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 | 42.1 | ||
Root | \(-7.49282i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.5.b.b.42.12 |
$q$-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 | \(-0.613952\pi\) | ||
0.350393 | − | 0.936603i | \(-0.386048\pi\) | |||||||
\(3\) | 14.5182i | 1.61313i | 0.591146 | + | 0.806564i | \(0.298676\pi\) | ||||
−0.591146 | + | 0.806564i | \(0.701324\pi\) | |||||||
\(4\) | −40.1424 | −2.50890 | ||||||||
\(5\) | 9.40180i | 0.376072i | 0.982162 | + | 0.188036i | \(0.0602122\pi\) | ||||
−0.982162 | + | 0.188036i | \(0.939788\pi\) | |||||||
\(6\) | 108.782 | 3.02172 | ||||||||
\(7\) | 53.5326i | 1.09250i | 0.837622 | + | 0.546251i | \(0.183945\pi\) | ||||
−0.837622 | + | 0.546251i | \(0.816055\pi\) | |||||||
\(8\) | 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 | \(0.138403\pi\) | ||||
−0.906952 | + | 0.421235i | \(0.861597\pi\) | |||||||
\(20\) | − | 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 | \(0.0510635\pi\) | ||||
−0.987160 | + | 0.159734i | \(0.948937\pi\) | |||||||
\(30\) | 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 | \(-0.858622\pi\) | ||
0.902975 | − | 0.429693i | \(-0.141378\pi\) | |||||||
\(38\) | 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 | \(0.290028\pi\) | ||||
−0.612839 | + | 0.790208i | \(0.709972\pi\) | |||||||
\(62\) | − | 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 | \(0.196702\pi\) | ||||
−0.815064 | + | 0.579371i | \(0.803298\pi\) | |||||||
\(72\) | − | 23475.9i | − | 4.52854i | ||||||
\(73\) | − | 663.511i | − | 0.124509i | −0.998060 | − | 0.0622547i | \(-0.980171\pi\) | ||
0.998060 | − | 0.0622547i | \(-0.0198291\pi\) | |||||||
\(74\) | −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 | \(0.0866037\pi\) | ||||
−0.963216 | + | 0.268729i | \(0.913396\pi\) | |||||||
\(90\) | −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 | \(0.199064\pi\) | ||||
−0.810742 | + | 0.585403i | \(0.800936\pi\) | |||||||
\(114\) | 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 | \(0.0703256\pi\) | ||||
−0.975693 | + | 0.219141i | \(0.929674\pi\) | |||||||
\(132\) | − | 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 | \(-0.863758\pi\) | ||
0.909790 | − | 0.415069i | \(-0.136242\pi\) | |||||||
\(138\) | −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 | \(-0.985566\pi\) | ||
0.998972 | − | 0.0453315i | \(-0.0144344\pi\) | |||||||
\(150\) | 58373.1 | 2.59436 | ||||||||
\(151\) | 7447.35i | 0.326624i | 0.986574 | + | 0.163312i | \(0.0522177\pi\) | ||||
−0.986574 | + | 0.163312i | \(0.947782\pi\) | |||||||
\(152\) | −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 | \(-0.892246\pi\) | ||
0.943248 | − | 0.332090i | \(-0.107754\pi\) | |||||||
\(158\) | − | 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 | \(-0.677225\pi\) | ||
0.528445 | − | 0.848967i | \(-0.322775\pi\) | |||||||
\(164\) | −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 | \(-0.710126\pi\) | ||
0.613220 | − | 0.789912i | \(-0.289874\pi\) | |||||||
\(180\) | 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 | \(0.239855\pi\) | ||||
−0.729280 | + | 0.684215i | \(0.760145\pi\) | |||||||
\(192\) | − | 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 | \(-0.728732\pi\) | ||
0.658319 | − | 0.752739i | \(-0.271268\pi\) | |||||||
\(200\) | 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 | \(-0.830198\pi\) | ||
0.861059 | − | 0.508506i | \(-0.169802\pi\) | |||||||
\(212\) | −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 | \(0.0842883\pi\) | ||||
−0.965145 | + | 0.261716i | \(0.915712\pi\) | |||||||
\(224\) | 131105. | 2.61290 | ||||||||
\(225\) | −69639.1 | −1.37559 | ||||||||
\(226\) | 112018. | 2.19316 | ||||||||
\(227\) | 57788.9i | 1.12148i | 0.827991 | + | 0.560741i | \(0.189484\pi\) | ||||
−0.827991 | + | 0.560741i | \(0.810516\pi\) | |||||||
\(228\) | 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 | \(-0.812749\pi\) | ||
0.831904 | − | 0.554919i | \(-0.187251\pi\) | |||||||
\(234\) | − | 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 | \(0.0321008\pi\) | ||||
−0.994919 | + | 0.100677i | \(0.967899\pi\) | |||||||
\(242\) | − | 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 | \(0.266559\pi\) | ||||
−0.669382 | + | 0.742919i | \(0.733441\pi\) | |||||||
\(258\) | 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 | \(-0.981591\pi\) | ||
0.998328 | − | 0.0578022i | \(-0.0184093\pi\) | |||||||
\(264\) | −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 | \(-0.855404\pi\) | ||
0.898586 | − | 0.438798i | \(-0.144596\pi\) | |||||||
\(278\) | − | 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 | \(0.114244\pi\) | ||||
−0.936280 | + | 0.351253i | \(0.885756\pi\) | |||||||
\(314\) | −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 | \(-0.909308\pi\) | ||
0.959685 | − | 0.281078i | \(-0.0906919\pi\) | |||||||
\(332\) | −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 | \(0.108363\pi\) | ||||
−0.942611 | + | 0.333893i | \(0.891637\pi\) | |||||||
\(348\) | 156580. | 1.29294 | ||||||||
\(349\) | − | 173808.i | − | 1.42698i | −0.700663 | − | 0.713492i | \(-0.747112\pi\) | ||
0.700663 | − | 0.713492i | \(-0.252888\pi\) | |||||||
\(350\) | 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 | \(0.271148\pi\) | ||||
−0.658603 | + | 0.752490i | \(0.728852\pi\) | |||||||
\(374\) | − | 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 | \(-0.943461\pi\) | ||
0.984267 | − | 0.176690i | \(-0.0565388\pi\) | |||||||
\(384\) | −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 | \(0.190069\pi\) | ||||
−0.826959 | + | 0.562262i | \(0.809931\pi\) | |||||||
\(390\) | − | 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 | \(-0.642163\pi\) | ||
0.431918 | − | 0.901913i | \(-0.357837\pi\) | |||||||
\(410\) | 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 | \(0.0140238\pi\) | ||||
−0.999030 | + | 0.0440430i | \(0.985976\pi\) | |||||||
\(420\) | 293322.i | 1.66282i | ||||||||
\(421\) | − | 218060.i | − | 1.23030i | −0.788409 | − | 0.615151i | \(-0.789095\pi\) | ||
0.788409 | − | 0.615151i | \(-0.210905\pi\) | |||||||
\(422\) | −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 | \(0.235326\pi\) | ||||
−0.738942 | + | 0.673769i | \(0.764674\pi\) | |||||||
\(434\) | 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 | \(0.184940\pi\) | ||||
−0.835911 | + | 0.548864i | \(0.815060\pi\) | |||||||
\(450\) | 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 | \(-0.939300\pi\) | ||
0.981873 | − | 0.189540i | \(-0.0606996\pi\) | |||||||
\(458\) | 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 | \(-0.726473\pi\) | ||
0.652960 | − | 0.757392i | \(-0.273527\pi\) | |||||||
\(464\) | 191599.i | 0.889932i | ||||||||
\(465\) | −90830.3 | −0.420073 | ||||||||
\(466\) | −451458. | −2.07896 | ||||||||
\(467\) | − | 48808.8i | − | 0.223802i | −0.993719 | − | 0.111901i | \(-0.964306\pi\) | ||
0.993719 | − | 0.111901i | \(-0.0356940\pi\) | |||||||
\(468\) | −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 | \(-0.838106\pi\) | ||
0.873425 | − | 0.486958i | \(-0.161894\pi\) | |||||||
\(492\) | − | 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 | \(-0.851714\pi\) | ||
0.893438 | − | 0.449186i | \(-0.148286\pi\) | |||||||
\(500\) | − | 438403.i | − | 1.75361i | ||||||
\(501\) | − | 351507.i | − | 1.40042i | ||||||
\(502\) | − | 714293.i | − | 2.83445i | ||||||
\(503\) | − | 171252.i | − | 0.676861i | −0.940991 | − | 0.338430i | \(-0.890104\pi\) | ||
0.940991 | − | 0.338430i | \(-0.109896\pi\) | |||||||
\(504\) | 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 | \(0.176825\pi\) | ||||
−0.849630 | + | 0.527378i | \(0.823175\pi\) | |||||||
\(522\) | −261255. | −0.958791 | ||||||||
\(523\) | 132186.i | 0.483263i | 0.970368 | + | 0.241631i | \(0.0776825\pi\) | ||||
−0.970368 | + | 0.241631i | \(0.922318\pi\) | |||||||
\(524\) | − | 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 | \(0.163076\pi\) | ||||
−0.871611 | + | 0.490198i | \(0.836924\pi\) | |||||||
\(572\) | 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 | \(0.291344\pi\) | ||||
−0.609565 | + | 0.792736i | \(0.708656\pi\) | |||||||
\(578\) | 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 | \(-0.689124\pi\) | ||
0.559804 | − | 0.828625i | \(-0.310876\pi\) | |||||||
\(588\) | 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 | \(0.296825\pi\) | ||||
−0.595824 | + | 0.803115i | \(0.703175\pi\) | |||||||
\(594\) | −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 | \(0.107576\pi\) | ||||
−0.943433 | + | 0.331563i | \(0.892424\pi\) | |||||||
\(602\) | 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 | \(-0.845188\pi\) | ||
0.884042 | − | 0.467408i | \(-0.154812\pi\) | |||||||
\(608\) | 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 | \(0.0827475\pi\) | ||||
−0.966400 | + | 0.257041i | \(0.917252\pi\) | |||||||
\(632\) | 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 | \(-0.883617\pi\) | ||
0.933900 | − | 0.357535i | \(-0.116383\pi\) | |||||||
\(642\) | −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 | \(0.0276846\pi\) | ||||
−0.996220 | + | 0.0868640i | \(0.972315\pi\) | |||||||
\(648\) | − | 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 | \(-0.869947\pi\) | ||
0.917688 | − | 0.397301i | \(-0.130053\pi\) | |||||||
\(654\) | 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 | \(-0.696364\pi\) | ||
0.578507 | − | 0.815678i | \(-0.303636\pi\) | |||||||
\(674\) | − | 397752.i | − | 0.875573i | ||||||
\(675\) | − | 379998.i | − | 0.834014i | ||||||
\(676\) | −2.95144e6 | −6.45863 | ||||||||
\(677\) | − | 227328.i | − | 0.495994i | −0.968761 | − | 0.247997i | \(-0.920228\pi\) | ||
0.968761 | − | 0.247997i | \(-0.0797723\pi\) | |||||||
\(678\) | 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 | \(-0.888631\pi\) | ||
0.939415 | − | 0.342783i | \(-0.111369\pi\) | |||||||
\(692\) | −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 | \(-0.869401\pi\) | ||
0.917005 | − | 0.398875i | \(-0.130599\pi\) | |||||||
\(728\) | 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 | \(0.169340\pi\) | ||||
−0.861796 | + | 0.507255i | \(0.830660\pi\) | |||||||
\(734\) | − | 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 | \(0.0912718\pi\) | ||||
−0.959171 | + | 0.282826i | \(0.908728\pi\) | |||||||
\(740\) | −444024. | −0.810855 | ||||||||
\(741\) | 1.41076e6 | 2.56932 | ||||||||
\(742\) | 1.06804e6 | 1.93991 | ||||||||
\(743\) | 1.03791e6i | 1.88011i | 0.341026 | + | 0.940054i | \(0.389225\pi\) | ||||
−0.341026 | + | 0.940054i | \(0.610775\pi\) | |||||||
\(744\) | −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 | \(0.0461041\pi\) | ||||
−0.989529 | + | 0.144334i | \(0.953896\pi\) | |||||||
\(752\) | −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 | \(-0.993238\pi\) | ||
0.999774 | − | 0.0212408i | \(-0.00676166\pi\) | |||||||
\(758\) | 689781.i | 1.20053i | ||||||||
\(759\) | − | 437361.i | − | 0.759201i | ||||||
\(760\) | − | 517247.i | − | 0.895511i | ||||||
\(761\) | − | 935074.i | − | 1.61464i | −0.590111 | − | 0.807322i | \(-0.700916\pi\) | ||
0.590111 | − | 0.807322i | \(-0.299084\pi\) | |||||||
\(762\) | −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 | \(-0.771444\pi\) | ||
0.753103 | − | 0.657903i | \(-0.228556\pi\) | |||||||
\(774\) | 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 | \(-0.749920\pi\) | ||
0.706930 | − | 0.707284i | \(-0.250080\pi\) | |||||||
\(812\) | 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 | \(-0.845611\pi\) | ||
0.884662 | − | 0.466233i | \(-0.154389\pi\) | |||||||
\(830\) | 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 | \(-0.912953\pi\) | ||
0.962841 | − | 0.270069i | \(-0.0870465\pi\) | |||||||
\(840\) | 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 | \(-0.717597\pi\) | ||
0.631589 | − | 0.775303i | \(-0.282403\pi\) | |||||||
\(860\) | −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 | \(0.0102951\pi\) | ||||
−0.999477 | + | 0.0323375i | \(0.989705\pi\) | |||||||
\(864\) | −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 | \(-0.919036\pi\) | ||
0.967826 | − | 0.251621i | \(-0.0809637\pi\) | |||||||
\(888\) | 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 | \(0.317147\pi\) | ||||
−0.543374 | + | 0.839491i | \(0.682853\pi\) | |||||||
\(912\) | −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 | \(0.0436450\pi\) | ||||
−0.990614 | + | 0.136686i | \(0.956355\pi\) | |||||||
\(930\) | 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 | \(0.342303\pi\) | ||||
−0.475401 | + | 0.879769i | \(0.657697\pi\) | |||||||
\(938\) | −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 | \(0.208242\pi\) | ||||
−0.793527 | + | 0.608535i | \(0.791758\pi\) | |||||||
\(954\) | 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 | \(-0.911764\pi\) | ||
0.961825 | − | 0.273666i | \(-0.0882364\pi\) | |||||||
\(984\) | −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 | \(-0.872306\pi\) | ||
0.920607 | − | 0.390490i | \(-0.127694\pi\) | |||||||
\(992\) | − | 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 | \(-0.844593\pi\) | ||
0.883166 | − | 0.469060i | \(-0.155407\pi\) | |||||||
\(998\) | −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.42.1 | ✓ | 12 | |
3.2 | odd | 2 | 387.5.b.c.343.12 | 12 | |||
4.3 | odd | 2 | 688.5.b.d.257.2 | 12 | |||
43.42 | odd | 2 | inner | 43.5.b.b.42.12 | yes | 12 | |
129.128 | even | 2 | 387.5.b.c.343.1 | 12 | |||
172.171 | even | 2 | 688.5.b.d.257.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.5.b.b.42.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
43.5.b.b.42.12 | yes | 12 | 43.42 | odd | 2 | inner | |
387.5.b.c.343.1 | 12 | 129.128 | even | 2 | |||
387.5.b.c.343.12 | 12 | 3.2 | odd | 2 | |||
688.5.b.d.257.2 | 12 | 4.3 | odd | 2 | |||
688.5.b.d.257.11 | 12 | 172.171 | even | 2 |