LMFDB - Embedded newform 847.1.bb.a.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,1,Mod(20,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([55, 76]))

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

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

chi := DirichletCharacter("847.20");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	847.bb (of order $110$, degree $40$, 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:	$0.422708065700$
Analytic rank:	$0$
Dimension:	$40$
Coefficient field:	$\Q(\zeta_{55})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{39} + x^{35} - x^{34} + x^{30} - x^{28} + x^{25} - x^{23} + x^{20} - x^{17} + x^{15} + \cdots + 1 $ x^40 - x^39 + x^35 - x^34 + x^30 - x^28 + x^25 - x^23 + x^20 - x^17 + x^15 - x^12 + x^10 - x^6 + x^5 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{55}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{55} - \cdots)$

Embedding invariants

Embedding label			433.1
Root			$0.696938 - 0.717132i$ of defining polynomial
Character	$\chi$	$=$	847.433
Dual form			847.1.bb.a.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07906 - 1.11032i) q^{2} +(-0.0398980 - 1.39661i) q^{4} +(0.774142 + 0.633012i) q^{7} +(-0.453058 - 0.415813i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(1.07906 - 1.11032i) q^{2} +(-0.0398980 - 1.39661i) q^{4} +(0.774142 + 0.633012i) q^{7} +(-0.453058 - 0.415813i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.466667 - 0.884433i) q^{11} +(1.53819 - 0.176491i) q^{14} +(0.444341 - 0.0254083i) q^{16} +(-1.52561 + 0.264017i) q^{18} +(-1.48557 - 0.436202i) q^{22} +(-0.427724 - 0.274882i) q^{23} +(0.516397 + 0.856349i) q^{25} +(0.853186 - 1.10643i) q^{28} +(-0.899302 + 1.49133i) q^{29} +(0.853963 - 0.985526i) q^{32} +(-0.788629 + 1.15333i) q^{36} +(-0.348845 - 0.510170i) q^{37} +(-0.829475 + 1.81630i) q^{43} +(-1.21659 + 0.687040i) q^{44} +(-0.766746 + 0.178299i) q^{46} +(0.198590 + 0.980083i) q^{49} +(1.50805 + 0.350681i) q^{50} +(-1.94485 - 0.111210i) q^{53} +(-0.0875163 - 0.608689i) q^{56} +(0.685455 + 2.60774i) q^{58} +(-0.254218 - 0.967147i) q^{63} +(-0.134691 - 1.56818i) q^{64} +(-0.0243572 + 0.169408i) q^{67} +(1.18956 + 0.276620i) q^{71} +(0.122123 + 0.602700i) q^{72} +(-0.942877 - 0.163171i) q^{74} +(0.198590 - 0.980083i) q^{77} +(0.374083 - 1.84617i) q^{79} +(0.309017 + 0.951057i) q^{81} +(1.12163 + 2.88087i) q^{86} +(-0.156331 + 0.594746i) q^{88} +(-0.366837 + 0.608332i) q^{92} +(1.30250 + 0.837065i) q^{98} +(-0.142315 + 0.989821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) $ 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9	$ 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46} + q^{49} + 2 q^{50} - 3 q^{53} - 7 q^{56} - 12 q^{58} + q^{63} - 9 q^{64} + 2 q^{67} - 3 q^{71} - q^{72} + 4 q^{74} + q^{77} - 3 q^{79} - 10 q^{81} - q^{86} - 12 q^{88} - 4 q^{92} - 9 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9 + q^11 - 3 * q^14 - 3 * q^18 + 2 * q^22 - 9 * q^23 + q^25 - 2 * q^28 + 2 * q^29 - 4 * q^32 + 3 * q^36 - 3 * q^37 + 2 * q^43 - 13 * q^44 - q^46 + q^49 + 2 * q^50 - 3 * q^53 - 7 * q^56 - 12 * q^58 + q^63 - 9 * q^64 + 2 * q^67 - 3 * q^71 - q^72 + 4 * q^74 + q^77 - 3 * q^79 - 10 * q^81 - q^86 - 12 * q^88 - 4 * q^92 - 9 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{41}{55}\right)$

Coefficient data

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

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

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

$2$	1.07906	−	1.11032i	1.07906	−	1.11032i	0.0855750	−	0.996332i	$-0.472727\pi$
$2$	1.07906	−	1.11032i	1.07906	−	1.11032i	0.993482	−	0.113991i	$-0.0363636\pi$
$3$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$3$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$4$	−0.0398980	−	1.39661i	−0.0398980	−	1.39661i
$5$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$5$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$6$		0			0
$7$	0.774142	+	0.633012i	0.774142	+	0.633012i
$7$	0.774142	+	0.633012i	0.774142	+	0.633012i
$8$	−0.453058	−	0.415813i	−0.453058	−	0.415813i
$9$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$10$		0			0
$11$	−0.466667	−	0.884433i	−0.466667	−	0.884433i
$11$	−0.466667	−	0.884433i	−0.466667	−	0.884433i
$12$		0			0
$13$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$13$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$14$	1.53819	−	0.176491i	1.53819	−	0.176491i
$15$		0			0
$16$	0.444341	−	0.0254083i	0.444341	−	0.0254083i
$17$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$17$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$18$	−1.52561	+	0.264017i	−1.52561	+	0.264017i
$19$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$19$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$20$		0			0
$21$		0			0
$22$	−1.48557	−	0.436202i	−1.48557	−	0.436202i
$23$	−0.427724	−	0.274882i	−0.427724	−	0.274882i	0.309017	−	0.951057i	$-0.400000\pi$
$23$	−0.427724	−	0.274882i	−0.427724	−	0.274882i	−0.736741	+	0.676175i	$0.763636\pi$
$24$		0			0
$25$	0.516397	+	0.856349i	0.516397	+	0.856349i
$26$		0			0
$27$		0			0
$28$	0.853186	−	1.10643i	0.853186	−	1.10643i
$29$	−0.899302	+	1.49133i	−0.899302	+	1.49133i	−0.0285561	+	0.999592i	$0.509091\pi$
$29$	−0.899302	+	1.49133i	−0.899302	+	1.49133i	−0.870746	+	0.491733i	$0.836364\pi$
$30$		0			0
$31$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$31$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$32$	0.853963	−	0.985526i	0.853963	−	0.985526i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.788629	+	1.15333i	−0.788629	+	1.15333i
$37$	−0.348845	−	0.510170i	−0.348845	−	0.510170i	0.610648	−	0.791902i	$-0.290909\pi$
$37$	−0.348845	−	0.510170i	−0.348845	−	0.510170i	−0.959493	+	0.281733i	$0.909091\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$41$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$42$		0			0
$43$	−0.829475	+	1.81630i	−0.829475	+	1.81630i	−0.362808	+	0.931864i	$0.618182\pi$
$43$	−0.829475	+	1.81630i	−0.829475	+	1.81630i	−0.466667	+	0.884433i	$0.654545\pi$
$44$	−1.21659	+	0.687040i	−1.21659	+	0.687040i
$45$		0			0
$46$	−0.766746	+	0.178299i	−0.766746	+	0.178299i
$47$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$47$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$48$		0			0
$49$	0.198590	+	0.980083i	0.198590	+	0.980083i
$50$	1.50805	+	0.350681i	1.50805	+	0.350681i
$51$		0			0
$52$		0			0
$53$	−1.94485	−	0.111210i	−1.94485	−	0.111210i	−0.959493	−	0.281733i	$-0.909091\pi$
$53$	−1.94485	−	0.111210i	−1.94485	−	0.111210i	−0.985354	+	0.170522i	$0.945455\pi$
$54$		0			0
$55$		0			0
$56$	−0.0875163	−	0.608689i	−0.0875163	−	0.608689i
$57$		0			0
$58$	0.685455	+	2.60774i	0.685455	+	2.60774i
$59$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$59$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$60$		0			0
$61$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$61$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$62$		0			0
$63$	−0.254218	−	0.967147i	−0.254218	−	0.967147i
$64$	−0.134691	−	1.56818i	−0.134691	−	1.56818i
$65$		0			0
$66$		0			0
$67$	−0.0243572	+	0.169408i	−0.0243572	+	0.169408i	−0.998369	−	0.0570888i	$-0.981818\pi$
$67$	−0.0243572	+	0.169408i	−0.0243572	+	0.169408i	0.974012	+	0.226497i	$0.0727273\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.18956	+	0.276620i	1.18956	+	0.276620i	0.774142	−	0.633012i	$-0.218182\pi$
$71$	1.18956	+	0.276620i	1.18956	+	0.276620i	0.415415	+	0.909632i	$0.363636\pi$
$72$	0.122123	+	0.602700i	0.122123	+	0.602700i
$73$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$73$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$74$	−0.942877	−	0.163171i	−0.942877	−	0.163171i
$75$		0			0
$76$		0			0
$77$	0.198590	−	0.980083i	0.198590	−	0.980083i
$78$		0			0
$79$	0.374083	−	1.84617i	0.374083	−	1.84617i	−0.142315	−	0.989821i	$-0.545455\pi$
$79$	0.374083	−	1.84617i	0.374083	−	1.84617i	0.516397	−	0.856349i	$-0.327273\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.309017	+	0.951057i
$82$		0			0
$83$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$83$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$84$		0			0
$85$		0			0
$86$	1.12163	+	2.88087i	1.12163	+	2.88087i
$87$		0			0
$88$	−0.156331	+	0.594746i	−0.156331	+	0.594746i
$89$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$89$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$90$		0			0
$91$		0			0
$92$	−0.366837	+	0.608332i	−0.366837	+	0.608332i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$97$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$98$	1.30250	+	0.837065i	1.30250	+	0.837065i
$99$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$100$	1.17538	−	0.755373i	1.17538	−	0.755373i
$101$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$101$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$102$		0			0
$103$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$103$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$104$		0			0
$105$		0			0
$106$	−2.22208	+	2.03941i	−2.22208	+	2.03941i
$107$	1.02606	−	0.117730i	1.02606	−	0.117730i	0.415415	−	0.909632i	$-0.363636\pi$
$107$	1.02606	−	0.117730i	1.02606	−	0.117730i	0.610648	+	0.791902i	$0.290909\pi$
$108$		0			0
$109$	1.89088	+	0.555213i	1.89088	+	0.555213i	0.993482	+	0.113991i	$0.0363636\pi$
$109$	1.89088	+	0.555213i	1.89088	+	0.555213i	0.897398	+	0.441221i	$0.145455\pi$
$110$		0			0
$111$		0			0
$112$	0.360066	+	0.261603i	0.360066	+	0.261603i
$113$	−1.02693	−	0.942503i	−1.02693	−	0.942503i	−0.0285561	−	0.999592i	$-0.509091\pi$
$113$	−1.02693	−	0.942503i	−1.02693	−	0.942503i	−0.998369	+	0.0570888i	$0.981818\pi$
$114$		0			0
$115$		0			0
$116$	2.11868	+	1.19647i	2.11868	+	1.19647i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.34816	−	0.761342i	−1.34816	−	0.761342i
$127$	−0.927251	−	1.75734i	−0.927251	−	1.75734i	−0.564443	−	0.825472i	$-0.690909\pi$
$127$	−0.927251	−	1.75734i	−0.927251	−	1.75734i	−0.362808	−	0.931864i	$-0.618182\pi$
$128$	−0.877015	−	0.717132i	−0.877015	−	0.717132i
$129$		0			0
$130$		0			0
$131$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$131$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$132$		0			0
$133$		0			0
$134$	0.161815	+	0.209845i	0.161815	+	0.209845i
$135$		0			0
$136$		0			0
$137$	0.0570190	−	0.00326046i	0.0570190	−	0.00326046i	−0.0285561	−	0.999592i	$-0.509091\pi$
$137$	0.0570190	−	0.00326046i	0.0570190	−	0.00326046i	0.0855750	+	0.996332i	$0.472727\pi$
$138$		0			0
$139$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$139$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$140$		0			0
$141$		0			0
$142$	1.59074	−	1.02230i	1.59074	−	1.02230i
$143$		0			0
$144$	−0.374414	−	0.240621i	−0.374414	−	0.240621i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.698590	+	0.507556i	−0.698590	+	0.507556i
$149$	−0.173809	+	0.225399i	−0.173809	+	0.225399i	−0.870746	−	0.491733i	$-0.836364\pi$
$149$	−0.173809	+	0.225399i	−0.173809	+	0.225399i	0.696938	+	0.717132i	$0.254545\pi$
$150$		0			0
$151$	0.0420768	−	1.47288i	0.0420768	−	1.47288i	−0.654861	−	0.755750i	$-0.727273\pi$
$151$	0.0420768	−	1.47288i	0.0420768	−	1.47288i	0.696938	−	0.717132i	$-0.254545\pi$
$152$		0			0
$153$		0			0
$154$	−0.873918	−	1.27806i	−0.873918	−	1.27806i
$155$		0			0
$156$		0			0
$157$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$157$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$158$	−1.64619	−	2.40748i	−1.64619	−	2.40748i
$159$		0			0
$160$		0			0
$161$	−0.157116	−	0.483552i	−0.157116	−	0.483552i
$162$	1.38943	+	0.683135i	1.38943	+	0.683135i
$163$	0.205103	−	1.01222i	0.205103	−	1.01222i	−0.736741	−	0.676175i	$-0.763636\pi$
$163$	0.205103	−	1.01222i	0.205103	−	1.01222i	0.941844	−	0.336049i	$-0.109091\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$167$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$168$		0			0
$169$	−0.254218	+	0.967147i	−0.254218	+	0.967147i
$170$		0			0
$171$		0			0
$172$	2.56975	+	1.08599i	2.56975	+	1.08599i
$173$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$173$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$174$		0			0
$175$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$176$	−0.229831	−	0.381132i	−0.229831	−	0.381132i
$177$		0			0
$178$		0			0
$179$	−0.505123	−	1.92169i	−0.505123	−	1.92169i	−0.362808	−	0.931864i	$-0.618182\pi$
$179$	−0.505123	−	1.92169i	−0.505123	−	1.92169i	−0.142315	−	0.989821i	$-0.545455\pi$
$180$		0			0
$181$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$181$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$182$		0			0
$183$		0			0
$184$	0.0794845	+	0.302390i	0.0794845	+	0.302390i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.73511	−	0.733264i	−1.73511	−	0.733264i	−0.998369	−	0.0570888i	$-0.981818\pi$
$191$	−1.73511	−	0.733264i	−1.73511	−	0.733264i	−0.736741	−	0.676175i	$-0.763636\pi$
$192$		0			0
$193$	0.276810	+	1.36611i	0.276810	+	1.36611i	0.841254	+	0.540641i	$0.181818\pi$
$193$	0.276810	+	1.36611i	0.276810	+	1.36611i	−0.564443	+	0.825472i	$0.690909\pi$
$194$		0			0
$195$		0			0
$196$	1.36087	−	0.316457i	1.36087	−	0.316457i
$197$	−0.0237252	−	0.0519510i	−0.0237252	−	0.0519510i	0.897398	−	0.441221i	$-0.145455\pi$
$197$	−0.0237252	−	0.0519510i	−0.0237252	−	0.0519510i	−0.921124	+	0.389270i	$0.872727\pi$
$198$	0.945456	+	1.22609i	0.945456	+	1.22609i
$199$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$199$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$200$	0.122123	−	0.602700i	0.122123	−	0.602700i
$201$		0			0
$202$		0			0
$203$	−1.64021	+	0.585227i	−1.64021	+	0.585227i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.184465	+	0.473794i	0.184465	+	0.473794i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.06324	−	0.379362i	−1.06324	−	0.379362i	−0.254218	−	0.967147i	$-0.581818\pi$
$211$	−1.06324	−	0.379362i	−1.06324	−	0.379362i	−0.809017	+	0.587785i	$0.800000\pi$
$212$	−0.0777222	+	2.72063i	−0.0777222	+	2.72063i
$213$		0			0
$214$	0.976462	−	1.26630i	0.976462	−	1.26630i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	2.65683	−	1.50038i	2.65683	−	1.50038i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$223$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$224$	1.28494	−	0.222367i	1.28494	−	0.222367i
$225$	0.0855750	−	0.996332i	0.0855750	−	0.996332i
$226$	−2.15459	+	0.123204i	−2.15459	+	0.123204i
$227$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$227$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$228$		0			0
$229$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$229$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$230$		0			0
$231$		0			0
$232$	1.02755	−	0.301715i	1.02755	−	0.301715i
$233$	1.05959	+	0.769835i	1.05959	+	0.769835i	0.974012	−	0.226497i	$-0.0727273\pi$
$233$	1.05959	+	0.769835i	1.05959	+	0.769835i	0.0855750	+	0.996332i	$0.472727\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.0528883	−	0.162773i	0.0528883	−	0.162773i	−0.921124	−	0.389270i	$-0.872727\pi$
$239$	0.0528883	−	0.162773i	0.0528883	−	0.162773i	0.974012	+	0.226497i	$0.0727273\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	0.307474	+	1.51745i	0.307474	+	1.51745i
$243$		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		−0.809017	−	0.587785i	$-0.800000\pi$
$251$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$252$	−1.34059	+	0.393631i	−1.34059	+	0.393631i
$253$	−0.0435095	+	0.506572i	−0.0435095	+	0.506572i
$254$	−2.95177	−	0.866717i	−2.95177	−	0.866717i
$255$		0			0
$256$	−0.178904	+	0.0205273i	−0.178904	+	0.0205273i
$257$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$257$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$258$		0			0
$259$	0.0528883	−	0.615767i	0.0528883	−	0.615767i
$260$		0			0
$261$	1.60413	−	0.677911i	1.60413	−	0.677911i
$262$		0			0
$263$	1.02742	−	0.660282i	1.02742	−	0.660282i	0.0855750	−	0.996332i	$-0.472727\pi$
$263$	1.02742	−	0.660282i	1.02742	−	0.660282i	0.941844	+	0.336049i	$0.109091\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.237569	+	0.0272585i	0.237569	+	0.0272585i
$269$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$269$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$270$		0			0
$271$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$271$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$272$		0			0
$273$		0			0
$274$	0.0579065	−	0.0668277i	0.0579065	−	0.0668277i
$275$	0.516397	−	0.856349i	0.516397	−	0.856349i
$276$		0			0
$277$	0.668382	+	1.71672i	0.668382	+	1.71672i	0.696938	+	0.717132i	$0.254545\pi$
$277$	0.668382	+	1.71672i	0.668382	+	1.71672i	−0.0285561	+	0.999592i	$0.509091\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.83474	−	0.654632i	1.83474	−	0.654632i	0.841254	−	0.540641i	$-0.181818\pi$
$281$	1.83474	−	0.654632i	1.83474	−	0.654632i	0.993482	−	0.113991i	$-0.0363636\pi$
$282$		0			0
$283$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$283$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$284$	0.338869	−	1.67238i	0.338869	−	1.67238i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.27015	+	0.295360i	−1.27015	+	0.295360i
$289$	−0.985354	−	0.170522i	−0.985354	−	0.170522i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$293$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$294$		0			0
$295$		0			0
$296$	−0.0540881	+	0.376191i	−0.0540881	+	0.376191i
$297$		0			0
$298$	0.0627163	+	0.436202i	0.0627163	+	0.436202i
$299$		0			0
$300$		0			0
$301$	−1.79187	+	0.881003i	−1.79187	+	0.881003i
$302$	−1.58997	−	1.63604i	−1.58997	−	1.63604i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$307$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$308$	−1.37672	−	0.238250i	−1.37672	−	0.238250i
$309$		0			0
$310$		0			0
$311$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$311$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$312$		0			0
$313$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$313$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$314$		0			0
$315$		0			0
$316$	−2.59331	−	0.448790i	−2.59331	−	0.448790i
$317$	−1.57598	+	0.366479i	−1.57598	+	0.366479i	−0.921124	−	0.389270i	$-0.872727\pi$
$317$	−1.57598	+	0.366479i	−1.57598	+	0.366479i	−0.654861	+	0.755750i	$0.727273\pi$
$318$		0			0
$319$	1.73865	+	0.0994197i	1.73865	+	0.0994197i
$320$		0			0
$321$		0			0
$322$	−0.706436	−	0.347331i	−0.706436	−	0.347331i
$323$		0			0
$324$	1.31593	−	0.469522i	1.31593	−	0.469522i
$325$		0			0
$326$	−0.902578	−	1.31998i	−0.902578	−	1.31998i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.17534	+	1.35642i	−1.17534	+	1.35642i	−0.254218	+	0.967147i	$0.581818\pi$
$331$	−1.17534	+	1.35642i	−1.17534	+	1.35642i	−0.921124	+	0.389270i	$0.872727\pi$
$332$		0			0
$333$	−0.0176486	+	0.617782i	−0.0176486	+	0.617782i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.78310	+	0.204591i	1.78310	+	0.204591i	0.941844	−	0.336049i	$-0.109091\pi$
$337$	1.78310	+	0.204591i	1.78310	+	0.204591i	0.841254	+	0.540641i	$0.181818\pi$
$338$	0.799530	+	1.32587i	0.799530	+	1.32587i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$344$	1.13104	−	0.477981i	1.13104	−	0.477981i
$345$		0			0
$346$		0			0
$347$	0.724432	−	0.0414245i	0.724432	−	0.0414245i	0.309017	−	0.951057i	$-0.400000\pi$
$347$	0.724432	−	0.0414245i	0.724432	−	0.0414245i	0.415415	+	0.909632i	$0.363636\pi$
$348$		0			0
$349$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$349$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$350$	0.945456	+	1.22609i	0.945456	+	1.22609i
$351$		0			0
$352$	−1.27015	−	0.295360i	−1.27015	−	0.295360i
$353$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$353$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−2.67875	−	1.51276i	−2.67875	−	1.51276i
$359$	−0.0512523	−	1.79406i	−0.0512523	−	1.79406i	−0.466667	−	0.884433i	$-0.654545\pi$
$359$	−0.0512523	−	1.79406i	−0.0512523	−	1.79406i	0.415415	−	0.909632i	$-0.363636\pi$
$360$		0			0
$361$	0.696938	−	0.717132i	0.696938	−	0.717132i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$367$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$368$	−0.197039	−	0.111273i	−0.197039	−	0.111273i
$369$		0			0
$370$		0			0
$371$	−1.43519	−	1.31720i	−1.43519	−	1.31720i
$372$		0			0
$373$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$373$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.47108	−	0.0841194i	1.47108	−	0.0841194i	0.696938	−	0.717132i	$-0.254545\pi$
$379$	1.47108	−	0.0841194i	1.47108	−	0.0841194i	0.774142	+	0.633012i	$0.218182\pi$
$380$		0			0
$381$		0			0
$382$	−2.68644	+	1.13530i	−2.68644	+	1.13530i
$383$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$383$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$384$		0			0
$385$		0			0
$386$	1.81552	+	1.16676i	1.81552	+	1.16676i
$387$	1.73865	−	0.981862i	1.73865	−	0.981862i
$388$		0			0
$389$	−1.46388	−	0.167964i	−1.46388	−	0.167964i	−0.654861	−	0.755750i	$-0.727273\pi$
$389$	−1.46388	−	0.167964i	−1.46388	−	0.167964i	−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$		0			0
$392$	0.317558	−	0.526611i	0.317558	−	0.526611i
$393$		0			0
$394$	−0.0832833	−	0.0297154i	−0.0832833	−	0.0297154i
$395$		0			0
$396$	1.38807	+	0.159267i	1.38807	+	0.159267i
$397$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$397$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$398$		0			0
$399$		0			0
$400$	0.251215	+	0.367390i	0.251215	+	0.367390i
$401$	0.409569	−	1.05197i	0.409569	−	1.05197i	−0.564443	−	0.825472i	$-0.690909\pi$
$401$	0.409569	−	1.05197i	0.409569	−	1.05197i	0.974012	−	0.226497i	$-0.0727273\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−1.12009	+	2.45266i	−1.12009	+	2.45266i
$407$	−0.288416	+	0.546610i	−0.288416	+	0.546610i
$408$		0			0
$409$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$409$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.725112	+	0.306435i	0.725112	+	0.306435i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$419$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$420$		0			0
$421$	−0.456270	−	1.73583i	−0.456270	−	1.73583i	−0.654861	−	0.755750i	$-0.727273\pi$
$421$	−0.456270	−	1.73583i	−0.456270	−	1.73583i	0.198590	−	0.980083i	$-0.436364\pi$
$422$	−1.56851	+	0.771182i	−1.56851	+	0.771182i
$423$		0			0
$424$	0.834886	+	0.859077i	0.834886	+	0.859077i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.205361	−	1.42831i	−0.205361	−	1.42831i
$429$		0			0
$430$		0			0
$431$	1.83924	+	0.105172i	1.83924	+	0.105172i	0.941844	−	0.336049i	$-0.109091\pi$
$431$	1.83924	+	0.105172i	1.83924	+	0.105172i	0.897398	+	0.441221i	$0.145455\pi$
$432$		0			0
$433$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$433$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$434$		0			0
$435$		0			0
$436$	0.699974	−	2.66298i	0.699974	−	2.66298i
$437$		0			0
$438$		0			0
$439$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$439$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$440$		0			0
$441$	0.415415	−	0.909632i	0.415415	−	0.909632i
$442$		0			0
$443$	−0.651166	−	0.320157i	−0.651166	−	0.320157i	0.0855750	−	0.996332i	$-0.472727\pi$
$443$	−0.651166	−	0.320157i	−0.651166	−	0.320157i	−0.736741	+	0.676175i	$0.763636\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.888407	−	1.29925i	0.888407	−	1.29925i
$449$	0.714988	+	1.83643i	0.714988	+	1.83643i	0.516397	+	0.856349i	$0.327273\pi$
$449$	0.714988	+	1.83643i	0.714988	+	1.83643i	0.198590	+	0.980083i	$0.436364\pi$
$450$	−1.01391	−	1.17011i	−1.01391	−	1.17011i
$451$		0			0
$452$	−1.27534	+	1.47182i	−1.27534	+	1.47182i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$457$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$461$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$462$		0			0
$463$	−0.785171	+	0.504599i	−0.785171	+	0.504599i	−0.870746	−	0.491733i	$-0.836364\pi$
$463$	−0.785171	+	0.504599i	−0.785171	+	0.504599i	0.0855750	+	0.996332i	$0.472727\pi$
$464$	−0.361704	+	0.685506i	−0.361704	+	0.685506i
$465$		0			0
$466$	1.99812	−	0.345788i	1.99812	−	0.345788i
$467$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$467$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$468$		0			0
$469$	−0.126093	+	0.115727i	−0.126093	+	0.115727i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.99348	−	0.113991i	1.99348	−	0.113991i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.50805	+	1.23312i	1.50805	+	1.23312i
$478$	−0.123662	−	0.234365i	−0.123662	−	0.234365i
$479$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$479$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.17538	+	0.755373i	1.17538	+	0.755373i
$485$		0			0
$486$		0			0
$487$	−0.617026	+	1.89901i	−0.617026	+	1.89901i	−0.254218	+	0.967147i	$0.581818\pi$
$487$	−0.617026	+	1.89901i	−0.617026	+	1.89901i	−0.362808	+	0.931864i	$0.618182\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.30250	+	1.06505i	1.30250	+	1.06505i	0.993482	+	0.113991i	$0.0363636\pi$
$491$	1.30250	+	1.06505i	1.30250	+	1.06505i	0.309017	+	0.951057i	$0.400000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.745782	+	0.967147i	0.745782	+	0.967147i
$498$		0			0
$499$	1.19207	−	1.09407i	1.19207	−	1.09407i	0.198590	−	0.980083i	$-0.436364\pi$
$499$	1.19207	−	1.09407i	1.19207	−	1.09407i	0.993482	−	0.113991i	$-0.0363636\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$503$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$504$	−0.286976	+	0.543881i	−0.286976	+	0.543881i
$505$		0			0
$506$	0.515509	+	0.594929i	0.515509	+	0.594929i
$507$		0			0
$508$	−2.41732	+	1.36512i	−2.41732	+	1.36512i
$509$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$509$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$510$		0			0
$511$		0			0
$512$	0.521540	−	0.676345i	0.521540	−	0.676345i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.626631	−	0.723170i	−0.626631	−	0.723170i
$519$		0			0
$520$		0			0
$521$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$521$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$522$	0.978247	−	2.51261i	0.978247	−	2.51261i
$523$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$523$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$524$		0			0
$525$		0			0
$526$	0.375517	−	1.85325i	0.375517	−	1.85325i
$527$		0			0
$528$		0			0
$529$	−0.308027	−	0.674485i	−0.308027	−	0.674485i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.0814772	−	0.0666236i	0.0814772	−	0.0666236i
$537$		0			0
$538$		0			0
$539$	0.774142	−	0.633012i	0.774142	−	0.633012i
$540$		0			0
$541$	−0.0966045	−	1.12475i	−0.0966045	−	1.12475i	−0.870746	−	0.491733i	$-0.836364\pi$
$541$	−0.0966045	−	1.12475i	−0.0966045	−	1.12475i	0.774142	−	0.633012i	$-0.218182\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.332955	+	1.26669i	0.332955	+	1.26669i	0.897398	+	0.441221i	$0.145455\pi$
$547$	0.332955	+	1.26669i	0.332955	+	1.26669i	−0.564443	+	0.825472i	$0.690909\pi$
$548$	−0.00682854	−	0.0795032i	−0.00682854	−	0.0795032i
$549$		0			0
$550$	−0.393602	−	1.49742i	−0.393602	−	1.49742i
$551$		0			0
$552$		0			0
$553$	1.45824	−	1.19240i	1.45824	−	1.19240i
$554$	2.62734	+	1.11032i	2.62734	+	1.11032i
$555$		0			0
$556$		0			0
$557$	0.411334	−	1.56488i	0.411334	−	1.56488i	−0.362808	−	0.931864i	$-0.618182\pi$
$557$	0.411334	−	1.56488i	0.411334	−	1.56488i	0.774142	−	0.633012i	$-0.218182\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.25293	−	2.74353i	1.25293	−	2.74353i
$563$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$563$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.362808	+	0.931864i	−0.362808	+	0.931864i
$568$	−0.423916	−	0.619958i	−0.423916	−	0.619958i
$569$	−0.468956	+	0.685827i	−0.468956	+	0.685827i	−0.985354	−	0.170522i	$-0.945455\pi$
$569$	−0.468956	+	0.685827i	−0.468956	+	0.685827i	0.516397	+	0.856349i	$0.327273\pi$
$570$		0			0
$571$	0.0374005	+	0.0431624i	0.0374005	+	0.0431624i	0.774142	−	0.633012i	$-0.218182\pi$
$571$	0.0374005	+	0.0431624i	0.0374005	+	0.0431624i	−0.736741	+	0.676175i	$0.763636\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.0145189	−	0.508229i	0.0145189	−	0.508229i
$576$	−0.812785	+	1.34785i	−0.812785	+	1.34785i
$577$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$577$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$578$	−1.25259	+	0.910058i	−1.25259	+	0.910058i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.809238	+	1.77198i	0.809238	+	1.77198i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$587$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.167969	−	0.217825i	−0.167969	−	0.217825i
$593$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$593$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$594$		0			0
$595$		0			0
$596$	0.321729	+	0.233750i	0.321729	+	0.233750i
$597$		0			0
$598$		0			0
$599$	0.919665	+	1.74296i	0.919665	+	1.74296i	0.610648	+	0.791902i	$0.290909\pi$
$599$	0.919665	+	1.74296i	0.919665	+	1.74296i	0.309017	+	0.951057i	$0.400000\pi$
$600$		0			0
$601$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$601$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$602$	−0.955331	+	2.94021i	−0.955331	+	2.94021i
$603$	0.119281	−	0.122737i	0.119281	−	0.122737i
$604$	−2.05872			−2.05872
$605$		0			0
$606$		0			0
$607$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$607$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.534591	+	0.490643i	0.534591	+	0.490643i	0.897398	−	0.441221i	$-0.145455\pi$
$613$	0.534591	+	0.490643i	0.534591	+	0.490643i	−0.362808	+	0.931864i	$0.618182\pi$
$614$		0			0
$615$		0			0
$616$	−0.497504	+	0.361458i	−0.497504	+	0.361458i
$617$	0.895528	+	0.262951i	0.895528	+	0.262951i	0.696938	−	0.717132i	$-0.254545\pi$
$617$	0.895528	+	0.262951i	0.895528	+	0.262951i	0.198590	+	0.980083i	$0.436364\pi$
$618$		0			0
$619$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$619$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.12153	−	0.128683i	−1.12153	−	0.128683i	−0.466667	−	0.884433i	$-0.654545\pi$
$631$	−1.12153	−	0.128683i	−1.12153	−	0.128683i	−0.654861	+	0.755750i	$0.727273\pi$
$632$	−0.937142	+	0.680874i	−0.937142	+	0.680874i
$633$		0			0
$634$	−1.29367	+	2.14530i	−1.29367	+	2.14530i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	1.98649	−	1.82319i	1.98649	−	1.82319i
$639$	−0.799779	−	0.922994i	−0.799779	−	0.922994i
$640$		0			0
$641$	0.409569	−	0.598975i	0.409569	−	0.598975i	−0.564443	−	0.825472i	$-0.690909\pi$
$641$	0.409569	−	0.598975i	0.409569	−	0.598975i	0.974012	+	0.226497i	$0.0727273\pi$
$642$		0			0
$643$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$643$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$644$	−0.669066	+	0.238722i	−0.669066	+	0.238722i
$645$		0			0
$646$		0			0
$647$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$647$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$648$	0.255459	−	0.559377i	0.255459	−	0.559377i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−1.42187	−	0.246064i	−1.42187	−	0.246064i
$653$	−0.505123	+	1.92169i	−0.505123	+	1.92169i	−0.142315	+	0.989821i	$0.545455\pi$
$653$	−0.505123	+	1.92169i	−0.505123	+	1.92169i	−0.362808	+	0.931864i	$0.618182\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$659$	−0.118239	+	0.822373i	−0.118239	+	0.822373i	−0.959493	+	0.281733i	$0.909091\pi$
$660$		0			0
$661$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$661$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$662$	0.237800	+	2.76866i	0.237800	+	2.76866i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.666894	+	0.686217i	0.666894	+	0.686217i
$667$	0.794591	−	0.390674i	0.794591	−	0.390674i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.724432	+	0.0414245i	0.724432	+	0.0414245i	0.415415	−	0.909632i	$-0.363636\pi$
$673$	0.724432	+	0.0414245i	0.724432	+	0.0414245i	0.309017	+	0.951057i	$0.400000\pi$
$674$	2.15123	−	1.75905i	2.15123	−	1.75905i
$675$		0			0
$676$	1.36087	+	0.316457i	1.36087	+	0.316457i
$677$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$677$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.468956	+	1.02687i	−0.468956	+	1.02687i	0.516397	+	0.856349i	$0.327273\pi$
$683$	−0.468956	+	1.02687i	−0.468956	+	1.02687i	−0.985354	+	0.170522i	$0.945455\pi$
$684$		0			0
$685$		0			0
$686$	0.478446	+	1.47250i	0.478446	+	1.47250i
$687$		0			0
$688$	−0.322420	+	0.828130i	−0.322420	+	0.828130i
$689$		0			0
$690$		0			0
$691$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$691$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$692$		0			0
$693$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$694$	0.735709	−	0.849053i	0.735709	−	0.849053i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	1.38807	+	0.159267i	1.38807	+	0.159267i
$701$	−0.760903	−	1.26182i	−0.760903	−	1.26182i	−0.959493	−	0.281733i	$-0.909091\pi$
$701$	−0.760903	−	1.26182i	−0.760903	−	1.26182i	0.198590	−	0.980083i	$-0.436364\pi$
$702$		0			0
$703$		0			0
$704$	−1.32409	+	0.850943i	−1.32409	+	0.850943i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.0620945	+	0.722954i	−0.0620945	+	0.722954i	0.897398	+	0.441221i	$0.145455\pi$
$709$	−0.0620945	+	0.722954i	−0.0620945	+	0.722954i	−0.959493	+	0.281733i	$0.909091\pi$
$710$		0			0
$711$	−1.38779	+	1.27370i	−1.38779	+	1.27370i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−2.66369	+	0.782131i	−2.66369	+	0.782131i
$717$		0			0
$718$	−2.04730	−	1.87899i	−2.04730	−	1.87899i
$719$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$719$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$720$		0			0
$721$		0			0
$722$	−0.0442129	−	1.54765i	−0.0442129	−	1.54765i
$723$		0			0
$724$		0			0
$725$	−1.74149			−1.74149
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.309017	−	0.951057i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$733$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$734$		0			0
$735$		0			0
$736$	−0.636163	+	0.186794i	−0.636163	+	0.186794i
$737$	0.161197	−	0.0575149i	0.161197	−	0.0575149i
$738$		0			0
$739$	−0.988049	−	1.28132i	−0.988049	−	1.28132i	−0.959493	−	0.281733i	$-0.909091\pi$
$739$	−0.988049	−	1.28132i	−0.988049	−	1.28132i	−0.0285561	−	0.999592i	$-0.509091\pi$
$740$		0			0
$741$		0			0
$742$	−3.01117	+	0.172185i	−3.01117	+	0.172185i
$743$	−0.138463	+	1.61210i	−0.138463	+	1.61210i	0.516397	+	0.856349i	$0.327273\pi$
$743$	−0.138463	+	1.61210i	−0.138463	+	1.61210i	−0.654861	+	0.755750i	$0.727273\pi$
$744$		0			0
$745$		0			0
$746$	−1.21567	+	2.30395i	−1.21567	+	2.30395i
$747$		0			0
$748$		0			0
$749$	0.868842	+	0.558371i	0.868842	+	0.558371i
$750$		0			0
$751$	−0.0294925	−	0.0489079i	−0.0294925	−	0.0489079i	0.841254	−	0.540641i	$-0.181818\pi$
$751$	−0.0294925	−	0.0489079i	−0.0294925	−	0.0489079i	−0.870746	+	0.491733i	$0.836364\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.879056	−	0.313647i	−0.879056	−	0.313647i	−0.142315	−	0.989821i	$-0.545455\pi$
$757$	−0.879056	−	0.313647i	−0.879056	−	0.313647i	−0.736741	+	0.676175i	$0.763636\pi$
$758$	1.49398	−	1.72414i	1.49398	−	1.72414i
$759$		0			0
$760$		0			0
$761$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$761$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$762$		0			0
$763$	1.11235	+	1.62676i	1.11235	+	1.62676i
$764$	−0.954857	+	2.45253i	−0.954857	+	2.45253i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$769$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$770$		0			0
$771$		0			0
$772$	1.89688	−	0.441101i	1.89688	−	0.441101i
$773$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$773$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$774$	0.785920	−	2.98995i	0.785920	−	2.98995i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.76610	+	1.44413i	−1.76610	+	1.44413i
$779$		0			0
$780$		0			0
$781$	−0.310476	−	1.18117i	−0.310476	−	1.18117i
$782$		0			0
$783$		0			0
$784$	0.113144	+	0.430445i	0.113144	+	0.430445i
$785$		0			0
$786$		0			0
$787$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$787$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$788$	−0.0716088	+	0.0352077i	−0.0716088	+	0.0352077i
$789$		0			0
$790$		0			0
$791$	−0.198369	−	1.37969i	−0.198369	−	1.37969i
$792$	0.476057	−	0.389270i	0.476057	−	0.389270i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$797$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$798$		0			0
$799$		0			0
$800$	1.28494	+	0.222367i	1.28494	+	0.222367i
$801$		0			0
$802$	−0.726077	−	1.58989i	−0.726077	−	1.58989i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.720886	+	1.85158i	−0.720886	+	1.85158i	−0.254218	+	0.967147i	$0.581818\pi$
$809$	−0.720886	+	1.85158i	−0.720886	+	1.85158i	−0.466667	+	0.884433i	$0.654545\pi$
$810$		0			0
$811$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$811$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$812$	0.882776	+	2.26739i	0.882776	+	2.26739i
$813$		0			0
$814$	0.295696	+	0.910058i	0.295696	+	0.910058i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.90648	−	0.218748i	−1.90648	−	0.218748i	−0.921124	−	0.389270i	$-0.872727\pi$
$821$	−1.90648	−	0.218748i	−1.90648	−	0.218748i	−0.985354	+	0.170522i	$0.945455\pi$
$822$		0			0
$823$	1.40890	−	0.795641i	1.40890	−	0.795641i	0.415415	−	0.909632i	$-0.363636\pi$
$823$	1.40890	−	0.795641i	1.40890	−	0.795641i	0.993482	+	0.113991i	$0.0363636\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.132827	−	0.251736i	0.132827	−	0.251736i	−0.809017	−	0.587785i	$-0.800000\pi$
$827$	0.132827	−	0.251736i	0.132827	−	0.251736i	0.941844	+	0.336049i	$0.109091\pi$
$828$	0.654346	−	0.276529i	0.654346	−	0.276529i
$829$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$829$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$830$		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		−0.736741	−	0.676175i	$-0.763636\pi$
$839$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$840$		0			0
$841$	−0.948639	−	1.79787i	−0.948639	−	1.79787i
$842$	−2.41968	−	1.36645i	−2.41968	−	1.36645i
$843$		0			0
$844$	−0.487400	+	1.50006i	−0.487400	+	1.50006i
$845$		0			0
$846$		0			0
$847$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$848$	−0.867000			−0.867000
$849$		0			0
$850$		0			0
$851$	0.00897320	+	0.314103i	0.00897320	+	0.314103i
$852$		0			0
$853$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$853$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$854$		0			0
$855$		0			0
$856$	−0.513819	−	0.373312i	−0.513819	−	0.373312i
$857$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$857$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$858$		0			0
$859$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$859$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$860$		0			0
$861$		0			0
$862$	2.10142	−	1.92867i	2.10142	−	1.92867i
$863$	1.91586	−	0.109553i	1.91586	−	0.109553i	0.941844	−	0.336049i	$-0.109091\pi$
$863$	1.91586	−	0.109553i	1.91586	−	0.109553i	0.974012	+	0.226497i	$0.0727273\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.80739	+	0.530696i	−1.80739	+	0.530696i
$870$		0			0
$871$		0			0
$872$	−0.625814	−	1.03780i	−0.625814	−	1.03780i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.0348754	+	1.22080i	−0.0348754	+	1.22080i	0.774142	+	0.633012i	$0.218182\pi$
$877$	−0.0348754	+	1.22080i	−0.0348754	+	1.22080i	−0.809017	+	0.587785i	$0.800000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$881$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$882$	−0.561729	−	1.44279i	−0.561729	−	1.44279i
$883$	0.739263	−	1.08114i	0.739263	−	1.08114i	−0.254218	−	0.967147i	$-0.581818\pi$
$883$	0.739263	−	1.08114i	0.739263	−	1.08114i	0.993482	−	0.113991i	$-0.0363636\pi$
$884$		0			0
$885$		0			0
$886$	−1.05812	+	0.377537i	−1.05812	+	0.377537i
$887$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$887$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$888$		0			0
$889$	0.394592	−	1.94739i	0.394592	−	1.94739i
$890$		0			0
$891$	0.696938	−	0.717132i	0.696938	−	0.717132i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.224981	−	1.11032i	−0.224981	−	1.11032i
$897$		0			0
$898$	2.81055	+	1.18775i	2.81055	+	1.18775i
$899$		0			0
$900$	−1.39490	−	0.0797634i	−1.39490	−	0.0797634i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.0733516	+	0.854017i	0.0733516	+	0.854017i
$905$		0			0
$906$		0			0
$907$	0.971444	+	0.999592i	0.971444	+	0.999592i	1.00000			$0$
$907$	0.971444	+	0.999592i	0.971444	+	0.999592i	−0.0285561	+	0.999592i	$0.509091\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.0243572	−	0.283586i	−0.0243572	−	0.283586i	−0.998369	−	0.0570888i	$-0.981818\pi$
$911$	−0.0243572	−	0.283586i	−0.0243572	−	0.283586i	0.974012	−	0.226497i	$-0.0727273\pi$
$912$		0			0
$913$		0			0
$914$	−0.136180	+	0.947152i	−0.136180	+	0.947152i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.0788763	+	0.389270i	0.0788763	+	0.389270i	1.00000			$0$
$919$	0.0788763	+	0.389270i	0.0788763	+	0.389270i	−0.921124	+	0.389270i	$0.872727\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.256741	−	0.562183i	0.256741	−	0.562183i
$926$	−0.286976	+	1.41628i	−0.286976	+	1.41628i
$927$		0			0
$928$	0.701769	+	2.15982i	0.701769	+	2.15982i
$929$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$929$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$930$		0			0
$931$		0			0
$932$	1.03288	−	1.51055i	1.03288	−	1.51055i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$937$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$938$	−0.00756703	+	0.264881i	−0.00756703	+	0.264881i
$939$		0			0
$940$		0			0
$941$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$941$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	2.02451	−	2.33641i	2.02451	−	2.33641i
$947$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$947$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.831697	−	0.763325i	0.831697	−	0.763325i	−0.142315	−	0.989821i	$-0.545455\pi$
$953$	0.831697	−	0.763325i	0.831697	−	0.763325i	0.974012	+	0.226497i	$0.0727273\pi$
$954$	2.99643	−	0.343809i	2.99643	−	0.343809i
$955$		0			0
$956$	−0.229441	−	0.0673700i	−0.229441	−	0.0673700i
$957$		0			0
$958$		0			0
$959$	0.0462047	+	0.0335697i	0.0462047	+	0.0335697i
$960$		0			0
$961$	0.774142	+	0.633012i	0.774142	+	0.633012i
$962$		0			0
$963$	−0.899302	−	0.507859i	−0.899302	−	0.507859i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.97071			−1.97071			−0.985354	−	0.170522i	$-0.945455\pi$
$967$	−1.97071			−1.97071			−0.985354	+	0.170522i	$0.945455\pi$
$968$	0.598967	−	0.139284i	0.598967	−	0.139284i
$969$		0			0
$970$		0			0
$971$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$971$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$972$		0			0
$973$		0			0
$974$	1.44271	+	2.73424i	1.44271	+	2.73424i
$975$		0			0
$976$		0			0
$977$	−1.45202	−	1.05496i	−1.45202	−	1.05496i	−0.985354	−	0.170522i	$-0.945455\pi$
$977$	−1.45202	−	1.05496i	−1.45202	−	1.05496i	−0.466667	−	0.884433i	$-0.654545\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.20341	−	1.56061i	−1.20341	−	1.56061i
$982$	2.58802	−	0.296947i	2.58802	−	0.296947i
$983$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$983$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.854053	−	0.548867i	0.854053	−	0.548867i
$990$		0			0
$991$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$991$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$992$		0			0
$993$		0			0
$994$	1.87859	+	0.215548i	1.87859	+	0.215548i
$995$		0			0
$996$		0			0
$997$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$997$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$998$	0.0715379	−	2.50415i	0.0715379	−	2.50415i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.1.bb.a.433.1	yes	40
7.6	odd	2	CM	847.1.bb.a.433.1	yes	40
121.102	even	55	inner	847.1.bb.a.223.1	✓	40
847.223	odd	110	inner	847.1.bb.a.223.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.1.bb.a.223.1	✓	40	121.102	even	55	inner
847.1.bb.a.223.1	✓	40	847.223	odd	110	inner
847.1.bb.a.433.1	yes	40	1.1	even	1	trivial
847.1.bb.a.433.1	yes	40	7.6	odd	2	CM

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	847.bb (of order \(110\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07906 - 1.11032i) q^{2} +(-0.0398980 - 1.39661i) q^{4} +(0.774142 + 0.633012i) q^{7} +(-0.453058 - 0.415813i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.07906 - 1.11032i) q^{2} +(-0.0398980 - 1.39661i) q^{4} +(0.774142 + 0.633012i) q^{7} +(-0.453058 - 0.415813i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.466667 - 0.884433i) q^{11} +(1.53819 - 0.176491i) q^{14} +(0.444341 - 0.0254083i) q^{16} +(-1.52561 + 0.264017i) q^{18} +(-1.48557 - 0.436202i) q^{22} +(-0.427724 - 0.274882i) q^{23} +(0.516397 + 0.856349i) q^{25} +(0.853186 - 1.10643i) q^{28} +(-0.899302 + 1.49133i) q^{29} +(0.853963 - 0.985526i) q^{32} +(-0.788629 + 1.15333i) q^{36} +(-0.348845 - 0.510170i) q^{37} +(-0.829475 + 1.81630i) q^{43} +(-1.21659 + 0.687040i) q^{44} +(-0.766746 + 0.178299i) q^{46} +(0.198590 + 0.980083i) q^{49} +(1.50805 + 0.350681i) q^{50} +(-1.94485 - 0.111210i) q^{53} +(-0.0875163 - 0.608689i) q^{56} +(0.685455 + 2.60774i) q^{58} +(-0.254218 - 0.967147i) q^{63} +(-0.134691 - 1.56818i) q^{64} +(-0.0243572 + 0.169408i) q^{67} +(1.18956 + 0.276620i) q^{71} +(0.122123 + 0.602700i) q^{72} +(-0.942877 - 0.163171i) q^{74} +(0.198590 - 0.980083i) q^{77} +(0.374083 - 1.84617i) q^{79} +(0.309017 + 0.951057i) q^{81} +(1.12163 + 2.88087i) q^{86} +(-0.156331 + 0.594746i) q^{88} +(-0.366837 + 0.608332i) q^{92} +(1.30250 + 0.837065i) q^{98} +(-0.142315 + 0.989821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46} + q^{49} + 2 q^{50} - 3 q^{53} - 7 q^{56} - 12 q^{58} + q^{63} - 9 q^{64} + 2 q^{67} - 3 q^{71} - q^{72} + 4 q^{74} + q^{77} - 3 q^{79} - 10 q^{81} - q^{86} - 12 q^{88} - 4 q^{92} - 9 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9 + q^11 - 3 * q^14 - 3 * q^18 + 2 * q^22 - 9 * q^23 + q^25 - 2 * q^28 + 2 * q^29 - 4 * q^32 + 3 * q^36 - 3 * q^37 + 2 * q^43 - 13 * q^44 - q^46 + q^49 + 2 * q^50 - 3 * q^53 - 7 * q^56 - 12 * q^58 + q^63 - 9 * q^64 + 2 * q^67 - 3 * q^71 - q^72 + 4 * q^74 + q^77 - 3 * q^79 - 10 * q^81 - q^86 - 12 * q^88 - 4 * q^92 - 9 * q^98 - 4 * q^99

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