Properties

Label 583.1.n.a.43.1
Level $583$
Weight $1$
Character 583.43
Analytic conductor $0.291$
Analytic rank $0$
Dimension $12$
Projective image $D_{26}$
CM discriminant -11
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [583,1,Mod(43,583)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(583, base_ring=CyclotomicField(26))
 
chi = DirichletCharacter(H, H._module([13, 11]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("583.43");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 583 = 11 \cdot 53 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 583.n (of order \(26\), degree \(12\), 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: \(0.290954902365\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\Q(\zeta_{26})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{26}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{26} - \cdots)\)

Embedding invariants

Embedding label 43.1
Root \(-0.885456 + 0.464723i\) of defining polynomial
Character \(\chi\) \(=\) 583.43
Dual form 583.1.n.a.461.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.53901 + 1.06230i) q^{3} +(-0.885456 + 0.464723i) q^{4} +(-1.53901 + 0.583668i) q^{5} +(0.885456 + 2.33476i) q^{9} +O(q^{10})\) \(q+(1.53901 + 1.06230i) q^{3} +(-0.885456 + 0.464723i) q^{4} +(-1.53901 + 0.583668i) q^{5} +(0.885456 + 2.33476i) q^{9} +(0.120537 - 0.992709i) q^{11} +(-1.85640 - 0.225408i) q^{12} +(-2.98857 - 0.736617i) q^{15} +(0.568065 - 0.822984i) q^{16} +(1.09148 - 1.23202i) q^{20} +1.98542i q^{23} +(1.27936 - 1.13342i) q^{25} +(-0.669959 + 2.71813i) q^{27} +(0.922670 - 0.112032i) q^{31} +(1.24006 - 1.39974i) q^{33} +(-1.86905 - 1.65583i) q^{36} +(0.402877 - 0.583668i) q^{37} +(0.354605 + 0.935016i) q^{44} +(-2.72545 - 3.07639i) q^{45} +(0.402877 - 1.06230i) q^{47} +(1.74851 - 0.663123i) q^{48} +(0.885456 - 0.464723i) q^{49} +(-0.748511 - 0.663123i) q^{53} +(0.393906 + 1.59814i) q^{55} +(0.627974 - 1.65583i) q^{59} +(2.98857 - 0.736617i) q^{60} +(-0.120537 + 0.992709i) q^{64} +(0.222431 + 0.423807i) q^{67} +(-2.10911 + 3.05557i) q^{69} +(-1.09148 + 0.753393i) q^{71} +(3.17297 - 0.385269i) q^{75} +(-0.393906 + 1.59814i) q^{80} +(-2.04949 + 1.81569i) q^{81} +(0.180446 + 0.159861i) q^{89} +(-0.922670 - 1.75800i) q^{92} +(1.53901 + 0.807733i) q^{93} +(-0.0854858 - 0.225408i) q^{97} +(2.42446 - 0.597576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + q^{4} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + q^{4} - q^{9} - q^{11} - 13 q^{15} - q^{16} - q^{25} - 12 q^{36} + 2 q^{37} + q^{44} + 2 q^{47} + 13 q^{48} - q^{49} - q^{53} + 2 q^{59} + 13 q^{60} + q^{64} - 14 q^{81} + 2 q^{89} - 2 q^{97} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/583\mathbb{Z}\right)^\times\).

\(n\) \(266\) \(320\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{26}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 −0.239316 0.970942i \(-0.576923\pi\)
0.239316 + 0.970942i \(0.423077\pi\)
\(3\) 1.53901 + 1.06230i 1.53901 + 1.06230i 0.970942 + 0.239316i \(0.0769231\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(4\) −0.885456 + 0.464723i −0.885456 + 0.464723i
\(5\) −1.53901 + 0.583668i −1.53901 + 0.583668i −0.970942 0.239316i \(-0.923077\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(6\) 0 0
\(7\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(8\) 0 0
\(9\) 0.885456 + 2.33476i 0.885456 + 2.33476i
\(10\) 0 0
\(11\) 0.120537 0.992709i 0.120537 0.992709i
\(12\) −1.85640 0.225408i −1.85640 0.225408i
\(13\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(14\) 0 0
\(15\) −2.98857 0.736617i −2.98857 0.736617i
\(16\) 0.568065 0.822984i 0.568065 0.822984i
\(17\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(18\) 0 0
\(19\) 0 0 0.464723 0.885456i \(-0.346154\pi\)
−0.464723 + 0.885456i \(0.653846\pi\)
\(20\) 1.09148 1.23202i 1.09148 1.23202i
\(21\) 0 0
\(22\) 0 0
\(23\) 1.98542i 1.98542i 0.120537 + 0.992709i \(0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(24\) 0 0
\(25\) 1.27936 1.13342i 1.27936 1.13342i
\(26\) 0 0
\(27\) −0.669959 + 2.71813i −0.669959 + 2.71813i
\(28\) 0 0
\(29\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(30\) 0 0
\(31\) 0.922670 0.112032i 0.922670 0.112032i 0.354605 0.935016i \(-0.384615\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(32\) 0 0
\(33\) 1.24006 1.39974i 1.24006 1.39974i
\(34\) 0 0
\(35\) 0 0
\(36\) −1.86905 1.65583i −1.86905 1.65583i
\(37\) 0.402877 0.583668i 0.402877 0.583668i −0.568065 0.822984i \(-0.692308\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(42\) 0 0
\(43\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(44\) 0.354605 + 0.935016i 0.354605 + 0.935016i
\(45\) −2.72545 3.07639i −2.72545 3.07639i
\(46\) 0 0
\(47\) 0.402877 1.06230i 0.402877 1.06230i −0.568065 0.822984i \(-0.692308\pi\)
0.970942 0.239316i \(-0.0769231\pi\)
\(48\) 1.74851 0.663123i 1.74851 0.663123i
\(49\) 0.885456 0.464723i 0.885456 0.464723i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.748511 0.663123i −0.748511 0.663123i
\(54\) 0 0
\(55\) 0.393906 + 1.59814i 0.393906 + 1.59814i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.627974 1.65583i 0.627974 1.65583i −0.120537 0.992709i \(-0.538462\pi\)
0.748511 0.663123i \(-0.230769\pi\)
\(60\) 2.98857 0.736617i 2.98857 0.736617i
\(61\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.120537 + 0.992709i −0.120537 + 0.992709i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.222431 + 0.423807i 0.222431 + 0.423807i 0.970942 0.239316i \(-0.0769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(68\) 0 0
\(69\) −2.10911 + 3.05557i −2.10911 + 3.05557i
\(70\) 0 0
\(71\) −1.09148 + 0.753393i −1.09148 + 0.753393i −0.970942 0.239316i \(-0.923077\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(72\) 0 0
\(73\) 0 0 0.663123 0.748511i \(-0.269231\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(74\) 0 0
\(75\) 3.17297 0.385269i 3.17297 0.385269i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.239316 0.970942i \(-0.423077\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(80\) −0.393906 + 1.59814i −0.393906 + 1.59814i
\(81\) −2.04949 + 1.81569i −2.04949 + 1.81569i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.180446 + 0.159861i 0.180446 + 0.159861i 0.748511 0.663123i \(-0.230769\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.922670 1.75800i −0.922670 1.75800i
\(93\) 1.53901 + 0.807733i 1.53901 + 0.807733i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.0854858 0.225408i −0.0854858 0.225408i 0.885456 0.464723i \(-0.153846\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(98\) 0 0
\(99\) 2.42446 0.597576i 2.42446 0.597576i
\(100\) −0.606094 + 1.59814i −0.606094 + 1.59814i
\(101\) 0 0 0.935016 0.354605i \(-0.115385\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(102\) 0 0
\(103\) −1.09148 0.753393i −1.09148 0.753393i −0.120537 0.992709i \(-0.538462\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −0.669959 2.71813i −0.669959 2.71813i
\(109\) 0 0 −0.822984 0.568065i \(-0.807692\pi\)
0.822984 + 0.568065i \(0.192308\pi\)
\(110\) 0 0
\(111\) 1.24006 0.470293i 1.24006 0.470293i
\(112\) 0 0
\(113\) −1.88546 + 0.464723i −1.88546 + 0.464723i −0.885456 + 0.464723i \(0.846154\pi\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) −1.15883 3.05557i −1.15883 3.05557i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.970942 0.239316i −0.970942 0.239316i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.764919 + 0.527986i −0.764919 + 0.527986i
\(125\) −0.542488 + 1.03363i −0.542488 + 1.03363i
\(126\) 0 0
\(127\) 0 0 −0.935016 0.354605i \(-0.884615\pi\)
0.935016 + 0.354605i \(0.115385\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(132\) −0.447528 + 1.81569i −0.447528 + 1.81569i
\(133\) 0 0
\(134\) 0 0
\(135\) −0.555415 4.57426i −0.555415 4.57426i
\(136\) 0 0
\(137\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(138\) 0 0
\(139\) 0 0 0.663123 0.748511i \(-0.269231\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(140\) 0 0
\(141\) 1.74851 1.20691i 1.74851 1.20691i
\(142\) 0 0
\(143\) 0 0
\(144\) 2.42446 + 0.597576i 2.42446 + 0.597576i
\(145\) 0 0
\(146\) 0 0
\(147\) 1.85640 + 0.225408i 1.85640 + 0.225408i
\(148\) −0.0854858 + 0.704039i −0.0854858 + 0.704039i
\(149\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(150\) 0 0
\(151\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.35460 + 0.710951i −1.35460 + 0.710951i
\(156\) 0 0
\(157\) −0.317391 1.28771i −0.317391 1.28771i −0.885456 0.464723i \(-0.846154\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(158\) 0 0
\(159\) −0.447528 1.81569i −0.447528 1.81569i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.56806 + 0.822984i −1.56806 + 0.822984i −0.568065 + 0.822984i \(0.692308\pi\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) −1.09148 + 2.87799i −1.09148 + 2.87799i
\(166\) 0 0
\(167\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(168\) 0 0
\(169\) 0.568065 + 0.822984i 0.568065 + 0.822984i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.464723 0.885456i \(-0.653846\pi\)
0.464723 + 0.885456i \(0.346154\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.748511 0.663123i −0.748511 0.663123i
\(177\) 2.72545 1.88124i 2.72545 1.88124i
\(178\) 0 0
\(179\) 0.879463 0.992709i 0.879463 0.992709i −0.120537 0.992709i \(-0.538462\pi\)
1.00000 \(0\)
\(180\) 3.84293 + 1.45743i 3.84293 + 1.45743i
\(181\) 0.475142 0.0576926i 0.475142 0.0576926i 0.120537 0.992709i \(-0.461538\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.279362 + 1.13342i −0.279362 + 1.13342i
\(186\) 0 0
\(187\) 0 0
\(188\) 0.136945 + 1.12785i 0.136945 + 1.12785i
\(189\) 0 0
\(190\) 0 0
\(191\) −1.85640 0.704039i −1.85640 0.704039i −0.970942 0.239316i \(-0.923077\pi\)
−0.885456 0.464723i \(-0.846154\pi\)
\(192\) −1.24006 + 1.39974i −1.24006 + 1.39974i
\(193\) 0 0 0.464723 0.885456i \(-0.346154\pi\)
−0.464723 + 0.885456i \(0.653846\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.568065 + 0.822984i −0.568065 + 0.822984i
\(197\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(198\) 0 0
\(199\) 1.71945 + 0.902438i 1.71945 + 0.902438i 0.970942 + 0.239316i \(0.0769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(200\) 0 0
\(201\) −0.107887 + 0.888530i −0.107887 + 0.888530i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −4.63547 + 1.75800i −4.63547 + 1.75800i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0.970942 + 0.239316i 0.970942 + 0.239316i
\(213\) −2.48012 −2.48012
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.09148 1.23202i −1.09148 1.23202i
\(221\) 0 0
\(222\) 0 0
\(223\) 0.136945 1.12785i 0.136945 1.12785i −0.748511 0.663123i \(-0.769231\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(224\) 0 0
\(225\) 3.77907 + 1.98341i 3.77907 + 1.98341i
\(226\) 0 0
\(227\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(228\) 0 0
\(229\) −0.180446 0.159861i −0.180446 0.159861i 0.568065 0.822984i \(-0.307692\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.935016 0.354605i \(-0.884615\pi\)
0.935016 + 0.354605i \(0.115385\pi\)
\(234\) 0 0
\(235\) 1.87003i 1.87003i
\(236\) 0.213460 + 1.75800i 0.213460 + 1.75800i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.239316 0.970942i \(-0.423077\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(240\) −2.30393 + 2.04110i −2.30393 + 2.04110i
\(241\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(242\) 0 0
\(243\) −2.30393 + 0.279747i −2.30393 + 0.279747i
\(244\) 0 0
\(245\) −1.09148 + 1.23202i −1.09148 + 1.23202i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.431935 0.822984i −0.431935 0.822984i 0.568065 0.822984i \(-0.307692\pi\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 1.97094 + 0.239316i 1.97094 + 0.239316i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.354605 0.935016i −0.354605 0.935016i
\(257\) 1.24006 + 1.39974i 1.24006 + 1.39974i 0.885456 + 0.464723i \(0.153846\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.239316 0.970942i \(-0.576923\pi\)
0.239316 + 0.970942i \(0.423077\pi\)
\(264\) 0 0
\(265\) 1.53901 + 0.583668i 1.53901 + 0.583668i
\(266\) 0 0
\(267\) 0.107887 + 0.437715i 0.107887 + 0.437715i
\(268\) −0.393906 0.271894i −0.393906 0.271894i
\(269\) 1.32555 0.695701i 1.32555 0.695701i 0.354605 0.935016i \(-0.384615\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(270\) 0 0
\(271\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.970942 1.40665i −0.970942 1.40665i
\(276\) 0.447528 3.68573i 0.447528 3.68573i
\(277\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(278\) 0 0
\(279\) 1.07855 + 2.05501i 1.07855 + 2.05501i
\(280\) 0 0
\(281\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(282\) 0 0
\(283\) 0 0 0.822984 0.568065i \(-0.192308\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(284\) 0.616337 1.17433i 0.616337 1.17433i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.120537 + 0.992709i 0.120537 + 0.992709i
\(290\) 0 0
\(291\) 0.107887 0.437715i 0.107887 0.437715i
\(292\) 0 0
\(293\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(294\) 0 0
\(295\) 2.91486i 2.91486i
\(296\) 0 0
\(297\) 2.61756 + 0.992709i 2.61756 + 0.992709i
\(298\) 0 0
\(299\) 0 0
\(300\) −2.63049 + 1.81569i −2.63049 + 1.81569i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(308\) 0 0
\(309\) −0.879463 2.31895i −0.879463 2.31895i
\(310\) 0 0
\(311\) 0.688601 0.169725i 0.688601 0.169725i 0.120537 0.992709i \(-0.461538\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(312\) 0 0
\(313\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.393906 1.59814i −0.393906 1.59814i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.970942 2.56016i 0.970942 2.56016i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.00599 0.527986i −1.00599 0.527986i −0.120537 0.992709i \(-0.538462\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(332\) 0 0
\(333\) 1.71945 + 0.423807i 1.71945 + 0.423807i
\(334\) 0 0
\(335\) −0.589686 0.522416i −0.589686 0.522416i
\(336\) 0 0
\(337\) 0 0 0.464723 0.885456i \(-0.346154\pi\)
−0.464723 + 0.885456i \(0.653846\pi\)
\(338\) 0 0
\(339\) −3.39540 1.28771i −3.39540 1.28771i
\(340\) 0 0
\(341\) 0.929446i 0.929446i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1.46249 5.93356i 1.46249 5.93356i
\(346\) 0 0
\(347\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(348\) 0 0
\(349\) 0 0 0.992709 0.120537i \(-0.0384615\pi\)
−0.992709 + 0.120537i \(0.961538\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.764919 + 0.527986i −0.764919 + 0.527986i −0.885456 0.464723i \(-0.846154\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(354\) 0 0
\(355\) 1.24006 1.79654i 1.24006 1.79654i
\(356\) −0.234068 0.0576926i −0.234068 0.0576926i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(360\) 0 0
\(361\) −0.568065 0.822984i −0.568065 0.822984i
\(362\) 0 0
\(363\) −1.24006 1.39974i −1.24006 1.39974i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.213460 + 0.112032i −0.213460 + 0.112032i −0.568065 0.822984i \(-0.692308\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(368\) 1.63397 + 1.12785i 1.63397 + 1.12785i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −1.73809 −1.73809
\(373\) 0 0 −0.239316 0.970942i \(-0.576923\pi\)
0.239316 + 0.970942i \(0.423077\pi\)
\(374\) 0 0
\(375\) −1.93291 + 1.01447i −1.93291 + 1.01447i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.31658 1.48611i −1.31658 1.48611i −0.748511 0.663123i \(-0.769231\pi\)
−0.568065 0.822984i \(-0.692308\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.63397 + 0.198399i 1.63397 + 0.198399i 0.885456 0.464723i \(-0.153846\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.180446 + 0.159861i 0.180446 + 0.159861i
\(389\) −1.53901 + 1.06230i −1.53901 + 1.06230i −0.568065 + 0.822984i \(0.692308\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −1.86905 + 1.65583i −1.86905 + 1.65583i
\(397\) −0.475142 + 1.92773i −0.475142 + 1.92773i −0.120537 + 0.992709i \(0.538462\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.206022 1.69675i −0.206022 1.69675i
\(401\) 1.32625i 1.32625i 0.748511 + 0.663123i \(0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 2.09442 3.99059i 2.09442 3.99059i
\(406\) 0 0
\(407\) −0.530851 0.470293i −0.530851 0.470293i
\(408\) 0 0
\(409\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.31658 + 0.159861i 1.31658 + 0.159861i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.85640 0.704039i 1.85640 0.704039i 0.885456 0.464723i \(-0.153846\pi\)
0.970942 0.239316i \(-0.0769231\pi\)
\(420\) 0 0
\(421\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(422\) 0 0
\(423\) 2.83694 2.83694
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(432\) 1.85640 + 2.09544i 1.85640 + 2.09544i
\(433\) 0.627974 + 1.65583i 0.627974 + 1.65583i 0.748511 + 0.663123i \(0.230769\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(440\) 0 0
\(441\) 1.86905 + 1.65583i 1.86905 + 1.65583i
\(442\) 0 0
\(443\) −0.222431 + 0.423807i −0.222431 + 0.423807i −0.970942 0.239316i \(-0.923077\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(444\) −0.879463 + 0.992709i −0.879463 + 0.992709i
\(445\) −0.371013 0.140707i −0.371013 0.140707i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.32555 + 1.17433i −1.32555 + 1.17433i −0.354605 + 0.935016i \(0.615385\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 1.45352 1.28771i 1.45352 1.28771i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.663123 0.748511i \(-0.269231\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 2.44608 + 2.16704i 2.44608 + 2.16704i
\(461\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(462\) 0 0
\(463\) 0.222431 + 0.423807i 0.222431 + 0.423807i 0.970942 0.239316i \(-0.0769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(464\) 0 0
\(465\) −2.83999 0.344837i −2.83999 0.344837i
\(466\) 0 0
\(467\) −0.136945 0.198399i −0.136945 0.198399i 0.748511 0.663123i \(-0.230769\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0.879463 2.31895i 0.879463 2.31895i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.885456 2.33476i 0.885456 2.33476i
\(478\) 0 0
\(479\) 0 0 −0.239316 0.970942i \(-0.576923\pi\)
0.239316 + 0.970942i \(0.423077\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.970942 0.239316i 0.970942 0.239316i
\(485\) 0.263126 + 0.297008i 0.263126 + 0.297008i
\(486\) 0 0
\(487\) −1.10312 1.59814i −1.10312 1.59814i −0.748511 0.663123i \(-0.769231\pi\)
−0.354605 0.935016i \(-0.615385\pi\)
\(488\) 0 0
\(489\) −3.28752 0.399177i −3.28752 0.399177i
\(490\) 0 0
\(491\) 0 0 −0.464723 0.885456i \(-0.653846\pi\)
0.464723 + 0.885456i \(0.346154\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −3.38248 + 2.33476i −3.38248 + 2.33476i
\(496\) 0.431935 0.822984i 0.431935 0.822984i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.85640 + 0.225408i −1.85640 + 0.225408i −0.970942 0.239316i \(-0.923077\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(500\) 1.16734i 1.16734i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.239316 0.970942i \(-0.423077\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.87003i 1.87003i
\(508\) 0 0
\(509\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.11952 + 0.522416i 2.11952 + 0.522416i
\(516\) 0 0
\(517\) −1.00599 0.527986i −1.00599 0.527986i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.402877 1.06230i −0.402877 1.06230i −0.970942 0.239316i \(-0.923077\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(522\) 0 0
\(523\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.447528 1.81569i −0.447528 1.81569i
\(529\) −2.94188 −2.94188
\(530\) 0 0
\(531\) 4.42201 4.42201
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.40805 0.593532i 2.40805 0.593532i
\(538\) 0 0
\(539\) −0.354605 0.935016i −0.354605 0.935016i
\(540\) 2.61756 + 3.79219i 2.61756 + 3.79219i
\(541\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(542\) 0 0
\(543\) 0.792533 + 0.415953i 0.792533 + 0.415953i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1.63397 + 1.44757i −1.63397 + 1.44757i
\(556\) 0 0
\(557\) 0 0 0.239316 0.970942i \(-0.423077\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.663123 0.748511i \(-0.269231\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(564\) −0.987350 + 1.88124i −0.987350 + 1.88124i
\(565\) 2.63049 1.81569i 2.63049 1.81569i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.464723 0.885456i \(-0.653846\pi\)
0.464723 + 0.885456i \(0.346154\pi\)
\(570\) 0 0
\(571\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(572\) 0 0
\(573\) −2.10911 3.05557i −2.10911 3.05557i
\(574\) 0 0
\(575\) 2.25030 + 2.54007i 2.25030 + 2.54007i
\(576\) −2.42446 + 0.597576i −2.42446 + 0.597576i
\(577\) −0.688601 + 1.81569i −0.688601 + 1.81569i −0.120537 + 0.992709i \(0.538462\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.56806 0.822984i 1.56806 0.822984i 0.568065 0.822984i \(-0.307692\pi\)
1.00000 \(0\)
\(588\) −1.74851 + 0.663123i −1.74851 + 0.663123i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.251489 0.663123i −0.251489 0.663123i
\(593\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.68759 + 3.21543i 1.68759 + 3.21543i
\(598\) 0 0
\(599\) 0.645395 0.935016i 0.645395 0.935016i −0.354605 0.935016i \(-0.615385\pi\)
1.00000 \(0\)
\(600\) 0 0
\(601\) 0 0 0.822984 0.568065i \(-0.192308\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(602\) 0 0
\(603\) −0.792533 + 0.894585i −0.792533 + 0.894585i
\(604\) 0 0
\(605\) 1.63397 0.198399i 1.63397 0.198399i
\(606\) 0 0
\(607\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(618\) 0 0
\(619\) −0.850405 0.753393i −0.850405 0.753393i 0.120537 0.992709i \(-0.461538\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(620\) 0.869047 1.25903i 0.869047 1.25903i
\(621\) −5.39663 1.33015i −5.39663 1.33015i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.0255765 0.210641i 0.0255765 0.210641i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.879463 + 0.992709i 0.879463 + 0.992709i
\(629\) 0 0
\(630\) 0 0
\(631\) 0.869047 0.329586i 0.869047 0.329586i 0.120537 0.992709i \(-0.461538\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 1.24006 + 1.39974i 1.24006 + 1.39974i
\(637\) 0 0
\(638\) 0 0
\(639\) −2.72545 1.88124i −2.72545 1.88124i
\(640\) 0 0
\(641\) 1.53901 0.583668i 1.53901 0.583668i 0.568065 0.822984i \(-0.307692\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(642\) 0 0
\(643\) −1.45352 + 0.358261i −1.45352 + 0.358261i −0.885456 0.464723i \(-0.846154\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.234068 + 1.92773i −0.234068 + 1.92773i 0.120537 + 0.992709i \(0.461538\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(648\) 0 0
\(649\) −1.56806 0.822984i −1.56806 0.822984i
\(650\) 0 0
\(651\) 0 0
\(652\) 1.00599 1.45743i 1.00599 1.45743i
\(653\) 1.45352 + 1.28771i 1.45352 + 1.28771i 0.885456 + 0.464723i \(0.153846\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) −0.371013 3.05557i −0.371013 3.05557i
\(661\) 1.32555 1.17433i 1.32555 1.17433i 0.354605 0.935016i \(-0.384615\pi\)
0.970942 0.239316i \(-0.0769231\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1.40887 1.59029i 1.40887 1.59029i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(674\) 0 0
\(675\) 2.22365 + 4.23682i 2.22365 + 4.23682i
\(676\) −0.885456 0.464723i −0.885456 0.464723i
\(677\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.688601 1.81569i 0.688601 1.81569i 0.120537 0.992709i \(-0.461538\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −0.107887 0.437715i −0.107887 0.437715i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.475142 1.92773i −0.475142 1.92773i −0.354605 0.935016i \(-0.615385\pi\)
−0.120537 0.992709i \(-0.538462\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.970942 + 0.239316i 0.970942 + 0.239316i
\(705\) −1.98653 + 2.87799i −1.98653 + 2.87799i
\(706\) 0 0
\(707\) 0 0
\(708\) −1.53901 + 2.93233i −1.53901 + 2.93233i
\(709\) 0.317391 0.358261i 0.317391 0.358261i −0.568065 0.822984i \(-0.692308\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.222431 + 1.83188i 0.222431 + 1.83188i
\(714\) 0 0
\(715\) 0 0
\(716\) −0.317391 + 1.28771i −0.317391 + 1.28771i
\(717\) 0 0
\(718\) 0 0
\(719\) 1.87003i 1.87003i −0.354605 0.935016i \(-0.615385\pi\)
0.354605 0.935016i \(-0.384615\pi\)
\(720\) −4.08005 + 0.495408i −4.08005 + 0.495408i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −0.393906 + 0.271894i −0.393906 + 0.271894i
\(725\) 0 0
\(726\) 0 0
\(727\) −1.94188 0.478631i −1.94188 0.478631i −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 0.239316i \(-0.923077\pi\)
\(728\) 0 0
\(729\) −1.41847 0.744470i −1.41847 0.744470i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(734\) 0 0
\(735\) −2.98857 + 0.736617i −2.98857 + 0.736617i
\(736\) 0 0
\(737\) 0.447528 0.169725i 0.447528 0.169725i
\(738\) 0 0
\(739\) 0 0 −0.822984 0.568065i \(-0.807692\pi\)
0.822984 + 0.568065i \(0.192308\pi\)
\(740\) −0.279362 1.13342i −0.279362 1.13342i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.688601 + 1.81569i 0.688601 + 1.81569i 0.568065 + 0.822984i \(0.307692\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(752\) −0.645395 0.935016i −0.645395 0.935016i
\(753\) 0.209504 1.72542i 0.209504 1.72542i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.234068 0.0576926i −0.234068 0.0576926i 0.120537 0.992709i \(-0.461538\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(758\) 0 0
\(759\) 2.77907 + 2.46204i 2.77907 + 2.46204i
\(760\) 0 0
\(761\) 0 0 0.464723 0.885456i \(-0.346154\pi\)
−0.464723 + 0.885456i \(0.653846\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1.97094 0.239316i 1.97094 0.239316i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.447528 1.81569i 0.447528 1.81569i
\(769\) 0 0 0.239316 0.970942i \(-0.423077\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(770\) 0 0
\(771\) 0.421519 + 3.47152i 0.421519 + 3.47152i
\(772\) 0 0
\(773\) −1.97094 + 0.239316i −1.97094 + 0.239316i −0.970942 + 0.239316i \(0.923077\pi\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 1.05345 1.18910i 1.05345 1.18910i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0.616337 + 1.17433i 0.616337 + 1.17433i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.120537 0.992709i 0.120537 0.992709i
\(785\) 1.24006 + 1.79654i 1.24006 + 1.79654i
\(786\) 0 0
\(787\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 1.74851 + 2.53316i 1.74851 + 2.53316i
\(796\) −1.94188 −1.94188
\(797\) 0.114544 + 0.464723i 0.114544 + 0.464723i 1.00000 \(0\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −0.213460 + 0.562847i −0.213460 + 0.562847i
\(802\) 0 0
\(803\) 0 0
\(804\) −0.317391 0.836892i −0.317391 0.836892i
\(805\) 0 0
\(806\) 0 0
\(807\) 2.77907 + 0.337440i 2.77907 + 0.337440i
\(808\) 0 0
\(809\) 0 0 −0.464723 0.885456i \(-0.653846\pi\)
0.464723 + 0.885456i \(0.346154\pi\)
\(810\) 0 0
\(811\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.93291 2.18181i 1.93291 2.18181i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.239316 0.970942i \(-0.423077\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(822\) 0 0
\(823\) 1.32555 1.17433i 1.32555 1.17433i 0.354605 0.935016i \(-0.384615\pi\)
0.970942 0.239316i \(-0.0769231\pi\)
\(824\) 0 0
\(825\) 3.19628i 3.19628i
\(826\) 0 0
\(827\) 0 0 −0.935016 0.354605i \(-0.884615\pi\)
0.935016 + 0.354605i \(0.115385\pi\)
\(828\) 3.28752 3.71084i 3.28752 3.71084i
\(829\) −0.922670 + 1.75800i −0.922670 + 1.75800i −0.354605 + 0.935016i \(0.615385\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −0.313632 + 2.58299i −0.313632 + 2.58299i
\(838\) 0 0
\(839\) 0.251489 + 0.663123i 0.251489 + 0.663123i 1.00000 \(0\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(840\) 0 0
\(841\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.35460 0.935016i −1.35460 0.935016i
\(846\) 0 0
\(847\) 0 0
\(848\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(849\) 0 0
\(850\) 0 0
\(851\) 1.15883 + 0.799879i 1.15883 + 0.799879i
\(852\) 2.19604 1.15257i 2.19604 1.15257i
\(853\) 0 0 0.935016 0.354605i \(-0.115385\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(858\) 0 0
\(859\) −0.180446 + 1.48611i −0.180446 + 1.48611i 0.568065 + 0.822984i \(0.307692\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.45352 0.358261i −1.45352 0.358261i −0.568065 0.822984i \(-0.692308\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −0.869047 + 1.65583i −0.869047 + 1.65583i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0.450578 0.399177i 0.450578 0.399177i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 1.53901 + 0.583668i 1.53901 + 0.583668i
\(881\) 0.317391 0.358261i 0.317391 0.358261i −0.568065 0.822984i \(-0.692308\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(882\) 0 0
\(883\) −0.393906 + 0.271894i −0.393906 + 0.271894i −0.748511 0.663123i \(-0.769231\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(884\) 0 0
\(885\) −3.09646 + 4.48599i −3.09646 + 4.48599i
\(886\) 0 0
\(887\) 0 0 −0.464723 0.885456i \(-0.653846\pi\)
0.464723 + 0.885456i \(0.346154\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.55542 + 2.25341i 1.55542 + 2.25341i
\(892\) 0.402877 + 1.06230i 0.402877 + 1.06230i
\(893\) 0 0
\(894\) 0 0
\(895\) −0.774087 + 2.04110i −0.774087 + 2.04110i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −4.26793 −4.26793
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −0.697573 + 0.366114i −0.697573 + 0.366114i
\(906\) 0 0
\(907\) −0.627974 + 1.65583i −0.627974 + 1.65583i 0.120537 + 0.992709i \(0.461538\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.136945 0.198399i −0.136945 0.198399i 0.748511 0.663123i \(-0.230769\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0.234068 + 0.0576926i 0.234068 + 0.0576926i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.822984 0.568065i \(-0.192308\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −0.146113 1.20335i −0.146113 1.20335i
\(926\) 0 0
\(927\) 0.792533 3.21543i 0.792533 3.21543i
\(928\) 0 0
\(929\) −0.530851 + 0.470293i −0.530851 + 0.470293i −0.885456 0.464723i \(-0.846154\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 1.24006 + 0.470293i 1.24006 + 0.470293i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −0.869047 1.65583i −0.869047 1.65583i
\(941\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1.00599 1.45743i −1.00599 1.45743i
\(945\) 0 0
\(946\) 0 0
\(947\) −1.10312 + 0.271894i −1.10312 + 0.271894i −0.748511 0.663123i \(-0.769231\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 2.30393 + 1.59029i 2.30393 + 1.59029i
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 3.26793 3.26793
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.09148 2.87799i 1.09148 2.87799i
\(961\) −0.132174 + 0.0325779i −0.132174 + 0.0325779i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.45352 1.28771i −1.45352 1.28771i −0.885456 0.464723i \(-0.846154\pi\)
−0.568065 0.822984i \(-0.692308\pi\)
\(972\) 1.91002 1.31839i 1.91002 1.31839i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.64597i 1.64597i 0.568065 + 0.822984i \(0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(978\) 0 0
\(979\) 0.180446 0.159861i 0.180446 0.159861i
\(980\) 0.393906 1.59814i 0.393906 1.59814i
\(981\) 0 0
\(982\) 0 0
\(983\) −0.180446 1.48611i −0.180446 1.48611i −0.748511 0.663123i \(-0.769231\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −0.645395 + 0.935016i −0.645395 + 0.935016i 0.354605 + 0.935016i \(0.384615\pi\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) −0.987350 1.88124i −0.987350 1.88124i
\(994\) 0 0
\(995\) −3.17297 0.385269i −3.17297 0.385269i
\(996\) 0 0
\(997\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(998\) 0 0
\(999\) 1.31658 + 1.48611i 1.31658 + 1.48611i
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 583.1.n.a.43.1 12
11.10 odd 2 CM 583.1.n.a.43.1 12
53.37 even 26 inner 583.1.n.a.461.1 yes 12
583.461 odd 26 inner 583.1.n.a.461.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
583.1.n.a.43.1 12 1.1 even 1 trivial
583.1.n.a.43.1 12 11.10 odd 2 CM
583.1.n.a.461.1 yes 12 53.37 even 26 inner
583.1.n.a.461.1 yes 12 583.461 odd 26 inner