LMFDB - Embedded newform 270.2.p.a.259.5

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			259.5
Character	$\chi$	$=$	270.259
Dual form			270.2.p.a.49.5

$q$-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 $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

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

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
$5$	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	0.273116	−	0.961981i	$-0.411946\pi$
$7$	0.531122	+	0.0936511i	0.200745	+	0.0353968i	−0.0723713	+	0.997378i	$0.523057\pi$
$8$	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	0.306637	−	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	0.500405	−	0.865792i	$-0.333185\pi$
$13$	−1.58330	−	1.88690i	−0.439128	−	0.523332i	−0.939533	+	0.342459i	$0.888740\pi$
$14$	−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	0.0236455	−	0.999720i	$-0.492473\pi$
$17$	3.71596	−	2.14541i	0.901252	−	0.520338i	0.877606	+	0.479383i	$0.159139\pi$
$18$	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	$0.0862799\pi$
$20$	0.823871	−	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	0.304921	−	0.952378i	$-0.401370\pi$
$23$	4.39867	−	0.775604i	0.917185	−	0.161725i	0.612264	+	0.790653i	$0.290259\pi$
$24$	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	0.589474	−	0.807787i	$-0.299335\pi$
$29$	−0.558330	−	0.468495i	−0.103679	−	0.0869973i	−0.693154	+	0.720790i	$0.743779\pi$
$30$	1.99018	+	3.32252i	0.363356	+	0.606607i
$31$	−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
$35$	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	−0.925965	−	0.377609i	$-0.876746\pi$
$37$	−6.45946	+	3.72937i	−1.06193	+	0.613105i	−0.135964	+	0.990714i	$0.543413\pi$
$38$	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	−0.971985	−	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	$0.0974264\pi$
$43$	2.73291	+	7.50862i	0.416765	+	1.14505i	−0.536759	+	0.843736i	$0.680351\pi$
$44$	−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	0.794126	−	0.607753i	$-0.207929\pi$
$47$	9.13513	+	1.61077i	1.33250	+	0.234955i	0.538370	+	0.842708i	$0.319040\pi$
$48$	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	$-0.997459\pi$
$53$		−	0.116236i		−	0.0159662i	0.999968	−	0.00798309i	$-0.00254112\pi$
$54$	−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	$0.862774\pi$
$60$	−3.82447	−	0.611109i	−0.493737	−	0.0788938i
$61$	−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
$65$	−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	0.246190	−	0.969221i	$-0.420821\pi$
$67$	−6.14767	−	7.32650i	−0.751057	−	0.895075i	−0.997247	+	0.0741468i	$0.976377\pi$
$68$	−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	0.898413	+	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	0.360770	−	0.932655i	$-0.382514\pi$
$73$	−2.27739	−	1.31485i	−0.266548	−	0.153892i	−0.627318	+	0.778763i	$0.715847\pi$
$74$	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	0.382297	−	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	$0.507407\pi$
$83$	−9.14477	+	10.8983i	−1.00377	+	1.19624i	−0.980501	+	0.196515i	$0.937037\pi$
$84$	−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	0.491900	+	0.870651i	$0.336302\pi$
$89$	−4.79299	+	8.30170i	−0.508056	+	0.879979i	−0.999956	+	0.00932743i	$0.997031\pi$
$90$	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	0.902506	−	0.430678i	$-0.141726\pi$
$97$	−0.646954	−	1.77749i	−0.0656882	−	0.180477i	−0.968194	+	0.250201i	$0.919503\pi$
$98$	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	−0.987867	−	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	−0.990911	−	0.134519i	$-0.957051\pi$
$103$	−1.47527	+	4.05326i	−0.145362	+	0.399380i	0.845549	+	0.533898i	$0.179273\pi$
$104$	−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	$-0.933214\pi$
$107$		−	4.30890i		−	0.416557i	0.978070	−	0.208279i	$-0.0667860\pi$
$108$	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	0.169384	+	0.985550i	$0.445822\pi$
$113$	−6.31294	+	17.3447i	−0.593871	+	1.63165i	−0.763255	+	0.646097i	$0.776400\pi$
$114$	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	0.0760690	−	0.997103i	$-0.475763\pi$
$127$	−8.44545	−	4.87598i	−0.749413	−	0.432674i	−0.825482	+	0.564429i	$0.809096\pi$
$128$	−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	−0.999201	−	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
$135$	1.21534	+	11.5552i	0.104600	+	0.994514i
$136$	4.29082			0.367934
$137$	4.54631	−	5.41808i	0.388417	−	0.462898i	−0.536035	−	0.844196i	$-0.680078\pi$
$137$	4.54631	−	5.41808i	0.388417	−	0.462898i	0.924452	+	0.381298i	$0.124523\pi$
$138$	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	$0.932927\pi$
$140$	0.632254	−	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	−0.788110	−	0.615535i	$-0.788940\pi$
$149$	−3.89120	+	3.26511i	−0.318780	+	0.267488i	0.469330	+	0.883023i	$0.344496\pi$
$150$	−0.105550	+	8.65961i	−0.00861812	+	0.707054i
$151$	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
$155$	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	−0.660222	−	0.751071i	$-0.729538\pi$
$157$	4.11379	−	11.3026i	0.328317	−	0.902042i	0.988538	−	0.150971i	$-0.0482401\pi$
$158$	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	$0.0247227\pi$
$163$			1.98122i			0.155181i	−0.996985	+	0.0775905i	$0.975277\pi$
$164$	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	−0.710139	−	0.704061i	$-0.751368\pi$
$167$	3.70137	−	10.1694i	0.286421	−	0.786934i	0.996560	−	0.0828733i	$-0.0264097\pi$
$168$	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	−0.674047	−	0.738688i	$-0.735446\pi$
$173$	−8.31946	−	22.8575i	−0.632517	−	1.73783i	0.0415308	−	0.999137i	$-0.486777\pi$
$174$	−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	0.946109	−	0.323848i	$-0.104977\pi$
$179$	2.57674	+	4.46304i	0.192594	+	0.333583i	−0.753515	+	0.657431i	$0.771643\pi$
$180$	0.405180	+	6.69596i	0.0302004	+	0.499087i
$181$	−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
$185$	−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	0.999961	+	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	−0.551569	−	0.834129i	$-0.685971\pi$
$193$	−10.8998	+	1.92193i	−0.784585	+	0.138344i	−0.233016	+	0.972473i	$0.574860\pi$
$194$	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	0.238004	−	0.971264i	$-0.423507\pi$
$197$	−6.79514	−	3.92318i	−0.484134	−	0.279515i	−0.722138	+	0.691749i	$0.756840\pi$
$198$	−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	$0.947409\pi$
$200$	−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	−0.747701	−	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
$220$	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	0.788258	−	0.615345i	$-0.210983\pi$
$223$	19.6897	+	3.47182i	1.31852	+	0.232490i	0.530260	+	0.847835i	$0.322094\pi$
$224$	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	−0.836360	−	0.548181i	$-0.815320\pi$
$227$	−8.25698	−	22.6859i	−0.548035	−	1.50571i	0.288325	−	0.957533i	$-0.406902\pi$
$228$	−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	$0.149011\pi$
$230$	−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	−0.859548	−	0.511055i	$-0.829255\pi$
$233$	−12.9249	+	7.46217i	−0.846735	+	0.488863i	0.0128126	+	0.999918i	$0.495922\pi$
$234$	−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	0.968606	+	0.248601i	$0.0799708\pi$
$239$	2.21754	+	12.5763i	0.143441	+	0.813492i	−0.825165	+	0.564891i	$0.808918\pi$
$240$	0.0622870	+	3.87248i	0.00402061	+	0.249968i
$241$	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
$245$	−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	−0.168908	−	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
$255$	−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	0.899658	+	0.436595i	$0.143816\pi$
$257$	18.8110	+	22.4180i	1.17340	+	1.39840i	0.273738	+	0.961804i	$0.411740\pi$
$258$	−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	0.437876	−	0.899035i	$-0.355731\pi$
$263$	8.78743	+	1.54946i	0.541856	+	0.0955439i	0.103980	+	0.994579i	$0.466842\pi$
$264$	−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	−0.402825	−	0.915277i	$-0.631972\pi$
$277$	−18.2145	−	3.21170i	−1.09440	−	0.192972i	−0.691575	+	0.722305i	$0.743083\pi$
$278$	−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	−0.844821	−	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	0.435957	−	0.899968i	$-0.356410\pi$
$283$	−8.84939	−	10.5463i	−0.526042	−	0.626912i	−0.961998	+	0.273056i	$0.911966\pi$
$284$	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	0.194672	−	0.980868i	$-0.437636\pi$
$293$	12.2060	−	2.15225i	0.713081	−	0.125736i	0.518409	+	0.855133i	$0.326524\pi$
$294$	−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	−0.590730	+	0.806870i	$0.701160\pi$
$307$	−27.7691	+	16.0325i	−1.58486	+	0.915022i	−0.994134	+	0.108152i	$0.965507\pi$
$308$	−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	−0.674133	−	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	$0.0593638\pi$
$313$	6.17591	+	16.9682i	0.349083	+	0.959097i	−0.633577	+	0.773680i	$0.718414\pi$
$314$	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	0.982831	−	0.184507i	$-0.0590690\pi$
$317$	32.8188	+	5.78683i	1.84329	+	0.325021i	0.860454	+	0.509528i	$0.170180\pi$
$318$	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	0.909072	+	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
$335$	−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	0.999943	−	0.0106706i	$-0.00339663\pi$
$337$	14.9760	+	17.8477i	0.815796	+	0.972228i	−0.184147	+	0.982899i	$0.558952\pi$
$338$	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	0.197792	−	0.980244i	$-0.436623\pi$
$347$	13.3920	−	2.36136i	0.718918	−	0.126765i	0.521127	+	0.853479i	$0.325512\pi$
$348$	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	−0.851398	−	0.524521i	$-0.824245\pi$
$353$	−3.51345	+	4.18717i	−0.187002	+	0.222861i	0.664396	+	0.747381i	$0.268689\pi$
$354$	−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	−0.770480	−	0.637464i	$-0.779984\pi$
$359$	3.16078	−	5.47463i	0.166820	−	0.288940i	0.937300	+	0.348524i	$0.113317\pi$
$360$	−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	−0.988090	−	0.153877i	$-0.950824\pi$
$367$	−6.32341	−	17.3734i	−0.330079	−	0.906886i	0.658011	−	0.753009i	$-0.271398\pi$
$368$	−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	−0.904183	−	0.427145i	$-0.859519\pi$
$373$	1.21721	−	3.34426i	0.0630248	−	0.173159i	0.967208	+	0.253986i	$0.0817416\pi$
$374$	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	−0.855785	−	0.517332i	$-0.826925\pi$
$383$	2.58954	−	7.11469i	0.132319	−	0.363544i	0.988104	+	0.153788i	$0.0491474\pi$
$384$	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	−0.773728	−	0.633518i	$-0.781610\pi$
$389$	−18.9188	+	6.88588i	−0.959221	+	0.349128i	−0.185493	+	0.982646i	$0.559388\pi$
$390$	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	0.761095	−	0.648640i	$-0.224662\pi$
$397$	11.5545	+	6.67099i	0.579903	+	0.334807i	−0.181192	+	0.983448i	$0.557995\pi$
$398$	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	−0.797046	−	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
$405$	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	0.781847	+	0.623470i	$0.214278\pi$
$409$	5.26607	+	29.8654i	0.260391	+	1.47675i	−0.521456	+	0.853278i	$0.674611\pi$
$410$	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	0.664857	−	0.746971i	$-0.268493\pi$
$419$	31.0303	−	26.0375i	1.51593	−	1.27202i	0.851074	−	0.525046i	$-0.175952\pi$
$420$	−1.97403	−	0.682739i	−0.0963226	−	0.0333142i
$421$	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
$425$	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	$0.149180\pi$
$433$			18.7982i			0.903385i	−0.892174	+	0.451693i	$0.850820\pi$
$434$	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	−0.809709	−	0.586831i	$-0.800375\pi$
$439$	3.18217	−	18.0470i	0.151877	−	0.861336i	0.961586	−	0.274504i	$-0.0885138\pi$
$440$	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	0.998076	+	0.0620063i	$0.0197499\pi$
$443$	5.75361	+	15.8079i	0.273362	+	0.751057i	−0.724713	+	0.689050i	$0.758028\pi$
$444$	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	0.790460	−	0.612514i	$-0.209842\pi$
$449$	−2.86531	−	4.96287i	−0.135222	−	0.234212i	−0.925682	+	0.378302i	$0.876508\pi$
$450$	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	−0.882509	−	0.470296i	$-0.844147\pi$
$457$	−5.68883	+	6.77968i	−0.266112	+	0.317140i	0.616397	+	0.787436i	$0.288592\pi$
$458$			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	−0.370505	−	0.928830i	$-0.620816\pi$
$463$	−8.62824	+	1.52139i	−0.400988	+	0.0707050i	−0.0304826	+	0.999535i	$0.509704\pi$
$464$	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	0.548727	−	0.836001i	$-0.315113\pi$
$467$	2.14140	+	1.23634i	0.0990924	+	0.0572110i	−0.449635	+	0.893212i	$0.648446\pi$
$468$	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	0.840129	+	0.542387i	$0.182479\pi$
$479$	−2.95115	+	16.7368i	−0.134841	+	0.764724i	−0.974970	+	0.222336i	$0.928632\pi$
$480$	−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	$0.228529\pi$
$487$			29.0344i			1.31567i	−0.753160	+	0.657837i	$0.771471\pi$
$488$	−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	−0.159136	−	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
$495$	−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	−0.611062	−	0.791583i	$-0.709257\pi$
$499$	1.39359	−	1.16936i	0.0623856	−	0.0523477i	0.673447	+	0.739235i	$0.264813\pi$
$500$	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	−0.0609321	−	0.998142i	$-0.519407\pi$
$503$	17.3370	−	10.0095i	0.773018	−	0.446302i	0.833950	+	0.551840i	$0.186074\pi$
$504$	−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	0.946574	+	0.322485i	$0.104518\pi$
$509$	3.77631	+	21.4165i	0.167382	+	0.949270i	−0.779192	+	0.626785i	$0.784371\pi$
$510$	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	−0.309243	−	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	0.330742	−	0.943721i	$-0.392701\pi$
$523$	30.0364	−	17.3415i	1.31340	−	0.758291i	0.982657	+	0.185430i	$0.0593678\pi$
$524$	−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	−0.123978	−	0.992285i	$-0.539565\pi$
$547$	−13.5618	−	2.39131i	−0.579860	−	0.102245i	−0.455883	+	0.890040i	$0.650676\pi$
$548$	−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	−0.858612	−	0.512626i	$-0.828673\pi$
$557$	−19.9184	+	11.4999i	−0.843970	+	0.487266i	0.0146417	+	0.999893i	$0.495339\pi$
$558$	−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	−0.602207	−	0.798340i	$-0.705712\pi$
$563$	−21.2374	+	3.74472i	−0.895048	+	0.157821i	−0.292841	+	0.956161i	$0.594601\pi$
$564$	−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	0.373741	−	0.927533i	$-0.378075\pi$
$569$	−11.3258	−	9.50345i	−0.474801	−	0.398405i	−0.848542	+	0.529128i	$0.822519\pi$
$570$	8.43537	−	0.135679i	0.353319	−	0.00568296i
$571$	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
$575$	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	−0.382554	−	0.923933i	$-0.624955\pi$
$577$	5.43636	−	3.13868i	0.226319	−	0.130665i	0.608873	+	0.793268i	$0.291622\pi$
$578$	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	−0.402746	−	0.915312i	$-0.631944\pi$
$587$	−26.5118	−	4.67475i	−1.09426	−	0.192947i	−0.691513	+	0.722364i	$0.743055\pi$
$588$	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	$-0.921125\pi$
$593$		−	11.9452i		−	0.490529i	0.969456	−	0.245264i	$-0.0788747\pi$
$594$	−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	$0.596601\pi$
$600$	8.54638	−	1.39978i	0.348905	−	0.0571457i
$601$	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
$605$	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	0.480686	−	0.876893i	$-0.340388\pi$
$607$	−11.4898	−	13.6930i	−0.466355	−	0.555781i	−0.947041	+	0.321112i	$0.895943\pi$
$608$	−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	−0.990599	−	0.136800i	$-0.956318\pi$
$613$	−39.7223	−	22.9337i	−1.60437	−	0.926284i	−0.613772	−	0.789483i	$-0.710349\pi$
$614$	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	−0.139817	−	0.990177i	$-0.544651\pi$
$617$	1.67563	−	0.295459i	0.0674583	−	0.0118947i	0.207275	+	0.978283i	$0.433540\pi$
$618$	−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
$625$	−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	0.965274	−	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
$635$	−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	0.888375	+	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	$-0.747578\pi$
$643$	7.44994	−	20.4685i	0.293797	−	0.807200i	0.995503	−	0.0947334i	$-0.0301999\pi$
$644$	−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	$-0.951197\pi$
$647$		−	7.76918i		−	0.305438i	0.988270	−	0.152719i	$-0.0488030\pi$
$648$	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	−0.694216	−	0.719767i	$-0.744249\pi$
$653$	7.67233	−	21.0796i	0.300241	−	0.824907i	0.994457	−	0.105140i	$-0.0335290\pi$
$654$	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	−0.652418	−	0.757859i	$-0.726245\pi$
$659$	−17.0727	+	6.21395i	−0.665057	+	0.242061i	−0.0126389	+	0.999920i	$0.504023\pi$
$660$	−15.4804	+	2.98708i	−0.602573	+	0.116272i
$661$	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
$665$	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	−0.282279	−	0.959332i	$-0.591090\pi$
$673$	18.4578	−	21.9972i	0.711497	−	0.847929i	0.993775	+	0.111404i	$0.0355347\pi$
$674$	−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	0.0546194	+	0.998507i	$0.482605\pi$
$677$	−24.4113	+	29.0923i	−0.938203	+	1.11811i	−0.992822	+	0.119599i	$0.961839\pi$
$678$	−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	0.990458	−	0.137812i	$-0.0440071\pi$
$683$	35.7083	+	20.6162i	1.36634	+	0.788856i	0.375880	+	0.926668i	$0.377340\pi$
$684$	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	−0.342084	−	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
$695$	−0.702781	+	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	−0.965601	−	0.260028i	$-0.916268\pi$
$709$	0.817504	−	4.63629i	0.0307020	−	0.174120i	0.996303	+	0.0859085i	$0.0273793\pi$
$710$	−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	0.661823	−	0.749660i	$-0.269783\pi$
$719$	−8.53531	−	14.7836i	−0.318313	−	0.551335i	−0.980136	+	0.198325i	$0.936450\pi$
$720$	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	−0.269899	−	0.962889i	$-0.586990\pi$
$727$	19.5543	−	23.3039i	0.725229	−	0.864294i	0.995128	+	0.0985945i	$0.0314347\pi$
$728$		−	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	0.738311	−	0.674460i	$-0.235623\pi$
$733$	45.0180	−	7.93788i	1.66278	−	0.293192i	0.924465	+	0.381268i	$0.124512\pi$
$734$	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	0.808047	−	0.589118i	$-0.200525\pi$
$739$	−2.88611	−	4.99888i	−0.106167	−	0.183887i	−0.914214	+	0.405231i	$0.867191\pi$
$740$	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	0.285053	−	0.958512i	$-0.407989\pi$
$743$	−19.3095	−	23.0121i	−0.708395	−	0.844233i	−0.993449	+	0.114279i	$0.963544\pi$
$744$	−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	0.0169082	−	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	$-0.781616\pi$
$757$		−	34.8600i		−	1.26701i	0.773739	−	0.633504i	$-0.218384\pi$
$758$	−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	0.640056	−	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
$765$	−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	−0.194824	−	0.980838i	$-0.562414\pi$
$769$	20.4455	−	17.1558i	0.737282	−	0.618653i	0.932106	+	0.362185i	$0.117969\pi$
$770$	−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	−0.240047	−	0.970761i	$-0.577163\pi$
$773$	13.3630	−	7.71514i	0.480634	−	0.277494i	0.720681	+	0.693267i	$0.243829\pi$
$774$	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	0.468586	−	0.883418i	$-0.344764\pi$
$787$	33.9745	−	5.99062i	1.21106	−	0.213542i	0.742473	+	0.669876i	$0.233653\pi$
$788$	−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	0.699054	−	0.715069i	$-0.253605\pi$
$797$	−3.57242	−	4.25745i	−0.126542	−	0.150806i	−0.825595	+	0.564263i	$0.809160\pi$
$798$	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	−0.168325	−	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	0.455661	−	0.890153i	$-0.349403\pi$
$823$	−14.3467	−	17.0977i	−0.500093	−	0.595988i	−0.955755	+	0.294165i	$0.904958\pi$
$824$	−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	−0.614920	−	0.788590i	$-0.710812\pi$
$827$	−6.88573	+	3.97548i	−0.239440	+	0.138241i	0.375479	+	0.926831i	$0.377478\pi$
$828$	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	$0.139938\pi$
$830$	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	0.395830	−	0.918324i	$-0.370457\pi$
$839$	−12.7392	−	10.6895i	−0.439807	−	0.369042i	−0.835637	+	0.549282i	$0.814901\pi$
$840$	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	−0.810899	−	0.585186i	$-0.801021\pi$
$853$	−16.5267	−	45.4068i	−0.565865	−	1.55470i	0.245034	−	0.969514i	$-0.421201\pi$
$854$	−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	0.0802178	−	0.996777i	$-0.474438\pi$
$857$	−5.42516	−	0.956602i	−0.185320	−	0.0326769i	−0.265538	+	0.964100i	$0.585550\pi$
$858$	−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	$0.476882\pi$
$860$	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	$0.113596\pi$
$863$			20.5253i			0.698689i	−0.936994	+	0.349344i	$0.886404\pi$
$864$	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	0.989190	+	0.146642i	$0.0468466\pi$
$877$	28.4839	+	33.9458i	0.961833	+	1.14627i	−0.0273565	+	0.999626i	$0.508709\pi$
$878$	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	0.924846	−	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	0.629996	−	0.776598i	$-0.283056\pi$
$883$	8.09566	+	4.67403i	0.272441	+	0.157294i	−0.357556	+	0.933892i	$0.616390\pi$
$884$	−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	−0.150588	−	0.988597i	$-0.548117\pi$
$887$	1.37077	−	0.241704i	0.0460260	−	0.00811563i	0.196614	+	0.980481i	$0.437005\pi$
$888$	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	0.958149	−	0.286270i	$-0.0924156\pi$
$907$	1.20927	+	3.32245i	0.0401532	+	0.110320i	−0.917996	+	0.396590i	$0.870193\pi$
$908$	−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	0.478633	+	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
$915$	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	−0.154633	−	0.987972i	$-0.549420\pi$
$929$	11.0326	−	4.01553i	0.361967	−	0.131745i	0.516600	+	0.856227i	$0.327197\pi$
$930$	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	0.817015	−	0.576616i	$-0.195627\pi$
$937$	22.2280	+	12.8334i	0.726159	+	0.419248i	−0.0908566	+	0.995864i	$0.528961\pi$
$938$	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	−0.983175	−	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
$945$	−0.436662	+	6.25104i	−0.0142046	+	0.203346i
$946$	−32.5273			−1.05755
$947$	−13.8601	+	16.5178i	−0.450392	+	0.536756i	−0.942690	−	0.333671i	$-0.891713\pi$
$947$	−13.8601	+	16.5178i	−0.450392	+	0.536756i	0.492298	+	0.870427i	$0.336157\pi$
$948$	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	0.536274	−	0.844044i	$-0.319831\pi$
$953$	2.26739	+	1.30908i	0.0734480	+	0.0424052i	−0.462826	+	0.886449i	$0.653165\pi$
$954$	−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	−0.848602	−	0.529031i	$-0.822555\pi$
$967$	4.40078	−	12.0910i	0.141520	−	0.388822i	0.990122	+	0.140209i	$0.0447776\pi$
$968$	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	0.610985	+	0.791642i	$0.290773\pi$
$977$	−11.4374	+	31.4239i	−0.365914	+	1.00534i	−0.976900	+	0.213699i	$0.931449\pi$
$978$	−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	0.996089	−	0.0883534i	$-0.0281605\pi$
$983$	5.52588	+	15.1822i	0.176248	+	0.484238i	−0.819841	+	0.572591i	$0.805938\pi$
$984$	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	−0.456440	−	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
$995$	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	−0.676177	−	0.736740i	$-0.736364\pi$
$997$	5.26635	−	6.27619i	0.166787	−	0.198769i	0.842964	+	0.537971i	$0.180809\pi$
$998$			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.259.5	yes	108
3.2	odd	2		810.2.p.a.289.10		108
5.4	even	2	inner	270.2.p.a.259.14	yes	108
15.14	odd	2		810.2.p.a.289.1		108
27.5	odd	18		810.2.p.a.199.1		108
27.22	even	9	inner	270.2.p.a.49.14	yes	108
135.49	even	18	inner	270.2.p.a.49.5	✓	108
135.59	odd	18		810.2.p.a.199.10		108

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

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.376104 - 1.69072i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.90411 + 1.17233i) q^{5} +(1.53692 + 0.798664i) q^{6} +(0.531122 + 0.0936511i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.71709 + 1.27178i) q^{9} +O(q^{10})\)	\(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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