LMFDB - Embedded newform 672.2.k.a.545.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(545,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))

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

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

chi := DirichletCharacter("672.545");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.k (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			545.6
Root			$1.17915 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	672.545
Dual form			672.2.k.a.545.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.848071 + 1.51022i) q^{3} -1.69614 q^{5} +(-2.56155 - 0.662153i) q^{7} +(-1.56155 + 2.56155i) q^{9} +O(q^{10})$	\(q+(0.848071 + 1.51022i) q^{3} -1.69614 q^{5} +(-2.56155 - 0.662153i) q^{7} +(-1.56155 + 2.56155i) q^{9} +4.00000i q^{11} -4.34475i q^{13} +(-1.43845 - 2.56155i) q^{15} -6.04090 q^{17} -3.02045i q^{19} +(-1.17238 - 4.43007i) q^{21} +1.12311i q^{23} -2.12311 q^{25} +(-5.19283 - 0.185917i) q^{27} -1.12311i q^{29} +4.71659i q^{31} +(-6.04090 + 3.39228i) q^{33} +(4.34475 + 1.12311i) q^{35} -8.24621 q^{37} +(6.56155 - 3.68466i) q^{39} -6.04090 q^{41} +8.00000 q^{43} +(2.64861 - 4.34475i) q^{45} -3.39228 q^{47} +(6.12311 + 3.39228i) q^{49} +(-5.12311 - 9.12311i) q^{51} +9.12311i q^{53} -6.78456i q^{55} +(4.56155 - 2.56155i) q^{57} +10.3857 q^{59} -11.1293i q^{61} +(5.69614 - 5.52757i) q^{63} +7.36932i q^{65} +2.24621 q^{67} +(-1.69614 + 0.952473i) q^{69} +14.2462i q^{71} +(-1.80054 - 3.20636i) q^{75} +(2.64861 - 10.2462i) q^{77} -5.12311 q^{79} +(-4.12311 - 8.00000i) q^{81} -17.1702 q^{83} +10.2462 q^{85} +(1.69614 - 0.952473i) q^{87} +9.43318 q^{89} +(-2.87689 + 11.1293i) q^{91} +(-7.12311 + 4.00000i) q^{93} +5.12311i q^{95} +15.4741i q^{97} +(-10.2462 - 6.24621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^7 + 4 * q^9	$ 8 q - 4 q^{7} + 4 q^{9} - 28 q^{15} + 8 q^{21} + 16 q^{25} + 36 q^{39} + 64 q^{43} + 16 q^{49} - 8 q^{51} + 20 q^{57} + 32 q^{63} - 48 q^{67} - 8 q^{79} + 16 q^{85} - 56 q^{91} - 24 q^{93} - 16 q^{99}+O(q^{100}) $ 8 * q - 4 * q^7 + 4 * q^9 - 28 * q^15 + 8 * q^21 + 16 * q^25 + 36 * q^39 + 64 * q^43 + 16 * q^49 - 8 * q^51 + 20 * q^57 + 32 * q^63 - 48 * q^67 - 8 * q^79 + 16 * q^85 - 56 * q^91 - 24 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.848071	+	1.51022i	0.489634	+	0.871928i
$3$	0.848071	+	1.51022i	0.489634	+	0.871928i
$4$		0			0
$5$	−1.69614			−0.758537			−0.379269	−	0.925287i	$-0.623824\pi$
$5$	−1.69614			−0.758537			−0.379269	+	0.925287i	$0.623824\pi$
$6$		0			0
$7$	−2.56155	−	0.662153i	−0.968176	−	0.250270i
$7$	−2.56155	−	0.662153i	−0.968176	−	0.250270i
$8$		0			0
$9$	−1.56155	+	2.56155i	−0.520518	+	0.853851i
$10$		0			0
$11$			4.00000i			1.20605i	0.797724	+	0.603023i	$0.206037\pi$
$11$			4.00000i			1.20605i	−0.797724	+	0.603023i	$0.793963\pi$
$12$		0			0
$13$		−	4.34475i		−	1.20502i	−0.798112	−	0.602509i	$-0.794168\pi$
$13$		−	4.34475i		−	1.20502i	0.798112	−	0.602509i	$-0.205832\pi$
$14$		0			0
$15$	−1.43845	−	2.56155i	−0.371405	−	0.661390i
$16$		0			0
$17$	−6.04090			−1.46513			−0.732566	−	0.680696i	$-0.761678\pi$
$17$	−6.04090			−1.46513			−0.732566	+	0.680696i	$0.761678\pi$
$18$		0			0
$19$		−	3.02045i		−	0.692938i	−0.938061	−	0.346469i	$-0.887381\pi$
$19$		−	3.02045i		−	0.692938i	0.938061	−	0.346469i	$-0.112619\pi$
$20$		0			0
$21$	−1.17238	−	4.43007i	−0.255834	−	0.966721i
$22$		0			0
$23$			1.12311i			0.234184i	0.993121	+	0.117092i	$0.0373572\pi$
$23$			1.12311i			0.234184i	−0.993121	+	0.117092i	$0.962643\pi$
$24$		0			0
$25$	−2.12311			−0.424621
$26$		0			0
$27$	−5.19283	−	0.185917i	−0.999360	−	0.0357798i
$28$		0			0
$29$		−	1.12311i		−	0.208555i	−0.994548	−	0.104278i	$-0.966747\pi$
$29$		−	1.12311i		−	0.208555i	0.994548	−	0.104278i	$-0.0332531\pi$
$30$		0			0
$31$			4.71659i			0.847124i	0.905867	+	0.423562i	$0.139220\pi$
$31$			4.71659i			0.847124i	−0.905867	+	0.423562i	$0.860780\pi$
$32$		0			0
$33$	−6.04090	+	3.39228i	−1.05158	+	0.590521i
$34$		0			0
$35$	4.34475	+	1.12311i	0.734398	+	0.189839i
$36$		0			0
$37$	−8.24621			−1.35567			−0.677834	−	0.735215i	$-0.737081\pi$
$37$	−8.24621			−1.35567			−0.677834	+	0.735215i	$0.737081\pi$
$38$		0			0
$39$	6.56155	−	3.68466i	1.05069	−	0.590018i
$40$		0			0
$41$	−6.04090			−0.943429			−0.471715	−	0.881751i	$-0.656365\pi$
$41$	−6.04090			−0.943429			−0.471715	+	0.881751i	$0.656365\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	2.64861	−	4.34475i	0.394832	−	0.647678i
$46$		0			0
$47$	−3.39228			−0.494815			−0.247408	−	0.968911i	$-0.579579\pi$
$47$	−3.39228			−0.494815			−0.247408	+	0.968911i	$0.579579\pi$
$48$		0			0
$49$	6.12311	+	3.39228i	0.874729	+	0.484612i
$50$		0			0
$51$	−5.12311	−	9.12311i	−0.717378	−	1.27749i
$52$		0			0
$53$			9.12311i			1.25315i	0.779359	+	0.626577i	$0.215545\pi$
$53$			9.12311i			1.25315i	−0.779359	+	0.626577i	$0.784455\pi$
$54$		0			0
$55$		−	6.78456i		−	0.914830i
$56$		0			0
$57$	4.56155	−	2.56155i	0.604192	−	0.339286i
$58$		0			0
$59$	10.3857			1.35210			0.676048	−	0.736857i	$-0.263691\pi$
$59$	10.3857			1.35210			0.676048	+	0.736857i	$0.263691\pi$
$60$		0			0
$61$		−	11.1293i		−	1.42496i	−0.701691	−	0.712482i	$-0.747571\pi$
$61$		−	11.1293i		−	1.42496i	0.701691	−	0.712482i	$-0.252429\pi$
$62$		0			0
$63$	5.69614	−	5.52757i	0.717646	−	0.696408i
$64$		0			0
$65$			7.36932i			0.914051i
$66$		0			0
$67$	2.24621			0.274418			0.137209	−	0.990542i	$-0.456187\pi$
$67$	2.24621			0.274418			0.137209	+	0.990542i	$0.456187\pi$
$68$		0			0
$69$	−1.69614	+	0.952473i	−0.204191	+	0.114664i
$70$		0			0
$71$			14.2462i			1.69071i	0.534202	+	0.845357i	$0.320612\pi$
$71$			14.2462i			1.69071i	−0.534202	+	0.845357i	$0.679388\pi$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−1.80054	−	3.20636i	−0.207909	−	0.370239i
$76$		0			0
$77$	2.64861	−	10.2462i	0.301838	−	1.16766i
$78$		0			0
$79$	−5.12311			−0.576394			−0.288197	−	0.957571i	$-0.593056\pi$
$79$	−5.12311			−0.576394			−0.288197	+	0.957571i	$0.593056\pi$
$80$		0			0
$81$	−4.12311	−	8.00000i	−0.458123	−	0.888889i
$82$		0			0
$83$	−17.1702			−1.88468			−0.942338	−	0.334663i	$-0.891378\pi$
$83$	−17.1702			−1.88468			−0.942338	+	0.334663i	$0.891378\pi$
$84$		0			0
$85$	10.2462			1.11136
$86$		0			0
$87$	1.69614	−	0.952473i	0.181845	−	0.102116i
$88$		0			0
$89$	9.43318			0.999915			0.499957	−	0.866050i	$-0.333349\pi$
$89$	9.43318			0.999915			0.499957	+	0.866050i	$0.333349\pi$
$90$		0			0
$91$	−2.87689	+	11.1293i	−0.301580	+	1.16667i
$92$		0			0
$93$	−7.12311	+	4.00000i	−0.738632	+	0.414781i
$94$		0			0
$95$			5.12311i			0.525620i
$96$		0			0
$97$			15.4741i			1.57115i	0.618764	+	0.785577i	$0.287634\pi$
$97$			15.4741i			1.57115i	−0.618764	+	0.785577i	$0.712366\pi$
$98$		0			0
$99$	−10.2462	−	6.24621i	−1.02978	−	0.627768i
$100$		0			0
$101$	5.08842			0.506317			0.253159	−	0.967425i	$-0.418531\pi$
$101$	5.08842			0.506317			0.253159	+	0.967425i	$0.418531\pi$
$102$		0			0
$103$			10.0138i			0.986691i	0.869834	+	0.493345i	$0.164226\pi$
$103$			10.0138i			0.986691i	−0.869834	+	0.493345i	$0.835774\pi$
$104$		0			0
$105$	1.98852	+	7.51403i	0.194059	+	0.733294i
$106$		0			0
$107$			14.2462i			1.37723i	0.725126	+	0.688617i	$0.241782\pi$
$107$			14.2462i			1.37723i	−0.725126	+	0.688617i	$0.758218\pi$
$108$		0			0
$109$	0.246211			0.0235828			0.0117914	−	0.999930i	$-0.496247\pi$
$109$	0.246211			0.0235828			0.0117914	+	0.999930i	$0.496247\pi$
$110$		0			0
$111$	−6.99337	−	12.4536i	−0.663781	−	1.18205i
$112$		0			0
$113$		−	5.12311i		−	0.481941i	−0.970532	−	0.240971i	$-0.922534\pi$
$113$		−	5.12311i		−	0.481941i	0.970532	−	0.240971i	$-0.0774657\pi$
$114$		0			0
$115$		−	1.90495i		−	0.177637i
$116$		0			0
$117$	11.1293	+	6.78456i	1.02891	+	0.627233i
$118$		0			0
$119$	15.4741	+	4.00000i	1.41851	+	0.366679i
$120$		0			0
$121$	−5.00000			−0.454545
$122$		0			0
$123$	−5.12311	−	9.12311i	−0.461935	−	0.822603i
$124$		0			0
$125$	12.0818			1.08063
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$		0			0
$129$	6.78456	+	12.0818i	0.597348	+	1.06374i
$130$		0			0
$131$	5.08842			0.444578			0.222289	−	0.974981i	$-0.428647\pi$
$131$	5.08842			0.444578			0.222289	+	0.974981i	$0.428647\pi$
$132$		0			0
$133$	−2.00000	+	7.73704i	−0.173422	+	0.670886i
$134$		0			0
$135$	8.80776	+	0.315342i	0.758052	+	0.0271403i
$136$		0			0
$137$		−	2.24621i		−	0.191907i	−0.995386	−	0.0959534i	$-0.969410\pi$
$137$		−	2.24621i		−	0.191907i	0.995386	−	0.0959534i	$-0.0305900\pi$
$138$		0			0
$139$		−	7.15640i		−	0.606998i	−0.952832	−	0.303499i	$-0.901845\pi$
$139$		−	7.15640i		−	0.606998i	0.952832	−	0.303499i	$-0.0981549\pi$
$140$		0			0
$141$	−2.87689	−	5.12311i	−0.242278	−	0.431443i
$142$		0			0
$143$	17.3790			1.45331
$144$		0			0
$145$			1.90495i			0.158197i
$146$		0			0
$147$	0.0697197	+	12.1242i	0.00575038	+	0.999983i
$148$		0			0
$149$		−	17.1231i		−	1.40278i	−0.712778	−	0.701390i	$-0.752563\pi$
$149$		−	17.1231i		−	1.40278i	0.712778	−	0.701390i	$-0.247437\pi$
$150$		0			0
$151$	−12.4924			−1.01662			−0.508309	−	0.861174i	$-0.669729\pi$
$151$	−12.4924			−1.01662			−0.508309	+	0.861174i	$0.669729\pi$
$152$		0			0
$153$	9.43318	−	15.4741i	0.762627	−	1.25100i
$154$		0			0
$155$		−	8.00000i		−	0.642575i
$156$		0			0
$157$		−	2.43981i		−	0.194718i	−0.995249	−	0.0973590i	$-0.968961\pi$
$157$		−	2.43981i		−	0.194718i	0.995249	−	0.0973590i	$-0.0310395\pi$
$158$		0			0
$159$	−13.7779	+	7.73704i	−1.09266	+	0.613587i
$160$		0			0
$161$	0.743668	−	2.87689i	0.0586093	−	0.226731i
$162$		0			0
$163$	18.2462			1.42915			0.714577	−	0.699557i	$-0.246619\pi$
$163$	18.2462			1.42915			0.714577	+	0.699557i	$0.246619\pi$
$164$		0			0
$165$	10.2462	−	5.75379i	0.797666	−	0.447932i
$166$		0			0
$167$	−20.7713			−1.60733			−0.803666	−	0.595081i	$-0.797120\pi$
$167$	−20.7713			−1.60733			−0.803666	+	0.595081i	$0.797120\pi$
$168$		0			0
$169$	−5.87689			−0.452069
$170$		0			0
$171$	7.73704	+	4.71659i	0.591666	+	0.360687i
$172$		0			0
$173$	−1.69614			−0.128955			−0.0644776	−	0.997919i	$-0.520538\pi$
$173$	−1.69614			−0.128955			−0.0644776	+	0.997919i	$0.520538\pi$
$174$		0			0
$175$	5.43845	+	1.40582i	0.411108	+	0.106270i
$176$		0			0
$177$	8.80776	+	15.6847i	0.662032	+	1.17893i
$178$		0			0
$179$			8.49242i			0.634753i	0.948300	+	0.317377i	$0.102802\pi$
$179$			8.49242i			0.634753i	−0.948300	+	0.317377i	$0.897198\pi$
$180$		0			0
$181$			11.1293i			0.827236i	0.910451	+	0.413618i	$0.135735\pi$
$181$			11.1293i			0.827236i	−0.910451	+	0.413618i	$0.864265\pi$
$182$		0			0
$183$	16.8078	−	9.43845i	1.24247	−	0.697710i
$184$		0			0
$185$	13.9867			1.02833
$186$		0			0
$187$		−	24.1636i		−	1.76702i
$188$		0			0
$189$	13.1786	+	3.91468i	0.958601	+	0.284751i
$190$		0			0
$191$		−	6.24621i		−	0.451960i	−0.974132	−	0.225980i	$-0.927442\pi$
$191$		−	6.24621i		−	0.451960i	0.974132	−	0.225980i	$-0.0725584\pi$
$192$		0			0
$193$	0.876894			0.0631202			0.0315601	−	0.999502i	$-0.489952\pi$
$193$	0.876894			0.0631202			0.0315601	+	0.999502i	$0.489952\pi$
$194$		0			0
$195$	−11.1293	+	6.24970i	−0.796987	+	0.447550i
$196$		0			0
$197$			11.3693i			0.810030i	0.914310	+	0.405015i	$0.132734\pi$
$197$			11.3693i			0.810030i	−0.914310	+	0.405015i	$0.867266\pi$
$198$		0			0
$199$			14.1498i			1.00305i	0.865143	+	0.501525i	$0.167228\pi$
$199$			14.1498i			1.00305i	−0.865143	+	0.501525i	$0.832772\pi$
$200$		0			0
$201$	1.90495	+	3.39228i	0.134364	+	0.239273i
$202$		0			0
$203$	−0.743668	+	2.87689i	−0.0521953	+	0.201918i
$204$		0			0
$205$	10.2462			0.715626
$206$		0			0
$207$	−2.87689	−	1.75379i	−0.199958	−	0.121897i
$208$		0			0
$209$	12.0818			0.835715
$210$		0			0
$211$	2.24621			0.154636			0.0773178	−	0.997006i	$-0.475364\pi$
$211$	2.24621			0.154636			0.0773178	+	0.997006i	$0.475364\pi$
$212$		0			0
$213$	−21.5150	+	12.0818i	−1.47418	+	0.827831i
$214$		0			0
$215$	−13.5691			−0.925407
$216$		0			0
$217$	3.12311	−	12.0818i	0.212010	−	0.820165i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			26.2462i			1.76551i
$222$		0			0
$223$		−	26.9752i		−	1.80639i	−0.429225	−	0.903197i	$-0.641213\pi$
$223$		−	26.9752i		−	1.80639i	0.429225	−	0.903197i	$-0.358787\pi$
$224$		0			0
$225$	3.31534	−	5.43845i	0.221023	−	0.362563i
$226$		0			0
$227$	8.48071			0.562884			0.281442	−	0.959578i	$-0.409187\pi$
$227$	8.48071			0.562884			0.281442	+	0.959578i	$0.409187\pi$
$228$		0			0
$229$			19.8188i			1.30967i	0.755774	+	0.654833i	$0.227261\pi$
$229$			19.8188i			1.30967i	−0.755774	+	0.654833i	$0.772739\pi$
$230$		0			0
$231$	17.7203	−	4.68951i	1.16591	−	0.308547i
$232$		0			0
$233$		−	20.4924i		−	1.34250i	−0.741230	−	0.671252i	$-0.765757\pi$
$233$		−	20.4924i		−	1.34250i	0.741230	−	0.671252i	$-0.234243\pi$
$234$		0			0
$235$	5.75379			0.375336
$236$		0			0
$237$	−4.34475	−	7.73704i	−0.282222	−	0.502575i
$238$		0			0
$239$		−	9.12311i		−	0.590125i	−0.955478	−	0.295062i	$-0.904660\pi$
$239$		−	9.12311i		−	0.590125i	0.955478	−	0.295062i	$-0.0953404\pi$
$240$		0			0
$241$		−	8.68951i		−	0.559741i	−0.960038	−	0.279870i	$-0.909709\pi$
$241$		−	8.68951i		−	0.559741i	0.960038	−	0.279870i	$-0.0902915\pi$
$242$		0			0
$243$	8.58511	−	13.0114i	0.550735	−	0.834680i
$244$		0			0
$245$	−10.3857	−	5.75379i	−0.663515	−	0.367596i
$246$		0			0
$247$	−13.1231			−0.835003
$248$		0			0
$249$	−14.5616	−	25.9309i	−0.922801	−	1.64330i
$250$		0			0
$251$	−17.1702			−1.08377			−0.541887	−	0.840451i	$-0.682290\pi$
$251$	−17.1702			−1.08377			−0.541887	+	0.840451i	$0.682290\pi$
$252$		0			0
$253$	−4.49242			−0.282436
$254$		0			0
$255$	8.68951	+	15.4741i	0.544158	+	0.969024i
$256$		0			0
$257$	−14.7304			−0.918857			−0.459429	−	0.888215i	$-0.651946\pi$
$257$	−14.7304			−0.918857			−0.459429	+	0.888215i	$0.651946\pi$
$258$		0			0
$259$	21.1231	+	5.46026i	1.31253	+	0.339284i
$260$		0			0
$261$	2.87689	+	1.75379i	0.178075	+	0.108557i
$262$		0			0
$263$		−	22.2462i		−	1.37176i	−0.727715	−	0.685880i	$-0.759417\pi$
$263$		−	22.2462i		−	1.37176i	0.727715	−	0.685880i	$-0.240583\pi$
$264$		0			0
$265$		−	15.4741i		−	0.950565i
$266$		0			0
$267$	8.00000	+	14.2462i	0.489592	+	0.871854i
$268$		0			0
$269$	5.08842			0.310247			0.155123	−	0.987895i	$-0.450423\pi$
$269$	5.08842			0.310247			0.155123	+	0.987895i	$0.450423\pi$
$270$		0			0
$271$			13.4061i			0.814362i	0.913347	+	0.407181i	$0.133488\pi$
$271$			13.4061i			0.814362i	−0.913347	+	0.407181i	$0.866512\pi$
$272$		0			0
$273$	−19.2476	+	5.09369i	−1.16492	+	0.308284i
$274$		0			0
$275$		−	8.49242i		−	0.512112i
$276$		0			0
$277$	2.00000			0.120168			0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000			0.120168			0.0600842	+	0.998193i	$0.480863\pi$
$278$		0			0
$279$	−12.0818	−	7.36520i	−0.723318	−	0.440943i
$280$		0			0
$281$			16.0000i			0.954480i	0.878773	+	0.477240i	$0.158363\pi$
$281$			16.0000i			0.954480i	−0.878773	+	0.477240i	$0.841637\pi$
$282$		0			0
$283$			15.8459i			0.941941i	0.882149	+	0.470971i	$0.156096\pi$
$283$			15.8459i			0.941941i	−0.882149	+	0.470971i	$0.843904\pi$
$284$		0			0
$285$	−7.73704	+	4.34475i	−0.458303	+	0.257361i
$286$		0			0
$287$	15.4741	+	4.00000i	0.913406	+	0.236113i
$288$		0			0
$289$	19.4924			1.14661
$290$		0			0
$291$	−23.3693	+	13.1231i	−1.36993	+	0.769290i
$292$		0			0
$293$	−27.7647			−1.62203			−0.811015	−	0.585026i	$-0.801084\pi$
$293$	−27.7647			−1.62203			−0.811015	+	0.585026i	$0.801084\pi$
$294$		0			0
$295$	−17.6155			−1.02562
$296$		0			0
$297$	0.743668	−	20.7713i	0.0431520	−	1.20527i
$298$		0			0
$299$	4.87962			0.282196
$300$		0			0
$301$	−20.4924	−	5.29723i	−1.18116	−	0.305327i
$302$		0			0
$303$	4.31534	+	7.68466i	0.247910	+	0.441472i
$304$		0			0
$305$			18.8769i			1.08089i
$306$		0			0
$307$			14.3586i			0.819487i	0.912201	+	0.409743i	$0.134382\pi$
$307$			14.3586i			0.819487i	−0.912201	+	0.409743i	$0.865618\pi$
$308$		0			0
$309$	−15.1231	+	8.49242i	−0.860323	+	0.483117i
$310$		0			0
$311$	6.78456			0.384717			0.192359	−	0.981325i	$-0.438386\pi$
$311$	6.78456			0.384717			0.192359	+	0.981325i	$0.438386\pi$
$312$		0			0
$313$		−	32.8531i		−	1.85697i	−0.371374	−	0.928483i	$-0.621113\pi$
$313$		−	32.8531i		−	1.85697i	0.371374	−	0.928483i	$-0.378887\pi$
$314$		0			0
$315$	−9.66146	+	9.37553i	−0.544362	+	0.528251i
$316$		0			0
$317$		−	9.12311i		−	0.512405i	−0.966623	−	0.256202i	$-0.917529\pi$
$317$		−	9.12311i		−	0.512405i	0.966623	−	0.256202i	$-0.0824713\pi$
$318$		0			0
$319$	4.49242			0.251527
$320$		0			0
$321$	−21.5150	+	12.0818i	−1.20085	+	0.674340i
$322$		0			0
$323$			18.2462i			1.01525i
$324$		0			0
$325$			9.22437i			0.511676i
$326$		0			0
$327$	0.208805	+	0.371834i	0.0115469	+	0.0205625i
$328$		0			0
$329$	8.68951	+	2.24621i	0.479068	+	0.123838i
$330$		0			0
$331$	−13.7538			−0.755977			−0.377988	−	0.925810i	$-0.623384\pi$
$331$	−13.7538			−0.755977			−0.377988	+	0.925810i	$0.623384\pi$
$332$		0			0
$333$	12.8769	−	21.1231i	0.705649	−	1.15754i
$334$		0			0
$335$	−3.80989			−0.208157
$336$		0			0
$337$	−31.6155			−1.72221			−0.861104	−	0.508429i	$-0.830226\pi$
$337$	−31.6155			−1.72221			−0.861104	+	0.508429i	$0.830226\pi$
$338$		0			0
$339$	7.73704	−	4.34475i	0.420218	−	0.235975i
$340$		0			0
$341$	−18.8664			−1.02167
$342$		0			0
$343$	−13.4384	−	12.7439i	−0.725608	−	0.688108i
$344$		0			0
$345$	2.87689	−	1.61553i	0.154887	−	0.0869771i
$346$		0			0
$347$		−	26.7386i		−	1.43541i	−0.696350	−	0.717703i	$-0.745194\pi$
$347$		−	26.7386i		−	1.43541i	0.696350	−	0.717703i	$-0.254806\pi$
$348$		0			0
$349$			4.34475i			0.232569i	0.993216	+	0.116285i	$0.0370985\pi$
$349$			4.34475i			0.232569i	−0.993216	+	0.116285i	$0.962902\pi$
$350$		0			0
$351$	−0.807764	+	22.5616i	−0.0431153	+	1.20425i
$352$		0			0
$353$	−28.2995			−1.50623			−0.753116	−	0.657888i	$-0.771450\pi$
$353$	−28.2995			−1.50623			−0.753116	+	0.657888i	$0.771450\pi$
$354$		0			0
$355$		−	24.1636i		−	1.28247i
$356$		0			0
$357$	7.08221	+	26.7616i	0.374830	+	1.41637i
$358$		0			0
$359$			11.3693i			0.600050i	0.953931	+	0.300025i	$0.0969950\pi$
$359$			11.3693i			0.600050i	−0.953931	+	0.300025i	$0.903005\pi$
$360$		0			0
$361$	9.87689			0.519837
$362$		0			0
$363$	−4.24035	−	7.55112i	−0.222561	−	0.396331i
$364$		0			0
$365$		0			0
$366$		0			0
$367$			10.7575i			0.561536i	0.959776	+	0.280768i	$0.0905892\pi$
$367$			10.7575i			0.561536i	−0.959776	+	0.280768i	$0.909411\pi$
$368$		0			0
$369$	9.43318	−	15.4741i	0.491072	−	0.805548i
$370$		0			0
$371$	6.04090	−	23.3693i	0.313628	−	1.21327i
$372$		0			0
$373$	14.0000			0.724893			0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000			0.724893			0.362446	+	0.932005i	$0.381942\pi$
$374$		0			0
$375$	10.2462	+	18.2462i	0.529112	+	0.942230i
$376$		0			0
$377$	−4.87962			−0.251313
$378$		0			0
$379$	−24.0000			−1.23280			−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000			−1.23280			−0.616399	+	0.787434i	$0.711409\pi$
$380$		0			0
$381$	−6.78456	−	12.0818i	−0.347584	−	0.618969i
$382$		0			0
$383$	−27.5559			−1.40804			−0.704019	−	0.710181i	$-0.748613\pi$
$383$	−27.5559			−1.40804			−0.704019	+	0.710181i	$0.748613\pi$
$384$		0			0
$385$	−4.49242	+	17.3790i	−0.228955	+	0.885717i
$386$		0			0
$387$	−12.4924	+	20.4924i	−0.635026	+	1.04169i
$388$		0			0
$389$			6.87689i			0.348672i	0.984686	+	0.174336i	$0.0557779\pi$
$389$			6.87689i			0.348672i	−0.984686	+	0.174336i	$0.944222\pi$
$390$		0			0
$391$		−	6.78456i		−	0.343110i
$392$		0			0
$393$	4.31534	+	7.68466i	0.217680	+	0.387640i
$394$		0			0
$395$	8.68951			0.437217
$396$		0			0
$397$		−	13.0343i		−	0.654171i	−0.944995	−	0.327085i	$-0.893933\pi$
$397$		−	13.0343i		−	0.654171i	0.944995	−	0.327085i	$-0.106067\pi$
$398$		0			0
$399$	−13.3808	+	3.54110i	−0.669878	+	0.177277i
$400$		0			0
$401$		−	13.1231i		−	0.655337i	−0.944793	−	0.327668i	$-0.893737\pi$
$401$		−	13.1231i		−	0.655337i	0.944793	−	0.327668i	$-0.106263\pi$
$402$		0			0
$403$	20.4924			1.02080
$404$		0			0
$405$	6.99337	+	13.5691i	0.347503	+	0.674255i
$406$		0			0
$407$		−	32.9848i		−	1.63500i
$408$		0			0
$409$		−	4.87962i		−	0.241282i	−0.992696	−	0.120641i	$-0.961505\pi$
$409$		−	4.87962i		−	0.241282i	0.992696	−	0.120641i	$-0.0384949\pi$
$410$		0			0
$411$	3.39228	−	1.90495i	0.167329	−	0.0939640i
$412$		0			0
$413$	−26.6034	−	6.87689i	−1.30907	−	0.338390i
$414$		0			0
$415$	29.1231			1.42960
$416$		0			0
$417$	10.8078	−	6.06913i	0.529258	−	0.297207i
$418$		0			0
$419$	−23.9548			−1.17027			−0.585134	−	0.810937i	$-0.698958\pi$
$419$	−23.9548			−1.17027			−0.585134	+	0.810937i	$0.698958\pi$
$420$		0			0
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$		0			0
$423$	5.29723	−	8.68951i	0.257560	−	0.422498i
$424$		0			0
$425$	12.8255			0.622126
$426$		0			0
$427$	−7.36932	+	28.5083i	−0.356626	+	1.37962i
$428$		0			0
$429$	14.7386	+	26.2462i	0.711588	+	1.26718i
$430$		0			0
$431$			33.1231i			1.59548i	0.602999	+	0.797742i	$0.293972\pi$
$431$			33.1231i			1.59548i	−0.602999	+	0.797742i	$0.706028\pi$
$432$		0			0
$433$		−	32.8531i		−	1.57882i	−0.613867	−	0.789409i	$-0.710387\pi$
$433$		−	32.8531i		−	1.57882i	0.613867	−	0.789409i	$-0.289613\pi$
$434$		0			0
$435$	−2.87689	+	1.61553i	−0.137937	+	0.0774586i
$436$		0			0
$437$	3.39228			0.162275
$438$		0			0
$439$			40.2183i			1.91951i	0.280831	+	0.959757i	$0.409390\pi$
$439$			40.2183i			1.91951i	−0.280831	+	0.959757i	$0.590610\pi$
$440$		0			0
$441$	−18.2511	+	10.3874i	−0.869098	+	0.494640i
$442$		0			0
$443$		−	38.2462i		−	1.81713i	−0.417741	−	0.908566i	$-0.637178\pi$
$443$		−	38.2462i		−	1.81713i	0.417741	−	0.908566i	$-0.362822\pi$
$444$		0			0
$445$	−16.0000			−0.758473
$446$		0			0
$447$	25.8597	−	14.5216i	1.22312	−	0.686848i
$448$		0			0
$449$			2.24621i			0.106005i	0.998594	+	0.0530026i	$0.0168792\pi$
$449$			2.24621i			0.106005i	−0.998594	+	0.0530026i	$0.983121\pi$
$450$		0			0
$451$		−	24.1636i		−	1.13782i
$452$		0			0
$453$	−10.5945	−	18.8664i	−0.497771	−	0.886419i
$454$		0			0
$455$	4.87962	−	18.8769i	0.228760	−	0.884962i
$456$		0			0
$457$	−13.3693			−0.625390			−0.312695	−	0.949854i	$-0.601232\pi$
$457$	−13.3693			−0.625390			−0.312695	+	0.949854i	$0.601232\pi$
$458$		0			0
$459$	31.3693	+	1.12311i	1.46419	+	0.0524221i
$460$		0			0
$461$	0.208805			0.00972500			0.00486250	−	0.999988i	$-0.498452\pi$
$461$	0.208805			0.00972500			0.00486250	+	0.999988i	$0.498452\pi$
$462$		0			0
$463$	31.3693			1.45786			0.728928	−	0.684590i	$-0.240019\pi$
$463$	31.3693			1.45786			0.728928	+	0.684590i	$0.240019\pi$
$464$		0			0
$465$	12.0818	−	6.78456i	0.560280	−	0.314627i
$466$		0			0
$467$	8.48071			0.392440			0.196220	−	0.980560i	$-0.437133\pi$
$467$	8.48071			0.392440			0.196220	+	0.980560i	$0.437133\pi$
$468$		0			0
$469$	−5.75379	−	1.48734i	−0.265685	−	0.0686788i
$470$		0			0
$471$	3.68466	−	2.06913i	0.169780	−	0.0953405i
$472$		0			0
$473$			32.0000i			1.47136i
$474$		0			0
$475$			6.41273i			0.294236i
$476$		0			0
$477$	−23.3693	−	14.2462i	−1.07001	−	0.652289i
$478$		0			0
$479$	−27.5559			−1.25906			−0.629530	−	0.776976i	$-0.716752\pi$
$479$	−27.5559			−1.25906			−0.629530	+	0.776976i	$0.716752\pi$
$480$		0			0
$481$			35.8278i			1.63361i
$482$		0			0
$483$	4.97544	−	1.31670i	0.226390	−	0.0599121i
$484$		0			0
$485$		−	26.2462i		−	1.19178i
$486$		0			0
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$		0			0
$489$	15.4741	+	27.5559i	0.699762	+	1.24612i
$490$		0			0
$491$		−	16.4924i		−	0.744293i	−0.928174	−	0.372146i	$-0.878622\pi$
$491$		−	16.4924i		−	0.744293i	0.928174	−	0.372146i	$-0.121378\pi$
$492$		0			0
$493$			6.78456i			0.305561i
$494$		0			0
$495$	17.3790	+	10.5945i	0.781129	+	0.476185i
$496$		0			0
$497$	9.43318	−	36.4924i	0.423136	−	1.63691i
$498$		0			0
$499$	−12.4924			−0.559238			−0.279619	−	0.960111i	$-0.590208\pi$
$499$	−12.4924			−0.559238			−0.279619	+	0.960111i	$0.590208\pi$
$500$		0			0
$501$	−17.6155	−	31.3693i	−0.787004	−	1.40148i
$502$		0			0
$503$	17.3790			0.774892			0.387446	−	0.921892i	$-0.373357\pi$
$503$	17.3790			0.774892			0.387446	+	0.921892i	$0.373357\pi$
$504$		0			0
$505$	−8.63068			−0.384060
$506$		0			0
$507$	−4.98402	−	8.87543i	−0.221348	−	0.394172i
$508$		0			0
$509$	29.2520			1.29657			0.648286	−	0.761397i	$-0.275486\pi$
$509$	29.2520			1.29657			0.648286	+	0.761397i	$0.275486\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−0.561553	+	15.6847i	−0.0247932	+	0.692495i
$514$		0			0
$515$		−	16.9848i		−	0.748442i
$516$		0			0
$517$		−	13.5691i		−	0.596770i
$518$		0			0
$519$	−1.43845	−	2.56155i	−0.0631408	−	0.112440i
$520$		0			0
$521$	−16.6354			−0.728808			−0.364404	−	0.931241i	$-0.618727\pi$
$521$	−16.6354			−0.728808			−0.364404	+	0.931241i	$0.618727\pi$
$522$		0			0
$523$		−	15.8459i		−	0.692893i	−0.938070	−	0.346447i	$-0.887388\pi$
$523$		−	15.8459i		−	0.692893i	0.938070	−	0.346447i	$-0.112612\pi$
$524$		0			0
$525$	2.48908	+	9.40551i	0.108632	+	0.410490i
$526$		0			0
$527$		−	28.4924i		−	1.24115i
$528$		0			0
$529$	21.7386			0.945158
$530$		0			0
$531$	−16.2177	+	26.6034i	−0.703790	+	1.15449i
$532$		0			0
$533$			26.2462i			1.13685i
$534$		0			0
$535$		−	24.1636i		−	1.04468i
$536$		0			0
$537$	−12.8255	+	7.20217i	−0.553459	+	0.310797i
$538$		0			0
$539$	−13.5691	+	24.4924i	−0.584464	+	1.05496i
$540$		0			0
$541$	14.4924			0.623078			0.311539	−	0.950233i	$-0.399156\pi$
$541$	14.4924			0.623078			0.311539	+	0.950233i	$0.399156\pi$
$542$		0			0
$543$	−16.8078	+	9.43845i	−0.721290	+	0.405043i
$544$		0			0
$545$	−0.417609			−0.0178884
$546$		0			0
$547$	38.7386			1.65634			0.828172	−	0.560474i	$-0.189381\pi$
$547$	38.7386			1.65634			0.828172	+	0.560474i	$0.189381\pi$
$548$		0			0
$549$	28.5083	+	17.3790i	1.21671	+	0.741718i
$550$		0			0
$551$	−3.39228			−0.144516
$552$		0			0
$553$	13.1231	+	3.39228i	0.558051	+	0.144255i
$554$		0			0
$555$	11.8617	+	21.1231i	0.503503	+	0.896626i
$556$		0			0
$557$			2.38447i			0.101033i	0.998723	+	0.0505167i	$0.0160868\pi$
$557$			2.38447i			0.101033i	−0.998723	+	0.0505167i	$0.983913\pi$
$558$		0			0
$559$		−	34.7580i		−	1.47011i
$560$		0			0
$561$	36.4924	−	20.4924i	1.54071	−	0.865191i
$562$		0			0
$563$	11.8730			0.500387			0.250193	−	0.968196i	$-0.419506\pi$
$563$	11.8730			0.500387			0.250193	+	0.968196i	$0.419506\pi$
$564$		0			0
$565$			8.68951i			0.365570i
$566$		0			0
$567$	5.26433	+	23.2226i	0.221081	+	0.975255i
$568$		0			0
$569$		−	39.3693i		−	1.65045i	−0.564806	−	0.825224i	$-0.691049\pi$
$569$		−	39.3693i		−	1.65045i	0.564806	−	0.825224i	$-0.308951\pi$
$570$		0			0
$571$	−22.7386			−0.951582			−0.475791	−	0.879558i	$-0.657838\pi$
$571$	−22.7386			−0.951582			−0.475791	+	0.879558i	$0.657838\pi$
$572$		0			0
$573$	9.43318	−	5.29723i	0.394077	−	0.221295i
$574$		0			0
$575$		−	2.38447i		−	0.0994394i
$576$		0			0
$577$			37.7327i			1.57083i	0.618967	+	0.785417i	$0.287551\pi$
$577$			37.7327i			1.57083i	−0.618967	+	0.785417i	$0.712449\pi$
$578$		0			0
$579$	0.743668	+	1.32431i	0.0309058	+	0.0550363i
$580$		0			0
$581$	43.9824	+	11.3693i	1.82470	+	0.471679i
$582$		0			0
$583$	−36.4924			−1.51136
$584$		0			0
$585$	−18.8769	−	11.5076i	−0.780464	−	0.475780i
$586$		0			0
$587$	3.18348			0.131396			0.0656981	−	0.997840i	$-0.479073\pi$
$587$	3.18348			0.131396			0.0656981	+	0.997840i	$0.479073\pi$
$588$		0			0
$589$	14.2462			0.587005
$590$		0			0
$591$	−17.1702	+	9.64198i	−0.706288	+	0.396618i
$592$		0			0
$593$	13.2431			0.543828			0.271914	−	0.962322i	$-0.412343\pi$
$593$	13.2431			0.543828			0.271914	+	0.962322i	$0.412343\pi$
$594$		0			0
$595$	−26.2462	−	6.78456i	−1.07599	−	0.278140i
$596$		0			0
$597$	−21.3693	+	12.0000i	−0.874588	+	0.491127i
$598$		0			0
$599$		−	6.24621i		−	0.255213i	−0.991825	−	0.127607i	$-0.959270\pi$
$599$		−	6.24621i		−	0.255213i	0.991825	−	0.127607i	$-0.0407295\pi$
$600$		0			0
$601$			17.3790i			0.708905i	0.935074	+	0.354452i	$0.115333\pi$
$601$			17.3790i			0.708905i	−0.935074	+	0.354452i	$0.884667\pi$
$602$		0			0
$603$	−3.50758	+	5.75379i	−0.142840	+	0.234312i
$604$		0			0
$605$	8.48071			0.344790
$606$		0			0
$607$			0.163030i			0.00661717i	0.999995	+	0.00330858i	$0.00105316\pi$
$607$			0.163030i			0.00661717i	−0.999995	+	0.00330858i	$0.998947\pi$
$608$		0			0
$609$	−4.97544	+	1.31670i	−0.201615	+	0.0533555i
$610$		0			0
$611$			14.7386i			0.596261i
$612$		0			0
$613$	−22.4924			−0.908460			−0.454230	−	0.890884i	$-0.650086\pi$
$613$	−22.4924			−0.908460			−0.454230	+	0.890884i	$0.650086\pi$
$614$		0			0
$615$	8.68951	+	15.4741i	0.350395	+	0.623975i
$616$		0			0
$617$			9.61553i			0.387107i	0.981090	+	0.193553i	$0.0620012\pi$
$617$			9.61553i			0.387107i	−0.981090	+	0.193553i	$0.937999\pi$
$618$		0			0
$619$			1.53311i			0.0616209i	0.999525	+	0.0308105i	$0.00980883\pi$
$619$			1.53311i			0.0616209i	−0.999525	+	0.0308105i	$0.990191\pi$
$620$		0			0
$621$	0.208805	−	5.83209i	0.00837904	−	0.234034i
$622$		0			0
$623$	−24.1636	−	6.24621i	−0.968094	−	0.250249i
$624$		0			0
$625$	−9.87689			−0.395076
$626$		0			0
$627$	10.2462	+	18.2462i	0.409194	+	0.728683i
$628$		0			0
$629$	49.8145			1.98623
$630$		0			0
$631$	5.12311			0.203948			0.101974	−	0.994787i	$-0.467484\pi$
$631$	5.12311			0.203948			0.101974	+	0.994787i	$0.467484\pi$
$632$		0			0
$633$	1.90495	+	3.39228i	0.0757148	+	0.134831i
$634$		0			0
$635$	13.5691			0.538474
$636$		0			0
$637$	14.7386	−	26.6034i	0.583966	−	1.05406i
$638$		0			0
$639$	−36.4924	−	22.2462i	−1.44362	−	0.880047i
$640$		0			0
$641$			38.1080i			1.50517i	0.658493	+	0.752587i	$0.271194\pi$
$641$			38.1080i			1.50517i	−0.658493	+	0.752587i	$0.728806\pi$
$642$		0			0
$643$			34.7123i			1.36892i	0.729051	+	0.684459i	$0.239962\pi$
$643$			34.7123i			1.36892i	−0.729051	+	0.684459i	$0.760038\pi$
$644$		0			0
$645$	−11.5076	−	20.4924i	−0.453110	−	0.806888i
$646$		0			0
$647$	−3.39228			−0.133364			−0.0666822	−	0.997774i	$-0.521241\pi$
$647$	−3.39228			−0.133364			−0.0666822	+	0.997774i	$0.521241\pi$
$648$		0			0
$649$			41.5426i			1.63069i
$650$		0			0
$651$	20.8948	−	5.52962i	0.818933	−	0.216723i
$652$		0			0
$653$			26.1080i			1.02168i	0.859675	+	0.510842i	$0.170666\pi$
$653$			26.1080i			1.02168i	−0.859675	+	0.510842i	$0.829334\pi$
$654$		0			0
$655$	−8.63068			−0.337229
$656$		0			0
$657$		0			0
$658$		0			0
$659$			9.75379i			0.379954i	0.981789	+	0.189977i	$0.0608413\pi$
$659$			9.75379i			0.379954i	−0.981789	+	0.189977i	$0.939159\pi$
$660$		0			0
$661$		−	40.1725i		−	1.56253i	−0.624200	−	0.781265i	$-0.714575\pi$
$661$		−	40.1725i		−	1.56253i	0.624200	−	0.781265i	$-0.285425\pi$
$662$		0			0
$663$	−39.6377	+	22.2586i	−1.53940	+	0.864454i
$664$		0			0
$665$	3.39228	−	13.1231i	0.131547	−	0.508892i
$666$		0			0
$667$	1.26137			0.0488403
$668$		0			0
$669$	40.7386	−	22.8769i	1.57505	−	0.884472i
$670$		0			0
$671$	44.5173			1.71857
$672$		0			0
$673$	−7.75379			−0.298887			−0.149443	−	0.988770i	$-0.547748\pi$
$673$	−7.75379			−0.298887			−0.149443	+	0.988770i	$0.547748\pi$
$674$		0			0
$675$	11.0249	+	0.394722i	0.424349	+	0.0151928i
$676$		0			0
$677$	0.208805			0.00802501			0.00401250	−	0.999992i	$-0.498723\pi$
$677$	0.208805			0.00802501			0.00401250	+	0.999992i	$0.498723\pi$
$678$		0			0
$679$	10.2462	−	39.6377i	0.393213	−	1.52115i
$680$		0			0
$681$	7.19224	+	12.8078i	0.275607	+	0.490795i
$682$		0			0
$683$			28.9848i			1.10907i	0.832159	+	0.554537i	$0.187105\pi$
$683$			28.9848i			1.10907i	−0.832159	+	0.554537i	$0.812895\pi$
$684$		0			0
$685$			3.80989i			0.145568i
$686$		0			0
$687$	−29.9309	+	16.8078i	−1.14193	+	0.641256i
$688$		0			0
$689$	39.6377			1.51007
$690$		0			0
$691$			1.11550i			0.0424357i	0.999775	+	0.0212179i	$0.00675436\pi$
$691$			1.11550i			0.0424357i	−0.999775	+	0.0212179i	$0.993246\pi$
$692$		0			0
$693$	22.1103	+	22.7846i	0.839899	+	0.865514i
$694$		0			0
$695$			12.1383i			0.460430i
$696$		0			0
$697$	36.4924			1.38225
$698$		0			0
$699$	30.9481	−	17.3790i	1.17057	−	0.657335i
$700$		0			0
$701$		−	44.3542i		−	1.67523i	−0.546258	−	0.837617i	$-0.683948\pi$
$701$		−	44.3542i		−	1.67523i	0.546258	−	0.837617i	$-0.316052\pi$
$702$		0			0
$703$			24.9073i			0.939395i
$704$		0			0
$705$	4.87962	+	8.68951i	0.183777	+	0.327266i
$706$		0			0
$707$	−13.0343	−	3.36932i	−0.490204	−	0.126716i
$708$		0			0
$709$	−28.2462			−1.06081			−0.530404	−	0.847745i	$-0.677960\pi$
$709$	−28.2462			−1.06081			−0.530404	+	0.847745i	$0.677960\pi$
$710$		0			0
$711$	8.00000	−	13.1231i	0.300023	−	0.492155i
$712$		0			0
$713$	−5.29723			−0.198383
$714$		0			0
$715$	−29.4773			−1.10239
$716$		0			0
$717$	13.7779	−	7.73704i	0.514546	−	0.288945i
$718$		0			0
$719$	31.3658			1.16975			0.584873	−	0.811125i	$-0.301144\pi$
$719$	31.3658			1.16975			0.584873	+	0.811125i	$0.301144\pi$
$720$		0			0
$721$	6.63068	−	25.6509i	0.246940	−	0.955290i
$722$		0			0
$723$	13.1231	−	7.36932i	0.488054	−	0.274068i
$724$		0			0
$725$			2.38447i			0.0885571i
$726$		0			0
$727$			47.7465i			1.77082i	0.464810	+	0.885410i	$0.346123\pi$
$727$			47.7465i			1.77082i	−0.464810	+	0.885410i	$0.653877\pi$
$728$		0			0
$729$	26.9309	+	1.93087i	0.997440	+	0.0715137i
$730$		0			0
$731$	−48.3272			−1.78744
$732$		0			0
$733$			31.4830i			1.16285i	0.813599	+	0.581426i	$0.197505\pi$
$733$			31.4830i			1.16285i	−0.813599	+	0.581426i	$0.802495\pi$
$734$		0			0
$735$	−0.118254	−	20.5643i	−0.00436188	−	0.758525i
$736$		0			0
$737$			8.98485i			0.330961i
$738$		0			0
$739$	−24.0000			−0.882854			−0.441427	−	0.897297i	$-0.645528\pi$
$739$	−24.0000			−0.882854			−0.441427	+	0.897297i	$0.645528\pi$
$740$		0			0
$741$	−11.1293	−	19.8188i	−0.408846	−	0.728063i
$742$		0			0
$743$			17.1231i			0.628186i	0.949392	+	0.314093i	$0.101700\pi$
$743$			17.1231i			0.628186i	−0.949392	+	0.314093i	$0.898300\pi$
$744$		0			0
$745$			29.0432i			1.06406i
$746$		0			0
$747$	26.8122	−	43.9824i	0.981007	−	1.60923i
$748$		0			0
$749$	9.43318	−	36.4924i	0.344681	−	1.33340i
$750$		0			0
$751$	32.9848			1.20363			0.601817	−	0.798634i	$-0.294444\pi$
$751$	32.9848			1.20363			0.601817	+	0.798634i	$0.294444\pi$
$752$		0			0
$753$	−14.5616	−	25.9309i	−0.530652	−	0.944973i
$754$		0			0
$755$	21.1889			0.771143
$756$		0			0
$757$	34.4924			1.25365			0.626824	−	0.779161i	$-0.284354\pi$
$757$	34.4924			1.25365			0.626824	+	0.779161i	$0.284354\pi$
$758$		0			0
$759$	−3.80989	−	6.78456i	−0.138290	−	0.246264i
$760$		0			0
$761$	−16.6354			−0.603031			−0.301516	−	0.953461i	$-0.597493\pi$
$761$	−16.6354			−0.603031			−0.301516	+	0.953461i	$0.597493\pi$
$762$		0			0
$763$	−0.630683	−	0.163030i	−0.0228323	−	0.00590207i
$764$		0			0
$765$	−16.0000	+	26.2462i	−0.578481	+	0.948934i
$766$		0			0
$767$		−	45.1231i		−	1.62930i
$768$		0			0
$769$			26.0685i			0.940055i	0.882652	+	0.470028i	$0.155756\pi$
$769$			26.0685i			0.940055i	−0.882652	+	0.470028i	$0.844244\pi$
$770$		0			0
$771$	−12.4924	−	22.2462i	−0.449904	−	0.801178i
$772$		0			0
$773$	−22.0498			−0.793077			−0.396539	−	0.918018i	$-0.629789\pi$
$773$	−22.0498			−0.793077			−0.396539	+	0.918018i	$0.629789\pi$
$774$		0			0
$775$		−	10.0138i		−	0.359707i
$776$		0			0
$777$	9.66767	+	36.5313i	0.346826	+	1.31055i
$778$		0			0
$779$			18.2462i			0.653738i
$780$		0			0
$781$	−56.9848			−2.03908
$782$		0			0
$783$	−0.208805	+	5.83209i	−0.00746206	+	0.208422i
$784$		0			0
$785$			4.13826i			0.147701i
$786$		0			0
$787$		−	17.3332i		−	0.617863i	−0.951084	−	0.308932i	$-0.900029\pi$
$787$		−	17.3332i		−	0.617863i	0.951084	−	0.308932i	$-0.0999715\pi$
$788$		0			0
$789$	33.5968	−	18.8664i	1.19608	−	0.671660i
$790$		0			0
$791$	−3.39228	+	13.1231i	−0.120616	+	0.466604i
$792$		0			0
$793$	−48.3542			−1.71711
$794$		0			0
$795$	23.3693	−	13.1231i	0.828824	−	0.465429i
$796$		0			0
$797$	−23.9548			−0.848522			−0.424261	−	0.905540i	$-0.639466\pi$
$797$	−23.9548			−0.848522			−0.424261	+	0.905540i	$0.639466\pi$
$798$		0			0
$799$	20.4924			0.724970
$800$		0			0
$801$	−14.7304	+	24.1636i	−0.520473	+	0.853778i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−1.26137	+	4.87962i	−0.0444573	+	0.171984i
$806$		0			0
$807$	4.31534	+	7.68466i	0.151907	+	0.270513i
$808$		0			0
$809$			33.6155i			1.18186i	0.806723	+	0.590930i	$0.201239\pi$
$809$			33.6155i			1.18186i	−0.806723	+	0.590930i	$0.798761\pi$
$810$		0			0
$811$			6.41273i			0.225181i	0.993641	+	0.112591i	$0.0359149\pi$
$811$			6.41273i			0.225181i	−0.993641	+	0.112591i	$0.964085\pi$
$812$		0			0
$813$	−20.2462	+	11.3693i	−0.710066	+	0.398739i
$814$		0			0
$815$	−30.9481			−1.08407
$816$		0			0
$817$		−	24.1636i		−	0.845377i
$818$		0			0
$819$	−24.0159	−	24.7483i	−0.839184	−	0.864777i
$820$		0			0
$821$		−	1.12311i		−	0.0391967i	−0.999808	−	0.0195983i	$-0.993761\pi$
$821$		−	1.12311i		−	0.0391967i	0.999808	−	0.0195983i	$-0.00623874\pi$
$822$		0			0
$823$	10.8769			0.379145			0.189572	−	0.981867i	$-0.439290\pi$
$823$	10.8769			0.379145			0.189572	+	0.981867i	$0.439290\pi$
$824$		0			0
$825$	12.8255	−	7.20217i	0.446525	−	0.250747i
$826$		0			0
$827$			18.7386i			0.651606i	0.945438	+	0.325803i	$0.105635\pi$
$827$			18.7386i			0.651606i	−0.945438	+	0.325803i	$0.894365\pi$
$828$		0			0
$829$			2.43981i			0.0847381i	0.999102	+	0.0423690i	$0.0134905\pi$
$829$			2.43981i			0.0847381i	−0.999102	+	0.0423690i	$0.986509\pi$
$830$		0			0
$831$	1.69614	+	3.02045i	0.0588385	+	0.104778i
$832$		0			0
$833$	−36.9890	−	20.4924i	−1.28159	−	0.710020i
$834$		0			0
$835$	35.2311			1.21922
$836$		0			0
$837$	0.876894	−	24.4924i	0.0303099	−	0.846582i
$838$		0			0
$839$	7.20217			0.248647			0.124323	−	0.992242i	$-0.460324\pi$
$839$	7.20217			0.248647			0.124323	+	0.992242i	$0.460324\pi$
$840$		0			0
$841$	27.7386			0.956505
$842$		0			0
$843$	−24.1636	+	13.5691i	−0.832238	+	0.467346i
$844$		0			0
$845$	9.96804			0.342911
$846$		0			0
$847$	12.8078	+	3.31077i	0.440080	+	0.113759i
$848$		0			0
$849$	−23.9309	+	13.4384i	−0.821305	+	0.461206i
$850$		0			0
$851$		−	9.26137i		−	0.317476i
$852$		0			0
$853$		−	14.9392i		−	0.511509i	−0.966742	−	0.255754i	$-0.917676\pi$
$853$		−	14.9392i		−	0.511509i	0.966742	−	0.255754i	$-0.0823238\pi$
$854$		0			0
$855$	−13.1231	−	8.00000i	−0.448801	−	0.273594i
$856$		0			0
$857$	0.743668			0.0254032			0.0127016	−	0.999919i	$-0.495957\pi$
$857$	0.743668			0.0254032			0.0127016	+	0.999919i	$0.495957\pi$
$858$		0			0
$859$			10.9663i			0.374165i	0.982344	+	0.187082i	$0.0599032\pi$
$859$			10.9663i			0.374165i	−0.982344	+	0.187082i	$0.940097\pi$
$860$		0			0
$861$	7.08221	+	26.7616i	0.241361	+	0.912033i
$862$		0			0
$863$			55.2311i			1.88009i	0.341055	+	0.940044i	$0.389216\pi$
$863$			55.2311i			1.88009i	−0.341055	+	0.940044i	$0.610784\pi$
$864$		0			0
$865$	2.87689			0.0978173
$866$		0			0
$867$	16.5309	+	29.4379i	0.561420	+	0.999764i
$868$		0			0
$869$		−	20.4924i		−	0.695158i
$870$		0			0
$871$		−	9.75924i		−	0.330679i
$872$		0			0
$873$	−39.6377	−	24.1636i	−1.34153	−	0.817813i
$874$		0			0
$875$	−30.9481	−	8.00000i	−1.04624	−	0.270449i
$876$		0			0
$877$	11.7538			0.396897			0.198449	−	0.980111i	$-0.436410\pi$
$877$	11.7538			0.396897			0.198449	+	0.980111i	$0.436410\pi$
$878$		0			0
$879$	−23.5464	−	41.9309i	−0.794200	−	1.41429i
$880$		0			0
$881$	−17.7051			−0.596499			−0.298250	−	0.954488i	$-0.596403\pi$
$881$	−17.7051			−0.596499			−0.298250	+	0.954488i	$0.596403\pi$
$882$		0			0
$883$	−22.7386			−0.765216			−0.382608	−	0.923911i	$-0.624974\pi$
$883$	−22.7386			−0.765216			−0.382608	+	0.923911i	$0.624974\pi$
$884$		0			0
$885$	−14.9392	−	26.6034i	−0.502176	−	0.894263i
$886$		0			0
$887$	−10.1768			−0.341705			−0.170853	−	0.985297i	$-0.554652\pi$
$887$	−10.1768			−0.341705			−0.170853	+	0.985297i	$0.554652\pi$
$888$		0			0
$889$	20.4924	+	5.29723i	0.687294	+	0.177663i
$890$		0			0
$891$	32.0000	−	16.4924i	1.07204	−	0.552517i
$892$		0			0
$893$			10.2462i			0.342876i
$894$		0			0
$895$		−	14.4043i		−	0.481484i
$896$		0			0
$897$	4.13826	+	7.36932i	0.138173	+	0.246054i
$898$		0			0
$899$	5.29723			0.176672
$900$		0			0
$901$		−	55.1117i		−	1.83604i
$902$		0			0
$903$	−9.37902	−	35.4406i	−0.312114	−	1.17939i
$904$		0			0
$905$		−	18.8769i		−	0.627489i
$906$		0			0
$907$	−24.0000			−0.796907			−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000			−0.796907			−0.398453	+	0.917189i	$0.630453\pi$
$908$		0			0
$909$	−7.94584	+	13.0343i	−0.263547	+	0.432319i
$910$		0			0
$911$			1.12311i			0.0372101i	0.999827	+	0.0186051i	$0.00592252\pi$
$911$			1.12311i			0.0372101i	−0.999827	+	0.0186051i	$0.994077\pi$
$912$		0			0
$913$		−	68.6809i		−	2.27300i
$914$		0			0
$915$	−28.5083	+	16.0089i	−0.942457	+	0.529239i
$916$		0			0
$917$	−13.0343	−	3.36932i	−0.430429	−	0.111265i
$918$		0			0
$919$	41.6155			1.37277			0.686385	−	0.727239i	$-0.259197\pi$
$919$	41.6155			1.37277			0.686385	+	0.727239i	$0.259197\pi$
$920$		0			0
$921$	−21.6847	+	12.1771i	−0.714534	+	0.401248i
$922$		0			0
$923$	61.8963			2.03734
$924$		0			0
$925$	17.5076			0.575646
$926$		0			0
$927$	−25.6509	−	15.6371i	−0.842487	−	0.513590i
$928$		0			0
$929$	−12.8255			−0.420790			−0.210395	−	0.977616i	$-0.567475\pi$
$929$	−12.8255			−0.420790			−0.210395	+	0.977616i	$0.567475\pi$
$930$		0			0
$931$	10.2462	−	18.4945i	0.335806	−	0.606133i
$932$		0			0
$933$	5.75379	+	10.2462i	0.188371	+	0.335446i
$934$		0			0
$935$			40.9848i			1.34035i
$936$		0			0
$937$			20.3537i			0.664926i	0.943116	+	0.332463i	$0.107880\pi$
$937$			20.3537i			0.664926i	−0.943116	+	0.332463i	$0.892120\pi$
$938$		0			0
$939$	49.6155	−	27.8617i	1.61914	−	0.909234i
$940$		0			0
$941$	−23.9548			−0.780903			−0.390452	−	0.920623i	$-0.627681\pi$
$941$	−23.9548			−0.780903			−0.390452	+	0.920623i	$0.627681\pi$
$942$		0			0
$943$		−	6.78456i		−	0.220936i
$944$		0			0
$945$	−22.3527	−	6.63986i	−0.727135	−	0.215995i
$946$		0			0
$947$		−	26.7386i		−	0.868889i	−0.900699	−	0.434444i	$-0.856945\pi$
$947$		−	26.7386i		−	0.868889i	0.900699	−	0.434444i	$-0.143055\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	13.7779	−	7.73704i	0.446780	−	0.250891i
$952$		0			0
$953$		−	2.24621i		−	0.0727619i	−0.999338	−	0.0363810i	$-0.988417\pi$
$953$		−	2.24621i		−	0.0727619i	0.999338	−	0.0363810i	$-0.0115830\pi$
$954$		0			0
$955$			10.5945i			0.342829i
$956$		0			0
$957$	3.80989	+	6.78456i	0.123156	+	0.219314i
$958$		0			0
$959$	−1.48734	+	5.75379i	−0.0480286	+	0.185800i
$960$		0			0
$961$	8.75379			0.282380
$962$		0			0
$963$	−36.4924	−	22.2462i	−1.17595	−	0.716874i
$964$		0			0
$965$	−1.48734			−0.0478791
$966$		0			0
$967$	−3.50758			−0.112796			−0.0563980	−	0.998408i	$-0.517962\pi$
$967$	−3.50758			−0.112796			−0.0563980	+	0.998408i	$0.517962\pi$
$968$		0			0
$969$	−27.5559	+	15.4741i	−0.885222	+	0.497099i
$970$		0			0
$971$	33.0619			1.06101			0.530503	−	0.847683i	$-0.322003\pi$
$971$	33.0619			1.06101			0.530503	+	0.847683i	$0.322003\pi$
$972$		0			0
$973$	−4.73863	+	18.3315i	−0.151914	+	0.587681i
$974$		0			0
$975$	−13.9309	+	7.82292i	−0.446145	+	0.250534i
$976$		0			0
$977$			29.7538i			0.951908i	0.879470	+	0.475954i	$0.157897\pi$
$977$			29.7538i			0.951908i	−0.879470	+	0.475954i	$0.842103\pi$
$978$		0			0
$979$			37.7327i			1.20594i
$980$		0			0
$981$	−0.384472	+	0.630683i	−0.0122752	+	0.0201362i
$982$		0			0
$983$	41.1250			1.31168			0.655842	−	0.754898i	$-0.272314\pi$
$983$	41.1250			1.31168			0.655842	+	0.754898i	$0.272314\pi$
$984$		0			0
$985$		−	19.2840i		−	0.614438i
$986$		0			0
$987$	3.97703	+	15.0281i	0.126590	+	0.478348i
$988$		0			0
$989$			8.98485i			0.285701i
$990$		0			0
$991$	37.1231			1.17925			0.589627	−	0.807676i	$-0.299275\pi$
$991$	37.1231			1.17925			0.589627	+	0.807676i	$0.299275\pi$
$992$		0			0
$993$	−11.6642	−	20.7713i	−0.370152	−	0.659157i
$994$		0			0
$995$		−	24.0000i		−	0.760851i
$996$		0			0
$997$			11.1293i			0.352469i	0.984348	+	0.176235i	$0.0563917\pi$
$997$			11.1293i			0.352469i	−0.984348	+	0.176235i	$0.943608\pi$
$998$		0			0
$999$	42.8211	+	1.53311i	1.35480	+	0.0485055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.k.a.545.6	yes	8
3.2	odd	2	inner	672.2.k.a.545.4	yes	8
4.3	odd	2		672.2.k.d.545.3	yes	8
7.6	odd	2	inner	672.2.k.a.545.3	✓	8
8.3	odd	2		1344.2.k.j.1217.6		8
8.5	even	2		1344.2.k.e.1217.3		8
12.11	even	2		672.2.k.d.545.5	yes	8
21.20	even	2	inner	672.2.k.a.545.5	yes	8
24.5	odd	2		1344.2.k.e.1217.5		8
24.11	even	2		1344.2.k.j.1217.4		8
28.27	even	2		672.2.k.d.545.6	yes	8
56.13	odd	2		1344.2.k.e.1217.6		8
56.27	even	2		1344.2.k.j.1217.3		8
84.83	odd	2		672.2.k.d.545.4	yes	8
168.83	odd	2		1344.2.k.j.1217.5		8
168.125	even	2		1344.2.k.e.1217.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.k.a.545.3	✓	8	7.6	odd	2	inner
672.2.k.a.545.4	yes	8	3.2	odd	2	inner
672.2.k.a.545.5	yes	8	21.20	even	2	inner
672.2.k.a.545.6	yes	8	1.1	even	1	trivial
672.2.k.d.545.3	yes	8	4.3	odd	2
672.2.k.d.545.4	yes	8	84.83	odd	2
672.2.k.d.545.5	yes	8	12.11	even	2
672.2.k.d.545.6	yes	8	28.27	even	2
1344.2.k.e.1217.3		8	8.5	even	2
1344.2.k.e.1217.4		8	168.125	even	2
1344.2.k.e.1217.5		8	24.5	odd	2
1344.2.k.e.1217.6		8	56.13	odd	2
1344.2.k.j.1217.3		8	56.27	even	2
1344.2.k.j.1217.4		8	24.11	even	2
1344.2.k.j.1217.5		8	168.83	odd	2
1344.2.k.j.1217.6		8	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.848071 + 1.51022i) q^{3} -1.69614 q^{5} +(-2.56155 - 0.662153i) q^{7} +(-1.56155 + 2.56155i) q^{9} +O(q^{10})\)	\(q+(0.848071 + 1.51022i) q^{3} -1.69614 q^{5} +(-2.56155 - 0.662153i) q^{7} +(-1.56155 + 2.56155i) q^{9} +4.00000i q^{11} -4.34475i q^{13} +(-1.43845 - 2.56155i) q^{15} -6.04090 q^{17} -3.02045i q^{19} +(-1.17238 - 4.43007i) q^{21} +1.12311i q^{23} -2.12311 q^{25} +(-5.19283 - 0.185917i) q^{27} -1.12311i q^{29} +4.71659i q^{31} +(-6.04090 + 3.39228i) q^{33} +(4.34475 + 1.12311i) q^{35} -8.24621 q^{37} +(6.56155 - 3.68466i) q^{39} -6.04090 q^{41} +8.00000 q^{43} +(2.64861 - 4.34475i) q^{45} -3.39228 q^{47} +(6.12311 + 3.39228i) q^{49} +(-5.12311 - 9.12311i) q^{51} +9.12311i q^{53} -6.78456i q^{55} +(4.56155 - 2.56155i) q^{57} +10.3857 q^{59} -11.1293i q^{61} +(5.69614 - 5.52757i) q^{63} +7.36932i q^{65} +2.24621 q^{67} +(-1.69614 + 0.952473i) q^{69} +14.2462i q^{71} +(-1.80054 - 3.20636i) q^{75} +(2.64861 - 10.2462i) q^{77} -5.12311 q^{79} +(-4.12311 - 8.00000i) q^{81} -17.1702 q^{83} +10.2462 q^{85} +(1.69614 - 0.952473i) q^{87} +9.43318 q^{89} +(-2.87689 + 11.1293i) q^{91} +(-7.12311 + 4.00000i) q^{93} +5.12311i q^{95} +15.4741i q^{97} +(-10.2462 - 6.24621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^7 + 4 * q^9	\( 8 q - 4 q^{7} + 4 q^{9} - 28 q^{15} + 8 q^{21} + 16 q^{25} + 36 q^{39} + 64 q^{43} + 16 q^{49} - 8 q^{51} + 20 q^{57} + 32 q^{63} - 48 q^{67} - 8 q^{79} + 16 q^{85} - 56 q^{91} - 24 q^{93} - 16 q^{99}+O(q^{100}) \) 8 * q - 4 * q^7 + 4 * q^9 - 28 * q^15 + 8 * q^21 + 16 * q^25 + 36 * q^39 + 64 * q^43 + 16 * q^49 - 8 * q^51 + 20 * q^57 + 32 * q^63 - 48 * q^67 - 8 * q^79 + 16 * q^85 - 56 * q^91 - 24 * q^93 - 16 * q^99

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