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 | 119.77 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.73459i | 1.93365i | 0.255443 | + | 0.966824i | \(0.417779\pi\) | ||||
−0.255443 | + | 0.966824i | \(0.582221\pi\) | |||||||
\(3\) | −8.52815 | + | 2.87588i | −0.947572 | + | 0.319542i | ||||
\(4\) | −43.8239 | −2.73899 | ||||||||
\(5\) | 0.620129i | 0.0248052i | 0.999923 | + | 0.0124026i | \(0.00394797\pi\) | ||||
−0.999923 | + | 0.0124026i | \(0.996052\pi\) | |||||||
\(6\) | −22.2437 | − | 65.9618i | −0.617881 | − | 1.83227i | ||||
\(7\) | 71.8012 | 1.46533 | 0.732666 | − | 0.680589i | \(-0.238276\pi\) | ||||
0.732666 | + | 0.680589i | \(0.238276\pi\) | |||||||
\(8\) | − | 215.207i | − | 3.36260i | ||||||
\(9\) | 64.4587 | − | 49.0518i | 0.795786 | − | 0.605578i | ||||
\(10\) | −4.79645 | −0.0479645 | ||||||||
\(11\) | 63.2025i | 0.522335i | 0.965294 | + | 0.261167i | \(0.0841075\pi\) | ||||
−0.965294 | + | 0.261167i | \(0.915893\pi\) | |||||||
\(12\) | 373.737 | − | 126.032i | 2.59540 | − | 0.875223i | ||||
\(13\) | 204.993 | 1.21298 | 0.606489 | − | 0.795092i | \(-0.292577\pi\) | ||||
0.606489 | + | 0.795092i | \(0.292577\pi\) | |||||||
\(14\) | 555.353i | 2.83344i | ||||||||
\(15\) | −1.78341 | − | 5.28856i | −0.00792629 | − | 0.0235047i | ||||
\(16\) | 963.353 | 3.76310 | ||||||||
\(17\) | − | 443.362i | − | 1.53412i | −0.641573 | − | 0.767062i | \(-0.721718\pi\) | ||
0.641573 | − | 0.767062i | \(-0.278282\pi\) | |||||||
\(18\) | 379.396 | + | 498.562i | 1.17097 | + | 1.53877i | ||||
\(19\) | −526.936 | −1.45966 | −0.729829 | − | 0.683630i | \(-0.760400\pi\) | ||||
−0.729829 | + | 0.683630i | \(0.760400\pi\) | |||||||
\(20\) | − | 27.1765i | − | 0.0679412i | ||||||
\(21\) | −612.332 | + | 206.491i | −1.38851 | + | 0.468235i | ||||
\(22\) | −488.846 | −1.01001 | ||||||||
\(23\) | − | 966.597i | − | 1.82722i | −0.406596 | − | 0.913608i | \(-0.633284\pi\) | ||
0.406596 | − | 0.913608i | \(-0.366716\pi\) | |||||||
\(24\) | 618.907 | + | 1835.31i | 1.07449 | + | 3.18631i | ||||
\(25\) | 624.615 | 0.999385 | ||||||||
\(26\) | 1585.54i | 2.34547i | ||||||||
\(27\) | −408.646 | + | 603.696i | −0.560558 | + | 0.828116i | ||||
\(28\) | −3146.61 | −4.01354 | ||||||||
\(29\) | − | 559.951i | − | 0.665816i | −0.942959 | − | 0.332908i | \(-0.891970\pi\) | ||
0.942959 | − | 0.332908i | \(-0.108030\pi\) | |||||||
\(30\) | 40.9048 | − | 13.7940i | 0.0454498 | − | 0.0153267i | ||||
\(31\) | 1278.62 | 1.33051 | 0.665256 | − | 0.746615i | \(-0.268322\pi\) | ||||
0.665256 | + | 0.746615i | \(0.268322\pi\) | |||||||
\(32\) | 4007.84i | 3.91390i | ||||||||
\(33\) | −181.763 | − | 539.001i | −0.166908 | − | 0.494950i | ||||
\(34\) | 3429.22 | 2.96645 | ||||||||
\(35\) | 44.5261i | 0.0363478i | ||||||||
\(36\) | −2824.83 | + | 2149.64i | −2.17965 | + | 1.65867i | ||||
\(37\) | 362.114 | 0.264510 | 0.132255 | − | 0.991216i | \(-0.457778\pi\) | ||||
0.132255 | + | 0.991216i | \(0.457778\pi\) | |||||||
\(38\) | − | 4075.64i | − | 2.82246i | ||||||
\(39\) | −1748.21 | + | 589.535i | −1.14938 | + | 0.387597i | ||||
\(40\) | 133.456 | 0.0834100 | ||||||||
\(41\) | 2028.46i | 1.20670i | 0.797477 | + | 0.603349i | \(0.206167\pi\) | ||||
−0.797477 | + | 0.603349i | \(0.793833\pi\) | |||||||
\(42\) | −1597.13 | − | 4736.14i | −0.905401 | − | 2.68488i | ||||
\(43\) | −487.652 | −0.263738 | −0.131869 | − | 0.991267i | \(-0.542098\pi\) | ||||
−0.131869 | + | 0.991267i | \(0.542098\pi\) | |||||||
\(44\) | − | 2769.78i | − | 1.43067i | ||||||
\(45\) | 30.4185 | + | 39.9727i | 0.0150215 | + | 0.0197396i | ||||
\(46\) | 7476.24 | 3.53319 | ||||||||
\(47\) | 34.7038i | 0.0157102i | 0.999969 | + | 0.00785510i | \(0.00250038\pi\) | ||||
−0.999969 | + | 0.00785510i | \(0.997500\pi\) | |||||||
\(48\) | −8215.62 | + | 2770.48i | −3.56581 | + | 1.20247i | ||||
\(49\) | 2754.42 | 1.14720 | ||||||||
\(50\) | 4831.15i | 1.93246i | ||||||||
\(51\) | 1275.05 | + | 3781.05i | 0.490216 | + | 1.45369i | ||||
\(52\) | −8983.61 | −3.32234 | ||||||||
\(53\) | − | 1648.43i | − | 0.586840i | −0.955984 | − | 0.293420i | \(-0.905207\pi\) | ||
0.955984 | − | 0.293420i | \(-0.0947934\pi\) | |||||||
\(54\) | −4669.34 | − | 3160.71i | −1.60128 | − | 1.08392i | ||||
\(55\) | −39.1937 | −0.0129566 | ||||||||
\(56\) | − | 15452.1i | − | 4.92733i | ||||||
\(57\) | 4493.79 | − | 1515.40i | 1.38313 | − | 0.466422i | ||||
\(58\) | 4330.99 | 1.28745 | ||||||||
\(59\) | 453.188i | 0.130189i | ||||||||
\(60\) | 78.1562 | + | 231.765i | 0.0217101 | + | 0.0643792i | ||||
\(61\) | −2514.15 | −0.675664 | −0.337832 | − | 0.941206i | \(-0.609694\pi\) | ||||
−0.337832 | + | 0.941206i | \(0.609694\pi\) | |||||||
\(62\) | 9889.62i | 2.57274i | ||||||||
\(63\) | 4628.21 | − | 3521.98i | 1.16609 | − | 0.887372i | ||||
\(64\) | −15585.3 | −3.80501 | ||||||||
\(65\) | 127.122i | 0.0300881i | ||||||||
\(66\) | 4168.95 | − | 1405.86i | 0.957059 | − | 0.322741i | ||||
\(67\) | −2378.22 | −0.529788 | −0.264894 | − | 0.964277i | \(-0.585337\pi\) | ||||
−0.264894 | + | 0.964277i | \(0.585337\pi\) | |||||||
\(68\) | 19429.8i | 4.20196i | ||||||||
\(69\) | 2779.81 | + | 8243.29i | 0.583872 | + | 1.73142i | ||||
\(70\) | −344.391 | −0.0702839 | ||||||||
\(71\) | 884.945i | 0.175550i | 0.996140 | + | 0.0877748i | \(0.0279756\pi\) | ||||
−0.996140 | + | 0.0877748i | \(0.972024\pi\) | |||||||
\(72\) | −10556.3 | − | 13871.9i | −2.03632 | − | 2.67591i | ||||
\(73\) | 7907.46 | 1.48385 | 0.741927 | − | 0.670480i | \(-0.233912\pi\) | ||||
0.741927 | + | 0.670480i | \(0.233912\pi\) | |||||||
\(74\) | 2800.80i | 0.511468i | ||||||||
\(75\) | −5326.81 | + | 1796.32i | −0.946989 | + | 0.319345i | ||||
\(76\) | 23092.4 | 3.99800 | ||||||||
\(77\) | 4538.02i | 0.765394i | ||||||||
\(78\) | −4559.82 | − | 13521.7i | −0.749477 | − | 2.22251i | ||||
\(79\) | −3006.62 | −0.481754 | −0.240877 | − | 0.970556i | \(-0.577435\pi\) | ||||
−0.240877 | + | 0.970556i | \(0.577435\pi\) | |||||||
\(80\) | 597.403i | 0.0933443i | ||||||||
\(81\) | 1748.84 | − | 6323.63i | 0.266551 | − | 0.963821i | ||||
\(82\) | −15689.3 | −2.33333 | ||||||||
\(83\) | − | 4564.48i | − | 0.662576i | −0.943530 | − | 0.331288i | \(-0.892517\pi\) | ||
0.943530 | − | 0.331288i | \(-0.107483\pi\) | |||||||
\(84\) | 26834.8 | − | 9049.26i | 3.80311 | − | 1.28249i | ||||
\(85\) | 274.942 | 0.0380542 | ||||||||
\(86\) | − | 3771.79i | − | 0.509977i | ||||||
\(87\) | 1610.35 | + | 4775.35i | 0.212756 | + | 0.630908i | ||||
\(88\) | 13601.6 | 1.75641 | ||||||||
\(89\) | 2010.89i | 0.253868i | 0.991911 | + | 0.126934i | \(0.0405137\pi\) | ||||
−0.991911 | + | 0.126934i | \(0.959486\pi\) | |||||||
\(90\) | −309.173 | + | 235.274i | −0.0381695 | + | 0.0290462i | ||||
\(91\) | 14718.8 | 1.77742 | ||||||||
\(92\) | 42360.1i | 5.00474i | ||||||||
\(93\) | −10904.3 | + | 3677.16i | −1.26076 | + | 0.425154i | ||||
\(94\) | −268.420 | −0.0303780 | ||||||||
\(95\) | − | 326.769i | − | 0.0362071i | ||||||
\(96\) | −11526.0 | − | 34179.4i | −1.25065 | − | 3.70870i | ||||
\(97\) | 7872.26 | 0.836673 | 0.418337 | − | 0.908292i | \(-0.362613\pi\) | ||||
0.418337 | + | 0.908292i | \(0.362613\pi\) | |||||||
\(98\) | 21304.3i | 2.21827i | ||||||||
\(99\) | 3100.20 | + | 4073.95i | 0.316314 | + | 0.415667i | ||||
\(100\) | −27373.1 | −2.73731 | ||||||||
\(101\) | − | 4233.74i | − | 0.415032i | −0.978232 | − | 0.207516i | \(-0.933462\pi\) | ||
0.978232 | − | 0.207516i | \(-0.0665380\pi\) | |||||||
\(102\) | −29244.9 | + | 9862.01i | −2.81093 | + | 0.947906i | ||||
\(103\) | 10764.8 | 1.01468 | 0.507341 | − | 0.861745i | \(-0.330628\pi\) | ||||
0.507341 | + | 0.861745i | \(0.330628\pi\) | |||||||
\(104\) | − | 44115.9i | − | 4.07877i | ||||||
\(105\) | −128.051 | − | 379.725i | −0.0116146 | − | 0.0344422i | ||||
\(106\) | 12750.0 | 1.13474 | ||||||||
\(107\) | − | 8243.20i | − | 0.719993i | −0.932954 | − | 0.359997i | \(-0.882778\pi\) | ||
0.932954 | − | 0.359997i | \(-0.117222\pi\) | |||||||
\(108\) | 17908.5 | − | 26456.3i | 1.53536 | − | 2.26820i | ||||
\(109\) | 4786.90 | 0.402903 | 0.201452 | − | 0.979498i | \(-0.435434\pi\) | ||||
0.201452 | + | 0.979498i | \(0.435434\pi\) | |||||||
\(110\) | − | 303.148i | − | 0.0250535i | ||||||
\(111\) | −3088.16 | + | 1041.39i | −0.250642 | + | 0.0845219i | ||||
\(112\) | 69169.9 | 5.51418 | ||||||||
\(113\) | − | 2505.20i | − | 0.196194i | −0.995177 | − | 0.0980971i | \(-0.968724\pi\) | ||
0.995177 | − | 0.0980971i | \(-0.0312756\pi\) | |||||||
\(114\) | 11721.0 | + | 34757.7i | 0.901895 | + | 2.67449i | ||||
\(115\) | 599.415 | 0.0453244 | ||||||||
\(116\) | 24539.2i | 1.82367i | ||||||||
\(117\) | 13213.6 | − | 10055.3i | 0.965272 | − | 0.734553i | ||||
\(118\) | −3505.22 | −0.251740 | ||||||||
\(119\) | − | 31833.9i | − | 2.24800i | ||||||
\(120\) | −1138.13 | + | 383.803i | −0.0790370 | + | 0.0266530i | ||||
\(121\) | 10646.4 | 0.727166 | ||||||||
\(122\) | − | 19445.9i | − | 1.30650i | ||||||
\(123\) | −5833.60 | − | 17299.0i | −0.385590 | − | 1.14343i | ||||
\(124\) | −56034.2 | −3.64427 | ||||||||
\(125\) | 774.923i | 0.0495951i | ||||||||
\(126\) | 27241.1 | + | 35797.3i | 1.71587 | + | 2.25481i | ||||
\(127\) | 16718.1 | 1.03652 | 0.518262 | − | 0.855222i | \(-0.326579\pi\) | ||||
0.518262 | + | 0.855222i | \(0.326579\pi\) | |||||||
\(128\) | − | 56420.8i | − | 3.44365i | ||||||
\(129\) | 4158.77 | − | 1402.43i | 0.249911 | − | 0.0842754i | ||||
\(130\) | −983.240 | −0.0581799 | ||||||||
\(131\) | 36.1996i | 0.00210941i | 0.999999 | + | 0.00105470i | \(0.000335723\pi\) | ||||
−0.999999 | + | 0.00105470i | \(0.999664\pi\) | |||||||
\(132\) | 7965.55 | + | 23621.1i | 0.457160 | + | 1.35567i | ||||
\(133\) | −37834.7 | −2.13888 | ||||||||
\(134\) | − | 18394.6i | − | 1.02442i | ||||||
\(135\) | −374.370 | − | 253.414i | −0.0205416 | − | 0.0139047i | ||||
\(136\) | −95414.4 | −5.15865 | ||||||||
\(137\) | − | 976.041i | − | 0.0520028i | −0.999662 | − | 0.0260014i | \(-0.991723\pi\) | ||
0.999662 | − | 0.0260014i | \(-0.00827744\pi\) | |||||||
\(138\) | −63758.5 | + | 21500.7i | −3.34796 | + | 1.12900i | ||||
\(139\) | −5174.94 | −0.267840 | −0.133920 | − | 0.990992i | \(-0.542757\pi\) | ||||
−0.133920 | + | 0.990992i | \(0.542757\pi\) | |||||||
\(140\) | − | 1951.31i | − | 0.0995564i | ||||||
\(141\) | −99.8039 | − | 295.959i | −0.00502006 | − | 0.0148865i | ||||
\(142\) | −6844.69 | −0.339451 | ||||||||
\(143\) | 12956.1i | 0.633581i | ||||||||
\(144\) | 62096.5 | − | 47254.2i | 2.99462 | − | 2.27885i | ||||
\(145\) | 347.242 | 0.0165157 | ||||||||
\(146\) | 61161.0i | 2.86925i | ||||||||
\(147\) | −23490.1 | + | 7921.36i | −1.08705 | + | 0.366577i | ||||
\(148\) | −15869.2 | −0.724490 | ||||||||
\(149\) | 24593.4i | 1.10776i | 0.832596 | + | 0.553881i | \(0.186854\pi\) | ||||
−0.832596 | + | 0.553881i | \(0.813146\pi\) | |||||||
\(150\) | −13893.8 | − | 41200.7i | −0.617501 | − | 1.83114i | ||||
\(151\) | 16890.9 | 0.740798 | 0.370399 | − | 0.928873i | \(-0.379221\pi\) | ||||
0.370399 | + | 0.928873i | \(0.379221\pi\) | |||||||
\(152\) | 113400.i | 4.90825i | ||||||||
\(153\) | −21747.7 | − | 28578.5i | −0.929031 | − | 1.22083i | ||||
\(154\) | −35099.7 | −1.48000 | ||||||||
\(155\) | 792.911i | 0.0330036i | ||||||||
\(156\) | 76613.6 | − | 25835.8i | 3.14816 | − | 1.06163i | ||||
\(157\) | −16131.7 | −0.654458 | −0.327229 | − | 0.944945i | \(-0.606115\pi\) | ||||
−0.327229 | + | 0.944945i | \(0.606115\pi\) | |||||||
\(158\) | − | 23255.0i | − | 0.931542i | ||||||
\(159\) | 4740.69 | + | 14058.1i | 0.187520 | + | 0.556073i | ||||
\(160\) | −2485.38 | −0.0970850 | ||||||||
\(161\) | − | 69402.9i | − | 2.67748i | ||||||
\(162\) | 48910.7 | + | 13526.6i | 1.86369 | + | 0.515416i | ||||
\(163\) | −40515.1 | −1.52490 | −0.762451 | − | 0.647046i | \(-0.776004\pi\) | ||||
−0.762451 | + | 0.647046i | \(0.776004\pi\) | |||||||
\(164\) | − | 88895.0i | − | 3.30514i | ||||||
\(165\) | 334.250 | − | 112.716i | 0.0122773 | − | 0.00414018i | ||||
\(166\) | 35304.4 | 1.28119 | ||||||||
\(167\) | 20215.8i | 0.724866i | 0.932010 | + | 0.362433i | \(0.118054\pi\) | ||||
−0.932010 | + | 0.362433i | \(0.881946\pi\) | |||||||
\(168\) | 44438.3 | + | 131778.i | 1.57449 | + | 4.66900i | ||||
\(169\) | 13461.3 | 0.471317 | ||||||||
\(170\) | 2126.56i | 0.0735834i | ||||||||
\(171\) | −33965.6 | + | 25847.2i | −1.16158 | + | 0.883936i | ||||
\(172\) | 21370.8 | 0.722378 | ||||||||
\(173\) | − | 49862.1i | − | 1.66601i | −0.553264 | − | 0.833006i | \(-0.686618\pi\) | ||
0.553264 | − | 0.833006i | \(-0.313382\pi\) | |||||||
\(174\) | −36935.3 | + | 12455.4i | −1.21995 | + | 0.411395i | ||||
\(175\) | 44848.2 | 1.46443 | ||||||||
\(176\) | 60886.3i | 1.96560i | ||||||||
\(177\) | −1303.31 | − | 3864.85i | −0.0416008 | − | 0.123363i | ||||
\(178\) | −15553.4 | −0.490892 | ||||||||
\(179\) | − | 32152.1i | − | 1.00347i | −0.865022 | − | 0.501733i | \(-0.832696\pi\) | ||
0.865022 | − | 0.501733i | \(-0.167304\pi\) | |||||||
\(180\) | −1333.06 | − | 1751.76i | −0.0411437 | − | 0.0540667i | ||||
\(181\) | 26929.6 | 0.822003 | 0.411001 | − | 0.911635i | \(-0.365179\pi\) | ||||
0.411001 | + | 0.911635i | \(0.365179\pi\) | |||||||
\(182\) | 113844.i | 3.43690i | ||||||||
\(183\) | 21441.0 | − | 7230.37i | 0.640240 | − | 0.215903i | ||||
\(184\) | −208018. | −6.14420 | ||||||||
\(185\) | 224.557i | 0.00656121i | ||||||||
\(186\) | −28441.3 | − | 84340.2i | −0.822098 | − | 2.43786i | ||||
\(187\) | 28021.6 | 0.801326 | ||||||||
\(188\) | − | 1520.86i | − | 0.0430302i | ||||||
\(189\) | −29341.3 | + | 43346.1i | −0.821403 | + | 1.21346i | ||||
\(190\) | 2527.42 | 0.0700117 | ||||||||
\(191\) | 32685.5i | 0.895958i | 0.894044 | + | 0.447979i | \(0.147856\pi\) | ||||
−0.894044 | + | 0.447979i | \(0.852144\pi\) | |||||||
\(192\) | 132914. | − | 44821.5i | 3.60552 | − | 1.21586i | ||||
\(193\) | 27244.8 | 0.731425 | 0.365712 | − | 0.930728i | \(-0.380825\pi\) | ||||
0.365712 | + | 0.930728i | \(0.380825\pi\) | |||||||
\(194\) | 60888.7i | 1.61783i | ||||||||
\(195\) | −365.588 | − | 1084.12i | −0.00961442 | − | 0.0285107i | ||||
\(196\) | −120709. | −3.14216 | ||||||||
\(197\) | 32019.8i | 0.825062i | 0.910944 | + | 0.412531i | \(0.135355\pi\) | ||||
−0.910944 | + | 0.412531i | \(0.864645\pi\) | |||||||
\(198\) | −31510.4 | + | 23978.8i | −0.803753 | + | 0.611641i | ||||
\(199\) | 25668.1 | 0.648169 | 0.324085 | − | 0.946028i | \(-0.394944\pi\) | ||||
0.324085 | + | 0.946028i | \(0.394944\pi\) | |||||||
\(200\) | − | 134421.i | − | 3.36053i | ||||||
\(201\) | 20281.8 | − | 6839.47i | 0.502013 | − | 0.169289i | ||||
\(202\) | 32746.3 | 0.802526 | ||||||||
\(203\) | − | 40205.2i | − | 0.975641i | ||||||
\(204\) | −55877.8 | − | 165701.i | −1.34270 | − | 3.98166i | ||||
\(205\) | −1257.91 | −0.0299323 | ||||||||
\(206\) | 83261.0i | 1.96204i | ||||||||
\(207\) | −47413.3 | − | 62305.6i | −1.10652 | − | 1.45407i | ||||
\(208\) | 197481. | 4.56456 | ||||||||
\(209\) | − | 33303.7i | − | 0.762430i | ||||||
\(210\) | 2937.02 | − | 990.425i | 0.0665990 | − | 0.0224586i | ||||
\(211\) | −42406.1 | −0.952497 | −0.476249 | − | 0.879311i | \(-0.658004\pi\) | ||||
−0.476249 | + | 0.879311i | \(0.658004\pi\) | |||||||
\(212\) | 72240.8i | 1.60735i | ||||||||
\(213\) | −2544.99 | − | 7546.95i | −0.0560954 | − | 0.166346i | ||||
\(214\) | 63757.8 | 1.39221 | ||||||||
\(215\) | − | 302.408i | − | 0.00654208i | ||||||
\(216\) | 129919. | + | 87943.4i | 2.78462 | + | 1.88493i | ||||
\(217\) | 91806.7 | 1.94964 | ||||||||
\(218\) | 37024.7i | 0.779073i | ||||||||
\(219\) | −67436.0 | + | 22740.9i | −1.40606 | + | 0.474153i | ||||
\(220\) | 1717.62 | 0.0354881 | ||||||||
\(221\) | − | 90886.2i | − | 1.86086i | ||||||
\(222\) | −8054.76 | − | 23885.7i | −0.163436 | − | 0.484653i | ||||
\(223\) | −53628.8 | −1.07842 | −0.539211 | − | 0.842171i | \(-0.681277\pi\) | ||||
−0.539211 | + | 0.842171i | \(0.681277\pi\) | |||||||
\(224\) | 287768.i | 5.73516i | ||||||||
\(225\) | 40261.9 | − | 30638.5i | 0.795297 | − | 0.605205i | ||||
\(226\) | 19376.7 | 0.379371 | ||||||||
\(227\) | 42594.5i | 0.826613i | 0.910592 | + | 0.413306i | \(0.135626\pi\) | ||||
−0.910592 | + | 0.413306i | \(0.864374\pi\) | |||||||
\(228\) | −196936. | + | 66410.9i | −3.78839 | + | 1.27753i | ||||
\(229\) | −15094.4 | −0.287836 | −0.143918 | − | 0.989590i | \(-0.545970\pi\) | ||||
−0.143918 | + | 0.989590i | \(0.545970\pi\) | |||||||
\(230\) | 4636.23i | 0.0876415i | ||||||||
\(231\) | −13050.8 | − | 38700.9i | −0.244575 | − | 0.725266i | ||||
\(232\) | −120505. | −2.23887 | ||||||||
\(233\) | 1764.28i | 0.0324979i | 0.999868 | + | 0.0162489i | \(0.00517243\pi\) | ||||
−0.999868 | + | 0.0162489i | \(0.994828\pi\) | |||||||
\(234\) | 77773.6 | + | 102202.i | 1.42037 | + | 1.86650i | ||||
\(235\) | −21.5209 | −0.000389694 | ||||||||
\(236\) | − | 19860.5i | − | 0.356587i | ||||||
\(237\) | 25640.9 | − | 8646.68i | 0.456496 | − | 0.153940i | ||||
\(238\) | 246222. | 4.34684 | ||||||||
\(239\) | 99155.8i | 1.73589i | 0.496659 | + | 0.867946i | \(0.334560\pi\) | ||||
−0.496659 | + | 0.867946i | \(0.665440\pi\) | |||||||
\(240\) | −1718.06 | − | 5094.75i | −0.0298274 | − | 0.0884505i | ||||
\(241\) | −73745.9 | −1.26971 | −0.634854 | − | 0.772632i | \(-0.718940\pi\) | ||||
−0.634854 | + | 0.772632i | \(0.718940\pi\) | |||||||
\(242\) | 82345.9i | 1.40608i | ||||||||
\(243\) | 3271.57 | + | 58958.3i | 0.0554044 | + | 0.998464i | ||||
\(244\) | 110180. | 1.85064 | ||||||||
\(245\) | 1708.10i | 0.0284564i | ||||||||
\(246\) | 133801. | − | 45120.5i | 2.21100 | − | 0.745596i | ||||
\(247\) | −108018. | −1.77053 | ||||||||
\(248\) | − | 275168.i | − | 4.47398i | ||||||
\(249\) | 13126.9 | + | 38926.6i | 0.211721 | + | 0.627838i | ||||
\(250\) | −5993.72 | −0.0958994 | ||||||||
\(251\) | 34624.4i | 0.549585i | 0.961504 | + | 0.274793i | \(0.0886092\pi\) | ||||
−0.961504 | + | 0.274793i | \(0.911391\pi\) | |||||||
\(252\) | −202826. | + | 154347.i | −3.19392 | + | 2.43051i | ||||
\(253\) | 61091.4 | 0.954419 | ||||||||
\(254\) | 129308.i | 2.00427i | ||||||||
\(255\) | −2344.74 | + | 790.698i | −0.0360591 | + | 0.0121599i | ||||
\(256\) | 187026. | 2.85380 | ||||||||
\(257\) | − | 85104.8i | − | 1.28851i | −0.764811 | − | 0.644255i | \(-0.777168\pi\) | ||
0.764811 | − | 0.644255i | \(-0.222832\pi\) | |||||||
\(258\) | 10847.2 | + | 32166.4i | 0.162959 | + | 0.483240i | ||||
\(259\) | 26000.2 | 0.387594 | ||||||||
\(260\) | − | 5571.00i | − | 0.0824113i | ||||||
\(261\) | −27466.6 | − | 36093.7i | −0.403203 | − | 0.529847i | ||||
\(262\) | −279.989 | −0.00407885 | ||||||||
\(263\) | 112176.i | 1.62176i | 0.585210 | + | 0.810882i | \(0.301012\pi\) | ||||
−0.585210 | + | 0.810882i | \(0.698988\pi\) | |||||||
\(264\) | −115997. | + | 39116.5i | −1.66432 | + | 0.561245i | ||||
\(265\) | 1022.24 | 0.0145567 | ||||||||
\(266\) | − | 292636.i | − | 4.13585i | ||||||
\(267\) | −5783.07 | − | 17149.2i | −0.0811215 | − | 0.240558i | ||||
\(268\) | 104223. | 1.45109 | ||||||||
\(269\) | − | 26041.8i | − | 0.359887i | −0.983677 | − | 0.179944i | \(-0.942408\pi\) | ||
0.983677 | − | 0.179944i | \(-0.0575915\pi\) | |||||||
\(270\) | 1960.05 | − | 2895.60i | 0.0268868 | − | 0.0397201i | ||||
\(271\) | −122251. | −1.66461 | −0.832307 | − | 0.554315i | \(-0.812980\pi\) | ||||
−0.832307 | + | 0.554315i | \(0.812980\pi\) | |||||||
\(272\) | − | 427114.i | − | 5.77306i | ||||||
\(273\) | −125524. | + | 42329.4i | −1.68423 | + | 0.567958i | ||||
\(274\) | 7549.28 | 0.100555 | ||||||||
\(275\) | 39477.3i | 0.522014i | ||||||||
\(276\) | −121822. | − | 361253.i | −1.59922 | − | 4.74235i | ||||
\(277\) | 27696.8 | 0.360969 | 0.180485 | − | 0.983578i | \(-0.442233\pi\) | ||||
0.180485 | + | 0.983578i | \(0.442233\pi\) | |||||||
\(278\) | − | 40026.0i | − | 0.517909i | ||||||
\(279\) | 82418.3 | − | 62718.7i | 1.05880 | − | 0.805728i | ||||
\(280\) | 9582.30 | 0.122223 | ||||||||
\(281\) | − | 138592.i | − | 1.75520i | −0.479396 | − | 0.877599i | \(-0.659144\pi\) | ||
0.479396 | − | 0.877599i | \(-0.340856\pi\) | |||||||
\(282\) | 2289.13 | − | 771.942i | 0.0287853 | − | 0.00970704i | ||||
\(283\) | 34002.8 | 0.424563 | 0.212281 | − | 0.977209i | \(-0.431911\pi\) | ||||
0.212281 | + | 0.977209i | \(0.431911\pi\) | |||||||
\(284\) | − | 38781.8i | − | 0.480829i | ||||||
\(285\) | 939.746 | + | 2786.73i | 0.0115697 | + | 0.0343088i | ||||
\(286\) | −100210. | −1.22512 | ||||||||
\(287\) | 145646.i | 1.76821i | ||||||||
\(288\) | 196592. | + | 258340.i | 2.37017 | + | 3.11463i | ||||
\(289\) | −113049. | −1.35353 | ||||||||
\(290\) | 2685.78i | 0.0319355i | ||||||||
\(291\) | −67135.8 | + | 22639.6i | −0.792808 | + | 0.267352i | ||||
\(292\) | −346536. | −4.06427 | ||||||||
\(293\) | − | 85177.2i | − | 0.992175i | −0.868272 | − | 0.496088i | \(-0.834769\pi\) | ||
0.868272 | − | 0.496088i | \(-0.165231\pi\) | |||||||
\(294\) | −61268.5 | − | 181686.i | −0.708831 | − | 2.10197i | ||||
\(295\) | −281.035 | −0.00322936 | ||||||||
\(296\) | − | 77929.3i | − | 0.889441i | ||||||
\(297\) | −38155.1 | − | 25827.5i | −0.432554 | − | 0.292799i | ||||
\(298\) | −190220. | −2.14202 | ||||||||
\(299\) | − | 198146.i | − | 2.21637i | ||||||
\(300\) | 233442. | − | 78721.6i | 2.59380 | − | 0.874685i | ||||
\(301\) | −35014.0 | −0.386464 | ||||||||
\(302\) | 130644.i | 1.43244i | ||||||||
\(303\) | 12175.7 | + | 36106.0i | 0.132620 | + | 0.393273i | ||||
\(304\) | −507626. | −5.49283 | ||||||||
\(305\) | − | 1559.10i | − | 0.0167600i | ||||||
\(306\) | 221043. | − | 168209.i | 2.36066 | − | 1.79642i | ||||
\(307\) | 181337. | 1.92402 | 0.962011 | − | 0.273009i | \(-0.0880190\pi\) | ||||
0.962011 | + | 0.273009i | \(0.0880190\pi\) | |||||||
\(308\) | − | 198874.i | − | 2.09641i | ||||||
\(309\) | −91803.5 | + | 30958.1i | −0.961485 | + | 0.324233i | ||||
\(310\) | −6132.84 | −0.0638173 | ||||||||
\(311\) | 54923.1i | 0.567851i | 0.958846 | + | 0.283925i | \(0.0916368\pi\) | ||||
−0.958846 | + | 0.283925i | \(0.908363\pi\) | |||||||
\(312\) | 126872. | + | 376227.i | 1.30334 | + | 3.86493i | ||||
\(313\) | 54353.5 | 0.554803 | 0.277401 | − | 0.960754i | \(-0.410527\pi\) | ||||
0.277401 | + | 0.960754i | \(0.410527\pi\) | |||||||
\(314\) | − | 124772.i | − | 1.26549i | ||||||
\(315\) | 2184.08 | + | 2870.09i | 0.0220114 | + | 0.0289251i | ||||
\(316\) | 131762. | 1.31952 | ||||||||
\(317\) | − | 22871.8i | − | 0.227605i | −0.993503 | − | 0.113802i | \(-0.963697\pi\) | ||
0.993503 | − | 0.113802i | \(-0.0363031\pi\) | |||||||
\(318\) | −108734. | + | 36667.3i | −1.07525 | + | 0.362597i | ||||
\(319\) | 35390.3 | 0.347779 | ||||||||
\(320\) | − | 9664.92i | − | 0.0943840i | ||||||
\(321\) | 23706.4 | + | 70299.3i | 0.230068 | + | 0.682246i | ||||
\(322\) | 536803. | 5.17730 | ||||||||
\(323\) | 233623.i | 2.23930i | ||||||||
\(324\) | −76641.1 | + | 277126.i | −0.730082 | + | 2.63990i | ||||
\(325\) | 128042. | 1.21223 | ||||||||
\(326\) | − | 313368.i | − | 2.94862i | ||||||
\(327\) | −40823.4 | + | 13766.5i | −0.381780 | + | 0.128744i | ||||
\(328\) | 436538. | 4.05765 | ||||||||
\(329\) | 2491.78i | 0.0230206i | ||||||||
\(330\) | 871.815 | + | 2585.29i | 0.00800565 | + | 0.0237400i | ||||
\(331\) | −77310.0 | −0.705634 | −0.352817 | − | 0.935692i | \(-0.614776\pi\) | ||||
−0.352817 | + | 0.935692i | \(0.614776\pi\) | |||||||
\(332\) | 200034.i | 1.81479i | ||||||||
\(333\) | 23341.4 | − | 17762.3i | 0.210493 | − | 0.160181i | ||||
\(334\) | −156361. | −1.40164 | ||||||||
\(335\) | − | 1474.80i | − | 0.0131415i | ||||||
\(336\) | −589892. | + | 198924.i | −5.22509 | + | 1.76201i | ||||
\(337\) | 4371.86 | 0.0384952 | 0.0192476 | − | 0.999815i | \(-0.493873\pi\) | ||||
0.0192476 | + | 0.999815i | \(0.493873\pi\) | |||||||
\(338\) | 104118.i | 0.911361i | ||||||||
\(339\) | 7204.65 | + | 21364.8i | 0.0626922 | + | 0.185908i | ||||
\(340\) | −12049.0 | −0.104230 | ||||||||
\(341\) | 80812.1i | 0.694973i | ||||||||
\(342\) | −199917. | − | 262710.i | −1.70922 | − | 2.24608i | ||||
\(343\) | 25375.9 | 0.215692 | ||||||||
\(344\) | 104946.i | 0.886848i | ||||||||
\(345\) | −5111.90 | + | 1723.84i | −0.0429482 | + | 0.0144830i | ||||
\(346\) | 385663. | 3.22148 | ||||||||
\(347\) | 71853.0i | 0.596741i | 0.954450 | + | 0.298370i | \(0.0964431\pi\) | ||||
−0.954450 | + | 0.298370i | \(0.903557\pi\) | |||||||
\(348\) | −70571.8 | − | 209274.i | −0.582737 | − | 1.72805i | ||||
\(349\) | 185348. | 1.52173 | 0.760863 | − | 0.648913i | \(-0.224776\pi\) | ||||
0.760863 | + | 0.648913i | \(0.224776\pi\) | |||||||
\(350\) | 346882.i | 2.83169i | ||||||||
\(351\) | −83769.8 | + | 123754.i | −0.679944 | + | 1.00449i | ||||
\(352\) | −253305. | −2.04437 | ||||||||
\(353\) | − | 146210.i | − | 1.17335i | −0.809822 | − | 0.586676i | \(-0.800436\pi\) | ||
0.809822 | − | 0.586676i | \(-0.199564\pi\) | |||||||
\(354\) | 29893.1 | − | 10080.6i | 0.238541 | − | 0.0804413i | ||||
\(355\) | −548.781 | −0.00435454 | ||||||||
\(356\) | − | 88125.1i | − | 0.695344i | ||||||
\(357\) | 91550.4 | + | 271484.i | 0.718330 | + | 2.13014i | ||||
\(358\) | 248683. | 1.94035 | ||||||||
\(359\) | − | 71968.3i | − | 0.558409i | −0.960232 | − | 0.279205i | \(-0.909929\pi\) | ||
0.960232 | − | 0.279205i | \(-0.0900708\pi\) | |||||||
\(360\) | 8602.39 | − | 6546.25i | 0.0663765 | − | 0.0505112i | ||||
\(361\) | 147341. | 1.13060 | ||||||||
\(362\) | 208290.i | 1.58946i | ||||||||
\(363\) | −90794.4 | + | 30617.8i | −0.689043 | + | 0.232360i | ||||
\(364\) | −645035. | −4.86833 | ||||||||
\(365\) | 4903.65i | 0.0368073i | ||||||||
\(366\) | 55924.0 | + | 165837.i | 0.417480 | + | 1.23800i | ||||
\(367\) | 263314. | 1.95498 | 0.977489 | − | 0.210988i | \(-0.0676681\pi\) | ||||
0.977489 | + | 0.210988i | \(0.0676681\pi\) | |||||||
\(368\) | − | 931174.i | − | 6.87599i | ||||||
\(369\) | 99499.6 | + | 130752.i | 0.730749 | + | 0.960273i | ||||
\(370\) | −1736.86 | −0.0126871 | ||||||||
\(371\) | − | 118360.i | − | 0.859915i | ||||||
\(372\) | 477868. | − | 161147.i | 3.45320 | − | 1.16449i | ||||
\(373\) | 94196.4 | 0.677043 | 0.338522 | − | 0.940959i | \(-0.390073\pi\) | ||||
0.338522 | + | 0.940959i | \(0.390073\pi\) | |||||||
\(374\) | 216735.i | 1.54948i | ||||||||
\(375\) | −2228.58 | − | 6608.66i | −0.0158477 | − | 0.0469949i | ||||
\(376\) | 7468.49 | 0.0528272 | ||||||||
\(377\) | − | 114786.i | − | 0.807620i | ||||||
\(378\) | −335265. | − | 226943.i | −2.34641 | − | 1.58830i | ||||
\(379\) | 102807. | 0.715720 | 0.357860 | − | 0.933775i | \(-0.383507\pi\) | ||||
0.357860 | + | 0.933775i | \(0.383507\pi\) | |||||||
\(380\) | 14320.3i | 0.0991710i | ||||||||
\(381\) | −142574. | + | 48079.2i | −0.982182 | + | 0.331213i | ||||
\(382\) | −252809. | −1.73247 | ||||||||
\(383\) | − | 58900.9i | − | 0.401536i | −0.979639 | − | 0.200768i | \(-0.935656\pi\) | ||
0.979639 | − | 0.200768i | \(-0.0643437\pi\) | |||||||
\(384\) | 162259. | + | 481165.i | 1.10039 | + | 3.26311i | ||||
\(385\) | −2814.16 | −0.0189857 | ||||||||
\(386\) | 210728.i | 1.41432i | ||||||||
\(387\) | −31433.4 | + | 23920.2i | −0.209879 | + | 0.159714i | ||||
\(388\) | −344993. | −2.29164 | ||||||||
\(389\) | 179102.i | 1.18359i | 0.806088 | + | 0.591795i | \(0.201581\pi\) | ||||
−0.806088 | + | 0.591795i | \(0.798419\pi\) | |||||||
\(390\) | 8385.22 | − | 2827.68i | 0.0551296 | − | 0.0185909i | ||||
\(391\) | −428552. | −2.80318 | ||||||||
\(392\) | − | 592769.i | − | 3.85757i | ||||||
\(393\) | −104.105 | − | 308.715i | −0.000674044 | − | 0.00199882i | ||||
\(394\) | −247660. | −1.59538 | ||||||||
\(395\) | − | 1864.50i | − | 0.0119500i | ||||||
\(396\) | −135863. | − | 178536.i | −0.866383 | − | 1.13851i | ||||
\(397\) | 45669.8 | 0.289767 | 0.144883 | − | 0.989449i | \(-0.453719\pi\) | ||||
0.144883 | + | 0.989449i | \(0.453719\pi\) | |||||||
\(398\) | 198533.i | 1.25333i | ||||||||
\(399\) | 322660. | − | 108808.i | 2.02675 | − | 0.683462i | ||||
\(400\) | 601725. | 3.76078 | ||||||||
\(401\) | 54669.9i | 0.339985i | 0.985445 | + | 0.169992i | \(0.0543743\pi\) | ||||
−0.985445 | + | 0.169992i | \(0.945626\pi\) | |||||||
\(402\) | 52900.5 | + | 156872.i | 0.327346 | + | 0.970716i | ||||
\(403\) | 262109. | 1.61388 | ||||||||
\(404\) | 185539.i | 1.13677i | ||||||||
\(405\) | 3921.47 | + | 1084.51i | 0.0239077 | + | 0.00661185i | ||||
\(406\) | 310971. | 1.88655 | ||||||||
\(407\) | 22886.5i | 0.138163i | ||||||||
\(408\) | 813708. | − | 274400.i | 4.88819 | − | 1.64840i | ||||
\(409\) | 259180. | 1.54937 | 0.774684 | − | 0.632348i | \(-0.217909\pi\) | ||||
0.774684 | + | 0.632348i | \(0.217909\pi\) | |||||||
\(410\) | − | 9729.40i | − | 0.0578786i | ||||||
\(411\) | 2806.97 | + | 8323.83i | 0.0166171 | + | 0.0492764i | ||||
\(412\) | −471754. | −2.77921 | ||||||||
\(413\) | 32539.4i | 0.190770i | ||||||||
\(414\) | 481908. | − | 366723.i | 2.81167 | − | 2.13962i | ||||
\(415\) | 2830.57 | 0.0164353 | ||||||||
\(416\) | 821580.i | 4.74748i | ||||||||
\(417\) | 44132.7 | − | 14882.5i | 0.253798 | − | 0.0855861i | ||||
\(418\) | 257591. | 1.47427 | ||||||||
\(419\) | − | 102683.i | − | 0.584888i | −0.956283 | − | 0.292444i | \(-0.905532\pi\) | ||
0.956283 | − | 0.292444i | \(-0.0944685\pi\) | |||||||
\(420\) | 5611.71 | + | 16641.0i | 0.0318124 | + | 0.0943369i | ||||
\(421\) | −216357. | −1.22069 | −0.610346 | − | 0.792135i | \(-0.708970\pi\) | ||||
−0.610346 | + | 0.792135i | \(0.708970\pi\) | |||||||
\(422\) | − | 327994.i | − | 1.84179i | ||||||
\(423\) | 1702.29 | + | 2236.96i | 0.00951375 | + | 0.0125020i | ||||
\(424\) | −354754. | −1.97331 | ||||||||
\(425\) | − | 276931.i | − | 1.53318i | ||||||
\(426\) | 58372.5 | − | 19684.5i | 0.321654 | − | 0.108469i | ||||
\(427\) | −180519. | −0.990072 | ||||||||
\(428\) | 361249.i | 1.97206i | ||||||||
\(429\) | −37260.1 | − | 110492.i | −0.202456 | − | 0.600364i | ||||
\(430\) | 2339.00 | 0.0126501 | ||||||||
\(431\) | 140988.i | 0.758976i | 0.925197 | + | 0.379488i | \(0.123900\pi\) | ||||
−0.925197 | + | 0.379488i | \(0.876100\pi\) | |||||||
\(432\) | −393671. | + | 581572.i | −2.10943 | + | 3.11628i | ||||
\(433\) | 133663. | 0.712911 | 0.356455 | − | 0.934312i | \(-0.383985\pi\) | ||||
0.356455 | + | 0.934312i | \(0.383985\pi\) | |||||||
\(434\) | 710087.i | 3.76992i | ||||||||
\(435\) | −2961.33 | + | 998.625i | −0.0156498 | + | 0.00527745i | ||||
\(436\) | −209780. | −1.10355 | ||||||||
\(437\) | 509335.i | 2.66711i | ||||||||
\(438\) | −175891. | − | 521590.i | −0.916846 | − | 2.71882i | ||||
\(439\) | −13250.2 | −0.0687531 | −0.0343765 | − | 0.999409i | \(-0.510945\pi\) | ||||
−0.0343765 | + | 0.999409i | \(0.510945\pi\) | |||||||
\(440\) | 8434.75i | 0.0435679i | ||||||||
\(441\) | 177546. | − | 135109.i | 0.912923 | − | 0.694717i | ||||
\(442\) | 702968. | 3.59825 | ||||||||
\(443\) | − | 195021.i | − | 0.993743i | −0.867824 | − | 0.496871i | \(-0.834482\pi\) | ||
0.867824 | − | 0.496871i | \(-0.165518\pi\) | |||||||
\(444\) | 135335. | − | 45638.0i | 0.686507 | − | 0.231505i | ||||
\(445\) | −1247.01 | −0.00629725 | ||||||||
\(446\) | − | 414797.i | − | 2.08529i | ||||||
\(447\) | −70727.6 | − | 209736.i | −0.353976 | − | 1.04968i | ||||
\(448\) | −1.11905e6 | −5.57560 | ||||||||
\(449\) | − | 62270.2i | − | 0.308879i | −0.988002 | − | 0.154439i | \(-0.950643\pi\) | ||
0.988002 | − | 0.154439i | \(-0.0493571\pi\) | |||||||
\(450\) | 236976. | + | 311409.i | 1.17025 | + | 1.53782i | ||||
\(451\) | −128204. | −0.630300 | ||||||||
\(452\) | 109788.i | 0.537375i | ||||||||
\(453\) | −144048. | + | 48576.2i | −0.701960 | + | 0.236716i | ||||
\(454\) | −329451. | −1.59838 | ||||||||
\(455\) | 9127.55i | 0.0440891i | ||||||||
\(456\) | −326125. | − | 967094.i | −1.56839 | − | 4.65092i | ||||
\(457\) | −178424. | −0.854319 | −0.427159 | − | 0.904176i | \(-0.640486\pi\) | ||||
−0.427159 | + | 0.904176i | \(0.640486\pi\) | |||||||
\(458\) | − | 116749.i | − | 0.556574i | ||||||
\(459\) | 267656. | + | 181178.i | 1.27043 | + | 0.859964i | ||||
\(460\) | −26268.7 | −0.124143 | ||||||||
\(461\) | − | 37707.0i | − | 0.177427i | −0.996057 | − | 0.0887135i | \(-0.971724\pi\) | ||
0.996057 | − | 0.0887135i | \(-0.0282756\pi\) | |||||||
\(462\) | 299336. | − | 100942.i | 1.40241 | − | 0.472922i | ||||
\(463\) | −234321. | −1.09308 | −0.546538 | − | 0.837435i | \(-0.684054\pi\) | ||||
−0.546538 | + | 0.837435i | \(0.684054\pi\) | |||||||
\(464\) | − | 539430.i | − | 2.50553i | ||||||
\(465\) | −2280.31 | − | 6762.07i | −0.0105460 | − | 0.0312733i | ||||
\(466\) | −13646.0 | −0.0628395 | ||||||||
\(467\) | 254624.i | 1.16753i | 0.811924 | + | 0.583763i | \(0.198420\pi\) | ||||
−0.811924 | + | 0.583763i | \(0.801580\pi\) | |||||||
\(468\) | −579072. | + | 440662.i | −2.64387 | + | 2.01194i | ||||
\(469\) | −170759. | −0.776316 | ||||||||
\(470\) | − | 166.455i | − | 0.000753532i | ||||||
\(471\) | 137574. | − | 46392.8i | 0.620146 | − | 0.209127i | ||||
\(472\) | 97529.0 | 0.437774 | ||||||||
\(473\) | − | 30820.9i | − | 0.137760i | ||||||
\(474\) | 66878.5 | + | 198322.i | 0.297667 | + | 0.882703i | ||||
\(475\) | −329133. | −1.45876 | ||||||||
\(476\) | 1.39509e6i | 6.15726i | ||||||||
\(477\) | −80858.6 | − | 106256.i | −0.355377 | − | 0.466999i | ||||
\(478\) | −766930. | −3.35660 | ||||||||
\(479\) | − | 157553.i | − | 0.686680i | −0.939211 | − | 0.343340i | \(-0.888442\pi\) | ||
0.939211 | − | 0.343340i | \(-0.111558\pi\) | |||||||
\(480\) | 21195.7 | − | 7147.63i | 0.0919951 | − | 0.0310227i | ||||
\(481\) | 74230.9 | 0.320844 | ||||||||
\(482\) | − | 570394.i | − | 2.45517i | ||||||
\(483\) | 199594. | + | 591878.i | 0.855566 | + | 2.53710i | ||||
\(484\) | −466569. | −1.99170 | ||||||||
\(485\) | 4881.82i | 0.0207538i | ||||||||
\(486\) | −456018. | + | 25304.3i | −1.93068 | + | 0.107133i | ||||
\(487\) | −9062.55 | −0.0382114 | −0.0191057 | − | 0.999817i | \(-0.506082\pi\) | ||||
−0.0191057 | + | 0.999817i | \(0.506082\pi\) | |||||||
\(488\) | 541061.i | 2.27199i | ||||||||
\(489\) | 345519. | − | 116516.i | 1.44495 | − | 0.487270i | ||||
\(490\) | −13211.4 | −0.0550247 | ||||||||
\(491\) | 200856.i | 0.833148i | 0.909102 | + | 0.416574i | \(0.136769\pi\) | ||||
−0.909102 | + | 0.416574i | \(0.863231\pi\) | |||||||
\(492\) | 255651. | + | 758110.i | 1.05613 | + | 3.13186i | ||||
\(493\) | −248261. | −1.02144 | ||||||||
\(494\) | − | 835479.i | − | 3.42359i | ||||||
\(495\) | −2526.38 | + | 1922.52i | −0.0103107 | + | 0.00784623i | ||||
\(496\) | 1.23176e6 | 5.00685 | ||||||||
\(497\) | 63540.2i | 0.257238i | ||||||||
\(498\) | −301081. | + | 101531.i | −1.21402 | + | 0.409393i | ||||
\(499\) | 280290. | 1.12566 | 0.562829 | − | 0.826573i | \(-0.309713\pi\) | ||||
0.562829 | + | 0.826573i | \(0.309713\pi\) | |||||||
\(500\) | − | 33960.2i | − | 0.135841i | ||||||
\(501\) | −58138.1 | − | 172403.i | −0.231625 | − | 0.686863i | ||||
\(502\) | −267806. | −1.06270 | ||||||||
\(503\) | − | 254469.i | − | 1.00577i | −0.864353 | − | 0.502886i | \(-0.832272\pi\) | ||
0.864353 | − | 0.502886i | \(-0.167728\pi\) | |||||||
\(504\) | −757953. | − | 996022.i | −2.98388 | − | 3.92110i | ||||
\(505\) | 2625.47 | 0.0102949 | ||||||||
\(506\) | 472517.i | 1.84551i | ||||||||
\(507\) | −114800. | + | 38713.0i | −0.446607 | + | 0.150605i | ||||
\(508\) | −732653. | −2.83904 | ||||||||
\(509\) | − | 250109.i | − | 0.965370i | −0.875794 | − | 0.482685i | \(-0.839662\pi\) | ||
0.875794 | − | 0.482685i | \(-0.160338\pi\) | |||||||
\(510\) | −6115.73 | − | 18135.6i | −0.0235130 | − | 0.0697256i | ||||
\(511\) | 567766. | 2.17434 | ||||||||
\(512\) | 543841.i | 2.07459i | ||||||||
\(513\) | 215331. | − | 318110.i | 0.818222 | − | 1.20877i | ||||
\(514\) | 658251. | 2.49153 | ||||||||
\(515\) | 6675.55i | 0.0251694i | ||||||||
\(516\) | −182254. | + | 61459.9i | −0.684505 | + | 0.230830i | ||||
\(517\) | −2193.37 | −0.00820599 | ||||||||
\(518\) | 201101.i | 0.749471i | ||||||||
\(519\) | 143397. | + | 425231.i | 0.532360 | + | 1.57867i | ||||
\(520\) | 27357.6 | 0.101175 | ||||||||
\(521\) | − | 190802.i | − | 0.702924i | −0.936202 | − | 0.351462i | \(-0.885685\pi\) | ||
0.936202 | − | 0.351462i | \(-0.114315\pi\) | |||||||
\(522\) | 279170. | − | 212443.i | 1.02454 | − | 0.779653i | ||||
\(523\) | −397545. | −1.45339 | −0.726697 | − | 0.686958i | \(-0.758946\pi\) | ||||
−0.726697 | + | 0.686958i | \(0.758946\pi\) | |||||||
\(524\) | − | 1586.41i | − | 0.00577766i | ||||||
\(525\) | −382472. | + | 128978.i | −1.38765 | + | 0.467946i | ||||
\(526\) | −867634. | −3.13592 | ||||||||
\(527\) | − | 566892.i | − | 2.04117i | ||||||
\(528\) | −175102. | − | 519248.i | −0.628090 | − | 1.86255i | ||||
\(529\) | −654469. | −2.33872 | ||||||||
\(530\) | 7906.62i | 0.0281475i | ||||||||
\(531\) | 22229.7 | + | 29211.9i | 0.0788395 | + | 0.103603i | ||||
\(532\) | 1.65806e6 | 5.85839 | ||||||||
\(533\) | 415821.i | 1.46370i | ||||||||
\(534\) | 132642. | − | 44729.7i | 0.465155 | − | 0.156860i | ||||
\(535\) | 5111.85 | 0.0178596 | ||||||||
\(536\) | 511809.i | 1.78147i | ||||||||
\(537\) | 92465.4 | + | 274198.i | 0.320649 | + | 0.950857i | ||||
\(538\) | 201423. | 0.695895 | ||||||||
\(539\) | 174086.i | 0.599221i | ||||||||
\(540\) | 16406.3 | + | 11105.6i | 0.0562632 | + | 0.0380850i | ||||
\(541\) | 43502.7 | 0.148635 | 0.0743177 | − | 0.997235i | \(-0.476322\pi\) | ||||
0.0743177 | + | 0.997235i | \(0.476322\pi\) | |||||||
\(542\) | − | 945561.i | − | 3.21878i | ||||||
\(543\) | −229660. | + | 77446.3i | −0.778907 | + | 0.262664i | ||||
\(544\) | 1.77692e6 | 6.00441 | ||||||||
\(545\) | 2968.49i | 0.00999409i | ||||||||
\(546\) | −327400. | − | 970877.i | −1.09823 | − | 3.25671i | ||||
\(547\) | −11223.2 | −0.0375095 | −0.0187547 | − | 0.999824i | \(-0.505970\pi\) | ||||
−0.0187547 | + | 0.999824i | \(0.505970\pi\) | |||||||
\(548\) | 42773.9i | 0.142435i | ||||||||
\(549\) | −162059. | + | 123323.i | −0.537684 | + | 0.409167i | ||||
\(550\) | −305341. | −1.00939 | ||||||||
\(551\) | 295059.i | 0.971863i | ||||||||
\(552\) | 1.77401e6 | − | 598234.i | 5.82208 | − | 1.96333i | ||||
\(553\) | −215879. | −0.705929 | ||||||||
\(554\) | 214224.i | 0.697988i | ||||||||
\(555\) | −645.799 | − | 1915.06i | −0.00209658 | − | 0.00621722i | ||||
\(556\) | 226786. | 0.733613 | ||||||||
\(557\) | 142448.i | 0.459140i | 0.973292 | + | 0.229570i | \(0.0737320\pi\) | ||||
−0.973292 | + | 0.229570i | \(0.926268\pi\) | |||||||
\(558\) | 485104. | + | 637472.i | 1.55800 | + | 2.04735i | ||||
\(559\) | −99965.5 | −0.319909 | ||||||||
\(560\) | 42894.3i | 0.136780i | ||||||||
\(561\) | −238972. | + | 80586.6i | −0.759314 | + | 0.256057i | ||||
\(562\) | 1.07195e6 | 3.39393 | ||||||||
\(563\) | 80736.3i | 0.254714i | 0.991857 | + | 0.127357i | \(0.0406493\pi\) | ||||
−0.991857 | + | 0.127357i | \(0.959351\pi\) | |||||||
\(564\) | 4373.80 | + | 12970.1i | 0.0137499 | + | 0.0407742i | ||||
\(565\) | 1553.55 | 0.00486663 | ||||||||
\(566\) | 262998.i | 0.820955i | ||||||||
\(567\) | 125569. | − | 454044.i | 0.390586 | − | 1.41232i | ||||
\(568\) | 190446. | 0.590304 | ||||||||
\(569\) | 597848.i | 1.84657i | 0.384112 | + | 0.923287i | \(0.374508\pi\) | ||||
−0.384112 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(570\) | −21554.2 | + | 7268.55i | −0.0663412 | + | 0.0223717i | ||||
\(571\) | 84790.5 | 0.260061 | 0.130030 | − | 0.991510i | \(-0.458492\pi\) | ||||
0.130030 | + | 0.991510i | \(0.458492\pi\) | |||||||
\(572\) | − | 567787.i | − | 1.73538i | ||||||
\(573\) | −93999.3 | − | 278746.i | −0.286296 | − | 0.848985i | ||||
\(574\) | −1.12651e6 | −3.41910 | ||||||||
\(575\) | − | 603752.i | − | 1.82609i | ||||||
\(576\) | −1.00461e6 | + | 764488.i | −3.02798 | + | 2.30423i | ||||
\(577\) | −315750. | −0.948402 | −0.474201 | − | 0.880417i | \(-0.657263\pi\) | ||||
−0.474201 | + | 0.880417i | \(0.657263\pi\) | |||||||
\(578\) | − | 874385.i | − | 2.61726i | ||||||
\(579\) | −232348. | + | 78352.8i | −0.693078 | + | 0.233721i | ||||
\(580\) | −15217.5 | −0.0452363 | ||||||||
\(581\) | − | 327736.i | − | 0.970893i | ||||||
\(582\) | −175108. | − | 519268.i | −0.516965 | − | 1.53301i | ||||
\(583\) | 104185. | 0.306527 | ||||||||
\(584\) | − | 1.70174e6i | − | 4.98961i | ||||||
\(585\) | 6235.58 | + | 8194.14i | 0.0182207 | + | 0.0239437i | ||||
\(586\) | 658811. | 1.91852 | ||||||||
\(587\) | 255826.i | 0.742454i | 0.928542 | + | 0.371227i | \(0.121063\pi\) | ||||
−0.928542 | + | 0.371227i | \(0.878937\pi\) | |||||||
\(588\) | 1.02943e6 | − | 347145.i | 2.97743 | − | 1.00405i | ||||
\(589\) | −673753. | −1.94209 | ||||||||
\(590\) | − | 2173.69i | − | 0.00624444i | ||||||
\(591\) | −92085.0 | − | 273070.i | −0.263642 | − | 0.781806i | ||||
\(592\) | 348843. | 0.995375 | ||||||||
\(593\) | − | 469997.i | − | 1.33655i | −0.743914 | − | 0.668275i | \(-0.767033\pi\) | ||
0.743914 | − | 0.668275i | \(-0.232967\pi\) | |||||||
\(594\) | 199765. | − | 295114.i | 0.566170 | − | 0.836407i | ||||
\(595\) | 19741.1 | 0.0557620 | ||||||||
\(596\) | − | 1.07778e6i | − | 3.03415i | ||||||
\(597\) | −218902. | + | 73818.4i | −0.614187 | + | 0.207117i | ||||
\(598\) | 1.53258e6 | 4.28569 | ||||||||
\(599\) | 407616.i | 1.13605i | 0.823011 | + | 0.568025i | \(0.192292\pi\) | ||||
−0.823011 | + | 0.568025i | \(0.807708\pi\) | |||||||
\(600\) | 386579. | + | 1.14637e6i | 1.07383 | + | 3.18435i | ||||
\(601\) | −222294. | −0.615431 | −0.307715 | − | 0.951478i | \(-0.599564\pi\) | ||||
−0.307715 | + | 0.951478i | \(0.599564\pi\) | |||||||
\(602\) | − | 270819.i | − | 0.747286i | ||||||
\(603\) | −153297. | + | 116656.i | −0.421598 | + | 0.320828i | ||||
\(604\) | −740227. | −2.02904 | ||||||||
\(605\) | 6602.17i | 0.0180375i | ||||||||
\(606\) | −279265. | + | 94174.2i | −0.760452 | + | 0.256441i | ||||
\(607\) | −163249. | −0.443071 | −0.221535 | − | 0.975152i | \(-0.571107\pi\) | ||||
−0.221535 | + | 0.975152i | \(0.571107\pi\) | |||||||
\(608\) | − | 2.11187e6i | − | 5.71296i | ||||||
\(609\) | 115625. | + | 342876.i | 0.311758 | + | 0.924490i | ||||
\(610\) | 12059.0 | 0.0324079 | ||||||||
\(611\) | 7114.06i | 0.0190561i | ||||||||
\(612\) | 953069. | + | 1.25242e6i | 2.54461 | + | 3.34386i | ||||
\(613\) | −288936. | −0.768919 | −0.384459 | − | 0.923142i | \(-0.625612\pi\) | ||||
−0.384459 | + | 0.923142i | \(0.625612\pi\) | |||||||
\(614\) | 1.40257e6i | 3.72038i | ||||||||
\(615\) | 10727.6 | − | 3617.58i | 0.0283631 | − | 0.00956463i | ||||
\(616\) | 976612. | 2.57372 | ||||||||
\(617\) | − | 412795.i | − | 1.08434i | −0.840270 | − | 0.542168i | \(-0.817604\pi\) | ||
0.840270 | − | 0.542168i | \(-0.182396\pi\) | |||||||
\(618\) | −239448. | − | 710063.i | −0.626953 | − | 1.85917i | ||||
\(619\) | 499803. | 1.30442 | 0.652211 | − | 0.758038i | \(-0.273842\pi\) | ||||
0.652211 | + | 0.758038i | \(0.273842\pi\) | |||||||
\(620\) | − | 34748.5i | − | 0.0903966i | ||||||
\(621\) | 583531. | + | 394997.i | 1.51315 | + | 1.02426i | ||||
\(622\) | −424808. | −1.09802 | ||||||||
\(623\) | 144384.i | 0.372001i | ||||||||
\(624\) | −1.68415e6 | + | 567931.i | −4.32525 | + | 1.45857i | ||||
\(625\) | 389904. | 0.998154 | ||||||||
\(626\) | 420402.i | 1.07279i | ||||||||
\(627\) | 95777.3 | + | 284019.i | 0.243628 | + | 0.722458i | ||||
\(628\) | 706955. | 1.79256 | ||||||||
\(629\) | − | 160547.i | − | 0.405790i | ||||||
\(630\) | −22199.0 | + | 16893.0i | −0.0559309 | + | 0.0425623i | ||||
\(631\) | −689137. | −1.73080 | −0.865400 | − | 0.501081i | \(-0.832936\pi\) | ||||
−0.865400 | + | 0.501081i | \(0.832936\pi\) | |||||||
\(632\) | 647045.i | 1.61995i | ||||||||
\(633\) | 361646. | − | 121955.i | 0.902560 | − | 0.304363i | ||||
\(634\) | 176904. | 0.440108 | ||||||||
\(635\) | 10367.4i | 0.0257112i | ||||||||
\(636\) | −207756. | − | 616080.i | −0.513616 | − | 1.52308i | ||||
\(637\) | 564638. | 1.39152 | ||||||||
\(638\) | 273730.i | 0.672482i | ||||||||
\(639\) | 43408.2 | + | 57042.4i | 0.106309 | + | 0.139700i | ||||
\(640\) | 34988.2 | 0.0854204 | ||||||||
\(641\) | − | 250518.i | − | 0.609710i | −0.952399 | − | 0.304855i | \(-0.901392\pi\) | ||
0.952399 | − | 0.304855i | \(-0.0986081\pi\) | |||||||
\(642\) | −543736. | + | 183360.i | −1.31922 | + | 0.444870i | ||||
\(643\) | 277817. | 0.671950 | 0.335975 | − | 0.941871i | \(-0.390934\pi\) | ||||
0.335975 | + | 0.941871i | \(0.390934\pi\) | |||||||
\(644\) | 3.04151e6i | 7.33360i | ||||||||
\(645\) | 869.687 | + | 2578.98i | 0.00209047 | + | 0.00619909i | ||||
\(646\) | −1.80698e6 | −4.33001 | ||||||||
\(647\) | 705078.i | 1.68434i | 0.539215 | + | 0.842168i | \(0.318721\pi\) | ||||
−0.539215 | + | 0.842168i | \(0.681279\pi\) | |||||||
\(648\) | −1.36089e6 | − | 376363.i | −3.24095 | − | 0.896306i | ||||
\(649\) | −28642.6 | −0.0680022 | ||||||||
\(650\) | 990353.i | 2.34403i | ||||||||
\(651\) | −782941. | + | 264025.i | −1.84743 | + | 0.622992i | ||||
\(652\) | 1.77553e6 | 4.17670 | ||||||||
\(653\) | 58074.5i | 0.136194i | 0.997679 | + | 0.0680972i | \(0.0216928\pi\) | ||||
−0.997679 | + | 0.0680972i | \(0.978307\pi\) | |||||||
\(654\) | −106478. | − | 315752.i | −0.248946 | − | 0.738228i | ||||
\(655\) | −22.4484 | −5.23242e−5 | ||||||||
\(656\) | 1.95412e6i | 4.54092i | ||||||||
\(657\) | 509705. | − | 387875.i | 1.18083 | − | 0.898589i | ||||
\(658\) | −19272.9 | −0.0445138 | ||||||||
\(659\) | − | 745763.i | − | 1.71724i | −0.512615 | − | 0.858619i | \(-0.671323\pi\) | ||
0.512615 | − | 0.858619i | \(-0.328677\pi\) | |||||||
\(660\) | −14648.1 | + | 4939.67i | −0.0336275 | + | 0.0113399i | ||||
\(661\) | 226416. | 0.518209 | 0.259104 | − | 0.965849i | \(-0.416573\pi\) | ||||
0.259104 | + | 0.965849i | \(0.416573\pi\) | |||||||
\(662\) | − | 597961.i | − | 1.36445i | ||||||
\(663\) | 261377. | + | 775091.i | 0.594622 | + | 1.76330i | ||||
\(664\) | −982307. | −2.22798 | ||||||||
\(665\) | − | 23462.4i | − | 0.0530554i | ||||||
\(666\) | 137384. | + | 180536.i | 0.309734 | + | 0.407020i | ||||
\(667\) | −541247. | −1.21659 | ||||||||
\(668\) | − | 885935.i | − | 1.98540i | ||||||
\(669\) | 457354. | − | 154230.i | 1.02188 | − | 0.344601i | ||||
\(670\) | 11407.0 | 0.0254110 | ||||||||
\(671\) | − | 158900.i | − | 0.352923i | ||||||
\(672\) | −827584. | − | 2.45412e6i | −1.83262 | − | 5.43448i | ||||
\(673\) | −515622. | −1.13842 | −0.569208 | − | 0.822194i | \(-0.692750\pi\) | ||||
−0.569208 | + | 0.822194i | \(0.692750\pi\) | |||||||
\(674\) | 33814.5i | 0.0744361i | ||||||||
\(675\) | −255247. | + | 377078.i | −0.560213 | + | 0.827606i | ||||
\(676\) | −589926. | −1.29093 | ||||||||
\(677\) | 722728.i | 1.57688i | 0.615114 | + | 0.788438i | \(0.289110\pi\) | ||||
−0.615114 | + | 0.788438i | \(0.710890\pi\) | |||||||
\(678\) | −165248. | + | 55725.1i | −0.359481 | + | 0.121225i | ||||
\(679\) | 565238. | 1.22600 | ||||||||
\(680\) | − | 59169.3i | − | 0.127961i | ||||||
\(681\) | −122497. | − | 363253.i | −0.264137 | − | 0.783275i | ||||
\(682\) | −625049. | −1.34383 | ||||||||
\(683\) | − | 821439.i | − | 1.76090i | −0.474142 | − | 0.880448i | \(-0.657242\pi\) | ||
0.474142 | − | 0.880448i | \(-0.342758\pi\) | |||||||
\(684\) | 1.48851e6 | − | 1.13272e6i | 3.18155 | − | 2.42110i | ||||
\(685\) | 605.272 | 0.00128994 | ||||||||
\(686\) | 196272.i | 0.417071i | ||||||||
\(687\) | 128727. | − | 43409.7i | 0.272745 | − | 0.0919756i | ||||
\(688\) | −469781. | −0.992473 | ||||||||
\(689\) | − | 337918.i | − | 0.711824i | ||||||
\(690\) | −13333.2 | − | 39538.5i | −0.0280051 | − | 0.0830466i | ||||
\(691\) | −506557. | −1.06089 | −0.530447 | − | 0.847718i | \(-0.677976\pi\) | ||||
−0.530447 | + | 0.847718i | \(0.677976\pi\) | |||||||
\(692\) | 2.18515e6i | 4.56320i | ||||||||
\(693\) | 222598. | + | 292515.i | 0.463505 | + | 0.609090i | ||||
\(694\) | −555753. | −1.15389 | ||||||||
\(695\) | − | 3209.13i | − | 0.00664382i | ||||||
\(696\) | 1.02769e6 | − | 346558.i | 2.12149 | − | 0.715414i | ||||
\(697\) | 899341. | 1.85122 | ||||||||
\(698\) | 1.43359e6i | 2.94248i | ||||||||
\(699\) | −5073.84 | − | 15046.0i | −0.0103844 | − | 0.0307941i | ||||
\(700\) | −1.96542e6 | −4.01107 | ||||||||
\(701\) | − | 831341.i | − | 1.69178i | −0.533360 | − | 0.845888i | \(-0.679071\pi\) | ||
0.533360 | − | 0.845888i | \(-0.320929\pi\) | |||||||
\(702\) | −957185. | − | 647925.i | −1.94232 | − | 1.31477i | ||||
\(703\) | −190811. | −0.386094 | ||||||||
\(704\) | − | 985032.i | − | 1.98749i | ||||||
\(705\) | 183.533 | − | 61.8913i | 0.000369263 | − | 0.000124524i | ||||
\(706\) | 1.13088e6 | 2.26885 | ||||||||
\(707\) | − | 303988.i | − | 0.608160i | ||||||
\(708\) | 57116.2 | + | 169373.i | 0.113944 | + | 0.337892i | ||||
\(709\) | −417159. | −0.829869 | −0.414935 | − | 0.909851i | \(-0.636196\pi\) | ||||
−0.414935 | + | 0.909851i | \(0.636196\pi\) | |||||||
\(710\) | − | 4244.59i | − | 0.00842014i | ||||||
\(711\) | −193803. | + | 147480.i | −0.383373 | + | 0.291739i | ||||
\(712\) | 432757. | 0.853658 | ||||||||
\(713\) | − | 1.23591e6i | − | 2.43113i | ||||||
\(714\) | −2.09982e6 | + | 708105.i | −4.11894 | + | 1.38900i | ||||
\(715\) | −8034.46 | −0.0157161 | ||||||||
\(716\) | 1.40903e6i | 2.74849i | ||||||||
\(717\) | −285160. | − | 845616.i | −0.554690 | − | 1.64488i | ||||
\(718\) | 556646. | 1.07977 | ||||||||
\(719\) | − | 150325.i | − | 0.290787i | −0.989374 | − | 0.145393i | \(-0.953555\pi\) | ||
0.989374 | − | 0.145393i | \(-0.0464448\pi\) | |||||||
\(720\) | 29303.7 | + | 38507.8i | 0.0565272 | + | 0.0742821i | ||||
\(721\) | 772923. | 1.48685 | ||||||||
\(722\) | 1.13962e6i | 2.18618i | ||||||||
\(723\) | 628916. | − | 212084.i | 1.20314 | − | 0.405725i | ||||
\(724\) | −1.18016e6 | −2.25146 | ||||||||
\(725\) | − | 349754.i | − | 0.665406i | ||||||
\(726\) | −236816. | − | 702258.i | −0.449302 | − | 1.33237i | ||||
\(727\) | −479152. | −0.906577 | −0.453289 | − | 0.891364i | \(-0.649749\pi\) | ||||
−0.453289 | + | 0.891364i | \(0.649749\pi\) | |||||||
\(728\) | − | 3.16758e6i | − | 5.97674i | ||||||
\(729\) | −197457. | − | 493397.i | −0.371551 | − | 0.928413i | ||||
\(730\) | −37927.7 | −0.0711723 | ||||||||
\(731\) | 216206.i | 0.404607i | ||||||||
\(732\) | −939629. | + | 316863.i | −1.75362 | + | 0.591357i | ||||
\(733\) | 1.03624e6 | 1.92865 | 0.964325 | − | 0.264720i | \(-0.0852796\pi\) | ||||
0.964325 | + | 0.264720i | \(0.0852796\pi\) | |||||||
\(734\) | 2.03663e6i | 3.78024i | ||||||||
\(735\) | −4912.27 | − | 14566.9i | −0.00909301 | − | 0.0269645i | ||||
\(736\) | 3.87396e6 | 7.15154 | ||||||||
\(737\) | − | 150310.i | − | 0.276727i | ||||||
\(738\) | −1.01131e6 | + | 769588.i | −1.85683 | + | 1.41301i | ||||
\(739\) | −900360. | −1.64865 | −0.824323 | − | 0.566120i | \(-0.808444\pi\) | ||||
−0.824323 | + | 0.566120i | \(0.808444\pi\) | |||||||
\(740\) | − | 9840.98i | − | 0.0179711i | ||||||
\(741\) | 921198. | − | 310648.i | 1.67771 | − | 0.565759i | ||||
\(742\) | 915463. | 1.66277 | ||||||||
\(743\) | 464398.i | 0.841226i | 0.907240 | + | 0.420613i | \(0.138185\pi\) | ||||
−0.907240 | + | 0.420613i | \(0.861815\pi\) | |||||||
\(744\) | 791349. | + | 2.34667e6i | 1.42962 | + | 4.23942i | ||||
\(745\) | −15251.1 | −0.0274782 | ||||||||
\(746\) | 728571.i | 1.30916i | ||||||||
\(747\) | −223896. | − | 294221.i | −0.401241 | − | 0.527269i | ||||
\(748\) | −1.22802e6 | −2.19483 | ||||||||
\(749\) | − | 591872.i | − | 1.05503i | ||||||
\(750\) | 51115.3 | − | 17237.2i | 0.0908716 | − | 0.0306439i | ||||
\(751\) | −469386. | −0.832243 | −0.416121 | − | 0.909309i | \(-0.636611\pi\) | ||||
−0.416121 | + | 0.909309i | \(0.636611\pi\) | |||||||
\(752\) | 33432.0i | 0.0591190i | ||||||||
\(753\) | −99575.5 | − | 295282.i | −0.175615 | − | 0.520772i | ||||
\(754\) | 887825. | 1.56165 | ||||||||
\(755\) | 10474.6i | 0.0183756i | ||||||||
\(756\) | 1.28585e6 | − | 1.89960e6i | 2.24982 | − | 3.32367i | ||||
\(757\) | −162448. | −0.283480 | −0.141740 | − | 0.989904i | \(-0.545270\pi\) | ||||
−0.141740 | + | 0.989904i | \(0.545270\pi\) | |||||||
\(758\) | 795168.i | 1.38395i | ||||||||
\(759\) | −520997. | + | 175691.i | −0.904381 | + | 0.304977i | ||||
\(760\) | −70322.8 | −0.121750 | ||||||||
\(761\) | 863476.i | 1.49101i | 0.666499 | + | 0.745506i | \(0.267792\pi\) | ||||
−0.666499 | + | 0.745506i | \(0.732208\pi\) | |||||||
\(762\) | −371873. | − | 1.10276e6i | −0.640449 | − | 1.89919i | ||||
\(763\) | 343705. | 0.590387 | ||||||||
\(764\) | − | 1.43240e6i | − | 2.45402i | ||||||
\(765\) | 17722.4 | − | 13486.4i | 0.0302830 | − | 0.0230448i | ||||
\(766\) | 455575. | 0.776429 | ||||||||
\(767\) | 92900.5i | 0.157916i | ||||||||
\(768\) | −1.59499e6 | + | 537865.i | −2.70418 | + | 0.911907i | ||||
\(769\) | −899906. | −1.52175 | −0.760877 | − | 0.648896i | \(-0.775231\pi\) | ||||
−0.760877 | + | 0.648896i | \(0.775231\pi\) | |||||||
\(770\) | − | 21766.4i | − | 0.0367117i | ||||||
\(771\) | 244751. | + | 725787.i | 0.411733 | + | 1.22096i | ||||
\(772\) | −1.19398e6 | −2.00337 | ||||||||
\(773\) | 736093.i | 1.23189i | 0.787787 | + | 0.615947i | \(0.211227\pi\) | ||||
−0.787787 | + | 0.615947i | \(0.788773\pi\) | |||||||
\(774\) | −185013. | − | 243125.i | −0.308831 | − | 0.405833i | ||||
\(775\) | 798647. | 1.32969 | ||||||||
\(776\) | − | 1.69416e6i | − | 2.81340i | ||||||
\(777\) | −221734. | + | 74773.4i | −0.367274 | + | 0.123853i | ||||
\(778\) | −1.38528e6 | −2.28865 | ||||||||
\(779\) | − | 1.06887e6i | − | 1.76137i | ||||||
\(780\) | 16021.5 | + | 47510.3i | 0.0263338 | + | 0.0780906i | ||||
\(781\) | −55930.8 | −0.0916957 | ||||||||
\(782\) | − | 3.31468e6i | − | 5.42035i | ||||||
\(783\) | 338040. | + | 228822.i | 0.551372 | + | 0.373228i | ||||
\(784\) | 2.65348e6 | 4.31701 | ||||||||
\(785\) | − | 10003.8i | − | 0.0162339i | ||||||
\(786\) | 2387.79 | − | 805.213i | 0.00386501 | − | 0.00130336i | ||||
\(787\) | −63528.7 | −0.102570 | −0.0512850 | − | 0.998684i | \(-0.516332\pi\) | ||||
−0.0512850 | + | 0.998684i | \(0.516332\pi\) | |||||||
\(788\) | − | 1.40323e6i | − | 2.25984i | ||||||
\(789\) | −322604. | − | 956652.i | −0.518221 | − | 1.53674i | ||||
\(790\) | 14421.1 | 0.0231071 | ||||||||
\(791\) | − | 179877.i | − | 0.287490i | ||||||
\(792\) | 876741. | − | 667183.i | 1.39772 | − | 1.06364i | ||||
\(793\) | −515383. | −0.819566 | ||||||||
\(794\) | 353237.i | 0.560307i | ||||||||
\(795\) | −8717.83 | + | 2939.84i | −0.0137935 | + | 0.00465146i | ||||
\(796\) | −1.12488e6 | −1.77533 | ||||||||
\(797\) | 854920.i | 1.34589i | 0.739694 | + | 0.672944i | \(0.234970\pi\) | ||||
−0.739694 | + | 0.672944i | \(0.765030\pi\) | |||||||
\(798\) | 841585. | + | 2.49564e6i | 1.32158 | + | 3.91901i | ||||
\(799\) | 15386.3 | 0.0241014 | ||||||||
\(800\) | 2.50336e6i | 3.91149i | ||||||||
\(801\) | 98637.8 | + | 129619.i | 0.153737 | + | 0.202025i | ||||
\(802\) | −422850. | −0.657411 | ||||||||
\(803\) | 499772.i | 0.775069i | ||||||||
\(804\) | −888829. | + | 299732.i | −1.37501 | + | 0.463683i | ||||
\(805\) | 43038.8 | 0.0664153 | ||||||||
\(806\) | 2.02731e6i | 3.12068i | ||||||||
\(807\) | 74892.9 | + | 222088.i | 0.114999 | + | 0.341019i | ||||
\(808\) | −911130. | −1.39559 | ||||||||
\(809\) | − | 32729.9i | − | 0.0500089i | −0.999687 | − | 0.0250045i | \(-0.992040\pi\) | ||
0.999687 | − | 0.0250045i | \(-0.00795999\pi\) | |||||||
\(810\) | −8388.23 | + | 30331.0i | −0.0127850 | + | 0.0462292i | ||||
\(811\) | 208112. | 0.316414 | 0.158207 | − | 0.987406i | \(-0.449429\pi\) | ||||
0.158207 | + | 0.987406i | \(0.449429\pi\) | |||||||
\(812\) | 1.76195e6i | 2.67227i | ||||||||
\(813\) | 1.04257e6 | − | 351578.i | 1.57734 | − | 0.531914i | ||||
\(814\) | −177018. | −0.267158 | ||||||||
\(815\) | − | 25124.6i | − | 0.0378255i | ||||||
\(816\) | 1.22833e6 | + | 3.64249e6i | 1.84473 | + | 5.47039i | ||||
\(817\) | 256962. | 0.384968 | ||||||||
\(818\) | 2.00465e6i | 2.99593i | ||||||||
\(819\) | 948753. | − | 721983.i | 1.41444 | − | 1.07636i | ||||
\(820\) | 55126.4 | 0.0819845 | ||||||||
\(821\) | 839175.i | 1.24499i | 0.782623 | + | 0.622496i | \(0.213881\pi\) | ||||
−0.782623 | + | 0.622496i | \(0.786119\pi\) | |||||||
\(822\) | −64381.4 | + | 21710.8i | −0.0952833 | + | 0.0321316i | ||||
\(823\) | 297088. | 0.438616 | 0.219308 | − | 0.975656i | \(-0.429620\pi\) | ||||
0.219308 | + | 0.975656i | \(0.429620\pi\) | |||||||
\(824\) | − | 2.31665e6i | − | 3.41197i | ||||||
\(825\) | −113532. | − | 336668.i | −0.166805 | − | 0.494646i | ||||
\(826\) | −251679. | −0.368882 | ||||||||
\(827\) | 609715.i | 0.891489i | 0.895160 | + | 0.445745i | \(0.147061\pi\) | ||||
−0.895160 | + | 0.445745i | \(0.852939\pi\) | |||||||
\(828\) | 2.07784e6 | + | 2.73047e6i | 3.03076 | + | 3.98270i | ||||
\(829\) | 66695.5 | 0.0970482 | 0.0485241 | − | 0.998822i | \(-0.484548\pi\) | ||||
0.0485241 | + | 0.998822i | \(0.484548\pi\) | |||||||
\(830\) | 21893.3i | 0.0317801i | ||||||||
\(831\) | −236203. | + | 79652.6i | −0.342045 | + | 0.115345i | ||||
\(832\) | −3.19489e6 | −4.61540 | ||||||||
\(833\) | − | 1.22120e6i | − | 1.75994i | ||||||
\(834\) | 115110. | + | 341348.i | 0.165493 | + | 0.490756i | ||||
\(835\) | −12536.4 | −0.0179804 | ||||||||
\(836\) | 1.45950e6i | 2.08829i | ||||||||
\(837\) | −522504. | + | 771899.i | −0.745829 | + | 1.10182i | ||||
\(838\) | 794215. | 1.13097 | ||||||||
\(839\) | − | 811996.i | − | 1.15353i | −0.816909 | − | 0.576766i | \(-0.804314\pi\) | ||
0.816909 | − | 0.576766i | \(-0.195686\pi\) | |||||||
\(840\) | −81719.3 | + | 27557.5i | −0.115815 | + | 0.0390554i | ||||
\(841\) | 393736. | 0.556690 | ||||||||
\(842\) | − | 1.67343e6i | − | 2.36039i | ||||||
\(843\) | 398574. | + | 1.18193e6i | 0.560859 | + | 1.66318i | ||||
\(844\) | 1.85840e6 | 2.60889 | ||||||||
\(845\) | 8347.74i | 0.0116911i | ||||||||
\(846\) | −17302.0 | + | 13166.5i | −0.0241744 | + | 0.0183962i | ||||
\(847\) | 764428. | 1.06554 | ||||||||
\(848\) | − | 1.58802e6i | − | 2.20834i | ||||||
\(849\) | −289981. | + | 97787.9i | −0.402304 | + | 0.135666i | ||||
\(850\) | 2.14194e6 | 2.96463 | ||||||||
\(851\) | − | 350018.i | − | 0.483316i | ||||||
\(852\) | 111532. | + | 330737.i | 0.153645 | + | 0.455620i | ||||
\(853\) | −146391. | −0.201195 | −0.100597 | − | 0.994927i | \(-0.532075\pi\) | ||||
−0.100597 | + | 0.994927i | \(0.532075\pi\) | |||||||
\(854\) | − | 1.39624e6i | − | 1.91445i | ||||||
\(855\) | −16028.6 | − | 21063.1i | −0.0219262 | − | 0.0288131i | ||||
\(856\) | −1.77399e6 | −2.42105 | ||||||||
\(857\) | − | 251181.i | − | 0.341999i | −0.985271 | − | 0.170999i | \(-0.945300\pi\) | ||
0.985271 | − | 0.170999i | \(-0.0546996\pi\) | |||||||
\(858\) | 854607. | − | 288192.i | 1.16089 | − | 0.391478i | ||||
\(859\) | 869910. | 1.17893 | 0.589465 | − | 0.807794i | \(-0.299339\pi\) | ||||
0.589465 | + | 0.807794i | \(0.299339\pi\) | |||||||
\(860\) | 13252.7i | 0.0179187i | ||||||||
\(861\) | −418859. | − | 1.24209e6i | −0.565018 | − | 1.67551i | ||||
\(862\) | −1.09049e6 | −1.46759 | ||||||||
\(863\) | 456928.i | 0.613516i | 0.951788 | + | 0.306758i | \(0.0992442\pi\) | ||||
−0.951788 | + | 0.306758i | \(0.900756\pi\) | |||||||
\(864\) | −2.41952e6 | − | 1.63779e6i | −3.24116 | − | 2.19397i | ||||
\(865\) | 30920.9 | 0.0413257 | ||||||||
\(866\) | 1.03383e6i | 1.37852i | ||||||||
\(867\) | 964095. | − | 325114.i | 1.28257 | − | 0.432511i | ||||
\(868\) | −4.02333e6 | −5.34006 | ||||||||
\(869\) | − | 190026.i | − | 0.251637i | ||||||
\(870\) | −7723.96 | − | 22904.7i | −0.0102047 | − | 0.0302612i | ||||
\(871\) | −487519. | −0.642622 | ||||||||
\(872\) | − | 1.03017e6i | − | 1.35480i | ||||||
\(873\) | 507435. | − | 386148.i | 0.665813 | − | 0.506671i | ||||
\(874\) | −3.93950e6 | −5.15725 | ||||||||
\(875\) | 55640.5i | 0.0726732i | ||||||||
\(876\) | 2.95531e6 | − | 996594.i | 3.85119 | − | 1.29870i | ||||
\(877\) | 382783. | 0.497684 | 0.248842 | − | 0.968544i | \(-0.419950\pi\) | ||||
0.248842 | + | 0.968544i | \(0.419950\pi\) | |||||||
\(878\) | − | 102485.i | − | 0.132944i | ||||||
\(879\) | 244959. | + | 726404.i | 0.317041 | + | 0.940158i | ||||
\(880\) | −37757.4 | −0.0487570 | ||||||||
\(881\) | 868608.i | 1.11911i | 0.828794 | + | 0.559554i | \(0.189028\pi\) | ||||
−0.828794 | + | 0.559554i | \(0.810972\pi\) | |||||||
\(882\) | 1.04501e6 | + | 1.37325e6i | 1.34334 | + | 1.76527i | ||||
\(883\) | 60577.1 | 0.0776939 | 0.0388470 | − | 0.999245i | \(-0.487632\pi\) | ||||
0.0388470 | + | 0.999245i | \(0.487632\pi\) | |||||||
\(884\) | 3.98299e6i | 5.09688i | ||||||||
\(885\) | 2396.71 | − | 808.222i | 0.00306005 | − | 0.00103191i | ||||
\(886\) | 1.50841e6 | 1.92155 | ||||||||
\(887\) | 1.22832e6i | 1.56122i | 0.625018 | + | 0.780610i | \(0.285092\pi\) | ||||
−0.625018 | + | 0.780610i | \(0.714908\pi\) | |||||||
\(888\) | 224115. | + | 664592.i | 0.284214 | + | 0.842810i | ||||
\(889\) | 1.20038e6 | 1.51885 | ||||||||
\(890\) | − | 9645.13i | − | 0.0121767i | ||||||
\(891\) | 399669. | + | 110531.i | 0.503437 | + | 0.139229i | ||||
\(892\) | 2.35022e6 | 2.95379 | ||||||||
\(893\) | − | 18286.7i | − | 0.0229315i | ||||||
\(894\) | 1.62222e6 | − | 547049.i | 2.02972 | − | 0.684465i | ||||
\(895\) | 19938.4 | 0.0248912 | ||||||||
\(896\) | − | 4.05108e6i | − | 5.04609i | ||||||
\(897\) | 569843. | + | 1.68982e6i | 0.708224 | + | 2.10017i | ||||
\(898\) | 481635. | 0.597263 | ||||||||
\(899\) | − | 715966.i | − | 0.885876i | ||||||
\(900\) | −1.76443e6 | + | 1.34270e6i | −2.17831 | + | 1.65765i | ||||
\(901\) | −730852. | −0.900285 | ||||||||
\(902\) | − | 991604.i | − | 1.21878i | ||||||
\(903\) | 298605. | − | 100696.i | 0.366203 | − | 0.123491i | ||||
\(904\) | −539136. | −0.659723 | ||||||||
\(905\) | 16699.9i | 0.0203899i | ||||||||
\(906\) | −375717. | − | 1.11416e6i | −0.457725 | − | 1.35734i | ||||
\(907\) | 298870. | 0.363302 | 0.181651 | − | 0.983363i | \(-0.441856\pi\) | ||||
0.181651 | + | 0.983363i | \(0.441856\pi\) | |||||||
\(908\) | − | 1.86666e6i | − | 2.26409i | ||||||
\(909\) | −207673. | − | 272902.i | −0.251334 | − | 0.330277i | ||||
\(910\) | −70597.9 | −0.0852528 | ||||||||
\(911\) | − | 563963.i | − | 0.679539i | −0.940509 | − | 0.339769i | \(-0.889651\pi\) | ||
0.940509 | − | 0.339769i | \(-0.110349\pi\) | |||||||
\(912\) | 4.32911e6 | − | 1.45987e6i | 5.20486 | − | 1.75519i | ||||
\(913\) | 288487. | 0.346086 | ||||||||
\(914\) | − | 1.38003e6i | − | 1.65195i | ||||||
\(915\) | 4483.77 | + | 13296.2i | 0.00535551 | + | 0.0158813i | ||||
\(916\) | 661496. | 0.788382 | ||||||||
\(917\) | 2599.17i | 0.00309098i | ||||||||
\(918\) | −1.40134e6 | + | 2.07021e6i | −1.66287 | + | 2.45657i | ||||
\(919\) | −1.39354e6 | −1.65002 | −0.825011 | − | 0.565116i | \(-0.808831\pi\) | ||||
−0.825011 | + | 0.565116i | \(0.808831\pi\) | |||||||
\(920\) | − | 128998.i | − | 0.152408i | ||||||
\(921\) | −1.54647e6 | + | 521503.i | −1.82315 | + | 0.614806i | ||||
\(922\) | 291648. | 0.343081 | ||||||||
\(923\) | 181408.i | 0.212938i | ||||||||
\(924\) | 571936. | + | 1.69603e6i | 0.669890 | + | 1.98650i | ||||
\(925\) | 226182. | 0.264347 | ||||||||
\(926\) | − | 1.81238e6i | − | 2.11362i | ||||||
\(927\) | 693882. | − | 528031.i | 0.807470 | − | 0.614469i | ||||
\(928\) | 2.24419e6 | 2.60594 | ||||||||
\(929\) | − | 343003.i | − | 0.397435i | −0.980057 | − | 0.198718i | \(-0.936322\pi\) | ||
0.980057 | − | 0.198718i | \(-0.0636776\pi\) | |||||||
\(930\) | 52301.8 | − | 17637.3i | 0.0604715 | − | 0.0203923i | ||||
\(931\) | −1.45140e6 | −1.67451 | ||||||||
\(932\) | − | 77317.6i | − | 0.0890115i | ||||||
\(933\) | −157952. | − | 468392.i | −0.181452 | − | 0.538080i | ||||
\(934\) | −1.96942e6 | −2.25758 | ||||||||
\(935\) | 17377.0i | 0.0198770i | ||||||||
\(936\) | −2.16397e6 | − | 2.84365e6i | −2.47001 | − | 3.24583i | ||||
\(937\) | −150942. | −0.171921 | −0.0859607 | − | 0.996299i | \(-0.527396\pi\) | ||||
−0.0859607 | + | 0.996299i | \(0.527396\pi\) | |||||||
\(938\) | − | 1.32075e6i | − | 1.50112i | ||||||
\(939\) | −463535. | + | 156314.i | −0.525716 | + | 0.177283i | ||||
\(940\) | 943.129 | 0.00106737 | ||||||||
\(941\) | 131326.i | 0.148310i | 0.997247 | + | 0.0741550i | \(0.0236260\pi\) | ||||
−0.997247 | + | 0.0741550i | \(0.976374\pi\) | |||||||
\(942\) | 358830. | + | 1.06408e6i | 0.404377 | + | 1.19914i | ||||
\(943\) | 1.96070e6 | 2.20490 | ||||||||
\(944\) | 436580.i | 0.489914i | ||||||||
\(945\) | −26880.2 | − | 18195.4i | −0.0301002 | − | 0.0203750i | ||||
\(946\) | 238387. | 0.266379 | ||||||||
\(947\) | − | 1.65428e6i | − | 1.84463i | −0.386441 | − | 0.922314i | \(-0.626296\pi\) | ||
0.386441 | − | 0.922314i | \(-0.373704\pi\) | |||||||
\(948\) | −1.12369e6 | + | 378931.i | −1.25034 | + | 0.421642i | ||||
\(949\) | 1.62098e6 | 1.79988 | ||||||||
\(950\) | − | 2.54571e6i | − | 2.82073i | ||||||
\(951\) | 65776.4 | + | 195054.i | 0.0727292 | + | 0.215672i | ||||
\(952\) | −6.85087e6 | −7.55913 | ||||||||
\(953\) | − | 151783.i | − | 0.167123i | −0.996503 | − | 0.0835615i | \(-0.973370\pi\) | ||
0.996503 | − | 0.0835615i | \(-0.0266295\pi\) | |||||||
\(954\) | 821845. | − | 625408.i | 0.903012 | − | 0.687174i | ||||
\(955\) | −20269.2 | −0.0222244 | ||||||||
\(956\) | − | 4.34540e6i | − | 4.75460i | ||||||
\(957\) | −301814. | + | 101778.i | −0.329545 | + | 0.111130i | ||||
\(958\) | 1.21860e6 | 1.32780 | ||||||||
\(959\) | − | 70081.0i | − | 0.0762014i | ||||||
\(960\) | 27795.1 | + | 82423.9i | 0.0301596 | + | 0.0894356i | ||||
\(961\) | 711354. | 0.770262 | ||||||||
\(962\) | 574146.i | 0.620400i | ||||||||
\(963\) | −404344. | − | 531346.i | −0.436012 | − | 0.572961i | ||||
\(964\) | 3.23183e6 | 3.47772 | ||||||||
\(965\) | 16895.3i | 0.0181431i | ||||||||
\(966\) | −4.57794e6 | + | 1.54378e6i | −4.90586 | + | 1.65436i | ||||
\(967\) | −1.21992e6 | −1.30461 | −0.652303 | − | 0.757959i | \(-0.726197\pi\) | ||||
−0.652303 | + | 0.757959i | \(0.726197\pi\) | |||||||
\(968\) | − | 2.29118e6i | − | 2.44517i | ||||||
\(969\) | −671872. | − | 1.99238e6i | −0.715548 | − | 2.12189i | ||||
\(970\) | −37758.9 | −0.0401306 | ||||||||
\(971\) | 1.47791e6i | 1.56751i | 0.621071 | + | 0.783754i | \(0.286698\pi\) | ||||
−0.621071 | + | 0.783754i | \(0.713302\pi\) | |||||||
\(972\) | −143373. | − | 2.58378e6i | −0.151752 | − | 2.73479i | ||||
\(973\) | −371567. | −0.392475 | ||||||||
\(974\) | − | 70095.2i | − | 0.0738874i | ||||||
\(975\) | −1.09196e6 | + | 368233.i | −1.14868 | + | 0.387359i | ||||
\(976\) | −2.42201e6 | −2.54259 | ||||||||
\(977\) | 442576.i | 0.463659i | 0.972756 | + | 0.231830i | \(0.0744712\pi\) | ||||
−0.972756 | + | 0.231830i | \(0.925529\pi\) | |||||||
\(978\) | 901207. | + | 2.67245e6i | 0.942208 | + | 2.79403i | ||||
\(979\) | −127093. | −0.132604 | ||||||||
\(980\) | − | 74855.4i | − | 0.0779419i | ||||||
\(981\) | 308557. | − | 234806.i | 0.320625 | − | 0.243989i | ||||
\(982\) | −1.55354e6 | −1.61102 | ||||||||
\(983\) | 1.41860e6i | 1.46809i | 0.679100 | + | 0.734046i | \(0.262370\pi\) | ||||
−0.679100 | + | 0.734046i | \(0.737630\pi\) | |||||||
\(984\) | −3.72286e6 | + | 1.25543e6i | −3.84491 | + | 1.29659i | ||||
\(985\) | −19856.4 | −0.0204658 | ||||||||
\(986\) | − | 1.92020e6i | − | 1.97511i | ||||||
\(987\) | −7166.04 | − | 21250.3i | −0.00735606 | − | 0.0218137i | ||||
\(988\) | 4.73379e6 | 4.84948 | ||||||||
\(989\) | 471363.i | 0.481907i | ||||||||
\(990\) | −14869.9 | − | 19540.5i | −0.0151719 | − | 0.0199372i | ||||
\(991\) | −331119. | −0.337161 | −0.168580 | − | 0.985688i | \(-0.553918\pi\) | ||||
−0.168580 | + | 0.985688i | \(0.553918\pi\) | |||||||
\(992\) | 5.12451e6i | 5.20749i | ||||||||
\(993\) | 659311. | − | 222334.i | 0.668639 | − | 0.225480i | ||||
\(994\) | −491457. | −0.497408 | ||||||||
\(995\) | 15917.6i | 0.0160780i | ||||||||
\(996\) | −575272. | − | 1.70592e6i | −0.579902 | − | 1.71965i | ||||
\(997\) | 115116. | 0.115809 | 0.0579047 | − | 0.998322i | \(-0.481558\pi\) | ||||
0.0579047 | + | 0.998322i | \(0.481558\pi\) | |||||||
\(998\) | 2.16793e6i | 2.17663i | ||||||||
\(999\) | −147976. | + | 218607.i | −0.148273 | + | 0.219045i |
(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.119.77 | yes | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.2 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.2 | ✓ | 78 | 3.2 | odd | 2 | inner | |
177.5.b.a.119.77 | yes | 78 | 1.1 | even | 1 | trivial |