Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,5,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, 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("43.42");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(4.44490841261\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 142x^{10} + 7173x^{8} + 157368x^{6} + 1510016x^{4} + 5098688x^{2} + 90352 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.12 | ||
Root | \(7.49282i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.5.b.b.42.1 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.49282i | 1.87321i | 0.350393 | + | 0.936603i | \(0.386048\pi\) | ||||
−0.350393 | + | 0.936603i | \(0.613952\pi\) | |||||||
\(3\) | − | 14.5182i | − | 1.61313i | −0.591146 | − | 0.806564i | \(-0.701324\pi\) | ||
0.591146 | − | 0.806564i | \(-0.298676\pi\) | |||||||
\(4\) | −40.1424 | −2.50890 | ||||||||
\(5\) | − | 9.40180i | − | 0.376072i | −0.982162 | − | 0.188036i | \(-0.939788\pi\) | ||
0.982162 | − | 0.188036i | \(-0.0602122\pi\) | |||||||
\(6\) | 108.782 | 3.02172 | ||||||||
\(7\) | − | 53.5326i | − | 1.09250i | −0.837622 | − | 0.546251i | \(-0.816055\pi\) | ||
0.837622 | − | 0.546251i | \(-0.183945\pi\) | |||||||
\(8\) | − | 180.895i | − | 2.82648i | ||||||
\(9\) | −129.777 | −1.60218 | ||||||||
\(10\) | 70.4460 | 0.704460 | ||||||||
\(11\) | 151.146 | 1.24914 | 0.624569 | − | 0.780970i | \(-0.285275\pi\) | ||||
0.624569 | + | 0.780970i | \(0.285275\pi\) | |||||||
\(12\) | 582.793i | 4.04718i | ||||||||
\(13\) | −319.508 | −1.89058 | −0.945289 | − | 0.326233i | \(-0.894221\pi\) | ||||
−0.945289 | + | 0.326233i | \(0.894221\pi\) | |||||||
\(14\) | 401.110 | 2.04648 | ||||||||
\(15\) | −136.497 | −0.606653 | ||||||||
\(16\) | 713.133 | 2.78568 | ||||||||
\(17\) | 32.2585 | 0.111621 | 0.0558106 | − | 0.998441i | \(-0.482226\pi\) | ||||
0.0558106 | + | 0.998441i | \(0.482226\pi\) | |||||||
\(18\) | − | 972.395i | − | 3.00122i | ||||||
\(19\) | − | 304.131i | − | 0.842469i | −0.906952 | − | 0.421235i | \(-0.861597\pi\) | ||
0.906952 | − | 0.421235i | \(-0.138403\pi\) | |||||||
\(20\) | 377.411i | 0.943527i | ||||||||
\(21\) | −777.194 | −1.76235 | ||||||||
\(22\) | 1132.51i | 2.33989i | ||||||||
\(23\) | −199.312 | −0.376771 | −0.188386 | − | 0.982095i | \(-0.560325\pi\) | ||||
−0.188386 | + | 0.982095i | \(0.560325\pi\) | |||||||
\(24\) | −2626.26 | −4.55947 | ||||||||
\(25\) | 536.606 | 0.858570 | ||||||||
\(26\) | − | 2394.02i | − | 3.54144i | ||||||
\(27\) | 708.150i | 0.971400i | ||||||||
\(28\) | 2148.92i | 2.74098i | ||||||||
\(29\) | − | 268.672i | − | 0.319467i | −0.987160 | − | 0.159734i | \(-0.948937\pi\) | ||
0.987160 | − | 0.159734i | \(-0.0510635\pi\) | |||||||
\(30\) | − | 1022.75i | − | 1.13639i | ||||||
\(31\) | 665.439 | 0.692444 | 0.346222 | − | 0.938153i | \(-0.387464\pi\) | ||||
0.346222 | + | 0.938153i | \(0.387464\pi\) | |||||||
\(32\) | 2449.06i | 2.39166i | ||||||||
\(33\) | − | 2194.36i | − | 2.01502i | ||||||
\(34\) | 241.707i | 0.209089i | ||||||||
\(35\) | −503.303 | −0.410859 | ||||||||
\(36\) | 5209.55 | 4.01972 | ||||||||
\(37\) | 1176.50i | 0.859387i | 0.902975 | + | 0.429693i | \(0.141378\pi\) | ||||
−0.902975 | + | 0.429693i | \(0.858622\pi\) | |||||||
\(38\) | 2278.80 | 1.57812 | ||||||||
\(39\) | 4638.66i | 3.04975i | ||||||||
\(40\) | −1700.74 | −1.06296 | ||||||||
\(41\) | 212.488 | 0.126406 | 0.0632028 | − | 0.998001i | \(-0.479868\pi\) | ||||
0.0632028 | + | 0.998001i | \(0.479868\pi\) | |||||||
\(42\) | − | 5823.38i | − | 3.30123i | ||||||
\(43\) | 1352.49 | + | 1260.78i | 0.731470 | + | 0.681873i | ||||
\(44\) | −6067.35 | −3.13396 | ||||||||
\(45\) | 1220.14i | 0.602537i | ||||||||
\(46\) | − | 1493.41i | − | 0.705770i | ||||||
\(47\) | −3100.78 | −1.40371 | −0.701853 | − | 0.712322i | \(-0.747643\pi\) | ||||
−0.701853 | + | 0.712322i | \(0.747643\pi\) | |||||||
\(48\) | − | 10353.4i | − | 4.49365i | ||||||
\(49\) | −464.736 | −0.193559 | ||||||||
\(50\) | 4020.69i | 1.60828i | ||||||||
\(51\) | − | 468.334i | − | 0.180059i | ||||||
\(52\) | 12825.8 | 4.74327 | ||||||||
\(53\) | 2662.72 | 0.947924 | 0.473962 | − | 0.880545i | \(-0.342823\pi\) | ||||
0.473962 | + | 0.880545i | \(0.342823\pi\) | |||||||
\(54\) | −5306.04 | −1.81963 | ||||||||
\(55\) | − | 1421.04i | − | 0.469766i | ||||||
\(56\) | −9683.75 | −3.08793 | ||||||||
\(57\) | −4415.43 | −1.35901 | ||||||||
\(58\) | 2013.11 | 0.598427 | ||||||||
\(59\) | 2748.48 | 0.789565 | 0.394783 | − | 0.918775i | \(-0.370820\pi\) | ||||
0.394783 | + | 0.918775i | \(0.370820\pi\) | |||||||
\(60\) | 5479.31 | 1.52203 | ||||||||
\(61\) | − | 5880.73i | − | 1.58042i | −0.612839 | − | 0.790208i | \(-0.709972\pi\) | ||
0.612839 | − | 0.790208i | \(-0.290028\pi\) | |||||||
\(62\) | 4986.02i | 1.29709i | ||||||||
\(63\) | 6947.29i | 1.75039i | ||||||||
\(64\) | −6940.28 | −1.69440 | ||||||||
\(65\) | 3003.95i | 0.710994i | ||||||||
\(66\) | 16441.9 | 3.77455 | ||||||||
\(67\) | −1093.36 | −0.243565 | −0.121782 | − | 0.992557i | \(-0.538861\pi\) | ||||
−0.121782 | + | 0.992557i | \(0.538861\pi\) | |||||||
\(68\) | −1294.93 | −0.280046 | ||||||||
\(69\) | 2893.64i | 0.607780i | ||||||||
\(70\) | − | 3771.16i | − | 0.769624i | ||||||
\(71\) | − | 5841.22i | − | 1.15874i | −0.815064 | − | 0.579371i | \(-0.803298\pi\) | ||
0.815064 | − | 0.579371i | \(-0.196702\pi\) | |||||||
\(72\) | 23475.9i | 4.52854i | ||||||||
\(73\) | 663.511i | 0.124509i | 0.998060 | + | 0.0622547i | \(0.0198291\pi\) | ||||
−0.998060 | + | 0.0622547i | \(0.980171\pi\) | |||||||
\(74\) | −8815.31 | −1.60981 | ||||||||
\(75\) | − | 7790.53i | − | 1.38498i | ||||||
\(76\) | 12208.6i | 2.11367i | ||||||||
\(77\) | − | 8091.21i | − | 1.36468i | ||||||
\(78\) | −34756.7 | −5.71280 | ||||||||
\(79\) | 6328.79 | 1.01407 | 0.507034 | − | 0.861926i | \(-0.330742\pi\) | ||||
0.507034 | + | 0.861926i | \(0.330742\pi\) | |||||||
\(80\) | − | 6704.74i | − | 1.04762i | ||||||
\(81\) | −230.889 | −0.0351911 | ||||||||
\(82\) | 1592.13i | 0.236784i | ||||||||
\(83\) | 8356.34 | 1.21300 | 0.606499 | − | 0.795084i | \(-0.292573\pi\) | ||||
0.606499 | + | 0.795084i | \(0.292573\pi\) | |||||||
\(84\) | 31198.4 | 4.42155 | ||||||||
\(85\) | − | 303.288i | − | 0.0419776i | ||||||
\(86\) | −9446.83 | + | 10134.0i | −1.27729 | + | 1.37019i | ||||
\(87\) | −3900.62 | −0.515341 | ||||||||
\(88\) | − | 27341.4i | − | 3.53066i | ||||||
\(89\) | − | 4257.21i | − | 0.537459i | −0.963216 | − | 0.268729i | \(-0.913396\pi\) | ||
0.963216 | − | 0.268729i | \(-0.0866037\pi\) | |||||||
\(90\) | −9142.27 | −1.12868 | ||||||||
\(91\) | 17104.1i | 2.06546i | ||||||||
\(92\) | 8000.85 | 0.945281 | ||||||||
\(93\) | − | 9660.95i | − | 1.11700i | ||||||
\(94\) | − | 23233.6i | − | 2.62943i | ||||||
\(95\) | −2859.38 | −0.316829 | ||||||||
\(96\) | 35555.9 | 3.85806 | ||||||||
\(97\) | −3585.40 | −0.381061 | −0.190530 | − | 0.981681i | \(-0.561021\pi\) | ||||
−0.190530 | + | 0.981681i | \(0.561021\pi\) | |||||||
\(98\) | − | 3482.18i | − | 0.362576i | ||||||
\(99\) | −19615.2 | −2.00135 | ||||||||
\(100\) | −21540.6 | −2.15406 | ||||||||
\(101\) | 3138.84 | 0.307699 | 0.153850 | − | 0.988094i | \(-0.450833\pi\) | ||||
0.153850 | + | 0.988094i | \(0.450833\pi\) | |||||||
\(102\) | 3509.14 | 0.337288 | ||||||||
\(103\) | −7225.57 | −0.681079 | −0.340539 | − | 0.940230i | \(-0.610610\pi\) | ||||
−0.340539 | + | 0.940230i | \(0.610610\pi\) | |||||||
\(104\) | 57797.2i | 5.34368i | ||||||||
\(105\) | 7307.03i | 0.662769i | ||||||||
\(106\) | 19951.3i | 1.77566i | ||||||||
\(107\) | −11372.2 | −0.993291 | −0.496645 | − | 0.867954i | \(-0.665435\pi\) | ||||
−0.496645 | + | 0.867954i | \(0.665435\pi\) | |||||||
\(108\) | − | 28426.8i | − | 2.43714i | ||||||
\(109\) | 6830.22 | 0.574886 | 0.287443 | − | 0.957798i | \(-0.407195\pi\) | ||||
0.287443 | + | 0.957798i | \(0.407195\pi\) | |||||||
\(110\) | 10647.6 | 0.879968 | ||||||||
\(111\) | 17080.6 | 1.38630 | ||||||||
\(112\) | − | 38175.8i | − | 3.04335i | ||||||
\(113\) | − | 14950.0i | − | 1.17081i | −0.810742 | − | 0.585403i | \(-0.800936\pi\) | ||
0.810742 | − | 0.585403i | \(-0.199064\pi\) | |||||||
\(114\) | − | 33084.0i | − | 2.54571i | ||||||
\(115\) | 1873.89i | 0.141693i | ||||||||
\(116\) | 10785.1i | 0.801511i | ||||||||
\(117\) | 41464.7 | 3.02905 | ||||||||
\(118\) | 20593.8i | 1.47902i | ||||||||
\(119\) | − | 1726.88i | − | 0.121946i | ||||||
\(120\) | 24691.5i | 1.71469i | ||||||||
\(121\) | 8204.00 | 0.560344 | ||||||||
\(122\) | 44063.3 | 2.96044 | ||||||||
\(123\) | − | 3084.93i | − | 0.203909i | ||||||
\(124\) | −26712.3 | −1.73727 | ||||||||
\(125\) | − | 10921.2i | − | 0.698956i | ||||||
\(126\) | −52054.8 | −3.27884 | ||||||||
\(127\) | −11093.6 | −0.687806 | −0.343903 | − | 0.939005i | \(-0.611749\pi\) | ||||
−0.343903 | + | 0.939005i | \(0.611749\pi\) | |||||||
\(128\) | − | 12817.2i | − | 0.782303i | ||||||
\(129\) | 18304.3 | − | 19635.6i | 1.09995 | − | 1.17996i | ||||
\(130\) | −22508.1 | −1.33184 | ||||||||
\(131\) | − | 7521.37i | − | 0.438283i | −0.975693 | − | 0.219141i | \(-0.929674\pi\) | ||
0.975693 | − | 0.219141i | \(-0.0703256\pi\) | |||||||
\(132\) | 88086.7i | 5.05548i | ||||||||
\(133\) | −16280.9 | −0.920399 | ||||||||
\(134\) | − | 8192.38i | − | 0.456247i | ||||||
\(135\) | 6657.89 | 0.365316 | ||||||||
\(136\) | − | 5835.39i | − | 0.315495i | ||||||
\(137\) | 15580.8i | 0.830137i | 0.909790 | + | 0.415069i | \(0.136242\pi\) | ||||
−0.909790 | + | 0.415069i | \(0.863758\pi\) | |||||||
\(138\) | −21681.5 | −1.13850 | ||||||||
\(139\) | 9394.31 | 0.486223 | 0.243111 | − | 0.969998i | \(-0.421832\pi\) | ||||
0.243111 | + | 0.969998i | \(0.421832\pi\) | |||||||
\(140\) | 20203.8 | 1.03080 | ||||||||
\(141\) | 45017.7i | 2.26436i | ||||||||
\(142\) | 43767.2 | 2.17056 | ||||||||
\(143\) | −48292.2 | −2.36159 | ||||||||
\(144\) | −92548.2 | −4.46316 | ||||||||
\(145\) | −2526.00 | −0.120143 | ||||||||
\(146\) | −4971.57 | −0.233232 | ||||||||
\(147\) | 6747.11i | 0.312236i | ||||||||
\(148\) | − | 47227.5i | − | 2.15611i | ||||||
\(149\) | 2012.81i | 0.0906630i | 0.998972 | + | 0.0453315i | \(0.0144344\pi\) | ||||
−0.998972 | + | 0.0453315i | \(0.985566\pi\) | |||||||
\(150\) | 58373.1 | 2.59436 | ||||||||
\(151\) | − | 7447.35i | − | 0.326624i | −0.986574 | − | 0.163312i | \(-0.947782\pi\) | ||
0.986574 | − | 0.163312i | \(-0.0522177\pi\) | |||||||
\(152\) | −55015.7 | −2.38122 | ||||||||
\(153\) | −4186.41 | −0.178838 | ||||||||
\(154\) | 60626.0 | 2.55633 | ||||||||
\(155\) | − | 6256.33i | − | 0.260409i | ||||||
\(156\) | − | 186207.i | − | 7.65151i | ||||||
\(157\) | 16371.4i | 0.664179i | 0.943248 | + | 0.332090i | \(0.107754\pi\) | ||||
−0.943248 | + | 0.332090i | \(0.892246\pi\) | |||||||
\(158\) | 47420.5i | 1.89956i | ||||||||
\(159\) | − | 38657.8i | − | 1.52912i | ||||||
\(160\) | 23025.6 | 0.899439 | ||||||||
\(161\) | 10669.7i | 0.411623i | ||||||||
\(162\) | − | 1730.01i | − | 0.0659202i | ||||||
\(163\) | 45112.4i | 1.69793i | 0.528445 | + | 0.848967i | \(0.322775\pi\) | ||||
−0.528445 | + | 0.848967i | \(0.677225\pi\) | |||||||
\(164\) | −8529.77 | −0.317139 | ||||||||
\(165\) | −20630.9 | −0.757793 | ||||||||
\(166\) | 62612.6i | 2.27219i | ||||||||
\(167\) | −24211.5 | −0.868139 | −0.434069 | − | 0.900879i | \(-0.642923\pi\) | ||||
−0.434069 | + | 0.900879i | \(0.642923\pi\) | |||||||
\(168\) | 140590.i | 4.98123i | ||||||||
\(169\) | 73524.2 | 2.57429 | ||||||||
\(170\) | 2272.48 | 0.0786327 | ||||||||
\(171\) | 39469.2i | 1.34979i | ||||||||
\(172\) | −54292.1 | − | 50610.9i | −1.83518 | − | 1.71075i | ||||
\(173\) | 36697.5 | 1.22615 | 0.613076 | − | 0.790024i | \(-0.289932\pi\) | ||||
0.613076 | + | 0.790024i | \(0.289932\pi\) | |||||||
\(174\) | − | 29226.6i | − | 0.965340i | ||||||
\(175\) | − | 28725.9i | − | 0.937989i | ||||||
\(176\) | 107787. | 3.47969 | ||||||||
\(177\) | − | 39902.8i | − | 1.27367i | ||||||
\(178\) | 31898.5 | 1.00677 | ||||||||
\(179\) | 50619.1i | 1.57982i | 0.613220 | + | 0.789912i | \(0.289874\pi\) | ||||
−0.613220 | + | 0.789912i | \(0.710126\pi\) | |||||||
\(180\) | − | 48979.2i | − | 1.51170i | ||||||
\(181\) | −31719.0 | −0.968194 | −0.484097 | − | 0.875014i | \(-0.660852\pi\) | ||||
−0.484097 | + | 0.875014i | \(0.660852\pi\) | |||||||
\(182\) | −128158. | −3.86903 | ||||||||
\(183\) | −85377.3 | −2.54941 | ||||||||
\(184\) | 36054.4i | 1.06494i | ||||||||
\(185\) | 11061.2 | 0.323191 | ||||||||
\(186\) | 72387.8 | 2.09237 | ||||||||
\(187\) | 4875.73 | 0.139430 | ||||||||
\(188\) | 124473. | 3.52175 | ||||||||
\(189\) | 37909.1 | 1.06126 | ||||||||
\(190\) | − | 21424.9i | − | 0.593486i | ||||||
\(191\) | − | 49921.7i | − | 1.36843i | −0.729280 | − | 0.684215i | \(-0.760145\pi\) | ||
0.729280 | − | 0.684215i | \(-0.239855\pi\) | |||||||
\(192\) | 100760.i | 2.73329i | ||||||||
\(193\) | 541.363 | 0.0145336 | 0.00726681 | − | 0.999974i | \(-0.497687\pi\) | ||||
0.00726681 | + | 0.999974i | \(0.497687\pi\) | |||||||
\(194\) | − | 26864.8i | − | 0.713805i | ||||||
\(195\) | 43611.8 | 1.14692 | ||||||||
\(196\) | 18655.6 | 0.485621 | ||||||||
\(197\) | −31142.6 | −0.802458 | −0.401229 | − | 0.915978i | \(-0.631417\pi\) | ||||
−0.401229 | + | 0.915978i | \(0.631417\pi\) | |||||||
\(198\) | − | 146973.i | − | 3.74894i | ||||||
\(199\) | 59618.5i | 1.50548i | 0.658319 | + | 0.752739i | \(0.271268\pi\) | ||||
−0.658319 | + | 0.752739i | \(0.728732\pi\) | |||||||
\(200\) | − | 97069.1i | − | 2.42673i | ||||||
\(201\) | 15873.6i | 0.392902i | ||||||||
\(202\) | 23518.8i | 0.576384i | ||||||||
\(203\) | −14382.7 | −0.349018 | ||||||||
\(204\) | 18800.0i | 0.451750i | ||||||||
\(205\) | − | 1997.77i | − | 0.0475377i | ||||||
\(206\) | − | 54139.9i | − | 1.27580i | ||||||
\(207\) | 25866.1 | 0.603656 | ||||||||
\(208\) | −227852. | −5.26654 | ||||||||
\(209\) | − | 45968.1i | − | 1.05236i | ||||||
\(210\) | −54750.3 | −1.24150 | ||||||||
\(211\) | 45278.4i | 1.01701i | 0.861059 | + | 0.508506i | \(0.169802\pi\) | ||||
−0.861059 | + | 0.508506i | \(0.830198\pi\) | |||||||
\(212\) | −106888. | −2.37825 | ||||||||
\(213\) | −84803.8 | −1.86920 | ||||||||
\(214\) | − | 85209.8i | − | 1.86064i | ||||||
\(215\) | 11853.6 | − | 12715.8i | 0.256434 | − | 0.275086i | ||||
\(216\) | 128101. | 2.74564 | ||||||||
\(217\) | − | 35622.7i | − | 0.756496i | ||||||
\(218\) | 51177.7i | 1.07688i | ||||||||
\(219\) | 9632.95 | 0.200850 | ||||||||
\(220\) | 57044.0i | 1.17860i | ||||||||
\(221\) | −10306.8 | −0.211029 | ||||||||
\(222\) | 127982.i | 2.59683i | ||||||||
\(223\) | − | 26029.7i | − | 0.523431i | −0.965145 | − | 0.261716i | \(-0.915712\pi\) | ||
0.965145 | − | 0.261716i | \(-0.0842883\pi\) | |||||||
\(224\) | 131105. | 2.61290 | ||||||||
\(225\) | −69639.1 | −1.37559 | ||||||||
\(226\) | 112018. | 2.19316 | ||||||||
\(227\) | − | 57788.9i | − | 1.12148i | −0.827991 | − | 0.560741i | \(-0.810516\pi\) | ||
0.827991 | − | 0.560741i | \(-0.189484\pi\) | |||||||
\(228\) | 177246. | 3.40962 | ||||||||
\(229\) | −15622.4 | −0.297905 | −0.148953 | − | 0.988844i | \(-0.547590\pi\) | ||||
−0.148953 | + | 0.988844i | \(0.547590\pi\) | |||||||
\(230\) | −14040.7 | −0.265420 | ||||||||
\(231\) | −117470. | −2.20141 | ||||||||
\(232\) | −48601.3 | −0.902967 | ||||||||
\(233\) | 60252.0i | 1.10984i | 0.831904 | + | 0.554919i | \(0.187251\pi\) | ||||
−0.831904 | + | 0.554919i | \(0.812749\pi\) | |||||||
\(234\) | 310688.i | 5.67404i | ||||||||
\(235\) | 29153.0i | 0.527894i | ||||||||
\(236\) | −110330. | −1.98094 | ||||||||
\(237\) | − | 91882.4i | − | 1.63582i | ||||||
\(238\) | 12939.2 | 0.228430 | ||||||||
\(239\) | 91262.4 | 1.59770 | 0.798851 | − | 0.601528i | \(-0.205441\pi\) | ||||
0.798851 | + | 0.601528i | \(0.205441\pi\) | |||||||
\(240\) | −97340.4 | −1.68994 | ||||||||
\(241\) | − | 11694.8i | − | 0.201354i | −0.994919 | − | 0.100677i | \(-0.967899\pi\) | ||
0.994919 | − | 0.100677i | \(-0.0321008\pi\) | |||||||
\(242\) | 61471.1i | 1.04964i | ||||||||
\(243\) | 60712.3i | 1.02817i | ||||||||
\(244\) | 236066.i | 3.96510i | ||||||||
\(245\) | 4369.36i | 0.0727923i | ||||||||
\(246\) | 23114.9 | 0.381963 | ||||||||
\(247\) | 97172.4i | 1.59275i | ||||||||
\(248\) | − | 120374.i | − | 1.95718i | ||||||
\(249\) | − | 121319.i | − | 1.95672i | ||||||
\(250\) | 81830.6 | 1.30929 | ||||||||
\(251\) | 95330.3 | 1.51316 | 0.756578 | − | 0.653904i | \(-0.226870\pi\) | ||||
0.756578 | + | 0.653904i | \(0.226870\pi\) | |||||||
\(252\) | − | 278881.i | − | 4.39155i | ||||||
\(253\) | −30125.1 | −0.470639 | ||||||||
\(254\) | − | 83122.6i | − | 1.28840i | ||||||
\(255\) | −4403.18 | −0.0677153 | ||||||||
\(256\) | −15007.1 | −0.228991 | ||||||||
\(257\) | − | 98138.1i | − | 1.48584i | −0.669382 | − | 0.742919i | \(-0.733441\pi\) | ||
0.669382 | − | 0.742919i | \(-0.266559\pi\) | |||||||
\(258\) | 147126. | + | 137151.i | 2.21030 | + | 2.06043i | ||||
\(259\) | 62981.1 | 0.938881 | ||||||||
\(260\) | − | 120586.i | − | 1.78381i | ||||||
\(261\) | 34867.4i | 0.511845i | ||||||||
\(262\) | 56356.3 | 0.820994 | ||||||||
\(263\) | 7996.23i | 0.115604i | 0.998328 | + | 0.0578022i | \(0.0184093\pi\) | ||||
−0.998328 | + | 0.0578022i | \(0.981591\pi\) | |||||||
\(264\) | −396947. | −5.69541 | ||||||||
\(265\) | − | 25034.4i | − | 0.356488i | ||||||
\(266\) | − | 121990.i | − | 1.72410i | ||||||
\(267\) | −61806.8 | −0.866990 | ||||||||
\(268\) | 43890.2 | 0.611080 | ||||||||
\(269\) | −42975.4 | −0.593903 | −0.296951 | − | 0.954893i | \(-0.595970\pi\) | ||||
−0.296951 | + | 0.954893i | \(0.595970\pi\) | |||||||
\(270\) | 49886.4i | 0.684313i | ||||||||
\(271\) | 22222.2 | 0.302585 | 0.151293 | − | 0.988489i | \(-0.451656\pi\) | ||||
0.151293 | + | 0.988489i | \(0.451656\pi\) | |||||||
\(272\) | 23004.6 | 0.310940 | ||||||||
\(273\) | 248320. | 3.33185 | ||||||||
\(274\) | −116744. | −1.55502 | ||||||||
\(275\) | 81105.7 | 1.07247 | ||||||||
\(276\) | − | 116158.i | − | 1.52486i | ||||||
\(277\) | 67337.1i | 0.877596i | 0.898586 | + | 0.438798i | \(0.144596\pi\) | ||||
−0.898586 | + | 0.438798i | \(0.855404\pi\) | |||||||
\(278\) | 70389.9i | 0.910795i | ||||||||
\(279\) | −86358.6 | −1.10942 | ||||||||
\(280\) | 91044.7i | 1.16129i | ||||||||
\(281\) | −14673.1 | −0.185828 | −0.0929138 | − | 0.995674i | \(-0.529618\pi\) | ||||
−0.0929138 | + | 0.995674i | \(0.529618\pi\) | |||||||
\(282\) | −337309. | −4.24161 | ||||||||
\(283\) | 25223.6 | 0.314944 | 0.157472 | − | 0.987523i | \(-0.449666\pi\) | ||||
0.157472 | + | 0.987523i | \(0.449666\pi\) | |||||||
\(284\) | 234481.i | 2.90717i | ||||||||
\(285\) | 41513.0i | 0.511086i | ||||||||
\(286\) | − | 361845.i | − | 4.42375i | ||||||
\(287\) | − | 11375.0i | − | 0.138098i | ||||||
\(288\) | − | 317832.i | − | 3.83189i | ||||||
\(289\) | −82480.4 | −0.987541 | ||||||||
\(290\) | − | 18926.9i | − | 0.225052i | ||||||
\(291\) | 52053.4i | 0.614700i | ||||||||
\(292\) | − | 26634.9i | − | 0.312382i | ||||||
\(293\) | 112480. | 1.31020 | 0.655102 | − | 0.755540i | \(-0.272626\pi\) | ||||
0.655102 | + | 0.755540i | \(0.272626\pi\) | |||||||
\(294\) | −50554.9 | −0.584882 | ||||||||
\(295\) | − | 25840.6i | − | 0.296933i | ||||||
\(296\) | 212823. | 2.42904 | ||||||||
\(297\) | 107034.i | 1.21341i | ||||||||
\(298\) | −15081.6 | −0.169830 | ||||||||
\(299\) | 63681.7 | 0.712315 | ||||||||
\(300\) | 312731.i | 3.47478i | ||||||||
\(301\) | 67493.0 | − | 72402.2i | 0.744948 | − | 0.799132i | ||||
\(302\) | 55801.7 | 0.611834 | ||||||||
\(303\) | − | 45570.2i | − | 0.496359i | ||||||
\(304\) | − | 216886.i | − | 2.34685i | ||||||
\(305\) | −55289.5 | −0.594351 | ||||||||
\(306\) | − | 31368.0i | − | 0.334999i | ||||||
\(307\) | 136783. | 1.45130 | 0.725648 | − | 0.688067i | \(-0.241540\pi\) | ||||
0.725648 | + | 0.688067i | \(0.241540\pi\) | |||||||
\(308\) | 324801.i | 3.42386i | ||||||||
\(309\) | 104902.i | 1.09867i | ||||||||
\(310\) | 46877.5 | 0.487800 | ||||||||
\(311\) | −46529.6 | −0.481070 | −0.240535 | − | 0.970640i | \(-0.577323\pi\) | ||||
−0.240535 | + | 0.970640i | \(0.577323\pi\) | |||||||
\(312\) | 839109. | 8.62004 | ||||||||
\(313\) | − | 68823.9i | − | 0.702507i | −0.936280 | − | 0.351253i | \(-0.885756\pi\) | ||
0.936280 | − | 0.351253i | \(-0.114244\pi\) | |||||||
\(314\) | −122668. | −1.24414 | ||||||||
\(315\) | 65317.1 | 0.658272 | ||||||||
\(316\) | −254053. | −2.54419 | ||||||||
\(317\) | −48726.3 | −0.484892 | −0.242446 | − | 0.970165i | \(-0.577950\pi\) | ||||
−0.242446 | + | 0.970165i | \(0.577950\pi\) | |||||||
\(318\) | 289656. | 2.86436 | ||||||||
\(319\) | − | 40608.6i | − | 0.399058i | ||||||
\(320\) | 65251.1i | 0.637218i | ||||||||
\(321\) | 165103.i | 1.60231i | ||||||||
\(322\) | −79946.0 | −0.771054 | ||||||||
\(323\) | − | 9810.83i | − | 0.0940374i | ||||||
\(324\) | 9268.43 | 0.0882910 | ||||||||
\(325\) | −171450. | −1.62319 | ||||||||
\(326\) | −338019. | −3.18058 | ||||||||
\(327\) | − | 99162.3i | − | 0.927366i | ||||||
\(328\) | − | 38437.9i | − | 0.357283i | ||||||
\(329\) | 165993.i | 1.53355i | ||||||||
\(330\) | − | 154584.i | − | 1.41950i | ||||||
\(331\) | 61590.4i | 0.562156i | 0.959685 | + | 0.281078i | \(0.0906919\pi\) | ||||
−0.959685 | + | 0.281078i | \(0.909308\pi\) | |||||||
\(332\) | −335444. | −3.04329 | ||||||||
\(333\) | − | 152683.i | − | 1.37690i | ||||||
\(334\) | − | 181413.i | − | 1.62620i | ||||||
\(335\) | 10279.6i | 0.0915980i | ||||||||
\(336\) | −554243. | −4.90932 | ||||||||
\(337\) | 53084.4 | 0.467420 | 0.233710 | − | 0.972306i | \(-0.424913\pi\) | ||||
0.233710 | + | 0.972306i | \(0.424913\pi\) | |||||||
\(338\) | 550904.i | 4.82217i | ||||||||
\(339\) | −217047. | −1.88866 | ||||||||
\(340\) | 12174.7i | 0.105318i | ||||||||
\(341\) | 100578. | 0.864958 | ||||||||
\(342\) | −295736. | −2.52844 | ||||||||
\(343\) | − | 103653.i | − | 0.881038i | ||||||
\(344\) | 228069. | − | 244658.i | 1.92730 | − | 2.06748i | ||||
\(345\) | 27205.4 | 0.228569 | ||||||||
\(346\) | 274968.i | 2.29683i | ||||||||
\(347\) | − | 80407.5i | − | 0.667787i | −0.942611 | − | 0.333893i | \(-0.891637\pi\) | ||
0.942611 | − | 0.333893i | \(-0.108363\pi\) | |||||||
\(348\) | 156580. | 1.29294 | ||||||||
\(349\) | 173808.i | 1.42698i | 0.700663 | + | 0.713492i | \(0.252888\pi\) | ||||
−0.700663 | + | 0.713492i | \(0.747112\pi\) | |||||||
\(350\) | 215238. | 1.75705 | ||||||||
\(351\) | − | 226260.i | − | 1.83651i | ||||||
\(352\) | 370165.i | 2.98752i | ||||||||
\(353\) | −80068.2 | −0.642556 | −0.321278 | − | 0.946985i | \(-0.604112\pi\) | ||||
−0.321278 | + | 0.946985i | \(0.604112\pi\) | |||||||
\(354\) | 298985. | 2.38585 | ||||||||
\(355\) | −54918.0 | −0.435771 | ||||||||
\(356\) | 170895.i | 1.34843i | ||||||||
\(357\) | −25071.1 | −0.196715 | ||||||||
\(358\) | −379280. | −2.95934 | ||||||||
\(359\) | 83187.2 | 0.645457 | 0.322729 | − | 0.946492i | \(-0.395400\pi\) | ||||
0.322729 | + | 0.946492i | \(0.395400\pi\) | |||||||
\(360\) | 220716. | 1.70306 | ||||||||
\(361\) | 37825.1 | 0.290245 | ||||||||
\(362\) | − | 237665.i | − | 1.81363i | ||||||
\(363\) | − | 119107.i | − | 0.903907i | ||||||
\(364\) | − | 686598.i | − | 5.18203i | ||||||
\(365\) | 6238.20 | 0.0468245 | ||||||||
\(366\) | − | 639717.i | − | 4.77558i | ||||||
\(367\) | 248797. | 1.84719 | 0.923597 | − | 0.383365i | \(-0.125235\pi\) | ||||
0.923597 | + | 0.383365i | \(0.125235\pi\) | |||||||
\(368\) | −142136. | −1.04956 | ||||||||
\(369\) | −27576.0 | −0.202525 | ||||||||
\(370\) | 82879.8i | 0.605404i | ||||||||
\(371\) | − | 142542.i | − | 1.03561i | ||||||
\(372\) | 387813.i | 2.80244i | ||||||||
\(373\) | − | 209386.i | − | 1.50498i | −0.658603 | − | 0.752490i | \(-0.728852\pi\) | ||
0.658603 | − | 0.752490i | \(-0.271148\pi\) | |||||||
\(374\) | 36533.0i | 0.261181i | ||||||||
\(375\) | −158556. | −1.12751 | ||||||||
\(376\) | 560915.i | 3.96754i | ||||||||
\(377\) | 85842.7i | 0.603978i | ||||||||
\(378\) | 284046.i | 1.98795i | ||||||||
\(379\) | −92058.9 | −0.640895 | −0.320448 | − | 0.947266i | \(-0.603833\pi\) | ||||
−0.320448 | + | 0.947266i | \(0.603833\pi\) | |||||||
\(380\) | 114783. | 0.794893 | ||||||||
\(381\) | 161059.i | 1.10952i | ||||||||
\(382\) | 374055. | 2.56335 | ||||||||
\(383\) | 51836.8i | 0.353379i | 0.984267 | + | 0.176690i | \(0.0565388\pi\) | ||||
−0.984267 | + | 0.176690i | \(0.943461\pi\) | |||||||
\(384\) | −186083. | −1.26195 | ||||||||
\(385\) | −76072.0 | −0.513220 | ||||||||
\(386\) | 4056.34i | 0.0272245i | ||||||||
\(387\) | −175522. | − | 163621.i | −1.17195 | − | 1.09249i | ||||
\(388\) | 143926. | 0.956043 | ||||||||
\(389\) | − | 170164.i | − | 1.12452i | −0.826959 | − | 0.562262i | \(-0.809931\pi\) | ||
0.826959 | − | 0.562262i | \(-0.190069\pi\) | |||||||
\(390\) | 326776.i | 2.14843i | ||||||||
\(391\) | −6429.50 | −0.0420556 | ||||||||
\(392\) | 84068.2i | 0.547091i | ||||||||
\(393\) | −109196. | −0.707007 | ||||||||
\(394\) | − | 233346.i | − | 1.50317i | ||||||
\(395\) | − | 59502.1i | − | 0.381362i | ||||||
\(396\) | 787401. | 5.02118 | ||||||||
\(397\) | −201719. | −1.27987 | −0.639936 | − | 0.768428i | \(-0.721039\pi\) | ||||
−0.639936 | + | 0.768428i | \(0.721039\pi\) | |||||||
\(398\) | −446711. | −2.82007 | ||||||||
\(399\) | 236369.i | 1.48472i | ||||||||
\(400\) | 382671. | 2.39170 | ||||||||
\(401\) | 38112.2 | 0.237015 | 0.118507 | − | 0.992953i | \(-0.462189\pi\) | ||||
0.118507 | + | 0.992953i | \(0.462189\pi\) | |||||||
\(402\) | −118938. | −0.735986 | ||||||||
\(403\) | −212613. | −1.30912 | ||||||||
\(404\) | −126001. | −0.771987 | ||||||||
\(405\) | 2170.77i | 0.0132344i | ||||||||
\(406\) | − | 107767.i | − | 0.653783i | ||||||
\(407\) | 177823.i | 1.07349i | ||||||||
\(408\) | −84719.1 | −0.508933 | ||||||||
\(409\) | 301746.i | 1.80383i | 0.431918 | + | 0.901913i | \(0.357837\pi\) | ||||
−0.431918 | + | 0.901913i | \(0.642163\pi\) | |||||||
\(410\) | 14968.9 | 0.0890478 | ||||||||
\(411\) | 226205. | 1.33912 | ||||||||
\(412\) | 290051. | 1.70876 | ||||||||
\(413\) | − | 147133.i | − | 0.862601i | ||||||
\(414\) | 193810.i | 1.13077i | ||||||||
\(415\) | − | 78564.7i | − | 0.456175i | ||||||
\(416\) | − | 782495.i | − | 4.52163i | ||||||
\(417\) | − | 136388.i | − | 0.784340i | ||||||
\(418\) | 344431. | 1.97129 | ||||||||
\(419\) | − | 15464.5i | − | 0.0880859i | −0.999030 | − | 0.0440430i | \(-0.985976\pi\) | ||
0.999030 | − | 0.0440430i | \(-0.0140238\pi\) | |||||||
\(420\) | − | 293322.i | − | 1.66282i | ||||||
\(421\) | 218060.i | 1.23030i | 0.788409 | + | 0.615151i | \(0.210905\pi\) | ||||
−0.788409 | + | 0.615151i | \(0.789095\pi\) | |||||||
\(422\) | −339263. | −1.90507 | ||||||||
\(423\) | 402410. | 2.24899 | ||||||||
\(424\) | − | 481672.i | − | 2.67929i | ||||||
\(425\) | 17310.1 | 0.0958345 | ||||||||
\(426\) | − | 635420.i | − | 3.50140i | ||||||
\(427\) | −314811. | −1.72661 | ||||||||
\(428\) | 456507. | 2.49207 | ||||||||
\(429\) | 701114.i | 3.80955i | ||||||||
\(430\) | 95277.5 | + | 88817.3i | 0.515292 | + | 0.480353i | ||||
\(431\) | −173738. | −0.935277 | −0.467639 | − | 0.883920i | \(-0.654895\pi\) | ||||
−0.467639 | + | 0.883920i | \(0.654895\pi\) | |||||||
\(432\) | 505005.i | 2.70600i | ||||||||
\(433\) | − | 252649.i | − | 1.34754i | −0.738942 | − | 0.673769i | \(-0.764674\pi\) | ||
0.738942 | − | 0.673769i | \(-0.235326\pi\) | |||||||
\(434\) | 266914. | 1.41707 | ||||||||
\(435\) | 36672.9i | 0.193806i | ||||||||
\(436\) | −274181. | −1.44233 | ||||||||
\(437\) | 60617.0i | 0.317418i | ||||||||
\(438\) | 72178.0i | 0.376233i | ||||||||
\(439\) | −197576. | −1.02519 | −0.512597 | − | 0.858630i | \(-0.671316\pi\) | ||||
−0.512597 | + | 0.858630i | \(0.671316\pi\) | |||||||
\(440\) | −257059. | −1.32778 | ||||||||
\(441\) | 60312.0 | 0.310118 | ||||||||
\(442\) | − | 77227.3i | − | 0.395300i | ||||||
\(443\) | 116118. | 0.591685 | 0.295842 | − | 0.955237i | \(-0.404400\pi\) | ||||
0.295842 | + | 0.955237i | \(0.404400\pi\) | |||||||
\(444\) | −685657. | −3.47809 | ||||||||
\(445\) | −40025.4 | −0.202123 | ||||||||
\(446\) | 195036. | 0.980495 | ||||||||
\(447\) | 29222.3 | 0.146251 | ||||||||
\(448\) | 371531.i | 1.85114i | ||||||||
\(449\) | − | 221303.i | − | 1.09773i | −0.835911 | − | 0.548864i | \(-0.815060\pi\) | ||
0.835911 | − | 0.548864i | \(-0.184940\pi\) | |||||||
\(450\) | − | 521793.i | − | 2.57676i | ||||||
\(451\) | 32116.6 | 0.157898 | ||||||||
\(452\) | 600130.i | 2.93744i | ||||||||
\(453\) | −108122. | −0.526886 | ||||||||
\(454\) | 433002. | 2.10077 | ||||||||
\(455\) | 160809. | 0.776762 | ||||||||
\(456\) | 798727.i | 3.84122i | ||||||||
\(457\) | 79170.3i | 0.379079i | 0.981873 | + | 0.189540i | \(0.0606996\pi\) | ||||
−0.981873 | + | 0.189540i | \(0.939300\pi\) | |||||||
\(458\) | − | 117056.i | − | 0.558038i | ||||||
\(459\) | 22843.9i | 0.108429i | ||||||||
\(460\) | − | 75222.5i | − | 0.355494i | ||||||
\(461\) | 272584. | 1.28262 | 0.641311 | − | 0.767281i | \(-0.278391\pi\) | ||||
0.641311 | + | 0.767281i | \(0.278391\pi\) | |||||||
\(462\) | − | 880178.i | − | 4.12370i | ||||||
\(463\) | 324723.i | 1.51478i | 0.652960 | + | 0.757392i | \(0.273527\pi\) | ||||
−0.652960 | + | 0.757392i | \(0.726473\pi\) | |||||||
\(464\) | − | 191599.i | − | 0.889932i | ||||||
\(465\) | −90830.3 | −0.420073 | ||||||||
\(466\) | −451458. | −2.07896 | ||||||||
\(467\) | 48808.8i | 0.223802i | 0.993719 | + | 0.111901i | \(0.0356940\pi\) | ||||
−0.993719 | + | 0.111901i | \(0.964306\pi\) | |||||||
\(468\) | −1.66449e6 | −7.59959 | ||||||||
\(469\) | 58530.5i | 0.266095i | ||||||||
\(470\) | −218438. | −0.988855 | ||||||||
\(471\) | 237682. | 1.07141 | ||||||||
\(472\) | − | 497184.i | − | 2.23169i | ||||||
\(473\) | 204423. | + | 190562.i | 0.913707 | + | 0.851754i | ||||
\(474\) | 688459. | 3.06423 | ||||||||
\(475\) | − | 163199.i | − | 0.723319i | ||||||
\(476\) | 69321.1i | 0.305951i | ||||||||
\(477\) | −345559. | −1.51875 | ||||||||
\(478\) | 683813.i | 2.99283i | ||||||||
\(479\) | 383151. | 1.66993 | 0.834966 | − | 0.550301i | \(-0.185487\pi\) | ||||
0.834966 | + | 0.550301i | \(0.185487\pi\) | |||||||
\(480\) | − | 334290.i | − | 1.45091i | ||||||
\(481\) | − | 375901.i | − | 1.62474i | ||||||
\(482\) | 87627.3 | 0.377177 | ||||||||
\(483\) | 154904. | 0.664001 | ||||||||
\(484\) | −329328. | −1.40585 | ||||||||
\(485\) | 33709.2i | 0.143306i | ||||||||
\(486\) | −454906. | −1.92597 | ||||||||
\(487\) | 296539. | 1.25033 | 0.625164 | − | 0.780494i | \(-0.285032\pi\) | ||||
0.625164 | + | 0.780494i | \(0.285032\pi\) | |||||||
\(488\) | −1.06379e6 | −4.46701 | ||||||||
\(489\) | 654949. | 2.73899 | ||||||||
\(490\) | −32738.8 | −0.136355 | ||||||||
\(491\) | 234793.i | 0.973916i | 0.873425 | + | 0.486958i | \(0.161894\pi\) | ||||
−0.873425 | + | 0.486958i | \(0.838106\pi\) | |||||||
\(492\) | 123837.i | 0.511586i | ||||||||
\(493\) | − | 8666.95i | − | 0.0356593i | ||||||
\(494\) | −728095. | −2.98356 | ||||||||
\(495\) | 184418.i | 0.752651i | ||||||||
\(496\) | 474546. | 1.92893 | ||||||||
\(497\) | −312696. | −1.26593 | ||||||||
\(498\) | 909019. | 3.66534 | ||||||||
\(499\) | 223696.i | 0.898372i | 0.893438 | + | 0.449186i | \(0.148286\pi\) | ||||
−0.893438 | + | 0.449186i | \(0.851714\pi\) | |||||||
\(500\) | 438403.i | 1.75361i | ||||||||
\(501\) | 351507.i | 1.40042i | ||||||||
\(502\) | 714293.i | 2.83445i | ||||||||
\(503\) | 171252.i | 0.676861i | 0.940991 | + | 0.338430i | \(0.109896\pi\) | ||||
−0.940991 | + | 0.338430i | \(0.890104\pi\) | |||||||
\(504\) | 1.25673e6 | 4.94743 | ||||||||
\(505\) | − | 29510.8i | − | 0.115717i | ||||||
\(506\) | − | 225722.i | − | 0.881603i | ||||||
\(507\) | − | 1.06744e6i | − | 4.15266i | ||||||
\(508\) | 445325. | 1.72564 | ||||||||
\(509\) | −489934. | −1.89105 | −0.945524 | − | 0.325554i | \(-0.894449\pi\) | ||||
−0.945524 | + | 0.325554i | \(0.894449\pi\) | |||||||
\(510\) | − | 32992.3i | − | 0.126845i | ||||||
\(511\) | 35519.4 | 0.136027 | ||||||||
\(512\) | − | 317522.i | − | 1.21125i | ||||||
\(513\) | 215371. | 0.818374 | ||||||||
\(514\) | 735331. | 2.78328 | ||||||||
\(515\) | 67933.4i | 0.256135i | ||||||||
\(516\) | −734777. | + | 788221.i | −2.75966 | + | 2.96039i | ||||
\(517\) | −468670. | −1.75342 | ||||||||
\(518\) | 471906.i | 1.75872i | ||||||||
\(519\) | − | 532780.i | − | 1.97794i | ||||||
\(520\) | 543398. | 2.00961 | ||||||||
\(521\) | − | 286304.i | − | 1.05476i | −0.849630 | − | 0.527378i | \(-0.823175\pi\) | ||
0.849630 | − | 0.527378i | \(-0.176825\pi\) | |||||||
\(522\) | −261255. | −0.958791 | ||||||||
\(523\) | − | 132186.i | − | 0.483263i | −0.970368 | − | 0.241631i | \(-0.922318\pi\) | ||
0.970368 | − | 0.241631i | \(-0.0776825\pi\) | |||||||
\(524\) | 301926.i | 1.09961i | ||||||||
\(525\) | −417047. | −1.51310 | ||||||||
\(526\) | −59914.4 | −0.216551 | ||||||||
\(527\) | 21466.1 | 0.0772914 | ||||||||
\(528\) | − | 1.56487e6i | − | 5.61319i | ||||||
\(529\) | −240116. | −0.858044 | ||||||||
\(530\) | 187578. | 0.667775 | ||||||||
\(531\) | −356689. | −1.26503 | ||||||||
\(532\) | 653556. | 2.30919 | ||||||||
\(533\) | −67891.6 | −0.238980 | ||||||||
\(534\) | − | 463108.i | − | 1.62405i | ||||||
\(535\) | 106919.i | 0.373549i | ||||||||
\(536\) | 197784.i | 0.688431i | ||||||||
\(537\) | 734897. | 2.54846 | ||||||||
\(538\) | − | 322007.i | − | 1.11250i | ||||||
\(539\) | −70242.8 | −0.241782 | ||||||||
\(540\) | −267264. | −0.916542 | ||||||||
\(541\) | 114352. | 0.390704 | 0.195352 | − | 0.980733i | \(-0.437415\pi\) | ||||
0.195352 | + | 0.980733i | \(0.437415\pi\) | |||||||
\(542\) | 166507.i | 0.566805i | ||||||||
\(543\) | 460501.i | 1.56182i | ||||||||
\(544\) | 79003.2i | 0.266960i | ||||||||
\(545\) | − | 64216.4i | − | 0.216199i | ||||||
\(546\) | 1.86061e6i | 6.24124i | ||||||||
\(547\) | 48485.5 | 0.162046 | 0.0810228 | − | 0.996712i | \(-0.474181\pi\) | ||||
0.0810228 | + | 0.996712i | \(0.474181\pi\) | |||||||
\(548\) | − | 625452.i | − | 2.08273i | ||||||
\(549\) | 763183.i | 2.53212i | ||||||||
\(550\) | 607710.i | 2.00896i | ||||||||
\(551\) | −81711.5 | −0.269141 | ||||||||
\(552\) | 523444. | 1.71788 | ||||||||
\(553\) | − | 338797.i | − | 1.10787i | ||||||
\(554\) | −504545. | −1.64392 | ||||||||
\(555\) | − | 160589.i | − | 0.521349i | ||||||
\(556\) | −377110. | −1.21988 | ||||||||
\(557\) | −96856.1 | −0.312188 | −0.156094 | − | 0.987742i | \(-0.549890\pi\) | ||||
−0.156094 | + | 0.987742i | \(0.549890\pi\) | |||||||
\(558\) | − | 647070.i | − | 2.07818i | ||||||
\(559\) | −432131. | − | 402830.i | −1.38290 | − | 1.28914i | ||||
\(560\) | −358922. | −1.14452 | ||||||||
\(561\) | − | 70786.6i | − | 0.224919i | ||||||
\(562\) | − | 109943.i | − | 0.348093i | ||||||
\(563\) | −26855.0 | −0.0847244 | −0.0423622 | − | 0.999102i | \(-0.513488\pi\) | ||||
−0.0423622 | + | 0.999102i | \(0.513488\pi\) | |||||||
\(564\) | − | 1.80712e6i | − | 5.68104i | ||||||
\(565\) | −140557. | −0.440308 | ||||||||
\(566\) | 188996.i | 0.589955i | ||||||||
\(567\) | 12360.1i | 0.0384464i | ||||||||
\(568\) | −1.05665e6 | −3.27516 | ||||||||
\(569\) | 228140. | 0.704654 | 0.352327 | − | 0.935877i | \(-0.385390\pi\) | ||||
0.352327 | + | 0.935877i | \(0.385390\pi\) | |||||||
\(570\) | −311049. | −0.957370 | ||||||||
\(571\) | − | 319649.i | − | 0.980396i | −0.871611 | − | 0.490198i | \(-0.836924\pi\) | ||
0.871611 | − | 0.490198i | \(-0.163076\pi\) | |||||||
\(572\) | 1.93856e6 | 5.92500 | ||||||||
\(573\) | −724771. | −2.20745 | ||||||||
\(574\) | 85231.1 | 0.258687 | ||||||||
\(575\) | −106952. | −0.323484 | ||||||||
\(576\) | 900688. | 2.71475 | ||||||||
\(577\) | − | 527850.i | − | 1.58547i | −0.609565 | − | 0.792736i | \(-0.708656\pi\) | ||
0.609565 | − | 0.792736i | \(-0.291344\pi\) | |||||||
\(578\) | − | 618011.i | − | 1.84987i | ||||||
\(579\) | − | 7859.59i | − | 0.0234446i | ||||||
\(580\) | 101400. | 0.301426 | ||||||||
\(581\) | − | 447336.i | − | 1.32520i | ||||||
\(582\) | −390027. | −1.15146 | ||||||||
\(583\) | 402458. | 1.18409 | ||||||||
\(584\) | 120025. | 0.351923 | ||||||||
\(585\) | − | 389843.i | − | 1.13914i | ||||||
\(586\) | 842791.i | 2.45428i | ||||||||
\(587\) | 571037.i | 1.65725i | 0.559804 | + | 0.828625i | \(0.310876\pi\) | ||||
−0.559804 | + | 0.828625i | \(0.689124\pi\) | |||||||
\(588\) | − | 270845.i | − | 0.783369i | ||||||
\(589\) | − | 202381.i | − | 0.583363i | ||||||
\(590\) | 193619. | 0.556217 | ||||||||
\(591\) | 452133.i | 1.29447i | ||||||||
\(592\) | 839001.i | 2.39397i | ||||||||
\(593\) | − | 564829.i | − | 1.60623i | −0.595824 | − | 0.803115i | \(-0.703175\pi\) | ||
0.595824 | − | 0.803115i | \(-0.296825\pi\) | |||||||
\(594\) | −801985. | −2.27297 | ||||||||
\(595\) | −16235.8 | −0.0458606 | ||||||||
\(596\) | − | 80799.0i | − | 0.227464i | ||||||
\(597\) | 865550. | 2.42853 | ||||||||
\(598\) | 477156.i | 1.33431i | ||||||||
\(599\) | 323806. | 0.902467 | 0.451233 | − | 0.892406i | \(-0.350984\pi\) | ||||
0.451233 | + | 0.892406i | \(0.350984\pi\) | |||||||
\(600\) | −1.40927e6 | −3.91463 | ||||||||
\(601\) | − | 239522.i | − | 0.663126i | −0.943433 | − | 0.331563i | \(-0.892424\pi\) | ||
0.943433 | − | 0.331563i | \(-0.107576\pi\) | |||||||
\(602\) | 542497. | + | 505713.i | 1.49694 | + | 1.39544i | ||||
\(603\) | 141893. | 0.390236 | ||||||||
\(604\) | 298954.i | 0.819466i | ||||||||
\(605\) | − | 77132.4i | − | 0.210730i | ||||||
\(606\) | 341449. | 0.929782 | ||||||||
\(607\) | 344432.i | 0.934816i | 0.884042 | + | 0.467408i | \(0.154812\pi\) | ||||
−0.884042 | + | 0.467408i | \(0.845188\pi\) | |||||||
\(608\) | 744838. | 2.01490 | ||||||||
\(609\) | 208810.i | 0.563011i | ||||||||
\(610\) | − | 414274.i | − | 1.11334i | ||||||
\(611\) | 990725. | 2.65382 | ||||||||
\(612\) | 168052. | 0.448685 | ||||||||
\(613\) | 446348. | 1.18783 | 0.593913 | − | 0.804529i | \(-0.297582\pi\) | ||||
0.593913 | + | 0.804529i | \(0.297582\pi\) | |||||||
\(614\) | 1.02489e6i | 2.71857i | ||||||||
\(615\) | −29003.9 | −0.0766844 | ||||||||
\(616\) | −1.46366e6 | −3.85725 | ||||||||
\(617\) | −663045. | −1.74170 | −0.870848 | − | 0.491552i | \(-0.836430\pi\) | ||||
−0.870848 | + | 0.491552i | \(0.836430\pi\) | |||||||
\(618\) | −786011. | −2.05803 | ||||||||
\(619\) | −298590. | −0.779281 | −0.389641 | − | 0.920967i | \(-0.627401\pi\) | ||||
−0.389641 | + | 0.920967i | \(0.627401\pi\) | |||||||
\(620\) | 251144.i | 0.653340i | ||||||||
\(621\) | − | 141143.i | − | 0.365995i | ||||||
\(622\) | − | 348638.i | − | 0.901143i | ||||||
\(623\) | −227899. | −0.587174 | ||||||||
\(624\) | 3.30798e6i | 8.49560i | ||||||||
\(625\) | 232700. | 0.595712 | ||||||||
\(626\) | 515685. | 1.31594 | ||||||||
\(627\) | −667373. | −1.69759 | ||||||||
\(628\) | − | 657185.i | − | 1.66636i | ||||||
\(629\) | 37952.1i | 0.0959257i | ||||||||
\(630\) | 489409.i | 1.23308i | ||||||||
\(631\) | − | 204687.i | − | 0.514082i | −0.966400 | − | 0.257041i | \(-0.917252\pi\) | ||
0.966400 | − | 0.257041i | \(-0.0827475\pi\) | |||||||
\(632\) | − | 1.14484e6i | − | 2.86624i | ||||||
\(633\) | 657358. | 1.64057 | ||||||||
\(634\) | − | 365098.i | − | 0.908303i | ||||||
\(635\) | 104300.i | 0.258665i | ||||||||
\(636\) | 1.55182e6i | 3.83642i | ||||||||
\(637\) | 148487. | 0.365939 | ||||||||
\(638\) | 304273. | 0.747518 | ||||||||
\(639\) | 758056.i | 1.85652i | ||||||||
\(640\) | −120505. | −0.294202 | ||||||||
\(641\) | 293809.i | 0.715070i | 0.933900 | + | 0.357535i | \(0.116383\pi\) | ||||
−0.933900 | + | 0.357535i | \(0.883617\pi\) | |||||||
\(642\) | −1.23709e6 | −3.00145 | ||||||||
\(643\) | −376164. | −0.909820 | −0.454910 | − | 0.890537i | \(-0.650329\pi\) | ||||
−0.454910 | + | 0.890537i | \(0.650329\pi\) | |||||||
\(644\) | − | 428306.i | − | 1.03272i | ||||||
\(645\) | −184610. | − | 172093.i | −0.443748 | − | 0.413660i | ||||
\(646\) | 73510.8 | 0.176151 | ||||||||
\(647\) | − | 72724.1i | − | 0.173728i | −0.996220 | − | 0.0868640i | \(-0.972315\pi\) | ||
0.996220 | − | 0.0868640i | \(-0.0276846\pi\) | |||||||
\(648\) | 41766.6i | 0.0994669i | ||||||||
\(649\) | 415420. | 0.986275 | ||||||||
\(650\) | − | 1.28464e6i | − | 3.04058i | ||||||
\(651\) | −517175. | −1.22033 | ||||||||
\(652\) | − | 1.81092e6i | − | 4.25995i | ||||||
\(653\) | 338825.i | 0.794602i | 0.917688 | + | 0.397301i | \(0.130053\pi\) | ||||
−0.917688 | + | 0.397301i | \(0.869947\pi\) | |||||||
\(654\) | 743005. | 1.73715 | ||||||||
\(655\) | −70714.5 | −0.164826 | ||||||||
\(656\) | 151532. | 0.352125 | ||||||||
\(657\) | − | 86108.3i | − | 0.199487i | ||||||
\(658\) | −1.24376e6 | −2.87265 | ||||||||
\(659\) | 548017. | 1.26189 | 0.630947 | − | 0.775826i | \(-0.282666\pi\) | ||||
0.630947 | + | 0.775826i | \(0.282666\pi\) | |||||||
\(660\) | 828174. | 1.90123 | ||||||||
\(661\) | 487460. | 1.11567 | 0.557836 | − | 0.829951i | \(-0.311632\pi\) | ||||
0.557836 | + | 0.829951i | \(0.311632\pi\) | |||||||
\(662\) | −461486. | −1.05303 | ||||||||
\(663\) | 149636.i | 0.340416i | ||||||||
\(664\) | − | 1.51162e6i | − | 3.42851i | ||||||
\(665\) | 153070.i | 0.346136i | ||||||||
\(666\) | 1.14402e6 | 2.57921 | ||||||||
\(667\) | 53549.5i | 0.120366i | ||||||||
\(668\) | 971908. | 2.17807 | ||||||||
\(669\) | −377904. | −0.844362 | ||||||||
\(670\) | −77023.1 | −0.171582 | ||||||||
\(671\) | − | 888846.i | − | 1.97416i | ||||||
\(672\) | − | 1.90340e6i | − | 4.21494i | ||||||
\(673\) | 738888.i | 1.63136i | 0.578507 | + | 0.815678i | \(0.303636\pi\) | ||||
−0.578507 | + | 0.815678i | \(0.696364\pi\) | |||||||
\(674\) | 397752.i | 0.875573i | ||||||||
\(675\) | 379998.i | 0.834014i | ||||||||
\(676\) | −2.95144e6 | −6.45863 | ||||||||
\(677\) | 227328.i | 0.495994i | 0.968761 | + | 0.247997i | \(0.0797723\pi\) | ||||
−0.968761 | + | 0.247997i | \(0.920228\pi\) | |||||||
\(678\) | − | 1.62629e6i | − | 3.53785i | ||||||
\(679\) | 191936.i | 0.416309i | ||||||||
\(680\) | −54863.2 | −0.118649 | ||||||||
\(681\) | −838988. | −1.80910 | ||||||||
\(682\) | 753615.i | 1.62024i | ||||||||
\(683\) | 161434. | 0.346061 | 0.173031 | − | 0.984916i | \(-0.444644\pi\) | ||||
0.173031 | + | 0.984916i | \(0.444644\pi\) | |||||||
\(684\) | − | 1.58439e6i | − | 3.38649i | ||||||
\(685\) | 146488. | 0.312191 | ||||||||
\(686\) | 776655. | 1.65036 | ||||||||
\(687\) | 226809.i | 0.480559i | ||||||||
\(688\) | 964504. | + | 899107.i | 2.03764 | + | 1.89948i | ||||
\(689\) | −850760. | −1.79213 | ||||||||
\(690\) | 203846.i | 0.428157i | ||||||||
\(691\) | 327344.i | 0.685565i | 0.939415 | + | 0.342783i | \(0.111369\pi\) | ||||
−0.939415 | + | 0.342783i | \(0.888631\pi\) | |||||||
\(692\) | −1.47312e6 | −3.07629 | ||||||||
\(693\) | 1.05005e6i | 2.18648i | ||||||||
\(694\) | 602479. | 1.25090 | ||||||||
\(695\) | − | 88323.4i | − | 0.182855i | ||||||
\(696\) | 705601.i | 1.45660i | ||||||||
\(697\) | 6854.54 | 0.0141095 | ||||||||
\(698\) | −1.30231e6 | −2.67303 | ||||||||
\(699\) | 874749. | 1.79031 | ||||||||
\(700\) | 1.15313e6i | 2.35332i | ||||||||
\(701\) | 436072. | 0.887406 | 0.443703 | − | 0.896174i | \(-0.353665\pi\) | ||||
0.443703 | + | 0.896174i | \(0.353665\pi\) | |||||||
\(702\) | 1.69532e6 | 3.44016 | ||||||||
\(703\) | 357811. | 0.724007 | ||||||||
\(704\) | −1.04899e6 | −2.11654 | ||||||||
\(705\) | 423247. | 0.851562 | ||||||||
\(706\) | − | 599937.i | − | 1.20364i | ||||||
\(707\) | − | 168030.i | − | 0.336162i | ||||||
\(708\) | 1.60179e6i | 3.19551i | ||||||||
\(709\) | −453704. | −0.902569 | −0.451285 | − | 0.892380i | \(-0.649034\pi\) | ||||
−0.451285 | + | 0.892380i | \(0.649034\pi\) | |||||||
\(710\) | − | 411491.i | − | 0.816289i | ||||||
\(711\) | −821331. | −1.62472 | ||||||||
\(712\) | −770106. | −1.51911 | ||||||||
\(713\) | −132630. | −0.260893 | ||||||||
\(714\) | − | 187853.i | − | 0.368488i | ||||||
\(715\) | 454034.i | 0.888129i | ||||||||
\(716\) | − | 2.03197e6i | − | 3.96362i | ||||||
\(717\) | − | 1.32496e6i | − | 2.57730i | ||||||
\(718\) | 623307.i | 1.20907i | ||||||||
\(719\) | −677749. | −1.31103 | −0.655513 | − | 0.755184i | \(-0.727547\pi\) | ||||
−0.655513 | + | 0.755184i | \(0.727547\pi\) | |||||||
\(720\) | 870120.i | 1.67847i | ||||||||
\(721\) | 386803.i | 0.744080i | ||||||||
\(722\) | 283417.i | 0.543689i | ||||||||
\(723\) | −169787. | −0.324810 | ||||||||
\(724\) | 1.27328e6 | 2.42910 | ||||||||
\(725\) | − | 144171.i | − | 0.274285i | ||||||
\(726\) | 892447. | 1.69320 | ||||||||
\(727\) | 421634.i | 0.797751i | 0.917005 | + | 0.398875i | \(0.130599\pi\) | ||||
−0.917005 | + | 0.398875i | \(0.869401\pi\) | |||||||
\(728\) | 3.09403e6 | 5.83798 | ||||||||
\(729\) | 862728. | 1.62338 | ||||||||
\(730\) | 46741.7i | 0.0877120i | ||||||||
\(731\) | 43629.2 | + | 40671.0i | 0.0816475 | + | 0.0761115i | ||||
\(732\) | 3.42725e6 | 6.39622 | ||||||||
\(733\) | − | 545085.i | − | 1.01451i | −0.861796 | − | 0.507255i | \(-0.830660\pi\) | ||
0.861796 | − | 0.507255i | \(-0.169340\pi\) | |||||||
\(734\) | 1.86419e6i | 3.46017i | ||||||||
\(735\) | 63435.0 | 0.117423 | ||||||||
\(736\) | − | 488128.i | − | 0.901110i | ||||||
\(737\) | −165257. | −0.304246 | ||||||||
\(738\) | − | 206622.i | − | 0.379371i | ||||||
\(739\) | − | 308914.i | − | 0.565651i | −0.959171 | − | 0.282826i | \(-0.908728\pi\) | ||
0.959171 | − | 0.282826i | \(-0.0912718\pi\) | |||||||
\(740\) | −444024. | −0.810855 | ||||||||
\(741\) | 1.41076e6 | 2.56932 | ||||||||
\(742\) | 1.06804e6 | 1.93991 | ||||||||
\(743\) | − | 1.03791e6i | − | 1.88011i | −0.341026 | − | 0.940054i | \(-0.610775\pi\) | ||
0.341026 | − | 0.940054i | \(-0.389225\pi\) | |||||||
\(744\) | −1.74761e6 | −3.15718 | ||||||||
\(745\) | 18924.0 | 0.0340958 | ||||||||
\(746\) | 1.56890e6 | 2.81914 | ||||||||
\(747\) | −1.08446e6 | −1.94345 | ||||||||
\(748\) | −195724. | −0.349816 | ||||||||
\(749\) | 608782.i | 1.08517i | ||||||||
\(750\) | − | 1.18803e6i | − | 2.11205i | ||||||
\(751\) | − | 162809.i | − | 0.288669i | −0.989529 | − | 0.144334i | \(-0.953896\pi\) | ||
0.989529 | − | 0.144334i | \(-0.0461041\pi\) | |||||||
\(752\) | −2.21127e6 | −3.91027 | ||||||||
\(753\) | − | 1.38402e6i | − | 2.44091i | ||||||
\(754\) | −643204. | −1.13137 | ||||||||
\(755\) | −70018.5 | −0.122834 | ||||||||
\(756\) | −1.52176e6 | −2.66258 | ||||||||
\(757\) | 24344.0i | 0.0424816i | 0.999774 | + | 0.0212408i | \(0.00676166\pi\) | ||||
−0.999774 | + | 0.0212408i | \(0.993238\pi\) | |||||||
\(758\) | − | 689781.i | − | 1.20053i | ||||||
\(759\) | 437361.i | 0.759201i | ||||||||
\(760\) | 517247.i | 0.895511i | ||||||||
\(761\) | 935074.i | 1.61464i | 0.590111 | + | 0.807322i | \(0.299084\pi\) | ||||
−0.590111 | + | 0.807322i | \(0.700916\pi\) | |||||||
\(762\) | −1.20679e6 | −2.07836 | ||||||||
\(763\) | − | 365639.i | − | 0.628064i | ||||||
\(764\) | 2.00398e6i | 3.43325i | ||||||||
\(765\) | 39359.8i | 0.0672558i | ||||||||
\(766\) | −388404. | −0.661952 | ||||||||
\(767\) | −878159. | −1.49273 | ||||||||
\(768\) | 217876.i | 0.369391i | ||||||||
\(769\) | 314204. | 0.531323 | 0.265662 | − | 0.964066i | \(-0.414410\pi\) | ||||
0.265662 | + | 0.964066i | \(0.414410\pi\) | |||||||
\(770\) | − | 569994.i | − | 0.961366i | ||||||
\(771\) | −1.42478e6 | −2.39685 | ||||||||
\(772\) | −21731.6 | −0.0364634 | ||||||||
\(773\) | 786232.i | 1.31581i | 0.753103 | + | 0.657903i | \(0.228556\pi\) | ||||
−0.753103 | + | 0.657903i | \(0.771444\pi\) | |||||||
\(774\) | 1.22598e6 | − | 1.31515e6i | 2.04645 | − | 2.19530i | ||||
\(775\) | 357079. | 0.594512 | ||||||||
\(776\) | 648579.i | 1.07706i | ||||||||
\(777\) | − | 914369.i | − | 1.51454i | ||||||
\(778\) | 1.27501e6 | 2.10646 | ||||||||
\(779\) | − | 64624.3i | − | 0.106493i | ||||||
\(780\) | −1.75068e6 | −2.87752 | ||||||||
\(781\) | − | 882875.i | − | 1.44743i | ||||||
\(782\) | − | 48175.1i | − | 0.0787788i | ||||||
\(783\) | 190260. | 0.310330 | ||||||||
\(784\) | −331418. | −0.539193 | ||||||||
\(785\) | 153920. | 0.249779 | ||||||||
\(786\) | − | 818190.i | − | 1.32437i | ||||||
\(787\) | 229414. | 0.370400 | 0.185200 | − | 0.982701i | \(-0.440707\pi\) | ||||
0.185200 | + | 0.982701i | \(0.440707\pi\) | |||||||
\(788\) | 1.25014e6 | 2.01329 | ||||||||
\(789\) | 116091. | 0.186485 | ||||||||
\(790\) | 445839. | 0.714370 | ||||||||
\(791\) | −800313. | −1.27911 | ||||||||
\(792\) | 3.54829e6i | 5.65677i | ||||||||
\(793\) | 1.87894e6i | 2.98790i | ||||||||
\(794\) | − | 1.51145e6i | − | 2.39746i | ||||||
\(795\) | −363453. | −0.575061 | ||||||||
\(796\) | − | 2.39323e6i | − | 3.77709i | ||||||
\(797\) | −1.10312e6 | −1.73663 | −0.868316 | − | 0.496011i | \(-0.834798\pi\) | ||||
−0.868316 | + | 0.496011i | \(0.834798\pi\) | |||||||
\(798\) | −1.77107e6 | −2.78119 | ||||||||
\(799\) | −100027. | −0.156683 | ||||||||
\(800\) | 1.31418e6i | 2.05341i | ||||||||
\(801\) | 552487.i | 0.861107i | ||||||||
\(802\) | 285568.i | 0.443977i | ||||||||
\(803\) | 100287.i | 0.155529i | ||||||||
\(804\) | − | 637205.i | − | 0.985751i | ||||||
\(805\) | 100314. | 0.154800 | ||||||||
\(806\) | − | 1.59307e6i | − | 2.45225i | ||||||
\(807\) | 623924.i | 0.958042i | ||||||||
\(808\) | − | 567800.i | − | 0.869706i | ||||||
\(809\) | 602078. | 0.919932 | 0.459966 | − | 0.887937i | \(-0.347862\pi\) | ||||
0.459966 | + | 0.887937i | \(0.347862\pi\) | |||||||
\(810\) | −16265.2 | −0.0247908 | ||||||||
\(811\) | 930391.i | 1.41457i | 0.706930 | + | 0.707284i | \(0.250080\pi\) | ||||
−0.706930 | + | 0.707284i | \(0.749920\pi\) | |||||||
\(812\) | 577356. | 0.875651 | ||||||||
\(813\) | − | 322625.i | − | 0.488109i | ||||||
\(814\) | −1.33240e6 | −2.01087 | ||||||||
\(815\) | 424138. | 0.638546 | ||||||||
\(816\) | − | 333984.i | − | 0.501587i | ||||||
\(817\) | 383444. | − | 411334.i | 0.574458 | − | 0.616241i | ||||
\(818\) | −2.26093e6 | −3.37894 | ||||||||
\(819\) | − | 2.21971e6i | − | 3.30925i | ||||||
\(820\) | 80195.3i | 0.119267i | ||||||||
\(821\) | −857913. | −1.27279 | −0.636395 | − | 0.771363i | \(-0.719575\pi\) | ||||
−0.636395 | + | 0.771363i | \(0.719575\pi\) | |||||||
\(822\) | 1.69491e6i | 2.50844i | ||||||||
\(823\) | −1.18057e6 | −1.74298 | −0.871488 | − | 0.490417i | \(-0.836845\pi\) | ||||
−0.871488 | + | 0.490417i | \(0.836845\pi\) | |||||||
\(824\) | 1.30707e6i | 1.92505i | ||||||||
\(825\) | − | 1.17750e6i | − | 1.73003i | ||||||
\(826\) | 1.10244e6 | 1.61583 | ||||||||
\(827\) | 48059.2 | 0.0702693 | 0.0351347 | − | 0.999383i | \(-0.488814\pi\) | ||||
0.0351347 | + | 0.999383i | \(0.488814\pi\) | |||||||
\(828\) | −1.03833e6 | −1.51451 | ||||||||
\(829\) | 640828.i | 0.932465i | 0.884662 | + | 0.466233i | \(0.154389\pi\) | ||||
−0.884662 | + | 0.466233i | \(0.845611\pi\) | |||||||
\(830\) | 588671. | 0.854509 | ||||||||
\(831\) | 977610. | 1.41568 | ||||||||
\(832\) | 2.21747e6 | 3.20340 | ||||||||
\(833\) | −14991.7 | −0.0216053 | ||||||||
\(834\) | 1.02193e6 | 1.46923 | ||||||||
\(835\) | 227632.i | 0.326483i | ||||||||
\(836\) | 1.84527e6i | 2.64027i | ||||||||
\(837\) | 471231.i | 0.672640i | ||||||||
\(838\) | 115872. | 0.165003 | ||||||||
\(839\) | 380215.i | 0.540138i | 0.962841 | + | 0.270069i | \(0.0870465\pi\) | ||||
−0.962841 | + | 0.270069i | \(0.912953\pi\) | |||||||
\(840\) | 1.32180e6 | 1.87330 | ||||||||
\(841\) | 635096. | 0.897941 | ||||||||
\(842\) | −1.63388e6 | −2.30461 | ||||||||
\(843\) | 213027.i | 0.299764i | ||||||||
\(844\) | − | 1.81758e6i | − | 2.55158i | ||||||
\(845\) | − | 691260.i | − | 0.968118i | ||||||
\(846\) | 3.01519e6i | 4.21283i | ||||||||
\(847\) | − | 439181.i | − | 0.612177i | ||||||
\(848\) | 1.89887e6 | 2.64061 | ||||||||
\(849\) | − | 366200.i | − | 0.508045i | ||||||
\(850\) | 129702.i | 0.179518i | ||||||||
\(851\) | − | 234490.i | − | 0.323792i | ||||||
\(852\) | 3.40423e6 | 4.68964 | ||||||||
\(853\) | 374276. | 0.514392 | 0.257196 | − | 0.966359i | \(-0.417201\pi\) | ||||
0.257196 | + | 0.966359i | \(0.417201\pi\) | |||||||
\(854\) | − | 2.35882e6i | − | 3.23429i | ||||||
\(855\) | 371082. | 0.507619 | ||||||||
\(856\) | 2.05717e6i | 2.80751i | ||||||||
\(857\) | 581564. | 0.791837 | 0.395918 | − | 0.918286i | \(-0.370426\pi\) | ||||
0.395918 | + | 0.918286i | \(0.370426\pi\) | |||||||
\(858\) | −5.25332e6 | −7.13607 | ||||||||
\(859\) | 1.14416e6i | 1.55061i | 0.631589 | + | 0.775303i | \(0.282403\pi\) | ||||
−0.631589 | + | 0.775303i | \(0.717597\pi\) | |||||||
\(860\) | −475834. | + | 510444.i | −0.643366 | + | 0.690162i | ||||
\(861\) | −165144. | −0.222770 | ||||||||
\(862\) | − | 1.30179e6i | − | 1.75197i | ||||||
\(863\) | − | 48167.9i | − | 0.0646750i | −0.999477 | − | 0.0323375i | \(-0.989705\pi\) | ||
0.999477 | − | 0.0323375i | \(-0.0102951\pi\) | |||||||
\(864\) | −1.73431e6 | −2.32326 | ||||||||
\(865\) | − | 345022.i | − | 0.461121i | ||||||
\(866\) | 1.89305e6 | 2.52422 | ||||||||
\(867\) | 1.19746e6i | 1.59303i | ||||||||
\(868\) | 1.42998e6i | 1.89797i | ||||||||
\(869\) | 956570. | 1.26671 | ||||||||
\(870\) | −274783. | −0.363038 | ||||||||
\(871\) | 349338. | 0.460479 | ||||||||
\(872\) | − | 1.23555e6i | − | 1.62490i | ||||||
\(873\) | 465302. | 0.610529 | ||||||||
\(874\) | −454192. | −0.594589 | ||||||||
\(875\) | −584640. | −0.763611 | ||||||||
\(876\) | −386690. | −0.503912 | ||||||||
\(877\) | −481656. | −0.626235 | −0.313118 | − | 0.949714i | \(-0.601373\pi\) | ||||
−0.313118 | + | 0.949714i | \(0.601373\pi\) | |||||||
\(878\) | − | 1.48040e6i | − | 1.92040i | ||||||
\(879\) | − | 1.63300e6i | − | 2.11353i | ||||||
\(880\) | − | 1.01339e6i | − | 1.30862i | ||||||
\(881\) | −771331. | −0.993777 | −0.496889 | − | 0.867814i | \(-0.665524\pi\) | ||||
−0.496889 | + | 0.867814i | \(0.665524\pi\) | |||||||
\(882\) | 451907.i | 0.580914i | ||||||||
\(883\) | 1.36525e6 | 1.75101 | 0.875507 | − | 0.483205i | \(-0.160527\pi\) | ||||
0.875507 | + | 0.483205i | \(0.160527\pi\) | |||||||
\(884\) | 413741. | 0.529449 | ||||||||
\(885\) | −375158. | −0.478992 | ||||||||
\(886\) | 870048.i | 1.10835i | ||||||||
\(887\) | 395935.i | 0.503242i | 0.967826 | + | 0.251621i | \(0.0809637\pi\) | ||||
−0.967826 | + | 0.251621i | \(0.919036\pi\) | |||||||
\(888\) | − | 3.08979e6i | − | 3.91835i | ||||||
\(889\) | 593870.i | 0.751429i | ||||||||
\(890\) | − | 299904.i | − | 0.378618i | ||||||
\(891\) | −34897.9 | −0.0439586 | ||||||||
\(892\) | 1.04490e6i | 1.31324i | ||||||||
\(893\) | 943046.i | 1.18258i | ||||||||
\(894\) | 218957.i | 0.273958i | ||||||||
\(895\) | 475911. | 0.594128 | ||||||||
\(896\) | −686140. | −0.854667 | ||||||||
\(897\) | − | 924541.i | − | 1.14906i | ||||||
\(898\) | 1.65819e6 | 2.05627 | ||||||||
\(899\) | − | 178785.i | − | 0.221213i | ||||||
\(900\) | 2.79548e6 | 3.45121 | ||||||||
\(901\) | 85895.3 | 0.105808 | ||||||||
\(902\) | 240644.i | 0.295776i | ||||||||
\(903\) | −1.05115e6 | − | 979874.i | −1.28910 | − | 1.20170i | ||||
\(904\) | −2.70438e6 | −3.30926 | ||||||||
\(905\) | 298216.i | 0.364111i | ||||||||
\(906\) | − | 810138.i | − | 0.986966i | ||||||
\(907\) | 1.02709e6 | 1.24852 | 0.624260 | − | 0.781216i | \(-0.285400\pi\) | ||||
0.624260 | + | 0.781216i | \(0.285400\pi\) | |||||||
\(908\) | 2.31978e6i | 2.81369i | ||||||||
\(909\) | −407349. | −0.492991 | ||||||||
\(910\) | 1.20491e6i | 1.45503i | ||||||||
\(911\) | − | 1.39342e6i | − | 1.67898i | −0.543374 | − | 0.839491i | \(-0.682853\pi\) | ||
0.543374 | − | 0.839491i | \(-0.317147\pi\) | |||||||
\(912\) | −3.14879e6 | −3.78576 | ||||||||
\(913\) | 1.26302e6 | 1.51520 | ||||||||
\(914\) | −593209. | −0.710094 | ||||||||
\(915\) | 802701.i | 0.958764i | ||||||||
\(916\) | 627122. | 0.747414 | ||||||||
\(917\) | −402638. | −0.478825 | ||||||||
\(918\) | −171165. | −0.203109 | ||||||||
\(919\) | −1.19770e6 | −1.41813 | −0.709064 | − | 0.705144i | \(-0.750882\pi\) | ||||
−0.709064 | + | 0.705144i | \(0.750882\pi\) | |||||||
\(920\) | 338977. | 0.400492 | ||||||||
\(921\) | − | 1.98584e6i | − | 2.34113i | ||||||
\(922\) | 2.04242e6i | 2.40261i | ||||||||
\(923\) | 1.86632e6i | 2.19069i | ||||||||
\(924\) | 4.71551e6 | 5.52312 | ||||||||
\(925\) | 631317.i | 0.737843i | ||||||||
\(926\) | −2.43309e6 | −2.83750 | ||||||||
\(927\) | 937711. | 1.09121 | ||||||||
\(928\) | 657995. | 0.764058 | ||||||||
\(929\) | − | 235931.i | − | 0.273371i | −0.990614 | − | 0.136686i | \(-0.956355\pi\) | ||
0.990614 | − | 0.136686i | \(-0.0436450\pi\) | |||||||
\(930\) | − | 680576.i | − | 0.786884i | ||||||
\(931\) | 141341.i | 0.163068i | ||||||||
\(932\) | − | 2.41866e6i | − | 2.78447i | ||||||
\(933\) | 675523.i | 0.776028i | ||||||||
\(934\) | −365715. | −0.419227 | ||||||||
\(935\) | − | 45840.7i | − | 0.0524358i | ||||||
\(936\) | − | 7.50074e6i | − | 8.56156i | ||||||
\(937\) | − | 1.54482e6i | − | 1.75954i | −0.475401 | − | 0.879769i | \(-0.657697\pi\) | ||
0.475401 | − | 0.879769i | \(-0.342303\pi\) | |||||||
\(938\) | −438559. | −0.498451 | ||||||||
\(939\) | −999196. | −1.13323 | ||||||||
\(940\) | − | 1.17027e6i | − | 1.32443i | ||||||
\(941\) | −573364. | −0.647517 | −0.323759 | − | 0.946140i | \(-0.604947\pi\) | ||||
−0.323759 | + | 0.946140i | \(0.604947\pi\) | |||||||
\(942\) | 1.78091e6i | 2.00696i | ||||||||
\(943\) | −42351.4 | −0.0476260 | ||||||||
\(944\) | 1.96003e6 | 2.19947 | ||||||||
\(945\) | − | 356414.i | − | 0.399109i | ||||||
\(946\) | −1.42785e6 | + | 1.53170e6i | −1.59551 | + | 1.71156i | ||||
\(947\) | 1.66137e6 | 1.85253 | 0.926265 | − | 0.376872i | \(-0.123000\pi\) | ||||
0.926265 | + | 0.376872i | \(0.123000\pi\) | |||||||
\(948\) | 3.68838e6i | 4.10411i | ||||||||
\(949\) | − | 211997.i | − | 0.235395i | ||||||
\(950\) | 1.22282e6 | 1.35492 | ||||||||
\(951\) | 707417.i | 0.782193i | ||||||||
\(952\) | −312383. | −0.344678 | ||||||||
\(953\) | − | 1.10535e6i | − | 1.21707i | −0.793527 | − | 0.608535i | \(-0.791758\pi\) | ||
0.793527 | − | 0.608535i | \(-0.208242\pi\) | |||||||
\(954\) | − | 2.58922e6i | − | 2.84493i | ||||||
\(955\) | −469354. | −0.514629 | ||||||||
\(956\) | −3.66349e6 | −4.00848 | ||||||||
\(957\) | −589562. | −0.643732 | ||||||||
\(958\) | 2.87088e6i | 3.12813i | ||||||||
\(959\) | 834083. | 0.906926 | ||||||||
\(960\) | 947326. | 1.02791 | ||||||||
\(961\) | −480712. | −0.520521 | ||||||||
\(962\) | 2.81656e6 | 3.04347 | ||||||||
\(963\) | 1.47585e6 | 1.59143 | ||||||||
\(964\) | 469458.i | 0.505176i | ||||||||
\(965\) | − | 5089.79i | − | 0.00546569i | ||||||
\(966\) | 1.16067e6i | 1.24381i | ||||||||
\(967\) | 352269. | 0.376723 | 0.188361 | − | 0.982100i | \(-0.439682\pi\) | ||||
0.188361 | + | 0.982100i | \(0.439682\pi\) | |||||||
\(968\) | − | 1.48406e6i | − | 1.58380i | ||||||
\(969\) | −142435. | −0.151694 | ||||||||
\(970\) | −252577. | −0.268442 | ||||||||
\(971\) | −697949. | −0.740262 | −0.370131 | − | 0.928980i | \(-0.620687\pi\) | ||||
−0.370131 | + | 0.928980i | \(0.620687\pi\) | |||||||
\(972\) | − | 2.43714e6i | − | 2.57957i | ||||||
\(973\) | − | 502901.i | − | 0.531199i | ||||||
\(974\) | 2.22191e6i | 2.34212i | ||||||||
\(975\) | 2.48914e6i | 2.61842i | ||||||||
\(976\) | − | 4.19374e6i | − | 4.40253i | ||||||
\(977\) | 84775.3 | 0.0888137 | 0.0444069 | − | 0.999014i | \(-0.485860\pi\) | ||||
0.0444069 | + | 0.999014i | \(0.485860\pi\) | |||||||
\(978\) | 4.90742e6i | 5.13069i | ||||||||
\(979\) | − | 643459.i | − | 0.671360i | ||||||
\(980\) | − | 175396.i | − | 0.182628i | ||||||
\(981\) | −886405. | −0.921073 | ||||||||
\(982\) | −1.75926e6 | −1.82435 | ||||||||
\(983\) | 528881.i | 0.547333i | 0.961825 | + | 0.273666i | \(0.0882364\pi\) | ||||
−0.961825 | + | 0.273666i | \(0.911764\pi\) | |||||||
\(984\) | −558048. | −0.576343 | ||||||||
\(985\) | 292796.i | 0.301782i | ||||||||
\(986\) | 64939.9 | 0.0667972 | ||||||||
\(987\) | 2.40991e6 | 2.47381 | ||||||||
\(988\) | − | 3.90073e6i | − | 3.99606i | ||||||
\(989\) | −269567. | − | 251289.i | −0.275597 | − | 0.256910i | ||||
\(990\) | −1.38181e6 | −1.40987 | ||||||||
\(991\) | 766986.i | 0.780980i | 0.920607 | + | 0.390490i | \(0.127694\pi\) | ||||
−0.920607 | + | 0.390490i | \(0.872306\pi\) | |||||||
\(992\) | 1.62970e6i | 1.65609i | ||||||||
\(993\) | 894178. | 0.906830 | ||||||||
\(994\) | − | 2.34297e6i | − | 2.37134i | ||||||
\(995\) | 560521. | 0.566169 | ||||||||
\(996\) | 4.87002e6i | 4.90922i | ||||||||
\(997\) | 932501.i | 0.938121i | 0.883166 | + | 0.469060i | \(0.155407\pi\) | ||||
−0.883166 | + | 0.469060i | \(0.844593\pi\) | |||||||
\(998\) | −1.67611e6 | −1.68284 | ||||||||
\(999\) | −833139. | −0.834808 |
(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 | 43.5.b.b.42.12 | yes | 12 | |
3.2 | odd | 2 | 387.5.b.c.343.1 | 12 | |||
4.3 | odd | 2 | 688.5.b.d.257.11 | 12 | |||
43.42 | odd | 2 | inner | 43.5.b.b.42.1 | ✓ | 12 | |
129.128 | even | 2 | 387.5.b.c.343.12 | 12 | |||
172.171 | even | 2 | 688.5.b.d.257.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.5.b.b.42.1 | ✓ | 12 | 43.42 | odd | 2 | inner | |
43.5.b.b.42.12 | yes | 12 | 1.1 | even | 1 | trivial | |
387.5.b.c.343.1 | 12 | 3.2 | odd | 2 | |||
387.5.b.c.343.12 | 12 | 129.128 | even | 2 | |||
688.5.b.d.257.2 | 12 | 172.171 | even | 2 | |||
688.5.b.d.257.11 | 12 | 4.3 | odd | 2 |