Properties

Label 583.1.n.a.197.1
Level $583$
Weight $1$
Character 583.197
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 197.1
Root \(-0.120537 - 0.992709i\) of defining polynomial
Character \(\chi\) \(=\) 583.197
Dual form 583.1.n.a.219.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.222431 - 0.902438i) q^{3} +(-0.120537 - 0.992709i) q^{4} +(0.222431 + 0.423807i) q^{5} +(0.120537 - 0.0632625i) q^{9} +O(q^{10})\) \(q+(-0.222431 - 0.902438i) q^{3} +(-0.120537 - 0.992709i) q^{4} +(0.222431 + 0.423807i) q^{5} +(0.120537 - 0.0632625i) q^{9} +(-0.354605 - 0.935016i) q^{11} +(-0.869047 + 0.329586i) q^{12} +(0.332984 - 0.294998i) q^{15} +(-0.970942 + 0.239316i) q^{16} +(0.393906 - 0.271894i) q^{20} +1.87003i q^{23} +(0.437928 - 0.634448i) q^{25} +(-0.700239 - 0.790406i) q^{27} +(-1.85640 - 0.704039i) q^{31} +(-0.764919 + 0.527986i) q^{33} +(-0.0773304 - 0.112032i) q^{36} +(1.71945 - 0.423807i) q^{37} +(-0.885456 + 0.464723i) q^{44} +(0.0536222 + 0.0370127i) q^{45} +(1.71945 + 0.902438i) q^{47} +(0.431935 + 0.822984i) q^{48} +(0.120537 + 0.992709i) q^{49} +(0.568065 + 0.822984i) q^{53} +(0.317391 - 0.358261i) q^{55} +(-0.213460 - 0.112032i) q^{59} +(-0.332984 - 0.294998i) q^{60} +(0.354605 + 0.935016i) q^{64} +(1.31658 - 0.159861i) q^{67} +(1.68759 - 0.415953i) q^{69} +(-0.393906 + 1.59814i) q^{71} +(-0.669959 - 0.254082i) q^{75} +(-0.317391 - 0.358261i) q^{80} +(-0.480207 + 0.695701i) q^{81} +(0.402877 + 0.583668i) q^{89} +(1.85640 - 0.225408i) q^{92} +(-0.222431 + 1.83188i) q^{93} +(-0.627974 + 0.329586i) q^{97} +(-0.101894 - 0.0902706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + q^{4} - q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/583\mathbb{Z}\right)^\times\).

\(n\) \(266\) \(320\)
\(\chi(n)\) \(-1\) \(e\left(\frac{19}{26}\right)\)

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 0.663123 0.748511i \(-0.269231\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(3\) −0.222431 0.902438i −0.222431 0.902438i −0.970942 0.239316i \(-0.923077\pi\)
0.748511 0.663123i \(-0.230769\pi\)
\(4\) −0.120537 0.992709i −0.120537 0.992709i
\(5\) 0.222431 + 0.423807i 0.222431 + 0.423807i 0.970942 0.239316i \(-0.0769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(6\) 0 0
\(7\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(8\) 0 0
\(9\) 0.120537 0.0632625i 0.120537 0.0632625i
\(10\) 0 0
\(11\) −0.354605 0.935016i −0.354605 0.935016i
\(12\) −0.869047 + 0.329586i −0.869047 + 0.329586i
\(13\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(14\) 0 0
\(15\) 0.332984 0.294998i 0.332984 0.294998i
\(16\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(17\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(18\) 0 0
\(19\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(20\) 0.393906 0.271894i 0.393906 0.271894i
\(21\) 0 0
\(22\) 0 0
\(23\) 1.87003i 1.87003i 0.354605 + 0.935016i \(0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(24\) 0 0
\(25\) 0.437928 0.634448i 0.437928 0.634448i
\(26\) 0 0
\(27\) −0.700239 0.790406i −0.700239 0.790406i
\(28\) 0 0
\(29\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(30\) 0 0
\(31\) −1.85640 0.704039i −1.85640 0.704039i −0.970942 0.239316i \(-0.923077\pi\)
−0.885456 0.464723i \(-0.846154\pi\)
\(32\) 0 0
\(33\) −0.764919 + 0.527986i −0.764919 + 0.527986i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.0773304 0.112032i −0.0773304 0.112032i
\(37\) 1.71945 0.423807i 1.71945 0.423807i 0.748511 0.663123i \(-0.230769\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.935016 0.354605i \(-0.115385\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(42\) 0 0
\(43\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(44\) −0.885456 + 0.464723i −0.885456 + 0.464723i
\(45\) 0.0536222 + 0.0370127i 0.0536222 + 0.0370127i
\(46\) 0 0
\(47\) 1.71945 + 0.902438i 1.71945 + 0.902438i 0.970942 + 0.239316i \(0.0769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(48\) 0.431935 + 0.822984i 0.431935 + 0.822984i
\(49\) 0.120537 + 0.992709i 0.120537 + 0.992709i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.568065 + 0.822984i 0.568065 + 0.822984i
\(54\) 0 0
\(55\) 0.317391 0.358261i 0.317391 0.358261i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.213460 0.112032i −0.213460 0.112032i 0.354605 0.935016i \(-0.384615\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(60\) −0.332984 0.294998i −0.332984 0.294998i
\(61\) 0 0 −0.822984 0.568065i \(-0.807692\pi\)
0.822984 + 0.568065i \(0.192308\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.354605 + 0.935016i 0.354605 + 0.935016i
\(65\) 0 0
\(66\) 0 0
\(67\) 1.31658 0.159861i 1.31658 0.159861i 0.568065 0.822984i \(-0.307692\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(68\) 0 0
\(69\) 1.68759 0.415953i 1.68759 0.415953i
\(70\) 0 0
\(71\) −0.393906 + 1.59814i −0.393906 + 1.59814i 0.354605 + 0.935016i \(0.384615\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(72\) 0 0
\(73\) 0 0 0.822984 0.568065i \(-0.192308\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(74\) 0 0
\(75\) −0.669959 0.254082i −0.669959 0.254082i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(80\) −0.317391 0.358261i −0.317391 0.358261i
\(81\) −0.480207 + 0.695701i −0.480207 + 0.695701i
\(82\) 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
\(89\) 0.402877 + 0.583668i 0.402877 + 0.583668i 0.970942 0.239316i \(-0.0769231\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.85640 0.225408i 1.85640 0.225408i
\(93\) −0.222431 + 1.83188i −0.222431 + 1.83188i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.627974 + 0.329586i −0.627974 + 0.329586i −0.748511 0.663123i \(-0.769231\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(98\) 0 0
\(99\) −0.101894 0.0902706i −0.101894 0.0902706i
\(100\) −0.682609 0.358261i −0.682609 0.358261i
\(101\) 0 0 −0.464723 0.885456i \(-0.653846\pi\)
0.464723 + 0.885456i \(0.346154\pi\)
\(102\) 0 0
\(103\) −0.393906 1.59814i −0.393906 1.59814i −0.748511 0.663123i \(-0.769231\pi\)
0.354605 0.935016i \(-0.384615\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −0.700239 + 0.790406i −0.700239 + 0.790406i
\(109\) 0 0 −0.239316 0.970942i \(-0.576923\pi\)
0.239316 + 0.970942i \(0.423077\pi\)
\(110\) 0 0
\(111\) −0.764919 1.45743i −0.764919 1.45743i
\(112\) 0 0
\(113\) −1.12054 0.992709i −1.12054 0.992709i −0.120537 0.992709i \(-0.538462\pi\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) −0.792533 + 0.415953i −0.792533 + 0.415953i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.475142 + 1.92773i −0.475142 + 1.92773i
\(125\) 0.841434 + 0.102169i 0.841434 + 0.102169i
\(126\) 0 0
\(127\) 0 0 0.464723 0.885456i \(-0.346154\pi\)
−0.464723 + 0.885456i \(0.653846\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(132\) 0.616337 + 0.695701i 0.616337 + 0.695701i
\(133\) 0 0
\(134\) 0 0
\(135\) 0.179225 0.472577i 0.179225 0.472577i
\(136\) 0 0
\(137\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(138\) 0 0
\(139\) 0 0 0.822984 0.568065i \(-0.192308\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(140\) 0 0
\(141\) 0.431935 1.75243i 0.431935 1.75243i
\(142\) 0 0
\(143\) 0 0
\(144\) −0.101894 + 0.0902706i −0.101894 + 0.0902706i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.869047 0.329586i 0.869047 0.329586i
\(148\) −0.627974 1.65583i −0.627974 1.65583i
\(149\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(150\) 0 0
\(151\) 0 0 −0.822984 0.568065i \(-0.807692\pi\)
0.822984 + 0.568065i \(0.192308\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.114544 0.943355i −0.114544 0.943355i
\(156\) 0 0
\(157\) −1.09148 + 1.23202i −1.09148 + 1.23202i −0.120537 + 0.992709i \(0.538462\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(158\) 0 0
\(159\) 0.616337 0.695701i 0.616337 0.695701i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −0.0290582 0.239316i −0.0290582 0.239316i 0.970942 0.239316i \(-0.0769231\pi\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) −0.393906 0.206738i −0.393906 0.206738i
\(166\) 0 0
\(167\) 0 0 −0.822984 0.568065i \(-0.807692\pi\)
0.822984 + 0.568065i \(0.192308\pi\)
\(168\) 0 0
\(169\) −0.970942 0.239316i −0.970942 0.239316i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.992709 0.120537i \(-0.0384615\pi\)
−0.992709 + 0.120537i \(0.961538\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.568065 + 0.822984i 0.568065 + 0.822984i
\(177\) −0.0536222 + 0.217554i −0.0536222 + 0.217554i
\(178\) 0 0
\(179\) 1.35460 0.935016i 1.35460 0.935016i 0.354605 0.935016i \(-0.384615\pi\)
1.00000 \(0\)
\(180\) 0.0302794 0.0576926i 0.0302794 0.0576926i
\(181\) −1.24006 0.470293i −1.24006 0.470293i −0.354605 0.935016i \(-0.615385\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.562072 + 0.634448i 0.562072 + 0.634448i
\(186\) 0 0
\(187\) 0 0
\(188\) 0.688601 1.81569i 0.688601 1.81569i
\(189\) 0 0
\(190\) 0 0
\(191\) −0.869047 + 1.65583i −0.869047 + 1.65583i −0.120537 + 0.992709i \(0.538462\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(192\) 0.764919 0.527986i 0.764919 0.527986i
\(193\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.970942 0.239316i 0.970942 0.239316i
\(197\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(198\) 0 0
\(199\) 0.180446 1.48611i 0.180446 1.48611i −0.568065 0.822984i \(-0.692308\pi\)
0.748511 0.663123i \(-0.230769\pi\)
\(200\) 0 0
\(201\) −0.437112 1.15257i −0.437112 1.15257i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.118303 + 0.225408i 0.118303 + 0.225408i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0.748511 0.663123i 0.748511 0.663123i
\(213\) 1.52984 1.52984
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.393906 0.271894i −0.393906 0.271894i
\(221\) 0 0
\(222\) 0 0
\(223\) 0.688601 + 1.81569i 0.688601 + 1.81569i 0.568065 + 0.822984i \(0.307692\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(224\) 0 0
\(225\) 0.0126496 0.104179i 0.0126496 0.104179i
\(226\) 0 0
\(227\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(228\) 0 0
\(229\) −0.402877 0.583668i −0.402877 0.583668i 0.568065 0.822984i \(-0.307692\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.464723 0.885456i \(-0.346154\pi\)
−0.464723 + 0.885456i \(0.653846\pi\)
\(234\) 0 0
\(235\) 0.929446i 0.929446i
\(236\) −0.0854858 + 0.225408i −0.0854858 + 0.225408i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(240\) −0.252710 + 0.366114i −0.252710 + 0.366114i
\(241\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(242\) 0 0
\(243\) −0.252710 0.0958405i −0.252710 0.0958405i
\(244\) 0 0
\(245\) −0.393906 + 0.271894i −0.393906 + 0.271894i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.97094 + 0.239316i −1.97094 + 0.239316i −0.970942 + 0.239316i \(0.923077\pi\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 1.74851 0.663123i 1.74851 0.663123i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.885456 0.464723i 0.885456 0.464723i
\(257\) −0.764919 0.527986i −0.764919 0.527986i 0.120537 0.992709i \(-0.461538\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.663123 0.748511i \(-0.269231\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(264\) 0 0
\(265\) −0.222431 + 0.423807i −0.222431 + 0.423807i
\(266\) 0 0
\(267\) 0.437112 0.493398i 0.437112 0.493398i
\(268\) −0.317391 1.28771i −0.317391 1.28771i
\(269\) −0.136945 1.12785i −0.136945 1.12785i −0.885456 0.464723i \(-0.846154\pi\)
0.748511 0.663123i \(-0.230769\pi\)
\(270\) 0 0
\(271\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.748511 0.184491i −0.748511 0.184491i
\(276\) −0.616337 1.62515i −0.616337 1.62515i
\(277\) 0 0 0.935016 0.354605i \(-0.115385\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(278\) 0 0
\(279\) −0.268303 + 0.0325779i −0.268303 + 0.0325779i
\(280\) 0 0
\(281\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(282\) 0 0
\(283\) 0 0 0.239316 0.970942i \(-0.423077\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(284\) 1.63397 + 0.198399i 1.63397 + 0.198399i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.354605 + 0.935016i −0.354605 + 0.935016i
\(290\) 0 0
\(291\) 0.437112 + 0.493398i 0.437112 + 0.493398i
\(292\) 0 0
\(293\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(294\) 0 0
\(295\) 0.115385i 0.115385i
\(296\) 0 0
\(297\) −0.490734 + 0.935016i −0.490734 + 0.935016i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.171475 + 0.695701i −0.171475 + 0.695701i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(308\) 0 0
\(309\) −1.35460 + 0.710951i −1.35460 + 0.710951i
\(310\) 0 0
\(311\) −1.32555 1.17433i −1.32555 1.17433i −0.970942 0.239316i \(-0.923077\pi\)
−0.354605 0.935016i \(-0.615385\pi\)
\(312\) 0 0
\(313\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.317391 + 0.358261i −0.317391 + 0.358261i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.748511 + 0.392849i 0.748511 + 0.392849i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.234068 1.92773i 0.234068 1.92773i −0.120537 0.992709i \(-0.538462\pi\)
0.354605 0.935016i \(-0.384615\pi\)
\(332\) 0 0
\(333\) 0.180446 0.159861i 0.180446 0.159861i
\(334\) 0 0
\(335\) 0.360598 + 0.522416i 0.360598 + 0.522416i
\(336\) 0 0
\(337\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(338\) 0 0
\(339\) −0.646616 + 1.23202i −0.646616 + 1.23202i
\(340\) 0 0
\(341\) 1.98542i 1.98542i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0.551656 + 0.622691i 0.551656 + 0.622691i
\(346\) 0 0
\(347\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(348\) 0 0
\(349\) 0 0 −0.935016 0.354605i \(-0.884615\pi\)
0.935016 + 0.354605i \(0.115385\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.475142 + 1.92773i −0.475142 + 1.92773i −0.120537 + 0.992709i \(0.538462\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(354\) 0 0
\(355\) −0.764919 + 0.188536i −0.764919 + 0.188536i
\(356\) 0.530851 0.470293i 0.530851 0.470293i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.935016 0.354605i \(-0.115385\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(360\) 0 0
\(361\) 0.970942 + 0.239316i 0.970942 + 0.239316i
\(362\) 0 0
\(363\) 0.764919 + 0.527986i 0.764919 + 0.527986i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0.0854858 + 0.704039i 0.0854858 + 0.704039i 0.970942 + 0.239316i \(0.0769231\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(368\) −0.447528 1.81569i −0.447528 1.81569i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 1.84534 1.84534
\(373\) 0 0 0.663123 0.748511i \(-0.269231\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(374\) 0 0
\(375\) −0.0949602 0.782068i −0.0949602 0.782068i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.53901 + 1.06230i 1.53901 + 1.06230i 0.970942 + 0.239316i \(0.0769231\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −0.447528 + 0.169725i −0.447528 + 0.169725i −0.568065 0.822984i \(-0.692308\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.402877 + 0.583668i 0.402877 + 0.583668i
\(389\) 0.222431 0.902438i 0.222431 0.902438i −0.748511 0.663123i \(-0.769231\pi\)
0.970942 0.239316i \(-0.0769231\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −0.0773304 + 0.112032i −0.0773304 + 0.112032i
\(397\) 1.24006 + 1.39974i 1.24006 + 1.39974i 0.885456 + 0.464723i \(0.153846\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.273369 + 0.720815i −0.273369 + 0.720815i
\(401\) 1.64597i 1.64597i −0.568065 0.822984i \(-0.692308\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −0.401656 0.0487698i −0.401656 0.0487698i
\(406\) 0 0
\(407\) −1.00599 1.45743i −1.00599 1.45743i
\(408\) 0 0
\(409\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.53901 + 0.583668i −1.53901 + 0.583668i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.869047 + 1.65583i 0.869047 + 1.65583i 0.748511 + 0.663123i \(0.230769\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(420\) 0 0
\(421\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(422\) 0 0
\(423\) 0.264348 0.264348
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(432\) 0.869047 + 0.599860i 0.869047 + 0.599860i
\(433\) −0.213460 + 0.112032i −0.213460 + 0.112032i −0.568065 0.822984i \(-0.692308\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(440\) 0 0
\(441\) 0.0773304 + 0.112032i 0.0773304 + 0.112032i
\(442\) 0 0
\(443\) −1.31658 0.159861i −1.31658 0.159861i −0.568065 0.822984i \(-0.692308\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(444\) −1.35460 + 0.935016i −1.35460 + 0.935016i
\(445\) −0.157750 + 0.300568i −0.157750 + 0.300568i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.136945 0.198399i 0.136945 0.198399i −0.748511 0.663123i \(-0.769231\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −0.850405 + 1.23202i −0.850405 + 1.23202i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.822984 0.568065i \(-0.192308\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0.508450 + 0.736617i 0.508450 + 0.736617i
\(461\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(462\) 0 0
\(463\) 1.31658 0.159861i 1.31658 0.159861i 0.568065 0.822984i \(-0.307692\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(464\) 0 0
\(465\) −0.825841 + 0.313200i −0.825841 + 0.313200i
\(466\) 0 0
\(467\) −0.688601 0.169725i −0.688601 0.169725i −0.120537 0.992709i \(-0.538462\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1.35460 + 0.710951i 1.35460 + 0.710951i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.120537 + 0.0632625i 0.120537 + 0.0632625i
\(478\) 0 0
\(479\) 0 0 0.663123 0.748511i \(-0.269231\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.748511 + 0.663123i 0.748511 + 0.663123i
\(485\) −0.279362 0.192830i −0.279362 0.192830i
\(486\) 0 0
\(487\) 1.45352 + 0.358261i 1.45352 + 0.358261i 0.885456 0.464723i \(-0.153846\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(488\) 0 0
\(489\) −0.209504 + 0.0794545i −0.209504 + 0.0794545i
\(490\) 0 0
\(491\) 0 0 0.992709 0.120537i \(-0.0384615\pi\)
−0.992709 + 0.120537i \(0.961538\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0.0155928 0.0632625i 0.0155928 0.0632625i
\(496\) 1.97094 + 0.239316i 1.97094 + 0.239316i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.869047 0.329586i −0.869047 0.329586i −0.120537 0.992709i \(-0.538462\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(500\) 0.847614i 0.847614i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.929446i 0.929446i
\(508\) 0 0
\(509\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.589686 0.522416i 0.589686 0.522416i
\(516\) 0 0
\(517\) 0.234068 1.92773i 0.234068 1.92773i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.71945 + 0.902438i −1.71945 + 0.902438i −0.748511 + 0.663123i \(0.769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(522\) 0 0
\(523\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.616337 0.695701i 0.616337 0.695701i
\(529\) −2.49702 −2.49702
\(530\) 0 0
\(531\) −0.0328172 −0.0328172
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.14510 1.01447i −1.14510 1.01447i
\(538\) 0 0
\(539\) 0.885456 0.464723i 0.885456 0.464723i
\(540\) −0.490734 0.120955i −0.490734 0.120955i
\(541\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(542\) 0 0
\(543\) −0.148582 + 1.22369i −0.148582 + 1.22369i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.447528 0.648356i 0.447528 0.648356i
\(556\) 0 0
\(557\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.822984 0.568065i \(-0.192308\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(564\) −1.79172 0.217554i −1.79172 0.217554i
\(565\) 0.171475 0.695701i 0.171475 0.695701i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.992709 0.120537i \(-0.0384615\pi\)
−0.992709 + 0.120537i \(0.961538\pi\)
\(570\) 0 0
\(571\) 0 0 0.935016 0.354605i \(-0.115385\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(572\) 0 0
\(573\) 1.68759 + 0.415953i 1.68759 + 0.415953i
\(574\) 0 0
\(575\) 1.18644 + 0.818940i 1.18644 + 0.818940i
\(576\) 0.101894 + 0.0902706i 0.101894 + 0.0902706i
\(577\) 1.32555 + 0.695701i 1.32555 + 0.695701i 0.970942 0.239316i \(-0.0769231\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.568065 0.822984i 0.568065 0.822984i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.0290582 + 0.239316i 0.0290582 + 0.239316i 1.00000 \(0\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(588\) −0.431935 0.822984i −0.431935 0.822984i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.56806 + 0.822984i −1.56806 + 0.822984i
\(593\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.38126 + 0.167715i −1.38126 + 0.167715i
\(598\) 0 0
\(599\) 1.88546 0.464723i 1.88546 0.464723i 0.885456 0.464723i \(-0.153846\pi\)
1.00000 \(0\)
\(600\) 0 0
\(601\) 0 0 0.239316 0.970942i \(-0.423077\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(602\) 0 0
\(603\) 0.148582 0.102559i 0.148582 0.102559i
\(604\) 0 0
\(605\) −0.447528 0.169725i −0.447528 0.169725i
\(606\) 0 0
\(607\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(608\) 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 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(618\) 0 0
\(619\) −1.10312 1.59814i −1.10312 1.59814i −0.748511 0.663123i \(-0.769231\pi\)
−0.354605 0.935016i \(-0.615385\pi\)
\(620\) −0.922670 + 0.227418i −0.922670 + 0.227418i
\(621\) 1.47808 1.30947i 1.47808 1.30947i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.129508 0.341484i −0.129508 0.341484i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.35460 + 0.935016i 1.35460 + 0.935016i
\(629\) 0 0
\(630\) 0 0
\(631\) −0.922670 1.75800i −0.922670 1.75800i −0.568065 0.822984i \(-0.692308\pi\)
−0.354605 0.935016i \(-0.615385\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −0.764919 0.527986i −0.764919 0.527986i
\(637\) 0 0
\(638\) 0 0
\(639\) 0.0536222 + 0.217554i 0.0536222 + 0.217554i
\(640\) 0 0
\(641\) −0.222431 0.423807i −0.222431 0.423807i 0.748511 0.663123i \(-0.230769\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(642\) 0 0
\(643\) 0.850405 + 0.753393i 0.850405 + 0.753393i 0.970942 0.239316i \(-0.0769231\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.530851 + 1.39974i 0.530851 + 1.39974i 0.885456 + 0.464723i \(0.153846\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(648\) 0 0
\(649\) −0.0290582 + 0.239316i −0.0290582 + 0.239316i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.234068 + 0.0576926i −0.234068 + 0.0576926i
\(653\) −0.850405 1.23202i −0.850405 1.23202i −0.970942 0.239316i \(-0.923077\pi\)
0.120537 0.992709i \(-0.461538\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) −0.157750 + 0.415953i −0.157750 + 0.415953i
\(661\) −0.136945 + 0.198399i −0.136945 + 0.198399i −0.885456 0.464723i \(-0.846154\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1.48538 1.02529i 1.48538 1.02529i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(674\) 0 0
\(675\) −0.808126 + 0.0981242i −0.808126 + 0.0981242i
\(676\) −0.120537 + 0.992709i −0.120537 + 0.992709i
\(677\) 0 0 0.935016 0.354605i \(-0.115385\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.32555 0.695701i −1.32555 0.695701i −0.354605 0.935016i \(-0.615385\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −0.437112 + 0.493398i −0.437112 + 0.493398i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 1.24006 1.39974i 1.24006 1.39974i 0.354605 0.935016i \(-0.384615\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(692\) 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 0.935016 0.354605i \(-0.115385\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.748511 0.663123i 0.748511 0.663123i
\(705\) 0.838768 0.206738i 0.838768 0.206738i
\(706\) 0 0
\(707\) 0 0
\(708\) 0.222431 + 0.0270080i 0.222431 + 0.0270080i
\(709\) 1.09148 0.753393i 1.09148 0.753393i 0.120537 0.992709i \(-0.461538\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.31658 3.47152i 1.31658 3.47152i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.09148 1.23202i −1.09148 1.23202i
\(717\) 0 0
\(718\) 0 0
\(719\) 0.929446i 0.929446i −0.885456 0.464723i \(-0.846154\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(720\) −0.0609218 0.0231046i −0.0609218 0.0231046i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −0.317391 + 1.28771i −0.317391 + 1.28771i
\(725\) 0 0
\(726\) 0 0
\(727\) −1.49702 + 1.32625i −1.49702 + 1.32625i −0.748511 + 0.663123i \(0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(728\) 0 0
\(729\) −0.132174 + 1.08855i −0.132174 + 1.08855i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(734\) 0 0
\(735\) 0.332984 + 0.294998i 0.332984 + 0.294998i
\(736\) 0 0
\(737\) −0.616337 1.17433i −0.616337 1.17433i
\(738\) 0 0
\(739\) 0 0 −0.239316 0.970942i \(-0.576923\pi\)
0.239316 + 0.970942i \(0.423077\pi\)
\(740\) 0.562072 0.634448i 0.562072 0.634448i
\(741\) 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
\(751\) −1.32555 + 0.695701i −1.32555 + 0.695701i −0.970942 0.239316i \(-0.923077\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(752\) −1.88546 0.464723i −1.88546 0.464723i
\(753\) 0.654366 + 1.72542i 0.654366 + 1.72542i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.530851 0.470293i 0.530851 0.470293i −0.354605 0.935016i \(-0.615385\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(758\) 0 0
\(759\) −0.987350 1.43042i −0.987350 1.43042i
\(760\) 0 0
\(761\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1.74851 + 0.663123i 1.74851 + 0.663123i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.616337 0.695701i −0.616337 0.695701i
\(769\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(770\) 0 0
\(771\) −0.306333 + 0.807733i −0.306333 + 0.807733i
\(772\) 0 0
\(773\) −1.74851 0.663123i −1.74851 0.663123i −0.748511 0.663123i \(-0.769231\pi\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) −1.25964 + 0.869470i −1.25964 + 0.869470i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 1.63397 0.198399i 1.63397 0.198399i
\(782\) 0 0
\(783\) 0 0
\(784\) −0.354605 0.935016i −0.354605 0.935016i
\(785\) −0.764919 0.188536i −0.764919 0.188536i
\(786\) 0 0
\(787\) 0 0 −0.822984 0.568065i \(-0.807692\pi\)
0.822984 + 0.568065i \(0.192308\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0.431935 + 0.106462i 0.431935 + 0.106462i
\(796\) −1.49702 −1.49702
\(797\) 0.879463 0.992709i 0.879463 0.992709i −0.120537 0.992709i \(-0.538462\pi\)
1.00000 \(0\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0.0854858 + 0.0448664i 0.0854858 + 0.0448664i
\(802\) 0 0
\(803\) 0 0
\(804\) −1.09148 + 0.572852i −1.09148 + 0.572852i
\(805\) 0 0
\(806\) 0 0
\(807\) −0.987350 + 0.374453i −0.987350 + 0.374453i
\(808\) 0 0
\(809\) 0 0 0.992709 0.120537i \(-0.0384615\pi\)
−0.992709 + 0.120537i \(0.961538\pi\)
\(810\) 0 0
\(811\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0.0949602 0.0655463i 0.0949602 0.0655463i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(822\) 0 0
\(823\) −0.136945 + 0.198399i −0.136945 + 0.198399i −0.885456 0.464723i \(-0.846154\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(824\) 0 0
\(825\) 0.716521i 0.716521i
\(826\) 0 0
\(827\) 0 0 0.464723 0.885456i \(-0.346154\pi\)
−0.464723 + 0.885456i \(0.653846\pi\)
\(828\) 0.209504 0.144610i 0.209504 0.144610i
\(829\) 1.85640 + 0.225408i 1.85640 + 0.225408i 0.970942 0.239316i \(-0.0769231\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0.743445 + 1.96030i 0.743445 + 1.96030i
\(838\) 0 0
\(839\) 1.56806 0.822984i 1.56806 0.822984i 0.568065 0.822984i \(-0.307692\pi\)
1.00000 \(0\)
\(840\) 0 0
\(841\) −0.748511 0.663123i −0.748511 0.663123i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −0.114544 0.464723i −0.114544 0.464723i
\(846\) 0 0
\(847\) 0 0
\(848\) −0.748511 0.663123i −0.748511 0.663123i
\(849\) 0 0
\(850\) 0 0
\(851\) 0.792533 + 3.21543i 0.792533 + 3.21543i
\(852\) −0.184402 1.51868i −0.184402 1.51868i
\(853\) 0 0 −0.464723 0.885456i \(-0.653846\pi\)
0.464723 + 0.885456i \(0.346154\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(858\) 0 0
\(859\) −0.402877 1.06230i −0.402877 1.06230i −0.970942 0.239316i \(-0.923077\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0.850405 0.753393i 0.850405 0.753393i −0.120537 0.992709i \(-0.538462\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0.922670 + 0.112032i 0.922670 + 0.112032i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −0.0548435 + 0.0794545i −0.0548435 + 0.0794545i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −0.222431 + 0.423807i −0.222431 + 0.423807i
\(881\) 1.09148 0.753393i 1.09148 0.753393i 0.120537 0.992709i \(-0.461538\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(882\) 0 0
\(883\) −0.317391 + 1.28771i −0.317391 + 1.28771i 0.568065 + 0.822984i \(0.307692\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(884\) 0 0
\(885\) −0.104128 + 0.0256653i −0.104128 + 0.0256653i
\(886\) 0 0
\(887\) 0 0 0.992709 0.120537i \(-0.0384615\pi\)
−0.992709 + 0.120537i \(0.961538\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.820775 + 0.202303i 0.820775 + 0.202303i
\(892\) 1.71945 0.902438i 1.71945 0.902438i
\(893\) 0 0
\(894\) 0 0
\(895\) 0.697573 + 0.366114i 0.697573 + 0.366114i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −0.104944 −0.104944
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −0.0765146 0.630154i −0.0765146 0.630154i
\(906\) 0 0
\(907\) 0.213460 + 0.112032i 0.213460 + 0.112032i 0.568065 0.822984i \(-0.307692\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.688601 0.169725i −0.688601 0.169725i −0.120537 0.992709i \(-0.538462\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.530851 + 0.470293i −0.530851 + 0.470293i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.239316 0.970942i \(-0.423077\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0.484113 1.27650i 0.484113 1.27650i
\(926\) 0 0
\(927\) −0.148582 0.167715i −0.148582 0.167715i
\(928\) 0 0
\(929\) −1.00599 + 1.45743i −1.00599 + 1.45743i −0.120537 + 0.992709i \(0.538462\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.764919 + 1.45743i −0.764919 + 1.45743i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0.922670 0.112032i 0.922670 0.112032i
\(941\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0.234068 + 0.0576926i 0.234068 + 0.0576926i
\(945\) 0 0
\(946\) 0 0
\(947\) 1.45352 + 1.28771i 1.45352 + 1.28771i 0.885456 + 0.464723i \(0.153846\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0.252710 + 1.02529i 0.252710 + 1.02529i
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) −0.895056 −0.895056
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0.393906 + 0.206738i 0.393906 + 0.206738i
\(961\) 2.20203 + 1.95083i 2.20203 + 1.95083i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0.850405 + 1.23202i 0.850405 + 1.23202i 0.970942 + 0.239316i \(0.0769231\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(972\) −0.0646808 + 0.262420i −0.0646808 + 0.262420i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0.478631i 0.478631i −0.970942 0.239316i \(-0.923077\pi\)
0.970942 0.239316i \(-0.0769231\pi\)
\(978\) 0 0
\(979\) 0.402877 0.583668i 0.402877 0.583668i
\(980\) 0.317391 + 0.358261i 0.317391 + 0.358261i
\(981\) 0 0
\(982\) 0 0
\(983\) −0.402877 + 1.06230i −0.402877 + 1.06230i 0.568065 + 0.822984i \(0.307692\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −1.88546 + 0.464723i −1.88546 + 0.464723i −0.885456 + 0.464723i \(0.846154\pi\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) −1.79172 + 0.217554i −1.79172 + 0.217554i
\(994\) 0 0
\(995\) 0.669959 0.254082i 0.669959 0.254082i
\(996\) 0 0
\(997\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(998\) 0 0
\(999\) −1.53901 1.06230i −1.53901 1.06230i
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.197.1 12
11.10 odd 2 CM 583.1.n.a.197.1 12
53.7 even 26 inner 583.1.n.a.219.1 yes 12
583.219 odd 26 inner 583.1.n.a.219.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
583.1.n.a.197.1 12 1.1 even 1 trivial
583.1.n.a.197.1 12 11.10 odd 2 CM
583.1.n.a.219.1 yes 12 53.7 even 26 inner
583.1.n.a.219.1 yes 12 583.219 odd 26 inner