Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(119,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.119");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.55 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.24 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.56380i | 0.890951i | 0.895294 | + | 0.445476i | \(0.146965\pi\) | ||||
−0.895294 | + | 0.445476i | \(0.853035\pi\) | |||||||
\(3\) | −1.54671 | + | 8.86610i | −0.171857 | + | 0.985122i | ||||
\(4\) | 3.29930 | 0.206206 | ||||||||
\(5\) | − | 32.9935i | − | 1.31974i | −0.751380 | − | 0.659870i | \(-0.770611\pi\) | ||
0.751380 | − | 0.659870i | \(-0.229389\pi\) | |||||||
\(6\) | −31.5970 | − | 5.51219i | −0.877695 | − | 0.153116i | ||||
\(7\) | −48.4204 | −0.988172 | −0.494086 | − | 0.869413i | \(-0.664497\pi\) | ||||
−0.494086 | + | 0.869413i | \(0.664497\pi\) | |||||||
\(8\) | 68.7789i | 1.07467i | ||||||||
\(9\) | −76.2153 | − | 27.4266i | −0.940930 | − | 0.338601i | ||||
\(10\) | 117.582 | 1.17582 | ||||||||
\(11\) | − | 143.870i | − | 1.18900i | −0.804094 | − | 0.594502i | \(-0.797349\pi\) | ||
0.804094 | − | 0.594502i | \(-0.202651\pi\) | |||||||
\(12\) | −5.10307 | + | 29.2519i | −0.0354380 | + | 0.203138i | ||||
\(13\) | 188.424 | 1.11494 | 0.557469 | − | 0.830198i | \(-0.311773\pi\) | ||||
0.557469 | + | 0.830198i | \(0.311773\pi\) | |||||||
\(14\) | − | 172.561i | − | 0.880413i | ||||||
\(15\) | 292.524 | + | 51.0315i | 1.30010 | + | 0.226807i | ||||
\(16\) | −192.326 | −0.751273 | ||||||||
\(17\) | − | 314.784i | − | 1.08922i | −0.838690 | − | 0.544610i | \(-0.816678\pi\) | ||
0.838690 | − | 0.544610i | \(-0.183322\pi\) | |||||||
\(18\) | 97.7432 | − | 271.617i | 0.301677 | − | 0.838323i | ||||
\(19\) | −1.38992 | −0.00385018 | −0.00192509 | − | 0.999998i | \(-0.500613\pi\) | ||||
−0.00192509 | + | 0.999998i | \(0.500613\pi\) | |||||||
\(20\) | − | 108.855i | − | 0.272138i | ||||||
\(21\) | 74.8926 | − | 429.300i | 0.169824 | − | 0.973470i | ||||
\(22\) | 512.723 | 1.05934 | ||||||||
\(23\) | − | 193.577i | − | 0.365931i | −0.983119 | − | 0.182965i | \(-0.941430\pi\) | ||
0.983119 | − | 0.182965i | \(-0.0585697\pi\) | |||||||
\(24\) | −609.801 | − | 106.381i | −1.05868 | − | 0.184690i | ||||
\(25\) | −463.571 | −0.741714 | ||||||||
\(26\) | 671.508i | 0.993355i | ||||||||
\(27\) | 361.051 | − | 633.311i | 0.495268 | − | 0.868740i | ||||
\(28\) | −159.753 | −0.203767 | ||||||||
\(29\) | − | 1266.29i | − | 1.50570i | −0.658191 | − | 0.752851i | \(-0.728678\pi\) | ||
0.658191 | − | 0.752851i | \(-0.271322\pi\) | |||||||
\(30\) | −181.866 | + | 1042.50i | −0.202074 | + | 1.15833i | ||||
\(31\) | 36.5072 | 0.0379888 | 0.0189944 | − | 0.999820i | \(-0.493954\pi\) | ||||
0.0189944 | + | 0.999820i | \(0.493954\pi\) | |||||||
\(32\) | 415.051i | 0.405323i | ||||||||
\(33\) | 1275.56 | + | 222.525i | 1.17131 | + | 0.204339i | ||||
\(34\) | 1121.83 | 0.970441 | ||||||||
\(35\) | 1597.56i | 1.30413i | ||||||||
\(36\) | −251.457 | − | 90.4886i | −0.194025 | − | 0.0698215i | ||||
\(37\) | 1485.40 | 1.08502 | 0.542512 | − | 0.840048i | \(-0.317473\pi\) | ||||
0.542512 | + | 0.840048i | \(0.317473\pi\) | |||||||
\(38\) | − | 4.95339i | − | 0.00343032i | ||||||
\(39\) | −291.439 | + | 1670.59i | −0.191610 | + | 1.09835i | ||||
\(40\) | 2269.26 | 1.41829 | ||||||||
\(41\) | 1972.66i | 1.17350i | 0.809768 | + | 0.586750i | \(0.199593\pi\) | ||||
−0.809768 | + | 0.586750i | \(0.800407\pi\) | |||||||
\(42\) | 1529.94 | + | 266.903i | 0.867314 | + | 0.151305i | ||||
\(43\) | 203.989 | 0.110324 | 0.0551620 | − | 0.998477i | \(-0.482432\pi\) | ||||
0.0551620 | + | 0.998477i | \(0.482432\pi\) | |||||||
\(44\) | − | 474.668i | − | 0.245180i | ||||||
\(45\) | −904.901 | + | 2514.61i | −0.446865 | + | 1.24178i | ||||
\(46\) | 689.872 | 0.326027 | ||||||||
\(47\) | − | 934.292i | − | 0.422948i | −0.977384 | − | 0.211474i | \(-0.932174\pi\) | ||
0.977384 | − | 0.211474i | \(-0.0678263\pi\) | |||||||
\(48\) | 297.473 | − | 1705.18i | 0.129112 | − | 0.740096i | ||||
\(49\) | −56.4629 | −0.0235164 | ||||||||
\(50\) | − | 1652.08i | − | 0.660831i | ||||||
\(51\) | 2790.91 | + | 486.882i | 1.07301 | + | 0.187190i | ||||
\(52\) | 621.668 | 0.229907 | ||||||||
\(53\) | − | 3283.35i | − | 1.16887i | −0.811442 | − | 0.584433i | \(-0.801317\pi\) | ||
0.811442 | − | 0.584433i | \(-0.198683\pi\) | |||||||
\(54\) | 2257.00 | + | 1286.71i | 0.774005 | + | 0.441260i | ||||
\(55\) | −4746.76 | −1.56918 | ||||||||
\(56\) | − | 3330.30i | − | 1.06196i | ||||||
\(57\) | 2.14980 | − | 12.3231i | 0.000661682 | − | 0.00379290i | ||||
\(58\) | 4512.83 | 1.34151 | ||||||||
\(59\) | − | 453.188i | − | 0.130189i | ||||||
\(60\) | 965.122 | + | 168.368i | 0.268089 | + | 0.0467689i | ||||
\(61\) | −5625.52 | −1.51183 | −0.755914 | − | 0.654670i | \(-0.772807\pi\) | ||||
−0.755914 | + | 0.654670i | \(0.772807\pi\) | |||||||
\(62\) | 130.105i | 0.0338461i | ||||||||
\(63\) | 3690.38 | + | 1328.01i | 0.929801 | + | 0.334596i | ||||
\(64\) | −4556.37 | −1.11240 | ||||||||
\(65\) | − | 6216.78i | − | 1.47143i | ||||||
\(66\) | −793.036 | + | 4545.85i | −0.182056 | + | 1.04358i | ||||
\(67\) | −4794.66 | −1.06809 | −0.534045 | − | 0.845456i | \(-0.679329\pi\) | ||||
−0.534045 | + | 0.845456i | \(0.679329\pi\) | |||||||
\(68\) | − | 1038.57i | − | 0.224604i | ||||||
\(69\) | 1716.28 | + | 299.409i | 0.360487 | + | 0.0628879i | ||||
\(70\) | −5693.39 | −1.16192 | ||||||||
\(71\) | 3643.38i | 0.722749i | 0.932421 | + | 0.361375i | \(0.117692\pi\) | ||||
−0.932421 | + | 0.361375i | \(0.882308\pi\) | |||||||
\(72\) | 1886.38 | − | 5242.01i | 0.363884 | − | 1.01119i | ||||
\(73\) | 2678.61 | 0.502649 | 0.251324 | − | 0.967903i | \(-0.419134\pi\) | ||||
0.251324 | + | 0.967903i | \(0.419134\pi\) | |||||||
\(74\) | 5293.67i | 0.966704i | ||||||||
\(75\) | 717.012 | − | 4110.07i | 0.127469 | − | 0.730678i | ||||
\(76\) | −4.58574 | −0.000793931 | ||||||||
\(77\) | 6966.22i | 1.17494i | ||||||||
\(78\) | −5953.66 | − | 1038.63i | −0.978576 | − | 0.170715i | ||||
\(79\) | 7113.29 | 1.13977 | 0.569884 | − | 0.821725i | \(-0.306988\pi\) | ||||
0.569884 | + | 0.821725i | \(0.306988\pi\) | |||||||
\(80\) | 6345.50i | 0.991485i | ||||||||
\(81\) | 5056.56 | + | 4180.66i | 0.770699 | + | 0.637199i | ||||
\(82\) | −7030.16 | −1.04553 | ||||||||
\(83\) | − | 9846.88i | − | 1.42936i | −0.699450 | − | 0.714681i | \(-0.746572\pi\) | ||
0.699450 | − | 0.714681i | \(-0.253428\pi\) | |||||||
\(84\) | 247.093 | − | 1416.39i | 0.0350188 | − | 0.200735i | ||||
\(85\) | −10385.8 | −1.43749 | ||||||||
\(86\) | 726.977i | 0.0982932i | ||||||||
\(87\) | 11227.1 | + | 1958.60i | 1.48330 | + | 0.258766i | ||||
\(88\) | 9895.19 | 1.27779 | ||||||||
\(89\) | − | 3149.01i | − | 0.397552i | −0.980045 | − | 0.198776i | \(-0.936303\pi\) | ||
0.980045 | − | 0.198776i | \(-0.0636967\pi\) | |||||||
\(90\) | −8961.58 | − | 3224.89i | −1.10637 | − | 0.398135i | ||||
\(91\) | −9123.59 | −1.10175 | ||||||||
\(92\) | − | 638.669i | − | 0.0754572i | ||||||
\(93\) | −56.4663 | + | 323.676i | −0.00652864 | + | 0.0374236i | ||||
\(94\) | 3329.63 | 0.376826 | ||||||||
\(95\) | 45.8582i | 0.00508124i | ||||||||
\(96\) | −3679.88 | − | 641.965i | −0.399293 | − | 0.0696577i | ||||
\(97\) | −13040.7 | −1.38598 | −0.692990 | − | 0.720947i | \(-0.743707\pi\) | ||||
−0.692990 | + | 0.720947i | \(0.743707\pi\) | |||||||
\(98\) | − | 201.223i | − | 0.0209520i | ||||||
\(99\) | −3945.86 | + | 10965.1i | −0.402598 | + | 1.11877i | ||||
\(100\) | −1529.46 | −0.152946 | ||||||||
\(101\) | − | 18350.4i | − | 1.79888i | −0.437042 | − | 0.899441i | \(-0.643974\pi\) | ||
0.437042 | − | 0.899441i | \(-0.356026\pi\) | |||||||
\(102\) | −1735.15 | + | 9946.25i | −0.166777 | + | 0.956003i | ||||
\(103\) | 5773.21 | 0.544180 | 0.272090 | − | 0.962272i | \(-0.412285\pi\) | ||||
0.272090 | + | 0.962272i | \(0.412285\pi\) | |||||||
\(104\) | 12959.6i | 1.19819i | ||||||||
\(105\) | −14164.1 | − | 2470.97i | −1.28473 | − | 0.224124i | ||||
\(106\) | 11701.2 | 1.04140 | ||||||||
\(107\) | − | 1010.41i | − | 0.0882531i | −0.999026 | − | 0.0441265i | \(-0.985950\pi\) | ||
0.999026 | − | 0.0441265i | \(-0.0140505\pi\) | |||||||
\(108\) | 1191.21 | − | 2089.48i | 0.102127 | − | 0.179139i | ||||
\(109\) | 3241.62 | 0.272841 | 0.136420 | − | 0.990651i | \(-0.456440\pi\) | ||||
0.136420 | + | 0.990651i | \(0.456440\pi\) | |||||||
\(110\) | − | 16916.5i | − | 1.39806i | ||||||
\(111\) | −2297.49 | + | 13169.7i | −0.186469 | + | 1.06888i | ||||
\(112\) | 9312.50 | 0.742387 | ||||||||
\(113\) | − | 14844.0i | − | 1.16250i | −0.813724 | − | 0.581252i | \(-0.802563\pi\) | ||
0.813724 | − | 0.581252i | \(-0.197437\pi\) | |||||||
\(114\) | 43.9172 | + | 7.66148i | 0.00337929 | + | 0.000589526i | ||||
\(115\) | −6386.80 | −0.482934 | ||||||||
\(116\) | − | 4177.88i | − | 0.310485i | ||||||
\(117\) | −14360.8 | − | 5167.85i | −1.04908 | − | 0.377519i | ||||
\(118\) | 1615.07 | 0.115992 | ||||||||
\(119\) | 15242.0i | 1.07634i | ||||||||
\(120\) | −3509.89 | + | 20119.5i | −0.243743 | + | 1.39718i | ||||
\(121\) | −6057.45 | −0.413732 | ||||||||
\(122\) | − | 20048.2i | − | 1.34697i | ||||||
\(123\) | −17489.8 | − | 3051.13i | −1.15604 | − | 0.201675i | ||||
\(124\) | 120.448 | 0.00783351 | ||||||||
\(125\) | − | 5326.10i | − | 0.340871i | ||||||
\(126\) | −4732.77 | + | 13151.8i | −0.298108 | + | 0.828407i | ||||
\(127\) | −8624.34 | −0.534710 | −0.267355 | − | 0.963598i | \(-0.586150\pi\) | ||||
−0.267355 | + | 0.963598i | \(0.586150\pi\) | |||||||
\(128\) | − | 9597.22i | − | 0.585768i | ||||||
\(129\) | −315.513 | + | 1808.59i | −0.0189600 | + | 0.108683i | ||||
\(130\) | 22155.4 | 1.31097 | ||||||||
\(131\) | 32219.3i | 1.87747i | 0.344635 | + | 0.938737i | \(0.388003\pi\) | ||||
−0.344635 | + | 0.938737i | \(0.611997\pi\) | |||||||
\(132\) | 4208.45 | + | 734.176i | 0.241532 | + | 0.0421359i | ||||
\(133\) | 67.3003 | 0.00380464 | ||||||||
\(134\) | − | 17087.2i | − | 0.951617i | ||||||
\(135\) | −20895.2 | − | 11912.3i | −1.14651 | − | 0.653626i | ||||
\(136\) | 21650.5 | 1.17055 | ||||||||
\(137\) | 8355.56i | 0.445179i | 0.974912 | + | 0.222589i | \(0.0714509\pi\) | ||||
−0.974912 | + | 0.222589i | \(0.928549\pi\) | |||||||
\(138\) | −1067.04 | + | 6116.47i | −0.0560300 | + | 0.321176i | ||||
\(139\) | −6883.91 | −0.356292 | −0.178146 | − | 0.984004i | \(-0.557010\pi\) | ||||
−0.178146 | + | 0.984004i | \(0.557010\pi\) | |||||||
\(140\) | 5270.82i | 0.268919i | ||||||||
\(141\) | 8283.52 | + | 1445.08i | 0.416655 | + | 0.0726866i | ||||
\(142\) | −12984.3 | −0.643934 | ||||||||
\(143\) | − | 27108.5i | − | 1.32567i | ||||||
\(144\) | 14658.2 | + | 5274.85i | 0.706896 | + | 0.254382i | ||||
\(145\) | −41779.5 | −1.98713 | ||||||||
\(146\) | 9546.06i | 0.447835i | ||||||||
\(147\) | 87.3320 | − | 500.606i | 0.00404147 | − | 0.0231665i | ||||
\(148\) | 4900.77 | 0.223739 | ||||||||
\(149\) | − | 31197.8i | − | 1.40524i | −0.711564 | − | 0.702622i | \(-0.752013\pi\) | ||
0.711564 | − | 0.702622i | \(-0.247987\pi\) | |||||||
\(150\) | 14647.5 | + | 2555.29i | 0.650999 | + | 0.113569i | ||||
\(151\) | 10047.5 | 0.440661 | 0.220330 | − | 0.975425i | \(-0.429286\pi\) | ||||
0.220330 | + | 0.975425i | \(0.429286\pi\) | |||||||
\(152\) | − | 95.5969i | − | 0.00413768i | ||||||
\(153\) | −8633.48 | + | 23991.4i | −0.368810 | + | 1.02488i | ||||
\(154\) | −24826.3 | −1.04681 | ||||||||
\(155\) | − | 1204.50i | − | 0.0501353i | ||||||
\(156\) | −961.544 | + | 5511.77i | −0.0395112 | + | 0.226486i | ||||
\(157\) | 33206.3 | 1.34717 | 0.673584 | − | 0.739111i | \(-0.264754\pi\) | ||||
0.673584 | + | 0.739111i | \(0.264754\pi\) | |||||||
\(158\) | 25350.4i | 1.01548i | ||||||||
\(159\) | 29110.5 | + | 5078.40i | 1.15148 | + | 0.200878i | ||||
\(160\) | 13694.0 | 0.534921 | ||||||||
\(161\) | 9373.10i | 0.361603i | ||||||||
\(162\) | −14899.1 | + | 18020.6i | −0.567713 | + | 0.686655i | ||||
\(163\) | 16842.0 | 0.633895 | 0.316947 | − | 0.948443i | \(-0.397342\pi\) | ||||
0.316947 | + | 0.948443i | \(0.397342\pi\) | |||||||
\(164\) | 6508.37i | 0.241983i | ||||||||
\(165\) | 7341.88 | − | 42085.2i | 0.269674 | − | 1.54583i | ||||
\(166\) | 35092.4 | 1.27349 | ||||||||
\(167\) | 47210.2i | 1.69279i | 0.532556 | + | 0.846395i | \(0.321232\pi\) | ||||
−0.532556 | + | 0.846395i | \(0.678768\pi\) | |||||||
\(168\) | 29526.8 | + | 5151.03i | 1.04616 | + | 0.182505i | ||||
\(169\) | 6942.79 | 0.243086 | ||||||||
\(170\) | − | 37013.1i | − | 1.28073i | ||||||
\(171\) | 105.933 | + | 38.1207i | 0.00362275 | + | 0.00130367i | ||||
\(172\) | 673.020 | 0.0227495 | ||||||||
\(173\) | − | 44614.6i | − | 1.49068i | −0.666683 | − | 0.745341i | \(-0.732287\pi\) | ||
0.666683 | − | 0.745341i | \(-0.267713\pi\) | |||||||
\(174\) | −6980.06 | + | 40011.2i | −0.230548 | + | 1.32155i | ||||
\(175\) | 22446.3 | 0.732941 | ||||||||
\(176\) | 27669.8i | 0.893267i | ||||||||
\(177\) | 4018.01 | + | 700.952i | 0.128252 | + | 0.0223739i | ||||
\(178\) | 11222.5 | 0.354200 | ||||||||
\(179\) | 42181.9i | 1.31650i | 0.752800 | + | 0.658249i | \(0.228703\pi\) | ||||
−0.752800 | + | 0.658249i | \(0.771297\pi\) | |||||||
\(180\) | −2985.54 | + | 8296.45i | −0.0921462 | + | 0.256063i | ||||
\(181\) | −60384.5 | −1.84318 | −0.921592 | − | 0.388160i | \(-0.873111\pi\) | ||||
−0.921592 | + | 0.388160i | \(0.873111\pi\) | |||||||
\(182\) | − | 32514.7i | − | 0.981606i | ||||||
\(183\) | 8701.07 | − | 49876.4i | 0.259819 | − | 1.48934i | ||||
\(184\) | 13314.1 | 0.393255 | ||||||||
\(185\) | − | 49008.5i | − | 1.43195i | ||||||
\(186\) | −1153.52 | − | 201.235i | −0.0333426 | − | 0.00581670i | ||||
\(187\) | −45287.9 | −1.29509 | ||||||||
\(188\) | − | 3082.50i | − | 0.0872144i | ||||||
\(189\) | −17482.2 | + | 30665.2i | −0.489410 | + | 0.858464i | ||||
\(190\) | −163.430 | −0.00452714 | ||||||||
\(191\) | 51191.6i | 1.40324i | 0.712551 | + | 0.701621i | \(0.247540\pi\) | ||||
−0.712551 | + | 0.701621i | \(0.752460\pi\) | |||||||
\(192\) | 7047.41 | − | 40397.3i | 0.191173 | − | 1.09585i | ||||
\(193\) | −22027.7 | −0.591364 | −0.295682 | − | 0.955286i | \(-0.595547\pi\) | ||||
−0.295682 | + | 0.955286i | \(0.595547\pi\) | |||||||
\(194\) | − | 46474.5i | − | 1.23484i | ||||||
\(195\) | 55118.6 | + | 9615.59i | 1.44954 | + | 0.252876i | ||||
\(196\) | −186.288 | −0.00484923 | ||||||||
\(197\) | 22961.1i | 0.591644i | 0.955243 | + | 0.295822i | \(0.0955936\pi\) | ||||
−0.955243 | + | 0.295822i | \(0.904406\pi\) | |||||||
\(198\) | −39077.4 | − | 14062.3i | −0.996770 | − | 0.358695i | ||||
\(199\) | 38265.0 | 0.966263 | 0.483132 | − | 0.875548i | \(-0.339499\pi\) | ||||
0.483132 | + | 0.875548i | \(0.339499\pi\) | |||||||
\(200\) | − | 31883.9i | − | 0.797098i | ||||||
\(201\) | 7415.97 | − | 42509.9i | 0.183559 | − | 1.05220i | ||||
\(202\) | 65397.2 | 1.60272 | ||||||||
\(203\) | 61314.5i | 1.48789i | ||||||||
\(204\) | 9208.03 | + | 1606.37i | 0.221262 | + | 0.0385997i | ||||
\(205\) | 65084.8 | 1.54872 | ||||||||
\(206\) | 20574.6i | 0.484838i | ||||||||
\(207\) | −5309.18 | + | 14753.6i | −0.123904 | + | 0.344315i | ||||
\(208\) | −36238.9 | −0.837623 | ||||||||
\(209\) | 199.967i | 0.00457788i | ||||||||
\(210\) | 8806.05 | − | 50478.1i | 0.199684 | − | 1.14463i | ||||
\(211\) | 34607.7 | 0.777335 | 0.388668 | − | 0.921378i | \(-0.372935\pi\) | ||||
0.388668 | + | 0.921378i | \(0.372935\pi\) | |||||||
\(212\) | − | 10832.7i | − | 0.241027i | ||||||
\(213\) | −32302.6 | − | 5635.27i | −0.711996 | − | 0.124210i | ||||
\(214\) | 3600.90 | 0.0786292 | ||||||||
\(215\) | − | 6730.31i | − | 0.145599i | ||||||
\(216\) | 43558.5 | + | 24832.7i | 0.933609 | + | 0.532251i | ||||
\(217\) | −1767.69 | −0.0375394 | ||||||||
\(218\) | 11552.5i | 0.243088i | ||||||||
\(219\) | −4143.05 | + | 23748.9i | −0.0863838 | + | 0.495170i | ||||
\(220\) | −15661.0 | −0.323574 | ||||||||
\(221\) | − | 59313.1i | − | 1.21441i | ||||||
\(222\) | −46934.2 | − | 8187.80i | −0.952321 | − | 0.166135i | ||||
\(223\) | 58364.2 | 1.17364 | 0.586822 | − | 0.809716i | \(-0.300379\pi\) | ||||
0.586822 | + | 0.809716i | \(0.300379\pi\) | |||||||
\(224\) | − | 20096.9i | − | 0.400529i | ||||||
\(225\) | 35331.2 | + | 12714.2i | 0.697901 | + | 0.251145i | ||||
\(226\) | 52901.2 | 1.03573 | ||||||||
\(227\) | − | 18653.8i | − | 0.362005i | −0.983483 | − | 0.181003i | \(-0.942066\pi\) | ||
0.983483 | − | 0.181003i | \(-0.0579343\pi\) | |||||||
\(228\) | 7.09284 | − | 40.6577i | 0.000136443 | − | 0.000782119i | ||||
\(229\) | −71930.2 | −1.37164 | −0.685820 | − | 0.727771i | \(-0.740556\pi\) | ||||
−0.685820 | + | 0.727771i | \(0.740556\pi\) | |||||||
\(230\) | − | 22761.3i | − | 0.430270i | ||||||
\(231\) | −61763.2 | − | 10774.8i | −1.15746 | − | 0.201922i | ||||
\(232\) | 87094.4 | 1.61813 | ||||||||
\(233\) | 72712.2i | 1.33935i | 0.742653 | + | 0.669677i | \(0.233567\pi\) | ||||
−0.742653 | + | 0.669677i | \(0.766433\pi\) | |||||||
\(234\) | 18417.2 | − | 51179.2i | 0.336351 | − | 0.934678i | ||||
\(235\) | −30825.6 | −0.558181 | ||||||||
\(236\) | − | 1495.20i | − | 0.0268457i | ||||||
\(237\) | −11002.2 | + | 63067.2i | −0.195877 | + | 1.12281i | ||||
\(238\) | −54319.5 | −0.958963 | ||||||||
\(239\) | − | 27801.0i | − | 0.486703i | −0.969938 | − | 0.243352i | \(-0.921753\pi\) | ||
0.969938 | − | 0.243352i | \(-0.0782469\pi\) | |||||||
\(240\) | −56259.9 | − | 9814.69i | −0.976734 | − | 0.170394i | ||||
\(241\) | 48259.9 | 0.830907 | 0.415454 | − | 0.909614i | \(-0.363623\pi\) | ||||
0.415454 | + | 0.909614i | \(0.363623\pi\) | |||||||
\(242\) | − | 21587.6i | − | 0.368615i | ||||||
\(243\) | −44887.2 | + | 38365.6i | −0.760169 | + | 0.649725i | ||||
\(244\) | −18560.2 | −0.311748 | ||||||||
\(245\) | 1862.91i | 0.0310356i | ||||||||
\(246\) | 10873.6 | − | 62330.1i | 0.179682 | − | 1.02998i | ||||
\(247\) | −261.894 | −0.00429271 | ||||||||
\(248\) | 2510.93i | 0.0408254i | ||||||||
\(249\) | 87303.4 | + | 15230.3i | 1.40810 | + | 0.245646i | ||||
\(250\) | 18981.2 | 0.303699 | ||||||||
\(251\) | − | 53937.3i | − | 0.856134i | −0.903747 | − | 0.428067i | \(-0.859195\pi\) | ||
0.903747 | − | 0.428067i | \(-0.140805\pi\) | |||||||
\(252\) | 12175.7 | + | 4381.50i | 0.191731 | + | 0.0689956i | ||||
\(253\) | −27849.9 | −0.435094 | ||||||||
\(254\) | − | 30735.5i | − | 0.476401i | ||||||
\(255\) | 16063.9 | − | 92081.8i | 0.247042 | − | 1.41610i | ||||
\(256\) | −38699.4 | −0.590506 | ||||||||
\(257\) | 69434.7i | 1.05126i | 0.850713 | + | 0.525630i | \(0.176170\pi\) | ||||
−0.850713 | + | 0.525630i | \(0.823830\pi\) | |||||||
\(258\) | −6445.45 | − | 1124.43i | −0.0968308 | − | 0.0168924i | ||||
\(259\) | −71923.6 | −1.07219 | ||||||||
\(260\) | − | 20511.0i | − | 0.303417i | ||||||
\(261\) | −34730.2 | + | 96511.1i | −0.509831 | + | 1.41676i | ||||
\(262\) | −114823. | −1.67274 | ||||||||
\(263\) | 96388.7i | 1.39352i | 0.717302 | + | 0.696762i | \(0.245377\pi\) | ||||
−0.717302 | + | 0.696762i | \(0.754623\pi\) | |||||||
\(264\) | −15305.0 | + | 87731.7i | −0.219597 | + | 1.25878i | ||||
\(265\) | −108329. | −1.54260 | ||||||||
\(266\) | 239.845i | 0.00338975i | ||||||||
\(267\) | 27919.5 | + | 4870.63i | 0.391638 | + | 0.0683223i | ||||
\(268\) | −15819.0 | −0.220247 | ||||||||
\(269\) | 62174.8i | 0.859230i | 0.903012 | + | 0.429615i | \(0.141351\pi\) | ||||
−0.903012 | + | 0.429615i | \(0.858649\pi\) | |||||||
\(270\) | 42453.2 | − | 74466.3i | 0.582349 | − | 1.02149i | ||||
\(271\) | 31459.2 | 0.428360 | 0.214180 | − | 0.976794i | \(-0.431292\pi\) | ||||
0.214180 | + | 0.976794i | \(0.431292\pi\) | |||||||
\(272\) | 60541.2i | 0.818301i | ||||||||
\(273\) | 14111.6 | − | 80890.7i | 0.189344 | − | 1.08536i | ||||
\(274\) | −29777.6 | −0.396632 | ||||||||
\(275\) | 66693.8i | 0.881901i | ||||||||
\(276\) | 5662.51 | + | 987.840i | 0.0743345 | + | 0.0129679i | ||||
\(277\) | 92427.3 | 1.20459 | 0.602297 | − | 0.798272i | \(-0.294252\pi\) | ||||
0.602297 | + | 0.798272i | \(0.294252\pi\) | |||||||
\(278\) | − | 24532.9i | − | 0.317438i | ||||||
\(279\) | −2782.41 | − | 1001.27i | −0.0357448 | − | 0.0128630i | ||||
\(280\) | −109878. | −1.40151 | ||||||||
\(281\) | 27532.2i | 0.348681i | 0.984685 | + | 0.174341i | \(0.0557794\pi\) | ||||
−0.984685 | + | 0.174341i | \(0.944221\pi\) | |||||||
\(282\) | −5149.99 | + | 29520.8i | −0.0647602 | + | 0.371219i | ||||
\(283\) | −93843.8 | −1.17174 | −0.585872 | − | 0.810404i | \(-0.699248\pi\) | ||||
−0.585872 | + | 0.810404i | \(0.699248\pi\) | |||||||
\(284\) | 12020.6i | 0.149035i | ||||||||
\(285\) | −406.583 | − | 70.9296i | −0.00500564 | − | 0.000873248i | ||||
\(286\) | 96609.6 | 1.18110 | ||||||||
\(287\) | − | 95516.8i | − | 1.15962i | ||||||
\(288\) | 11383.5 | − | 31633.2i | 0.137243 | − | 0.381381i | ||||
\(289\) | −15568.2 | −0.186399 | ||||||||
\(290\) | − | 148894.i | − | 1.77044i | ||||||
\(291\) | 20170.2 | − | 115620.i | 0.238191 | − | 1.36536i | ||||
\(292\) | 8837.54 | 0.103649 | ||||||||
\(293\) | − | 95388.5i | − | 1.11112i | −0.831477 | − | 0.555560i | \(-0.812504\pi\) | ||
0.831477 | − | 0.555560i | \(-0.187496\pi\) | |||||||
\(294\) | 1784.06 | + | 311.234i | 0.0206403 | + | 0.00360075i | ||||
\(295\) | −14952.2 | −0.171816 | ||||||||
\(296\) | 102164.i | 1.16604i | ||||||||
\(297\) | −91114.2 | − | 51944.2i | −1.03294 | − | 0.588876i | ||||
\(298\) | 111183. | 1.25200 | ||||||||
\(299\) | − | 36474.7i | − | 0.407990i | ||||||
\(300\) | 2365.64 | − | 13560.3i | 0.0262848 | − | 0.150670i | ||||
\(301\) | −9877.23 | −0.109019 | ||||||||
\(302\) | 35807.4i | 0.392607i | ||||||||
\(303\) | 162696. | + | 28382.8i | 1.77212 | + | 0.309151i | ||||
\(304\) | 267.317 | 0.00289254 | ||||||||
\(305\) | 185605.i | 1.99522i | ||||||||
\(306\) | −85500.7 | − | 30768.0i | −0.913117 | − | 0.328592i | ||||
\(307\) | −34270.2 | −0.363613 | −0.181807 | − | 0.983334i | \(-0.558194\pi\) | ||||
−0.181807 | + | 0.983334i | \(0.558194\pi\) | |||||||
\(308\) | 22983.6i | 0.242280i | ||||||||
\(309\) | −8929.50 | + | 51185.8i | −0.0935213 | + | 0.536084i | ||||
\(310\) | 4292.61 | 0.0446681 | ||||||||
\(311\) | 137459.i | 1.42119i | 0.703602 | + | 0.710594i | \(0.251574\pi\) | ||||
−0.703602 | + | 0.710594i | \(0.748426\pi\) | |||||||
\(312\) | −114901. | − | 20044.9i | −1.18036 | − | 0.205918i | ||||
\(313\) | 147882. | 1.50948 | 0.754739 | − | 0.656026i | \(-0.227764\pi\) | ||||
0.754739 | + | 0.656026i | \(0.227764\pi\) | |||||||
\(314\) | 118341.i | 1.20026i | ||||||||
\(315\) | 43815.7 | − | 121759.i | 0.441579 | − | 1.22710i | ||||
\(316\) | 23468.9 | 0.235027 | ||||||||
\(317\) | 105626.i | 1.05112i | 0.850758 | + | 0.525558i | \(0.176143\pi\) | ||||
−0.850758 | + | 0.525558i | \(0.823857\pi\) | |||||||
\(318\) | −18098.4 | + | 103744.i | −0.178973 | + | 1.02591i | ||||
\(319\) | −182181. | −1.79029 | ||||||||
\(320\) | 150331.i | 1.46807i | ||||||||
\(321\) | 8958.39 | + | 1562.82i | 0.0869400 | + | 0.0151669i | ||||
\(322\) | −33403.9 | −0.322170 | ||||||||
\(323\) | 437.524i | 0.00419369i | ||||||||
\(324\) | 16683.1 | + | 13793.2i | 0.158923 | + | 0.131394i | ||||
\(325\) | −87348.2 | −0.826965 | ||||||||
\(326\) | 60021.4i | 0.564769i | ||||||||
\(327\) | −5013.87 | + | 28740.5i | −0.0468897 | + | 0.268782i | ||||
\(328\) | −135677. | −1.26113 | ||||||||
\(329\) | 45238.8i | 0.417945i | ||||||||
\(330\) | 149984. | + | 26165.0i | 1.37726 | + | 0.240267i | ||||
\(331\) | −142699. | −1.30246 | −0.651230 | − | 0.758880i | \(-0.725747\pi\) | ||||
−0.651230 | + | 0.758880i | \(0.725747\pi\) | |||||||
\(332\) | − | 32487.8i | − | 0.294743i | ||||||
\(333\) | −113210. | − | 40739.5i | −1.02093 | − | 0.367390i | ||||
\(334\) | −168248. | −1.50819 | ||||||||
\(335\) | 158193.i | 1.40960i | ||||||||
\(336\) | −14403.8 | + | 82565.5i | −0.127585 | + | 0.731342i | ||||
\(337\) | −100324. | −0.883377 | −0.441689 | − | 0.897168i | \(-0.645620\pi\) | ||||
−0.441689 | + | 0.897168i | \(0.645620\pi\) | |||||||
\(338\) | 24742.8i | 0.216578i | ||||||||
\(339\) | 131608. | + | 22959.5i | 1.14521 | + | 0.199785i | ||||
\(340\) | −34266.0 | −0.296418 | ||||||||
\(341\) | − | 5252.28i | − | 0.0451688i | ||||||
\(342\) | −135.855 | + | 377.524i | −0.00116151 | + | 0.00322770i | ||||
\(343\) | 118991. | 1.01141 | ||||||||
\(344\) | 14030.1i | 0.118562i | ||||||||
\(345\) | 9878.56 | − | 56626.0i | 0.0829956 | − | 0.475749i | ||||
\(346\) | 158998. | 1.32813 | ||||||||
\(347\) | − | 181469.i | − | 1.50710i | −0.657388 | − | 0.753552i | \(-0.728339\pi\) | ||
0.657388 | − | 0.753552i | \(-0.271661\pi\) | |||||||
\(348\) | 37041.5 | + | 6461.99i | 0.305865 | + | 0.0533590i | ||||
\(349\) | 149731. | 1.22931 | 0.614656 | − | 0.788795i | \(-0.289295\pi\) | ||||
0.614656 | + | 0.788795i | \(0.289295\pi\) | |||||||
\(350\) | 79994.3i | 0.653014i | ||||||||
\(351\) | 68030.8 | − | 119331.i | 0.552194 | − | 0.968591i | ||||
\(352\) | 59713.2 | 0.481931 | ||||||||
\(353\) | − | 29293.1i | − | 0.235080i | −0.993068 | − | 0.117540i | \(-0.962499\pi\) | ||
0.993068 | − | 0.117540i | \(-0.0375008\pi\) | |||||||
\(354\) | −2498.06 | + | 14319.4i | −0.0199341 | + | 0.114266i | ||||
\(355\) | 120208. | 0.953841 | ||||||||
\(356\) | − | 10389.5i | − | 0.0819777i | ||||||
\(357\) | −135137. | − | 23575.0i | −1.06032 | − | 0.184976i | ||||
\(358\) | −150328. | −1.17294 | ||||||||
\(359\) | − | 10042.8i | − | 0.0779227i | −0.999241 | − | 0.0389614i | \(-0.987595\pi\) | ||
0.999241 | − | 0.0389614i | \(-0.0124049\pi\) | |||||||
\(360\) | −172952. | − | 62238.1i | −1.33451 | − | 0.480232i | ||||
\(361\) | −130319. | −0.999985 | ||||||||
\(362\) | − | 215199.i | − | 1.64219i | ||||||
\(363\) | 9369.14 | − | 53705.9i | 0.0711028 | − | 0.407576i | ||||
\(364\) | −30101.4 | −0.227188 | ||||||||
\(365\) | − | 88376.9i | − | 0.663366i | ||||||
\(366\) | 177750. | + | 31008.9i | 1.32693 | + | 0.231486i | ||||
\(367\) | 139800. | 1.03795 | 0.518974 | − | 0.854790i | \(-0.326314\pi\) | ||||
0.518974 | + | 0.854790i | \(0.326314\pi\) | |||||||
\(368\) | 37230.0i | 0.274914i | ||||||||
\(369\) | 54103.3 | − | 150347.i | 0.397348 | − | 1.10418i | ||||
\(370\) | 174657. | 1.27580 | ||||||||
\(371\) | 158981.i | 1.15504i | ||||||||
\(372\) | −186.299 | + | 1067.90i | −0.00134625 | + | 0.00771697i | ||||
\(373\) | −120658. | −0.867238 | −0.433619 | − | 0.901096i | \(-0.642764\pi\) | ||||
−0.433619 | + | 0.901096i | \(0.642764\pi\) | |||||||
\(374\) | − | 161397.i | − | 1.15386i | ||||||
\(375\) | 47221.8 | + | 8237.97i | 0.335799 | + | 0.0585811i | ||||
\(376\) | 64259.6 | 0.454530 | ||||||||
\(377\) | − | 238601.i | − | 1.67876i | ||||||
\(378\) | −109285. | − | 62303.2i | −0.764850 | − | 0.436041i | ||||
\(379\) | 160981. | 1.12072 | 0.560358 | − | 0.828251i | \(-0.310664\pi\) | ||||
0.560358 | + | 0.828251i | \(0.310664\pi\) | |||||||
\(380\) | 151.300i | 0.00104778i | ||||||||
\(381\) | 13339.4 | − | 76464.2i | 0.0918938 | − | 0.526755i | ||||
\(382\) | −182437. | −1.25022 | ||||||||
\(383\) | − | 267800.i | − | 1.82563i | −0.408374 | − | 0.912815i | \(-0.633904\pi\) | ||
0.408374 | − | 0.912815i | \(-0.366096\pi\) | |||||||
\(384\) | 85089.8 | + | 14844.2i | 0.577052 | + | 0.100668i | ||||
\(385\) | 229840. | 1.55062 | ||||||||
\(386\) | − | 78502.4i | − | 0.526876i | ||||||
\(387\) | −15547.1 | − | 5594.73i | −0.103807 | − | 0.0373558i | ||||
\(388\) | −43025.1 | −0.285797 | ||||||||
\(389\) | 2697.04i | 0.0178233i | 0.999960 | + | 0.00891165i | \(0.00283670\pi\) | ||||
−0.999960 | + | 0.00891165i | \(0.997163\pi\) | |||||||
\(390\) | −34268.1 | + | 196432.i | −0.225300 | + | 1.29147i | ||||
\(391\) | −60935.2 | −0.398579 | ||||||||
\(392\) | − | 3883.46i | − | 0.0252724i | ||||||
\(393\) | −285660. | − | 49834.1i | −1.84954 | − | 0.322657i | ||||
\(394\) | −81829.0 | −0.527126 | ||||||||
\(395\) | − | 234692.i | − | 1.50420i | ||||||
\(396\) | −13018.6 | + | 36177.0i | −0.0830181 | + | 0.230697i | ||||
\(397\) | −34899.8 | −0.221433 | −0.110716 | − | 0.993852i | \(-0.535314\pi\) | ||||
−0.110716 | + | 0.993852i | \(0.535314\pi\) | |||||||
\(398\) | 136369.i | 0.860893i | ||||||||
\(399\) | −104.094 | + | 596.691i | −0.000653855 | + | 0.00374804i | ||||
\(400\) | 89156.7 | 0.557230 | ||||||||
\(401\) | − | 61105.8i | − | 0.380009i | −0.981783 | − | 0.190004i | \(-0.939150\pi\) | ||
0.981783 | − | 0.190004i | \(-0.0608503\pi\) | |||||||
\(402\) | 151497. | + | 26429.1i | 0.937459 | + | 0.163542i | ||||
\(403\) | 6878.85 | 0.0423551 | ||||||||
\(404\) | − | 60543.4i | − | 0.370940i | ||||||
\(405\) | 137935. | − | 166834.i | 0.840937 | − | 1.01712i | ||||
\(406\) | −218513. | −1.32564 | ||||||||
\(407\) | − | 213704.i | − | 1.29010i | ||||||
\(408\) | −33487.2 | + | 191956.i | −0.201168 | + | 1.15314i | ||||
\(409\) | 245183. | 1.46569 | 0.732847 | − | 0.680394i | \(-0.238191\pi\) | ||||
0.732847 | + | 0.680394i | \(0.238191\pi\) | |||||||
\(410\) | 231949.i | 1.37983i | ||||||||
\(411\) | −74081.2 | − | 12923.7i | −0.438555 | − | 0.0765071i | ||||
\(412\) | 19047.5 | 0.112213 | ||||||||
\(413\) | 21943.5i | 0.128649i | ||||||||
\(414\) | −52578.9 | − | 18920.9i | −0.306768 | − | 0.110393i | ||||
\(415\) | −324883. | −1.88639 | ||||||||
\(416\) | 78205.7i | 0.451910i | ||||||||
\(417\) | 10647.4 | − | 61033.4i | 0.0612313 | − | 0.350991i | ||||
\(418\) | −712.642 | −0.00407867 | ||||||||
\(419\) | 89352.9i | 0.508956i | 0.967079 | + | 0.254478i | \(0.0819037\pi\) | ||||
−0.967079 | + | 0.254478i | \(0.918096\pi\) | |||||||
\(420\) | −46731.6 | − | 8152.46i | −0.264918 | − | 0.0462157i | ||||
\(421\) | −137615. | −0.776431 | −0.388215 | − | 0.921569i | \(-0.626908\pi\) | ||||
−0.388215 | + | 0.921569i | \(0.626908\pi\) | |||||||
\(422\) | 123335.i | 0.692568i | ||||||||
\(423\) | −25624.5 | + | 71207.4i | −0.143210 | + | 0.397964i | ||||
\(424\) | 225825. | 1.25615 | ||||||||
\(425\) | 145925.i | 0.807889i | ||||||||
\(426\) | 20083.0 | − | 115120.i | 0.110665 | − | 0.634354i | ||||
\(427\) | 272390. | 1.49395 | ||||||||
\(428\) | − | 3333.64i | − | 0.0181983i | ||||||
\(429\) | 240347. | + | 41929.2i | 1.30594 | + | 0.227825i | ||||
\(430\) | 23985.5 | 0.129722 | ||||||||
\(431\) | 260720.i | 1.40353i | 0.712411 | + | 0.701763i | \(0.247603\pi\) | ||||
−0.712411 | + | 0.701763i | \(0.752397\pi\) | |||||||
\(432\) | −69439.4 | + | 121802.i | −0.372082 | + | 0.652661i | ||||
\(433\) | 223240. | 1.19068 | 0.595341 | − | 0.803473i | \(-0.297017\pi\) | ||||
0.595341 | + | 0.803473i | \(0.297017\pi\) | |||||||
\(434\) | − | 6299.72i | − | 0.0334458i | ||||||
\(435\) | 64621.0 | − | 370421.i | 0.341503 | − | 1.95757i | ||||
\(436\) | 10695.1 | 0.0562614 | ||||||||
\(437\) | 269.056i | 0.00140890i | ||||||||
\(438\) | −84636.3 | − | 14765.0i | −0.441172 | − | 0.0769637i | ||||
\(439\) | 210890. | 1.09428 | 0.547138 | − | 0.837042i | \(-0.315717\pi\) | ||||
0.547138 | + | 0.837042i | \(0.315717\pi\) | |||||||
\(440\) | − | 326477.i | − | 1.68635i | ||||||
\(441\) | 4303.34 | + | 1548.59i | 0.0221273 | + | 0.00796267i | ||||
\(442\) | 211380. | 1.08198 | ||||||||
\(443\) | − | 94013.2i | − | 0.479051i | −0.970890 | − | 0.239525i | \(-0.923008\pi\) | ||
0.970890 | − | 0.239525i | \(-0.0769918\pi\) | |||||||
\(444\) | −7580.09 | + | 43450.7i | −0.0384511 | + | 0.220410i | ||||
\(445\) | −103897. | −0.524666 | ||||||||
\(446\) | 207999.i | 1.04566i | ||||||||
\(447\) | 276603. | + | 48254.1i | 1.38434 | + | 0.241501i | ||||
\(448\) | 220622. | 1.09924 | ||||||||
\(449\) | 251762.i | 1.24881i | 0.781100 | + | 0.624406i | \(0.214659\pi\) | ||||
−0.781100 | + | 0.624406i | \(0.785341\pi\) | |||||||
\(450\) | −45310.9 | + | 125914.i | −0.223758 | + | 0.621796i | ||||
\(451\) | 283805. | 1.39530 | ||||||||
\(452\) | − | 48974.8i | − | 0.239715i | ||||||
\(453\) | −15540.6 | + | 89082.2i | −0.0757308 | + | 0.434105i | ||||
\(454\) | 66478.4 | 0.322529 | ||||||||
\(455\) | 301019.i | 1.45402i | ||||||||
\(456\) | 847.572 | + | 147.861i | 0.00407612 | + | 0.000711090i | ||||
\(457\) | 202155. | 0.967946 | 0.483973 | − | 0.875083i | \(-0.339193\pi\) | ||||
0.483973 | + | 0.875083i | \(0.339193\pi\) | |||||||
\(458\) | − | 256345.i | − | 1.22206i | ||||||
\(459\) | −199357. | − | 113653.i | −0.946248 | − | 0.539456i | ||||
\(460\) | −21071.9 | −0.0995838 | ||||||||
\(461\) | 180886.i | 0.851143i | 0.904925 | + | 0.425572i | \(0.139927\pi\) | ||||
−0.904925 | + | 0.425572i | \(0.860073\pi\) | |||||||
\(462\) | 38399.1 | − | 220112.i | 0.179903 | − | 1.03124i | ||||
\(463\) | −121417. | −0.566394 | −0.283197 | − | 0.959062i | \(-0.591395\pi\) | ||||
−0.283197 | + | 0.959062i | \(0.591395\pi\) | |||||||
\(464\) | 243541.i | 1.13119i | ||||||||
\(465\) | 10679.2 | + | 1863.02i | 0.0493894 | + | 0.00861611i | ||||
\(466\) | −259132. | −1.19330 | ||||||||
\(467\) | − | 220885.i | − | 1.01282i | −0.862293 | − | 0.506409i | \(-0.830973\pi\) | ||
0.862293 | − | 0.506409i | \(-0.169027\pi\) | |||||||
\(468\) | −47380.7 | − | 17050.3i | −0.216326 | − | 0.0778466i | ||||
\(469\) | 232159. | 1.05546 | ||||||||
\(470\) | − | 109856.i | − | 0.497312i | ||||||
\(471\) | −51360.7 | + | 294411.i | −0.231520 | + | 1.32712i | ||||
\(472\) | 31169.8 | 0.139910 | ||||||||
\(473\) | − | 29347.8i | − | 0.131176i | ||||||
\(474\) | −224759. | − | 39209.8i | −1.00037 | − | 0.174517i | ||||
\(475\) | 644.325 | 0.00285573 | ||||||||
\(476\) | 50287.8i | 0.221947i | ||||||||
\(477\) | −90051.2 | + | 250241.i | −0.395779 | + | 1.09982i | ||||
\(478\) | 99077.2 | 0.433629 | ||||||||
\(479\) | 9680.62i | 0.0421922i | 0.999777 | + | 0.0210961i | \(0.00671559\pi\) | ||||
−0.999777 | + | 0.0210961i | \(0.993284\pi\) | |||||||
\(480\) | −21180.7 | + | 121412.i | −0.0919300 | + | 0.526962i | ||||
\(481\) | 279885. | 1.20973 | ||||||||
\(482\) | 171989.i | 0.740298i | ||||||||
\(483\) | −83102.8 | − | 14497.5i | −0.356223 | − | 0.0621440i | ||||
\(484\) | −19985.3 | −0.0853140 | ||||||||
\(485\) | 430258.i | 1.82913i | ||||||||
\(486\) | −136728. | − | 159969.i | −0.578874 | − | 0.677273i | ||||
\(487\) | 431822. | 1.82074 | 0.910368 | − | 0.413799i | \(-0.135798\pi\) | ||||
0.910368 | + | 0.413799i | \(0.135798\pi\) | |||||||
\(488\) | − | 386917.i | − | 1.62472i | ||||||
\(489\) | −26049.7 | + | 149322.i | −0.108939 | + | 0.624464i | ||||
\(490\) | −6639.04 | −0.0276512 | ||||||||
\(491\) | − | 25060.0i | − | 0.103948i | −0.998648 | − | 0.0519742i | \(-0.983449\pi\) | ||
0.998648 | − | 0.0519742i | \(-0.0165514\pi\) | |||||||
\(492\) | −57703.9 | − | 10066.6i | −0.238383 | − | 0.0415865i | ||||
\(493\) | −398610. | −1.64004 | ||||||||
\(494\) | − | 933.340i | − | 0.00382460i | ||||||
\(495\) | 361776. | + | 130188.i | 1.47649 | + | 0.531324i | ||||
\(496\) | −7021.28 | −0.0285399 | ||||||||
\(497\) | − | 176414.i | − | 0.714201i | ||||||
\(498\) | −54277.9 | + | 311132.i | −0.218859 | + | 1.25455i | ||||
\(499\) | 172187. | 0.691511 | 0.345755 | − | 0.938325i | \(-0.387623\pi\) | ||||
0.345755 | + | 0.938325i | \(0.387623\pi\) | |||||||
\(500\) | − | 17572.4i | − | 0.0702896i | ||||||
\(501\) | −418570. | − | 73020.8i | −1.66760 | − | 0.290918i | ||||
\(502\) | 192222. | 0.762773 | ||||||||
\(503\) | 451517.i | 1.78459i | 0.451455 | + | 0.892294i | \(0.350905\pi\) | ||||
−0.451455 | + | 0.892294i | \(0.649095\pi\) | |||||||
\(504\) | −91339.1 | + | 253820.i | −0.359580 | + | 0.999230i | ||||
\(505\) | −605444. | −2.37406 | ||||||||
\(506\) | − | 99251.6i | − | 0.387647i | ||||||
\(507\) | −10738.5 | + | 61555.5i | −0.0417762 | + | 0.239470i | ||||
\(508\) | −28454.2 | −0.110260 | ||||||||
\(509\) | 171453.i | 0.661773i | 0.943670 | + | 0.330887i | \(0.107348\pi\) | ||||
−0.943670 | + | 0.330887i | \(0.892652\pi\) | |||||||
\(510\) | 328162. | + | 57248.7i | 1.26168 | + | 0.220103i | ||||
\(511\) | −129700. | −0.496703 | ||||||||
\(512\) | − | 291473.i | − | 1.11188i | ||||||
\(513\) | −501.830 | + | 880.250i | −0.00190687 | + | 0.00334481i | ||||
\(514\) | −247452. | −0.936622 | ||||||||
\(515\) | − | 190478.i | − | 0.718176i | ||||||
\(516\) | −1040.97 | + | 5967.06i | −0.00390966 | + | 0.0224110i | ||||
\(517\) | −134416. | −0.502887 | ||||||||
\(518\) | − | 256322.i | − | 0.955270i | ||||||
\(519\) | 395558. | + | 69006.1i | 1.46850 | + | 0.256185i | ||||
\(520\) | 427584. | 1.58130 | ||||||||
\(521\) | − | 497867.i | − | 1.83416i | −0.398701 | − | 0.917081i | \(-0.630539\pi\) | ||
0.398701 | − | 0.917081i | \(-0.369461\pi\) | |||||||
\(522\) | −343947. | − | 123772.i | −1.26226 | − | 0.454235i | ||||
\(523\) | 93268.9 | 0.340984 | 0.170492 | − | 0.985359i | \(-0.445464\pi\) | ||||
0.170492 | + | 0.985359i | \(0.445464\pi\) | |||||||
\(524\) | 106301.i | 0.387146i | ||||||||
\(525\) | −34718.0 | + | 199011.i | −0.125961 | + | 0.722036i | ||||
\(526\) | −343511. | −1.24156 | ||||||||
\(527\) | − | 11491.9i | − | 0.0413781i | ||||||
\(528\) | −245323. | − | 42797.4i | −0.879977 | − | 0.153514i | ||||
\(529\) | 242369. | 0.866095 | ||||||||
\(530\) | − | 386064.i | − | 1.37438i | ||||||
\(531\) | −12429.4 | + | 34539.8i | −0.0440820 | + | 0.122499i | ||||
\(532\) | 222.044 | 0.000784540 | ||||||||
\(533\) | 371697.i | 1.30838i | ||||||||
\(534\) | −17358.0 | + | 99499.5i | −0.0608718 | + | 0.348930i | ||||
\(535\) | −33336.9 | −0.116471 | ||||||||
\(536\) | − | 329772.i | − | 1.14785i | ||||||
\(537\) | −373989. | − | 65243.4i | −1.29691 | − | 0.226250i | ||||
\(538\) | −221579. | −0.765532 | ||||||||
\(539\) | 8123.29i | 0.0279611i | ||||||||
\(540\) | −68939.3 | − | 39302.3i | −0.236417 | − | 0.134782i | ||||
\(541\) | −239967. | −0.819891 | −0.409946 | − | 0.912110i | \(-0.634452\pi\) | ||||
−0.409946 | + | 0.912110i | \(0.634452\pi\) | |||||||
\(542\) | 112114.i | 0.381648i | ||||||||
\(543\) | 93397.7 | − | 535375.i | 0.316764 | − | 1.81576i | ||||
\(544\) | 130652. | 0.441486 | ||||||||
\(545\) | − | 106953.i | − | 0.360079i | ||||||
\(546\) | 288279. | + | 50291.0i | 0.967001 | + | 0.168696i | ||||
\(547\) | −305510. | −1.02106 | −0.510529 | − | 0.859860i | \(-0.670551\pi\) | ||||
−0.510529 | + | 0.859860i | \(0.670551\pi\) | |||||||
\(548\) | 27567.5i | 0.0917985i | ||||||||
\(549\) | 428751. | + | 154289.i | 1.42253 | + | 0.511906i | ||||
\(550\) | −237684. | −0.785731 | ||||||||
\(551\) | 1760.04i | 0.00579723i | ||||||||
\(552\) | −20593.0 | + | 118044.i | −0.0675838 | + | 0.387404i | ||||
\(553\) | −344429. | −1.12629 | ||||||||
\(554\) | 329393.i | 1.07323i | ||||||||
\(555\) | 434514. | + | 75802.2i | 1.41065 | + | 0.246091i | ||||
\(556\) | −22712.1 | −0.0734695 | ||||||||
\(557\) | − | 351391.i | − | 1.13261i | −0.824196 | − | 0.566305i | \(-0.808373\pi\) | ||
0.824196 | − | 0.566305i | \(-0.191627\pi\) | |||||||
\(558\) | 3568.33 | − | 9915.97i | 0.0114603 | − | 0.0318469i | ||||
\(559\) | 38436.5 | 0.123004 | ||||||||
\(560\) | − | 307252.i | − | 0.979758i | ||||||
\(561\) | 70047.4 | − | 401527.i | 0.222570 | − | 1.27582i | ||||
\(562\) | −98119.5 | −0.310658 | ||||||||
\(563\) | − | 234536.i | − | 0.739934i | −0.929045 | − | 0.369967i | \(-0.879369\pi\) | ||
0.929045 | − | 0.369967i | \(-0.120631\pi\) | |||||||
\(564\) | 27329.8 | + | 4767.76i | 0.0859168 | + | 0.0149884i | ||||
\(565\) | −489756. | −1.53420 | ||||||||
\(566\) | − | 334441.i | − | 1.04397i | ||||||
\(567\) | −244841. | − | 202429.i | −0.761583 | − | 0.629662i | ||||
\(568\) | −250588. | −0.776718 | ||||||||
\(569\) | − | 111484.i | − | 0.344340i | −0.985067 | − | 0.172170i | \(-0.944922\pi\) | ||
0.985067 | − | 0.172170i | \(-0.0550778\pi\) | |||||||
\(570\) | 252.779 | − | 1448.98i | 0.000778021 | − | 0.00445978i | ||||
\(571\) | 12151.4 | 0.0372696 | 0.0186348 | − | 0.999826i | \(-0.494068\pi\) | ||||
0.0186348 | + | 0.999826i | \(0.494068\pi\) | |||||||
\(572\) | − | 89439.1i | − | 0.273360i | ||||||
\(573\) | −453870. | − | 79178.9i | −1.38236 | − | 0.241157i | ||||
\(574\) | 340403. | 1.03317 | ||||||||
\(575\) | 89736.9i | 0.271416i | ||||||||
\(576\) | 347266. | + | 124966.i | 1.04669 | + | 0.376658i | ||||
\(577\) | 414975. | 1.24644 | 0.623218 | − | 0.782048i | \(-0.285825\pi\) | ||||
0.623218 | + | 0.782048i | \(0.285825\pi\) | |||||||
\(578\) | − | 55482.0i | − | 0.166072i | ||||||
\(579\) | 34070.6 | − | 195300.i | 0.101630 | − | 0.582565i | ||||
\(580\) | −137843. | −0.409759 | ||||||||
\(581\) | 476790.i | 1.41246i | ||||||||
\(582\) | 412047. | + | 71882.7i | 1.21647 | + | 0.212216i | ||||
\(583\) | −472374. | −1.38979 | ||||||||
\(584\) | 184232.i | 0.540182i | ||||||||
\(585\) | −170506. | + | 473814.i | −0.498226 | + | 1.38451i | ||||
\(586\) | 339946. | 0.989953 | ||||||||
\(587\) | − | 325482.i | − | 0.944606i | −0.881436 | − | 0.472303i | \(-0.843423\pi\) | ||
0.881436 | − | 0.472303i | \(-0.156577\pi\) | |||||||
\(588\) | 288.134 | − | 1651.65i | 0.000833375 | − | 0.00477708i | ||||
\(589\) | −50.7420 | −0.000146264 | ||||||||
\(590\) | − | 53286.9i | − | 0.153079i | ||||||
\(591\) | −203576. | − | 35514.3i | −0.582842 | − | 0.101678i | ||||
\(592\) | −285681. | −0.815150 | ||||||||
\(593\) | − | 208866.i | − | 0.593962i | −0.954883 | − | 0.296981i | \(-0.904020\pi\) | ||
0.954883 | − | 0.296981i | \(-0.0959798\pi\) | |||||||
\(594\) | 185119. | − | 324713.i | 0.524660 | − | 0.920295i | ||||
\(595\) | 502887. | 1.42048 | ||||||||
\(596\) | − | 102931.i | − | 0.289770i | ||||||
\(597\) | −59185.0 | + | 339261.i | −0.166059 | + | 0.951887i | ||||
\(598\) | 129989. | 0.363499 | ||||||||
\(599\) | − | 199894.i | − | 0.557116i | −0.960419 | − | 0.278558i | \(-0.910144\pi\) | ||
0.960419 | − | 0.278558i | \(-0.0898565\pi\) | |||||||
\(600\) | 282686. | + | 49315.3i | 0.785239 | + | 0.136987i | ||||
\(601\) | 110370. | 0.305565 | 0.152782 | − | 0.988260i | \(-0.451177\pi\) | ||||
0.152782 | + | 0.988260i | \(0.451177\pi\) | |||||||
\(602\) | − | 35200.5i | − | 0.0971306i | ||||||
\(603\) | 365427. | + | 131501.i | 1.00500 | + | 0.361656i | ||||
\(604\) | 33149.7 | 0.0908669 | ||||||||
\(605\) | 199856.i | 0.546018i | ||||||||
\(606\) | −101151. | + | 579818.i | −0.275438 | + | 1.57887i | ||||
\(607\) | −671627. | −1.82285 | −0.911425 | − | 0.411466i | \(-0.865017\pi\) | ||||
−0.911425 | + | 0.411466i | \(0.865017\pi\) | |||||||
\(608\) | − | 576.886i | − | 0.00156057i | ||||||
\(609\) | −543621. | − | 94836.1i | −1.46575 | − | 0.255705i | ||||
\(610\) | −661462. | −1.77764 | ||||||||
\(611\) | − | 176043.i | − | 0.471560i | ||||||
\(612\) | −28484.4 | + | 79154.7i | −0.0760509 | + | 0.211336i | ||||
\(613\) | 400715. | 1.06639 | 0.533193 | − | 0.845993i | \(-0.320992\pi\) | ||||
0.533193 | + | 0.845993i | \(0.320992\pi\) | |||||||
\(614\) | − | 122132.i | − | 0.323961i | ||||||
\(615\) | −100668. | + | 577048.i | −0.266158 | + | 1.52567i | ||||
\(616\) | −479129. | −1.26267 | ||||||||
\(617\) | 353491.i | 0.928556i | 0.885690 | + | 0.464278i | \(0.153686\pi\) | ||||
−0.885690 | + | 0.464278i | \(0.846314\pi\) | |||||||
\(618\) | −182416. | − | 31823.0i | −0.477624 | − | 0.0833229i | ||||
\(619\) | 106626. | 0.278279 | 0.139139 | − | 0.990273i | \(-0.455566\pi\) | ||||
0.139139 | + | 0.990273i | \(0.455566\pi\) | |||||||
\(620\) | − | 3974.00i | − | 0.0103382i | ||||||
\(621\) | −122595. | − | 69891.3i | −0.317899 | − | 0.181234i | ||||
\(622\) | −489876. | −1.26621 | ||||||||
\(623\) | 152477.i | 0.392850i | ||||||||
\(624\) | 56051.3 | − | 321298.i | 0.143952 | − | 0.825161i | ||||
\(625\) | −465459. | −1.19157 | ||||||||
\(626\) | 527022.i | 1.34487i | ||||||||
\(627\) | −1772.92 | − | 309.291i | −0.00450977 | − | 0.000786742i | ||||
\(628\) | 109558. | 0.277794 | ||||||||
\(629\) | − | 467580.i | − | 1.18183i | ||||||
\(630\) | 433924. | + | 156151.i | 1.09328 | + | 0.393425i | ||||
\(631\) | −699848. | −1.75770 | −0.878851 | − | 0.477097i | \(-0.841689\pi\) | ||||
−0.878851 | + | 0.477097i | \(0.841689\pi\) | |||||||
\(632\) | 489245.i | 1.22488i | ||||||||
\(633\) | −53528.3 | + | 306836.i | −0.133591 | + | 0.765770i | ||||
\(634\) | −376429. | −0.936492 | ||||||||
\(635\) | 284547.i | 0.705678i | ||||||||
\(636\) | 96044.1 | + | 16755.2i | 0.237441 | + | 0.0414223i | ||||
\(637\) | −10639.0 | −0.0262193 | ||||||||
\(638\) | − | 649258.i | − | 1.59506i | ||||||
\(639\) | 99925.7 | − | 277681.i | 0.244723 | − | 0.680057i | ||||
\(640\) | −316646. | −0.773061 | ||||||||
\(641\) | 300253.i | 0.730754i | 0.930860 | + | 0.365377i | \(0.119060\pi\) | ||||
−0.930860 | + | 0.365377i | \(0.880940\pi\) | |||||||
\(642\) | −5569.57 | + | 31925.9i | −0.0135130 | + | 0.0774593i | ||||
\(643\) | 466427. | 1.12814 | 0.564069 | − | 0.825728i | \(-0.309235\pi\) | ||||
0.564069 | + | 0.825728i | \(0.309235\pi\) | |||||||
\(644\) | 30924.6i | 0.0745646i | ||||||||
\(645\) | 59671.6 | + | 10409.9i | 0.143433 | + | 0.0250222i | ||||
\(646\) | −1559.25 | −0.00373638 | ||||||||
\(647\) | − | 107628.i | − | 0.257109i | −0.991702 | − | 0.128554i | \(-0.958966\pi\) | ||
0.991702 | − | 0.128554i | \(-0.0410336\pi\) | |||||||
\(648\) | −287541. | + | 347785.i | −0.684779 | + | 0.828248i | ||||
\(649\) | −65199.9 | −0.154795 | ||||||||
\(650\) | − | 311292.i | − | 0.736785i | ||||||
\(651\) | 2734.12 | − | 15672.6i | 0.00645142 | − | 0.0369809i | ||||
\(652\) | 55566.6 | 0.130713 | ||||||||
\(653\) | 509956.i | 1.19593i | 0.801522 | + | 0.597966i | \(0.204024\pi\) | ||||
−0.801522 | + | 0.597966i | \(0.795976\pi\) | |||||||
\(654\) | −102426. | − | 17868.4i | −0.239471 | − | 0.0417764i | ||||
\(655\) | 1.06303e6 | 2.47778 | ||||||||
\(656\) | − | 379393.i | − | 0.881620i | ||||||
\(657\) | −204152. | − | 73465.4i | −0.472957 | − | 0.170197i | ||||
\(658\) | −161222. | −0.372369 | ||||||||
\(659\) | − | 547617.i | − | 1.26097i | −0.776200 | − | 0.630486i | \(-0.782855\pi\) | ||
0.776200 | − | 0.630486i | \(-0.217145\pi\) | |||||||
\(660\) | 24223.1 | − | 138852.i | 0.0556085 | − | 0.318760i | ||||
\(661\) | 341882. | 0.782480 | 0.391240 | − | 0.920289i | \(-0.372046\pi\) | ||||
0.391240 | + | 0.920289i | \(0.372046\pi\) | |||||||
\(662\) | − | 508551.i | − | 1.16043i | ||||||
\(663\) | 525876. | + | 91740.4i | 1.19634 | + | 0.208705i | ||||
\(664\) | 677258. | 1.53609 | ||||||||
\(665\) | − | 2220.47i | − | 0.00502114i | ||||||
\(666\) | 145188. | − | 403459.i | 0.327326 | − | 0.909601i | ||||
\(667\) | −245126. | −0.550983 | ||||||||
\(668\) | 155761.i | 0.349064i | ||||||||
\(669\) | −90272.7 | + | 517462.i | −0.201699 | + | 1.15618i | ||||
\(670\) | −563768. | −1.25589 | ||||||||
\(671\) | 809340.i | 1.79757i | ||||||||
\(672\) | 178181. | + | 31084.2i | 0.394570 | + | 0.0688338i | ||||
\(673\) | −318066. | −0.702244 | −0.351122 | − | 0.936330i | \(-0.614200\pi\) | ||||
−0.351122 | + | 0.936330i | \(0.614200\pi\) | |||||||
\(674\) | − | 357536.i | − | 0.787046i | ||||||
\(675\) | −167373. | + | 293585.i | −0.367347 | + | 0.644356i | ||||
\(676\) | 22906.3 | 0.0501259 | ||||||||
\(677\) | − | 793472.i | − | 1.73123i | −0.500711 | − | 0.865615i | \(-0.666928\pi\) | ||
0.500711 | − | 0.865615i | \(-0.333072\pi\) | |||||||
\(678\) | −81823.0 | + | 469027.i | −0.177998 | + | 1.02032i | ||||
\(679\) | 631435. | 1.36959 | ||||||||
\(680\) | − | 714327.i | − | 1.54482i | ||||||
\(681\) | 165386. | + | 28852.1i | 0.356619 | + | 0.0622132i | ||||
\(682\) | 18718.1 | 0.0402432 | ||||||||
\(683\) | 208408.i | 0.446759i | 0.974732 | + | 0.223379i | \(0.0717089\pi\) | ||||
−0.974732 | + | 0.223379i | \(0.928291\pi\) | |||||||
\(684\) | 349.504 | + | 125.772i | 0.000747034 | + | 0.000268825i | ||||
\(685\) | 275679. | 0.587520 | ||||||||
\(686\) | 424062.i | 0.901117i | ||||||||
\(687\) | 111255. | − | 637740.i | 0.235726 | − | 1.35123i | ||||
\(688\) | −39232.4 | −0.0828834 | ||||||||
\(689\) | − | 618663.i | − | 1.30321i | ||||||
\(690\) | 201804. | + | 35205.2i | 0.423869 | + | 0.0739451i | ||||
\(691\) | 543662. | 1.13860 | 0.569302 | − | 0.822128i | \(-0.307213\pi\) | ||||
0.569302 | + | 0.822128i | \(0.307213\pi\) | |||||||
\(692\) | − | 147197.i | − | 0.307388i | ||||||
\(693\) | 191060. | − | 530933.i | 0.397836 | − | 1.10554i | ||||
\(694\) | 646720. | 1.34276 | ||||||||
\(695\) | 227124.i | 0.470212i | ||||||||
\(696\) | −134710. | + | 772187.i | −0.278088 | + | 1.59406i | ||||
\(697\) | 620961. | 1.27820 | ||||||||
\(698\) | 533614.i | 1.09526i | ||||||||
\(699\) | −644673. | − | 112465.i | −1.31943 | − | 0.230178i | ||||
\(700\) | 74057.0 | 0.151137 | ||||||||
\(701\) | 72520.4i | 0.147579i | 0.997274 | + | 0.0737894i | \(0.0235093\pi\) | ||||
−0.997274 | + | 0.0737894i | \(0.976491\pi\) | |||||||
\(702\) | 425274. | + | 242448.i | 0.862967 | + | 0.491978i | ||||
\(703\) | −2064.58 | −0.00417754 | ||||||||
\(704\) | 655524.i | 1.32264i | ||||||||
\(705\) | 47678.3 | − | 273302.i | 0.0959274 | − | 0.549876i | ||||
\(706\) | 104395. | 0.209445 | ||||||||
\(707\) | 888534.i | 1.77761i | ||||||||
\(708\) | 13256.6 | + | 2312.65i | 0.0264463 | + | 0.00461363i | ||||
\(709\) | 112277. | 0.223356 | 0.111678 | − | 0.993744i | \(-0.464378\pi\) | ||||
0.111678 | + | 0.993744i | \(0.464378\pi\) | |||||||
\(710\) | 428397.i | 0.849826i | ||||||||
\(711\) | −542142. | − | 195094.i | −1.07244 | − | 0.385926i | ||||
\(712\) | 216586. | 0.427238 | ||||||||
\(713\) | − | 7066.97i | − | 0.0139013i | ||||||
\(714\) | 84016.7 | − | 481602.i | 0.164805 | − | 0.944695i | ||||
\(715\) | −894406. | −1.74953 | ||||||||
\(716\) | 139171.i | 0.271470i | ||||||||
\(717\) | 246486. | + | 43000.2i | 0.479462 | + | 0.0836434i | ||||
\(718\) | 35790.4 | 0.0694254 | ||||||||
\(719\) | 315016.i | 0.609361i | 0.952455 | + | 0.304681i | \(0.0985498\pi\) | ||||
−0.952455 | + | 0.304681i | \(0.901450\pi\) | |||||||
\(720\) | 174036. | − | 483625.i | 0.335717 | − | 0.932918i | ||||
\(721\) | −279541. | −0.537743 | ||||||||
\(722\) | − | 464432.i | − | 0.890938i | ||||||
\(723\) | −74644.3 | + | 427877.i | −0.142797 | + | 0.818545i | ||||
\(724\) | −199226. | −0.380076 | ||||||||
\(725\) | 587018.i | 1.11680i | ||||||||
\(726\) | 191397. | + | 33389.8i | 0.363130 | + | 0.0633491i | ||||
\(727\) | −886179. | −1.67669 | −0.838345 | − | 0.545141i | \(-0.816476\pi\) | ||||
−0.838345 | + | 0.545141i | \(0.816476\pi\) | |||||||
\(728\) | − | 627511.i | − | 1.18402i | ||||||
\(729\) | −270726. | − | 457315.i | −0.509418 | − | 0.860519i | ||||
\(730\) | 314958. | 0.591026 | ||||||||
\(731\) | − | 64212.5i | − | 0.120167i | ||||||
\(732\) | 28707.4 | − | 164557.i | 0.0535762 | − | 0.307110i | ||||
\(733\) | 530184. | 0.986775 | 0.493388 | − | 0.869810i | \(-0.335758\pi\) | ||||
0.493388 | + | 0.869810i | \(0.335758\pi\) | |||||||
\(734\) | 498220.i | 0.924760i | ||||||||
\(735\) | −16516.7 | − | 2881.39i | −0.0305738 | − | 0.00533368i | ||||
\(736\) | 80344.5 | 0.148320 | ||||||||
\(737\) | 689806.i | 1.26996i | ||||||||
\(738\) | 535806. | + | 192814.i | 0.983773 | + | 0.354018i | ||||
\(739\) | 703143. | 1.28752 | 0.643761 | − | 0.765226i | \(-0.277373\pi\) | ||||
0.643761 | + | 0.765226i | \(0.277373\pi\) | |||||||
\(740\) | − | 161694.i | − | 0.295277i | ||||||
\(741\) | 405.076 | − | 2321.98i | 0.000737734 | − | 0.00422885i | ||||
\(742\) | −566577. | −1.02909 | ||||||||
\(743\) | − | 201327.i | − | 0.364690i | −0.983235 | − | 0.182345i | \(-0.941631\pi\) | ||
0.983235 | − | 0.182345i | \(-0.0583688\pi\) | |||||||
\(744\) | −22262.1 | − | 3883.69i | −0.0402180 | − | 0.00701614i | ||||
\(745\) | −1.02932e6 | −1.85456 | ||||||||
\(746\) | − | 430001.i | − | 0.772666i | ||||||
\(747\) | −270067. | + | 750483.i | −0.483983 | + | 1.34493i | ||||
\(748\) | −149418. | −0.267055 | ||||||||
\(749\) | 48924.4i | 0.0872092i | ||||||||
\(750\) | −29358.5 | + | 168289.i | −0.0521929 | + | 0.299181i | ||||
\(751\) | 362775. | 0.643217 | 0.321609 | − | 0.946873i | \(-0.395776\pi\) | ||||
0.321609 | + | 0.946873i | \(0.395776\pi\) | |||||||
\(752\) | 179688.i | 0.317749i | ||||||||
\(753\) | 478213. | + | 83425.6i | 0.843396 | + | 0.147133i | ||||
\(754\) | 850327. | 1.49570 | ||||||||
\(755\) | − | 331503.i | − | 0.581558i | ||||||
\(756\) | −57679.0 | + | 101174.i | −0.100919 | + | 0.177021i | ||||
\(757\) | 494359. | 0.862682 | 0.431341 | − | 0.902189i | \(-0.358041\pi\) | ||||
0.431341 | + | 0.902189i | \(0.358041\pi\) | |||||||
\(758\) | 573704.i | 0.998503i | ||||||||
\(759\) | 43075.9 | − | 246920.i | 0.0747740 | − | 0.428620i | ||||
\(760\) | −3154.08 | −0.00546066 | ||||||||
\(761\) | − | 1.04816e6i | − | 1.80992i | −0.425498 | − | 0.904959i | \(-0.639901\pi\) | ||
0.425498 | − | 0.904959i | \(-0.360099\pi\) | |||||||
\(762\) | 272504. | + | 47539.0i | 0.469313 | + | 0.0818729i | ||||
\(763\) | −156961. | −0.269614 | ||||||||
\(764\) | 168896.i | 0.289357i | ||||||||
\(765\) | 791560. | + | 284849.i | 1.35257 | + | 0.486734i | ||||
\(766\) | 954386. | 1.62655 | ||||||||
\(767\) | − | 85391.6i | − | 0.145153i | ||||||
\(768\) | 59856.9 | − | 343113.i | 0.101483 | − | 0.581720i | ||||
\(769\) | −145986. | −0.246865 | −0.123432 | − | 0.992353i | \(-0.539390\pi\) | ||||
−0.123432 | + | 0.992353i | \(0.539390\pi\) | |||||||
\(770\) | 819105.i | 1.38152i | ||||||||
\(771\) | −615615. | − | 107396.i | −1.03562 | − | 0.180667i | ||||
\(772\) | −72675.9 | −0.121943 | ||||||||
\(773\) | 929338.i | 1.55530i | 0.628696 | + | 0.777651i | \(0.283589\pi\) | ||||
−0.628696 | + | 0.777651i | \(0.716411\pi\) | |||||||
\(774\) | 19938.5 | − | 55406.8i | 0.0332822 | − | 0.0924871i | ||||
\(775\) | −16923.7 | −0.0281768 | ||||||||
\(776\) | − | 896924.i | − | 1.48947i | ||||||
\(777\) | 111245. | − | 637682.i | 0.184264 | − | 1.05624i | ||||
\(778\) | −9611.72 | −0.0158797 | ||||||||
\(779\) | − | 2741.82i | − | 0.00451819i | ||||||
\(780\) | 181853. | + | 31724.7i | 0.298903 | + | 0.0521445i | ||||
\(781\) | 524171. | 0.859352 | ||||||||
\(782\) | − | 217161.i | − | 0.355114i | ||||||
\(783\) | −801959. | − | 457197.i | −1.30806 | − | 0.745726i | ||||
\(784\) | 10859.3 | 0.0176672 | ||||||||
\(785\) | − | 1.09559e6i | − | 1.77791i | ||||||
\(786\) | 177599. | − | 1.01804e6i | 0.287472 | − | 1.64785i | ||||
\(787\) | 1.09920e6 | 1.77470 | 0.887352 | − | 0.461092i | \(-0.152542\pi\) | ||||
0.887352 | + | 0.461092i | \(0.152542\pi\) | |||||||
\(788\) | 75755.6i | 0.122001i | ||||||||
\(789\) | −854592. | − | 149086.i | −1.37279 | − | 0.239487i | ||||
\(790\) | 836398. | 1.34017 | ||||||||
\(791\) | 718753.i | 1.14875i | ||||||||
\(792\) | −754166. | − | 271392.i | −1.20231 | − | 0.432660i | ||||
\(793\) | −1.05998e6 | −1.68560 | ||||||||
\(794\) | − | 124376.i | − | 0.197286i | ||||||
\(795\) | 167554. | − | 960456.i | 0.265107 | − | 1.51965i | ||||
\(796\) | 126248. | 0.199249 | ||||||||
\(797\) | 871729.i | 1.37235i | 0.727437 | + | 0.686175i | \(0.240711\pi\) | ||||
−0.727437 | + | 0.686175i | \(0.759289\pi\) | |||||||
\(798\) | −2126.49 | − | 370.972i | −0.00333932 | − | 0.000582553i | ||||
\(799\) | −294100. | −0.460683 | ||||||||
\(800\) | − | 192406.i | − | 0.300634i | ||||||
\(801\) | −86366.9 | + | 240003.i | −0.134612 | + | 0.374069i | ||||
\(802\) | 217769. | 0.338569 | ||||||||
\(803\) | − | 385371.i | − | 0.597651i | ||||||
\(804\) | 24467.5 | − | 140253.i | 0.0378510 | − | 0.216970i | ||||
\(805\) | 309251. | 0.477222 | ||||||||
\(806\) | 24514.9i | 0.0377363i | ||||||||
\(807\) | −551248. | − | 96166.6i | −0.846447 | − | 0.147665i | ||||
\(808\) | 1.26212e6 | 1.93321 | ||||||||
\(809\) | 631887.i | 0.965478i | 0.875764 | + | 0.482739i | \(0.160358\pi\) | ||||
−0.875764 | + | 0.482739i | \(0.839642\pi\) | |||||||
\(810\) | 594562. | + | 491572.i | 0.906207 | + | 0.749234i | ||||
\(811\) | −1.25367e6 | −1.90608 | −0.953042 | − | 0.302839i | \(-0.902065\pi\) | ||||
−0.953042 | + | 0.302839i | \(0.902065\pi\) | |||||||
\(812\) | 202295.i | 0.306812i | ||||||||
\(813\) | −48658.4 | + | 278920.i | −0.0736168 | + | 0.421987i | ||||
\(814\) | 761598. | 1.14942 | ||||||||
\(815\) | − | 555675.i | − | 0.836576i | ||||||
\(816\) | −536764. | − | 93640.0i | −0.806126 | − | 0.140631i | ||||
\(817\) | −283.528 | −0.000424767 | ||||||||
\(818\) | 873783.i | 1.30586i | ||||||||
\(819\) | 695358. | + | 250230.i | 1.03667 | + | 0.373053i | ||||
\(820\) | 214734. | 0.319355 | ||||||||
\(821\) | − | 891043.i | − | 1.32194i | −0.750411 | − | 0.660971i | \(-0.770145\pi\) | ||
0.750411 | − | 0.660971i | \(-0.229855\pi\) | |||||||
\(822\) | 46057.4 | − | 264011.i | 0.0681641 | − | 0.390731i | ||||
\(823\) | −577380. | −0.852436 | −0.426218 | − | 0.904620i | \(-0.640154\pi\) | ||||
−0.426218 | + | 0.904620i | \(0.640154\pi\) | |||||||
\(824\) | 397075.i | 0.584814i | ||||||||
\(825\) | −591313. | − | 103156.i | −0.868780 | − | 0.151561i | ||||
\(826\) | −78202.5 | −0.114620 | ||||||||
\(827\) | − | 978522.i | − | 1.43074i | −0.698747 | − | 0.715368i | \(-0.746259\pi\) | ||
0.698747 | − | 0.715368i | \(-0.253741\pi\) | |||||||
\(828\) | −17516.6 | + | 48676.4i | −0.0255498 | + | 0.0709999i | ||||
\(829\) | −1.22664e6 | −1.78488 | −0.892439 | − | 0.451169i | \(-0.851007\pi\) | ||||
−0.892439 | + | 0.451169i | \(0.851007\pi\) | |||||||
\(830\) | − | 1.15782e6i | − | 1.68068i | ||||||
\(831\) | −142959. | + | 819469.i | −0.207018 | + | 1.18667i | ||||
\(832\) | −858533. | −1.24025 | ||||||||
\(833\) | 17773.6i | 0.0256145i | ||||||||
\(834\) | 217511. | + | 37945.4i | 0.312715 | + | 0.0545541i | ||||
\(835\) | 1.55763e6 | 2.23404 | ||||||||
\(836\) | 659.749i | 0.000943987i | ||||||||
\(837\) | 13181.0 | − | 23120.4i | 0.0188146 | − | 0.0330024i | ||||
\(838\) | −318436. | −0.453455 | ||||||||
\(839\) | 221493.i | 0.314657i | 0.987546 | + | 0.157328i | \(0.0502881\pi\) | ||||
−0.987546 | + | 0.157328i | \(0.949712\pi\) | |||||||
\(840\) | 169951. | − | 974193.i | 0.240860 | − | 1.38066i | ||||
\(841\) | −896222. | −1.26714 | ||||||||
\(842\) | − | 490434.i | − | 0.691762i | ||||||
\(843\) | −244103. | − | 42584.5i | −0.343494 | − | 0.0599234i | ||||
\(844\) | 114181. | 0.160291 | ||||||||
\(845\) | − | 229067.i | − | 0.320811i | ||||||
\(846\) | −253769. | − | 91320.7i | −0.354567 | − | 0.127593i | ||||
\(847\) | 293304. | 0.408838 | ||||||||
\(848\) | 631473.i | 0.878138i | ||||||||
\(849\) | 145150. | − | 832028.i | 0.201373 | − | 1.15431i | ||||
\(850\) | −520048. | −0.719790 | ||||||||
\(851\) | − | 287540.i | − | 0.397044i | ||||||
\(852\) | −106576. | − | 18592.4i | −0.146818 | − | 0.0256128i | ||||
\(853\) | 1.07567e6 | 1.47836 | 0.739179 | − | 0.673509i | \(-0.235214\pi\) | ||||
0.739179 | + | 0.673509i | \(0.235214\pi\) | |||||||
\(854\) | 970744.i | 1.33103i | ||||||||
\(855\) | 1257.74 | − | 3495.10i | 0.00172051 | − | 0.00478109i | ||||
\(856\) | 69494.9 | 0.0948430 | ||||||||
\(857\) | − | 967907.i | − | 1.31787i | −0.752200 | − | 0.658934i | \(-0.771007\pi\) | ||
0.752200 | − | 0.658934i | \(-0.228993\pi\) | |||||||
\(858\) | −149427. | + | 856550.i | −0.202981 | + | 1.16353i | ||||
\(859\) | 476618. | 0.645928 | 0.322964 | − | 0.946411i | \(-0.395321\pi\) | ||||
0.322964 | + | 0.946411i | \(0.395321\pi\) | |||||||
\(860\) | − | 22205.3i | − | 0.0300234i | ||||||
\(861\) | 846861. | + | 147737.i | 1.14237 | + | 0.199289i | ||||
\(862\) | −929156. | −1.25047 | ||||||||
\(863\) | − | 682724.i | − | 0.916692i | −0.888774 | − | 0.458346i | \(-0.848442\pi\) | ||
0.888774 | − | 0.458346i | \(-0.151558\pi\) | |||||||
\(864\) | 262856. | + | 149854.i | 0.352120 | + | 0.200744i | ||||
\(865\) | −1.47199e6 | −1.96731 | ||||||||
\(866\) | 795584.i | 1.06084i | ||||||||
\(867\) | 24079.6 | − | 138029.i | 0.0320340 | − | 0.183625i | ||||
\(868\) | −5832.15 | −0.00774086 | ||||||||
\(869\) | − | 1.02339e6i | − | 1.35519i | ||||||
\(870\) | 1.32011e6 | + | 230297.i | 1.74410 | + | 0.304263i | ||||
\(871\) | −903431. | −1.19085 | ||||||||
\(872\) | 222955.i | 0.293214i | ||||||||
\(873\) | 993900. | + | 357662.i | 1.30411 | + | 0.469294i | ||||
\(874\) | −958.865 | −0.00125526 | ||||||||
\(875\) | 257892.i | 0.336839i | ||||||||
\(876\) | −13669.2 | + | 78354.5i | −0.0178129 | + | 0.102107i | ||||
\(877\) | −716340. | −0.931365 | −0.465683 | − | 0.884952i | \(-0.654191\pi\) | ||||
−0.465683 | + | 0.884952i | \(0.654191\pi\) | |||||||
\(878\) | 751571.i | 0.974947i | ||||||||
\(879\) | 845724. | + | 147539.i | 1.09459 | + | 0.190954i | ||||
\(880\) | 912925. | 1.17888 | ||||||||
\(881\) | − | 304540.i | − | 0.392367i | −0.980567 | − | 0.196183i | \(-0.937145\pi\) | ||
0.980567 | − | 0.196183i | \(-0.0628548\pi\) | |||||||
\(882\) | −5518.87 | + | 15336.3i | −0.00709435 | + | 0.0197143i | ||||
\(883\) | 408396. | 0.523794 | 0.261897 | − | 0.965096i | \(-0.415652\pi\) | ||||
0.261897 | + | 0.965096i | \(0.415652\pi\) | |||||||
\(884\) | − | 195691.i | − | 0.250419i | ||||||
\(885\) | 23126.9 | − | 132568.i | 0.0295277 | − | 0.169259i | ||||
\(886\) | 335045. | 0.426811 | ||||||||
\(887\) | 657288.i | 0.835427i | 0.908579 | + | 0.417713i | \(0.137168\pi\) | ||||
−0.908579 | + | 0.417713i | \(0.862832\pi\) | |||||||
\(888\) | −905797. | − | 158019.i | −1.14870 | − | 0.200393i | ||||
\(889\) | 417594. | 0.528385 | ||||||||
\(890\) | − | 370269.i | − | 0.467452i | ||||||
\(891\) | 601470. | − | 727485.i | 0.757633 | − | 0.916365i | ||||
\(892\) | 192561. | 0.242013 | ||||||||
\(893\) | 1298.59i | 0.00162843i | ||||||||
\(894\) | −171968. | + | 985758.i | −0.215166 | + | 1.23338i | ||||
\(895\) | 1.39173e6 | 1.73744 | ||||||||
\(896\) | 464701.i | 0.578839i | ||||||||
\(897\) | 323389. | + | 56416.0i | 0.401920 | + | 0.0701161i | ||||
\(898\) | −897229. | −1.11263 | ||||||||
\(899\) | − | 46228.9i | − | 0.0571998i | ||||||
\(900\) | 116568. | + | 41947.9i | 0.143911 | + | 0.0517876i | ||||
\(901\) | −1.03355e6 | −1.27315 | ||||||||
\(902\) | 1.01143e6i | 1.24314i | ||||||||
\(903\) | 15277.3 | − | 87572.5i | 0.0187357 | − | 0.107397i | ||||
\(904\) | 1.02096e6 | 1.24931 | ||||||||
\(905\) | 1.99230e6i | 2.43252i | ||||||||
\(906\) | −317472. | − | 55383.8i | −0.386766 | − | 0.0674724i | ||||
\(907\) | 1.35437e6 | 1.64636 | 0.823179 | − | 0.567783i | \(-0.192199\pi\) | ||||
0.823179 | + | 0.567783i | \(0.192199\pi\) | |||||||
\(908\) | − | 61544.3i | − | 0.0746477i | ||||||
\(909\) | −503290. | + | 1.39858e6i | −0.609103 | + | 1.69262i | ||||
\(910\) | −1.07277e6 | −1.29546 | ||||||||
\(911\) | 29604.9i | 0.0356719i | 0.999841 | + | 0.0178360i | \(0.00567766\pi\) | ||||
−0.999841 | + | 0.0178360i | \(0.994322\pi\) | |||||||
\(912\) | −413.463 | + | 2370.06i | −0.000497104 | + | 0.00284950i | ||||
\(913\) | −1.41667e6 | −1.69952 | ||||||||
\(914\) | 720439.i | 0.862393i | ||||||||
\(915\) | −1.64560e6 | − | 287079.i | −1.96554 | − | 0.342893i | ||||
\(916\) | −237319. | −0.282840 | ||||||||
\(917\) | − | 1.56007e6i | − | 1.85527i | ||||||
\(918\) | 405038. | − | 710468.i | 0.480629 | − | 0.843061i | ||||
\(919\) | −792378. | −0.938213 | −0.469106 | − | 0.883142i | \(-0.655424\pi\) | ||||
−0.469106 | + | 0.883142i | \(0.655424\pi\) | |||||||
\(920\) | − | 439277.i | − | 0.518995i | ||||||
\(921\) | 53006.2 | − | 303843.i | 0.0624895 | − | 0.358203i | ||||
\(922\) | −644642. | −0.758327 | ||||||||
\(923\) | 686502.i | 0.805821i | ||||||||
\(924\) | −203775. | − | 35549.1i | −0.238675 | − | 0.0416375i | ||||
\(925\) | −688588. | −0.804778 | ||||||||
\(926\) | − | 432708.i | − | 0.504630i | ||||||
\(927\) | −440007. | − | 158340.i | −0.512035 | − | 0.184260i | ||||
\(928\) | 525577. | 0.610295 | ||||||||
\(929\) | 678039.i | 0.785639i | 0.919616 | + | 0.392820i | \(0.128500\pi\) | ||||
−0.919616 | + | 0.392820i | \(0.871500\pi\) | |||||||
\(930\) | −6639.44 | + | 38058.7i | −0.00767654 | + | 0.0440035i | ||||
\(931\) | 78.4787 | 9.05425e−5 | ||||||||
\(932\) | 239899.i | 0.276183i | ||||||||
\(933\) | −1.21872e6 | − | 212610.i | −1.40004 | − | 0.244242i | ||||
\(934\) | 787189. | 0.902372 | ||||||||
\(935\) | 1.49421e6i | 1.70918i | ||||||||
\(936\) | 355439. | − | 987723.i | 0.405708 | − | 1.12741i | ||||
\(937\) | −1.48025e6 | −1.68599 | −0.842996 | − | 0.537920i | \(-0.819210\pi\) | ||||
−0.842996 | + | 0.537920i | \(0.819210\pi\) | |||||||
\(938\) | 827371.i | 0.940361i | ||||||||
\(939\) | −228731. | + | 1.31114e6i | −0.259415 | + | 1.48702i | ||||
\(940\) | −101703. | −0.115100 | ||||||||
\(941\) | 149475.i | 0.168807i | 0.996432 | + | 0.0844034i | \(0.0268984\pi\) | ||||
−0.996432 | + | 0.0844034i | \(0.973102\pi\) | |||||||
\(942\) | −1.04922e6 | − | 183040.i | −1.18240 | − | 0.206273i | ||||
\(943\) | 381862. | 0.429420 | ||||||||
\(944\) | 87159.7i | 0.0978074i | ||||||||
\(945\) | 1.01175e6 | + | 576800.i | 1.13295 | + | 0.645894i | ||||
\(946\) | 104590. | 0.116871 | ||||||||
\(947\) | 533086.i | 0.594425i | 0.954811 | + | 0.297213i | \(0.0960570\pi\) | ||||
−0.954811 | + | 0.297213i | \(0.903943\pi\) | |||||||
\(948\) | −36299.6 | + | 208077.i | −0.0403911 | + | 0.231530i | ||||
\(949\) | 504717. | 0.560422 | ||||||||
\(950\) | 2296.25i | 0.00254432i | ||||||||
\(951\) | −936486. | − | 163373.i | −1.03548 | − | 0.180642i | ||||
\(952\) | −1.04833e6 | −1.15671 | ||||||||
\(953\) | − | 551784.i | − | 0.607552i | −0.952743 | − | 0.303776i | \(-0.901753\pi\) | ||
0.952743 | − | 0.303776i | \(-0.0982475\pi\) | |||||||
\(954\) | −891812. | − | 320925.i | −0.979888 | − | 0.352620i | ||||
\(955\) | 1.68899e6 | 1.85191 | ||||||||
\(956\) | − | 91723.6i | − | 0.100361i | ||||||
\(957\) | 281782. | − | 1.61524e6i | 0.307674 | − | 1.76365i | ||||
\(958\) | −34499.8 | −0.0375912 | ||||||||
\(959\) | − | 404580.i | − | 0.439913i | ||||||
\(960\) | −1.33285e6 | − | 232519.i | −1.44623 | − | 0.252299i | ||||
\(961\) | −922188. | −0.998557 | ||||||||
\(962\) | 997457.i | 1.07781i | ||||||||
\(963\) | −27712.1 | + | 77008.7i | −0.0298825 | + | 0.0830400i | ||||
\(964\) | 159224. | 0.171338 | ||||||||
\(965\) | 726771.i | 0.780446i | ||||||||
\(966\) | 51666.3 | − | 296162.i | 0.0553673 | − | 0.317377i | ||||
\(967\) | 436427. | 0.466723 | 0.233361 | − | 0.972390i | \(-0.425027\pi\) | ||||
0.233361 | + | 0.972390i | \(0.425027\pi\) | |||||||
\(968\) | − | 416625.i | − | 0.444625i | ||||||
\(969\) | −3879.13 | − | 676.725i | −0.00413130 | − | 0.000720716i | ||||
\(970\) | −1.53335e6 | −1.62967 | ||||||||
\(971\) | − | 61610.5i | − | 0.0653456i | −0.999466 | − | 0.0326728i | \(-0.989598\pi\) | ||
0.999466 | − | 0.0326728i | \(-0.0104019\pi\) | |||||||
\(972\) | −148096. | + | 126580.i | −0.156751 | + | 0.133977i | ||||
\(973\) | 333322. | 0.352077 | ||||||||
\(974\) | 1.53893e6i | 1.62219i | ||||||||
\(975\) | 135103. | − | 774437.i | 0.142120 | − | 0.814661i | ||||
\(976\) | 1.08193e6 | 1.13580 | ||||||||
\(977\) | 432087.i | 0.452671i | 0.974049 | + | 0.226335i | \(0.0726745\pi\) | ||||
−0.974049 | + | 0.226335i | \(0.927325\pi\) | |||||||
\(978\) | −532156. | − | 92836.0i | −0.556367 | − | 0.0970597i | ||||
\(979\) | −453047. | −0.472692 | ||||||||
\(980\) | 6146.29i | 0.00639972i | ||||||||
\(981\) | −247061. | − | 88906.9i | −0.256724 | − | 0.0923841i | ||||
\(982\) | 89308.9 | 0.0926130 | ||||||||
\(983\) | − | 901970.i | − | 0.933437i | −0.884406 | − | 0.466718i | \(-0.845436\pi\) | ||
0.884406 | − | 0.466718i | \(-0.154564\pi\) | |||||||
\(984\) | 209854. | − | 1.20293e6i | 0.216734 | − | 1.24236i | ||||
\(985\) | 757568. | 0.780817 | ||||||||
\(986\) | − | 1.42057e6i | − | 1.46119i | ||||||
\(987\) | −401092. | − | 69971.5i | −0.411727 | − | 0.0718269i | ||||
\(988\) | −864.067 | −0.000885184 | ||||||||
\(989\) | − | 39487.7i | − | 0.0403709i | ||||||
\(990\) | −463964. | + | 1.28930e6i | −0.473384 | + | 1.31548i | ||||
\(991\) | 310140. | 0.315799 | 0.157899 | − | 0.987455i | \(-0.449528\pi\) | ||||
0.157899 | + | 0.987455i | \(0.449528\pi\) | |||||||
\(992\) | 15152.3i | 0.0153977i | ||||||||
\(993\) | 220714. | − | 1.26518e6i | 0.223837 | − | 1.28308i | ||||
\(994\) | 628705. | 0.636318 | ||||||||
\(995\) | − | 1.26250e6i | − | 1.27522i | ||||||
\(996\) | 288040. | + | 50249.3i | 0.290358 | + | 0.0506537i | ||||
\(997\) | 922449. | 0.928008 | 0.464004 | − | 0.885833i | \(-0.346412\pi\) | ||||
0.464004 | + | 0.885833i | \(0.346412\pi\) | |||||||
\(998\) | 613641.i | 0.616103i | ||||||||
\(999\) | 536304. | − | 940720.i | 0.537378 | − | 0.942604i |
(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 | 177.5.b.a.119.55 | yes | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.24 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.24 | ✓ | 78 | 3.2 | odd | 2 | inner | |
177.5.b.a.119.55 | yes | 78 | 1.1 | even | 1 | trivial |