LMFDB - Embedded newform 2100.2.x.c.1693.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1357,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("2100.1357");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.x (of order $4$, degree $2$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.478584585616890104119296.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 31x^{12} + 336x^{8} - 19375x^{4} + 390625 $ x^16 - 31x^12 + 336x^8 - 19375*x^4 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1693.5
Root			$-1.97578 + 1.04705i$ of defining polynomial
Character	$\chi$	$=$	2100.1693
Dual form			2100.2.x.c.1357.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-2.49342 + 0.884806i) q^{7} -1.00000i q^{9} +O(q^{10})$	$q+(0.707107 - 0.707107i) q^{3} +(-2.49342 + 0.884806i) q^{7} -1.00000i q^{9} +3.27492 q^{11} +(3.02282 - 3.02282i) q^{13} +(-1.41421 - 1.41421i) q^{17} +2.15068 q^{19} +(-1.13746 + 2.38876i) q^{21} +(0.296014 + 0.296014i) q^{23} +(-0.707107 - 0.707107i) q^{27} +0.725083i q^{29} +1.31342i q^{31} +(2.31572 - 2.31572i) q^{33} +(-1.56145 + 1.56145i) q^{37} -4.27492i q^{39} -5.25370i q^{41} +(-0.632717 - 0.632717i) q^{43} +(-1.41421 - 1.41421i) q^{47} +(5.43424 - 4.41238i) q^{49} -2.00000 q^{51} +(-3.71492 - 3.71492i) q^{53} +(1.52076 - 1.52076i) q^{57} +8.71780 q^{59} -1.31342i q^{61} +(0.884806 + 2.49342i) q^{63} +(3.08221 - 3.08221i) q^{67} +0.418627 q^{69} +9.27492 q^{71} +(7.07107 - 7.07107i) q^{73} +(-8.16573 + 2.89767i) q^{77} -11.8248i q^{79} -1.00000 q^{81} +(11.7025 - 11.7025i) q^{83} +(0.512711 + 0.512711i) q^{87} +18.2728 q^{89} +(-4.86254 + 10.2118i) q^{91} +(0.928731 + 0.928731i) q^{93} +(-7.26546 - 7.26546i) q^{97} -3.27492i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} + 12 q^{21} - 32 q^{51} + 88 q^{71} - 16 q^{81} - 108 q^{91}+O(q^{100}) $ 16 * q - 8 * q^11 + 12 * q^21 - 32 * q^51 + 88 * q^71 - 16 * q^81 - 108 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.49342	+	0.884806i	−0.942422	+	0.334425i
$7$	−2.49342	+	0.884806i	−0.942422	+	0.334425i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	3.27492			0.987425			0.493712	−	0.869625i	$-0.335640\pi$
$11$	3.27492			0.987425			0.493712	+	0.869625i	$0.335640\pi$
$12$		0			0
$13$	3.02282	−	3.02282i	0.838380	−	0.838380i	−0.150265	−	0.988646i	$-0.548013\pi$
$13$	3.02282	−	3.02282i	0.838380	−	0.838380i	0.988646	+	0.150265i	$0.0480128\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	0.514496	−	0.857493i	$-0.327979\pi$
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	−0.857493	+	0.514496i	$0.827979\pi$
$18$		0			0
$19$	2.15068			0.493399			0.246700	−	0.969092i	$-0.420654\pi$
$19$	2.15068			0.493399			0.246700	+	0.969092i	$0.420654\pi$
$20$		0			0
$21$	−1.13746	+	2.38876i	−0.248214	+	0.521271i
$22$		0			0
$23$	0.296014	+	0.296014i	0.0617231	+	0.0617231i	0.737295	−	0.675571i	$-0.236103\pi$
$23$	0.296014	+	0.296014i	0.0617231	+	0.0617231i	−0.675571	+	0.737295i	$0.736103\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			0.725083i			0.134644i	0.997731	+	0.0673222i	$0.0214456\pi$
$29$			0.725083i			0.134644i	−0.997731	+	0.0673222i	$0.978554\pi$
$30$		0			0
$31$			1.31342i			0.235898i	0.993020	+	0.117949i	$0.0376319\pi$
$31$			1.31342i			0.235898i	−0.993020	+	0.117949i	$0.962368\pi$
$32$		0			0
$33$	2.31572	−	2.31572i	0.403114	−	0.403114i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.56145	+	1.56145i	−0.256701	+	0.256701i	−0.823711	−	0.567010i	$-0.808100\pi$
$37$	−1.56145	+	1.56145i	−0.256701	+	0.256701i	0.567010	+	0.823711i	$0.308100\pi$
$38$		0			0
$39$		−	4.27492i		−	0.684535i
$40$		0			0
$41$		−	5.25370i		−	0.820490i	−0.911975	−	0.410245i	$-0.865443\pi$
$41$		−	5.25370i		−	0.820490i	0.911975	−	0.410245i	$-0.134557\pi$
$42$		0			0
$43$	−0.632717	−	0.632717i	−0.0964885	−	0.0964885i	0.657215	−	0.753703i	$-0.271734\pi$
$43$	−0.632717	−	0.632717i	−0.0964885	−	0.0964885i	−0.753703	+	0.657215i	$0.771734\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.41421	−	1.41421i	−0.206284	−	0.206284i	0.596402	−	0.802686i	$-0.296597\pi$
$47$	−1.41421	−	1.41421i	−0.206284	−	0.206284i	−0.802686	+	0.596402i	$0.796597\pi$
$48$		0			0
$49$	5.43424	−	4.41238i	0.776320	−	0.630339i
$50$		0			0
$51$	−2.00000			−0.280056
$52$		0			0
$53$	−3.71492	−	3.71492i	−0.510284	−	0.510284i	0.404329	−	0.914613i	$-0.367505\pi$
$53$	−3.71492	−	3.71492i	−0.510284	−	0.510284i	−0.914613	+	0.404329i	$0.867505\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.52076	−	1.52076i	0.201429	−	0.201429i
$58$		0			0
$59$	8.71780			1.13496			0.567480	−	0.823387i	$-0.307918\pi$
$59$	8.71780			1.13496			0.567480	+	0.823387i	$0.307918\pi$
$60$		0			0
$61$		−	1.31342i		−	0.168167i	−0.996459	−	0.0840834i	$-0.973204\pi$
$61$		−	1.31342i		−	0.168167i	0.996459	−	0.0840834i	$-0.0267962\pi$
$62$		0			0
$63$	0.884806	+	2.49342i	0.111475	+	0.314141i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.08221	−	3.08221i	0.376552	−	0.376552i	−0.493305	−	0.869856i	$-0.664211\pi$
$67$	3.08221	−	3.08221i	0.376552	−	0.376552i	0.869856	+	0.493305i	$0.164211\pi$
$68$		0			0
$69$	0.418627			0.0503967
$70$		0			0
$71$	9.27492			1.10073			0.550365	−	0.834924i	$-0.314489\pi$
$71$	9.27492			1.10073			0.550365	+	0.834924i	$0.314489\pi$
$72$		0			0
$73$	7.07107	−	7.07107i	0.827606	−	0.827606i	−0.159579	−	0.987185i	$-0.551014\pi$
$73$	7.07107	−	7.07107i	0.827606	−	0.827606i	0.987185	+	0.159579i	$0.0510137\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.16573	+	2.89767i	−0.930571	+	0.330220i
$78$		0			0
$79$		−	11.8248i		−	1.33039i	−0.746670	−	0.665194i	$-0.768349\pi$
$79$		−	11.8248i		−	1.33039i	0.746670	−	0.665194i	$-0.231651\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	11.7025	−	11.7025i	1.28452	−	1.28452i	0.346447	−	0.938070i	$-0.387388\pi$
$83$	11.7025	−	11.7025i	1.28452	−	1.28452i	0.938070	−	0.346447i	$-0.112612\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.512711	+	0.512711i	0.0549684	+	0.0549684i
$88$		0			0
$89$	18.2728			1.93692			0.968459	−	0.249173i	$-0.0801587\pi$
$89$	18.2728			1.93692			0.968459	+	0.249173i	$0.0801587\pi$
$90$		0			0
$91$	−4.86254	+	10.2118i	−0.509733	+	1.07048i
$92$		0			0
$93$	0.928731	+	0.928731i	0.0963049	+	0.0963049i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.26546	−	7.26546i	−0.737696	−	0.737696i	0.234436	−	0.972132i	$-0.424676\pi$
$97$	−7.26546	−	7.26546i	−0.737696	−	0.737696i	−0.972132	+	0.234436i	$0.924676\pi$
$98$		0			0
$99$		−	3.27492i		−	0.329142i
$100$		0			0
$101$		−	7.76546i		−	0.772692i	−0.922354	−	0.386346i	$-0.873737\pi$
$101$		−	7.76546i		−	0.772692i	0.922354	−	0.386346i	$-0.126263\pi$
$102$		0			0
$103$	4.63143	−	4.63143i	0.456349	−	0.456349i	−0.441106	−	0.897455i	$-0.645414\pi$
$103$	4.63143	−	4.63143i	0.456349	−	0.456349i	0.897455	+	0.441106i	$0.145414\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.30695	+	4.30695i	−0.416369	+	0.416369i	−0.883950	−	0.467581i	$-0.845126\pi$
$107$	−4.30695	+	4.30695i	−0.416369	+	0.416369i	0.467581	+	0.883950i	$0.345126\pi$
$108$		0			0
$109$		−	1.00000i		−	0.0957826i	−0.998853	−	0.0478913i	$-0.984750\pi$
$109$		−	1.00000i		−	0.0957826i	0.998853	−	0.0478913i	$-0.0152501\pi$
$110$		0			0
$111$			2.20822i			0.209595i
$112$		0			0
$113$	−11.3594	−	11.3594i	−1.06860	−	1.06860i	−0.997467	−	0.0711366i	$-0.977337\pi$
$113$	−11.3594	−	11.3594i	−1.06860	−	1.06860i	−0.0711366	−	0.997467i	$-0.522663\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.02282	−	3.02282i	−0.279460	−	0.279460i
$118$		0			0
$119$	4.77753	+	2.27492i	0.437955	+	0.208541i
$120$		0			0
$121$	−0.274917			−0.0249925
$122$		0			0
$123$	−3.71492	−	3.71492i	−0.334963	−	0.334963i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.50195	−	9.50195i	0.843161	−	0.843161i	−0.146107	−	0.989269i	$-0.546675\pi$
$127$	9.50195	−	9.50195i	0.843161	−	0.843161i	0.989269	+	0.146107i	$0.0466745\pi$
$128$		0			0
$129$	−0.894797			−0.0787825
$130$		0			0
$131$			19.9474i			1.74281i	0.490566	+	0.871404i	$0.336790\pi$
$131$			19.9474i			1.74281i	−0.490566	+	0.871404i	$0.663210\pi$
$132$		0			0
$133$	−5.36253	+	1.90293i	−0.464990	+	0.165005i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15.3703	+	15.3703i	−1.31318	+	1.31318i	−0.394117	+	0.919060i	$0.628949\pi$
$137$	−15.3703	+	15.3703i	−1.31318	+	1.31318i	−0.919060	+	0.394117i	$0.871051\pi$
$138$		0			0
$139$	3.46410			0.293821			0.146911	−	0.989150i	$-0.453067\pi$
$139$	3.46410			0.293821			0.146911	+	0.989150i	$0.453067\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$		0			0
$143$	9.89949	−	9.89949i	0.827837	−	0.827837i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.722565	−	6.96261i	0.0595962	−	0.574266i
$148$		0			0
$149$			23.2749i			1.90676i	0.301779	+	0.953378i	$0.402419\pi$
$149$			23.2749i			1.90676i	−0.301779	+	0.953378i	$0.597581\pi$
$150$		0			0
$151$	−11.0000			−0.895167			−0.447584	−	0.894242i	$-0.647715\pi$
$151$	−11.0000			−0.895167			−0.447584	+	0.894242i	$0.647715\pi$
$152$		0			0
$153$	−1.41421	+	1.41421i	−0.114332	+	0.114332i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.65426	−	7.65426i	−0.610876	−	0.610876i	0.332298	−	0.943174i	$-0.392176\pi$
$157$	−7.65426	−	7.65426i	−0.610876	−	0.610876i	−0.943174	+	0.332298i	$0.892176\pi$
$158$		0			0
$159$	−5.25370			−0.416645
$160$		0			0
$161$	−1.00000	−	0.476171i	−0.0788110	−	0.0375275i
$162$		0			0
$163$	−15.7070	−	15.7070i	−1.23027	−	1.23027i	−0.963859	−	0.266412i	$-0.914162\pi$
$163$	−15.7070	−	15.7070i	−1.23027	−	1.23027i	−0.266412	−	0.963859i	$-0.585838\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.45986	+	7.45986i	0.577261	+	0.577261i	0.934148	−	0.356886i	$-0.116162\pi$
$167$	7.45986	+	7.45986i	0.577261	+	0.577261i	−0.356886	+	0.934148i	$0.616162\pi$
$168$		0			0
$169$		−	5.27492i		−	0.405763i
$170$		0			0
$171$		−	2.15068i		−	0.164466i
$172$		0			0
$173$	−13.5055	+	13.5055i	−1.02680	+	1.02680i	−0.0271738	+	0.999631i	$0.508651\pi$
$173$	−13.5055	+	13.5055i	−1.02680	+	1.02680i	−0.999631	+	0.0271738i	$0.991349\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.16441	−	6.16441i	0.463346	−	0.463346i
$178$		0			0
$179$			7.45017i			0.556852i	0.960458	+	0.278426i	$0.0898126\pi$
$179$			7.45017i			0.556852i	−0.960458	+	0.278426i	$0.910187\pi$
$180$		0			0
$181$			3.10302i			0.230646i	0.993328	+	0.115323i	$0.0367902\pi$
$181$			3.10302i			0.230646i	−0.993328	+	0.115323i	$0.963210\pi$
$182$		0			0
$183$	−0.928731	−	0.928731i	−0.0686538	−	0.0686538i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−4.63143	−	4.63143i	−0.338684	−	0.338684i
$188$		0			0
$189$	2.38876	+	1.13746i	0.173757	+	0.0827379i
$190$		0			0
$191$	12.5498			0.908074			0.454037	−	0.890983i	$-0.349983\pi$
$191$	12.5498			0.908074			0.454037	+	0.890983i	$0.349983\pi$
$192$		0			0
$193$	13.5536	+	13.5536i	0.975608	+	0.975608i	0.999710	−	0.0241020i	$-0.00767264\pi$
$193$	13.5536	+	13.5536i	0.975608	+	0.975608i	−0.0241020	+	0.999710i	$0.507673\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.0328	+	12.0328i	−0.857303	+	0.857303i	−0.991020	−	0.133717i	$-0.957309\pi$
$197$	−12.0328	+	12.0328i	−0.857303	+	0.857303i	0.133717	+	0.991020i	$0.457309\pi$
$198$		0			0
$199$	−15.1698			−1.07536			−0.537680	−	0.843149i	$-0.680699\pi$
$199$	−15.1698			−1.07536			−0.537680	+	0.843149i	$0.680699\pi$
$200$		0			0
$201$		−	4.35890i		−	0.307453i
$202$		0			0
$203$	−0.641557	−	1.80793i	−0.0450285	−	0.126892i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.296014	−	0.296014i	0.0205744	−	0.0205744i
$208$		0			0
$209$	7.04329			0.487195
$210$		0			0
$211$	1.72508			0.118760			0.0593798	−	0.998235i	$-0.481088\pi$
$211$	1.72508			0.118760			0.0593798	+	0.998235i	$0.481088\pi$
$212$		0			0
$213$	6.55836	−	6.55836i	0.449371	−	0.449371i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−1.16213	−	3.27491i	−0.0788902	−	0.222315i
$218$		0			0
$219$		−	10.0000i		−	0.675737i
$220$		0			0
$221$	−8.54983			−0.575124
$222$		0			0
$223$	−3.41161	+	3.41161i	−0.228459	+	0.228459i	−0.812049	−	0.583590i	$-0.801648\pi$
$223$	−3.41161	+	3.41161i	−0.228459	+	0.228459i	0.583590	+	0.812049i	$0.301648\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.8943	+	13.8943i	0.922197	+	0.922197i	0.997184	−	0.0749876i	$-0.0238917\pi$
$227$	13.8943	+	13.8943i	0.922197	+	0.922197i	−0.0749876	+	0.997184i	$0.523892\pi$
$228$		0			0
$229$	12.5430			0.828864			0.414432	−	0.910080i	$-0.363980\pi$
$229$	12.5430			0.828864			0.414432	+	0.910080i	$0.363980\pi$
$230$		0			0
$231$	−3.72508	+	7.82300i	−0.245092	+	0.514716i
$232$		0			0
$233$	6.46043	+	6.46043i	0.423237	+	0.423237i	0.886317	−	0.463080i	$-0.153256\pi$
$233$	6.46043	+	6.46043i	0.423237	+	0.423237i	−0.463080	+	0.886317i	$0.653256\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−8.36136	−	8.36136i	−0.543129	−	0.543129i
$238$		0			0
$239$			9.09967i			0.588609i	0.955712	+	0.294304i	$0.0950879\pi$
$239$			9.09967i			0.588609i	−0.955712	+	0.294304i	$0.904912\pi$
$240$		0			0
$241$		−	28.1890i		−	1.81581i	−0.419174	−	0.907906i	$-0.637680\pi$
$241$		−	28.1890i		−	1.81581i	0.419174	−	0.907906i	$-0.362320\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.50112	−	6.50112i	0.413656	−	0.413656i
$248$		0			0
$249$		−	16.5498i		−	1.04880i
$250$		0			0
$251$		−	6.09095i		−	0.384457i	−0.981350	−	0.192229i	$-0.938428\pi$
$251$		−	6.09095i		−	0.384457i	0.981350	−	0.192229i	$-0.0615715\pi$
$252$		0			0
$253$	0.969421	+	0.969421i	0.0609470	+	0.0609470i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.60601	+	3.60601i	0.224937	+	0.224937i	0.810574	−	0.585637i	$-0.199156\pi$
$257$	3.60601	+	3.60601i	0.224937	+	0.224937i	−0.585637	+	0.810574i	$0.699156\pi$
$258$		0			0
$259$	2.51176	−	5.27492i	0.156073	−	0.327767i
$260$		0			0
$261$	0.725083			0.0448815
$262$		0			0
$263$	7.05246	+	7.05246i	0.434873	+	0.434873i	0.890282	−	0.455409i	$-0.150507\pi$
$263$	7.05246	+	7.05246i	0.434873	+	0.434873i	−0.455409	+	0.890282i	$0.650507\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	12.9209	−	12.9209i	0.790744	−	0.790744i
$268$		0			0
$269$	−18.1578			−1.10710			−0.553549	−	0.832817i	$-0.686727\pi$
$269$	−18.1578			−1.10710			−0.553549	+	0.832817i	$0.686727\pi$
$270$		0			0
$271$			22.5742i			1.37129i	0.727938	+	0.685643i	$0.240479\pi$
$271$			22.5742i			1.37129i	−0.727938	+	0.685643i	$0.759521\pi$
$272$		0			0
$273$	3.78247	+	10.6591i	0.228926	+	0.645121i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.97025	+	3.97025i	−0.238549	+	0.238549i	−0.816249	−	0.577700i	$-0.803950\pi$
$277$	−3.97025	+	3.97025i	−0.238549	+	0.238549i	0.577700	+	0.816249i	$0.303950\pi$
$278$		0			0
$279$	1.31342			0.0786326
$280$		0			0
$281$	12.7251			0.759115			0.379557	−	0.925168i	$-0.376076\pi$
$281$	12.7251			0.759115			0.379557	+	0.925168i	$0.376076\pi$
$282$		0			0
$283$	18.9680	−	18.9680i	1.12753	−	1.12753i	0.136951	−	0.990578i	$-0.456270\pi$
$283$	18.9680	−	18.9680i	1.12753	−	1.12753i	0.990578	−	0.136951i	$-0.0437301\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.64850	+	13.0996i	0.274392	+	0.773248i
$288$		0			0
$289$		−	13.0000i		−	0.764706i
$290$		0			0
$291$	−10.2749			−0.602326
$292$		0			0
$293$	−10.6771	+	10.6771i	−0.623762	+	0.623762i	−0.946491	−	0.322730i	$-0.895400\pi$
$293$	−10.6771	+	10.6771i	−0.623762	+	0.623762i	0.322730	+	0.946491i	$0.395400\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.31572	−	2.31572i	−0.134371	−	0.134371i
$298$		0			0
$299$	1.78959			0.103495
$300$		0			0
$301$	2.13746	+	1.01779i	0.123201	+	0.0586647i
$302$		0			0
$303$	−5.49101	−	5.49101i	−0.315450	−	0.315450i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	11.1193	+	11.1193i	0.634613	+	0.634613i	0.949221	−	0.314609i	$-0.101873\pi$
$307$	11.1193	+	11.1193i	0.634613	+	0.634613i	−0.314609	+	0.949221i	$0.601873\pi$
$308$		0			0
$309$		−	6.54983i		−	0.372607i
$310$		0			0
$311$		−	33.0816i		−	1.87589i	−0.346790	−	0.937943i	$-0.612729\pi$
$311$		−	33.0816i		−	1.87589i	0.346790	−	0.937943i	$-0.387271\pi$
$312$		0			0
$313$	−19.6046	+	19.6046i	−1.10812	+	1.10812i	−0.114719	+	0.993398i	$0.536597\pi$
$313$	−19.6046	+	19.6046i	−1.10812	+	1.10812i	−0.993398	+	0.114719i	$0.963403\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.64448	−	7.64448i	0.429357	−	0.429357i	−0.459052	−	0.888409i	$-0.651811\pi$
$317$	7.64448	−	7.64448i	0.429357	−	0.429357i	0.888409	+	0.459052i	$0.151811\pi$
$318$		0			0
$319$			2.37459i			0.132951i
$320$		0			0
$321$			6.09095i			0.339964i
$322$		0			0
$323$	−3.04152	−	3.04152i	−0.169235	−	0.169235i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.707107	−	0.707107i	−0.0391031	−	0.0391031i
$328$		0			0
$329$	4.77753	+	2.27492i	0.263394	+	0.125420i
$330$		0			0
$331$	10.3746			0.570239			0.285119	−	0.958492i	$-0.407967\pi$
$331$	10.3746			0.570239			0.285119	+	0.958492i	$0.407967\pi$
$332$		0			0
$333$	1.56145	+	1.56145i	0.0855668	+	0.0855668i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	12.5842	−	12.5842i	0.685502	−	0.685502i	−0.275732	−	0.961235i	$-0.588920\pi$
$337$	12.5842	−	12.5842i	0.685502	−	0.685502i	0.961235	+	0.275732i	$0.0889203\pi$
$338$		0			0
$339$	−16.0646			−0.872511
$340$		0			0
$341$			4.30136i			0.232931i
$342$		0			0
$343$	−9.64572	+	15.8101i	−0.520820	+	0.853667i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.50195	+	9.50195i	−0.510091	+	0.510091i	−0.914554	−	0.404463i	$-0.867458\pi$
$347$	−9.50195	+	9.50195i	−0.510091	+	0.510091i	0.404463	+	0.914554i	$0.367458\pi$
$348$		0			0
$349$	−18.2728			−0.978123			−0.489062	−	0.872249i	$-0.662661\pi$
$349$	−18.2728			−0.978123			−0.489062	+	0.872249i	$0.662661\pi$
$350$		0			0
$351$	−4.27492			−0.228178
$352$		0			0
$353$	5.26806	−	5.26806i	0.280391	−	0.280391i	−0.552874	−	0.833265i	$-0.686469\pi$
$353$	5.26806	−	5.26806i	0.280391	−	0.280391i	0.833265	+	0.552874i	$0.186469\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	4.98683	−	1.76961i	0.263931	−	0.0936578i
$358$		0			0
$359$			26.3746i			1.39200i	0.718043	+	0.695999i	$0.245038\pi$
$359$			26.3746i			1.39200i	−0.718043	+	0.695999i	$0.754962\pi$
$360$		0			0
$361$	−14.3746			−0.756557
$362$		0			0
$363$	−0.194396	+	0.194396i	−0.0102031	+	0.0102031i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	18.9680	+	18.9680i	0.990120	+	0.990120i	0.999952	−	0.00983201i	$-0.00312968\pi$
$367$	18.9680	+	18.9680i	0.990120	+	0.990120i	−0.00983201	+	0.999952i	$0.503130\pi$
$368$		0			0
$369$	−5.25370			−0.273497
$370$		0			0
$371$	12.5498	+	5.97586i	0.651555	+	0.310251i
$372$		0			0
$373$	12.9615	+	12.9615i	0.671123	+	0.671123i	0.957975	−	0.286852i	$-0.0926087\pi$
$373$	12.9615	+	12.9615i	0.671123	+	0.671123i	−0.286852	+	0.957975i	$0.592609\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.19180	+	2.19180i	0.112883	+	0.112883i
$378$		0			0
$379$			15.0000i			0.770498i	0.922813	+	0.385249i	$0.125884\pi$
$379$			15.0000i			0.770498i	−0.922813	+	0.385249i	$0.874116\pi$
$380$		0			0
$381$		−	13.4378i		−	0.688438i
$382$		0			0
$383$	−15.1676	+	15.1676i	−0.775026	+	0.775026i	−0.978980	−	0.203954i	$-0.934621\pi$
$383$	−15.1676	+	15.1676i	−0.775026	+	0.775026i	0.203954	+	0.978980i	$0.434621\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.632717	+	0.632717i	−0.0321628	+	0.0321628i
$388$		0			0
$389$			18.3746i			0.931628i	0.884883	+	0.465814i	$0.154239\pi$
$389$			18.3746i			0.931628i	−0.884883	+	0.465814i	$0.845761\pi$
$390$		0			0
$391$		−	0.837253i		−	0.0423417i
$392$		0			0
$393$	14.1049	+	14.1049i	0.711499	+	0.711499i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−4.43704	−	4.43704i	−0.222688	−	0.222688i	0.586941	−	0.809630i	$-0.300332\pi$
$397$	−4.43704	−	4.43704i	−0.222688	−	0.222688i	−0.809630	+	0.586941i	$0.800332\pi$
$398$		0			0
$399$	−2.44631	+	5.13746i	−0.122469	+	0.257195i
$400$		0			0
$401$	−1.27492			−0.0636663			−0.0318332	−	0.999493i	$-0.510135\pi$
$401$	−1.27492			−0.0636663			−0.0318332	+	0.999493i	$0.510135\pi$
$402$		0			0
$403$	3.97025	+	3.97025i	0.197772	+	0.197772i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.11361	+	5.11361i	−0.253472	+	0.253472i
$408$		0			0
$409$	−31.7682			−1.57084			−0.785418	−	0.618966i	$-0.787552\pi$
$409$	−31.7682			−1.57084			−0.785418	+	0.618966i	$0.787552\pi$
$410$		0			0
$411$			21.7370i			1.07220i
$412$		0			0
$413$	−21.7371	+	7.71356i	−1.06961	+	0.379559i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.44949	−	2.44949i	0.119952	−	0.119952i
$418$		0			0
$419$	−12.1819			−0.595125			−0.297562	−	0.954702i	$-0.596174\pi$
$419$	−12.1819			−0.595125			−0.297562	+	0.954702i	$0.596174\pi$
$420$		0			0
$421$	0.725083			0.0353384			0.0176692	−	0.999844i	$-0.494375\pi$
$421$	0.725083			0.0353384			0.0176692	+	0.999844i	$0.494375\pi$
$422$		0			0
$423$	−1.41421	+	1.41421i	−0.0687614	+	0.0687614i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.16213	+	3.27491i	0.0562392	+	0.158484i
$428$		0			0
$429$		−	14.0000i		−	0.675926i
$430$		0			0
$431$	25.6495			1.23549			0.617747	−	0.786377i	$-0.288046\pi$
$431$	25.6495			1.23549			0.617747	+	0.786377i	$0.288046\pi$
$432$		0			0
$433$	−4.43704	+	4.43704i	−0.213230	+	0.213230i	−0.805638	−	0.592408i	$-0.798177\pi$
$433$	−4.43704	+	4.43704i	−0.213230	+	0.213230i	0.592408	+	0.805638i	$0.298177\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.636630	+	0.636630i	0.0304542	+	0.0304542i
$438$		0			0
$439$	−33.4427			−1.59613			−0.798066	−	0.602570i	$-0.794143\pi$
$439$	−33.4427			−1.59613			−0.798066	+	0.602570i	$0.794143\pi$
$440$		0			0
$441$	−4.41238	−	5.43424i	−0.210113	−	0.258773i
$442$		0			0
$443$	19.0039	+	19.0039i	0.902902	+	0.902902i	0.995686	−	0.0927842i	$-0.0295767\pi$
$443$	19.0039	+	19.0039i	0.902902	+	0.902902i	−0.0927842	+	0.995686i	$0.529577\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	16.4579	+	16.4579i	0.778430	+	0.778430i
$448$		0			0
$449$			7.82475i			0.369273i	0.982807	+	0.184636i	$0.0591108\pi$
$449$			7.82475i			0.369273i	−0.982807	+	0.184636i	$0.940889\pi$
$450$		0			0
$451$		−	17.2054i		−	0.810172i
$452$		0			0
$453$	−7.77817	+	7.77817i	−0.365451	+	0.365451i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.86840	+	5.86840i	−0.274512	+	0.274512i	−0.830914	−	0.556401i	$-0.812182\pi$
$457$	−5.86840	+	5.86840i	−0.274512	+	0.274512i	0.556401	+	0.830914i	$0.312182\pi$
$458$		0			0
$459$			2.00000i			0.0933520i
$460$		0			0
$461$		−	21.6219i		−	1.00703i	−0.863986	−	0.503515i	$-0.832040\pi$
$461$		−	21.6219i		−	1.00703i	0.863986	−	0.503515i	$-0.167960\pi$
$462$		0			0
$463$	14.7783	+	14.7783i	0.686807	+	0.686807i	0.961525	−	0.274718i	$-0.0885845\pi$
$463$	14.7783	+	14.7783i	0.686807	+	0.686807i	−0.274718	+	0.961525i	$0.588585\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.388792	+	0.388792i	0.0179911	+	0.0179911i	0.716045	−	0.698054i	$-0.245950\pi$
$467$	0.388792	+	0.388792i	0.0179911	+	0.0179911i	−0.698054	+	0.716045i	$0.745950\pi$
$468$		0			0
$469$	−4.95807	+	10.4124i	−0.228942	+	0.480799i
$470$		0			0
$471$	−10.8248			−0.498778
$472$		0			0
$473$	−2.07210	−	2.07210i	−0.0952751	−	0.0952751i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.71492	+	3.71492i	−0.170095	+	0.170095i
$478$		0			0
$479$	−24.2487			−1.10795			−0.553976	−	0.832533i	$-0.686890\pi$
$479$	−24.2487			−1.10795			−0.553976	+	0.832533i	$0.686890\pi$
$480$		0			0
$481$			9.43996i			0.430425i
$482$		0			0
$483$	−1.04381	+	0.370403i	−0.0474950	+	0.0168539i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	15.4110	−	15.4110i	0.698341	−	0.698341i	−0.265712	−	0.964052i	$-0.585607\pi$
$487$	15.4110	−	15.4110i	0.698341	−	0.698341i	0.964052	+	0.265712i	$0.0856070\pi$
$488$		0			0
$489$	−22.2131			−1.00451
$490$		0			0
$491$	28.9244			1.30534			0.652670	−	0.757642i	$-0.273649\pi$
$491$	28.9244			1.30534			0.652670	+	0.757642i	$0.273649\pi$
$492$		0			0
$493$	1.02542	−	1.02542i	0.0461827	−	0.0461827i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−23.1262	+	8.20650i	−1.03735	+	0.368112i
$498$		0			0
$499$		−	9.17525i		−	0.410741i	−0.978684	−	0.205370i	$-0.934160\pi$
$499$		−	9.17525i		−	0.410741i	0.978684	−	0.205370i	$-0.0658399\pi$
$500$		0			0
$501$	10.5498			0.471332
$502$		0			0
$503$	−8.48528	+	8.48528i	−0.378340	+	0.378340i	−0.870503	−	0.492163i	$-0.836206\pi$
$503$	−8.48528	+	8.48528i	−0.378340	+	0.378340i	0.492163	+	0.870503i	$0.336206\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−3.72993	−	3.72993i	−0.165652	−	0.165652i
$508$		0			0
$509$	17.3205			0.767718			0.383859	−	0.923392i	$-0.374595\pi$
$509$	17.3205			0.767718			0.383859	+	0.923392i	$0.374595\pi$
$510$		0			0
$511$	−11.3746	+	23.8876i	−0.503182	+	1.05673i
$512$		0			0
$513$	−1.52076	−	1.52076i	−0.0671431	−	0.0671431i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−4.63143	−	4.63143i	−0.203690	−	0.203690i
$518$		0			0
$519$			19.0997i			0.838382i
$520$		0			0
$521$		−	32.0142i		−	1.40257i	−0.712883	−	0.701283i	$-0.752611\pi$
$521$		−	32.0142i		−	1.40257i	0.712883	−	0.701283i	$-0.247389\pi$
$522$		0			0
$523$	−20.1343	+	20.1343i	−0.880413	+	0.880413i	−0.993576	−	0.113163i	$-0.963902\pi$
$523$	−20.1343	+	20.1343i	−0.880413	+	0.880413i	0.113163	+	0.993576i	$0.463902\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.85746	−	1.85746i	0.0809123	−	0.0809123i
$528$		0			0
$529$		−	22.8248i		−	0.992381i
$530$		0			0
$531$		−	8.71780i		−	0.378320i
$532$		0			0
$533$	−15.8810	−	15.8810i	−0.687882	−	0.687882i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	5.26806	+	5.26806i	0.227334	+	0.227334i
$538$		0			0
$539$	17.7967	−	14.4502i	0.766557	−	0.622413i
$540$		0			0
$541$	−33.1993			−1.42735			−0.713676	−	0.700476i	$-0.752971\pi$
$541$	−33.1993			−1.42735			−0.713676	+	0.700476i	$0.752971\pi$
$542$		0			0
$543$	2.19417	+	2.19417i	0.0941607	+	0.0941607i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	5.19499	−	5.19499i	0.222122	−	0.222122i	−0.587270	−	0.809391i	$-0.699797\pi$
$547$	5.19499	−	5.19499i	0.222122	−	0.222122i	0.809391	+	0.587270i	$0.199797\pi$
$548$		0			0
$549$	−1.31342			−0.0560556
$550$		0			0
$551$			1.55942i			0.0664335i
$552$		0			0
$553$	10.4626	+	29.4840i	0.444915	+	1.25379i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	16.9318	−	16.9318i	0.717423	−	0.717423i	−0.250654	−	0.968077i	$-0.580646\pi$
$557$	16.9318	−	16.9318i	0.717423	−	0.717423i	0.968077	+	0.250654i	$0.0806455\pi$
$558$		0			0
$559$	−3.82518			−0.161788
$560$		0			0
$561$	−6.54983			−0.276534
$562$		0			0
$563$	19.4102	−	19.4102i	0.818042	−	0.818042i	−0.167782	−	0.985824i	$-0.553660\pi$
$563$	19.4102	−	19.4102i	0.818042	−	0.818042i	0.985824	+	0.167782i	$0.0536604\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.49342	−	0.884806i	0.104714	−	0.0371583i
$568$		0			0
$569$			41.8248i			1.75338i	0.481051	+	0.876692i	$0.340255\pi$
$569$			41.8248i			1.75338i	−0.481051	+	0.876692i	$0.659745\pi$
$570$		0			0
$571$	18.0997			0.757448			0.378724	−	0.925510i	$-0.376363\pi$
$571$	18.0997			0.757448			0.378724	+	0.925510i	$0.376363\pi$
$572$		0			0
$573$	8.87407	−	8.87407i	0.370720	−	0.370720i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	8.67968	+	8.67968i	0.361340	+	0.361340i	0.864306	−	0.502966i	$-0.167758\pi$
$577$	8.67968	+	8.67968i	0.361340	+	0.361340i	−0.502966	+	0.864306i	$0.667758\pi$
$578$		0			0
$579$	19.1676			0.796580
$580$		0			0
$581$	−18.8248	+	39.5336i	−0.780982	+	1.64013i
$582$		0			0
$583$	−12.1661	−	12.1661i	−0.503867	−	0.503867i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.63143	+	4.63143i	0.191160	+	0.191160i	0.796197	−	0.605037i	$-0.206842\pi$
$587$	4.63143	+	4.63143i	0.191160	+	0.191160i	−0.605037	+	0.796197i	$0.706842\pi$
$588$		0			0
$589$			2.82475i			0.116392i
$590$		0			0
$591$			17.0170i			0.699985i
$592$		0			0
$593$	−14.1421	+	14.1421i	−0.580748	+	0.580748i	−0.935109	−	0.354361i	$-0.884698\pi$
$593$	−14.1421	+	14.1421i	−0.580748	+	0.580748i	0.354361	+	0.935109i	$0.384698\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.7267	+	10.7267i	−0.439014	+	0.439014i
$598$		0			0
$599$			22.3746i			0.914201i	0.889415	+	0.457100i	$0.151112\pi$
$599$			22.3746i			0.914201i	−0.889415	+	0.457100i	$0.848888\pi$
$600$		0			0
$601$		−	24.0027i		−	0.979091i	−0.871978	−	0.489546i	$-0.837163\pi$
$601$		−	24.0027i		−	0.979091i	0.871978	−	0.489546i	$-0.162837\pi$
$602$		0			0
$603$	−3.08221	−	3.08221i	−0.125517	−	0.125517i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	5.40902	+	5.40902i	0.219545	+	0.219545i	0.808307	−	0.588762i	$-0.200384\pi$
$607$	5.40902	+	5.40902i	0.219545	+	0.219545i	−0.588762	+	0.808307i	$0.700384\pi$
$608$		0			0
$609$	−1.73205	−	0.824752i	−0.0701862	−	0.0334206i
$610$		0			0
$611$	−8.54983			−0.345889
$612$		0			0
$613$	−29.7713	−	29.7713i	−1.20245	−	1.20245i	−0.973419	−	0.229031i	$-0.926444\pi$
$613$	−29.7713	−	29.7713i	−1.20245	−	1.20245i	−0.229031	−	0.973419i	$-0.573556\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.27637	−	5.27637i	0.212419	−	0.212419i	−0.592875	−	0.805294i	$-0.702007\pi$
$617$	5.27637	−	5.27637i	0.212419	−	0.212419i	0.805294	+	0.592875i	$0.202007\pi$
$618$		0			0
$619$	−8.12654			−0.326633			−0.163317	−	0.986574i	$-0.552219\pi$
$619$	−8.12654			−0.326633			−0.163317	+	0.986574i	$0.552219\pi$
$620$		0			0
$621$		−	0.418627i		−	0.0167989i
$622$		0			0
$623$	−45.5618	+	16.1679i	−1.82539	+	0.647754i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	4.98036	−	4.98036i	0.198896	−	0.198896i
$628$		0			0
$629$	4.41644			0.176095
$630$		0			0
$631$	−29.0000			−1.15447			−0.577236	−	0.816577i	$-0.695869\pi$
$631$	−29.0000			−1.15447			−0.577236	+	0.816577i	$0.695869\pi$
$632$		0			0
$633$	1.21982	−	1.21982i	0.0484834	−	0.0484834i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	3.08891	−	29.7646i	0.122387	−	1.17932i
$638$		0			0
$639$		−	9.27492i		−	0.366910i
$640$		0			0
$641$	−13.2749			−0.524328			−0.262164	−	0.965023i	$-0.584436\pi$
$641$	−13.2749			−0.524328			−0.262164	+	0.965023i	$0.584436\pi$
$642$		0			0
$643$	21.3542	−	21.3542i	0.842126	−	0.842126i	−0.147009	−	0.989135i	$-0.546965\pi$
$643$	21.3542	−	21.3542i	0.842126	−	0.842126i	0.989135	+	0.147009i	$0.0469647\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17.7481	+	17.7481i	0.697752	+	0.697752i	0.963925	−	0.266174i	$-0.0857594\pi$
$647$	17.7481	+	17.7481i	0.697752	+	0.697752i	−0.266174	+	0.963925i	$0.585759\pi$
$648$		0			0
$649$	28.5501			1.12069
$650$		0			0
$651$	−3.13746	−	1.49397i	−0.122967	−	0.0585531i
$652$		0			0
$653$	14.0235	+	14.0235i	0.548783	+	0.548783i	0.926089	−	0.377306i	$-0.123149\pi$
$653$	14.0235	+	14.0235i	0.548783	+	0.548783i	−0.377306	+	0.926089i	$0.623149\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−7.07107	−	7.07107i	−0.275869	−	0.275869i
$658$		0			0
$659$		−	33.0997i		−	1.28938i	−0.764444	−	0.644690i	$-0.776986\pi$
$659$		−	33.0997i		−	1.28938i	0.764444	−	0.644690i	$-0.223014\pi$
$660$		0			0
$661$		−	33.8038i		−	1.31481i	−0.753536	−	0.657407i	$-0.771653\pi$
$661$		−	33.8038i		−	1.31481i	0.753536	−	0.657407i	$-0.228347\pi$
$662$		0			0
$663$	−6.04565	+	6.04565i	−0.234793	+	0.234793i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.214635	+	0.214635i	−0.00831068	+	0.00831068i
$668$		0			0
$669$			4.82475i			0.186536i
$670$		0			0
$671$		−	4.30136i		−	0.166052i
$672$		0			0
$673$	7.26709	+	7.26709i	0.280126	+	0.280126i	0.833159	−	0.553033i	$-0.186530\pi$
$673$	7.26709	+	7.26709i	0.280126	+	0.280126i	−0.553033	+	0.833159i	$0.686530\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.26806	+	5.26806i	0.202468	+	0.202468i	0.801057	−	0.598589i	$-0.204272\pi$
$677$	5.26806	+	5.26806i	0.202468	+	0.202468i	−0.598589	+	0.801057i	$0.704272\pi$
$678$		0			0
$679$	24.5443	+	11.6873i	0.941925	+	0.448517i
$680$		0			0
$681$	19.6495			0.752971
$682$		0			0
$683$	13.7275	+	13.7275i	0.525269	+	0.525269i	0.919158	−	0.393889i	$-0.128871\pi$
$683$	13.7275	+	13.7275i	0.525269	+	0.525269i	−0.393889	+	0.919158i	$0.628871\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	8.86923	−	8.86923i	0.338382	−	0.338382i
$688$		0			0
$689$	−22.4591			−0.855624
$690$		0			0
$691$			47.7753i			1.81746i	0.417388	+	0.908728i	$0.362945\pi$
$691$			47.7753i			1.81746i	−0.417388	+	0.908728i	$0.637055\pi$
$692$		0			0
$693$	2.89767	+	8.16573i	0.110073	+	0.310190i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−7.42985	+	7.42985i	−0.281426	+	0.281426i
$698$		0			0
$699$	9.13642			0.345571
$700$		0			0
$701$	−45.2990			−1.71092			−0.855460	−	0.517869i	$-0.826725\pi$
$701$	−45.2990			−1.71092			−0.855460	+	0.517869i	$0.826725\pi$
$702$		0			0
$703$	−3.35817	+	3.35817i	−0.126656	+	0.126656i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.87092	+	19.3625i	0.258408	+	0.728202i
$708$		0			0
$709$		−	4.27492i		−	0.160548i	−0.996773	−	0.0802739i	$-0.974420\pi$
$709$		−	4.27492i		−	0.160548i	0.996773	−	0.0802739i	$-0.0255795\pi$
$710$		0			0
$711$	−11.8248			−0.443463
$712$		0			0
$713$	−0.388792	+	0.388792i	−0.0145604	+	0.0145604i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	6.43444	+	6.43444i	0.240298	+	0.240298i
$718$		0			0
$719$	−32.2443			−1.20251			−0.601256	−	0.799057i	$-0.705333\pi$
$719$	−32.2443			−1.20251			−0.601256	+	0.799057i	$0.705333\pi$
$720$		0			0
$721$	−7.45017	+	15.6460i	−0.277459	+	0.582688i
$722$		0			0
$723$	−19.9326	−	19.9326i	−0.741302	−	0.741302i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	20.7710	+	20.7710i	0.770353	+	0.770353i	0.978168	−	0.207815i	$-0.0666353\pi$
$727$	20.7710	+	20.7710i	0.770353	+	0.770353i	−0.207815	+	0.978168i	$0.566635\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			1.78959i			0.0661905i
$732$		0			0
$733$	−16.5818	+	16.5818i	−0.612462	+	0.612462i	−0.943587	−	0.331125i	$-0.892572\pi$
$733$	−16.5818	+	16.5818i	−0.612462	+	0.612462i	0.331125	+	0.943587i	$0.392572\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.0940	−	10.0940i	0.371816	−	0.371816i
$738$		0			0
$739$			13.6254i			0.501219i	0.968088	+	0.250609i	$0.0806310\pi$
$739$			13.6254i			0.501219i	−0.968088	+	0.250609i	$0.919369\pi$
$740$		0			0
$741$		−	9.19397i		−	0.337749i
$742$		0			0
$743$	−4.30695	−	4.30695i	−0.158007	−	0.158007i	0.623676	−	0.781683i	$-0.285638\pi$
$743$	−4.30695	−	4.30695i	−0.158007	−	0.158007i	−0.781683	+	0.623676i	$0.785638\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−11.7025	−	11.7025i	−0.428172	−	0.428172i
$748$		0			0
$749$	6.92820	−	14.5498i	0.253151	−	0.531639i
$750$		0			0
$751$	24.0000			0.875772			0.437886	−	0.899030i	$-0.355727\pi$
$751$	24.0000			0.875772			0.437886	+	0.899030i	$0.355727\pi$
$752$		0			0
$753$	−4.30695	−	4.30695i	−0.156954	−	0.156954i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−9.16524	+	9.16524i	−0.333116	+	0.333116i	−0.853769	−	0.520652i	$-0.825689\pi$
$757$	−9.16524	+	9.16524i	−0.333116	+	0.333116i	0.520652	+	0.853769i	$0.325689\pi$
$758$		0			0
$759$	1.37097			0.0497630
$760$		0			0
$761$		−	13.8564i		−	0.502294i	−0.967949	−	0.251147i	$-0.919192\pi$
$761$		−	13.8564i		−	0.502294i	0.967949	−	0.251147i	$-0.0808078\pi$
$762$		0			0
$763$	0.884806	+	2.49342i	0.0320321	+	0.0902677i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	26.3524	−	26.3524i	0.951529	−	0.951529i
$768$		0			0
$769$	−37.8591			−1.36523			−0.682617	−	0.730776i	$-0.739158\pi$
$769$	−37.8591			−1.36523			−0.682617	+	0.730776i	$0.739158\pi$
$770$		0			0
$771$	5.09967			0.183660
$772$		0			0
$773$	16.9706	−	16.9706i	0.610389	−	0.610389i	−0.332659	−	0.943047i	$-0.607946\pi$
$773$	16.9706	−	16.9706i	0.610389	−	0.610389i	0.943047	+	0.332659i	$0.107946\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.95385	−	5.50601i	−0.0700939	−	0.197527i
$778$		0			0
$779$		−	11.2990i		−	0.404829i
$780$		0			0
$781$	30.3746			1.08689
$782$		0			0
$783$	0.512711	−	0.512711i	0.0183228	−	0.0183228i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−24.3770	−	24.3770i	−0.868945	−	0.868945i	0.123410	−	0.992356i	$-0.460617\pi$
$787$	−24.3770	−	24.3770i	−0.868945	−	0.868945i	−0.992356	+	0.123410i	$0.960617\pi$
$788$		0			0
$789$	9.97368			0.355072
$790$		0			0
$791$	38.3746	+	18.2728i	1.36444	+	0.649708i
$792$		0			0
$793$	−3.97025	−	3.97025i	−0.140988	−	0.140988i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.1167	−	13.1167i	−0.464618	−	0.464618i	0.435548	−	0.900166i	$-0.356555\pi$
$797$	−13.1167	−	13.1167i	−0.464618	−	0.464618i	−0.900166	+	0.435548i	$0.856555\pi$
$798$		0			0
$799$			4.00000i			0.141510i
$800$		0			0
$801$		−	18.2728i		−	0.645639i
$802$		0			0
$803$	23.1572	−	23.1572i	0.817198	−	0.817198i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−12.8395	+	12.8395i	−0.451971	+	0.451971i
$808$		0			0
$809$			6.72508i			0.236441i	0.992987	+	0.118221i	$0.0377190\pi$
$809$			6.72508i			0.236441i	−0.992987	+	0.118221i	$0.962281\pi$
$810$		0			0
$811$		−	19.4712i		−	0.683726i	−0.939750	−	0.341863i	$-0.888942\pi$
$811$		−	19.4712i		−	0.683726i	0.939750	−	0.341863i	$-0.111058\pi$
$812$		0			0
$813$	15.9624	+	15.9624i	0.559825	+	0.559825i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.36077	−	1.36077i	−0.0476073	−	0.0476073i
$818$		0			0
$819$	10.2118	+	4.86254i	0.356828	+	0.169911i
$820$		0			0
$821$	−34.0000			−1.18661			−0.593304	−	0.804978i	$-0.702177\pi$
$821$	−34.0000			−1.18661			−0.593304	+	0.804978i	$0.702177\pi$
$822$		0			0
$823$	−6.20510	−	6.20510i	−0.216296	−	0.216296i	0.590639	−	0.806936i	$-0.298876\pi$
$823$	−6.20510	−	6.20510i	−0.216296	−	0.216296i	−0.806936	+	0.590639i	$0.798876\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−37.2011	+	37.2011i	−1.29361	+	1.29361i	−0.361072	+	0.932538i	$0.617589\pi$
$827$	−37.2011	+	37.2011i	−1.29361	+	1.29361i	−0.932538	+	0.361072i	$0.882411\pi$
$828$		0			0
$829$	35.7084			1.24021			0.620103	−	0.784521i	$-0.287091\pi$
$829$	35.7084			1.24021			0.620103	+	0.784521i	$0.287091\pi$
$830$		0			0
$831$			5.61478i			0.194775i
$832$		0			0
$833$	−13.9252	−	1.44513i	−0.482480	−	0.0500708i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.928731	−	0.928731i	0.0321016	−	0.0321016i
$838$		0			0
$839$	−19.2252			−0.663727			−0.331864	−	0.943327i	$-0.607677\pi$
$839$	−19.2252			−0.663727			−0.331864	+	0.943327i	$0.607677\pi$
$840$		0			0
$841$	28.4743			0.981871
$842$		0			0
$843$	8.99799	−	8.99799i	0.309907	−	0.309907i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.685483	−	0.243248i	0.0235535	−	0.00835811i
$848$		0			0
$849$		−	26.8248i		−	0.920623i
$850$		0			0
$851$	−0.924421			−0.0316887
$852$		0			0
$853$	24.2360	−	24.2360i	0.829826	−	0.829826i	−0.157667	−	0.987492i	$-0.550397\pi$
$853$	24.2360	−	24.2360i	0.829826	−	0.829826i	0.987492	+	0.157667i	$0.0503971\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.26286	−	9.26286i	−0.316413	−	0.316413i	0.530974	−	0.847388i	$-0.321826\pi$
$857$	−9.26286	−	9.26286i	−0.316413	−	0.316413i	−0.847388	+	0.530974i	$0.821826\pi$
$858$		0			0
$859$	51.3544			1.75219			0.876096	−	0.482138i	$-0.160139\pi$
$859$	51.3544			1.75219			0.876096	+	0.482138i	$0.160139\pi$
$860$		0			0
$861$	12.5498	+	5.97586i	0.427697	+	0.203657i
$862$		0			0
$863$	29.7713	+	29.7713i	1.01343	+	1.01343i	0.999909	+	0.0135172i	$0.00430278\pi$
$863$	29.7713	+	29.7713i	1.01343	+	1.01343i	0.0135172	+	0.999909i	$0.495697\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−9.19239	−	9.19239i	−0.312190	−	0.312190i
$868$		0			0
$869$		−	38.7251i		−	1.31366i
$870$		0			0
$871$		−	18.6339i		−	0.631387i
$872$		0			0
$873$	−7.26546	+	7.26546i	−0.245899	+	0.245899i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−23.0555	+	23.0555i	−0.778530	+	0.778530i	−0.979581	−	0.201051i	$-0.935564\pi$
$877$	−23.0555	+	23.0555i	−0.778530	+	0.778530i	0.201051	+	0.979581i	$0.435564\pi$
$878$		0			0
$879$			15.0997i			0.509299i
$880$		0			0
$881$			45.1484i			1.52109i	0.649286	+	0.760544i	$0.275068\pi$
$881$			45.1484i			1.52109i	−0.649286	+	0.760544i	$0.724932\pi$
$882$		0			0
$883$	−20.9834	−	20.9834i	−0.706148	−	0.706148i	0.259575	−	0.965723i	$-0.416418\pi$
$883$	−20.9834	−	20.9834i	−0.706148	−	0.706148i	−0.965723	+	0.259575i	$0.916418\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.26806	−	5.26806i	−0.176884	−	0.176884i	0.613112	−	0.789996i	$-0.289917\pi$
$887$	−5.26806	−	5.26806i	−0.176884	−	0.176884i	−0.789996	+	0.613112i	$0.789917\pi$
$888$		0			0
$889$	−15.2849	+	32.0997i	−0.512640	+	1.07659i
$890$		0			0
$891$	−3.27492			−0.109714
$892$		0			0
$893$	−3.04152	−	3.04152i	−0.101780	−	0.101780i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.26543	−	1.26543i	0.0422516	−	0.0422516i
$898$		0			0
$899$	−0.952341			−0.0317624
$900$		0			0
$901$			10.5074i			0.350052i
$902$		0			0
$903$	2.23110	−	0.791722i	0.0742464	−	0.0263469i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−22.2082	+	22.2082i	−0.737410	+	0.737410i	−0.972076	−	0.234666i	$-0.924600\pi$
$907$	−22.2082	+	22.2082i	−0.737410	+	0.737410i	0.234666	+	0.972076i	$0.424600\pi$
$908$		0			0
$909$	−7.76546			−0.257564
$910$		0			0
$911$	−12.7251			−0.421601			−0.210800	−	0.977529i	$-0.567607\pi$
$911$	−12.7251			−0.421601			−0.210800	+	0.977529i	$0.567607\pi$
$912$		0			0
$913$	38.3247	−	38.3247i	1.26836	−	1.26836i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−17.6495	−	49.7370i	−0.582839	−	1.64246i
$918$		0			0
$919$			36.2990i			1.19739i	0.800976	+	0.598697i	$0.204315\pi$
$919$			36.2990i			1.19739i	−0.800976	+	0.598697i	$0.795685\pi$
$920$		0			0
$921$	15.7251			0.518159
$922$		0			0
$923$	28.0364	−	28.0364i	0.922830	−	0.922830i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−4.63143	−	4.63143i	−0.152116	−	0.152116i
$928$		0			0
$929$	39.7796			1.30513			0.652564	−	0.757734i	$-0.273694\pi$
$929$	39.7796			1.30513			0.652564	+	0.757734i	$0.273694\pi$
$930$		0			0
$931$	11.6873	−	9.48960i	0.383036	−	0.311009i
$932$		0			0
$933$	−23.3922	−	23.3922i	−0.765827	−	0.765827i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−24.6248	−	24.6248i	−0.804458	−	0.804458i	0.179331	−	0.983789i	$-0.442607\pi$
$937$	−24.6248	−	24.6248i	−0.804458	−	0.804458i	−0.983789	+	0.179331i	$0.942607\pi$
$938$		0			0
$939$			27.7251i			0.904774i
$940$		0			0
$941$		−	7.65037i		−	0.249395i	−0.992195	−	0.124697i	$-0.960204\pi$
$941$		−	7.65037i		−	0.249395i	0.992195	−	0.124697i	$-0.0397960\pi$
$942$		0			0
$943$	1.55517	−	1.55517i	0.0506432	−	0.0506432i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.71658	−	9.71658i	0.315746	−	0.315746i	−0.531384	−	0.847131i	$-0.678328\pi$
$947$	9.71658	−	9.71658i	0.315746	−	0.315746i	0.847131	+	0.531384i	$0.178328\pi$
$948$		0			0
$949$		−	42.7492i		−	1.38770i
$950$		0			0
$951$		−	10.8109i		−	0.350568i
$952$		0			0
$953$	−9.42057	−	9.42057i	−0.305162	−	0.305162i	0.537867	−	0.843029i	$-0.319230\pi$
$953$	−9.42057	−	9.42057i	−0.305162	−	0.305162i	−0.843029	+	0.537867i	$0.819230\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.67909	+	1.67909i	0.0542771	+	0.0542771i
$958$		0			0
$959$	24.7249	−	51.9244i	0.798408	−	1.67673i
$960$		0			0
$961$	29.2749			0.944352
$962$		0			0
$963$	4.30695	+	4.30695i	0.138790	+	0.138790i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−24.5763	+	24.5763i	−0.790320	+	0.790320i	−0.981546	−	0.191226i	$-0.938754\pi$
$967$	−24.5763	+	24.5763i	−0.790320	+	0.790320i	0.191226	+	0.981546i	$0.438754\pi$
$968$		0			0
$969$	−4.30136			−0.138179
$970$		0			0
$971$			25.9232i			0.831916i	0.909384	+	0.415958i	$0.136554\pi$
$971$			25.9232i			0.831916i	−0.909384	+	0.415958i	$0.863446\pi$
$972$		0			0
$973$	−8.63744	+	3.06506i	−0.276904	+	0.0982612i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.0328	+	12.0328i	−0.384964	+	0.384964i	−0.872887	−	0.487923i	$-0.837755\pi$
$977$	−12.0328	+	12.0328i	−0.384964	+	0.384964i	0.487923	+	0.872887i	$0.337755\pi$
$978$		0			0
$979$	59.8421			1.91256
$980$		0			0
$981$	−1.00000			−0.0319275
$982$		0			0
$983$	30.6170	−	30.6170i	0.976531	−	0.976531i	−0.0231995	−	0.999731i	$-0.507385\pi$
$983$	30.6170	−	30.6170i	0.976531	−	0.976531i	0.999731	+	0.0231995i	$0.00738530\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	4.98683	−	1.76961i	0.158733	−	0.0563274i
$988$		0			0
$989$		−	0.374586i		−	0.0119111i
$990$		0			0
$991$	−21.5498			−0.684553			−0.342277	−	0.939599i	$-0.611198\pi$
$991$	−21.5498			−0.684553			−0.342277	+	0.939599i	$0.611198\pi$
$992$		0			0
$993$	7.33594	−	7.33594i	0.232799	−	0.232799i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	32.0312	+	32.0312i	1.01444	+	1.01444i	0.999894	+	0.0145452i	$0.00463003\pi$
$997$	32.0312	+	32.0312i	1.01444	+	1.01444i	0.0145452	+	0.999894i	$0.495370\pi$
$998$		0			0
$999$	2.20822			0.0698650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.x.c.1693.5	yes	16
5.2	odd	4	inner	2100.2.x.c.1357.3	✓	16
5.3	odd	4	inner	2100.2.x.c.1357.6	yes	16
5.4	even	2	inner	2100.2.x.c.1693.4	yes	16
7.6	odd	2	inner	2100.2.x.c.1693.3	yes	16
35.13	even	4	inner	2100.2.x.c.1357.4	yes	16
35.27	even	4	inner	2100.2.x.c.1357.5	yes	16
35.34	odd	2	inner	2100.2.x.c.1693.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.x.c.1357.3	✓	16	5.2	odd	4	inner
2100.2.x.c.1357.4	yes	16	35.13	even	4	inner
2100.2.x.c.1357.5	yes	16	35.27	even	4	inner
2100.2.x.c.1357.6	yes	16	5.3	odd	4	inner
2100.2.x.c.1693.3	yes	16	7.6	odd	2	inner
2100.2.x.c.1693.4	yes	16	5.4	even	2	inner
2100.2.x.c.1693.5	yes	16	1.1	even	1	trivial
2100.2.x.c.1693.6	yes	16	35.34	odd	2	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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.49342 + 0.884806i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.49342 + 0.884806i) q^{7} -1.00000i q^{9} +3.27492 q^{11} +(3.02282 - 3.02282i) q^{13} +(-1.41421 - 1.41421i) q^{17} +2.15068 q^{19} +(-1.13746 + 2.38876i) q^{21} +(0.296014 + 0.296014i) q^{23} +(-0.707107 - 0.707107i) q^{27} +0.725083i q^{29} +1.31342i q^{31} +(2.31572 - 2.31572i) q^{33} +(-1.56145 + 1.56145i) q^{37} -4.27492i q^{39} -5.25370i q^{41} +(-0.632717 - 0.632717i) q^{43} +(-1.41421 - 1.41421i) q^{47} +(5.43424 - 4.41238i) q^{49} -2.00000 q^{51} +(-3.71492 - 3.71492i) q^{53} +(1.52076 - 1.52076i) q^{57} +8.71780 q^{59} -1.31342i q^{61} +(0.884806 + 2.49342i) q^{63} +(3.08221 - 3.08221i) q^{67} +0.418627 q^{69} +9.27492 q^{71} +(7.07107 - 7.07107i) q^{73} +(-8.16573 + 2.89767i) q^{77} -11.8248i q^{79} -1.00000 q^{81} +(11.7025 - 11.7025i) q^{83} +(0.512711 + 0.512711i) q^{87} +18.2728 q^{89} +(-4.86254 + 10.2118i) q^{91} +(0.928731 + 0.928731i) q^{93} +(-7.26546 - 7.26546i) q^{97} -3.27492i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} + 12 q^{21} - 32 q^{51} + 88 q^{71} - 16 q^{81} - 108 q^{91}+O(q^{100}) \) 16 * q - 8 * q^11 + 12 * q^21 - 32 * q^51 + 88 * q^71 - 16 * q^81 - 108 * q^91

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