Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(557,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.557");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.i (of order \(4\), degree \(2\), 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: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 557.14 | ||
Character | \(\chi\) | \(=\) | 1500.557 |
Dual form | 1500.2.i.a.1193.14 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 1.51726 | − | 0.835422i | 0.875989 | − | 0.482331i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.05575 | − | 1.05575i | −0.399037 | − | 0.399037i | 0.478857 | − | 0.877893i | \(-0.341051\pi\) |
−0.877893 | + | 0.478857i | \(0.841051\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.60414 | − | 2.53510i | 0.534713 | − | 0.845034i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.36443i | − | 1.61744i | −0.588196 | − | 0.808719i | \(-0.700161\pi\) | ||
0.588196 | − | 0.808719i | \(-0.299839\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50979 | + | 2.50979i | −0.696090 | + | 0.696090i | −0.963565 | − | 0.267475i | \(-0.913811\pi\) |
0.267475 | + | 0.963565i | \(0.413811\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.79257 | − | 4.79257i | 1.16237 | − | 1.16237i | 0.178414 | − | 0.983955i | \(-0.442903\pi\) |
0.983955 | − | 0.178414i | \(-0.0570967\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.75159i | 0.631258i | 0.948883 | + | 0.315629i | \(0.102216\pi\) | ||||
−0.948883 | + | 0.315629i | \(0.897784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.48384 | − | 0.719849i | −0.542019 | − | 0.157084i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.68934 | + | 3.68934i | 0.769281 | + | 0.769281i | 0.977980 | − | 0.208699i | \(-0.0669230\pi\) |
−0.208699 | + | 0.977980i | \(0.566923\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.316015 | − | 5.18653i | 0.0608170 | − | 0.998149i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.14208 | −0.583469 | −0.291734 | − | 0.956499i | \(-0.594232\pi\) | ||||
−0.291734 | + | 0.956499i | \(0.594232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.41986 | −1.69186 | −0.845928 | − | 0.533297i | \(-0.820953\pi\) | ||||
−0.845928 | + | 0.533297i | \(0.820953\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.48157 | − | 8.13923i | −0.780140 | − | 1.41686i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00517 | − | 3.00517i | −0.494047 | − | 0.494047i | 0.415532 | − | 0.909579i | \(-0.363595\pi\) |
−0.909579 | + | 0.415532i | \(0.863595\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.71126 | + | 5.90473i | −0.274021 | + | 0.945513i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.8360i | − | 1.69230i | −0.532947 | − | 0.846148i | \(-0.678916\pi\) | ||
0.532947 | − | 0.846148i | \(-0.321084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.30996 | − | 1.30996i | 0.199767 | − | 0.199767i | −0.600133 | − | 0.799900i | \(-0.704886\pi\) |
0.799900 | + | 0.600133i | \(0.204886\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.22241 | + | 3.22241i | −0.470037 | + | 0.470037i | −0.901926 | − | 0.431890i | \(-0.857847\pi\) |
0.431890 | + | 0.901926i | \(0.357847\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.77078i | − | 0.681540i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.26775 | − | 11.2754i | 0.457576 | − | 1.57887i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.347725 | − | 0.347725i | −0.0477638 | − | 0.0477638i | 0.682821 | − | 0.730585i | \(-0.260753\pi\) |
−0.730585 | + | 0.682821i | \(0.760753\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.29874 | + | 4.17487i | 0.304475 | + | 0.552975i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.13898 | −0.538849 | −0.269425 | − | 0.963021i | \(-0.586833\pi\) | ||||
−0.269425 | + | 0.963021i | \(0.586833\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.72055 | 0.476367 | 0.238184 | − | 0.971220i | \(-0.423448\pi\) | ||||
0.238184 | + | 0.971220i | \(0.423448\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.37001 | + | 0.982863i | −0.550569 | + | 0.123829i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.11379 | + | 8.11379i | 0.991257 | + | 0.991257i | 0.999962 | − | 0.00870492i | \(-0.00277090\pi\) |
−0.00870492 | + | 0.999962i | \(0.502771\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.67983 | + | 2.51552i | 1.04493 | + | 0.302833i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.87034i | − | 0.815359i | −0.913125 | − | 0.407679i | \(-0.866338\pi\) | ||
0.913125 | − | 0.407679i | \(-0.133662\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.19983 | − | 1.19983i | 0.140429 | − | 0.140429i | −0.633397 | − | 0.773827i | \(-0.718340\pi\) |
0.773827 | + | 0.633397i | \(0.218340\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.66351 | + | 5.66351i | −0.645417 | + | 0.645417i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.55468i | − | 0.849968i | −0.905201 | − | 0.424984i | \(-0.860280\pi\) | ||
0.905201 | − | 0.424984i | \(-0.139720\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.85347 | − | 8.13331i | −0.428163 | − | 0.903701i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.29515 | + | 8.29515i | 0.910511 | + | 0.910511i | 0.996312 | − | 0.0858016i | \(-0.0273451\pi\) |
−0.0858016 | + | 0.996312i | \(0.527345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.76734 | + | 2.62496i | −0.511112 | + | 0.281425i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.1454 | 1.81741 | 0.908706 | − | 0.417437i | \(-0.137072\pi\) | ||||
0.908706 | + | 0.417437i | \(0.137072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.29942 | 0.555531 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.2923 | + | 7.86956i | −1.48205 | + | 0.816035i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.70248 | − | 7.70248i | −0.782068 | − | 0.782068i | 0.198112 | − | 0.980179i | \(-0.436519\pi\) |
−0.980179 | + | 0.198112i | \(0.936519\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.5994 | − | 8.60530i | −1.36679 | − | 0.864865i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.4893i | − | 1.04373i | −0.853029 | − | 0.521864i | \(-0.825237\pi\) | ||
0.853029 | − | 0.521864i | \(-0.174763\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.62286 | − | 9.62286i | 0.948168 | − | 0.948168i | −0.0505529 | − | 0.998721i | \(-0.516098\pi\) |
0.998721 | + | 0.0505529i | \(0.0160984\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.132819 | − | 0.132819i | 0.0128401 | − | 0.0128401i | −0.700658 | − | 0.713498i | \(-0.747110\pi\) |
0.713498 | + | 0.700658i | \(0.247110\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.32624i | 0.797509i | 0.917058 | + | 0.398754i | \(0.130557\pi\) | ||||
−0.917058 | + | 0.398754i | \(0.869443\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.07020 | − | 2.04903i | −0.671074 | − | 0.194485i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.2412 | + | 10.2412i | 0.963409 | + | 0.963409i | 0.999354 | − | 0.0359451i | \(-0.0114441\pi\) |
−0.0359451 | + | 0.999354i | \(0.511444\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.33651 | + | 10.3886i | 0.216011 | + | 0.960428i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.1195 | −0.927656 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.7771 | −1.61610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.05262 | − | 16.4410i | −0.816247 | − | 1.48243i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3812 | + | 11.3812i | 1.00992 | + | 1.00992i | 0.999950 | + | 0.00996950i | \(0.00317344\pi\) |
0.00996950 | + | 0.999950i | \(0.496827\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.893175 | − | 3.08191i | 0.0786397 | − | 0.271347i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.06681i | 0.617430i | 0.951155 | + | 0.308715i | \(0.0998989\pi\) | ||||
−0.951155 | + | 0.308715i | \(0.900101\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.90500 | − | 2.90500i | 0.251895 | − | 0.251895i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.590772 | + | 0.590772i | −0.0504730 | + | 0.0504730i | −0.731893 | − | 0.681420i | \(-0.761363\pi\) |
0.681420 | + | 0.731893i | \(0.261363\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.1515i | 1.11549i | 0.830011 | + | 0.557747i | \(0.188334\pi\) | ||||
−0.830011 | + | 0.557747i | \(0.811666\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.19715 | + | 7.58130i | −0.185034 | + | 0.638461i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.4636 | + | 13.4636i | 1.12588 | + | 1.12588i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.98561 | − | 7.23850i | −0.328728 | − | 0.597021i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.57868 | 0.457023 | 0.228511 | − | 0.973541i | \(-0.426614\pi\) | ||||
0.228511 | + | 0.973541i | \(0.426614\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.114853 | −0.00934659 | −0.00467330 | − | 0.999989i | \(-0.501488\pi\) | ||||
−0.00467330 | + | 0.999989i | \(0.501488\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.46170 | − | 19.8376i | −0.360707 | − | 1.60378i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1232 | + | 10.1232i | 0.807921 | + | 0.807921i | 0.984319 | − | 0.176398i | \(-0.0564446\pi\) |
−0.176398 | + | 0.984319i | \(0.556445\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.818086 | − | 0.237091i | −0.0648785 | − | 0.0188026i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.79005i | − | 0.613942i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.6706 | + | 10.6706i | −0.835783 | + | 0.835783i | −0.988301 | − | 0.152518i | \(-0.951262\pi\) |
0.152518 | + | 0.988301i | \(0.451262\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.6490 | + | 10.6490i | −0.824041 | + | 0.824041i | −0.986685 | − | 0.162644i | \(-0.947998\pi\) |
0.162644 | + | 0.986685i | \(0.447998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.401935i | 0.0309181i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.97556 | + | 4.41394i | 0.533434 | + | 0.337542i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.435013 | − | 0.435013i | −0.0330734 | − | 0.0330734i | 0.690377 | − | 0.723450i | \(-0.257445\pi\) |
−0.723450 | + | 0.690377i | \(0.757445\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.27990 | + | 3.45779i | −0.472026 | + | 0.259904i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.58679 | −0.567063 | −0.283532 | − | 0.958963i | \(-0.591506\pi\) | ||||
−0.283532 | + | 0.958963i | \(0.591506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.59257 | 0.564351 | 0.282176 | − | 0.959363i | \(-0.408944\pi\) | ||||
0.282176 | + | 0.959363i | \(0.408944\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.64503 | − | 3.10823i | 0.417292 | − | 0.229767i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.7094 | − | 25.7094i | −1.88006 | − | 1.88006i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.80932 | + | 5.14206i | −0.422566 | + | 0.374030i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.91066i | − | 0.355323i | −0.984092 | − | 0.177661i | \(-0.943147\pi\) | ||
0.984092 | − | 0.177661i | \(-0.0568532\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.3811 | + | 18.3811i | −1.32310 | + | 1.32310i | −0.411846 | + | 0.911253i | \(0.635116\pi\) |
−0.911253 | + | 0.411846i | \(0.864884\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.71657 | − | 6.71657i | 0.478536 | − | 0.478536i | −0.426127 | − | 0.904663i | \(-0.640122\pi\) |
0.904663 | + | 0.426127i | \(0.140122\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0825425i | 0.00585128i | 0.999996 | + | 0.00292564i | \(0.000931262\pi\) | ||||
−0.999996 | + | 0.00292564i | \(0.999069\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.0891 | + | 5.53227i | 1.34644 | + | 0.390216i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.31725 | + | 3.31725i | 0.232825 | + | 0.232825i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.2711 | − | 3.43463i | 1.06141 | − | 0.238723i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.7607 | 1.02102 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.0889 | 1.03876 | 0.519382 | − | 0.854542i | \(-0.326162\pi\) | ||||
0.519382 | + | 0.854542i | \(0.326162\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.73963 | − | 10.4241i | −0.393273 | − | 0.714245i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.94503 | + | 9.94503i | 0.675112 | + | 0.675112i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.818086 | − | 2.82282i | 0.0552812 | − | 0.190748i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.0567i | 1.61823i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.66264 | + | 3.66264i | −0.245268 | + | 0.245268i | −0.819025 | − | 0.573757i | \(-0.805485\pi\) |
0.573757 | + | 0.819025i | \(0.305485\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.4232 | − | 16.4232i | 1.09005 | − | 1.09005i | 0.0945253 | − | 0.995522i | \(-0.469867\pi\) |
0.995522 | − | 0.0945253i | \(-0.0301333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 26.1344i | − | 1.72701i | −0.504339 | − | 0.863506i | \(-0.668264\pi\) | ||
0.504339 | − | 0.863506i | \(-0.331736\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.86158 | + | 13.3244i | −0.254073 | + | 0.876682i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.407782 | + | 0.407782i | 0.0267147 | + | 0.0267147i | 0.720338 | − | 0.693623i | \(-0.243987\pi\) |
−0.693623 | + | 0.720338i | \(0.743987\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.31134 | − | 11.4624i | −0.409966 | − | 0.744562i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.1595 | −1.04527 | −0.522636 | − | 0.852556i | \(-0.675051\pi\) | ||||
−0.522636 | + | 0.852556i | \(0.675051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.476850 | 0.0307166 | 0.0153583 | − | 0.999882i | \(-0.495111\pi\) | ||||
0.0153583 | + | 0.999882i | \(0.495111\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.6415 | − | 9.12106i | −0.810950 | − | 0.585116i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.90591 | − | 6.90591i | −0.439412 | − | 0.439412i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.5158 | + | 5.65592i | 1.23676 | + | 0.358430i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9243i | 1.51009i | 0.655675 | + | 0.755043i | \(0.272384\pi\) | ||||
−0.655675 | + | 0.755043i | \(0.727616\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.7912 | − | 19.7912i | 1.24426 | − | 1.24426i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.0938 | − | 10.0938i | 0.629636 | − | 0.629636i | −0.318341 | − | 0.947976i | \(-0.603126\pi\) |
0.947976 | + | 0.318341i | \(0.103126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.34542i | 0.394286i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.04033 | + | 7.96548i | −0.311989 | + | 0.493051i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.16000 | + | 7.16000i | 0.441504 | + | 0.441504i | 0.892517 | − | 0.451013i | \(-0.148937\pi\) |
−0.451013 | + | 0.892517i | \(0.648937\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.0140 | − | 14.3237i | 1.59203 | − | 0.876594i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.8893 | 1.27364 | 0.636822 | − | 0.771011i | \(-0.280249\pi\) | ||||
0.636822 | + | 0.771011i | \(0.280249\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.08128 | 0.126429 | 0.0632143 | − | 0.998000i | \(-0.479865\pi\) | ||||
0.0632143 | + | 0.998000i | \(0.479865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.04059 | − | 4.42726i | 0.486639 | − | 0.267950i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.1913 | − | 10.1913i | −0.612335 | − | 0.612335i | 0.331219 | − | 0.943554i | \(-0.392540\pi\) |
−0.943554 | + | 0.331219i | \(0.892540\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.1108 | + | 23.8803i | −0.904658 | + | 1.42968i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.85316i | 0.528135i | 0.964504 | + | 0.264068i | \(0.0850642\pi\) | ||||
−0.964504 | + | 0.264068i | \(0.914936\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.65052 | − | 7.65052i | 0.454776 | − | 0.454776i | −0.442160 | − | 0.896936i | \(-0.645788\pi\) |
0.896936 | + | 0.442160i | \(0.145788\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.4401 | + | 11.4401i | −0.675288 | + | 0.675288i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 28.9375i | − | 1.70221i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.1215 | − | 5.25182i | −1.06230 | − | 0.307867i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.5842 | + | 16.5842i | 0.968858 | + | 0.968858i | 0.999530 | − | 0.0306711i | \(-0.00976446\pi\) |
−0.0306711 | + | 0.999530i | \(0.509764\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −27.8228 | − | 1.69524i | −1.61444 | − | 0.0983677i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.5189 | −1.07098 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.76598 | −0.159428 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.76302 | − | 15.9150i | −0.503422 | − | 0.914294i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.09776 | + | 1.09776i | 0.0626522 | + | 0.0626522i | 0.737739 | − | 0.675086i | \(-0.235894\pi\) |
−0.675086 | + | 0.737739i | \(0.735894\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.56121 | − | 22.6395i | 0.373254 | − | 1.28792i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.1988i | 1.54230i | 0.636654 | + | 0.771150i | \(0.280318\pi\) | ||||
−0.636654 | + | 0.771150i | \(0.719682\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.2574 | + | 17.2574i | −0.975444 | + | 0.975444i | −0.999706 | − | 0.0242613i | \(-0.992277\pi\) |
0.0242613 | + | 0.999706i | \(0.492277\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.1703 | − | 19.1703i | 1.07671 | − | 1.07671i | 0.0799087 | − | 0.996802i | \(-0.474537\pi\) |
0.996802 | − | 0.0799087i | \(-0.0254629\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.8555i | 0.943724i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0905609 | − | 0.312481i | 0.00505462 | − | 0.0174410i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.1872 | + | 13.1872i | 0.733755 | + | 0.733755i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.95592 | + | 12.6330i | 0.384663 | + | 0.698609i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.80413 | 0.375124 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.87878 | −0.268162 | −0.134081 | − | 0.990970i | \(-0.542808\pi\) | ||||
−0.134081 | + | 0.990970i | \(0.542808\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.4391 | + | 2.79769i | −0.681660 | + | 0.153313i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.854739 | + | 0.854739i | 0.0465606 | + | 0.0465606i | 0.730004 | − | 0.683443i | \(-0.239518\pi\) |
−0.683443 | + | 0.730004i | \(0.739518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.0942 | + | 6.98280i | 1.30862 | + | 0.379253i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 50.5322i | 2.73647i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.4270 | + | 12.4270i | −0.670996 | + | 0.670996i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.5114 | + | 16.5114i | −0.886380 | + | 0.886380i | −0.994173 | − | 0.107794i | \(-0.965621\pi\) |
0.107794 | + | 0.994173i | \(0.465621\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.2298i | 1.67169i | 0.548964 | + | 0.835846i | \(0.315023\pi\) | ||||
−0.548964 | + | 0.835846i | \(0.684977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.2240 | + | 13.8102i | 0.652467 | + | 0.737135i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.2055 | + | 16.2055i | 0.862529 | + | 0.862529i | 0.991631 | − | 0.129102i | \(-0.0412095\pi\) |
−0.129102 | + | 0.991631i | \(0.541210\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.3539 | + | 8.45408i | −0.812616 | + | 0.447437i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.5938 | −1.45635 | −0.728174 | − | 0.685393i | \(-0.759631\pi\) | ||||
−0.728174 | + | 0.685393i | \(0.759631\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.4287 | 0.601513 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.9725 | + | 14.8514i | −1.41569 | + | 0.779497i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.1487 | + | 19.1487i | 0.999553 | + | 0.999553i | 1.00000 | 0.000446897i | \(-0.000142252\pi\) | |
−0.000446897 | 1.00000i | \(0.500142\pi\) | ||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.4703 | − | 17.3824i | −1.43005 | − | 0.904894i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.734223i | 0.0381190i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.4168 | − | 23.4168i | 1.21247 | − | 1.21247i | 0.242264 | − | 0.970210i | \(-0.422110\pi\) |
0.970210 | − | 0.242264i | \(-0.0778899\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.88594 | − | 7.88594i | 0.406147 | − | 0.406147i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.72957i | 0.397042i | 0.980097 | + | 0.198521i | \(0.0636137\pi\) | ||||
−0.980097 | + | 0.198521i | \(0.936386\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.7764 | + | 7.76012i | 1.37179 | + | 0.397563i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.6062 | − | 23.6062i | −1.20622 | − | 1.20622i | −0.972242 | − | 0.233976i | \(-0.924826\pi\) |
−0.233976 | − | 0.972242i | \(-0.575174\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.21952 | − | 5.42223i | −0.0619916 | − | 0.275627i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.18514 | −0.415003 | −0.207502 | − | 0.978235i | \(-0.566533\pi\) | ||||
−0.207502 | + | 0.978235i | \(0.566533\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.3629 | 1.78838 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.90377 | + | 10.7222i | 0.297806 | + | 0.540862i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.88292 | − | 6.88292i | −0.345444 | − | 0.345444i | 0.512965 | − | 0.858409i | \(-0.328547\pi\) |
−0.858409 | + | 0.512965i | \(0.828547\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.98073 | − | 6.83452i | 0.0991605 | − | 0.342154i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.2267i | − | 0.510695i | −0.966849 | − | 0.255347i | \(-0.917810\pi\) | ||
0.966849 | − | 0.255347i | \(-0.0821898\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.6418 | − | 23.6418i | 1.17768 | − | 1.17768i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.1210 | + | 16.1210i | −0.799090 | + | 0.799090i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.9396i | 1.48042i | 0.672378 | + | 0.740208i | \(0.265273\pi\) | ||||
−0.672378 | + | 0.740208i | \(0.734727\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.402809 | + | 1.38990i | −0.0198691 | + | 0.0685585i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.36973 | + | 4.36973i | 0.215021 | + | 0.215021i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.9870 | + | 19.9542i | 0.538037 | + | 0.977160i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.20518 | −0.205437 | −0.102718 | − | 0.994710i | \(-0.532754\pi\) | ||||
−0.102718 | + | 0.994710i | \(0.532754\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0724 | 0.685846 | 0.342923 | − | 0.939364i | \(-0.388583\pi\) | ||||
0.342923 | + | 0.939364i | \(0.388583\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.99994 | + | 13.3383i | 0.145862 | + | 0.648532i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.92797 | − | 3.92797i | −0.190088 | − | 0.190088i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.6755 | + | 9.17995i | 1.52931 | + | 0.443212i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 19.6714i | − | 0.947537i | −0.880649 | − | 0.473769i | \(-0.842893\pi\) | ||
0.880649 | − | 0.473769i | \(-0.157107\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5624 | − | 18.5624i | 0.892050 | − | 0.892050i | −0.102666 | − | 0.994716i | \(-0.532737\pi\) |
0.994716 | + | 0.102666i | \(0.0327373\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.1516 | + | 10.1516i | −0.485615 | + | 0.485615i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 30.8707i | − | 1.47338i | −0.676231 | − | 0.736689i | \(-0.736388\pi\) | ||
0.676231 | − | 0.736689i | \(-0.263612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.0944 | − | 7.65300i | −0.575924 | − | 0.364428i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.2069 | − | 17.2069i | −0.817523 | − | 0.817523i | 0.168225 | − | 0.985749i | \(-0.446196\pi\) |
−0.985749 | + | 0.168225i | \(0.946196\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.46429 | − | 4.66055i | 0.400347 | − | 0.220436i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.6598 | 0.597453 | 0.298726 | − | 0.954339i | \(-0.403438\pi\) | ||||
0.298726 | + | 0.954339i | \(0.403438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −58.1289 | −2.73718 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.174261 | + | 0.0959506i | −0.00818751 | + | 0.00450815i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.9120 | + | 20.9120i | 0.978220 | + | 0.978220i | 0.999768 | − | 0.0215478i | \(-0.00685941\pi\) |
−0.0215478 | + | 0.999768i | \(0.506859\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −23.3423 | − | 26.3714i | −1.08953 | − | 1.23091i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0486i | 1.02690i | 0.858118 | + | 0.513452i | \(0.171634\pi\) | ||||
−0.858118 | + | 0.513452i | \(0.828366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.8425 | + | 11.8425i | −0.550367 | + | 0.550367i | −0.926547 | − | 0.376180i | \(-0.877238\pi\) |
0.376180 | + | 0.926547i | \(0.377238\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.82588 | − | 7.82588i | 0.362139 | − | 0.362139i | −0.502461 | − | 0.864600i | \(-0.667572\pi\) |
0.864600 | + | 0.502461i | \(0.167572\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 17.1323i | − | 0.791096i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.8167 | + | 6.90237i | 1.09741 | + | 0.318044i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.02718 | − | 7.02718i | −0.323110 | − | 0.323110i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.43932 | + | 0.323719i | −0.0659019 | + | 0.0148221i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.4902 | 1.48451 | 0.742257 | − | 0.670115i | \(-0.233755\pi\) | ||||
0.742257 | + | 0.670115i | \(0.233755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.0847 | 0.687802 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.50798 | − | 11.8195i | −0.296123 | − | 0.537807i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.1604 | − | 20.1604i | −0.913553 | − | 0.913553i | 0.0829964 | − | 0.996550i | \(-0.473551\pi\) |
−0.996550 | + | 0.0829964i | \(0.973551\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.27556 | + | 25.1044i | −0.329012 | + | 1.13526i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.99751i | 0.360923i | 0.983582 | + | 0.180461i | \(0.0577590\pi\) | ||||
−0.983582 | + | 0.180461i | \(0.942241\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.0586 | + | 15.0586i | −0.678206 | + | 0.678206i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.25337 | + | 7.25337i | −0.325358 | + | 0.325358i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.1515i | − | 0.723039i | −0.932364 | − | 0.361520i | \(-0.882258\pi\) | ||
0.932364 | − | 0.361520i | \(-0.117742\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.26084 | + | 25.0536i | −0.324390 | + | 1.11931i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.1740 | − | 20.1740i | −0.899516 | − | 0.899516i | 0.0958769 | − | 0.995393i | \(-0.469434\pi\) |
−0.995393 | + | 0.0958769i | \(0.969434\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.335785 | + | 0.609839i | 0.0149127 | + | 0.0270839i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.4502 | 1.17239 | 0.586193 | − | 0.810172i | \(-0.300626\pi\) | ||||
0.586193 | + | 0.810172i | \(0.300626\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.53344 | −0.112073 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.2712 | + | 0.869543i | 0.630090 | + | 0.0383912i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.2864 | + | 17.2864i | 0.760255 | + | 0.760255i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.02345 | − | 0.296607i | −0.0449243 | − | 0.0130196i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.4508i | − | 1.24645i | −0.782041 | − | 0.623226i | \(-0.785821\pi\) | ||
0.782041 | − | 0.623226i | \(-0.214179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.2736 | + | 27.2736i | −1.19259 | + | 1.19259i | −0.216254 | + | 0.976337i | \(0.569384\pi\) |
−0.976337 | + | 0.216254i | \(0.930616\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −45.1454 | + | 45.1454i | −1.96656 | + | 1.96656i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.22246i | 0.183585i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.63950 | + | 10.4927i | −0.288130 | + | 0.455346i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.1960 | + | 27.1960i | 1.17799 | + | 1.17799i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.5111 | + | 6.33817i | −0.496741 | + | 0.273512i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.5925 | −1.10235 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.79711 | −0.378217 | −0.189109 | − | 0.981956i | \(-0.560560\pi\) | ||||
−0.189109 | + | 0.981956i | \(0.560560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.5199 | − | 6.34300i | 0.494365 | − | 0.272204i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.84963 | + | 7.84963i | 0.335626 | + | 0.335626i | 0.854718 | − | 0.519092i | \(-0.173730\pi\) |
−0.519092 | + | 0.854718i | \(0.673730\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.96828 | − | 9.43196i | 0.254720 | − | 0.402546i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.64570i | − | 0.368319i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.97586 | + | 7.97586i | −0.339168 | + | 0.339168i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.0351 | − | 23.0351i | 0.976029 | − | 0.976029i | −0.0236902 | − | 0.999719i | \(-0.507542\pi\) |
0.999719 | + | 0.0236902i | \(0.00754152\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.57543i | 0.278111i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −60.4861 | − | 17.5296i | −2.55372 | − | 0.740100i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.4247 | + | 15.4247i | 0.650072 | + | 0.650072i | 0.953010 | − | 0.302938i | \(-0.0979675\pi\) |
−0.302938 | + | 0.953010i | \(0.597967\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.51845 | + | 12.6551i | −0.189757 | + | 0.531463i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.584046 | −0.0244845 | −0.0122422 | − | 0.999925i | \(-0.503897\pi\) | ||||
−0.0122422 | + | 0.999925i | \(0.503897\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.69247 | 0.238222 | 0.119111 | − | 0.992881i | \(-0.461996\pi\) | ||||
0.119111 | + | 0.992881i | \(0.461996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.10247 | − | 7.45073i | −0.171383 | − | 0.311259i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.97443 | − | 4.97443i | −0.207088 | − | 0.207088i | 0.595940 | − | 0.803029i | \(-0.296779\pi\) |
−0.803029 | + | 0.595940i | \(0.796779\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.5329 | + | 43.2448i | −0.520848 | + | 1.79719i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 17.5152i | − | 0.726654i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.86535 | + | 1.86535i | −0.0772549 | + | 0.0772549i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.00375 | − | 2.00375i | 0.0827036 | − | 0.0827036i | −0.664545 | − | 0.747248i | \(-0.731375\pi\) |
0.747248 | + | 0.664545i | \(0.231375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 25.9196i | − | 1.06800i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.57960 | − | 15.8019i | 0.188379 | − | 0.650005i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.29289 | − | 2.29289i | −0.0941577 | − | 0.0941577i | 0.658459 | − | 0.752617i | \(-0.271209\pi\) |
−0.752617 | + | 0.658459i | \(0.771209\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.0689578 | + | 0.125238i | 0.00282226 | + | 0.00512566i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.30110 | −0.134879 | −0.0674395 | − | 0.997723i | \(-0.521483\pi\) | ||||
−0.0674395 | + | 0.997723i | \(0.521483\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.1115 | −1.10590 | −0.552951 | − | 0.833214i | \(-0.686498\pi\) | ||||
−0.552951 | + | 0.833214i | \(0.686498\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.5849 | − | 7.55362i | 1.36768 | − | 0.307607i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.725530 | + | 0.725530i | 0.0294483 | + | 0.0294483i | 0.721678 | − | 0.692229i | \(-0.243371\pi\) |
−0.692229 | + | 0.721678i | \(0.743371\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.80443 | + | 2.26182i | 0.316251 | + | 0.0916535i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 16.1751i | − | 0.654376i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.54878 | − | 2.54878i | 0.102944 | − | 0.102944i | −0.653759 | − | 0.756703i | \(-0.726809\pi\) |
0.756703 | + | 0.653759i | \(0.226809\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.7733 | + | 13.7733i | −0.554493 | + | 0.554493i | −0.927734 | − | 0.373241i | \(-0.878246\pi\) |
0.373241 | + | 0.927734i | \(0.378246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5.31656i | − | 0.213691i | −0.994276 | − | 0.106845i | \(-0.965925\pi\) | ||
0.994276 | − | 0.106845i | \(-0.0340750\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.3008 | − | 17.9690i | 0.814642 | − | 0.721071i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.1013 | − | 18.1013i | −0.725214 | − | 0.725214i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22.3958 | − | 12.3314i | 0.894403 | − | 0.492470i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.8050 | −1.14853 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.9595 | 0.595529 | 0.297765 | − | 0.954639i | \(-0.403759\pi\) | ||||
0.297765 | + | 0.954639i | \(0.403759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.8938 | − | 12.6056i | 0.909945 | − | 0.501028i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.9736 | + | 11.9736i | 0.474413 | + | 0.474413i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.4170 | − | 11.0210i | −0.689005 | − | 0.435983i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 43.0294i | − | 1.69956i | −0.527139 | − | 0.849779i | \(-0.676735\pi\) | ||
0.527139 | − | 0.849779i | \(-0.323265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.86447 | + | 4.86447i | −0.191836 | + | 0.191836i | −0.796489 | − | 0.604653i | \(-0.793312\pi\) |
0.604653 | + | 0.796489i | \(0.293312\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.8140 | − | 30.8140i | 1.21142 | − | 1.21142i | 0.240866 | − | 0.970558i | \(-0.422569\pi\) |
0.970558 | − | 0.240866i | \(-0.0774314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.2033i | 0.871555i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.3975 | + | 6.78087i | 0.917019 | + | 0.265763i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.4625 | − | 29.4625i | −1.15296 | − | 1.15296i | −0.985957 | − | 0.167002i | \(-0.946591\pi\) |
−0.167002 | − | 0.985957i | \(-0.553409\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.11699 | − | 4.96638i | −0.0435781 | − | 0.193757i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.5130 | 0.838026 | 0.419013 | − | 0.907980i | \(-0.362376\pi\) | ||||
0.419013 | + | 0.907980i | \(0.362376\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.8754 | 1.27871 | 0.639353 | − | 0.768913i | \(-0.279202\pi\) | ||||
0.639353 | + | 0.768913i | \(0.279202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.0975 | + | 36.5002i | 0.780521 | + | 1.41755i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.5922 | − | 11.5922i | −0.448851 | − | 0.448851i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.49732 | + | 8.61701i | −0.0965518 | + | 0.333153i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 19.9586i | − | 0.770494i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0746 | − | 20.0746i | 0.773817 | − | 0.773817i | −0.204954 | − | 0.978772i | \(-0.565705\pi\) |
0.978772 | + | 0.204954i | \(0.0657045\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.7207 | − | 23.7207i | 0.911662 | − | 0.911662i | −0.0847414 | − | 0.996403i | \(-0.527006\pi\) |
0.996403 | + | 0.0847414i | \(0.0270064\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.2638i | 0.624147i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.1979 | − | 38.6386i | 0.429106 | − | 1.48063i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.5593 | + | 11.5593i | 0.442305 | + | 0.442305i | 0.892786 | − | 0.450481i | \(-0.148748\pi\) |
−0.450481 | + | 0.892786i | \(0.648748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.8333 | − | 39.6526i | −0.832991 | − | 1.51284i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.74543 | 0.0664957 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.3522 | 0.393816 | 0.196908 | − | 0.980422i | \(-0.436910\pi\) | ||||
0.196908 | + | 0.980422i | \(0.436910\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.27250 | + | 23.4426i | 0.200286 | + | 0.890512i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.9323 | − | 51.9323i | −1.96707 | − | 1.96707i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.959380 | + | 0.278040i | 0.0362871 | + | 0.0105164i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.1863i | 0.649119i | 0.945865 | + | 0.324560i | \(0.105216\pi\) | ||||
−0.945865 | + | 0.324560i | \(0.894784\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.26900 | − | 8.26900i | 0.311871 | − | 0.311871i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.0741 | + | 11.0741i | −0.416486 | + | 0.416486i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.73580i | 0.365636i | 0.983147 | + | 0.182818i | \(0.0585219\pi\) | ||||
−0.983147 | + | 0.182818i | \(0.941478\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.1519 | − | 12.1188i | −0.718251 | − | 0.454489i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34.7531 | − | 34.7531i | −1.30151 | − | 1.30151i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.5181 | + | 13.5000i | −0.915646 | + | 0.504167i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.0470 | 0.784921 | 0.392461 | − | 0.919769i | \(-0.371624\pi\) | ||||
0.392461 | + | 0.919769i | \(0.371624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.3187 | −0.756708 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.723504 | − | 0.398371i | 0.0269074 | − | 0.0148156i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.6156 | + | 27.6156i | 1.02421 | + | 1.02421i | 0.999700 | + | 0.0245068i | \(0.00780153\pi\) |
0.0245068 | + | 0.999700i | \(0.492198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.8003 | − | 3.27804i | −0.992603 | − | 0.121409i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 12.5561i | − | 0.464405i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.4480 | + | 26.4480i | −0.976879 | + | 0.976879i | −0.999739 | − | 0.0228597i | \(-0.992723\pi\) |
0.0228597 | + | 0.999739i | \(0.492723\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.5259 | − | 43.5259i | 1.60330 | − | 1.60330i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.90172i | 0.0699559i | 0.999388 | + | 0.0349779i | \(0.0111361\pi\) | ||||
−0.999388 | + | 0.0349779i | \(0.988864\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.2474 | − | 4.70869i | −0.596863 | − | 0.172978i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.31527 | − | 1.31527i | −0.0482527 | − | 0.0482527i | 0.682569 | − | 0.730821i | \(-0.260863\pi\) |
−0.730821 | + | 0.682569i | \(0.760863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.3356 | − | 7.72245i | 1.25627 | − | 0.282550i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.280448 | −0.0102474 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.0085 | −1.35046 | −0.675230 | − | 0.737608i | \(-0.735955\pi\) | ||||
−0.675230 | + | 0.737608i | \(0.735955\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.9869 | + | 36.2993i | 0.728362 | + | 1.32282i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0860 | − | 15.0860i | −0.548308 | − | 0.548308i | 0.377643 | − | 0.925951i | \(-0.376735\pi\) |
−0.925951 | + | 0.377643i | \(0.876735\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.4944 | − | 46.5624i | 0.489814 | − | 1.69011i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 43.9192i | − | 1.59207i | −0.605252 | − | 0.796034i | \(-0.706928\pi\) | ||
0.605252 | − | 0.796034i | \(-0.293072\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.79044 | − | 8.79044i | 0.318235 | − | 0.318235i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.3880 | − | 10.3880i | 0.375087 | − | 0.375087i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.7444i | − | 0.495637i | −0.968806 | − | 0.247819i | \(-0.920286\pi\) | ||
0.968806 | − | 0.247819i | \(-0.0797137\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.88233 | − | 23.7475i | 0.247861 | − | 0.855247i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.2220 | − | 12.2220i | −0.439594 | − | 0.439594i | 0.452281 | − | 0.891875i | \(-0.350610\pi\) |
−0.891875 | + | 0.452281i | \(0.850610\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.30111 | + | 9.62764i | 0.190176 | + | 0.345390i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.8162 | 1.06828 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.8555 | −1.31879 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.992941 | + | 16.2965i | −0.0354848 | + | 0.582389i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.67770 | − | 6.67770i | −0.238034 | − | 0.238034i | 0.578001 | − | 0.816036i | \(-0.303833\pi\) |
−0.816036 | + | 0.578001i | \(0.803833\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.8452 | + | 4.88194i | 0.599704 | + | 0.173802i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 21.6243i | − | 0.768871i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.33778 | + | 9.33778i | −0.331594 | + | 0.331594i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.9958 | + | 13.9958i | −0.495756 | + | 0.495756i | −0.910114 | − | 0.414358i | \(-0.864006\pi\) |
0.414358 | + | 0.910114i | \(0.364006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.8873i | 1.09271i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.5037 | − | 43.4654i | 0.971794 | − | 1.53577i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.43641 | − | 6.43641i | −0.227136 | − | 0.227136i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.6945 | − | 17.4514i | 1.11570 | − | 0.614318i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.9116 | −1.71964 | −0.859821 | − | 0.510596i | \(-0.829425\pi\) | ||||
−0.859821 | + | 0.510596i | \(0.829425\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.91061 | 0.348009 | 0.174004 | − | 0.984745i | \(-0.444329\pi\) | ||||
0.174004 | + | 0.984745i | \(0.444329\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.15783 | − | 1.73874i | 0.110750 | − | 0.0609804i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.60447 | + | 3.60447i | 0.126104 | + | 0.126104i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.50102 | − | 13.4346i | 0.297050 | − | 0.469442i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.3930i | 1.09562i | 0.836602 | + | 0.547811i | \(0.184539\pi\) | ||||
−0.836602 | + | 0.547811i | \(0.815461\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.4174 | − | 14.4174i | 0.502560 | − | 0.502560i | −0.409673 | − | 0.912233i | \(-0.634357\pi\) |
0.912233 | + | 0.409673i | \(0.134357\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.76302 | − | 2.76302i | 0.0960795 | − | 0.0960795i | −0.657433 | − | 0.753513i | \(-0.728358\pi\) |
0.753513 | + | 0.657433i | \(0.228358\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 31.5824i | − | 1.09690i | −0.836183 | − | 0.548450i | \(-0.815218\pi\) | ||
0.836183 | − | 0.548450i | \(-0.184782\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.9768 | − | 6.94878i | −0.831747 | − | 0.241050i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.8643 | − | 22.8643i | −0.792201 | − | 0.792201i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.97681 | + | 48.8564i | −0.102894 | + | 1.68872i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0505 | 0.416028 | 0.208014 | − | 0.978126i | \(-0.433300\pi\) | ||||
0.208014 | + | 0.978126i | \(0.433300\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.1274 | −0.659564 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.39613 | + | 13.4325i | 0.254736 | + | 0.462641i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.7682 | + | 18.7682i | 0.644884 | + | 0.644884i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.21639 | − | 17.9992i | 0.179026 | − | 0.617732i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 22.1742i | − | 0.760121i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.5979 | + | 23.5979i | −0.807978 | + | 0.807978i | −0.984328 | − | 0.176350i | \(-0.943571\pi\) |
0.176350 | + | 0.984328i | \(0.443571\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.51855 | − | 2.51855i | 0.0860319 | − | 0.0860319i | −0.662781 | − | 0.748813i | \(-0.730624\pi\) |
0.748813 | + | 0.662781i | \(0.230624\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.2203i | 0.621668i | 0.950464 | + | 0.310834i | \(0.100608\pi\) | ||||
−0.950464 | + | 0.310834i | \(0.899392\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.80027 | + | 26.9149i | −0.265833 | + | 0.917258i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.0844 | − | 22.0844i | −0.751763 | − | 0.751763i | 0.223045 | − | 0.974808i | \(-0.428400\pi\) |
−0.974808 | + | 0.223045i | \(0.928400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24.1750 | − | 43.9057i | −0.821027 | − | 1.49111i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.5266 | −1.37477 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.7278 | −1.38001 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.8824 | + | 7.17070i | −1.07906 | + | 0.242691i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8814 | − | 26.8814i | −0.907719 | − | 0.907719i | 0.0883686 | − | 0.996088i | \(-0.471835\pi\) |
−0.996088 | + | 0.0883686i | \(0.971835\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 39.0173 | + | 11.3077i | 1.31602 | + | 0.381399i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 21.6378i | − | 0.728998i | −0.931204 | − | 0.364499i | \(-0.881240\pi\) | ||
0.931204 | − | 0.364499i | \(-0.118760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.7073 | − | 12.7073i | 0.427634 | − | 0.427634i | −0.460188 | − | 0.887822i | \(-0.652218\pi\) |
0.887822 | + | 0.460188i | \(0.152218\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.7681 | + | 36.7681i | −1.23455 | + | 1.23455i | −0.272356 | + | 0.962197i | \(0.587803\pi\) |
−0.962197 | + | 0.272356i | \(0.912197\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 24.0315i | − | 0.805990i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −43.6306 | + | 20.6717i | −1.46168 | + | 0.692527i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.86676 | − | 8.86676i | −0.296715 | − | 0.296715i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.0980 | + | 15.4711i | −0.938164 | + | 0.516565i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.5979 | 0.987145 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.33300 | −0.111038 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.19670 | + | 2.31076i | −0.139658 | + | 0.0768973i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.52831 | + | 1.52831i | 0.0507468 | + | 0.0507468i | 0.732025 | − | 0.681278i | \(-0.238576\pi\) |
−0.681278 | + | 0.732025i | \(0.738576\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.5915 | − | 16.8264i | −0.881985 | − | 0.558095i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 14.7675i | − | 0.489269i | −0.969615 | − | 0.244635i | \(-0.921332\pi\) | ||
0.969615 | − | 0.244635i | \(-0.0786680\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.4988 | − | 44.4988i | 1.47269 | − | 1.47269i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.46080 | − | 7.46080i | 0.246377 | − | 0.246377i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.7950i | 1.37869i | 0.724433 | + | 0.689345i | \(0.242102\pi\) | ||||
−0.724433 | + | 0.689345i | \(0.757898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.58267 | + | 0.748488i | 0.0851017 | + | 0.0246635i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.2431 | + | 17.2431i | 0.567563 | + | 0.567563i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.95850 | − | 39.8313i | −0.294236 | − | 1.30823i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.468082 | 0.0153573 | 0.00767863 | − | 0.999971i | \(-0.497556\pi\) | ||||
0.00767863 | + | 0.999971i | \(0.497556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.1272 | 0.430227 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.7224 | + | 41.2675i | 0.743899 | + | 1.35104i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4650 | + | 29.4650i | 0.962578 | + | 0.962578i | 0.999325 | − | 0.0367464i | \(-0.0116994\pi\) |
−0.0367464 | + | 0.999325i | \(0.511699\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.7667 | + | 40.6011i | −0.383991 | + | 1.32497i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 7.77228i | − | 0.253369i | −0.991943 | − | 0.126685i | \(-0.959566\pi\) | ||
0.991943 | − | 0.126685i | \(-0.0404336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.9776 | − | 39.9776i | 1.30185 | − | 1.30185i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.7465 | + | 22.7465i | −0.739163 | + | 0.739163i | −0.972416 | − | 0.233253i | \(-0.925063\pi\) |
0.233253 | + | 0.972416i | \(0.425063\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.02264i | 0.195503i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.0710 | − | 45.1016i | 0.423856 | − | 1.46252i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.75462 | − | 2.75462i | −0.0892309 | − | 0.0892309i | 0.661082 | − | 0.750313i | \(-0.270097\pi\) |
−0.750313 | + | 0.661082i | \(0.770097\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.0814 | + | 25.5741i | 0.455188 | + | 0.826692i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.24742 | 0.0402812 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.7337 | 1.86238 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.123650 | − | 0.549771i | −0.00398455 | − | 0.0177161i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.1302 | − | 13.1302i | −0.422240 | − | 0.422240i | 0.463735 | − | 0.885974i | \(-0.346509\pi\) |
−0.885974 | + | 0.463735i | \(0.846509\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.0253 | + | 8.99150i | 0.996675 | + | 0.288849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 47.3723i | − | 1.52025i | −0.649776 | − | 0.760125i | \(-0.725137\pi\) | ||
0.649776 | − | 0.760125i | \(-0.274863\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.8847 | − | 13.8847i | 0.445123 | − | 0.445123i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.897303 | + | 0.897303i | −0.0287073 | + | 0.0287073i | −0.721315 | − | 0.692607i | \(-0.756462\pi\) |
0.692607 | + | 0.721315i | \(0.256462\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 91.9755i | − | 2.93955i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.1079 | + | 13.3565i | 0.673922 | + | 0.426439i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.0539 | − | 29.0539i | −0.926676 | − | 0.926676i | 0.0708140 | − | 0.997490i | \(-0.477440\pi\) |
−0.997490 | + | 0.0708140i | \(0.977440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.3236 | − | 5.68432i | 0.328604 | − | 0.180934i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.66576 | 0.307353 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.3697 | 1.79064 | 0.895321 | − | 0.445421i | \(-0.146946\pi\) | ||||
0.895321 | + | 0.445421i | \(0.146946\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.40237 | + | 4.07584i | −0.234907 | + | 0.129343i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.9840 | + | 17.9840i | 0.569560 | + | 0.569560i | 0.932005 | − | 0.362445i | \(-0.118058\pi\) |
−0.362445 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.5361 | + | 14.6367i | −0.523179 | + | 0.463086i |
(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 | 1500.2.i.a.557.14 | yes | 32 | |
3.2 | odd | 2 | inner | 1500.2.i.a.557.11 | yes | 32 | |
5.2 | odd | 4 | inner | 1500.2.i.a.1193.6 | yes | 32 | |
5.3 | odd | 4 | inner | 1500.2.i.a.1193.11 | yes | 32 | |
5.4 | even | 2 | inner | 1500.2.i.a.557.3 | ✓ | 32 | |
15.2 | even | 4 | inner | 1500.2.i.a.1193.3 | yes | 32 | |
15.8 | even | 4 | inner | 1500.2.i.a.1193.14 | yes | 32 | |
15.14 | odd | 2 | inner | 1500.2.i.a.557.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1500.2.i.a.557.3 | ✓ | 32 | 5.4 | even | 2 | inner | |
1500.2.i.a.557.6 | yes | 32 | 15.14 | odd | 2 | inner | |
1500.2.i.a.557.11 | yes | 32 | 3.2 | odd | 2 | inner | |
1500.2.i.a.557.14 | yes | 32 | 1.1 | even | 1 | trivial | |
1500.2.i.a.1193.3 | yes | 32 | 15.2 | even | 4 | inner | |
1500.2.i.a.1193.6 | yes | 32 | 5.2 | odd | 4 | inner | |
1500.2.i.a.1193.11 | yes | 32 | 5.3 | odd | 4 | inner | |
1500.2.i.a.1193.14 | yes | 32 | 15.8 | even | 4 | inner |