LMFDB - Embedded newform 324.2.l.a.179.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.1
Character	$\chi$	$=$	324.179
Dual form			324.2.l.a.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36831 + 0.357407i) q^{2} +(1.74452 - 0.978083i) q^{4} +(-0.532084 - 0.0938207i) q^{5} +(-1.18790 - 1.41568i) q^{7} +(-2.03746 + 1.96182i) q^{8} +O(q^{10})$	\(q+(-1.36831 + 0.357407i) q^{2} +(1.74452 - 0.978083i) q^{4} +(-0.532084 - 0.0938207i) q^{5} +(-1.18790 - 1.41568i) q^{7} +(-2.03746 + 1.96182i) q^{8} +(0.761586 - 0.0617949i) q^{10} +(-0.867520 - 4.91995i) q^{11} +(-1.52553 + 0.555249i) q^{13} +(2.13138 + 1.51252i) q^{14} +(2.08671 - 3.41257i) q^{16} +(0.683630 + 0.394694i) q^{17} +(-2.86200 + 1.65238i) q^{19} +(-1.02000 + 0.356750i) q^{20} +(2.94546 + 6.42194i) q^{22} +(-3.15234 - 2.64512i) q^{23} +(-4.42415 - 1.61026i) q^{25} +(1.88895 - 1.30499i) q^{26} +(-3.45697 - 1.30783i) q^{28} +(3.24174 - 8.90660i) q^{29} +(3.70462 - 4.41499i) q^{31} +(-1.63558 + 5.41525i) q^{32} +(-1.07648 - 0.295728i) q^{34} +(0.499242 + 0.864712i) q^{35} +(5.53013 - 9.57846i) q^{37} +(3.32552 - 3.28386i) q^{38} +(1.26816 - 0.852696i) q^{40} +(2.62821 + 7.22095i) q^{41} +(-7.88044 + 1.38953i) q^{43} +(-6.32553 - 7.73445i) q^{44} +(5.25874 + 2.49267i) q^{46} +(-2.39693 + 2.01126i) q^{47} +(0.622483 - 3.53027i) q^{49} +(6.62911 + 0.622106i) q^{50} +(-2.11825 + 2.46074i) q^{52} +0.933485i q^{53} +2.69922i q^{55} +(5.19762 + 0.553960i) q^{56} +(-1.25241 + 13.3456i) q^{58} +(0.461077 - 2.61490i) q^{59} +(-4.29949 + 3.60770i) q^{61} +(-3.49110 + 7.36511i) q^{62} +(0.302524 - 7.99428i) q^{64} +(0.863806 - 0.152312i) q^{65} +(2.15593 + 5.92336i) q^{67} +(1.57865 + 0.0199049i) q^{68} +(-0.992169 - 1.00476i) q^{70} +(-4.53203 + 7.84970i) q^{71} +(5.77108 + 9.99580i) q^{73} +(-4.14350 + 15.0828i) q^{74} +(-3.37666 + 5.68189i) q^{76} +(-5.93457 + 7.07254i) q^{77} +(-0.275423 + 0.756719i) q^{79} +(-1.43047 + 1.62000i) q^{80} +(-6.17702 - 8.94113i) q^{82} +(15.0247 + 5.46855i) q^{83} +(-0.326718 - 0.274149i) q^{85} +(10.2862 - 4.71783i) q^{86} +(11.4196 + 8.32231i) q^{88} +(5.41508 - 3.12640i) q^{89} +(2.59824 + 1.50009i) q^{91} +(-8.08647 - 1.53123i) q^{92} +(2.56089 - 3.60870i) q^{94} +(1.67785 - 0.610689i) q^{95} +(1.63933 + 9.29708i) q^{97} +(0.409997 + 5.05297i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.36831	+	0.357407i	−0.967538	+	0.252725i
$2$	−1.36831	+	0.357407i	−0.967538	+	0.252725i
$3$		0			0
$3$		0			0
$4$	1.74452	−	0.978083i	0.872260	−	0.489042i
$5$	−0.532084	−	0.0938207i	−0.237955	−	0.0419579i	0.0533987	−	0.998573i	$-0.482995\pi$
$5$	−0.532084	−	0.0938207i	−0.237955	−	0.0419579i	−0.291354	+	0.956615i	$0.594106\pi$
$6$		0			0
$7$	−1.18790	−	1.41568i	−0.448984	−	0.535078i	0.493315	−	0.869851i	$-0.335785\pi$
$7$	−1.18790	−	1.41568i	−0.448984	−	0.535078i	−0.942299	+	0.334773i	$0.891341\pi$
$8$	−2.03746	+	1.96182i	−0.720352	+	0.693608i
$9$		0			0
$10$	0.761586	−	0.0617949i	0.240835	−	0.0195413i
$11$	−0.867520	−	4.91995i	−0.261567	−	1.48342i	−0.778635	−	0.627477i	$-0.784088\pi$
$11$	−0.867520	−	4.91995i	−0.261567	−	1.48342i	0.517068	−	0.855944i	$-0.327023\pi$
$12$		0			0
$13$	−1.52553	+	0.555249i	−0.423107	+	0.153998i	−0.544793	−	0.838570i	$-0.683392\pi$
$13$	−1.52553	+	0.555249i	−0.423107	+	0.153998i	0.121687	+	0.992569i	$0.461170\pi$
$14$	2.13138	+	1.51252i	0.569637	+	0.404239i
$15$		0			0
$16$	2.08671	−	3.41257i	0.521677	−	0.853143i
$17$	0.683630	+	0.394694i	0.165805	+	0.0957273i	0.580606	−	0.814185i	$-0.302816\pi$
$17$	0.683630	+	0.394694i	0.165805	+	0.0957273i	−0.414802	+	0.909912i	$0.636149\pi$
$18$		0			0
$19$	−2.86200	+	1.65238i	−0.656589	+	0.379082i	−0.790976	−	0.611847i	$-0.790427\pi$
$19$	−2.86200	+	1.65238i	−0.656589	+	0.379082i	0.134387	+	0.990929i	$0.457093\pi$
$20$	−1.02000	+	0.356750i	−0.228078	+	0.0797717i
$21$		0			0
$22$	2.94546	+	6.42194i	0.627973	+	1.36916i
$23$	−3.15234	−	2.64512i	−0.657307	−	0.551546i	0.251971	−	0.967735i	$-0.418921\pi$
$23$	−3.15234	−	2.64512i	−0.657307	−	0.551546i	−0.909278	+	0.416188i	$0.863366\pi$
$24$		0			0
$25$	−4.42415	−	1.61026i	−0.884830	−	0.322052i
$26$	1.88895	−	1.30499i	0.370453	−	0.255929i
$27$		0			0
$28$	−3.45697	−	1.30783i	−0.653306	−	0.247156i
$29$	3.24174	−	8.90660i	0.601976	−	1.65391i	−0.145290	−	0.989389i	$-0.546412\pi$
$29$	3.24174	−	8.90660i	0.601976	−	1.65391i	0.747266	−	0.664525i	$-0.231366\pi$
$30$		0			0
$31$	3.70462	−	4.41499i	0.665369	−	0.792956i	−0.322777	−	0.946475i	$-0.604616\pi$
$31$	3.70462	−	4.41499i	0.665369	−	0.792956i	0.988146	+	0.153519i	$0.0490607\pi$
$32$	−1.63558	+	5.41525i	−0.289132	+	0.957289i
$33$		0			0
$34$	−1.07648	−	0.295728i	−0.184615	−	0.0507169i
$35$	0.499242	+	0.864712i	0.0843873	+	0.146163i
$36$		0			0
$37$	5.53013	−	9.57846i	0.909147	−	1.57469i	0.0938963	−	0.995582i	$-0.470068\pi$
$37$	5.53013	−	9.57846i	0.909147	−	1.57469i	0.815251	−	0.579108i	$-0.196599\pi$
$38$	3.32552	−	3.28386i	0.539471	−	0.532712i
$39$		0			0
$40$	1.26816	−	0.852696i	0.200514	−	0.134823i
$41$	2.62821	+	7.22095i	0.410458	+	1.12772i	0.956948	+	0.290258i	$0.0937412\pi$
$41$	2.62821	+	7.22095i	0.410458	+	1.12772i	−0.546491	+	0.837465i	$0.684037\pi$
$42$		0			0
$43$	−7.88044	+	1.38953i	−1.20176	+	0.211902i	−0.738458	−	0.674300i	$-0.764445\pi$
$43$	−7.88044	+	1.38953i	−1.20176	+	0.211902i	−0.463299	+	0.886202i	$0.653334\pi$
$44$	−6.32553	−	7.73445i	−0.953609	−	1.16601i
$45$		0			0
$46$	5.25874	+	2.49267i	0.775359	+	0.367524i
$47$	−2.39693	+	2.01126i	−0.349628	+	0.293372i	−0.800640	−	0.599145i	$-0.795507\pi$
$47$	−2.39693	+	2.01126i	−0.349628	+	0.293372i	0.451013	+	0.892517i	$0.351063\pi$
$48$		0			0
$49$	0.622483	−	3.53027i	0.0889261	−	0.504325i
$50$	6.62911	+	0.622106i	0.937498	+	0.0879791i
$51$		0			0
$52$	−2.11825	+	2.46074i	−0.293748	+	0.341243i
$53$			0.933485i			0.128224i	0.997943	+	0.0641120i	$0.0204215\pi$
$53$			0.933485i			0.128224i	−0.997943	+	0.0641120i	$0.979579\pi$
$54$		0			0
$55$			2.69922i			0.363962i
$56$	5.19762	+	0.553960i	0.694561	+	0.0740260i
$57$		0			0
$58$	−1.25241	+	13.3456i	−0.164449	+	1.75236i
$59$	0.461077	−	2.61490i	0.0600271	−	0.340431i	−0.939973	−	0.341250i	$-0.889150\pi$
$59$	0.461077	−	2.61490i	0.0600271	−	0.340431i	1.00000		0.000819421i	$0.000260830\pi$
$60$		0			0
$61$	−4.29949	+	3.60770i	−0.550493	+	0.461919i	−0.875108	−	0.483928i	$-0.839210\pi$
$61$	−4.29949	+	3.60770i	−0.550493	+	0.461919i	0.324615	+	0.945846i	$0.394765\pi$
$62$	−3.49110	+	7.36511i	−0.443370	+	0.935370i
$63$		0			0
$64$	0.302524	−	7.99428i	0.0378154	−	0.999285i
$65$	0.863806	−	0.152312i	0.107142	−	0.0188920i
$66$		0			0
$67$	2.15593	+	5.92336i	0.263388	+	0.723653i	0.998933	+	0.0461775i	$0.0147040\pi$
$67$	2.15593	+	5.92336i	0.263388	+	0.723653i	−0.735545	+	0.677476i	$0.763074\pi$
$68$	1.57865	+	0.0199049i	0.191439	+	0.00241383i
$69$		0			0
$70$	−0.992169	−	1.00476i	−0.118587	−	0.120092i
$71$	−4.53203	+	7.84970i	−0.537853	+	0.931588i	0.461167	+	0.887313i	$0.347431\pi$
$71$	−4.53203	+	7.84970i	−0.537853	+	0.931588i	−0.999019	+	0.0442746i	$0.985902\pi$
$72$		0			0
$73$	5.77108	+	9.99580i	0.675454	+	1.16992i	0.976336	+	0.216259i	$0.0693855\pi$
$73$	5.77108	+	9.99580i	0.675454	+	1.16992i	−0.300882	+	0.953661i	$0.597281\pi$
$74$	−4.14350	+	15.0828i	−0.481672	+	1.75334i
$75$		0			0
$76$	−3.37666	+	5.68189i	−0.387330	+	0.651757i
$77$	−5.93457	+	7.07254i	−0.676307	+	0.805991i
$78$		0			0
$79$	−0.275423	+	0.756719i	−0.0309875	+	0.0851375i	−0.954222	−	0.299100i	$-0.903313\pi$
$79$	−0.275423	+	0.756719i	−0.0309875	+	0.0851375i	0.923234	+	0.384238i	$0.125536\pi$
$80$	−1.43047	+	1.62000i	−0.159932	+	0.181121i
$81$		0			0
$82$	−6.17702	−	8.94113i	−0.682137	−	0.987383i
$83$	15.0247	+	5.46855i	1.64918	+	0.600252i	0.988608	−	0.150513i	$-0.0480925\pi$
$83$	15.0247	+	5.46855i	1.64918	+	0.600252i	0.660570	+	0.750765i	$0.270315\pi$
$84$		0			0
$85$	−0.326718	−	0.274149i	−0.0354375	−	0.0297356i
$86$	10.2862	−	4.71783i	1.10919	−	0.508737i
$87$		0			0
$88$	11.4196	+	8.32231i	1.21733	+	0.887161i
$89$	5.41508	−	3.12640i	0.573997	−	0.331398i	−0.184747	−	0.982786i	$-0.559147\pi$
$89$	5.41508	−	3.12640i	0.573997	−	0.331398i	0.758744	+	0.651389i	$0.225813\pi$
$90$		0			0
$91$	2.59824	+	1.50009i	0.272369	+	0.157252i
$92$	−8.08647	−	1.53123i	−0.843072	−	0.159641i
$93$		0			0
$94$	2.56089	−	3.60870i	0.264136	−	0.372208i
$95$	1.67785	−	0.610689i	0.172144	−	0.0626553i
$96$		0			0
$97$	1.63933	+	9.29708i	0.166448	+	0.943975i	0.947559	+	0.319582i	$0.103543\pi$
$97$	1.63933	+	9.29708i	0.166448	+	0.943975i	−0.781110	+	0.624393i	$0.785346\pi$
$98$	0.409997	+	5.05297i	0.0414160	+	0.510427i
$99$		0			0
$100$	−9.29299	+	1.51806i	−0.929299	+	0.151806i
$101$	−6.31653	−	7.52775i	−0.628518	−	0.749039i	0.353992	−	0.935249i	$-0.384824\pi$
$101$	−6.31653	−	7.52775i	−0.628518	−	0.749039i	−0.982510	+	0.186210i	$0.940380\pi$
$102$		0			0
$103$	−6.85056	−	1.20794i	−0.675005	−	0.119022i	−0.174370	−	0.984680i	$-0.555789\pi$
$103$	−6.85056	−	1.20794i	−0.675005	−	0.119022i	−0.500635	+	0.865658i	$0.666900\pi$
$104$	2.01892	−	4.12412i	0.197972	−	0.404403i
$105$		0			0
$106$	−0.333634	−	1.27729i	−0.0324054	−	0.124062i
$107$	−2.51779			−0.243404			−0.121702	−	0.992567i	$-0.538835\pi$
$107$	−2.51779			−0.243404			−0.121702	+	0.992567i	$0.538835\pi$
$108$		0			0
$109$	5.76924			0.552593			0.276296	−	0.961072i	$-0.410893\pi$
$109$	5.76924			0.552593			0.276296	+	0.961072i	$0.410893\pi$
$110$	−0.964718	−	3.69335i	−0.0919823	−	0.352148i
$111$		0			0
$112$	−7.30992	+	1.09968i	−0.690723	+	0.103910i
$113$	−4.36693	−	0.770007i	−0.410806	−	0.0724362i	−0.0355738	−	0.999367i	$-0.511326\pi$
$113$	−4.36693	−	0.770007i	−0.410806	−	0.0724362i	−0.375232	+	0.926931i	$0.622437\pi$
$114$		0			0
$115$	1.42914	+	1.70318i	0.133268	+	0.158823i
$116$	−3.05612	−	18.7084i	−0.283753	−	1.73704i
$117$		0			0
$118$	0.303687	+	3.74277i	0.0279567	+	0.344550i
$119$	−0.253322	−	1.43666i	−0.0232220	−	0.131698i
$120$		0			0
$121$	−13.1167	+	4.77409i	−1.19243	+	0.434008i
$122$	4.59360	−	6.47310i	0.415885	−	0.586047i
$123$		0			0
$124$	2.14455	−	11.3255i	0.192587	−	1.01706i
$125$	4.54248	+	2.62260i	0.406292	+	0.234573i
$126$		0			0
$127$	3.47118	−	2.00409i	0.308018	−	0.177834i	−0.338021	−	0.941138i	$-0.609758\pi$
$127$	3.47118	−	2.00409i	0.308018	−	0.177834i	0.646039	+	0.763304i	$0.276424\pi$
$128$	2.44326	+	11.0467i	0.215956	+	0.976403i
$129$		0			0
$130$	−1.12751	+	0.517140i	−0.0988894	+	0.0453561i
$131$	1.84218	+	1.54577i	0.160952	+	0.135055i	0.719707	−	0.694278i	$-0.244276\pi$
$131$	1.84218	+	1.54577i	0.160952	+	0.135055i	−0.558755	+	0.829333i	$0.688721\pi$
$132$		0			0
$133$	5.73902	+	2.08883i	0.497636	+	0.181125i
$134$	−5.06701	−	7.33442i	−0.437723	−	0.633598i
$135$		0			0
$136$	−2.16719	+	0.536984i	−0.185835	+	0.0460460i
$137$	−1.46523	+	4.02570i	−0.125183	+	0.343939i	−0.986415	−	0.164275i	$-0.947472\pi$
$137$	−1.46523	+	4.02570i	−0.125183	+	0.343939i	0.861231	+	0.508213i	$0.169694\pi$
$138$		0			0
$139$	11.4619	−	13.6598i	0.972187	−	1.15861i	−0.0151364	−	0.999885i	$-0.504818\pi$
$139$	11.4619	−	13.6598i	0.972187	−	1.15861i	0.987323	−	0.158722i	$-0.0507373\pi$
$140$	1.71670	+	1.02021i	0.145087	+	0.0862233i
$141$		0			0
$142$	3.39566	−	12.3606i	0.284958	−	1.03728i
$143$	4.05523	+	7.02386i	0.339115	+	0.587365i
$144$		0			0
$145$	−2.56050	+	4.43492i	−0.212638	+	0.368300i
$146$	−11.4692	−	11.6147i	−0.949195	−	0.961239i
$147$		0			0
$148$	0.278891	−	22.1188i	0.0229247	−	1.81815i
$149$	−4.08657	−	11.2278i	−0.334785	−	0.919814i	−0.986848	−	0.161650i	$-0.948319\pi$
$149$	−4.08657	−	11.2278i	−0.334785	−	0.919814i	0.652063	−	0.758165i	$-0.273904\pi$
$150$		0			0
$151$	18.0852	−	3.18891i	1.47175	−	0.259510i	0.620475	−	0.784226i	$-0.286940\pi$
$151$	18.0852	−	3.18891i	1.47175	−	0.259510i	0.851277	+	0.524716i	$0.175829\pi$
$152$	2.58956	−	8.98140i	0.210041	−	0.728488i
$153$		0			0
$154$	5.59253	−	11.7985i	0.450659	−	0.950746i
$155$	−2.38539	+	2.00158i	−0.191599	+	0.160770i
$156$		0			0
$157$	3.60079	−	20.4211i	0.287374	−	1.62978i	−0.409306	−	0.912397i	$-0.634229\pi$
$157$	3.60079	−	20.4211i	0.287374	−	1.62978i	0.696680	−	0.717382i	$-0.254660\pi$
$158$	0.106407	−	1.13386i	0.00846526	−	0.0902051i
$159$		0			0
$160$	1.37833	−	2.72791i	0.108966	−	0.215661i
$161$			7.60485i			0.599346i
$162$		0			0
$163$		−	2.03697i		−	0.159548i	−0.996813	−	0.0797739i	$-0.974580\pi$
$163$		−	2.03697i		−	0.159548i	0.996813	−	0.0797739i	$-0.0254198\pi$
$164$	11.6477	+	10.0265i	0.909530	+	0.782938i
$165$		0			0
$166$	−22.5129	−	2.11272i	−1.74734	−	0.163978i
$167$	1.07213	−	6.08034i	0.0829637	−	0.470511i	−0.914814	−	0.403876i	$-0.867663\pi$
$167$	1.07213	−	6.08034i	0.0829637	−	0.470511i	0.997777	−	0.0666346i	$-0.0212262\pi$
$168$		0			0
$169$	−7.93963	+	6.66214i	−0.610741	+	0.512472i
$170$	0.545033	+	0.258348i	0.0418021	+	0.0198144i
$171$		0			0
$172$	−12.3885	+	10.1318i	−0.944616	+	0.772543i
$173$	−14.6443	+	2.58218i	−1.11338	+	0.196320i	−0.699934	−	0.714207i	$-0.746787\pi$
$173$	−14.6443	+	2.58218i	−1.11338	+	0.196320i	−0.413450	+	0.910527i	$0.635676\pi$
$174$		0			0
$175$	2.97583	+	8.17603i	0.224952	+	0.618050i
$176$	−18.5999	−	7.30602i	−1.40202	−	0.550712i
$177$		0			0
$178$	−6.29209	+	6.21325i	−0.471612	+	0.465703i
$179$	2.80761	−	4.86292i	0.209850	−	0.363472i	−0.741817	−	0.670603i	$-0.766036\pi$
$179$	2.80761	−	4.86292i	0.209850	−	0.363472i	0.951667	+	0.307131i	$0.0993690\pi$
$180$		0			0
$181$	−3.04279	−	5.27027i	−0.226169	−	0.391736i	0.730500	−	0.682912i	$-0.239287\pi$
$181$	−3.04279	−	5.27027i	−0.226169	−	0.391736i	−0.956670	+	0.291176i	$0.905954\pi$
$182$	−4.09133	−	1.12396i	−0.303269	−	0.0833133i
$183$		0			0
$184$	11.6120	−	0.794970i	0.856050	−	0.0586059i
$185$	−3.84115	+	4.57770i	−0.282407	+	0.336560i
$186$		0			0
$187$	1.34881	−	3.70583i	0.0986349	−	0.270997i
$188$	−2.21431	+	5.85308i	−0.161495	+	0.426880i
$189$		0			0
$190$	−2.07755	+	1.43528i	−0.150721	+	0.104126i
$191$	4.55974	+	1.65961i	0.329931	+	0.120085i	0.501674	−	0.865057i	$-0.332718\pi$
$191$	4.55974	+	1.65961i	0.329931	+	0.120085i	−0.171743	+	0.985142i	$0.554940\pi$
$192$		0			0
$193$	4.04332	+	3.39275i	0.291044	+	0.244215i	0.776605	−	0.629988i	$-0.216940\pi$
$193$	4.04332	+	3.39275i	0.291044	+	0.244215i	−0.485561	+	0.874203i	$0.661385\pi$
$194$	−5.56594	−	12.1353i	−0.399611	−	0.871266i
$195$		0			0
$196$	−2.36697	−	6.76748i	−0.169069	−	0.483391i
$197$	−2.31117	+	1.33435i	−0.164664	+	0.0950687i	−0.580067	−	0.814569i	$-0.696974\pi$
$197$	−2.31117	+	1.33435i	−0.164664	+	0.0950687i	0.415403	+	0.909637i	$0.363640\pi$
$198$		0			0
$199$	9.82614	+	5.67313i	0.696557	+	0.402157i	0.806064	−	0.591829i	$-0.201594\pi$
$199$	9.82614	+	5.67313i	0.696557	+	0.402157i	−0.109507	+	0.993986i	$0.534927\pi$
$200$	12.1731	−	5.39854i	0.860768	−	0.381735i
$201$		0			0
$202$	11.3334	+	8.04269i	0.797416	+	0.565882i
$203$	−16.4598	+	5.99087i	−1.15525	+	0.420477i
$204$		0			0
$205$	−0.720954	−	4.08873i	−0.0503536	−	0.285570i
$206$	9.80538	−	0.795606i	0.683173	−	0.0554325i
$207$		0			0
$208$	−1.28851	+	6.36464i	−0.0893424	+	0.441308i
$209$	10.6125	+	12.6474i	0.734080	+	0.874842i
$210$		0			0
$211$	−4.51015	−	0.795260i	−0.310491	−	0.0547480i	0.0162314	−	0.999868i	$-0.494833\pi$
$211$	−4.51015	−	0.795260i	−0.310491	−	0.0547480i	−0.326723	+	0.945120i	$0.605944\pi$
$212$	0.913026	+	1.62848i	0.0627069	+	0.111845i
$213$		0			0
$214$	3.44510	−	0.899874i	0.235502	−	0.0615141i
$215$	4.32342			0.294855
$216$		0			0
$217$	−10.6509			−0.723033
$218$	−7.89408	+	2.06196i	−0.534655	+	0.139654i
$219$		0			0
$220$	2.64006	+	4.70884i	0.177993	+	0.317470i
$221$	−1.26205	−	0.222534i	−0.0848949	−	0.0149693i
$222$		0			0
$223$	−11.8712	−	14.1475i	−0.794953	−	0.947388i	0.204552	−	0.978856i	$-0.434426\pi$
$223$	−11.8712	−	14.1475i	−0.794953	−	0.947388i	−0.999505	+	0.0314676i	$0.989982\pi$
$224$	9.60918	−	4.11731i	0.642040	−	0.275099i
$225$		0			0
$226$	6.25050	−	0.507164i	0.415777	−	0.0337360i
$227$	−2.30342	−	13.0633i	−0.152883	−	0.867043i	−0.960696	−	0.277604i	$-0.910460\pi$
$227$	−2.30342	−	13.0633i	−0.152883	−	0.867043i	0.807813	−	0.589439i	$-0.200651\pi$
$228$		0			0
$229$	3.24361	−	1.18058i	0.214344	−	0.0780147i	−0.232617	−	0.972569i	$-0.574729\pi$
$229$	3.24361	−	1.18058i	0.214344	−	0.0780147i	0.446960	+	0.894554i	$0.352507\pi$
$230$	−2.56423	−	1.81969i	−0.169080	−	0.119987i
$231$		0			0
$232$	10.8682	+	24.5066i	0.713534	+	1.60894i
$233$	14.1574	+	8.17379i	0.927483	+	0.535483i	0.886015	−	0.463657i	$-0.153463\pi$
$233$	14.1574	+	8.17379i	0.927483	+	0.535483i	0.0414686	+	0.999140i	$0.486796\pi$
$234$		0			0
$235$	1.46406	−	0.845277i	0.0955050	−	0.0551398i
$236$	−1.75323	−	5.01271i	−0.114125	−	0.326300i
$237$		0			0
$238$	0.860094	+	1.87525i	0.0557516	+	0.121554i
$239$	0.797855	+	0.669480i	0.0516089	+	0.0433050i	0.668227	−	0.743957i	$-0.267053\pi$
$239$	0.797855	+	0.669480i	0.0516089	+	0.0433050i	−0.616618	+	0.787262i	$0.711498\pi$
$240$		0			0
$241$	15.4743	+	5.63219i	0.996788	+	0.362801i	0.788345	−	0.615233i	$-0.210938\pi$
$241$	15.4743	+	5.63219i	0.996788	+	0.362801i	0.208443	+	0.978035i	$0.433160\pi$
$242$	16.2414	−	11.2204i	1.04403	−	0.721275i
$243$		0			0
$244$	−3.97192	+	10.4990i	−0.254276	+	0.672128i
$245$	−0.662426	+	1.82000i	−0.0423208	+	0.116276i
$246$		0			0
$247$	3.44860	−	4.10988i	0.219429	−	0.261506i
$248$	1.11339	+	16.2632i	0.0707005	+	1.03271i
$249$		0			0
$250$	−7.15283	−	1.96501i	−0.452385	−	0.124278i
$251$	−6.70961	−	11.6214i	−0.423507	−	0.733535i	0.572773	−	0.819714i	$-0.305868\pi$
$251$	−6.70961	−	11.6214i	−0.423507	−	0.733535i	−0.996280	+	0.0861790i	$0.972534\pi$
$252$		0			0
$253$	−10.2792	+	17.8040i	−0.646245	+	1.11933i
$254$	−4.03337	+	3.98283i	−0.253076	+	0.249905i
$255$		0			0
$256$	−7.29131	−	14.2421i	−0.455707	−	0.890130i
$257$	−0.987706	−	2.71370i	−0.0616114	−	0.169276i	0.905068	−	0.425268i	$-0.139820\pi$
$257$	−0.987706	−	2.71370i	−0.0616114	−	0.169276i	−0.966679	+	0.255992i	$0.917598\pi$
$258$		0			0
$259$	−20.1293	+	3.54934i	−1.25077	+	0.220545i
$260$	1.35795	−	1.11059i	0.0842167	−	0.0688756i
$261$		0			0
$262$	−3.07313	−	1.45668i	−0.189859	−	0.0899940i
$263$	−10.7439	+	9.01519i	−0.662496	+	0.555900i	−0.910834	−	0.412773i	$-0.864560\pi$
$263$	−10.7439	+	9.01519i	−0.662496	+	0.555900i	0.248338	+	0.968674i	$0.420116\pi$
$264$		0			0
$265$	0.0875803	−	0.496692i	0.00538001	−	0.0305116i
$266$	−8.59929	−	0.806997i	−0.527257	−	0.0494802i
$267$		0			0
$268$	9.55460	+	8.22475i	0.583640	+	0.502406i
$269$		−	20.1185i		−	1.22665i	−0.789831	−	0.613325i	$-0.789832\pi$
$269$		−	20.1185i		−	1.22665i	0.789831	−	0.613325i	$-0.210168\pi$
$270$		0			0
$271$			19.1968i			1.16612i	0.812428	+	0.583062i	$0.198145\pi$
$271$			19.1968i			1.16612i	−0.812428	+	0.583062i	$0.801855\pi$
$272$	2.77346	−	1.50933i	0.168165	−	0.0915163i
$273$		0			0
$274$	0.566077	−	6.03207i	0.0341980	−	0.364411i
$275$	−4.08436	+	23.1635i	−0.246296	+	1.39681i
$276$		0			0
$277$	20.3674	−	17.0903i	1.22376	−	1.02686i	0.225141	−	0.974326i	$-0.427716\pi$
$277$	20.3674	−	17.0903i	1.22376	−	1.02686i	0.998619	−	0.0525311i	$-0.0167289\pi$
$278$	−10.8013	+	22.7873i	−0.647819	+	1.36669i
$279$		0			0
$280$	−2.71360	−	0.782398i	−0.162168	−	0.0467572i
$281$	−2.17919	+	0.384249i	−0.129999	+	0.0229224i	−0.238269	−	0.971199i	$-0.576580\pi$
$281$	−2.17919	+	0.384249i	−0.129999	+	0.0229224i	0.108270	+	0.994122i	$0.465469\pi$
$282$		0			0
$283$	8.19432	+	22.5137i	0.487102	+	1.33830i	0.903293	+	0.429024i	$0.141142\pi$
$283$	8.19432	+	22.5137i	0.487102	+	1.33830i	−0.416192	+	0.909277i	$0.636635\pi$
$284$	−0.228556	+	18.1267i	−0.0135623	+	1.07562i
$285$		0			0
$286$	−8.05916	−	8.16142i	−0.476548	−	0.482595i
$287$	7.10053	−	12.2985i	0.419131	−	0.725957i
$288$		0			0
$289$	−8.18843	−	14.1828i	−0.481673	−	0.834281i
$290$	1.91848	−	6.98346i	0.112657	−	0.410083i
$291$		0			0
$292$	19.8445	+	11.7933i	1.16131	+	0.690150i
$293$	17.5281	−	20.8891i	1.02400	−	1.22036i	0.0488514	−	0.998806i	$-0.484444\pi$
$293$	17.5281	−	20.8891i	1.02400	−	1.22036i	0.975149	−	0.221550i	$-0.0711116\pi$
$294$		0			0
$295$	−0.490663	+	1.34809i	−0.0285675	+	0.0784886i
$296$	7.52378	+	30.3649i	0.437311	+	1.76492i
$297$		0			0
$298$	9.60456	+	13.9024i	0.556377	+	0.805347i
$299$	6.27769	+	2.28489i	0.363048	+	0.132139i
$300$		0			0
$301$	11.3283	+	9.50559i	0.652953	+	0.547893i
$302$	−23.6063	+	10.8272i	−1.35839	+	0.623034i
$303$		0			0
$304$	−0.333300	+	13.2148i	−0.0191161	+	0.757922i
$305$	2.62617	−	1.51622i	0.150374	−	0.0868184i
$306$		0			0
$307$	−21.0055	−	12.1276i	−1.19885	−	0.692156i	−0.238551	−	0.971130i	$-0.576672\pi$
$307$	−21.0055	−	12.1276i	−1.19885	−	0.692156i	−0.960299	+	0.278974i	$0.910006\pi$
$308$	−3.43544	+	18.1427i	−0.195753	+	1.03378i
$309$		0			0
$310$	2.54856	−	3.59132i	0.144748	−	0.203973i
$311$	18.0900	−	6.58424i	1.02579	−	0.373358i	0.226315	−	0.974054i	$-0.427332\pi$
$311$	18.0900	−	6.58424i	1.02579	−	0.373358i	0.799477	+	0.600696i	$0.205110\pi$
$312$		0			0
$313$	−1.18433	−	6.71666i	−0.0669422	−	0.379648i	−0.999811	−	0.0194321i	$-0.993814\pi$
$313$	−1.18433	−	6.71666i	−0.0669422	−	0.379648i	0.932869	−	0.360216i	$-0.117297\pi$
$314$	2.37165	+	29.2292i	0.133840	+	1.64950i
$315$		0			0
$316$	0.259652	+	1.58950i	0.0146066	+	0.0894163i
$317$	7.41728	+	8.83957i	0.416596	+	0.496480i	0.933006	−	0.359862i	$-0.117176\pi$
$317$	7.41728	+	8.83957i	0.416596	+	0.496480i	−0.516409	+	0.856342i	$0.672732\pi$
$318$		0			0
$319$	−46.6323	−	8.22253i	−2.61091	−	0.460373i
$320$	−0.910997	+	4.22524i	−0.0509263	+	0.236198i
$321$		0			0
$322$	−2.71802	−	10.4058i	−0.151470	−	0.579890i
$323$	−2.60873			−0.145154
$324$		0			0
$325$	7.64329			0.423973
$326$	0.728026	+	2.78720i	0.0403217	+	0.154369i
$327$		0			0
$328$	−19.5211	−	9.55636i	−1.07787	−	0.527662i
$329$	5.69461	+	1.00411i	0.313954	+	0.0553586i
$330$		0			0
$331$	13.2173	+	15.7517i	0.726487	+	0.865793i	0.995244	−	0.0974147i	$-0.0310573\pi$
$331$	13.2173	+	15.7517i	0.726487	+	0.865793i	−0.268757	+	0.963208i	$0.586613\pi$
$332$	31.5596	−	5.15543i	1.73206	−	0.282941i
$333$		0			0
$334$	0.706155	+	8.70295i	0.0386391	+	0.476204i
$335$	−0.591400	−	3.35399i	−0.0323116	−	0.183248i
$336$		0			0
$337$	−10.0326	+	3.65156i	−0.546509	+	0.198913i	−0.600495	−	0.799629i	$-0.705030\pi$
$337$	−10.0326	+	3.65156i	−0.546509	+	0.198913i	0.0539858	+	0.998542i	$0.482807\pi$
$338$	8.48274	−	11.9535i	0.461400	−	0.650186i
$339$		0			0
$340$	−0.838107	−	0.158701i	−0.0454527	−	0.00860678i
$341$	−24.9354	−	14.3964i	−1.35033	−	0.779611i
$342$		0			0
$343$	−16.9404	+	9.78053i	−0.914694	+	0.528099i
$344$	13.3301	−	18.2911i	0.718711	−	0.986192i
$345$		0			0
$346$	19.1150	−	8.76718i	1.02763	−	0.471327i
$347$	−0.957389	−	0.803344i	−0.0513953	−	0.0431258i	0.616728	−	0.787176i	$-0.288458\pi$
$347$	−0.957389	−	0.803344i	−0.0513953	−	0.0431258i	−0.668123	+	0.744050i	$0.732902\pi$
$348$		0			0
$349$	−18.0738	−	6.57834i	−0.967470	−	0.352130i	−0.190514	−	0.981685i	$-0.561015\pi$
$349$	−18.0738	−	6.57834i	−0.967470	−	0.352130i	−0.776957	+	0.629554i	$0.783238\pi$
$350$	−6.99401	−	10.1237i	−0.373846	−	0.541136i
$351$		0			0
$352$	28.0616	+	3.34912i	1.49569	+	0.178509i
$353$	2.12947	−	5.85067i	0.113340	−	0.311400i	−0.870034	−	0.492992i	$-0.835903\pi$
$353$	2.12947	−	5.85067i	0.113340	−	0.311400i	0.983374	+	0.181593i	$0.0581253\pi$
$354$		0			0
$355$	3.14788	−	3.75150i	0.167072	−	0.199109i
$356$	6.38884	−	10.7505i	0.338608	−	0.569774i
$357$		0			0
$358$	−2.10363	+	7.65742i	−0.111180	+	0.404707i
$359$	4.51666	+	7.82308i	0.238380	+	0.412886i	0.960250	−	0.279143i	$-0.0900503\pi$
$359$	4.51666	+	7.82308i	0.238380	+	0.412886i	−0.721870	+	0.692029i	$0.756717\pi$
$360$		0			0
$361$	−4.03929	+	6.99626i	−0.212594	+	0.368224i
$362$	6.04710	+	6.12383i	0.317829	+	0.321861i
$363$		0			0
$364$	5.99989	+	0.0756516i	0.314480	+	0.00396522i
$365$	−2.13288	−	5.86005i	−0.111640	−	0.306729i
$366$		0			0
$367$	7.28951	−	1.28534i	0.380509	−	0.0670941i	0.0198778	−	0.999802i	$-0.493672\pi$
$367$	7.28951	−	1.28534i	0.380509	−	0.0670941i	0.360632	+	0.932708i	$0.382561\pi$
$368$	−15.6047	+	5.23798i	−0.813450	+	0.273048i
$369$		0			0
$370$	3.61977	−	7.63655i	0.188183	−	0.397005i
$371$	1.32152	−	1.10889i	0.0686099	−	0.0575705i
$372$		0			0
$373$	0.532880	−	3.02211i	0.0275915	−	0.156479i	−0.967899	−	0.251339i	$-0.919129\pi$
$373$	0.532880	−	3.02211i	0.0275915	−	0.156479i	0.995491	+	0.0948598i	$0.0302403\pi$
$374$	−0.521098	+	5.55278i	−0.0269454	+	0.287127i
$375$		0			0
$376$	0.937922	−	8.80021i	0.0483696	−	0.453836i
$377$			15.3873i			0.792486i
$378$		0			0
$379$		−	30.1832i		−	1.55041i	−0.631712	−	0.775203i	$-0.717647\pi$
$379$		−	30.1832i		−	1.55041i	0.631712	−	0.775203i	$-0.282353\pi$
$380$	2.32975	−	2.70644i	0.119513	−	0.138837i
$381$		0			0
$382$	−6.83228	−	0.641172i	−0.349570	−	0.0328052i
$383$	3.37652	−	19.1492i	0.172532	−	0.978479i	−0.768422	−	0.639944i	$-0.778958\pi$
$383$	3.37652	−	19.1492i	0.172532	−	0.978479i	0.940954	−	0.338535i	$-0.109931\pi$
$384$		0			0
$385$	3.82124	−	3.20640i	0.194748	−	0.163413i
$386$	−6.74509	−	3.19721i	−0.343316	−	0.162733i
$387$		0			0
$388$	11.9532	+	14.6155i	0.606829	+	0.741992i
$389$	20.0904	−	3.54247i	1.01862	−	0.179610i	0.360688	−	0.932687i	$-0.382542\pi$
$389$	20.0904	−	3.54247i	1.01862	−	0.179610i	0.657933	+	0.753076i	$0.271431\pi$
$390$		0			0
$391$	−1.11102	−	3.05249i	−0.0561865	−	0.154371i
$392$	5.65748	+	8.41401i	0.285746	+	0.424972i
$393$		0			0
$394$	2.68548	−	2.65183i	0.135292	−	0.133597i
$395$	0.217544	−	0.376797i	0.0109458	−	0.0189587i
$396$		0			0
$397$	−8.78858	−	15.2223i	−0.441086	−	0.763984i	0.556684	−	0.830724i	$-0.312073\pi$
$397$	−8.78858	−	15.2223i	−0.441086	−	0.763984i	−0.997770	+	0.0667406i	$0.978740\pi$
$398$	−15.4728	−	4.25064i	−0.775580	−	0.213065i
$399$		0			0
$400$	−14.7270	+	11.7376i	−0.736352	+	0.586880i
$401$	15.5813	−	18.5691i	0.778094	−	0.927297i	−0.220751	−	0.975330i	$-0.570851\pi$
$401$	15.5813	−	18.5691i	0.778094	−	0.927297i	0.998846	+	0.0480334i	$0.0152954\pi$
$402$		0			0
$403$	−3.20010	+	8.79220i	−0.159408	+	0.437971i
$404$	−18.3821	−	6.95422i	−0.914543	−	0.345986i
$405$		0			0
$406$	20.3808	−	14.0802i	1.01148	−	0.698788i
$407$	−51.9231	−	18.8984i	−2.57373	−	0.936761i
$408$		0			0
$409$	15.8369	+	13.2887i	0.783085	+	0.657086i	0.944024	−	0.329878i	$-0.107008\pi$
$409$	15.8369	+	13.2887i	0.783085	+	0.657086i	−0.160939	+	0.986964i	$0.551452\pi$
$410$	2.44783	+	5.33696i	0.120890	+	0.263574i
$411$		0			0
$412$	−13.1324	+	4.59314i	−0.646987	+	0.226288i
$413$	−4.24958	+	2.45350i	−0.209108	+	0.120729i
$414$		0			0
$415$	−7.48135	−	4.31936i	−0.367245	−	0.212029i
$416$	−0.511682	−	9.16929i	−0.0250873	−	0.449561i
$417$		0			0
$418$	−19.0414	−	13.5126i	−0.931344	−	0.660923i
$419$	8.00463	−	2.91345i	0.391052	−	0.142331i	−0.139009	−	0.990291i	$-0.544392\pi$
$419$	8.00463	−	2.91345i	0.391052	−	0.142331i	0.530060	+	0.847960i	$0.322169\pi$
$420$		0			0
$421$	−2.47727	−	14.0493i	−0.120735	−	0.684721i	−0.983750	−	0.179543i	$-0.942538\pi$
$421$	−2.47727	−	14.0493i	−0.120735	−	0.684721i	0.863015	−	0.505178i	$-0.168573\pi$
$422$	6.45549	−	0.523797i	0.314248	−	0.0254980i
$423$		0			0
$424$	−1.83133	−	1.90194i	−0.0889372	−	0.0923665i
$425$	−2.38892	−	2.84701i	−0.115880	−	0.138100i
$426$		0			0
$427$	10.2147	+	1.80113i	0.494325	+	0.0871629i
$428$	−4.39233	+	2.46261i	−0.212311	+	0.119035i
$429$		0			0
$430$	−5.91577	+	1.54522i	−0.285284	+	0.0745172i
$431$	1.49028			0.0717841			0.0358920	−	0.999356i	$-0.488573\pi$
$431$	1.49028			0.0717841			0.0358920	+	0.999356i	$0.488573\pi$
$432$		0			0
$433$	2.83288			0.136139			0.0680697	−	0.997681i	$-0.478316\pi$
$433$	2.83288			0.136139			0.0680697	+	0.997681i	$0.478316\pi$
$434$	14.5738	−	3.80672i	0.699562	−	0.182728i
$435$		0			0
$436$	10.0646	−	5.64280i	0.482005	−	0.270241i
$437$	13.3927	+	2.36150i	0.640662	+	0.112966i
$438$		0			0
$439$	17.2666	+	20.5775i	0.824089	+	0.982112i	0.999997	−	0.00229504i	$-0.000730536\pi$
$439$	17.2666	+	20.5775i	0.824089	+	0.982112i	−0.175908	+	0.984407i	$0.556286\pi$
$440$	−5.29538	−	5.49956i	−0.252447	−	0.262181i
$441$		0			0
$442$	1.80641	−	0.146572i	0.0859222	−	0.00697170i
$443$	4.52430	+	25.6586i	0.214956	+	1.21908i	0.880983	+	0.473148i	$0.156882\pi$
$443$	4.52430	+	25.6586i	0.214956	+	1.21908i	−0.666027	+	0.745928i	$0.732006\pi$
$444$		0			0
$445$	−3.17460	+	1.15546i	−0.150490	+	0.0547740i
$446$	21.2998	+	15.1153i	1.00858	+	0.715730i
$447$		0			0
$448$	−11.6767	+	9.06812i	−0.551674	+	0.428429i
$449$	−19.5356	−	11.2789i	−0.921940	−	0.532282i	−0.0376867	−	0.999290i	$-0.511999\pi$
$449$	−19.5356	−	11.2789i	−0.921940	−	0.532282i	−0.884254	+	0.467007i	$0.845332\pi$
$450$		0			0
$451$	33.2467	−	19.1950i	1.56553	−	0.903857i
$452$	−8.37133	+	2.92792i	−0.393754	+	0.137718i
$453$		0			0
$454$	7.82069	+	17.0514i	0.367043	+	0.800260i
$455$	−1.24174	−	1.04194i	−0.0582137	−	0.0488471i
$456$		0			0
$457$	−13.9247	−	5.06817i	−0.651370	−	0.237079i	−0.00486385	−	0.999988i	$-0.501548\pi$
$457$	−13.9247	−	5.06817i	−0.651370	−	0.237079i	−0.646506	+	0.762909i	$0.723770\pi$
$458$	−4.01630	+	2.77468i	−0.187669	+	0.129652i
$459$		0			0
$460$	4.15902	+	1.57342i	0.193915	+	0.0733611i
$461$	−10.5924	+	29.1025i	−0.493339	+	1.35544i	0.404267	+	0.914641i	$0.367527\pi$
$461$	−10.5924	+	29.1025i	−0.493339	+	1.35544i	−0.897606	+	0.440798i	$0.854696\pi$
$462$		0			0
$463$	−14.7162	+	17.5380i	−0.683918	+	0.815062i	−0.990606	−	0.136748i	$-0.956335\pi$
$463$	−14.7162	+	17.5380i	−0.683918	+	0.815062i	0.306687	+	0.951810i	$0.400779\pi$
$464$	−23.6299	−	29.6481i	−1.09699	−	1.37638i
$465$		0			0
$466$	−22.2930	−	6.12429i	−1.03271	−	0.283702i
$467$	−17.9763	−	31.1359i	−0.831844	−	1.44080i	−0.896575	−	0.442893i	$-0.853952\pi$
$467$	−17.9763	−	31.1359i	−0.831844	−	1.44080i	0.0647308	−	0.997903i	$-0.479381\pi$
$468$		0			0
$469$	5.82458	−	10.0885i	0.268954	−	0.465842i
$470$	−1.70118	+	1.67986i	−0.0784695	+	0.0774863i
$471$		0			0
$472$	4.19053	+	6.23231i	0.192885	+	0.286865i
$473$	13.6729	+	37.5659i	0.628680	+	1.72728i
$474$		0			0
$475$	15.3227	−	2.70181i	0.703054	−	0.123967i
$476$	−1.84710	−	2.25851i	−0.0846616	−	0.103519i
$477$		0			0
$478$	−1.33099	−	0.630894i	−0.0608779	−	0.0288564i
$479$	15.6682	−	13.1472i	0.715899	−	0.600711i	−0.210348	−	0.977627i	$-0.567460\pi$
$479$	15.6682	−	13.1472i	0.715899	−	0.600711i	0.926248	+	0.376916i	$0.123015\pi$
$480$		0			0
$481$	−3.11797	+	17.6829i	−0.142167	+	0.806269i
$482$	−23.1866	−	2.17593i	−1.05612	−	0.0991111i
$483$		0			0
$484$	−18.2129	+	21.1577i	−0.827859	+	0.961714i
$485$		−	5.10063i		−	0.231608i
$486$		0			0
$487$		−	17.0248i		−	0.771469i	−0.922610	−	0.385734i	$-0.873948\pi$
$487$		−	17.0248i		−	0.771469i	0.922610	−	0.385734i	$-0.126052\pi$
$488$	1.68240	−	15.7854i	0.0761586	−	0.714571i
$489$		0			0
$490$	0.255921	−	2.72707i	0.0115613	−	0.123197i
$491$	−2.46802	+	13.9968i	−0.111380	+	0.631668i	0.877099	+	0.480310i	$0.159476\pi$
$491$	−2.46802	+	13.9968i	−0.111380	+	0.631668i	−0.988479	+	0.151358i	$0.951635\pi$
$492$		0			0
$493$	5.73153	−	4.80932i	0.258135	−	0.216601i
$494$	−3.24984	+	6.85613i	−0.146217	+	0.308472i
$495$		0			0
$496$	−7.33603	−	21.8551i	−0.329397	−	0.981322i
$497$	16.4963	−	2.90874i	0.739960	−	0.130475i
$498$		0			0
$499$	2.45044	+	6.73253i	0.109697	+	0.301390i	0.982379	−	0.186899i	$-0.0598436\pi$
$499$	2.45044	+	6.73253i	0.109697	+	0.301390i	−0.872682	+	0.488288i	$0.837621\pi$
$500$	10.4896	+	0.132261i	0.469108	+	0.00591490i
$501$		0			0
$502$	13.3344	+	13.5035i	0.595141	+	0.602693i
$503$	−2.15953	+	3.74041i	−0.0962886	+	0.166777i	−0.910146	−	0.414288i	$-0.864031\pi$
$503$	−2.15953	+	3.74041i	−0.0962886	+	0.166777i	0.813857	+	0.581065i	$0.197364\pi$
$504$		0			0
$505$	2.65467	+	4.59802i	0.118131	+	0.204609i
$506$	7.70176	−	28.0352i	0.342385	−	1.24632i
$507$		0			0
$508$	4.09539	−	6.89128i	0.181703	−	0.305751i
$509$	−25.4341	+	30.3112i	−1.12735	+	1.34352i	−0.195488	+	0.980706i	$0.562629\pi$
$509$	−25.4341	+	30.3112i	−1.12735	+	1.34352i	−0.931861	+	0.362816i	$0.881815\pi$
$510$		0			0
$511$	7.29543	−	20.0440i	0.322731	−	0.886696i
$512$	15.0670	+	16.8816i	0.665872	+	0.746066i
$513$		0			0
$514$	2.32138	+	3.36016i	0.102392	+	0.148210i
$515$	3.53174	+	1.28545i	0.155627	+	0.0566436i
$516$		0			0
$517$	11.9747	+	10.0479i	0.526646	+	0.441908i
$518$	26.2745	−	12.0509i	1.15443	−	0.529488i
$519$		0			0
$520$	−1.46116	+	2.00496i	−0.0640763	+	0.0879234i
$521$	−39.1169	+	22.5841i	−1.71374	+	0.989429i	−0.784360	+	0.620305i	$0.787009\pi$
$521$	−39.1169	+	22.5841i	−1.71374	+	0.989429i	−0.929380	+	0.369123i	$0.879658\pi$
$522$		0			0
$523$	−2.99933	−	1.73166i	−0.131152	−	0.0757204i	0.432989	−	0.901399i	$-0.357459\pi$
$523$	−2.99933	−	1.73166i	−0.131152	−	0.0757204i	−0.564140	+	0.825679i	$0.690792\pi$
$524$	4.72561	+	0.894827i	0.206439	+	0.0390907i
$525$		0			0
$526$	11.4788	−	16.1755i	0.500501	−	0.705284i
$527$	4.27516	−	1.55603i	0.186229	−	0.0677817i
$528$		0			0
$529$	−1.05337	−	5.97395i	−0.0457986	−	0.259737i
$530$	0.0576846	+	0.710929i	0.00250566	+	0.0308808i
$531$		0			0
$532$	12.0549	−	1.96923i	0.522646	−	0.0853768i
$533$	−8.01885	−	9.55650i	−0.347335	−	0.413938i
$534$		0			0
$535$	1.33967	+	0.236221i	0.0579192	+	0.0102127i
$536$	−16.0132	−	7.83909i	−0.691664	−	0.338597i
$537$		0			0
$538$	7.19050	+	27.5283i	0.310005	+	1.18683i
$539$	−17.9088			−0.771386
$540$		0			0
$541$	−14.6206			−0.628588			−0.314294	−	0.949326i	$-0.601768\pi$
$541$	−14.6206			−0.628588			−0.314294	+	0.949326i	$0.601768\pi$
$542$	−6.86107	−	26.2671i	−0.294708	−	1.12827i
$543$		0			0
$544$	−3.25549	+	3.05647i	−0.139578	+	0.131045i
$545$	−3.06972	−	0.541274i	−0.131492	−	0.0231856i
$546$		0			0
$547$	−8.74169	−	10.4179i	−0.373768	−	0.445439i	0.546069	−	0.837740i	$-0.316124\pi$
$547$	−8.74169	−	10.4179i	−0.373768	−	0.445439i	−0.919837	+	0.392301i	$0.871679\pi$
$548$	1.38134	+	8.45603i	0.0590077	+	0.361224i
$549$		0			0
$550$	−2.69015	−	33.1546i	−0.114709	−	1.41372i
$551$	5.43921	+	30.8473i	0.231718	+	1.31414i
$552$		0			0
$553$	1.39845	−	0.508994i	0.0594681	−	0.0216446i
$554$	−21.7607	+	30.6642i	−0.924523	+	1.30280i
$555$		0			0
$556$	6.63515	−	35.0405i	0.281393	−	1.48605i
$557$	−5.66207	−	3.26900i	−0.239909	−	0.138512i	0.375226	−	0.926933i	$-0.377565\pi$
$557$	−5.66207	−	3.26900i	−0.239909	−	0.138512i	−0.615135	+	0.788422i	$0.710899\pi$
$558$		0			0
$559$	11.2503	−	6.49539i	0.475839	−	0.274726i
$560$	3.99266	+	0.100702i	0.168721	+	0.00425542i
$561$		0			0
$562$	2.84446	−	1.30463i	0.119986	−	0.0550323i
$563$	18.1068	+	15.1934i	0.763110	+	0.640325i	0.938934	−	0.344096i	$-0.111815\pi$
$563$	18.1068	+	15.1934i	0.763110	+	0.640325i	−0.175824	+	0.984422i	$0.556259\pi$
$564$		0			0
$565$	2.25133	+	0.819417i	0.0947141	+	0.0344731i
$566$	−19.2589	−	27.8769i	−0.809511	−	1.17175i
$567$		0			0
$568$	−6.16586	−	24.8845i	−0.258714	−	1.04413i
$569$	−3.88872	+	10.6842i	−0.163024	+	0.447904i	−0.994128	−	0.108213i	$-0.965487\pi$
$569$	−3.88872	+	10.6842i	−0.163024	+	0.447904i	0.831104	+	0.556117i	$0.187709\pi$
$570$		0			0
$571$	14.2613	−	16.9960i	0.596818	−	0.711260i	−0.380083	−	0.924952i	$-0.624105\pi$
$571$	14.2613	−	16.9960i	0.596818	−	0.711260i	0.976901	+	0.213692i	$0.0685490\pi$
$572$	13.9443	+	8.28692i	0.583042	+	0.346494i
$573$		0			0
$574$	−5.32014	+	19.3659i	−0.222058	+	0.808316i
$575$	9.68708	+	16.7785i	0.403979	+	0.699712i
$576$		0			0
$577$	5.30268	−	9.18452i	0.220754	−	0.382357i	−0.734283	−	0.678843i	$-0.762482\pi$
$577$	5.30268	−	9.18452i	0.220754	−	0.382357i	0.955037	+	0.296487i	$0.0958150\pi$
$578$	16.2733	+	16.4798i	0.676880	+	0.685469i
$579$		0			0
$580$	−0.129129	+	10.2412i	−0.00536180	+	0.425242i
$581$	−10.1061	−	27.7664i	−0.419273	−	1.15194i
$582$		0			0
$583$	4.59270	−	0.809817i	0.190210	−	0.0335392i
$584$	−31.3683	−	9.04427i	−1.29803	−	0.374255i
$585$		0			0
$586$	−16.5178	+	34.8474i	−0.682345	+	1.43953i
$587$	8.09141	−	6.78950i	0.333968	−	0.280233i	−0.460346	−	0.887740i	$-0.652275\pi$
$587$	8.09141	−	6.78950i	0.333968	−	0.280233i	0.794314	+	0.607507i	$0.207830\pi$
$588$		0			0
$589$	−3.30739	+	18.7572i	−0.136279	+	0.772875i
$590$	0.189562	−	2.01996i	0.00780416	−	0.0831604i
$591$		0			0
$592$	−21.1474	−	38.8594i	−0.869155	−	1.59711i
$593$		−	27.5676i		−	1.13207i	−0.824383	−	0.566033i	$-0.808478\pi$
$593$		−	27.5676i		−	1.13207i	0.824383	−	0.566033i	$-0.191522\pi$
$594$		0			0
$595$			0.788191i			0.0323127i
$596$	−18.1108	−	15.5901i	−0.741847	−	0.638594i
$597$		0			0
$598$	−9.40644	−	0.882744i	−0.384658	−	0.0360981i
$599$	2.13432	−	12.1044i	0.0872061	−	0.494571i	−0.909653	−	0.415370i	$-0.863652\pi$
$599$	2.13432	−	12.1044i	0.0872061	−	0.494571i	0.996859	−	0.0792006i	$-0.0252368\pi$
$600$		0			0
$601$	−9.68745	+	8.12873i	−0.395159	+	0.331578i	−0.818619	−	0.574337i	$-0.805260\pi$
$601$	−9.68745	+	8.12873i	−0.395159	+	0.331578i	0.423460	+	0.905915i	$0.360815\pi$
$602$	−18.8980	−	8.95773i	−0.770223	−	0.365090i
$603$		0			0
$604$	28.4310	−	23.2519i	1.15684	−	0.946108i
$605$	7.42709	−	1.30960i	0.301954	−	0.0532427i
$606$		0			0
$607$	2.12432	+	5.83652i	0.0862235	+	0.236897i	0.975309	−	0.220844i	$-0.0708810\pi$
$607$	2.12432	+	5.83652i	0.0862235	+	0.236897i	−0.889086	+	0.457741i	$0.848659\pi$
$608$	−4.26701	−	18.2010i	−0.173050	−	0.738150i
$609$		0			0
$610$	−3.05149	+	3.01326i	−0.123551	+	0.122003i
$611$	2.53984	−	4.39913i	0.102751	−	0.177970i
$612$		0			0
$613$	12.5009	+	21.6522i	0.504907	+	0.874524i	0.999984	+	0.00567529i	$0.00180651\pi$
$613$	12.5009	+	21.6522i	0.504907	+	0.874524i	−0.495077	+	0.868849i	$0.664860\pi$
$614$	33.0765	+	9.08668i	1.33486	+	0.366709i
$615$		0			0
$616$	−1.78358	−	26.0526i	−0.0718627	−	1.04969i
$617$	20.9893	−	25.0141i	0.844997	−	1.00703i	−0.154821	−	0.987943i	$-0.549480\pi$
$617$	20.9893	−	25.0141i	0.844997	−	1.00703i	0.999818	−	0.0190859i	$-0.00607561\pi$
$618$		0			0
$619$	−13.2843	+	36.4984i	−0.533942	+	1.46699i	0.320401	+	0.947282i	$0.396182\pi$
$619$	−13.2843	+	36.4984i	−0.533942	+	1.46699i	−0.854342	+	0.519711i	$0.826040\pi$
$620$	−2.20365	+	5.82490i	−0.0885006	+	0.233933i
$621$		0			0
$622$	−22.3995	+	15.4748i	−0.898136	+	0.620481i
$623$	−10.8586	−	3.95219i	−0.435039	−	0.158341i
$624$		0			0
$625$	15.8621	+	13.3099i	0.634483	+	0.532395i
$626$	4.02110	+	8.76715i	0.160715	+	0.350406i
$627$		0			0
$628$	−13.6919	−	39.1468i	−0.546365	−	1.56213i
$629$	7.56112	−	4.36541i	0.301482	−	0.174060i
$630$		0			0
$631$	27.2601	+	15.7386i	1.08521	+	0.626544i	0.932296	−	0.361696i	$-0.117802\pi$
$631$	27.2601	+	15.7386i	1.08521	+	0.626544i	0.152911	+	0.988240i	$0.451135\pi$
$632$	−0.923381	−	2.08212i	−0.0367301	−	0.0828222i
$633$		0			0
$634$	−13.3084	−	9.44425i	−0.528545	−	0.375079i
$635$	−2.03499	+	0.740675i	−0.0807560	+	0.0293928i
$636$		0			0
$637$	1.01056	+	5.73118i	0.0400399	+	0.227078i
$638$	66.7460	−	5.41576i	2.64250	−	0.214412i
$639$		0			0
$640$	−0.263608	−	6.10702i	−0.0104200	−	0.241401i
$641$	−6.98262	−	8.32156i	−0.275797	−	0.328682i	0.610310	−	0.792163i	$-0.291045\pi$
$641$	−6.98262	−	8.32156i	−0.275797	−	0.328682i	−0.886107	+	0.463481i	$0.846600\pi$
$642$		0			0
$643$	10.8032	+	1.90489i	0.426036	+	0.0751217i	0.382555	−	0.923933i	$-0.375044\pi$
$643$	10.8032	+	1.90489i	0.426036	+	0.0751217i	0.0434808	+	0.999054i	$0.486155\pi$
$644$	7.43818	+	13.2668i	0.293105	+	0.522786i
$645$		0			0
$646$	3.56955	−	0.932379i	0.140442	−	0.0366840i
$647$	47.2138			1.85616			0.928082	−	0.372375i	$-0.121456\pi$
$647$	47.2138			1.85616			0.928082	+	0.372375i	$0.121456\pi$
$648$		0			0
$649$	−13.2652			−0.520703
$650$	−10.4584	+	2.73176i	−0.410210	+	0.107149i
$651$		0			0
$652$	−1.99233	−	3.55354i	−0.0780255	−	0.139167i
$653$	28.9484	+	5.10438i	1.13284	+	0.199750i	0.708471	−	0.705740i	$-0.249385\pi$
$653$	28.9484	+	5.10438i	1.13284	+	0.199750i	0.424367	+	0.905490i	$0.360497\pi$
$654$		0			0
$655$	−0.835168	−	0.995314i	−0.0326327	−	0.0388902i
$656$	30.1263	+	6.09905i	1.17624	+	0.238128i
$657$		0			0
$658$	−8.15085	+	0.661358i	−0.317753	+	0.0257824i
$659$	0.0149056	+	0.0845336i	0.000580638	+	0.00329296i	0.985097	−	0.172001i	$-0.0550234\pi$
$659$	0.0149056	+	0.0845336i	0.000580638	+	0.00329296i	−0.984516	+	0.175294i	$0.943912\pi$
$660$		0			0
$661$	−12.6865	+	4.61752i	−0.493449	+	0.179601i	−0.576745	−	0.816924i	$-0.695677\pi$
$661$	−12.6865	+	4.61752i	−0.493449	+	0.179601i	0.0832963	+	0.996525i	$0.473455\pi$
$662$	−23.7150	−	16.8292i	−0.921711	−	0.654087i
$663$		0			0
$664$	−41.3407	+	18.3338i	−1.60433	+	0.711490i
$665$	−2.85766	−	1.64987i	−0.110815	−	0.0639793i
$666$		0			0
$667$	−33.7781	+	19.5018i	−1.30789	+	0.755113i
$668$	−4.07673	−	11.6559i	−0.157733	−	0.450981i
$669$		0			0
$670$	2.00796	+	4.37792i	0.0775741	+	0.169134i
$671$	21.4796	+	18.0235i	0.829211	+	0.695790i
$672$		0			0
$673$	−5.01426	−	1.82504i	−0.193285	−	0.0703501i	0.243564	−	0.969885i	$-0.421683\pi$
$673$	−5.01426	−	1.82504i	−0.193285	−	0.0703501i	−0.436849	+	0.899535i	$0.643906\pi$
$674$	12.4225	−	8.58215i	0.478498	−	0.330572i
$675$		0			0
$676$	−7.33472	+	19.3879i	−0.282105	+	0.745687i
$677$	8.95953	−	24.6161i	0.344343	−	0.946074i	−0.639776	−	0.768562i	$-0.720973\pi$
$677$	8.95953	−	24.6161i	0.344343	−	0.946074i	0.984119	−	0.177512i	$-0.0568050\pi$
$678$		0			0
$679$	11.2144	−	13.3648i	0.430368	−	0.512892i
$680$	1.20351	−	0.0823932i	0.0461524	−	0.00315963i
$681$		0			0
$682$	39.2646	+	10.7867i	1.50352	+	0.413043i
$683$	16.4032	+	28.4113i	0.627653	+	1.08713i	0.988021	+	0.154317i	$0.0493176\pi$
$683$	16.4032	+	28.4113i	0.627653	+	1.08713i	−0.360369	+	0.932810i	$0.617349\pi$
$684$		0			0
$685$	1.15732	−	2.00454i	0.0442190	−	0.0765895i
$686$	19.6840	−	19.4373i	0.751538	−	0.742121i
$687$		0			0
$688$	−11.7023	+	29.7921i	−0.446145	+	1.13581i
$689$	−0.518316	−	1.42406i	−0.0197463	−	0.0542525i
$690$		0			0
$691$	−5.03144	+	0.887178i	−0.191405	+	0.0337498i	−0.268529	−	0.963272i	$-0.586537\pi$
$691$	−5.03144	+	0.887178i	−0.191405	+	0.0337498i	0.0771239	+	0.997022i	$0.475426\pi$
$692$	−23.0217	+	18.8280i	−0.875153	+	0.715733i
$693$		0			0
$694$	1.59712	+	0.757044i	0.0606259	+	0.0287370i
$695$	−7.38027	+	6.19278i	−0.279950	+	0.234906i
$696$		0			0
$697$	−1.05334	+	5.97380i	−0.0398982	+	0.226274i
$698$	27.0817	+	2.54147i	1.02506	+	0.0961960i
$699$		0			0
$700$	13.1882	+	11.3526i	0.498468	+	0.429089i
$701$			40.9095i			1.54513i	0.634936	+	0.772565i	$0.281026\pi$
$701$			40.9095i			1.54513i	−0.634936	+	0.772565i	$0.718974\pi$
$702$		0			0
$703$			36.5515i			1.37856i
$704$	−39.5939	+	5.44679i	−1.49225	+	0.205284i
$705$		0			0
$706$	−0.822697	+	8.76659i	−0.0309626	+	0.329935i
$707$	−3.15351	+	17.8844i	−0.118600	+	0.672613i
$708$		0			0
$709$	−12.2104	+	10.2458i	−0.458572	+	0.384787i	−0.842605	−	0.538532i	$-0.818979\pi$
$709$	−12.2104	+	10.2458i	−0.458572	+	0.384787i	0.384033	+	0.923319i	$0.374535\pi$
$710$	−2.96646	+	6.25827i	−0.111329	+	0.234869i
$711$		0			0
$712$	−4.89960	+	16.9933i	−0.183620	+	0.636852i
$713$	−23.3564	+	4.11836i	−0.874704	+	0.154234i
$714$		0			0
$715$	−1.49874	−	4.11775i	−0.0560496	−	0.153995i
$716$	0.141591	−	11.2295i	0.00529151	−	0.419667i
$717$		0			0
$718$	−8.97619	−	9.09008i	−0.334988	−	0.339239i
$719$	−15.8103	+	27.3843i	−0.589626	+	1.02126i	0.404655	+	0.914469i	$0.367392\pi$
$719$	−15.8103	+	27.3843i	−0.589626	+	1.02126i	−0.994281	+	0.106793i	$0.965942\pi$
$720$		0			0
$721$	6.42772	+	11.1331i	0.239381	+	0.414619i
$722$	3.02648	−	11.0167i	0.112634	−	0.409999i
$723$		0			0
$724$	−10.4630	−	6.21800i	−0.388854	−	0.231090i
$725$	−28.6839	+	34.1841i	−1.06529	+	1.26957i
$726$		0			0
$727$	9.85979	−	27.0896i	0.365680	−	1.00470i	−0.611307	−	0.791394i	$-0.709356\pi$
$727$	9.85979	−	27.0896i	0.365680	−	1.00470i	0.976986	−	0.213302i	$-0.0684220\pi$
$728$	−8.23673	+	2.04089i	−0.305273	+	0.0756403i
$729$		0			0
$730$	5.01286	+	7.25603i	0.185534	+	0.268558i
$731$	−5.93575	−	2.16044i	−0.219542	−	0.0799066i
$732$		0			0
$733$	−25.8057	−	21.6536i	−0.953157	−	0.799793i	0.0266696	−	0.999644i	$-0.491510\pi$
$733$	−25.8057	−	21.6536i	−0.953157	−	0.799793i	−0.979826	+	0.199851i	$0.935954\pi$
$734$	−9.51489	+	4.36405i	−0.351201	+	0.161080i
$735$		0			0
$736$	19.4799	−	12.7444i	0.718038	−	0.469764i
$737$	27.2723	−	15.7457i	1.00459	−	0.580000i
$738$		0			0
$739$	−10.3214	−	5.95905i	−0.379678	−	0.219207i	0.298000	−	0.954566i	$-0.403680\pi$
$739$	−10.3214	−	5.95905i	−0.379678	−	0.219207i	−0.677678	+	0.735359i	$0.737014\pi$
$740$	−2.22359	+	11.7429i	−0.0817409	+	0.431676i
$741$		0			0
$742$	−1.41192	+	1.98962i	−0.0518332	+	0.0730411i
$743$	−9.08444	+	3.30647i	−0.333276	+	0.121302i	−0.503237	−	0.864148i	$-0.667858\pi$
$743$	−9.08444	+	3.30647i	−0.333276	+	0.121302i	0.169962	+	0.985451i	$0.445636\pi$
$744$		0			0
$745$	1.12100	+	6.35752i	0.0410703	+	0.232921i
$746$	0.350981	+	4.32563i	0.0128503	+	0.158373i
$747$		0			0
$748$	−1.27158	−	7.78415i	−0.0464935	−	0.284617i
$749$	2.99088	+	3.56439i	0.109284	+	0.130240i
$750$		0			0
$751$	22.0213	+	3.88295i	0.803570	+	0.141691i	0.560324	−	0.828274i	$-0.310677\pi$
$751$	22.0213	+	3.88295i	0.803570	+	0.141691i	0.243246	+	0.969965i	$0.421788\pi$
$752$	1.86189	+	12.3766i	0.0678961	+	0.451328i
$753$		0			0
$754$	−5.49952	−	21.0545i	−0.200281	−	0.766760i
$755$	−9.92203			−0.361100
$756$		0			0
$757$	3.40365			0.123708			0.0618540	−	0.998085i	$-0.480299\pi$
$757$	3.40365			0.123708			0.0618540	+	0.998085i	$0.480299\pi$
$758$	10.7877	+	41.2998i	0.391826	+	1.50008i
$759$		0			0
$760$	−2.22051	+	4.53590i	−0.0805462	+	0.164534i
$761$	−43.2514	−	7.62639i	−1.56786	−	0.276457i	−0.678829	−	0.734297i	$-0.737512\pi$
$761$	−43.2514	−	7.62639i	−1.56786	−	0.276457i	−0.889034	+	0.457840i	$0.848623\pi$
$762$		0			0
$763$	−6.85328	−	8.16742i	−0.248105	−	0.295680i
$764$	9.57780	−	1.56458i	0.346513	−	0.0566046i
$765$		0			0
$766$	2.22394	+	27.4088i	0.0803542	+	0.990319i
$767$	0.748530	+	4.24513i	0.0270279	+	0.153283i
$768$		0			0
$769$	43.4127	−	15.8009i	1.56550	−	0.569797i	0.593514	−	0.804823i	$-0.297740\pi$
$769$	43.4127	−	15.8009i	1.56550	−	0.569797i	0.971989	+	0.235027i	$0.0755178\pi$
$770$	−4.08263	+	5.75307i	−0.147128	+	0.207326i
$771$		0			0
$772$	10.3720	+	1.96402i	0.373298	+	0.0706865i
$773$	35.3857	+	20.4299i	1.27273	+	0.734813i	0.975502	−	0.219992i	$-0.0706031\pi$
$773$	35.3857	+	20.4299i	1.27273	+	0.734813i	0.297232	+	0.954805i	$0.403936\pi$
$774$		0			0
$775$	−23.4991	+	13.5672i	−0.844112	+	0.487348i
$776$	−21.5793	−	15.7264i	−0.774650	−	0.564545i
$777$		0			0
$778$	−26.2236	+	12.0276i	−0.940163	+	0.431211i
$779$	−19.4537	−	16.3236i	−0.697001	−	0.584853i
$780$		0			0
$781$	42.5518	+	15.4876i	1.52262	+	0.554189i
$782$	2.61119	+	3.77966i	0.0933760	+	0.135160i
$783$		0			0
$784$	−10.7484	−	9.49091i	−0.383871	−	0.338961i
$785$	−3.83184	+	10.5279i	−0.136764	+	0.375757i
$786$		0			0
$787$	−26.6313	+	31.7379i	−0.949302	+	1.13133i	0.0419189	+	0.999121i	$0.486653\pi$
$787$	−26.6313	+	31.7379i	−0.949302	+	1.13133i	−0.991221	+	0.132214i	$0.957792\pi$
$788$	−2.72677	+	4.58832i	−0.0971372	+	0.163452i
$789$		0			0
$790$	−0.162997	+	0.593326i	−0.00579917	+	0.0211096i
$791$	4.09738	+	7.09688i	0.145686	+	0.252336i
$792$		0			0
$793$	4.55584	−	7.89095i	0.161783	−	0.280216i
$794$	17.4660	+	17.6876i	0.619845	+	0.627710i
$795$		0			0
$796$	22.6907	+	0.286103i	0.804251	+	0.0101407i
$797$	−4.25196	−	11.6822i	−0.150612	−	0.413803i	0.841326	−	0.540528i	$-0.181776\pi$
$797$	−4.25196	−	11.6822i	−0.150612	−	0.413803i	−0.991938	+	0.126725i	$0.959553\pi$
$798$		0			0
$799$	−2.43244	+	0.428905i	−0.0860536	+	0.0151736i
$800$	15.9560	−	21.3242i	0.564129	−	0.753923i
$801$		0			0
$802$	−14.6833	+	30.9771i	−0.518485	+	1.09384i
$803$	44.1723	−	37.0650i	1.55881	−	1.30799i
$804$		0			0
$805$	0.713493	−	4.04642i	0.0251473	−	0.142618i
$806$	1.23632	−	13.1742i	0.0435476	−	0.464040i
$807$		0			0
$808$	27.6378	+	2.94562i	0.972294	+	0.103627i
$809$			4.57993i			0.161022i	0.996754	+	0.0805109i	$0.0256552\pi$
$809$			4.57993i			0.161022i	−0.996754	+	0.0805109i	$0.974345\pi$
$810$		0			0
$811$		−	23.9708i		−	0.841727i	−0.907124	−	0.420864i	$-0.861727\pi$
$811$		−	23.9708i		−	0.841727i	0.907124	−	0.420864i	$-0.138273\pi$
$812$	−22.8549	+	26.5502i	−0.802049	+	0.931731i
$813$		0			0
$814$	77.8010	+	7.30121i	2.72692	+	0.255907i
$815$	−0.191110	+	1.08384i	−0.00669429	+	0.0379652i
$816$		0			0
$817$	20.2578	−	16.9983i	0.708731	−	0.594696i
$818$	−26.4192	−	12.5229i	−0.923726	−	0.437851i
$819$		0			0
$820$	−5.25684	−	6.42773i	−0.183577	−	0.224466i
$821$	−7.46457	+	1.31620i	−0.260515	+	0.0459359i	−0.302380	−	0.953187i	$-0.597781\pi$
$821$	−7.46457	+	1.31620i	−0.260515	+	0.0459359i	0.0418649	+	0.999123i	$0.486670\pi$
$822$		0			0
$823$	−15.9886	−	43.9282i	−0.557326	−	1.53124i	−0.823500	−	0.567316i	$-0.807982\pi$
$823$	−15.9886	−	43.9282i	−0.557326	−	1.53124i	0.266174	−	0.963925i	$-0.414240\pi$
$824$	16.3275	−	10.9784i	0.568796	−	0.382452i
$825$		0			0
$826$	4.93783	−	4.87596i	0.171809	−	0.169656i
$827$	15.4331	−	26.7308i	0.536660	−	0.929522i	−0.462421	−	0.886661i	$-0.653019\pi$
$827$	15.4331	−	26.7308i	0.536660	−	0.929522i	0.999081	−	0.0428620i	$-0.0136476\pi$
$828$		0			0
$829$	5.56407	+	9.63724i	0.193248	+	0.334715i	0.946325	−	0.323217i	$-0.104764\pi$
$829$	5.56407	+	9.63724i	0.193248	+	0.334715i	−0.753077	+	0.657933i	$0.771431\pi$
$830$	11.7805	+	3.23632i	0.408909	+	0.112334i
$831$		0			0
$832$	3.97730	+	12.3635i	0.137888	+	0.428628i
$833$	1.81892	−	2.16771i	0.0630220	−	0.0751067i
$834$		0			0
$835$	−1.14092	+	3.13466i	−0.0394833	+	0.108479i
$836$	30.8839	+	11.6839i	1.06814	+	0.404095i
$837$		0			0
$838$	−9.91149	+	6.84739i	−0.342387	+	0.236539i
$839$	−8.74658	−	3.18349i	−0.301965	−	0.109906i	0.186594	−	0.982437i	$-0.440255\pi$
$839$	−8.74658	−	3.18349i	−0.301965	−	0.109906i	−0.488559	+	0.872531i	$0.662477\pi$
$840$		0			0
$841$	−46.6034	−	39.1049i	−1.60701	−	1.34844i
$842$	8.41098	+	18.3384i	0.289862	+	0.631981i
$843$		0			0
$844$	−8.64587	+	3.02395i	−0.297603	+	0.104089i
$845$	4.84959	−	2.79991i	0.166831	−	0.0963200i
$846$		0			0
$847$	22.3399	+	12.8980i	0.767609	+	0.443179i
$848$	3.18559	+	1.94791i	0.109393	+	0.0668915i
$849$		0			0
$850$	4.28632	+	3.04176i	0.147019	+	0.104331i
$851$	−42.7690	+	15.5667i	−1.46610	+	0.533618i
$852$		0			0
$853$	2.28870	+	12.9798i	0.0783634	+	0.444421i	0.998592	+	0.0530406i	$0.0168913\pi$
$853$	2.28870	+	12.9798i	0.0783634	+	0.444421i	−0.920229	+	0.391381i	$0.871998\pi$
$854$	−14.6206	+	1.18631i	−0.500307	+	0.0405948i
$855$		0			0
$856$	5.12990	−	4.93945i	0.175336	−	0.168827i
$857$	9.69516	+	11.5542i	0.331180	+	0.394685i	0.905779	−	0.423750i	$-0.139286\pi$
$857$	9.69516	+	11.5542i	0.331180	+	0.394685i	−0.574599	+	0.818435i	$0.694842\pi$
$858$		0			0
$859$	24.5457	+	4.32808i	0.837490	+	0.147672i	0.575914	−	0.817511i	$-0.304646\pi$
$859$	24.5457	+	4.32808i	0.837490	+	0.147672i	0.261577	+	0.965183i	$0.415758\pi$
$860$	7.54230	−	4.22867i	0.257190	−	0.144196i
$861$		0			0
$862$	−2.03915	+	0.532634i	−0.0694538	+	0.0181416i
$863$	−22.0216			−0.749626			−0.374813	−	0.927101i	$-0.622293\pi$
$863$	−22.0216			−0.749626			−0.374813	+	0.927101i	$0.622293\pi$
$864$		0			0
$865$	8.03425			0.273173
$866$	−3.87624	+	1.01249i	−0.131720	+	0.0344058i
$867$		0			0
$868$	−18.5808	+	10.4175i	−0.630673	+	0.353593i
$869$	3.96195	+	0.698599i	0.134400	+	0.0236984i
$870$		0			0
$871$	−6.57787	−	7.83921i	−0.222883	−	0.265621i
$872$	−11.7546	+	11.3182i	−0.398062	+	0.383283i
$873$		0			0
$874$	−19.1694	+	1.55540i	−0.648414	+	0.0526121i
$875$	−1.68323	−	9.54610i	−0.0569037	−	0.322717i
$876$		0			0
$877$	−20.5090	+	7.46466i	−0.692539	+	0.252064i	−0.664222	−	0.747535i	$-0.731237\pi$
$877$	−20.5090	+	7.46466i	−0.692539	+	0.252064i	−0.0283170	+	0.999599i	$0.509015\pi$
$878$	−30.9805	−	21.9851i	−1.04554	−	0.741963i
$879$		0			0
$880$	9.21128	+	5.63248i	0.310512	+	0.189871i
$881$	7.29454	+	4.21150i	0.245759	+	0.141889i	0.617821	−	0.786319i	$-0.288016\pi$
$881$	7.29454	+	4.21150i	0.245759	+	0.141889i	−0.372062	+	0.928208i	$0.621349\pi$
$882$		0			0
$883$	21.6426	−	12.4953i	0.728330	−	0.420502i	−0.0894807	−	0.995989i	$-0.528521\pi$
$883$	21.6426	−	12.4953i	0.728330	−	0.420502i	0.817811	+	0.575487i	$0.195187\pi$
$884$	−2.41934	+	0.846178i	−0.0813710	+	0.0284600i
$885$		0			0
$886$	−15.3612	−	33.4918i	−0.516069	−	1.12518i
$887$	−34.3044	−	28.7848i	−1.15183	−	0.966499i	−0.152068	−	0.988370i	$-0.548593\pi$
$887$	−34.3044	−	28.7848i	−1.15183	−	0.966499i	−0.999761	+	0.0218707i	$0.993038\pi$
$888$		0			0
$889$	−6.96058	−	2.53344i	−0.233450	−	0.0849689i
$890$	3.93085	−	2.71564i	0.131762	−	0.0910286i
$891$		0			0
$892$	−34.5470	−	13.0696i	−1.15672	−	0.437604i
$893$	3.53665	−	9.71686i	0.118349	−	0.325162i
$894$		0			0
$895$	−1.95013	+	2.32407i	−0.0651855	+	0.0776850i
$896$	12.7363	−	16.5813i	0.425491	−	0.553943i
$897$		0			0
$898$	30.7618	+	8.45079i	1.02653	+	0.282007i
$899$	−27.3132	−	47.3078i	−0.910945	−	1.57780i
$900$		0			0
$901$	−0.368441	+	0.638158i	−0.0122745	+	0.0212601i
$902$	−38.6312	+	38.1472i	−1.28628	+	1.27016i
$903$		0			0
$904$	10.4081	−	6.99826i	0.346167	−	0.232759i
$905$	1.12456	+	3.08970i	0.0373817	+	0.102705i
$906$		0			0
$907$	−31.5142	+	5.55680i	−1.04641	+	0.184511i	−0.670320	−	0.742072i	$-0.733843\pi$
$907$	−31.5142	+	5.55680i	−1.04641	+	0.184511i	−0.376091	+	0.926583i	$0.622732\pi$
$908$	−16.7954	−	20.5363i	−0.557374	−	0.681521i
$909$		0			0
$910$	2.07148	+	0.981891i	0.0686688	+	0.0325494i
$911$	−21.9054	+	18.3808i	−0.725757	+	0.608983i	−0.928971	−	0.370152i	$-0.879306\pi$
$911$	−21.9054	+	18.3808i	−0.725757	+	0.608983i	0.203214	+	0.979134i	$0.434861\pi$
$912$		0			0
$913$	13.8708	−	78.6650i	0.459055	−	2.60343i
$914$	20.8646	+	1.95803i	0.690141	+	0.0647660i
$915$		0			0
$916$	4.50384	−	5.23206i	0.148811	−	0.172872i
$917$		−	4.44416i		−	0.146759i
$918$		0			0
$919$			27.7726i			0.916132i	0.888918	+	0.458066i	$0.151458\pi$
$919$			27.7726i			0.916132i	−0.888918	+	0.458066i	$0.848542\pi$
$920$	−6.25316	−	0.666458i	−0.206160	−	0.0219725i
$921$		0			0
$922$	4.09227	−	43.6069i	0.134772	−	1.43612i
$923$	2.55522	−	14.4914i	0.0841062	−	0.476990i
$924$		0			0
$925$	−39.8899	+	33.4716i	−1.31157	+	1.10054i
$926$	13.8680	−	29.2571i	0.455731	−	0.961447i
$927$		0			0
$928$	42.9293	+	32.1222i	1.40922	+	1.05446i
$929$	9.40060	−	1.65758i	0.308424	−	0.0543834i	−0.0172941	−	0.999850i	$-0.505505\pi$
$929$	9.40060	−	1.65758i	0.308424	−	0.0543834i	0.325718	+	0.945467i	$0.394394\pi$
$930$		0			0
$931$	4.05180	+	11.1322i	0.132792	+	0.364844i
$932$	32.6926	+	0.412215i	1.07088	+	0.0135025i
$933$		0			0
$934$	35.7252	+	36.1785i	1.16897	+	1.18380i
$935$	−1.06536	+	1.84527i	−0.0348411	+	0.0603466i
$936$		0			0
$937$	−1.13866	−	1.97222i	−0.0371986	−	0.0644298i	0.846827	−	0.531869i	$-0.178510\pi$
$937$	−1.13866	−	1.97222i	−0.0371986	−	0.0644298i	−0.884025	+	0.467439i	$0.845177\pi$
$938$	−4.36412	+	15.8858i	−0.142494	+	0.518691i
$939$		0			0
$940$	1.72734	−	2.90658i	0.0563395	−	0.0948022i
$941$	4.48164	−	5.34101i	0.146097	−	0.174112i	−0.688033	−	0.725679i	$-0.741526\pi$
$941$	4.48164	−	5.34101i	0.146097	−	0.174112i	0.834130	+	0.551567i	$0.185970\pi$
$942$		0			0
$943$	10.8153	−	29.7148i	0.352195	−	0.967647i
$944$	−7.96140	−	7.02998i	−0.259121	−	0.228806i
$945$		0			0
$946$	−32.1350	−	46.5149i	−1.04480	−	1.51233i
$947$	42.9198	+	15.6215i	1.39471	+	0.507631i	0.926603	−	0.376042i	$-0.122715\pi$
$947$	42.9198	+	15.6215i	1.39471	+	0.507631i	0.468103	+	0.883674i	$0.344937\pi$
$948$		0			0
$949$	−14.3541	−	12.0445i	−0.465955	−	0.390982i
$950$	−20.0005	+	9.17333i	−0.648902	+	0.297622i
$951$		0			0
$952$	3.33460	+	2.43017i	0.108075	+	0.0787623i
$953$	26.2534	−	15.1574i	0.850431	−	0.490997i	−0.0103652	−	0.999946i	$-0.503299\pi$
$953$	26.2534	−	15.1574i	0.850431	−	0.490997i	0.860796	+	0.508950i	$0.169966\pi$
$954$		0			0
$955$	−2.27046	−	1.31085i	−0.0734704	−	0.0424181i
$956$	2.04668	+	0.387553i	0.0661944	+	0.0125344i
$957$		0			0
$958$	−16.7400	+	23.5893i	−0.540846	+	0.762136i
$959$	7.43966	−	2.70782i	0.240239	−	0.0874400i
$960$		0			0
$961$	−0.384864	−	2.18267i	−0.0124150	−	0.0704089i
$962$	−2.05364	−	25.3099i	−0.0662121	−	0.816025i
$963$		0			0
$964$	32.5040	−	5.30969i	1.04688	−	0.171014i
$965$	−1.83307	−	2.18457i	−0.0590088	−	0.0703239i
$966$		0			0
$967$	−30.8569	−	5.44090i	−0.992290	−	0.174967i	−0.346144	−	0.938181i	$-0.612509\pi$
$967$	−30.8569	−	5.44090i	−0.992290	−	0.174967i	−0.646146	+	0.763214i	$0.723620\pi$
$968$	17.3589	−	35.4596i	0.557936	−	1.13972i
$969$		0			0
$970$	1.82300	+	6.97922i	0.0585329	+	0.224089i
$971$	1.61116			0.0517047			0.0258523	−	0.999666i	$-0.491770\pi$
$971$	1.61116			0.0517047			0.0258523	+	0.999666i	$0.491770\pi$
$972$		0			0
$973$	−32.9535			−1.05644
$974$	6.08479	+	23.2952i	0.194969	+	0.746426i
$975$		0			0
$976$	3.33977	+	22.2005i	0.106903	+	0.710622i
$977$	−26.4012	−	4.65524i	−0.844648	−	0.148934i	−0.265453	−	0.964124i	$-0.585522\pi$
$977$	−26.4012	−	4.65524i	−0.844648	−	0.148934i	−0.579194	+	0.815190i	$0.696633\pi$
$978$		0			0
$979$	−20.0794	−	23.9297i	−0.641741	−	0.764797i
$980$	0.624496	+	3.82294i	0.0199488	+	0.122119i
$981$		0			0
$982$	−1.62556	−	20.0340i	−0.0518736	−	0.639312i
$983$	−4.56612	−	25.8958i	−0.145637	−	0.825947i	−0.966854	−	0.255331i	$-0.917816\pi$
$983$	−4.56612	−	25.8958i	−0.145637	−	0.825947i	0.821217	−	0.570616i	$-0.193296\pi$
$984$		0			0
$985$	1.35492	−	0.493152i	0.0431715	−	0.0157131i
$986$	−6.12360	+	8.62911i	−0.195015	+	0.274807i
$987$		0			0
$988$	1.99635	−	10.5428i	0.0635123	−	0.335411i
$989$	28.5173	+	16.4645i	0.906797	+	0.523540i
$990$		0			0
$991$	20.2827	−	11.7102i	0.644302	−	0.371988i	−0.141968	−	0.989871i	$-0.545343\pi$
$991$	20.2827	−	11.7102i	0.644302	−	0.371988i	0.786270	+	0.617883i	$0.212010\pi$
$992$	17.8491	+	27.2825i	0.566709	+	0.866219i
$993$		0			0
$994$	−21.5324	+	9.87593i	−0.682965	+	0.313245i
$995$	−4.69607	−	3.94047i	−0.148876	−	0.124921i
$996$		0			0
$997$	5.48788	+	1.99742i	0.173803	+	0.0632590i	0.427456	−	0.904036i	$-0.359410\pi$
$997$	5.48788	+	1.99742i	0.173803	+	0.0632590i	−0.253653	+	0.967295i	$0.581632\pi$
$998$	−5.75921	−	8.33636i	−0.182304	−	0.263883i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.179.1		96
3.2	odd	2		108.2.l.a.23.16	yes	96
4.3	odd	2	inner	324.2.l.a.179.12		96
9.2	odd	6		972.2.l.c.215.5		96
9.4	even	3		972.2.l.a.863.10		96
9.5	odd	6		972.2.l.d.863.7		96
9.7	even	3		972.2.l.b.215.12		96
12.11	even	2		108.2.l.a.23.5	✓	96
27.2	odd	18		972.2.l.a.107.1		96
27.7	even	9		108.2.l.a.47.5	yes	96
27.11	odd	18		972.2.l.b.755.11		96
27.16	even	9		972.2.l.c.755.6		96
27.20	odd	18	inner	324.2.l.a.143.12		96
27.25	even	9		972.2.l.d.107.16		96
36.7	odd	6		972.2.l.b.215.11		96
36.11	even	6		972.2.l.c.215.6		96
36.23	even	6		972.2.l.d.863.16		96
36.31	odd	6		972.2.l.a.863.1		96
108.7	odd	18		108.2.l.a.47.16	yes	96
108.11	even	18		972.2.l.b.755.12		96
108.43	odd	18		972.2.l.c.755.5		96
108.47	even	18	inner	324.2.l.a.143.1		96
108.79	odd	18		972.2.l.d.107.7		96
108.83	even	18		972.2.l.a.107.10		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.5	✓	96	12.11	even	2
108.2.l.a.23.16	yes	96	3.2	odd	2
108.2.l.a.47.5	yes	96	27.7	even	9
108.2.l.a.47.16	yes	96	108.7	odd	18
324.2.l.a.143.1		96	108.47	even	18	inner
324.2.l.a.143.12		96	27.20	odd	18	inner
324.2.l.a.179.1		96	1.1	even	1	trivial
324.2.l.a.179.12		96	4.3	odd	2	inner
972.2.l.a.107.1		96	27.2	odd	18
972.2.l.a.107.10		96	108.83	even	18
972.2.l.a.863.1		96	36.31	odd	6
972.2.l.a.863.10		96	9.4	even	3
972.2.l.b.215.11		96	36.7	odd	6
972.2.l.b.215.12		96	9.7	even	3
972.2.l.b.755.11		96	27.11	odd	18
972.2.l.b.755.12		96	108.11	even	18
972.2.l.c.215.5		96	9.2	odd	6
972.2.l.c.215.6		96	36.11	even	6
972.2.l.c.755.5		96	108.43	odd	18
972.2.l.c.755.6		96	27.16	even	9
972.2.l.d.107.7		96	108.79	odd	18
972.2.l.d.107.16		96	27.25	even	9
972.2.l.d.863.7		96	9.5	odd	6
972.2.l.d.863.16		96	36.23	even	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36831 + 0.357407i) q^{2} +(1.74452 - 0.978083i) q^{4} +(-0.532084 - 0.0938207i) q^{5} +(-1.18790 - 1.41568i) q^{7} +(-2.03746 + 1.96182i) q^{8} +O(q^{10})\)	\(q+(-1.36831 + 0.357407i) q^{2} +(1.74452 - 0.978083i) q^{4} +(-0.532084 - 0.0938207i) q^{5} +(-1.18790 - 1.41568i) q^{7} +(-2.03746 + 1.96182i) q^{8} +(0.761586 - 0.0617949i) q^{10} +(-0.867520 - 4.91995i) q^{11} +(-1.52553 + 0.555249i) q^{13} +(2.13138 + 1.51252i) q^{14} +(2.08671 - 3.41257i) q^{16} +(0.683630 + 0.394694i) q^{17} +(-2.86200 + 1.65238i) q^{19} +(-1.02000 + 0.356750i) q^{20} +(2.94546 + 6.42194i) q^{22} +(-3.15234 - 2.64512i) q^{23} +(-4.42415 - 1.61026i) q^{25} +(1.88895 - 1.30499i) q^{26} +(-3.45697 - 1.30783i) q^{28} +(3.24174 - 8.90660i) q^{29} +(3.70462 - 4.41499i) q^{31} +(-1.63558 + 5.41525i) q^{32} +(-1.07648 - 0.295728i) q^{34} +(0.499242 + 0.864712i) q^{35} +(5.53013 - 9.57846i) q^{37} +(3.32552 - 3.28386i) q^{38} +(1.26816 - 0.852696i) q^{40} +(2.62821 + 7.22095i) q^{41} +(-7.88044 + 1.38953i) q^{43} +(-6.32553 - 7.73445i) q^{44} +(5.25874 + 2.49267i) q^{46} +(-2.39693 + 2.01126i) q^{47} +(0.622483 - 3.53027i) q^{49} +(6.62911 + 0.622106i) q^{50} +(-2.11825 + 2.46074i) q^{52} +0.933485i q^{53} +2.69922i q^{55} +(5.19762 + 0.553960i) q^{56} +(-1.25241 + 13.3456i) q^{58} +(0.461077 - 2.61490i) q^{59} +(-4.29949 + 3.60770i) q^{61} +(-3.49110 + 7.36511i) q^{62} +(0.302524 - 7.99428i) q^{64} +(0.863806 - 0.152312i) q^{65} +(2.15593 + 5.92336i) q^{67} +(1.57865 + 0.0199049i) q^{68} +(-0.992169 - 1.00476i) q^{70} +(-4.53203 + 7.84970i) q^{71} +(5.77108 + 9.99580i) q^{73} +(-4.14350 + 15.0828i) q^{74} +(-3.37666 + 5.68189i) q^{76} +(-5.93457 + 7.07254i) q^{77} +(-0.275423 + 0.756719i) q^{79} +(-1.43047 + 1.62000i) q^{80} +(-6.17702 - 8.94113i) q^{82} +(15.0247 + 5.46855i) q^{83} +(-0.326718 - 0.274149i) q^{85} +(10.2862 - 4.71783i) q^{86} +(11.4196 + 8.32231i) q^{88} +(5.41508 - 3.12640i) q^{89} +(2.59824 + 1.50009i) q^{91} +(-8.08647 - 1.53123i) q^{92} +(2.56089 - 3.60870i) q^{94} +(1.67785 - 0.610689i) q^{95} +(1.63933 + 9.29708i) q^{97} +(0.409997 + 5.05297i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

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