Properties

Label 959.1.t.a.804.1
Level $959$
Weight $1$
Character 959.804
Analytic conductor $0.479$
Analytic rank $0$
Dimension $16$
Projective image $D_{17}$
CM discriminant -7
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [959,1,Mod(34,959)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(959, base_ring=CyclotomicField(34))
 
chi = DirichletCharacter(H, H._module([17, 12]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("959.34");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 959 = 7 \cdot 137 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 959.t (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: \(0.478603347115\)
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 804.1
Root \(-0.0922684 + 0.995734i\) of defining polynomial
Character \(\chi\) \(=\) 959.804
Dual form 959.1.t.a.860.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.58561 + 0.614268i) q^{2} +(1.39782 - 1.27428i) q^{4} +(-0.602635 + 0.798017i) q^{7} +(-0.675694 + 1.35698i) q^{8} +(-0.850217 - 0.526432i) q^{9} +O(q^{10})\) \(q+(-1.58561 + 0.614268i) q^{2} +(1.39782 - 1.27428i) q^{4} +(-0.602635 + 0.798017i) q^{7} +(-0.675694 + 1.35698i) q^{8} +(-0.850217 - 0.526432i) q^{9} +(1.37821 - 1.25640i) q^{11} +(0.465346 - 1.63552i) q^{14} +(0.0633152 - 0.683280i) q^{16} +(1.67148 + 0.312454i) q^{18} +(-1.41353 + 2.83876i) q^{22} +(0.0170269 - 0.183750i) q^{23} +(0.739009 + 0.673696i) q^{25} +(0.174523 + 1.88341i) q^{28} +(0.172075 - 1.85699i) q^{29} +(-0.0955212 - 0.335722i) q^{32} +(-1.85927 + 0.347558i) q^{36} +1.47802 q^{37} +(-0.181395 - 0.0339085i) q^{43} +(0.325477 - 3.51245i) q^{44} +(0.0858734 + 0.301814i) q^{46} +(-0.273663 - 0.961826i) q^{49} +(-1.58561 - 0.614268i) q^{50} +(0.538007 + 0.100571i) q^{53} +(-0.675694 - 1.35698i) q^{56} +(0.867844 + 3.05016i) q^{58} +(0.932472 - 0.361242i) q^{63} +(0.771215 + 1.02125i) q^{64} +(1.02474 - 1.35698i) q^{67} +(1.09227 + 0.995734i) q^{71} +(1.28884 - 0.798017i) q^{72} +(-2.34356 + 0.907899i) q^{74} +(0.172075 + 1.85699i) q^{77} +(0.538007 + 1.89090i) q^{79} +(0.445738 + 0.895163i) q^{81} +(0.308450 - 0.0576592i) q^{86} +(0.773663 + 2.71914i) q^{88} +(-0.210348 - 0.278545i) q^{92} +(1.02474 + 1.35698i) q^{98} +(-1.83319 + 0.342683i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} - 3 q^{4} - q^{7} - 4 q^{8} - q^{9} - 2 q^{11} - 2 q^{14} - 5 q^{16} - 2 q^{18} - 4 q^{22} + 15 q^{23} - q^{25} - 3 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 2 q^{37} - 2 q^{43} + 11 q^{44} - 4 q^{46} - q^{49} - 2 q^{50} - 2 q^{53} - 4 q^{56} - 4 q^{58} - q^{63} + 10 q^{64} - 2 q^{67} + 15 q^{71} + 13 q^{72} - 4 q^{74} - 2 q^{77} - 2 q^{79} - q^{81} - 4 q^{86} + 9 q^{88} - 6 q^{92} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/959\mathbb{Z}\right)^\times\).

\(n\) \(414\) \(549\)
\(\chi(n)\) \(e\left(\frac{10}{17}\right)\) \(-1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58561 + 0.614268i −1.58561 + 0.614268i −0.982973 0.183750i \(-0.941176\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(3\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(4\) 1.39782 1.27428i 1.39782 1.27428i
\(5\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(6\) 0 0
\(7\) −0.602635 + 0.798017i −0.602635 + 0.798017i
\(8\) −0.675694 + 1.35698i −0.675694 + 1.35698i
\(9\) −0.850217 0.526432i −0.850217 0.526432i
\(10\) 0 0
\(11\) 1.37821 1.25640i 1.37821 1.25640i 0.445738 0.895163i \(-0.352941\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(12\) 0 0
\(13\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(14\) 0.465346 1.63552i 0.465346 1.63552i
\(15\) 0 0
\(16\) 0.0633152 0.683280i 0.0633152 0.683280i
\(17\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(18\) 1.67148 + 0.312454i 1.67148 + 0.312454i
\(19\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.41353 + 2.83876i −1.41353 + 2.83876i
\(23\) 0.0170269 0.183750i 0.0170269 0.183750i −0.982973 0.183750i \(-0.941176\pi\)
1.00000 \(0\)
\(24\) 0 0
\(25\) 0.739009 + 0.673696i 0.739009 + 0.673696i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.174523 + 1.88341i 0.174523 + 1.88341i
\(29\) 0.172075 1.85699i 0.172075 1.85699i −0.273663 0.961826i \(-0.588235\pi\)
0.445738 0.895163i \(-0.352941\pi\)
\(30\) 0 0
\(31\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(32\) −0.0955212 0.335722i −0.0955212 0.335722i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −1.85927 + 0.347558i −1.85927 + 0.347558i
\(37\) 1.47802 1.47802 0.739009 0.673696i \(-0.235294\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −0.181395 0.0339085i −0.181395 0.0339085i 0.0922684 0.995734i \(-0.470588\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(44\) 0.325477 3.51245i 0.325477 3.51245i
\(45\) 0 0
\(46\) 0.0858734 + 0.301814i 0.0858734 + 0.301814i
\(47\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(48\) 0 0
\(49\) −0.273663 0.961826i −0.273663 0.961826i
\(50\) −1.58561 0.614268i −1.58561 0.614268i
\(51\) 0 0
\(52\) 0 0
\(53\) 0.538007 + 0.100571i 0.538007 + 0.100571i 0.445738 0.895163i \(-0.352941\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.675694 1.35698i −0.675694 1.35698i
\(57\) 0 0
\(58\) 0.867844 + 3.05016i 0.867844 + 3.05016i
\(59\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(60\) 0 0
\(61\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(62\) 0 0
\(63\) 0.932472 0.361242i 0.932472 0.361242i
\(64\) 0.771215 + 1.02125i 0.771215 + 1.02125i
\(65\) 0 0
\(66\) 0 0
\(67\) 1.02474 1.35698i 1.02474 1.35698i 0.0922684 0.995734i \(-0.470588\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.09227 + 0.995734i 1.09227 + 0.995734i 1.00000 \(0\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(72\) 1.28884 0.798017i 1.28884 0.798017i
\(73\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(74\) −2.34356 + 0.907899i −2.34356 + 0.907899i
\(75\) 0 0
\(76\) 0 0
\(77\) 0.172075 + 1.85699i 0.172075 + 1.85699i
\(78\) 0 0
\(79\) 0.538007 + 1.89090i 0.538007 + 1.89090i 0.445738 + 0.895163i \(0.352941\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(80\) 0 0
\(81\) 0.445738 + 0.895163i 0.445738 + 0.895163i
\(82\) 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
\(86\) 0.308450 0.0576592i 0.308450 0.0576592i
\(87\) 0 0
\(88\) 0.773663 + 2.71914i 0.773663 + 2.71914i
\(89\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.210348 0.278545i −0.210348 0.278545i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(98\) 1.02474 + 1.35698i 1.02474 + 1.35698i
\(99\) −1.83319 + 0.342683i −1.83319 + 0.342683i
\(100\) 1.89148 1.89148
\(101\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(102\) 0 0
\(103\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −0.914845 + 0.171014i −0.914845 + 0.171014i
\(107\) −0.0505009 + 0.177492i −0.0505009 + 0.177492i −0.982973 0.183750i \(-0.941176\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(108\) 0 0
\(109\) −0.156896 1.69318i −0.156896 1.69318i −0.602635 0.798017i \(-0.705882\pi\)
0.445738 0.895163i \(-0.352941\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.507113 + 0.462295i 0.507113 + 0.462295i
\(113\) −0.890705 0.811985i −0.890705 0.811985i 0.0922684 0.995734i \(-0.470588\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.12579 2.81500i −2.12579 2.81500i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.228643 2.46745i 0.228643 2.46745i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −1.25664 + 1.14558i −1.25664 + 1.14558i
\(127\) −1.70043 −1.70043 −0.850217 0.526432i \(-0.823529\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(128\) −1.55340 0.961826i −1.55340 0.961826i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.791290 + 2.78110i −0.791290 + 2.78110i
\(135\) 0 0
\(136\) 0 0
\(137\) 1.00000 1.00000
\(138\) 0 0
\(139\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2.34356 0.907899i −2.34356 0.907899i
\(143\) 0 0
\(144\) −0.413532 + 0.547605i −0.413532 + 0.547605i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 2.06600 1.88341i 2.06600 1.88341i
\(149\) −0.243964 0.489946i −0.243964 0.489946i 0.739009 0.673696i \(-0.235294\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(150\) 0 0
\(151\) −0.547326 + 1.92365i −0.547326 + 1.92365i −0.273663 + 0.961826i \(0.588235\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −1.41353 2.83876i −1.41353 2.83876i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(158\) −2.01458 2.66774i −2.01458 2.66774i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.136374 + 0.124322i 0.136374 + 0.124322i
\(162\) −1.25664 1.14558i −1.25664 1.14558i
\(163\) −0.243964 + 0.857445i −0.243964 + 0.857445i 0.739009 + 0.673696i \(0.235294\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(168\) 0 0
\(169\) −0.273663 0.961826i −0.273663 0.961826i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.296766 + 0.183750i −0.296766 + 0.183750i
\(173\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(174\) 0 0
\(175\) −0.982973 + 0.183750i −0.982973 + 0.183750i
\(176\) −0.771215 1.02125i −0.771215 1.02125i
\(177\) 0 0
\(178\) 0 0
\(179\) −1.70043 1.05286i −1.70043 1.05286i −0.850217 0.526432i \(-0.823529\pi\)
−0.850217 0.526432i \(-0.823529\pi\)
\(180\) 0 0
\(181\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.237839 + 0.147263i 0.237839 + 0.147263i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.757949 + 1.52217i −0.757949 + 1.52217i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(192\) 0 0
\(193\) −0.757949 1.52217i −0.757949 1.52217i −0.850217 0.526432i \(-0.823529\pi\)
0.0922684 0.995734i \(-0.470588\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.60817 0.995734i −1.60817 0.995734i
\(197\) 0.0822551 + 0.887674i 0.0822551 + 0.887674i 0.932472 + 0.361242i \(0.117647\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(198\) 2.69622 1.66943i 2.69622 1.66943i
\(199\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(200\) −1.41353 + 0.547605i −1.41353 + 0.547605i
\(201\) 0 0
\(202\) 0 0
\(203\) 1.37821 + 1.25640i 1.37821 + 1.25640i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.111208 + 0.147263i −0.111208 + 0.147263i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −0.510366 + 0.197717i −0.510366 + 0.197717i −0.602635 0.798017i \(-0.705882\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(212\) 0.880191 0.544991i 0.880191 0.544991i
\(213\) 0 0
\(214\) −0.0289531 0.312454i −0.0289531 0.312454i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 1.28884 + 2.58834i 1.28884 + 2.58834i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(224\) 0.325477 + 0.126090i 0.325477 + 0.126090i
\(225\) −0.273663 0.961826i −0.273663 0.961826i
\(226\) 1.91108 + 0.740358i 1.91108 + 0.740358i
\(227\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(228\) 0 0
\(229\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.40362 + 1.48826i 2.40362 + 1.48826i
\(233\) −1.96595 −1.96595 −0.982973 0.183750i \(-0.941176\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.67148 1.03494i 1.67148 1.03494i 0.739009 0.673696i \(-0.235294\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(240\) 0 0
\(241\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(242\) 1.15314 + 4.05285i 1.15314 + 4.05285i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(252\) 0.843104 1.69318i 0.843104 1.69318i
\(253\) −0.207397 0.274638i −0.207397 0.274638i
\(254\) 2.69622 1.04452i 2.69622 1.04452i
\(255\) 0 0
\(256\) 1.79596 + 0.335722i 1.79596 + 0.335722i
\(257\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(258\) 0 0
\(259\) −0.890705 + 1.17948i −0.890705 + 1.17948i
\(260\) 0 0
\(261\) −1.12388 + 1.48826i −1.12388 + 1.48826i
\(262\) 0 0
\(263\) −1.45285 + 1.32445i −1.45285 + 1.32445i −0.602635 + 0.798017i \(0.705882\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.296766 3.20261i −0.296766 3.20261i
\(269\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(270\) 0 0
\(271\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −1.58561 + 0.614268i −1.58561 + 0.614268i
\(275\) 1.86494 1.86494
\(276\) 0 0
\(277\) −0.510366 + 1.79375i −0.510366 + 1.79375i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.329838 0.436776i 0.329838 0.436776i −0.602635 0.798017i \(-0.705882\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(282\) 0 0
\(283\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(284\) 2.79564 2.79564
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.0955212 + 0.335722i −0.0955212 + 0.335722i
\(289\) −0.602635 + 0.798017i −0.602635 + 0.798017i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.998687 + 2.00563i −0.998687 + 2.00563i
\(297\) 0 0
\(298\) 0.687790 + 0.627003i 0.687790 + 0.627003i
\(299\) 0 0
\(300\) 0 0
\(301\) 0.136374 0.124322i 0.136374 0.124322i
\(302\) −0.313793 3.38636i −0.313793 3.38636i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(308\) 2.60685 + 2.37646i 2.60685 + 2.37646i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 3.16157 + 1.95756i 3.16157 + 1.95756i
\(317\) −1.45285 0.271585i −1.45285 0.271585i −0.602635 0.798017i \(-0.705882\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(318\) 0 0
\(319\) −2.09597 2.77552i −2.09597 2.77552i
\(320\) 0 0
\(321\) 0 0
\(322\) −0.292603 0.113355i −0.292603 0.113355i
\(323\) 0 0
\(324\) 1.76375 + 0.683280i 1.76375 + 0.683280i
\(325\) 0 0
\(326\) −0.139869 1.50943i −0.139869 1.50943i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.658809 1.32307i 0.658809 1.32307i −0.273663 0.961826i \(-0.588235\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(332\) 0 0
\(333\) −1.25664 0.778076i −1.25664 0.778076i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.73901 0.673696i 1.73901 0.673696i 0.739009 0.673696i \(-0.235294\pi\)
1.00000 \(0\)
\(338\) 1.02474 + 1.35698i 1.02474 + 1.35698i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.932472 + 0.361242i 0.932472 + 0.361242i
\(344\) 0.168580 0.223236i 0.168580 0.223236i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.726337 + 0.961826i 0.726337 + 0.961826i 1.00000 \(0\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(348\) 0 0
\(349\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(350\) 1.44574 0.895163i 1.44574 0.895163i
\(351\) 0 0
\(352\) −0.553451 0.342683i −0.553451 0.342683i
\(353\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 3.34296 + 0.624908i 3.34296 + 0.624908i
\(359\) 0.172075 + 1.85699i 0.172075 + 1.85699i 0.445738 + 0.895163i \(0.352941\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(360\) 0 0
\(361\) 0.932472 + 0.361242i 0.932472 + 0.361242i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(368\) −0.124474 0.0232683i −0.124474 0.0232683i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.404479 + 0.368731i −0.404479 + 0.368731i
\(372\) 0 0
\(373\) 1.18475 0.221468i 1.18475 0.221468i 0.445738 0.895163i \(-0.352941\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.149783 + 0.526432i 0.149783 + 0.526432i 1.00000 \(0\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.266792 2.87914i 0.266792 2.87914i
\(383\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.13683 + 1.94798i 2.13683 + 1.94798i
\(387\) 0.136374 + 0.124322i 0.136374 + 0.124322i
\(388\) 0 0
\(389\) −0.537235 + 1.07891i −0.537235 + 1.07891i 0.445738 + 0.895163i \(0.352941\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.49009 + 0.278545i 1.49009 + 0.278545i
\(393\) 0 0
\(394\) −0.675694 1.35698i −0.675694 1.35698i
\(395\) 0 0
\(396\) −2.12579 + 2.81500i −2.12579 + 2.81500i
\(397\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.507113 0.462295i 0.507113 0.462295i
\(401\) −1.20527 −1.20527 −0.602635 0.798017i \(-0.705882\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) −2.95707 1.14558i −2.95707 1.14558i
\(407\) 2.03702 1.85699i 2.03702 1.85699i
\(408\) 0 0
\(409\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.0858734 0.301814i 0.0858734 0.301814i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(420\) 0 0
\(421\) 1.47802 1.47802 0.739009 0.673696i \(-0.235294\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(422\) 0.687790 0.627003i 0.687790 0.627003i
\(423\) 0 0
\(424\) −0.500000 + 0.662107i −0.500000 + 0.662107i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0.155584 + 0.312454i 0.155584 + 0.312454i
\(429\) 0 0
\(430\) 0 0
\(431\) −1.58561 + 0.614268i −1.58561 + 0.614268i −0.982973 0.183750i \(-0.941176\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(432\) 0 0
\(433\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.37690 2.16683i −2.37690 2.16683i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(440\) 0 0
\(441\) −0.273663 + 0.961826i −0.273663 + 0.961826i
\(442\) 0 0
\(443\) 0.329838 + 1.15926i 0.329838 + 1.15926i 0.932472 + 0.361242i \(0.117647\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −1.27974 −1.27974
\(449\) 0.538007 0.100571i 0.538007 0.100571i 0.0922684 0.995734i \(-0.470588\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(450\) 1.02474 + 1.35698i 1.02474 + 1.35698i
\(451\) 0 0
\(452\) −2.27974 −2.27974
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.547326 1.92365i −0.547326 1.92365i −0.273663 0.961826i \(-0.588235\pi\)
−0.273663 0.961826i \(-0.588235\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(462\) 0 0
\(463\) 0.0822551 + 0.887674i 0.0822551 + 0.887674i 0.932472 + 0.361242i \(0.117647\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(464\) −1.25795 0.235151i −1.25795 0.235151i
\(465\) 0 0
\(466\) 3.11722 1.20762i 3.11722 1.20762i
\(467\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(468\) 0 0
\(469\) 0.465346 + 1.63552i 0.465346 + 1.63552i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −0.292603 + 0.181172i −0.292603 + 0.181172i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.404479 0.368731i −0.404479 0.368731i
\(478\) −2.01458 + 2.66774i −2.01458 + 2.66774i
\(479\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −2.82462 3.74040i −2.82462 3.74040i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.67148 1.03494i 1.67148 1.03494i 0.739009 0.673696i \(-0.235294\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0.831277 1.66943i 0.831277 1.66943i 0.0922684 0.995734i \(-0.470588\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.45285 + 0.271585i −1.45285 + 0.271585i
\(498\) 0 0
\(499\) 0.149783 + 0.526432i 0.149783 + 0.526432i 1.00000 \(0\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(504\) −0.139869 + 1.50943i −0.139869 + 1.50943i
\(505\) 0 0
\(506\) 0.497552 + 0.308071i 0.497552 + 0.308071i
\(507\) 0 0
\(508\) −2.37690 + 2.16683i −2.37690 + 2.16683i
\(509\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.25795 + 0.235151i −1.25795 + 0.235151i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0.687790 2.41733i 0.687790 2.41733i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(522\) 0.867844 3.05016i 0.867844 3.05016i
\(523\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 1.49009 2.99250i 1.49009 2.99250i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.949499 + 0.177492i 0.949499 + 0.177492i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 1.14897 + 2.30745i 1.14897 + 2.30745i
\(537\) 0 0
\(538\) 0 0
\(539\) −1.58561 0.981767i −1.58561 0.981767i
\(540\) 0 0
\(541\) −0.537235 + 0.711414i −0.537235 + 0.711414i −0.982973 0.183750i \(-0.941176\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.96595 −1.96595 −0.982973 0.183750i \(-0.941176\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(548\) 1.39782 1.27428i 1.39782 1.27428i
\(549\) 0 0
\(550\) −2.95707 + 1.14558i −2.95707 + 1.14558i
\(551\) 0 0
\(552\) 0 0
\(553\) −1.83319 0.710182i −1.83319 0.710182i
\(554\) −0.292603 3.15769i −0.292603 3.15769i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.67148 + 1.03494i 1.67148 + 1.03494i 0.932472 + 0.361242i \(0.117647\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.254696 + 0.895163i −0.254696 + 0.895163i
\(563\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.982973 0.183750i −0.982973 0.183750i
\(568\) −2.08923 + 0.809370i −2.08923 + 0.809370i
\(569\) 0.726337 + 0.961826i 0.726337 + 0.961826i 1.00000 \(0\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(570\) 0 0
\(571\) −0.181395 + 1.95756i −0.181395 + 1.95756i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.136374 0.124322i 0.136374 0.124322i
\(576\) −0.118079 1.27428i −0.118079 1.27428i
\(577\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(578\) 0.465346 1.63552i 0.465346 1.63552i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.867844 0.537346i 0.867844 0.537346i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.0935810 1.00990i 0.0935810 1.00990i
\(593\) 0 0 −0.602635 0.798017i \(-0.705882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.965346 0.373977i −0.965346 0.373977i
\(597\) 0 0
\(598\) 0 0
\(599\) 0.538007 0.100571i 0.538007 0.100571i 0.0922684 0.995734i \(-0.470588\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(600\) 0 0
\(601\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(602\) −0.139869 + 0.280896i −0.139869 + 0.280896i
\(603\) −1.58561 + 0.614268i −1.58561 + 0.614268i
\(604\) 1.68621 + 3.38636i 1.68621 + 3.38636i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.156896 + 0.0971461i −0.156896 + 0.0971461i −0.602635 0.798017i \(-0.705882\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −2.63616 1.02125i −2.63616 1.02125i
\(617\) −1.83319 0.710182i −1.83319 0.710182i −0.982973 0.183750i \(-0.941176\pi\)
−0.850217 0.526432i \(-0.823529\pi\)
\(618\) 0 0
\(619\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.0922684 + 0.995734i 0.0922684 + 0.995734i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 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 \(-0.117647\pi\)
\(632\) −2.92943 0.547605i −2.92943 0.547605i
\(633\) 0 0
\(634\) 2.47048 0.461813i 2.47048 0.461813i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 5.02830 + 3.11339i 5.02830 + 3.11339i
\(639\) −0.404479 1.42160i −0.404479 1.42160i
\(640\) 0 0
\(641\) −0.0505009 + 0.544991i −0.0505009 + 0.544991i 0.932472 + 0.361242i \(0.117647\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(642\) 0 0
\(643\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(644\) 0.349047 0.349047
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(648\) −1.51590 −1.51590
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.751607 + 1.50943i 0.751607 + 1.50943i
\(653\) 0.149783 + 0.526432i 0.149783 + 0.526432i 1.00000 \(0\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −0.243964 + 0.857445i −0.243964 + 0.857445i 0.739009 + 0.673696i \(0.235294\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(660\) 0 0
\(661\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(662\) −0.231896 + 2.50255i −0.231896 + 2.50255i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 2.47048 + 0.461813i 2.47048 + 0.461813i
\(667\) −0.338291 0.0632375i −0.338291 0.0632375i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.831277 + 1.66943i 0.831277 + 1.66943i 0.739009 + 0.673696i \(0.235294\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(674\) −2.34356 + 2.13643i −2.34356 + 2.13643i
\(675\) 0 0
\(676\) −1.60817 0.995734i −1.60817 0.995734i
\(677\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.172075 0.0666624i 0.172075 0.0666624i −0.273663 0.961826i \(-0.588235\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.70043 −1.70043
\(687\) 0 0
\(688\) −0.0346541 + 0.121796i −0.0346541 + 0.121796i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(692\) 0 0
\(693\) 0.831277 1.66943i 0.831277 1.66943i
\(694\) −1.74250 1.07891i −1.74250 1.07891i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.13987 + 1.50943i −1.13987 + 1.50943i
\(701\) 0.136374 1.47171i 0.136374 1.47171i −0.602635 0.798017i \(-0.705882\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 2.34600 + 0.438544i 2.34600 + 0.438544i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.37821 + 1.25640i 1.37821 + 1.25640i 0.932472 + 0.361242i \(0.117647\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(710\) 0 0
\(711\) 0.538007 1.89090i 0.538007 1.89090i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −3.71854 + 0.695116i −3.71854 + 0.695116i
\(717\) 0 0
\(718\) −1.41353 2.83876i −1.41353 2.83876i
\(719\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.70043 −1.70043
\(723\) 0 0
\(724\) 0 0
\(725\) 1.37821 1.25640i 1.37821 1.25640i
\(726\) 0 0
\(727\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(728\) 0 0
\(729\) 0.0922684 0.995734i 0.0922684 0.995734i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.0633152 + 0.0118357i −0.0633152 + 0.0118357i
\(737\) −0.292603 3.15769i −0.292603 3.15769i
\(738\) 0 0
\(739\) −0.876298 + 1.75984i −0.876298 + 1.75984i −0.273663 + 0.961826i \(0.588235\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.414845 0.833121i 0.414845 0.833121i
\(743\) −0.243964 0.857445i −0.243964 0.857445i −0.982973 0.183750i \(-0.941176\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −1.74250 + 1.07891i −1.74250 + 1.07891i
\(747\) 0 0
\(748\) 0 0
\(749\) −0.111208 0.147263i −0.111208 0.147263i
\(750\) 0 0
\(751\) −0.890705 0.811985i −0.890705 0.811985i 0.0922684 0.995734i \(-0.470588\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.25664 + 0.778076i −1.25664 + 0.778076i −0.982973 0.183750i \(-0.941176\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(758\) −0.560867 0.742708i −0.560867 0.742708i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(762\) 0 0
\(763\) 1.44574 + 0.895163i 1.44574 + 0.895163i
\(764\) 0.880191 + 3.09355i 0.880191 + 3.09355i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.99914 1.16187i −2.99914 1.16187i
\(773\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(774\) −0.292603 0.113355i −0.292603 0.113355i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.189102 2.04074i 0.189102 2.04074i
\(779\) 0 0
\(780\) 0 0
\(781\) 2.75642 2.75642
\(782\) 0 0
\(783\) 0 0
\(784\) −0.674523 + 0.126090i −0.674523 + 0.126090i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(788\) 1.24612 + 1.13599i 1.24612 + 1.13599i
\(789\) 0 0
\(790\) 0 0
\(791\) 1.18475 0.221468i 1.18475 0.221468i
\(792\) 0.773663 2.71914i 0.773663 2.71914i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.155584 0.312454i 0.155584 0.312454i
\(801\) 0 0
\(802\) 1.91108 0.740358i 1.91108 0.740358i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −0.537235 + 0.711414i −0.537235 + 0.711414i −0.982973 0.183750i \(-0.941176\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(810\) 0 0
\(811\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(812\) 3.52750 3.52750
\(813\) 0 0
\(814\) −2.08923 + 4.19573i −2.08923 + 4.19573i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −0.547326 −0.547326 −0.273663 0.961826i \(-0.588235\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(822\) 0 0
\(823\) −0.547326 −0.547326 −0.273663 0.961826i \(-0.588235\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0.172075 + 0.0666624i 0.172075 + 0.0666624i 0.445738 0.895163i \(-0.352941\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(828\) 0.0322060 + 0.347558i 0.0322060 + 0.347558i
\(829\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(840\) 0 0
\(841\) −2.43582 0.455335i −2.43582 0.455335i
\(842\) −2.34356 + 0.907899i −2.34356 + 0.907899i
\(843\) 0 0
\(844\) −0.461453 + 0.926722i −0.461453 + 0.926722i
\(845\) 0 0
\(846\) 0 0
\(847\) 1.83128 + 1.66943i 1.83128 + 1.66943i
\(848\) 0.102782 0.361242i 0.102782 0.361242i
\(849\) 0 0
\(850\) 0 0
\(851\) 0.0251661 0.271585i 0.0251661 0.271585i
\(852\) 0 0
\(853\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −0.206729 0.188459i −0.206729 0.188459i
\(857\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 2.13683 1.94798i 2.13683 1.94798i
\(863\) −1.96595 −1.96595 −0.982973 0.183750i \(-0.941176\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 3.11722 + 1.93010i 3.11722 + 1.93010i
\(870\) 0 0
\(871\) 0 0
\(872\) 2.40362 + 0.931167i 2.40362 + 0.931167i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.86494 0.722483i 1.86494 0.722483i 0.932472 0.361242i \(-0.117647\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(882\) −0.156896 1.69318i −0.156896 1.69318i
\(883\) −0.156896 + 0.0971461i −0.156896 + 0.0971461i −0.602635 0.798017i \(-0.705882\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.23509 1.63552i −1.23509 1.63552i
\(887\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(888\) 0 0
\(889\) 1.02474 1.35698i 1.02474 1.35698i
\(890\) 0 0
\(891\) 1.73901 + 0.673696i 1.73901 + 0.673696i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 1.70369 0.660012i 1.70369 0.660012i
\(897\) 0 0
\(898\) −0.791290 + 0.489946i −0.791290 + 0.489946i
\(899\) 0 0
\(900\) −1.60817 0.995734i −1.60817 0.995734i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 1.70369 0.660012i 1.70369 0.660012i
\(905\) 0 0
\(906\) 0 0
\(907\) −0.111208 1.20013i −0.111208 1.20013i −0.850217 0.526432i \(-0.823529\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.510366 0.197717i −0.510366 0.197717i 0.0922684 0.995734i \(-0.470588\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 2.04948 + 2.71395i 2.04948 + 2.71395i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0.658809 0.600584i 0.658809 0.600584i −0.273663 0.961826i \(-0.588235\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.09227 + 0.995734i 1.09227 + 0.995734i
\(926\) −0.675694 1.35698i −0.675694 1.35698i
\(927\) 0 0
\(928\) −0.639869 + 0.119612i −0.639869 + 0.119612i
\(929\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −2.74804 + 2.50517i −2.74804 + 2.50517i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.445738 0.895163i \(-0.352941\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(938\) −1.74250 2.30745i −1.74250 2.30745i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0.352665 0.467004i 0.352665 0.467004i
\(947\) 0.0822551 + 0.165190i 0.0822551 + 0.165190i 0.932472 0.361242i \(-0.117647\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.184537 + 1.99147i 0.184537 + 1.99147i 0.0922684 + 0.995734i \(0.470588\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(954\) 0.867844 + 0.336205i 0.867844 + 0.336205i
\(955\) 0 0
\(956\) 1.01763 3.57659i 1.01763 3.57659i
\(957\) 0 0
\(958\) 0 0
\(959\) −0.602635 + 0.798017i −0.602635 + 0.798017i
\(960\) 0 0
\(961\) 0.932472 0.361242i 0.932472 0.361242i
\(962\) 0 0
\(963\) 0.136374 0.124322i 0.136374 0.124322i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0.0822551 0.165190i 0.0822551 0.165190i −0.850217 0.526432i \(-0.823529\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(968\) 3.19377 + 1.97750i 3.19377 + 1.97750i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.445738 0.895163i \(-0.647059\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −2.01458 + 2.66774i −2.01458 + 2.66774i
\(975\) 0 0
\(976\) 0 0
\(977\) −0.876298 0.163808i −0.876298 0.163808i −0.273663 0.961826i \(-0.588235\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −0.757949 + 1.52217i −0.757949 + 1.52217i
\(982\) −0.292603 + 3.15769i −0.292603 + 3.15769i
\(983\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.00931926 + 0.0327538i −0.00931926 + 0.0327538i
\(990\) 0 0
\(991\) −0.0505009 0.177492i −0.0505009 0.177492i 0.932472 0.361242i \(-0.117647\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 2.13683 1.32307i 2.13683 1.32307i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(998\) −0.560867 0.742708i −0.560867 0.742708i
\(999\) 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 959.1.t.a.804.1 16
7.6 odd 2 CM 959.1.t.a.804.1 16
137.38 even 17 inner 959.1.t.a.860.1 yes 16
959.860 odd 34 inner 959.1.t.a.860.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
959.1.t.a.804.1 16 1.1 even 1 trivial
959.1.t.a.804.1 16 7.6 odd 2 CM
959.1.t.a.860.1 yes 16 137.38 even 17 inner
959.1.t.a.860.1 yes 16 959.860 odd 34 inner