Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (of order \(4\), degree \(2\), not 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.534694406811304329216.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1201.6 | ||
Root | \(-0.841995 - 1.13624i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1201 |
Dual form | 1600.2.l.h.401.6 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.734294 | − | 0.734294i | 0.423945 | − | 0.423945i | −0.462615 | − | 0.886559i | \(-0.653089\pi\) |
0.886559 | + | 0.462615i | \(0.153089\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.71452i | 0.648029i | 0.946052 | + | 0.324015i | \(0.105033\pi\) | ||||
−0.946052 | + | 0.324015i | \(0.894967\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.92163i | 0.640542i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.82684 | − | 2.82684i | −0.852324 | − | 0.852324i | 0.138095 | − | 0.990419i | \(-0.455902\pi\) |
−0.990419 | + | 0.138095i | \(0.955902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.59462 | − | 2.59462i | 0.719618 | − | 0.719618i | −0.248909 | − | 0.968527i | \(-0.580072\pi\) |
0.968527 | + | 0.248909i | \(0.0800720\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.89939 | −0.460671 | −0.230335 | − | 0.973111i | \(-0.573982\pi\) | ||||
−0.230335 | + | 0.973111i | \(0.573982\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.89623 | − | 2.89623i | 0.664440 | − | 0.664440i | −0.291983 | − | 0.956423i | \(-0.594315\pi\) |
0.956423 | + | 0.291983i | \(0.0943151\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.25896 | + | 1.25896i | 0.274729 | + | 0.274729i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.00613i | − | 0.418306i | −0.977883 | − | 0.209153i | \(-0.932929\pi\) | ||
0.977883 | − | 0.209153i | \(-0.0670707\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.61392 | + | 3.61392i | 0.695499 | + | 0.695499i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.72307 | − | 6.72307i | 1.24844 | − | 1.24844i | 0.292034 | − | 0.956408i | \(-0.405668\pi\) |
0.956408 | − | 0.292034i | \(-0.0943321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.11778 | 1.27839 | 0.639195 | − | 0.769044i | \(-0.279268\pi\) | ||||
0.639195 | + | 0.769044i | \(0.279268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.15146 | −0.722676 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.25207 | − | 2.25207i | −0.370237 | − | 0.370237i | 0.497326 | − | 0.867564i | \(-0.334315\pi\) |
−0.867564 | + | 0.497326i | \(0.834315\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.81042i | − | 0.610156i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.59630i | − | 0.249301i | −0.992201 | − | 0.124650i | \(-0.960219\pi\) | ||
0.992201 | − | 0.124650i | \(-0.0397809\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.06886 | + | 8.06886i | 1.23049 | + | 1.23049i | 0.963776 | + | 0.266715i | \(0.0859381\pi\) |
0.266715 | + | 0.963776i | \(0.414062\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.43823 | 0.647383 | 0.323691 | − | 0.946163i | \(-0.395076\pi\) | ||||
0.323691 | + | 0.946163i | \(0.395076\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.06040 | 0.580058 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.39471 | + | 1.39471i | −0.195299 | + | 0.195299i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.481758 | + | 0.481758i | 0.0661746 | + | 0.0661746i | 0.739420 | − | 0.673245i | \(-0.235100\pi\) |
−0.673245 | + | 0.739420i | \(0.735100\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.25336i | − | 0.563372i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.08580 | + | 3.08580i | 0.401737 | + | 0.401737i | 0.878845 | − | 0.477108i | \(-0.158315\pi\) |
−0.477108 | + | 0.878845i | \(0.658315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.46410 | − | 3.46410i | 0.443533 | − | 0.443533i | −0.449665 | − | 0.893197i | \(-0.648457\pi\) |
0.893197 | + | 0.449665i | \(0.148457\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.29468 | −0.415090 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.80454 | + | 1.80454i | −0.220460 | + | 0.220460i | −0.808692 | − | 0.588232i | \(-0.799824\pi\) |
0.588232 | + | 0.808692i | \(0.299824\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.47309 | − | 1.47309i | −0.177339 | − | 0.177339i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.379150i | 0.0449969i | 0.999747 | + | 0.0224984i | \(0.00716208\pi\) | ||||
−0.999747 | + | 0.0224984i | \(0.992838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.37718i | 0.980475i | 0.871589 | + | 0.490237i | \(0.163090\pi\) | ||||
−0.871589 | + | 0.490237i | \(0.836910\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.84668 | − | 4.84668i | 0.552331 | − | 0.552331i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.2566 | 1.26646 | 0.633231 | − | 0.773963i | \(-0.281728\pi\) | ||||
0.633231 | + | 0.773963i | \(0.281728\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.457524 | −0.0508360 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.24890 | + | 8.24890i | −0.905435 | + | 0.905435i | −0.995900 | − | 0.0904649i | \(-0.971165\pi\) |
0.0904649 | + | 0.995900i | \(0.471165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 9.87341i | − | 1.05854i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 11.9820i | − | 1.27009i | −0.772474 | − | 0.635046i | \(-0.780981\pi\) | ||
0.772474 | − | 0.635046i | \(-0.219019\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.44854 | + | 4.44854i | 0.466334 | + | 0.466334i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.22654 | − | 5.22654i | 0.541967 | − | 0.541967i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.50543 | −0.660526 | −0.330263 | − | 0.943889i | \(-0.607137\pi\) | ||||
−0.330263 | + | 0.943889i | \(0.607137\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.43213 | − | 5.43213i | 0.545949 | − | 0.545949i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.72307 | − | 6.72307i | −0.668970 | − | 0.668970i | 0.288508 | − | 0.957478i | \(-0.406841\pi\) |
−0.957478 | + | 0.288508i | \(0.906841\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.1733i | − | 1.49506i | −0.664225 | − | 0.747532i | \(-0.731238\pi\) | ||
0.664225 | − | 0.747532i | \(-0.268762\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.69781 | − | 1.69781i | −0.164134 | − | 0.164134i | 0.620262 | − | 0.784395i | \(-0.287026\pi\) |
−0.784395 | + | 0.620262i | \(0.787026\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.11120 | + | 3.11120i | −0.297999 | + | 0.297999i | −0.840230 | − | 0.542231i | \(-0.817580\pi\) |
0.542231 | + | 0.840230i | \(0.317580\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.30735 | −0.313920 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.8259 | −1.48877 | −0.744387 | − | 0.667748i | \(-0.767258\pi\) | ||||
−0.744387 | + | 0.667748i | \(0.767258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.98589 | + | 4.98589i | 0.460946 | + | 0.460946i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.25656i | − | 0.298528i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.98203i | 0.452912i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.17216 | − | 1.17216i | −0.105690 | − | 0.105690i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.3239 | −1.62598 | −0.812991 | − | 0.582276i | \(-0.802162\pi\) | ||||
−0.812991 | + | 0.582276i | \(0.802162\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.8498 | 1.04332 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2036 | − | 10.2036i | 0.891491 | − | 0.891491i | −0.103172 | − | 0.994663i | \(-0.532899\pi\) |
0.994663 | + | 0.103172i | \(0.0328994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.96565 | + | 4.96565i | 0.430577 | + | 0.430577i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.9845i | 1.28021i | 0.768286 | + | 0.640107i | \(0.221110\pi\) | ||||
−0.768286 | + | 0.640107i | \(0.778890\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.29094 | − | 8.29094i | −0.703228 | − | 0.703228i | 0.261874 | − | 0.965102i | \(-0.415660\pi\) |
−0.965102 | + | 0.261874i | \(0.915660\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.25896 | − | 3.25896i | 0.274454 | − | 0.274454i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.6691 | −1.22670 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.98153 | − | 2.98153i | 0.245912 | − | 0.245912i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.30735 | + | 7.30735i | 0.598642 | + | 0.598642i | 0.939951 | − | 0.341309i | \(-0.110870\pi\) |
−0.341309 | + | 0.939951i | \(0.610870\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.56873i | − | 0.371798i | −0.982569 | − | 0.185899i | \(-0.940480\pi\) | ||
0.982569 | − | 0.185899i | \(-0.0595197\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 3.64992i | − | 0.295079i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.52966 | + | 1.52966i | −0.122080 | + | 0.122080i | −0.765507 | − | 0.643427i | \(-0.777512\pi\) |
0.643427 | + | 0.765507i | \(0.277512\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.707504 | 0.0561087 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.43955 | 0.271075 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1361 | − | 10.1361i | 0.793918 | − | 0.793918i | −0.188211 | − | 0.982129i | \(-0.560269\pi\) |
0.982129 | + | 0.188211i | \(0.0602689\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.57967i | 0.199621i | 0.995006 | + | 0.0998105i | \(0.0318237\pi\) | ||||
−0.995006 | + | 0.0998105i | \(0.968176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 0.464102i | − | 0.0357001i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.56547 | + | 5.56547i | 0.425602 | + | 0.425602i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1773 | − | 14.1773i | 1.07788 | − | 1.07788i | 0.0811779 | − | 0.996700i | \(-0.474132\pi\) |
0.996700 | − | 0.0811779i | \(-0.0258682\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.53177 | 0.340629 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.88067 | + | 9.88067i | −0.738516 | + | 0.738516i | −0.972291 | − | 0.233775i | \(-0.924892\pi\) |
0.233775 | + | 0.972291i | \(0.424892\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.20514 | + | 6.20514i | 0.461224 | + | 0.461224i | 0.899057 | − | 0.437832i | \(-0.144254\pi\) |
−0.437832 | + | 0.899057i | \(0.644254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.08733i | − | 0.376067i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.36928 | + | 5.36928i | 0.392641 | + | 0.392641i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.19615 | + | 6.19615i | −0.450704 | + | 0.450704i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.9282 | −1.36960 | −0.684798 | − | 0.728733i | \(-0.740110\pi\) | ||||
−0.684798 | + | 0.728733i | \(0.740110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.42987 | −0.318869 | −0.159434 | − | 0.987209i | \(-0.550967\pi\) | ||||
−0.159434 | + | 0.987209i | \(0.550967\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.39341 | + | 6.39341i | 0.455511 | + | 0.455511i | 0.897179 | − | 0.441667i | \(-0.145613\pi\) |
−0.441667 | + | 0.897179i | \(0.645613\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.85641i | 0.415150i | 0.978219 | + | 0.207575i | \(0.0665570\pi\) | ||||
−0.978219 | + | 0.207575i | \(0.933443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.65013i | 0.186926i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.5269 | + | 11.5269i | 0.809027 | + | 0.809027i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.85503 | 0.267943 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.3743 | −1.13264 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.60373 | + | 7.60373i | −0.523462 | + | 0.523462i | −0.918615 | − | 0.395153i | \(-0.870692\pi\) |
0.395153 | + | 0.918615i | \(0.370692\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.278408 | + | 0.278408i | 0.0190762 | + | 0.0190762i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.2036i | 0.828435i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.15131 | + | 6.15131i | 0.415667 | + | 0.415667i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.92820 | + | 4.92820i | −0.331507 | + | 0.331507i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.22430 | 0.617705 | 0.308853 | − | 0.951110i | \(-0.400055\pi\) | ||||
0.308853 | + | 0.951110i | \(0.400055\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.21725 | + | 9.21725i | −0.611770 | + | 0.611770i | −0.943407 | − | 0.331637i | \(-0.892399\pi\) |
0.331637 | + | 0.943407i | \(0.392399\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.63811 | − | 1.63811i | −0.108250 | − | 0.108250i | 0.650907 | − | 0.759157i | \(-0.274389\pi\) |
−0.759157 | + | 0.650907i | \(0.774389\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 7.11778i | − | 0.468315i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.3798i | 0.811026i | 0.914089 | + | 0.405513i | \(0.132907\pi\) | ||||
−0.914089 | + | 0.405513i | \(0.867093\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.26562 | − | 8.26562i | 0.536910 | − | 0.536910i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.77449 | −0.502890 | −0.251445 | − | 0.967872i | \(-0.580906\pi\) | ||||
−0.251445 | + | 0.967872i | \(0.580906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.47068 | −0.223566 | −0.111783 | − | 0.993733i | \(-0.535656\pi\) | ||||
−0.111783 | + | 0.993733i | \(0.535656\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.1777 | + | 11.1777i | −0.717051 | + | 0.717051i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 15.0292i | − | 0.956286i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.1142i | 0.767708i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.94765 | − | 8.94765i | −0.564771 | − | 0.564771i | 0.365888 | − | 0.930659i | \(-0.380765\pi\) |
−0.930659 | + | 0.365888i | \(0.880765\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.67100 | + | 5.67100i | −0.356533 | + | 0.356533i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.62228 | 0.225952 | 0.112976 | − | 0.993598i | \(-0.463962\pi\) | ||||
0.112976 | + | 0.993598i | \(0.463962\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.86122 | − | 3.86122i | 0.239925 | − | 0.239925i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.9192 | + | 12.9192i | 0.799680 | + | 0.799680i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 13.7416i | − | 0.847345i | −0.905815 | − | 0.423673i | \(-0.860741\pi\) | ||
0.905815 | − | 0.423673i | \(-0.139259\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.79833 | − | 8.79833i | −0.538449 | − | 0.538449i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.22240 | − | 4.22240i | 0.257444 | − | 0.257444i | −0.566570 | − | 0.824014i | \(-0.691730\pi\) |
0.824014 | + | 0.566570i | \(0.191730\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.40015 | 0.328036 | 0.164018 | − | 0.986457i | \(-0.447555\pi\) | ||||
0.164018 | + | 0.986457i | \(0.447555\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.53307 | 0.395399 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.08733 | − | 5.08733i | −0.305668 | − | 0.305668i | 0.537558 | − | 0.843227i | \(-0.319347\pi\) |
−0.843227 | + | 0.537558i | \(0.819347\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.6777i | 0.818863i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.2780i | − | 1.26934i | −0.772784 | − | 0.634669i | \(-0.781136\pi\) | ||
0.772784 | − | 0.634669i | \(-0.218864\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.08521 | + | 4.08521i | 0.242840 | + | 0.242840i | 0.818024 | − | 0.575184i | \(-0.195069\pi\) |
−0.575184 | + | 0.818024i | \(0.695069\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.73690 | 0.161554 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3923 | −0.787783 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.77689 | + | 4.77689i | −0.280026 | + | 0.280026i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.40400 | + | 7.40400i | 0.432547 | + | 0.432547i | 0.889494 | − | 0.456947i | \(-0.151057\pi\) |
−0.456947 | + | 0.889494i | \(0.651057\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 20.4319i | − | 1.18558i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.20514 | − | 5.20514i | −0.301021 | − | 0.301021i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.8343 | + | 13.8343i | −0.797394 | + | 0.797394i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.87341 | −0.567212 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.6634 | − | 16.6634i | 0.951030 | − | 0.951030i | −0.0478262 | − | 0.998856i | \(-0.515229\pi\) |
0.998856 | + | 0.0478262i | \(0.0152294\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.1416 | − | 11.1416i | −0.633825 | − | 0.633825i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.9072i | 1.24224i | 0.783714 | + | 0.621122i | \(0.213323\pi\) | ||||
−0.783714 | + | 0.621122i | \(0.786677\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4820i | 0.705525i | 0.935713 | + | 0.352763i | \(0.114758\pi\) | ||||
−0.935713 | + | 0.352763i | \(0.885242\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.24325 | + | 4.24325i | −0.238324 | + | 0.238324i | −0.816156 | − | 0.577832i | \(-0.803899\pi\) |
0.577832 | + | 0.816156i | \(0.303899\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −38.0100 | −2.12815 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.49338 | −0.139167 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.50108 | + | 5.50108i | −0.306088 | + | 0.306088i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.56907i | 0.252670i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.60946i | 0.419523i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.10377 | − | 1.10377i | −0.0606688 | − | 0.0606688i | 0.676121 | − | 0.736790i | \(-0.263659\pi\) |
−0.736790 | + | 0.676121i | \(0.763659\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.32763 | − | 4.32763i | 0.237152 | − | 0.237152i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.47635 | −0.407263 | −0.203631 | − | 0.979048i | \(-0.565274\pi\) | ||||
−0.203631 | + | 0.979048i | \(0.565274\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.6208 | + | 11.6208i | −0.631158 | + | 0.631158i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.1208 | − | 20.1208i | −1.08960 | − | 1.08960i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.9633i | 1.02392i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.56074 | + | 8.56074i | 0.459565 | + | 0.459565i | 0.898512 | − | 0.438948i | \(-0.144649\pi\) |
−0.438948 | + | 0.898512i | \(0.644649\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.91567 | + | 7.91567i | −0.423716 | + | 0.423716i | −0.886481 | − | 0.462765i | \(-0.846857\pi\) |
0.462765 | + | 0.886481i | \(0.346857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.7535 | 1.00099 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.67314 | 0.514849 | 0.257425 | − | 0.966298i | \(-0.417126\pi\) | ||||
0.257425 | + | 0.966298i | \(0.417126\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.39127 | − | 2.39127i | −0.126559 | − | 0.126559i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 17.0867i | − | 0.901799i | −0.892575 | − | 0.450900i | \(-0.851103\pi\) | ||
0.892575 | − | 0.450900i | \(-0.148897\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.22373i | 0.117038i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.65827 | + | 3.65827i | 0.192010 | + | 0.192010i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.4500 | 0.702086 | 0.351043 | − | 0.936359i | \(-0.385827\pi\) | ||||
0.351043 | + | 0.936359i | \(0.385827\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.06750 | 0.159688 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.825987 | + | 0.825987i | −0.0428831 | + | 0.0428831i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0271 | − | 12.0271i | −0.622740 | − | 0.622740i | 0.323491 | − | 0.946231i | \(-0.395143\pi\) |
−0.946231 | + | 0.323491i | \(0.895143\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 34.8876i | − | 1.79680i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.1552 | + | 19.1552i | 0.983936 | + | 0.983936i | 0.999873 | − | 0.0159369i | \(-0.00507308\pi\) |
−0.0159369 | + | 0.999873i | \(0.505073\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.4551 | + | 13.4551i | −0.689327 | + | 0.689327i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.7503 | 0.907000 | 0.453500 | − | 0.891256i | \(-0.350175\pi\) | ||||
0.453500 | + | 0.891256i | \(0.350175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.5053 | + | 15.5053i | −0.788181 | + | 0.788181i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.18654 | + | 1.18654i | 0.0601602 | + | 0.0601602i | 0.736547 | − | 0.676387i | \(-0.236455\pi\) |
−0.676387 | + | 0.736547i | \(0.736455\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.81042i | 0.192701i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 14.9848i | − | 0.755886i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.74478 | + | 4.74478i | −0.238134 | + | 0.238134i | −0.816077 | − | 0.577943i | \(-0.803855\pi\) |
0.577943 | + | 0.816077i | \(0.303855\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.29250 | 0.365081 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.632677 | 0.0315944 | 0.0157972 | − | 0.999875i | \(-0.494971\pi\) | ||||
0.0157972 | + | 0.999875i | \(0.494971\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.4679 | − | 18.4679i | 0.919953 | − | 0.919953i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.7324i | 0.631124i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.3809i | 1.30445i | 0.758024 | + | 0.652226i | \(0.226165\pi\) | ||||
−0.758024 | + | 0.652226i | \(0.773835\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.0030 | + | 11.0030i | 0.542739 | + | 0.542739i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.29069 | + | 5.29069i | −0.260338 | + | 0.260338i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.1760 | −0.596260 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.37589 | + | 1.37589i | −0.0672167 | + | 0.0672167i | −0.739916 | − | 0.672699i | \(-0.765135\pi\) |
0.672699 | + | 0.739916i | \(0.265135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.65671 | + | 6.65671i | 0.324428 | + | 0.324428i | 0.850463 | − | 0.526035i | \(-0.176322\pi\) |
−0.526035 | + | 0.850463i | \(0.676322\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.52862i | 0.414676i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.93929 | + | 5.93929i | 0.287422 | + | 0.287422i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.7715 | + | 10.7715i | −0.520051 | + | 0.520051i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.08798 | −0.196911 | −0.0984556 | − | 0.995141i | \(-0.531390\pi\) | ||||
−0.0984556 | + | 0.995141i | \(0.531390\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.2913 | −1.40765 | −0.703826 | − | 0.710373i | \(-0.748526\pi\) | ||||
−0.703826 | + | 0.710373i | \(0.748526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.81020 | − | 5.81020i | −0.277940 | − | 0.277940i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.9790i | 1.28764i | 0.765178 | + | 0.643819i | \(0.222651\pi\) | ||||
−0.765178 | + | 0.643819i | \(0.777349\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.80258i | 0.371551i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.5286 | − | 14.5286i | −0.690276 | − | 0.690276i | 0.272017 | − | 0.962293i | \(-0.412309\pi\) |
−0.962293 | + | 0.272017i | \(0.912309\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.7315 | 0.507582 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.1572 | −1.09286 | −0.546428 | − | 0.837506i | \(-0.684013\pi\) | ||||
−0.546428 | + | 0.837506i | \(0.684013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.51249 | + | 4.51249i | −0.212485 | + | 0.212485i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.35479 | − | 3.35479i | −0.157622 | − | 0.157622i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.7026i | 1.76365i | 0.471572 | + | 0.881827i | \(0.343687\pi\) | ||||
−0.471572 | + | 0.881827i | \(0.656313\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.86425 | − | 6.86425i | −0.320396 | − | 0.320396i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.3737 | − | 11.3737i | 0.529727 | − | 0.529727i | −0.390764 | − | 0.920491i | \(-0.627789\pi\) |
0.920491 | + | 0.390764i | \(0.127789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.94895 | −0.369419 | −0.184710 | − | 0.982793i | \(-0.559134\pi\) | ||||
−0.184710 | + | 0.982793i | \(0.559134\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.34999 | + | 5.34999i | −0.247568 | + | 0.247568i | −0.819972 | − | 0.572404i | \(-0.806011\pi\) |
0.572404 | + | 0.819972i | \(0.306011\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.09394 | − | 3.09394i | −0.142865 | − | 0.142865i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.24643i | 0.103510i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 45.6187i | − | 2.09755i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.925759 | + | 0.925759i | −0.0423876 | + | 0.0423876i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.58973 | −0.438166 | −0.219083 | − | 0.975706i | \(-0.570307\pi\) | ||||
−0.219083 | + | 0.975706i | \(0.570307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.6865 | −0.532859 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.52564 | − | 2.52564i | 0.114921 | − | 0.114921i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.6487i | 1.66071i | 0.557232 | + | 0.830357i | \(0.311863\pi\) | ||||
−0.557232 | + | 0.830357i | \(0.688137\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 14.8857i | − | 0.673154i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.4273 | − | 23.4273i | −1.05726 | − | 1.05726i | −0.998258 | − | 0.0590019i | \(-0.981208\pi\) |
−0.0590019 | − | 0.998258i | \(-0.518792\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7697 | + | 12.7697i | −0.575120 | + | 0.575120i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.650063 | −0.0291593 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.50152 | + | 9.50152i | −0.425346 | + | 0.425346i | −0.887040 | − | 0.461693i | \(-0.847242\pi\) |
0.461693 | + | 0.887040i | \(0.347242\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.89424 | + | 1.89424i | 0.0846283 | + | 0.0846283i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.6875i | 0.922411i | 0.887293 | + | 0.461206i | \(0.152583\pi\) | ||||
−0.887293 | + | 0.461206i | \(0.847417\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.340787 | − | 0.340787i | −0.0151349 | − | 0.0151349i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.6381 | + | 11.6381i | −0.515850 | + | 0.515850i | −0.916313 | − | 0.400463i | \(-0.868849\pi\) |
0.400463 | + | 0.916313i | \(0.368849\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.3629 | −0.635377 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.9335 | 0.924235 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.5462 | − | 12.5462i | −0.551780 | − | 0.551780i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 20.8205i | − | 0.913921i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.18654i | 0.227227i | 0.993525 | + | 0.113613i | \(0.0362425\pi\) | ||||
−0.993525 | + | 0.113613i | \(0.963758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.9589 | − | 26.9589i | −1.17883 | − | 1.17883i | −0.980043 | − | 0.198788i | \(-0.936300\pi\) |
−0.198788 | − | 0.980043i | \(-0.563700\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.5195 | −0.588917 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.9755 | 0.825020 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.92976 | + | 5.92976i | −0.257330 | + | 0.257330i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.14180 | − | 4.14180i | −0.179401 | − | 0.179401i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.5106i | 0.626179i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.4781 | − | 11.4781i | −0.494397 | − | 0.494397i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.4945 | − | 27.4945i | 1.18208 | − | 1.18208i | 0.202878 | − | 0.979204i | \(-0.434971\pi\) |
0.979204 | − | 0.202878i | \(-0.0650294\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.11278 | 0.391067 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.5197 | − | 22.5197i | 0.962873 | − | 0.962873i | −0.0364619 | − | 0.999335i | \(-0.511609\pi\) |
0.999335 | + | 0.0364619i | \(0.0116088\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.65671 | + | 6.65671i | 0.284101 | + | 0.284101i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 38.9431i | − | 1.65903i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.2996i | 0.820704i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.7333 | + | 13.7333i | −0.581897 | + | 0.581897i | −0.935424 | − | 0.353527i | \(-0.884982\pi\) |
0.353527 | + | 0.935424i | \(0.384982\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.8713 | 1.77097 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.88525 | 0.332916 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.229223 | − | 0.229223i | 0.00966061 | − | 0.00966061i | −0.702260 | − | 0.711921i | \(-0.747826\pi\) |
0.711921 | + | 0.702260i | \(0.247826\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.784437i | − | 0.0329433i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 23.0376i | − | 0.965787i | −0.875679 | − | 0.482894i | \(-0.839586\pi\) | ||
0.875679 | − | 0.482894i | \(-0.160414\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.8610 | + | 11.8610i | 0.496367 | + | 0.496367i | 0.910305 | − | 0.413938i | \(-0.135847\pi\) |
−0.413938 | + | 0.910305i | \(0.635847\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.8989 | + | 13.8989i | −0.580633 | + | 0.580633i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.7168 | 1.65343 | 0.826715 | − | 0.562621i | \(-0.190207\pi\) | ||||
0.826715 | + | 0.562621i | \(0.190207\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.25282 | + | 3.25282i | −0.135183 | + | 0.135183i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.1429 | − | 14.1429i | −0.586748 | − | 0.586748i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.72371i | − | 0.112804i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.63887 | − | 8.63887i | −0.356564 | − | 0.356564i | 0.505980 | − | 0.862545i | \(-0.331131\pi\) |
−0.862545 | + | 0.505980i | \(0.831131\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.6147 | − | 20.6147i | 0.849414 | − | 0.849414i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.38927 | 0.386223 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.8229 | 1.88172 | 0.940860 | − | 0.338795i | \(-0.110019\pi\) | ||||
0.940860 | + | 0.338795i | \(0.110019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.30032 | + | 4.30032i | 0.176000 | + | 0.176000i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0609i | 0.697090i | 0.937292 | + | 0.348545i | \(0.113324\pi\) | ||||
−0.937292 | + | 0.348545i | \(0.886676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0363i | 1.55153i | 0.631020 | + | 0.775766i | \(0.282636\pi\) | ||||
−0.631020 | + | 0.775766i | \(0.717364\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.46766 | − | 3.46766i | −0.141214 | − | 0.141214i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.67169 | −0.351973 | −0.175987 | − | 0.984393i | \(-0.556312\pi\) | ||||
−0.175987 | + | 0.984393i | \(0.556312\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.9282 | 0.685965 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.5155 | − | 11.5155i | 0.465868 | − | 0.465868i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.9739 | − | 13.9739i | −0.564401 | − | 0.564401i | 0.366153 | − | 0.930554i | \(-0.380675\pi\) |
−0.930554 | + | 0.366153i | \(0.880675\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 37.3904i | − | 1.50528i | −0.658431 | − | 0.752641i | \(-0.728780\pi\) | ||
0.658431 | − | 0.752641i | \(-0.271220\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.2754 | − | 23.2754i | −0.935516 | − | 0.935516i | 0.0625269 | − | 0.998043i | \(-0.480084\pi\) |
−0.998043 | + | 0.0625269i | \(0.980084\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.24998 | − | 7.24998i | 0.290932 | − | 0.290932i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.5435 | 0.823058 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.0236 | + | 12.0236i | −0.480175 | + | 0.480175i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.27756 | + | 4.27756i | 0.170557 | + | 0.170557i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.1834i | 0.763680i | 0.924228 | + | 0.381840i | \(0.124710\pi\) | ||||
−0.924228 | + | 0.381840i | \(0.875290\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.1667i | 0.443838i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.5352 | − | 10.5352i | 0.417420 | − | 0.417420i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.728585 | −0.0288224 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.1765 | −0.638933 | −0.319466 | − | 0.947598i | \(-0.603504\pi\) | ||||
−0.319466 | + | 0.947598i | \(0.603504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.0289 | + | 15.0289i | −0.592681 | + | 0.592681i | −0.938355 | − | 0.345674i | \(-0.887650\pi\) |
0.345674 | + | 0.938355i | \(0.387650\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 49.3812i | − | 1.94138i | −0.240345 | − | 0.970688i | \(-0.577261\pi\) | ||
0.240345 | − | 0.970688i | \(-0.422739\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 17.4461i | − | 0.684821i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.96103 | + | 8.96103i | 0.351210 | + | 0.351210i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.8685 | + | 19.8685i | −0.777514 | + | 0.777514i | −0.979408 | − | 0.201893i | \(-0.935291\pi\) |
0.201893 | + | 0.979408i | \(0.435291\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.0978 | −0.628035 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.94765 | − | 4.94765i | 0.192733 | − | 0.192733i | −0.604143 | − | 0.796876i | \(-0.706484\pi\) |
0.796876 | + | 0.604143i | \(0.206484\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.1602 | + | 12.1602i | 0.472977 | + | 0.472977i | 0.902877 | − | 0.429899i | \(-0.141451\pi\) |
−0.429899 | + | 0.902877i | \(0.641451\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.23750i | 0.281081i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.4873 | − | 13.4873i | −0.522231 | − | 0.522231i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.77335 | − | 6.77335i | 0.261873 | − | 0.261873i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.5849 | −0.756067 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.9882 | 1.27160 | 0.635801 | − | 0.771853i | \(-0.280670\pi\) | ||||
0.635801 | + | 0.771853i | \(0.280670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.4610 | + | 18.4610i | 0.709513 | + | 0.709513i | 0.966433 | − | 0.256920i | \(-0.0827076\pi\) |
−0.256920 | + | 0.966433i | \(0.582708\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 11.1537i | − | 0.428040i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.5363i | 0.518713i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.2374 | − | 12.2374i | −0.468251 | − | 0.468251i | 0.433097 | − | 0.901347i | \(-0.357421\pi\) |
−0.901347 | + | 0.433097i | \(0.857421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.40571 | −0.0917837 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.49996 | 0.0952409 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.46014 | − | 9.46014i | 0.359881 | − | 0.359881i | −0.503888 | − | 0.863769i | \(-0.668098\pi\) |
0.863769 | + | 0.503888i | \(0.168098\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.31352 | + | 9.31352i | 0.353791 | + | 0.353791i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.03201i | 0.114845i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.09039 | + | 9.09039i | 0.343830 | + | 0.343830i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.14714 | + | 5.14714i | −0.194405 | + | 0.194405i | −0.797596 | − | 0.603192i | \(-0.793895\pi\) |
0.603192 | + | 0.797596i | \(0.293895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.0450 | −0.492001 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.5269 | − | 11.5269i | 0.433512 | − | 0.433512i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0125 | + | 18.0125i | 0.676472 | + | 0.676472i | 0.959200 | − | 0.282728i | \(-0.0912395\pi\) |
−0.282728 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.6309i | 0.811222i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 14.2792i | − | 0.534759i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.70875 | + | 5.70875i | −0.213197 | + | 0.213197i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.5017 | 1.28669 | 0.643347 | − | 0.765574i | \(-0.277545\pi\) | ||||
0.643347 | + | 0.765574i | \(0.277545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.0149 | 0.968846 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.54850 | + | 2.54850i | −0.0947796 | + | 0.0947796i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8421i | 0.476288i | 0.971230 | + | 0.238144i | \(0.0765391\pi\) | ||||
−0.971230 | + | 0.238144i | \(0.923461\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.0429i | 0.557143i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.3259 | − | 15.3259i | −0.566851 | − | 0.566851i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.1490 | + | 24.1490i | −0.891965 | + | 0.891965i | −0.994708 | − | 0.102743i | \(-0.967238\pi\) |
0.102743 | + | 0.994708i | \(0.467238\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.2023 | 0.375807 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.9398 | − | 35.9398i | 1.32207 | − | 1.32207i | 0.409966 | − | 0.912101i | \(-0.365540\pi\) |
0.912101 | − | 0.409966i | \(-0.134460\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.0359 | − | 11.0359i | −0.405412 | − | 0.405412i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.9502i | 1.68575i | 0.538109 | + | 0.842875i | \(0.319139\pi\) | ||||
−0.538109 | + | 0.842875i | \(0.680861\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.8513 | − | 15.8513i | −0.579969 | − | 0.579969i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.91094 | − | 2.91094i | 0.106363 | − | 0.106363i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.4820 | 0.893361 | 0.446680 | − | 0.894694i | \(-0.352606\pi\) | ||||
0.446680 | + | 0.894694i | \(0.352606\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.1404 | −0.478863 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.0328 | − | 17.0328i | −0.619067 | − | 0.619067i | 0.326225 | − | 0.945292i | \(-0.394223\pi\) |
−0.945292 | + | 0.326225i | \(0.894223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.32835i | 0.302300i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8.53590i | − | 0.309426i | −0.987959 | − | 0.154713i | \(-0.950555\pi\) | ||
0.987959 | − | 0.154713i | \(-0.0494453\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.33423 | − | 5.33423i | −0.193112 | − | 0.193112i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.0130 | 0.578195 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.87438 | 0.0675917 | 0.0337959 | − | 0.999429i | \(-0.489240\pi\) | ||||
0.0337959 | + | 0.999429i | \(0.489240\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.65982 | − | 2.65982i | 0.0957911 | − | 0.0957911i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.5374 | + | 21.5374i | 0.774645 | + | 0.774645i | 0.978915 | − | 0.204270i | \(-0.0654820\pi\) |
−0.204270 | + | 0.978915i | \(0.565482\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 5.67054i | − | 0.203429i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.62326 | − | 4.62326i | −0.165645 | − | 0.165645i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.07180 | − | 1.07180i | 0.0383519 | − | 0.0383519i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 48.5932 | 1.73658 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.03687 | − | 7.03687i | 0.250837 | − | 0.250837i | −0.570477 | − | 0.821314i | \(-0.693241\pi\) |
0.821314 | + | 0.570477i | \(0.193241\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.0904 | − | 10.0904i | −0.359227 | − | 0.359227i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 27.1339i | − | 0.964770i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 17.9761i | − | 0.638348i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.07933 | + | 8.07933i | −0.286185 | + | 0.286185i | −0.835569 | − | 0.549385i | \(-0.814862\pi\) |
0.549385 | + | 0.835569i | \(0.314862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.42995 | −0.298230 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.0250 | 0.813548 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.6809 | − | 23.6809i | 0.835682 | − | 0.835682i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6.20097i | − | 0.218284i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.40185i | 0.189919i | 0.995481 | + | 0.0949595i | \(0.0302722\pi\) | ||||
−0.995481 | + | 0.0949595i | \(0.969728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3478 | + | 10.3478i | 0.363360 | + | 0.363360i | 0.865049 | − | 0.501688i | \(-0.167288\pi\) |
−0.501688 | + | 0.865049i | \(0.667288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.96530 | − | 3.96530i | 0.139069 | − | 0.139069i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.7385 | 1.63517 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.54843 | + | 8.54843i | −0.298706 | + | 0.298706i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.7321 | + | 10.7321i | 0.374551 | + | 0.374551i | 0.869132 | − | 0.494581i | \(-0.164678\pi\) |
−0.494581 | + | 0.869132i | \(0.664678\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.51588i | 0.122556i | 0.998121 | + | 0.0612780i | \(0.0195176\pi\) | ||||
−0.998121 | + | 0.0612780i | \(0.980482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.7375 | − | 27.7375i | −0.964529 | − | 0.964529i | 0.0348631 | − | 0.999392i | \(-0.488900\pi\) |
−0.999392 | + | 0.0348631i | \(0.988900\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.5849 | − | 19.5849i | 0.680212 | − | 0.680212i | −0.279836 | − | 0.960048i | \(-0.590280\pi\) |
0.960048 | + | 0.279836i | \(0.0902800\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.47119 | −0.259173 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.71231 | −0.267216 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.7231 | + | 25.7231i | 0.889119 | + | 0.889119i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 40.0520i | − | 1.38275i | −0.722496 | − | 0.691375i | \(-0.757005\pi\) | ||
0.722496 | − | 0.691375i | \(-0.242995\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 61.3992i | − | 2.11722i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.6243 | − | 15.6243i | −0.538129 | − | 0.538129i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.54182 | −0.293500 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.99948 | 0.205902 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.51793 | + | 4.51793i | −0.154873 | + | 0.154873i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.7328 | − | 13.7328i | −0.470202 | − | 0.470202i | 0.431778 | − | 0.901980i | \(-0.357886\pi\) |
−0.901980 | + | 0.431778i | \(0.857886\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.9485i | 1.36462i | 0.731065 | + | 0.682308i | \(0.239024\pi\) | ||||
−0.731065 | + | 0.682308i | \(0.760976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.6366 | + | 33.6366i | 1.14766 | + | 1.14766i | 0.987011 | + | 0.160654i | \(0.0513602\pi\) |
0.160654 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.00969 | − | 2.00969i | 0.0684900 | − | 0.0684900i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.5303 | −0.562697 | −0.281349 | − | 0.959606i | \(-0.590782\pi\) | ||||
−0.281349 | + | 0.959606i | \(0.590782\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.83388 | + | 9.83388i | −0.333976 | + | 0.333976i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.8205 | − | 31.8205i | −1.07944 | − | 1.07944i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.36421i | 0.317294i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 12.5010i | − | 0.423095i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.66381 | − | 9.66381i | 0.326324 | − | 0.326324i | −0.524863 | − | 0.851187i | \(-0.675883\pi\) |
0.851187 | + | 0.524863i | \(0.175883\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.8734 | 0.366752 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.4299 | −1.46319 | −0.731596 | − | 0.681739i | \(-0.761224\pi\) | ||||
−0.731596 | + | 0.681739i | \(0.761224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.3879 | − | 22.3879i | 0.753413 | − | 0.753413i | −0.221701 | − | 0.975115i | \(-0.571161\pi\) |
0.975115 | + | 0.221701i | \(0.0711610\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.6913i | 1.06409i | 0.846716 | + | 0.532045i | \(0.178576\pi\) | ||||
−0.846716 | + | 0.532045i | \(0.821424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 31.4168i | − | 1.05368i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.29335 | + | 1.29335i | 0.0433288 | + | 0.0433288i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.8541 | − | 12.8541i | 0.430147 | − | 0.430147i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.64420 | −0.255232 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 47.8533 | − | 47.8533i | 1.59600 | − | 1.59600i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.915049 | − | 0.915049i | −0.0304847 | − | 0.0304847i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.3168i | 0.676102i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.9184 | + | 24.9184i | 0.827401 | + | 0.827401i | 0.987157 | − | 0.159755i | \(-0.0510705\pi\) |
−0.159755 | + | 0.987157i | \(0.551071\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.9192 | − | 12.9192i | 0.428503 | − | 0.428503i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.0459 | 1.55870 | 0.779350 | − | 0.626589i | \(-0.215549\pi\) | ||||
0.779350 | + | 0.626589i | \(0.215549\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.6366 | 1.54345 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.4943 | + | 17.4943i | 0.577712 | + | 0.577712i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 12.5442i | − | 0.413796i | −0.978362 | − | 0.206898i | \(-0.933663\pi\) | ||
0.978362 | − | 0.206898i | \(-0.0663369\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 24.4716i | − | 0.806368i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.983751 | + | 0.983751i | 0.0323806 | + | 0.0323806i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.1573 | 0.957652 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.7421 | 0.877380 | 0.438690 | − | 0.898639i | \(-0.355443\pi\) | ||||
0.438690 | + | 0.898639i | \(0.355443\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.7599 | − | 11.7599i | 0.385414 | − | 0.385414i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.0863 | + | 16.0863i | 0.526642 | + | 0.526642i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.06580i | 0.100155i | 0.998745 | + | 0.0500777i | \(0.0159469\pi\) | ||||
−0.998745 | + | 0.0500777i | \(0.984053\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.16546 | + | 9.16546i | 0.299104 | + | 0.299104i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.6023 | + | 14.6023i | −0.476020 | + | 0.476020i | −0.903856 | − | 0.427836i | \(-0.859276\pi\) |
0.427836 | + | 0.903856i | \(0.359276\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.20239 | −0.104284 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.4872 | + | 29.4872i | −0.958204 | + | 0.958204i | −0.999161 | − | 0.0409570i | \(-0.986959\pi\) |
0.0409570 | + | 0.999161i | \(0.486959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.7356 | + | 21.7356i | 0.705567 | + | 0.705567i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.23158i | 0.202073i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.6807i | 1.09103i | 0.838103 | + | 0.545513i | \(0.183665\pi\) | ||||
−0.838103 | + | 0.545513i | \(0.816335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −27.9105 | + | 27.9105i | −0.902219 | + | 0.902219i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.6913 | −0.829616 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.6628 | 0.634283 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.26256 | − | 3.26256i | 0.105134 | − | 0.105134i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.70089i | 0.279802i | 0.990166 | + | 0.139901i | \(0.0446784\pi\) | ||||
−0.990166 | + | 0.139901i | \(0.955322\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.07881i | 0.259529i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.87523 | + | 5.87523i | 0.188545 | + | 0.188545i | 0.795067 | − | 0.606522i | \(-0.207436\pi\) |
−0.606522 | + | 0.795067i | \(0.707436\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.2150 | − | 14.2150i | 0.455713 | − | 0.455713i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.8541 | −1.33903 | −0.669516 | − | 0.742798i | \(-0.733498\pi\) | ||||
−0.669516 | + | 0.742798i | \(0.733498\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.8713 | + | 33.8713i | −1.08253 | + | 1.08253i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.97856 | − | 5.97856i | −0.190881 | − | 0.190881i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 57.4539i | − | 1.83250i | −0.400612 | − | 0.916248i | \(-0.631203\pi\) | ||
0.400612 | − | 0.916248i | \(-0.368797\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.58758 | + | 5.58758i | 0.177854 | + | 0.177854i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.1872 | − | 16.1872i | 0.514722 | − | 0.514722i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.8205 | −0.407258 | −0.203629 | − | 0.979048i | \(-0.565274\pi\) | ||||
−0.203629 | + | 0.979048i | \(0.565274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.62099 | −0.0514404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.0860 | − | 15.0860i | −0.477777 | − | 0.477777i | 0.426643 | − | 0.904420i | \(-0.359696\pi\) |
−0.904420 | + | 0.426643i | \(0.859696\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 16.2776i | − | 0.514999i |
(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 | 1600.2.l.h.1201.6 | 16 | ||
4.3 | odd | 2 | 400.2.l.i.101.8 | 16 | |||
5.2 | odd | 4 | 320.2.q.c.49.3 | 16 | |||
5.3 | odd | 4 | 320.2.q.c.49.6 | 16 | |||
5.4 | even | 2 | inner | 1600.2.l.h.1201.3 | 16 | ||
16.3 | odd | 4 | 400.2.l.i.301.8 | 16 | |||
16.13 | even | 4 | inner | 1600.2.l.h.401.6 | 16 | ||
20.3 | even | 4 | 80.2.q.c.69.5 | yes | 16 | ||
20.7 | even | 4 | 80.2.q.c.69.4 | yes | 16 | ||
20.19 | odd | 2 | 400.2.l.i.101.1 | 16 | |||
40.3 | even | 4 | 640.2.q.e.609.6 | 16 | |||
40.13 | odd | 4 | 640.2.q.f.609.3 | 16 | |||
40.27 | even | 4 | 640.2.q.e.609.3 | 16 | |||
40.37 | odd | 4 | 640.2.q.f.609.6 | 16 | |||
60.23 | odd | 4 | 720.2.bm.f.469.4 | 16 | |||
60.47 | odd | 4 | 720.2.bm.f.469.5 | 16 | |||
80.3 | even | 4 | 80.2.q.c.29.4 | ✓ | 16 | ||
80.13 | odd | 4 | 320.2.q.c.209.3 | 16 | |||
80.19 | odd | 4 | 400.2.l.i.301.1 | 16 | |||
80.27 | even | 4 | 640.2.q.e.289.6 | 16 | |||
80.29 | even | 4 | inner | 1600.2.l.h.401.3 | 16 | ||
80.37 | odd | 4 | 640.2.q.f.289.3 | 16 | |||
80.43 | even | 4 | 640.2.q.e.289.3 | 16 | |||
80.53 | odd | 4 | 640.2.q.f.289.6 | 16 | |||
80.67 | even | 4 | 80.2.q.c.29.5 | yes | 16 | ||
80.77 | odd | 4 | 320.2.q.c.209.6 | 16 | |||
240.83 | odd | 4 | 720.2.bm.f.109.5 | 16 | |||
240.227 | odd | 4 | 720.2.bm.f.109.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.q.c.29.4 | ✓ | 16 | 80.3 | even | 4 | ||
80.2.q.c.29.5 | yes | 16 | 80.67 | even | 4 | ||
80.2.q.c.69.4 | yes | 16 | 20.7 | even | 4 | ||
80.2.q.c.69.5 | yes | 16 | 20.3 | even | 4 | ||
320.2.q.c.49.3 | 16 | 5.2 | odd | 4 | |||
320.2.q.c.49.6 | 16 | 5.3 | odd | 4 | |||
320.2.q.c.209.3 | 16 | 80.13 | odd | 4 | |||
320.2.q.c.209.6 | 16 | 80.77 | odd | 4 | |||
400.2.l.i.101.1 | 16 | 20.19 | odd | 2 | |||
400.2.l.i.101.8 | 16 | 4.3 | odd | 2 | |||
400.2.l.i.301.1 | 16 | 80.19 | odd | 4 | |||
400.2.l.i.301.8 | 16 | 16.3 | odd | 4 | |||
640.2.q.e.289.3 | 16 | 80.43 | even | 4 | |||
640.2.q.e.289.6 | 16 | 80.27 | even | 4 | |||
640.2.q.e.609.3 | 16 | 40.27 | even | 4 | |||
640.2.q.e.609.6 | 16 | 40.3 | even | 4 | |||
640.2.q.f.289.3 | 16 | 80.37 | odd | 4 | |||
640.2.q.f.289.6 | 16 | 80.53 | odd | 4 | |||
640.2.q.f.609.3 | 16 | 40.13 | odd | 4 | |||
640.2.q.f.609.6 | 16 | 40.37 | odd | 4 | |||
720.2.bm.f.109.4 | 16 | 240.227 | odd | 4 | |||
720.2.bm.f.109.5 | 16 | 240.83 | odd | 4 | |||
720.2.bm.f.469.4 | 16 | 60.23 | odd | 4 | |||
720.2.bm.f.469.5 | 16 | 60.47 | odd | 4 | |||
1600.2.l.h.401.3 | 16 | 80.29 | even | 4 | inner | ||
1600.2.l.h.401.6 | 16 | 16.13 | even | 4 | inner | ||
1600.2.l.h.1201.3 | 16 | 5.4 | even | 2 | inner | ||
1600.2.l.h.1201.6 | 16 | 1.1 | even | 1 | trivial |