LMFDB - Embedded newform 378.2.u.c.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			211.2
Character	$\chi$	$=$	378.211
Dual form			378.2.u.c.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-0.762464 - 1.55520i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.51130 + 0.550067i) q^{5} +(1.58375 + 0.701250i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.83730 + 2.37157i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.762464 - 1.55520i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.51130 + 0.550067i) q^{5} +(1.58375 + 0.701250i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.83730 + 2.37157i) q^{9} +(0.804144 - 1.39282i) q^{10} +(-2.33948 - 0.851501i) q^{11} +(-1.66397 + 0.480823i) q^{12} +(1.41023 + 1.18332i) q^{13} +(0.766044 + 0.642788i) q^{14} +(2.00777 + 1.93096i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.68369 + 2.91623i) q^{17} +(-0.116964 - 2.99772i) q^{18} +(0.754514 + 1.30686i) q^{19} +(0.279276 + 1.58385i) q^{20} +(-1.39917 + 1.02094i) q^{21} +(2.33948 - 0.851501i) q^{22} +(-0.880064 + 4.99109i) q^{23} +(0.965611 - 1.43791i) q^{24} +(-1.84878 + 1.55131i) q^{25} -1.84092 q^{26} +(5.08914 + 1.04913i) q^{27} -1.00000 q^{28} +(-6.12677 + 5.14097i) q^{29} +(-2.77924 - 0.188631i) q^{30} +(0.0299215 - 0.169693i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.459515 + 4.28760i) q^{33} +(-0.584738 - 3.31622i) q^{34} +(0.804144 + 1.39282i) q^{35} +(2.01650 + 2.22120i) q^{36} +(-1.62826 + 2.82023i) q^{37} +(-1.41802 - 0.516118i) q^{38} +(0.765053 - 3.09542i) q^{39} +(-1.23202 - 1.03379i) q^{40} +(2.71635 + 2.27929i) q^{41} +(0.415582 - 1.68146i) q^{42} +(-5.45095 - 1.98398i) q^{43} +(-1.24481 + 2.15608i) q^{44} +(1.47218 - 4.59478i) q^{45} +(-2.53404 - 4.38909i) q^{46} +(-0.690703 - 3.91717i) q^{47} +(0.184572 + 1.72219i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(0.419085 - 2.37675i) q^{50} +(5.81907 + 0.394949i) q^{51} +(1.41023 - 1.18332i) q^{52} -5.82891 q^{53} +(-4.57287 + 2.46756i) q^{54} +4.00403 q^{55} +(0.766044 - 0.642788i) q^{56} +(1.45713 - 2.16985i) q^{57} +(1.38883 - 7.87642i) q^{58} +(2.71002 - 0.986366i) q^{59} +(2.25027 - 1.64196i) q^{60} +(-2.55663 - 14.4993i) q^{61} +(0.0861556 + 0.149226i) q^{62} +(2.65458 + 1.39757i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.78217 - 1.01263i) q^{65} +(-3.10803 - 2.98912i) q^{66} +(-2.47139 - 2.07374i) q^{67} +(2.57956 + 2.16451i) q^{68} +(8.43316 - 2.43685i) q^{69} +(-1.51130 - 0.550067i) q^{70} +(1.00056 - 1.73303i) q^{71} +(-2.97249 - 0.405361i) q^{72} +(7.20098 + 12.4725i) q^{73} +(-0.565489 - 3.20705i) q^{74} +(3.82223 + 1.69241i) q^{75} +(1.41802 - 0.516118i) q^{76} +(-0.432319 + 2.45180i) q^{77} +(1.40364 + 2.86300i) q^{78} +(-3.41045 + 2.86171i) q^{79} +1.60829 q^{80} +(-2.24868 - 8.71455i) q^{81} -3.54594 q^{82} +(-4.13117 + 3.46647i) q^{83} +(0.762464 + 1.55520i) q^{84} +(0.940427 - 5.33343i) q^{85} +(5.45095 - 1.98398i) q^{86} +(12.6667 + 5.60855i) q^{87} +(-0.432319 - 2.45180i) q^{88} +(-5.53774 - 9.59164i) q^{89} +(1.82571 + 4.46610i) q^{90} +(0.920460 - 1.59428i) q^{91} +(4.76244 + 1.73339i) q^{92} +(-0.286721 + 0.0828512i) q^{93} +(3.04702 + 2.55675i) q^{94} +(-1.85915 - 1.56001i) q^{95} +(-1.24839 - 1.20063i) q^{96} +(4.39293 + 1.59890i) q^{97} +(0.500000 - 0.866025i) q^{98} +(6.31771 - 3.98378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−0.762464	−	1.55520i	−0.440209	−	0.897895i
$3$	−0.762464	−	1.55520i	−0.440209	−	0.897895i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−1.51130	+	0.550067i	−0.675872	+	0.245997i	−0.657074	−	0.753826i	$-0.728206\pi$
$5$	−1.51130	+	0.550067i	−0.675872	+	0.245997i	−0.0187978	+	0.999823i	$0.505984\pi$
$6$	1.58375	+	0.701250i	0.646561	+	0.286284i
$7$	−0.173648	−	0.984808i	−0.0656328	−	0.372222i
$7$	−0.173648	−	0.984808i	−0.0656328	−	0.372222i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.83730	+	2.37157i	−0.612432	+	0.790523i
$10$	0.804144	−	1.39282i	0.254293	−	0.440448i
$11$	−2.33948	−	0.851501i	−0.705380	−	0.256737i	−0.0356738	−	0.999363i	$-0.511358\pi$
$11$	−2.33948	−	0.851501i	−0.705380	−	0.256737i	−0.669706	+	0.742626i	$0.733580\pi$
$12$	−1.66397	+	0.480823i	−0.480348	+	0.138802i
$13$	1.41023	+	1.18332i	0.391126	+	0.328194i	0.817052	−	0.576564i	$-0.195607\pi$
$13$	1.41023	+	1.18332i	0.391126	+	0.328194i	−0.425925	+	0.904758i	$0.640051\pi$
$14$	0.766044	+	0.642788i	0.204734	+	0.171792i
$15$	2.00777	+	1.93096i	0.518405	+	0.498572i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−1.68369	+	2.91623i	−0.408354	+	0.707290i	−0.994705	−	0.102767i	$-0.967230\pi$
$17$	−1.68369	+	2.91623i	−0.408354	+	0.707290i	0.586351	+	0.810057i	$0.300564\pi$
$18$	−0.116964	−	2.99772i	−0.0275688	−	0.706569i
$19$	0.754514	+	1.30686i	0.173097	+	0.299813i	0.939501	−	0.342546i	$-0.111289\pi$
$19$	0.754514	+	1.30686i	0.173097	+	0.299813i	−0.766404	+	0.642359i	$0.777956\pi$
$20$	0.279276	+	1.58385i	0.0624480	+	0.354160i
$21$	−1.39917	+	1.02094i	−0.305325	+	0.222787i
$22$	2.33948	−	0.851501i	0.498779	−	0.181541i
$23$	−0.880064	+	4.99109i	−0.183506	+	1.04071i	0.744354	+	0.667785i	$0.232758\pi$
$23$	−0.880064	+	4.99109i	−0.183506	+	1.04071i	−0.927860	+	0.372929i	$0.878354\pi$
$24$	0.965611	−	1.43791i	0.197105	−	0.293513i
$25$	−1.84878	+	1.55131i	−0.369756	+	0.310262i
$26$	−1.84092			−0.361034
$27$	5.08914	+	1.04913i	0.979405	+	0.201905i
$28$	−1.00000			−0.188982
$29$	−6.12677	+	5.14097i	−1.13771	+	0.954654i	−0.999362	−	0.0357293i	$-0.988625\pi$
$29$	−6.12677	+	5.14097i	−1.13771	+	0.954654i	−0.138351	+	0.990383i	$0.544180\pi$
$30$	−2.77924	−	0.188631i	−0.507418	−	0.0344391i
$31$	0.0299215	−	0.169693i	0.00537407	−	0.0304778i	−0.982003	−	0.188866i	$-0.939519\pi$
$31$	0.0299215	−	0.169693i	0.00537407	−	0.0304778i	0.987377	+	0.158388i	$0.0506298\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.459515	+	4.28760i	0.0799913	+	0.746375i
$34$	−0.584738	−	3.31622i	−0.100282	−	0.568726i
$35$	0.804144	+	1.39282i	0.135925	+	0.235429i
$36$	2.01650	+	2.22120i	0.336083	+	0.370200i
$37$	−1.62826	+	2.82023i	−0.267684	+	0.463643i	−0.968263	−	0.249932i	$-0.919592\pi$
$37$	−1.62826	+	2.82023i	−0.267684	+	0.463643i	0.700579	+	0.713575i	$0.252925\pi$
$38$	−1.41802	−	0.516118i	−0.230034	−	0.0837254i
$39$	0.765053	−	3.09542i	0.122507	−	0.495665i
$40$	−1.23202	−	1.03379i	−0.194799	−	0.163456i
$41$	2.71635	+	2.27929i	0.424222	+	0.355965i	0.829767	−	0.558111i	$-0.188474\pi$
$41$	2.71635	+	2.27929i	0.424222	+	0.355965i	−0.405544	+	0.914075i	$0.632918\pi$
$42$	0.415582	−	1.68146i	0.0641257	−	0.259454i
$43$	−5.45095	−	1.98398i	−0.831261	−	0.302554i	−0.108885	−	0.994054i	$-0.534728\pi$
$43$	−5.45095	−	1.98398i	−0.831261	−	0.302554i	−0.722376	+	0.691500i	$0.756950\pi$
$44$	−1.24481	+	2.15608i	−0.187662	+	0.325041i
$45$	1.47218	−	4.59478i	0.219459	−	0.684949i
$46$	−2.53404	−	4.38909i	−0.373624	−	0.647136i
$47$	−0.690703	−	3.91717i	−0.100749	−	0.571378i	−0.992833	−	0.119508i	$-0.961868\pi$
$47$	−0.690703	−	3.91717i	−0.100749	−	0.571378i	0.892084	−	0.451870i	$-0.149243\pi$
$48$	0.184572	+	1.72219i	0.0266407	+	0.248576i
$49$	−0.939693	+	0.342020i	−0.134242	+	0.0488600i
$50$	0.419085	−	2.37675i	0.0592675	−	0.336123i
$51$	5.81907	+	0.394949i	0.814833	+	0.0553039i
$52$	1.41023	−	1.18332i	0.195563	−	0.164097i
$53$	−5.82891			−0.800662			−0.400331	−	0.916371i	$-0.631105\pi$
$53$	−5.82891			−0.800662			−0.400331	+	0.916371i	$0.631105\pi$
$54$	−4.57287	+	2.46756i	−0.622289	+	0.335792i
$55$	4.00403			0.539903
$56$	0.766044	−	0.642788i	0.102367	−	0.0858961i
$57$	1.45713	−	2.16985i	0.193002	−	0.287404i
$58$	1.38883	−	7.87642i	0.182362	−	1.03422i
$59$	2.71002	−	0.986366i	0.352814	−	0.128414i	−0.159532	−	0.987193i	$-0.550999\pi$
$59$	2.71002	−	0.986366i	0.352814	−	0.128414i	0.512347	+	0.858779i	$0.328776\pi$
$60$	2.25027	−	1.64196i	0.290509	−	0.211976i
$61$	−2.55663	−	14.4993i	−0.327342	−	1.85645i	−0.492675	−	0.870213i	$-0.663981\pi$
$61$	−2.55663	−	14.4993i	−0.327342	−	1.85645i	0.165333	−	0.986238i	$-0.447130\pi$
$62$	0.0861556	+	0.149226i	0.0109418	+	0.0189517i
$63$	2.65458	+	1.39757i	0.334446	+	0.176077i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.78217	−	1.01263i	−0.345086	−	0.125601i
$66$	−3.10803	−	2.98912i	−0.382571	−	0.367935i
$67$	−2.47139	−	2.07374i	−0.301928	−	0.253348i	0.479218	−	0.877696i	$-0.340920\pi$
$67$	−2.47139	−	2.07374i	−0.301928	−	0.253348i	−0.781146	+	0.624348i	$0.785365\pi$
$68$	2.57956	+	2.16451i	0.312817	+	0.262485i
$69$	8.43316	−	2.43685i	1.01523	−	0.293362i
$70$	−1.51130	−	0.550067i	−0.180634	−	0.0657455i
$71$	1.00056	−	1.73303i	0.118745	−	0.205672i	−0.800526	−	0.599299i	$-0.795446\pi$
$71$	1.00056	−	1.73303i	0.118745	−	0.205672i	0.919271	+	0.393626i	$0.128780\pi$
$72$	−2.97249	−	0.405361i	−0.350311	−	0.0477723i
$73$	7.20098	+	12.4725i	0.842811	+	1.45979i	0.887509	+	0.460791i	$0.152434\pi$
$73$	7.20098	+	12.4725i	0.842811	+	1.45979i	−0.0446978	+	0.999001i	$0.514232\pi$
$74$	−0.565489	−	3.20705i	−0.0657367	−	0.372812i
$75$	3.82223	+	1.69241i	0.441353	+	0.195422i
$76$	1.41802	−	0.516118i	0.162658	−	0.0592028i
$77$	−0.432319	+	2.45180i	−0.0492673	+	0.279409i
$78$	1.40364	+	2.86300i	0.158930	+	0.324171i
$79$	−3.41045	+	2.86171i	−0.383706	+	0.321968i	−0.814155	−	0.580647i	$-0.802800\pi$
$79$	−3.41045	+	2.86171i	−0.383706	+	0.321968i	0.430449	+	0.902615i	$0.358355\pi$
$80$	1.60829			0.179812
$81$	−2.24868	−	8.71455i	−0.249854	−	0.968284i
$82$	−3.54594			−0.391584
$83$	−4.13117	+	3.46647i	−0.453455	+	0.380494i	−0.840716	−	0.541476i	$-0.817866\pi$
$83$	−4.13117	+	3.46647i	−0.453455	+	0.380494i	0.387261	+	0.921970i	$0.373421\pi$
$84$	0.762464	+	1.55520i	0.0831917	+	0.169686i
$85$	0.940427	−	5.33343i	0.102004	−	0.578491i
$86$	5.45095	−	1.98398i	0.587791	−	0.213938i
$87$	12.6667	+	5.60855i	1.35801	+	0.601299i
$88$	−0.432319	−	2.45180i	−0.0460853	−	0.261363i
$89$	−5.53774	−	9.59164i	−0.586999	−	1.01671i	−0.994623	−	0.103562i	$-0.966976\pi$
$89$	−5.53774	−	9.59164i	−0.586999	−	1.01671i	0.407624	−	0.913150i	$-0.366357\pi$
$90$	1.82571	+	4.46610i	0.192447	+	0.470768i
$91$	0.920460	−	1.59428i	0.0964904	−	0.167126i
$92$	4.76244	+	1.73339i	0.496519	+	0.180718i
$93$	−0.286721	+	0.0828512i	−0.0297316	+	0.00859127i
$94$	3.04702	+	2.55675i	0.314276	+	0.263709i
$95$	−1.85915	−	1.56001i	−0.190745	−	0.160054i
$96$	−1.24839	−	1.20063i	−0.127413	−	0.122539i
$97$	4.39293	+	1.59890i	0.446035	+	0.162343i	0.555266	−	0.831673i	$-0.312617\pi$
$97$	4.39293	+	1.59890i	0.446035	+	0.162343i	−0.109231	+	0.994016i	$0.534839\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	6.31771	−	3.98378i	0.634954	−	0.400385i
$100$	1.20671	+	2.09008i	0.120671	+	0.209008i
$101$	−1.34027	−	7.60103i	−0.133362	−	0.756331i	−0.975987	−	0.217830i	$-0.930102\pi$
$101$	−1.34027	−	7.60103i	−0.133362	−	0.756331i	0.842625	−	0.538501i	$-0.181009\pi$
$102$	−4.71154	+	3.43788i	−0.466512	+	0.340401i
$103$	5.98150	−	2.17709i	0.589374	−	0.214515i	−0.0300799	−	0.999547i	$-0.509576\pi$
$103$	5.98150	−	2.17709i	0.589374	−	0.214515i	0.619454	+	0.785033i	$0.287354\pi$
$104$	−0.319672	+	1.81295i	−0.0313465	+	0.177775i
$105$	1.55298	−	2.31258i	0.151555	−	0.225684i
$106$	4.46520	−	3.74675i	0.433699	−	0.363916i
$107$	19.5911			1.89394			0.946970	−	0.321323i	$-0.104128\pi$
$107$	19.5911			1.89394			0.946970	+	0.321323i	$0.104128\pi$
$108$	1.91691	−	4.82964i	0.184455	−	0.464733i
$109$	−7.72080			−0.739519			−0.369759	−	0.929128i	$-0.620560\pi$
$109$	−7.72080			−0.739519			−0.369759	+	0.929128i	$0.620560\pi$
$110$	−3.06726	+	2.57374i	−0.292452	+	0.245396i
$111$	5.62751	+	0.381947i	0.534140	+	0.0362528i
$112$	−0.173648	+	0.984808i	−0.0164082	+	0.0930556i
$113$	−9.98006	+	3.63244i	−0.938845	+	0.341712i	−0.765710	−	0.643186i	$-0.777612\pi$
$113$	−9.98006	+	3.63244i	−0.938845	+	0.341712i	−0.173135	+	0.984898i	$0.555390\pi$
$114$	0.278524	+	2.59883i	0.0260862	+	0.243403i
$115$	−1.41540	−	8.02710i	−0.131986	−	0.748531i
$116$	3.99896	+	6.92641i	0.371294	+	0.643101i
$117$	−5.39733	+	1.17034i	−0.498983	+	0.108198i
$118$	−1.44197	+	2.49757i	−0.132744	+	0.229920i
$119$	3.16430	+	1.15171i	0.290071	+	0.105577i
$120$	−0.668375	+	2.70426i	−0.0610140	+	0.246864i
$121$	−3.67837	−	3.08652i	−0.334398	−	0.280593i
$122$	11.2785	+	9.46378i	1.02111	+	0.856810i
$123$	1.47363	−	5.96234i	0.132873	−	0.537606i
$124$	−0.161920	−	0.0589339i	−0.0145408	−	0.00529242i
$125$	5.96145	−	10.3255i	0.533208	−	0.923544i
$126$	−2.93187	+	0.635736i	−0.261191	+	0.0566359i
$127$	10.1898	+	17.6492i	0.904194	+	1.56611i	0.821995	+	0.569495i	$0.192861\pi$
$127$	10.1898	+	17.6492i	0.904194	+	1.56611i	0.0821992	+	0.996616i	$0.473806\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	1.07066	+	9.99003i	0.0942665	+	0.879573i
$130$	2.78217	−	1.01263i	0.244013	−	0.0888134i
$131$	2.43858	−	13.8299i	0.213059	−	1.20832i	−0.671183	−	0.741292i	$-0.734213\pi$
$131$	2.43858	−	13.8299i	0.213059	−	1.20832i	0.884242	−	0.467028i	$-0.154675\pi$
$132$	4.30226	+	0.292000i	0.374463	+	0.0254153i
$133$	1.15598	−	0.969984i	0.100236	−	0.0841083i
$134$	3.22617			0.278699
$135$	−8.26828	+	1.21382i	−0.711620	+	0.104469i
$136$	−3.36737			−0.288750
$137$	−15.5973	+	13.0877i	−1.33257	+	1.11816i	−0.349097	+	0.937087i	$0.613511\pi$
$137$	−15.5973	+	13.0877i	−1.33257	+	1.11816i	−0.983470	+	0.181070i	$0.942044\pi$
$138$	−4.89380	+	7.28747i	−0.416588	+	0.620351i
$139$	−1.32238	+	7.49957i	−0.112163	+	0.636105i	0.875953	+	0.482396i	$0.160233\pi$
$139$	−1.32238	+	7.49957i	−0.112163	+	0.636105i	−0.988116	+	0.153710i	$0.950878\pi$
$140$	1.51130	−	0.550067i	0.127728	−	0.0464891i
$141$	−5.56535	+	4.06088i	−0.468687	+	0.341988i
$142$	0.347492	+	1.97073i	0.0291609	+	0.165380i
$143$	−2.29160	−	3.96917i	−0.191633	−	0.331918i
$144$	2.53762	−	1.60015i	0.211468	−	0.133346i
$145$	6.43148	−	11.1397i	0.534106	−	0.925098i
$146$	−13.5334	−	4.92576i	−1.12003	−	0.407659i
$147$	1.24839	+	1.20063i	0.102966	+	0.0990265i
$148$	2.49464	+	2.09325i	0.205058	+	0.172064i
$149$	6.91613	+	5.80333i	0.566592	+	0.475427i	0.880513	−	0.474022i	$-0.157198\pi$
$149$	6.91613	+	5.80333i	0.566592	+	0.475427i	−0.313921	+	0.949449i	$0.601643\pi$
$150$	−4.01586	+	1.16042i	−0.327893	+	0.0947482i
$151$	−17.2987	−	6.29622i	−1.40775	−	0.512379i	−0.477281	−	0.878751i	$-0.658378\pi$
$151$	−17.2987	−	6.29622i	−1.40775	−	0.512379i	−0.930468	+	0.366372i	$0.880600\pi$
$152$	−0.754514	+	1.30686i	−0.0611992	+	0.106000i
$153$	−3.82261	−	9.35096i	−0.309040	−	0.755980i
$154$	−1.24481	−	2.15608i	−0.100310	−	0.173742i
$155$	0.0481224	+	0.272916i	0.00386529	+	0.0219211i
$156$	−2.91555	−	1.29095i	−0.233431	−	0.103358i
$157$	−13.4960	+	4.91215i	−1.07710	+	0.392033i	−0.818828	−	0.574039i	$-0.805376\pi$
$157$	−13.4960	+	4.91215i	−1.07710	+	0.392033i	−0.258273	+	0.966072i	$0.583153\pi$
$158$	0.773087	−	4.38439i	0.0615035	−	0.348804i
$159$	4.44433	+	9.06512i	0.352458	+	0.718911i
$160$	−1.23202	+	1.03379i	−0.0973997	+	0.0817280i
$161$	5.06809			0.399421
$162$	7.32420	+	5.23031i	0.575443	+	0.410932i
$163$	−15.1851			−1.18939			−0.594695	−	0.803951i	$-0.702727\pi$
$163$	−15.1851			−1.18939			−0.594695	+	0.803951i	$0.702727\pi$
$164$	2.71635	−	2.27929i	0.212111	−	0.177982i
$165$	−3.05293	−	6.22707i	−0.237670	−	0.484777i
$166$	0.936461	−	5.31093i	0.0726835	−	0.412208i
$167$	−10.2325	+	3.72431i	−0.791811	+	0.288196i	−0.706089	−	0.708123i	$-0.749542\pi$
$167$	−10.2325	+	3.72431i	−0.791811	+	0.288196i	−0.0857224	+	0.996319i	$0.527320\pi$
$168$	−1.58375	−	0.701250i	−0.122189	−	0.0541026i
$169$	−1.66893	−	9.46500i	−0.128380	−	0.728077i
$170$	2.70785	+	4.69014i	0.207683	+	0.359717i
$171$	−4.48557	−	0.611701i	−0.343020	−	0.0467779i
$172$	−2.90039	+	5.02362i	−0.221152	+	0.383047i
$173$	−21.2112	−	7.72026i	−1.61266	−	0.586961i	−0.630697	−	0.776029i	$-0.717231\pi$
$173$	−21.2112	−	7.72026i	−1.61266	−	0.586961i	−0.981964	+	0.189068i	$0.939453\pi$
$174$	−13.3083	+	3.84559i	−1.00890	+	0.291533i
$175$	1.84878	+	1.55131i	0.139755	+	0.117268i
$176$	1.90716	+	1.60030i	0.143758	+	0.120627i
$177$	−3.60029	−	3.46255i	−0.270614	−	0.260261i
$178$	10.4075	+	3.78803i	0.780078	+	0.283925i
$179$	7.41065	−	12.8356i	0.553898	−	0.959379i	−0.444090	−	0.895982i	$-0.646473\pi$
$179$	7.41065	−	12.8356i	0.553898	−	0.959379i	0.997988	−	0.0633974i	$-0.0201936\pi$
$180$	−4.26933	−	2.24769i	−0.318217	−	0.167533i
$181$	8.55254	+	14.8134i	0.635706	+	1.10107i	0.986365	+	0.164571i	$0.0526241\pi$
$181$	8.55254	+	14.8134i	0.635706	+	1.10107i	−0.350660	+	0.936503i	$0.614043\pi$
$182$	0.319672	+	1.81295i	0.0236957	+	0.134385i
$183$	−20.6001	+	15.0313i	−1.52280	+	1.11115i
$184$	−4.76244	+	1.73339i	−0.351092	+	0.127787i
$185$	0.909468	−	5.15785i	0.0668654	−	0.379213i
$186$	0.166386	−	0.247769i	0.0122000	−	0.0181673i
$187$	6.42213	−	5.38880i	0.469632	−	0.394068i
$188$	−3.97760			−0.290096
$189$	0.149470	−	5.19400i	0.0108723	−	0.377808i
$190$	2.42695			0.176069
$191$	4.00143	−	3.35760i	0.289533	−	0.242947i	−0.486439	−	0.873715i	$-0.661704\pi$
$191$	4.00143	−	3.35760i	0.289533	−	0.242947i	0.775972	+	0.630768i	$0.217260\pi$
$192$	1.72808	+	0.117287i	0.124713	+	0.00846445i
$193$	−3.09719	+	17.5650i	−0.222941	+	1.26436i	0.643643	+	0.765326i	$0.277422\pi$
$193$	−3.09719	+	17.5650i	−0.222941	+	1.26436i	−0.866583	+	0.499032i	$0.833689\pi$
$194$	−4.39293	+	1.59890i	−0.315394	+	0.114794i
$195$	0.546468	+	5.09893i	0.0391334	+	0.365142i
$196$	0.173648	+	0.984808i	0.0124034	+	0.0703434i
$197$	−3.83234	−	6.63781i	−0.273043	−	0.472924i	0.696596	−	0.717463i	$-0.254697\pi$
$197$	−3.83234	−	6.63781i	−0.273043	−	0.472924i	−0.969640	+	0.244539i	$0.921363\pi$
$198$	−2.27893	+	7.11270i	−0.161956	+	0.505478i
$199$	−12.3176	+	21.3347i	−0.873172	+	1.51238i	−0.0144747	+	0.999895i	$0.504608\pi$
$199$	−12.3176	+	21.3347i	−0.873172	+	1.51238i	−0.858697	+	0.512483i	$0.828726\pi$
$200$	−2.26787	−	0.825436i	−0.160362	−	0.0583671i
$201$	−1.34074	+	5.42466i	−0.0945684	+	0.382626i
$202$	5.91255	+	4.96122i	0.416006	+	0.349070i
$203$	6.12677	+	5.14097i	0.430015	+	0.360825i
$204$	1.39942	−	5.66209i	0.0979790	−	0.396425i
$205$	−5.35896	−	1.95050i	−0.374286	−	0.136229i
$206$	−3.18269	+	5.51258i	−0.221748	+	0.384079i
$207$	−10.2198	−	11.2572i	−0.710324	−	0.782433i
$208$	−0.920460	−	1.59428i	−0.0638224	−	0.110544i
$209$	−0.652381	−	3.69983i	−0.0451261	−	0.255923i
$210$	0.296845	+	2.76977i	0.0204842	+	0.191133i
$211$	13.6212	−	4.95773i	0.937725	−	0.341304i	0.172458	−	0.985017i	$-0.444829\pi$
$211$	13.6212	−	4.95773i	0.937725	−	0.341304i	0.765267	+	0.643713i	$0.222607\pi$
$212$	−1.01218	+	5.74035i	−0.0695167	+	0.394249i
$213$	−3.45810	−	0.234706i	−0.236945	−	0.0160818i
$214$	−15.0076	+	12.5929i	−1.02590	+	0.860832i
$215$	9.32931			0.636254
$216$	1.63600	+	4.93189i	0.111316	+	0.335572i
$217$	−0.172311			−0.0116973
$218$	5.91448	−	4.96284i	0.400579	−	0.336126i
$219$	13.9067	−	20.7088i	0.939727	−	1.39937i
$220$	0.695292	−	3.94320i	0.0468766	−	0.265850i
$221$	−5.82522	+	2.12021i	−0.391846	+	0.142620i
$222$	−4.55643	+	3.32471i	−0.305808	+	0.223140i
$223$	2.57166	+	14.5846i	0.172211	+	0.976658i	0.941314	+	0.337532i	$0.109592\pi$
$223$	2.57166	+	14.5846i	0.172211	+	0.976658i	−0.769103	+	0.639125i	$0.779297\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−0.282283	−	7.23473i	−0.0188189	−	0.482316i
$226$	5.31028	−	9.19767i	0.353234	−	0.611820i
$227$	15.3577	+	5.58975i	1.01933	+	0.371005i	0.797008	−	0.603969i	$-0.206415\pi$
$227$	15.3577	+	5.58975i	1.01933	+	0.371005i	0.222319	+	0.974974i	$0.428637\pi$
$228$	−1.88386	−	1.81179i	−0.124762	−	0.119989i
$229$	17.2037	+	14.4356i	1.13685	+	0.953933i	0.999331	−	0.0365652i	$-0.0116417\pi$
$229$	17.2037	+	14.4356i	1.13685	+	0.953933i	0.137522	+	0.990499i	$0.456086\pi$
$230$	6.24398	+	5.23932i	0.411716	+	0.345471i
$231$	4.14267	−	1.19707i	0.272568	−	0.0787613i
$232$	−7.51559	−	2.73545i	−0.493423	−	0.179591i
$233$	11.4950	−	19.9099i	0.753063	−	1.30434i	−0.193268	−	0.981146i	$-0.561909\pi$
$233$	11.4950	−	19.9099i	0.753063	−	1.30434i	0.946331	−	0.323198i	$-0.104758\pi$
$234$	3.38232	−	4.36587i	0.221109	−	0.285406i
$235$	3.19856	+	5.54007i	0.208651	+	0.361394i
$236$	−0.500791	−	2.84013i	−0.0325987	−	0.184877i
$237$	7.05088	+	3.12199i	0.458004	+	0.202795i
$238$	−3.16430	+	1.15171i	−0.205111	+	0.0746542i
$239$	1.11911	−	6.34676i	0.0723889	−	0.410538i	−0.926983	−	0.375103i	$-0.877607\pi$
$239$	1.11911	−	6.34676i	0.0723889	−	0.410538i	0.999372	−	0.0354348i	$-0.0112816\pi$
$240$	−1.22626	−	2.50121i	−0.0791548	−	0.161452i
$241$	−1.02174	+	0.857344i	−0.0658162	+	0.0552264i	−0.675102	−	0.737724i	$-0.735901\pi$
$241$	−1.02174	+	0.857344i	−0.0658162	+	0.0552264i	0.609286	+	0.792950i	$0.291456\pi$
$242$	4.80178			0.308670
$243$	−11.8383	+	10.1417i	−0.759430	+	0.650589i
$244$	−14.7230			−0.942545
$245$	1.23202	−	1.03379i	0.0787108	−	0.0660462i
$246$	2.70365	+	5.51465i	0.172379	+	0.351601i
$247$	−0.482395	+	2.73580i	−0.0306940	+	0.174074i
$248$	0.161920	−	0.0589339i	0.0102819	−	0.00374231i
$249$	8.54092	+	3.78175i	0.541259	+	0.239658i
$250$	2.07039	+	11.7418i	0.130943	+	0.742614i
$251$	−7.27870	−	12.6071i	−0.459427	−	0.795751i	0.539504	−	0.841983i	$-0.318612\pi$
$251$	−7.27870	−	12.6071i	−0.459427	−	0.795751i	−0.998931	+	0.0462321i	$0.985279\pi$
$252$	1.83730	−	2.37157i	0.115739	−	0.149395i
$253$	6.30881	−	10.9272i	0.396632	−	0.686986i
$254$	−19.1505	−	6.97020i	−1.20161	−	0.437349i
$255$	−9.01159	+	2.60399i	−0.564328	+	0.163068i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	11.8719	+	9.96173i	0.740551	+	0.621396i	0.932986	−	0.359914i	$-0.117194\pi$
$257$	11.8719	+	9.96173i	0.740551	+	0.621396i	−0.192435	+	0.981310i	$0.561638\pi$
$258$	−7.24164	−	6.96460i	−0.450845	−	0.433597i
$259$	3.06013	+	1.11380i	0.190147	+	0.0692079i
$260$	−1.48036	+	2.56407i	−0.0918083	+	0.159017i
$261$	−0.935473	−	23.9755i	−0.0579043	−	1.48405i
$262$	7.02160	+	12.1618i	0.433796	+	0.751357i
$263$	2.12085	+	12.0279i	0.130777	+	0.741674i	0.977708	+	0.209971i	$0.0673368\pi$
$263$	2.12085	+	12.0279i	0.130777	+	0.741674i	−0.846931	+	0.531704i	$0.821552\pi$
$264$	−3.48341	+	2.54175i	−0.214389	+	0.156434i
$265$	8.80920	−	3.20629i	0.541145	−	0.196961i
$266$	−0.262040	+	1.48610i	−0.0160667	+	0.0911188i
$267$	−10.6946	+	15.9256i	−0.654499	+	0.974629i
$268$	−2.47139	+	2.07374i	−0.150964	+	0.126674i
$269$	−12.7339			−0.776399			−0.388200	−	0.921575i	$-0.626903\pi$
$269$	−12.7339			−0.776399			−0.388200	+	0.921575i	$0.626903\pi$
$270$	5.55364	−	6.24459i	0.337984	−	0.380034i
$271$	−5.74985			−0.349278			−0.174639	−	0.984633i	$-0.555876\pi$
$271$	−5.74985			−0.349278			−0.174639	+	0.984633i	$0.555876\pi$
$272$	2.57956	−	2.16451i	0.156409	−	0.131242i
$273$	−3.18125	−	0.215916i	−0.192538	−	0.0130678i
$274$	3.53562	−	20.0515i	0.213595	−	1.21136i
$275$	5.64613	−	2.05502i	0.340475	−	0.123923i
$276$	−0.935427	−	8.72820i	−0.0563061	−	0.525376i
$277$	2.59066	+	14.6923i	0.155658	+	0.882778i	0.958182	+	0.286159i	$0.0923785\pi$
$277$	2.59066	+	14.6923i	0.155658	+	0.882778i	−0.802525	+	0.596619i	$0.796510\pi$
$278$	−3.80763	−	6.59501i	−0.228367	−	0.395543i
$279$	0.347465	+	0.382738i	0.0208022	+	0.0229139i
$280$	−0.804144	+	1.39282i	−0.0480568	+	0.0832368i
$281$	22.2060	+	8.08232i	1.32470	+	0.482151i	0.904961	−	0.425495i	$-0.139900\pi$
$281$	22.2060	+	8.08232i	1.32470	+	0.482151i	0.419738	+	0.907645i	$0.362122\pi$
$282$	1.65302	−	6.68815i	0.0984358	−	0.398274i
$283$	−10.6611	−	8.94576i	−0.633739	−	0.531770i	0.268349	−	0.963322i	$-0.413522\pi$
$283$	−10.6611	−	8.94576i	−0.633739	−	0.531770i	−0.902088	+	0.431551i	$0.857966\pi$
$284$	−1.53295	−	1.28630i	−0.0909640	−	0.0763278i
$285$	−1.00860	+	4.08081i	−0.0597441	+	0.241726i
$286$	4.30680	+	1.56755i	0.254666	+	0.0926909i
$287$	1.77297	−	3.07087i	0.104655	−	0.181268i
$288$	−0.915370	+	2.85694i	−0.0539387	+	0.168347i
$289$	2.83040	+	4.90239i	0.166494	+	0.288376i
$290$	2.23363	+	12.6675i	0.131163	+	0.743864i
$291$	−0.862849	−	8.05099i	−0.0505811	−	0.471958i
$292$	13.5334	−	4.92576i	0.791983	−	0.288258i
$293$	−3.84408	+	21.8009i	−0.224574	+	1.27362i	0.638925	+	0.769269i	$0.279380\pi$
$293$	−3.84408	+	21.8009i	−0.224574	+	1.27362i	−0.863498	+	0.504352i	$0.831732\pi$
$294$	−1.72808	−	0.117287i	−0.100783	−	0.00684031i
$295$	−3.55307	+	2.98138i	−0.206868	+	0.173583i
$296$	−3.25652			−0.189281
$297$	−11.0126	−	6.78782i	−0.639016	−	0.393869i
$298$	−9.02837			−0.523000
$299$	−7.14715	+	5.99717i	−0.413330	+	0.346825i
$300$	2.33042	−	3.47028i	0.134547	−	0.200357i
$301$	−1.00729	+	5.71265i	−0.0580595	+	0.329272i
$302$	17.2987	−	6.29622i	0.995429	−	0.362307i
$303$	−10.7992	+	7.87990i	−0.620399	+	0.452688i
$304$	−0.262040	−	1.48610i	−0.0150290	−	0.0852338i
$305$	11.8394	+	20.5065i	0.677923	+	1.17420i
$306$	8.93897	+	4.70612i	0.511007	+	0.269031i
$307$	8.71894	−	15.1016i	0.497616	−	0.861897i	−0.502380	−	0.864647i	$-0.667542\pi$
$307$	8.71894	−	15.1016i	0.497616	−	0.861897i	0.999996	+	0.00275037i	$0.000875471\pi$
$308$	2.33948	+	0.851501i	0.133304	+	0.0485188i
$309$	−7.94648	−	7.64247i	−0.452060	−	0.434765i
$310$	−0.212291	−	0.178133i	−0.0120573	−	0.0101173i
$311$	7.19780	+	6.03967i	0.408150	+	0.342479i	0.823634	−	0.567122i	$-0.191943\pi$
$311$	7.19780	+	6.03967i	0.408150	+	0.342479i	−0.415484	+	0.909601i	$0.636388\pi$
$312$	3.06324	−	0.885157i	0.173422	−	0.0501121i
$313$	32.0035	+	11.6483i	1.80895	+	0.658403i	0.997232	+	0.0743484i	$0.0236877\pi$
$313$	32.0035	+	11.6483i	1.80895	+	0.658403i	0.811714	+	0.584054i	$0.198535\pi$
$314$	7.18109	−	12.4380i	0.405252	−	0.701918i
$315$	−4.78061	−	0.651937i	−0.269357	−	0.0367325i
$316$	2.22602	+	3.85557i	0.125223	+	0.216893i
$317$	−0.0957832	−	0.543214i	−0.00537972	−	0.0305099i	0.982000	−	0.188882i	$-0.0604865\pi$
$317$	−0.0957832	−	0.543214i	−0.00537972	−	0.0305099i	−0.987379	+	0.158372i	$0.949375\pi$
$318$	−9.23150	−	4.08752i	−0.517677	−	0.229217i
$319$	18.7110	−	6.81025i	1.04761	−	0.381301i
$320$	0.279276	−	1.58385i	0.0156120	−	0.0885401i
$321$	−14.9375	−	30.4680i	−0.833729	−	1.70056i
$322$	−3.88238	+	3.25770i	−0.216356	+	0.181545i
$323$	−5.08146			−0.282740
$324$	−8.97264	+	0.701253i	−0.498480	+	0.0389585i
$325$	−4.44290			−0.246448
$326$	11.6325	−	9.76080i	0.644263	−	0.540601i
$327$	5.88684	+	12.0074i	0.325543	+	0.664010i
$328$	−0.615746	+	3.49207i	−0.0339989	+	0.192817i
$329$	−3.73772	+	1.36042i	−0.206067	+	0.0750023i
$330$	6.34136	+	2.80783i	0.349080	+	0.154566i
$331$	−2.03287	−	11.5290i	−0.111737	−	0.633690i	−0.988314	−	0.152430i	$-0.951290\pi$
$331$	−2.03287	−	11.5290i	−0.111737	−	0.633690i	0.876578	−	0.481261i	$-0.159821\pi$
$332$	2.69643	+	4.67036i	0.147986	+	0.256319i
$333$	−3.69677	−	9.04313i	−0.202582	−	0.495560i
$334$	5.44458	−	9.43028i	0.297914	−	0.516002i
$335$	4.87570	+	1.77461i	0.266388	+	0.0969572i
$336$	1.66397	−	0.480823i	0.0907772	−	0.0262310i
$337$	2.57157	+	2.15780i	0.140082	+	0.117543i	0.710136	−	0.704064i	$-0.248633\pi$
$337$	2.57157	+	2.15780i	0.140082	+	0.117543i	−0.570054	+	0.821607i	$0.693078\pi$
$338$	7.36246	+	6.17784i	0.400465	+	0.336030i
$339$	13.2586	+	12.7514i	0.720109	+	0.692560i
$340$	−5.08910	−	1.85228i	−0.275995	−	0.100454i
$341$	−0.214495	+	0.371516i	−0.0116156	+	0.0201187i
$342$	3.82934	−	2.41468i	0.207067	−	0.130571i
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$	−1.00729	−	5.71265i	−0.0543096	−	0.308005i
$345$	−11.4046	+	8.32160i	−0.614001	+	0.448020i
$346$	21.2112	−	7.72026i	1.14032	−	0.415044i
$347$	4.36056	−	24.7300i	0.234087	−	1.32757i	−0.610441	−	0.792062i	$-0.709008\pi$
$347$	4.36056	−	24.7300i	0.234087	−	1.32757i	0.844528	−	0.535512i	$-0.179881\pi$
$348$	7.72289	−	11.5003i	0.413990	−	0.616482i
$349$	10.9493	−	9.18759i	0.586105	−	0.491800i	−0.300841	−	0.953674i	$-0.597267\pi$
$349$	10.9493	−	9.18759i	0.586105	−	0.491800i	0.886946	+	0.461874i	$0.152823\pi$
$350$	−2.41341			−0.129002
$351$	5.93538	+	7.50159i	0.316807	+	0.400405i
$352$	−2.48962			−0.132697
$353$	12.8138	−	10.7521i	0.682010	−	0.572274i	−0.234583	−	0.972096i	$-0.575372\pi$
$353$	12.8138	−	10.7521i	0.682010	−	0.572274i	0.916593	+	0.399822i	$0.130928\pi$
$354$	4.98367	+	0.338248i	0.264879	+	0.0179777i
$355$	−0.558867	+	3.16949i	−0.0296616	+	0.168219i
$356$	−10.4075	+	3.78803i	−0.551598	+	0.200765i
$357$	−0.621523	−	5.79925i	−0.0328945	−	0.306929i
$358$	2.57369	+	14.5961i	0.136024	+	0.771429i
$359$	−0.375708	−	0.650746i	−0.0198291	−	0.0343450i	0.855941	−	0.517074i	$-0.172979\pi$
$359$	−0.375708	−	0.650746i	−0.0198291	−	0.0343450i	−0.875770	+	0.482729i	$0.839646\pi$
$360$	4.71528	−	1.02245i	0.248517	−	0.0538876i
$361$	8.36142	−	14.4824i	0.440075	−	0.762232i
$362$	−16.0735	−	5.85028i	−0.844806	−	0.307484i
$363$	−1.99553	+	8.07397i	−0.104738	+	0.423774i
$364$	−1.41023	−	1.18332i	−0.0739160	−	0.0620229i
$365$	−17.7435	−	14.8886i	−0.928737	−	0.779303i
$366$	6.11863	−	24.7561i	0.319826	−	1.29402i
$367$	−14.0331	−	5.10763i	−0.732521	−	0.266616i	−0.0512896	−	0.998684i	$-0.516333\pi$
$367$	−14.0331	−	5.10763i	−0.732521	−	0.266616i	−0.681232	+	0.732068i	$0.738555\pi$
$368$	2.53404	−	4.38909i	0.132096	−	0.228797i
$369$	−10.3962	+	2.25428i	−0.541206	+	0.117353i
$370$	2.61871	+	4.53574i	0.136140	+	0.235802i
$371$	1.01218	+	5.74035i	0.0525497	+	0.298024i
$372$	0.0318039	+	0.296752i	0.00164895	+	0.0153859i
$373$	−2.49201	+	0.907016i	−0.129031	+	0.0469635i	−0.405729	−	0.913994i	$-0.632982\pi$
$373$	−2.49201	+	0.907016i	−0.129031	+	0.0469635i	0.276698	+	0.960957i	$0.410760\pi$
$374$	−1.45578	+	8.25613i	−0.0752765	+	0.426914i
$375$	−20.6037	−	1.39840i	−1.06397	−	0.0722130i
$376$	3.04702	−	2.55675i	0.157138	−	0.131854i
$377$	−14.7235			−0.758301
$378$	3.22414	+	4.07491i	0.165832	+	0.209591i
$379$	−0.380171			−0.0195281			−0.00976403	−	0.999952i	$-0.503108\pi$
$379$	−0.380171			−0.0195281			−0.00976403	+	0.999952i	$0.503108\pi$
$380$	−1.85915	+	1.56001i	−0.0953724	+	0.0800270i
$381$	19.6787	−	29.3040i	1.00817	−	1.50129i
$382$	−0.907050	+	5.14413i	−0.0464087	+	0.263197i
$383$	−19.4340	+	7.07341i	−0.993033	+	0.361434i	−0.786894	−	0.617089i	$-0.788312\pi$
$383$	−19.4340	+	7.07341i	−0.993033	+	0.361434i	−0.206139	+	0.978523i	$0.566090\pi$
$384$	−1.39917	+	1.02094i	−0.0714012	+	0.0520995i
$385$	−0.695292	−	3.94320i	−0.0354354	−	0.200964i
$386$	−8.91800	−	15.4464i	−0.453914	−	0.786202i
$387$	14.7202	−	9.28213i	0.748267	−	0.471837i
$388$	2.33743	−	4.04855i	0.118665	−	0.205534i
$389$	27.6850	+	10.0765i	1.40368	+	0.510899i	0.929269	−	0.369403i	$-0.120438\pi$
$389$	27.6850	+	10.0765i	1.40368	+	0.510899i	0.474414	+	0.880302i	$0.342660\pi$
$390$	−3.69615	−	3.55475i	−0.187162	−	0.180002i
$391$	−13.0734	−	10.9699i	−0.661151	−	0.554772i
$392$	−0.766044	−	0.642788i	−0.0386911	−	0.0324657i
$393$	−23.3675	+	6.75229i	−1.17874	+	0.340608i
$394$	7.20245	+	2.62148i	0.362854	+	0.132068i
$395$	3.58007	−	6.20086i	0.180133	−	0.311999i
$396$	−2.82620	−	6.91351i	−0.142022	−	0.347417i
$397$	−1.94160	−	3.36294i	−0.0974459	−	0.168781i	0.813181	−	0.582011i	$-0.197734\pi$
$397$	−1.94160	−	3.36294i	−0.0974459	−	0.168781i	−0.910627	+	0.413230i	$0.864401\pi$
$398$	−4.27786	−	24.2609i	−0.214430	−	1.21609i
$399$	−2.38991	−	1.05821i	−0.119645	−	0.0529766i
$400$	2.26787	−	0.825436i	0.113393	−	0.0412718i
$401$	−4.87513	+	27.6482i	−0.243452	+	1.38069i	0.580607	+	0.814184i	$0.302815\pi$
$401$	−4.87513	+	27.6482i	−0.243452	+	1.38069i	−0.824060	+	0.566503i	$0.808296\pi$
$402$	−2.45984	−	5.01734i	−0.122686	−	0.250242i
$403$	0.242998	−	0.203899i	0.0121046	−	0.0101570i
$404$	−7.71829			−0.383999
$405$	8.19201	+	11.9333i	0.407064	+	0.592972i
$406$	−7.99793			−0.396931
$407$	6.21071	−	5.21140i	0.307853	−	0.258320i
$408$	2.56750	+	5.23694i	0.127110	+	0.259267i
$409$	0.274351	−	1.55592i	0.0135658	−	0.0769354i	−0.977273	−	0.211983i	$-0.932008\pi$
$409$	0.274351	−	1.55592i	0.0135658	−	0.0769354i	0.990839	+	0.135048i	$0.0431189\pi$
$410$	5.35896	−	1.95050i	0.264660	−	0.0963285i
$411$	32.2464	+	14.2780i	1.59060	+	0.704283i
$412$	−1.10534	−	6.26867i	−0.0544560	−	0.308835i
$413$	−1.44197	−	2.49757i	−0.0709548	−	0.122897i
$414$	15.0648	+	2.05440i	0.740396	+	0.100968i
$415$	4.33664	−	7.51127i	0.212877	−	0.368714i
$416$	1.72990	+	0.629632i	0.0848153	+	0.0308702i
$417$	12.6716	−	3.66159i	0.620531	−	0.179309i
$418$	2.87796	+	2.41490i	0.140766	+	0.118116i
$419$	−14.7393	−	12.3678i	−0.720063	−	0.604205i	0.207340	−	0.978269i	$-0.433519\pi$
$419$	−14.7393	−	12.3678i	−0.720063	−	0.604205i	−0.927403	+	0.374064i	$0.877964\pi$
$420$	−2.00777	−	1.93096i	−0.0979693	−	0.0942213i
$421$	−31.1074	−	11.3222i	−1.51608	−	0.551809i	−0.555917	−	0.831238i	$-0.687633\pi$
$421$	−31.1074	−	11.3222i	−1.51608	−	0.551809i	−0.960166	+	0.279429i	$0.909855\pi$
$422$	−7.24771	+	12.5534i	−0.352813	+	0.611090i
$423$	10.5589	+	5.55895i	0.513389	+	0.270286i
$424$	−2.91445	−	5.04798i	−0.141538	−	0.245152i
$425$	−1.41121	−	8.00340i	−0.0684540	−	0.388222i
$426$	2.79992	−	2.04303i	0.135657	−	0.0989850i
$427$	−13.8351	+	5.03557i	−0.669528	+	0.243688i
$428$	3.40195	−	19.2934i	0.164440	−	0.932583i
$429$	−4.42559	+	6.59024i	−0.213669	+	0.318180i
$430$	−7.14667	+	5.99677i	−0.344643	+	0.289190i
$431$	20.6717			0.995723			0.497861	−	0.867257i	$-0.334119\pi$
$431$	20.6717			0.995723			0.497861	+	0.867257i	$0.334119\pi$
$432$	−4.42340	−	2.72645i	−0.212821	−	0.131176i
$433$	15.7189			0.755402			0.377701	−	0.925928i	$-0.376715\pi$
$433$	15.7189			0.755402			0.377701	+	0.925928i	$0.376715\pi$
$434$	0.131998	−	0.110760i	0.00633611	−	0.00531663i
$435$	−22.2282	−	1.50866i	−1.06576	−	0.0723345i
$436$	−1.34070	+	7.60351i	−0.0642080	+	0.364142i
$437$	−7.18666	+	2.61573i	−0.343784	+	0.125127i
$438$	2.65820	+	24.8029i	0.127014	+	1.18513i
$439$	−0.200767	−	1.13861i	−0.00958209	−	0.0543427i	0.979642	−	0.200753i	$-0.0643390\pi$
$439$	−0.200767	−	1.13861i	−0.00958209	−	0.0543427i	−0.989224	+	0.146411i	$0.953228\pi$
$440$	2.00201	+	3.46759i	0.0954423	+	0.165311i
$441$	0.915370	−	2.85694i	0.0435890	−	0.136045i
$442$	3.09953	−	5.36855i	0.147430	−	0.255356i
$443$	19.6044	+	7.13540i	0.931431	+	0.339013i	0.762777	−	0.646662i	$-0.223836\pi$
$443$	19.6044	+	7.13540i	0.931431	+	0.339013i	0.168655	+	0.985675i	$0.446058\pi$
$444$	1.35335	−	5.47569i	0.0642272	−	0.259865i
$445$	13.6452	+	11.4497i	0.646844	+	0.542767i
$446$	−11.3448	−	9.51943i	−0.537192	−	0.450758i
$447$	3.75203	−	15.1808i	0.177465	−	0.718027i
$448$	0.939693	+	0.342020i	0.0443963	+	0.0161589i
$449$	−16.5903	+	28.7352i	−0.782944	+	1.35610i	0.147276	+	0.989095i	$0.452950\pi$
$449$	−16.5903	+	28.7352i	−0.782944	+	1.35610i	−0.930220	+	0.367003i	$0.880384\pi$
$450$	4.86664	+	5.36068i	0.229416	+	0.252705i
$451$	−4.41403	−	7.64532i	−0.207848	−	0.360004i
$452$	1.84424	+	10.4592i	0.0867458	+	0.491960i
$453$	3.39777	+	31.7036i	0.159641	+	1.48957i
$454$	−15.3577	+	5.58975i	−0.720773	+	0.262340i
$455$	−0.514125	+	2.91575i	−0.0241026	+	0.136692i
$456$	2.60771	+	0.176989i	0.122117	+	0.00828827i
$457$	−18.8178	+	15.7900i	−0.880259	+	0.738625i	−0.966232	−	0.257672i	$-0.917045\pi$
$457$	−18.8178	+	15.7900i	−0.880259	+	0.738625i	0.0859729	+	0.996297i	$0.472600\pi$
$458$	−22.4579			−1.04939
$459$	−11.6280	+	13.0747i	−0.542749	+	0.610275i
$460$	−8.15094			−0.380039
$461$	5.27363	−	4.42510i	0.245617	−	0.206097i	−0.511665	−	0.859185i	$-0.670971\pi$
$461$	5.27363	−	4.42510i	0.245617	−	0.206097i	0.757282	+	0.653088i	$0.226527\pi$
$462$	−2.40401	+	3.57986i	−0.111845	+	0.166550i
$463$	4.03029	−	22.8569i	0.187303	−	1.06225i	−0.735657	−	0.677354i	$-0.763126\pi$
$463$	4.03029	−	22.8569i	0.187303	−	1.06225i	0.922960	−	0.384895i	$-0.125762\pi$
$464$	7.51559	−	2.73545i	0.348903	−	0.126990i
$465$	0.387747	−	0.282929i	0.0179813	−	0.0131205i
$466$	3.99217	+	22.6407i	0.184934	+	1.04881i
$467$	−8.35450	−	14.4704i	−0.386600	−	0.669611i	0.605389	−	0.795929i	$-0.293017\pi$
$467$	−8.35450	−	14.4704i	−0.386600	−	0.669611i	−0.991990	+	0.126318i	$0.959684\pi$
$468$	0.215322	+	5.51856i	0.00995327	+	0.255096i
$469$	−1.61309	+	2.79395i	−0.0744854	+	0.129012i
$470$	−6.01133	−	2.18794i	−0.277282	−	0.100922i
$471$	17.9296	+	17.2437i	0.826154	+	0.794547i
$472$	2.20923	+	1.85376i	0.101688	+	0.0853263i
$473$	11.0630	+	9.28297i	0.508678	+	0.426832i
$474$	−7.40806	+	2.14064i	−0.340264	+	0.0983228i
$475$	−3.42227	−	1.24561i	−0.157025	−	0.0571523i
$476$	1.68369	−	2.91623i	0.0771717	−	0.133665i
$477$	10.7094	−	13.8237i	0.490351	−	0.632942i
$478$	3.22234	+	5.58125i	0.147386	+	0.255280i
$479$	3.76307	+	21.3414i	0.171939	+	0.975115i	0.941618	+	0.336684i	$0.109305\pi$
$479$	3.76307	+	21.3414i	0.171939	+	0.975115i	−0.769679	+	0.638431i	$0.779584\pi$
$480$	2.54712	+	1.12781i	0.116259	+	0.0514773i
$481$	−5.63345	+	2.05041i	−0.256863	+	0.0934906i
$482$	0.231610	−	1.31353i	0.0105496	−	0.0598295i
$483$	−3.86423	−	7.88189i	−0.175829	−	0.358638i
$484$	−3.67837	+	3.08652i	−0.167199	+	0.140296i
$485$	−7.51852			−0.341398
$486$	2.54974	−	15.3785i	0.115659	−	0.697584i
$487$	−30.5474			−1.38423			−0.692116	−	0.721786i	$-0.743321\pi$
$487$	−30.5474			−1.38423			−0.692116	+	0.721786i	$0.743321\pi$
$488$	11.2785	−	9.46378i	0.510553	−	0.428405i
$489$	11.5781	+	23.6159i	0.523580	+	1.06795i
$490$	−0.279276	+	1.58385i	−0.0126164	+	0.0715512i
$491$	−19.1950	+	6.98642i	−0.866259	+	0.315293i	−0.736651	−	0.676273i	$-0.763594\pi$
$491$	−19.1950	+	6.98642i	−0.866259	+	0.315293i	−0.129608	+	0.991565i	$0.541372\pi$
$492$	−5.61587	−	2.48659i	−0.253183	−	0.112104i
$493$	−4.67669	−	26.5229i	−0.210628	−	1.19453i
$494$	−1.38900	−	2.40582i	−0.0624940	−	0.108243i
$495$	−7.35659	+	9.49583i	−0.330654	+	0.426806i
$496$	−0.0861556	+	0.149226i	−0.00386850	+	0.00670044i
$497$	−1.88044	−	0.684426i	−0.0843494	−	0.0307007i
$498$	−8.97358	+	2.59301i	−0.402116	+	0.116196i
$499$	−0.676249	−	0.567441i	−0.0302731	−	0.0254021i	0.627526	−	0.778596i	$-0.284068\pi$
$499$	−0.676249	−	0.567441i	−0.0302731	−	0.0254021i	−0.657799	+	0.753194i	$0.728512\pi$
$500$	−9.13347	−	7.66389i	−0.408461	−	0.342740i
$501$	13.5939	+	13.0739i	0.607332	+	0.584097i
$502$	13.6795	+	4.97892i	0.610545	+	0.222220i
$503$	3.40900	−	5.90457i	0.152000	−	0.263272i	−0.779963	−	0.625826i	$-0.784762\pi$
$503$	3.40900	−	5.90457i	0.152000	−	0.263272i	0.931963	+	0.362554i	$0.118095\pi$
$504$	0.116964	+	2.99772i	0.00521001	+	0.133529i
$505$	6.20661	+	10.7502i	0.276191	+	0.478376i
$506$	2.19103	+	12.4259i	0.0974030	+	0.552400i
$507$	−13.4475	+	9.81225i	−0.597223	+	0.435777i
$508$	19.1505	−	6.97020i	0.849665	−	0.309253i
$509$	0.0561186	−	0.318265i	0.00248742	−	0.0141068i	−0.983539	−	0.180697i	$-0.942165\pi$
$509$	0.0561186	−	0.318265i	0.00248742	−	0.0141068i	0.986026	+	0.166590i	$0.0532757\pi$
$510$	5.22946	−	7.78731i	0.231564	−	0.344828i
$511$	11.0325	−	9.25740i	0.488051	−	0.409523i
$512$	−1.00000			−0.0441942
$513$	2.46877	+	7.44235i	0.108999	+	0.328588i
$514$	−15.4977			−0.683575
$515$	−7.84226	+	6.58044i	−0.345571	+	0.289969i
$516$	10.0242	+	0.680355i	0.441290	+	0.0299509i
$517$	−1.71959	+	9.75227i	−0.0756274	+	0.428905i
$518$	−3.06013	+	1.11380i	−0.134454	+	0.0489374i
$519$	4.16626	+	38.8742i	0.182879	+	1.70639i
$520$	−0.514125	−	2.91575i	−0.0225459	−	0.127864i
$521$	11.3906	+	19.7291i	0.499031	+	0.864346i	0.999999	−	0.00111901i	$-0.000356192\pi$
$521$	11.3906	+	19.7291i	0.499031	+	0.864346i	−0.500969	+	0.865465i	$0.667023\pi$
$522$	16.1278	+	17.7650i	0.705894	+	0.777554i
$523$	15.4596	−	26.7768i	0.676000	−	1.17087i	−0.300176	−	0.953884i	$-0.597045\pi$
$523$	15.4596	−	26.7768i	0.676000	−	1.17087i	0.976176	−	0.216982i	$-0.0696213\pi$
$524$	−13.1963	−	4.80306i	−0.576483	−	0.209823i
$525$	1.00297	−	4.05805i	0.0437733	−	0.177108i
$526$	−9.35607	−	7.85068i	−0.407944	−	0.342306i
$527$	0.444487	+	0.372969i	0.0193622	+	0.0162468i
$528$	1.03464	−	4.18619i	0.0450271	−	0.182181i
$529$	−2.52353	−	0.918491i	−0.109719	−	0.0399344i
$530$	−4.68728	+	8.11860i	−0.203602	+	0.352650i
$531$	−2.63987	+	8.23924i	−0.114561	+	0.357553i
$532$	−0.754514	−	1.30686i	−0.0327123	−	0.0566594i
$533$	1.13354	+	6.42862i	0.0490990	+	0.278454i
$534$	−2.04422	−	19.0741i	−0.0884622	−	0.825415i
$535$	−29.6079	+	10.7764i	−1.28006	+	0.465904i
$536$	0.560219	−	3.17716i	0.0241978	−	0.137232i
$537$	−25.6123	−	1.73834i	−1.10525	−	0.0750151i
$538$	9.75473	−	8.18519i	0.420556	−	0.352889i
$539$	2.48962			0.107236
$540$	−0.240390	+	8.35345i	−0.0103448	+	0.359475i
$541$	−8.16919			−0.351221			−0.175611	−	0.984460i	$-0.556190\pi$
$541$	−8.16919			−0.351221			−0.175611	+	0.984460i	$0.556190\pi$
$542$	4.40464	−	3.69593i	0.189195	−	0.158754i
$543$	16.5169	−	24.5956i	0.708806	−	1.05550i
$544$	−0.584738	+	3.31622i	−0.0250704	+	0.142182i
$545$	11.6684	−	4.24696i	0.499820	−	0.181920i
$546$	2.57577	−	1.87947i	0.110233	−	0.0804337i
$547$	3.26261	+	18.5032i	0.139499	+	0.791138i	0.971621	+	0.236545i	$0.0760150\pi$
$547$	3.26261	+	18.5032i	0.139499	+	0.791138i	−0.832122	+	0.554593i	$0.812874\pi$
$548$	10.1804	+	17.6330i	0.434886	+	0.753244i
$549$	39.0835	+	20.5764i	1.66804	+	0.878179i
$550$	−3.00424	+	5.20350i	−0.128101	+	0.221878i
$551$	−11.3412	−	4.12787i	−0.483153	−	0.175853i
$552$	6.32696	+	6.08491i	0.269293	+	0.258991i
$553$	3.41045	+	2.86171i	0.145027	+	0.121692i
$554$	−11.4286	−	9.58975i	−0.485555	−	0.407429i
$555$	−8.71493	+	2.51827i	−0.369928	+	0.106895i
$556$	7.15601	+	2.60457i	0.303482	+	0.110459i
$557$	−19.0189	+	32.9417i	−0.805857	+	1.39579i	0.109854	+	0.993948i	$0.464962\pi$
$557$	−19.0189	+	32.9417i	−0.805857	+	1.39579i	−0.915711	+	0.401837i	$0.868372\pi$
$558$	−0.512193	−	0.0698483i	−0.0216829	−	0.00295691i
$559$	−5.33938	−	9.24808i	−0.225832	−	0.391152i
$560$	−0.279276	−	1.58385i	−0.0118016	−	0.0669300i
$561$	−13.2773	−	5.87892i	−0.560569	−	0.248208i
$562$	−22.2060	+	8.08232i	−0.936703	+	0.340932i
$563$	6.75273	−	38.2966i	0.284594	−	1.61401i	−0.422139	−	0.906531i	$-0.638721\pi$
$563$	6.75273	−	38.2966i	0.284594	−	1.61401i	0.706733	−	0.707480i	$-0.250168\pi$
$564$	3.03278	+	6.18596i	0.127703	+	0.260476i
$565$	13.0847	−	10.9794i	0.550479	−	0.461907i
$566$	13.9171			0.584981
$567$	−8.19168	+	3.72779i	−0.344018	+	0.156552i
$568$	2.00113			0.0839654
$569$	−5.85040	+	4.90907i	−0.245262	+	0.205799i	−0.757129	−	0.653266i	$-0.773398\pi$
$569$	−5.85040	+	4.90907i	−0.245262	+	0.205799i	0.511867	+	0.859065i	$0.328954\pi$
$570$	−1.85046	−	3.77439i	−0.0775073	−	0.158092i
$571$	5.36935	−	30.4511i	0.224700	−	1.27434i	−0.638557	−	0.769575i	$-0.720468\pi$
$571$	5.36935	−	30.4511i	0.224700	−	1.27434i	0.863257	−	0.504765i	$-0.168421\pi$
$572$	−4.30680	+	1.56755i	−0.180076	+	0.0655424i
$573$	−8.27268	−	3.66297i	−0.345596	−	0.153023i
$574$	0.615746	+	3.49207i	0.0257007	+	0.145756i
$575$	−6.11569	−	10.5927i	−0.255042	−	0.441746i
$576$	−1.13519	−	2.77693i	−0.0472996	−	0.115705i
$577$	9.02608	−	15.6336i	0.375761	−	0.650837i	−0.614680	−	0.788777i	$-0.710715\pi$
$577$	9.02608	−	15.6336i	0.375761	−	0.650837i	0.990441	+	0.137940i	$0.0440481\pi$
$578$	−5.31941	−	1.93611i	−0.221258	−	0.0805314i
$579$	29.6786	−	8.57596i	1.23340	−	0.356405i
$580$	−9.85360	−	8.26815i	−0.409149	−	0.343316i
$581$	4.13117	+	3.46647i	0.171390	+	0.143813i
$582$	5.83606	+	5.61279i	0.241912	+	0.232658i
$583$	13.6366	+	4.96332i	0.564771	+	0.205560i
$584$	−7.20098	+	12.4725i	−0.297979	+	0.516114i
$585$	7.51320	−	4.73762i	0.310633	−	0.195876i
$586$	−11.0686	−	19.1714i	−0.457239	−	0.791962i
$587$	1.46253	+	8.29445i	0.0603653	+	0.342348i	1.00000		0.000169268i	$5.38797e-5\pi$
$587$	1.46253	+	8.29445i	0.0603653	+	0.342348i	−0.939635	+	0.342179i	$0.888835\pi$
$588$	1.39917	−	1.02094i	0.0577009	−	0.0421028i
$589$	0.244341	−	0.0889329i	0.0100679	−	0.00366442i
$590$	0.805416	−	4.56774i	0.0331585	−	0.188051i
$591$	−7.40110	+	11.0212i	−0.304441	+	0.453350i
$592$	2.49464	−	2.09325i	0.102529	−	0.0860321i
$593$	37.7543			1.55038			0.775191	−	0.631727i	$-0.217654\pi$
$593$	37.7543			1.55038			0.775191	+	0.631727i	$0.217654\pi$
$594$	12.7993	−	1.87899i	0.525161	−	0.0770960i
$595$	−5.41570			−0.222022
$596$	6.91613	−	5.80333i	0.283296	−	0.237713i
$597$	42.5715	+	2.88939i	1.74234	+	0.118255i
$598$	1.62013	−	9.18820i	0.0662519	−	0.375733i
$599$	16.2902	−	5.92916i	0.665601	−	0.242259i	0.0129484	−	0.999916i	$-0.495878\pi$
$599$	16.2902	−	5.92916i	0.665601	−	0.242259i	0.652653	+	0.757657i	$0.273656\pi$
$600$	0.445449	+	4.15635i	0.0181854	+	0.169682i
$601$	−4.36483	−	24.7542i	−0.178045	−	1.00975i	−0.934570	−	0.355780i	$-0.884215\pi$
$601$	−4.36483	−	24.7542i	−0.178045	−	1.00975i	0.756524	−	0.653965i	$-0.226896\pi$
$602$	−2.90039	−	5.02362i	−0.118211	−	0.204747i
$603$	9.45870	−	2.05099i	0.385188	−	0.0835229i
$604$	−9.20445	+	15.9426i	−0.374524	+	0.648694i
$605$	7.25690	+	2.64130i	0.295035	+	0.107384i
$606$	3.20758	−	12.9780i	0.130299	−	0.527193i
$607$	−15.8312	−	13.2840i	−0.642569	−	0.539179i	0.262237	−	0.965003i	$-0.415540\pi$
$607$	−15.8312	−	13.2840i	−0.642569	−	0.539179i	−0.904806	+	0.425824i	$0.859984\pi$
$608$	1.15598	+	0.969984i	0.0468813	+	0.0393381i
$609$	3.32380	−	13.4482i	0.134687	−	0.544947i
$610$	−22.2508	−	8.09864i	−0.900910	−	0.327904i
$611$	3.66122	−	6.34142i	0.148117	−	0.256546i
$612$	−9.87269	+	2.14076i	−0.399080	+	0.0865351i
$613$	15.0995	+	26.1532i	0.609864	+	1.05632i	0.991262	+	0.131905i	$0.0421094\pi$
$613$	15.0995	+	26.1532i	0.609864	+	1.05632i	−0.381398	+	0.924411i	$0.624557\pi$
$614$	3.02806	+	17.1730i	0.122202	+	0.693044i
$615$	1.05259	+	9.82145i	0.0424447	+	0.396039i
$616$	−2.33948	+	0.851501i	−0.0942604	+	0.0343080i
$617$	−1.32472	+	7.51285i	−0.0533311	+	0.302456i	−0.999793	−	0.0203606i	$-0.993519\pi$
$617$	−1.32472	+	7.51285i	−0.0533311	+	0.302456i	0.946462	+	0.322817i	$0.104630\pi$
$618$	10.9998	+	0.746575i	0.442479	+	0.0300316i
$619$	−19.6118	+	16.4563i	−0.788265	+	0.661433i	−0.945315	−	0.326158i	$-0.894246\pi$
$619$	−19.6118	+	16.4563i	−0.788265	+	0.661433i	0.157051	+	0.987591i	$0.449801\pi$
$620$	0.277126			0.0111296
$621$	−9.71506	+	24.4770i	−0.389852	+	0.982230i
$622$	−9.39607			−0.376748
$623$	−8.48430	+	7.11918i	−0.339916	+	0.285224i
$624$	−1.77761	+	2.64708i	−0.0711615	+	0.105968i
$625$	−1.23436	+	7.00038i	−0.0493742	+	0.280015i
$626$	−32.0035	+	11.6483i	−1.27912	+	0.465561i
$627$	−5.25657	+	3.83557i	−0.209927	+	0.153178i
$628$	2.49397	+	14.1440i	0.0995201	+	0.564406i
$629$	−5.48296	−	9.49676i	−0.218620	−	0.378661i
$630$	4.08122	−	2.57351i	0.162600	−	0.102531i
$631$	−4.40210	+	7.62466i	−0.175245	+	0.303533i	−0.940246	−	0.340496i	$-0.889405\pi$
$631$	−4.40210	+	7.62466i	−0.175245	+	0.303533i	0.765001	+	0.644029i	$0.222738\pi$
$632$	−4.18354	−	1.52268i	−0.166412	−	0.0605691i
$633$	−18.0960	−	17.4037i	−0.719250	−	0.691734i
$634$	0.422545	+	0.354558i	0.0167814	+	0.0140813i
$635$	−25.1079	−	21.0681i	−0.996378	−	0.836061i
$636$	9.69915	−	2.80267i	0.384596	−	0.111133i
$637$	−1.72990	−	0.629632i	−0.0685411	−	0.0249469i
$638$	−9.95591	+	17.2441i	−0.394158	+	0.682702i
$639$	2.27166	+	5.55699i	0.0898655	+	0.219831i
$640$	0.804144	+	1.39282i	0.0317866	+	0.0550559i
$641$	1.99371	+	11.3069i	0.0787468	+	0.446595i	0.998532	+	0.0541722i	$0.0172520\pi$
$641$	1.99371	+	11.3069i	0.0787468	+	0.446595i	−0.919785	+	0.392423i	$0.871637\pi$
$642$	31.0272	+	13.7382i	1.22455	+	0.542205i
$643$	−17.4282	+	6.34334i	−0.687301	+	0.250157i	−0.661979	−	0.749522i	$-0.730283\pi$
$643$	−17.4282	+	6.34334i	−0.687301	+	0.250157i	−0.0253218	+	0.999679i	$0.508061\pi$
$644$	0.880064	−	4.99109i	0.0346794	−	0.196676i
$645$	−7.11327	−	14.5089i	−0.280085	−	0.571289i
$646$	3.89262	−	3.26630i	0.153153	−	0.128511i
$647$	−22.8590			−0.898680			−0.449340	−	0.893361i	$-0.648341\pi$
$647$	−22.8590			−0.898680			−0.449340	+	0.893361i	$0.648341\pi$
$648$	6.42268	−	6.30469i	0.252307	−	0.247672i
$649$	−7.17993			−0.281837
$650$	3.40346	−	2.85584i	0.133495	−	0.112015i
$651$	0.131381	+	0.267979i	0.00514923	+	0.0105029i
$652$	−2.63687	+	14.9544i	−0.103268	+	0.585660i
$653$	−1.22941	+	0.447470i	−0.0481107	+	0.0175109i	−0.365963	−	0.930629i	$-0.619260\pi$
$653$	−1.22941	+	0.447470i	−0.0481107	+	0.0175109i	0.317853	+	0.948140i	$0.397038\pi$
$654$	−12.2278	−	5.41421i	−0.478144	−	0.211712i
$655$	3.92193	+	22.2424i	0.153243	+	0.869082i
$656$	−1.77297	−	3.07087i	−0.0692229	−	0.119898i
$657$	−42.8096	−	5.83799i	−1.67016	−	0.227762i
$658$	1.98880	−	3.44470i	0.0775314	−	0.134288i
$659$	17.5778	+	6.39778i	0.684732	+	0.249222i	0.660878	−	0.750493i	$-0.270184\pi$
$659$	17.5778	+	6.39778i	0.684732	+	0.249222i	0.0238541	+	0.999715i	$0.492406\pi$
$660$	−6.66260	+	1.92523i	−0.259341	+	0.0749394i
$661$	−33.5878	−	28.1835i	−1.30642	−	1.09621i	−0.988998	−	0.147926i	$-0.952740\pi$
$661$	−33.5878	−	28.1835i	−1.30642	−	1.09621i	−0.317417	−	0.948286i	$-0.602815\pi$
$662$	8.96796	+	7.52501i	0.348550	+	0.292468i
$663$	7.73886	+	7.44280i	0.300553	+	0.289054i
$664$	−5.06763	−	1.84447i	−0.196662	−	0.0715792i
$665$	−1.21347	+	2.10180i	−0.0470565	+	0.0815043i
$666$	8.64470	+	4.55120i	0.334975	+	0.176355i
$667$	−20.2671	−	35.1036i	−0.784745	−	1.35922i
$668$	1.89088	+	10.7237i	0.0731604	+	0.414913i
$669$	20.7212	−	15.1197i	0.801127	−	0.584561i
$670$	−4.87570	+	1.77461i	−0.188365	+	0.0685591i
$671$	−6.36504	+	36.0979i	−0.245719	+	1.39354i
$672$	−0.965611	+	1.43791i	−0.0372493	+	0.0554687i
$673$	30.3790	−	25.4910i	1.17103	−	0.982608i	0.171030	−	0.985266i	$-0.445291\pi$
$673$	30.3790	−	25.4910i	1.17103	−	0.982608i	0.999996	+	0.00265831i	$0.000846167\pi$
$674$	−3.35694			−0.129305
$675$	−11.0362	+	5.95523i	−0.424785	+	0.229217i
$676$	−9.61101			−0.369654
$677$	−21.0764	+	17.6852i	−0.810031	+	0.679697i	−0.950615	−	0.310372i	$-0.899546\pi$
$677$	−21.0764	+	17.6852i	−0.810031	+	0.679697i	0.140584	+	0.990069i	$0.455102\pi$
$678$	−18.3531	−	1.24565i	−0.704847	−	0.0478390i
$679$	0.811781	−	4.60384i	0.0311533	−	0.176679i
$680$	5.08910	−	1.85228i	0.195158	−	0.0710317i
$681$	−3.01652	−	28.1463i	−0.115593	−	1.07857i
$682$	−0.0744933	−	0.422473i	−0.00285250	−	0.0161773i
$683$	22.0309	+	38.1586i	0.842987	+	1.46010i	0.887358	+	0.461081i	$0.152538\pi$
$683$	22.0309	+	38.1586i	0.842987	+	1.46010i	−0.0443706	+	0.999015i	$0.514128\pi$
$684$	−1.38132	+	4.31120i	−0.0528160	+	0.164843i
$685$	16.3730	−	28.3589i	0.625581	−	1.08354i
$686$	−0.939693	−	0.342020i	−0.0358776	−	0.0130584i
$687$	9.33308	−	37.7619i	0.356079	−	1.44071i
$688$	4.44365	+	3.72867i	0.169413	+	0.142154i
$689$	−8.22008	−	6.89747i	−0.313160	−	0.262773i
$690$	3.38738	−	13.7054i	0.128955	−	0.521757i
$691$	21.6601	+	7.88363i	0.823989	+	0.299907i	0.719389	−	0.694607i	$-0.244422\pi$
$691$	21.6601	+	7.88363i	0.823989	+	0.299907i	0.104600	+	0.994514i	$0.466644\pi$
$692$	−11.2863	+	19.5484i	−0.429040	+	0.743118i
$693$	−5.02032	−	5.52996i	−0.190706	−	0.210066i
$694$	12.5557	+	21.7472i	0.476609	+	0.825511i
$695$	−2.12676	−	12.0615i	−0.0806727	−	0.457517i
$696$	1.47619	+	13.7739i	0.0559550	+	0.522100i
$697$	−11.2204	+	4.08389i	−0.425003	+	0.154688i
$698$	−2.48202	+	14.0762i	−0.0939457	+	0.532792i
$699$	−39.7285	−	2.69643i	−1.50267	−	0.101988i
$700$	1.84878	−	1.55131i	0.0698774	−	0.0586341i
$701$	−48.0725			−1.81567			−0.907837	−	0.419323i	$-0.862268\pi$
$701$	−48.0725			−1.81567			−0.907837	+	0.419323i	$0.862268\pi$
$702$	−9.36870	−	1.93136i	−0.353599	−	0.0728945i
$703$	−4.91418			−0.185342
$704$	1.90716	−	1.60030i	0.0718789	−	0.0603135i
$705$	6.17713	−	9.19850i	0.232644	−	0.346436i
$706$	−2.90465	+	16.4731i	−0.109318	+	0.619974i
$707$	−7.25282	+	2.63981i	−0.272770	+	0.0992803i
$708$	−4.03513	+	2.94433i	−0.151650	+	0.110655i
$709$	5.59346	+	31.7221i	0.210067	+	1.19135i	0.889265	+	0.457392i	$0.151216\pi$
$709$	5.59346	+	31.7221i	0.210067	+	1.19135i	−0.679198	+	0.733955i	$0.737672\pi$
$710$	−1.60919	−	2.78720i	−0.0603919	−	0.104602i
$711$	−0.520729	−	13.3459i	−0.0195289	−	0.500512i
$712$	5.53774	−	9.59164i	0.207535	−	0.359462i
$713$	0.820622	+	0.298682i	0.0307325	+	0.0111857i
$714$	4.20380	+	4.04298i	0.157323	+	0.151305i
$715$	5.64659	+	4.73805i	0.211170	+	0.177193i
$716$	−11.3538	−	9.52695i	−0.424310	−	0.356039i
$717$	−10.7238	+	3.09875i	−0.400486	+	0.115725i
$718$	0.706100	+	0.256999i	0.0263514	+	0.00959114i
$719$	3.10067	−	5.37052i	0.115636	−	0.200287i	−0.802398	−	0.596789i	$-0.796443\pi$
$719$	3.10067	−	5.37052i	0.115636	−	0.200287i	0.918034	+	0.396503i	$0.129776\pi$
$720$	−2.95490	+	3.81416i	−0.110123	+	0.142146i
$721$	−3.18269	−	5.51258i	−0.118529	−	0.205299i
$722$	2.90389	+	16.4688i	0.108072	+	0.612904i
$723$	2.11238	+	0.935320i	0.0785604	+	0.0347849i
$724$	16.0735	−	5.85028i	0.597368	−	0.217424i
$725$	3.35181	−	19.0091i	0.124483	−	0.705979i
$726$	−3.66118	−	7.46772i	−0.135879	−	0.277153i
$727$	23.1480	−	19.4235i	0.858511	−	0.720376i	−0.103136	−	0.994667i	$-0.532888\pi$
$727$	23.1480	−	19.4235i	0.858511	−	0.720376i	0.961647	+	0.274291i	$0.0884431\pi$
$728$	1.84092			0.0682290
$729$	24.7987	+	10.6783i	0.918469	+	0.395493i
$730$	23.1625			0.857282
$731$	14.9634	−	12.5558i	0.553443	−	0.464393i
$732$	11.2258	+	22.8973i	0.414917	+	0.846307i
$733$	−3.01849	+	17.1187i	−0.111490	+	0.632293i	0.876938	+	0.480604i	$0.159582\pi$
$733$	−3.01849	+	17.1187i	−0.111490	+	0.632293i	−0.988428	+	0.151689i	$0.951529\pi$
$734$	14.0331	−	5.10763i	0.517971	−	0.188526i
$735$	−2.54712	−	1.12781i	−0.0939518	−	0.0416000i
$736$	0.880064	+	4.99109i	0.0324396	+	0.183974i
$737$	4.01598	+	6.95587i	0.147930	+	0.256223i
$738$	6.51494	−	8.40944i	0.239818	−	0.309556i
$739$	20.1518	−	34.9040i	0.741297	−	1.28396i	−0.210608	−	0.977571i	$-0.567544\pi$
$739$	20.1518	−	34.9040i	0.741297	−	1.28396i	0.951905	−	0.306394i	$-0.0991224\pi$
$740$	−4.92156	−	1.79130i	−0.180920	−	0.0658496i
$741$	4.62252	−	1.33573i	0.169812	−	0.0490691i
$742$	−4.46520	−	3.74675i	−0.163923	−	0.137547i
$743$	−21.8612	−	18.3437i	−0.802010	−	0.672967i	0.146676	−	0.989185i	$-0.453142\pi$
$743$	−21.8612	−	18.3437i	−0.802010	−	0.672967i	−0.948687	+	0.316218i	$0.897587\pi$
$744$	−0.215112	−	0.206882i	−0.00788639	−	0.00758468i
$745$	−13.6445	−	4.96621i	−0.499897	−	0.181948i
$746$	1.32597	−	2.29665i	0.0485472	−	0.0840862i
$747$	−0.630773	−	16.1663i	−0.0230788	−	0.591494i
$748$	−4.19175	−	7.26032i	−0.153265	−	0.265463i
$749$	−3.40195	−	19.2934i	−0.124305	−	0.704966i
$750$	16.6822	−	12.1725i	0.609148	−	0.444478i
$751$	−10.9650	+	3.99094i	−0.400119	+	0.145631i	−0.534238	−	0.845334i	$-0.679402\pi$
$751$	−10.9650	+	3.99094i	−0.400119	+	0.145631i	0.134120	+	0.990965i	$0.457179\pi$
$752$	−0.690703	+	3.91717i	−0.0251873	+	0.142844i
$753$	−14.0568	+	20.9323i	−0.512257	+	0.762814i
$754$	11.2789	−	9.46411i	0.410753	−	0.344663i
$755$	29.6068			1.07750
$756$	−5.08914	−	1.04913i	−0.185090	−	0.0381564i
$757$	53.0899			1.92958			0.964792	−	0.263014i	$-0.0847165\pi$
$757$	53.0899			1.92958			0.964792	+	0.263014i	$0.0847165\pi$
$758$	0.291228	−	0.244369i	0.0105779	−	0.00887588i
$759$	−21.8042	−	1.47988i	−0.791442	−	0.0537163i
$760$	0.421435	−	2.39008i	0.0152871	−	0.0866973i
$761$	15.0462	−	5.47637i	0.545424	−	0.198518i	−0.0545880	−	0.998509i	$-0.517385\pi$
$761$	15.0462	−	5.47637i	0.545424	−	0.198518i	0.600012	+	0.799991i	$0.295162\pi$
$762$	3.76149	+	35.0973i	0.136264	+	1.27144i
$763$	1.34070	+	7.60351i	0.0485367	+	0.275265i
$764$	−2.61175	−	4.52368i	−0.0944896	−	0.163661i
$765$	10.9207	+	12.0294i	0.394840	+	0.434923i
$766$	10.3406	−	17.9105i	0.373622	−	0.647133i
$767$	4.98893	+	1.81582i	0.180140	+	0.0655655i
$768$	0.415582	−	1.68146i	0.0149960	−	0.0606743i
$769$	−17.1882	−	14.4226i	−0.619823	−	0.520093i	0.277925	−	0.960603i	$-0.410353\pi$
$769$	−17.1882	−	14.4226i	−0.619823	−	0.520093i	−0.897748	+	0.440509i	$0.854798\pi$
$770$	3.06726	+	2.57374i	0.110537	+	0.0927512i
$771$	6.44057	−	26.0587i	0.231951	−	0.938481i
$772$	16.7604	+	6.10027i	0.603218	+	0.219554i
$773$	10.1456	−	17.5727i	0.364912	−	0.632045i	−0.623850	−	0.781544i	$-0.714433\pi$
$773$	10.1456	−	17.5727i	0.364912	−	0.632045i	0.988762	+	0.149498i	$0.0477659\pi$
$774$	−5.30985	+	16.5725i	−0.190859	+	0.595685i
$775$	0.207929	+	0.360144i	0.00746903	+	0.0129367i
$776$	0.811781	+	4.60384i	0.0291413	+	0.165268i
$777$	−0.601063	−	5.60834i	−0.0215630	−	0.201198i
$778$	−27.6850	+	10.0765i	−0.992554	+	0.361260i
$779$	−0.929178	+	5.26963i	−0.0332913	+	0.188804i
$780$	5.11636	+	0.347254i	0.183195	+	0.0124337i
$781$	−3.81647	+	3.20240i	−0.136564	+	0.114591i
$782$	17.0661			0.610284
$783$	−36.5735	+	19.7353i	−1.30703	+	0.705283i
$784$	1.00000			0.0357143
$785$	17.6945	−	14.8474i	0.631543	−	0.529928i
$786$	13.5603	−	20.1929i	0.483679	−	0.720257i
$787$	0.145268	−	0.823857i	0.00517825	−	0.0293673i	−0.982109	−	0.188313i	$-0.939698\pi$
$787$	0.145268	−	0.823857i	0.00517825	−	0.0293673i	0.987287	+	0.158945i	$0.0508093\pi$
$788$	−7.20245	+	2.62148i	−0.256577	+	0.0933862i
$789$	17.0888	−	12.4692i	0.608377	−	0.443916i
$790$	1.24335	+	7.05136i	0.0442363	+	0.250876i
$791$	5.31028	+	9.19767i	0.188812	+	0.327032i
$792$	6.60891	+	3.47941i	0.234837	+	0.123635i
$793$	13.5520	−	23.4727i	0.481244	−	0.833539i
$794$	3.64901	+	1.32813i	0.129498	+	0.0471335i
$795$	−11.7031	−	11.2554i	−0.415067	−	0.399188i
$796$	18.8717	+	15.8352i	0.668889	+	0.561264i
$797$	6.37913	+	5.35272i	0.225960	+	0.189603i	0.748738	−	0.662866i	$-0.230660\pi$
$797$	6.37913	+	5.35272i	0.225960	+	0.189603i	−0.522778	+	0.852469i	$0.675104\pi$
$798$	2.51098	−	0.725575i	0.0888878	−	0.0256851i
$799$	12.5863	+	4.58104i	0.445271	+	0.162065i
$800$	−1.20671	+	2.09008i	−0.0426635	+	0.0738954i
$801$	32.9217	+	4.48956i	1.16323	+	0.158631i
$802$	−14.0374	−	24.3134i	−0.495677	−	0.858538i
$803$	−6.22623	−	35.3107i	−0.219719	−	1.24609i
$804$	5.10943	+	2.26235i	0.180196	+	0.0797870i
$805$	−7.65937	+	2.78778i	−0.269957	+	0.0982565i
$806$	−0.0550832	+	0.312392i	−0.00194022	+	0.0110035i
$807$	9.70914	+	19.8038i	0.341778	+	0.697125i
$808$	5.91255	−	4.96122i	0.208003	−	0.174535i
$809$	−28.2868			−0.994510			−0.497255	−	0.867604i	$-0.665659\pi$
$809$	−28.2868			−0.994510			−0.497255	+	0.867604i	$0.665659\pi$
$810$	−13.9460	−	3.87575i	−0.490014	−	0.136180i
$811$	−39.0770			−1.37218			−0.686090	−	0.727517i	$-0.740674\pi$
$811$	−39.0770			−1.37218			−0.686090	+	0.727517i	$0.740674\pi$
$812$	6.12677	−	5.14097i	0.215007	−	0.180413i
$813$	4.38405	+	8.94216i	0.153755	+	0.313615i
$814$	−1.40785	+	7.98434i	−0.0493452	+	0.279851i
$815$	22.9492	−	8.35282i	0.803875	−	0.292587i
$816$	−5.33306	−	2.36137i	−0.186694	−	0.0826645i
$817$	−1.52003	−	8.62054i	−0.0531793	−	0.301595i
$818$	0.789962	+	1.36825i	0.0276204	+	0.0478399i
$819$	2.08980	+	5.11211i	0.0730234	+	0.178631i
$820$	−2.85144	+	4.93885i	−0.0995768	+	0.172472i
$821$	−5.27071	−	1.91838i	−0.183949	−	0.0669520i	0.248403	−	0.968657i	$-0.420094\pi$
$821$	−5.27071	−	1.91838i	−0.183949	−	0.0669520i	−0.432353	+	0.901705i	$0.642316\pi$
$822$	−33.8799	+	9.78995i	−1.18170	+	0.341464i
$823$	−5.91714	−	4.96507i	−0.206258	−	0.173071i	0.533807	−	0.845606i	$-0.320761\pi$
$823$	−5.91714	−	4.96507i	−0.206258	−	0.173071i	−0.740065	+	0.672535i	$0.765205\pi$
$824$	4.87616	+	4.09158i	0.169869	+	0.142537i
$825$	−7.50095	−	7.21399i	−0.261149	−	0.251159i
$826$	2.71002	+	0.986366i	0.0942936	+	0.0343201i
$827$	−24.1509	+	41.8306i	−0.839808	+	1.45459i	0.0502461	+	0.998737i	$0.483999\pi$
$827$	−24.1509	+	41.8306i	−0.839808	+	1.45459i	−0.890055	+	0.455854i	$0.849334\pi$
$828$	−12.8609	+	8.10971i	−0.446946	+	0.281832i
$829$	23.4965	+	40.6972i	0.816069	+	1.41347i	0.908558	+	0.417759i	$0.137184\pi$
$829$	23.4965	+	40.6972i	0.816069	+	1.41347i	−0.0924894	+	0.995714i	$0.529482\pi$
$830$	1.50610	+	8.54151i	0.0522774	+	0.296480i
$831$	20.8743	−	15.2314i	0.724120	−	0.528371i
$832$	−1.72990	+	0.629632i	−0.0599735	+	0.0218286i
$833$	0.584738	−	3.31622i	0.0202600	−	0.114900i
$834$	−7.35338	+	10.9501i	−0.254627	+	0.379171i
$835$	13.4156	−	11.2571i	0.464268	−	0.389567i
$836$	−3.75691			−0.129935
$837$	0.330305	−	0.832202i	0.0114170	−	0.0287651i
$838$	19.2408			0.664663
$839$	−18.9009	+	15.8598i	−0.652533	+	0.547540i	−0.907838	−	0.419320i	$-0.862268\pi$
$839$	−18.9009	+	15.8598i	−0.652533	+	0.547540i	0.255305	+	0.966860i	$0.417824\pi$
$840$	2.77924	+	0.188631i	0.0958929	+	0.00650839i
$841$	6.07193	−	34.4356i	0.209377	−	1.18744i
$842$	31.1074	−	11.3222i	1.07203	−	0.390188i
$843$	−4.36165	−	40.6973i	−0.150223	−	1.40169i
$844$	−2.51710	−	14.2752i	−0.0866423	−	0.491373i
$845$	7.72863	+	13.3864i	0.265873	+	0.460506i
$846$	−11.6618	+	2.52870i	−0.400940	+	0.0869385i
$847$	−2.40089	+	4.15846i	−0.0824955	+	0.142886i
$848$	5.47738	+	1.99360i	0.188094	+	0.0684606i
$849$	−5.78371	+	23.4010i	−0.198496	+	0.803122i
$850$	6.22554	+	5.22385i	0.213534	+	0.179176i
$851$	−12.6430	−	10.6088i	−0.433398	−	0.363664i
$852$	−0.831632	+	3.36480i	−0.0284913	+	0.115276i
$853$	43.1026	+	15.6881i	1.47581	+	0.537150i	0.949670	−	0.313251i	$-0.101418\pi$
$853$	43.1026	+	15.6881i	1.47581	+	0.537150i	0.526136	+	0.850401i	$0.323640\pi$
$854$	7.36151	−	12.7505i	0.251906	−	0.436314i
$855$	7.11549	−	1.54290i	0.243345	−	0.0527660i
$856$	9.79553	+	16.9664i	0.334804	+	0.579898i
$857$	−5.15646	−	29.2437i	−0.176141	−	0.998947i	−0.936818	−	0.349817i	$-0.886244\pi$
$857$	−5.15646	−	29.2437i	−0.176141	−	0.998947i	0.760677	−	0.649131i	$-0.224867\pi$
$858$	−0.845930	−	7.89313i	−0.0288796	−	0.269467i
$859$	−37.9617	+	13.8169i	−1.29524	+	0.471427i	−0.895442	−	0.445177i	$-0.853141\pi$
$859$	−37.9617	+	13.8169i	−1.29524	+	0.471427i	−0.399794	+	0.916605i	$0.630918\pi$
$860$	1.62002	−	9.18758i	0.0552421	−	0.313294i
$861$	−6.12765	−	0.415892i	−0.208830	−	0.0141736i
$862$	−15.8355	+	13.2875i	−0.539358	+	0.452575i
$863$	14.5654			0.495813			0.247907	−	0.968784i	$-0.420257\pi$
$863$	14.5654			0.495813			0.247907	+	0.968784i	$0.420257\pi$
$864$	5.14105	−	0.754730i	0.174902	−	0.0256764i
$865$	36.3031			1.23434
$866$	−12.0414	+	10.1039i	−0.409183	+	0.343345i
$867$	5.46613	−	8.13973i	0.185639	−	0.276440i
$868$	−0.0299215	+	0.169693i	−0.00101560	+	0.00575977i
$869$	10.4154	−	3.79091i	0.353320	−	0.128598i
$870$	17.9975	−	13.1323i	0.610173	−	0.445226i
$871$	−1.03132	−	5.84889i	−0.0349449	−	0.198182i
$872$	−3.86040	−	6.68641i	−0.130730	−	0.226430i
$873$	−11.8630	+	7.48050i	−0.401502	+	0.253177i
$874$	3.82394	−	6.62326i	0.129347	−	0.224035i
$875$	−11.2039	−	4.07787i	−0.378759	−	0.137857i
$876$	−17.9793	−	17.2915i	−0.607464	−	0.584224i
$877$	32.3812	+	27.1710i	1.09343	+	0.917500i	0.996966	−	0.0778361i	$-0.0248011\pi$
$877$	32.3812	+	27.1710i	1.09343	+	0.917500i	0.0964677	+	0.995336i	$0.469246\pi$
$878$	0.885678	+	0.743172i	0.0298902	+	0.0250809i
$879$	36.8357	−	10.6441i	1.24244	−	0.359016i
$880$	−3.76256	−	1.36946i	−0.126836	−	0.0461644i
$881$	−3.84139	+	6.65348i	−0.129420	+	0.224162i	−0.923452	−	0.383714i	$-0.874645\pi$
$881$	−3.84139	+	6.65348i	−0.129420	+	0.224162i	0.794032	+	0.607876i	$0.207978\pi$
$882$	1.13519	+	2.77693i	0.0382239	+	0.0935041i
$883$	24.1261	+	41.7877i	0.811909	+	1.40627i	0.911526	+	0.411243i	$0.134905\pi$
$883$	24.1261	+	41.7877i	0.811909	+	1.40627i	−0.0996165	+	0.995026i	$0.531762\pi$
$884$	1.07646	+	6.10489i	0.0362052	+	0.205330i
$885$	7.34574	+	3.25254i	0.246924	+	0.109333i
$886$	−19.6044	+	7.13540i	−0.658621	+	0.239719i
$887$	0.316524	−	1.79509i	0.0106278	−	0.0602734i	−0.979033	−	0.203704i	$-0.934702\pi$
$887$	0.316524	−	1.79509i	0.0106278	−	0.0602734i	0.989660	+	0.143430i	$0.0458132\pi$
$888$	2.48298	+	5.06454i	0.0833233	+	0.169955i
$889$	15.6116	−	13.0997i	0.523596	−	0.439350i
$890$	−17.8125			−0.597078
$891$	−2.15971	+	22.3023i	−0.0723529	+	0.747155i
$892$	14.8096			0.495862
$893$	4.59803	−	3.85821i	0.153867	−	0.129110i
$894$	6.88381	+	14.0409i	0.230229	+	0.469599i
$895$	−4.13923	+	23.4748i	−0.138359	+	0.784675i
$896$	−0.939693	+	0.342020i	−0.0313929	+	0.0114261i
$897$	14.7762	+	6.54262i	0.493364	+	0.218452i
$898$	−5.76175	−	32.6765i	−0.192272	−	1.09043i
$899$	0.689067	+	1.19350i	0.0229817	+	0.0398054i
$900$	−7.17384	−	0.978303i	−0.239128	−	0.0326101i
$901$	9.81405	−	16.9984i	0.326954	−	0.566300i
$902$	8.29566	+	3.01937i	0.276215	+	0.100534i
$903$	9.65234	−	2.78915i	0.321210	−	0.0928169i
$904$	−8.13582	−	6.82676i	−0.270593	−	0.227055i
$905$	−21.0738	−	17.6830i	−0.700517	−	0.587803i
$906$	−22.9815	−	22.1023i	−0.763510	−	0.734301i
$907$	−11.9238	−	4.33990i	−0.395923	−	0.144104i	0.136383	−	0.990656i	$-0.456452\pi$
$907$	−11.9238	−	4.33990i	−0.395923	−	0.144104i	−0.532306	+	0.846552i	$0.678674\pi$
$908$	8.17167	−	14.1537i	0.271186	−	0.469708i
$909$	20.4888	+	10.7868i	0.679572	+	0.357776i
$910$	−1.48036	−	2.56407i	−0.0490736	−	0.0849979i
$911$	−1.85203	−	10.5034i	−0.0613605	−	0.347992i	−0.999995	−	0.00307981i	$-0.999020\pi$
$911$	−1.85203	−	10.5034i	−0.0613605	−	0.347992i	0.938635	−	0.344913i	$-0.112091\pi$
$912$	−2.11139	+	1.54062i	−0.0699151	+	0.0510152i
$913$	12.6165	−	4.59203i	0.417545	−	0.151974i
$914$	4.26565	−	24.1917i	0.141095	−	0.800190i
$915$	22.8646	−	34.0481i	0.755879	−	1.12560i
$916$	17.2037	−	14.4356i	0.568427	−	0.476967i
$917$	−14.0432			−0.463747
$918$	0.503321	−	17.4901i	0.0166121	−	0.577261i
$919$	−60.5489			−1.99732			−0.998662	−	0.0517212i	$-0.983529\pi$
$919$	−60.5489			−1.99732			−0.998662	+	0.0517212i	$0.983529\pi$
$920$	6.24398	−	5.23932i	0.205858	−	0.172735i
$921$	−30.1340	−	2.04523i	−0.992948	−	0.0673928i
$922$	−1.19543	+	6.77965i	−0.0393695	+	0.223276i
$923$	3.46175	−	1.25997i	0.113945	−	0.0414725i
$924$	−0.459515	−	4.28760i	−0.0151169	−	0.141052i
$925$	−1.36476	−	7.73993i	−0.0448730	−	0.254487i
$926$	11.6047	+	20.1000i	0.381356	+	0.660527i
$927$	−5.82667	+	18.1855i	−0.191373	+	0.597290i
$928$	−3.99896	+	6.92641i	−0.131272	+	0.227371i
$929$	14.2058	+	5.17049i	0.466077	+	0.169638i	0.564375	−	0.825519i	$-0.309117\pi$
$929$	14.2058	+	5.17049i	0.466077	+	0.169638i	−0.0982972	+	0.995157i	$0.531340\pi$
$930$	−0.115169	+	0.465975i	−0.00377653	+	0.0152799i
$931$	−1.15598	−	0.969984i	−0.0378858	−	0.0317899i
$932$	−17.6114	−	14.7777i	−0.576880	−	0.484060i
$933$	3.90484	−	15.7991i	0.127839	−	0.517238i
$934$	15.7013	+	5.71482i	0.513763	+	0.186995i
$935$	−6.74153	+	11.6767i	−0.220472	+	0.381868i
$936$	−3.71221	−	4.08906i	−0.121337	−	0.133655i
$937$	−23.5067	−	40.7147i	−0.767929	−	1.33009i	−0.938684	−	0.344779i	$-0.887954\pi$
$937$	−23.5067	−	40.7147i	−0.767929	−	1.33009i	0.170755	−	0.985314i	$-0.445379\pi$
$938$	−0.560219	−	3.17716i	−0.0182918	−	0.103738i
$939$	−6.28606	−	58.6534i	−0.205138	−	1.91408i
$940$	6.01133	−	2.18794i	0.196068	−	0.0713628i
$941$	2.91518	−	16.5328i	0.0950323	−	0.538955i	−0.899705	−	0.436498i	$-0.856219\pi$
$941$	2.91518	−	16.5328i	0.0950323	−	0.538955i	0.994737	−	0.102457i	$-0.0326704\pi$
$942$	−24.8189	−	1.68449i	−0.808644	−	0.0548838i
$943$	−13.7667	+	11.5516i	−0.448305	+	0.376172i
$944$	−2.88394			−0.0938643
$945$	2.63115	+	7.93189i	0.0855914	+	0.258024i
$946$	−14.4417			−0.469542
$947$	−16.0923	+	13.5030i	−0.522928	+	0.438789i	−0.865651	−	0.500648i	$-0.833095\pi$
$947$	−16.0923	+	13.5030i	−0.522928	+	0.438789i	0.342723	+	0.939437i	$0.388651\pi$
$948$	4.29893	−	6.40163i	0.139623	−	0.207915i
$949$	−4.60391	+	26.1101i	−0.149449	+	0.847569i
$950$	3.42227	−	1.24561i	0.111033	−	0.0404128i
$951$	−0.771775	+	0.563143i	−0.0250265	+	0.0182612i
$952$	0.584738	+	3.31622i	0.0189515	+	0.107479i
$953$	2.87515	+	4.97991i	0.0931354	+	0.161315i	0.908829	−	0.417169i	$-0.136978\pi$
$953$	2.87515	+	4.97991i	0.0931354	+	0.161315i	−0.815694	+	0.578484i	$0.803644\pi$
$954$	0.681775	+	17.4734i	0.0220733	+	0.565723i
$955$	−4.20044	+	7.27537i	−0.135923	+	0.235425i
$956$	−6.05601	−	2.20421i	−0.195865	−	0.0712892i
$957$	−24.8578	−	23.9068i	−0.803537	−	0.772797i
$958$	−16.6007	−	13.9296i	−0.536344	−	0.450046i
$959$	15.5973	+	13.0877i	0.503663	+	0.422623i
$960$	−2.67615	+	0.773301i	−0.0863723	+	0.0249582i
$961$	29.1026	+	10.5925i	0.938793	+	0.341693i
$962$	2.99750	−	5.19182i	0.0966432	−	0.167391i
$963$	−35.9946	+	46.4616i	−1.15991	+	1.49720i
$964$	0.666895	+	1.15510i	0.0214792	+	0.0372031i
$965$	−4.98117	−	28.2496i	−0.160349	−	0.909387i
$966$	8.02655	+	3.55400i	0.258250	+	0.114348i
$967$	36.5097	−	13.2884i	1.17407	−	0.427327i	0.319967	−	0.947429i	$-0.396328\pi$
$967$	36.5097	−	13.2884i	1.17407	−	0.427327i	0.854104	+	0.520102i	$0.174106\pi$
$968$	0.833820	−	4.72883i	0.0268000	−	0.151990i
$969$	3.87443	+	7.90269i	0.124465	+	0.253871i
$970$	5.75952	−	4.83281i	0.184927	−	0.155172i
$971$	36.9685			1.18637			0.593187	−	0.805065i	$-0.297869\pi$
$971$	36.9685			1.18637			0.593187	+	0.805065i	$0.297869\pi$
$972$	7.93190	+	13.4196i	0.254416	+	0.430433i
$973$	7.61526			0.244134
$974$	23.4006	−	19.6355i	0.749804	−	0.629161i
$975$	3.38755	+	6.90960i	0.108489	+	0.221284i
$976$	−2.55663	+	14.4993i	−0.0818356	+	0.464113i
$977$	25.6803	−	9.34688i	0.821587	−	0.299033i	0.103186	−	0.994662i	$-0.467096\pi$
$977$	25.6803	−	9.34688i	0.821587	−	0.299033i	0.718401	+	0.695629i	$0.244874\pi$
$978$	−24.0493	−	10.6486i	−0.769013	−	0.340504i
$979$	4.78813	+	27.1548i	0.153029	+	0.867873i
$980$	−0.804144	−	1.39282i	−0.0256874	−	0.0444919i
$981$	14.1854	−	18.3104i	0.452905	−	0.584607i
$982$	10.2135	−	17.6902i	0.325925	−	0.564518i
$983$	17.5614	+	6.39183i	0.560122	+	0.203868i	0.606538	−	0.795054i	$-0.292558\pi$
$983$	17.5614	+	6.39183i	0.560122	+	0.203868i	−0.0464159	+	0.998922i	$0.514780\pi$
$984$	5.90035	−	1.70497i	0.188096	−	0.0543524i
$985$	9.44304	+	7.92365i	0.300880	+	0.252468i
$986$	20.6311	+	17.3116i	0.657029	+	0.551313i
$987$	4.96560	+	4.77563i	0.158057	+	0.152010i
$988$	2.61047	+	0.950132i	0.0830500	+	0.0302277i
$989$	14.6994	−	25.4601i	0.467414	−	0.809585i
$990$	−0.468329	−	12.0030i	−0.0148845	−	0.381479i
$991$	−4.91454	−	8.51223i	−0.156115	−	0.270400i	0.777349	−	0.629069i	$-0.216564\pi$
$991$	−4.91454	−	8.51223i	−0.156115	−	0.270400i	−0.933465	+	0.358669i	$0.883231\pi$
$992$	−0.0299215	−	0.169693i	−0.000950010	−	0.00538777i
$993$	−16.3799	+	11.9520i	−0.519800	+	0.379284i
$994$	1.88044	−	0.684426i	0.0596441	−	0.0217087i
$995$	6.88003	−	39.0186i	0.218112	−	1.23697i
$996$	5.20741	−	7.75447i	0.165003	−	0.245710i
$997$	−42.5815	+	35.7301i	−1.34857	+	1.13158i	−0.369235	+	0.929336i	$0.620380\pi$
$997$	−42.5815	+	35.7301i	−1.34857	+	1.13158i	−0.979334	+	0.202248i	$0.935175\pi$
$998$	0.882781			0.0279439
$999$	−11.2452	+	12.6443i	−0.355783	+	0.400047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.c.211.2	yes	24
27.16	even	9	inner	378.2.u.c.43.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.c.43.2	✓	24	27.16	even	9	inner
378.2.u.c.211.2	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.762464 - 1.55520i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.51130 + 0.550067i) q^{5} +(1.58375 + 0.701250i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.83730 + 2.37157i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.762464 - 1.55520i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.51130 + 0.550067i) q^{5} +(1.58375 + 0.701250i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.83730 + 2.37157i) q^{9} +(0.804144 - 1.39282i) q^{10} +(-2.33948 - 0.851501i) q^{11} +(-1.66397 + 0.480823i) q^{12} +(1.41023 + 1.18332i) q^{13} +(0.766044 + 0.642788i) q^{14} +(2.00777 + 1.93096i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-1.68369 + 2.91623i) q^{17} +(-0.116964 - 2.99772i) q^{18} +(0.754514 + 1.30686i) q^{19} +(0.279276 + 1.58385i) q^{20} +(-1.39917 + 1.02094i) q^{21} +(2.33948 - 0.851501i) q^{22} +(-0.880064 + 4.99109i) q^{23} +(0.965611 - 1.43791i) q^{24} +(-1.84878 + 1.55131i) q^{25} -1.84092 q^{26} +(5.08914 + 1.04913i) q^{27} -1.00000 q^{28} +(-6.12677 + 5.14097i) q^{29} +(-2.77924 - 0.188631i) q^{30} +(0.0299215 - 0.169693i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.459515 + 4.28760i) q^{33} +(-0.584738 - 3.31622i) q^{34} +(0.804144 + 1.39282i) q^{35} +(2.01650 + 2.22120i) q^{36} +(-1.62826 + 2.82023i) q^{37} +(-1.41802 - 0.516118i) q^{38} +(0.765053 - 3.09542i) q^{39} +(-1.23202 - 1.03379i) q^{40} +(2.71635 + 2.27929i) q^{41} +(0.415582 - 1.68146i) q^{42} +(-5.45095 - 1.98398i) q^{43} +(-1.24481 + 2.15608i) q^{44} +(1.47218 - 4.59478i) q^{45} +(-2.53404 - 4.38909i) q^{46} +(-0.690703 - 3.91717i) q^{47} +(0.184572 + 1.72219i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(0.419085 - 2.37675i) q^{50} +(5.81907 + 0.394949i) q^{51} +(1.41023 - 1.18332i) q^{52} -5.82891 q^{53} +(-4.57287 + 2.46756i) q^{54} +4.00403 q^{55} +(0.766044 - 0.642788i) q^{56} +(1.45713 - 2.16985i) q^{57} +(1.38883 - 7.87642i) q^{58} +(2.71002 - 0.986366i) q^{59} +(2.25027 - 1.64196i) q^{60} +(-2.55663 - 14.4993i) q^{61} +(0.0861556 + 0.149226i) q^{62} +(2.65458 + 1.39757i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.78217 - 1.01263i) q^{65} +(-3.10803 - 2.98912i) q^{66} +(-2.47139 - 2.07374i) q^{67} +(2.57956 + 2.16451i) q^{68} +(8.43316 - 2.43685i) q^{69} +(-1.51130 - 0.550067i) q^{70} +(1.00056 - 1.73303i) q^{71} +(-2.97249 - 0.405361i) q^{72} +(7.20098 + 12.4725i) q^{73} +(-0.565489 - 3.20705i) q^{74} +(3.82223 + 1.69241i) q^{75} +(1.41802 - 0.516118i) q^{76} +(-0.432319 + 2.45180i) q^{77} +(1.40364 + 2.86300i) q^{78} +(-3.41045 + 2.86171i) q^{79} +1.60829 q^{80} +(-2.24868 - 8.71455i) q^{81} -3.54594 q^{82} +(-4.13117 + 3.46647i) q^{83} +(0.762464 + 1.55520i) q^{84} +(0.940427 - 5.33343i) q^{85} +(5.45095 - 1.98398i) q^{86} +(12.6667 + 5.60855i) q^{87} +(-0.432319 - 2.45180i) q^{88} +(-5.53774 - 9.59164i) q^{89} +(1.82571 + 4.46610i) q^{90} +(0.920460 - 1.59428i) q^{91} +(4.76244 + 1.73339i) q^{92} +(-0.286721 + 0.0828512i) q^{93} +(3.04702 + 2.55675i) q^{94} +(-1.85915 - 1.56001i) q^{95} +(-1.24839 - 1.20063i) q^{96} +(4.39293 + 1.59890i) q^{97} +(0.500000 - 0.866025i) q^{98} +(6.31771 - 3.98378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

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