LMFDB - Embedded newform 847.1.bb.a.48.1

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			48.1
Root			$-0.870746 + 0.491733i$ of defining polynomial
Character	$\chi$	$=$	847.48
Dual form			847.1.bb.a.300.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.56281 + 0.882561i) q^{2} +(1.14707 - 1.90220i) q^{4} +(0.897398 - 0.441221i) q^{7} +(-0.0625942 + 2.19108i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.198590 + 0.980083i) q^{11} +(-1.01306 + 1.48155i) q^{14} +(-0.799335 - 1.51491i) q^{16} +(1.78310 + 0.204591i) q^{18} +(-1.17534 - 1.35642i) q^{22} +(0.280461 - 1.95065i) q^{23} +(0.774142 - 0.633012i) q^{25} +(0.190087 - 2.21315i) q^{28} +(1.45824 + 1.19240i) q^{29} +(0.742201 + 0.476984i) q^{32} +(-2.04609 + 0.864684i) q^{36} +(-0.569286 - 0.240582i) q^{37} +(0.895528 - 0.262951i) q^{43} +(2.09211 + 0.746465i) q^{44} +(1.28326 + 3.29602i) q^{46} +(0.610648 - 0.791902i) q^{49} +(-0.651166 + 1.67251i) q^{50} +(0.338621 - 0.641758i) q^{53} +(0.910580 + 1.99389i) q^{56} +(-3.33132 - 0.576508i) q^{58} +(-0.985354 - 0.170522i) q^{63} +(0.129177 + 0.00738662i) q^{64} +(-0.829475 + 1.81630i) q^{67} +(-0.0620945 + 0.159489i) q^{71} +(1.33853 - 1.73583i) q^{72} +(1.10202 - 0.126444i) q^{74} +(0.610648 + 0.791902i) q^{77} +(1.18956 + 1.54264i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-1.16747 + 1.20130i) q^{86} +(-2.15987 + 0.373781i) q^{88} +(-3.38882 - 2.77103i) q^{92} +(-0.255426 + 1.77653i) q^{98} +(0.415415 - 0.909632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{46}{55}\right)$

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 $

$2$	−1.56281	+	0.882561i	−1.56281	+	0.882561i	−0.564443	+	0.825472i	$0.690909\pi$
$2$	−1.56281	+	0.882561i	−1.56281	+	0.882561i	−0.998369	+	0.0570888i	$0.981818\pi$
$3$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$3$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$4$	1.14707	−	1.90220i	1.14707	−	1.90220i
$5$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$5$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$6$		0			0
$7$	0.897398	−	0.441221i	0.897398	−	0.441221i
$7$	0.897398	−	0.441221i	0.897398	−	0.441221i
$8$	−0.0625942	+	2.19108i	−0.0625942	+	2.19108i
$9$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$10$		0			0
$11$	0.198590	+	0.980083i	0.198590	+	0.980083i
$11$	0.198590	+	0.980083i	0.198590	+	0.980083i
$12$		0			0
$13$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$13$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$14$	−1.01306	+	1.48155i	−1.01306	+	1.48155i
$15$		0			0
$16$	−0.799335	−	1.51491i	−0.799335	−	1.51491i
$17$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$17$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$18$	1.78310	+	0.204591i	1.78310	+	0.204591i
$19$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$19$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$20$		0			0
$21$		0			0
$22$	−1.17534	−	1.35642i	−1.17534	−	1.35642i
$23$	0.280461	−	1.95065i	0.280461	−	1.95065i	−0.0285561	−	0.999592i	$-0.509091\pi$
$23$	0.280461	−	1.95065i	0.280461	−	1.95065i	0.309017	−	0.951057i	$-0.400000\pi$
$24$		0			0
$25$	0.774142	−	0.633012i	0.774142	−	0.633012i
$26$		0			0
$27$		0			0
$28$	0.190087	−	2.21315i	0.190087	−	2.21315i
$29$	1.45824	+	1.19240i	1.45824	+	1.19240i	0.941844	+	0.336049i	$0.109091\pi$
$29$	1.45824	+	1.19240i	1.45824	+	1.19240i	0.516397	+	0.856349i	$0.327273\pi$
$30$		0			0
$31$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$31$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$32$	0.742201	+	0.476984i	0.742201	+	0.476984i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−2.04609	+	0.864684i	−2.04609	+	0.864684i
$37$	−0.569286	−	0.240582i	−0.569286	−	0.240582i	0.0855750	−	0.996332i	$-0.472727\pi$
$37$	−0.569286	−	0.240582i	−0.569286	−	0.240582i	−0.654861	+	0.755750i	$0.727273\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$41$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$42$		0			0
$43$	0.895528	−	0.262951i	0.895528	−	0.262951i	0.198590	−	0.980083i	$-0.436364\pi$
$43$	0.895528	−	0.262951i	0.895528	−	0.262951i	0.696938	+	0.717132i	$0.254545\pi$
$44$	2.09211	+	0.746465i	2.09211	+	0.746465i
$45$		0			0
$46$	1.28326	+	3.29602i	1.28326	+	3.29602i
$47$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$47$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$48$		0			0
$49$	0.610648	−	0.791902i	0.610648	−	0.791902i
$50$	−0.651166	+	1.67251i	−0.651166	+	1.67251i
$51$		0			0
$52$		0			0
$53$	0.338621	−	0.641758i	0.338621	−	0.641758i	−0.654861	−	0.755750i	$-0.727273\pi$
$53$	0.338621	−	0.641758i	0.338621	−	0.641758i	0.993482	+	0.113991i	$0.0363636\pi$
$54$		0			0
$55$		0			0
$56$	0.910580	+	1.99389i	0.910580	+	1.99389i
$57$		0			0
$58$	−3.33132	−	0.576508i	−3.33132	−	0.576508i
$59$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$59$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$60$		0			0
$61$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$61$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$62$		0			0
$63$	−0.985354	−	0.170522i	−0.985354	−	0.170522i
$64$	0.129177	+	0.00738662i	0.129177	+	0.00738662i
$65$		0			0
$66$		0			0
$67$	−0.829475	+	1.81630i	−0.829475	+	1.81630i	−0.362808	+	0.931864i	$0.618182\pi$
$67$	−0.829475	+	1.81630i	−0.829475	+	1.81630i	−0.466667	+	0.884433i	$0.654545\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.0620945	+	0.159489i	−0.0620945	+	0.159489i	−0.959493	−	0.281733i	$-0.909091\pi$
$71$	−0.0620945	+	0.159489i	−0.0620945	+	0.159489i	0.897398	+	0.441221i	$0.145455\pi$
$72$	1.33853	−	1.73583i	1.33853	−	1.73583i
$73$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$73$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$74$	1.10202	−	0.126444i	1.10202	−	0.126444i
$75$		0			0
$76$		0			0
$77$	0.610648	+	0.791902i	0.610648	+	0.791902i
$78$		0			0
$79$	1.18956	+	1.54264i	1.18956	+	1.54264i	0.774142	+	0.633012i	$0.218182\pi$
$79$	1.18956	+	1.54264i	1.18956	+	1.54264i	0.415415	+	0.909632i	$0.363636\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.309017	+	0.951057i
$82$		0			0
$83$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$83$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$84$		0			0
$85$		0			0
$86$	−1.16747	+	1.20130i	−1.16747	+	1.20130i
$87$		0			0
$88$	−2.15987	+	0.373781i	−2.15987	+	0.373781i
$89$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$89$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$90$		0			0
$91$		0			0
$92$	−3.38882	−	2.77103i	−3.38882	−	2.77103i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$97$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$98$	−0.255426	+	1.77653i	−0.255426	+	1.77653i
$99$	0.415415	−	0.909632i	0.415415	−	0.909632i
$100$	−0.316123	−	2.19869i	−0.316123	−	2.19869i
$101$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$101$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$102$		0			0
$103$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$103$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$104$		0			0
$105$		0			0
$106$	0.0371895	+	1.30180i	0.0371895	+	1.30180i
$107$	−0.873918	+	1.27806i	−0.873918	+	1.27806i	0.0855750	+	0.996332i	$0.472727\pi$
$107$	−0.873918	+	1.27806i	−0.873918	+	1.27806i	−0.959493	+	0.281733i	$0.909091\pi$
$108$		0			0
$109$	−1.30118	−	1.50165i	−1.30118	−	1.50165i	−0.736741	−	0.676175i	$-0.763636\pi$
$109$	−1.30118	−	1.50165i	−1.30118	−	1.50165i	−0.564443	−	0.825472i	$-0.690909\pi$
$110$		0			0
$111$		0			0
$112$	−1.38573	−	1.00679i	−1.38573	−	1.00679i
$113$	0.0497301	−	1.74078i	0.0497301	−	1.74078i	−0.466667	−	0.884433i	$-0.654545\pi$
$113$	0.0497301	−	1.74078i	0.0497301	−	1.74078i	0.516397	−	0.856349i	$-0.327273\pi$
$114$		0			0
$115$		0			0
$116$	3.94089	−	1.40611i	3.94089	−	1.40611i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	1.69042	−	0.603140i	1.69042	−	0.603140i
$127$	−0.224186	−	1.10640i	−0.224186	−	1.10640i	−0.921124	−	0.389270i	$-0.872727\pi$
$127$	−0.224186	−	1.10640i	−0.224186	−	1.10640i	0.696938	−	0.717132i	$-0.254545\pi$
$128$	−1.00013	+	0.491733i	−1.00013	+	0.491733i
$129$		0			0
$130$		0			0
$131$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$131$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$132$		0			0
$133$		0			0
$134$	−0.306679	−	3.57059i	−0.306679	−	3.57059i
$135$		0			0
$136$		0			0
$137$	−0.481972	−	0.913438i	−0.481972	−	0.913438i	−0.998369	−	0.0570888i	$-0.981818\pi$
$137$	−0.481972	−	0.913438i	−0.481972	−	0.913438i	0.516397	−	0.856349i	$-0.327273\pi$
$138$		0			0
$139$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$139$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$140$		0			0
$141$		0			0
$142$	−0.0437162	−	0.304053i	−0.0437162	−	0.304053i
$143$		0			0
$144$	−0.243765	+	1.69542i	−0.243765	+	1.69542i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−1.11065	+	0.806933i	−1.11065	+	0.806933i
$149$	0.0710983	−	0.827782i	0.0710983	−	0.827782i	−0.870746	−	0.491733i	$-0.836364\pi$
$149$	0.0710983	−	0.827782i	0.0710983	−	0.827782i	0.941844	−	0.336049i	$-0.109091\pi$
$150$		0			0
$151$	−0.0294925	−	0.0489079i	−0.0294925	−	0.0489079i	0.841254	−	0.540641i	$-0.181818\pi$
$151$	−0.0294925	−	0.0489079i	−0.0294925	−	0.0489079i	−0.870746	+	0.491733i	$0.836364\pi$
$152$		0			0
$153$		0			0
$154$	−1.65323	−	0.698661i	−1.65323	−	0.698661i
$155$		0			0
$156$		0			0
$157$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$157$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$158$	−3.22053	−	1.36101i	−3.22053	−	1.36101i
$159$		0			0
$160$		0			0
$161$	−0.608982	−	1.87425i	−0.608982	−	1.87425i
$162$	−1.32230	−	1.21360i	−1.32230	−	1.21360i
$163$	0.945456	+	1.22609i	0.945456	+	1.22609i	0.974012	+	0.226497i	$0.0727273\pi$
$163$	0.945456	+	1.22609i	0.945456	+	1.22609i	−0.0285561	+	0.999592i	$0.509091\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$167$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$168$		0			0
$169$	−0.985354	+	0.170522i	−0.985354	+	0.170522i
$170$		0			0
$171$		0			0
$172$	0.527049	−	2.00510i	0.527049	−	2.00510i
$173$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$173$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$174$		0			0
$175$	0.415415	−	0.909632i	0.415415	−	0.909632i
$176$	1.32600	−	1.08426i	1.32600	−	1.08426i
$177$		0			0
$178$		0			0
$179$	1.11235	+	0.192500i	1.11235	+	0.192500i	0.696938	−	0.717132i	$-0.254545\pi$
$179$	1.11235	+	0.192500i	1.11235	+	0.192500i	0.415415	+	0.909632i	$0.363636\pi$
$180$		0			0
$181$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$181$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$182$		0			0
$183$		0			0
$184$	4.25648	+	0.736613i	4.25648	+	0.736613i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.495223	+	1.88403i	−0.495223	+	1.88403i	−0.0285561	+	0.999592i	$0.509091\pi$
$191$	−0.495223	+	1.88403i	−0.495223	+	1.88403i	−0.466667	+	0.884433i	$0.654545\pi$
$192$		0			0
$193$	−1.06344	+	1.37909i	−1.06344	+	1.37909i	−0.142315	+	0.989821i	$0.545455\pi$
$193$	−1.06344	+	1.37909i	−1.06344	+	1.37909i	−0.921124	+	0.389270i	$0.872727\pi$
$194$		0			0
$195$		0			0
$196$	−0.805903	−	2.06995i	−0.805903	−	2.06995i
$197$	−0.990959	−	0.290972i	−0.990959	−	0.290972i	−0.254218	−	0.967147i	$-0.581818\pi$
$197$	−0.990959	−	0.290972i	−0.990959	−	0.290972i	−0.736741	+	0.676175i	$0.763636\pi$
$198$	0.153590	+	1.78821i	0.153590	+	1.78821i
$199$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$199$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$200$	1.33853	+	1.73583i	1.33853	+	1.73583i
$201$		0			0
$202$		0			0
$203$	1.83474	+	0.426649i	1.83474	+	0.426649i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.37346	+	1.41326i	−1.37346	+	1.41326i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.79437	+	0.417263i	−1.79437	+	0.417263i	−0.985354	−	0.170522i	$-0.945455\pi$
$211$	−1.79437	+	0.417263i	−1.79437	+	0.417263i	−0.809017	+	0.587785i	$0.800000\pi$
$212$	−0.832333	−	1.38027i	−0.832333	−	1.38027i
$213$		0			0
$214$	0.237800	−	2.76866i	0.237800	−	2.76866i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	3.35880	+	1.19842i	3.35880	+	1.19842i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$223$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$224$	0.876506	+	0.100570i	0.876506	+	0.100570i
$225$	−0.998369	+	0.0570888i	−0.998369	+	0.0570888i
$226$	1.45863	+	2.76441i	1.45863	+	2.76441i
$227$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$227$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$228$		0			0
$229$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$229$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$230$		0			0
$231$		0			0
$232$	−2.70392	+	3.12049i	−2.70392	+	3.12049i
$233$	−1.36118	−	0.988953i	−1.36118	−	0.988953i	−0.998369	−	0.0570888i	$-0.981818\pi$
$233$	−1.36118	−	0.988953i	−1.36118	−	0.988953i	−0.362808	−	0.931864i	$-0.618182\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.617026	+	1.89901i	−0.617026	+	1.89901i	−0.254218	+	0.967147i	$0.581818\pi$
$239$	−0.617026	+	1.89901i	−0.617026	+	1.89901i	−0.362808	+	0.931864i	$0.618182\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	1.09599	−	1.42130i	1.09599	−	1.42130i
$243$		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	$0.200000\pi$
$252$	−1.45464	+	1.67874i	−1.45464	+	1.67874i
$253$	1.96749	−	0.112505i	1.96749	−	0.112505i
$254$	1.32683	+	1.53124i	1.32683	+	1.53124i
$255$		0			0
$256$	1.05601	−	1.54436i	1.05601	−	1.54436i
$257$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$257$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$258$		0			0
$259$	−0.617026	+	0.0352828i	−0.617026	+	0.0352828i
$260$		0			0
$261$	−0.478868	−	1.82180i	−0.478868	−	1.82180i
$262$		0			0
$263$	−0.0243572	−	0.169408i	−0.0243572	−	0.169408i	0.974012	−	0.226497i	$-0.0727273\pi$
$263$	−0.0243572	−	0.169408i	−0.0243572	−	0.169408i	−0.998369	+	0.0570888i	$0.981818\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	2.50350	+	3.66125i	2.50350	+	3.66125i
$269$		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		−0.774142	−	0.633012i	$-0.781818\pi$
$271$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$272$		0			0
$273$		0			0
$274$	1.55940	+	1.00216i	1.55940	+	1.00216i
$275$	0.774142	+	0.633012i	0.774142	+	0.633012i
$276$		0			0
$277$	−0.354349	+	0.364616i	−0.354349	+	0.364616i	−0.870746	−	0.491733i	$-0.836364\pi$
$277$	−0.354349	+	0.364616i	−0.354349	+	0.364616i	0.516397	+	0.856349i	$0.327273\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.706758	−	0.164350i	−0.706758	−	0.164350i	−0.142315	−	0.989821i	$-0.545455\pi$
$281$	−0.706758	−	0.164350i	−0.706758	−	0.164350i	−0.564443	+	0.825472i	$0.690909\pi$
$282$		0			0
$283$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$283$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$284$	0.232153	+	0.301061i	0.232153	+	0.301061i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.320089	−	0.822143i	−0.320089	−	0.822143i
$289$	0.993482	−	0.113991i	0.993482	−	0.113991i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$293$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$294$		0			0
$295$		0			0
$296$	0.562770	−	1.23229i	0.562770	−	1.23229i
$297$		0			0
$298$	0.619455	+	1.35642i	0.619455	+	1.35642i
$299$		0			0
$300$		0			0
$301$	0.687626	−	0.631097i	0.687626	−	0.631097i
$302$	0.0892555	+	0.0504049i	0.0892555	+	0.0504049i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$307$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$308$	2.20682	−	0.253209i	2.20682	−	0.253209i
$309$		0			0
$310$		0			0
$311$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$311$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$312$		0			0
$313$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$313$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$314$		0			0
$315$		0			0
$316$	4.29893	−	0.493256i	4.29893	−	0.493256i
$317$	0.587035	+	1.50779i	0.587035	+	1.50779i	0.841254	+	0.540641i	$0.181818\pi$
$317$	0.587035	+	1.50779i	0.587035	+	1.50779i	−0.254218	+	0.967147i	$0.581818\pi$
$318$		0			0
$319$	−0.879056	+	1.66600i	−0.879056	+	1.66600i
$320$		0			0
$321$		0			0
$322$	2.60587	+	2.39164i	2.60587	+	2.39164i
$323$		0			0
$324$	2.16357	+	0.503116i	2.16357	+	0.503116i
$325$		0			0
$326$	−2.55967	−	1.08172i	−2.55967	−	1.08172i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.23957	−	0.796625i	−1.23957	−	0.796625i	−0.254218	−	0.967147i	$-0.581818\pi$
$331$	−1.23957	−	0.796625i	−1.23957	−	0.796625i	−0.985354	+	0.170522i	$0.945455\pi$
$332$		0			0
$333$	0.319151	+	0.529253i	0.319151	+	0.529253i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.831697	+	1.21632i	0.831697	+	1.21632i	0.974012	+	0.226497i	$0.0727273\pi$
$337$	0.831697	+	1.21632i	0.831697	+	1.21632i	−0.142315	+	0.989821i	$0.545455\pi$
$338$	1.38943	−	1.13613i	1.38943	−	1.13613i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.198590	−	0.980083i	0.198590	−	0.980083i
$344$	0.520092	+	1.97864i	0.520092	+	1.97864i
$345$		0			0
$346$		0			0
$347$	−0.650476	−	1.23279i	−0.650476	−	1.23279i	−0.959493	−	0.281733i	$-0.909091\pi$
$347$	−0.650476	−	1.23279i	−0.650476	−	1.23279i	0.309017	−	0.951057i	$-0.400000\pi$
$348$		0			0
$349$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$349$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$350$	0.153590	+	1.78821i	0.153590	+	1.78821i
$351$		0			0
$352$	−0.320089	+	0.822143i	−0.320089	+	0.822143i
$353$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$353$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.90829	+	0.680877i	−1.90829	+	0.680877i
$359$	−0.760903	+	1.26182i	−0.760903	+	1.26182i	0.198590	+	0.980083i	$0.436364\pi$
$359$	−0.760903	+	1.26182i	−0.760903	+	1.26182i	−0.959493	+	0.281733i	$0.909091\pi$
$360$		0			0
$361$	−0.870746	+	0.491733i	−0.870746	+	0.491733i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$367$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$368$	−3.17924	+	1.13435i	−3.17924	+	1.13435i
$369$		0			0
$370$		0			0
$371$	0.0207207	−	0.725319i	0.0207207	−	0.725319i
$372$		0			0
$373$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$373$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.0266524	+	0.0505118i	0.0266524	+	0.0505118i	0.897398	−	0.441221i	$-0.145455\pi$
$379$	0.0266524	+	0.0505118i	0.0266524	+	0.0505118i	−0.870746	+	0.491733i	$0.836364\pi$
$380$		0			0
$381$		0			0
$382$	−0.888825	−	3.38144i	−0.888825	−	3.38144i
$383$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$383$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$384$		0			0
$385$		0			0
$386$	0.444823	−	3.09381i	0.444823	−	3.09381i
$387$	−0.879056	−	0.313647i	−0.879056	−	0.313647i
$388$		0			0
$389$	0.0322365	+	0.0471444i	0.0322365	+	0.0471444i	0.841254	−	0.540641i	$-0.181818\pi$
$389$	0.0322365	+	0.0471444i	0.0322365	+	0.0471444i	−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$		0			0
$392$	1.69690	+	1.38755i	1.69690	+	1.38755i
$393$		0			0
$394$	1.80548	−	0.419847i	1.80548	−	0.419847i
$395$		0			0
$396$	−1.25380	−	1.83362i	−1.25380	−	1.83362i
$397$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$397$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$398$		0			0
$399$		0			0
$400$	−1.57776	−	0.666765i	−1.57776	−	0.666765i
$401$	−1.28393	−	1.32113i	−1.28393	−	1.32113i	−0.921124	−	0.389270i	$-0.872727\pi$
$401$	−1.28393	−	1.32113i	−1.28393	−	1.32113i	−0.362808	−	0.931864i	$-0.618182\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−3.24389	+	0.952492i	−3.24389	+	0.952492i
$407$	0.122736	−	0.605724i	0.122736	−	0.605724i
$408$		0			0
$409$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$409$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.899175	−	3.42082i	0.899175	−	3.42082i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$419$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$420$		0			0
$421$	1.45190	+	0.251261i	1.45190	+	0.251261i	0.841254	−	0.540641i	$-0.181818\pi$
$421$	1.45190	+	0.251261i	1.45190	+	0.251261i	0.610648	+	0.791902i	$0.290909\pi$
$422$	2.43600	−	2.23575i	2.43600	−	2.23575i
$423$		0			0
$424$	1.38495	+	0.782117i	1.38495	+	0.782117i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	1.42869	+	3.12840i	1.42869	+	3.12840i
$429$		0			0
$430$		0			0
$431$	0.237271	−	0.449678i	0.237271	−	0.449678i	−0.736741	−	0.676175i	$-0.763636\pi$
$431$	0.237271	−	0.449678i	0.237271	−	0.449678i	0.974012	+	0.226497i	$0.0727273\pi$
$432$		0			0
$433$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$433$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$434$		0			0
$435$		0			0
$436$	−4.34899	+	0.752622i	−4.34899	+	0.752622i
$437$		0			0
$438$		0			0
$439$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$439$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$440$		0			0
$441$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$442$		0			0
$443$	−1.02693	−	0.942503i	−1.02693	−	0.942503i	−0.0285561	−	0.999592i	$-0.509091\pi$
$443$	−1.02693	−	0.942503i	−1.02693	−	0.942503i	−0.998369	+	0.0570888i	$0.981818\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.119183	−	0.0503670i	0.119183	−	0.0503670i
$449$	1.38479	−	1.42491i	1.38479	−	1.42491i	0.610648	−	0.791902i	$-0.290909\pi$
$449$	1.38479	−	1.42491i	1.38479	−	1.42491i	0.774142	−	0.633012i	$-0.218182\pi$
$450$	1.50988	−	0.970340i	1.50988	−	0.970340i
$451$		0			0
$452$	−3.25428	−	2.09140i	−3.25428	−	2.09140i
$453$		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		0.142315	−	0.989821i	$-0.454545\pi$
$461$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$462$		0			0
$463$	−0.0565247	−	0.393138i	−0.0565247	−	0.393138i	−0.998369	−	0.0570888i	$-0.981818\pi$
$463$	−0.0565247	−	0.393138i	−0.0565247	−	0.393138i	0.941844	−	0.336049i	$-0.109091\pi$
$464$	0.640751	−	3.16223i	0.640751	−	3.16223i
$465$		0			0
$466$	3.00007	+	0.344227i	3.00007	+	0.344227i
$467$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$467$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$468$		0			0
$469$	0.0570190	+	1.99592i	0.0570190	+	1.99592i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.435557	+	0.825472i	0.435557	+	0.825472i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.651166	+	0.320157i	−0.651166	+	0.320157i
$478$	−0.711696	−	3.51236i	−0.711696	−	3.51236i
$479$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$479$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.316123	+	2.19869i	−0.316123	+	2.19869i
$485$		0			0
$486$		0			0
$487$	−0.288416	+	0.887654i	−0.288416	+	0.887654i	0.696938	+	0.717132i	$0.254545\pi$
$487$	−0.288416	+	0.887654i	−0.288416	+	0.887654i	−0.985354	+	0.170522i	$0.945455\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.255426	+	0.125585i	−0.255426	+	0.125585i	−0.564443	−	0.825472i	$-0.690909\pi$
$491$	−0.255426	+	0.125585i	−0.255426	+	0.125585i	0.309017	+	0.951057i	$0.400000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.0146462	+	0.170522i	0.0146462	+	0.170522i
$498$		0			0
$499$	0.0462047	+	1.61737i	0.0462047	+	1.61737i	0.610648	+	0.791902i	$0.290909\pi$
$499$	0.0462047	+	1.61737i	0.0462047	+	1.61737i	−0.564443	+	0.825472i	$0.690909\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$503$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$504$	0.435306	−	2.14832i	0.435306	−	2.14832i
$505$		0			0
$506$	−2.97553	+	1.91226i	−2.97553	+	1.91226i
$507$		0			0
$508$	−2.36176	−	0.842674i	−2.36176	−	0.842674i
$509$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$509$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$510$		0			0
$511$		0			0
$512$	−0.191976	+	2.23514i	−0.191976	+	2.23514i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.933157	−	0.599703i	0.933157	−	0.599703i
$519$		0			0
$520$		0			0
$521$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$521$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$522$	2.35623	+	2.42451i	2.35623	+	2.42451i
$523$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$523$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$524$		0			0
$525$		0			0
$526$	0.187579	+	0.243256i	0.187579	+	0.243256i
$527$		0			0
$528$		0			0
$529$	−2.76688	−	0.812429i	−2.76688	−	0.812429i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−3.92774	−	1.93114i	−3.92774	−	1.93114i
$537$		0			0
$538$		0			0
$539$	0.897398	+	0.441221i	0.897398	+	0.441221i
$540$		0			0
$541$	1.83924	+	0.105172i	1.83924	+	0.105172i	0.941844	−	0.336049i	$-0.109091\pi$
$541$	1.83924	+	0.105172i	1.83924	+	0.105172i	0.897398	+	0.441221i	$0.145455\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.65786	−	0.286905i	−1.65786	−	0.286905i	−0.736741	−	0.676175i	$-0.763636\pi$
$547$	−1.65786	−	0.286905i	−1.65786	−	0.286905i	−0.921124	+	0.389270i	$0.872727\pi$
$548$	−2.29040	−	0.130970i	−2.29040	−	0.130970i
$549$		0			0
$550$	−1.76851	−	0.306053i	−1.76851	−	0.306053i
$551$		0			0
$552$		0			0
$553$	1.74815	+	0.859509i	1.74815	+	0.859509i
$554$	0.231985	−	0.882561i	0.231985	−	0.882561i
$555$		0			0
$556$		0			0
$557$	1.59434	−	0.275911i	1.59434	−	0.275911i	0.696938	−	0.717132i	$-0.254545\pi$
$557$	1.59434	−	0.275911i	1.59434	−	0.275911i	0.897398	+	0.441221i	$0.145455\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.24958	−	0.366909i	1.24958	−	0.366909i
$563$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$563$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.696938	+	0.717132i	0.696938	+	0.717132i
$568$	−0.345566	−	0.146037i	−0.345566	−	0.146037i
$569$	1.76762	−	0.747004i	1.76762	−	0.747004i	0.774142	−	0.633012i	$-0.218182\pi$
$569$	1.76762	−	0.747004i	1.76762	−	0.747004i	0.993482	−	0.113991i	$-0.0363636\pi$
$570$		0			0
$571$	0.868842	−	0.558371i	0.868842	−	0.558371i	−0.0285561	−	0.999592i	$-0.509091\pi$
$571$	0.868842	−	0.558371i	0.868842	−	0.558371i	0.897398	+	0.441221i	$0.145455\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.01767	−	1.68761i	−1.01767	−	1.68761i
$576$	−0.100165	−	0.0819044i	−0.100165	−	0.0819044i
$577$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$577$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$578$	−1.45202	+	1.05496i	−1.45202	+	1.05496i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.696223	+	0.204429i	0.696223	+	0.204429i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$587$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.0905901	+	1.05472i	0.0905901	+	1.05472i
$593$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$593$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$594$		0			0
$595$		0			0
$596$	−1.49306	−	1.08477i	−1.49306	−	1.08477i
$597$		0			0
$598$		0			0
$599$	0.394592	+	1.94739i	0.394592	+	1.94739i	0.309017	+	0.951057i	$0.400000\pi$
$599$	0.394592	+	1.94739i	0.394592	+	1.94739i	0.0855750	+	0.996332i	$0.472727\pi$
$600$		0			0
$601$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$601$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$602$	−0.517649	+	1.59316i	−0.517649	+	1.59316i
$603$	1.73865	−	0.981862i	1.73865	−	0.981862i
$604$	−0.126863			−0.126863
$605$		0			0
$606$		0			0
$607$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$607$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.0398036	+	1.39331i	−0.0398036	+	1.39331i	0.696938	+	0.717132i	$0.254545\pi$
$613$	−0.0398036	+	1.39331i	−0.0398036	+	1.39331i	−0.736741	+	0.676175i	$0.763636\pi$
$614$		0			0
$615$		0			0
$616$	−1.77335	+	1.28841i	−1.77335	+	1.28841i
$617$	−0.260098	−	0.300169i	−0.260098	−	0.300169i	0.610648	−	0.791902i	$-0.290909\pi$
$617$	−0.260098	−	0.300169i	−0.260098	−	0.300169i	−0.870746	+	0.491733i	$0.836364\pi$
$618$		0			0
$619$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$619$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.198590	−	0.980083i	0.198590	−	0.980083i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.03984	+	1.52072i	1.03984	+	1.52072i	0.841254	+	0.540641i	$0.181818\pi$
$631$	1.03984	+	1.52072i	1.03984	+	1.52072i	0.198590	+	0.980083i	$0.436364\pi$
$632$	−3.45452	+	2.50986i	−3.45452	+	2.50986i
$633$		0			0
$634$	−2.24814	−	1.83829i	−2.24814	−	1.83829i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.0965434	−	3.37946i	−0.0965434	−	3.37946i
$639$	0.143981	−	0.0925307i	0.143981	−	0.0925307i
$640$		0			0
$641$	−1.28393	+	0.542594i	−1.28393	+	0.542594i	−0.921124	−	0.389270i	$-0.872727\pi$
$641$	−1.28393	+	0.542594i	−1.28393	+	0.542594i	−0.362808	+	0.931864i	$0.618182\pi$
$642$		0			0
$643$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$643$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$644$	−4.26376	−	0.991495i	−4.26376	−	0.991495i
$645$		0			0
$646$		0			0
$647$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$647$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$648$	−2.10319	+	0.617552i	−2.10319	+	0.617552i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	3.41678	−	0.392039i	3.41678	−	0.392039i
$653$	1.11235	−	0.192500i	1.11235	−	0.192500i	0.415415	−	0.909632i	$-0.363636\pi$
$653$	1.11235	−	0.192500i	1.11235	−	0.192500i	0.696938	+	0.717132i	$0.254545\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$659$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$660$		0			0
$661$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$661$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$662$	2.64029	+	0.150977i	2.64029	+	0.150977i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.965871	−	0.545453i	−0.965871	−	0.545453i
$667$	2.73493	−	2.51010i	2.73493	−	2.51010i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.650476	+	1.23279i	−0.650476	+	1.23279i	0.309017	+	0.951057i	$0.400000\pi$
$673$	−0.650476	+	1.23279i	−0.650476	+	1.23279i	−0.959493	+	0.281733i	$0.909091\pi$
$674$	−2.37326	−	1.16685i	−2.37326	−	1.16685i
$675$		0			0
$676$	−0.805903	+	2.06995i	−0.805903	+	2.06995i
$677$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$677$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.76762	−	0.519021i	1.76762	−	0.519021i	0.774142	−	0.633012i	$-0.218182\pi$
$683$	1.76762	−	0.519021i	1.76762	−	0.519021i	0.993482	+	0.113991i	$0.0363636\pi$
$684$		0			0
$685$		0			0
$686$	0.554623	+	1.70695i	0.554623	+	1.70695i
$687$		0			0
$688$	−1.11417	−	1.14646i	−1.11417	−	1.14646i
$689$		0			0
$690$		0			0
$691$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$691$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$692$		0			0
$693$	−0.0285561	−	0.999592i	−0.0285561	−	0.999592i
$694$	2.10458	+	1.35253i	2.10458	+	1.35253i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−1.25380	−	1.83362i	−1.25380	−	1.83362i
$701$	−0.0442129	+	0.0361527i	−0.0442129	+	0.0361527i	−0.654861	−	0.755750i	$-0.727273\pi$
$701$	−0.0442129	+	0.0361527i	−0.0442129	+	0.0361527i	0.610648	+	0.791902i	$0.290909\pi$
$702$		0			0
$703$		0			0
$704$	0.0184139	+	0.128071i	0.0184139	+	0.128071i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.39160	+	0.0795747i	−1.39160	+	0.0795747i	−0.736741	−	0.676175i	$-0.763636\pi$
$709$	−1.39160	+	0.0795747i	−1.39160	+	0.0795747i	−0.654861	+	0.755750i	$0.727273\pi$
$710$		0			0
$711$	−0.0556279	−	1.94723i	−0.0556279	−	1.94723i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.64212	−	1.89511i	1.64212	−	1.89511i
$717$		0			0
$718$	0.0755194	−	2.64352i	0.0755194	−	2.64352i
$719$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$719$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$720$		0			0
$721$		0			0
$722$	0.926829	−	1.53697i	0.926829	−	1.53697i
$723$		0			0
$724$		0			0
$725$	1.88369			1.88369
$726$		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		0.897398	−	0.441221i	$-0.145455\pi$
$733$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$734$		0			0
$735$		0			0
$736$	1.13859	−	1.31400i	1.13859	−	1.31400i
$737$	−1.94485	−	0.452255i	−1.94485	−	0.452255i
$738$		0			0
$739$	−0.138463	−	1.61210i	−0.138463	−	1.61210i	−0.654861	−	0.755750i	$-0.727273\pi$
$739$	−0.138463	−	1.61210i	−0.138463	−	1.61210i	0.516397	−	0.856349i	$-0.327273\pi$
$740$		0			0
$741$		0			0
$742$	0.607756	+	1.15183i	0.607756	+	1.15183i
$743$	1.61540	−	0.0923716i	1.61540	−	0.0923716i	0.774142	−	0.633012i	$-0.218182\pi$
$743$	1.61540	−	0.0923716i	1.61540	−	0.0923716i	0.841254	+	0.540641i	$0.181818\pi$
$744$		0			0
$745$		0			0
$746$	−0.101450	+	0.500678i	−0.101450	+	0.500678i
$747$		0			0
$748$		0			0
$749$	−0.220344	+	1.53252i	−0.220344	+	1.53252i
$750$		0			0
$751$	0.799530	−	0.653772i	0.799530	−	0.653772i	−0.142315	−	0.989821i	$-0.545455\pi$
$751$	0.799530	−	0.653772i	0.799530	−	0.653772i	0.941844	+	0.336049i	$0.109091\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.386859	−	0.0899602i	0.386859	−	0.0899602i	−0.0285561	−	0.999592i	$-0.509091\pi$
$757$	0.386859	−	0.0899602i	0.386859	−	0.0899602i	0.415415	+	0.909632i	$0.363636\pi$
$758$	−0.0862324	−	0.0554182i	−0.0862324	−	0.0554182i
$759$		0			0
$760$		0			0
$761$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$761$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$762$		0			0
$763$	−1.83024	−	0.773465i	−1.83024	−	0.773465i
$764$	3.01574	+	3.10313i	3.01574	+	3.10313i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$769$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$770$		0			0
$771$		0			0
$772$	1.40347	+	3.60479i	1.40347	+	3.60479i
$773$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$773$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$774$	1.65061	−	0.285650i	1.65061	−	0.285650i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.0919875	−	0.0452272i	−0.0919875	−	0.0452272i
$779$		0			0
$780$		0			0
$781$	−0.168643	−	0.0291849i	−0.168643	−	0.0291849i
$782$		0			0
$783$		0			0
$784$	−1.68777	−	0.292080i	−1.68777	−	0.292080i
$785$		0			0
$786$		0			0
$787$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$787$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$788$	−1.69019	+	1.55124i	−1.69019	+	1.55124i
$789$		0			0
$790$		0			0
$791$	−0.723442	−	1.58412i	−0.723442	−	1.58412i
$792$	1.96708	+	0.967147i	1.96708	+	0.967147i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$797$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$798$		0			0
$799$		0			0
$800$	0.876506	−	0.100570i	0.876506	−	0.100570i
$801$		0			0
$802$	3.17252	+	0.931537i	3.17252	+	0.931537i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.786763	−	0.809560i	−0.786763	−	0.809560i	0.198590	−	0.980083i	$-0.436364\pi$
$809$	−0.786763	−	0.809560i	−0.786763	−	0.809560i	−0.985354	+	0.170522i	$0.945455\pi$
$810$		0			0
$811$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$811$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$812$	2.91615	−	3.00064i	2.91615	−	3.00064i
$813$		0			0
$814$	0.342776	+	1.05496i	0.342776	+	1.05496i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.739263	+	1.08114i	0.739263	+	1.08114i	0.993482	+	0.113991i	$0.0363636\pi$
$821$	0.739263	+	1.08114i	0.739263	+	1.08114i	−0.254218	+	0.967147i	$0.581818\pi$
$822$		0			0
$823$	−1.52394	−	0.543739i	−1.52394	−	0.543739i	−0.564443	−	0.825472i	$-0.690909\pi$
$823$	−1.52394	−	0.543739i	−1.52394	−	0.543739i	−0.959493	+	0.281733i	$0.909091\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.164995	−	0.814282i	0.164995	−	0.814282i	−0.809017	−	0.587785i	$-0.800000\pi$
$827$	0.164995	−	0.814282i	0.164995	−	0.814282i	0.974012	−	0.226497i	$-0.0727273\pi$
$828$	1.11285	+	4.23371i	1.11285	+	4.23371i
$829$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$829$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$830$		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		0.0285561	−	0.999592i	$-0.490909\pi$
$839$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$840$		0			0
$841$	0.506065	+	2.49753i	0.506065	+	2.49753i
$842$	−2.49080	+	0.888717i	−2.49080	+	0.888717i
$843$		0			0
$844$	−1.26455	+	3.89189i	−1.26455	+	3.89189i
$845$		0			0
$846$		0			0
$847$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$848$	−1.24288			−1.24288
$849$		0			0
$850$		0			0
$851$	−0.628954	+	1.04300i	−0.628954	+	1.04300i
$852$		0			0
$853$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$853$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$854$		0			0
$855$		0			0
$856$	−2.74564	−	1.99483i	−2.74564	−	1.99483i
$857$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$857$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$858$		0			0
$859$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$859$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$860$		0			0
$861$		0			0
$862$	0.0260586	+	0.912168i	0.0260586	+	0.912168i
$863$	0.611204	+	1.15836i	0.611204	+	1.15836i	0.974012	+	0.226497i	$0.0727273\pi$
$863$	0.611204	+	1.15836i	0.611204	+	1.15836i	−0.362808	+	0.931864i	$0.618182\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.27568	+	1.47222i	−1.27568	+	1.47222i
$870$		0			0
$871$		0			0
$872$	3.37168	−	2.75701i	3.37168	−	2.75701i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.0883814	+	0.146564i	0.0883814	+	0.146564i	0.897398	−	0.441221i	$-0.145455\pi$
$877$	0.0883814	+	0.146564i	0.0883814	+	0.146564i	−0.809017	+	0.587785i	$0.800000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$881$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$882$	1.25086	−	1.28711i	1.25086	−	1.28711i
$883$	−1.54980	+	0.654950i	−1.54980	+	0.654950i	−0.985354	−	0.170522i	$-0.945455\pi$
$883$	−1.54980	+	0.654950i	−1.54980	+	0.654950i	−0.564443	+	0.825472i	$0.690909\pi$
$884$		0			0
$885$		0			0
$886$	2.43671	+	0.566632i	2.43671	+	0.566632i
$887$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$887$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$888$		0			0
$889$	−0.689352	−	0.893968i	−0.689352	−	0.893968i
$890$		0			0
$891$	−0.870746	+	0.491733i	−0.870746	+	0.491733i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.680556	+	0.882561i	−0.680556	+	0.882561i
$897$		0			0
$898$	−0.906592	+	3.44904i	−0.906592	+	3.44904i
$899$		0			0
$900$	−1.03661	+	1.96459i	−1.03661	+	1.96459i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	3.81109	+	0.217926i	3.81109	+	0.217926i
$905$		0			0
$906$		0			0
$907$	1.51640	+	0.856349i	1.51640	+	0.856349i	1.00000			$0$
$907$	1.51640	+	0.856349i	1.51640	+	0.856349i	0.516397	+	0.856349i	$0.327273\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.829475	−	0.0474311i	−0.829475	−	0.0474311i	−0.362808	−	0.931864i	$-0.618182\pi$
$911$	−0.829475	−	0.0474311i	−0.829475	−	0.0474311i	−0.466667	+	0.884433i	$0.654545\pi$
$912$		0			0
$913$		0			0
$914$	0.460797	−	1.00901i	0.460797	−	1.00901i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.745782	−	0.967147i	0.745782	−	0.967147i	−0.254218	−	0.967147i	$-0.581818\pi$
$919$	0.745782	−	0.967147i	0.745782	−	0.967147i	1.00000			$0$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.592999	+	0.174120i	−0.592999	+	0.174120i
$926$	0.435306	+	0.564515i	0.435306	+	0.564515i
$927$		0			0
$928$	0.513554	+	1.58056i	0.513554	+	1.58056i
$929$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$929$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$930$		0			0
$931$		0			0
$932$	−3.44256	+	1.45484i	−3.44256	+	1.45484i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$937$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$938$	−1.85063	−	3.06893i	−1.85063	−	3.06893i
$939$		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
$946$	−1.40922	−	0.905652i	−1.40922	−	0.905652i
$947$	0.273100	+	1.89945i	0.273100	+	1.89945i	0.415415	+	0.909632i	$0.363636\pi$
$947$	0.273100	+	1.89945i	0.273100	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.0526073	+	1.84150i	0.0526073	+	1.84150i	0.415415	+	0.909632i	$0.363636\pi$
$953$	0.0526073	+	1.84150i	0.0526073	+	1.84150i	−0.362808	+	0.931864i	$0.618182\pi$
$954$	0.735093	−	1.07504i	0.735093	−	1.07504i
$955$		0			0
$956$	2.90453	+	3.35201i	2.90453	+	3.35201i
$957$		0			0
$958$		0			0
$959$	−0.835549	−	0.607062i	−0.835549	−	0.607062i
$960$		0			0
$961$	0.897398	−	0.441221i	0.897398	−	0.441221i
$962$		0			0
$963$	1.45824	−	0.520300i	1.45824	−	0.520300i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.98696			1.98696			0.993482	−	0.113991i	$-0.0363636\pi$
$967$	1.98696			1.98696			0.993482	+	0.113991i	$0.0363636\pi$
$968$	−0.795266	−	2.04263i	−0.795266	−	2.04263i
$969$		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
$974$	−0.332668	−	1.64178i	−0.332668	−	1.64178i
$975$		0			0
$976$		0			0
$977$	1.19207	+	0.866091i	1.19207	+	0.866091i	0.993482	−	0.113991i	$-0.0363636\pi$
$977$	1.19207	+	0.866091i	1.19207	+	0.866091i	0.198590	+	0.980083i	$0.436364\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.170034	+	1.97967i	0.170034	+	1.97967i
$982$	0.288347	−	0.421694i	0.288347	−	0.421694i
$983$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$983$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.261764	−	1.82061i	−0.261764	−	1.82061i
$990$		0			0
$991$	0.273100	−	1.89945i	0.273100	−	1.89945i	−0.142315	−	0.989821i	$-0.545455\pi$
$991$	0.273100	−	1.89945i	0.273100	−	1.89945i	0.415415	−	0.909632i	$-0.363636\pi$
$992$		0			0
$993$		0			0
$994$	−0.173385	−	0.253568i	−0.173385	−	0.253568i
$995$		0			0
$996$		0			0
$997$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$997$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$998$	−1.49964	−	2.48687i	−1.49964	−	2.48687i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.1.bb.a.48.1	✓	40
7.6	odd	2	CM	847.1.bb.a.48.1	✓	40
121.58	even	55	inner	847.1.bb.a.300.1	yes	40
847.300	odd	110	inner	847.1.bb.a.300.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.1.bb.a.48.1	✓	40	1.1	even	1	trivial
847.1.bb.a.48.1	✓	40	7.6	odd	2	CM
847.1.bb.a.300.1	yes	40	121.58	even	55	inner
847.1.bb.a.300.1	yes	40	847.300	odd	110	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.56281 + 0.882561i) q^{2} +(1.14707 - 1.90220i) q^{4} +(0.897398 - 0.441221i) q^{7} +(-0.0625942 + 2.19108i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.198590 + 0.980083i) q^{11} +(-1.01306 + 1.48155i) q^{14} +(-0.799335 - 1.51491i) q^{16} +(1.78310 + 0.204591i) q^{18} +(-1.17534 - 1.35642i) q^{22} +(0.280461 - 1.95065i) q^{23} +(0.774142 - 0.633012i) q^{25} +(0.190087 - 2.21315i) q^{28} +(1.45824 + 1.19240i) q^{29} +(0.742201 + 0.476984i) q^{32} +(-2.04609 + 0.864684i) q^{36} +(-0.569286 - 0.240582i) q^{37} +(0.895528 - 0.262951i) q^{43} +(2.09211 + 0.746465i) q^{44} +(1.28326 + 3.29602i) q^{46} +(0.610648 - 0.791902i) q^{49} +(-0.651166 + 1.67251i) q^{50} +(0.338621 - 0.641758i) q^{53} +(0.910580 + 1.99389i) q^{56} +(-3.33132 - 0.576508i) q^{58} +(-0.985354 - 0.170522i) q^{63} +(0.129177 + 0.00738662i) q^{64} +(-0.829475 + 1.81630i) q^{67} +(-0.0620945 + 0.159489i) q^{71} +(1.33853 - 1.73583i) q^{72} +(1.10202 - 0.126444i) q^{74} +(0.610648 + 0.791902i) q^{77} +(1.18956 + 1.54264i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-1.16747 + 1.20130i) q^{86} +(-2.15987 + 0.373781i) q^{88} +(-3.38882 - 2.77103i) q^{92} +(-0.255426 + 1.77653i) q^{98} +(0.415415 - 0.909632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46}+ \cdots - 4 q^{99}+O(q^{100}) \) 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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