LMFDB - Embedded newform 2940.2.q.p.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2940,2,Mod(361,2940)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2940, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2940.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,2,0,0,0,-2,0,4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2940.361
Dual form			2940.2.q.p.961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -2.82843 q^{13} -1.00000 q^{15} +(0.585786 - 1.01461i) q^{17} +(-2.70711 - 4.68885i) q^{19} +(3.70711 + 6.42090i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +3.65685 q^{29} +(-2.12132 + 3.67423i) q^{31} +(1.00000 + 1.73205i) q^{33} +(5.24264 + 9.08052i) q^{37} +(1.41421 - 2.44949i) q^{39} -2.00000 q^{41} +1.65685 q^{43} +(0.500000 - 0.866025i) q^{45} +(5.24264 + 9.08052i) q^{47} +(0.585786 + 1.01461i) q^{51} +(2.29289 - 3.97141i) q^{53} +2.00000 q^{55} +5.41421 q^{57} +(-1.41421 + 2.44949i) q^{59} +(4.94975 + 8.57321i) q^{61} +(-1.41421 - 2.44949i) q^{65} +(3.41421 - 5.91359i) q^{67} -7.41421 q^{69} -10.4853 q^{71} +(-2.24264 + 3.88437i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(5.00000 + 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -4.82843 q^{83} +1.17157 q^{85} +(-1.82843 + 3.16693i) q^{87} +(2.41421 + 4.18154i) q^{89} +(-2.12132 - 3.67423i) q^{93} +(2.70711 - 4.68885i) q^{95} +4.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{5} - 2 q^{9} + 4 q^{11} - 4 q^{15} + 8 q^{17} - 8 q^{19} + 12 q^{23} - 2 q^{25} + 4 q^{27} - 8 q^{29} + 4 q^{33} + 4 q^{37} - 8 q^{41} - 16 q^{43} + 2 q^{45} + 4 q^{47} + 8 q^{51} + 12 q^{53}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^5 - 2 * q^9 + 4 * q^11 - 4 * q^15 + 8 * q^17 - 8 * q^19 + 12 * q^23 - 2 * q^25 + 4 * q^27 - 8 * q^29 + 4 * q^33 + 4 * q^37 - 8 * q^41 - 16 * q^43 + 2 * q^45 + 4 * q^47 + 8 * q^51 + 12 * q^53 + 8 * q^55 + 16 * q^57 + 8 * q^67 - 24 * q^69 - 8 * q^71 + 8 * q^73 - 2 * q^75 + 20 * q^79 - 2 * q^81 - 8 * q^83 + 16 * q^85 + 4 * q^87 + 4 * q^89 + 8 * q^95 + 16 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		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
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−2.82843			−0.784465			−0.392232	−	0.919866i	$-0.628297\pi$
$13$	−2.82843			−0.784465			−0.392232	+	0.919866i	$0.628297\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	0.585786	−	1.01461i	0.142074	−	0.246080i	−0.786203	−	0.617968i	$-0.787956\pi$
$17$	0.585786	−	1.01461i	0.142074	−	0.246080i	0.928278	+	0.371888i	$0.121290\pi$
$18$		0			0
$19$	−2.70711	−	4.68885i	−0.621053	−	1.07570i	−0.989290	−	0.145963i	$-0.953372\pi$
$19$	−2.70711	−	4.68885i	−0.621053	−	1.07570i	0.368237	−	0.929732i	$-0.379961\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.70711	+	6.42090i	0.772985	+	1.33885i	0.935920	+	0.352213i	$0.114571\pi$
$23$	3.70711	+	6.42090i	0.772985	+	1.33885i	−0.162935	+	0.986637i	$0.552096\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	3.65685			0.679061			0.339530	−	0.940595i	$-0.389732\pi$
$29$	3.65685			0.679061			0.339530	+	0.940595i	$0.389732\pi$
$30$		0			0
$31$	−2.12132	+	3.67423i	−0.381000	+	0.659912i	−0.991206	−	0.132331i	$-0.957754\pi$
$31$	−2.12132	+	3.67423i	−0.381000	+	0.659912i	0.610205	+	0.792243i	$0.291087\pi$
$32$		0			0
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.24264	+	9.08052i	0.861885	+	1.49283i	0.870107	+	0.492862i	$0.164049\pi$
$37$	5.24264	+	9.08052i	0.861885	+	1.49283i	−0.00822261	+	0.999966i	$0.502617\pi$
$38$		0			0
$39$	1.41421	−	2.44949i	0.226455	−	0.392232i
$40$		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
$43$	1.65685			0.252668			0.126334	−	0.991988i	$-0.459679\pi$
$43$	1.65685			0.252668			0.126334	+	0.991988i	$0.459679\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	5.24264	+	9.08052i	0.764718	+	1.32453i	0.940396	+	0.340082i	$0.110455\pi$
$47$	5.24264	+	9.08052i	0.764718	+	1.32453i	−0.175678	+	0.984448i	$0.556212\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.585786	+	1.01461i	0.0820265	+	0.142074i
$52$		0			0
$53$	2.29289	−	3.97141i	0.314953	−	0.545515i	−0.664474	−	0.747311i	$-0.731345\pi$
$53$	2.29289	−	3.97141i	0.314953	−	0.545515i	0.979428	+	0.201796i	$0.0646779\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$		0			0
$57$	5.41421			0.717130
$58$		0			0
$59$	−1.41421	+	2.44949i	−0.184115	+	0.318896i	−0.943278	−	0.332004i	$-0.892275\pi$
$59$	−1.41421	+	2.44949i	−0.184115	+	0.318896i	0.759163	+	0.650901i	$0.225609\pi$
$60$		0			0
$61$	4.94975	+	8.57321i	0.633750	+	1.09769i	0.986778	+	0.162075i	$0.0518186\pi$
$61$	4.94975	+	8.57321i	0.633750	+	1.09769i	−0.353028	+	0.935613i	$0.614848\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.41421	−	2.44949i	−0.175412	−	0.303822i
$66$		0			0
$67$	3.41421	−	5.91359i	0.417113	−	0.722460i	−0.578535	−	0.815657i	$-0.696375\pi$
$67$	3.41421	−	5.91359i	0.417113	−	0.722460i	0.995648	+	0.0931973i	$0.0297087\pi$
$68$		0			0
$69$	−7.41421			−0.892566
$70$		0			0
$71$	−10.4853			−1.24437			−0.622187	−	0.782869i	$-0.713756\pi$
$71$	−10.4853			−1.24437			−0.622187	+	0.782869i	$0.713756\pi$
$72$		0			0
$73$	−2.24264	+	3.88437i	−0.262481	+	0.454631i	−0.966901	−	0.255153i	$-0.917874\pi$
$73$	−2.24264	+	3.88437i	−0.262481	+	0.454631i	0.704419	+	0.709784i	$0.251207\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−4.82843			−0.529989			−0.264994	−	0.964250i	$-0.585370\pi$
$83$	−4.82843			−0.529989			−0.264994	+	0.964250i	$0.585370\pi$
$84$		0			0
$85$	1.17157			0.127075
$86$		0			0
$87$	−1.82843	+	3.16693i	−0.196028	+	0.339530i
$88$		0			0
$89$	2.41421	+	4.18154i	0.255906	+	0.443242i	0.965141	−	0.261730i	$-0.0842929\pi$
$89$	2.41421	+	4.18154i	0.255906	+	0.443242i	−0.709235	+	0.704972i	$0.750960\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.12132	−	3.67423i	−0.219971	−	0.381000i
$94$		0			0
$95$	2.70711	−	4.68885i	0.277743	−	0.481065i
$96$		0			0
$97$	4.00000			0.406138			0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000			0.406138			0.203069	+	0.979164i	$0.434908\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$		0			0
$101$	−5.82843	+	10.0951i	−0.579950	+	1.00450i	0.415534	+	0.909578i	$0.363595\pi$
$101$	−5.82843	+	10.0951i	−0.579950	+	1.00450i	−0.995484	+	0.0949256i	$0.969739\pi$
$102$		0			0
$103$	−1.41421	−	2.44949i	−0.139347	−	0.241355i	0.787903	−	0.615800i	$-0.211167\pi$
$103$	−1.41421	−	2.44949i	−0.139347	−	0.241355i	−0.927249	+	0.374444i	$0.877834\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.53553	−	4.39167i	−0.245119	−	0.424559i	0.717046	−	0.697026i	$-0.245494\pi$
$107$	−2.53553	−	4.39167i	−0.245119	−	0.424559i	−0.962165	+	0.272467i	$0.912160\pi$
$108$		0			0
$109$	2.17157	−	3.76127i	0.207999	−	0.360265i	−0.743085	−	0.669197i	$-0.766638\pi$
$109$	2.17157	−	3.76127i	0.207999	−	0.360265i	0.951084	+	0.308932i	$0.0999716\pi$
$110$		0			0
$111$	−10.4853			−0.995219
$112$		0			0
$113$	−6.24264			−0.587258			−0.293629	−	0.955919i	$-0.594863\pi$
$113$	−6.24264			−0.587258			−0.293629	+	0.955919i	$0.594863\pi$
$114$		0			0
$115$	−3.70711	+	6.42090i	−0.345689	+	0.598752i
$116$		0			0
$117$	1.41421	+	2.44949i	0.130744	+	0.226455i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	1.00000	−	1.73205i	0.0901670	−	0.156174i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	14.1421			1.25491			0.627456	−	0.778652i	$-0.284096\pi$
$127$	14.1421			1.25491			0.627456	+	0.778652i	$0.284096\pi$
$128$		0			0
$129$	−0.828427	+	1.43488i	−0.0729389	+	0.126334i
$130$		0			0
$131$	−5.65685	−	9.79796i	−0.494242	−	0.856052i	0.505736	−	0.862688i	$-0.331221\pi$
$131$	−5.65685	−	9.79796i	−0.494242	−	0.856052i	−0.999978	+	0.00663646i	$0.997888\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$		0			0
$137$	3.94975	−	6.84116i	0.337450	−	0.584480i	−0.646503	−	0.762912i	$-0.723769\pi$
$137$	3.94975	−	6.84116i	0.337450	−	0.584480i	0.983952	+	0.178432i	$0.0571024\pi$
$138$		0			0
$139$	−7.55635			−0.640921			−0.320461	−	0.947262i	$-0.603838\pi$
$139$	−7.55635			−0.640921			−0.320461	+	0.947262i	$0.603838\pi$
$140$		0			0
$141$	−10.4853			−0.883020
$142$		0			0
$143$	−2.82843	+	4.89898i	−0.236525	+	0.409673i
$144$		0			0
$145$	1.82843	+	3.16693i	0.151843	+	0.262999i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.82843	+	17.0233i	0.805176	+	1.39461i	0.916172	+	0.400785i	$0.131263\pi$
$149$	9.82843	+	17.0233i	0.805176	+	1.39461i	−0.110996	+	0.993821i	$0.535404\pi$
$150$		0			0
$151$	−2.65685	+	4.60181i	−0.216212	+	0.374490i	−0.953647	−	0.300928i	$-0.902703\pi$
$151$	−2.65685	+	4.60181i	−0.216212	+	0.374490i	0.737435	+	0.675418i	$0.236037\pi$
$152$		0			0
$153$	−1.17157			−0.0947161
$154$		0			0
$155$	−4.24264			−0.340777
$156$		0			0
$157$	−5.07107	+	8.78335i	−0.404715	+	0.700987i	−0.994288	−	0.106728i	$-0.965963\pi$
$157$	−5.07107	+	8.78335i	−0.404715	+	0.700987i	0.589573	+	0.807715i	$0.299296\pi$
$158$		0			0
$159$	2.29289	+	3.97141i	0.181838	+	0.314953i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	9.07107	+	15.7116i	0.710501	+	1.23062i	0.964669	+	0.263464i	$0.0848649\pi$
$163$	9.07107	+	15.7116i	0.710501	+	1.23062i	−0.254168	+	0.967160i	$0.581802\pi$
$164$		0			0
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$		0			0
$167$	−16.0000			−1.23812			−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000			−1.23812			−0.619059	+	0.785345i	$0.712486\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$		0			0
$171$	−2.70711	+	4.68885i	−0.207018	+	0.358565i
$172$		0			0
$173$	7.07107	+	12.2474i	0.537603	+	0.931156i	0.999032	+	0.0439792i	$0.0140035\pi$
$173$	7.07107	+	12.2474i	0.537603	+	0.931156i	−0.461429	+	0.887177i	$0.652663\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.41421	−	2.44949i	−0.106299	−	0.184115i
$178$		0			0
$179$	5.24264	−	9.08052i	0.391853	−	0.678710i	−0.600841	−	0.799369i	$-0.705167\pi$
$179$	5.24264	−	9.08052i	0.391853	−	0.678710i	0.992694	+	0.120659i	$0.0385007\pi$
$180$		0			0
$181$	24.2426			1.80194			0.900971	−	0.433880i	$-0.142856\pi$
$181$	24.2426			1.80194			0.900971	+	0.433880i	$0.142856\pi$
$182$		0			0
$183$	−9.89949			−0.731792
$184$		0			0
$185$	−5.24264	+	9.08052i	−0.385447	+	0.667613i
$186$		0			0
$187$	−1.17157	−	2.02922i	−0.0856739	−	0.148392i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.48528	−	12.9649i	−0.541616	−	0.938106i	−0.998811	−	0.0487401i	$-0.984479\pi$
$191$	−7.48528	−	12.9649i	−0.541616	−	0.938106i	0.457196	−	0.889366i	$-0.348854\pi$
$192$		0			0
$193$	−6.41421	+	11.1097i	−0.461705	+	0.799697i	−0.999046	−	0.0436683i	$-0.986096\pi$
$193$	−6.41421	+	11.1097i	−0.461705	+	0.799697i	0.537341	+	0.843365i	$0.319429\pi$
$194$		0			0
$195$	2.82843			0.202548
$196$		0			0
$197$	13.0711			0.931275			0.465638	−	0.884976i	$-0.345825\pi$
$197$	13.0711			0.931275			0.465638	+	0.884976i	$0.345825\pi$
$198$		0			0
$199$	−4.12132	+	7.13834i	−0.292153	+	0.506023i	−0.974319	−	0.225174i	$-0.927705\pi$
$199$	−4.12132	+	7.13834i	−0.292153	+	0.506023i	0.682166	+	0.731197i	$0.261038\pi$
$200$		0			0
$201$	3.41421	+	5.91359i	0.240820	+	0.417113i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$		0			0
$207$	3.70711	−	6.42090i	0.257662	−	0.446283i
$208$		0			0
$209$	−10.8284			−0.749018
$210$		0			0
$211$	−17.6569			−1.21555			−0.607774	−	0.794110i	$-0.707937\pi$
$211$	−17.6569			−1.21555			−0.607774	+	0.794110i	$0.707937\pi$
$212$		0			0
$213$	5.24264	−	9.08052i	0.359220	−	0.622187i
$214$		0			0
$215$	0.828427	+	1.43488i	0.0564983	+	0.0978579i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−2.24264	−	3.88437i	−0.151544	−	0.262481i
$220$		0			0
$221$	−1.65685	+	2.86976i	−0.111452	+	0.193041i
$222$		0			0
$223$	5.17157			0.346314			0.173157	−	0.984894i	$-0.444603\pi$
$223$	5.17157			0.346314			0.173157	+	0.984894i	$0.444603\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	−0.791989	−	0.610535i	$-0.790954\pi$
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	0.924734	+	0.380615i	$0.124288\pi$
$228$		0			0
$229$	2.70711	+	4.68885i	0.178891	+	0.309848i	0.941501	−	0.337011i	$-0.109416\pi$
$229$	2.70711	+	4.68885i	0.178891	+	0.309848i	−0.762610	+	0.646858i	$0.776082\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.36396	−	2.36245i	−0.0893561	−	0.154769i	0.817883	−	0.575384i	$-0.195148\pi$
$233$	−1.36396	−	2.36245i	−0.0893561	−	0.154769i	−0.907239	+	0.420615i	$0.861814\pi$
$234$		0			0
$235$	−5.24264	+	9.08052i	−0.341992	+	0.592348i
$236$		0			0
$237$	−10.0000			−0.649570
$238$		0			0
$239$	−19.6569			−1.27150			−0.635748	−	0.771897i	$-0.719308\pi$
$239$	−19.6569			−1.27150			−0.635748	+	0.771897i	$0.719308\pi$
$240$		0			0
$241$	−14.7071	+	25.4735i	−0.947368	+	1.64089i	−0.196429	+	0.980518i	$0.562935\pi$
$241$	−14.7071	+	25.4735i	−0.947368	+	1.64089i	−0.750939	+	0.660372i	$0.770399\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.65685	+	13.2621i	0.487194	+	0.843845i
$248$		0			0
$249$	2.41421	−	4.18154i	0.152995	−	0.264994i
$250$		0			0
$251$	11.5147			0.726803			0.363401	−	0.931633i	$-0.381615\pi$
$251$	11.5147			0.726803			0.363401	+	0.931633i	$0.381615\pi$
$252$		0			0
$253$	14.8284			0.932255
$254$		0			0
$255$	−0.585786	+	1.01461i	−0.0366834	+	0.0635375i
$256$		0			0
$257$	10.6569	+	18.4582i	0.664756	+	1.15139i	0.979351	+	0.202166i	$0.0647980\pi$
$257$	10.6569	+	18.4582i	0.664756	+	1.15139i	−0.314595	+	0.949226i	$0.601869\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.82843	−	3.16693i	−0.113177	−	0.196028i
$262$		0			0
$263$	8.53553	−	14.7840i	0.526324	−	0.911619i	−0.473206	−	0.880952i	$-0.656903\pi$
$263$	8.53553	−	14.7840i	0.526324	−	0.911619i	0.999530	−	0.0306674i	$-0.00976327\pi$
$264$		0			0
$265$	4.58579			0.281703
$266$		0			0
$267$	−4.82843			−0.295495
$268$		0			0
$269$	7.58579	−	13.1390i	0.462514	−	0.801097i	−0.536572	−	0.843855i	$-0.680281\pi$
$269$	7.58579	−	13.1390i	0.462514	−	0.801097i	0.999085	+	0.0427576i	$0.0136143\pi$
$270$		0			0
$271$	−10.1213	−	17.5306i	−0.614826	−	1.06491i	−0.990415	−	0.138124i	$-0.955893\pi$
$271$	−10.1213	−	17.5306i	−0.614826	−	1.06491i	0.375589	−	0.926787i	$-0.377441\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.00000	+	1.73205i	0.0603023	+	0.104447i
$276$		0			0
$277$	−2.65685	+	4.60181i	−0.159635	+	0.276496i	−0.934737	−	0.355340i	$-0.884365\pi$
$277$	−2.65685	+	4.60181i	−0.159635	+	0.276496i	0.775102	+	0.631836i	$0.217698\pi$
$278$		0			0
$279$	4.24264			0.254000
$280$		0			0
$281$	−2.97056			−0.177209			−0.0886045	−	0.996067i	$-0.528241\pi$
$281$	−2.97056			−0.177209			−0.0886045	+	0.996067i	$0.528241\pi$
$282$		0			0
$283$	4.24264	−	7.34847i	0.252199	−	0.436821i	−0.711932	−	0.702248i	$-0.752180\pi$
$283$	4.24264	−	7.34847i	0.252199	−	0.436821i	0.964131	+	0.265427i	$0.0855130\pi$
$284$		0			0
$285$	2.70711	+	4.68885i	0.160355	+	0.277743i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.81371	+	13.5337i	0.459630	+	0.796102i
$290$		0			0
$291$	−2.00000	+	3.46410i	−0.117242	+	0.203069i
$292$		0			0
$293$	−3.65685			−0.213636			−0.106818	−	0.994279i	$-0.534066\pi$
$293$	−3.65685			−0.213636			−0.106818	+	0.994279i	$0.534066\pi$
$294$		0			0
$295$	−2.82843			−0.164677
$296$		0			0
$297$	1.00000	−	1.73205i	0.0580259	−	0.100504i
$298$		0			0
$299$	−10.4853	−	18.1610i	−0.606379	−	1.05028i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−5.82843	−	10.0951i	−0.334834	−	0.579950i
$304$		0			0
$305$	−4.94975	+	8.57321i	−0.283422	+	0.490901i
$306$		0			0
$307$	1.65685			0.0945617			0.0472808	−	0.998882i	$-0.484944\pi$
$307$	1.65685			0.0945617			0.0472808	+	0.998882i	$0.484944\pi$
$308$		0			0
$309$	2.82843			0.160904
$310$		0			0
$311$	−4.34315	+	7.52255i	−0.246277	+	0.426565i	−0.962490	−	0.271317i	$-0.912541\pi$
$311$	−4.34315	+	7.52255i	−0.246277	+	0.426565i	0.716213	+	0.697882i	$0.245874\pi$
$312$		0			0
$313$	−14.2426	−	24.6690i	−0.805042	−	1.39437i	−0.916263	−	0.400577i	$-0.868810\pi$
$313$	−14.2426	−	24.6690i	−0.805042	−	1.39437i	0.111221	−	0.993796i	$-0.464524\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.0502525	−	0.0870399i	−0.00282246	−	0.00488865i	0.864611	−	0.502442i	$-0.167565\pi$
$317$	−0.0502525	−	0.0870399i	−0.00282246	−	0.00488865i	−0.867433	+	0.497554i	$0.834232\pi$
$318$		0			0
$319$	3.65685	−	6.33386i	0.204745	−	0.354628i
$320$		0			0
$321$	5.07107			0.283039
$322$		0			0
$323$	−6.34315			−0.352942
$324$		0			0
$325$	1.41421	−	2.44949i	0.0784465	−	0.135873i
$326$		0			0
$327$	2.17157	+	3.76127i	0.120088	+	0.207999i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	17.3137	+	29.9882i	0.951647	+	1.64830i	0.741860	+	0.670555i	$0.233944\pi$
$331$	17.3137	+	29.9882i	0.951647	+	1.64830i	0.209787	+	0.977747i	$0.432723\pi$
$332$		0			0
$333$	5.24264	−	9.08052i	0.287295	−	0.497609i
$334$		0			0
$335$	6.82843			0.373077
$336$		0			0
$337$	33.7990			1.84115			0.920574	−	0.390568i	$-0.127721\pi$
$337$	33.7990			1.84115			0.920574	+	0.390568i	$0.127721\pi$
$338$		0			0
$339$	3.12132	−	5.40629i	0.169527	−	0.293629i
$340$		0			0
$341$	4.24264	+	7.34847i	0.229752	+	0.397942i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−3.70711	−	6.42090i	−0.199584	−	0.345689i
$346$		0			0
$347$	−6.29289	+	10.8996i	−0.337820	+	0.585122i	−0.984022	−	0.178044i	$-0.943023\pi$
$347$	−6.29289	+	10.8996i	−0.337820	+	0.585122i	0.646202	+	0.763166i	$0.276356\pi$
$348$		0			0
$349$	29.2132			1.56375			0.781873	−	0.623437i	$-0.214264\pi$
$349$	29.2132			1.56375			0.781873	+	0.623437i	$0.214264\pi$
$350$		0			0
$351$	−2.82843			−0.150970
$352$		0			0
$353$	−15.1421	+	26.2269i	−0.805935	+	1.39592i	0.109724	+	0.993962i	$0.465003\pi$
$353$	−15.1421	+	26.2269i	−0.805935	+	1.39592i	−0.915658	+	0.401957i	$0.868330\pi$
$354$		0			0
$355$	−5.24264	−	9.08052i	−0.278250	−	0.481944i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−13.4853	−	23.3572i	−0.711726	−	1.23275i	−0.964209	−	0.265144i	$-0.914580\pi$
$359$	−13.4853	−	23.3572i	−0.711726	−	1.23275i	0.252483	−	0.967601i	$-0.418753\pi$
$360$		0			0
$361$	−5.15685	+	8.93193i	−0.271413	+	0.470102i
$362$		0			0
$363$	−7.00000			−0.367405
$364$		0			0
$365$	−4.48528			−0.234770
$366$		0			0
$367$	15.4142	−	26.6982i	0.804615	−	1.39363i	−0.111935	−	0.993716i	$-0.535705\pi$
$367$	15.4142	−	26.6982i	0.804615	−	1.39363i	0.916550	−	0.399919i	$-0.130962\pi$
$368$		0			0
$369$	1.00000	+	1.73205i	0.0520579	+	0.0901670i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.34315	−	2.32640i	−0.0695455	−	0.120456i	0.829156	−	0.559018i	$-0.188822\pi$
$373$	−1.34315	−	2.32640i	−0.0695455	−	0.120456i	−0.898701	+	0.438561i	$0.855488\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	−10.3431			−0.532699
$378$		0			0
$379$	31.9411			1.64071			0.820353	−	0.571858i	$-0.193777\pi$
$379$	31.9411			1.64071			0.820353	+	0.571858i	$0.193777\pi$
$380$		0			0
$381$	−7.07107	+	12.2474i	−0.362262	+	0.627456i
$382$		0			0
$383$	1.92893	+	3.34101i	0.0985638	+	0.170718i	0.911090	−	0.412207i	$-0.135242\pi$
$383$	1.92893	+	3.34101i	0.0985638	+	0.170718i	−0.812527	+	0.582924i	$0.801908\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.828427	−	1.43488i	−0.0421113	−	0.0729389i
$388$		0			0
$389$	−3.58579	+	6.21076i	−0.181807	+	0.314898i	−0.942496	−	0.334218i	$-0.891528\pi$
$389$	−3.58579	+	6.21076i	−0.181807	+	0.314898i	0.760689	+	0.649116i	$0.224861\pi$
$390$		0			0
$391$	8.68629			0.439285
$392$		0			0
$393$	11.3137			0.570701
$394$		0			0
$395$	−5.00000	+	8.66025i	−0.251577	+	0.435745i
$396$		0			0
$397$	14.1421	+	24.4949i	0.709773	+	1.22936i	0.964941	+	0.262467i	$0.0845360\pi$
$397$	14.1421	+	24.4949i	0.709773	+	1.22936i	−0.255168	+	0.966897i	$0.582131\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−19.2426	−	33.3292i	−0.960932	−	1.66438i	−0.720169	−	0.693798i	$-0.755936\pi$
$401$	−19.2426	−	33.3292i	−0.960932	−	1.66438i	−0.240762	−	0.970584i	$-0.577397\pi$
$402$		0			0
$403$	6.00000	−	10.3923i	0.298881	−	0.517678i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	20.9706			1.03947
$408$		0			0
$409$	12.3640	−	21.4150i	0.611359	−	1.05890i	−0.379653	−	0.925129i	$-0.623957\pi$
$409$	12.3640	−	21.4150i	0.611359	−	1.05890i	0.991012	−	0.133775i	$-0.0427100\pi$
$410$		0			0
$411$	3.94975	+	6.84116i	0.194827	+	0.337450i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.41421	−	4.18154i	−0.118509	−	0.205264i
$416$		0			0
$417$	3.77817	−	6.54399i	0.185018	−	0.320461i
$418$		0			0
$419$	−32.9706			−1.61072			−0.805359	−	0.592788i	$-0.798027\pi$
$419$	−32.9706			−1.61072			−0.805359	+	0.592788i	$0.798027\pi$
$420$		0			0
$421$	−32.2843			−1.57344			−0.786720	−	0.617311i	$-0.788222\pi$
$421$	−32.2843			−1.57344			−0.786720	+	0.617311i	$0.788222\pi$
$422$		0			0
$423$	5.24264	−	9.08052i	0.254906	−	0.441510i
$424$		0			0
$425$	0.585786	+	1.01461i	0.0284148	+	0.0492159i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.82843	−	4.89898i	−0.136558	−	0.236525i
$430$		0			0
$431$	−19.2426	+	33.3292i	−0.926885	+	1.60541i	−0.138385	+	0.990379i	$0.544191\pi$
$431$	−19.2426	+	33.3292i	−0.926885	+	1.60541i	−0.788501	+	0.615034i	$0.789142\pi$
$432$		0			0
$433$	13.1716			0.632985			0.316493	−	0.948595i	$-0.397495\pi$
$433$	13.1716			0.632985			0.316493	+	0.948595i	$0.397495\pi$
$434$		0			0
$435$	−3.65685			−0.175333
$436$		0			0
$437$	20.0711	−	34.7641i	0.960129	−	1.66299i
$438$		0			0
$439$	−12.3640	−	21.4150i	−0.590100	−	1.02208i	−0.994218	−	0.107376i	$-0.965755\pi$
$439$	−12.3640	−	21.4150i	−0.590100	−	1.02208i	0.404119	−	0.914707i	$-0.367578\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.2929	+	17.8278i	0.489030	+	0.847025i	0.999920	−	0.0126209i	$-0.00401748\pi$
$443$	10.2929	+	17.8278i	0.489030	+	0.847025i	−0.510890	+	0.859646i	$0.670684\pi$
$444$		0			0
$445$	−2.41421	+	4.18154i	−0.114445	+	0.198224i
$446$		0			0
$447$	−19.6569			−0.929737
$448$		0			0
$449$	22.0000			1.03824			0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000			1.03824			0.519122	+	0.854700i	$0.326259\pi$
$450$		0			0
$451$	−2.00000	+	3.46410i	−0.0941763	+	0.163118i
$452$		0			0
$453$	−2.65685	−	4.60181i	−0.124830	−	0.216212i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.75736	−	8.23999i	−0.222540	−	0.385450i	0.733039	−	0.680187i	$-0.238101\pi$
$457$	−4.75736	−	8.23999i	−0.222540	−	0.385450i	−0.955579	+	0.294737i	$0.904768\pi$
$458$		0			0
$459$	0.585786	−	1.01461i	0.0273422	−	0.0473580i
$460$		0			0
$461$	11.4558			0.533552			0.266776	−	0.963759i	$-0.414042\pi$
$461$	11.4558			0.533552			0.266776	+	0.963759i	$0.414042\pi$
$462$		0			0
$463$	−5.85786			−0.272238			−0.136119	−	0.990692i	$-0.543463\pi$
$463$	−5.85786			−0.272238			−0.136119	+	0.990692i	$0.543463\pi$
$464$		0			0
$465$	2.12132	−	3.67423i	0.0983739	−	0.170389i
$466$		0			0
$467$	−14.9706	−	25.9298i	−0.692755	−	1.19989i	−0.970932	−	0.239357i	$-0.923063\pi$
$467$	−14.9706	−	25.9298i	−0.692755	−	1.19989i	0.278177	−	0.960530i	$-0.410270\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−5.07107	−	8.78335i	−0.233662	−	0.404715i
$472$		0			0
$473$	1.65685	−	2.86976i	0.0761822	−	0.131952i
$474$		0			0
$475$	5.41421			0.248421
$476$		0			0
$477$	−4.58579			−0.209969
$478$		0			0
$479$	16.9706	−	29.3939i	0.775405	−	1.34304i	−0.159162	−	0.987252i	$-0.550879\pi$
$479$	16.9706	−	29.3939i	0.775405	−	1.34304i	0.934567	−	0.355788i	$-0.115787\pi$
$480$		0			0
$481$	−14.8284	−	25.6836i	−0.676118	−	1.17107i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.00000	+	3.46410i	0.0908153	+	0.157297i
$486$		0			0
$487$	10.1421	−	17.5667i	0.459584	−	0.796023i	−0.539355	−	0.842079i	$-0.681332\pi$
$487$	10.1421	−	17.5667i	0.459584	−	0.796023i	0.998939	+	0.0460557i	$0.0146652\pi$
$488$		0			0
$489$	−18.1421			−0.820416
$490$		0			0
$491$	−29.1127			−1.31384			−0.656919	−	0.753961i	$-0.728141\pi$
$491$	−29.1127			−1.31384			−0.656919	+	0.753961i	$0.728141\pi$
$492$		0			0
$493$	2.14214	−	3.71029i	0.0964769	−	0.167103i
$494$		0			0
$495$	−1.00000	−	1.73205i	−0.0449467	−	0.0778499i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	15.1421	+	26.2269i	0.677855	+	1.17408i	0.975626	+	0.219442i	$0.0704237\pi$
$499$	15.1421	+	26.2269i	0.677855	+	1.17408i	−0.297770	+	0.954637i	$0.596243\pi$
$500$		0			0
$501$	8.00000	−	13.8564i	0.357414	−	0.619059i
$502$		0			0
$503$	−32.8284			−1.46375			−0.731874	−	0.681440i	$-0.761354\pi$
$503$	−32.8284			−1.46375			−0.731874	+	0.681440i	$0.761354\pi$
$504$		0			0
$505$	−11.6569			−0.518723
$506$		0			0
$507$	2.50000	−	4.33013i	0.111029	−	0.192308i
$508$		0			0
$509$	19.2426	+	33.3292i	0.852915	+	1.47729i	0.878566	+	0.477621i	$0.158501\pi$
$509$	19.2426	+	33.3292i	0.852915	+	1.47729i	−0.0256508	+	0.999671i	$0.508166\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.70711	−	4.68885i	−0.119522	−	0.207018i
$514$		0			0
$515$	1.41421	−	2.44949i	0.0623177	−	0.107937i
$516$		0			0
$517$	20.9706			0.922284
$518$		0			0
$519$	−14.1421			−0.620771
$520$		0			0
$521$	10.5563	−	18.2841i	0.462482	−	0.801042i	−0.536602	−	0.843836i	$-0.680292\pi$
$521$	10.5563	−	18.2841i	0.462482	−	0.801042i	0.999084	+	0.0427931i	$0.0136256\pi$
$522$		0			0
$523$	6.58579	+	11.4069i	0.287976	+	0.498790i	0.973327	−	0.229424i	$-0.0736842\pi$
$523$	6.58579	+	11.4069i	0.287976	+	0.498790i	−0.685350	+	0.728214i	$0.740351\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.48528	+	4.30463i	0.108261	+	0.187513i
$528$		0			0
$529$	−15.9853	+	27.6873i	−0.695012	+	1.20380i
$530$		0			0
$531$	2.82843			0.122743
$532$		0			0
$533$	5.65685			0.245026
$534$		0			0
$535$	2.53553	−	4.39167i	0.109621	−	0.189869i
$536$		0			0
$537$	5.24264	+	9.08052i	0.226237	+	0.391853i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−18.1421	−	31.4231i	−0.779991	−	1.35098i	−0.931946	−	0.362597i	$-0.881890\pi$
$541$	−18.1421	−	31.4231i	−0.779991	−	1.35098i	0.151955	−	0.988387i	$-0.451443\pi$
$542$		0			0
$543$	−12.1213	+	20.9947i	−0.520176	+	0.900971i
$544$		0			0
$545$	4.34315			0.186040
$546$		0			0
$547$	27.1127			1.15926			0.579628	−	0.814881i	$-0.303198\pi$
$547$	27.1127			1.15926			0.579628	+	0.814881i	$0.303198\pi$
$548$		0			0
$549$	4.94975	−	8.57321i	0.211250	−	0.365896i
$550$		0			0
$551$	−9.89949	−	17.1464i	−0.421733	−	0.730462i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−5.24264	−	9.08052i	−0.222538	−	0.385447i
$556$		0			0
$557$	15.8492	−	27.4517i	0.671554	−	1.16317i	−0.305909	−	0.952061i	$-0.598960\pi$
$557$	15.8492	−	27.4517i	0.671554	−	1.16317i	0.977463	−	0.211105i	$-0.0677062\pi$
$558$		0			0
$559$	−4.68629			−0.198209
$560$		0			0
$561$	2.34315			0.0989277
$562$		0			0
$563$	19.2426	−	33.3292i	0.810981	−	1.40466i	−0.101198	−	0.994866i	$-0.532267\pi$
$563$	19.2426	−	33.3292i	0.810981	−	1.40466i	0.912178	−	0.409793i	$-0.134399\pi$
$564$		0			0
$565$	−3.12132	−	5.40629i	−0.131315	−	0.227444i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−17.2426	−	29.8651i	−0.722849	−	1.25201i	−0.959853	−	0.280503i	$-0.909499\pi$
$569$	−17.2426	−	29.8651i	−0.722849	−	1.25201i	0.237004	−	0.971509i	$-0.423835\pi$
$570$		0			0
$571$	−10.1421	+	17.5667i	−0.424435	+	0.735143i	−0.996368	−	0.0851575i	$-0.972861\pi$
$571$	−10.1421	+	17.5667i	−0.424435	+	0.735143i	0.571932	+	0.820301i	$0.306194\pi$
$572$		0			0
$573$	14.9706			0.625404
$574$		0			0
$575$	−7.41421			−0.309194
$576$		0			0
$577$	1.41421	−	2.44949i	0.0588745	−	0.101974i	−0.835086	−	0.550119i	$-0.814582\pi$
$577$	1.41421	−	2.44949i	0.0588745	−	0.101974i	0.893960	+	0.448146i	$0.147915\pi$
$578$		0			0
$579$	−6.41421	−	11.1097i	−0.266566	−	0.461705i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−4.58579	−	7.94282i	−0.189924	−	0.328958i
$584$		0			0
$585$	−1.41421	+	2.44949i	−0.0584705	+	0.101274i
$586$		0			0
$587$	16.8284			0.694584			0.347292	−	0.937757i	$-0.387101\pi$
$587$	16.8284			0.694584			0.347292	+	0.937757i	$0.387101\pi$
$588$		0			0
$589$	22.9706			0.946486
$590$		0			0
$591$	−6.53553	+	11.3199i	−0.268836	+	0.465638i
$592$		0			0
$593$	1.48528	+	2.57258i	0.0609932	+	0.105643i	0.894910	−	0.446247i	$-0.147240\pi$
$593$	1.48528	+	2.57258i	0.0609932	+	0.105643i	−0.833916	+	0.551891i	$0.813907\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.12132	−	7.13834i	−0.168674	−	0.292153i
$598$		0			0
$599$	7.00000	−	12.1244i	0.286012	−	0.495388i	−0.686842	−	0.726807i	$-0.741004\pi$
$599$	7.00000	−	12.1244i	0.286012	−	0.495388i	0.972854	+	0.231419i	$0.0743369\pi$
$600$		0			0
$601$	19.7574			0.805919			0.402960	−	0.915218i	$-0.367981\pi$
$601$	19.7574			0.805919			0.402960	+	0.915218i	$0.367981\pi$
$602$		0			0
$603$	−6.82843			−0.278075
$604$		0			0
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$		0			0
$607$	−10.7279	−	18.5813i	−0.435433	−	0.754192i	0.561898	−	0.827207i	$-0.310071\pi$
$607$	−10.7279	−	18.5813i	−0.435433	−	0.754192i	−0.997331	+	0.0730146i	$0.976738\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−14.8284	−	25.6836i	−0.599894	−	1.03905i
$612$		0			0
$613$	−18.6569	+	32.3146i	−0.753543	+	1.30518i	0.192552	+	0.981287i	$0.438324\pi$
$613$	−18.6569	+	32.3146i	−0.753543	+	1.30518i	−0.946095	+	0.323888i	$0.895010\pi$
$614$		0			0
$615$	2.00000			0.0806478
$616$		0			0
$617$	35.6985			1.43717			0.718583	−	0.695441i	$-0.244791\pi$
$617$	35.6985			1.43717			0.718583	+	0.695441i	$0.244791\pi$
$618$		0			0
$619$	7.05025	−	12.2114i	0.283374	−	0.490817i	−0.688840	−	0.724914i	$-0.741880\pi$
$619$	7.05025	−	12.2114i	0.283374	−	0.490817i	0.972213	+	0.234096i	$0.0752130\pi$
$620$		0			0
$621$	3.70711	+	6.42090i	0.148761	+	0.257662i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	5.41421	−	9.37769i	0.216223	−	0.374509i
$628$		0			0
$629$	12.2843			0.489806
$630$		0			0
$631$	6.68629			0.266177			0.133089	−	0.991104i	$-0.457511\pi$
$631$	6.68629			0.266177			0.133089	+	0.991104i	$0.457511\pi$
$632$		0			0
$633$	8.82843	−	15.2913i	0.350898	−	0.607774i
$634$		0			0
$635$	7.07107	+	12.2474i	0.280607	+	0.486025i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	5.24264	+	9.08052i	0.207396	+	0.359220i
$640$		0			0
$641$	−4.51472	+	7.81972i	−0.178321	+	0.308860i	−0.941305	−	0.337556i	$-0.890400\pi$
$641$	−4.51472	+	7.81972i	−0.178321	+	0.308860i	0.762985	+	0.646416i	$0.223733\pi$
$642$		0			0
$643$	32.2843			1.27317			0.636584	−	0.771208i	$-0.280347\pi$
$643$	32.2843			1.27317			0.636584	+	0.771208i	$0.280347\pi$
$644$		0			0
$645$	−1.65685			−0.0652386
$646$		0			0
$647$	17.6569	−	30.5826i	0.694163	−	1.20232i	−0.276300	−	0.961072i	$-0.589108\pi$
$647$	17.6569	−	30.5826i	0.694163	−	1.20232i	0.970462	−	0.241253i	$-0.0775585\pi$
$648$		0			0
$649$	2.82843	+	4.89898i	0.111025	+	0.192302i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.29289	−	14.3637i	−0.324526	−	0.562096i	0.656890	−	0.753986i	$-0.271871\pi$
$653$	−8.29289	−	14.3637i	−0.324526	−	0.562096i	−0.981416	+	0.191891i	$0.938538\pi$
$654$		0			0
$655$	5.65685	−	9.79796i	0.221032	−	0.382838i
$656$		0			0
$657$	4.48528			0.174987
$658$		0			0
$659$	9.79899			0.381714			0.190857	−	0.981618i	$-0.438873\pi$
$659$	9.79899			0.381714			0.190857	+	0.981618i	$0.438873\pi$
$660$		0			0
$661$	−17.8787	+	30.9668i	−0.695400	+	1.20447i	0.274646	+	0.961546i	$0.411439\pi$
$661$	−17.8787	+	30.9668i	−0.695400	+	1.20447i	−0.970046	+	0.242923i	$0.921894\pi$
$662$		0			0
$663$	−1.65685	−	2.86976i	−0.0643469	−	0.111452i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	13.5563	+	23.4803i	0.524904	+	0.909160i
$668$		0			0
$669$	−2.58579	+	4.47871i	−0.0999723	+	0.173157i
$670$		0			0
$671$	19.7990			0.764332
$672$		0			0
$673$	40.8284			1.57382			0.786910	−	0.617068i	$-0.211680\pi$
$673$	40.8284			1.57382			0.786910	+	0.617068i	$0.211680\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$		0			0
$677$	−21.4853	−	37.2136i	−0.825746	−	1.43023i	−0.901347	−	0.433097i	$-0.857421\pi$
$677$	−21.4853	−	37.2136i	−0.825746	−	1.43023i	0.0756010	−	0.997138i	$-0.475912\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.00000	+	3.46410i	0.0766402	+	0.132745i
$682$		0			0
$683$	1.22183	−	2.11626i	0.0467518	−	0.0809766i	−0.841703	−	0.539942i	$-0.818446\pi$
$683$	1.22183	−	2.11626i	0.0467518	−	0.0809766i	0.888454	+	0.458965i	$0.151780\pi$
$684$		0			0
$685$	7.89949			0.301824
$686$		0			0
$687$	−5.41421			−0.206565
$688$		0			0
$689$	−6.48528	+	11.2328i	−0.247070	+	0.427937i
$690$		0			0
$691$	9.63604	+	16.6901i	0.366572	+	0.634922i	0.989027	−	0.147734i	$-0.0471979\pi$
$691$	9.63604	+	16.6901i	0.366572	+	0.634922i	−0.622455	+	0.782656i	$0.713865\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.77817	−	6.54399i	−0.143314	−	0.248228i
$696$		0			0
$697$	−1.17157	+	2.02922i	−0.0443765	+	0.0768623i
$698$		0			0
$699$	2.72792			0.103179
$700$		0			0
$701$	−30.9706			−1.16974			−0.584871	−	0.811126i	$-0.698855\pi$
$701$	−30.9706			−1.16974			−0.584871	+	0.811126i	$0.698855\pi$
$702$		0			0
$703$	28.3848	−	49.1639i	1.07055	−	1.85425i
$704$		0			0
$705$	−5.24264	−	9.08052i	−0.197449	−	0.341992i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−4.34315	−	7.52255i	−0.163110	−	0.282515i	0.772872	−	0.634562i	$-0.218819\pi$
$709$	−4.34315	−	7.52255i	−0.163110	−	0.282515i	−0.935983	+	0.352046i	$0.885486\pi$
$710$		0			0
$711$	5.00000	−	8.66025i	0.187515	−	0.324785i
$712$		0			0
$713$	−31.4558			−1.17803
$714$		0			0
$715$	−5.65685			−0.211554
$716$		0			0
$717$	9.82843	−	17.0233i	0.367049	−	0.635748i
$718$		0			0
$719$	−6.24264	−	10.8126i	−0.232811	−	0.403241i	0.725823	−	0.687881i	$-0.241459\pi$
$719$	−6.24264	−	10.8126i	−0.232811	−	0.403241i	−0.958634	+	0.284641i	$0.908126\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−14.7071	−	25.4735i	−0.546963	−	0.947368i
$724$		0			0
$725$	−1.82843	+	3.16693i	−0.0679061	+	0.117617i
$726$		0			0
$727$	−43.5980			−1.61696			−0.808480	−	0.588524i	$-0.799709\pi$
$727$	−43.5980			−1.61696			−0.808480	+	0.588524i	$0.799709\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.970563	−	1.68106i	0.0358976	−	0.0621764i
$732$		0			0
$733$	−12.2426	−	21.2049i	−0.452192	−	0.783220i	0.546330	−	0.837570i	$-0.316025\pi$
$733$	−12.2426	−	21.2049i	−0.452192	−	0.783220i	−0.998522	+	0.0543503i	$0.982691\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.82843	−	11.8272i	−0.251528	−	0.435660i
$738$		0			0
$739$	3.31371	−	5.73951i	0.121897	−	0.211131i	−0.798619	−	0.601837i	$-0.794436\pi$
$739$	3.31371	−	5.73951i	0.121897	−	0.211131i	0.920516	+	0.390706i	$0.127769\pi$
$740$		0			0
$741$	−15.3137			−0.562563
$742$		0			0
$743$	−18.0416			−0.661883			−0.330942	−	0.943651i	$-0.607366\pi$
$743$	−18.0416			−0.661883			−0.330942	+	0.943651i	$0.607366\pi$
$744$		0			0
$745$	−9.82843	+	17.0233i	−0.360086	+	0.623687i
$746$		0			0
$747$	2.41421	+	4.18154i	0.0883315	+	0.152995i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−6.82843	−	11.8272i	−0.249173	−	0.431580i	0.714124	−	0.700020i	$-0.246825\pi$
$751$	−6.82843	−	11.8272i	−0.249173	−	0.431580i	−0.963297	+	0.268440i	$0.913492\pi$
$752$		0			0
$753$	−5.75736	+	9.97204i	−0.209810	+	0.363401i
$754$		0			0
$755$	−5.31371			−0.193386
$756$		0			0
$757$	0.828427			0.0301097			0.0150548	−	0.999887i	$-0.495208\pi$
$757$	0.828427			0.0301097			0.0150548	+	0.999887i	$0.495208\pi$
$758$		0			0
$759$	−7.41421	+	12.8418i	−0.269119	+	0.466128i
$760$		0			0
$761$	−3.24264	−	5.61642i	−0.117546	−	0.203595i	0.801249	−	0.598331i	$-0.204169\pi$
$761$	−3.24264	−	5.61642i	−0.117546	−	0.203595i	−0.918794	+	0.394736i	$0.870836\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.585786	−	1.01461i	−0.0211792	−	0.0366834i
$766$		0			0
$767$	4.00000	−	6.92820i	0.144432	−	0.250163i
$768$		0			0
$769$	−13.2132			−0.476480			−0.238240	−	0.971206i	$-0.576571\pi$
$769$	−13.2132			−0.476480			−0.238240	+	0.971206i	$0.576571\pi$
$770$		0			0
$771$	−21.3137			−0.767594
$772$		0			0
$773$	−18.7279	+	32.4377i	−0.673597	+	1.16670i	0.303280	+	0.952901i	$0.401918\pi$
$773$	−18.7279	+	32.4377i	−0.673597	+	1.16670i	−0.976877	+	0.213802i	$0.931415\pi$
$774$		0			0
$775$	−2.12132	−	3.67423i	−0.0762001	−	0.131982i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.41421	+	9.37769i	0.193984	+	0.335991i
$780$		0			0
$781$	−10.4853	+	18.1610i	−0.375193	+	0.649853i
$782$		0			0
$783$	3.65685			0.130685
$784$		0			0
$785$	−10.1421			−0.361988
$786$		0			0
$787$	19.5563	−	33.8726i	0.697109	−	1.20743i	−0.272356	−	0.962197i	$-0.587803\pi$
$787$	19.5563	−	33.8726i	0.697109	−	1.20743i	0.969465	−	0.245231i	$-0.0788638\pi$
$788$		0			0
$789$	8.53553	+	14.7840i	0.303873	+	0.526324i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−14.0000	−	24.2487i	−0.497155	−	0.861097i
$794$		0			0
$795$	−2.29289	+	3.97141i	−0.0813205	+	0.140851i
$796$		0			0
$797$	15.1127			0.535319			0.267660	−	0.963514i	$-0.413750\pi$
$797$	15.1127			0.535319			0.267660	+	0.963514i	$0.413750\pi$
$798$		0			0
$799$	12.2843			0.434586
$800$		0			0
$801$	2.41421	−	4.18154i	0.0853020	−	0.147747i
$802$		0			0
$803$	4.48528	+	7.76874i	0.158282	+	0.274153i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	7.58579	+	13.1390i	0.267032	+	0.462514i
$808$		0			0
$809$	−2.75736	+	4.77589i	−0.0969436	+	0.167911i	−0.910418	−	0.413689i	$-0.864240\pi$
$809$	−2.75736	+	4.77589i	−0.0969436	+	0.167911i	0.813475	+	0.581601i	$0.197573\pi$
$810$		0			0
$811$	−1.89949			−0.0667003			−0.0333501	−	0.999444i	$-0.510618\pi$
$811$	−1.89949			−0.0667003			−0.0333501	+	0.999444i	$0.510618\pi$
$812$		0			0
$813$	20.2426			0.709940
$814$		0			0
$815$	−9.07107	+	15.7116i	−0.317746	+	0.550352i
$816$		0			0
$817$	−4.48528	−	7.76874i	−0.156920	−	0.271794i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−20.2132	−	35.0103i	−0.705446	−	1.22187i	−0.966530	−	0.256552i	$-0.917414\pi$
$821$	−20.2132	−	35.0103i	−0.705446	−	1.22187i	0.261085	−	0.965316i	$-0.415920\pi$
$822$		0			0
$823$	−12.7279	+	22.0454i	−0.443667	+	0.768455i	−0.997958	−	0.0638684i	$-0.979656\pi$
$823$	−12.7279	+	22.0454i	−0.443667	+	0.768455i	0.554291	+	0.832323i	$0.312990\pi$
$824$		0			0
$825$	−2.00000			−0.0696311
$826$		0			0
$827$	−14.2426			−0.495265			−0.247633	−	0.968854i	$-0.579653\pi$
$827$	−14.2426			−0.495265			−0.247633	+	0.968854i	$0.579653\pi$
$828$		0			0
$829$	−1.53553	+	2.65962i	−0.0533313	+	0.0923725i	−0.891459	−	0.453102i	$-0.850317\pi$
$829$	−1.53553	+	2.65962i	−0.0533313	+	0.0923725i	0.838127	+	0.545475i	$0.183651\pi$
$830$		0			0
$831$	−2.65685	−	4.60181i	−0.0921653	−	0.159635i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−8.00000	−	13.8564i	−0.276851	−	0.479521i
$836$		0			0
$837$	−2.12132	+	3.67423i	−0.0733236	+	0.127000i
$838$		0			0
$839$	32.4853			1.12152			0.560758	−	0.827980i	$-0.310510\pi$
$839$	32.4853			1.12152			0.560758	+	0.827980i	$0.310510\pi$
$840$		0			0
$841$	−15.6274			−0.538876
$842$		0			0
$843$	1.48528	−	2.57258i	0.0511558	−	0.0886045i
$844$		0			0
$845$	−2.50000	−	4.33013i	−0.0860026	−	0.148961i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.24264	+	7.34847i	0.145607	+	0.252199i
$850$		0			0
$851$	−38.8701	+	67.3249i	−1.33245	+	2.30787i
$852$		0			0
$853$	40.2843			1.37931			0.689654	−	0.724139i	$-0.257763\pi$
$853$	40.2843			1.37931			0.689654	+	0.724139i	$0.257763\pi$
$854$		0			0
$855$	−5.41421			−0.185162
$856$		0			0
$857$	12.7279	−	22.0454i	0.434778	−	0.753057i	−0.562500	−	0.826797i	$-0.690160\pi$
$857$	12.7279	−	22.0454i	0.434778	−	0.753057i	0.997277	+	0.0737406i	$0.0234937\pi$
$858$		0			0
$859$	−5.05025	−	8.74729i	−0.172312	−	0.298454i	0.766916	−	0.641748i	$-0.221791\pi$
$859$	−5.05025	−	8.74729i	−0.172312	−	0.298454i	−0.939228	+	0.343294i	$0.888457\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	17.9497	+	31.0899i	0.611017	+	1.05831i	0.991069	+	0.133347i	$0.0425724\pi$
$863$	17.9497	+	31.0899i	0.611017	+	1.05831i	−0.380053	+	0.924965i	$0.624094\pi$
$864$		0			0
$865$	−7.07107	+	12.2474i	−0.240424	+	0.416426i
$866$		0			0
$867$	−15.6274			−0.530735
$868$		0			0
$869$	20.0000			0.678454
$870$		0			0
$871$	−9.65685	+	16.7262i	−0.327210	+	0.566744i
$872$		0			0
$873$	−2.00000	−	3.46410i	−0.0676897	−	0.117242i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	23.4853	+	40.6777i	0.793042	+	1.37359i	0.924075	+	0.382210i	$0.124837\pi$
$877$	23.4853	+	40.6777i	0.793042	+	1.37359i	−0.131034	+	0.991378i	$0.541830\pi$
$878$		0			0
$879$	1.82843	−	3.16693i	0.0616713	−	0.106818i
$880$		0			0
$881$	46.0000			1.54978			0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000			1.54978			0.774890	+	0.632096i	$0.217805\pi$
$882$		0			0
$883$	−16.9706			−0.571105			−0.285552	−	0.958363i	$-0.592177\pi$
$883$	−16.9706			−0.571105			−0.285552	+	0.958363i	$0.592177\pi$
$884$		0			0
$885$	1.41421	−	2.44949i	0.0475383	−	0.0823387i
$886$		0			0
$887$	13.5858	+	23.5313i	0.456166	+	0.790103i	0.998754	−	0.0498959i	$-0.0158890\pi$
$887$	13.5858	+	23.5313i	0.456166	+	0.790103i	−0.542588	+	0.839999i	$0.682556\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$		0			0
$893$	28.3848	−	49.1639i	0.949860	−	1.64521i
$894$		0			0
$895$	10.4853			0.350484
$896$		0			0
$897$	20.9706			0.700187
$898$		0			0
$899$	−7.75736	+	13.4361i	−0.258722	+	0.448120i
$900$		0			0
$901$	−2.68629	−	4.65279i	−0.0894933	−	0.155007i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.1213	+	20.9947i	0.402926	+	0.697889i
$906$		0			0
$907$	−16.8284	+	29.1477i	−0.558779	+	0.967833i	0.438820	+	0.898575i	$0.355397\pi$
$907$	−16.8284	+	29.1477i	−0.558779	+	0.967833i	−0.997599	+	0.0692582i	$0.977937\pi$
$908$		0			0
$909$	11.6569			0.386633
$910$		0			0
$911$	−47.9411			−1.58836			−0.794180	−	0.607682i	$-0.792099\pi$
$911$	−47.9411			−1.58836			−0.794180	+	0.607682i	$0.792099\pi$
$912$		0			0
$913$	−4.82843	+	8.36308i	−0.159798	+	0.276778i
$914$		0			0
$915$	−4.94975	−	8.57321i	−0.163634	−	0.283422i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−14.1421	−	24.4949i	−0.466506	−	0.808012i	0.532762	−	0.846265i	$-0.321154\pi$
$919$	−14.1421	−	24.4949i	−0.466506	−	0.808012i	−0.999268	+	0.0382530i	$0.987821\pi$
$920$		0			0
$921$	−0.828427	+	1.43488i	−0.0272976	+	0.0472808i
$922$		0			0
$923$	29.6569			0.976167
$924$		0			0
$925$	−10.4853			−0.344754
$926$		0			0
$927$	−1.41421	+	2.44949i	−0.0464489	+	0.0804518i
$928$		0			0
$929$	−9.58579	−	16.6031i	−0.314499	−	0.544729i	0.664832	−	0.746993i	$-0.268503\pi$
$929$	−9.58579	−	16.6031i	−0.314499	−	0.544729i	−0.979331	+	0.202264i	$0.935170\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−4.34315	−	7.52255i	−0.142188	−	0.246277i
$934$		0			0
$935$	1.17157	−	2.02922i	0.0383145	−	0.0663627i
$936$		0			0
$937$	−17.6569			−0.576824			−0.288412	−	0.957506i	$-0.593127\pi$
$937$	−17.6569			−0.576824			−0.288412	+	0.957506i	$0.593127\pi$
$938$		0			0
$939$	28.4853			0.929582
$940$		0			0
$941$	25.6274	−	44.3880i	0.835430	−	1.44701i	−0.0582500	−	0.998302i	$-0.518552\pi$
$941$	25.6274	−	44.3880i	0.835430	−	1.44701i	0.893680	−	0.448705i	$-0.148115\pi$
$942$		0			0
$943$	−7.41421	−	12.8418i	−0.241440	−	0.418186i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.4645	−	19.8570i	−0.372545	−	0.645267i	0.617411	−	0.786641i	$-0.288181\pi$
$947$	−11.4645	−	19.8570i	−0.372545	−	0.645267i	−0.989956	+	0.141374i	$0.954848\pi$
$948$		0			0
$949$	6.34315	−	10.9867i	0.205907	−	0.356642i
$950$		0			0
$951$	0.100505			0.00325910
$952$		0			0
$953$	46.0416			1.49143			0.745717	−	0.666262i	$-0.232107\pi$
$953$	46.0416			1.49143			0.745717	+	0.666262i	$0.232107\pi$
$954$		0			0
$955$	7.48528	−	12.9649i	0.242218	−	0.419534i
$956$		0			0
$957$	3.65685	+	6.33386i	0.118209	+	0.204745i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	6.50000	+	11.2583i	0.209677	+	0.363172i
$962$		0			0
$963$	−2.53553	+	4.39167i	−0.0817064	+	0.141520i
$964$		0			0
$965$	−12.8284			−0.412962
$966$		0			0
$967$	−20.2010			−0.649621			−0.324810	−	0.945779i	$-0.605300\pi$
$967$	−20.2010			−0.649621			−0.324810	+	0.945779i	$0.605300\pi$
$968$		0			0
$969$	3.17157	−	5.49333i	0.101886	−	0.176471i
$970$		0			0
$971$	−10.2426	−	17.7408i	−0.328702	−	0.569329i	0.653553	−	0.756881i	$-0.273278\pi$
$971$	−10.2426	−	17.7408i	−0.328702	−	0.569329i	−0.982255	+	0.187553i	$0.939945\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.41421	+	2.44949i	0.0452911	+	0.0784465i
$976$		0			0
$977$	−15.0208	+	26.0168i	−0.480558	+	0.832352i	−0.999751	−	0.0223055i	$-0.992899\pi$
$977$	−15.0208	+	26.0168i	−0.480558	+	0.832352i	0.519193	+	0.854657i	$0.326233\pi$
$978$		0			0
$979$	9.65685			0.308634
$980$		0			0
$981$	−4.34315			−0.138666
$982$		0			0
$983$	−27.7990	+	48.1493i	−0.886650	+	1.53572i	−0.0428394	+	0.999082i	$0.513640\pi$
$983$	−27.7990	+	48.1493i	−0.886650	+	1.53572i	−0.843811	+	0.536641i	$0.819693\pi$
$984$		0			0
$985$	6.53553	+	11.3199i	0.208239	+	0.360681i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	6.14214	+	10.6385i	0.195309	+	0.338284i
$990$		0			0
$991$	5.65685	−	9.79796i	0.179696	−	0.311242i	−0.762080	−	0.647482i	$-0.775822\pi$
$991$	5.65685	−	9.79796i	0.179696	−	0.311242i	0.941776	+	0.336240i	$0.109155\pi$
$992$		0			0
$993$	−34.6274			−1.09887
$994$		0			0
$995$	−8.24264			−0.261309
$996$		0			0
$997$	−1.65685	+	2.86976i	−0.0524731	+	0.0908861i	−0.891069	−	0.453868i	$-0.850044\pi$
$997$	−1.65685	+	2.86976i	−0.0524731	+	0.0908861i	0.838596	+	0.544754i	$0.183377\pi$
$998$		0			0
$999$	5.24264	+	9.08052i	0.165870	+	0.287295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.q.p.361.1		4
7.2	even	3	inner	2940.2.q.p.961.1		4
7.3	odd	6		2940.2.a.o.1.2	✓	2
7.4	even	3		2940.2.a.q.1.1	yes	2
7.5	odd	6		2940.2.q.r.961.2		4
7.6	odd	2		2940.2.q.r.361.2		4
21.11	odd	6		8820.2.a.bm.1.1		2
21.17	even	6		8820.2.a.bh.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2940.2.a.o.1.2	✓	2	7.3	odd	6
2940.2.a.q.1.1	yes	2	7.4	even	3
2940.2.q.p.361.1		4	1.1	even	1	trivial
2940.2.q.p.961.1		4	7.2	even	3	inner
2940.2.q.r.361.2		4	7.6	odd	2
2940.2.q.r.961.2		4	7.5	odd	6
8820.2.a.bh.1.2		2	21.17	even	6
8820.2.a.bm.1.1		2	21.11	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -2.82843 q^{13} -1.00000 q^{15} +(0.585786 - 1.01461i) q^{17} +(-2.70711 - 4.68885i) q^{19} +(3.70711 + 6.42090i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +3.65685 q^{29} +(-2.12132 + 3.67423i) q^{31} +(1.00000 + 1.73205i) q^{33} +(5.24264 + 9.08052i) q^{37} +(1.41421 - 2.44949i) q^{39} -2.00000 q^{41} +1.65685 q^{43} +(0.500000 - 0.866025i) q^{45} +(5.24264 + 9.08052i) q^{47} +(0.585786 + 1.01461i) q^{51} +(2.29289 - 3.97141i) q^{53} +2.00000 q^{55} +5.41421 q^{57} +(-1.41421 + 2.44949i) q^{59} +(4.94975 + 8.57321i) q^{61} +(-1.41421 - 2.44949i) q^{65} +(3.41421 - 5.91359i) q^{67} -7.41421 q^{69} -10.4853 q^{71} +(-2.24264 + 3.88437i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(5.00000 + 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -4.82843 q^{83} +1.17157 q^{85} +(-1.82843 + 3.16693i) q^{87} +(2.41421 + 4.18154i) q^{89} +(-2.12132 - 3.67423i) q^{93} +(2.70711 - 4.68885i) q^{95} +4.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5} - 2 q^{9} + 4 q^{11} - 4 q^{15} + 8 q^{17} - 8 q^{19} + 12 q^{23} - 2 q^{25} + 4 q^{27} - 8 q^{29} + 4 q^{33} + 4 q^{37} - 8 q^{41} - 16 q^{43} + 2 q^{45} + 4 q^{47} + 8 q^{51} + 12 q^{53}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^5 - 2 * q^9 + 4 * q^11 - 4 * q^15 + 8 * q^17 - 8 * q^19 + 12 * q^23 - 2 * q^25 + 4 * q^27 - 8 * q^29 + 4 * q^33 + 4 * q^37 - 8 * q^41 - 16 * q^43 + 2 * q^45 + 4 * q^47 + 8 * q^51 + 12 * q^53 + 8 * q^55 + 16 * q^57 + 8 * q^67 - 24 * q^69 - 8 * q^71 + 8 * q^73 - 2 * q^75 + 20 * q^79 - 2 * q^81 - 8 * q^83 + 16 * q^85 + 4 * q^87 + 4 * q^89 + 8 * q^95 + 16 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more