LMFDB - Embedded newform 270.2.p.a.259.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(49,270)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("270.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.p (of order $18$, degree $6$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			259.14
Character	$\chi$	$=$	270.259
Dual form			270.2.p.a.49.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(0.376104 + 1.69072i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.21219 + 0.325886i) q^{5} +(1.53692 + 0.798664i) q^{6} +(-0.531122 - 0.0936511i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.71709 + 1.27178i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(0.376104 + 1.69072i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.21219 + 0.325886i) q^{5} +(1.53692 + 0.798664i) q^{6} +(-0.531122 - 0.0936511i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.71709 + 1.27178i) q^{9} +(1.67161 - 1.48516i) q^{10} +(3.82525 - 1.39228i) q^{11} +(1.59973 - 0.663981i) q^{12} +(1.58330 + 1.88690i) q^{13} +(-0.413139 + 0.346665i) q^{14} +(0.281031 + 3.86277i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.71596 + 2.14541i) q^{17} +(-0.772277 + 2.89889i) q^{18} +(1.08914 - 1.88645i) q^{19} +(-0.0632081 - 2.23517i) q^{20} +(-0.0414188 - 0.933203i) q^{21} +(1.39228 - 3.82525i) q^{22} +(-4.39867 + 0.775604i) q^{23} +(0.519646 - 1.65226i) q^{24} +(4.78760 + 1.44185i) q^{25} +2.46317 q^{26} +(-3.17213 - 4.11553i) q^{27} +0.539315i q^{28} +(-0.558330 - 0.468495i) q^{29} +(3.13970 + 2.26766i) q^{30} +(-1.28782 - 7.30358i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(3.79265 + 5.94380i) q^{33} +(-0.745092 + 4.22563i) q^{34} +(-1.14442 - 0.380260i) q^{35} +(1.72427 + 2.45497i) q^{36} +(6.45946 - 3.72937i) q^{37} +(-0.745018 - 2.04692i) q^{38} +(-2.59474 + 3.38659i) q^{39} +(-1.75287 - 1.38832i) q^{40} +(-5.82235 + 4.88553i) q^{41} +(-0.741498 - 0.568122i) q^{42} +(-2.73291 - 7.50862i) q^{43} +(-2.03537 - 3.52537i) q^{44} +(-6.42519 + 1.92795i) q^{45} +(-2.23326 + 3.86812i) q^{46} +(-9.13513 - 1.61077i) q^{47} +(-0.931683 - 1.46013i) q^{48} +(-6.30453 - 2.29466i) q^{49} +(4.18193 - 2.74071i) q^{50} +(-5.02488 - 5.47576i) q^{51} +(1.58330 - 1.88690i) q^{52} +0.116236i q^{53} +(-5.19169 - 0.215421i) q^{54} +(8.91592 - 1.83339i) q^{55} +(0.413139 + 0.346665i) q^{56} +(3.59910 + 1.13194i) q^{57} +(-0.717776 + 0.126563i) q^{58} +(-10.2609 - 3.73464i) q^{59} +(3.75529 - 0.947525i) q^{60} +(-1.35199 + 7.66749i) q^{61} +(-6.42266 - 3.70813i) q^{62} +(1.56221 - 0.421009i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.88765 + 4.69016i) q^{65} +(6.99109 + 0.915265i) q^{66} +(6.14767 + 7.32650i) q^{67} +(2.75808 + 3.28696i) q^{68} +(-2.96569 - 7.14522i) q^{69} +(-1.02692 + 0.632254i) q^{70} +(6.98968 + 12.1065i) q^{71} +(2.98896 + 0.257156i) q^{72} +(2.27739 + 1.31485i) q^{73} +(1.29520 - 7.34543i) q^{74} +(-0.637130 + 8.63679i) q^{75} +(-2.04692 - 0.745018i) q^{76} +(-2.16206 + 0.381230i) q^{77} +(0.926409 + 4.16455i) q^{78} +(-4.10029 - 3.44055i) q^{79} +(-2.19024 + 0.450382i) q^{80} +(5.76518 - 6.91106i) q^{81} +7.60054i q^{82} +(9.14477 - 10.8983i) q^{83} +(-0.911833 + 0.202839i) q^{84} +(-8.91957 + 3.53508i) q^{85} +(-7.50862 - 2.73291i) q^{86} +(0.582105 - 1.12019i) q^{87} +(-4.00891 - 0.706878i) q^{88} +(-4.79299 + 8.30170i) q^{89} +(-2.65313 + 6.16124i) q^{90} +(-0.664214 - 1.15045i) q^{91} +(1.52764 + 4.19716i) q^{92} +(11.8640 - 4.92425i) q^{93} +(-7.10587 + 5.96254i) q^{94} +(3.02416 - 3.81826i) q^{95} +(-1.71740 - 0.224840i) q^{96} +(0.646954 + 1.77749i) q^{97} +(-5.81028 + 3.35457i) q^{98} +(-8.62290 + 8.64781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9}+O(q^{10}) $ 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9	$ 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9} - 12 q^{11} + 6 q^{14} + 18 q^{15} + 12 q^{20} - 72 q^{21} - 18 q^{25} - 72 q^{26} + 6 q^{29} + 36 q^{30} + 36 q^{31} + 18 q^{35} - 30 q^{36} - 48 q^{39} - 12 q^{41} - 12 q^{44} - 66 q^{45} + 18 q^{49} - 12 q^{50} + 48 q^{51} - 36 q^{54} - 6 q^{56} - 84 q^{59} + 18 q^{60} - 18 q^{61} + 54 q^{64} - 6 q^{65} - 60 q^{69} - 48 q^{74} + 12 q^{75} - 72 q^{79} - 12 q^{81} - 36 q^{86} - 132 q^{89} + 30 q^{90} - 36 q^{94} - 18 q^{95} - 36 q^{99}+O(q^{100}) $ 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9 - 12 * q^11 + 6 * q^14 + 18 * q^15 + 12 * q^20 - 72 * q^21 - 18 * q^25 - 72 * q^26 + 6 * q^29 + 36 * q^30 + 36 * q^31 + 18 * q^35 - 30 * q^36 - 48 * q^39 - 12 * q^41 - 12 * q^44 - 66 * q^45 + 18 * q^49 - 12 * q^50 + 48 * q^51 - 36 * q^54 - 6 * q^56 - 84 * q^59 + 18 * q^60 - 18 * q^61 + 54 * q^64 - 6 * q^65 - 60 * q^69 - 48 * q^74 + 12 * q^75 - 72 * q^79 - 12 * q^81 - 36 * q^86 - 132 * q^89 + 30 * q^90 - 36 * q^94 - 18 * q^95 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	0.376104	+	1.69072i	0.217144	+	0.976140i
$3$	0.376104	+	1.69072i	0.217144	+	0.976140i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	2.21219	+	0.325886i	0.989323	+	0.145741i
$5$	2.21219	+	0.325886i	0.989323	+	0.145741i
$6$	1.53692	+	0.798664i	0.627447	+	0.326053i
$7$	−0.531122	−	0.0936511i	−0.200745	−	0.0353968i	0.0723713	−	0.997378i	$-0.476943\pi$
$7$	−0.531122	−	0.0936511i	−0.200745	−	0.0353968i	−0.273116	+	0.961981i	$0.588054\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−2.71709	+	1.27178i	−0.905697	+	0.423925i
$10$	1.67161	−	1.48516i	0.528611	−	0.469650i
$11$	3.82525	−	1.39228i	1.15336	−	0.419788i	0.306637	−	0.951826i	$-0.400796\pi$
$11$	3.82525	−	1.39228i	1.15336	−	0.419788i	0.846720	+	0.532039i	$0.178574\pi$
$12$	1.59973	−	0.663981i	0.461802	−	0.191675i
$13$	1.58330	+	1.88690i	0.439128	+	0.523332i	0.939533	−	0.342459i	$-0.111260\pi$
$13$	1.58330	+	1.88690i	0.439128	+	0.523332i	−0.500405	+	0.865792i	$0.666815\pi$
$14$	−0.413139	+	0.346665i	−0.110416	+	0.0926502i
$15$	0.281031	+	3.86277i	0.0725618	+	0.997364i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−3.71596	+	2.14541i	−0.901252	+	0.520338i	−0.877606	−	0.479383i	$-0.840861\pi$
$17$	−3.71596	+	2.14541i	−0.901252	+	0.520338i	−0.0236455	+	0.999720i	$0.507527\pi$
$18$	−0.772277	+	2.89889i	−0.182027	+	0.683276i
$19$	1.08914	−	1.88645i	0.249867	−	0.432782i	−0.713622	−	0.700531i	$-0.752947\pi$
$19$	1.08914	−	1.88645i	0.249867	−	0.432782i	0.963489	+	0.267749i	$0.0862799\pi$
$20$	−0.0632081	−	2.23517i	−0.0141338	−	0.499800i
$21$	−0.0414188	−	0.933203i	−0.00903832	−	0.203642i
$22$	1.39228	−	3.82525i	0.296835	−	0.815547i
$23$	−4.39867	+	0.775604i	−0.917185	+	0.161725i	−0.612264	−	0.790653i	$-0.709741\pi$
$23$	−4.39867	+	0.775604i	−0.917185	+	0.161725i	−0.304921	+	0.952378i	$0.598630\pi$
$24$	0.519646	−	1.65226i	0.106072	−	0.337266i
$25$	4.78760	+	1.44185i	0.957519	+	0.288369i
$26$	2.46317			0.483068
$27$	−3.17213	−	4.11553i	−0.610476	−	0.792034i
$28$			0.539315i			0.101921i
$29$	−0.558330	−	0.468495i	−0.103679	−	0.0869973i	0.589474	−	0.807787i	$-0.299335\pi$
$29$	−0.558330	−	0.468495i	−0.103679	−	0.0869973i	−0.693154	+	0.720790i	$0.743779\pi$
$30$	3.13970	+	2.26766i	0.573228	+	0.414016i
$31$	−1.28782	−	7.30358i	−0.231299	−	1.31176i	−0.850269	−	0.526348i	$-0.823561\pi$
$31$	−1.28782	−	7.30358i	−0.231299	−	1.31176i	0.618970	−	0.785414i	$-0.287550\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	3.79265	+	5.94380i	0.660216	+	1.03468i
$34$	−0.745092	+	4.22563i	−0.127782	+	0.724689i
$35$	−1.14442	−	0.380260i	−0.193443	−	0.0642756i
$36$	1.72427	+	2.45497i	0.287379	+	0.409162i
$37$	6.45946	−	3.72937i	1.06193	−	0.613105i	0.135964	−	0.990714i	$-0.456587\pi$
$37$	6.45946	−	3.72937i	1.06193	−	0.613105i	0.925965	+	0.377609i	$0.123254\pi$
$38$	−0.745018	−	2.04692i	−0.120858	−	0.332054i
$39$	−2.59474	+	3.38659i	−0.415491	+	0.542288i
$40$	−1.75287	−	1.38832i	−0.277153	−	0.219513i
$41$	−5.82235	+	4.88553i	−0.909298	+	0.762992i	−0.971985	−	0.235042i	$-0.924477\pi$
$41$	−5.82235	+	4.88553i	−0.909298	+	0.762992i	0.0626873	+	0.998033i	$0.480033\pi$
$42$	−0.741498	−	0.568122i	−0.114416	−	0.0876632i
$43$	−2.73291	−	7.50862i	−0.416765	−	1.14505i	−0.953524	−	0.301317i	$-0.902574\pi$
$43$	−2.73291	−	7.50862i	−0.416765	−	1.14505i	0.536759	−	0.843736i	$-0.319649\pi$
$44$	−2.03537	−	3.52537i	−0.306844	−	0.531470i
$45$	−6.42519	+	1.92795i	−0.957810	+	0.287402i
$46$	−2.23326	+	3.86812i	−0.329276	+	0.570324i
$47$	−9.13513	−	1.61077i	−1.33250	−	0.234955i	−0.538370	−	0.842708i	$-0.680960\pi$
$47$	−9.13513	−	1.61077i	−1.33250	−	0.234955i	−0.794126	+	0.607753i	$0.792071\pi$
$48$	−0.931683	−	1.46013i	−0.134477	−	0.210751i
$49$	−6.30453	−	2.29466i	−0.900647	−	0.327809i
$50$	4.18193	−	2.74071i	0.591414	−	0.387595i
$51$	−5.02488	−	5.47576i	−0.703623	−	0.766759i
$52$	1.58330	−	1.88690i	0.219564	−	0.261666i
$53$			0.116236i			0.0159662i	0.999968	+	0.00798309i	$0.00254112\pi$
$53$			0.116236i			0.0159662i	−0.999968	+	0.00798309i	$0.997459\pi$
$54$	−5.19169	−	0.215421i	−0.706499	−	0.0293151i
$55$	8.91592	−	1.83339i	1.20222	−	0.247214i
$56$	0.413139	+	0.346665i	0.0552081	+	0.0463251i
$57$	3.59910	+	1.13194i	0.476712	+	0.149929i
$58$	−0.717776	+	0.126563i	−0.0942486	+	0.0166186i
$59$	−10.2609	−	3.73464i	−1.33585	−	0.486209i	−0.427346	−	0.904088i	$-0.640551\pi$
$59$	−10.2609	−	3.73464i	−1.33585	−	0.486209i	−0.908503	+	0.417879i	$0.862774\pi$
$60$	3.75529	−	0.947525i	0.484806	−	0.122325i
$61$	−1.35199	+	7.66749i	−0.173104	+	0.981721i	0.767206	+	0.641401i	$0.221647\pi$
$61$	−1.35199	+	7.66749i	−0.173104	+	0.981721i	−0.940310	+	0.340320i	$0.889465\pi$
$62$	−6.42266	−	3.70813i	−0.815679	−	0.470932i
$63$	1.56221	−	0.421009i	0.196820	−	0.0530421i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	2.88765	+	4.69016i	0.358168	+	0.581743i
$66$	6.99109	+	0.915265i	0.860543	+	0.112661i
$67$	6.14767	+	7.32650i	0.751057	+	0.895075i	0.997247	−	0.0741468i	$-0.0236233\pi$
$67$	6.14767	+	7.32650i	0.751057	+	0.895075i	−0.246190	+	0.969221i	$0.579179\pi$
$68$	2.75808	+	3.28696i	0.334467	+	0.398602i
$69$	−2.96569	−	7.14522i	−0.357027	−	0.860184i
$70$	−1.02692	+	0.632254i	−0.122740	+	0.0755688i
$71$	6.98968	+	12.1065i	0.829522	+	1.43677i	0.898413	+	0.439151i	$0.144721\pi$
$71$	6.98968	+	12.1065i	0.829522	+	1.43677i	−0.0688910	+	0.997624i	$0.521946\pi$
$72$	2.98896	+	0.257156i	0.352252	+	0.0303062i
$73$	2.27739	+	1.31485i	0.266548	+	0.153892i	0.627318	−	0.778763i	$-0.284153\pi$
$73$	2.27739	+	1.31485i	0.266548	+	0.153892i	−0.360770	+	0.932655i	$0.617486\pi$
$74$	1.29520	−	7.34543i	0.150564	−	0.853889i
$75$	−0.637130	+	8.63679i	−0.0735695	+	0.997290i
$76$	−2.04692	−	0.745018i	−0.234798	−	0.0854594i
$77$	−2.16206	+	0.381230i	−0.246390	+	0.0434452i
$78$	0.926409	+	4.16455i	0.104895	+	0.471542i
$79$	−4.10029	−	3.44055i	−0.461318	−	0.387092i	0.382297	−	0.924039i	$-0.375133\pi$
$79$	−4.10029	−	3.44055i	−0.461318	−	0.387092i	−0.843616	+	0.536947i	$0.819577\pi$
$80$	−2.19024	+	0.450382i	−0.244876	+	0.0503542i
$81$	5.76518	−	6.91106i	0.640575	−	0.767895i
$82$			7.60054i			0.839339i
$83$	9.14477	−	10.8983i	1.00377	−	1.19624i	0.0232678	−	0.999729i	$-0.492593\pi$
$83$	9.14477	−	10.8983i	1.00377	−	1.19624i	0.980501	−	0.196515i	$-0.0629626\pi$
$84$	−0.911833	+	0.202839i	−0.0994891	+	0.0221315i
$85$	−8.91957	+	3.53508i	−0.967463	+	0.383433i
$86$	−7.50862	−	2.73291i	−0.809675	−	0.294698i
$87$	0.582105	−	1.12019i	0.0624082	−	0.120096i
$88$	−4.00891	−	0.706878i	−0.427351	−	0.0753535i
$89$	−4.79299	+	8.30170i	−0.508056	+	0.879979i	0.491900	+	0.870651i	$0.336302\pi$
$89$	−4.79299	+	8.30170i	−0.508056	+	0.879979i	−0.999956	+	0.00932743i	$0.997031\pi$
$90$	−2.65313	+	6.16124i	−0.279665	+	0.649452i
$91$	−0.664214	−	1.15045i	−0.0696285	−	0.120600i
$92$	1.52764	+	4.19716i	0.159268	+	0.437584i
$93$	11.8640	−	4.92425i	1.23024	−	0.510621i
$94$	−7.10587	+	5.96254i	−0.732915	+	0.614989i
$95$	3.02416	−	3.81826i	0.310273	−	0.391745i
$96$	−1.71740	−	0.224840i	−0.175281	−	0.0229476i
$97$	0.646954	+	1.77749i	0.0656882	+	0.180477i	0.968194	−	0.250201i	$-0.0804967\pi$
$97$	0.646954	+	1.77749i	0.0656882	+	0.180477i	−0.902506	+	0.430678i	$0.858274\pi$
$98$	−5.81028	+	3.35457i	−0.586927	+	0.338863i
$99$	−8.62290	+	8.64781i	−0.866634	+	0.869137i
$100$	0.588584	−	4.96524i	0.0588584	−	0.496524i
$101$	−0.0649104	+	0.368125i	−0.00645883	+	0.0366298i	−0.987867	−	0.155303i	$-0.950365\pi$
$101$	−0.0649104	+	0.368125i	−0.00645883	+	0.0366298i	0.981408	+	0.191933i	$0.0614757\pi$
$102$	−7.42460	+	0.329530i	−0.735145	+	0.0326283i
$103$	1.47527	−	4.05326i	0.145362	−	0.399380i	−0.845549	−	0.533898i	$-0.820727\pi$
$103$	1.47527	−	4.05326i	0.145362	−	0.399380i	0.990911	+	0.134519i	$0.0429488\pi$
$104$	−0.427726	−	2.42575i	−0.0419420	−	0.237865i
$105$	0.212491	−	2.07792i	0.0207370	−	0.202784i
$106$	0.0890416	+	0.0747148i	0.00864849	+	0.00725694i
$107$			4.30890i			0.416557i	0.978070	+	0.208279i	$0.0667860\pi$
$107$			4.30890i			0.416557i	−0.978070	+	0.208279i	$0.933214\pi$
$108$	−3.50217	+	3.83859i	−0.336997	+	0.369369i
$109$	19.7643			1.89308			0.946538	−	0.322594i	$-0.104555\pi$
$109$	19.7643			1.89308			0.946538	+	0.322594i	$0.104555\pi$
$110$	4.32658	−	8.00847i	0.412524	−	0.763578i
$111$	8.73477	+	9.51853i	0.829067	+	0.903459i
$112$	0.531122	−	0.0936511i	0.0501863	−	0.00884920i
$113$	6.31294	−	17.3447i	0.593871	−	1.63165i	−0.169384	−	0.985550i	$-0.554178\pi$
$113$	6.31294	−	17.3447i	0.593871	−	1.63165i	0.763255	−	0.646097i	$-0.223600\pi$
$114$	3.18057	−	2.02947i	0.297888	−	0.190078i
$115$	−9.98346	+	0.282320i	−0.930962	+	0.0263265i
$116$	−0.364424	+	0.631201i	−0.0338360	+	0.0586056i
$117$	−6.70168	−	3.11328i	−0.619570	−	0.287823i
$118$	−9.45645	+	5.45968i	−0.870537	+	0.502605i
$119$	2.17454	−	0.791470i	0.199340	−	0.0725539i
$120$	1.68801	−	3.48578i	0.154093	−	0.318206i
$121$	4.26763	−	3.58097i	0.387966	−	0.325543i
$122$	5.00460	+	5.96425i	0.453095	+	0.539978i
$123$	−10.4499	−	8.00651i	−0.942235	−	0.721923i
$124$	−6.96900	+	2.53651i	−0.625834	+	0.227785i
$125$	10.1212	+	4.74985i	0.905269	+	0.424840i
$126$	0.681658	−	1.46734i	0.0607269	−	0.130721i
$127$	8.44545	+	4.87598i	0.749413	+	0.432674i	0.825482	−	0.564429i	$-0.190904\pi$
$127$	8.44545	+	4.87598i	0.749413	+	0.432674i	−0.0760690	+	0.997103i	$0.524237\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	11.6671	−	7.44462i	1.02723	−	0.655462i
$130$	5.44902	+	0.802714i	0.477910	+	0.0704027i
$131$	−0.846116	−	4.79856i	−0.0739255	−	0.419253i	−0.999201	−	0.0399576i	$-0.987278\pi$
$131$	−0.846116	−	4.79856i	−0.0739255	−	0.419253i	0.925276	−	0.379295i	$-0.123833\pi$
$132$	5.19492	−	4.76716i	0.452160	−	0.414928i
$133$	−0.755136	+	0.899936i	−0.0654786	+	0.0780343i
$134$	9.56407			0.826210
$135$	−5.67617	−	10.1381i	−0.488527	−	0.872549i
$136$	4.29082			0.367934
$137$	−4.54631	+	5.41808i	−0.388417	+	0.462898i	−0.924452	−	0.381298i	$-0.875477\pi$
$137$	−4.54631	+	5.41808i	−0.388417	+	0.462898i	0.536035	+	0.844196i	$0.319922\pi$
$138$	−7.37986	−	2.32101i	−0.628216	−	0.197578i
$139$	0.148126	+	0.840064i	0.0125639	+	0.0712533i	0.990445	−	0.137908i	$-0.0440378\pi$
$139$	0.148126	+	0.840064i	0.0125639	+	0.0712533i	−0.977881	+	0.209161i	$0.932927\pi$
$140$	−0.175755	+	1.19307i	−0.0148540	+	0.100833i
$141$	−0.712391	−	16.0508i	−0.0599941	−	1.35172i
$142$	13.7670	+	2.42749i	1.15530	+	0.203710i
$143$	8.68361	+	5.01348i	0.726160	+	0.419248i
$144$	2.11826	−	2.12438i	0.176522	−	0.177031i
$145$	−1.08246	−	1.21835i	−0.0898933	−	0.101179i
$146$	2.47111	−	0.899411i	0.204511	−	0.0744358i
$147$	1.50848	−	11.5222i	0.124417	−	0.950339i
$148$	−4.79439	−	5.71373i	−0.394096	−	0.469666i
$149$	−3.89120	+	3.26511i	−0.318780	+	0.267488i	−0.788110	−	0.615535i	$-0.788940\pi$
$149$	−3.89120	+	3.26511i	−0.318780	+	0.267488i	0.469330	+	0.883023i	$0.344496\pi$
$150$	6.20662	+	6.03969i	0.506769	+	0.493139i
$151$	3.86669	−	1.40736i	0.314667	−	0.114529i	−0.179859	−	0.983692i	$-0.557564\pi$
$151$	3.86669	−	1.40736i	0.314667	−	0.114529i	0.494525	+	0.869163i	$0.335342\pi$
$152$	−1.88645	+	1.08914i	−0.153011	+	0.0883412i
$153$	7.36812	−	10.5551i	0.595677	−	0.853332i
$154$	−1.09771	+	1.90129i	−0.0884559	+	0.153210i
$155$	−0.468767	−	16.5766i	−0.0376523	−	1.33147i
$156$	3.78571	+	1.96725i	0.303100	+	0.157506i
$157$	−4.11379	+	11.3026i	−0.328317	+	0.902042i	0.660222	+	0.751071i	$0.270462\pi$
$157$	−4.11379	+	11.3026i	−0.328317	+	0.902042i	−0.988538	+	0.150971i	$0.951760\pi$
$158$	−5.27123	+	0.929460i	−0.419356	+	0.0739439i
$159$	−0.196522	+	0.0437167i	−0.0155852	+	0.00346696i
$160$	−1.06285	+	1.96732i	−0.0840255	+	0.155530i
$161$	2.40886			0.189845
$162$	−1.58839	−	8.85872i	−0.124796	−	0.696007i
$163$		−	1.98122i		−	0.155181i	−0.996985	−	0.0775905i	$-0.975277\pi$
$163$		−	1.98122i		−	0.155181i	0.996985	−	0.0775905i	$-0.0247227\pi$
$164$	5.82235	+	4.88553i	0.454649	+	0.381496i
$165$	6.45307	+	14.3848i	0.502371	+	1.11986i
$166$	−2.47045	−	14.0106i	−0.191744	−	1.08743i
$167$	−3.70137	+	10.1694i	−0.286421	+	0.786934i	0.710139	+	0.704061i	$0.248632\pi$
$167$	−3.70137	+	10.1694i	−0.286421	+	0.786934i	−0.996560	+	0.0828733i	$0.973590\pi$
$168$	−0.430732	+	0.828887i	−0.0332317	+	0.0639500i
$169$	1.20386	−	6.82745i	0.0926049	−	0.525188i
$170$	−3.02536	+	9.10509i	−0.232035	+	0.698329i
$171$	−0.560160	+	6.51081i	−0.0428365	+	0.497894i
$172$	−6.91998	+	3.99525i	−0.527643	+	0.304635i
$173$	8.31946	+	22.8575i	0.632517	+	1.73783i	0.674047	+	0.738688i	$0.264554\pi$
$173$	8.31946	+	22.8575i	0.632517	+	1.73783i	−0.0415308	+	0.999137i	$0.513223\pi$
$174$	−0.483942	−	1.16596i	−0.0366875	−	0.0883912i
$175$	−2.40777	−	1.21416i	−0.182010	−	0.0917818i
$176$	−3.11837	+	2.61663i	−0.235056	+	0.197236i
$177$	2.45511	−	18.7529i	0.184537	−	1.40955i
$178$	3.27860	+	9.00788i	0.245741	+	0.675169i
$179$	2.57674	+	4.46304i	0.192594	+	0.333583i	0.946109	−	0.323848i	$-0.104977\pi$
$179$	2.57674	+	4.46304i	0.192594	+	0.333583i	−0.753515	+	0.657431i	$0.771643\pi$
$180$	3.01438	+	5.99279i	0.224679	+	0.446676i
$181$	−4.22810	+	7.32328i	−0.314272	+	0.544335i	−0.979282	−	0.202499i	$-0.935094\pi$
$181$	−4.22810	+	7.32328i	−0.314272	+	0.544335i	0.665011	+	0.746834i	$0.268427\pi$
$182$	−1.30825	−	0.230679i	−0.0969736	−	0.0170991i
$183$	−13.4721	+	0.597939i	−0.995886	+	0.0442009i
$184$	4.19716	+	1.52764i	0.309419	+	0.112619i
$185$	15.5049	−	6.14504i	1.13995	−	0.451792i
$186$	3.85383	−	12.2536i	0.282576	−	0.898477i
$187$	−11.2275	+	13.3804i	−0.821033	+	0.978470i
$188$			9.27606i			0.676526i
$189$	1.29936	+	2.48292i	0.0945147	+	0.180606i
$190$	−0.981060	−	4.77097i	−0.0711736	−	0.346123i
$191$	16.3395	+	13.7105i	1.18229	+	0.992057i	0.999961	+	0.00881893i	$0.00280719\pi$
$191$	16.3395	+	13.7105i	1.18229	+	0.992057i	0.182326	+	0.983238i	$0.441637\pi$
$192$	−1.27616	+	1.17108i	−0.0920987	+	0.0845152i
$193$	10.8998	−	1.92193i	0.784585	−	0.138344i	0.233016	−	0.972473i	$-0.425140\pi$
$193$	10.8998	−	1.92193i	0.784585	−	0.138344i	0.551569	+	0.834129i	$0.314029\pi$
$194$	1.77749	+	0.646954i	0.127616	+	0.0464486i
$195$	−6.84372	+	6.64620i	−0.490089	+	0.475944i
$196$	−1.16503	+	6.60721i	−0.0832164	+	0.471944i
$197$	6.79514	+	3.92318i	0.484134	+	0.279515i	0.722138	−	0.691749i	$-0.243160\pi$
$197$	6.79514	+	3.92318i	0.484134	+	0.279515i	−0.238004	+	0.971264i	$0.576493\pi$
$198$	1.08191	+	12.1642i	0.0768882	+	0.864474i
$199$	−4.94805	−	8.57027i	−0.350758	−	0.607530i	0.635625	−	0.771998i	$-0.280743\pi$
$199$	−4.94805	−	8.57027i	−0.350758	−	0.607530i	−0.986382	+	0.164468i	$0.947409\pi$
$200$	−3.42526	−	3.64247i	−0.242202	−	0.257562i
$201$	−10.0749	+	13.1495i	−0.710631	+	0.927496i
$202$	0.240277	+	0.286351i	0.0169058	+	0.0201476i
$203$	0.252666	+	0.301116i	0.0177337	+	0.0211342i
$204$	−4.52001	+	5.89939i	−0.316464	+	0.413040i
$205$	−14.4723	+	8.91031i	−1.01079	+	0.622323i
$206$	−2.15669	−	3.73550i	−0.150264	−	0.260265i
$207$	10.9652	−	7.70150i	0.762133	−	0.535291i
$208$	−2.13317	−	1.23159i	−0.147909	−	0.0853952i
$209$	1.53978	−	8.73254i	0.106509	−	0.604043i
$210$	−1.45519	−	1.49844i	−0.100418	−	0.103402i
$211$	−25.3811	−	9.23797i	−1.74731	−	0.635968i	−0.747701	−	0.664035i	$-0.768842\pi$
$211$	−25.3811	−	9.23797i	−1.74731	−	0.635968i	−0.999606	+	0.0280677i	$0.991065\pi$
$212$	0.114470	−	0.0201841i	0.00786181	−	0.00138625i
$213$	−17.8399	+	16.3709i	−1.22237	+	1.12172i
$214$	3.30081	+	2.76971i	0.225639	+	0.189333i
$215$	−3.59878	−	17.5011i	−0.245435	−	1.19357i
$216$	0.689378	+	5.15022i	0.0469062	+	0.350428i
$217$			3.99970i			0.271517i
$218$	12.7042	−	15.1403i	0.860439	−	1.02543i
$219$	−1.36651	+	4.34495i	−0.0923405	+	0.293605i
$220$	−3.35377	−	8.46210i	−0.226111	−	0.570515i
$221$	−9.93164	−	3.61482i	−0.668074	−	0.243159i
$222$	12.9062	−	0.572823i	0.866209	−	0.0384454i
$223$	−19.6897	−	3.47182i	−1.31852	−	0.232490i	−0.530260	−	0.847835i	$-0.677906\pi$
$223$	−19.6897	−	3.47182i	−1.31852	−	0.232490i	−0.788258	+	0.615345i	$0.789017\pi$
$224$	0.269658	−	0.467061i	0.0180173	−	0.0312068i
$225$	−14.8420	+	2.17112i	−0.989470	+	0.144741i
$226$	−9.22890	−	15.9849i	−0.613897	−	1.06330i
$227$	8.25698	+	22.6859i	0.548035	+	1.50571i	0.836360	+	0.548181i	$0.184680\pi$
$227$	8.25698	+	22.6859i	0.548035	+	1.50571i	−0.288325	+	0.957533i	$0.593098\pi$
$228$	0.489765	−	3.74098i	0.0324355	−	0.247752i
$229$	9.12526	−	7.65700i	0.603014	−	0.505989i	−0.289399	−	0.957209i	$-0.593455\pi$
$229$	9.12526	−	7.65700i	0.603014	−	0.505989i	0.892413	+	0.451220i	$0.149011\pi$
$230$	−6.20097	+	7.82925i	−0.408880	+	0.516245i
$231$	−1.45772	−	3.51207i	−0.0959106	−	0.231077i
$232$	0.249281	+	0.684894i	0.0163661	+	0.0449655i
$233$	12.9249	−	7.46217i	0.846735	−	0.488863i	−0.0128126	−	0.999918i	$-0.504078\pi$
$233$	12.9249	−	7.46217i	0.846735	−	0.488863i	0.859548	+	0.511055i	$0.170745\pi$
$234$	−6.69267	+	3.13260i	−0.437514	+	0.204785i
$235$	−19.6838	−	6.54035i	−1.28403	−	0.426645i
$236$	−1.89613	+	10.7535i	−0.123427	+	0.699992i
$237$	4.27488	−	8.22646i	0.277684	−	0.534366i
$238$	0.791470	−	2.17454i	0.0513034	−	0.140955i
$239$	2.21754	+	12.5763i	0.143441	+	0.813492i	0.968606	+	0.248601i	$0.0799708\pi$
$239$	2.21754	+	12.5763i	0.143441	+	0.813492i	−0.825165	+	0.564891i	$0.808918\pi$
$240$	−1.58523	−	3.53370i	−0.102326	−	0.228099i
$241$	18.6632	+	15.6602i	1.20220	+	1.00877i	0.999564	+	0.0295107i	$0.00939492\pi$
$241$	18.6632	+	15.6602i	1.20220	+	1.00877i	0.202635	+	0.979254i	$0.435050\pi$
$242$		−	5.57100i		−	0.358117i
$243$	13.8530	+	7.14804i	0.888670	+	0.458547i
$244$	7.78577			0.498433
$245$	−13.1990	−	7.13079i	−0.843255	−	0.455570i
$246$	−12.8504	+	2.85859i	−0.819312	+	0.182257i
$247$	5.28398	−	0.931709i	0.336212	−	0.0592832i
$248$	−2.53651	+	6.96900i	−0.161068	+	0.442532i
$249$	21.8654	+	11.3624i	1.38566	+	0.720061i
$250$	10.1444	−	4.70015i	0.641587	−	0.297264i
$251$	12.1853	−	21.1055i	0.769128	−	1.33217i	−0.168908	−	0.985632i	$-0.554024\pi$
$251$	12.1853	−	21.1055i	0.769128	−	1.33217i	0.938036	−	0.346537i	$-0.112643\pi$
$252$	−0.685888	−	1.46537i	−0.0432069	−	0.0923096i
$253$	−15.7462	+	9.09105i	−0.989952	+	0.571549i
$254$	9.16385	−	3.33537i	0.574991	−	0.209280i
$255$	−9.33152	−	13.7510i	−0.584363	−	0.861119i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−18.8110	−	22.4180i	−1.17340	−	1.39840i	−0.899658	−	0.436595i	$-0.856184\pi$
$257$	−18.8110	−	22.4180i	−1.17340	−	1.39840i	−0.273738	−	0.961804i	$-0.588260\pi$
$258$	1.79658	−	13.7229i	0.111850	−	0.854348i
$259$	−3.78002	+	1.37582i	−0.234879	+	0.0854890i
$260$	4.11748	−	3.65821i	0.255355	−	0.226873i
$261$	2.11286	+	0.562873i	0.130782	+	0.0348410i
$262$	−4.21979	−	2.43630i	−0.260699	−	0.150515i
$263$	−8.78743	−	1.54946i	−0.541856	−	0.0955439i	−0.103980	−	0.994579i	$-0.533158\pi$
$263$	−8.78743	−	1.54946i	−0.541856	−	0.0955439i	−0.437876	+	0.899035i	$0.644269\pi$
$264$	−0.312629	−	7.04381i	−0.0192410	−	0.433517i
$265$	−0.0378796	+	0.257136i	−0.00232692	+	0.0157957i
$266$	0.203999	+	1.15694i	0.0125080	+	0.0709362i
$267$	−15.8385	−	4.98132i	−0.969303	−	0.304852i
$268$	6.14767	−	7.32650i	0.375528	−	0.447537i
$269$	−9.14408			−0.557525			−0.278762	−	0.960360i	$-0.589924\pi$
$269$	−9.14408			−0.557525			−0.278762	+	0.960360i	$0.589924\pi$
$270$	−11.4148	−	2.16845i	−0.694683	−	0.131968i
$271$	−20.6295			−1.25315			−0.626576	−	0.779360i	$-0.715544\pi$
$271$	−20.6295			−1.25315			−0.626576	+	0.779360i	$0.715544\pi$
$272$	2.75808	−	3.28696i	0.167233	−	0.199301i
$273$	1.69528	−	1.55569i	0.102603	−	0.0941547i
$274$	1.22818	+	6.96535i	0.0741970	+	0.420792i
$275$	20.3212	−	1.15024i	1.22542	−	0.0693621i
$276$	−6.52168	+	4.16139i	−0.392559	+	0.250486i
$277$	18.2145	+	3.21170i	1.09440	+	0.192972i	0.691575	−	0.722305i	$-0.256917\pi$
$277$	18.2145	+	3.21170i	1.09440	+	0.192972i	0.402825	+	0.915277i	$0.368028\pi$
$278$	0.738740	+	0.426512i	0.0443067	+	0.0255805i
$279$	12.7876	+	18.2067i	0.765576	+	1.09001i
$280$	0.800971	+	0.901527i	0.0478672	+	0.0538765i
$281$	−19.2451	+	7.00466i	−1.14807	+	0.417863i	−0.844821	−	0.535049i	$-0.820293\pi$
$281$	−19.2451	+	7.00466i	−1.14807	+	0.417863i	−0.303247	+	0.952912i	$0.598071\pi$
$282$	−12.7535	−	9.77153i	−0.759463	−	0.581886i
$283$	8.84939	+	10.5463i	0.526042	+	0.626912i	0.961998	−	0.273056i	$-0.0880343\pi$
$283$	8.84939	+	10.5463i	0.526042	+	0.626912i	−0.435957	+	0.899968i	$0.643590\pi$
$284$	10.7088	−	8.98576i	0.635451	−	0.533207i
$285$	7.59302	+	3.67696i	0.449771	+	0.217804i
$286$	9.42226	−	3.42942i	0.557150	−	0.202786i
$287$	3.54991	−	2.04954i	0.209545	−	0.120981i
$288$	−0.265777	−	2.98820i	−0.0156611	−	0.176082i
$289$	0.705549	−	1.22205i	0.0415029	−	0.0718851i
$290$	−1.62910	+	0.0460691i	−0.0956643	+	0.00270527i
$291$	−2.76192	+	1.76234i	−0.161907	+	0.103310i
$292$	0.899411	−	2.47111i	0.0526340	−	0.144611i
$293$	−12.2060	+	2.15225i	−0.713081	+	0.125736i	−0.518409	−	0.855133i	$-0.673476\pi$
$293$	−12.2060	+	2.15225i	−0.713081	+	0.125736i	−0.194672	+	0.980868i	$0.562364\pi$
$294$	−7.85692	−	8.56192i	−0.458225	−	0.499341i
$295$	−21.4819	−	11.6056i	−1.25073	−	0.675706i
$296$	−7.45874			−0.433531
$297$	−17.8642	−	11.3265i	−1.03658	−	0.657228i
$298$			5.07960i			0.294254i
$299$	−8.42789	−	7.07184i	−0.487397	−	0.408975i
$300$	8.61621	−	0.872311i	0.497457	−	0.0503629i
$301$	0.748319	+	4.24393i	0.0431324	+	0.244616i
$302$	1.40736	−	3.86669i	0.0809845	−	0.222503i
$303$	−0.646811	+	0.0287078i	−0.0371583	+	0.00164922i
$304$	−0.378255	+	2.14519i	−0.0216944	+	0.123035i
$305$	−5.48958	+	16.5214i	−0.314333	+	0.946011i
$306$	−3.34956	−	12.4290i	−0.191482	−	0.710519i
$307$	27.7691	−	16.0325i	1.58486	−	0.915022i	0.590730	−	0.806870i	$-0.298840\pi$
$307$	27.7691	−	16.0325i	1.58486	−	0.915022i	0.994134	−	0.108152i	$-0.0344934\pi$
$308$	0.750877	+	2.06302i	0.0427852	+	0.117551i
$309$	7.40779	+	0.969820i	0.421415	+	0.0551711i
$310$	−12.9997	−	10.2961i	−0.738336	−	0.584782i
$311$	−1.12523	+	0.944177i	−0.0638058	+	0.0535394i	−0.674133	−	0.738610i	$-0.735482\pi$
$311$	−1.12523	+	0.944177i	−0.0638058	+	0.0535394i	0.610327	+	0.792150i	$0.291038\pi$
$312$	3.94041	−	1.63550i	0.223082	−	0.0925920i
$313$	−6.17591	−	16.9682i	−0.349083	−	0.959097i	−0.982660	−	0.185418i	$-0.940636\pi$
$313$	−6.17591	−	16.9682i	−0.349083	−	0.959097i	0.633577	−	0.773680i	$-0.281586\pi$
$314$	6.01396	+	10.4165i	0.339388	+	0.587837i
$315$	3.59311	−	0.422250i	0.202449	−	0.0237911i
$316$	−2.67627	+	4.63544i	−0.150552	+	0.260764i
$317$	−32.8188	−	5.78683i	−1.84329	−	0.325021i	−0.860454	−	0.509528i	$-0.829820\pi$
$317$	−32.8188	−	5.78683i	−1.84329	−	0.325021i	−0.982831	+	0.184507i	$0.940931\pi$
$318$	−0.0928332	+	0.178645i	−0.00520583	+	0.0100179i
$319$	−2.78803	−	1.01476i	−0.156100	−	0.0568157i
$320$	0.823871	+	2.07876i	0.0460558	+	0.116206i
$321$	−7.28516	+	1.62059i	−0.406618	+	0.0904527i
$322$	1.54839	−	1.84530i	0.0862883	−	0.102834i
$323$			9.34662i			0.520060i
$324$	−7.80718	−	4.47750i	−0.433732	−	0.248750i
$325$	4.85957	+	11.3166i	0.269560	+	0.627732i
$326$	−1.51770	−	1.27350i	−0.0840577	−	0.0705328i
$327$	7.43342	+	33.4159i	0.411069	+	1.84791i
$328$	7.48507	−	1.31982i	0.413294	−	0.0728748i
$329$	4.70102	+	1.71103i	0.259176	+	0.0943322i
$330$	15.1674	+	4.30304i	0.834936	+	0.236875i
$331$	−1.59511	+	9.04632i	−0.0876752	+	0.497231i	0.909072	+	0.416639i	$0.136792\pi$
$331$	−1.59511	+	9.04632i	−0.0876752	+	0.497231i	−0.996747	+	0.0805917i	$0.974319\pi$
$332$	−12.3207	−	7.11337i	−0.676187	−	0.390397i
$333$	−12.8080	+	18.3480i	−0.701876	+	1.00547i
$334$	5.41104	+	9.37220i	0.296079	+	0.512824i
$335$	11.2122	+	18.2111i	0.612589	+	0.994977i
$336$	0.358095	+	0.862758i	0.0195357	+	0.0470673i
$337$	−14.9760	−	17.8477i	−0.815796	−	0.972228i	0.184147	−	0.982899i	$-0.441048\pi$
$337$	−14.9760	−	17.8477i	−0.815796	−	0.972228i	−0.999943	+	0.0106706i	$0.996603\pi$
$338$	−4.45630	−	5.31081i	−0.242391	−	0.288870i
$339$	31.6993	+	4.15004i	1.72167	+	0.225399i
$340$	5.03024	+	8.17020i	0.272803	+	0.443091i
$341$	−15.0948	−	26.1450i	−0.817432	−	1.41583i
$342$	4.62750	+	4.61417i	0.250227	+	0.249506i
$343$	6.40300	+	3.69677i	0.345729	+	0.199607i
$344$	−1.38754	+	7.86911i	−0.0748109	+	0.424274i
$345$	−4.23214	−	16.7731i	−0.227851	−	0.903033i
$346$	22.8575	+	8.31946i	1.22883	+	0.447257i
$347$	−13.3920	+	2.36136i	−0.718918	+	0.126765i	−0.521127	−	0.853479i	$-0.674488\pi$
$347$	−13.3920	+	2.36136i	−0.718918	+	0.126765i	−0.197792	+	0.980244i	$0.563377\pi$
$348$	−1.20425	−	0.378744i	−0.0645545	−	0.0203028i
$349$	−3.05394	−	2.56256i	−0.163474	−	0.137171i	0.557381	−	0.830257i	$-0.311806\pi$
$349$	−3.05394	−	2.56256i	−0.163474	−	0.137171i	−0.720855	+	0.693086i	$0.756251\pi$
$350$	−2.47778	+	1.06401i	−0.132443	+	0.0568737i
$351$	2.74318	−	12.5016i	0.146420	−	0.667286i
$352$			4.07075i			0.216972i
$353$	3.51345	−	4.18717i	0.187002	−	0.222861i	−0.664396	−	0.747381i	$-0.731311\pi$
$353$	3.51345	−	4.18717i	0.187002	−	0.222861i	0.851398	+	0.524521i	$0.175755\pi$
$354$	−12.7874	−	13.9348i	−0.679644	−	0.740628i
$355$	11.5172	+	29.0597i	0.611269	+	1.54233i
$356$	9.00788	+	3.27860i	0.477417	+	0.173765i
$357$	2.15601	+	3.37888i	0.114108	+	0.178829i
$358$	5.07518	+	0.894891i	0.268232	+	0.0472965i
$359$	3.16078	−	5.47463i	0.166820	−	0.288940i	−0.770480	−	0.637464i	$-0.779984\pi$
$359$	3.16078	−	5.47463i	0.166820	−	0.288940i	0.937300	+	0.348524i	$0.113317\pi$
$360$	6.52835	+	1.54294i	0.344074	+	0.0813201i
$361$	7.12754	+	12.3453i	0.375133	+	0.649750i
$362$	2.89219	+	7.94622i	0.152010	+	0.417644i
$363$	7.65950	+	5.86857i	0.402019	+	0.308020i
$364$	−1.01763	+	0.853897i	−0.0533385	+	0.0447563i
$365$	4.60953	+	3.65087i	0.241274	+	0.191095i
$366$	−8.20165	+	10.7046i	−0.428707	+	0.559537i
$367$	6.32341	+	17.3734i	0.330079	+	0.906886i	0.988090	+	0.153877i	$0.0491760\pi$
$367$	6.32341	+	17.3734i	0.330079	+	0.906886i	−0.658011	+	0.753009i	$0.728602\pi$
$368$	3.86812	−	2.23326i	0.201640	−	0.116417i
$369$	9.60656	−	20.6792i	0.500098	−	1.07651i
$370$	5.25900	−	15.8274i	0.273402	−	0.822828i
$371$	0.0108856	−	0.0617353i	0.000565152	−	0.00320514i
$372$	−6.90960	−	10.8287i	−0.358246	−	0.561440i
$373$	−1.21721	+	3.34426i	−0.0630248	+	0.173159i	−0.967208	−	0.253986i	$-0.918258\pi$
$373$	−1.21721	+	3.34426i	−0.0630248	+	0.173159i	0.904183	+	0.427145i	$0.140481\pi$
$374$	3.03308	+	17.2015i	0.156837	+	0.889467i
$375$	−4.22406	+	18.8986i	−0.218130	+	0.975920i
$376$	7.10587	+	5.96254i	0.366457	+	0.307494i
$377$		−	1.79528i		−	0.0924617i
$378$	2.73724	+	0.600622i	0.140789	+	0.0308927i
$379$	1.04628			0.0537435			0.0268718	−	0.999639i	$-0.491445\pi$
$379$	1.04628			0.0537435			0.0268718	+	0.999639i	$0.491445\pi$
$380$	−4.28539	−	2.31519i	−0.219836	−	0.118767i
$381$	−5.06757	+	16.1128i	−0.259620	+	0.825484i
$382$	21.0057	−	3.70387i	1.07475	−	0.189507i
$383$	−2.58954	+	7.11469i	−0.132319	+	0.363544i	−0.988104	−	0.153788i	$-0.950853\pi$
$383$	−2.58954	+	7.11469i	−0.132319	+	0.363544i	0.855785	+	0.517332i	$0.173075\pi$
$384$	0.0767989	+	1.73035i	0.00391913	+	0.0883014i
$385$	−4.90714	+	0.138768i	−0.250091	+	0.00707228i
$386$	5.53398	−	9.58513i	0.281672	−	0.487870i
$387$	16.9748	+	16.9260i	0.862880	+	0.860394i
$388$	1.63815	−	0.945783i	0.0831642	−	0.0480149i
$389$	−18.9188	+	6.88588i	−0.959221	+	0.349128i	−0.773728	−	0.633518i	$-0.781610\pi$
$389$	−18.9188	+	6.88588i	−0.959221	+	0.349128i	−0.185493	+	0.982646i	$0.559388\pi$
$390$	0.692228	+	9.51469i	0.0350523	+	0.481795i
$391$	14.6813	−	12.3190i	0.742463	−	0.623001i
$392$	4.31255	+	5.13950i	0.217817	+	0.259584i
$393$	7.79482	−	3.23531i	0.393197	−	0.163200i
$394$	7.37316	−	2.68361i	0.371454	−	0.135198i
$395$	−7.94940	−	8.94739i	−0.399978	−	0.450192i
$396$	10.0138	+	6.99022i	0.503211	+	0.351272i
$397$	−11.5545	−	6.67099i	−0.579903	−	0.334807i	0.181192	−	0.983448i	$-0.442005\pi$
$397$	−11.5545	−	6.67099i	−0.579903	−	0.334807i	−0.761095	+	0.648640i	$0.775338\pi$
$398$	−9.74575	−	1.71844i	−0.488510	−	0.0861375i
$399$	−1.80555	−	0.938257i	−0.0903907	−	0.0469716i
$400$	−4.99201	+	0.282562i	−0.249600	+	0.0141281i
$401$	−5.09876	−	28.9165i	−0.254620	−	1.44402i	−0.797046	−	0.603918i	$-0.793605\pi$
$401$	−5.09876	−	28.9165i	−0.254620	−	1.44402i	0.542426	−	0.840103i	$-0.317506\pi$
$402$	3.59708	+	16.1702i	0.179406	+	0.806496i
$403$	11.7421	−	13.9937i	0.584917	−	0.697077i
$404$	0.373804			0.0185975
$405$	15.0059	−	13.4098i	0.745649	−	0.666339i
$406$	0.393079			0.0195082
$407$	19.5168	−	23.2592i	0.967409	−	1.15291i
$408$	1.61379	+	7.25458i	0.0798946	+	0.359155i
$409$	5.26607	+	29.8654i	0.260391	+	1.47675i	0.781847	+	0.623470i	$0.214278\pi$
$409$	5.26607	+	29.8654i	0.260391	+	1.47675i	−0.521456	+	0.853278i	$0.674611\pi$
$410$	−2.47691	+	16.8139i	−0.122326	+	0.830377i
$411$	−10.8704	−	5.64879i	−0.536195	−	0.278634i
$412$	−4.24786	−	0.749012i	−0.209277	−	0.0369012i
$413$	5.10001	+	2.94449i	0.250955	+	0.144889i
$414$	1.14860	−	13.3503i	0.0564504	−	0.656129i
$415$	23.7816	−	21.1290i	1.16739	−	1.03718i
$416$	−2.31463	+	0.842455i	−0.113484	+	0.0413048i
$417$	−1.36461	+	0.566392i	−0.0668250	+	0.0277363i
$418$	−5.69976	−	6.79271i	−0.278784	−	0.332242i
$419$	31.0303	−	26.0375i	1.51593	−	1.27202i	0.664857	−	0.746971i	$-0.268493\pi$
$419$	31.0303	−	26.0375i	1.51593	−	1.27202i	0.851074	−	0.525046i	$-0.175952\pi$
$420$	−2.08325	+	0.151564i	−0.101652	+	0.00739558i
$421$	25.0173	−	9.10554i	1.21927	−	0.443777i	0.349358	−	0.936989i	$-0.386400\pi$
$421$	25.0173	−	9.10554i	1.21927	−	0.443777i	0.869909	+	0.493213i	$0.164178\pi$
$422$	−23.3914	+	13.5050i	−1.13867	+	0.657413i
$423$	26.8695	−	7.24122i	1.30644	−	0.352080i
$424$	0.0581178	−	0.100663i	0.00282245	−	0.00488863i
$425$	−20.8838	+	4.91351i	−1.01302	+	0.238340i
$426$	1.07360	+	24.1891i	0.0520160	+	1.17197i
$427$	1.43614	−	3.94576i	0.0694996	−	0.190949i
$428$	4.24344	−	0.748233i	0.205114	−	0.0361672i
$429$	−5.21047	+	16.5672i	−0.251564	+	0.799870i
$430$	−15.7199	−	8.49269i	−0.758080	−	0.409554i
$431$	23.7321			1.14314			0.571568	−	0.820555i	$-0.306335\pi$
$431$	23.7321			1.14314			0.571568	+	0.820555i	$0.306335\pi$
$432$	4.38842	+	2.78240i	0.211138	+	0.133868i
$433$		−	18.7982i		−	0.903385i	−0.892174	−	0.451693i	$-0.850820\pi$
$433$		−	18.7982i		−	0.903385i	0.892174	−	0.451693i	$-0.149180\pi$
$434$	3.06395	+	2.57096i	0.147074	+	0.123410i
$435$	1.65278	−	2.28837i	0.0792448	−	0.109719i
$436$	−3.43203	−	19.4640i	−0.164365	−	0.932157i
$437$	−3.32764	+	9.14261i	−0.159183	+	0.437350i
$438$	2.45005	+	3.83969i	0.117068	+	0.183468i
$439$	3.18217	−	18.0470i	0.151877	−	0.861336i	−0.809709	−	0.586831i	$-0.800375\pi$
$439$	3.18217	−	18.0470i	0.151877	−	0.861336i	0.961586	−	0.274504i	$-0.0885138\pi$
$440$	−8.63811	−	2.87020i	−0.411806	−	0.136831i
$441$	20.0483	−	1.78314i	0.954680	−	0.0849113i
$442$	−9.15305	+	5.28451i	−0.435366	+	0.251359i
$443$	−5.75361	−	15.8079i	−0.273362	−	0.751057i	−0.998076	−	0.0620063i	$-0.980250\pi$
$443$	−5.75361	−	15.8079i	−0.273362	−	0.751057i	0.724713	−	0.689050i	$-0.241972\pi$
$444$	7.85715	−	10.2549i	0.372884	−	0.486678i
$445$	−13.3084	+	16.8030i	−0.630880	+	0.796539i
$446$	−15.3158	+	12.8515i	−0.725226	+	0.608537i
$447$	−6.98389	−	5.35093i	−0.330327	−	0.253090i
$448$	−0.184457	−	0.506791i	−0.00871476	−	0.0239436i
$449$	−2.86531	−	4.96287i	−0.135222	−	0.234212i	0.790460	−	0.612514i	$-0.209842\pi$
$449$	−2.86531	−	4.96287i	−0.135222	−	0.234212i	−0.925682	+	0.378302i	$0.876508\pi$
$450$	−7.87711	+	12.7652i	−0.371331	+	0.601759i
$451$	−15.4699	+	26.7947i	−0.728451	+	1.26171i
$452$	−18.1774	−	3.20516i	−0.854992	−	0.150758i
$453$	3.83373	+	6.00819i	0.180124	+	0.282289i
$454$	22.6859	+	8.25698i	1.06470	+	0.387519i
$455$	−1.09445	−	2.76148i	−0.0513087	−	0.129460i
$456$	−2.55094	−	2.77984i	−0.119459	−	0.130178i
$457$	5.68883	−	6.77968i	0.266112	−	0.317140i	−0.616397	−	0.787436i	$-0.711408\pi$
$457$	5.68883	−	6.77968i	0.266112	−	0.317140i	0.882509	+	0.470296i	$0.155853\pi$
$458$		−	11.9122i		−	0.556620i
$459$	20.6170	+	8.48762i	0.962318	+	0.396168i
$460$	2.01164	+	9.78276i	0.0937932	+	0.456124i
$461$	15.8273	+	13.2806i	0.737149	+	0.618541i	0.932070	−	0.362277i	$-0.118001\pi$
$461$	15.8273	+	13.2806i	0.737149	+	0.618541i	−0.194921	+	0.980819i	$0.562445\pi$
$462$	−3.62740	−	1.14084i	−0.168762	−	0.0530767i
$463$	8.62824	−	1.52139i	0.400988	−	0.0707050i	0.0304826	−	0.999535i	$-0.490296\pi$
$463$	8.62824	−	1.52139i	0.400988	−	0.0707050i	0.370505	+	0.928830i	$0.379184\pi$
$464$	0.684894	+	0.249281i	0.0317954	+	0.0115726i
$465$	27.8502	−	7.02708i	1.29152	−	0.325873i
$466$	2.59158	−	14.6976i	0.120053	−	0.680853i
$467$	−2.14140	−	1.23634i	−0.0990924	−	0.0572110i	0.449635	−	0.893212i	$-0.351554\pi$
$467$	−2.14140	−	1.23634i	−0.0990924	−	0.0572110i	−0.548727	+	0.836001i	$0.684887\pi$
$468$	−1.90225	+	7.14048i	−0.0879316	+	0.330069i
$469$	−2.57902	−	4.46700i	−0.119088	−	0.206267i
$470$	−17.6627	+	10.8746i	−0.814718	+	0.501607i
$471$	−20.6567	−	2.70435i	−0.951811	−	0.124610i
$472$	7.01884	+	8.36472i	0.323068	+	0.385018i
$473$	−20.9082	−	24.9174i	−0.961358	−	1.14570i
$474$	−3.55399	−	8.56262i	−0.163240	−	0.393294i
$475$	7.93435	−	7.46119i	0.364053	−	0.342343i
$476$	−1.15705	−	2.00407i	−0.0530333	−	0.0918565i
$477$	−0.147826	−	0.315823i	−0.00676847	−	0.0144605i
$478$	11.0594	+	6.38515i	0.505845	+	0.292050i
$479$	−2.95115	+	16.7368i	−0.134841	+	0.764724i	0.840129	+	0.542387i	$0.182479\pi$
$479$	−2.95115	+	16.7368i	−0.134841	+	0.764724i	−0.974970	+	0.222336i	$0.928632\pi$
$480$	−3.72594	−	1.05706i	−0.170065	−	0.0482481i
$481$	17.2642	+	6.28366i	0.787180	+	0.286510i
$482$	23.9929	−	4.23059i	1.09285	−	0.192698i
$483$	0.905983	+	4.07272i	0.0412236	+	0.185315i
$484$	−4.26763	−	3.58097i	−0.193983	−	0.162771i
$485$	0.851927	+	4.14299i	0.0386840	+	0.188123i
$486$	14.3803	−	6.01734i	0.652302	−	0.272952i
$487$		−	29.0344i		−	1.31567i	−0.753160	−	0.657837i	$-0.771471\pi$
$487$		−	29.0344i		−	1.31567i	0.753160	−	0.657837i	$-0.228529\pi$
$488$	5.00460	−	5.96425i	0.226548	−	0.269989i
$489$	3.34969	−	0.745144i	0.151478	−	0.0336966i
$490$	−13.9467	+	5.52746i	−0.630047	+	0.249705i
$491$	−20.2892	−	7.38465i	−0.915637	−	0.333265i	−0.159136	−	0.987257i	$-0.550871\pi$
$491$	−20.2892	−	7.38465i	−0.915637	−	0.333265i	−0.756501	+	0.653992i	$0.773093\pi$
$492$	−6.07027	+	11.6814i	−0.273669	+	0.526640i
$493$	3.07984	+	0.543060i	0.138709	+	0.0244582i
$494$	2.68275	−	4.64666i	0.120703	−	0.209063i
$495$	−21.8937	+	16.3205i	−0.984049	+	0.733554i
$496$	3.70813	+	6.42266i	0.166500	+	0.288386i
$497$	−2.57859	−	7.08461i	−0.115665	−	0.317788i
$498$	22.7589	−	9.44628i	1.01985	−	0.423298i
$499$	1.39359	−	1.16936i	0.0623856	−	0.0523477i	−0.611062	−	0.791583i	$-0.709257\pi$
$499$	1.39359	−	1.16936i	0.0623856	−	0.0523477i	0.673447	+	0.739235i	$0.264813\pi$
$500$	2.92016	−	10.7922i	0.130594	−	0.482644i
$501$	−18.5858	−	2.43323i	−0.830352	−	0.108709i
$502$	−8.33522	−	22.9008i	−0.372019	−	1.02211i
$503$	−17.3370	+	10.0095i	−0.773018	+	0.446302i	−0.833950	−	0.551840i	$-0.813926\pi$
$503$	−17.3370	+	10.0095i	−0.773018	+	0.446302i	0.0609321	+	0.998142i	$0.480593\pi$
$504$	−1.56342	−	0.416501i	−0.0696402	−	0.0185524i
$505$	−0.263561	+	0.793211i	−0.0117283	+	0.0352974i
$506$	−3.15729	+	17.9059i	−0.140359	+	0.796013i
$507$	11.9961	−	0.532429i	0.532766	−	0.0236460i
$508$	3.33537	−	9.16385i	0.147983	−	0.406580i
$509$	3.77631	+	21.4165i	0.167382	+	0.949270i	0.946574	+	0.322485i	$0.104518\pi$
$509$	3.77631	+	21.4165i	0.167382	+	0.949270i	−0.779192	+	0.626785i	$0.784371\pi$
$510$	−16.5320	−	1.69059i	−0.732051	−	0.0748606i
$511$	−1.08643	−	0.911626i	−0.0480610	−	0.0403279i
$512$		−	1.00000i		−	0.0441942i
$513$	−11.2187	+	1.50166i	−0.495316	+	0.0663000i
$514$	−29.2647			−1.29081
$515$	4.58447	−	8.48582i	0.202016	−	0.373930i
$516$	−9.35750	−	10.1971i	−0.411941	−	0.448904i
$517$	−37.1868	+	6.55704i	−1.63548	+	0.288378i
$518$	−1.37582	+	3.78002i	−0.0604498	+	0.166085i
$519$	−35.5168	+	22.6627i	−1.55901	+	0.994782i
$520$	−0.155692	−	5.50562i	−0.00682757	−	0.241438i
$521$	15.2692	−	26.4470i	0.668954	−	1.15866i	−0.309243	−	0.950983i	$-0.600076\pi$
$521$	15.2692	−	26.4470i	0.668954	−	1.15866i	0.978197	−	0.207679i	$-0.0665910\pi$
$522$	1.78930	−	1.25673i	0.0783157	−	0.0550057i
$523$	−30.0364	+	17.3415i	−1.31340	+	0.758291i	−0.982657	−	0.185430i	$-0.940632\pi$
$523$	−30.0364	+	17.3415i	−1.31340	+	0.758291i	−0.330742	+	0.943721i	$0.607299\pi$
$524$	−4.57874	+	1.66652i	−0.200023	+	0.0728024i
$525$	1.14724	−	4.52752i	0.0500696	−	0.197597i
$526$	−6.83541	+	5.73559i	−0.298038	+	0.250084i
$527$	20.4546	+	24.3769i	0.891018	+	1.06187i
$528$	−5.59683	−	4.28819i	−0.243571	−	0.186619i
$529$	−2.86622	+	1.04322i	−0.124618	+	0.0453574i
$530$	0.172629	+	0.194301i	0.00749852	+	0.00843990i
$531$	32.6293	−	2.90212i	1.41599	−	0.125941i
$532$	1.01739	+	0.587391i	0.0441095	+	0.0254666i
$533$	−18.4370	−	3.25094i	−0.798596	−	0.140814i
$534$	−13.9967	+	8.93110i	−0.605698	+	0.386487i
$535$	−1.40421	+	9.53212i	−0.0607093	+	0.412109i
$536$	−1.66078	−	9.41877i	−0.0717349	−	0.406829i
$537$	−6.57665	+	6.03512i	−0.283803	+	0.260434i
$538$	−5.87770	+	7.00477i	−0.253406	+	0.301997i
$539$	−27.3112			−1.17638
$540$	−8.99843	+	7.35040i	−0.387231	+	0.316311i
$541$	−35.7367			−1.53644			−0.768221	−	0.640185i	$-0.778858\pi$
$541$	−35.7367			−1.53644			−0.768221	+	0.640185i	$0.778858\pi$
$542$	−13.2604	+	15.8031i	−0.569582	+	0.678802i
$543$	−13.9718	−	4.39423i	−0.599589	−	0.188574i
$544$	−0.745092	−	4.22563i	−0.0319456	−	0.181172i
$545$	43.7224	+	6.44091i	1.87286	+	0.275898i
$546$	−0.102022	−	2.29864i	−0.00436613	−	0.0983727i
$547$	13.5618	+	2.39131i	0.579860	+	0.102245i	0.455883	−	0.890040i	$-0.349324\pi$
$547$	13.5618	+	2.39131i	0.579860	+	0.102245i	0.123978	+	0.992285i	$0.460435\pi$
$548$	6.12522	+	3.53640i	0.261657	+	0.151068i
$549$	−6.07785	−	22.5527i	−0.259396	−	0.962526i
$550$	12.1811	−	16.3063i	0.519404	−	0.695304i
$551$	−1.49189	+	0.543005i	−0.0635568	+	0.0231328i
$552$	−1.00425	+	7.67079i	−0.0427438	+	0.326490i
$553$	1.85554	+	2.21135i	0.0789056	+	0.0940361i
$554$	14.1683	−	11.8886i	0.601955	−	0.505100i
$555$	16.2210	+	23.9034i	0.688544	+	1.01464i
$556$	0.801580	−	0.291751i	0.0339946	−	0.0123730i
$557$	19.9184	−	11.4999i	0.843970	−	0.487266i	−0.0146417	−	0.999893i	$-0.504661\pi$
$557$	19.9184	−	11.4999i	0.843970	−	0.487266i	0.858612	+	0.512626i	$0.171327\pi$
$558$	22.1669	+	1.90714i	0.938398	+	0.0807355i
$559$	9.84100	−	17.0451i	0.416230	−	0.720931i
$560$	1.20546	−	0.0340891i	0.0509401	−	0.00144053i
$561$	−26.8452	−	13.9501i	−1.13341	−	0.588975i
$562$	−7.00466	+	19.2451i	−0.295474	+	0.811807i
$563$	21.2374	−	3.74472i	0.895048	−	0.157821i	0.292841	−	0.956161i	$-0.405399\pi$
$563$	21.2374	−	3.74472i	0.895048	−	0.157821i	0.602207	+	0.798340i	$0.294288\pi$
$564$	−15.6832	+	3.48876i	−0.660384	+	0.146903i
$565$	19.6178	−	36.3124i	0.825328	−	1.52768i
$566$	13.7672			0.578679
$567$	−3.70924	+	3.13070i	−0.155773	+	0.131477i
$568$		−	13.9794i		−	0.586561i
$569$	−11.3258	−	9.50345i	−0.474801	−	0.398405i	0.373741	−	0.927533i	$-0.378075\pi$
$569$	−11.3258	−	9.50345i	−0.474801	−	0.398405i	−0.848542	+	0.529128i	$0.822519\pi$
$570$	7.69741	−	3.45308i	0.322409	−	0.144634i
$571$	1.39101	+	7.88879i	0.0582118	+	0.330136i	0.999981	−	0.00612376i	$-0.00194927\pi$
$571$	1.39101	+	7.88879i	0.0582118	+	0.330136i	−0.941769	+	0.336259i	$0.890838\pi$
$572$	3.42942	−	9.42226i	0.143391	−	0.393965i
$573$	−17.0353	+	32.7822i	−0.711660	+	1.36950i
$574$	0.711799	−	4.03681i	0.0297099	−	0.168493i
$575$	−22.1773	−	2.62892i	−0.924859	−	0.109634i
$576$	−2.45994	−	1.71718i	−0.102497	−	0.0715493i
$577$	−5.43636	+	3.13868i	−0.226319	+	0.130665i	−0.608873	−	0.793268i	$-0.708378\pi$
$577$	−5.43636	+	3.13868i	−0.226319	+	0.130665i	0.382554	+	0.923933i	$0.375045\pi$
$578$	−0.482624	−	1.32600i	−0.0200745	−	0.0551542i
$579$	7.34891	+	17.7057i	0.305410	+	0.735825i
$580$	−1.01188	+	1.27758i	−0.0420159	+	0.0530486i
$581$	−5.87762	+	4.93191i	−0.243845	+	0.204610i
$582$	−0.425299	+	3.24857i	−0.0176292	+	0.134657i
$583$	0.161832	+	0.444631i	0.00670241	+	0.0184147i
$584$	−1.31485	−	2.27739i	−0.0544089	−	0.0942390i
$585$	−13.8108	−	9.07117i	−0.571008	−	0.375047i
$586$	−6.19714	+	10.7338i	−0.256002	+	0.443408i
$587$	26.5118	+	4.67475i	1.09426	+	0.192947i	0.691513	−	0.722364i	$-0.256945\pi$
$587$	26.5118	+	4.67475i	1.09426	+	0.192947i	0.402746	+	0.915312i	$0.368056\pi$
$588$	−11.6091	+	0.515254i	−0.478753	+	0.0212487i
$589$	−15.1805	−	5.52524i	−0.625500	−	0.227663i
$590$	−22.6987	+	8.99615i	−0.934492	+	0.370366i
$591$	−4.07733	+	12.9642i	−0.167719	+	0.533277i
$592$	−4.79439	+	5.71373i	−0.197048	+	0.234833i
$593$			11.9452i			0.490529i	0.969456	+	0.245264i	$0.0788747\pi$
$593$			11.9452i			0.490529i	−0.969456	+	0.245264i	$0.921125\pi$
$594$	−20.1594	+	6.40423i	−0.827152	+	0.262769i
$595$	5.06844	−	1.04223i	0.207786	−	0.0427272i
$596$	3.89120	+	3.26511i	0.159390	+	0.133744i
$597$	12.6290	−	11.5891i	0.516869	−	0.474310i
$598$	−10.8347	+	1.91045i	−0.443063	+	0.0781240i
$599$	2.09601	+	0.762886i	0.0856408	+	0.0311707i	0.384485	−	0.923131i	$-0.374379\pi$
$599$	2.09601	+	0.762886i	0.0856408	+	0.0311707i	−0.298844	+	0.954302i	$0.596601\pi$
$600$	4.87016	−	7.16111i	0.198824	−	0.292351i
$601$	5.05104	−	28.6459i	0.206036	−	1.16849i	−0.689764	−	0.724034i	$-0.742286\pi$
$601$	5.05104	−	28.6459i	0.206036	−	1.16849i	0.895801	−	0.444456i	$-0.146603\pi$
$602$	3.73205	+	2.15470i	0.152107	+	0.0878190i
$603$	−26.0214	−	12.0883i	−1.05967	−	0.492275i
$604$	−2.05742	−	3.56356i	−0.0837153	−	0.144999i
$605$	10.6078	−	6.53103i	0.431269	−	0.265524i
$606$	−0.393771	+	0.513939i	−0.0159959	+	0.0208774i
$607$	11.4898	+	13.6930i	0.466355	+	0.555781i	0.947041	−	0.321112i	$-0.104057\pi$
$607$	11.4898	+	13.6930i	0.466355	+	0.555781i	−0.480686	+	0.876893i	$0.659612\pi$
$608$	1.40018	+	1.66866i	0.0567846	+	0.0676733i
$609$	−0.414075	+	0.540440i	−0.0167792	+	0.0218997i
$610$	9.12747	+	14.8250i	0.369561	+	0.600247i
$611$	−11.4243	−	19.7874i	−0.462177	−	0.800513i
$612$	−11.6742	−	5.42330i	−0.471903	−	0.219224i
$613$	39.7223	+	22.9337i	1.60437	+	0.926284i	0.990599	+	0.136800i	$0.0436818\pi$
$613$	39.7223	+	22.9337i	1.60437	+	0.926284i	0.613772	+	0.789483i	$0.289651\pi$
$614$	5.56802	−	31.5778i	0.224707	−	1.27438i
$615$	−20.5080	−	21.1174i	−0.826961	−	0.851537i
$616$	2.06302	+	0.750877i	0.0831213	+	0.0302537i
$617$	−1.67563	+	0.295459i	−0.0674583	+	0.0118947i	−0.207275	−	0.978283i	$-0.566460\pi$
$617$	−1.67563	+	0.295459i	−0.0674583	+	0.0118947i	0.139817	+	0.990177i	$0.455349\pi$
$618$	5.50456	−	5.05131i	0.221426	−	0.203194i
$619$	−16.5836	−	13.9153i	−0.666550	−	0.559302i	0.245492	−	0.969399i	$-0.421050\pi$
$619$	−16.5836	−	13.9153i	−0.666550	−	0.559302i	−0.912042	+	0.410097i	$0.865495\pi$
$620$	−16.2434	+	3.34014i	−0.652350	+	0.134143i
$621$	17.1452	+	15.6425i	0.688011	+	0.627713i
$622$			1.46888i			0.0588967i
$623$	3.32313	−	3.96035i	0.133138	−	0.158668i
$624$	1.27998	−	4.06981i	0.0512402	−	0.162923i
$625$	20.8422	+	13.8060i	0.833686	+	0.552238i
$626$	−16.9682	−	6.17591i	−0.678184	−	0.246839i
$627$	15.3434	−	0.680995i	0.612758	−	0.0271963i
$628$	11.8452	+	2.08863i	0.472675	+	0.0833453i
$629$	−16.0020	+	27.7164i	−0.638043	+	1.10512i
$630$	1.98614	−	3.02390i	0.0791299	−	0.120475i
$631$	6.44066	+	11.1555i	0.256398	+	0.444095i	0.965274	−	0.261238i	$-0.0841307\pi$
$631$	6.44066	+	11.1555i	0.256398	+	0.444095i	−0.708876	+	0.705333i	$0.750797\pi$
$632$	1.83068	+	5.02975i	0.0728205	+	0.200073i
$633$	6.07292	−	46.3869i	0.241377	−	1.84371i
$634$	−25.5285	+	21.4209i	−1.01386	+	0.850733i
$635$	17.0940	+	13.5389i	0.678353	+	0.537274i
$636$	0.0771782	+	0.185945i	0.00306032	+	0.00737321i
$637$	−5.65215	−	15.5292i	−0.223946	−	0.615287i
$638$	−2.56946	+	1.48348i	−0.101726	+	0.0587315i
$639$	−34.3883	−	24.0051i	−1.36038	−	0.949628i
$640$	2.12200	+	0.705079i	0.0838792	+	0.0278707i
$641$	−2.61920	+	14.8542i	−0.103452	+	0.586706i	0.888375	+	0.459118i	$0.151835\pi$
$641$	−2.61920	+	14.8542i	−0.103452	+	0.586706i	−0.991827	+	0.127588i	$0.959276\pi$
$642$	−3.44136	+	6.62245i	−0.135820	+	0.261367i
$643$	−7.44994	+	20.4685i	−0.293797	+	0.807200i	0.701706	+	0.712467i	$0.252422\pi$
$643$	−7.44994	+	20.4685i	−0.293797	+	0.807200i	−0.995503	+	0.0947334i	$0.969800\pi$
$644$	−0.418295	−	2.37227i	−0.0164831	−	0.0934805i
$645$	28.2361	−	12.6668i	1.11179	−	0.498754i
$646$	7.15993	+	6.00789i	0.281704	+	0.236377i
$647$			7.76918i			0.305438i	0.988270	+	0.152719i	$0.0488030\pi$
$647$			7.76918i			0.305438i	−0.988270	+	0.152719i	$0.951197\pi$
$648$	−8.44832	+	3.10256i	−0.331881	+	0.121880i
$649$	−44.4500			−1.74482
$650$	11.7927	+	3.55152i	0.462547	+	0.139302i
$651$	−6.76238	+	1.50430i	−0.265039	+	0.0589582i
$652$	−1.95112	+	0.344035i	−0.0764118	+	0.0134735i
$653$	−7.67233	+	21.0796i	−0.300241	+	0.824907i	0.694216	+	0.719767i	$0.255751\pi$
$653$	−7.67233	+	21.0796i	−0.300241	+	0.824907i	−0.994457	+	0.105140i	$0.966471\pi$
$654$	30.3762	+	15.7850i	1.18780	+	0.617243i
$655$	−0.307987	−	10.8911i	−0.0120340	−	0.425550i
$656$	3.80027	−	6.58226i	0.148376	−	0.256994i
$657$	−7.86007	−	0.676245i	−0.306650	−	0.0263828i
$658$	4.33248	−	2.50136i	0.168898	−	0.0975132i
$659$	−17.0727	+	6.21395i	−0.665057	+	0.242061i	−0.652418	−	0.757859i	$-0.726245\pi$
$659$	−17.0727	+	6.21395i	−0.665057	+	0.242061i	−0.0126389	+	0.999920i	$0.504023\pi$
$660$	13.0457	−	8.85293i	0.507804	−	0.344600i
$661$	33.8258	−	28.3832i	1.31567	−	1.10398i	0.328468	−	0.944515i	$-0.393468\pi$
$661$	33.8258	−	28.3832i	1.31567	−	1.10398i	0.987204	−	0.159465i	$-0.0509768\pi$
$662$	5.90457	+	7.03679i	0.229487	+	0.273493i
$663$	2.37634	−	18.1512i	0.0922892	−	0.704934i
$664$	−13.3688	+	4.86583i	−0.518808	+	0.188831i
$665$	−1.96378	+	1.74474i	−0.0761522	+	0.0676583i
$666$	5.82256	+	21.6054i	0.225620	+	0.837192i
$667$	2.81928	+	1.62771i	0.109163	+	0.0630252i
$668$	10.6577	+	1.87924i	0.412358	+	0.0727098i
$669$	−1.53547	−	34.5955i	−0.0593647	−	1.33754i
$670$	21.1576	+	3.11680i	0.817388	+	0.120412i
$671$	5.50359	+	31.2124i	0.212464	+	1.20494i
$672$	0.891090	+	0.280253i	0.0343745	+	0.0108110i
$673$	−18.4578	+	21.9972i	−0.711497	+	0.847929i	−0.993775	−	0.111404i	$-0.964465\pi$
$673$	−18.4578	+	21.9972i	−0.711497	+	0.847929i	0.282279	+	0.959332i	$0.408910\pi$
$674$	−23.2986			−0.897427
$675$	−9.25291	−	24.2772i	−0.356145	−	0.934431i
$676$	−6.93277			−0.266645
$677$	24.4113	−	29.0923i	0.938203	−	1.11811i	−0.0546194	−	0.998507i	$-0.517395\pi$
$677$	24.4113	−	29.0923i	0.938203	−	1.11811i	0.992822	−	0.119599i	$-0.0381610\pi$
$678$	23.5551	−	21.6155i	0.904626	−	0.830138i
$679$	−0.177147	−	1.00465i	−0.00679829	−	0.0385550i
$680$	9.49211	+	1.39832i	0.364006	+	0.0536230i
$681$	−35.2500	+	22.4925i	−1.35078	+	0.861915i
$682$	−29.7310	−	5.24239i	−1.13846	−	0.200741i
$683$	−35.7083	−	20.6162i	−1.36634	−	0.788856i	−0.375880	−	0.926668i	$-0.622660\pi$
$683$	−35.7083	−	20.6162i	−1.36634	−	0.788856i	−0.990458	+	0.137812i	$0.955993\pi$
$684$	6.50916	−	0.578939i	0.248884	−	0.0221363i
$685$	−11.8230	+	10.5043i	−0.451733	+	0.401347i
$686$	6.94766	−	2.52874i	0.265263	−	0.0965478i
$687$	16.3779	+	12.5485i	0.624857	+	0.478754i
$688$	5.13620	+	6.12108i	0.195816	+	0.233364i
$689$	−0.219325	+	0.184036i	−0.00835562	+	0.00701120i
$690$	−15.5693	−	7.53952i	−0.592713	−	0.287025i
$691$	−0.00336697	+	0.00122548i	−0.000128086	+	4.66193e-5i	−0.342084	−	0.939669i	$-0.611133\pi$
$691$	−0.00336697	+	0.00122548i	−0.000128086	+	4.66193e-5i	0.341956	+	0.939716i	$0.388911\pi$
$692$	21.0656	−	12.1622i	0.800794	−	0.462339i
$693$	5.38969	−	3.78550i	0.204737	−	0.143799i
$694$	−6.79928	+	11.7767i	−0.258097	+	0.447037i
$695$	0.0539180	+	1.90666i	0.00204523	+	0.0723236i
$696$	−1.06421	+	0.679056i	−0.0403388	+	0.0257396i
$697$	11.1541	−	30.6457i	0.422493	−	1.16079i
$698$	−3.92607	+	0.692272i	−0.148604	+	0.0262029i
$699$	17.4775	+	19.0458i	0.661062	+	0.720379i
$700$	−0.777610	+	2.58202i	−0.0293909	+	0.0975913i
$701$	11.4392			0.432052			0.216026	−	0.976388i	$-0.430690\pi$
$701$	11.4392			0.432052			0.216026	+	0.976388i	$0.430690\pi$
$702$	−7.81351	−	10.1373i	−0.294902	−	0.382607i
$703$		−	16.2473i		−	0.612778i
$704$	3.11837	+	2.61663i	0.117528	+	0.0986178i
$705$	3.65479	−	35.7396i	0.137647	−	1.34603i
$706$	−0.949154	−	5.38292i	−0.0357219	−	0.202589i
$707$	0.0689507	−	0.189441i	0.00259316	−	0.00712464i
$708$	−18.8943	+	0.838595i	−0.710091	+	0.0315163i
$709$	0.817504	−	4.63629i	0.0307020	−	0.174120i	−0.965601	−	0.260028i	$-0.916268\pi$
$709$	0.817504	−	4.63629i	0.0307020	−	0.174120i	0.996303	+	0.0859085i	$0.0273793\pi$
$710$	29.6641	+	9.85655i	1.11328	+	0.369910i
$711$	15.5165	+	4.13365i	0.581913	+	0.155024i
$712$	8.30170	−	4.79299i	0.311120	−	0.179625i
$713$	11.3294	+	31.1272i	0.424288	+	1.16572i
$714$	3.97423	+	0.520302i	0.148732	+	0.0194718i
$715$	17.5760	+	13.9207i	0.657305	+	0.520603i
$716$	3.94779	−	3.31259i	0.147536	−	0.123797i
$717$	−20.4290	+	8.47923i	−0.762935	+	0.316663i
$718$	−2.16210	−	5.94032i	−0.0806889	−	0.221691i
$719$	−8.53531	−	14.7836i	−0.318313	−	0.551335i	0.661823	−	0.749660i	$-0.269783\pi$
$719$	−8.53531	−	14.7836i	−0.318313	−	0.551335i	−0.980136	+	0.198325i	$0.936450\pi$
$720$	5.37830	−	4.00922i	0.200437	−	0.149415i
$721$	−1.16314	+	2.01461i	−0.0433175	+	0.0750282i
$722$	14.0385	+	2.47537i	0.522459	+	0.0921236i
$723$	−19.4579	+	37.4441i	−0.723646	+	1.39256i
$724$	7.94622	+	2.89219i	0.295319	+	0.107487i
$725$	−1.99756	−	3.04799i	−0.0741876	−	0.113200i
$726$	9.41902	−	2.09527i	0.349572	−	0.0777629i
$727$	−19.5543	+	23.3039i	−0.725229	+	0.864294i	−0.995128	−	0.0985945i	$-0.968565\pi$
$727$	−19.5543	+	23.3039i	−0.725229	+	0.864294i	0.269899	+	0.962889i	$0.413010\pi$
$728$			1.32843i			0.0492348i
$729$	−6.87520	+	26.1100i	−0.254637	+	0.967037i
$730$	5.75968	−	1.18437i	0.213175	−	0.0438355i
$731$	26.2644	+	22.0385i	0.971425	+	0.815122i
$732$	2.92826	+	13.1636i	0.108232	+	0.486540i
$733$	−45.0180	+	7.93788i	−1.66278	+	0.293192i	−0.924465	−	0.381268i	$-0.875488\pi$
$733$	−45.0180	+	7.93788i	−1.66278	+	0.293192i	−0.738311	+	0.674460i	$0.764377\pi$
$734$	17.3734	+	6.32341i	0.641265	+	0.233401i
$735$	7.09199	−	24.9978i	0.261592	−	0.922059i
$736$	0.775604	−	4.39867i	0.0285891	−	0.162137i
$737$	33.7169	+	19.4665i	1.24198	+	0.717056i
$738$	−9.66617	−	20.6514i	−0.355817	−	0.760187i
$739$	−2.88611	−	4.99888i	−0.106167	−	0.183887i	0.808047	−	0.589118i	$-0.200525\pi$
$739$	−2.88611	−	4.99888i	−0.106167	−	0.183887i	−0.914214	+	0.405231i	$0.867191\pi$
$740$	−8.74409	−	14.2023i	−0.321439	−	0.522087i
$741$	3.56259	+	8.58334i	0.130875	+	0.315317i
$742$	−0.0402948	−	0.0480215i	−0.00147927	−	0.00176293i
$743$	19.3095	+	23.0121i	0.708395	+	0.844233i	0.993449	−	0.114279i	$-0.0364557\pi$
$743$	19.3095	+	23.0121i	0.708395	+	0.844233i	−0.285053	+	0.958512i	$0.592011\pi$
$744$	−12.7366	−	1.66747i	−0.466948	−	0.0611323i
$745$	−9.67214	+	5.95496i	−0.354360	+	0.218173i
$746$	1.77944	+	3.08209i	0.0651501	+	0.112843i
$747$	−10.9870	+	41.2418i	−0.401992	+	1.50896i
$748$	15.1267	+	8.73342i	0.553088	+	0.319325i
$749$	0.403533	−	2.28855i	0.0147448	−	0.0836218i
$750$	11.7620	+	15.3836i	0.429487	+	0.561730i
$751$	−16.7944	−	6.11265i	−0.612835	−	0.223054i	0.0169082	−	0.999857i	$-0.494618\pi$
$751$	−16.7944	−	6.11265i	−0.612835	−	0.223054i	−0.629743	+	0.776803i	$0.716840\pi$
$752$	9.13513	−	1.61077i	0.333124	−	0.0587388i
$753$	40.2665	+	12.6641i	1.46739	+	0.461504i
$754$	−1.37527	−	1.15398i	−0.0500842	−	0.0420256i
$755$	9.01250	−	1.85325i	0.327999	−	0.0674467i
$756$	2.21957	−	1.71078i	0.0807249	−	0.0622204i
$757$			34.8600i			1.26701i	0.773739	+	0.633504i	$0.218384\pi$
$757$			34.8600i			1.26701i	−0.773739	+	0.633504i	$0.781616\pi$
$758$	0.672533	−	0.801493i	0.0244275	−	0.0291115i
$759$	−21.2926	−	23.2032i	−0.772874	−	0.842223i
$760$	−4.52813	+	1.79463i	−0.164253	+	0.0650979i
$761$	17.5585	+	6.39077i	0.636495	+	0.231665i	0.640056	−	0.768328i	$-0.278911\pi$
$761$	17.5585	+	6.39077i	0.636495	+	0.231665i	−0.00356090	+	0.999994i	$0.501133\pi$
$762$	9.08575	+	14.2391i	0.329142	+	0.515828i
$763$	−10.4972	−	1.85095i	−0.380026	−	0.0670088i
$764$	10.6649	−	18.4721i	0.385842	−	0.668297i
$765$	19.7395	−	20.9488i	0.713682	−	0.757406i
$766$	3.78565	+	6.55694i	0.136781	+	0.236912i
$767$	−9.19908	−	25.2743i	−0.332160	−	0.912601i
$768$	1.37489	+	1.05341i	0.0496120	+	0.0380118i
$769$	20.4455	−	17.1558i	0.737282	−	0.618653i	−0.194824	−	0.980838i	$-0.562414\pi$
$769$	20.4455	−	17.1558i	0.737282	−	0.618653i	0.932106	+	0.362185i	$0.117969\pi$
$770$	−3.04795	+	3.84829i	−0.109840	+	0.138683i
$771$	30.8278	−	40.2357i	1.11024	−	1.44905i
$772$	−3.78546	−	10.4005i	−0.136242	−	0.374321i
$773$	−13.3630	+	7.71514i	−0.480634	+	0.277494i	−0.720681	−	0.693267i	$-0.756171\pi$
$773$	−13.3630	+	7.71514i	−0.480634	+	0.277494i	0.240047	+	0.970761i	$0.422837\pi$
$774$	23.8773	−	2.12370i	0.858250	−	0.0763347i
$775$	4.36509	−	36.8234i	0.156799	−	1.32274i
$776$	0.328467	−	1.86283i	0.0117913	−	0.0668717i
$777$	−3.74780	−	5.87352i	−0.134452	−	0.210711i
$778$	−6.88588	+	18.9188i	−0.246871	+	0.678271i
$779$	2.87494	+	16.3046i	0.103006	+	0.584173i
$780$	7.73363	+	5.58564i	0.276908	+	0.199998i
$781$	43.5929	+	36.5788i	1.55988	+	1.30889i
$782$		−	19.1650i		−	0.685340i
$783$	−0.157010	+	3.78395i	−0.00561107	+	0.135227i
$784$	6.70914			0.239612
$785$	−12.7839	+	23.6628i	−0.456275	+	0.844562i
$786$	2.53202	−	8.05079i	0.0903143	−	0.287162i
$787$	−33.9745	+	5.99062i	−1.21106	+	0.213542i	−0.742473	−	0.669876i	$-0.766347\pi$
$787$	−33.9745	+	5.99062i	−1.21106	+	0.213542i	−0.468586	+	0.883418i	$0.655236\pi$
$788$	2.68361	−	7.37316i	0.0955997	−	0.262658i
$789$	−0.685276	−	15.4399i	−0.0243965	−	0.549674i
$790$	−11.9639	+	0.338324i	−0.425656	+	0.0120370i
$791$	−4.97728	+	8.62091i	−0.176972	+	0.306524i
$792$	11.7916	−	3.17777i	0.418995	−	0.112917i
$793$	−16.6084	+	9.58886i	−0.589781	+	0.340510i
$794$	−12.5374	+	4.56323i	−0.444934	+	0.161943i
$795$	−0.448992	+	0.0326658i	−0.0159241	+	0.00115854i
$796$	−7.58085	+	6.36108i	−0.268696	+	0.225463i
$797$	3.57242	+	4.25745i	0.126542	+	0.150806i	0.825595	−	0.564263i	$-0.190840\pi$
$797$	3.57242	+	4.25745i	0.126542	+	0.150806i	−0.699054	+	0.715069i	$0.746395\pi$
$798$	−1.87933	+	0.780033i	−0.0665277	+	0.0276129i
$799$	37.4015	−	13.6130i	1.32317	−	0.481595i
$800$	−2.99235	+	4.00573i	−0.105795	+	0.141624i
$801$	2.46510	−	28.6521i	0.0870999	−	1.01237i
$802$	−25.4288	−	14.6813i	−0.897920	−	0.518415i
$803$	10.5422	+	1.85888i	0.372027	+	0.0655984i
$804$	14.6992	+	7.63848i	0.518403	+	0.269388i
$805$	5.32887	+	0.785015i	0.187818	+	0.0276682i
$806$	−3.17212	−	17.9900i	−0.111733	−	0.633671i
$807$	−3.43912	−	15.4601i	−0.121063	−	0.544222i
$808$	0.240277	−	0.286351i	0.00845291	−	0.0100738i
$809$	1.58313			0.0556599			0.0278299	−	0.999613i	$-0.491140\pi$
$809$	1.58313			0.0556599			0.0278299	+	0.999613i	$0.491140\pi$
$810$	−0.626899	−	20.1148i	−0.0220270	−	0.706764i
$811$	−22.1659			−0.778351			−0.389175	−	0.921164i	$-0.627240\pi$
$811$	−22.1659			−0.778351			−0.389175	+	0.921164i	$0.627240\pi$
$812$	0.252666	−	0.301116i	0.00886685	−	0.0105671i
$813$	−7.75883	−	34.8788i	−0.272114	−	1.22325i
$814$	−5.27242	−	29.9014i	−0.184798	−	1.04804i
$815$	0.645652	−	4.38284i	0.0226162	−	0.153524i
$816$	6.59466	+	3.42692i	0.230859	+	0.119966i
$817$	−17.1412	−	3.02245i	−0.599694	−	0.105742i
$818$	26.2632	+	15.1631i	0.918271	+	0.530164i
$819$	3.26785	+	2.28115i	0.114188	+	0.0797099i
$820$	11.2880	+	12.7052i	0.394195	+	0.443683i
$821$	9.63738	−	3.50772i	0.336347	−	0.122420i	−0.168325	−	0.985732i	$-0.553836\pi$
$821$	9.63738	−	3.50772i	0.336347	−	0.122420i	0.504672	+	0.863311i	$0.331614\pi$
$822$	−11.3146	+	4.69620i	−0.394640	+	0.163799i
$823$	14.3467	+	17.0977i	0.500093	+	0.595988i	0.955755	−	0.294165i	$-0.0950416\pi$
$823$	14.3467	+	17.0977i	0.500093	+	0.595988i	−0.455661	+	0.890153i	$0.650597\pi$
$824$	−3.30425	+	2.77259i	−0.115109	+	0.0965878i
$825$	9.58762	+	33.9249i	0.333798	+	1.18112i
$826$	5.53383	−	2.01415i	0.192547	−	0.0700813i
$827$	6.88573	−	3.97548i	0.239440	−	0.138241i	−0.375479	−	0.926831i	$-0.622522\pi$
$827$	6.88573	−	3.97548i	0.239440	−	0.138241i	0.614920	+	0.788590i	$0.289188\pi$
$828$	−9.48858	−	9.46125i	−0.329751	−	0.328801i
$829$	2.41490	−	4.18273i	0.0838731	−	0.145272i	−0.821037	−	0.570874i	$-0.806604\pi$
$829$	2.41490	−	4.18273i	0.0838731	−	0.145272i	0.904910	+	0.425602i	$0.139938\pi$
$830$	−0.899244	−	31.7992i	−0.0312132	−	1.10377i
$831$	1.42043	+	32.0035i	0.0492741	+	1.11019i
$832$	−0.842455	+	2.31463i	−0.0292069	+	0.0802452i
$833$	28.3503	−	4.99893i	0.982281	−	0.173203i
$834$	−0.443271	+	1.40942i	−0.0153492	+	0.0488042i
$835$	−11.5022	+	21.2905i	−0.398051	+	0.736789i
$836$	−8.86726			−0.306680
$837$	−25.9730	+	28.4680i	−0.897758	+	0.983997i
$838$		−	40.5072i		−	1.39930i
$839$	−12.7392	−	10.6895i	−0.439807	−	0.369042i	0.395830	−	0.918324i	$-0.370457\pi$
$839$	−12.7392	−	10.6895i	−0.439807	−	0.369042i	−0.835637	+	0.549282i	$0.814901\pi$
$840$	−1.22298	+	1.69329i	−0.0421970	+	0.0584240i
$841$	−4.94355	−	28.0363i	−0.170467	−	0.966768i
$842$	9.10554	−	25.0173i	0.313798	−	0.862152i
$843$	−19.0811	−	29.9037i	−0.657188	−	1.02994i
$844$	−4.69024	+	26.5997i	−0.161445	+	0.915598i
$845$	4.88815	−	14.7113i	0.168157	−	0.506084i
$846$	11.7243	−	25.2378i	0.403090	−	0.867694i
$847$	−2.60199	+	1.50226i	−0.0894056	+	0.0516183i
$848$	−0.0397549	−	0.109226i	−0.00136519	−	0.00375083i
$849$	−14.5026	+	18.9284i	−0.497727	+	0.649620i
$850$	−9.65991	+	19.1563i	−0.331332	+	0.657055i
$851$	−25.5205	+	21.4142i	−0.874832	+	0.734071i
$852$	19.2201	+	14.7261i	0.658468	+	0.504506i
$853$	16.5267	+	45.4068i	0.565865	+	1.55470i	0.810899	+	0.585186i	$0.198979\pi$
$853$	16.5267	+	45.4068i	0.565865	+	1.55470i	−0.245034	+	0.969514i	$0.578799\pi$
$854$	−2.09949	−	3.63643i	−0.0718432	−	0.124436i
$855$	−3.36096	+	14.2206i	−0.114943	+	0.486335i
$856$	2.15445	−	3.73162i	0.0736376	−	0.127544i
$857$	5.42516	+	0.956602i	0.185320	+	0.0326769i	0.265538	−	0.964100i	$-0.414450\pi$
$857$	5.42516	+	0.956602i	0.185320	+	0.0326769i	−0.0802178	+	0.996777i	$0.525562\pi$
$858$	9.34196	+	14.6406i	0.318929	+	0.499823i
$859$	22.5455	+	8.20589i	0.769242	+	0.279981i	0.696679	−	0.717383i	$-0.254660\pi$
$859$	22.5455	+	8.20589i	0.769242	+	0.279981i	0.0725627	+	0.997364i	$0.476882\pi$
$860$	−16.6103	+	6.58314i	−0.566407	+	0.224483i
$861$	4.80034	+	5.23108i	0.163595	+	0.178275i
$862$	15.2547	−	18.1799i	0.519577	−	0.619208i
$863$		−	20.5253i		−	0.698689i	−0.936994	−	0.349344i	$-0.886404\pi$
$863$		−	20.5253i		−	0.698689i	0.936994	−	0.349344i	$-0.113596\pi$
$864$	4.95227	−	1.57323i	0.168480	−	0.0535224i
$865$	10.9553	+	53.2764i	0.372491	+	1.81145i
$866$	−14.4003	−	12.0833i	−0.489341	−	0.410606i
$867$	2.33150	+	0.733272i	0.0791820	+	0.0249032i
$868$	3.93893	−	0.694540i	0.133696	−	0.0235742i
$869$	−20.4748	−	7.45223i	−0.694561	−	0.252800i
$870$	−0.690602	−	2.73704i	−0.0234136	−	0.0927943i
$871$	−4.09080	+	23.2001i	−0.138611	+	0.786104i
$872$	−17.1164	−	9.88214i	−0.579633	−	0.334652i
$873$	−4.01840	−	4.00683i	−0.136002	−	0.135611i
$874$	4.86468	+	8.42588i	0.164550	+	0.285010i
$875$	−4.93077	−	3.47061i	−0.166690	−	0.117328i
$876$	4.51624	+	0.591261i	0.152590	+	0.0199769i
$877$	−28.4839	−	33.9458i	−0.961833	−	1.14627i	−0.989190	−	0.146642i	$-0.953153\pi$
$877$	−28.4839	−	33.9458i	−0.961833	−	1.14627i	0.0273565	−	0.999626i	$-0.491291\pi$
$878$	−11.7793	−	14.0381i	−0.397533	−	0.473762i
$879$	−8.22957	−	19.8275i	−0.277577	−	0.668764i
$880$	−7.75117	+	4.77225i	−0.261292	+	0.160872i
$881$	3.94879	+	6.83950i	0.133038	+	0.230429i	0.924846	−	0.380341i	$-0.124193\pi$
$881$	3.94879	+	6.83950i	0.133038	+	0.230429i	−0.791808	+	0.610770i	$0.790860\pi$
$882$	11.5208	−	16.5040i	0.387926	−	0.555720i
$883$	−8.09566	−	4.67403i	−0.272441	−	0.157294i	0.357556	−	0.933892i	$-0.383610\pi$
$883$	−8.09566	−	4.67403i	−0.272441	−	0.157294i	−0.629996	+	0.776598i	$0.716944\pi$
$884$	−1.83529	+	10.4085i	−0.0617276	+	0.350074i
$885$	11.5425	−	40.6849i	0.387996	−	1.36761i
$886$	−15.8079	−	5.75361i	−0.531077	−	0.193296i
$887$	−1.37077	+	0.241704i	−0.0460260	+	0.00811563i	−0.196614	−	0.980481i	$-0.562995\pi$
$887$	−1.37077	+	0.241704i	−0.0460260	+	0.00811563i	0.150588	+	0.988597i	$0.451883\pi$
$888$	−2.80526	−	12.6107i	−0.0941384	−	0.423187i
$889$	−4.02892	−	3.38067i	−0.135126	−	0.113384i
$890$	4.31735	+	20.9956i	0.144718	+	0.703775i
$891$	12.4311	−	34.4633i	0.416459	−	1.15456i
$892$			19.9934i			0.669429i
$893$	−12.9881	+	15.4786i	−0.434630	+	0.517972i
$894$	−8.58821	+	1.91046i	−0.287233	+	0.0638953i
$895$	4.24580	+	10.7128i	0.141921	+	0.358090i
$896$	−0.506791	−	0.184457i	−0.0169307	−	0.00616226i
$897$	8.78676	−	16.9090i	0.293381	−	0.564574i
$898$	−5.64357	−	0.995113i	−0.188328	−	0.0332073i
$899$	−2.70266	+	4.68115i	−0.0901388	+	0.156125i
$900$	4.71543	+	14.2395i	0.157181	+	0.474652i
$901$	−0.249373	−	0.431926i	−0.00830781	−	0.0143896i
$902$	10.5821	+	29.0740i	0.352344	+	0.968057i
$903$	−6.89387	+	2.86136i	−0.229414	+	0.0952201i
$904$	−14.1395	+	11.8644i	−0.470272	+	0.394605i
$905$	−11.7399	+	14.8226i	−0.390248	+	0.492721i
$906$	7.06682	+	0.925180i	0.234779	+	0.0307370i
$907$	−1.20927	−	3.32245i	−0.0401532	−	0.110320i	0.917996	−	0.396590i	$-0.129807\pi$
$907$	−1.20927	−	3.32245i	−0.0401532	−	0.110320i	−0.958149	+	0.286270i	$0.907584\pi$
$908$	20.9074	−	12.0709i	0.693837	−	0.400587i
$909$	−0.291805	−	1.08278i	−0.00967856	−	0.0359136i
$910$	−2.81892	−	0.936646i	−0.0934462	−	0.0310495i
$911$	−8.19262	+	46.4627i	−0.271434	+	1.53938i	0.478633	+	0.878015i	$0.341132\pi$
$911$	−8.19262	+	46.4627i	−0.271434	+	1.53938i	−0.750067	+	0.661362i	$0.769979\pi$
$912$	−3.76919	+	0.167290i	−0.124810	+	0.00553952i
$913$	19.8076	−	54.4208i	0.655535	−	1.80107i
$914$	−1.53683	−	8.71579i	−0.0508338	−	0.288293i
$915$	−29.9977	−	3.06761i	−0.991694	−	0.101412i
$916$	−9.12526	−	7.65700i	−0.301507	−	0.252995i
$917$			2.62786i			0.0867797i
$918$	19.7542	−	10.3378i	0.651987	−	0.341198i
$919$	29.2135			0.963666			0.481833	−	0.876263i	$-0.339971\pi$
$919$	29.2135			0.963666			0.481833	+	0.876263i	$0.339971\pi$
$920$	8.78709	+	4.74723i	0.289702	+	0.156512i
$921$	37.5505	+	40.9199i	1.23733	+	1.34836i
$922$	20.3471	−	3.58775i	0.670097	−	0.118156i
$923$	−11.7770	+	32.3570i	−0.387644	+	1.06504i
$924$	−3.20558	+	2.04543i	−0.105456	+	0.0672898i
$925$	36.3025	−	8.54118i	1.19362	−	0.280832i
$926$	4.38067	−	7.58754i	0.143958	−	0.249342i
$927$	1.14640	+	12.8893i	0.0376528	+	0.423340i
$928$	0.631201	−	0.364424i	0.0207202	−	0.0119628i
$929$	11.0326	−	4.01553i	0.361967	−	0.131745i	−0.154633	−	0.987972i	$-0.549420\pi$
$929$	11.0326	−	4.01553i	0.361967	−	0.131745i	0.516600	+	0.856227i	$0.327197\pi$
$930$	12.5187	−	25.8514i	0.410504	−	0.847700i
$931$	−11.1953	+	9.39397i	−0.366911	+	0.307875i
$932$	−9.59318	−	11.4327i	−0.314235	−	0.374491i
$933$	−2.01955	−	1.54734i	−0.0661169	−	0.0506576i
$934$	−2.32356	+	0.845707i	−0.0760292	+	0.0276724i
$935$	−29.1978	+	25.9411i	−0.954870	+	0.848364i
$936$	4.24718	+	6.04702i	0.138823	+	0.197653i
$937$	−22.2280	−	12.8334i	−0.726159	−	0.419248i	0.0908566	−	0.995864i	$-0.471039\pi$
$937$	−22.2280	−	12.8334i	−0.726159	−	0.419248i	−0.817015	+	0.576616i	$0.804373\pi$
$938$	−5.07969	−	0.895686i	−0.165858	−	0.0292452i
$939$	26.3657	−	16.8235i	0.860412	−	0.549016i
$940$	−3.02294	+	20.5204i	−0.0985974	+	0.669303i
$941$	−3.73531	−	21.1840i	−0.121768	−	0.690578i	−0.983175	−	0.182664i	$-0.941528\pi$
$941$	−3.73531	−	21.1840i	−0.121768	−	0.690578i	0.861408	−	0.507914i	$-0.169583\pi$
$942$	−15.3495	+	14.0856i	−0.500115	+	0.458935i
$943$	21.8213	−	26.0057i	0.710600	−	0.846861i
$944$	10.9194			0.355395
$945$	2.06529	+	5.91615i	0.0671839	+	0.192452i
$946$	−32.5273			−1.05755
$947$	13.8601	−	16.5178i	0.450392	−	0.536756i	−0.492298	−	0.870427i	$-0.663843\pi$
$947$	13.8601	−	16.5178i	0.450392	−	0.536756i	0.942690	+	0.333671i	$0.108287\pi$
$948$	−8.84380	−	2.78143i	−0.287233	−	0.0903367i
$949$	1.12479	+	6.37901i	0.0365123	+	0.207071i
$950$	−0.615501	−	10.8740i	−0.0199695	−	0.352800i
$951$	−2.55933	−	57.6639i	−0.0829918	−	1.86988i
$952$	−2.27895	−	0.401840i	−0.0738611	−	0.0130237i
$953$	−2.26739	−	1.30908i	−0.0734480	−	0.0424052i	0.462826	−	0.886449i	$-0.346835\pi$
$953$	−2.26739	−	1.30908i	−0.0734480	−	0.0424052i	−0.536274	+	0.844044i	$0.680169\pi$
$954$	−0.336955	−	0.0897661i	−0.0109093	−	0.00290628i
$955$	31.6782	+	35.6551i	1.02508	+	1.15377i
$956$	12.0002	−	4.36770i	0.388113	−	0.141261i
$957$	0.667090	−	5.09544i	0.0215640	−	0.164712i
$958$	10.9242	+	13.0189i	0.352944	+	0.420622i
$959$	2.92205	−	2.45189i	0.0943580	−	0.0791758i
$960$	−3.20474	+	2.17477i	−0.103433	+	0.0701903i
$961$	−22.5534	+	8.20875i	−0.727528	+	0.264798i
$962$	15.9108	−	9.18609i	0.512984	−	0.296172i
$963$	−5.47995	−	11.7077i	−0.176589	−	0.377275i
$964$	12.1815	−	21.0990i	0.392340	−	0.679553i
$965$	24.7388	−	0.699584i	0.796371	−	0.0225204i
$966$	3.70224	+	1.92387i	0.119118	+	0.0618996i
$967$	−4.40078	+	12.0910i	−0.141520	+	0.388822i	−0.990122	−	0.140209i	$-0.955222\pi$
$967$	−4.40078	+	12.0910i	−0.141520	+	0.388822i	0.848602	+	0.529031i	$0.177445\pi$
$968$	−5.48636	+	0.967393i	−0.176338	+	0.0310932i
$969$	−15.8026	+	3.51530i	−0.507651	+	0.112928i
$970$	3.72132	+	2.01045i	0.119484	+	0.0645516i
$971$	15.9136			0.510691			0.255345	−	0.966850i	$-0.417811\pi$
$971$	15.9136			0.510691			0.255345	+	0.966850i	$0.417811\pi$
$972$	4.63390	−	14.8838i	0.148632	−	0.477398i
$973$		−	0.460049i		−	0.0147485i
$974$	−22.2417	−	18.6630i	−0.712668	−	0.598000i
$975$	−17.3055	+	12.4724i	−0.554220	+	0.399437i
$976$	−1.35199	−	7.66749i	−0.0432760	−	0.245430i
$977$	11.4374	−	31.4239i	0.365914	−	1.00534i	−0.610985	−	0.791642i	$-0.709227\pi$
$977$	11.4374	−	31.4239i	0.365914	−	1.00534i	0.976900	−	0.213699i	$-0.0685512\pi$
$978$	1.58233	−	3.04498i	0.0505973	−	0.0973678i
$979$	−6.77612	+	38.4293i	−0.216566	+	1.22821i
$980$	−4.73047	+	14.2368i	−0.151109	+	0.454777i
$981$	−53.7014	+	25.1357i	−1.71455	+	0.802522i
$982$	−18.6986	+	10.7956i	−0.596696	+	0.344503i
$983$	−5.52588	−	15.1822i	−0.176248	−	0.484238i	0.819841	−	0.572591i	$-0.194062\pi$
$983$	−5.52588	−	15.1822i	−0.176248	−	0.484238i	−0.996089	+	0.0883534i	$0.971840\pi$
$984$	5.04661	+	12.1588i	0.160880	+	0.387608i
$985$	13.7537	+	10.8933i	0.438228	+	0.347088i
$986$	2.39569	−	2.01023i	0.0762944	−	0.0640186i
$987$	−1.12481	+	8.59165i	−0.0358031	+	0.273475i
$988$	−1.83511	−	5.04192i	−0.0583826	−	0.160405i
$989$	17.8449	+	30.9082i	0.567434	+	0.982825i
$990$	−1.57075	+	27.2622i	−0.0499218	+	0.866450i
$991$	17.0726	−	29.5706i	0.542329	−	0.939342i	−0.456440	−	0.889754i	$-0.650876\pi$
$991$	17.0726	−	29.5706i	0.542329	−	0.939342i	0.998770	−	0.0495881i	$-0.0157909\pi$
$992$	7.30358	+	1.28782i	0.231889	+	0.0408883i
$993$	−15.8948	+	0.705465i	−0.504405	+	0.0223872i
$994$	−7.08461	−	2.57859i	−0.224710	−	0.0817878i
$995$	−8.15310	−	20.5716i	−0.258471	−	0.652163i
$996$	7.39287	−	23.5063i	0.234252	−	0.744825i
$997$	−5.26635	+	6.27619i	−0.166787	+	0.198769i	−0.842964	−	0.537971i	$-0.819191\pi$
$997$	−5.26635	+	6.27619i	−0.166787	+	0.198769i	0.676177	+	0.736740i	$0.263636\pi$
$998$		−	1.81920i		−	0.0575858i
$999$	−35.8386	−	14.7541i	−1.13388	−	0.466798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.p.a.259.14	yes	108
3.2	odd	2		810.2.p.a.289.1		108
5.4	even	2	inner	270.2.p.a.259.5	yes	108
15.14	odd	2		810.2.p.a.289.10		108
27.5	odd	18		810.2.p.a.199.10		108
27.22	even	9	inner	270.2.p.a.49.5	✓	108
135.49	even	18	inner	270.2.p.a.49.14	yes	108
135.59	odd	18		810.2.p.a.199.1		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.p.a.49.5	✓	108	27.22	even	9	inner
270.2.p.a.49.14	yes	108	135.49	even	18	inner
270.2.p.a.259.5	yes	108	5.4	even	2	inner
270.2.p.a.259.14	yes	108	1.1	even	1	trivial
810.2.p.a.199.1		108	135.59	odd	18
810.2.p.a.199.10		108	27.5	odd	18
810.2.p.a.289.1		108	3.2	odd	2
810.2.p.a.289.10		108	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.376104 + 1.69072i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.21219 + 0.325886i) q^{5} +(1.53692 + 0.798664i) q^{6} +(-0.531122 - 0.0936511i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.71709 + 1.27178i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.376104 + 1.69072i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.21219 + 0.325886i) q^{5} +(1.53692 + 0.798664i) q^{6} +(-0.531122 - 0.0936511i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.71709 + 1.27178i) q^{9} +(1.67161 - 1.48516i) q^{10} +(3.82525 - 1.39228i) q^{11} +(1.59973 - 0.663981i) q^{12} +(1.58330 + 1.88690i) q^{13} +(-0.413139 + 0.346665i) q^{14} +(0.281031 + 3.86277i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.71596 + 2.14541i) q^{17} +(-0.772277 + 2.89889i) q^{18} +(1.08914 - 1.88645i) q^{19} +(-0.0632081 - 2.23517i) q^{20} +(-0.0414188 - 0.933203i) q^{21} +(1.39228 - 3.82525i) q^{22} +(-4.39867 + 0.775604i) q^{23} +(0.519646 - 1.65226i) q^{24} +(4.78760 + 1.44185i) q^{25} +2.46317 q^{26} +(-3.17213 - 4.11553i) q^{27} +0.539315i q^{28} +(-0.558330 - 0.468495i) q^{29} +(3.13970 + 2.26766i) q^{30} +(-1.28782 - 7.30358i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(3.79265 + 5.94380i) q^{33} +(-0.745092 + 4.22563i) q^{34} +(-1.14442 - 0.380260i) q^{35} +(1.72427 + 2.45497i) q^{36} +(6.45946 - 3.72937i) q^{37} +(-0.745018 - 2.04692i) q^{38} +(-2.59474 + 3.38659i) q^{39} +(-1.75287 - 1.38832i) q^{40} +(-5.82235 + 4.88553i) q^{41} +(-0.741498 - 0.568122i) q^{42} +(-2.73291 - 7.50862i) q^{43} +(-2.03537 - 3.52537i) q^{44} +(-6.42519 + 1.92795i) q^{45} +(-2.23326 + 3.86812i) q^{46} +(-9.13513 - 1.61077i) q^{47} +(-0.931683 - 1.46013i) q^{48} +(-6.30453 - 2.29466i) q^{49} +(4.18193 - 2.74071i) q^{50} +(-5.02488 - 5.47576i) q^{51} +(1.58330 - 1.88690i) q^{52} +0.116236i q^{53} +(-5.19169 - 0.215421i) q^{54} +(8.91592 - 1.83339i) q^{55} +(0.413139 + 0.346665i) q^{56} +(3.59910 + 1.13194i) q^{57} +(-0.717776 + 0.126563i) q^{58} +(-10.2609 - 3.73464i) q^{59} +(3.75529 - 0.947525i) q^{60} +(-1.35199 + 7.66749i) q^{61} +(-6.42266 - 3.70813i) q^{62} +(1.56221 - 0.421009i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.88765 + 4.69016i) q^{65} +(6.99109 + 0.915265i) q^{66} +(6.14767 + 7.32650i) q^{67} +(2.75808 + 3.28696i) q^{68} +(-2.96569 - 7.14522i) q^{69} +(-1.02692 + 0.632254i) q^{70} +(6.98968 + 12.1065i) q^{71} +(2.98896 + 0.257156i) q^{72} +(2.27739 + 1.31485i) q^{73} +(1.29520 - 7.34543i) q^{74} +(-0.637130 + 8.63679i) q^{75} +(-2.04692 - 0.745018i) q^{76} +(-2.16206 + 0.381230i) q^{77} +(0.926409 + 4.16455i) q^{78} +(-4.10029 - 3.44055i) q^{79} +(-2.19024 + 0.450382i) q^{80} +(5.76518 - 6.91106i) q^{81} +7.60054i q^{82} +(9.14477 - 10.8983i) q^{83} +(-0.911833 + 0.202839i) q^{84} +(-8.91957 + 3.53508i) q^{85} +(-7.50862 - 2.73291i) q^{86} +(0.582105 - 1.12019i) q^{87} +(-4.00891 - 0.706878i) q^{88} +(-4.79299 + 8.30170i) q^{89} +(-2.65313 + 6.16124i) q^{90} +(-0.664214 - 1.15045i) q^{91} +(1.52764 + 4.19716i) q^{92} +(11.8640 - 4.92425i) q^{93} +(-7.10587 + 5.96254i) q^{94} +(3.02416 - 3.81826i) q^{95} +(-1.71740 - 0.224840i) q^{96} +(0.646954 + 1.77749i) q^{97} +(-5.81028 + 3.35457i) q^{98} +(-8.62290 + 8.64781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9	\( 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9} - 12 q^{11} + 6 q^{14} + 18 q^{15} + 12 q^{20} - 72 q^{21} - 18 q^{25} - 72 q^{26} + 6 q^{29} + 36 q^{30} + 36 q^{31} + 18 q^{35} - 30 q^{36} - 48 q^{39} - 12 q^{41} - 12 q^{44} - 66 q^{45} + 18 q^{49} - 12 q^{50} + 48 q^{51} - 36 q^{54} - 6 q^{56} - 84 q^{59} + 18 q^{60} - 18 q^{61} + 54 q^{64} - 6 q^{65} - 60 q^{69} - 48 q^{74} + 12 q^{75} - 72 q^{79} - 12 q^{81} - 36 q^{86} - 132 q^{89} + 30 q^{90} - 36 q^{94} - 18 q^{95} - 36 q^{99}+O(q^{100}) \) 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9 - 12 * q^11 + 6 * q^14 + 18 * q^15 + 12 * q^20 - 72 * q^21 - 18 * q^25 - 72 * q^26 + 6 * q^29 + 36 * q^30 + 36 * q^31 + 18 * q^35 - 30 * q^36 - 48 * q^39 - 12 * q^41 - 12 * q^44 - 66 * q^45 + 18 * q^49 - 12 * q^50 + 48 * q^51 - 36 * q^54 - 6 * q^56 - 84 * q^59 + 18 * q^60 - 18 * q^61 + 54 * q^64 - 6 * q^65 - 60 * q^69 - 48 * q^74 + 12 * q^75 - 72 * q^79 - 12 * q^81 - 36 * q^86 - 132 * q^89 + 30 * q^90 - 36 * q^94 - 18 * q^95 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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