Properties

Label 1096.1.u.a.651.1
Level $1096$
Weight $1$
Character 1096.651
Analytic conductor $0.547$
Analytic rank $0$
Dimension $16$
Projective image $D_{34}$
CM discriminant -8
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1096,1,Mod(99,1096)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1096, base_ring=CyclotomicField(34))
 
chi = DirichletCharacter(H, H._module([17, 17, 31]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1096.99");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1096 = 2^{3} \cdot 137 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1096.u (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: \(0.546975253846\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{34}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{34} - \cdots)\)

Embedding invariants

Embedding label 651.1
Root \(-0.0922684 + 0.995734i\) of defining polynomial
Character \(\chi\) \(=\) 1096.651
Dual form 1096.1.u.a.963.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0922684 + 0.995734i) q^{2} +(-1.72198 + 0.857445i) q^{3} +(-0.982973 - 0.183750i) q^{4} +(-0.694903 - 1.79375i) q^{6} +(0.273663 - 0.961826i) q^{8} +(1.62738 - 2.15499i) q^{9} +O(q^{10})\) \(q+(-0.0922684 + 0.995734i) q^{2} +(-1.72198 + 0.857445i) q^{3} +(-0.982973 - 0.183750i) q^{4} +(-0.694903 - 1.79375i) q^{6} +(0.273663 - 0.961826i) q^{8} +(1.62738 - 2.15499i) q^{9} +(1.83319 + 0.342683i) q^{11} +(1.85022 - 0.526432i) q^{12} +(0.932472 + 0.361242i) q^{16} +(-0.510366 - 1.79375i) q^{17} +(1.99565 + 1.81927i) q^{18} +(-0.404479 - 0.368731i) q^{19} +(-0.510366 + 1.79375i) q^{22} +(0.353470 + 1.89090i) q^{24} +(0.982973 - 0.183750i) q^{25} +(-0.601052 + 3.21535i) q^{27} +(-0.445738 + 0.895163i) q^{32} +(-3.45055 + 0.981767i) q^{33} +(1.83319 - 0.342683i) q^{34} +(-1.99565 + 1.81927i) q^{36} +(0.404479 - 0.368731i) q^{38} +1.79033i q^{41} +(0.486734 - 0.533922i) q^{43} +(-1.73901 - 0.673696i) q^{44} +(-1.91545 + 0.177492i) q^{48} +(0.445738 - 0.895163i) q^{49} +(0.0922684 + 0.995734i) q^{50} +(2.41689 + 2.65120i) q^{51} +(-3.14617 - 0.895163i) q^{54} +(1.01267 + 0.288130i) q^{57} +(-0.111208 + 0.147263i) q^{59} +(-0.850217 - 0.526432i) q^{64} +(-0.659202 - 3.52642i) q^{66} +(-1.01267 - 1.63552i) q^{67} +(0.172075 + 1.85699i) q^{68} +(-1.62738 - 2.15499i) q^{72} +(0.757949 + 0.469302i) q^{73} +(-1.53511 + 1.15926i) q^{75} +(0.329838 + 0.436776i) q^{76} +(-0.982973 - 3.45479i) q^{81} +(-1.78269 - 0.165190i) q^{82} +(1.01267 + 0.288130i) q^{83} +(0.486734 + 0.533922i) q^{86} +(0.831277 - 1.66943i) q^{88} +(1.34164 - 0.124322i) q^{89} -1.92365i q^{96} +(0.0675278 - 0.361242i) q^{97} +(0.850217 + 0.526432i) q^{98} +(3.72177 - 3.39284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{2} - q^{4} + q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + q^{2} - q^{4} + q^{8} - q^{9} + 2 q^{11} + 17 q^{12} - q^{16} - 2 q^{17} + q^{18} - 2 q^{19} - 2 q^{22} + q^{25} + q^{32} + 2 q^{34} - q^{36} + 2 q^{38} - 15 q^{44} - q^{49} - q^{50} - 17 q^{54} - 2 q^{59} - q^{64} - 2 q^{68} + q^{72} + 2 q^{73} - 2 q^{76} - q^{81} - 2 q^{88} + 17 q^{97} + q^{98} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1096\mathbb{Z}\right)^\times\).

\(n\) \(549\) \(823\) \(825\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{29}{34}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0922684 + 0.995734i −0.0922684 + 0.995734i
\(3\) −1.72198 + 0.857445i −1.72198 + 0.857445i −0.739009 + 0.673696i \(0.764706\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(4\) −0.982973 0.183750i −0.982973 0.183750i
\(5\) 0 0 0.995734 0.0922684i \(-0.0294118\pi\)
−0.995734 + 0.0922684i \(0.970588\pi\)
\(6\) −0.694903 1.79375i −0.694903 1.79375i
\(7\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(8\) 0.273663 0.961826i 0.273663 0.961826i
\(9\) 1.62738 2.15499i 1.62738 2.15499i
\(10\) 0 0
\(11\) 1.83319 + 0.342683i 1.83319 + 0.342683i 0.982973 0.183750i \(-0.0588235\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(12\) 1.85022 0.526432i 1.85022 0.526432i
\(13\) 0 0 −0.526432 0.850217i \(-0.676471\pi\)
0.526432 + 0.850217i \(0.323529\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.932472 + 0.361242i 0.932472 + 0.361242i
\(17\) −0.510366 1.79375i −0.510366 1.79375i −0.602635 0.798017i \(-0.705882\pi\)
0.0922684 0.995734i \(-0.470588\pi\)
\(18\) 1.99565 + 1.81927i 1.99565 + 1.81927i
\(19\) −0.404479 0.368731i −0.404479 0.368731i 0.445738 0.895163i \(-0.352941\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.510366 + 1.79375i −0.510366 + 1.79375i
\(23\) 0 0 0.361242 0.932472i \(-0.382353\pi\)
−0.361242 + 0.932472i \(0.617647\pi\)
\(24\) 0.353470 + 1.89090i 0.353470 + 1.89090i
\(25\) 0.982973 0.183750i 0.982973 0.183750i
\(26\) 0 0
\(27\) −0.601052 + 3.21535i −0.601052 + 3.21535i
\(28\) 0 0
\(29\) 0 0 0.361242 0.932472i \(-0.382353\pi\)
−0.361242 + 0.932472i \(0.617647\pi\)
\(30\) 0 0
\(31\) 0 0 −0.673696 0.739009i \(-0.735294\pi\)
0.673696 + 0.739009i \(0.264706\pi\)
\(32\) −0.445738 + 0.895163i −0.445738 + 0.895163i
\(33\) −3.45055 + 0.981767i −3.45055 + 0.981767i
\(34\) 1.83319 0.342683i 1.83319 0.342683i
\(35\) 0 0
\(36\) −1.99565 + 1.81927i −1.99565 + 1.81927i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0.404479 0.368731i 0.404479 0.368731i
\(39\) 0 0
\(40\) 0 0
\(41\) 1.79033i 1.79033i 0.445738 + 0.895163i \(0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(42\) 0 0
\(43\) 0.486734 0.533922i 0.486734 0.533922i −0.445738 0.895163i \(-0.647059\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(44\) −1.73901 0.673696i −1.73901 0.673696i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.798017 0.602635i \(-0.794118\pi\)
0.798017 + 0.602635i \(0.205882\pi\)
\(48\) −1.91545 + 0.177492i −1.91545 + 0.177492i
\(49\) 0.445738 0.895163i 0.445738 0.895163i
\(50\) 0.0922684 + 0.995734i 0.0922684 + 0.995734i
\(51\) 2.41689 + 2.65120i 2.41689 + 2.65120i
\(52\) 0 0
\(53\) 0 0 0.673696 0.739009i \(-0.264706\pi\)
−0.673696 + 0.739009i \(0.735294\pi\)
\(54\) −3.14617 0.895163i −3.14617 0.895163i
\(55\) 0 0
\(56\) 0 0
\(57\) 1.01267 + 0.288130i 1.01267 + 0.288130i
\(58\) 0 0
\(59\) −0.111208 + 0.147263i −0.111208 + 0.147263i −0.850217 0.526432i \(-0.823529\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(60\) 0 0
\(61\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.850217 0.526432i −0.850217 0.526432i
\(65\) 0 0
\(66\) −0.659202 3.52642i −0.659202 3.52642i
\(67\) −1.01267 1.63552i −1.01267 1.63552i −0.739009 0.673696i \(-0.764706\pi\)
−0.273663 0.961826i \(-0.588235\pi\)
\(68\) 0.172075 + 1.85699i 0.172075 + 1.85699i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.183750 0.982973i \(-0.558824\pi\)
0.183750 + 0.982973i \(0.441176\pi\)
\(72\) −1.62738 2.15499i −1.62738 2.15499i
\(73\) 0.757949 + 0.469302i 0.757949 + 0.469302i 0.850217 0.526432i \(-0.176471\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(74\) 0 0
\(75\) −1.53511 + 1.15926i −1.53511 + 1.15926i
\(76\) 0.329838 + 0.436776i 0.329838 + 0.436776i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.895163 0.445738i \(-0.852941\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(80\) 0 0
\(81\) −0.982973 3.45479i −0.982973 3.45479i
\(82\) −1.78269 0.165190i −1.78269 0.165190i
\(83\) 1.01267 + 0.288130i 1.01267 + 0.288130i 0.739009 0.673696i \(-0.235294\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.486734 + 0.533922i 0.486734 + 0.533922i
\(87\) 0 0
\(88\) 0.831277 1.66943i 0.831277 1.66943i
\(89\) 1.34164 0.124322i 1.34164 0.124322i 0.602635 0.798017i \(-0.294118\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.92365i 1.92365i
\(97\) 0.0675278 0.361242i 0.0675278 0.361242i −0.932472 0.361242i \(-0.882353\pi\)
1.00000 \(0\)
\(98\) 0.850217 + 0.526432i 0.850217 + 0.526432i
\(99\) 3.72177 3.39284i 3.72177 3.39284i
\(100\) −1.00000 −1.00000
\(101\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(102\) −2.86289 + 2.16195i −2.86289 + 2.16195i
\(103\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.757949 + 1.52217i 0.757949 + 1.52217i 0.850217 + 0.526432i \(0.176471\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(108\) 1.18164 3.05016i 1.18164 3.05016i
\(109\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.328972 + 1.75984i 0.328972 + 1.75984i 0.602635 + 0.798017i \(0.294118\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(114\) −0.380338 + 0.981767i −0.380338 + 0.981767i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.136374 0.124322i −0.136374 0.124322i
\(119\) 0 0
\(120\) 0 0
\(121\) 2.31068 + 0.895163i 2.31068 + 0.895163i
\(122\) 0 0
\(123\) −1.53511 3.08291i −1.53511 3.08291i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0.602635 0.798017i 0.602635 0.798017i
\(129\) −0.380338 + 1.33675i −0.380338 + 1.33675i
\(130\) 0 0
\(131\) −0.260991 0.673696i −0.260991 0.673696i 0.739009 0.673696i \(-0.235294\pi\)
−1.00000 \(\pi\)
\(132\) 3.57220 0.331013i 3.57220 0.331013i
\(133\) 0 0
\(134\) 1.72198 0.857445i 1.72198 0.857445i
\(135\) 0 0
\(136\) −1.86494 −1.86494
\(137\) −0.739009 + 0.673696i −0.739009 + 0.673696i
\(138\) 0 0
\(139\) 0.0505009 0.544991i 0.0505009 0.544991i −0.932472 0.361242i \(-0.882353\pi\)
0.982973 0.183750i \(-0.0588235\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 2.29596 1.42160i 2.29596 1.42160i
\(145\) 0 0
\(146\) −0.537235 + 0.711414i −0.537235 + 0.711414i
\(147\) 1.92365i 1.92365i
\(148\) 0 0
\(149\) 0 0 0.961826 0.273663i \(-0.0882353\pi\)
−0.961826 + 0.273663i \(0.911765\pi\)
\(150\) −1.01267 1.63552i −1.01267 1.63552i
\(151\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(152\) −0.465346 + 0.288130i −0.465346 + 0.288130i
\(153\) −4.69608 1.81927i −4.69608 1.81927i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.995734 0.0922684i \(-0.970588\pi\)
0.995734 + 0.0922684i \(0.0294118\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 3.53075 0.660012i 3.53075 0.660012i
\(163\) −0.328972 + 0.163808i −0.328972 + 0.163808i −0.602635 0.798017i \(-0.705882\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(164\) 0.328972 1.75984i 0.328972 1.75984i
\(165\) 0 0
\(166\) −0.380338 + 0.981767i −0.380338 + 0.981767i
\(167\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(168\) 0 0
\(169\) −0.445738 + 0.895163i −0.445738 + 0.895163i
\(170\) 0 0
\(171\) −1.45285 + 0.271585i −1.45285 + 0.271585i
\(172\) −0.576554 + 0.435393i −0.576554 + 0.435393i
\(173\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.58561 + 0.981767i 1.58561 + 0.981767i
\(177\) 0.0652282 0.348940i 0.0652282 0.348940i
\(178\) 1.34739i 1.34739i
\(179\) −1.42871 1.07891i −1.42871 1.07891i −0.982973 0.183750i \(-0.941176\pi\)
−0.445738 0.895163i \(-0.647059\pi\)
\(180\) 0 0
\(181\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.320911 3.46318i −0.320911 3.46318i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.961826 0.273663i \(-0.911765\pi\)
0.961826 + 0.273663i \(0.0882353\pi\)
\(192\) 1.91545 + 0.177492i 1.91545 + 0.177492i
\(193\) −0.538007 1.89090i −0.538007 1.89090i −0.445738 0.895163i \(-0.647059\pi\)
−0.0922684 0.995734i \(-0.529412\pi\)
\(194\) 0.353470 + 0.100571i 0.353470 + 0.100571i
\(195\) 0 0
\(196\) −0.602635 + 0.798017i −0.602635 + 0.798017i
\(197\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(198\) 3.03496 + 4.01894i 3.03496 + 4.01894i
\(199\) 0 0 0.798017 0.602635i \(-0.205882\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(200\) 0.0922684 0.995734i 0.0922684 0.995734i
\(201\) 3.14617 + 1.94803i 3.14617 + 1.94803i
\(202\) 0 0
\(203\) 0 0
\(204\) −1.88858 3.05016i −1.88858 3.05016i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.615129 0.814562i −0.615129 0.814562i
\(210\) 0 0
\(211\) −0.0170269 + 0.183750i −0.0170269 + 0.183750i 0.982973 + 0.183750i \(0.0588235\pi\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.58561 + 0.614268i −1.58561 + 0.614268i
\(215\) 0 0
\(216\) 2.92812 + 1.45803i 2.92812 + 1.45803i
\(217\) 0 0
\(218\) 0 0
\(219\) −1.70757 0.158230i −1.70757 0.158230i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.673696 0.739009i \(-0.735294\pi\)
0.673696 + 0.739009i \(0.264706\pi\)
\(224\) 0 0
\(225\) 1.20369 2.41733i 1.20369 2.41733i
\(226\) −1.78269 + 0.165190i −1.78269 + 0.165190i
\(227\) −0.840204 0.634493i −0.840204 0.634493i 0.0922684 0.995734i \(-0.470588\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(228\) −0.942485 0.469302i −0.942485 0.469302i
\(229\) 0 0 0.526432 0.850217i \(-0.323529\pi\)
−0.526432 + 0.850217i \(0.676471\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.367499i 0.367499i 0.982973 + 0.183750i \(0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.136374 0.124322i 0.136374 0.124322i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.798017 0.602635i \(-0.205882\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(240\) 0 0
\(241\) −0.353470 + 0.100571i −0.353470 + 0.100571i −0.445738 0.895163i \(-0.647059\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(242\) −1.10455 + 2.21823i −1.10455 + 2.21823i
\(243\) 2.45127 + 2.68891i 2.45127 + 2.68891i
\(244\) 0 0
\(245\) 0 0
\(246\) 3.21140 1.24410i 3.21140 1.24410i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.99086 + 0.372156i −1.99086 + 0.372156i
\(250\) 0 0
\(251\) −0.260991 + 0.673696i −0.260991 + 0.673696i 0.739009 + 0.673696i \(0.235294\pi\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.739009 + 0.673696i 0.739009 + 0.673696i
\(257\) 0.243964 + 0.857445i 0.243964 + 0.857445i 0.982973 + 0.183750i \(0.0588235\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(258\) −1.29596 0.502056i −1.29596 0.502056i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.694903 0.197717i 0.694903 0.197717i
\(263\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(264\) 3.58750i 3.58750i
\(265\) 0 0
\(266\) 0 0
\(267\) −2.20369 + 1.36447i −2.20369 + 1.36447i
\(268\) 0.694903 + 1.79375i 0.694903 + 1.79375i
\(269\) 0 0 0.995734 0.0922684i \(-0.0294118\pi\)
−0.995734 + 0.0922684i \(0.970588\pi\)
\(270\) 0 0
\(271\) 0 0 0.895163 0.445738i \(-0.147059\pi\)
−0.895163 + 0.445738i \(0.852941\pi\)
\(272\) 0.172075 1.85699i 0.172075 1.85699i
\(273\) 0 0
\(274\) −0.602635 0.798017i −0.602635 0.798017i
\(275\) 1.86494 1.86494
\(276\) 0 0
\(277\) 0 0 0.895163 0.445738i \(-0.147059\pi\)
−0.895163 + 0.445738i \(0.852941\pi\)
\(278\) 0.538007 + 0.100571i 0.538007 + 0.100571i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.465346 + 0.288130i −0.465346 + 0.288130i −0.739009 0.673696i \(-0.764706\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(282\) 0 0
\(283\) 0.726337 0.961826i 0.726337 0.961826i −0.273663 0.961826i \(-0.588235\pi\)
1.00000 \(0\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.20369 + 2.41733i 1.20369 + 2.41733i
\(289\) −2.10685 + 1.30451i −2.10685 + 1.30451i
\(290\) 0 0
\(291\) 0.193463 + 0.679953i 0.193463 + 0.679953i
\(292\) −0.658809 0.600584i −0.658809 0.600584i
\(293\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(294\) −1.91545 0.177492i −1.91545 0.177492i
\(295\) 0 0
\(296\) 0 0
\(297\) −2.20369 + 5.68837i −2.20369 + 5.68837i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.72198 0.857445i 1.72198 0.857445i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.243964 0.489946i −0.243964 0.489946i
\(305\) 0 0
\(306\) 2.24481 4.50819i 2.24481 4.50819i
\(307\) 1.85022 0.526432i 1.85022 0.526432i 0.850217 0.526432i \(-0.176471\pi\)
1.00000 \(0\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −1.25664 0.778076i −1.25664 0.778076i −0.273663 0.961826i \(-0.588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.673696 0.739009i \(-0.264706\pi\)
−0.673696 + 0.739009i \(0.735294\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −2.61035 1.97124i −2.61035 1.97124i
\(322\) 0 0
\(323\) −0.454980 + 0.913722i −0.454980 + 0.913722i
\(324\) 0.331420 + 3.57659i 0.331420 + 3.57659i
\(325\) 0 0
\(326\) −0.132756 0.342683i −0.132756 0.342683i
\(327\) 0 0
\(328\) 1.72198 + 0.489946i 1.72198 + 0.489946i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(332\) −0.942485 0.469302i −0.942485 0.469302i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.0822551 + 0.887674i −0.0822551 + 0.887674i 0.850217 + 0.526432i \(0.176471\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(338\) −0.850217 0.526432i −0.850217 0.526432i
\(339\) −2.07545 2.74834i −2.07545 2.74834i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.136374 1.47171i −0.136374 1.47171i
\(343\) 0 0
\(344\) −0.380338 0.614268i −0.380338 0.614268i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.02474 + 0.634493i 1.02474 + 0.634493i 0.932472 0.361242i \(-0.117647\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(348\) 0 0
\(349\) 0 0 0.798017 0.602635i \(-0.205882\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.12388 + 1.48826i −1.12388 + 1.48826i
\(353\) 0.942485 + 0.469302i 0.942485 + 0.469302i 0.850217 0.526432i \(-0.176471\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(354\) 0.341433 + 0.0971461i 0.341433 + 0.0971461i
\(355\) 0 0
\(356\) −1.34164 0.124322i −1.34164 0.124322i
\(357\) 0 0
\(358\) 1.20614 1.32307i 1.20614 1.32307i
\(359\) 0 0 −0.361242 0.932472i \(-0.617647\pi\)
0.361242 + 0.932472i \(0.382353\pi\)
\(360\) 0 0
\(361\) −0.0646279 0.697446i −0.0646279 0.697446i
\(362\) 0 0
\(363\) −4.74651 + 0.439829i −4.74651 + 0.439829i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(368\) 0 0
\(369\) 3.85814 + 2.91353i 3.85814 + 2.91353i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(374\) 3.47802 3.47802
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.876298 1.75984i 0.876298 1.75984i 0.273663 0.961826i \(-0.411765\pi\)
0.602635 0.798017i \(-0.294118\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(384\) −0.353470 + 1.89090i −0.353470 + 1.89090i
\(385\) 0 0
\(386\) 1.93247 0.361242i 1.93247 0.361242i
\(387\) −0.358499 1.91780i −0.358499 1.91780i
\(388\) −0.132756 + 0.342683i −0.132756 + 0.342683i
\(389\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.739009 0.673696i −0.739009 0.673696i
\(393\) 1.02708 + 0.936306i 1.02708 + 0.936306i
\(394\) 0 0
\(395\) 0 0
\(396\) −4.28183 + 2.65120i −4.28183 + 2.65120i
\(397\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.982973 + 0.183750i 0.982973 + 0.183750i
\(401\) 1.59603i 1.59603i −0.602635 0.798017i \(-0.705882\pi\)
0.602635 0.798017i \(-0.294118\pi\)
\(402\) −2.23001 + 2.95301i −2.23001 + 2.95301i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 3.21140 1.59909i 3.21140 1.59909i
\(409\) 0.181395 1.95756i 0.181395 1.95756i −0.0922684 0.995734i \(-0.529412\pi\)
0.273663 0.961826i \(-0.411765\pi\)
\(410\) 0 0
\(411\) 0.694903 1.79375i 0.694903 1.79375i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.380338 + 0.981767i 0.380338 + 0.981767i
\(418\) 0.867844 0.537346i 0.867844 0.537346i
\(419\) −0.538007 + 1.89090i −0.538007 + 1.89090i −0.0922684 + 0.995734i \(0.529412\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) −0.181395 0.0339085i −0.181395 0.0339085i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.831277 1.66943i −0.831277 1.66943i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.465346 1.63552i −0.465346 1.63552i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.995734 0.0922684i \(-0.970588\pi\)
0.995734 + 0.0922684i \(0.0294118\pi\)
\(432\) −1.72198 + 2.78110i −1.72198 + 2.78110i
\(433\) −0.538007 + 1.89090i −0.538007 + 1.89090i −0.0922684 + 0.995734i \(0.529412\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.315110 1.68569i 0.315110 1.68569i
\(439\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(440\) 0 0
\(441\) −1.20369 2.41733i −1.20369 2.41733i
\(442\) 0 0
\(443\) −0.876298 + 1.75984i −0.876298 + 1.75984i −0.273663 + 0.961826i \(0.588235\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.45285 + 1.32445i −1.45285 + 1.32445i −0.602635 + 0.798017i \(0.705882\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(450\) 2.29596 + 1.42160i 2.29596 + 1.42160i
\(451\) −0.613514 + 3.28201i −0.613514 + 3.28201i
\(452\) 1.79033i 1.79033i
\(453\) 0 0
\(454\) 0.709310 0.778076i 0.709310 0.778076i
\(455\) 0 0
\(456\) 0.554262 0.895163i 0.554262 0.895163i
\(457\) 0.646741 + 0.322039i 0.646741 + 0.322039i 0.739009 0.673696i \(-0.235294\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(458\) 0 0
\(459\) 6.07429 0.562866i 6.07429 0.562866i
\(460\) 0 0
\(461\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(462\) 0 0
\(463\) 0 0 −0.361242 0.932472i \(-0.617647\pi\)
0.361242 + 0.932472i \(0.382353\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.365931 0.0339085i −0.365931 0.0339085i
\(467\) −0.243964 0.857445i −0.243964 0.857445i −0.982973 0.183750i \(-0.941176\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.111208 + 0.147263i 0.111208 + 0.147263i
\(473\) 1.07524 0.811985i 1.07524 0.811985i
\(474\) 0 0
\(475\) −0.465346 0.288130i −0.465346 0.288130i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.0675278 0.361242i −0.0675278 0.361242i
\(483\) 0 0
\(484\) −2.10685 1.30451i −2.10685 1.30451i
\(485\) 0 0
\(486\) −2.90362 + 2.19271i −2.90362 + 2.19271i
\(487\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(488\) 0 0
\(489\) 0.426027 0.564150i 0.426027 0.564150i
\(490\) 0 0
\(491\) −1.91545 0.544991i −1.91545 0.544991i −0.982973 0.183750i \(-0.941176\pi\)
−0.932472 0.361242i \(-0.882353\pi\)
\(492\) 0.942485 + 3.31249i 0.942485 + 3.31249i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.186875 2.01670i −0.186875 2.01670i
\(499\) −0.537235 + 1.07891i −0.537235 + 1.07891i 0.445738 + 0.895163i \(0.352941\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.646741 0.322039i −0.646741 0.322039i
\(503\) 0 0 0.526432 0.850217i \(-0.323529\pi\)
−0.526432 + 0.850217i \(0.676471\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.92365i 1.92365i
\(508\) 0 0
\(509\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.739009 + 0.673696i −0.739009 + 0.673696i
\(513\) 1.42871 1.07891i 1.42871 1.07891i
\(514\) −0.876298 + 0.163808i −0.876298 + 0.163808i
\(515\) 0 0
\(516\) 0.619490 1.24410i 0.619490 1.24410i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.328972 1.75984i 0.328972 1.75984i −0.273663 0.961826i \(-0.588235\pi\)
0.602635 0.798017i \(-0.294118\pi\)
\(522\) 0 0
\(523\) −1.18475 + 0.221468i −1.18475 + 0.221468i −0.739009 0.673696i \(-0.764706\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(524\) 0.132756 + 0.710182i 0.132756 + 0.710182i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −3.57220 0.331013i −3.57220 0.331013i
\(529\) −0.739009 0.673696i −0.739009 0.673696i
\(530\) 0 0
\(531\) 0.136374 + 0.479306i 0.136374 + 0.479306i
\(532\) 0 0
\(533\) 0 0
\(534\) −1.15531 2.32018i −1.15531 2.32018i
\(535\) 0 0
\(536\) −1.85022 + 0.526432i −1.85022 + 0.526432i
\(537\) 3.38532 + 0.632827i 3.38532 + 0.632827i
\(538\) 0 0
\(539\) 1.12388 1.48826i 1.12388 1.48826i
\(540\) 0 0
\(541\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.83319 + 0.342683i 1.83319 + 0.342683i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.891477 0.891477 0.445738 0.895163i \(-0.352941\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(548\) 0.850217 0.526432i 0.850217 0.526432i
\(549\) 0 0
\(550\) −0.172075 + 1.85699i −0.172075 + 1.85699i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.149783 + 0.526432i −0.149783 + 0.526432i
\(557\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 3.52209 + 5.68837i 3.52209 + 5.68837i
\(562\) −0.243964 0.489946i −0.243964 0.489946i
\(563\) 1.44574 0.895163i 1.44574 0.895163i 0.445738 0.895163i \(-0.352941\pi\)
1.00000 \(0\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.890705 + 0.811985i 0.890705 + 0.811985i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.840204 + 1.35698i −0.840204 + 1.35698i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(570\) 0 0
\(571\) −0.380338 + 0.981767i −0.380338 + 0.981767i 0.602635 + 0.798017i \(0.294118\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −2.51808 + 0.975509i −2.51808 + 0.975509i
\(577\) −0.576554 + 1.48826i −0.576554 + 1.48826i 0.273663 + 0.961826i \(0.411765\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(578\) −1.10455 2.21823i −1.10455 2.21823i
\(579\) 2.54778 + 2.79478i 2.54778 + 2.79478i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.694903 + 0.129900i −0.694903 + 0.129900i
\(583\) 0 0
\(584\) 0.658809 0.600584i 0.658809 0.600584i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.25664 + 0.778076i 1.25664 + 0.778076i 0.982973 0.183750i \(-0.0588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(588\) 0.353470 1.89090i 0.353470 1.89090i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.04837 1.69318i 1.04837 1.69318i 0.445738 0.895163i \(-0.352941\pi\)
0.602635 0.798017i \(-0.294118\pi\)
\(594\) −5.46078 2.71914i −5.46078 2.71914i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.673696 0.739009i \(-0.735294\pi\)
0.673696 + 0.739009i \(0.264706\pi\)
\(600\) 0.694903 + 1.79375i 0.694903 + 1.79375i
\(601\) 0.709310 0.778076i 0.709310 0.778076i −0.273663 0.961826i \(-0.588235\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(602\) 0 0
\(603\) −5.17253 0.479306i −5.17253 0.479306i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(608\) 0.510366 0.197717i 0.510366 0.197717i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 4.28183 + 2.65120i 4.28183 + 2.65120i
\(613\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(614\) 0.353470 + 1.89090i 0.353470 + 1.89090i
\(615\) 0 0
\(616\) 0 0
\(617\) 0.136374 + 1.47171i 0.136374 + 1.47171i 0.739009 + 0.673696i \(0.235294\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(618\) 0 0
\(619\) 0.293271 + 1.56886i 0.293271 + 1.56886i 0.739009 + 0.673696i \(0.235294\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.932472 0.361242i 0.932472 0.361242i
\(626\) 0.890705 1.17948i 0.890705 1.17948i
\(627\) 1.75768 + 0.875222i 1.75768 + 0.875222i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.961826 0.273663i \(-0.911765\pi\)
0.961826 + 0.273663i \(0.0882353\pi\)
\(632\) 0 0
\(633\) −0.128235 0.331013i −0.128235 0.331013i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.12388 0.435393i −1.12388 0.435393i −0.273663 0.961826i \(-0.588235\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(642\) 2.20369 2.41733i 2.20369 2.41733i
\(643\) −1.27366 0.961826i −1.27366 0.961826i −0.273663 0.961826i \(-0.588235\pi\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.867844 0.537346i −0.867844 0.537346i
\(647\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(648\) −3.59191 −3.59191
\(649\) −0.254330 + 0.231853i −0.254330 + 0.231853i
\(650\) 0 0
\(651\) 0 0
\(652\) 0.353470 0.100571i 0.353470 0.100571i
\(653\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.646741 + 1.66943i −0.646741 + 1.66943i
\(657\) 2.24481 0.869644i 2.24481 0.869644i
\(658\) 0 0
\(659\) 0.942485 0.469302i 0.942485 0.469302i 0.0922684 0.995734i \(-0.470588\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(660\) 0 0
\(661\) 0 0 −0.183750 0.982973i \(-0.558824\pi\)
0.183750 + 0.982973i \(0.441176\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.554262 0.895163i 0.554262 0.895163i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.694903 0.197717i 0.694903 0.197717i 0.0922684 0.995734i \(-0.470588\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(674\) −0.876298 0.163808i −0.876298 0.163808i
\(675\) 3.27104i 3.27104i
\(676\) 0.602635 0.798017i 0.602635 0.798017i
\(677\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(678\) 2.92812 1.81301i 2.92812 1.81301i
\(679\) 0 0
\(680\) 0 0
\(681\) 1.99086 + 0.372156i 1.99086 + 0.372156i
\(682\) 0 0
\(683\) 0.0822551 0.887674i 0.0822551 0.887674i −0.850217 0.526432i \(-0.823529\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(684\) 1.47802 1.47802
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.646741 0.322039i 0.646741 0.322039i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.726337 + 0.961826i −0.726337 + 0.961826i
\(695\) 0 0
\(696\) 0 0
\(697\) 3.21140 0.913722i 3.21140 0.913722i
\(698\) 0 0
\(699\) −0.315110 0.632827i −0.315110 0.632827i
\(700\) 0 0
\(701\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.37821 1.25640i −1.37821 1.25640i
\(705\) 0 0
\(706\) −0.554262 + 0.895163i −0.554262 + 0.895163i
\(707\) 0 0
\(708\) −0.128235 + 0.331013i −0.128235 + 0.331013i
\(709\) 0 0 −0.183750 0.982973i \(-0.558824\pi\)
0.183750 + 0.982973i \(0.441176\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.247582 1.32445i 0.247582 1.32445i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.20614 + 1.32307i 1.20614 + 1.32307i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.700434 0.700434
\(723\) 0.522435 0.476262i 0.522435 0.476262i
\(724\) 0 0
\(725\) 0 0
\(726\) 4.76684i 4.76684i
\(727\) 0 0 −0.798017 0.602635i \(-0.794118\pi\)
0.798017 + 0.602635i \(0.205882\pi\)
\(728\) 0 0
\(729\) −3.17728 1.23089i −3.17728 1.23089i
\(730\) 0 0
\(731\) −1.20614 0.600584i −1.20614 0.600584i
\(732\) 0 0
\(733\) 0 0 0.995734 0.0922684i \(-0.0294118\pi\)
−0.995734 + 0.0922684i \(0.970588\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.29596 3.34525i −1.29596 3.34525i
\(738\) −3.25709 + 3.57286i −3.25709 + 3.57286i
\(739\) −1.91545 0.544991i −1.91545 0.544991i −0.982973 0.183750i \(-0.941176\pi\)
−0.932472 0.361242i \(-0.882353\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.895163 0.445738i \(-0.852941\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.26892 1.71341i 2.26892 1.71341i
\(748\) −0.320911 + 3.46318i −0.320911 + 3.46318i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.183750 0.982973i \(-0.558824\pi\)
0.183750 + 0.982973i \(0.441176\pi\)
\(752\) 0 0
\(753\) −0.128235 1.38388i −0.128235 1.38388i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(758\) 1.67148 + 1.03494i 1.67148 + 1.03494i
\(759\) 0 0
\(760\) 0 0
\(761\) −1.02474 1.35698i −1.02474 1.35698i −0.932472 0.361242i \(-0.882353\pi\)
−0.0922684 0.995734i \(-0.529412\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.85022 0.526432i −1.85022 0.526432i
\(769\) −1.34164 + 1.47171i −1.34164 + 1.47171i −0.602635 + 0.798017i \(0.705882\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(770\) 0 0
\(771\) −1.15531 1.26732i −1.15531 1.26732i
\(772\) 0.181395 + 1.95756i 0.181395 + 1.95756i
\(773\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(774\) 1.94270 0.180017i 1.94270 0.180017i
\(775\) 0 0
\(776\) −0.328972 0.163808i −0.328972 0.163808i
\(777\) 0 0
\(778\) 0 0
\(779\) 0.660149 0.724149i 0.660149 0.724149i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.739009 0.673696i 0.739009 0.673696i
\(785\) 0 0
\(786\) −1.02708 + 0.936306i −1.02708 + 0.936306i
\(787\) −0.293271 + 0.221468i −0.293271 + 0.221468i −0.739009 0.673696i \(-0.764706\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −2.24481 4.50819i −2.24481 4.50819i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.273663 + 0.961826i −0.273663 + 0.961826i
\(801\) 1.91545 3.09355i 1.91545 3.09355i
\(802\) 1.58923 + 0.147263i 1.58923 + 0.147263i
\(803\) 1.22864 + 1.12006i 1.22864 + 1.12006i
\(804\) −2.73465 2.49297i −2.73465 2.49297i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.04837 + 1.69318i 1.04837 + 1.69318i 0.602635 + 0.798017i \(0.294118\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(810\) 0 0
\(811\) −0.181395 0.0339085i −0.181395 0.0339085i 0.0922684 0.995734i \(-0.470588\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 1.29596 + 3.34525i 1.29596 + 3.34525i
\(817\) −0.393747 + 0.0364860i −0.393747 + 0.0364860i
\(818\) 1.93247 + 0.361242i 1.93247 + 0.361242i
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 1.72198 + 0.857445i 1.72198 + 0.857445i
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) −3.21140 + 1.59909i −3.21140 + 1.59909i
\(826\) 0 0
\(827\) −1.78269 + 0.165190i −1.78269 + 0.165190i −0.932472 0.361242i \(-0.882353\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(828\) 0 0
\(829\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.83319 0.342683i −1.83319 0.342683i
\(834\) −1.01267 + 0.288130i −1.01267 + 0.288130i
\(835\) 0 0
\(836\) 0.454980 + 0.913722i 0.454980 + 0.913722i
\(837\) 0 0
\(838\) −1.83319 0.710182i −1.83319 0.710182i
\(839\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(840\) 0 0
\(841\) −0.739009 0.673696i −0.739009 0.673696i
\(842\) 0 0
\(843\) 0.554262 0.895163i 0.554262 0.895163i
\(844\) 0.0505009 0.177492i 0.0505009 0.177492i
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −0.426027 + 2.27904i −0.426027 + 2.27904i
\(850\) 1.73901 0.673696i 1.73901 0.673696i
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.673696 0.739009i \(-0.735294\pi\)
0.673696 + 0.739009i \(0.264706\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1.67148 0.312454i 1.67148 0.312454i
\(857\) −1.53511 + 1.15926i −1.53511 + 1.15926i −0.602635 + 0.798017i \(0.705882\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(858\) 0 0
\(859\) −0.891477 −0.891477 −0.445738 0.895163i \(-0.647059\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) −2.61035 1.97124i −2.61035 1.97124i
\(865\) 0 0
\(866\) −1.83319 0.710182i −1.83319 0.710182i
\(867\) 2.50942 4.05285i 2.50942 4.05285i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −0.668580 0.733398i −0.668580 0.733398i
\(874\) 0 0
\(875\) 0 0
\(876\) 1.64943 + 0.469302i 1.64943 + 0.469302i
\(877\) 0 0 −0.995734 0.0922684i \(-0.970588\pi\)
0.995734 + 0.0922684i \(0.0294118\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.18475 + 1.56886i −1.18475 + 1.56886i −0.445738 + 0.895163i \(0.647059\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(882\) 2.51808 0.975509i 2.51808 0.975509i
\(883\) −0.329838 0.436776i −0.329838 0.436776i 0.602635 0.798017i \(-0.294118\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.67148 1.03494i −1.67148 1.03494i
\(887\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.618079 6.67014i −0.618079 6.67014i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −1.18475 1.56886i −1.18475 1.56886i
\(899\) 0 0
\(900\) −1.62738 + 2.15499i −1.62738 + 2.15499i
\(901\) 0 0
\(902\) −3.21140 0.913722i −3.21140 0.913722i
\(903\) 0 0
\(904\) 1.78269 + 0.165190i 1.78269 + 0.165190i
\(905\) 0 0
\(906\) 0 0
\(907\) 0.380338 + 0.981767i 0.380338 + 0.981767i 0.982973 + 0.183750i \(0.0588235\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(908\) 0.709310 + 0.778076i 0.709310 + 0.778076i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 0.995734 0.0922684i \(-0.0294118\pi\)
−0.995734 + 0.0922684i \(0.970588\pi\)
\(912\) 0.840204 + 0.634493i 0.840204 + 0.634493i
\(913\) 1.75768 + 0.875222i 1.75768 + 0.875222i
\(914\) −0.380338 + 0.614268i −0.380338 + 0.614268i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 6.10031i 6.10031i
\(919\) 0 0 0.183750 0.982973i \(-0.441176\pi\)
−0.183750 + 0.982973i \(0.558824\pi\)
\(920\) 0 0
\(921\) −2.73465 + 2.49297i −2.73465 + 2.49297i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0.658809 + 1.32307i 0.658809 + 1.32307i 0.932472 + 0.361242i \(0.117647\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(930\) 0 0
\(931\) −0.510366 + 0.197717i −0.510366 + 0.197717i
\(932\) 0.0675278 0.361242i 0.0675278 0.361242i
\(933\) 0 0
\(934\) 0.876298 0.163808i 0.876298 0.163808i
\(935\) 0 0
\(936\) 0 0
\(937\) −0.329838 + 1.15926i −0.329838 + 1.15926i 0.602635 + 0.798017i \(0.294118\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(938\) 0 0
\(939\) 2.83106 + 0.262337i 2.83106 + 0.262337i
\(940\) 0 0
\(941\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −0.156896 + 0.0971461i −0.156896 + 0.0971461i
\(945\) 0 0
\(946\) 0.709310 + 1.14558i 0.709310 + 1.14558i
\(947\) 1.91545 0.544991i 1.91545 0.544991i 0.932472 0.361242i \(-0.117647\pi\)
0.982973 0.183750i \(-0.0588235\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0.329838 0.436776i 0.329838 0.436776i
\(951\) 0 0
\(952\) 0 0
\(953\) −0.486734 1.25640i −0.486734 1.25640i −0.932472 0.361242i \(-0.882353\pi\)
0.445738 0.895163i \(-0.352941\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.0922684 + 0.995734i −0.0922684 + 0.995734i
\(962\) 0 0
\(963\) 4.51372 + 0.843761i 4.51372 + 0.843761i
\(964\) 0.365931 0.0339085i 0.365931 0.0339085i
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(968\) 1.49334 1.97750i 1.49334 1.97750i
\(969\) 1.96353i 1.96353i
\(970\) 0 0
\(971\) −1.53511 + 0.436776i −1.53511 + 0.436776i −0.932472 0.361242i \(-0.882353\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(972\) −1.91545 3.09355i −1.91545 3.09355i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1.47802 1.34739i −1.47802 1.34739i −0.739009 0.673696i \(-0.764706\pi\)
−0.739009 0.673696i \(-0.764706\pi\)
\(978\) 0.522435 + 0.476262i 0.522435 + 0.476262i
\(979\) 2.50209 + 0.231853i 2.50209 + 0.231853i
\(980\) 0 0
\(981\) 0 0
\(982\) 0.719401 1.85699i 0.719401 1.85699i
\(983\) 0 0 −0.183750 0.982973i \(-0.558824\pi\)
0.183750 + 0.982973i \(0.441176\pi\)
\(984\) −3.38532 + 0.632827i −3.38532 + 0.632827i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 2.02534 2.02534
\(997\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(998\) −1.02474 0.634493i −1.02474 0.634493i
\(999\) 0 0
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 1096.1.u.a.651.1 16
8.3 odd 2 CM 1096.1.u.a.651.1 16
137.4 even 34 inner 1096.1.u.a.963.1 yes 16
1096.963 odd 34 inner 1096.1.u.a.963.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1096.1.u.a.651.1 16 1.1 even 1 trivial
1096.1.u.a.651.1 16 8.3 odd 2 CM
1096.1.u.a.963.1 yes 16 137.4 even 34 inner
1096.1.u.a.963.1 yes 16 1096.963 odd 34 inner