Properties

Label 1096.1.s.a.187.1
Level $1096$
Weight $1$
Character 1096.187
Analytic conductor $0.547$
Analytic rank $0$
Dimension $16$
Projective image $D_{17}$
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(59,1096)]
 
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, 26]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1096.59");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1096 = 2^{3} \cdot 137 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1096.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: \(0.546975253846\)
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: \(D_{17}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{17} - \cdots)\)

Embedding invariants

Embedding label 187.1
Root \(0.850217 - 0.526432i\) of defining polynomial
Character \(\chi\) \(=\) 1096.187
Dual form 1096.1.s.a.211.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.739009 - 0.673696i) q^{2} +(1.02474 + 0.634493i) q^{3} +(0.0922684 - 0.995734i) q^{4} +(1.18475 - 0.221468i) q^{6} +(-0.602635 - 0.798017i) q^{8} +(0.201774 + 0.405217i) q^{9} +O(q^{10})\) \(q+(0.739009 - 0.673696i) q^{2} +(1.02474 + 0.634493i) q^{3} +(0.0922684 - 0.995734i) q^{4} +(1.18475 - 0.221468i) q^{6} +(-0.602635 - 0.798017i) q^{8} +(0.201774 + 0.405217i) q^{9} +(-0.181395 + 1.95756i) q^{11} +(0.726337 - 0.961826i) q^{12} +(-0.982973 - 0.183750i) q^{16} +(1.18475 - 1.56886i) q^{17} +(0.422106 + 0.163525i) q^{18} +(-1.12388 - 0.435393i) q^{19} +(1.18475 + 1.56886i) q^{22} +(-0.111208 - 1.20013i) q^{24} +(0.0922684 + 0.995734i) q^{25} +(0.0608671 - 0.656861i) q^{27} +(-0.850217 + 0.526432i) q^{32} +(-1.42794 + 1.89090i) q^{33} +(-0.181395 - 1.95756i) q^{34} +(0.422106 - 0.163525i) q^{36} +(-1.12388 + 0.435393i) q^{38} -1.70043 q^{41} +(-1.83319 - 0.710182i) q^{43} +(1.93247 + 0.361242i) q^{44} +(-0.890705 - 0.811985i) q^{48} +(-0.850217 + 0.526432i) q^{49} +(0.739009 + 0.673696i) q^{50} +(2.20949 - 0.855960i) q^{51} +(-0.397543 - 0.526432i) q^{54} +(-0.875432 - 1.15926i) q^{57} +(0.658809 + 1.32307i) q^{59} +(-0.273663 + 0.961826i) q^{64} +(0.218629 + 2.35939i) q^{66} +(0.329838 + 1.15926i) q^{67} +(-1.45285 - 1.32445i) q^{68} +(0.201774 - 0.405217i) q^{72} +(0.465346 - 1.63552i) q^{73} +(-0.537235 + 1.07891i) q^{75} +(-0.537235 + 1.07891i) q^{76} +(0.751944 - 0.995734i) q^{81} +(-1.25664 + 1.14558i) q^{82} +(0.329838 + 0.436776i) q^{83} +(-1.83319 + 0.710182i) q^{86} +(1.67148 - 1.03494i) q^{88} +(1.37821 + 1.25640i) q^{89} -1.20527 q^{96} +(0.0170269 - 0.183750i) q^{97} +(-0.273663 + 0.961826i) q^{98} +(-0.829838 + 0.321481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - q^{8} - 3 q^{9} - 2 q^{11} + 15 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{22} - 2 q^{24} - q^{25} - 4 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} - 2 q^{38} - 2 q^{41} - 2 q^{43} + 15 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} + 13 q^{54} - 4 q^{57} - 2 q^{59} - q^{64} - 4 q^{66} - 2 q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} - 2 q^{75} - 2 q^{76} - 5 q^{81} - 2 q^{82} - 2 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} + 15 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(549\) \(823\) \(825\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{17}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.739009 0.673696i 0.739009 0.673696i
\(3\) 1.02474 + 0.634493i 1.02474 + 0.634493i 0.932472 0.361242i \(-0.117647\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(4\) 0.0922684 0.995734i 0.0922684 0.995734i
\(5\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(6\) 1.18475 0.221468i 1.18475 0.221468i
\(7\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(8\) −0.602635 0.798017i −0.602635 0.798017i
\(9\) 0.201774 + 0.405217i 0.201774 + 0.405217i
\(10\) 0 0
\(11\) −0.181395 + 1.95756i −0.181395 + 1.95756i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(12\) 0.726337 0.961826i 0.726337 0.961826i
\(13\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.982973 0.183750i −0.982973 0.183750i
\(17\) 1.18475 1.56886i 1.18475 1.56886i 0.445738 0.895163i \(-0.352941\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(18\) 0.422106 + 0.163525i 0.422106 + 0.163525i
\(19\) −1.12388 0.435393i −1.12388 0.435393i −0.273663 0.961826i \(-0.588235\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.18475 + 1.56886i 1.18475 + 1.56886i
\(23\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(24\) −0.111208 1.20013i −0.111208 1.20013i
\(25\) 0.0922684 + 0.995734i 0.0922684 + 0.995734i
\(26\) 0 0
\(27\) 0.0608671 0.656861i 0.0608671 0.656861i
\(28\) 0 0
\(29\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(30\) 0 0
\(31\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(32\) −0.850217 + 0.526432i −0.850217 + 0.526432i
\(33\) −1.42794 + 1.89090i −1.42794 + 1.89090i
\(34\) −0.181395 1.95756i −0.181395 1.95756i
\(35\) 0 0
\(36\) 0.422106 0.163525i 0.422106 0.163525i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −1.12388 + 0.435393i −1.12388 + 0.435393i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.70043 −1.70043 −0.850217 0.526432i \(-0.823529\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(42\) 0 0
\(43\) −1.83319 0.710182i −1.83319 0.710182i −0.982973 0.183750i \(-0.941176\pi\)
−0.850217 0.526432i \(-0.823529\pi\)
\(44\) 1.93247 + 0.361242i 1.93247 + 0.361242i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(48\) −0.890705 0.811985i −0.890705 0.811985i
\(49\) −0.850217 + 0.526432i −0.850217 + 0.526432i
\(50\) 0.739009 + 0.673696i 0.739009 + 0.673696i
\(51\) 2.20949 0.855960i 2.20949 0.855960i
\(52\) 0 0
\(53\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(54\) −0.397543 0.526432i −0.397543 0.526432i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.875432 1.15926i −0.875432 1.15926i
\(58\) 0 0
\(59\) 0.658809 + 1.32307i 0.658809 + 1.32307i 0.932472 + 0.361242i \(0.117647\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(60\) 0 0
\(61\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.273663 + 0.961826i −0.273663 + 0.961826i
\(65\) 0 0
\(66\) 0.218629 + 2.35939i 0.218629 + 2.35939i
\(67\) 0.329838 + 1.15926i 0.329838 + 1.15926i 0.932472 + 0.361242i \(0.117647\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(68\) −1.45285 1.32445i −1.45285 1.32445i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(72\) 0.201774 0.405217i 0.201774 0.405217i
\(73\) 0.465346 1.63552i 0.465346 1.63552i −0.273663 0.961826i \(-0.588235\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(74\) 0 0
\(75\) −0.537235 + 1.07891i −0.537235 + 1.07891i
\(76\) −0.537235 + 1.07891i −0.537235 + 1.07891i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(80\) 0 0
\(81\) 0.751944 0.995734i 0.751944 0.995734i
\(82\) −1.25664 + 1.14558i −1.25664 + 1.14558i
\(83\) 0.329838 + 0.436776i 0.329838 + 0.436776i 0.932472 0.361242i \(-0.117647\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.83319 + 0.710182i −1.83319 + 0.710182i
\(87\) 0 0
\(88\) 1.67148 1.03494i 1.67148 1.03494i
\(89\) 1.37821 + 1.25640i 1.37821 + 1.25640i 0.932472 + 0.361242i \(0.117647\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −1.20527 −1.20527
\(97\) 0.0170269 0.183750i 0.0170269 0.183750i −0.982973 0.183750i \(-0.941176\pi\)
1.00000 \(0\)
\(98\) −0.273663 + 0.961826i −0.273663 + 0.961826i
\(99\) −0.829838 + 0.321481i −0.829838 + 0.321481i
\(100\) 1.00000 1.00000
\(101\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(102\) 1.05617 2.12108i 1.05617 2.12108i
\(103\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.465346 + 0.288130i 0.465346 + 0.288130i 0.739009 0.673696i \(-0.235294\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(108\) −0.648443 0.121215i −0.648443 0.121215i
\(109\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.156896 1.69318i −0.156896 1.69318i −0.602635 0.798017i \(-0.705882\pi\)
0.445738 0.895163i \(-0.352941\pi\)
\(114\) −1.42794 0.266928i −1.42794 0.266928i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.37821 + 0.533922i 1.37821 + 0.533922i
\(119\) 0 0
\(120\) 0 0
\(121\) −2.81616 0.526432i −2.81616 0.526432i
\(122\) 0 0
\(123\) −1.74250 1.07891i −1.74250 1.07891i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0.445738 + 0.895163i 0.445738 + 0.895163i
\(129\) −1.42794 1.89090i −1.42794 1.89090i
\(130\) 0 0
\(131\) 1.93247 0.361242i 1.93247 0.361242i 0.932472 0.361242i \(-0.117647\pi\)
1.00000 \(0\)
\(132\) 1.75108 + 1.59632i 1.75108 + 1.59632i
\(133\) 0 0
\(134\) 1.02474 + 0.634493i 1.02474 + 0.634493i
\(135\) 0 0
\(136\) −1.96595 −1.96595
\(137\) 0.932472 0.361242i 0.932472 0.361242i
\(138\) 0 0
\(139\) −0.890705 + 0.811985i −0.890705 + 0.811985i −0.982973 0.183750i \(-0.941176\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.123880 0.435393i −0.123880 0.435393i
\(145\) 0 0
\(146\) −0.757949 1.52217i −0.757949 1.52217i
\(147\) −1.20527 −1.20527
\(148\) 0 0
\(149\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(150\) 0.329838 + 1.15926i 0.329838 + 1.15926i
\(151\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(152\) 0.329838 + 1.15926i 0.329838 + 1.15926i
\(153\) 0.874780 + 0.163525i 0.874780 + 0.163525i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.115129 1.24244i −0.115129 1.24244i
\(163\) −0.156896 0.0971461i −0.156896 0.0971461i 0.445738 0.895163i \(-0.352941\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(164\) −0.156896 + 1.69318i −0.156896 + 1.69318i
\(165\) 0 0
\(166\) 0.538007 + 0.100571i 0.538007 + 0.100571i
\(167\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(168\) 0 0
\(169\) −0.850217 + 0.526432i −0.850217 + 0.526432i
\(170\) 0 0
\(171\) −0.0503411 0.543267i −0.0503411 0.543267i
\(172\) −0.876298 + 1.75984i −0.876298 + 1.75984i
\(173\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.538007 1.89090i 0.538007 1.89090i
\(177\) −0.164368 + 1.77381i −0.164368 + 1.77381i
\(178\) 1.86494 1.86494
\(179\) −0.757949 1.52217i −0.757949 1.52217i −0.850217 0.526432i \(-0.823529\pi\)
0.0922684 0.995734i \(-0.470588\pi\)
\(180\) 0 0
\(181\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.85623 + 2.60380i 2.85623 + 2.60380i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(192\) −0.890705 + 0.811985i −0.890705 + 0.811985i
\(193\) −0.111208 + 0.147263i −0.111208 + 0.147263i −0.850217 0.526432i \(-0.823529\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(194\) −0.111208 0.147263i −0.111208 0.147263i
\(195\) 0 0
\(196\) 0.445738 + 0.895163i 0.445738 + 0.895163i
\(197\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(198\) −0.396677 + 0.796635i −0.396677 + 0.796635i
\(199\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(200\) 0.739009 0.673696i 0.739009 0.673696i
\(201\) −0.397543 + 1.39722i −0.397543 + 1.39722i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.648443 2.27904i −0.648443 2.27904i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.05617 2.12108i 1.05617 2.12108i
\(210\) 0 0
\(211\) 1.09227 0.995734i 1.09227 0.995734i 0.0922684 0.995734i \(-0.470588\pi\)
1.00000 \(0\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.538007 0.100571i 0.538007 0.100571i
\(215\) 0 0
\(216\) −0.560867 + 0.347274i −0.560867 + 0.347274i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.51458 1.38073i 1.51458 1.38073i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(224\) 0 0
\(225\) −0.384871 + 0.238302i −0.384871 + 0.238302i
\(226\) −1.25664 1.14558i −1.25664 1.14558i
\(227\) −0.243964 0.489946i −0.243964 0.489946i 0.739009 0.673696i \(-0.235294\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(228\) −1.23509 + 0.764734i −1.23509 + 0.764734i
\(229\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.184537 0.184537 0.0922684 0.995734i \(-0.470588\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.37821 0.533922i 1.37821 0.533922i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(240\) 0 0
\(241\) −0.111208 + 0.147263i −0.111208 + 0.147263i −0.850217 0.526432i \(-0.823529\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(242\) −2.43582 + 1.50820i −2.43582 + 1.50820i
\(243\) 0.787204 0.304965i 0.787204 0.304965i
\(244\) 0 0
\(245\) 0 0
\(246\) −2.01458 + 0.376591i −2.01458 + 0.376591i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.0608671 + 0.656861i 0.0608671 + 0.656861i
\(250\) 0 0
\(251\) 1.93247 + 0.361242i 1.93247 + 0.361242i 1.00000 \(0\)
0.932472 + 0.361242i \(0.117647\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.932472 + 0.361242i 0.932472 + 0.361242i
\(257\) 1.02474 1.35698i 1.02474 1.35698i 0.0922684 0.995734i \(-0.470588\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(258\) −2.32915 0.435393i −2.32915 0.435393i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.18475 1.56886i 1.18475 1.56886i
\(263\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(264\) 2.36949 2.36949
\(265\) 0 0
\(266\) 0 0
\(267\) 0.615129 + 2.16195i 0.615129 + 2.16195i
\(268\) 1.18475 0.221468i 1.18475 0.221468i
\(269\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(270\) 0 0
\(271\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(272\) −1.45285 + 1.32445i −1.45285 + 1.32445i
\(273\) 0 0
\(274\) 0.445738 0.895163i 0.445738 0.895163i
\(275\) −1.96595 −1.96595
\(276\) 0 0
\(277\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(278\) −0.111208 + 1.20013i −0.111208 + 1.20013i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.329838 + 1.15926i 0.329838 + 1.15926i 0.932472 + 0.361242i \(0.117647\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(282\) 0 0
\(283\) 0.397365 + 0.798017i 0.397365 + 0.798017i 1.00000 \(0\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.384871 0.238302i −0.384871 0.238302i
\(289\) −0.784029 2.75558i −0.784029 2.75558i
\(290\) 0 0
\(291\) 0.134036 0.177492i 0.134036 0.177492i
\(292\) −1.58561 0.614268i −1.58561 0.614268i
\(293\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(294\) −0.890705 + 0.811985i −0.890705 + 0.811985i
\(295\) 0 0
\(296\) 0 0
\(297\) 1.27480 + 0.238302i 1.27480 + 0.238302i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.02474 + 0.634493i 1.02474 + 0.634493i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.02474 + 0.634493i 1.02474 + 0.634493i
\(305\) 0 0
\(306\) 0.756636 0.468489i 0.756636 0.468489i
\(307\) 0.726337 0.961826i 0.726337 0.961826i −0.273663 0.961826i \(-0.588235\pi\)
1.00000 \(0\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) −0.510366 + 1.79375i −0.510366 + 1.79375i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0.294043 + 0.590517i 0.294043 + 0.590517i
\(322\) 0 0
\(323\) −2.01458 + 1.24738i −2.01458 + 1.24738i
\(324\) −0.922106 0.840611i −0.922106 0.840611i
\(325\) 0 0
\(326\) −0.181395 + 0.0339085i −0.181395 + 0.0339085i
\(327\) 0 0
\(328\) 1.02474 + 1.35698i 1.02474 + 1.35698i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.20527 1.59603i −1.20527 1.59603i −0.602635 0.798017i \(-0.705882\pi\)
−0.602635 0.798017i \(-0.705882\pi\)
\(332\) 0.465346 0.288130i 0.465346 0.288130i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.25664 + 1.14558i −1.25664 + 1.14558i −0.273663 + 0.961826i \(0.588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(338\) −0.273663 + 0.961826i −0.273663 + 0.961826i
\(339\) 0.913532 1.83462i 0.913532 1.83462i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.403199 0.367564i −0.403199 0.367564i
\(343\) 0 0
\(344\) 0.538007 + 1.89090i 0.538007 + 1.89090i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.243964 + 0.857445i −0.243964 + 0.857445i 0.739009 + 0.673696i \(0.235294\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(348\) 0 0
\(349\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.876298 1.75984i −0.876298 1.75984i
\(353\) 0.465346 0.288130i 0.465346 0.288130i −0.273663 0.961826i \(-0.588235\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(354\) 1.07354 + 1.42160i 1.07354 + 1.42160i
\(355\) 0 0
\(356\) 1.37821 1.25640i 1.37821 1.25640i
\(357\) 0 0
\(358\) −1.58561 0.614268i −1.58561 0.614268i
\(359\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(360\) 0 0
\(361\) 0.334530 + 0.304965i 0.334530 + 0.304965i
\(362\) 0 0
\(363\) −2.55182 2.32629i −2.55182 2.32629i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(368\) 0 0
\(369\) −0.343104 0.689045i −0.343104 0.689045i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(374\) 3.86494 3.86494
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.156896 + 0.0971461i −0.156896 + 0.0971461i −0.602635 0.798017i \(-0.705882\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(384\) −0.111208 + 1.20013i −0.111208 + 1.20013i
\(385\) 0 0
\(386\) 0.0170269 + 0.183750i 0.0170269 + 0.183750i
\(387\) −0.0821126 0.886136i −0.0821126 0.886136i
\(388\) −0.181395 0.0339085i −0.181395 0.0339085i
\(389\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.932472 + 0.361242i 0.932472 + 0.361242i
\(393\) 2.20949 + 0.855960i 2.20949 + 0.855960i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.243542 + 0.855960i 0.243542 + 0.855960i
\(397\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.0922684 0.995734i 0.0922684 0.995734i
\(401\) 0.891477 0.891477 0.445738 0.895163i \(-0.352941\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(402\) 0.647513 + 1.30038i 0.647513 + 1.30038i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −2.01458 1.24738i −2.01458 1.24738i
\(409\) 0.136374 0.124322i 0.136374 0.124322i −0.602635 0.798017i \(-0.705882\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(410\) 0 0
\(411\) 1.18475 + 0.221468i 1.18475 + 0.221468i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.42794 + 0.266928i −1.42794 + 0.266928i
\(418\) −0.648443 2.27904i −0.648443 2.27904i
\(419\) −0.111208 0.147263i −0.111208 0.147263i 0.739009 0.673696i \(-0.235294\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0.136374 1.47171i 0.136374 1.47171i
\(423\) 0 0
\(424\) 0 0
\(425\) 1.67148 + 1.03494i 1.67148 + 1.03494i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.329838 0.436776i 0.329838 0.436776i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(432\) −0.180529 + 0.634493i −0.180529 + 0.634493i
\(433\) −0.111208 0.147263i −0.111208 0.147263i 0.739009 0.673696i \(-0.235294\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.189102 2.04074i 0.189102 2.04074i
\(439\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(440\) 0 0
\(441\) −0.384871 0.238302i −0.384871 0.238302i
\(442\) 0 0
\(443\) −0.156896 + 0.0971461i −0.156896 + 0.0971461i −0.602635 0.798017i \(-0.705882\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.172075 0.0666624i 0.172075 0.0666624i −0.273663 0.961826i \(-0.588235\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(450\) −0.123880 + 0.435393i −0.123880 + 0.435393i
\(451\) 0.308450 3.32870i 0.308450 3.32870i
\(452\) −1.70043 −1.70043
\(453\) 0 0
\(454\) −0.510366 0.197717i −0.510366 0.197717i
\(455\) 0 0
\(456\) −0.397543 + 1.39722i −0.397543 + 1.39722i
\(457\) 1.67148 1.03494i 1.67148 1.03494i 0.739009 0.673696i \(-0.235294\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(458\) 0 0
\(459\) −0.958410 0.873706i −0.958410 0.873706i
\(460\) 0 0
\(461\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(462\) 0 0
\(463\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.136374 0.124322i 0.136374 0.124322i
\(467\) 1.02474 1.35698i 1.02474 1.35698i 0.0922684 0.995734i \(-0.470588\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.658809 1.32307i 0.658809 1.32307i
\(473\) 1.72275 3.45976i 1.72275 3.45976i
\(474\) 0 0
\(475\) 0.329838 1.15926i 0.329838 1.15926i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.0170269 + 0.183750i 0.0170269 + 0.183750i
\(483\) 0 0
\(484\) −0.784029 + 2.75558i −0.784029 + 2.75558i
\(485\) 0 0
\(486\) 0.376298 0.755708i 0.376298 0.755708i
\(487\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(488\) 0 0
\(489\) −0.0991395 0.199099i −0.0991395 0.199099i
\(490\) 0 0
\(491\) −0.890705 1.17948i −0.890705 1.17948i −0.982973 0.183750i \(-0.941176\pi\)
0.0922684 0.995734i \(-0.470588\pi\)
\(492\) −1.23509 + 1.63552i −1.23509 + 1.63552i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.487506 + 0.444420i 0.487506 + 0.444420i
\(499\) −0.757949 + 0.469302i −0.757949 + 0.469302i −0.850217 0.526432i \(-0.823529\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.67148 1.03494i 1.67148 1.03494i
\(503\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.20527 −1.20527
\(508\) 0 0
\(509\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.932472 0.361242i 0.932472 0.361242i
\(513\) −0.354400 + 0.711732i −0.354400 + 0.711732i
\(514\) −0.156896 1.69318i −0.156896 1.69318i
\(515\) 0 0
\(516\) −2.01458 + 1.24738i −2.01458 + 1.24738i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.156896 + 1.69318i −0.156896 + 1.69318i 0.445738 + 0.895163i \(0.352941\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(522\) 0 0
\(523\) 0.0822551 + 0.887674i 0.0822551 + 0.887674i 0.932472 + 0.361242i \(0.117647\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(524\) −0.181395 1.95756i −0.181395 1.95756i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 1.75108 1.59632i 1.75108 1.59632i
\(529\) 0.932472 + 0.361242i 0.932472 + 0.361242i
\(530\) 0 0
\(531\) −0.403199 + 0.533922i −0.403199 + 0.533922i
\(532\) 0 0
\(533\) 0 0
\(534\) 1.91108 + 1.18329i 1.91108 + 1.18329i
\(535\) 0 0
\(536\) 0.726337 0.961826i 0.726337 0.961826i
\(537\) 0.189102 2.04074i 0.189102 2.04074i
\(538\) 0 0
\(539\) −0.876298 1.75984i −0.876298 1.75984i
\(540\) 0 0
\(541\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.181395 + 1.95756i −0.181395 + 1.95756i
\(545\) 0 0
\(546\) 0 0
\(547\) −1.70043 −1.70043 −0.850217 0.526432i \(-0.823529\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(548\) −0.273663 0.961826i −0.273663 0.961826i
\(549\) 0 0
\(550\) −1.45285 + 1.32445i −1.45285 + 1.32445i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.726337 + 0.961826i 0.726337 + 0.961826i
\(557\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 1.27480 + 4.48047i 1.27480 + 4.48047i
\(562\) 1.02474 + 0.634493i 1.02474 + 0.634493i
\(563\) 0.149783 + 0.526432i 0.149783 + 0.526432i 1.00000 \(0\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.831277 + 0.322039i 0.831277 + 0.322039i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.243964 + 0.857445i −0.243964 + 0.857445i 0.739009 + 0.673696i \(0.235294\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(570\) 0 0
\(571\) 0.538007 + 0.100571i 0.538007 + 0.100571i 0.445738 0.895163i \(-0.352941\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.444966 + 0.0831786i −0.444966 + 0.0831786i
\(577\) −0.876298 0.163808i −0.876298 0.163808i −0.273663 0.961826i \(-0.588235\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(578\) −2.43582 1.50820i −2.43582 1.50820i
\(579\) −0.207397 + 0.0803461i −0.207397 + 0.0803461i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.0205220 0.221468i −0.0205220 0.221468i
\(583\) 0 0
\(584\) −1.58561 + 0.614268i −1.58561 + 0.614268i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.510366 + 1.79375i −0.510366 + 1.79375i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(588\) −0.111208 + 1.20013i −0.111208 + 1.20013i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.404479 + 1.42160i −0.404479 + 1.42160i 0.445738 + 0.895163i \(0.352941\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(594\) 1.10263 0.682722i 1.10263 0.682722i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(600\) 1.18475 0.221468i 1.18475 0.221468i
\(601\) −0.510366 0.197717i −0.510366 0.197717i 0.0922684 0.995734i \(-0.470588\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(602\) 0 0
\(603\) −0.403199 + 0.367564i −0.403199 + 0.367564i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(608\) 1.18475 0.221468i 1.18475 0.221468i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.243542 0.855960i 0.243542 0.855960i
\(613\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(614\) −0.111208 1.20013i −0.111208 1.20013i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.37821 + 1.25640i 1.37821 + 1.25640i 0.932472 + 0.361242i \(0.117647\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(618\) 0 0
\(619\) 0.0822551 + 0.887674i 0.0822551 + 0.887674i 0.932472 + 0.361242i \(0.117647\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.982973 + 0.183750i −0.982973 + 0.183750i
\(626\) 0.831277 + 1.66943i 0.831277 + 1.66943i
\(627\) 2.42812 1.50343i 2.42812 1.50343i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(632\) 0 0
\(633\) 1.75108 0.327333i 1.75108 0.327333i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.876298 0.163808i −0.876298 0.163808i −0.273663 0.961826i \(-0.588235\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(642\) 0.615129 + 0.238302i 0.615129 + 0.238302i
\(643\) 0.397365 + 0.798017i 0.397365 + 0.798017i 1.00000 \(0\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.648443 + 2.27904i −0.648443 + 2.27904i
\(647\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(648\) −1.24776 −1.24776
\(649\) −2.70949 + 1.04966i −2.70949 + 1.04966i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.111208 + 0.147263i −0.111208 + 0.147263i
\(653\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.67148 + 0.312454i 1.67148 + 0.312454i
\(657\) 0.756636 0.141440i 0.756636 0.141440i
\(658\) 0 0
\(659\) 0.465346 + 0.288130i 0.465346 + 0.288130i 0.739009 0.673696i \(-0.235294\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(660\) 0 0
\(661\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(662\) −1.96595 0.367499i −1.96595 0.367499i
\(663\) 0 0
\(664\) 0.149783 0.526432i 0.149783 0.526432i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.18475 1.56886i 1.18475 1.56886i 0.445738 0.895163i \(-0.352941\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(674\) −0.156896 + 1.69318i −0.156896 + 1.69318i
\(675\) 0.659675 0.659675
\(676\) 0.445738 + 0.895163i 0.445738 + 0.895163i
\(677\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(678\) −0.560867 1.97124i −0.560867 1.97124i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.0608671 0.656861i 0.0608671 0.656861i
\(682\) 0 0
\(683\) −1.25664 + 1.14558i −1.25664 + 1.14558i −0.273663 + 0.961826i \(0.588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(684\) −0.545594 −0.545594
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.67148 + 1.03494i 1.67148 + 1.03494i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.96595 + 0.367499i −1.96595 + 0.367499i −0.982973 + 0.183750i \(0.941176\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.397365 + 0.798017i 0.397365 + 0.798017i
\(695\) 0 0
\(696\) 0 0
\(697\) −2.01458 + 2.66774i −2.01458 + 2.66774i
\(698\) 0 0
\(699\) 0.189102 + 0.117087i 0.189102 + 0.117087i
\(700\) 0 0
\(701\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.83319 0.710182i −1.83319 0.710182i
\(705\) 0 0
\(706\) 0.149783 0.526432i 0.149783 0.526432i
\(707\) 0 0
\(708\) 1.75108 + 0.327333i 1.75108 + 0.327333i
\(709\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.172075 1.85699i 0.172075 1.85699i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.58561 + 0.614268i −1.58561 + 0.614268i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.452674 0.452674
\(723\) −0.207397 + 0.0803461i −0.207397 + 0.0803461i
\(724\) 0 0
\(725\) 0 0
\(726\) −3.45303 −3.45303
\(727\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(728\) 0 0
\(729\) −0.226337 0.0423097i −0.226337 0.0423097i
\(730\) 0 0
\(731\) −3.28604 + 2.03463i −3.28604 + 2.03463i
\(732\) 0 0
\(733\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.32915 + 0.435393i −2.32915 + 0.435393i
\(738\) −0.717763 0.278063i −0.717763 0.278063i
\(739\) −0.890705 1.17948i −0.890705 1.17948i −0.982973 0.183750i \(-0.941176\pi\)
0.0922684 0.995734i \(-0.470588\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.110436 + 0.221786i −0.110436 + 0.221786i
\(748\) 2.85623 2.60380i 2.85623 2.60380i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(752\) 0 0
\(753\) 1.75108 + 1.59632i 1.75108 + 1.59632i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(758\) −0.0505009 + 0.177492i −0.0505009 + 0.177492i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.243964 + 0.489946i −0.243964 + 0.489946i −0.982973 0.183750i \(-0.941176\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.726337 + 0.961826i 0.726337 + 0.961826i
\(769\) 1.37821 + 0.533922i 1.37821 + 0.533922i 0.932472 0.361242i \(-0.117647\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(770\) 0 0
\(771\) 1.91108 0.740358i 1.91108 0.740358i
\(772\) 0.136374 + 0.124322i 0.136374 + 0.124322i
\(773\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(774\) −0.657668 0.599544i −0.657668 0.599544i
\(775\) 0 0
\(776\) −0.156896 + 0.0971461i −0.156896 + 0.0971461i
\(777\) 0 0
\(778\) 0 0
\(779\) 1.91108 + 0.740358i 1.91108 + 0.740358i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.932472 0.361242i 0.932472 0.361242i
\(785\) 0 0
\(786\) 2.20949 0.855960i 2.20949 0.855960i
\(787\) 0.0822551 0.165190i 0.0822551 0.165190i −0.850217 0.526432i \(-0.823529\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.756636 + 0.468489i 0.756636 + 0.468489i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.602635 0.798017i −0.602635 0.798017i
\(801\) −0.231030 + 0.811985i −0.231030 + 0.811985i
\(802\) 0.658809 0.600584i 0.658809 0.600584i
\(803\) 3.11722 + 1.20762i 3.11722 + 1.20762i
\(804\) 1.35458 + 0.524766i 1.35458 + 0.524766i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −0.404479 1.42160i −0.404479 1.42160i −0.850217 0.526432i \(-0.823529\pi\)
0.445738 0.895163i \(-0.352941\pi\)
\(810\) 0 0
\(811\) 0.136374 1.47171i 0.136374 1.47171i −0.602635 0.798017i \(-0.705882\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −2.32915 + 0.435393i −2.32915 + 0.435393i
\(817\) 1.75108 + 1.59632i 1.75108 + 1.59632i
\(818\) 0.0170269 0.183750i 0.0170269 0.183750i
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 1.02474 0.634493i 1.02474 0.634493i
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) −2.01458 1.24738i −2.01458 1.24738i
\(826\) 0 0
\(827\) −1.25664 1.14558i −1.25664 1.14558i −0.982973 0.183750i \(-0.941176\pi\)
−0.273663 0.961826i \(-0.588235\pi\)
\(828\) 0 0
\(829\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −0.181395 + 1.95756i −0.181395 + 1.95756i
\(834\) −0.875432 + 1.15926i −0.875432 + 1.15926i
\(835\) 0 0
\(836\) −2.01458 1.24738i −2.01458 1.24738i
\(837\) 0 0
\(838\) −0.181395 0.0339085i −0.181395 0.0339085i
\(839\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(840\) 0 0
\(841\) 0.932472 + 0.361242i 0.932472 + 0.361242i
\(842\) 0 0
\(843\) −0.397543 + 1.39722i −0.397543 + 1.39722i
\(844\) −0.890705 1.17948i −0.890705 1.17948i
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −0.0991395 + 1.06989i −0.0991395 + 1.06989i
\(850\) 1.93247 0.361242i 1.93247 0.361242i
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −0.0505009 0.544991i −0.0505009 0.544991i
\(857\) −0.537235 + 1.07891i −0.537235 + 1.07891i 0.445738 + 0.895163i \(0.352941\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(858\) 0 0
\(859\) −1.70043 −1.70043 −0.850217 0.526432i \(-0.823529\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0.294043 + 0.590517i 0.294043 + 0.590517i
\(865\) 0 0
\(866\) −0.181395 0.0339085i −0.181395 0.0339085i
\(867\) 0.944966 3.32121i 0.944966 3.32121i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0.0778940 0.0301763i 0.0778940 0.0301763i
\(874\) 0 0
\(875\) 0 0
\(876\) −1.23509 1.63552i −1.23509 1.63552i
\(877\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0.0822551 + 0.165190i 0.0822551 + 0.165190i 0.932472 0.361242i \(-0.117647\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(882\) −0.444966 + 0.0831786i −0.444966 + 0.0831786i
\(883\) −0.537235 + 1.07891i −0.537235 + 1.07891i 0.445738 + 0.895163i \(0.352941\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −0.0505009 + 0.177492i −0.0505009 + 0.177492i
\(887\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.81281 + 1.65260i 1.81281 + 1.65260i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0.0822551 0.165190i 0.0822551 0.165190i
\(899\) 0 0
\(900\) 0.201774 + 0.405217i 0.201774 + 0.405217i
\(901\) 0 0
\(902\) −2.01458 2.66774i −2.01458 2.66774i
\(903\) 0 0
\(904\) −1.25664 + 1.14558i −1.25664 + 1.14558i
\(905\) 0 0
\(906\) 0 0
\(907\) 0.538007 0.100571i 0.538007 0.100571i 0.0922684 0.995734i \(-0.470588\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(908\) −0.510366 + 0.197717i −0.510366 + 0.197717i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(912\) 0.647513 + 1.30038i 0.647513 + 1.30038i
\(913\) −0.914845 + 0.566448i −0.914845 + 0.566448i
\(914\) 0.538007 1.89090i 0.538007 1.89090i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) −1.29689 −1.29689
\(919\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(920\) 0 0
\(921\) 1.35458 0.524766i 1.35458 0.524766i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.58561 0.981767i −1.58561 0.981767i −0.982973 0.183750i \(-0.941176\pi\)
−0.602635 0.798017i \(-0.705882\pi\)
\(930\) 0 0
\(931\) 1.18475 0.221468i 1.18475 0.221468i
\(932\) 0.0170269 0.183750i 0.0170269 0.183750i
\(933\) 0 0
\(934\) −0.156896 1.69318i −0.156896 1.69318i
\(935\) 0 0
\(936\) 0 0
\(937\) −0.537235 0.711414i −0.537235 0.711414i 0.445738 0.895163i \(-0.352941\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(938\) 0 0
\(939\) −1.66111 + 1.51431i −1.66111 + 1.51431i
\(940\) 0 0
\(941\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −0.404479 1.42160i −0.404479 1.42160i
\(945\) 0 0
\(946\) −1.05769 3.71740i −1.05769 3.71740i
\(947\) −0.890705 + 1.17948i −0.890705 + 1.17948i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −0.537235 1.07891i −0.537235 1.07891i
\(951\) 0 0
\(952\) 0 0
\(953\) −1.83319 + 0.342683i −1.83319 + 0.342683i −0.982973 0.183750i \(-0.941176\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 0.739009 0.673696i 0.739009 0.673696i
\(962\) 0 0
\(963\) −0.0228604 + 0.246703i −0.0228604 + 0.246703i
\(964\) 0.136374 + 0.124322i 0.136374 + 0.124322i
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(968\) 1.27702 + 2.56459i 1.27702 + 2.56459i
\(969\) −2.85588 −2.85588
\(970\) 0 0
\(971\) −0.537235 + 0.711414i −0.537235 + 0.711414i −0.982973 0.183750i \(-0.941176\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(972\) −0.231030 0.811985i −0.231030 0.811985i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.86494 + 0.722483i 1.86494 + 0.722483i 0.932472 + 0.361242i \(0.117647\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(978\) −0.207397 0.0803461i −0.207397 0.0803461i
\(979\) −2.70949 + 2.47002i −2.70949 + 2.47002i
\(980\) 0 0
\(981\) 0 0
\(982\) −1.45285 0.271585i −1.45285 0.271585i
\(983\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(984\) 0.189102 + 2.04074i 0.189102 + 2.04074i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(992\) 0 0
\(993\) −0.222416 2.40026i −0.222416 2.40026i
\(994\) 0 0
\(995\) 0 0
\(996\) 0.659675 0.659675
\(997\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(998\) −0.243964 + 0.857445i −0.243964 + 0.857445i
\(999\) 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.s.a.187.1 16
8.3 odd 2 CM 1096.1.s.a.187.1 16
137.74 even 17 inner 1096.1.s.a.211.1 yes 16
1096.211 odd 34 inner 1096.1.s.a.211.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1096.1.s.a.187.1 16 1.1 even 1 trivial
1096.1.s.a.187.1 16 8.3 odd 2 CM
1096.1.s.a.211.1 yes 16 137.74 even 17 inner
1096.1.s.a.211.1 yes 16 1096.211 odd 34 inner