LMFDB - Embedded newform 693.2.i.i.298.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(100,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("693.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.i (of order $3$, degree $2$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.10423593216.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			298.3
Root			$0.643668 + 1.11487i$ of defining polynomial
Character	$\chi$	$=$	693.298
Dual form			693.2.i.i.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.643668 + 1.11487i) q^{2} +(0.171383 - 0.296844i) q^{4} +(1.95872 + 3.39260i) q^{5} +(-0.234193 + 2.63537i) q^{7} +3.01593 q^{8} +O(q^{10})$	\(q+(0.643668 + 1.11487i) q^{2} +(0.171383 - 0.296844i) q^{4} +(1.95872 + 3.39260i) q^{5} +(-0.234193 + 2.63537i) q^{7} +3.01593 q^{8} +(-2.52153 + 4.36742i) q^{10} +(-0.500000 + 0.866025i) q^{11} -3.04306 q^{13} +(-3.08882 + 1.43521i) q^{14} +(1.59849 + 2.76866i) q^{16} +(1.98643 - 3.44061i) q^{17} +(-3.79530 - 6.57365i) q^{19} +1.34277 q^{20} -1.28734 q^{22} +(2.25572 + 3.90703i) q^{23} +(-5.17316 + 8.96018i) q^{25} +(-1.95872 - 3.39260i) q^{26} +(0.742157 + 0.521177i) q^{28} -3.75572 q^{29} +(3.37168 - 5.83991i) q^{31} +(0.958135 - 1.65954i) q^{32} +5.11442 q^{34} +(-9.39946 + 4.36742i) q^{35} +(-0.171383 - 0.296844i) q^{37} +(4.88582 - 8.46250i) q^{38} +(5.90735 + 10.2318i) q^{40} +2.79182 q^{41} +11.1222 q^{43} +(0.171383 + 0.296844i) q^{44} +(-2.90387 + 5.02965i) q^{46} +(0.828617 + 1.43521i) q^{47} +(-6.89031 - 1.23437i) q^{49} -13.3192 q^{50} +(-0.521529 + 0.903315i) q^{52} +(-6.47016 + 11.2067i) q^{53} -3.91744 q^{55} +(-0.706310 + 7.94807i) q^{56} +(-2.41744 - 4.18713i) q^{58} +(-1.83039 + 3.17034i) q^{59} +(0.234193 + 0.405635i) q^{61} +8.68096 q^{62} +8.86084 q^{64} +(-5.96050 - 10.3239i) q^{65} +(1.28911 - 2.23281i) q^{67} +(-0.680883 - 1.17932i) q^{68} +(-10.9192 - 7.66797i) q^{70} +5.00355 q^{71} +(4.36878 - 7.56694i) q^{73} +(0.220628 - 0.382139i) q^{74} -2.60180 q^{76} +(-2.16520 - 1.52050i) q^{77} +(-0.359814 - 0.623216i) q^{79} +(-6.26198 + 10.8461i) q^{80} +(1.79700 + 3.11250i) q^{82} +11.5976 q^{83} +15.5635 q^{85} +(7.15901 + 12.3998i) q^{86} +(-1.50796 + 2.61187i) q^{88} +(-6.17764 - 10.7000i) q^{89} +(0.712664 - 8.01957i) q^{91} +1.54637 q^{92} +(-1.06671 + 1.84759i) q^{94} +(14.8679 - 25.7519i) q^{95} -13.1687 q^{97} +(-3.05891 - 8.47629i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8	$ 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8} - 10 q^{10} - 4 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{17} - 4 q^{22} + 4 q^{23} - 4 q^{25} - 4 q^{26} - 22 q^{28} - 16 q^{29} + 12 q^{31} + 26 q^{32} - 32 q^{34} + 2 q^{35} + 4 q^{37} + 8 q^{38} + 6 q^{40} - 4 q^{41} + 36 q^{43} - 4 q^{44} + 14 q^{46} + 12 q^{47} - 4 q^{49} - 4 q^{50} + 6 q^{52} - 12 q^{53} - 8 q^{55} - 48 q^{56} + 4 q^{58} + 12 q^{59} - 2 q^{61} + 52 q^{62} + 112 q^{64} - 4 q^{65} - 28 q^{67} - 48 q^{68} - 32 q^{70} - 24 q^{71} - 6 q^{73} - 16 q^{74} - 36 q^{76} - 4 q^{77} - 2 q^{79} + 16 q^{80} + 12 q^{82} + 24 q^{83} + 36 q^{85} + 36 q^{86} + 12 q^{88} + 8 q^{89} + 12 q^{91} + 32 q^{92} - 20 q^{94} + 34 q^{95} - 88 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8 - 10 * q^10 - 4 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^17 - 4 * q^22 + 4 * q^23 - 4 * q^25 - 4 * q^26 - 22 * q^28 - 16 * q^29 + 12 * q^31 + 26 * q^32 - 32 * q^34 + 2 * q^35 + 4 * q^37 + 8 * q^38 + 6 * q^40 - 4 * q^41 + 36 * q^43 - 4 * q^44 + 14 * q^46 + 12 * q^47 - 4 * q^49 - 4 * q^50 + 6 * q^52 - 12 * q^53 - 8 * q^55 - 48 * q^56 + 4 * q^58 + 12 * q^59 - 2 * q^61 + 52 * q^62 + 112 * q^64 - 4 * q^65 - 28 * q^67 - 48 * q^68 - 32 * q^70 - 24 * q^71 - 6 * q^73 - 16 * q^74 - 36 * q^76 - 4 * q^77 - 2 * q^79 + 16 * q^80 + 12 * q^82 + 24 * q^83 + 36 * q^85 + 36 * q^86 + 12 * q^88 + 8 * q^89 + 12 * q^91 + 32 * q^92 - 20 * q^94 + 34 * q^95 - 88 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.643668	+	1.11487i	0.455142	+	0.788329i	0.998696	−	0.0510450i	$-0.0162552\pi$
$2$	0.643668	+	1.11487i	0.455142	+	0.788329i	−0.543554	+	0.839374i	$0.682922\pi$
$3$		0			0
$3$		0			0
$4$	0.171383	−	0.296844i	0.0856916	−	0.148422i
$5$	1.95872	+	3.39260i	0.875966	+	1.51722i	0.855730	+	0.517422i	$0.173108\pi$
$5$	1.95872	+	3.39260i	0.875966	+	1.51722i	0.0202354	+	0.999795i	$0.493558\pi$
$6$		0			0
$7$	−0.234193	+	2.63537i	−0.0885168	+	0.996075i
$7$	−0.234193	+	2.63537i	−0.0885168	+	0.996075i
$8$	3.01593			1.06629
$9$		0			0
$10$	−2.52153	+	4.36742i	−0.797378	+	1.38110i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	−3.04306			−0.843993			−0.421996	−	0.906598i	$-0.638670\pi$
$13$	−3.04306			−0.843993			−0.421996	+	0.906598i	$0.638670\pi$
$14$	−3.08882	+	1.43521i	−0.825522	+	0.383575i
$15$		0			0
$16$	1.59849	+	2.76866i	0.399622	+	0.692166i
$17$	1.98643	−	3.44061i	0.481781	−	0.834469i	−0.518000	−	0.855380i	$-0.673323\pi$
$17$	1.98643	−	3.44061i	0.481781	−	0.834469i	0.999781	+	0.0209111i	$0.00665670\pi$
$18$		0			0
$19$	−3.79530	−	6.57365i	−0.870701	−	1.50810i	−0.861272	−	0.508144i	$-0.830332\pi$
$19$	−3.79530	−	6.57365i	−0.870701	−	1.50810i	−0.00942900	−	0.999956i	$-0.503001\pi$
$20$	1.34277			0.300252
$21$		0			0
$22$	−1.28734			−0.274461
$23$	2.25572	+	3.90703i	0.470351	+	0.814671i	0.999425	−	0.0339042i	$-0.0107941\pi$
$23$	2.25572	+	3.90703i	0.470351	+	0.814671i	−0.529074	+	0.848575i	$0.677461\pi$
$24$		0			0
$25$	−5.17316	+	8.96018i	−1.03463	+	1.79204i
$26$	−1.95872	−	3.39260i	−0.384136	−	0.665344i
$27$		0			0
$28$	0.742157	+	0.521177i	0.140254	+	0.0984931i
$29$	−3.75572			−0.697420			−0.348710	−	0.937231i	$-0.613380\pi$
$29$	−3.75572			−0.697420			−0.348710	+	0.937231i	$0.613380\pi$
$30$		0			0
$31$	3.37168	−	5.83991i	0.605571	−	1.04888i	−0.386390	−	0.922335i	$-0.626278\pi$
$31$	3.37168	−	5.83991i	0.605571	−	1.04888i	0.991961	−	0.126544i	$-0.0403885\pi$
$32$	0.958135	−	1.65954i	0.169376	−	0.293368i
$33$		0			0
$34$	5.11442			0.877115
$35$	−9.39946	+	4.36742i	−1.58880	+	0.738228i
$36$		0			0
$37$	−0.171383	−	0.296844i	−0.0281752	−	0.0488009i	0.851594	−	0.524202i	$-0.175636\pi$
$37$	−0.171383	−	0.296844i	−0.0281752	−	0.0488009i	−0.879769	+	0.475401i	$0.842303\pi$
$38$	4.88582	−	8.46250i	0.792585	−	1.37280i
$39$		0			0
$40$	5.90735	+	10.2318i	0.934035	+	1.61780i
$41$	2.79182			0.436009			0.218004	−	0.975948i	$-0.430045\pi$
$41$	2.79182			0.436009			0.218004	+	0.975948i	$0.430045\pi$
$42$		0			0
$43$	11.1222			1.69612			0.848061	−	0.529899i	$-0.177770\pi$
$43$	11.1222			1.69612			0.848061	+	0.529899i	$0.177770\pi$
$44$	0.171383	+	0.296844i	0.0258370	+	0.0447510i
$45$		0			0
$46$	−2.90387	+	5.02965i	−0.428153	+	0.741582i
$47$	0.828617	+	1.43521i	0.120866	+	0.209346i	0.920109	−	0.391661i	$-0.128099\pi$
$47$	0.828617	+	1.43521i	0.120866	+	0.209346i	−0.799243	+	0.601008i	$0.794766\pi$
$48$		0			0
$49$	−6.89031	−	1.23437i	−0.984330	−	0.176339i
$50$	−13.3192			−1.88362
$51$		0			0
$52$	−0.521529	+	0.903315i	−0.0723231	+	0.125267i
$53$	−6.47016	+	11.2067i	−0.888745	+	1.53935i	−0.0473857	+	0.998877i	$0.515089\pi$
$53$	−6.47016	+	11.2067i	−0.888745	+	1.53935i	−0.841360	+	0.540476i	$0.818244\pi$
$54$		0			0
$55$	−3.91744			−0.528227
$56$	−0.706310	+	7.94807i	−0.0943847	+	1.06211i
$57$		0			0
$58$	−2.41744	−	4.18713i	−0.317425	−	0.549797i
$59$	−1.83039	+	3.17034i	−0.238297	+	0.412743i	−0.960226	−	0.279225i	$-0.909923\pi$
$59$	−1.83039	+	3.17034i	−0.238297	+	0.412743i	0.721929	+	0.691967i	$0.243256\pi$
$60$		0			0
$61$	0.234193	+	0.405635i	0.0299854	+	0.0519362i	0.880629	−	0.473807i	$-0.157121\pi$
$61$	0.234193	+	0.405635i	0.0299854	+	0.0519362i	−0.850643	+	0.525743i	$0.823787\pi$
$62$	8.68096			1.10248
$63$		0			0
$64$	8.86084			1.10760
$65$	−5.96050	−	10.3239i	−0.739309	−	1.28052i
$66$		0			0
$67$	1.28911	−	2.23281i	0.157490	−	0.272781i	−0.776473	−	0.630151i	$-0.782993\pi$
$67$	1.28911	−	2.23281i	0.157490	−	0.272781i	0.933963	+	0.357370i	$0.116326\pi$
$68$	−0.680883	−	1.17932i	−0.0825692	−	0.143014i
$69$		0			0
$70$	−10.9192	−	7.66797i	−1.30510	−	0.916498i
$71$	5.00355			0.593813			0.296906	−	0.954907i	$-0.404045\pi$
$71$	5.00355			0.593813			0.296906	+	0.954907i	$0.404045\pi$
$72$		0			0
$73$	4.36878	−	7.56694i	0.511327	−	0.885644i	−0.488587	−	0.872515i	$-0.662488\pi$
$73$	4.36878	−	7.56694i	0.511327	−	0.885644i	0.999914	−	0.0131288i	$-0.00417914\pi$
$74$	0.220628	−	0.382139i	0.0256475	−	0.0444227i
$75$		0			0
$76$	−2.60180			−0.298447
$77$	−2.16520	−	1.52050i	−0.246747	−	0.173277i
$78$		0			0
$79$	−0.359814	−	0.623216i	−0.0404822	−	0.0701172i	0.845074	−	0.534649i	$-0.179556\pi$
$79$	−0.359814	−	0.623216i	−0.0404822	−	0.0701172i	−0.885557	+	0.464532i	$0.846223\pi$
$80$	−6.26198	+	10.8461i	−0.700111	+	1.21263i
$81$		0			0
$82$	1.79700	+	3.11250i	0.198446	+	0.343718i
$83$	11.5976			1.27300			0.636499	−	0.771278i	$-0.280382\pi$
$83$	11.5976			1.27300			0.636499	+	0.771278i	$0.280382\pi$
$84$		0			0
$85$	15.5635			1.68810
$86$	7.15901	+	12.3998i	0.771976	+	1.33710i
$87$		0			0
$88$	−1.50796	+	2.61187i	−0.160749	+	0.278426i
$89$	−6.17764	−	10.7000i	−0.654829	−	1.13420i	−0.981937	−	0.189210i	$-0.939407\pi$
$89$	−6.17764	−	10.7000i	−0.654829	−	1.13420i	0.327108	−	0.944987i	$-0.393926\pi$
$90$		0			0
$91$	0.712664	−	8.01957i	0.0747075	−	0.840680i
$92$	1.54637			0.161220
$93$		0			0
$94$	−1.06671	+	1.84759i	−0.110023	+	0.190565i
$95$	14.8679	−	25.7519i	1.52541	−	2.64209i
$96$		0			0
$97$	−13.1687			−1.33708			−0.668538	−	0.743678i	$-0.733080\pi$
$97$	−13.1687			−1.33708			−0.668538	+	0.743678i	$0.733080\pi$
$98$	−3.05891	−	8.47629i	−0.308997	−	0.856235i
$99$		0			0
$100$	1.77319	+	3.07125i	0.177319	+	0.307125i
$101$	3.53509	−	6.12296i	0.351755	−	0.609258i	−0.634802	−	0.772675i	$-0.718918\pi$
$101$	3.53509	−	6.12296i	0.351755	−	0.609258i	0.986557	+	0.163417i	$0.0522517\pi$
$102$		0			0
$103$	−1.16868	−	2.02421i	−0.115153	−	0.199451i	0.802688	−	0.596400i	$-0.203403\pi$
$103$	−1.16868	−	2.02421i	−0.115153	−	0.199451i	−0.917841	+	0.396948i	$0.870069\pi$
$104$	−9.17764			−0.899942
$105$		0			0
$106$	−16.6585			−1.61802
$107$	−5.42660	−	9.39914i	−0.524609	−	0.908649i	−0.999589	−	0.0286528i	$-0.990878\pi$
$107$	−5.42660	−	9.39914i	−0.524609	−	0.908649i	0.474981	−	0.879996i	$-0.342455\pi$
$108$		0			0
$109$	1.09620	−	1.89868i	0.104997	−	0.181860i	−0.808740	−	0.588166i	$-0.799850\pi$
$109$	1.09620	−	1.89868i	0.104997	−	0.181860i	0.913737	+	0.406306i	$0.133183\pi$
$110$	−2.52153	−	4.36742i	−0.240418	−	0.416417i
$111$		0			0
$112$	−7.67080	+	3.56420i	−0.724822	+	0.336785i
$113$	11.6415			1.09514			0.547568	−	0.836761i	$-0.315554\pi$
$113$	11.6415			1.09514			0.547568	+	0.836761i	$0.315554\pi$
$114$		0			0
$115$	−8.83665	+	15.3055i	−0.824022	+	1.42725i
$116$	−0.643668	+	1.11487i	−0.0597631	+	0.103513i
$117$		0			0
$118$	−4.71266			−0.433836
$119$	8.60204	+	6.04075i	0.788548	+	0.553755i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.301486	+	0.522188i	−0.0272952	+	0.0472767i
$123$		0			0
$124$	−1.15570	−	2.00173i	−0.103785	−	0.179760i
$125$	−20.9439			−1.87328
$126$		0			0
$127$	5.41837			0.480802			0.240401	−	0.970674i	$-0.422721\pi$
$127$	5.41837			0.480802			0.240401	+	0.970674i	$0.422721\pi$
$128$	3.78717	+	6.55957i	0.334742	+	0.579789i
$129$		0			0
$130$	7.67316	−	13.2903i	0.672981	−	1.16564i
$131$	−1.03297	−	1.78916i	−0.0902514	−	0.156320i	0.817365	−	0.576120i	$-0.195434\pi$
$131$	−1.03297	−	1.78916i	−0.0902514	−	0.156320i	−0.907617	+	0.419800i	$0.862100\pi$
$132$		0			0
$133$	18.2128	−	8.46250i	1.57925	−	0.733792i
$134$	3.31904			0.286722
$135$		0			0
$136$	5.99094	−	10.3766i	0.513719	−	0.889787i
$137$	−2.09153	+	3.62263i	−0.178691	+	0.309502i	−0.941432	−	0.337202i	$-0.890520\pi$
$137$	−2.09153	+	3.62263i	−0.178691	+	0.309502i	0.762741	+	0.646704i	$0.223853\pi$
$138$		0			0
$139$	3.61077			0.306261			0.153131	−	0.988206i	$-0.451064\pi$
$139$	3.61077			0.306261			0.153131	+	0.988206i	$0.451064\pi$
$140$	−0.314467	+	3.53868i	−0.0265773	+	0.299073i
$141$		0			0
$142$	3.22063	+	5.57829i	0.270269	+	0.468120i
$143$	1.52153	−	2.63537i	0.127237	−	0.220380i
$144$		0			0
$145$	−7.35641	−	12.7417i	−0.610916	−	1.05814i
$146$	11.2482			0.930905
$147$		0			0
$148$	−0.117489			−0.00965752
$149$	6.65960	+	11.5348i	0.545575	+	0.944964i	0.998570	+	0.0534512i	$0.0170221\pi$
$149$	6.65960	+	11.5348i	0.545575	+	0.944964i	−0.452995	+	0.891513i	$0.649645\pi$
$150$		0			0
$151$	3.52160	−	6.09959i	0.286584	−	0.496378i	−0.686408	−	0.727217i	$-0.740814\pi$
$151$	3.52160	−	6.09959i	0.286584	−	0.496378i	0.972992	+	0.230839i	$0.0741469\pi$
$152$	−11.4463	−	19.8257i	−0.928421	−	1.60807i
$153$		0			0
$154$	0.301486	−	3.39260i	0.0242944	−	0.273384i
$155$	26.4167			2.12184
$156$		0			0
$157$	−6.37793	+	11.0469i	−0.509015	+	0.881639i	0.490931	+	0.871199i	$0.336657\pi$
$157$	−6.37793	+	11.0469i	−0.509015	+	0.881639i	−0.999945	+	0.0104406i	$0.996677\pi$
$158$	0.463201	−	0.802288i	0.0368503	−	0.0638266i
$159$		0			0
$160$	7.50687			0.593470
$161$	−10.8247	+	5.02965i	−0.853107	+	0.396392i
$162$		0			0
$163$	−5.70207	−	9.87627i	−0.446621	−	0.773569i	0.551543	−	0.834146i	$-0.314039\pi$
$163$	−5.70207	−	9.87627i	−0.446621	−	0.773569i	−0.998164	+	0.0605770i	$0.980706\pi$
$164$	0.478471	−	0.828736i	0.0373623	−	0.0647134i
$165$		0			0
$166$	7.46498	+	12.9297i	0.579395	+	1.00354i
$167$	−12.1109			−0.937167			−0.468583	−	0.883419i	$-0.655235\pi$
$167$	−12.1109			−0.937167			−0.468583	+	0.883419i	$0.655235\pi$
$168$		0			0
$169$	−3.73980			−0.287677
$170$	10.0177	+	17.3512i	0.768323	+	1.33077i
$171$		0			0
$172$	1.90616	−	3.30157i	0.145343	−	0.251742i
$173$	1.82124	+	3.15448i	0.138466	+	0.239830i	0.926916	−	0.375268i	$-0.122449\pi$
$173$	1.82124	+	3.15448i	0.138466	+	0.239830i	−0.788450	+	0.615099i	$0.789116\pi$
$174$		0			0
$175$	−22.4018	−	15.7316i	−1.69342	−	1.18920i
$176$	−3.19698			−0.240981
$177$		0			0
$178$	7.95270	−	13.7745i	0.596080	−	1.03244i
$179$	4.96320	−	8.59652i	0.370967	−	0.642534i	−0.618748	−	0.785590i	$-0.712360\pi$
$179$	4.96320	−	8.59652i	0.370967	−	0.642534i	0.989715	+	0.143056i	$0.0456929\pi$
$180$		0			0
$181$	−8.07219			−0.600001			−0.300001	−	0.953939i	$-0.596987\pi$
$181$	−8.07219			−0.600001			−0.300001	+	0.953939i	$0.596987\pi$
$182$	9.39946	−	4.36742i	0.696735	−	0.323734i
$183$		0			0
$184$	6.80310	+	11.7833i	0.501531	+	0.868677i
$185$	0.671383	−	1.16287i	0.0493611	−	0.0854959i
$186$		0			0
$187$	1.98643	+	3.44061i	0.145262	+	0.251602i
$188$	0.568044			0.0414289
$189$		0			0
$190$	38.2798			2.77711
$191$	2.79182	+	4.83557i	0.202009	+	0.349890i	0.949176	−	0.314747i	$-0.101920\pi$
$191$	2.79182	+	4.83557i	0.202009	+	0.349890i	−0.747167	+	0.664637i	$0.768586\pi$
$192$		0			0
$193$	−5.56688	+	9.64211i	−0.400712	+	0.694054i	−0.993812	−	0.111075i	$-0.964571\pi$
$193$	−5.56688	+	9.64211i	−0.400712	+	0.694054i	0.593100	+	0.805129i	$0.297904\pi$
$194$	−8.47626	−	14.6813i	−0.608560	−	1.05406i
$195$		0			0
$196$	−1.54730	+	1.83380i	−0.110521	+	0.130986i
$197$	0.644475			0.0459170			0.0229585	−	0.999736i	$-0.492691\pi$
$197$	0.644475			0.0459170			0.0229585	+	0.999736i	$0.492691\pi$
$198$		0			0
$199$	12.6177	−	21.8545i	0.894447	−	1.54923i	0.0599599	−	0.998201i	$-0.480903\pi$
$199$	12.6177	−	21.8545i	0.894447	−	1.54923i	0.834487	−	0.551027i	$-0.185764\pi$
$200$	−15.6019	+	27.0232i	−1.10322	+	1.91083i
$201$		0			0
$202$	9.10171			0.640394
$203$	0.879565	−	9.89770i	0.0617334	−	0.694683i
$204$		0			0
$205$	5.46839	+	9.47152i	0.381929	+	0.661520i
$206$	1.50448	−	2.60584i	0.104822	−	0.181557i
$207$		0			0
$208$	−4.86430	−	8.42521i	−0.337278	−	0.584183i
$209$	7.59060			0.525053
$210$		0			0
$211$	−17.6357			−1.21409			−0.607044	−	0.794668i	$-0.707645\pi$
$211$	−17.6357			−1.21409			−0.607044	+	0.794668i	$0.707645\pi$
$212$	2.21776	+	3.84127i	0.152316	+	0.263819i
$213$		0			0
$214$	6.98585	−	12.0998i	0.477543	−	0.827129i
$215$	21.7853	+	37.7332i	1.48574	+	2.57338i
$216$		0			0
$217$	14.6007	+	10.2533i	0.991159	+	0.696037i
$218$	2.82236			0.191154
$219$		0			0
$220$	−0.671383	+	1.16287i	−0.0452646	+	0.0784007i
$221$	−6.04484	+	10.4700i	−0.406620	+	0.704286i
$222$		0			0
$223$	16.5853			1.11064			0.555318	−	0.831638i	$-0.312596\pi$
$223$	16.5853			1.11064			0.555318	+	0.831638i	$0.312596\pi$
$224$	4.14910	+	2.91369i	0.277224	+	0.194679i
$225$		0			0
$226$	7.49323	+	12.9787i	0.498442	+	0.863327i
$227$	−1.17409	+	2.03358i	−0.0779269	+	0.134973i	−0.902355	−	0.430993i	$-0.858163\pi$
$227$	−1.17409	+	2.03358i	−0.0779269	+	0.134973i	0.824428	+	0.565966i	$0.191497\pi$
$228$		0			0
$229$	8.72518	+	15.1125i	0.576576	+	0.998660i	0.995868	+	0.0908081i	$0.0289450\pi$
$229$	8.72518	+	15.1125i	0.576576	+	0.998660i	−0.419292	+	0.907851i	$0.637722\pi$
$230$	−22.7515			−1.50019
$231$		0			0
$232$	−11.3270			−0.743653
$233$	−2.79530	−	4.84160i	−0.183126	−	0.317184i	0.759817	−	0.650137i	$-0.225288\pi$
$233$	−2.79530	−	4.84160i	−0.183126	−	0.317184i	−0.942943	+	0.332953i	$0.891955\pi$
$234$		0			0
$235$	−3.24605	+	5.62233i	−0.211749	+	0.366760i
$236$	0.627398	+	1.08668i	0.0408401	+	0.0707372i
$237$		0			0
$238$	−1.19776	+	13.4784i	−0.0776394	+	0.873672i
$239$	−17.8147			−1.15234			−0.576169	−	0.817331i	$-0.695453\pi$
$239$	−17.8147			−1.15234			−0.576169	+	0.817331i	$0.695453\pi$
$240$		0			0
$241$	−1.49211	+	2.58441i	−0.0961152	+	0.166476i	−0.910074	−	0.414447i	$-0.863975\pi$
$241$	−1.49211	+	2.58441i	−0.0961152	+	0.166476i	0.813958	+	0.580923i	$0.197308\pi$
$242$	0.643668	−	1.11487i	0.0413765	−	0.0716663i
$243$		0			0
$244$	0.160547			0.0102780
$245$	−9.30845	−	25.7938i	−0.594695	−	1.64791i
$246$		0			0
$247$	11.5493	+	20.0040i	0.734866	+	1.27282i
$248$	10.1687	−	17.6128i	0.645715	−	1.11841i
$249$		0			0
$250$	−13.4809	−	23.3496i	−0.852607	−	1.47676i
$251$	−25.0829			−1.58322			−0.791608	−	0.611029i	$-0.790756\pi$
$251$	−25.0829			−1.58322			−0.791608	+	0.611029i	$0.790756\pi$
$252$		0			0
$253$	−4.51145			−0.283632
$254$	3.48763	+	6.04075i	0.218833	+	0.379030i
$255$		0			0
$256$	3.98548	−	6.90306i	0.249093	−	0.431441i
$257$	−11.2785	−	19.5350i	−0.703535	−	1.21856i	−0.967218	−	0.253948i	$-0.918271\pi$
$257$	−11.2785	−	19.5350i	−0.703535	−	1.21856i	0.263683	−	0.964609i	$-0.415063\pi$
$258$		0			0
$259$	0.822431	−	0.382139i	0.0511034	−	0.0237449i
$260$	−4.08612			−0.253410
$261$		0			0
$262$	1.32978	−	2.30326i	0.0821544	−	0.142296i
$263$	12.8779	−	22.3052i	0.794087	−	1.37540i	−0.129330	−	0.991602i	$-0.541283\pi$
$263$	12.8779	−	22.3052i	0.794087	−	1.37540i	0.923417	−	0.383798i	$-0.125384\pi$
$264$		0			0
$265$	−50.6929			−3.11404
$266$	21.1575	+	14.8578i	1.29725	+	0.910990i
$267$		0			0
$268$	−0.441865	−	0.765332i	−0.0269912	−	0.0467501i
$269$	−10.3481	+	17.9234i	−0.630935	+	1.09281i	0.356426	+	0.934323i	$0.383995\pi$
$269$	−10.3481	+	17.9234i	−0.630935	+	1.09281i	−0.987361	+	0.158488i	$0.949338\pi$
$270$		0			0
$271$	−1.53390	−	2.65680i	−0.0931779	−	0.161389i	0.815669	−	0.578519i	$-0.196369\pi$
$271$	−1.53390	−	2.65680i	−0.0931779	−	0.161389i	−0.908847	+	0.417130i	$0.863036\pi$
$272$	12.7012			0.770122
$273$		0			0
$274$	−5.38499			−0.325319
$275$	−5.17316	−	8.96018i	−0.311953	−	0.540319i
$276$		0			0
$277$	3.34277	−	5.78984i	0.200847	−	0.347878i	−0.747954	−	0.663750i	$-0.768964\pi$
$277$	3.34277	−	5.78984i	0.200847	−	0.347878i	0.948802	+	0.315872i	$0.102297\pi$
$278$	2.32413	+	4.02552i	0.139392	+	0.241435i
$279$		0			0
$280$	−28.3481	+	13.1718i	−1.69412	+	0.787166i
$281$	−3.11286			−0.185698			−0.0928489	−	0.995680i	$-0.529597\pi$
$281$	−3.11286			−0.185698			−0.0928489	+	0.995680i	$0.529597\pi$
$282$		0			0
$283$	11.1799	−	19.3642i	0.664578	−	1.15108i	−0.314822	−	0.949151i	$-0.601945\pi$
$283$	11.1799	−	19.3642i	0.664578	−	1.15108i	0.979400	−	0.201932i	$-0.0647220\pi$
$284$	0.857525	−	1.48528i	0.0508848	−	0.0881350i
$285$		0			0
$286$	3.91744			0.231643
$287$	−0.653825	+	7.35746i	−0.0385941	+	0.434297i
$288$		0			0
$289$	0.608157	+	1.05336i	0.0357739	+	0.0619623i
$290$	9.47016	−	16.4028i	0.556107	−	0.963206i
$291$		0			0
$292$	−1.49747	−	2.59370i	−0.0876328	−	0.151785i
$293$	−10.6291			−0.620958			−0.310479	−	0.950580i	$-0.600489\pi$
$293$	−10.6291			−0.620958			−0.310479	+	0.950580i	$0.600489\pi$
$294$		0			0
$295$	−14.3409			−0.834960
$296$	−0.516879	−	0.895261i	−0.0300430	−	0.0520360i
$297$		0			0
$298$	−8.57314	+	14.8491i	−0.496628	+	0.860186i
$299$	−6.86430	−	11.8893i	−0.396972	−	0.687576i
$300$		0			0
$301$	−2.60475	+	29.3111i	−0.150135	+	1.68946i
$302$	9.06697			0.521746
$303$		0			0
$304$	12.1335	−	21.0158i	0.695903	−	1.20534i
$305$	−0.917438	+	1.58905i	−0.0525324	+	0.0909887i
$306$		0			0
$307$	−18.5229			−1.05716			−0.528580	−	0.848883i	$-0.677275\pi$
$307$	−18.5229			−1.05716			−0.528580	+	0.848883i	$0.677275\pi$
$308$	−0.822431	+	0.382139i	−0.0468623	+	0.0217744i
$309$		0			0
$310$	17.0036	+	29.4510i	0.965737	+	1.67271i
$311$	−9.92192	+	17.1853i	−0.562620	+	0.974487i	0.434646	+	0.900601i	$0.356873\pi$
$311$	−9.92192	+	17.1853i	−0.562620	+	0.974487i	−0.997267	+	0.0738860i	$0.976460\pi$
$312$		0			0
$313$	10.5572	+	18.2856i	0.596729	+	1.03356i	0.993300	+	0.115561i	$0.0368665\pi$
$313$	10.5572	+	18.2856i	0.596729	+	1.03356i	−0.396572	+	0.918004i	$0.629800\pi$
$314$	−16.4211			−0.926696
$315$		0			0
$316$	−0.246664			−0.0138759
$317$	−7.90329	−	13.6889i	−0.443893	−	0.768845i	0.554081	−	0.832462i	$-0.313070\pi$
$317$	−7.90329	−	13.6889i	−0.443893	−	0.768845i	−0.997974	+	0.0636174i	$0.979736\pi$
$318$		0			0
$319$	1.87786	−	3.25255i	0.105140	−	0.182108i
$320$	17.3559	+	30.0613i	0.970224	+	1.68048i
$321$		0			0
$322$	−12.5749	−	8.83068i	−0.700772	−	0.492114i
$323$	−30.1565			−1.67795
$324$		0			0
$325$	15.7422	−	27.2663i	0.873222	−	1.51246i
$326$	7.34048	−	12.7141i	0.406551	−	0.704168i
$327$		0			0
$328$	8.41992			0.464912
$329$	−3.97635	+	1.84759i	−0.219223	+	0.101861i
$330$		0			0
$331$	4.58163	+	7.93562i	0.251829	+	0.436181i	0.964030	−	0.265795i	$-0.0856345\pi$
$331$	4.58163	+	7.93562i	0.251829	+	0.436181i	−0.712200	+	0.701976i	$0.752301\pi$
$332$	1.98763	−	3.44267i	0.109085	−	0.188941i
$333$		0			0
$334$	−7.79537	−	13.5020i	−0.426544	−	0.738796i
$335$	10.1000			0.551824
$336$		0			0
$337$	−12.7174			−0.692760			−0.346380	−	0.938094i	$-0.612589\pi$
$337$	−12.7174			−0.692760			−0.346380	+	0.938094i	$0.612589\pi$
$338$	−2.40719	−	4.16937i	−0.130934	−	0.226784i
$339$		0			0
$340$	2.66732	−	4.61993i	0.144656	−	0.250551i
$341$	3.37168	+	5.83991i	0.182586	+	0.316249i
$342$		0			0
$343$	4.86668	−	17.8694i	0.262776	−	0.964857i
$344$	33.5438			1.80856
$345$		0			0
$346$	−2.34454	+	4.06087i	−0.126043	+	0.218314i
$347$	1.27370	−	2.20611i	0.0683756	−	0.118430i	−0.829811	−	0.558045i	$-0.811552\pi$
$347$	1.27370	−	2.20611i	0.0683756	−	0.118430i	0.898186	+	0.439615i	$0.144885\pi$
$348$		0			0
$349$	−25.0183			−1.33920			−0.669600	−	0.742722i	$-0.733534\pi$
$349$	−25.0183			−1.33920			−0.669600	+	0.742722i	$0.733534\pi$
$350$	3.11927	−	35.1009i	0.166732	−	1.87622i
$351$		0			0
$352$	0.958135	+	1.65954i	0.0510688	+	0.0884537i
$353$	−5.71444	+	9.89770i	−0.304149	+	0.526802i	−0.977072	−	0.212911i	$-0.931705\pi$
$353$	−5.71444	+	9.89770i	−0.304149	+	0.526802i	0.672922	+	0.739713i	$0.265039\pi$
$354$		0			0
$355$	9.80056	+	16.9751i	0.520160	+	0.900943i
$356$	−4.23498			−0.224453
$357$		0			0
$358$	12.7786			0.675371
$359$	14.9811	+	25.9480i	0.790672	+	1.36948i	0.925551	+	0.378622i	$0.123602\pi$
$359$	14.9811	+	25.9480i	0.790672	+	1.36948i	−0.134879	+	0.990862i	$0.543065\pi$
$360$		0			0
$361$	−19.3086	+	33.4435i	−1.01624	+	1.76018i
$362$	−5.19581	−	8.99941i	−0.273086	−	0.472998i
$363$		0			0
$364$	−2.25843	−	1.58597i	−0.118374	−	0.0831275i
$365$	34.2288			1.79162
$366$		0			0
$367$	7.23130	−	12.5250i	0.377471	−	0.653798i	−0.613223	−	0.789910i	$-0.710127\pi$
$367$	7.23130	−	12.5250i	0.377471	−	0.653798i	0.990693	+	0.136112i	$0.0434606\pi$
$368$	−7.21150	+	12.4907i	−0.375925	+	0.651122i
$369$		0			0
$370$	1.72859			0.0898652
$371$	−28.0184	−	19.6758i	−1.45464	−	1.02152i
$372$		0			0
$373$	−15.0726	−	26.1066i	−0.780431	−	1.35175i	−0.931691	−	0.363252i	$-0.881666\pi$
$373$	−15.0726	−	26.1066i	−0.780431	−	1.35175i	0.151260	−	0.988494i	$-0.451667\pi$
$374$	−2.55721	+	4.42921i	−0.132230	+	0.229029i
$375$		0			0
$376$	2.49905	+	4.32848i	0.128879	+	0.223224i
$377$	11.4289			0.588617
$378$		0			0
$379$	−11.7452			−0.603311			−0.301655	−	0.953417i	$-0.597539\pi$
$379$	−11.7452			−0.603311			−0.301655	+	0.953417i	$0.597539\pi$
$380$	−5.09620	−	8.82688i	−0.261430	−	0.452809i
$381$		0			0
$382$	−3.59401	+	6.22500i	−0.183885	+	0.318499i
$383$	13.9685	+	24.1942i	0.713759	+	1.23627i	0.963436	+	0.267937i	$0.0863420\pi$
$383$	13.9685	+	24.1942i	0.713759	+	1.23627i	−0.249678	+	0.968329i	$0.580325\pi$
$384$		0			0
$385$	0.917438	−	10.3239i	0.0467570	−	0.526154i
$386$	−14.3329			−0.729524
$387$		0			0
$388$	−2.25689	+	3.90905i	−0.114576	+	0.198452i
$389$	−7.87896	+	13.6468i	−0.399479	+	0.691918i	−0.993662	−	0.112412i	$-0.964142\pi$
$389$	−7.87896	+	13.6468i	−0.399479	+	0.691918i	0.594183	+	0.804330i	$0.297476\pi$
$390$		0			0
$391$	17.9234			0.906424
$392$	−20.7807	−	3.72277i	−1.04958	−	0.188028i
$393$		0			0
$394$	0.414828	+	0.718503i	0.0208987	+	0.0361977i
$395$	1.40955	−	2.44141i	0.0709221	−	0.122841i
$396$		0			0
$397$	−6.40446	−	11.0928i	−0.321430	−	0.556734i	0.659353	−	0.751834i	$-0.270830\pi$
$397$	−6.40446	−	11.0928i	−0.321430	−	0.556734i	−0.980783	+	0.195100i	$0.937497\pi$
$398$	32.4865			1.62840
$399$		0			0
$400$	−33.0770			−1.65385
$401$	−5.49033	−	9.50953i	−0.274174	−	0.474883i	0.695752	−	0.718282i	$-0.255071\pi$
$401$	−5.49033	−	9.50953i	−0.274174	−	0.474883i	−0.969926	+	0.243398i	$0.921738\pi$
$402$		0			0
$403$	−10.2602	+	17.7712i	−0.511097	+	0.885246i
$404$	−1.21171	−	2.09875i	−0.0602849	−	0.104417i
$405$		0			0
$406$	11.6008	−	5.39024i	0.575736	−	0.267513i
$407$	0.342766			0.0169903
$408$		0			0
$409$	−9.01281	+	15.6106i	−0.445655	+	0.771896i	−0.998098	−	0.0616543i	$-0.980362\pi$
$409$	−9.01281	+	15.6106i	−0.445655	+	0.771896i	0.552443	+	0.833551i	$0.313696\pi$
$410$	−7.03965	+	12.1930i	−0.347664	+	0.602171i
$411$		0			0
$412$	−0.801168			−0.0394707
$413$	−7.92633	−	5.56623i	−0.390029	−	0.273896i
$414$		0			0
$415$	22.7164	+	39.3459i	1.11510	+	1.93141i
$416$	−2.91566	+	5.05007i	−0.142952	+	0.247600i
$417$		0			0
$418$	4.88582	+	8.46250i	0.238974	+	0.413914i
$419$	−11.8542			−0.579116			−0.289558	−	0.957160i	$-0.593508\pi$
$419$	−11.8542			−0.579116			−0.289558	+	0.957160i	$0.593508\pi$
$420$		0			0
$421$	26.4890			1.29100			0.645498	−	0.763762i	$-0.276650\pi$
$421$	26.4890			1.29100			0.645498	+	0.763762i	$0.276650\pi$
$422$	−11.3515	−	19.6614i	−0.552583	−	0.957101i
$423$		0			0
$424$	−19.5135	+	33.7985i	−0.947661	+	1.64140i
$425$	20.5523	+	35.5976i	0.996932	+	1.72674i
$426$		0			0
$427$	−1.12384	+	0.522188i	−0.0543866	+	0.0252705i
$428$	−3.72011			−0.179818
$429$		0			0
$430$	−28.0450	+	48.5753i	−1.35245	+	2.34251i
$431$	−1.08841	+	1.88517i	−0.0524266	+	0.0908056i	−0.891048	−	0.453910i	$-0.850029\pi$
$431$	−1.08841	+	1.88517i	−0.0524266	+	0.0908056i	0.838621	+	0.544715i	$0.183362\pi$
$432$		0			0
$433$	−16.4831			−0.792129			−0.396065	−	0.918223i	$-0.629624\pi$
$433$	−16.4831			−0.792129			−0.396065	+	0.918223i	$0.629624\pi$
$434$	−2.03302	+	22.8775i	−0.0975882	+	1.09815i
$435$		0			0
$436$	−0.375741	−	0.650802i	−0.0179947	−	0.0311678i
$437$	17.1223	−	29.6567i	0.819070	−	1.41867i
$438$		0			0
$439$	0.376500	+	0.652117i	0.0179694	+	0.0311239i	0.874870	−	0.484357i	$-0.160947\pi$
$439$	0.376500	+	0.652117i	0.0179694	+	0.0311239i	−0.856901	+	0.515481i	$0.827613\pi$
$440$	−11.8147			−0.563244
$441$		0			0
$442$	−15.5635			−0.740279
$443$	20.0309	+	34.6946i	0.951698	+	1.64839i	0.741750	+	0.670677i	$0.233996\pi$
$443$	20.0309	+	34.6946i	0.951698	+	1.64839i	0.209949	+	0.977712i	$0.432670\pi$
$444$		0			0
$445$	24.2005	−	41.9166i	1.14722	−	1.98704i
$446$	10.6754	+	18.4904i	0.505497	+	0.875547i
$447$		0			0
$448$	−2.07515	+	23.3516i	−0.0980416	+	1.10326i
$449$	7.71924			0.364294			0.182147	−	0.983271i	$-0.441695\pi$
$449$	7.71924			0.364294			0.182147	+	0.983271i	$0.441695\pi$
$450$		0			0
$451$	−1.39591	+	2.41779i	−0.0657308	+	0.113849i
$452$	1.99515	−	3.45570i	0.0938440	−	0.162543i
$453$		0			0
$454$	−3.02289			−0.141871
$455$	28.6031	−	13.2903i	1.34093	−	0.623059i
$456$		0			0
$457$	−13.1823	−	22.8324i	−0.616643	−	1.06806i	−0.990094	−	0.140407i	$-0.955159\pi$
$457$	−13.1823	−	22.8324i	−0.616643	−	1.06806i	0.373451	−	0.927650i	$-0.378174\pi$
$458$	−11.2322	+	19.4548i	−0.524848	+	0.909064i
$459$		0			0
$460$	3.02891	+	5.24622i	0.141224	+	0.244606i
$461$	−12.4685			−0.580718			−0.290359	−	0.956918i	$-0.593775\pi$
$461$	−12.4685			−0.580718			−0.290359	+	0.956918i	$0.593775\pi$
$462$		0			0
$463$	37.7630			1.75499			0.877497	−	0.479582i	$-0.159212\pi$
$463$	37.7630			1.75499			0.877497	+	0.479582i	$0.159212\pi$
$464$	−6.00348	−	10.3983i	−0.278705	−	0.482731i
$465$		0			0
$466$	3.59849	−	6.23277i	0.166697	−	0.288727i
$467$	11.0104	+	19.0706i	0.509502	+	0.882483i	0.999939	+	0.0110065i	$0.00350356\pi$
$467$	11.0104	+	19.0706i	0.509502	+	0.882483i	−0.490438	+	0.871476i	$0.663163\pi$
$468$		0			0
$469$	5.58237	+	3.92019i	0.257770	+	0.181018i
$470$	−8.35753			−0.385504
$471$		0			0
$472$	−5.52034	+	9.56150i	−0.254094	+	0.440104i
$473$	−5.56111	+	9.63212i	−0.255700	+	0.442885i
$474$		0			0
$475$	78.5348			3.60342
$476$	3.26741	−	1.51819i	0.149761	−	0.0695860i
$477$		0			0
$478$	−11.4668	−	19.8610i	−0.524477	−	0.908421i
$479$	−4.72401	+	8.18223i	−0.215846	+	0.373856i	−0.953534	−	0.301286i	$-0.902584\pi$
$479$	−4.72401	+	8.18223i	−0.215846	+	0.373856i	0.737688	+	0.675142i	$0.235918\pi$
$480$		0			0
$481$	0.521529	+	0.903315i	0.0237797	+	0.0411876i
$482$	−3.84169			−0.174984
$483$		0			0
$484$	−0.342766			−0.0155803
$485$	−25.7937	−	44.6761i	−1.17123	−	2.02864i
$486$		0			0
$487$	−20.1170	+	34.8437i	−0.911589	+	1.57892i	−0.0997702	+	0.995011i	$0.531811\pi$
$487$	−20.1170	+	34.8437i	−0.911589	+	1.57892i	−0.811819	+	0.583909i	$0.801523\pi$
$488$	0.706310	+	1.22337i	0.0319732	+	0.0553791i
$489$		0			0
$490$	22.7651	−	26.9803i	1.02842	−	1.21885i
$491$	−20.2964			−0.915966			−0.457983	−	0.888961i	$-0.651428\pi$
$491$	−20.2964			−0.915966			−0.457983	+	0.888961i	$0.651428\pi$
$492$		0			0
$493$	−7.46050	+	12.9220i	−0.336004	+	0.581976i
$494$	−14.8679	+	25.7519i	−0.668936	+	1.15863i
$495$		0			0
$496$	21.5583			0.967998
$497$	−1.17180	+	13.1862i	−0.0525624	+	0.591482i
$498$		0			0
$499$	−18.1477	−	31.4328i	−0.812403	−	1.40712i	−0.911178	−	0.412014i	$-0.864826\pi$
$499$	−18.1477	−	31.4328i	−0.812403	−	1.40712i	0.0987744	−	0.995110i	$-0.468508\pi$
$500$	−3.58943	+	6.21708i	−0.160524	+	0.278036i
$501$		0			0
$502$	−16.1450	−	27.9640i	−0.720588	−	1.24809i
$503$	27.6923			1.23474			0.617368	−	0.786674i	$-0.288199\pi$
$503$	27.6923			1.23474			0.617368	+	0.786674i	$0.288199\pi$
$504$		0			0
$505$	27.6970			1.23250
$506$	−2.90387	−	5.02965i	−0.129093	−	0.223595i
$507$		0			0
$508$	0.928617	−	1.60841i	0.0412007	−	0.0713617i
$509$	4.54399	+	7.87041i	0.201409	+	0.348850i	0.948983	−	0.315329i	$-0.102115\pi$
$509$	4.54399	+	7.87041i	0.201409	+	0.348850i	−0.747574	+	0.664179i	$0.768781\pi$
$510$		0			0
$511$	18.9185	+	13.2855i	0.836906	+	0.587714i
$512$	25.4100			1.12297
$513$		0			0
$514$	14.5192	−	25.1481i	0.640416	−	1.10923i
$515$	4.57823	−	7.92972i	0.201741	−	0.349425i
$516$		0			0
$517$	−1.65723			−0.0728850
$518$	0.955405	+	0.670929i	0.0419781	+	0.0294789i
$519$		0			0
$520$	−17.9764	−	31.1361i	−0.788318	−	1.36541i
$521$	19.4255	−	33.6459i	0.851046	−	1.47405i	−0.0292202	−	0.999573i	$-0.509302\pi$
$521$	19.4255	−	33.6459i	0.851046	−	1.47405i	0.880266	−	0.474481i	$-0.157364\pi$
$522$		0			0
$523$	10.7500	+	18.6196i	0.470066	+	0.814178i	0.999414	−	0.0342267i	$-0.0108968\pi$
$523$	10.7500	+	18.6196i	0.470066	+	0.814178i	−0.529348	+	0.848405i	$0.677564\pi$
$524$	−0.708138			−0.0309352
$525$		0			0
$526$	33.1565			1.44569
$527$	−13.3952	−	23.2012i	−0.583505	−	1.01066i
$528$		0			0
$529$	1.32343	−	2.29225i	0.0575405	−	0.0996630i
$530$	−32.6294	−	56.5158i	−1.41733	−	2.45489i
$531$		0			0
$532$	0.609325	−	6.85670i	0.0264176	−	0.297276i
$533$	−8.49566			−0.367988
$534$		0			0
$535$	21.2584	−	36.8205i	0.919079	−	1.59189i
$536$	3.88787	−	6.73399i	0.167930	−	0.290864i
$537$		0			0
$538$	−26.6430			−1.14866
$539$	4.51415	−	5.35000i	0.194438	−	0.230441i
$540$		0			0
$541$	14.9470	+	25.8890i	0.642622	+	1.11305i	0.984845	+	0.173435i	$0.0554867\pi$
$541$	14.9470	+	25.8890i	0.642622	+	1.11305i	−0.342223	+	0.939619i	$0.611180\pi$
$542$	1.97465	−	3.42019i	0.0848183	−	0.146910i
$543$		0			0
$544$	−3.80654	−	6.59313i	−0.163204	−	0.282678i
$545$	8.58860			0.367895
$546$		0			0
$547$	−31.9072			−1.36425			−0.682127	−	0.731234i	$-0.738945\pi$
$547$	−31.9072			−1.36425			−0.682127	+	0.731234i	$0.738945\pi$
$548$	0.716905	+	1.24172i	0.0306247	+	0.0530435i
$549$		0			0
$550$	6.65960	−	11.5348i	0.283966	−	0.491844i
$551$	14.2541	+	24.6888i	0.607245	+	1.05178i
$552$		0			0
$553$	1.72667	−	0.802288i	0.0734254	−	0.0341167i
$554$	8.60653			0.365656
$555$		0			0
$556$	0.618825	−	1.07184i	0.0262440	−	0.0454560i
$557$	−7.30446	+	12.6517i	−0.309500	+	0.536069i	−0.978253	−	0.207415i	$-0.933495\pi$
$557$	−7.30446	+	12.6517i	−0.309500	+	0.536069i	0.668753	+	0.743484i	$0.266828\pi$
$558$		0			0
$559$	−33.8455			−1.43151
$560$	−27.1169	−	19.0427i	−1.14590	−	0.804701i
$561$		0			0
$562$	−2.00365	−	3.47042i	−0.0845189	−	0.146391i
$563$	−4.24116	+	7.34590i	−0.178743	+	0.309593i	−0.941450	−	0.337151i	$-0.890537\pi$
$563$	−4.24116	+	7.34590i	−0.178743	+	0.309593i	0.762707	+	0.646744i	$0.223870\pi$
$564$		0			0
$565$	22.8023	+	39.4948i	0.959301	+	1.66156i
$566$	28.7847			1.20991
$567$		0			0
$568$	15.0904			0.633177
$569$	10.3529	+	17.9318i	0.434017	+	0.751740i	0.997215	−	0.0745824i	$-0.0237624\pi$
$569$	10.3529	+	17.9318i	0.434017	+	0.751740i	−0.563198	+	0.826322i	$0.690429\pi$
$570$		0			0
$571$	−0.504409	+	0.873661i	−0.0211088	+	0.0365616i	−0.876387	−	0.481608i	$-0.840053\pi$
$571$	−0.504409	+	0.873661i	−0.0211088	+	0.0365616i	0.855278	+	0.518169i	$0.173386\pi$
$572$	−0.521529	−	0.903315i	−0.0218062	−	0.0377695i
$573$		0			0
$574$	−8.62343	+	4.00683i	−0.359935	+	0.167242i
$575$	−46.6769			−1.94656
$576$		0			0
$577$	19.1925	−	33.2425i	0.798996	−	1.38390i	−0.121274	−	0.992619i	$-0.538698\pi$
$577$	19.1925	−	33.2425i	0.798996	−	1.38390i	0.920270	−	0.391283i	$-0.127969\pi$
$578$	−0.782902	+	1.35603i	−0.0325644	+	0.0564033i
$579$		0			0
$580$	−5.04306			−0.209402
$581$	−2.71607	+	30.5638i	−0.112682	+	1.26800i
$582$		0			0
$583$	−6.47016	−	11.2067i	−0.267967	−	0.464132i
$584$	13.1759	−	22.8214i	0.545223	−	0.944354i
$585$		0			0
$586$	−6.84160	−	11.8500i	−0.282624	−	0.489519i
$587$	−3.95733			−0.163336			−0.0816682	−	0.996660i	$-0.526025\pi$
$587$	−3.95733			−0.163336			−0.0816682	+	0.996660i	$0.526025\pi$
$588$		0			0
$589$	−51.1861			−2.10909
$590$	−9.23079	−	15.9882i	−0.380025	−	0.658223i
$591$		0			0
$592$	0.547908	−	0.949005i	0.0225189	−	0.0390039i
$593$	4.25131	+	7.36349i	0.174581	+	0.302382i	0.940016	−	0.341130i	$-0.110810\pi$
$593$	4.25131	+	7.36349i	0.174581	+	0.302382i	−0.765435	+	0.643513i	$0.777476\pi$
$594$		0			0
$595$	−3.64486	+	41.0154i	−0.149425	+	1.68147i
$596$	4.56537			0.187005
$597$		0			0
$598$	8.83665	−	15.3055i	0.361358	−	0.625890i
$599$	−3.48076	+	6.02885i	−0.142220	+	0.246332i	−0.928332	−	0.371751i	$-0.878757\pi$
$599$	−3.48076	+	6.02885i	−0.142220	+	0.246332i	0.786112	+	0.618084i	$0.212091\pi$
$600$		0			0
$601$	31.8738			1.30016			0.650081	−	0.759865i	$-0.274735\pi$
$601$	31.8738			1.30016			0.650081	+	0.759865i	$0.274735\pi$
$602$	−34.3545	+	15.9627i	−1.40019	+	0.650590i
$603$		0			0
$604$	−1.20709	−	2.09074i	−0.0491157	−	0.0850709i
$605$	1.95872	−	3.39260i	0.0796333	−	0.137929i
$606$		0			0
$607$	−1.67204	−	2.89606i	−0.0678660	−	0.117547i	0.830096	−	0.557621i	$-0.188286\pi$
$607$	−1.67204	−	2.89606i	−0.0678660	−	0.117547i	−0.897962	+	0.440074i	$0.854952\pi$
$608$	−14.5456			−0.589903
$609$		0			0
$610$	−2.36210			−0.0956387
$611$	−2.52153	−	4.36742i	−0.102010	−	0.176687i
$612$		0			0
$613$	2.11325	−	3.66025i	0.0853533	−	0.147836i	−0.820188	−	0.572093i	$-0.806131\pi$
$613$	2.11325	−	3.66025i	0.0853533	−	0.147836i	0.905542	+	0.424257i	$0.139465\pi$
$614$	−11.9226	−	20.6506i	−0.481158	−	0.833390i
$615$		0			0
$616$	−6.53008	−	4.58572i	−0.263104	−	0.184764i
$617$	−3.91266			−0.157518			−0.0787590	−	0.996894i	$-0.525096\pi$
$617$	−3.91266			−0.157518			−0.0787590	+	0.996894i	$0.525096\pi$
$618$		0			0
$619$	−0.869194	+	1.50549i	−0.0349359	+	0.0605107i	−0.882965	−	0.469439i	$-0.844456\pi$
$619$	−0.869194	+	1.50549i	−0.0349359	+	0.0605107i	0.848029	+	0.529950i	$0.177789\pi$
$620$	4.52737	−	7.84164i	0.181824	−	0.314928i
$621$		0			0
$622$	−25.5457			−1.02429
$623$	29.6452	−	13.7745i	1.18771	−	0.551863i
$624$		0			0
$625$	−15.1574	−	26.2534i	−0.606295	−	1.05013i
$626$	−13.5907	+	23.5397i	−0.543193	+	0.940837i
$627$		0			0
$628$	2.18614	+	3.78651i	0.0872366	+	0.151098i
$629$	−1.36177			−0.0542972
$630$		0			0
$631$	−13.3994			−0.533420			−0.266710	−	0.963777i	$-0.585937\pi$
$631$	−13.3994			−0.533420			−0.266710	+	0.963777i	$0.585937\pi$
$632$	−1.08517	−	1.87957i	−0.0431658	−	0.0747654i
$633$		0			0
$634$	10.1742	−	17.6222i	0.404069	−	0.699867i
$635$	10.6131	+	18.3824i	0.421166	+	0.729481i
$636$		0			0
$637$	20.9676	+	3.75626i	0.830767	+	0.148829i
$638$	4.83488			0.191415
$639$		0			0
$640$	−14.8360	+	25.6967i	−0.586444	+	1.01575i
$641$	5.39101	−	9.33750i	0.212932	−	0.368809i	−0.739699	−	0.672938i	$-0.765032\pi$
$641$	5.39101	−	9.33750i	0.212932	−	0.368809i	0.952631	+	0.304129i	$0.0983653\pi$
$642$		0			0
$643$	30.1180			1.18774			0.593868	−	0.804562i	$-0.297600\pi$
$643$	30.1180			1.18774			0.593868	+	0.804562i	$0.297600\pi$
$644$	−0.362150	+	4.07526i	−0.0142707	+	0.160588i
$645$		0			0
$646$	−19.4107	−	33.6204i	−0.763705	−	1.32278i
$647$	−6.32343	+	10.9525i	−0.248600	+	0.430587i	−0.963138	−	0.269009i	$-0.913304\pi$
$647$	−6.32343	+	10.9525i	−0.248600	+	0.430587i	0.714538	+	0.699597i	$0.246637\pi$
$648$		0			0
$649$	−1.83039	−	3.17034i	−0.0718493	−	0.124447i
$650$	40.5311			1.58976
$651$		0			0
$652$	−3.90896			−0.153087
$653$	0.751146	+	1.30102i	0.0293946	+	0.0509130i	0.880348	−	0.474327i	$-0.157309\pi$
$653$	0.751146	+	1.30102i	0.0293946	+	0.0509130i	−0.850954	+	0.525240i	$0.823975\pi$
$654$		0			0
$655$	4.04661	−	7.00894i	0.158114	−	0.273862i
$656$	4.46269	+	7.72961i	0.174239	+	0.301790i
$657$		0			0
$658$	−4.61927	−	3.24386i	−0.180078	−	0.126459i
$659$	14.4079			0.561251			0.280626	−	0.959817i	$-0.409458\pi$
$659$	14.4079			0.561251			0.280626	+	0.959817i	$0.409458\pi$
$660$		0			0
$661$	8.39269	−	14.5366i	0.326438	−	0.565407i	−0.655364	−	0.755313i	$-0.727485\pi$
$661$	8.39269	−	14.5366i	0.326438	−	0.565407i	0.981802	+	0.189906i	$0.0608182\pi$
$662$	−5.89810	+	10.2158i	−0.229236	+	0.397049i
$663$		0			0
$664$	34.9774			1.35739
$665$	64.3837	+	45.2131i	2.49669	+	1.75329i
$666$		0			0
$667$	−8.47187	−	14.6737i	−0.328032	−	0.568168i
$668$	−2.07560	+	3.59504i	−0.0803073	+	0.139096i
$669$		0			0
$670$	6.50107	+	11.2602i	0.251158	+	0.435019i
$671$	−0.468387			−0.0180819
$672$		0			0
$673$	−48.1663			−1.85667			−0.928337	−	0.371740i	$-0.878761\pi$
$673$	−48.1663			−1.85667			−0.928337	+	0.371740i	$0.878761\pi$
$674$	−8.18577	−	14.1782i	−0.315304	−	0.546123i
$675$		0			0
$676$	−0.640938	+	1.11014i	−0.0246515	+	0.0426976i
$677$	−5.85741	−	10.1453i	−0.225118	−	0.389916i	0.731237	−	0.682124i	$-0.238944\pi$
$677$	−5.85741	−	10.1453i	−0.225118	−	0.389916i	−0.956355	+	0.292207i	$0.905610\pi$
$678$		0			0
$679$	3.08402	−	34.7043i	0.118354	−	1.33183i
$680$	46.9383			1.80000
$681$		0			0
$682$	−4.34048	+	7.51793i	−0.166206	+	0.287876i
$683$	5.70996	−	9.88994i	0.218486	−	0.378428i	−0.735860	−	0.677134i	$-0.763222\pi$
$683$	5.70996	−	9.88994i	0.218486	−	0.378428i	0.954345	+	0.298706i	$0.0965550\pi$
$684$		0			0
$685$	−16.3868			−0.626109
$686$	23.0545	−	6.07626i	0.880225	−	0.231993i
$687$		0			0
$688$	17.7787	+	30.7937i	0.677808	+	1.17400i
$689$	19.6891	−	34.1025i	0.750095	−	1.29920i
$690$		0			0
$691$	11.4596	+	19.8486i	0.435943	+	0.755075i	0.997372	−	0.0724499i	$-0.0230817\pi$
$691$	11.4596	+	19.8486i	0.435943	+	0.755075i	−0.561429	+	0.827525i	$0.689748\pi$
$692$	1.24852			0.0474615
$693$		0			0
$694$	3.27935			0.124482
$695$	7.07248	+	12.2499i	0.268274	+	0.464665i
$696$		0			0
$697$	5.54576	−	9.60554i	0.210061	−	0.363836i
$698$	−16.1035	−	27.8921i	−0.609526	−	1.05573i
$699$		0			0
$700$	−8.50913	+	3.95373i	−0.321615	+	0.149437i
$701$	−25.3982			−0.959277			−0.479638	−	0.877466i	$-0.659232\pi$
$701$	−25.3982			−0.959277			−0.479638	+	0.877466i	$0.659232\pi$
$702$		0			0
$703$	−1.30090	+	2.25323i	−0.0490644	+	0.0849821i
$704$	−4.43042	+	7.67371i	−0.166978	+	0.289214i
$705$		0			0
$706$	−14.7128			−0.553724
$707$	15.3084	+	10.7502i	0.575730	+	0.404304i
$708$		0			0
$709$	8.25054	+	14.2903i	0.309855	+	0.536685i	0.978331	−	0.207049i	$-0.0663860\pi$
$709$	8.25054	+	14.2903i	0.309855	+	0.536685i	−0.668475	+	0.743735i	$0.733053\pi$
$710$	−12.6166	+	21.8526i	−0.473493	+	0.820114i
$711$		0			0
$712$	−18.6313	−	32.2704i	−0.698238	−	1.20938i
$713$	30.4223			1.13932
$714$		0			0
$715$	11.9210			0.445820
$716$	−1.70122	−	2.94660i	−0.0635775	−	0.110120i
$717$		0			0
$718$	−19.2857	+	33.4038i	−0.719736	+	1.24662i
$719$	−17.9149	−	31.0295i	−0.668112	−	1.15720i	−0.978431	−	0.206572i	$-0.933769\pi$
$719$	−17.9149	−	31.0295i	−0.668112	−	1.15720i	0.310319	−	0.950632i	$-0.399564\pi$
$720$		0			0
$721$	5.60823	−	2.60584i	0.208862	−	0.0970465i
$722$	−49.7133			−1.85014
$723$		0			0
$724$	−1.38344	+	2.39619i	−0.0514151	+	0.0890535i
$725$	19.4290	−	33.6519i	0.721573	−	1.24980i
$726$		0			0
$727$	−18.7401			−0.695031			−0.347516	−	0.937674i	$-0.612975\pi$
$727$	−18.7401			−0.695031			−0.347516	+	0.937674i	$0.612975\pi$
$728$	2.14934	−	24.1864i	0.0796600	−	0.896409i
$729$		0			0
$730$	22.0320	+	38.1605i	0.815441	+	1.41239i
$731$	22.0935	−	38.2671i	0.817159	−	1.41536i
$732$		0			0
$733$	−23.9039	−	41.4028i	−0.882912	−	1.52925i	−0.848088	−	0.529856i	$-0.822246\pi$
$733$	−23.9039	−	41.4028i	−0.882912	−	1.52925i	−0.0348246	−	0.999393i	$-0.511087\pi$
$734$	18.6182			0.687211
$735$		0			0
$736$	8.64515			0.318664
$737$	1.28911	+	2.23281i	0.0474851	+	0.0822466i
$738$		0			0
$739$	6.07009	−	10.5137i	0.223292	−	0.386753i	−0.732514	−	0.680752i	$-0.761653\pi$
$739$	6.07009	−	10.5137i	0.223292	−	0.386753i	0.955806	+	0.293999i	$0.0949864\pi$
$740$	−0.230128	−	0.398593i	−0.00845966	−	0.0146526i
$741$		0			0
$742$	3.90132	−	43.9014i	0.143222	−	1.61167i
$743$	−30.9615			−1.13587			−0.567934	−	0.823074i	$-0.692257\pi$
$743$	−30.9615			−1.13587			−0.567934	+	0.823074i	$0.692257\pi$
$744$		0			0
$745$	−26.0886	+	45.1867i	−0.955811	+	1.65551i
$746$	19.4035	−	33.6079i	0.710414	−	1.23047i
$747$		0			0
$748$	1.36177			0.0497911
$749$	26.0410	−	12.0998i	0.951519	−	0.442119i
$750$		0			0
$751$	16.0219	+	27.7507i	0.584646	+	1.01264i	0.994919	+	0.100674i	$0.0321000\pi$
$751$	16.0219	+	27.7507i	0.584646	+	1.01264i	−0.410273	+	0.911963i	$0.634567\pi$
$752$	−2.64907	+	4.58832i	−0.0966016	+	0.167319i
$753$		0			0
$754$	7.35641	+	12.7417i	0.267904	+	0.464024i
$755$	27.5913			1.00415
$756$		0			0
$757$	32.5209			1.18199			0.590996	−	0.806675i	$-0.298735\pi$
$757$	32.5209			1.18199			0.590996	+	0.806675i	$0.298735\pi$
$758$	−7.56001	−	13.0943i	−0.274592	−	0.475607i
$759$		0			0
$760$	44.8404	−	77.6658i	1.62653	−	2.81723i
$761$	−1.23181	−	2.13355i	−0.0446530	−	0.0773412i	0.842835	−	0.538172i	$-0.180885\pi$
$761$	−1.23181	−	2.13355i	−0.0446530	−	0.0773412i	−0.887488	+	0.460831i	$0.847552\pi$
$762$		0			0
$763$	4.74698	+	3.33355i	0.171852	+	0.120683i
$764$	1.91388			0.0692419
$765$		0			0
$766$	−17.9822	+	31.1461i	−0.649723	+	1.12535i
$767$	5.57000	−	9.64752i	0.201121	−	0.348352i
$768$		0			0
$769$	49.0232			1.76782			0.883911	−	0.467656i	$-0.154901\pi$
$769$	49.0232			1.76782			0.883911	+	0.467656i	$0.154901\pi$
$770$	12.1003	−	5.62233i	0.436063	−	0.202615i
$771$		0			0
$772$	1.90814	+	3.30499i	0.0686754	+	0.118949i
$773$	0.208182	−	0.360582i	0.00748779	−	0.0129692i	−0.862257	−	0.506471i	$-0.830950\pi$
$773$	0.208182	−	0.360582i	0.00748779	−	0.0129692i	0.869745	+	0.493501i	$0.164283\pi$
$774$		0			0
$775$	34.8844	+	60.4216i	1.25309	+	2.17041i
$776$	−39.7158			−1.42571
$777$		0			0
$778$	−20.2857			−0.727278
$779$	−10.5958	−	18.3524i	−0.379633	−	0.657544i
$780$		0			0
$781$	−2.50178	+	4.33321i	−0.0895206	+	0.155054i
$782$	11.5367	+	19.9822i	0.412552	+

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.643668 + 1.11487i) q^{2} +(0.171383 - 0.296844i) q^{4} +(1.95872 + 3.39260i) q^{5} +(-0.234193 + 2.63537i) q^{7} +3.01593 q^{8} +O(q^{10})\)	\(q+(0.643668 + 1.11487i) q^{2} +(0.171383 - 0.296844i) q^{4} +(1.95872 + 3.39260i) q^{5} +(-0.234193 + 2.63537i) q^{7} +3.01593 q^{8} +(-2.52153 + 4.36742i) q^{10} +(-0.500000 + 0.866025i) q^{11} -3.04306 q^{13} +(-3.08882 + 1.43521i) q^{14} +(1.59849 + 2.76866i) q^{16} +(1.98643 - 3.44061i) q^{17} +(-3.79530 - 6.57365i) q^{19} +1.34277 q^{20} -1.28734 q^{22} +(2.25572 + 3.90703i) q^{23} +(-5.17316 + 8.96018i) q^{25} +(-1.95872 - 3.39260i) q^{26} +(0.742157 + 0.521177i) q^{28} -3.75572 q^{29} +(3.37168 - 5.83991i) q^{31} +(0.958135 - 1.65954i) q^{32} +5.11442 q^{34} +(-9.39946 + 4.36742i) q^{35} +(-0.171383 - 0.296844i) q^{37} +(4.88582 - 8.46250i) q^{38} +(5.90735 + 10.2318i) q^{40} +2.79182 q^{41} +11.1222 q^{43} +(0.171383 + 0.296844i) q^{44} +(-2.90387 + 5.02965i) q^{46} +(0.828617 + 1.43521i) q^{47} +(-6.89031 - 1.23437i) q^{49} -13.3192 q^{50} +(-0.521529 + 0.903315i) q^{52} +(-6.47016 + 11.2067i) q^{53} -3.91744 q^{55} +(-0.706310 + 7.94807i) q^{56} +(-2.41744 - 4.18713i) q^{58} +(-1.83039 + 3.17034i) q^{59} +(0.234193 + 0.405635i) q^{61} +8.68096 q^{62} +8.86084 q^{64} +(-5.96050 - 10.3239i) q^{65} +(1.28911 - 2.23281i) q^{67} +(-0.680883 - 1.17932i) q^{68} +(-10.9192 - 7.66797i) q^{70} +5.00355 q^{71} +(4.36878 - 7.56694i) q^{73} +(0.220628 - 0.382139i) q^{74} -2.60180 q^{76} +(-2.16520 - 1.52050i) q^{77} +(-0.359814 - 0.623216i) q^{79} +(-6.26198 + 10.8461i) q^{80} +(1.79700 + 3.11250i) q^{82} +11.5976 q^{83} +15.5635 q^{85} +(7.15901 + 12.3998i) q^{86} +(-1.50796 + 2.61187i) q^{88} +(-6.17764 - 10.7000i) q^{89} +(0.712664 - 8.01957i) q^{91} +1.54637 q^{92} +(-1.06671 + 1.84759i) q^{94} +(14.8679 - 25.7519i) q^{95} -13.1687 q^{97} +(-3.05891 - 8.47629i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8	\( 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8} - 10 q^{10} - 4 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{17} - 4 q^{22} + 4 q^{23} - 4 q^{25} - 4 q^{26} - 22 q^{28} - 16 q^{29} + 12 q^{31} + 26 q^{32} - 32 q^{34} + 2 q^{35} + 4 q^{37} + 8 q^{38} + 6 q^{40} - 4 q^{41} + 36 q^{43} - 4 q^{44} + 14 q^{46} + 12 q^{47} - 4 q^{49} - 4 q^{50} + 6 q^{52} - 12 q^{53} - 8 q^{55} - 48 q^{56} + 4 q^{58} + 12 q^{59} - 2 q^{61} + 52 q^{62} + 112 q^{64} - 4 q^{65} - 28 q^{67} - 48 q^{68} - 32 q^{70} - 24 q^{71} - 6 q^{73} - 16 q^{74} - 36 q^{76} - 4 q^{77} - 2 q^{79} + 16 q^{80} + 12 q^{82} + 24 q^{83} + 36 q^{85} + 36 q^{86} + 12 q^{88} + 8 q^{89} + 12 q^{91} + 32 q^{92} - 20 q^{94} + 34 q^{95} - 88 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 - 24 * q^8 - 10 * q^10 - 4 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^17 - 4 * q^22 + 4 * q^23 - 4 * q^25 - 4 * q^26 - 22 * q^28 - 16 * q^29 + 12 * q^31 + 26 * q^32 - 32 * q^34 + 2 * q^35 + 4 * q^37 + 8 * q^38 + 6 * q^40 - 4 * q^41 + 36 * q^43 - 4 * q^44 + 14 * q^46 + 12 * q^47 - 4 * q^49 - 4 * q^50 + 6 * q^52 - 12 * q^53 - 8 * q^55 - 48 * q^56 + 4 * q^58 + 12 * q^59 - 2 * q^61 + 52 * q^62 + 112 * q^64 - 4 * q^65 - 28 * q^67 - 48 * q^68 - 32 * q^70 - 24 * q^71 - 6 * q^73 - 16 * q^74 - 36 * q^76 - 4 * q^77 - 2 * q^79 + 16 * q^80 + 12 * q^82 + 24 * q^83 + 36 * q^85 + 36 * q^86 + 12 * q^88 + 8 * q^89 + 12 * q^91 + 32 * q^92 - 20 * q^94 + 34 * q^95 - 88 * q^97 - 16 * q^98

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