LMFDB - Embedded newform 135.2.q.a.38.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			38.10
Character	$\chi$	$=$	135.38
Dual form			135.2.q.a.32.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0559313 + 0.639298i) q^{2} +(0.432570 + 1.67717i) q^{3} +(1.56404 - 0.275783i) q^{4} +(2.15338 - 0.602474i) q^{5} +(-1.04801 + 0.370347i) q^{6} +(-2.47086 - 3.52875i) q^{7} +(0.595975 + 2.22421i) q^{8} +(-2.62577 + 1.45098i) q^{9} +O(q^{10})$	\(q+(0.0559313 + 0.639298i) q^{2} +(0.432570 + 1.67717i) q^{3} +(1.56404 - 0.275783i) q^{4} +(2.15338 - 0.602474i) q^{5} +(-1.04801 + 0.370347i) q^{6} +(-2.47086 - 3.52875i) q^{7} +(0.595975 + 2.22421i) q^{8} +(-2.62577 + 1.45098i) q^{9} +(0.505601 + 1.34295i) q^{10} +(-0.157893 - 0.433806i) q^{11} +(1.13909 + 2.50386i) q^{12} +(-5.28596 - 0.462462i) q^{13} +(2.11772 - 1.77698i) q^{14} +(1.94193 + 3.35095i) q^{15} +(1.59619 - 0.580964i) q^{16} +(-1.32114 + 4.93057i) q^{17} +(-1.07447 - 1.59749i) q^{18} +(-1.03667 - 0.598524i) q^{19} +(3.20182 - 1.53616i) q^{20} +(4.84948 - 5.67047i) q^{21} +(0.268500 - 0.125204i) q^{22} +(-2.25381 - 1.57814i) q^{23} +(-3.47256 + 1.96168i) q^{24} +(4.27405 - 2.59470i) q^{25} -3.40517i q^{26} +(-3.56937 - 3.77619i) q^{27} +(-4.83770 - 4.83770i) q^{28} +(0.00462297 + 0.00387914i) q^{29} +(-2.03364 + 1.42890i) q^{30} +(-0.387533 - 2.19781i) q^{31} +(2.40699 + 5.16180i) q^{32} +(0.659265 - 0.452464i) q^{33} +(-3.22599 - 0.568830i) q^{34} +(-7.44667 - 6.11010i) q^{35} +(-3.70665 + 2.99354i) q^{36} +(7.25290 + 1.94341i) q^{37} +(0.324653 - 0.696220i) q^{38} +(-1.51093 - 9.06548i) q^{39} +(2.62339 + 4.43050i) q^{40} +(3.02828 + 3.60897i) q^{41} +(3.89636 + 2.78310i) q^{42} +(1.72881 + 0.806157i) q^{43} +(-0.366587 - 0.634947i) q^{44} +(-4.78008 + 4.70647i) q^{45} +(0.882840 - 1.52912i) q^{46} +(9.24502 - 6.47343i) q^{47} +(1.66484 + 2.42576i) q^{48} +(-3.95281 + 10.8602i) q^{49} +(1.89784 + 2.58727i) q^{50} +(-8.84086 - 0.0829548i) q^{51} +(-8.39501 + 0.734468i) q^{52} +(-3.94023 + 3.94023i) q^{53} +(2.21447 - 2.49310i) q^{54} +(-0.601359 - 0.839022i) q^{55} +(6.37611 - 7.59875i) q^{56} +(0.555389 - 1.99758i) q^{57} +(-0.00222135 + 0.00317242i) q^{58} +(0.388624 + 0.141448i) q^{59} +(3.96140 + 4.70548i) q^{60} +(0.399307 - 2.26458i) q^{61} +(1.38338 - 0.370675i) q^{62} +(11.6081 + 5.68050i) q^{63} +(-0.223194 + 0.128861i) q^{64} +(-11.6613 + 2.18880i) q^{65} +(0.326133 + 0.396160i) q^{66} +(-0.511475 + 5.84619i) q^{67} +(-0.706556 + 8.07597i) q^{68} +(1.67186 - 4.46267i) q^{69} +(3.48967 - 5.10238i) q^{70} +(0.648656 - 0.374502i) q^{71} +(-4.79218 - 4.97550i) q^{72} +(11.1032 - 2.97508i) q^{73} +(-0.836752 + 4.74546i) q^{74} +(6.20057 + 6.04590i) q^{75} +(-1.78647 - 0.650220i) q^{76} +(-1.14066 + 1.62904i) q^{77} +(5.71103 - 1.47297i) q^{78} +(1.01095 - 1.20481i) q^{79} +(3.08717 - 2.21269i) q^{80} +(4.78929 - 7.61989i) q^{81} +(-2.13783 + 2.13783i) q^{82} +(-10.6371 + 0.930629i) q^{83} +(6.02097 - 10.2063i) q^{84} +(0.125623 + 11.4133i) q^{85} +(-0.418680 + 1.15031i) q^{86} +(-0.00450619 + 0.00943149i) q^{87} +(0.870776 - 0.609724i) q^{88} +(-6.36010 + 11.0160i) q^{89} +(-3.27619 - 2.79265i) q^{90} +(11.4289 + 19.7955i) q^{91} +(-3.96028 - 1.84671i) q^{92} +(3.51845 - 1.60066i) q^{93} +(4.65554 + 5.54825i) q^{94} +(-2.59294 - 0.664279i) q^{95} +(-7.61600 + 6.26976i) q^{96} +(-3.62057 + 7.76434i) q^{97} +(-7.16401 - 1.91959i) q^{98} +(1.04404 + 0.909974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.0559313	+	0.639298i	0.0395494	+	0.452052i	0.989989	+	0.141143i	$0.0450777\pi$
$2$	0.0559313	+	0.639298i	0.0395494	+	0.452052i	−0.950440	+	0.310909i	$0.899367\pi$
$3$	0.432570	+	1.67717i	0.249745	+	0.968312i
$3$	0.432570	+	1.67717i	0.249745	+	0.968312i
$4$	1.56404	−	0.275783i	0.782021	−	0.137891i
$5$	2.15338	−	0.602474i	0.963019	−	0.269434i
$5$	2.15338	−	0.602474i	0.963019	−	0.269434i
$6$	−1.04801	+	0.370347i	−0.427850	+	0.151194i
$7$	−2.47086	−	3.52875i	−0.933897	−	1.33374i	−0.942651	−	0.333781i	$-0.891675\pi$
$7$	−2.47086	−	3.52875i	−0.933897	−	1.33374i	0.00875387	−	0.999962i	$-0.497214\pi$
$8$	0.595975	+	2.22421i	0.210709	+	0.786377i
$9$	−2.62577	+	1.45098i	−0.875255	+	0.483661i
$10$	0.505601	+	1.34295i	0.159885	+	0.424678i
$11$	−0.157893	−	0.433806i	−0.0476064	−	0.130798i	0.913611	−	0.406590i	$-0.133282\pi$
$11$	−0.157893	−	0.433806i	−0.0476064	−	0.130798i	−0.961217	+	0.275792i	$0.911060\pi$
$12$	1.13909	+	2.50386i	0.328828	+	0.722803i
$13$	−5.28596	−	0.462462i	−1.46606	−	0.128264i	−0.674012	−	0.738720i	$-0.735430\pi$
$13$	−5.28596	−	0.462462i	−1.46606	−	0.128264i	−0.792050	+	0.610457i	$0.790986\pi$
$14$	2.11772	−	1.77698i	0.565986	−	0.474918i
$15$	1.94193	+	3.35095i	0.501405	+	0.865213i
$16$	1.59619	−	0.580964i	0.399047	−	0.145241i
$17$	−1.32114	+	4.93057i	−0.320424	+	1.19584i	0.598409	+	0.801191i	$0.295800\pi$
$17$	−1.32114	+	4.93057i	−0.320424	+	1.19584i	−0.918833	+	0.394647i	$0.870867\pi$
$18$	−1.07447	−	1.59749i	−0.253256	−	0.376532i
$19$	−1.03667	−	0.598524i	−0.237829	−	0.137311i	0.376349	−	0.926478i	$-0.377179\pi$
$19$	−1.03667	−	0.598524i	−0.237829	−	0.137311i	−0.614179	+	0.789167i	$0.710513\pi$
$20$	3.20182	−	1.53616i	0.715948	−	0.343495i
$21$	4.84948	−	5.67047i	1.05824	−	1.23740i
$22$	0.268500	−	0.125204i	0.0572444	−	0.0266935i
$23$	−2.25381	−	1.57814i	−0.469952	−	0.329064i	0.314496	−	0.949259i	$-0.398165\pi$
$23$	−2.25381	−	1.57814i	−0.469952	−	0.329064i	−0.784448	+	0.620195i	$0.787054\pi$
$24$	−3.47256	+	1.96168i	−0.708834	+	0.400425i
$25$	4.27405	−	2.59470i	0.854810	−	0.518941i
$26$		−	3.40517i		−	0.667808i
$27$	−3.56937	−	3.77619i	−0.686925	−	0.726728i
$28$	−4.83770	−	4.83770i	−0.914239	−	0.914239i
$29$	0.00462297	+	0.00387914i	0.000858465	+	0.000720337i	0.643217	−	0.765684i	$-0.277599\pi$
$29$	0.00462297	+	0.00387914i	0.000858465	+	0.000720337i	−0.642358	+	0.766404i	$0.722044\pi$
$30$	−2.03364	+	1.42890i	−0.371290	+	0.260880i
$31$	−0.387533	−	2.19781i	−0.0696030	−	0.394738i	−0.999629	−	0.0272441i	$-0.991327\pi$
$31$	−0.387533	−	2.19781i	−0.0696030	−	0.394738i	0.930026	−	0.367494i	$-0.119784\pi$
$32$	2.40699	+	5.16180i	0.425499	+	0.912486i
$33$	0.659265	−	0.452464i	0.114763	−	0.0787638i
$34$	−3.22599	−	0.568830i	−0.553253	−	0.0975535i
$35$	−7.44667	−	6.11010i	−1.25872	−	1.03280i
$36$	−3.70665	+	2.99354i	−0.617775	+	0.498924i
$37$	7.25290	+	1.94341i	1.19237	+	0.319494i	0.799822	−	0.600238i	$-0.204927\pi$
$37$	7.25290	+	1.94341i	1.19237	+	0.319494i	0.392547	+	0.919732i	$0.371594\pi$
$38$	0.324653	−	0.696220i	0.0526656	−	0.112942i
$39$	−1.51093	−	9.06548i	−0.241942	−	1.45164i
$40$	2.62339	+	4.43050i	0.414794	+	0.700523i
$41$	3.02828	+	3.60897i	0.472939	+	0.563626i	0.948793	−	0.315898i	$-0.102306\pi$
$41$	3.02828	+	3.60897i	0.472939	+	0.563626i	−0.475855	+	0.879524i	$0.657861\pi$
$42$	3.89636	+	2.78310i	0.601221	+	0.429442i
$43$	1.72881	+	0.806157i	0.263641	+	0.122938i	0.549945	−	0.835201i	$-0.314649\pi$
$43$	1.72881	+	0.806157i	0.263641	+	0.122938i	−0.286304	+	0.958139i	$0.592427\pi$
$44$	−0.366587	−	0.634947i	−0.0552651	−	0.0957219i
$45$	−4.78008	+	4.70647i	−0.712572	+	0.701599i
$46$	0.882840	−	1.52912i	0.130168	−	0.225457i
$47$	9.24502	−	6.47343i	1.34853	−	0.944247i	0.348549	−	0.937290i	$-0.386674\pi$
$47$	9.24502	−	6.47343i	1.34853	−	0.944247i	0.999976	−	0.00695690i	$-0.00221447\pi$
$48$	1.66484	+	2.42576i	0.240298	+	0.350128i
$49$	−3.95281	+	10.8602i	−0.564687	+	1.55146i
$50$	1.89784	+	2.58727i	0.268395	+	0.365895i
$51$	−8.84086	−	0.0829548i	−1.23797	−	0.0116160i
$52$	−8.39501	+	0.734468i	−1.16418	+	0.101852i
$53$	−3.94023	+	3.94023i	−0.541233	+	0.541233i	−0.923890	−	0.382657i	$-0.875009\pi$
$53$	−3.94023	+	3.94023i	−0.541233	+	0.541233i	0.382657	+	0.923890i	$0.375009\pi$
$54$	2.21447	−	2.49310i	0.301351	−	0.339267i
$55$	−0.601359	−	0.839022i	−0.0810872	−	0.113134i
$56$	6.37611	−	7.59875i	0.852044	−	1.01543i
$57$	0.555389	−	1.99758i	0.0735631	−	0.264586i
$58$	−0.00222135	+	0.00317242i	−0.000291678	+	0.000416559i
$59$	0.388624	+	0.141448i	0.0505945	+	0.0184149i	0.367193	−	0.930145i	$-0.380319\pi$
$59$	0.388624	+	0.141448i	0.0505945	+	0.0184149i	−0.316599	+	0.948559i	$0.602541\pi$
$60$	3.96140	+	4.70548i	0.511415	+	0.607475i
$61$	0.399307	−	2.26458i	0.0511260	−	0.289950i	−0.948515	−	0.316731i	$-0.897415\pi$
$61$	0.399307	−	2.26458i	0.0511260	−	0.289950i	0.999641	+	0.0267812i	$0.00852575\pi$
$62$	1.38338	−	0.370675i	0.175689	−	0.0470758i
$63$	11.6081	+	5.68050i	1.46248	+	0.715676i
$64$	−0.223194	+	0.128861i	−0.0278993	+	0.0161077i
$65$	−11.6613	+	2.18880i	−1.44640	+	0.271487i
$66$	0.326133	+	0.396160i	0.0401441	+	0.0487639i
$67$	−0.511475	+	5.84619i	−0.0624866	+	0.714226i	0.898743	+	0.438476i	$0.144482\pi$
$67$	−0.511475	+	5.84619i	−0.0624866	+	0.714226i	−0.961230	+	0.275750i	$0.911074\pi$
$68$	−0.706556	+	8.07597i	−0.0856824	+	0.979355i
$69$	1.67186	−	4.46267i	0.201269	−	0.537242i
$70$	3.48967	−	5.10238i	0.417095	−	0.609851i
$71$	0.648656	−	0.374502i	0.0769813	−	0.0444452i	−0.461015	−	0.887392i	$-0.652515\pi$
$71$	0.648656	−	0.374502i	0.0769813	−	0.0444452i	0.537997	+	0.842947i	$0.319181\pi$
$72$	−4.79218	−	4.97550i	−0.564764	−	0.586368i
$73$	11.1032	−	2.97508i	1.29953	−	0.348207i	0.458255	−	0.888821i	$-0.348475\pi$
$73$	11.1032	−	2.97508i	1.29953	−	0.348207i	0.841271	+	0.540614i	$0.181808\pi$
$74$	−0.836752	+	4.74546i	−0.0972705	+	0.551648i
$75$	6.20057	+	6.04590i	0.715981	+	0.698120i
$76$	−1.78647	−	0.650220i	−0.204922	−	0.0745854i
$77$	−1.14066	+	1.62904i	−0.129991	+	0.185646i
$78$	5.71103	−	1.47297i	0.646647	−	0.166782i
$79$	1.01095	−	1.20481i	0.113741	−	0.135551i	−0.706170	−	0.708043i	$-0.749578\pi$
$79$	1.01095	−	1.20481i	0.113741	−	0.135551i	0.819911	+	0.572491i	$0.194023\pi$
$80$	3.08717	−	2.21269i	0.345156	−	0.247387i
$81$	4.78929	−	7.61989i	0.532143	−	0.846654i
$82$	−2.13783	+	2.13783i	−0.236084	+	0.236084i
$83$	−10.6371	+	0.930629i	−1.16758	+	0.102150i	−0.654411	−	0.756139i	$-0.727083\pi$
$83$	−10.6371	+	0.930629i	−1.16758	+	0.102150i	−0.513167	+	0.858289i	$0.671528\pi$
$84$	6.02097	−	10.2063i	0.656942	−	1.11359i
$85$	0.125623	+	11.4133i	0.0136257	+	1.23795i
$86$	−0.418680	+	1.15031i	−0.0451474	+	0.124041i
$87$	−0.00450619	+	0.00943149i	−0.000483114	+	0.00101116i
$88$	0.870776	−	0.609724i	0.0928250	−	0.0649968i
$89$	−6.36010	+	11.0160i	−0.674169	+	1.16770i	0.302542	+	0.953136i	$0.402165\pi$
$89$	−6.36010	+	11.0160i	−0.674169	+	1.16770i	−0.976711	+	0.214559i	$0.931168\pi$
$90$	−3.27619	−	2.79265i	−0.345341	−	0.294372i
$91$	11.4289	+	19.7955i	1.19808	+	2.07513i
$92$	−3.96028	−	1.84671i	−0.412888	−	0.192533i
$93$	3.51845	−	1.60066i	0.364847	−	0.165981i
$94$	4.65554	+	5.54825i	0.480182	+	0.572259i
$95$	−2.59294	−	0.664279i	−0.266030	−	0.0681535i
$96$	−7.61600	+	6.26976i	−0.777305	+	0.639904i
$97$	−3.62057	+	7.76434i	−0.367613	+	0.788349i	0.632294	+	0.774729i	$0.282114\pi$
$97$	−3.62057	+	7.76434i	−0.367613	+	0.788349i	−0.999907	+	0.0136208i	$0.995664\pi$
$98$	−7.16401	−	1.91959i	−0.723675	−	0.193908i
$99$	1.04404	+	0.909974i	0.104929	+	0.0914558i
$100$	5.96922	−	5.23694i	0.596922	−	0.523694i
$101$	−15.4590	−	2.72585i	−1.53823	−	0.271232i	−0.660663	−	0.750682i	$-0.729725\pi$
$101$	−15.4590	−	2.72585i	−1.53823	−	0.271232i	−0.877569	+	0.479450i	$0.840836\pi$
$102$	−0.441448	−	5.65658i	−0.0437099	−	0.560085i
$103$	−5.91592	−	12.6867i	−0.582912	−	1.25006i	−0.947758	−	0.318992i	$-0.896656\pi$
$103$	−5.91592	−	12.6867i	−0.582912	−	1.25006i	0.364845	−	0.931068i	$-0.381122\pi$
$104$	−2.12169	−	12.0327i	−0.208049	−	1.17990i
$105$	7.02644	−	15.1323i	0.685710	−	1.47676i
$106$	−2.73936	−	2.29860i	−0.266071	−	0.223260i
$107$	−2.86472	−	2.86472i	−0.276943	−	0.276943i	0.554945	−	0.831887i	$-0.312739\pi$
$107$	−2.86472	−	2.86472i	−0.276943	−	0.276943i	−0.831887	+	0.554945i	$0.812739\pi$
$108$	−6.62405	−	4.92175i	−0.637400	−	0.473596i
$109$			6.64284i			0.636269i	0.948046	+	0.318134i	$0.103056\pi$
$109$			6.64284i			0.636269i	−0.948046	+	0.318134i	$0.896944\pi$
$110$	0.502750	−	0.431375i	0.0479353	−	0.0411300i
$111$	−0.122027	+	13.0050i	−0.0115823	+	1.23438i
$112$	−5.99403	−	4.19706i	−0.566382	−	0.396585i
$113$	6.36611	−	2.96857i	0.598874	−	0.279259i	−0.0994488	−	0.995043i	$-0.531708\pi$
$113$	6.36611	−	2.96857i	0.598874	−	0.279259i	0.698322	+	0.715783i	$0.253930\pi$
$114$	1.30811	+	0.243332i	0.122516	+	0.0227901i
$115$	−5.80409	−	2.04046i	−0.541234	−	0.190274i
$116$	0.00830033	+	0.00479220i	0.000770666	+	0.000444944i
$117$	14.5507	−	6.45553i	1.34521	−	0.596814i
$118$	−0.0686908	+	0.256358i	−0.00632350	+	0.0235996i
$119$	20.6631	−	7.52076i	1.89418	−	0.689427i
$120$	−6.29588	+	6.31635i	−0.574732	+	0.576601i
$121$	8.26323	−	6.93367i	0.751203	−	0.630334i
$122$	1.47008	+	0.128615i	0.133094	+	0.0116443i
$123$	−4.74289	+	6.64007i	−0.427652	+	0.598715i
$124$	−1.21224	−	3.33059i	−0.108862	−	0.299096i
$125$	7.64040	−	8.16237i	0.683378	−	0.730065i
$126$	−2.98227	+	7.73872i	−0.265682	+	0.689420i
$127$	−2.17007	−	8.09882i	−0.192563	−	0.718654i	−0.992884	−	0.119083i	$-0.962005\pi$
$127$	−2.17007	−	8.09882i	−0.192563	−	0.718654i	0.800322	−	0.599571i	$-0.204662\pi$
$128$	6.43865	+	9.19534i	0.569102	+	0.812761i
$129$	−0.604227	+	3.24822i	−0.0531992	+	0.285990i
$130$	−2.05152	−	7.33260i	−0.179931	−	0.643112i
$131$	−11.2646	+	1.98625i	−0.984193	+	0.173540i	−0.642512	−	0.766276i	$-0.722108\pi$
$131$	−11.2646	+	1.98625i	−0.984193	+	0.173540i	−0.341682	+	0.939816i	$0.610996\pi$
$132$	0.906337	−	0.889487i	0.0788865	−	0.0774199i
$133$	0.449432	+	5.13704i	0.0389707	+	0.445437i
$134$	−3.76606			−0.325338
$135$	−9.96124	−	5.98110i	−0.857327	−	0.514771i
$136$	−11.7540			−1.00790
$137$	−0.898508	−	10.2700i	−0.0767647	−	0.877424i	−0.932773	−	0.360463i	$-0.882619\pi$
$137$	−0.898508	−	10.2700i	−0.0767647	−	0.877424i	0.856009	−	0.516961i	$-0.172937\pi$
$138$	2.94648	+	0.819214i	0.250821	+	0.0697362i
$139$	1.70385	−	0.300434i	0.144518	−	0.0254825i	−0.100921	−	0.994894i	$-0.532179\pi$
$139$	1.70385	−	0.300434i	0.144518	−	0.0254825i	0.245439	+	0.969412i	$0.421068\pi$
$140$	−13.3320	−	7.50279i	−1.12676	−	0.634102i
$141$	14.8561	+	12.7052i	1.25111	+	1.06997i
$142$	0.275698	+	0.393738i	0.0231361	+	0.0330417i
$143$	0.633995	+	2.36610i	0.0530173	+	0.197863i
$144$	−3.34824	+	3.84152i	−0.279020	+	0.320126i
$145$	0.0122921	+	0.00556802i	0.00102080	+	0.000462399i
$146$	2.52298	+	6.93182i	0.208803	+	0.573681i
$147$	−19.9243	−	1.93169i	−1.64333	−	0.159323i
$148$	11.8798	+	1.03935i	0.976513	+	0.0854339i
$149$	3.51771	−	2.95171i	0.288182	−	0.241813i	−0.487223	−	0.873277i	$-0.661990\pi$
$149$	3.51771	−	2.95171i	0.288182	−	0.241813i	0.775405	+	0.631464i	$0.217546\pi$
$150$	−3.51832	+	4.30217i	−0.287270	+	0.351270i
$151$	−4.16351	+	1.51539i	−0.338821	+	0.123321i	−0.505827	−	0.862635i	$-0.668813\pi$
$151$	−4.16351	+	1.51539i	−0.338821	+	0.123321i	0.167005	+	0.985956i	$0.446590\pi$
$152$	0.713411	−	2.66249i	0.0578653	−	0.215956i
$153$	−3.68517	−	14.8635i	−0.297928	−	1.20164i
$154$	−1.10524	−	0.638110i	−0.0890627	−	0.0514204i
$155$	−2.15863	−	4.49923i	−0.173385	−	0.361387i
$156$	−4.86326	−	13.7621i	−0.389372	−	1.10185i
$157$	0.754412	−	0.351788i	0.0602086	−	0.0280757i	−0.392281	−	0.919846i	$-0.628314\pi$
$157$	0.754412	−	0.351788i	0.0602086	−	0.0280757i	0.452489	+	0.891770i	$0.350536\pi$
$158$	0.826774	+	0.578913i	0.0657746	+	0.0460559i
$159$	−8.31285	−	4.90400i	−0.659252	−	0.388912i
$160$	8.29300	+	9.66515i	0.655619	+	0.764097i
$161$			11.8525i			0.934107i
$162$	5.13925	+	2.63559i	0.403777	+	0.207072i
$163$	−10.1572	−	10.1572i	−0.795571	−	0.795571i	0.186823	−	0.982394i	$-0.440181\pi$
$163$	−10.1572	−	10.1572i	−0.795571	−	0.795571i	−0.982394	+	0.186823i	$0.940181\pi$
$164$	5.73166	+	4.80943i	0.447567	+	0.375554i
$165$	1.14705	−	1.37151i	0.0892976	−	0.106772i
$166$	−1.18990	−	6.74824i	−0.0923540	−	0.523765i
$167$	9.48250	+	20.3353i	0.733778	+	1.57359i	0.816718	+	0.577038i	$0.195791\pi$
$167$	9.48250	+	20.3353i	0.733778	+	1.57359i	−0.0829395	+	0.996555i	$0.526431\pi$
$168$	15.5025	+	7.40680i	1.19604	+	0.571447i
$169$	14.9250	+	2.63168i	1.14808	+	0.202437i
$170$	−7.28948	+	0.718672i	−0.559078	+	0.0551196i
$171$	3.59051	+	0.0673863i	0.274573	+	0.00515316i
$172$	2.92626	+	0.784088i	0.223125	+	0.0597861i
$173$	−0.976093	+	2.09324i	−0.0742110	+	0.159146i	−0.939913	−	0.341413i	$-0.889094\pi$
$173$	−0.976093	+	2.09324i	−0.0742110	+	0.159146i	0.865702	+	0.500559i	$0.166872\pi$
$174$	−0.00628157	−	0.00235328i	−0.000476204	−	0.000178402i
$175$	−19.7166	−	8.67092i	−1.49044	−	0.655460i
$176$	−0.504052	−	0.600706i	−0.0379943	−	0.0452799i
$177$	−0.0691237	+	0.712973i	−0.00519565	+	0.0535903i
$178$	−7.39824	−	3.44986i	−0.554522	−	0.258578i
$179$	10.3891	+	17.9945i	0.776520	+	1.34497i	0.933936	+	0.357440i	$0.116350\pi$
$179$	10.3891	+	17.9945i	0.776520	+	1.34497i	−0.157416	+	0.987532i	$0.550316\pi$
$180$	−6.17828	+	8.67938i	−0.460502	+	0.646923i
$181$	1.61486	−	2.79701i	0.120031	−	0.207900i	−0.799748	−	0.600335i	$-0.795034\pi$
$181$	1.61486	−	2.79701i	0.120031	−	0.207900i	0.919780	+	0.392435i	$0.128367\pi$
$182$	−12.0160	+	8.41369i	−0.890685	+	0.623664i
$183$	3.97081	−	0.309888i	0.293531	−	0.0229076i
$184$	2.16689	−	5.95348i	0.159745	−	0.438896i
$185$	16.7891	−	0.184792i	1.23436	−	0.0135862i
$186$	1.22009	+	2.15981i	0.0894615	+	0.158365i
$187$	2.34751	−	0.205381i	0.171667	−	0.0150189i
$188$	12.6743	−	12.6743i	0.924372	−	0.924372i
$189$	−4.50583	+	21.9258i	−0.327751	+	1.59487i
$190$	0.279645	−	1.69482i	0.0202876	−	0.122955i
$191$	0.296698	−	0.353591i	0.0214683	−	0.0255850i	−0.755203	−	0.655490i	$-0.772462\pi$
$191$	0.296698	−	0.353591i	0.0214683	−	0.0255850i	0.776672	+	0.629905i	$0.216906\pi$
$192$	−0.312669	−	0.318592i	−0.0225649	−	0.0229924i
$193$	1.30491	−	1.86360i	0.0939292	−	0.134145i	−0.769437	−	0.638723i	$-0.779463\pi$
$193$	1.30491	−	1.86360i	0.0939292	−	0.134145i	0.863366	+	0.504578i	$0.168352\pi$
$194$	−5.16623	−	1.88035i	−0.370914	−	0.135001i
$195$	−8.71530	−	18.6111i	−0.624116	−	1.33277i
$196$	−3.18729	+	18.0760i	−0.227663	+	1.29114i
$197$	25.7926	−	6.91110i	1.83765	−	0.492396i	0.838986	−	0.544153i	$-0.183149\pi$
$197$	25.7926	−	6.91110i	1.83765	−	0.492396i	0.998660	+	0.0517571i	$0.0164821\pi$
$198$	−0.523350	+	0.718345i	−0.0371929	+	0.0510506i
$199$	−20.6539	+	11.9246i	−1.46412	+	0.845309i	−0.999198	−	0.0400428i	$-0.987251\pi$
$199$	−20.6539	+	11.9246i	−1.46412	+	0.845309i	−0.464921	+	0.885352i	$0.653917\pi$
$200$	8.31839	+	7.96001i	0.588199	+	0.562857i
$201$	−10.0263	+	1.67106i	−0.707199	+	0.117867i
$202$	0.877983	−	10.0354i	0.0617747	−	0.706088i
$203$	0.00226579	−	0.0258981i	0.000159027	−	0.00181769i
$204$	−13.8504	+	2.30841i	−0.969720	+	0.161621i
$205$	8.69534	+	5.94700i	0.607309	+	0.415357i
$206$	7.77970	−	4.49161i	0.542038	−	0.312946i
$207$	8.20783	+	0.873570i	0.570484	+	0.0607173i
$208$	−8.70605	+	2.33278i	−0.603656	+	0.161749i
$209$	−0.0959604	+	0.544219i	−0.00663772	+	0.0376444i
$210$	10.0671	+	3.64561i	0.694693	+	0.251571i
$211$	20.3867	+	7.42015i	1.40348	+	0.510825i	0.929209	−	0.369555i	$-0.120490\pi$
$211$	20.3867	+	7.42015i	1.40348	+	0.510825i	0.474270	+	0.880379i	$0.342712\pi$
$212$	−5.07605	+	7.24934i	−0.348624	+	0.497887i
$213$	0.908691	+	0.925905i	0.0622625	+	0.0634420i
$214$	1.67118	−	1.99163i	0.114239	−	0.136145i
$215$	4.20846	+	0.694397i	0.287015	+	0.0473575i
$216$	6.27178	−	10.1895i	0.426741	−	0.693310i
$217$	−6.79799	+	6.79799i	−0.461477	+	0.461477i
$218$	−4.24675	+	0.371543i	−0.287626	+	0.0251640i
$219$	9.79260	+	17.3349i	0.661722	+	1.17138i
$220$	−1.17194	−	1.14642i	−0.0790121	−	0.0772917i
$221$	9.26370	−	25.4518i	0.623144	−	1.71207i
$222$	−8.32087	+	0.649373i	−0.558460	+	0.0435831i
$223$	9.00598	−	6.30605i	0.603085	−	0.422285i	−0.231757	−	0.972774i	$-0.574448\pi$
$223$	9.00598	−	6.30605i	0.603085	−	0.422285i	0.834842	+	0.550489i	$0.185559\pi$
$224$	12.2674	−	21.2477i	0.819649	−	1.41967i
$225$	−7.45778	+	13.0147i	−0.497186	+	0.867644i
$226$	2.25386	+	3.90381i	0.149925	+	0.259677i
$227$	−8.96865	−	4.18215i	−0.595270	−	0.277579i	0.101544	−	0.994831i	$-0.467622\pi$
$227$	−8.96865	−	4.18215i	−0.595270	−	0.277579i	−0.696814	+	0.717252i	$0.745400\pi$
$228$	0.317755	−	3.27746i	0.0210438	−	0.217055i
$229$	−6.25137	−	7.45009i	−0.413102	−	0.492316i	0.518866	−	0.854855i	$-0.326354\pi$
$229$	−6.25137	−	7.45009i	−0.413102	−	0.492316i	−0.931968	+	0.362540i	$0.881910\pi$
$230$	0.979829	−	3.82466i	0.0646080	−	0.252191i
$231$	−3.22558	−	1.20841i	−0.212228	−	0.0795075i
$232$	−0.00587283	+	0.0125943i	−0.000385570	+	0.000826858i
$233$	−9.77279	−	2.61861i	−0.640236	−	0.171551i	−0.0759259	−	0.997113i	$-0.524191\pi$
$233$	−9.77279	−	2.61861i	−0.640236	−	0.171551i	−0.564311	+	0.825563i	$0.690858\pi$
$234$	4.94084	+	8.94117i	0.322993	+	0.584503i
$235$	16.0079	−	19.5096i	1.04424	−	1.27267i
$236$	0.646833	+	0.114054i	0.0421053	+	0.00742429i
$237$	2.45797	+	1.17437i	0.159662	+	0.0762836i
$238$	5.96371	+	12.7892i	0.386570	+	0.829002i
$239$	0.554723	+	3.14599i	0.0358821	+	0.203497i	0.997478	−	0.0709702i	$-0.0226095\pi$
$239$	0.554723	+	3.14599i	0.0358821	+	0.203497i	−0.961596	+	0.274468i	$0.911498\pi$
$240$	5.04647	+	4.22055i	0.325748	+	0.272435i
$241$	−15.5334	−	13.0341i	−1.00060	−	0.839600i	−0.0135291	−	0.999908i	$-0.504307\pi$
$241$	−15.5334	−	13.0341i	−1.00060	−	0.839600i	−0.987067	+	0.160309i	$0.948751\pi$
$242$	4.89485	+	4.89485i	0.314653	+	0.314653i
$243$	14.8515	+	4.73629i	0.952725	+	0.303833i
$244$		−	3.65203i		−	0.233797i
$245$	−1.96886	+	25.7676i	−0.125786	+	1.64623i
$246$	−4.51025	−	2.66073i	−0.287563	−	0.169642i
$247$	5.20303	+	3.64320i	0.331061	+	0.231811i
$248$	4.65743	−	2.17179i	0.295747	−	0.137909i
$249$	−6.16213	−	17.4377i	−0.390509	−	1.10507i
$250$	5.64552	+	4.42795i	0.357054	+	0.280048i
$251$	12.3046	+	7.10409i	0.776662	+	0.448406i	0.835246	−	0.549876i	$-0.185325\pi$
$251$	12.3046	+	7.10409i	0.776662	+	0.448406i	−0.0585840	+	0.998282i	$0.518659\pi$
$252$	19.7221	+	5.68324i	1.24237	+	0.358010i
$253$	−0.328745	+	1.22689i	−0.0206680	+	0.0771341i
$254$	5.05618	−	1.84030i	0.317253	−	0.115471i
$255$	−19.0877	+	5.14775i	−1.19532	+	0.322365i
$256$	−5.91329	+	4.96184i	−0.369581	+	0.310115i
$257$	−28.1859	−	2.46595i	−1.75819	−	0.153822i	−0.838096	−	0.545522i	$-0.816331\pi$
$257$	−28.1859	−	2.46595i	−1.75819	−	0.153822i	−0.920093	+	0.391701i	$0.871887\pi$
$258$	−2.11037	−	0.204604i	−0.131386	−	0.0127381i
$259$	−11.0631	−	30.3956i	−0.687426	−	1.88869i
$260$	−17.6351	+	6.63935i	−1.09368	+	0.411755i
$261$	−0.0177674	−	0.00347784i	−0.00109978	−	0.000215273i
$262$	−1.89985	−	7.09034i	−0.117373	−	0.438043i
$263$	−3.01081	−	4.29988i	−0.185655	−	0.265142i	0.715526	−	0.698586i	$-0.246187\pi$
$263$	−3.01081	−	4.29988i	−0.185655	−	0.265142i	−0.901181	+	0.433444i	$0.857298\pi$
$264$	1.39928	+	1.19669i	0.0861197	+	0.0736510i
$265$	−6.11092	+	10.8587i	−0.375391	+	0.667044i
$266$	−3.25896	+	0.574642i	−0.199819	+	0.0352336i
$267$	−21.2269	−	5.90173i	−1.29906	−	0.361180i
$268$	0.812310	+	9.28474i	0.0496197	+	0.567156i
$269$	−11.2342			−0.684961			−0.342480	−	0.939525i	$-0.611267\pi$
$269$	−11.2342			−0.684961			−0.342480	+	0.939525i	$0.611267\pi$
$270$	3.26656	−	6.70273i	0.198796	−	0.407915i
$271$	−15.3871			−0.934699			−0.467349	−	0.884073i	$-0.654791\pi$
$271$	−15.3871			−0.934699			−0.467349	+	0.884073i	$0.654791\pi$
$272$	0.755696	+	8.63764i	0.0458208	+	0.523734i
$273$	−28.2565	+	27.7312i	−1.71016	+	1.67837i
$274$	6.51532	−	1.14883i	0.393605	−	0.0694032i
$275$	−1.80044	−	1.44443i	−0.108571	−	0.0871022i
$276$	1.38414	−	7.44087i	0.0833152	−	0.447888i
$277$	9.41860	+	13.4512i	0.565909	+	0.808202i	0.995494	−	0.0948247i	$-0.0302291\pi$
$277$	9.41860	+	13.4512i	0.565909	+	0.808202i	−0.429585	+	0.903026i	$0.641340\pi$
$278$	0.287365	+	1.07246i	0.0172350	+	0.0643219i
$279$	4.20656	+	5.20863i	0.251840	+	0.311832i
$280$	9.15211	−	20.2044i	0.546943	−	1.20744i
$281$	−3.30030	−	9.06751i	−0.196880	−	0.540922i	0.801490	−	0.598009i	$-0.204041\pi$
$281$	−3.30030	−	9.06751i	−0.196880	−	0.540922i	−0.998369	+	0.0570865i	$0.981819\pi$
$282$	−7.29149	+	10.2081i	−0.434202	+	0.607884i
$283$	−15.4609	−	1.35265i	−0.919054	−	0.0804068i	−0.382198	−	0.924080i	$-0.624833\pi$
$283$	−15.4609	−	1.35265i	−0.919054	−	0.0804068i	−0.536856	+	0.843674i	$0.680388\pi$
$284$	0.911245	−	0.764625i	0.0540724	−	0.0453721i
$285$	−0.00752639	−	4.63614i	−0.000445825	−	0.274621i
$286$	−1.47718	+	0.537651i	−0.0873477	+	0.0317920i
$287$	5.25269	−	19.6033i	0.310057	−	1.15715i
$288$	−13.8099	−	10.0612i	−0.813755	−	0.592861i
$289$	−7.84266	−	4.52796i	−0.461333	−	0.266351i
$290$	−0.00287211	+	0.00816972i	−0.000168656	+	0.000479742i
$291$	−14.5882	−	2.71367i	−0.855177	−	0.159078i
$292$	16.5453	−	7.71521i	0.968242	−	0.451499i
$293$	7.90208	+	5.53310i	0.461645	+	0.323247i	0.781157	−	0.624335i	$-0.214630\pi$
$293$	7.90208	+	5.53310i	0.461645	+	0.323247i	−0.319512	+	0.947582i	$0.603519\pi$
$294$	0.120532	−	12.8456i	0.00702954	−	0.749170i
$295$	0.922072	+	0.0704540i	0.0536851	+	0.00410199i
$296$			17.2902i			1.00497i
$297$	−1.07456	+	2.14465i	−0.0623522	+	0.124445i
$298$	2.08377	+	2.08377i	0.120709	+	0.120709i
$299$	11.1837	+	9.38426i	0.646772	+	0.542706i
$300$	11.3653	+	7.74603i	0.656177	+	0.447217i
$301$	−1.42692	−	8.09244i	−0.0822460	−	0.466440i
$302$	−1.20166	−	2.57696i	−0.0691476	−	0.148288i
$303$	−2.11543	−	27.1065i	−0.121528	−	1.55723i
$304$	−2.00245	−	0.353085i	−0.114848	−	0.0202508i
$305$	−0.504493	−	5.11707i	−0.0288872	−	0.293003i
$306$	9.29607	−	3.18725i	0.531421	−	0.182203i
$307$	4.23478	+	1.13471i	0.241692	+	0.0647610i	0.377631	−	0.925956i	$-0.376739\pi$
$307$	4.23478	+	1.13471i	0.241692	+	0.0647610i	−0.135940	+	0.990717i	$0.543405\pi$
$308$	−1.33479	+	2.86246i	−0.0760566	+	0.163104i
$309$	18.7187	−	15.4099i	1.06487	−	0.876637i
$310$	2.75561	−	1.63165i	0.156508	−	0.0926716i
$311$	−5.33012	−	6.35219i	−0.302243	−	0.360199i	0.593451	−	0.804870i	$-0.297765\pi$
$311$	−5.33012	−	6.35219i	−0.302243	−	0.360199i	−0.895694	+	0.444671i	$0.853321\pi$
$312$	19.2630	−	8.76341i	1.09055	−	0.496131i
$313$	9.38140	+	4.37462i	0.530268	+	0.247268i	0.669264	−	0.743025i	$-0.266610\pi$
$313$	9.38140	+	4.37462i	0.530268	+	0.247268i	−0.138996	+	0.990293i	$0.544387\pi$
$314$	0.267093	+	0.462618i	0.0150729	+	0.0261070i
$315$	28.4189	+	5.23870i	1.60122	+	0.295167i
$316$	1.24891	−	2.16317i	0.0702566	−	0.121688i
$317$	−1.11253	+	0.779004i	−0.0624861	+	0.0437532i	−0.604402	−	0.796679i	$-0.706588\pi$
$317$	−1.11253	+	0.779004i	−0.0624861	+	0.0437532i	0.541916	+	0.840433i	$0.317699\pi$
$318$	2.67016	−	5.58867i	0.149735	−	0.313397i
$319$	0.000952860	−	0.00261796i	5.33499e−5	−	0.000146578i
$320$	−0.402986	+	0.411955i	−0.0225276	+	0.0230290i
$321$	3.56541	−	6.04379i	0.199002	−	0.337332i
$322$	−7.57727	+	0.662925i	−0.422265	+	0.0369434i
$323$	4.32066	−	4.32066i	0.240408	−	0.240408i
$324$	5.38922	−	13.2386i	0.299401	−	0.735480i
$325$	−23.7924	+	11.7389i	−1.31977	+	0.651158i
$326$	5.92535	−	7.06156i	0.328175	−	0.391104i
$327$	−11.1411	+	2.87350i	−0.616106	+	0.158905i
$328$	−6.22232	+	8.88639i	−0.343570	+	0.490669i
$329$	−45.6863	−	16.6284i	−2.51877	−	0.916756i
$330$	0.940962	+	0.656594i	0.0517982	+	0.0361443i
$331$	1.24032	−	7.03423i	0.0681744	−	0.386636i	−0.931560	−	0.363588i	$-0.881552\pi$
$331$	1.24032	−	7.03423i	0.0681744	−	0.386636i	0.999734	−	0.0230485i	$-0.00733722\pi$
$332$	−16.3803	+	4.38908i	−0.898985	+	0.240882i
$333$	−21.8643	+	5.42091i	−1.19815	+	0.297064i
$334$	−12.4699	+	7.19952i	−0.682324	+	0.393940i
$335$	2.42078	+	12.8972i	0.132261	+	0.704649i
$336$	4.44633	−	11.8685i	0.242567	−	0.647480i
$337$	2.50617	−	28.6457i	0.136520	−	1.56043i	−0.551151	−	0.834406i	$-0.685811\pi$
$337$	2.50617	−	28.6457i	0.136520	−	1.56043i	0.687671	−	0.726023i	$-0.258633\pi$
$338$	−0.847653	+	9.68871i	−0.0461062	+	0.526997i
$339$	7.73257	+	9.39291i	0.419976	+	0.510153i
$340$	3.34408	+	17.8163i	0.181358	+	0.966223i
$341$	−0.892235	+	0.515132i	−0.0483172	+	0.0278960i
$342$	0.157742	+	2.29918i	0.00852972	+	0.124325i
$343$	18.9628	−	5.08105i	1.02389	−	0.274351i
$344$	−0.762735	+	4.32568i	−0.0411239	+	0.233225i
$345$	0.911506	−	10.6171i	0.0490739	−	0.571603i
$346$	−1.39280	−	0.506936i	−0.0748772	−	0.0272531i
$347$	16.9146	−	24.1565i	0.908021	−	1.29679i	−0.0465844	−	0.998914i	$-0.514834\pi$
$347$	16.9146	−	24.1565i	0.908021	−	1.29679i	0.954605	−	0.297874i	$-0.0962775\pi$
$348$	−0.00444683	+	0.0159940i	−0.000238375	+	0.000857367i
$349$	13.2402	−	15.7790i	0.708730	−	0.844632i	−0.284754	−	0.958601i	$-0.591912\pi$
$349$	13.2402	−	15.7790i	0.708730	−	0.844632i	0.993484	+	0.113969i	$0.0363563\pi$
$350$	4.44052	−	13.0898i	0.237356	−	0.699678i
$351$	17.1212	+	21.6115i	0.913862	+	1.15354i
$352$	1.85918	−	1.85918i	0.0990944	−	0.0990944i
$353$	−1.74696	+	0.152839i	−0.0929814	+	0.00813482i	−0.133552	−	0.991042i	$-0.542638\pi$
$353$	−1.74696	+	0.152839i	−0.0929814	+	0.00813482i	0.0405701	+	0.999177i	$0.487083\pi$
$354$	−0.459668	−	0.00431311i	−0.0244311	−	0.000229239i
$355$	1.17117	−	1.19724i	0.0621594	−	0.0635430i
$356$	−6.90944	+	18.9835i	−0.366199	+	1.00612i
$357$	21.5518	+	31.4022i	1.14064	+	1.66198i
$358$	−10.9228	+	7.64820i	−0.577286	+	0.404220i
$359$	−9.41628	+	16.3095i	−0.496972	+	0.860781i	−0.999994	−	0.00349274i	$-0.998888\pi$
$359$	−9.41628	+	16.3095i	−0.496972	+	0.860781i	0.503022	+	0.864274i	$0.332222\pi$
$360$	−13.3170	−	7.82696i	−0.701866	−	0.412517i
$361$	−8.78354	−	15.2135i	−0.462291	−	0.800712i
$362$	1.87844	+	0.875933i	0.0987288	+	0.0460380i
$363$	15.2033	+	10.8595i	0.797969	+	0.569976i
$364$	23.3346	+	27.8091i	1.22307	+	1.45759i
$365$	22.1168	−	13.0958i	1.15765	−	0.685467i
$366$	0.420203	+	2.52120i	0.0219644	+	0.131785i
$367$	−11.3614	+	24.3645i	−0.593058	+	1.27182i	0.349237	+	0.937034i	$0.386441\pi$
$367$	−11.3614	+	24.3645i	−0.593058	+	1.27182i	−0.942295	+	0.334783i	$0.891337\pi$
$368$	−4.51434	−	1.20961i	−0.235326	−	0.0630555i
$369$	−13.1881	−	5.08231i	−0.686546	−	0.264575i
$370$	1.05717	+	10.7229i	0.0549597	+	0.557456i
$371$	23.6399	+	4.16835i	1.22732	+	0.216410i
$372$	5.06158	−	3.47384i	0.262431	−	0.180110i
$373$	1.33439	+	2.86161i	0.0690922	+	0.148169i	0.937821	−	0.347120i	$-0.112840\pi$
$373$	1.33439	+	2.86161i	0.0690922	+	0.148169i	−0.868729	+	0.495288i	$0.835062\pi$
$374$	0.262599	+	1.48927i	0.0135786	+	0.0770083i
$375$	16.9947	+	9.28340i	0.877600	+	0.479393i
$376$	19.9081	+	16.7049i	1.02668	+	0.861487i
$377$	−0.0226429	−	0.0226429i	−0.00116617	−	0.00116617i
$378$	−14.2692	−	1.65423i	−0.733926	−	0.0850842i
$379$			7.29800i			0.374873i	0.982277	+	0.187436i	$0.0600179\pi$
$379$			7.29800i			0.374873i	−0.982277	+	0.187436i	$0.939982\pi$
$380$	−4.23867	−	0.323870i	−0.217439	−	0.0166142i
$381$	12.6443	−	7.14288i	0.647789	−	0.365941i
$382$	0.242645	+	0.169902i	0.0124148	+	0.00869293i
$383$	16.6615	−	7.76938i	0.851362	−	0.396997i	0.0525799	−	0.998617i	$-0.483256\pi$
$383$	16.6615	−	7.76938i	0.851362	−	0.396997i	0.798783	+	0.601620i	$0.205478\pi$
$384$	−12.6369	+	14.7763i	−0.644876	+	0.754051i
$385$	−1.47483	+	4.19515i	−0.0751641	+	0.213805i
$386$	1.26438	+	0.729990i	0.0643552	+	0.0371555i
$387$	−5.70917	+	0.391696i	−0.290213	+	0.0199110i
$388$	−3.52146	+	13.1423i	−0.178775	+	0.667197i
$389$	−19.7491	+	7.18808i	−1.00132	+	0.364450i	−0.790093	−	0.612987i	$-0.789968\pi$
$389$	−19.7491	+	7.18808i	−1.00132	+	0.364450i	−0.211226	+	0.977437i	$0.567746\pi$
$390$	11.4106	−	6.61261i	0.577796	−	0.334843i
$391$	10.7587	−	9.02763i	0.544091	−	0.456547i
$392$	−26.5112	−	2.31943i	−1.33902	−	0.117149i
$393$	−8.20401	−	18.0334i	−0.413838	−	0.909665i
$394$	5.86086	+	16.1026i	0.295266	+	0.811237i
$395$	1.45110	−	3.20347i	0.0730126	−	0.161184i
$396$	1.88387	+	1.13531i	0.0946681	+	0.0570515i
$397$	8.78326	+	32.7796i	0.440819	+	1.64516i	0.726745	+	0.686907i	$0.241032\pi$
$397$	8.78326	+	32.7796i	0.440819	+	1.64516i	−0.285926	+	0.958252i	$0.592301\pi$
$398$	−8.77854	−	12.5371i	−0.440029	−	0.628426i
$399$	−8.42125	+	2.97590i	−0.421590	+	0.148981i
$400$	5.31475	−	6.62470i	0.265738	−	0.331235i
$401$	−26.7887	+	4.72357i	−1.33776	+	0.235884i	−0.796332	−	0.604860i	$-0.793229\pi$
$401$	−26.7887	+	4.72357i	−1.33776	+	0.235884i	−0.541433	+	0.840744i	$0.682118\pi$
$402$	−1.62909	−	6.31631i	−0.0812515	−	0.315029i
$403$	1.03208	+	11.7968i	0.0514117	+	0.587638i
$404$	−24.9303			−1.24033
$405$	5.72236	−	19.2939i	0.284346	−	0.958722i
$406$	0.0166833			0.000827980
$407$	−0.302116	−	3.45320i	−0.0149753	−	0.171169i
$408$	−5.08443	−	19.7134i	−0.251717	−	0.975957i
$409$	13.3695	−	2.35741i	0.661081	−	0.116566i	0.166965	−	0.985963i	$-0.446603\pi$
$409$	13.3695	−	2.35741i	0.661081	−	0.116566i	0.494115	+	0.869396i	$0.335492\pi$
$410$	−3.31556	+	5.89153i	−0.163744	+	0.290962i
$411$	16.8358	−	5.94944i	0.830449	−	0.293464i
$412$	−12.7515	−	18.2111i	−0.628222	−	0.897195i
$413$	−0.461102	−	1.72085i	−0.0226893	−	0.0846777i
$414$	−0.0993966	+	5.29610i	−0.00488508	+	0.260289i
$415$	−22.3451	+	8.41259i	−1.09688	+	0.412958i
$416$	−10.3361	−	28.3982i	−0.506769	−	1.39234i
$417$	1.24091	+	2.72767i	0.0607677	+	0.133575i
$418$	−0.353285	−	0.0309084i	−0.0172797	−	0.00151178i
$419$	9.78730	−	8.21252i	0.478141	−	0.401208i	−0.371613	−	0.928388i	$-0.621195\pi$
$419$	9.78730	−	8.21252i	0.478141	−	0.401208i	0.849754	+	0.527180i	$0.176751\pi$
$420$	6.81641	−	25.6054i	0.332607	−	1.24942i
$421$	16.9246	−	6.16004i	0.824853	−	0.300222i	0.105108	−	0.994461i	$-0.466481\pi$
$421$	16.9246	−	6.16004i	0.824853	−	0.300222i	0.719745	+	0.694239i	$0.244259\pi$
$422$	−3.60343	+	13.4482i	−0.175412	+	0.654648i
$423$	−14.8824	+	30.4121i	−0.723608	+	1.47869i
$424$	−11.1122	−	6.41562i	−0.539656	−	0.311570i
$425$	7.14674	+	24.5015i	0.346668	+	1.18850i
$426$	−0.541105	+	0.632711i	−0.0262166	+	0.0306549i
$427$	−8.97778	+	4.18641i	−0.434465	+	0.202595i
$428$	−5.27058	−	3.69050i	−0.254763	−	0.178387i
$429$	−3.69410	+	2.08682i	−0.178353	+	0.100753i
$430$	−0.208541	+	2.72930i	−0.0100568	+	0.131618i
$431$			4.80209i			0.231309i	0.993290	+	0.115654i	$0.0368965\pi$
$431$			4.80209i			0.231309i	−0.993290	+	0.115654i	$0.963104\pi$
$432$	−7.89121	−	3.95383i	−0.379666	−	0.190229i
$433$	23.6615	+	23.6615i	1.13710	+	1.13710i	0.988968	+	0.148130i	$0.0473253\pi$
$433$	23.6615	+	23.6615i	1.13710	+	1.13710i	0.148130	+	0.988968i	$0.452675\pi$
$434$	−4.72616	−	3.96572i	−0.226863	−	0.190360i
$435$	−0.00402129	+	0.0230244i	−0.000192806	+	0.00110394i
$436$	1.83198	+	10.3897i	0.0877360	+	0.497576i
$437$	1.39192	+	2.98497i	0.0665844	+	0.142791i
$438$	−10.5344	+	7.22994i	−0.503355	+	0.345460i
$439$	−0.531654	−	0.0937450i	−0.0253745	−	0.00447420i	0.160947	−	0.986963i	$-0.448545\pi$
$439$	−0.531654	−	0.0937450i	−0.0253745	−	0.00447420i	−0.186321	+	0.982489i	$0.559656\pi$
$440$	1.50777	−	1.83758i	0.0718799	−	0.0876034i
$441$	−5.37890	−	34.2519i	−0.256138	−	1.63104i
$442$	16.7894	+	4.49871i	0.798591	+	0.213982i
$443$	−2.19821	+	4.71408i	−0.104440	+	0.223973i	−0.951583	−	0.307393i	$-0.900543\pi$
$443$	−2.19821	+	4.71408i	−0.104440	+	0.223973i	0.847142	+	0.531366i	$0.178321\pi$
$444$	3.39569	+	20.3740i	0.161152	+	0.966906i
$445$	−7.05882	+	27.5534i	−0.334620	+	1.30616i
$446$	4.53516	+	5.40479i	0.214746	+	0.255924i
$447$	6.47215	+	4.62295i	0.306122	+	0.218658i
$448$	1.00620	+	0.469199i	0.0475385	+	0.0221676i
$449$	−6.99817	−	12.1212i	−0.330264	−	0.572034i	0.652300	−	0.757961i	$-0.273804\pi$
$449$	−6.99817	−	12.1212i	−0.330264	−	0.572034i	−0.982564	+	0.185927i	$0.940471\pi$
$450$	−8.73737	−	4.03982i	−0.411883	−	0.190439i
$451$	1.08745	−	1.88352i	0.0512060	−	0.0886914i
$452$	9.13819	−	6.39863i	0.429824	−	0.300966i
$453$	−4.34257	−	6.32738i	−0.204032	−	0.297286i
$454$	2.17201	−	5.96755i	0.101937	−	0.280071i
$455$	36.5371	+	35.7415i	1.71289	+	1.67559i
$456$	4.77403	+	0.0447952i	0.223564	+	0.00209773i
$457$	3.82420	−	0.334574i	0.178888	−	0.0156507i	0.00264047	−	0.999997i	$-0.499160\pi$
$457$	3.82420	−	0.334574i	0.178888	−	0.0156507i	0.176248	+	0.984346i	$0.443604\pi$
$458$	4.41318	−	4.41318i	0.206214	−	0.206214i
$459$	23.3344	−	12.6101i	1.08916	−	0.588591i
$460$	−9.64056	−	1.59069i	−0.449493	−	0.0741664i
$461$	−14.3235	+	17.0701i	−0.667111	+	0.795032i	−0.988388	−	0.151953i	$-0.951444\pi$
$461$	−14.3235	+	17.0701i	−0.667111	+	0.795032i	0.321276	+	0.946985i	$0.395888\pi$
$462$	0.592122	−	2.12970i	0.0275480	−	0.0990824i
$463$	0.684383	−	0.977400i	0.0318060	−	0.0454236i	−0.802934	−	0.596068i	$-0.796729\pi$
$463$	0.684383	−	0.977400i	0.0318060	−	0.0454236i	0.834740	+	0.550644i	$0.185618\pi$
$464$	0.00963277	+	0.00350604i	0.000447190	+	0.000162764i
$465$	6.61220	−	5.56661i	0.306633	−	0.258145i
$466$	1.12747	−	6.39418i	0.0522289	−	0.296205i
$467$	0.869824	−	0.233069i	0.0402506	−	0.0107851i	−0.238638	−	0.971109i	$-0.576701\pi$
$467$	0.869824	−	0.233069i	0.0402506	−	0.0107851i	0.278888	+	0.960324i	$0.410034\pi$
$468$	20.9776	−	14.1096i	0.969691	−	0.652215i
$469$	21.8935	−	12.6402i	1.01095	−	0.583672i
$470$	13.3678	+	9.14263i	0.616610	+	0.421718i
$471$	0.916343	+	1.11310i	0.0422229	+	0.0512890i
$472$	−0.0829988	+	0.948680i	−0.00382033	+	0.0436665i
$473$	0.0767499	−	0.877255i	0.00352896	−	0.0403362i
$474$	−0.613295	+	1.63706i	−0.0281696	+	0.0751925i
$475$	−5.98379	+	0.131739i	−0.274555	+	0.00604462i
$476$	30.2439	−	17.4613i	1.38623	−	0.800338i
$477$	4.62891	−	16.0634i	0.211943	−	0.735490i
$478$	−1.98020	+	0.530593i	−0.0905722	+	0.0242687i
$479$	5.10504	−	28.9521i	0.233255	−	1.32286i	−0.613001	−	0.790082i	$-0.710038\pi$
$479$	5.10504	−	28.9521i	0.233255	−	1.32286i	0.846257	−	0.532775i	$-0.178851\pi$
$480$	−12.6227	+	18.0896i	−0.576147	+	0.825673i
$481$	−37.4398	−	13.6270i	−1.70711	−	0.621336i
$482$	7.46386	−	10.6595i	0.339969	−	0.485527i
$483$	−19.8786	+	5.12704i	−0.904507	+	0.233288i
$484$	11.0119	−	13.1234i	0.500539	−	0.596519i
$485$	−3.11864	+	18.9008i	−0.141610	+	0.858243i
$486$	−2.19724	+	9.75944i	−0.0996686	+	0.442697i
$487$	22.6006	−	22.6006i	1.02413	−	1.02413i	0.0244298	−	0.999702i	$-0.492223\pi$
$487$	22.6006	−	22.6006i	1.02413	−	1.02413i	0.999702	−	0.0244298i	$-0.00777702\pi$
$488$	5.27488	−	0.461492i	0.238783	−	0.0208908i
$489$	12.6416	−	21.4289i	0.571671	−	0.969050i
$490$	−16.5833	+	0.182527i	−0.749158	+	0.00824575i
$491$	−4.34237	+	11.9306i	−0.195968	+	0.538419i	−0.998289	−	0.0584746i	$-0.981376\pi$
$491$	−4.34237	+	11.9306i	−0.195968	+	0.538419i	0.802320	+	0.596894i	$0.203599\pi$
$492$	−5.58687	+	11.6934i	−0.251875	+	0.527177i
$493$	−0.0252339	+	0.0176690i	−0.00113648	+	0.000795772i
$494$	−2.03808	+	3.53005i	−0.0916974	+	0.158824i
$495$	2.79643	+	1.33051i	0.125690	+	0.0598021i
$496$	−1.89542	−	3.28297i	−0.0851071	−	0.147410i
$497$	−2.92426	−	1.36361i	−0.131171	−	0.0611661i
$498$	10.8032	−	4.91475i	0.484103	−	0.220235i
$499$	7.76871	+	9.25839i	0.347775	+	0.414463i	0.911369	−	0.411589i	$-0.135026\pi$
$499$	7.76871	+	9.25839i	0.347775	+	0.414463i	−0.563594	+	0.826052i	$0.690582\pi$
$500$	9.69886	−	14.8734i	0.433746	−	0.665158i
$501$	−30.0038	+	24.7002i	−1.34047	+	1.10352i
$502$	−3.85341	+	8.26367i	−0.171986	+	0.368825i
$503$	21.0910	+	5.65132i	0.940402	+	0.251980i	0.696285	−	0.717766i	$-0.254835\pi$
$503$	21.0910	+	5.65132i	0.940402	+	0.251980i	0.244117	+	0.969746i	$0.421502\pi$
$504$	−5.71650	+	29.2042i	−0.254633	+	1.30086i
$505$	−34.9314	+	3.44389i	−1.55443	+	0.153251i
$506$	−0.802737	−	0.141544i	−0.0356860	−	0.00629241i
$507$	2.04235	+	26.1701i	0.0907041	+	1.16225i
$508$	−5.62760	−	12.0684i	−0.249684	−	0.535450i
$509$	0.934268	+	5.29850i	0.0414107	+	0.234852i	0.998487	−	0.0549834i	$-0.0175106\pi$
$509$	0.934268	+	5.29850i	0.0414107	+	0.234852i	−0.957077	+	0.289835i	$0.906399\pi$
$510$	−4.35854	−	11.9148i	−0.193000	−	0.527596i
$511$	−37.9326	−	31.8293i	−1.67804	−	1.40804i
$512$	12.3723	+	12.3723i	0.546785	+	0.546785i
$513$	1.44013	+	6.05103i	0.0635834	+	0.267160i
$514$		−	18.1571i		−	0.800876i
$515$	−20.3826	−	23.7551i	−0.898165	−	1.04677i
$516$	−0.0492331	+	5.24699i	−0.00216736	+	0.230986i
$517$	−4.26794	−	2.98844i	−0.187704	−	0.131432i
$518$	18.8130	−	8.77266i	0.826597	−	0.385449i
$519$	−3.93293	−	0.731596i	−0.172637	−	0.0321135i
$520$	−11.8182	−	24.6327i	−0.518261	−	1.08021i
$521$	−2.74885	−	1.58705i	−0.120429	−	0.0695300i	0.438575	−	0.898694i	$-0.355483\pi$
$521$	−2.74885	−	1.58705i	−0.120429	−	0.0695300i	−0.559005	+	0.829165i	$0.688817\pi$
$522$	0.00122962	−	0.0115532i	5.38190e−5	−	0.000505669i
$523$	3.10969	−	11.6055i	0.135977	−	0.507473i	−0.864015	−	0.503466i	$-0.832058\pi$
$523$	3.10969	−	11.6055i	0.135977	−	0.507473i	0.999992	−	0.00400710i	$-0.00127550\pi$
$524$	−17.0706	+	6.21317i	−0.745731	+	0.271424i
$525$	6.01373	−	36.8188i	0.262461	−	1.60691i
$526$	2.58051	−	2.16530i	0.112515	−	0.0944116i
$527$	11.3484	+	0.992860i	0.494346	+	0.0432496i
$528$	0.789445	−	1.10523i	0.0343562	−	0.0480988i
$529$	−5.27731	−	14.4993i	−0.229448	−	0.630404i
$530$	−7.28373	−	3.29935i	−0.316385	−	0.143315i
$531$	−1.22567	+	0.192479i	−0.0531897	+	0.00835288i
$532$	2.11964	+	7.91060i	0.0918980	+	0.342968i
$533$	−14.3384	−	20.4773i	−0.621064	−	0.886972i
$534$	2.58572	−	13.9004i	0.111895	−	0.601528i
$535$	−7.89473	−	4.44289i	−0.341319	−	0.192083i
$536$	−13.3080	+	2.34655i	−0.574817	+	0.101356i
$537$	−25.6857	+	25.2082i	−1.10842	+	1.08781i
$538$	−0.628343	−	7.18199i	−0.0270898	−	0.309638i
$539$	5.33536			0.229810
$540$	−17.2293	−	6.60756i	−0.741431	−	0.284344i
$541$	33.7781			1.45223			0.726116	−	0.687572i	$-0.241324\pi$
$541$	33.7781			1.45223			0.726116	+	0.687572i	$0.241324\pi$
$542$	−0.860619	−	9.83692i	−0.0369668	−	0.422532i
$543$	5.38959	+	1.49847i	0.231289	+	0.0643057i
$544$	−28.6306	+	5.04834i	−1.22753	+	0.216446i
$545$	4.00214	+	14.3045i	0.171433	+	0.612739i
$546$	−19.3089	−	16.5133i	−0.826345	−	0.706704i
$547$	−8.22365	−	11.7446i	−0.351618	−	0.502162i	0.603914	−	0.797049i	$-0.293607\pi$
$547$	−8.22365	−	11.7446i	−0.351618	−	0.502162i	−0.955532	+	0.294887i	$0.904718\pi$
$548$	−4.23759	−	15.8149i	−0.181021	−	0.675579i
$549$	2.23739	+	6.52565i	0.0954894	+	0.278508i
$550$	0.822717	−	1.23181i	0.0350808	−	0.0525244i
$551$	−0.00247076	−	0.00678836i	−0.000105258	−	0.000289194i
$552$	10.9223	+	1.05893i	0.464884	+	0.0450711i
$553$	−6.74939	−	0.590495i	−0.287013	−	0.0251104i
$554$	−8.07250	+	6.77363i	−0.342968	+	0.287784i
$555$	7.57238	+	28.0781i	0.321430	+	1.19185i
$556$	2.58203	−	0.939783i	0.109503	−	0.0398557i
$557$	−2.61958	+	9.77642i	−0.110995	+	0.414240i	−0.998956	−	0.0456789i	$-0.985455\pi$
$557$	−2.61958	+	9.77642i	−0.110995	+	0.414240i	0.887961	+	0.459919i	$0.152122\pi$
$558$	−3.09459	+	2.98057i	−0.131004	+	0.126177i
$559$	−8.76560	−	5.06082i	−0.370745	−	0.214050i
$560$	−15.4360	−	5.42661i	−0.652291	−	0.229316i
$561$	1.35992	+	3.84832i	0.0574159	+	0.162476i
$562$	5.61224	−	2.61703i	0.236738	−	0.110393i
$563$	−23.0577	−	16.1451i	−0.971765	−	0.680437i	−0.0241016	−	0.999710i	$-0.507673\pi$
$563$	−23.0577	−	16.1451i	−0.971765	−	0.680437i	−0.947663	+	0.319273i	$0.896561\pi$
$564$	26.7395	+	15.7744i	1.12594	+	0.664223i
$565$	11.9201	−	10.2279i	0.501484	−	0.430289i
$566$		−	9.95976i		−	0.418640i
$567$	−38.7224	+	1.92745i	−1.62619	+	0.0809453i
$568$	1.21955	+	1.21955i	0.0511713	+	0.0511713i
$569$	7.66040	+	6.42784i	0.321141	+	0.269469i	0.789078	−	0.614292i	$-0.210558\pi$
$569$	7.66040	+	6.42784i	0.321141	+	0.269469i	−0.467938	+	0.883761i	$0.655003\pi$
$570$	2.96345	−	0.264117i	0.124125	−	0.0110626i
$571$	4.25288	+	24.1193i	0.177978	+	1.00936i	0.934651	+	0.355568i	$0.115712\pi$
$571$	4.25288	+	24.1193i	0.177978	+	1.00936i	−0.756673	+	0.653794i	$0.773176\pi$
$572$	1.64413	+	3.52584i	0.0687444	+	0.147423i
$573$	0.721374	+	0.344659i	0.0301358	+	0.0143983i
$574$	12.8261	+	2.26159i	0.535353	+	0.0943971i
$575$	−13.7277	−	0.897060i	−0.572485	−	0.0374100i
$576$	0.399080	−	0.662211i	0.0166283	−	0.0275921i
$577$	15.4493	+	4.13963i	0.643163	+	0.172335i	0.565636	−	0.824655i	$-0.308631\pi$
$577$	15.4493	+	4.13963i	0.643163	+	0.172335i	0.0775272	+	0.996990i	$0.475298\pi$
$578$	2.45606	−	5.26705i	0.102159	−	0.219080i
$579$	3.69003	+	1.38240i	0.153352	+	0.0574508i
$580$	0.0207609	+	0.00531867i	0.000862049	+	0.000220846i
$581$	29.5668	+	35.2364i	1.22664	+	1.46185i
$582$	0.918905	−	9.47800i	0.0380898	−	0.392876i
$583$	2.33143	+	1.08716i	0.0965581	+	0.0450258i
$584$	13.2344	+	22.9227i	0.547643	+	0.948546i
$585$	27.4439	−	22.6676i	1.13466	−	0.937190i
$586$	−3.09532	+	5.36125i	−0.127867	+	0.221471i
$587$	−16.2765	+	11.3970i	−0.671805	+	0.470403i	−0.859037	−	0.511913i	$-0.828937\pi$
$587$	−16.2765	+	11.3970i	−0.671805	+	0.470403i	0.187233	+	0.982316i	$0.440048\pi$
$588$	−31.6952	+	2.47354i	−1.30709	+	0.102007i
$589$	−0.913697	+	2.51036i	−0.0376482	+	0.103438i
$590$	0.00653158	+	0.593419i	0.000268901	+	0.0244307i
$591$	22.7482	+	40.2689i	0.935735	+	1.65644i
$592$	12.7060	−	1.11163i	0.522214	−	0.0456878i
$593$	24.0438	−	24.0438i	0.987362	−	0.987362i	−0.0125593	−	0.999921i	$-0.503998\pi$
$593$	24.0438	−	24.0438i	0.987362	−	0.987362i	0.999921	+	0.0125593i	$0.00399784\pi$
$594$	−1.43117	−	0.567010i	−0.0587216	−	0.0232647i
$595$	39.9644	−	28.6440i	1.63838	−	1.17429i
$596$	4.68781	−	5.58672i	0.192020	−	0.228841i
$597$	−28.9337	−	29.4819i	−1.18418	−	1.20661i
$598$	−5.37382	+	7.67460i	−0.219752	+	0.313838i
$599$	32.8027	+	11.9392i	1.34028	+	0.487823i	0.909901	−	0.414825i	$-0.136157\pi$
$599$	32.8027	+	11.9392i	1.34028	+	0.487823i	0.430381	+	0.902647i	$0.358379\pi$
$600$	−9.75195	+	17.3946i	−0.398122	+	0.710131i
$601$	−4.52626	+	25.6697i	−0.184630	+	1.04709i	0.741800	+	0.670621i	$0.233972\pi$
$601$	−4.52626	+	25.6697i	−0.184630	+	1.04709i	−0.926430	+	0.376467i	$0.877139\pi$
$602$	5.09367	−	1.36484i	0.207602	−	0.0556269i
$603$	−7.13971	−	16.0929i	−0.290752	−	0.655352i
$604$	−6.09398	+	3.51836i	−0.247961	+	0.143160i
$605$	13.6165	−	19.9092i	0.553589	−	0.809423i
$606$	17.2108	−	2.86849i	0.699141	−	0.116524i
$607$	−0.312022	+	3.56643i	−0.0126646	+	0.144757i	−0.999894	−	0.0145470i	$-0.995369\pi$
$607$	−0.312022	+	3.56643i	−0.0126646	+	0.144757i	0.987230	+	0.159304i	$0.0509249\pi$
$608$	0.594201	−	6.79175i	0.0240980	−	0.275442i
$609$	0.0444155	−	0.00740266i	0.00179981	−	0.000299971i
$610$	3.24311	−	0.608726i	0.131310	−	0.0246466i
$611$	−51.8625	+	29.9428i	−2.09813	+	1.21136i
$612$	−9.86285	−	22.2308i	−0.398682	−	0.898627i
$613$	−17.6112	+	4.71891i	−0.711310	+	0.190595i	−0.596291	−	0.802768i	$-0.703360\pi$
$613$	−17.6112	+	4.71891i	−0.711310	+	0.190595i	−0.115019	+	0.993363i	$0.536693\pi$
$614$	−0.488558	+	2.77075i	−0.0197166	+	0.111818i
$615$	−6.21276	+	17.1560i	−0.250523	+	0.691798i
$616$	−4.30313	−	1.56621i	−0.173378	−	0.0631044i
$617$	1.76647	−	2.52278i	0.0711153	−	0.101563i	−0.782019	−	0.623255i	$-0.785810\pi$
$617$	1.76647	−	2.52278i	0.0711153	−	0.101563i	0.853134	+	0.521692i	$0.174699\pi$
$618$	10.8984	+	11.1049i	0.438400	+	0.446705i
$619$	−22.9284	+	27.3250i	−0.921572	+	1.09829i	0.0733171	+	0.997309i	$0.476641\pi$
$619$	−22.9284	+	27.3250i	−0.921572	+	1.09829i	−0.994889	+	0.100978i	$0.967803\pi$
$620$	−4.61699	−	6.44168i	−0.185423	−	0.258704i
$621$	2.08534	+	14.1438i	0.0836820	+	0.567570i
$622$	3.76282	−	3.76282i	0.150875	−	0.150875i
$623$	54.5877	−	4.77580i	2.18701	−	0.191339i
$624$	−7.67844	−	13.5924i	−0.307383	−	0.544131i
$625$	11.5350	−	22.1798i	0.461401	−	0.887192i
$626$	−2.27197	+	6.24218i	−0.0908062	+	0.249488i
$627$	−0.954254	+	0.0744714i	−0.0381092	+	0.00297410i
$628$	1.08292	−	0.758266i	0.0432130	−	0.0302581i
$629$	−19.1642	+	33.1934i	−0.764127	+	1.32351i
$630$	−1.75958	+	18.4611i	−0.0701035	+	0.735508i
$631$	0.459598	+	0.796047i	0.0182963	+	0.0316901i	0.875029	−	0.484071i	$-0.160842\pi$
$631$	0.459598	+	0.796047i	0.0182963	+	0.0316901i	−0.856732	+	0.515761i	$0.827509\pi$
$632$	3.28225	+	1.53054i	0.130561	+	0.0608815i
$633$	−3.62614	+	37.4016i	−0.144126	+	1.48658i
$634$	−0.560241	−	0.667669i	−0.0222500	−	0.0265165i
$635$	−9.55230	−	16.1324i	−0.379072	−	0.640194i
$636$	−14.3541	−	5.37751i	−0.569177	−	0.213232i
$637$	25.9168	−	55.5788i	1.02686	−	2.20211i
$638$	0.00172695		0.000462735i	6.83707e−5		1.83199e-5i
$639$	−1.15982	+	1.92454i	−0.0458819	+	0.0761338i
$640$	19.4048	+	15.9219i	0.767041	+	0.629369i
$641$	28.1175	+	4.95787i	1.11057	+	0.195824i	0.698699	−	0.715416i	$-0.253763\pi$
$641$	28.1175	+	4.95787i	1.11057	+	0.195824i	0.411875	+	0.911240i	$0.364874\pi$
$642$	4.06320	+	1.94132i	0.160362	+	0.0766178i
$643$	16.0061	+	34.3252i	0.631220	+	1.35365i	0.918352	+	0.395764i	$0.129520\pi$
$643$	16.0061	+	34.3252i	0.631220	+	1.35365i	−0.287133	+	0.957891i	$0.592702\pi$
$644$	3.26871	+	18.5378i	0.128805	+	0.730492i
$645$	0.655839	+	7.35866i	0.0258236	+	0.289747i
$646$	3.00385	+	2.52053i	0.118185	+	0.0991688i
$647$	−30.2410	−	30.2410i	−1.18890	−	1.18890i	−0.977373	−	0.211525i	$-0.932157\pi$
$647$	−30.2410	−	30.2410i	−1.18890	−	1.18890i	−0.211525	−	0.977373i	$-0.567843\pi$
$648$	19.8025	+	6.11112i	0.777917	+	0.240067i
$649$		−	0.190921i		−	0.00749431i
$650$	−8.83540	−	14.5539i	−0.346553	−	0.570849i
$651$	−14.3420	−	8.46074i	−0.562105	−	0.331602i
$652$	−18.6874	−	13.0851i	−0.731856	−	0.512451i
$653$	−33.1747	+	15.4696i	−1.29823	+	0.605374i	−0.944049	−	0.329804i	$-0.893017\pi$
$653$	−33.1747	+	15.4696i	−1.29823	+	0.605374i	−0.354178	+	0.935178i	$0.615239\pi$
$654$	−2.46016	−	6.96178i	−0.0961998	−	0.272227i
$655$	−23.0603	+	11.0638i	−0.901039	+	0.432298i
$656$	6.93039	+	4.00126i	0.270586	+	0.156223i
$657$	−24.8375	+	23.9224i	−0.969002	+	0.933300i
$658$	8.07523	−	30.1372i	0.314805	−	1.17487i
$659$	29.4659	−	10.7247i	1.14783	−	0.417776i	0.303095	−	0.952960i	$-0.401980\pi$
$659$	29.4659	−	10.7247i	1.14783	−	0.417776i	0.844735	+	0.535184i	$0.179758\pi$
$660$	1.41579	−	2.46144i	0.0551096	−	0.0958115i
$661$	3.28171	−	2.75368i	0.127644	−	0.107106i	−0.576731	−	0.816934i	$-0.695672\pi$
$661$	3.28171	−	2.75368i	0.127644	−	0.107106i	0.704375	+	0.709828i	$0.251227\pi$
$662$	4.56634	+	0.399503i	0.177476	+	0.0155271i
$663$	46.6941	+	4.52706i	1.81345	+	0.175816i
$664$	−8.40938	−	23.1046i	−0.326347	−	0.896632i
$665$	4.06272	+	10.7912i	0.157546	+	0.418465i
$666$	−4.68847	−	13.6746i	−0.181674	−	0.529879i
$667$	−0.00429751	−	0.0160385i	−0.000166400	−	0.000621014i
$668$	20.4392	+	29.1901i	0.790815	+	1.12940i
$669$	14.4720	+	12.3767i	0.559520	+	0.478511i
$670$	−8.10974	+	2.26895i	−0.313307	+	0.0876573i
$671$	−1.04544	+	0.184339i	−0.0403587	+	0.00711633i
$672$	40.9425	+	11.3833i	1.57939	+	0.439120i
$673$	2.48234	+	28.3733i	0.0956872	+	1.09371i	0.880522	+	0.474005i	$0.157192\pi$
$673$	2.48234	+	28.3733i	0.0956872	+	1.09371i	−0.784835	+	0.619705i	$0.787252\pi$
$674$	18.4533			0.710793
$675$	−25.0538	−	6.87817i	−0.964320	−	0.264741i
$676$	24.0691			0.925735
$677$	−3.71607	−	42.4749i	−0.142820	−	1.63244i	−0.642537	−	0.766255i	$-0.722118\pi$
$677$	−3.71607	−	42.4749i	−0.142820	−	1.63244i	0.499717	−	0.866189i	$-0.333437\pi$
$678$	−5.57237	+	5.46877i	−0.214006	+	0.210027i
$679$	36.3444	−	6.40849i	1.39477	−	0.245935i
$680$	−25.3107	+	7.08146i	−0.970623	+	0.271562i
$681$	3.13458	−	16.8510i	0.120118	−	0.645731i
$682$	−0.379227	−	0.541592i	−0.0145213	−	0.0207386i
$683$	−4.42899	−	16.5292i	−0.169471	−	0.632473i	−0.997428	−	0.0716812i	$-0.977164\pi$
$683$	−4.42899	−	16.5292i	−0.169471	−	0.632473i	0.827957	−	0.560792i	$-0.189503\pi$
$684$	5.63430	−	0.884807i	0.215433	−	0.0338314i
$685$	−8.12222	−	21.5738i	−0.310334	−	0.824293i
$686$	4.30892	+	11.8386i	0.164515	+	0.452002i
$687$	9.79087	−	13.7073i	0.373545	−	0.522965i
$688$	3.22785	+	0.282400i	0.123061	+	0.0107664i
$689$	22.6501	−	19.0057i	0.862901	−	0.724060i
$690$	6.83844	−	0.0111016i	0.260335	−	0.000422632i
$691$	−28.7479	+	10.4634i	−1.09362	+	0.398045i	−0.824961	−	0.565190i	$-0.808803\pi$
$691$	−28.7479	+	10.4634i	−1.09362	+	0.398045i	−0.268660	+	0.963235i	$0.586581\pi$
$692$	−0.949372	+	3.54310i	−0.0360897	+	0.134689i
$693$	0.631410	−	5.93256i	0.0239853	−	0.225359i
$694$	16.3892	+	9.46233i	0.622127	+	0.359185i
$695$	3.48802	−	1.67347i	0.132308	−	0.0634783i
$696$	−0.0236632	−	0.00440177i	−0.000896951	−	0.000166849i
$697$	−21.7951	+	10.1632i	−0.825547	+	0.384959i
$698$	10.8280	+	7.58187i	0.409847	+	0.286978i
$699$	0.164423	−	17.5233i	0.00621905	−	0.662792i
$700$	−33.2290	−	8.12418i	−1.25594	−	0.307065i
$701$		−	33.1045i		−	1.25034i	−0.780488	−	0.625171i	$-0.785029\pi$
$701$		−	33.1045i		−	1.25034i	0.780488	−	0.625171i	$-0.214971\pi$
$702$	−12.8586	+	12.1543i	−0.485315	+	0.458734i
$703$	−6.35572	−	6.35572i	−0.239710	−	0.239710i
$704$	0.0911416	+	0.0764768i	0.00343503	+	0.00288233i
$705$	39.6454	+	18.4087i	1.49313	+	0.693310i
$706$	−0.195420	−	1.10828i	−0.00735472	−	0.0417107i
$707$	28.5783	+	61.2863i	1.07480	+	2.30491i
$708$	0.0885133	+	1.13418i	0.00332653	+	0.0426252i
$709$	−36.6991	−	6.47105i	−1.37827	−	0.243025i	−0.565083	−	0.825034i	$-0.691156\pi$
$709$	−36.6991	−	6.47105i	−1.37827	−	0.243025i	−0.813182	+	0.582009i	$0.802267\pi$
$710$	0.830898	+	0.681765i	0.0311831	+	0.0255862i
$711$	−0.906370	+	4.63042i	−0.0339915	+	0.173654i
$712$	−28.2924	−	7.58092i	−1.06030	−	0.284107i
$713$	−2.59502	+	5.56503i	−0.0971841	+	0.208412i
$714$	−18.8699	+	15.5344i	−0.706189	+	0.581359i
$715$	2.79074	+	4.71314i	0.104368	+	0.176262i
$716$	21.2116	+	25.2790i	0.792716	+	0.944722i
$717$	−5.03639	+	2.29123i	−0.188087	+	0.0855674i
$718$	−10.9533	−	5.10759i	−0.408772	−	0.190614i
$719$	−21.5770	−	37.3725i	−0.804687	−	1.39376i	−0.916502	−	0.400029i	$-0.869000\pi$
$719$	−21.5770	−	37.3725i	−0.804687	−	1.39376i	0.111816	−	0.993729i	$-0.464333\pi$
$720$	−4.89561	+	10.2895i	−0.182449	+	0.383465i
$721$	−30.1509	+	52.2229i	−1.12288	+	1.94488i
$722$	9.23470	−	6.46621i	0.343680	−	0.240647i
$723$	15.1410	−	31.6903i	0.563101	−	1.17857i
$724$	1.75433	−	4.82000i	0.0651993	−	0.179134i
$725$	0.0298240	+	0.00458438i	0.00110764	+	0.000170260i
$726$	−6.09211	+	10.3268i	−0.226099	+	0.383265i
$727$	6.75332	−	0.590839i	0.250467	−	0.0219130i	0.0387690	−	0.999248i	$-0.487656\pi$
$727$	6.75332	−	0.590839i	0.250467	−	0.0219130i	0.211698	+	0.977335i	$0.432101\pi$
$728$	−37.2180	+	37.2180i	−1.37939	+	1.37939i
$729$	−1.51922	+	26.9572i	−0.0562673	+	0.998416i
$730$	9.60915	+	13.4068i	0.355651	+	0.496207i
$731$	−6.25882	+	7.45897i	−0.231491	+	0.275880i
$732$	6.12505	−	1.57976i	0.226388	−	0.0583896i
$733$	14.5660	−	20.8024i	0.538006	−	0.768353i	−0.454474	−	0.890760i	$-0.650173\pi$
$733$	14.5660	−	20.8024i	0.538006	−	0.768353i	0.992480	+	0.122408i	$0.0390615\pi$
$734$	−16.2116	−	5.90055i	−0.598382	−	0.217793i
$735$	−44.0683	+	7.84421i	−1.62548	+	0.289338i
$736$	2.72113	−	15.4323i	0.100302	−	0.568841i
$737$	2.61687	−	0.701189i	0.0963937	−	0.0258286i
$738$	2.51148	−	8.71539i	0.0924489	−	0.320818i
$739$	31.3022	−	18.0723i	1.15147	−	0.664801i	0.202224	−	0.979339i	$-0.435183\pi$
$739$	31.3022	−	18.0723i	1.15147	−	0.664801i	0.949245	+	0.314538i	$0.101850\pi$
$740$	26.2078	−	4.91916i	0.963420	−	0.180832i
$741$	−3.85957	+	10.3023i	−0.141785	+	0.378463i
$742$	−1.34261	+	15.3461i	−0.0492886	+	0.563371i
$743$	−3.12862	+	35.7603i	−0.114778	+	1.31192i	0.692358	+	0.721554i	$0.256572\pi$
$743$	−3.12862	+	35.7603i	−0.114778	+	1.31192i	−0.807136	+	0.590365i	$0.798984\pi$
$744$	5.65712	+	6.87182i	0.207400	+	0.251933i
$745$	5.79662	−	8.47546i	0.212372	−	0.310517i
$746$	−1.75479	+	1.01313i	−0.0642473	+	0.0370932i
$747$	26.5803	−	17.8779i	0.972522	−	0.654119i
$748$	3.61497	−	0.968627i	0.132176	−	0.0354165i
$749$	−3.03056	+	17.1872i	−0.110734	+	0.628006i
$750$	−4.98432	+	11.3839i	−0.182002	+	0.415680i
$751$	20.6234	+	7.50630i	0.752558	+	0.273909i	0.689682	−	0.724113i	$-0.257750\pi$
$751$	20.6234	+	7.50630i	0.752558	+	0.273909i	0.0628763	+	0.998021i	$0.479973\pi$
$752$	10.9959	−	15.7038i	0.400981	−	0.572660i
$753$	−6.59210	+	23.7099i	−0.240230	+	0.864038i
$754$	0.0132091	−	0.0157420i	0.000481047	−	0.000573290i
$755$	−8.05261	+	5.77161i	−0.293065	+	0.210051i
$756$	−1.00054	+	35.5356i	−0.0363892	+	1.29242i
$757$	−19.9998	+	19.9998i	−0.726906	+	0.726906i	−0.970002	−	0.243096i	$-0.921837\pi$
$757$	−19.9998	+	19.9998i	−0.726906	+	0.726906i	0.243096	+	0.970002i	$0.421837\pi$
$758$	−4.66559	+	0.408186i	−0.169462	+	0.0148260i
$759$	−2.19991	−	0.0206420i	−0.0798516	−	0.000749256i
$760$	−0.0678358	−	6.16314i	−0.00246066	−	0.223561i
$761$	17.7365	−	48.7306i	0.642947	−	1.76648i	0.000683402	−	1.00000i	$-0.499782\pi$
$761$	17.7365	−	48.7306i	0.642947	−	1.76648i	0.642264	−	0.766484i	$-0.277995\pi$
$762$	5.27364	+	7.68399i	0.191044	+	0.278362i
$763$	23.4409	−	16.4135i	0.848619	−	0.594209i
$764$	0.366534	−	0.634856i	0.0132607	−	0.0229683i
$765$	−16.8904	−	29.7864i	−0.610674	−	1.07693i
$766$	5.89884	+	10.2171i	0.213134	+	0.369159i
$767$	−1.98884	−	0.927410i	−0.0718127	−	0.0334868i
$768$	−10.8797	−	7.77122i	−0.392589	−	0.280420i
$769$	−28.9226	−	34.4686i	−1.04298	−	1.24297i	−0.969350	−	0.245684i	$-0.920987\pi$
$769$	−28.9226	−	34.4686i	−1.04298	−	1.24297i	−0.0736257	−	0.997286i	$-0.523457\pi$
$770$	−2.76444	−	0.708213i	−0.0996234	−	0.0255222i
$771$	−8.05659	−	48.3391i	−0.290151	−	1.74089i
$772$	1.52698	−	3.27462i	0.0549572	−	0.117856i
$773$	23.2025	+	6.21709i	0.834536	+	0.223613i	0.650691	−	0.759342i	$-0.274479\pi$
$773$	23.2025	+	6.21709i	0.834536	+	0.223613i	0.183844	+	0.982955i	$0.441146\pi$
$774$	−0.569731	−	3.62795i	−0.0204786	−	0.130404i
$775$	−7.35900	−	8.38802i	−0.264343	−	0.301306i
$776$	−19.4273	−	3.42556i	−0.697399	−	0.122970i
$777$	46.1928	−	31.7028i	1.65716	−	1.13733i
$778$	−5.69992	−	12.2235i	−0.204352	−	0.438234i
$779$	−0.979290	−	5.55383i	−0.0350867	−	0.198987i
$780$	−18.7637	−	26.7050i	−0.671849	−	0.956192i
$781$	−0.264879	−	0.222260i	−0.00947813	−	0.00795309i
$782$	6.37309	+	6.37309i	0.227901	+	0.227901i
$783$	−0.00185275	−	0.0313033i	−6.62117e−5	−	0.00111869i
$784$			19.6314i			0.701122i
$785$	1.41259	−	1.21205i	0.0504175	−	0.0432597i
$786$	11.0699	−	6.25344i	0.394849	−	0.223053i
$787$	26.9699	+	18.8846i	0.961375	+	0.673162i	0.945126	−	0.326706i	$-0.105939\pi$
$787$	26.9699	+	18.8846i	0.961375	+	0.673162i	0.0162488	+	0.999868i	$0.494828\pi$
$788$	38.4347	−	17.9224i	1.36918	−	0.638460i
$789$	5.90923	−	6.90963i	0.210374	−	0.245989i
$790$	2.12913	+	0.748508i	0.0757512	+	0.0266307i
$791$	−26.2051	−	15.1295i	−0.931746	−	0.537944i
$792$	−1.40175	+	2.86447i	−0.0498092	+	0.101785i
$793$	−3.15800	+	11.7858i	−0.112144	+	0.418527i
$794$	−20.4646	+	7.44852i	−0.726263	+	0.264338i
$795$	−20.8552	−	5.55187i	−0.739658	−	0.196904i
$796$	−29.0150	+	24.3465i	−1.02841	+	0.862939i
$797$	−46.3175	−	4.05225i	−1.64065	−	0.143538i	−0.770874	−	0.636988i	$-0.780180\pi$
$797$	−46.3175	−	4.05225i	−1.64065	−	0.143538i	−0.869774	+	0.493449i	$0.835736\pi$
$798$	−2.37350	−	5.21724i	−0.0840209	−	0.184688i
$799$	19.7037	+	54.1355i	0.697068	+	1.91518i
$800$	23.6809	+	15.8164i	0.837247	+	0.559194i
$801$	0.716067	−	38.1539i	0.0253010	−	1.34810i
$802$	−4.51810	−	16.8618i	−0.159540	−	0.595410i
$803$	−3.04371	−	4.34687i	−0.107410	−	0.153398i
$804$	−15.2207	+	5.37868i	−0.536792	+	0.189692i
$805$	7.14081	+	25.5229i	0.251681	+	0.899563i
$806$	−7.48391	+	1.31962i	−0.263610	+	0.0464815i
$807$	−4.85958	−	18.8416i	−0.171065	−	0.663256i
$808$	−3.15035	−	36.0087i	−0.110829	−	1.26678i
$809$	14.6731			0.515879			0.257939	−	0.966161i	$-0.416957\pi$
$809$	14.6731			0.515879			0.257939	+	0.966161i	$0.416957\pi$
$810$	12.6546	+	2.57916i	0.444637	+	0.0906223i
$811$	30.4369			1.06878			0.534392	−	0.845237i	$-0.320541\pi$
$811$	30.4369			1.06878			0.534392	+	0.845237i	$0.320541\pi$
$812$	−0.00359846	−	0.0411306i	−0.000126281	−	0.00144340i
$813$	−6.65600	−	25.8067i	−0.233436	−	0.905080i
$814$	2.19073	−	0.386284i	0.0767849	−	0.0135393i
$815$	−27.9916	−	15.7528i	−0.980504	−	0.551796i
$816$	−14.1599	+	5.00381i	−0.495694	+	0.175169i
$817$	−1.30971	−	1.87046i	−0.0458209	−	0.0654390i
$818$	2.25486	+	8.41525i	0.0788393	+	0.294232i
$819$	−58.7327	−	35.3952i	−2.05229	−	1.23681i
$820$	15.2400	+	6.90334i	0.532203	+	0.241075i
$821$	5.06906	+	13.9271i	0.176911	+	0.486060i	0.996177	−	0.0873536i	$-0.0278410\pi$
$821$	5.06906	+	13.9271i	0.176911	+	0.486060i	−0.819266	+	0.573414i	$0.805619\pi$
$822$	4.74511	+	10.4303i	0.165505	+	0.363799i
$823$	−11.9027	−	1.04135i	−0.414903	−	0.0362993i	−0.122206	−	0.992505i	$-0.538997\pi$
$823$	−11.9027	−	1.04135i	−0.414903	−	0.0362993i	−0.292696	+	0.956205i	$0.594553\pi$
$824$	24.6922	−	20.7192i	0.860193	−	0.721788i
$825$	1.64372	−	3.64445i	0.0572271	−	0.126884i
$826$	1.07435	−	0.391031i	0.0373813	−	0.0136057i
$827$	1.44038	−	5.37558i	0.0500870	−	0.186927i	−0.936350	−	0.351068i	$-0.885819\pi$
$827$	1.44038	−	5.37558i	0.0500870	−	0.186927i	0.986437	+	0.164141i	$0.0524852\pi$
$828$	13.0783	−	0.897279i	0.454503	−	0.0311826i
$829$	34.1754	+	19.7312i	1.18696	+	0.685293i	0.957615	−	0.288052i	$-0.0930076\pi$
$829$	34.1754	+	19.7312i	1.18696	+	0.685293i	0.229347	+	0.973345i	$0.426341\pi$
$830$	−6.62793	−	13.8146i	−0.230059	−	0.479512i
$831$	−18.4856	+	21.6151i	−0.641258	+	0.749820i
$832$	1.23939	−	0.577937i	0.0429681	−	0.0200364i
$833$	−48.3250	−	33.8375i	−1.67436	−	1.17240i
$834$	−1.67439	+	0.945873i	−0.0579793	+	0.0327529i
$835$	32.6709	+	38.0766i	1.13062	+	1.31769i
$836$			0.877645i			0.0303540i
$837$	−6.91610	+	9.30819i	−0.239055	+	0.321738i
$838$	5.79766	+	5.79766i	0.200277	+	0.200277i
$839$	−34.4322	−	28.8921i	−1.18873	−	0.997464i	−0.999881	−	0.0154586i	$-0.995079\pi$
$839$	−34.4322	−	28.8921i	−1.18873	−	0.997464i	−0.188851	−	0.982006i	$-0.560476\pi$
$840$	37.8451	+	6.60978i	1.30578	+	0.228059i
$841$	−5.03579	−	28.5594i	−0.173648	−	0.984807i
$842$	4.88471	+	10.4753i	0.168338	+	0.361003i
$843$	13.7801	−	9.45749i	0.474612	−	0.325733i
$844$	33.9320	+	5.98313i	1.16799	+	0.205948i
$845$	33.7247	−	3.32492i	1.16016	−	0.114381i
$846$	−20.2748	−	7.81330i	−0.697061	−	0.268627i
$847$	−44.8845	−	12.0268i	−1.54225	−	0.413244i
$848$	−4.00021	+	8.57848i	−0.137368	+	0.294586i
$849$	−4.41930	−	26.5156i	−0.151670	−	0.910012i
$850$	−15.2640	+	5.93929i	−0.523551	+	0.203716i
$851$	−13.2797	−	15.8261i	−0.455222	−	0.542513i
$852$	1.67658	+	1.19755i	0.0574387	+	0.0410275i
$853$	−7.95489	−	3.70943i	−0.272370	−	0.127008i	0.281635	−	0.959522i	$-0.409123\pi$
$853$	−7.95489	−	3.70943i	−0.272370	−	0.127008i	−0.554005	+	0.832513i	$0.686901\pi$
$854$	−3.17850	−	5.50532i	−0.108766	−	0.188388i
$855$	7.77232	−	2.01808i	0.265808	−	0.0690169i
$856$	4.66443	−	8.07903i	0.159427	−	0.276135i
$857$	−28.3204	+	19.8301i	−0.967406	+	0.677385i	−0.946604	−	0.322399i	$-0.895511\pi$
$857$	−28.3204	+	19.8301i	−0.967406	+	0.677385i	−0.0208017	+	0.999784i	$0.506622\pi$
$858$	−1.54072	−	2.24491i	−0.0525991	−	0.0766399i
$859$	−6.70299	+	18.4163i	−0.228703	+	0.628357i	−0.999967	−	0.00815913i	$-0.997403\pi$
$859$	−6.70299	+	18.4163i	−0.228703	+	0.628357i	0.771264	+	0.636516i	$0.219625\pi$
$860$	6.77372	−	0.0745562i	0.230982	−	0.00254235i
$861$	35.1502	+	0.329818i	1.19791	+	0.0112402i
$862$	−3.06997	+	0.268587i	−0.104563	+	0.00914812i
$863$	−29.8911	+	29.8911i	−1.01750	+	1.01750i	−0.0176605	+	0.999844i	$0.505622\pi$
$863$	−29.8911	+	29.8911i	−1.01750	+	1.01750i	−0.999844	+	0.0176605i	$0.994378\pi$
$864$	10.9005	−	27.5136i	0.370843	−	0.936032i
$865$	−0.840774	+	5.09560i	−0.0285872	+	0.173255i
$866$	−13.8033	+	16.4501i	−0.469055	+	0.558998i
$867$	4.20164	−	15.1121i	0.142695	−	0.513234i
$868$	−8.75757	+	12.5071i	−0.297251	+	0.424519i
$869$	−0.682275	−	0.248328i	−0.0231446	−	0.00842394i
$870$	−0.0149444	−	0.00128302i	−0.000506661	−	4.34984e-5i
$871$	5.40728	−	30.6662i	0.183219	−	1.03908i
$872$	−14.7751	+	3.95897i	−0.500347	+	0.134068i
$873$	−1.75916	−	25.6407i	−0.0595386	−	0.867807i
$874$	−1.83043	+	1.05680i	−0.0619154	+	0.0357469i
$875$	−47.6813	−	6.79299i	−1.61192	−	0.229645i
$876$	20.0967	+	24.4119i	0.679005	+	0.824801i
$877$	−2.86019	+	32.6921i	−0.0965817	+	1.10393i	0.781008	+	0.624521i	$0.214706\pi$
$877$	−2.86019	+	32.6921i	−0.0965817	+	1.10393i	−0.877590	+	0.479413i	$0.840850\pi$
$878$	0.0301948	−	0.345129i	0.00101903	−	0.0116475i
$879$	−5.86171	+	15.6465i	−0.197711	+	0.527745i
$880$	−1.44732	−	0.989867i	−0.0487892	−	0.0333684i
$881$	−10.5631	+	6.09860i	−0.355879	+	0.205467i	−0.667272	−	0.744814i	$-0.732538\pi$
$881$	−10.5631	+	6.09860i	−0.355879	+	0.205467i	0.311392	+	0.950281i	$0.399205\pi$
$882$	21.5963	−	5.35447i	0.727186	−	0.180294i
$883$	−34.3877	+	9.21415i	−1.15724	+	0.310081i	−0.785862	−	0.618402i	$-0.787780\pi$
$883$	−34.3877	+	9.21415i	−1.15724	+	0.310081i	−0.371376	+	0.928483i	$0.621114\pi$
$884$	7.46965	−	42.3625i	0.251232	−	1.42480i
$885$	0.280698	+	1.57694i	0.00943556	+	0.0530083i
$886$	−3.13665	−	1.14165i	−0.105378	−	0.0383544i
$887$	5.74909	−	8.21054i	0.193035	−	0.275683i	−0.710954	−	0.703239i	$-0.751736\pi$
$887$	5.74909	−	8.21054i	0.193035	−	0.275683i	0.903989	+	0.427556i	$0.140625\pi$
$888$	−28.9985	+	7.47922i	−0.973126	+	0.250986i
$889$	−23.2168	+	27.6687i	−0.778666	+	0.927978i
$890$	−18.0096	−	2.97159i	−0.603684	−	0.0996080i
$891$	−4.06175	−	0.874500i	−0.136074	−	0.0292969i
$892$	12.3466	−	12.3466i	0.413396	−	0.413396i
$893$	−13.4586	+	1.17747i	−0.450374	+	0.0394027i
$894$	−2.59345	+	4.39620i	−0.0867378	+	0.147031i
$895$	33.2129	+	32.4897i	1.11019	+	1.08601i
$896$	16.5391	−	45.4408i	0.552532	−	1.51807i
$897$	−10.9012	+	22.8163i	−0.363981	+	0.761815i
$898$	7.35763	−	5.15187i	0.245527	−	0.171920i
$899$	0.00673405	−	0.0116637i	0.000224593	−	0.000389007i
$900$	−8.07507	+	22.4122i	−0.269169	+	0.747074i
$901$	−14.2220	−	24.6332i	−0.473803	−	0.820651i
$902$	1.26495	+	0.589856i	0.0421183	+	0.0196401i
$903$	12.9551	−	5.89372i	0.431119	−	0.196131i
$904$	10.3968	+	12.3904i	0.345791	+	0.412098i
$905$	1.79226	−	6.99592i	0.0595769	−	0.232552i
$906$	3.80219	−	3.13010i	0.126319	−	0.103990i
$907$	−7.47482	+	16.0298i	−0.248197	+	0.532261i	−0.990452	−	0.137857i	$-0.955979\pi$
$907$	−7.47482	+	16.0298i	−0.248197	+	0.532261i	0.742255	+	0.670118i	$0.233756\pi$
$908$	−15.1807	−	4.06766i	−0.503790	−	0.134990i
$909$	44.5470	−	15.2734i	1.47753	−	0.506587i
$910$	−20.8059	+	25.3571i	−0.689709	+	0.840581i
$911$	15.2588	+	2.69054i	0.505547	+	0.0891416i	0.420604	−	0.907244i	$-0.361818\pi$
$911$	15.2588	+	2.69054i	0.505547	+	0.0891416i	0.0849428	+	0.996386i	$0.472929\pi$
$912$	−0.274017	−	3.51117i	−0.00907360	−	0.116266i
$913$	2.08324	+	4.46752i	0.0689451	+	0.147853i
$914$	0.427785	+	2.42609i	0.0141499	+	0.0802478i
$915$	8.36394	−	3.05961i	0.276503	−	0.101148i
$916$	−11.8320	−	9.92824i	−0.390941	−	0.328038i
$917$	34.8423	+	34.8423i	1.15059	+	1.15059i
$918$	9.36675	+	14.2123i	0.309149	+	0.469077i
$919$		−	18.6392i		−	0.614851i	−0.951572	−	0.307426i	$-0.900532\pi$
$919$		−	18.6392i		−	0.614851i	0.951572	−	0.307426i	$-0.0994676\pi$
$920$	1.07931	−	14.1256i	0.0355839	−	0.465706i
$921$	−0.0712484	+	7.59326i	−0.00234771	+	0.250206i
$922$	−11.7140	−	8.20222i	−0.385779	−	0.270126i
$923$	−3.60196	+	1.67962i	−0.118560	+	0.0552855i
$924$	−5.37821	−	1.00044i	−0.176930	−	0.0329121i
$925$	36.0418	−	10.5129i	1.18505	−	0.345662i
$926$	0.663128	+	0.382857i	0.0217917	+	0.0125815i
$927$	33.9420	+	24.7285i	1.11480	+	0.812189i
$928$	−0.00889589	+	0.0331999i	−0.000292022	+	0.00108984i
$929$	9.92982	−	3.61416i	0.325787	−	0.118577i	−0.173949	−	0.984755i	$-0.555653\pi$
$929$	9.92982	−	3.61416i	0.325787	−	0.118577i	0.499736	+	0.866178i	$0.333431\pi$
$930$	3.92855	+	3.91581i	0.128822	+	0.128405i
$931$	10.5979	−	8.89269i	0.347332	−	0.291446i
$932$	−16.0072	−	1.40045i	−0.524334	−	0.0458733i
$933$	8.34801	−	11.6873i	0.273302	−	0.382623i
$934$	0.197650	+	0.543040i	0.00646732	+	0.0177688i
$935$	4.93133	−	1.85657i	0.161272	−	0.0607165i
$936$	23.0303	+	28.5165i	0.752769	+	0.932091i
$937$	3.84529	+	14.3508i	0.125620	+	0.468820i	0.999861	−	0.0166719i	$-0.00530709\pi$
$937$	3.84529	+	14.3508i	0.125620	+	0.468820i	−0.874241	+	0.485492i	$0.838640\pi$
$938$	9.30540	+	13.2895i	0.303832	+	0.433917i
$939$	−3.27884	+	17.6265i	−0.107001	+	0.575219i
$940$	19.6567	−	34.9286i	0.641130	−	1.13924i
$941$	16.9600	−	2.99051i	0.552882	−	0.0974879i	0.109774	−	0.993957i	$-0.464987\pi$
$941$	16.9600	−	2.99051i	0.552882	−	0.0974879i	0.443107	+	0.896469i	$0.353876\pi$
$942$	−0.660350	+	0.648073i	−0.0215154	+	0.0211154i
$943$	−1.12974	−	12.9130i	−0.0367894	−	0.420504i
$944$	0.702492			0.0228642
$945$	3.50700	+	49.9292i	0.114083	+	1.62420i
$946$	0.565120			0.0183736
$947$	5.19344	+	59.3613i	0.168764	+	1.92898i	0.333704	+	0.942678i	$0.391701\pi$
$947$	5.19344	+	59.3613i	0.168764	+	1.92898i	−0.164940	+	0.986304i	$0.552743\pi$
$948$	4.16824	+	1.15890i	0.135378	+	0.0376394i
$949$	−60.0667	+	10.5914i	−1.94985	+	0.343811i
$950$	−0.418902	−	3.81806i	−0.0135910	−	0.123874i
$951$	−1.78777	−	1.52893i	−0.0579723	−	0.0495789i
$952$	29.0424	+	41.4769i	0.941271	+	1.34427i
$953$	−2.03332	−	7.58847i	−0.0658658	−	0.245815i	0.925141	−	0.379623i	$-0.123946\pi$
$953$	−2.03332	−	7.58847i	−0.0658658	−	0.245815i	−0.991007	+	0.133808i	$0.957279\pi$
$954$	10.5282	+	2.06081i	0.340862	+	0.0667212i
$955$	0.425874	−	0.940168i	0.0137809	−	0.0304231i
$956$	1.73522	+	4.76748i	0.0561211	+	0.154191i
$957$	0.00480293		0.000465651i	0.000155257		1.50524e-5i
$958$	18.7946	+	1.64431i	0.607225	+	0.0531253i
$959$	−34.0202	+	28.5463i	−1.09857	+	0.921808i
$960$	−0.865237	−	0.497674i	−0.0279254	−	0.0160623i
$961$	24.4503	−	8.89918i	0.788719	−	0.287070i
$962$	6.61763	−	24.6973i	0.213361	−	0.796274i
$963$	11.6787	+	3.36542i	0.376342	+	0.108449i
$964$	−27.8895	−	16.1020i	−0.898261	−	0.518611i
$965$	1.68718	−	4.79920i	0.0543123	−	0.154492i
$966$	−4.38954	−	12.4216i	−0.141231	−	0.399657i
$967$	−28.2347	+	13.1660i	−0.907966	+	0.423392i	−0.819758	−	0.572710i	$-0.805892\pi$
$967$	−28.2347	+	13.1660i	−0.907966	+	0.423392i	−0.0882085	+	0.996102i	$0.528114\pi$
$968$	20.3466	+	14.2469i	0.653965	+	0.457911i
$969$	9.11545	+	5.37747i	0.292830	+	0.172749i
$970$	−12.2577	−	0.936590i	−0.393571	−	0.0300721i
$971$		−	46.4614i		−	1.49102i	−0.666496	−	0.745509i	$-0.732207\pi$
$971$		−	46.4614i		−	1.49102i	0.666496	−	0.745509i	$-0.267793\pi$
$972$	24.5346	+	3.31197i	0.786947	+	0.106231i
$973$	−5.27012	−	5.27012i	−0.168952	−	0.168952i
$974$	15.7126	+	13.1844i	0.503464	+	0.422456i
$975$	−29.9800	−	34.8259i	−0.960128	−	1.11532i
$976$	−0.678273	−	3.84668i	−0.0217110	−	0.123129i
$977$	−14.4520	−	30.9924i	−0.462360	−	0.991534i	−0.989869	−	0.141985i	$-0.954652\pi$
$977$	−14.4520	−	30.9924i	−0.462360	−	0.991534i	0.527509	−	0.849549i	$-0.323126\pi$
$978$	14.4065	+	6.88317i	0.460670	+	0.220100i
$979$	5.78303	+	1.01970i	0.184826	+	0.0325899i
$980$	4.02689	+	40.8447i	0.128634	+	1.30474i
$981$	−9.63865	−	17.4425i	−0.307739	−	0.556897i
$982$	−7.87006	−	2.10878i	−0.251144	−	0.0672937i
$983$	−15.0350	+	32.2428i	−0.479543	+	1.02838i	0.506553	+	0.862209i	$0.330919\pi$
$983$	−15.0350	+	32.2428i	−0.479543	+	1.02838i	−0.986096	+	0.166175i	$0.946858\pi$
$984$	−17.5955	−	6.59187i	−0.560925	−	0.210141i
$985$	51.3774	−	30.4216i	1.63702	−	0.969311i
$986$	−0.0127071	−	0.0151438i	−0.000404677	−	0.000482275i
$987$	8.12612	−	83.8164i	0.258657	−	2.66791i
$988$	9.14249	+	4.26321i	0.290861	+	0.135631i
$989$	−2.62418	−	4.54522i	−0.0834442	−	0.144530i
$990$	−0.694185	+	1.86217i	−0.0220627	+	0.0591837i
$991$	−2.77369	+	4.80418i	−0.0881092	+	0.152610i	−0.906712	−	0.421751i	$-0.861416\pi$
$991$	−2.77369	+	4.80418i	−0.0881092	+	0.152610i	0.818603	+	0.574360i	$0.194749\pi$
$992$	10.4119	−	7.29047i	0.330577	−	0.231473i
$993$	12.3341	−	0.962571i	0.391411	−	0.0305463i
$994$	0.708192	−	1.94574i	0.0224625	−	0.0617152i
$995$	−37.2915	+	38.1215i	−1.18222	+	1.20853i
$996$	−14.4468	−	25.5739i	−0.457766	−	0.810338i
$997$	30.3931	−	2.65905i	0.962558	−	0.0842129i	0.404969	−	0.914330i	$-0.367282\pi$
$997$	30.3931	−	2.65905i	0.962558	−	0.0842129i	0.557589	+	0.830117i	$0.311727\pi$
$998$	−5.48435	+	5.48435i	−0.173604	+	0.173604i
$999$	−18.5496	−	34.3251i	−0.586883	−	1.08600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.38.10	yes	192
3.2	odd	2		405.2.r.a.278.7		192
5.2	odd	4	inner	135.2.q.a.92.7	yes	192
5.3	odd	4		675.2.ba.b.632.10		192
5.4	even	2		675.2.ba.b.443.7		192
15.2	even	4		405.2.r.a.197.10		192
27.5	odd	18	inner	135.2.q.a.113.7	yes	192
27.22	even	9		405.2.r.a.368.10		192
135.22	odd	36		405.2.r.a.287.7		192
135.32	even	36	inner	135.2.q.a.32.10	✓	192
135.59	odd	18		675.2.ba.b.518.10		192
135.113	even	36		675.2.ba.b.32.7		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.10	✓	192	135.32	even	36	inner
135.2.q.a.38.10	yes	192	1.1	even	1	trivial
135.2.q.a.92.7	yes	192	5.2	odd	4	inner
135.2.q.a.113.7	yes	192	27.5	odd	18	inner
405.2.r.a.197.10		192	15.2	even	4
405.2.r.a.278.7		192	3.2	odd	2
405.2.r.a.287.7		192	135.22	odd	36
405.2.r.a.368.10		192	27.22	even	9
675.2.ba.b.32.7		192	135.113	even	36
675.2.ba.b.443.7		192	5.4	even	2
675.2.ba.b.518.10		192	135.59	odd	18
675.2.ba.b.632.10		192	5.3	odd	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0559313 + 0.639298i) q^{2} +(0.432570 + 1.67717i) q^{3} +(1.56404 - 0.275783i) q^{4} +(2.15338 - 0.602474i) q^{5} +(-1.04801 + 0.370347i) q^{6} +(-2.47086 - 3.52875i) q^{7} +(0.595975 + 2.22421i) q^{8} +(-2.62577 + 1.45098i) q^{9} +O(q^{10})\)	\(q+(0.0559313 + 0.639298i) q^{2} +(0.432570 + 1.67717i) q^{3} +(1.56404 - 0.275783i) q^{4} +(2.15338 - 0.602474i) q^{5} +(-1.04801 + 0.370347i) q^{6} +(-2.47086 - 3.52875i) q^{7} +(0.595975 + 2.22421i) q^{8} +(-2.62577 + 1.45098i) q^{9} +(0.505601 + 1.34295i) q^{10} +(-0.157893 - 0.433806i) q^{11} +(1.13909 + 2.50386i) q^{12} +(-5.28596 - 0.462462i) q^{13} +(2.11772 - 1.77698i) q^{14} +(1.94193 + 3.35095i) q^{15} +(1.59619 - 0.580964i) q^{16} +(-1.32114 + 4.93057i) q^{17} +(-1.07447 - 1.59749i) q^{18} +(-1.03667 - 0.598524i) q^{19} +(3.20182 - 1.53616i) q^{20} +(4.84948 - 5.67047i) q^{21} +(0.268500 - 0.125204i) q^{22} +(-2.25381 - 1.57814i) q^{23} +(-3.47256 + 1.96168i) q^{24} +(4.27405 - 2.59470i) q^{25} -3.40517i q^{26} +(-3.56937 - 3.77619i) q^{27} +(-4.83770 - 4.83770i) q^{28} +(0.00462297 + 0.00387914i) q^{29} +(-2.03364 + 1.42890i) q^{30} +(-0.387533 - 2.19781i) q^{31} +(2.40699 + 5.16180i) q^{32} +(0.659265 - 0.452464i) q^{33} +(-3.22599 - 0.568830i) q^{34} +(-7.44667 - 6.11010i) q^{35} +(-3.70665 + 2.99354i) q^{36} +(7.25290 + 1.94341i) q^{37} +(0.324653 - 0.696220i) q^{38} +(-1.51093 - 9.06548i) q^{39} +(2.62339 + 4.43050i) q^{40} +(3.02828 + 3.60897i) q^{41} +(3.89636 + 2.78310i) q^{42} +(1.72881 + 0.806157i) q^{43} +(-0.366587 - 0.634947i) q^{44} +(-4.78008 + 4.70647i) q^{45} +(0.882840 - 1.52912i) q^{46} +(9.24502 - 6.47343i) q^{47} +(1.66484 + 2.42576i) q^{48} +(-3.95281 + 10.8602i) q^{49} +(1.89784 + 2.58727i) q^{50} +(-8.84086 - 0.0829548i) q^{51} +(-8.39501 + 0.734468i) q^{52} +(-3.94023 + 3.94023i) q^{53} +(2.21447 - 2.49310i) q^{54} +(-0.601359 - 0.839022i) q^{55} +(6.37611 - 7.59875i) q^{56} +(0.555389 - 1.99758i) q^{57} +(-0.00222135 + 0.00317242i) q^{58} +(0.388624 + 0.141448i) q^{59} +(3.96140 + 4.70548i) q^{60} +(0.399307 - 2.26458i) q^{61} +(1.38338 - 0.370675i) q^{62} +(11.6081 + 5.68050i) q^{63} +(-0.223194 + 0.128861i) q^{64} +(-11.6613 + 2.18880i) q^{65} +(0.326133 + 0.396160i) q^{66} +(-0.511475 + 5.84619i) q^{67} +(-0.706556 + 8.07597i) q^{68} +(1.67186 - 4.46267i) q^{69} +(3.48967 - 5.10238i) q^{70} +(0.648656 - 0.374502i) q^{71} +(-4.79218 - 4.97550i) q^{72} +(11.1032 - 2.97508i) q^{73} +(-0.836752 + 4.74546i) q^{74} +(6.20057 + 6.04590i) q^{75} +(-1.78647 - 0.650220i) q^{76} +(-1.14066 + 1.62904i) q^{77} +(5.71103 - 1.47297i) q^{78} +(1.01095 - 1.20481i) q^{79} +(3.08717 - 2.21269i) q^{80} +(4.78929 - 7.61989i) q^{81} +(-2.13783 + 2.13783i) q^{82} +(-10.6371 + 0.930629i) q^{83} +(6.02097 - 10.2063i) q^{84} +(0.125623 + 11.4133i) q^{85} +(-0.418680 + 1.15031i) q^{86} +(-0.00450619 + 0.00943149i) q^{87} +(0.870776 - 0.609724i) q^{88} +(-6.36010 + 11.0160i) q^{89} +(-3.27619 - 2.79265i) q^{90} +(11.4289 + 19.7955i) q^{91} +(-3.96028 - 1.84671i) q^{92} +(3.51845 - 1.60066i) q^{93} +(4.65554 + 5.54825i) q^{94} +(-2.59294 - 0.664279i) q^{95} +(-7.61600 + 6.26976i) q^{96} +(-3.62057 + 7.76434i) q^{97} +(-7.16401 - 1.91959i) q^{98} +(1.04404 + 0.909974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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