Properties

Label 1133.1.s.a.890.1
Level $1133$
Weight $1$
Character 1133.890
Analytic conductor $0.565$
Analytic rank $0$
Dimension $16$
Projective image $D_{17}$
CM discriminant -11
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1133,1,Mod(76,1133)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1133, base_ring=CyclotomicField(34))
 
chi = DirichletCharacter(H, H._module([17, 22]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1133.76");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1133 = 11 \cdot 103 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1133.s (of order \(34\), degree \(16\), 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: \(0.565440659313\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\Q(\zeta_{34})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{17}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{17} - \cdots)\)

Embedding invariants

Embedding label 890.1
Root \(0.602635 + 0.798017i\) of defining polynomial
Character \(\chi\) \(=\) 1133.890
Dual form 1133.1.s.a.373.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.538007 + 0.100571i) q^{3} +(0.739009 + 0.673696i) q^{4} +(-0.0505009 - 0.177492i) q^{5} +(-0.653136 - 0.253026i) q^{9} +O(q^{10})\) \(q+(0.538007 + 0.100571i) q^{3} +(0.739009 + 0.673696i) q^{4} +(-0.0505009 - 0.177492i) q^{5} +(-0.653136 - 0.253026i) q^{9} +(0.932472 + 0.361242i) q^{11} +(0.329838 + 0.436776i) q^{12} +(-0.00931926 - 0.100571i) q^{15} +(0.0922684 + 0.995734i) q^{16} +(0.0822551 - 0.165190i) q^{20} +(-0.510366 + 0.197717i) q^{23} +(0.821264 - 0.508505i) q^{25} +(-0.791290 - 0.489946i) q^{27} +(-0.0505009 - 0.544991i) q^{31} +(0.465346 + 0.288130i) q^{33} +(-0.312210 - 0.627003i) q^{36} +(0.726337 + 0.961826i) q^{37} +(0.445738 + 0.895163i) q^{44} +(-0.0119262 + 0.128704i) q^{45} -1.70043 q^{47} +(-0.0505009 + 0.544991i) q^{48} +(-0.602635 - 0.798017i) q^{49} +(-1.45285 + 0.271585i) q^{53} +(0.0170269 - 0.183750i) q^{55} +(-0.537235 - 1.07891i) q^{59} +(0.0608671 - 0.0806011i) q^{60} +(-0.602635 + 0.798017i) q^{64} +(0.397365 + 0.798017i) q^{67} +(-0.294465 + 0.0550451i) q^{69} +(0.538007 - 1.89090i) q^{71} +(0.492986 - 0.190984i) q^{75} +(0.172075 - 0.0666624i) q^{80} +(0.141182 + 0.128704i) q^{81} +(0.136374 - 0.124322i) q^{89} +(-0.510366 - 0.197717i) q^{92} +(0.0276404 - 0.298288i) q^{93} +(-0.156896 - 0.0971461i) q^{97} +(-0.517627 - 0.471880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{3} - q^{4} - 2 q^{5} - 3 q^{9} - q^{11} - 2 q^{12} - 4 q^{15} - q^{16} - 2 q^{20} - 2 q^{23} - 3 q^{25} - 4 q^{27} - 2 q^{31} - 2 q^{33} - 3 q^{36} + 15 q^{37} - q^{44} + 11 q^{45} - 2 q^{47} - 2 q^{48} - q^{49} - 2 q^{53} + 15 q^{55} - 2 q^{59} - 4 q^{60} - q^{64} + 15 q^{67} - 4 q^{69} - 2 q^{71} - 6 q^{75} - 2 q^{80} - 5 q^{81} - 2 q^{89} - 2 q^{92} - 4 q^{93} - 2 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1133\mathbb{Z}\right)^\times\).

\(n\) \(310\) \(1035\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{17}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(3\) 0.538007 + 0.100571i 0.538007 + 0.100571i 0.445738 0.895163i \(-0.352941\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(4\) 0.739009 + 0.673696i 0.739009 + 0.673696i
\(5\) −0.0505009 0.177492i −0.0505009 0.177492i 0.932472 0.361242i \(-0.117647\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(6\) 0 0
\(7\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(8\) 0 0
\(9\) −0.653136 0.253026i −0.653136 0.253026i
\(10\) 0 0
\(11\) 0.932472 + 0.361242i 0.932472 + 0.361242i
\(12\) 0.329838 + 0.436776i 0.329838 + 0.436776i
\(13\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(14\) 0 0
\(15\) −0.00931926 0.100571i −0.00931926 0.100571i
\(16\) 0.0922684 + 0.995734i 0.0922684 + 0.995734i
\(17\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(18\) 0 0
\(19\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(20\) 0.0822551 0.165190i 0.0822551 0.165190i
\(21\) 0 0
\(22\) 0 0
\(23\) −0.510366 + 0.197717i −0.510366 + 0.197717i −0.602635 0.798017i \(-0.705882\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(24\) 0 0
\(25\) 0.821264 0.508505i 0.821264 0.508505i
\(26\) 0 0
\(27\) −0.791290 0.489946i −0.791290 0.489946i
\(28\) 0 0
\(29\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(30\) 0 0
\(31\) −0.0505009 0.544991i −0.0505009 0.544991i −0.982973 0.183750i \(-0.941176\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(32\) 0 0
\(33\) 0.465346 + 0.288130i 0.465346 + 0.288130i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.312210 0.627003i −0.312210 0.627003i
\(37\) 0.726337 + 0.961826i 0.726337 + 0.961826i 1.00000 \(0\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(42\) 0 0
\(43\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(44\) 0.445738 + 0.895163i 0.445738 + 0.895163i
\(45\) −0.0119262 + 0.128704i −0.0119262 + 0.128704i
\(46\) 0 0
\(47\) −1.70043 −1.70043 −0.850217 0.526432i \(-0.823529\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(48\) −0.0505009 + 0.544991i −0.0505009 + 0.544991i
\(49\) −0.602635 0.798017i −0.602635 0.798017i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.45285 + 0.271585i −1.45285 + 0.271585i −0.850217 0.526432i \(-0.823529\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(54\) 0 0
\(55\) 0.0170269 0.183750i 0.0170269 0.183750i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.537235 1.07891i −0.537235 1.07891i −0.982973 0.183750i \(-0.941176\pi\)
0.445738 0.895163i \(-0.352941\pi\)
\(60\) 0.0608671 0.0806011i 0.0608671 0.0806011i
\(61\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.602635 + 0.798017i −0.602635 + 0.798017i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.397365 + 0.798017i 0.397365 + 0.798017i 1.00000 \(0\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(68\) 0 0
\(69\) −0.294465 + 0.0550451i −0.294465 + 0.0550451i
\(70\) 0 0
\(71\) 0.538007 1.89090i 0.538007 1.89090i 0.0922684 0.995734i \(-0.470588\pi\)
0.445738 0.895163i \(-0.352941\pi\)
\(72\) 0 0
\(73\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(74\) 0 0
\(75\) 0.492986 0.190984i 0.492986 0.190984i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(80\) 0.172075 0.0666624i 0.172075 0.0666624i
\(81\) 0.141182 + 0.128704i 0.141182 + 0.128704i
\(82\) 0 0
\(83\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.136374 0.124322i 0.136374 0.124322i −0.602635 0.798017i \(-0.705882\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.510366 0.197717i −0.510366 0.197717i
\(93\) 0.0276404 0.298288i 0.0276404 0.298288i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.156896 0.0971461i −0.156896 0.0971461i 0.445738 0.895163i \(-0.352941\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(98\) 0 0
\(99\) −0.517627 0.471880i −0.517627 0.471880i
\(100\) 0.949499 + 0.177492i 0.949499 + 0.177492i
\(101\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(102\) 0 0
\(103\) 0.0922684 + 0.995734i 0.0922684 + 0.995734i
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(108\) −0.254696 0.895163i −0.254696 0.895163i
\(109\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(110\) 0 0
\(111\) 0.294043 + 0.590517i 0.294043 + 0.590517i
\(112\) 0 0
\(113\) 0.136374 1.47171i 0.136374 1.47171i −0.602635 0.798017i \(-0.705882\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(114\) 0 0
\(115\) 0.0608671 + 0.0806011i 0.0608671 + 0.0806011i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.739009 + 0.673696i 0.739009 + 0.673696i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.329838 0.436776i 0.329838 0.436776i
\(125\) −0.268104 0.244410i −0.268104 0.244410i
\(126\) 0 0
\(127\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(132\) 0.149783 + 0.526432i 0.149783 + 0.526432i
\(133\) 0 0
\(134\) 0 0
\(135\) −0.0470007 + 0.165190i −0.0470007 + 0.165190i
\(136\) 0 0
\(137\) −0.181395 + 0.0339085i −0.181395 + 0.0339085i −0.273663 0.961826i \(-0.588235\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(138\) 0 0
\(139\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(140\) 0 0
\(141\) −0.914845 0.171014i −0.914845 0.171014i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.191683 0.673696i 0.191683 0.673696i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.243964 0.489946i −0.243964 0.489946i
\(148\) −0.111208 + 1.20013i −0.111208 + 1.20013i
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.0941813 + 0.0364860i −0.0941813 + 0.0364860i
\(156\) 0 0
\(157\) −1.12388 1.48826i −1.12388 1.48826i −0.850217 0.526432i \(-0.823529\pi\)
−0.273663 0.961826i \(-0.588235\pi\)
\(158\) 0 0
\(159\) −0.808958 −0.808958
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −0.537235 + 0.711414i −0.537235 + 0.711414i −0.982973 0.183750i \(-0.941176\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(164\) 0 0
\(165\) 0.0276404 0.0971461i 0.0276404 0.0971461i
\(166\) 0 0
\(167\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(168\) 0 0
\(169\) −0.602635 0.798017i −0.602635 0.798017i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.273663 + 0.961826i −0.273663 + 0.961826i
\(177\) −0.180529 0.634493i −0.180529 0.634493i
\(178\) 0 0
\(179\) −0.757949 0.469302i −0.757949 0.469302i 0.0922684 0.995734i \(-0.470588\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(180\) −0.0955212 + 0.0870791i −0.0955212 + 0.0870791i
\(181\) 1.02474 0.634493i 1.02474 0.634493i 0.0922684 0.995734i \(-0.470588\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.134036 0.177492i 0.134036 0.177492i
\(186\) 0 0
\(187\) 0 0
\(188\) −1.25664 1.14558i −1.25664 1.14558i
\(189\) 0 0
\(190\) 0 0
\(191\) 0.172075 + 1.85699i 0.172075 + 1.85699i 0.445738 + 0.895163i \(0.352941\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(192\) −0.404479 + 0.368731i −0.404479 + 0.368731i
\(193\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.0922684 0.995734i 0.0922684 0.995734i
\(197\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(198\) 0 0
\(199\) −0.876298 + 1.75984i −0.876298 + 1.75984i −0.273663 + 0.961826i \(0.588235\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(200\) 0 0
\(201\) 0.133528 + 0.469302i 0.133528 + 0.469302i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.383366 0.383366
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(212\) −1.25664 0.778076i −1.25664 0.778076i
\(213\) 0.479620 0.963208i 0.479620 0.963208i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.136374 0.124322i 0.136374 0.124322i
\(221\) 0 0
\(222\) 0 0
\(223\) −1.25664 + 0.778076i −1.25664 + 0.778076i −0.982973 0.183750i \(-0.941176\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(224\) 0 0
\(225\) −0.665062 + 0.124322i −0.665062 + 0.124322i
\(226\) 0 0
\(227\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(228\) 0 0
\(229\) 1.73901 0.673696i 1.73901 0.673696i 0.739009 0.673696i \(-0.235294\pi\)
1.00000 \(0\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(234\) 0 0
\(235\) 0.0858734 + 0.301814i 0.0858734 + 0.301814i
\(236\) 0.329838 1.15926i 0.329838 1.15926i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(240\) 0.0992820 0.0185590i 0.0992820 0.0185590i
\(241\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(242\) 0 0
\(243\) 0.623880 + 0.826151i 0.623880 + 0.826151i
\(244\) 0 0
\(245\) −0.111208 + 0.147263i −0.111208 + 0.147263i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.111208 + 1.20013i −0.111208 + 1.20013i 0.739009 + 0.673696i \(0.235294\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(252\) 0 0
\(253\) −0.547326 −0.547326
\(254\) 0 0
\(255\) 0 0
\(256\) −0.982973 + 0.183750i −0.982973 + 0.183750i
\(257\) 1.73901 0.673696i 1.73901 0.673696i 0.739009 0.673696i \(-0.235294\pi\)
1.00000 \(0\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0.121574 + 0.244155i 0.121574 + 0.244155i
\(266\) 0 0
\(267\) 0.0858734 0.0531706i 0.0858734 0.0531706i
\(268\) −0.243964 + 0.857445i −0.243964 + 0.857445i
\(269\) −0.890705 + 0.811985i −0.890705 + 0.811985i −0.982973 0.183750i \(-0.941176\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(270\) 0 0
\(271\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.949499 0.177492i 0.949499 0.177492i
\(276\) −0.254696 0.157701i −0.254696 0.157701i
\(277\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(278\) 0 0
\(279\) −0.104913 + 0.368731i −0.104913 + 0.368731i
\(280\) 0 0
\(281\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(282\) 0 0
\(283\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(284\) 1.67148 1.03494i 1.67148 1.03494i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.445738 0.895163i 0.445738 0.895163i
\(290\) 0 0
\(291\) −0.0746412 0.0680444i −0.0746412 0.0680444i
\(292\) 0 0
\(293\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(294\) 0 0
\(295\) −0.164368 + 0.149841i −0.164368 + 0.149841i
\(296\) 0 0
\(297\) −0.560867 0.742708i −0.560867 0.742708i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.492986 + 0.190984i 0.492986 + 0.190984i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(308\) 0 0
\(309\) −0.0505009 + 0.544991i −0.0505009 + 0.544991i
\(310\) 0 0
\(311\) 0.172075 + 0.0666624i 0.172075 + 0.0666624i 0.445738 0.895163i \(-0.352941\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(312\) 0 0
\(313\) −1.25664 1.14558i −1.25664 1.14558i −0.982973 0.183750i \(-0.941176\pi\)
−0.273663 0.961826i \(-0.588235\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.891477 + 1.79033i 0.891477 + 1.79033i 0.445738 + 0.895163i \(0.352941\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.172075 + 0.0666624i 0.172075 + 0.0666624i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.0176272 + 0.190227i 0.0176272 + 0.190227i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.37821 + 1.25640i 1.37821 + 1.25640i 0.932472 + 0.361242i \(0.117647\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(332\) 0 0
\(333\) −0.231030 0.811985i −0.231030 0.811985i
\(334\) 0 0
\(335\) 0.121574 0.110830i 0.121574 0.110830i
\(336\) 0 0
\(337\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(338\) 0 0
\(339\) 0.221382 0.778076i 0.221382 0.778076i
\(340\) 0 0
\(341\) 0.149783 0.526432i 0.149783 0.526432i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0.0246408 + 0.0494854i 0.0246408 + 0.0494854i
\(346\) 0 0
\(347\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(348\) 0 0
\(349\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.831277 + 1.66943i 0.831277 + 1.66943i 0.739009 + 0.673696i \(0.235294\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(354\) 0 0
\(355\) −0.362789 −0.362789
\(356\) 0.184537 0.184537
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(360\) 0 0
\(361\) 0.932472 0.361242i 0.932472 0.361242i
\(362\) 0 0
\(363\) 0.329838 + 0.436776i 0.329838 + 0.436776i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0.0822551 0.887674i 0.0822551 0.887674i −0.850217 0.526432i \(-0.823529\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(368\) −0.243964 0.489946i −0.243964 0.489946i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0.221382 0.201816i 0.221382 0.201816i
\(373\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(374\) 0 0
\(375\) −0.119662 0.158457i −0.119662 0.158457i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.156896 0.0971461i −0.156896 0.0971461i 0.445738 0.895163i \(-0.352941\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.465346 + 1.63552i 0.465346 + 1.63552i 0.739009 + 0.673696i \(0.235294\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.0505009 0.177492i −0.0505009 0.177492i
\(389\) 0.172075 0.0666624i 0.172075 0.0666624i −0.273663 0.961826i \(-0.588235\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −0.0646279 0.697446i −0.0646279 0.697446i
\(397\) 0.0822551 + 0.887674i 0.0822551 + 0.887674i 0.932472 + 0.361242i \(0.117647\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.582113 + 0.770842i 0.582113 + 0.770842i
\(401\) 0.831277 + 0.322039i 0.831277 + 0.322039i 0.739009 0.673696i \(-0.235294\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.0157142 0.0315584i 0.0157142 0.0315584i
\(406\) 0 0
\(407\) 0.329838 + 1.15926i 0.329838 + 1.15926i
\(408\) 0 0
\(409\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(410\) 0 0
\(411\) −0.101002 −0.101002
\(412\) −0.602635 + 0.798017i −0.602635 + 0.798017i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.658809 1.32307i 0.658809 1.32307i −0.273663 0.961826i \(-0.588235\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(420\) 0 0
\(421\) 1.73901 + 0.673696i 1.73901 + 0.673696i 1.00000 \(0\)
0.739009 + 0.673696i \(0.235294\pi\)
\(422\) 0 0
\(423\) 1.11061 + 0.430254i 1.11061 + 0.430254i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(432\) 0.414845 0.833121i 0.414845 0.833121i
\(433\) 1.02474 1.35698i 1.02474 1.35698i 0.0922684 0.995734i \(-0.470588\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(440\) 0 0
\(441\) 0.191683 + 0.673696i 0.191683 + 0.673696i
\(442\) 0 0
\(443\) 0.0822551 + 0.887674i 0.0822551 + 0.887674i 0.932472 + 0.361242i \(0.117647\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(444\) −0.180529 + 0.634493i −0.180529 + 0.634493i
\(445\) −0.0289531 0.0179270i −0.0289531 0.0179270i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.02474 + 1.35698i 1.02474 + 1.35698i 0.932472 + 0.361242i \(0.117647\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 1.09227 0.995734i 1.09227 0.995734i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.00931926 + 0.100571i −0.00931926 + 0.100571i
\(461\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(462\) 0 0
\(463\) 0.172075 0.0666624i 0.172075 0.0666624i −0.273663 0.961826i \(-0.588235\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(464\) 0 0
\(465\) −0.0543396 + 0.0101578i −0.0543396 + 0.0101578i
\(466\) 0 0
\(467\) 0.136374 1.47171i 0.136374 1.47171i −0.602635 0.798017i \(-0.705882\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.454980 0.913722i −0.454980 0.913722i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.01763 + 0.190227i 1.01763 + 0.190227i
\(478\) 0 0
\(479\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.0922684 + 0.995734i 0.0922684 + 0.995734i
\(485\) −0.00931926 + 0.0327538i −0.00931926 + 0.0327538i
\(486\) 0 0
\(487\) −1.83319 + 0.710182i −1.83319 + 0.710182i −0.850217 + 0.526432i \(0.823529\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(488\) 0 0
\(489\) −0.360583 + 0.328715i −0.360583 + 0.328715i
\(490\) 0 0
\(491\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −0.0576143 + 0.115705i −0.0576143 + 0.115705i
\(496\) 0.538007 0.100571i 0.538007 0.100571i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.184537 + 1.99147i 0.184537 + 1.99147i 0.0922684 + 0.995734i \(0.470588\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(500\) −0.0334740 0.361242i −0.0334740 0.361242i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.243964 0.489946i −0.243964 0.489946i
\(508\) 0 0
\(509\) −0.757949 0.469302i −0.757949 0.469302i 0.0922684 0.995734i \(-0.470588\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.172075 0.0666624i 0.172075 0.0666624i
\(516\) 0 0
\(517\) −1.58561 0.614268i −1.58561 0.614268i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.757949 0.469302i −0.757949 0.469302i 0.0922684 0.995734i \(-0.470588\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(522\) 0 0
\(523\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.243964 + 0.489946i −0.243964 + 0.489946i
\(529\) −0.517627 + 0.471880i −0.517627 + 0.471880i
\(530\) 0 0
\(531\) 0.0778940 + 0.840611i 0.0778940 + 0.840611i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −0.360583 0.328715i −0.360583 0.328715i
\(538\) 0 0
\(539\) −0.273663 0.961826i −0.273663 0.961826i
\(540\) −0.146022 + 0.0904131i −0.146022 + 0.0904131i
\(541\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(542\) 0 0
\(543\) 0.615129 0.238302i 0.615129 0.238302i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(548\) −0.156896 0.0971461i −0.156896 0.0971461i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.0899627 0.0820119i 0.0899627 0.0820119i
\(556\) 0 0
\(557\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(564\) −0.560867 0.742708i −0.560867 0.742708i
\(565\) −0.268104 + 0.0501174i −0.268104 + 0.0501174i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) −0.0941813 + 1.01638i −0.0941813 + 1.01638i
\(574\) 0 0
\(575\) −0.318605 + 0.421902i −0.318605 + 0.421902i
\(576\) 0.595521 0.368731i 0.595521 0.368731i
\(577\) −0.404479 + 1.42160i −0.404479 + 1.42160i 0.445738 + 0.895163i \(0.352941\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.45285 0.271585i −1.45285 0.271585i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.136374 + 1.47171i 0.136374 + 1.47171i 0.739009 + 0.673696i \(0.235294\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(588\) 0.149783 0.526432i 0.149783 0.526432i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.890705 + 0.811985i −0.890705 + 0.811985i
\(593\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.648443 + 0.858677i −0.648443 + 0.858677i
\(598\) 0 0
\(599\) −0.876298 + 0.163808i −0.876298 + 0.163808i −0.602635 0.798017i \(-0.705882\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(600\) 0 0
\(601\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(602\) 0 0
\(603\) −0.0576143 0.621757i −0.0576143 0.621757i
\(604\) 0 0
\(605\) 0.0822551 0.165190i 0.0822551 0.165190i
\(606\) 0 0
\(607\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.96595 −1.96595 −0.982973 0.183750i \(-0.941176\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(618\) 0 0
\(619\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(620\) −0.0941813 0.0364860i −0.0941813 0.0364860i
\(621\) 0.500718 + 0.0936005i 0.500718 + 0.0936005i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.400718 0.804750i 0.400718 0.804750i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.172075 1.85699i 0.172075 1.85699i
\(629\) 0 0
\(630\) 0 0
\(631\) 0.658809 1.32307i 0.658809 1.32307i −0.273663 0.961826i \(-0.588235\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −0.597827 0.544991i −0.597827 0.544991i
\(637\) 0 0
\(638\) 0 0
\(639\) −0.829838 + 1.09888i −0.829838 + 1.09888i
\(640\) 0 0
\(641\) 1.37821 0.533922i 1.37821 0.533922i 0.445738 0.895163i \(-0.352941\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(642\) 0 0
\(643\) 1.67148 1.03494i 1.67148 1.03494i 0.739009 0.673696i \(-0.235294\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.329838 + 1.15926i 0.329838 + 1.15926i 0.932472 + 0.361242i \(0.117647\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(648\) 0 0
\(649\) −0.111208 1.20013i −0.111208 1.20013i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.876298 + 0.163808i −0.876298 + 0.163808i
\(653\) −0.876298 0.163808i −0.876298 0.163808i −0.273663 0.961826i \(-0.588235\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(660\) 0.0858734 0.0531706i 0.0858734 0.0531706i
\(661\) 1.02474 1.35698i 1.02474 1.35698i 0.0922684 0.995734i \(-0.470588\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −0.754330 + 0.292229i −0.754330 + 0.292229i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(674\) 0 0
\(675\) −0.898998 −0.898998
\(676\) 0.0922684 0.995734i 0.0922684 0.995734i
\(677\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.18475 + 0.221468i 1.18475 + 0.221468i 0.739009 0.673696i \(-0.235294\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(684\) 0 0
\(685\) 0.0151791 + 0.0304837i 0.0151791 + 0.0304837i
\(686\) 0 0
\(687\) 1.00335 0.187559i 1.00335 0.187559i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.0505009 + 0.177492i −0.0505009 + 0.177492i −0.982973 0.183750i \(-0.941176\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.850217 + 0.526432i −0.850217 + 0.526432i
\(705\) 0.0158468 + 0.171014i 0.0158468 + 0.171014i
\(706\) 0 0
\(707\) 0 0
\(708\) 0.294043 0.590517i 0.294043 0.590517i
\(709\) 0.726337 + 0.961826i 0.726337 + 0.961826i 1.00000 \(0\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.133528 + 0.268160i 0.133528 + 0.268160i
\(714\) 0 0
\(715\) 0 0
\(716\) −0.243964 0.857445i −0.243964 0.857445i
\(717\) 0 0
\(718\) 0 0
\(719\) −1.83319 0.710182i −1.83319 0.710182i −0.982973 0.183750i \(-0.941176\pi\)
−0.850217 0.526432i \(-0.823529\pi\)
\(720\) −0.129256 −0.129256
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 1.18475 + 0.221468i 1.18475 + 0.221468i
\(725\) 0 0
\(726\) 0 0
\(727\) −0.757949 0.469302i −0.757949 0.469302i 0.0922684 0.995734i \(-0.470588\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(728\) 0 0
\(729\) 0.167410 + 0.336205i 0.167410 + 0.336205i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(734\) 0 0
\(735\) −0.0746412 + 0.0680444i −0.0746412 + 0.0680444i
\(736\) 0 0
\(737\) 0.0822551 + 0.887674i 0.0822551 + 0.887674i
\(738\) 0 0
\(739\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(740\) 0.218629 0.0408689i 0.218629 0.0408689i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.0505009 + 0.177492i −0.0505009 + 0.177492i −0.982973 0.183750i \(-0.941176\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(752\) −0.156896 1.69318i −0.156896 1.69318i
\(753\) −0.180529 + 0.634493i −0.180529 + 0.634493i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.243964 0.489946i −0.243964 0.489946i 0.739009 0.673696i \(-0.235294\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(758\) 0 0
\(759\) −0.294465 0.0550451i −0.294465 0.0550451i
\(760\) 0 0
\(761\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.12388 + 1.48826i −1.12388 + 1.48826i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.547326 −0.547326
\(769\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(770\) 0 0
\(771\) 1.00335 0.187559i 1.00335 0.187559i
\(772\) 0 0
\(773\) 0.172075 0.0666624i 0.172075 0.0666624i −0.273663 0.961826i \(-0.588235\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(774\) 0 0
\(775\) −0.318605 0.421902i −0.318605 0.421902i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 1.18475 1.56886i 1.18475 1.56886i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.739009 0.673696i 0.739009 0.673696i
\(785\) −0.207397 + 0.274638i −0.207397 + 0.274638i
\(786\) 0 0
\(787\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0.0408531 + 0.143584i 0.0408531 + 0.143584i
\(796\) −1.83319 + 0.710182i −1.83319 + 0.710182i
\(797\) −1.58561 0.981767i −1.58561 0.981767i −0.982973 0.183750i \(-0.941176\pi\)
−0.602635 0.798017i \(-0.705882\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −0.120527 + 0.0466926i −0.120527 + 0.0466926i
\(802\) 0 0
\(803\) 0 0
\(804\) −0.217488 + 0.436776i −0.217488 + 0.436776i
\(805\) 0 0
\(806\) 0 0
\(807\) −0.560867 + 0.347274i −0.560867 + 0.347274i
\(808\) 0 0
\(809\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(810\) 0 0
\(811\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0.153401 + 0.0594279i 0.153401 + 0.0594279i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(822\) 0 0
\(823\) −1.70043 −1.70043 −0.850217 0.526432i \(-0.823529\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(824\) 0 0
\(825\) 0.528687 0.528687
\(826\) 0 0
\(827\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(828\) 0.283311 + 0.258272i 0.283311 + 0.258272i
\(829\) −0.404479 1.42160i −0.404479 1.42160i −0.850217 0.526432i \(-0.823529\pi\)
0.445738 0.895163i \(-0.352941\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −0.227055 + 0.455989i −0.227055 + 0.455989i
\(838\) 0 0
\(839\) 0.136374 + 1.47171i 0.136374 + 1.47171i 0.739009 + 0.673696i \(0.235294\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(840\) 0 0
\(841\) −0.850217 + 0.526432i −0.850217 + 0.526432i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −0.111208 + 0.147263i −0.111208 + 0.147263i
\(846\) 0 0
\(847\) 0 0
\(848\) −0.404479 1.42160i −0.404479 1.42160i
\(849\) 0 0
\(850\) 0 0
\(851\) −0.560867 0.347274i −0.560867 0.347274i
\(852\) 1.00335 0.388701i 1.00335 0.388701i
\(853\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(858\) 0 0
\(859\) −1.83319 0.342683i −1.83319 0.342683i −0.850217 0.526432i \(-0.823529\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0.726337 0.961826i 0.726337 0.961826i −0.273663 0.961826i \(-0.588235\pi\)
1.00000 \(0\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0.329838 0.436776i 0.329838 0.436776i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0.0778940 + 0.103148i 0.0778940 + 0.103148i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0.184537 0.184537
\(881\) −1.20527 −1.20527 −0.602635 0.798017i \(-0.705882\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(882\) 0 0
\(883\) −0.757949 1.52217i −0.757949 1.52217i −0.850217 0.526432i \(-0.823529\pi\)
0.0922684 0.995734i \(-0.470588\pi\)
\(884\) 0 0
\(885\) −0.103501 + 0.0640848i −0.103501 + 0.0640848i
\(886\) 0 0
\(887\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.0851549 + 0.171014i 0.0851549 + 0.171014i
\(892\) −1.45285 0.271585i −1.45285 0.271585i
\(893\) 0 0
\(894\) 0 0
\(895\) −0.0450203 + 0.158230i −0.0450203 + 0.158230i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −0.575241 0.356174i −0.575241 0.356174i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −0.164368 0.149841i −0.164368 0.149841i
\(906\) 0 0
\(907\) −0.243964 + 0.489946i −0.243964 + 0.489946i −0.982973 0.183750i \(-0.941176\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0.0822551 + 0.887674i 0.0822551 + 0.887674i 0.932472 + 0.361242i \(0.117647\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.73901 + 0.673696i 1.73901 + 0.673696i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.08561 + 0.420567i 1.08561 + 0.420567i
\(926\) 0 0
\(927\) 0.191683 0.673696i 0.191683 0.673696i
\(928\) 0 0
\(929\) −0.510366 0.197717i −0.510366 0.197717i 0.0922684 0.995734i \(-0.470588\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0.0858734 + 0.0531706i 0.0858734 + 0.0531706i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(938\) 0 0
\(939\) −0.560867 0.742708i −0.560867 0.742708i
\(940\) −0.139869 + 0.280896i −0.139869 + 0.280896i
\(941\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 1.02474 0.634493i 1.02474 0.634493i
\(945\) 0 0
\(946\) 0 0
\(947\) −0.243964 + 0.489946i −0.243964 + 0.489946i −0.982973 0.183750i \(-0.941176\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0.299566 + 1.05286i 0.299566 + 1.05286i
\(952\) 0 0
\(953\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(954\) 0 0
\(955\) 0.320911 0.124322i 0.320911 0.124322i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0.0858734 + 0.0531706i 0.0858734 + 0.0531706i
\(961\) 0.688508 0.128704i 0.688508 0.128704i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0.397365 + 0.798017i 0.397365 + 0.798017i 1.00000 \(0\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(972\) −0.0955212 + 1.03084i −0.0955212 + 1.03084i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.18475 0.221468i 1.18475 0.221468i 0.445738 0.895163i \(-0.352941\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(978\) 0 0
\(979\) 0.172075 0.0666624i 0.172075 0.0666624i
\(980\) −0.181395 + 0.0339085i −0.181395 + 0.0339085i
\(981\) 0 0
\(982\) 0 0
\(983\) −0.547326 −0.547326 −0.273663 0.961826i \(-0.588235\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −0.890705 + 1.17948i −0.890705 + 1.17948i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(992\) 0 0
\(993\) 0.615129 + 0.814562i 0.615129 + 0.814562i
\(994\) 0 0
\(995\) 0.356612 + 0.0666624i 0.356612 + 0.0666624i
\(996\) 0 0
\(997\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(998\) 0 0
\(999\) −0.103501 1.11695i −0.103501 1.11695i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 1133.1.s.a.890.1 yes 16
11.10 odd 2 CM 1133.1.s.a.890.1 yes 16
103.64 even 17 inner 1133.1.s.a.373.1 16
1133.373 odd 34 inner 1133.1.s.a.373.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1133.1.s.a.373.1 16 103.64 even 17 inner
1133.1.s.a.373.1 16 1133.373 odd 34 inner
1133.1.s.a.890.1 yes 16 1.1 even 1 trivial
1133.1.s.a.890.1 yes 16 11.10 odd 2 CM