LMFDB - Embedded newform 270.2.p.a.49.5

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			49.5
Character	$\chi$	$=$	270.49
Dual form			270.2.p.a.259.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 - 0.766044i) q^{2} +(-0.376104 + 1.69072i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.90411 - 1.17233i) q^{5} +(1.53692 - 0.798664i) q^{6} +(0.531122 - 0.0936511i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.71709 - 1.27178i) q^{9} +O(q^{10})$	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.376104 + 1.69072i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.90411 - 1.17233i) 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} +(-2.12200 - 0.705079i) 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} +(1.26594 + 3.66025i) 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} +(0.823871 + 2.07876i) 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} +(2.25130 - 4.46449i) q^{25} +2.46317 q^{26} +(3.17213 - 4.11553i) q^{27} +0.539315i q^{28} +(-0.558330 + 0.468495i) q^{29} +(1.99018 - 3.32252i) 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} +(0.901527 - 0.800971i) 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} +(1.06285 - 1.96732i) 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} +(-6.66459 + 0.763716i) 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} +(-4.86710 + 1.14512i) 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} +(-3.82447 + 0.611109i) 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} +(-0.802714 + 5.44902i) 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} +(-1.19307 - 0.175755i) 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} +(6.70149 + 5.48543i) 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} +(9.59072 - 0.271214i) 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} +(4.86896 + 4.61446i) 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} +(4.28539 + 2.31519i) 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 $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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
$5$	1.90411	−	1.17233i	0.851546	−	0.524281i
$5$	1.90411	−	1.17233i	0.851546	−	0.524281i
$6$	1.53692	−	0.798664i	0.627447	−	0.326053i
$7$	0.531122	−	0.0936511i	0.200745	−	0.0353968i	−0.0723713	−	0.997378i	$-0.523057\pi$
$7$	0.531122	−	0.0936511i	0.200745	−	0.0353968i	0.273116	+	0.961981i	$0.411946\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−2.71709	−	1.27178i	−0.905697	−	0.423925i
$10$	−2.12200	−	0.705079i	−0.671034	−	0.222965i
$11$	3.82525	+	1.39228i	1.15336	+	0.419788i	0.846720	−	0.532039i	$-0.178574\pi$
$11$	3.82525	+	1.39228i	1.15336	+	0.419788i	0.306637	+	0.951826i	$0.400796\pi$
$12$	−1.59973	−	0.663981i	−0.461802	−	0.191675i
$13$	−1.58330	+	1.88690i	−0.439128	+	0.523332i	−0.939533	−	0.342459i	$-0.888740\pi$
$13$	−1.58330	+	1.88690i	−0.439128	+	0.523332i	0.500405	+	0.865792i	$0.333185\pi$
$14$	−0.413139	−	0.346665i	−0.110416	−	0.0926502i
$15$	1.26594	+	3.66025i	0.326863	+	0.945072i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.71596	+	2.14541i	0.901252	+	0.520338i	0.877606	−	0.479383i	$-0.159139\pi$
$17$	3.71596	+	2.14541i	0.901252	+	0.520338i	0.0236455	+	0.999720i	$0.492473\pi$
$18$	0.772277	+	2.89889i	0.182027	+	0.683276i
$19$	1.08914	+	1.88645i	0.249867	+	0.432782i	0.963489	−	0.267749i	$-0.0862799\pi$
$19$	1.08914	+	1.88645i	0.249867	+	0.432782i	−0.713622	+	0.700531i	$0.752947\pi$
$20$	0.823871	+	2.07876i	0.184223	+	0.464825i
$21$	−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	$-0.290259\pi$
$23$	4.39867	+	0.775604i	0.917185	+	0.161725i	0.304921	+	0.952378i	$0.401370\pi$
$24$	0.519646	+	1.65226i	0.106072	+	0.337266i
$25$	2.25130	−	4.46449i	0.450260	−	0.892898i
$26$	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	−0.693154	−	0.720790i	$-0.743779\pi$
$29$	−0.558330	+	0.468495i	−0.103679	+	0.0869973i	0.589474	+	0.807787i	$0.299335\pi$
$30$	1.99018	−	3.32252i	0.363356	−	0.606607i
$31$	−1.28782	+	7.30358i	−0.231299	+	1.31176i	0.618970	+	0.785414i	$0.287550\pi$
$31$	−1.28782	+	7.30358i	−0.231299	+	1.31176i	−0.850269	+	0.526348i	$0.823561\pi$
$32$	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
$35$	0.901527	−	0.800971i	0.152386	−	0.135389i
$36$	1.72427	−	2.45497i	0.287379	−	0.409162i
$37$	−6.45946	−	3.72937i	−1.06193	−	0.613105i	−0.135964	−	0.990714i	$-0.543413\pi$
$37$	−6.45946	−	3.72937i	−1.06193	−	0.613105i	−0.925965	+	0.377609i	$0.876746\pi$
$38$	0.745018	−	2.04692i	0.120858	−	0.332054i
$39$	−2.59474	−	3.38659i	−0.415491	−	0.542288i
$40$	1.06285	−	1.96732i	0.168051	−	0.311061i
$41$	−5.82235	−	4.88553i	−0.909298	−	0.762992i	0.0626873	−	0.998033i	$-0.480033\pi$
$41$	−5.82235	−	4.88553i	−0.909298	−	0.762992i	−0.971985	+	0.235042i	$0.924477\pi$
$42$	0.741498	−	0.568122i	0.114416	−	0.0876632i
$43$	2.73291	−	7.50862i	0.416765	−	1.14505i	−0.536759	−	0.843736i	$-0.680351\pi$
$43$	2.73291	−	7.50862i	0.416765	−	1.14505i	0.953524	−	0.301317i	$-0.0974264\pi$
$44$	−2.03537	+	3.52537i	−0.306844	+	0.531470i
$45$	−6.66459	+	0.763716i	−0.993498	+	0.113848i
$46$	−2.23326	−	3.86812i	−0.329276	−	0.570324i
$47$	9.13513	−	1.61077i	1.33250	−	0.234955i	0.538370	−	0.842708i	$-0.319040\pi$
$47$	9.13513	−	1.61077i	1.33250	−	0.234955i	0.794126	+	0.607753i	$0.207929\pi$
$48$	0.931683	−	1.46013i	0.134477	−	0.210751i
$49$	−6.30453	+	2.29466i	−0.900647	+	0.327809i
$50$	−4.86710	+	1.14512i	−0.688312	+	0.161945i
$51$	−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	−0.908503	−	0.417879i	$-0.862774\pi$
$59$	−10.2609	+	3.73464i	−1.33585	+	0.486209i	−0.427346	+	0.904088i	$0.640551\pi$
$60$	−3.82447	+	0.611109i	−0.493737	+	0.0788938i
$61$	−1.35199	−	7.66749i	−0.173104	−	0.981721i	−0.940310	−	0.340320i	$-0.889465\pi$
$61$	−1.35199	−	7.66749i	−0.173104	−	0.981721i	0.767206	−	0.641401i	$-0.221647\pi$
$62$	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
$65$	−0.802714	+	5.44902i	−0.0995645	+	0.675867i
$66$	6.99109	−	0.915265i	0.860543	−	0.112661i
$67$	−6.14767	+	7.32650i	−0.751057	+	0.895075i	−0.997247	−	0.0741468i	$-0.976377\pi$
$67$	−6.14767	+	7.32650i	−0.751057	+	0.895075i	0.246190	+	0.969221i	$0.420821\pi$
$68$	−2.75808	+	3.28696i	−0.334467	+	0.398602i
$69$	−2.96569	+	7.14522i	−0.357027	+	0.860184i
$70$	−1.19307	−	0.175755i	−0.142599	−	0.0210068i
$71$	6.98968	−	12.1065i	0.829522	−	1.43677i	−0.0688910	−	0.997624i	$-0.521946\pi$
$71$	6.98968	−	12.1065i	0.829522	−	1.43677i	0.898413	−	0.439151i	$-0.144721\pi$
$72$	−2.98896	+	0.257156i	−0.352252	+	0.0303062i
$73$	−2.27739	+	1.31485i	−0.266548	+	0.153892i	−0.627318	−	0.778763i	$-0.715847\pi$
$73$	−2.27739	+	1.31485i	−0.266548	+	0.153892i	0.360770	+	0.932655i	$0.382514\pi$
$74$	1.29520	+	7.34543i	0.150564	+	0.853889i
$75$	6.70149	+	5.48543i	0.773822	+	0.633403i
$76$	−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	−0.843616	−	0.536947i	$-0.819577\pi$
$79$	−4.10029	+	3.44055i	−0.461318	+	0.387092i	0.382297	+	0.924039i	$0.375133\pi$
$80$	−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	−0.980501	−	0.196515i	$-0.937037\pi$
$83$	−9.14477	−	10.8983i	−1.00377	−	1.19624i	−0.0232678	−	0.999729i	$-0.507407\pi$
$84$	−0.911833	−	0.202839i	−0.0994891	−	0.0221315i
$85$	9.59072	−	0.271214i	1.04026	−	0.0294173i
$86$	−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	−0.999956	−	0.00932743i	$-0.997031\pi$
$89$	−4.79299	−	8.30170i	−0.508056	−	0.879979i	0.491900	−	0.870651i	$-0.336302\pi$
$90$	4.86896	+	4.61446i	0.513233	+	0.486407i
$91$	−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
$95$	4.28539	+	2.31519i	0.439672	+	0.237533i
$96$	−1.71740	+	0.224840i	−0.175281	+	0.0229476i
$97$	−0.646954	+	1.77749i	−0.0656882	+	0.180477i	−0.968194	−	0.250201i	$-0.919503\pi$
$97$	−0.646954	+	1.77749i	−0.0656882	+	0.180477i	0.902506	+	0.430678i	$0.141726\pi$
$98$	5.81028	+	3.35457i	0.586927	+	0.338863i
$99$	−8.62290	−	8.64781i	−0.866634	−	0.869137i
$100$	4.00573	+	2.99235i	0.400573	+	0.299235i
$101$	−0.0649104	−	0.368125i	−0.00645883	−	0.0366298i	0.981408	−	0.191933i	$-0.0614757\pi$
$101$	−0.0649104	−	0.368125i	−0.00645883	−	0.0366298i	−0.987867	+	0.155303i	$0.950365\pi$
$102$	7.42460	+	0.329530i	0.735145	+	0.0326283i
$103$	−1.47527	−	4.05326i	−0.145362	−	0.399380i	0.845549	−	0.533898i	$-0.179273\pi$
$103$	−1.47527	−	4.05326i	−0.145362	−	0.399380i	−0.990911	+	0.134519i	$0.957051\pi$
$104$	−0.427726	+	2.42575i	−0.0419420	+	0.237865i
$105$	1.01515	+	1.82548i	0.0990687	+	0.178149i
$106$	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	$0.104555\pi$
$110$	−7.13550	−	5.65151i	−0.680344	−	0.538850i
$111$	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	−0.763255	−	0.646097i	$-0.776400\pi$
$113$	−6.31294	−	17.3447i	−0.593871	−	1.63165i	0.169384	−	0.985550i	$-0.445822\pi$
$114$	3.18057	+	2.02947i	0.297888	+	0.190078i
$115$	9.28482	−	3.67984i	0.865814	−	0.343147i
$116$	−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
$120$	2.92646	+	2.53690i	0.267148	+	0.231586i
$121$	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
$125$	−0.947111	−	11.1402i	−0.0847122	−	0.996405i
$126$	0.681658	+	1.46734i	0.0607269	+	0.130721i
$127$	−8.44545	+	4.87598i	−0.749413	+	0.432674i	−0.825482	−	0.564429i	$-0.809096\pi$
$127$	−8.44545	+	4.87598i	−0.749413	+	0.432674i	0.0760690	+	0.997103i	$0.475763\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	11.6671	+	7.44462i	1.02723	+	0.655462i
$130$	4.69016	−	2.88765i	0.411355	−	0.253263i
$131$	−0.846116	+	4.79856i	−0.0739255	+	0.419253i	0.925276	+	0.379295i	$0.123833\pi$
$131$	−0.846116	+	4.79856i	−0.0739255	+	0.419253i	−0.999201	+	0.0399576i	$0.987278\pi$
$132$	−5.19492	−	4.76716i	−0.452160	−	0.414928i
$133$	0.755136	+	0.899936i	0.0654786	+	0.0780343i
$134$	9.56407			0.826210
$135$	1.21534	−	11.5552i	0.104600	−	0.994514i
$136$	4.29082			0.367934
$137$	4.54631	+	5.41808i	0.388417	+	0.462898i	0.924452	−	0.381298i	$-0.124523\pi$
$137$	4.54631	+	5.41808i	0.388417	+	0.462898i	−0.536035	+	0.844196i	$0.680078\pi$
$138$	7.37986	−	2.32101i	0.628216	−	0.197578i
$139$	0.148126	−	0.840064i	0.0125639	−	0.0712533i	−0.977881	−	0.209161i	$-0.932927\pi$
$139$	0.148126	−	0.840064i	0.0125639	−	0.0712533i	0.990445	+	0.137908i	$0.0440378\pi$
$140$	0.632254	+	1.02692i	0.0534352	+	0.0867904i
$141$	−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
$145$	−0.513896	+	1.54661i	−0.0426767	+	0.128439i
$146$	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	0.469330	−	0.883023i	$-0.344496\pi$
$149$	−3.89120	−	3.26511i	−0.318780	−	0.267488i	−0.788110	+	0.615535i	$0.788940\pi$
$150$	−0.105550	−	8.65961i	−0.00861812	−	0.707054i
$151$	3.86669	+	1.40736i	0.314667	+	0.114529i	0.494525	−	0.869163i	$-0.335342\pi$
$151$	3.86669	+	1.40736i	0.314667	+	0.114529i	−0.179859	+	0.983692i	$0.557564\pi$
$152$	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
$155$	6.11003	+	15.4166i	0.490770	+	1.23829i
$156$	3.78571	−	1.96725i	0.303100	−	0.157506i
$157$	4.11379	+	11.3026i	0.328317	+	0.902042i	0.988538	+	0.150971i	$0.0482401\pi$
$157$	4.11379	+	11.3026i	0.328317	+	0.902042i	−0.660222	+	0.751071i	$0.729538\pi$
$158$	5.27123	+	0.929460i	0.419356	+	0.0739439i
$159$	−0.196522	−	0.0437167i	−0.0155852	−	0.00346696i
$160$	1.75287	+	1.38832i	0.138577	+	0.109757i
$161$	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
$165$	−0.253555	+	15.7639i	−0.0197392	+	1.22722i
$166$	−2.47045	+	14.0106i	−0.191744	+	1.08743i
$167$	3.70137	+	10.1694i	0.286421	+	0.786934i	0.996560	+	0.0828733i	$0.0264097\pi$
$167$	3.70137	+	10.1694i	0.286421	+	0.786934i	−0.710139	+	0.704061i	$0.751368\pi$
$168$	0.430732	+	0.828887i	0.0332317	+	0.0639500i
$169$	1.20386	+	6.82745i	0.0926049	+	0.525188i
$170$	−6.37256	−	7.17259i	−0.488753	−	0.550112i
$171$	−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	0.0415308	+	0.999137i	$0.486777\pi$
$173$	−8.31946	+	22.8575i	−0.632517	+	1.73783i	−0.674047	+	0.738688i	$0.735446\pi$
$174$	−0.483942	+	1.16596i	−0.0366875	+	0.0883912i
$175$	0.777610	−	2.58202i	0.0587818	−	0.195183i
$176$	−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	−0.753515	−	0.657431i	$-0.771643\pi$
$179$	2.57674	−	4.46304i	0.192594	−	0.333583i	0.946109	+	0.323848i	$0.104977\pi$
$180$	0.405180	−	6.69596i	0.0302004	−	0.499087i
$181$	−4.22810	−	7.32328i	−0.314272	−	0.544335i	0.665011	−	0.746834i	$-0.268427\pi$
$181$	−4.22810	−	7.32328i	−0.314272	−	0.544335i	−0.979282	+	0.202499i	$0.935094\pi$
$182$	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
$185$	−16.6716	+	0.471453i	−1.22572	+	0.0346619i
$186$	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	0.182326	−	0.983238i	$-0.441637\pi$
$191$	16.3395	−	13.7105i	1.18229	−	0.992057i	0.999961	−	0.00881893i	$-0.00280719\pi$
$192$	1.27616	+	1.17108i	0.0920987	+	0.0845152i
$193$	−10.8998	−	1.92193i	−0.784585	−	0.138344i	−0.233016	−	0.972473i	$-0.574860\pi$
$193$	−10.8998	−	1.92193i	−0.784585	−	0.138344i	−0.551569	+	0.834129i	$0.685971\pi$
$194$	1.77749	−	0.646954i	0.127616	−	0.0464486i
$195$	−8.91088	−	3.40656i	−0.638121	−	0.243949i
$196$	−1.16503	−	6.60721i	−0.0832164	−	0.471944i
$197$	−6.79514	+	3.92318i	−0.484134	+	0.279515i	−0.722138	−	0.691749i	$-0.756840\pi$
$197$	−6.79514	+	3.92318i	−0.484134	+	0.279515i	0.238004	+	0.971264i	$0.423507\pi$
$198$	−1.08191	+	12.1642i	−0.0768882	+	0.864474i
$199$	−4.94805	+	8.57027i	−0.350758	+	0.607530i	−0.986382	−	0.164468i	$-0.947409\pi$
$199$	−4.94805	+	8.57027i	−0.350758	+	0.607530i	0.635625	+	0.771998i	$0.280743\pi$
$200$	−0.282562	−	4.99201i	−0.0199802	−	0.352988i
$201$	−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
$205$	−16.8139	−	2.47691i	−1.17433	−	0.172995i
$206$	−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
$210$	0.745872	−	1.95105i	0.0514700	−	0.134635i
$211$	−25.3811	+	9.23797i	−1.74731	+	0.635968i	−0.999606	−	0.0280677i	$-0.991065\pi$
$211$	−25.3811	+	9.23797i	−1.74731	+	0.635968i	−0.747701	+	0.664035i	$0.768842\pi$
$212$	−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
$220$	0.257304	+	9.09883i	0.0173474	+	0.613443i
$221$	−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	$-0.322094\pi$
$223$	19.6897	−	3.47182i	1.31852	−	0.232490i	0.788258	+	0.615345i	$0.210983\pi$
$224$	0.269658	+	0.467061i	0.0180173	+	0.0312068i
$225$	−11.7948	+	9.26728i	−0.786321	+	0.617819i
$226$	−9.22890	+	15.9849i	−0.613897	+	1.06330i
$227$	−8.25698	+	22.6859i	−0.548035	+	1.50571i	0.288325	+	0.957533i	$0.406902\pi$
$227$	−8.25698	+	22.6859i	−0.548035	+	1.50571i	−0.836360	+	0.548181i	$0.815320\pi$
$228$	−0.489765	−	3.74098i	−0.0324355	−	0.247752i
$229$	9.12526	+	7.65700i	0.603014	+	0.505989i	0.892413	−	0.451220i	$-0.149011\pi$
$229$	9.12526	+	7.65700i	0.603014	+	0.505989i	−0.289399	+	0.957209i	$0.593455\pi$
$230$	−8.78709	−	4.74723i	−0.579403	−	0.313023i
$231$	−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	$-0.495922\pi$
$233$	−12.9249	−	7.46217i	−0.846735	−	0.488863i	−0.859548	+	0.511055i	$0.829255\pi$
$234$	−6.69267	−	3.13260i	−0.437514	−	0.204785i
$235$	15.5060	−	13.7765i	1.01150	−	0.898677i
$236$	−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	−0.825165	−	0.564891i	$-0.808918\pi$
$239$	2.21754	−	12.5763i	0.143441	−	0.813492i	0.968606	−	0.248601i	$-0.0799708\pi$
$240$	0.0622870	−	3.87248i	0.00402061	−	0.249968i
$241$	18.6632	−	15.6602i	1.20220	−	1.00877i	0.202635	−	0.979254i	$-0.435050\pi$
$241$	18.6632	−	15.6602i	1.20220	−	1.00877i	0.999564	−	0.0295107i	$-0.00939492\pi$
$242$		−	5.57100i		−	0.358117i
$243$	−13.8530	+	7.14804i	−0.888670	+	0.458547i
$244$	7.78577			0.498433
$245$	−9.31445	+	11.7603i	−0.595078	+	0.751336i
$246$	−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
$250$	−7.92506	+	7.88628i	−0.501225	+	0.498772i
$251$	12.1853	+	21.1055i	0.769128	+	1.33217i	0.938036	+	0.346537i	$0.112643\pi$
$251$	12.1853	+	21.1055i	0.769128	+	1.33217i	−0.168908	+	0.985632i	$0.554024\pi$
$252$	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
$255$	−3.14856	+	16.3173i	−0.197170	+	1.02183i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	18.8110	−	22.4180i	1.17340	−	1.39840i	0.273738	−	0.961804i	$-0.411740\pi$
$257$	18.8110	−	22.4180i	1.17340	−	1.39840i	0.899658	−	0.436595i	$-0.143816\pi$
$258$	−1.79658	−	13.7229i	−0.111850	−	0.854348i
$259$	−3.78002	−	1.37582i	−0.234879	−	0.0854890i
$260$	−5.22684	−	1.73673i	−0.324155	−	0.107708i
$261$	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	$-0.466842\pi$
$263$	8.78743	−	1.54946i	0.541856	−	0.0955439i	0.437876	+	0.899035i	$0.355731\pi$
$264$	−0.312629	+	7.04381i	−0.0192410	+	0.433517i
$265$	0.136266	+	0.221326i	0.00837076	+	0.0135959i
$266$	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	$0.589924\pi$
$270$	−9.63301	+	6.49654i	−0.586247	+	0.395367i
$271$	−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
$275$	14.8276	−	13.9434i	0.894138	−	0.840816i
$276$	−6.52168	−	4.16139i	−0.392559	−	0.250486i
$277$	−18.2145	+	3.21170i	−1.09440	+	0.192972i	−0.691575	−	0.722305i	$-0.743083\pi$
$277$	−18.2145	+	3.21170i	−1.09440	+	0.192972i	−0.402825	+	0.915277i	$0.631972\pi$
$278$	−0.738740	+	0.426512i	−0.0443067	+	0.0255805i
$279$	12.7876	−	18.2067i	0.765576	−	1.09001i
$280$	0.380260	−	1.14442i	0.0227249	−	0.0683924i
$281$	−19.2451	−	7.00466i	−1.14807	−	0.417863i	−0.303247	−	0.952912i	$-0.598071\pi$
$281$	−19.2451	−	7.00466i	−1.14807	−	0.417863i	−0.844821	+	0.535049i	$0.820293\pi$
$282$	12.7535	−	9.77153i	0.759463	−	0.581886i
$283$	−8.84939	+	10.5463i	−0.526042	+	0.626912i	−0.961998	−	0.273056i	$-0.911966\pi$
$283$	−8.84939	+	10.5463i	−0.526042	+	0.626912i	0.435957	+	0.899968i	$0.356410\pi$
$284$	10.7088	+	8.98576i	0.635451	+	0.533207i
$285$	−5.52609	+	6.37466i	−0.327337	+	0.377602i
$286$	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
$290$	1.51510	−	0.600477i	0.0889698	−	0.0352612i
$291$	−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	$-0.326524\pi$
$293$	12.2060	+	2.15225i	0.713081	+	0.125736i	0.194672	+	0.980868i	$0.437636\pi$
$294$	−7.85692	+	8.56192i	−0.458225	+	0.499341i
$295$	−15.1596	+	19.1403i	−0.882626	+	1.11439i
$296$	−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
$300$	−6.56580	+	5.64715i	−0.379077	+	0.326038i
$301$	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
$305$	−11.5631	−	13.0148i	−0.662103	−	0.745225i
$306$	−3.34956	+	12.4290i	−0.191482	+	0.710519i
$307$	−27.7691	−	16.0325i	−1.58486	−	0.915022i	−0.994134	−	0.108152i	$-0.965507\pi$
$307$	−27.7691	−	16.0325i	−1.58486	−	0.915022i	−0.590730	−	0.806870i	$-0.701160\pi$
$308$	−0.750877	+	2.06302i	−0.0427852	+	0.117551i
$309$	7.40779	−	0.969820i	0.421415	−	0.0551711i
$310$	7.88234	−	14.5902i	0.447687	−	0.828665i
$311$	−1.12523	−	0.944177i	−0.0638058	−	0.0535394i	0.610327	−	0.792150i	$-0.291038\pi$
$311$	−1.12523	−	0.944177i	−0.0638058	−	0.0535394i	−0.674133	+	0.738610i	$0.735482\pi$
$312$	−3.94041	−	1.63550i	−0.223082	−	0.0925920i
$313$	6.17591	−	16.9682i	0.349083	−	0.959097i	−0.633577	−	0.773680i	$-0.718414\pi$
$313$	6.17591	−	16.9682i	0.349083	−	0.959097i	0.982660	−	0.185418i	$-0.0593638\pi$
$314$	6.01396	−	10.4165i	0.339388	−	0.587837i
$315$	−3.46819	+	1.02977i	−0.195410	+	0.0580211i
$316$	−2.67627	−	4.63544i	−0.150552	−	0.260764i
$317$	32.8188	−	5.78683i	1.84329	−	0.325021i	0.860454	−	0.509528i	$-0.170180\pi$
$317$	32.8188	−	5.78683i	1.84329	−	0.325021i	0.982831	+	0.184507i	$0.0590690\pi$
$318$	0.0928332	+	0.178645i	0.00520583	+	0.0100179i
$319$	−2.78803	+	1.01476i	−0.156100	+	0.0568157i
$320$	−0.0632081	−	2.23517i	−0.00353344	−	0.124950i
$321$	−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
$330$	12.2388	−	9.93861i	0.673726	−	0.547102i
$331$	−1.59511	−	9.04632i	−0.0876752	−	0.497231i	−0.996747	−	0.0805917i	$-0.974319\pi$
$331$	−1.59511	−	9.04632i	−0.0876752	−	0.497231i	0.909072	−	0.416639i	$-0.136792\pi$
$332$	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
$335$	−3.11680	+	21.1576i	−0.170289	+	1.15596i
$336$	0.358095	−	0.862758i	0.0195357	−	0.0470673i
$337$	14.9760	−	17.8477i	0.815796	−	0.972228i	−0.184147	−	0.982899i	$-0.558952\pi$
$337$	14.9760	−	17.8477i	0.815796	−	0.972228i	0.999943	+	0.0106706i	$0.00339663\pi$
$338$	4.45630	−	5.31081i	0.242391	−	0.288870i
$339$	31.6993	−	4.15004i	1.72167	−	0.225399i
$340$	−1.39832	+	9.49211i	−0.0758344	+	0.514782i
$341$	−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
$345$	2.72953	+	17.0821i	0.146953	+	0.919668i
$346$	22.8575	−	8.31946i	1.22883	−	0.447257i
$347$	13.3920	+	2.36136i	0.718918	+	0.126765i	0.521127	−	0.853479i	$-0.325512\pi$
$347$	13.3920	+	2.36136i	0.718918	+	0.126765i	0.197792	+	0.980244i	$0.436623\pi$
$348$	1.20425	−	0.378744i	0.0645545	−	0.0203028i
$349$	−3.05394	+	2.56256i	−0.163474	+	0.137171i	−0.720855	−	0.693086i	$-0.756251\pi$
$349$	−3.05394	+	2.56256i	−0.163474	+	0.137171i	0.557381	+	0.830257i	$0.311806\pi$
$350$	−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	$-0.268689\pi$
$353$	−3.51345	−	4.18717i	−0.187002	−	0.222861i	−0.851398	+	0.524521i	$0.824245\pi$
$354$	−12.7874	+	13.9348i	−0.679644	+	0.740628i
$355$	−0.883608	−	31.2463i	−0.0468971	−	1.65838i
$356$	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	0.937300	−	0.348524i	$-0.113317\pi$
$359$	3.16078	+	5.47463i	0.166820	+	0.288940i	−0.770480	+	0.637464i	$0.779984\pi$
$360$	−5.38984	+	3.99369i	−0.284070	+	0.210486i
$361$	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
$365$	−2.79497	+	5.17347i	−0.146295	+	0.270792i
$366$	−8.20165	−	10.7046i	−0.428707	−	0.559537i
$367$	−6.32341	+	17.3734i	−0.330079	+	0.906886i	0.658011	+	0.753009i	$0.271398\pi$
$367$	−6.32341	+	17.3734i	−0.330079	+	0.906886i	−0.988090	+	0.153877i	$0.950824\pi$
$368$	−3.86812	−	2.23326i	−0.201640	−	0.116417i
$369$	9.60656	+	20.6792i	0.500098	+	1.07651i
$370$	11.0774	+	12.4681i	0.575889	+	0.648188i
$371$	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	$-0.0817416\pi$
$373$	1.21721	+	3.34426i	0.0630248	+	0.173159i	−0.904183	+	0.427145i	$0.859519\pi$
$374$	3.03308	−	17.2015i	0.156837	−	0.889467i
$375$	19.1911	+	2.58855i	0.991026	+	0.133672i
$376$	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	$0.491445\pi$
$380$	−3.02416	+	3.81826i	−0.155136	+	0.195872i
$381$	−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	$-0.0491474\pi$
$383$	2.58954	+	7.11469i	0.132319	+	0.363544i	−0.855785	+	0.517332i	$0.826925\pi$
$384$	0.0767989	−	1.73035i	0.00391913	−	0.0883014i
$385$	4.56374	−	1.80874i	0.232590	−	0.0921819i
$386$	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	−0.185493	−	0.982646i	$-0.559388\pi$
$389$	−18.9188	−	6.88588i	−0.959221	−	0.349128i	−0.773728	+	0.633518i	$0.781610\pi$
$390$	3.11822	+	9.01583i	0.157897	+	0.456534i
$391$	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
$395$	−3.77396	+	11.3581i	−0.189889	+	0.571487i
$396$	10.0138	−	6.99022i	0.503211	−	0.351272i
$397$	11.5545	−	6.67099i	0.579903	−	0.334807i	−0.181192	−	0.983448i	$-0.557995\pi$
$397$	11.5545	−	6.67099i	0.579903	−	0.334807i	0.761095	+	0.648640i	$0.224662\pi$
$398$	9.74575	−	1.71844i	0.488510	−	0.0861375i
$399$	−1.80555	+	0.938257i	−0.0903907	+	0.0469716i
$400$	−3.64247	+	3.42526i	−0.182124	+	0.171263i
$401$	−5.09876	+	28.9165i	−0.254620	+	1.44402i	0.542426	+	0.840103i	$0.317506\pi$
$401$	−5.09876	+	28.9165i	−0.254620	+	1.44402i	−0.797046	+	0.603918i	$0.793605\pi$
$402$	−3.59708	+	16.1702i	−0.179406	+	0.806496i
$403$	−11.7421	−	13.9937i	−0.584917	−	0.697077i
$404$	0.373804			0.0185975
$405$	19.0796	+	6.40077i	0.948072	+	0.318057i
$406$	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	−0.521456	−	0.853278i	$-0.674611\pi$
$409$	5.26607	−	29.8654i	0.260391	−	1.47675i	0.781847	−	0.623470i	$-0.214278\pi$
$410$	8.91031	+	14.4723i	0.440049	+	0.714735i
$411$	−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
$415$	−30.1891	−	10.0310i	−1.48192	−	0.492401i
$416$	−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	0.851074	+	0.525046i	$0.175952\pi$
$419$	31.0303	+	26.0375i	1.51593	+	1.27202i	0.664857	+	0.746971i	$0.268493\pi$
$420$	−1.97403	+	0.682739i	−0.0963226	+	0.0333142i
$421$	25.0173	+	9.10554i	1.21927	+	0.443777i	0.869909	−	0.493213i	$-0.164178\pi$
$421$	25.0173	+	9.10554i	1.21927	+	0.443777i	0.349358	+	0.936989i	$0.386400\pi$
$422$	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
$425$	17.9439	−	11.7599i	0.870406	−	0.570438i
$426$	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
$430$	−11.0934	+	14.0063i	−0.534971	+	0.675445i
$431$	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
$435$	−2.42162	−	1.45054i	−0.116108	−	0.0695482i
$436$	−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	0.961586	+	0.274504i	$0.0885138\pi$
$439$	3.18217	+	18.0470i	0.151877	+	0.861336i	−0.809709	+	0.586831i	$0.800375\pi$
$440$	6.80472	−	6.04572i	0.324402	−	0.288219i
$441$	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	−0.724713	−	0.689050i	$-0.758028\pi$
$443$	5.75361	−	15.8079i	0.273362	−	0.751057i	0.998076	−	0.0620063i	$-0.0197499\pi$
$444$	7.85715	+	10.2549i	0.372884	+	0.486678i
$445$	−18.8587	−	10.1884i	−0.893989	−	0.482978i
$446$	−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	−0.925682	−	0.378302i	$-0.876508\pi$
$449$	−2.86531	+	4.96287i	−0.135222	+	0.234212i	0.790460	+	0.612514i	$0.209842\pi$
$450$	14.6807	+	3.07846i	0.692055	+	0.145120i
$451$	−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
$455$	0.0839673	+	2.96927i	0.00393645	+	0.139201i
$456$	−2.55094	+	2.77984i	−0.119459	+	0.130178i
$457$	−5.68883	−	6.77968i	−0.266112	−	0.317140i	0.616397	−	0.787436i	$-0.288592\pi$
$457$	−5.68883	−	6.77968i	−0.266112	−	0.317140i	−0.882509	+	0.470296i	$0.844147\pi$
$458$		−	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	−0.194921	−	0.980819i	$-0.562445\pi$
$461$	15.8273	−	13.2806i	0.737149	−	0.618541i	0.932070	+	0.362277i	$0.118001\pi$
$462$	3.62740	−	1.14084i	0.168762	−	0.0530767i
$463$	−8.62824	−	1.52139i	−0.400988	−	0.0707050i	−0.0304826	−	0.999535i	$-0.509704\pi$
$463$	−8.62824	−	1.52139i	−0.400988	−	0.0707050i	−0.370505	+	0.928830i	$0.620816\pi$
$464$	0.684894	−	0.249281i	0.0317954	−	0.0115726i
$465$	−28.3632	+	4.53214i	−1.31531	+	0.210173i
$466$	2.59158	+	14.6976i	0.120053	+	0.680853i
$467$	2.14140	−	1.23634i	0.0990924	−	0.0572110i	−0.449635	−	0.893212i	$-0.648446\pi$
$467$	2.14140	−	1.23634i	0.0990924	−	0.0572110i	0.548727	+	0.836001i	$0.315113\pi$
$468$	1.90225	+	7.14048i	0.0879316	+	0.330069i
$469$	−2.57902	+	4.46700i	−0.119088	+	0.206267i
$470$	−20.5204	−	3.02294i	−0.946537	−	0.139438i
$471$	−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
$475$	10.8740	−	0.615501i	0.498934	−	0.0282411i
$476$	−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	−0.974970	−	0.222336i	$-0.928632\pi$
$479$	−2.95115	−	16.7368i	−0.134841	−	0.764724i	0.840129	−	0.542387i	$-0.182479\pi$
$480$	−3.00653	+	2.44147i	−0.137229	+	0.111437i
$481$	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
$490$	14.9961	−	0.424072i	0.677455	−	0.0191576i
$491$	−20.2892	+	7.38465i	−0.915637	+	0.333265i	−0.756501	−	0.653992i	$-0.773093\pi$
$491$	−20.2892	+	7.38465i	−0.915637	+	0.333265i	−0.159136	+	0.987257i	$0.550871\pi$
$492$	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
$495$	−26.5570	−	6.35755i	−1.19365	−	0.285751i
$496$	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	0.673447	−	0.739235i	$-0.264813\pi$
$499$	1.39359	+	1.16936i	0.0623856	+	0.0523477i	−0.611062	+	0.791583i	$0.709257\pi$
$500$	11.1354	+	1.00174i	0.497989	+	0.0447994i
$501$	−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	$-0.186074\pi$
$503$	17.3370	+	10.0095i	0.773018	+	0.446302i	−0.0609321	+	0.998142i	$0.519407\pi$
$504$	−1.56342	+	0.416501i	−0.0696402	+	0.0185524i
$505$	−0.555160	−	0.624856i	−0.0247043	−	0.0278057i
$506$	−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	−0.779192	−	0.626785i	$-0.784371\pi$
$509$	3.77631	−	21.4165i	0.167382	−	0.949270i	0.946574	−	0.322485i	$-0.104518\pi$
$510$	14.5236	−	8.07660i	0.643116	−	0.357638i
$511$	−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
$515$	−7.56082	−	5.98837i	−0.333170	−	0.263879i
$516$	−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
$520$	2.02934	+	5.12034i	0.0889923	+	0.224542i
$521$	15.2692	+	26.4470i	0.668954	+	1.15866i	0.978197	+	0.207679i	$0.0665910\pi$
$521$	15.2692	+	26.4470i	0.668954	+	1.15866i	−0.309243	+	0.950983i	$0.600076\pi$
$522$	−1.78930	−	1.25673i	−0.0783157	−	0.0550057i
$523$	30.0364	+	17.3415i	1.31340	+	0.758291i	0.982657	−	0.185430i	$-0.0593678\pi$
$523$	30.0364	+	17.3415i	1.31340	+	0.758291i	0.330742	+	0.943721i	$0.392701\pi$
$524$	−4.57874	−	1.66652i	−0.200023	−	0.0728024i
$525$	4.07303	+	2.28583i	0.177761	+	0.0997619i
$526$	−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
$530$	0.0819552	−	0.246651i	0.00355991	−	0.0107139i
$531$	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
$535$	5.05144	+	8.20464i	0.218393	+	0.354717i
$536$	−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
$540$	11.1686	+	3.20342i	0.480621	+	0.137853i
$541$	−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
$545$	37.6334	−	23.1702i	1.61204	−	0.992502i
$546$	−0.102022	+	2.29864i	−0.00436613	+	0.0983727i
$547$	−13.5618	+	2.39131i	−0.579860	+	0.102245i	−0.455883	−	0.890040i	$-0.650676\pi$
$547$	−13.5618	+	2.39131i	−0.579860	+	0.102245i	−0.123978	+	0.992285i	$0.539565\pi$
$548$	−6.12522	+	3.53640i	−0.261657	+	0.151068i
$549$	−6.07785	+	22.5527i	−0.259396	+	0.962526i
$550$	−20.2122	−	2.39598i	−0.861852	−	0.102165i
$551$	−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
$555$	5.47315	−	28.3644i	0.232322	−	1.20400i
$556$	0.801580	+	0.291751i	0.0339946	+	0.0123730i
$557$	−19.9184	−	11.4999i	−0.843970	−	0.487266i	0.0146417	−	0.999893i	$-0.495339\pi$
$557$	−19.9184	−	11.4999i	−0.843970	−	0.487266i	−0.858612	+	0.512626i	$0.828673\pi$
$558$	−22.1669	+	1.90714i	−0.938398	+	0.0807355i
$559$	9.84100	+	17.0451i	0.416230	+	0.720931i
$560$	−1.12111	+	0.444326i	−0.0473754	+	0.0187762i
$561$	−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	$-0.594601\pi$
$563$	−21.2374	−	3.74472i	−0.895048	−	0.157821i	−0.602207	+	0.798340i	$0.705712\pi$
$564$	−15.6832	−	3.48876i	−0.660384	−	0.146903i
$565$	−32.3542	−	25.6254i	−1.36115	−	1.07807i
$566$	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	−0.848542	−	0.529128i	$-0.822519\pi$
$569$	−11.3258	+	9.50345i	−0.474801	+	0.398405i	0.373741	+	0.927533i	$0.378075\pi$
$570$	8.43537	+	0.135679i	0.353319	+	0.00568296i
$571$	1.39101	−	7.88879i	0.0582118	−	0.330136i	−0.941769	−	0.336259i	$-0.890838\pi$
$571$	1.39101	−	7.88879i	0.0582118	−	0.330136i	0.999981	+	0.00612376i	$0.00194927\pi$
$572$	−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
$575$	13.3654	−	17.8917i	0.557375	−	0.746135i
$576$	−2.45994	+	1.71718i	−0.102497	+	0.0715493i
$577$	5.43636	+	3.13868i	0.226319	+	0.130665i	0.608873	−	0.793268i	$-0.291622\pi$
$577$	5.43636	+	3.13868i	0.226319	+	0.130665i	−0.382554	+	0.923933i	$0.624955\pi$
$578$	0.482624	−	1.32600i	0.0200745	−	0.0551542i
$579$	7.34891	−	17.7057i	0.305410	−	0.735825i
$580$	−1.43388	−	0.774655i	−0.0595386	−	0.0321658i
$581$	−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
$585$	9.11097	−	13.7846i	0.376692	−	0.569923i
$586$	−6.19714	−	10.7338i	−0.256002	−	0.443408i
$587$	−26.5118	+	4.67475i	−1.09426	+	0.192947i	−0.691513	−	0.722364i	$-0.743055\pi$
$587$	−26.5118	+	4.67475i	−1.09426	+	0.192947i	−0.402746	+	0.915312i	$0.631944\pi$
$588$	11.6091	+	0.515254i	0.478753	+	0.0212487i
$589$	−15.1805	+	5.52524i	−0.625500	+	0.227663i
$590$	24.4067	−	0.690192i	1.00481	−	0.0284148i
$591$	−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	−0.298844	−	0.954302i	$-0.596601\pi$
$599$	2.09601	−	0.762886i	0.0856408	−	0.0311707i	0.384485	+	0.923131i	$0.374379\pi$
$600$	8.54638	+	1.39978i	0.348905	+	0.0571457i
$601$	5.05104	+	28.6459i	0.206036	+	1.16849i	0.895801	+	0.444456i	$0.146603\pi$
$601$	5.05104	+	28.6459i	0.206036	+	1.16849i	−0.689764	+	0.724034i	$0.742286\pi$
$602$	−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
$605$	12.3241	+	1.81551i	0.501047	+	0.0738110i
$606$	−0.393771	−	0.513939i	−0.0159959	−	0.0208774i
$607$	−11.4898	+	13.6930i	−0.466355	+	0.555781i	−0.947041	−	0.321112i	$-0.895943\pi$
$607$	−11.4898	+	13.6930i	−0.466355	+	0.555781i	0.480686	+	0.876893i	$0.340388\pi$
$608$	−1.40018	+	1.66866i	−0.0567846	+	0.0676733i
$609$	−0.414075	−	0.540440i	−0.0167792	−	0.0218997i
$610$	−2.53728	+	17.2236i	−0.102731	+	0.697364i
$611$	−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	−0.613772	+	0.789483i	$0.710349\pi$
$613$	−39.7223	+	22.9337i	−1.60437	+	0.926284i	−0.990599	+	0.136800i	$0.956318\pi$
$614$	5.56802	+	31.5778i	0.224707	+	1.27438i
$615$	10.5115	−	27.4960i	0.423865	−	1.10875i
$616$	2.06302	−	0.750877i	0.0831213	−	0.0302537i
$617$	1.67563	+	0.295459i	0.0674583	+	0.0118947i	0.207275	−	0.978283i	$-0.433540\pi$
$617$	1.67563	+	0.295459i	0.0674583	+	0.0118947i	−0.139817	+	0.990177i	$0.544651\pi$
$618$	−5.50456	−	5.05131i	−0.221426	−	0.203194i
$619$	−16.5836	+	13.9153i	−0.666550	+	0.559302i	−0.912042	−	0.410097i	$-0.865495\pi$
$619$	−16.5836	+	13.9153i	−0.666550	+	0.559302i	0.245492	+	0.969399i	$0.421050\pi$
$620$	−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
$625$	−14.8633	−	20.1018i	−0.594532	−	0.804072i
$626$	−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
$630$	3.01816	+	1.99486i	0.120246	+	0.0794771i
$631$	6.44066	−	11.1555i	0.256398	−	0.444095i	−0.708876	−	0.705333i	$-0.750797\pi$
$631$	6.44066	−	11.1555i	0.256398	−	0.444095i	0.965274	+	0.261238i	$0.0841307\pi$
$632$	−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
$635$	−10.3649	+	19.1853i	−0.411317	+	0.761344i
$636$	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
$640$	−1.67161	+	1.48516i	−0.0660763	+	0.0587062i
$641$	−2.61920	−	14.8542i	−0.103452	−	0.586706i	−0.991827	−	0.127588i	$-0.959276\pi$
$641$	−2.61920	−	14.8542i	−0.103452	−	0.586706i	0.888375	−	0.459118i	$-0.151835\pi$
$642$	3.44136	+	6.62245i	0.135820	+	0.261367i
$643$	7.44994	+	20.4685i	0.293797	+	0.807200i	0.995503	+	0.0947334i	$0.0301999\pi$
$643$	7.44994	+	20.4685i	0.293797	+	0.807200i	−0.701706	+	0.712467i	$0.747578\pi$
$644$	−0.418295	+	2.37227i	−0.0164831	+	0.0934805i
$645$	30.9431	+	0.497704i	1.21838	+	0.0195971i
$646$	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
$650$	5.54534	−	10.9968i	0.217506	−	0.431330i
$651$	−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	0.994457	+	0.105140i	$0.0335290\pi$
$653$	7.67233	+	21.0796i	0.300241	+	0.824907i	−0.694216	+	0.719767i	$0.744249\pi$
$654$	30.3762	−	15.7850i	1.18780	−	0.617243i
$655$	4.01438	+	10.1289i	0.156855	+	0.395770i
$656$	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	−0.0126389	−	0.999920i	$-0.504023\pi$
$659$	−17.0727	−	6.21395i	−0.665057	−	0.242061i	−0.652418	+	0.757859i	$0.726245\pi$
$660$	−15.4804	−	2.98708i	−0.602573	−	0.116272i
$661$	33.8258	+	28.3832i	1.31567	+	1.10398i	0.987204	+	0.159465i	$0.0509768\pi$
$661$	33.8258	+	28.3832i	1.31567	+	1.10398i	0.328468	+	0.944515i	$0.393468\pi$
$662$	−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
$665$	2.49288	+	0.828314i	0.0966699	+	0.0321206i
$666$	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
$670$	18.2111	−	11.2122i	0.703555	−	0.433166i
$671$	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	$-0.0355347\pi$
$673$	18.4578	+	21.9972i	0.711497	+	0.847929i	−0.282279	+	0.959332i	$0.591090\pi$
$674$	−23.2986			−0.897427
$675$	−11.2323	−	23.4272i	−0.432333	−	0.901714i
$676$	−6.93277			−0.266645
$677$	−24.4113	−	29.0923i	−0.938203	−	1.11811i	−0.992822	−	0.119599i	$-0.961839\pi$
$677$	−24.4113	−	29.0923i	−0.938203	−	1.11811i	0.0546194	−	0.998507i	$-0.482605\pi$
$678$	−23.5551	−	21.6155i	−0.904626	−	0.830138i
$679$	−0.177147	+	1.00465i	−0.00679829	+	0.0385550i
$680$	8.17020	−	5.03024i	0.313313	−	0.192901i
$681$	−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	$-0.377340\pi$
$683$	35.7083	−	20.6162i	1.36634	−	0.788856i	0.990458	+	0.137812i	$0.0440071\pi$
$684$	6.50916	+	0.578939i	0.248884	+	0.0221363i
$685$	15.0084	+	4.98688i	0.573443	+	0.190539i
$686$	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
$690$	11.3311	−	13.0711i	0.431368	−	0.497608i
$691$	−0.00336697	−	0.00122548i	−0.000128086	−	4.66193e-5i	0.341956	−	0.939716i	$-0.388911\pi$
$691$	−0.00336697	−	0.00122548i	−0.000128086	−	4.66193e-5i	−0.342084	+	0.939669i	$0.611133\pi$
$692$	−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
$695$	−0.702781	−	1.77323i	−0.0266580	−	0.0672625i
$696$	−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
$700$	2.40777	+	1.21416i	0.0910050	+	0.0458909i
$701$	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
$705$	17.4603	+	31.3977i	0.657594	+	1.18251i
$706$	−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	0.996303	−	0.0859085i	$-0.0273793\pi$
$709$	0.817504	+	4.63629i	0.0307020	+	0.174120i	−0.965601	+	0.260028i	$0.916268\pi$
$710$	−23.3681	+	20.7616i	−0.876989	+	0.779170i
$711$	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
$715$	−10.6571	+	19.7263i	−0.398554	+	0.737721i
$716$	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	−0.980136	−	0.198325i	$-0.936450\pi$
$719$	−8.53531	+	14.7836i	−0.318313	+	0.551335i	0.661823	+	0.749660i	$0.269783\pi$
$720$	6.52387	+	1.56177i	0.243130	+	0.0582036i
$721$	−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
$725$	0.834621	+	3.54738i	0.0309971	+	0.131746i
$726$	9.41902	+	2.09527i	0.349572	+	0.0777629i
$727$	19.5543	+	23.3039i	0.725229	+	0.864294i	0.995128	−	0.0985945i	$-0.0314347\pi$
$727$	19.5543	+	23.3039i	0.725229	+	0.864294i	−0.269899	+	0.962889i	$0.586990\pi$
$728$			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	$-0.124512\pi$
$733$	45.0180	+	7.93788i	1.66278	+	0.293192i	0.738311	+	0.674460i	$0.235623\pi$
$734$	17.3734	−	6.32341i	0.641265	−	0.233401i
$735$	−16.3802	−	20.1712i	−0.604191	−	0.744027i
$736$	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	−0.914214	−	0.405231i	$-0.867191\pi$
$739$	−2.88611	+	4.99888i	−0.106167	+	0.183887i	0.808047	+	0.589118i	$0.200525\pi$
$740$	2.43070	−	16.5002i	0.0893544	−	0.606559i
$741$	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	$-0.963544\pi$
$743$	−19.3095	+	23.0121i	−0.708395	+	0.844233i	0.285053	+	0.958512i	$0.407989\pi$
$744$	−12.7366	+	1.66747i	−0.466948	+	0.0611323i
$745$	−11.2371	−	1.65537i	−0.411694	−	0.0606482i
$746$	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
$750$	−10.3529	−	16.3651i	−0.378034	−	0.597571i
$751$	−16.7944	+	6.11265i	−0.612835	+	0.223054i	−0.629743	−	0.776803i	$-0.716840\pi$
$751$	−16.7944	+	6.11265i	−0.612835	+	0.223054i	0.0169082	+	0.999857i	$0.494618\pi$
$752$	−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
$760$	4.86885	−	0.137685i	0.176612	−	0.00499437i
$761$	17.5585	−	6.39077i	0.636495	−	0.231665i	−0.00356090	−	0.999994i	$-0.501133\pi$
$761$	17.5585	−	6.39077i	0.636495	−	0.231665i	0.640056	+	0.768328i	$0.278911\pi$
$762$	−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
$765$	−26.4038	−	11.4603i	−0.954631	−	0.414349i
$766$	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	0.932106	−	0.362185i	$-0.117969\pi$
$769$	20.4455	+	17.1558i	0.737282	+	0.618653i	−0.194824	+	0.980838i	$0.562414\pi$
$770$	−4.31909	−	2.33339i	−0.155649	−	0.0840897i
$771$	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	$-0.243829\pi$
$773$	13.3630	+	7.71514i	0.480634	+	0.277494i	−0.240047	+	0.970761i	$0.577163\pi$
$774$	23.8773	+	2.12370i	0.858250	+	0.0763347i
$775$	29.7075	+	22.1920i	1.06712	+	0.797160i
$776$	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
$780$	4.90217	−	8.18396i	0.175526	−	0.293033i
$781$	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
$785$	21.0834	+	16.6986i	0.752500	+	0.596000i
$786$	2.53202	+	8.05079i	0.0903143	+	0.287162i
$787$	33.9745	+	5.99062i	1.21106	+	0.213542i	0.742473	−	0.669876i	$-0.233653\pi$
$787$	33.9745	+	5.99062i	1.21106	+	0.213542i	0.468586	+	0.883418i	$0.344764\pi$
$788$	−2.68361	−	7.37316i	−0.0955997	−	0.262658i
$789$	−0.685276	+	15.4399i	−0.0243965	+	0.549674i
$790$	11.1266	−	4.40981i	0.395868	−	0.156894i
$791$	−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
$795$	−0.425451	+	0.147147i	−0.0150892	+	0.00521876i
$796$	−7.58085	−	6.36108i	−0.268696	−	0.225463i
$797$	−3.57242	+	4.25745i	−0.126542	+	0.150806i	−0.825595	−	0.564263i	$-0.809160\pi$
$797$	−3.57242	+	4.25745i	−0.126542	+	0.150806i	0.699054	+	0.715069i	$0.253605\pi$
$798$	1.87933	+	0.780033i	0.0665277	+	0.0276129i
$799$	37.4015	+	13.6130i	1.32317	+	0.481595i
$800$	4.96524	+	0.588584i	0.175548	+	0.0208096i
$801$	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
$805$	4.58675	−	2.82398i	0.161662	−	0.0995321i
$806$	−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	$0.491140\pi$
$810$	−7.36084	−	18.7301i	−0.258634	−	0.658110i
$811$	−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
$815$	−2.32264	−	3.77247i	−0.0813584	−	0.132144i
$816$	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
$820$	5.35897	−	16.1283i	0.187144	−	0.563225i
$821$	9.63738	+	3.50772i	0.336347	+	0.122420i	0.504672	−	0.863311i	$-0.331614\pi$
$821$	9.63738	+	3.50772i	0.336347	+	0.122420i	−0.168325	+	0.985732i	$0.553836\pi$
$822$	11.3146	+	4.69620i	0.394640	+	0.163799i
$823$	−14.3467	+	17.0977i	−0.500093	+	0.595988i	−0.955755	−	0.294165i	$-0.904958\pi$
$823$	−14.3467	+	17.0977i	−0.500093	+	0.595988i	0.455661	+	0.890153i	$0.349403\pi$
$824$	−3.30425	−	2.77259i	−0.115109	−	0.0965878i
$825$	17.9977	+	30.3135i	0.626598	+	1.05538i
$826$	5.53383	+	2.01415i	0.192547	+	0.0700813i
$827$	−6.88573	−	3.97548i	−0.239440	−	0.138241i	0.375479	−	0.926831i	$-0.377478\pi$
$827$	−6.88573	−	3.97548i	−0.239440	−	0.138241i	−0.614920	+	0.788590i	$0.710812\pi$
$828$	9.48858	−	9.46125i	0.329751	−	0.328801i
$829$	2.41490	+	4.18273i	0.0838731	+	0.145272i	0.904910	−	0.425602i	$-0.139938\pi$
$829$	2.41490	+	4.18273i	0.0838731	+	0.145272i	−0.821037	+	0.570874i	$0.806604\pi$
$830$	11.7210	+	29.5739i	0.406841	+	1.02653i
$831$	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
$835$	18.9697	+	15.0245i	0.656475	+	0.519946i
$836$	−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	−0.835637	−	0.549282i	$-0.814901\pi$
$839$	−12.7392	+	10.6895i	−0.439807	+	0.369042i	0.395830	+	0.918324i	$0.370457\pi$
$840$	1.79189	+	1.07334i	0.0618260	+	0.0370336i
$841$	−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
$845$	10.2963	+	11.5889i	0.354203	+	0.398671i
$846$	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
$850$	−20.5427	−	6.18670i	−0.704609	−	0.212202i
$851$	−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	0.245034	+	0.969514i	$0.421201\pi$
$853$	−16.5267	+	45.4068i	−0.565865	+	1.55470i	−0.810899	+	0.585186i	$0.801021\pi$
$854$	−2.09949	+	3.63643i	−0.0718432	+	0.124436i
$855$	−8.69940	−	11.7406i	−0.297513	−	0.401521i
$856$	2.15445	+	3.73162i	0.0736376	+	0.127544i
$857$	−5.42516	+	0.956602i	−0.185320	+	0.0326769i	−0.265538	−	0.964100i	$-0.585550\pi$
$857$	−5.42516	+	0.956602i	−0.185320	+	0.0326769i	0.0802178	+	0.996777i	$0.474438\pi$
$858$	−9.34196	+	14.6406i	−0.318929	+	0.499823i
$859$	22.5455	−	8.20589i	0.769242	−	0.279981i	0.0725627	−	0.997364i	$-0.476882\pi$
$859$	22.5455	−	8.20589i	0.769242	−	0.279981i	0.696679	+	0.717383i	$0.254660\pi$
$860$	17.8602	−	0.505064i	0.609027	−	0.0172225i
$861$	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
$870$	0.445406	+	2.78746i	0.0151007	+	0.0945037i
$871$	−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
$875$	−1.54632	−	5.82808i	−0.0522751	−	0.197025i
$876$	4.51624	−	0.591261i	0.152590	−	0.0199769i
$877$	28.4839	−	33.9458i	0.961833	−	1.14627i	−0.0273565	−	0.999626i	$-0.508709\pi$
$877$	28.4839	−	33.9458i	0.961833	−	1.14627i	0.989190	−	0.146642i	$-0.0468466\pi$
$878$	11.7793	−	14.0381i	0.397533	−	0.473762i
$879$	−8.22957	+	19.8275i	−0.277577	+	0.668764i
$880$	−9.00528	−	1.32660i	−0.303568	−	0.0447197i
$881$	3.94879	−	6.83950i	0.133038	−	0.230429i	−0.791808	−	0.610770i	$-0.790860\pi$
$881$	3.94879	−	6.83950i	0.133038	−	0.230429i	0.924846	+	0.380341i	$0.124193\pi$
$882$	−11.5208	−	16.5040i	−0.387926	−	0.555720i
$883$	8.09566	−	4.67403i	0.272441	−	0.157294i	−0.357556	−	0.933892i	$-0.616390\pi$
$883$	8.09566	−	4.67403i	0.272441	−	0.157294i	0.629996	+	0.776598i	$0.283056\pi$
$884$	−1.83529	−	10.4085i	−0.0617276	−	0.350074i
$885$	−26.6593	−	32.8294i	−0.896143	−	1.10355i
$886$	−15.8079	+	5.75361i	−0.531077	+	0.193296i
$887$	1.37077	+	0.241704i	0.0460260	+	0.00811563i	0.196614	−	0.980481i	$-0.437005\pi$
$887$	1.37077	+	0.241704i	0.0460260	+	0.00811563i	−0.150588	+	0.988597i	$0.548117\pi$
$888$	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
$895$	−0.325741	−	11.5189i	−0.0108883	−	0.385035i
$896$	−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
$900$	−7.07834	−	13.2249i	−0.235945	−	0.440829i
$901$	−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
$905$	−16.6361	−	8.98764i	−0.553001	−	0.298759i
$906$	7.06682	−	0.925180i	0.234779	−	0.0307370i
$907$	1.20927	−	3.32245i	0.0401532	−	0.110320i	−0.917996	−	0.396590i	$-0.870193\pi$
$907$	1.20927	−	3.32245i	0.0401532	−	0.110320i	0.958149	+	0.286270i	$0.0924156\pi$
$908$	−20.9074	−	12.0709i	−0.693837	−	0.400587i
$909$	−0.291805	+	1.08278i	−0.00967856	+	0.0359136i
$910$	2.22062	−	1.97293i	0.0736127	−	0.0654020i
$911$	−8.19262	−	46.4627i	−0.271434	−	1.53938i	−0.750067	−	0.661362i	$-0.769979\pi$
$911$	−8.19262	−	46.4627i	−0.271434	−	1.53938i	0.478633	−	0.878015i	$-0.341132\pi$
$912$	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
$915$	26.3534	−	14.6552i	0.871216	−	0.484484i
$916$	−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	$0.339971\pi$
$920$	6.20097	−	7.82925i	0.204440	−	0.258123i
$921$	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
$925$	−31.1919	+	20.4423i	−1.02558	+	0.672137i
$926$	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	0.516600	−	0.856227i	$-0.327197\pi$
$929$	11.0326	+	4.01553i	0.361967	+	0.131745i	−0.154633	+	0.987972i	$0.549420\pi$
$930$	21.7033	+	18.8143i	0.711680	+	0.616944i
$931$	−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
$935$	37.0645	+	12.3155i	1.21214	+	0.402760i
$936$	4.24718	−	6.04702i	0.138823	−	0.197653i
$937$	22.2280	−	12.8334i	0.726159	−	0.419248i	−0.0908566	−	0.995864i	$-0.528961\pi$
$937$	22.2280	−	12.8334i	0.726159	−	0.419248i	0.817015	+	0.576616i	$0.195627\pi$
$938$	5.07969	−	0.895686i	0.165858	−	0.0292452i
$939$	26.3657	+	16.8235i	0.860412	+	0.549016i
$940$	10.8746	+	17.6627i	0.354689	+	0.576093i
$941$	−3.73531	+	21.1840i	−0.121768	+	0.690578i	0.861408	+	0.507914i	$0.169583\pi$
$941$	−3.73531	+	21.1840i	−0.121768	+	0.690578i	−0.983175	+	0.182664i	$0.941528\pi$
$942$	15.3495	+	14.0856i	0.500115	+	0.458935i
$943$	−21.8213	−	26.0057i	−0.710600	−	0.846861i
$944$	10.9194			0.355395
$945$	−0.436662	−	6.25104i	−0.0142046	−	0.203346i
$946$	−32.5273			−1.05755
$947$	−13.8601	−	16.5178i	−0.450392	−	0.536756i	0.492298	−	0.870427i	$-0.336157\pi$
$947$	−13.8601	−	16.5178i	−0.450392	−	0.536756i	−0.942690	+	0.333671i	$0.891713\pi$
$948$	8.84380	−	2.78143i	0.287233	−	0.0903367i
$949$	1.12479	−	6.37901i	0.0365123	−	0.207071i
$950$	−7.46119	−	7.93435i	−0.242073	−	0.257424i
$951$	−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	$-0.653165\pi$
$953$	2.26739	−	1.30908i	0.0734480	−	0.0424052i	0.536274	+	0.844044i	$0.319831\pi$
$954$	−0.336955	+	0.0897661i	−0.0109093	+	0.00290628i
$955$	15.0392	−	45.2616i	0.486655	−	1.46463i
$956$	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
$960$	3.80283	+	0.733790i	0.122736	+	0.0236830i
$961$	−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
$965$	−23.0076	+	9.11857i	−0.740641	+	0.293537i
$966$	3.70224	−	1.92387i	0.119118	−	0.0618996i
$967$	4.40078	+	12.0910i	0.141520	+	0.388822i	0.990122	−	0.140209i	$-0.0447776\pi$
$967$	4.40078	+	12.0910i	0.141520	+	0.388822i	−0.848602	+	0.529031i	$0.822555\pi$
$968$	5.48636	+	0.967393i	0.176338	+	0.0310932i
$969$	−15.8026	−	3.51530i	−0.507651	−	0.112928i
$970$	2.62610	−	3.31568i	0.0843191	−	0.106460i
$971$	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
$975$	−20.9609	+	3.95998i	−0.671287	+	0.126821i
$976$	−1.35199	+	7.66749i	−0.0432760	+	0.245430i
$977$	−11.4374	−	31.4239i	−0.365914	−	1.00534i	−0.976900	−	0.213699i	$-0.931449\pi$
$977$	−11.4374	−	31.4239i	−0.365914	−	1.00534i	0.610985	−	0.791642i	$-0.290773\pi$
$978$	−1.58233	−	3.04498i	−0.0505973	−	0.0973678i
$979$	−6.77612	−	38.4293i	−0.216566	−	1.22821i
$980$	−9.96416	−	11.2151i	−0.318293	−	0.358253i
$981$	−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	$-0.805938\pi$
$983$	5.52588	−	15.1822i	0.176248	−	0.484238i	0.996089	+	0.0883534i	$0.0281605\pi$
$984$	5.04661	−	12.1588i	0.160880	−	0.387608i
$985$	−8.33948	+	15.4363i	−0.265718	+	0.491841i
$986$	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
$990$	12.2004	+	24.4304i	0.387753	+	0.776450i
$991$	17.0726	+	29.5706i	0.542329	+	0.939342i	0.998770	+	0.0495881i	$0.0157909\pi$
$991$	17.0726	+	29.5706i	0.542329	+	0.939342i	−0.456440	+	0.889754i	$0.650876\pi$
$992$	−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
$995$	0.625513	+	22.1195i	0.0198301	+	0.701235i
$996$	7.39287	+	23.5063i	0.234252	+	0.744825i
$997$	5.26635	+	6.27619i	0.166787	+	0.198769i	0.842964	−	0.537971i	$-0.180809\pi$
$997$	5.26635	+	6.27619i	0.166787	+	0.198769i	−0.676177	+	0.736740i	$0.736364\pi$
$998$		−	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.49.5	✓	108
3.2	odd	2		810.2.p.a.199.10		108
5.4	even	2	inner	270.2.p.a.49.14	yes	108
15.14	odd	2		810.2.p.a.199.1		108
27.11	odd	18		810.2.p.a.289.1		108
27.16	even	9	inner	270.2.p.a.259.14	yes	108
135.119	odd	18		810.2.p.a.289.10		108
135.124	even	18	inner	270.2.p.a.259.5	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.p.a.49.5	✓	108	1.1	even	1	trivial
270.2.p.a.49.14	yes	108	5.4	even	2	inner
270.2.p.a.259.5	yes	108	135.124	even	18	inner
270.2.p.a.259.14	yes	108	27.16	even	9	inner
810.2.p.a.199.1		108	15.14	odd	2
810.2.p.a.199.10		108	3.2	odd	2
810.2.p.a.289.1		108	27.11	odd	18
810.2.p.a.289.10		108	135.119	odd	18

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)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.376104 + 1.69072i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.90411 - 1.17233i) q^{5} +(1.53692 - 0.798664i) q^{6} +(0.531122 - 0.0936511i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.71709 - 1.27178i) q^{9} +O(q^{10})\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.376104 + 1.69072i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.90411 - 1.17233i) 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} +(-2.12200 - 0.705079i) 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} +(1.26594 + 3.66025i) 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} +(0.823871 + 2.07876i) 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} +(2.25130 - 4.46449i) q^{25} +2.46317 q^{26} +(3.17213 - 4.11553i) q^{27} +0.539315i q^{28} +(-0.558330 + 0.468495i) q^{29} +(1.99018 - 3.32252i) 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} +(0.901527 - 0.800971i) 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} +(1.06285 - 1.96732i) 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} +(-6.66459 + 0.763716i) 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} +(-4.86710 + 1.14512i) 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} +(-3.82447 + 0.611109i) 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} +(-0.802714 + 5.44902i) 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} +(-1.19307 - 0.175755i) 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} +(6.70149 + 5.48543i) 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} +(9.59072 - 0.271214i) 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} +(4.86896 + 4.61446i) 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} +(4.28539 + 2.31519i) 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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