LMFDB - Embedded newform 2790.2.e.a.2789.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2790,2,Mod(2789,2790)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2790, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("2790.2789");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2790.e (of order $2$, degree $1$, 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:	$22.2782621639$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2789.3
Character	$\chi$	$=$	2790.2789
Dual form			2790.2.e.a.2789.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-2.18226 + 0.487576i) q^{5} +4.29689i q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.18226 + 0.487576i) q^{5} +4.29689i q^{7} -1.00000 q^{8} +(2.18226 - 0.487576i) q^{10} -6.60801 q^{11} -1.29946 q^{13} -4.29689i q^{14} +1.00000 q^{16} +5.98631i q^{17} -5.77875 q^{19} +(-2.18226 + 0.487576i) q^{20} +6.60801 q^{22} +4.49127i q^{23} +(4.52454 - 2.12804i) q^{25} +1.29946 q^{26} +4.29689i q^{28} -6.18784 q^{29} +(3.92488 + 3.94909i) q^{31} -1.00000 q^{32} -5.98631i q^{34} +(-2.09506 - 9.37694i) q^{35} +6.75195 q^{37} +5.77875 q^{38} +(2.18226 - 0.487576i) q^{40} -4.72669i q^{41} -6.68877 q^{43} -6.60801 q^{44} -4.49127i q^{46} +2.99416 q^{47} -11.4632 q^{49} +(-4.52454 + 2.12804i) q^{50} -1.29946 q^{52} +0.154894i q^{53} +(14.4204 - 3.22190i) q^{55} -4.29689i q^{56} +6.18784 q^{58} -7.02972i q^{59} -5.19654i q^{61} +(-3.92488 - 3.94909i) q^{62} +1.00000 q^{64} +(2.83577 - 0.633587i) q^{65} +3.32789i q^{67} +5.98631i q^{68} +(2.09506 + 9.37694i) q^{70} -0.985624i q^{71} -9.67138 q^{73} -6.75195 q^{74} -5.77875 q^{76} -28.3939i q^{77} +16.7416i q^{79} +(-2.18226 + 0.487576i) q^{80} +4.72669i q^{82} +0.977557i q^{83} +(-2.91878 - 13.0637i) q^{85} +6.68877 q^{86} +6.60801 q^{88} +15.5550 q^{89} -5.58365i q^{91} +4.49127i q^{92} -2.99416 q^{94} +(12.6108 - 2.81758i) q^{95} -11.5566i q^{97} +11.4632 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} + 32 q^{4} - 4 q^{5} - 32 q^{8}+O(q^{10}) $ 32 * q - 32 * q^2 + 32 * q^4 - 4 * q^5 - 32 * q^8	$ 32 q - 32 q^{2} + 32 q^{4} - 4 q^{5} - 32 q^{8} + 4 q^{10} + 32 q^{16} - 16 q^{19} - 4 q^{20} + 4 q^{25} - 32 q^{32} - 8 q^{35} + 16 q^{38} + 4 q^{40} + 8 q^{47} - 24 q^{49} - 4 q^{50} + 32 q^{64} + 8 q^{70} - 16 q^{76} - 4 q^{80} - 8 q^{94} + 4 q^{95} + 24 q^{98}+O(q^{100}) $ 32 * q - 32 * q^2 + 32 * q^4 - 4 * q^5 - 32 * q^8 + 4 * q^10 + 32 * q^16 - 16 * q^19 - 4 * q^20 + 4 * q^25 - 32 * q^32 - 8 * q^35 + 16 * q^38 + 4 * q^40 + 8 * q^47 - 24 * q^49 - 4 * q^50 + 32 * q^64 + 8 * q^70 - 16 * q^76 - 4 * q^80 - 8 * q^94 + 4 * q^95 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2790\mathbb{Z}\right)^\times$.

$n$	$1117$	$1801$	$2171$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−2.18226	+	0.487576i	−0.975937	+	0.218051i
$5$	−2.18226	+	0.487576i	−0.975937	+	0.218051i
$6$		0			0
$7$			4.29689i			1.62407i	0.583608	+	0.812035i	$0.301640\pi$
$7$			4.29689i			1.62407i	−0.583608	+	0.812035i	$0.698360\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	2.18226	−	0.487576i	0.690092	−	0.154185i
$11$	−6.60801			−1.99239			−0.996194	−	0.0871583i	$-0.972221\pi$
$11$	−6.60801			−1.99239			−0.996194	+	0.0871583i	$0.972221\pi$
$12$		0			0
$13$	−1.29946			−0.360406			−0.180203	−	0.983629i	$-0.557676\pi$
$13$	−1.29946			−0.360406			−0.180203	+	0.983629i	$0.557676\pi$
$14$		−	4.29689i		−	1.14839i
$15$		0			0
$16$	1.00000			0.250000
$17$			5.98631i			1.45189i	0.687750	+	0.725947i	$0.258598\pi$
$17$			5.98631i			1.45189i	−0.687750	+	0.725947i	$0.741402\pi$
$18$		0			0
$19$	−5.77875			−1.32574			−0.662868	−	0.748736i	$-0.730661\pi$
$19$	−5.77875			−1.32574			−0.662868	+	0.748736i	$0.730661\pi$
$20$	−2.18226	+	0.487576i	−0.487969	+	0.109025i
$21$		0			0
$22$	6.60801			1.40883
$23$			4.49127i			0.936494i	0.883597	+	0.468247i	$0.155114\pi$
$23$			4.49127i			0.936494i	−0.883597	+	0.468247i	$0.844886\pi$
$24$		0			0
$25$	4.52454	−	2.12804i	0.904908	−	0.425607i
$26$	1.29946			0.254846
$27$		0			0
$28$			4.29689i			0.812035i
$29$	−6.18784			−1.14905			−0.574526	−	0.818486i	$-0.694814\pi$
$29$	−6.18784			−1.14905			−0.574526	+	0.818486i	$0.694814\pi$
$30$		0			0
$31$	3.92488	+	3.94909i	0.704930	+	0.709277i
$31$	3.92488	+	3.94909i	0.704930	+	0.709277i
$32$	−1.00000			−0.176777
$33$		0			0
$34$		−	5.98631i		−	1.02664i
$35$	−2.09506	−	9.37694i	−0.354129	−	1.58499i
$36$		0			0
$37$	6.75195			1.11001			0.555007	−	0.831846i	$-0.312716\pi$
$37$	6.75195			1.11001			0.555007	+	0.831846i	$0.312716\pi$
$38$	5.77875			0.937437
$39$		0			0
$40$	2.18226	−	0.487576i	0.345046	−	0.0770925i
$41$		−	4.72669i		−	0.738186i	−0.929393	−	0.369093i	$-0.879668\pi$
$41$		−	4.72669i		−	0.738186i	0.929393	−	0.369093i	$-0.120332\pi$
$42$		0			0
$43$	−6.68877			−1.02003			−0.510014	−	0.860166i	$-0.670360\pi$
$43$	−6.68877			−1.02003			−0.510014	+	0.860166i	$0.670360\pi$
$44$	−6.60801			−0.996194
$45$		0			0
$46$		−	4.49127i		−	0.662202i
$47$	2.99416			0.436743			0.218371	−	0.975866i	$-0.429926\pi$
$47$	2.99416			0.436743			0.218371	+	0.975866i	$0.429926\pi$
$48$		0			0
$49$	−11.4632			−1.63761
$50$	−4.52454	+	2.12804i	−0.639867	+	0.300950i
$51$		0			0
$52$	−1.29946			−0.180203
$53$			0.154894i			0.0212763i	0.999943	+	0.0106381i	$0.00338629\pi$
$53$			0.154894i			0.0212763i	−0.999943	+	0.0106381i	$0.996614\pi$
$54$		0			0
$55$	14.4204	−	3.22190i	1.94445	−	0.434441i
$56$		−	4.29689i		−	0.574196i
$57$		0			0
$58$	6.18784			0.812503
$59$		−	7.02972i		−	0.915191i	−0.889160	−	0.457596i	$-0.848711\pi$
$59$		−	7.02972i		−	0.915191i	0.889160	−	0.457596i	$-0.151289\pi$
$60$		0			0
$61$		−	5.19654i		−	0.665348i	−0.943042	−	0.332674i	$-0.892049\pi$
$61$		−	5.19654i		−	0.665348i	0.943042	−	0.332674i	$-0.107951\pi$
$62$	−3.92488	−	3.94909i	−0.498461	−	0.501535i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.83577	−	0.633587i	0.351734	−	0.0785868i
$66$		0			0
$67$			3.32789i			0.406567i	0.979120	+	0.203283i	$0.0651612\pi$
$67$			3.32789i			0.406567i	−0.979120	+	0.203283i	$0.934839\pi$
$68$			5.98631i			0.725947i
$69$		0			0
$70$	2.09506	+	9.37694i	0.250407	+	1.12076i
$71$		−	0.985624i		−	0.116972i	−0.998288	−	0.0584860i	$-0.981373\pi$
$71$		−	0.985624i		−	0.116972i	0.998288	−	0.0584860i	$-0.0186273\pi$
$72$		0			0
$73$	−9.67138			−1.13195			−0.565975	−	0.824423i	$-0.691500\pi$
$73$	−9.67138			−1.13195			−0.565975	+	0.824423i	$0.691500\pi$
$74$	−6.75195			−0.784898
$75$		0			0
$76$	−5.77875			−0.662868
$77$		−	28.3939i		−	3.23578i
$78$		0			0
$79$			16.7416i			1.88358i	0.336204	+	0.941789i	$0.390857\pi$
$79$			16.7416i			1.88358i	−0.336204	+	0.941789i	$0.609143\pi$
$80$	−2.18226	+	0.487576i	−0.243984	+	0.0545126i
$81$		0			0
$82$			4.72669i			0.521976i
$83$			0.977557i			0.107301i	0.998560	+	0.0536504i	$0.0170857\pi$
$83$			0.977557i			0.107301i	−0.998560	+	0.0536504i	$0.982914\pi$
$84$		0			0
$85$	−2.91878	−	13.0637i	−0.316586	−	1.41696i
$86$	6.68877			0.721269
$87$		0			0
$88$	6.60801			0.704416
$89$	15.5550			1.64883			0.824415	−	0.565986i	$-0.191504\pi$
$89$	15.5550			1.64883			0.824415	+	0.565986i	$0.191504\pi$
$90$		0			0
$91$		−	5.58365i		−	0.585325i
$92$			4.49127i			0.468247i
$93$		0			0
$94$	−2.99416			−0.308824
$95$	12.6108	−	2.81758i	1.29384	−	0.289078i
$96$		0			0
$97$		−	11.5566i		−	1.17340i	−0.809805	−	0.586699i	$-0.800427\pi$
$97$		−	11.5566i		−	1.17340i	0.809805	−	0.586699i	$-0.199573\pi$
$98$	11.4632			1.15796
$99$		0			0
$100$	4.52454	−	2.12804i	0.452454	−	0.212804i
$101$			15.2957i			1.52198i	0.648763	+	0.760991i	$0.275287\pi$
$101$			15.2957i			1.52198i	−0.648763	+	0.760991i	$0.724713\pi$
$102$		0			0
$103$			15.6546i			1.54249i	0.636536	+	0.771247i	$0.280367\pi$
$103$			15.6546i			1.54249i	−0.636536	+	0.771247i	$0.719633\pi$
$104$	1.29946			0.127423
$105$		0			0
$106$		−	0.154894i		−	0.0150446i
$107$	3.79191			0.366578			0.183289	−	0.983059i	$-0.441326\pi$
$107$	3.79191			0.366578			0.183289	+	0.983059i	$0.441326\pi$
$108$		0			0
$109$	17.2931			1.65638			0.828191	−	0.560445i	$-0.189370\pi$
$109$	17.2931			1.65638			0.828191	+	0.560445i	$0.189370\pi$
$110$	−14.4204	+	3.22190i	−1.37493	+	0.307196i
$111$		0			0
$112$			4.29689i			0.406018i
$113$	8.46604			0.796418			0.398209	−	0.917295i	$-0.369632\pi$
$113$	8.46604			0.796418			0.398209	+	0.917295i	$0.369632\pi$
$114$		0			0
$115$	−2.18983	−	9.80113i	−0.204203	−	0.913960i
$116$	−6.18784			−0.574526
$117$		0			0
$118$			7.02972i			0.647138i
$119$	−25.7225			−2.35798
$120$		0			0
$121$	32.6658			2.96961
$122$			5.19654i			0.470472i
$123$		0			0
$124$	3.92488	+	3.94909i	0.352465	+	0.354639i
$125$	−8.83615	+	6.84999i	−0.790330	+	0.612682i
$126$		0			0
$127$	−9.03004			−0.801286			−0.400643	−	0.916234i	$-0.631213\pi$
$127$	−9.03004			−0.801286			−0.400643	+	0.916234i	$0.631213\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−2.83577	+	0.633587i	−0.248713	+	0.0555692i
$131$		−	12.7992i		−	1.11827i	−0.829076	−	0.559136i	$-0.811133\pi$
$131$		−	12.7992i		−	1.11827i	0.829076	−	0.559136i	$-0.188867\pi$
$132$		0			0
$133$		−	24.8306i		−	2.15309i
$134$		−	3.32789i		−	0.287486i
$135$		0			0
$136$		−	5.98631i		−	0.513322i
$137$		−	11.3902i		−	0.973129i	−0.873645	−	0.486564i	$-0.838250\pi$
$137$		−	11.3902i		−	0.973129i	0.873645	−	0.486564i	$-0.161750\pi$
$138$		0			0
$139$		−	3.28843i		−	0.278921i	−0.990228	−	0.139461i	$-0.955463\pi$
$139$		−	3.28843i		−	0.278921i	0.990228	−	0.139461i	$-0.0445369\pi$
$140$	−2.09506	−	9.37694i	−0.177065	−	0.792496i
$141$		0			0
$142$			0.985624i			0.0827117i
$143$	8.58686			0.718069
$144$		0			0
$145$	13.5035	−	3.01704i	1.12140	−	0.250552i
$146$	9.67138			0.800409
$147$		0			0
$148$	6.75195			0.555007
$149$		−	2.75453i		−	0.225660i	−0.993614	−	0.112830i	$-0.964009\pi$
$149$		−	2.75453i		−	0.225660i	0.993614	−	0.112830i	$-0.0359915\pi$
$150$		0			0
$151$		−	16.4613i		−	1.33960i	−0.742540	−	0.669802i	$-0.766379\pi$
$151$		−	16.4613i		−	1.33960i	0.742540	−	0.669802i	$-0.233621\pi$
$152$	5.77875			0.468719
$153$		0			0
$154$			28.3939i			2.28804i
$155$	−10.4906	−	6.70427i	−0.842626	−	0.538500i
$156$		0			0
$157$			7.30627i			0.583104i	0.956555	+	0.291552i	$0.0941716\pi$
$157$			7.30627i			0.583104i	−0.956555	+	0.291552i	$0.905828\pi$
$158$		−	16.7416i		−	1.33189i
$159$		0			0
$160$	2.18226	−	0.487576i	0.172523	−	0.0385463i
$161$	−19.2985			−1.52093
$162$		0			0
$163$		−	13.2198i		−	1.03545i	−0.855547	−	0.517726i	$-0.826779\pi$
$163$		−	13.2198i		−	1.03545i	0.855547	−	0.517726i	$-0.173221\pi$
$164$		−	4.72669i		−	0.369093i
$165$		0			0
$166$		−	0.977557i		−	0.0758732i
$167$			22.1337i			1.71276i	0.516347	+	0.856379i	$0.327291\pi$
$167$			22.1337i			1.71276i	−0.516347	+	0.856379i	$0.672709\pi$
$168$		0			0
$169$	−11.3114			−0.870107
$170$	2.91878	+	13.0637i	0.223860	+	1.00194i
$171$		0			0
$172$	−6.68877			−0.510014
$173$	−10.6801			−0.811993			−0.405997	−	0.913875i	$-0.633076\pi$
$173$	−10.6801			−0.811993			−0.405997	+	0.913875i	$0.633076\pi$
$174$		0			0
$175$	9.14393	+	19.4414i	0.691216	+	1.46963i
$176$	−6.60801			−0.498097
$177$		0			0
$178$	−15.5550			−1.16590
$179$	−10.5930			−0.791758			−0.395879	−	0.918303i	$-0.629560\pi$
$179$	−10.5930			−0.791758			−0.395879	+	0.918303i	$0.629560\pi$
$180$		0			0
$181$			20.3240i			1.51067i	0.655336	+	0.755337i	$0.272527\pi$
$181$			20.3240i			1.51067i	−0.655336	+	0.755337i	$0.727473\pi$
$182$			5.58365i			0.413887i
$183$		0			0
$184$		−	4.49127i		−	0.331101i
$185$	−14.7345	+	3.29209i	−1.08330	+	0.242039i
$186$		0			0
$187$		−	39.5576i		−	2.89274i
$188$	2.99416			0.218371
$189$		0			0
$190$	−12.6108	+	2.81758i	−0.914880	+	0.204409i
$191$		−	12.0603i		−	0.872656i	−0.899788	−	0.436328i	$-0.856279\pi$
$191$		−	12.0603i		−	0.872656i	0.899788	−	0.436328i	$-0.143721\pi$
$192$		0			0
$193$			0.987462i			0.0710791i	0.999368	+	0.0355396i	$0.0113150\pi$
$193$			0.987462i			0.0710791i	−0.999368	+	0.0355396i	$0.988685\pi$
$194$			11.5566i			0.829718i
$195$		0			0
$196$	−11.4632			−0.818803
$197$			11.0469i			0.787059i	0.919312	+	0.393530i	$0.128746\pi$
$197$			11.0469i			0.787059i	−0.919312	+	0.393530i	$0.871254\pi$
$198$		0			0
$199$		−	14.3284i		−	1.01571i	−0.861441	−	0.507857i	$-0.830438\pi$
$199$		−	14.3284i		−	1.01571i	0.861441	−	0.507857i	$-0.169562\pi$
$200$	−4.52454	+	2.12804i	−0.319933	+	0.150475i
$201$		0			0
$202$		−	15.2957i		−	1.07620i
$203$		−	26.5884i		−	1.86614i
$204$		0			0
$205$	2.30462	+	10.3149i	0.160962	+	0.720423i
$206$		−	15.6546i		−	1.09071i
$207$		0			0
$208$	−1.29946			−0.0901016
$209$	38.1860			2.64138
$210$		0			0
$211$	1.46324			0.100734			0.0503668	−	0.998731i	$-0.483961\pi$
$211$	1.46324			0.100734			0.0503668	+	0.998731i	$0.483961\pi$
$212$			0.154894i			0.0106381i
$213$		0			0
$214$	−3.79191			−0.259210
$215$	14.5967	−	3.26128i	0.995484	−	0.222418i
$216$		0			0
$217$	−16.9688	+	16.8648i	−1.15192	+	1.14486i
$218$	−17.2931			−1.17124
$219$		0			0
$220$	14.4204	−	3.22190i	0.972224	−	0.217221i
$221$		−	7.77899i		−	0.523272i
$222$		0			0
$223$	−24.7896			−1.66003			−0.830016	−	0.557739i	$-0.811669\pi$
$223$	−24.7896			−1.66003			−0.830016	+	0.557739i	$0.811669\pi$
$224$		−	4.29689i		−	0.287098i
$225$		0			0
$226$	−8.46604			−0.563152
$227$	12.3341			0.818641			0.409321	−	0.912391i	$-0.365766\pi$
$227$	12.3341			0.818641			0.409321	+	0.912391i	$0.365766\pi$
$228$		0			0
$229$		−	28.0772i		−	1.85540i	−0.373331	−	0.927698i	$-0.621784\pi$
$229$		−	28.0772i		−	1.85540i	0.373331	−	0.927698i	$-0.378216\pi$
$230$	2.18983	+	9.80113i	0.144393	+	0.646267i
$231$		0			0
$232$	6.18784			0.406251
$233$	−19.1236			−1.25283			−0.626415	−	0.779490i	$-0.715479\pi$
$233$	−19.1236			−1.25283			−0.626415	+	0.779490i	$0.715479\pi$
$234$		0			0
$235$	−6.53404	+	1.45988i	−0.426234	+	0.0952320i
$236$		−	7.02972i		−	0.457596i
$237$		0			0
$238$	25.7225			1.66734
$239$	9.05540			0.585745			0.292872	−	0.956152i	$-0.405389\pi$
$239$	9.05540			0.585745			0.292872	+	0.956152i	$0.405389\pi$
$240$		0			0
$241$		−	7.78866i		−	0.501711i	−0.968024	−	0.250856i	$-0.919288\pi$
$241$		−	7.78866i		−	0.501711i	0.968024	−	0.250856i	$-0.0807120\pi$
$242$	−32.6658			−2.09983
$243$		0			0
$244$		−	5.19654i		−	0.332674i
$245$	25.0158	−	5.58920i	1.59820	−	0.357081i
$246$		0			0
$247$	7.50928			0.477804
$248$	−3.92488	−	3.94909i	−0.249230	−	0.250767i
$249$		0			0
$250$	8.83615	−	6.84999i	0.558847	−	0.433231i
$251$	−8.71034			−0.549792			−0.274896	−	0.961474i	$-0.588643\pi$
$251$	−8.71034			−0.549792			−0.274896	+	0.961474i	$0.588643\pi$
$252$		0			0
$253$		−	29.6783i		−	1.86586i
$254$	9.03004			0.566595
$255$		0			0
$256$	1.00000			0.0625000
$257$	−2.40058			−0.149744			−0.0748719	−	0.997193i	$-0.523855\pi$
$257$	−2.40058			−0.149744			−0.0748719	+	0.997193i	$0.523855\pi$
$258$		0			0
$259$			29.0124i			1.80274i
$260$	2.83577	−	0.633587i	0.175867	−	0.0392934i
$261$		0			0
$262$			12.7992i			0.790738i
$263$			9.34137i			0.576014i	0.957628	+	0.288007i	$0.0929926\pi$
$263$			9.34137i			0.576014i	−0.957628	+	0.288007i	$0.907007\pi$
$264$		0			0
$265$	−0.0755223	−	0.338018i	−0.00463930	−	0.0207643i
$266$			24.8306i			1.52246i
$267$		0			0
$268$			3.32789i			0.203283i
$269$	10.6837			0.651395			0.325698	−	0.945474i	$-0.394401\pi$
$269$	10.6837			0.651395			0.325698	+	0.945474i	$0.394401\pi$
$270$		0			0
$271$		−	17.0593i		−	1.03628i	−0.855297	−	0.518139i	$-0.826625\pi$
$271$		−	17.0593i		−	1.03628i	0.855297	−	0.518139i	$-0.173375\pi$
$272$			5.98631i			0.362974i
$273$		0			0
$274$			11.3902i			0.688106i
$275$	−29.8982	+	14.0621i	−1.80293	+	0.847975i
$276$		0			0
$277$	−27.7890			−1.66968			−0.834840	−	0.550493i	$-0.814440\pi$
$277$	−27.7890			−1.66968			−0.834840	+	0.550493i	$0.814440\pi$
$278$			3.28843i			0.197227i
$279$		0			0
$280$	2.09506	+	9.37694i	0.125204	+	0.560379i
$281$			11.9267i			0.711489i	0.934583	+	0.355745i	$0.115773\pi$
$281$			11.9267i			0.711489i	−0.934583	+	0.355745i	$0.884227\pi$
$282$		0			0
$283$		−	12.1177i		−	0.720325i	−0.932890	−	0.360163i	$-0.882721\pi$
$283$		−	12.1177i		−	0.720325i	0.932890	−	0.360163i	$-0.117279\pi$
$284$		−	0.985624i		−	0.0584860i
$285$		0			0
$286$	−8.58686			−0.507752
$287$	20.3101			1.19887
$288$		0			0
$289$	−18.8360			−1.10800
$290$	−13.5035	+	3.01704i	−0.792952	+	0.177167i
$291$		0			0
$292$	−9.67138			−0.565975
$293$	28.1066			1.64201			0.821004	−	0.570923i	$-0.193415\pi$
$293$	28.1066			1.64201			0.821004	+	0.570923i	$0.193415\pi$
$294$		0			0
$295$	3.42752	+	15.3407i	0.199558	+	0.893169i
$296$	−6.75195			−0.392449
$297$		0			0
$298$			2.75453i			0.159565i
$299$		−	5.83624i		−	0.337518i
$300$		0			0
$301$		−	28.7409i		−	1.65660i
$302$			16.4613i			0.947243i
$303$		0			0
$304$	−5.77875			−0.331434
$305$	2.53371	+	11.3402i	0.145080	+	0.649338i
$306$		0			0
$307$			16.6046i			0.947677i	0.880612	+	0.473838i	$0.157132\pi$
$307$			16.6046i			0.947677i	−0.880612	+	0.473838i	$0.842868\pi$
$308$		−	28.3939i		−	1.61789i
$309$		0			0
$310$	10.4906	+	6.70427i	0.595826	+	0.380777i
$311$		−	8.39888i		−	0.476257i	−0.971234	−	0.238128i	$-0.923466\pi$
$311$		−	8.39888i		−	0.476257i	0.971234	−	0.238128i	$-0.0765339\pi$
$312$		0			0
$313$	−20.8912			−1.18084			−0.590420	−	0.807096i	$-0.701038\pi$
$313$	−20.8912			−1.18084			−0.590420	+	0.807096i	$0.701038\pi$
$314$		−	7.30627i		−	0.412317i
$315$		0			0
$316$			16.7416i			0.941789i
$317$	17.4559			0.980423			0.490211	−	0.871604i	$-0.336920\pi$
$317$	17.4559			0.980423			0.490211	+	0.871604i	$0.336920\pi$
$318$		0			0
$319$	40.8893			2.28936
$320$	−2.18226	+	0.487576i	−0.121992	+	0.0272563i
$321$		0			0
$322$	19.2985			1.07546
$323$		−	34.5934i		−	1.92483i
$324$		0			0
$325$	−5.87947	+	2.76531i	−0.326134	+	0.153392i
$326$			13.2198i			0.732175i
$327$		0			0
$328$			4.72669i			0.260988i
$329$			12.8656i			0.709301i
$330$		0			0
$331$			21.4257i			1.17766i	0.808255	+	0.588832i	$0.200412\pi$
$331$			21.4257i			1.17766i	−0.808255	+	0.588832i	$0.799588\pi$
$332$			0.977557i			0.0536504i
$333$		0			0
$334$		−	22.1337i		−	1.21110i
$335$	−1.62260	−	7.26233i	−0.0886521	−	0.396784i
$336$		0			0
$337$	7.69750			0.419309			0.209655	−	0.977776i	$-0.432766\pi$
$337$	7.69750			0.419309			0.209655	+	0.977776i	$0.432766\pi$
$338$	11.3114			0.615259
$339$		0			0
$340$	−2.91878	−	13.0637i	−0.158293	−	0.708479i
$341$	−25.9356	−	26.0956i	−1.40449	−	1.41316i
$342$		0			0
$343$		−	19.1780i		−	1.03552i
$344$	6.68877			0.360634
$345$		0			0
$346$	10.6801			0.574166
$347$		−	4.34040i		−	0.233005i	−0.993190	−	0.116503i	$-0.962832\pi$
$347$		−	4.34040i		−	0.233005i	0.993190	−	0.116503i	$-0.0371683\pi$
$348$		0			0
$349$	3.61613			0.193567			0.0967836	−	0.995305i	$-0.469145\pi$
$349$	3.61613			0.193567			0.0967836	+	0.995305i	$0.469145\pi$
$350$	−9.14393	−	19.4414i	−0.488764	−	1.03919i
$351$		0			0
$352$	6.60801			0.352208
$353$		−	8.87197i		−	0.472208i	−0.971728	−	0.236104i	$-0.924129\pi$
$353$		−	8.87197i		−	0.472208i	0.971728	−	0.236104i	$-0.0758705\pi$
$354$		0			0
$355$	0.480566	+	2.15089i	0.0255058	+	0.114157i
$356$	15.5550			0.824415
$357$		0			0
$358$	10.5930			0.559857
$359$			30.4101i			1.60498i	0.596663	+	0.802492i	$0.296493\pi$
$359$			30.4101i			1.60498i	−0.596663	+	0.802492i	$0.703507\pi$
$360$		0			0
$361$	14.3940			0.757578
$362$		−	20.3240i		−	1.06821i
$363$		0			0
$364$		−	5.58365i		−	0.292663i
$365$	21.1055	−	4.71553i	1.10471	−	0.246822i
$366$		0			0
$367$	25.2595			1.31853			0.659267	−	0.751909i	$-0.270867\pi$
$367$	25.2595			1.31853			0.659267	+	0.751909i	$0.270867\pi$
$368$			4.49127i			0.234124i
$369$		0			0
$370$	14.7345	−	3.29209i	0.766012	−	0.171147i
$371$	−0.665560			−0.0345542
$372$		0			0
$373$		−	25.4731i		−	1.31895i	−0.751728	−	0.659474i	$-0.770779\pi$
$373$		−	25.4731i		−	1.31895i	0.751728	−	0.659474i	$-0.229221\pi$
$374$			39.5576i			2.04547i
$375$		0			0
$376$	−2.99416			−0.154412
$377$	8.04087			0.414126
$378$		0			0
$379$	2.28086			0.117160			0.0585799	−	0.998283i	$-0.481343\pi$
$379$	2.28086			0.117160			0.0585799	+	0.998283i	$0.481343\pi$
$380$	12.6108	−	2.81758i	0.646918	−	0.144539i
$381$		0			0
$382$			12.0603i			0.617061i
$383$		−	22.7602i		−	1.16299i	−0.813549	−	0.581497i	$-0.802467\pi$
$383$		−	22.7602i		−	1.16299i	0.813549	−	0.581497i	$-0.197533\pi$
$384$		0			0
$385$	13.8442	+	61.9629i	0.705564	+	3.15792i
$386$		−	0.987462i		−	0.0502605i
$387$		0			0
$388$		−	11.5566i		−	0.586699i
$389$	−6.31866			−0.320369			−0.160184	−	0.987087i	$-0.551209\pi$
$389$	−6.31866			−0.320369			−0.160184	+	0.987087i	$0.551209\pi$
$390$		0			0
$391$	−26.8861			−1.35969
$392$	11.4632			0.578981
$393$		0			0
$394$		−	11.0469i		−	0.556535i
$395$	−8.16280	−	36.5346i	−0.410715	−	1.83825i
$396$		0			0
$397$			12.4324i			0.623962i	0.950088	+	0.311981i	$0.100993\pi$
$397$			12.4324i			0.623962i	−0.950088	+	0.311981i	$0.899007\pi$
$398$			14.3284i			0.718219i
$399$		0			0
$400$	4.52454	−	2.12804i	0.226227	−	0.106402i
$401$	2.65118			0.132394			0.0661968	−	0.997807i	$-0.478913\pi$
$401$	2.65118			0.132394			0.0661968	+	0.997807i	$0.478913\pi$
$402$		0			0
$403$	−5.10024	−	5.13170i	−0.254061	−	0.255628i
$404$			15.2957i			0.760991i
$405$		0			0
$406$			26.5884i			1.31956i
$407$	−44.6169			−2.21158
$408$		0			0
$409$			3.01814i			0.149237i	0.997212	+	0.0746186i	$0.0237739\pi$
$409$			3.01814i			0.149237i	−0.997212	+	0.0746186i	$0.976226\pi$
$410$	−2.30462	−	10.3149i	−0.113817	−	0.509416i
$411$		0			0
$412$			15.6546i			0.771247i
$413$	30.2059			1.48634
$414$		0			0
$415$	−0.476633	−	2.13329i	−0.0233970	−	0.104719i
$416$	1.29946			0.0637114
$417$		0			0
$418$	−38.1860			−1.86774
$419$			26.5832i			1.29867i	0.760501	+	0.649336i	$0.224953\pi$
$419$			26.5832i			1.29867i	−0.760501	+	0.649336i	$0.775047\pi$
$420$		0			0
$421$	−12.1951			−0.594351			−0.297175	−	0.954823i	$-0.596045\pi$
$421$	−12.1951			−0.594351			−0.297175	+	0.954823i	$0.596045\pi$
$422$	−1.46324			−0.0712295
$423$		0			0
$424$		−	0.154894i		−	0.00752229i
$425$	12.7391	+	27.0853i	0.617937	+	1.31383i
$426$		0			0
$427$	22.3289			1.08057
$428$	3.79191			0.183289
$429$		0			0
$430$	−14.5967	+	3.26128i	−0.703913	+	0.157273i
$431$		−	6.46374i		−	0.311347i	−0.987809	−	0.155674i	$-0.950245\pi$
$431$		−	6.46374i		−	0.311347i	0.987809	−	0.155674i	$-0.0497548\pi$
$432$		0			0
$433$	−11.1240			−0.534587			−0.267294	−	0.963615i	$-0.586129\pi$
$433$	−11.1240			−0.534587			−0.267294	+	0.963615i	$0.586129\pi$
$434$	16.9688	−	16.8648i	0.814528	−	0.809535i
$435$		0			0
$436$	17.2931			0.828191
$437$		−	25.9539i		−	1.24155i
$438$		0			0
$439$	−30.0405			−1.43376			−0.716878	−	0.697199i	$-0.754430\pi$
$439$	−30.0405			−1.43376			−0.716878	+	0.697199i	$0.754430\pi$
$440$	−14.4204	+	3.22190i	−0.687466	+	0.153598i
$441$		0			0
$442$			7.77899i			0.370009i
$443$	−21.0674			−1.00094			−0.500470	−	0.865754i	$-0.666839\pi$
$443$	−21.0674			−1.00094			−0.500470	+	0.865754i	$0.666839\pi$
$444$		0			0
$445$	−33.9452	+	7.58426i	−1.60916	+	0.359528i
$446$	24.7896			1.17382
$447$		0			0
$448$			4.29689i			0.203009i
$449$	3.94056			0.185966			0.0929832	−	0.995668i	$-0.470360\pi$
$449$	3.94056			0.185966			0.0929832	+	0.995668i	$0.470360\pi$
$450$		0			0
$451$			31.2340i			1.47075i
$452$	8.46604			0.398209
$453$		0			0
$454$	−12.3341			−0.578867
$455$	2.72245	+	12.1850i	0.127630	+	0.571241i
$456$		0			0
$457$	6.36435			0.297712			0.148856	−	0.988859i	$-0.452441\pi$
$457$	6.36435			0.297712			0.148856	+	0.988859i	$0.452441\pi$
$458$			28.0772i			1.31196i
$459$		0			0
$460$	−2.18983	−	9.80113i	−0.102102	−	0.456980i
$461$	13.9588			0.650125			0.325063	−	0.945693i	$-0.394615\pi$
$461$	13.9588			0.650125			0.325063	+	0.945693i	$0.394615\pi$
$462$		0			0
$463$	16.3980			0.762080			0.381040	−	0.924559i	$-0.375566\pi$
$463$	16.3980			0.762080			0.381040	+	0.924559i	$0.375566\pi$
$464$	−6.18784			−0.287263
$465$		0			0
$466$	19.1236			0.885885
$467$	−28.7497			−1.33038			−0.665188	−	0.746676i	$-0.731648\pi$
$467$	−28.7497			−1.33038			−0.665188	+	0.746676i	$0.731648\pi$
$468$		0			0
$469$	−14.2996			−0.660293
$470$	6.53404	−	1.45988i	0.301393	−	0.0673392i
$471$		0			0
$472$			7.02972i			0.323569i
$473$	44.1994			2.03229
$474$		0			0
$475$	−26.1462	+	12.2974i	−1.19967	+	0.564243i
$476$	−25.7225			−1.17899
$477$		0			0
$478$	−9.05540			−0.414184
$479$			29.6502i			1.35475i	0.735638	+	0.677375i	$0.236883\pi$
$479$			29.6502i			1.35475i	−0.735638	+	0.677375i	$0.763117\pi$
$480$		0			0
$481$	−8.77391			−0.400056
$482$			7.78866i			0.354764i
$483$		0			0
$484$	32.6658			1.48481
$485$	5.63473	+	25.2196i	0.255860	+	1.14516i
$486$		0			0
$487$	−5.40645			−0.244990			−0.122495	−	0.992469i	$-0.539090\pi$
$487$	−5.40645			−0.244990			−0.122495	+	0.992469i	$0.539090\pi$
$488$			5.19654i			0.235236i
$489$		0			0
$490$	−25.0158	+	5.58920i	−1.13010	+	0.252494i
$491$	−3.12044			−0.140823			−0.0704117	−	0.997518i	$-0.522431\pi$
$491$	−3.12044			−0.140823			−0.0704117	+	0.997518i	$0.522431\pi$
$492$		0			0
$493$		−	37.0423i		−	1.66830i
$494$	−7.50928			−0.337858
$495$		0			0
$496$	3.92488	+	3.94909i	0.176232	+	0.177319i
$497$	4.23511			0.189971
$498$		0			0
$499$		−	5.17275i		−	0.231564i	−0.993275	−	0.115782i	$-0.963063\pi$
$499$		−	5.17275i		−	0.231564i	0.993275	−	0.115782i	$-0.0369374\pi$
$500$	−8.83615	+	6.84999i	−0.395165	+	0.306341i
$501$		0			0
$502$	8.71034			0.388761
$503$	12.7174			0.567039			0.283519	−	0.958966i	$-0.408498\pi$
$503$	12.7174			0.567039			0.283519	+	0.958966i	$0.408498\pi$
$504$		0			0
$505$	−7.45783	−	33.3793i	−0.331869	−	1.48536i
$506$			29.6783i			1.31936i
$507$		0			0
$508$	−9.03004			−0.400643
$509$	−16.8301			−0.745980			−0.372990	−	0.927835i	$-0.621667\pi$
$509$	−16.8301			−0.745980			−0.372990	+	0.927835i	$0.621667\pi$
$510$		0			0
$511$		−	41.5568i		−	1.83837i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	2.40058			0.105885
$515$	−7.63280	−	34.1625i	−0.336342	−	1.50538i
$516$		0			0
$517$	−19.7854			−0.870161
$518$		−	29.0124i		−	1.27473i
$519$		0			0
$520$	−2.83577	+	0.633587i	−0.124357	+	0.0277846i
$521$		−	8.27443i		−	0.362509i	−0.983436	−	0.181255i	$-0.941984\pi$
$521$		−	8.27443i		−	0.362509i	0.983436	−	0.181255i	$-0.0580158\pi$
$522$		0			0
$523$	11.5000			0.502861			0.251430	−	0.967875i	$-0.419099\pi$
$523$	11.5000			0.502861			0.251430	+	0.967875i	$0.419099\pi$
$524$		−	12.7992i		−	0.559136i
$525$		0			0
$526$		−	9.34137i		−	0.407303i
$527$	−23.6405	+	23.4956i	−1.02980	+	1.02348i
$528$		0			0
$529$	2.82850			0.122978
$530$	0.0755223	+	0.338018i	0.00328048	+	0.0146826i
$531$		0			0
$532$		−	24.8306i		−	1.07655i
$533$			6.14216i			0.266047i
$534$		0			0
$535$	−8.27494	+	1.84884i	−0.357757	+	0.0799324i
$536$		−	3.32789i		−	0.143743i
$537$		0			0
$538$	−10.6837			−0.460606
$539$	75.7492			3.26275
$540$		0			0
$541$	13.0921			0.562873			0.281437	−	0.959580i	$-0.409189\pi$
$541$	13.0921			0.562873			0.281437	+	0.959580i	$0.409189\pi$
$542$			17.0593i			0.732759i
$543$		0			0
$544$		−	5.98631i		−	0.256661i
$545$	−37.7382	+	8.43172i	−1.61653	+	0.361175i
$546$		0			0
$547$			19.7056i			0.842552i	0.906932	+	0.421276i	$0.138418\pi$
$547$			19.7056i			0.842552i	−0.906932	+	0.421276i	$0.861582\pi$
$548$		−	11.3902i		−	0.486564i
$549$		0			0
$550$	29.8982	−	14.0621i	1.27486	−	0.599609i
$551$	35.7580			1.52334
$552$		0			0
$553$	−71.9368			−3.05906
$554$	27.7890			1.18064
$555$		0			0
$556$		−	3.28843i		−	0.139461i
$557$		−	38.9920i		−	1.65214i	−0.563565	−	0.826072i	$-0.690570\pi$
$557$		−	38.9920i		−	1.65214i	0.563565	−	0.826072i	$-0.309430\pi$
$558$		0			0
$559$	8.69181			0.367624
$560$	−2.09506	−	9.37694i	−0.0885324	−	0.396248i
$561$		0			0
$562$		−	11.9267i		−	0.503099i
$563$	−16.4081			−0.691518			−0.345759	−	0.938323i	$-0.612379\pi$
$563$	−16.4081			−0.691518			−0.345759	+	0.938323i	$0.612379\pi$
$564$		0			0
$565$	−18.4751	+	4.12783i	−0.777254	+	0.173659i
$566$			12.1177i			0.509347i
$567$		0			0
$568$			0.985624i			0.0413559i
$569$	18.5966			0.779608			0.389804	−	0.920898i	$-0.372543\pi$
$569$	18.5966			0.779608			0.389804	+	0.920898i	$0.372543\pi$
$570$		0			0
$571$			13.5989i			0.569095i	0.958662	+	0.284547i	$0.0918433\pi$
$571$			13.5989i			0.569095i	−0.958662	+	0.284547i	$0.908157\pi$
$572$	8.58686			0.359035
$573$		0			0
$574$	−20.3101			−0.847726
$575$	9.55759	+	20.3209i	0.398579	+	0.847441i
$576$		0			0
$577$			1.91524i			0.0797325i	0.999205	+	0.0398663i	$0.0126932\pi$
$577$			1.91524i			0.0797325i	−0.999205	+	0.0398663i	$0.987307\pi$
$578$	18.8360			0.783472
$579$		0			0
$580$	13.5035	−	3.01704i	0.560702	−	0.125276i
$581$	−4.20045			−0.174264
$582$		0			0
$583$		−	1.02354i		−	0.0423906i
$584$	9.67138			0.400204
$585$		0			0
$586$	−28.1066			−1.16107
$587$			38.9605i			1.60807i	0.594581	+	0.804036i	$0.297318\pi$
$587$			38.9605i			1.60807i	−0.594581	+	0.804036i	$0.702682\pi$
$588$		0			0
$589$	−22.6809	−	22.8208i	−0.934551	−	0.940315i
$590$	−3.42752	−	15.3407i	−0.141109	−	0.631566i
$591$		0			0
$592$	6.75195			0.277503
$593$	−10.5262			−0.432260			−0.216130	−	0.976365i	$-0.569344\pi$
$593$	−10.5262			−0.432260			−0.216130	+	0.976365i	$0.569344\pi$
$594$		0			0
$595$	56.1333	−	12.5417i	2.30124	−	0.514159i
$596$		−	2.75453i		−	0.112830i
$597$		0			0
$598$			5.83624i			0.238662i
$599$			9.34149i			0.381683i	0.981621	+	0.190842i	$0.0611217\pi$
$599$			9.34149i			0.381683i	−0.981621	+	0.190842i	$0.938878\pi$
$600$		0			0
$601$		−	3.61259i		−	0.147361i	−0.997282	−	0.0736803i	$-0.976526\pi$
$601$		−	3.61259i		−	0.147361i	0.997282	−	0.0736803i	$-0.0234744\pi$
$602$			28.7409i			1.17139i
$603$		0			0
$604$		−	16.4613i		−	0.669802i
$605$	−71.2852	+	15.9270i	−2.89816	+	0.647526i
$606$		0			0
$607$		−	26.5898i		−	1.07925i	−0.841906	−	0.539624i	$-0.818566\pi$
$607$		−	26.5898i		−	1.07925i	0.841906	−	0.539624i	$-0.181434\pi$
$608$	5.77875			0.234359
$609$		0			0
$610$	−2.53371	−	11.3402i	−0.102587	−	0.459152i
$611$	−3.89080			−0.157405
$612$		0			0
$613$	−35.9800			−1.45322			−0.726610	−	0.687051i	$-0.758905\pi$
$613$	−35.9800			−1.45322			−0.726610	+	0.687051i	$0.758905\pi$
$614$		−	16.6046i		−	0.670109i
$615$		0			0
$616$			28.3939i			1.14402i
$617$	34.7261			1.39802			0.699010	−	0.715112i	$-0.253624\pi$
$617$	34.7261			1.39802			0.699010	+	0.715112i	$0.253624\pi$
$618$		0			0
$619$			42.9054i			1.72452i	0.506470	+	0.862258i	$0.330950\pi$
$619$			42.9054i			1.72452i	−0.506470	+	0.862258i	$0.669050\pi$
$620$	−10.4906	−	6.70427i	−0.421313	−	0.269250i
$621$		0			0
$622$			8.39888i			0.336765i
$623$			66.8382i			2.67782i
$624$		0			0
$625$	15.9429	−	19.2568i	0.637717	−	0.770271i
$626$	20.8912			0.834980
$627$		0			0
$628$			7.30627i			0.291552i
$629$			40.4193i			1.61162i
$630$		0			0
$631$		−	9.34336i		−	0.371953i	−0.982554	−	0.185977i	$-0.940455\pi$
$631$		−	9.34336i		−	0.371953i	0.982554	−	0.185977i	$-0.0595449\pi$
$632$		−	16.7416i		−	0.665945i
$633$		0			0
$634$	−17.4559			−0.693263
$635$	19.7059	−	4.40283i	0.782005	−	0.174721i
$636$		0			0
$637$	14.8961			0.590203
$638$	−40.8893			−1.61882
$639$		0			0
$640$	2.18226	−	0.487576i	0.0862615	−	0.0192731i
$641$	8.92870			0.352662			0.176331	−	0.984331i	$-0.443577\pi$
$641$	8.92870			0.352662			0.176331	+	0.984331i	$0.443577\pi$
$642$		0			0
$643$	6.70061			0.264246			0.132123	−	0.991233i	$-0.457821\pi$
$643$	6.70061			0.264246			0.132123	+	0.991233i	$0.457821\pi$
$644$	−19.2985			−0.760467
$645$		0			0
$646$			34.5934i			1.36106i
$647$			0.794969i			0.0312535i	0.999878	+	0.0156267i	$0.00497435\pi$
$647$			0.794969i			0.0312535i	−0.999878	+	0.0156267i	$0.995026\pi$
$648$		0			0
$649$			46.4524i			1.82342i
$650$	5.87947	−	2.76531i	0.230612	−	0.108464i
$651$		0			0
$652$		−	13.2198i		−	0.517726i
$653$	42.4245			1.66020			0.830099	−	0.557617i	$-0.188284\pi$
$653$	42.4245			1.66020			0.830099	+	0.557617i	$0.188284\pi$
$654$		0			0
$655$	6.24059	+	27.9312i	0.243840	+	1.09136i
$656$		−	4.72669i		−	0.184546i
$657$		0			0
$658$		−	12.8656i		−	0.501552i
$659$			39.2544i			1.52914i	0.644543	+	0.764568i	$0.277048\pi$
$659$			39.2544i			1.52914i	−0.644543	+	0.764568i	$0.722952\pi$
$660$		0			0
$661$	15.2294			0.592355			0.296178	−	0.955133i	$-0.404288\pi$
$661$	15.2294			0.592355			0.296178	+	0.955133i	$0.404288\pi$
$662$		−	21.4257i		−	0.832735i
$663$		0			0
$664$		−	0.977557i		−	0.0379366i
$665$	12.1068	+	54.1870i	0.469482	+	2.10128i
$666$		0			0
$667$		−	27.7912i		−	1.07608i
$668$			22.1337i			0.856379i
$669$		0			0
$670$	1.62260	+	7.26233i	0.0626865	+	0.280568i
$671$			34.3388i			1.32563i
$672$		0			0
$673$	8.40017			0.323803			0.161901	−	0.986807i	$-0.448237\pi$
$673$	8.40017			0.323803			0.161901	+	0.986807i	$0.448237\pi$
$674$	−7.69750			−0.296496
$675$		0			0
$676$	−11.3114			−0.435054
$677$			18.6843i			0.718098i	0.933319	+	0.359049i	$0.116899\pi$
$677$			18.6843i			0.718098i	−0.933319	+	0.359049i	$0.883101\pi$
$678$		0			0
$679$	49.6576			1.90568
$680$	2.91878	+	13.0637i	0.111930	+	0.500970i
$681$		0			0
$682$	25.9356	+	26.0956i	0.993127	+	0.999252i
$683$	13.1308			0.502437			0.251218	−	0.967930i	$-0.419169\pi$
$683$	13.1308			0.502437			0.251218	+	0.967930i	$0.419169\pi$
$684$		0			0
$685$	5.55358	+	24.8564i	0.212191	+	0.949713i
$686$			19.1780i			0.732221i
$687$		0			0
$688$	−6.68877			−0.255007
$689$		−	0.201278i		−	0.00766810i
$690$		0			0
$691$	−26.8976			−1.02323			−0.511617	−	0.859213i	$-0.670953\pi$
$691$	−26.8976			−1.02323			−0.511617	+	0.859213i	$0.670953\pi$
$692$	−10.6801			−0.405997
$693$		0			0
$694$			4.34040i			0.164759i
$695$	1.60336	+	7.17623i	0.0608189	+	0.272210i
$696$		0			0
$697$	28.2955			1.07177
$698$	−3.61613			−0.136873
$699$		0			0
$700$	9.14393	+	19.4414i	0.345608	+	0.734817i
$701$		−	29.2723i		−	1.10560i	−0.833314	−	0.552800i	$-0.813559\pi$
$701$		−	29.2723i		−	1.10560i	0.833314	−	0.552800i	$-0.186441\pi$
$702$		0			0
$703$	−39.0178			−1.47159
$704$	−6.60801			−0.249049
$705$		0			0
$706$			8.87197i			0.333901i
$707$	−65.7240			−2.47181
$708$		0			0
$709$		−	1.01161i		−	0.0379919i	−0.999820	−	0.0189959i	$-0.993953\pi$
$709$		−	1.01161i		−	0.0379919i	0.999820	−	0.0189959i	$-0.00604696\pi$
$710$	−0.480566	−	2.15089i	−0.0180353	−	0.0807215i
$711$		0			0
$712$	−15.5550			−0.582950
$713$	−17.7364	+	17.6277i	−0.664234	+	0.660163i
$714$		0			0
$715$	−18.7388	+	4.18675i	−0.700791	+	0.156575i
$716$	−10.5930			−0.395879
$717$		0			0
$718$		−	30.4101i		−	1.13489i
$719$	34.0208			1.26876			0.634380	−	0.773021i	$-0.281255\pi$
$719$	34.0208			1.26876			0.634380	+	0.773021i	$0.281255\pi$
$720$		0			0
$721$	−67.2661			−2.50512
$722$	−14.3940			−0.535688
$723$		0			0
$724$			20.3240i			0.755337i
$725$	−27.9971	+	13.1679i	−1.03979	+	0.489045i
$726$		0			0
$727$			13.4828i			0.500048i	0.968240	+	0.250024i	$0.0804385\pi$
$727$			13.4828i			0.500048i	−0.968240	+	0.250024i	$0.919561\pi$
$728$			5.58365i			0.206944i
$729$		0			0
$730$	−21.1055	+	4.71553i	−0.781149	+	0.174530i
$731$		−	40.0411i		−	1.48097i
$732$		0			0
$733$			30.7041i			1.13408i	0.823690	+	0.567040i	$0.191912\pi$
$733$			30.7041i			1.13408i	−0.823690	+	0.567040i	$0.808088\pi$
$734$	−25.2595			−0.932345
$735$		0			0
$736$		−	4.49127i		−	0.165550i
$737$		−	21.9907i		−	0.810039i
$738$		0			0
$739$			39.6477i			1.45846i	0.684267	+	0.729232i	$0.260123\pi$
$739$			39.6477i			1.45846i	−0.684267	+	0.729232i	$0.739877\pi$
$740$	−14.7345	+	3.29209i	−0.541652	+	0.121020i
$741$		0			0
$742$	0.665560			0.0244335
$743$		−	11.4146i		−	0.418761i	−0.977834	−	0.209381i	$-0.932855\pi$
$743$		−	11.4146i		−	0.418761i	0.977834	−	0.209381i	$-0.0671448\pi$
$744$		0			0
$745$	1.34304	+	6.01110i	0.0492052	+	0.220230i
$746$			25.4731i			0.932637i
$747$		0			0
$748$		−	39.5576i		−	1.44637i
$749$			16.2934i			0.595348i
$750$		0			0
$751$	20.8513			0.760875			0.380437	−	0.924807i	$-0.375773\pi$
$751$	20.8513			0.760875			0.380437	+	0.924807i	$0.375773\pi$
$752$	2.99416			0.109186
$753$		0			0
$754$	−8.04087			−0.292831
$755$	8.02614	+	35.9229i	0.292101	+	1.30737i
$756$		0			0
$757$	−9.56162			−0.347523			−0.173762	−	0.984788i	$-0.555592\pi$
$757$	−9.56162			−0.347523			−0.173762	+	0.984788i	$0.555592\pi$
$758$	−2.28086			−0.0828444
$759$		0			0
$760$	−12.6108	+	2.81758i	−0.457440	+	0.102204i
$761$	14.5650			0.527983			0.263991	−	0.964525i	$-0.414961\pi$
$761$	14.5650			0.527983			0.263991	+	0.964525i	$0.414961\pi$
$762$		0			0
$763$			74.3067i			2.69008i
$764$		−	12.0603i		−	0.436328i
$765$		0			0
$766$			22.7602i			0.822360i
$767$			9.13486i			0.329841i
$768$		0			0
$769$	−28.1510			−1.01515			−0.507575	−	0.861607i	$-0.669458\pi$
$769$	−28.1510			−1.01515			−0.507575	+	0.861607i	$0.669458\pi$
$770$	−13.8442	−	61.9629i	−0.498909	−	2.23299i
$771$		0			0
$772$			0.987462i			0.0355396i
$773$		−	39.8810i		−	1.43442i	−0.696857	−	0.717210i	$-0.745419\pi$
$773$		−	39.8810i		−	1.43442i	0.696857	−	0.717210i	$-0.254581\pi$
$774$		0			0
$775$	26.1621	+	9.51551i	0.939770	+	0.341807i
$776$			11.5566i			0.414859i
$777$		0			0
$778$	6.31866			0.226535
$779$			27.3144i			0.978640i
$780$		0			0
$781$			6.51301i			0.233054i
$782$	26.8861			0.961447
$783$		0			0
$784$	−11.4632			−0.409401
$785$	−3.56236	−	15.9442i	−0.127146	−	0.569073i
$786$		0			0
$787$	18.1462			0.646842			0.323421	−	0.946255i	$-0.395167\pi$
$787$	18.1462			0.646842			0.323421	+	0.946255i	$0.395167\pi$
$788$			11.0469i			0.393530i
$789$		0			0
$790$	8.16280	+	36.5346i	0.290420	+	1.29984i
$791$			36.3776i			1.29344i
$792$		0			0
$793$			6.75271i			0.239796i
$794$		−	12.4324i		−	0.441208i
$795$		0			0
$796$		−	14.3284i		−	0.507857i
$797$			43.0105i			1.52351i	0.647866	+	0.761754i	$0.275662\pi$
$797$			43.0105i			1.52351i	−0.647866	+	0.761754i	$0.724338\pi$
$798$		0			0
$799$			17.9240i			0.634104i
$800$	−4.52454	+	2.12804i	−0.159967	+	0.0752375i
$801$		0			0
$802$	−2.65118			−0.0936164
$803$	63.9085			2.25528
$804$		0			0
$805$	42.1143	−	9.40947i	1.48434	−	0.331640i
$806$	5.10024	+	5.13170i	0.179648	+	0.180756i
$807$		0			0
$808$		−	15.2957i		−	0.538102i
$809$	1.92772			0.0677750			0.0338875	−	0.999426i	$-0.489211\pi$
$809$	1.92772			0.0677750			0.0338875	+	0.999426i	$0.489211\pi$
$810$		0			0
$811$	−3.78310			−0.132843			−0.0664213	−	0.997792i	$-0.521158\pi$
$811$	−3.78310			−0.132843			−0.0664213	+	0.997792i	$0.521158\pi$
$812$		−	26.5884i		−	0.933071i
$813$		0			0
$814$	44.6169			1.56382
$815$	6.44564	+	28.8490i	0.225781	+	1.01054i
$816$		0			0
$817$	38.6527			1.35229
$818$		−	3.01814i		−	0.105527i
$819$		0			0
$820$	2.30462	+	10.3149i	0.0804809	+	0.360211i
$821$	−5.07023			−0.176952			−0.0884760	−	0.996078i	$-0.528200\pi$
$821$	−5.07023			−0.176952			−0.0884760	+	0.996078i	$0.528200\pi$
$822$		0			0
$823$	3.84012			0.133858			0.0669292	−	0.997758i	$-0.478680\pi$
$823$	3.84012			0.133858			0.0669292	+	0.997758i	$0.478680\pi$
$824$		−	15.6546i		−	0.545354i
$825$		0			0
$826$	−30.2059			−1.05100
$827$			47.3032i			1.64489i	0.568843	+	0.822446i	$0.307391\pi$
$827$			47.3032i			1.64489i	−0.568843	+	0.822446i	$0.692609\pi$
$828$		0			0
$829$			22.0475i			0.765743i	0.923802	+	0.382871i	$0.125065\pi$
$829$			22.0475i			0.765743i	−0.923802	+	0.382871i	$0.874935\pi$
$830$	0.476633	+	2.13329i	0.0165442	+	0.0740475i
$831$		0			0
$832$	−1.29946			−0.0450508
$833$		−	68.6225i		−	2.37763i
$834$		0			0
$835$	−10.7919	−	48.3016i	−0.373468	−	1.67155i
$836$	38.1860			1.32069
$837$		0			0
$838$		−	26.5832i		−	0.918300i
$839$		−	39.8048i		−	1.37421i	−0.726556	−	0.687107i	$-0.758880\pi$
$839$		−	39.8048i		−	1.37421i	0.726556	−	0.687107i	$-0.241120\pi$
$840$		0			0
$841$	9.28934			0.320322
$842$	12.1951			0.420270
$843$		0			0
$844$	1.46324			0.0503668
$845$	24.6844	−	5.51516i	0.849170	−	0.189727i
$846$		0			0
$847$			140.361i			4.82286i
$848$			0.154894i			0.00531907i
$849$		0			0
$850$	−12.7391	−	27.0853i	−0.436947	−	0.929019i
$851$			30.3248i			1.03952i
$852$		0			0
$853$			12.3157i			0.421683i	0.977520	+	0.210841i	$0.0676204\pi$
$853$			12.3157i			0.421683i	−0.977520	+	0.210841i	$0.932380\pi$
$854$	−22.3289			−0.764080
$855$		0			0
$856$	−3.79191			−0.129605
$857$	−39.7971			−1.35944			−0.679722	−	0.733470i	$-0.737899\pi$
$857$	−39.7971			−1.35944			−0.679722	+	0.733470i	$0.737899\pi$
$858$		0			0
$859$		−	10.0371i		−	0.342461i	−0.985231	−	0.171231i	$-0.945226\pi$
$859$		−	10.0371i		−	0.342461i	0.985231	−	0.171231i	$-0.0547744\pi$
$860$	14.5967	−	3.26128i	0.497742	−	0.111209i
$861$		0			0
$862$			6.46374i			0.220156i
$863$		−	12.4242i		−	0.422925i	−0.977386	−	0.211462i	$-0.932177\pi$
$863$		−	12.4242i		−	0.422925i	0.977386	−	0.211462i	$-0.0678226\pi$
$864$		0			0
$865$	23.3068	−	5.20736i	0.792455	−	0.177056i
$866$	11.1240			0.378010
$867$		0			0
$868$	−16.9688	+	16.8648i	−0.575958	+	0.572428i
$869$		−	110.629i		−	3.75282i
$870$		0			0
$871$		−	4.32447i		−	0.146529i
$872$	−17.2931			−0.585620
$873$		0			0
$874$			25.9539i			0.877905i
$875$	−29.4336	−	37.9680i	−0.995039	−	1.28355i
$876$		0			0
$877$			9.07886i			0.306571i	0.988182	+	0.153286i	$0.0489854\pi$
$877$			9.07886i			0.306571i	−0.988182	+	0.153286i	$0.951015\pi$
$878$	30.0405			1.01382
$879$		0			0
$880$	14.4204	−	3.22190i	0.486112	−	0.108610i
$881$	−5.98703			−0.201708			−0.100854	−	0.994901i	$-0.532158\pi$
$881$	−5.98703			−0.201708			−0.100854	+	0.994901i	$0.532158\pi$
$882$		0			0
$883$	43.6900			1.47029			0.735143	−	0.677912i	$-0.237115\pi$
$883$	43.6900			1.47029			0.735143	+	0.677912i	$0.237115\pi$
$884$		−	7.77899i		−	0.261636i
$885$		0			0
$886$	21.0674			0.707772
$887$	−50.3233			−1.68969			−0.844846	−	0.535010i	$-0.820308\pi$
$887$	−50.3233			−1.68969			−0.844846	+	0.535010i	$0.820308\pi$
$888$		0			0
$889$		−	38.8011i		−	1.30135i
$890$	33.9452	−	7.58426i	1.13784	−	0.254225i
$891$		0			0
$892$	−24.7896			−0.830016
$893$	−17.3025			−0.579006
$894$		0			0
$895$	23.1167	−	5.16489i	0.772706	−	0.172643i
$896$		−	4.29689i		−	0.143549i
$897$		0			0
$898$	−3.94056			−0.131498
$899$	−24.2865	−	24.4363i	−0.810001	−	0.814997i
$900$		0			0
$901$	−0.927241			−0.0308909
$902$		−	31.2340i		−	1.03998i
$903$		0			0
$904$	−8.46604			−0.281576
$905$	−9.90951	−	44.3524i	−0.329403	−	1.47432i
$906$		0			0
$907$		−	1.12840i		−	0.0374680i	−0.999825	−	0.0187340i	$-0.994036\pi$
$907$		−	1.12840i		−	0.0374680i	0.999825	−	0.0187340i	$-0.00596357\pi$
$908$	12.3341			0.409321
$909$		0			0
$910$	−2.72245	−	12.1850i	−0.0902484	−	0.403928i
$911$	−46.3517			−1.53570			−0.767851	−	0.640629i	$-0.778674\pi$
$911$	−46.3517			−1.53570			−0.767851	+	0.640629i	$0.778674\pi$
$912$		0			0
$913$		−	6.45971i		−	0.213785i
$914$	−6.36435			−0.210514
$915$		0			0
$916$		−	28.0772i		−	0.927698i
$917$	54.9968			1.81615
$918$		0			0
$919$	−45.3355			−1.49548			−0.747741	−	0.663991i	$-0.768861\pi$
$919$	−45.3355			−1.49548			−0.747741	+	0.663991i	$0.768861\pi$
$920$	2.18983	+	9.80113i	0.0721967	+	0.323134i
$921$		0			0
$922$	−13.9588			−0.459708
$923$			1.28078i			0.0421574i
$924$		0			0
$925$	30.5495	−	14.3684i	1.00446	−	0.472430i
$926$	−16.3980			−0.538872
$927$		0			0
$928$	6.18784			0.203126
$929$	−41.4856			−1.36110			−0.680549	−	0.732703i	$-0.738259\pi$
$929$	−41.4856			−1.36110			−0.680549	+	0.732703i	$0.738259\pi$
$930$		0			0
$931$	66.2432			2.17103
$932$	−19.1236			−0.626415
$933$		0			0
$934$	28.7497			0.940718
$935$	19.2873	+	86.3251i	0.630763	+	2.82313i
$936$		0			0
$937$		−	0.355403i		−	0.0116105i	−0.999983	−	0.00580526i	$-0.998152\pi$
$937$		−	0.355403i		−	0.0116105i	0.999983	−	0.00580526i	$-0.00184788\pi$
$938$	14.2996			0.466898
$939$		0			0
$940$	−6.53404	+	1.45988i	−0.213117	+	0.0476160i
$941$	−15.4712			−0.504348			−0.252174	−	0.967682i	$-0.581146\pi$
$941$	−15.4712			−0.504348			−0.252174	+	0.967682i	$0.581146\pi$
$942$		0			0
$943$	21.2289			0.691307
$944$		−	7.02972i		−	0.228798i
$945$		0			0
$946$	−44.1994			−1.43705
$947$			12.4734i			0.405330i	0.979248	+	0.202665i	$0.0649603\pi$
$947$			12.4734i			0.405330i	−0.979248	+	0.202665i	$0.935040\pi$
$948$		0			0
$949$	12.5676			0.407962
$950$	26.1462	−	12.2974i	0.848295	−	0.398980i
$951$		0			0
$952$	25.7225			0.833672
$953$			36.6679i			1.18779i	0.804542	+	0.593896i	$0.202411\pi$
$953$			36.6679i			1.18779i	−0.804542	+	0.593896i	$0.797589\pi$
$954$		0			0
$955$	5.88033	+	26.3188i	0.190283	+	0.851657i
$956$	9.05540			0.292872
$957$		0			0
$958$		−	29.6502i		−	0.957953i
$959$	48.9423			1.58043
$960$		0			0
$961$	−0.190600	+	30.9994i	−0.00614839	+	0.999981i
$962$	8.77391			0.282882
$963$		0			0
$964$		−	7.78866i		−	0.250856i
$965$	−0.481463	−	2.15490i	−0.0154988	−	0.0693688i
$966$		0			0
$967$	−31.4446			−1.01119			−0.505594	−	0.862771i	$-0.668727\pi$
$967$	−31.4446			−1.01119			−0.505594	+	0.862771i	$0.668727\pi$
$968$	−32.6658			−1.04992
$969$		0			0
$970$	−5.63473	−	25.2196i	−0.180920	−	0.809753i
$971$		−	21.2154i		−	0.680834i	−0.940275	−	0.340417i	$-0.889432\pi$
$971$		−	21.2154i		−	0.680834i	0.940275	−	0.340417i	$-0.110568\pi$
$972$		0			0
$973$	14.1300			0.452988
$974$	5.40645			0.173234
$975$		0			0
$976$		−	5.19654i		−	0.166337i
$977$	−28.0660			−0.897911			−0.448956	−	0.893554i	$-0.648204\pi$
$977$	−28.0660			−0.897911			−0.448956	+	0.893554i	$0.648204\pi$
$978$		0			0
$979$	−102.788			−3.28511
$980$	25.0158	−	5.58920i	0.799100	−	0.178540i
$981$		0			0
$982$	3.12044			0.0995772
$983$		−	42.8011i		−	1.36514i	−0.730818	−	0.682572i	$-0.760861\pi$
$983$		−	42.8011i		−	1.36514i	0.730818	−	0.682572i	$-0.239139\pi$
$984$		0			0
$985$	−5.38620	−	24.1072i	−0.171619	−	0.768121i
$986$			37.0423i			1.17967i
$987$		0			0
$988$	7.50928			0.238902
$989$		−	30.0411i		−	0.955251i
$990$		0			0
$991$		−	27.1264i		−	0.861699i	−0.902424	−	0.430849i	$-0.858214\pi$
$991$		−	27.1264i		−	0.861699i	0.902424	−	0.430849i	$-0.141786\pi$
$992$	−3.92488	−	3.94909i	−0.124615	−	0.125384i
$993$		0			0
$994$	−4.23511			−0.134330
$995$	6.98619	+	31.2684i	0.221477	+	0.991274i
$996$		0			0
$997$		−	33.2795i		−	1.05397i	−0.849874	−	0.526985i	$-0.823322\pi$
$997$		−	33.2795i		−	1.05397i	0.849874	−	0.526985i	$-0.176678\pi$
$998$			5.17275i			0.163741i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2790.2.e.a.2789.3	yes	32
3.2	odd	2		2790.2.e.b.2789.29	yes	32
5.4	even	2		2790.2.e.b.2789.32	yes	32
15.14	odd	2	inner	2790.2.e.a.2789.2	yes	32
31.30	odd	2	inner	2790.2.e.a.2789.4	yes	32
93.92	even	2		2790.2.e.b.2789.30	yes	32
155.154	odd	2		2790.2.e.b.2789.31	yes	32
465.464	even	2	inner	2790.2.e.a.2789.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2790.2.e.a.2789.1	✓	32	465.464	even	2	inner
2790.2.e.a.2789.2	yes	32	15.14	odd	2	inner
2790.2.e.a.2789.3	yes	32	1.1	even	1	trivial
2790.2.e.a.2789.4	yes	32	31.30	odd	2	inner
2790.2.e.b.2789.29	yes	32	3.2	odd	2
2790.2.e.b.2789.30	yes	32	93.92	even	2
2790.2.e.b.2789.31	yes	32	155.154	odd	2
2790.2.e.b.2789.32	yes	32	5.4	even	2

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:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.18226 + 0.487576i) q^{5} +4.29689i q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.18226 + 0.487576i) q^{5} +4.29689i q^{7} -1.00000 q^{8} +(2.18226 - 0.487576i) q^{10} -6.60801 q^{11} -1.29946 q^{13} -4.29689i q^{14} +1.00000 q^{16} +5.98631i q^{17} -5.77875 q^{19} +(-2.18226 + 0.487576i) q^{20} +6.60801 q^{22} +4.49127i q^{23} +(4.52454 - 2.12804i) q^{25} +1.29946 q^{26} +4.29689i q^{28} -6.18784 q^{29} +(3.92488 + 3.94909i) q^{31} -1.00000 q^{32} -5.98631i q^{34} +(-2.09506 - 9.37694i) q^{35} +6.75195 q^{37} +5.77875 q^{38} +(2.18226 - 0.487576i) q^{40} -4.72669i q^{41} -6.68877 q^{43} -6.60801 q^{44} -4.49127i q^{46} +2.99416 q^{47} -11.4632 q^{49} +(-4.52454 + 2.12804i) q^{50} -1.29946 q^{52} +0.154894i q^{53} +(14.4204 - 3.22190i) q^{55} -4.29689i q^{56} +6.18784 q^{58} -7.02972i q^{59} -5.19654i q^{61} +(-3.92488 - 3.94909i) q^{62} +1.00000 q^{64} +(2.83577 - 0.633587i) q^{65} +3.32789i q^{67} +5.98631i q^{68} +(2.09506 + 9.37694i) q^{70} -0.985624i q^{71} -9.67138 q^{73} -6.75195 q^{74} -5.77875 q^{76} -28.3939i q^{77} +16.7416i q^{79} +(-2.18226 + 0.487576i) q^{80} +4.72669i q^{82} +0.977557i q^{83} +(-2.91878 - 13.0637i) q^{85} +6.68877 q^{86} +6.60801 q^{88} +15.5550 q^{89} -5.58365i q^{91} +4.49127i q^{92} -2.99416 q^{94} +(12.6108 - 2.81758i) q^{95} -11.5566i q^{97} +11.4632 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} + 32 q^{4} - 4 q^{5} - 32 q^{8}+O(q^{10}) \) 32 * q - 32 * q^2 + 32 * q^4 - 4 * q^5 - 32 * q^8	\( 32 q - 32 q^{2} + 32 q^{4} - 4 q^{5} - 32 q^{8} + 4 q^{10} + 32 q^{16} - 16 q^{19} - 4 q^{20} + 4 q^{25} - 32 q^{32} - 8 q^{35} + 16 q^{38} + 4 q^{40} + 8 q^{47} - 24 q^{49} - 4 q^{50} + 32 q^{64} + 8 q^{70} - 16 q^{76} - 4 q^{80} - 8 q^{94} + 4 q^{95} + 24 q^{98}+O(q^{100}) \) 32 * q - 32 * q^2 + 32 * q^4 - 4 * q^5 - 32 * q^8 + 4 * q^10 + 32 * q^16 - 16 * q^19 - 4 * q^20 + 4 * q^25 - 32 * q^32 - 8 * q^35 + 16 * q^38 + 4 * q^40 + 8 * q^47 - 24 * q^49 - 4 * q^50 + 32 * q^64 + 8 * q^70 - 16 * q^76 - 4 * q^80 - 8 * q^94 + 4 * q^95 + 24 * q^98

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