LMFDB - Embedded newform 855.2.bs.b.766.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			766.2
Root			$0.296923 + 0.514286i$ of defining polynomial
Character	$\chi$	$=$	855.766
Dual form			855.2.bs.b.586.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.454913 - 0.381717i) q^{2} +(-0.286059 + 1.62232i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.530259 + 0.918436i) q^{7} +(1.08298 + 1.87578i) q^{8} +O(q^{10})$	\(q+(0.454913 - 0.381717i) q^{2} +(-0.286059 + 1.62232i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.530259 + 0.918436i) q^{7} +(1.08298 + 1.87578i) q^{8} +(0.454913 + 0.381717i) q^{10} +(0.0983263 + 0.170306i) q^{11} +(4.96388 - 1.80671i) q^{13} +(0.109361 + 0.620217i) q^{14} +(-1.88732 - 0.686928i) q^{16} +(-0.540035 + 0.453143i) q^{17} +(-4.24646 + 0.983648i) q^{19} -1.64735 q^{20} +(0.109739 + 0.0399416i) q^{22} +(-1.15007 + 6.52236i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(1.56848 - 2.71669i) q^{26} +(-1.33831 - 1.12298i) q^{28} +(2.59020 + 2.17343i) q^{29} +(-3.95912 + 6.85739i) q^{31} +(-5.19146 + 1.88954i) q^{32} +(-0.0726963 + 0.412281i) q^{34} +(-0.996561 - 0.362719i) q^{35} -1.09727 q^{37} +(-1.55629 + 2.06842i) q^{38} +(-1.65922 + 1.39225i) q^{40} +(-1.27293 - 0.463310i) q^{41} +(1.56424 + 8.87125i) q^{43} +(-0.304418 + 0.110799i) q^{44} +(1.96652 + 3.40611i) q^{46} +(-3.69186 - 3.09784i) q^{47} +(2.93765 + 5.08816i) q^{49} +(-0.296923 + 0.514286i) q^{50} +(1.51109 + 8.56982i) q^{52} +(0.924537 - 5.24331i) q^{53} +(-0.150645 + 0.126406i) q^{55} -2.29704 q^{56} +2.00795 q^{58} +(8.41282 - 7.05920i) q^{59} +(2.04079 - 11.5739i) q^{61} +(0.816531 + 4.63078i) q^{62} +(0.368050 - 0.637482i) q^{64} +(2.64123 + 4.57474i) q^{65} +(-2.34103 - 1.96435i) q^{67} +(-0.580661 - 1.00573i) q^{68} +(-0.591804 + 0.215399i) q^{70} +(-0.434950 - 2.46672i) q^{71} +(-6.15894 - 2.24167i) q^{73} +(-0.499161 + 0.418846i) q^{74} +(-0.381053 - 7.17050i) q^{76} -0.208554 q^{77} +(11.5236 + 4.19426i) q^{79} +(0.348762 - 1.97793i) q^{80} +(-0.755927 + 0.275135i) q^{82} +(-2.01588 + 3.49160i) q^{83} +(-0.540035 - 0.453143i) q^{85} +(4.09790 + 3.43855i) q^{86} +(-0.212971 + 0.368877i) q^{88} +(16.4684 - 5.99401i) q^{89} +(-0.972801 + 5.51703i) q^{91} +(-10.2524 - 3.73156i) q^{92} -2.86197 q^{94} +(-1.70609 - 4.01114i) q^{95} +(-1.02612 + 0.861014i) q^{97} +(3.27861 + 1.19332i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.454913	−	0.381717i	0.321672	−	0.269915i	−0.467624	−	0.883927i	$-0.654890\pi$
$2$	0.454913	−	0.381717i	0.321672	−	0.269915i	0.789296	+	0.614012i	$0.210446\pi$
$3$		0			0
$3$		0			0
$4$	−0.286059	+	1.62232i	−0.143029	+	0.811160i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$6$		0			0
$7$	−0.530259	+	0.918436i	−0.200419	+	0.347136i	−0.948664	−	0.316287i	$-0.897564\pi$
$7$	−0.530259	+	0.918436i	−0.200419	+	0.347136i	0.748244	+	0.663423i	$0.230897\pi$
$8$	1.08298	+	1.87578i	0.382892	+	0.663188i
$9$		0			0
$10$	0.454913	+	0.381717i	0.143856	+	0.120710i
$11$	0.0983263	+	0.170306i	0.0296465	+	0.0513492i	0.880468	−	0.474106i	$-0.157229\pi$
$11$	0.0983263	+	0.170306i	0.0296465	+	0.0513492i	−0.850821	+	0.525455i	$0.823895\pi$
$12$		0			0
$13$	4.96388	−	1.80671i	1.37673	−	0.501090i	0.455547	−	0.890212i	$-0.349444\pi$
$13$	4.96388	−	1.80671i	1.37673	−	0.501090i	0.921186	+	0.389122i	$0.127222\pi$
$14$	0.109361	+	0.620217i	0.0292280	+	0.165760i
$15$		0			0
$16$	−1.88732	−	0.686928i	−0.471830	−	0.171732i
$17$	−0.540035	+	0.453143i	−0.130978	+	0.109903i	−0.705923	−	0.708288i	$-0.749468\pi$
$17$	−0.540035	+	0.453143i	−0.130978	+	0.109903i	0.574946	+	0.818192i	$0.305023\pi$
$18$		0			0
$19$	−4.24646	+	0.983648i	−0.974205	+	0.225664i
$19$	−4.24646	+	0.983648i	−0.974205	+	0.225664i
$20$	−1.64735			−0.368358
$21$		0			0
$22$	0.109739	+	0.0399416i	0.0233964	+	0.00851558i
$23$	−1.15007	+	6.52236i	−0.239806	+	1.36001i	0.592447	+	0.805610i	$0.298162\pi$
$23$	−1.15007	+	6.52236i	−0.239806	+	1.36001i	−0.832253	+	0.554397i	$0.812949\pi$
$24$		0			0
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	1.56848	−	2.71669i	0.307605	−	0.532787i
$27$		0			0
$28$	−1.33831	−	1.12298i	−0.252917	−	0.212223i
$29$	2.59020	+	2.17343i	0.480988	+	0.403597i	0.850783	−	0.525516i	$-0.176128\pi$
$29$	2.59020	+	2.17343i	0.480988	+	0.403597i	−0.369796	+	0.929113i	$0.620572\pi$
$30$		0			0
$31$	−3.95912	+	6.85739i	−0.711078	+	1.23162i	0.253375	+	0.967368i	$0.418459\pi$
$31$	−3.95912	+	6.85739i	−0.711078	+	1.23162i	−0.964453	+	0.264255i	$0.914874\pi$
$32$	−5.19146	+	1.88954i	−0.917729	+	0.334026i
$33$		0			0
$34$	−0.0726963	+	0.412281i	−0.0124673	+	0.0707056i
$35$	−0.996561	−	0.362719i	−0.168450	−	0.0613106i
$36$		0			0
$37$	−1.09727			−0.180390			−0.0901949	−	0.995924i	$-0.528749\pi$
$37$	−1.09727			−0.180390			−0.0901949	+	0.995924i	$0.528749\pi$
$38$	−1.55629	+	2.06842i	−0.252464	+	0.335542i
$39$		0			0
$40$	−1.65922	+	1.39225i	−0.262346	+	0.220135i
$41$	−1.27293	−	0.463310i	−0.198799	−	0.0723568i	0.240702	−	0.970599i	$-0.422622\pi$
$41$	−1.27293	−	0.463310i	−0.198799	−	0.0723568i	−0.439501	+	0.898242i	$0.644845\pi$
$42$		0			0
$43$	1.56424	+	8.87125i	0.238544	+	1.35285i	0.835019	+	0.550221i	$0.185456\pi$
$43$	1.56424	+	8.87125i	0.238544	+	1.35285i	−0.596475	+	0.802632i	$0.703432\pi$
$44$	−0.304418	+	0.110799i	−0.0458928	+	0.0167036i
$45$		0			0
$46$	1.96652	+	3.40611i	0.289947	+	0.502203i
$47$	−3.69186	−	3.09784i	−0.538513	−	0.451866i	0.332516	−	0.943098i	$-0.392102\pi$
$47$	−3.69186	−	3.09784i	−0.538513	−	0.451866i	−0.871029	+	0.491232i	$0.836547\pi$
$48$		0			0
$49$	2.93765	+	5.08816i	0.419664	+	0.726880i
$50$	−0.296923	+	0.514286i	−0.0419913	+	0.0727310i
$51$		0			0
$52$	1.51109	+	8.56982i	0.209551	+	1.18842i
$53$	0.924537	−	5.24331i	0.126995	−	0.720224i	−0.853108	−	0.521734i	$-0.825285\pi$
$53$	0.924537	−	5.24331i	0.126995	−	0.720224i	0.980103	−	0.198490i	$-0.0636037\pi$
$54$		0			0
$55$	−0.150645	+	0.126406i	−0.0203129	+	0.0170446i
$56$	−2.29704			−0.306955
$57$		0			0
$58$	2.00795			0.263657
$59$	8.41282	−	7.05920i	1.09526	−	0.919029i	0.0981591	−	0.995171i	$-0.468705\pi$
$59$	8.41282	−	7.05920i	1.09526	−	0.919029i	0.997097	+	0.0761417i	$0.0242601\pi$
$60$		0			0
$61$	2.04079	−	11.5739i	0.261297	−	1.48189i	−0.518081	−	0.855332i	$-0.673353\pi$
$61$	2.04079	−	11.5739i	0.261297	−	1.48189i	0.779378	−	0.626555i	$-0.215535\pi$
$62$	0.816531	+	4.63078i	0.103700	+	0.588109i
$63$		0			0
$64$	0.368050	−	0.637482i	0.0460063	−	0.0796852i
$65$	2.64123	+	4.57474i	0.327604	+	0.567426i
$66$		0			0
$67$	−2.34103	−	1.96435i	−0.286002	−	0.239984i	0.488488	−	0.872571i	$-0.337549\pi$
$67$	−2.34103	−	1.96435i	−0.286002	−	0.239984i	−0.774489	+	0.632587i	$0.781993\pi$
$68$	−0.580661	−	1.00573i	−0.0704155	−	0.121963i
$69$		0			0
$70$	−0.591804	+	0.215399i	−0.0707342	+	0.0257451i
$71$	−0.434950	−	2.46672i	−0.0516191	−	0.292746i	0.948060	−	0.318093i	$-0.103042\pi$
$71$	−0.434950	−	2.46672i	−0.0516191	−	0.292746i	−0.999679	+	0.0253463i	$0.991931\pi$
$72$		0			0
$73$	−6.15894	−	2.24167i	−0.720849	−	0.262368i	−0.0445630	−	0.999007i	$-0.514190\pi$
$73$	−6.15894	−	2.24167i	−0.720849	−	0.262368i	−0.676286	+	0.736639i	$0.736412\pi$
$74$	−0.499161	+	0.418846i	−0.0580263	+	0.0486899i
$75$		0			0
$76$	−0.381053	−	7.17050i	−0.0437098	−	0.822513i
$77$	−0.208554			−0.0237669
$78$		0			0
$79$	11.5236	+	4.19426i	1.29651	+	0.471892i	0.895859	−	0.444339i	$-0.146561\pi$
$79$	11.5236	+	4.19426i	1.29651	+	0.471892i	0.400652	+	0.916230i	$0.368784\pi$
$80$	0.348762	−	1.97793i	0.0389928	−	0.221139i
$81$		0			0
$82$	−0.755927	+	0.275135i	−0.0834782	+	0.0303836i
$83$	−2.01588	+	3.49160i	−0.221271	+	0.383253i	−0.955194	−	0.295980i	$-0.904354\pi$
$83$	−2.01588	+	3.49160i	−0.221271	+	0.383253i	0.733923	+	0.679233i	$0.237687\pi$
$84$		0			0
$85$	−0.540035	−	0.453143i	−0.0585750	−	0.0491502i
$86$	4.09790	+	3.43855i	0.441888	+	0.370788i
$87$		0			0
$88$	−0.212971	+	0.368877i	−0.0227028	+	0.0393224i
$89$	16.4684	−	5.99401i	1.74565	−	0.635364i	0.746112	−	0.665821i	$-0.231918\pi$
$89$	16.4684	−	5.99401i	1.74565	−	0.635364i	0.999536	+	0.0304568i	$0.00969621\pi$
$90$		0			0
$91$	−0.972801	+	5.51703i	−0.101977	+	0.578342i
$92$	−10.2524	−	3.73156i	−1.06888	−	0.389042i
$93$		0			0
$94$	−2.86197			−0.295190
$95$	−1.70609	−	4.01114i	−0.175042	−	0.411534i
$96$		0			0
$97$	−1.02612	+	0.861014i	−0.104186	+	0.0874227i	−0.693393	−	0.720560i	$-0.743885\pi$
$97$	−1.02612	+	0.861014i	−0.104186	+	0.0874227i	0.589206	+	0.807983i	$0.299440\pi$
$98$	3.27861	+	1.19332i	0.331190	+	0.120543i
$99$		0			0
$100$	−0.286059	−	1.62232i	−0.0286059	−	0.162232i
$101$	−16.8532	+	6.13405i	−1.67695	+	0.610361i	−0.992887	−	0.119060i	$-0.962012\pi$
$101$	−16.8532	+	6.13405i	−1.67695	+	0.610361i	−0.684065	+	0.729421i	$0.739790\pi$
$102$		0			0
$103$	5.81168	+	10.0661i	0.572641	+	0.991844i	0.996293	+	0.0860191i	$0.0274146\pi$
$103$	5.81168	+	10.0661i	0.572641	+	0.991844i	−0.423652	+	0.905825i	$0.639252\pi$
$104$	8.76477	+	7.35452i	0.859457	+	0.721170i
$105$		0			0
$106$	−1.58088	−	2.73816i	−0.153549	−	0.265954i
$107$	1.24823	−	2.16199i	0.120671	−	0.209007i	−0.799362	−	0.600850i	$-0.794829\pi$
$107$	1.24823	−	2.16199i	0.120671	−	0.209007i	0.920032	+	0.391843i	$0.128162\pi$
$108$		0			0
$109$	−0.360621	−	2.04518i	−0.0345412	−	0.195893i	0.962654	−	0.270734i	$-0.0872663\pi$
$109$	−0.360621	−	2.04518i	−0.0345412	−	0.195893i	−0.997195	+	0.0748407i	$0.976155\pi$
$110$	−0.0202789	+	0.115007i	−0.00193352	+	0.0109655i
$111$		0			0
$112$	1.63167	−	1.36913i	0.154178	−	0.129371i
$113$	15.3786			1.44669			0.723347	−	0.690484i	$-0.242603\pi$
$113$	15.3786			1.44669			0.723347	+	0.690484i	$0.242603\pi$
$114$		0			0
$115$	−6.62298			−0.617596
$116$	−4.26695	+	3.58040i	−0.396177	+	0.332432i
$117$		0			0
$118$	1.13248	−	6.42264i	0.104254	−	0.591252i
$119$	−0.129824	−	0.736270i	−0.0119010	−	0.0674938i
$120$		0			0
$121$	5.48066	−	9.49279i	0.498242	−	0.862981i
$122$	−3.48957	−	6.04412i	−0.315931	−	0.547209i
$123$		0			0
$124$	−9.99234	−	8.38457i	−0.897338	−	0.752956i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	7.14848	−	2.60183i	0.634325	−	0.230875i	−0.00478767	−	0.999989i	$-0.501524\pi$
$127$	7.14848	−	2.60183i	0.634325	−	0.230875i	0.639113	+	0.769113i	$0.279302\pi$
$128$	−1.99459	−	11.3119i	−0.176299	−	0.999840i
$129$		0			0
$130$	2.94778	+	1.07291i	0.258538	+	0.0941000i
$131$	15.9798	−	13.4087i	1.39616	−	1.17152i	0.433392	−	0.901205i	$-0.357317\pi$
$131$	15.9798	−	13.4087i	1.39616	−	1.17152i	0.962772	−	0.270315i	$-0.0871279\pi$
$132$		0			0
$133$	1.34831	−	4.42169i	0.116913	−	0.383409i
$134$	−1.81479			−0.156774
$135$		0			0
$136$	−1.43484	−	0.522240i	−0.123037	−	0.0447818i
$137$	−3.33683	+	18.9241i	−0.285085	+	1.61680i	0.419897	+	0.907572i	$0.362066\pi$
$137$	−3.33683	+	18.9241i	−0.285085	+	1.61680i	−0.704982	+	0.709225i	$0.749045\pi$
$138$		0			0
$139$	18.4635	−	6.72016i	1.56605	−	0.569997i	0.593940	−	0.804509i	$-0.297572\pi$
$139$	18.4635	−	6.72016i	1.56605	−	0.569997i	0.972113	+	0.234513i	$0.0753494\pi$
$140$	0.873520	−	1.51298i	0.0738260	−	0.127870i
$141$		0			0
$142$	−1.13945	−	0.956116i	−0.0956209	−	0.0802355i
$143$	0.795773	+	0.667733i	0.0665459	+	0.0558386i
$144$		0			0
$145$	−1.69063	+	2.92826i	−0.140399	+	0.243179i
$146$	−3.65746	+	1.33121i	−0.302694	+	0.110172i
$147$		0			0
$148$	0.313883	−	1.78012i	0.0258010	−	0.146325i
$149$	−8.13270	−	2.96006i	−0.666257	−	0.242498i	−0.0133215	−	0.999911i	$-0.504241\pi$
$149$	−8.13270	−	2.96006i	−0.666257	−	0.242498i	−0.652935	+	0.757414i	$0.726463\pi$
$150$		0			0
$151$	−4.95316			−0.403083			−0.201541	−	0.979480i	$-0.564595\pi$
$151$	−4.95316			−0.403083			−0.201541	+	0.979480i	$0.564595\pi$
$152$	−6.44395	−	6.90015i	−0.522673	−	0.559676i
$153$		0			0
$154$	−0.0948738	+	0.0796085i	−0.00764515	+	0.00641504i
$155$	−7.44070	−	2.70819i	−0.597652	−	0.217527i
$156$		0			0
$157$	−2.40761	−	13.6542i	−0.192148	−	1.08973i	−0.916422	−	0.400214i	$-0.868936\pi$
$157$	−2.40761	−	13.6542i	−0.192148	−	1.08973i	0.724273	−	0.689513i	$-0.242175\pi$
$158$	6.84328	−	2.49075i	0.544422	−	0.198153i
$159$		0			0
$160$	−2.76232	−	4.78447i	−0.218380	−	0.378246i
$161$	−5.38053	−	4.51480i	−0.424046	−	0.355816i
$162$		0			0
$163$	3.17547	+	5.50007i	0.248722	+	0.430799i	0.963171	−	0.268888i	$-0.0866562\pi$
$163$	3.17547	+	5.50007i	0.248722	+	0.430799i	−0.714450	+	0.699687i	$0.753323\pi$
$164$	1.11577	−	1.93257i	0.0871270	−	0.150908i
$165$		0			0
$166$	0.415756	+	2.35787i	0.0322689	+	0.183006i
$167$	−3.42089	+	19.4008i	−0.264716	+	1.50128i	0.505126	+	0.863046i	$0.331446\pi$
$167$	−3.42089	+	19.4008i	−0.264716	+	1.50128i	−0.769842	+	0.638234i	$0.779665\pi$
$168$		0			0
$169$	11.4174	−	9.58030i	0.878258	−	0.736946i
$170$	−0.418641			−0.0321083
$171$		0			0
$172$	−14.8395			−1.13150
$173$	−6.83133	+	5.73217i	−0.519377	+	0.435809i	−0.864414	−	0.502780i	$-0.832311\pi$
$173$	−6.83133	+	5.73217i	−0.519377	+	0.435809i	0.345038	+	0.938589i	$0.387866\pi$
$174$		0			0
$175$	0.184157	−	1.04441i	0.0139210	−	0.0789497i
$176$	−0.0685850	−	0.388965i	−0.00516979	−	0.0293193i
$177$		0			0
$178$	5.20367	−	9.01303i	0.390032	−	0.675555i
$179$	0.886039	+	1.53466i	0.0662257	+	0.114706i	0.897237	−	0.441549i	$-0.145571\pi$
$179$	0.886039	+	1.53466i	0.0662257	+	0.114706i	−0.831011	+	0.556255i	$0.812238\pi$
$180$		0			0
$181$	6.54881	+	5.49510i	0.486769	+	0.408448i	0.852867	−	0.522129i	$-0.174862\pi$
$181$	6.54881	+	5.49510i	0.486769	+	0.408448i	−0.366098	+	0.930576i	$0.619306\pi$
$182$	1.66340	+	2.88110i	0.123300	+	0.213561i
$183$		0			0
$184$	−13.4800	+	4.90632i	−0.993760	+	0.361699i
$185$	−0.190539	−	1.08060i	−0.0140087	−	0.0794471i
$186$		0			0
$187$	−0.130273	−	0.0474154i	−0.00952648	−	0.00346735i
$188$	6.08177	−	5.10321i	0.443558	−	0.372190i
$189$		0			0
$190$	−2.30725	−	1.17347i	−0.167385	−	0.0851327i
$191$	12.3918			0.896636			0.448318	−	0.893874i	$-0.352023\pi$
$191$	12.3918			0.896636			0.448318	+	0.893874i	$0.352023\pi$
$192$		0			0
$193$	−1.43370	−	0.521824i	−0.103200	−	0.0375617i	0.289904	−	0.957056i	$-0.406377\pi$
$193$	−1.43370	−	0.521824i	−0.103200	−	0.0375617i	−0.393104	+	0.919494i	$0.628599\pi$
$194$	−0.138130	+	0.783373i	−0.00991714	+	0.0562429i
$195$		0			0
$196$	−9.09496	+	3.31030i	−0.649640	+	0.236450i
$197$	6.88125	−	11.9187i	0.490269	−	0.849171i	−0.509668	−	0.860371i	$-0.670232\pi$
$197$	6.88125	−	11.9187i	0.490269	−	0.849171i	0.999937	+	0.0112002i	$0.00356521\pi$
$198$		0			0
$199$	−10.9481	−	9.18652i	−0.776088	−	0.651215i	0.166172	−	0.986097i	$-0.446859\pi$
$199$	−10.9481	−	9.18652i	−0.776088	−	0.651215i	−0.942260	+	0.334881i	$0.891304\pi$
$200$	−1.65922	−	1.39225i	−0.117325	−	0.0984473i
$201$		0			0
$202$	−5.32525	+	9.22360i	−0.374683	+	0.648970i
$203$	−3.36964	+	1.22645i	−0.236502	+	0.0860797i
$204$		0			0
$205$	0.235229	−	1.33405i	0.0164291	−	0.0931739i
$206$	6.48622	+	2.36079i	0.451916	+	0.164484i
$207$		0			0
$208$	−10.6095			−0.735637
$209$	−0.585060	−	0.626480i	−0.0404695	−	0.0433345i
$210$		0			0
$211$	1.34520	−	1.12876i	0.0926074	−	0.0777068i	−0.595309	−	0.803497i	$-0.702970\pi$
$211$	1.34520	−	1.12876i	0.0926074	−	0.0777068i	0.687916	+	0.725790i	$0.258526\pi$
$212$	8.24186	+	2.99979i	0.566053	+	0.206026i
$213$		0			0
$214$	−0.257435	−	1.45999i	−0.0175979	−	0.0998026i
$215$	−8.46485	+	3.08095i	−0.577298	+	0.210119i
$216$		0			0
$217$	−4.19871	−	7.27239i	−0.285027	−	0.493682i
$218$	−0.944732	−	0.792724i	−0.0639853	−	0.0536901i
$219$		0			0
$220$	−0.161977	−	0.280553i	−0.0109205	−	0.0189149i
$221$	−1.86197	+	3.22503i	−0.125250	+	0.216939i
$222$		0			0
$223$	−2.90718	−	16.4874i	−0.194679	−	1.10408i	−0.912875	−	0.408240i	$-0.866143\pi$
$223$	−2.90718	−	16.4874i	−0.194679	−	1.10408i	0.718196	−	0.695841i	$-0.244968\pi$
$224$	1.01740	−	5.76996i	0.0679779	−	0.385522i
$225$		0			0
$226$	6.99591	−	5.87027i	0.465361	−	0.390484i
$227$	−16.3212			−1.08328			−0.541638	−	0.840612i	$-0.682196\pi$
$227$	−16.3212			−1.08328			−0.541638	+	0.840612i	$0.682196\pi$
$228$		0			0
$229$	10.0335			0.663033			0.331517	−	0.943449i	$-0.392440\pi$
$229$	10.0335			0.663033			0.331517	+	0.943449i	$0.392440\pi$
$230$	−3.01288	+	2.52810i	−0.198663	+	0.166698i
$231$		0			0
$232$	−1.27175	+	7.21243i	−0.0834942	+	0.473519i
$233$	−1.89676	−	10.7570i	−0.124261	−	0.704718i	−0.981744	−	0.190206i	$-0.939084\pi$
$233$	−1.89676	−	10.7570i	−0.124261	−	0.704718i	0.857483	−	0.514511i	$-0.172027\pi$
$234$		0			0
$235$	2.40969	−	4.17370i	0.157191	−	0.272262i
$236$	9.04571	+	15.6676i	0.588826	+	1.01988i
$237$		0			0
$238$	−0.340106	−	0.285383i	−0.0220458	−	0.0184986i
$239$	−5.93326	−	10.2767i	−0.383790	−	0.664745i	0.607810	−	0.794082i	$-0.292048\pi$
$239$	−5.93326	−	10.2767i	−0.383790	−	0.664745i	−0.991601	+	0.129338i	$0.958715\pi$
$240$		0			0
$241$	−3.03169	+	1.10344i	−0.195288	+	0.0710791i	−0.437813	−	0.899066i	$-0.644247\pi$
$241$	−3.03169	+	1.10344i	−0.195288	+	0.0710791i	0.242525	+	0.970145i	$0.422025\pi$
$242$	−1.13034	−	6.41045i	−0.0726608	−	0.412080i
$243$		0			0
$244$	18.1928	+	6.62163i	1.16467	+	0.423906i
$245$	−4.50074	+	3.77657i	−0.287542	+	0.241276i
$246$		0			0
$247$	−19.3018	+	12.5548i	−1.22814	+	0.798844i
$248$	−17.1506			−1.08906
$249$		0			0
$250$	−0.558033	−	0.203107i	−0.0352931	−	0.0128456i
$251$	0.304723	−	1.72817i	0.0192340	−	0.109081i	−0.973679	−	0.227922i	$-0.926807\pi$
$251$	0.304723	−	1.72817i	0.0192340	−	0.109081i	0.992913	+	0.118841i	$0.0379179\pi$
$252$		0			0
$253$	−1.22388	+	0.445456i	−0.0769447	+	0.0280056i
$254$	2.25877	−	3.91231i	0.141728	−	0.245480i
$255$		0			0
$256$	−4.09754	−	3.43824i	−0.256096	−	0.214890i
$257$	−18.5637	−	15.5768i	−1.15797	−	0.971656i	−0.158098	−	0.987423i	$-0.550536\pi$
$257$	−18.5637	−	15.5768i	−1.15797	−	0.971656i	−0.999876	+	0.0157678i	$0.994981\pi$
$258$		0			0
$259$	0.581836	−	1.00777i	0.0361535	−	0.0626198i
$260$	−8.17723	+	2.97627i	−0.507130	+	0.184580i
$261$		0			0
$262$	2.15111	−	12.1995i	0.132896	−	0.753691i
$263$	11.9270	+	4.34108i	0.735451	+	0.267682i	0.682470	−	0.730913i	$-0.260906\pi$
$263$	11.9270	+	4.34108i	0.735451	+	0.267682i	0.0529807	+	0.998596i	$0.483128\pi$
$264$		0			0
$265$	5.32420			0.327063
$266$	−1.07447	−	2.52616i	−0.0658801	−	0.154889i
$267$		0			0
$268$	3.85648	−	3.23597i	0.235572	−	0.197668i
$269$	26.5616	+	9.66763i	1.61949	+	0.589446i	0.983285	−	0.182075i	$-0.0582813\pi$
$269$	26.5616	+	9.66763i	1.61949	+	0.589446i	0.636204	+	0.771521i	$0.280504\pi$
$270$		0			0
$271$	1.42161	+	8.06236i	0.0863568	+	0.489754i	0.997056	+	0.0766825i	$0.0244328\pi$
$271$	1.42161	+	8.06236i	0.0863568	+	0.489754i	−0.910699	+	0.413071i	$0.864456\pi$
$272$	1.33049	−	0.484260i	0.0806730	−	0.0293626i
$273$		0			0
$274$	5.70570	+	9.88255i	0.344694	+	0.597027i
$275$	−0.150645	−	0.126406i	−0.00908421	−	0.00762256i
$276$		0			0
$277$	12.5287	+	21.7004i	0.752779	+	1.30385i	0.946471	+	0.322789i	$0.104620\pi$
$277$	12.5287	+	21.7004i	0.752779	+	1.30385i	−0.193692	+	0.981062i	$0.562046\pi$
$278$	5.83408	−	10.1049i	0.349905	−	0.606053i
$279$		0			0
$280$	−0.398878	−	2.26215i	−0.0238375	−	0.135189i
$281$	4.26163	−	24.1689i	0.254228	−	1.44180i	−0.543820	−	0.839202i	$-0.683022\pi$
$281$	4.26163	−	24.1689i	0.254228	−	1.44180i	0.798047	−	0.602595i	$-0.205866\pi$
$282$		0			0
$283$	19.7102	−	16.5388i	1.17165	−	0.983129i	0.171650	−	0.985158i	$-0.445090\pi$
$283$	19.7102	−	16.5388i	1.17165	−	0.983129i	0.999998	+	0.00202873i	$0.000645767\pi$
$284$	4.12623			0.244847
$285$		0			0
$286$	0.616893			0.0364776
$287$	1.10050	−	0.923433i	0.0649608	−	0.0545085i
$288$		0			0
$289$	−2.86572	+	16.2523i	−0.168572	+	0.956018i
$290$	0.348677	+	1.97745i	0.0204750	+	0.116120i
$291$		0			0
$292$	5.39852	−	9.35052i	0.315925	−	0.547198i
$293$	−2.72924	−	4.72718i	−0.159444	−	0.276165i	0.775224	−	0.631686i	$-0.217637\pi$
$293$	−2.72924	−	4.72718i	−0.159444	−	0.276165i	−0.934668	+	0.355521i	$0.884303\pi$
$294$		0			0
$295$	8.41282	+	7.05920i	0.489813	+	0.411002i
$296$	−1.18832	−	2.05823i	−0.0690698	−	0.119632i
$297$		0			0
$298$	−4.82958	+	1.75782i	−0.279770	+	0.101828i
$299$	6.07518	+	34.4541i	0.351337	+	1.99253i
$300$		0			0
$301$	−8.97712	−	3.26741i	−0.517433	−	0.188330i
$302$	−2.25326	+	1.89071i	−0.129660	+	0.108798i
$303$		0			0
$304$	8.69012	+	1.06056i	0.498413	+	0.0608271i
$305$	11.7524			0.672943
$306$		0			0
$307$	3.48291	+	1.26768i	0.198780	+	0.0723501i	0.439492	−	0.898247i	$-0.355159\pi$
$307$	3.48291	+	1.26768i	0.198780	+	0.0723501i	−0.240712	+	0.970597i	$0.577381\pi$
$308$	0.0596586	−	0.338341i	0.00339936	−	0.0192788i
$309$		0			0
$310$	−4.41864	+	1.60825i	−0.250962	+	0.0913426i
$311$	−0.867259	+	1.50214i	−0.0491777	+	0.0851784i	−0.889566	−	0.456806i	$-0.848993\pi$
$311$	−0.867259	+	1.50214i	−0.0491777	+	0.0851784i	0.840389	+	0.541984i	$0.182327\pi$
$312$		0			0
$313$	3.04002	+	2.55088i	0.171832	+	0.144184i	0.724648	−	0.689119i	$-0.242002\pi$
$313$	3.04002	+	2.55088i	0.171832	+	0.144184i	−0.552816	+	0.833303i	$0.686447\pi$
$314$	−6.30731	−	5.29246i	−0.355942	−	0.298671i
$315$		0			0
$316$	−10.1009	+	17.4952i	−0.568219	+	0.984183i
$317$	−25.1047	+	9.13738i	−1.41002	+	0.513206i	−0.931137	−	0.364670i	$-0.881182\pi$
$317$	−25.1047	+	9.13738i	−1.41002	+	0.513206i	−0.478887	+	0.877877i	$0.658959\pi$
$318$		0			0
$319$	−0.115465	+	0.654833i	−0.00646478	+	0.0366636i
$320$	0.691708	+	0.251761i	0.0386677	+	0.0140739i
$321$		0			0
$322$	−4.17105			−0.232444
$323$	1.84750	−	2.45546i	0.102798	−	0.136625i
$324$		0			0
$325$	−4.04659	+	3.39549i	−0.224465	+	0.188348i
$326$	3.54403	+	1.28992i	0.196286	+	0.0714422i
$327$		0			0
$328$	−0.509497	−	2.88950i	−0.0281322	−	0.159546i
$329$	4.80280	−	1.74808i	0.264787	−	0.0963746i
$330$		0			0
$331$	9.55725	+	16.5536i	0.525314	+	0.909871i	0.999565	+	0.0294810i	$0.00938546\pi$
$331$	9.55725	+	16.5536i	0.525314	+	0.909871i	−0.474251	+	0.880389i	$0.657281\pi$
$332$	−5.08783	−	4.26920i	−0.279231	−	0.234303i
$333$		0			0
$334$	5.84942	+	10.1315i	0.320066	+	0.554370i
$335$	1.52800	−	2.64657i	0.0834833	−	0.144597i
$336$		0			0
$337$	−2.12149	−	12.0315i	−0.115565	−	0.655400i	−0.986469	−	0.163947i	$-0.947577\pi$
$337$	−2.12149	−	12.0315i	−0.115565	−	0.655400i	0.870904	−	0.491452i	$-0.163534\pi$
$338$	1.53694	−	8.71640i	0.0835983	−	0.474110i
$339$		0			0
$340$	0.889624	−	0.746483i	0.0482466	−	0.0404837i
$341$	−1.55714			−0.0843239
$342$		0			0
$343$	−13.6545			−0.737273
$344$	−14.9465	+	12.5416i	−0.805859	+	0.676196i
$345$		0			0
$346$	−0.919594	+	5.21528i	−0.0494377	+	0.280375i
$347$	0.688384	+	3.90402i	0.0369544	+	0.209579i	0.997694	−	0.0678729i	$-0.0216212\pi$
$347$	0.688384	+	3.90402i	0.0369544	+	0.209579i	−0.960740	+	0.277452i	$0.910510\pi$
$348$		0			0
$349$	12.4163	−	21.5056i	0.664628	−	1.15117i	−0.314758	−	0.949172i	$-0.601923\pi$
$349$	12.4163	−	21.5056i	0.664628	−	1.15117i	0.979386	−	0.201998i	$-0.0647435\pi$
$350$	−0.314893	−	0.545410i	−0.0168317	−	0.0291534i
$351$		0			0
$352$	−0.832257	−	0.698346i	−0.0443594	−	0.0372220i
$353$	7.01082	+	12.1431i	0.373148	+	0.646312i	0.990048	−	0.140730i	$-0.0449449\pi$
$353$	7.01082	+	12.1431i	0.373148	+	0.646312i	−0.616900	+	0.787042i	$0.711612\pi$
$354$		0			0
$355$	2.35372	−	0.856684i	0.124922	−	0.0454681i
$356$	5.01327	+	28.4317i	0.265703	+	1.50687i
$357$		0			0
$358$	0.988878	+	0.359922i	0.0522638	+	0.0190225i
$359$	13.4157	−	11.2571i	0.708056	−	0.594129i	−0.215997	−	0.976394i	$-0.569300\pi$
$359$	13.4157	−	11.2571i	0.708056	−	0.594129i	0.924053	+	0.382265i	$0.124856\pi$
$360$		0			0
$361$	17.0649	−	8.35404i	0.898151	−	0.439686i
$362$	5.07671			0.266826
$363$		0			0
$364$	−8.67210	−	3.15639i	−0.454542	−	0.165440i
$365$	1.13813	−	6.45463i	0.0595722	−	0.337851i
$366$		0			0
$367$	−17.1931	+	6.25776i	−0.897470	+	0.326653i	−0.749239	−	0.662300i	$-0.769580\pi$
$367$	−17.1931	+	6.25776i	−0.897470	+	0.326653i	−0.148232	+	0.988953i	$0.547358\pi$
$368$	6.65094	−	11.5198i	0.346704	−	0.600509i
$369$		0			0
$370$	−0.499161	−	0.418846i	−0.0259502	−	0.0217748i
$371$	4.32540	+	3.62944i	0.224564	+	0.188431i
$372$		0			0
$373$	−3.85669	+	6.67999i	−0.199692	+	0.345877i	−0.948429	−	0.316991i	$-0.897328\pi$
$373$	−3.85669	+	6.67999i	−0.199692	+	0.345877i	0.748736	+	0.662868i	$0.230661\pi$
$374$	−0.0773620	+	0.0281574i	−0.00400029	+	0.00145599i
$375$		0			0
$376$	1.81264	−	10.2800i	0.0934799	−	0.530151i
$377$	16.7842	+	6.10895i	0.864430	+	0.314627i
$378$		0			0
$379$	−12.7900			−0.656977			−0.328488	−	0.944508i	$-0.606539\pi$
$379$	−12.7900			−0.656977			−0.328488	+	0.944508i	$0.606539\pi$
$380$	6.99539	−	1.62041i	0.358856	−	0.0831252i
$381$		0			0
$382$	5.63717	−	4.73014i	0.288423	−	0.242015i
$383$	15.2106	+	5.53621i	0.777225	+	0.282887i	0.700015	−	0.714128i	$-0.253177\pi$
$383$	15.2106	+	5.53621i	0.777225	+	0.282887i	0.0772102	+	0.997015i	$0.475399\pi$
$384$		0			0
$385$	−0.0362150	−	0.205385i	−0.00184569	−	0.0104674i
$386$	−0.851397	+	0.309883i	−0.0433350	+	0.0157726i
$387$		0			0
$388$	−1.10331	−	1.91099i	−0.0560121	−	0.0970158i
$389$	2.12224	+	1.78077i	0.107602	+	0.0902888i	0.695001	−	0.719008i	$-0.255404\pi$
$389$	2.12224	+	1.78077i	0.107602	+	0.0902888i	−0.587399	+	0.809297i	$0.699848\pi$
$390$		0			0
$391$	−2.33448	−	4.04345i	−0.118060	−	0.204486i
$392$	−6.36284	+	11.0208i	−0.321372	+	0.556633i
$393$		0			0
$394$	−1.41919	−	8.04865i	−0.0714980	−	0.405485i
$395$	−2.12948	+	12.0769i	−0.107146	+	0.607655i
$396$		0			0
$397$	20.7920	−	17.4465i	1.04352	−	0.875617i	0.0511222	−	0.998692i	$-0.483720\pi$
$397$	20.7920	−	17.4465i	1.04352	−	0.875617i	0.992397	+	0.123076i	$0.0392758\pi$
$398$	−8.48707			−0.425418
$399$		0			0
$400$	2.00844			0.100422
$401$	9.16769	−	7.69261i	0.457813	−	0.384151i	−0.384513	−	0.923120i	$-0.625631\pi$
$401$	9.16769	−	7.69261i	0.457813	−	0.384151i	0.842326	+	0.538969i	$0.181186\pi$
$402$		0			0
$403$	−7.26330	+	41.1922i	−0.361811	+	2.05193i
$404$	−5.13039	−	29.0959i	−0.255247	−	1.44758i
$405$		0			0
$406$	−1.06473	+	1.84417i	−0.0528419	+	0.0915249i
$407$	−0.107890	−	0.186871i	−0.00534792	−	0.00926288i
$408$		0			0
$409$	−22.5628	−	18.9324i	−1.11566	−	0.936147i	−0.117279	−	0.993099i	$-0.537417\pi$
$409$	−22.5628	−	18.9324i	−1.11566	−	0.936147i	−0.998377	+	0.0569521i	$0.981862\pi$
$410$	−0.402220	−	0.696666i	−0.0198642	−	0.0344059i
$411$		0			0
$412$	−17.9929	+	6.54889i	−0.886448	+	0.322641i
$413$	2.02244	+	11.4698i	0.0995179	+	0.564394i
$414$		0			0
$415$	−3.78861	−	1.37894i	−0.185975	−	0.0676895i
$416$	−22.3559	+	18.7589i	−1.09609	+	0.919729i
$417$		0			0
$418$	−0.505290	−	0.0616664i	−0.0247145	−	0.00301620i
$419$	−19.9013			−0.972243			−0.486121	−	0.873891i	$-0.661589\pi$
$419$	−19.9013			−0.972243			−0.486121	+	0.873891i	$0.661589\pi$
$420$		0			0
$421$	15.1697	+	5.52131i	0.739325	+	0.269092i	0.684107	−	0.729382i	$-0.260192\pi$
$421$	15.1697	+	5.52131i	0.739325	+	0.269092i	0.0552182	+	0.998474i	$0.482415\pi$
$422$	0.181083	−	1.02697i	0.00881498	−	0.0499922i
$423$		0			0
$424$	10.8366	−	3.94418i	0.526270	−	0.191547i
$425$	0.352483	−	0.610518i	0.0170979	−	0.0296145i
$426$		0			0
$427$	9.54774	+	8.01150i	0.462047	+	0.387704i
$428$	3.15037	+	2.64348i	0.152279	+	0.127777i
$429$		0			0
$430$	−2.67471	+	4.63274i	−0.128986	+	0.223411i
$431$	13.5155	−	4.91925i	0.651020	−	0.236952i	0.00466545	−	0.999989i	$-0.498515\pi$
$431$	13.5155	−	4.91925i	0.651020	−	0.236952i	0.646355	+	0.763037i	$0.276293\pi$
$432$		0			0
$433$	−5.43145	+	30.8033i	−0.261019	+	1.48031i	0.519119	+	0.854702i	$0.326260\pi$
$433$	−5.43145	+	30.8033i	−0.261019	+	1.48031i	−0.780138	+	0.625608i	$0.784851\pi$
$434$	−4.68604	−	1.70558i	−0.224937	−	0.0818705i
$435$		0			0
$436$	3.42110			0.163841
$437$	−1.53198	−	28.8282i	−0.0732847	−	1.37904i
$438$		0			0
$439$	−2.38632	+	2.00236i	−0.113893	+	0.0955673i	−0.697955	−	0.716141i	$-0.745907\pi$
$439$	−2.38632	+	2.00236i	−0.113893	+	0.0955673i	0.584063	+	0.811709i	$0.301462\pi$
$440$	−0.400255	−	0.145681i	−0.0190814	−	0.00694507i
$441$		0			0
$442$	0.384014	+	2.17785i	0.0182657	+	0.103590i
$443$	−19.5293	+	7.10807i	−0.927863	+	0.337715i	−0.761362	−	0.648327i	$-0.775469\pi$
$443$	−19.5293	+	7.10807i	−0.927863	+	0.337715i	−0.166501	+	0.986041i	$0.553247\pi$
$444$		0			0
$445$	8.76266	+	15.1774i	0.415390	+	0.719476i
$446$	−7.61605	−	6.39063i	−0.360631	−	0.302605i
$447$		0			0
$448$	0.390324	+	0.676061i	0.0184411	+	0.0319409i
$449$	−7.88665	+	13.6601i	−0.372194	+	0.644659i	−0.989903	−	0.141748i	$-0.954728\pi$
$449$	−7.88665	+	13.6601i	−0.372194	+	0.644659i	0.617709	+	0.786407i	$0.288061\pi$
$450$		0			0
$451$	−0.0462583	−	0.262344i	−0.00217822	−	0.0123533i
$452$	−4.39917	+	24.9490i	−0.206920	+	1.17350i
$453$		0			0
$454$	−7.42472	+	6.23008i	−0.348459	+	0.292392i
$455$	−5.60214			−0.262632
$456$		0			0
$457$	−26.9899			−1.26254			−0.631268	−	0.775565i	$-0.717465\pi$
$457$	−26.9899			−1.26254			−0.631268	+	0.775565i	$0.717465\pi$
$458$	4.56437	−	3.82996i	0.213279	−	0.178962i
$459$		0			0
$460$	1.89456	−	10.7446i	0.0883343	−	0.500969i
$461$	1.26456	+	7.17170i	0.0588966	+	0.334019i	0.999991	−	0.00412323i	$-0.00131247\pi$
$461$	1.26456	+	7.17170i	0.0588966	+	0.334019i	−0.941095	+	0.338143i	$0.890201\pi$
$462$		0			0
$463$	−6.10730	+	10.5781i	−0.283830	+	0.491608i	−0.972325	−	0.233633i	$-0.924939\pi$
$463$	−6.10730	+	10.5781i	−0.283830	+	0.491608i	0.688495	+	0.725241i	$0.258272\pi$
$464$	−3.39554	−	5.88124i	−0.157634	−	0.273030i
$465$		0			0
$466$	−4.96901	−	4.16949i	−0.230185	−	0.193148i
$467$	−5.28685	−	9.15710i	−0.244646	−	0.423740i	0.717386	−	0.696676i	$-0.245339\pi$
$467$	−5.28685	−	9.15710i	−0.244646	−	0.423740i	−0.962032	+	0.272936i	$0.912005\pi$
$468$		0			0
$469$	3.04548	−	1.10847i	0.140627	−	0.0511842i
$470$	−0.496976	−	2.81849i	−0.0229238	−	0.130007i
$471$		0			0
$472$	22.3524	+	8.13562i	1.02885	+	0.374472i
$473$	−1.35702	+	1.13868i	−0.0623959	+	0.0523564i
$474$		0			0
$475$	3.65394	−	2.37670i	0.167654	−	0.109051i
$476$	1.23160			0.0564504
$477$		0			0
$478$	−6.62191	−	2.41018i	−0.302879	−	0.110239i
$479$	−0.264352	+	1.49922i	−0.0120786	+	0.0685009i	−0.990251	−	0.139293i	$-0.955517\pi$
$479$	−0.264352	+	1.49922i	−0.0120786	+	0.0685009i	0.978173	+	0.207794i	$0.0666282\pi$
$480$		0			0
$481$	−5.44671	+	1.98244i	−0.248348	+	0.0903914i
$482$	−0.957950	+	1.65922i	−0.0436334	+	0.0755753i
$483$		0			0
$484$	13.8325	+	11.6069i	0.628752	+	0.527586i
$485$	−1.02612	−	0.861014i	−0.0465936	−	0.0390966i
$486$		0			0
$487$	−14.4652	+	25.0545i	−0.655482	+	1.13533i	0.326291	+	0.945270i	$0.394201\pi$
$487$	−14.4652	+	25.0545i	−0.655482	+	1.13533i	−0.981773	+	0.190059i	$0.939132\pi$
$488$	23.9202	−	8.70625i	1.08282	−	0.394113i
$489$		0			0
$490$	−0.605863	+	3.43602i	−0.0273701	+	0.155224i
$491$	−13.8681	−	5.04759i	−0.625860	−	0.227795i	0.00956815	−	0.999954i	$-0.496954\pi$
$491$	−13.8681	−	5.04759i	−0.625860	−	0.227795i	−0.635429	+	0.772160i	$0.719177\pi$
$492$		0			0
$493$	−2.38367			−0.107355
$494$	−3.98824	+	13.0792i	−0.179439	+	0.588459i
$495$		0			0
$496$	12.1826	−	10.2225i	0.547017	−	0.459002i
$497$	2.49616	+	0.908529i	0.111968	+	0.0407531i
$498$		0			0
$499$	3.89908	+	22.1128i	0.174547	+	0.989904i	0.938666	+	0.344829i	$0.112063\pi$
$499$	3.89908	+	22.1128i	0.174547	+	0.989904i	−0.764119	+	0.645076i	$0.776826\pi$
$500$	1.54800	−	0.563426i	0.0692286	−	0.0251972i
$501$		0			0
$502$	−0.521050	−	0.902485i	−0.0232556	−	0.0402799i
$503$	33.7053	+	28.2821i	1.50284	+	1.26104i	0.876415	+	0.481557i	$0.159929\pi$
$503$	33.7053	+	28.2821i	1.50284	+	1.26104i	0.626429	+	0.779479i	$0.284516\pi$
$504$		0			0
$505$	−8.96738	−	15.5320i	−0.399043	−	0.691163i
$506$	−0.386721	+	0.669820i	−0.0171918	+	0.0297771i
$507$		0			0
$508$	2.17612	+	12.3414i	0.0965498	+	0.547561i
$509$	2.42105	−	13.7305i	0.107311	−	0.608592i	−0.882961	−	0.469447i	$-0.844453\pi$
$509$	2.42105	−	13.7305i	0.107311	−	0.608592i	0.990272	−	0.139145i	$-0.0444355\pi$
$510$		0			0
$511$	5.32466	−	4.46792i	0.235549	−	0.197649i
$512$	19.7963			0.874883
$513$		0			0
$514$	−14.3908			−0.634752
$515$	−8.90400	+	7.47135i	−0.392357	+	0.329227i
$516$		0			0
$517$	0.164574	−	0.933345i	0.00723795	−	0.0410485i
$518$	−0.119998	−	0.680544i	−0.00527242	−	0.0299014i
$519$		0			0
$520$	−5.72080	+	9.90872i	−0.250874	+	0.434526i
$521$	12.8847	+	22.3170i	0.564489	+	0.977724i	0.997097	+	0.0761420i	$0.0242602\pi$
$521$	12.8847	+	22.3170i	0.564489	+	0.977724i	−0.432608	+	0.901582i	$0.642406\pi$
$522$		0			0
$523$	−16.0475	−	13.4655i	−0.701709	−	0.588803i	0.220551	−	0.975376i	$-0.429215\pi$
$523$	−16.0475	−	13.4655i	−0.701709	−	0.588803i	−0.922259	+	0.386572i	$0.873659\pi$
$524$	17.1820	+	29.7601i	0.750598	+	1.30007i
$525$		0			0
$526$	7.08281	−	2.57793i	0.308825	−	0.112403i
$527$	−0.969317	−	5.49727i	−0.0422241	−	0.239465i
$528$		0			0
$529$	−19.6056	−	7.13585i	−0.852417	−	0.310255i
$530$	2.42205	−	2.03234i	0.105207	−	0.0882791i
$531$		0			0
$532$	6.78770	+	3.45225i	0.294284	+	0.149674i
$533$	−7.15575			−0.309950
$534$		0			0
$535$	2.34590	+	0.853837i	0.101422	+	0.0369146i
$536$	1.14941	−	6.51861i	0.0496468	−	0.281561i
$537$		0			0
$538$	15.7735	−	5.74109i	0.680044	−	0.247516i
$539$	−0.577697	+	1.00060i	−0.0248832	+	0.0430989i
$540$		0			0
$541$	7.30219	+	6.12727i	0.313946	+	0.263432i	0.786121	−	0.618073i	$-0.212086\pi$
$541$	7.30219	+	6.12727i	0.313946	+	0.263432i	−0.472175	+	0.881505i	$0.656531\pi$
$542$	3.72425	+	3.12502i	0.159970	+	0.134231i
$543$		0			0
$544$	1.94734	−	3.37289i	0.0834914	−	0.144611i
$545$	1.95149	−	0.710284i	0.0835927	−	0.0304252i
$546$		0			0
$547$	2.37095	−	13.4463i	0.101375	−	0.574924i	−0.891232	−	0.453548i	$-0.850158\pi$
$547$	2.37095	−	13.4463i	0.101375	−	0.574924i	0.992607	−	0.121376i	$-0.0387307\pi$
$548$	−29.7464	−	10.8268i	−1.27071	−	0.462499i
$549$		0			0
$550$	−0.116781			−0.00497958
$551$	−13.1371	−	6.68156i	−0.559658	−	0.284644i
$552$		0			0
$553$	−9.96268	+	8.35968i	−0.423656	+	0.355490i
$554$	13.9829	+	5.08936i	0.594077	+	0.216226i
$555$		0			0
$556$	5.62061	+	31.8760i	0.238367	+	1.35185i
$557$	8.04670	−	2.92876i	0.340950	−	0.124096i	−0.165870	−	0.986148i	$-0.553043\pi$
$557$	8.04670	−	2.92876i	0.340950	−	0.124096i	0.506820	+	0.862052i	$0.330821\pi$
$558$		0			0
$559$	23.7924	+	41.2097i	1.00631	+	1.74298i
$560$	1.63167	+	1.36913i	0.0689505	+	0.0578564i
$561$		0			0
$562$	−7.28702	−	12.6215i	−0.307384	−	0.532405i
$563$	−7.10954	+	12.3141i	−0.299631	+	0.518977i	−0.976052	−	0.217539i	$-0.930197\pi$
$563$	−7.10954	+	12.3141i	−0.299631	+	0.518977i	0.676420	+	0.736516i	$0.263530\pi$
$564$		0			0
$565$	2.67046	+	15.1449i	0.112347	+	0.637152i
$566$	2.65327	−	15.0474i	0.111525	−	0.632490i
$567$		0			0
$568$	4.15599	−	3.48729i	0.174381	−	0.146323i
$569$	−30.2404			−1.26774			−0.633872	−	0.773438i	$-0.718535\pi$
$569$	−30.2404			−1.26774			−0.633872	+	0.773438i	$0.718535\pi$
$570$		0			0
$571$	−32.2109			−1.34798			−0.673992	−	0.738739i	$-0.735422\pi$
$571$	−32.2109			−1.34798			−0.673992	+	0.738739i	$0.735422\pi$
$572$	−1.31091	+	1.09999i	−0.0548121	+	0.0459928i
$573$		0			0
$574$	0.148143	−	0.840163i	0.00618339	−	0.0350677i
$575$	−1.15007	−	6.52236i	−0.0479612	−	0.272001i
$576$		0			0
$577$	22.3966	−	38.7920i	0.932381	−	1.61493i	0.153141	−	0.988204i	$-0.451061\pi$
$577$	22.3966	−	38.7920i	0.932381	−	1.61493i	0.779239	−	0.626726i	$-0.215606\pi$
$578$	4.90013	+	8.48728i	0.203819	+	0.353024i
$579$		0			0
$580$	−4.26695	−	3.58040i	−0.177176	−	0.148668i
$581$	−2.13787	−	3.70290i	−0.0886939	−	0.153622i
$582$		0			0
$583$	0.983875	−	0.358101i	0.0407479	−	0.0148310i
$584$	−2.46514	−	13.9805i	−0.102008	−	0.578517i
$585$		0			0
$586$	−3.04601	−	1.10866i	−0.125830	−	0.0457982i
$587$	6.71729	−	5.63648i	0.277252	−	0.232642i	−0.493549	−	0.869718i	$-0.664301\pi$
$587$	6.71729	−	5.63648i	0.277252	−	0.232642i	0.770801	+	0.637076i	$0.219856\pi$
$588$		0			0
$589$	10.0670	−	33.0140i	0.414803	−	1.36032i
$590$	6.52172			0.268495
$591$		0			0
$592$	2.07089	+	0.753744i	0.0851132	+	0.0309787i
$593$	−1.80952	+	10.2623i	−0.0743082	+	0.421423i	0.924847	+	0.380338i	$0.124192\pi$
$593$	−1.80952	+	10.2623i	−0.0743082	+	0.421423i	−0.999156	+	0.0410846i	$0.986919\pi$
$594$		0			0
$595$	0.702541	−	0.255704i	0.0288014	−	0.0104828i
$596$	7.12860	−	12.3471i	0.291999	−	0.505757i
$597$		0			0
$598$	15.9154	+	13.3546i	0.650828	+	0.546110i
$599$	−14.5133	−	12.1781i	−0.592998	−	0.497584i	0.296188	−	0.955130i	$-0.404284\pi$
$599$	−14.5133	−	12.1781i	−0.592998	−	0.497584i	−0.889186	+	0.457545i	$0.848729\pi$
$600$		0			0
$601$	2.41826	−	4.18855i	0.0986429	−	0.170855i	−0.812480	−	0.582989i	$-0.801883\pi$
$601$	2.41826	−	4.18855i	0.0986429	−	0.170855i	0.911123	+	0.412134i	$0.135217\pi$
$602$	−5.33103	+	1.94034i	−0.217277	+	0.0790822i
$603$		0			0
$604$	1.41690	−	8.03561i	0.0576526	−	0.326964i
$605$	10.3003	+	3.74899i	0.418766	+	0.152418i
$606$		0			0
$607$	−19.4767			−0.790537			−0.395268	−	0.918566i	$-0.629348\pi$
$607$	−19.4767			−0.790537			−0.395268	+	0.918566i	$0.629348\pi$
$608$	20.1867	−	13.1304i	0.818678	−	0.532508i
$609$		0			0
$610$	5.34634	−	4.48611i	0.216467	−	0.181637i
$611$	−23.9228	−	8.70719i	−0.967813	−	0.352255i
$612$		0			0
$613$	−6.45316	−	36.5977i	−0.260641	−	1.47817i	−0.781167	−	0.624322i	$-0.785375\pi$
$613$	−6.45316	−	36.5977i	−0.260641	−	1.47817i	0.520526	−	0.853846i	$-0.325736\pi$
$614$	2.06832	−	0.752805i	0.0834704	−	0.0303807i
$615$		0			0
$616$	−0.225860	−	0.391201i	−0.00910015	−	0.0157619i
$617$	10.8292	+	9.08679i	0.435968	+	0.365821i	0.834198	−	0.551465i	$-0.185931\pi$
$617$	10.8292	+	9.08679i	0.435968	+	0.365821i	−0.398230	+	0.917286i	$0.630375\pi$
$618$		0			0
$619$	−15.9555	−	27.6357i	−0.641306	−	1.11077i	−0.985142	−	0.171744i	$-0.945060\pi$
$619$	−15.9555	−	27.6357i	−0.641306	−	1.11077i	0.343836	−	0.939030i	$-0.388274\pi$
$620$	6.52203	−	11.2965i	0.261931	−	0.453678i
$621$		0			0
$622$	0.178864	+	1.01439i	0.00717180	+	0.0406733i
$623$	−3.22741	+	18.3036i	−0.129303	+	0.733316i
$624$		0			0
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	2.35666			0.0941912
$627$		0			0
$628$	22.8403			0.911426
$629$	0.592563	−	0.497219i	0.0236270	−	0.0198254i
$630$		0			0
$631$	0.747749	−	4.24069i	0.0297674	−	0.168819i	−0.966300	−	0.257419i	$-0.917128\pi$
$631$	0.747749	−	4.24069i	0.0297674	−	0.168819i	0.996067	+	0.0885995i	$0.0282391\pi$
$632$	4.61238	+	26.1581i	0.183471	+	1.04051i
$633$		0			0
$634$	−7.93258	+	13.7396i	−0.315043	+	0.545670i
$635$	3.80363	+	6.58807i	0.150942	+	0.261440i
$636$		0			0
$637$	23.7750	+	19.9496i	0.941998	+	0.790430i
$638$	0.197435	+	0.341967i	0.00781651	+	0.0135386i
$639$		0			0
$640$	10.7937	−	3.92858i	0.426658	−	0.155291i
$641$	−5.57212	−	31.6011i	−0.220086	−	1.24817i	−0.871860	−	0.489755i	$-0.837086\pi$
$641$	−5.57212	−	31.6011i	−0.220086	−	1.24817i	0.651775	−	0.758413i	$-0.274025\pi$
$642$		0			0
$643$	18.1242	+	6.59666i	0.714747	+	0.260147i	0.673694	−	0.739010i	$-0.264706\pi$
$643$	18.1242	+	6.59666i	0.714747	+	0.260147i	0.0410531	+	0.999157i	$0.486929\pi$
$644$	8.86360	−	7.43745i	0.349275	−	0.293076i
$645$		0			0
$646$	−0.0968373	−	1.82224i	−0.00381001	−	0.0716952i
$647$	−7.19470			−0.282853			−0.141426	−	0.989949i	$-0.545169\pi$
$647$	−7.19470			−0.282853			−0.141426	+	0.989949i	$0.545169\pi$
$648$		0			0
$649$	2.02943	+	0.738651i	0.0796620	+	0.0289946i
$650$	−0.544728	+	3.08931i	−0.0213660	+	0.121173i
$651$		0			0
$652$	−9.83124	+	3.57828i	−0.385021	+	0.140136i
$653$	−22.4349	+	38.8583i	−0.877944	+	1.52064i	−0.0243514	+	0.999703i	$0.507752\pi$
$653$	−22.4349	+	38.8583i	−0.877944	+	1.52064i	−0.853593	+	0.520941i	$0.825581\pi$
$654$		0			0
$655$	15.9798	+	13.4087i	0.624384	+	0.523920i
$656$	2.08417	+	1.74883i	0.0813732	+	0.0682802i
$657$		0			0
$658$	1.51759	−	2.62854i	0.0591617	−	0.102471i
$659$	−4.66645	+	1.69845i	−0.181779	+	0.0661621i	−0.431306	−	0.902206i	$-0.641947\pi$
$659$	−4.66645	+	1.69845i	−0.181779	+	0.0661621i	0.249527	+	0.968368i	$0.419725\pi$
$660$		0			0
$661$	−0.292511	+	1.65891i	−0.0113773	+	0.0645242i	−0.989968	−	0.141293i	$-0.954874\pi$
$661$	−0.292511	+	1.65891i	−0.0113773	+	0.0645242i	0.978590	+	0.205817i	$0.0659852\pi$
$662$	10.6665	+	3.88230i	0.414566	+	0.150890i
$663$		0			0
$664$	−8.73263			−0.338892
$665$	4.58865	+	0.560006i	0.177940	+	0.0217161i
$666$		0			0
$667$	−17.1548	+	14.3946i	−0.664238	+	0.557362i
$668$	−30.4957	−	11.0995i	−1.17992	−	0.429454i
$669$		0			0
$670$	−0.315135	−	1.78722i	−0.0121747	−	0.0690463i
$671$	2.17177	−	0.790460i	0.0838403	−	0.0305154i
$672$		0			0
$673$	0.214798	+	0.372041i	0.00827986	+	0.0143411i	0.870136	−	0.492812i	$-0.164031\pi$
$673$	0.214798	+	0.372041i	0.00827986	+	0.0143411i	−0.861856	+	0.507153i	$0.830698\pi$
$674$	−5.55774	−	4.66350i	−0.214076	−	0.179631i
$675$		0			0
$676$	12.2763	+	21.2631i	0.472164	+	0.817813i
$677$	6.95294	−	12.0428i	0.267223	−	0.462844i	−0.700920	−	0.713239i	$-0.747227\pi$
$677$	6.95294	−	12.0428i	0.267223	−	0.462844i	0.968144	+	0.250395i	$0.0805606\pi$
$678$		0			0
$679$	−0.246678	−	1.39898i	−0.00946665	−	0.0536880i
$680$	0.265148	−	1.50373i	0.0101680	−	0.0576655i
$681$		0			0
$682$	−0.708363	+	0.594388i	−0.0271246	+	0.0227603i
$683$	−19.7531			−0.755831			−0.377916	−	0.925840i	$-0.623359\pi$
$683$	−19.7531			−0.755831			−0.377916	+	0.925840i	$0.623359\pi$
$684$		0			0
$685$	−19.2161			−0.734208
$686$	−6.21160	+	5.21215i	−0.237160	+	0.199001i
$687$		0			0
$688$	3.14169	−	17.8174i	0.119776	−	0.679282i
$689$	−4.88382	−	27.6975i	−0.186059	−	1.05519i
$690$		0			0
$691$	−6.05650	+	10.4902i	−0.230400	+	0.399065i	−0.957926	−	0.287016i	$-0.907337\pi$
$691$	−6.05650	+	10.4902i	−0.230400	+	0.399065i	0.727526	+	0.686080i	$0.240670\pi$
$692$	−7.34525	−	12.7223i	−0.279224	−	0.483631i
$693$		0			0
$694$	1.80339	+	1.51322i	0.0684556	+	0.0574411i
$695$	9.82422	+	17.0160i	0.372654	+	0.645455i
$696$		0			0
$697$	0.897374	−	0.326617i	0.0339904	−	0.0123715i
$698$	−2.56074	−	14.5227i	−0.0969256	−	0.549692i
$699$		0			0
$700$	1.64168	+	0.597523i	0.0620497	+	0.0225843i
$701$	15.5903	−	13.0818i	0.588836	−	0.494092i	−0.299000	−	0.954253i	$-0.596653\pi$
$701$	15.5903	−	13.0818i	0.588836	−	0.494092i	0.887835	+	0.460161i	$0.152208\pi$
$702$		0			0
$703$	4.65951	−	1.07932i	0.175737	−	0.0407075i
$704$	0.144756			0.00545570
$705$		0			0
$706$	7.82454	+	2.84790i	0.294481	+	0.107182i
$707$	3.30281	−	18.7312i	0.124215	−	0.704459i
$708$		0			0
$709$	−37.4832	+	13.6428i	−1.40771	+	0.512364i	−0.930457	−	0.366402i	$-0.880590\pi$
$709$	−37.4832	+	13.6428i	−1.40771	+	0.512364i	−0.477253	+	0.878766i	$0.658367\pi$
$710$	0.743726	−	1.28817i	0.0279116	−	0.0483442i
$711$		0			0
$712$	29.0784	+	24.3997i	1.08976	+	0.914418i
$713$	−40.1731	−	33.7092i	−1.50449	−	1.26242i
$714$		0			0
$715$	−0.519404	+	0.899634i	−0.0194246	+	0.0336444i
$716$	−2.74318	+	0.998434i	−0.102517	+	0.0373132i
$717$		0			0
$718$	1.80595	−	10.2420i	0.0673974	−	0.382229i
$719$	22.6968	+	8.26097i	0.846449	+	0.308082i	0.728592	−	0.684948i	$-0.240175\pi$
$719$	22.6968	+	8.26097i	0.846449	+	0.308082i	0.117857	+	0.993031i	$0.462397\pi$
$720$		0			0
$721$	−12.3268			−0.459073
$722$	4.57415	−	10.3143i	0.170232	−	0.383859i
$723$		0			0
$724$	−10.7882	+	9.05233i	−0.400938	+	0.336427i
$725$	−3.17735	−	1.15646i	−0.118004	−	0.0429499i
$726$		0			0
$727$	−5.75274	−	32.6254i	−0.213357	−	1.21001i	−0.883734	−	0.467989i	$-0.844979\pi$
$727$	−5.75274	−	32.6254i	−0.213357	−	1.21001i	0.670377	−	0.742021i	$-0.266132\pi$
$728$	−11.4023	+	4.15008i	−0.422596	+	0.153812i
$729$		0			0
$730$	−1.94610	−	3.37074i	−0.0720283	−	0.124757i
$731$	−4.86469	−	4.08196i	−0.179927	−	0.150977i
$732$		0			0
$733$	10.1387	+	17.5607i	0.374481	+	0.648620i	0.990249	−	0.139307i	$-0.0444875\pi$
$733$	10.1387	+	17.5607i	0.374481	+	0.648620i	−0.615768	+	0.787927i	$0.711154\pi$
$734$	−5.43265	+	9.40962i	−0.200523	+	0.347315i
$735$		0			0
$736$	−6.35371	−	36.0337i	−0.234201	−	1.32822i
$737$	0.104357	−	0.591839i	0.00384405	−	0.0218007i
$738$		0			0
$739$	−19.6216	+	16.4645i	−0.721792	+	0.605655i	−0.927880	−	0.372878i	$-0.878371\pi$
$739$	−19.6216	+	16.4645i	−0.721792	+	0.605655i	0.206088	+	0.978533i	$0.433927\pi$
$740$	1.80758			0.0664480
$741$		0			0
$742$	3.35310			0.123096
$743$	−18.2970	+	15.3530i	−0.671250	+	0.563246i	−0.913435	−	0.406984i	$-0.866580\pi$
$743$	−18.2970	+	15.3530i	−0.671250	+	0.563246i	0.242185	+	0.970230i	$0.422136\pi$
$744$		0			0
$745$	1.50286	−	8.52316i	0.0550606	−	0.312264i
$746$	0.795408	+	4.51098i	0.0291219	+	0.165159i
$747$		0			0
$748$	0.114188	−	0.197780i	0.00417514	−	0.00723156i
$749$	1.32377	+	2.29283i	0.0483694	+	0.0837782i
$750$		0			0
$751$	−37.6199	−	31.5669i	−1.37277	−	1.15189i	−0.971802	−	0.235800i	$-0.924229\pi$
$751$	−37.6199	−	31.5669i	−1.37277	−	1.15189i	−0.400969	−	0.916092i	$-0.631327\pi$
$752$	4.83972	+	8.38264i	0.176486	+	0.305684i
$753$		0			0
$754$	9.96723	−	3.62778i	0.362985	−	0.132116i
$755$	−0.860108	−	4.87791i	−0.0313025	−	0.177525i
$756$		0			0
$757$	20.0398	+	7.29390i	0.728360	+	0.265101i	0.679470	−	0.733703i	$-0.262210\pi$
$757$	20.0398	+	7.29390i	0.728360	+	0.265101i	0.0488893	+	0.998804i	$0.484432\pi$
$758$	−5.81832	+	4.88215i	−0.211331	+	0.177328i
$759$		0			0
$760$	5.67635	−	7.54425i	0.205903	−	0.273659i
$761$	−11.4807			−0.416176			−0.208088	−	0.978110i	$-0.566724\pi$
$761$	−11.4807			−0.416176			−0.208088	+	0.978110i	$0.566724\pi$
$762$		0			0
$763$	2.06959	+	0.753270i	0.0749242	+	0.0272702i
$764$	−3.54477	+	20.1034i	−0.128245	+	0.727315i
$765$		0			0
$766$	9.03276	−	3.28766i	0.326367	−	0.118788i
$767$	29.0064	−	50.2405i	1.04736	−	1.81408i
$768$		0			0
$769$	0.0886493	+	0.0743856i	0.00319677	+	0.00268241i	0.644385	−	0.764702i	$-0.277114\pi$
$769$	0.0886493	+	0.0743856i	0.00319677	+	0.00268241i	−0.641188	+	0.767384i	$0.721558\pi$
$770$	−0.0948738	−	0.0796085i	−0.00341901	−	0.00286889i
$771$		0			0
$772$	1.25669	−	2.17665i	0.0452292	−	0.0783392i
$773$	32.2920	−	11.7533i	1.16146	−	0.422738i	0.311843	−	0.950133i	$-0.399054\pi$
$773$	32.2920	−	11.7533i	1.16146	−	0.422738i	0.849620	+	0.527395i	$0.176831\pi$
$774$		0			0
$775$	1.37499	−	7.79794i	0.0493910	−	0.280110i
$776$	−2.72634	−	0.992306i	−0.0978698	−	0.0356217i
$777$		0			0
$778$	1.64519			0.0589829
$779$	5.86120	+	0.715310i	0.209999	+	0.0256286i
$780$		0			0
$781$	0.377331	−	0.316618i	0.0135020	−	0.0113295i
$782$	−2.60544	−	0.948302i	−0.0931703	−	0.0339112i
$783$		0			0
$784$	−2.04908	−	11.6209i	−0.0731816	−	0.415033i
$785$	13.0287	−	4.74207i	0.465015	−	0.169252i
$786$		0			0
$787$	−2.85365	−	4.94268i	−0.101722	−	0.176187i	0.810672	−	0.585500i	$-0.199102\pi$
$787$	−2.85365	−	4.94268i	−0.101722	−	0.176187i	−0.912394	+	0.409313i	$0.865768\pi$
$788$	17.3675	+	14.5730i	0.618690	+	0.519143i
$789$		0			0
$790$	3.64123	+	6.30680i	0.129549	+	0.224386i
$791$	−8.15463	+	14.1242i	−0.289945	+	0.502200i
$792$		0			0
$793$	−10.7804	−	61.1386i	−0.382823	−	2.17109i
$794$	2.79889	−	15.8733i	0.0993290	−	0.563323i
$795$		0			0
$796$	18.0353	−	15.1334i	0.639243	−	0.536389i
$797$	39.6776			1.40545			0.702726	−	0.711461i	$-0.251966\pi$
$797$	39.6776			1.40545			0.702726	+	0.711461i	$0.251966\pi$
$798$		0			0
$799$	3.39749			0.120195
$800$	4.23212	−	3.55117i	0.149628	−	0.125553i
$801$		0			0
$802$	1.23410	−	6.99893i	0.0435776	−	0.247141i
$803$	−0.223815	−	1.26932i	−0.00789828	−	0.0447934i
$804$		0			0
$805$	3.51189	−	6.08278i	0.123778	−	0.214390i
$806$	12.4196	+	21.5114i	0.437462	+	0.757707i
$807$		0			0
$808$	−29.7578	−	24.9698i	−1.04688	−	0.878433i
$809$	−11.8967	−	20.6056i	−0.418264	−	0.724455i	0.577501	−	0.816390i	$-0.304028\pi$
$809$	−11.8967	−	20.6056i	−0.418264	−	0.724455i	−0.995765	+	0.0919355i	$0.970695\pi$
$810$		0			0
$811$	14.6389	−	5.32813i	0.514042	−	0.187096i	−0.0719573	−	0.997408i	$-0.522925\pi$
$811$	14.6389	−	5.32813i	0.514042	−	0.187096i	0.585999	+	0.810312i	$0.300702\pi$
$812$	−1.02578	−	5.81746i	−0.0359977	−	0.204153i
$813$		0			0
$814$	−0.120413	−	0.0438267i	−0.00422046	−	0.00153612i
$815$	−4.86510	+	4.08230i	−0.170417	+	0.142997i
$816$		0			0
$817$	−15.3687	−	36.1328i	−0.537682	−	1.26412i
$818$	−17.4909			−0.611555
$819$		0			0
$820$	2.09696	+	0.763232i	0.0732291	+	0.0266532i
$821$	−8.57507	+	48.6316i	−0.299272	+	1.69726i	0.350041	+	0.936735i	$0.386168\pi$
$821$	−8.57507	+	48.6316i	−0.299272	+	1.69726i	−0.649313	+	0.760522i	$0.724943\pi$
$822$		0			0
$823$	−7.11258	+	2.58877i	−0.247929	+	0.0902387i	−0.462995	−	0.886361i	$-0.653225\pi$
$823$	−7.11258	+	2.58877i	−0.247929	+	0.0902387i	0.215067	+	0.976599i	$0.431003\pi$
$824$	−12.5879	+	21.8028i	−0.438520	+	0.759538i
$825$		0			0
$826$	5.29827	+	4.44578i	0.184350	+	0.154688i
$827$	24.5604	+	20.6086i	0.854048	+	0.716631i	0.960677	−	0.277668i	$-0.0895614\pi$
$827$	24.5604	+	20.6086i	0.854048	+	0.716631i	−0.106629	+	0.994299i	$0.534006\pi$
$828$		0			0
$829$	−6.51811	+	11.2897i	−0.226383	+	0.392107i	−0.956734	−	0.290966i	$-0.906023\pi$
$829$	−6.51811	+	11.2897i	−0.226383	+	0.392107i	0.730350	+	0.683073i	$0.239357\pi$
$830$	−2.24985	+	0.818879i	−0.0780935	+	0.0284237i
$831$		0			0
$832$	0.675216	−	3.82934i	0.0234089	−	0.132758i
$833$	−3.89210	−	1.41661i	−0.134853	−	0.0490825i
$834$		0			0
$835$	−19.7001			−0.681750
$836$	1.18371	−	0.769944i	0.0409396	−	0.0266291i
$837$		0			0
$838$	−9.05336	+	7.59667i	−0.312743	+	0.262423i
$839$	−8.46469	−	3.08090i	−0.292234	−	0.106364i	0.191743	−	0.981445i	$-0.438586\pi$
$839$	−8.46469	−	3.08090i	−0.292234	−	0.106364i	−0.483977	+	0.875081i	$0.660808\pi$
$840$		0			0
$841$	−3.05049	−	17.3002i	−0.105189	−	0.596558i
$842$	9.00846	−	3.27881i	0.310452	−	0.112995i
$843$		0			0
$844$	1.44640	+	2.50524i	0.0497871	+	0.0862338i
$845$	11.4174	+	9.58030i	0.392769	+	0.329572i
$846$		0			0
$847$	5.81234	+	10.0673i	0.199715	+	0.345916i
$848$	−5.34667	+	9.26071i	−0.183606	+	0.318014i
$849$		0			0
$850$	−0.0726963	−	0.412281i	−0.00249346	−	0.0141411i
$851$	1.26193	−	7.15678i	0.0432585	−	0.245331i
$852$		0			0
$853$	14.9550	−	12.5488i	0.512050	−	0.429661i	−0.349800	−	0.936825i	$-0.613750\pi$
$853$	14.9550	−	12.5488i	0.512050	−	0.429661i	0.861850	+	0.507163i	$0.169306\pi$
$854$	7.40152			0.253275
$855$		0			0
$856$	5.40722			0.184815
$857$	15.7946	−	13.2532i	0.539533	−	0.452722i	−0.331845	−	0.943334i	$-0.607671\pi$
$857$	15.7946	−	13.2532i	0.539533	−	0.452722i	0.871378	+	0.490612i	$0.163227\pi$
$858$		0			0
$859$	2.94700	−	16.7133i	0.100550	−	0.570249i	−0.892354	−	0.451336i	$-0.850948\pi$
$859$	2.94700	−	16.7133i	0.100550	−	0.570249i	0.992905	−	0.118914i	$-0.0379412\pi$
$860$	−2.57685	−	14.6140i	−0.0878697	−	0.498334i
$861$		0			0
$862$	4.27062	−	7.39694i	0.145458	−	0.251941i
$863$	−3.58869	−	6.21580i	−0.122161	−	0.211588i	0.798459	−	0.602049i	$-0.205649\pi$
$863$	−3.58869	−	6.21580i	−0.122161	−	0.211588i	−0.920619	+	0.390461i	$0.872316\pi$
$864$		0			0
$865$	−6.83133	−	5.73217i	−0.232272	−	0.194900i
$866$	9.28730	+	16.0861i	0.315595	+	0.546627i
$867$		0			0
$868$	12.9992	−	4.73133i	0.441222	−	0.160592i
$869$	0.418769	+	2.37495i	0.0142057	+	0.0805648i
$870$		0			0
$871$	−15.1696	−	5.52128i	−0.514002	−	0.187081i
$872$	3.44577	−	2.89134i	0.116688	−	0.0979131i
$873$		0			0
$874$	−11.7011	−	12.5295i	−0.395797	−	0.423818i
$875$	1.06052			0.0358521
$876$		0			0
$877$	1.43115	+	0.520896i	0.0483265	+	0.0175894i	0.366070	−	0.930587i	$-0.380703\pi$
$877$	1.43115	+	0.520896i	0.0483265	+	0.0175894i	−0.317744	+	0.948177i	$0.602925\pi$
$878$	−0.321232	+	1.82180i	−0.0108410	+	0.0614826i
$879$		0			0
$880$	0.371146	−	0.135086i	0.0125113	−	0.00455375i
$881$	25.7569	−	44.6123i	0.867774	−	1.50303i	0.00350703	−	0.999994i	$-0.498884\pi$
$881$	25.7569	−	44.6123i	0.867774	−	1.50303i	0.864267	−	0.503034i	$-0.167783\pi$
$882$		0			0
$883$	2.64236	+	2.21720i	0.0889224	+	0.0746147i	0.686165	−	0.727446i	$-0.259293\pi$
$883$	2.64236	+	2.21720i	0.0889224	+	0.0746147i	−0.597243	+	0.802060i	$0.703737\pi$
$884$	−4.69940	−	3.94326i	−0.158058	−	0.132626i
$885$		0			0
$886$	−6.17084	+	10.6882i	−0.207313	+	0.359077i
$887$	−34.7236	+	12.6383i	−1.16590	+	0.424354i	−0.851203	−	0.524837i	$-0.824126\pi$
$887$	−34.7236	+	12.6383i	−1.16590	+	0.424354i	−0.314700	+	0.949191i	$0.601904\pi$
$888$		0			0
$889$	−1.40093	+	7.94507i	−0.0469857	+	0.266469i
$890$	9.77971	+	3.55952i	0.327817	+	0.119315i
$891$		0			0
$892$	27.5795			0.923431
$893$	18.7245	+	9.52336i	0.626592	+	0.318687i
$894$		0			0
$895$	−1.35749	+	1.13907i	−0.0453759	+	0.0380749i
$896$	11.4469	+	4.16633i	0.382414	+	0.139187i
$897$		0			0
$898$	1.62655	+	9.22462i	0.0542786	+	0.307830i
$899$	−25.1590	+	9.15712i	−0.839099	+	0.305407i
$900$		0			0
$901$	1.87669	+	3.25052i	0.0625215	+	0.108290i
$902$	−0.121185	−	0.101686i	−0.00403501	−	0.00338577i
$903$		0			0
$904$	16.6547	+	28.8468i	0.553928	+	0.959431i
$905$	−4.27443	+	7.40353i	−0.142087	+	0.246102i
$906$		0			0
$907$	−4.00543	−	22.7159i	−0.132998	−	0.754269i	−0.976233	−	0.216724i	$-0.930463\pi$
$907$	−4.00543	−	22.7159i	−0.132998	−	0.754269i	0.843235	−	0.537545i	$-0.180648\pi$
$908$	4.66882	−	26.4782i	0.154940	−	0.878709i
$909$		0			0
$910$	−2.54848	+	2.13843i	−0.0844814	+	0.0708883i
$911$	−22.8760			−0.757915			−0.378957	−	0.925414i	$-0.623717\pi$
$911$	−22.8760			−0.757915			−0.378957	+	0.925414i	$0.623717\pi$
$912$		0			0
$913$	−0.792855			−0.0262397
$914$	−12.2781	+	10.3025i	−0.406122	+	0.340777i
$915$		0			0
$916$	−2.87017	+	16.2776i	−0.0948332	+	0.537826i
$917$	3.84155	+	21.7865i	0.126859	+	0.719454i
$918$		0			0
$919$	6.46621	−	11.1998i	0.213301	−	0.369448i	−0.739445	−	0.673217i	$-0.764912\pi$
$919$	6.46621	−	11.1998i	0.213301	−	0.369448i	0.952746	+	0.303769i	$0.0982453\pi$
$920$	−7.17257	−	12.4232i	−0.236472	−	0.409582i
$921$		0			0
$922$	3.31283	+	2.77979i	0.109102	+	0.0915476i
$923$	−6.61568	−	11.4587i	−0.217758	−	0.377168i
$924$		0			0
$925$	1.03109	−	0.375288i	0.0339022	−	0.0123394i
$926$	1.25957	+	7.14340i	0.0413921	+	0.234747i
$927$		0			0
$928$	−17.5537	−	6.38902i	−0.576228	−	0.209730i
$929$	9.48977	−	7.96286i	0.311349	−	0.261253i	−0.473700	−	0.880686i	$-0.657082\pi$
$929$	9.48977	−	7.96286i	0.311349	−	0.261253i	0.785049	+	0.619433i	$0.212638\pi$
$930$		0			0
$931$	−17.4796	−	18.7171i	−0.572870	−	0.613427i
$932$	17.9939			0.589411
$933$		0			0
$934$	−5.90048	−	2.14760i	−0.193070	−	0.0702716i
$935$	0.0240734	−	0.136527i	0.000787285	−	0.00446491i
$936$		0			0
$937$	10.0261	−	3.64922i	0.327540	−	0.119215i	−0.173016	−	0.984919i	$-0.555351\pi$
$937$	10.0261	−	3.64922i	0.327540	−	0.119215i	0.500556	+	0.865704i	$0.333129\pi$
$938$	0.962309	−	1.66677i	0.0314205	−	0.0544219i
$939$		0			0
$940$	6.08177	+	5.10321i	0.198365	+	0.166448i
$941$	−9.79712	−	8.22076i	−0.319377	−	0.267989i	0.468978	−	0.883210i	$-0.344622\pi$
$941$	−9.79712	−	8.22076i	−0.319377	−	0.267989i	−0.788355	+	0.615221i	$0.789067\pi$
$942$		0			0
$943$	4.48583	−	7.76969i	0.146079	−	0.253016i
$944$	−20.7268	+	7.54395i	−0.674601	+	0.245535i
$945$		0			0
$946$	−0.182674	+	1.03600i	−0.00593925	+	0.0336832i
$947$	13.2645	+	4.82790i	0.431040	+	0.156886i	0.548423	−	0.836201i	$-0.315228\pi$
$947$	13.2645	+	4.82790i	0.431040	+	0.156886i	−0.117383	+	0.993087i	$0.537451\pi$
$948$		0			0
$949$	−34.6223			−1.12389
$950$	0.754997	−	2.47596i	0.0244953	−	0.0803309i
$951$		0			0
$952$	1.24048	−	1.04089i	0.0402043	−	0.0337354i
$953$	−41.0653	−	14.9465i	−1.33023	−	0.484166i	−0.423511	−	0.905891i	$-0.639202\pi$
$953$	−41.0653	−	14.9465i	−1.33023	−	0.484166i	−0.906724	+	0.421725i	$0.861425\pi$
$954$		0			0
$955$	2.15181	+	12.2035i	0.0696308	+	0.394896i
$956$	18.3694	−	6.68590i	0.594107	−	0.216237i
$957$		0			0
$958$	0.452019	+	0.782920i	0.0146041	+	0.0252950i
$959$	−15.6112	−	13.0994i	−0.504112	−	0.423000i
$960$		0			0
$961$	−15.8492	−	27.4516i	−0.511264	−	0.885536i
$962$	−1.72105	+	2.98094i	−0.0554887	+	0.0961093i
$963$		0			0
$964$	−0.922899	−	5.23402i	−0.0297246	−	0.168576i
$965$	0.264937	−	1.50253i	0.00852862	−	0.0483682i
$966$		0			0
$967$	1.75708	−	1.47437i	0.0565039	−	0.0474124i	−0.614098	−	0.789230i	$-0.710480\pi$
$967$	1.75708	−	1.47437i	0.0565039	−	0.0474124i	0.670602	+	0.741817i	$0.266036\pi$
$968$	23.7418			0.763092
$969$		0			0
$970$	−0.795457			−0.0255406
$971$	22.6553	−	19.0100i	0.727042	−	0.610061i	−0.202281	−	0.979327i	$-0.564835\pi$
$971$	22.6553	−	19.0100i	0.727042	−	0.610061i	0.929324	+	0.369266i	$0.120391\pi$
$972$		0			0
$973$	−3.61840	+	20.5210i	−0.116001	+	0.657872i
$974$	2.98332	+	16.9192i	0.0955917	+	0.542128i
$975$		0			0
$976$	−11.8021	+	20.4418i	−0.377775	+	0.654325i
$977$	8.19487	+	14.1939i	0.262177	+	0.454104i	0.966820	−	0.255458i	$-0.0822262\pi$
$977$	8.19487	+	14.1939i	0.262177	+	0.454104i	−0.704643	+	0.709562i	$0.748893\pi$
$978$		0			0
$979$	2.64010	+	2.21530i	0.0843778	+	0.0708014i
$980$	−4.83933	−	8.38196i	−0.154587	−	0.267752i
$981$		0			0
$982$	−8.23555	+	2.99749i	−0.262807	+	0.0956539i
$983$	−8.92083	−	50.5925i	−0.284530	−	1.61365i	−0.706958	−	0.707255i	$-0.749933\pi$
$983$	−8.92083	−	50.5925i	−0.284530	−	1.61365i	0.422428	−	0.906396i	$-0.361178\pi$
$984$		0			0
$985$	12.9325	+	4.70705i	0.412065	+	0.149979i
$986$	−1.08436	+	0.909889i	−0.0345332	+	0.0289768i
$987$		0			0
$988$	−14.8465	−	34.9051i	−0.472329	−	1.11048i
$989$	−59.6605			−1.89709
$990$		0			0
$991$	45.9315	+	16.7177i	1.45906	+	0.531055i	0.945107	−	0.326761i	$-0.105957\pi$
$991$	45.9315	+	16.7177i	1.45906	+	0.531055i	0.513956	+	0.857817i	$0.328180\pi$
$992$	7.59630	−	43.0807i	0.241183	−	1.36781i
$993$		0			0
$994$	1.48234	−	0.539527i	0.0470169	−	0.0171128i
$995$	7.14585	−	12.3770i	0.226539	−	0.392376i
$996$		0			0
$997$	14.7253	+	12.3560i	0.466355	+	0.391318i	0.845463	−	0.534034i	$-0.179325\pi$
$997$	14.7253	+	12.3560i	0.466355	+	0.391318i	−0.379108	+	0.925352i	$0.623769\pi$
$998$	10.2146	+	8.57105i	0.323337	+	0.271312i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.b.766.2		18
3.2	odd	2		95.2.k.b.6.2	✓	18
15.2	even	4		475.2.u.c.424.3		36
15.8	even	4		475.2.u.c.424.4		36
15.14	odd	2		475.2.l.b.101.2		18
19.16	even	9	inner	855.2.bs.b.586.2		18
57.23	odd	18		1805.2.a.t.1.5		9
57.35	odd	18		95.2.k.b.16.2	yes	18
57.53	even	18		1805.2.a.u.1.5		9
285.92	even	36		475.2.u.c.149.4		36
285.149	odd	18		475.2.l.b.301.2		18
285.194	odd	18		9025.2.a.ce.1.5		9
285.224	even	18		9025.2.a.cd.1.5		9
285.263	even	36		475.2.u.c.149.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.6.2	✓	18	3.2	odd	2
95.2.k.b.16.2	yes	18	57.35	odd	18
475.2.l.b.101.2		18	15.14	odd	2
475.2.l.b.301.2		18	285.149	odd	18
475.2.u.c.149.3		36	285.263	even	36
475.2.u.c.149.4		36	285.92	even	36
475.2.u.c.424.3		36	15.2	even	4
475.2.u.c.424.4		36	15.8	even	4
855.2.bs.b.586.2		18	19.16	even	9	inner
855.2.bs.b.766.2		18	1.1	even	1	trivial
1805.2.a.t.1.5		9	57.23	odd	18
1805.2.a.u.1.5		9	57.53	even	18
9025.2.a.cd.1.5		9	285.224	even	18
9025.2.a.ce.1.5		9	285.194	odd	18

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.454913 - 0.381717i) q^{2} +(-0.286059 + 1.62232i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.530259 + 0.918436i) q^{7} +(1.08298 + 1.87578i) q^{8} +O(q^{10})\)	\(q+(0.454913 - 0.381717i) q^{2} +(-0.286059 + 1.62232i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.530259 + 0.918436i) q^{7} +(1.08298 + 1.87578i) q^{8} +(0.454913 + 0.381717i) q^{10} +(0.0983263 + 0.170306i) q^{11} +(4.96388 - 1.80671i) q^{13} +(0.109361 + 0.620217i) q^{14} +(-1.88732 - 0.686928i) q^{16} +(-0.540035 + 0.453143i) q^{17} +(-4.24646 + 0.983648i) q^{19} -1.64735 q^{20} +(0.109739 + 0.0399416i) q^{22} +(-1.15007 + 6.52236i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(1.56848 - 2.71669i) q^{26} +(-1.33831 - 1.12298i) q^{28} +(2.59020 + 2.17343i) q^{29} +(-3.95912 + 6.85739i) q^{31} +(-5.19146 + 1.88954i) q^{32} +(-0.0726963 + 0.412281i) q^{34} +(-0.996561 - 0.362719i) q^{35} -1.09727 q^{37} +(-1.55629 + 2.06842i) q^{38} +(-1.65922 + 1.39225i) q^{40} +(-1.27293 - 0.463310i) q^{41} +(1.56424 + 8.87125i) q^{43} +(-0.304418 + 0.110799i) q^{44} +(1.96652 + 3.40611i) q^{46} +(-3.69186 - 3.09784i) q^{47} +(2.93765 + 5.08816i) q^{49} +(-0.296923 + 0.514286i) q^{50} +(1.51109 + 8.56982i) q^{52} +(0.924537 - 5.24331i) q^{53} +(-0.150645 + 0.126406i) q^{55} -2.29704 q^{56} +2.00795 q^{58} +(8.41282 - 7.05920i) q^{59} +(2.04079 - 11.5739i) q^{61} +(0.816531 + 4.63078i) q^{62} +(0.368050 - 0.637482i) q^{64} +(2.64123 + 4.57474i) q^{65} +(-2.34103 - 1.96435i) q^{67} +(-0.580661 - 1.00573i) q^{68} +(-0.591804 + 0.215399i) q^{70} +(-0.434950 - 2.46672i) q^{71} +(-6.15894 - 2.24167i) q^{73} +(-0.499161 + 0.418846i) q^{74} +(-0.381053 - 7.17050i) q^{76} -0.208554 q^{77} +(11.5236 + 4.19426i) q^{79} +(0.348762 - 1.97793i) q^{80} +(-0.755927 + 0.275135i) q^{82} +(-2.01588 + 3.49160i) q^{83} +(-0.540035 - 0.453143i) q^{85} +(4.09790 + 3.43855i) q^{86} +(-0.212971 + 0.368877i) q^{88} +(16.4684 - 5.99401i) q^{89} +(-0.972801 + 5.51703i) q^{91} +(-10.2524 - 3.73156i) q^{92} -2.86197 q^{94} +(-1.70609 - 4.01114i) q^{95} +(-1.02612 + 0.861014i) q^{97} +(3.27861 + 1.19332i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Introduction

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