LMFDB - Embedded newform 2592.2.s.j.1727.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(863,2592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("2592.863");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.s (of order $6$, degree $2$, not 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:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 49x^{12} - 12x^{10} - 600x^{8} + 108x^{6} + 4057x^{4} + 18252x^{2} + 28561 $ x^16 - 12x^14 + 49x^12 - 12x^10 - 600x^8 + 108x^6 + 4057x^4 + 18252*x^2 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1727.7
Root			$-0.115299 - 1.50155i$ of defining polynomial
Character	$\chi$	$=$	2592.1727
Dual form			2592.2.s.j.863.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.35218 - 1.35803i) q^{5} +(3.67803 + 2.12351i) q^{7} +O(q^{10})$	$q+(2.35218 - 1.35803i) q^{5} +(3.67803 + 2.12351i) q^{7} +(1.09921 - 1.90389i) q^{11} +(-1.25749 - 2.17803i) q^{13} +7.93806i q^{17} -5.13799i q^{19} +(0.868614 + 1.50448i) q^{23} +(1.18849 - 2.05853i) q^{25} +(0.230858 + 0.133286i) q^{29} +(8.69251 - 5.01862i) q^{31} +11.5352 q^{35} +9.24703 q^{37} +(-2.18363 + 1.26072i) q^{41} +(-1.14214 - 0.659412i) q^{43} +(-0.860601 + 1.49061i) q^{47} +(5.51862 + 9.55853i) q^{49} +0.306989i q^{53} -5.97105i q^{55} +(-5.83153 - 10.1005i) q^{59} +(-4.64214 + 8.04041i) q^{61} +(-5.91567 - 3.41542i) q^{65} +(-5.59895 + 3.23255i) q^{67} -9.46463 q^{71} +6.62301 q^{73} +(8.08587 - 4.66838i) q^{77} +(-9.83464 - 5.67803i) q^{79} +(-6.41148 + 11.1050i) q^{83} +(10.7801 + 18.6717i) q^{85} -9.42422i q^{89} -10.6812i q^{91} +(-6.97754 - 12.0855i) q^{95} +(-4.12766 + 7.14932i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{7}+O(q^{10}) $ 16 * q + 12 * q^7	$ 16 q + 12 q^{7} + 4 q^{13} + 24 q^{25} + 72 q^{31} + 72 q^{37} + 84 q^{43} + 24 q^{49} + 28 q^{61} + 36 q^{67} + 96 q^{73} + 12 q^{79} + 12 q^{85} + 16 q^{97}+O(q^{100}) $ 16 * q + 12 * q^7 + 4 * q^13 + 24 * q^25 + 72 * q^31 + 72 * q^37 + 84 * q^43 + 24 * q^49 + 28 * q^61 + 36 * q^67 + 96 * q^73 + 12 * q^79 + 12 * q^85 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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			0
$3$		0			0
$4$		0			0
$5$	2.35218	−	1.35803i	1.05193	−	0.607330i	0.128738	−	0.991679i	$-0.458907\pi$
$5$	2.35218	−	1.35803i	1.05193	−	0.607330i	0.923188	+	0.384349i	$0.125574\pi$
$6$		0			0
$7$	3.67803	+	2.12351i	1.39017	+	0.802613i	0.993333	−	0.115278i	$-0.0367759\pi$
$7$	3.67803	+	2.12351i	1.39017	+	0.802613i	0.396833	+	0.917891i	$0.370109\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.09921	−	1.90389i	0.331425	−	0.574045i	−0.651367	−	0.758763i	$-0.725804\pi$
$11$	1.09921	−	1.90389i	0.331425	−	0.574045i	0.982791	+	0.184719i	$0.0591374\pi$
$12$		0			0
$13$	−1.25749	−	2.17803i	−0.348765	−	0.604078i	0.637266	−	0.770644i	$-0.280065\pi$
$13$	−1.25749	−	2.17803i	−0.348765	−	0.604078i	−0.986030	+	0.166566i	$0.946732\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			7.93806i			1.92526i	0.270818	+	0.962631i	$0.412706\pi$
$17$			7.93806i			1.92526i	−0.270818	+	0.962631i	$0.587294\pi$
$18$		0			0
$19$		−	5.13799i		−	1.17874i	−0.807865	−	0.589368i	$-0.799377\pi$
$19$		−	5.13799i		−	1.17874i	0.807865	−	0.589368i	$-0.200623\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.868614	+	1.50448i	0.181119	+	0.313707i	0.942262	−	0.334877i	$-0.108695\pi$
$23$	0.868614	+	1.50448i	0.181119	+	0.313707i	−0.761143	+	0.648584i	$0.775362\pi$
$24$		0			0
$25$	1.18849	−	2.05853i	0.237699	−	0.411707i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.230858	+	0.133286i	0.0428692	+	0.0247506i	0.521281	−	0.853385i	$-0.325454\pi$
$29$	0.230858	+	0.133286i	0.0428692	+	0.0247506i	−0.478412	+	0.878135i	$0.658788\pi$
$30$		0			0
$31$	8.69251	−	5.01862i	1.56122	−	0.901371i	0.564086	−	0.825716i	$-0.309228\pi$
$31$	8.69251	−	5.01862i	1.56122	−	0.901371i	0.997134	−	0.0756553i	$-0.0241049\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	11.5352			1.94980
$36$		0			0
$37$	9.24703			1.52020			0.760101	−	0.649805i	$-0.225149\pi$
$37$	9.24703			1.52020			0.760101	+	0.649805i	$0.225149\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.18363	+	1.26072i	−0.341026	+	0.196891i	−0.660725	−	0.750628i	$-0.729751\pi$
$41$	−2.18363	+	1.26072i	−0.341026	+	0.196891i	0.319700	+	0.947519i	$0.396418\pi$
$42$		0			0
$43$	−1.14214	−	0.659412i	−0.174174	−	0.100559i	0.410379	−	0.911915i	$-0.365397\pi$
$43$	−1.14214	−	0.659412i	−0.174174	−	0.100559i	−0.584553	+	0.811356i	$0.698730\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.860601	+	1.49061i	−0.125532	+	0.217427i	−0.921941	−	0.387331i	$-0.873397\pi$
$47$	−0.860601	+	1.49061i	−0.125532	+	0.217427i	0.796409	+	0.604758i	$0.206730\pi$
$48$		0			0
$49$	5.51862	+	9.55853i	0.788375	+	1.36550i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			0.306989i			0.0421682i	0.999778	+	0.0210841i	$0.00671177\pi$
$53$			0.306989i			0.0421682i	−0.999778	+	0.0210841i	$0.993288\pi$
$54$		0			0
$55$		−	5.97105i		−	0.805137i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.83153	−	10.1005i	−0.759200	−	1.31497i	−0.943259	−	0.332058i	$-0.892257\pi$
$59$	−5.83153	−	10.1005i	−0.759200	−	1.31497i	0.184058	−	0.982915i	$-0.441076\pi$
$60$		0			0
$61$	−4.64214	+	8.04041i	−0.594365	+	1.02947i	0.399272	+	0.916833i	$0.369263\pi$
$61$	−4.64214	+	8.04041i	−0.594365	+	1.02947i	−0.993636	+	0.112637i	$0.964070\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.91567	−	3.41542i	−0.733749	−	0.423630i
$66$		0			0
$67$	−5.59895	+	3.23255i	−0.684020	+	0.394919i	−0.801368	−	0.598172i	$-0.795894\pi$
$67$	−5.59895	+	3.23255i	−0.684020	+	0.394919i	0.117348	+	0.993091i	$0.462561\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.46463			−1.12325			−0.561623	−	0.827393i	$-0.689823\pi$
$71$	−9.46463			−1.12325			−0.561623	+	0.827393i	$0.689823\pi$
$72$		0			0
$73$	6.62301			0.775165			0.387582	−	0.921835i	$-0.373310\pi$
$73$	6.62301			0.775165			0.387582	+	0.921835i	$0.373310\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.08587	−	4.66838i	0.921471	−	0.532012i
$78$		0			0
$79$	−9.83464	−	5.67803i	−1.10648	−	0.638829i	−0.168567	−	0.985690i	$-0.553914\pi$
$79$	−9.83464	−	5.67803i	−1.10648	−	0.638829i	−0.937916	+	0.346861i	$0.887247\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.41148	+	11.1050i	−0.703751	+	1.21893i	0.263389	+	0.964690i	$0.415160\pi$
$83$	−6.41148	+	11.1050i	−0.703751	+	1.21893i	−0.967140	+	0.254243i	$0.918174\pi$
$84$		0			0
$85$	10.7801	+	18.6717i	1.16927	+	2.02523i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	9.42422i		−	0.998965i	−0.866324	−	0.499483i	$-0.833523\pi$
$89$		−	9.42422i		−	0.998965i	0.866324	−	0.499483i	$-0.166477\pi$
$90$		0			0
$91$		−	10.6812i		−	1.11969i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.97754	−	12.0855i	−0.715881	−	1.23994i
$96$		0			0
$97$	−4.12766	+	7.14932i	−0.419101	+	0.725903i	−0.995849	−	0.0910182i	$-0.970988\pi$
$97$	−4.12766	+	7.14932i	−0.419101	+	0.725903i	0.576749	+	0.816922i	$0.304321\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.61883	−	4.97608i	−0.857605	−	0.495139i	0.00560428	−	0.999984i	$-0.498216\pi$
$101$	−8.61883	−	4.97608i	−0.857605	−	0.495139i	−0.863210	+	0.504846i	$0.831549\pi$
$102$		0			0
$103$	15.4641	−	8.92820i	1.52372	−	0.879722i	0.524117	−	0.851646i	$-0.324395\pi$
$103$	15.4641	−	8.92820i	1.52372	−	0.879722i	0.999606	−	0.0280760i	$-0.00893804\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.9160			1.53866			0.769329	−	0.638852i	$-0.220591\pi$
$107$	15.9160			1.53866			0.769329	+	0.638852i	$0.220591\pi$
$108$		0			0
$109$	−0.435890			−0.0417507			−0.0208754	−	0.999782i	$-0.506645\pi$
$109$	−0.435890			−0.0417507			−0.0208754	+	0.999782i	$0.506645\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.82122	−	5.67028i	0.923902	−	0.533415i	0.0390244	−	0.999238i	$-0.487575\pi$
$113$	9.82122	−	5.67028i	0.923902	−	0.533415i	0.884878	+	0.465823i	$0.154242\pi$
$114$		0			0
$115$	4.08627	+	2.35921i	0.381047	+	0.219997i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−16.8566	+	29.1964i	−1.54524	+	2.67643i
$120$		0			0
$121$	3.08347	+	5.34072i	0.280315	+	0.485520i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			7.12426i			0.637213i
$126$		0			0
$127$			9.39331i			0.833522i	0.909016	+	0.416761i	$0.136835\pi$
$127$			9.39331i			0.833522i	−0.909016	+	0.416761i	$0.863165\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.50759	+	7.80737i	0.393830	+	0.682133i	0.992951	−	0.118525i	$-0.0378167\pi$
$131$	4.50759	+	7.80737i	0.393830	+	0.682133i	−0.599121	+	0.800658i	$0.704483\pi$
$132$		0			0
$133$	10.9106	−	18.8977i	0.946068	−	1.63864i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.0488813	+	0.0282216i	0.00417621	+	0.00241114i	0.502087	−	0.864817i	$-0.332566\pi$
$137$	0.0488813	+	0.0282216i	0.00417621	+	0.00241114i	−0.497910	+	0.867228i	$0.665899\pi$
$138$		0			0
$139$	16.2052	−	9.35607i	1.37451	−	0.793571i	0.383014	−	0.923742i	$-0.374886\pi$
$139$	16.2052	−	9.35607i	1.37451	−	0.793571i	0.991492	+	0.130171i	$0.0415527\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.52898			−0.462357
$144$		0			0
$145$	0.724025			0.0601270
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−15.5329	+	8.96792i	−1.27250	+	0.734680i	−0.975459	−	0.220183i	$-0.929335\pi$
$149$	−15.5329	+	8.96792i	−1.27250	+	0.734680i	−0.297045	+	0.954863i	$0.596001\pi$
$150$		0			0
$151$	−1.54319	−	0.890960i	−0.125583	−	0.0725053i	0.435893	−	0.899999i	$-0.356433\pi$
$151$	−1.54319	−	0.890960i	−0.125583	−	0.0725053i	−0.561475	+	0.827493i	$0.689766\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	13.6309	−	23.6094i	1.09486	−	1.89635i
$156$		0			0
$157$	5.50415	+	9.53346i	0.439279	+	0.760853i	0.997634	−	0.0687488i	$-0.0219007\pi$
$157$	5.50415	+	9.53346i	0.439279	+	0.760853i	−0.558355	+	0.829602i	$0.688567\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			7.37806i			0.581472i
$162$		0			0
$163$		−	23.1835i		−	1.81587i	−0.419107	−	0.907937i	$-0.637657\pi$
$163$		−	23.1835i		−	1.81587i	0.419107	−	0.907937i	$-0.362343\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.40176	+	2.42791i	0.108471	+	0.187878i	0.915151	−	0.403111i	$-0.132071\pi$
$167$	1.40176	+	2.42791i	0.108471	+	0.187878i	−0.806680	+	0.590989i	$0.798738\pi$
$168$		0			0
$169$	3.33745	−	5.78063i	0.256727	−	0.444664i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−15.2303	−	8.79324i	−1.15794	−	0.668538i	−0.207132	−	0.978313i	$-0.566413\pi$
$173$	−15.2303	−	8.79324i	−1.15794	−	0.668538i	−0.950810	+	0.309775i	$0.899746\pi$
$174$		0			0
$175$	8.74265	−	5.04757i	0.660882	−	0.381560i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.54074			−0.339391			−0.169696	−	0.985497i	$-0.554278\pi$
$179$	−4.54074			−0.339391			−0.169696	+	0.985497i	$0.554278\pi$
$180$		0			0
$181$	3.34777			0.248838			0.124419	−	0.992230i	$-0.460293\pi$
$181$	3.34777			0.248838			0.124419	+	0.992230i	$0.460293\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	21.7507	−	12.5577i	1.59914	−	0.923264i
$186$		0			0
$187$	15.1132	+	8.72560i	1.10519	+	0.638079i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.16390	+	5.48003i	−0.228932	+	0.396521i	−0.957492	−	0.288461i	$-0.906857\pi$
$191$	−3.16390	+	5.48003i	−0.228932	+	0.396521i	0.728560	+	0.684982i	$0.240190\pi$
$192$		0			0
$193$	−5.20384	−	9.01331i	−0.374581	−	0.648793i	0.615684	−	0.787993i	$-0.288880\pi$
$193$	−5.20384	−	9.01331i	−0.374581	−	0.648793i	−0.990264	+	0.139201i	$0.955547\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			18.0477i			1.28584i	0.765932	+	0.642922i	$0.222278\pi$
$197$			18.0477i			1.28584i	−0.765932	+	0.642922i	$0.777722\pi$
$198$		0			0
$199$		−	0.913624i		−	0.0647651i	−0.999476	−	0.0323825i	$-0.989691\pi$
$199$		−	0.913624i		−	0.0647651i	0.999476	−	0.0323825i	$-0.0103095\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.566068	+	0.980459i	0.0397302	+	0.0688148i
$204$		0			0
$205$	−3.42419	+	5.93087i	−0.239156	+	0.414230i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.78217	−	5.64774i	−0.676647	−	0.390662i
$210$		0			0
$211$	4.82735	−	2.78707i	0.332329	−	0.191870i	−0.324546	−	0.945870i	$-0.605211\pi$
$211$	4.82735	−	2.78707i	0.332329	−	0.191870i	0.656875	+	0.754000i	$0.271878\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.58201			−0.244291
$216$		0			0
$217$	42.6284			2.89381
$218$		0			0
$219$		0			0
$220$		0			0
$221$	17.2894	−	9.98201i	1.16301	−	0.671463i
$222$		0			0
$223$	−6.98553	−	4.03310i	−0.467785	−	0.270076i	0.247527	−	0.968881i	$-0.420382\pi$
$223$	−6.98553	−	4.03310i	−0.467785	−	0.270076i	−0.715312	+	0.698805i	$0.753716\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.1675	−	22.8069i	0.873960	−	1.51374i	0.0160945	−	0.999870i	$-0.494877\pi$
$227$	13.1675	−	22.8069i	0.873960	−	1.51374i	0.857866	−	0.513873i	$-0.171790\pi$
$228$		0			0
$229$	−9.90013	−	17.1475i	−0.654219	−	1.13314i	−0.982089	−	0.188417i	$-0.939664\pi$
$229$	−9.90013	−	17.1475i	−0.654219	−	1.13314i	0.327870	−	0.944723i	$-0.393669\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	7.08515i		−	0.464164i	−0.972696	−	0.232082i	$-0.925446\pi$
$233$		−	7.08515i		−	0.464164i	0.972696	−	0.232082i	$-0.0745537\pi$
$234$		0			0
$235$			4.67489i			0.304956i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.50268	−	12.9950i	−0.485308	−	0.840578i	0.514550	−	0.857461i	$-0.327959\pi$
$239$	−7.50268	−	12.9950i	−0.485308	−	0.840578i	−0.999857	+	0.0168829i	$0.994626\pi$
$240$		0			0
$241$	−1.50037	+	2.59871i	−0.0966472	+	0.167398i	−0.910295	−	0.413960i	$-0.864145\pi$
$241$	−1.50037	+	2.59871i	−0.0966472	+	0.167398i	0.813648	+	0.581358i	$0.197479\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	25.9616	+	14.9889i	1.65862	+	0.957607i
$246$		0			0
$247$	−11.1907	+	6.46096i	−0.712048	+	0.411101i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	23.6594			1.49337			0.746685	−	0.665177i	$-0.231644\pi$
$251$	23.6594			1.49337			0.746685	+	0.665177i	$0.231644\pi$
$252$		0			0
$253$	3.81916			0.240109
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−18.3321	+	10.5841i	−1.14353	+	0.660215i	−0.947301	−	0.320344i	$-0.896202\pi$
$257$	−18.3321	+	10.5841i	−1.14353	+	0.660215i	−0.196225	+	0.980559i	$0.562868\pi$
$258$		0			0
$259$	34.0109	+	19.6362i	2.11333	+	1.22013i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.59783	+	4.49957i	−0.160189	+	0.277456i	−0.934936	−	0.354815i	$-0.884544\pi$
$263$	−2.59783	+	4.49957i	−0.160189	+	0.277456i	0.774747	+	0.632271i	$0.217877\pi$
$264$		0			0
$265$	0.416901	+	0.722093i	0.0256100	+	0.0443578i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			2.25487i			0.137482i	0.997635	+	0.0687408i	$0.0218982\pi$
$269$			2.25487i			0.137482i	−0.997635	+	0.0687408i	$0.978102\pi$
$270$		0			0
$271$		−	10.7038i		−	0.650212i	−0.945678	−	0.325106i	$-0.894600\pi$
$271$		−	10.7038i		−	0.650212i	0.945678	−	0.325106i	$-0.105400\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.61281	−	4.52553i	−0.157559	−	0.272900i
$276$		0			0
$277$	−3.56585	+	6.17624i	−0.214251	+	0.371094i	−0.953041	−	0.302842i	$-0.902064\pi$
$277$	−3.56585	+	6.17624i	−0.214251	+	0.371094i	0.738789	+	0.673936i	$0.235398\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	4.47068	+	2.58115i	0.266698	+	0.153978i	0.627386	−	0.778708i	$-0.284125\pi$
$281$	4.47068	+	2.58115i	0.266698	+	0.153978i	−0.360688	+	0.932687i	$0.617458\pi$
$282$		0			0
$283$	−13.3561	+	7.71113i	−0.793936	+	0.458379i	−0.841346	−	0.540496i	$-0.818236\pi$
$283$	−13.3561	+	7.71113i	−0.793936	+	0.458379i	0.0474105	+	0.998875i	$0.484903\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.7086			−0.632110
$288$		0			0
$289$	−46.0127			−2.70663
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−18.2214	+	10.5201i	−1.06450	+	0.614592i	−0.926675	−	0.375864i	$-0.877346\pi$
$293$	−18.2214	+	10.5201i	−1.06450	+	0.614592i	−0.137830	+	0.990456i	$0.544013\pi$
$294$		0			0
$295$	−27.4336	−	15.8388i	−1.59725	−	0.922170i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.18454	−	3.78374i	0.126335	−	0.218819i
$300$		0			0
$301$	−2.80054	−	4.85068i	−0.161421	−	0.279589i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			25.2166i			1.44390i
$306$		0			0
$307$		−	1.54319i		−	0.0880744i	−0.999030	−	0.0440372i	$-0.985978\pi$
$307$		−	1.54319i		−	0.0880744i	0.999030	−	0.0440372i	$-0.0140220\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.48218	+	9.49541i	0.310866	+	0.538435i	0.978550	−	0.206009i	$-0.0660477\pi$
$311$	5.48218	+	9.49541i	0.310866	+	0.538435i	−0.667684	+	0.744445i	$0.732714\pi$
$312$		0			0
$313$	−8.43954	+	14.6177i	−0.477031	+	0.826241i	−0.999654	−	0.0263226i	$-0.991620\pi$
$313$	−8.43954	+	14.6177i	−0.477031	+	0.826241i	0.522623	+	0.852564i	$0.324954\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.93192	+	4.00214i	0.389335	+	0.224783i	0.681872	−	0.731471i	$-0.261166\pi$
$317$	6.93192	+	4.00214i	0.389335	+	0.224783i	−0.292537	+	0.956254i	$0.594499\pi$
$318$		0			0
$319$	0.507523	−	0.293019i	0.0284158	−	0.0164059i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	40.7856			2.26937
$324$		0			0
$325$	−5.97807			−0.331604
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.33064	+	3.65500i	−0.349020	+	0.201507i
$330$		0			0
$331$	−9.83464	−	5.67803i	−0.540561	−	0.312093i	0.204745	−	0.978815i	$-0.434363\pi$
$331$	−9.83464	−	5.67803i	−0.540561	−	0.312093i	−0.745306	+	0.666722i	$0.767697\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−8.77981	+	15.2071i	−0.479692	+	0.830852i
$336$		0			0
$337$	12.2956	+	21.2966i	0.669784	+	1.16010i	0.977964	+	0.208772i	$0.0669467\pi$
$337$	12.2956	+	21.2966i	0.669784	+	1.16010i	−0.308180	+	0.951328i	$0.599720\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	22.0661i		−	1.19495i
$342$		0			0
$343$			17.1463i			0.925812i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.60189	+	14.8989i	0.461773	+	0.799815i	0.999049	−	0.0435914i	$-0.0138800\pi$
$347$	8.60189	+	14.8989i	0.461773	+	0.799815i	−0.537276	+	0.843407i	$0.680547\pi$
$348$		0			0
$349$	−10.8015	+	18.7088i	−0.578194	+	1.00146i	0.417493	+	0.908680i	$0.362909\pi$
$349$	−10.8015	+	18.7088i	−0.578194	+	1.00146i	−0.995687	+	0.0927805i	$0.970425\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	20.0675	+	11.5860i	1.06808	+	0.616658i	0.927657	−	0.373433i	$-0.121819\pi$
$353$	20.0675	+	11.5860i	1.06808	+	0.616658i	0.140426	+	0.990091i	$0.455153\pi$
$354$		0			0
$355$	−22.2625	+	12.8533i	−1.18157	+	0.682180i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.26471			0.172305			0.0861524	−	0.996282i	$-0.472543\pi$
$359$	3.26471			0.172305			0.0861524	+	0.996282i	$0.472543\pi$
$360$		0			0
$361$	−7.39892			−0.389417
$362$		0			0
$363$		0			0
$364$		0			0
$365$	15.5785	−	8.99425i	0.815416	−	0.470781i
$366$		0			0
$367$	−5.22841	−	3.01862i	−0.272921	−	0.157571i	0.357294	−	0.933992i	$-0.383700\pi$
$367$	−5.22841	−	3.01862i	−0.272921	−	0.157571i	−0.630214	+	0.776421i	$0.717033\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.651895	+	1.12912i	−0.0338447	+	0.0586208i
$372$		0			0
$373$	3.60209	+	6.23900i	0.186509	+	0.323043i	0.944084	−	0.329705i	$-0.106949\pi$
$373$	3.60209	+	6.23900i	0.186509	+	0.323043i	−0.757575	+	0.652748i	$0.773616\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	0.670421i		−	0.0345285i
$378$		0			0
$379$		−	0.0971502i		−	0.00499027i	−0.999997	−	0.00249514i	$-0.999206\pi$
$379$		−	0.0971502i		−	0.00499027i	0.999997	−	0.00249514i	$-0.000794227\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.53976	+	4.39899i	0.129776	+	0.224778i	0.923590	−	0.383383i	$-0.125241\pi$
$383$	2.53976	+	4.39899i	0.129776	+	0.224778i	−0.793814	+	0.608161i	$0.791908\pi$
$384$		0			0
$385$	12.6796	−	21.9617i	0.646213	−	1.11927i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.84234	−	5.68248i	−0.499026	−	0.288113i	0.229285	−	0.973359i	$-0.426361\pi$
$389$	−9.84234	−	5.68248i	−0.499026	−	0.288113i	−0.728311	+	0.685246i	$0.759695\pi$
$390$		0			0
$391$	−11.9427	+	6.89511i	−0.603967	+	0.348701i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−30.8438			−1.55192
$396$		0			0
$397$	10.6693			0.535476			0.267738	−	0.963492i	$-0.413724\pi$
$397$	10.6693			0.535476			0.267738	+	0.963492i	$0.413724\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−30.6353	+	17.6873i	−1.52986	+	0.883263i	−0.530489	+	0.847692i	$0.677992\pi$
$401$	−30.6353	+	17.6873i	−1.52986	+	0.883263i	−0.999367	+	0.0355709i	$0.988675\pi$
$402$		0			0
$403$	−21.8615	−	12.6217i	−1.08900	−	0.628732i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	10.1644	−	17.6053i	0.503833	−	0.872664i
$408$		0			0
$409$	−9.25833	−	16.0359i	−0.457795	−	0.792924i	0.541049	−	0.840991i	$-0.318027\pi$
$409$	−9.25833	−	16.0359i	−0.457795	−	0.792924i	−0.998844	+	0.0480668i	$0.984694\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	49.5333i		−	2.43738i
$414$		0			0
$415$			34.8279i			1.70964i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.11495	+	5.39525i	0.152175	+	0.263575i	0.932027	−	0.362389i	$-0.118039\pi$
$419$	3.11495	+	5.39525i	0.152175	+	0.263575i	−0.779852	+	0.625964i	$0.784706\pi$
$420$		0			0
$421$	6.63117	−	11.4855i	0.323184	−	0.559770i	−0.657960	−	0.753053i	$-0.728580\pi$
$421$	6.63117	−	11.4855i	0.323184	−	0.559770i	0.981143	+	0.193283i	$0.0619136\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	16.3407	+	9.43434i	0.792643	+	0.457633i
$426$		0			0
$427$	−34.1479	+	19.7153i	−1.65253	+	0.954089i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−34.6333			−1.66823			−0.834114	−	0.551592i	$-0.814021\pi$
$431$	−34.6333			−1.66823			−0.834114	+	0.551592i	$0.814021\pi$
$432$		0			0
$433$	−5.67288			−0.272621			−0.136311	−	0.990666i	$-0.543525\pi$
$433$	−5.67288			−0.272621			−0.136311	+	0.990666i	$0.543525\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.73002	−	4.46293i	0.369777	−	0.213491i
$438$		0			0
$439$	17.4771	+	10.0904i	0.834137	+	0.481589i	0.855267	−	0.518187i	$-0.173393\pi$
$439$	17.4771	+	10.0904i	0.834137	+	0.481589i	−0.0211298	+	0.999777i	$0.506726\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.16349	+	12.4075i	−0.340347	+	0.589499i	−0.984497	−	0.175400i	$-0.943878\pi$
$443$	−7.16349	+	12.4075i	−0.340347	+	0.589499i	0.644150	+	0.764899i	$0.277211\pi$
$444$		0			0
$445$	−12.7984	−	22.1674i	−0.606701	−	1.05084i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	23.4094i		−	1.10476i	−0.833593	−	0.552379i	$-0.813720\pi$
$449$		−	23.4094i		−	1.10476i	0.833593	−	0.552379i	$-0.186280\pi$
$450$		0			0
$451$			5.54319i			0.261019i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−14.5054	−	25.1240i	−0.680022	−	1.17783i
$456$		0			0
$457$	0.786939	−	1.36302i	0.0368115	−	0.0637593i	−0.847033	−	0.531541i	$-0.821613\pi$
$457$	0.786939	−	1.36302i	0.0368115	−	0.0637593i	0.883844	+	0.467781i	$0.154947\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.10140	−	2.36794i	−0.191021	−	0.110286i	0.401439	−	0.915886i	$-0.368510\pi$
$461$	−4.10140	−	2.36794i	−0.191021	−	0.110286i	−0.592461	+	0.805599i	$0.701843\pi$
$462$		0			0
$463$	3.54824	−	2.04858i	0.164901	−	0.0952054i	−0.415279	−	0.909694i	$-0.636316\pi$
$463$	3.54824	−	2.04858i	0.164901	−	0.0952054i	0.580179	+	0.814489i	$0.302983\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−41.3565			−1.91375			−0.956874	−	0.290502i	$-0.906178\pi$
$467$	−41.3565			−1.91375			−0.956874	+	0.290502i	$0.906178\pi$
$468$		0			0
$469$	−27.4575			−1.26787
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.51090	+	1.44967i	−0.115451	+	0.0666558i
$474$		0			0
$475$	−10.5767	−	6.10647i	−0.485293	−	0.280184i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.03763	+	3.52927i	−0.0931016	+	0.161257i	−0.908815	−	0.417200i	$-0.863011\pi$
$479$	−2.03763	+	3.52927i	−0.0931016	+	0.161257i	0.815713	+	0.578457i	$0.196345\pi$
$480$		0			0
$481$	−11.6280	−	20.1403i	−0.530193	−	0.918320i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			22.4220i			1.01813i
$486$		0			0
$487$			23.4449i			1.06239i	0.847249	+	0.531195i	$0.178257\pi$
$487$			23.4449i			1.06239i	−0.847249	+	0.531195i	$0.821743\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.12020	−	10.6005i	−0.276201	−	0.478393i	0.694237	−	0.719747i	$-0.255742\pi$
$491$	−6.12020	−	10.6005i	−0.276201	−	0.478393i	−0.970437	+	0.241353i	$0.922409\pi$
$492$		0			0
$493$	−1.05803	+	1.83256i	−0.0476513	+	0.0825344i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−34.8112	−	20.0983i	−1.56150	−	0.901531i
$498$		0			0
$499$	18.1385	−	10.4723i	0.811993	−	0.468804i	−0.0356548	−	0.999364i	$-0.511352\pi$
$499$	18.1385	−	10.4723i	0.811993	−	0.468804i	0.847647	+	0.530560i	$0.178018\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−33.1123			−1.47641			−0.738203	−	0.674578i	$-0.764325\pi$
$503$	−33.1123			−1.47641			−0.738203	+	0.674578i	$0.764325\pi$
$504$		0			0
$505$	−27.0307			−1.20285
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.04353	−	5.22128i	0.400847	−	0.231429i	−0.286002	−	0.958229i	$-0.592326\pi$
$509$	9.04353	−	5.22128i	0.400847	−	0.231429i	0.686850	+	0.726800i	$0.258993\pi$
$510$		0			0
$511$	24.3597	+	14.0641i	1.07761	+	0.622157i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	24.2495	−	42.0014i	1.06856	−	1.85080i
$516$		0			0
$517$	1.89197	+	3.27698i	0.0832086	+	0.144121i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	27.4658i		−	1.20330i	−0.798760	−	0.601649i	$-0.794511\pi$
$521$		−	27.4658i		−	1.20330i	0.798760	−	0.601649i	$-0.205489\pi$
$522$		0			0
$523$		−	11.4140i		−	0.499098i	−0.968362	−	0.249549i	$-0.919718\pi$
$523$		−	11.4140i		−	0.499098i	0.968362	−	0.249549i	$-0.0802823\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	39.8381	+	69.0016i	1.73537	+	3.00576i
$528$		0			0
$529$	9.99102	−	17.3050i	0.434392	−	0.752389i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.49178	+	3.17068i	0.237875	+	0.137337i
$534$		0			0
$535$	37.4373	−	21.6144i	1.61856	−	0.934473i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	24.2645			1.04515
$540$		0			0
$541$	−17.4658			−0.750915			−0.375458	−	0.926840i	$-0.622514\pi$
$541$	−17.4658			−0.750915			−0.375458	+	0.926840i	$0.622514\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.02529	+	0.591952i	−0.0439187	+	0.0253565i
$546$		0			0
$547$	−19.6998	−	11.3737i	−0.842303	−	0.486304i	0.0157437	−	0.999876i	$-0.494988\pi$
$547$	−19.6998	−	11.3737i	−0.842303	−	0.486304i	−0.858046	+	0.513572i	$0.828322\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.684821	−	1.18614i	0.0291743	−	0.0505314i
$552$		0			0
$553$	−24.1148	−	41.7680i	−1.02546	−	1.77616i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	36.8213i		−	1.56017i	−0.625674	−	0.780085i	$-0.715176\pi$
$557$		−	36.8213i		−	1.56017i	0.625674	−	0.780085i	$-0.284824\pi$
$558$		0			0
$559$			3.31681i			0.140286i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.41299	+	4.17943i	0.101696	+	0.176142i	0.912383	−	0.409337i	$-0.134240\pi$
$563$	2.41299	+	4.17943i	0.101696	+	0.176142i	−0.810688	+	0.585479i	$0.800907\pi$
$564$		0			0
$565$	15.4008	−	26.6750i	0.647918	−	1.12223i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.1950	−	7.61816i	−0.553165	−	0.319370i	0.197233	−	0.980357i	$-0.436805\pi$
$569$	−13.1950	−	7.61816i	−0.553165	−	0.319370i	−0.750397	+	0.660987i	$0.770138\pi$
$570$		0			0
$571$	−8.64237	+	4.98967i	−0.361672	+	0.208811i	−0.669814	−	0.742529i	$-0.733626\pi$
$571$	−8.64237	+	4.98967i	−0.361672	+	0.208811i	0.308142	+	0.951340i	$0.400293\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.12937			0.172207
$576$		0			0
$577$	−14.1236			−0.587974			−0.293987	−	0.955809i	$-0.594982\pi$
$577$	−14.1236			−0.587974			−0.293987	+	0.955809i	$0.594982\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−47.1633	+	27.2297i	−1.95666	+	1.12968i
$582$		0			0
$583$	0.584474	+	0.337446i	0.0242064	+	0.0139756i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.6504	+	21.9112i	−0.522139	+	0.904371i	0.477529	+	0.878616i	$0.341532\pi$
$587$	−12.6504	+	21.9112i	−0.522139	+	0.904371i	−0.999668	+	0.0257553i	$0.991801\pi$
$588$		0			0
$589$	−25.7856	−	44.6620i	−1.06248	−	1.84027i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			29.9811i			1.23118i	0.788068	+	0.615588i	$0.211081\pi$
$593$			29.9811i			1.23118i	−0.788068	+	0.615588i	$0.788919\pi$
$594$		0			0
$595$			91.5670i			3.75388i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.05626	−	10.4898i	−0.247452	−	0.428600i	0.715366	−	0.698750i	$-0.246260\pi$
$599$	−6.05626	−	10.4898i	−0.247452	−	0.428600i	−0.962818	+	0.270150i	$0.912927\pi$
$600$		0			0
$601$	−3.19251	+	5.52959i	−0.130225	+	0.225556i	−0.923763	−	0.382964i	$-0.874903\pi$
$601$	−3.19251	+	5.52959i	−0.130225	+	0.225556i	0.793538	+	0.608520i	$0.208237\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	14.5057	+	8.37489i	0.589742	+	0.340488i
$606$		0			0
$607$	−26.7050	+	15.4181i	−1.08392	+	0.625802i	−0.931951	−	0.362583i	$-0.881895\pi$
$607$	−26.7050	+	15.4181i	−1.08392	+	0.625802i	−0.151969	+	0.988385i	$0.548561\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.32878			0.175124
$612$		0			0
$613$	−13.7839			−0.556728			−0.278364	−	0.960476i	$-0.589792\pi$
$613$	−13.7839			−0.556728			−0.278364	+	0.960476i	$0.589792\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	26.6496	−	15.3862i	1.07287	−	0.619424i	0.143909	−	0.989591i	$-0.454033\pi$
$617$	26.6496	−	15.3862i	1.07287	−	0.619424i	0.928965	+	0.370167i	$0.120700\pi$
$618$		0			0
$619$	28.2973	+	16.3374i	1.13736	+	0.656657i	0.945776	−	0.324818i	$-0.105303\pi$
$619$	28.2973	+	16.3374i	1.13736	+	0.656657i	0.191587	+	0.981476i	$0.438636\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	20.0125	−	34.6626i	0.801782	−	1.38873i
$624$		0			0
$625$	15.6174	+	27.0502i	0.624697	+	1.08201i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			73.4034i			2.92679i
$630$		0			0
$631$			10.1436i			0.403810i	0.979405	+	0.201905i	$0.0647132\pi$
$631$			10.1436i			0.403810i	−0.979405	+	0.201905i	$0.935287\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	12.7564	+	22.0947i	0.506222	+	0.876803i
$636$		0			0
$637$	13.8792	−	24.0395i	0.549914	−	0.952479i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	37.5666	+	21.6891i	1.48379	+	0.856666i	0.999830	−	0.0184242i	$-0.00586495\pi$
$641$	37.5666	+	21.6891i	1.48379	+	0.856666i	0.483959	+	0.875091i	$0.339198\pi$
$642$		0			0
$643$	−24.2487	+	14.0000i	−0.956276	+	0.552106i	−0.895025	−	0.446016i	$-0.852842\pi$
$643$	−24.2487	+	14.0000i	−0.956276	+	0.552106i	−0.0612510	+	0.998122i	$0.519509\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−17.4413			−0.685687			−0.342844	−	0.939392i	$-0.611390\pi$
$647$	−17.4413			−0.685687			−0.342844	+	0.939392i	$0.611390\pi$
$648$		0			0
$649$	−25.6403			−1.00647
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.7870	+	11.4241i	−0.774327	+	0.447058i	−0.834416	−	0.551135i	$-0.814195\pi$
$653$	−19.7870	+	11.4241i	−0.774327	+	0.447058i	0.0600892	+	0.998193i	$0.480861\pi$
$654$		0			0
$655$	21.2053	+	12.2429i	0.828559	+	0.478369i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−15.0517	+	26.0703i	−0.586331	+	1.01555i	0.408378	+	0.912813i	$0.366095\pi$
$659$	−15.0517	+	26.0703i	−0.586331	+	1.01555i	−0.994708	+	0.102741i	$0.967239\pi$
$660$		0			0
$661$	9.17500	+	15.8916i	0.356866	+	0.618110i	0.987435	−	0.158023i	$-0.0505119\pi$
$661$	9.17500	+	15.8916i	0.356866	+	0.618110i	−0.630569	+	0.776133i	$0.717179\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	59.2676i		−	2.29830i
$666$		0			0
$667$			0.463096i			0.0179311i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	10.2054	+	17.6762i	0.393974	+	0.682383i
$672$		0			0
$673$	−0.145944	+	0.252783i	−0.00562574	+	0.00974406i	−0.868825	−	0.495120i	$-0.835124\pi$
$673$	−0.145944	+	0.252783i	−0.00562574	+	0.00974406i	0.863199	+	0.504864i	$0.168457\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.1176	−	12.1922i	−0.811614	−	0.468586i	0.0359018	−	0.999355i	$-0.488570\pi$
$677$	−21.1176	−	12.1922i	−0.811614	−	0.468586i	−0.847516	+	0.530770i	$0.821903\pi$
$678$		0			0
$679$	−30.3634	+	17.5303i	−1.16524	+	0.672751i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−26.4127			−1.01065			−0.505326	−	0.862928i	$-0.668628\pi$
$683$	−26.4127			−1.01065			−0.505326	+	0.862928i	$0.668628\pi$
$684$		0			0
$685$	0.153303			0.00585742
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.668633	−	0.386035i	0.0254729	−	0.0147068i
$690$		0			0
$691$	−22.0056	−	12.7050i	−0.837133	−	0.483319i	0.0191555	−	0.999817i	$-0.493902\pi$
$691$	−22.0056	−	12.7050i	−0.837133	−	0.483319i	−0.856289	+	0.516497i	$0.827236\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	25.4117	−	44.0143i	0.963919	−	1.66956i
$696$		0			0
$697$	−10.0077	−	17.3338i	−0.379067	−	0.656563i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			2.37948i			0.0898719i	0.998990	+	0.0449359i	$0.0143084\pi$
$701$			2.37948i			0.0898719i	−0.998990	+	0.0449359i	$0.985692\pi$
$702$		0			0
$703$		−	47.5111i		−	1.79192i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−21.1336	−	36.6044i	−0.794809	−	1.37665i
$708$		0			0
$709$	−21.9001	+	37.9321i	−0.822477	+	1.42457i	0.0813562	+	0.996685i	$0.474075\pi$
$709$	−21.9001	+	37.9321i	−0.822477	+	1.42457i	−0.903833	+	0.427886i	$0.859258\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	15.1009	+	8.71849i	0.565532	+	0.326510i
$714$		0			0
$715$	−13.0052	+	7.50853i	−0.486365	+	0.280803i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	31.1749			1.16263			0.581314	−	0.813680i	$-0.302539\pi$
$719$	31.1749			1.16263			0.581314	+	0.813680i	$0.302539\pi$
$720$		0			0
$721$	75.8367			2.82430
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.548746	−	0.316819i	0.0203799	−	0.0117664i
$726$		0			0
$727$	−20.8114	−	12.0155i	−0.771853	−	0.445629i	0.0616823	−	0.998096i	$-0.480353\pi$
$727$	−20.8114	−	12.0155i	−0.771853	−	0.445629i	−0.833535	+	0.552466i	$0.813687\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.23445	−	9.06633i	0.193603	−	0.335330i
$732$		0			0
$733$	−6.32611	−	10.9572i	−0.233660	−	0.404712i	0.725222	−	0.688515i	$-0.241737\pi$
$733$	−6.32611	−	10.9572i	−0.233660	−	0.404712i	−0.958883	+	0.283803i	$0.908404\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			14.2130i			0.523544i
$738$		0			0
$739$		−	27.4097i		−	1.00828i	−0.863621	−	0.504141i	$-0.831809\pi$
$739$		−	27.4097i		−	1.00828i	0.863621	−	0.504141i	$-0.168191\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	13.2005	+	22.8639i	0.484278	+	0.838794i	0.999837	−	0.0180598i	$-0.00574894\pi$
$743$	13.2005	+	22.8639i	0.484278	+	0.838794i	−0.515559	+	0.856854i	$0.672416\pi$
$744$		0			0
$745$	−24.3574	+	42.1883i	−0.892387	+	1.54566i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	58.5396	+	33.7979i	2.13899	+	1.23495i
$750$		0			0
$751$	−34.6599	+	20.0109i	−1.26476	+	0.730207i	−0.973991	−	0.226587i	$-0.927243\pi$
$751$	−34.6599	+	20.0109i	−1.26476	+	0.730207i	−0.290765	+	0.956794i	$0.593910\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.83980			−0.176139
$756$		0			0
$757$	−50.3671			−1.83062			−0.915311	−	0.402748i	$-0.868055\pi$
$757$	−50.3671			−1.83062			−0.915311	+	0.402748i	$0.868055\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	42.3409	−	24.4455i	1.53486	−	0.886150i	0.535729	−	0.844390i	$-0.320037\pi$
$761$	42.3409	−	24.4455i	1.53486	−	0.886150i	0.999128	−	0.0417602i	$-0.0132965\pi$
$762$		0			0
$763$	−1.60322	−	0.925619i	−0.0580404	−	0.0335097i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−14.6662	+	25.4025i	−0.529564	+	0.917232i
$768$		0			0
$769$	−5.74703	−	9.95414i	−0.207243	−	0.358956i	0.743602	−	0.668623i	$-0.233116\pi$
$769$	−5.74703	−	9.95414i	−0.207243	−	0.358956i	−0.950845	+	0.309667i	$0.899782\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	31.8866i		−	1.14688i	−0.819247	−	0.573441i	$-0.805608\pi$
$773$		−	31.8866i		−	1.14688i	0.819247	−	0.573441i	$-0.194392\pi$
$774$		0			0
$775$		−	23.8584i		−	0.857020i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.47756	+	11.2195i	0.232083	+	0.401979i
$780$		0			0
$781$	−10.4036	+	18.0196i	−0.372271	+	0.644793i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	25.8935	+	14.9496i	0.924178	+	0.533574i
$786$		0			0
$787$	13.4161	−	7.74579i	0.478232	−	0.276108i	−0.241447	−	0.970414i	$-0.577622\pi$
$787$	13.4161	−	7.74579i	0.478232	−	0.276108i	0.719680	+	0.694306i	$0.244289\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	48.1637			1.71250
$792$		0			0
$793$	23.3497			0.829173
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.99393	+	2.30589i	−0.141472	+	0.0816790i	−0.569065	−	0.822292i	$-0.692695\pi$
$797$	−3.99393	+	2.30589i	−0.141472	+	0.0816790i	0.427593	+	0.903971i	$0.359362\pi$
$798$		0			0
$799$	−11.8325	−	6.83150i	−0.418604	−	0.241681i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	7.28009	−	12.6095i	0.256909	−	0.444979i
$804$		0			0
$805$	10.0196	+	17.3545i	0.353145	+	0.611666i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	9.23050i		−	0.324527i	−0.986747	−	0.162263i	$-0.948121\pi$
$809$		−	9.23050i		−	0.324527i	0.986747	−	0.162263i	$-0.0518795\pi$
$810$		0			0
$811$			14.4920i			0.508884i	0.967088	+	0.254442i	$0.0818919\pi$
$811$			14.4920i			0.508884i	−0.967088	+	0.254442i	$0.918108\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−31.4839	−	54.5318i	−1.10283	−	1.91017i
$816$		0			0
$817$	−3.38805	+	5.86828i	−0.118533	+	0.205305i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.64787	−	3.83815i	−0.232012	−	0.133952i	0.379488	−	0.925197i	$-0.376100\pi$
$821$	−6.64787	−	3.83815i	−0.232012	−	0.133952i	−0.611500	+	0.791244i	$0.709434\pi$
$822$		0			0
$823$	−18.1619	+	10.4858i	−0.633083	+	0.365511i	−0.781945	−	0.623347i	$-0.785772\pi$
$823$	−18.1619	+	10.4858i	−0.633083	+	0.365511i	0.148862	+	0.988858i	$0.452439\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−22.2620			−0.774127			−0.387064	−	0.922053i	$-0.626511\pi$
$827$	−22.2620			−0.774127			−0.387064	+	0.922053i	$0.626511\pi$
$828$		0			0
$829$	24.1198			0.837716			0.418858	−	0.908052i	$-0.362431\pi$
$829$	24.1198			0.837716			0.418858	+	0.908052i	$0.362431\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−75.8762	+	43.8071i	−2.62895	+	1.51783i
$834$		0			0
$835$	6.59437	+	3.80726i	0.228207	+	0.131756i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	16.1238	−	27.9273i	0.556657	−	0.964158i	−0.441116	−	0.897450i	$-0.645417\pi$
$839$	16.1238	−	27.9273i	0.556657	−	0.964158i	0.997773	−	0.0667076i	$-0.0212495\pi$
$840$		0			0
$841$	−14.4645	−	25.0532i	−0.498775	−	0.863903i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	18.1294i		−	0.623671i
$846$		0			0
$847$			26.1911i			0.899938i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	8.03210	+	13.9120i	0.275337	+	0.476897i
$852$		0			0
$853$	15.4714	−	26.7972i	0.529730	−	0.917520i	−0.469668	−	0.882843i	$-0.655626\pi$
$853$	15.4714	−	26.7972i	0.529730	−	0.917520i	0.999399	−	0.0346769i	$-0.0110402\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.22025	+	0.704509i	0.0416828	+	0.0240656i	0.520697	−	0.853742i	$-0.325672\pi$
$857$	1.22025	+	0.704509i	0.0416828	+	0.0240656i	−0.479014	+	0.877807i	$0.659006\pi$
$858$		0			0
$859$	−12.9478	+	7.47543i	−0.441774	+	0.255059i	−0.704350	−	0.709853i	$-0.748761\pi$
$859$	−12.9478	+	7.47543i	−0.441774	+	0.255059i	0.262576	+	0.964911i	$0.415428\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	44.6593			1.52022			0.760109	−	0.649795i	$-0.225145\pi$
$863$	44.6593			1.52022			0.760109	+	0.649795i	$0.225145\pi$
$864$		0			0
$865$	−47.7660			−1.62409
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−21.6207	+	12.4827i	−0.733432	+	0.423447i
$870$		0			0
$871$	14.0812	+	8.12980i	0.477124	+	0.275468i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−15.1285	+	26.2033i	−0.511435	+	0.885832i
$876$		0			0
$877$	14.4364	+	25.0046i	0.487482	+	0.844344i	0.999896	−	0.0143943i	$-0.00458201\pi$
$877$	14.4364	+	25.0046i	0.487482	+	0.844344i	−0.512414	+	0.858739i	$0.671249\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			14.1962i			0.478283i	0.970985	+	0.239142i	$0.0768660\pi$
$881$			14.1962i			0.478283i	−0.970985	+	0.239142i	$0.923134\pi$
$882$		0			0
$883$		−	33.8730i		−	1.13992i	−0.821673	−	0.569959i	$-0.806959\pi$
$883$		−	33.8730i		−	1.13992i	0.821673	−	0.569959i	$-0.193041\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.8373	−	27.4310i	−0.531765	−	0.921044i	−0.999312	−	0.0370762i	$-0.988196\pi$
$887$	−15.8373	−	27.4310i	−0.531765	−	0.921044i	0.467547	−	0.883968i	$-0.345138\pi$
$888$		0			0
$889$	−19.9468	+	34.5489i	−0.668995	+	1.15873i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.65871	+	4.42176i	0.256289	+	0.147969i
$894$		0			0
$895$	−10.6806	+	6.16647i	−0.357014	+	0.206122i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.67564			0.0892377
$900$		0			0
$901$	−2.43690			−0.0811848
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.87456	−	4.54638i	0.261759	−	0.151127i
$906$		0			0
$907$	−21.2072	−	12.2440i	−0.704174	−	0.406555i	0.104726	−	0.994501i	$-0.466603\pi$
$907$	−21.2072	−	12.2440i	−0.704174	−	0.406555i	−0.808900	+	0.587946i	$0.799937\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.29162	+	10.8974i	−0.208451	+	0.361047i	−0.951227	−	0.308493i	$-0.900175\pi$
$911$	−6.29162	+	10.8974i	−0.208451	+	0.361047i	0.742776	+	0.669540i	$0.233509\pi$
$912$		0			0
$913$	14.0951	+	24.4135i	0.466481	+	0.807969i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			38.2877i			1.26437i
$918$		0			0
$919$			23.2890i			0.768232i	0.923285	+	0.384116i	$0.125494\pi$
$919$			23.2890i			0.768232i	−0.923285	+	0.384116i	$0.874506\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	11.9017	+	20.6143i	0.391748	+	0.678528i
$924$		0			0
$925$	10.9900	−	19.0353i	0.361350	−	0.625877i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−31.3620	−	18.1069i	−1.02895	−	0.594067i	−0.112269	−	0.993678i	$-0.535812\pi$
$929$	−31.3620	−	18.1069i	−1.02895	−	0.594067i	−0.916685	+	0.399611i	$0.869145\pi$
$930$		0			0
$931$	49.1116	−	28.3546i	1.60957	−	0.929285i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	47.3985			1.55010
$936$		0			0
$937$	−2.31254			−0.0755474			−0.0377737	−	0.999286i	$-0.512027\pi$
$937$	−2.31254			−0.0755474			−0.0377737	+	0.999286i	$0.512027\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.97067	−	2.86982i	0.162039	−	0.0935533i	−0.416788	−	0.909004i	$-0.636844\pi$
$941$	4.97067	−	2.86982i	0.162039	−	0.0935533i	0.578827	+	0.815451i	$0.303511\pi$
$942$		0			0
$943$	−3.79346	−	2.19016i	−0.123532	−	0.0713213i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.67639	+	8.09975i	−0.151962	+	0.263207i	−0.931949	−	0.362590i	$-0.881893\pi$
$947$	−4.67639	+	8.09975i	−0.151962	+	0.263207i	0.779986	+	0.625796i	$0.215226\pi$
$948$		0			0
$949$	−8.32836	−	14.4251i	−0.270350	−	0.468260i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			47.4501i			1.53706i	0.639814	+	0.768530i	$0.279012\pi$
$953$			47.4501i			1.53706i	−0.639814	+	0.768530i	$0.720988\pi$
$954$		0			0
$955$			17.1867i			0.556148i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.119858	+	0.207600i	0.00387042	+	0.00670376i
$960$		0			0
$961$	34.8731	−	60.4020i	1.12494	−	1.94845i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−24.4807	−	14.1339i	−0.788062	−	0.454988i
$966$		0			0
$967$	6.35617	−	3.66974i	0.204401	−	0.118011i	−0.394306	−	0.918979i	$-0.629015\pi$
$967$	6.35617	−	3.66974i	0.204401	−	0.118011i	0.598707	+	0.800968i	$0.295682\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−39.9568			−1.28228			−0.641138	−	0.767425i	$-0.721537\pi$
$971$	−39.9568			−1.28228			−0.641138	+	0.767425i	$0.721537\pi$
$972$		0			0
$973$	79.4710			2.54772
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.03700	−	4.06281i	0.225133	−	0.129981i	−0.383192	−	0.923669i	$-0.625175\pi$
$977$	7.03700	−	4.06281i	0.225133	−	0.129981i	0.608325	+	0.793688i	$0.291842\pi$
$978$		0			0
$979$	−17.9427	−	10.3592i	−0.573450	−	0.331082i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.20579	−	10.7487i	0.197934	−	0.342832i	−0.749924	−	0.661524i	$-0.769910\pi$
$983$	6.20579	−	10.7487i	0.197934	−	0.342832i	0.947858	+	0.318692i	$0.103243\pi$
$984$		0			0
$985$	24.5093	+	42.4514i	0.780931	+	1.35261i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	2.29110i		−	0.0728527i
$990$		0			0
$991$		−	30.6327i		−	0.973080i	−0.873658	−	0.486540i	$-0.838259\pi$
$991$		−	30.6327i		−	0.973080i	0.873658	−	0.486540i	$-0.161741\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.24073	−	2.14901i	−0.0393338	−	0.0681281i
$996$		0			0
$997$	−26.5182	+	45.9308i	−0.839839	+	1.45464i	0.0501902	+	0.998740i	$0.484017\pi$
$997$	−26.5182	+	45.9308i	−0.839839	+	1.45464i	−0.890029	+	0.455904i	$0.849316\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.s.j.1727.7		16
3.2	odd	2	inner	2592.2.s.j.1727.2		16
4.3	odd	2		2592.2.s.i.1727.7		16
9.2	odd	6		2592.2.c.b.2591.3	✓	16
9.4	even	3		2592.2.s.i.863.2		16
9.5	odd	6		2592.2.s.i.863.7		16
9.7	even	3		2592.2.c.b.2591.13	yes	16
12.11	even	2		2592.2.s.i.1727.2		16
36.7	odd	6		2592.2.c.b.2591.14	yes	16
36.11	even	6		2592.2.c.b.2591.4	yes	16
36.23	even	6	inner	2592.2.s.j.863.7		16
36.31	odd	6	inner	2592.2.s.j.863.2		16
72.11	even	6		5184.2.c.l.5183.14		16
72.29	odd	6		5184.2.c.l.5183.13		16
72.43	odd	6		5184.2.c.l.5183.4		16
72.61	even	6		5184.2.c.l.5183.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2592.2.c.b.2591.3	✓	16	9.2	odd	6
2592.2.c.b.2591.4	yes	16	36.11	even	6
2592.2.c.b.2591.13	yes	16	9.7	even	3
2592.2.c.b.2591.14	yes	16	36.7	odd	6
2592.2.s.i.863.2		16	9.4	even	3
2592.2.s.i.863.7		16	9.5	odd	6
2592.2.s.i.1727.2		16	12.11	even	2
2592.2.s.i.1727.7		16	4.3	odd	2
2592.2.s.j.863.2		16	36.31	odd	6	inner
2592.2.s.j.863.7		16	36.23	even	6	inner
2592.2.s.j.1727.2		16	3.2	odd	2	inner
2592.2.s.j.1727.7		16	1.1	even	1	trivial
5184.2.c.l.5183.3		16	72.61	even	6
5184.2.c.l.5183.4		16	72.43	odd	6
5184.2.c.l.5183.13		16	72.29	odd	6
5184.2.c.l.5183.14		16	72.11	even	6

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:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.35218 - 1.35803i) q^{5} +(3.67803 + 2.12351i) q^{7} +O(q^{10})\)	\(q+(2.35218 - 1.35803i) q^{5} +(3.67803 + 2.12351i) q^{7} +(1.09921 - 1.90389i) q^{11} +(-1.25749 - 2.17803i) q^{13} +7.93806i q^{17} -5.13799i q^{19} +(0.868614 + 1.50448i) q^{23} +(1.18849 - 2.05853i) q^{25} +(0.230858 + 0.133286i) q^{29} +(8.69251 - 5.01862i) q^{31} +11.5352 q^{35} +9.24703 q^{37} +(-2.18363 + 1.26072i) q^{41} +(-1.14214 - 0.659412i) q^{43} +(-0.860601 + 1.49061i) q^{47} +(5.51862 + 9.55853i) q^{49} +0.306989i q^{53} -5.97105i q^{55} +(-5.83153 - 10.1005i) q^{59} +(-4.64214 + 8.04041i) q^{61} +(-5.91567 - 3.41542i) q^{65} +(-5.59895 + 3.23255i) q^{67} -9.46463 q^{71} +6.62301 q^{73} +(8.08587 - 4.66838i) q^{77} +(-9.83464 - 5.67803i) q^{79} +(-6.41148 + 11.1050i) q^{83} +(10.7801 + 18.6717i) q^{85} -9.42422i q^{89} -10.6812i q^{91} +(-6.97754 - 12.0855i) q^{95} +(-4.12766 + 7.14932i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7}+O(q^{10}) \) 16 * q + 12 * q^7	\( 16 q + 12 q^{7} + 4 q^{13} + 24 q^{25} + 72 q^{31} + 72 q^{37} + 84 q^{43} + 24 q^{49} + 28 q^{61} + 36 q^{67} + 96 q^{73} + 12 q^{79} + 12 q^{85} + 16 q^{97}+O(q^{100}) \) 16 * q + 12 * q^7 + 4 * q^13 + 24 * q^25 + 72 * q^31 + 72 * q^37 + 84 * q^43 + 24 * q^49 + 28 * q^61 + 36 * q^67 + 96 * q^73 + 12 * q^79 + 12 * q^85 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more