Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,5,Mod(37,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.37");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(3.92805859719\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 450x^{6} + 68229x^{4} + 4001228x^{2} + 77475204 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(-13.9305i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.37 |
Dual form | 38.5.b.a.37.8 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.82843i | − | 0.707107i | ||||||
\(3\) | − | 15.3447i | − | 1.70497i | −0.522755 | − | 0.852483i | \(-0.675096\pi\) | ||
0.522755 | − | 0.852483i | \(-0.324904\pi\) | |||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 41.6240 | 1.66496 | 0.832480 | − | 0.554055i | \(-0.186920\pi\) | ||||
0.832480 | + | 0.554055i | \(0.186920\pi\) | |||||||
\(6\) | −43.4013 | −1.20559 | ||||||||
\(7\) | −62.4342 | −1.27417 | −0.637084 | − | 0.770794i | \(-0.719860\pi\) | ||||
−0.637084 | + | 0.770794i | \(0.719860\pi\) | |||||||
\(8\) | 22.6274i | 0.353553i | ||||||||
\(9\) | −154.460 | −1.90691 | ||||||||
\(10\) | − | 117.730i | − | 1.17730i | ||||||
\(11\) | 122.938 | 1.01601 | 0.508007 | − | 0.861353i | \(-0.330382\pi\) | ||||
0.508007 | + | 0.861353i | \(0.330382\pi\) | |||||||
\(12\) | 122.758i | 0.852483i | ||||||||
\(13\) | 68.9610i | 0.408053i | 0.978965 | + | 0.204027i | \(0.0654029\pi\) | ||||
−0.978965 | + | 0.204027i | \(0.934597\pi\) | |||||||
\(14\) | 176.591i | 0.900973i | ||||||||
\(15\) | − | 638.707i | − | 2.83870i | ||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 297.375 | 1.02898 | 0.514490 | − | 0.857496i | \(-0.327981\pi\) | ||||
0.514490 | + | 0.857496i | \(0.327981\pi\) | |||||||
\(18\) | 436.878i | 1.34839i | ||||||||
\(19\) | −195.642 | − | 303.390i | −0.541944 | − | 0.840415i | ||||
\(20\) | −332.992 | −0.832480 | ||||||||
\(21\) | 958.034i | 2.17241i | ||||||||
\(22\) | − | 347.721i | − | 0.718431i | ||||||
\(23\) | 268.685 | 0.507911 | 0.253956 | − | 0.967216i | \(-0.418268\pi\) | ||||
0.253956 | + | 0.967216i | \(0.418268\pi\) | |||||||
\(24\) | 347.211 | 0.602796 | ||||||||
\(25\) | 1107.56 | 1.77209 | ||||||||
\(26\) | 195.051 | 0.288537 | ||||||||
\(27\) | 1127.21i | 1.54625i | ||||||||
\(28\) | 499.474 | 0.637084 | ||||||||
\(29\) | − | 561.405i | − | 0.667545i | −0.942654 | − | 0.333772i | \(-0.891678\pi\) | ||
0.942654 | − | 0.333772i | \(-0.108322\pi\) | |||||||
\(30\) | −1806.54 | −2.00726 | ||||||||
\(31\) | − | 252.423i | − | 0.262667i | −0.991338 | − | 0.131333i | \(-0.958074\pi\) | ||
0.991338 | − | 0.131333i | \(-0.0419259\pi\) | |||||||
\(32\) | − | 181.019i | − | 0.176777i | ||||||
\(33\) | − | 1886.44i | − | 1.73227i | ||||||
\(34\) | − | 841.104i | − | 0.727599i | ||||||
\(35\) | −2598.76 | −2.12144 | ||||||||
\(36\) | 1235.68 | 0.953454 | ||||||||
\(37\) | 2407.33i | 1.75846i | 0.476400 | + | 0.879228i | \(0.341941\pi\) | ||||
−0.476400 | + | 0.879228i | \(0.658059\pi\) | |||||||
\(38\) | −858.116 | + | 553.358i | −0.594263 | + | 0.383212i | ||||
\(39\) | 1058.18 | 0.695717 | ||||||||
\(40\) | 941.843i | 0.588652i | ||||||||
\(41\) | − | 690.246i | − | 0.410616i | −0.978697 | − | 0.205308i | \(-0.934180\pi\) | ||
0.978697 | − | 0.205308i | \(-0.0658197\pi\) | |||||||
\(42\) | 2709.73 | 1.53613 | ||||||||
\(43\) | 218.905 | 0.118391 | 0.0591954 | − | 0.998246i | \(-0.481146\pi\) | ||||
0.0591954 | + | 0.998246i | \(0.481146\pi\) | |||||||
\(44\) | −983.502 | −0.508007 | ||||||||
\(45\) | −6429.22 | −3.17493 | ||||||||
\(46\) | − | 759.956i | − | 0.359148i | ||||||
\(47\) | −83.1049 | −0.0376211 | −0.0188105 | − | 0.999823i | \(-0.505988\pi\) | ||||
−0.0188105 | + | 0.999823i | \(0.505988\pi\) | |||||||
\(48\) | − | 982.060i | − | 0.426241i | ||||||
\(49\) | 1497.03 | 0.623505 | ||||||||
\(50\) | − | 3132.64i | − | 1.25306i | ||||||
\(51\) | − | 4563.13i | − | 1.75438i | ||||||
\(52\) | − | 551.688i | − | 0.204027i | ||||||
\(53\) | 4389.68i | 1.56272i | 0.624080 | + | 0.781360i | \(0.285474\pi\) | ||||
−0.624080 | + | 0.781360i | \(0.714526\pi\) | |||||||
\(54\) | 3188.24 | 1.09336 | ||||||||
\(55\) | 5117.16 | 1.69162 | ||||||||
\(56\) | − | 1412.73i | − | 0.450486i | ||||||
\(57\) | −4655.42 | + | 3002.06i | −1.43288 | + | 0.923996i | ||||
\(58\) | −1587.89 | −0.472025 | ||||||||
\(59\) | − | 476.981i | − | 0.137024i | −0.997650 | − | 0.0685120i | \(-0.978175\pi\) | ||
0.997650 | − | 0.0685120i | \(-0.0218252\pi\) | |||||||
\(60\) | 5109.66i | 1.41935i | ||||||||
\(61\) | 3965.09 | 1.06560 | 0.532799 | − | 0.846242i | \(-0.321140\pi\) | ||||
0.532799 | + | 0.846242i | \(0.321140\pi\) | |||||||
\(62\) | −713.960 | −0.185734 | ||||||||
\(63\) | 9643.57 | 2.42972 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | 2870.43i | 0.679392i | ||||||||
\(66\) | −5335.66 | −1.22490 | ||||||||
\(67\) | 5111.96i | 1.13878i | 0.822069 | + | 0.569388i | \(0.192820\pi\) | ||||
−0.822069 | + | 0.569388i | \(0.807180\pi\) | |||||||
\(68\) | −2379.00 | −0.514490 | ||||||||
\(69\) | − | 4122.89i | − | 0.865972i | ||||||
\(70\) | 7350.41i | 1.50008i | ||||||||
\(71\) | 8182.93i | 1.62327i | 0.584161 | + | 0.811637i | \(0.301423\pi\) | ||||
−0.584161 | + | 0.811637i | \(0.698577\pi\) | |||||||
\(72\) | − | 3495.02i | − | 0.674194i | ||||||
\(73\) | −7345.23 | −1.37835 | −0.689175 | − | 0.724595i | \(-0.742027\pi\) | ||||
−0.689175 | + | 0.724595i | \(0.742027\pi\) | |||||||
\(74\) | 6808.95 | 1.24342 | ||||||||
\(75\) | − | 16995.1i | − | 3.02135i | ||||||
\(76\) | 1565.13 | + | 2427.12i | 0.270972 | + | 0.420207i | ||||
\(77\) | −7675.53 | −1.29457 | ||||||||
\(78\) | − | 2993.00i | − | 0.491946i | ||||||
\(79\) | − | 1485.61i | − | 0.238041i | −0.992892 | − | 0.119021i | \(-0.962025\pi\) | ||
0.992892 | − | 0.119021i | \(-0.0379754\pi\) | |||||||
\(80\) | 2663.94 | 0.416240 | ||||||||
\(81\) | 4785.54 | 0.729391 | ||||||||
\(82\) | −1952.31 | −0.290350 | ||||||||
\(83\) | 5347.30 | 0.776209 | 0.388104 | − | 0.921615i | \(-0.373130\pi\) | ||||
0.388104 | + | 0.921615i | \(0.373130\pi\) | |||||||
\(84\) | − | 7664.27i | − | 1.08621i | ||||||
\(85\) | 12377.9 | 1.71321 | ||||||||
\(86\) | − | 619.156i | − | 0.0837150i | ||||||
\(87\) | −8614.59 | −1.13814 | ||||||||
\(88\) | 2781.76i | 0.359215i | ||||||||
\(89\) | − | 11172.3i | − | 1.41047i | −0.708975 | − | 0.705234i | \(-0.750842\pi\) | ||
0.708975 | − | 0.705234i | \(-0.249158\pi\) | |||||||
\(90\) | 18184.6i | 2.24501i | ||||||||
\(91\) | − | 4305.53i | − | 0.519928i | ||||||
\(92\) | −2149.48 | −0.253956 | ||||||||
\(93\) | −3873.35 | −0.447838 | ||||||||
\(94\) | 235.056i | 0.0266021i | ||||||||
\(95\) | −8143.39 | − | 12628.3i | −0.902315 | − | 1.39926i | ||||
\(96\) | −2777.69 | −0.301398 | ||||||||
\(97\) | 1078.13i | 0.114585i | 0.998357 | + | 0.0572927i | \(0.0182468\pi\) | ||||
−0.998357 | + | 0.0572927i | \(0.981753\pi\) | |||||||
\(98\) | − | 4234.25i | − | 0.440884i | ||||||
\(99\) | −18988.9 | −1.93745 | ||||||||
\(100\) | −8860.45 | −0.886045 | ||||||||
\(101\) | 1393.71 | 0.136625 | 0.0683126 | − | 0.997664i | \(-0.478238\pi\) | ||||
0.0683126 | + | 0.997664i | \(0.478238\pi\) | |||||||
\(102\) | −12906.5 | −1.24053 | ||||||||
\(103\) | 11163.2i | 1.05224i | 0.850411 | + | 0.526119i | \(0.176353\pi\) | ||||
−0.850411 | + | 0.526119i | \(0.823647\pi\) | |||||||
\(104\) | −1560.41 | −0.144269 | ||||||||
\(105\) | 39877.2i | 3.61698i | ||||||||
\(106\) | 12415.9 | 1.10501 | ||||||||
\(107\) | 502.078i | 0.0438534i | 0.999760 | + | 0.0219267i | \(0.00698005\pi\) | ||||
−0.999760 | + | 0.0219267i | \(0.993020\pi\) | |||||||
\(108\) | − | 9017.72i | − | 0.773124i | ||||||
\(109\) | − | 11387.7i | − | 0.958477i | −0.877685 | − | 0.479238i | \(-0.840913\pi\) | ||
0.877685 | − | 0.479238i | \(-0.159087\pi\) | |||||||
\(110\) | − | 14473.5i | − | 1.19616i | ||||||
\(111\) | 36939.7 | 2.99811 | ||||||||
\(112\) | −3995.79 | −0.318542 | ||||||||
\(113\) | 4779.02i | 0.374267i | 0.982334 | + | 0.187133i | \(0.0599197\pi\) | ||||
−0.982334 | + | 0.187133i | \(0.940080\pi\) | |||||||
\(114\) | 8491.12 | + | 13167.5i | 0.653364 | + | 1.01320i | ||||
\(115\) | 11183.7 | 0.845652 | ||||||||
\(116\) | 4491.24i | 0.333772i | ||||||||
\(117\) | − | 10651.7i | − | 0.778120i | ||||||
\(118\) | −1349.11 | −0.0968906 | ||||||||
\(119\) | −18566.4 | −1.31109 | ||||||||
\(120\) | 14452.3 | 1.00363 | ||||||||
\(121\) | 472.695 | 0.0322857 | ||||||||
\(122\) | − | 11215.0i | − | 0.753491i | ||||||
\(123\) | −10591.6 | −0.700087 | ||||||||
\(124\) | 2019.38i | 0.131333i | ||||||||
\(125\) | 20085.9 | 1.28550 | ||||||||
\(126\) | − | 27276.1i | − | 1.71807i | ||||||
\(127\) | − | 17552.6i | − | 1.08826i | −0.839001 | − | 0.544130i | \(-0.816860\pi\) | ||
0.839001 | − | 0.544130i | \(-0.183140\pi\) | |||||||
\(128\) | 1448.15i | 0.0883883i | ||||||||
\(129\) | − | 3359.02i | − | 0.201852i | ||||||
\(130\) | 8118.80 | 0.480403 | ||||||||
\(131\) | −7401.84 | −0.431317 | −0.215659 | − | 0.976469i | \(-0.569190\pi\) | ||||
−0.215659 | + | 0.976469i | \(0.569190\pi\) | |||||||
\(132\) | 15091.5i | 0.866135i | ||||||||
\(133\) | 12214.7 | + | 18941.9i | 0.690528 | + | 1.07083i | ||||
\(134\) | 14458.8 | 0.805236 | ||||||||
\(135\) | 46919.2i | 2.57444i | ||||||||
\(136\) | 6728.83i | 0.363799i | ||||||||
\(137\) | 1692.77 | 0.0901896 | 0.0450948 | − | 0.998983i | \(-0.485641\pi\) | ||||
0.0450948 | + | 0.998983i | \(0.485641\pi\) | |||||||
\(138\) | −11661.3 | −0.612334 | ||||||||
\(139\) | −37366.7 | −1.93399 | −0.966996 | − | 0.254791i | \(-0.917993\pi\) | ||||
−0.966996 | + | 0.254791i | \(0.917993\pi\) | |||||||
\(140\) | 20790.1 | 1.06072 | ||||||||
\(141\) | 1275.22i | 0.0641426i | ||||||||
\(142\) | 23144.8 | 1.14783 | ||||||||
\(143\) | 8477.91i | 0.414588i | ||||||||
\(144\) | −9885.41 | −0.476727 | ||||||||
\(145\) | − | 23367.9i | − | 1.11143i | ||||||
\(146\) | 20775.4i | 0.974641i | ||||||||
\(147\) | − | 22971.5i | − | 1.06305i | ||||||
\(148\) | − | 19258.6i | − | 0.879228i | ||||||
\(149\) | −6037.22 | −0.271935 | −0.135967 | − | 0.990713i | \(-0.543414\pi\) | ||||
−0.135967 | + | 0.990713i | \(0.543414\pi\) | |||||||
\(150\) | −48069.4 | −2.13642 | ||||||||
\(151\) | 20619.1i | 0.904307i | 0.891940 | + | 0.452153i | \(0.149344\pi\) | ||||
−0.891940 | + | 0.452153i | \(0.850656\pi\) | |||||||
\(152\) | 6864.92 | − | 4426.87i | 0.297131 | − | 0.191606i | ||||
\(153\) | −45932.4 | −1.96217 | ||||||||
\(154\) | 21709.7i | 0.915402i | ||||||||
\(155\) | − | 10506.8i | − | 0.437330i | ||||||
\(156\) | −8465.48 | −0.347858 | ||||||||
\(157\) | −1043.55 | −0.0423362 | −0.0211681 | − | 0.999776i | \(-0.506739\pi\) | ||||
−0.0211681 | + | 0.999776i | \(0.506739\pi\) | |||||||
\(158\) | −4201.95 | −0.168321 | ||||||||
\(159\) | 67358.3 | 2.66439 | ||||||||
\(160\) | − | 7534.75i | − | 0.294326i | ||||||
\(161\) | −16775.2 | −0.647165 | ||||||||
\(162\) | − | 13535.5i | − | 0.515757i | ||||||
\(163\) | 1587.92 | 0.0597658 | 0.0298829 | − | 0.999553i | \(-0.490487\pi\) | ||||
0.0298829 | + | 0.999553i | \(0.490487\pi\) | |||||||
\(164\) | 5521.97i | 0.205308i | ||||||||
\(165\) | − | 78521.3i | − | 2.88416i | ||||||
\(166\) | − | 15124.5i | − | 0.548862i | ||||||
\(167\) | − | 21277.9i | − | 0.762948i | −0.924380 | − | 0.381474i | \(-0.875417\pi\) | ||
0.924380 | − | 0.381474i | \(-0.124583\pi\) | |||||||
\(168\) | −21677.8 | −0.768064 | ||||||||
\(169\) | 23805.4 | 0.833493 | ||||||||
\(170\) | − | 35010.1i | − | 1.21142i | ||||||
\(171\) | 30218.7 | + | 46861.4i | 1.03344 | + | 1.60259i | ||||
\(172\) | −1751.24 | −0.0591954 | ||||||||
\(173\) | 23629.3i | 0.789513i | 0.918786 | + | 0.394756i | \(0.129171\pi\) | ||||
−0.918786 | + | 0.394756i | \(0.870829\pi\) | |||||||
\(174\) | 24365.7i | 0.804787i | ||||||||
\(175\) | −69149.5 | −2.25794 | ||||||||
\(176\) | 7868.02 | 0.254004 | ||||||||
\(177\) | −7319.12 | −0.233621 | ||||||||
\(178\) | −31600.1 | −0.997351 | ||||||||
\(179\) | 54580.1i | 1.70345i | 0.523993 | + | 0.851723i | \(0.324442\pi\) | ||||
−0.523993 | + | 0.851723i | \(0.675558\pi\) | |||||||
\(180\) | 51433.8 | 1.58746 | ||||||||
\(181\) | − | 48461.8i | − | 1.47925i | −0.673017 | − | 0.739627i | \(-0.735002\pi\) | ||
0.673017 | − | 0.739627i | \(-0.264998\pi\) | |||||||
\(182\) | −12177.9 | −0.367645 | ||||||||
\(183\) | − | 60843.0i | − | 1.81681i | ||||||
\(184\) | 6079.65i | 0.179574i | ||||||||
\(185\) | 100203.i | 2.92776i | ||||||||
\(186\) | 10955.5i | 0.316669i | ||||||||
\(187\) | 36558.6 | 1.04546 | ||||||||
\(188\) | 664.839 | 0.0188105 | ||||||||
\(189\) | − | 70376.8i | − | 1.97018i | ||||||
\(190\) | −35718.2 | + | 23033.0i | −0.989424 | + | 0.638033i | ||||
\(191\) | 10718.8 | 0.293819 | 0.146909 | − | 0.989150i | \(-0.453067\pi\) | ||||
0.146909 | + | 0.989150i | \(0.453067\pi\) | |||||||
\(192\) | 7856.48i | 0.213121i | ||||||||
\(193\) | − | 25358.2i | − | 0.680776i | −0.940285 | − | 0.340388i | \(-0.889442\pi\) | ||
0.940285 | − | 0.340388i | \(-0.110558\pi\) | |||||||
\(194\) | 3049.42 | 0.0810241 | ||||||||
\(195\) | 44045.9 | 1.15834 | ||||||||
\(196\) | −11976.3 | −0.311752 | ||||||||
\(197\) | −4536.94 | −0.116904 | −0.0584521 | − | 0.998290i | \(-0.518617\pi\) | ||||
−0.0584521 | + | 0.998290i | \(0.518617\pi\) | |||||||
\(198\) | 53708.8i | 1.36998i | ||||||||
\(199\) | −67698.1 | −1.70951 | −0.854753 | − | 0.519035i | \(-0.826291\pi\) | ||||
−0.854753 | + | 0.519035i | \(0.826291\pi\) | |||||||
\(200\) | 25061.1i | 0.626529i | ||||||||
\(201\) | 78441.5 | 1.94157 | ||||||||
\(202\) | − | 3942.01i | − | 0.0966085i | ||||||
\(203\) | 35050.9i | 0.850564i | ||||||||
\(204\) | 36505.0i | 0.877188i | ||||||||
\(205\) | − | 28730.8i | − | 0.683660i | ||||||
\(206\) | 31574.2 | 0.744044 | ||||||||
\(207\) | −41501.0 | −0.968540 | ||||||||
\(208\) | 4413.50i | 0.102013i | ||||||||
\(209\) | −24051.8 | − | 37298.1i | −0.550623 | − | 0.853874i | ||||
\(210\) | 112790. | 2.55759 | ||||||||
\(211\) | − | 2816.81i | − | 0.0632691i | −0.999500 | − | 0.0316346i | \(-0.989929\pi\) | ||
0.999500 | − | 0.0316346i | \(-0.0100713\pi\) | |||||||
\(212\) | − | 35117.5i | − | 0.781360i | ||||||
\(213\) | 125565. | 2.76763 | ||||||||
\(214\) | 1420.09 | 0.0310090 | ||||||||
\(215\) | 9111.68 | 0.197116 | ||||||||
\(216\) | −25506.0 | −0.546681 | ||||||||
\(217\) | 15759.8i | 0.334682i | ||||||||
\(218\) | −32209.2 | −0.677746 | ||||||||
\(219\) | 112710.i | 2.35004i | ||||||||
\(220\) | −40937.3 | −0.845812 | ||||||||
\(221\) | 20507.3i | 0.419878i | ||||||||
\(222\) | − | 104481.i | − | 2.11998i | ||||||
\(223\) | − | 36870.4i | − | 0.741426i | −0.928747 | − | 0.370713i | \(-0.879113\pi\) | ||
0.928747 | − | 0.370713i | \(-0.120887\pi\) | |||||||
\(224\) | 11301.8i | 0.225243i | ||||||||
\(225\) | −171073. | −3.37921 | ||||||||
\(226\) | 13517.1 | 0.264647 | ||||||||
\(227\) | − | 56826.9i | − | 1.10281i | −0.834236 | − | 0.551407i | \(-0.814091\pi\) | ||
0.834236 | − | 0.551407i | \(-0.185909\pi\) | |||||||
\(228\) | 37243.4 | − | 24016.5i | 0.716439 | − | 0.461998i | ||||
\(229\) | 7632.64 | 0.145547 | 0.0727736 | − | 0.997348i | \(-0.476815\pi\) | ||||
0.0727736 | + | 0.997348i | \(0.476815\pi\) | |||||||
\(230\) | − | 31632.4i | − | 0.597966i | ||||||
\(231\) | 117779.i | 2.20720i | ||||||||
\(232\) | 12703.1 | 0.236013 | ||||||||
\(233\) | 91249.2 | 1.68080 | 0.840402 | − | 0.541964i | \(-0.182319\pi\) | ||||
0.840402 | + | 0.541964i | \(0.182319\pi\) | |||||||
\(234\) | −30127.5 | −0.550214 | ||||||||
\(235\) | −3459.16 | −0.0626375 | ||||||||
\(236\) | 3815.85i | 0.0685120i | ||||||||
\(237\) | −22796.3 | −0.405852 | ||||||||
\(238\) | 52513.7i | 0.927083i | ||||||||
\(239\) | −110161. | −1.92856 | −0.964280 | − | 0.264884i | \(-0.914666\pi\) | ||||
−0.964280 | + | 0.264884i | \(0.914666\pi\) | |||||||
\(240\) | − | 40877.3i | − | 0.709675i | ||||||
\(241\) | 58423.0i | 1.00589i | 0.864319 | + | 0.502944i | \(0.167750\pi\) | ||||
−0.864319 | + | 0.502944i | \(0.832250\pi\) | |||||||
\(242\) | − | 1336.98i | − | 0.0228295i | ||||||
\(243\) | 17871.8i | 0.302661i | ||||||||
\(244\) | −31720.7 | −0.532799 | ||||||||
\(245\) | 62312.6 | 1.03811 | ||||||||
\(246\) | 29957.6i | 0.495036i | ||||||||
\(247\) | 20922.0 | − | 13491.6i | 0.342934 | − | 0.221142i | ||||
\(248\) | 5711.68 | 0.0928668 | ||||||||
\(249\) | − | 82052.7i | − | 1.32341i | ||||||
\(250\) | − | 56811.6i | − | 0.908985i | ||||||
\(251\) | −17258.3 | −0.273936 | −0.136968 | − | 0.990575i | \(-0.543736\pi\) | ||||
−0.136968 | + | 0.990575i | \(0.543736\pi\) | |||||||
\(252\) | −77148.5 | −1.21486 | ||||||||
\(253\) | 33031.5 | 0.516045 | ||||||||
\(254\) | −49646.1 | −0.769517 | ||||||||
\(255\) | − | 189936.i | − | 2.92096i | ||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 41195.7i | 0.623714i | 0.950129 | + | 0.311857i | \(0.100951\pi\) | ||||
−0.950129 | + | 0.311857i | \(0.899049\pi\) | |||||||
\(258\) | −9500.75 | −0.142731 | ||||||||
\(259\) | − | 150300.i | − | 2.24057i | ||||||
\(260\) | − | 22963.4i | − | 0.339696i | ||||||
\(261\) | 86714.4i | 1.27295i | ||||||||
\(262\) | 20935.6i | 0.304987i | ||||||||
\(263\) | −41179.7 | −0.595349 | −0.297675 | − | 0.954667i | \(-0.596211\pi\) | ||||
−0.297675 | + | 0.954667i | \(0.596211\pi\) | |||||||
\(264\) | 42685.3 | 0.612450 | ||||||||
\(265\) | 182716.i | 2.60187i | ||||||||
\(266\) | 53575.8 | − | 34548.5i | 0.757191 | − | 0.488277i | ||||
\(267\) | −171436. | −2.40480 | ||||||||
\(268\) | − | 40895.7i | − | 0.569388i | ||||||
\(269\) | − | 19858.8i | − | 0.274440i | −0.990541 | − | 0.137220i | \(-0.956183\pi\) | ||
0.990541 | − | 0.137220i | \(-0.0438168\pi\) | |||||||
\(270\) | 132707. | 1.82040 | ||||||||
\(271\) | 110976. | 1.51110 | 0.755549 | − | 0.655093i | \(-0.227370\pi\) | ||||
0.755549 | + | 0.655093i | \(0.227370\pi\) | |||||||
\(272\) | 19032.0 | 0.257245 | ||||||||
\(273\) | −66067.0 | −0.886460 | ||||||||
\(274\) | − | 4787.87i | − | 0.0637737i | ||||||
\(275\) | 136161. | 1.80047 | ||||||||
\(276\) | 32983.1i | 0.432986i | ||||||||
\(277\) | −87534.8 | −1.14083 | −0.570415 | − | 0.821357i | \(-0.693218\pi\) | ||||
−0.570415 | + | 0.821357i | \(0.693218\pi\) | |||||||
\(278\) | 105689.i | 1.36754i | ||||||||
\(279\) | 38989.1i | 0.500882i | ||||||||
\(280\) | − | 58803.3i | − | 0.750042i | ||||||
\(281\) | − | 133298.i | − | 1.68815i | −0.536228 | − | 0.844073i | \(-0.680151\pi\) | ||
0.536228 | − | 0.844073i | \(-0.319849\pi\) | |||||||
\(282\) | 3606.86 | 0.0453557 | ||||||||
\(283\) | 29905.8 | 0.373407 | 0.186704 | − | 0.982416i | \(-0.440220\pi\) | ||||
0.186704 | + | 0.982416i | \(0.440220\pi\) | |||||||
\(284\) | − | 65463.4i | − | 0.811637i | ||||||
\(285\) | −193777. | + | 124958.i | −2.38568 | + | 1.53842i | ||||
\(286\) | 23979.1 | 0.293158 | ||||||||
\(287\) | 43095.0i | 0.523194i | ||||||||
\(288\) | 27960.2i | 0.337097i | ||||||||
\(289\) | 4910.99 | 0.0587994 | ||||||||
\(290\) | −66094.5 | −0.785903 | ||||||||
\(291\) | 16543.6 | 0.195364 | ||||||||
\(292\) | 58761.8 | 0.689175 | ||||||||
\(293\) | − | 42625.4i | − | 0.496516i | −0.968694 | − | 0.248258i | \(-0.920142\pi\) | ||
0.968694 | − | 0.248258i | \(-0.0798580\pi\) | |||||||
\(294\) | −64973.3 | −0.751693 | ||||||||
\(295\) | − | 19853.8i | − | 0.228140i | ||||||
\(296\) | −54471.6 | −0.621708 | ||||||||
\(297\) | 138577.i | 1.57101i | ||||||||
\(298\) | 17075.8i | 0.192287i | ||||||||
\(299\) | 18528.8i | 0.207255i | ||||||||
\(300\) | 135961.i | 1.51068i | ||||||||
\(301\) | −13667.1 | −0.150850 | ||||||||
\(302\) | 58319.6 | 0.639441 | ||||||||
\(303\) | − | 21386.1i | − | 0.232941i | ||||||
\(304\) | −12521.1 | − | 19416.9i | −0.135486 | − | 0.210104i | ||||
\(305\) | 165043. | 1.77418 | ||||||||
\(306\) | 129917.i | 1.38746i | ||||||||
\(307\) | 39047.5i | 0.414302i | 0.978309 | + | 0.207151i | \(0.0664191\pi\) | ||||
−0.978309 | + | 0.207151i | \(0.933581\pi\) | |||||||
\(308\) | 61404.2 | 0.647287 | ||||||||
\(309\) | 171296. | 1.79403 | ||||||||
\(310\) | −29717.9 | −0.309239 | ||||||||
\(311\) | 79232.0 | 0.819180 | 0.409590 | − | 0.912270i | \(-0.365672\pi\) | ||||
0.409590 | + | 0.912270i | \(0.365672\pi\) | |||||||
\(312\) | 23944.0i | 0.245973i | ||||||||
\(313\) | −107079. | −1.09298 | −0.546492 | − | 0.837464i | \(-0.684037\pi\) | ||||
−0.546492 | + | 0.837464i | \(0.684037\pi\) | |||||||
\(314\) | 2951.59i | 0.0299362i | ||||||||
\(315\) | 401404. | 4.04539 | ||||||||
\(316\) | 11884.9i | 0.119021i | ||||||||
\(317\) | − | 132924.i | − | 1.32277i | −0.750046 | − | 0.661385i | \(-0.769969\pi\) | ||
0.750046 | − | 0.661385i | \(-0.230031\pi\) | |||||||
\(318\) | − | 190518.i | − | 1.88401i | ||||||
\(319\) | − | 69017.9i | − | 0.678235i | ||||||
\(320\) | −21311.5 | −0.208120 | ||||||||
\(321\) | 7704.23 | 0.0747686 | ||||||||
\(322\) | 47447.3i | 0.457614i | ||||||||
\(323\) | −58179.0 | − | 90220.6i | −0.557649 | − | 0.864770i | ||||
\(324\) | −38284.3 | −0.364696 | ||||||||
\(325\) | 76378.2i | 0.723107i | ||||||||
\(326\) | − | 4491.31i | − | 0.0422608i | ||||||
\(327\) | −174740. | −1.63417 | ||||||||
\(328\) | 15618.5 | 0.145175 | ||||||||
\(329\) | 5188.59 | 0.0479356 | ||||||||
\(330\) | −222092. | −2.03941 | ||||||||
\(331\) | − | 44623.1i | − | 0.407290i | −0.979045 | − | 0.203645i | \(-0.934721\pi\) | ||
0.979045 | − | 0.203645i | \(-0.0652788\pi\) | |||||||
\(332\) | −42778.4 | −0.388104 | ||||||||
\(333\) | − | 371835.i | − | 3.35322i | ||||||
\(334\) | −60182.9 | −0.539486 | ||||||||
\(335\) | 212780.i | 1.89602i | ||||||||
\(336\) | 61314.2i | 0.543103i | ||||||||
\(337\) | 5142.51i | 0.0452810i | 0.999744 | + | 0.0226405i | \(0.00720730\pi\) | ||||
−0.999744 | + | 0.0226405i | \(0.992793\pi\) | |||||||
\(338\) | − | 67331.8i | − | 0.589368i | ||||||
\(339\) | 73332.5 | 0.638112 | ||||||||
\(340\) | −99023.5 | −0.856605 | ||||||||
\(341\) | − | 31032.3i | − | 0.266873i | ||||||
\(342\) | 132544. | − | 85471.5i | 1.13320 | − | 0.730751i | ||||
\(343\) | 56438.4 | 0.479718 | ||||||||
\(344\) | 4953.25i | 0.0418575i | ||||||||
\(345\) | − | 171611.i | − | 1.44181i | ||||||
\(346\) | 66833.8 | 0.558270 | ||||||||
\(347\) | −175661. | −1.45887 | −0.729436 | − | 0.684049i | \(-0.760218\pi\) | ||||
−0.729436 | + | 0.684049i | \(0.760218\pi\) | |||||||
\(348\) | 68916.7 | 0.569070 | ||||||||
\(349\) | 137125. | 1.12581 | 0.562906 | − | 0.826521i | \(-0.309683\pi\) | ||||
0.562906 | + | 0.826521i | \(0.309683\pi\) | |||||||
\(350\) | 195584.i | 1.59661i | ||||||||
\(351\) | −77733.8 | −0.630951 | ||||||||
\(352\) | − | 22254.1i | − | 0.179608i | ||||||
\(353\) | −199391. | −1.60013 | −0.800065 | − | 0.599913i | \(-0.795202\pi\) | ||||
−0.800065 | + | 0.599913i | \(0.795202\pi\) | |||||||
\(354\) | 20701.6i | 0.165195i | ||||||||
\(355\) | 340606.i | 2.70269i | ||||||||
\(356\) | 89378.5i | 0.705234i | ||||||||
\(357\) | 284896.i | 2.23537i | ||||||||
\(358\) | 154376. | 1.20452 | ||||||||
\(359\) | 6307.95 | 0.0489440 | 0.0244720 | − | 0.999701i | \(-0.492210\pi\) | ||||
0.0244720 | + | 0.999701i | \(0.492210\pi\) | |||||||
\(360\) | − | 145477.i | − | 1.12251i | ||||||
\(361\) | −53769.6 | + | 118711.i | −0.412594 | + | 0.910915i | ||||
\(362\) | −137071. | −1.04599 | ||||||||
\(363\) | − | 7253.36i | − | 0.0550460i | ||||||
\(364\) | 34444.2i | 0.259964i | ||||||||
\(365\) | −305738. | −2.29490 | ||||||||
\(366\) | −172090. | −1.28468 | ||||||||
\(367\) | 52946.3 | 0.393100 | 0.196550 | − | 0.980494i | \(-0.437026\pi\) | ||||
0.196550 | + | 0.980494i | \(0.437026\pi\) | |||||||
\(368\) | 17195.8 | 0.126978 | ||||||||
\(369\) | 106615.i | 0.783008i | ||||||||
\(370\) | 283416. | 2.07024 | ||||||||
\(371\) | − | 274067.i | − | 1.99117i | ||||||
\(372\) | 30986.8 | 0.223919 | ||||||||
\(373\) | − | 9312.99i | − | 0.0669378i | −0.999440 | − | 0.0334689i | \(-0.989345\pi\) | ||
0.999440 | − | 0.0334689i | \(-0.0106555\pi\) | |||||||
\(374\) | − | 103403.i | − | 0.739251i | ||||||
\(375\) | − | 308212.i | − | 2.19173i | ||||||
\(376\) | − | 1880.45i | − | 0.0133011i | ||||||
\(377\) | 38715.0 | 0.272394 | ||||||||
\(378\) | −199056. | −1.39313 | ||||||||
\(379\) | − | 178291.i | − | 1.24123i | −0.784117 | − | 0.620613i | \(-0.786884\pi\) | ||
0.784117 | − | 0.620613i | \(-0.213116\pi\) | |||||||
\(380\) | 65147.1 | + | 101026.i | 0.451157 | + | 0.699628i | ||||
\(381\) | −269339. | −1.85545 | ||||||||
\(382\) | − | 30317.3i | − | 0.207761i | ||||||
\(383\) | 27764.8i | 0.189276i | 0.995512 | + | 0.0946382i | \(0.0301694\pi\) | ||||
−0.995512 | + | 0.0946382i | \(0.969831\pi\) | |||||||
\(384\) | 22221.5 | 0.150699 | ||||||||
\(385\) | −319486. | −2.15541 | ||||||||
\(386\) | −71723.9 | −0.481381 | ||||||||
\(387\) | −33811.9 | −0.225760 | ||||||||
\(388\) | − | 8625.07i | − | 0.0572927i | ||||||
\(389\) | 241135. | 1.59353 | 0.796765 | − | 0.604289i | \(-0.206543\pi\) | ||||
0.796765 | + | 0.604289i | \(0.206543\pi\) | |||||||
\(390\) | − | 124581.i | − | 0.819070i | ||||||
\(391\) | 79900.3 | 0.522631 | ||||||||
\(392\) | 33874.0i | 0.220442i | ||||||||
\(393\) | 113579.i | 0.735381i | ||||||||
\(394\) | 12832.4i | 0.0826638i | ||||||||
\(395\) | − | 61837.2i | − | 0.396329i | ||||||
\(396\) | 151911. | 0.968723 | ||||||||
\(397\) | 234920. | 1.49052 | 0.745261 | − | 0.666772i | \(-0.232325\pi\) | ||||
0.745261 | + | 0.666772i | \(0.232325\pi\) | |||||||
\(398\) | 191479.i | 1.20880i | ||||||||
\(399\) | 290658. | − | 187432.i | 1.82573 | − | 1.17733i | ||||
\(400\) | 70883.6 | 0.443023 | ||||||||
\(401\) | − | 311500.i | − | 1.93718i | −0.248667 | − | 0.968589i | \(-0.579993\pi\) | ||
0.248667 | − | 0.968589i | \(-0.420007\pi\) | |||||||
\(402\) | − | 221866.i | − | 1.37290i | ||||||
\(403\) | 17407.3 | 0.107182 | ||||||||
\(404\) | −11149.7 | −0.0683126 | ||||||||
\(405\) | 199193. | 1.21441 | ||||||||
\(406\) | 99138.9 | 0.601440 | ||||||||
\(407\) | 295951.i | 1.78662i | ||||||||
\(408\) | 103252. | 0.620265 | ||||||||
\(409\) | 243636.i | 1.45645i | 0.685338 | + | 0.728225i | \(0.259655\pi\) | ||||
−0.685338 | + | 0.728225i | \(0.740345\pi\) | |||||||
\(410\) | −81263.0 | −0.483420 | ||||||||
\(411\) | − | 25975.0i | − | 0.153770i | ||||||
\(412\) | − | 89305.5i | − | 0.526119i | ||||||
\(413\) | 29779.9i | 0.174592i | ||||||||
\(414\) | 117383.i | 0.684862i | ||||||||
\(415\) | 222576. | 1.29236 | ||||||||
\(416\) | 12483.3 | 0.0721343 | ||||||||
\(417\) | 573380.i | 3.29739i | ||||||||
\(418\) | −105495. | + | 68028.7i | −0.603780 | + | 0.389349i | ||||
\(419\) | −193805. | −1.10392 | −0.551960 | − | 0.833871i | \(-0.686120\pi\) | ||||
−0.551960 | + | 0.833871i | \(0.686120\pi\) | |||||||
\(420\) | − | 319018.i | − | 1.80849i | ||||||
\(421\) | 136536.i | 0.770339i | 0.922846 | + | 0.385169i | \(0.125857\pi\) | ||||
−0.922846 | + | 0.385169i | \(0.874143\pi\) | |||||||
\(422\) | −7967.13 | −0.0447380 | ||||||||
\(423\) | 12836.3 | 0.0717399 | ||||||||
\(424\) | −99327.2 | −0.552505 | ||||||||
\(425\) | 329360. | 1.82345 | ||||||||
\(426\) | − | 355150.i | − | 1.95701i | ||||||
\(427\) | −247557. | −1.35775 | ||||||||
\(428\) | − | 4016.62i | − | 0.0219267i | ||||||
\(429\) | 130091. | 0.706858 | ||||||||
\(430\) | − | 25771.7i | − | 0.139382i | ||||||
\(431\) | 323841.i | 1.74332i | 0.490113 | + | 0.871659i | \(0.336956\pi\) | ||||
−0.490113 | + | 0.871659i | \(0.663044\pi\) | |||||||
\(432\) | 72141.7i | 0.386562i | ||||||||
\(433\) | 286129.i | 1.52611i | 0.646333 | + | 0.763056i | \(0.276302\pi\) | ||||
−0.646333 | + | 0.763056i | \(0.723698\pi\) | |||||||
\(434\) | 44575.5 | 0.236656 | ||||||||
\(435\) | −358574. | −1.89496 | ||||||||
\(436\) | 91101.3i | 0.479238i | ||||||||
\(437\) | −52566.0 | − | 81516.3i | −0.275259 | − | 0.426856i | ||||
\(438\) | 318793. | 1.66173 | ||||||||
\(439\) | − | 26283.3i | − | 0.136380i | −0.997672 | − | 0.0681901i | \(-0.978278\pi\) | ||
0.997672 | − | 0.0681901i | \(-0.0217224\pi\) | |||||||
\(440\) | 115788.i | 0.598079i | ||||||||
\(441\) | −231231. | −1.18897 | ||||||||
\(442\) | 58003.3 | 0.296899 | ||||||||
\(443\) | −317887. | −1.61981 | −0.809907 | − | 0.586558i | \(-0.800482\pi\) | ||||
−0.809907 | + | 0.586558i | \(0.800482\pi\) | |||||||
\(444\) | −295518. | −1.49905 | ||||||||
\(445\) | − | 465036.i | − | 2.34837i | ||||||
\(446\) | −104285. | −0.524267 | ||||||||
\(447\) | 92639.3i | 0.463639i | ||||||||
\(448\) | 31966.3 | 0.159271 | ||||||||
\(449\) | − | 68728.7i | − | 0.340915i | −0.985365 | − | 0.170457i | \(-0.945476\pi\) | ||
0.985365 | − | 0.170457i | \(-0.0545245\pi\) | |||||||
\(450\) | 483867.i | 2.38947i | ||||||||
\(451\) | − | 84857.3i | − | 0.417192i | ||||||
\(452\) | − | 38232.1i | − | 0.187133i | ||||||
\(453\) | 316394. | 1.54181 | ||||||||
\(454\) | −160731. | −0.779808 | ||||||||
\(455\) | − | 179213.i | − | 0.865660i | ||||||
\(456\) | −67928.9 | − | 105340.i | −0.326682 | − | 0.506599i | ||||
\(457\) | 182859. | 0.875555 | 0.437778 | − | 0.899083i | \(-0.355766\pi\) | ||||
0.437778 | + | 0.899083i | \(0.355766\pi\) | |||||||
\(458\) | − | 21588.4i | − | 0.102917i | ||||||
\(459\) | 335206.i | 1.59106i | ||||||||
\(460\) | −89470.0 | −0.422826 | ||||||||
\(461\) | 142804. | 0.671951 | 0.335976 | − | 0.941871i | \(-0.390934\pi\) | ||||
0.335976 | + | 0.941871i | \(0.390934\pi\) | |||||||
\(462\) | 333128. | 1.56073 | ||||||||
\(463\) | 96212.9 | 0.448819 | 0.224409 | − | 0.974495i | \(-0.427955\pi\) | ||||
0.224409 | + | 0.974495i | \(0.427955\pi\) | |||||||
\(464\) | − | 35929.9i | − | 0.166886i | ||||||
\(465\) | −161224. | −0.745632 | ||||||||
\(466\) | − | 258092.i | − | 1.18851i | ||||||
\(467\) | 287321. | 1.31745 | 0.658724 | − | 0.752384i | \(-0.271096\pi\) | ||||
0.658724 | + | 0.752384i | \(0.271096\pi\) | |||||||
\(468\) | 85213.5i | 0.389060i | ||||||||
\(469\) | − | 319162.i | − | 1.45099i | ||||||
\(470\) | 9783.98i | 0.0442914i | ||||||||
\(471\) | 16012.9i | 0.0721818i | ||||||||
\(472\) | 10792.8 | 0.0484453 | ||||||||
\(473\) | 26911.6 | 0.120287 | ||||||||
\(474\) | 64477.7i | 0.286981i | ||||||||
\(475\) | −216684. | − | 336021.i | −0.960374 | − | 1.48929i | ||||
\(476\) | 148531. | 0.655547 | ||||||||
\(477\) | − | 678029.i | − | 2.97997i | ||||||
\(478\) | 311583.i | 1.36370i | ||||||||
\(479\) | 101492. | 0.442346 | 0.221173 | − | 0.975235i | \(-0.429011\pi\) | ||||
0.221173 | + | 0.975235i | \(0.429011\pi\) | |||||||
\(480\) | −115618. | −0.501816 | ||||||||
\(481\) | −166012. | −0.717544 | ||||||||
\(482\) | 165245. | 0.711270 | ||||||||
\(483\) | 257410.i | 1.10339i | ||||||||
\(484\) | −3781.56 | −0.0161429 | ||||||||
\(485\) | 44876.2i | 0.190780i | ||||||||
\(486\) | 50549.1 | 0.214014 | ||||||||
\(487\) | 203340.i | 0.857363i | 0.903456 | + | 0.428682i | \(0.141022\pi\) | ||||
−0.903456 | + | 0.428682i | \(0.858978\pi\) | |||||||
\(488\) | 89719.7i | 0.376745i | ||||||||
\(489\) | − | 24366.1i | − | 0.101899i | ||||||
\(490\) | − | 176247.i | − | 0.734055i | ||||||
\(491\) | −227758. | −0.944735 | −0.472368 | − | 0.881402i | \(-0.656601\pi\) | ||||
−0.472368 | + | 0.881402i | \(0.656601\pi\) | |||||||
\(492\) | 84732.9 | 0.350043 | ||||||||
\(493\) | − | 166948.i | − | 0.686890i | ||||||
\(494\) | −38160.1 | − | 59176.5i | −0.156371 | − | 0.242491i | ||||
\(495\) | −790394. | −3.22577 | ||||||||
\(496\) | − | 16155.1i | − | 0.0656667i | ||||||
\(497\) | − | 510895.i | − | 2.06833i | ||||||
\(498\) | −232080. | −0.935792 | ||||||||
\(499\) | −132829. | −0.533447 | −0.266724 | − | 0.963773i | \(-0.585941\pi\) | ||||
−0.266724 | + | 0.963773i | \(0.585941\pi\) | |||||||
\(500\) | −160687. | −0.642750 | ||||||||
\(501\) | −326502. | −1.30080 | ||||||||
\(502\) | 48813.8i | 0.193702i | ||||||||
\(503\) | 279294. | 1.10389 | 0.551945 | − | 0.833880i | \(-0.313886\pi\) | ||||
0.551945 | + | 0.833880i | \(0.313886\pi\) | |||||||
\(504\) | 218209.i | 0.859036i | ||||||||
\(505\) | 58011.9 | 0.227475 | ||||||||
\(506\) | − | 93427.3i | − | 0.364899i | ||||||
\(507\) | − | 365286.i | − | 1.42108i | ||||||
\(508\) | 140420.i | 0.544130i | ||||||||
\(509\) | 304788.i | 1.17642i | 0.808709 | + | 0.588209i | \(0.200167\pi\) | ||||
−0.808709 | + | 0.588209i | \(0.799833\pi\) | |||||||
\(510\) | −537219. | −2.06543 | ||||||||
\(511\) | 458594. | 1.75625 | ||||||||
\(512\) | − | 11585.2i | − | 0.0441942i | ||||||
\(513\) | 341985. | − | 220530.i | 1.29949 | − | 0.837980i | ||||
\(514\) | 116519. | 0.441032 | ||||||||
\(515\) | 464656.i | 1.75193i | ||||||||
\(516\) | 26872.2i | 0.100926i | ||||||||
\(517\) | −10216.7 | −0.0382235 | ||||||||
\(518\) | −425112. | −1.58432 | ||||||||
\(519\) | 362585. | 1.34609 | ||||||||
\(520\) | −64950.4 | −0.240201 | ||||||||
\(521\) | − | 181301.i | − | 0.667919i | −0.942587 | − | 0.333959i | \(-0.891615\pi\) | ||
0.942587 | − | 0.333959i | \(-0.108385\pi\) | |||||||
\(522\) | 245265. | 0.900109 | ||||||||
\(523\) | 5966.86i | 0.0218144i | 0.999941 | + | 0.0109072i | \(0.00347193\pi\) | ||||
−0.999941 | + | 0.0109072i | \(0.996528\pi\) | |||||||
\(524\) | 59214.7 | 0.215659 | ||||||||
\(525\) | 1.06108e6i | 3.84971i | ||||||||
\(526\) | 116474.i | 0.420976i | ||||||||
\(527\) | − | 75064.3i | − | 0.270279i | ||||||
\(528\) | − | 120732.i | − | 0.433068i | ||||||
\(529\) | −207649. | −0.742026 | ||||||||
\(530\) | 516799. | 1.83980 | ||||||||
\(531\) | 73674.2i | 0.261292i | ||||||||
\(532\) | −97718.0 | − | 151535.i | −0.345264 | − | 0.535415i | ||||
\(533\) | 47600.1 | 0.167553 | ||||||||
\(534\) | 484893.i | 1.70045i | ||||||||
\(535\) | 20898.5i | 0.0730142i | ||||||||
\(536\) | −115671. | −0.402618 | ||||||||
\(537\) | 837515. | 2.90432 | ||||||||
\(538\) | −56169.1 | −0.194058 | ||||||||
\(539\) | 184042. | 0.633490 | ||||||||
\(540\) | − | 375353.i | − | 1.28722i | ||||||
\(541\) | −121383. | −0.414727 | −0.207364 | − | 0.978264i | \(-0.566488\pi\) | ||||
−0.207364 | + | 0.978264i | \(0.566488\pi\) | |||||||
\(542\) | − | 313889.i | − | 1.06851i | ||||||
\(543\) | −743632. | −2.52208 | ||||||||
\(544\) | − | 53830.7i | − | 0.181900i | ||||||
\(545\) | − | 474000.i | − | 1.59583i | ||||||
\(546\) | 186866.i | 0.626822i | ||||||||
\(547\) | 297533.i | 0.994399i | 0.867636 | + | 0.497200i | \(0.165638\pi\) | ||||
−0.867636 | + | 0.497200i | \(0.834362\pi\) | |||||||
\(548\) | −13542.2 | −0.0450948 | ||||||||
\(549\) | −612446. | −2.03200 | ||||||||
\(550\) | − | 385120.i | − | 1.27312i | ||||||
\(551\) | −170325. | + | 109834.i | −0.561014 | + | 0.361772i | ||||
\(552\) | 93290.4 | 0.306167 | ||||||||
\(553\) | 92753.2i | 0.303304i | ||||||||
\(554\) | 247586.i | 0.806689i | ||||||||
\(555\) | 1.53758e6 | 4.99173 | ||||||||
\(556\) | 298933. | 0.966996 | ||||||||
\(557\) | 192568. | 0.620687 | 0.310344 | − | 0.950624i | \(-0.399556\pi\) | ||||
0.310344 | + | 0.950624i | \(0.399556\pi\) | |||||||
\(558\) | 110278. | 0.354177 | ||||||||
\(559\) | 15095.9i | 0.0483097i | ||||||||
\(560\) | −166321. | −0.530360 | ||||||||
\(561\) | − | 560981.i | − | 1.78247i | ||||||
\(562\) | −377023. | −1.19370 | ||||||||
\(563\) | 21470.7i | 0.0677376i | 0.999426 | + | 0.0338688i | \(0.0107828\pi\) | ||||
−0.999426 | + | 0.0338688i | \(0.989217\pi\) | |||||||
\(564\) | − | 10201.8i | − | 0.0320713i | ||||||
\(565\) | 198922.i | 0.623139i | ||||||||
\(566\) | − | 84586.4i | − | 0.264039i | ||||||
\(567\) | −298781. | −0.929367 | ||||||||
\(568\) | −185159. | −0.573914 | ||||||||
\(569\) | 51249.7i | 0.158295i | 0.996863 | + | 0.0791474i | \(0.0252198\pi\) | ||||
−0.996863 | + | 0.0791474i | \(0.974780\pi\) | |||||||
\(570\) | 353434. | + | 548085.i | 1.08782 | + | 1.68693i | ||||
\(571\) | 515089. | 1.57983 | 0.789914 | − | 0.613218i | \(-0.210125\pi\) | ||||
0.789914 | + | 0.613218i | \(0.210125\pi\) | |||||||
\(572\) | − | 67823.3i | − | 0.207294i | ||||||
\(573\) | − | 164477.i | − | 0.500951i | ||||||
\(574\) | 121891. | 0.369954 | ||||||||
\(575\) | 297584. | 0.900065 | ||||||||
\(576\) | 79083.3 | 0.238364 | ||||||||
\(577\) | −419849. | −1.26108 | −0.630538 | − | 0.776159i | \(-0.717166\pi\) | ||||
−0.630538 | + | 0.776159i | \(0.717166\pi\) | |||||||
\(578\) | − | 13890.4i | − | 0.0415775i | ||||||
\(579\) | −389114. | −1.16070 | ||||||||
\(580\) | 186943.i | 0.555717i | ||||||||
\(581\) | −333855. | −0.989020 | ||||||||
\(582\) | − | 46792.5i | − | 0.138143i | ||||||
\(583\) | 539658.i | 1.58775i | ||||||||
\(584\) | − | 166204.i | − | 0.487320i | ||||||
\(585\) | − | 443366.i | − | 1.29554i | ||||||
\(586\) | −120563. | −0.351090 | ||||||||
\(587\) | 311469. | 0.903939 | 0.451970 | − | 0.892033i | \(-0.350722\pi\) | ||||
0.451970 | + | 0.892033i | \(0.350722\pi\) | |||||||
\(588\) | 183772.i | 0.531527i | ||||||||
\(589\) | −76582.5 | + | 49384.5i | −0.220749 | + | 0.142351i | ||||
\(590\) | −56155.1 | −0.161319 | ||||||||
\(591\) | 69617.9i | 0.199318i | ||||||||
\(592\) | 154069.i | 0.439614i | ||||||||
\(593\) | −131604. | −0.374247 | −0.187124 | − | 0.982336i | \(-0.559917\pi\) | ||||
−0.187124 | + | 0.982336i | \(0.559917\pi\) | |||||||
\(594\) | 391956. | 1.11087 | ||||||||
\(595\) | −772807. | −2.18292 | ||||||||
\(596\) | 48297.8 | 0.135967 | ||||||||
\(597\) | 1.03881e6i | 2.91465i | ||||||||
\(598\) | 52407.3 | 0.146551 | ||||||||
\(599\) | 199776.i | 0.556788i | 0.960467 | + | 0.278394i | \(0.0898021\pi\) | ||||
−0.960467 | + | 0.278394i | \(0.910198\pi\) | |||||||
\(600\) | 384556. | 1.06821 | ||||||||
\(601\) | − | 328476.i | − | 0.909399i | −0.890645 | − | 0.454700i | \(-0.849747\pi\) | ||
0.890645 | − | 0.454700i | \(-0.150253\pi\) | |||||||
\(602\) | 38656.5i | 0.106667i | ||||||||
\(603\) | − | 789592.i | − | 2.17154i | ||||||
\(604\) | − | 164953.i | − | 0.452153i | ||||||
\(605\) | 19675.5 | 0.0537544 | ||||||||
\(606\) | −60489.0 | −0.164714 | ||||||||
\(607\) | − | 275312.i | − | 0.747219i | −0.927586 | − | 0.373610i | \(-0.878120\pi\) | ||
0.927586 | − | 0.373610i | \(-0.121880\pi\) | |||||||
\(608\) | −54919.4 | + | 35414.9i | −0.148566 | + | 0.0958031i | ||||
\(609\) | 537845. | 1.45018 | ||||||||
\(610\) | − | 466811.i | − | 1.25453i | ||||||
\(611\) | − | 5731.00i | − | 0.0153514i | ||||||
\(612\) | 367460. | 0.981085 | ||||||||
\(613\) | −473140. | −1.25912 | −0.629562 | − | 0.776950i | \(-0.716766\pi\) | ||||
−0.629562 | + | 0.776950i | \(0.716766\pi\) | |||||||
\(614\) | 110443. | 0.292956 | ||||||||
\(615\) | −440865. | −1.16562 | ||||||||
\(616\) | − | 173677.i | − | 0.457701i | ||||||
\(617\) | 10864.2 | 0.0285382 | 0.0142691 | − | 0.999898i | \(-0.495458\pi\) | ||||
0.0142691 | + | 0.999898i | \(0.495458\pi\) | |||||||
\(618\) | − | 484497.i | − | 1.26857i | ||||||
\(619\) | 8963.62 | 0.0233939 | 0.0116969 | − | 0.999932i | \(-0.496277\pi\) | ||||
0.0116969 | + | 0.999932i | \(0.496277\pi\) | |||||||
\(620\) | 84054.8i | 0.218665i | ||||||||
\(621\) | 302866.i | 0.785357i | ||||||||
\(622\) | − | 224102.i | − | 0.579248i | ||||||
\(623\) | 697535.i | 1.79717i | ||||||||
\(624\) | 67723.8 | 0.173929 | ||||||||
\(625\) | 143834. | 0.368214 | ||||||||
\(626\) | 302864.i | 0.772857i | ||||||||
\(627\) | −572327. | + | 369067.i | −1.45583 | + | 0.938793i | ||||
\(628\) | 8348.36 | 0.0211681 | ||||||||
\(629\) | 715879.i | 1.80942i | ||||||||
\(630\) | − | 1.13534e6i | − | 2.86052i | ||||||
\(631\) | −439268. | −1.10324 | −0.551621 | − | 0.834095i | \(-0.685991\pi\) | ||||
−0.551621 | + | 0.834095i | \(0.685991\pi\) | |||||||
\(632\) | 33615.6 | 0.0841603 | ||||||||
\(633\) | −43223.0 | −0.107872 | ||||||||
\(634\) | −375966. | −0.935340 | ||||||||
\(635\) | − | 730608.i | − | 1.81191i | ||||||
\(636\) | −538867. | −1.33219 | ||||||||
\(637\) | 103237.i | 0.254423i | ||||||||
\(638\) | −195212. | −0.479585 | ||||||||
\(639\) | − | 1.26393e6i | − | 3.09544i | ||||||
\(640\) | 60278.0i | 0.147163i | ||||||||
\(641\) | − | 351470.i | − | 0.855406i | −0.903919 | − | 0.427703i | \(-0.859323\pi\) | ||
0.903919 | − | 0.427703i | \(-0.140677\pi\) | |||||||
\(642\) | − | 21790.8i | − | 0.0528694i | ||||||
\(643\) | −257336. | −0.622412 | −0.311206 | − | 0.950342i | \(-0.600733\pi\) | ||||
−0.311206 | + | 0.950342i | \(0.600733\pi\) | |||||||
\(644\) | 134201. | 0.323582 | ||||||||
\(645\) | − | 139816.i | − | 0.336076i | ||||||
\(646\) | −255182. | + | 164555.i | −0.611485 | + | 0.394318i | ||||
\(647\) | 352433. | 0.841915 | 0.420957 | − | 0.907080i | \(-0.361694\pi\) | ||||
0.420957 | + | 0.907080i | \(0.361694\pi\) | |||||||
\(648\) | 108284.i | 0.257879i | ||||||||
\(649\) | − | 58639.0i | − | 0.139218i | ||||||
\(650\) | 216030. | 0.511314 | ||||||||
\(651\) | 241830. | 0.570621 | ||||||||
\(652\) | −12703.3 | −0.0298829 | ||||||||
\(653\) | −51680.8 | −0.121200 | −0.0606001 | − | 0.998162i | \(-0.519301\pi\) | ||||
−0.0606001 | + | 0.998162i | \(0.519301\pi\) | |||||||
\(654\) | 494240.i | 1.15553i | ||||||||
\(655\) | −308094. | −0.718126 | ||||||||
\(656\) | − | 44175.8i | − | 0.102654i | ||||||
\(657\) | 1.13454e6 | 2.62839 | ||||||||
\(658\) | − | 14675.6i | − | 0.0338956i | ||||||
\(659\) | 144227.i | 0.332105i | 0.986117 | + | 0.166053i | \(0.0531021\pi\) | ||||
−0.986117 | + | 0.166053i | \(0.946898\pi\) | |||||||
\(660\) | 628170.i | 1.44208i | ||||||||
\(661\) | − | 615181.i | − | 1.40799i | −0.710205 | − | 0.703995i | \(-0.751398\pi\) | ||
0.710205 | − | 0.703995i | \(-0.248602\pi\) | |||||||
\(662\) | −126213. | −0.287997 | ||||||||
\(663\) | 314678. | 0.715878 | ||||||||
\(664\) | 120996.i | 0.274431i | ||||||||
\(665\) | 508426. | + | 788438.i | 1.14970 | + | 1.78289i | ||||
\(666\) | −1.05171e6 | −2.37108 | ||||||||
\(667\) | − | 150841.i | − | 0.339054i | ||||||
\(668\) | 170223.i | 0.381474i | ||||||||
\(669\) | −565765. | −1.26411 | ||||||||
\(670\) | 601834. | 1.34069 | ||||||||
\(671\) | 487459. | 1.08266 | ||||||||
\(672\) | 173423. | 0.384032 | ||||||||
\(673\) | 334936.i | 0.739489i | 0.929133 | + | 0.369745i | \(0.120555\pi\) | ||||
−0.929133 | + | 0.369745i | \(0.879445\pi\) | |||||||
\(674\) | 14545.2 | 0.0320185 | ||||||||
\(675\) | 1.24845e6i | 2.74009i | ||||||||
\(676\) | −190443. | −0.416746 | ||||||||
\(677\) | − | 504808.i | − | 1.10141i | −0.834700 | − | 0.550705i | \(-0.814359\pi\) | ||
0.834700 | − | 0.550705i | \(-0.185641\pi\) | |||||||
\(678\) | − | 207416.i | − | 0.451214i | ||||||
\(679\) | − | 67312.5i | − | 0.146001i | ||||||
\(680\) | 280081.i | 0.605711i | ||||||||
\(681\) | −871992. | −1.88026 | ||||||||
\(682\) | −87772.6 | −0.188708 | ||||||||
\(683\) | 690506.i | 1.48022i | 0.672486 | + | 0.740110i | \(0.265227\pi\) | ||||
−0.672486 | + | 0.740110i | \(0.734773\pi\) | |||||||
\(684\) | −241750. | − | 374892.i | −0.516719 | − | 0.801297i | ||||
\(685\) | 70459.8 | 0.150162 | ||||||||
\(686\) | − | 159632.i | − | 0.339212i | ||||||
\(687\) | − | 117121.i | − | 0.248153i | ||||||
\(688\) | 14009.9 | 0.0295977 | ||||||||
\(689\) | −302717. | −0.637673 | ||||||||
\(690\) | −485390. | −1.01951 | ||||||||
\(691\) | 461905. | 0.967379 | 0.483690 | − | 0.875240i | \(-0.339296\pi\) | ||||
0.483690 | + | 0.875240i | \(0.339296\pi\) | |||||||
\(692\) | − | 189035.i | − | 0.394756i | ||||||
\(693\) | 1.18556e6 | 2.46863 | ||||||||
\(694\) | 496846.i | 1.03158i | ||||||||
\(695\) | −1.55535e6 | −3.22002 | ||||||||
\(696\) | − | 194926.i | − | 0.402394i | ||||||
\(697\) | − | 205262.i | − | 0.422516i | ||||||
\(698\) | − | 387848.i | − | 0.796069i | ||||||
\(699\) | − | 1.40019e6i | − | 2.86571i | ||||||
\(700\) | 553196. | 1.12897 | ||||||||
\(701\) | −410170. | −0.834694 | −0.417347 | − | 0.908747i | \(-0.637040\pi\) | ||||
−0.417347 | + | 0.908747i | \(0.637040\pi\) | |||||||
\(702\) | 219864.i | 0.446150i | ||||||||
\(703\) | 730358. | − | 470974.i | 1.47783 | − | 0.952985i | ||||
\(704\) | −62944.1 | −0.127002 | ||||||||
\(705\) | 53079.7i | 0.106795i | ||||||||
\(706\) | 563962.i | 1.13146i | ||||||||
\(707\) | −87015.4 | −0.174083 | ||||||||
\(708\) | 58553.0 | 0.116811 | ||||||||
\(709\) | 368245. | 0.732562 | 0.366281 | − | 0.930504i | \(-0.380631\pi\) | ||||
0.366281 | + | 0.930504i | \(0.380631\pi\) | |||||||
\(710\) | 963380. | 1.91109 | ||||||||
\(711\) | 229467.i | 0.453923i | ||||||||
\(712\) | 252801. | 0.498675 | ||||||||
\(713\) | − | 67822.3i | − | 0.133411i | ||||||
\(714\) | 805806. | 1.58064 | ||||||||
\(715\) | 352884.i | 0.690272i | ||||||||
\(716\) | − | 436641.i | − | 0.851723i | ||||||
\(717\) | 1.69039e6i | 3.28813i | ||||||||
\(718\) | − | 17841.6i | − | 0.0346086i | ||||||
\(719\) | −460066. | −0.889943 | −0.444971 | − | 0.895545i | \(-0.646786\pi\) | ||||
−0.444971 | + | 0.895545i | \(0.646786\pi\) | |||||||
\(720\) | −411470. | −0.793731 | ||||||||
\(721\) | − | 696965.i | − | 1.34073i | ||||||
\(722\) | 335766. | + | 152083.i | 0.644114 | + | 0.291748i | ||||
\(723\) | 896482. | 1.71500 | ||||||||
\(724\) | 387695.i | 0.739627i | ||||||||
\(725\) | − | 621788.i | − | 1.18295i | ||||||
\(726\) | −20515.6 | −0.0389234 | ||||||||
\(727\) | 196263. | 0.371339 | 0.185670 | − | 0.982612i | \(-0.440555\pi\) | ||||
0.185670 | + | 0.982612i | \(0.440555\pi\) | |||||||
\(728\) | 97422.9 | 0.183822 | ||||||||
\(729\) | 661866. | 1.24542 | ||||||||
\(730\) | 864757.i | 1.62274i | ||||||||
\(731\) | 65096.8 | 0.121822 | ||||||||
\(732\) | 486744.i | 0.908403i | ||||||||
\(733\) | 578892. | 1.07743 | 0.538716 | − | 0.842487i | \(-0.318910\pi\) | ||||
0.538716 | + | 0.842487i | \(0.318910\pi\) | |||||||
\(734\) | − | 149755.i | − | 0.277964i | ||||||
\(735\) | − | 956167.i | − | 1.76994i | ||||||
\(736\) | − | 48637.2i | − | 0.0897869i | ||||||
\(737\) | 628453.i | 1.15701i | ||||||||
\(738\) | 301553. | 0.553670 | ||||||||
\(739\) | 721624. | 1.32136 | 0.660681 | − | 0.750667i | \(-0.270268\pi\) | ||||
0.660681 | + | 0.750667i | \(0.270268\pi\) | |||||||
\(740\) | − | 801621.i | − | 1.46388i | ||||||
\(741\) | −207025. | − | 321042.i | −0.377039 | − | 0.584690i | ||||
\(742\) | −775177. | −1.40797 | ||||||||
\(743\) | − | 963975.i | − | 1.74618i | −0.487562 | − | 0.873088i | \(-0.662114\pi\) | ||
0.487562 | − | 0.873088i | \(-0.337886\pi\) | |||||||
\(744\) | − | 87643.9i | − | 0.158335i | ||||||
\(745\) | −251293. | −0.452760 | ||||||||
\(746\) | −26341.1 | −0.0473322 | ||||||||
\(747\) | −825942. | −1.48016 | ||||||||
\(748\) | −292469. | −0.522729 | ||||||||
\(749\) | − | 31346.8i | − | 0.0558766i | ||||||
\(750\) | −871756. | −1.54979 | ||||||||
\(751\) | − | 632486.i | − | 1.12143i | −0.828010 | − | 0.560713i | \(-0.810527\pi\) | ||
0.828010 | − | 0.560713i | \(-0.189473\pi\) | |||||||
\(752\) | −5318.71 | −0.00940526 | ||||||||
\(753\) | 264823.i | 0.467052i | ||||||||
\(754\) | − | 109503.i | − | 0.192611i | ||||||
\(755\) | 858249.i | 1.50563i | ||||||||
\(756\) | 563014.i | 0.985090i | ||||||||
\(757\) | 684418. | 1.19434 | 0.597172 | − | 0.802113i | \(-0.296291\pi\) | ||||
0.597172 | + | 0.802113i | \(0.296291\pi\) | |||||||
\(758\) | −504283. | −0.877680 | ||||||||
\(759\) | − | 506859.i | − | 0.879840i | ||||||
\(760\) | 285746. | − | 184264.i | 0.494712 | − | 0.319016i | ||||
\(761\) | −201444. | −0.347845 | −0.173923 | − | 0.984759i | \(-0.555644\pi\) | ||||
−0.173923 | + | 0.984759i | \(0.555644\pi\) | |||||||
\(762\) | 761805.i | 1.31200i | ||||||||
\(763\) | 710980.i | 1.22126i | ||||||||
\(764\) | −85750.4 | −0.146909 | ||||||||
\(765\) | −1.91189e6 | −3.26693 | ||||||||
\(766\) | 78530.6 | 0.133839 | ||||||||
\(767\) | 32893.1 | 0.0559131 | ||||||||
\(768\) | − | 62851.9i | − | 0.106560i | ||||||
\(769\) | 343992. | 0.581695 | 0.290847 | − | 0.956769i | \(-0.406063\pi\) | ||||
0.290847 | + | 0.956769i | \(0.406063\pi\) | |||||||
\(770\) | 903643.i | 1.52411i | ||||||||
\(771\) | 632135. | 1.06341 | ||||||||
\(772\) | 202866.i | 0.340388i | ||||||||
\(773\) | − | 323326.i | − | 0.541105i | −0.962705 | − | 0.270553i | \(-0.912794\pi\) | ||
0.962705 | − | 0.270553i | \(-0.0872064\pi\) | |||||||
\(774\) | 95634.5i | 0.159637i | ||||||||
\(775\) | − | 279573.i | − | 0.465469i | ||||||
\(776\) | −24395.4 | −0.0405121 | ||||||||
\(777\) | −2.30630e6 | −3.82010 | ||||||||
\(778\) | − | 682032.i | − | 1.12680i | ||||||
\(779\) | −209414. | + | 135041.i | −0.345088 | + | 0.222531i | ||||
\(780\) | −352367. | −0.579170 | ||||||||
\(781\) | 1.00599e6i | 1.64927i | ||||||||
\(782\) | − | 225992.i | − | 0.369556i | ||||||
\(783\) | 632824. | 1.03219 | ||||||||
\(784\) | 95810.2 | 0.155876 | ||||||||
\(785\) | −43436.5 | −0.0704881 | ||||||||
\(786\) | 321250. | 0.519993 | ||||||||
\(787\) | − | 526771.i | − | 0.850496i | −0.905077 | − | 0.425248i | \(-0.860187\pi\) | ||
0.905077 | − | 0.425248i | \(-0.139813\pi\) | |||||||
\(788\) | 36295.5 | 0.0584521 | ||||||||
\(789\) | 631890.i | 1.01505i | ||||||||
\(790\) | −174902. | −0.280247 | ||||||||
\(791\) | − | 298374.i | − | 0.476879i | ||||||
\(792\) | − | 429670.i | − | 0.684991i | ||||||
\(793\) | 273436.i | 0.434820i | ||||||||
\(794\) | − | 664454.i | − | 1.05396i | ||||||
\(795\) | 2.80372e6 | 4.43609 | ||||||||
\(796\) | 541585. | 0.854753 | ||||||||
\(797\) | 937353.i | 1.47566i | 0.674986 | + | 0.737831i | \(0.264150\pi\) | ||||
−0.674986 | + | 0.737831i | \(0.735850\pi\) | |||||||
\(798\) | −530136. | − | 822104.i | −0.832495 | − | 1.29098i | ||||
\(799\) | −24713.3 | −0.0387113 | ||||||||
\(800\) | − | 200489.i | − | 0.313264i | ||||||
\(801\) | 1.72567e6i | 2.68963i | ||||||||
\(802\) | −881055. | −1.36979 | ||||||||
\(803\) | −903006. | −1.40042 | ||||||||
\(804\) | −627532. | −0.970787 | ||||||||
\(805\) | −698249. | −1.07750 | ||||||||
\(806\) | − | 49235.4i | − | 0.0757891i | ||||||
\(807\) | −304727. | −0.467911 | ||||||||
\(808\) | 31536.1i | 0.0483043i | ||||||||
\(809\) | −339941. | −0.519405 | −0.259702 | − | 0.965689i | \(-0.583624\pi\) | ||||
−0.259702 | + | 0.965689i | \(0.583624\pi\) | |||||||
\(810\) | − | 563403.i | − | 0.858715i | ||||||
\(811\) | − | 421572.i | − | 0.640958i | −0.947256 | − | 0.320479i | \(-0.896156\pi\) | ||
0.947256 | − | 0.320479i | \(-0.103844\pi\) | |||||||
\(812\) | − | 280407.i | − | 0.425282i | ||||||
\(813\) | − | 1.70290e6i | − | 2.57637i | ||||||
\(814\) | 837077. | 1.26333 | ||||||||
\(815\) | 66095.4 | 0.0995076 | ||||||||
\(816\) | − | 292040.i | − | 0.438594i | ||||||
\(817\) | −42826.9 | − | 66413.4i | −0.0641612 | − | 0.0994974i | ||||
\(818\) | 689108. | 1.02987 | ||||||||
\(819\) | 665030.i | 0.991456i | ||||||||
\(820\) | 229846.i | 0.341830i | ||||||||
\(821\) | −832671. | −1.23534 | −0.617671 | − | 0.786437i | \(-0.711923\pi\) | ||||
−0.617671 | + | 0.786437i | \(0.711923\pi\) | |||||||
\(822\) | −73468.5 | −0.108732 | ||||||||
\(823\) | 193463. | 0.285627 | 0.142813 | − | 0.989750i | \(-0.454385\pi\) | ||||
0.142813 | + | 0.989750i | \(0.454385\pi\) | |||||||
\(824\) | −252594. | −0.372022 | ||||||||
\(825\) | − | 2.08934e6i | − | 3.06974i | ||||||
\(826\) | 84230.4 | 0.123455 | ||||||||
\(827\) | − | 414119.i | − | 0.605500i | −0.953070 | − | 0.302750i | \(-0.902095\pi\) | ||
0.953070 | − | 0.302750i | \(-0.0979047\pi\) | |||||||
\(828\) | 332008. | 0.484270 | ||||||||
\(829\) | − | 1.10281e6i | − | 1.60469i | −0.596858 | − | 0.802347i | \(-0.703585\pi\) | ||
0.596858 | − | 0.802347i | \(-0.296415\pi\) | |||||||
\(830\) | − | 629540.i | − | 0.913834i | ||||||
\(831\) | 1.34319e6i | 1.94508i | ||||||||
\(832\) | − | 35308.0i | − | 0.0510066i | ||||||
\(833\) | 445181. | 0.641574 | ||||||||
\(834\) | 1.62176e6 | 2.33161 | ||||||||
\(835\) | − | 885669.i | − | 1.27028i | ||||||
\(836\) | 192414. | + | 298384.i | 0.275311 | + | 0.426937i | ||||
\(837\) | 284535. | 0.406148 | ||||||||
\(838\) | 548164.i | 0.780589i | ||||||||
\(839\) | 420379.i | 0.597196i | 0.954379 | + | 0.298598i | \(0.0965189\pi\) | ||||
−0.954379 | + | 0.298598i | \(0.903481\pi\) | |||||||
\(840\) | −902318. | −1.27880 | ||||||||
\(841\) | 392105. | 0.554384 | ||||||||
\(842\) | 386181. | 0.544712 | ||||||||
\(843\) | −2.04541e6 | −2.87823 | ||||||||
\(844\) | 22534.4i | 0.0316346i | ||||||||
\(845\) | 990875. | 1.38773 | ||||||||
\(846\) | − | 36306.7i | − | 0.0507278i | ||||||
\(847\) | −29512.4 | −0.0411374 | ||||||||
\(848\) | 280940.i | 0.390680i | ||||||||
\(849\) | − | 458895.i | − | 0.636646i | ||||||
\(850\) | − | 931570.i | − | 1.28937i | ||||||
\(851\) | 646813.i | 0.893140i | ||||||||
\(852\) | −1.00452e6 | −1.38381 | ||||||||
\(853\) | −1.00746e6 | −1.38462 | −0.692310 | − | 0.721600i | \(-0.743407\pi\) | ||||
−0.692310 | + | 0.721600i | \(0.743407\pi\) | |||||||
\(854\) | 700198.i | 0.960074i | ||||||||
\(855\) | 1.25782e6 | + | 1.95056e6i | 1.72063 | + | 2.66825i | ||||
\(856\) | −11360.7 | −0.0155045 | ||||||||
\(857\) | − | 425334.i | − | 0.579119i | −0.957160 | − | 0.289560i | \(-0.906491\pi\) | ||
0.957160 | − | 0.289560i | \(-0.0935089\pi\) | |||||||
\(858\) | − | 367953.i | − | 0.499824i | ||||||
\(859\) | −101991. | −0.138221 | −0.0691105 | − | 0.997609i | \(-0.522016\pi\) | ||||
−0.0691105 | + | 0.997609i | \(0.522016\pi\) | |||||||
\(860\) | −72893.5 | −0.0985580 | ||||||||
\(861\) | 661280. | 0.892029 | ||||||||
\(862\) | 915959. | 1.23271 | ||||||||
\(863\) | − | 295578.i | − | 0.396872i | −0.980114 | − | 0.198436i | \(-0.936414\pi\) | ||
0.980114 | − | 0.198436i | \(-0.0635862\pi\) | |||||||
\(864\) | 204048. | 0.273341 | ||||||||
\(865\) | 983547.i | 1.31451i | ||||||||
\(866\) | 809295. | 1.07912 | ||||||||
\(867\) | − | 75357.6i | − | 0.100251i | ||||||
\(868\) | − | 126079.i | − | 0.167341i | ||||||
\(869\) | − | 182638.i | − | 0.241853i | ||||||
\(870\) | 1.01420e6i | 1.33994i | ||||||||
\(871\) | −352526. | −0.464681 | ||||||||
\(872\) | 257673. | 0.338873 | ||||||||
\(873\) | − | 166528.i | − | 0.218504i | ||||||
\(874\) | −230563. | + | 148679.i | −0.301833 | + | 0.194638i | ||||
\(875\) | −1.25405e6 | −1.63794 | ||||||||
\(876\) | − | 901682.i | − | 1.17502i | ||||||
\(877\) | 267600.i | 0.347926i | 0.984752 | + | 0.173963i | \(0.0556573\pi\) | ||||
−0.984752 | + | 0.173963i | \(0.944343\pi\) | |||||||
\(878\) | −74340.5 | −0.0964354 | ||||||||
\(879\) | −654073. | −0.846542 | ||||||||
\(880\) | 327498. | 0.422906 | ||||||||
\(881\) | 1.32998e6 | 1.71353 | 0.856765 | − | 0.515707i | \(-0.172471\pi\) | ||||
0.856765 | + | 0.515707i | \(0.172471\pi\) | |||||||
\(882\) | 654021.i | 0.840726i | ||||||||
\(883\) | −229460. | −0.294296 | −0.147148 | − | 0.989114i | \(-0.547009\pi\) | ||||
−0.147148 | + | 0.989114i | \(0.547009\pi\) | |||||||
\(884\) | − | 164058.i | − | 0.209939i | ||||||
\(885\) | −304651. | −0.388970 | ||||||||
\(886\) | 899120.i | 1.14538i | ||||||||
\(887\) | 161937.i | 0.205825i | 0.994690 | + | 0.102913i | \(0.0328162\pi\) | ||||
−0.994690 | + | 0.102913i | \(0.967184\pi\) | |||||||
\(888\) | 835850.i | 1.05999i | ||||||||
\(889\) | 1.09588e6i | 1.38663i | ||||||||
\(890\) | −1.31532e6 | −1.66055 | ||||||||
\(891\) | 588323. | 0.741072 | ||||||||
\(892\) | 294963.i | 0.370713i | ||||||||
\(893\) | 16258.8 | + | 25213.2i | 0.0203885 | + | 0.0316173i | ||||
\(894\) | 262023. | 0.327842 | ||||||||
\(895\) | 2.27184e6i | 2.83617i | ||||||||
\(896\) | − | 90414.4i | − | 0.112622i | ||||||
\(897\) | 284319. | 0.353362 | ||||||||
\(898\) | −194394. | −0.241063 | ||||||||
\(899\) | −141711. | −0.175342 | ||||||||
\(900\) | 1.36858e6 | 1.68961 | ||||||||
\(901\) | 1.30538e6i | 1.60801i | ||||||||
\(902\) | −240013. | −0.295000 | ||||||||
\(903\) | 209718.i | 0.257194i | ||||||||
\(904\) | −108137. | −0.132323 | ||||||||
\(905\) | − | 2.01717e6i | − | 2.46290i | ||||||
\(906\) | − | 894897.i | − | 1.09023i | ||||||
\(907\) | − | 530320.i | − | 0.644649i | −0.946629 | − | 0.322325i | \(-0.895536\pi\) | ||
0.946629 | − | 0.322325i | \(-0.104464\pi\) | |||||||
\(908\) | 454615.i | 0.551407i | ||||||||
\(909\) | −215272. | −0.260532 | ||||||||
\(910\) | −506891. | −0.612114 | ||||||||
\(911\) | 969623.i | 1.16833i | 0.811634 | + | 0.584166i | \(0.198578\pi\) | ||||
−0.811634 | + | 0.584166i | \(0.801422\pi\) | |||||||
\(912\) | −297947. | + | 192132.i | −0.358220 | + | 0.230999i | ||||
\(913\) | 657385. | 0.788639 | ||||||||
\(914\) | − | 517203.i | − | 0.619111i | ||||||
\(915\) | − | 2.53253e6i | − | 3.02491i | ||||||
\(916\) | −61061.1 | −0.0727736 | ||||||||
\(917\) | 462128. | 0.549571 | ||||||||
\(918\) | 948105. | 1.12505 | ||||||||
\(919\) | 853445. | 1.01052 | 0.505260 | − | 0.862967i | \(-0.331397\pi\) | ||||
0.505260 | + | 0.862967i | \(0.331397\pi\) | |||||||
\(920\) | 253059.i | 0.298983i | ||||||||
\(921\) | 599172. | 0.706370 | ||||||||
\(922\) | − | 403910.i | − | 0.475141i | ||||||
\(923\) | −564303. | −0.662382 | ||||||||
\(924\) | − | 942229.i | − | 1.10360i | ||||||
\(925\) | 2.66625e6i | 3.11614i | ||||||||
\(926\) | − | 272131.i | − | 0.317363i | ||||||
\(927\) | − | 1.72426e6i | − | 2.00652i | ||||||
\(928\) | −101625. | −0.118006 | ||||||||
\(929\) | 580185. | 0.672257 | 0.336128 | − | 0.941816i | \(-0.390882\pi\) | ||||
0.336128 | + | 0.941816i | \(0.390882\pi\) | |||||||
\(930\) | 456011.i | 0.527242i | ||||||||
\(931\) | −292882. | − | 454185.i | −0.337905 | − | 0.524002i | ||||
\(932\) | −729993. | −0.840402 | ||||||||
\(933\) | − | 1.21579e6i | − | 1.39667i | ||||||
\(934\) | − | 812667.i | − | 0.931577i | ||||||
\(935\) | 1.52172e6 | 1.74065 | ||||||||
\(936\) | 241020. | 0.275107 | ||||||||
\(937\) | −173996. | −0.198180 | −0.0990901 | − | 0.995078i | \(-0.531593\pi\) | ||||
−0.0990901 | + | 0.995078i | \(0.531593\pi\) | |||||||
\(938\) | −902725. | −1.02601 | ||||||||
\(939\) | 1.64309e6i | 1.86350i | ||||||||
\(940\) | 27673.3 | 0.0313188 | ||||||||
\(941\) | 288487.i | 0.325797i | 0.986643 | + | 0.162899i | \(0.0520844\pi\) | ||||
−0.986643 | + | 0.162899i | \(0.947916\pi\) | |||||||
\(942\) | 45291.3 | 0.0510402 | ||||||||
\(943\) | − | 185459.i | − | 0.208557i | ||||||
\(944\) | − | 30526.8i | − | 0.0342560i | ||||||
\(945\) | − | 2.92936e6i | − | 3.28027i | ||||||
\(946\) | − | 76117.6i | − | 0.0850556i | ||||||
\(947\) | 484204. | 0.539919 | 0.269959 | − | 0.962872i | \(-0.412990\pi\) | ||||
0.269959 | + | 0.962872i | \(0.412990\pi\) | |||||||
\(948\) | 182370. | 0.202926 | ||||||||
\(949\) | − | 506534.i | − | 0.562440i | ||||||
\(950\) | −950412. | + | 612876.i | −1.05309 | + | 0.679087i | ||||
\(951\) | −2.03968e6 | −2.25528 | ||||||||
\(952\) | − | 420110.i | − | 0.463542i | ||||||
\(953\) | 834271.i | 0.918590i | 0.888284 | + | 0.459295i | \(0.151898\pi\) | ||||
−0.888284 | + | 0.459295i | \(0.848102\pi\) | |||||||
\(954\) | −1.91775e6 | −2.10715 | ||||||||
\(955\) | 446159. | 0.489196 | ||||||||
\(956\) | 881290. | 0.964280 | ||||||||
\(957\) | −1.05906e6 | −1.15637 | ||||||||
\(958\) | − | 287064.i | − | 0.312786i | ||||||
\(959\) | −105687. | −0.114917 | ||||||||
\(960\) | 327018.i | 0.354837i | ||||||||
\(961\) | 859804. | 0.931006 | ||||||||
\(962\) | 469552.i | 0.507380i | ||||||||
\(963\) | − | 77550.7i | − | 0.0836244i | ||||||
\(964\) | − | 467384.i | − | 0.502944i | ||||||
\(965\) | − | 1.05551e6i | − | 1.13346i | ||||||
\(966\) | 728064. | 0.780217 | ||||||||
\(967\) | −268509. | −0.287148 | −0.143574 | − | 0.989640i | \(-0.545859\pi\) | ||||
−0.143574 | + | 0.989640i | \(0.545859\pi\) | |||||||
\(968\) | 10695.9i | 0.0114147i | ||||||||
\(969\) | −1.38441e6 | + | 892739.i | −1.47440 | + | 0.950773i | ||||
\(970\) | 126929. | 0.134902 | ||||||||
\(971\) | − | 513847.i | − | 0.544999i | −0.962156 | − | 0.272499i | \(-0.912150\pi\) | ||
0.962156 | − | 0.272499i | \(-0.0878503\pi\) | |||||||
\(972\) | − | 142975.i | − | 0.151330i | ||||||
\(973\) | 2.33296e6 | 2.46423 | ||||||||
\(974\) | 575132. | 0.606248 | ||||||||
\(975\) | 1.17200e6 | 1.23287 | ||||||||
\(976\) | 253766. | 0.266399 | ||||||||
\(977\) | − | 880047.i | − | 0.921970i | −0.887408 | − | 0.460985i | \(-0.847496\pi\) | ||
0.887408 | − | 0.460985i | \(-0.152504\pi\) | |||||||
\(978\) | −68917.7 | −0.0720532 | ||||||||
\(979\) | − | 1.37350e6i | − | 1.43306i | ||||||
\(980\) | −498500. | −0.519055 | ||||||||
\(981\) | 1.75893e6i | 1.82773i | ||||||||
\(982\) | 644196.i | 0.668029i | ||||||||
\(983\) | 1.15115e6i | 1.19131i | 0.803239 | + | 0.595656i | \(0.203108\pi\) | ||||
−0.803239 | + | 0.595656i | \(0.796892\pi\) | |||||||
\(984\) | − | 239661.i | − | 0.247518i | ||||||
\(985\) | −188845. | −0.194641 | ||||||||
\(986\) | −472200. | −0.485705 | ||||||||
\(987\) | − | 79617.3i | − | 0.0817285i | ||||||
\(988\) | −167376. | + | 107933.i | −0.171467 | + | 0.110571i | ||||
\(989\) | 58816.4 | 0.0601320 | ||||||||
\(990\) | 2.23557e6i | 2.28096i | ||||||||
\(991\) | − | 1.55344e6i | − | 1.58178i | −0.611956 | − | 0.790892i | \(-0.709617\pi\) | ||
0.611956 | − | 0.790892i | \(-0.290383\pi\) | |||||||
\(992\) | −45693.4 | −0.0464334 | ||||||||
\(993\) | −684727. | −0.694415 | ||||||||
\(994\) | −1.44503e6 | −1.46253 | ||||||||
\(995\) | −2.81787e6 | −2.84626 | ||||||||
\(996\) | 656422.i | 0.661705i | ||||||||
\(997\) | −1.19520e6 | −1.20240 | −0.601200 | − | 0.799099i | \(-0.705310\pi\) | ||||
−0.601200 | + | 0.799099i | \(0.705310\pi\) | |||||||
\(998\) | 375697.i | 0.377204i | ||||||||
\(999\) | −2.71357e6 | −2.71901 |
(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 | 38.5.b.a.37.1 | ✓ | 8 | |
3.2 | odd | 2 | 342.5.d.a.37.5 | 8 | |||
4.3 | odd | 2 | 304.5.e.e.113.8 | 8 | |||
19.18 | odd | 2 | inner | 38.5.b.a.37.8 | yes | 8 | |
57.56 | even | 2 | 342.5.d.a.37.1 | 8 | |||
76.75 | even | 2 | 304.5.e.e.113.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.5.b.a.37.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
38.5.b.a.37.8 | yes | 8 | 19.18 | odd | 2 | inner | |
304.5.e.e.113.1 | 8 | 76.75 | even | 2 | |||
304.5.e.e.113.8 | 8 | 4.3 | odd | 2 | |||
342.5.d.a.37.1 | 8 | 57.56 | even | 2 | |||
342.5.d.a.37.5 | 8 | 3.2 | odd | 2 |