LMFDB - Embedded newform 324.2.l.a.143.1

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			143.1
Character	$\chi$	$=$	324.143
Dual form			324.2.l.a.179.1

$q$-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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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	−0.291354	−	0.956615i	$-0.594106\pi$
$5$	−0.532084	+	0.0938207i	−0.237955	+	0.0419579i	0.0533987	+	0.998573i	$0.482995\pi$
$6$		0			0
$7$	−1.18790	+	1.41568i	−0.448984	+	0.535078i	−0.942299	−	0.334773i	$-0.891341\pi$
$7$	−1.18790	+	1.41568i	−0.448984	+	0.535078i	0.493315	+	0.869851i	$0.335785\pi$
$8$	−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	0.517068	+	0.855944i	$0.327023\pi$
$11$	−0.867520	+	4.91995i	−0.261567	+	1.48342i	−0.778635	+	0.627477i	$0.784088\pi$
$12$		0			0
$13$	−1.52553	−	0.555249i	−0.423107	−	0.153998i	0.121687	−	0.992569i	$-0.461170\pi$
$13$	−1.52553	−	0.555249i	−0.423107	−	0.153998i	−0.544793	+	0.838570i	$0.683392\pi$
$14$	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	−0.414802	−	0.909912i	$-0.636149\pi$
$17$	0.683630	−	0.394694i	0.165805	−	0.0957273i	0.580606	+	0.814185i	$0.302816\pi$
$18$		0			0
$19$	−2.86200	−	1.65238i	−0.656589	−	0.379082i	0.134387	−	0.990929i	$-0.457093\pi$
$19$	−2.86200	−	1.65238i	−0.656589	−	0.379082i	−0.790976	+	0.611847i	$0.790427\pi$
$20$	−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	−0.909278	−	0.416188i	$-0.863366\pi$
$23$	−3.15234	+	2.64512i	−0.657307	+	0.551546i	0.251971	+	0.967735i	$0.418921\pi$
$24$		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	0.747266	+	0.664525i	$0.231366\pi$
$29$	3.24174	+	8.90660i	0.601976	+	1.65391i	−0.145290	+	0.989389i	$0.546412\pi$
$30$		0			0
$31$	3.70462	+	4.41499i	0.665369	+	0.792956i	0.988146	−	0.153519i	$-0.0490607\pi$
$31$	3.70462	+	4.41499i	0.665369	+	0.792956i	−0.322777	+	0.946475i	$0.604616\pi$
$32$	−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	0.815251	+	0.579108i	$0.196599\pi$
$37$	5.53013	+	9.57846i	0.909147	+	1.57469i	0.0938963	+	0.995582i	$0.470068\pi$
$38$	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	−0.546491	−	0.837465i	$-0.684037\pi$
$41$	2.62821	−	7.22095i	0.410458	−	1.12772i	0.956948	−	0.290258i	$-0.0937412\pi$
$42$		0			0
$43$	−7.88044	−	1.38953i	−1.20176	−	0.211902i	−0.463299	−	0.886202i	$-0.653334\pi$
$43$	−7.88044	−	1.38953i	−1.20176	−	0.211902i	−0.738458	+	0.674300i	$0.764445\pi$
$44$	−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	0.451013	−	0.892517i	$-0.351063\pi$
$47$	−2.39693	−	2.01126i	−0.349628	−	0.293372i	−0.800640	+	0.599145i	$0.795507\pi$
$48$		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	$-0.979579\pi$
$53$		−	0.933485i		−	0.128224i	0.997943	−	0.0641120i	$-0.0204215\pi$
$54$		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	1.00000		0.000819421i	$-0.000260830\pi$
$59$	0.461077	+	2.61490i	0.0600271	+	0.340431i	−0.939973	+	0.341250i	$0.889150\pi$
$60$		0			0
$61$	−4.29949	−	3.60770i	−0.550493	−	0.461919i	0.324615	−	0.945846i	$-0.394765\pi$
$61$	−4.29949	−	3.60770i	−0.550493	−	0.461919i	−0.875108	+	0.483928i	$0.839210\pi$
$62$	−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	−0.735545	−	0.677476i	$-0.763074\pi$
$67$	2.15593	−	5.92336i	0.263388	−	0.723653i	0.998933	−	0.0461775i	$-0.0147040\pi$
$68$	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	−0.999019	−	0.0442746i	$-0.985902\pi$
$71$	−4.53203	−	7.84970i	−0.537853	−	0.931588i	0.461167	−	0.887313i	$-0.347431\pi$
$72$		0			0
$73$	5.77108	−	9.99580i	0.675454	−	1.16992i	−0.300882	−	0.953661i	$-0.597281\pi$
$73$	5.77108	−	9.99580i	0.675454	−	1.16992i	0.976336	−	0.216259i	$-0.0693855\pi$
$74$	−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	0.923234	−	0.384238i	$-0.125536\pi$
$79$	−0.275423	−	0.756719i	−0.0309875	−	0.0851375i	−0.954222	+	0.299100i	$0.903313\pi$
$80$	−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	0.660570	−	0.750765i	$-0.270315\pi$
$83$	15.0247	−	5.46855i	1.64918	−	0.600252i	0.988608	+	0.150513i	$0.0480925\pi$
$84$		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	0.758744	−	0.651389i	$-0.225813\pi$
$89$	5.41508	+	3.12640i	0.573997	+	0.331398i	−0.184747	+	0.982786i	$0.559147\pi$
$90$		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	−0.781110	−	0.624393i	$-0.785346\pi$
$97$	1.63933	−	9.29708i	0.166448	−	0.943975i	0.947559	−	0.319582i	$-0.103543\pi$
$98$	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	−0.982510	−	0.186210i	$-0.940380\pi$
$101$	−6.31653	+	7.52775i	−0.628518	+	0.749039i	0.353992	+	0.935249i	$0.384824\pi$
$102$		0			0
$103$	−6.85056	+	1.20794i	−0.675005	+	0.119022i	−0.500635	−	0.865658i	$-0.666900\pi$
$103$	−6.85056	+	1.20794i	−0.675005	+	0.119022i	−0.174370	+	0.984680i	$0.555789\pi$
$104$	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	−0.375232	−	0.926931i	$-0.622437\pi$
$113$	−4.36693	+	0.770007i	−0.410806	+	0.0724362i	−0.0355738	+	0.999367i	$0.511326\pi$
$114$		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	0.646039	−	0.763304i	$-0.276424\pi$
$127$	3.47118	+	2.00409i	0.308018	+	0.177834i	−0.338021	+	0.941138i	$0.609758\pi$
$128$	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	−0.558755	−	0.829333i	$-0.688721\pi$
$131$	1.84218	−	1.54577i	0.160952	−	0.135055i	0.719707	+	0.694278i	$0.244276\pi$
$132$		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	0.861231	−	0.508213i	$-0.169694\pi$
$137$	−1.46523	−	4.02570i	−0.125183	−	0.343939i	−0.986415	+	0.164275i	$0.947472\pi$
$138$		0			0
$139$	11.4619	+	13.6598i	0.972187	+	1.15861i	0.987323	+	0.158722i	$0.0507373\pi$
$139$	11.4619	+	13.6598i	0.972187	+	1.15861i	−0.0151364	+	0.999885i	$0.504818\pi$
$140$	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	0.652063	+	0.758165i	$0.273904\pi$
$149$	−4.08657	+	11.2278i	−0.334785	+	0.919814i	−0.986848	+	0.161650i	$0.948319\pi$
$150$		0			0
$151$	18.0852	+	3.18891i	1.47175	+	0.259510i	0.851277	−	0.524716i	$-0.175829\pi$
$151$	18.0852	+	3.18891i	1.47175	+	0.259510i	0.620475	+	0.784226i	$0.286940\pi$
$152$	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	0.696680	+	0.717382i	$0.254660\pi$
$157$	3.60079	+	20.4211i	0.287374	+	1.62978i	−0.409306	+	0.912397i	$0.634229\pi$
$158$	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	$0.0254198\pi$
$163$			2.03697i			0.159548i	−0.996813	+	0.0797739i	$0.974580\pi$
$164$	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	0.997777	+	0.0666346i	$0.0212262\pi$
$167$	1.07213	+	6.08034i	0.0829637	+	0.470511i	−0.914814	+	0.403876i	$0.867663\pi$
$168$		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	−0.413450	−	0.910527i	$-0.635676\pi$
$173$	−14.6443	−	2.58218i	−1.11338	−	0.196320i	−0.699934	+	0.714207i	$0.746787\pi$
$174$		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	0.951667	−	0.307131i	$-0.0993690\pi$
$179$	2.80761	+	4.86292i	0.209850	+	0.363472i	−0.741817	+	0.670603i	$0.766036\pi$
$180$		0			0
$181$	−3.04279	+	5.27027i	−0.226169	+	0.391736i	−0.956670	−	0.291176i	$-0.905954\pi$
$181$	−3.04279	+	5.27027i	−0.226169	+	0.391736i	0.730500	+	0.682912i	$0.239287\pi$
$182$	−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	−0.171743	−	0.985142i	$-0.554940\pi$
$191$	4.55974	−	1.65961i	0.329931	−	0.120085i	0.501674	+	0.865057i	$0.332718\pi$
$192$		0			0
$193$	4.04332	−	3.39275i	0.291044	−	0.244215i	−0.485561	−	0.874203i	$-0.661385\pi$
$193$	4.04332	−	3.39275i	0.291044	−	0.244215i	0.776605	+	0.629988i	$0.216940\pi$
$194$	−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	0.415403	−	0.909637i	$-0.363640\pi$
$197$	−2.31117	−	1.33435i	−0.164664	−	0.0950687i	−0.580067	+	0.814569i	$0.696974\pi$
$198$		0			0
$199$	9.82614	−	5.67313i	0.696557	−	0.402157i	−0.109507	−	0.993986i	$-0.534927\pi$
$199$	9.82614	−	5.67313i	0.696557	−	0.402157i	0.806064	+	0.591829i	$0.201594\pi$
$200$	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	−0.326723	−	0.945120i	$-0.605944\pi$
$211$	−4.51015	+	0.795260i	−0.310491	+	0.0547480i	0.0162314	+	0.999868i	$0.494833\pi$
$212$	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	−0.999505	−	0.0314676i	$-0.989982\pi$
$223$	−11.8712	+	14.1475i	−0.794953	+	0.947388i	0.204552	+	0.978856i	$0.434426\pi$
$224$	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	0.807813	+	0.589439i	$0.200651\pi$
$227$	−2.30342	+	13.0633i	−0.152883	+	0.867043i	−0.960696	+	0.277604i	$0.910460\pi$
$228$		0			0
$229$	3.24361	+	1.18058i	0.214344	+	0.0780147i	0.446960	−	0.894554i	$-0.352507\pi$
$229$	3.24361	+	1.18058i	0.214344	+	0.0780147i	−0.232617	+	0.972569i	$0.574729\pi$
$230$	−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	0.0414686	−	0.999140i	$-0.486796\pi$
$233$	14.1574	−	8.17379i	0.927483	−	0.535483i	0.886015	+	0.463657i	$0.153463\pi$
$234$		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	−0.616618	−	0.787262i	$-0.711498\pi$
$239$	0.797855	−	0.669480i	0.0516089	−	0.0433050i	0.668227	+	0.743957i	$0.267053\pi$
$240$		0			0
$241$	15.4743	−	5.63219i	0.996788	−	0.362801i	0.208443	−	0.978035i	$-0.433160\pi$
$241$	15.4743	−	5.63219i	0.996788	−	0.362801i	0.788345	+	0.615233i	$0.210938\pi$
$242$	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	−0.996280	−	0.0861790i	$-0.972534\pi$
$251$	−6.70961	+	11.6214i	−0.423507	+	0.733535i	0.572773	+	0.819714i	$0.305868\pi$
$252$		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	−0.966679	−	0.255992i	$-0.917598\pi$
$257$	−0.987706	+	2.71370i	−0.0616114	+	0.169276i	0.905068	+	0.425268i	$0.139820\pi$
$258$		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	0.248338	−	0.968674i	$-0.420116\pi$
$263$	−10.7439	−	9.01519i	−0.662496	−	0.555900i	−0.910834	+	0.412773i	$0.864560\pi$
$264$		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	$0.210168\pi$
$269$			20.1185i			1.22665i	−0.789831	+	0.613325i	$0.789832\pi$
$270$		0			0
$271$		−	19.1968i		−	1.16612i	−0.812428	−	0.583062i	$-0.801855\pi$
$271$		−	19.1968i		−	1.16612i	0.812428	−	0.583062i	$-0.198145\pi$
$272$	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	0.998619	+	0.0525311i	$0.0167289\pi$
$277$	20.3674	+	17.0903i	1.22376	+	1.02686i	0.225141	+	0.974326i	$0.427716\pi$
$278$	−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	0.108270	−	0.994122i	$-0.465469\pi$
$281$	−2.17919	−	0.384249i	−0.129999	−	0.0229224i	−0.238269	+	0.971199i	$0.576580\pi$
$282$		0			0
$283$	8.19432	−	22.5137i	0.487102	−	1.33830i	−0.416192	−	0.909277i	$-0.636635\pi$
$283$	8.19432	−	22.5137i	0.487102	−	1.33830i	0.903293	−	0.429024i	$-0.141142\pi$
$284$	−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	0.975149	+	0.221550i	$0.0711116\pi$
$293$	17.5281	+	20.8891i	1.02400	+	1.22036i	0.0488514	+	0.998806i	$0.484444\pi$
$294$		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	−0.960299	−	0.278974i	$-0.910006\pi$
$307$	−21.0055	+	12.1276i	−1.19885	+	0.692156i	−0.238551	+	0.971130i	$0.576672\pi$
$308$	−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	0.799477	−	0.600696i	$-0.205110\pi$
$311$	18.0900	+	6.58424i	1.02579	+	0.373358i	0.226315	+	0.974054i	$0.427332\pi$
$312$		0			0
$313$	−1.18433	+	6.71666i	−0.0669422	+	0.379648i	0.932869	+	0.360216i	$0.117297\pi$
$313$	−1.18433	+	6.71666i	−0.0669422	+	0.379648i	−0.999811	+	0.0194321i	$0.993814\pi$
$314$	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	−0.516409	−	0.856342i	$-0.672732\pi$
$317$	7.41728	−	8.83957i	0.416596	−	0.496480i	0.933006	+	0.359862i	$0.117176\pi$
$318$		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	−0.268757	−	0.963208i	$-0.586613\pi$
$331$	13.2173	−	15.7517i	0.726487	−	0.865793i	0.995244	+	0.0974147i	$0.0310573\pi$
$332$	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	0.0539858	−	0.998542i	$-0.482807\pi$
$337$	−10.0326	−	3.65156i	−0.546509	−	0.198913i	−0.600495	+	0.799629i	$0.705030\pi$
$338$	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	−0.668123	−	0.744050i	$-0.732902\pi$
$347$	−0.957389	+	0.803344i	−0.0513953	+	0.0431258i	0.616728	+	0.787176i	$0.288458\pi$
$348$		0			0
$349$	−18.0738	+	6.57834i	−0.967470	+	0.352130i	−0.776957	−	0.629554i	$-0.783238\pi$
$349$	−18.0738	+	6.57834i	−0.967470	+	0.352130i	−0.190514	+	0.981685i	$0.561015\pi$
$350$	−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	0.983374	−	0.181593i	$-0.0581253\pi$
$353$	2.12947	+	5.85067i	0.113340	+	0.311400i	−0.870034	+	0.492992i	$0.835903\pi$
$354$		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	−0.721870	−	0.692029i	$-0.756717\pi$
$359$	4.51666	−	7.82308i	0.238380	−	0.412886i	0.960250	+	0.279143i	$0.0900503\pi$
$360$		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	0.360632	−	0.932708i	$-0.382561\pi$
$367$	7.28951	+	1.28534i	0.380509	+	0.0670941i	0.0198778	+	0.999802i	$0.493672\pi$
$368$	−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	0.995491	−	0.0948598i	$-0.0302403\pi$
$373$	0.532880	+	3.02211i	0.0275915	+	0.156479i	−0.967899	+	0.251339i	$0.919129\pi$
$374$	−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	$0.282353\pi$
$379$			30.1832i			1.55041i	−0.631712	+	0.775203i	$0.717647\pi$
$380$	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	0.940954	+	0.338535i	$0.109931\pi$
$383$	3.37652	+	19.1492i	0.172532	+	0.978479i	−0.768422	+	0.639944i	$0.778958\pi$
$384$		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	0.657933	−	0.753076i	$-0.271431\pi$
$389$	20.0904	+	3.54247i	1.01862	+	0.179610i	0.360688	+	0.932687i	$0.382542\pi$
$390$		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	−0.997770	−	0.0667406i	$-0.978740\pi$
$397$	−8.78858	+	15.2223i	−0.441086	+	0.763984i	0.556684	+	0.830724i	$0.312073\pi$
$398$	−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	0.998846	−	0.0480334i	$-0.0152954\pi$
$401$	15.5813	+	18.5691i	0.778094	+	0.927297i	−0.220751	+	0.975330i	$0.570851\pi$
$402$		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	−0.160939	−	0.986964i	$-0.551452\pi$
$409$	15.8369	−	13.2887i	0.783085	−	0.657086i	0.944024	+	0.329878i	$0.107008\pi$
$410$	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	0.530060	−	0.847960i	$-0.322169\pi$
$419$	8.00463	+	2.91345i	0.391052	+	0.142331i	−0.139009	+	0.990291i	$0.544392\pi$
$420$		0			0
$421$	−2.47727	+	14.0493i	−0.120735	+	0.684721i	0.863015	+	0.505178i	$0.168573\pi$
$421$	−2.47727	+	14.0493i	−0.120735	+	0.684721i	−0.983750	+	0.179543i	$0.942538\pi$
$422$	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	−0.175908	−	0.984407i	$-0.556286\pi$
$439$	17.2666	−	20.5775i	0.824089	−	0.982112i	0.999997	+	0.00229504i	$0.000730536\pi$
$440$	−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	−0.666027	−	0.745928i	$-0.732006\pi$
$443$	4.52430	−	25.6586i	0.214956	−	1.21908i	0.880983	−	0.473148i	$-0.156882\pi$
$444$		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	−0.884254	−	0.467007i	$-0.845332\pi$
$449$	−19.5356	+	11.2789i	−0.921940	+	0.532282i	−0.0376867	+	0.999290i	$0.511999\pi$
$450$		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	−0.646506	−	0.762909i	$-0.723770\pi$
$457$	−13.9247	+	5.06817i	−0.651370	+	0.237079i	−0.00486385	+	0.999988i	$0.501548\pi$
$458$	−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	−0.897606	−	0.440798i	$-0.854696\pi$
$461$	−10.5924	−	29.1025i	−0.493339	−	1.35544i	0.404267	−	0.914641i	$-0.367527\pi$
$462$		0			0
$463$	−14.7162	−	17.5380i	−0.683918	−	0.815062i	0.306687	−	0.951810i	$-0.400779\pi$
$463$	−14.7162	−	17.5380i	−0.683918	−	0.815062i	−0.990606	+	0.136748i	$0.956335\pi$
$464$	−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	0.0647308	+	0.997903i	$0.479381\pi$
$467$	−17.9763	+	31.1359i	−0.831844	+	1.44080i	−0.896575	+	0.442893i	$0.853952\pi$
$468$		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	0.926248	−	0.376916i	$-0.123015\pi$
$479$	15.6682	+	13.1472i	0.715899	+	0.600711i	−0.210348	+	0.977627i	$0.567460\pi$
$480$		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	$0.126052\pi$
$487$			17.0248i			0.771469i	−0.922610	+	0.385734i	$0.873948\pi$
$488$	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	−0.988479	−	0.151358i	$-0.951635\pi$
$491$	−2.46802	−	13.9968i	−0.111380	−	0.631668i	0.877099	−	0.480310i	$-0.159476\pi$
$492$		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	−0.872682	−	0.488288i	$-0.837621\pi$
$499$	2.45044	−	6.73253i	0.109697	−	0.301390i	0.982379	+	0.186899i	$0.0598436\pi$
$500$	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	0.813857	−	0.581065i	$-0.197364\pi$
$503$	−2.15953	−	3.74041i	−0.0962886	−	0.166777i	−0.910146	+	0.414288i	$0.864031\pi$
$504$		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	−0.931861	−	0.362816i	$-0.881815\pi$
$509$	−25.4341	−	30.3112i	−1.12735	−	1.34352i	−0.195488	−	0.980706i	$-0.562629\pi$
$510$		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	−0.929380	−	0.369123i	$-0.879658\pi$
$521$	−39.1169	−	22.5841i	−1.71374	−	0.989429i	−0.784360	−	0.620305i	$-0.787009\pi$
$522$		0			0
$523$	−2.99933	+	1.73166i	−0.131152	+	0.0757204i	−0.564140	−	0.825679i	$-0.690792\pi$
$523$	−2.99933	+	1.73166i	−0.131152	+	0.0757204i	0.432989	+	0.901399i	$0.357459\pi$
$524$	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	−0.919837	−	0.392301i	$-0.871679\pi$
$547$	−8.74169	+	10.4179i	−0.373768	+	0.445439i	0.546069	+	0.837740i	$0.316124\pi$
$548$	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	−0.615135	−	0.788422i	$-0.710899\pi$
$557$	−5.66207	+	3.26900i	−0.239909	+	0.138512i	0.375226	+	0.926933i	$0.377565\pi$
$558$		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	−0.175824	−	0.984422i	$-0.556259\pi$
$563$	18.1068	−	15.1934i	0.763110	−	0.640325i	0.938934	+	0.344096i	$0.111815\pi$
$564$		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	0.831104	−	0.556117i	$-0.187709\pi$
$569$	−3.88872	−	10.6842i	−0.163024	−	0.447904i	−0.994128	+	0.108213i	$0.965487\pi$
$570$		0			0
$571$	14.2613	+	16.9960i	0.596818	+	0.711260i	0.976901	−	0.213692i	$-0.0685490\pi$
$571$	14.2613	+	16.9960i	0.596818	+	0.711260i	−0.380083	+	0.924952i	$0.624105\pi$
$572$	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	0.955037	−	0.296487i	$-0.0958150\pi$
$577$	5.30268	+	9.18452i	0.220754	+	0.382357i	−0.734283	+	0.678843i	$0.762482\pi$
$578$	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	0.794314	−	0.607507i	$-0.207830\pi$
$587$	8.09141	+	6.78950i	0.333968	+	0.280233i	−0.460346	+	0.887740i	$0.652275\pi$
$588$		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	$0.191522\pi$
$593$			27.5676i			1.13207i	−0.824383	+	0.566033i	$0.808478\pi$
$594$		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	0.996859	+	0.0792006i	$0.0252368\pi$
$599$	2.13432	+	12.1044i	0.0872061	+	0.494571i	−0.909653	+	0.415370i	$0.863652\pi$
$600$		0			0
$601$	−9.68745	−	8.12873i	−0.395159	−	0.331578i	0.423460	−	0.905915i	$-0.360815\pi$
$601$	−9.68745	−	8.12873i	−0.395159	−	0.331578i	−0.818619	+	0.574337i	$0.805260\pi$
$602$	−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	−0.889086	−	0.457741i	$-0.848659\pi$
$607$	2.12432	−	5.83652i	0.0862235	−	0.236897i	0.975309	+	0.220844i	$0.0708810\pi$
$608$	−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	−0.495077	−	0.868849i	$-0.664860\pi$
$613$	12.5009	−	21.6522i	0.504907	−	0.874524i	0.999984	−	0.00567529i	$-0.00180651\pi$
$614$	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	0.999818	+	0.0190859i	$0.00607561\pi$
$617$	20.9893	+	25.0141i	0.844997	+	1.00703i	−0.154821	+	0.987943i	$0.549480\pi$
$618$		0			0
$619$	−13.2843	−	36.4984i	−0.533942	−	1.46699i	−0.854342	−	0.519711i	$-0.826040\pi$
$619$	−13.2843	−	36.4984i	−0.533942	−	1.46699i	0.320401	−	0.947282i	$-0.396182\pi$
$620$	−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	0.152911	−	0.988240i	$-0.451135\pi$
$631$	27.2601	−	15.7386i	1.08521	−	0.626544i	0.932296	+	0.361696i	$0.117802\pi$
$632$	−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	−0.886107	−	0.463481i	$-0.846600\pi$
$641$	−6.98262	+	8.32156i	−0.275797	+	0.328682i	0.610310	+	0.792163i	$0.291045\pi$
$642$		0			0
$643$	10.8032	−	1.90489i	0.426036	−	0.0751217i	0.0434808	−	0.999054i	$-0.486155\pi$
$643$	10.8032	−	1.90489i	0.426036	−	0.0751217i	0.382555	+	0.923933i	$0.375044\pi$
$644$	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	0.424367	−	0.905490i	$-0.360497\pi$
$653$	28.9484	−	5.10438i	1.13284	−	0.199750i	0.708471	+	0.705740i	$0.249385\pi$
$654$		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	−0.984516	−	0.175294i	$-0.943912\pi$
$659$	0.0149056	−	0.0845336i	0.000580638	−	0.00329296i	0.985097	+	0.172001i	$0.0550234\pi$
$660$		0			0
$661$	−12.6865	−	4.61752i	−0.493449	−	0.179601i	0.0832963	−	0.996525i	$-0.473455\pi$
$661$	−12.6865	−	4.61752i	−0.493449	−	0.179601i	−0.576745	+	0.816924i	$0.695677\pi$
$662$	−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	−0.436849	−	0.899535i	$-0.643906\pi$
$673$	−5.01426	+	1.82504i	−0.193285	+	0.0703501i	0.243564	+	0.969885i	$0.421683\pi$
$674$	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	0.984119	+	0.177512i	$0.0568050\pi$
$677$	8.95953	+	24.6161i	0.344343	+	0.946074i	−0.639776	+	0.768562i	$0.720973\pi$
$678$		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	−0.360369	−	0.932810i	$-0.617349\pi$
$683$	16.4032	−	28.4113i	0.627653	−	1.08713i	0.988021	−	0.154317i	$-0.0493176\pi$
$684$		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	0.0771239	−	0.997022i	$-0.475426\pi$
$691$	−5.03144	−	0.887178i	−0.191405	−	0.0337498i	−0.268529	+	0.963272i	$0.586537\pi$
$692$	−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	$-0.718974\pi$
$701$		−	40.9095i		−	1.54513i	0.634936	−	0.772565i	$-0.281026\pi$
$702$		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	0.384033	−	0.923319i	$-0.374535\pi$
$709$	−12.2104	−	10.2458i	−0.458572	−	0.384787i	−0.842605	+	0.538532i	$0.818979\pi$
$710$	−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	−0.994281	−	0.106793i	$-0.965942\pi$
$719$	−15.8103	−	27.3843i	−0.589626	−	1.02126i	0.404655	−	0.914469i	$-0.367392\pi$
$720$		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	0.976986	+	0.213302i	$0.0684220\pi$
$727$	9.85979	+	27.0896i	0.365680	+	1.00470i	−0.611307	+	0.791394i	$0.709356\pi$
$728$	−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	−0.979826	−	0.199851i	$-0.935954\pi$
$733$	−25.8057	+	21.6536i	−0.953157	+	0.799793i	0.0266696	+	0.999644i	$0.491510\pi$
$734$	−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	−0.677678	−	0.735359i	$-0.737014\pi$
$739$	−10.3214	+	5.95905i	−0.379678	+	0.219207i	0.298000	+	0.954566i	$0.403680\pi$
$740$	−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	0.169962	−	0.985451i	$-0.445636\pi$
$743$	−9.08444	−	3.30647i	−0.333276	−	0.121302i	−0.503237	+	0.864148i	$0.667858\pi$
$744$		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	0.243246	−	0.969965i	$-0.421788\pi$
$751$	22.0213	−	3.88295i	0.803570	−	0.141691i	0.560324	+	0.828274i	$0.310677\pi$
$752$	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	−0.889034	−	0.457840i	$-0.848623\pi$
$761$	−43.2514	+	7.62639i	−1.56786	+	0.276457i	−0.678829	+	0.734297i	$0.737512\pi$
$762$		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	0.971989	−	0.235027i	$-0.0755178\pi$
$769$	43.4127	+	15.8009i	1.56550	+	0.569797i	0.593514	+	0.804823i	$0.297740\pi$
$770$	−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	0.297232	−	0.954805i	$-0.403936\pi$
$773$	35.3857	−	20.4299i	1.27273	−	0.734813i	0.975502	+	0.219992i	$0.0706031\pi$
$774$		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	−0.991221	−	0.132214i	$-0.957792\pi$
$787$	−26.6313	−	31.7379i	−0.949302	−	1.13133i	0.0419189	−	0.999121i	$-0.486653\pi$
$788$	−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	−0.991938	−	0.126725i	$-0.959553\pi$
$797$	−4.25196	+	11.6822i	−0.150612	+	0.413803i	0.841326	+	0.540528i	$0.181776\pi$
$798$		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	$-0.974345\pi$
$809$		−	4.57993i		−	0.161022i	0.996754	−	0.0805109i	$-0.0256552\pi$
$810$		0			0
$811$			23.9708i			0.841727i	0.907124	+	0.420864i	$0.138273\pi$
$811$			23.9708i			0.841727i	−0.907124	+	0.420864i	$0.861727\pi$
$812$	−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	0.0418649	−	0.999123i	$-0.486670\pi$
$821$	−7.46457	−	1.31620i	−0.260515	−	0.0459359i	−0.302380	+	0.953187i	$0.597781\pi$
$822$		0			0
$823$	−15.9886	+	43.9282i	−0.557326	+	1.53124i	0.266174	+	0.963925i	$0.414240\pi$
$823$	−15.9886	+	43.9282i	−0.557326	+	1.53124i	−0.823500	+	0.567316i	$0.807982\pi$
$824$	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	0.999081	+	0.0428620i	$0.0136476\pi$
$827$	15.4331	+	26.7308i	0.536660	+	0.929522i	−0.462421	+	0.886661i	$0.653019\pi$
$828$		0			0
$829$	5.56407	−	9.63724i	0.193248	−	0.334715i	−0.753077	−	0.657933i	$-0.771431\pi$
$829$	5.56407	−	9.63724i	0.193248	−	0.334715i	0.946325	+	0.323217i	$0.104764\pi$
$830$	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	−0.488559	−	0.872531i	$-0.662477\pi$
$839$	−8.74658	+	3.18349i	−0.301965	+	0.109906i	0.186594	+	0.982437i	$0.440255\pi$
$840$		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	−0.920229	−	0.391381i	$-0.871998\pi$
$853$	2.28870	−	12.9798i	0.0783634	−	0.444421i	0.998592	−	0.0530406i	$-0.0168913\pi$
$854$	−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	−0.574599	−	0.818435i	$-0.694842\pi$
$857$	9.69516	−	11.5542i	0.331180	−	0.394685i	0.905779	+	0.423750i	$0.139286\pi$
$858$		0			0
$859$	24.5457	−	4.32808i	0.837490	−	0.147672i	0.261577	−	0.965183i	$-0.415758\pi$
$859$	24.5457	−	4.32808i	0.837490	−	0.147672i	0.575914	+	0.817511i	$0.304646\pi$
$860$	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	−0.0283170	−	0.999599i	$-0.509015\pi$
$877$	−20.5090	−	7.46466i	−0.692539	−	0.252064i	−0.664222	+	0.747535i	$0.731237\pi$
$878$	−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	−0.372062	−	0.928208i	$-0.621349\pi$
$881$	7.29454	−	4.21150i	0.245759	−	0.141889i	0.617821	+	0.786319i	$0.288016\pi$
$882$		0			0
$883$	21.6426	+	12.4953i	0.728330	+	0.420502i	0.817811	−	0.575487i	$-0.195187\pi$
$883$	21.6426	+	12.4953i	0.728330	+	0.420502i	−0.0894807	+	0.995989i	$0.528521\pi$
$884$	−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	−0.999761	−	0.0218707i	$-0.993038\pi$
$887$	−34.3044	+	28.7848i	−1.15183	+	0.966499i	−0.152068	+	0.988370i	$0.548593\pi$
$888$		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	−0.376091	−	0.926583i	$-0.622732\pi$
$907$	−31.5142	−	5.55680i	−1.04641	−	0.184511i	−0.670320	+	0.742072i	$0.733843\pi$
$908$	−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	0.203214	−	0.979134i	$-0.434861\pi$
$911$	−21.9054	−	18.3808i	−0.725757	−	0.608983i	−0.928971	+	0.370152i	$0.879306\pi$
$912$		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	$-0.848542\pi$
$919$		−	27.7726i		−	0.916132i	0.888918	−	0.458066i	$-0.151458\pi$
$920$	−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	0.325718	−	0.945467i	$-0.394394\pi$
$929$	9.40060	+	1.65758i	0.308424	+	0.0543834i	−0.0172941	+	0.999850i	$0.505505\pi$
$930$		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	−0.884025	−	0.467439i	$-0.845177\pi$
$937$	−1.13866	+	1.97222i	−0.0371986	+	0.0644298i	0.846827	+	0.531869i	$0.178510\pi$
$938$	−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	0.834130	−	0.551567i	$-0.185970\pi$
$941$	4.48164	+	5.34101i	0.146097	+	0.174112i	−0.688033	+	0.725679i	$0.741526\pi$
$942$		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	0.468103	−	0.883674i	$-0.344937\pi$
$947$	42.9198	−	15.6215i	1.39471	−	0.507631i	0.926603	+	0.376042i	$0.122715\pi$
$948$		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	0.860796	−	0.508950i	$-0.169966\pi$
$953$	26.2534	+	15.1574i	0.850431	+	0.490997i	−0.0103652	+	0.999946i	$0.503299\pi$
$954$		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	−0.646146	−	0.763214i	$-0.723620\pi$
$967$	−30.8569	+	5.44090i	−0.992290	+	0.174967i	−0.346144	+	0.938181i	$0.612509\pi$
$968$	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	−0.579194	−	0.815190i	$-0.696633\pi$
$977$	−26.4012	+	4.65524i	−0.844648	+	0.148934i	−0.265453	+	0.964124i	$0.585522\pi$
$978$		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	0.821217	+	0.570616i	$0.193296\pi$
$983$	−4.56612	+	25.8958i	−0.145637	+	0.825947i	−0.966854	+	0.255331i	$0.917816\pi$
$984$		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	0.786270	−	0.617883i	$-0.212010\pi$
$991$	20.2827	+	11.7102i	0.644302	+	0.371988i	−0.141968	+	0.989871i	$0.545343\pi$
$992$	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	−0.253653	−	0.967295i	$-0.581632\pi$
$997$	5.48788	−	1.99742i	0.173803	−	0.0632590i	0.427456	+	0.904036i	$0.359410\pi$
$998$	−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.143.1		96
3.2	odd	2		108.2.l.a.47.16	yes	96
4.3	odd	2	inner	324.2.l.a.143.12		96
9.2	odd	6		972.2.l.d.107.7		96
9.4	even	3		972.2.l.b.755.12		96
9.5	odd	6		972.2.l.c.755.5		96
9.7	even	3		972.2.l.a.107.10		96
12.11	even	2		108.2.l.a.47.5	yes	96
27.4	even	9		108.2.l.a.23.5	✓	96
27.5	odd	18		972.2.l.b.215.11		96
27.13	even	9		972.2.l.d.863.16		96
27.14	odd	18		972.2.l.a.863.1		96
27.22	even	9		972.2.l.c.215.6		96
27.23	odd	18	inner	324.2.l.a.179.12		96
36.7	odd	6		972.2.l.a.107.1		96
36.11	even	6		972.2.l.d.107.16		96
36.23	even	6		972.2.l.c.755.6		96
36.31	odd	6		972.2.l.b.755.11		96
108.23	even	18	inner	324.2.l.a.179.1		96
108.31	odd	18		108.2.l.a.23.16	yes	96
108.59	even	18		972.2.l.b.215.12		96
108.67	odd	18		972.2.l.d.863.7		96
108.95	even	18		972.2.l.a.863.10		96
108.103	odd	18		972.2.l.c.215.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.5	✓	96	27.4	even	9
108.2.l.a.23.16	yes	96	108.31	odd	18
108.2.l.a.47.5	yes	96	12.11	even	2
108.2.l.a.47.16	yes	96	3.2	odd	2
324.2.l.a.143.1		96	1.1	even	1	trivial
324.2.l.a.143.12		96	4.3	odd	2	inner
324.2.l.a.179.1		96	108.23	even	18	inner
324.2.l.a.179.12		96	27.23	odd	18	inner
972.2.l.a.107.1		96	36.7	odd	6
972.2.l.a.107.10		96	9.7	even	3
972.2.l.a.863.1		96	27.14	odd	18
972.2.l.a.863.10		96	108.95	even	18
972.2.l.b.215.11		96	27.5	odd	18
972.2.l.b.215.12		96	108.59	even	18
972.2.l.b.755.11		96	36.31	odd	6
972.2.l.b.755.12		96	9.4	even	3
972.2.l.c.215.5		96	108.103	odd	18
972.2.l.c.215.6		96	27.22	even	9
972.2.l.c.755.5		96	9.5	odd	6
972.2.l.c.755.6		96	36.23	even	6
972.2.l.d.107.7		96	9.2	odd	6
972.2.l.d.107.16		96	36.11	even	6
972.2.l.d.863.7		96	108.67	odd	18
972.2.l.d.863.16		96	27.13	even	9

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

L-functions

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