LMFDB - Embedded newform 1728.2.z.a.1583.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1728,2,Mod(143,1728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1728, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1728.143"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1583.9
Character	$\chi$	$=$	1728.1583
Dual form			1728.2.z.a.143.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05401 + 0.282421i) q^{5} +(1.93586 + 3.35301i) q^{7} +(3.53182 + 0.946349i) q^{11} +(3.87946 - 1.03950i) q^{13} +1.55026i q^{17} +(-4.06175 + 4.06175i) q^{19} +(-3.86595 - 2.23201i) q^{23} +(-3.29895 + 1.90465i) q^{25} +(4.28493 + 1.14814i) q^{29} +(-1.85935 - 1.07349i) q^{31} +(-2.98738 - 2.98738i) q^{35} +(6.04318 - 6.04318i) q^{37} +(-1.59725 + 2.76652i) q^{41} +(1.47814 - 5.51650i) q^{43} +(0.0494357 + 0.0856252i) q^{47} +(-3.99512 + 6.91976i) q^{49} +(1.72094 + 1.72094i) q^{53} -3.98985 q^{55} +(3.58531 + 13.3806i) q^{59} +(-2.33005 + 8.69586i) q^{61} +(-3.79542 + 2.19129i) q^{65} +(-0.251689 - 0.939315i) q^{67} -7.11471i q^{71} +10.4116i q^{73} +(3.66400 + 13.6742i) q^{77} +(-14.2402 + 8.22160i) q^{79} +(-4.02380 + 15.0170i) q^{83} +(-0.437828 - 1.63399i) q^{85} +11.2398 q^{89} +(10.9956 + 10.9956i) q^{91} +(3.13400 - 5.42825i) q^{95} +(0.0532804 + 0.0922843i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.05401	+	0.282421i	−0.471368	+	0.126303i	−0.486681	−	0.873580i	$-0.661792\pi$
$5$	−1.05401	+	0.282421i	−0.471368	+	0.126303i	0.0153123	+	0.999883i	$0.495126\pi$
$6$		0			0
$7$	1.93586	+	3.35301i	0.731687	+	1.26732i	0.956162	+	0.292839i	$0.0946001\pi$
$7$	1.93586	+	3.35301i	0.731687	+	1.26732i	−0.224475	+	0.974480i	$0.572067\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.53182	+	0.946349i	1.06488	+	0.285335i	0.748390	−	0.663259i	$-0.230827\pi$
$11$	3.53182	+	0.946349i	1.06488	+	0.285335i	0.316495	+	0.948594i	$0.397494\pi$
$12$		0			0
$13$	3.87946	−	1.03950i	1.07597	−	0.288305i	0.323025	−	0.946390i	$-0.395300\pi$
$13$	3.87946	−	1.03950i	1.07597	−	0.288305i	0.752943	+	0.658085i	$0.228633\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			1.55026i			0.375994i	0.982170	+	0.187997i	$0.0601995\pi$
$17$			1.55026i			0.375994i	−0.982170	+	0.187997i	$0.939800\pi$
$18$		0			0
$19$	−4.06175	+	4.06175i	−0.931829	+	0.931829i	−0.997820	−	0.0659916i	$-0.978979\pi$
$19$	−4.06175	+	4.06175i	−0.931829	+	0.931829i	0.0659916	+	0.997820i	$0.478979\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.86595	−	2.23201i	−0.806106	−	0.465405i	0.0394958	−	0.999220i	$-0.487425\pi$
$23$	−3.86595	−	2.23201i	−0.806106	−	0.465405i	−0.845602	+	0.533814i	$0.820758\pi$
$24$		0			0
$25$	−3.29895	+	1.90465i	−0.659790	+	0.380930i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.28493	+	1.14814i	0.795691	+	0.213205i	0.633691	−	0.773586i	$-0.281539\pi$
$29$	4.28493	+	1.14814i	0.795691	+	0.213205i	0.162000	+	0.986791i	$0.448206\pi$
$30$		0			0
$31$	−1.85935	−	1.07349i	−0.333948	−	0.192805i	0.323644	−	0.946179i	$-0.395092\pi$
$31$	−1.85935	−	1.07349i	−0.333948	−	0.192805i	−0.657593	+	0.753374i	$0.728425\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.98738	−	2.98738i	−0.504960	−	0.504960i
$36$		0			0
$37$	6.04318	−	6.04318i	0.993493	−	0.993493i	−0.00648560	−	0.999979i	$-0.502064\pi$
$37$	6.04318	−	6.04318i	0.993493	−	0.993493i	0.999979	+	0.00648560i	$0.00206445\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.59725	+	2.76652i	−0.249449	+	0.432058i	−0.963373	−	0.268165i	$-0.913583\pi$
$41$	−1.59725	+	2.76652i	−0.249449	+	0.432058i	0.713924	+	0.700223i	$0.246916\pi$
$42$		0			0
$43$	1.47814	−	5.51650i	0.225415	−	0.841259i	−0.756823	−	0.653619i	$-0.773250\pi$
$43$	1.47814	−	5.51650i	0.225415	−	0.841259i	0.982238	−	0.187639i	$-0.0600836\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.0494357	+	0.0856252i	0.00721094	+	0.0124897i	0.869608	−	0.493742i	$-0.164371\pi$
$47$	0.0494357	+	0.0856252i	0.00721094	+	0.0124897i	−0.862397	+	0.506232i	$0.831038\pi$
$48$		0			0
$49$	−3.99512	+	6.91976i	−0.570732	+	0.988537i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.72094	+	1.72094i	0.236389	+	0.236389i	0.815353	−	0.578964i	$-0.196543\pi$
$53$	1.72094	+	1.72094i	0.236389	+	0.236389i	−0.578964	+	0.815353i	$0.696543\pi$
$54$		0			0
$55$	−3.98985			−0.537991
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.58531	+	13.3806i	0.466768	+	1.74200i	0.650960	+	0.759112i	$0.274367\pi$
$59$	3.58531	+	13.3806i	0.466768	+	1.74200i	−0.184192	+	0.982890i	$0.558967\pi$
$60$		0			0
$61$	−2.33005	+	8.69586i	−0.298332	+	1.11339i	0.640203	+	0.768206i	$0.278850\pi$
$61$	−2.33005	+	8.69586i	−0.298332	+	1.11339i	−0.938535	+	0.345184i	$0.887816\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.79542	+	2.19129i	−0.470764	+	0.271796i
$66$		0			0
$67$	−0.251689	−	0.939315i	−0.0307487	−	0.114756i	0.948846	−	0.315740i	$-0.102253\pi$
$67$	−0.251689	−	0.939315i	−0.0307487	−	0.114756i	−0.979594	+	0.200984i	$0.935586\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.11471i		−	0.844361i	−0.906512	−	0.422180i	$-0.861265\pi$
$71$		−	7.11471i		−	0.844361i	0.906512	−	0.422180i	$-0.138735\pi$
$72$		0			0
$73$			10.4116i			1.21859i	0.792945	+	0.609293i	$0.208547\pi$
$73$			10.4116i			1.21859i	−0.792945	+	0.609293i	$0.791453\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.66400	+	13.6742i	0.417552	+	1.55832i
$78$		0			0
$79$	−14.2402	+	8.22160i	−1.60215	+	0.925003i	−0.611095	+	0.791557i	$0.709271\pi$
$79$	−14.2402	+	8.22160i	−1.60215	+	0.925003i	−0.991056	+	0.133446i	$0.957396\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.02380	+	15.0170i	−0.441669	+	1.64833i	0.282915	+	0.959145i	$0.408698\pi$
$83$	−4.02380	+	15.0170i	−0.441669	+	1.64833i	−0.724584	+	0.689186i	$0.757968\pi$
$84$		0			0
$85$	−0.437828	−	1.63399i	−0.0474891	−	0.177232i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	11.2398			1.19142			0.595710	−	0.803200i	$-0.296871\pi$
$89$	11.2398			1.19142			0.595710	+	0.803200i	$0.296871\pi$
$90$		0			0
$91$	10.9956	+	10.9956i	1.15265	+	1.15265i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.13400	−	5.42825i	0.321542	−	0.556927i
$96$		0			0
$97$	0.0532804	+	0.0922843i	0.00540980	+	0.00937005i	0.868718	−	0.495308i	$-0.164945\pi$
$97$	0.0532804	+	0.0922843i	0.00540980	+	0.00937005i	−0.863308	+	0.504678i	$0.831611\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.12101	−	4.18366i	0.111545	−	0.416290i	−0.887461	−	0.460883i	$-0.847533\pi$
$101$	1.12101	−	4.18366i	0.111545	−	0.416290i	0.999005	+	0.0445936i	$0.0141993\pi$
$102$		0			0
$103$	1.25063	−	2.16615i	0.123228	−	0.213437i	−0.797811	−	0.602908i	$-0.794009\pi$
$103$	1.25063	−	2.16615i	0.123228	−	0.213437i	0.921039	+	0.389470i	$0.127342\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.01074	−	6.01074i	0.581080	−	0.581080i	−0.354120	−	0.935200i	$-0.615220\pi$
$107$	6.01074	−	6.01074i	0.581080	−	0.581080i	0.935200	+	0.354120i	$0.115220\pi$
$108$		0			0
$109$	0.880973	+	0.880973i	0.0843819	+	0.0843819i	0.748038	−	0.663656i	$-0.230996\pi$
$109$	0.880973	+	0.880973i	0.0843819	+	0.0843819i	−0.663656	+	0.748038i	$0.730996\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.13357	−	1.23182i	−0.200709	−	0.115880i	0.396277	−	0.918131i	$-0.370302\pi$
$113$	−2.13357	−	1.23182i	−0.200709	−	0.115880i	−0.596986	+	0.802251i	$0.703635\pi$
$114$		0			0
$115$	4.70512	+	1.26073i	0.438755	+	0.117564i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−5.19805	+	3.00110i	−0.476504	+	0.275110i
$120$		0			0
$121$	2.05191	+	1.18467i	0.186538	+	0.107698i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.79716	−	6.79716i	0.607957	−	0.607957i
$126$		0			0
$127$		−	3.76697i		−	0.334264i	−0.985934	−	0.167132i	$-0.946549\pi$
$127$		−	3.76697i		−	0.334264i	0.985934	−	0.167132i	$-0.0534507\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.28665	−	0.344757i	0.112415	−	0.0301216i	−0.202173	−	0.979350i	$-0.564800\pi$
$131$	1.28665	−	0.344757i	0.112415	−	0.0301216i	0.314588	+	0.949228i	$0.398134\pi$
$132$		0			0
$133$	−21.4821	−	5.75610i	−1.86273	−	0.499117i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.59673	+	9.69382i	0.478161	+	0.828199i	0.999687	−	0.0250365i	$-0.00797020\pi$
$137$	5.59673	+	9.69382i	0.478161	+	0.828199i	−0.521526	+	0.853236i	$0.674637\pi$
$138$		0			0
$139$	3.01559	−	0.808026i	0.255779	−	0.0685359i	−0.128651	−	0.991690i	$-0.541065\pi$
$139$	3.01559	−	0.808026i	0.255779	−	0.0685359i	0.384430	+	0.923154i	$0.374398\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	14.6853			1.22805
$144$		0			0
$145$	−4.84062			−0.401992
$146$		0			0
$147$		0			0
$148$		0			0
$149$	14.4685	−	3.87683i	1.18531	−	0.317602i	0.388277	−	0.921543i	$-0.373070\pi$
$149$	14.4685	−	3.87683i	1.18531	−	0.317602i	0.797029	+	0.603941i	$0.206404\pi$
$150$		0			0
$151$	0.301388	+	0.522019i	0.0245266	+	0.0424813i	0.878028	−	0.478609i	$-0.158859\pi$
$151$	0.301388	+	0.522019i	0.0245266	+	0.0424813i	−0.853502	+	0.521090i	$0.825525\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.26295	+	0.606355i	0.181764	+	0.0487036i
$156$		0			0
$157$	6.72554	−	1.80210i	0.536756	−	0.143823i	0.0197500	−	0.999805i	$-0.493713\pi$
$157$	6.72554	−	1.80210i	0.536756	−	0.143823i	0.517006	+	0.855981i	$0.327046\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	17.2834i		−	1.36212i
$162$		0			0
$163$	−7.73897	+	7.73897i	−0.606163	+	0.606163i	−0.941941	−	0.335778i	$-0.891001\pi$
$163$	−7.73897	+	7.73897i	−0.606163	+	0.606163i	0.335778	+	0.941941i	$0.391001\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	16.3533	+	9.44158i	1.26546	+	0.730611i	0.974125	−	0.226011i	$-0.0725684\pi$
$167$	16.3533	+	9.44158i	1.26546	+	0.730611i	0.291331	+	0.956622i	$0.405902\pi$
$168$		0			0
$169$	2.71133	−	1.56539i	0.208564	−	0.120414i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−16.3589	−	4.38336i	−1.24375	−	0.333261i	−0.423829	−	0.905742i	$-0.639314\pi$
$173$	−16.3589	−	4.38336i	−1.24375	−	0.333261i	−0.819918	+	0.572481i	$0.805981\pi$
$174$		0			0
$175$	−12.7726	−	7.37428i	−0.965519	−	0.557443i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.85114	+	4.85114i	0.362591	+	0.362591i	0.864766	−	0.502175i	$-0.167467\pi$
$179$	4.85114	+	4.85114i	0.362591	+	0.362591i	−0.502175	+	0.864766i	$0.667467\pi$
$180$		0			0
$181$	−1.98842	+	1.98842i	−0.147798	+	0.147798i	−0.777134	−	0.629336i	$-0.783327\pi$
$181$	−1.98842	+	1.98842i	−0.147798	+	0.147798i	0.629336	+	0.777134i	$0.283327\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.66286	+	8.07631i	−0.342820	+	0.593782i
$186$		0			0
$187$	−1.46709	+	5.47525i	−0.107284	+	0.400390i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.1997	−	17.6664i	−0.738025	−	1.27830i	−0.953383	−	0.301762i	$-0.902425\pi$
$191$	−10.1997	−	17.6664i	−0.738025	−	1.27830i	0.215358	−	0.976535i	$-0.430908\pi$
$192$		0			0
$193$	−8.30403	+	14.3830i	−0.597737	+	1.03531i	0.395417	+	0.918502i	$0.370600\pi$
$193$	−8.30403	+	14.3830i	−0.597737	+	1.03531i	−0.993154	+	0.116809i	$0.962733\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.03806	−	2.03806i	−0.145206	−	0.145206i	0.630767	−	0.775972i	$-0.282740\pi$
$197$	−2.03806	−	2.03806i	−0.145206	−	0.145206i	−0.775972	+	0.630767i	$0.782740\pi$
$198$		0			0
$199$	9.19698			0.651956			0.325978	−	0.945377i	$-0.394306\pi$
$199$	9.19698			0.651956			0.325978	+	0.945377i	$0.394306\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.44529	+	16.5901i	0.311999	+	1.16439i
$204$		0			0
$205$	0.902196	−	3.36704i	0.0630121	−	0.235164i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−18.1892	+	10.5015i	−1.25817	+	0.726407i
$210$		0			0
$211$	−3.99524	−	14.9104i	−0.275043	−	1.02648i	−0.955812	−	0.293978i	$-0.905021\pi$
$211$	−3.99524	−	14.9104i	−0.275043	−	1.02648i	0.680769	−	0.732498i	$-0.261646\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			6.23192i			0.425013i
$216$		0			0
$217$		−	8.31254i		−	0.564292i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.61150	+	6.01418i	0.108401	+	0.404558i
$222$		0			0
$223$	15.1760	−	8.76186i	1.01626	−	0.586738i	0.103241	−	0.994656i	$-0.467079\pi$
$223$	15.1760	−	8.76186i	1.01626	−	0.586738i	0.913018	+	0.407918i	$0.133745\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.24944	−	19.5912i	0.348418	−	1.30031i	−0.540150	−	0.841569i	$-0.681633\pi$
$227$	5.24944	−	19.5912i	0.348418	−	1.30031i	0.888568	−	0.458745i	$-0.151701\pi$
$228$		0			0
$229$	−4.02901	−	15.0365i	−0.266244	−	0.993638i	−0.961484	−	0.274860i	$-0.911369\pi$
$229$	−4.02901	−	15.0365i	−0.266244	−	0.993638i	0.695240	−	0.718778i	$-0.255298\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−27.1681			−1.77984			−0.889920	−	0.456116i	$-0.849240\pi$
$233$	−27.1681			−1.77984			−0.889920	+	0.456116i	$0.849240\pi$
$234$		0			0
$235$	−0.0762882	−	0.0762882i	−0.00497649	−	0.00497649i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.48037	+	4.29612i	−0.160442	+	0.277893i	−0.935027	−	0.354576i	$-0.884625\pi$
$239$	−2.48037	+	4.29612i	−0.160442	+	0.277893i	0.774586	+	0.632469i	$0.217959\pi$
$240$		0			0
$241$	−4.93768	−	8.55231i	−0.318064	−	0.550903i	0.662020	−	0.749486i	$-0.269699\pi$
$241$	−4.93768	−	8.55231i	−0.318064	−	0.550903i	−0.980084	+	0.198583i	$0.936366\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.25662	−	8.42181i	0.144170	−	0.538050i
$246$		0			0
$247$	−11.5352	+	19.9796i	−0.733968	+	1.27127i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.77292	+	1.77292i	−0.111906	+	0.111906i	−0.760842	−	0.648937i	$-0.775214\pi$
$251$	−1.77292	+	1.77292i	−0.111906	+	0.111906i	0.648937	+	0.760842i	$0.275214\pi$
$252$		0			0
$253$	−11.5416	−	11.5416i	−0.725613	−	0.725613i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.6473	−	8.45663i	−0.913674	−	0.527510i	−0.0320628	−	0.999486i	$-0.510208\pi$
$257$	−14.6473	−	8.45663i	−0.913674	−	0.527510i	−0.881612	+	0.471976i	$0.843541\pi$
$258$		0			0
$259$	31.9616	+	8.56410i	1.98600	+	0.532147i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−17.9408	+	10.3581i	−1.10627	+	0.638708i	−0.937862	−	0.347009i	$-0.887197\pi$
$263$	−17.9408	+	10.3581i	−1.10627	+	0.638708i	−0.168413	+	0.985717i	$0.553864\pi$
$264$		0			0
$265$	−2.29992	−	1.32786i	−0.141283	−	0.0815696i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	15.1523	−	15.1523i	0.923853	−	0.923853i	−0.0734463	−	0.997299i	$-0.523400\pi$
$269$	15.1523	−	15.1523i	0.923853	−	0.923853i	0.997299	+	0.0734463i	$0.0233998\pi$
$270$		0			0
$271$		−	20.0322i		−	1.21687i	−0.793603	−	0.608436i	$-0.791797\pi$
$271$		−	20.0322i		−	1.21687i	0.793603	−	0.608436i	$-0.208203\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−13.4538	+	3.60493i	−0.811293	+	0.217385i
$276$		0			0
$277$	26.8731	+	7.20063i	1.61465	+	0.432644i	0.949424	−	0.313998i	$-0.101669\pi$
$277$	26.8731	+	7.20063i	1.61465	+	0.432644i	0.665226	+	0.746642i	$0.268335\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.83494	−	15.3026i	−0.527048	−	0.912874i	−0.999503	−	0.0315195i	$-0.989965\pi$
$281$	−8.83494	−	15.3026i	−0.527048	−	0.912874i	0.472455	−	0.881355i	$-0.343368\pi$
$282$		0			0
$283$	23.5142	−	6.30060i	1.39777	−	0.374532i	0.520228	−	0.854028i	$-0.325847\pi$
$283$	23.5142	−	6.30060i	1.39777	−	0.374532i	0.877544	+	0.479496i	$0.159180\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.3682			−0.730074
$288$		0			0
$289$	14.5967			0.858629
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.03527	−	1.34920i	0.294164	−	0.0788209i	−0.108719	−	0.994073i	$-0.534675\pi$
$293$	5.03527	−	1.34920i	0.294164	−	0.0788209i	0.402883	+	0.915252i	$0.368008\pi$
$294$		0			0
$295$	−7.55792	−	13.0907i	−0.440039	−	0.762170i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−17.3180	−	4.64033i	−1.00152	−	0.268357i
$300$		0			0
$301$	21.3584	−	5.72296i	1.23108	−	0.329866i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	9.82358i		−	0.562497i
$306$		0			0
$307$	−2.82663	+	2.82663i	−0.161324	+	0.161324i	−0.783153	−	0.621829i	$-0.786390\pi$
$307$	−2.82663	+	2.82663i	−0.161324	+	0.161324i	0.621829	+	0.783153i	$0.286390\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.51789	−	1.45371i	−0.142777	−	0.0824322i	0.426910	−	0.904294i	$-0.359602\pi$
$311$	−2.51789	−	1.45371i	−0.142777	−	0.0824322i	−0.569687	+	0.821862i	$0.692935\pi$
$312$		0			0
$313$	18.0136	−	10.4002i	1.01819	−	0.587852i	0.104611	−	0.994513i	$-0.466640\pi$
$313$	18.0136	−	10.4002i	1.01819	−	0.587852i	0.913579	+	0.406661i	$0.133307\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.1525	+	2.72034i	0.570219	+	0.152790i	0.532397	−	0.846495i	$-0.321291\pi$
$317$	10.1525	+	2.72034i	0.570219	+	0.152790i	0.0378219	+	0.999284i	$0.487958\pi$
$318$		0			0
$319$	14.0471	+	8.11008i	0.786485	+	0.454077i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−6.29678	−	6.29678i	−0.350362	−	0.350362i
$324$		0			0
$325$	−10.8183	+	10.8183i	−0.600089	+	0.600089i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.191401	+	0.331517i	−0.0105523	+	0.0182771i
$330$		0			0
$331$	1.99815	−	7.45721i	0.109828	−	0.409885i	−0.889020	−	0.457869i	$-0.848613\pi$
$331$	1.99815	−	7.45721i	0.109828	−	0.409885i	0.998848	+	0.0479837i	$0.0152795\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.530565	+	0.918966i	0.0289879	+	0.0502085i
$336$		0			0
$337$	−15.1525	+	26.2448i	−0.825407	+	1.42965i	0.0762015	+	0.997092i	$0.475721\pi$
$337$	−15.1525	+	26.2448i	−0.825407	+	1.42965i	−0.901608	+	0.432554i	$0.857613\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.55098	−	5.55098i	−0.300602	−	0.300602i
$342$		0			0
$343$	−3.83397			−0.207015
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.40762	−	27.6456i	−0.397662	−	1.48409i	−0.817199	−	0.576356i	$-0.804474\pi$
$347$	−7.40762	−	27.6456i	−0.397662	−	1.48409i	0.419537	−	0.907738i	$-0.362192\pi$
$348$		0			0
$349$	−1.32426	+	4.94221i	−0.0708861	+	0.264551i	−0.992269	−	0.124105i	$-0.960394\pi$
$349$	−1.32426	+	4.94221i	−0.0708861	+	0.264551i	0.921383	+	0.388656i	$0.127061\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.6375	+	6.14156i	−0.566176	+	0.326882i	−0.755621	−	0.655009i	$-0.772665\pi$
$353$	−10.6375	+	6.14156i	−0.566176	+	0.326882i	0.189444	+	0.981891i	$0.439331\pi$
$354$		0			0
$355$	2.00935	+	7.49899i	0.106645	+	0.398005i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	8.35783i		−	0.441109i	−0.975375	−	0.220555i	$-0.929213\pi$
$359$		−	8.35783i		−	0.441109i	0.975375	−	0.220555i	$-0.0707867\pi$
$360$		0			0
$361$		−	13.9956i		−	0.736609i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.94046	−	10.9739i	−0.153911	−	0.574403i
$366$		0			0
$367$	−5.59831	+	3.23218i	−0.292229	+	0.168719i	−0.638947	−	0.769251i	$-0.720630\pi$
$367$	−5.59831	+	3.23218i	−0.292229	+	0.168719i	0.346718	+	0.937970i	$0.387296\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.43882	+	9.10182i	−0.126617	+	0.472543i
$372$		0			0
$373$	−3.08351	−	11.5078i	−0.159658	−	0.595853i	−0.998661	−	0.0517262i	$-0.983528\pi$
$373$	−3.08351	−	11.5078i	−0.159658	−	0.595853i	0.839003	−	0.544127i	$-0.183139\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	17.8167			0.917607
$378$		0			0
$379$	−7.76444	−	7.76444i	−0.398833	−	0.398833i	0.478988	−	0.877821i	$-0.341004\pi$
$379$	−7.76444	−	7.76444i	−0.398833	−	0.398833i	−0.877821	+	0.478988i	$0.841004\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.86264	−	4.95824i	0.146274	−	0.253354i	−0.783573	−	0.621299i	$-0.786605\pi$
$383$	2.86264	−	4.95824i	0.146274	−	0.253354i	0.929848	+	0.367945i	$0.119939\pi$
$384$		0			0
$385$	−7.72380	−	13.3780i	−0.393641	−	0.681807i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.82769	+	6.82104i	−0.0926677	+	0.345841i	−0.996656	−	0.0817177i	$-0.973959\pi$
$389$	−1.82769	+	6.82104i	−0.0926677	+	0.345841i	0.903988	+	0.427558i	$0.140626\pi$
$390$		0			0
$391$	3.46020	−	5.99324i	0.174990	−	0.303091i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.6874	−	12.6874i	0.638373	−	0.638373i
$396$		0			0
$397$	−1.86429	−	1.86429i	−0.0935661	−	0.0935661i	0.658774	−	0.752340i	$-0.271075\pi$
$397$	−1.86429	−	1.86429i	−0.0935661	−	0.0935661i	−0.752340	+	0.658774i	$0.771075\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	34.3098	+	19.8088i	1.71335	+	0.989204i	0.929949	+	0.367688i	$0.119851\pi$
$401$	34.3098	+	19.8088i	1.71335	+	0.989204i	0.783402	+	0.621516i	$0.213483\pi$
$402$		0			0
$403$	−8.32915	−	2.23179i	−0.414905	−	0.111173i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	27.0624	−	15.6245i	1.34143	−	0.774477i
$408$		0			0
$409$	19.5426	+	11.2829i	0.966317	+	0.557903i	0.898111	−	0.439768i	$-0.144939\pi$
$409$	19.5426	+	11.2829i	0.966317	+	0.557903i	0.0682056	+	0.997671i	$0.478273\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−37.9245	+	37.9245i	−1.86614	+	1.86614i
$414$		0			0
$415$		−	16.9645i		−	0.832755i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.541167	+	0.145005i	−0.0264377	+	0.00708397i	−0.272014	−	0.962293i	$-0.587690\pi$
$419$	−0.541167	+	0.145005i	−0.0264377	+	0.00708397i	0.245576	+	0.969377i	$0.421023\pi$
$420$		0			0
$421$	21.1102	+	5.65647i	1.02885	+	0.275679i	0.733485	−	0.679706i	$-0.237892\pi$
$421$	21.1102	+	5.65647i	1.02885	+	0.275679i	0.295364	+	0.955385i	$0.404559\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.95271	−	5.11424i	−0.143227	−	0.248077i
$426$		0			0
$427$	−33.6680	+	9.02130i	−1.62931	+	0.436571i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.09784			−0.390059			−0.195030	−	0.980797i	$-0.562480\pi$
$431$	−8.09784			−0.390059			−0.195030	+	0.980797i	$0.562480\pi$
$432$		0			0
$433$	28.0379			1.34742			0.673708	−	0.738997i	$-0.264700\pi$
$433$	28.0379			1.34742			0.673708	+	0.738997i	$0.264700\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	24.7683	−	6.63666i	1.18483	−	0.317474i
$438$		0			0
$439$	−14.3003	−	24.7689i	−0.682518	−	1.18216i	−0.974210	−	0.225644i	$-0.927551\pi$
$439$	−14.3003	−	24.7689i	−0.682518	−	1.18216i	0.291692	−	0.956512i	$-0.405782\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.49785	−	1.74109i	−0.308722	−	0.0827218i	0.101132	−	0.994873i	$-0.467754\pi$
$443$	−6.49785	−	1.74109i	−0.308722	−	0.0827218i	−0.409854	+	0.912151i	$0.634420\pi$
$444$		0			0
$445$	−11.8469	+	3.17437i	−0.561597	+	0.150479i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			34.1293i			1.61066i	0.592827	+	0.805330i	$0.298012\pi$
$449$			34.1293i			1.61066i	−0.592827	+	0.805330i	$0.701988\pi$
$450$		0			0
$451$	−8.25930	+	8.25930i	−0.388915	+	0.388915i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−14.6948	−	8.48405i	−0.688903	−	0.397739i
$456$		0			0
$457$	0.228748	−	0.132067i	0.0107004	−	0.00617786i	−0.494640	−	0.869098i	$-0.664700\pi$
$457$	0.228748	−	0.132067i	0.0107004	−	0.00617786i	0.505341	+	0.862920i	$0.331367\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−22.1554	−	5.93653i	−1.03188	−	0.276492i	−0.297136	−	0.954835i	$-0.596032\pi$
$461$	−22.1554	−	5.93653i	−1.03188	−	0.276492i	−0.734745	+	0.678343i	$0.762698\pi$
$462$		0			0
$463$	25.1678	+	14.5306i	1.16964	+	0.675295i	0.953596	−	0.301088i	$-0.0973498\pi$
$463$	25.1678	+	14.5306i	1.16964	+	0.675295i	0.216048	+	0.976383i	$0.430683\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.46976	+	1.46976i	0.0680123	+	0.0680123i	0.740295	−	0.672282i	$-0.234686\pi$
$467$	1.46976	+	1.46976i	0.0680123	+	0.0680123i	−0.672282	+	0.740295i	$0.734686\pi$
$468$		0			0
$469$	2.66230	−	2.66230i	0.122934	−	0.122934i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	10.4411	−	18.0845i	0.480081	−	0.831525i
$474$		0			0
$475$	5.66329	−	21.1357i	0.259850	−	0.969772i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−11.8147	−	20.4636i	−0.539826	−	0.935006i	−0.998913	−	0.0466149i	$-0.985157\pi$
$479$	−11.8147	−	20.4636i	−0.539826	−	0.935006i	0.459087	−	0.888391i	$-0.348177\pi$
$480$		0			0
$481$	17.1624	−	29.7262i	0.782539	−	1.35540i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.0822212	−	0.0822212i	−0.00373347	−	0.00373347i
$486$		0			0
$487$	8.44298			0.382588			0.191294	−	0.981533i	$-0.438732\pi$
$487$	8.44298			0.382588			0.191294	+	0.981533i	$0.438732\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.32013	+	4.92678i	0.0595765	+	0.222342i	0.989295	−	0.145928i	$-0.0466167\pi$
$491$	1.32013	+	4.92678i	0.0595765	+	0.222342i	−0.929719	+	0.368270i	$0.879950\pi$
$492$		0			0
$493$	−1.77992	+	6.64277i	−0.0801638	+	0.299175i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	23.8557	−	13.7731i	1.07007	−	0.617808i
$498$		0			0
$499$	−5.34256	−	19.9387i	−0.239166	−	0.892579i	−0.976227	−	0.216753i	$-0.930454\pi$
$499$	−5.34256	−	19.9387i	−0.239166	−	0.892579i	0.737061	−	0.675827i	$-0.236213\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	25.8852i		−	1.15417i	−0.816686	−	0.577083i	$-0.804191\pi$
$503$		−	25.8852i		−	1.15417i	0.816686	−	0.577083i	$-0.195809\pi$
$504$		0			0
$505$			4.72622i			0.210314i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.39138	−	12.6568i	−0.150320	−	0.561003i	−0.999461	−	0.0328359i	$-0.989546\pi$
$509$	−3.39138	−	12.6568i	−0.150320	−	0.561003i	0.849140	−	0.528167i	$-0.177121\pi$
$510$		0			0
$511$	−34.9102	+	20.1554i	−1.54434	+	0.891623i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.706409	+	2.63635i	−0.0311281	+	0.116172i
$516$		0			0
$517$	0.0935669	+	0.349196i	0.00411507	+	0.0153576i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	15.9529			0.698909			0.349454	−	0.936953i	$-0.386367\pi$
$521$	15.9529			0.698909			0.349454	+	0.936953i	$0.386367\pi$
$522$		0			0
$523$	−8.00417	−	8.00417i	−0.349998	−	0.349998i	0.510111	−	0.860109i	$-0.329604\pi$
$523$	−8.00417	−	8.00417i	−0.349998	−	0.349998i	−0.860109	+	0.510111i	$0.829604\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.66420	−	2.88247i	0.0724936	−	0.125563i
$528$		0			0
$529$	−1.53630	−	2.66094i	−0.0667955	−	0.115693i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.32068	+	12.3929i	−0.143835	+	0.536798i
$534$		0			0
$535$	−4.63782	+	8.03294i	−0.200511	+	0.347294i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−20.6586	+	20.6586i	−0.889828	+	0.889828i
$540$		0			0
$541$	−16.5746	−	16.5746i	−0.712599	−	0.712599i	0.254479	−	0.967078i	$-0.418096\pi$
$541$	−16.5746	−	16.5746i	−0.712599	−	0.712599i	−0.967078	+	0.254479i	$0.918096\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.17736	−	0.679750i	−0.0504326	−	0.0291173i
$546$		0			0
$547$	−3.72043	−	0.996886i	−0.159074	−	0.0426238i	0.178403	−	0.983957i	$-0.442907\pi$
$547$	−3.72043	−	0.996886i	−0.159074	−	0.0426238i	−0.337477	+	0.941334i	$0.609574\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−22.0678	+	12.7408i	−0.940118	+	0.542778i
$552$		0			0
$553$	−55.1343	−	31.8318i	−2.34455	−	1.35362i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.2615	−	14.2615i	0.604278	−	0.604278i	−0.337167	−	0.941445i	$-0.609469\pi$
$557$	14.2615	−	14.2615i	0.604278	−	0.604278i	0.941445	+	0.337167i	$0.109469\pi$
$558$		0			0
$559$		−	22.9376i		−	0.970156i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	35.1298	−	9.41300i	1.48054	−	0.396711i	0.574012	−	0.818847i	$-0.305386\pi$
$563$	35.1298	−	9.41300i	1.48054	−	0.396711i	0.906532	+	0.422136i	$0.138720\pi$
$564$		0			0
$565$	2.59670	+	0.695783i	0.109244	+	0.0292718i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.2488	−	21.2155i	−0.513496	−	0.889402i	−0.999877	−	0.0156550i	$-0.995017\pi$
$569$	−12.2488	−	21.2155i	−0.513496	−	0.889402i	0.486381	−	0.873747i	$-0.338317\pi$
$570$		0			0
$571$	−7.91280	+	2.12023i	−0.331140	+	0.0887288i	−0.420559	−	0.907265i	$-0.638166\pi$
$571$	−7.91280	+	2.12023i	−0.331140	+	0.0887288i	0.0894183	+	0.995994i	$0.471499\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	17.0048			0.709147
$576$		0			0
$577$	−19.0192			−0.791779			−0.395889	−	0.918298i	$-0.629564\pi$
$577$	−19.0192			−0.791779			−0.395889	+	0.918298i	$0.629564\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−58.1417	+	15.5790i	−2.41213	+	0.646327i
$582$		0			0
$583$	4.44944	+	7.70665i	0.184277	+	0.319177i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.79477	−	2.62450i	−0.404274	−	0.108325i	0.0509516	−	0.998701i	$-0.483775\pi$
$587$	−9.79477	−	2.62450i	−0.404274	−	0.108325i	−0.455225	+	0.890376i	$0.650441\pi$
$588$		0			0
$589$	11.9124	−	3.19193i	0.490844	−	0.131521i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	16.0166i		−	0.657724i	−0.944378	−	0.328862i	$-0.893335\pi$
$593$		−	16.0166i		−	0.657724i	0.944378	−	0.328862i	$-0.106665\pi$
$594$		0			0
$595$	4.63123	−	4.63123i	0.189862	−	0.189862i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.72485	+	1.57319i	0.111334	+	0.0642790i	0.554633	−	0.832095i	$-0.312859\pi$
$599$	2.72485	+	1.57319i	0.111334	+	0.0642790i	−0.443299	+	0.896374i	$0.646192\pi$
$600$		0			0
$601$	6.88132	−	3.97293i	0.280695	−	0.162059i	−0.353043	−	0.935607i	$-0.614853\pi$
$601$	6.88132	−	3.97293i	0.280695	−	0.162059i	0.633738	+	0.773548i	$0.281520\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.49732	−	0.669154i	−0.101530	−	0.0272050i
$606$		0			0
$607$	28.2159	+	16.2905i	1.14525	+	0.661209i	0.947725	−	0.319089i	$-0.103377\pi$
$607$	28.2159	+	16.2905i	1.14525	+	0.661209i	0.197523	+	0.980298i	$0.436710\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.280791	+	0.280791i	0.0113596	+	0.0113596i
$612$		0			0
$613$	1.74081	−	1.74081i	0.0703105	−	0.0703105i	−0.671077	−	0.741388i	$-0.734168\pi$
$613$	1.74081	−	1.74081i	0.0703105	−	0.0703105i	0.741388	+	0.671077i	$0.234168\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8.76552	+	15.1823i	−0.352887	+	0.611218i	−0.986754	−	0.162224i	$-0.948133\pi$
$617$	−8.76552	+	15.1823i	−0.352887	+	0.611218i	0.633867	+	0.773442i	$0.281467\pi$
$618$		0			0
$619$	−3.30420	+	12.3314i	−0.132807	+	0.495643i	−0.999997	−	0.00233438i	$-0.999257\pi$
$619$	−3.30420	+	12.3314i	−0.132807	+	0.495643i	0.867190	+	0.497977i	$0.165924\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	21.7588	+	37.6873i	0.871746	+	1.50991i
$624$		0			0
$625$	4.27862	−	7.41079i	0.171145	−	0.296432i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	9.36852	+	9.36852i	0.373548	+	0.373548i
$630$		0			0
$631$	24.1690			0.962153			0.481076	−	0.876679i	$-0.340246\pi$
$631$	24.1690			0.962153			0.481076	+	0.876679i	$0.340246\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.06387	+	3.97043i	0.0422185	+	0.157562i
$636$		0			0
$637$	−8.30585	+	30.9979i	−0.329090	+	1.22818i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	19.3938	−	11.1970i	0.766010	−	0.442256i	−0.0654392	−	0.997857i	$-0.520845\pi$
$641$	19.3938	−	11.1970i	0.766010	−	0.442256i	0.831450	+	0.555600i	$0.187511\pi$
$642$		0			0
$643$	−1.00422	−	3.74778i	−0.0396024	−	0.147798i	0.943294	−	0.331960i	$-0.107710\pi$
$643$	−1.00422	−	3.74778i	−0.0396024	−	0.147798i	−0.982896	+	0.184161i	$0.941043\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			36.0008i			1.41534i	0.706544	+	0.707669i	$0.250253\pi$
$647$			36.0008i			1.41534i	−0.706544	+	0.707669i	$0.749747\pi$
$648$		0			0
$649$			50.6508i			1.98822i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.19679	−	4.46647i	−0.0468339	−	0.174786i	0.938547	−	0.345151i	$-0.112172\pi$
$653$	−1.19679	−	4.46647i	−0.0468339	−	0.174786i	−0.985381	+	0.170364i	$0.945506\pi$
$654$		0			0
$655$	−1.25878	+	0.726755i	−0.0491845	+	0.0283967i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.49427	−	35.4331i	0.369844	−	1.38028i	−0.490889	−	0.871222i	$-0.663328\pi$
$659$	9.49427	−	35.4331i	0.369844	−	1.38028i	0.860734	−	0.509056i	$-0.170005\pi$
$660$		0			0
$661$	6.83035	+	25.4912i	0.265670	+	0.991493i	0.961839	+	0.273616i	$0.0882196\pi$
$661$	6.83035	+	25.4912i	0.265670	+	0.991493i	−0.696169	+	0.717878i	$0.745114\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	24.2680			0.941072
$666$		0			0
$667$	−14.0027	−	14.0027i	−0.542185	−	0.542185i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−16.4586	+	28.5072i	−0.635378	+	1.10051i
$672$		0			0
$673$	−11.8530	−	20.5299i	−0.456898	−	0.791371i	0.541897	−	0.840445i	$-0.317706\pi$
$673$	−11.8530	−	20.5299i	−0.456898	−	0.791371i	−0.998795	+	0.0490741i	$0.984373\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.158680	−	0.592200i	0.00609855	−	0.0227601i	−0.962810	−	0.270181i	$-0.912916\pi$
$677$	0.158680	−	0.592200i	0.00609855	−	0.0227601i	0.968908	+	0.247421i	$0.0795831\pi$
$678$		0			0
$679$	−0.206287	+	0.357299i	−0.00791656	+	0.0137119i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	7.92296	−	7.92296i	0.303164	−	0.303164i	−0.539087	−	0.842250i	$-0.681230\pi$
$683$	7.92296	−	7.92296i	0.303164	−	0.303164i	0.842250	+	0.539087i	$0.181230\pi$
$684$		0			0
$685$	−8.63676	−	8.63676i	−0.329994	−	0.329994i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	8.46522	+	4.88739i	0.322499	+	0.186195i
$690$		0			0
$691$	−10.1756	−	2.72654i	−0.387097	−	0.103722i	0.0600214	−	0.998197i	$-0.480883\pi$
$691$	−10.1756	−	2.72654i	−0.387097	−	0.103722i	−0.447118	+	0.894475i	$0.647550\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.95027	+	1.70334i	−0.111910	+	0.0646112i
$696$		0			0
$697$	−4.28883	−	2.47616i	−0.162451	−	0.0937912i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	17.1029	−	17.1029i	0.645968	−	0.645968i	−0.306048	−	0.952016i	$-0.599007\pi$
$701$	17.1029	−	17.1029i	0.645968	−	0.645968i	0.952016	+	0.306048i	$0.0990068\pi$
$702$		0			0
$703$			49.0918i			1.85153i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	16.1980	−	4.34024i	0.609188	−	0.163231i
$708$		0			0
$709$	1.33738	+	0.358349i	0.0502263	+	0.0134581i	0.283845	−	0.958870i	$-0.408390\pi$
$709$	1.33738	+	0.358349i	0.0502263	+	0.0134581i	−0.233618	+	0.972328i	$0.575057\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.79209	+	8.30014i	0.179465	+	0.310843i
$714$		0			0
$715$	−15.4785	+	4.14744i	−0.578862	+	0.155106i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	3.58660			0.133758			0.0668789	−	0.997761i	$-0.478696\pi$
$719$	3.58660			0.133758			0.0668789	+	0.997761i	$0.478696\pi$
$720$		0			0
$721$	9.68418			0.360658
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−16.3226	+	4.37362i	−0.606205	+	0.162432i
$726$		0			0
$727$	19.8338	+	34.3531i	0.735594	+	1.27409i	0.954462	+	0.298331i	$0.0964301\pi$
$727$	19.8338	+	34.3531i	0.735594	+	1.27409i	−0.218869	+	0.975754i	$0.570237\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.55203	+	2.29151i	0.316308	+	0.0847545i
$732$		0			0
$733$	7.45317	−	1.99707i	0.275289	−	0.0737635i	−0.118533	−	0.992950i	$-0.537819\pi$
$733$	7.45317	−	1.99707i	0.275289	−	0.0737635i	0.393822	+	0.919187i	$0.371153\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	3.55568i		−	0.130975i
$738$		0			0
$739$	3.67791	−	3.67791i	0.135294	−	0.135294i	−0.636216	−	0.771511i	$-0.719501\pi$
$739$	3.67791	−	3.67791i	0.135294	−	0.135294i	0.771511	+	0.636216i	$0.219501\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	29.0142	+	16.7513i	1.06443	+	0.614547i	0.926654	−	0.375917i	$-0.122672\pi$
$743$	29.0142	+	16.7513i	1.06443	+	0.614547i	0.137773	+	0.990464i	$0.456005\pi$
$744$		0			0
$745$	−14.1551	+	8.17244i	−0.518602	+	0.299415i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	31.7900	+	8.51811i	1.16158	+	0.311245i
$750$		0			0
$751$	28.3480	+	16.3667i	1.03443	+	0.597231i	0.918252	−	0.395997i	$-0.129601\pi$
$751$	28.3480	+	16.3667i	1.03443	+	0.597231i	0.116182	+	0.993228i	$0.462934\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.465095	−	0.465095i	−0.0169265	−	0.0169265i
$756$		0			0
$757$	−32.1096	+	32.1096i	−1.16704	+	1.16704i	−0.184143	+	0.982900i	$0.558951\pi$
$757$	−32.1096	+	32.1096i	−1.16704	+	1.16704i	−0.982900	+	0.184143i	$0.941049\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	11.3534	−	19.6647i	0.411562	−	0.712847i	−0.583499	−	0.812114i	$-0.698317\pi$
$761$	11.3534	−	19.6647i	0.411562	−	0.712847i	0.995061	+	0.0992676i	$0.0316500\pi$
$762$		0			0
$763$	−1.24847	+	4.65936i	−0.0451977	+	0.168680i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	27.8182	+	48.1825i	1.00446	+	1.73977i
$768$		0			0
$769$	23.6477	−	40.9590i	0.852757	−	1.47702i	−0.0259531	−	0.999663i	$-0.508262\pi$
$769$	23.6477	−	40.9590i	0.852757	−	1.47702i	0.878710	−	0.477356i	$-0.158405\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−13.5761	−	13.5761i	−0.488297	−	0.488297i	0.419472	−	0.907768i	$-0.362215\pi$
$773$	−13.5761	−	13.5761i	−0.488297	−	0.488297i	−0.907768	+	0.419472i	$0.862215\pi$
$774$		0			0
$775$	8.17852			0.293781
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.74927	−	17.7245i	−0.170160	−	0.635047i
$780$		0			0
$781$	6.73300	−	25.1279i	0.240926	−	0.899147i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.57984	+	3.79887i	−0.234845	+	0.135588i
$786$		0			0
$787$	2.13054	+	7.95128i	0.0759455	+	0.283432i	0.993446	−	0.114302i	$-0.0364632\pi$
$787$	2.13054	+	7.95128i	0.0759455	+	0.283432i	−0.917501	+	0.397735i	$0.869797\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	9.53851i		−	0.339150i
$792$		0			0
$793$			36.1573i			1.28398i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.57723	+	35.7427i	0.339243	+	1.26607i	0.899195	+	0.437547i	$0.144153\pi$
$797$	9.57723	+	35.7427i	0.339243	+	1.26607i	−0.559953	+	0.828525i	$0.689181\pi$
$798$		0			0
$799$	−0.132742	+	0.0766384i	−0.00469606	+	0.00271127i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−9.85301	+	36.7719i	−0.347705	+	1.29765i
$804$		0			0
$805$	4.88121	+	18.2169i	0.172040	+	0.642062i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−42.6915			−1.50095			−0.750477	−	0.660897i	$-0.770176\pi$
$809$	−42.6915			−1.50095			−0.750477	+	0.660897i	$0.770176\pi$
$810$		0			0
$811$	21.6324	+	21.6324i	0.759616	+	0.759616i	0.976252	−	0.216637i	$-0.0695087\pi$
$811$	21.6324	+	21.6324i	0.759616	+	0.759616i	−0.216637	+	0.976252i	$0.569509\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.97131	−	10.3426i	0.209166	−	0.362286i
$816$		0			0
$817$	16.4028	+	28.4105i	0.573861	+	0.993957i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.1896	+	41.7600i	−0.390519	+	1.45744i	0.438762	+	0.898603i	$0.355417\pi$
$821$	−11.1896	+	41.7600i	−0.390519	+	1.45744i	−0.829281	+	0.558832i	$0.811250\pi$
$822$		0			0
$823$	7.47369	−	12.9448i	0.260516	−	0.451227i	−0.705863	−	0.708348i	$-0.749441\pi$
$823$	7.47369	−	12.9448i	0.260516	−	0.451227i	0.966379	+	0.257121i	$0.0827739\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.17437	+	3.17437i	−0.110384	+	0.110384i	−0.760141	−	0.649758i	$-0.774870\pi$
$827$	−3.17437	+	3.17437i	−0.110384	+	0.110384i	0.649758	+	0.760141i	$0.274870\pi$
$828$		0			0
$829$	−6.24227	−	6.24227i	−0.216803	−	0.216803i	0.590347	−	0.807150i	$-0.298991\pi$
$829$	−6.24227	−	6.24227i	−0.216803	−	0.216803i	−0.807150	+	0.590347i	$0.798991\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−10.7274	−	6.19349i	−0.371684	−	0.214592i
$834$		0			0
$835$	−19.9031	−	5.33301i	−0.688774	−	0.184556i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.61601	−	4.97446i	0.297458	−	0.171737i	−0.343842	−	0.939027i	$-0.611729\pi$
$839$	8.61601	−	4.97446i	0.297458	−	0.171737i	0.641300	+	0.767290i	$0.278395\pi$
$840$		0			0
$841$	−8.07235	−	4.66057i	−0.278357	−	0.160709i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.41567	+	2.41567i	−0.0831016	+	0.0831016i
$846$		0			0
$847$			9.17346i			0.315204i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−36.8511	+	9.87421i	−1.26324	+	0.338484i
$852$		0			0
$853$	20.6477	+	5.53253i	0.706963	+	0.189430i	0.594347	−	0.804208i	$-0.297410\pi$
$853$	20.6477	+	5.53253i	0.706963	+	0.189430i	0.112616	+	0.993639i	$0.464077\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.86646	+	11.8931i	0.234554	+	0.406259i	0.959143	−	0.282922i	$-0.0913038\pi$
$857$	6.86646	+	11.8931i	0.234554	+	0.406259i	−0.724589	+	0.689181i	$0.757970\pi$
$858$		0			0
$859$	−13.6273	+	3.65143i	−0.464958	+	0.124585i	−0.483690	−	0.875239i	$-0.660704\pi$
$859$	−13.6273	+	3.65143i	−0.464958	+	0.124585i	0.0187321	+	0.999825i	$0.494037\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−30.6861			−1.04457			−0.522284	−	0.852772i	$-0.674920\pi$
$863$	−30.6861			−1.04457			−0.522284	+	0.852772i	$0.674920\pi$
$864$		0			0
$865$	18.4805			0.628355
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−58.0745	+	15.5610i	−1.97004	+	0.527871i
$870$		0			0
$871$	−1.95283	−	3.38240i	−0.0661692	−	0.114608i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	35.9493	+	9.63260i	1.21531	+	0.325641i
$876$		0			0
$877$	−21.1730	+	5.67328i	−0.714960	+	0.191573i	−0.597922	−	0.801554i	$-0.704007\pi$
$877$	−21.1730	+	5.67328i	−0.714960	+	0.191573i	−0.117038	+	0.993127i	$0.537340\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			15.7695i			0.531287i	0.964071	+	0.265644i	$0.0855845\pi$
$881$			15.7695i			0.531287i	−0.964071	+	0.265644i	$0.914416\pi$
$882$		0			0
$883$	32.1210	−	32.1210i	1.08096	−	1.08096i	0.0845378	−	0.996420i	$-0.473059\pi$
$883$	32.1210	−	32.1210i	1.08096	−	1.08096i	0.996420	−	0.0845378i	$-0.0269414\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.68281	+	3.28097i	0.190810	+	0.110164i	0.592362	−	0.805672i	$-0.298196\pi$
$887$	5.68281	+	3.28097i	0.190810	+	0.110164i	−0.401552	+	0.915836i	$0.631529\pi$
$888$		0			0
$889$	12.6307	−	7.29233i	0.423620	−	0.244577i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.548583	−	0.146992i	−0.0183576	−	0.00491891i
$894$		0			0
$895$	−6.48322	−	3.74309i	−0.216710	−	0.125118i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.73464	−	6.73464i	−0.224613	−	0.224613i
$900$		0			0
$901$	−2.66790	+	2.66790i	−0.0888808	+	0.0888808i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.53424	−	2.65738i	0.0509999	−	0.0883344i
$906$		0			0
$907$	−5.88760	+	21.9728i	−0.195495	+	0.729596i	0.796644	+	0.604449i	$0.206607\pi$
$907$	−5.88760	+	21.9728i	−0.195495	+	0.729596i	−0.992138	+	0.125147i	$0.960060\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.27703	−	9.14009i	−0.174836	−	0.302825i	0.765269	−	0.643711i	$-0.222606\pi$
$911$	−5.27703	−	9.14009i	−0.174836	−	0.302825i	−0.940104	+	0.340887i	$0.889273\pi$
$912$		0			0
$913$	−28.4227	+	49.2295i	−0.940653	+	1.62926i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.64675	+	3.64675i	0.120426	+	0.120426i
$918$		0			0
$919$	0.366138			0.0120778			0.00603890	−	0.999982i	$-0.498078\pi$
$919$	0.366138			0.0120778			0.00603890	+	0.999982i	$0.498078\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−7.39573	−	27.6012i	−0.243433	−	0.908506i
$924$		0			0
$925$	−8.42601	+	31.4463i	−0.277046	+	1.03395i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	40.6720	−	23.4820i	1.33440	−	0.770419i	0.348433	−	0.937334i	$-0.386714\pi$
$929$	40.6720	−	23.4820i	1.33440	−	0.770419i	0.985971	+	0.166915i	$0.0533806\pi$
$930$		0			0
$931$	−11.8791	−	44.3335i	−0.389323	−	1.45297i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	6.18532i		−	0.202281i
$936$		0			0
$937$		−	52.8156i		−	1.72541i	−0.505706	−	0.862706i	$-0.668768\pi$
$937$		−	52.8156i		−	1.72541i	0.505706	−	0.862706i	$-0.331232\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−14.2433	−	53.1569i	−0.464320	−	1.73286i	−0.659135	−	0.752024i	$-0.729078\pi$
$941$	−14.2433	−	53.1569i	−0.464320	−	1.73286i	0.194816	−	0.980840i	$-0.437589\pi$
$942$		0			0
$943$	12.3498	−	7.13015i	0.402164	−	0.232190i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.03273	−	18.7824i	0.163542	−	0.610346i	−0.834680	−	0.550735i	$-0.814347\pi$
$947$	5.03273	−	18.7824i	0.163542	−	0.610346i	0.998222	−	0.0596105i	$-0.0189859\pi$
$948$		0			0
$949$	10.8228	+	40.3914i	0.351324	+	1.31116i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−32.2129			−1.04348			−0.521739	−	0.853105i	$-0.674717\pi$
$953$	−32.2129			−1.04348			−0.521739	+	0.853105i	$0.674717\pi$
$954$		0			0
$955$	15.7400	+	15.7400i	0.509334	+	0.509334i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−21.6690	+	37.5318i	−0.699729	+	1.21197i
$960$		0			0
$961$	−13.1952	−	22.8548i	−0.425652	−	0.737251i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.69047	−	17.5051i	0.150992	−	0.563508i
$966$		0			0
$967$	6.78008	−	11.7434i	0.218033	−	0.377644i	−0.736174	−	0.676793i	$-0.763369\pi$
$967$	6.78008	−	11.7434i	0.218033	−	0.377644i	0.954206	+	0.299149i	$0.0967028\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.29201	−	1.29201i	0.0414626	−	0.0414626i	−0.686072	−	0.727534i	$-0.740666\pi$
$971$	1.29201	−	1.29201i	0.0414626	−	0.0414626i	0.727534	+	0.686072i	$0.240666\pi$
$972$		0			0
$973$	8.54709	+	8.54709i	0.274007	+	0.274007i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.8504	+	17.8115i	0.986993	+	0.569841i	0.904374	−	0.426741i	$-0.140338\pi$
$977$	30.8504	+	17.8115i	0.986993	+	0.569841i	0.0826189	+	0.996581i	$0.473672\pi$
$978$		0			0
$979$	39.6971	+	10.6368i	1.26872	+	0.339954i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	44.7746	−	25.8506i	1.42809	−	0.824507i	0.431118	−	0.902295i	$-0.358119\pi$
$983$	44.7746	−	25.8506i	1.42809	−	0.824507i	0.996970	+	0.0777882i	$0.0247858\pi$
$984$		0			0
$985$	2.72373	+	1.57254i	0.0867852	+	0.0501054i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−18.0273	+	18.0273i	−0.573235	+	0.573235i
$990$		0			0
$991$		−	27.3724i		−	0.869513i	−0.900548	−	0.434756i	$-0.856834\pi$
$991$		−	27.3724i		−	0.869513i	0.900548	−	0.434756i	$-0.143166\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.69372	+	2.59742i	−0.307311	+	0.0823439i
$996$		0			0
$997$	−52.2174	−	13.9916i	−1.65374	−	0.443119i	−0.693085	−	0.720856i	$-0.743749\pi$
$997$	−52.2174	−	13.9916i	−1.65374	−	0.443119i	−0.960657	+	0.277737i	$0.910416\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.z.a.1583.9		88
3.2	odd	2		576.2.y.a.239.21		88
4.3	odd	2		432.2.v.a.179.18		88
9.2	odd	6	inner	1728.2.z.a.1007.9		88
9.7	even	3		576.2.y.a.47.13		88
12.11	even	2		144.2.u.a.131.5	yes	88
16.5	even	4		432.2.v.a.395.19		88
16.11	odd	4	inner	1728.2.z.a.719.9		88
36.7	odd	6		144.2.u.a.83.4	yes	88
36.11	even	6		432.2.v.a.35.19		88
48.5	odd	4		144.2.u.a.59.4	yes	88
48.11	even	4		576.2.y.a.527.13		88
144.11	even	12	inner	1728.2.z.a.143.9		88
144.43	odd	12		576.2.y.a.335.21		88
144.101	odd	12		432.2.v.a.251.18		88
144.133	even	12		144.2.u.a.11.5	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.5	✓	88	144.133	even	12
144.2.u.a.59.4	yes	88	48.5	odd	4
144.2.u.a.83.4	yes	88	36.7	odd	6
144.2.u.a.131.5	yes	88	12.11	even	2
432.2.v.a.35.19		88	36.11	even	6
432.2.v.a.179.18		88	4.3	odd	2
432.2.v.a.251.18		88	144.101	odd	12
432.2.v.a.395.19		88	16.5	even	4
576.2.y.a.47.13		88	9.7	even	3
576.2.y.a.239.21		88	3.2	odd	2
576.2.y.a.335.21		88	144.43	odd	12
576.2.y.a.527.13		88	48.11	even	4
1728.2.z.a.143.9		88	144.11	even	12	inner
1728.2.z.a.719.9		88	16.11	odd	4	inner
1728.2.z.a.1007.9		88	9.2	odd	6	inner
1728.2.z.a.1583.9		88	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.05401 + 0.282421i) q^{5} +(1.93586 + 3.35301i) q^{7} +(3.53182 + 0.946349i) q^{11} +(3.87946 - 1.03950i) q^{13} +1.55026i q^{17} +(-4.06175 + 4.06175i) q^{19} +(-3.86595 - 2.23201i) q^{23} +(-3.29895 + 1.90465i) q^{25} +(4.28493 + 1.14814i) q^{29} +(-1.85935 - 1.07349i) q^{31} +(-2.98738 - 2.98738i) q^{35} +(6.04318 - 6.04318i) q^{37} +(-1.59725 + 2.76652i) q^{41} +(1.47814 - 5.51650i) q^{43} +(0.0494357 + 0.0856252i) q^{47} +(-3.99512 + 6.91976i) q^{49} +(1.72094 + 1.72094i) q^{53} -3.98985 q^{55} +(3.58531 + 13.3806i) q^{59} +(-2.33005 + 8.69586i) q^{61} +(-3.79542 + 2.19129i) q^{65} +(-0.251689 - 0.939315i) q^{67} -7.11471i q^{71} +10.4116i q^{73} +(3.66400 + 13.6742i) q^{77} +(-14.2402 + 8.22160i) q^{79} +(-4.02380 + 15.0170i) q^{83} +(-0.437828 - 1.63399i) q^{85} +11.2398 q^{89} +(10.9956 + 10.9956i) q^{91} +(3.13400 - 5.42825i) q^{95} +(0.0532804 + 0.0922843i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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