Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} + 28 x^{13} + 373 x^{12} - 920 x^{11} + 1088 x^{10} - 168 x^{9} + 16460 x^{8} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.11 | ||
Root | \(1.30491 - 1.30491i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.b.1471.3 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.482745 | −0.182460 | −0.0912302 | − | 0.995830i | \(-0.529080\pi\) | ||||
−0.0912302 | + | 0.995830i | \(0.529080\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.10189 | −0.332232 | −0.166116 | − | 0.986106i | \(-0.553123\pi\) | ||||
−0.166116 | + | 0.986106i | \(0.553123\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.25517 | 0.625471 | 0.312735 | − | 0.949840i | \(-0.398755\pi\) | ||||
0.312735 | + | 0.949840i | \(0.398755\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.03534i | 1.46379i | 0.681420 | + | 0.731893i | \(0.261363\pi\) | ||||
−0.681420 | + | 0.731893i | \(0.738637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.48254 | 0.340118 | 0.170059 | − | 0.985434i | \(-0.445604\pi\) | ||||
0.170059 | + | 0.985434i | \(0.445604\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.482745i | − | 0.105344i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.55260 | + | 1.50793i | 0.949283 | + | 0.314424i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.68679 | −1.42740 | −0.713700 | − | 0.700451i | \(-0.752982\pi\) | ||||
−0.713700 | + | 0.700451i | \(0.752982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.12465i | − | 0.920414i | −0.887812 | − | 0.460207i | \(-0.847775\pi\) | ||
0.887812 | − | 0.460207i | \(-0.152225\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.10189i | − | 0.191814i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 0.482745i | − | 0.0815987i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.83765i | 0.959705i | 0.877349 | + | 0.479852i | \(0.159310\pi\) | ||||
−0.877349 | + | 0.479852i | \(0.840690\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.25517i | 0.361116i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.27767 | 0.199538 | 0.0997689 | − | 0.995011i | \(-0.468190\pi\) | ||||
0.0997689 | + | 0.995011i | \(0.468190\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.46629 | 1.29110 | 0.645548 | − | 0.763720i | \(-0.276629\pi\) | ||||
0.645548 | + | 0.763720i | \(0.276629\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.2632i | 1.64290i | 0.570278 | + | 0.821452i | \(0.306836\pi\) | ||||
−0.570278 | + | 0.821452i | \(0.693164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.76696 | −0.966708 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.03534 | −0.845117 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.81467i | − | 1.21079i | −0.795926 | − | 0.605394i | \(-0.793015\pi\) | ||
0.795926 | − | 0.605394i | \(-0.206985\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.10189i | − | 0.148579i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.48254i | 0.196367i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.08002i | 1.05193i | 0.850507 | + | 0.525964i | \(0.176295\pi\) | ||||
−0.850507 | + | 0.525964i | \(0.823705\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.0392191i | − | 0.00502149i | −0.999997 | − | 0.00251075i | \(-0.999201\pi\) | ||
0.999997 | − | 0.00251075i | \(-0.000799197\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.482745 | 0.0608201 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.25517i | 0.279719i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.39370 | 1.02545 | 0.512727 | − | 0.858552i | \(-0.328635\pi\) | ||||
0.512727 | + | 0.858552i | \(0.328635\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.50793 | + | 4.55260i | −0.181533 | + | 0.548069i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.25598i | − | 0.149058i | −0.997219 | − | 0.0745289i | \(-0.976255\pi\) | ||
0.997219 | − | 0.0745289i | \(-0.0237453\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.47480 | −0.406694 | −0.203347 | − | 0.979107i | \(-0.565182\pi\) | ||||
−0.203347 | + | 0.979107i | \(0.565182\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.531931 | 0.0606192 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.61831 | 0.407092 | 0.203546 | − | 0.979065i | \(-0.434753\pi\) | ||||
0.203546 | + | 0.979065i | \(0.434753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.12164 | −1.00123 | −0.500615 | − | 0.865670i | \(-0.666893\pi\) | ||||
−0.500615 | + | 0.865670i | \(0.666893\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.03534 | −0.654625 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.68679i | − | 0.824110i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.85106i | − | 0.726211i | −0.931748 | − | 0.363105i | \(-0.881717\pi\) | ||
0.931748 | − | 0.363105i | \(-0.118283\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.08867 | −0.114124 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.12465 | 0.531401 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.48254i | 0.152105i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.330286i | − | 0.0335355i | −0.999859 | − | 0.0167677i | \(-0.994662\pi\) | ||
0.999859 | − | 0.0167677i | \(-0.00533759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.10189 | 0.110744 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.89119 | −0.387188 | −0.193594 | − | 0.981082i | \(-0.562014\pi\) | ||||
−0.193594 | + | 0.981082i | \(0.562014\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2588 | −1.10937 | −0.554683 | − | 0.832062i | \(-0.687160\pi\) | ||||
−0.554683 | + | 0.832062i | \(0.687160\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.482745 | 0.0471111 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.801493 | 0.0774833 | 0.0387416 | − | 0.999249i | \(-0.487665\pi\) | ||||
0.0387416 | + | 0.999249i | \(0.487665\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.25885i | 0.120576i | 0.998181 | + | 0.0602880i | \(0.0192019\pi\) | ||||
−0.998181 | + | 0.0602880i | \(0.980798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.83765 | −0.554086 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.70667i | 0.819054i | 0.912298 | + | 0.409527i | \(0.134306\pi\) | ||||
−0.912298 | + | 0.409527i | \(0.865694\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.50793 | + | 4.55260i | −0.140615 | + | 0.424532i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.25517 | −0.208490 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.91353i | − | 0.267083i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.78584 | −0.889622 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.27767i | 0.115203i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.51836i | − | 0.489676i | −0.969564 | − | 0.244838i | \(-0.921265\pi\) | ||
0.969564 | − | 0.244838i | \(-0.0787347\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.46629i | 0.745415i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.5197i | 1.26859i | 0.773089 | + | 0.634297i | \(0.218711\pi\) | ||||
−0.773089 | + | 0.634297i | \(0.781289\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.715687 | −0.0620580 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.50448i | 0.384844i | 0.981312 | + | 0.192422i | \(0.0616342\pi\) | ||||
−0.981312 | + | 0.192422i | \(0.938366\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.13377i | 0.180984i | 0.995897 | + | 0.0904921i | \(0.0288440\pi\) | ||||
−0.995897 | + | 0.0904921i | \(0.971156\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.2632 | −0.948531 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.48494 | −0.207801 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.68679i | − | 0.638353i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 6.76696i | − | 0.558129i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.9315i | 0.977468i | 0.872433 | + | 0.488734i | \(0.162541\pi\) | ||||
−0.872433 | + | 0.488734i | \(0.837459\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.63555i | 0.784130i | 0.919937 | + | 0.392065i | \(0.128239\pi\) | ||||
−0.919937 | + | 0.392065i | \(0.871761\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.03534i | − | 0.487929i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.12465 | 0.411622 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.935197i | − | 0.0746368i | −0.999303 | − | 0.0373184i | \(-0.988118\pi\) | ||
0.999303 | − | 0.0373184i | \(-0.0118816\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.81467 | 0.699049 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.19774 | − | 0.727943i | −0.173206 | − | 0.0573700i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.8165i | 1.08220i | 0.840960 | + | 0.541098i | \(0.181991\pi\) | ||||
−0.840960 | + | 0.541098i | \(0.818009\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.10189 | 0.0857820 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.69307i | 0.517925i | 0.965887 | + | 0.258963i | \(0.0833807\pi\) | ||||
−0.965887 | + | 0.258963i | \(0.916619\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.91423 | −0.608787 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.48254 | −0.113373 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.6878 | −1.87698 | −0.938490 | − | 0.345305i | \(-0.887775\pi\) | ||||
−0.938490 | + | 0.345305i | \(0.887775\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.482745 | 0.0364921 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.08002 | −0.607331 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.65679i | − | 0.348065i | −0.984740 | − | 0.174032i | \(-0.944320\pi\) | ||
0.984740 | − | 0.174032i | \(-0.0556797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.4913i | 0.779809i | 0.920855 | + | 0.389905i | \(0.127492\pi\) | ||||
−0.920855 | + | 0.389905i | \(0.872508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0392191 | 0.00289916 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.83765 | −0.429193 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.65028i | − | 0.486317i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.482745i | 0.0351145i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1702 | 0.735886 | 0.367943 | − | 0.929848i | \(-0.380062\pi\) | ||||
0.367943 | + | 0.929848i | \(0.380062\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.3593 | −0.961626 | −0.480813 | − | 0.876823i | \(-0.659658\pi\) | ||||
−0.480813 | + | 0.876823i | \(0.659658\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.25517 | −0.161496 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.65615 | −0.189243 | −0.0946216 | − | 0.995513i | \(-0.530164\pi\) | ||||
−0.0946216 | + | 0.995513i | \(0.530164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.43038 | −0.597614 | −0.298807 | − | 0.954314i | \(-0.596589\pi\) | ||||
−0.298807 | + | 0.954314i | \(0.596589\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.39370i | 0.592046i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.71075 | 0.260444 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.27767i | 0.0892360i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.55260 | − | 1.50793i | −0.316428 | − | 0.104808i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.63359 | −0.112998 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 0.771524i | − | 0.0531139i | −0.999647 | − | 0.0265570i | \(-0.991546\pi\) | ||
0.999647 | − | 0.0265570i | \(-0.00845434\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.25598 | 0.0860586 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.46629i | 0.577396i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.47390i | 0.167939i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 3.47480i | − | 0.234805i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.6107i | 0.915555i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.0727i | − | 1.27720i | −0.769538 | − | 0.638601i | \(-0.779513\pi\) | ||
0.769538 | − | 0.638601i | \(-0.220487\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.95607 | 0.461691 | 0.230845 | − | 0.972990i | \(-0.425851\pi\) | ||||
0.230845 | + | 0.972990i | \(0.425851\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.27163i | 0.0840316i | 0.999117 | + | 0.0420158i | \(0.0133780\pi\) | ||||
−0.999117 | + | 0.0420158i | \(0.986622\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.531931i | 0.0349985i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.90098 | −0.648635 | −0.324317 | − | 0.945948i | \(-0.605135\pi\) | ||||
−0.324317 | + | 0.945948i | \(0.605135\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2632 | −0.734729 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.61831i | 0.235035i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3420i | − | 0.668968i | −0.942401 | − | 0.334484i | \(-0.891438\pi\) | ||
0.942401 | − | 0.334484i | \(-0.108562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.9888i | 0.707852i | 0.935273 | + | 0.353926i | \(0.115153\pi\) | ||||
−0.935273 | + | 0.353926i | \(0.884847\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 6.76696i | − | 0.432325i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.34337 | 0.212734 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 9.12164i | − | 0.578061i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.22629 | −0.519239 | −0.259619 | − | 0.965711i | \(-0.583597\pi\) | ||||
−0.259619 | + | 0.965711i | \(0.583597\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.01646 | − | 1.66157i | −0.315382 | − | 0.104462i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 6.03534i | − | 0.377948i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.1958 | −1.88357 | −0.941783 | − | 0.336223i | \(-0.890851\pi\) | ||||
−0.941783 | + | 0.336223i | \(0.890851\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.81810i | − | 0.175108i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.68679 | 0.475800 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.7029 | 1.21493 | 0.607466 | − | 0.794346i | \(-0.292186\pi\) | ||||
0.607466 | + | 0.794346i | \(0.292186\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.81467 | 0.541481 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.85106 | 0.419278 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.1993 | 0.743805 | 0.371902 | − | 0.928272i | \(-0.378706\pi\) | ||||
0.371902 | + | 0.928272i | \(0.378706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 17.7526i | − | 1.07840i | −0.842179 | − | 0.539198i | \(-0.818727\pi\) | ||
0.842179 | − | 0.539198i | \(-0.181273\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.08867i | − | 0.0658893i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.10189 | 0.0664465 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.0510 | −1.02449 | −0.512246 | − | 0.858839i | \(-0.671187\pi\) | ||||
−0.512246 | + | 0.858839i | \(0.671187\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.12465i | 0.306805i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.4880i | − | 1.16256i | −0.813705 | − | 0.581278i | \(-0.802553\pi\) | ||
0.813705 | − | 0.581278i | \(-0.197447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.52826 | −0.269177 | −0.134589 | − | 0.990902i | \(-0.542971\pi\) | ||||
−0.134589 | + | 0.990902i | \(0.542971\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.48254 | −0.0878180 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.616786 | −0.0364077 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.4254 | −1.14267 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.330286 | 0.0193617 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.3433i | − | 0.837942i | −0.908000 | − | 0.418971i | \(-0.862391\pi\) | ||
0.908000 | − | 0.418971i | \(-0.137609\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.08002 | −0.470437 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.10189i | 0.0639381i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2669 | + | 3.40062i | 0.593748 | + | 0.196663i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.08705 | −0.235574 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.89119i | − | 0.223543i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0392191 | 0.00224568 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.1488i | − | 1.14995i | −0.818170 | − | 0.574976i | \(-0.805011\pi\) | ||
0.818170 | − | 0.574976i | \(-0.194989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 11.2588i | − | 0.640493i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.50388i | − | 0.425506i | −0.977106 | − | 0.212753i | \(-0.931757\pi\) | ||
0.977106 | − | 0.212753i | \(-0.0682430\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 27.7341i | − | 1.56763i | −0.620997 | − | 0.783813i | \(-0.713272\pi\) | ||
0.620997 | − | 0.783813i | \(-0.286728\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.482745i | 0.0271996i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.7305 | 1.33284 | 0.666419 | − | 0.745577i | \(-0.267826\pi\) | ||||
0.666419 | + | 0.745577i | \(0.267826\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.46999 | 0.474228 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.801493i | 0.0447350i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.94763i | 0.497859i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.25517 | −0.125094 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.25885 | −0.0696146 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 5.43724i | − | 0.299765i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 14.4675i | − | 0.795205i | −0.917558 | − | 0.397602i | \(-0.869842\pi\) | ||
0.917558 | − | 0.397602i | \(-0.130158\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.83765i | − | 0.319902i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.39370i | 0.458597i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.09258i | 0.113990i | 0.998374 | + | 0.0569950i | \(0.0181519\pi\) | ||||
−0.998374 | + | 0.0569950i | \(0.981848\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.70667 | −0.472881 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.64680i | 0.305791i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.64593 | 0.358846 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.55260 | − | 1.50793i | −0.245104 | − | 0.0811840i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.3150i | 1.89581i | 0.318552 | + | 0.947905i | \(0.396804\pi\) | ||||
−0.318552 | + | 0.947905i | \(0.603196\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.4994 | 1.36495 | 0.682477 | − | 0.730907i | \(-0.260903\pi\) | ||||
0.682477 | + | 0.730907i | \(0.260903\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.25517i | − | 0.120372i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.8722 | −1.21737 | −0.608683 | − | 0.793414i | \(-0.708302\pi\) | ||||
−0.608683 | + | 0.793414i | \(0.708302\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.25598 | 0.0666607 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.91353 | 0.154200 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.5592 | −1.56008 | −0.780038 | − | 0.625732i | \(-0.784800\pi\) | ||||
−0.780038 | + | 0.625732i | \(0.784800\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8021 | −0.884320 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 9.78584i | − | 0.513623i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.47480i | − | 0.181879i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.9579 | 0.728598 | 0.364299 | − | 0.931282i | \(-0.381309\pi\) | ||||
0.364299 | + | 0.931282i | \(0.381309\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.27767 | −0.0665126 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.25524i | 0.220921i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.8723i | 0.977170i | 0.872516 | + | 0.488585i | \(0.162487\pi\) | ||||
−0.872516 | + | 0.488585i | \(0.837513\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.3350 | −0.892797 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7908 | −0.811121 | −0.405560 | − | 0.914068i | \(-0.632924\pi\) | ||||
−0.405560 | + | 0.914068i | \(0.632924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.51836 | 0.282714 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.4419 | −0.635749 | −0.317875 | − | 0.948133i | \(-0.602969\pi\) | ||||
−0.317875 | + | 0.948133i | \(0.602969\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.531931i | 0.0271097i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.46629 | −0.430365 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.3784i | 0.678312i | 0.940730 | + | 0.339156i | \(0.110142\pi\) | ||||
−0.940730 | + | 0.339156i | \(0.889858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.10085 | + | 27.4765i | −0.460250 | + | 1.38955i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.5197 | −0.732424 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.61831i | 0.182057i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.8329 | 1.14595 | 0.572976 | − | 0.819572i | \(-0.305789\pi\) | ||||
0.572976 | + | 0.819572i | \(0.305789\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 0.715687i | − | 0.0358292i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.0495i | 1.20098i | 0.799634 | + | 0.600488i | \(0.205027\pi\) | ||||
−0.799634 | + | 0.600488i | \(0.794973\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 11.5569i | − | 0.575692i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.43245i | − | 0.318845i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5572 | −0.967042 | −0.483521 | − | 0.875333i | \(-0.660642\pi\) | ||||
−0.483521 | + | 0.875333i | \(0.660642\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.50448 | −0.222190 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.90059i | − | 0.191935i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 9.12164i | − | 0.447764i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.13377 | −0.104491 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.0411 | 1.27219 | 0.636095 | − | 0.771611i | \(-0.280549\pi\) | ||||
0.636095 | + | 0.771611i | \(0.280549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.9967i | 1.85185i | 0.377711 | + | 0.925924i | \(0.376711\pi\) | ||||
−0.377711 | + | 0.925924i | \(0.623289\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 11.2632i | − | 0.547635i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 6.03534i | − | 0.292757i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0189328i | 0.000916224i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 2.48494i | − | 0.119974i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −41.2449 | −1.98670 | −0.993348 | − | 0.115152i | \(-0.963265\pi\) | ||||
−0.993348 | + | 0.115152i | \(0.963265\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.54638i | − | 0.122371i | −0.998126 | − | 0.0611856i | \(-0.980512\pi\) | ||
0.998126 | − | 0.0611856i | \(-0.0194882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.68679 | 0.368553 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.74940 | + | 2.23556i | 0.322868 | + | 0.106941i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.22800i | 0.440428i | 0.975452 | + | 0.220214i | \(0.0706756\pi\) | ||||
−0.975452 | + | 0.220214i | \(0.929324\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.76696 | 0.322236 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.8713i | 0.516511i | 0.966077 | + | 0.258256i | \(0.0831477\pi\) | ||||
−0.966077 | + | 0.258256i | \(0.916852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.85106 | 0.324771 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.9315 | −0.564341 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.3548 | −0.583061 | −0.291530 | − | 0.956562i | \(-0.594164\pi\) | ||||
−0.291530 | + | 0.956562i | \(0.594164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.40785 | −0.0662929 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.63555 | −0.452718 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.08867i | − | 0.0510376i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.0224i | 1.68506i | 0.538651 | + | 0.842529i | \(0.318934\pi\) | ||||
−0.538651 | + | 0.842529i | \(0.681066\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.03534 | 0.281706 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.41328 | −0.0658229 | −0.0329115 | − | 0.999458i | \(-0.510478\pi\) | ||||
−0.0329115 | + | 0.999458i | \(0.510478\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.3322i | − | 1.03787i | −0.854815 | − | 0.518934i | \(-0.826329\pi\) | ||
0.854815 | − | 0.518934i | \(-0.173671\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.12465i | 0.237650i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.6777 | 0.632930 | 0.316465 | − | 0.948604i | \(-0.397504\pi\) | ||||
0.316465 | + | 0.948604i | \(0.397504\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.05201 | −0.187105 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.935197 | 0.0430916 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.32891 | −0.428944 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.48254 | −0.0680235 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.81467i | 0.403596i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.9153 | 0.909954 | 0.454977 | − | 0.890503i | \(-0.349647\pi\) | ||||
0.454977 | + | 0.890503i | \(0.349647\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.1649i | 0.600267i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.727943 | − | 2.19774i | 0.0331226 | − | 0.100001i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.330286 | 0.0149975 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 36.4307i | − | 1.65083i | −0.564524 | − | 0.825417i | \(-0.690940\pi\) | ||
0.564524 | − | 0.825417i | \(-0.309060\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.8165 | −0.624806 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.4791i | 0.833948i | 0.908918 | + | 0.416974i | \(0.136909\pi\) | ||||
−0.908918 | + | 0.416974i | \(0.863091\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 46.3924i | − | 2.08941i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.10189i | 0.0495263i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.606320i | 0.0271971i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 11.1690i | − | 0.499993i | −0.968247 | − | 0.249997i | \(-0.919571\pi\) | ||
0.968247 | − | 0.249997i | \(-0.0804295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.69307 | −0.299024 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.27100 | 0.279610 | 0.139805 | − | 0.990179i | \(-0.455352\pi\) | ||||
0.139805 | + | 0.990179i | \(0.455352\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.89119i | − | 0.173156i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 7.91423i | − | 0.351483i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 39.1536 | 1.73545 | 0.867726 | − | 0.497043i | \(-0.165581\pi\) | ||||
0.867726 | + | 0.497043i | \(0.165581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.67744 | 0.0742056 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.48254i | − | 0.0654557i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 11.2588i | − | 0.496124i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 12.4108i | − | 0.545826i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 24.6878i | − | 1.08368i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.4123i | 1.63906i | 0.573035 | + | 0.819531i | \(0.305766\pi\) | ||||
−0.573035 | + | 0.819531i | \(0.694234\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.7986 | 0.647098 | 0.323549 | − | 0.946211i | \(-0.395124\pi\) | ||||
0.323549 | + | 0.946211i | \(0.395124\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.482745i | 0.0210687i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.9290 | 1.34729 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.4523 | + | 13.7300i | 0.802275 | + | 0.596955i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 8.08002i | − | 0.350643i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.88135 | 0.124805 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.801493i | 0.0346516i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.65679 | 0.200955 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.45644 | 0.321172 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.29246 | 0.0555670 | 0.0277835 | − | 0.999614i | \(-0.491155\pi\) | ||||
0.0277835 | + | 0.999614i | \(0.491155\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.4913 | −0.450223 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.25885 | −0.0539232 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.2259i | 0.522741i | 0.965239 | + | 0.261370i | \(0.0841744\pi\) | ||||
−0.965239 | + | 0.261370i | \(0.915826\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.0392191i | 0.00167383i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.3960 | −0.485484 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.74672 | −0.0742781 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 5.83765i | − | 0.247795i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 17.1020i | − | 0.724637i | −0.932054 | − | 0.362318i | \(-0.881985\pi\) | ||
0.932054 | − | 0.362318i | \(-0.118015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.0929 | 0.807543 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.65028 | 0.280775 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.9801 | −1.01064 | −0.505321 | − | 0.862931i | \(-0.668626\pi\) | ||||
−0.505321 | + | 0.862931i | \(0.668626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.70667 | −0.366292 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.482745 | −0.0202734 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.83032i | 0.118653i | 0.998239 | + | 0.0593265i | \(0.0188953\pi\) | ||||
−0.998239 | + | 0.0593265i | \(0.981105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.44436 | 0.311537 | 0.155768 | − | 0.987794i | \(-0.450215\pi\) | ||||
0.155768 | + | 0.987794i | \(0.450215\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.1702i | 0.424864i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.55260 | − | 1.50793i | −0.189857 | − | 0.0628849i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.4658 | −0.435695 | −0.217848 | − | 0.975983i | \(-0.569904\pi\) | ||||
−0.217848 | + | 0.975983i | \(0.569904\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 13.3593i | − | 0.555195i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.40342 | 0.182685 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.71280i | 0.402263i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.25517i | − | 0.0932396i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.27783i | 0.217839i | 0.994051 | + | 0.108920i | \(0.0347391\pi\) | ||||
−0.994051 | + | 0.108920i | \(0.965261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 7.59749i | − | 0.313049i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 2.65615i | − | 0.109260i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.1506 | 0.745357 | 0.372679 | − | 0.927960i | \(-0.378439\pi\) | ||||
0.372679 | + | 0.927960i | \(0.378439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.91353 | 0.119443 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 8.43038i | − | 0.345033i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0499i | 0.614921i | 0.951561 | + | 0.307460i | \(0.0994792\pi\) | ||||
−0.951561 | + | 0.307460i | \(0.900521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.8769 | 0.729213 | 0.364607 | − | 0.931162i | \(-0.381203\pi\) | ||||
0.364607 | + | 0.931162i | \(0.381203\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.39370 | −0.341818 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 9.78584i | − | 0.397851i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.8849i | 0.685336i | 0.939457 | + | 0.342668i | \(0.111331\pi\) | ||||
−0.939457 | + | 0.342668i | \(0.888669\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.71075i | 0.150367i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.4003i | 1.02759i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 25.0275i | − | 1.01085i | −0.862871 | − | 0.505425i | \(-0.831336\pi\) | ||
0.862871 | − | 0.505425i | \(-0.168664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.27767 | −0.0515204 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.3884i | 1.30391i | 0.758259 | + | 0.651953i | \(0.226050\pi\) | ||||
−0.758259 | + | 0.651953i | \(0.773950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.1700 | −1.37341 | −0.686703 | − | 0.726938i | \(-0.740943\pi\) | ||||
−0.686703 | + | 0.726938i | \(0.740943\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.50793 | − | 4.55260i | 0.0605110 | − | 0.182690i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.30731i | 0.132505i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1.63359i | − | 0.0652394i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.2323 | −1.40480 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.12167 | −0.323319 | −0.161659 | − | 0.986847i | \(-0.551685\pi\) | ||||
−0.161659 | + | 0.986847i | \(0.551685\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.771524 | 0.0306653 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.51836 | 0.218990 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.2606 | −0.604648 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.25598i | 0.0496860i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.8333i | 1.29684i | 0.761285 | + | 0.648418i | \(0.224569\pi\) | ||||
−0.761285 | + | 0.648418i | \(0.775431\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.4559 | 0.451776 | 0.225888 | − | 0.974153i | \(-0.427472\pi\) | ||||
0.225888 | + | 0.974153i | \(0.427472\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.46629 | −0.333360 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.8499i | 0.465867i | 0.972493 | + | 0.232933i | \(0.0748324\pi\) | ||||
−0.972493 | + | 0.232933i | \(0.925168\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.90329i | − | 0.349485i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.47390 | −0.0969597 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.4675 | 0.761821 | 0.380911 | − | 0.924612i | \(-0.375611\pi\) | ||||
0.380911 | + | 0.924612i | \(0.375611\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.5197 | −0.567333 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.47480 | 0.135565 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.7108 | 1.50796 | 0.753980 | − | 0.656897i | \(-0.228131\pi\) | ||||
0.753980 | + | 0.656897i | \(0.228131\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 23.6248i | − | 0.918900i | −0.888204 | − | 0.459450i | \(-0.848047\pi\) | ||
0.888204 | − | 0.459450i | \(-0.151953\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.6107 | −0.528596 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 0.715687i | − | 0.0277532i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.9949 | − | 11.5911i | −1.35501 | − | 0.448809i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.0727 | 0.737393 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0432152i | 0.00166830i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.6743 | −1.60643 | −0.803213 | − | 0.595692i | \(-0.796878\pi\) | ||||
−0.803213 | + | 0.595692i | \(0.796878\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.61727i | 0.100590i | 0.998734 | + | 0.0502948i | \(0.0160161\pi\) | ||||
−0.998734 | + | 0.0502948i | \(0.983984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.159444i | 0.00611890i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.95607i | 0.266557i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.4757i | 0.668688i | 0.942451 | + | 0.334344i | \(0.108515\pi\) | ||||
−0.942451 | + | 0.334344i | \(0.891485\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.50448 | −0.172107 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.27163 | −0.0485157 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 19.8786i | − | 0.757313i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 33.9569i | − | 1.29178i | −0.763430 | − | 0.645890i | \(-0.776486\pi\) | ||
0.763430 | − | 0.645890i | \(-0.223514\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.531931 | −0.0202064 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.13377 | −0.0809386 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.71115i | 0.292081i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 9.90098i | − | 0.374489i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.9294i | 0.677183i | 0.940933 | + | 0.338592i | \(0.109951\pi\) | ||||
−0.940933 | + | 0.338592i | \(0.890049\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.65455i | 0.326412i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 11.2632i | − | 0.424196i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.87845 | 0.0706464 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.2328i | 0.872526i | 0.899819 | + | 0.436263i | \(0.143698\pi\) | ||||
−0.899819 | + | 0.436263i | \(0.856302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.61831 | −0.135697 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.72759 | − | 23.3305i | 0.289401 | − | 0.873733i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.48494i | − | 0.0929317i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.3420 | 0.386229 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.5036i | 1.28677i | 0.765544 | + | 0.643384i | \(0.222470\pi\) | ||||
−0.765544 | + | 0.643384i | \(0.777530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.43514 | 0.202415 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.9888 | −0.408678 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.68679 | 0.285480 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.7234 | 1.69579 | 0.847893 | − | 0.530168i | \(-0.177871\pi\) | ||||
0.847893 | + | 0.530168i | \(0.177871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 51.0969i | 1.88989i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.56648i | − | 0.168667i | −0.996438 | − | 0.0843333i | \(-0.973124\pi\) | ||
0.996438 | − | 0.0843333i | \(-0.0268760\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.76696 | 0.249603 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.24893 | −0.340689 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 8.71551i | − | 0.320605i | −0.987068 | − | 0.160303i | \(-0.948753\pi\) | ||
0.987068 | − | 0.160303i | \(-0.0512470\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.34337i | 0.122822i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.8622 | 1.46240 | 0.731202 | − | 0.682161i | \(-0.238960\pi\) | ||||
0.731202 | + | 0.682161i | \(0.238960\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.9315 | −0.437137 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.12164 | 0.333743 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.386917 | −0.0141376 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.71643 | 0.245086 | 0.122543 | − | 0.992463i | \(-0.460895\pi\) | ||||
0.122543 | + | 0.992463i | \(0.460895\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 8.22629i | − | 0.299783i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.63555 | −0.350674 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 39.8926i | − | 1.44992i | −0.688790 | − | 0.724961i | \(-0.741858\pi\) | ||
0.688790 | − | 0.724961i | \(-0.258142\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.66157 | − | 5.01646i | 0.0603111 | − | 0.182086i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.24308 | 0.0813116 | 0.0406558 | − | 0.999173i | \(-0.487055\pi\) | ||||
0.0406558 | + | 0.999173i | \(0.487055\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 0.607703i | − | 0.0220003i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.03534 | 0.218208 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.2218i | 0.657950i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.5172i | 0.956233i | 0.878296 | + | 0.478117i | \(0.158680\pi\) | ||||
−0.878296 | + | 0.478117i | \(0.841320\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 30.1958i | − | 1.08748i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 49.8502i | − | 1.79299i | −0.443057 | − | 0.896493i | \(-0.646106\pi\) | ||
0.443057 | − | 0.896493i | \(-0.353894\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.12465i | 0.184083i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.81810 | 0.101099 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.89419 | 0.0678663 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.38396i | 0.0495218i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.68679i | 0.274703i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.935197 | 0.0333786 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.8578 | −0.921732 | −0.460866 | − | 0.887470i | \(-0.652461\pi\) | ||||
−0.460866 | + | 0.887470i | \(0.652461\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.7029i | 0.701441i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.20310i | − | 0.149445i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.0884456i | − | 0.00314080i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.81467i | 0.312624i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.23771i | 0.185529i | 0.995688 | + | 0.0927647i | \(0.0295704\pi\) | ||||
−0.995688 | + | 0.0927647i | \(0.970430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −67.9772 | −2.40486 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.85106i | 0.242070i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.82884 | 0.135117 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.727943 | − | 2.19774i | 0.0256566 | − | 0.0774603i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.1993i | 0.429436i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.3522 | −0.399123 | −0.199562 | − | 0.979885i | \(-0.563952\pi\) | ||||
−0.199562 | + | 0.979885i | \(0.563952\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 21.9307i | − | 0.770092i | −0.922897 | − | 0.385046i | \(-0.874186\pi\) | ||
0.922897 | − | 0.385046i | \(-0.125814\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.7526 | 0.622612 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.8165 | −0.483973 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.5516 | 0.439125 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.08867 | 0.0380412 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.5030 | 0.645758 | 0.322879 | − | 0.946440i | \(-0.395349\pi\) | ||||
0.322879 | + | 0.946440i | \(0.395349\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 29.3898i | − | 1.02446i | −0.858848 | − | 0.512231i | \(-0.828819\pi\) | ||
0.858848 | − | 0.512231i | \(-0.171181\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.10189i | 0.0383629i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.4155 | 1.05765 | 0.528826 | − | 0.848730i | \(-0.322632\pi\) | ||||
0.528826 | + | 0.848730i | \(0.322632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.00083 | 0.243149 | 0.121574 | − | 0.992582i | \(-0.461206\pi\) | ||||
0.121574 | + | 0.992582i | \(0.461206\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 17.0510i | − | 0.591491i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 40.8409i | − | 1.41505i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.69307 | −0.231623 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.12465 | −0.177134 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.9514 | 0.619750 | 0.309875 | − | 0.950777i | \(-0.399713\pi\) | ||||
0.309875 | + | 0.950777i | \(0.399713\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.0867 | 1.03747 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.4880 | 0.671202 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 7.91423i | − | 0.272258i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.72406 | 0.162321 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 4.52826i | − | 0.155410i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.80275 | + | 26.5765i | −0.301754 | + | 0.911031i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.2089 | 0.965853 | 0.482926 | − | 0.875661i | \(-0.339574\pi\) | ||||
0.482926 | + | 0.875661i | \(0.339574\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.48254i | − | 0.0507017i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.0494 | 1.50470 | 0.752349 | − | 0.658765i | \(-0.228921\pi\) | ||||
0.752349 | + | 0.658765i | \(0.228921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.9359i | 0.509607i | 0.966993 | + | 0.254804i | \(0.0820108\pi\) | ||||
−0.966993 | + | 0.254804i | \(0.917989\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 0.616786i | − | 0.0210200i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 50.8360i | 1.73048i | 0.501361 | + | 0.865238i | \(0.332833\pi\) | ||||
−0.501361 | + | 0.865238i | \(0.667167\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 24.6878i | − | 0.839411i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 19.4254i | − | 0.659720i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.98698 | −0.135249 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.9292 | 0.641391 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.330286i | 0.0111785i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.482745i | 0.0163197i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.5651 | 1.09965 | 0.549823 | − | 0.835281i | \(-0.314695\pi\) | ||||
0.549823 | + | 0.835281i | \(0.314695\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.3433 | 0.483786 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.91908i | 0.132037i | 0.997818 | + | 0.0660187i | \(0.0210297\pi\) | ||||
−0.997818 | + | 0.0660187i | \(0.978970\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.11783i | 0.138576i | 0.997597 | + | 0.0692880i | \(0.0220727\pi\) | ||||
−0.997597 | + | 0.0692880i | \(0.977927\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 8.08002i | − | 0.271607i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 53.8097i | − | 1.80675i | −0.428850 | − | 0.903376i | \(-0.641081\pi\) | ||
0.428850 | − | 0.903376i | \(-0.358919\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.66396i | 0.0893464i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.10189 | −0.0369147 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.6981i | 0.558781i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.65679 | 0.155659 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.40062 | + | 10.2669i | −0.113543 | + | 0.342801i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.3921i | 1.31380i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.1996 | 1.77234 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 4.08705i | − | 0.136009i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.4913 | −0.348741 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.1782 | −1.33409 | −0.667047 | − | 0.745016i | \(-0.732442\pi\) | ||||
−0.667047 | + | 0.745016i | \(0.732442\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.89119 | 0.129063 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.6169 | 0.451147 | 0.225574 | − | 0.974226i | \(-0.427574\pi\) | ||||
0.225574 | + | 0.974226i | \(0.427574\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.0510 | 0.332641 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.0392191i | 0.00129654i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7.00932i | − | 0.231468i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.9380 | −1.25146 | −0.625729 | − | 0.780040i | \(-0.715198\pi\) | ||||
−0.625729 | + | 0.780040i | \(0.715198\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.1488 | 0.663925 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2.83245i | − | 0.0932313i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 5.83765i | − | 0.191941i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.2588 | 0.369789 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.09450 | 0.134336 | 0.0671681 | − | 0.997742i | \(-0.478604\pi\) | ||||
0.0671681 | + | 0.997742i | \(0.478604\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.0323 | −0.328794 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.50388 | 0.245666 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.65028 | 0.217488 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6199i | 0.673621i | 0.941572 | + | 0.336811i | \(0.109348\pi\) | ||||
−0.941572 | + | 0.336811i | \(0.890652\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.7341 | 0.905069 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 8.99208i | − | 0.293133i | −0.989201 | − | 0.146567i | \(-0.953178\pi\) | ||
0.989201 | − | 0.146567i | \(-0.0468223\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.81670 | + | 1.92662i | 0.189418 | + | 0.0627395i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.482745 | −0.0157037 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.5823i | 0.408870i | 0.978880 | + | 0.204435i | \(0.0655357\pi\) | ||||
−0.978880 | + | 0.204435i | \(0.934464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.83624 | −0.254375 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.7305i | 0.769515i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 18.1150i | − | 0.586801i | −0.955990 | − | 0.293401i | \(-0.905213\pi\) | ||
0.955990 | − | 0.293401i | \(-0.0947870\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.1702i | 0.329098i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.46999i | 0.273796i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 2.17451i | − | 0.0702187i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.73797 | 0.152838 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.801493 | −0.0258278 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 13.3593i | − | 0.430052i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.6245i | 1.37071i | 0.728209 | + | 0.685355i | \(0.240353\pi\) | ||||
−0.728209 | + | 0.685355i | \(0.759647\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.94763 | −0.287439 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.0477 | 0.900094 | 0.450047 | − | 0.893005i | \(-0.351407\pi\) | ||||
0.450047 | + | 0.893005i | \(0.351407\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.03007i | − | 0.0330224i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 2.25517i | − | 0.0722231i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.7913i | 0.793145i | 0.918003 | + | 0.396573i | \(0.129801\pi\) | ||||
−0.918003 | + | 0.396573i | \(0.870199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.54911i | 0.241271i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.25885i | − | 0.0401920i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.0003 | −1.43529 | −0.717644 | − | 0.696411i | \(-0.754779\pi\) | ||||
−0.717644 | + | 0.696411i | \(0.754779\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2.65615i | − | 0.0846321i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.43724 | 0.173069 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.5436 | + | 12.7665i | 1.22562 | + | 0.405952i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 47.7981i | − | 1.51836i | −0.650883 | − | 0.759178i | \(-0.725601\pi\) | ||
0.650883 | − | 0.759178i | \(-0.274399\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.4675 | 0.459112 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 8.43038i | − | 0.267261i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.9172 | 0.820807 | 0.410404 | − | 0.911904i | \(-0.365388\pi\) | ||||
0.410404 | + | 0.911904i | \(0.365388\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.83765 | 0.184695 |
(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 | 5520.2.be.b.1471.11 | yes | 16 | |
4.3 | odd | 2 | 5520.2.be.a.1471.6 | ✓ | 16 | ||
23.22 | odd | 2 | 5520.2.be.a.1471.14 | yes | 16 | ||
92.91 | even | 2 | inner | 5520.2.be.b.1471.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.a.1471.6 | ✓ | 16 | 4.3 | odd | 2 | ||
5520.2.be.a.1471.14 | yes | 16 | 23.22 | odd | 2 | ||
5520.2.be.b.1471.3 | yes | 16 | 92.91 | even | 2 | inner | |
5520.2.be.b.1471.11 | yes | 16 | 1.1 | even | 1 | trivial |