LMFDB - Embedded newform 1960.2.q.j.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.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:	$15.6506787962$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.j.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} +1.00000 q^{13} -1.00000 q^{15} +(2.50000 + 4.33013i) q^{17} +(3.00000 - 5.19615i) q^{19} +(-0.500000 - 0.866025i) q^{25} +5.00000 q^{27} -5.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(1.50000 - 2.59808i) q^{33} +(2.00000 - 3.46410i) q^{37} +(0.500000 + 0.866025i) q^{39} -2.00000 q^{41} +10.0000 q^{43} +(1.00000 + 1.73205i) q^{45} +(4.50000 - 7.79423i) q^{47} +(-2.50000 + 4.33013i) q^{51} +(-3.00000 - 5.19615i) q^{53} +3.00000 q^{55} +6.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(6.00000 - 10.3923i) q^{61} +(-0.500000 + 0.866025i) q^{65} +(1.00000 + 1.73205i) q^{67} +(7.00000 + 12.1244i) q^{73} +(0.500000 - 0.866025i) q^{75} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} -5.00000 q^{85} +(-2.50000 - 4.33013i) q^{87} +(1.00000 - 1.73205i) q^{93} +(3.00000 + 5.19615i) q^{95} -9.00000 q^{97} -6.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - q^{5} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 - q^5 + 2 * q^9	$ 2 q + q^{3} - q^{5} + 2 q^{9} - 3 q^{11} + 2 q^{13} - 2 q^{15} + 5 q^{17} + 6 q^{19} - q^{25} + 10 q^{27} - 10 q^{29} - 2 q^{31} + 3 q^{33} + 4 q^{37} + q^{39} - 4 q^{41} + 20 q^{43} + 2 q^{45} + 9 q^{47} - 5 q^{51} - 6 q^{53} + 6 q^{55} + 12 q^{57} + 6 q^{59} + 12 q^{61} - q^{65} + 2 q^{67} + 14 q^{73} + q^{75} - q^{79} - q^{81} + 24 q^{83} - 10 q^{85} - 5 q^{87} + 2 q^{93} + 6 q^{95} - 18 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q + q^3 - q^5 + 2 * q^9 - 3 * q^11 + 2 * q^13 - 2 * q^15 + 5 * q^17 + 6 * q^19 - q^25 + 10 * q^27 - 10 * q^29 - 2 * q^31 + 3 * q^33 + 4 * q^37 + q^39 - 4 * q^41 + 20 * q^43 + 2 * q^45 + 9 * q^47 - 5 * q^51 - 6 * q^53 + 6 * q^55 + 12 * q^57 + 6 * q^59 + 12 * q^61 - q^65 + 2 * q^67 + 14 * q^73 + q^75 - q^79 - q^81 + 24 * q^83 - 10 * q^85 - 5 * q^87 + 2 * q^93 + 6 * q^95 - 18 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$		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
$7$		0			0
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	0.991838	+	0.127502i	$0.0406959\pi$
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	−0.385499	+	0.922708i	$0.625971\pi$
$18$		0			0
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$		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
$27$	5.00000			0.962250
$28$		0			0
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$		0			0
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$		0			0
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$		0			0
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	−0.325150	−	0.945662i	$-0.605415\pi$
$47$	4.50000	−	7.79423i	0.656392	−	1.13691i	0.981543	−	0.191243i	$-0.0612518\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.50000	+	4.33013i	−0.350070	+	0.606339i
$52$		0			0
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	3.00000			0.404520
$56$		0			0
$57$	6.00000			0.794719
$58$		0			0
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	6.00000	−	10.3923i	0.768221	−	1.33060i	−0.170305	−	0.985391i	$-0.554475\pi$
$61$	6.00000	−	10.3923i	0.768221	−	1.33060i	0.938527	−	0.345207i	$-0.112191\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	0.906208	+	0.422833i	$0.138964\pi$
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	−0.0869195	+	0.996215i	$0.527702\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	−0.892781	−	0.450490i	$-0.851249\pi$
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	0.836527	+	0.547926i	$0.184582\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−5.00000			−0.542326
$86$		0			0
$87$	−2.50000	−	4.33013i	−0.268028	−	0.464238i
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.00000	−	1.73205i	0.103695	−	0.179605i
$94$		0			0
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$		0			0
$97$	−9.00000			−0.913812			−0.456906	−	0.889515i	$-0.651042\pi$
$97$	−9.00000			−0.913812			−0.456906	+	0.889515i	$0.651042\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$		0			0
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$		0			0
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	−0.840341	−	0.542059i	$-0.817645\pi$
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	0.889607	+	0.456727i	$0.150978\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	−0.910306	−	0.413936i	$-0.864154\pi$
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	0.813632	+	0.581380i	$0.197487\pi$
$108$		0			0
$109$	9.50000	+	16.4545i	0.909935	+	1.57605i	0.814152	+	0.580651i	$0.197202\pi$
$109$	9.50000	+	16.4545i	0.909935	+	1.57605i	0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$	−4.00000			−0.376288			−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000			−0.376288			−0.188144	+	0.982141i	$0.560247\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−6.00000			−0.532414			−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000			−0.532414			−0.266207	+	0.963916i	$0.585770\pi$
$128$		0			0
$129$	5.00000	+	8.66025i	0.440225	+	0.762493i
$130$		0			0
$131$	8.00000	−	13.8564i	0.698963	−	1.21064i	−0.269863	−	0.962899i	$-0.586978\pi$
$131$	8.00000	−	13.8564i	0.698963	−	1.21064i	0.968826	−	0.247741i	$-0.0796882\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$		0			0
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	0.767853	−	0.640626i	$-0.221325\pi$
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	−0.938725	+	0.344668i	$0.887992\pi$
$138$		0			0
$139$	16.0000			1.35710			0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000			1.35710			0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$	9.00000			0.757937
$142$		0			0
$143$	−1.50000	−	2.59808i	−0.125436	−	0.217262i
$144$		0			0
$145$	2.50000	−	4.33013i	0.207614	−	0.359597i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$		0			0
$151$	−4.50000	−	7.79423i	−0.366205	−	0.634285i	0.622764	−	0.782410i	$-0.286010\pi$
$151$	−4.50000	−	7.79423i	−0.366205	−	0.634285i	−0.988969	+	0.148124i	$0.952676\pi$
$152$		0			0
$153$	10.0000			0.808452
$154$		0			0
$155$	2.00000			0.160644
$156$		0			0
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	0.903167	−	0.429289i	$-0.141236\pi$
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	−0.823359	+	0.567521i	$0.807902\pi$
$158$		0			0
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$		0			0
$165$	1.50000	+	2.59808i	0.116775	+	0.202260i
$166$		0			0
$167$	−5.00000			−0.386912			−0.193456	−	0.981109i	$-0.561970\pi$
$167$	−5.00000			−0.386912			−0.193456	+	0.981109i	$0.561970\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−6.00000	−	10.3923i	−0.458831	−	0.794719i
$172$		0			0
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	0.426329	+	0.904568i	$0.359807\pi$
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	−0.996544	+	0.0830722i	$0.973527\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$		0			0
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	0.949048	+	0.315130i	$0.102048\pi$
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	−0.201613	+	0.979465i	$0.564618\pi$
$180$		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
$183$	12.0000			0.887066
$184$		0			0
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$		0			0
$187$	7.50000	−	12.9904i	0.548454	−	0.949951i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.5000	−	21.6506i	0.904468	−	1.56658i	0.0828388	−	0.996563i	$-0.473601\pi$
$191$	12.5000	−	21.6506i	0.904468	−	1.56658i	0.821629	−	0.570022i	$-0.193065\pi$
$192$		0			0
$193$	−12.0000	−	20.7846i	−0.863779	−	1.49611i	−0.868255	−	0.496119i	$-0.834758\pi$
$193$	−12.0000	−	20.7846i	−0.863779	−	1.49611i	0.00447566	−	0.999990i	$-0.498575\pi$
$194$		0			0
$195$	−1.00000			−0.0716115
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	−11.0000	−	19.0526i	−0.779769	−	1.35060i	−0.932075	−	0.362267i	$-0.882003\pi$
$199$	−11.0000	−	19.0526i	−0.779769	−	1.35060i	0.152305	−	0.988334i	$-0.451330\pi$
$200$		0			0
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−18.0000			−1.24509
$210$		0			0
$211$	−11.0000			−0.757271			−0.378636	−	0.925546i	$-0.623607\pi$
$211$	−11.0000			−0.757271			−0.378636	+	0.925546i	$0.623607\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.00000	+	8.66025i	−0.340997	+	0.590624i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$		0			0
$221$	2.50000	+	4.33013i	0.168168	+	0.291276i
$222$		0			0
$223$	11.0000			0.736614			0.368307	−	0.929704i	$-0.379937\pi$
$223$	11.0000			0.736614			0.368307	+	0.929704i	$0.379937\pi$
$224$		0			0
$225$	−2.00000			−0.133333
$226$		0			0
$227$	8.50000	+	14.7224i	0.564165	+	0.977162i	0.997127	+	0.0757500i	$0.0241351\pi$
$227$	8.50000	+	14.7224i	0.564165	+	0.977162i	−0.432962	+	0.901412i	$0.642532\pi$
$228$		0			0
$229$	−1.00000	+	1.73205i	−0.0660819	+	0.114457i	−0.897173	−	0.441679i	$-0.854383\pi$
$229$	−1.00000	+	1.73205i	−0.0660819	+	0.114457i	0.831092	+	0.556136i	$0.187717\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	−0.142166	−	0.989843i	$-0.545407\pi$
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	0.928312	−	0.371802i	$-0.121260\pi$
$234$		0			0
$235$	4.50000	+	7.79423i	0.293548	+	0.508439i
$236$		0			0
$237$	−1.00000			−0.0649570
$238$		0			0
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$		0			0
$241$	−2.00000	−	3.46410i	−0.128831	−	0.223142i	0.794393	−	0.607404i	$-0.207789\pi$
$241$	−2.00000	−	3.46410i	−0.128831	−	0.223142i	−0.923224	+	0.384262i	$0.874456\pi$
$242$		0			0
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.00000	−	5.19615i	0.190885	−	0.330623i
$248$		0			0
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−2.50000	−	4.33013i	−0.156556	−	0.271163i
$256$		0			0
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	−0.997429	−	0.0716680i	$-0.977168\pi$
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	0.560781	+	0.827964i	$0.310501\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−5.00000	+	8.66025i	−0.309492	+	0.536056i
$262$		0			0
$263$	−13.0000	−	22.5167i	−0.801614	−	1.38844i	−0.918553	−	0.395298i	$-0.870641\pi$
$263$	−13.0000	−	22.5167i	−0.801614	−	1.38844i	0.116939	−	0.993139i	$-0.462692\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.00000	+	13.8564i	0.487769	+	0.844840i	0.999901	−	0.0140665i	$-0.00447764\pi$
$269$	8.00000	+	13.8564i	0.487769	+	0.844840i	−0.512132	+	0.858906i	$0.671144\pi$
$270$		0			0
$271$	−14.0000	+	24.2487i	−0.850439	+	1.47300i	0.0303728	+	0.999539i	$0.490331\pi$
$271$	−14.0000	+	24.2487i	−0.850439	+	1.47300i	−0.880812	+	0.473466i	$0.843003\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$		0			0
$277$	−2.00000	−	3.46410i	−0.120168	−	0.208138i	0.799666	−	0.600446i	$-0.205010\pi$
$277$	−2.00000	−	3.46410i	−0.120168	−	0.208138i	−0.919834	+	0.392308i	$0.871677\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	27.0000			1.61068			0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000			1.61068			0.805342	+	0.592810i	$0.201981\pi$
$282$		0			0
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	0.850782	−	0.525519i	$-0.176129\pi$
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	−0.880504	+	0.474039i	$0.842796\pi$
$284$		0			0
$285$	−3.00000	+	5.19615i	−0.177705	+	0.307794i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	−4.50000	−	7.79423i	−0.263795	−	0.456906i
$292$		0			0
$293$	−29.0000			−1.69420			−0.847099	−	0.531435i	$-0.821653\pi$
$293$	−29.0000			−1.69420			−0.847099	+	0.531435i	$0.821653\pi$
$294$		0			0
$295$	−6.00000			−0.349334
$296$		0			0
$297$	−7.50000	−	12.9904i	−0.435194	−	0.753778i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−9.00000	+	15.5885i	−0.517036	+	0.895533i
$304$		0			0
$305$	6.00000	+	10.3923i	0.343559	+	0.595062i
$306$		0			0
$307$	25.0000			1.42683			0.713413	−	0.700744i	$-0.247149\pi$
$307$	25.0000			1.42683			0.713413	+	0.700744i	$0.247149\pi$
$308$		0			0
$309$	1.00000			0.0568880
$310$		0			0
$311$	−11.0000	−	19.0526i	−0.623753	−	1.08037i	−0.988781	−	0.149375i	$-0.952274\pi$
$311$	−11.0000	−	19.0526i	−0.623753	−	1.08037i	0.365028	−	0.930997i	$-0.381059\pi$
$312$		0			0
$313$	−6.50000	+	11.2583i	−0.367402	+	0.636358i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−6.50000	+	11.2583i	−0.367402	+	0.636358i	0.621757	+	0.783210i	$0.286419\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	−0.971589	−	0.236675i	$-0.923942\pi$
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	0.690761	+	0.723083i	$0.257276\pi$
$318$		0			0
$319$	7.50000	+	12.9904i	0.419919	+	0.727322i
$320$		0			0
$321$	−2.00000			−0.111629
$322$		0			0
$323$	30.0000			1.66924
$324$		0			0
$325$	−0.500000	−	0.866025i	−0.0277350	−	0.0480384i
$326$		0			0
$327$	−9.50000	+	16.4545i	−0.525351	+	0.909935i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$		0			0
$333$	−4.00000	−	6.92820i	−0.219199	−	0.379663i
$334$		0			0
$335$	−2.00000			−0.109272
$336$		0			0
$337$	32.0000			1.74315			0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000			1.74315			0.871576	+	0.490261i	$0.163099\pi$
$338$		0			0
$339$	−2.00000	−	3.46410i	−0.108625	−	0.188144i
$340$		0			0
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−18.0000	−	31.1769i	−0.966291	−	1.67366i	−0.706107	−	0.708105i	$-0.749550\pi$
$347$	−18.0000	−	31.1769i	−0.966291	−	1.67366i	−0.260184	−	0.965559i	$-0.583783\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$		0			0
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	0.823343	−	0.567545i	$-0.192107\pi$
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	−0.903179	+	0.429263i	$0.858773\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$		0			0
$363$	2.00000			0.104973
$364$		0			0
$365$	−14.0000			−0.732793
$366$		0			0
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	−0.992776	−	0.119982i	$-0.961716\pi$
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	0.392481	−	0.919760i	$-0.371617\pi$
$368$		0			0
$369$	−2.00000	+	3.46410i	−0.104116	+	0.180334i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	12.0000	−	20.7846i	0.621336	−	1.07619i	−0.367901	−	0.929865i	$-0.619923\pi$
$373$	12.0000	−	20.7846i	0.621336	−	1.07619i	0.989237	−	0.146321i	$-0.0467433\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	−5.00000			−0.257513
$378$		0			0
$379$	−32.0000			−1.64373			−0.821865	−	0.569683i	$-0.807066\pi$
$379$	−32.0000			−1.64373			−0.821865	+	0.569683i	$0.807066\pi$
$380$		0			0
$381$	−3.00000	−	5.19615i	−0.153695	−	0.266207i
$382$		0			0
$383$	−16.0000	+	27.7128i	−0.817562	+	1.41606i	0.0899119	+	0.995950i	$0.471341\pi$
$383$	−16.0000	+	27.7128i	−0.817562	+	1.41606i	−0.907474	+	0.420109i	$0.861992\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	10.0000	−	17.3205i	0.508329	−	0.880451i
$388$		0			0
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	0.991100	−	0.133120i	$-0.0424994\pi$
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	−0.610835	+	0.791758i	$0.709166\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	16.0000			0.807093
$394$		0			0
$395$	−0.500000	−	0.866025i	−0.0251577	−	0.0435745i
$396$		0			0
$397$	−5.50000	+	9.52628i	−0.276037	+	0.478110i	−0.970396	−	0.241518i	$-0.922355\pi$
$397$	−5.50000	+	9.52628i	−0.276037	+	0.478110i	0.694359	+	0.719629i	$0.255688\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.50000	+	11.2583i	−0.324595	+	0.562214i	−0.981430	−	0.191820i	$-0.938561\pi$
$401$	−6.50000	+	11.2583i	−0.324595	+	0.562214i	0.656836	+	0.754034i	$0.271895\pi$
$402$		0			0
$403$	−1.00000	−	1.73205i	−0.0498135	−	0.0862796i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−12.0000			−0.594818
$408$		0			0
$409$	−17.0000	−	29.4449i	−0.840596	−	1.45595i	−0.889392	−	0.457146i	$-0.848872\pi$
$409$	−17.0000	−	29.4449i	−0.840596	−	1.45595i	0.0487958	−	0.998809i	$-0.484462\pi$
$410$		0			0
$411$	2.00000	−	3.46410i	0.0986527	−	0.170872i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$		0			0
$417$	8.00000	+	13.8564i	0.391762	+	0.678551i
$418$		0			0
$419$	−22.0000			−1.07477			−0.537385	−	0.843337i	$-0.680588\pi$
$419$	−22.0000			−1.07477			−0.537385	+	0.843337i	$0.680588\pi$
$420$		0			0
$421$	13.0000			0.633581			0.316791	−	0.948495i	$-0.397395\pi$
$421$	13.0000			0.633581			0.316791	+	0.948495i	$0.397395\pi$
$422$		0			0
$423$	−9.00000	−	15.5885i	−0.437595	−	0.757937i
$424$		0			0
$425$	2.50000	−	4.33013i	0.121268	−	0.210042i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1.50000	−	2.59808i	0.0724207	−	0.125436i
$430$		0			0
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	0.827636	−	0.561266i	$-0.189685\pi$
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	−0.899888	+	0.436121i	$0.856352\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	5.00000			0.239732
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	0.310228	+	0.950662i	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.00000	+	15.5885i	−0.427603	+	0.740630i	−0.996660	−	0.0816684i	$-0.973975\pi$
$443$	−9.00000	+	15.5885i	−0.427603	+	0.740630i	0.569057	+	0.822298i	$0.307309\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−18.0000			−0.851371
$448$		0			0
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$		0			0
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$		0			0
$453$	4.50000	−	7.79423i	0.211428	−	0.366205i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	−0.996038	−	0.0889312i	$-0.971655\pi$
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	0.575036	+	0.818128i	$0.304988\pi$
$458$		0			0
$459$	12.5000	+	21.6506i	0.583450	+	1.01057i
$460$		0			0
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$	40.0000			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$464$		0			0
$465$	1.00000	+	1.73205i	0.0463739	+	0.0803219i
$466$		0			0
$467$	1.50000	−	2.59808i	0.0694117	−	0.120225i	−0.829231	−	0.558906i	$-0.811221\pi$
$467$	1.50000	−	2.59808i	0.0694117	−	0.120225i	0.898642	+	0.438682i	$0.144554\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.00000	+	1.73205i	−0.0460776	+	0.0798087i
$472$		0			0
$473$	−15.0000	−	25.9808i	−0.689701	−	1.19460i
$474$		0			0
$475$	−6.00000			−0.275299
$476$		0			0
$477$	−12.0000			−0.549442
$478$		0			0
$479$	2.00000	+	3.46410i	0.0913823	+	0.158279i	0.908093	−	0.418769i	$-0.137538\pi$
$479$	2.00000	+	3.46410i	0.0913823	+	0.158279i	−0.816711	+	0.577047i	$0.804205\pi$
$480$		0			0
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.50000	−	7.79423i	0.204334	−	0.353918i
$486$		0			0
$487$	14.0000	+	24.2487i	0.634401	+	1.09881i	0.986642	+	0.162905i	$0.0520863\pi$
$487$	14.0000	+	24.2487i	0.634401	+	1.09881i	−0.352241	+	0.935909i	$0.614580\pi$
$488$		0			0
$489$	8.00000			0.361773
$490$		0			0
$491$	−3.00000			−0.135388			−0.0676941	−	0.997706i	$-0.521564\pi$
$491$	−3.00000			−0.135388			−0.0676941	+	0.997706i	$0.521564\pi$
$492$		0			0
$493$	−12.5000	−	21.6506i	−0.562972	−	0.975096i
$494$		0			0
$495$	3.00000	−	5.19615i	0.134840	−	0.233550i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−3.50000	+	6.06218i	−0.156682	+	0.271380i	−0.933670	−	0.358134i	$-0.883413\pi$
$499$	−3.50000	+	6.06218i	−0.156682	+	0.271380i	0.776989	+	0.629515i	$0.216746\pi$
$500$		0			0
$501$	−2.50000	−	4.33013i	−0.111692	−	0.193456i
$502$		0			0
$503$	−39.0000			−1.73892			−0.869462	−	0.494000i	$-0.835534\pi$
$503$	−39.0000			−1.73892			−0.869462	+	0.494000i	$0.835534\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$		0			0
$509$	−20.0000	+	34.6410i	−0.886484	+	1.53544i	−0.0424816	+	0.999097i	$0.513526\pi$
$509$	−20.0000	+	34.6410i	−0.886484	+	1.53544i	−0.844003	+	0.536339i	$0.819807\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	15.0000	−	25.9808i	0.662266	−	1.14708i
$514$		0			0
$515$	0.500000	+	0.866025i	0.0220326	+	0.0381616i
$516$		0			0
$517$	−27.0000			−1.18746
$518$		0			0
$519$	−15.0000			−0.658427
$520$		0			0
$521$	13.0000	+	22.5167i	0.569540	+	0.986473i	0.996611	+	0.0822547i	$0.0262121\pi$
$521$	13.0000	+	22.5167i	0.569540	+	0.986473i	−0.427071	+	0.904218i	$0.640455\pi$
$522$		0			0
$523$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$523$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.00000	−	8.66025i	0.217803	−	0.377247i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	12.0000			0.520756
$532$		0			0
$533$	−2.00000			−0.0866296
$534$		0			0
$535$	−1.00000	−	1.73205i	−0.0432338	−	0.0748831i
$536$		0			0
$537$	−10.0000	+	17.3205i	−0.431532	+	0.747435i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−7.50000	+	12.9904i	−0.322450	+	0.558500i	−0.980993	−	0.194043i	$-0.937840\pi$
$541$	−7.50000	+	12.9904i	−0.322450	+	0.558500i	0.658543	+	0.752543i	$0.271173\pi$
$542$		0			0
$543$	−5.00000	−	8.66025i	−0.214571	−	0.371647i
$544$		0			0
$545$	−19.0000			−0.813871
$546$		0			0
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$		0			0
$549$	−12.0000	−	20.7846i	−0.512148	−	0.887066i
$550$		0			0
$551$	−15.0000	+	25.9808i	−0.639021	+	1.10682i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$		0			0
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	0.964686	−	0.263404i	$-0.0848453\pi$
$557$	6.00000	+	10.3923i	0.254228	+	0.440336i	−0.710457	+	0.703740i	$0.751512\pi$
$558$		0			0
$559$	10.0000			0.422955
$560$		0			0
$561$	15.0000			0.633300
$562$		0			0
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	0.996082	−	0.0884397i	$-0.0281881\pi$
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	−0.574632	+	0.818412i	$0.694855\pi$
$564$		0			0
$565$	2.00000	−	3.46410i	0.0841406	−	0.145736i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.00000	+	1.73205i	−0.0419222	+	0.0726113i	−0.886225	−	0.463255i	$-0.846681\pi$
$569$	−1.00000	+	1.73205i	−0.0419222	+	0.0726113i	0.844303	+	0.535866i	$0.180015\pi$
$570$		0			0
$571$	−18.0000	−	31.1769i	−0.753277	−	1.30471i	−0.946227	−	0.323505i	$-0.895139\pi$
$571$	−18.0000	−	31.1769i	−0.753277	−	1.30471i	0.192950	−	0.981209i	$-0.438194\pi$
$572$		0			0
$573$	25.0000			1.04439
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−4.50000	−	7.79423i	−0.187337	−	0.324478i	0.757024	−	0.653387i	$-0.226652\pi$
$577$	−4.50000	−	7.79423i	−0.187337	−	0.324478i	−0.944362	+	0.328909i	$0.893319\pi$
$578$		0			0
$579$	12.0000	−	20.7846i	0.498703	−	0.863779i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$		0			0
$585$	1.00000	+	1.73205i	0.0413449	+	0.0716115i
$586$		0			0
$587$	−20.0000			−0.825488			−0.412744	−	0.910847i	$-0.635430\pi$
$587$	−20.0000			−0.825488			−0.412744	+	0.910847i	$0.635430\pi$
$588$		0			0
$589$	−12.0000			−0.494451
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$		0			0
$593$	1.50000	−	2.59808i	0.0615976	−	0.106690i	−0.833582	−	0.552396i	$-0.813714\pi$
$593$	1.50000	−	2.59808i	0.0615976	−	0.106690i	0.895180	+	0.445705i	$0.147047\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	11.0000	−	19.0526i	0.450200	−	0.779769i
$598$		0			0
$599$	8.50000	+	14.7224i	0.347301	+	0.601542i	0.985769	−	0.168106i	$-0.0537650\pi$
$599$	8.50000	+	14.7224i	0.347301	+	0.601542i	−0.638468	+	0.769648i	$0.720432\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$	4.00000			0.162893
$604$		0			0
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$		0			0
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	−0.967256	−	0.253804i	$-0.918318\pi$
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	0.703429	+	0.710766i	$0.251651\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.50000	−	7.79423i	0.182051	−	0.315321i
$612$		0			0
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	0.553716	−	0.832705i	$-0.313209\pi$
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	−0.998002	+	0.0631797i	$0.979876\pi$
$614$		0			0
$615$	2.00000			0.0806478
$616$		0			0
$617$	−12.0000			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$618$		0			0
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.846566	+	0.532284i	$0.178666\pi$
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.0376891	+	0.999290i	$0.488000\pi$
$620$		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
$627$	−9.00000	−	15.5885i	−0.359425	−	0.622543i
$628$		0			0
$629$	20.0000			0.797452
$630$		0			0
$631$	−37.0000			−1.47295			−0.736473	−	0.676467i	$-0.763510\pi$
$631$	−37.0000			−1.47295			−0.736473	+	0.676467i	$0.763510\pi$
$632$		0			0
$633$	−5.50000	−	9.52628i	−0.218605	−	0.378636i
$634$		0			0
$635$	3.00000	−	5.19615i	0.119051	−	0.206203i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	5.00000	+	8.66025i	0.197488	+	0.342059i	0.947713	−	0.319123i	$-0.103388\pi$
$641$	5.00000	+	8.66025i	0.197488	+	0.342059i	−0.750225	+	0.661182i	$0.770055\pi$
$642$		0			0
$643$	−9.00000			−0.354925			−0.177463	−	0.984128i	$-0.556789\pi$
$643$	−9.00000			−0.354925			−0.177463	+	0.984128i	$0.556789\pi$
$644$		0			0
$645$	−10.0000			−0.393750
$646$		0			0
$647$	10.0000	+	17.3205i	0.393141	+	0.680939i	0.992862	−	0.119269i	$-0.0380552\pi$
$647$	10.0000	+	17.3205i	0.393141	+	0.680939i	−0.599721	+	0.800209i	$0.704722\pi$
$648$		0			0
$649$	9.00000	−	15.5885i	0.353281	−	0.611900i
$650$		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
$655$	8.00000	+	13.8564i	0.312586	+	0.541415i
$656$		0			0
$657$	28.0000			1.09238
$658$		0			0
$659$	−33.0000			−1.28550			−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000			−1.28550			−0.642749	+	0.766077i	$0.722206\pi$
$660$		0			0
$661$	−22.0000	−	38.1051i	−0.855701	−	1.48212i	−0.875993	−	0.482323i	$-0.839793\pi$
$661$	−22.0000	−	38.1051i	−0.855701	−	1.48212i	0.0202925	−	0.999794i	$-0.493540\pi$
$662$		0			0
$663$	−2.50000	+	4.33013i	−0.0970920	+	0.168168i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	5.50000	+	9.52628i	0.212642	+	0.368307i
$670$		0			0
$671$	−36.0000			−1.38976
$672$		0			0
$673$	−40.0000			−1.54189			−0.770943	−	0.636904i	$-0.780215\pi$
$673$	−40.0000			−1.54189			−0.770943	+	0.636904i	$0.780215\pi$
$674$		0			0
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$		0			0
$677$	1.50000	−	2.59808i	0.0576497	−	0.0998522i	−0.835760	−	0.549095i	$-0.814973\pi$
$677$	1.50000	−	2.59808i	0.0576497	−	0.0998522i	0.893410	+	0.449242i	$0.148306\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−8.50000	+	14.7224i	−0.325721	+	0.564165i
$682$		0			0
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	0.972242	+	0.233977i	$0.0751739\pi$
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	−0.283491	+	0.958975i	$0.591493\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$		0			0
$687$	−2.00000			−0.0763048
$688$		0			0
$689$	−3.00000	−	5.19615i	−0.114291	−	0.197958i
$690$		0			0
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	−0.957290	−	0.289130i	$-0.906634\pi$
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	0.729039	+	0.684472i	$0.239967\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.00000	+	13.8564i	−0.303457	+	0.525603i
$696$		0			0
$697$	−5.00000	−	8.66025i	−0.189389	−	0.328031i
$698$		0			0
$699$	24.0000			0.907763
$700$		0			0
$701$	27.0000			1.01978			0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000			1.01978			0.509888	+	0.860241i	$0.329687\pi$
$702$		0			0
$703$	−12.0000	−	20.7846i	−0.452589	−	0.783906i
$704$		0			0
$705$	−4.50000	+	7.79423i	−0.169480	+	0.293548i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−13.5000	+	23.3827i	−0.507003	+	0.878155i	0.492964	+	0.870050i	$0.335913\pi$
$709$	−13.5000	+	23.3827i	−0.507003	+	0.878155i	−0.999967	+	0.00810550i	$0.997420\pi$
$710$		0			0
$711$	1.00000	+	1.73205i	0.0375029	+	0.0649570i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	3.00000			0.112194
$716$		0			0
$717$	−7.50000	−	12.9904i	−0.280093	−	0.485135i
$718$		0			0
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	−0.998224	−	0.0595683i	$-0.981028\pi$
$719$	−12.0000	+	20.7846i	−0.447524	+	0.775135i	0.550700	+	0.834703i	$0.314361\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.00000	−	3.46410i	0.0743808	−	0.128831i
$724$		0			0
$725$	2.50000	+	4.33013i	0.0928477	+	0.160817i
$726$		0			0
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	25.0000	+	43.3013i	0.924658	+	1.60156i
$732$		0			0
$733$	25.5000	−	44.1673i	0.941864	−	1.63136i	0.179952	−	0.983675i	$-0.442406\pi$
$733$	25.5000	−	44.1673i	0.941864	−	1.63136i	0.761912	−	0.647681i	$-0.224261\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.00000	−	5.19615i	0.110506	−	0.191403i
$738$		0			0
$739$	16.5000	+	28.5788i	0.606962	+	1.05129i	0.991738	+	0.128279i	$0.0409454\pi$
$739$	16.5000	+	28.5788i	0.606962	+	1.05129i	−0.384776	+	0.923010i	$0.625721\pi$
$740$		0			0
$741$	6.00000			0.220416
$742$		0			0
$743$	54.0000			1.98107			0.990534	−	0.137268i	$-0.0438322\pi$
$743$	54.0000			1.98107			0.990534	+	0.137268i	$0.0438322\pi$
$744$		0			0
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$		0			0
$747$	12.0000	−	20.7846i	0.439057	−	0.760469i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$		0			0
$753$	−6.00000	−	10.3923i	−0.218652	−	0.378717i
$754$		0			0
$755$	9.00000			0.327544
$756$		0			0
$757$	24.0000			0.872295			0.436147	−	0.899875i	$-0.356343\pi$
$757$	24.0000			0.872295			0.436147	+	0.899875i	$0.356343\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.0000	+	20.7846i	−0.435000	+	0.753442i	−0.997296	−	0.0734946i	$-0.976585\pi$
$761$	−12.0000	+	20.7846i	−0.435000	+	0.753442i	0.562296	+	0.826936i	$0.309918\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−5.00000	+	8.66025i	−0.180775	+	0.313112i
$766$		0			0
$767$	3.00000	+	5.19615i	0.108324	+	0.187622i
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$	−14.0000			−0.504198
$772$		0			0
$773$	11.5000	+	19.9186i	0.413626	+	0.716422i	0.995283	−	0.0970125i	$-0.0309287\pi$
$773$	11.5000	+	19.9186i	0.413626	+	0.716422i	−0.581657	+	0.813434i	$0.697595\pi$
$774$		0			0
$775$	−1.00000	+	1.73205i	−0.0359211	+	0.0622171i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−25.0000			−0.893427
$784$		0			0
$785$	−2.00000			−0.0713831
$786$		0			0
$787$	22.5000	+	38.9711i	0.802038	+	1.38917i	0.918272	+	0.395949i	$0.129584\pi$
$787$	22.5000	+	38.9711i	0.802038	+	1.38917i	−0.116234	+	0.993222i	$0.537082\pi$
$788$		0			0
$789$	13.0000	−	22.5167i	0.462812	−	0.801614i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6.00000	−	10.3923i	0.213066	−	0.369042i
$794$		0			0
$795$	3.00000	+	5.19615i	0.106399	+	0.184289i
$796$		0			0
$797$	39.0000			1.38145			0.690725	−	0.723117i	$-0.257291\pi$
$797$	39.0000			1.38145			0.690725	+	0.723117i	$0.257291\pi$
$798$		0			0
$799$	45.0000			1.59199
$800$		0			0
$801$		0			0
$802$		0			0
$803$	21.0000	−	36.3731i	0.741074	−	1.28358i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−8.00000	+	13.8564i	−0.281613	+	0.487769i
$808$		0			0
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	0.891189	−	0.453632i	$-0.149872\pi$
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	−0.838452	+	0.544976i	$0.816539\pi$
$810$		0			0
$811$	40.0000			1.40459			0.702295	−	0.711886i	$-0.252159\pi$
$811$	40.0000			1.40459			0.702295	+	0.711886i	$0.252159\pi$
$812$		0			0
$813$	−28.0000			−0.982003
$814$		0			0
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$		0			0
$817$	30.0000	−	51.9615i	1.04957	−	1.81790i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.50000	+	4.33013i	−0.0872506	+	0.151122i	−0.906348	−	0.422532i	$-0.861141\pi$
$821$	−2.50000	+	4.33013i	−0.0872506	+	0.151122i	0.819097	+	0.573654i	$0.194475\pi$
$822$		0			0
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	0.545428	−	0.838157i	$-0.316367\pi$
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	−0.998580	+	0.0532760i	$0.983034\pi$
$824$		0			0
$825$	−3.00000			−0.104447
$826$		0			0
$827$	−8.00000			−0.278187			−0.139094	−	0.990279i	$-0.544419\pi$
$827$	−8.00000			−0.278187			−0.139094	+	0.990279i	$0.544419\pi$
$828$		0			0
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	0.939696	−	0.342012i	$-0.111108\pi$
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	−0.766039	+	0.642795i	$0.777775\pi$
$830$		0			0
$831$	2.00000	−	3.46410i	0.0693792	−	0.120168i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.50000	−	4.33013i	0.0865161	−	0.149850i
$836$		0			0
$837$	−5.00000	−	8.66025i	−0.172825	−	0.299342i
$838$		0			0
$839$	−52.0000			−1.79524			−0.897620	−	0.440771i	$-0.854705\pi$
$839$	−52.0000			−1.79524			−0.897620	+	0.440771i	$0.854705\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$		0			0
$843$	13.5000	+	23.3827i	0.464965	+	0.805342i
$844$		0			0
$845$	6.00000	−	10.3923i	0.206406	−	0.357506i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.500000	−	0.866025i	0.0171600	−	0.0297219i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−22.0000			−0.753266			−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000			−0.753266			−0.376633	+	0.926363i	$0.622918\pi$
$854$		0			0
$855$	12.0000			0.410391
$856$		0			0
$857$	19.0000	+	32.9090i	0.649028	+	1.12415i	0.983355	+	0.181692i	$0.0581574\pi$
$857$	19.0000	+	32.9090i	0.649028	+	1.12415i	−0.334328	+	0.942457i	$0.608509\pi$
$858$		0			0
$859$	10.0000	−	17.3205i	0.341196	−	0.590968i	−0.643459	−	0.765480i	$-0.722501\pi$
$859$	10.0000	−	17.3205i	0.341196	−	0.590968i	0.984655	+	0.174512i	$0.0558348\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.00000	−	15.5885i	0.306364	−	0.530637i	−0.671200	−	0.741276i	$-0.734221\pi$
$863$	9.00000	−	15.5885i	0.306364	−	0.530637i	0.977564	+	0.210639i	$0.0675543\pi$
$864$		0			0
$865$	−7.50000	−	12.9904i	−0.255008	−	0.441686i
$866$		0			0
$867$	−8.00000			−0.271694
$868$		0			0
$869$	3.00000			0.101768
$870$		0			0
$871$	1.00000	+	1.73205i	0.0338837	+	0.0586883i
$872$		0			0
$873$	−9.00000	+	15.5885i	−0.304604	+	0.527589i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−15.0000	+	25.9808i	−0.506514	+	0.877308i	0.493458	+	0.869770i	$0.335733\pi$
$877$	−15.0000	+	25.9808i	−0.506514	+	0.877308i	−0.999972	+	0.00753813i	$0.997601\pi$
$878$		0			0
$879$	−14.5000	−	25.1147i	−0.489073	−	0.847099i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	36.0000			1.21150			0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000			1.21150			0.605748	+	0.795656i	$0.292874\pi$
$884$		0			0
$885$	−3.00000	−	5.19615i	−0.100844	−	0.174667i
$886$		0			0
$887$	−16.0000	+	27.7128i	−0.537227	+	0.930505i	0.461825	+	0.886971i	$0.347195\pi$
$887$	−16.0000	+	27.7128i	−0.537227	+	0.930505i	−0.999052	+	0.0435339i	$0.986138\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$		0			0
$893$	−27.0000	−	46.7654i	−0.903521	−	1.56494i
$894$		0			0
$895$	−20.0000			−0.668526
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.00000	+	8.66025i	0.166759	+	0.288836i
$900$		0			0
$901$	15.0000	−	25.9808i	0.499722	−	0.865545i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$		0			0
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	0.650868	−	0.759191i	$-0.274405\pi$
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	−0.982913	+	0.184073i	$0.941072\pi$
$908$		0			0
$909$	36.0000			1.19404
$910$		0			0
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$		0			0
$913$	−18.0000	−	31.1769i	−0.595713	−	1.03181i
$914$		0			0
$915$	−6.00000	+	10.3923i	−0.198354	+	0.343559i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−8.50000	+	14.7224i	−0.280389	+	0.485648i	−0.971481	−	0.237119i	$-0.923797\pi$
$919$	−8.50000	+	14.7224i	−0.280389	+	0.485648i	0.691091	+	0.722767i	$0.257130\pi$
$920$		0			0
$921$	12.5000	+	21.6506i	0.411889	+	0.713413i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−4.00000			−0.131519
$926$		0			0
$927$	−1.00000	−	1.73205i	−0.0328443	−	0.0568880i
$928$		0			0
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	−0.283178	−	0.959067i	$-0.591389\pi$
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	0.972166	−	0.234294i	$-0.0752779\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	11.0000	−	19.0526i	0.360124	−	0.623753i
$934$		0			0
$935$	7.50000	+	12.9904i	0.245276	+	0.424831i
$936$		0			0
$937$	43.0000			1.40475			0.702374	−	0.711808i	$-0.252123\pi$
$937$	43.0000			1.40475			0.702374	+	0.711808i	$0.252123\pi$
$938$		0			0
$939$	−13.0000			−0.424239
$940$		0			0
$941$	6.00000	+	10.3923i	0.195594	+	0.338779i	0.947095	−	0.320953i	$-0.104003\pi$
$941$	6.00000	+	10.3923i	0.195594	+	0.338779i	−0.751501	+	0.659732i	$0.770670\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.0000	−	22.5167i	0.422443	−	0.731693i	−0.573735	−	0.819041i	$-0.694506\pi$
$947$	13.0000	−	22.5167i	0.422443	−	0.731693i	0.996178	+	0.0873481i	$0.0278392\pi$
$948$		0			0
$949$	7.00000	+	12.1244i	0.227230	+	0.393573i
$950$		0			0
$951$	−10.0000			−0.324272
$952$		0			0
$953$	−34.0000			−1.10137			−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000			−1.10137			−0.550684	+	0.834714i	$0.685633\pi$
$954$		0			0
$955$	12.5000	+	21.6506i	0.404491	+	0.700598i
$956$		0			0
$957$	−7.50000	+	12.9904i	−0.242441	+	0.419919i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		0			0
$963$	2.00000	+	3.46410i	0.0644491	+	0.111629i
$964$		0			0
$965$	24.0000			0.772587
$966$		0			0
$967$	−50.0000			−1.60789			−0.803946	−	0.594703i	$-0.797270\pi$
$967$	−50.0000			−1.60789			−0.803946	+	0.594703i	$0.797270\pi$
$968$		0			0
$969$	15.0000	+	25.9808i	0.481869	+	0.834622i
$970$		0			0
$971$	7.00000	−	12.1244i	0.224641	−	0.389089i	−0.731571	−	0.681765i	$-0.761212\pi$
$971$	7.00000	−	12.1244i	0.224641	−	0.389089i	0.956212	+	0.292676i	$0.0945458\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$		0			0
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	38.0000			1.21325
$982$		0			0
$983$	17.5000	+	30.3109i	0.558163	+	0.966767i	0.997650	+	0.0685181i	$0.0218271\pi$
$983$	17.5000	+	30.3109i	0.558163	+	0.966767i	−0.439487	+	0.898249i	$0.644840\pi$
$984$		0			0
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−18.0000	−	31.1769i	−0.571789	−	0.990367i	−0.996382	−	0.0849833i	$-0.972916\pi$
$991$	−18.0000	−	31.1769i	−0.571789	−	0.990367i	0.424594	−	0.905384i	$-0.360417\pi$
$992$		0			0
$993$	20.0000			0.634681
$994$		0			0
$995$	22.0000			0.697447
$996$		0			0
$997$	−7.50000	−	12.9904i	−0.237527	−	0.411409i	0.722477	−	0.691395i	$-0.243004\pi$
$997$	−7.50000	−	12.9904i	−0.237527	−	0.411409i	−0.960004	+	0.279986i	$0.909670\pi$
$998$		0			0
$999$	10.0000	−	17.3205i	0.316386	−	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.j.961.1		2
7.2	even	3		1960.2.a.f.1.1	✓	1
7.3	odd	6		1960.2.q.f.361.1		2
7.4	even	3	inner	1960.2.q.j.361.1		2
7.5	odd	6		1960.2.a.j.1.1	yes	1
7.6	odd	2		1960.2.q.f.961.1		2
28.19	even	6		3920.2.a.l.1.1		1
28.23	odd	6		3920.2.a.x.1.1		1
35.9	even	6		9800.2.a.bd.1.1		1
35.19	odd	6		9800.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.f.1.1	✓	1	7.2	even	3
1960.2.a.j.1.1	yes	1	7.5	odd	6
1960.2.q.f.361.1		2	7.3	odd	6
1960.2.q.f.961.1		2	7.6	odd	2
1960.2.q.j.361.1		2	7.4	even	3	inner
1960.2.q.j.961.1		2	1.1	even	1	trivial
3920.2.a.l.1.1		1	28.19	even	6
3920.2.a.x.1.1		1	28.23	odd	6
9800.2.a.t.1.1		1	35.19	odd	6
9800.2.a.bd.1.1		1	35.9	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:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} +1.00000 q^{13} -1.00000 q^{15} +(2.50000 + 4.33013i) q^{17} +(3.00000 - 5.19615i) q^{19} +(-0.500000 - 0.866025i) q^{25} +5.00000 q^{27} -5.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(1.50000 - 2.59808i) q^{33} +(2.00000 - 3.46410i) q^{37} +(0.500000 + 0.866025i) q^{39} -2.00000 q^{41} +10.0000 q^{43} +(1.00000 + 1.73205i) q^{45} +(4.50000 - 7.79423i) q^{47} +(-2.50000 + 4.33013i) q^{51} +(-3.00000 - 5.19615i) q^{53} +3.00000 q^{55} +6.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(6.00000 - 10.3923i) q^{61} +(-0.500000 + 0.866025i) q^{65} +(1.00000 + 1.73205i) q^{67} +(7.00000 + 12.1244i) q^{73} +(0.500000 - 0.866025i) q^{75} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} -5.00000 q^{85} +(-2.50000 - 4.33013i) q^{87} +(1.00000 - 1.73205i) q^{93} +(3.00000 + 5.19615i) q^{95} -9.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - q^{5} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 - q^5 + 2 * q^9	\( 2 q + q^{3} - q^{5} + 2 q^{9} - 3 q^{11} + 2 q^{13} - 2 q^{15} + 5 q^{17} + 6 q^{19} - q^{25} + 10 q^{27} - 10 q^{29} - 2 q^{31} + 3 q^{33} + 4 q^{37} + q^{39} - 4 q^{41} + 20 q^{43} + 2 q^{45} + 9 q^{47} - 5 q^{51} - 6 q^{53} + 6 q^{55} + 12 q^{57} + 6 q^{59} + 12 q^{61} - q^{65} + 2 q^{67} + 14 q^{73} + q^{75} - q^{79} - q^{81} + 24 q^{83} - 10 q^{85} - 5 q^{87} + 2 q^{93} + 6 q^{95} - 18 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q + q^3 - q^5 + 2 * q^9 - 3 * q^11 + 2 * q^13 - 2 * q^15 + 5 * q^17 + 6 * q^19 - q^25 + 10 * q^27 - 10 * q^29 - 2 * q^31 + 3 * q^33 + 4 * q^37 + q^39 - 4 * q^41 + 20 * q^43 + 2 * q^45 + 9 * q^47 - 5 * q^51 - 6 * q^53 + 6 * q^55 + 12 * q^57 + 6 * q^59 + 12 * q^61 - q^65 + 2 * q^67 + 14 * q^73 + q^75 - q^79 - q^81 + 24 * q^83 - 10 * q^85 - 5 * q^87 + 2 * q^93 + 6 * q^95 - 18 * q^97 - 12 * q^99

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