Properties

Label 1340.1.bl.a.1239.1
Level $1340$
Weight $1$
Character 1340.1239
Analytic conductor $0.669$
Analytic rank $0$
Dimension $20$
Projective image $D_{33}$
CM discriminant -20
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1340,1,Mod(19,1340)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1340, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([33, 33, 10]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1340.19");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1340.bl (of order \(66\), degree \(20\), 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: \(0.668747116928\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{33})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{33}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{33} - \cdots)\)

Embedding invariants

Embedding label 1239.1
Root \(0.723734 - 0.690079i\) of defining polynomial
Character \(\chi\) \(=\) 1340.1239
Dual form 1340.1.bl.a.199.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0475819 - 0.998867i) q^{2} +(-1.91030 + 0.560914i) q^{3} +(-0.995472 + 0.0950560i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(0.651174 + 1.88144i) q^{6} +(0.419102 + 0.216062i) q^{7} +(0.142315 + 0.989821i) q^{8} +(2.49336 - 1.60238i) q^{9} +O(q^{10})\) \(q+(-0.0475819 - 0.998867i) q^{2} +(-1.91030 + 0.560914i) q^{3} +(-0.995472 + 0.0950560i) q^{4} +(-0.654861 - 0.755750i) q^{5} +(0.651174 + 1.88144i) q^{6} +(0.419102 + 0.216062i) q^{7} +(0.142315 + 0.989821i) q^{8} +(2.49336 - 1.60238i) q^{9} +(-0.723734 + 0.690079i) q^{10} +(1.84833 - 0.739959i) q^{12} +(0.195876 - 0.428908i) q^{14} +(1.67489 + 1.07639i) q^{15} +(0.981929 - 0.189251i) q^{16} +(-1.71921 - 2.41429i) q^{18} +(0.723734 + 0.690079i) q^{20} +(-0.921801 - 0.177663i) q^{21} +(0.235759 - 0.971812i) q^{23} +(-0.827068 - 1.81103i) q^{24} +(-0.142315 + 0.989821i) q^{25} +(-2.56046 + 2.95493i) q^{27} +(-0.437742 - 0.175245i) q^{28} +(-0.723734 - 1.25354i) q^{29} +(0.995472 - 1.72421i) q^{30} +(-0.235759 - 0.971812i) q^{32} +(-0.111165 - 0.458227i) q^{35} +(-2.32975 + 1.83214i) q^{36} +(0.654861 - 0.755750i) q^{40} +(-0.911911 + 1.28060i) q^{41} +(-0.133600 + 0.929210i) q^{42} +(-0.481929 - 1.05528i) q^{43} +(-2.84380 - 0.835015i) q^{45} +(-0.981929 - 0.189251i) q^{46} +(-1.34378 - 1.28129i) q^{47} +(-1.76962 + 0.912303i) q^{48} +(-0.451093 - 0.633472i) q^{49} +(0.995472 + 0.0950560i) q^{50} +(3.07341 + 2.41696i) q^{54} +(-0.154218 + 0.445585i) q^{56} +(-1.21769 + 0.782560i) q^{58} +(-1.76962 - 0.912303i) q^{60} +(0.428368 + 1.23769i) q^{61} +(1.39118 - 0.132842i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.580057 - 0.814576i) q^{67} +(0.0947329 + 1.98869i) q^{69} +(-0.452418 + 0.132842i) q^{70} +(1.94091 + 2.23993i) q^{72} +(-0.283341 - 1.97068i) q^{75} +(-0.786053 - 0.618159i) q^{80} +(2.00255 - 4.38497i) q^{81} +(1.32254 + 0.849945i) q^{82} +(1.74555 - 0.336426i) q^{83} +(0.934515 + 0.0892353i) q^{84} +(-1.03115 + 0.531595i) q^{86} +(2.08568 + 1.98869i) q^{87} +(-1.61435 - 0.474017i) q^{89} +(-0.698756 + 2.88031i) q^{90} +(-0.142315 + 0.989821i) q^{92} +(-1.21590 + 1.40323i) q^{94} +(0.995472 + 1.72421i) q^{96} +(-0.611291 + 0.480724i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{10} + q^{12} + 2 q^{14} - 2 q^{15} + q^{16} + q^{20} - 10 q^{21} + q^{23} - 9 q^{24} - 2 q^{25} + 2 q^{27} + q^{28} - q^{29} - q^{30} - q^{32} - 21 q^{35} + 2 q^{40} - q^{41} - 20 q^{42} + 9 q^{43} - q^{46} + q^{47} + q^{48} - q^{50} + q^{54} - q^{56} - 2 q^{58} + q^{60} - 9 q^{61} + 11 q^{63} - 2 q^{64} - q^{67} + q^{69} - 9 q^{70} + 11 q^{72} - 2 q^{75} + q^{80} + 2 q^{81} - 2 q^{82} + q^{83} + q^{84} - q^{86} - q^{87} - 4 q^{89} - 2 q^{92} + 2 q^{94} - q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times\).

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{16}{33}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0475819 0.998867i −0.0475819 0.998867i
\(3\) −1.91030 + 0.560914i −1.91030 + 0.560914i −0.928368 + 0.371662i \(0.878788\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(4\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(5\) −0.654861 0.755750i −0.654861 0.755750i
\(6\) 0.651174 + 1.88144i 0.651174 + 1.88144i
\(7\) 0.419102 + 0.216062i 0.419102 + 0.216062i 0.654861 0.755750i \(-0.272727\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(8\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(9\) 2.49336 1.60238i 2.49336 1.60238i
\(10\) −0.723734 + 0.690079i −0.723734 + 0.690079i
\(11\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(12\) 1.84833 0.739959i 1.84833 0.739959i
\(13\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(14\) 0.195876 0.428908i 0.195876 0.428908i
\(15\) 1.67489 + 1.07639i 1.67489 + 1.07639i
\(16\) 0.981929 0.189251i 0.981929 0.189251i
\(17\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(18\) −1.71921 2.41429i −1.71921 2.41429i
\(19\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(20\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(21\) −0.921801 0.177663i −0.921801 0.177663i
\(22\) 0 0
\(23\) 0.235759 0.971812i 0.235759 0.971812i −0.723734 0.690079i \(-0.757576\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(24\) −0.827068 1.81103i −0.827068 1.81103i
\(25\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(26\) 0 0
\(27\) −2.56046 + 2.95493i −2.56046 + 2.95493i
\(28\) −0.437742 0.175245i −0.437742 0.175245i
\(29\) −0.723734 1.25354i −0.723734 1.25354i −0.959493 0.281733i \(-0.909091\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(30\) 0.995472 1.72421i 0.995472 1.72421i
\(31\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(32\) −0.235759 0.971812i −0.235759 0.971812i
\(33\) 0 0
\(34\) 0 0
\(35\) −0.111165 0.458227i −0.111165 0.458227i
\(36\) −2.32975 + 1.83214i −2.32975 + 1.83214i
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.654861 0.755750i 0.654861 0.755750i
\(41\) −0.911911 + 1.28060i −0.911911 + 1.28060i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(42\) −0.133600 + 0.929210i −0.133600 + 0.929210i
\(43\) −0.481929 1.05528i −0.481929 1.05528i −0.981929 0.189251i \(-0.939394\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(44\) 0 0
\(45\) −2.84380 0.835015i −2.84380 0.835015i
\(46\) −0.981929 0.189251i −0.981929 0.189251i
\(47\) −1.34378 1.28129i −1.34378 1.28129i −0.928368 0.371662i \(-0.878788\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(48\) −1.76962 + 0.912303i −1.76962 + 0.912303i
\(49\) −0.451093 0.633472i −0.451093 0.633472i
\(50\) 0.995472 + 0.0950560i 0.995472 + 0.0950560i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(54\) 3.07341 + 2.41696i 3.07341 + 2.41696i
\(55\) 0 0
\(56\) −0.154218 + 0.445585i −0.154218 + 0.445585i
\(57\) 0 0
\(58\) −1.21769 + 0.782560i −1.21769 + 0.782560i
\(59\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(60\) −1.76962 0.912303i −1.76962 0.912303i
\(61\) 0.428368 + 1.23769i 0.428368 + 1.23769i 0.928368 + 0.371662i \(0.121212\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 1.39118 0.132842i 1.39118 0.132842i
\(64\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.580057 0.814576i −0.580057 0.814576i
\(68\) 0 0
\(69\) 0.0947329 + 1.98869i 0.0947329 + 1.98869i
\(70\) −0.452418 + 0.132842i −0.452418 + 0.132842i
\(71\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(72\) 1.94091 + 2.23993i 1.94091 + 2.23993i
\(73\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(74\) 0 0
\(75\) −0.283341 1.97068i −0.283341 1.97068i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(80\) −0.786053 0.618159i −0.786053 0.618159i
\(81\) 2.00255 4.38497i 2.00255 4.38497i
\(82\) 1.32254 + 0.849945i 1.32254 + 0.849945i
\(83\) 1.74555 0.336426i 1.74555 0.336426i 0.786053 0.618159i \(-0.212121\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(84\) 0.934515 + 0.0892353i 0.934515 + 0.0892353i
\(85\) 0 0
\(86\) −1.03115 + 0.531595i −1.03115 + 0.531595i
\(87\) 2.08568 + 1.98869i 2.08568 + 1.98869i
\(88\) 0 0
\(89\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(90\) −0.698756 + 2.88031i −0.698756 + 2.88031i
\(91\) 0 0
\(92\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(93\) 0 0
\(94\) −1.21590 + 1.40323i −1.21590 + 1.40323i
\(95\) 0 0
\(96\) 0.995472 + 1.72421i 0.995472 + 1.72421i
\(97\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) −0.611291 + 0.480724i −0.611291 + 0.480724i
\(99\) 0 0
\(100\) 0.0475819 0.998867i 0.0475819 0.998867i
\(101\) 0.0800569 1.68060i 0.0800569 1.68060i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(102\) 0 0
\(103\) 0.0748038 0.0588264i 0.0748038 0.0588264i −0.580057 0.814576i \(-0.696970\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(104\) 0 0
\(105\) 0.469383 + 0.812995i 0.469383 + 0.812995i
\(106\) 0 0
\(107\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(108\) 2.26798 3.18493i 2.26798 3.18493i
\(109\) −0.0135432 + 0.0941952i −0.0135432 + 0.0941952i −0.995472 0.0950560i \(-0.969697\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.452418 + 0.132842i 0.452418 + 0.132842i
\(113\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(114\) 0 0
\(115\) −0.888835 + 0.458227i −0.888835 + 0.458227i
\(116\) 0.839614 + 1.17907i 0.839614 + 1.17907i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.827068 + 1.81103i −0.827068 + 1.81103i
\(121\) −0.786053 0.618159i −0.786053 0.618159i
\(122\) 1.21590 0.486774i 1.21590 0.486774i
\(123\) 1.02371 2.95783i 1.02371 2.95783i
\(124\) 0 0
\(125\) 0.841254 0.540641i 0.841254 0.540641i
\(126\) −0.198887 1.38329i −0.198887 1.38329i
\(127\) −0.581419 0.299742i −0.581419 0.299742i 0.142315 0.989821i \(-0.454545\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(128\) 0.327068 + 0.945001i 0.327068 + 0.945001i
\(129\) 1.51255 + 1.74557i 1.51255 + 1.74557i
\(130\) 0 0
\(131\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(135\) 3.90993 3.90993
\(136\) 0 0
\(137\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(138\) 1.98193 0.189251i 1.98193 0.189251i
\(139\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(140\) 0.154218 + 0.445585i 0.154218 + 0.445585i
\(141\) 3.28572 + 1.69391i 3.28572 + 1.69391i
\(142\) 0 0
\(143\) 0 0
\(144\) 2.14504 2.04530i 2.14504 2.04530i
\(145\) −0.473420 + 1.36786i −0.473420 + 1.36786i
\(146\) 0 0
\(147\) 1.21705 + 0.957095i 1.21705 + 0.957095i
\(148\) 0 0
\(149\) −1.32254 0.849945i −1.32254 0.849945i −0.327068 0.945001i \(-0.606061\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(150\) −1.95496 + 0.376789i −1.95496 + 0.376789i
\(151\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.580057 + 0.814576i −0.580057 + 0.814576i
\(161\) 0.308779 0.356349i 0.308779 0.356349i
\(162\) −4.47528 1.79163i −4.47528 1.79163i
\(163\) 0.415415 + 0.719520i 0.415415 + 0.719520i 0.995472 0.0950560i \(-0.0303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(164\) 0.786053 1.36148i 0.786053 1.36148i
\(165\) 0 0
\(166\) −0.419102 1.72756i −0.419102 1.72756i
\(167\) 0.0913090 1.91681i 0.0913090 1.91681i −0.235759 0.971812i \(-0.575758\pi\)
0.327068 0.945001i \(-0.393939\pi\)
\(168\) 0.0446683 0.937702i 0.0446683 0.937702i
\(169\) 0.235759 + 0.971812i 0.235759 + 0.971812i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.580057 + 1.00469i 0.580057 + 1.00469i
\(173\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(174\) 1.88720 2.17794i 1.88720 2.17794i
\(175\) −0.273507 + 0.384087i −0.273507 + 0.384087i
\(176\) 0 0
\(177\) 0 0
\(178\) −0.396666 + 1.63508i −0.396666 + 1.63508i
\(179\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(180\) 2.91030 + 0.560914i 2.91030 + 0.560914i
\(181\) 0.601300 + 0.573338i 0.601300 + 0.573338i 0.928368 0.371662i \(-0.121212\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(182\) 0 0
\(183\) −1.51255 2.12407i −1.51255 2.12407i
\(184\) 0.995472 + 0.0950560i 0.995472 + 0.0950560i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 1.45949 + 1.14776i 1.45949 + 1.14776i
\(189\) −1.71154 + 0.685198i −1.71154 + 0.685198i
\(190\) 0 0
\(191\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(192\) 1.67489 1.07639i 1.67489 1.07639i
\(193\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.509266 + 0.587724i 0.509266 + 0.587724i
\(197\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(198\) 0 0
\(199\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(200\) −1.00000 −1.00000
\(201\) 1.56499 + 1.23072i 1.56499 + 1.23072i
\(202\) −1.68251 −1.68251
\(203\) −0.0324750 0.681734i −0.0324750 0.681734i
\(204\) 0 0
\(205\) 1.56499 0.149438i 1.56499 0.149438i
\(206\) −0.0623191 0.0719200i −0.0623191 0.0719200i
\(207\) −0.969383 2.80085i −0.969383 2.80085i
\(208\) 0 0
\(209\) 0 0
\(210\) 0.789740 0.507535i 0.789740 0.507535i
\(211\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.223734 + 0.175946i 0.223734 + 0.175946i
\(215\) −0.481929 + 1.05528i −0.481929 + 1.05528i
\(216\) −3.28924 2.11387i −3.28924 2.11387i
\(217\) 0 0
\(218\) 0.0947329 + 0.00904590i 0.0947329 + 0.00904590i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.25667 0.368991i −1.25667 0.368991i −0.415415 0.909632i \(-0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(224\) 0.111165 0.458227i 0.111165 0.458227i
\(225\) 1.23123 + 2.69602i 1.23123 + 2.69602i
\(226\) 0 0
\(227\) −0.975950 + 1.37053i −0.975950 + 1.37053i −0.0475819 + 0.998867i \(0.515152\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(228\) 0 0
\(229\) −0.607279 0.243118i −0.607279 0.243118i 0.0475819 0.998867i \(-0.484848\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(230\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(231\) 0 0
\(232\) 1.13779 0.894765i 1.13779 0.894765i
\(233\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(234\) 0 0
\(235\) −0.0883470 + 1.85463i −0.0883470 + 1.85463i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 1.84833 + 0.739959i 1.84833 + 0.739959i
\(241\) −0.0623191 + 0.0719200i −0.0623191 + 0.0719200i −0.786053 0.618159i \(-0.787879\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(242\) −0.580057 + 0.814576i −0.580057 + 0.814576i
\(243\) −0.809430 + 5.62971i −0.809430 + 5.62971i
\(244\) −0.544078 1.19136i −0.544078 1.19136i
\(245\) −0.183343 + 0.755750i −0.183343 + 0.755750i
\(246\) −3.00319 0.881816i −3.00319 0.881816i
\(247\) 0 0
\(248\) 0 0
\(249\) −3.14580 + 1.62177i −3.14580 + 1.62177i
\(250\) −0.580057 0.814576i −0.580057 0.814576i
\(251\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(252\) −1.37226 + 0.264481i −1.37226 + 0.264481i
\(253\) 0 0
\(254\) −0.271738 + 0.595023i −0.271738 + 0.595023i
\(255\) 0 0
\(256\) 0.928368 0.371662i 0.928368 0.371662i
\(257\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(258\) 1.67162 1.59389i 1.67162 1.59389i
\(259\) 0 0
\(260\) 0 0
\(261\) −3.81318 1.96583i −3.81318 1.96583i
\(262\) 0 0
\(263\) 1.28605 + 1.48418i 1.28605 + 1.48418i 0.786053 + 0.618159i \(0.212121\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3.34978 3.34978
\(268\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(269\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(270\) −0.186042 3.90550i −0.186042 3.90550i
\(271\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.283341 1.97068i −0.283341 1.97068i
\(277\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.437742 0.175245i 0.437742 0.175245i
\(281\) −1.45949 1.14776i −1.45949 1.14776i −0.959493 0.281733i \(-0.909091\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(282\) 1.53565 3.36260i 1.53565 3.36260i
\(283\) −1.65210 1.06174i −1.65210 1.06174i −0.928368 0.371662i \(-0.878788\pi\)
−0.723734 0.690079i \(-0.757576\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.658873 + 0.339672i −0.658873 + 0.339672i
\(288\) −2.14504 2.04530i −2.14504 2.04530i
\(289\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(290\) 1.38884 + 0.407799i 1.38884 + 0.407799i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(294\) 0.898102 1.26121i 0.898102 1.26121i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.786053 + 1.36148i −0.786053 + 1.36148i
\(299\) 0 0
\(300\) 0.469383 + 1.93482i 0.469383 + 1.93482i
\(301\) 0.0260280 0.546395i 0.0260280 0.546395i
\(302\) 0 0
\(303\) 0.789740 + 3.25535i 0.789740 + 3.25535i
\(304\) 0 0
\(305\) 0.654861 1.13425i 0.654861 1.13425i
\(306\) 0 0
\(307\) 0.264241 + 0.105786i 0.264241 + 0.105786i 0.500000 0.866025i \(-0.333333\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(308\) 0 0
\(309\) −0.109901 + 0.154334i −0.109901 + 0.154334i
\(310\) 0 0
\(311\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(312\) 0 0
\(313\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(314\) 0 0
\(315\) −1.01143 0.964394i −1.01143 0.964394i
\(316\) 0 0
\(317\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(321\) 0.235408 0.515472i 0.235408 0.515472i
\(322\) −0.370638 0.291473i −0.370638 0.291473i
\(323\) 0 0
\(324\) −1.57666 + 4.55546i −1.57666 + 4.55546i
\(325\) 0 0
\(326\) 0.698939 0.449181i 0.698939 0.449181i
\(327\) −0.0269638 0.187537i −0.0269638 0.187537i
\(328\) −1.39734 0.720381i −1.39734 0.720381i
\(329\) −0.286343 0.827333i −0.286343 0.827333i
\(330\) 0 0
\(331\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(332\) −1.70566 + 0.500828i −1.70566 + 0.500828i
\(333\) 0 0
\(334\) −1.91899 −1.91899
\(335\) −0.235759 + 0.971812i −0.235759 + 0.971812i
\(336\) −0.938766 −0.938766
\(337\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(338\) 0.959493 0.281733i 0.959493 0.281733i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.119289 0.829672i −0.119289 0.829672i
\(344\) 0.975950 0.627205i 0.975950 0.627205i
\(345\) 1.44091 1.37391i 1.44091 1.37391i
\(346\) 0 0
\(347\) 1.21590 0.486774i 1.21590 0.486774i 0.327068 0.945001i \(-0.393939\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(348\) −2.26527 1.78143i −2.26527 1.78143i
\(349\) 0.481929 1.05528i 0.481929 1.05528i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(350\) 0.396666 + 0.254922i 0.396666 + 0.254922i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.65210 + 0.318417i 1.65210 + 0.318417i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(360\) 0.421801 2.93369i 0.421801 2.93369i
\(361\) 0.580057 0.814576i 0.580057 0.814576i
\(362\) 0.544078 0.627899i 0.544078 0.627899i
\(363\) 1.84833 + 0.739959i 1.84833 + 0.739959i
\(364\) 0 0
\(365\) 0 0
\(366\) −2.04970 + 1.61190i −2.04970 + 1.61190i
\(367\) −0.0224357 0.0924813i −0.0224357 0.0924813i 0.959493 0.281733i \(-0.0909091\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(368\) 0.0475819 0.998867i 0.0475819 0.998867i
\(369\) −0.221708 + 4.65422i −0.221708 + 4.65422i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0 0
\(375\) −1.30379 + 1.50465i −1.30379 + 1.50465i
\(376\) 1.07701 1.51245i 1.07701 1.51245i
\(377\) 0 0
\(378\) 0.765860 + 1.67700i 0.765860 + 1.67700i
\(379\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(380\) 0 0
\(381\) 1.27881 + 0.246471i 1.27881 + 0.246471i
\(382\) 0 0
\(383\) 1.65033 0.850806i 1.65033 0.850806i 0.654861 0.755750i \(-0.272727\pi\)
0.995472 0.0950560i \(-0.0303030\pi\)
\(384\) −1.15486 1.62177i −1.15486 1.62177i
\(385\) 0 0
\(386\) 0 0
\(387\) −2.89258 1.85895i −2.89258 1.85895i
\(388\) 0 0
\(389\) −0.0748038 0.0588264i −0.0748038 0.0588264i 0.580057 0.814576i \(-0.303030\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.562827 0.536654i 0.562827 0.536654i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(401\) 0.471518 0.471518 0.235759 0.971812i \(-0.424242\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(402\) 1.15486 1.62177i 1.15486 1.62177i
\(403\) 0 0
\(404\) 0.0800569 + 1.68060i 0.0800569 + 1.68060i
\(405\) −4.62533 + 1.35812i −4.62533 + 1.35812i
\(406\) −0.679417 + 0.0648764i −0.679417 + 0.0648764i
\(407\) 0 0
\(408\) 0 0
\(409\) −0.738471 0.380708i −0.738471 0.380708i 0.0475819 0.998867i \(-0.484848\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(410\) −0.223734 1.55610i −0.223734 1.55610i
\(411\) 0 0
\(412\) −0.0688733 + 0.0656706i −0.0688733 + 0.0656706i
\(413\) 0 0
\(414\) −2.75155 + 1.10155i −2.75155 + 1.10155i
\(415\) −1.39734 1.09888i −1.39734 1.09888i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(420\) −0.544537 0.764696i −0.544537 0.764696i
\(421\) 1.70566 0.879330i 1.70566 0.879330i 0.723734 0.690079i \(-0.242424\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(422\) 0 0
\(423\) −5.40365 1.04147i −5.40365 1.04147i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.0878875 + 0.611271i −0.0878875 + 0.611271i
\(428\) 0.165101 0.231852i 0.165101 0.231852i
\(429\) 0 0
\(430\) 1.07701 + 0.431171i 1.07701 + 0.431171i
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) −1.95496 + 3.38610i −1.95496 + 3.38610i
\(433\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(434\) 0 0
\(435\) 0.137123 2.87856i 0.137123 2.87856i
\(436\) 0.00452808 0.0950560i 0.00452808 0.0950560i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) −2.13980 0.856647i −2.13980 0.856647i
\(442\) 0 0
\(443\) −0.839614 + 1.17907i −0.839614 + 1.17907i 0.142315 + 0.989821i \(0.454545\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(444\) 0 0
\(445\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(446\) −0.308779 + 1.27280i −0.308779 + 1.27280i
\(447\) 3.00319 + 0.881816i 3.00319 + 0.881816i
\(448\) −0.462997 0.0892353i −0.462997 0.0892353i
\(449\) 1.34378 + 1.28129i 1.34378 + 1.28129i 0.928368 + 0.371662i \(0.121212\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(450\) 2.63438 1.35812i 2.63438 1.35812i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(458\) −0.213947 + 0.618159i −0.213947 + 0.618159i
\(459\) 0 0
\(460\) 0.841254 0.540641i 0.841254 0.540641i
\(461\) 0.252989 + 1.75958i 0.252989 + 1.75958i 0.580057 + 0.814576i \(0.303030\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(462\) 0 0
\(463\) 0.271738 + 0.785135i 0.271738 + 0.785135i 0.995472 + 0.0950560i \(0.0303030\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(464\) −0.947890 1.09392i −0.947890 1.09392i
\(465\) 0 0
\(466\) 0 0
\(467\) 0.0311250 + 0.653395i 0.0311250 + 0.653395i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(468\) 0 0
\(469\) −0.0671040 0.466718i −0.0671040 0.466718i
\(470\) 1.85674 1.85674
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(480\) 0.651174 1.88144i 0.651174 1.88144i
\(481\) 0 0
\(482\) 0.0748038 + 0.0588264i 0.0748038 + 0.0588264i
\(483\) −0.389977 + 0.853931i −0.389977 + 0.853931i
\(484\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(485\) 0 0
\(486\) 5.66185 + 0.540641i 5.66185 + 0.540641i
\(487\) 1.03115 + 1.44805i 1.03115 + 1.44805i 0.888835 + 0.458227i \(0.151515\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(488\) −1.16413 + 0.600149i −1.16413 + 0.600149i
\(489\) −1.19715 1.14148i −1.19715 1.14148i
\(490\) 0.763617 + 0.147175i 0.763617 + 0.147175i
\(491\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(492\) −0.737920 + 3.04175i −0.737920 + 3.04175i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.76962 + 3.06507i 1.76962 + 3.06507i
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) −0.786053 + 0.618159i −0.786053 + 0.618159i
\(501\) 0.900739 + 3.71290i 0.900739 + 3.71290i
\(502\) 0 0
\(503\) 0.0748038 1.57033i 0.0748038 1.57033i −0.580057 0.814576i \(-0.696970\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(504\) 0.329476 + 1.35812i 0.329476 + 1.35812i
\(505\) −1.32254 + 1.04006i −1.32254 + 1.04006i
\(506\) 0 0
\(507\) −0.995472 1.72421i −0.995472 1.72421i
\(508\) 0.607279 + 0.243118i 0.607279 + 0.243118i
\(509\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.415415 0.909632i −0.415415 0.909632i
\(513\) 0 0
\(514\) 0 0
\(515\) −0.0934441 0.0180099i −0.0934441 0.0180099i
\(516\) −1.67162 1.59389i −1.67162 1.59389i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.841254 0.540641i −0.841254 0.540641i 0.0475819 0.998867i \(-0.484848\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(522\) −1.78217 + 3.90240i −1.78217 + 3.90240i
\(523\) 0.911911 + 0.717135i 0.911911 + 0.717135i 0.959493 0.281733i \(-0.0909091\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(524\) 0 0
\(525\) 0.307040 0.887134i 0.307040 0.887134i
\(526\) 1.42131 1.35522i 1.42131 1.35522i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.159389 3.34598i −0.159389 3.34598i
\(535\) 0.284630 0.284630
\(536\) 0.723734 0.690079i 0.723734 0.690079i
\(537\) 0 0
\(538\) −0.0395325 0.829889i −0.0395325 0.829889i
\(539\) 0 0
\(540\) −3.89223 + 0.371662i −3.89223 + 0.371662i
\(541\) −0.759713 0.876756i −0.759713 0.876756i 0.235759 0.971812i \(-0.424242\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(542\) 0 0
\(543\) −1.47025 0.757969i −1.47025 0.757969i
\(544\) 0 0
\(545\) 0.0800569 0.0514495i 0.0800569 0.0514495i
\(546\) 0 0
\(547\) −0.213947 + 0.618159i −0.213947 + 0.618159i 0.786053 + 0.618159i \(0.212121\pi\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 3.05132 + 2.39959i 3.05132 + 2.39959i
\(550\) 0 0
\(551\) 0 0
\(552\) −1.95496 + 0.376789i −1.95496 + 0.376789i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.195876 0.428908i −0.195876 0.428908i
\(561\) 0 0
\(562\) −1.07701 + 1.51245i −1.07701 + 1.51245i
\(563\) 0.759713 0.876756i 0.759713 0.876756i −0.235759 0.971812i \(-0.575758\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(564\) −3.43186 1.37391i −3.43186 1.37391i
\(565\) 0 0
\(566\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(567\) 1.78670 1.40507i 1.78670 1.40507i
\(568\) 0 0
\(569\) −0.0913090 + 1.91681i −0.0913090 + 1.91681i 0.235759 + 0.971812i \(0.424242\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(570\) 0 0
\(571\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.370638 + 0.641964i 0.370638 + 0.641964i
\(575\) 0.928368 + 0.371662i 0.928368 + 0.371662i
\(576\) −1.94091 + 2.23993i −1.94091 + 2.23993i
\(577\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(578\) 0.142315 0.989821i 0.142315 0.989821i
\(579\) 0 0
\(580\) 0.341254 1.40667i 0.341254 1.40667i
\(581\) 0.804250 + 0.236149i 0.804250 + 0.236149i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.279486 0.0538665i 0.279486 0.0538665i −0.0475819 0.998867i \(-0.515152\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(588\) −1.30251 0.837074i −1.30251 0.837074i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.39734 + 0.720381i 1.39734 + 0.720381i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(600\) 1.91030 0.560914i 1.91030 0.560914i
\(601\) 0.0552004 + 1.15880i 0.0552004 + 1.15880i 0.841254 + 0.540641i \(0.181818\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(602\) −0.547014 −0.547014
\(603\) −2.75155 1.10155i −2.75155 1.10155i
\(604\) 0 0
\(605\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(606\) 3.21409 0.943741i 3.21409 0.943741i
\(607\) 1.84833 0.176494i 1.84833 0.176494i 0.888835 0.458227i \(-0.151515\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(608\) 0 0
\(609\) 0.444431 + 1.28410i 0.444431 + 1.28410i
\(610\) −1.16413 0.600149i −1.16413 0.600149i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(614\) 0.0930932 0.268975i 0.0930932 0.268975i
\(615\) −2.90577 + 1.16329i −2.90577 + 1.16329i
\(616\) 0 0
\(617\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(618\) 0.159389 + 0.102433i 0.159389 + 0.102433i
\(619\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(620\) 0 0
\(621\) 2.26798 + 3.18493i 2.26798 + 3.18493i
\(622\) 0 0
\(623\) −0.574161 0.547462i −0.574161 0.547462i
\(624\) 0 0
\(625\) −0.959493 0.281733i −0.959493 0.281733i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −0.915176 + 1.05617i −0.915176 + 1.05617i
\(631\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.154218 + 0.635697i 0.154218 + 0.635697i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.500000 0.866025i
\(641\) −0.981929 1.70075i −0.981929 1.70075i −0.654861 0.755750i \(-0.727273\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(642\) −0.526089 0.210614i −0.526089 0.210614i
\(643\) 0.947890 1.09392i 0.947890 1.09392i −0.0475819 0.998867i \(-0.515152\pi\)
0.995472 0.0950560i \(-0.0303030\pi\)
\(644\) −0.273507 + 0.384087i −0.273507 + 0.384087i
\(645\) 0.328708 2.28621i 0.328708 2.28621i
\(646\) 0 0
\(647\) −0.437742 + 1.80440i −0.437742 + 1.80440i 0.142315 + 0.989821i \(0.454545\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(648\) 4.62533 + 1.35812i 4.62533 + 1.35812i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.481929 0.676774i −0.481929 0.676774i
\(653\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(654\) −0.186042 + 0.0358566i −0.186042 + 0.0358566i
\(655\) 0 0
\(656\) −0.653077 + 1.43004i −0.653077 + 1.43004i
\(657\) 0 0
\(658\) −0.812771 + 0.325385i −0.812771 + 0.325385i
\(659\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(660\) 0 0
\(661\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.581419 + 1.67990i 0.581419 + 1.67990i
\(665\) 0 0
\(666\) 0 0
\(667\) −1.38884 + 0.407799i −1.38884 + 0.407799i
\(668\) 0.0913090 + 1.91681i 0.0913090 + 1.91681i
\(669\) 2.60758 2.60758
\(670\) 0.981929 + 0.189251i 0.981929 + 0.189251i
\(671\) 0 0
\(672\) 0.0446683 + 0.937702i 0.0446683 + 0.937702i
\(673\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(674\) 0 0
\(675\) −2.56046 2.95493i −2.56046 2.95493i
\(676\) −0.327068 0.945001i −0.327068 0.945001i
\(677\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.09560 3.16554i 1.09560 3.16554i
\(682\) 0 0
\(683\) −0.223734 0.175946i −0.223734 0.175946i 0.500000 0.866025i \(-0.333333\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.823056 + 0.158631i −0.823056 + 0.158631i
\(687\) 1.29645 + 0.123796i 1.29645 + 0.123796i
\(688\) −0.672932 0.945001i −0.672932 0.945001i
\(689\) 0 0
\(690\) −1.44091 1.37391i −1.44091 1.37391i
\(691\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.544078 1.19136i −0.544078 1.19136i
\(695\) 0 0
\(696\) −1.67162 + 2.34747i −1.67162 + 2.34747i
\(697\) 0 0
\(698\) −1.07701 0.431171i −1.07701 0.431171i
\(699\) 0 0
\(700\) 0.235759 0.408346i 0.235759 0.408346i
\(701\) 0.786053 0.618159i 0.786053 0.618159i −0.142315 0.989821i \(-0.545455\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −0.871520 3.59245i −0.871520 3.59245i
\(706\) 0 0
\(707\) 0.396666 0.687046i 0.396666 0.687046i
\(708\) 0 0
\(709\) −0.928368 0.371662i −0.928368 0.371662i −0.142315 0.989821i \(-0.545455\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.239446 1.66538i 0.239446 1.66538i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(720\) −2.95044 0.281733i −2.95044 0.281733i
\(721\) 0.0440606 0.00849198i 0.0440606 0.00849198i
\(722\) −0.841254 0.540641i −0.841254 0.540641i
\(723\) 0.0787070 0.172344i 0.0787070 0.172344i
\(724\) −0.653077 0.513585i −0.653077 0.513585i
\(725\) 1.34378 0.537970i 1.34378 0.537970i
\(726\) 0.651174 1.88144i 0.651174 1.88144i
\(727\) 1.13779 1.08488i 1.13779 1.08488i 0.142315 0.989821i \(-0.454545\pi\)
0.995472 0.0950560i \(-0.0303030\pi\)
\(728\) 0 0
\(729\) −0.925488 6.43691i −0.925488 6.43691i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.70760 + 1.97068i 1.70760 + 1.97068i
\(733\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(734\) −0.0913090 + 0.0268107i −0.0913090 + 0.0268107i
\(735\) −0.0736710 1.54655i −0.0736710 1.54655i
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) 4.65950 4.65950
\(739\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.271738 + 0.785135i 0.271738 + 0.785135i 0.995472 + 0.0950560i \(0.0303030\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(744\) 0 0
\(745\) 0.223734 + 1.55610i 0.223734 + 1.55610i
\(746\) 0 0
\(747\) 3.81318 3.63586i 3.81318 3.63586i
\(748\) 0 0
\(749\) −0.124594 + 0.0498801i −0.124594 + 0.0498801i
\(750\) 1.56499 + 1.23072i 1.56499 + 1.23072i
\(751\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(752\) −1.56199 1.00383i −1.56199 1.00383i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.63866 0.844787i 1.63866 0.844787i
\(757\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.345139 + 0.755750i 0.345139 + 0.755750i 1.00000 \(0\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(762\) 0.185343 1.28909i 0.185343 1.28909i
\(763\) −0.0260280 + 0.0365512i −0.0260280 + 0.0365512i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.928368 1.60798i −0.928368 1.60798i
\(767\) 0 0
\(768\) −1.56499 + 1.23072i −1.56499 + 1.23072i
\(769\) −0.469383 1.93482i −0.469383 1.93482i −0.327068 0.945001i \(-0.606061\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(774\) −1.71921 + 2.97775i −1.71921 + 2.97775i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.0552004 + 0.0775182i −0.0552004 + 0.0775182i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 5.55722 + 1.07107i 5.55722 + 1.07107i
\(784\) −0.562827 0.536654i −0.562827 0.536654i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.651174 0.0621796i −0.651174 0.0621796i −0.235759 0.971812i \(-0.575758\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(788\) 0 0
\(789\) −3.28924 2.11387i −3.28924 2.11387i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.995472 0.0950560i 0.995472 0.0950560i
\(801\) −4.78471 + 1.40492i −4.78471 + 1.40492i
\(802\) −0.0224357 0.470984i −0.0224357 0.470984i
\(803\) 0 0
\(804\) −1.67489 1.07639i −1.67489 1.07639i
\(805\) −0.471518 −0.471518
\(806\) 0 0
\(807\) −1.58713 + 0.466024i −1.58713 + 0.466024i
\(808\) 1.67489 0.159932i 1.67489 0.159932i
\(809\) 0.428368 + 0.494363i 0.428368 + 0.494363i 0.928368 0.371662i \(-0.121212\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) 1.57666 + 4.55546i 1.57666 + 4.55546i
\(811\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(812\) 0.0971309 + 0.675560i 0.0971309 + 0.675560i
\(813\) 0 0
\(814\) 0 0
\(815\) 0.271738 0.785135i 0.271738 0.785135i
\(816\) 0 0
\(817\) 0 0
\(818\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(819\) 0 0
\(820\) −1.54370 + 0.297523i −1.54370 + 0.297523i
\(821\) 1.30379 + 0.124497i 1.30379 + 0.124497i 0.723734 0.690079i \(-0.242424\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(822\) 0 0
\(823\) 1.28656 0.663268i 1.28656 0.663268i 0.327068 0.945001i \(-0.393939\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(824\) 0.0688733 + 0.0656706i 0.0688733 + 0.0656706i
\(825\) 0 0
\(826\) 0 0
\(827\) 0.370638 1.52779i 0.370638 1.52779i −0.415415 0.909632i \(-0.636364\pi\)
0.786053 0.618159i \(-0.212121\pi\)
\(828\) 1.23123 + 2.69602i 1.23123 + 2.69602i
\(829\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(830\) −1.03115 + 1.44805i −1.03115 + 1.44805i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −1.50842 + 1.18624i −1.50842 + 1.18624i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(840\) −0.737920 + 0.580306i −0.737920 + 0.580306i
\(841\) −0.547582 + 0.948440i −0.547582 + 0.948440i
\(842\) −0.959493 1.66189i −0.959493 1.66189i
\(843\) 3.43186 + 1.37391i 3.43186 + 1.37391i
\(844\) 0 0
\(845\) 0.580057 0.814576i 0.580057 0.814576i
\(846\) −0.783173 + 5.44709i −0.783173 + 5.44709i
\(847\) −0.195876 0.428908i −0.195876 0.428908i
\(848\) 0 0
\(849\) 3.75155 + 1.10155i 3.75155 + 1.10155i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(854\) 0.614761 + 0.0587025i 0.614761 + 0.0587025i
\(855\) 0 0
\(856\) −0.239446 0.153882i −0.239446 0.153882i
\(857\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(858\) 0 0
\(859\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(860\) 0.379436 1.09631i 0.379436 1.09631i
\(861\) 1.06812 1.01845i 1.06812 1.01845i
\(862\) 0 0
\(863\) 0.279486 + 1.94387i 0.279486 + 1.94387i 0.327068 + 0.945001i \(0.393939\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(864\) 3.47528 + 1.79163i 3.47528 + 1.79163i
\(865\) 0 0
\(866\) 0 0
\(867\) −1.98193 + 0.189251i −1.98193 + 0.189251i
\(868\) 0 0
\(869\) 0 0
\(870\) −2.88183 −2.88183
\(871\) 0 0
\(872\) −0.0951638 −0.0951638
\(873\) 0 0
\(874\) 0 0
\(875\) 0.469383 0.0448206i 0.469383 0.0448206i
\(876\) 0 0
\(877\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −0.723734 + 0.690079i −0.723734 + 0.690079i −0.959493 0.281733i \(-0.909091\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(882\) −0.753861 + 2.17814i −0.753861 + 2.17814i
\(883\) 0.264241 0.105786i 0.264241 0.105786i −0.235759 0.971812i \(-0.575758\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.21769 + 0.782560i 1.21769 + 0.782560i
\(887\) −1.42131 + 0.273935i −1.42131 + 0.273935i −0.841254 0.540641i \(-0.818182\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(888\) 0 0
\(889\) −0.178911 0.251245i −0.178911 0.251245i
\(890\) 1.49547 0.770969i 1.49547 0.770969i
\(891\) 0 0
\(892\) 1.28605 + 0.247866i 1.28605 + 0.247866i
\(893\) 0 0
\(894\) 0.737920 3.04175i 0.737920 3.04175i
\(895\) 0 0
\(896\) −0.0671040 + 0.466718i −0.0671040 + 0.466718i
\(897\) 0 0
\(898\) 1.21590 1.40323i 1.21590 1.40323i
\(899\) 0 0
\(900\) −1.48193 2.56678i −1.48193 2.56678i
\(901\) 0 0
\(902\) 0 0
\(903\) 0.256759 + 1.05838i 0.256759 + 1.05838i
\(904\) 0 0
\(905\) 0.0395325 0.829889i 0.0395325 0.829889i
\(906\) 0 0
\(907\) −1.02951 + 0.809616i −1.02951 + 0.809616i −0.981929 0.189251i \(-0.939394\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(908\) 0.841254 1.45709i 0.841254 1.45709i
\(909\) −2.49336 4.31862i −2.49336 4.31862i
\(910\) 0 0
\(911\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −0.614761 + 2.53408i −0.614761 + 2.53408i
\(916\) 0.627639 + 0.184291i 0.627639 + 0.184291i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(920\) −0.580057 0.814576i −0.580057 0.814576i
\(921\) −0.564116 0.0538665i −0.564116 0.0538665i
\(922\) 1.74555 0.336426i 1.74555 0.336426i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0.771316 0.308788i 0.771316 0.308788i
\(927\) 0.0922502 0.266539i 0.0922502 0.266539i
\(928\) −1.04758 + 0.998867i −1.04758 + 0.998867i
\(929\) −1.49547 + 0.961081i −1.49547 + 0.961081i −0.500000 + 0.866025i \(0.666667\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0.651174 0.0621796i 0.651174 0.0621796i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) −0.462997 + 0.0892353i −0.462997 + 0.0892353i
\(939\) 0 0
\(940\) −0.0883470 1.85463i −0.0883470 1.85463i
\(941\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(942\) 0 0
\(943\) 1.02951 + 1.18812i 1.02951 + 1.18812i
\(944\) 0 0
\(945\) 1.63866 + 0.844787i 1.63866 + 0.844787i
\(946\) 0 0
\(947\) −0.975950 + 0.627205i −0.975950 + 0.627205i −0.928368 0.371662i \(-0.878788\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −1.91030 0.560914i −1.91030 0.560914i
\(961\) 0.235759 0.971812i 0.235759 0.971812i
\(962\) 0 0
\(963\) −0.120057 + 0.835015i −0.120057 + 0.835015i
\(964\) 0.0552004 0.0775182i 0.0552004 0.0775182i
\(965\) 0 0
\(966\) 0.871520 + 0.348904i 0.871520 + 0.348904i
\(967\) −0.142315 0.246497i −0.142315 0.246497i 0.786053 0.618159i \(-0.212121\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(968\) 0.500000 0.866025i 0.500000 0.866025i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(972\) 0.270627 5.68116i 0.270627 5.68116i
\(973\) 0 0
\(974\) 1.39734 1.09888i 1.39734 1.09888i
\(975\) 0 0
\(976\) 0.654861 + 1.13425i 0.654861 + 1.13425i
\(977\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(978\) −1.08323 + 1.25011i −1.08323 + 1.25011i
\(979\) 0 0
\(980\) 0.110674 0.769755i 0.110674 0.769755i
\(981\) 0.117169 + 0.256564i 0.117169 + 0.256564i
\(982\) 0 0
\(983\) −1.84125 0.540641i −1.84125 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
−1.00000 \(\pi\)
\(984\) 3.07341 + 0.592352i 3.07341 + 0.592352i
\(985\) 0 0
\(986\) 0 0
\(987\) 1.01106 + 1.41984i 1.01106 + 1.41984i
\(988\) 0 0
\(989\) −1.13915 + 0.219553i −1.13915 + 0.219553i
\(990\) 0 0
\(991\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 2.97740 1.91346i 2.97740 1.91346i
\(997\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(998\) 0 0
\(999\) 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 1340.1.bl.a.1239.1 yes 20
4.3 odd 2 1340.1.bl.b.1239.1 yes 20
5.4 even 2 1340.1.bl.b.1239.1 yes 20
20.19 odd 2 CM 1340.1.bl.a.1239.1 yes 20
67.65 even 33 inner 1340.1.bl.a.199.1 20
268.199 odd 66 1340.1.bl.b.199.1 yes 20
335.199 even 66 1340.1.bl.b.199.1 yes 20
1340.199 odd 66 inner 1340.1.bl.a.199.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1340.1.bl.a.199.1 20 67.65 even 33 inner
1340.1.bl.a.199.1 20 1340.199 odd 66 inner
1340.1.bl.a.1239.1 yes 20 1.1 even 1 trivial
1340.1.bl.a.1239.1 yes 20 20.19 odd 2 CM
1340.1.bl.b.199.1 yes 20 268.199 odd 66
1340.1.bl.b.199.1 yes 20 335.199 even 66
1340.1.bl.b.1239.1 yes 20 4.3 odd 2
1340.1.bl.b.1239.1 yes 20 5.4 even 2