LMFDB - Embedded newform 3997.1.ce.a.944.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3997,1,Mod(258,3997)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3997, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([57, 86]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3997.258");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3997 = 7 \cdot 571 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3997.ce (of order $114$, degree $36$, 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:	$1.99476285549$
Analytic rank:	$0$
Dimension:	$36$
Coefficient field:	$\Q(\zeta_{57})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{36} - x^{35} + x^{33} - x^{32} + x^{30} - x^{29} + x^{27} - x^{26} + x^{24} - x^{23} + x^{21} + \cdots + 1 $ x^36 - x^35 + x^33 - x^32 + x^30 - x^29 + x^27 - x^26 + x^24 - x^23 + x^21 - x^20 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{57}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{57} - \cdots)$

Embedding invariants

Embedding label			944.1
Root			$0.993931 - 0.110008i$ of defining polynomial
Character	$\chi$	$=$	3997.944
Dual form			3997.1.ce.a.1266.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.427940 + 0.416307i) q^{2} +(-0.0177328 + 0.643311i) q^{4} +(0.789141 - 0.614213i) q^{7} +(-0.664583 - 0.721930i) q^{8} +(0.904357 - 0.426776i) q^{9} +O(q^{10})$	\(q+(-0.427940 + 0.416307i) q^{2} +(-0.0177328 + 0.643311i) q^{4} +(0.789141 - 0.614213i) q^{7} +(-0.664583 - 0.721930i) q^{8} +(0.904357 - 0.426776i) q^{9} +(1.52274 + 1.05585i) q^{11} +(-0.0820041 + 0.591371i) q^{14} +(-0.0576318 - 0.00317964i) q^{16} +(-0.209341 + 0.559125i) q^{18} +(-1.09120 + 0.182089i) q^{22} +(1.30345 - 1.41593i) q^{23} +(-0.754107 + 0.656752i) q^{25} +(0.381136 + 0.518555i) q^{28} +(-1.91286 + 0.211715i) q^{29} +(0.765955 - 0.667071i) q^{32} +(0.258513 + 0.589351i) q^{36} +(1.16832 - 1.58955i) q^{37} +(1.29645 + 0.611812i) q^{43} +(-0.706241 + 0.960876i) q^{44} +(0.0316601 + 1.14857i) q^{46} +(0.245485 - 0.969400i) q^{49} +(0.0493023 - 0.594990i) q^{50} +(-1.17807 - 1.14605i) q^{53} +(-0.967868 - 0.161509i) q^{56} +(0.730450 - 0.886936i) q^{58} +(0.451533 - 0.892254i) q^{63} +(-0.0453105 + 0.546816i) q^{64} +(-1.37947 + 0.390078i) q^{67} +(0.0825793 - 0.143032i) q^{71} +(-0.909124 - 0.369254i) q^{72} +(0.161771 + 1.16661i) q^{74} +(1.85017 - 0.102077i) q^{77} +(-0.508621 + 0.312648i) q^{79} +(0.635724 - 0.771917i) q^{81} +(-0.809507 + 0.277904i) q^{86} +(-0.249743 - 1.80101i) q^{88} +(0.887768 + 0.863634i) q^{92} +(0.298515 + 0.517043i) q^{98} +(1.82772 + 0.304992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 2 q^{7} - 21 q^{8} + q^{9}+O(q^{10}) $ 36 * q - q^2 - 2 * q^7 - 21 * q^8 + q^9	$ 36 q - q^{2} - 2 q^{7} - 21 q^{8} + q^{9} - q^{11} - q^{14} - q^{16} - q^{18} - 21 q^{22} + 2 q^{23} + q^{25} - q^{29} + 2 q^{37} - q^{43} + 39 q^{46} - 2 q^{49} + 2 q^{50} - q^{53} - 2 q^{56} + q^{58} + q^{63} - 21 q^{64} - 20 q^{67} + 2 q^{71} - 18 q^{72} + 36 q^{74} - q^{77} - q^{79} + q^{81} - 2 q^{86} - q^{88} - 19 q^{92} - q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - q^2 - 2 * q^7 - 21 * q^8 + q^9 - q^11 - q^14 - q^16 - q^18 - 21 * q^22 + 2 * q^23 + q^25 - q^29 + 2 * q^37 - q^43 + 39 * q^46 - 2 * q^49 + 2 * q^50 - q^53 - 2 * q^56 + q^58 + q^63 - 21 * q^64 - 20 * q^67 + 2 * q^71 - 18 * q^72 + 36 * q^74 - q^77 - q^79 + q^81 - 2 * q^86 - q^88 - 19 * q^92 - q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times$.

$n$	$1716$	$2285$
$\chi(n)$	$e\left(\frac{53}{57}\right)$	$-1$

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 $

$2$	−0.427940	+	0.416307i	−0.427940	+	0.416307i	−0.879474	−	0.475947i	$-0.842105\pi$
$2$	−0.427940	+	0.416307i	−0.427940	+	0.416307i	0.451533	+	0.892254i	$0.350877\pi$
$3$		0			0		0.975796	−	0.218681i	$-0.0701754\pi$
$3$		0			0		−0.975796	+	0.218681i	$0.929825\pi$
$4$	−0.0177328	+	0.643311i	−0.0177328	+	0.643311i
$5$		0			0		−0.350638	−	0.936511i	$-0.614035\pi$
$5$		0			0		0.350638	+	0.936511i	$0.385965\pi$
$6$		0			0
$7$	0.789141	−	0.614213i	0.789141	−	0.614213i
$7$	0.789141	−	0.614213i	0.789141	−	0.614213i
$8$	−0.664583	−	0.721930i	−0.664583	−	0.721930i
$9$	0.904357	−	0.426776i	0.904357	−	0.426776i
$10$		0			0
$11$	1.52274	+	1.05585i	1.52274	+	1.05585i	0.975796	+	0.218681i	$0.0701754\pi$
$11$	1.52274	+	1.05585i	1.52274	+	1.05585i	0.546948	+	0.837166i	$0.315789\pi$
$12$		0			0
$13$		0			0		−0.592235	−	0.805765i	$-0.701754\pi$
$13$		0			0		0.592235	+	0.805765i	$0.298246\pi$
$14$	−0.0820041	+	0.591371i	−0.0820041	+	0.591371i
$15$		0			0
$16$	−0.0576318	−	0.00317964i	−0.0576318	−	0.00317964i
$17$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$17$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$18$	−0.209341	+	0.559125i	−0.209341	+	0.559125i
$19$		0			0		0.975796	−	0.218681i	$-0.0701754\pi$
$19$		0			0		−0.975796	+	0.218681i	$0.929825\pi$
$20$		0			0
$21$		0			0
$22$	−1.09120	+	0.182089i	−1.09120	+	0.182089i
$23$	1.30345	−	1.41593i	1.30345	−	1.41593i	0.451533	−	0.892254i	$-0.350877\pi$
$23$	1.30345	−	1.41593i	1.30345	−	1.41593i	0.851919	−	0.523673i	$-0.175439\pi$
$24$		0			0
$25$	−0.754107	+	0.656752i	−0.754107	+	0.656752i
$26$		0			0
$27$		0			0
$28$	0.381136	+	0.518555i	0.381136	+	0.518555i
$29$	−1.91286	+	0.211715i	−1.91286	+	0.211715i	−0.986361	−	0.164595i	$-0.947368\pi$
$29$	−1.91286	+	0.211715i	−1.91286	+	0.211715i	−0.926494	+	0.376309i	$0.877193\pi$
$30$		0			0
$31$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$31$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$32$	0.765955	−	0.667071i	0.765955	−	0.667071i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.258513	+	0.589351i	0.258513	+	0.589351i
$37$	1.16832	−	1.58955i	1.16832	−	1.58955i	0.451533	−	0.892254i	$-0.350877\pi$
$37$	1.16832	−	1.58955i	1.16832	−	1.58955i	0.716783	−	0.697297i	$-0.245614\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.350638	−	0.936511i	$-0.614035\pi$
$41$		0			0		0.350638	+	0.936511i	$0.385965\pi$
$42$		0			0
$43$	1.29645	+	0.611812i	1.29645	+	0.611812i	0.945817	−	0.324699i	$-0.105263\pi$
$43$	1.29645	+	0.611812i	1.29645	+	0.611812i	0.350638	+	0.936511i	$0.385965\pi$
$44$	−0.706241	+	0.960876i	−0.706241	+	0.960876i
$45$		0			0
$46$	0.0316601	+	1.14857i	0.0316601	+	1.14857i
$47$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$47$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$48$		0			0
$49$	0.245485	−	0.969400i	0.245485	−	0.969400i
$50$	0.0493023	−	0.594990i	0.0493023	−	0.594990i
$51$		0			0
$52$		0			0
$53$	−1.17807	−	1.14605i	−1.17807	−	1.14605i	−0.986361	−	0.164595i	$-0.947368\pi$
$53$	−1.17807	−	1.14605i	−1.17807	−	1.14605i	−0.191711	−	0.981451i	$-0.561404\pi$
$54$		0			0
$55$		0			0
$56$	−0.967868	−	0.161509i	−0.967868	−	0.161509i
$57$		0			0
$58$	0.730450	−	0.886936i	0.730450	−	0.886936i
$59$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$59$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$60$		0			0
$61$		0			0		−0.962268	−	0.272103i	$-0.912281\pi$
$61$		0			0		0.962268	+	0.272103i	$0.0877193\pi$
$62$		0			0
$63$	0.451533	−	0.892254i	0.451533	−	0.892254i
$64$	−0.0453105	+	0.546816i	−0.0453105	+	0.546816i
$65$		0			0
$66$		0			0
$67$	−1.37947	+	0.390078i	−1.37947	+	0.390078i	−0.879474	−	0.475947i	$-0.842105\pi$
$67$	−1.37947	+	0.390078i	−1.37947	+	0.390078i	−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.0825793	−	0.143032i	0.0825793	−	0.143032i	−0.821778	−	0.569808i	$-0.807018\pi$
$71$	0.0825793	−	0.143032i	0.0825793	−	0.143032i	0.904357	+	0.426776i	$0.140351\pi$
$72$	−0.909124	−	0.369254i	−0.909124	−	0.369254i
$73$		0			0		−0.993931	−	0.110008i	$-0.964912\pi$
$73$		0			0		0.993931	+	0.110008i	$0.0350877\pi$
$74$	0.161771	+	1.16661i	0.161771	+	1.16661i
$75$		0			0
$76$		0			0
$77$	1.85017	−	0.102077i	1.85017	−	0.102077i
$78$		0			0
$79$	−0.508621	+	0.312648i	−0.508621	+	0.312648i	−0.754107	−	0.656752i	$-0.771930\pi$
$79$	−0.508621	+	0.312648i	−0.508621	+	0.312648i	0.245485	+	0.969400i	$0.421053\pi$
$80$		0			0
$81$	0.635724	−	0.771917i	0.635724	−	0.771917i
$82$		0			0
$83$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$83$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$84$		0			0
$85$		0			0
$86$	−0.809507	+	0.277904i	−0.809507	+	0.277904i
$87$		0			0
$88$	−0.249743	−	1.80101i	−0.249743	−	1.80101i
$89$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$89$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$90$		0			0
$91$		0			0
$92$	0.887768	+	0.863634i	0.887768	+	0.863634i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.0275543	−	0.999620i	$-0.491228\pi$
$97$		0			0		−0.0275543	+	0.999620i	$0.508772\pi$
$98$	0.298515	+	0.517043i	0.298515	+	0.517043i
$99$	1.82772	+	0.304992i	1.82772	+	0.304992i
$100$	−0.409124	−	0.496771i	−0.409124	−	0.496771i
$101$		0			0		−0.0275543	−	0.999620i	$-0.508772\pi$
$101$		0			0		0.0275543	+	0.999620i	$0.491228\pi$
$102$		0			0
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$		0			0
$105$		0			0
$106$	0.981251			0.981251
$107$	−1.57588	+	0.0869440i	−1.57588	+	0.0869440i	−0.821778	−	0.569808i	$-0.807018\pi$
$107$	−1.57588	+	0.0869440i	−1.57588	+	0.0869440i	−0.754107	+	0.656752i	$0.771930\pi$
$108$		0			0
$109$	−0.245485	+	0.425193i	−0.245485	+	0.425193i	−0.962268	−	0.272103i	$-0.912281\pi$
$109$	−0.245485	+	0.425193i	−0.245485	+	0.425193i	0.716783	+	0.697297i	$0.245614\pi$
$110$		0			0
$111$		0			0
$112$	−0.0474326	+	0.0328890i	−0.0474326	+	0.0328890i
$113$	1.18267	+	1.60908i	1.18267	+	1.60908i	0.635724	+	0.771917i	$0.280702\pi$
$113$	1.18267	+	1.60908i	1.18267	+	1.60908i	0.546948	+	0.837166i	$0.315789\pi$
$114$		0			0
$115$		0			0
$116$	−0.102278	−	1.23432i	−0.102278	−	1.23432i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.853299	+	2.27906i	0.853299	+	2.27906i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.178222	+	0.569808i	0.178222	+	0.569808i
$127$	1.71071	+	0.807305i	1.71071	+	0.807305i	0.993931	+	0.110008i	$0.0350877\pi$
$127$	1.71071	+	0.807305i	1.71071	+	0.807305i	0.716783	+	0.697297i	$0.245614\pi$
$128$	0.437459	+	0.531177i	0.437459	+	0.531177i
$129$		0			0
$130$		0			0
$131$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$131$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$132$		0			0
$133$		0			0
$134$	0.427940	−	0.741215i	0.427940	−	0.741215i
$135$		0			0
$136$		0			0
$137$	−0.207158	−	0.180414i	−0.207158	−	0.180414i	0.546948	−	0.837166i	$-0.315789\pi$
$137$	−0.207158	−	0.180414i	−0.207158	−	0.180414i	−0.754107	+	0.656752i	$0.771930\pi$
$138$		0			0
$139$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$139$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$140$		0			0
$141$		0			0
$142$	0.0242060	+	0.0955874i	0.0242060	+	0.0955874i
$143$		0			0
$144$	−0.0534768	+	0.0217204i	−0.0534768	+	0.0217204i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	1.00186	+	0.779778i	1.00186	+	0.779778i
$149$	−0.611630	−	0.664408i	−0.611630	−	0.664408i	0.350638	−	0.936511i	$-0.385965\pi$
$149$	−0.611630	−	0.664408i	−0.611630	−	0.664408i	−0.962268	+	0.272103i	$0.912281\pi$
$150$		0			0
$151$	−0.350638	+	0.936511i	−0.350638	+	0.936511i	0.635724	+	0.771917i	$0.280702\pi$
$151$	−0.350638	+	0.936511i	−0.350638	+	0.936511i	−0.986361	+	0.164595i	$0.947368\pi$
$152$		0			0
$153$		0			0
$154$	−0.749269	+	0.813923i	−0.749269	+	0.813923i
$155$		0			0
$156$		0			0
$157$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$157$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$158$	0.0875019	−	0.345537i	0.0875019	−	0.345537i
$159$		0			0
$160$		0			0
$161$	0.158927	−	1.91796i	0.158927	−	1.91796i
$162$	0.0493023	+	0.594990i	0.0493023	+	0.594990i
$163$	−0.130333	−	0.101443i	−0.130333	−	0.101443i	0.546948	−	0.837166i	$-0.315789\pi$
$163$	−0.130333	−	0.101443i	−0.130333	−	0.101443i	−0.677282	+	0.735724i	$0.736842\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		0			0
$169$	−0.298515	+	0.954405i	−0.298515	+	0.954405i
$170$		0			0
$171$		0			0
$172$	−0.416575	+	0.823175i	−0.416575	+	0.823175i
$173$		0			0		0.926494	−	0.376309i	$-0.122807\pi$
$173$		0			0		−0.926494	+	0.376309i	$0.877193\pi$
$174$		0			0
$175$	−0.191711	+	0.981451i	−0.191711	+	0.981451i
$176$	−0.0844013	−	0.0656922i	−0.0844013	−	0.0656922i
$177$		0			0
$178$		0			0
$179$	−1.74827	+	0.946117i	−1.74827	+	0.946117i	−0.821778	+	0.569808i	$0.807018\pi$
$179$	−1.74827	+	0.946117i	−1.74827	+	0.946117i	−0.926494	+	0.376309i	$0.877193\pi$
$180$		0			0
$181$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$181$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$182$		0			0
$183$		0			0
$184$	−1.88845			−1.88845
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.326644	+	0.200787i	−0.326644	+	0.200787i	−0.677282	−	0.735724i	$-0.736842\pi$
$191$	−0.326644	+	0.200787i	−0.326644	+	0.200787i	0.350638	+	0.936511i	$0.385965\pi$
$192$		0			0
$193$	0.998482	+	1.72942i	0.998482	+	1.72942i	0.546948	+	0.837166i	$0.315789\pi$
$193$	0.998482	+	1.72942i	0.998482	+	1.72942i	0.451533	+	0.892254i	$0.350877\pi$
$194$		0			0
$195$		0			0
$196$	0.619273	+	0.175114i	0.619273	+	0.175114i
$197$	−1.91286	+	0.211715i	−1.91286	+	0.211715i	−0.986361	−	0.164595i	$-0.947368\pi$
$197$	−1.91286	+	0.211715i	−1.91286	+	0.211715i	−0.926494	+	0.376309i	$0.877193\pi$
$198$	−0.909124	+	0.630372i	−0.909124	+	0.630372i
$199$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$199$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$200$	0.975296	+	0.107946i	0.975296	+	0.107946i
$201$		0			0
$202$		0			0
$203$	−1.37947	+	1.34197i	−1.37947	+	1.34197i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.574503	−	1.83679i	0.574503	−	1.83679i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.0469482	−	1.70319i	0.0469482	−	1.70319i	−0.500000	−	0.866025i	$-0.666667\pi$
$211$	0.0469482	−	1.70319i	0.0469482	−	1.70319i	0.546948	−	0.837166i	$-0.315789\pi$
$212$	0.758155	−	0.737544i	0.758155	−	0.737544i
$213$		0			0
$214$	0.638189	−	0.693258i	0.638189	−	0.693258i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.0719577	−	0.284155i	−0.0719577	−	0.284155i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$223$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$224$	0.194723	−	0.996872i	0.194723	−	0.996872i
$225$	−0.401695	+	0.915773i	−0.401695	+	0.915773i
$226$	−1.17599	−	0.196237i	−1.17599	−	0.196237i
$227$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$227$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$228$		0			0
$229$		0			0		0.137354	−	0.990522i	$-0.456140\pi$
$229$		0			0		−0.137354	+	0.990522i	$0.543860\pi$
$230$		0			0
$231$		0			0
$232$	1.42410	+	1.24025i	1.42410	+	1.24025i
$233$	0.854136	+	1.68782i	0.854136	+	1.68782i	0.716783	+	0.697297i	$0.245614\pi$
$233$	0.854136	+	1.68782i	0.854136	+	1.68782i	0.137354	+	0.990522i	$0.456140\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.07118	+	0.505504i	−1.07118	+	0.505504i	−0.879474	−	0.475947i	$-0.842105\pi$
$239$	−1.07118	+	0.505504i	−1.07118	+	0.505504i	−0.191711	+	0.981451i	$0.561404\pi$
$240$		0			0
$241$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$241$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$242$	−1.31395	−	0.620068i	−1.31395	−	0.620068i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$251$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$252$	0.565990	+	0.306299i	0.565990	+	0.306299i
$253$	3.47983	−	0.779848i	3.47983	−	0.779848i
$254$	−1.06817	+	0.366703i	−1.06817	+	0.366703i
$255$		0			0
$256$	−0.953699	−	0.105555i	−0.953699	−	0.105555i
$257$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$257$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$258$		0			0
$259$	−0.0543571	−	1.97197i	−0.0543571	−	1.97197i
$260$		0			0
$261$	−1.63955	+	1.00783i	−1.63955	+	1.00783i
$262$		0			0
$263$	−0.0221369	−	0.803086i	−0.0221369	−	0.803086i	−0.926494	−	0.376309i	$-0.877193\pi$
$263$	−0.0221369	−	0.803086i	−0.0221369	−	0.803086i	0.904357	−	0.426776i	$-0.140351\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.226480	−	0.894348i	−0.226480	−	0.894348i
$269$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$269$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$270$		0			0
$271$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$271$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$272$		0			0
$273$		0			0
$274$	0.163759	−	0.00903485i	0.163759	−	0.00903485i
$275$	−1.84174	+	0.203844i	−1.84174	+	0.203844i
$276$		0			0
$277$	0.917421	+	0.996584i	0.917421	+	0.996584i	1.00000			$0$
$277$	0.917421	+	0.996584i	0.917421	+	0.996584i	−0.0825793	+	0.996584i	$0.526316\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.0521227	+	0.0178938i	0.0521227	+	0.0178938i	0.350638	−	0.936511i	$-0.385965\pi$
$281$	0.0521227	+	0.0178938i	0.0521227	+	0.0178938i	−0.298515	+	0.954405i	$0.596491\pi$
$282$		0			0
$283$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$283$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$284$	0.0905495	+	0.0556606i	0.0905495	+	0.0556606i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.408007	−	0.930162i	0.408007	−	0.930162i
$289$	0.993931	+	0.110008i	0.993931	+	0.110008i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.191711	−	0.981451i	$-0.438596\pi$
$293$		0			0		−0.191711	+	0.981451i	$0.561404\pi$
$294$		0			0
$295$		0			0
$296$	−1.92399	+	0.212947i	−1.92399	+	0.212947i
$297$		0			0
$298$	0.538339	+	0.0297010i	0.538339	+	0.0297010i
$299$		0			0
$300$		0			0
$301$	1.39887	−	0.313494i	1.39887	−	0.313494i
$302$	−0.239824	−	0.546744i	−0.239824	−	0.546744i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.350638	−	0.936511i	$-0.614035\pi$
$307$		0			0		0.350638	+	0.936511i	$0.385965\pi$
$308$	0.0328586	+	1.19205i	0.0328586	+	1.19205i
$309$		0			0
$310$		0			0
$311$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$311$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$312$		0			0
$313$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$313$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$314$		0			0
$315$		0			0
$316$	−0.192111	−	0.332746i	−0.192111	−	0.332746i
$317$	−1.82026	+	0.624896i	−1.82026	+	0.624896i	−0.821778	+	0.569808i	$0.807018\pi$
$317$	−1.82026	+	0.624896i	−1.82026	+	0.624896i	−0.998482	+	0.0550878i	$0.982456\pi$
$318$		0			0
$319$	−3.13633	−	1.69730i	−3.13633	−	1.69730i
$320$		0			0
$321$		0			0
$322$	0.730450	+	0.886936i	0.730450	+	0.886936i
$323$		0			0
$324$	0.485310	+	0.422656i	0.485310	+	0.422656i
$325$		0			0
$326$	0.0980062	−	0.0108473i	0.0980062	−	0.0108473i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.677282	+	1.17309i	0.677282	+	1.17309i	0.975796	+	0.218681i	$0.0701754\pi$
$331$	0.677282	+	1.17309i	0.677282	+	1.17309i	−0.298515	+	0.954405i	$0.596491\pi$
$332$		0			0
$333$	0.378192	−	1.93613i	0.378192	−	1.93613i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.868992	+	0.245728i	−0.868992	+	0.245728i	−0.677282	−	0.735724i	$-0.736842\pi$
$337$	−0.868992	+	0.245728i	−0.868992	+	0.245728i	−0.191711	+	0.981451i	$0.561404\pi$
$338$	−0.269579	−	0.532702i	−0.269579	−	0.532702i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.401695	−	0.915773i	−0.401695	−	0.915773i
$344$	−0.419917	−	1.34255i	−0.419917	−	1.34255i
$345$		0			0
$346$		0			0
$347$	0.259684	−	1.32944i	0.259684	−	1.32944i	−0.592235	−	0.805765i	$-0.701754\pi$
$347$	0.259684	−	1.32944i	0.259684	−	1.32944i	0.851919	−	0.523673i	$-0.175439\pi$
$348$		0			0
$349$		0			0		−0.350638	−	0.936511i	$-0.614035\pi$
$349$		0			0		0.350638	+	0.936511i	$0.385965\pi$
$350$	−0.326544	−	0.499813i	−0.326544	−	0.499813i
$351$		0			0
$352$	1.87068	−	0.207047i	1.87068	−	0.207047i
$353$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$353$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.354281	−	1.13270i	0.354281	−	1.13270i
$359$	0.351919	−	0.342352i	0.351919	−	0.342352i	−0.500000	−	0.866025i	$-0.666667\pi$
$359$	0.351919	−	0.342352i	0.351919	−	0.342352i	0.851919	+	0.523673i	$0.175439\pi$
$360$		0			0
$361$	0.904357	−	0.426776i	0.904357	−	0.426776i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.137354	−	0.990522i	$-0.543860\pi$
$367$		0			0		0.137354	+	0.990522i	$0.456140\pi$
$368$	−0.0796225	+	0.0774580i	−0.0796225	+	0.0774580i
$369$		0			0
$370$		0			0
$371$	−1.63358	−	0.180805i	−1.63358	−	0.180805i
$372$		0			0
$373$	1.11315	−	0.771841i	1.11315	−	0.771841i	0.137354	−	0.990522i	$-0.456140\pi$
$373$	1.11315	−	0.771841i	1.11315	−	0.771841i	0.975796	+	0.218681i	$0.0701754\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.254515	−	1.83543i	−0.254515	−	1.83543i	−0.500000	−	0.866025i	$-0.666667\pi$
$379$	−0.254515	−	1.83543i	−0.254515	−	1.83543i	0.245485	−	0.969400i	$-0.421053\pi$
$380$		0			0
$381$		0			0
$382$	0.0561950	−	0.221909i	0.0561950	−	0.221909i
$383$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$383$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$384$		0			0
$385$		0			0
$386$	−1.14726	−	0.324414i	−1.14726	−	0.324414i
$387$	1.43357			1.43357
$388$		0			0
$389$	0.337209	−	0.182488i	0.337209	−	0.182488i	−0.298515	−	0.954405i	$-0.596491\pi$
$389$	0.337209	−	0.182488i	0.337209	−	0.182488i	0.635724	+	0.771917i	$0.280702\pi$
$390$		0			0
$391$		0			0
$392$	−0.862985	+	0.467024i	−0.862985	+	0.467024i
$393$		0			0
$394$	0.730450	−	0.886936i	0.730450	−	0.886936i
$395$		0			0
$396$	−0.228615	+	1.17038i	−0.228615	+	1.17038i
$397$		0			0		0.451533	−	0.892254i	$-0.350877\pi$
$397$		0			0		−0.451533	+	0.892254i	$0.649123\pi$
$398$		0			0
$399$		0			0
$400$	0.0455488	−	0.0354520i	0.0455488	−	0.0354520i
$401$	−1.49848	−	0.810938i	−1.49848	−	0.810938i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−1.49848	−	0.810938i	−1.49848	−	0.810938i	−0.998482	+	0.0550878i	$0.982456\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.0316601	−	1.14857i	0.0316601	−	1.14857i
$407$	3.45737	−	1.18692i	3.45737	−	1.18692i
$408$		0			0
$409$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$409$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.518814	+	1.02520i	0.518814	+	1.02520i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$419$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$420$		0			0
$421$	0.273040	+	1.96902i	0.273040	+	1.96902i	0.245485	+	0.969400i	$0.421053\pi$
$421$	0.273040	+	1.96902i	0.273040	+	1.96902i	0.0275543	+	0.999620i	$0.491228\pi$
$422$	0.688959	+	0.748409i	0.688959	+	0.748409i
$423$		0			0
$424$	−0.0444380	+	1.61213i	−0.0444380	+	1.61213i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.0279873	−	1.01533i	−0.0279873	−	1.01533i
$429$		0			0
$430$		0			0
$431$	1.06742	−	1.63381i	1.06742	−	1.63381i	0.350638	−	0.936511i	$-0.385965\pi$
$431$	1.06742	−	1.63381i	1.06742	−	1.63381i	0.716783	−	0.697297i	$-0.245614\pi$
$432$		0			0
$433$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$433$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$434$		0			0
$435$		0			0
$436$	−0.269179	−	0.165463i	−0.269179	−	0.165463i
$437$		0			0
$438$		0			0
$439$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$439$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$440$		0			0
$441$	−0.191711	−	0.981451i	−0.191711	−	0.981451i
$442$		0			0
$443$	−1.17799	−	1.43035i	−1.17799	−	1.43035i	−0.879474	−	0.475947i	$-0.842105\pi$
$443$	−1.17799	−	1.43035i	−1.17799	−	1.43035i	−0.298515	−	0.954405i	$-0.596491\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.300105	+	0.459345i	0.300105	+	0.459345i
$449$	1.75628	−	0.950449i	1.75628	−	0.950449i	0.851919	−	0.523673i	$-0.175439\pi$
$449$	1.75628	−	0.950449i	1.75628	−	0.950449i	0.904357	−	0.426776i	$-0.140351\pi$
$450$	−0.209341	−	0.559125i	−0.209341	−	0.559125i
$451$		0			0
$452$	−1.05611	+	0.732293i	−1.05611	+	0.732293i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.691711	+	1.84748i	−0.691711	+	1.84748i	−0.191711	+	0.981451i	$0.561404\pi$
$457$	−0.691711	+	1.84748i	−0.691711	+	1.84748i	−0.500000	+	0.866025i	$0.666667\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$461$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$462$		0			0
$463$	−0.752996	−	1.02449i	−0.752996	−	1.02449i	−0.998482	−	0.0550878i	$-0.982456\pi$
$463$	−0.752996	−	1.02449i	−0.752996	−	1.02449i	0.245485	−	0.969400i	$-0.421053\pi$
$464$	0.110915	−	0.00611933i	0.110915	−	0.00611933i
$465$		0			0
$466$	−1.06817	−	0.366703i	−1.06817	−	0.366703i
$467$		0			0		0.191711	−	0.981451i	$-0.438596\pi$
$467$		0			0		−0.191711	+	0.981451i	$0.561404\pi$
$468$		0			0
$469$	−0.849008	+	1.15512i	−0.849008	+	1.15512i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.32819	+	2.30049i	1.32819	+	2.30049i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.55450	−	0.533662i	−1.55450	−	0.533662i
$478$	0.247958	−	0.662267i	0.247958	−	0.662267i
$479$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$479$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.48128	+	0.508523i	−1.48128	+	0.508523i
$485$		0			0
$486$		0			0
$487$	1.02149	+	0.889612i	1.02149	+	0.889612i	0.993931	−	0.110008i	$-0.0350877\pi$
$487$	1.02149	+	0.889612i	1.02149	+	0.889612i	0.0275543	+	0.999620i	$0.491228\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.588887	+	1.88278i	0.588887	+	1.88278i	0.451533	+	0.892254i	$0.350877\pi$
$491$	0.588887	+	1.88278i	0.588887	+	1.88278i	0.137354	+	0.990522i	$0.456140\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.0226851	−	0.163593i	−0.0226851	−	0.163593i
$498$		0			0
$499$	−0.254515	−	0.103375i	−0.254515	−	0.103375i	0.245485	−	0.969400i	$-0.421053\pi$
$499$	−0.254515	−	0.103375i	−0.254515	−	0.103375i	−0.500000	+	0.866025i	$0.666667\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$503$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$504$	−0.944227	+	0.267002i	−0.944227	+	0.267002i
$505$		0			0
$506$	−1.16450	+	1.78240i	−1.16450	+	1.78240i
$507$		0			0
$508$	−0.549684	+	1.08621i	−0.549684	+	1.08621i
$509$		0			0		−0.191711	−	0.981451i	$-0.561404\pi$
$509$		0			0		0.191711	+	0.981451i	$0.438596\pi$
$510$		0			0
$511$		0			0
$512$	−0.0909592	+	0.0707964i	−0.0909592	+	0.0707964i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.844208	+	0.821258i	0.844208	+	0.821258i
$519$		0			0
$520$		0			0
$521$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$521$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$522$	0.282064	−	1.11385i	0.282064	−	1.11385i
$523$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$523$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$524$		0			0
$525$		0			0
$526$	0.343803	+	0.334457i	0.343803	+	0.334457i
$527$		0			0
$528$		0			0
$529$	−0.223281	−	2.69460i	−0.223281	−	2.69460i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	1.19838	+	0.736644i	1.19838	+	0.736644i
$537$		0			0
$538$		0			0
$539$	1.39735	−	1.21695i	1.39735	−	1.21695i
$540$		0			0
$541$	−1.47171	−	0.329818i	−1.47171	−	0.329818i	−0.592235	−	0.805765i	$-0.701754\pi$
$541$	−1.47171	−	0.329818i	−1.47171	−	0.329818i	−0.879474	+	0.475947i	$0.842105\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.64356	−	1.13962i	−1.64356	−	1.13962i	−0.821778	−	0.569808i	$-0.807018\pi$
$547$	−1.64356	−	1.13962i	−1.64356	−	1.13962i	−0.821778	−	0.569808i	$-0.807018\pi$
$548$	0.119736	−	0.130068i	0.119736	−	0.130068i
$549$		0			0
$550$	0.703294	−	0.853963i	0.703294	−	0.853963i
$551$		0			0
$552$		0			0
$553$	−0.209341	+	0.559125i	−0.209341	+	0.559125i
$554$	−0.807486	−	0.0445503i	−0.807486	−	0.0445503i
$555$		0			0
$556$		0			0
$557$	0.196905	−	1.41998i	0.196905	−	1.41998i	−0.592235	−	0.805765i	$-0.701754\pi$
$557$	0.196905	−	1.41998i	0.196905	−	1.41998i	0.789141	−	0.614213i	$-0.210526\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.0297547	+	0.0140416i	−0.0297547	+	0.0140416i
$563$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$563$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.0275543	−	0.999620i	0.0275543	−	0.999620i
$568$	−0.158140	+	0.0354399i	−0.158140	+	0.0354399i
$569$	−1.08106	+	1.05167i	−1.08106	+	1.05167i	−0.0825793	+	0.996584i	$0.526316\pi$
$569$	−1.08106	+	1.05167i	−1.08106	+	1.05167i	−0.998482	+	0.0550878i	$0.982456\pi$
$570$		0			0
$571$	−0.998482	−	0.0550878i	−0.998482	−	0.0550878i
$571$	−0.998482	−	0.0550878i	−0.998482	−	0.0550878i
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.0530293	+	1.92381i	−0.0530293	+	1.92381i
$576$	0.192391	+	0.513855i	0.192391	+	0.513855i
$577$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$577$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$578$	−0.471140	+	0.366703i	−0.471140	+	0.366703i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.583853	−	2.98900i	−0.583853	−	2.98900i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$587$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.0723864	+	0.0878939i	−0.0723864	+	0.0878939i
$593$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$593$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$594$		0			0
$595$		0			0
$596$	0.438267	−	0.381687i	0.438267	−	0.381687i
$597$		0			0
$598$		0			0
$599$	−1.07118	−	1.45740i	−1.07118	−	1.45740i	−0.879474	−	0.475947i	$-0.842105\pi$
$599$	−1.07118	−	1.45740i	−1.07118	−	1.45740i	−0.191711	−	0.981451i	$-0.561404\pi$
$600$		0			0
$601$		0			0		−0.975796	−	0.218681i	$-0.929825\pi$
$601$		0			0		0.975796	+	0.218681i	$0.0701754\pi$
$602$	−0.468122	+	0.716515i	−0.468122	+	0.716515i
$603$	−1.08106	+	0.941497i	−1.08106	+	0.941497i
$604$	−0.596250	−	0.242176i	−0.596250	−	0.242176i
$605$		0			0
$606$		0			0
$607$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$607$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.145253	+	1.75294i	0.145253	+	1.75294i	0.546948	+	0.837166i	$0.315789\pi$
$613$	0.145253	+	1.75294i	0.145253	+	1.75294i	−0.401695	+	0.915773i	$0.631579\pi$
$614$		0			0
$615$		0			0
$616$	−1.30329	−	1.26786i	−1.30329	−	1.26786i
$617$	−0.0415578	−	1.50764i	−0.0415578	−	1.50764i	−0.677282	−	0.735724i	$-0.736842\pi$
$617$	−0.0415578	−	1.50764i	−0.0415578	−	1.50764i	0.635724	−	0.771917i	$-0.280702\pi$
$618$		0			0
$619$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$619$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.137354	−	0.990522i	0.137354	−	0.990522i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.234028	−	0.143857i	0.234028	−	0.143857i	−0.401695	−	0.915773i	$-0.631579\pi$
$631$	0.234028	−	0.143857i	0.234028	−	0.143857i	0.635724	+	0.771917i	$0.280702\pi$
$632$	0.563731	+	0.159408i	0.563731	+	0.159408i
$633$		0			0
$634$	0.518814	−	1.02520i	0.518814	−	1.02520i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	2.04876	−	0.579333i	2.04876	−	0.579333i
$639$	0.0136387	−	0.164595i	0.0136387	−	0.164595i
$640$		0			0
$641$	−0.582579	+	0.130559i	−0.582579	+	0.130559i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	−0.582579	+	0.130559i	−0.582579	+	0.130559i	−0.0825793	+	0.996584i	$0.526316\pi$
$642$		0			0
$643$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$643$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$644$	1.23103	+	0.136250i	1.23103	+	0.136250i
$645$		0			0
$646$		0			0
$647$		0			0		−0.191711	−	0.981451i	$-0.561404\pi$
$647$		0			0		0.191711	+	0.981451i	$0.438596\pi$
$648$	−0.979761	+	0.0540549i	−0.979761	+	0.0540549i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.0675703	−	0.0820461i	0.0675703	−	0.0820461i
$653$	−1.36396	−	0.643670i	−1.36396	−	0.643670i	−0.401695	−	0.915773i	$-0.631579\pi$
$653$	−1.36396	−	0.643670i	−1.36396	−	0.643670i	−0.962268	+	0.272103i	$0.912281\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.0377320	+	0.272103i	0.0377320	+	0.272103i	1.00000			$0$
$659$	0.0377320	+	0.272103i	0.0377320	+	0.272103i	−0.962268	+	0.272103i	$0.912281\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	−0.778200	−	0.220054i	−0.778200	−	0.220054i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.644181	+	0.985993i	0.644181	+	0.985993i
$667$	−2.19354	+	2.98442i	−2.19354	+	2.98442i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.973372	−	1.32432i	0.973372	−	1.32432i	0.0275543	−	0.999620i	$-0.491228\pi$
$673$	0.973372	−	1.32432i	0.973372	−	1.32432i	0.945817	−	0.324699i	$-0.105263\pi$
$674$	0.269579	−	0.466924i	0.269579	−	0.466924i
$675$		0			0
$676$	−0.608686	−	0.208962i	−0.608686	−	0.208962i
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.60378	+	1.11203i	−1.60378	+	1.11203i	−0.677282	+	0.735724i	$0.736842\pi$
$683$	−1.60378	+	1.11203i	−1.60378	+	1.11203i	−0.926494	+	0.376309i	$0.877193\pi$
$684$		0			0
$685$		0			0
$686$	0.553144	+	0.224668i	0.553144	+	0.224668i
$687$		0			0
$688$	−0.0727717	−	0.0393821i	−0.0727717	−	0.0393821i
$689$		0			0
$690$		0			0
$691$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$691$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$692$		0			0
$693$	1.62965	−	0.881925i	1.62965	−	0.881925i
$694$	0.442325	+	0.677029i	0.442325	+	0.677029i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.627979	−	0.140733i	−0.627979	−	0.140733i
$701$	0.289141	+	1.48024i	0.289141	+	1.48024i	0.789141	+	0.614213i	$0.210526\pi$
$701$	0.289141	+	1.48024i	0.289141	+	1.48024i	−0.500000	+	0.866025i	$0.666667\pi$
$702$		0			0
$703$		0			0
$704$	−0.646351	+	0.784821i	−0.646351	+	0.784821i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.0941244	−	0.371689i	−0.0941244	−	0.371689i	0.904357	−	0.426776i	$-0.140351\pi$
$709$	−0.0941244	−	0.371689i	−0.0941244	−	0.371689i	−0.998482	+	0.0550878i	$0.982456\pi$
$710$		0			0
$711$	−0.326544	+	0.499813i	−0.326544	+	0.499813i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.577646	−	1.14146i	−0.577646	−	1.14146i
$717$		0			0
$718$	−0.00807684	+	0.293013i	−0.00807684	+	0.293013i
$719$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$719$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$720$		0			0
$721$		0			0
$722$	−0.209341	+	0.559125i	−0.209341	+	0.559125i
$723$		0			0
$724$		0			0
$725$	1.30345	−	1.41593i	1.30345	−	1.41593i
$726$		0			0
$727$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$727$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$728$		0			0
$729$	0.245485	−	0.969400i	0.245485	−	0.969400i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$733$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$734$		0			0
$735$		0			0
$736$	0.0538625	−	1.95403i	0.0538625	−	1.95403i
$737$	−2.51245	−	0.862525i	−2.51245	−	0.862525i
$738$		0			0
$739$	−1.98484	+	0.109507i	−1.98484	+	0.109507i	−0.998482	−	0.0550878i	$-0.982456\pi$
$739$	−1.98484	+	0.109507i	−1.98484	+	0.109507i	−0.986361	+	0.164595i	$0.947368\pi$
$740$		0			0
$741$		0			0
$742$	0.774345	−	0.602697i	0.774345	−	0.602697i
$743$	−0.794223	+	1.56943i	−0.794223	+	1.56943i	0.0275543	+	0.999620i	$0.491228\pi$
$743$	−0.794223	+	1.56943i	−0.794223	+	1.56943i	−0.821778	+	0.569808i	$0.807018\pi$
$744$		0			0
$745$		0			0
$746$	−0.155039	+	0.793714i	−0.155039	+	0.793714i
$747$		0			0
$748$		0			0
$749$	−1.19019	+	1.03654i	−1.19019	+	1.03654i
$750$		0			0
$751$	−0.575857	+	0.560202i	−0.575857	+	0.560202i	−0.926494	−	0.376309i	$-0.877193\pi$
$751$	−0.575857	+	0.560202i	−0.575857	+	0.560202i	0.350638	+	0.936511i	$0.385965\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.322718	+	0.735724i	0.322718	+	0.735724i	1.00000			$0$
$757$	0.322718	+	0.735724i	0.322718	+	0.735724i	−0.677282	+	0.735724i	$0.736842\pi$
$758$	0.873017	+	0.679497i	0.873017	+	0.679497i
$759$		0			0
$760$		0			0
$761$		0			0		−0.975796	−	0.218681i	$-0.929825\pi$
$761$		0			0		0.975796	+	0.218681i	$0.0701754\pi$
$762$		0			0
$763$	0.0674366	+	0.486318i	0.0674366	+	0.486318i
$764$	−0.123376	−	0.213694i	−0.123376	−	0.213694i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$769$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$770$		0			0
$771$		0			0
$772$	−1.13026	+	0.611667i	−1.13026	+	0.611667i
$773$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$773$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$774$	−0.613480	+	0.596803i	−0.613480	+	0.596803i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.0683342	+	0.218477i	−0.0683342	+	0.218477i
$779$		0			0
$780$		0			0
$781$	0.276767	−	0.130609i	0.276767	−	0.130609i
$782$		0			0
$783$		0			0
$784$	−0.0172301	+	0.0550878i	−0.0172301	+	0.0550878i
$785$		0			0
$786$		0			0
$787$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$787$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$788$	−0.102278	−	1.23432i	−0.102278	−	1.23432i
$789$		0			0
$790$		0			0
$791$	1.92161	+	0.543381i	1.92161	+	0.543381i
$792$	−0.994487	−	1.52218i	−0.994487	−	1.52218i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$797$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$798$		0			0
$799$		0			0
$800$	−0.139512	+	1.00608i	−0.139512	+	1.00608i
$801$		0			0
$802$	0.978860	−	0.276795i	0.978860	−	0.276795i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.346750	+	1.77517i	−0.346750	+	1.77517i	0.245485	+	0.969400i	$0.421053\pi$
$809$	−0.346750	+	1.77517i	−0.346750	+	1.77517i	−0.592235	+	0.805765i	$0.701754\pi$
$810$		0			0
$811$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$811$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$812$	−0.838844	−	0.911228i	−0.838844	−	0.911228i
$813$		0			0
$814$	−0.985427	+	1.94726i	−0.985427	+	1.94726i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.92161	−	0.543381i	1.92161	−	0.543381i	0.945817	−	0.324699i	$-0.105263\pi$
$821$	1.92161	−	0.543381i	1.92161	−	0.543381i	0.975796	−	0.218681i	$-0.0701754\pi$
$822$		0			0
$823$	−1.71637	−	0.928855i	−1.71637	−	0.928855i	−0.962268	−	0.272103i	$-0.912281\pi$
$823$	−1.71637	−	0.928855i	−1.71637	−	0.928855i	−0.754107	−	0.656752i	$-0.771930\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.42486	+	0.157704i	1.42486	+	0.157704i	0.789141	−	0.614213i	$-0.210526\pi$
$827$	1.42486	+	0.157704i	1.42486	+	0.157704i	0.635724	+	0.771917i	$0.280702\pi$
$828$	1.17144	+	0.402155i	1.17144	+	0.402155i
$829$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$829$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$839$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$840$		0			0
$841$	2.63840	−	0.591278i	2.63840	−	0.591278i
$842$	−0.936562	−	0.728955i	−0.936562	−	0.728955i
$843$		0			0
$844$	1.09485	+	0.0604046i	1.09485	+	0.0604046i
$845$		0			0
$846$		0			0
$847$	2.07320	+	1.27439i	2.07320	+	1.27439i
$848$	0.0642504	+	0.0697946i	0.0642504	+	0.0697946i
$849$		0			0
$850$		0			0
$851$	−0.727844	−	3.72615i	−0.727844	−	3.72615i
$852$		0			0
$853$		0			0		−0.993931	−	0.110008i	$-0.964912\pi$
$853$		0			0		0.993931	+	0.110008i	$0.0350877\pi$
$854$		0			0
$855$		0			0
$856$	1.11007	+	1.07990i	1.11007	+	1.07990i
$857$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$857$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$858$		0			0
$859$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$859$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$860$		0			0
$861$		0			0
$862$	0.223373	+	1.14355i	0.223373	+	1.14355i
$863$	0.234028	−	1.68769i	0.234028	−	1.68769i	−0.401695	−	0.915773i	$-0.631579\pi$
$863$	0.234028	−	1.68769i	0.234028	−	1.68769i	0.635724	−	0.771917i	$-0.280702\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.10461	−	0.0609430i	−1.10461	−	0.0609430i
$870$		0			0
$871$		0			0
$872$	0.470105	−	0.105353i	0.470105	−	0.105353i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.706561	−	1.61080i	0.706561	−	1.61080i	−0.0825793	−	0.996584i	$-0.526316\pi$
$877$	0.706561	−	1.61080i	0.706561	−	1.61080i	0.789141	−	0.614213i	$-0.210526\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$881$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$882$	0.490626	+	0.340192i	0.490626	+	0.340192i
$883$	−0.0275543	−	0.999620i	−0.0275543	−	0.999620i	−0.879474	−	0.475947i	$-0.842105\pi$
$883$	−0.0275543	−	0.999620i	−0.0275543	−	0.999620i	0.851919	−	0.523673i	$-0.175439\pi$
$884$		0			0
$885$		0			0
$886$	1.09957	+	0.121701i	1.09957	+	0.121701i
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$	1.84585	−	0.413665i	1.84585	−	0.413665i
$890$		0			0
$891$	1.78307	−	0.504204i	1.78307	−	0.504204i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.671472	+	0.150480i	0.671472	+	0.150480i
$897$		0			0
$898$	−0.355903	+	1.13789i	−0.355903	+	1.13789i
$899$		0			0
$900$	−0.582004	−	0.274654i	−0.582004	−	0.274654i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.375661	−	1.92318i	0.375661	−	1.92318i
$905$		0			0
$906$		0			0
$907$	−0.474961	+	0.515945i	−0.474961	+	0.515945i	−0.926494	−	0.376309i	$-0.877193\pi$
$907$	−0.474961	+	0.515945i	−0.474961	+	0.515945i	0.451533	+	0.892254i	$0.350877\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.472446	+	0.133595i	−0.472446	+	0.133595i	−0.500000	−	0.866025i	$-0.666667\pi$
$911$	−0.472446	+	0.133595i	−0.472446	+	0.133595i	0.0275543	+	0.999620i	$0.491228\pi$
$912$		0			0
$913$		0			0
$914$	−0.473106	−	1.07857i	−0.473106	−	1.07857i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.239824	+	0.766760i	0.239824	+	0.766760i	0.993931	+	0.110008i	$0.0350877\pi$
$919$	0.239824	+	0.766760i	0.239824	+	0.766760i	−0.754107	+	0.656752i	$0.771930\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.162906	+	1.96598i	0.162906	+	1.96598i
$926$	0.748739	+	0.124942i	0.748739	+	0.124942i
$927$		0			0
$928$	−1.32393	+	1.43817i	−1.32393	+	1.43817i
$929$		0			0		0.298515	−	0.954405i	$-0.403509\pi$
$929$		0			0		−0.298515	+	0.954405i	$0.596491\pi$
$930$		0			0
$931$		0			0
$932$	−1.10094	+	0.519546i	−1.10094	+	0.519546i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$937$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$938$	−0.117558	−	0.847769i	−0.117558	−	0.847769i
$939$		0			0
$940$		0			0
$941$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$941$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−1.52610	−	0.431539i	−1.52610	−	0.431539i
$947$	0.445817	−	1.19072i	0.445817	−	1.19072i	−0.500000	−	0.866025i	$-0.666667\pi$
$947$	0.445817	−	1.19072i	0.445817	−	1.19072i	0.945817	−	0.324699i	$-0.105263\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.0941244	+	0.371689i	−0.0941244	+	0.371689i	−0.998482	−	0.0550878i	$-0.982456\pi$
$953$	−0.0941244	+	0.371689i	−0.0941244	+	0.371689i	0.904357	+	0.426776i	$0.140351\pi$
$954$	0.887402	−	0.418775i	0.887402	−	0.418775i
$955$		0			0
$956$	−0.306201	−	0.698069i	−0.306201	−	0.698069i
$957$		0			0
$958$		0			0
$959$	−0.274290	−	0.0151330i	−0.274290	−	0.0151330i
$960$		0			0
$961$	−0.401695	−	0.915773i	−0.401695	−	0.915773i
$962$		0			0
$963$	−1.38806	+	0.751179i	−1.38806	+	0.751179i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.191711	−	0.981451i	0.191711	−	0.981451i	−0.754107	−	0.656752i	$-0.771930\pi$
$967$	0.191711	−	0.981451i	0.191711	−	0.981451i	0.945817	−	0.324699i	$-0.105263\pi$
$968$	1.07823	−	2.13065i	1.07823	−	2.13065i
$969$		0			0
$970$		0			0
$971$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$971$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$972$		0			0
$973$		0			0
$974$	−0.807486	+	0.0445503i	−0.807486	+	0.0445503i
$975$		0			0
$976$		0			0
$977$	0.0135284	−	0.490785i	0.0135284	−	0.490785i	−0.962268	−	0.272103i	$-0.912281\pi$
$977$	0.0135284	−	0.490785i	0.0135284	−	0.490785i	0.975796	−	0.218681i	$-0.0701754\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.0405441	+	0.489294i	−0.0405441	+	0.489294i
$982$	−1.03582	−	0.560558i	−1.03582	−	0.560558i
$983$		0			0		−0.851919	−	0.523673i	$-0.824561\pi$
$983$		0			0		0.851919	+	0.523673i	$0.175439\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.55615	−	1.03822i	2.55615	−	1.03822i
$990$		0			0
$991$	0.0963226	−	0.257266i	0.0963226	−	0.257266i	−0.879474	−	0.475947i	$-0.842105\pi$
$991$	0.0963226	−	0.257266i	0.0963226	−	0.257266i	0.975796	+	0.218681i	$0.0701754\pi$
$992$		0			0
$993$		0			0
$994$	0.0778129	+	0.0605642i	0.0778129	+	0.0605642i
$995$		0			0
$996$		0			0
$997$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$997$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$998$	0.151953	−	0.0617179i	0.151953	−	0.0617179i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3997.1.ce.a.944.1	✓	36
7.6	odd	2	CM	3997.1.ce.a.944.1	✓	36
571.124	even	57	inner	3997.1.ce.a.1266.1	yes	36
3997.1266	odd	114	inner	3997.1.ce.a.1266.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3997.1.ce.a.944.1	✓	36	1.1	even	1	trivial
3997.1.ce.a.944.1	✓	36	7.6	odd	2	CM
3997.1.ce.a.1266.1	yes	36	571.124	even	57	inner
3997.1.ce.a.1266.1	yes	36	3997.1266	odd	114	inner

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:	\( N \)	\(=\)	\( 3997 = 7 \cdot 571 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3997.ce (of order \(114\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.427940 + 0.416307i) q^{2} +(-0.0177328 + 0.643311i) q^{4} +(0.789141 - 0.614213i) q^{7} +(-0.664583 - 0.721930i) q^{8} +(0.904357 - 0.426776i) q^{9} +O(q^{10})\)	\(q+(-0.427940 + 0.416307i) q^{2} +(-0.0177328 + 0.643311i) q^{4} +(0.789141 - 0.614213i) q^{7} +(-0.664583 - 0.721930i) q^{8} +(0.904357 - 0.426776i) q^{9} +(1.52274 + 1.05585i) q^{11} +(-0.0820041 + 0.591371i) q^{14} +(-0.0576318 - 0.00317964i) q^{16} +(-0.209341 + 0.559125i) q^{18} +(-1.09120 + 0.182089i) q^{22} +(1.30345 - 1.41593i) q^{23} +(-0.754107 + 0.656752i) q^{25} +(0.381136 + 0.518555i) q^{28} +(-1.91286 + 0.211715i) q^{29} +(0.765955 - 0.667071i) q^{32} +(0.258513 + 0.589351i) q^{36} +(1.16832 - 1.58955i) q^{37} +(1.29645 + 0.611812i) q^{43} +(-0.706241 + 0.960876i) q^{44} +(0.0316601 + 1.14857i) q^{46} +(0.245485 - 0.969400i) q^{49} +(0.0493023 - 0.594990i) q^{50} +(-1.17807 - 1.14605i) q^{53} +(-0.967868 - 0.161509i) q^{56} +(0.730450 - 0.886936i) q^{58} +(0.451533 - 0.892254i) q^{63} +(-0.0453105 + 0.546816i) q^{64} +(-1.37947 + 0.390078i) q^{67} +(0.0825793 - 0.143032i) q^{71} +(-0.909124 - 0.369254i) q^{72} +(0.161771 + 1.16661i) q^{74} +(1.85017 - 0.102077i) q^{77} +(-0.508621 + 0.312648i) q^{79} +(0.635724 - 0.771917i) q^{81} +(-0.809507 + 0.277904i) q^{86} +(-0.249743 - 1.80101i) q^{88} +(0.887768 + 0.863634i) q^{92} +(0.298515 + 0.517043i) q^{98} +(1.82772 + 0.304992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 2 q^{7} - 21 q^{8} + q^{9}+O(q^{10}) \) 36 * q - q^2 - 2 * q^7 - 21 * q^8 + q^9	\( 36 q - q^{2} - 2 q^{7} - 21 q^{8} + q^{9} - q^{11} - q^{14} - q^{16} - q^{18} - 21 q^{22} + 2 q^{23} + q^{25} - q^{29} + 2 q^{37} - q^{43} + 39 q^{46} - 2 q^{49} + 2 q^{50} - q^{53} - 2 q^{56} + q^{58} + q^{63} - 21 q^{64} - 20 q^{67} + 2 q^{71} - 18 q^{72} + 36 q^{74} - q^{77} - q^{79} + q^{81} - 2 q^{86} - q^{88} - 19 q^{92} - q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - q^2 - 2 * q^7 - 21 * q^8 + q^9 - q^11 - q^14 - q^16 - q^18 - 21 * q^22 + 2 * q^23 + q^25 - q^29 + 2 * q^37 - q^43 + 39 * q^46 - 2 * q^49 + 2 * q^50 - q^53 - 2 * q^56 + q^58 + q^63 - 21 * q^64 - 20 * q^67 + 2 * q^71 - 18 * q^72 + 36 * q^74 - q^77 - q^79 + q^81 - 2 * q^86 - q^88 - 19 * q^92 - q^98 + 2 * q^99

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