813621 | − | 0.996685i | \(-0.525927\pi\) | ||||
−0.0813621 | + | 0.996685i | \(0.525927\pi\) | |||||||
\(744\) | 855536. | − | 87372.1i | 1.54558 | − | 0.157843i | ||||
\(745\) | 436433.i | 0.786330i | ||||||||
\(746\) | −249076. | + | 69200.2i | −0.447563 | + | 0.124345i | ||||
\(747\) | −662064. | − | 489871.i | −1.18648 | − | 0.877890i | ||||
\(748\) | 50355.1 | − | 202770.i | 0.0899995 | − | 0.362410i | ||||
\(749\) | 81131.4 | + | 81131.4i | 0.144619 | + | 0.144619i | ||||
\(750\) | 527375. | − | 189634.i | 0.937555 | − | 0.337127i | ||||
\(751\) | −717332. | −1.27186 | −0.635931 | − | 0.771746i | \(-0.719384\pi\) | ||||
−0.635931 | + | 0.771746i | \(0.719384\pi\) | |||||||
\(752\) | 482746. | + | 255525.i | 0.853656 | + | 0.451854i | ||||
\(753\) | −546349. | + | 634089.i | −0.963563 | + | 1.11830i | ||||
\(754\) | 80861.7 | − | 143078.i | 0.142233 | − | 0.251670i | ||||
\(755\) | 258829. | + | 258829.i | 0.454066 | + | 0.454066i | ||||
\(756\) | 559523. | − | 536678.i | 0.978981 | − | 0.939010i | ||||
\(757\) | −176774. | − | 176774.i | −0.308479 | − | 0.308479i | 0.535840 | − | 0.844319i | \(-0.319995\pi\) |
−0.844319 | + | 0.535840i | \(0.819995\pi\) | |||||||
\(758\) | −594912. | + | 165283.i | −1.03541 | + | 0.287667i | ||||
\(759\) | 187961. | − | 218146.i | 0.326276 | − | 0.378673i | ||||
\(760\) | 27741.4 | + | 1.00556e6i | 0.0480287 | + | 1.74093i | ||||
\(761\) | 621827. | 1.07374 | 0.536871 | − | 0.843664i | \(-0.319606\pi\) | ||||
0.536871 | + | 0.843664i | \(0.319606\pi\) | |||||||
\(762\) | 266196. | − | 565122.i | 0.458449 | − | 0.973267i | ||||
\(763\) | −510692. | − | 510692.i | −0.877223 | − | 0.877223i | ||||
\(764\) | −577698. | + | 347851.i | −0.989723 | + | 0.595945i | ||||
\(765\) | 121220. | + | 89692.1i | 0.207133 | + | 0.153261i | ||||
\(766\) | −118707. | − | 67087.8i | −0.202310 | − | 0.114337i | ||||
\(767\) | 289111.i | 0.491444i | ||||||||
\(768\) | −366892. | − | 461826.i | −0.622036 | − | 0.782989i | ||||
\(769\) | −648676. | −1.09692 | −0.548460 | − | 0.836177i | \(-0.684786\pi\) | ||||
−0.548460 | + | 0.836177i | \(0.684786\pi\) | |||||||
\(770\) | −577660. | + | 1.02212e6i | −0.974296 | + | 1.72394i | ||||
\(771\) | −10453.0 | − | 140634.i | −0.0175847 | − | 0.236581i | ||||
\(772\) | 66487.4 | + | 110420.i | 0.111559 | + | 0.185273i | ||||
\(773\) | 804458. | − | 804458.i | 1.34631 | − | 1.34631i | 0.456674 | − | 0.889634i | \(-0.349040\pi\) |
0.889634 | − | 0.456674i | \(-0.150960\pi\) | |||||||
\(774\) | 533428. | − | 237816.i | 0.890418 | − | 0.396971i | ||||
\(775\) | − | 6796.12i | − | 0.0113151i | ||||||
\(776\) | 419249. | − | 11566.2i | 0.696223 | − | 0.0192074i | ||||
\(777\) | −270632. | + | 314093.i | −0.448267 | + | 0.520255i | ||||
\(778\) | 142005. | + | 511126.i | 0.234609 | + | 0.844440i | ||||
\(779\) | 489250. | − | 489250.i | 0.806224 | − | 0.806224i | ||||
\(780\) | −266883. | + | 188994.i | −0.438664 | + | 0.310642i | ||||
\(781\) | −112097. | + | 112097.i | −0.183777 | + | 0.183777i | ||||
\(782\) | −46972.1 | − | 26546.6i | −0.0768116 | − | 0.0434106i | ||||
\(783\) | 279879. | + | 176573.i | 0.456507 | + | 0.288005i | ||||
\(784\) | 241583. | − | 456406.i | 0.393037 | − | 0.742538i | ||||
\(785\) | 206226.i | 0.334660i | ||||||||
\(786\) | −908452. | + | 326662.i | −1.47047 | + | 0.528754i | ||||
\(787\) | −381072. | + | 381072.i | −0.615258 | + | 0.615258i | −0.944311 | − | 0.329054i | \(-0.893270\pi\) |
0.329054 | + | 0.944311i | \(0.393270\pi\) | |||||||
\(788\) | 461941. | + | 114717.i | 0.743934 | + | 0.184746i | ||||
\(789\) | −755619. | + | 56163.7i | −1.21380 | + | 0.0902198i | ||||
\(790\) | −233713. | − | 841215.i | −0.374480 | − | 1.34789i | ||||
\(791\) | −581045. | −0.928660 | ||||||||
\(792\) | −522230. | + | 748099.i | −0.832552 | + | 1.19264i | ||||
\(793\) | − | 336864.i | − | 0.535684i | ||||||
\(794\) | −97598.0 | − | 351290.i | −0.154810 | − | 0.557217i | ||||
\(795\) | −16750.9 | − | 225365.i | −0.0265036 | − | 0.356575i | ||||
\(796\) | −535130. | + | 322219.i | −0.844564 | + | 0.508540i | ||||
\(797\) | 816658. | + | 816658.i | 1.28565 | + | 1.28565i | 0.937401 | + | 0.348252i | \(0.113225\pi\) |
0.348252 | + | 0.937401i | \(0.386775\pi\) | |||||||
\(798\) | −1.41058e6 | + | 507217.i | −2.21509 | + | 0.796505i | ||||
\(799\) | −158306. | −0.247973 | ||||||||
\(800\) | −3925.31 | + | 2513.60i | −0.00613330 | + | 0.00392750i | ||||
\(801\) | 765150. | − | 114376.i | 1.19256 | − | 0.178267i | ||||
\(802\) | −91567.8 | − | 51750.1i | −0.142362 | − | 0.0804568i | ||||
\(803\) | −469773. | − | 469773.i | −0.728546 | − | 0.728546i | ||||
\(804\) | 755722. | + | 129118.i | 1.16910 | + | 0.199745i | ||||
\(805\) | 214392. | + | 214392.i | 0.330839 | + | 0.330839i | ||||
\(806\) | −144697. | − | 520818.i | −0.222736 | − | 0.801707i | ||||
\(807\) | −679108. | − | 585139.i | −1.04278 | − | 0.898487i | ||||
\(808\) | −478659. | + | 505818.i | −0.733167 | + | 0.774768i | ||||
\(809\) | 34063.6 | 0.0520468 | 0.0260234 | − | 0.999661i | \(-0.491716\pi\) | ||||
0.0260234 | + | 0.999661i | \(0.491716\pi\) | |||||||
\(810\) | −354097. | − | 555174.i | −0.539699 | − | 0.846172i | ||||
\(811\) | 834839. | + | 834839.i | 1.26929 | + | 1.26929i | 0.946455 | + | 0.322835i | \(0.104636\pi\) |
0.322835 | + | 0.946455i | \(0.395364\pi\) | |||||||
\(812\) | 468541. | + | 116356.i | 0.710616 | + | 0.176472i | ||||
\(813\) | −579513. | + | 43074.1i | −0.876763 | + | 0.0651682i | ||||
\(814\) | 240051. | − | 424751.i | 0.362288 | − | 0.641041i | ||||
\(815\) | 933156.i | 1.40488i | ||||||||
\(816\) | 156601. | + | 68554.3i | 0.235187 | + | 0.102957i | ||||
\(817\) | −1.12921e6 | −1.69173 | ||||||||
\(818\) | 166371. | + | 94025.8i | 0.248641 | + | 0.140521i | ||||
\(819\) | −391740. | − | 289854.i | −0.584024 | − | 0.432127i | ||||
\(820\) | 430338. | + | 106868.i | 0.640003 | + | 0.158936i | ||||
\(821\) | 189132. | − | 189132.i | 0.280594 | − | 0.280594i | −0.552752 | − | 0.833346i | \(-0.686422\pi\) |
0.833346 | + | 0.552752i | \(0.186422\pi\) | |||||||
\(822\) | −212741. | + | 451641.i | −0.314854 | + | 0.668420i | ||||
\(823\) | − | 43766.5i | − | 0.0646164i | −0.999478 | − | 0.0323082i | \(-0.989714\pi\) | ||
0.999478 | − | 0.0323082i | \(-0.0102858\pi\) | |||||||
\(824\) | 4000.84 | + | 145021.i | 0.00589247 | + | 0.213588i | ||||
\(825\) | 5462.04 | + | 4706.25i | 0.00802504 | + | 0.00691461i | ||||
\(826\) | −818273. | + | 227339.i | −1.19933 | + | 0.333206i | ||||
\(827\) | −96321.9 | + | 96321.9i | −0.140836 | + | 0.140836i | −0.774010 | − | 0.633174i | \(-0.781752\pi\) |
0.633174 | + | 0.774010i | \(0.281752\pi\) | |||||||
\(828\) | 150040. | + | 181656.i | 0.218851 | + | 0.264966i | ||||
\(829\) | −211562. | + | 211562.i | −0.307843 | + | 0.307843i | −0.844072 | − | 0.536229i | \(-0.819848\pi\) |
0.536229 | + | 0.844072i | \(0.319848\pi\) | |||||||
\(830\) | −502091. | + | 888411.i | −0.728830 | + | 1.28961i | ||||
\(831\) | −182022. | − | 156835.i | −0.263585 | − | 0.227112i | ||||
\(832\) | −247297. | + | 276203.i | −0.357249 | + | 0.399008i | ||||
\(833\) | 149668.i | 0.215695i | ||||||||
\(834\) | 315476. | − | 113439.i | 0.453559 | − | 0.163091i | ||||
\(835\) | −300304. | + | 300304.i | −0.430713 | + | 0.430713i | ||||
\(836\) | 1.51117e6 | − | 909925.i | 2.16222 | − | 1.30195i | ||||
\(837\) | 1.06157e6 | − | 240260.i | 1.51530 | − | 0.342949i | ||||
\(838\) | −549461. | + | 152655.i | −0.782436 | + | 0.217382i | ||||
\(839\) | −362437. | −0.514883 | −0.257442 | − | 0.966294i | \(-0.582880\pi\) | ||||
−0.257442 | + | 0.966294i | \(0.582880\pi\) | |||||||
\(840\) | −744772. | − | 606747.i | −1.05552 | − | 0.859902i | ||||
\(841\) | − | 501218.i | − | 0.708654i | ||||||
\(842\) | −646989. | + | 179751.i | −0.912584 | + | 0.253541i | ||||
\(843\) | −243594. | + | 18105.9i | −0.342778 | + | 0.0254780i | ||||
\(844\) | −126520. | − | 31419.6i | −0.177613 | − | 0.0441078i | ||||
\(845\) | −361380. | − | 361380.i | −0.506117 | − | 0.506117i | ||||
\(846\) | 645495. | + | 247414.i | 0.901888 | + | 0.345688i | ||||
\(847\) | 1.08561e6 | 1.51323 | ||||||||
\(848\) | −75360.5 | − | 244856.i | −0.104798 | − | 0.340502i | ||||
\(849\) | −623333. | − | 537081.i | −0.864778 | − | 0.745118i | ||||
\(850\) | 664.686 | − | 1176.11i | 0.000919980 | − | 0.00162783i | ||||
\(851\) | −89092.0 | − | 89092.0i | −0.123021 | − | 0.123021i | ||||
\(852\) | −74962.6 | − | 105856.i | −0.103268 | − | 0.145827i | ||||
\(853\) | 923944. | + | 923944.i | 1.26984 | + | 1.26984i | 0.946172 | + | 0.323663i | \(0.104915\pi\) |
0.323663 | + | 0.946172i | \(0.395085\pi\) | |||||||
\(854\) | 953430. | − | 264889.i | 1.30729 | − | 0.363202i | ||||
\(855\) | 188221. | + | 1.25916e6i | 0.257476 | + | 1.72245i | ||||
\(856\) | 75933.2 | − | 80241.8i | 0.103630 | − | 0.109510i | ||||
\(857\) | −95031.7 | −0.129392 | −0.0646959 | − | 0.997905i | \(-0.520608\pi\) | ||||
−0.0646959 | + | 0.997905i | \(0.520608\pi\) | |||||||
\(858\) | 518783. | + | 244368.i | 0.704711 | + | 0.331948i | ||||
\(859\) | −93950.8 | − | 93950.8i | −0.127325 | − | 0.127325i | 0.640572 | − | 0.767898i | \(-0.278697\pi\) |
−0.767898 | + | 0.640572i | \(0.778697\pi\) | |||||||
\(860\) | −373290. | − | 619947.i | −0.504719 | − | 0.838219i | ||||
\(861\) | 48976.7 | + | 658926.i | 0.0660668 | + | 0.888854i | ||||
\(862\) | −734424. | − | 415065.i | −0.988400 | − | 0.558600i | ||||
\(863\) | 80586.9i | 0.108204i | 0.998535 | + | 0.0541019i | \(0.0172296\pi\) | ||||
−0.998535 | + | 0.0541019i | \(0.982770\pi\) | |||||||
\(864\) | −531400. | − | 524281.i | −0.711859 | − | 0.702322i | ||||
\(865\) | −672236. | −0.898441 | ||||||||
\(866\) | 214310. | − | 379205.i | 0.285764 | − | 0.505636i | ||||
\(867\) | 700211. | − | 52045.4i | 0.931517 | − | 0.0692379i | ||||
\(868\) | 1.36029e6 | − | 819076.i | 1.80548 | − | 1.08714i | ||||
\(869\) | −1.08257e6 | + | 1.08257e6i | −1.43356 | + | 1.43356i | ||||
\(870\) | 174728. | − | 370940.i | 0.230847 | − | 0.490079i | ||||
\(871\) | − | 481893.i | − | 0.635205i | ||||||
\(872\) | −477972. | + | 505092.i | −0.628592 | + | 0.664260i | ||||
\(873\) | 524981. | − | 78475.2i | 0.688834 | − | 0.102968i | ||||
\(874\) | −121942. | − | 438911.i | −0.159635 | − | 0.574584i | ||||
\(875\) | 731692. | − | 731692.i | 0.955679 | − | 0.955679i | ||||
\(876\) | 443620. | − | 314151.i | 0.578099 | − | 0.409384i | ||||
\(877\) | 579137. | − | 579137.i | 0.752978 | − | 0.752978i | −0.222056 | − | 0.975034i | \(-0.571277\pi\) |
0.975034 | + | 0.222056i | \(0.0712767\pi\) | |||||||
\(878\) | 310433. | + | 175443.i | 0.402698 | + | 0.227587i | ||||
\(879\) | 626851. | − | 727519.i | 0.811309 | − | 0.941600i | ||||
\(880\) | 999116. | + | 528847.i | 1.29018 | + | 0.682913i | ||||
\(881\) | 1.14232e6i | 1.47175i | 0.677115 | + | 0.735877i | \(0.263230\pi\) | ||||
−0.677115 | + | 0.735877i | \(0.736770\pi\) | |||||||
\(882\) | 233914. | − | 610275.i | 0.300690 | − | 0.784491i | ||||
\(883\) | 879289. | − | 879289.i | 1.12774 | − | 1.12774i | 0.137200 | − | 0.990543i | \(-0.456190\pi\) |
0.990543 | − | 0.137200i | \(-0.0438102\pi\) | |||||||
\(884\) | 25897.1 | − | 104282.i | 0.0331396 | − | 0.133446i | ||||
\(885\) | 53465.9 | + | 719323.i | 0.0682638 | + | 0.918411i | ||||
\(886\) | 91932.2 | + | 330896.i | 0.117112 | + | 0.421526i | ||||
\(887\) | 453147. | 0.575959 | 0.287980 | − | 0.957637i | \(-0.407016\pi\) | ||||
0.287980 | + | 0.957637i | \(0.407016\pi\) | |||||||
\(888\) | 309495. | + | 252138.i | 0.392490 | + | 0.319752i | ||||
\(889\) | − | 1.15339e6i | − | 1.45939i | ||||||
\(890\) | −256605. | − | 923614.i | −0.323956 | − | 1.16603i | ||||
\(891\) | −542031. | + | 1.01956e6i | −0.682761 | + | 1.28428i | ||||
\(892\) | −287674. | − | 477759.i | −0.361552 | − | 0.600453i | ||||
\(893\) | −945095. | − | 945095.i | −1.18515 | − | 1.18515i | ||||
\(894\) | 211883. | + | 589250.i | 0.265107 | + | 0.737267i | ||||
\(895\) | 484362. | 0.604678 | ||||||||
\(896\) | −976198. | − | 482736.i | −1.21597 | − | 0.601304i | ||||
\(897\) | 96666.5 | − | 112190.i | 0.120141 | − | 0.139435i | ||||
\(898\) | −365583. | − | 206611.i | −0.453349 | − | 0.256213i | ||||
\(899\) | 479241. | + | 479241.i | 0.592973 | + | 0.592973i | ||||
\(900\) | −4548.39 | + | 3756.78i | −0.00561530 | + | 0.00463800i | ||||
\(901\) | 52504.0 | + | 52504.0i | 0.0646759 | + | 0.0646759i | ||||
\(902\) | −208139. | − | 749165.i | −0.255823 | − | 0.920798i | ||||
\(903\) | 703894. | − | 816934.i | 0.863240 | − | 1.00187i | ||||
\(904\) | 15428.5 | + | 559245.i | 0.0188793 | + | 0.684330i | ||||
\(905\) | 1.43460e6 | 1.75159 | ||||||||
\(906\) | 475116. | + | 223799.i | 0.578820 | + | 0.272648i | ||||
\(907\) | −901139. | − | 901139.i | −1.09541 | − | 1.09541i | −0.994940 | − | 0.100472i | \(-0.967965\pi\) |
−0.100472 | − | 0.994940i | \(-0.532035\pi\) | |||||||
\(908\) | 233464. | − | 940113.i | 0.283171 | − | 1.14027i | ||||
\(909\) | −524240. | + | 708515.i | −0.634458 | + | 0.857475i | ||||
\(910\) | −297085. | + | 525668.i | −0.358755 | + | 0.634789i | ||||
\(911\) | 479905.i | 0.578254i | 0.957291 | + | 0.289127i | \(0.0933649\pi\) | ||||
−0.957291 | + | 0.289127i | \(0.906635\pi\) | |||||||
\(912\) | 525643. | + | 1.34419e6i | 0.631977 | + | 1.61611i | ||||
\(913\) | 1.78946e6 | 2.14674 | ||||||||
\(914\) | −931011. | − | 526167.i | −1.11445 | − | 0.629841i | ||||
\(915\) | −62297.0 | − | 838136.i | −0.0744090 | − | 1.00109i | ||||
\(916\) | −88639.6 | + | 356934.i | −0.105642 | + | 0.425400i | ||||
\(917\) | −1.26041e6 | + | 1.26041e6i | −1.49890 | + | 1.49890i | ||||
\(918\) | 207209. | + | 62247.1i | 0.245880 | + | 0.0738642i | ||||
\(919\) | 1.08958e6i | 1.29011i | 0.764135 | + | 0.645056i | \(0.223166\pi\) | ||||
−0.764135 | + | 0.645056i | \(0.776834\pi\) | |||||||
\(920\) | 200655. | − | 212041.i | 0.237069 | − | 0.250521i | ||||
\(921\) | −117180. | + | 135999.i | −0.138145 | + | 0.160330i | ||||
\(922\) | 217941. | − | 60550.1i | 0.256376 | − | 0.0712284i | ||||
\(923\) | −57650.3 | + | 57650.3i | −0.0676704 | + | 0.0676704i | ||||
\(924\) | −283699. | + | 1.66047e6i | −0.332287 | + | 1.94485i | ||||
\(925\) | 2230.72 | − | 2230.72i | 0.00260713 | − | 0.00260713i | ||||
\(926\) | −150705. | + | 266661.i | −0.175755 | + | 0.310984i | ||||
\(927\) | 27145.1 | + | 181595.i | 0.0315888 | + | 0.211321i | ||||
\(928\) | 99549.0 | − | 454052.i | 0.115596 | − | 0.527241i | ||||
\(929\) | 643655.i | 0.745799i | 0.927872 | + | 0.372899i | \(0.121636\pi\) | ||||
−0.927872 | + | 0.372899i | \(0.878364\pi\) | |||||||
\(930\) | −456331. | − | 1.26906e6i | −0.527611 | − | 1.46729i | ||||
\(931\) | −893527. | + | 893527.i | −1.03088 | + | 1.03088i | ||||
\(932\) | −291461. | − | 484047.i | −0.335543 | − | 0.557257i | ||||
\(933\) | 721691. | − | 53642.0i | 0.829064 | − | 0.0616228i | ||||
\(934\) | 1.38156e6 | − | 383836.i | 1.58371 | − | 0.439999i | ||||
\(935\) | −327638. | −0.374775 | ||||||||
\(936\) | −268578. | + | 384740.i | −0.306562 | + | 0.439152i | ||||
\(937\) | 336071.i | 0.382782i | 0.981514 | + | 0.191391i | \(0.0612999\pi\) | ||||
−0.981514 | + | 0.191391i | \(0.938700\pi\) | |||||||
\(938\) | 1.36390e6 | − | 378930.i | 1.55017 | − | 0.430679i | ||||
\(939\) | −66458.9 | − | 894128.i | −0.0753740 | − | 1.01407i | ||||
\(940\) | 206440. | − | 831293.i | 0.233635 | − | 0.940803i | ||||
\(941\) | 277322. | + | 277322.i | 0.313188 | + | 0.313188i | 0.846143 | − | 0.532955i | \(-0.178919\pi\) |
−0.532955 | + | 0.846143i | \(0.678919\pi\) | |||||||
\(942\) | 100120. | + | 278436.i | 0.112829 | + | 0.313779i | ||||
\(943\) | −200795. | −0.225803 | ||||||||
\(944\) | 240537. | + | 781537.i | 0.269922 | + | 0.877012i | ||||
\(945\) | −1.02827e6 | − | 648726.i | −1.15145 | − | 0.726437i | ||||
\(946\) | −624355. | + | 1.10475e6i | −0.697669 | + | 1.23447i | ||||
\(947\) | −1.12072e6 | − | 1.12072e6i | −1.24967 | − | 1.24967i | −0.955865 | − | 0.293806i | \(-0.905078\pi\) |
−0.293806 | − | 0.955865i | \(-0.594922\pi\) | |||||||
\(948\) | −723948. | − | 1.02230e6i | −0.805547 | − | 1.13753i | ||||
\(949\) | −241600. | − | 241600.i | −0.268265 | − | 0.268265i | ||||
\(950\) | 10989.6 | − | 3053.23i | 0.0121769 | − | 0.00338308i | ||||
\(951\) | −1.07460e6 | − | 925905.i | −1.18819 | − | 1.02378i | ||||
\(952\) | 315515. | − | 8704.44i | 0.348134 | − | 0.00960432i | ||||
\(953\) | −154472. | −0.170084 | −0.0850421 | − | 0.996377i | \(-0.527102\pi\) | ||||
−0.0850421 | + | 0.996377i | \(0.527102\pi\) | |||||||
\(954\) | −132028. | − | 296144.i | −0.145067 | − | 0.325391i | ||||
\(955\) | 747756. | + | 747756.i | 0.819885 | + | 0.819885i | ||||
\(956\) | −1.51394e6 | + | 911592.i | −1.65650 | + | 0.997435i | ||||
\(957\) | −717036. | + | 53295.9i | −0.782920 | + | 0.0581929i | ||||
\(958\) | −564947. | − | 319284.i | −0.615569 | − | 0.347893i | ||||
\(959\) | 921779.i | 1.00228i | ||||||||
\(960\) | −564208. | + | 732941.i | −0.612204 | + | 0.795292i | ||||
\(961\) | 1.30562e6 | 1.41374 | ||||||||
\(962\) | 123456. | − | 218445.i | 0.133402 | − | 0.236044i | ||||
\(963\) | 83164.2 | − | 112397.i | 0.0896776 | − | 0.121200i | ||||
\(964\) | −114561. | − | 190258.i | −0.123277 | − | 0.204734i | ||||
\(965\) | 142924. | − | 142924.i | 0.153480 | − | 0.153480i | ||||
\(966\) | 393546. | + | 185376.i | 0.421736 | + | 0.198655i | ||||
\(967\) | 785704.i | 0.840245i | 0.907467 | + | 0.420123i | \(0.138013\pi\) | ||||
−0.907467 | + | 0.420123i | \(0.861987\pi\) | |||||||
\(968\) | −28826.1 | − | 1.04488e6i | −0.0307635 | − | 1.11510i | ||||
\(969\) | −316905. | − | 273054.i | −0.337506 | − | 0.290805i | ||||
\(970\) | −176061. | − | 633705.i | −0.187119 | − | 0.673509i | ||||
\(971\) | 117692. | − | 117692.i | 0.124827 | − | 0.124827i | −0.641933 | − | 0.766760i | \(-0.721867\pi\) |
0.766760 | + | 0.641933i | \(0.221867\pi\) | |||||||
\(972\) | −747615. | − | 577658.i | −0.791308 | − | 0.611418i | ||||
\(973\) | 437698. | − | 437698.i | 0.462327 | − | 0.462327i | ||||
\(974\) | −58740.2 | − | 33197.4i | −0.0619181 | − | 0.0349934i | ||||
\(975\) | 2809.07 | + | 2420.38i | 0.00295498 | + | 0.00254609i | ||||
\(976\) | −280267. | − | 910626.i | −0.294221 | − | 0.955961i | ||||
\(977\) | − | 1.13635e6i | − | 1.19048i | −0.803547 | − | 0.595241i | \(-0.797056\pi\) | ||
0.803547 | − | 0.595241i | \(-0.202944\pi\) | |||||||
\(978\) | 453037. | + | 1.25990e6i | 0.473648 | + | 1.31722i | ||||
\(979\) | −1.18861e6 | + | 1.18861e6i | −1.24015 | + | 1.24015i | ||||
\(980\) | −785935. | − | 195176.i | −0.818341 | − | 0.203224i | ||||
\(981\) | −523488. | + | 707499.i | −0.543962 | + | 0.735170i | ||||
\(982\) | 193214. | + | 695447.i | 0.200362 | + | 0.721176i | ||||
\(983\) | 917825. | 0.949845 | 0.474923 | − | 0.880028i | \(-0.342476\pi\) | ||||
0.474923 | + | 0.880028i | \(0.342476\pi\) | |||||||
\(984\) | 632904. | − | 64635.7i | 0.653654 | − | 0.0667548i | ||||
\(985\) | − | 746410.i | − | 0.769317i | ||||||
\(986\) | 36064.0 | + | 129807.i | 0.0370954 | + | 0.133519i | ||||
\(987\) | 1.27286e6 | − | 94609.5i | 1.30661 | − | 0.0971181i | ||||
\(988\) | 777180. | − | 467965.i | 0.796173 | − | 0.479402i | ||||
\(989\) | 231722. | + | 231722.i | 0.236905 | + | 0.236905i | ||||
\(990\) | 1.33595e6 | + | 512061.i | 1.36307 | + | 0.522458i | ||||
\(991\) | 503498. | 0.512684 | 0.256342 | − | 0.966586i | \(-0.417483\pi\) | ||||
0.256342 | + | 0.966586i | \(0.417483\pi\) | |||||||
\(992\) | −824467. | − | 1.28751e6i | −0.837818 | − | 1.30836i | ||||
\(993\) | 570277. | + | 491367.i | 0.578345 | + | 0.498319i | ||||
\(994\) | −208501. | − | 117836.i | −0.211025 | − | 0.119262i | ||||
\(995\) | 692657. | + | 692657.i | 0.699636 | + | 0.699636i | ||||
\(996\) | −246585. | + | 1.44325e6i | −0.248570 | + | 1.45486i | ||||
\(997\) | −597685. | − | 597685.i | −0.601288 | − | 0.601288i | 0.339367 | − | 0.940654i | \(-0.389787\pi\) |
−0.940654 | + | 0.339367i | \(0.889787\pi\) | |||||||
\(998\) | 444229. | + | 1.59894e6i | 0.446011 | + | 1.60535i | ||||
\(999\) | 427306. | + | 269583.i | 0.428162 | + | 0.270123i |
(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 | 48.5.i.a.5.12 | ✓ | 60 | |
3.2 | odd | 2 | inner | 48.5.i.a.5.19 | yes | 60 | |
4.3 | odd | 2 | 192.5.i.a.113.1 | 60 | |||
12.11 | even | 2 | 192.5.i.a.113.15 | 60 | |||
16.3 | odd | 4 | 192.5.i.a.17.15 | 60 | |||
16.13 | even | 4 | inner | 48.5.i.a.29.19 | yes | 60 | |
48.29 | odd | 4 | inner | 48.5.i.a.29.12 | yes | 60 | |
48.35 | even | 4 | 192.5.i.a.17.1 | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.5.i.a.5.12 | ✓ | 60 | 1.1 | even | 1 | trivial | |
48.5.i.a.5.19 | yes | 60 | 3.2 | odd | 2 | inner | |
48.5.i.a.29.12 | yes | 60 | 48.29 | odd | 4 | inner | |
48.5.i.a.29.19 | yes | 60 | 16.13 | even | 4 | inner | |
192.5.i.a.17.1 | 60 | 48.35 | even | 4 | |||
192.5.i.a.17.15 | 60 | 16.3 | odd | 4 | |||
192.5.i.a.113.1 | 60 | 4.3 | odd | 2 | |||
192.5.i.a.113.15 | 60 | 12.11 | even | 2 |