LMFDB - Embedded newform 3240.2.q.q.1081.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1081.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3240.1081
Dual form			3240.2.q.q.2161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(-2.00000 - 3.46410i) q^{11} +(-3.00000 + 5.19615i) q^{13} +6.00000 q^{17} -4.00000 q^{19} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{29} +(4.00000 - 6.92820i) q^{31} -2.00000 q^{37} +(-3.00000 + 5.19615i) q^{41} +(-6.00000 - 10.3923i) q^{43} +(4.00000 + 6.92820i) q^{47} +(3.50000 - 6.06218i) q^{49} -6.00000 q^{53} -4.00000 q^{55} +(6.00000 - 10.3923i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(3.00000 + 5.19615i) q^{65} +(-2.00000 + 3.46410i) q^{67} -8.00000 q^{71} -6.00000 q^{73} +(4.00000 + 6.92820i) q^{79} +(-6.00000 - 10.3923i) q^{83} +(3.00000 - 5.19615i) q^{85} -10.0000 q^{89} +(-2.00000 + 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{5}+O(q^{10}) $ 2 * q + q^5	$ 2 q + q^{5} - 4 q^{11} - 6 q^{13} + 12 q^{17} - 8 q^{19} - q^{25} - 2 q^{29} + 8 q^{31} - 4 q^{37} - 6 q^{41} - 12 q^{43} + 8 q^{47} + 7 q^{49} - 12 q^{53} - 8 q^{55} + 12 q^{59} - 14 q^{61} + 6 q^{65} - 4 q^{67} - 16 q^{71} - 12 q^{73} + 8 q^{79} - 12 q^{83} + 6 q^{85} - 20 q^{89} - 4 q^{95} - 2 q^{97}+O(q^{100}) $ 2 * q + q^5 - 4 * q^11 - 6 * q^13 + 12 * q^17 - 8 * q^19 - q^25 - 2 * q^29 + 8 * q^31 - 4 * q^37 - 6 * q^41 - 12 * q^43 + 8 * q^47 + 7 * q^49 - 12 * q^53 - 8 * q^55 + 12 * q^59 - 14 * q^61 + 6 * q^65 - 4 * q^67 - 16 * q^71 - 12 * q^73 + 8 * q^79 - 12 * q^83 + 6 * q^85 - 20 * q^89 - 4 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	0.0643593	+	0.997927i	$0.479500\pi$
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	−0.896410	+	0.443227i	$0.853834\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	0.758115	−	0.652121i	$-0.226120\pi$
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	−0.943811	+	0.330487i	$0.892787\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	−6.00000	−	10.3923i	−0.914991	−	1.58481i	−0.806914	−	0.590669i	$-0.798864\pi$
$43$	−6.00000	−	10.3923i	−0.914991	−	1.58481i	−0.108078	−	0.994142i	$-0.534469\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$		0			0
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	−4.00000			−0.539360
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.0640184	−	0.997949i	$-0.520392\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$		0			0
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$103$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$		0			0
$109$	−18.0000			−1.72409			−0.862044	−	0.506834i	$-0.830816\pi$
$109$	−18.0000			−1.72409			−0.862044	+	0.506834i	$0.830816\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	24.0000			2.00698
$144$		0			0
$145$	−2.00000			−0.166091
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$		0			0
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	−0.982873	−	0.184284i	$-0.941004\pi$
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	0.331842	−	0.943335i	$-0.392330\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.00000	−	6.92820i	−0.321288	−	0.556487i
$156$		0			0
$157$	−3.00000	+	5.19615i	−0.239426	+	0.414698i	−0.960550	−	0.278108i	$-0.910293\pi$
$157$	−3.00000	+	5.19615i	−0.239426	+	0.414698i	0.721124	+	0.692806i	$0.243626\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.00000	−	13.8564i	0.619059	−	1.07224i	−0.370599	−	0.928793i	$-0.620848\pi$
$167$	8.00000	−	13.8564i	0.619059	−	1.07224i	0.989658	−	0.143448i	$-0.0458190\pi$
$168$		0			0
$169$	−11.5000	−	19.9186i	−0.884615	−	1.53220i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.00000	+	1.73205i	−0.0735215	+	0.127343i
$186$		0			0
$187$	−12.0000	−	20.7846i	−0.877527	−	1.51992i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.0000			0.712470			0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000			0.712470			0.356235	+	0.934396i	$0.384060\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.00000	+	13.8564i	0.553372	+	0.958468i
$210$		0			0
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	−0.995222	−	0.0976347i	$-0.968872\pi$
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	0.582165	+	0.813070i	$0.302206\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−12.0000			−0.818393
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−18.0000	+	31.1769i	−1.21081	+	2.09719i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.0000	−	24.2487i	−0.929213	−	1.60944i	−0.784642	−	0.619949i	$-0.787153\pi$
$227$	−14.0000	−	24.2487i	−0.929213	−	1.60944i	−0.144571	−	0.989494i	$-0.546180\pi$
$228$		0			0
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.00000			−0.131024			−0.0655122	−	0.997852i	$-0.520868\pi$
$233$	−2.00000			−0.131024			−0.0655122	+	0.997852i	$0.520868\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	0.998443	−	0.0557856i	$-0.0177663\pi$
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	−0.547533	+	0.836784i	$0.684433\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.50000	−	6.06218i	−0.223607	−	0.387298i
$246$		0			0
$247$	12.0000	−	20.7846i	0.763542	−	1.32249i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−28.0000			−1.76734			−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000			−1.76734			−0.883672	+	0.468106i	$0.844936\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.00000	−	8.66025i	0.311891	−	0.540212i	−0.666880	−	0.745165i	$-0.732371\pi$
$257$	5.00000	−	8.66025i	0.311891	−	0.540212i	0.978772	+	0.204953i	$0.0657041\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$	−3.00000	+	5.19615i	−0.184289	+	0.319197i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$		0			0
$271$	−24.0000			−1.45790			−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000			−1.45790			−0.728948	+	0.684569i	$0.759990\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.0000	−	19.0526i	−0.656205	−	1.13658i	−0.981590	−	0.190999i	$-0.938827\pi$
$281$	−11.0000	−	19.0526i	−0.656205	−	1.13658i	0.325385	−	0.945582i	$-0.394506\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$		0			0
$292$		0			0
$293$	11.0000	−	19.0526i	0.642627	−	1.11306i	−0.342217	−	0.939621i	$-0.611178\pi$
$293$	11.0000	−	19.0526i	0.642627	−	1.11306i	0.984844	−	0.173442i	$-0.0554888\pi$
$294$		0			0
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−14.0000			−0.801638
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	−0.730044	−	0.683400i	$-0.760501\pi$
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	0.956864	+	0.290537i	$0.0938340\pi$
$312$		0			0
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	0.689412	−	0.724370i	$-0.257869\pi$
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	−0.972028	+	0.234863i	$0.924536\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.00000	+	12.1244i	0.393159	+	0.680972i	0.992864	−	0.119249i	$-0.0380488\pi$
$317$	7.00000	+	12.1244i	0.393159	+	0.680972i	−0.599705	+	0.800221i	$0.704715\pi$
$318$		0			0
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−24.0000			−1.33540
$324$		0			0
$325$	6.00000			0.332820
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$		0			0
$337$	−1.00000	+	1.73205i	−0.0544735	+	0.0943508i	−0.891976	−	0.452082i	$-0.850681\pi$
$337$	−1.00000	+	1.73205i	−0.0544735	+	0.0943508i	0.837503	+	0.546433i	$0.184015\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−32.0000			−1.73290
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	13.0000	+	22.5167i	0.691920	+	1.19844i	0.971208	+	0.238233i	$0.0765683\pi$
$353$	13.0000	+	22.5167i	0.691920	+	1.19844i	−0.279288	+	0.960207i	$0.590098\pi$
$354$		0			0
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.00000	+	5.19615i	−0.157027	+	0.271979i
$366$		0			0
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1.00000	−	1.73205i	0.0517780	−	0.0896822i	−0.838975	−	0.544170i	$-0.816844\pi$
$373$	1.00000	−	1.73205i	0.0517780	−	0.0896822i	0.890753	+	0.454488i	$0.150178\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	−0.377531	−	0.925997i	$-0.623227\pi$
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	0.990702	−	0.136047i	$-0.0434398\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.00000			0.402524
$396$		0			0
$397$	38.0000			1.90717			0.953583	−	0.301131i	$-0.0973643\pi$
$397$	38.0000			1.90717			0.953583	+	0.301131i	$0.0973643\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.00000	+	12.1244i	−0.349563	+	0.605461i	−0.986172	−	0.165726i	$-0.947003\pi$
$401$	−7.00000	+	12.1244i	−0.349563	+	0.605461i	0.636609	+	0.771187i	$0.280337\pi$
$402$		0			0
$403$	24.0000	+	41.5692i	1.19553	+	2.07071i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.00000	+	6.92820i	0.198273	+	0.343418i
$408$		0			0
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	0.341994	+	0.939702i	$0.388898\pi$
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	−0.984803	+	0.173675i	$0.944436\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−12.0000			−0.589057
$416$		0			0
$417$		0			0
$418$		0			0
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.0273103	−	0.999627i	$-0.491306\pi$
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.852047	−	0.523465i	$-0.175361\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	16.0000			0.770693			0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000			0.770693			0.385346	+	0.922772i	$0.374082\pi$
$432$		0			0
$433$	−30.0000			−1.44171			−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000			−1.44171			−0.720854	+	0.693087i	$0.756250\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	0.609503	−	0.792784i	$-0.291369\pi$
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	−0.991322	+	0.131453i	$0.958036\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	0.814595	−	0.580030i	$-0.196959\pi$
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	−0.909618	+	0.415445i	$0.863626\pi$
$444$		0			0
$445$	−5.00000	+	8.66025i	−0.237023	+	0.410535i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	24.0000			1.13012
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.00000	+	12.1244i	0.326023	+	0.564688i	0.981719	−	0.190337i	$-0.0609581\pi$
$461$	7.00000	+	12.1244i	0.326023	+	0.564688i	−0.655696	+	0.755025i	$0.727625\pi$
$462$		0			0
$463$	−4.00000	+	6.92820i	−0.185896	+	0.321981i	−0.943878	−	0.330294i	$-0.892852\pi$
$463$	−4.00000	+	6.92820i	−0.185896	+	0.321981i	0.757982	+	0.652275i	$0.226185\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	28.0000			1.29569			0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000			1.29569			0.647843	+	0.761774i	$0.275671\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−24.0000	+	41.5692i	−1.10352	+	1.91135i
$474$		0			0
$475$	2.00000	+	3.46410i	0.0917663	+	0.158944i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−16.0000	−	27.7128i	−0.731059	−	1.26623i	−0.956431	−	0.291958i	$-0.905693\pi$
$479$	−16.0000	−	27.7128i	−0.731059	−	1.26623i	0.225372	−	0.974273i	$-0.427640\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.00000			−0.0908153
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−18.0000	+	31.1769i	−0.812329	+	1.40699i	0.0989017	+	0.995097i	$0.468467\pi$
$491$	−18.0000	+	31.1769i	−0.812329	+	1.40699i	−0.911230	+	0.411897i	$0.864866\pi$
$492$		0			0
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	−0.550572	−	0.834788i	$-0.685590\pi$
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	0.998233	+	0.0594153i	$0.0189236\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	16.0000			0.713405			0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000			0.713405			0.356702	+	0.934218i	$0.383901\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.00000	+	1.73205i	−0.0443242	+	0.0767718i	−0.887336	−	0.461123i	$-0.847447\pi$
$509$	−1.00000	+	1.73205i	−0.0443242	+	0.0767718i	0.843012	+	0.537895i	$0.180780\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$	16.0000	−	27.7128i	0.703679	−	1.21881i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$		0			0
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	24.0000	−	41.5692i	1.04546	−	1.81078i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−18.0000	−	31.1769i	−0.779667	−	1.35042i
$534$		0			0
$535$	2.00000	−	3.46410i	0.0864675	−	0.149766i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−28.0000			−1.20605
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−9.00000	+	15.5885i	−0.385518	+	0.667736i
$546$		0			0
$547$	−18.0000	−	31.1769i	−0.769624	−	1.33303i	−0.937767	−	0.347266i	$-0.887110\pi$
$547$	−18.0000	−	31.1769i	−0.769624	−	1.33303i	0.168142	−	0.985763i	$-0.446223\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.00000	+	6.92820i	0.170406	+	0.295151i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$		0			0
$559$	72.0000			3.04528
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$		0			0
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	−0.712735	−	0.701434i	$-0.752544\pi$
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	0.963827	+	0.266529i	$0.0858769\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.00000	−	3.46410i	−0.0825488	−	0.142979i	0.821795	−	0.569783i	$-0.192973\pi$
$587$	−2.00000	−	3.46410i	−0.0825488	−	0.142979i	−0.904344	+	0.426804i	$0.859639\pi$
$588$		0			0
$589$	−16.0000	+	27.7128i	−0.659269	+	1.14189i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−20.0000	+	34.6410i	−0.817178	+	1.41539i	0.0905757	+	0.995890i	$0.471129\pi$
$599$	−20.0000	+	34.6410i	−0.817178	+	1.41539i	−0.907754	+	0.419504i	$0.862204\pi$
$600$		0			0
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.50000	+	4.33013i	0.101639	+	0.176045i
$606$		0			0
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	0.0998457	+	0.995003i	$0.468165\pi$
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	−0.911621	+	0.411033i	$0.865168\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−48.0000			−1.94187
$612$		0			0
$613$	−2.00000			−0.0807792			−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000			−0.0807792			−0.0403896	+	0.999184i	$0.512860\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.00000	−	1.73205i	0.0402585	−	0.0697297i	−0.845194	−	0.534460i	$-0.820515\pi$
$617$	1.00000	−	1.73205i	0.0402585	−	0.0697297i	0.885453	+	0.464730i	$0.153849\pi$
$618$		0			0
$619$	14.0000	+	24.2487i	0.562708	+	0.974638i	0.997259	+	0.0739910i	$0.0235736\pi$
$619$	14.0000	+	24.2487i	0.562708	+	0.974638i	−0.434551	+	0.900647i	$0.643093\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$		0			0
$637$	21.0000	+	36.3731i	0.832050	+	1.44115i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$		0			0
$643$	−2.00000	+	3.46410i	−0.0788723	+	0.136611i	−0.902764	−	0.430137i	$-0.858465\pi$
$643$	−2.00000	+	3.46410i	−0.0788723	+	0.136611i	0.823891	+	0.566748i	$0.191799\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	48.0000			1.88707			0.943537	−	0.331266i	$-0.107476\pi$
$647$	48.0000			1.88707			0.943537	+	0.331266i	$0.107476\pi$
$648$		0			0
$649$	−48.0000			−1.88416
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.00000	−	12.1244i	0.273931	−	0.474463i	−0.695934	−	0.718106i	$-0.745009\pi$
$653$	7.00000	−	12.1244i	0.273931	−	0.474463i	0.969865	+	0.243643i	$0.0783426\pi$
$654$		0			0
$655$	−2.00000	−	3.46410i	−0.0781465	−	0.135354i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.00000	+	3.46410i	0.0779089	+	0.134942i	0.902348	−	0.431009i	$-0.141842\pi$
$659$	2.00000	+	3.46410i	0.0779089	+	0.134942i	−0.824439	+	0.565951i	$0.808509\pi$
$660$		0			0
$661$	−3.00000	+	5.19615i	−0.116686	+	0.202107i	−0.918453	−	0.395531i	$-0.870561\pi$
$661$	−3.00000	+	5.19615i	−0.116686	+	0.202107i	0.801766	+	0.597638i	$0.203894\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−28.0000	+	48.4974i	−1.08093	+	1.87222i
$672$		0			0
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	0.968818	−	0.247774i	$-0.0796991\pi$
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	−0.698988	+	0.715134i	$0.746366\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.0000	+	32.9090i	0.730229	+	1.26479i	0.956785	+	0.290796i	$0.0939201\pi$
$677$	19.0000	+	32.9090i	0.730229	+	1.26479i	−0.226556	+	0.973998i	$0.572747\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−28.0000			−1.07139			−0.535695	−	0.844411i	$-0.679950\pi$
$683$	−28.0000			−1.07139			−0.535695	+	0.844411i	$0.679950\pi$
$684$		0			0
$685$	2.00000			0.0764161
$686$		0			0
$687$		0			0
$688$		0			0
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$		0			0
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	0.991122	−	0.132956i	$-0.0424468\pi$
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	−0.610704	+	0.791859i	$0.709113\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.00000	+	3.46410i	0.0758643	+	0.131401i
$696$		0			0
$697$	−18.0000	+	31.1769i	−0.681799	+	1.18091i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	8.00000			0.301726
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	12.0000	−	20.7846i	0.448775	−	0.777300i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.00000	+	1.73205i	−0.0371391	+	0.0643268i
$726$		0			0
$727$	16.0000	+	27.7128i	0.593407	+	1.02781i	0.993770	+	0.111454i	$0.0355509\pi$
$727$	16.0000	+	27.7128i	0.593407	+	1.02781i	−0.400362	+	0.916357i	$0.631116\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−36.0000	−	62.3538i	−1.33151	−	2.30624i
$732$		0			0
$733$	13.0000	−	22.5167i	0.480166	−	0.831672i	−0.519575	−	0.854425i	$-0.673910\pi$
$733$	13.0000	−	22.5167i	0.480166	−	0.831672i	0.999741	+	0.0227529i	$0.00724310\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	16.0000			0.589368
$738$		0			0
$739$	−4.00000			−0.147142			−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000			−0.147142			−0.0735712	+	0.997290i	$0.523440\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8.00000	+	13.8564i	−0.293492	+	0.508342i	−0.974633	−	0.223810i	$-0.928151\pi$
$743$	−8.00000	+	13.8564i	−0.293492	+	0.508342i	0.681141	+	0.732152i	$0.261484\pi$
$744$		0			0
$745$	5.00000	+	8.66025i	0.183186	+	0.317287i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	−0.929731	−	0.368238i	$-0.879961\pi$
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	0.783769	+	0.621052i	$0.213294\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−16.0000			−0.582300
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.0000	−	22.5167i	0.471250	−	0.816228i	−0.528209	−	0.849114i	$-0.677136\pi$
$761$	13.0000	−	22.5167i	0.471250	−	0.816228i	0.999459	+	0.0328858i	$0.0104698\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	36.0000	+	62.3538i	1.29988	+	2.25147i
$768$		0			0
$769$	15.0000	−	25.9808i	0.540914	−	0.936890i	−0.457938	−	0.888984i	$-0.651412\pi$
$769$	15.0000	−	25.9808i	0.540914	−	0.936890i	0.998852	−	0.0479061i	$-0.0152548\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	42.0000			1.51064			0.755318	−	0.655359i	$-0.227483\pi$
$773$	42.0000			1.51064			0.755318	+	0.655359i	$0.227483\pi$
$774$		0			0
$775$	−8.00000			−0.287368
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.0000	−	20.7846i	0.429945	−	0.744686i
$780$		0			0
$781$	16.0000	+	27.7128i	0.572525	+	0.991642i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	3.00000	+	5.19615i	0.107075	+	0.185459i
$786$		0			0
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	−0.899468	−	0.436987i	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	84.0000			2.98293
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	−0.883193	−	0.469010i	$-0.844611\pi$
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	0.847771	+	0.530362i	$0.177944\pi$
$798$		0			0
$799$	24.0000	+	41.5692i

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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(-2.00000 - 3.46410i) q^{11} +(-3.00000 + 5.19615i) q^{13} +6.00000 q^{17} -4.00000 q^{19} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{29} +(4.00000 - 6.92820i) q^{31} -2.00000 q^{37} +(-3.00000 + 5.19615i) q^{41} +(-6.00000 - 10.3923i) q^{43} +(4.00000 + 6.92820i) q^{47} +(3.50000 - 6.06218i) q^{49} -6.00000 q^{53} -4.00000 q^{55} +(6.00000 - 10.3923i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(3.00000 + 5.19615i) q^{65} +(-2.00000 + 3.46410i) q^{67} -8.00000 q^{71} -6.00000 q^{73} +(4.00000 + 6.92820i) q^{79} +(-6.00000 - 10.3923i) q^{83} +(3.00000 - 5.19615i) q^{85} -10.0000 q^{89} +(-2.00000 + 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{5}+O(q^{10}) \) 2 * q + q^5	\( 2 q + q^{5} - 4 q^{11} - 6 q^{13} + 12 q^{17} - 8 q^{19} - q^{25} - 2 q^{29} + 8 q^{31} - 4 q^{37} - 6 q^{41} - 12 q^{43} + 8 q^{47} + 7 q^{49} - 12 q^{53} - 8 q^{55} + 12 q^{59} - 14 q^{61} + 6 q^{65} - 4 q^{67} - 16 q^{71} - 12 q^{73} + 8 q^{79} - 12 q^{83} + 6 q^{85} - 20 q^{89} - 4 q^{95} - 2 q^{97}+O(q^{100}) \) 2 * q + q^5 - 4 * q^11 - 6 * q^13 + 12 * q^17 - 8 * q^19 - q^25 - 2 * q^29 + 8 * q^31 - 4 * q^37 - 6 * q^41 - 12 * q^43 + 8 * q^47 + 7 * q^49 - 12 * q^53 - 8 * q^55 + 12 * q^59 - 14 * q^61 + 6 * q^65 - 4 * q^67 - 16 * q^71 - 12 * q^73 + 8 * q^79 - 12 * q^83 + 6 * q^85 - 20 * q^89 - 4 * q^95 - 2 * q^97

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