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 | 1471.14 | ||
Root | \(1.30491 + 1.30491i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.a.1471.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | \(-0.470920\pi\) | ||||
0.0912302 | + | 0.995830i | \(0.470920\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.10189 | 0.332232 | 0.166116 | − | 0.986106i | \(-0.446877\pi\) | ||||
0.166116 | + | 0.986106i | \(0.446877\pi\) | |||||||
\(12\) | 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 | \(-0.738637\pi\) | ||
0.681420 | − | 0.731893i | \(-0.261363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.48254 | −0.340118 | −0.170059 | − | 0.985434i | \(-0.554396\pi\) | ||||
−0.170059 | + | 0.985434i | \(0.554396\pi\) | |||||||
\(20\) | 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 | \(-0.840690\pi\) | ||
0.877349 | − | 0.479852i | \(-0.159310\pi\) | |||||||
\(38\) | 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 | \(-0.723371\pi\) | ||||
−0.645548 | + | 0.763720i | \(0.723371\pi\) | |||||||
\(44\) | 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 | \(0.206985\pi\) | ||||
−0.795926 | + | 0.605394i | \(0.793015\pi\) | |||||||
\(54\) | 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 | \(0.000799197\pi\) | ||||
−0.999997 | + | 0.00251075i | \(0.999201\pi\) | |||||||
\(62\) | 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 | \(-0.671365\pi\) | ||||
−0.512727 | + | 0.858552i | \(0.671365\pi\) | |||||||
\(68\) | 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 | \(-0.565247\pi\) | ||||
−0.203546 | + | 0.979065i | \(0.565247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.12164 | 1.00123 | 0.500615 | − | 0.865670i | \(-0.333107\pi\) | ||||
0.500615 | + | 0.865670i | \(0.333107\pi\) | |||||||
\(84\) | 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 | \(0.118283\pi\) | ||||
−0.931748 | + | 0.363105i | \(0.881717\pi\) | |||||||
\(90\) | 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 | \(0.00533759\pi\) | ||||
−0.999859 | + | 0.0167677i | \(0.994662\pi\) | |||||||
\(98\) | 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 | \(-0.312840\pi\) | ||||
0.554683 | + | 0.832062i | \(0.312840\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.482745 | 0.0471111 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.801493 | −0.0774833 | −0.0387416 | − | 0.999249i | \(-0.512335\pi\) | ||||
−0.0387416 | + | 0.999249i | \(0.512335\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.25885i | − | 0.120576i | −0.998181 | − | 0.0602880i | \(-0.980798\pi\) | ||
0.998181 | − | 0.0602880i | \(-0.0192019\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.83765 | 0.554086 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.70667i | − | 0.819054i | −0.912298 | − | 0.409527i | \(-0.865694\pi\) | ||
0.912298 | − | 0.409527i | \(-0.134306\pi\) | |||||||
\(114\) | 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 | \(-0.938366\pi\) | ||
0.981312 | − | 0.192422i | \(-0.0616342\pi\) | |||||||
\(138\) | 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 | \(-0.837459\pi\) | ||
0.872433 | − | 0.488734i | \(-0.162541\pi\) | |||||||
\(150\) | 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 | \(0.0118816\pi\) | ||||
−0.999303 | + | 0.0373184i | \(0.988118\pi\) | |||||||
\(158\) | 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 | \(-0.872508\pi\) | ||
0.920855 | − | 0.389905i | \(-0.127492\pi\) | |||||||
\(182\) | 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 | \(-0.619938\pi\) | ||||
−0.367943 | + | 0.929848i | \(0.619938\pi\) | |||||||
\(192\) | 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 | \(-0.403411\pi\) | ||||
0.298807 | + | 0.954314i | \(0.403411\pi\) | |||||||
\(200\) | 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 | \(-0.574149\pi\) | ||||
−0.230845 | + | 0.972990i | \(0.574149\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.27163i | − | 0.0840316i | −0.999117 | − | 0.0420158i | \(-0.986622\pi\) | ||
0.999117 | − | 0.0420158i | \(-0.0133780\pi\) | |||||||
\(230\) | 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 | \(-0.884847\pi\) | ||
0.935273 | − | 0.353926i | \(-0.115153\pi\) | |||||||
\(242\) | 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 | \(-0.416403\pi\) | ||||
0.259619 | + | 0.965711i | \(0.416403\pi\) | |||||||
\(252\) | 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 | \(-0.707814\pi\) | ||||
−0.607466 | + | 0.794346i | \(0.707814\pi\) | |||||||
\(264\) | 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 | \(0.197447\pi\) | ||||
−0.813705 | + | 0.581278i | \(0.802553\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.52826 | 0.269177 | 0.134589 | − | 0.990902i | \(-0.457029\pi\) | ||||
0.134589 | + | 0.990902i | \(0.457029\pi\) | |||||||
\(284\) | 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 | \(0.137609\pi\) | ||||
−0.908000 | + | 0.418971i | \(0.862391\pi\) | |||||||
\(294\) | 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 | \(0.286728\pi\) | ||||
−0.620997 | + | 0.783813i | \(0.713272\pi\) | |||||||
\(314\) | 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 | \(-0.981848\pi\) | ||
0.998374 | − | 0.0569950i | \(-0.0181519\pi\) | |||||||
\(338\) | 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 | \(-0.215200\pi\) | ||||
0.780038 | + | 0.625732i | \(0.215200\pi\) | |||||||
\(360\) | 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 | \(-0.618691\pi\) | ||||
−0.364299 | + | 0.931282i | \(0.618691\pi\) | |||||||
\(368\) | 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 | \(-0.837513\pi\) | ||
0.872516 | − | 0.488585i | \(-0.162487\pi\) | |||||||
\(374\) | 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 | \(-0.367076\pi\) | ||||
0.405560 | + | 0.914068i | \(0.367076\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.51836 | 0.282714 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.4419 | 0.635749 | 0.317875 | − | 0.948133i | \(-0.397031\pi\) | ||||
0.317875 | + | 0.948133i | \(0.397031\pi\) | |||||||
\(384\) | 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 | \(-0.889858\pi\) | ||
0.940730 | − | 0.339156i | \(-0.110142\pi\) | |||||||
\(390\) | 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 | \(-0.794973\pi\) | ||
0.799634 | − | 0.600488i | \(-0.205027\pi\) | |||||||
\(402\) | 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 | \(-0.719451\pi\) | ||||
−0.636095 | + | 0.771611i | \(0.719451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 37.9967i | − | 1.85185i | −0.377711 | − | 0.925924i | \(-0.623289\pi\) | ||
0.377711 | − | 0.925924i | \(-0.376711\pi\) | |||||||
\(422\) | 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 | \(-0.0367354\pi\) | ||||
0.993348 | + | 0.115152i | \(0.0367354\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.54638i | 0.122371i | 0.998126 | + | 0.0611856i | \(0.0194882\pi\) | ||||
−0.998126 | + | 0.0611856i | \(0.980512\pi\) | |||||||
\(434\) | 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 | \(-0.681066\pi\) | ||
0.538651 | − | 0.842529i | \(-0.318934\pi\) | |||||||
\(458\) | 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 | \(-0.602496\pi\) | ||||
−0.316465 | + | 0.948604i | \(0.602496\pi\) | |||||||
\(468\) | 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 | \(-0.650353\pi\) | ||||
−0.454977 | + | 0.890503i | \(0.650353\pi\) | |||||||
\(480\) | 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 | \(-0.544648\pi\) | ||||
−0.139805 | + | 0.990179i | \(0.544648\pi\) | |||||||
\(504\) | 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 | \(-0.694234\pi\) | ||
0.573035 | − | 0.819531i | \(-0.305766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.7986 | −0.647098 | −0.323549 | − | 0.946211i | \(-0.604876\pi\) | ||||
−0.323549 | + | 0.946211i | \(0.604876\pi\) | |||||||
\(524\) | 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 | \(0.118015\pi\) | ||||
−0.932054 | + | 0.362318i | \(0.881985\pi\) | |||||||
\(558\) | 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 | \(-0.331374\pi\) | ||||
0.505321 | + | 0.862931i | \(0.331374\pi\) | |||||||
\(564\) | 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 | \(-0.981105\pi\) | ||
0.998239 | − | 0.0593265i | \(-0.0188953\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.44436 | −0.311537 | −0.155768 | − | 0.987794i | \(-0.549785\pi\) | ||||
−0.155768 | + | 0.987794i | \(0.549785\pi\) | |||||||
\(572\) | 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 | \(0.168664\pi\) | ||||
−0.862871 | + | 0.505425i | \(0.831336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.27767 | 0.0515204 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 32.3884i | − | 1.30391i | −0.758259 | − | 0.651953i | \(-0.773950\pi\) | ||
0.758259 | − | 0.651953i | \(-0.226050\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.1700 | 1.37341 | 0.686703 | − | 0.726938i | \(-0.259057\pi\) | ||||
0.686703 | + | 0.726938i | \(0.259057\pi\) | |||||||
\(620\) | 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 | \(-0.448315\pi\) | ||||
0.161659 | + | 0.986847i | \(0.448315\pi\) | |||||||
\(632\) | 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 | \(-0.775431\pi\) | ||
0.761285 | − | 0.648418i | \(-0.224569\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.4559 | −0.451776 | −0.225888 | − | 0.974153i | \(-0.572528\pi\) | ||||
−0.225888 | + | 0.974153i | \(0.572528\pi\) | |||||||
\(644\) | 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 | \(-0.771869\pi\) | ||||
−0.753980 | + | 0.656897i | \(0.771869\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.6248i | 0.918900i | 0.888204 | + | 0.459450i | \(0.151953\pi\) | ||||
−0.888204 | + | 0.459450i | \(0.848047\pi\) | |||||||
\(662\) | 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 | \(-0.983984\pi\) | ||
0.998734 | − | 0.0502948i | \(-0.0160161\pi\) | |||||||
\(678\) | 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 | \(-0.890049\pi\) | ||
0.940933 | − | 0.338592i | \(-0.109951\pi\) | |||||||
\(702\) | 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 | \(-0.856302\pi\) | ||
0.899819 | − | 0.436263i | \(-0.143698\pi\) | |||||||
\(710\) | 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 | \(-0.822129\pi\) | ||||
−0.847893 | + | 0.530168i | \(0.822129\pi\) | |||||||
\(728\) | 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 | \(0.0268760\pi\) | ||||
−0.996438 | + | 0.0843333i | \(0.973124\pi\) | |||||||
\(734\) | 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 | \(-0.761040\pi\) | ||||
−0.731202 | + | 0.682161i | \(0.761040\pi\) | |||||||
\(744\) | 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 | \(-0.539105\pi\) | ||||
−0.122543 | + | 0.992463i | \(0.539105\pi\) | |||||||
\(752\) | 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 | \(0.258142\pi\) | ||||
−0.688790 | + | 0.724961i | \(0.741858\pi\) | |||||||
\(758\) | 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 | \(-0.841320\pi\) | ||
0.878296 | − | 0.478117i | \(-0.158680\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 30.1958i | − | 1.08748i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.8502i | 1.79299i | 0.443057 | + | 0.896493i | \(0.353894\pi\) | ||||
−0.443057 | + | 0.896493i | \(0.646106\pi\) | |||||||
\(774\) | 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 | \(-0.347539\pi\) | ||||
0.460866 | + | 0.887470i | \(0.347539\pi\) | |||||||
\(788\) | 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 | \(-0.970430\pi\) | ||
0.995688 | − | 0.0927647i | \(-0.0295704\pi\) | |||||||
\(798\) | 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 | \(-0.677368\pi\) | ||||
−0.528826 | + | 0.848730i | \(0.677368\pi\) | |||||||
\(828\) | 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 | \(-0.600287\pi\) | ||||
−0.309875 | + | 0.950777i | \(0.600287\pi\) | |||||||
\(840\) | 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 | \(-0.978970\pi\) | ||
0.997818 | − | 0.0660187i | \(-0.0210297\pi\) | |||||||
\(882\) | 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 | \(-0.267558\pi\) | ||||
0.667047 | + | 0.745016i | \(0.267558\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.89119 | 0.129063 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.6169 | −0.451147 | −0.225574 | − | 0.974226i | \(-0.572426\pi\) | ||||
−0.225574 | + | 0.974226i | \(0.572426\pi\) | |||||||
\(912\) | 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 | \(-0.284802\pi\) | ||||
0.625729 | + | 0.780040i | \(0.284802\pi\) | |||||||
\(920\) | 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 | \(-0.890652\pi\) | ||
0.941572 | − | 0.336811i | \(-0.109348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.7341 | −0.905069 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.99208i | 0.293133i | 0.989201 | + | 0.146567i | \(0.0468223\pi\) | ||||
−0.989201 | + | 0.146567i | \(0.953178\pi\) | |||||||
\(942\) | 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 | \(0.0947870\pi\) | ||||
−0.955990 | + | 0.293401i | \(0.905213\pi\) | |||||||
\(954\) | 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 | \(-0.648593\pi\) | ||||
−0.450047 | + | 0.893005i | \(0.648593\pi\) | |||||||
\(972\) | 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 | \(-0.870199\pi\) | ||
0.918003 | − | 0.396573i | \(-0.129801\pi\) | |||||||
\(978\) | 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 | \(-0.245221\pi\) | ||||
0.717644 | + | 0.696411i | \(0.245221\pi\) | |||||||
\(984\) | 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.a.1471.14 | yes | 16 | |
4.3 | odd | 2 | 5520.2.be.b.1471.3 | yes | 16 | ||
23.22 | odd | 2 | 5520.2.be.b.1471.11 | yes | 16 | ||
92.91 | even | 2 | inner | 5520.2.be.a.1471.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.a.1471.6 | ✓ | 16 | 92.91 | even | 2 | inner | |
5520.2.be.a.1471.14 | yes | 16 | 1.1 | even | 1 | trivial | |
5520.2.be.b.1471.3 | yes | 16 | 4.3 | odd | 2 | ||
5520.2.be.b.1471.11 | yes | 16 | 23.22 | odd | 2 |