LMFDB - Embedded newform 3900.2.bw.g.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.g.49.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(-0.741181 - 1.28376i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.85872 - 1.07313i) q^{11} +(1.86250 - 3.08725i) q^{13} +(-5.88512 + 3.39778i) q^{17} +(-2.54516 + 1.46945i) q^{19} -1.48236i q^{21} +(7.65427 + 4.41920i) q^{23} +1.00000i q^{27} +(1.41774 - 2.45559i) q^{29} +8.32780i q^{31} +(-1.07313 - 1.85872i) q^{33} +(-3.64929 + 6.32076i) q^{37} +(3.15660 - 1.74238i) q^{39} +(-0.417738 - 0.241181i) q^{41} +(-6.91239 + 3.99087i) q^{43} +12.1891 q^{47} +(2.40130 - 4.15918i) q^{49} -6.79555 q^{51} -0.565122i q^{53} -2.93890 q^{57} +(7.39483 - 4.26941i) q^{59} +(5.92953 + 10.2702i) q^{61} +(0.741181 - 1.28376i) q^{63} +(-5.66510 + 9.81225i) q^{67} +(4.41920 + 7.65427i) q^{69} +(3.63713 - 2.09990i) q^{71} +11.4317 q^{73} +3.18154i q^{77} +9.19615 q^{79} +(-0.500000 + 0.866025i) q^{81} +9.28132 q^{83} +(2.45559 - 1.41774i) q^{87} +(10.8228 + 6.24857i) q^{89} +(-5.34374 - 0.102802i) q^{91} +(-4.16390 + 7.21209i) q^{93} +(8.32660 + 14.4221i) q^{97} -2.14626i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−0.741181	−	1.28376i	−0.280140	−	0.485217i	0.691279	−	0.722588i	$-0.257048\pi$
$7$	−0.741181	−	1.28376i	−0.280140	−	0.485217i	−0.971419	+	0.237371i	$0.923714\pi$
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.85872	−	1.07313i	−0.560425	−	0.323562i	0.192891	−	0.981220i	$-0.438214\pi$
$11$	−1.85872	−	1.07313i	−0.560425	−	0.323562i	−0.753316	+	0.657659i	$0.771547\pi$
$12$		0			0
$13$	1.86250	−	3.08725i	0.516565	−	0.856248i
$13$	1.86250	−	3.08725i	0.516565	−	0.856248i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.88512	+	3.39778i	−1.42735	+	0.824082i	−0.996911	−	0.0785367i	$-0.974975\pi$
$17$	−5.88512	+	3.39778i	−1.42735	+	0.824082i	−0.430441	+	0.902619i	$0.641642\pi$
$18$		0			0
$19$	−2.54516	+	1.46945i	−0.583900	+	0.337115i	−0.762682	−	0.646774i	$-0.776118\pi$
$19$	−2.54516	+	1.46945i	−0.583900	+	0.337115i	0.178782	+	0.983889i	$0.442784\pi$
$20$		0			0
$21$		−	1.48236i		−	0.323478i
$22$		0			0
$23$	7.65427	+	4.41920i	1.59603	+	0.921466i	0.992242	+	0.124319i	$0.0396745\pi$
$23$	7.65427	+	4.41920i	1.59603	+	0.921466i	0.603784	+	0.797148i	$0.293659\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	1.41774	−	2.45559i	0.263267	−	0.455992i	−0.703841	−	0.710358i	$-0.748533\pi$
$29$	1.41774	−	2.45559i	0.263267	−	0.455992i	0.967108	+	0.254365i	$0.0818666\pi$
$30$		0			0
$31$			8.32780i			1.49572i	0.663858	+	0.747859i	$0.268918\pi$
$31$			8.32780i			1.49572i	−0.663858	+	0.747859i	$0.731082\pi$
$32$		0			0
$33$	−1.07313	−	1.85872i	−0.186808	−	0.323562i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.64929	+	6.32076i	−0.599940	+	1.03913i	0.392890	+	0.919586i	$0.371475\pi$
$37$	−3.64929	+	6.32076i	−0.599940	+	1.03913i	−0.992829	+	0.119540i	$0.961858\pi$
$38$		0			0
$39$	3.15660	−	1.74238i	0.505460	−	0.279005i
$40$		0			0
$41$	−0.417738	−	0.241181i	−0.0652397	−	0.0376661i	0.467025	−	0.884244i	$-0.345326\pi$
$41$	−0.417738	−	0.241181i	−0.0652397	−	0.0376661i	−0.532265	+	0.846578i	$0.678659\pi$
$42$		0			0
$43$	−6.91239	+	3.99087i	−1.05413	+	0.608602i	−0.923803	−	0.382869i	$-0.874936\pi$
$43$	−6.91239	+	3.99087i	−1.05413	+	0.608602i	−0.130327	+	0.991471i	$0.541603\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	12.1891			1.77796			0.888982	−	0.457943i	$-0.151413\pi$
$47$	12.1891			1.77796			0.888982	+	0.457943i	$0.151413\pi$
$48$		0			0
$49$	2.40130	−	4.15918i	0.343043	−	0.594168i
$50$		0			0
$51$	−6.79555			−0.951568
$52$		0			0
$53$		−	0.565122i		−	0.0776255i	−0.999247	−	0.0388127i	$-0.987642\pi$
$53$		−	0.565122i		−	0.0776255i	0.999247	−	0.0388127i	$-0.0123576\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.93890			−0.389267
$58$		0			0
$59$	7.39483	−	4.26941i	0.962725	−	0.555830i	0.0657145	−	0.997838i	$-0.479067\pi$
$59$	7.39483	−	4.26941i	0.962725	−	0.555830i	0.897011	+	0.442009i	$0.145734\pi$
$60$		0			0
$61$	5.92953	+	10.2702i	0.759198	+	1.31497i	0.943260	+	0.332056i	$0.107742\pi$
$61$	5.92953	+	10.2702i	0.759198	+	1.31497i	−0.184061	+	0.982915i	$0.558925\pi$
$62$		0			0
$63$	0.741181	−	1.28376i	0.0933800	−	0.161739i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.66510	+	9.81225i	−0.692103	+	1.19876i	0.279045	+	0.960278i	$0.409982\pi$
$67$	−5.66510	+	9.81225i	−0.692103	+	1.19876i	−0.971148	+	0.238479i	$0.923351\pi$
$68$		0			0
$69$	4.41920	+	7.65427i	0.532009	+	0.921466i
$70$		0			0
$71$	3.63713	−	2.09990i	0.431648	−	0.249212i	−0.268400	−	0.963307i	$-0.586495\pi$
$71$	3.63713	−	2.09990i	0.431648	−	0.249212i	0.700049	+	0.714095i	$0.253162\pi$
$72$		0			0
$73$	11.4317			1.33798			0.668992	−	0.743269i	$-0.266726\pi$
$73$	11.4317			1.33798			0.668992	+	0.743269i	$0.266726\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			3.18154i			0.362570i
$78$		0			0
$79$	9.19615			1.03465			0.517324	−	0.855790i	$-0.326928\pi$
$79$	9.19615			1.03465			0.517324	+	0.855790i	$0.326928\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	9.28132			1.01876			0.509378	−	0.860543i	$-0.329875\pi$
$83$	9.28132			1.01876			0.509378	+	0.860543i	$0.329875\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.45559	−	1.41774i	0.263267	−	0.151997i
$88$		0			0
$89$	10.8228	+	6.24857i	1.14722	+	0.662347i	0.948208	−	0.317650i	$-0.102894\pi$
$89$	10.8228	+	6.24857i	1.14722	+	0.662347i	0.199011	+	0.979997i	$0.436227\pi$
$90$		0			0
$91$	−5.34374	−	0.102802i	−0.560176	−	0.0107766i
$92$		0			0
$93$	−4.16390	+	7.21209i	−0.431777	+	0.747859i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	8.32660	+	14.4221i	0.845438	+	1.46434i	0.885240	+	0.465135i	$0.153994\pi$
$97$	8.32660	+	14.4221i	0.845438	+	1.46434i	−0.0398015	+	0.999208i	$0.512673\pi$
$98$		0			0
$99$		−	2.14626i		−	0.215708i
$100$		0			0
$101$	5.67253	−	9.82512i	0.564438	−	0.977636i	−0.432663	−	0.901556i	$-0.642426\pi$
$101$	5.67253	−	9.82512i	0.564438	−	0.977636i	0.997102	−	0.0760803i	$-0.0242405\pi$
$102$		0			0
$103$		−	15.8089i		−	1.55770i	−0.627211	−	0.778850i	$-0.715803\pi$
$103$		−	15.8089i		−	1.55770i	0.627211	−	0.778850i	$-0.284197\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−16.9677	−	9.79631i	−1.64033	−	0.947045i	−0.980715	−	0.195441i	$-0.937386\pi$
$107$	−16.9677	−	9.79631i	−1.64033	−	0.947045i	−0.659615	−	0.751604i	$-0.729281\pi$
$108$		0			0
$109$			6.00945i			0.575601i	0.957690	+	0.287801i	$0.0929240\pi$
$109$			6.00945i			0.575601i	−0.957690	+	0.287801i	$0.907076\pi$
$110$		0			0
$111$	−6.32076	+	3.64929i	−0.599940	+	0.346375i
$112$		0			0
$113$	−17.3631	+	10.0246i	−1.63338	+	0.943033i	−0.650341	+	0.759642i	$0.725374\pi$
$113$	−17.3631	+	10.0246i	−1.63338	+	0.943033i	−0.983040	+	0.183391i	$0.941293\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.60488	+	0.0693504i	0.333272	+	0.00641144i
$118$		0			0
$119$	8.72388	+	5.03674i	0.799717	+	0.461717i
$120$		0			0
$121$	−3.19677	−	5.53698i	−0.290616	−	0.503361i
$122$		0			0
$123$	−0.241181	−	0.417738i	−0.0217466	−	0.0376661i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	4.31892	+	2.49353i	0.383242	+	0.221265i	0.679228	−	0.733927i	$-0.262315\pi$
$127$	4.31892	+	2.49353i	0.383242	+	0.221265i	−0.295986	+	0.955192i	$0.595648\pi$
$128$		0			0
$129$	−7.98174			−0.702753
$130$		0			0
$131$	7.32076			0.639617			0.319809	−	0.947482i	$-0.396381\pi$
$131$	7.32076			0.639617			0.319809	+	0.947482i	$0.396381\pi$
$132$		0			0
$133$	3.77285	+	2.17826i	0.327148	+	0.188879i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.60514	+	7.97634i	0.393444	+	0.681465i	0.992901	−	0.118942i	$-0.0379502\pi$
$137$	4.60514	+	7.97634i	0.393444	+	0.681465i	−0.599457	+	0.800407i	$0.704617\pi$
$138$		0			0
$139$	3.77792	+	6.54354i	0.320439	+	0.555016i	0.980579	−	0.196127i	$-0.0628363\pi$
$139$	3.77792	+	6.54354i	0.320439	+	0.555016i	−0.660140	+	0.751143i	$0.729503\pi$
$140$		0			0
$141$	10.5561	+	6.09455i	0.888982	+	0.513254i
$142$		0			0
$143$	−6.77489	+	3.73961i	−0.566545	+	0.312722i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	4.15918	−	2.40130i	0.343043	−	0.198056i
$148$		0			0
$149$	−2.90496	+	1.67718i	−0.237984	+	0.137400i	−0.614250	−	0.789112i	$-0.710541\pi$
$149$	−2.90496	+	1.67718i	−0.237984	+	0.137400i	0.376266	+	0.926512i	$0.377208\pi$
$150$		0			0
$151$		−	13.6310i		−	1.10928i	−0.832091	−	0.554639i	$-0.812856\pi$
$151$		−	13.6310i		−	1.10928i	0.832091	−	0.554639i	$-0.187144\pi$
$152$		0			0
$153$	−5.88512	−	3.39778i	−0.475784	−	0.274694i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			8.00897i			0.639186i	0.947555	+	0.319593i	$0.103546\pi$
$157$			8.00897i			0.639186i	−0.947555	+	0.319593i	$0.896454\pi$
$158$		0			0
$159$	0.282561	−	0.489410i	0.0224086	−	0.0388127i
$160$		0			0
$161$		−	13.1017i		−	1.03256i
$162$		0			0
$163$	4.52677	+	7.84059i	0.354564	+	0.614123i	0.987043	−	0.160455i	$-0.0512960\pi$
$163$	4.52677	+	7.84059i	0.354564	+	0.614123i	−0.632479	+	0.774577i	$0.717963\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.51764	+	9.55683i	−0.426968	+	0.739530i	−0.996602	−	0.0823686i	$-0.973752\pi$
$167$	−5.51764	+	9.55683i	−0.426968	+	0.739530i	0.569634	+	0.821898i	$0.307085\pi$
$168$		0			0
$169$	−6.06218	−	11.5000i	−0.466321	−	0.884615i
$170$		0			0
$171$	−2.54516	−	1.46945i	−0.194633	−	0.112372i
$172$		0			0
$173$	−7.69137	+	4.44062i	−0.584764	+	0.337614i	−0.763025	−	0.646370i	$-0.776286\pi$
$173$	−7.69137	+	4.44062i	−0.584764	+	0.337614i	0.178260	+	0.983983i	$0.442953\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.53882			0.641817
$178$		0			0
$179$	−0.323941	+	0.561083i	−0.0242125	+	0.0419373i	−0.877878	−	0.478885i	$-0.841041\pi$
$179$	−0.323941	+	0.561083i	−0.0242125	+	0.0419373i	0.853665	+	0.520822i	$0.174374\pi$
$180$		0			0
$181$	4.78851			0.355927			0.177963	−	0.984037i	$-0.443049\pi$
$181$	4.78851			0.355927			0.177963	+	0.984037i	$0.443049\pi$
$182$		0			0
$183$			11.8591i			0.876647i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	14.5851			1.06657
$188$		0			0
$189$	1.28376	−	0.741181i	0.0933800	−	0.0539130i
$190$		0			0
$191$	−6.23289	−	10.7957i	−0.450996	−	0.781148i	0.547452	−	0.836837i	$-0.315598\pi$
$191$	−6.23289	−	10.7957i	−0.450996	−	0.781148i	−0.998448	+	0.0556890i	$0.982264\pi$
$192$		0			0
$193$	−6.43331	+	11.1428i	−0.463080	+	0.802078i	−0.999113	−	0.0421193i	$-0.986589\pi$
$193$	−6.43331	+	11.1428i	−0.463080	+	0.802078i	0.536033	+	0.844197i	$0.319922\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.21235	+	5.56395i	−0.228870	+	0.396415i	−0.957474	−	0.288521i	$-0.906837\pi$
$197$	−3.21235	+	5.56395i	−0.228870	+	0.396415i	0.728603	+	0.684936i	$0.240170\pi$
$198$		0			0
$199$	−2.83850	−	4.91643i	−0.201216	−	0.348516i	0.747704	−	0.664032i	$-0.231156\pi$
$199$	−2.83850	−	4.91643i	−0.201216	−	0.348516i	−0.948921	+	0.315515i	$0.897823\pi$
$200$		0			0
$201$	−9.81225	+	5.66510i	−0.692103	+	0.399586i
$202$		0			0
$203$	−4.20320			−0.295007
$204$		0			0
$205$		0			0
$206$		0			0
$207$			8.83839i			0.614311i
$208$		0			0
$209$	6.30766			0.436310
$210$		0			0
$211$	−6.04222	+	10.4654i	−0.415963	+	0.720470i	−0.995529	−	0.0944558i	$-0.969889\pi$
$211$	−6.04222	+	10.4654i	−0.415963	+	0.720470i	0.579566	+	0.814926i	$0.303222\pi$
$212$		0			0
$213$	4.19980			0.287766
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.6909	−	6.17241i	0.725748	−	0.419011i
$218$		0			0
$219$	9.90018	+	5.71587i	0.668992	+	0.386243i
$220$		0			0
$221$	−0.471274	+	24.4972i	−0.0317013	+	1.64786i
$222$		0			0
$223$	−0.166929	+	0.289129i	−0.0111784	+	0.0193615i	−0.871560	−	0.490288i	$-0.836892\pi$
$223$	−0.166929	+	0.289129i	−0.0111784	+	0.0193615i	0.860382	+	0.509650i	$0.170225\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.33427	+	9.23923i	0.354048	+	0.613229i	0.986955	−	0.160999i	$-0.0514716\pi$
$227$	5.33427	+	9.23923i	0.354048	+	0.613229i	−0.632906	+	0.774228i	$0.718138\pi$
$228$		0			0
$229$			21.8530i			1.44409i	0.691847	+	0.722044i	$0.256797\pi$
$229$			21.8530i			1.44409i	−0.691847	+	0.722044i	$0.743203\pi$
$230$		0			0
$231$	−1.59077	+	2.75529i	−0.104665	+	0.181285i
$232$		0			0
$233$		−	0.825259i		−	0.0540645i	−0.999635	−	0.0270323i	$-0.991394\pi$
$233$		−	0.825259i		−	0.0540645i	0.999635	−	0.0270323i	$-0.00860568\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	7.96410	+	4.59808i	0.517324	+	0.298677i
$238$		0			0
$239$		−	8.44609i		−	0.546332i	−0.961967	−	0.273166i	$-0.911929\pi$
$239$		−	8.44609i		−	0.546332i	0.961967	−	0.273166i	$-0.0880709\pi$
$240$		0			0
$241$	−5.15526	+	2.97639i	−0.332080	+	0.191726i	−0.656764	−	0.754096i	$-0.728075\pi$
$241$	−5.15526	+	2.97639i	−0.332080	+	0.191726i	0.324684	+	0.945822i	$0.394742\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.203814	+	10.5944i	−0.0129684	+	0.674105i
$248$		0			0
$249$	8.03786	+	4.64066i	0.509378	+	0.294090i
$250$		0			0
$251$	−8.34349	−	14.4513i	−0.526636	−	0.912161i	−0.999518	−	0.0310349i	$-0.990120\pi$
$251$	−8.34349	−	14.4513i	−0.526636	−	0.912161i	0.472882	−	0.881126i	$-0.343214\pi$
$252$		0			0
$253$	−9.48477	−	16.4281i	−0.596302	−	1.03283i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−25.5710	−	14.7634i	−1.59508	−	0.920918i	−0.992417	−	0.122920i	$-0.960774\pi$
$257$	−25.5710	−	14.7634i	−1.59508	−	0.920918i	−0.602660	−	0.797998i	$-0.705893\pi$
$258$		0			0
$259$	10.8191			0.672269
$260$		0			0
$261$	2.83548			0.175512
$262$		0			0
$263$	13.5113	+	7.80078i	0.833145	+	0.481017i	0.854928	−	0.518746i	$-0.173601\pi$
$263$	13.5113	+	7.80078i	0.833145	+	0.481017i	−0.0217831	+	0.999763i	$0.506934\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	6.24857	+	10.8228i	0.382406	+	0.662347i
$268$		0			0
$269$	3.53835	+	6.12861i	0.215737	+	0.373668i	0.953500	−	0.301392i	$-0.0974512\pi$
$269$	3.53835	+	6.12861i	0.215737	+	0.373668i	−0.737763	+	0.675060i	$0.764118\pi$
$270$		0			0
$271$	−5.10989	−	2.95019i	−0.310403	−	0.179212i	0.336704	−	0.941611i	$-0.390688\pi$
$271$	−5.10989	−	2.95019i	−0.310403	−	0.179212i	−0.647107	+	0.762399i	$0.724021\pi$
$272$		0			0
$273$	−4.57642	−	2.76090i	−0.276977	−	0.167097i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−21.4582	+	12.3889i	−1.28930	+	0.744377i	−0.978529	−	0.206108i	$-0.933920\pi$
$277$	−21.4582	+	12.3889i	−1.28930	+	0.744377i	−0.310770	+	0.950485i	$0.600587\pi$
$278$		0			0
$279$	−7.21209	+	4.16390i	−0.431777	+	0.249286i
$280$		0			0
$281$		−	31.8253i		−	1.89854i	−0.314465	−	0.949269i	$-0.601825\pi$
$281$		−	31.8253i		−	1.89854i	0.314465	−	0.949269i	$-0.398175\pi$
$282$		0			0
$283$	−1.49978	−	0.865901i	−0.0891529	−	0.0514725i	0.454761	−	0.890614i	$-0.349725\pi$
$283$	−1.49978	−	0.865901i	−0.0891529	−	0.0514725i	−0.543914	+	0.839141i	$0.683058\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			0.715035i			0.0422072i
$288$		0			0
$289$	14.5898	−	25.2702i	0.858223	−	1.48649i
$290$		0			0
$291$			16.6532i			0.976228i
$292$		0			0
$293$	4.12742	+	7.14891i	0.241127	+	0.417644i	0.961036	−	0.276425i	$-0.0891497\pi$
$293$	4.12742	+	7.14891i	0.241127	+	0.417644i	−0.719909	+	0.694069i	$0.755816\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.07313	−	1.85872i	0.0622694	−	0.107854i
$298$		0			0
$299$	27.8992	−	15.3999i	1.61346	−	0.890597i
$300$		0			0
$301$	10.2467	+	5.91591i	0.590608	+	0.340988i
$302$		0			0
$303$	9.82512	−	5.67253i	0.564438	−	0.325879i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−6.30903			−0.360075			−0.180038	−	0.983660i	$-0.557622\pi$
$307$	−6.30903			−0.360075			−0.180038	+	0.983660i	$0.557622\pi$
$308$		0			0
$309$	7.90446	−	13.6909i	0.449669	−	0.778850i
$310$		0			0
$311$	−1.16417			−0.0660142			−0.0330071	−	0.999455i	$-0.510508\pi$
$311$	−1.16417			−0.0660142			−0.0330071	+	0.999455i	$0.510508\pi$
$312$		0			0
$313$			19.7018i			1.11361i	0.830642	+	0.556807i	$0.187974\pi$
$313$			19.7018i			1.11361i	−0.830642	+	0.556807i	$0.812026\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.882212			−0.0495500			−0.0247750	−	0.999693i	$-0.507887\pi$
$317$	−0.882212			−0.0495500			−0.0247750	+	0.999693i	$0.507887\pi$
$318$		0			0
$319$	−5.27035	+	3.04284i	−0.295083	+	0.170366i
$320$		0			0
$321$	−9.79631	−	16.9677i	−0.546777	−	0.947045i
$322$		0			0
$323$	9.98573	−	17.2958i	0.555621	−	0.962363i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−3.00473	+	5.20434i	−0.166162	+	0.287801i
$328$		0			0
$329$	−9.03433	−	15.6479i	−0.498079	−	0.862698i
$330$		0			0
$331$	17.0020	−	9.81614i	0.934517	−	0.539544i	0.0462798	−	0.998929i	$-0.485263\pi$
$331$	17.0020	−	9.81614i	0.934517	−	0.539544i	0.888237	+	0.459385i	$0.151930\pi$
$332$		0			0
$333$	−7.29858			−0.399960
$334$		0			0
$335$		0			0
$336$		0			0
$337$			2.36724i			0.128952i	0.997919	+	0.0644760i	$0.0205376\pi$
$337$			2.36724i			0.128952i	−0.997919	+	0.0644760i	$0.979462\pi$
$338$		0			0
$339$	−20.0492			−1.08892
$340$		0			0
$341$	8.93684	−	15.4791i	0.483957	−	0.838238i
$342$		0			0
$343$	−17.4957			−0.944681
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.6862	+	7.32441i	−0.681033	+	0.393195i	−0.800244	−	0.599674i	$-0.795297\pi$
$347$	−12.6862	+	7.32441i	−0.681033	+	0.393195i	0.119211	+	0.992869i	$0.461963\pi$
$348$		0			0
$349$	−26.9424	−	15.5552i	−1.44219	−	0.832651i	−0.444198	−	0.895928i	$-0.646512\pi$
$349$	−26.9424	−	15.5552i	−1.44219	−	0.832651i	−0.997996	+	0.0632770i	$0.979845\pi$
$350$		0			0
$351$	3.08725	+	1.86250i	0.164785	+	0.0994130i
$352$		0			0
$353$	0.295838	−	0.512406i	0.0157458	−	0.0272726i	−0.858045	−	0.513574i	$-0.828321\pi$
$353$	0.295838	−	0.512406i	0.0157458	−	0.0272726i	0.873791	+	0.486302i	$0.161654\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.03674	+	8.72388i	0.266572	+	0.461717i
$358$		0			0
$359$		−	13.8253i		−	0.729671i	−0.931072	−	0.364836i	$-0.881125\pi$
$359$		−	13.8253i		−	0.729671i	0.931072	−	0.364836i	$-0.118875\pi$
$360$		0			0
$361$	−5.18143	+	8.97451i	−0.272707	+	0.472342i
$362$		0			0
$363$		−	6.39355i		−	0.335574i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	21.0335	+	12.1437i	1.09794	+	0.633896i	0.935679	−	0.352852i	$-0.114788\pi$
$367$	21.0335	+	12.1437i	1.09794	+	0.633896i	0.162261	+	0.986748i	$0.448121\pi$
$368$		0			0
$369$		−	0.482362i		−	0.0251108i
$370$		0			0
$371$	−0.725483	+	0.418858i	−0.0376652	+	0.0217460i
$372$		0			0
$373$	−9.12012	+	5.26550i	−0.472222	+	0.272637i	−0.717169	−	0.696899i	$-0.754563\pi$
$373$	−9.12012	+	5.26550i	−0.472222	+	0.272637i	0.244948	+	0.969536i	$0.421229\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.94048	−	8.95045i	−0.254448	−	0.460972i
$378$		0			0
$379$	1.41022	+	0.814189i	0.0724380	+	0.0418221i	0.535782	−	0.844357i	$-0.320017\pi$
$379$	1.41022	+	0.814189i	0.0724380	+	0.0418221i	−0.463344	+	0.886179i	$0.653350\pi$
$380$		0			0
$381$	2.49353	+	4.31892i	0.127747	+	0.221265i
$382$		0			0
$383$	4.81199	+	8.33461i	0.245881	+	0.425879i	0.962379	−	0.271711i	$-0.0875893\pi$
$383$	4.81199	+	8.33461i	0.245881	+	0.425879i	−0.716498	+	0.697589i	$0.754256\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.91239	−	3.99087i	−0.351376	−	0.202867i
$388$		0			0
$389$	−15.4741			−0.784566			−0.392283	−	0.919844i	$-0.628315\pi$
$389$	−15.4741			−0.784566			−0.392283	+	0.919844i	$0.628315\pi$
$390$		0			0
$391$	−60.0618			−3.03746
$392$		0			0
$393$	6.33996	+	3.66038i	0.319809	+	0.184642i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−10.7103	−	18.5509i	−0.537537	−	0.931041i	−0.999036	−	0.0439006i	$-0.986022\pi$
$397$	−10.7103	−	18.5509i	−0.537537	−	0.931041i	0.461499	−	0.887141i	$-0.347312\pi$
$398$		0			0
$399$	2.17826	+	3.77285i	0.109049	+	0.188879i
$400$		0			0
$401$	27.7026	+	15.9941i	1.38340	+	0.798708i	0.992561	−	0.121750i	$-0.0388506\pi$
$401$	27.7026	+	15.9941i	1.38340	+	0.798708i	0.390842	+	0.920458i	$0.372184\pi$
$402$		0			0
$403$	25.7100	+	15.5105i	1.28071	+	0.772635i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	13.5660	−	7.83234i	0.672442	−	0.388235i
$408$		0			0
$409$	23.5525	−	13.5981i	1.16460	−	0.672380i	0.212196	−	0.977227i	$-0.431939\pi$
$409$	23.5525	−	13.5981i	1.16460	−	0.672380i	0.952401	+	0.304847i	$0.0986053\pi$
$410$		0			0
$411$			9.21028i			0.454310i
$412$		0			0
$413$	−10.9618	−	6.32881i	−0.539396	−	0.311420i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			7.55583i			0.370011i
$418$		0			0
$419$	0.325349	−	0.563522i	0.0158944	−	0.0275298i	−0.857969	−	0.513702i	$-0.828274\pi$
$419$	0.325349	−	0.563522i	0.0158944	−	0.0275298i	0.873863	+	0.486172i	$0.161607\pi$
$420$		0			0
$421$			35.7471i			1.74221i	0.491098	+	0.871104i	$0.336596\pi$
$421$			35.7471i			1.74221i	−0.491098	+	0.871104i	$0.663404\pi$
$422$		0			0
$423$	6.09455	+	10.5561i	0.296327	+	0.513254i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	8.78971	−	15.2242i	0.425364	−	0.736752i
$428$		0			0
$429$	−7.73703	−	0.148844i	−0.373548	−	0.00718627i
$430$		0			0
$431$	18.1241	+	10.4639i	0.873005	+	0.504030i	0.868346	−	0.495960i	$-0.165184\pi$
$431$	18.1241	+	10.4639i	0.873005	+	0.504030i	0.00465921	+	0.999989i	$0.498517\pi$
$432$		0			0
$433$	−21.3903	+	12.3497i	−1.02795	+	0.593487i	−0.916397	−	0.400271i	$-0.868916\pi$
$433$	−21.3903	+	12.3497i	−1.02795	+	0.593487i	−0.111553	+	0.993758i	$0.535583\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−25.9752			−1.24256
$438$		0			0
$439$	−13.9137	+	24.0992i	−0.664063	+	1.15019i	0.315475	+	0.948934i	$0.397836\pi$
$439$	−13.9137	+	24.0992i	−0.664063	+	1.15019i	−0.979538	+	0.201258i	$0.935497\pi$
$440$		0			0
$441$	4.80260			0.228695
$442$		0			0
$443$		−	27.8356i		−	1.32251i	−0.750161	−	0.661256i	$-0.770024\pi$
$443$		−	27.8356i		−	1.32251i	0.750161	−	0.661256i	$-0.229976\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−3.35436			−0.158656
$448$		0			0
$449$	5.88828	−	3.39960i	0.277885	−	0.160437i	−0.354580	−	0.935026i	$-0.615376\pi$
$449$	5.88828	−	3.39960i	0.277885	−	0.160437i	0.632466	+	0.774588i	$0.282043\pi$
$450$		0			0
$451$	0.517638	+	0.896575i	0.0243746	+	0.0422181i
$452$		0			0
$453$	6.81552	−	11.8048i	0.320221	−	0.554639i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.798482	+	1.38301i	−0.0373514	+	0.0646945i	−0.884097	−	0.467304i	$-0.845225\pi$
$457$	−0.798482	+	1.38301i	−0.0373514	+	0.0646945i	0.846745	+	0.531998i	$0.178559\pi$
$458$		0			0
$459$	−3.39778	−	5.88512i	−0.158595	−	0.274694i
$460$		0			0
$461$	6.32097	−	3.64941i	0.294397	−	0.169970i	−0.345526	−	0.938409i	$-0.612300\pi$
$461$	6.32097	−	3.64941i	0.294397	−	0.169970i	0.639923	+	0.768439i	$0.278966\pi$
$462$		0			0
$463$	12.7038			0.590397			0.295198	−	0.955436i	$-0.404614\pi$
$463$	12.7038			0.590397			0.295198	+	0.955436i	$0.404614\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	1.65053i		−	0.0763777i	−0.999271	−	0.0381888i	$-0.987841\pi$
$467$		−	1.65053i		−	0.0763777i	0.999271	−	0.0381888i	$-0.0121588\pi$
$468$		0			0
$469$	16.7955			0.775543
$470$		0			0
$471$	−4.00449	+	6.93597i	−0.184517	+	0.319593i
$472$		0			0
$473$	17.1309			0.787681
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.489410	−	0.282561i	0.0224086	−	0.0129376i
$478$		0			0
$479$	−23.8712	−	13.7821i	−1.09070	−	0.629719i	−0.156941	−	0.987608i	$-0.550163\pi$
$479$	−23.8712	−	13.7821i	−1.09070	−	0.629719i	−0.933764	+	0.357890i	$0.883496\pi$
$480$		0			0
$481$	12.7169	+	23.0387i	0.579842	+	1.05047i
$482$		0			0
$483$	6.55085	−	11.3464i	0.298074	−	0.516279i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	20.8850	+	36.1739i	0.946390	+	1.63919i	0.752945	+	0.658084i	$0.228633\pi$
$487$	20.8850	+	36.1739i	0.946390	+	1.63919i	0.193445	+	0.981111i	$0.438034\pi$
$488$		0			0
$489$			9.05354i			0.409415i
$490$		0			0
$491$	8.51463	−	14.7478i	0.384260	−	0.665558i	−0.607406	−	0.794391i	$-0.707790\pi$
$491$	8.51463	−	14.7478i	0.384260	−	0.665558i	0.991666	+	0.128834i	$0.0411233\pi$
$492$		0			0
$493$			19.2686i			0.867815i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.39155	−	3.11281i	−0.241844	−	0.139629i
$498$		0			0
$499$			27.7591i			1.24267i	0.783546	+	0.621333i	$0.213409\pi$
$499$			27.7591i			1.24267i	−0.783546	+	0.621333i	$0.786591\pi$
$500$		0			0
$501$	−9.55683	+	5.51764i	−0.426968	+	0.246510i
$502$		0			0
$503$	−7.23126	+	4.17497i	−0.322426	+	0.186153i	−0.652473	−	0.757812i	$-0.726269\pi$
$503$	−7.23126	+	4.17497i	−0.322426	+	0.186153i	0.330047	+	0.943964i	$0.392935\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.500000	−	12.9904i	0.0222058	−	0.576923i
$508$		0			0
$509$	−4.29338	−	2.47879i	−0.190301	−	0.109870i	0.401823	−	0.915718i	$-0.368377\pi$
$509$	−4.29338	−	2.47879i	−0.190301	−	0.109870i	−0.592123	+	0.805847i	$0.701710\pi$
$510$		0			0
$511$	−8.47299	−	14.6757i	−0.374823	−	0.649213i
$512$		0			0
$513$	−1.46945	−	2.54516i	−0.0648778	−	0.112372i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−22.6561	−	13.0805i	−0.996415	−	0.575281i
$518$		0			0
$519$	−8.88123			−0.389843
$520$		0			0
$521$	−27.0863			−1.18667			−0.593337	−	0.804954i	$-0.702190\pi$
$521$	−27.0863			−1.18667			−0.593337	+	0.804954i	$0.702190\pi$
$522$		0			0
$523$	4.39492	+	2.53741i	0.192177	+	0.110953i	0.593001	−	0.805202i	$-0.297943\pi$
$523$	4.39492	+	2.53741i	0.192177	+	0.110953i	−0.400825	+	0.916155i	$0.631276\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−28.2960	−	49.0102i	−1.23259	−	2.13492i
$528$		0			0
$529$	27.5586	+	47.7329i	1.19820	+	2.07534i
$530$		0			0
$531$	7.39483	+	4.26941i	0.320908	+	0.185277i
$532$		0			0
$533$	−1.52262	+	0.840459i	−0.0659521	+	0.0364043i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.561083	+	0.323941i	−0.0242125	+	0.0139791i
$538$		0			0
$539$	−8.92669	+	5.15383i	−0.384500	+	0.221991i
$540$		0			0
$541$			4.65826i			0.200274i	0.994974	+	0.100137i	$0.0319282\pi$
$541$			4.65826i			0.200274i	−0.994974	+	0.100137i	$0.968072\pi$
$542$		0			0
$543$	4.14697	+	2.39425i	0.177963	+	0.102747i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	30.0649i		−	1.28548i	−0.766083	−	0.642742i	$-0.777797\pi$
$547$		−	30.0649i		−	1.28548i	0.766083	−	0.642742i	$-0.222203\pi$
$548$		0			0
$549$	−5.92953	+	10.2702i	−0.253066	+	0.438323i
$550$		0			0
$551$			8.33318i			0.355005i
$552$		0			0
$553$	−6.81601	−	11.8057i	−0.289846	−	0.502029i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.89640	−	10.2129i	0.249838	−	0.432733i	−0.713642	−	0.700510i	$-0.752956\pi$
$557$	5.89640	−	10.2129i	0.249838	−	0.432733i	0.963481	+	0.267777i	$0.0862891\pi$
$558$		0			0
$559$	−0.553536	+	28.7732i	−0.0234121	+	1.21698i
$560$		0			0
$561$	12.6310	+	7.29253i	0.533283	+	0.307891i
$562$		0			0
$563$	31.5200	−	18.1981i	1.32841	−	0.766957i	0.343356	−	0.939205i	$-0.388436\pi$
$563$	31.5200	−	18.1981i	1.32841	−	0.766957i	0.985054	+	0.172248i	$0.0551030\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.48236			0.0622533
$568$		0			0
$569$	2.14532	−	3.71580i	0.0899365	−	0.155775i	−0.817548	−	0.575861i	$-0.804667\pi$
$569$	2.14532	−	3.71580i	0.0899365	−	0.155775i	0.907484	+	0.420086i	$0.138000\pi$
$570$		0			0
$571$	25.7016			1.07558			0.537789	−	0.843080i	$-0.319260\pi$
$571$	25.7016			1.07558			0.537789	+	0.843080i	$0.319260\pi$
$572$		0			0
$573$		−	12.4658i		−	0.520765i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	33.8695			1.41001			0.705004	−	0.709204i	$-0.250945\pi$
$577$	33.8695			1.41001			0.705004	+	0.709204i	$0.250945\pi$
$578$		0			0
$579$	−11.1428	+	6.43331i	−0.463080	+	0.267359i
$580$		0			0
$581$	−6.87914	−	11.9150i	−0.285395	−	0.494318i
$582$		0			0
$583$	−0.606451	+	1.05040i	−0.0251166	+	0.0435033i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.33943	+	4.05202i	−0.0965587	+	0.167245i	−0.910258	−	0.414041i	$-0.864117\pi$
$587$	−2.33943	+	4.05202i	−0.0965587	+	0.167245i	0.813699	+	0.581286i	$0.197450\pi$
$588$		0			0
$589$	−12.2373	−	21.1956i	−0.504229	−	0.873350i
$590$		0			0
$591$	−5.56395	+	3.21235i	−0.228870	+	0.132138i
$592$		0			0
$593$	−18.6055			−0.764036			−0.382018	−	0.924155i	$-0.624771\pi$
$593$	−18.6055			−0.764036			−0.382018	+	0.924155i	$0.624771\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	5.67700i		−	0.232344i
$598$		0			0
$599$	−4.77008			−0.194900			−0.0974501	−	0.995240i	$-0.531069\pi$
$599$	−4.77008			−0.194900			−0.0974501	+	0.995240i	$0.531069\pi$
$600$		0			0
$601$	−1.84890	+	3.20239i	−0.0754183	+	0.130628i	−0.901268	−	0.433262i	$-0.857363\pi$
$601$	−1.84890	+	3.20239i	−0.0754183	+	0.130628i	0.825850	+	0.563890i	$0.190696\pi$
$602$		0			0
$603$	−11.3302			−0.461402
$604$		0			0
$605$		0			0
$606$		0			0
$607$	35.2571	−	20.3557i	1.43104	−	0.826211i	0.433839	−	0.900990i	$-0.357158\pi$
$607$	35.2571	−	20.3557i	1.43104	−	0.826211i	0.997200	+	0.0747791i	$0.0238252\pi$
$608$		0			0
$609$	−3.64008	−	2.10160i	−0.147503	−	0.0851611i
$610$		0			0
$611$	22.7022	−	37.6308i	0.918434	−	1.52238i
$612$		0			0
$613$	17.3962	−	30.1310i	0.702624	−	1.21698i	−0.264918	−	0.964271i	$-0.585345\pi$
$613$	17.3962	−	30.1310i	0.702624	−	1.21698i	0.967542	−	0.252710i	$-0.0813218\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.20454	+	15.9427i	0.370561	+	0.641830i	0.989652	−	0.143489i	$-0.0458322\pi$
$617$	9.20454	+	15.9427i	0.370561	+	0.641830i	−0.619091	+	0.785319i	$0.712499\pi$
$618$		0			0
$619$		−	25.3957i		−	1.02074i	−0.859955	−	0.510370i	$-0.829509\pi$
$619$		−	25.3957i		−	1.02074i	0.859955	−	0.510370i	$-0.170491\pi$
$620$		0			0
$621$	−4.41920	+	7.65427i	−0.177336	+	0.307155i
$622$		0			0
$623$		−	18.5253i		−	0.742200i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	5.46259	+	3.15383i	0.218155	+	0.125952i
$628$		0			0
$629$		−	49.5979i		−	1.97760i
$630$		0			0
$631$	0.747989	−	0.431852i	0.0297770	−	0.0171917i	−0.485038	−	0.874493i	$-0.661194\pi$
$631$	0.747989	−	0.431852i	0.0297770	−	0.0171917i	0.514815	+	0.857302i	$0.327861\pi$
$632$		0			0
$633$	−10.4654	+	6.04222i	−0.415963	+	0.240157i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−8.36797	−	15.1599i	−0.331551	−	0.600656i
$638$		0			0
$639$	3.63713	+	2.09990i	0.143883	+	0.0830708i
$640$		0			0
$641$	1.27633	+	2.21067i	0.0504121	+	0.0873163i	0.890130	−	0.455706i	$-0.150613\pi$
$641$	1.27633	+	2.21067i	0.0504121	+	0.0873163i	−0.839718	+	0.543022i	$0.817280\pi$
$642$		0			0
$643$	−7.83515	−	13.5709i	−0.308988	−	0.535183i	0.669153	−	0.743125i	$-0.266657\pi$
$643$	−7.83515	−	13.5709i	−0.308988	−	0.535183i	−0.978141	+	0.207941i	$0.933324\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.6010	−	11.8940i	−0.809909	−	0.467601i	0.0370152	−	0.999315i	$-0.488215\pi$
$647$	−20.6010	−	11.8940i	−0.809909	−	0.467601i	−0.846924	+	0.531713i	$0.821548\pi$
$648$		0			0
$649$	−18.3266			−0.719380
$650$		0			0
$651$	12.3448			0.483832
$652$		0			0
$653$	21.6447	+	12.4966i	0.847022	+	0.489028i	0.859645	−	0.510892i	$-0.170685\pi$
$653$	21.6447	+	12.4966i	0.847022	+	0.489028i	−0.0126233	+	0.999920i	$0.504018\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	5.71587	+	9.90018i	0.222997	+	0.386243i
$658$		0			0
$659$	11.3259	+	19.6171i	0.441195	+	0.764172i	0.997778	−	0.0666195i	$-0.0212214\pi$
$659$	11.3259	+	19.6171i	0.441195	+	0.764172i	−0.556583	+	0.830792i	$0.687888\pi$
$660$		0			0
$661$	−25.0675	−	14.4727i	−0.975014	−	0.562924i	−0.0742527	−	0.997239i	$-0.523657\pi$
$661$	−25.0675	−	14.4727i	−0.975014	−	0.562924i	−0.900761	+	0.434315i	$0.856990\pi$
$662$		0			0
$663$	−12.6567	+	20.9796i	−0.491547	+	0.814778i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	21.7035	−	12.5305i	0.840363	−	0.485184i
$668$		0			0
$669$	−0.289129	+	0.166929i	−0.0111784	+	0.00645384i
$670$		0			0
$671$		−	25.4527i		−	0.982590i
$672$		0			0
$673$	−5.52072	−	3.18739i	−0.212808	−	0.122865i	0.389808	−	0.920896i	$-0.372541\pi$
$673$	−5.52072	−	3.18739i	−0.212808	−	0.122865i	−0.602616	+	0.798032i	$0.705875\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			2.18855i			0.0841129i	0.999115	+	0.0420565i	$0.0133909\pi$
$677$			2.18855i			0.0841129i	−0.999115	+	0.0420565i	$0.986609\pi$
$678$		0			0
$679$	12.3430	−	21.3788i	0.473682	−	0.820442i
$680$		0			0
$681$			10.6685i			0.408820i
$682$		0			0
$683$	−7.93261	−	13.7397i	−0.303533	−	0.525734i	0.673401	−	0.739278i	$-0.264833\pi$
$683$	−7.93261	−	13.7397i	−0.303533	−	0.525734i	−0.976934	+	0.213543i	$0.931500\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−10.9265	+	18.9253i	−0.416872	+	0.722044i
$688$		0			0
$689$	−1.74467	−	1.05254i	−0.0664667	−	0.0400986i
$690$		0			0
$691$	−30.6956	−	17.7221i	−1.16772	−	0.674182i	−0.214576	−	0.976707i	$-0.568837\pi$
$691$	−30.6956	−	17.7221i	−1.16772	−	0.674182i	−0.953141	+	0.302525i	$0.902170\pi$
$692$		0			0
$693$	−2.75529	+	1.59077i	−0.104665	+	0.0604284i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	3.27792			0.124160
$698$		0			0
$699$	0.412630	−	0.714695i	0.0156071	−	0.0270323i
$700$		0			0
$701$	48.8074			1.84343			0.921714	−	0.387869i	$-0.126789\pi$
$701$	48.8074			1.84343			0.921714	+	0.387869i	$0.126789\pi$
$702$		0			0
$703$		−	21.4498i		−	0.808994i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−16.8175			−0.632487
$708$		0			0
$709$	−29.3654	+	16.9541i	−1.10284	+	0.636725i	−0.936965	−	0.349422i	$-0.886378\pi$
$709$	−29.3654	+	16.9541i	−1.10284	+	0.636725i	−0.165874	+	0.986147i	$0.553045\pi$
$710$		0			0
$711$	4.59808	+	7.96410i	0.172441	+	0.298677i
$712$		0			0
$713$	−36.8022	+	63.7433i	−1.37825	+	2.38721i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.22304	−	7.31453i	0.157713	−	0.273166i
$718$		0			0
$719$	15.8458	+	27.4458i	0.590950	+	1.02356i	0.994105	+	0.108423i	$0.0345802\pi$
$719$	15.8458	+	27.4458i	0.590950	+	1.02356i	−0.403155	+	0.915132i	$0.632086\pi$
$720$		0			0
$721$	−20.2949	+	11.7173i	−0.755822	+	0.436374i
$722$		0			0
$723$	−5.95278			−0.221386
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	41.4882i		−	1.53871i	−0.638820	−	0.769356i	$-0.720577\pi$
$727$		−	41.4882i		−	1.53871i	0.638820	−	0.769356i	$-0.279423\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	27.1202	−	46.9735i	1.00308	−	1.73738i
$732$		0			0
$733$	−24.7661			−0.914757			−0.457379	−	0.889272i	$-0.651212\pi$
$733$	−24.7661			−0.914757			−0.457379	+	0.889272i	$0.651212\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	21.0597	−	12.1588i	0.775743	−	0.447876i
$738$		0			0
$739$	16.8459	+	9.72600i	0.619687	+	0.357777i	0.776747	−	0.629812i	$-0.216868\pi$
$739$	16.8459	+	9.72600i	0.619687	+	0.357777i	−0.157060	+	0.987589i	$0.550202\pi$
$740$		0			0
$741$	−5.47370	+	9.07311i	−0.201082	+	0.333309i
$742$		0			0
$743$	24.7123	−	42.8030i	0.906607	−	1.57029i	0.0878606	−	0.996133i	$-0.471997\pi$
$743$	24.7123	−	42.8030i	0.906607	−	1.57029i	0.818746	−	0.574156i	$-0.194670\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.64066	+	8.03786i	0.169793	+	0.294090i
$748$		0			0
$749$			29.0434i			1.06122i
$750$		0			0
$751$	22.6941	−	39.3073i	0.828119	−	1.43434i	−0.0713924	−	0.997448i	$-0.522744\pi$
$751$	22.6941	−	39.3073i	0.828119	−	1.43434i	0.899512	−	0.436897i	$-0.143922\pi$
$752$		0			0
$753$		−	16.6870i		−	0.608107i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−32.6723	−	18.8633i	−1.18749	−	0.685600i	−0.229757	−	0.973248i	$-0.573793\pi$
$757$	−32.6723	−	18.8633i	−1.18749	−	0.685600i	−0.957736	+	0.287648i	$0.907127\pi$
$758$		0			0
$759$		−	18.9695i		−	0.688550i
$760$		0			0
$761$	15.9074	−	9.18412i	0.576641	−	0.332924i	−0.183156	−	0.983084i	$-0.558631\pi$
$761$	15.9074	−	9.18412i	0.576641	−	0.332924i	0.759798	+	0.650160i	$0.225298\pi$
$762$		0			0
$763$	7.71471	−	4.45409i	0.279291	−	0.161249i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.592170	−	30.7815i	0.0213820	−	1.11145i
$768$		0			0
$769$	−2.16546	−	1.25023i	−0.0780885	−	0.0450844i	0.460447	−	0.887687i	$-0.347689\pi$
$769$	−2.16546	−	1.25023i	−0.0780885	−	0.0450844i	−0.538536	+	0.842603i	$0.681022\pi$
$770$		0			0
$771$	−14.7634	−	25.5710i	−0.531692	−	0.920918i
$772$		0			0
$773$	−0.326221	−	0.565031i	−0.0117333	−	0.0203228i	0.860099	−	0.510127i	$-0.170402\pi$
$773$	−0.326221	−	0.565031i	−0.0117333	−	0.0203228i	−0.871832	+	0.489804i	$0.837068\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	9.36965	+	5.40957i	0.336134	+	0.194067i
$778$		0			0
$779$	1.41761			0.0507913
$780$		0			0
$781$	−9.01388			−0.322542
$782$		0			0
$783$	2.45559	+	1.41774i	0.0877558	+	0.0506658i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	14.2101	+	24.6126i	0.506535	+	0.877344i	0.999971	+	0.00756251i	$0.00240724\pi$
$787$	14.2101	+	24.6126i	0.506535	+	0.877344i	−0.493436	+	0.869782i	$0.664259\pi$
$788$		0			0
$789$	7.80078	+	13.5113i	0.277715	+	0.481017i
$790$		0			0
$791$	25.7384	+	14.8601i	0.915151	+	0.528363i
$792$		0			0
$793$	42.7505	+	0.822430i	1.51812	+	0.0292053i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−28.4774	+	16.4414i	−1.00872	+	0.582386i	−0.910817	−	0.412810i	$-0.864547\pi$
$797$	−28.4774	+	16.4414i	−1.00872	+	0.582386i	−0.0979044	+	0.995196i	$0.531214\pi$
$798$		0			0
$799$	−71.7344	+	41.4159i	−2.53778	+	1.46519i
$800$		0			0
$801$			12.4971i			0.441565i
$802$		0			0
$803$	−21.2484	−	12.2678i	−0.749840	−	0.432920i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			7.07671i			0.249112i
$808$		0			0
$809$	−9.83715	+	17.0384i	−0.345856	+	0.599040i	−0.985509	−	0.169624i	$-0.945745\pi$
$809$	−9.83715	+	17.0384i	−0.345856	+	0.599040i	0.639653	+	0.768664i	$0.279078\pi$
$810$		0			0
$811$			1.86785i			0.0655891i	0.999462	+	0.0327945i	$0.0104407\pi$
$811$			1.86785i			0.0655891i	−0.999462	+	0.0327945i	$0.989559\pi$
$812$		0			0
$813$	−2.95019	−	5.10989i	−0.103468	−	0.179212i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	11.7288	−	20.3148i	0.410338	−	0.710726i
$818$		0			0
$819$	−2.58284	−	4.67922i	−0.0902518	−	0.163505i
$820$		0			0
$821$	−2.22390	−	1.28397i	−0.0776146	−	0.0448108i	0.460690	−	0.887561i	$-0.347602\pi$
$821$	−2.22390	−	1.28397i	−0.0776146	−	0.0448108i	−0.538305	+	0.842750i	$0.680935\pi$
$822$		0			0
$823$	25.0698	−	14.4741i	0.873879	−	0.504534i	0.00524374	−	0.999986i	$-0.498331\pi$
$823$	25.0698	−	14.4741i	0.873879	−	0.504534i	0.868635	+	0.495452i	$0.164998\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.30704			0.0454502			0.0227251	−	0.999742i	$-0.492766\pi$
$827$	1.30704			0.0454502			0.0227251	+	0.999742i	$0.492766\pi$
$828$		0			0
$829$	−16.5976	+	28.7479i	−0.576458	+	0.998455i	0.419423	+	0.907791i	$0.362232\pi$
$829$	−16.5976	+	28.7479i	−0.576458	+	0.998455i	−0.995882	+	0.0906643i	$0.971101\pi$
$830$		0			0
$831$	−24.7778			−0.859533
$832$		0			0
$833$			32.6364i			1.13078i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−8.32780			−0.287851
$838$		0			0
$839$	−17.7161	+	10.2284i	−0.611626	+	0.353122i	−0.773602	−	0.633672i	$-0.781547\pi$
$839$	−17.7161	+	10.2284i	−0.611626	+	0.353122i	0.161975	+	0.986795i	$0.448213\pi$
$840$		0			0
$841$	10.4800	+	18.1520i	0.361381	+	0.625930i
$842$		0			0
$843$	15.9126	−	27.5615i	0.548061	−	0.949269i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−4.73878	+	8.20780i	−0.162826	+	0.282023i
$848$		0			0
$849$	−0.865901	−	1.49978i	−0.0297176	−	0.0514725i
$850$		0			0
$851$	−55.8653	+	32.2539i	−1.91504	+	1.10565i
$852$		0			0
$853$	−35.4366			−1.21332			−0.606662	−	0.794960i	$-0.707492\pi$
$853$	−35.4366			−1.21332			−0.606662	+	0.794960i	$0.707492\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	34.6965i		−	1.18521i	−0.805494	−	0.592604i	$-0.798100\pi$
$857$		−	34.6965i		−	1.18521i	0.805494	−	0.592604i	$-0.201900\pi$
$858$		0			0
$859$	−3.72422			−0.127069			−0.0635344	−	0.997980i	$-0.520237\pi$
$859$	−3.72422			−0.127069			−0.0635344	+	0.997980i	$0.520237\pi$
$860$		0			0
$861$	−0.357517	+	0.619238i	−0.0121842	+	0.0211036i
$862$		0			0
$863$	29.9610			1.01988			0.509942	−	0.860209i	$-0.329667\pi$
$863$	29.9610			1.01988			0.509942	+	0.860209i	$0.329667\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	25.2702	−	14.5898i	0.858223	−	0.495495i
$868$		0			0
$869$	−17.0931	−	9.86869i	−0.579843	−	0.334772i
$870$		0			0
$871$	19.7416	+	35.7649i	0.668917	+	1.21185i
$872$		0			0
$873$	−8.32660	+	14.4221i	−0.281813	+	0.488114i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19.8199	+	34.3290i	0.669270	+	1.15921i	0.978109	+	0.208095i	$0.0667264\pi$
$877$	19.8199	+	34.3290i	0.669270	+	1.15921i	−0.308839	+	0.951114i	$0.599940\pi$
$878$		0			0
$879$			8.25485i			0.278429i
$880$		0			0
$881$	−15.5498	+	26.9330i	−0.523885	+	0.907396i	0.475728	+	0.879592i	$0.342185\pi$
$881$	−15.5498	+	26.9330i	−0.523885	+	0.907396i	−0.999613	+	0.0278037i	$0.991149\pi$
$882$		0			0
$883$		−	8.19692i		−	0.275848i	−0.990443	−	0.137924i	$-0.955957\pi$
$883$		−	8.19692i		−	0.275848i	0.990443	−	0.137924i	$-0.0440430\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.11703	+	3.53167i	0.205390	+	0.118582i	0.599167	−	0.800624i	$-0.295499\pi$
$887$	6.11703	+	3.53167i	0.205390	+	0.118582i	−0.393777	+	0.919206i	$0.628832\pi$
$888$		0			0
$889$		−	7.39263i		−	0.247941i
$890$		0			0
$891$	1.85872	−	1.07313i	0.0622694	−	0.0359513i
$892$		0			0
$893$	−31.0232	+	17.9113i	−1.03815	+	0.599378i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	31.8614	+	0.612946i	1.06382	+	0.0204657i
$898$		0			0
$899$	20.4497	+	11.8066i	0.682036	+	0.393774i
$900$		0			0
$901$	1.92016	+	3.32581i	0.0639698	+	0.110799i
$902$		0			0
$903$	5.91591	+	10.2467i	0.196869	+	0.340988i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	25.5097	+	14.7280i	0.847036	+	0.489036i	0.859650	−	0.510884i	$-0.170682\pi$
$907$	25.5097	+	14.7280i	0.847036	+	0.489036i	−0.0126137	+	0.999920i	$0.504015\pi$
$908$		0			0
$909$	11.3451			0.376292
$910$		0			0
$911$	−3.27384			−0.108467			−0.0542335	−	0.998528i	$-0.517272\pi$
$911$	−3.27384			−0.108467			−0.0542335	+	0.998528i	$0.517272\pi$
$912$		0			0
$913$	−17.2514	−	9.96008i	−0.570937	−	0.329631i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.42601	−	9.39812i	−0.179182	−	0.310353i
$918$		0			0
$919$	−20.5422	−	35.5801i	−0.677624	−	1.17368i	−0.975694	−	0.219136i	$-0.929676\pi$
$919$	−20.5422	−	35.5801i	−0.677624	−	1.17368i	0.298070	−	0.954544i	$-0.403657\pi$
$920$		0			0
$921$	−5.46378	−	3.15451i	−0.180038	−	0.103945i
$922$		0			0
$923$	0.291258	−	15.1398i	0.00958686	−	0.498332i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	13.6909	−	7.90446i	0.449669	−	0.259617i
$928$		0			0
$929$	−26.1187	+	15.0796i	−0.856926	+	0.494747i	−0.862982	−	0.505235i	$-0.831406\pi$
$929$	−26.1187	+	15.0796i	−0.856926	+	0.494747i	0.00605561	+	0.999982i	$0.498072\pi$
$930$		0			0
$931$			14.1144i			0.462580i
$932$		0			0
$933$	−1.00820	−	0.582087i	−0.0330071	−	0.0190567i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	48.4005i		−	1.58117i	−0.612350	−	0.790587i	$-0.709775\pi$
$937$		−	48.4005i		−	1.58117i	0.612350	−	0.790587i	$-0.290225\pi$
$938$		0			0
$939$	−9.85092	+	17.0623i	−0.321473	+	0.556807i
$940$		0			0
$941$		−	12.6829i		−	0.413452i	−0.978399	−	0.206726i	$-0.933719\pi$
$941$		−	12.6829i		−	0.413452i	0.978399	−	0.206726i	$-0.0662809\pi$
$942$		0			0
$943$	−2.13165	−	3.69213i	−0.0694162	−	0.120232i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.2105	+	24.6133i	−0.461780	+	0.799826i	−0.999050	−	0.0435841i	$-0.986122\pi$
$947$	−14.2105	+	24.6133i	−0.461780	+	0.799826i	0.537270	+	0.843410i	$0.319456\pi$
$948$		0			0
$949$	21.2916	−	35.2926i	0.691156	−	1.14565i
$950$		0			0
$951$	−0.764018	−	0.441106i	−0.0247750	−	0.0143038i
$952$		0			0
$953$	15.0381	−	8.68225i	0.487132	−	0.281246i	−0.236252	−	0.971692i	$-0.575919\pi$
$953$	15.0381	−	8.68225i	0.487132	−	0.281246i	0.723384	+	0.690446i	$0.242586\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−6.08568			−0.196722
$958$		0			0
$959$	6.82649	−	11.8238i	0.220439	−	0.381811i
$960$		0			0
$961$	−38.3523			−1.23717
$962$		0			0
$963$		−	19.5926i		−	0.631363i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−26.3359			−0.846906			−0.423453	−	0.905918i	$-0.639182\pi$
$967$	−26.3359			−0.846906			−0.423453	+	0.905918i	$0.639182\pi$
$968$		0			0
$969$	17.2958	−	9.98573i	0.555621	−	0.320788i
$970$		0			0
$971$	−12.4170	−	21.5068i	−0.398479	−	0.690186i	0.595059	−	0.803682i	$-0.297129\pi$
$971$	−12.4170	−	21.5068i	−0.398479	−	0.690186i	−0.993538	+	0.113496i	$0.963795\pi$
$972$		0			0
$973$	5.60024	−	9.69990i	0.179535	−	0.310965i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.4281	−	31.9184i	0.589567	−	1.02116i	−0.404722	−	0.914440i	$-0.632632\pi$
$977$	18.4281	−	31.9184i	0.589567	−	1.02116i	0.994289	−	0.106720i	$-0.0340349\pi$
$978$		0			0
$979$	−13.4111	−	23.2287i	−0.428620	−	0.742392i
$980$		0			0
$981$	−5.20434	+	3.00473i	−0.166162	+	0.0959335i
$982$		0			0
$983$	5.00673			0.159690			0.0798450	−	0.996807i	$-0.474557\pi$
$983$	5.00673			0.159690			0.0798450	+	0.996807i	$0.474557\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	18.0687i		−	0.575132i
$988$		0			0
$989$	−70.5458			−2.24322
$990$		0			0
$991$	9.01343	−	15.6117i	0.286321	−	0.495922i	−0.686608	−	0.727028i	$-0.740901\pi$
$991$	9.01343	−	15.6117i	0.286321	−	0.495922i	0.972929	+	0.231106i	$0.0742343\pi$
$992$		0			0
$993$	19.6323			0.623011
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−49.9853	+	28.8590i	−1.58305	+	0.913974i	−0.588639	+	0.808396i	$0.700336\pi$
$997$	−49.9853	+	28.8590i	−1.58305	+	0.913974i	−0.994411	+	0.105578i	$0.966331\pi$
$998$		0			0
$999$	−6.32076	−	3.64929i	−0.199980	−	0.115458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3900.2.bw.g.2149.4		8
5.2	odd	4		3900.2.cd.l.901.3		8
5.3	odd	4		780.2.cc.b.121.2	✓	8
5.4	even	2		3900.2.bw.l.2149.1		8
13.10	even	6		3900.2.bw.l.49.1		8
15.8	even	4		2340.2.dj.c.901.4		8
65.23	odd	12		780.2.cc.b.361.4	yes	8
65.49	even	6	inner	3900.2.bw.g.49.4		8
65.62	odd	12		3900.2.cd.l.2701.3		8
195.23	even	12		2340.2.dj.c.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.cc.b.121.2	✓	8	5.3	odd	4
780.2.cc.b.361.4	yes	8	65.23	odd	12
2340.2.dj.c.361.2		8	195.23	even	12
2340.2.dj.c.901.4		8	15.8	even	4
3900.2.bw.g.49.4		8	65.49	even	6	inner
3900.2.bw.g.2149.4		8	1.1	even	1	trivial
3900.2.bw.l.49.1		8	13.10	even	6
3900.2.bw.l.2149.1		8	5.4	even	2
3900.2.cd.l.901.3		8	5.2	odd	4
3900.2.cd.l.2701.3		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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-0.741181 - 1.28376i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.85872 - 1.07313i) q^{11} +(1.86250 - 3.08725i) q^{13} +(-5.88512 + 3.39778i) q^{17} +(-2.54516 + 1.46945i) q^{19} -1.48236i q^{21} +(7.65427 + 4.41920i) q^{23} +1.00000i q^{27} +(1.41774 - 2.45559i) q^{29} +8.32780i q^{31} +(-1.07313 - 1.85872i) q^{33} +(-3.64929 + 6.32076i) q^{37} +(3.15660 - 1.74238i) q^{39} +(-0.417738 - 0.241181i) q^{41} +(-6.91239 + 3.99087i) q^{43} +12.1891 q^{47} +(2.40130 - 4.15918i) q^{49} -6.79555 q^{51} -0.565122i q^{53} -2.93890 q^{57} +(7.39483 - 4.26941i) q^{59} +(5.92953 + 10.2702i) q^{61} +(0.741181 - 1.28376i) q^{63} +(-5.66510 + 9.81225i) q^{67} +(4.41920 + 7.65427i) q^{69} +(3.63713 - 2.09990i) q^{71} +11.4317 q^{73} +3.18154i q^{77} +9.19615 q^{79} +(-0.500000 + 0.866025i) q^{81} +9.28132 q^{83} +(2.45559 - 1.41774i) q^{87} +(10.8228 + 6.24857i) q^{89} +(-5.34374 - 0.102802i) q^{91} +(-4.16390 + 7.21209i) q^{93} +(8.32660 + 14.4221i) q^{97} -2.14626i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7} + 4 q^{9} - 12 q^{11} - 12 q^{19} + 12 q^{23} + 8 q^{29} + 4 q^{33} - 8 q^{37} - 24 q^{43} + 40 q^{47} + 4 q^{49} - 8 q^{51} - 24 q^{57} - 24 q^{59} + 8 q^{61} + 8 q^{63} - 4 q^{69} - 12 q^{71}+ \cdots + 24 q^{97}+O(q^{100}) \) 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

Related objects

Downloads

Learn more