Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(39,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, 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("76.39");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 39.17 | ||
Character | \(\chi\) | \(=\) | 76.39 |
Dual form | 76.5.b.a.39.18 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.591318 | − | 3.95605i | −0.147830 | − | 0.989013i | ||||
\(3\) | 4.43430i | 0.492700i | 0.969181 | + | 0.246350i | \(0.0792312\pi\) | ||||
−0.969181 | + | 0.246350i | \(0.920769\pi\) | |||||||
\(4\) | −15.3007 | + | 4.67857i | −0.956293 | + | 0.292411i | ||||
\(5\) | 13.1035 | 0.524141 | 0.262070 | − | 0.965049i | \(-0.415595\pi\) | ||||
0.262070 | + | 0.965049i | \(0.415595\pi\) | |||||||
\(6\) | 17.5423 | − | 2.62208i | 0.487286 | − | 0.0728356i | ||||
\(7\) | − | 8.96798i | − | 0.183020i | −0.995804 | − | 0.0915100i | \(-0.970831\pi\) | ||
0.995804 | − | 0.0915100i | \(-0.0291693\pi\) | |||||||
\(8\) | 27.5562 | + | 57.7638i | 0.430566 | + | 0.902559i | ||||
\(9\) | 61.3370 | 0.757247 | ||||||||
\(10\) | −7.74835 | − | 51.8382i | −0.0774835 | − | 0.518382i | ||||
\(11\) | − | 193.669i | − | 1.60057i | −0.599618 | − | 0.800287i | \(-0.704681\pi\) | ||
0.599618 | − | 0.800287i | \(-0.295319\pi\) | |||||||
\(12\) | −20.7462 | − | 67.8478i | −0.144071 | − | 0.471165i | ||||
\(13\) | 173.528 | 1.02679 | 0.513396 | − | 0.858152i | \(-0.328387\pi\) | ||||
0.513396 | + | 0.858152i | \(0.328387\pi\) | |||||||
\(14\) | −35.4778 | + | 5.30293i | −0.181009 | + | 0.0270557i | ||||
\(15\) | 58.1049i | 0.258244i | ||||||||
\(16\) | 212.222 | − | 143.171i | 0.828992 | − | 0.559260i | ||||
\(17\) | 83.2927 | 0.288210 | 0.144105 | − | 0.989562i | \(-0.453970\pi\) | ||||
0.144105 | + | 0.989562i | \(0.453970\pi\) | |||||||
\(18\) | −36.2697 | − | 242.652i | −0.111943 | − | 0.748927i | ||||
\(19\) | − | 82.8191i | − | 0.229416i | ||||||
\(20\) | −200.493 | + | 61.3057i | −0.501232 | + | 0.153264i | ||||
\(21\) | 39.7667 | 0.0901738 | ||||||||
\(22\) | −766.166 | + | 114.520i | −1.58299 | + | 0.236612i | ||||
\(23\) | − | 684.081i | − | 1.29316i | −0.762846 | − | 0.646580i | \(-0.776199\pi\) | ||
0.762846 | − | 0.646580i | \(-0.223801\pi\) | |||||||
\(24\) | −256.142 | + | 122.193i | −0.444691 | + | 0.212140i | ||||
\(25\) | −453.298 | −0.725276 | ||||||||
\(26\) | −102.610 | − | 686.485i | −0.151790 | − | 1.01551i | ||||
\(27\) | 631.165i | 0.865795i | ||||||||
\(28\) | 41.9573 | + | 137.216i | 0.0535170 | + | 0.175021i | ||||
\(29\) | 1433.18 | 1.70414 | 0.852071 | − | 0.523426i | \(-0.175346\pi\) | ||||
0.852071 | + | 0.523426i | \(0.175346\pi\) | |||||||
\(30\) | 229.866 | − | 34.3585i | 0.255407 | − | 0.0381761i | ||||
\(31\) | 750.769i | 0.781237i | 0.920553 | + | 0.390619i | \(0.127739\pi\) | ||||
−0.920553 | + | 0.390619i | \(0.872261\pi\) | |||||||
\(32\) | −691.881 | − | 754.902i | −0.675665 | − | 0.737209i | ||||
\(33\) | 858.787 | 0.788602 | ||||||||
\(34\) | −49.2525 | − | 329.510i | −0.0426059 | − | 0.285043i | ||||
\(35\) | − | 117.512i | − | 0.0959282i | ||||||
\(36\) | −938.498 | + | 286.969i | −0.724150 | + | 0.221427i | ||||
\(37\) | 437.540 | 0.319606 | 0.159803 | − | 0.987149i | \(-0.448914\pi\) | ||||
0.159803 | + | 0.987149i | \(0.448914\pi\) | |||||||
\(38\) | −327.637 | + | 48.9724i | −0.226895 | + | 0.0339144i | ||||
\(39\) | 769.474i | 0.505900i | ||||||||
\(40\) | 361.084 | + | 756.909i | 0.225677 | + | 0.473068i | ||||
\(41\) | 895.241 | 0.532565 | 0.266282 | − | 0.963895i | \(-0.414205\pi\) | ||||
0.266282 | + | 0.963895i | \(0.414205\pi\) | |||||||
\(42\) | −23.5147 | − | 157.319i | −0.0133304 | − | 0.0891831i | ||||
\(43\) | 928.943i | 0.502403i | 0.967935 | + | 0.251202i | \(0.0808257\pi\) | ||||
−0.967935 | + | 0.251202i | \(0.919174\pi\) | |||||||
\(44\) | 906.096 | + | 2963.27i | 0.468025 | + | 1.53062i | ||||
\(45\) | 803.731 | 0.396904 | ||||||||
\(46\) | −2706.26 | + | 404.510i | −1.27895 | + | 0.191167i | ||||
\(47\) | 2116.78i | 0.958252i | 0.877746 | + | 0.479126i | \(0.159046\pi\) | ||||
−0.877746 | + | 0.479126i | \(0.840954\pi\) | |||||||
\(48\) | 634.861 | + | 941.055i | 0.275547 | + | 0.408444i | ||||
\(49\) | 2320.58 | 0.966504 | ||||||||
\(50\) | 268.043 | + | 1793.27i | 0.107217 | + | 0.717308i | ||||
\(51\) | 369.344i | 0.142001i | ||||||||
\(52\) | −2655.09 | + | 811.862i | −0.981914 | + | 0.300245i | ||||
\(53\) | −3581.37 | −1.27496 | −0.637481 | − | 0.770466i | \(-0.720024\pi\) | ||||
−0.637481 | + | 0.770466i | \(0.720024\pi\) | |||||||
\(54\) | 2496.92 | − | 373.219i | 0.856282 | − | 0.127990i | ||||
\(55\) | − | 2537.75i | − | 0.838926i | ||||||
\(56\) | 518.024 | − | 247.124i | 0.165186 | − | 0.0788022i | ||||
\(57\) | 367.244 | 0.113033 | ||||||||
\(58\) | −847.467 | − | 5669.75i | −0.251922 | − | 1.68542i | ||||
\(59\) | 306.954i | 0.0881797i | 0.999028 | + | 0.0440899i | \(0.0140388\pi\) | ||||
−0.999028 | + | 0.0440899i | \(0.985961\pi\) | |||||||
\(60\) | −271.848 | − | 889.045i | −0.0755133 | − | 0.246957i | ||||
\(61\) | −7090.53 | −1.90554 | −0.952772 | − | 0.303687i | \(-0.901782\pi\) | ||||
−0.952772 | + | 0.303687i | \(0.901782\pi\) | |||||||
\(62\) | 2970.08 | − | 443.943i | 0.772654 | − | 0.115490i | ||||
\(63\) | − | 550.069i | − | 0.138591i | ||||||
\(64\) | −2577.31 | + | 3183.50i | −0.629226 | + | 0.777223i | ||||
\(65\) | 2273.83 | 0.538184 | ||||||||
\(66\) | −507.817 | − | 3397.41i | −0.116579 | − | 0.779937i | ||||
\(67\) | − | 4562.45i | − | 1.01636i | −0.861250 | − | 0.508181i | \(-0.830318\pi\) | ||
0.861250 | − | 0.508181i | \(-0.169682\pi\) | |||||||
\(68\) | −1274.43 | + | 389.691i | −0.275613 | + | 0.0842756i | ||||
\(69\) | 3033.42 | 0.637139 | ||||||||
\(70\) | −464.884 | + | 69.4870i | −0.0948742 | + | 0.0141810i | ||||
\(71\) | 149.139i | 0.0295853i | 0.999891 | + | 0.0147926i | \(0.00470882\pi\) | ||||
−0.999891 | + | 0.0147926i | \(0.995291\pi\) | |||||||
\(72\) | 1690.22 | + | 3543.06i | 0.326045 | + | 0.683460i | ||||
\(73\) | −2829.51 | −0.530964 | −0.265482 | − | 0.964116i | \(-0.585531\pi\) | ||||
−0.265482 | + | 0.964116i | \(0.585531\pi\) | |||||||
\(74\) | −258.725 | − | 1730.93i | −0.0472471 | − | 0.316094i | ||||
\(75\) | − | 2010.06i | − | 0.357343i | ||||||
\(76\) | 387.475 | + | 1267.19i | 0.0670836 | + | 0.219389i | ||||
\(77\) | −1736.82 | −0.292937 | ||||||||
\(78\) | 3044.08 | − | 455.004i | 0.500342 | − | 0.0747870i | ||||
\(79\) | − | 6895.61i | − | 1.10489i | −0.833550 | − | 0.552444i | \(-0.813695\pi\) | ||
0.833550 | − | 0.552444i | \(-0.186305\pi\) | |||||||
\(80\) | 2780.86 | − | 1876.04i | 0.434509 | − | 0.293131i | ||||
\(81\) | 2169.53 | 0.330670 | ||||||||
\(82\) | −529.372 | − | 3541.62i | −0.0787288 | − | 0.526713i | ||||
\(83\) | 7842.11i | 1.13835i | 0.822216 | + | 0.569176i | \(0.192738\pi\) | ||||
−0.822216 | + | 0.569176i | \(0.807262\pi\) | |||||||
\(84\) | −608.457 | + | 186.051i | −0.0862326 | + | 0.0263678i | ||||
\(85\) | 1091.43 | 0.151063 | ||||||||
\(86\) | 3674.95 | − | 549.301i | 0.496883 | − | 0.0742700i | ||||
\(87\) | 6355.16i | 0.839630i | ||||||||
\(88\) | 11187.1 | − | 5336.80i | 1.44461 | − | 0.689153i | ||||
\(89\) | −8713.81 | −1.10009 | −0.550045 | − | 0.835135i | \(-0.685389\pi\) | ||||
−0.550045 | + | 0.835135i | \(0.685389\pi\) | |||||||
\(90\) | −475.261 | − | 3179.60i | −0.0586742 | − | 0.392543i | ||||
\(91\) | − | 1556.19i | − | 0.187923i | ||||||
\(92\) | 3200.52 | + | 10466.9i | 0.378134 | + | 1.23664i | ||||
\(93\) | −3329.13 | −0.384915 | ||||||||
\(94\) | 8374.09 | − | 1251.69i | 0.947724 | − | 0.141658i | ||||
\(95\) | − | 1085.22i | − | 0.120246i | ||||||
\(96\) | 3347.46 | − | 3068.01i | 0.363222 | − | 0.332900i | ||||
\(97\) | −2174.99 | −0.231161 | −0.115580 | − | 0.993298i | \(-0.536873\pi\) | ||||
−0.115580 | + | 0.993298i | \(0.536873\pi\) | |||||||
\(98\) | −1372.20 | − | 9180.32i | −0.142878 | − | 0.955885i | ||||
\(99\) | − | 11879.1i | − | 1.21203i | ||||||
\(100\) | 6935.77 | − | 2120.78i | 0.693577 | − | 0.212078i | ||||
\(101\) | −4516.78 | −0.442778 | −0.221389 | − | 0.975186i | \(-0.571059\pi\) | ||||
−0.221389 | + | 0.975186i | \(0.571059\pi\) | |||||||
\(102\) | 1461.15 | − | 218.400i | 0.140441 | − | 0.0209919i | ||||
\(103\) | − | 2460.95i | − | 0.231968i | −0.993251 | − | 0.115984i | \(-0.962998\pi\) | ||
0.993251 | − | 0.115984i | \(-0.0370021\pi\) | |||||||
\(104\) | 4781.77 | + | 10023.6i | 0.442102 | + | 0.926740i | ||||
\(105\) | 521.083 | 0.0472638 | ||||||||
\(106\) | 2117.73 | + | 14168.1i | 0.188477 | + | 1.26095i | ||||
\(107\) | 8505.12i | 0.742870i | 0.928459 | + | 0.371435i | \(0.121134\pi\) | ||||
−0.928459 | + | 0.371435i | \(0.878866\pi\) | |||||||
\(108\) | −2952.95 | − | 9657.25i | −0.253168 | − | 0.827954i | ||||
\(109\) | −2706.22 | −0.227777 | −0.113888 | − | 0.993494i | \(-0.536331\pi\) | ||||
−0.113888 | + | 0.993494i | \(0.536331\pi\) | |||||||
\(110\) | −10039.5 | + | 1500.62i | −0.829709 | + | 0.124018i | ||||
\(111\) | 1940.18i | 0.157470i | ||||||||
\(112\) | −1283.95 | − | 1903.20i | −0.102356 | − | 0.151722i | ||||
\(113\) | 6191.77 | 0.484907 | 0.242453 | − | 0.970163i | \(-0.422048\pi\) | ||||
0.242453 | + | 0.970163i | \(0.422048\pi\) | |||||||
\(114\) | −217.158 | − | 1452.84i | −0.0167096 | − | 0.111791i | ||||
\(115\) | − | 8963.88i | − | 0.677798i | ||||||
\(116\) | −21928.7 | + | 6705.25i | −1.62966 | + | 0.498309i | ||||
\(117\) | 10643.7 | 0.777535 | ||||||||
\(118\) | 1214.32 | − | 181.507i | 0.0872109 | − | 0.0130356i | ||||
\(119\) | − | 746.967i | − | 0.0527482i | ||||||
\(120\) | −3356.36 | + | 1601.15i | −0.233081 | + | 0.111191i | ||||
\(121\) | −22866.8 | −1.56184 | ||||||||
\(122\) | 4192.76 | + | 28050.5i | 0.281696 | + | 1.88461i | ||||
\(123\) | 3969.77i | 0.262394i | ||||||||
\(124\) | −3512.53 | − | 11487.3i | −0.228442 | − | 0.747092i | ||||
\(125\) | −14129.5 | −0.904288 | ||||||||
\(126\) | −2176.10 | + | 325.266i | −0.137069 | + | 0.0204879i | ||||
\(127\) | − | 2796.70i | − | 0.173396i | −0.996235 | − | 0.0866979i | \(-0.972369\pi\) | ||
0.996235 | − | 0.0866979i | \(-0.0276315\pi\) | |||||||
\(128\) | 14118.1 | + | 8313.50i | 0.861701 | + | 0.507416i | ||||
\(129\) | −4119.21 | −0.247534 | ||||||||
\(130\) | −1344.55 | − | 8995.37i | −0.0795594 | − | 0.532271i | ||||
\(131\) | 24318.3i | 1.41707i | 0.705676 | + | 0.708535i | \(0.250644\pi\) | ||||
−0.705676 | + | 0.708535i | \(0.749356\pi\) | |||||||
\(132\) | −13140.0 | + | 4017.90i | −0.754134 | + | 0.230596i | ||||
\(133\) | −742.719 | −0.0419876 | ||||||||
\(134\) | −18049.3 | + | 2697.86i | −1.00520 | + | 0.150248i | ||||
\(135\) | 8270.48i | 0.453799i | ||||||||
\(136\) | 2295.23 | + | 4811.30i | 0.124093 | + | 0.260126i | ||||
\(137\) | 24493.0 | 1.30497 | 0.652485 | − | 0.757801i | \(-0.273726\pi\) | ||||
0.652485 | + | 0.757801i | \(0.273726\pi\) | |||||||
\(138\) | −1793.72 | − | 12000.4i | −0.0941880 | − | 0.630139i | ||||
\(139\) | 30575.5i | 1.58250i | 0.611493 | + | 0.791250i | \(0.290569\pi\) | ||||
−0.611493 | + | 0.791250i | \(0.709431\pi\) | |||||||
\(140\) | 549.788 | + | 1798.02i | 0.0280504 | + | 0.0917355i | ||||
\(141\) | −9386.43 | −0.472131 | ||||||||
\(142\) | 590.003 | − | 88.1889i | 0.0292602 | − | 0.00437358i | ||||
\(143\) | − | 33607.0i | − | 1.64346i | ||||||
\(144\) | 13017.1 | − | 8781.66i | 0.627752 | − | 0.423498i | ||||
\(145\) | 18779.8 | 0.893211 | ||||||||
\(146\) | 1673.14 | + | 11193.7i | 0.0784922 | + | 0.525131i | ||||
\(147\) | 10290.1i | 0.476196i | ||||||||
\(148\) | −6694.66 | + | 2047.06i | −0.305637 | + | 0.0934561i | ||||
\(149\) | 42569.0 | 1.91744 | 0.958718 | − | 0.284357i | \(-0.0917802\pi\) | ||||
0.958718 | + | 0.284357i | \(0.0917802\pi\) | |||||||
\(150\) | −7951.89 | + | 1188.58i | −0.353417 | + | 0.0528259i | ||||
\(151\) | − | 32464.1i | − | 1.42380i | −0.702280 | − | 0.711901i | \(-0.747834\pi\) | ||
0.702280 | − | 0.711901i | \(-0.252166\pi\) | |||||||
\(152\) | 4783.94 | − | 2282.18i | 0.207061 | − | 0.0987786i | ||||
\(153\) | 5108.92 | 0.218246 | ||||||||
\(154\) | 1027.01 | + | 6870.96i | 0.0433047 | + | 0.289718i | ||||
\(155\) | 9837.72i | 0.409479i | ||||||||
\(156\) | −3600.04 | − | 11773.5i | −0.147931 | − | 0.483789i | ||||
\(157\) | 195.182 | 0.00791845 | 0.00395923 | − | 0.999992i | \(-0.498740\pi\) | ||||
0.00395923 | + | 0.999992i | \(0.498740\pi\) | |||||||
\(158\) | −27279.4 | + | 4077.50i | −1.09275 | + | 0.163335i | ||||
\(159\) | − | 15880.8i | − | 0.628173i | ||||||
\(160\) | −9066.08 | − | 9891.87i | −0.354144 | − | 0.386401i | ||||
\(161\) | −6134.82 | −0.236674 | ||||||||
\(162\) | −1282.88 | − | 8582.76i | −0.0488828 | − | 0.327037i | ||||
\(163\) | 21326.3i | 0.802678i | 0.915930 | + | 0.401339i | \(0.131455\pi\) | ||||
−0.915930 | + | 0.401339i | \(0.868545\pi\) | |||||||
\(164\) | −13697.8 | + | 4188.45i | −0.509288 | + | 0.155728i | ||||
\(165\) | 11253.1 | 0.413339 | ||||||||
\(166\) | 31023.8 | − | 4637.18i | 1.12585 | − | 0.168282i | ||||
\(167\) | 20994.1i | 0.752774i | 0.926462 | + | 0.376387i | \(0.122834\pi\) | ||||
−0.926462 | + | 0.376387i | \(0.877166\pi\) | |||||||
\(168\) | 1095.82 | + | 2297.07i | 0.0388258 | + | 0.0813872i | ||||
\(169\) | 1550.90 | 0.0543015 | ||||||||
\(170\) | −645.381 | − | 4317.74i | −0.0223315 | − | 0.149403i | ||||
\(171\) | − | 5079.87i | − | 0.173724i | ||||||
\(172\) | −4346.13 | − | 14213.5i | −0.146908 | − | 0.480445i | ||||
\(173\) | 34458.3 | 1.15134 | 0.575668 | − | 0.817684i | \(-0.304742\pi\) | ||||
0.575668 | + | 0.817684i | \(0.304742\pi\) | |||||||
\(174\) | 25141.3 | − | 3757.92i | 0.830405 | − | 0.124122i | ||||
\(175\) | 4065.16i | 0.132740i | ||||||||
\(176\) | −27727.8 | − | 41100.9i | −0.895137 | − | 1.32686i | ||||
\(177\) | −1361.12 | −0.0434461 | ||||||||
\(178\) | 5152.63 | + | 34472.3i | 0.162626 | + | 1.08800i | ||||
\(179\) | 26297.9i | 0.820756i | 0.911915 | + | 0.410378i | \(0.134603\pi\) | ||||
−0.911915 | + | 0.410378i | \(0.865397\pi\) | |||||||
\(180\) | −12297.6 | + | 3760.31i | −0.379557 | + | 0.116059i | ||||
\(181\) | −24396.4 | −0.744677 | −0.372339 | − | 0.928097i | \(-0.621444\pi\) | ||||
−0.372339 | + | 0.928097i | \(0.621444\pi\) | |||||||
\(182\) | −6156.38 | + | 920.205i | −0.185859 | + | 0.0277806i | ||||
\(183\) | − | 31441.5i | − | 0.938861i | ||||||
\(184\) | 39515.1 | − | 18850.7i | 1.16715 | − | 0.556791i | ||||
\(185\) | 5733.32 | 0.167518 | ||||||||
\(186\) | 1968.58 | + | 13170.2i | 0.0569019 | + | 0.380686i | ||||
\(187\) | − | 16131.2i | − | 0.461301i | ||||||
\(188\) | −9903.50 | − | 32388.2i | −0.280203 | − | 0.916370i | ||||
\(189\) | 5660.27 | 0.158458 | ||||||||
\(190\) | −4293.19 | + | 641.711i | −0.118925 | + | 0.0177759i | ||||
\(191\) | − | 20922.9i | − | 0.573527i | −0.958001 | − | 0.286764i | \(-0.907421\pi\) | ||
0.958001 | − | 0.286764i | \(-0.0925795\pi\) | |||||||
\(192\) | −14116.6 | − | 11428.5i | −0.382937 | − | 0.310019i | ||||
\(193\) | 55571.2 | 1.49188 | 0.745942 | − | 0.666011i | \(-0.232000\pi\) | ||||
0.745942 | + | 0.666011i | \(0.232000\pi\) | |||||||
\(194\) | 1286.11 | + | 8604.37i | 0.0341723 | + | 0.228621i | ||||
\(195\) | 10082.8i | 0.265163i | ||||||||
\(196\) | −35506.4 | + | 10857.0i | −0.924261 | + | 0.282616i | ||||
\(197\) | −50210.5 | −1.29378 | −0.646892 | − | 0.762582i | \(-0.723932\pi\) | ||||
−0.646892 | + | 0.762582i | \(0.723932\pi\) | |||||||
\(198\) | −46994.3 | + | 7024.33i | −1.19871 | + | 0.179174i | ||||
\(199\) | − | 4943.87i | − | 0.124842i | −0.998050 | − | 0.0624211i | \(-0.980118\pi\) | ||
0.998050 | − | 0.0624211i | \(-0.0198822\pi\) | |||||||
\(200\) | −12491.2 | − | 26184.2i | −0.312279 | − | 0.654605i | ||||
\(201\) | 20231.3 | 0.500761 | ||||||||
\(202\) | 2670.86 | + | 17868.6i | 0.0654557 | + | 0.437914i | ||||
\(203\) | − | 12852.8i | − | 0.311892i | ||||||
\(204\) | −1728.00 | − | 5651.22i | −0.0415226 | − | 0.135794i | ||||
\(205\) | 11730.8 | 0.279139 | ||||||||
\(206\) | −9735.63 | + | 1455.20i | −0.229419 | + | 0.0342917i | ||||
\(207\) | − | 41959.5i | − | 0.979241i | ||||||
\(208\) | 36826.4 | − | 24844.1i | 0.851202 | − | 0.574244i | ||||
\(209\) | −16039.5 | −0.367197 | ||||||||
\(210\) | −308.126 | − | 2061.43i | −0.00698699 | − | 0.0467445i | ||||
\(211\) | − | 67805.4i | − | 1.52300i | −0.648166 | − | 0.761499i | \(-0.724464\pi\) | ||
0.648166 | − | 0.761499i | \(-0.275536\pi\) | |||||||
\(212\) | 54797.4 | − | 16755.7i | 1.21924 | − | 0.372812i | ||||
\(213\) | −661.329 | −0.0145767 | ||||||||
\(214\) | 33646.7 | − | 5029.23i | 0.734708 | − | 0.109818i | ||||
\(215\) | 12172.4i | 0.263330i | ||||||||
\(216\) | −36458.4 | + | 17392.5i | −0.781431 | + | 0.372782i | ||||
\(217\) | 6732.88 | 0.142982 | ||||||||
\(218\) | 1600.24 | + | 10705.9i | 0.0336721 | + | 0.225274i | ||||
\(219\) | − | 12546.9i | − | 0.261606i | ||||||
\(220\) | 11873.0 | + | 38829.3i | 0.245311 | + | 0.802259i | ||||
\(221\) | 14453.6 | 0.295932 | ||||||||
\(222\) | 7675.46 | − | 1147.26i | 0.155739 | − | 0.0232786i | ||||
\(223\) | 35884.4i | 0.721598i | 0.932644 | + | 0.360799i | \(0.117496\pi\) | ||||
−0.932644 | + | 0.360799i | \(0.882504\pi\) | |||||||
\(224\) | −6769.94 | + | 6204.77i | −0.134924 | + | 0.123660i | ||||
\(225\) | −27803.9 | −0.549213 | ||||||||
\(226\) | −3661.31 | − | 24495.0i | −0.0716835 | − | 0.479579i | ||||
\(227\) | 79862.5i | 1.54985i | 0.632050 | + | 0.774927i | \(0.282214\pi\) | ||||
−0.632050 | + | 0.774927i | \(0.717786\pi\) | |||||||
\(228\) | −5619.09 | + | 1718.18i | −0.108093 | + | 0.0330521i | ||||
\(229\) | −56160.1 | −1.07092 | −0.535460 | − | 0.844561i | \(-0.679862\pi\) | ||||
−0.535460 | + | 0.844561i | \(0.679862\pi\) | |||||||
\(230\) | −35461.6 | + | 5300.50i | −0.670351 | + | 0.100199i | ||||
\(231\) | − | 7701.58i | − | 0.144330i | ||||||
\(232\) | 39493.1 | + | 82786.1i | 0.733746 | + | 1.53809i | ||||
\(233\) | −71608.6 | −1.31903 | −0.659513 | − | 0.751694i | \(-0.729237\pi\) | ||||
−0.659513 | + | 0.751694i | \(0.729237\pi\) | |||||||
\(234\) | −6293.80 | − | 42106.9i | −0.114943 | − | 0.768992i | ||||
\(235\) | 27737.3i | 0.502259i | ||||||||
\(236\) | −1436.10 | − | 4696.60i | −0.0257847 | − | 0.0843256i | ||||
\(237\) | 30577.2 | 0.544378 | ||||||||
\(238\) | −2955.04 | + | 441.695i | −0.0521686 | + | 0.00779773i | ||||
\(239\) | 11359.8i | 0.198873i | 0.995044 | + | 0.0994366i | \(0.0317040\pi\) | ||||
−0.995044 | + | 0.0994366i | \(0.968296\pi\) | |||||||
\(240\) | 8318.92 | + | 12331.1i | 0.144426 | + | 0.214082i | ||||
\(241\) | −42161.8 | −0.725914 | −0.362957 | − | 0.931806i | \(-0.618233\pi\) | ||||
−0.362957 | + | 0.931806i | \(0.618233\pi\) | |||||||
\(242\) | 13521.6 | + | 90462.3i | 0.230885 | + | 1.54467i | ||||
\(243\) | 60744.7i | 1.02872i | ||||||||
\(244\) | 108490. | − | 33173.5i | 1.82226 | − | 0.557201i | ||||
\(245\) | 30407.7 | 0.506584 | ||||||||
\(246\) | 15704.6 | − | 2347.39i | 0.259511 | − | 0.0387896i | ||||
\(247\) | − | 14371.4i | − | 0.235562i | ||||||
\(248\) | −43367.3 | + | 20688.4i | −0.705113 | + | 0.336374i | ||||
\(249\) | −34774.2 | −0.560866 | ||||||||
\(250\) | 8355.03 | + | 55897.0i | 0.133680 | + | 0.894352i | ||||
\(251\) | − | 7549.02i | − | 0.119824i | −0.998204 | − | 0.0599119i | \(-0.980918\pi\) | ||
0.998204 | − | 0.0599119i | \(-0.0190820\pi\) | |||||||
\(252\) | 2573.54 | + | 8416.43i | 0.0405256 | + | 0.132534i | ||||
\(253\) | −132486. | −2.06980 | ||||||||
\(254\) | −11063.9 | + | 1653.74i | −0.171491 | + | 0.0256330i | ||||
\(255\) | 4839.71i | 0.0744285i | ||||||||
\(256\) | 24540.3 | − | 60767.9i | 0.374456 | − | 0.927245i | ||||
\(257\) | −24834.0 | −0.375994 | −0.187997 | − | 0.982170i | \(-0.560200\pi\) | ||||
−0.187997 | + | 0.982170i | \(0.560200\pi\) | |||||||
\(258\) | 2435.76 | + | 16295.8i | 0.0365928 | + | 0.244814i | ||||
\(259\) | − | 3923.85i | − | 0.0584942i | ||||||
\(260\) | −34791.1 | + | 10638.3i | −0.514661 | + | 0.157371i | ||||
\(261\) | 87907.2 | 1.29046 | ||||||||
\(262\) | 96204.6 | − | 14379.9i | 1.40150 | − | 0.209485i | ||||
\(263\) | − | 10991.3i | − | 0.158905i | −0.996839 | − | 0.0794527i | \(-0.974683\pi\) | ||
0.996839 | − | 0.0794527i | \(-0.0253173\pi\) | |||||||
\(264\) | 23664.9 | + | 49606.8i | 0.339545 | + | 0.711760i | ||||
\(265\) | −46928.5 | −0.668260 | ||||||||
\(266\) | 439.183 | + | 2938.24i | 0.00620701 | + | 0.0415263i | ||||
\(267\) | − | 38639.6i | − | 0.542014i | ||||||
\(268\) | 21345.7 | + | 69808.6i | 0.297195 | + | 0.971940i | ||||
\(269\) | 123859. | 1.71168 | 0.855839 | − | 0.517242i | \(-0.173041\pi\) | ||||
0.855839 | + | 0.517242i | \(0.173041\pi\) | |||||||
\(270\) | 32718.4 | − | 4890.48i | 0.448813 | − | 0.0670848i | ||||
\(271\) | − | 38457.3i | − | 0.523649i | −0.965116 | − | 0.261824i | \(-0.915676\pi\) | ||
0.965116 | − | 0.261824i | \(-0.0843241\pi\) | |||||||
\(272\) | 17676.5 | − | 11925.1i | 0.238924 | − | 0.161184i | ||||
\(273\) | 6900.62 | 0.0925898 | ||||||||
\(274\) | −14483.2 | − | 96895.6i | −0.192913 | − | 1.29063i | ||||
\(275\) | 87789.9i | 1.16086i | ||||||||
\(276\) | −46413.4 | + | 14192.1i | −0.609292 | + | 0.186306i | ||||
\(277\) | −63456.0 | −0.827015 | −0.413508 | − | 0.910501i | \(-0.635696\pi\) | ||||
−0.413508 | + | 0.910501i | \(0.635696\pi\) | |||||||
\(278\) | 120958. | − | 18079.8i | 1.56511 | − | 0.233940i | ||||
\(279\) | 46049.9i | 0.591590i | ||||||||
\(280\) | 6787.94 | − | 3238.19i | 0.0865809 | − | 0.0413034i | ||||
\(281\) | −49117.0 | −0.622041 | −0.311020 | − | 0.950403i | \(-0.600671\pi\) | ||||
−0.311020 | + | 0.950403i | \(0.600671\pi\) | |||||||
\(282\) | 5550.37 | + | 37133.2i | 0.0697948 | + | 0.466943i | ||||
\(283\) | 71155.9i | 0.888460i | 0.895913 | + | 0.444230i | \(0.146523\pi\) | ||||
−0.895913 | + | 0.444230i | \(0.853477\pi\) | |||||||
\(284\) | −697.759 | − | 2281.94i | −0.00865105 | − | 0.0282922i | ||||
\(285\) | 4812.20 | 0.0592453 | ||||||||
\(286\) | −132951. | + | 19872.4i | −1.62540 | + | 0.242951i | ||||
\(287\) | − | 8028.50i | − | 0.0974699i | ||||||
\(288\) | −42437.9 | − | 46303.4i | −0.511645 | − | 0.558249i | ||||
\(289\) | −76583.3 | −0.916935 | ||||||||
\(290\) | −11104.8 | − | 74293.7i | −0.132043 | − | 0.883397i | ||||
\(291\) | − | 9644.55i | − | 0.113893i | ||||||
\(292\) | 43293.4 | − | 13238.1i | 0.507758 | − | 0.155260i | ||||
\(293\) | 2819.70 | 0.0328448 | 0.0164224 | − | 0.999865i | \(-0.494772\pi\) | ||||
0.0164224 | + | 0.999865i | \(0.494772\pi\) | |||||||
\(294\) | 40708.2 | − | 6084.73i | 0.470964 | − | 0.0703958i | ||||
\(295\) | 4022.17i | 0.0462186i | ||||||||
\(296\) | 12057.0 | + | 25274.0i | 0.137611 | + | 0.288463i | ||||
\(297\) | 122237. | 1.38577 | ||||||||
\(298\) | −25171.8 | − | 168405.i | −0.283454 | − | 1.89637i | ||||
\(299\) | − | 118707.i | − | 1.32781i | ||||||
\(300\) | 9404.19 | + | 30755.2i | 0.104491 | + | 0.341725i | ||||
\(301\) | 8330.74 | 0.0919498 | ||||||||
\(302\) | −128430. | + | 19196.6i | −1.40816 | + | 0.210480i | ||||
\(303\) | − | 20028.8i | − | 0.218157i | ||||||
\(304\) | −11857.3 | − | 17576.0i | −0.128303 | − | 0.190184i | ||||
\(305\) | −92910.9 | −0.998774 | ||||||||
\(306\) | −3021.00 | − | 20211.2i | −0.0322632 | − | 0.215848i | ||||
\(307\) | 161051.i | 1.70878i | 0.519631 | + | 0.854391i | \(0.326069\pi\) | ||||
−0.519631 | + | 0.854391i | \(0.673931\pi\) | |||||||
\(308\) | 26574.6 | − | 8125.84i | 0.280133 | − | 0.0856578i | ||||
\(309\) | 10912.6 | 0.114290 | ||||||||
\(310\) | 38918.5 | − | 5817.22i | 0.404980 | − | 0.0605330i | ||||
\(311\) | − | 138439.i | − | 1.43133i | −0.698446 | − | 0.715663i | \(-0.746125\pi\) | ||
0.698446 | − | 0.715663i | \(-0.253875\pi\) | |||||||
\(312\) | −44447.7 | + | 21203.8i | −0.456605 | + | 0.217823i | ||||
\(313\) | 26633.8 | 0.271860 | 0.135930 | − | 0.990718i | \(-0.456598\pi\) | ||||
0.135930 | + | 0.990718i | \(0.456598\pi\) | |||||||
\(314\) | −115.415 | − | 772.150i | −0.00117058 | − | 0.00783145i | ||||
\(315\) | − | 7207.84i | − | 0.0726414i | ||||||
\(316\) | 32261.6 | + | 105508.i | 0.323081 | + | 1.05660i | ||||
\(317\) | −45290.4 | −0.450700 | −0.225350 | − | 0.974278i | \(-0.572353\pi\) | ||||
−0.225350 | + | 0.974278i | \(0.572353\pi\) | |||||||
\(318\) | −62825.4 | + | 9390.63i | −0.621271 | + | 0.0928625i | ||||
\(319\) | − | 277564.i | − | 2.72760i | ||||||
\(320\) | −33771.8 | + | 41715.1i | −0.329803 | + | 0.407374i | ||||
\(321\) | −37714.2 | −0.366012 | ||||||||
\(322\) | 3627.63 | + | 24269.7i | 0.0349874 | + | 0.234074i | ||||
\(323\) | − | 6898.22i | − | 0.0661199i | ||||||
\(324\) | −33195.3 | + | 10150.3i | −0.316218 | + | 0.0966915i | ||||
\(325\) | −78659.8 | −0.744708 | ||||||||
\(326\) | 84368.1 | − | 12610.7i | 0.793859 | − | 0.118659i | ||||
\(327\) | − | 12000.2i | − | 0.112226i | ||||||
\(328\) | 24669.5 | + | 51712.5i | 0.229304 | + | 0.480671i | ||||
\(329\) | 18983.2 | 0.175379 | ||||||||
\(330\) | −6654.19 | − | 44518.0i | −0.0611036 | − | 0.408797i | ||||
\(331\) | 1136.55i | 0.0103737i | 0.999987 | + | 0.00518685i | \(0.00165103\pi\) | ||||
−0.999987 | + | 0.00518685i | \(0.998349\pi\) | |||||||
\(332\) | −36689.9 | − | 119990.i | −0.332866 | − | 1.08860i | ||||
\(333\) | 26837.4 | 0.242020 | ||||||||
\(334\) | 83053.8 | − | 12414.2i | 0.744504 | − | 0.111282i | ||||
\(335\) | − | 59784.2i | − | 0.532717i | ||||||
\(336\) | 8439.36 | − | 5693.42i | 0.0747534 | − | 0.0504307i | ||||
\(337\) | 126361. | 1.11263 | 0.556317 | − | 0.830970i | \(-0.312214\pi\) | ||||
0.556317 | + | 0.830970i | \(0.312214\pi\) | |||||||
\(338\) | −917.078 | − | 6135.46i | −0.00802736 | − | 0.0537049i | ||||
\(339\) | 27456.2i | 0.238913i | ||||||||
\(340\) | −16699.6 | + | 5106.32i | −0.144460 | + | 0.0441723i | ||||
\(341\) | 145401. | 1.25043 | ||||||||
\(342\) | −20096.2 | + | 3003.82i | −0.171816 | + | 0.0256816i | ||||
\(343\) | − | 42343.0i | − | 0.359909i | ||||||
\(344\) | −53659.3 | + | 25598.2i | −0.453449 | + | 0.216318i | ||||
\(345\) | 39748.5 | 0.333951 | ||||||||
\(346\) | −20375.8 | − | 136319.i | −0.170201 | − | 1.13869i | ||||
\(347\) | 164302.i | 1.36453i | 0.731103 | + | 0.682267i | \(0.239006\pi\) | ||||
−0.731103 | + | 0.682267i | \(0.760994\pi\) | |||||||
\(348\) | −29733.1 | − | 97238.3i | −0.245517 | − | 0.802932i | ||||
\(349\) | −57342.3 | −0.470787 | −0.235394 | − | 0.971900i | \(-0.575638\pi\) | ||||
−0.235394 | + | 0.971900i | \(0.575638\pi\) | |||||||
\(350\) | 16082.0 | − | 2403.80i | 0.131282 | − | 0.0196229i | ||||
\(351\) | 109525.i | 0.888991i | ||||||||
\(352\) | −146201. | + | 133996.i | −1.17996 | + | 1.08145i | ||||
\(353\) | 229162. | 1.83905 | 0.919524 | − | 0.393034i | \(-0.128575\pi\) | ||||
0.919524 | + | 0.393034i | \(0.128575\pi\) | |||||||
\(354\) | 804.857 | + | 5384.67i | 0.00642262 | + | 0.0429688i | ||||
\(355\) | 1954.25i | 0.0155069i | ||||||||
\(356\) | 133327. | − | 40768.2i | 1.05201 | − | 0.321678i | ||||
\(357\) | 3312.27 | 0.0259890 | ||||||||
\(358\) | 104036. | − | 15550.4i | 0.811739 | − | 0.121332i | ||||
\(359\) | − | 140525.i | − | 1.09035i | −0.838322 | − | 0.545175i | \(-0.816463\pi\) | ||
0.838322 | − | 0.545175i | \(-0.183537\pi\) | |||||||
\(360\) | 22147.8 | + | 46426.5i | 0.170894 | + | 0.358229i | ||||
\(361\) | −6859.00 | −0.0526316 | ||||||||
\(362\) | 14426.0 | + | 96513.3i | 0.110085 | + | 0.736495i | ||||
\(363\) | − | 101398.i | − | 0.769516i | ||||||
\(364\) | 7280.76 | + | 23810.8i | 0.0549508 | + | 0.179710i | ||||
\(365\) | −37076.5 | −0.278300 | ||||||||
\(366\) | −124384. | + | 18591.9i | −0.928545 | + | 0.138791i | ||||
\(367\) | 181307.i | 1.34612i | 0.739589 | + | 0.673059i | \(0.235020\pi\) | ||||
−0.739589 | + | 0.673059i | \(0.764980\pi\) | |||||||
\(368\) | −97940.4 | − | 145177.i | −0.723213 | − | 1.07202i | ||||
\(369\) | 54911.4 | 0.403283 | ||||||||
\(370\) | −3390.21 | − | 22681.3i | −0.0247642 | − | 0.165678i | ||||
\(371\) | 32117.6i | 0.233343i | ||||||||
\(372\) | 50938.0 | − | 15575.6i | 0.368092 | − | 0.112553i | ||||
\(373\) | 181780. | 1.30656 | 0.653280 | − | 0.757117i | \(-0.273393\pi\) | ||||
0.653280 | + | 0.757117i | \(0.273393\pi\) | |||||||
\(374\) | −63816.0 | + | 9538.69i | −0.456233 | + | 0.0681939i | ||||
\(375\) | − | 62654.4i | − | 0.445542i | ||||||
\(376\) | −122273. | + | 58330.5i | −0.864879 | + | 0.412591i | ||||
\(377\) | 248697. | 1.74980 | ||||||||
\(378\) | −3347.02 | − | 22392.3i | −0.0234247 | − | 0.156717i | ||||
\(379\) | 151291.i | 1.05326i | 0.850095 | + | 0.526629i | \(0.176544\pi\) | ||||
−0.850095 | + | 0.526629i | \(0.823456\pi\) | |||||||
\(380\) | 5077.29 | + | 16604.6i | 0.0351613 | + | 0.114991i | ||||
\(381\) | 12401.4 | 0.0854320 | ||||||||
\(382\) | −82771.9 | + | 12372.1i | −0.567226 | + | 0.0847843i | ||||
\(383\) | 150881.i | 1.02858i | 0.857616 | + | 0.514290i | \(0.171945\pi\) | ||||
−0.857616 | + | 0.514290i | \(0.828055\pi\) | |||||||
\(384\) | −36864.5 | + | 62603.9i | −0.250004 | + | 0.424560i | ||||
\(385\) | −22758.5 | −0.153540 | ||||||||
\(386\) | −32860.2 | − | 219842.i | −0.220544 | − | 1.47549i | ||||
\(387\) | 56978.6i | 0.380443i | ||||||||
\(388\) | 33278.8 | − | 10175.8i | 0.221057 | − | 0.0675938i | ||||
\(389\) | −1428.09 | −0.00943750 | −0.00471875 | − | 0.999989i | \(-0.501502\pi\) | ||||
−0.00471875 | + | 0.999989i | \(0.501502\pi\) | |||||||
\(390\) | 39888.2 | − | 5962.15i | 0.262250 | − | 0.0391989i | ||||
\(391\) | − | 56979.0i | − | 0.372701i | ||||||
\(392\) | 63946.3 | + | 134045.i | 0.416144 | + | 0.872327i | ||||
\(393\) | −107835. | −0.698190 | ||||||||
\(394\) | 29690.4 | + | 198635.i | 0.191259 | + | 1.27957i | ||||
\(395\) | − | 90356.8i | − | 0.579117i | ||||||
\(396\) | 55577.2 | + | 181758.i | 0.354410 | + | 1.15906i | ||||
\(397\) | −208771. | −1.32461 | −0.662307 | − | 0.749233i | \(-0.730423\pi\) | ||||
−0.662307 | + | 0.749233i | \(0.730423\pi\) | |||||||
\(398\) | −19558.2 | + | 2923.40i | −0.123471 | + | 0.0184554i | ||||
\(399\) | − | 3293.44i | − | 0.0206873i | ||||||
\(400\) | −96199.7 | + | 64898.9i | −0.601248 | + | 0.405618i | ||||
\(401\) | 237252. | 1.47544 | 0.737719 | − | 0.675108i | \(-0.235903\pi\) | ||||
0.737719 | + | 0.675108i | \(0.235903\pi\) | |||||||
\(402\) | −11963.1 | − | 80035.9i | −0.0740273 | − | 0.495259i | ||||
\(403\) | 130279.i | 0.802168i | ||||||||
\(404\) | 69109.9 | − | 21132.1i | 0.423426 | − | 0.129473i | ||||
\(405\) | 28428.4 | 0.173318 | ||||||||
\(406\) | −50846.2 | + | 7600.07i | −0.308465 | + | 0.0461068i | ||||
\(407\) | − | 84738.1i | − | 0.511552i | ||||||
\(408\) | −21334.7 | + | 10177.7i | −0.128164 | + | 0.0611408i | ||||
\(409\) | −315975. | −1.88889 | −0.944443 | − | 0.328676i | \(-0.893397\pi\) | ||||
−0.944443 | + | 0.328676i | \(0.893397\pi\) | |||||||
\(410\) | −6936.64 | − | 46407.7i | −0.0412650 | − | 0.276072i | ||||
\(411\) | 108609.i | 0.642959i | ||||||||
\(412\) | 11513.7 | + | 37654.2i | 0.0678298 | + | 0.221829i | ||||
\(413\) | 2752.75 | 0.0161386 | ||||||||
\(414\) | −165994. | + | 24811.4i | −0.968482 | + | 0.144761i | ||||
\(415\) | 102759.i | 0.596657i | ||||||||
\(416\) | −120061. | − | 130996.i | −0.693767 | − | 0.756960i | ||||
\(417\) | −135581. | −0.779697 | ||||||||
\(418\) | 9484.46 | + | 63453.2i | 0.0542825 | + | 0.363162i | ||||
\(419\) | − | 233329.i | − | 1.32905i | −0.747266 | − | 0.664525i | \(-0.768634\pi\) | ||
0.747266 | − | 0.664525i | \(-0.231366\pi\) | |||||||
\(420\) | −7972.93 | + | 2437.92i | −0.0451980 | + | 0.0138204i | ||||
\(421\) | −162883. | −0.918992 | −0.459496 | − | 0.888180i | \(-0.651970\pi\) | ||||
−0.459496 | + | 0.888180i | \(0.651970\pi\) | |||||||
\(422\) | −268242. | + | 40094.6i | −1.50626 | + | 0.225144i | ||||
\(423\) | 129837.i | 0.725634i | ||||||||
\(424\) | −98689.0 | − | 206873.i | −0.548955 | − | 1.15073i | ||||
\(425\) | −37756.4 | −0.209032 | ||||||||
\(426\) | 391.056 | + | 2616.25i | 0.00215486 | + | 0.0144165i | ||||
\(427\) | 63587.7i | 0.348752i | ||||||||
\(428\) | −39791.8 | − | 130134.i | −0.217223 | − | 0.710401i | ||||
\(429\) | 149024. | 0.809730 | ||||||||
\(430\) | 48154.8 | − | 7197.78i | 0.260437 | − | 0.0389280i | ||||
\(431\) | 353158.i | 1.90114i | 0.310512 | + | 0.950570i | \(0.399500\pi\) | ||||
−0.310512 | + | 0.950570i | \(0.600500\pi\) | |||||||
\(432\) | 90364.2 | + | 133947.i | 0.484205 | + | 0.717737i | ||||
\(433\) | 107507. | 0.573406 | 0.286703 | − | 0.958020i | \(-0.407441\pi\) | ||||
0.286703 | + | 0.958020i | \(0.407441\pi\) | |||||||
\(434\) | −3981.27 | − | 26635.6i | −0.0211370 | − | 0.141411i | ||||
\(435\) | 83275.0i | 0.440085i | ||||||||
\(436\) | 41407.0 | − | 12661.2i | 0.217821 | − | 0.0666044i | ||||
\(437\) | −56655.0 | −0.296671 | ||||||||
\(438\) | −49636.1 | + | 7419.20i | −0.258732 | + | 0.0386731i | ||||
\(439\) | − | 365722.i | − | 1.89767i | −0.315766 | − | 0.948837i | \(-0.602261\pi\) | ||
0.315766 | − | 0.948837i | \(-0.397739\pi\) | |||||||
\(440\) | 146590. | − | 69930.9i | 0.757180 | − | 0.361213i | ||||
\(441\) | 142337. | 0.731882 | ||||||||
\(442\) | −8546.67 | − | 57179.2i | −0.0437474 | − | 0.292680i | ||||
\(443\) | 11929.3i | 0.0607867i | 0.999538 | + | 0.0303934i | \(0.00967600\pi\) | ||||
−0.999538 | + | 0.0303934i | \(0.990324\pi\) | |||||||
\(444\) | −9077.28 | − | 29686.1i | −0.0460458 | − | 0.150587i | ||||
\(445\) | −114182. | −0.576602 | ||||||||
\(446\) | 141960. | − | 21219.1i | 0.713670 | − | 0.106674i | ||||
\(447\) | 188764.i | 0.944720i | ||||||||
\(448\) | 28549.6 | + | 23113.2i | 0.142247 | + | 0.115161i | ||||
\(449\) | −85864.7 | −0.425914 | −0.212957 | − | 0.977062i | \(-0.568309\pi\) | ||||
−0.212957 | + | 0.977062i | \(0.568309\pi\) | |||||||
\(450\) | 16441.0 | + | 109994.i | 0.0811899 | + | 0.543179i | ||||
\(451\) | − | 173381.i | − | 0.852409i | ||||||
\(452\) | −94738.4 | + | 28968.6i | −0.463713 | + | 0.141792i | ||||
\(453\) | 143955. | 0.701507 | ||||||||
\(454\) | 315940. | − | 47224.1i | 1.53283 | − | 0.229114i | ||||
\(455\) | − | 20391.6i | − | 0.0984983i | ||||||
\(456\) | 10119.9 | + | 21213.4i | 0.0486682 | + | 0.102019i | ||||
\(457\) | −281117. | −1.34603 | −0.673015 | − | 0.739629i | \(-0.735001\pi\) | ||||
−0.673015 | + | 0.739629i | \(0.735001\pi\) | |||||||
\(458\) | 33208.5 | + | 222172.i | 0.158313 | + | 1.05915i | ||||
\(459\) | 52571.4i | 0.249531i | ||||||||
\(460\) | 41938.1 | + | 137153.i | 0.198195 | + | 0.648173i | ||||
\(461\) | −7044.46 | −0.0331471 | −0.0165736 | − | 0.999863i | \(-0.505276\pi\) | ||||
−0.0165736 | + | 0.999863i | \(0.505276\pi\) | |||||||
\(462\) | −30467.9 | + | 4554.09i | −0.142744 | + | 0.0213362i | ||||
\(463\) | − | 216166.i | − | 1.00838i | −0.863592 | − | 0.504192i | \(-0.831791\pi\) | ||
0.863592 | − | 0.504192i | \(-0.168209\pi\) | |||||||
\(464\) | 304153. | − | 205190.i | 1.41272 | − | 0.953059i | ||||
\(465\) | −43623.4 | −0.201750 | ||||||||
\(466\) | 42343.4 | + | 283287.i | 0.194991 | + | 1.30453i | ||||
\(467\) | − | 211192.i | − | 0.968373i | −0.874965 | − | 0.484187i | \(-0.839116\pi\) | ||
0.874965 | − | 0.484187i | \(-0.160884\pi\) | |||||||
\(468\) | −162856. | + | 49797.2i | −0.743551 | + | 0.227360i | ||||
\(469\) | −40915.9 | −0.186014 | ||||||||
\(470\) | 109730. | − | 16401.6i | 0.496741 | − | 0.0742488i | ||||
\(471\) | 865.495i | 0.00390142i | ||||||||
\(472\) | −17730.8 | + | 8458.49i | −0.0795874 | + | 0.0379672i | ||||
\(473\) | 179908. | 0.804133 | ||||||||
\(474\) | −18080.8 | − | 120965.i | −0.0804752 | − | 0.538397i | ||||
\(475\) | 37541.7i | 0.166390i | ||||||||
\(476\) | 3494.73 | + | 11429.1i | 0.0154241 | + | 0.0504427i | ||||
\(477\) | −219670. | −0.965461 | ||||||||
\(478\) | 44940.1 | − | 6717.28i | 0.196688 | − | 0.0293993i | ||||
\(479\) | − | 318333.i | − | 1.38743i | −0.720251 | − | 0.693714i | \(-0.755973\pi\) | ||
0.720251 | − | 0.693714i | \(-0.244027\pi\) | |||||||
\(480\) | 43863.5 | − | 40201.7i | 0.190380 | − | 0.174487i | ||||
\(481\) | 75925.4 | 0.328168 | ||||||||
\(482\) | 24931.1 | + | 166794.i | 0.107312 | + | 0.717939i | ||||
\(483\) | − | 27203.6i | − | 0.116609i | ||||||
\(484\) | 349878. | − | 106984.i | 1.49357 | − | 0.456697i | ||||
\(485\) | −28500.0 | −0.121161 | ||||||||
\(486\) | 240309. | − | 35919.4i | 1.01741 | − | 0.152075i | ||||
\(487\) | − | 158377.i | − | 0.667780i | −0.942612 | − | 0.333890i | \(-0.891639\pi\) | ||
0.942612 | − | 0.333890i | \(-0.108361\pi\) | |||||||
\(488\) | −195388. | − | 409576.i | −0.820463 | − | 1.71987i | ||||
\(489\) | −94567.3 | −0.395479 | ||||||||
\(490\) | −17980.6 | − | 120294.i | −0.0748881 | − | 0.501018i | ||||
\(491\) | − | 38055.1i | − | 0.157852i | −0.996880 | − | 0.0789260i | \(-0.974851\pi\) | ||
0.996880 | − | 0.0789260i | \(-0.0251491\pi\) | |||||||
\(492\) | −18572.8 | − | 60740.1i | −0.0767269 | − | 0.250926i | ||||
\(493\) | 119374. | 0.491151 | ||||||||
\(494\) | −56854.1 | + | 8498.08i | −0.232974 | + | 0.0348230i | ||||
\(495\) | − | 155658.i | − | 0.635274i | ||||||
\(496\) | 107488. | + | 159330.i | 0.436915 | + | 0.647640i | ||||
\(497\) | 1337.48 | 0.00541470 | ||||||||
\(498\) | 20562.6 | + | 137569.i | 0.0829125 | + | 0.554704i | ||||
\(499\) | 477988.i | 1.91962i | 0.280644 | + | 0.959812i | \(0.409452\pi\) | ||||
−0.280644 | + | 0.959812i | \(0.590548\pi\) | |||||||
\(500\) | 216191. | − | 66105.8i | 0.864764 | − | 0.264423i | ||||
\(501\) | −93094.2 | −0.370892 | ||||||||
\(502\) | −29864.3 | + | 4463.87i | −0.118507 | + | 0.0177135i | ||||
\(503\) | 157454.i | 0.622327i | 0.950356 | + | 0.311163i | \(0.100719\pi\) | ||||
−0.950356 | + | 0.311163i | \(0.899281\pi\) | |||||||
\(504\) | 31774.1 | − | 15157.8i | 0.125087 | − | 0.0596727i | ||||
\(505\) | −59185.8 | −0.232078 | ||||||||
\(506\) | 78341.1 | + | 524120.i | 0.305977 | + | 2.04706i | ||||
\(507\) | 6877.17i | 0.0267543i | ||||||||
\(508\) | 13084.6 | + | 42791.4i | 0.0507028 | + | 0.165817i | ||||
\(509\) | −85407.2 | −0.329654 | −0.164827 | − | 0.986322i | \(-0.552707\pi\) | ||||
−0.164827 | + | 0.986322i | \(0.552707\pi\) | |||||||
\(510\) | 19146.2 | − | 2861.81i | 0.0736107 | − | 0.0110027i | ||||
\(511\) | 25375.0i | 0.0971771i | ||||||||
\(512\) | −254912. | − | 61149.7i | −0.972413 | − | 0.233267i | ||||
\(513\) | 52272.5 | 0.198627 | ||||||||
\(514\) | 14684.8 | + | 98244.7i | 0.0555830 | + | 0.371863i | ||||
\(515\) | − | 32247.1i | − | 0.121584i | ||||||
\(516\) | 63026.8 | − | 19272.0i | 0.236715 | − | 0.0723815i | ||||
\(517\) | 409955. | 1.53375 | ||||||||
\(518\) | −15522.9 | + | 2320.24i | −0.0578515 | + | 0.00864717i | ||||
\(519\) | 152798.i | 0.567263i | ||||||||
\(520\) | 62658.1 | + | 131345.i | 0.231724 | + | 0.485743i | ||||
\(521\) | −181842. | −0.669915 | −0.334957 | − | 0.942233i | \(-0.608722\pi\) | ||||
−0.334957 | + | 0.942233i | \(0.608722\pi\) | |||||||
\(522\) | −51981.1 | − | 347765.i | −0.190768 | − | 1.27628i | ||||
\(523\) | − | 479579.i | − | 1.75330i | −0.481128 | − | 0.876651i | \(-0.659773\pi\) | ||
0.481128 | − | 0.876651i | \(-0.340227\pi\) | |||||||
\(524\) | −113775. | − | 372087.i | −0.414366 | − | 1.35513i | ||||
\(525\) | −18026.1 | −0.0654009 | ||||||||
\(526\) | −43482.2 | + | 6499.37i | −0.157159 | + | 0.0234909i | ||||
\(527\) | 62533.6i | 0.225160i | ||||||||
\(528\) | 182254. | − | 122953.i | 0.653745 | − | 0.441034i | ||||
\(529\) | −188126. | −0.672262 | ||||||||
\(530\) | 27749.7 | + | 185652.i | 0.0987885 | + | 0.660917i | ||||
\(531\) | 18827.6i | 0.0667738i | ||||||||
\(532\) | 11364.1 | − | 3474.86i | 0.0401525 | − | 0.0122776i | ||||
\(533\) | 155349. | 0.546833 | ||||||||
\(534\) | −152860. | + | 22848.3i | −0.536058 | + | 0.0801256i | ||||
\(535\) | 111447.i | 0.389368i | ||||||||
\(536\) | 263544. | − | 125724.i | 0.917327 | − | 0.437611i | ||||
\(537\) | −116612. | −0.404386 | ||||||||
\(538\) | −73239.9 | − | 489992.i | −0.253037 | − | 1.69287i | ||||
\(539\) | − | 449424.i | − | 1.54696i | ||||||
\(540\) | −38694.0 | − | 126544.i | −0.132696 | − | 0.433964i | ||||
\(541\) | −90387.3 | −0.308825 | −0.154413 | − | 0.988006i | \(-0.549349\pi\) | ||||
−0.154413 | + | 0.988006i | \(0.549349\pi\) | |||||||
\(542\) | −152139. | + | 22740.5i | −0.517895 | + | 0.0774107i | ||||
\(543\) | − | 108181.i | − | 0.366902i | ||||||
\(544\) | −57628.6 | − | 62877.8i | −0.194733 | − | 0.212471i | ||||
\(545\) | −35461.0 | −0.119387 | ||||||||
\(546\) | −4080.46 | − | 27299.2i | −0.0136875 | − | 0.0915725i | ||||
\(547\) | 106106.i | 0.354622i | 0.984155 | + | 0.177311i | \(0.0567398\pi\) | ||||
−0.984155 | + | 0.177311i | \(0.943260\pi\) | |||||||
\(548\) | −374760. | + | 114592.i | −1.24793 | + | 0.381587i | ||||
\(549\) | −434912. | −1.44297 | ||||||||
\(550\) | 347301. | − | 51911.7i | 1.14810 | − | 0.171609i | ||||
\(551\) | − | 118695.i | − | 0.390957i | ||||||
\(552\) | 83589.6 | + | 175222.i | 0.274331 | + | 0.575056i | ||||
\(553\) | −61839.7 | −0.202217 | ||||||||
\(554\) | 37522.7 | + | 251035.i | 0.122257 | + | 0.817929i | ||||
\(555\) | 25423.2i | 0.0825362i | ||||||||
\(556\) | −143049. | − | 467826.i | −0.462740 | − | 1.51333i | ||||
\(557\) | −566621. | −1.82634 | −0.913171 | − | 0.407576i | \(-0.866374\pi\) | ||||
−0.913171 | + | 0.407576i | \(0.866374\pi\) | |||||||
\(558\) | 182176. | − | 27230.2i | 0.585090 | − | 0.0874544i | ||||
\(559\) | 161198.i | 0.515863i | ||||||||
\(560\) | −16824.3 | − | 24938.6i | −0.0536489 | − | 0.0795237i | ||||
\(561\) | 71530.7 | 0.227283 | ||||||||
\(562\) | 29043.7 | + | 194309.i | 0.0919560 | + | 0.615206i | ||||
\(563\) | − | 568120.i | − | 1.79235i | −0.443698 | − | 0.896176i | \(-0.646334\pi\) | ||
0.443698 | − | 0.896176i | \(-0.353666\pi\) | |||||||
\(564\) | 143619. | − | 43915.1i | 0.451495 | − | 0.138056i | ||||
\(565\) | 81134.0 | 0.254159 | ||||||||
\(566\) | 281496. | − | 42075.8i | 0.878699 | − | 0.131341i | ||||
\(567\) | − | 19456.3i | − | 0.0605192i | ||||||
\(568\) | −8614.86 | + | 4109.72i | −0.0267025 | + | 0.0127384i | ||||
\(569\) | −86245.2 | −0.266386 | −0.133193 | − | 0.991090i | \(-0.542523\pi\) | ||||
−0.133193 | + | 0.991090i | \(0.542523\pi\) | |||||||
\(570\) | −2845.54 | − | 19037.3i | −0.00875820 | − | 0.0585943i | ||||
\(571\) | − | 75126.1i | − | 0.230419i | −0.993341 | − | 0.115210i | \(-0.963246\pi\) | ||
0.993341 | − | 0.115210i | \(-0.0367540\pi\) | |||||||
\(572\) | 157233. | + | 514211.i | 0.480564 | + | 1.57162i | ||||
\(573\) | 92778.2 | 0.282577 | ||||||||
\(574\) | −31761.2 | + | 4747.40i | −0.0963990 | + | 0.0144089i | ||||
\(575\) | 310092.i | 0.937898i | ||||||||
\(576\) | −158084. | + | 195267.i | −0.476479 | + | 0.588550i | ||||
\(577\) | 489075. | 1.46901 | 0.734504 | − | 0.678604i | \(-0.237415\pi\) | ||||
0.734504 | + | 0.678604i | \(0.237415\pi\) | |||||||
\(578\) | 45285.1 | + | 302968.i | 0.135550 | + | 0.906861i | ||||
\(579\) | 246419.i | 0.735050i | ||||||||
\(580\) | −287343. | + | 87862.4i | −0.854171 | + | 0.261184i | ||||
\(581\) | 70327.9 | 0.208341 | ||||||||
\(582\) | −38154.3 | + | 5703.00i | −0.112641 | + | 0.0168367i | ||||
\(583\) | 693601.i | 2.04067i | ||||||||
\(584\) | −77970.6 | − | 163443.i | −0.228615 | − | 0.479227i | ||||
\(585\) | 139470. | 0.407538 | ||||||||
\(586\) | −1667.34 | − | 11154.9i | −0.00485544 | − | 0.0324840i | ||||
\(587\) | 562634.i | 1.63286i | 0.577442 | + | 0.816432i | \(0.304051\pi\) | ||||
−0.577442 | + | 0.816432i | \(0.695949\pi\) | |||||||
\(588\) | −48143.0 | − | 157446.i | −0.139245 | − | 0.455383i | ||||
\(589\) | 62178.0 | 0.179228 | ||||||||
\(590\) | 15911.9 | − | 2378.38i | 0.0457108 | − | 0.00683247i | ||||
\(591\) | − | 222648.i | − | 0.637447i | ||||||
\(592\) | 92855.6 | − | 62642.9i | 0.264951 | − | 0.178743i | ||||
\(593\) | −354885. | −1.00920 | −0.504602 | − | 0.863352i | \(-0.668361\pi\) | ||||
−0.504602 | + | 0.863352i | \(0.668361\pi\) | |||||||
\(594\) | −72281.1 | − | 483577.i | −0.204857 | − | 1.37054i | ||||
\(595\) | − | 9787.89i | − | 0.0276475i | ||||||
\(596\) | −651335. | + | 199162.i | −1.83363 | + | 0.560679i | ||||
\(597\) | 21922.6 | 0.0615097 | ||||||||
\(598\) | −469612. | + | 70193.7i | −1.31322 | + | 0.196289i | ||||
\(599\) | 214683.i | 0.598333i | 0.954201 | + | 0.299167i | \(0.0967087\pi\) | ||||
−0.954201 | + | 0.299167i | \(0.903291\pi\) | |||||||
\(600\) | 116108. | − | 55389.6i | 0.322523 | − | 0.153860i | ||||
\(601\) | 79153.3 | 0.219139 | 0.109570 | − | 0.993979i | \(-0.465053\pi\) | ||||
0.109570 | + | 0.993979i | \(0.465053\pi\) | |||||||
\(602\) | −4926.12 | − | 32956.8i | −0.0135929 | − | 0.0909395i | ||||
\(603\) | − | 279847.i | − | 0.769637i | ||||||
\(604\) | 151886. | + | 496723.i | 0.416335 | + | 1.36157i | ||||
\(605\) | −299636. | −0.818622 | ||||||||
\(606\) | −79234.8 | + | 11843.4i | −0.215760 | + | 0.0322500i | ||||
\(607\) | 483102.i | 1.31118i | 0.755118 | + | 0.655589i | \(0.227580\pi\) | ||||
−0.755118 | + | 0.655589i | \(0.772420\pi\) | |||||||
\(608\) | −62520.3 | + | 57301.0i | −0.169127 | + | 0.155008i | ||||
\(609\) | 56992.9 | 0.153669 | ||||||||
\(610\) | 54939.9 | + | 367560.i | 0.147648 | + | 0.987800i | ||||
\(611\) | 367320.i | 0.983926i | ||||||||
\(612\) | −78170.0 | + | 23902.5i | −0.208707 | + | 0.0638175i | ||||
\(613\) | 199537. | 0.531010 | 0.265505 | − | 0.964109i | \(-0.414461\pi\) | ||||
0.265505 | + | 0.964109i | \(0.414461\pi\) | |||||||
\(614\) | 637126. | − | 95232.3i | 1.69001 | − | 0.252608i | ||||
\(615\) | 52017.9i | 0.137532i | ||||||||
\(616\) | −47860.3 | − | 100325.i | −0.126129 | − | 0.264393i | ||||
\(617\) | 121881. | 0.320159 | 0.160079 | − | 0.987104i | \(-0.448825\pi\) | ||||
0.160079 | + | 0.987104i | \(0.448825\pi\) | |||||||
\(618\) | −6452.80 | − | 43170.7i | −0.0168955 | − | 0.113035i | ||||
\(619\) | 133551.i | 0.348550i | 0.984697 | + | 0.174275i | \(0.0557582\pi\) | ||||
−0.984697 | + | 0.174275i | \(0.944242\pi\) | |||||||
\(620\) | −46026.5 | − | 150524.i | −0.119736 | − | 0.391581i | ||||
\(621\) | 431768. | 1.11961 | ||||||||
\(622\) | −547673. | + | 81861.7i | −1.41560 | + | 0.211592i | ||||
\(623\) | 78145.2i | 0.201338i | ||||||||
\(624\) | 110166. | + | 163299.i | 0.282930 | + | 0.419387i | ||||
\(625\) | 98164.8 | 0.251302 | ||||||||
\(626\) | −15749.1 | − | 105365.i | −0.0401889 | − | 0.268873i | ||||
\(627\) | − | 71124.0i | − | 0.180918i | ||||||
\(628\) | −2986.42 | + | 913.172i | −0.00757236 | + | 0.00231544i | ||||
\(629\) | 36443.9 | 0.0921135 | ||||||||
\(630\) | −28514.6 | + | 4262.13i | −0.0718432 | + | 0.0107385i | ||||
\(631\) | − | 559153.i | − | 1.40434i | −0.712010 | − | 0.702169i | \(-0.752215\pi\) | ||
0.712010 | − | 0.702169i | \(-0.247785\pi\) | |||||||
\(632\) | 398316. | − | 190017.i | 0.997227 | − | 0.475728i | ||||
\(633\) | 300669. | 0.750380 | ||||||||
\(634\) | 26781.0 | + | 179171.i | 0.0666267 | + | 0.445748i | ||||
\(635\) | − | 36646.6i | − | 0.0908838i | ||||||
\(636\) | 74299.6 | + | 242988.i | 0.183685 | + | 0.600718i | ||||
\(637\) | 402684. | 0.992398 | ||||||||
\(638\) | −1.09806e6 | + | 164128.i | −2.69764 | + | 0.403220i | ||||
\(639\) | 9147.77i | 0.0224034i | ||||||||
\(640\) | 184997. | + | 108936.i | 0.451653 | + | 0.265957i | ||||
\(641\) | 523535. | 1.27418 | 0.637089 | − | 0.770791i | \(-0.280139\pi\) | ||||
0.637089 | + | 0.770791i | \(0.280139\pi\) | |||||||
\(642\) | 22301.1 | + | 149199.i | 0.0541073 | + | 0.361990i | ||||
\(643\) | − | 508744.i | − | 1.23049i | −0.788337 | − | 0.615244i | \(-0.789057\pi\) | ||
0.788337 | − | 0.615244i | \(-0.210943\pi\) | |||||||
\(644\) | 93867.0 | − | 28702.2i | 0.226330 | − | 0.0692060i | ||||
\(645\) | −53976.2 | −0.129743 | ||||||||
\(646\) | −27289.7 | + | 4079.04i | −0.0653934 | + | 0.00977447i | ||||
\(647\) | − | 303404.i | − | 0.724792i | −0.932024 | − | 0.362396i | \(-0.881959\pi\) | ||
0.932024 | − | 0.362396i | \(-0.118041\pi\) | |||||||
\(648\) | 59784.0 | + | 125320.i | 0.142375 | + | 0.298449i | ||||
\(649\) | 59447.5 | 0.141138 | ||||||||
\(650\) | 46512.9 | + | 311182.i | 0.110090 | + | 0.736526i | ||||
\(651\) | 29855.6i | 0.0704472i | ||||||||
\(652\) | −99776.8 | − | 326308.i | −0.234711 | − | 0.767595i | ||||
\(653\) | 479003. | 1.12334 | 0.561671 | − | 0.827361i | \(-0.310159\pi\) | ||||
0.561671 | + | 0.827361i | \(0.310159\pi\) | |||||||
\(654\) | −47473.3 | + | 7095.92i | −0.110993 | + | 0.0165903i | ||||
\(655\) | 318656.i | 0.742745i | ||||||||
\(656\) | 189990. | − | 128172.i | 0.441492 | − | 0.297842i | ||||
\(657\) | −173554. | −0.402071 | ||||||||
\(658\) | −11225.1 | − | 75098.6i | −0.0259262 | − | 0.173452i | ||||
\(659\) | − | 28254.6i | − | 0.0650606i | −0.999471 | − | 0.0325303i | \(-0.989643\pi\) | ||
0.999471 | − | 0.0325303i | \(-0.0103565\pi\) | |||||||
\(660\) | −172181. | + | 52648.6i | −0.395273 | + | 0.120865i | ||||
\(661\) | 546615. | 1.25106 | 0.625530 | − | 0.780200i | \(-0.284883\pi\) | ||||
0.625530 | + | 0.780200i | \(0.284883\pi\) | |||||||
\(662\) | 4496.26 | − | 672.065i | 0.0102597 | − | 0.00153354i | ||||
\(663\) | 64091.5i | 0.145805i | ||||||||
\(664\) | −452990. | + | 216099.i | −1.02743 | + | 0.490136i | ||||
\(665\) | −9732.24 | −0.0220074 | ||||||||
\(666\) | −15869.4 | − | 106170.i | −0.0357778 | − | 0.239361i | ||||
\(667\) | − | 980414.i | − | 2.20373i | ||||||
\(668\) | −98222.5 | − | 321225.i | −0.220119 | − | 0.719873i | ||||
\(669\) | −159122. | −0.355531 | ||||||||
\(670\) | −236509. | + | 35351.5i | −0.526864 | + | 0.0787513i | ||||
\(671\) | 1.37322e6i | 3.04996i | ||||||||
\(672\) | −27513.8 | − | 30019.9i | −0.0609273 | − | 0.0664769i | ||||
\(673\) | 146970. | 0.324489 | 0.162244 | − | 0.986751i | \(-0.448127\pi\) | ||||
0.162244 | + | 0.986751i | \(0.448127\pi\) | |||||||
\(674\) | −74719.3 | − | 499889.i | −0.164480 | − | 1.10041i | ||||
\(675\) | − | 286105.i | − | 0.627941i | ||||||
\(676\) | −23729.9 | + | 7256.02i | −0.0519281 | + | 0.0158783i | ||||
\(677\) | −636186. | −1.38806 | −0.694028 | − | 0.719948i | \(-0.744166\pi\) | ||||
−0.694028 | + | 0.719948i | \(0.744166\pi\) | |||||||
\(678\) | 108618. | − | 16235.3i | 0.236288 | − | 0.0353184i | ||||
\(679\) | 19505.2i | 0.0423070i | ||||||||
\(680\) | 30075.6 | + | 63045.0i | 0.0650425 | + | 0.136343i | ||||
\(681\) | −354134. | −0.763613 | ||||||||
\(682\) | −85978.2 | − | 575214.i | −0.184850 | − | 1.23669i | ||||
\(683\) | − | 471150.i | − | 1.00999i | −0.863122 | − | 0.504996i | \(-0.831494\pi\) | ||
0.863122 | − | 0.504996i | \(-0.168506\pi\) | |||||||
\(684\) | 23766.5 | + | 77725.6i | 0.0507989 | + | 0.166131i | ||||
\(685\) | 320945. | 0.683989 | ||||||||
\(686\) | −167511. | + | 25038.2i | −0.355955 | + | 0.0532052i | ||||
\(687\) | − | 249030.i | − | 0.527641i | ||||||
\(688\) | 132997. | + | 197142.i | 0.280974 | + | 0.416488i | ||||
\(689\) | −621467. | −1.30912 | ||||||||
\(690\) | −23504.0 | − | 157247.i | −0.0493678 | − | 0.330282i | ||||
\(691\) | 727652.i | 1.52394i | 0.647613 | + | 0.761970i | \(0.275767\pi\) | ||||
−0.647613 | + | 0.761970i | \(0.724233\pi\) | |||||||
\(692\) | −527236. | + | 161216.i | −1.10101 | + | 0.336663i | ||||
\(693\) | −106531. | −0.221826 | ||||||||
\(694\) | 649988. | − | 97154.8i | 1.34954 | − | 0.201718i | ||||
\(695\) | 400646.i | 0.829453i | ||||||||
\(696\) | −367098. | + | 175124.i | −0.757816 | + | 0.361516i | ||||
\(697\) | 74567.0 | 0.153490 | ||||||||
\(698\) | 33907.6 | + | 226849.i | 0.0695962 | + | 0.465614i | ||||
\(699\) | − | 317534.i | − | 0.649883i | ||||||
\(700\) | −19019.1 | − | 62199.8i | −0.0388146 | − | 0.126938i | ||||
\(701\) | 610269. | 1.24190 | 0.620948 | − | 0.783852i | \(-0.286748\pi\) | ||||
0.620948 | + | 0.783852i | \(0.286748\pi\) | |||||||
\(702\) | 433285. | − | 64763.9i | 0.879224 | − | 0.131419i | ||||
\(703\) | − | 36236.7i | − | 0.0733226i | ||||||
\(704\) | 616547. | + | 499146.i | 1.24400 | + | 1.00712i | ||||
\(705\) | −122995. | −0.247463 | ||||||||
\(706\) | −135508. | − | 906576.i | −0.271866 | − | 1.81884i | ||||
\(707\) | 40506.4i | 0.0810373i | ||||||||
\(708\) | 20826.1 | − | 6368.11i | 0.0415472 | − | 0.0127041i | ||||
\(709\) | 31766.6 | 0.0631943 | 0.0315972 | − | 0.999501i | \(-0.489941\pi\) | ||||
0.0315972 | + | 0.999501i | \(0.489941\pi\) | |||||||
\(710\) | 7731.12 | − | 1155.58i | 0.0153365 | − | 0.00229237i | ||||
\(711\) | − | 422956.i | − | 0.836674i | ||||||
\(712\) | −240120. | − | 503342.i | −0.473661 | − | 0.992896i | ||||
\(713\) | 513587. | 1.01026 | ||||||||
\(714\) | −1958.61 | − | 13103.5i | −0.00384194 | − | 0.0257035i | ||||
\(715\) | − | 440370.i | − | 0.861402i | ||||||
\(716\) | −123036. | − | 402375.i | −0.239998 | − | 0.784883i | ||||
\(717\) | −50372.9 | −0.0979848 | ||||||||
\(718\) | −555926. | + | 83095.2i | −1.07837 | + | 0.161186i | ||||
\(719\) | − | 63172.8i | − | 0.122200i | −0.998132 | − | 0.0611001i | \(-0.980539\pi\) | ||
0.998132 | − | 0.0611001i | \(-0.0194609\pi\) | |||||||
\(720\) | 170569. | − | 115071.i | 0.329030 | − | 0.221973i | ||||
\(721\) | −22069.7 | −0.0424547 | ||||||||
\(722\) | 4055.85 | + | 27134.6i | 0.00778050 | + | 0.0520533i | ||||
\(723\) | − | 186958.i | − | 0.357658i | ||||||
\(724\) | 373281. | − | 114140.i | 0.712130 | − | 0.217752i | ||||
\(725\) | −649659. | −1.23597 | ||||||||
\(726\) | −401137. | + | 59958.6i | −0.761061 | + | 0.113757i | ||||
\(727\) | 259499.i | 0.490984i | 0.969399 | + | 0.245492i | \(0.0789496\pi\) | ||||
−0.969399 | + | 0.245492i | \(0.921050\pi\) | |||||||
\(728\) | 89891.6 | − | 42882.8i | 0.169612 | − | 0.0809134i | ||||
\(729\) | −93628.2 | −0.176178 | ||||||||
\(730\) | 21924.0 | + | 146677.i | 0.0411410 | + | 0.275242i | ||||
\(731\) | 77374.2i | 0.144798i | ||||||||
\(732\) | 147101. | + | 481077.i | 0.274533 | + | 0.897826i | ||||
\(733\) | −176670. | −0.328817 | −0.164409 | − | 0.986392i | \(-0.552572\pi\) | ||||
−0.164409 | + | 0.986392i | \(0.552572\pi\) | |||||||
\(734\) | 717261. | − | 107210.i | 1.33133 | − | 0.198996i | ||||
\(735\) | 134837.i | 0.249594i | ||||||||
\(736\) | −516414. | + | 473303.i | −0.953328 | + | 0.873743i | ||||
\(737\) | −883607. | −1.62676 | ||||||||
\(738\) | −32470.1 | − | 217232.i | −0.0596171 | − | 0.398852i | ||||
\(739\) | − | 309358.i | − | 0.566465i | −0.959051 | − | 0.283232i | \(-0.908593\pi\) | ||
0.959051 | − | 0.283232i | \(-0.0914068\pi\) | |||||||
\(740\) | −87723.7 | + | 26823.7i | −0.160197 | + | 0.0489841i | ||||
\(741\) | 63727.1 | 0.116061 | ||||||||
\(742\) | 127059. | − | 18991.7i | 0.230780 | − | 0.0344950i | ||||
\(743\) | − | 173374.i | − | 0.314055i | −0.987594 | − | 0.157028i | \(-0.949809\pi\) | ||
0.987594 | − | 0.157028i | \(-0.0501911\pi\) | |||||||
\(744\) | −91738.4 | − | 192303.i | −0.165732 | − | 0.347409i | ||||
\(745\) | 557804. | 1.00501 | ||||||||
\(746\) | −107490. | − | 719132.i | −0.193148 | − | 1.29220i | ||||
\(747\) | 481012.i | 0.862014i | ||||||||
\(748\) | 75471.1 | + | 246819.i | 0.134889 | + | 0.441139i | ||||
\(749\) | 76273.7 | 0.135960 | ||||||||
\(750\) | −247864. | + | 37048.7i | −0.440647 | + | 0.0658643i | ||||
\(751\) | − | 357686.i | − | 0.634194i | −0.948393 | − | 0.317097i | \(-0.897292\pi\) | ||
0.948393 | − | 0.317097i | \(-0.102708\pi\) | |||||||
\(752\) | 303061. | + | 449227.i | 0.535913 | + | 0.794384i | ||||
\(753\) | 33474.6 | 0.0590372 | ||||||||
\(754\) | −147059. | − | 983859.i | −0.258672 | − | 1.73057i | ||||
\(755\) | − | 425394.i | − | 0.746273i | ||||||
\(756\) | −86606.0 | + | 26482.0i | −0.151532 | + | 0.0463347i | ||||
\(757\) | 423414. | 0.738880 | 0.369440 | − | 0.929255i | \(-0.379550\pi\) | ||||
0.369440 | + | 0.929255i | \(0.379550\pi\) | |||||||
\(758\) | 598515. | − | 89461.1i | 1.04169 | − | 0.155703i | ||||
\(759\) | − | 587481.i | − | 1.01979i | ||||||
\(760\) | 62686.5 | − | 29904.6i | 0.108529 | − | 0.0517739i | ||||
\(761\) | 660959. | 1.14131 | 0.570657 | − | 0.821189i | \(-0.306689\pi\) | ||||
0.570657 | + | 0.821189i | \(0.306689\pi\) | |||||||
\(762\) | −7333.17 | − | 49060.6i | −0.0126294 | − | 0.0844934i | ||||
\(763\) | 24269.3i | 0.0416877i | ||||||||
\(764\) | 97889.0 | + | 320134.i | 0.167706 | + | 0.548460i | ||||
\(765\) | 66944.9 | 0.114392 | ||||||||
\(766\) | 596895. | − | 89218.9i | 1.01728 | − | 0.152055i | ||||
\(767\) | 53265.0i | 0.0905422i | ||||||||
\(768\) | 269463. | + | 108819.i | 0.456853 | + | 0.184494i | ||||
\(769\) | −557564. | −0.942849 | −0.471424 | − | 0.881906i | \(-0.656260\pi\) | ||||
−0.471424 | + | 0.881906i | \(0.656260\pi\) | |||||||
\(770\) | 13457.5 | + | 90033.8i | 0.0226978 | + | 0.151853i | ||||
\(771\) | − | 110121.i | − | 0.185252i | ||||||
\(772\) | −850277. | + | 259993.i | −1.42668 | + | 0.436242i | ||||
\(773\) | 159973. | 0.267725 | 0.133862 | − | 0.991000i | \(-0.457262\pi\) | ||||
0.133862 | + | 0.991000i | \(0.457262\pi\) | |||||||
\(774\) | 225410. | − | 33692.5i | 0.376263 | − | 0.0562408i | ||||
\(775\) | − | 340322.i | − | 0.566613i | ||||||
\(776\) | −59934.5 | − | 125636.i | −0.0995299 | − | 0.208636i | ||||
\(777\) | 17399.5 | 0.0288201 | ||||||||
\(778\) | 844.457 | + | 5649.61i | 0.00139514 | + | 0.00933381i | ||||
\(779\) | − | 74143.1i | − | 0.122179i | ||||||
\(780\) | −47173.2 | − | 154274.i | −0.0775364 | − | 0.253573i | ||||
\(781\) | 28883.7 | 0.0473534 | ||||||||
\(782\) | −225412. | + | 33692.7i | −0.368606 | + | 0.0550963i | ||||
\(783\) | 904575.i | 1.47544i | ||||||||
\(784\) | 492477. | − | 332238.i | 0.801224 | − | 0.540527i | ||||
\(785\) | 2557.57 | 0.00415038 | ||||||||
\(786\) | 63764.6 | + | 426600.i | 0.103213 | + | 0.690519i | ||||
\(787\) | 536068.i | 0.865506i | 0.901512 | + | 0.432753i | \(0.142458\pi\) | ||||
−0.901512 | + | 0.432753i | \(0.857542\pi\) | |||||||
\(788\) | 768254. | − | 234913.i | 1.23724 | − | 0.378316i | ||||
\(789\) | 48738.8 | 0.0782926 | ||||||||
\(790\) | −357456. | + | 53429.6i | −0.572755 | + | 0.0856106i | ||||
\(791\) | − | 55527.7i | − | 0.0887476i | ||||||
\(792\) | 686182. | − | 327343.i | 1.09393 | − | 0.521859i | ||||
\(793\) | −1.23040e6 | −1.95660 | ||||||||
\(794\) | 123450. | + | 825909.i | 0.195817 | + | 1.31006i | ||||
\(795\) | − | 208095.i | − | 0.329251i | ||||||
\(796\) | 23130.3 | + | 75644.7i | 0.0365052 | + | 0.119386i | ||||
\(797\) | 169520. | 0.266873 | 0.133437 | − | 0.991057i | \(-0.457399\pi\) | ||||
0.133437 | + | 0.991057i | \(0.457399\pi\) | |||||||
\(798\) | −13029.0 | + | 1947.47i | −0.0204600 | + | 0.00305819i | ||||
\(799\) | 176312.i | 0.276178i | ||||||||
\(800\) | 313628. | + | 342195.i | 0.490044 | + | 0.534680i | ||||
\(801\) | −534479. | −0.833039 | ||||||||
\(802\) | −140291. | − | 938581.i | −0.218113 | − | 1.45923i | ||||
\(803\) | 547989.i | 0.849848i | ||||||||
\(804\) | −309552. | + | 94653.3i | −0.478874 | + | 0.146428i | ||||
\(805\) | −80387.8 | −0.124050 | ||||||||
\(806\) | 515392. | − | 77036.5i | 0.793355 | − | 0.118584i | ||||
\(807\) | 549226.i | 0.843343i | ||||||||
\(808\) | −124466. | − | 260906.i | −0.190645 | − | 0.399634i | ||||
\(809\) | −951147. | −1.45328 | −0.726642 | − | 0.687016i | \(-0.758920\pi\) | ||||
−0.726642 | + | 0.687016i | \(0.758920\pi\) | |||||||
\(810\) | −16810.3 | − | 112464.i | −0.0256215 | − | 0.171414i | ||||
\(811\) | 418188.i | 0.635814i | 0.948122 | + | 0.317907i | \(0.102980\pi\) | ||||
−0.948122 | + | 0.317907i | \(0.897020\pi\) | |||||||
\(812\) | 60132.5 | + | 196656.i | 0.0912005 | + | 0.298260i | ||||
\(813\) | 170531. | 0.258002 | ||||||||
\(814\) | −335228. | + | 50107.2i | −0.505932 | + | 0.0756225i | ||||
\(815\) | 279450.i | 0.420716i | ||||||||
\(816\) | 52879.3 | + | 78383.0i | 0.0794155 | + | 0.117718i | ||||
\(817\) | 76934.2 | 0.115259 | ||||||||
\(818\) | 186842. | + | 1.25001e6i | 0.279233 | + | 1.86813i | ||||
\(819\) | − | 95452.2i | − | 0.142304i | ||||||
\(820\) | −179490. | + | 54883.4i | −0.266939 | + | 0.0816232i | ||||
\(821\) | −754344. | −1.11914 | −0.559568 | − | 0.828784i | \(-0.689033\pi\) | ||||
−0.559568 | + | 0.828784i | \(0.689033\pi\) | |||||||
\(822\) | 429664. | − | 64222.6i | 0.635894 | − | 0.0950483i | ||||
\(823\) | 520834.i | 0.768953i | 0.923135 | + | 0.384477i | \(0.125618\pi\) | ||||
−0.923135 | + | 0.384477i | \(0.874382\pi\) | |||||||
\(824\) | 142154. | − | 67814.4i | 0.209365 | − | 0.0998774i | ||||
\(825\) | −389286. | −0.571954 | ||||||||
\(826\) | −1627.75 | − | 10890.0i | −0.00238577 | − | 0.0159613i | ||||
\(827\) | − | 633719.i | − | 0.926585i | −0.886205 | − | 0.463293i | \(-0.846668\pi\) | ||
0.886205 | − | 0.463293i | \(-0.153332\pi\) | |||||||
\(828\) | 196310. | + | 642009.i | 0.286341 | + | 0.936441i | ||||
\(829\) | 68381.2 | 0.0995011 | 0.0497505 | − | 0.998762i | \(-0.484157\pi\) | ||||
0.0497505 | + | 0.998762i | \(0.484157\pi\) | |||||||
\(830\) | 406521. | − | 60763.4i | 0.590102 | − | 0.0882035i | ||||
\(831\) | − | 281383.i | − | 0.407470i | ||||||
\(832\) | −447235. | + | 552427.i | −0.646084 | + | 0.798046i | ||||
\(833\) | 193287. | 0.278556 | ||||||||
\(834\) | 80171.3 | + | 536364.i | 0.115262 | + | 0.771130i | ||||
\(835\) | 275097.i | 0.394560i | ||||||||
\(836\) | 245416. | − | 75042.0i | 0.351148 | − | 0.107372i | ||||
\(837\) | −473859. | −0.676391 | ||||||||
\(838\) | −923062. | + | 137972.i | −1.31445 | + | 0.196473i | ||||
\(839\) | 57238.5i | 0.0813139i | 0.999173 | + | 0.0406569i | \(0.0129451\pi\) | ||||
−0.999173 | + | 0.0406569i | \(0.987055\pi\) | |||||||
\(840\) | 14359.1 | + | 30099.7i | 0.0203502 | + | 0.0426584i | ||||
\(841\) | 1.34673e6 | 1.90410 | ||||||||
\(842\) | 96315.7 | + | 644373.i | 0.135854 | + | 0.908895i | ||||
\(843\) | − | 217799.i | − | 0.306479i | ||||||
\(844\) | 317232. | + | 1.03747e6i | 0.445341 | + | 1.45643i | ||||
\(845\) | 20322.3 | 0.0284616 | ||||||||
\(846\) | 513642. | − | 76774.9i | 0.717661 | − | 0.107270i | ||||
\(847\) | 205069.i | 0.285847i | ||||||||
\(848\) | −760045. | + | 512747.i | −1.05693 | + | 0.713036i | ||||
\(849\) | −315526. | −0.437744 | ||||||||
\(850\) | 22326.0 | + | 149366.i | 0.0309011 | + | 0.206735i | ||||
\(851\) | − | 299313.i | − | 0.413301i | ||||||
\(852\) | 10118.8 | − | 3094.07i | 0.0139396 | − | 0.00426237i | ||||
\(853\) | −158388. | −0.217684 | −0.108842 | − | 0.994059i | \(-0.534714\pi\) | ||||
−0.108842 | + | 0.994059i | \(0.534714\pi\) | |||||||
\(854\) | 251556. | − | 37600.5i | 0.344921 | − | 0.0515559i | ||||
\(855\) | − | 66564.3i | − | 0.0910561i | ||||||
\(856\) | −491288. | + | 234369.i | −0.670484 | + | 0.319855i | ||||
\(857\) | 958773. | 1.30543 | 0.652716 | − | 0.757603i | \(-0.273630\pi\) | ||||
0.652716 | + | 0.757603i | \(0.273630\pi\) | |||||||
\(858\) | −88120.3 | − | 589545.i | −0.119702 | − | 0.800833i | ||||
\(859\) | − | 1.28765e6i | − | 1.74507i | −0.488555 | − | 0.872533i | \(-0.662476\pi\) | ||
0.488555 | − | 0.872533i | \(-0.337524\pi\) | |||||||
\(860\) | −56949.6 | − | 186247.i | −0.0770005 | − | 0.251821i | ||||
\(861\) | 35600.8 | 0.0480234 | ||||||||
\(862\) | 1.39711e6 | − | 208828.i | 1.88025 | − | 0.281044i | ||||
\(863\) | 1.04487e6i | 1.40295i | 0.712696 | + | 0.701473i | \(0.247474\pi\) | ||||
−0.712696 | + | 0.701473i | \(0.752526\pi\) | |||||||
\(864\) | 476467. | − | 436691.i | 0.638272 | − | 0.584988i | ||||
\(865\) | 451526. | 0.603462 | ||||||||
\(866\) | −63571.0 | − | 425304.i | −0.0847663 | − | 0.567106i | ||||
\(867\) | − | 339593.i | − | 0.451774i | ||||||
\(868\) | −103018. | + | 31500.2i | −0.136733 | + | 0.0418094i | ||||
\(869\) | −1.33547e6 | −1.76846 | ||||||||
\(870\) | 329440. | − | 49242.0i | 0.435249 | − | 0.0650575i | ||||
\(871\) | − | 791712.i | − | 1.04359i | ||||||
\(872\) | −74573.1 | − | 156321.i | −0.0980730 | − | 0.205582i | ||||
\(873\) | −133407. | −0.175046 | ||||||||
\(874\) | 33501.1 | + | 224130.i | 0.0438568 | + | 0.293412i | ||||
\(875\) | 126713.i | 0.165503i | ||||||||
\(876\) | 58701.5 | + | 191976.i | 0.0764964 | + | 0.250172i | ||||
\(877\) | −1.30314e6 | −1.69431 | −0.847156 | − | 0.531344i | \(-0.821687\pi\) | ||||
−0.847156 | + | 0.531344i | \(0.821687\pi\) | |||||||
\(878\) | −1.44681e6 | + | 216258.i | −1.87682 | + | 0.280532i | ||||
\(879\) | 12503.4i | 0.0161826i | ||||||||
\(880\) | −363331. | − | 538567.i | −0.469178 | − | 0.695463i | ||||
\(881\) | −1.09260e6 | −1.40769 | −0.703846 | − | 0.710353i | \(-0.748535\pi\) | ||||
−0.703846 | + | 0.710353i | \(0.748535\pi\) | |||||||
\(882\) | −84166.5 | − | 563093.i | −0.108194 | − | 0.723841i | ||||
\(883\) | 941564.i | 1.20761i | 0.797130 | + | 0.603807i | \(0.206350\pi\) | ||||
−0.797130 | + | 0.603807i | \(0.793650\pi\) | |||||||
\(884\) | −221150. | + | 67622.1i | −0.282997 | + | 0.0865335i | ||||
\(885\) | −17835.5 | −0.0227719 | ||||||||
\(886\) | 47193.0 | − | 7054.03i | 0.0601188 | − | 0.00898607i | ||||
\(887\) | − | 1.09323e6i | − | 1.38952i | −0.719242 | − | 0.694759i | \(-0.755511\pi\) | ||
0.719242 | − | 0.694759i | \(-0.244489\pi\) | |||||||
\(888\) | −112072. | + | 53464.1i | −0.142126 | + | 0.0678011i | ||||
\(889\) | −25080.7 | −0.0317349 | ||||||||
\(890\) | 67517.6 | + | 451708.i | 0.0852388 | + | 0.570267i | ||||
\(891\) | − | 420171.i | − | 0.529262i | ||||||
\(892\) | −167888. | − | 549055.i | −0.211003 | − | 0.690059i | ||||
\(893\) | 175310. | 0.219838 | ||||||||
\(894\) | 746759. | − | 111619.i | 0.934341 | − | 0.139658i | ||||
\(895\) | 344595.i | 0.430192i | ||||||||
\(896\) | 74555.3 | − | 126611.i | 0.0928672 | − | 0.157709i | ||||
\(897\) | 526383. | 0.654209 | ||||||||
\(898\) | 50773.4 | + | 339685.i | 0.0629627 | + | 0.421235i | ||||
\(899\) | 1.07599e6i | 1.33134i | ||||||||
\(900\) | 425419. | − | 130083.i | 0.525209 | − | 0.160596i | ||||
\(901\) | −298302. | −0.367457 | ||||||||
\(902\) | −685903. | + | 102523.i | −0.843043 | + | 0.126011i | ||||
\(903\) | 36941.0i | 0.0453036i | ||||||||
\(904\) | 170622. | + | 357660.i | 0.208784 | + | 0.437657i | ||||
\(905\) | −319678. | −0.390316 | ||||||||
\(906\) | −85123.5 | − | 569495.i | −0.103703 | − | 0.693799i | ||||
\(907\) | − | 543026.i | − | 0.660095i | −0.943964 | − | 0.330047i | \(-0.892935\pi\) | ||
0.943964 | − | 0.330047i | \(-0.107065\pi\) | |||||||
\(908\) | −373642. | − | 1.22195e6i | −0.453194 | − | 1.48211i | ||||
\(909\) | −277046. | −0.335293 | ||||||||
\(910\) | −80670.3 | + | 12057.9i | −0.0974161 | + | 0.0145610i | ||||
\(911\) | 1.63167e6i | 1.96606i | 0.183454 | + | 0.983028i | \(0.441272\pi\) | ||||
−0.183454 | + | 0.983028i | \(0.558728\pi\) | |||||||
\(912\) | 77937.3 | − | 52578.6i | 0.0937035 | − | 0.0632149i | ||||
\(913\) | 1.51878e6 | 1.82202 | ||||||||
\(914\) | 166229. | + | 1.11211e6i | 0.198983 | + | 1.33124i | ||||
\(915\) | − | 411995.i | − | 0.492095i | ||||||
\(916\) | 859287. | − | 262749.i | 1.02411 | − | 0.313148i | ||||
\(917\) | 218086. | 0.259352 | ||||||||
\(918\) | 207975. | − | 31086.4i | 0.246789 | − | 0.0368880i | ||||
\(919\) | − | 327137.i | − | 0.387346i | −0.981066 | − | 0.193673i | \(-0.937960\pi\) | ||
0.981066 | − | 0.193673i | \(-0.0620401\pi\) | |||||||
\(920\) | 517787. | − | 247011.i | 0.611753 | − | 0.291837i | ||||
\(921\) | −714148. | −0.841916 | ||||||||
\(922\) | 4165.52 | + | 27868.3i | 0.00490013 | + | 0.0327829i | ||||
\(923\) | 25879.8i | 0.0303779i | ||||||||
\(924\) | 36032.4 | + | 117840.i | 0.0422036 | + | 0.138022i | ||||
\(925\) | −198336. | −0.231802 | ||||||||
\(926\) | −855164. | + | 127823.i | −0.997304 | + | 0.149069i | ||||
\(927\) | − | 150947.i | − | 0.175657i | ||||||
\(928\) | −991593. | − | 1.08191e6i | −1.15143 | − | 1.25631i | ||||
\(929\) | −16017.8 | −0.0185598 | −0.00927988 | − | 0.999957i | \(-0.502954\pi\) | ||||
−0.00927988 | + | 0.999957i | \(0.502954\pi\) | |||||||
\(930\) | 25795.3 | + | 172576.i | 0.0298246 | + | 0.199533i | ||||
\(931\) | − | 192188.i | − | 0.221731i | ||||||
\(932\) | 1.09566e6 | − | 335026.i | 1.26137 | − | 0.385697i | ||||
\(933\) | 613881. | 0.705214 | ||||||||
\(934\) | −835485. | + | 124881.i | −0.957733 | + | 0.143154i | ||||
\(935\) | − | 211376.i | − | 0.241787i | ||||||
\(936\) | 293300. | + | 614819.i | 0.334780 | + | 0.701771i | ||||
\(937\) | 753326. | 0.858032 | 0.429016 | − | 0.903297i | \(-0.358860\pi\) | ||||
0.429016 | + | 0.903297i | \(0.358860\pi\) | |||||||
\(938\) | 24194.3 | + | 161866.i | 0.0274984 | + | 0.183971i | ||||
\(939\) | 118102.i | 0.133945i | ||||||||
\(940\) | −129771. | − | 424399.i | −0.146866 | − | 0.480307i | ||||
\(941\) | −433839. | −0.489947 | −0.244974 | − | 0.969530i | \(-0.578779\pi\) | ||||
−0.244974 | + | 0.969530i | \(0.578779\pi\) | |||||||
\(942\) | 3423.94 | − | 511.783i | 0.00385855 | − | 0.000576745i | ||||
\(943\) | − | 612418.i | − | 0.688691i | ||||||
\(944\) | 43946.7 | + | 65142.3i | 0.0493154 | + | 0.0731003i | ||||
\(945\) | 74169.5 | 0.0830542 | ||||||||
\(946\) | −106383. | − | 711725.i | −0.118875 | − | 0.795298i | ||||
\(947\) | 495248.i | 0.552233i | 0.961124 | + | 0.276117i | \(0.0890476\pi\) | ||||
−0.961124 | + | 0.276117i | \(0.910952\pi\) | |||||||
\(948\) | −467852. | + | 143057.i | −0.520585 | + | 0.159182i | ||||
\(949\) | −490999. | −0.545190 | ||||||||
\(950\) | 148517. | − | 22199.1i | 0.164562 | − | 0.0245973i | ||||
\(951\) | − | 200831.i | − | 0.222060i | ||||||
\(952\) | 43147.6 | − | 20583.6i | 0.0476083 | − | 0.0227116i | ||||
\(953\) | 655146. | 0.721360 | 0.360680 | − | 0.932690i | \(-0.382545\pi\) | ||||
0.360680 | + | 0.932690i | \(0.382545\pi\) | |||||||
\(954\) | 129895. | + | 869027.i | 0.142724 | + | 0.954853i | ||||
\(955\) | − | 274163.i | − | 0.300609i | ||||||
\(956\) | −53147.8 | − | 173813.i | −0.0581526 | − | 0.190181i | ||||
\(957\) | 1.23080e6 | 1.34389 | ||||||||
\(958\) | −1.25934e6 | + | 188236.i | −1.37218 | + | 0.205103i | ||||
\(959\) | − | 219653.i | − | 0.238836i | ||||||
\(960\) | −184977. | − | 149754.i | −0.200713 | − | 0.162494i | ||||
\(961\) | 359867. | 0.389668 | ||||||||
\(962\) | −44896.0 | − | 300365.i | −0.0485130 | − | 0.324563i | ||||
\(963\) | 521678.i | 0.562536i | ||||||||
\(964\) | 645105. | − | 197257.i | 0.694187 | − | 0.212265i | ||||
\(965\) | 728178. | 0.781957 | ||||||||
\(966\) | −107619. | + | 16086.0i | −0.115328 | + | 0.0172383i | ||||
\(967\) | 300375.i | 0.321226i | 0.987017 | + | 0.160613i | \(0.0513471\pi\) | ||||
−0.987017 | + | 0.160613i | \(0.948653\pi\) | |||||||
\(968\) | −630124. | − | 1.32087e6i | −0.672473 | − | 1.40965i | ||||
\(969\) | 30588.8 | 0.0325772 | ||||||||
\(970\) | 16852.6 | + | 112748.i | 0.0179111 | + | 0.119829i | ||||
\(971\) | − | 994951.i | − | 1.05527i | −0.849471 | − | 0.527635i | \(-0.823079\pi\) | ||
0.849471 | − | 0.527635i | \(-0.176921\pi\) | |||||||
\(972\) | −284198. | − | 929435.i | −0.300807 | − | 0.983754i | ||||
\(973\) | 274200. | 0.289629 | ||||||||
\(974\) | −626547. | + | 93651.1i | −0.660443 | + | 0.0987177i | ||||
\(975\) | − | 348801.i | − | 0.366917i | ||||||
\(976\) | −1.50477e6 | + | 1.01516e6i | −1.57968 | + | 1.06570i | ||||
\(977\) | 1.39627e6 | 1.46278 | 0.731391 | − | 0.681959i | \(-0.238872\pi\) | ||||
0.731391 | + | 0.681959i | \(0.238872\pi\) | |||||||
\(978\) | 55919.4 | + | 374113.i | 0.0584635 | + | 0.391134i | ||||
\(979\) | 1.68760e6i | 1.76077i | ||||||||
\(980\) | −465259. | + | 142265.i | −0.484443 | + | 0.148131i | ||||
\(981\) | −165991. | −0.172483 | ||||||||
\(982\) | −150548. | + | 22502.7i | −0.156118 | + | 0.0233352i | ||||
\(983\) | − | 1.17073e6i | − | 1.21157i | −0.795629 | − | 0.605784i | \(-0.792859\pi\) | ||
0.795629 | − | 0.605784i | \(-0.207141\pi\) | |||||||
\(984\) | −229309. | + | 109392.i | −0.236826 | + | 0.112978i | ||||
\(985\) | −657934. | −0.678125 | ||||||||
\(986\) | −70587.8 | − | 472248.i | −0.0726066 | − | 0.485754i | ||||
\(987\) | 84177.3i | 0.0864093i | ||||||||
\(988\) | 67237.7 | + | 219892.i | 0.0688809 | + | 0.225266i | ||||
\(989\) | 635473. | 0.649687 | ||||||||
\(990\) | −615791. | + | 92043.4i | −0.628294 | + | 0.0939123i | ||||
\(991\) | 28788.9i | 0.0293142i | 0.999893 | + | 0.0146571i | \(0.00466567\pi\) | ||||
−0.999893 | + | 0.0146571i | \(0.995334\pi\) | |||||||
\(992\) | 566757. | − | 519443.i | 0.575935 | − | 0.527855i | ||||
\(993\) | −5039.82 | −0.00511112 | ||||||||
\(994\) | −790.876 | − | 5291.14i | −0.000800452 | − | 0.00535521i | ||||
\(995\) | − | 64782.2i | − | 0.0654349i | ||||||
\(996\) | 532070. | − | 162694.i | 0.536352 | − | 0.164003i | ||||
\(997\) | 954503. | 0.960256 | 0.480128 | − | 0.877198i | \(-0.340590\pi\) | ||||
0.480128 | + | 0.877198i | \(0.340590\pi\) | |||||||
\(998\) | 1.89095e6 | − | 282643.i | 1.89853 | − | 0.283777i | ||||
\(999\) | 276160.i | 0.276713i |
(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 | 76.5.b.a.39.17 | ✓ | 36 | |
4.3 | odd | 2 | inner | 76.5.b.a.39.18 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.b.a.39.17 | ✓ | 36 | 1.1 | even | 1 | trivial | |
76.5.b.a.39.18 | yes | 36 | 4.3 | odd | 2 | inner |