LMFDB - Embedded newform 1620.2.i.h.1081.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(541,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1620.541");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.i (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:	$12.9357651274$
Analytic rank:	$1$
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 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1081.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1620.1081
Dual form			1620.2.i.h.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{13} -6.00000 q^{17} -4.00000 q^{19} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 - 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} -2.00000 q^{35} +2.00000 q^{37} +(-3.00000 + 5.19615i) q^{41} +(5.00000 + 8.66025i) q^{43} +(3.00000 + 5.19615i) q^{47} +(1.50000 - 2.59808i) q^{49} -6.00000 q^{53} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(1.00000 + 1.73205i) q^{65} +(-1.00000 + 1.73205i) q^{67} -12.0000 q^{71} +2.00000 q^{73} +(-4.00000 - 6.92820i) q^{79} +(-3.00000 - 5.19615i) q^{83} +(-3.00000 + 5.19615i) q^{85} -6.00000 q^{89} +4.00000 q^{91} +(-2.00000 + 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{5} - 2 q^{7} - 2 q^{13} - 12 q^{17} - 8 q^{19} - 6 q^{23} - q^{25} - 6 q^{29} + 4 q^{31} - 4 q^{35} + 4 q^{37} - 6 q^{41} + 10 q^{43} + 6 q^{47} + 3 q^{49} - 12 q^{53} - 12 q^{59} - 2 q^{61}+ \cdots - 2 q^{97}+O(q^{100}) $ 2 * q + q^5 - 2 * q^7 - 2 * q^13 - 12 * q^17 - 8 * q^19 - 6 * q^23 - q^25 - 6 * q^29 + 4 * q^31 - 4 * q^35 + 4 * q^37 - 6 * q^41 + 10 * q^43 + 6 * q^47 + 3 * q^49 - 12 * q^53 - 12 * q^59 - 2 * q^61 + 2 * q^65 - 2 * q^67 - 24 * q^71 + 4 * q^73 - 8 * q^79 - 6 * q^83 - 6 * q^85 - 12 * q^89 + 8 * q^91 - 4 * q^95 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		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
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.00000			−0.338062
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		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
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		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
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	0.653079	−	0.757290i	$-0.273477\pi$
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	−0.982372	+	0.186938i	$0.940144\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$		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	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$		0			0
$115$	3.00000	+	5.19615i	0.279751	+	0.484544i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.00000	+	10.3923i	0.550019	+	0.952661i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−6.00000			−0.498273
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	−0.910195	−	0.414181i	$-0.864068\pi$
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	0.0964061	−	0.995342i	$-0.469265\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.00000	−	3.46410i	−0.160644	−	0.278243i
$156$		0			0
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.0242497	−	0.999706i	$-0.492280\pi$
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.853646	−	0.520854i	$-0.174386\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	12.0000			0.945732
$162$		0			0
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	−1.00000	+	1.73205i	−0.0755929	+	0.130931i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		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
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	−13.0000	+	22.5167i	−0.935760	+	1.62078i	−0.162488	+	0.986710i	$0.551952\pi$
$193$	−13.0000	+	22.5167i	−0.935760	+	1.62078i	−0.773272	+	0.634074i	$0.781381\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.00000	+	10.3923i	−0.421117	+	0.729397i
$204$		0			0
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	0.998221	−	0.0596196i	$-0.0189888\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	10.0000			0.681994
$216$		0			0
$217$	−8.00000			−0.543075
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	0.983451	−	0.181173i	$-0.0579895\pi$
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	−0.648626	+	0.761107i	$0.724656\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.00000	+	5.19615i	0.199117	+	0.344881i	0.948242	−	0.317547i	$-0.102859\pi$
$227$	3.00000	+	5.19615i	0.199117	+	0.344881i	−0.749125	+	0.662428i	$0.769526\pi$
$228$		0			0
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	6.00000			0.391397
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.0000	−	20.7846i	0.776215	−	1.34444i	−0.157893	−	0.987456i	$-0.550470\pi$
$239$	12.0000	−	20.7846i	0.776215	−	1.34444i	0.934109	−	0.356988i	$-0.116196\pi$
$240$		0			0
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	−2.00000	−	3.46410i	−0.124274	−	0.215249i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	0.997906	+	0.0646755i	$0.0206012\pi$
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	−0.442943	+	0.896550i	$0.646065\pi$
$264$		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
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−13.0000	−	22.5167i	−0.781094	−	1.35290i	−0.931305	−	0.364241i	$-0.881328\pi$
$277$	−13.0000	−	22.5167i	−0.781094	−	1.35290i	0.150210	−	0.988654i	$-0.452005\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$		0			0
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.0000			0.708338
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$		0			0
$292$		0			0
$293$	15.0000	−	25.9808i	0.876309	−	1.51781i	0.0209480	−	0.999781i	$-0.493332\pi$
$293$	15.0000	−	25.9808i	0.876309	−	1.51781i	0.855361	−	0.518032i	$-0.173335\pi$
$294$		0			0
$295$	6.00000	+	10.3923i	0.349334	+	0.605063i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$		0			0
$301$	10.0000	−	17.3205i	0.576390	−	0.998337i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.00000			−0.114520
$306$		0			0
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	−0.984475	−	0.175525i	$-0.943838\pi$
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	0.644246	+	0.764818i	$0.277171\pi$
$312$		0			0
$313$	11.0000	+	19.0526i	0.621757	+	1.07691i	0.989158	+	0.146852i	$0.0469141\pi$
$313$	11.0000	+	19.0526i	0.621757	+	1.07691i	−0.367402	+	0.930062i	$0.619753\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	24.0000			1.33540
$324$		0			0
$325$	2.00000			0.110940
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.00000	+	1.73205i	0.0546358	+	0.0946320i
$336$		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
$341$		0			0
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	−0.110885	−	0.993833i	$-0.535369\pi$
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	0.916127	−	0.400887i	$-0.131298\pi$
$348$		0			0
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$		0			0
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$		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
$365$	1.00000	−	1.73205i	0.0523424	−	0.0906597i
$366$		0			0
$367$	11.0000	+	19.0526i	0.574195	+	0.994535i	0.996129	+	0.0879086i	$0.0280183\pi$
$367$	11.0000	+	19.0526i	0.574195	+	0.994535i	−0.421933	+	0.906627i	$0.638648\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$		0			0
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	0.303902	+	0.952703i	$0.401711\pi$
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	−0.977016	+	0.213165i	$0.931623\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$		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
$391$	18.0000	−	31.1769i	0.910299	−	1.57668i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.00000			−0.402524
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	−0.199207	−	0.979957i	$-0.563837\pi$
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	0.948272	−	0.317460i	$-0.102830\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	17.0000	−	29.4449i	0.840596	−	1.45595i	−0.0487958	−	0.998809i	$-0.515538\pi$
$409$	17.0000	−	29.4449i	0.840596	−	1.45595i	0.889392	−	0.457146i	$-0.151128\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0000			1.18096
$414$		0			0
$415$	−6.00000			−0.294528
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−18.0000	+	31.1769i	−0.879358	+	1.52309i	−0.0273103	+	0.999627i	$0.508694\pi$
$419$	−18.0000	+	31.1769i	−0.879358	+	1.52309i	−0.852047	+	0.523465i	$0.824639\pi$
$420$		0			0
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	−0.986814	−	0.161859i	$-0.948251\pi$
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	0.353233	−	0.935536i	$-0.385082\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$		0			0
$427$	−2.00000	+	3.46410i	−0.0967868	+	0.167640i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	36.0000			1.73406			0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000			1.73406			0.867029	+	0.498257i	$0.166026\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.0000	−	20.7846i	0.574038	−	0.994263i
$438$		0			0
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	0.785916	−	0.618333i	$-0.212192\pi$
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	−0.928450	+	0.371457i	$0.878858\pi$
$444$		0			0
$445$	−3.00000	+	5.19615i	−0.142214	+	0.246321i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.00000	−	3.46410i	0.0937614	−	0.162400i
$456$		0			0
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	−0.991551	−	0.129718i	$-0.958593\pi$
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	0.383437	−	0.923567i	$-0.374740\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	−0.968945	−	0.247276i	$-0.920465\pi$
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	0.270326	−	0.962769i	$-0.412869\pi$
$462$		0			0
$463$	−7.00000	+	12.1244i	−0.325318	+	0.563467i	−0.981577	−	0.191069i	$-0.938805\pi$
$463$	−7.00000	+	12.1244i	−0.325318	+	0.563467i	0.656259	+	0.754536i	$0.272138\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−30.0000			−1.38823			−0.694117	−	0.719862i	$-0.744205\pi$
$467$	−30.0000			−1.38823			−0.694117	+	0.719862i	$0.744205\pi$
$468$		0			0
$469$	4.00000			0.184703
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	2.00000	+	3.46410i	0.0917663	+	0.158944i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.00000			−0.0908153
$486$		0			0
$487$	26.0000			1.17817			0.589086	−	0.808070i	$-0.299488\pi$
$487$	26.0000			1.17817			0.589086	+	0.808070i	$0.299488\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$	18.0000	+	31.1769i	0.810679	+	1.40414i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.0000	+	20.7846i	0.538274	+	0.932317i
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−18.0000			−0.802580			−0.401290	−	0.915951i	$-0.631438\pi$
$503$	−18.0000			−0.802580			−0.401290	+	0.915951i	$0.631438\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.00000	+	12.1244i	0.308457	+	0.534263i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$		0			0
$523$	14.0000			0.612177			0.306089	−	0.952003i	$-0.400980\pi$
$523$	14.0000			0.612177			0.306089	+	0.952003i	$0.400980\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.00000	−	10.3923i	−0.259889	−	0.450141i
$534$		0			0
$535$	−3.00000	+	5.19615i	−0.129701	+	0.224649i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	14.0000			0.601907			0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000			0.601907			0.300954	+	0.953639i	$0.402695\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.00000	−	1.73205i	0.0428353	−	0.0741929i
$546$		0			0
$547$	−13.0000	−	22.5167i	−0.555840	−	0.962743i	−0.997838	−	0.0657267i	$-0.979063\pi$
$547$	−13.0000	−	22.5167i	−0.555840	−	0.962743i	0.441998	−	0.897016i	$-0.354270\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.0000	+	20.7846i	0.511217	+	0.885454i
$552$		0			0
$553$	−8.00000	+	13.8564i	−0.340195	+	0.589234i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$		0			0
$559$	−20.0000			−0.845910
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.00000	−	15.5885i	0.379305	−	0.656975i	−0.611656	−	0.791123i	$-0.709497\pi$
$563$	9.00000	−	15.5885i	0.379305	−	0.656975i	0.990961	+	0.134148i	$0.0428299\pi$
$564$		0			0
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$		0			0
$571$	−4.00000	+	6.92820i	−0.167395	+	0.289936i	−0.937503	−	0.347977i	$-0.886869\pi$
$571$	−4.00000	+	6.92820i	−0.167395	+	0.289936i	0.770108	+	0.637913i	$0.220202\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	6.00000			0.250217
$576$		0			0
$577$	−22.0000			−0.915872			−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.00000	+	10.3923i	−0.248922	+	0.431145i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.00000	+	5.19615i	0.123823	+	0.214468i	0.921272	−	0.388918i	$-0.127151\pi$
$587$	3.00000	+	5.19615i	0.123823	+	0.214468i	−0.797449	+	0.603386i	$0.793818\pi$
$588$		0			0
$589$	−8.00000	+	13.8564i	−0.329634	+	0.570943i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	18.0000			0.739171			0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$		0			0
$595$	12.0000			0.491952
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	0.949799	−	0.312861i	$-0.101287\pi$
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	−0.745845	+	0.666120i	$0.767954\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.50000	−	9.52628i	−0.223607	−	0.387298i
$606$		0			0
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	−0.551678	−	0.834058i	$-0.686012\pi$
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	0.998154	+	0.0607380i	$0.0193454\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−12.0000			−0.485468
$612$		0			0
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	−0.799298	−	0.600935i	$-0.794795\pi$
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	0.920074	+	0.391745i	$0.128129\pi$
$618$		0			0
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6.00000	+	10.3923i	0.240385	+	0.416359i
$624$		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
$631$	−28.0000			−1.11466			−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000			−1.11466			−0.557331	+	0.830290i	$0.688175\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.00000	−	1.73205i	0.0396838	−	0.0687343i
$636$		0			0
$637$	3.00000	+	5.19615i	0.118864	+	0.205879i
$638$		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
$643$	−7.00000	+	12.1244i	−0.276053	+	0.478138i	−0.970400	−	0.241502i	$-0.922360\pi$
$643$	−7.00000	+	12.1244i	−0.276053	+	0.478138i	0.694347	+	0.719640i	$0.255693\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	42.0000			1.65119			0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000			1.65119			0.825595	+	0.564263i	$0.190840\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.0000	+	36.3731i	−0.821794	+	1.42339i	0.0825519	+	0.996587i	$0.473693\pi$
$653$	−21.0000	+	36.3731i	−0.821794	+	1.42339i	−0.904345	+	0.426801i	$0.859640\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$		0			0
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	−0.568831	−	0.822454i	$-0.692604\pi$
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	0.996682	+	0.0813955i	$0.0259377\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	8.00000			0.310227
$666$		0			0
$667$	36.0000			1.39393
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	23.0000	+	39.8372i	0.886585	+	1.53561i	0.843886	+	0.536522i	$0.180262\pi$
$673$	23.0000	+	39.8372i	0.886585	+	1.53561i	0.0426985	+	0.999088i	$0.486405\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	0.639618	−	0.768693i	$-0.279092\pi$
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	−0.985517	+	0.169580i	$0.945759\pi$
$678$		0			0
$679$	−2.00000	+	3.46410i	−0.0767530	+	0.132940i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−42.0000			−1.60709			−0.803543	−	0.595247i	$-0.797054\pi$
$683$	−42.0000			−1.60709			−0.803543	+	0.595247i	$0.797054\pi$
$684$		0			0
$685$	−18.0000			−0.687745
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$		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
$707$	−6.00000	+	10.3923i	−0.225653	+	0.390843i
$708$		0			0
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	0.985773	+	0.168080i	$0.0537568\pi$
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	−0.347325	+	0.937745i	$0.612910\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.0000	+	20.7846i	0.449404	+	0.778390i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		0			0
$721$	28.0000			1.04277
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	23.0000	+	39.8372i	0.853023	+	1.47748i	0.878467	+	0.477803i	$0.158567\pi$
$727$	23.0000	+	39.8372i	0.853023	+	1.47748i	−0.0254445	+	0.999676i	$0.508100\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−30.0000	−	51.9615i	−1.10959	−	1.92187i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	−0.915794	−	0.401648i	$-0.868437\pi$
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	0.805735	+	0.592277i	$0.201771\pi$
$744$		0			0
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.00000	+	10.3923i	0.219235	+	0.379727i
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−20.0000			−0.727875
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$		0			0
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.0000	−	20.7846i	−0.433295	−	0.750489i
$768$		0			0
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−30.0000			−1.07903			−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000			−1.07903			−0.539513	+	0.841978i	$0.681391\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.0000	−	20.7846i	0.429945	−	0.744686i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−11.0000	−	19.0526i	−0.392607	−	0.680015i
$786$		0			0
$787$	−13.0000	+	22.5167i	−0.463400	+	0.802632i	−0.999128	−	0.0417585i	$-0.986704\pi$
$787$	−13.0000	+	22.5167i	−0.463400	+	0.802632i	0.535728	+	0.844391i	$0.320037\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.0000			−0.426671
$792$		0			0
$793$	4.00000			0.142044
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−21.0000	+	36.3731i	−0.743858	+	1.28840i	0.206868	+	0.978369i	$0.433673\pi$
$797$	−21.0000	+	36.3731i	−0.743858	+	1.28840i	−0.950726	+	0.310031i	$0.899660\pi$
$798$		0			0
$799$	−18.0000	−	31.1769i	−0.636794	−	1.10296i
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$	6.00000	−	10.3923i	0.211472	−	0.366281i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.00000	+	8.66025i	−0.175142	+	0.303355i
$816$		0			0
$817$	−20.0000	−	34.6410i	−0.699711	−	1.21194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	27.0000	+	46.7654i	0.942306	+	1.63212i	0.761056	+	0.648686i	$0.224681\pi$
$821$	27.0000	+	46.7654i	0.942306	+	1.63212i	0.181250	+	0.983437i	$0.441986\pi$
$822$		0			0
$823$	−19.0000	+	32.9090i	−0.662298	+	1.14713i	0.317712	+	0.948187i	$0.397086\pi$
$823$	−19.0000	+	32.9090i	−0.662298	+	1.14713i	−0.980010	+	0.198947i	$0.936248\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	2.00000			0.0694629			0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000			0.0694629			0.0347314	+	0.999397i	$0.488942\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−9.00000	+	15.5885i	−0.311832	+	0.540108i
$834$		0			0
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	0.899158	+	0.437623i	$0.144180\pi$
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	−0.0705865	+	0.997506i	$0.522487\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	9.00000			0.309609
$846$		0			0
$847$	−22.0000			−0.755929
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	−25.0000	−	43.3013i	−0.855984	−	1.48261i	−0.875729	−	0.482802i	$-0.839619\pi$
$853$	−25.0000	−	43.3013i	−0.855984	−	1.48261i	0.0197457	−	0.999805i	$-0.493714\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.00000			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$		0			0
$865$	6.00000			0.204006
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.00000	+	1.73205i	0.0338062	+	0.0585540i
$876$		0			0
$877$	−13.0000	+	22.5167i	−0.438979	+	0.760334i	−0.997611	−	0.0690819i	$-0.977993\pi$
$877$	−13.0000	+	22.5167i	−0.438979	+	0.760334i	0.558632	+	0.829416i	$0.311326\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	14.0000			0.471138			0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000			0.471138			0.235569	+	0.971858i	$0.424305\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.00000	+	15.5885i	−0.302190	+	0.523409i	−0.976632	−	0.214919i	$-0.931051\pi$
$887$	−9.00000	+	15.5885i	−0.302190	+	0.523409i	0.674441	+	0.738328i	$0.264385\pi$
$888$		0			0
$889$	−2.00000	−	3.46410i	−0.0670778	−	0.116182i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.0000	−	20.7846i	−0.401565	−	0.695530i
$894$		0			0
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−24.0000			−0.800445
$900$		0			0
$901$	36.0000			1.19933
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.00000	+	8.66025i	−0.166206	+	0.287877i
$906$		0			0
$907$	23.0000	+	39.8372i	0.763702	+	1.32277i	0.940930	+	0.338602i	$0.109954\pi$
$907$	23.0000	+	39.8372i	0.763702	+	1.32277i	−0.177227	+	0.984170i	$0.556713\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.00000	−	10.3923i	−0.198789	−	0.344312i	0.749347	−	0.662177i	$-0.230367\pi$
$911$	−6.00000	−	10.3923i	−0.198789	−	0.344312i	−0.948136	+	0.317865i	$0.897034\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	12.0000	−	20.7846i	0.394985	−	0.684134i
$924$		0			0
$925$	−1.00000	−	1.73205i	−0.0328798	−	0.0569495i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	21.0000	+	36.3731i	0.688988	+	1.19336i	0.972166	+	0.234294i	$0.0752779\pi$
$929$	21.0000	+	36.3731i	0.688988	+	1.19336i	−0.283178	+	0.959067i	$0.591389\pi$
$930$		0			0
$931$	−6.00000	+	10.3923i	−0.196642	+	0.340594i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$		0			0
$943$	−18.0000	−	31.1769i	−0.586161	−	1.01526i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$	12.0000			0.388311
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−18.0000	+	31.1769i	−0.581250	+	1.00676i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.0000	+	22.5167i	0.418485	+	0.724837i
$966$		0			0
$967$	11.0000	−	19.0526i	0.353736	−	0.612689i	−0.633165	−	0.774017i	$-0.718244\pi$
$967$	11.0000	−	19.0526i	0.353736	−	0.612689i	0.986901	+	0.161328i	$0.0515777\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−24.0000			−0.770197			−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000			−0.770197			−0.385098	+	0.922876i	$0.625832\pi$
$972$		0			0
$973$	−8.00000			−0.256468
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	0.973106	−	0.230360i	$-0.0739903\pi$
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	−0.686050	+	0.727554i	$0.740657\pi$
$984$		0			0
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−60.0000			−1.90789
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.00000	−	6.92820i	0.126809	−	0.219639i
$996$		0			0
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.i.h.1081.1		2
3.2	odd	2		1620.2.i.b.1081.1		2
9.2	odd	6		1620.2.i.b.541.1		2
9.4	even	3		20.2.a.a.1.1	✓	1
9.5	odd	6		180.2.a.a.1.1		1
9.7	even	3	inner	1620.2.i.h.541.1		2
36.23	even	6		720.2.a.h.1.1		1
36.31	odd	6		80.2.a.b.1.1		1
45.4	even	6		100.2.a.a.1.1		1
45.13	odd	12		100.2.c.a.49.1		2
45.14	odd	6		900.2.a.b.1.1		1
45.22	odd	12		100.2.c.a.49.2		2
45.23	even	12		900.2.d.c.649.1		2
45.32	even	12		900.2.d.c.649.2		2
63.4	even	3		980.2.i.i.961.1		2
63.13	odd	6		980.2.a.h.1.1		1
63.31	odd	6		980.2.i.c.961.1		2
63.40	odd	6		980.2.i.c.361.1		2
63.41	even	6		8820.2.a.g.1.1		1
63.58	even	3		980.2.i.i.361.1		2
72.5	odd	6		2880.2.a.m.1.1		1
72.13	even	6		320.2.a.f.1.1		1
72.59	even	6		2880.2.a.f.1.1		1
72.67	odd	6		320.2.a.a.1.1		1
99.76	odd	6		2420.2.a.a.1.1		1
117.31	odd	12		3380.2.f.b.3041.2		2
117.103	even	6		3380.2.a.c.1.1		1
117.112	odd	12		3380.2.f.b.3041.1		2
144.13	even	12		1280.2.d.c.641.1		2
144.67	odd	12		1280.2.d.g.641.2		2
144.85	even	12		1280.2.d.c.641.2		2
144.139	odd	12		1280.2.d.g.641.1		2
153.4	even	12		5780.2.c.a.5201.2		2
153.13	even	12		5780.2.c.a.5201.1		2
153.67	even	6		5780.2.a.f.1.1		1
171.94	odd	6		7220.2.a.f.1.1		1
180.23	odd	12		3600.2.f.j.2449.2		2
180.59	even	6		3600.2.a.be.1.1		1
180.67	even	12		400.2.c.b.49.1		2
180.103	even	12		400.2.c.b.49.2		2
180.139	odd	6		400.2.a.c.1.1		1
180.167	odd	12		3600.2.f.j.2449.1		2
252.139	even	6		3920.2.a.h.1.1		1
315.13	even	12		4900.2.e.f.2549.2		2
315.139	odd	6		4900.2.a.e.1.1		1
315.202	even	12		4900.2.e.f.2549.1		2
360.13	odd	12		1600.2.c.d.449.2		2
360.67	even	12		1600.2.c.e.449.2		2
360.139	odd	6		1600.2.a.w.1.1		1
360.157	odd	12		1600.2.c.d.449.1		2
360.229	even	6		1600.2.a.c.1.1		1
360.283	even	12		1600.2.c.e.449.1		2
396.175	even	6		9680.2.a.ba.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.2.a.a.1.1	✓	1	9.4	even	3
80.2.a.b.1.1		1	36.31	odd	6
100.2.a.a.1.1		1	45.4	even	6
100.2.c.a.49.1		2	45.13	odd	12
100.2.c.a.49.2		2	45.22	odd	12
180.2.a.a.1.1		1	9.5	odd	6
320.2.a.a.1.1		1	72.67	odd	6
320.2.a.f.1.1		1	72.13	even	6
400.2.a.c.1.1		1	180.139	odd	6
400.2.c.b.49.1		2	180.67	even	12
400.2.c.b.49.2		2	180.103	even	12
720.2.a.h.1.1		1	36.23	even	6
900.2.a.b.1.1		1	45.14	odd	6
900.2.d.c.649.1		2	45.23	even	12
900.2.d.c.649.2		2	45.32	even	12
980.2.a.h.1.1		1	63.13	odd	6
980.2.i.c.361.1		2	63.40	odd	6
980.2.i.c.961.1		2	63.31	odd	6
980.2.i.i.361.1		2	63.58	even	3
980.2.i.i.961.1		2	63.4	even	3
1280.2.d.c.641.1		2	144.13	even	12
1280.2.d.c.641.2		2	144.85	even	12
1280.2.d.g.641.1		2	144.139	odd	12
1280.2.d.g.641.2		2	144.67	odd	12
1600.2.a.c.1.1		1	360.229	even	6
1600.2.a.w.1.1		1	360.139	odd	6
1600.2.c.d.449.1		2	360.157	odd	12
1600.2.c.d.449.2		2	360.13	odd	12
1600.2.c.e.449.1		2	360.283	even	12
1600.2.c.e.449.2		2	360.67	even	12
1620.2.i.b.541.1		2	9.2	odd	6
1620.2.i.b.1081.1		2	3.2	odd	2
1620.2.i.h.541.1		2	9.7	even	3	inner
1620.2.i.h.1081.1		2	1.1	even	1	trivial
2420.2.a.a.1.1		1	99.76	odd	6
2880.2.a.f.1.1		1	72.59	even	6
2880.2.a.m.1.1		1	72.5	odd	6
3380.2.a.c.1.1		1	117.103	even	6
3380.2.f.b.3041.1		2	117.112	odd	12
3380.2.f.b.3041.2		2	117.31	odd	12
3600.2.a.be.1.1		1	180.59	even	6
3600.2.f.j.2449.1		2	180.167	odd	12
3600.2.f.j.2449.2		2	180.23	odd	12
3920.2.a.h.1.1		1	252.139	even	6
4900.2.a.e.1.1		1	315.139	odd	6
4900.2.e.f.2549.1		2	315.202	even	12
4900.2.e.f.2549.2		2	315.13	even	12
5780.2.a.f.1.1		1	153.67	even	6
5780.2.c.a.5201.1		2	153.13	even	12
5780.2.c.a.5201.2		2	153.4	even	12
7220.2.a.f.1.1		1	171.94	odd	6
8820.2.a.g.1.1		1	63.41	even	6
9680.2.a.ba.1.1		1	396.175	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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{13} -6.00000 q^{17} -4.00000 q^{19} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 - 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} -2.00000 q^{35} +2.00000 q^{37} +(-3.00000 + 5.19615i) q^{41} +(5.00000 + 8.66025i) q^{43} +(3.00000 + 5.19615i) q^{47} +(1.50000 - 2.59808i) q^{49} -6.00000 q^{53} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(1.00000 + 1.73205i) q^{65} +(-1.00000 + 1.73205i) q^{67} -12.0000 q^{71} +2.00000 q^{73} +(-4.00000 - 6.92820i) q^{79} +(-3.00000 - 5.19615i) q^{83} +(-3.00000 + 5.19615i) q^{85} -6.00000 q^{89} +4.00000 q^{91} +(-2.00000 + 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{5} - 2 q^{7} - 2 q^{13} - 12 q^{17} - 8 q^{19} - 6 q^{23} - q^{25} - 6 q^{29} + 4 q^{31} - 4 q^{35} + 4 q^{37} - 6 q^{41} + 10 q^{43} + 6 q^{47} + 3 q^{49} - 12 q^{53} - 12 q^{59} - 2 q^{61}+ \cdots - 2 q^{97}+O(q^{100}) \) 2 * q + q^5 - 2 * q^7 - 2 * q^13 - 12 * q^17 - 8 * q^19 - 6 * q^23 - q^25 - 6 * q^29 + 4 * q^31 - 4 * q^35 + 4 * q^37 - 6 * q^41 + 10 * q^43 + 6 * q^47 + 3 * q^49 - 12 * q^53 - 12 * q^59 - 2 * q^61 + 2 * q^65 - 2 * q^67 - 24 * q^71 + 4 * q^73 - 8 * q^79 - 6 * q^83 - 6 * q^85 - 12 * q^89 + 8 * q^91 - 4 * q^95 - 2 * q^97

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