LMFDB - Embedded newform 3900.2.bw.l.2149.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3900,2,Mod(49,3900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3900.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3900.bw (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,8,0,4,0,-12,0,0,0,0,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$31.1416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 780)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2149.4
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	3900.2149
Dual form			3900.2.bw.l.49.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{3} +(1.96593 + 3.40508i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.14128 - 0.658919i) q^{11} +(-3.08725 - 1.86250i) q^{13} +(0.478838 - 0.276457i) q^{17} +(-4.69748 + 2.71209i) q^{19} +3.93185i q^{21} +(0.411634 + 0.237657i) q^{23} +1.00000i q^{27} +(-1.53906 + 2.66573i) q^{29} +3.49938i q^{31} +(-0.658919 - 1.14128i) q^{33} +(-0.235077 + 0.407165i) q^{37} +(-1.74238 - 3.15660i) q^{39} +(2.53906 + 1.46593i) q^{41} +(1.20893 - 0.697977i) q^{43} -7.71039 q^{47} +(-4.22973 + 7.32611i) q^{49} +0.552914 q^{51} -3.43488i q^{53} -5.42418 q^{57} +(-11.2735 + 6.50877i) q^{59} +(0.313111 + 0.542324i) q^{61} +(-1.96593 + 3.40508i) q^{63} +(-6.37221 + 11.0370i) q^{67} +(0.237657 + 0.411634i) q^{69} +(-4.51581 + 2.60721i) q^{71} -6.95303 q^{73} -5.18154i q^{77} -1.19615 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.9382 q^{83} +(-2.66573 + 1.53906i) q^{87} +(15.5117 + 8.95568i) q^{89} +(0.272675 - 14.1739i) q^{91} +(-1.74969 + 3.03055i) q^{93} +(-2.62314 - 4.54342i) q^{97} -1.31784i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7} + 4 q^{9} - 12 q^{11} - 12 q^{19} - 12 q^{23} + 8 q^{29} - 4 q^{33} + 8 q^{37} + 24 q^{43} - 40 q^{47} + 4 q^{49} - 8 q^{51} + 24 q^{57} - 24 q^{59} + 8 q^{61} - 8 q^{63} - 4 q^{69} - 12 q^{71}+ \cdots - 24 q^{97}+O(q^{100}) $ 8 * q + 8 * q^7 + 4 * q^9 - 12 * q^11 - 12 * q^19 - 12 * q^23 + 8 * q^29 - 4 * q^33 + 8 * q^37 + 24 * q^43 - 40 * q^47 + 4 * q^49 - 8 * q^51 + 24 * q^57 - 24 * q^59 + 8 * q^61 - 8 * q^63 - 4 * q^69 - 12 * q^71 + 32 * q^79 - 4 * q^81 - 8 * q^83 - 12 * q^87 + 12 * q^89 + 8 * q^91 + 4 * q^93 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1951$	$3277$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$-1$

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
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.96593	+	3.40508i	0.743050	+	1.28700i	0.951100	+	0.308882i	$0.0999550\pi$
$7$	1.96593	+	3.40508i	0.743050	+	1.28700i	−0.208050	+	0.978118i	$0.566712\pi$
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.14128	−	0.658919i	−0.344109	−	0.198671i	0.317979	−	0.948098i	$-0.396996\pi$
$11$	−1.14128	−	0.658919i	−0.344109	−	0.198671i	−0.662088	+	0.749426i	$0.730329\pi$
$12$		0			0
$13$	−3.08725	−	1.86250i	−0.856248	−	0.516565i
$13$	−3.08725	−	1.86250i	−0.856248	−	0.516565i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.478838	−	0.276457i	0.116135	−	0.0670507i	−0.440807	−	0.897602i	$-0.645308\pi$
$17$	0.478838	−	0.276457i	0.116135	−	0.0670507i	0.556942	+	0.830551i	$0.311974\pi$
$18$		0			0
$19$	−4.69748	+	2.71209i	−1.07768	+	0.622196i	−0.930268	−	0.366880i	$-0.880426\pi$
$19$	−4.69748	+	2.71209i	−1.07768	+	0.622196i	−0.147407	+	0.989076i	$0.547093\pi$
$20$		0			0
$21$			3.93185i			0.858000i
$22$		0			0
$23$	0.411634	+	0.237657i	0.0858316	+	0.0495549i	0.542301	−	0.840184i	$-0.317553\pi$
$23$	0.411634	+	0.237657i	0.0858316	+	0.0495549i	−0.456470	+	0.889739i	$0.650886\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−1.53906	+	2.66573i	−0.285796	+	0.495013i	−0.972802	−	0.231639i	$-0.925591\pi$
$29$	−1.53906	+	2.66573i	−0.285796	+	0.495013i	0.687006	+	0.726652i	$0.258925\pi$
$30$		0			0
$31$			3.49938i			0.628507i	0.949339	+	0.314253i	$0.101754\pi$
$31$			3.49938i			0.628507i	−0.949339	+	0.314253i	$0.898246\pi$
$32$		0			0
$33$	−0.658919	−	1.14128i	−0.114703	−	0.198671i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.235077	+	0.407165i	−0.0386464	+	0.0669376i	−0.884702	−	0.466158i	$-0.845638\pi$
$37$	−0.235077	+	0.407165i	−0.0386464	+	0.0669376i	0.846055	+	0.533095i	$0.178971\pi$
$38$		0			0
$39$	−1.74238	−	3.15660i	−0.279005	−	0.505460i
$40$		0			0
$41$	2.53906	+	1.46593i	0.396534	+	0.228939i	0.684987	−	0.728555i	$-0.259808\pi$
$41$	2.53906	+	1.46593i	0.396534	+	0.228939i	−0.288453	+	0.957494i	$0.593141\pi$
$42$		0			0
$43$	1.20893	−	0.697977i	0.184360	−	0.106440i	−0.404979	−	0.914326i	$-0.632721\pi$
$43$	1.20893	−	0.697977i	0.184360	−	0.106440i	0.589340	+	0.807885i	$0.299388\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.71039			−1.12468			−0.562338	−	0.826907i	$-0.690098\pi$
$47$	−7.71039			−1.12468			−0.562338	+	0.826907i	$0.690098\pi$
$48$		0			0
$49$	−4.22973	+	7.32611i	−0.604247	+	1.04659i
$50$		0			0
$51$	0.552914			0.0774235
$52$		0			0
$53$		−	3.43488i		−	0.471817i	−0.971775	−	0.235908i	$-0.924193\pi$
$53$		−	3.43488i		−	0.471817i	0.971775	−	0.235908i	$-0.0758065\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−5.42418			−0.718450
$58$		0			0
$59$	−11.2735	+	6.50877i	−1.46769	+	0.847369i	−0.999345	−	0.0361787i	$-0.988481\pi$
$59$	−11.2735	+	6.50877i	−1.46769	+	0.847369i	−0.468341	+	0.883548i	$0.655148\pi$
$60$		0			0
$61$	0.313111	+	0.542324i	0.0400898	+	0.0694375i	0.885374	−	0.464879i	$-0.153902\pi$
$61$	0.313111	+	0.542324i	0.0400898	+	0.0694375i	−0.845284	+	0.534317i	$0.820569\pi$
$62$		0			0
$63$	−1.96593	+	3.40508i	−0.247683	+	0.429000i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.37221	+	11.0370i	−0.778490	+	1.34838i	0.154323	+	0.988020i	$0.450680\pi$
$67$	−6.37221	+	11.0370i	−0.778490	+	1.34838i	−0.932812	+	0.360363i	$0.882653\pi$
$68$		0			0
$69$	0.237657	+	0.411634i	0.0286105	+	0.0495549i
$70$		0			0
$71$	−4.51581	+	2.60721i	−0.535929	+	0.309418i	−0.743427	−	0.668817i	$-0.766801\pi$
$71$	−4.51581	+	2.60721i	−0.535929	+	0.309418i	0.207499	+	0.978235i	$0.433468\pi$
$72$		0			0
$73$	−6.95303			−0.813791			−0.406895	−	0.913475i	$-0.633389\pi$
$73$	−6.95303			−0.813791			−0.406895	+	0.913475i	$0.633389\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	5.18154i		−	0.590491i
$78$		0			0
$79$	−1.19615			−0.134578			−0.0672888	−	0.997734i	$-0.521435\pi$
$79$	−1.19615			−0.134578			−0.0672888	+	0.997734i	$0.521435\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	12.9382			1.42015			0.710074	−	0.704127i	$-0.248661\pi$
$83$	12.9382			1.42015			0.710074	+	0.704127i	$0.248661\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.66573	+	1.53906i	−0.285796	+	0.165004i
$88$		0			0
$89$	15.5117	+	8.95568i	1.64424	+	0.949300i	0.979304	+	0.202395i	$0.0648726\pi$
$89$	15.5117	+	8.95568i	1.64424	+	0.949300i	0.664931	+	0.746904i	$0.268461\pi$
$90$		0			0
$91$	0.272675	−	14.1739i	0.0285841	−	1.48583i
$92$		0			0
$93$	−1.74969	+	3.03055i	−0.181434	+	0.314253i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.62314	−	4.54342i	−0.266340	−	0.461314i	0.701574	−	0.712597i	$-0.252481\pi$
$97$	−2.62314	−	4.54342i	−0.266340	−	0.461314i	−0.967914	+	0.251282i	$0.919148\pi$
$98$		0			0
$99$		−	1.31784i		−	0.132448i
$100$		0			0
$101$	6.98432	−	12.0972i	0.694966	−	1.20372i	−0.275226	−	0.961379i	$-0.588753\pi$
$101$	6.98432	−	12.0972i	0.694966	−	1.20372i	0.970192	−	0.242337i	$-0.0779138\pi$
$102$		0			0
$103$			17.2231i			1.69705i	0.529158	+	0.848523i	$0.322508\pi$
$103$			17.2231i			1.69705i	−0.529158	+	0.848523i	$0.677492\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.33167	−	4.81029i	−0.805453	−	0.465028i	0.0399215	−	0.999203i	$-0.487289\pi$
$107$	−8.33167	−	4.81029i	−0.805453	−	0.465028i	−0.845374	+	0.534174i	$0.820623\pi$
$108$		0			0
$109$			12.1516i			1.16391i	0.813221	+	0.581956i	$0.197712\pi$
$109$			12.1516i			1.16391i	−0.813221	+	0.581956i	$0.802288\pi$
$110$		0			0
$111$	−0.407165	+	0.235077i	−0.0386464	+	0.0223125i
$112$		0			0
$113$	0.636919	−	0.367725i	0.0599163	−	0.0345927i	−0.469743	−	0.882803i	$-0.655653\pi$
$113$	0.636919	−	0.367725i	0.0599163	−	0.0345927i	0.529659	+	0.848211i	$0.322320\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.0693504	−	3.60488i	0.00641144	−	0.333272i
$118$		0			0
$119$	1.88272	+	1.08699i	0.172589	+	0.0996441i
$120$		0			0
$121$	−4.63165	−	8.02226i	−0.421059	−	0.729296i
$122$		0			0
$123$	1.46593	+	2.53906i	0.132178	+	0.228939i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−16.5303	−	9.54378i	−1.46683	−	0.846874i	−0.467517	−	0.883984i	$-0.654851\pi$
$127$	−16.5303	−	9.54378i	−1.46683	−	0.846874i	−0.999311	+	0.0371100i	$0.988185\pi$
$128$		0			0
$129$	1.39595			0.122907
$130$		0			0
$131$	1.40717			0.122945			0.0614723	−	0.998109i	$-0.480420\pi$
$131$	1.40717			0.122945			0.0614723	+	0.998109i	$0.480420\pi$
$132$		0			0
$133$	−18.4698	−	10.6635i	−1.60153	−	0.924646i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.82989	−	10.0977i	−0.498081	−	0.862701i	0.501917	−	0.864916i	$-0.332628\pi$
$137$	−5.82989	−	10.0977i	−0.498081	−	0.862701i	−0.999998	+	0.00221463i	$0.999295\pi$
$138$		0			0
$139$	−1.12106	−	1.94174i	−0.0950873	−	0.164696i	0.814558	−	0.580082i	$-0.196980\pi$
$139$	−1.12106	−	1.94174i	−0.0950873	−	0.164696i	−0.909645	+	0.415386i	$0.863646\pi$
$140$		0			0
$141$	−6.67739	−	3.85520i	−0.562338	−	0.324666i
$142$		0			0
$143$	2.29618	+	4.15988i	0.192016	+	0.347867i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.32611	+	4.22973i	−0.604247	+	0.348862i
$148$		0			0
$149$	16.1476	−	9.32282i	1.32286	−	0.763755i	0.338678	−	0.940902i	$-0.390020\pi$
$149$	16.1476	−	9.32282i	1.32286	−	0.763755i	0.984184	+	0.177147i	$0.0566868\pi$
$150$		0			0
$151$			0.368970i			0.0300263i	0.999887	+	0.0150132i	$0.00477902\pi$
$151$			0.368970i			0.0300263i	−0.999887	+	0.0150132i	$0.995221\pi$
$152$		0			0
$153$	0.478838	+	0.276457i	0.0387117	+	0.0223502i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			4.71895i			0.376613i	0.982110	+	0.188307i	$0.0602999\pi$
$157$			4.71895i			0.376613i	−0.982110	+	0.188307i	$0.939700\pi$
$158$		0			0
$159$	1.71744	−	2.97469i	0.136202	−	0.235908i
$160$		0			0
$161$			1.86886i			0.147287i
$162$		0			0
$163$	−6.76612	−	11.7193i	−0.529964	−	0.917924i	−0.999389	−	0.0349520i	$-0.988872\pi$
$163$	−6.76612	−	11.7193i	−0.529964	−	0.917924i	0.469425	−	0.882972i	$-0.344461\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.06815	−	5.31419i	0.237420	−	0.411224i	−0.722553	−	0.691316i	$-0.757031\pi$
$167$	3.06815	−	5.31419i	0.237420	−	0.411224i	0.959973	+	0.280091i	$0.0903648\pi$
$168$		0			0
$169$	6.06218	+	11.5000i	0.466321	+	0.884615i
$170$		0			0
$171$	−4.69748	−	2.71209i	−0.359225	−	0.207399i
$172$		0			0
$173$	0.429946	−	0.248229i	0.0326882	−	0.0188725i	−0.483567	−	0.875307i	$-0.660659\pi$
$173$	0.429946	−	0.248229i	0.0326882	−	0.0188725i	0.516255	+	0.856435i	$0.327326\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−13.0175			−0.978458
$178$		0			0
$179$	−1.96895	+	3.41032i	−0.147166	+	0.254900i	−0.930179	−	0.367106i	$-0.880349\pi$
$179$	−1.96895	+	3.41032i	−0.147166	+	0.254900i	0.783013	+	0.622006i	$0.213682\pi$
$180$		0			0
$181$	3.35363			0.249273			0.124637	−	0.992202i	$-0.460223\pi$
$181$	3.35363			0.249273			0.124637	+	0.992202i	$0.460223\pi$
$182$		0			0
$183$			0.626222i			0.0462917i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.728651			−0.0532842
$188$		0			0
$189$	−3.40508	+	1.96593i	−0.247683	+	0.143000i
$190$		0			0
$191$	10.2831	+	17.8109i	0.744062	+	1.28875i	0.950632	+	0.310321i	$0.100437\pi$
$191$	10.2831	+	17.8109i	0.744062	+	1.28875i	−0.206570	+	0.978432i	$0.566230\pi$
$192$		0			0
$193$	2.75908	−	4.77886i	0.198603	−	0.343990i	−0.749473	−	0.662035i	$-0.769693\pi$
$193$	2.75908	−	4.77886i	0.198603	−	0.343990i	0.948076	+	0.318045i	$0.103026\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.92979	−	6.80659i	0.279986	−	0.484950i	−0.691395	−	0.722477i	$-0.743004\pi$
$197$	3.92979	−	6.80659i	0.279986	−	0.484950i	0.971381	+	0.237527i	$0.0763369\pi$
$198$		0			0
$199$	3.49536	+	6.05413i	0.247779	+	0.429166i	0.962909	−	0.269825i	$-0.0869659\pi$
$199$	3.49536	+	6.05413i	0.247779	+	0.429166i	−0.715130	+	0.698991i	$0.753633\pi$
$200$		0			0
$201$	−11.0370	+	6.37221i	−0.778490	+	0.449461i
$202$		0			0
$203$	−12.1027			−0.849443
$204$		0			0
$205$		0			0
$206$		0			0
$207$			0.475314i			0.0330366i
$208$		0			0
$209$	7.14819			0.494451
$210$		0			0
$211$	6.79958	−	11.7772i	0.468102	−	0.810777i	−0.531233	−	0.847226i	$-0.678271\pi$
$211$	6.79958	−	11.7772i	0.468102	−	0.810777i	0.999336	+	0.0364488i	$0.0116046\pi$
$212$		0			0
$213$	−5.21441			−0.357286
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−11.9157	+	6.87952i	−0.808889	+	0.467012i
$218$		0			0
$219$	−6.02150	−	3.47652i	−0.406895	−	0.234921i
$220$		0			0
$221$	−1.99319	−	0.0383448i	−0.134077	−	0.00257935i
$222$		0			0
$223$	−6.16693	+	10.6814i	−0.412968	+	0.715282i	−0.995213	−	0.0977319i	$-0.968841\pi$
$223$	−6.16693	+	10.6814i	−0.412968	+	0.715282i	0.582245	+	0.813014i	$0.302175\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.54441	−	9.60319i	−0.367995	−	0.637386i	0.621257	−	0.783607i	$-0.286622\pi$
$227$	−5.54441	−	9.60319i	−0.367995	−	0.637386i	−0.989252	+	0.146221i	$0.953289\pi$
$228$		0			0
$229$		−	11.4607i		−	0.757344i	−0.925531	−	0.378672i	$-0.876381\pi$
$229$		−	11.4607i		−	0.757344i	0.925531	−	0.378672i	$-0.123619\pi$
$230$		0			0
$231$	2.59077	−	4.48735i	0.170460	−	0.295246i
$232$		0			0
$233$			25.4527i			1.66746i	0.552172	+	0.833730i	$0.313799\pi$
$233$			25.4527i			1.66746i	−0.552172	+	0.833730i	$0.686201\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.03590	−	0.598076i	−0.0672888	−	0.0388492i
$238$		0			0
$239$			20.8676i			1.34981i	0.737903	+	0.674907i	$0.235816\pi$
$239$			20.8676i			1.34981i	−0.737903	+	0.674907i	$0.764184\pi$
$240$		0			0
$241$	−15.8447	+	9.14796i	−1.02065	+	0.589272i	−0.914292	−	0.405056i	$-0.867252\pi$
$241$	−15.8447	+	9.14796i	−1.02065	+	0.589272i	−0.106357	+	0.994328i	$0.533919\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	19.5535	+	0.376169i	1.24416	+	0.0239351i
$248$		0			0
$249$	11.2048	+	6.46909i	0.710074	+	0.409962i
$250$		0			0
$251$	2.17191	+	3.76186i	0.137090	+	0.237447i	0.926394	−	0.376556i	$-0.122892\pi$
$251$	2.17191	+	3.76186i	0.137090	+	0.237447i	−0.789304	+	0.614003i	$0.789558\pi$
$252$		0			0
$253$	−0.313193	−	0.542466i	−0.0196903	−	0.0341046i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.20706	−	2.42895i	−0.262429	−	0.151514i	0.363013	−	0.931784i	$-0.381748\pi$
$257$	−4.20706	−	2.42895i	−0.262429	−	0.151514i	−0.625442	+	0.780270i	$0.715081\pi$
$258$		0			0
$259$	−1.84858			−0.114865
$260$		0			0
$261$	−3.07812			−0.190531
$262$		0			0
$263$	−19.3379	−	11.1647i	−1.19243	−	0.688447i	−0.233570	−	0.972340i	$-0.575041\pi$
$263$	−19.3379	−	11.1647i	−1.19243	−	0.688447i	−0.958856	+	0.283893i	$0.908374\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	8.95568	+	15.5117i	0.548078	+	0.949300i
$268$		0			0
$269$	4.16875	+	7.22049i	0.254173	+	0.440241i	0.964671	−	0.263459i	$-0.0848633\pi$
$269$	4.16875	+	7.22049i	0.254173	+	0.440241i	−0.710497	+	0.703700i	$0.751530\pi$
$270$		0			0
$271$	−9.58860	−	5.53598i	−0.582466	−	0.336287i	0.179647	−	0.983731i	$-0.442504\pi$
$271$	−9.58860	−	5.53598i	−0.582466	−	0.336287i	−0.762113	+	0.647444i	$0.775838\pi$
$272$		0			0
$273$	7.32308	−	12.1386i	0.443213	−	0.734661i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−15.4582	+	8.92480i	−0.928794	+	0.536239i	−0.886430	−	0.462863i	$-0.846822\pi$
$277$	−15.4582	+	8.92480i	−0.928794	+	0.536239i	−0.0423641	+	0.999102i	$0.513489\pi$
$278$		0			0
$279$	−3.03055	+	1.74969i	−0.181434	+	0.104751i
$280$		0			0
$281$			30.2163i			1.80256i	0.433242	+	0.901278i	$0.357370\pi$
$281$			30.2163i			1.80256i	−0.433242	+	0.901278i	$0.642630\pi$
$282$		0			0
$283$	26.3789	+	15.2299i	1.56806	+	0.905321i	0.996395	+	0.0848360i	$0.0270366\pi$
$283$	26.3789	+	15.2299i	1.56806	+	0.905321i	0.571668	+	0.820485i	$0.306297\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			11.5276i			0.680453i
$288$		0			0
$289$	−8.34714	+	14.4577i	−0.491008	+	0.850452i
$290$		0			0
$291$		−	5.24629i		−	0.307543i
$292$		0			0
$293$	−9.23654	−	15.9982i	−0.539604	−	0.934622i	−0.998925	−	0.0463516i	$-0.985241\pi$
$293$	−9.23654	−	15.9982i	−0.539604	−	0.934622i	0.459321	−	0.888270i	$-0.348093\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.658919	−	1.14128i	0.0382343	−	0.0662238i
$298$		0			0
$299$	−0.828178	−	1.50037i	−0.0478948	−	0.0867688i
$300$		0			0
$301$	4.75334	+	2.74434i	0.273978	+	0.158181i
$302$		0			0
$303$	12.0972	−	6.98432i	0.694966	−	0.401239i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−24.6938			−1.40935			−0.704675	−	0.709530i	$-0.748907\pi$
$307$	−24.6938			−1.40935			−0.704675	+	0.709530i	$0.748907\pi$
$308$		0			0
$309$	−8.61157	+	14.9157i	−0.489895	+	0.848523i
$310$		0			0
$311$	33.5489			1.90239			0.951193	−	0.308596i	$-0.0998591\pi$
$311$	33.5489			1.90239			0.951193	+	0.308596i	$0.0998591\pi$
$312$		0			0
$313$		−	22.2876i		−	1.25977i	−0.776688	−	0.629886i	$-0.783102\pi$
$313$		−	22.2876i		−	1.25977i	0.776688	−	0.629886i	$-0.216898\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	34.0884			1.91459			0.957296	−	0.289109i	$-0.0933589\pi$
$317$	34.0884			1.91459			0.957296	+	0.289109i	$0.0933589\pi$
$318$		0			0
$319$	3.51299	−	2.02823i	0.196690	−	0.113559i
$320$		0			0
$321$	−4.81029	−	8.33167i	−0.268484	−	0.465028i
$322$		0			0
$323$	−1.49955	+	2.59730i	−0.0834374	+	0.144518i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.07579	+	10.5236i	−0.335992	+	0.581956i
$328$		0			0
$329$	−15.1581	−	26.2545i	−0.835691	−	1.44746i
$330$		0			0
$331$	−26.0020	+	15.0123i	−1.42920	+	0.825150i	−0.997058	−	0.0766545i	$-0.975576\pi$
$331$	−26.0020	+	15.0123i	−1.42920	+	0.825150i	−0.432144	+	0.901805i	$0.642243\pi$
$332$		0			0
$333$	−0.470154			−0.0257643
$334$		0			0
$335$		0			0
$336$		0			0
$337$			6.84596i			0.372923i	0.982462	+	0.186462i	$0.0597020\pi$
$337$			6.84596i			0.372923i	−0.982462	+	0.186462i	$0.940298\pi$
$338$		0			0
$339$	0.735451			0.0399442
$340$		0			0
$341$	2.30581	−	3.99377i	0.124866	−	0.216275i
$342$		0			0
$343$	−5.73837			−0.309843
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−22.2010	+	12.8177i	−1.19181	+	0.688092i	−0.958717	−	0.284363i	$-0.908218\pi$
$347$	−22.2010	+	12.8177i	−1.19181	+	0.688092i	−0.233093	+	0.972454i	$0.574885\pi$
$348$		0			0
$349$	−10.5134	−	6.06993i	−0.562771	−	0.324916i	0.191486	−	0.981495i	$-0.438669\pi$
$349$	−10.5134	−	6.06993i	−0.562771	−	0.324916i	−0.754257	+	0.656579i	$0.772003\pi$
$350$		0			0
$351$	1.86250	−	3.08725i	0.0994130	−	0.164785i
$352$		0			0
$353$	−15.2899	+	26.4830i	−0.813802	+	1.40955i	0.0963832	+	0.995344i	$0.469273\pi$
$353$	−15.2899	+	26.4830i	−0.813802	+	1.40955i	−0.910185	+	0.414202i	$0.864061\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.08699	+	1.88272i	0.0575295	+	0.0996441i
$358$		0			0
$359$			12.2163i			0.644754i	0.946611	+	0.322377i	$0.104482\pi$
$359$			12.2163i			0.644754i	−0.946611	+	0.322377i	$0.895518\pi$
$360$		0			0
$361$	5.21087	−	9.02549i	0.274256	−	0.475026i
$362$		0			0
$363$		−	9.26330i		−	0.486197i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	22.4269	+	12.9482i	1.17068	+	0.675890i	0.953839	−	0.300318i	$-0.0970930\pi$
$367$	22.4269	+	12.9482i	1.17068	+	0.675890i	0.216836	+	0.976208i	$0.430426\pi$
$368$		0			0
$369$			2.93185i			0.152626i
$370$		0			0
$371$	11.6960	−	6.75272i	0.607228	−	0.350584i
$372$		0			0
$373$	15.2438	−	8.80104i	0.789296	−	0.455700i	−0.0504185	−	0.998728i	$-0.516056\pi$
$373$	15.2438	−	8.80104i	0.789296	−	0.455700i	0.839715	+	0.543028i	$0.182722\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.71637	−	5.36326i	0.500419	−	0.276222i
$378$		0			0
$379$	24.3471	+	14.0568i	1.25063	+	0.722051i	0.971234	−	0.238126i	$-0.0765330\pi$
$379$	24.3471	+	14.0568i	1.25063	+	0.722051i	0.279394	+	0.960176i	$0.409866\pi$
$380$		0			0
$381$	−9.54378	−	16.5303i	−0.488943	−	0.846874i
$382$		0			0
$383$	−1.13776	−	1.97065i	−0.0581366	−	0.100696i	0.835492	−	0.549502i	$-0.185183\pi$
$383$	−1.13776	−	1.97065i	−0.0581366	−	0.100696i	−0.893629	+	0.448807i	$0.851849\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.20893	+	0.697977i	0.0614534	+	0.0354801i
$388$		0			0
$389$	−0.182785			−0.00926757			−0.00463378	−	0.999989i	$-0.501475\pi$
$389$	−0.182785			−0.00926757			−0.00463378	+	0.999989i	$0.501475\pi$
$390$		0			0
$391$	0.262808			0.0132908
$392$		0			0
$393$	1.21864	+	0.703583i	0.0614723	+	0.0354911i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−14.5890	−	25.2689i	−0.732202	−	1.26821i	−0.955940	−	0.293562i	$-0.905159\pi$
$397$	−14.5890	−	25.2689i	−0.732202	−	1.26821i	0.223738	−	0.974649i	$-0.428174\pi$
$398$		0			0
$399$	−10.6635	−	18.4698i	−0.533845	−	0.924646i
$400$		0			0
$401$	24.2385	+	13.9941i	1.21041	+	0.698833i	0.962849	−	0.270039i	$-0.0870366\pi$
$401$	24.2385	+	13.9941i	1.21041	+	0.698833i	0.247564	+	0.968872i	$0.420370\pi$
$402$		0			0
$403$	6.51760	−	10.8034i	0.324665	−	0.538158i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.536578	−	0.309793i	0.0265972	−	0.0153559i
$408$		0			0
$409$	15.6607	−	9.04170i	0.774371	−	0.447083i	−0.0600606	−	0.998195i	$-0.519129\pi$
$409$	15.6607	−	9.04170i	0.774371	−	0.447083i	0.834432	+	0.551111i	$0.185796\pi$
$410$		0			0
$411$		−	11.6598i		−	0.575134i
$412$		0			0
$413$	−44.3258	−	25.5915i	−2.18113	−	1.25928i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	2.24213i		−	0.109797i
$418$		0			0
$419$	−5.20403	+	9.01364i	−0.254233	+	0.440345i	−0.964687	−	0.263399i	$-0.915156\pi$
$419$	−5.20403	+	9.01364i	−0.254233	+	0.440345i	0.710454	+	0.703744i	$0.248490\pi$
$420$		0			0
$421$		−	5.16456i		−	0.251705i	−0.992049	−	0.125853i	$-0.959833\pi$
$421$		−	5.16456i		−	0.251705i	0.992049	−	0.125853i	$-0.0401666\pi$
$422$		0			0
$423$	−3.85520	−	6.67739i	−0.187446	−	0.324666i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.23111	+	2.13234i	−0.0595774	+	0.103191i
$428$		0			0
$429$	−0.0913925	+	4.75065i	−0.00441247	+	0.229364i
$430$		0			0
$431$	29.0597	+	16.7776i	1.39976	+	0.808150i	0.994367	−	0.105993i	$-0.0338023\pi$
$431$	29.0597	+	16.7776i	1.39976	+	0.808150i	0.405390	+	0.914144i	$0.367136\pi$
$432$		0			0
$433$	14.6722	−	8.47099i	0.705100	−	0.407090i	−0.104144	−	0.994562i	$-0.533210\pi$
$433$	14.6722	−	8.47099i	0.705100	−	0.407090i	0.809244	+	0.587472i	$0.199877\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.57819			−0.123331
$438$		0			0
$439$	13.3279	−	23.0846i	0.636105	−	1.10177i	−0.350174	−	0.936684i	$-0.613878\pi$
$439$	13.3279	−	23.0846i	0.636105	−	1.10177i	0.986280	−	0.165082i	$-0.0527890\pi$
$440$		0			0
$441$	−8.45946			−0.402831
$442$		0			0
$443$			8.90671i			0.423170i	0.977360	+	0.211585i	$0.0678626\pi$
$443$			8.90671i			0.423170i	−0.977360	+	0.211585i	$0.932137\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	18.6456			0.881909
$448$		0			0
$449$	−9.40300	+	5.42883i	−0.443755	+	0.256202i	−0.705189	−	0.709019i	$-0.749138\pi$
$449$	−9.40300	+	5.42883i	−0.443755	+	0.256202i	0.261434	+	0.965221i	$0.415805\pi$
$450$		0			0
$451$	−1.93185	−	3.34607i	−0.0909673	−	0.157560i
$452$		0			0
$453$	−0.184485	+	0.319537i	−0.00866785	+	0.0150132i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.89036	+	6.73831i	−0.181984	+	0.315205i	−0.942556	−	0.334048i	$-0.891585\pi$
$457$	−3.89036	+	6.73831i	−0.181984	+	0.315205i	0.760572	+	0.649253i	$0.224918\pi$
$458$		0			0
$459$	0.276457	+	0.478838i	0.0129039	+	0.0223502i
$460$		0			0
$461$	−24.4717	+	14.1288i	−1.13976	+	0.658042i	−0.946372	−	0.323080i	$-0.895282\pi$
$461$	−24.4717	+	14.1288i	−1.13976	+	0.658042i	−0.193390	+	0.981122i	$0.561948\pi$
$462$		0			0
$463$	−8.22511			−0.382253			−0.191127	−	0.981565i	$-0.561214\pi$
$463$	−8.22511			−0.382253			−0.191127	+	0.981565i	$0.561214\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	21.4205i		−	0.991224i	−0.868544	−	0.495612i	$-0.834944\pi$
$467$		−	21.4205i		−	0.991224i	0.868544	−	0.495612i	$-0.165056\pi$
$468$		0			0
$469$	−50.1092			−2.31383
$470$		0			0
$471$	−2.35948	+	4.08673i	−0.108719	+	0.188307i
$472$		0			0
$473$	−1.83964			−0.0845867
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.97469	−	1.71744i	0.136202	−	0.0786361i
$478$		0			0
$479$	30.7499	+	17.7535i	1.40500	+	0.811177i	0.994900	−	0.100864i	$-0.0321607\pi$
$479$	30.7499	+	17.7535i	1.40500	+	0.811177i	0.410099	+	0.912041i	$0.365494\pi$
$480$		0			0
$481$	1.48409	−	0.819188i	0.0676685	−	0.0373518i
$482$		0			0
$483$	−0.934431	+	1.61848i	−0.0425181	+	0.0736435i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1.11500	−	1.93124i	−0.0505255	−	0.0875128i	0.839657	−	0.543118i	$-0.182756\pi$
$487$	−1.11500	−	1.93124i	−0.0505255	−	0.0875128i	−0.890182	+	0.455605i	$0.849423\pi$
$488$		0			0
$489$		−	13.5322i		−	0.611949i
$490$		0			0
$491$	18.8199	−	32.5970i	0.849330	−	1.47108i	−0.0324772	−	0.999472i	$-0.510340\pi$
$491$	18.8199	−	32.5970i	0.849330	−	1.47108i	0.881807	−	0.471610i	$-0.156327\pi$
$492$		0			0
$493$			1.70193i			0.0766513i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.7555	−	10.2511i	−0.796443	−	0.459827i
$498$		0			0
$499$		−	26.3242i		−	1.17843i	−0.807975	−	0.589216i	$-0.799437\pi$
$499$		−	26.3242i		−	1.17843i	0.807975	−	0.589216i	$-0.200563\pi$
$500$		0			0
$501$	5.31419	−	3.06815i	0.237420	−	0.137075i
$502$		0			0
$503$	22.7687	−	13.1455i	1.01521	−	0.586130i	0.102496	−	0.994733i	$-0.467317\pi$
$503$	22.7687	−	13.1455i	1.01521	−	0.586130i	0.912712	+	0.408603i	$0.133984\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.500000	+	12.9904i	−0.0222058	+	0.576923i
$508$		0			0
$509$	3.35226	+	1.93543i	0.148586	+	0.0857863i	0.572450	−	0.819940i	$-0.305993\pi$
$509$	3.35226	+	1.93543i	0.148586	+	0.0857863i	−0.423864	+	0.905726i	$0.639326\pi$
$510$		0			0
$511$	−13.6691	−	23.6757i	−0.604687	−	1.04735i
$512$		0			0
$513$	−2.71209	−	4.69748i	−0.119742	−	0.207399i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	8.79972	+	5.08052i	0.387011	+	0.223441i
$518$		0			0
$519$	0.496458			0.0217921
$520$		0			0
$521$	20.6427			0.904372			0.452186	−	0.891924i	$-0.350644\pi$
$521$	20.6427			0.904372			0.452186	+	0.891924i	$0.350644\pi$
$522$		0			0
$523$	24.5787	+	14.1905i	1.07475	+	0.620508i	0.929476	−	0.368883i	$-0.120260\pi$
$523$	24.5787	+	14.1905i	1.07475	+	0.620508i	0.145275	+	0.989391i	$0.453593\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.967428	+	1.67563i	0.0421418	+	0.0729918i
$528$		0			0
$529$	−11.3870	−	19.7229i	−0.495089	−	0.857519i
$530$		0			0
$531$	−11.2735	−	6.50877i	−0.489229	−	0.282456i
$532$		0			0
$533$	−5.10841	−	9.25467i	−0.221270	−	0.400864i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.41032	+	1.96895i	−0.147166	+	0.0849666i
$538$		0			0
$539$	9.65461	−	5.57409i	0.415854	−	0.240093i
$540$		0			0
$541$			2.51613i			0.108177i	0.998536	+	0.0540884i	$0.0172253\pi$
$541$			2.51613i			0.108177i	−0.998536	+	0.0540884i	$0.982775\pi$
$542$		0			0
$543$	2.90433	+	1.67681i	0.124637	+	0.0719590i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			28.6507i			1.22502i	0.790464	+	0.612508i	$0.209839\pi$
$547$			28.6507i			1.22502i	−0.790464	+	0.612508i	$0.790161\pi$
$548$		0			0
$549$	−0.313111	+	0.542324i	−0.0133633	+	0.0231458i
$550$		0			0
$551$		−	16.6963i		−	0.711285i
$552$		0			0
$553$	−2.35155	−	4.07300i	−0.0999979	−	0.173202i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.9675	−	20.7283i	0.507078	−	0.878285i	−0.492889	−	0.870092i	$-0.664059\pi$
$557$	11.9675	−	20.7283i	0.507078	−	0.878285i	0.999966	−	0.00819220i	$-0.00260769\pi$
$558$		0			0
$559$	−5.03225	−	0.0968099i	−0.212841	−	0.00409462i
$560$		0			0
$561$	−0.631030	−	0.364326i	−0.0266421	−	0.0153818i
$562$		0			0
$563$	18.0641	−	10.4293i	0.761313	−	0.439544i	−0.0684539	−	0.997654i	$-0.521807\pi$
$563$	18.0641	−	10.4293i	0.761313	−	0.439544i	0.829767	+	0.558110i	$0.188473\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−3.93185			−0.165122
$568$		0			0
$569$	9.70392	−	16.8077i	0.406810	−	0.704615i	−0.587721	−	0.809064i	$-0.699975\pi$
$569$	9.70392	−	16.8077i	0.406810	−	0.704615i	0.994530	+	0.104449i	$0.0333079\pi$
$570$		0			0
$571$	2.64156			0.110546			0.0552730	−	0.998471i	$-0.482397\pi$
$571$	2.64156			0.110546			0.0552730	+	0.998471i	$0.482397\pi$
$572$		0			0
$573$			20.5663i			0.859169i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−24.0716			−1.00211			−0.501057	−	0.865415i	$-0.667055\pi$
$577$	−24.0716			−1.00211			−0.501057	+	0.865415i	$0.667055\pi$
$578$		0			0
$579$	4.77886	−	2.75908i	0.198603	−	0.114663i
$580$		0			0
$581$	25.4355	+	44.0556i	1.05524	+	1.82773i
$582$		0			0
$583$	−2.26330	+	3.92016i	−0.0937365	+	0.162356i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.6814	−	32.3571i	0.771063	−	1.33552i	−0.165918	−	0.986140i	$-0.553059\pi$
$587$	18.6814	−	32.3571i	0.771063	−	1.33552i	0.936981	−	0.349381i	$-0.113608\pi$
$588$		0			0
$589$	−9.49063	−	16.4383i	−0.391055	−	0.677326i
$590$		0			0
$591$	6.80659	−	3.92979i	0.279986	−	0.161650i
$592$		0			0
$593$	45.4778			1.86755			0.933774	−	0.357863i	$-0.116495\pi$
$593$	45.4778			1.86755			0.933774	+	0.357863i	$0.116495\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			6.99071i			0.286111i
$598$		0			0
$599$	−24.7863			−1.01274			−0.506370	−	0.862316i	$-0.669013\pi$
$599$	−24.7863			−1.01274			−0.506370	+	0.862316i	$0.669013\pi$
$600$		0			0
$601$	−12.3643	+	21.4156i	−0.504350	+	0.873560i	0.495637	+	0.868530i	$0.334935\pi$
$601$	−12.3643	+	21.4156i	−0.504350	+	0.873560i	−0.999987	+	0.00503065i	$0.998399\pi$
$602$		0			0
$603$	−12.7444			−0.518993
$604$		0			0
$605$		0			0
$606$		0			0
$607$	4.52913	−	2.61489i	0.183832	−	0.106135i	−0.405260	−	0.914201i	$-0.632819\pi$
$607$	4.52913	−	2.61489i	0.183832	−	0.106135i	0.589092	+	0.808066i	$0.299486\pi$
$608$		0			0
$609$	−10.4812	−	6.05135i	−0.424721	−	0.245213i
$610$		0			0
$611$	23.8039	+	14.3606i	0.963002	+	0.580968i
$612$		0			0
$613$	−6.96780	+	12.0686i	−0.281427	+	0.487446i	−0.971736	−	0.236069i	$-0.924141\pi$
$613$	−6.96780	+	12.0686i	−0.281427	+	0.487446i	0.690310	+	0.723514i	$0.257474\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	22.6898	+	39.2999i	0.913458	+	1.58216i	0.809144	+	0.587611i	$0.199931\pi$
$617$	22.6898	+	39.2999i	0.913458	+	1.58216i	0.104314	+	0.994544i	$0.466735\pi$
$618$		0			0
$619$		−	12.7094i		−	0.510834i	−0.966831	−	0.255417i	$-0.917787\pi$
$619$		−	12.7094i		−	0.510834i	0.966831	−	0.255417i	$-0.0822128\pi$
$620$		0			0
$621$	−0.237657	+	0.411634i	−0.00953684	+	0.0165183i
$622$		0			0
$623$			70.4248i			2.82151i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.19051	+	3.57409i	0.247225	+	0.142736i
$628$		0			0
$629$			0.259955i			0.0103651i
$630$		0			0
$631$	3.49465	−	2.01764i	0.139120	−	0.0803209i	−0.428825	−	0.903388i	$-0.641072\pi$
$631$	3.49465	−	2.01764i	0.139120	−	0.0803209i	0.567944	+	0.823067i	$0.307739\pi$
$632$		0			0
$633$	11.7772	−	6.79958i	0.468102	−	0.270259i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	26.7031	−	14.7396i	1.05802	−	0.584005i
$638$		0			0
$639$	−4.51581	−	2.60721i	−0.178643	−	0.103139i
$640$		0			0
$641$	−16.7616	−	29.0320i	−0.662044	−	1.14669i	−0.980078	−	0.198614i	$-0.936356\pi$
$641$	−16.7616	−	29.0320i	−0.662044	−	1.14669i	0.318034	−	0.948079i	$-0.396977\pi$
$642$		0			0
$643$	24.7714	+	42.9054i	0.976891	+	1.69202i	0.673550	+	0.739142i	$0.264769\pi$
$643$	24.7714	+	42.9054i	0.976891	+	1.69202i	0.303341	+	0.952882i	$0.401898\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.8731	−	6.27758i	−0.427465	−	0.246797i	0.270801	−	0.962635i	$-0.412711\pi$
$647$	−10.8731	−	6.27758i	−0.427465	−	0.246797i	−0.698266	+	0.715838i	$0.746045\pi$
$648$		0			0
$649$	17.1550			0.673392
$650$		0			0
$651$	−13.7590			−0.539259
$652$		0			0
$653$	0.0675086	+	0.0389761i	0.00264181	+	0.00152525i	0.501320	−	0.865262i	$-0.332848\pi$
$653$	0.0675086	+	0.0389761i	0.00264181	+	0.00152525i	−0.498679	+	0.866787i	$0.666181\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.47652	−	6.02150i	−0.135632	−	0.234921i
$658$		0			0
$659$	21.5441	+	37.3155i	0.839241	+	1.45361i	0.890531	+	0.454924i	$0.150333\pi$
$659$	21.5441	+	37.3155i	0.839241	+	1.45361i	−0.0512899	+	0.998684i	$0.516333\pi$
$660$		0			0
$661$	−15.6898	−	9.05853i	−0.610264	−	0.352336i	0.162805	−	0.986658i	$-0.447946\pi$
$661$	−15.6898	−	9.05853i	−0.610264	−	0.352336i	−0.773069	+	0.634322i	$0.781279\pi$
$662$		0			0
$663$	−1.70698	−	1.02980i	−0.0662937	−	0.0399943i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.26706	+	0.731535i	−0.0490606	+	0.0283252i
$668$		0			0
$669$	−10.6814	+	6.16693i	−0.412968	+	0.238427i
$670$		0			0
$671$		−	0.825259i		−	0.0318588i
$672$		0			0
$673$	8.60060	+	4.96556i	0.331529	+	0.191408i	0.656520	−	0.754309i	$-0.272028\pi$
$673$	8.60060	+	4.96556i	0.331529	+	0.191408i	−0.324991	+	0.945717i	$0.605361\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	36.7571i		−	1.41269i	−0.707868	−	0.706345i	$-0.750343\pi$
$677$		−	36.7571i		−	1.41269i	0.707868	−	0.706345i	$-0.249657\pi$
$678$		0			0
$679$	10.3138	−	17.8641i	0.395808	−	0.685559i
$680$		0			0
$681$		−	11.0888i		−	0.424924i
$682$		0			0
$683$	7.84557	+	13.5889i	0.300202	+	0.519966i	0.976182	−	0.216955i	$-0.0696125\pi$
$683$	7.84557	+	13.5889i	0.300202	+	0.519966i	−0.675979	+	0.736921i	$0.736279\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.73035	−	9.92526i	0.218627	−	0.378672i
$688$		0			0
$689$	−6.39746	+	10.6043i	−0.243724	+	0.403992i
$690$		0			0
$691$	−17.7308	−	10.2369i	−0.674510	−	0.389428i	0.123273	−	0.992373i	$-0.460661\pi$
$691$	−17.7308	−	10.2369i	−0.674510	−	0.389428i	−0.797783	+	0.602944i	$0.793994\pi$
$692$		0			0
$693$	4.48735	−	2.59077i	0.170460	−	0.0984152i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.62106			0.0614021
$698$		0			0
$699$	−12.7263	+	22.0427i	−0.481354	+	0.833730i
$700$		0			0
$701$	−23.8368			−0.900303			−0.450152	−	0.892952i	$-0.648630\pi$
$701$	−23.8368			−0.900303			−0.450152	+	0.892952i	$0.648630\pi$
$702$		0			0
$703$		−	2.55020i		−	0.0961826i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	54.9226			2.06558
$708$		0			0
$709$	1.63746	−	0.945386i	0.0614960	−	0.0355047i	−0.468937	−	0.883232i	$-0.655363\pi$
$709$	1.63746	−	0.945386i	0.0614960	−	0.0355047i	0.530433	+	0.847727i	$0.322029\pi$
$710$		0			0
$711$	−0.598076	−	1.03590i	−0.0224296	−	0.0388492i
$712$		0			0
$713$	−0.831651	+	1.44046i	−0.0311456	+	0.0539457i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−10.4338	+	18.0719i	−0.389658	+	0.674907i
$718$		0			0
$719$	−2.99659	−	5.19025i	−0.111754	−	0.193564i	0.804724	−	0.593650i	$-0.202314\pi$
$719$	−2.99659	−	5.19025i	−0.111754	−	0.193564i	−0.916478	+	0.400086i	$0.868980\pi$
$720$		0			0
$721$	−58.6462	+	33.8594i	−2.18410	+	1.26099i
$722$		0			0
$723$	−18.2959			−0.680433
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	39.0387i		−	1.44787i	−0.689870	−	0.723933i	$-0.742333\pi$
$727$		−	39.0387i		−	1.44787i	0.689870	−	0.723933i	$-0.257667\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	0.385921	−	0.668435i	0.0142738	−	0.0247230i
$732$		0			0
$733$	17.4176			0.643336			0.321668	−	0.946853i	$-0.395757\pi$
$733$	17.4176			0.643336			0.321668	+	0.946853i	$0.395757\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	14.5450	−	8.39754i	0.535771	−	0.309327i
$738$		0			0
$739$	−12.3018	−	7.10243i	−0.452528	−	0.261267i	0.256369	−	0.966579i	$-0.417474\pi$
$739$	−12.3018	−	7.10243i	−0.452528	−	0.261267i	−0.708897	+	0.705312i	$0.750807\pi$
$740$		0			0
$741$	16.7458	+	10.1025i	0.615172	+	0.371126i
$742$		0			0
$743$	4.34834	−	7.53155i	0.159525	−	0.276306i	−0.775172	−	0.631750i	$-0.782337\pi$
$743$	4.34834	−	7.53155i	0.159525	−	0.276306i	0.934698	+	0.355444i	$0.115670\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	6.46909	+	11.2048i	0.236691	+	0.409962i
$748$		0			0
$749$		−	37.8267i		−	1.38216i
$750$		0			0
$751$	−9.79460	+	16.9647i	−0.357410	+	0.619052i	−0.987527	−	0.157448i	$-0.949673\pi$
$751$	−9.79460	+	16.9647i	−0.357410	+	0.619052i	0.630117	+	0.776500i	$0.283007\pi$
$752$		0			0
$753$			4.34383i			0.158298i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−12.1870	−	7.03616i	−0.442943	−	0.255733i	0.261902	−	0.965094i	$-0.415650\pi$
$757$	−12.1870	−	7.03616i	−0.442943	−	0.255733i	−0.704845	+	0.709361i	$0.748984\pi$
$758$		0			0
$759$		−	0.626386i		−	0.0227364i
$760$		0			0
$761$	−15.3926	+	8.88695i	−0.557983	+	0.322152i	−0.752336	−	0.658780i	$-0.771073\pi$
$761$	−15.3926	+	8.88695i	−0.557983	+	0.322152i	0.194353	+	0.980932i	$0.437739\pi$
$762$		0			0
$763$	−41.3772	+	23.8891i	−1.49795	+	0.864844i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	46.9267	+	0.902770i	1.69442	+	0.0325972i
$768$		0			0
$769$	39.1066	+	22.5782i	1.41022	+	0.814191i	0.995409	−	0.0957170i	$-0.0305144\pi$
$769$	39.1066	+	22.5782i	1.41022	+	0.814191i	0.414811	+	0.909908i	$0.363848\pi$
$770$		0			0
$771$	−2.42895	−	4.20706i	−0.0874765	−	0.151514i
$772$		0			0
$773$	−24.6399	−	42.6776i	−0.886237	−	1.53501i	−0.844290	−	0.535887i	$-0.819977\pi$
$773$	−24.6399	−	42.6776i	−0.886237	−	1.53501i	−0.0419470	−	0.999120i	$-0.513356\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.60091	−	0.924288i	−0.0574325	−	0.0331586i
$778$		0			0
$779$	−15.9029			−0.569780
$780$		0			0
$781$	6.87175			0.245890
$782$		0			0
$783$	−2.66573	−	1.53906i	−0.0952653	−	0.0550014i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	15.9883	+	27.6925i	0.569920	+	0.987131i	0.996573	+	0.0827152i	$0.0263592\pi$
$787$	15.9883	+	27.6925i	0.569920	+	0.987131i	−0.426653	+	0.904415i	$0.640307\pi$
$788$		0			0
$789$	−11.1647	−	19.3379i	−0.397475	−	0.688447i
$790$		0			0
$791$	2.50427	+	1.44584i	0.0890416	+	0.0514082i
$792$		0			0
$793$	0.0434287	−	2.25746i	0.00154220	−	0.0801647i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	23.6145	−	13.6338i	0.836468	−	0.482935i	−0.0195943	−	0.999808i	$-0.506237\pi$
$797$	23.6145	−	13.6338i	0.836468	−	0.482935i	0.856062	+	0.516873i	$0.172904\pi$
$798$		0			0
$799$	−3.69203	+	2.13159i	−0.130615	+	0.0754103i
$800$		0			0
$801$			17.9114i			0.632866i
$802$		0			0
$803$	7.93536	+	4.58148i	0.280033	+	0.161677i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			8.33751i			0.293494i
$808$		0			0
$809$	22.1803	−	38.4174i	0.779818	−	1.35068i	−0.152229	−	0.988345i	$-0.548645\pi$
$809$	22.1803	−	38.4174i	0.779818	−	1.35068i	0.932047	−	0.362339i	$-0.118022\pi$
$810$		0			0
$811$			54.1521i			1.90154i	0.309900	+	0.950769i	$0.399704\pi$
$811$			54.1521i			1.90154i	−0.309900	+	0.950769i	$0.600296\pi$
$812$		0			0
$813$	−5.53598	−	9.58860i	−0.194155	−	0.336287i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.78595	+	6.55746i	−0.132454	+	0.229417i
$818$		0			0
$819$	12.4113	−	6.85079i	0.433685	−	0.239386i
$820$		0			0
$821$	−7.71723	−	4.45554i	−0.269333	−	0.155499i	0.359251	−	0.933241i	$-0.383032\pi$
$821$	−7.71723	−	4.45554i	−0.269333	−	0.155499i	−0.628584	+	0.777741i	$0.716365\pi$
$822$		0			0
$823$	−1.41546	+	0.817215i	−0.0493398	+	0.0284863i	−0.524467	−	0.851431i	$-0.675735\pi$
$823$	−1.41546	+	0.817215i	−0.0493398	+	0.0284863i	0.475127	+	0.879917i	$0.342402\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	19.5497			0.679809			0.339904	−	0.940460i	$-0.389605\pi$
$827$	19.5497			0.679809			0.339904	+	0.940460i	$0.389605\pi$
$828$		0			0
$829$	−26.2725	+	45.5052i	−0.912480	+	1.58046i	−0.101931	+	0.994791i	$0.532502\pi$
$829$	−26.2725	+	45.5052i	−0.912480	+	1.58046i	−0.810549	+	0.585671i	$0.800831\pi$
$830$		0			0
$831$	−17.8496			−0.619196
$832$		0			0
$833$			4.67735i			0.162061i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.49938			−0.120956
$838$		0			0
$839$	3.01757	−	1.74219i	0.104178	−	0.0601472i	−0.447006	−	0.894531i	$-0.647510\pi$
$839$	3.01757	−	1.74219i	0.104178	−	0.0601472i	0.551184	+	0.834384i	$0.314176\pi$
$840$		0			0
$841$	9.76260	+	16.9093i	0.336641	+	0.583080i
$842$		0			0
$843$	−15.1082	+	26.1681i	−0.520353	+	0.901278i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	18.2110	−	31.5423i	0.625736	−	1.08381i
$848$		0			0
$849$	15.2299	+	26.3789i	0.522688	+	0.905321i
$850$		0			0
$851$	−0.193531	+	0.111735i	−0.00663417	+	0.00383024i
$852$		0			0
$853$	6.46294			0.221287			0.110643	−	0.993860i	$-0.464709\pi$
$853$	6.46294			0.221287			0.110643	+	0.993860i	$0.464709\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	20.1736i		−	0.689117i	−0.938765	−	0.344559i	$-0.888029\pi$
$857$		−	20.1736i		−	0.689117i	0.938765	−	0.344559i	$-0.111971\pi$
$858$		0			0
$859$	−15.3052			−0.522207			−0.261104	−	0.965311i	$-0.584086\pi$
$859$	−15.3052			−0.522207			−0.261104	+	0.965311i	$0.584086\pi$
$860$		0			0
$861$	−5.76380	+	9.98320i	−0.196430	+	0.340227i
$862$		0			0
$863$	36.1031			1.22896			0.614482	−	0.788931i	$-0.289365\pi$
$863$	36.1031			1.22896			0.614482	+	0.788931i	$0.289365\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−14.4577	+	8.34714i	−0.491008	+	0.283484i
$868$		0			0
$869$	1.36515	+	0.788167i	0.0463094	+	0.0267367i
$870$		0			0
$871$	40.2290	−	22.2057i	1.36311	−	0.752410i
$872$		0			0
$873$	2.62314	−	4.54342i	0.0887800	−	0.153771i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	26.6483	+	46.1562i	0.899850	+	1.55859i	0.827685	+	0.561192i	$0.189657\pi$
$877$	26.6483	+	46.1562i	0.899850	+	1.55859i	0.0721642	+	0.997393i	$0.477009\pi$
$878$		0			0
$879$		−	18.4731i		−	0.623081i
$880$		0			0
$881$	−6.59235	+	11.4183i	−0.222102	+	0.384692i	−0.955446	−	0.295166i	$-0.904625\pi$
$881$	−6.59235	+	11.4183i	−0.222102	+	0.384692i	0.733344	+	0.679858i	$0.237958\pi$
$882$		0			0
$883$		−	36.3300i		−	1.22260i	−0.791398	−	0.611301i	$-0.790647\pi$
$883$		−	36.3300i		−	1.22260i	0.791398	−	0.611301i	$-0.209353\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.4516	+	17.0039i	0.988886	+	0.570934i	0.904941	−	0.425537i	$-0.139915\pi$
$887$	29.4516	+	17.0039i	0.988886	+	0.570934i	0.0839452	+	0.996470i	$0.473248\pi$
$888$		0			0
$889$		−	75.0495i		−	2.51708i
$890$		0			0
$891$	1.14128	−	0.658919i	0.0382343	−	0.0220746i
$892$		0			0
$893$	36.2194	−	20.9113i	1.21204	−	0.699769i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.0329632	−	1.71345i	0.00110061	−	0.0572105i
$898$		0			0
$899$	−9.32838	−	5.38575i	−0.311119	−	0.179625i
$900$		0			0
$901$	−0.949596	−	1.64475i	−0.0316356	−	0.0547945i
$902$		0			0
$903$	2.74434	+	4.75334i	0.0913259	+	0.158181i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−12.2476	−	7.07118i	−0.406677	−	0.234795i	0.282684	−	0.959213i	$-0.408775\pi$
$907$	−12.2476	−	7.07118i	−0.406677	−	0.234795i	−0.689361	+	0.724418i	$0.742108\pi$
$908$		0			0
$909$	13.9686			0.463311
$910$		0			0
$911$	−36.7262			−1.21679			−0.608396	−	0.793634i	$-0.708187\pi$
$911$	−36.7262			−1.21679			−0.608396	+	0.793634i	$0.708187\pi$
$912$		0			0
$913$	−14.7661	−	8.52520i	−0.488686	−	0.282143i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.76638	+	4.79152i	0.0913540	+	0.158230i
$918$		0			0
$919$	9.74320	+	16.8757i	0.321399	+	0.556679i	0.980777	−	0.195133i	$-0.0625137\pi$
$919$	9.74320	+	16.8757i	0.321399	+	0.556679i	−0.659378	+	0.751811i	$0.729180\pi$
$920$		0			0
$921$	−21.3855	−	12.3469i	−0.704675	−	0.406844i
$922$		0			0
$923$	18.7974	+	0.361621i	0.618722	+	0.0119029i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−14.9157	+	8.61157i	−0.489895	+	0.282841i
$928$		0			0
$929$	24.0598	−	13.8909i	0.789377	−	0.455747i	−0.0503664	−	0.998731i	$-0.516039\pi$
$929$	24.0598	−	13.8909i	0.789377	−	0.455747i	0.839743	+	0.542984i	$0.182706\pi$
$930$		0			0
$931$		−	45.8856i		−	1.50384i
$932$		0			0
$933$	29.0542	+	16.7745i	0.951193	+	0.549172i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			49.0868i			1.60359i	0.597596	+	0.801797i	$0.296123\pi$
$937$			49.0868i			1.60359i	−0.597596	+	0.801797i	$0.703877\pi$
$938$		0			0
$939$	11.1438	−	19.3017i	0.363665	−	0.629886i
$940$		0			0
$941$			7.01554i			0.228700i	0.993441	+	0.114350i	$0.0364785\pi$
$941$			7.01554i			0.228700i	−0.993441	+	0.114350i	$0.963521\pi$
$942$		0			0
$943$	0.696775	+	1.20685i	0.0226901	+	0.0393004i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.22450	−	15.9773i	0.299756	−	0.519193i	−0.676324	−	0.736604i	$-0.736428\pi$
$947$	9.22450	−	15.9773i	0.299756	−	0.519193i	0.976080	+	0.217412i	$0.0697614\pi$
$948$		0			0
$949$	21.4657	+	12.9500i	0.696807	+	0.420376i
$950$		0			0
$951$	29.5214	+	17.0442i	0.957296	+	0.552695i
$952$		0			0
$953$	−46.9325	+	27.0965i	−1.52029	+	0.877741i	−0.520578	+	0.853814i	$0.674283\pi$
$953$	−46.9325	+	27.0965i	−1.52029	+	0.877741i	−0.999714	+	0.0239264i	$0.992383\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	4.05646			0.131127
$958$		0			0
$959$	22.9223	−	39.7025i	0.740198	−	1.28206i
$960$		0			0
$961$	18.7544			0.604979
$962$		0			0
$963$		−	9.62058i		−	0.310019i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	52.8600			1.69986			0.849932	−	0.526892i	$-0.176643\pi$
$967$	52.8600			1.69986			0.849932	+	0.526892i	$0.176643\pi$
$968$		0			0
$969$	−2.59730	+	1.49955i	−0.0834374	+	0.0481726i
$970$		0			0
$971$	10.3459	+	17.9196i	0.332015	+	0.575068i	0.982907	−	0.184103i	$-0.0589381\pi$
$971$	10.3459	+	17.9196i	0.332015	+	0.575068i	−0.650892	+	0.759171i	$0.725605\pi$
$972$		0			0
$973$	4.40785	−	7.63462i	0.141309	−	0.244755i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.54247	+	4.40368i	−0.0813407	+	0.140886i	−0.903826	−	0.427900i	$-0.859254\pi$
$977$	−2.54247	+	4.40368i	−0.0813407	+	0.140886i	0.822485	+	0.568786i	$0.192587\pi$
$978$		0			0
$979$	−11.8021	−	20.4419i	−0.377197	−	0.653325i
$980$		0			0
$981$	−10.5236	+	6.07579i	−0.335992	+	0.193985i
$982$		0			0
$983$	16.8646			0.537897			0.268949	−	0.963155i	$-0.413324\pi$
$983$	16.8646			0.537897			0.268949	+	0.963155i	$0.413324\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	30.3161i		−	0.964972i
$988$		0			0
$989$	0.663516			0.0210986
$990$		0			0
$991$	25.4424	−	44.0676i	0.808205	−	1.39985i	−0.105901	−	0.994377i	$-0.533773\pi$
$991$	25.4424	−	44.0676i	0.808205	−	1.39985i	0.914106	−	0.405475i	$-0.132894\pi$
$992$		0			0
$993$	−30.0246			−0.952801
$994$		0			0
$995$		0			0
$996$		0			0
$997$	21.0477	−	12.1519i	0.666588	−	0.384855i	−0.128194	−	0.991749i	$-0.540918\pi$
$997$	21.0477	−	12.1519i	0.666588	−	0.384855i	0.794783	+	0.606894i	$0.207585\pi$
$998$		0			0
$999$	−0.407165	−	0.235077i	−0.0128821	−	0.00743751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3900.2.bw.l.2149.4		8
5.2	odd	4		3900.2.cd.l.901.1		8
5.3	odd	4		780.2.cc.b.121.4	✓	8
5.4	even	2		3900.2.bw.g.2149.1		8
13.10	even	6		3900.2.bw.g.49.1		8
15.8	even	4		2340.2.dj.c.901.2		8
65.23	odd	12		780.2.cc.b.361.2	yes	8
65.49	even	6	inner	3900.2.bw.l.49.4		8
65.62	odd	12		3900.2.cd.l.2701.1		8
195.23	even	12		2340.2.dj.c.361.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.cc.b.121.4	✓	8	5.3	odd	4
780.2.cc.b.361.2	yes	8	65.23	odd	12
2340.2.dj.c.361.4		8	195.23	even	12
2340.2.dj.c.901.2		8	15.8	even	4
3900.2.bw.g.49.1		8	13.10	even	6
3900.2.bw.g.2149.1		8	5.4	even	2
3900.2.bw.l.49.4		8	65.49	even	6	inner
3900.2.bw.l.2149.4		8	1.1	even	1	trivial
3900.2.cd.l.901.1		8	5.2	odd	4
3900.2.cd.l.2701.1		8	65.62	odd	12

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:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3900.bw (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(1.96593 + 3.40508i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.14128 - 0.658919i) q^{11} +(-3.08725 - 1.86250i) q^{13} +(0.478838 - 0.276457i) q^{17} +(-4.69748 + 2.71209i) q^{19} +3.93185i q^{21} +(0.411634 + 0.237657i) q^{23} +1.00000i q^{27} +(-1.53906 + 2.66573i) q^{29} +3.49938i q^{31} +(-0.658919 - 1.14128i) q^{33} +(-0.235077 + 0.407165i) q^{37} +(-1.74238 - 3.15660i) q^{39} +(2.53906 + 1.46593i) q^{41} +(1.20893 - 0.697977i) q^{43} -7.71039 q^{47} +(-4.22973 + 7.32611i) q^{49} +0.552914 q^{51} -3.43488i q^{53} -5.42418 q^{57} +(-11.2735 + 6.50877i) q^{59} +(0.313111 + 0.542324i) q^{61} +(-1.96593 + 3.40508i) q^{63} +(-6.37221 + 11.0370i) q^{67} +(0.237657 + 0.411634i) q^{69} +(-4.51581 + 2.60721i) q^{71} -6.95303 q^{73} -5.18154i q^{77} -1.19615 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.9382 q^{83} +(-2.66573 + 1.53906i) q^{87} +(15.5117 + 8.95568i) q^{89} +(0.272675 - 14.1739i) q^{91} +(-1.74969 + 3.03055i) q^{93} +(-2.62314 - 4.54342i) q^{97} -1.31784i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7} + 4 q^{9} - 12 q^{11} - 12 q^{19} - 12 q^{23} + 8 q^{29} - 4 q^{33} + 8 q^{37} + 24 q^{43} - 40 q^{47} + 4 q^{49} - 8 q^{51} + 24 q^{57} - 24 q^{59} + 8 q^{61} - 8 q^{63} - 4 q^{69} - 12 q^{71}+ \cdots - 24 q^{97}+O(q^{100}) \) 8 * q + 8 * q^7 + 4 * q^9 - 12 * q^11 - 12 * q^19 - 12 * q^23 + 8 * q^29 - 4 * q^33 + 8 * q^37 + 24 * q^43 - 40 * q^47 + 4 * q^49 - 8 * q^51 + 24 * q^57 - 24 * q^59 + 8 * q^61 - 8 * q^63 - 4 * q^69 - 12 * q^71 + 32 * q^79 - 4 * q^81 - 8 * q^83 - 12 * q^87 + 12 * q^89 + 8 * q^91 + 4 * q^93 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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