Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(257,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.257");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.e (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: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 32 x^{14} + 356 x^{13} + 1348 x^{12} - 8992 x^{11} + 22064 x^{10} + 391324 x^{9} + 724325 x^{8} - 2262056 x^{7} + 45109352 x^{6} + \cdots + 21479188203 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{54}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Root | \(-1.10373 + 0.840249i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.257 |
Dual form | 384.5.e.d.257.1 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −8.70713 | + | 2.27724i | −0.967459 | + | 0.253026i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 28.9306i | 1.15722i | 0.815603 | + | 0.578612i | \(0.196405\pi\) | ||||
−0.815603 | + | 0.578612i | \(0.803595\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.36161 | −0.0481961 | −0.0240981 | − | 0.999710i | \(-0.507671\pi\) | ||||
−0.0240981 | + | 0.999710i | \(0.507671\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 70.6284 | − | 39.6564i | 0.871955 | − | 0.489585i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 21.1756i | − | 0.175005i | −0.996164 | − | 0.0875024i | \(-0.972111\pi\) | ||
0.996164 | − | 0.0875024i | \(-0.0278885\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −259.705 | −1.53671 | −0.768357 | − | 0.640022i | \(-0.778925\pi\) | ||||
−0.768357 | + | 0.640022i | \(0.778925\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −65.8818 | − | 251.903i | −0.292808 | − | 1.11957i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 350.061i | 1.21129i | 0.795737 | + | 0.605643i | \(0.207084\pi\) | ||||
−0.795737 | + | 0.605643i | \(0.792916\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −308.733 | −0.855216 | −0.427608 | − | 0.903964i | \(-0.640644\pi\) | ||||
−0.427608 | + | 0.903964i | \(0.640644\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 20.5629 | − | 5.37795i | 0.0466278 | − | 0.0121949i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 282.768i | − | 0.534532i | −0.963623 | − | 0.267266i | \(-0.913880\pi\) | ||
0.963623 | − | 0.267266i | \(-0.0861203\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −211.979 | −0.339166 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −524.664 | + | 506.131i | −0.719703 | + | 0.694282i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1236.29i | 1.47003i | 0.678051 | + | 0.735015i | \(0.262825\pi\) | ||||
−0.678051 | + | 0.735015i | \(0.737175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −158.246 | −0.164668 | −0.0823338 | − | 0.996605i | \(-0.526237\pi\) | ||||
−0.0823338 | + | 0.996605i | \(0.526237\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 48.2218 | + | 184.379i | 0.0442808 | + | 0.169310i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 68.3228i | − | 0.0557737i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −890.346 | −0.650363 | −0.325181 | − | 0.945652i | \(-0.605425\pi\) | ||||
−0.325181 | + | 0.945652i | \(0.605425\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2261.28 | − | 591.409i | 1.48671 | − | 0.388829i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1787.97i | − | 1.06364i | −0.846858 | − | 0.531819i | \(-0.821509\pi\) | ||
0.846858 | − | 0.531819i | \(-0.178491\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3446.41 | 1.86393 | 0.931965 | − | 0.362549i | \(-0.118094\pi\) | ||||
0.931965 | + | 0.362549i | \(0.118094\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1147.28 | + | 2043.32i | 0.566560 | + | 1.00905i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3405.32i | − | 1.54157i | −0.637097 | − | 0.770784i | \(-0.719865\pi\) | ||
0.637097 | − | 0.770784i | \(-0.280135\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2395.42 | −0.997677 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −797.173 | − | 3048.03i | −0.306487 | − | 1.17187i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 580.891i | 0.206797i | 0.994640 | + | 0.103398i | \(0.0329716\pi\) | ||||
−0.994640 | + | 0.103398i | \(0.967028\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 612.622 | 0.202520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2688.18 | − | 703.058i | 0.827387 | − | 0.216392i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 3755.71i | − | 1.07892i | −0.842012 | − | 0.539458i | \(-0.818629\pi\) | ||
0.842012 | − | 0.539458i | \(-0.181371\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 205.602 | 0.0552544 | 0.0276272 | − | 0.999618i | \(-0.491205\pi\) | ||||
0.0276272 | + | 0.999618i | \(0.491205\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −166.797 | + | 93.6530i | −0.0420249 | + | 0.0235961i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7513.41i | − | 1.77832i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −610.202 | −0.135933 | −0.0679664 | − | 0.997688i | \(-0.521651\pi\) | ||||
−0.0679664 | + | 0.997688i | \(0.521651\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 643.929 | + | 2462.10i | 0.135251 | + | 0.517138i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3017.17i | 0.598527i | 0.954171 | + | 0.299263i | \(0.0967409\pi\) | ||||
−0.954171 | + | 0.299263i | \(0.903259\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5237.06 | 0.982746 | 0.491373 | − | 0.870949i | \(-0.336495\pi\) | ||||
0.491373 | + | 0.870949i | \(0.336495\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1845.73 | − | 482.727i | 0.328130 | − | 0.0858181i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 50.0084i | 0.00843455i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6540.29 | −1.04796 | −0.523978 | − | 0.851732i | \(-0.675553\pi\) | ||||
−0.523978 | + | 0.851732i | \(0.675553\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3415.74 | − | 5601.74i | 0.520612 | − | 0.853793i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13003.3i | − | 1.88754i | −0.330599 | − | 0.943771i | \(-0.607251\pi\) | ||
0.330599 | − | 0.943771i | \(-0.392749\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10127.5 | −1.40173 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2815.34 | − | 10764.6i | −0.371956 | − | 1.42219i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5444.47i | − | 0.687346i | −0.939089 | − | 0.343673i | \(-0.888329\pi\) | ||
0.939089 | − | 0.343673i | \(-0.111671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 613.321 | 0.0740636 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1377.87 | − | 360.363i | 0.159309 | − | 0.0416653i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 8931.83i | − | 0.989676i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1878.51 | 0.199650 | 0.0998250 | − | 0.995005i | \(-0.468172\pi\) | ||||
0.0998250 | + | 0.995005i | \(0.468172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −839.748 | − | 1495.60i | −0.0856798 | − | 0.152596i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10462.0i | 1.02559i | 0.858511 | + | 0.512795i | \(0.171390\pi\) | ||||
−0.858511 | + | 0.512795i | \(0.828610\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8522.68 | 0.803345 | 0.401672 | − | 0.915783i | \(-0.368429\pi\) | ||||
0.401672 | + | 0.915783i | \(0.368429\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 155.587 | + | 594.895i | 0.0141122 | + | 0.0539588i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 21110.3i | − | 1.84385i | −0.387365 | − | 0.921926i | \(-0.626615\pi\) | ||
0.387365 | − | 0.921926i | \(-0.373385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14321.8 | 1.20544 | 0.602718 | − | 0.797954i | \(-0.294084\pi\) | ||||
0.602718 | + | 0.797954i | \(0.294084\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7752.36 | − | 2027.53i | 0.629199 | − | 0.164559i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14376.1i | − | 1.12586i | −0.826505 | − | 0.562929i | \(-0.809674\pi\) | ||
0.826505 | − | 0.562929i | \(-0.190326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8180.63 | 0.618573 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18342.5 | + | 10299.0i | −1.33995 | + | 0.752352i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 826.709i | − | 0.0583793i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14192.6 | 0.969373 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4071.64 | + | 15568.1i | 0.269128 | + | 1.02903i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11948.9i | 0.764732i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19839.4 | 1.23004 | 0.615022 | − | 0.788510i | \(-0.289147\pi\) | ||||
0.615022 | + | 0.788510i | \(0.289147\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −30008.3 | + | 7848.28i | −1.80328 | + | 0.471623i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 26627.1i | 1.55160i | 0.630977 | + | 0.775801i | \(0.282654\pi\) | ||||
−0.630977 | + | 0.775801i | \(0.717346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 729.107 | 0.0412181 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14642.7 | − | 15178.8i | −0.803439 | − | 0.832858i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2627.82i | 0.140009i | 0.997547 | + | 0.0700044i | \(0.0223013\pi\) | ||||
−0.997547 | + | 0.0700044i | \(0.977699\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18817.8 | −0.973958 | −0.486979 | − | 0.873414i | \(-0.661901\pi\) | ||||
−0.486979 | + | 0.873414i | \(0.661901\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7754.73 | + | 29650.6i | 0.390057 | + | 1.49140i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5499.39i | 0.268932i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −35766.7 | −1.70115 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20857.3 | − | 5454.95i | 0.965212 | − | 0.252439i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 40235.0i | − | 1.81231i | −0.422951 | − | 0.906153i | \(-0.639006\pi\) | ||
0.422951 | − | 0.906153i | \(-0.360994\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3711.55 | 0.162780 | 0.0813902 | − | 0.996682i | \(-0.474064\pi\) | ||||
0.0813902 | + | 0.996682i | \(0.474064\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13882.2 | + | 24724.3i | 0.593028 | + | 1.05619i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4578.14i | − | 0.190557i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18538.0 | 0.752079 | 0.376040 | − | 0.926604i | \(-0.377286\pi\) | ||||
0.376040 | + | 0.926604i | \(0.377286\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1322.83 | − | 5057.90i | −0.0523250 | − | 0.200067i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 667.787i | 0.0257624i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18342.9 | −0.690387 | −0.345194 | − | 0.938531i | \(-0.612187\pi\) | ||||
−0.345194 | + | 0.938531i | \(0.612187\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5334.18 | + | 1395.09i | −0.195930 | + | 0.0512428i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 118.074i | − | 0.00423372i | −0.999998 | − | 0.00211686i | \(-0.999326\pi\) | ||
0.999998 | − | 0.00211686i | \(-0.000673819\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 38885.4 | 1.36149 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21805.3 | + | 12243.2i | −0.745710 | + | 0.418701i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 11073.2i | − | 0.369982i | −0.982740 | − | 0.184991i | \(-0.940774\pi\) | ||
0.982740 | − | 0.184991i | \(-0.0592256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 500.612 | 0.0163465 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8552.64 | + | 32701.4i | 0.272994 | + | 1.04381i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 21979.1i | − | 0.685969i | −0.939341 | − | 0.342984i | \(-0.888562\pi\) | ||
0.939341 | − | 0.342984i | \(-0.111438\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −60261.6 | −1.83943 | −0.919716 | − | 0.392584i | \(-0.871581\pi\) | ||||
−0.919716 | + | 0.392584i | \(0.871581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1790.20 | + | 468.204i | −0.0534564 | + | 0.0139808i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 25758.2i | − | 0.752615i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7412.75 | 0.211981 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1239.05 | − | 1195.28i | 0.0346869 | − | 0.0334617i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 64427.5i | 1.76606i | 0.469321 | + | 0.883028i | \(0.344499\pi\) | ||||
−0.469321 | + | 0.883028i | \(0.655501\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3486.80 | −0.0936080 | −0.0468040 | − | 0.998904i | \(-0.514904\pi\) | ||||
−0.0468040 | + | 0.998904i | \(0.514904\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17109.8 | + | 65420.2i | 0.449962 | + | 1.72045i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 37789.8i | − | 0.973737i | −0.873475 | − | 0.486869i | \(-0.838139\pi\) | ||
0.873475 | − | 0.486869i | \(-0.161861\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −54178.5 | −1.36811 | −0.684054 | − | 0.729431i | \(-0.739785\pi\) | ||||
−0.684054 | + | 0.729431i | \(0.739785\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5313.11 | − | 1389.57i | 0.131509 | − | 0.0343946i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2919.65i | − | 0.0708497i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 51727.1 | 1.23087 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11213.6 | − | 19971.4i | −0.261699 | − | 0.466088i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6537.60i | 0.149667i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23635.9 | −0.530894 | −0.265447 | − | 0.964126i | \(-0.585519\pi\) | ||||
−0.265447 | + | 0.964126i | \(0.585519\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6870.82 | − | 26270.9i | −0.151443 | − | 0.579050i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 99706.5i | 2.15698i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 373.714 | 0.00793634 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −45599.7 | + | 11926.0i | −0.950767 | + | 0.248661i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 90912.6i | − | 1.86140i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −47287.6 | −0.950906 | −0.475453 | − | 0.879741i | \(-0.657716\pi\) | ||||
−0.475453 | + | 0.879741i | \(0.657716\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14971.7 | + | 8406.33i | −0.295738 | + | 0.166051i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 48999.1i | − | 0.950902i | −0.879742 | − | 0.475451i | \(-0.842285\pi\) | ||
0.879742 | − | 0.475451i | \(-0.157715\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 46911.9 | 0.894565 | 0.447283 | − | 0.894393i | \(-0.352392\pi\) | ||||
0.447283 | + | 0.894393i | \(0.352392\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −113.881 | − | 435.430i | −0.00213416 | − | 0.00816008i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 54299.1i | 1.00019i | 0.865971 | + | 0.500093i | \(0.166701\pi\) | ||||
−0.865971 | + | 0.500093i | \(0.833299\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 98518.0 | 1.78394 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 56947.2 | − | 14893.8i | 1.01386 | − | 0.265161i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 76506.0i | 1.33937i | 0.742647 | + | 0.669683i | \(0.233570\pi\) | ||||
−0.742647 | + | 0.669683i | \(0.766430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −71695.7 | −1.23441 | −0.617205 | − | 0.786803i | \(-0.711735\pi\) | ||||
−0.617205 | + | 0.786803i | \(0.711735\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16984.8 | + | 56553.5i | −0.287639 | + | 0.957739i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 69301.0i | − | 1.15454i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 80179.3 | 1.31422 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 29611.6 | + | 113221.i | 0.477598 | + | 1.82612i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 46313.1i | 0.735118i | 0.930000 | + | 0.367559i | \(0.119806\pi\) | ||||
−0.930000 | + | 0.367559i | \(0.880194\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5987.77 | −0.0935457 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 88181.4 | − | 23062.7i | 1.35611 | − | 0.354674i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 72961.7i | − | 1.10466i | −0.833625 | − | 0.552330i | \(-0.813739\pi\) | ||
0.833625 | − | 0.552330i | \(-0.186261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2102.65 | 0.0313449 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 49027.0 | + | 87317.5i | 0.719705 | + | 1.28180i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 40584.1i | 0.586738i | 0.955999 | + | 0.293369i | \(0.0947765\pi\) | ||||
−0.955999 | + | 0.293369i | \(0.905224\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16805.5 | −0.239310 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12398.3 | + | 47405.7i | 0.173917 | + | 0.664979i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 42063.7i | − | 0.581304i | −0.956829 | − | 0.290652i | \(-0.906128\pi\) | ||
0.956829 | − | 0.290652i | \(-0.0938722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −129290. | −1.76046 | −0.880228 | − | 0.474551i | \(-0.842611\pi\) | ||||
−0.880228 | + | 0.474551i | \(0.842611\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5340.27 | + | 1396.68i | −0.0716535 | + | 0.0187400i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4488.78i | 0.0593557i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −114230. | −1.48874 | −0.744372 | − | 0.667766i | \(-0.767251\pi\) | ||||
−0.744372 | + | 0.667766i | \(0.767251\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11176.6 | + | 6275.46i | −0.143583 | + | 0.0806189i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 26580.0i | − | 0.336621i | −0.985734 | − | 0.168311i | \(-0.946169\pi\) | ||
0.985734 | − | 0.168311i | \(-0.0538312\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3293.98 | −0.0411290 | −0.0205645 | − | 0.999789i | \(-0.506546\pi\) | ||||
−0.0205645 | + | 0.999789i | \(0.506546\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 20339.9 | + | 77770.6i | 0.250414 | + | 0.957471i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4222.50i | 0.0512632i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −39022.0 | −0.467212 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16356.4 | + | 4277.81i | −0.193153 | + | 0.0505167i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4332.67i | 0.0504685i | 0.999682 | + | 0.0252342i | \(0.00803316\pi\) | ||||
−0.999682 | + | 0.0252342i | \(0.991967\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 108655. | 1.24855 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10717.6 | + | 11110.1i | 0.121503 | + | 0.125951i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 73436.0i | 0.821423i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8139.06 | −0.0898342 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −23824.6 | − | 91094.4i | −0.259501 | − | 0.992217i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5948.18i | 0.0639417i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −102988. | −1.09272 | −0.546360 | − | 0.837551i | \(-0.683987\pi\) | ||||
−0.546360 | + | 0.837551i | \(0.683987\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −74208.2 | + | 19408.2i | −0.777203 | + | 0.203267i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 97799.9i | − | 1.01115i | −0.862781 | − | 0.505577i | \(-0.831280\pi\) | ||
0.862781 | − | 0.505577i | \(-0.168720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −39759.3 | −0.405836 | −0.202918 | − | 0.979196i | \(-0.565042\pi\) | ||||
−0.202918 | + | 0.979196i | \(0.565042\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2709.44 | − | 4825.53i | −0.0273060 | − | 0.0486322i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 33537.2i | − | 0.333740i | −0.985979 | − | 0.166870i | \(-0.946634\pi\) | ||
0.985979 | − | 0.166870i | \(-0.0533661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26179.3 | 0.257262 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 48073.1 | + | 183810.i | 0.466543 | + | 1.78385i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 108076.i | − | 1.03591i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 55051.9 | 0.521202 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −124702. | + | 32614.1i | −1.16621 | + | 0.305007i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8042.04i | 0.0742976i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −36151.9 | −0.329971 | −0.164985 | − | 0.986296i | \(-0.552758\pi\) | ||||
−0.164985 | + | 0.986296i | \(0.552758\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −62883.7 | + | 35308.0i | −0.567087 | + | 0.318408i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 17653.5i | − | 0.157305i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 212846. | 1.87415 | 0.937077 | − | 0.349123i | \(-0.113520\pi\) | ||||
0.937077 | + | 0.349123i | \(0.113520\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 32737.8 | + | 125175.i | 0.284872 | + | 1.08922i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3350.94i | 0.0288176i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11327.3 | 0.0962803 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −71229.9 | + | 18629.2i | −0.598445 | + | 0.156515i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 161089.i | − | 1.33785i | −0.743329 | − | 0.668926i | \(-0.766754\pi\) | ||
0.743329 | − | 0.668926i | \(-0.233246\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −112340. | −0.922327 | −0.461164 | − | 0.887315i | \(-0.652568\pi\) | ||||
−0.461164 | + | 0.887315i | \(0.652568\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 136258. | − | 131445.i | 1.10598 | − | 1.06691i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 13780.1i | − | 0.110586i | −0.998470 | − | 0.0552932i | \(-0.982391\pi\) | ||
0.998470 | − | 0.0552932i | \(-0.0176094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −87288.6 | −0.692629 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1882.61 | + | 7198.26i | 0.0147715 | + | 0.0564796i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 12567.6i | − | 0.0975132i | −0.998811 | − | 0.0487566i | \(-0.984474\pi\) | ||
0.998811 | − | 0.0487566i | \(-0.0155259\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35005.0 | −0.268606 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −123577. | + | 32319.9i | −0.937829 | + | 0.245277i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 151511.i | 1.13726i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −169054. | −1.25514 | −0.627571 | − | 0.778559i | \(-0.715951\pi\) | ||||
−0.627571 | + | 0.778559i | \(0.715951\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −70904.6 | − | 126282.i | −0.520741 | − | 0.927444i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1371.84i | − | 0.00996679i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 238003. | 1.71066 | 0.855331 | − | 0.518082i | \(-0.173354\pi\) | ||||
0.855331 | + | 0.518082i | \(0.173354\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −27210.6 | − | 104041.i | −0.193497 | − | 0.739847i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 321071.i | − | 2.25901i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 203118. | 1.41407 | 0.707034 | − | 0.707180i | \(-0.250033\pi\) | ||||
0.707034 | + | 0.707180i | \(0.250033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −172744. | + | 45179.0i | −1.19002 | + | 0.311234i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 160683.i | 1.09540i | 0.836676 | + | 0.547699i | \(0.184496\pi\) | ||||
−0.836676 | + | 0.547699i | \(0.815504\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1446.77 | −0.00976066 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 243414. | − | 136672.i | 1.62526 | − | 0.912553i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 38824.4i | 0.256570i | 0.991737 | + | 0.128285i | \(0.0409472\pi\) | ||||
−0.991737 | + | 0.128285i | \(0.959053\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 98986.0 | 0.647471 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −60636.1 | − | 231845.i | −0.392596 | − | 1.50111i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 189215.i | − | 1.21272i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −100549. | −0.637967 | −0.318983 | − | 0.947760i | \(-0.603341\pi\) | ||||
−0.318983 | + | 0.947760i | \(0.603341\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6348.43 | + | 1660.35i | −0.0398768 | + | 0.0104293i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25766.4i | 0.160238i | 0.996785 | + | 0.0801189i | \(0.0255300\pi\) | ||||
−0.996785 | + | 0.0801189i | \(0.974470\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 41097.1 | 0.253047 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 162062. | + | 98819.3i | 0.988030 | + | 0.602465i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18853.6i | 0.113817i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 135050. | 0.807324 | 0.403662 | − | 0.914908i | \(-0.367737\pi\) | ||||
0.403662 | + | 0.914908i | \(0.367737\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5984.18 | − | 22880.8i | −0.0354259 | − | 0.135453i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8869.51i | 0.0519996i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 376193. | 2.18431 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 163849. | − | 42852.7i | 0.942265 | − | 0.246437i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 222868.i | − | 1.26946i | −0.772732 | − | 0.634732i | \(-0.781110\pi\) | ||
0.772732 | − | 0.634732i | \(-0.218890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 77824.4 | 0.439088 | 0.219544 | − | 0.975603i | \(-0.429543\pi\) | ||||
0.219544 | + | 0.975603i | \(0.429543\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −135043. | − | 240512.i | −0.754729 | − | 1.34418i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 74205.7i | − | 0.410827i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −485.551 | −0.00266305 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12523.4 | − | 47883.9i | −0.0680469 | − | 0.260181i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 296695.i | − | 1.59718i | −0.601872 | − | 0.798592i | \(-0.705578\pi\) | ||
0.601872 | − | 0.798592i | \(-0.294422\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 155246. | 0.828027 | 0.414014 | − | 0.910271i | \(-0.364127\pi\) | ||||
0.414014 | + | 0.910271i | \(0.364127\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 311426. | − | 81449.4i | 1.64580 | − | 0.430437i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 87299.7i | 0.457141i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 126457. | 0.656165 | 0.328082 | − | 0.944649i | \(-0.393598\pi\) | ||||
0.328082 | + | 0.944649i | \(0.393598\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −169185. | + | 94993.9i | −0.869930 | + | 0.488448i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 145466.i | − | 0.741230i | −0.928787 | − | 0.370615i | \(-0.879147\pi\) | ||
0.928787 | − | 0.370615i | \(-0.120853\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 157512. | 0.795413 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 91624.6 | + | 350331.i | 0.458561 | + | 1.75333i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 287619.i | − | 1.42668i | −0.700820 | − | 0.713338i | \(-0.747182\pi\) | ||
0.700820 | − | 0.713338i | \(-0.252818\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37861.4 | −0.186142 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32317.0 | + | 8452.09i | −0.157483 | + | 0.0411877i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17743.7i | 0.0857082i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −267619. | −1.28140 | −0.640701 | − | 0.767791i | \(-0.721356\pi\) | ||||
−0.640701 | + | 0.767791i | \(0.721356\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −177177. | − | 183665.i | −0.840973 | − | 0.871766i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 85209.3i | − | 0.400945i | −0.979699 | − | 0.200473i | \(-0.935752\pi\) | ||
0.979699 | − | 0.200473i | \(-0.0642478\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −239522. | −1.11734 | −0.558668 | − | 0.829391i | \(-0.688687\pi\) | ||||
−0.558668 | + | 0.829391i | \(0.688687\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10425.5 | + | 39862.5i | 0.0482160 | + | 0.184356i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 225161.i | 1.03243i | 0.856459 | + | 0.516214i | \(0.172659\pi\) | ||||
−0.856459 | + | 0.516214i | \(0.827341\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1441.06 | 0.00655143 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −161413. | + | 42215.4i | −0.727606 | + | 0.190296i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 72979.6i | − | 0.326196i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 65444.9 | 0.290061 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23036.1 | + | 41027.4i | 0.101245 | + | 0.180317i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 210999.i | − | 0.919622i | −0.888017 | − | 0.459811i | \(-0.847917\pi\) | ||
0.888017 | − | 0.459811i | \(-0.152083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 231227. | 0.999421 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1520.71 | − | 5814.51i | −0.00651856 | − | 0.0249241i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 54346.3i | 0.231040i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −346874. | −1.46256 | −0.731280 | − | 0.682077i | \(-0.761077\pi\) | ||||
−0.731280 | + | 0.682077i | \(0.761077\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 159714. | − | 41771.1i | 0.667922 | − | 0.174686i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 46005.6i | 0.190831i | 0.995438 | + | 0.0954153i | \(0.0304179\pi\) | ||||
−0.995438 | + | 0.0954153i | \(0.969582\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −432779. | −1.78063 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 43268.5 | − | 24294.4i | 0.176588 | − | 0.0991507i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 7125.39i | − | 0.0288467i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −266428. | −1.06999 | −0.534994 | − | 0.844856i | \(-0.679686\pi\) | ||||
−0.534994 | + | 0.844856i | \(0.679686\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 268.883 | + | 1028.09i | 0.00107124 | + | 0.00409596i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 54796.2i | − | 0.216578i | −0.994119 | − | 0.108289i | \(-0.965463\pi\) | ||
0.994119 | − | 0.108289i | \(-0.0345372\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −302673. | −1.18684 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −338581. | + | 88551.4i | −1.31718 | + | 0.344492i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 76722.7i | 0.296134i | 0.988977 | + | 0.148067i | \(0.0473052\pi\) | ||||
−0.988977 | + | 0.148067i | \(0.952695\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12367.9 | −0.0473646 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 161981. | − | 156259.i | 0.615502 | − | 0.593761i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 246566.i | 0.929649i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −72109.7 | −0.269782 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25216.3 | + | 96415.8i | 0.0936152 | + | 0.357943i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 400136.i | 1.47412i | 0.675828 | + | 0.737060i | \(0.263786\pi\) | ||||
−0.675828 | + | 0.737060i | \(0.736214\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 285364. | 1.04327 | 0.521634 | − | 0.853169i | \(-0.325323\pi\) | ||||
0.521634 | + | 0.853169i | \(0.325323\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4358.89 | + | 1140.01i | −0.0158146 | + | 0.00413610i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 55395.7i | − | 0.199460i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 199884. | 0.714275 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −148938. | − | 265259.i | −0.528222 | − | 0.940767i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 464345.i | 1.63451i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 610732. | 2.13375 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 50051.7 | + | 191375.i | 0.173568 | + | 0.663647i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 50724.5i | 0.174598i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −321140. | −1.09724 | −0.548619 | − | 0.836073i | \(-0.684846\pi\) | ||||
−0.548619 | + | 0.836073i | \(0.684846\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 524706. | − | 137230.i | 1.77958 | − | 0.465425i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 414338.i | 1.39496i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2543.76 | 0.00850160 | 0.00425080 | − | 0.999991i | \(-0.498647\pi\) | ||||
0.00425080 | + | 0.999991i | \(0.498647\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14521.3 | − | 8153.43i | 0.0481794 | − | 0.0270518i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 381685.i | − | 1.25719i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15445.6 | 0.0505074 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 58657.6 | + | 224280.i | 0.190431 | + | 0.728124i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 265139.i | − | 0.854602i | −0.904109 | − | 0.427301i | \(-0.859464\pi\) | ||
0.904109 | − | 0.427301i | \(-0.140536\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −895047. | −2.86432 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −64543.8 | + | 16880.6i | −0.205083 | + | 0.0536367i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 77729.4i | − | 0.245227i | −0.992454 | − | 0.122614i | \(-0.960872\pi\) | ||
0.992454 | − | 0.122614i | \(-0.0391276\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 415909. | 1.30287 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8066.64 | + | 13229.1i | −0.0250915 | + | 0.0411495i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 147003.i | 0.454047i | 0.973889 | + | 0.227023i | \(0.0728994\pi\) | ||||
−0.973889 | + | 0.227023i | \(0.927101\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −113294. | −0.347484 | −0.173742 | − | 0.984791i | \(-0.555586\pi\) | ||||
−0.173742 | + | 0.984791i | \(0.555586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −146717. | − | 560979.i | −0.446859 | − | 1.70859i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 59940.8i | 0.181295i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −300139. | −0.901512 | −0.450756 | − | 0.892647i | \(-0.648845\pi\) | ||||
−0.450756 | + | 0.892647i | \(0.648845\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30360.1 | − | 7940.28i | 0.0905619 | − | 0.0236853i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30708.7i | 0.0909722i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12300.7 | 0.0361904 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −297955. | − | 530660.i | −0.870640 | − | 1.55062i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 340321.i | 0.987673i | 0.869555 | + | 0.493836i | \(0.164406\pi\) | ||||
−0.869555 | + | 0.493836i | \(0.835594\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48855.6 | 0.140826 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 86056.3 | + | 329041.i | 0.246381 | + | 0.942051i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 457414.i | 1.30077i | 0.759605 | + | 0.650385i | \(0.225392\pi\) | ||||
−0.759605 | + | 0.650385i | \(0.774608\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23917.2 | 0.0675578 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 471739. | − | 123377.i | 1.32359 | − | 0.346168i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 527946.i | 1.47142i | 0.677297 | + | 0.735709i | \(0.263151\pi\) | ||||
−0.677297 | + | 0.735709i | \(0.736849\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −229399. | −0.635101 | −0.317551 | − | 0.948241i | \(-0.602860\pi\) | ||||
−0.317551 | + | 0.948241i | \(0.602860\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −43097.6 | + | 24198.4i | −0.118527 | + | 0.0665507i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 410600.i | 1.12178i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 287358. | 0.779912 | 0.389956 | − | 0.920834i | \(-0.372490\pi\) | ||||
0.389956 | + | 0.920834i | \(0.372490\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6648.73 | + | 25421.7i | 0.0179268 | + | 0.0685442i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 884378.i | 2.36895i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −282301. | −0.751262 | −0.375631 | − | 0.926769i | \(-0.622574\pi\) | ||||
−0.375631 | + | 0.926769i | \(0.622574\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −450395. | + | 117795.i | −1.19081 | + | 0.311442i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 284331.i | 0.746885i | 0.927653 | + | 0.373442i | \(0.121823\pi\) | ||||
−0.927653 | + | 0.373442i | \(0.878177\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 448233. | 1.16983 | 0.584915 | − | 0.811094i | \(-0.301128\pi\) | ||||
0.584915 | + | 0.811094i | \(0.301128\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 143118. | + | 148358.i | 0.371116 | + | 0.384705i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12857.7i | 0.0331274i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −478177. | −1.22413 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14887.7 | − | 56923.7i | −0.0378697 | − | 0.144797i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 311676.i | − | 0.787775i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 564174. | 1.41695 | 0.708475 | − | 0.705736i | \(-0.249383\pi\) | ||||
0.708475 | + | 0.705736i | \(0.249383\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 205801. | − | 53824.6i | 0.513618 | − | 0.134330i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 573965.i | 1.42344i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 622102. | 1.53314 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 119650. | + | 213098.i | 0.293030 | + | 0.521889i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 376472.i | 0.916257i | 0.888886 | + | 0.458128i | \(0.151480\pi\) | ||||
−0.888886 | + | 0.458128i | \(0.848520\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −531024. | −1.28438 | −0.642188 | − | 0.766547i | \(-0.721973\pi\) | ||||
−0.642188 | + | 0.766547i | \(0.721973\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −227055. | − | 868158.i | −0.545774 | − | 2.08679i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 482001.i | 1.15144i | 0.817649 | + | 0.575718i | \(0.195277\pi\) | ||||
−0.817649 | + | 0.575718i | \(0.804723\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −79529.2 | −0.188815 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3253.98 | + | 851.036i | −0.00767809 | + | 0.00200810i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 47193.4i | − | 0.110676i | −0.998468 | − | 0.0553382i | \(-0.982376\pi\) | ||
0.998468 | − | 0.0553382i | \(-0.0176237\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −770336. | −1.79555 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 369885. | − | 207683.i | 0.856911 | − | 0.481138i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 344237.i | − | 0.792660i | −0.918108 | − | 0.396330i | \(-0.870284\pi\) | ||
0.918108 | − | 0.396330i | \(-0.129716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23725.6 | −0.0543018 | −0.0271509 | − | 0.999631i | \(-0.508643\pi\) | ||||
−0.0271509 | + | 0.999631i | \(0.508643\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 207029. | + | 791588.i | 0.470983 | + | 1.80083i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21093.5i | 0.0476985i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 349584. | 0.785778 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 411739. | − | 107685.i | 0.919962 | − | 0.240604i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4353.73i | − | 0.00966979i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 201011. | 0.443804 | 0.221902 | − | 0.975069i | \(-0.428774\pi\) | ||||
0.221902 | + | 0.975069i | \(0.428774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 111218. | − | 107289.i | 0.244099 | − | 0.235477i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 726242.i | − | 1.58454i | −0.610169 | − | 0.792272i | \(-0.708898\pi\) | ||
0.610169 | − | 0.792272i | \(-0.291102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4436.30 | −0.00962235 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 111582. | + | 426641.i | 0.240603 | + | 0.919960i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 316498.i | − | 0.678468i | −0.940702 | − | 0.339234i | \(-0.889832\pi\) | ||
0.940702 | − | 0.339234i | \(-0.110168\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −76024.5 | −0.162021 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −408468. | + | 106829.i | −0.865455 | + | 0.226349i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 150860.i | − | 0.317787i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −299153. | −0.626524 | −0.313262 | − | 0.949667i | \(-0.601422\pi\) | ||||
−0.313262 | + | 0.949667i | \(0.601422\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1983.16 | + | 3532.02i | 0.00412943 | + | 0.00735455i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 544411.i | − | 1.12709i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 625901. | 1.28837 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −123652. | − | 472790.i | −0.253074 | − | 0.967640i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 185762.i | 0.378024i | 0.981975 | + | 0.189012i | \(0.0605286\pi\) | ||||
−0.981975 | + | 0.189012i | \(0.939471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 274879. | 0.556200 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −857810. | + | 224349.i | −1.72589 | + | 0.451383i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 24707.3i | − | 0.0494295i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −279476. | −0.555970 | −0.277985 | − | 0.960585i | \(-0.589667\pi\) | ||||
−0.277985 | + | 0.960585i | \(0.589667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −461930. | + | 259365.i | −0.913771 | + | 0.513064i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 44746.7i | 0.0880202i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −159101. | −0.311215 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −174222. | − | 666148.i | −0.338895 | − | 1.29578i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 252618.i | − | 0.488659i | −0.969692 | − | 0.244330i | \(-0.921432\pi\) | ||
0.969692 | − | 0.244330i | \(-0.0785679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20127.3 | −0.0387181 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 624264. | − | 163268.i | 1.19424 | − | 0.312338i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 262069.i | − | 0.498585i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −478683. | −0.905689 | −0.452844 | − | 0.891590i | \(-0.649591\pi\) | ||||
−0.452844 | + | 0.891590i | \(0.649591\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19103.0 | − | 531098.i | 0.0359457 | − | 0.999354i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.20645e6i | 2.25775i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 554036. | 1.03117 | 0.515585 | − | 0.856838i | \(-0.327575\pi\) | ||||
0.515585 | + | 0.856838i | \(0.327575\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 157815. | + | 603413.i | 0.292128 | + | 1.11697i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12921.4i | 0.0237889i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −268187. | −0.491077 | −0.245538 | − | 0.969387i | \(-0.578965\pi\) | ||||
−0.245538 | + | 0.969387i | \(0.578965\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −698132. | + | 182587.i | −1.27146 | + | 0.332533i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 487745.i | − | 0.883517i | −0.897134 | − | 0.441758i | \(-0.854355\pi\) | ||
0.897134 | − | 0.441758i | \(-0.145645\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.16402e6 | 2.09724 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −515664. | − | 918401.i | −0.924113 | − | 1.64585i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49854.2i | 0.0888665i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −256091. | −0.454061 | −0.227031 | − | 0.973888i | \(-0.572902\pi\) | ||||
−0.227031 | + | 0.973888i | \(0.572902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −105466. | − | 403255.i | −0.186004 | − | 0.711197i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 107377.i | 0.188373i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 138602. | 0.241867 | 0.120934 | − | 0.992661i | \(-0.461411\pi\) | ||||
0.120934 | + | 0.992661i | \(0.461411\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 52136.3 | − | 13635.6i | 0.0905016 | − | 0.0236695i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 487206.i | 0.841286i | 0.907226 | + | 0.420643i | \(0.138195\pi\) | ||||
−0.907226 | + | 0.420643i | \(0.861805\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33822.5 | −0.0580973 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −715288. | + | 401620.i | −1.22224 | + | 0.686266i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 975374.i | 1.65798i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35520.3 | 0.0600654 | 0.0300327 | − | 0.999549i | \(-0.490439\pi\) | ||||
0.0300327 | + | 0.999549i | \(0.490439\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 166151. | + | 635288.i | 0.279508 | + | 1.06871i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 813847.i | 1.36202i | 0.732274 | + | 0.681010i | \(0.238459\pi\) | ||||
−0.732274 | + | 0.681010i | \(0.761541\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33544.8 | 0.0558497 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18308.1 | + | 4788.23i | −0.0303250 | + | 0.00793110i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 552006.i | 0.909639i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 63890.4 | 0.104745 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −625728. | − | 648639.i | −1.02061 | − | 1.05799i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 536315.i | 0.870324i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 100644. | 0.162494 | 0.0812470 | − | 0.996694i | \(-0.474110\pi\) | ||||
0.0812470 | + | 0.996694i | \(0.474110\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −92419.6 | − | 353371.i | −0.148460 | − | 0.567645i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33950.7i | 0.0542620i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53395.7 | −0.0849102 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 146328. | − | 38270.2i | 0.231523 | − | 0.0605517i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 603149.i | − | 0.949529i | −0.880113 | − | 0.474764i | \(-0.842533\pi\) | ||
0.880113 | − | 0.474764i | \(-0.157467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.19207e6 | 1.86728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −215908. | − | 384534.i | −0.336515 | − | 0.599335i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 110898.i | − | 0.171985i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19319.5 | −0.0298128 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 95789.1 | + | 366255.i | 0.147085 | + | 0.562388i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 443718.i | 0.677970i | 0.940792 | + | 0.338985i | \(0.110084\pi\) | ||||
−0.940792 | + | 0.338985i | \(0.889916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −782028. | −1.18900 | −0.594498 | − | 0.804097i | \(-0.702649\pi\) | ||||
−0.594498 | + | 0.804097i | \(0.702649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.12574e6 | − | 294423.i | 1.70317 | − | 0.445442i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 530671.i | − | 0.798933i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.06402e6 | −1.59406 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 43317.8 | − | 24322.1i | 0.0645802 | − | 0.0362605i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.21496e6i | 1.80251i | 0.433292 | + | 0.901254i | \(0.357352\pi\) | ||||
−0.433292 | + | 0.901254i | \(0.642648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 126836. | 0.187260 | 0.0936299 | − | 0.995607i | \(-0.470153\pi\) | ||||
0.0936299 | + | 0.995607i | \(0.470153\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10222.0 | − | 39084.4i | −0.0150186 | − | 0.0574243i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.11286e6i | − | 1.62715i | −0.581458 | − | 0.813577i | \(-0.697517\pi\) | ||
0.581458 | − | 0.813577i | \(-0.302483\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 759496. | 1.10514 | 0.552569 | − | 0.833467i | \(-0.313648\pi\) | ||||
0.552569 | + | 0.833467i | \(0.313648\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 994614. | − | 260128.i | 1.44030 | − | 0.376691i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 838545.i | − | 1.20847i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3415.96 | 0.00489937 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 83025.7 | − | 80093.1i | 0.118512 | − | 0.114326i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 965454.i | − | 1.37154i | −0.727820 | − | 0.685769i | \(-0.759466\pi\) | ||
0.727820 | − | 0.685769i | \(-0.240534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −821144. | −1.16099 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 60528.9 | + | 231435.i | 0.0851741 | + | 0.325668i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.12498e6i | 1.57555i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33517.4 | −0.0467200 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28681.1 | − | 7501.17i | 0.0397906 | − | 0.0104067i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 251761.i | 0.347640i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.09387e6 | −1.50337 | −0.751686 | − | 0.659522i | \(-0.770759\pi\) | ||||
−0.751686 | + | 0.659522i | \(0.770759\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −354204. | − | 630840.i | −0.484531 | − | 0.862953i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.10568e6i | 1.50545i | 0.658333 | + | 0.752727i | \(0.271262\pi\) | ||||
−0.658333 | + | 0.752727i | \(0.728738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 780160. | 1.05730 | 0.528649 | − | 0.848841i | \(-0.322699\pi\) | ||||
0.528649 | + | 0.848841i | \(0.322699\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9615.63 | − | 36765.8i | −0.0129709 | − | 0.0495950i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 610965.i | − | 0.820341i | −0.912009 | − | 0.410170i | \(-0.865469\pi\) | ||
0.912009 | − | 0.410170i | \(-0.134531\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 320354. | 0.428152 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 339770. | − | 88862.4i | 0.452009 | − | 0.118217i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 138494.i | 0.183397i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 158472. | 0.208890 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 132676. | − | 74494.9i | 0.174086 | − | 0.0977457i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 28218.7i | − | 0.0368571i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −141276. | −0.183684 | −0.0918419 | − | 0.995774i | \(-0.529275\pi\) | ||||
−0.0918419 | + | 0.995774i | \(0.529275\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9866.51 | − | 37725.1i | −0.0127699 | − | 0.0488262i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 410601.i | − | 0.529016i | −0.964384 | − | 0.264508i | \(-0.914791\pi\) | ||
0.964384 | − | 0.264508i | \(-0.0852095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 609192. | 0.781327 | 0.390663 | − | 0.920534i | \(-0.372246\pi\) | ||||
0.390663 | + | 0.920534i | \(0.372246\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −946072. | + | 247433.i | −1.20792 | + | 0.315915i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 797723.i | − | 1.01392i | −0.861969 | − | 0.506961i | \(-0.830769\pi\) | ||
0.861969 | − | 0.506961i | \(-0.169231\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −46852.9 | −0.0592834 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −118620. | − | 72330.2i | −0.149418 | − | 0.0911096i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.05134e6i | 1.31837i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 635869. | 0.793819 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −167231. | − | 639417.i | −0.207842 | − | 0.794693i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 195638.i | − | 0.242066i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −203348. | −0.250490 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 70867.9 | − | 18534.6i | 0.0869109 | − | 0.0227304i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.74340e6i | − | 2.12863i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 71090.1 | 0.0864161 | 0.0432081 | − | 0.999066i | \(-0.486242\pi\) | ||||
0.0432081 | + | 0.999066i | \(0.486242\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 414887. | + | 738917.i | 0.502114 | + | 0.894269i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4036.23i | − | 0.00486339i | −0.999997 | − | 0.00243169i | \(-0.999226\pi\) | ||
0.999997 | − | 0.00243169i | \(-0.000774033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −275352. | −0.330329 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13545.4 | − | 51791.6i | −0.0161789 | − | 0.0618610i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 62882.7i | − | 0.0747812i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 604713. | 0.716009 | 0.358004 | − | 0.933720i | \(-0.383457\pi\) | ||||
0.358004 | + | 0.933720i | \(0.383457\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 896728. | − | 234528.i | 1.05716 | − | 0.276487i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 783574.i | − | 0.919764i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 188735. | 0.220581 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 601943. | − | 337979.i | 0.700481 | − | 0.393306i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 136984.i | 0.158722i | 0.996846 | + | 0.0793612i | \(0.0252880\pi\) | ||||
−0.996846 | + | 0.0793612i | \(0.974712\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 739546. | 0.853229 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 222714. | + | 851557.i | 0.255849 | + | 0.978251i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 214455.i | 0.245309i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.68479e6 | 1.91897 | 0.959483 | − | 0.281768i | \(-0.0909209\pi\) | ||||
0.959483 | + | 0.281768i | \(0.0909209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 346190. | − | 90541.5i | 0.392630 | − | 0.102687i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 347602.i | 0.392557i | 0.980548 | + | 0.196278i | \(0.0628857\pi\) | ||||
−0.980548 | + | 0.196278i | \(0.937114\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −505581. | −0.568548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 34580.3 | + | 35846.5i | 0.0387226 | + | 0.0401405i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 67955.1i | 0.0757743i | 0.999282 | + | 0.0378871i | \(0.0120627\pi\) | ||||
−0.999282 | + | 0.0378871i | \(0.987937\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.36009e6 | −1.51020 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 76372.2 | + | 292013.i | 0.0844451 | + | 0.322880i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 760779.i | − | 0.837669i | −0.908063 | − | 0.418835i | \(-0.862439\pi\) | ||
0.908063 | − | 0.418835i | \(-0.137561\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.86392e6 | −2.04372 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −227946. | + | 59616.4i | −0.248891 | + | 0.0650941i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 6205.90i | − | 0.00674788i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −898479. | −0.972885 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −837158. | − | 1.49098e6i | −0.902723 | − | 1.60776i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 100875.i | − | 0.108325i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.63961e6 | −1.75343 | −0.876716 | − | 0.481009i | \(-0.840270\pi\) | ||||
−0.876716 | + | 0.481009i | \(0.840270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 246114. | + | 941028.i | 0.262113 | + | 1.00220i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 487147.i | − | 0.516680i | −0.966054 | − | 0.258340i | \(-0.916825\pi\) | ||
0.966054 | − | 0.258340i | \(-0.0831755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44440.4 | 0.0469410 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −479344. | + | 125366.i | −0.504241 | + | 0.131878i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.10091e6i | − | 1.15336i | −0.816971 | − | 0.576678i | \(-0.804349\pi\) | ||
0.816971 | − | 0.576678i | \(-0.195651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −115290. | −0.120289 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.01152e6 | − | 567951.i | 1.05109 | − | 0.590164i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 812256.i | − | 0.840593i | −0.907387 | − | 0.420297i | \(-0.861926\pi\) | ||
0.907387 | − | 0.420297i | \(-0.138074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.09328e6 | 1.12683 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18313.6 | − | 70023.2i | −0.0187992 | − | 0.0718799i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 974532.i | − | 0.996330i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.01281e6 | −1.03129 | −0.515646 | − | 0.856802i | \(-0.672448\pi\) | ||||
−0.515646 | + | 0.856802i | \(0.672448\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 314780. | − | 82326.5i | 0.319233 | − | 0.0834913i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.56741e6i | − | 1.58321i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 571619. | 0.575064 | 0.287532 | − | 0.957771i | \(-0.407165\pi\) | ||||
0.287532 | + | 0.957771i | \(0.407165\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 467132. | − | 450632.i | 0.468068 | − | 0.451535i |
(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 | 384.5.e.d.257.2 | yes | 16 | |
3.2 | odd | 2 | inner | 384.5.e.d.257.1 | yes | 16 | |
4.3 | odd | 2 | 384.5.e.a.257.15 | ✓ | 16 | ||
8.3 | odd | 2 | 384.5.e.c.257.2 | yes | 16 | ||
8.5 | even | 2 | 384.5.e.b.257.15 | yes | 16 | ||
12.11 | even | 2 | 384.5.e.a.257.16 | yes | 16 | ||
24.5 | odd | 2 | 384.5.e.b.257.16 | yes | 16 | ||
24.11 | even | 2 | 384.5.e.c.257.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.e.a.257.15 | ✓ | 16 | 4.3 | odd | 2 | ||
384.5.e.a.257.16 | yes | 16 | 12.11 | even | 2 | ||
384.5.e.b.257.15 | yes | 16 | 8.5 | even | 2 | ||
384.5.e.b.257.16 | yes | 16 | 24.5 | odd | 2 | ||
384.5.e.c.257.1 | yes | 16 | 24.11 | even | 2 | ||
384.5.e.c.257.2 | yes | 16 | 8.3 | odd | 2 | ||
384.5.e.d.257.1 | yes | 16 | 3.2 | odd | 2 | inner | |
384.5.e.d.257.2 | yes | 16 | 1.1 | even | 1 | trivial |