Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,5,Mod(63,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.63");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.b (of order \(2\), degree \(1\), 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: | \(12.8178754224\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 63.6 | ||
Character | \(\chi\) | \(=\) | 124.63 |
Dual form | 124.5.b.a.63.5 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.71949 | + | 1.47153i | −0.929872 | + | 0.367883i | ||||
\(3\) | − | 6.32028i | − | 0.702254i | −0.936328 | − | 0.351127i | \(-0.885799\pi\) | ||
0.936328 | − | 0.351127i | \(-0.114201\pi\) | |||||||
\(4\) | 11.6692 | − | 10.9467i | 0.729324 | − | 0.684169i | ||||
\(5\) | −34.2840 | −1.37136 | −0.685681 | − | 0.727902i | \(-0.740495\pi\) | ||||
−0.685681 | + | 0.727902i | \(0.740495\pi\) | |||||||
\(6\) | 9.30050 | + | 23.5082i | 0.258347 | + | 0.653006i | ||||
\(7\) | 45.8539i | 0.935795i | 0.883783 | + | 0.467897i | \(0.154988\pi\) | ||||
−0.883783 | + | 0.467897i | \(0.845012\pi\) | |||||||
\(8\) | −27.2950 | + | 57.8877i | −0.426484 | + | 0.904495i | ||||
\(9\) | 41.0540 | 0.506840 | ||||||||
\(10\) | 127.519 | − | 50.4501i | 1.27519 | − | 0.504501i | ||||
\(11\) | 74.0573i | 0.612044i | 0.952024 | + | 0.306022i | \(0.0989981\pi\) | ||||
−0.952024 | + | 0.306022i | \(0.901002\pi\) | |||||||
\(12\) | −69.1862 | − | 73.7525i | −0.480460 | − | 0.512170i | ||||
\(13\) | 233.059 | 1.37905 | 0.689523 | − | 0.724264i | \(-0.257820\pi\) | ||||
0.689523 | + | 0.724264i | \(0.257820\pi\) | |||||||
\(14\) | −67.4756 | − | 170.553i | −0.344263 | − | 0.870169i | ||||
\(15\) | 216.685i | 0.963044i | ||||||||
\(16\) | 16.3397 | − | 255.478i | 0.0638269 | − | 0.997961i | ||||
\(17\) | −427.011 | −1.47755 | −0.738774 | − | 0.673953i | \(-0.764595\pi\) | ||||
−0.738774 | + | 0.673953i | \(0.764595\pi\) | |||||||
\(18\) | −152.700 | + | 60.4123i | −0.471296 | + | 0.186458i | ||||
\(19\) | − | 535.858i | − | 1.48437i | −0.670194 | − | 0.742186i | \(-0.733789\pi\) | ||
0.670194 | − | 0.742186i | \(-0.266211\pi\) | |||||||
\(20\) | −400.067 | + | 375.297i | −1.00017 | + | 0.938243i | ||||
\(21\) | 289.810 | 0.657165 | ||||||||
\(22\) | −108.978 | − | 275.455i | −0.225161 | − | 0.569122i | ||||
\(23\) | − | 625.741i | − | 1.18288i | −0.806351 | − | 0.591438i | \(-0.798561\pi\) | ||
0.806351 | − | 0.591438i | \(-0.201439\pi\) | |||||||
\(24\) | 365.867 | + | 172.512i | 0.635185 | + | 0.299500i | ||||
\(25\) | 550.396 | 0.880634 | ||||||||
\(26\) | −866.860 | + | 342.954i | −1.28234 | + | 0.507328i | ||||
\(27\) | − | 771.416i | − | 1.05818i | ||||||
\(28\) | 501.949 | + | 535.078i | 0.640241 | + | 0.682497i | ||||
\(29\) | 1347.30 | 1.60202 | 0.801012 | − | 0.598649i | \(-0.204296\pi\) | ||||
0.801012 | + | 0.598649i | \(0.204296\pi\) | |||||||
\(30\) | −318.859 | − | 805.957i | −0.354288 | − | 0.895508i | ||||
\(31\) | 172.601i | 0.179605i | ||||||||
\(32\) | 315.169 | + | 974.292i | 0.307782 | + | 0.951457i | ||||
\(33\) | 468.063 | 0.429810 | ||||||||
\(34\) | 1588.26 | − | 628.361i | 1.37393 | − | 0.543565i | ||||
\(35\) | − | 1572.06i | − | 1.28331i | ||||||
\(36\) | 479.067 | − | 449.406i | 0.369650 | − | 0.346764i | ||||
\(37\) | 345.621 | 0.252463 | 0.126231 | − | 0.992001i | \(-0.459712\pi\) | ||||
0.126231 | + | 0.992001i | \(0.459712\pi\) | |||||||
\(38\) | 788.533 | + | 1993.12i | 0.546075 | + | 1.38028i | ||||
\(39\) | − | 1473.00i | − | 0.968440i | ||||||
\(40\) | 935.782 | − | 1984.62i | 0.584864 | − | 1.24039i | ||||
\(41\) | 686.886 | 0.408617 | 0.204309 | − | 0.978907i | \(-0.434505\pi\) | ||||
0.204309 | + | 0.978907i | \(0.434505\pi\) | |||||||
\(42\) | −1077.94 | + | 426.465i | −0.611079 | + | 0.241760i | ||||
\(43\) | − | 973.443i | − | 0.526470i | −0.964732 | − | 0.263235i | \(-0.915211\pi\) | ||
0.964732 | − | 0.263235i | \(-0.0847895\pi\) | |||||||
\(44\) | 810.683 | + | 864.188i | 0.418741 | + | 0.446378i | ||||
\(45\) | −1407.50 | −0.695061 | ||||||||
\(46\) | 920.798 | + | 2327.44i | 0.435160 | + | 1.09992i | ||||
\(47\) | − | 2390.64i | − | 1.08223i | −0.840950 | − | 0.541113i | \(-0.818003\pi\) | ||
0.840950 | − | 0.541113i | \(-0.181997\pi\) | |||||||
\(48\) | −1614.69 | − | 103.271i | −0.700822 | − | 0.0448227i | ||||
\(49\) | 298.417 | 0.124288 | ||||||||
\(50\) | −2047.19 | + | 809.926i | −0.818876 | + | 0.323970i | ||||
\(51\) | 2698.83i | 1.03761i | ||||||||
\(52\) | 2719.61 | − | 2551.22i | 1.00577 | − | 0.943500i | ||||
\(53\) | 611.221 | 0.217594 | 0.108797 | − | 0.994064i | \(-0.465300\pi\) | ||||
0.108797 | + | 0.994064i | \(0.465300\pi\) | |||||||
\(54\) | 1135.16 | + | 2869.27i | 0.389288 | + | 0.983975i | ||||
\(55\) | − | 2538.98i | − | 0.839333i | ||||||
\(56\) | −2654.38 | − | 1251.58i | −0.846422 | − | 0.399101i | ||||
\(57\) | −3386.77 | −1.04240 | ||||||||
\(58\) | −5011.27 | + | 1982.60i | −1.48968 | + | 0.589357i | ||||
\(59\) | 4381.91i | 1.25881i | 0.777078 | + | 0.629404i | \(0.216701\pi\) | ||||
−0.777078 | + | 0.629404i | \(0.783299\pi\) | |||||||
\(60\) | 2371.98 | + | 2528.54i | 0.658884 | + | 0.702371i | ||||
\(61\) | 3155.99 | 0.848156 | 0.424078 | − | 0.905626i | \(-0.360598\pi\) | ||||
0.424078 | + | 0.905626i | \(0.360598\pi\) | |||||||
\(62\) | −253.988 | − | 641.986i | −0.0660738 | − | 0.167010i | ||||
\(63\) | 1882.49i | 0.474298i | ||||||||
\(64\) | −2605.97 | − | 3160.09i | −0.636223 | − | 0.771505i | ||||
\(65\) | −7990.20 | −1.89117 | ||||||||
\(66\) | −1740.95 | + | 688.770i | −0.399668 | + | 0.158120i | ||||
\(67\) | 4953.41i | 1.10346i | 0.834024 | + | 0.551728i | \(0.186031\pi\) | ||||
−0.834024 | + | 0.551728i | \(0.813969\pi\) | |||||||
\(68\) | −4982.87 | + | 4674.36i | −1.07761 | + | 1.01089i | ||||
\(69\) | −3954.86 | −0.830679 | ||||||||
\(70\) | 2313.34 | + | 5847.25i | 0.472109 | + | 1.19332i | ||||
\(71\) | − | 6469.57i | − | 1.28339i | −0.766960 | − | 0.641695i | \(-0.778231\pi\) | ||
0.766960 | − | 0.641695i | \(-0.221769\pi\) | |||||||
\(72\) | −1120.57 | + | 2376.52i | −0.216159 | + | 0.458434i | ||||
\(73\) | 7051.59 | 1.32325 | 0.661624 | − | 0.749836i | \(-0.269868\pi\) | ||||
0.661624 | + | 0.749836i | \(0.269868\pi\) | |||||||
\(74\) | −1285.53 | + | 508.593i | −0.234758 | + | 0.0928768i | ||||
\(75\) | − | 3478.66i | − | 0.618428i | ||||||
\(76\) | −5865.87 | − | 6253.03i | −1.01556 | − | 1.08259i | ||||
\(77\) | −3395.82 | −0.572747 | ||||||||
\(78\) | 2167.56 | + | 5478.80i | 0.356273 | + | 0.900526i | ||||
\(79\) | − | 8207.15i | − | 1.31504i | −0.753438 | − | 0.657519i | \(-0.771606\pi\) | ||
0.753438 | − | 0.657519i | \(-0.228394\pi\) | |||||||
\(80\) | −560.190 | + | 8758.82i | −0.0875297 | + | 1.36857i | ||||
\(81\) | −1550.19 | −0.236273 | ||||||||
\(82\) | −2554.86 | + | 1010.77i | −0.379962 | + | 0.150323i | ||||
\(83\) | − | 4403.54i | − | 0.639213i | −0.947550 | − | 0.319606i | \(-0.896449\pi\) | ||
0.947550 | − | 0.319606i | \(-0.103551\pi\) | |||||||
\(84\) | 3381.84 | − | 3172.46i | 0.479286 | − | 0.449612i | ||||
\(85\) | 14639.7 | 2.02625 | ||||||||
\(86\) | 1432.45 | + | 3620.71i | 0.193679 | + | 0.489550i | ||||
\(87\) | − | 8515.33i | − | 1.12503i | ||||||
\(88\) | −4287.01 | − | 2021.39i | −0.553591 | − | 0.261027i | ||||
\(89\) | 10025.2 | 1.26565 | 0.632824 | − | 0.774296i | \(-0.281896\pi\) | ||||
0.632824 | + | 0.774296i | \(0.281896\pi\) | |||||||
\(90\) | 5235.17 | − | 2071.18i | 0.646318 | − | 0.255701i | ||||
\(91\) | 10686.7i | 1.29050i | ||||||||
\(92\) | −6849.80 | − | 7301.89i | −0.809286 | − | 0.862699i | ||||
\(93\) | 1090.89 | 0.126128 | ||||||||
\(94\) | 3517.90 | + | 8891.95i | 0.398133 | + | 1.00633i | ||||
\(95\) | 18371.4i | 2.03561i | ||||||||
\(96\) | 6157.80 | − | 1991.96i | 0.668164 | − | 0.216141i | ||||
\(97\) | −13502.1 | −1.43502 | −0.717512 | − | 0.696546i | \(-0.754719\pi\) | ||||
−0.717512 | + | 0.696546i | \(0.754719\pi\) | |||||||
\(98\) | −1109.96 | + | 439.130i | −0.115572 | + | 0.0457236i | ||||
\(99\) | 3040.35i | 0.310208i | ||||||||
\(100\) | 6422.67 | − | 6025.02i | 0.642267 | − | 0.602502i | ||||
\(101\) | −12189.6 | −1.19494 | −0.597470 | − | 0.801892i | \(-0.703827\pi\) | ||||
−0.597470 | + | 0.801892i | \(0.703827\pi\) | |||||||
\(102\) | −3971.42 | − | 10038.3i | −0.381720 | − | 0.964848i | ||||
\(103\) | − | 13419.0i | − | 1.26487i | −0.774613 | − | 0.632436i | \(-0.782055\pi\) | ||
0.774613 | − | 0.632436i | \(-0.217945\pi\) | |||||||
\(104\) | −6361.33 | + | 13491.2i | −0.588141 | + | 1.24734i | ||||
\(105\) | −9935.85 | −0.901211 | ||||||||
\(106\) | −2273.43 | + | 899.431i | −0.202334 | + | 0.0800491i | ||||
\(107\) | 12335.1i | 1.07740i | 0.842498 | + | 0.538699i | \(0.181084\pi\) | ||||
−0.842498 | + | 0.538699i | \(0.818916\pi\) | |||||||
\(108\) | −8444.46 | − | 9001.79i | −0.723976 | − | 0.771759i | ||||
\(109\) | 11823.9 | 0.995193 | 0.497597 | − | 0.867409i | \(-0.334216\pi\) | ||||
0.497597 | + | 0.867409i | \(0.334216\pi\) | |||||||
\(110\) | 3736.20 | + | 9443.72i | 0.308777 | + | 0.780473i | ||||
\(111\) | − | 2184.43i | − | 0.177293i | ||||||
\(112\) | 11714.7 | + | 749.239i | 0.933887 | + | 0.0597288i | ||||
\(113\) | 10630.5 | 0.832524 | 0.416262 | − | 0.909245i | \(-0.363340\pi\) | ||||
0.416262 | + | 0.909245i | \(0.363340\pi\) | |||||||
\(114\) | 12597.1 | − | 4983.75i | 0.969303 | − | 0.383483i | ||||
\(115\) | 21452.9i | 1.62215i | ||||||||
\(116\) | 15721.9 | − | 14748.5i | 1.16839 | − | 1.09605i | ||||
\(117\) | 9568.01 | 0.698956 | ||||||||
\(118\) | −6448.12 | − | 16298.5i | −0.463094 | − | 1.17053i | ||||
\(119\) | − | 19580.2i | − | 1.38268i | ||||||
\(120\) | −12543.4 | − | 5914.41i | −0.871068 | − | 0.410723i | ||||
\(121\) | 9156.52 | 0.625403 | ||||||||
\(122\) | −11738.7 | + | 4644.14i | −0.788676 | + | 0.312022i | ||||
\(123\) | − | 4341.31i | − | 0.286953i | ||||||
\(124\) | 1889.41 | + | 2014.11i | 0.122880 | + | 0.130990i | ||||
\(125\) | 2557.73 | 0.163695 | ||||||||
\(126\) | −2770.14 | − | 7001.90i | −0.174486 | − | 0.441036i | ||||
\(127\) | 15848.4i | 0.982602i | 0.870990 | + | 0.491301i | \(0.163479\pi\) | ||||
−0.870990 | + | 0.491301i | \(0.836521\pi\) | |||||||
\(128\) | 14343.0 | + | 7919.13i | 0.875430 | + | 0.483345i | ||||
\(129\) | −6152.43 | −0.369715 | ||||||||
\(130\) | 29719.5 | − | 11757.8i | 1.75855 | − | 0.695730i | ||||
\(131\) | − | 32191.2i | − | 1.87583i | −0.346860 | − | 0.937917i | \(-0.612752\pi\) | ||
0.346860 | − | 0.937917i | \(-0.387248\pi\) | |||||||
\(132\) | 5461.91 | − | 5123.74i | 0.313471 | − | 0.294062i | ||||
\(133\) | 24571.2 | 1.38907 | ||||||||
\(134\) | −7289.11 | − | 18424.2i | −0.405943 | − | 1.02607i | ||||
\(135\) | 26447.3i | 1.45115i | ||||||||
\(136\) | 11655.3 | − | 24718.7i | 0.630150 | − | 1.33644i | ||||
\(137\) | −20862.7 | −1.11155 | −0.555776 | − | 0.831332i | \(-0.687579\pi\) | ||||
−0.555776 | + | 0.831332i | \(0.687579\pi\) | |||||||
\(138\) | 14710.1 | − | 5819.71i | 0.772425 | − | 0.305593i | ||||
\(139\) | − | 224.364i | − | 0.0116124i | −0.999983 | − | 0.00580621i | \(-0.998152\pi\) | ||
0.999983 | − | 0.00580621i | \(-0.00184819\pi\) | |||||||
\(140\) | −17208.8 | − | 18344.6i | −0.878002 | − | 0.935951i | ||||
\(141\) | −15109.5 | −0.759997 | ||||||||
\(142\) | 9520.18 | + | 24063.5i | 0.472138 | + | 1.19339i | ||||
\(143\) | 17259.7i | 0.844037i | ||||||||
\(144\) | 670.810 | − | 10488.4i | 0.0323500 | − | 0.505806i | ||||
\(145\) | −46190.9 | −2.19695 | ||||||||
\(146\) | −26228.3 | + | 10376.6i | −1.23045 | + | 0.486801i | ||||
\(147\) | − | 1886.08i | − | 0.0872820i | ||||||
\(148\) | 4033.12 | − | 3783.41i | 0.184127 | − | 0.172727i | ||||
\(149\) | 3811.74 | 0.171692 | 0.0858462 | − | 0.996308i | \(-0.472641\pi\) | ||||
0.0858462 | + | 0.996308i | \(0.472641\pi\) | |||||||
\(150\) | 5118.96 | + | 12938.8i | 0.227509 | + | 0.575059i | ||||
\(151\) | − | 9236.23i | − | 0.405080i | −0.979274 | − | 0.202540i | \(-0.935080\pi\) | ||
0.979274 | − | 0.202540i | \(-0.0649196\pi\) | |||||||
\(152\) | 31019.6 | + | 14626.2i | 1.34261 | + | 0.633060i | ||||
\(153\) | −17530.5 | −0.748880 | ||||||||
\(154\) | 12630.7 | − | 4997.06i | 0.532582 | − | 0.210704i | ||||
\(155\) | − | 5917.45i | − | 0.246304i | ||||||
\(156\) | −16124.5 | − | 17188.7i | −0.662576 | − | 0.706307i | ||||
\(157\) | −29667.1 | −1.20358 | −0.601790 | − | 0.798654i | \(-0.705546\pi\) | ||||
−0.601790 | + | 0.798654i | \(0.705546\pi\) | |||||||
\(158\) | 12077.1 | + | 30526.4i | 0.483780 | + | 1.22282i | ||||
\(159\) | − | 3863.09i | − | 0.152806i | ||||||
\(160\) | −10805.3 | − | 33402.7i | −0.422081 | − | 1.30479i | ||||
\(161\) | 28692.7 | 1.10693 | ||||||||
\(162\) | 5765.91 | − | 2281.15i | 0.219704 | − | 0.0869210i | ||||
\(163\) | 20133.9i | 0.757796i | 0.925438 | + | 0.378898i | \(0.123697\pi\) | ||||
−0.925438 | + | 0.378898i | \(0.876303\pi\) | |||||||
\(164\) | 8015.39 | − | 7519.13i | 0.298014 | − | 0.279563i | ||||
\(165\) | −16047.1 | −0.589425 | ||||||||
\(166\) | 6479.95 | + | 16378.9i | 0.235156 | + | 0.594386i | ||||
\(167\) | 7545.07i | 0.270539i | 0.990809 | + | 0.135270i | \(0.0431901\pi\) | ||||
−0.990809 | + | 0.135270i | \(0.956810\pi\) | |||||||
\(168\) | −7910.35 | + | 16776.4i | −0.280270 | + | 0.594403i | ||||
\(169\) | 25755.4 | 0.901769 | ||||||||
\(170\) | −54452.1 | + | 21542.8i | −1.88416 | + | 0.745424i | ||||
\(171\) | − | 21999.1i | − | 0.752339i | ||||||
\(172\) | −10656.0 | − | 11359.3i | −0.360194 | − | 0.383967i | ||||
\(173\) | −6029.10 | −0.201447 | −0.100723 | − | 0.994914i | \(-0.532116\pi\) | ||||
−0.100723 | + | 0.994914i | \(0.532116\pi\) | |||||||
\(174\) | 12530.6 | + | 31672.7i | 0.413878 | + | 1.04613i | ||||
\(175\) | 25237.8i | 0.824092i | ||||||||
\(176\) | 18920.0 | + | 1210.07i | 0.610796 | + | 0.0390648i | ||||
\(177\) | 27694.9 | 0.884002 | ||||||||
\(178\) | −37288.6 | + | 14752.4i | −1.17689 | + | 0.465610i | ||||
\(179\) | 59397.2i | 1.85379i | 0.375325 | + | 0.926893i | \(0.377531\pi\) | ||||
−0.375325 | + | 0.926893i | \(0.622469\pi\) | |||||||
\(180\) | −16424.4 | + | 15407.5i | −0.506925 | + | 0.475539i | ||||
\(181\) | −3752.62 | −0.114545 | −0.0572727 | − | 0.998359i | \(-0.518240\pi\) | ||||
−0.0572727 | + | 0.998359i | \(0.518240\pi\) | |||||||
\(182\) | −15725.8 | − | 39748.9i | −0.474755 | − | 1.20000i | ||||
\(183\) | − | 19946.7i | − | 0.595620i | ||||||
\(184\) | 36222.7 | + | 17079.6i | 1.06991 | + | 0.504477i | ||||
\(185\) | −11849.3 | −0.346218 | ||||||||
\(186\) | −4057.53 | + | 1605.27i | −0.117283 | + | 0.0464005i | ||||
\(187\) | − | 31623.3i | − | 0.904324i | ||||||
\(188\) | −26169.6 | − | 27896.8i | −0.740425 | − | 0.789294i | ||||
\(189\) | 35372.5 | 0.990243 | ||||||||
\(190\) | −27034.1 | − | 68332.1i | −0.748867 | − | 1.89286i | ||||
\(191\) | − | 8999.22i | − | 0.246682i | −0.992364 | − | 0.123341i | \(-0.960639\pi\) | ||
0.992364 | − | 0.123341i | \(-0.0393610\pi\) | |||||||
\(192\) | −19972.6 | + | 16470.5i | −0.541792 | + | 0.446790i | ||||
\(193\) | −2072.92 | −0.0556504 | −0.0278252 | − | 0.999613i | \(-0.508858\pi\) | ||||
−0.0278252 | + | 0.999613i | \(0.508858\pi\) | |||||||
\(194\) | 50221.0 | − | 19868.8i | 1.33439 | − | 0.527921i | ||||
\(195\) | 50500.3i | 1.32808i | ||||||||
\(196\) | 3482.28 | − | 3266.68i | 0.0906465 | − | 0.0850342i | ||||
\(197\) | 31507.8 | 0.811869 | 0.405935 | − | 0.913902i | \(-0.366946\pi\) | ||||
0.405935 | + | 0.913902i | \(0.366946\pi\) | |||||||
\(198\) | −4473.97 | − | 11308.5i | −0.114120 | − | 0.288454i | ||||
\(199\) | − | 10209.6i | − | 0.257811i | −0.991657 | − | 0.128906i | \(-0.958854\pi\) | ||
0.991657 | − | 0.128906i | \(-0.0411465\pi\) | |||||||
\(200\) | −15023.0 | + | 31861.2i | −0.375576 | + | 0.796529i | ||||
\(201\) | 31307.0 | 0.774906 | ||||||||
\(202\) | 45339.0 | − | 17937.4i | 1.11114 | − | 0.439598i | ||||
\(203\) | 61779.1i | 1.49916i | ||||||||
\(204\) | 29543.3 | + | 31493.2i | 0.709902 | + | 0.756756i | ||||
\(205\) | −23549.2 | −0.560362 | ||||||||
\(206\) | 19746.5 | + | 49911.9i | 0.465325 | + | 1.17617i | ||||
\(207\) | − | 25689.2i | − | 0.599528i | ||||||
\(208\) | 3808.11 | − | 59541.4i | 0.0880202 | − | 1.37623i | ||||
\(209\) | 39684.2 | 0.908500 | ||||||||
\(210\) | 36956.3 | − | 14620.9i | 0.838011 | − | 0.331540i | ||||
\(211\) | − | 46275.0i | − | 1.03940i | −0.854350 | − | 0.519698i | \(-0.826044\pi\) | ||
0.854350 | − | 0.519698i | \(-0.173956\pi\) | |||||||
\(212\) | 7132.45 | − | 6690.85i | 0.158696 | − | 0.148871i | ||||
\(213\) | −40889.5 | −0.901265 | ||||||||
\(214\) | −18151.5 | − | 45880.4i | −0.396357 | − | 1.00184i | ||||
\(215\) | 33373.6i | 0.721981i | ||||||||
\(216\) | 44655.5 | + | 21055.8i | 0.957122 | + | 0.451298i | ||||
\(217\) | −7914.42 | −0.168074 | ||||||||
\(218\) | −43978.8 | + | 17399.2i | −0.925403 | + | 0.366115i | ||||
\(219\) | − | 44568.0i | − | 0.929256i | ||||||
\(220\) | −27793.5 | − | 29627.9i | −0.574246 | − | 0.612146i | ||||
\(221\) | −99518.8 | −2.03761 | ||||||||
\(222\) | 3214.45 | + | 8124.94i | 0.0652231 | + | 0.164860i | ||||
\(223\) | 34523.1i | 0.694225i | 0.937824 | + | 0.347112i | \(0.112838\pi\) | ||||
−0.937824 | + | 0.347112i | \(0.887162\pi\) | |||||||
\(224\) | −44675.1 | + | 14451.7i | −0.890368 | + | 0.288021i | ||||
\(225\) | 22596.0 | 0.446340 | ||||||||
\(226\) | −39540.0 | + | 15643.1i | −0.774141 | + | 0.306272i | ||||
\(227\) | 26009.3i | 0.504751i | 0.967629 | + | 0.252376i | \(0.0812118\pi\) | ||||
−0.967629 | + | 0.252376i | \(0.918788\pi\) | |||||||
\(228\) | −39520.9 | + | 37074.0i | −0.760251 | + | 0.713181i | ||||
\(229\) | 86590.4 | 1.65120 | 0.825598 | − | 0.564259i | \(-0.190838\pi\) | ||||
0.825598 | + | 0.564259i | \(0.190838\pi\) | |||||||
\(230\) | −31568.7 | − | 79794.0i | −0.596762 | − | 1.50839i | ||||
\(231\) | 21462.5i | 0.402214i | ||||||||
\(232\) | −36774.5 | + | 77992.2i | −0.683237 | + | 1.44902i | ||||
\(233\) | −27675.0 | −0.509772 | −0.254886 | − | 0.966971i | \(-0.582038\pi\) | ||||
−0.254886 | + | 0.966971i | \(0.582038\pi\) | |||||||
\(234\) | −35588.1 | + | 14079.6i | −0.649939 | + | 0.257134i | ||||
\(235\) | 81960.8i | 1.48412i | ||||||||
\(236\) | 47967.4 | + | 51133.3i | 0.861236 | + | 0.918078i | ||||
\(237\) | −51871.5 | −0.923490 | ||||||||
\(238\) | 28812.8 | + | 72828.1i | 0.508665 | + | 1.28572i | ||||
\(239\) | 3547.80i | 0.0621102i | 0.999518 | + | 0.0310551i | \(0.00988674\pi\) | ||||
−0.999518 | + | 0.0310551i | \(0.990113\pi\) | |||||||
\(240\) | 55358.2 | + | 3540.56i | 0.961080 | + | 0.0614681i | ||||
\(241\) | −76033.0 | −1.30909 | −0.654543 | − | 0.756025i | \(-0.727139\pi\) | ||||
−0.654543 | + | 0.756025i | \(0.727139\pi\) | |||||||
\(242\) | −34057.6 | + | 13474.1i | −0.581544 | + | 0.230075i | ||||
\(243\) | − | 52687.1i | − | 0.892260i | ||||||
\(244\) | 36827.8 | − | 34547.6i | 0.618580 | − | 0.580281i | ||||
\(245\) | −10230.9 | −0.170444 | ||||||||
\(246\) | 6388.38 | + | 16147.5i | 0.105565 | + | 0.266829i | ||||
\(247\) | − | 124886.i | − | 2.04702i | ||||||
\(248\) | −9991.46 | − | 4711.13i | −0.162452 | − | 0.0765988i | ||||
\(249\) | −27831.6 | −0.448890 | ||||||||
\(250\) | −9513.44 | + | 3763.78i | −0.152215 | + | 0.0602205i | ||||
\(251\) | − | 61927.9i | − | 0.982967i | −0.870887 | − | 0.491484i | \(-0.836455\pi\) | ||
0.870887 | − | 0.491484i | \(-0.163545\pi\) | |||||||
\(252\) | 20607.0 | + | 21967.1i | 0.324500 | + | 0.345917i | ||||
\(253\) | 46340.7 | 0.723971 | ||||||||
\(254\) | −23321.4 | − | 58947.9i | −0.361483 | − | 0.913694i | ||||
\(255\) | − | 92526.9i | − | 1.42294i | ||||||
\(256\) | −65002.0 | − | 8348.86i | −0.991852 | − | 0.127393i | ||||
\(257\) | 4753.43 | 0.0719683 | 0.0359841 | − | 0.999352i | \(-0.488543\pi\) | ||||
0.0359841 | + | 0.999352i | \(0.488543\pi\) | |||||||
\(258\) | 22883.9 | − | 9053.51i | 0.343788 | − | 0.136012i | ||||
\(259\) | 15848.1i | 0.236253i | ||||||||
\(260\) | −93239.1 | + | 87466.3i | −1.37928 | + | 1.29388i | ||||
\(261\) | 55312.2 | 0.811969 | ||||||||
\(262\) | 47370.4 | + | 119735.i | 0.690088 | + | 1.74429i | ||||
\(263\) | − | 40642.1i | − | 0.587578i | −0.955870 | − | 0.293789i | \(-0.905084\pi\) | ||
0.955870 | − | 0.293789i | \(-0.0949162\pi\) | |||||||
\(264\) | −12775.8 | + | 27095.1i | −0.183307 | + | 0.388761i | ||||
\(265\) | −20955.1 | −0.298400 | ||||||||
\(266\) | −91392.3 | + | 36157.3i | −1.29165 | + | 0.511014i | ||||
\(267\) | − | 63362.0i | − | 0.888805i | ||||||
\(268\) | 54223.5 | + | 57802.3i | 0.754950 | + | 0.804777i | ||||
\(269\) | −1417.58 | −0.0195904 | −0.00979520 | − | 0.999952i | \(-0.503118\pi\) | ||||
−0.00979520 | + | 0.999952i | \(0.503118\pi\) | |||||||
\(270\) | −38918.0 | − | 98370.3i | −0.533855 | − | 1.34939i | ||||
\(271\) | − | 8685.84i | − | 0.118270i | −0.998250 | − | 0.0591348i | \(-0.981166\pi\) | ||
0.998250 | − | 0.0591348i | \(-0.0188342\pi\) | |||||||
\(272\) | −6977.23 | + | 109092.i | −0.0943073 | + | 1.47454i | ||||
\(273\) | 67542.7 | 0.906261 | ||||||||
\(274\) | 77598.7 | − | 30700.2i | 1.03360 | − | 0.408922i | ||||
\(275\) | 40760.8i | 0.538986i | ||||||||
\(276\) | −46150.0 | + | 43292.7i | −0.605834 | + | 0.568324i | ||||
\(277\) | 64381.4 | 0.839075 | 0.419538 | − | 0.907738i | \(-0.362192\pi\) | ||||
0.419538 | + | 0.907738i | \(0.362192\pi\) | |||||||
\(278\) | 330.159 | + | 834.518i | 0.00427202 | + | 0.0107981i | ||||
\(279\) | 7085.95i | 0.0910311i | ||||||||
\(280\) | 91002.8 | + | 42909.3i | 1.16075 | + | 0.547312i | ||||
\(281\) | −104740. | −1.32647 | −0.663237 | − | 0.748410i | \(-0.730818\pi\) | ||||
−0.663237 | + | 0.748410i | \(0.730818\pi\) | |||||||
\(282\) | 56199.6 | − | 22234.1i | 0.706700 | − | 0.279590i | ||||
\(283\) | − | 86277.0i | − | 1.07726i | −0.842541 | − | 0.538632i | \(-0.818941\pi\) | ||
0.842541 | − | 0.538632i | \(-0.181059\pi\) | |||||||
\(284\) | −70820.4 | − | 75494.6i | −0.878055 | − | 0.936007i | ||||
\(285\) | 116112. | 1.42951 | ||||||||
\(286\) | −25398.2 | − | 64197.3i | −0.310507 | − | 0.784846i | ||||
\(287\) | 31496.4i | 0.382382i | ||||||||
\(288\) | 12939.0 | + | 39998.6i | 0.155996 | + | 0.482236i | ||||
\(289\) | 98817.7 | 1.18315 | ||||||||
\(290\) | 171807. | − | 67971.5i | 2.04289 | − | 0.808222i | ||||
\(291\) | 85337.3i | 1.00775i | ||||||||
\(292\) | 82286.3 | − | 77191.6i | 0.965077 | − | 0.905325i | ||||
\(293\) | 118.705 | 0.00138272 | 0.000691358 | − | 1.00000i | \(-0.499780\pi\) | ||||
0.000691358 | 1.00000i | \(0.499780\pi\) | ||||||||
\(294\) | 2775.42 | + | 7015.24i | 0.0321096 | + | 0.0811611i | ||||
\(295\) | − | 150230.i | − | 1.72628i | ||||||
\(296\) | −9433.73 | + | 20007.2i | −0.107671 | + | 0.228351i | ||||
\(297\) | 57129.0 | 0.647655 | ||||||||
\(298\) | −14177.7 | + | 5609.10i | −0.159652 | + | 0.0631627i | ||||
\(299\) | − | 145835.i | − | 1.63124i | ||||||
\(300\) | −38079.8 | − | 40593.1i | −0.423109 | − | 0.451034i | ||||
\(301\) | 44636.2 | 0.492668 | ||||||||
\(302\) | 13591.4 | + | 34354.0i | 0.149022 | + | 0.376673i | ||||
\(303\) | 77041.6i | 0.839150i | ||||||||
\(304\) | −136900. | − | 8755.75i | −1.48134 | − | 0.0947428i | ||||
\(305\) | −108200. | −1.16313 | ||||||||
\(306\) | 65204.6 | − | 25796.8i | 0.696363 | − | 0.275500i | ||||
\(307\) | − | 56068.2i | − | 0.594895i | −0.954738 | − | 0.297447i | \(-0.903865\pi\) | ||
0.954738 | − | 0.297447i | \(-0.0961353\pi\) | |||||||
\(308\) | −39626.4 | + | 37173.0i | −0.417718 | + | 0.391856i | ||||
\(309\) | −84812.0 | −0.888260 | ||||||||
\(310\) | 8707.72 | + | 22009.9i | 0.0906110 | + | 0.229031i | ||||
\(311\) | − | 11136.2i | − | 0.115137i | −0.998342 | − | 0.0575686i | \(-0.981665\pi\) | ||
0.998342 | − | 0.0575686i | \(-0.0183348\pi\) | |||||||
\(312\) | 85268.4 | + | 40205.4i | 0.875950 | + | 0.413024i | ||||
\(313\) | −125438. | −1.28038 | −0.640192 | − | 0.768215i | \(-0.721145\pi\) | ||||
−0.640192 | + | 0.768215i | \(0.721145\pi\) | |||||||
\(314\) | 110346. | − | 43656.0i | 1.11918 | − | 0.442777i | ||||
\(315\) | − | 64539.3i | − | 0.650434i | ||||||
\(316\) | −89841.2 | − | 95770.8i | −0.899708 | − | 0.959089i | ||||
\(317\) | 44565.5 | 0.443486 | 0.221743 | − | 0.975105i | \(-0.428825\pi\) | ||||
0.221743 | + | 0.975105i | \(0.428825\pi\) | |||||||
\(318\) | 5684.66 | + | 14368.7i | 0.0562148 | + | 0.142090i | ||||
\(319\) | 99777.5i | 0.980508i | ||||||||
\(320\) | 89343.2 | + | 108341.i | 0.872492 | + | 1.05801i | ||||
\(321\) | 77961.5 | 0.756607 | ||||||||
\(322\) | −106722. | + | 42222.2i | −1.02930 | + | 0.407220i | ||||
\(323\) | 228817.i | 2.19323i | ||||||||
\(324\) | −18089.4 | + | 16969.5i | −0.172320 | + | 0.161651i | ||||
\(325\) | 128275. | 1.21443 | ||||||||
\(326\) | −29627.7 | − | 74887.7i | −0.278780 | − | 0.704653i | ||||
\(327\) | − | 74730.3i | − | 0.698878i | ||||||
\(328\) | −18748.5 | + | 39762.2i | −0.174269 | + | 0.369592i | ||||
\(329\) | 109620. | 1.01274 | ||||||||
\(330\) | 59687.0 | − | 23613.8i | 0.548090 | − | 0.216839i | ||||
\(331\) | 76858.6i | 0.701514i | 0.936466 | + | 0.350757i | \(0.114076\pi\) | ||||
−0.936466 | + | 0.350757i | \(0.885924\pi\) | |||||||
\(332\) | −48204.2 | − | 51385.7i | −0.437329 | − | 0.466193i | ||||
\(333\) | 14189.2 | 0.127958 | ||||||||
\(334\) | −11102.8 | − | 28063.8i | −0.0995269 | − | 0.251567i | ||||
\(335\) | − | 169823.i | − | 1.51324i | ||||||
\(336\) | 4735.40 | − | 74040.0i | 0.0419448 | − | 0.655825i | ||||
\(337\) | −140790. | −1.23968 | −0.619842 | − | 0.784727i | \(-0.712803\pi\) | ||||
−0.619842 | + | 0.784727i | \(0.712803\pi\) | |||||||
\(338\) | −95797.0 | + | 37900.0i | −0.838530 | + | 0.331746i | ||||
\(339\) | − | 67187.8i | − | 0.584643i | ||||||
\(340\) | 170833. | − | 160256.i | 1.47779 | − | 1.38630i | ||||
\(341\) | −12782.3 | −0.109926 | ||||||||
\(342\) | 32372.4 | + | 81825.5i | 0.276773 | + | 0.699579i | ||||
\(343\) | 123779.i | 1.05210i | ||||||||
\(344\) | 56350.4 | + | 26570.1i | 0.476190 | + | 0.224531i | ||||
\(345\) | 135589. | 1.13916 | ||||||||
\(346\) | 22425.2 | − | 8872.02i | 0.187320 | − | 0.0741089i | ||||
\(347\) | 86322.6i | 0.716911i | 0.933547 | + | 0.358456i | \(0.116697\pi\) | ||||
−0.933547 | + | 0.358456i | \(0.883303\pi\) | |||||||
\(348\) | −93214.7 | − | 99366.9i | −0.769708 | − | 0.820509i | ||||
\(349\) | −89643.9 | −0.735986 | −0.367993 | − | 0.929828i | \(-0.619955\pi\) | ||||
−0.367993 | + | 0.929828i | \(0.619955\pi\) | |||||||
\(350\) | −37138.3 | − | 93871.8i | −0.303170 | − | 0.766300i | ||||
\(351\) | − | 179785.i | − | 1.45928i | ||||||
\(352\) | −72153.4 | + | 23340.6i | −0.582333 | + | 0.188376i | ||||
\(353\) | 117441. | 0.942478 | 0.471239 | − | 0.882006i | \(-0.343807\pi\) | ||||
0.471239 | + | 0.882006i | \(0.343807\pi\) | |||||||
\(354\) | −103011. | + | 40754.0i | −0.822009 | + | 0.325209i | ||||
\(355\) | 221803.i | 1.75999i | ||||||||
\(356\) | 116986. | − | 109743.i | 0.923067 | − | 0.865916i | ||||
\(357\) | −123752. | −0.970993 | ||||||||
\(358\) | −87404.9 | − | 220927.i | −0.681977 | − | 1.72378i | ||||
\(359\) | − | 208824.i | − | 1.62029i | −0.586233 | − | 0.810143i | \(-0.699390\pi\) | ||
0.586233 | − | 0.810143i | \(-0.300610\pi\) | |||||||
\(360\) | 38417.6 | − | 81476.8i | 0.296432 | − | 0.628679i | ||||
\(361\) | −156823. | −1.20336 | ||||||||
\(362\) | 13957.8 | − | 5522.11i | 0.106513 | − | 0.0421393i | ||||
\(363\) | − | 57871.8i | − | 0.439191i | ||||||
\(364\) | 116984. | + | 124705.i | 0.882922 | + | 0.941196i | ||||
\(365\) | −241757. | −1.81465 | ||||||||
\(366\) | 29352.3 | + | 74191.6i | 0.219119 | + | 0.553851i | ||||
\(367\) | 25998.4i | 0.193025i | 0.995332 | + | 0.0965127i | \(0.0307688\pi\) | ||||
−0.995332 | + | 0.0965127i | \(0.969231\pi\) | |||||||
\(368\) | −159863. | − | 10224.4i | −1.18046 | − | 0.0754992i | ||||
\(369\) | 28199.4 | 0.207104 | ||||||||
\(370\) | 44073.3 | − | 17436.6i | 0.321938 | − | 0.127368i | ||||
\(371\) | 28026.9i | 0.203623i | ||||||||
\(372\) | 12729.7 | − | 11941.6i | 0.0919885 | − | 0.0862931i | ||||
\(373\) | 61928.2 | 0.445114 | 0.222557 | − | 0.974920i | \(-0.428560\pi\) | ||||
0.222557 | + | 0.974920i | \(0.428560\pi\) | |||||||
\(374\) | 46534.7 | + | 117623.i | 0.332686 | + | 0.840906i | ||||
\(375\) | − | 16165.6i | − | 0.114955i | ||||||
\(376\) | 138389. | + | 65252.4i | 0.978869 | + | 0.461552i | ||||
\(377\) | 314001. | 2.20926 | ||||||||
\(378\) | −131567. | + | 52051.7i | −0.920799 | + | 0.364294i | ||||
\(379\) | 215762.i | 1.50210i | 0.660248 | + | 0.751048i | \(0.270451\pi\) | ||||
−0.660248 | + | 0.751048i | \(0.729549\pi\) | |||||||
\(380\) | 201106. | + | 214379.i | 1.39270 | + | 1.48462i | ||||
\(381\) | 100166. | 0.690036 | ||||||||
\(382\) | 13242.6 | + | 33472.5i | 0.0907503 | + | 0.229383i | ||||
\(383\) | 104151.i | 0.710013i | 0.934864 | + | 0.355006i | \(0.115521\pi\) | ||||
−0.934864 | + | 0.355006i | \(0.884479\pi\) | |||||||
\(384\) | 50051.1 | − | 90652.1i | 0.339431 | − | 0.614774i | ||||
\(385\) | 116422. | 0.785444 | ||||||||
\(386\) | 7710.20 | − | 3050.37i | 0.0517477 | − | 0.0204728i | ||||
\(387\) | − | 39963.8i | − | 0.266836i | ||||||
\(388\) | −157559. | + | 147804.i | −1.04660 | + | 0.981798i | ||||
\(389\) | 42415.3 | 0.280300 | 0.140150 | − | 0.990130i | \(-0.455241\pi\) | ||||
0.140150 | + | 0.990130i | \(0.455241\pi\) | |||||||
\(390\) | −74312.9 | − | 187835.i | −0.488579 | − | 1.23495i | ||||
\(391\) | 267199.i | 1.74776i | ||||||||
\(392\) | −8145.27 | + | 17274.6i | −0.0530070 | + | 0.112418i | ||||
\(393\) | −203457. | −1.31731 | ||||||||
\(394\) | −117193. | + | 46364.8i | −0.754934 | + | 0.298673i | ||||
\(395\) | 281374.i | 1.80339i | ||||||||
\(396\) | 33281.8 | + | 35478.4i | 0.212235 | + | 0.226242i | ||||
\(397\) | −159398. | −1.01135 | −0.505674 | − | 0.862724i | \(-0.668756\pi\) | ||||
−0.505674 | + | 0.862724i | \(0.668756\pi\) | |||||||
\(398\) | 15023.7 | + | 37974.5i | 0.0948445 | + | 0.239732i | ||||
\(399\) | − | 155297.i | − | 0.975477i | ||||||
\(400\) | 8993.29 | − | 140614.i | 0.0562081 | − | 0.878838i | ||||
\(401\) | −16058.4 | −0.0998650 | −0.0499325 | − | 0.998753i | \(-0.515901\pi\) | ||||
−0.0499325 | + | 0.998753i | \(0.515901\pi\) | |||||||
\(402\) | −116446. | + | 46069.2i | −0.720563 | + | 0.285075i | ||||
\(403\) | 40226.1i | 0.247684i | ||||||||
\(404\) | −142242. | + | 133436.i | −0.871498 | + | 0.817540i | ||||
\(405\) | 53146.8 | 0.324016 | ||||||||
\(406\) | −90909.9 | − | 229787.i | −0.551517 | − | 1.39403i | ||||
\(407\) | 25595.8i | 0.154518i | ||||||||
\(408\) | −156229. | − | 73664.5i | −0.938516 | − | 0.442525i | ||||
\(409\) | 125083. | 0.747741 | 0.373870 | − | 0.927481i | \(-0.378030\pi\) | ||||
0.373870 | + | 0.927481i | \(0.378030\pi\) | |||||||
\(410\) | 87591.0 | − | 34653.4i | 0.521065 | − | 0.206148i | ||||
\(411\) | 131858.i | 0.780592i | ||||||||
\(412\) | −146894. | − | 156589.i | −0.865385 | − | 0.922501i | ||||
\(413\) | −200928. | −1.17799 | ||||||||
\(414\) | 37802.5 | + | 95550.7i | 0.220556 | + | 0.557485i | ||||
\(415\) | 150971.i | 0.876592i | ||||||||
\(416\) | 73452.9 | + | 227067.i | 0.424446 | + | 1.31210i | ||||
\(417\) | −1418.04 | −0.00815487 | ||||||||
\(418\) | −147605. | + | 58396.6i | −0.844789 | + | 0.334222i | ||||
\(419\) | − | 181403.i | − | 1.03328i | −0.856204 | − | 0.516638i | \(-0.827183\pi\) | ||
0.856204 | − | 0.516638i | \(-0.172817\pi\) | |||||||
\(420\) | −115943. | + | 108765.i | −0.657275 | + | 0.616580i | ||||
\(421\) | −76021.6 | −0.428916 | −0.214458 | − | 0.976733i | \(-0.568799\pi\) | ||||
−0.214458 | + | 0.976733i | \(0.568799\pi\) | |||||||
\(422\) | 68095.2 | + | 172119.i | 0.382377 | + | 0.966506i | ||||
\(423\) | − | 98145.4i | − | 0.548516i | ||||||
\(424\) | −16683.3 | + | 35382.2i | −0.0928002 | + | 0.196813i | ||||
\(425\) | −235025. | −1.30118 | ||||||||
\(426\) | 152088. | − | 60170.3i | 0.838062 | − | 0.331560i | ||||
\(427\) | 144714.i | 0.793699i | ||||||||
\(428\) | 135029. | + | 143941.i | 0.737122 | + | 0.785772i | ||||
\(429\) | 109086. | 0.592728 | ||||||||
\(430\) | −49110.3 | − | 124133.i | −0.265605 | − | 0.671350i | ||||
\(431\) | − | 346086.i | − | 1.86307i | −0.363651 | − | 0.931535i | \(-0.618470\pi\) | ||
0.363651 | − | 0.931535i | \(-0.381530\pi\) | |||||||
\(432\) | −197080. | − | 12604.7i | −1.05603 | − | 0.0675406i | ||||
\(433\) | −236255. | −1.26010 | −0.630049 | − | 0.776555i | \(-0.716965\pi\) | ||||
−0.630049 | + | 0.776555i | \(0.716965\pi\) | |||||||
\(434\) | 29437.6 | − | 11646.3i | 0.156287 | − | 0.0618315i | ||||
\(435\) | 291940.i | 1.54282i | ||||||||
\(436\) | 137975. | − | 129433.i | 0.725818 | − | 0.680880i | ||||
\(437\) | −335308. | −1.75583 | ||||||||
\(438\) | 65583.3 | + | 165770.i | 0.341858 | + | 0.864089i | ||||
\(439\) | 281888.i | 1.46268i | 0.682015 | + | 0.731338i | \(0.261104\pi\) | ||||
−0.682015 | + | 0.731338i | \(0.738896\pi\) | |||||||
\(440\) | 146976. | + | 69301.5i | 0.759173 | + | 0.357962i | ||||
\(441\) | 12251.2 | 0.0629943 | ||||||||
\(442\) | 370159. | − | 146445.i | 1.89471 | − | 0.749601i | ||||
\(443\) | 11327.7i | 0.0577209i | 0.999583 | + | 0.0288605i | \(0.00918785\pi\) | ||||
−0.999583 | + | 0.0288605i | \(0.990812\pi\) | |||||||
\(444\) | −23912.2 | − | 25490.5i | −0.121298 | − | 0.129304i | ||||
\(445\) | −343704. | −1.73566 | ||||||||
\(446\) | −50801.9 | − | 128408.i | −0.255394 | − | 0.645540i | ||||
\(447\) | − | 24091.3i | − | 0.120572i | ||||||
\(448\) | 144902. | − | 119494.i | 0.721970 | − | 0.595374i | ||||
\(449\) | 49613.7 | 0.246098 | 0.123049 | − | 0.992401i | \(-0.460733\pi\) | ||||
0.123049 | + | 0.992401i | \(0.460733\pi\) | |||||||
\(450\) | −84045.5 | + | 33250.7i | −0.415039 | + | 0.164201i | ||||
\(451\) | 50868.9i | 0.250092i | ||||||||
\(452\) | 124049. | − | 116369.i | 0.607180 | − | 0.569587i | ||||
\(453\) | −58375.6 | −0.284469 | ||||||||
\(454\) | −38273.6 | − | 96741.4i | −0.185689 | − | 0.469354i | ||||
\(455\) | − | 366382.i | − | 1.76975i | ||||||
\(456\) | 92441.9 | − | 196053.i | 0.444569 | − | 0.942850i | ||||
\(457\) | −96047.8 | −0.459891 | −0.229946 | − | 0.973203i | \(-0.573855\pi\) | ||||
−0.229946 | + | 0.973203i | \(0.573855\pi\) | |||||||
\(458\) | −322072. | + | 127421.i | −1.53540 | + | 0.607447i | ||||
\(459\) | 329403.i | 1.56352i | ||||||||
\(460\) | 234839. | + | 250338.i | 1.10982 | + | 1.18307i | ||||
\(461\) | 261473. | 1.23034 | 0.615169 | − | 0.788395i | \(-0.289088\pi\) | ||||
0.615169 | + | 0.788395i | \(0.289088\pi\) | |||||||
\(462\) | −31582.8 | − | 79829.6i | −0.147968 | − | 0.374007i | ||||
\(463\) | 203922.i | 0.951266i | 0.879644 | + | 0.475633i | \(0.157781\pi\) | ||||
−0.879644 | + | 0.475633i | \(0.842219\pi\) | |||||||
\(464\) | 22014.5 | − | 344206.i | 0.102252 | − | 1.59876i | ||||
\(465\) | −37400.0 | −0.172968 | ||||||||
\(466\) | 102937. | − | 40724.7i | 0.474023 | − | 0.187537i | ||||
\(467\) | 318175.i | 1.45892i | 0.684021 | + | 0.729462i | \(0.260230\pi\) | ||||
−0.684021 | + | 0.729462i | \(0.739770\pi\) | |||||||
\(468\) | 111651. | − | 104738.i | 0.509765 | − | 0.478204i | ||||
\(469\) | −227133. | −1.03261 | ||||||||
\(470\) | −120608. | − | 304852.i | −0.545984 | − | 1.38005i | ||||
\(471\) | 187504.i | 0.845219i | ||||||||
\(472\) | −253659. | − | 119604.i | −1.13859 | − | 0.536861i | ||||
\(473\) | 72090.5 | 0.322223 | ||||||||
\(474\) | 192936. | − | 76330.6i | 0.858728 | − | 0.339737i | ||||
\(475\) | − | 294934.i | − | 1.30719i | ||||||
\(476\) | −214338. | − | 228484.i | −0.945987 | − | 1.00842i | ||||
\(477\) | 25093.1 | 0.110285 | ||||||||
\(478\) | −5220.70 | − | 13196.0i | −0.0228493 | − | 0.0577546i | ||||
\(479\) | − | 326676.i | − | 1.42379i | −0.702286 | − | 0.711895i | \(-0.747837\pi\) | ||
0.702286 | − | 0.711895i | \(-0.252163\pi\) | |||||||
\(480\) | −211114. | + | 68292.3i | −0.916295 | + | 0.296408i | ||||
\(481\) | 80550.1 | 0.348158 | ||||||||
\(482\) | 282804. | − | 111885.i | 1.21728 | − | 0.481591i | ||||
\(483\) | − | 181346.i | − | 0.777344i | ||||||
\(484\) | 106849. | − | 100234.i | 0.456121 | − | 0.427881i | ||||
\(485\) | 462908. | 1.96794 | ||||||||
\(486\) | 77530.7 | + | 195969.i | 0.328247 | + | 0.829687i | ||||
\(487\) | − | 312827.i | − | 1.31901i | −0.751702 | − | 0.659503i | \(-0.770767\pi\) | ||
0.751702 | − | 0.659503i | \(-0.229233\pi\) | |||||||
\(488\) | −86142.6 | + | 182693.i | −0.361725 | + | 0.767153i | ||||
\(489\) | 127252. | 0.532165 | ||||||||
\(490\) | 38053.8 | − | 15055.1i | 0.158492 | − | 0.0627036i | ||||
\(491\) | 178766.i | 0.741517i | 0.928729 | + | 0.370759i | \(0.120902\pi\) | ||||
−0.928729 | + | 0.370759i | \(0.879098\pi\) | |||||||
\(492\) | −47523.0 | − | 50659.6i | −0.196324 | − | 0.209282i | ||||
\(493\) | −575313. | −2.36707 | ||||||||
\(494\) | 183774. | + | 464514.i | 0.753063 | + | 1.90346i | ||||
\(495\) | − | 104236.i | − | 0.425408i | ||||||
\(496\) | 44095.7 | + | 2820.24i | 0.179239 | + | 0.0114636i | ||||
\(497\) | 296655. | 1.20099 | ||||||||
\(498\) | 103519. | − | 40955.1i | 0.417410 | − | 0.165139i | ||||
\(499\) | − | 122318.i | − | 0.491236i | −0.969367 | − | 0.245618i | \(-0.921009\pi\) | ||
0.969367 | − | 0.245618i | \(-0.0789908\pi\) | |||||||
\(500\) | 29846.6 | − | 27998.7i | 0.119386 | − | 0.111995i | ||||
\(501\) | 47687.0 | 0.189987 | ||||||||
\(502\) | 91129.0 | + | 230340.i | 0.361617 | + | 0.914034i | ||||
\(503\) | − | 248135.i | − | 0.980734i | −0.871516 | − | 0.490367i | \(-0.836863\pi\) | ||
0.871516 | − | 0.490367i | \(-0.163137\pi\) | |||||||
\(504\) | −108973. | − | 51382.5i | −0.429000 | − | 0.202280i | ||||
\(505\) | 417908. | 1.63869 | ||||||||
\(506\) | −172364. | + | 68191.8i | −0.673201 | + | 0.266337i | ||||
\(507\) | − | 162782.i | − | 0.633271i | ||||||
\(508\) | 173487. | + | 184938.i | 0.672265 | + | 0.716635i | ||||
\(509\) | 334708. | 1.29191 | 0.645953 | − | 0.763377i | \(-0.276460\pi\) | ||||
0.645953 | + | 0.763377i | \(0.276460\pi\) | |||||||
\(510\) | 136156. | + | 344153.i | 0.523477 | + | 1.32316i | ||||
\(511\) | 323343.i | 1.23829i | ||||||||
\(512\) | 254060. | − | 64599.1i | 0.969162 | − | 0.246426i | ||||
\(513\) | −413369. | −1.57074 | ||||||||
\(514\) | −17680.3 | + | 6994.83i | −0.0669213 | + | 0.0264759i | ||||
\(515\) | 460058.i | 1.73460i | ||||||||
\(516\) | −71793.9 | + | 67348.8i | −0.269642 | + | 0.252948i | ||||
\(517\) | 177044. | 0.662370 | ||||||||
\(518\) | −23321.0 | − | 58946.8i | −0.0869136 | − | 0.219685i | ||||
\(519\) | 38105.6i | 0.141467i | ||||||||
\(520\) | 218092. | − | 462534.i | 0.806554 | − | 1.71056i | ||||
\(521\) | 340339. | 1.25382 | 0.626912 | − | 0.779090i | \(-0.284318\pi\) | ||||
0.626912 | + | 0.779090i | \(0.284318\pi\) | |||||||
\(522\) | −205733. | + | 81393.6i | −0.755027 | + | 0.298710i | ||||
\(523\) | 28259.2i | 0.103313i | 0.998665 | + | 0.0516567i | \(0.0164502\pi\) | ||||
−0.998665 | + | 0.0516567i | \(0.983550\pi\) | |||||||
\(524\) | −352387. | − | 375645.i | −1.28339 | − | 1.36809i | ||||
\(525\) | 159510. | 0.578722 | ||||||||
\(526\) | 59806.2 | + | 151168.i | 0.216160 | + | 0.546372i | ||||
\(527\) | − | 73702.5i | − | 0.265375i | ||||||
\(528\) | 7648.00 | − | 119580.i | 0.0274334 | − | 0.428933i | ||||
\(529\) | −111711. | −0.399194 | ||||||||
\(530\) | 77942.3 | − | 30836.2i | 0.277474 | − | 0.109776i | ||||
\(531\) | 179895.i | 0.638014i | ||||||||
\(532\) | 286726. | − | 268973.i | 1.01308 | − | 0.950356i | ||||
\(533\) | 160085. | 0.563502 | ||||||||
\(534\) | 93239.3 | + | 235674.i | 0.326977 | + | 0.826475i | ||||
\(535\) | − | 422898.i | − | 1.47750i | ||||||
\(536\) | −286742. | − | 135203.i | −0.998070 | − | 0.470606i | ||||
\(537\) | 375407. | 1.30183 | ||||||||
\(538\) | 5272.68 | − | 2086.02i | 0.0182166 | − | 0.00720698i | ||||
\(539\) | 22099.9i | 0.0760700i | ||||||||
\(540\) | 289510. | + | 308618.i | 0.992833 | + | 1.05836i | ||||
\(541\) | 496161. | 1.69523 | 0.847614 | − | 0.530614i | \(-0.178039\pi\) | ||||
0.847614 | + | 0.530614i | \(0.178039\pi\) | |||||||
\(542\) | 12781.5 | + | 32306.9i | 0.0435094 | + | 0.109976i | ||||
\(543\) | 23717.6i | 0.0804400i | ||||||||
\(544\) | −134581. | − | 416034.i | −0.454763 | − | 1.40582i | ||||
\(545\) | −405371. | −1.36477 | ||||||||
\(546\) | −251224. | + | 99391.4i | −0.842707 | + | 0.333398i | ||||
\(547\) | 122088.i | 0.408034i | 0.978967 | + | 0.204017i | \(0.0653998\pi\) | ||||
−0.978967 | + | 0.204017i | \(0.934600\pi\) | |||||||
\(548\) | −243451. | + | 228378.i | −0.810682 | + | 0.760489i | ||||
\(549\) | 129566. | 0.429879 | ||||||||
\(550\) | −59980.9 | − | 151609.i | −0.198284 | − | 0.501188i | ||||
\(551\) | − | 721962.i | − | 2.37800i | ||||||
\(552\) | 107948. | − | 228938.i | 0.354271 | − | 0.751345i | ||||
\(553\) | 376330. | 1.23061 | ||||||||
\(554\) | −239466. | + | 94739.4i | −0.780233 | + | 0.308682i | ||||
\(555\) | 74890.9i | 0.243133i | ||||||||
\(556\) | −2456.04 | − | 2618.14i | −0.00794486 | − | 0.00846922i | ||||
\(557\) | −324387. | −1.04557 | −0.522785 | − | 0.852464i | \(-0.675107\pi\) | ||||
−0.522785 | + | 0.852464i | \(0.675107\pi\) | |||||||
\(558\) | −10427.2 | − | 26356.1i | −0.0334888 | − | 0.0846473i | ||||
\(559\) | − | 226870.i | − | 0.726027i | ||||||
\(560\) | −401626. | − | 25686.9i | −1.28070 | − | 0.0819099i | ||||
\(561\) | −199868. | −0.635065 | ||||||||
\(562\) | 389578. | − | 154128.i | 1.23345 | − | 0.487987i | ||||
\(563\) | − | 180882.i | − | 0.570662i | −0.958429 | − | 0.285331i | \(-0.907897\pi\) | ||
0.958429 | − | 0.285331i | \(-0.0921035\pi\) | |||||||
\(564\) | −176316. | + | 165399.i | −0.554284 | + | 0.519966i | ||||
\(565\) | −364457. | −1.14169 | ||||||||
\(566\) | 126959. | + | 320906.i | 0.396307 | + | 1.00172i | ||||
\(567\) | − | 71082.3i | − | 0.221103i | ||||||
\(568\) | 374509. | + | 176587.i | 1.16082 | + | 0.547345i | ||||
\(569\) | 345837. | 1.06819 | 0.534093 | − | 0.845426i | \(-0.320653\pi\) | ||||
0.534093 | + | 0.845426i | \(0.320653\pi\) | |||||||
\(570\) | −431878. | + | 170863.i | −1.32927 | + | 0.525894i | ||||
\(571\) | − | 239120.i | − | 0.733405i | −0.930338 | − | 0.366703i | \(-0.880487\pi\) | ||
0.930338 | − | 0.366703i | \(-0.119513\pi\) | |||||||
\(572\) | 188937. | + | 201407.i | 0.577463 | + | 0.615576i | ||||
\(573\) | −56877.6 | −0.173234 | ||||||||
\(574\) | −46348.0 | − | 117151.i | −0.140672 | − | 0.355566i | ||||
\(575\) | − | 344405.i | − | 1.04168i | ||||||
\(576\) | −106986. | − | 129734.i | −0.322463 | − | 0.391030i | ||||
\(577\) | 78021.8 | 0.234350 | 0.117175 | − | 0.993111i | \(-0.462616\pi\) | ||||
0.117175 | + | 0.993111i | \(0.462616\pi\) | |||||||
\(578\) | −367551. | + | 145413.i | −1.10018 | + | 0.435260i | ||||
\(579\) | 13101.4i | 0.0390807i | ||||||||
\(580\) | −539011. | + | 505638.i | −1.60229 | + | 1.50309i | ||||
\(581\) | 201920. | 0.598172 | ||||||||
\(582\) | −125577. | − | 317411.i | −0.370734 | − | 0.937079i | ||||
\(583\) | 45265.4i | 0.133177i | ||||||||
\(584\) | −192473. | + | 408200.i | −0.564344 | + | 1.19687i | ||||
\(585\) | −328030. | −0.958521 | ||||||||
\(586\) | −441.521 | + | 174.678i | −0.00128575 | + | 0.000508678i | ||||
\(587\) | − | 619048.i | − | 1.79659i | −0.439396 | − | 0.898293i | \(-0.644808\pi\) | ||
0.439396 | − | 0.898293i | \(-0.355192\pi\) | |||||||
\(588\) | −20646.3 | − | 22009.0i | −0.0597156 | − | 0.0636569i | ||||
\(589\) | 92489.5 | 0.266601 | ||||||||
\(590\) | 221068. | + | 558777.i | 0.635070 | + | 1.60522i | ||||
\(591\) | − | 199138.i | − | 0.570138i | ||||||
\(592\) | 5647.34 | − | 88298.7i | 0.0161139 | − | 0.251948i | ||||
\(593\) | −501794. | −1.42697 | −0.713486 | − | 0.700669i | \(-0.752885\pi\) | ||||
−0.713486 | + | 0.700669i | \(0.752885\pi\) | |||||||
\(594\) | −212491. | + | 84067.1i | −0.602236 | + | 0.238261i | ||||
\(595\) | 671287.i | 1.89616i | ||||||||
\(596\) | 44479.9 | − | 41726.0i | 0.125219 | − | 0.117467i | ||||
\(597\) | −64527.5 | −0.181049 | ||||||||
\(598\) | 214600. | + | 542430.i | 0.600106 | + | 1.51684i | ||||
\(599\) | 290536.i | 0.809742i | 0.914374 | + | 0.404871i | \(0.132684\pi\) | ||||
−0.914374 | + | 0.404871i | \(0.867316\pi\) | |||||||
\(600\) | 201371. | + | 94949.9i | 0.559365 | + | 0.263750i | ||||
\(601\) | −126251. | −0.349532 | −0.174766 | − | 0.984610i | \(-0.555917\pi\) | ||||
−0.174766 | + | 0.984610i | \(0.555917\pi\) | |||||||
\(602\) | −166024. | + | 65683.6i | −0.458118 | + | 0.181244i | ||||
\(603\) | 203358.i | 0.559275i | ||||||||
\(604\) | −101106. | − | 107779.i | −0.277143 | − | 0.295435i | ||||
\(605\) | −313923. | −0.857653 | ||||||||
\(606\) | −113369. | − | 286555.i | −0.308709 | − | 0.780302i | ||||
\(607\) | − | 392034.i | − | 1.06401i | −0.846741 | − | 0.532006i | \(-0.821439\pi\) | ||
0.846741 | − | 0.532006i | \(-0.178561\pi\) | |||||||
\(608\) | 522082. | − | 168886.i | 1.41232 | − | 0.456863i | ||||
\(609\) | 390461. | 1.05279 | ||||||||
\(610\) | 402449. | − | 159220.i | 1.08156 | − | 0.427895i | ||||
\(611\) | − | 557159.i | − | 1.49244i | ||||||
\(612\) | −204567. | + | 191901.i | −0.546176 | + | 0.512360i | ||||
\(613\) | 186670. | 0.496767 | 0.248384 | − | 0.968662i | \(-0.420101\pi\) | ||||
0.248384 | + | 0.968662i | \(0.420101\pi\) | |||||||
\(614\) | 82506.2 | + | 208545.i | 0.218852 | + | 0.553176i | ||||
\(615\) | 148838.i | 0.393516i | ||||||||
\(616\) | 92688.7 | − | 196576.i | 0.244267 | − | 0.518047i | ||||
\(617\) | 318253. | 0.835992 | 0.417996 | − | 0.908449i | \(-0.362733\pi\) | ||||
0.417996 | + | 0.908449i | \(0.362733\pi\) | |||||||
\(618\) | 315457. | − | 124804.i | 0.825968 | − | 0.326776i | ||||
\(619\) | − | 166643.i | − | 0.434917i | −0.976070 | − | 0.217458i | \(-0.930223\pi\) | ||
0.976070 | − | 0.217458i | \(-0.0697766\pi\) | |||||||
\(620\) | −64776.5 | − | 69051.8i | −0.168513 | − | 0.179635i | ||||
\(621\) | −482707. | −1.25170 | ||||||||
\(622\) | 16387.2 | + | 41420.9i | 0.0423570 | + | 0.107063i | ||||
\(623\) | 459695.i | 1.18439i | ||||||||
\(624\) | −376319. | − | 24068.3i | −0.966466 | − | 0.0618125i | ||||
\(625\) | −431687. | −1.10512 | ||||||||
\(626\) | 466565. | − | 184586.i | 1.19059 | − | 0.471032i | ||||
\(627\) | − | 250815.i | − | 0.637997i | ||||||
\(628\) | −346190. | + | 324756.i | −0.877800 | + | 0.823452i | ||||
\(629\) | −147584. | −0.373026 | ||||||||
\(630\) | 94971.7 | + | 240053.i | 0.239284 | + | 0.604821i | ||||
\(631\) | 546542.i | 1.37266i | 0.727288 | + | 0.686332i | \(0.240780\pi\) | ||||
−0.727288 | + | 0.686332i | \(0.759220\pi\) | |||||||
\(632\) | 475093. | + | 224014.i | 1.18945 | + | 0.560843i | ||||
\(633\) | −292471. | −0.729920 | ||||||||
\(634\) | −165761. | + | 65579.5i | −0.412385 | + | 0.163151i | ||||
\(635\) | − | 543347.i | − | 1.34750i | ||||||
\(636\) | −42288.1 | − | 45079.1i | −0.104545 | − | 0.111445i | ||||
\(637\) | 69548.6 | 0.171400 | ||||||||
\(638\) | −146826. | − | 371121.i | −0.360712 | − | 0.911747i | ||||
\(639\) | − | 265602.i | − | 0.650473i | ||||||
\(640\) | −491738. | − | 271500.i | −1.20053 | − | 0.662841i | ||||
\(641\) | −85487.5 | −0.208059 | −0.104030 | − | 0.994574i | \(-0.533174\pi\) | ||||
−0.104030 | + | 0.994574i | \(0.533174\pi\) | |||||||
\(642\) | −289977. | + | 114723.i | −0.703547 | + | 0.278343i | ||||
\(643\) | 662876.i | 1.60328i | 0.597805 | + | 0.801641i | \(0.296040\pi\) | ||||
−0.597805 | + | 0.801641i | \(0.703960\pi\) | |||||||
\(644\) | 334820. | − | 314090.i | 0.807309 | − | 0.757326i | ||||
\(645\) | 210930. | 0.507014 | ||||||||
\(646\) | −336712. | − | 851084.i | −0.806852 | − | 2.03942i | ||||
\(647\) | 295935.i | 0.706948i | 0.935444 | + | 0.353474i | \(0.115000\pi\) | ||||
−0.935444 | + | 0.353474i | \(0.885000\pi\) | |||||||
\(648\) | 42312.4 | − | 89736.9i | 0.100767 | − | 0.213708i | ||||
\(649\) | −324512. | −0.770445 | ||||||||
\(650\) | −477116. | + | 188760.i | −1.12927 | + | 0.446770i | ||||
\(651\) | 50021.4i | 0.118030i | ||||||||
\(652\) | 220399. | + | 234946.i | 0.518460 | + | 0.552679i | ||||
\(653\) | 623598. | 1.46244 | 0.731221 | − | 0.682141i | \(-0.238951\pi\) | ||||
0.731221 | + | 0.682141i | \(0.238951\pi\) | |||||||
\(654\) | 109968. | + | 277959.i | 0.257105 | + | 0.649867i | ||||
\(655\) | 1.10364e6i | 2.57245i | ||||||||
\(656\) | 11223.5 | − | 175484.i | 0.0260808 | − | 0.407784i | ||||
\(657\) | 289496. | 0.670675 | ||||||||
\(658\) | −407731. | + | 161310.i | −0.941720 | + | 0.372571i | ||||
\(659\) | 360136.i | 0.829269i | 0.909988 | + | 0.414635i | \(0.136091\pi\) | ||||
−0.909988 | + | 0.414635i | \(0.863909\pi\) | |||||||
\(660\) | −187256. | + | 175663.i | −0.429882 | + | 0.403266i | ||||
\(661\) | 605534. | 1.38591 | 0.692955 | − | 0.720980i | \(-0.256308\pi\) | ||||
0.692955 | + | 0.720980i | \(0.256308\pi\) | |||||||
\(662\) | −113100. | − | 285875.i | −0.258075 | − | 0.652319i | ||||
\(663\) | 628987.i | 1.43092i | ||||||||
\(664\) | 254911. | + | 120194.i | 0.578165 | + | 0.272614i | ||||
\(665\) | −842400. | −1.90491 | ||||||||
\(666\) | −52776.4 | + | 20879.8i | −0.118985 | + | 0.0470737i | ||||
\(667\) | − | 843062.i | − | 1.89499i | ||||||
\(668\) | 82593.6 | + | 88044.8i | 0.185095 | + | 0.197311i | ||||
\(669\) | 218196. | 0.487522 | ||||||||
\(670\) | 249900. | + | 631655.i | 0.556694 | + | 1.40712i | ||||
\(671\) | 233724.i | 0.519108i | ||||||||
\(672\) | 91339.1 | + | 282359.i | 0.202264 | + | 0.625264i | ||||
\(673\) | −502267. | −1.10893 | −0.554465 | − | 0.832207i | \(-0.687077\pi\) | ||||
−0.554465 | + | 0.832207i | \(0.687077\pi\) | |||||||
\(674\) | 523665. | − | 207177.i | 1.15275 | − | 0.456059i | ||||
\(675\) | − | 424584.i | − | 0.931872i | ||||||
\(676\) | 300545. | − | 281937.i | 0.657682 | − | 0.616962i | ||||
\(677\) | −544296. | −1.18757 | −0.593783 | − | 0.804625i | \(-0.702366\pi\) | ||||
−0.593783 | + | 0.804625i | \(0.702366\pi\) | |||||||
\(678\) | 98869.0 | + | 249904.i | 0.215080 | + | 0.543643i | ||||
\(679\) | − | 619126.i | − | 1.34289i | ||||||
\(680\) | −399590. | + | 847457.i | −0.864164 | + | 1.83274i | ||||
\(681\) | 164386. | 0.354463 | ||||||||
\(682\) | 47543.8 | − | 18809.6i | 0.102217 | − | 0.0404400i | ||||
\(683\) | − | 204667.i | − | 0.438739i | −0.975642 | − | 0.219370i | \(-0.929600\pi\) | ||
0.975642 | − | 0.219370i | \(-0.0704001\pi\) | |||||||
\(684\) | −240818. | − | 256712.i | −0.514726 | − | 0.548699i | ||||
\(685\) | 715259. | 1.52434 | ||||||||
\(686\) | −182145. | − | 460394.i | −0.387051 | − | 0.978321i | ||||
\(687\) | − | 547275.i | − | 1.15956i | ||||||
\(688\) | −248693. | − | 15905.7i | −0.525396 | − | 0.0336029i | ||||
\(689\) | 142450. | 0.300072 | ||||||||
\(690\) | −504320. | + | 199523.i | −1.05927 | + | 0.419078i | ||||
\(691\) | 329946.i | 0.691015i | 0.938416 | + | 0.345507i | \(0.112293\pi\) | ||||
−0.938416 | + | 0.345507i | \(0.887707\pi\) | |||||||
\(692\) | −70354.7 | + | 65998.8i | −0.146920 | + | 0.137824i | ||||
\(693\) | −139412. | −0.290291 | ||||||||
\(694\) | −127026. | − | 321076.i | −0.263740 | − | 0.666636i | ||||
\(695\) | 7692.10i | 0.0159248i | ||||||||
\(696\) | 492933. | + | 232426.i | 1.01758 | + | 0.479806i | ||||
\(697\) | −293308. | −0.603752 | ||||||||
\(698\) | 333429. | − | 131914.i | 0.684373 | − | 0.270757i | ||||
\(699\) | 174914.i | 0.357989i | ||||||||
\(700\) | 276271. | + | 294505.i | 0.563818 | + | 0.601030i | ||||
\(701\) | 144602. | 0.294264 | 0.147132 | − | 0.989117i | \(-0.452996\pi\) | ||||
0.147132 | + | 0.989117i | \(0.452996\pi\) | |||||||
\(702\) | 264560. | + | 668709.i | 0.536846 | + | 1.35695i | ||||
\(703\) | − | 185204.i | − | 0.374748i | ||||||
\(704\) | 234027. | − | 192991.i | 0.472195 | − | 0.389396i | ||||
\(705\) | 518015. | 1.04223 | ||||||||
\(706\) | −436821. | + | 172819.i | −0.876384 | + | 0.346722i | ||||
\(707\) | − | 558940.i | − | 1.11822i | ||||||
\(708\) | 323177. | − | 303168.i | 0.644724 | − | 0.604806i | ||||
\(709\) | 15096.1 | 0.0300312 | 0.0150156 | − | 0.999887i | \(-0.495220\pi\) | ||||
0.0150156 | + | 0.999887i | \(0.495220\pi\) | |||||||
\(710\) | −326390. | − | 824994.i | −0.647472 | − | 1.63657i | ||||
\(711\) | − | 336937.i | − | 0.666514i | ||||||
\(712\) | −273637. | + | 580335.i | −0.539778 | + | 1.14477i | ||||
\(713\) | 108003. | 0.212451 | ||||||||
\(714\) | 460294. | − | 182105.i | 0.902899 | − | 0.357212i | ||||
\(715\) | − | 591733.i | − | 1.15748i | ||||||
\(716\) | 650203. | + | 693117.i | 1.26830 | + | 1.35201i | ||||
\(717\) | 22423.1 | 0.0436171 | ||||||||
\(718\) | 307291. | + | 776718.i | 0.596076 | + | 1.50666i | ||||
\(719\) | − | 181074.i | − | 0.350267i | −0.984545 | − | 0.175133i | \(-0.943964\pi\) | ||
0.984545 | − | 0.175133i | \(-0.0560356\pi\) | |||||||
\(720\) | −22998.1 | + | 359585.i | −0.0443636 | + | 0.693644i | ||||
\(721\) | 615315. | 1.18366 | ||||||||
\(722\) | 583301. | − | 230770.i | 1.11897 | − | 0.442695i | ||||
\(723\) | 480550.i | 0.919310i | ||||||||
\(724\) | −43790.1 | + | 41078.8i | −0.0835407 | + | 0.0783684i | ||||
\(725\) | 741549. | 1.41080 | ||||||||
\(726\) | 85160.2 | + | 215253.i | 0.161571 | + | 0.408392i | ||||
\(727\) | 504679.i | 0.954874i | 0.878666 | + | 0.477437i | \(0.158434\pi\) | ||||
−0.878666 | + | 0.477437i | \(0.841566\pi\) | |||||||
\(728\) | −618626. | − | 291692.i | −1.16725 | − | 0.550379i | ||||
\(729\) | −458562. | −0.862866 | ||||||||
\(730\) | 899212. | − | 355753.i | 1.68739 | − | 0.667580i | ||||
\(731\) | 415671.i | 0.777885i | ||||||||
\(732\) | −218351. | − | 232762.i | −0.407505 | − | 0.434400i | ||||
\(733\) | 212915. | 0.396276 | 0.198138 | − | 0.980174i | \(-0.436511\pi\) | ||||
0.198138 | + | 0.980174i | \(0.436511\pi\) | |||||||
\(734\) | −38257.5 | − | 96700.7i | −0.0710108 | − | 0.179489i | ||||
\(735\) | 64662.3i | 0.119695i | ||||||||
\(736\) | 609654. | − | 197214.i | 1.12545 | − | 0.364068i | ||||
\(737\) | −366836. | −0.675363 | ||||||||
\(738\) | −104887. | + | 41496.4i | −0.192580 | + | 0.0761899i | ||||
\(739\) | 61157.0i | 0.111984i | 0.998431 | + | 0.0559921i | \(0.0178322\pi\) | ||||
−0.998431 | + | 0.0559921i | \(0.982168\pi\) | |||||||
\(740\) | −138272. | + | 129711.i | −0.252505 | + | 0.236871i | ||||
\(741\) | −789318. | −1.43752 | ||||||||
\(742\) | −41242.5 | − | 104246.i | −0.0749095 | − | 0.189343i | ||||
\(743\) | 56723.7i | 0.102751i | 0.998679 | + | 0.0513756i | \(0.0163606\pi\) | ||||
−0.998679 | + | 0.0513756i | \(0.983639\pi\) | |||||||
\(744\) | −29775.7 | + | 63148.8i | −0.0537918 | + | 0.114083i | ||||
\(745\) | −130682. | −0.235452 | ||||||||
\(746\) | −230341. | + | 91129.4i | −0.413899 | + | 0.163750i | ||||
\(747\) | − | 180783.i | − | 0.323979i | ||||||
\(748\) | −346171. | − | 369018.i | −0.618710 | − | 0.659545i | ||||
\(749\) | −565614. | −1.00822 | ||||||||
\(750\) | 23788.2 | + | 60127.6i | 0.0422901 | + | 0.106894i | ||||
\(751\) | 214929.i | 0.381080i | 0.981679 | + | 0.190540i | \(0.0610238\pi\) | ||||
−0.981679 | + | 0.190540i | \(0.938976\pi\) | |||||||
\(752\) | −610756. | − | 39062.3i | −1.08002 | − | 0.0690751i | ||||
\(753\) | −391402. | −0.690292 | ||||||||
\(754\) | −1.16792e6 | + | 462062.i | −2.05433 | + | 0.812751i | ||||
\(755\) | 316655.i | 0.555511i | ||||||||
\(756\) | 412768. | − | 387212.i | 0.722208 | − | 0.677493i | ||||
\(757\) | −821257. | −1.43314 | −0.716568 | − | 0.697517i | \(-0.754288\pi\) | ||||
−0.716568 | + | 0.697517i | \(0.754288\pi\) | |||||||
\(758\) | −317502. | − | 802526.i | −0.552596 | − | 1.39676i | ||||
\(759\) | − | 292886.i | − | 0.508412i | ||||||
\(760\) | −1.06348e6 | − | 501446.i | −1.84120 | − | 0.868155i | ||||
\(761\) | −901445. | −1.55657 | −0.778287 | − | 0.627909i | \(-0.783911\pi\) | ||||
−0.778287 | + | 0.627909i | \(0.783911\pi\) | |||||||
\(762\) | −372567. | + | 147398.i | −0.641645 | + | 0.253853i | ||||
\(763\) | 542172.i | 0.931297i | ||||||||
\(764\) | −98511.7 | − | 105014.i | −0.168772 | − | 0.179911i | ||||
\(765\) | 601018. | 1.02699 | ||||||||
\(766\) | −153262. | − | 387389.i | −0.261202 | − | 0.660221i | ||||
\(767\) | 1.02124e6i | 1.73595i | ||||||||
\(768\) | −52767.1 | + | 410831.i | −0.0894625 | + | 0.696532i | ||||
\(769\) | −1.14370e6 | −1.93402 | −0.967009 | − | 0.254744i | \(-0.918009\pi\) | ||||
−0.967009 | + | 0.254744i | \(0.918009\pi\) | |||||||
\(770\) | −433032. | + | 171319.i | −0.730362 | + | 0.288952i | ||||
\(771\) | − | 30043.0i | − | 0.0505400i | ||||||
\(772\) | −24189.3 | + | 22691.6i | −0.0405871 | + | 0.0380742i | ||||
\(773\) | 1.12591e6 | 1.88427 | 0.942136 | − | 0.335232i | \(-0.108815\pi\) | ||||
0.942136 | + | 0.335232i | \(0.108815\pi\) | |||||||
\(774\) | 58808.0 | + | 148645.i | 0.0981645 | + | 0.248123i | ||||
\(775\) | 94998.7i | 0.158166i | ||||||||
\(776\) | 368540. | − | 781608.i | 0.612014 | − | 1.29797i | ||||
\(777\) | 100164. | 0.165910 | ||||||||
\(778\) | −157763. | + | 62415.6i | −0.260644 | + | 0.103118i | ||||
\(779\) | − | 368073.i | − | 0.606540i | ||||||
\(780\) | 552812. | + | 589298.i | 0.908632 | + | 0.968602i | ||||
\(781\) | 479119. | 0.785491 | ||||||||
\(782\) | −393191. | − | 993842.i | −0.642970 | − | 1.62519i | ||||
\(783\) | − | 1.03933e6i | − | 1.69523i | ||||||
\(784\) | 4876.03 | − | 76238.9i | 0.00793294 | − | 0.124035i | ||||
\(785\) | 1.01711e6 | 1.65054 | ||||||||
\(786\) | 756757. | − | 299394.i | 1.22493 | − | 0.484616i | ||||
\(787\) | − | 764877.i | − | 1.23493i | −0.786599 | − | 0.617465i | \(-0.788160\pi\) | ||
0.786599 | − | 0.617465i | \(-0.211840\pi\) | |||||||
\(788\) | 367671. | − | 344907.i | 0.592116 | − | 0.555455i | ||||
\(789\) | −256870. | −0.412628 | ||||||||
\(790\) | −414052. | − | 1.04657e6i | −0.663438 | − | 1.67692i | ||||
\(791\) | 487450.i | 0.779072i | ||||||||
\(792\) | −175999. | − | 82986.3i | −0.280582 | − | 0.132299i | ||||
\(793\) | 735531. | 1.16965 | ||||||||
\(794\) | 592878. | − | 234559.i | 0.940425 | − | 0.372058i | ||||
\(795\) | 132442.i | 0.209552i | ||||||||
\(796\) | −111761. | − | 119138.i | −0.176386 | − | 0.188028i | ||||
\(797\) | 2005.12 | 0.00315663 | 0.00157832 | − | 0.999999i | \(-0.499498\pi\) | ||||
0.00157832 | + | 0.999999i | \(0.499498\pi\) | |||||||
\(798\) | 228524. | + | 577625.i | 0.358862 | + | 0.907069i | ||||
\(799\) | 1.02083e6i | 1.59904i | ||||||||
\(800\) | 173468. | + | 536246.i | 0.271043 | + | 0.837885i | ||||
\(801\) | 411575. | 0.641481 | ||||||||
\(802\) | 59729.0 | − | 23630.4i | 0.0928617 | − | 0.0367387i | ||||
\(803\) | 522222.i | 0.809886i | ||||||||
\(804\) | 365327. | − | 342708.i | 0.565157 | − | 0.530166i | ||||
\(805\) | −983702. | −1.51800 | ||||||||
\(806\) | −59194.1 | − | 149621.i | −0.0911188 | − | 0.230314i | ||||
\(807\) | 8959.51i | 0.0137574i | ||||||||
\(808\) | 332714. | − | 705626.i | 0.509622 | − | 1.08082i | ||||
\(809\) | 1.07187e6 | 1.63775 | 0.818874 | − | 0.573974i | \(-0.194599\pi\) | ||||
0.818874 | + | 0.573974i | \(0.194599\pi\) | |||||||
\(810\) | −197679. | + | 78207.2i | −0.301294 | + | 0.119200i | ||||
\(811\) | 1.17100e6i | 1.78039i | 0.455576 | + | 0.890197i | \(0.349433\pi\) | ||||
−0.455576 | + | 0.890197i | \(0.650567\pi\) | |||||||
\(812\) | 676277. | + | 720911.i | 1.02568 | + | 1.09338i | ||||
\(813\) | −54897.0 | −0.0830553 | ||||||||
\(814\) | −37665.0 | − | 95203.2i | −0.0568446 | − | 0.143682i | ||||
\(815\) | − | 690271.i | − | 1.03921i | ||||||
\(816\) | 689492. | + | 44098.1i | 1.03550 | + | 0.0662276i | ||||
\(817\) | −521627. | −0.781477 | ||||||||
\(818\) | −465244. | + | 184063.i | −0.695303 | + | 0.275081i | ||||
\(819\) | 438731.i | 0.654079i | ||||||||
\(820\) | −274800. | + | 257786.i | −0.408686 | + | 0.383382i | ||||
\(821\) | −429054. | −0.636540 | −0.318270 | − | 0.948000i | \(-0.603102\pi\) | ||||
−0.318270 | + | 0.948000i | \(0.603102\pi\) | |||||||
\(822\) | −194034. | − | 490446.i | −0.287167 | − | 0.725851i | ||||
\(823\) | 141782.i | 0.209326i | 0.994508 | + | 0.104663i | \(0.0333764\pi\) | ||||
−0.994508 | + | 0.104663i | \(0.966624\pi\) | |||||||
\(824\) | 776796. | + | 366272.i | 1.14407 | + | 0.539447i | ||||
\(825\) | 257620. | 0.378505 | ||||||||
\(826\) | 747348. | − | 295672.i | 1.09538 | − | 0.433361i | ||||
\(827\) | 408769.i | 0.597677i | 0.954304 | + | 0.298838i | \(0.0965992\pi\) | ||||
−0.954304 | + | 0.298838i | \(0.903401\pi\) | |||||||
\(828\) | −281212. | − | 299772.i | −0.410179 | − | 0.437250i | ||||
\(829\) | −735343. | −1.06999 | −0.534997 | − | 0.844854i | \(-0.679687\pi\) | ||||
−0.534997 | + | 0.844854i | \(0.679687\pi\) | |||||||
\(830\) | −222159. | − | 561535.i | −0.322484 | − | 0.815119i | ||||
\(831\) | − | 406909.i | − | 0.589244i | ||||||
\(832\) | −607344. | − | 736486.i | −0.877381 | − | 1.06394i | ||||
\(833\) | −127427. | −0.183642 | ||||||||
\(834\) | 5274.39 | − | 2086.70i | 0.00758298 | − | 0.00300004i | ||||
\(835\) | − | 258676.i | − | 0.371007i | ||||||
\(836\) | 463082. | − | 434411.i | 0.662591 | − | 0.621567i | ||||
\(837\) | 133147. | 0.190055 | ||||||||
\(838\) | 266940. | + | 674726.i | 0.380125 | + | 0.960815i | ||||
\(839\) | − | 245759.i | − | 0.349128i | −0.984646 | − | 0.174564i | \(-0.944148\pi\) | ||
0.984646 | − | 0.174564i | \(-0.0558517\pi\) | |||||||
\(840\) | 271199. | − | 575164.i | 0.384352 | − | 0.815141i | ||||
\(841\) | 1.10794e6 | 1.56648 | ||||||||
\(842\) | 282761. | − | 111868.i | 0.398837 | − | 0.157791i | ||||
\(843\) | 661984.i | 0.931521i | ||||||||
\(844\) | −506558. | − | 539991.i | −0.711123 | − | 0.758057i | ||||
\(845\) | −883000. | −1.23665 | ||||||||
\(846\) | 144424. | + | 365050.i | 0.201790 | + | 0.510049i | ||||
\(847\) | 419862.i | 0.585248i | ||||||||
\(848\) | 9987.15 | − | 156153.i | 0.0138883 | − | 0.217150i | ||||
\(849\) | −545295. | −0.756513 | ||||||||
\(850\) | 874174. | − | 345847.i | 1.20993 | − | 0.478682i | ||||
\(851\) | − | 216270.i | − | 0.298632i | ||||||
\(852\) | −477147. | + | 447605.i | −0.657315 | + | 0.616617i | ||||
\(853\) | 528771. | 0.726724 | 0.363362 | − | 0.931648i | \(-0.381629\pi\) | ||||
0.363362 | + | 0.931648i | \(0.381629\pi\) | |||||||
\(854\) | −212952. | − | 538264.i | −0.291989 | − | 0.738039i | ||||
\(855\) | 754219.i | 1.03173i | ||||||||
\(856\) | −714052. | − | 336687.i | −0.974501 | − | 0.459493i | ||||
\(857\) | 1.36027e6 | 1.85209 | 0.926045 | − | 0.377412i | \(-0.123186\pi\) | ||||
0.926045 | + | 0.377412i | \(0.123186\pi\) | |||||||
\(858\) | −405745. | + | 160524.i | −0.551161 | + | 0.218055i | ||||
\(859\) | − | 286244.i | − | 0.387927i | −0.981009 | − | 0.193964i | \(-0.937866\pi\) | ||
0.981009 | − | 0.193964i | \(-0.0621344\pi\) | |||||||
\(860\) | 365330. | + | 389442.i | 0.493957 | + | 0.526558i | ||||
\(861\) | 199066. | 0.268529 | ||||||||
\(862\) | 509277. | + | 1.28726e6i | 0.685392 | + | 1.73242i | ||||
\(863\) | − | 32079.7i | − | 0.0430733i | −0.999768 | − | 0.0215367i | \(-0.993144\pi\) | ||
0.999768 | − | 0.0215367i | \(-0.00685586\pi\) | |||||||
\(864\) | 751584. | − | 243126.i | 1.00682 | − | 0.325690i | ||||
\(865\) | 206702. | 0.276257 | ||||||||
\(866\) | 878747. | − | 347656.i | 1.17173 | − | 0.463569i | ||||
\(867\) | − | 624556.i | − | 0.830870i | ||||||
\(868\) | −92354.8 | + | 86636.8i | −0.122580 | + | 0.114991i | ||||
\(869\) | 607800. | 0.804861 | ||||||||
\(870\) | −429599. | − | 1.08587e6i | −0.567577 | − | 1.43462i | ||||
\(871\) | 1.15444e6i | 1.52172i | ||||||||
\(872\) | −322733. | + | 684458.i | −0.424434 | + | 0.900148i | ||||
\(873\) | −554317. | −0.727327 | ||||||||
\(874\) | 1.24718e6 | − | 493417.i | 1.63269 | − | 0.645939i | ||||
\(875\) | 117282.i | 0.153185i | ||||||||
\(876\) | −487873. | − | 520073.i | −0.635767 | − | 0.677728i | ||||
\(877\) | 1.01706e6 | 1.32236 | 0.661179 | − | 0.750228i | \(-0.270056\pi\) | ||||
0.661179 | + | 0.750228i | \(0.270056\pi\) | |||||||
\(878\) | −414808. | − | 1.04848e6i | −0.538094 | − | 1.36010i | ||||
\(879\) | − | 750.248i | − | 0.000971017i | ||||||
\(880\) | −648654. | − | 41486.2i | −0.837622 | − | 0.0535720i | ||||
\(881\) | 236693. | 0.304954 | 0.152477 | − | 0.988307i | \(-0.451275\pi\) | ||||
0.152477 | + | 0.988307i | \(0.451275\pi\) | |||||||
\(882\) | −45568.2 | + | 18028.0i | −0.0585767 | + | 0.0231746i | ||||
\(883\) | − | 1.22889e6i | − | 1.57613i | −0.615590 | − | 0.788067i | \(-0.711082\pi\) | ||
0.615590 | − | 0.788067i | \(-0.288918\pi\) | |||||||
\(884\) | −1.16130e6 | + | 1.08940e6i | −1.48608 | + | 1.39407i | ||||
\(885\) | −949493. | −1.21229 | ||||||||
\(886\) | −16669.0 | − | 42133.2i | −0.0212346 | − | 0.0536731i | ||||
\(887\) | 715067.i | 0.908865i | 0.890781 | + | 0.454433i | \(0.150158\pi\) | ||||
−0.890781 | + | 0.454433i | \(0.849842\pi\) | |||||||
\(888\) | 126451. | + | 59623.8i | 0.160361 | + | 0.0756125i | ||||
\(889\) | −726711. | −0.919514 | ||||||||
\(890\) | 1.27840e6 | − | 505772.i | 1.61394 | − | 0.638520i | ||||
\(891\) | − | 114803.i | − | 0.144610i | ||||||
\(892\) | 377914. | + | 402856.i | 0.474967 | + | 0.506315i | ||||
\(893\) | −1.28104e6 | −1.60643 | ||||||||
\(894\) | 35451.1 | + | 89607.3i | 0.0443563 | + | 0.112116i | ||||
\(895\) | − | 2.03638e6i | − | 2.54221i | ||||||
\(896\) | −363123. | + | 657685.i | −0.452312 | + | 0.819222i | ||||
\(897\) | −921715. | −1.14554 | ||||||||
\(898\) | −184537. | + | 73008.2i | −0.228840 | + | 0.0905355i | ||||
\(899\) | 232545.i | 0.287732i | ||||||||
\(900\) | 263677. | − | 247351.i | 0.325527 | − | 0.305372i | ||||
\(901\) | −260998. | −0.321505 | ||||||||
\(902\) | −74855.2 | − | 189206.i | −0.0920045 | − | 0.232553i | ||||
\(903\) | − | 282113.i | − | 0.345978i | ||||||
\(904\) | −290159. | + | 615375.i | −0.355058 | + | 0.753014i | ||||
\(905\) | 128655. | 0.157083 | ||||||||
\(906\) | 217127. | − | 85901.6i | 0.264520 | − | 0.104651i | ||||
\(907\) | 739435.i | 0.898846i | 0.893319 | + | 0.449423i | \(0.148370\pi\) | ||||
−0.893319 | + | 0.449423i | \(0.851630\pi\) | |||||||
\(908\) | 284716. | + | 303508.i | 0.345335 | + | 0.368127i | ||||
\(909\) | −500431. | −0.605643 | ||||||||
\(910\) | 539143. | + | 1.36275e6i | 0.651061 | + | 1.64564i | ||||
\(911\) | − | 1.43700e6i | − | 1.73148i | −0.500490 | − | 0.865742i | \(-0.666847\pi\) | ||
0.500490 | − | 0.865742i | \(-0.333153\pi\) | |||||||
\(912\) | −55338.8 | + | 865246.i | −0.0665335 | + | 1.04028i | ||||
\(913\) | 326114. | 0.391226 | ||||||||
\(914\) | 357249. | − | 141337.i | 0.427640 | − | 0.169186i | ||||
\(915\) | 683855.i | 0.816811i | ||||||||
\(916\) | 1.01044e6 | − | 947878.i | 1.20426 | − | 1.12970i | ||||
\(917\) | 1.47609e6 | 1.75539 | ||||||||
\(918\) | −484728. | − | 1.22521e6i | −0.575192 | − | 1.45387i | ||||
\(919\) | 1.53081e6i | 1.81255i | 0.422684 | + | 0.906277i | \(0.361088\pi\) | ||||
−0.422684 | + | 0.906277i | \(0.638912\pi\) | |||||||
\(920\) | −1.24186e6 | − | 585557.i | −1.46723 | − | 0.691821i | ||||
\(921\) | −354367. | −0.417767 | ||||||||
\(922\) | −972545. | + | 384766.i | −1.14406 | + | 0.452621i | ||||
\(923\) | − | 1.50779e6i | − | 1.76986i | ||||||
\(924\) | 234944. | + | 250450.i | 0.275182 | + | 0.293344i | ||||
\(925\) | 190229. | 0.222327 | ||||||||
\(926\) | −300078. | − | 758485.i | −0.349955 | − | 0.884555i | ||||
\(927\) | − | 550905.i | − | 0.641087i | ||||||
\(928\) | 424628. | + | 1.31266e6i | 0.493074 | + | 1.52426i | ||||
\(929\) | −766377. | −0.887997 | −0.443998 | − | 0.896028i | \(-0.646440\pi\) | ||||
−0.443998 | + | 0.896028i | \(0.646440\pi\) | |||||||
\(930\) | 139109. | − | 55035.3i | 0.160838 | − | 0.0636319i | ||||
\(931\) | − | 159909.i | − | 0.184490i | ||||||
\(932\) | −322945. | + | 302950.i | −0.371789 | + | 0.348770i | ||||
\(933\) | −70383.8 | −0.0808554 | ||||||||
\(934\) | −468205. | − | 1.18345e6i | −0.536714 | − | 1.35661i | ||||
\(935\) | 1.08417e6i | 1.24016i | ||||||||
\(936\) | −261158. | + | 553870.i | −0.298093 | + | 0.632202i | ||||
\(937\) | −152632. | −0.173847 | −0.0869235 | − | 0.996215i | \(-0.527704\pi\) | ||||
−0.0869235 | + | 0.996215i | \(0.527704\pi\) | |||||||
\(938\) | 844820. | − | 334234.i | 0.960193 | − | 0.379879i | ||||
\(939\) | 792803.i | 0.899154i | ||||||||
\(940\) | 897200. | + | 956415.i | 1.01539 | + | 1.08241i | ||||
\(941\) | −829824. | −0.937145 | −0.468573 | − | 0.883425i | \(-0.655232\pi\) | ||||
−0.468573 | + | 0.883425i | \(0.655232\pi\) | |||||||
\(942\) | −275918. | − | 697420.i | −0.310942 | − | 0.785945i | ||||
\(943\) | − | 429813.i | − | 0.483343i | ||||||
\(944\) | 1.11948e6 | + | 71599.0i | 1.25624 | + | 0.0803457i | ||||
\(945\) | −1.21271e6 | −1.35798 | ||||||||
\(946\) | −268140. | + | 106084.i | −0.299626 | + | 0.118540i | ||||
\(947\) | − | 874022.i | − | 0.974591i | −0.873237 | − | 0.487296i | \(-0.837983\pi\) | ||
0.873237 | − | 0.487296i | \(-0.162017\pi\) | |||||||
\(948\) | −605298. | + | 567822.i | −0.673524 | + | 0.631823i | ||||
\(949\) | 1.64344e6 | 1.82482 | ||||||||
\(950\) | 434005. | + | 1.09700e6i | 0.480892 | + | 1.21552i | ||||
\(951\) | − | 281666.i | − | 0.311440i | ||||||
\(952\) | 1.13345e6 | + | 534440.i | 1.25063 | + | 0.589691i | ||||
\(953\) | −195337. | −0.215079 | −0.107540 | − | 0.994201i | \(-0.534297\pi\) | ||||
−0.107540 | + | 0.994201i | \(0.534297\pi\) | |||||||
\(954\) | −93333.4 | + | 36925.3i | −0.102551 | + | 0.0405721i | ||||
\(955\) | 308530.i | 0.338291i | ||||||||
\(956\) | 38836.7 | + | 41399.9i | 0.0424939 | + | 0.0452985i | ||||
\(957\) | 630622. | 0.688565 | ||||||||
\(958\) | 480714. | + | 1.21507e6i | 0.523788 | + | 1.32394i | ||||
\(959\) | − | 956638.i | − | 1.04019i | ||||||
\(960\) | 684743. | − | 564674.i | 0.742993 | − | 0.612711i | ||||
\(961\) | −29791.0 | −0.0322581 | ||||||||
\(962\) | −299605. | + | 118532.i | −0.323742 | + | 0.128081i | ||||
\(963\) | 506407.i | 0.546068i | ||||||||
\(964\) | −887243. | + | 832310.i | −0.954748 | + | 0.895635i | ||||
\(965\) | 71068.1 | 0.0763168 | ||||||||
\(966\) | 266856. | + | 674514.i | 0.285972 | + | 0.722831i | ||||
\(967\) | − | 323652.i | − | 0.346119i | −0.984911 | − | 0.173060i | \(-0.944635\pi\) | ||
0.984911 | − | 0.173060i | \(-0.0553653\pi\) | |||||||
\(968\) | −249927. | + | 530050.i | −0.266724 | + | 0.565674i | ||||
\(969\) | 1.44619e6 | 1.54020 | ||||||||
\(970\) | −1.72178e6 | + | 681184.i | −1.82993 | + | 0.723971i | ||||
\(971\) | 655388.i | 0.695120i | 0.937658 | + | 0.347560i | \(0.112990\pi\) | ||||
−0.937658 | + | 0.347560i | \(0.887010\pi\) | |||||||
\(972\) | −576749. | − | 614815.i | −0.610456 | − | 0.650747i | ||||
\(973\) | 10288.0 | 0.0108668 | ||||||||
\(974\) | 460336. | + | 1.16356e6i | 0.485240 | + | 1.22651i | ||||
\(975\) | − | 810732.i | − | 0.852841i | ||||||
\(976\) | 51567.8 | − | 806285.i | 0.0541351 | − | 0.846426i | ||||
\(977\) | 477188. | 0.499920 | 0.249960 | − | 0.968256i | \(-0.419583\pi\) | ||||
0.249960 | + | 0.968256i | \(0.419583\pi\) | |||||||
\(978\) | −473311. | + | 187255.i | −0.494845 | + | 0.195774i | ||||
\(979\) | 742439.i | 0.774631i | ||||||||
\(980\) | −119387. | + | 111995.i | −0.124309 | + | 0.116613i | ||||
\(981\) | 485418. | 0.504404 | ||||||||
\(982\) | −263060. | − | 664917.i | −0.272792 | − | 0.689516i | ||||
\(983\) | 1.23297e6i | 1.27599i | 0.770041 | + | 0.637995i | \(0.220236\pi\) | ||||
−0.770041 | + | 0.637995i | \(0.779764\pi\) | |||||||
\(984\) | 251308. | + | 118496.i | 0.259548 | + | 0.122381i | ||||
\(985\) | −1.08022e6 | −1.11337 | ||||||||
\(986\) | 2.13987e6 | − | 846592.i | 2.20107 | − | 0.870804i | ||||
\(987\) | − | 692831.i | − | 0.711202i | ||||||
\(988\) | −1.36709e6 | − | 1.45732e6i | −1.40050 | − | 1.49294i | ||||
\(989\) | −609123. | −0.622748 | ||||||||
\(990\) | 153386. | + | 387703.i | 0.156500 | + | 0.395575i | ||||
\(991\) | 151177.i | 0.153936i | 0.997034 | + | 0.0769679i | \(0.0245239\pi\) | ||||
−0.997034 | + | 0.0769679i | \(0.975476\pi\) | |||||||
\(992\) | −168163. | + | 54398.4i | −0.170887 | + | 0.0552793i | ||||
\(993\) | 485768. | 0.492641 | ||||||||
\(994\) | −1.10341e6 | + | 436538.i | −1.11677 | + | 0.441824i | ||||
\(995\) | 350026.i | 0.353553i | ||||||||
\(996\) | −324772. | + | 304664.i | −0.327386 | + | 0.307116i | ||||
\(997\) | 6029.29 | 0.00606563 | 0.00303282 | − | 0.999995i | \(-0.499035\pi\) | ||||
0.00303282 | + | 0.999995i | \(0.499035\pi\) | |||||||
\(998\) | 179995. | + | 454961.i | 0.180717 | + | 0.456786i | ||||
\(999\) | − | 266618.i | − | 0.267152i |
(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 | 124.5.b.a.63.6 | yes | 60 | |
4.3 | odd | 2 | inner | 124.5.b.a.63.5 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.5.b.a.63.5 | ✓ | 60 | 4.3 | odd | 2 | inner | |
124.5.b.a.63.6 | yes | 60 | 1.1 | even | 1 | trivial |