LMFDB - Embedded newform 3240.2.q.bd.2161.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3240,2,Mod(1081,3240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3240, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3240.1081");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3240 = 2^{3} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3240.q (of order $3$, 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:	$25.8715302549$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2161.2
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	3240.2161
Dual form			3240.2.q.bd.1081.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{5} +(1.18614 - 2.05446i) q^{7} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{5} +(1.18614 - 2.05446i) q^{7} +(-1.68614 + 2.92048i) q^{11} +(-1.18614 - 2.05446i) q^{13} -4.74456 q^{17} +1.00000 q^{19} +(-0.186141 - 0.322405i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.68614 + 2.92048i) q^{29} +(3.05842 + 5.29734i) q^{31} +2.37228 q^{35} +6.00000 q^{37} +(5.87228 + 10.1711i) q^{41} +(-3.37228 + 5.84096i) q^{43} +(-1.81386 + 3.14170i) q^{47} +(0.686141 + 1.18843i) q^{49} +7.11684 q^{53} -3.37228 q^{55} +(2.50000 + 4.33013i) q^{59} +(-0.627719 + 1.08724i) q^{61} +(1.18614 - 2.05446i) q^{65} +(-5.37228 - 9.30506i) q^{67} -1.37228 q^{71} +3.25544 q^{73} +(4.00000 + 6.92820i) q^{77} +(-4.37228 + 7.57301i) q^{79} +(-5.00000 + 8.66025i) q^{83} +(-2.37228 - 4.10891i) q^{85} -1.37228 q^{89} -5.62772 q^{91} +(0.500000 + 0.866025i) q^{95} +(-3.37228 + 5.84096i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - q^{7}+O(q^{10}) $ 4 * q + 2 * q^5 - q^7	$ 4 q + 2 q^{5} - q^{7} - q^{11} + q^{13} + 4 q^{17} + 4 q^{19} + 5 q^{23} - 2 q^{25} - q^{29} - 5 q^{31} - 2 q^{35} + 24 q^{37} + 12 q^{41} - 2 q^{43} - 13 q^{47} - 3 q^{49} - 6 q^{53} - 2 q^{55} + 10 q^{59} - 14 q^{61} - q^{65} - 10 q^{67} + 6 q^{71} + 36 q^{73} + 16 q^{77} - 6 q^{79} - 20 q^{83} + 2 q^{85} + 6 q^{89} - 34 q^{91} + 2 q^{95} - 2 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 - q^7 - q^11 + q^13 + 4 * q^17 + 4 * q^19 + 5 * q^23 - 2 * q^25 - q^29 - 5 * q^31 - 2 * q^35 + 24 * q^37 + 12 * q^41 - 2 * q^43 - 13 * q^47 - 3 * q^49 - 6 * q^53 - 2 * q^55 + 10 * q^59 - 14 * q^61 - q^65 - 10 * q^67 + 6 * q^71 + 36 * q^73 + 16 * q^77 - 6 * q^79 - 20 * q^83 + 2 * q^85 + 6 * q^89 - 34 * q^91 + 2 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times$.

$n$	$1297$	$1621$	$2431$	$3161$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	1.18614	−	2.05446i	0.448319	−	0.776511i	−0.549958	−	0.835192i	$-0.685356\pi$
$7$	1.18614	−	2.05446i	0.448319	−	0.776511i	0.998277	+	0.0586811i	$0.0186895\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.68614	+	2.92048i	−0.508391	+	0.880558i	0.491562	+	0.870842i	$0.336426\pi$
$11$	−1.68614	+	2.92048i	−0.508391	+	0.880558i	−0.999953	+	0.00971581i	$0.996907\pi$
$12$		0			0
$13$	−1.18614	−	2.05446i	−0.328976	−	0.569804i	0.653333	−	0.757071i	$-0.273370\pi$
$13$	−1.18614	−	2.05446i	−0.328976	−	0.569804i	−0.982309	+	0.187267i	$0.940037\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.74456			−1.15073			−0.575363	−	0.817898i	$-0.695139\pi$
$17$	−4.74456			−1.15073			−0.575363	+	0.817898i	$0.695139\pi$
$18$		0			0
$19$	1.00000			0.229416			0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000			0.229416			0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.186141	−	0.322405i	−0.0388130	−	0.0672261i	0.845966	−	0.533236i	$-0.179024\pi$
$23$	−0.186141	−	0.322405i	−0.0388130	−	0.0672261i	−0.884779	+	0.466010i	$0.845691\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.68614	+	2.92048i	−0.313108	+	0.542320i	−0.979034	−	0.203699i	$-0.934704\pi$
$29$	−1.68614	+	2.92048i	−0.313108	+	0.542320i	0.665925	+	0.746019i	$0.268037\pi$
$30$		0			0
$31$	3.05842	+	5.29734i	0.549309	+	0.951431i	0.998322	+	0.0579057i	$0.0184423\pi$
$31$	3.05842	+	5.29734i	0.549309	+	0.951431i	−0.449013	+	0.893525i	$0.648224\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.37228			0.400989
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.87228	+	10.1711i	0.917096	+	1.58846i	0.803803	+	0.594896i	$0.202807\pi$
$41$	5.87228	+	10.1711i	0.917096	+	1.58846i	0.113293	+	0.993562i	$0.463860\pi$
$42$		0			0
$43$	−3.37228	+	5.84096i	−0.514268	+	0.890738i	0.485595	+	0.874184i	$0.338603\pi$
$43$	−3.37228	+	5.84096i	−0.514268	+	0.890738i	−0.999863	+	0.0165545i	$0.994730\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.81386	+	3.14170i	−0.264579	+	0.458264i	−0.967453	−	0.253050i	$-0.918566\pi$
$47$	−1.81386	+	3.14170i	−0.264579	+	0.458264i	0.702875	+	0.711314i	$0.251900\pi$
$48$		0			0
$49$	0.686141	+	1.18843i	0.0980201	+	0.169776i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.11684			0.977574			0.488787	−	0.872403i	$-0.337440\pi$
$53$	7.11684			0.977574			0.488787	+	0.872403i	$0.337440\pi$
$54$		0			0
$55$	−3.37228			−0.454718
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	0.981608	−	0.190909i	$-0.0611434\pi$
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	−0.656136	+	0.754643i	$0.727810\pi$
$60$		0			0
$61$	−0.627719	+	1.08724i	−0.0803711	+	0.139207i	−0.903409	−	0.428779i	$-0.858944\pi$
$61$	−0.627719	+	1.08724i	−0.0803711	+	0.139207i	0.823038	+	0.567986i	$0.192277\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.18614	−	2.05446i	0.147123	−	0.254824i
$66$		0			0
$67$	−5.37228	−	9.30506i	−0.656329	−	1.13679i	−0.981559	−	0.191160i	$-0.938775\pi$
$67$	−5.37228	−	9.30506i	−0.656329	−	1.13679i	0.325230	−	0.945635i	$-0.394558\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.37228			−0.162860			−0.0814299	−	0.996679i	$-0.525949\pi$
$71$	−1.37228			−0.162860			−0.0814299	+	0.996679i	$0.525949\pi$
$72$		0			0
$73$	3.25544			0.381020			0.190510	−	0.981685i	$-0.438986\pi$
$73$	3.25544			0.381020			0.190510	+	0.981685i	$0.438986\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.00000	+	6.92820i	0.455842	+	0.789542i
$78$		0			0
$79$	−4.37228	+	7.57301i	−0.491920	+	0.852031i	−0.999957	−	0.00930489i	$-0.997038\pi$
$79$	−4.37228	+	7.57301i	−0.491920	+	0.852031i	0.508037	+	0.861335i	$0.330371\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.00000	+	8.66025i	−0.548821	+	0.950586i	0.449534	+	0.893263i	$0.351590\pi$
$83$	−5.00000	+	8.66025i	−0.548821	+	0.950586i	−0.998356	+	0.0573233i	$0.981743\pi$
$84$		0			0
$85$	−2.37228	−	4.10891i	−0.257310	−	0.445674i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.37228			−0.145462			−0.0727308	−	0.997352i	$-0.523171\pi$
$89$	−1.37228			−0.145462			−0.0727308	+	0.997352i	$0.523171\pi$
$90$		0			0
$91$	−5.62772			−0.589945
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$		0			0
$97$	−3.37228	+	5.84096i	−0.342403	+	0.593060i	−0.984878	−	0.173247i	$-0.944574\pi$
$97$	−3.37228	+	5.84096i	−0.342403	+	0.593060i	0.642475	+	0.766306i	$0.277908\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.43070	−	11.1383i	0.639879	−	1.10830i	−0.345580	−	0.938389i	$-0.612318\pi$
$101$	6.43070	−	11.1383i	0.639879	−	1.10830i	0.985459	−	0.169913i	$-0.0543488\pi$
$102$		0			0
$103$	−8.55842	−	14.8236i	−0.843286	−	1.46061i	−0.887101	−	0.461575i	$-0.847284\pi$
$103$	−8.55842	−	14.8236i	−0.843286	−	1.46061i	0.0438147	−	0.999040i	$-0.486049\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.00000			0.580042			0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000			0.580042			0.290021	+	0.957020i	$0.406338\pi$
$108$		0			0
$109$	18.1168			1.73528			0.867639	−	0.497194i	$-0.165636\pi$
$109$	18.1168			1.73528			0.867639	+	0.497194i	$0.165636\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.62772	+	2.81929i	0.153123	+	0.265217i	0.932374	−	0.361495i	$-0.117734\pi$
$113$	1.62772	+	2.81929i	0.153123	+	0.265217i	−0.779251	+	0.626712i	$0.784400\pi$
$114$		0			0
$115$	0.186141	−	0.322405i	0.0173577	−	0.0300644i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−5.62772	+	9.74749i	−0.515892	+	0.893551i
$120$		0			0
$121$	−0.186141	−	0.322405i	−0.0169219	−	0.0293096i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	15.8614			1.40747			0.703736	−	0.710461i	$-0.251514\pi$
$127$	15.8614			1.40747			0.703736	+	0.710461i	$0.251514\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.87228	+	15.3672i	0.775175	+	1.34264i	0.934696	+	0.355448i	$0.115672\pi$
$131$	8.87228	+	15.3672i	0.775175	+	1.34264i	−0.159521	+	0.987194i	$0.550995\pi$
$132$		0			0
$133$	1.18614	−	2.05446i	0.102851	−	0.178144i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.37228	+	14.5012i	−0.715292	+	1.23892i	0.247554	+	0.968874i	$0.420373\pi$
$137$	−8.37228	+	14.5012i	−0.715292	+	1.23892i	−0.962847	+	0.270049i	$0.912960\pi$
$138$		0			0
$139$	−7.50000	−	12.9904i	−0.636142	−	1.10183i	−0.986272	−	0.165129i	$-0.947196\pi$
$139$	−7.50000	−	12.9904i	−0.636142	−	1.10183i	0.350130	−	0.936701i	$-0.386137\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.00000			0.668994
$144$		0			0
$145$	−3.37228			−0.280053
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.74456	−	3.02167i	−0.142920	−	0.247545i	0.785675	−	0.618640i	$-0.212316\pi$
$149$	−1.74456	−	3.02167i	−0.142920	−	0.247545i	−0.928595	+	0.371095i	$0.878983\pi$
$150$		0			0
$151$	−9.31386	+	16.1321i	−0.757951	+	1.31281i	0.185943	+	0.982561i	$0.440466\pi$
$151$	−9.31386	+	16.1321i	−0.757951	+	1.31281i	−0.943894	+	0.330249i	$0.892867\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.05842	+	5.29734i	−0.245658	+	0.425493i
$156$		0			0
$157$	2.93070	+	5.07613i	0.233896	+	0.405119i	0.958951	−	0.283571i	$-0.0915193\pi$
$157$	2.93070	+	5.07613i	0.233896	+	0.405119i	−0.725056	+	0.688690i	$0.758186\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.883156			−0.0696024
$162$		0			0
$163$	−13.4891			−1.05655			−0.528275	−	0.849073i	$-0.677161\pi$
$163$	−13.4891			−1.05655			−0.528275	+	0.849073i	$0.677161\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	3.68614	−	6.38458i	0.283549	−	0.491122i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.93070	+	12.0043i	−0.526932	+	0.912672i	0.472576	+	0.881290i	$0.343324\pi$
$173$	−6.93070	+	12.0043i	−0.526932	+	0.912672i	−0.999507	+	0.0313823i	$0.990009\pi$
$174$		0			0
$175$	1.18614	+	2.05446i	0.0896638	+	0.155302i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	15.7446			1.17680			0.588402	−	0.808569i	$-0.299757\pi$
$179$	15.7446			1.17680			0.588402	+	0.808569i	$0.299757\pi$
$180$		0			0
$181$	14.8614			1.10464			0.552320	−	0.833632i	$-0.313743\pi$
$181$	14.8614			1.10464			0.552320	+	0.833632i	$0.313743\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	8.00000	−	13.8564i	0.585018	−	1.01328i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.68614	+	9.84868i	−0.411435	+	0.712626i	−0.995047	−	0.0994067i	$-0.968306\pi$
$191$	−5.68614	+	9.84868i	−0.411435	+	0.712626i	0.583612	+	0.812033i	$0.301639\pi$
$192$		0			0
$193$	5.37228	+	9.30506i	0.386705	+	0.669793i	0.992004	−	0.126205i	$-0.0402797\pi$
$193$	5.37228	+	9.30506i	0.386705	+	0.669793i	−0.605299	+	0.795998i	$0.706946\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.37228			0.454006			0.227003	−	0.973894i	$-0.427107\pi$
$197$	6.37228			0.454006			0.227003	+	0.973894i	$0.427107\pi$
$198$		0			0
$199$	−9.48913			−0.672666			−0.336333	−	0.941743i	$-0.609187\pi$
$199$	−9.48913			−0.672666			−0.336333	+	0.941743i	$0.609187\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.00000	+	6.92820i	0.280745	+	0.486265i
$204$		0			0
$205$	−5.87228	+	10.1711i	−0.410138	+	0.710380i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.68614	+	2.92048i	−0.116633	+	0.202014i
$210$		0			0
$211$	−8.50000	−	14.7224i	−0.585164	−	1.01353i	−0.994855	−	0.101310i	$-0.967697\pi$
$211$	−8.50000	−	14.7224i	−0.585164	−	1.01353i	0.409691	−	0.912224i	$-0.365637\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.74456			−0.459975
$216$		0			0
$217$	14.5109			0.985062
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.62772	+	9.74749i	0.378561	+	0.655687i
$222$		0			0
$223$	−1.25544	+	2.17448i	−0.0840703	+	0.145614i	−0.904995	−	0.425423i	$-0.860125\pi$
$223$	−1.25544	+	2.17448i	−0.0840703	+	0.145614i	0.820924	+	0.571037i	$0.193459\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.74456	−	4.75372i	0.182163	−	0.315516i	−0.760454	−	0.649392i	$-0.775023\pi$
$227$	2.74456	−	4.75372i	0.182163	−	0.315516i	0.942617	+	0.333876i	$0.108357\pi$
$228$		0			0
$229$	2.62772	+	4.55134i	0.173645	+	0.300761i	0.939691	−	0.342024i	$-0.111112\pi$
$229$	2.62772	+	4.55134i	0.173645	+	0.300761i	−0.766047	+	0.642785i	$0.777779\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−20.2337			−1.32555			−0.662776	−	0.748817i	$-0.730622\pi$
$233$	−20.2337			−1.32555			−0.662776	+	0.748817i	$0.730622\pi$
$234$		0			0
$235$	−3.62772			−0.236646
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.11684	+	12.3267i	0.460350	+	0.797350i	0.998978	−	0.0451935i	$-0.0143905\pi$
$239$	7.11684	+	12.3267i	0.460350	+	0.797350i	−0.538628	+	0.842544i	$0.681057\pi$
$240$		0			0
$241$	−14.8030	+	25.6395i	−0.953544	+	1.65159i	−0.215879	+	0.976420i	$0.569262\pi$
$241$	−14.8030	+	25.6395i	−0.953544	+	1.65159i	−0.737665	+	0.675167i	$0.764072\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.686141	+	1.18843i	−0.0438359	+	0.0759260i
$246$		0			0
$247$	−1.18614	−	2.05446i	−0.0754723	−	0.130722i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−15.8614			−1.00116			−0.500582	−	0.865689i	$-0.666880\pi$
$251$	−15.8614			−1.00116			−0.500582	+	0.865689i	$0.666880\pi$
$252$		0			0
$253$	1.25544			0.0789287
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.7446	+	20.3422i	0.732606	+	1.26891i	0.955766	+	0.294128i	$0.0950294\pi$
$257$	11.7446	+	20.3422i	0.732606	+	1.26891i	−0.223160	+	0.974782i	$0.571637\pi$
$258$		0			0
$259$	7.11684	−	12.3267i	0.442219	−	0.765946i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.55842	+	11.3595i	−0.404410	+	0.700458i	−0.994253	−	0.107060i	$-0.965856\pi$
$263$	−6.55842	+	11.3595i	−0.404410	+	0.700458i	0.589843	+	0.807518i	$0.299190\pi$
$264$		0			0
$265$	3.55842	+	6.16337i	0.218592	+	0.378613i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.1168			−0.738777			−0.369389	−	0.929275i	$-0.620433\pi$
$269$	−12.1168			−0.738777			−0.369389	+	0.929275i	$0.620433\pi$
$270$		0			0
$271$	−20.7446			−1.26014			−0.630071	−	0.776537i	$-0.716974\pi$
$271$	−20.7446			−1.26014			−0.630071	+	0.776537i	$0.716974\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.68614	−	2.92048i	−0.101678	−	0.176112i
$276$		0			0
$277$	8.55842	−	14.8236i	0.514226	−	0.890665i	−0.485638	−	0.874160i	$-0.661413\pi$
$277$	8.55842	−	14.8236i	0.514226	−	0.890665i	0.999864	−	0.0165051i	$-0.00525398\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.81386	−	10.0699i	0.346826	−	0.600720i	−0.638858	−	0.769325i	$-0.720593\pi$
$281$	5.81386	−	10.0699i	0.346826	−	0.600720i	0.985684	+	0.168605i	$0.0539262\pi$
$282$		0			0
$283$	−2.62772	−	4.55134i	−0.156202	−	0.270549i	0.777294	−	0.629137i	$-0.216592\pi$
$283$	−2.62772	−	4.55134i	−0.156202	−	0.270549i	−0.933496	+	0.358588i	$0.883258\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	27.8614			1.64461
$288$		0			0
$289$	5.51087			0.324169
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.93070	+	12.0043i	0.404896	+	0.701300i	0.994309	−	0.106531i	$-0.0339744\pi$
$293$	6.93070	+	12.0043i	0.404896	+	0.701300i	−0.589413	+	0.807832i	$0.700641\pi$
$294$		0			0
$295$	−2.50000	+	4.33013i	−0.145556	+	0.252110i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.441578	+	0.764836i	−0.0255371	+	0.0442316i
$300$		0			0
$301$	8.00000	+	13.8564i	0.461112	+	0.798670i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.25544			−0.0718861
$306$		0			0
$307$	−10.7446			−0.613225			−0.306612	−	0.951834i	$-0.599195\pi$
$307$	−10.7446			−0.613225			−0.306612	+	0.951834i	$0.599195\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.43070	−	9.40625i	−0.307947	−	0.533380i	0.669966	−	0.742392i	$-0.266309\pi$
$311$	−5.43070	−	9.40625i	−0.307947	−	0.533380i	−0.977913	+	0.209012i	$0.932975\pi$
$312$		0			0
$313$	2.00000	−	3.46410i	0.113047	−	0.195803i	−0.803951	−	0.594696i	$-0.797272\pi$
$313$	2.00000	−	3.46410i	0.113047	−	0.195803i	0.916997	+	0.398894i	$0.130606\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.18614	+	14.1788i	−0.459779	+	0.796361i	−0.998949	−	0.0458359i	$-0.985405\pi$
$317$	−8.18614	+	14.1788i	−0.459779	+	0.796361i	0.539170	+	0.842197i	$0.318738\pi$
$318$		0			0
$319$	−5.68614	−	9.84868i	−0.318363	−	0.551420i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−4.74456			−0.263995
$324$		0			0
$325$	2.37228			0.131590
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.30298	+	7.45299i	0.237231	+	0.410897i
$330$		0			0
$331$	−9.68614	+	16.7769i	−0.532398	+	0.922141i	0.466886	+	0.884318i	$0.345376\pi$
$331$	−9.68614	+	16.7769i	−0.532398	+	0.922141i	−0.999284	+	0.0378236i	$0.987957\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.37228	−	9.30506i	0.293519	−	0.508390i
$336$		0			0
$337$	−0.372281	−	0.644810i	−0.0202795	−	0.0351250i	0.855708	−	0.517460i	$-0.173122\pi$
$337$	−0.372281	−	0.644810i	−0.0202795	−	0.0351250i	−0.875987	+	0.482335i	$0.839789\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−20.6277			−1.11705
$342$		0			0
$343$	19.8614			1.07242
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.1168	−	26.1831i	−0.811515	−	1.40558i	−0.911804	−	0.410626i	$-0.865310\pi$
$347$	−15.1168	−	26.1831i	−0.811515	−	1.40558i	0.100289	−	0.994958i	$-0.468023\pi$
$348$		0			0
$349$	12.6861	−	21.9730i	0.679074	−	1.17619i	−0.296187	−	0.955130i	$-0.595715\pi$
$349$	12.6861	−	21.9730i	0.679074	−	1.17619i	0.975260	−	0.221060i	$-0.0709516\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.4891	−	21.6318i	0.664729	−	1.15134i	−0.314630	−	0.949215i	$-0.601880\pi$
$353$	12.4891	−	21.6318i	0.664729	−	1.15134i	0.979359	−	0.202130i	$-0.0647864\pi$
$354$		0			0
$355$	−0.686141	−	1.18843i	−0.0364166	−	0.0630753i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.6277			0.560910			0.280455	−	0.959867i	$-0.409515\pi$
$359$	10.6277			0.560910			0.280455	+	0.959867i	$0.409515\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.62772	+	2.81929i	0.0851987	+	0.147568i
$366$		0			0
$367$	−2.11684	+	3.66648i	−0.110498	+	0.191389i	−0.915971	−	0.401244i	$-0.868578\pi$
$367$	−2.11684	+	3.66648i	−0.110498	+	0.191389i	0.805473	+	0.592633i	$0.201911\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	8.44158	−	14.6212i	0.438265	−	0.759097i
$372$		0			0
$373$	−0.372281	−	0.644810i	−0.0192760	−	0.0333870i	0.856226	−	0.516601i	$-0.172803\pi$
$373$	−0.372281	−	0.644810i	−0.0192760	−	0.0333870i	−0.875502	+	0.483214i	$0.839469\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.00000			0.412021
$378$		0			0
$379$	25.3505			1.30217			0.651085	−	0.759005i	$-0.274314\pi$
$379$	25.3505			1.30217			0.651085	+	0.759005i	$0.274314\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.81386	−	11.8020i	−0.348172	−	0.603052i	0.637753	−	0.770241i	$-0.279864\pi$
$383$	−6.81386	−	11.8020i	−0.348172	−	0.603052i	−0.985925	+	0.167190i	$0.946531\pi$
$384$		0			0
$385$	−4.00000	+	6.92820i	−0.203859	+	0.353094i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.62772	−	8.01544i	0.234635	−	0.406399i	−0.724532	−	0.689241i	$-0.757944\pi$
$389$	4.62772	−	8.01544i	0.234635	−	0.406399i	0.959166	+	0.282842i	$0.0912773\pi$
$390$		0			0
$391$	0.883156	+	1.52967i	0.0446631	+	0.0773588i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.74456			−0.439987
$396$		0			0
$397$	34.0000			1.70641			0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000			1.70641			0.853206	+	0.521575i	$0.174655\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.67527	−	13.2940i	−0.383284	−	0.663868i	0.608245	−	0.793749i	$-0.291874\pi$
$401$	−7.67527	−	13.2940i	−0.383284	−	0.663868i	−0.991530	+	0.129881i	$0.958540\pi$
$402$		0			0
$403$	7.25544	−	12.5668i	0.361419	−	0.625996i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.1168	+	17.5229i	−0.501473	+	0.868577i
$408$		0			0
$409$	7.81386	+	13.5340i	0.386370	+	0.669213i	0.991958	−	0.126565i	$-0.0403953\pi$
$409$	7.81386	+	13.5340i	0.386370	+	0.669213i	−0.605588	+	0.795778i	$0.707062\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	11.8614			0.583662
$414$		0			0
$415$	−10.0000			−0.490881
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5.48913	−	9.50744i	−0.268161	−	0.464469i	0.700226	−	0.713922i	$-0.253083\pi$
$419$	−5.48913	−	9.50744i	−0.268161	−	0.464469i	−0.968387	+	0.249452i	$0.919749\pi$
$420$		0			0
$421$	−11.3139	+	19.5962i	−0.551404	+	0.955059i	0.446770	+	0.894649i	$0.352574\pi$
$421$	−11.3139	+	19.5962i	−0.551404	+	0.955059i	−0.998174	+	0.0604104i	$0.980759\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.37228	−	4.10891i	0.115073	−	0.199311i
$426$		0			0
$427$	1.48913	+	2.57924i	0.0720638	+	0.124818i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.3723			−0.740457			−0.370228	−	0.928941i	$-0.620721\pi$
$431$	−15.3723			−0.740457			−0.370228	+	0.928941i	$0.620721\pi$
$432$		0			0
$433$	39.2119			1.88441			0.942203	−	0.335043i	$-0.108751\pi$
$433$	39.2119			1.88441			0.942203	+	0.335043i	$0.108751\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.186141	−	0.322405i	−0.00890432	−	0.0154227i
$438$		0			0
$439$	−15.5475	+	26.9291i	−0.742044	+	1.28526i	0.209519	+	0.977805i	$0.432810\pi$
$439$	−15.5475	+	26.9291i	−0.742044	+	1.28526i	−0.951563	+	0.307453i	$0.900523\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.48913	−	14.7036i	0.403331	−	0.698589i	−0.590795	−	0.806822i	$-0.701186\pi$
$443$	8.48913	−	14.7036i	0.403331	−	0.698589i	0.994126	+	0.108233i	$0.0345192\pi$
$444$		0			0
$445$	−0.686141	−	1.18843i	−0.0325262	−	0.0563370i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	22.7228			1.07236			0.536178	−	0.844105i	$-0.319868\pi$
$449$	22.7228			1.07236			0.536178	+	0.844105i	$0.319868\pi$
$450$		0			0
$451$	−39.6060			−1.86497
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.81386	−	4.87375i	−0.131916	−	0.228485i
$456$		0			0
$457$	20.1168	−	34.8434i	0.941026	−	1.62991i	0.177508	−	0.984119i	$-0.443197\pi$
$457$	20.1168	−	34.8434i	0.941026	−	1.62991i	0.763519	−	0.645786i	$-0.223470\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.94158	−	12.0232i	0.323302	−	0.559975i	−0.657866	−	0.753135i	$-0.728541\pi$
$461$	6.94158	−	12.0232i	0.323302	−	0.559975i	0.981167	+	0.193161i	$0.0618739\pi$
$462$		0			0
$463$	10.9307	+	18.9325i	0.507993	+	0.879869i	0.999957	+	0.00925409i	$0.00294571\pi$
$463$	10.9307	+	18.9325i	0.507993	+	0.879869i	−0.491964	+	0.870615i	$0.663721\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	18.2337			0.843754			0.421877	−	0.906653i	$-0.361371\pi$
$467$	18.2337			0.843754			0.421877	+	0.906653i	$0.361371\pi$
$468$		0			0
$469$	−25.4891			−1.17698
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11.3723	−	19.6974i	−0.522898	−	0.905686i
$474$		0			0
$475$	−0.500000	+	0.866025i	−0.0229416	+	0.0397360i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.0584	+	20.8858i	−0.550963	+	0.954297i	0.447242	+	0.894413i	$0.352406\pi$
$479$	−12.0584	+	20.8858i	−0.550963	+	0.954297i	−0.998205	+	0.0598836i	$0.980927\pi$
$480$		0			0
$481$	−7.11684	−	12.3267i	−0.324500	−	0.562051i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.74456			−0.306255
$486$		0			0
$487$	−20.6060			−0.933746			−0.466873	−	0.884324i	$-0.654619\pi$
$487$	−20.6060			−0.933746			−0.466873	+	0.884324i	$0.654619\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.98913	+	17.3017i	0.450803	+	0.780814i	0.998436	−	0.0559050i	$-0.0178044\pi$
$491$	9.98913	+	17.3017i	0.450803	+	0.780814i	−0.547633	+	0.836719i	$0.684471\pi$
$492$		0			0
$493$	8.00000	−	13.8564i	0.360302	−	0.624061i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.62772	+	2.81929i	−0.0730132	+	0.126463i
$498$		0			0
$499$	−4.12772	−	7.14942i	−0.184782	−	0.320052i	0.758721	−	0.651416i	$-0.225825\pi$
$499$	−4.12772	−	7.14942i	−0.184782	−	0.320052i	−0.943503	+	0.331364i	$0.892491\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	34.9783			1.55960			0.779802	−	0.626027i	$-0.215320\pi$
$503$	34.9783			1.55960			0.779802	+	0.626027i	$0.215320\pi$
$504$		0			0
$505$	12.8614			0.572325
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−19.0000	−	32.9090i	−0.842160	−	1.45866i	−0.888065	−	0.459718i	$-0.847950\pi$
$509$	−19.0000	−	32.9090i	−0.842160	−	1.45866i	0.0459045	−	0.998946i	$-0.485383\pi$
$510$		0			0
$511$	3.86141	−	6.68815i	0.170819	−	0.295866i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.55842	−	14.8236i	0.377129	−	0.653207i
$516$		0			0
$517$	−6.11684	−	10.5947i	−0.269018	−	0.465954i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.1168			−0.749903			−0.374951	−	0.927045i	$-0.622341\pi$
$521$	−17.1168			−0.749903			−0.374951	+	0.927045i	$0.622341\pi$
$522$		0			0
$523$	−5.76631			−0.252143			−0.126072	−	0.992021i	$-0.540237\pi$
$523$	−5.76631			−0.252143			−0.126072	+	0.992021i	$0.540237\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.5109	−	25.1336i	−0.632104	−	1.09484i
$528$		0			0
$529$	11.4307	−	19.7986i	0.496987	−	0.860807i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	13.9307	−	24.1287i	0.603406	−	1.04513i
$534$		0			0
$535$	3.00000	+	5.19615i	0.129701	+	0.224649i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4.62772			−0.199330
$540$		0			0
$541$	−38.3505			−1.64882			−0.824409	−	0.565994i	$-0.808492\pi$
$541$	−38.3505			−1.64882			−0.824409	+	0.565994i	$0.808492\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9.05842	+	15.6896i	0.388020	+	0.672071i
$546$		0			0
$547$	20.0000	−	34.6410i	0.855138	−	1.48114i	−0.0213785	−	0.999771i	$-0.506805\pi$
$547$	20.0000	−	34.6410i	0.855138	−	1.48114i	0.876517	−	0.481371i	$-0.159861\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.68614	+	2.92048i	−0.0718320	+	0.124417i
$552$		0			0
$553$	10.3723	+	17.9653i	0.441074	+	0.763963i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.60597			−0.364647			−0.182323	−	0.983239i	$-0.558362\pi$
$557$	−8.60597			−0.364647			−0.182323	+	0.983239i	$0.558362\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.1168	+	20.9870i	0.510664	+	0.884496i	0.999924	+	0.0123579i	$0.00393375\pi$
$563$	12.1168	+	20.9870i	0.510664	+	0.884496i	−0.489260	+	0.872138i	$0.662733\pi$
$564$		0			0
$565$	−1.62772	+	2.81929i	−0.0684786	+	0.118608i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.6168	−	37.4415i	0.906225	−	1.56963i	0.0869612	−	0.996212i	$-0.472284\pi$
$569$	21.6168	−	37.4415i	0.906225	−	1.56963i	0.819264	−	0.573416i	$-0.194382\pi$
$570$		0			0
$571$	−7.05842	−	12.2255i	−0.295386	−	0.511623i	0.679689	−	0.733501i	$-0.262115\pi$
$571$	−7.05842	−	12.2255i	−0.295386	−	0.511623i	−0.975075	+	0.221877i	$0.928782\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.372281			0.0155252
$576$		0			0
$577$	13.4891			0.561560			0.280780	−	0.959772i	$-0.409407\pi$
$577$	13.4891			0.561560			0.280780	+	0.959772i	$0.409407\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	11.8614	+	20.5446i	0.492094	+	0.852332i
$582$		0			0
$583$	−12.0000	+	20.7846i	−0.496989	+	0.860811i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.0000	−	25.9808i	0.619116	−	1.07234i	−0.370531	−	0.928820i	$-0.620824\pi$
$587$	15.0000	−	25.9808i	0.619116	−	1.07234i	0.989647	−	0.143521i	$-0.0458424\pi$
$588$		0			0
$589$	3.05842	+	5.29734i	0.126020	+	0.218273i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16.9783			−0.697213			−0.348607	−	0.937269i	$-0.613345\pi$
$593$	−16.9783			−0.697213			−0.348607	+	0.937269i	$0.613345\pi$
$594$		0			0
$595$	−11.2554			−0.461428
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−18.1753	−	31.4805i	−0.742621	−	1.28626i	−0.951298	−	0.308273i	$-0.900249\pi$
$599$	−18.1753	−	31.4805i	−0.742621	−	1.28626i	0.208677	−	0.977985i	$-0.433084\pi$
$600$		0			0
$601$	−6.50000	+	11.2583i	−0.265141	+	0.459237i	−0.967600	−	0.252486i	$-0.918752\pi$
$601$	−6.50000	+	11.2583i	−0.265141	+	0.459237i	0.702460	+	0.711723i	$0.252085\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.186141	−	0.322405i	0.00756769	−	0.0131076i
$606$		0			0
$607$	16.6277	+	28.8001i	0.674898	+	1.16896i	0.976499	+	0.215524i	$0.0691458\pi$
$607$	16.6277	+	28.8001i	0.674898	+	1.16896i	−0.301600	+	0.953434i	$0.597521\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.60597			0.348160
$612$		0			0
$613$	−33.3505			−1.34702			−0.673508	−	0.739180i	$-0.735213\pi$
$613$	−33.3505			−1.34702			−0.673508	+	0.739180i	$0.735213\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−21.8614	−	37.8651i	−0.880107	−	1.52439i	−0.851221	−	0.524807i	$-0.824137\pi$
$617$	−21.8614	−	37.8651i	−0.880107	−	1.52439i	−0.0288861	−	0.999583i	$-0.509196\pi$
$618$		0			0
$619$	19.1861	−	33.2314i	0.771156	−	1.33568i	−0.165774	−	0.986164i	$-0.553012\pi$
$619$	19.1861	−	33.2314i	0.771156	−	1.33568i	0.936930	−	0.349518i	$-0.113655\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.62772	+	2.81929i	−0.0652132	+	0.112953i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−28.4674			−1.13507
$630$		0			0
$631$	−36.6277			−1.45813			−0.729063	−	0.684446i	$-0.760044\pi$
$631$	−36.6277			−1.45813			−0.729063	+	0.684446i	$0.760044\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.93070	+	13.7364i	0.314720	+	0.545112i
$636$		0			0
$637$	1.62772	−	2.81929i	0.0644926	−	0.111704i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.19702	−	2.07329i	0.0472793	−	0.0818901i	−0.841417	−	0.540386i	$-0.818278\pi$
$641$	1.19702	−	2.07329i	0.0472793	−	0.0818901i	0.888697	+	0.458496i	$0.151612\pi$
$642$		0			0
$643$	−10.6277	−	18.4077i	−0.419116	−	0.725931i	0.576734	−	0.816932i	$-0.304327\pi$
$643$	−10.6277	−	18.4077i	−0.419116	−	0.725931i	−0.995851	+	0.0910009i	$0.970993\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−25.7228			−1.01127			−0.505634	−	0.862748i	$-0.668741\pi$
$647$	−25.7228			−1.01127			−0.505634	+	0.862748i	$0.668741\pi$
$648$		0			0
$649$	−16.8614			−0.661868
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.3723	−	21.4294i	−0.484165	−	0.838598i	0.515670	−	0.856787i	$-0.327543\pi$
$653$	−12.3723	−	21.4294i	−0.484165	−	0.838598i	−0.999835	+	0.0181894i	$0.994210\pi$
$654$		0			0
$655$	−8.87228	+	15.3672i	−0.346669	+	0.600448i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−23.7921	+	41.2091i	−0.926809	+	1.60528i	−0.138183	+	0.990407i	$0.544126\pi$
$659$	−23.7921	+	41.2091i	−0.926809	+	1.60528i	−0.788626	+	0.614874i	$0.789207\pi$
$660$		0			0
$661$	22.5475	+	39.0535i	0.876998	+	1.51901i	0.854619	+	0.519255i	$0.173791\pi$
$661$	22.5475	+	39.0535i	0.876998	+	1.51901i	0.0223789	+	0.999750i	$0.492876\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.37228			0.0919931
$666$		0			0
$667$	1.25544			0.0486107
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.11684	−	3.66648i	−0.0817199	−	0.141543i
$672$		0			0
$673$	0.255437	−	0.442430i	0.00984639	−	0.0170544i	−0.861060	−	0.508503i	$-0.830199\pi$
$673$	0.255437	−	0.442430i	0.00984639	−	0.0170544i	0.870907	+	0.491449i	$0.163532\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.5584	+	18.2877i	−0.405793	+	0.702854i	−0.994413	−	0.105555i	$-0.966338\pi$
$677$	−10.5584	+	18.2877i	−0.405793	+	0.702854i	0.588620	+	0.808410i	$0.299671\pi$
$678$		0			0
$679$	8.00000	+	13.8564i	0.307012	+	0.531760i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−38.2337			−1.46297			−0.731486	−	0.681857i	$-0.761173\pi$
$683$	−38.2337			−1.46297			−0.731486	+	0.681857i	$0.761173\pi$
$684$		0			0
$685$	−16.7446			−0.639777
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.44158	−	14.6212i	−0.321599	−	0.557025i
$690$		0			0
$691$	−20.6753	+	35.8106i	−0.786524	+	1.36230i	0.141560	+	0.989930i	$0.454788\pi$
$691$	−20.6753	+	35.8106i	−0.786524	+	1.36230i	−0.928084	+	0.372370i	$0.878545\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.50000	−	12.9904i	0.284491	−	0.492753i
$696$		0			0
$697$	−27.8614	−	48.2574i	−1.05533	−	1.82788i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	8.11684			0.306569			0.153284	−	0.988182i	$-0.451015\pi$
$701$	8.11684			0.306569			0.153284	+	0.988182i	$0.451015\pi$
$702$		0			0
$703$	6.00000			0.226294
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.2554	−	26.4232i	−0.573740	−	0.993746i
$708$		0			0
$709$	−9.23369	+	15.9932i	−0.346778	+	0.600638i	−0.985675	−	0.168655i	$-0.946058\pi$
$709$	−9.23369	+	15.9932i	−0.346778	+	0.600638i	0.638897	+	0.769292i	$0.279391\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.13859	−	1.97210i	0.0426407	−	0.0738558i
$714$		0			0
$715$	4.00000	+	6.92820i	0.149592	+	0.259100i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.3940			0.387632			0.193816	−	0.981038i	$-0.437914\pi$
$719$	10.3940			0.387632			0.193816	+	0.981038i	$0.437914\pi$
$720$		0			0
$721$	−40.6060			−1.51225
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.68614	−	2.92048i	−0.0626217	−	0.108464i
$726$		0			0
$727$	23.5584	−	40.8044i	0.873734	−	1.51335i	0.0156277	−	0.999878i	$-0.495025\pi$
$727$	23.5584	−	40.8044i	0.873734	−	1.51335i	0.858106	−	0.513473i	$-0.171641\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	16.0000	−	27.7128i	0.591781	−	1.02500i
$732$		0			0
$733$	14.4891	+	25.0959i	0.535168	+	0.926938i	0.999155	+	0.0410963i	$0.0130851\pi$
$733$	14.4891	+	25.0959i	0.535168	+	0.926938i	−0.463987	+	0.885842i	$0.653582\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	36.2337			1.33469
$738$		0			0
$739$	−12.8614			−0.473114			−0.236557	−	0.971618i	$-0.576019\pi$
$739$	−12.8614			−0.473114			−0.236557	+	0.971618i	$0.576019\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−14.7446	−	25.5383i	−0.540926	−	0.936911i	−0.998851	−	0.0479200i	$-0.984741\pi$
$743$	−14.7446	−	25.5383i	−0.540926	−	0.936911i	0.457926	−	0.888991i	$-0.348593\pi$
$744$		0			0
$745$	1.74456	−	3.02167i	0.0639158	−	0.110705i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.11684	−	12.3267i	0.260044	−	0.450409i
$750$		0			0
$751$	19.1168	+	33.1113i	0.697584	+	1.20825i	0.969302	+	0.245873i	$0.0790747\pi$
$751$	19.1168	+	33.1113i	0.697584	+	1.20825i	−0.271718	+	0.962377i	$0.587592\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−18.6277			−0.677932
$756$		0			0
$757$	27.1168			0.985578			0.492789	−	0.870149i	$-0.335977\pi$
$757$	27.1168			0.985578			0.492789	+	0.870149i	$0.335977\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−8.61684	−	14.9248i	−0.312360	−	0.541024i	0.666513	−	0.745494i	$-0.267786\pi$
$761$	−8.61684	−	14.9248i	−0.312360	−	0.541024i	−0.978873	+	0.204470i	$0.934453\pi$
$762$		0			0
$763$	21.4891	−	37.2203i	0.777959	−	1.34746i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.93070	−	10.2723i	0.214145	−	0.370911i
$768$		0			0
$769$	16.1753	+	28.0164i	0.583295	+	1.01030i	0.995086	+	0.0990181i	$0.0315702\pi$
$769$	16.1753	+	28.0164i	0.583295	+	1.01030i	−0.411791	+	0.911278i	$0.635096\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−18.0000			−0.647415			−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000			−0.647415			−0.323708	+	0.946157i	$0.604929\pi$
$774$		0			0
$775$	−6.11684			−0.219724
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.87228	+	10.1711i	0.210396	+	0.364417i
$780$		0			0
$781$	2.31386	−	4.00772i	0.0827964	−	0.143408i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.93070	+	5.07613i	−0.104601	+	0.181175i
$786$		0			0
$787$	−7.86141	−	13.6164i	−0.280229	−	0.485371i	0.691212	−	0.722652i	$-0.257077\pi$
$787$	−7.86141	−	13.6164i	−0.280229	−	0.485371i	−0.971441	+	0.237281i	$0.923744\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	7.72281			0.274592
$792$		0			0
$793$	2.97825			0.105761
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.11684	+	12.3267i	0.252092	+	0.436635i	0.964101	−	0.265534i	$-0.0855483\pi$
$797$	7.11684	+	12.3267i	0.252092	+	0.436635i	−0.712010	+	0.702169i	$0.752215\pi$
$798$		0			0
$799$	8.60597	−	14.9060i	0.304457	−	0.527336i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.48913	+	9.50744i	−0.193707	+	0.335510i
$804$		0			0
$805$	−0.441578	−	0.764836i	−0.0155636	−	0.0269569i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	34.2119			1.20283			0.601414	−	0.798938i	$-0.294604\pi$
$809$	34.2119			1.20283			0.601414	+	0.798938i	$0.294604\pi$
$810$		0			0
$811$	14.3505			0.503915			0.251958	−	0.967738i	$-0.418926\pi$
$811$	14.3505			0.503915			0.251958	+	0.967738i	$0.418926\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.74456	−	11.6819i	−0.236252	−	0.409200i
$816$		0			0
$817$	−3.37228	+	5.84096i	−0.117981	+	0.204349i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	20.6861	−	35.8294i	0.721951	−	1.25046i	−0.238265	−	0.971200i	$-0.576579\pi$
$821$	20.6861	−	35.8294i	0.721951	−	1.25046i	0.960217	−	0.279256i	$-0.0900879\pi$
$822$		0			0
$823$	17.3723	+	30.0897i	0.605560	+	1.04886i	0.991963	+	0.126530i	$0.0403840\pi$
$823$	17.3723	+	30.0897i	0.605560	+	1.04886i	−0.386403	+	0.922330i	$0.626283\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−45.9565			−1.59806			−0.799032	−	0.601288i	$-0.794654\pi$
$827$	−45.9565			−1.59806			−0.799032	+	0.601288i	$0.794654\pi$
$828$		0			0
$829$	42.5842			1.47901			0.739506	−	0.673150i	$-0.235059\pi$
$829$	42.5842			1.47901			0.739506	+	0.673150i	$0.235059\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.25544	−	5.63858i	−0.112794	−	0.195365i
$834$		0			0
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.80298	−	10.0511i	0.200341	−	0.347001i	−0.748297	−	0.663364i	$-0.769128\pi$
$839$	5.80298	−	10.0511i	0.200341	−	0.347001i	0.948638	+	0.316362i	$0.102462\pi$
$840$		0			0
$841$	8.81386	+	15.2661i	0.303926	+	0.526416i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	7.37228			0.253614
$846$		0			0
$847$	−0.883156			−0.0303456
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.11684	−	1.93443i	−0.0382849	−	0.0663114i
$852$		0			0
$853$	0.372281	−	0.644810i	0.0127467	−	0.0220779i	−0.859582	−	0.510998i	$-0.829276\pi$
$853$	0.372281	−	0.644810i	0.0127467	−	0.0220779i	0.872328	+	0.488920i	$0.162609\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.3723	+	38.7499i	−0.764223	+	1.32367i	0.176434	+	0.984312i	$0.443544\pi$
$857$	−22.3723	+	38.7499i	−0.764223	+	1.32367i	−0.940657	+	0.339360i	$0.889790\pi$
$858$		0			0
$859$	−25.1753	−	43.6048i	−0.858969	−	1.48778i	−0.872913	−	0.487875i	$-0.837772\pi$
$859$	−25.1753	−	43.6048i	−0.858969	−	1.48778i	0.0139444	−	0.999903i	$-0.495561\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	11.3940			0.387857			0.193929	−	0.981016i	$-0.437877\pi$
$863$	11.3940			0.387857			0.193929	+	0.981016i	$0.437877\pi$
$864$		0			0
$865$	−13.8614			−0.471302
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−14.7446	−	25.5383i	−0.500175	−	0.866329i
$870$		0			0
$871$	−12.7446	+	22.0742i	−0.431833	+	0.747957i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.18614	+	2.05446i	−0.0400989	+	0.0694533i
$876$		0			0
$877$	−4.44158	−	7.69304i	−0.149981	−	0.259775i	0.781239	−	0.624232i	$-0.214588\pi$
$877$	−4.44158	−	7.69304i	−0.149981	−	0.259775i	−0.931220	+	0.364457i	$0.881255\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−25.3723			−0.854814			−0.427407	−	0.904059i	$-0.640573\pi$
$881$	−25.3723			−0.854814			−0.427407	+	0.904059i	$0.640573\pi$
$882$		0			0
$883$	5.76631			0.194052			0.0970259	−	0.995282i	$-0.469067\pi$
$883$	5.76631			0.194052			0.0970259	+	0.995282i	$0.469067\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.9307	−	36.2530i	−0.702784	−	1.21726i	−0.967485	−	0.252927i	$-0.918607\pi$
$887$	−20.9307	−	36.2530i	−0.702784	−	1.21726i	0.264701	−	0.964331i	$-0.414727\pi$
$888$		0			0
$889$	18.8139	−	32.5866i	0.630997	−	1.09292i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.81386	+	3.14170i	−0.0606985	+	0.105133i
$894$		0			0
$895$	7.87228	+	13.6352i	0.263141	+	0.455774i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−20.6277			−0.687973
$900$		0			0
$901$	−33.7663			−1.12492
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.43070	+	12.8704i	0.247005	+	0.427825i
$906$		0			0
$907$	17.7446	−	30.7345i	0.589199	−	1.02052i	−0.405139	−	0.914255i	$-0.632777\pi$
$907$	17.7446	−	30.7345i	0.589199	−	1.02052i	0.994338	−	0.106267i	$-0.0338897\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	27.0367	−	46.8289i	0.895765	−	1.55151i	0.0629099	−	0.998019i	$-0.479962\pi$
$911$	27.0367	−	46.8289i	0.895765	−	1.55151i	0.832855	−	0.553491i	$-0.186705\pi$
$912$		0			0
$913$	−16.8614	−	29.2048i	−0.558031	−	0.966538i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	42.0951			1.39010
$918$		0			0
$919$	42.1168			1.38931			0.694653	−	0.719345i	$-0.255558\pi$
$919$	42.1168			1.38931			0.694653	+	0.719345i	$0.255558\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.62772	+	2.81929i	0.0535770	+	0.0927981i
$924$		0			0
$925$	−3.00000	+	5.19615i	−0.0986394	+	0.170848i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.43070	+	2.47805i	−0.0469399	+	0.0813022i	−0.888541	−	0.458798i	$-0.848280\pi$
$929$	−1.43070	+	2.47805i	−0.0469399	+	0.0813022i	0.841601	+	0.540100i	$0.181614\pi$
$930$		0			0
$931$	0.686141	+	1.18843i	0.0224874	+	0.0389492i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	16.0000			0.523256
$936$		0			0
$937$	42.7446			1.39640			0.698202	−	0.715901i	$-0.253984\pi$
$937$	42.7446			1.39640			0.698202	+	0.715901i	$0.253984\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	13.2337	+	22.9214i	0.431406	+	0.747217i	0.996995	−	0.0774705i	$-0.0246844\pi$
$941$	13.2337	+	22.9214i	0.431406	+	0.747217i	−0.565589	+	0.824687i	$0.691351\pi$
$942$		0			0
$943$	2.18614	−	3.78651i	0.0711905	−	0.123306i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.6277	−	32.2642i	0.605320	−	1.04844i	−0.386681	−	0.922213i	$-0.626379\pi$
$947$	18.6277	−	32.2642i	0.605320	−	1.04844i	0.992001	−	0.126231i	$-0.0402880\pi$
$948$		0			0
$949$	−3.86141	−	6.68815i	−0.125347	−	0.217107i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	12.0000			0.388718			0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000			0.388718			0.194359	+	0.980930i	$0.437737\pi$
$954$		0			0
$955$	−11.3723			−0.367998
$956$		0			0
$957$		0			0
$958$		0			0
$959$	19.8614	+	34.4010i	0.641358	+	1.11087i
$960$		0			0
$961$	−3.20789	+	5.55623i	−0.103480	+	0.179233i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5.37228	+	9.30506i	−0.172940	+	0.299541i
$966$		0			0
$967$	9.25544	+	16.0309i	0.297635	+	0.515519i	0.975594	−	0.219581i	$-0.0704689\pi$
$967$	9.25544	+	16.0309i	0.297635	+	0.515519i	−0.677960	+	0.735099i	$0.737136\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.72281			0.279928			0.139964	−	0.990157i	$-0.455301\pi$
$971$	8.72281			0.279928			0.139964	+	0.990157i	$0.455301\pi$
$972$		0			0
$973$	−35.5842			−1.14078
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.88316	+	15.3861i	0.284197	+	0.492244i	0.972414	−	0.233261i	$-0.0749396\pi$
$977$	8.88316	+	15.3861i	0.284197	+	0.492244i	−0.688217	+	0.725505i	$0.741606\pi$
$978$		0			0
$979$	2.31386	−	4.00772i	0.0739513	−	0.128087i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−2.74456	+	4.75372i	−0.0875380	+	0.151620i	−0.906470	−	0.422271i	$-0.861233\pi$
$983$	−2.74456	+	4.75372i	−0.0875380	+	0.151620i	0.818932	+	0.573891i	$0.194567\pi$
$984$		0			0
$985$	3.18614	+	5.51856i	0.101519	+	0.175836i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.51087			0.0798412
$990$		0			0
$991$	3.37228			0.107124			0.0535620	−	0.998565i	$-0.482943\pi$
$991$	3.37228			0.107124			0.0535620	+	0.998565i	$0.482943\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.74456	−	8.21782i	−0.150413	−	0.260523i
$996$		0			0
$997$	−4.67527	+	8.09780i	−0.148067	+	0.256460i	−0.930513	−	0.366259i	$-0.880639\pi$
$997$	−4.67527	+	8.09780i	−0.148067	+	0.256460i	0.782446	+	0.622719i	$0.213972\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3240.2.q.bd.2161.2		4
3.2	odd	2		3240.2.q.ba.2161.2		4
9.2	odd	6		3240.2.a.m.1.1	yes	2
9.4	even	3	inner	3240.2.q.bd.1081.2		4
9.5	odd	6		3240.2.q.ba.1081.2		4
9.7	even	3		3240.2.a.i.1.1	✓	2
36.7	odd	6		6480.2.a.bd.1.2		2
36.11	even	6		6480.2.a.bo.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3240.2.a.i.1.1	✓	2	9.7	even	3
3240.2.a.m.1.1	yes	2	9.2	odd	6
3240.2.q.ba.1081.2		4	9.5	odd	6
3240.2.q.ba.2161.2		4	3.2	odd	2
3240.2.q.bd.1081.2		4	9.4	even	3	inner
3240.2.q.bd.2161.2		4	1.1	even	1	trivial
6480.2.a.bd.1.2		2	36.7	odd	6
6480.2.a.bo.1.2		2	36.11	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:	\( N \)	\(=\)	\( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3240.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{5} +(1.18614 - 2.05446i) q^{7} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{5} +(1.18614 - 2.05446i) q^{7} +(-1.68614 + 2.92048i) q^{11} +(-1.18614 - 2.05446i) q^{13} -4.74456 q^{17} +1.00000 q^{19} +(-0.186141 - 0.322405i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.68614 + 2.92048i) q^{29} +(3.05842 + 5.29734i) q^{31} +2.37228 q^{35} +6.00000 q^{37} +(5.87228 + 10.1711i) q^{41} +(-3.37228 + 5.84096i) q^{43} +(-1.81386 + 3.14170i) q^{47} +(0.686141 + 1.18843i) q^{49} +7.11684 q^{53} -3.37228 q^{55} +(2.50000 + 4.33013i) q^{59} +(-0.627719 + 1.08724i) q^{61} +(1.18614 - 2.05446i) q^{65} +(-5.37228 - 9.30506i) q^{67} -1.37228 q^{71} +3.25544 q^{73} +(4.00000 + 6.92820i) q^{77} +(-4.37228 + 7.57301i) q^{79} +(-5.00000 + 8.66025i) q^{83} +(-2.37228 - 4.10891i) q^{85} -1.37228 q^{89} -5.62772 q^{91} +(0.500000 + 0.866025i) q^{95} +(-3.37228 + 5.84096i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - q^{7}+O(q^{10}) \) 4 * q + 2 * q^5 - q^7	\( 4 q + 2 q^{5} - q^{7} - q^{11} + q^{13} + 4 q^{17} + 4 q^{19} + 5 q^{23} - 2 q^{25} - q^{29} - 5 q^{31} - 2 q^{35} + 24 q^{37} + 12 q^{41} - 2 q^{43} - 13 q^{47} - 3 q^{49} - 6 q^{53} - 2 q^{55} + 10 q^{59} - 14 q^{61} - q^{65} - 10 q^{67} + 6 q^{71} + 36 q^{73} + 16 q^{77} - 6 q^{79} - 20 q^{83} + 2 q^{85} + 6 q^{89} - 34 q^{91} + 2 q^{95} - 2 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 - q^7 - q^11 + q^13 + 4 * q^17 + 4 * q^19 + 5 * q^23 - 2 * q^25 - q^29 - 5 * q^31 - 2 * q^35 + 24 * q^37 + 12 * q^41 - 2 * q^43 - 13 * q^47 - 3 * q^49 - 6 * q^53 - 2 * q^55 + 10 * q^59 - 14 * q^61 - q^65 - 10 * q^67 + 6 * q^71 + 36 * q^73 + 16 * q^77 - 6 * q^79 - 20 * q^83 + 2 * q^85 + 6 * q^89 - 34 * q^91 + 2 * q^95 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more