LMFDB - Embedded newform 847.1.bb.a.412.1

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			412.1
Root			$-0.921124 - 0.389270i$ of defining polynomial
Character	$\chi$	$=$	847.412
Dual form			847.1.bb.a.405.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73511 - 0.733264i) q^{2} +(1.77599 + 1.82745i) q^{4} +(0.941844 - 0.336049i) q^{7} +(-1.05812 - 2.71777i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.516397 + 0.856349i) q^{11} +(-1.88062 - 0.107538i) q^{14} +(-0.0841108 + 2.94426i) q^{16} +(0.161197 - 1.87678i) q^{18} +(-0.268077 - 1.86452i) q^{22} +(-1.17182 + 0.344079i) q^{23} +(-0.870746 + 0.491733i) q^{25} +(2.28683 + 1.12436i) q^{28} +(0.442719 + 0.250015i) q^{29} +(1.09331 - 2.39402i) q^{32} +(-1.18920 + 2.25379i) q^{36} +(0.755084 + 1.43104i) q^{37} +(-0.0480458 - 0.0308771i) q^{43} +(-0.647820 + 2.46456i) q^{44} +(2.28555 + 0.262242i) q^{46} +(0.774142 - 0.633012i) q^{49} +(1.87141 - 0.214724i) q^{50} +(-0.0567398 - 1.98615i) q^{53} +(-1.90989 - 2.20413i) q^{56} +(-0.584840 - 0.758434i) q^{58} +(0.610648 + 0.791902i) q^{63} +(-1.48242 + 1.36055i) q^{64} +(0.964926 - 1.11358i) q^{67} +(1.78310 - 0.204591i) q^{71} +(2.25777 - 1.84617i) q^{72} +(-0.260822 - 3.03669i) q^{74} +(0.774142 + 0.633012i) q^{77} +(-1.52561 - 1.24748i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.0607236 + 0.0888054i) q^{86} +(1.78094 - 2.30957i) q^{88} +(-2.70994 - 1.53037i) q^{92} +(-1.80739 + 0.530696i) q^{98} +(-0.654861 + 0.755750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{7}{55}\right)$

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 $

$2$	−1.73511	−	0.733264i	−1.73511	−	0.733264i	−0.998369	−	0.0570888i	$-0.981818\pi$
$2$	−1.73511	−	0.733264i	−1.73511	−	0.733264i	−0.736741	−	0.676175i	$-0.763636\pi$
$3$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$3$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$4$	1.77599	+	1.82745i	1.77599	+	1.82745i
$5$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$5$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$6$		0			0
$7$	0.941844	−	0.336049i	0.941844	−	0.336049i
$7$	0.941844	−	0.336049i	0.941844	−	0.336049i
$8$	−1.05812	−	2.71777i	−1.05812	−	2.71777i
$9$	0.309017	+	0.951057i	0.309017	+	0.951057i
$10$		0			0
$11$	0.516397	+	0.856349i	0.516397	+	0.856349i
$11$	0.516397	+	0.856349i	0.516397	+	0.856349i
$12$		0			0
$13$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$13$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$14$	−1.88062	−	0.107538i	−1.88062	−	0.107538i
$15$		0			0
$16$	−0.0841108	+	2.94426i	−0.0841108	+	2.94426i
$17$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$17$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$18$	0.161197	−	1.87678i	0.161197	−	1.87678i
$19$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$19$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$20$		0			0
$21$		0			0
$22$	−0.268077	−	1.86452i	−0.268077	−	1.86452i
$23$	−1.17182	+	0.344079i	−1.17182	+	0.344079i	−0.809017	−	0.587785i	$-0.800000\pi$
$23$	−1.17182	+	0.344079i	−1.17182	+	0.344079i	−0.362808	+	0.931864i	$0.618182\pi$
$24$		0			0
$25$	−0.870746	+	0.491733i	−0.870746	+	0.491733i
$26$		0			0
$27$		0			0
$28$	2.28683	+	1.12436i	2.28683	+	1.12436i
$29$	0.442719	+	0.250015i	0.442719	+	0.250015i	0.696938	−	0.717132i	$-0.254545\pi$
$29$	0.442719	+	0.250015i	0.442719	+	0.250015i	−0.254218	+	0.967147i	$0.581818\pi$
$30$		0			0
$31$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$31$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$32$	1.09331	−	2.39402i	1.09331	−	2.39402i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−1.18920	+	2.25379i	−1.18920	+	2.25379i
$37$	0.755084	+	1.43104i	0.755084	+	1.43104i	0.897398	+	0.441221i	$0.145455\pi$
$37$	0.755084	+	1.43104i	0.755084	+	1.43104i	−0.142315	+	0.989821i	$0.545455\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$41$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$42$		0			0
$43$	−0.0480458	−	0.0308771i	−0.0480458	−	0.0308771i	0.516397	−	0.856349i	$-0.327273\pi$
$43$	−0.0480458	−	0.0308771i	−0.0480458	−	0.0308771i	−0.564443	+	0.825472i	$0.690909\pi$
$44$	−0.647820	+	2.46456i	−0.647820	+	2.46456i
$45$		0			0
$46$	2.28555	+	0.262242i	2.28555	+	0.262242i
$47$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$47$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$48$		0			0
$49$	0.774142	−	0.633012i	0.774142	−	0.633012i
$50$	1.87141	−	0.214724i	1.87141	−	0.214724i
$51$		0			0
$52$		0			0
$53$	−0.0567398	−	1.98615i	−0.0567398	−	1.98615i	−0.142315	−	0.989821i	$-0.545455\pi$
$53$	−0.0567398	−	1.98615i	−0.0567398	−	1.98615i	0.0855750	−	0.996332i	$-0.472727\pi$
$54$		0			0
$55$		0			0
$56$	−1.90989	−	2.20413i	−1.90989	−	2.20413i
$57$		0			0
$58$	−0.584840	−	0.758434i	−0.584840	−	0.758434i
$59$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$59$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$60$		0			0
$61$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$61$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$62$		0			0
$63$	0.610648	+	0.791902i	0.610648	+	0.791902i
$64$	−1.48242	+	1.36055i	−1.48242	+	1.36055i
$65$		0			0
$66$		0			0
$67$	0.964926	−	1.11358i	0.964926	−	1.11358i	−0.0285561	−	0.999592i	$-0.509091\pi$
$67$	0.964926	−	1.11358i	0.964926	−	1.11358i	0.993482	−	0.113991i	$-0.0363636\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.78310	−	0.204591i	1.78310	−	0.204591i	0.841254	−	0.540641i	$-0.181818\pi$
$71$	1.78310	−	0.204591i	1.78310	−	0.204591i	0.941844	+	0.336049i	$0.109091\pi$
$72$	2.25777	−	1.84617i	2.25777	−	1.84617i
$73$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$73$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$74$	−0.260822	−	3.03669i	−0.260822	−	3.03669i
$75$		0			0
$76$		0			0
$77$	0.774142	+	0.633012i	0.774142	+	0.633012i
$78$		0			0
$79$	−1.52561	−	1.24748i	−1.52561	−	1.24748i	−0.870746	−	0.491733i	$-0.836364\pi$
$79$	−1.52561	−	1.24748i	−1.52561	−	1.24748i	−0.654861	−	0.755750i	$-0.727273\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$82$		0			0
$83$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$83$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$84$		0			0
$85$		0			0
$86$	0.0607236	+	0.0888054i	0.0607236	+	0.0888054i
$87$		0			0
$88$	1.78094	−	2.30957i	1.78094	−	2.30957i
$89$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$89$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$90$		0			0
$91$		0			0
$92$	−2.70994	−	1.53037i	−2.70994	−	1.53037i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$97$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$98$	−1.80739	+	0.530696i	−1.80739	+	0.530696i
$99$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$100$	−2.44506	−	0.717934i	−2.44506	−	0.717934i
$101$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$101$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$102$		0			0
$103$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$103$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$104$		0			0
$105$		0			0
$106$	−1.35792	+	3.48780i	−1.35792	+	3.48780i
$107$	1.73865	+	0.0994197i	1.73865	+	0.0994197i	0.897398	−	0.441221i	$-0.145455\pi$
$107$	1.73865	+	0.0994197i	1.73865	+	0.0994197i	0.841254	+	0.540641i	$0.181818\pi$
$108$		0			0
$109$	−0.0243572	−	0.169408i	−0.0243572	−	0.169408i	0.974012	−	0.226497i	$-0.0727273\pi$
$109$	−0.0243572	−	0.169408i	−0.0243572	−	0.169408i	−0.998369	+	0.0570888i	$0.981818\pi$
$110$		0			0
$111$		0			0
$112$	0.910198	+	2.80130i	0.910198	+	2.80130i
$113$	0.668382	+	1.71672i	0.668382	+	1.71672i	0.696938	+	0.717132i	$0.254545\pi$
$113$	0.668382	+	1.71672i	0.668382	+	1.71672i	−0.0285561	+	0.999592i	$0.509091\pi$
$114$		0			0
$115$		0			0
$116$	0.329376	+	1.25307i	0.329376	+	1.25307i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.478868	−	1.82180i	−0.478868	−	1.82180i
$127$	−1.03111	−	1.70990i	−1.03111	−	1.70990i	−0.564443	−	0.825472i	$-0.690909\pi$
$127$	−1.03111	−	1.70990i	−1.03111	−	1.70990i	−0.466667	−	0.884433i	$-0.654545\pi$
$128$	1.09101	−	0.389270i	1.09101	−	0.389270i
$129$		0			0
$130$		0			0
$131$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$131$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$132$		0			0
$133$		0			0
$134$	−2.49080	+	1.22465i	−2.49080	+	1.22465i
$135$		0			0
$136$		0			0
$137$	−0.0398036	+	1.39331i	−0.0398036	+	1.39331i	0.696938	+	0.717132i	$0.254545\pi$
$137$	−0.0398036	+	1.39331i	−0.0398036	+	1.39331i	−0.736741	+	0.676175i	$0.763636\pi$
$138$		0			0
$139$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$139$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$140$		0			0
$141$		0			0
$142$	−3.24389	−	0.952492i	−3.24389	−	0.952492i
$143$		0			0
$144$	−2.82615	+	0.829833i	−2.82615	+	0.829833i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−1.27414	+	3.92140i	−1.27414	+	3.92140i
$149$	−1.17534	−	0.577877i	−1.17534	−	0.577877i	−0.254218	−	0.967147i	$-0.581818\pi$
$149$	−1.17534	−	0.577877i	−1.17534	−	0.577877i	−0.921124	+	0.389270i	$0.872727\pi$
$150$		0			0
$151$	−0.505709	+	0.520362i	−0.505709	+	0.520362i	−0.921124	−	0.389270i	$-0.872727\pi$
$151$	−0.505709	+	0.520362i	−0.505709	+	0.520362i	0.415415	+	0.909632i	$0.363636\pi$
$152$		0			0
$153$		0			0
$154$	−0.879056	−	1.66600i	−0.879056	−	1.66600i
$155$		0			0
$156$		0			0
$157$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$157$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$158$	1.73236	+	3.28319i	1.73236	+	3.28319i
$159$		0			0
$160$		0			0
$161$	−0.988049	+	0.717860i	−0.988049	+	0.717860i
$162$	1.83474	−	0.426649i	1.83474	−	0.426649i
$163$	−1.34816	−	1.10239i	−1.34816	−	1.10239i	−0.985354	−	0.170522i	$-0.945455\pi$
$163$	−1.34816	−	1.10239i	−1.34816	−	1.10239i	−0.362808	−	0.931864i	$-0.618182\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$167$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$168$		0			0
$169$	0.610648	−	0.791902i	0.610648	−	0.791902i
$170$		0			0
$171$		0			0
$172$	−0.0289024	−	0.142639i	−0.0289024	−	0.142639i
$173$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$173$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$174$		0			0
$175$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$176$	−2.56475	+	1.44838i	−2.56475	+	1.44838i
$177$		0			0
$178$		0			0
$179$	−1.21930	−	1.58122i	−1.21930	−	1.58122i	−0.654861	−	0.755750i	$-0.727273\pi$
$179$	−1.21930	−	1.58122i	−1.21930	−	1.58122i	−0.564443	−	0.825472i	$-0.690909\pi$
$180$		0			0
$181$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$181$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$182$		0			0
$183$		0			0
$184$	2.17506	+	2.82067i	2.17506	+	2.82067i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.391364	−	1.93146i	−0.391364	−	1.93146i	−0.362808	−	0.931864i	$-0.618182\pi$
$191$	−0.391364	−	1.93146i	−0.391364	−	1.93146i	−0.0285561	−	0.999592i	$-0.509091\pi$
$192$		0			0
$193$	−1.42616	+	1.16617i	−1.42616	+	1.16617i	−0.466667	+	0.884433i	$0.654545\pi$
$193$	−1.42616	+	1.16617i	−1.42616	+	1.16617i	−0.959493	+	0.281733i	$0.909091\pi$
$194$		0			0
$195$		0			0
$196$	2.53167	+	0.290482i	2.53167	+	0.290482i
$197$	1.17260	−	0.753586i	1.17260	−	0.753586i	0.198590	−	0.980083i	$-0.436364\pi$
$197$	1.17260	−	0.753586i	1.17260	−	0.753586i	0.974012	+	0.226497i	$0.0727273\pi$
$198$	1.69042	−	0.831123i	1.69042	−	0.831123i
$199$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$199$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$200$	2.25777	+	1.84617i	2.25777	+	1.84617i
$201$		0			0
$202$		0			0
$203$	0.500990	+	0.0866997i	0.500990	+	0.0866997i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.689352	−	1.00815i	−0.689352	−	1.00815i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.919665	−	0.159154i	0.919665	−	0.159154i	0.309017	−	0.951057i	$-0.400000\pi$
$211$	0.919665	−	0.159154i	0.919665	−	0.159154i	0.610648	+	0.791902i	$0.290909\pi$
$212$	3.52884	−	3.63109i	3.52884	−	3.63109i
$213$		0			0
$214$	−2.94385	−	1.44739i	−2.94385	−	1.44739i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.0819583	+	0.311802i	−0.0819583	+	0.311802i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$223$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$224$	0.225221	−	2.62220i	0.225221	−	2.62220i
$225$	−0.736741	−	0.676175i	−0.736741	−	0.676175i
$226$	0.0990958	−	3.46881i	0.0990958	−	3.46881i
$227$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$227$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$228$		0			0
$229$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$229$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$230$		0			0
$231$		0			0
$232$	0.211031	−	1.46775i	0.211031	−	1.46775i
$233$	0.256741	+	0.790166i	0.256741	+	0.790166i	0.993482	+	0.113991i	$0.0363636\pi$
$233$	0.256741	+	0.790166i	0.256741	+	0.790166i	−0.736741	+	0.676175i	$0.763636\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.19207	+	0.866091i	1.19207	+	0.866091i	0.993482	−	0.113991i	$-0.0363636\pi$
$239$	1.19207	+	0.866091i	1.19207	+	0.866091i	0.198590	+	0.980083i	$0.436364\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	1.45824	−	1.19240i	1.45824	−	1.19240i
$243$		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		−0.309017	−	0.951057i	$-0.600000\pi$
$251$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$252$	−0.362659	+	2.52235i	−0.362659	+	2.52235i
$253$	−0.899779	−	0.825810i	−0.899779	−	0.825810i
$254$	0.535279	+	3.72295i	0.535279	+	3.72295i
$255$		0			0
$256$	−0.169605	−	0.00969837i	−0.169605	−	0.00969837i
$257$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$257$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$258$		0			0
$259$	1.19207	+	1.09407i	1.19207	+	1.09407i
$260$		0			0
$261$	−0.100971	+	0.498310i	−0.100971	+	0.498310i
$262$		0			0
$263$	−1.72209	−	0.505653i	−1.72209	−	0.505653i	−0.736741	−	0.676175i	$-0.763636\pi$
$263$	−1.72209	−	0.505653i	−1.72209	−	0.505653i	−0.985354	+	0.170522i	$0.945455\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	3.74873	−	0.214360i	3.74873	−	0.214360i
$269$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$269$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$270$		0			0
$271$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$271$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$272$		0			0
$273$		0			0
$274$	1.09072	−	2.38835i	1.09072	−	2.38835i
$275$	−0.870746	−	0.491733i	−0.870746	−	0.491733i
$276$		0			0
$277$	−0.224186	−	0.327862i	−0.224186	−	0.327862i	0.696938	−	0.717132i	$-0.254545\pi$
$277$	−0.224186	−	0.327862i	−0.224186	−	0.327862i	−0.921124	+	0.389270i	$0.872727\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.95786	−	0.338821i	−1.95786	−	0.338821i	−0.998369	−	0.0570888i	$-0.981818\pi$
$281$	−1.95786	−	0.338821i	−1.95786	−	0.338821i	−0.959493	−	0.281733i	$-0.909091\pi$
$282$		0			0
$283$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$283$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$284$	3.54065	+	2.89518i	3.54065	+	2.89518i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.61470	+	0.300009i	2.61470	+	0.300009i
$289$	0.0855750	+	0.996332i	0.0855750	+	0.996332i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$293$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$294$		0			0
$295$		0			0
$296$	3.09027	−	3.56636i	3.09027	−	3.56636i
$297$		0			0
$298$	1.61561	+	1.86452i	1.61561	+	1.86452i
$299$		0			0
$300$		0			0
$301$	−0.0556279	−	0.0129357i	−0.0556279	−	0.0129357i
$302$	1.25902	−	0.532067i	1.25902	−	0.532067i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$307$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$308$	0.218069	+	2.53894i	0.218069	+	2.53894i
$309$		0			0
$310$		0			0
$311$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$311$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$312$		0			0
$313$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$313$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$314$		0			0
$315$		0			0
$316$	−0.429751	−	5.00350i	−0.429751	−	5.00350i
$317$	0.614005	+	0.0704506i	0.614005	+	0.0704506i	0.415415	−	0.909632i	$-0.363636\pi$
$317$	0.614005	+	0.0704506i	0.614005	+	0.0704506i	0.198590	+	0.980083i	$0.436364\pi$
$318$		0			0
$319$	0.0145189	+	0.508229i	0.0145189	+	0.508229i
$320$		0			0
$321$		0			0
$322$	2.24075	−	0.521065i	2.24075	−	0.521065i
$323$		0			0
$324$	−2.51096	−	0.434539i	−2.51096	−	0.434539i
$325$		0			0
$326$	1.53087	+	2.90132i	1.53087	+	2.90132i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.809238	−	1.77198i	0.809238	−	1.77198i	0.198590	−	0.980083i	$-0.436364\pi$
$331$	0.809238	−	1.77198i	0.809238	−	1.77198i	0.610648	−	0.791902i	$-0.290909\pi$
$332$		0			0
$333$	−1.12767	+	1.16034i	−1.12767	+	1.16034i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.94485	+	0.111210i	−1.94485	+	0.111210i	−0.985354	−	0.170522i	$-0.945455\pi$
$337$	−1.94485	+	0.111210i	−1.94485	+	0.111210i	−0.959493	+	0.281733i	$0.909091\pi$
$338$	−1.64021	+	0.926272i	−1.64021	+	0.926272i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.516397	−	0.856349i	0.516397	−	0.856349i
$344$	−0.0330785	+	0.163249i	−0.0330785	+	0.163249i
$345$		0			0
$346$		0			0
$347$	0.0322365	−	1.12843i	0.0322365	−	1.12843i	−0.809017	−	0.587785i	$-0.800000\pi$
$347$	0.0322365	−	1.12843i	0.0322365	−	1.12843i	0.841254	−	0.540641i	$-0.181818\pi$
$348$		0			0
$349$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$349$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$350$	1.69042	−	0.831123i	1.69042	−	0.831123i
$351$		0			0
$352$	2.61470	−	0.300009i	2.61470	−	0.300009i
$353$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$353$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.956174	+	3.63766i	0.956174	+	3.63766i
$359$	1.35765	+	1.39699i	1.35765	+	1.39699i	0.841254	+	0.540641i	$0.181818\pi$
$359$	1.35765	+	1.39699i	1.35765	+	1.39699i	0.516397	+	0.856349i	$0.327273\pi$
$360$		0			0
$361$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$367$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$368$	−0.914495	−	3.47910i	−0.914495	−	3.47910i
$369$		0			0
$370$		0			0
$371$	−0.720886	−	1.85158i	−0.720886	−	1.85158i
$372$		0			0
$373$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$373$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.0207207	−	0.725319i	0.0207207	−	0.725319i	−0.921124	−	0.389270i	$-0.872727\pi$
$379$	0.0207207	−	0.725319i	0.0207207	−	0.725319i	0.941844	−	0.336049i	$-0.109091\pi$
$380$		0			0
$381$		0			0
$382$	−0.737207	+	3.63826i	−0.737207	+	3.63826i
$383$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$383$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$384$		0			0
$385$		0			0
$386$	3.32965	−	0.977674i	3.32965	−	0.977674i
$387$	0.0145189	−	0.0552358i	0.0145189	−	0.0552358i
$388$		0			0
$389$	0.724432	−	0.0414245i	0.724432	−	0.0414245i	0.309017	−	0.951057i	$-0.400000\pi$
$389$	0.724432	−	0.0414245i	0.724432	−	0.0414245i	0.415415	+	0.909632i	$0.363636\pi$
$390$		0			0
$391$		0			0
$392$	−2.53952	−	1.43413i	−2.53952	−	1.43413i
$393$		0			0
$394$	−2.58717	+	0.447728i	−2.58717	+	0.447728i
$395$		0			0
$396$	−2.54413	+	0.145478i	−2.54413	+	0.145478i
$397$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$397$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$398$		0			0
$399$		0			0
$400$	−1.37455	−	2.60507i	−1.37455	−	2.60507i
$401$	0.526814	−	0.770442i	0.526814	−	0.770442i	−0.466667	−	0.884433i	$-0.654545\pi$
$401$	0.526814	−	0.770442i	0.526814	−	0.770442i	0.993482	+	0.113991i	$0.0363636\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.805699	−	0.517791i	−0.805699	−	0.517791i
$407$	−0.835549	+	1.38560i	−0.835549	+	1.38560i
$408$		0			0
$409$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$409$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.456866	+	2.25472i	0.456866	+	2.25472i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$419$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$420$		0			0
$421$	1.18956	+	1.54264i	1.18956	+	1.54264i	0.774142	+	0.633012i	$0.218182\pi$
$421$	1.18956	+	1.54264i	1.18956	+	1.54264i	0.415415	+	0.909632i	$0.363636\pi$
$422$	−1.71242	−	0.398207i	−1.71242	−	0.398207i
$423$		0			0
$424$	−5.33786	+	2.25580i	−5.33786	+	2.25580i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	2.90615	+	3.35388i	2.90615	+	3.35388i
$429$		0			0
$430$		0			0
$431$	−0.0113419	−	0.397019i	−0.0113419	−	0.397019i	−0.985354	−	0.170522i	$-0.945455\pi$
$431$	−0.0113419	−	0.397019i	−0.0113419	−	0.397019i	0.974012	−	0.226497i	$-0.0727273\pi$
$432$		0			0
$433$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$433$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$434$		0			0
$435$		0			0
$436$	0.266327	−	0.345379i	0.266327	−	0.345379i
$437$		0			0
$438$		0			0
$439$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$439$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$440$		0			0
$441$	0.841254	+	0.540641i	0.841254	+	0.540641i
$442$		0			0
$443$	−1.09955	+	0.255689i	−1.09955	+	0.255689i	−0.736741	−	0.676175i	$-0.763636\pi$
$443$	−1.09955	+	0.255689i	−1.09955	+	0.255689i	−0.362808	+	0.931864i	$0.618182\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.938995	+	1.77959i	−0.938995	+	1.77959i
$449$	−0.0966045	−	0.141280i	−0.0966045	−	0.141280i	0.774142	−	0.633012i	$-0.218182\pi$
$449$	−0.0966045	−	0.141280i	−0.0966045	−	0.141280i	−0.870746	+	0.491733i	$0.836364\pi$
$450$	0.782513	+	1.71346i	0.782513	+	1.71346i
$451$		0			0
$452$	−1.95019	+	4.27033i	−1.95019	+	4.27033i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$457$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$461$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$462$		0			0
$463$	−0.990959	−	0.290972i	−0.990959	−	0.290972i	−0.254218	−	0.967147i	$-0.581818\pi$
$463$	−0.990959	−	0.290972i	−0.990959	−	0.290972i	−0.736741	+	0.676175i	$0.763636\pi$
$464$	−0.773348	+	1.28245i	−0.773348	+	1.28245i
$465$		0			0
$466$	0.133927	−	1.55928i	0.133927	−	1.55928i
$467$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$467$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$468$		0			0
$469$	0.534591	−	1.37309i	0.534591	−	1.37309i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.00163090	−	0.0570888i	0.00163090	−	0.0570888i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.87141	−	0.667718i	1.87141	−	0.667718i
$478$	−1.43330	−	2.37687i	−1.43330	−	2.37687i
$479$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$479$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−2.44506	+	0.717934i	−2.44506	+	0.717934i
$485$		0			0
$486$		0			0
$487$	0.0462047	+	0.0335697i	0.0462047	+	0.0335697i	0.610648	−	0.791902i	$-0.290909\pi$
$487$	0.0462047	+	0.0335697i	0.0462047	+	0.0335697i	−0.564443	+	0.825472i	$0.690909\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.80739	+	0.644874i	−1.80739	+	0.644874i	−0.809017	+	0.587785i	$0.800000\pi$
$491$	−1.80739	+	0.644874i	−1.80739	+	0.644874i	−0.998369	+	0.0570888i	$0.981818\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.61065	−	0.791902i	1.61065	−	0.791902i
$498$		0			0
$499$	−0.224227	+	0.575924i	−0.224227	+	0.575924i	−0.998369	−	0.0570888i	$-0.981818\pi$
$499$	−0.224227	+	0.575924i	−0.224227	+	0.575924i	0.774142	+	0.633012i	$0.218182\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$503$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$504$	1.50606	−	2.49753i	1.50606	−	2.49753i
$505$		0			0
$506$	0.955679	+	2.09265i	0.955679	+	2.09265i
$507$		0			0
$508$	1.29353	−	4.92109i	1.29353	−	4.92109i
$509$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$509$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$510$		0			0
$511$		0			0
$512$	−0.752349	−	0.369905i	−0.752349	−	0.369905i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−1.26613	−	2.77244i	−1.26613	−	2.77244i
$519$		0			0
$520$		0			0
$521$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$521$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$522$	0.540588	−	0.790585i	0.540588	−	0.790585i
$523$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$523$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$524$		0			0
$525$		0			0
$526$	2.61725	+	2.14011i	2.61725	+	2.14011i
$527$		0			0
$528$		0			0
$529$	0.413529	−	0.265759i	0.413529	−	0.265759i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−4.04747	−	1.44413i	−4.04747	−	1.44413i
$537$		0			0
$538$		0			0
$539$	0.941844	+	0.336049i	0.941844	+	0.336049i
$540$		0			0
$541$	0.687626	−	0.631097i	0.687626	−	0.631097i	−0.254218	−	0.967147i	$-0.581818\pi$
$541$	0.687626	−	0.631097i	0.687626	−	0.631097i	0.941844	+	0.336049i	$0.109091\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.507345	+	0.657936i	0.507345	+	0.657936i	0.974012	−	0.226497i	$-0.0727273\pi$
$547$	0.507345	+	0.657936i	0.507345	+	0.657936i	−0.466667	+	0.884433i	$0.654545\pi$
$548$	−2.61690	+	2.40177i	−2.61690	+	2.40177i
$549$		0			0
$550$	1.15027	+	1.49170i	1.15027	+	1.49170i
$551$		0			0
$552$		0			0
$553$	−1.85610	−	0.662255i	−1.85610	−	0.662255i
$554$	0.148578	+	0.733264i	0.148578	+	0.733264i
$555$		0			0
$556$		0			0
$557$	0.377401	−	0.489423i	0.377401	−	0.489423i	−0.564443	−	0.825472i	$-0.690909\pi$
$557$	0.377401	−	0.489423i	0.377401	−	0.489423i	0.941844	+	0.336049i	$0.109091\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	3.14866	+	2.02352i	3.14866	+	2.02352i
$563$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$563$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$568$	−2.44277	−	4.62956i	−2.44277	−	4.62956i
$569$	−0.785171	+	1.48806i	−0.785171	+	1.48806i	0.0855750	+	0.996332i	$0.472727\pi$
$569$	−0.785171	+	1.48806i	−0.785171	+	1.48806i	−0.870746	+	0.491733i	$0.836364\pi$
$570$		0			0
$571$	0.579037	+	1.26791i	0.579037	+	1.26791i	0.941844	+	0.336049i	$0.109091\pi$
$571$	0.579037	+	1.26791i	0.579037	+	1.26791i	−0.362808	+	0.931864i	$0.618182\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.851167	−	0.875830i	0.851167	−	0.875830i
$576$	−1.75205	−	0.989430i	−1.75205	−	0.989430i
$577$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$577$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$578$	0.582092	−	1.79149i	0.582092	−	1.79149i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.67154	−	1.07423i	1.67154	−	1.07423i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$587$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−4.27688	+	2.10280i	−4.27688	+	2.10280i
$593$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$593$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$594$		0			0
$595$		0			0
$596$	−1.03136	−	3.17419i	−1.03136	−	3.17419i
$597$		0			0
$598$		0			0
$599$	0.0883814	+	0.146564i	0.0883814	+	0.146564i	0.897398	−	0.441221i	$-0.145455\pi$
$599$	0.0883814	+	0.146564i	0.0883814	+	0.146564i	−0.809017	+	0.587785i	$0.800000\pi$
$600$		0			0
$601$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$601$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$602$	0.0870352	+	0.0632348i	0.0870352	+	0.0632348i
$603$	1.35726	+	0.573583i	1.35726	+	0.573583i
$604$	−1.84907			−1.84907
$605$		0			0
$606$		0			0
$607$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$607$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.409569	+	1.05197i	0.409569	+	1.05197i	0.974012	+	0.226497i	$0.0727273\pi$
$613$	0.409569	+	1.05197i	0.409569	+	1.05197i	−0.564443	+	0.825472i	$0.690909\pi$
$614$		0			0
$615$		0			0
$616$	0.901243	−	2.77374i	0.901243	−	2.77374i
$617$	−0.146982	−	1.02228i	−0.146982	−	1.02228i	−0.921124	−	0.389270i	$-0.872727\pi$
$617$	−0.146982	−	1.02228i	−0.146982	−	1.02228i	0.774142	−	0.633012i	$-0.218182\pi$
$618$		0			0
$619$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$619$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.516397	−	0.856349i	0.516397	−	0.856349i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.931812	−	0.0532830i	0.931812	−	0.0532830i	0.415415	−	0.909632i	$-0.363636\pi$
$631$	0.931812	−	0.0532830i	0.931812	−	0.0532830i	0.516397	+	0.856349i	$0.327273\pi$
$632$	−1.77609	+	5.46623i	−1.77609	+	5.46623i
$633$		0			0
$634$	−1.01371	−	0.572467i	−1.01371	−	0.572467i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.347474	−	0.892480i	0.347474	−	0.892480i
$639$	0.745586	+	1.63260i	0.745586	+	1.63260i
$640$		0			0
$641$	0.526814	−	0.998424i	0.526814	−	0.998424i	−0.466667	−	0.884433i	$-0.654545\pi$
$641$	0.526814	−	0.998424i	0.526814	−	0.998424i	0.993482	−	0.113991i	$-0.0363636\pi$
$642$		0			0
$643$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$643$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$644$	−3.06663	−	0.530700i	−3.06663	−	0.530700i
$645$		0			0
$646$		0			0
$647$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$647$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$648$	2.45350	+	1.57677i	2.45350	+	1.57677i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.379766	−	4.42154i	−0.379766	−	4.42154i
$653$	−1.21930	+	1.58122i	−1.21930	+	1.58122i	−0.564443	+	0.825472i	$0.690909\pi$
$653$	−1.21930	+	1.58122i	−1.21930	+	1.58122i	−0.654861	+	0.755750i	$0.727273\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$659$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$660$		0			0
$661$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$661$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$662$	−2.70345	+	2.48120i	−2.70345	+	2.48120i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	2.80747	−	1.18645i	2.80747	−	1.18645i
$667$	−0.604814	−	0.140644i	−0.604814	−	0.140644i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.0322365	+	1.12843i	0.0322365	+	1.12843i	0.841254	+	0.540641i	$0.181818\pi$
$673$	0.0322365	+	1.12843i	0.0322365	+	1.12843i	−0.809017	+	0.587785i	$0.800000\pi$
$674$	3.45607	+	1.23312i	3.45607	+	1.23312i
$675$		0			0
$676$	2.53167	−	0.290482i	2.53167	−	0.290482i
$677$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$677$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.785171	−	0.504599i	−0.785171	−	0.504599i	0.0855750	−	0.996332i	$-0.472727\pi$
$683$	−0.785171	−	0.504599i	−0.785171	−	0.504599i	−0.870746	+	0.491733i	$0.836364\pi$
$684$		0			0
$685$		0			0
$686$	−1.52394	+	1.10720i	−1.52394	+	1.10720i
$687$		0			0
$688$	0.0949516	−	0.138862i	0.0949516	−	0.138862i
$689$		0			0
$690$		0			0
$691$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$691$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$692$		0			0
$693$	−0.362808	+	0.931864i	−0.362808	+	0.931864i
$694$	−0.883368	+	1.93431i	−0.883368	+	1.93431i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−2.54413	+	0.145478i	−2.54413	+	0.145478i
$701$	0.631827	−	0.356809i	0.631827	−	0.356809i	−0.142315	−	0.989821i	$-0.545455\pi$
$701$	0.631827	−	0.356809i	0.631827	−	0.356809i	0.774142	+	0.633012i	$0.218182\pi$
$702$		0			0
$703$		0			0
$704$	−1.93062	−	0.566882i	−1.93062	−	0.566882i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.831697	+	0.763325i	0.831697	+	0.763325i	0.974012	−	0.226497i	$-0.0727273\pi$
$709$	0.831697	+	0.763325i	0.831697	+	0.763325i	−0.142315	+	0.989821i	$0.545455\pi$
$710$		0			0
$711$	0.714988	−	1.83643i	0.714988	−	1.83643i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.724134	−	5.03646i	0.724134	−	5.03646i
$717$		0			0
$718$	−1.33131	−	3.41945i	−1.33131	−	3.41945i
$719$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$719$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$720$		0			0
$721$		0			0
$722$	1.31281	+	1.35085i	1.31281	+	1.35085i
$723$		0			0
$724$		0			0
$725$	−0.508437			−0.508437
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$733$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$734$		0			0
$735$		0			0
$736$	−0.457439	+	3.18156i	−0.457439	+	3.18156i
$737$	1.45190	+	0.251261i	1.45190	+	0.251261i
$738$		0			0
$739$	0.554623	−	0.272690i	0.554623	−	0.272690i	−0.142315	−	0.989821i	$-0.545455\pi$
$739$	0.554623	−	0.272690i	0.554623	−	0.272690i	0.696938	+	0.717132i	$0.254545\pi$
$740$		0			0
$741$		0			0
$742$	−0.106880	+	3.74129i	−0.106880	+	3.74129i
$743$	−0.455331	−	0.417899i	−0.455331	−	0.417899i	0.415415	−	0.909632i	$-0.363636\pi$
$743$	−0.455331	−	0.417899i	−0.455331	−	0.417899i	−0.870746	+	0.491733i	$0.836364\pi$
$744$		0			0
$745$		0			0
$746$	−1.86666	+	3.09551i	−1.86666	+	3.09551i
$747$		0			0
$748$		0			0
$749$	1.67095	−	0.490635i	1.67095	−	0.490635i
$750$		0			0
$751$	−1.21371	+	0.685414i	−1.21371	+	0.685414i	−0.959493	−	0.281733i	$-0.909091\pi$
$751$	−1.21371	+	0.685414i	−1.21371	+	0.685414i	−0.254218	+	0.967147i	$0.581818\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.01767	+	0.176114i	−1.01767	+	0.176114i	−0.654861	−	0.755750i	$-0.727273\pi$
$757$	−1.01767	+	0.176114i	−1.01767	+	0.176114i	−0.362808	+	0.931864i	$0.618182\pi$
$758$	−0.567803	+	1.24332i	−0.567803	+	1.24332i
$759$		0			0
$760$		0			0
$761$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$761$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$762$		0			0
$763$	−0.0798701	−	0.151371i	−0.0798701	−	0.151371i
$764$	2.83459	−	4.14545i	2.83459	−	4.14545i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$769$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$770$		0			0
$771$		0			0
$772$	−4.66397	−	0.535140i	−4.66397	−	0.535140i
$773$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$773$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$774$	−0.0656944	+	0.0851940i	−0.0656944	+	0.0851940i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.28734	−	0.459324i	−1.28734	−	0.459324i
$779$		0			0
$780$		0			0
$781$	1.09599	+	1.42130i	1.09599	+	1.42130i
$782$		0			0
$783$		0			0
$784$	1.79864	+	2.33252i	1.79864	+	2.33252i
$785$		0			0
$786$		0			0
$787$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$787$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$788$	3.45968	+	0.804514i	3.45968	+	0.804514i
$789$		0			0
$790$		0			0
$791$	1.20642	+	1.39228i	1.20642	+	1.39228i
$792$	2.74687	+	0.980083i	2.74687	+	0.980083i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$797$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$798$		0			0
$799$		0			0
$800$	0.225221	+	2.62220i	0.225221	+	2.62220i
$801$		0			0
$802$	−1.47902	+	0.950507i	−1.47902	+	0.950507i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.12705	−	1.64825i	1.12705	−	1.64825i	0.516397	−	0.856349i	$-0.327273\pi$
$809$	1.12705	−	1.64825i	1.12705	−	1.64825i	0.610648	−	0.791902i	$-0.290909\pi$
$810$		0			0
$811$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$811$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$812$	0.731316	+	1.06951i	0.731316	+	1.06951i
$813$		0			0
$814$	2.46578	−	1.79149i	2.46578	−	1.79149i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.284165	−	0.0162492i	0.284165	−	0.0162492i	0.0855750	−	0.996332i	$-0.472727\pi$
$821$	0.284165	−	0.0162492i	0.284165	−	0.0162492i	0.198590	+	0.980083i	$0.436364\pi$
$822$		0			0
$823$	−0.157116	+	0.597730i	−0.157116	+	0.597730i	0.841254	+	0.540641i	$0.181818\pi$
$823$	−0.157116	+	0.597730i	−0.157116	+	0.597730i	−0.998369	+	0.0570888i	$0.981818\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.676337	+	1.12158i	−0.676337	+	1.12158i	0.309017	+	0.951057i	$0.400000\pi$
$827$	−0.676337	+	1.12158i	−0.676337	+	1.12158i	−0.985354	+	0.170522i	$0.945455\pi$
$828$	0.618055	−	3.05022i	0.618055	−	3.05022i
$829$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$829$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$830$		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		−0.362808	−	0.931864i	$-0.618182\pi$
$839$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$840$		0			0
$841$	−0.382905	−	0.634976i	−0.382905	−	0.634976i
$842$	−0.932847	−	3.54892i	−0.932847	−	3.54892i
$843$		0			0
$844$	1.92417	+	1.39799i	1.92417	+	1.39799i
$845$		0			0
$846$		0			0
$847$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$848$	5.85253			5.85253
$849$		0			0
$850$		0			0
$851$	−1.37722	−	1.41712i	−1.37722	−	1.41712i
$852$		0			0
$853$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$853$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$854$		0			0
$855$		0			0
$856$	−1.56951	−	4.83045i	−1.56951	−	4.83045i
$857$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$857$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$858$		0			0
$859$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$859$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$860$		0			0
$861$		0			0
$862$	−0.271440	+	0.697188i	−0.271440	+	0.697188i
$863$	0.00812790	−	0.284514i	0.00812790	−	0.284514i	−0.985354	−	0.170522i	$-0.945455\pi$
$863$	0.00812790	−	0.284514i	0.00812790	−	0.284514i	0.993482	−	0.113991i	$-0.0363636\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.280461	−	1.95065i	0.280461	−	1.95065i
$870$		0			0
$871$		0			0
$872$	−0.434638	+	0.245452i	−0.434638	+	0.245452i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.25086	−	1.28711i	1.25086	−	1.28711i	0.309017	−	0.951057i	$-0.400000\pi$
$877$	1.25086	−	1.28711i	1.25086	−	1.28711i	0.941844	−	0.336049i	$-0.109091\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$881$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$882$	−1.06324	−	1.55493i	−1.06324	−	1.55493i
$883$	−0.387721	+	0.734813i	−0.387721	+	0.734813i	−0.998369	−	0.0570888i	$-0.981818\pi$
$883$	−0.387721	+	0.734813i	−0.387721	+	0.734813i	0.610648	+	0.791902i	$0.290909\pi$
$884$		0			0
$885$		0			0
$886$	2.09533	+	0.362610i	2.09533	+	0.362610i
$887$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$887$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$888$		0			0
$889$	−1.54576	−	1.26396i	−1.54576	−	1.26396i
$890$		0			0
$891$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.896744	−	0.733264i	0.896744	−	0.733264i
$897$		0			0
$898$	0.0640242	+	0.315972i	0.0640242	+	0.315972i
$899$		0			0
$900$	−0.0727689	−	2.54724i	−0.0727689	−	2.54724i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	3.95842	−	3.63301i	3.95842	−	3.63301i
$905$		0			0
$906$		0			0
$907$	1.69694	−	0.717132i	1.69694	−	0.717132i	0.696938	−	0.717132i	$-0.254545\pi$
$907$	1.69694	−	0.717132i	1.69694	−	0.717132i	1.00000			$0$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.964926	−	0.885601i	0.964926	−	0.885601i	−0.0285561	−	0.999592i	$-0.509091\pi$
$911$	0.964926	−	0.885601i	0.964926	−	0.885601i	0.993482	+	0.113991i	$0.0363636\pi$
$912$		0			0
$913$		0			0
$914$	1.99593	−	2.30343i	1.99593	−	2.30343i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.19859	−	0.980083i	1.19859	−	0.980083i	0.198590	−	0.980083i	$-0.436364\pi$
$919$	1.19859	−	0.980083i	1.19859	−	0.980083i	1.00000			$0$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.36118	−	0.874775i	−1.36118	−	0.874775i
$926$	1.50606	+	1.23150i	1.50606	+	1.23150i
$927$		0			0
$928$	1.08257	−	0.786534i	1.08257	−	0.786534i
$929$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$929$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$930$		0			0
$931$		0			0
$932$	−0.988023	+	1.87251i	−0.988023	+	1.87251i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$937$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$938$	−1.93441	+	1.99046i	−1.93441	+	1.99046i
$939$		0			0
$940$		0			0
$941$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$941$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.0446909	+	0.0978595i	−0.0446909	+	0.0978595i
$947$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$947$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.338621	−	0.869741i	0.338621	−	0.869741i	−0.654861	−	0.755750i	$-0.727273\pi$
$953$	0.338621	−	0.869741i	0.338621	−	0.869741i	0.993482	−	0.113991i	$-0.0363636\pi$
$954$	−3.73672	−	0.213673i	−3.73672	−	0.213673i
$955$		0			0
$956$	0.534371	+	3.71663i	0.534371	+	3.71663i
$957$		0			0
$958$		0			0
$959$	0.430731	+	1.32565i	0.430731	+	1.32565i
$960$		0			0
$961$	0.941844	−	0.336049i	0.941844	−	0.336049i
$962$		0			0
$963$	0.442719	+	1.68428i	0.442719	+	1.68428i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.171150			0.171150			0.0855750	−	0.996332i	$-0.472727\pi$
$967$	0.171150			0.171150			0.0855750	+	0.996332i	$0.472727\pi$
$968$	2.89747	+	0.332454i	2.89747	+	0.332454i
$969$		0			0
$970$		0			0
$971$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$971$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$972$		0			0
$973$		0			0
$974$	−0.0555548	−	0.0921272i	−0.0555548	−	0.0921272i
$975$		0			0
$976$		0			0
$977$	0.601972	+	1.85268i	0.601972	+	1.85268i	0.516397	+	0.856349i	$0.327273\pi$
$977$	0.601972	+	1.85268i	0.601972	+	1.85268i	0.0855750	+	0.996332i	$0.472727\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.153590	−	0.0755150i	0.153590	−	0.0755150i
$982$	3.60888	+	0.206363i	3.60888	+	0.206363i
$983$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$983$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.0669254	+	0.0196511i	0.0669254	+	0.0196511i
$990$		0			0
$991$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$991$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$992$		0			0
$993$		0			0
$994$	−3.37532	+	0.193008i	−3.37532	+	0.193008i
$995$		0			0
$996$		0			0
$997$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$997$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$998$	0.811363	−	0.834873i	0.811363	−	0.834873i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.1.bb.a.412.1	yes	40
7.6	odd	2	CM	847.1.bb.a.412.1	yes	40
121.42	even	55	inner	847.1.bb.a.405.1	✓	40
847.405	odd	110	inner	847.1.bb.a.405.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.1.bb.a.405.1	✓	40	121.42	even	55	inner
847.1.bb.a.405.1	✓	40	847.405	odd	110	inner
847.1.bb.a.412.1	yes	40	1.1	even	1	trivial
847.1.bb.a.412.1	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)

\(f(q)\)	\(=\)	\(q+(-1.73511 - 0.733264i) q^{2} +(1.77599 + 1.82745i) q^{4} +(0.941844 - 0.336049i) q^{7} +(-1.05812 - 2.71777i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.516397 + 0.856349i) q^{11} +(-1.88062 - 0.107538i) q^{14} +(-0.0841108 + 2.94426i) q^{16} +(0.161197 - 1.87678i) q^{18} +(-0.268077 - 1.86452i) q^{22} +(-1.17182 + 0.344079i) q^{23} +(-0.870746 + 0.491733i) q^{25} +(2.28683 + 1.12436i) q^{28} +(0.442719 + 0.250015i) q^{29} +(1.09331 - 2.39402i) q^{32} +(-1.18920 + 2.25379i) q^{36} +(0.755084 + 1.43104i) q^{37} +(-0.0480458 - 0.0308771i) q^{43} +(-0.647820 + 2.46456i) q^{44} +(2.28555 + 0.262242i) q^{46} +(0.774142 - 0.633012i) q^{49} +(1.87141 - 0.214724i) q^{50} +(-0.0567398 - 1.98615i) q^{53} +(-1.90989 - 2.20413i) q^{56} +(-0.584840 - 0.758434i) q^{58} +(0.610648 + 0.791902i) q^{63} +(-1.48242 + 1.36055i) q^{64} +(0.964926 - 1.11358i) q^{67} +(1.78310 - 0.204591i) q^{71} +(2.25777 - 1.84617i) q^{72} +(-0.260822 - 3.03669i) q^{74} +(0.774142 + 0.633012i) q^{77} +(-1.52561 - 1.24748i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.0607236 + 0.0888054i) q^{86} +(1.78094 - 2.30957i) q^{88} +(-2.70994 - 1.53037i) q^{92} +(-1.80739 + 0.530696i) q^{98} +(-0.654861 + 0.755750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46}+ \cdots - 4 q^{99}+O(q^{100}) \) 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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