LMFDB - Embedded newform 1728.2.z.a.1007.21

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)

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);

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")

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			1007.21
Character	$\chi$	$=$	1728.1007
Dual form			1728.2.z.a.719.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.961558 - 3.58858i) q^{5} +(1.29216 - 2.23809i) q^{7} +(-0.541286 - 2.02011i) q^{11} +(0.267433 - 0.998074i) q^{13} -4.13788i q^{17} +(-2.49279 + 2.49279i) q^{19} +(7.01915 - 4.05251i) q^{23} +(-7.62322 - 4.40127i) q^{25} +(1.88218 + 7.02439i) q^{29} +(-2.03331 + 1.17393i) q^{31} +(-6.78909 - 6.78909i) q^{35} +(-4.75590 + 4.75590i) q^{37} +(0.636217 + 1.10196i) q^{41} +(1.45505 - 0.389880i) q^{43} +(3.60814 - 6.24948i) q^{47} +(0.160635 + 0.278228i) q^{49} +(0.546616 + 0.546616i) q^{53} -7.76980 q^{55} +(-8.00411 - 2.14469i) q^{59} +(-6.77407 + 1.81511i) q^{61} +(-3.32452 - 1.91941i) q^{65} +(2.80643 + 0.751980i) q^{67} +6.59449i q^{71} +8.78699i q^{73} +(-5.22061 - 1.39886i) q^{77} +(5.64940 + 3.26168i) q^{79} +(7.71754 - 2.06791i) q^{83} +(-14.8491 - 3.97882i) q^{85} -14.1938 q^{89} +(-1.88821 - 1.88821i) q^{91} +(6.54863 + 11.3426i) q^{95} +(6.54551 - 11.3372i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

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

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
$5$	0.961558	−	3.58858i	0.430022	−	1.60486i	−0.322684	−	0.946507i	$-0.604585\pi$
$5$	0.961558	−	3.58858i	0.430022	−	1.60486i	0.752706	−	0.658357i	$-0.228748\pi$
$6$		0			0
$7$	1.29216	−	2.23809i	0.488391	−	0.845919i	−0.511520	−	0.859272i	$-0.670917\pi$
$7$	1.29216	−	2.23809i	0.488391	−	0.845919i	0.999911	+	0.0133531i	$0.00425055\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.541286	−	2.02011i	−0.163204	−	0.609085i	−0.998262	−	0.0589240i	$-0.981233\pi$
$11$	−0.541286	−	2.02011i	−0.163204	−	0.609085i	0.835059	−	0.550161i	$-0.185434\pi$
$12$		0			0
$13$	0.267433	−	0.998074i	0.0741726	−	0.276816i	−0.918872	−	0.394556i	$-0.870898\pi$
$13$	0.267433	−	0.998074i	0.0741726	−	0.276816i	0.993044	+	0.117740i	$0.0375650\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	4.13788i		−	1.00358i	−0.864988	−	0.501792i	$-0.832674\pi$
$17$		−	4.13788i		−	1.00358i	0.864988	−	0.501792i	$-0.167326\pi$
$18$		0			0
$19$	−2.49279	+	2.49279i	−0.571886	+	0.571886i	−0.932655	−	0.360769i	$-0.882514\pi$
$19$	−2.49279	+	2.49279i	−0.571886	+	0.571886i	0.360769	+	0.932655i	$0.382514\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.01915	−	4.05251i	1.46359	−	0.845006i	0.464418	−	0.885616i	$-0.346264\pi$
$23$	7.01915	−	4.05251i	1.46359	−	0.845006i	0.999175	+	0.0406102i	$0.0129302\pi$
$24$		0			0
$25$	−7.62322	−	4.40127i	−1.52464	−	0.880253i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.88218	+	7.02439i	0.349512	+	1.30440i	0.887252	+	0.461286i	$0.152612\pi$
$29$	1.88218	+	7.02439i	0.349512	+	1.30440i	−0.537740	+	0.843111i	$0.680722\pi$
$30$		0			0
$31$	−2.03331	+	1.17393i	−0.365194	+	0.210845i	−0.671357	−	0.741134i	$-0.734288\pi$
$31$	−2.03331	+	1.17393i	−0.365194	+	0.210845i	0.306163	+	0.951979i	$0.400955\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.78909	−	6.78909i	−1.14757	−	1.14757i
$36$		0			0
$37$	−4.75590	+	4.75590i	−0.781865	+	0.781865i	−0.980145	−	0.198280i	$-0.936464\pi$
$37$	−4.75590	+	4.75590i	−0.781865	+	0.781865i	0.198280	+	0.980145i	$0.436464\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.636217	+	1.10196i	0.0993604	+	0.172097i	0.911420	−	0.411477i	$-0.134987\pi$
$41$	0.636217	+	1.10196i	0.0993604	+	0.172097i	−0.812060	+	0.583574i	$0.801654\pi$
$42$		0			0
$43$	1.45505	−	0.389880i	0.221894	−	0.0594562i	−0.146159	−	0.989261i	$-0.546691\pi$
$43$	1.45505	−	0.389880i	0.221894	−	0.0594562i	0.368053	+	0.929805i	$0.380025\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.60814	−	6.24948i	0.526301	−	0.911580i	−0.473230	−	0.880939i	$-0.656912\pi$
$47$	3.60814	−	6.24948i	0.526301	−	0.911580i	0.999530	−	0.0306407i	$-0.00975476\pi$
$48$		0			0
$49$	0.160635	+	0.278228i	0.0229479	+	0.0397469i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.546616	+	0.546616i	0.0750835	+	0.0750835i	0.743651	−	0.668568i	$-0.233092\pi$
$53$	0.546616	+	0.546616i	0.0750835	+	0.0750835i	−0.668568	+	0.743651i	$0.733092\pi$
$54$		0			0
$55$	−7.76980			−1.04768
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.00411	−	2.14469i	−1.04205	−	0.279215i	−0.303085	−	0.952963i	$-0.598017\pi$
$59$	−8.00411	−	2.14469i	−1.04205	−	0.279215i	−0.738961	+	0.673748i	$0.764683\pi$
$60$		0			0
$61$	−6.77407	+	1.81511i	−0.867331	+	0.232401i	−0.664933	−	0.746903i	$-0.731540\pi$
$61$	−6.77407	+	1.81511i	−0.867331	+	0.232401i	−0.202398	+	0.979303i	$0.564873\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.32452	−	1.91941i	−0.412356	−	0.238074i
$66$		0			0
$67$	2.80643	+	0.751980i	0.342860	+	0.0918690i	0.426140	−	0.904657i	$-0.359873\pi$
$67$	2.80643	+	0.751980i	0.342860	+	0.0918690i	−0.0832804	+	0.996526i	$0.526540\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			6.59449i			0.782622i	0.920258	+	0.391311i	$0.127978\pi$
$71$			6.59449i			0.782622i	−0.920258	+	0.391311i	$0.872022\pi$
$72$		0			0
$73$			8.78699i			1.02844i	0.857658	+	0.514220i	$0.171918\pi$
$73$			8.78699i			1.02844i	−0.857658	+	0.514220i	$0.828082\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.22061	−	1.39886i	−0.594944	−	0.159415i
$78$		0			0
$79$	5.64940	+	3.26168i	0.635607	+	0.366968i	0.782920	−	0.622122i	$-0.213729\pi$
$79$	5.64940	+	3.26168i	0.635607	+	0.366968i	−0.147313	+	0.989090i	$0.547063\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.71754	−	2.06791i	0.847110	−	0.226982i	0.190946	−	0.981601i	$-0.438845\pi$
$83$	7.71754	−	2.06791i	0.847110	−	0.226982i	0.656164	+	0.754618i	$0.272178\pi$
$84$		0			0
$85$	−14.8491	−	3.97882i	−1.61062	−	0.431563i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−14.1938			−1.50454			−0.752272	−	0.658852i	$-0.771042\pi$
$89$	−14.1938			−1.50454			−0.752272	+	0.658852i	$0.771042\pi$
$90$		0			0
$91$	−1.88821	−	1.88821i	−0.197939	−	0.197939i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.54863	+	11.3426i	0.671875	+	1.16372i
$96$		0			0
$97$	6.54551	−	11.3372i	0.664596	−	1.15111i	−0.314799	−	0.949158i	$-0.601937\pi$
$97$	6.54551	−	11.3372i	0.664596	−	1.15111i	0.979395	−	0.201955i	$-0.0647295\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.94498	−	1.05705i	0.392540	−	0.105181i	−0.0571499	−	0.998366i	$-0.518201\pi$
$101$	3.94498	−	1.05705i	0.392540	−	0.105181i	0.449690	+	0.893185i	$0.351535\pi$
$102$		0			0
$103$	−2.22868	−	3.86019i	−0.219599	−	0.380356i	0.735087	−	0.677973i	$-0.237141\pi$
$103$	−2.22868	−	3.86019i	−0.219599	−	0.380356i	−0.954685	+	0.297617i	$0.903808\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.01417	+	4.01417i	−0.388064	+	0.388064i	−0.873996	−	0.485932i	$-0.838480\pi$
$107$	−4.01417	+	4.01417i	−0.388064	+	0.388064i	0.485932	+	0.873996i	$0.338480\pi$
$108$		0			0
$109$	−6.84996	−	6.84996i	−0.656107	−	0.656107i	0.298349	−	0.954457i	$-0.403564\pi$
$109$	−6.84996	−	6.84996i	−0.656107	−	0.656107i	−0.954457	+	0.298349i	$0.903564\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.97546	−	4.60464i	0.750268	−	0.433168i	−0.0755225	−	0.997144i	$-0.524062\pi$
$113$	7.97546	−	4.60464i	0.750268	−	0.433168i	0.825791	+	0.563976i	$0.190729\pi$
$114$		0			0
$115$	−7.79344	−	29.0855i	−0.726742	−	2.71224i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.26095	−	5.34681i	−0.848950	−	0.490142i
$120$		0			0
$121$	5.73844	−	3.31309i	0.521676	−	0.301190i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.98936	+	9.98936i	−0.893475	+	0.893475i
$126$		0			0
$127$			4.75792i			0.422197i	0.977465	+	0.211099i	$0.0677041\pi$
$127$			4.75792i			0.422197i	−0.977465	+	0.211099i	$0.932296\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.24125	−	8.36446i	0.195819	−	0.730806i	−0.796234	−	0.604988i	$-0.793178\pi$
$131$	2.24125	−	8.36446i	0.195819	−	0.730806i	0.992053	−	0.125818i	$-0.0401555\pi$
$132$		0			0
$133$	2.35800	+	8.80019i	0.204465	+	0.763073i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.29570	−	14.3686i	0.708750	−	1.22759i	−0.256571	−	0.966525i	$-0.582593\pi$
$137$	8.29570	−	14.3686i	0.708750	−	1.22759i	0.965321	−	0.261065i	$-0.0840738\pi$
$138$		0			0
$139$	−1.84191	+	6.87408i	−0.156228	+	0.583052i	0.842769	+	0.538276i	$0.180924\pi$
$139$	−1.84191	+	6.87408i	−0.156228	+	0.583052i	−0.998997	+	0.0447763i	$0.985743\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.16097			−0.180710
$144$		0			0
$145$	27.0175			2.24368
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.969882	+	3.61965i	−0.0794558	+	0.296533i	−0.994207	−	0.107485i	$-0.965720\pi$
$149$	−0.969882	+	3.61965i	−0.0794558	+	0.296533i	0.914751	+	0.404018i	$0.132387\pi$
$150$		0			0
$151$	−1.35324	+	2.34389i	−0.110125	+	0.190743i	−0.915821	−	0.401588i	$-0.868459\pi$
$151$	−1.35324	+	2.34389i	−0.110125	+	0.190743i	0.805695	+	0.592330i	$0.201792\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.25761	+	8.42553i	0.181336	+	0.676755i
$156$		0			0
$157$	−1.28460	+	4.79418i	−0.102522	+	0.382617i	−0.998052	−	0.0623832i	$-0.980130\pi$
$157$	−1.28460	+	4.79418i	−0.102522	+	0.382617i	0.895530	+	0.445001i	$0.146797\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	20.9460i		−	1.65077i
$162$		0			0
$163$	8.40242	−	8.40242i	0.658129	−	0.658129i	−0.296808	−	0.954937i	$-0.595922\pi$
$163$	8.40242	−	8.40242i	0.658129	−	0.658129i	0.954937	+	0.296808i	$0.0959223\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.11596	+	4.10840i	−0.550650	+	0.317918i	−0.749384	−	0.662136i	$-0.769650\pi$
$167$	−7.11596	+	4.10840i	−0.550650	+	0.317918i	0.198734	+	0.980053i	$0.436317\pi$
$168$		0			0
$169$	10.3337	+	5.96616i	0.794900	+	0.458936i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.66438	−	24.8718i	−0.506683	−	1.89097i	−0.451012	−	0.892518i	$-0.648937\pi$
$173$	−6.66438	−	24.8718i	−0.506683	−	1.89097i	−0.0556715	−	0.998449i	$-0.517730\pi$
$174$		0			0
$175$	−19.7009	+	11.3743i	−1.48925	+	0.859816i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−14.5908	−	14.5908i	−1.09057	−	1.09057i	−0.995467	−	0.0951034i	$-0.969682\pi$
$179$	−14.5908	−	14.5908i	−1.09057	−	1.09057i	−0.0951034	−	0.995467i	$-0.530318\pi$
$180$		0			0
$181$	8.19403	−	8.19403i	0.609057	−	0.609057i	−0.333642	−	0.942700i	$-0.608278\pi$
$181$	8.19403	−	8.19403i	0.609057	−	0.609057i	0.942700	+	0.333642i	$0.108278\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	12.4939	+	21.6400i	0.918568	+	1.59101i
$186$		0			0
$187$	−8.35896	+	2.23978i	−0.611268	+	0.163789i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.80582	−	4.85981i	0.203022	−	0.351644i	−0.746479	−	0.665409i	$-0.768257\pi$
$191$	2.80582	−	4.85981i	0.203022	−	0.351644i	0.949501	+	0.313765i	$0.101590\pi$
$192$		0			0
$193$	−12.5728	−	21.7767i	−0.905008	−	1.56752i	−0.820906	−	0.571063i	$-0.806531\pi$
$193$	−12.5728	−	21.7767i	−0.905008	−	1.56752i	−0.0841024	−	0.996457i	$-0.526802\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.31684	+	4.31684i	0.307562	+	0.307562i	0.843963	−	0.536401i	$-0.180216\pi$
$197$	4.31684	+	4.31684i	0.307562	+	0.307562i	−0.536401	+	0.843963i	$0.680216\pi$
$198$		0			0
$199$	14.6645			1.03954			0.519769	−	0.854307i	$-0.326018\pi$
$199$	14.6645			1.03954			0.519769	+	0.854307i	$0.326018\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	18.1533	+	4.86416i	1.27411	+	0.341397i
$204$		0			0
$205$	4.56624	−	1.22352i	0.318920	−	0.0854543i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.38502	+	3.68639i	0.441661	+	0.254993i
$210$		0			0
$211$	2.25661	+	0.604656i	0.155351	+	0.0416263i	0.335656	−	0.941984i	$-0.391042\pi$
$211$	2.25661	+	0.604656i	0.155351	+	0.0416263i	−0.180305	+	0.983611i	$0.557709\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	5.59648i		−	0.381677i
$216$		0			0
$217$			6.06766i			0.411899i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.12991	−	1.10661i	−0.277808	−	0.0744385i
$222$		0			0
$223$	24.9105	+	14.3821i	1.66813	+	0.963094i	0.968646	+	0.248445i	$0.0799195\pi$
$223$	24.9105	+	14.3821i	1.66813	+	0.963094i	0.699483	+	0.714650i	$0.253414\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.06995	+	2.16234i	−0.535621	+	0.143519i	−0.516483	−	0.856298i	$-0.672759\pi$
$227$	−8.06995	+	2.16234i	−0.535621	+	0.143519i	−0.0191384	+	0.999817i	$0.506092\pi$
$228$		0			0
$229$	18.5393	+	4.96759i	1.22511	+	0.328268i	0.812674	−	0.582718i	$-0.198011\pi$
$229$	18.5393	+	4.96759i	1.22511	+	0.328268i	0.412438	+	0.910986i	$0.364677\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.96265			0.194090			0.0970450	−	0.995280i	$-0.469061\pi$
$233$	2.96265			0.194090			0.0970450	+	0.995280i	$0.469061\pi$
$234$		0			0
$235$	−18.9573	−	18.9573i	−1.23664	−	1.23664i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	5.14390	+	8.90950i	0.332731	+	0.576307i	0.983046	−	0.183357i	$-0.0586965\pi$
$239$	5.14390	+	8.90950i	0.332731	+	0.576307i	−0.650315	+	0.759665i	$0.725363\pi$
$240$		0			0
$241$	−12.8722	+	22.2954i	−0.829173	+	1.43617i	0.0695144	+	0.997581i	$0.477855\pi$
$241$	−12.8722	+	22.2954i	−0.829173	+	1.43617i	−0.898688	+	0.438589i	$0.855478\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.15290	−	0.308920i	0.0736564	−	0.0197362i
$246$		0			0
$247$	1.82134	+	3.15465i	0.115889	+	0.200725i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−16.7668	+	16.7668i	−1.05831	+	1.05831i	−0.0601228	+	0.998191i	$0.519149\pi$
$251$	−16.7668	+	16.7668i	−1.05831	+	1.05831i	−0.998191	+	0.0601228i	$0.980851\pi$
$252$		0			0
$253$	−11.9859	−	11.9859i	−0.753544	−	0.753544i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.74821	−	3.89608i	0.420942	−	0.243031i	−0.274538	−	0.961576i	$-0.588525\pi$
$257$	6.74821	−	3.89608i	0.420942	−	0.243031i	0.695480	+	0.718545i	$0.255192\pi$
$258$		0			0
$259$	4.49874	+	16.7895i	0.279538	+	1.04325i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.3513	+	7.13103i	0.761615	+	0.439718i	0.829875	−	0.557949i	$-0.188412\pi$
$263$	12.3513	+	7.13103i	0.761615	+	0.439718i	−0.0682606	+	0.997668i	$0.521745\pi$
$264$		0			0
$265$	2.48718	−	1.43597i	0.152786	−	0.0882112i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.70265	+	1.70265i	−0.103812	+	0.103812i	−0.757105	−	0.653293i	$-0.773387\pi$
$269$	−1.70265	+	1.70265i	−0.103812	+	0.103812i	0.653293	+	0.757105i	$0.273387\pi$
$270$		0			0
$271$			9.55642i			0.580511i	0.956949	+	0.290256i	$0.0937403\pi$
$271$			9.55642i			0.580511i	−0.956949	+	0.290256i	$0.906260\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.76469	+	17.7821i	−0.287321	+	1.07230i
$276$		0			0
$277$	0.571577	+	2.13315i	0.0343427	+	0.128169i	0.980969	−	0.194164i	$-0.0621995\pi$
$277$	0.571577	+	2.13315i	0.0343427	+	0.128169i	−0.946626	+	0.322333i	$0.895533\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	8.26158	−	14.3095i	0.492845	−	0.853632i	−0.507121	−	0.861875i	$-0.669290\pi$
$281$	8.26158	−	14.3095i	0.492845	−	0.853632i	0.999966	+	0.00824250i	$0.00262370\pi$
$282$		0			0
$283$	1.95433	−	7.29366i	0.116173	−	0.433563i	−0.883199	−	0.468998i	$-0.844615\pi$
$283$	1.95433	−	7.29366i	0.116173	−	0.433563i	0.999372	+	0.0354353i	$0.0112818\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.28838			0.194107
$288$		0			0
$289$	−0.122073			−0.00718078
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.12613	+	22.8630i	−0.357892	+	1.33567i	0.518913	+	0.854827i	$0.326337\pi$
$293$	−6.12613	+	22.8630i	−0.357892	+	1.33567i	−0.876805	+	0.480845i	$0.840330\pi$
$294$		0			0
$295$	−15.3928	+	26.6612i	−0.896206	+	1.55227i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.16755	−	8.08940i	−0.125353	−	0.467822i
$300$		0			0
$301$	1.00758	−	3.76033i	0.0580758	−	0.216742i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			26.0547i			1.49189i
$306$		0			0
$307$	−12.9528	+	12.9528i	−0.739255	+	0.739255i	−0.972434	−	0.233179i	$-0.925087\pi$
$307$	−12.9528	+	12.9528i	−0.739255	+	0.739255i	0.233179	+	0.972434i	$0.425087\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.74301	+	2.16103i	−0.212247	+	0.122541i	−0.602355	−	0.798228i	$-0.705771\pi$
$311$	−3.74301	+	2.16103i	−0.212247	+	0.122541i	0.390108	+	0.920769i	$0.372438\pi$
$312$		0			0
$313$	−13.7859	−	7.95932i	−0.779228	−	0.449887i	0.0569286	−	0.998378i	$-0.481869\pi$
$313$	−13.7859	−	7.95932i	−0.779228	−	0.449887i	−0.836157	+	0.548491i	$0.815203\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.69292	+	28.7104i	0.432077	+	1.61253i	0.747965	+	0.663738i	$0.231031\pi$
$317$	7.69292	+	28.7104i	0.432077	+	1.61253i	−0.315888	+	0.948797i	$0.602302\pi$
$318$		0			0
$319$	13.1712	−	7.60441i	0.737447	−	0.425765i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	10.3149	+	10.3149i	0.573935	+	0.573935i
$324$		0			0
$325$	−6.43149	+	6.43149i	−0.356755	+	0.356755i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−9.32459	−	16.1507i	−0.514082	−	0.890415i
$330$		0			0
$331$	1.90112	−	0.509403i	0.104495	−	0.0279993i	−0.206193	−	0.978511i	$-0.566107\pi$
$331$	1.90112	−	0.509403i	0.104495	−	0.0279993i	0.310688	+	0.950512i	$0.399441\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.39709	−	9.34803i	0.294874	−	0.510738i
$336$		0			0
$337$	9.46585	+	16.3953i	0.515638	+	0.893111i	0.999835	+	0.0181522i	$0.00577834\pi$
$337$	9.46585	+	16.3953i	0.515638	+	0.893111i	−0.484197	+	0.874959i	$0.660888\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.47208	+	3.47208i	0.188024	+	0.188024i
$342$		0			0
$343$	18.9205			1.02161
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.06413	−	0.821032i	−0.164491	−	0.0440753i	0.175634	−	0.984456i	$-0.443803\pi$
$347$	−3.06413	−	0.821032i	−0.164491	−	0.0440753i	−0.340125	+	0.940380i	$0.610469\pi$
$348$		0			0
$349$	15.9915	−	4.28490i	0.856003	−	0.229365i	0.195978	−	0.980608i	$-0.437212\pi$
$349$	15.9915	−	4.28490i	0.856003	−	0.229365i	0.660026	+	0.751243i	$0.270545\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−19.7145	−	11.3822i	−1.04930	−	0.605813i	−0.126846	−	0.991922i	$-0.540486\pi$
$353$	−19.7145	−	11.3822i	−1.04930	−	0.605813i	−0.922453	+	0.386109i	$0.873819\pi$
$354$		0			0
$355$	23.6649	+	6.34099i	1.25600	+	0.336545i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			7.54182i			0.398042i	0.979995	+	0.199021i	$0.0637762\pi$
$359$			7.54182i			0.398042i	−0.979995	+	0.199021i	$0.936224\pi$
$360$		0			0
$361$			6.57197i			0.345893i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	31.5329	+	8.44921i	1.65051	+	0.442252i
$366$		0			0
$367$	−20.6334	−	11.9127i	−1.07706	−	0.621839i	−0.146955	−	0.989143i	$-0.546947\pi$
$367$	−20.6334	−	11.9127i	−1.07706	−	0.621839i	−0.930101	+	0.367304i	$0.880281\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.92969	−	0.517059i	0.100185	−	0.0268444i
$372$		0			0
$373$	8.84822	+	2.37087i	0.458143	+	0.122759i	0.480507	−	0.876991i	$-0.340453\pi$
$373$	8.84822	+	2.37087i	0.458143	+	0.122759i	−0.0223639	+	0.999750i	$0.507119\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	7.51422			0.387002
$378$		0			0
$379$	−0.636018	−	0.636018i	−0.0326701	−	0.0326701i	0.690583	−	0.723253i	$-0.257354\pi$
$379$	−0.636018	−	0.636018i	−0.0326701	−	0.0326701i	−0.723253	+	0.690583i	$0.757354\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.80598	−	11.7883i	−0.347769	−	0.602354i	0.638084	−	0.769967i	$-0.279727\pi$
$383$	−6.80598	−	11.7883i	−0.347769	−	0.602354i	−0.985853	+	0.167613i	$0.946394\pi$
$384$		0			0
$385$	−10.0398	+	17.3895i	−0.511678	+	0.886252i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.00251	−	2.14427i	0.405744	−	0.108719i	−0.0501744	−	0.998740i	$-0.515978\pi$
$389$	8.00251	−	2.14427i	0.405744	−	0.108719i	0.455918	+	0.890022i	$0.349311\pi$
$390$		0			0
$391$	−16.7688	−	29.0444i	−0.848034	−	1.46884i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	17.1370	−	17.1370i	0.862258	−	0.862258i
$396$		0			0
$397$	−6.79264	−	6.79264i	−0.340913	−	0.340913i	0.515798	−	0.856710i	$-0.327496\pi$
$397$	−6.79264	−	6.79264i	−0.340913	−	0.340913i	−0.856710	+	0.515798i	$0.827496\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.01378	+	2.89471i	−0.250376	+	0.144555i	−0.619936	−	0.784652i	$-0.712842\pi$
$401$	−5.01378	+	2.89471i	−0.250376	+	0.144555i	0.369560	+	0.929207i	$0.379508\pi$
$402$		0			0
$403$	0.627898	+	2.34335i	0.0312778	+	0.116731i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	12.1817	+	7.03312i	0.603826	+	0.348619i
$408$		0			0
$409$	11.5152	−	6.64832i	0.569392	−	0.328738i	−0.187515	−	0.982262i	$-0.560043\pi$
$409$	11.5152	−	6.64832i	0.569392	−	0.328738i	0.756906	+	0.653523i	$0.226710\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−15.1426	+	15.1426i	−0.745120	+	0.745120i
$414$		0			0
$415$		−	29.6834i		−	1.45710i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.29438	+	12.2948i	−0.160941	+	0.600639i	0.837582	+	0.546311i	$0.183968\pi$
$419$	−3.29438	+	12.2948i	−0.160941	+	0.600639i	−0.998523	+	0.0543282i	$0.982698\pi$
$420$		0			0
$421$	1.72149	+	6.42470i	0.0839004	+	0.313121i	0.995104	−	0.0988365i	$-0.0315121\pi$
$421$	1.72149	+	6.42470i	0.0839004	+	0.313121i	−0.911203	+	0.411957i	$0.864845\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−18.2119	+	31.5440i	−0.883408	+	1.53011i
$426$		0			0
$427$	−4.69083	+	17.5064i	−0.227005	+	0.847194i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	37.3843			1.80074			0.900370	−	0.435126i	$-0.143296\pi$
$431$	37.3843			1.80074			0.900370	+	0.435126i	$0.143296\pi$
$432$		0			0
$433$	−18.8561			−0.906166			−0.453083	−	0.891468i	$-0.649676\pi$
$433$	−18.8561			−0.906166			−0.453083	+	0.891468i	$0.649676\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.39522	+	27.5993i	−0.353761	+	1.32026i
$438$		0			0
$439$	4.21577	−	7.30192i	0.201208	−	0.348502i	−0.747710	−	0.664025i	$-0.768847\pi$
$439$	4.21577	−	7.30192i	0.201208	−	0.348502i	0.948918	+	0.315523i	$0.102180\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.46777	−	9.20983i	−0.117247	−	0.437572i	0.882198	−	0.470879i	$-0.156063\pi$
$443$	−2.46777	−	9.20983i	−0.117247	−	0.437572i	−0.999445	+	0.0333063i	$0.989396\pi$
$444$		0			0
$445$	−13.6482	+	50.9358i	−0.646987	+	2.41459i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	7.54348i		−	0.355999i	−0.984031	−	0.177999i	$-0.943038\pi$
$449$		−	7.54348i		−	0.355999i	0.984031	−	0.177999i	$-0.0569625\pi$
$450$		0			0
$451$	1.88170	−	1.88170i	0.0886058	−	0.0886058i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.59164	+	4.96039i	−0.402782	+	0.232546i
$456$		0			0
$457$	−5.15261	−	2.97486i	−0.241029	−	0.139158i	0.374621	−	0.927178i	$-0.377773\pi$
$457$	−5.15261	−	2.97486i	−0.241029	−	0.139158i	−0.615649	+	0.788020i	$0.711106\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.37780	−	23.8023i	−0.297044	−	1.10858i	−0.939581	−	0.342328i	$-0.888785\pi$
$461$	−6.37780	−	23.8023i	−0.297044	−	1.10858i	0.642537	−	0.766255i	$-0.277882\pi$
$462$		0			0
$463$	20.8183	−	12.0194i	0.967507	−	0.558590i	0.0690315	−	0.997614i	$-0.478009\pi$
$463$	20.8183	−	12.0194i	0.967507	−	0.558590i	0.898475	+	0.439024i	$0.144676\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.3702	+	25.3702i	1.17399	+	1.17399i	0.981249	+	0.192744i	$0.0617388\pi$
$467$	25.3702	+	25.3702i	1.17399	+	1.17399i	0.192744	+	0.981249i	$0.438261\pi$
$468$		0			0
$469$	5.30936	−	5.30936i	0.245163	−	0.245163i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.57520	−	2.72833i	−0.0724278	−	0.125449i
$474$		0			0
$475$	29.9745	−	8.03166i	1.37533	−	0.368518i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.498647	−	0.863682i	0.0227838	−	0.0394626i	−0.854409	−	0.519602i	$-0.826080\pi$
$479$	0.498647	−	0.863682i	0.0227838	−	0.0394626i	0.877192	+	0.480139i	$0.159414\pi$
$480$		0			0
$481$	3.47486	+	6.01863i	0.158440	+	0.274426i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−34.3904	−	34.3904i	−1.56159	−	1.56159i
$486$		0			0
$487$	18.8397			0.853709			0.426855	−	0.904320i	$-0.359622\pi$
$487$	18.8397			0.853709			0.426855	+	0.904320i	$0.359622\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.535020	+	0.143358i	0.0241451	+	0.00646966i	0.270871	−	0.962616i	$-0.412688\pi$
$491$	0.535020	+	0.143358i	0.0241451	+	0.00646966i	−0.246726	+	0.969085i	$0.579355\pi$
$492$		0			0
$493$	29.0661	−	7.78824i	1.30907	−	0.350765i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	14.7591	+	8.52115i	0.662035	+	0.382226i
$498$		0			0
$499$	42.1874	+	11.3041i	1.88857	+	0.506041i	0.998764	+	0.0497007i	$0.0158267\pi$
$499$	42.1874	+	11.3041i	1.88857	+	0.506041i	0.889805	+	0.456340i	$0.150840\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	20.7324i		−	0.924412i	−0.886773	−	0.462206i	$-0.847058\pi$
$503$		−	20.7324i		−	0.924412i	0.886773	−	0.462206i	$-0.152942\pi$
$504$		0			0
$505$		−	15.1733i		−	0.675203i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.69736	+	2.59840i	0.429828	+	0.115172i	0.467245	−	0.884128i	$-0.345246\pi$
$509$	9.69736	+	2.59840i	0.429828	+	0.115172i	−0.0374174	+	0.999300i	$0.511913\pi$
$510$		0			0
$511$	19.6661	+	11.3542i	0.869976	+	0.502281i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−15.9956	+	4.28602i	−0.704852	+	0.188865i
$516$		0			0
$517$	−14.5776	−	3.90607i	−0.641124	−	0.171789i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.20573			0.140445			0.0702227	−	0.997531i	$-0.477629\pi$
$521$	3.20573			0.140445			0.0702227	+	0.997531i	$0.477629\pi$
$522$		0			0
$523$	28.1479	+	28.1479i	1.23082	+	1.23082i	0.963648	+	0.267175i	$0.0860902\pi$
$523$	28.1479	+	28.1479i	1.23082	+	1.23082i	0.267175	+	0.963648i	$0.413910\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.85760	+	8.41362i	0.211601	+	0.366503i
$528$		0			0
$529$	21.3456	−	36.9717i	0.928070	−	1.60746i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.26998	−	0.340291i	0.0550091	−	0.0147396i
$534$		0			0
$535$	10.5453	+	18.2650i	0.455914	+	0.789666i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.475101	−	0.475101i	0.0204640	−	0.0204640i
$540$		0			0
$541$	14.6373	+	14.6373i	0.629307	+	0.629307i	0.947894	−	0.318586i	$-0.103208\pi$
$541$	14.6373	+	14.6373i	0.629307	+	0.629307i	−0.318586	+	0.947894i	$0.603208\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−31.1683	+	17.9950i	−1.33510	+	0.770822i
$546$		0			0
$547$	−4.55558	−	17.0017i	−0.194783	−	0.726938i	−0.992323	−	0.123673i	$-0.960533\pi$
$547$	−4.55558	−	17.0017i	−0.194783	−	0.726938i	0.797541	−	0.603265i	$-0.206134\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−22.2022	−	12.8185i	−0.945847	−	0.546085i
$552$		0			0
$553$	14.5999	−	8.42924i	0.620850	−	0.358448i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.32037	−	8.32037i	0.352546	−	0.352546i	−0.508510	−	0.861056i	$-0.669804\pi$
$557$	8.32037	−	8.32037i	0.352546	−	0.352546i	0.861056	+	0.508510i	$0.169804\pi$
$558$		0			0
$559$		−	1.55652i		−	0.0658337i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5.81439	−	21.6996i	0.245047	−	0.914529i	−0.728312	−	0.685245i	$-0.759695\pi$
$563$	5.81439	−	21.6996i	0.245047	−	0.914529i	0.973360	−	0.229284i	$-0.0736383\pi$
$564$		0			0
$565$	−8.85525	−	33.0482i	−0.372543	−	1.39035i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.57037	+	13.1123i	−0.317367	+	0.549695i	−0.979938	−	0.199304i	$-0.936132\pi$
$569$	−7.57037	+	13.1123i	−0.317367	+	0.549695i	0.662571	+	0.748999i	$0.269465\pi$
$570$		0			0
$571$	8.82715	−	32.9434i	0.369405	−	1.37864i	−0.491945	−	0.870626i	$-0.663714\pi$
$571$	8.82715	−	32.9434i	0.369405	−	1.37864i	0.861350	−	0.508012i	$-0.169619\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−71.3446			−2.97528
$576$		0			0
$577$	19.9524			0.830629			0.415315	−	0.909678i	$-0.363671\pi$
$577$	19.9524			0.830629			0.415315	+	0.909678i	$0.363671\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.34414	−	19.9446i	0.221712	−	0.827442i
$582$		0			0
$583$	0.808347	−	1.40010i	0.0334783	−	0.0579861i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.04265	−	30.0156i	−0.331955	−	1.23887i	−0.907132	−	0.420846i	$-0.861733\pi$
$587$	−8.04265	−	30.0156i	−0.331955	−	1.23887i	0.575177	−	0.818029i	$-0.304933\pi$
$588$		0			0
$589$	2.14226	−	7.99501i	0.0882701	−	0.329429i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			38.3863i			1.57634i	0.615460	+	0.788168i	$0.288970\pi$
$593$			38.3863i			1.57634i	−0.615460	+	0.788168i	$0.711030\pi$
$594$		0			0
$595$	−28.0924	+	28.0924i	−1.15168	+	1.15168i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−24.9602	+	14.4108i	−1.01985	+	0.588809i	−0.914060	−	0.405580i	$-0.867070\pi$
$599$	−24.9602	+	14.4108i	−1.01985	+	0.588809i	−0.105787	+	0.994389i	$0.533736\pi$
$600$		0			0
$601$	−19.8695	−	11.4716i	−0.810492	−	0.467938i	0.0366348	−	0.999329i	$-0.488336\pi$
$601$	−19.8695	−	11.4716i	−0.810492	−	0.467938i	−0.847127	+	0.531391i	$0.821670\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.37146	−	23.7786i	−0.259037	−	0.966738i
$606$		0			0
$607$	−16.8592	+	9.73364i	−0.684292	+	0.395076i	−0.801470	−	0.598035i	$-0.795949\pi$
$607$	−16.8592	+	9.73364i	−0.684292	+	0.395076i	0.117178	+	0.993111i	$0.462615\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.27251	−	5.27251i	−0.213303	−	0.213303i
$612$		0			0
$613$	−10.5918	+	10.5918i	−0.427797	+	0.427797i	−0.887877	−	0.460080i	$-0.847821\pi$
$613$	−10.5918	+	10.5918i	−0.427797	+	0.427797i	0.460080	+	0.887877i	$0.347821\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.33080	+	16.1614i	0.375644	+	0.650634i	0.990423	−	0.138065i	$-0.0440882\pi$
$617$	9.33080	+	16.1614i	0.375644	+	0.650634i	−0.614779	+	0.788699i	$0.710755\pi$
$618$		0			0
$619$	−21.0028	+	5.62767i	−0.844172	+	0.226195i	−0.654887	−	0.755727i	$-0.727284\pi$
$619$	−21.0028	+	5.62767i	−0.844172	+	0.226195i	−0.189285	+	0.981922i	$0.560617\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−18.3407	+	31.7671i	−0.734807	+	1.27272i
$624$		0			0
$625$	4.23597	+	7.33691i	0.169439	+	0.293477i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	19.6794	+	19.6794i	0.784667	+	0.784667i
$630$		0			0
$631$	−26.5211			−1.05579			−0.527894	−	0.849310i	$-0.677018\pi$
$631$	−26.5211			−1.05579			−0.527894	+	0.849310i	$0.677018\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	17.0742	+	4.57502i	0.677569	+	0.181554i
$636$		0			0
$637$	0.320651	−	0.0859183i	0.0127047	−	0.00340421i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.35222	−	0.780702i	−0.0534093	−	0.0308359i	0.473058	−	0.881032i	$-0.343150\pi$
$641$	−1.35222	−	0.780702i	−0.0534093	−	0.0308359i	−0.526467	+	0.850196i	$0.676484\pi$
$642$		0			0
$643$	−33.6691	−	9.02160i	−1.32778	−	0.355777i	−0.475892	−	0.879503i	$-0.657875\pi$
$643$	−33.6691	−	9.02160i	−1.32778	−	0.355777i	−0.851887	+	0.523726i	$0.824542\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			7.73678i			0.304164i	0.988368	+	0.152082i	$0.0485978\pi$
$647$			7.73678i			0.304164i	−0.988368	+	0.152082i	$0.951402\pi$
$648$		0			0
$649$			17.3300i			0.680264i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−14.2429	−	3.81636i	−0.557366	−	0.149346i	−0.0308703	−	0.999523i	$-0.509828\pi$
$653$	−14.2429	−	3.81636i	−0.557366	−	0.149346i	−0.526496	+	0.850178i	$0.676495\pi$
$654$		0			0
$655$	−27.8615	−	16.0858i	−1.08864	−	0.628526i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	33.8013	−	9.05703i	1.31671	−	0.352812i	0.468967	−	0.883216i	$-0.344626\pi$
$659$	33.8013	−	9.05703i	1.31671	−	0.352812i	0.847745	+	0.530404i	$0.177960\pi$
$660$		0			0
$661$	35.8049	+	9.59389i	1.39265	+	0.373159i	0.875699	−	0.482857i	$-0.160401\pi$
$661$	35.8049	+	9.59389i	1.39265	+	0.373159i	0.516949	+	0.856016i	$0.327068\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	33.8476			1.31255
$666$		0			0
$667$	41.6777	+	41.6777i	1.61377	+	1.61377i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	7.33342	+	12.7019i	0.283103	+	0.490350i
$672$		0			0
$673$	−14.5046	+	25.1226i	−0.559109	+	0.968406i	0.438462	+	0.898750i	$0.355523\pi$
$673$	−14.5046	+	25.1226i	−0.559109	+	0.968406i	−0.997571	+	0.0696559i	$0.977810\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.8441	−	5.58517i	0.801105	−	0.214655i	0.165036	−	0.986288i	$-0.447226\pi$
$677$	20.8441	−	5.58517i	0.801105	−	0.214655i	0.636069	+	0.771632i	$0.280559\pi$
$678$		0			0
$679$	−16.9157	−	29.2989i	−0.649165	−	1.12439i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−19.1487	+	19.1487i	−0.732704	+	0.732704i	−0.971155	−	0.238451i	$-0.923360\pi$
$683$	−19.1487	+	19.1487i	−0.732704	+	0.732704i	0.238451	+	0.971155i	$0.423360\pi$
$684$		0			0
$685$	−43.5861	−	43.5861i	−1.66534	−	1.66534i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.691747	−	0.399380i	0.0263534	−	0.0152152i
$690$		0			0
$691$	−8.78531	−	32.7872i	−0.334209	−	1.24728i	−0.904724	−	0.425997i	$-0.859923\pi$
$691$	−8.78531	−	32.7872i	−0.334209	−	1.24728i	0.570516	−	0.821287i	$-0.306743\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	22.8971	+	13.2197i	0.868538	+	0.501450i
$696$		0			0
$697$	4.55978	−	2.63259i	0.172714	−	0.0997165i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	28.6582	−	28.6582i	1.08240	−	1.08240i	0.0861190	−	0.996285i	$-0.472553\pi$
$701$	28.6582	−	28.6582i	1.08240	−	1.08240i	0.996285	−	0.0861190i	$-0.0274465\pi$
$702$		0			0
$703$		−	23.7109i		−	0.894275i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.73177	−	10.1951i	0.102739	−	0.383426i
$708$		0			0
$709$	2.14398	+	8.00146i	0.0805190	+	0.300501i	0.994428	−	0.105418i	$-0.0336181\pi$
$709$	2.14398	+	8.00146i	0.0805190	+	0.300501i	−0.913909	+	0.405919i	$0.866951\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.51476	+	16.4800i	−0.356330	+	0.617182i
$714$		0			0
$715$	−2.07790	+	7.75484i	−0.0777091	+	0.290014i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−17.3387			−0.646625			−0.323312	−	0.946292i	$-0.604796\pi$
$719$	−17.3387			−0.646625			−0.323312	+	0.946292i	$0.604796\pi$
$720$		0			0
$721$	−11.5193			−0.429001
$722$		0			0
$723$		0			0
$724$		0			0
$725$	16.5680	−	61.8325i	0.615318	−	2.29640i
$726$		0			0
$727$	−25.1782	+	43.6100i	−0.933809	+	1.61741i	−0.157066	+	0.987588i	$0.550204\pi$
$727$	−25.1782	+	43.6100i	−0.933809	+	1.61741i	−0.776743	+	0.629817i	$0.783130\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.61328	−	6.02084i	−0.0596693	−	0.222689i
$732$		0			0
$733$	−0.123620	+	0.461357i	−0.00456602	+	0.0170406i	−0.968171	−	0.250289i	$-0.919474\pi$
$733$	−0.123620	+	0.461357i	−0.00456602	+	0.0170406i	0.963605	+	0.267329i	$0.0861411\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	6.07632i		−	0.223824i
$738$		0			0
$739$	−35.7895	+	35.7895i	−1.31654	+	1.31654i	−0.400038	+	0.916499i	$0.631003\pi$
$739$	−35.7895	+	35.7895i	−1.31654	+	1.31654i	−0.916499	+	0.400038i	$0.868997\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	40.8564	−	23.5884i	1.49888	−	0.865376i	0.498877	−	0.866673i	$-0.333746\pi$
$743$	40.8564	−	23.5884i	1.49888	−	0.865376i	0.999999	+	0.00129681i	$0.000412789\pi$
$744$		0			0
$745$	12.0568	+	6.96101i	0.441728	+	0.255032i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.79711	+	14.1710i	0.138743	+	0.517798i
$750$		0			0
$751$	12.6419	−	7.29878i	0.461308	−	0.266336i	−0.251286	−	0.967913i	$-0.580853\pi$
$751$	12.6419	−	7.29878i	0.461308	−	0.266336i	0.712594	+	0.701577i	$0.247520\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.11001	+	7.11001i	0.258760	+	0.258760i
$756$		0			0
$757$	22.1300	−	22.1300i	0.804329	−	0.804329i	−0.179440	−	0.983769i	$-0.557429\pi$
$757$	22.1300	−	22.1300i	0.804329	−	0.804329i	0.983769	+	0.179440i	$0.0574286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.0131	−	22.5393i	−0.471724	−	0.817050i	0.527753	−	0.849398i	$-0.323035\pi$
$761$	−13.0131	−	22.5393i	−0.471724	−	0.817050i	−0.999477	+	0.0323484i	$0.989701\pi$
$762$		0			0
$763$	−24.1821	+	6.47957i	−0.875451	+	0.234576i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.28113	+	7.41513i	−0.154583	+	0.267745i
$768$		0			0
$769$	−17.7312	−	30.7114i	−0.639404	−	1.10748i	−0.985564	−	0.169305i	$-0.945848\pi$
$769$	−17.7312	−	30.7114i	−0.639404	−	1.10748i	0.346159	−	0.938176i	$-0.387486\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.23556	−	3.23556i	−0.116375	−	0.116375i	0.646521	−	0.762896i	$-0.276223\pi$
$773$	−3.23556	−	3.23556i	−0.116375	−	0.116375i	−0.762896	+	0.646521i	$0.776223\pi$
$774$		0			0
$775$	20.6672			0.742388
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.33291	−	1.16100i	−0.155243	−	0.0415972i
$780$		0			0
$781$	13.3216	−	3.56951i	0.476683	−	0.127727i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	15.9691	+	9.21977i	0.569962	+	0.329068i
$786$		0			0
$787$	−24.4646	−	6.55528i	−0.872070	−	0.233671i	−0.205087	−	0.978744i	$-0.565748\pi$
$787$	−24.4646	−	6.55528i	−0.872070	−	0.233671i	−0.666983	+	0.745073i	$0.732415\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	23.7997i		−	0.846221i
$792$		0			0
$793$			7.24645i			0.257329i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−30.4414	−	8.15674i	−1.07829	−	0.288927i	−0.324394	−	0.945922i	$-0.605160\pi$
$797$	−30.4414	−	8.15674i	−1.07829	−	0.288927i	−0.753895	+	0.656995i	$0.771827\pi$
$798$		0			0
$799$	−25.8596	−	14.9300i	−0.914847	−	0.528187i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	17.7507	−	4.75628i	0.626407	−	0.167845i
$804$		0			0
$805$	−75.1664	−	20.1408i	−2.64927	−	0.709869i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−46.7989			−1.64536			−0.822681	−	0.568503i	$-0.807523\pi$
$809$	−46.7989			−1.64536			−0.822681	+	0.568503i	$0.807523\pi$
$810$		0			0
$811$	−32.5365	−	32.5365i	−1.14251	−	1.14251i	−0.987989	−	0.154522i	$-0.950616\pi$
$811$	−32.5365	−	32.5365i	−1.14251	−	1.14251i	−0.154522	−	0.987989i	$-0.549384\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−22.0734	−	38.2322i	−0.773197	−	1.33922i
$816$		0			0
$817$	−2.65526	+	4.59904i	−0.0928956	+	0.160900i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.3044	+	2.76106i	−0.359627	+	0.0963618i	−0.434108	−	0.900861i	$-0.642937\pi$
$821$	−10.3044	+	2.76106i	−0.359627	+	0.0963618i	0.0744814	+	0.997222i	$0.476270\pi$
$822$		0			0
$823$	9.53960	+	16.5231i	0.332530	+	0.575958i	0.983007	−	0.183567i	$-0.0587645\pi$
$823$	9.53960	+	16.5231i	0.332530	+	0.575958i	−0.650478	+	0.759526i	$0.725431\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.6788	−	11.6788i	0.406113	−	0.406113i	−0.474268	−	0.880381i	$-0.657287\pi$
$827$	11.6788	−	11.6788i	0.406113	−	0.406113i	0.880381	+	0.474268i	$0.157287\pi$
$828$		0			0
$829$	29.2209	+	29.2209i	1.01488	+	1.01488i	0.999888	+	0.0149948i	$0.00477317\pi$
$829$	29.2209	+	29.2209i	1.01488	+	1.01488i	0.0149948	+	0.999888i	$0.495227\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.15127	−	0.664689i	0.0398893	−	0.0230301i
$834$		0			0
$835$	7.90094	+	29.4867i	0.273423	+	1.02043i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.64393	−	2.68117i	−0.160326	−	0.0925643i	0.417690	−	0.908589i	$-0.362840\pi$
$839$	−4.64393	−	2.68117i	−0.160326	−	0.0925643i	−0.578016	+	0.816025i	$0.696173\pi$
$840$		0			0
$841$	−20.6847	+	11.9423i	−0.713267	+	0.411805i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	31.3465	−	31.3465i	1.07835	−	1.07835i
$846$		0			0
$847$		−	17.1242i		−	0.588394i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−14.1090	+	52.6557i	−0.483652	+	1.80501i
$852$		0			0
$853$	5.89168	+	21.9880i	0.201727	+	0.752856i	0.990422	+	0.138072i	$0.0440904\pi$
$853$	5.89168	+	21.9880i	0.201727	+	0.752856i	−0.788695	+	0.614785i	$0.789243\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.7367	−	37.6490i	0.742510	−	1.28607i	−0.208839	−	0.977950i	$-0.566968\pi$
$857$	21.7367	−	37.6490i	0.742510	−	1.28607i	0.951349	−	0.308115i	$-0.0996983\pi$
$858$		0			0
$859$	−0.490831	+	1.83181i	−0.0167469	+	0.0625005i	−0.973794	−	0.227433i	$-0.926967\pi$
$859$	−0.490831	+	1.83181i	−0.0167469	+	0.0625005i	0.957047	+	0.289934i	$0.0936333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.75112			0.195770			0.0978852	−	0.995198i	$-0.468792\pi$
$863$	5.75112			0.195770			0.0978852	+	0.995198i	$0.468792\pi$
$864$		0			0
$865$	−95.6627			−3.25263
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.53100	−	13.1779i	0.119781	−	0.447029i
$870$		0			0
$871$	1.50106	−	2.59992i	0.0508616	−	0.0880949i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	9.44921	+	35.2649i	0.319442	+	1.19217i
$876$		0			0
$877$	−10.6306	+	39.6739i	−0.358969	+	1.33969i	0.516446	+	0.856320i	$0.327255\pi$
$877$	−10.6306	+	39.6739i	−0.358969	+	1.33969i	−0.875415	+	0.483372i	$0.839412\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	7.20282i		−	0.242669i	−0.992612	−	0.121335i	$-0.961283\pi$
$881$		−	7.20282i		−	0.242669i	0.992612	−	0.121335i	$-0.0387174\pi$
$882$		0			0
$883$	30.8474	−	30.8474i	1.03810	−	1.03810i	0.0388519	−	0.999245i	$-0.487630\pi$
$883$	30.8474	−	30.8474i	1.03810	−	1.03810i	0.999245	−	0.0388519i	$-0.0123701\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	34.5994	−	19.9760i	1.16173	−	0.670728i	0.210016	−	0.977698i	$-0.432649\pi$
$887$	34.5994	−	19.9760i	1.16173	−	0.670728i	0.951719	+	0.306970i	$0.0993152\pi$
$888$		0			0
$889$	10.6487	+	6.14801i	0.357145	+	0.206198i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.58431	+	24.5730i	0.220336	+	0.822304i
$894$		0			0
$895$	−66.3904	+	38.3305i	−2.21919	+	1.28125i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.0732	−	12.0732i	−0.402665	−	0.402665i
$900$		0			0
$901$	2.26183	−	2.26183i	0.0753526	−	0.0753526i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−21.5259	−	37.2840i	−0.715546	−	1.23936i
$906$		0			0
$907$	43.5725	−	11.6752i	1.44680	−	0.387670i	0.551892	−	0.833916i	$-0.313906\pi$
$907$	43.5725	−	11.6752i	1.44680	−	0.387670i	0.894910	+	0.446246i	$0.147239\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.452588	+	0.783905i	−0.0149949	+	0.0259719i	−0.873425	−	0.486958i	$-0.838107\pi$
$911$	−0.452588	+	0.783905i	−0.0149949	+	0.0259719i	0.858431	+	0.512930i	$0.171440\pi$
$912$		0			0
$913$	−8.35479	−	14.4709i	−0.276503	−	0.478917i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.8244	−	15.8244i	−0.522566	−	0.522566i
$918$		0			0
$919$	0.631829			0.0208421			0.0104211	−	0.999946i	$-0.496683\pi$
$919$	0.631829			0.0208421			0.0104211	+	0.999946i	$0.496683\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.58179	+	1.76359i	0.216642	+	0.0580492i
$924$		0			0
$925$	57.1873	−	15.3233i	1.88031	−	0.503826i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	21.7169	+	12.5383i	0.712509	+	0.411367i	0.811989	−	0.583672i	$-0.198385\pi$
$929$	21.7169	+	12.5383i	0.712509	+	0.411367i	−0.0994805	+	0.995040i	$0.531718\pi$
$930$		0			0
$931$	−1.09399	−	0.293135i	−0.0358542	−	0.00960711i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			32.1505i			1.05143i
$936$		0			0
$937$			40.0398i			1.30804i	0.756476	+	0.654021i	$0.226919\pi$
$937$			40.0398i			1.30804i	−0.756476	+	0.654021i	$0.773081\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.3853	+	2.78273i	0.338551	+	0.0907146i	0.424089	−	0.905620i	$-0.360594\pi$
$941$	10.3853	+	2.78273i	0.338551	+	0.0907146i	−0.0855380	+	0.996335i	$0.527261\pi$
$942$		0			0
$943$	8.93140	+	5.15654i	0.290846	+	0.167920i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−37.6297	+	10.0828i	−1.22280	+	0.327648i	−0.811772	−	0.583975i	$-0.801497\pi$
$947$	−37.6297	+	10.0828i	−1.22280	+	0.327648i	−0.411028	+	0.911623i	$0.634830\pi$
$948$		0			0
$949$	8.77007	+	2.34993i	0.284689	+	0.0762821i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	7.83389			0.253765			0.126882	−	0.991918i	$-0.459503\pi$
$953$	7.83389			0.253765			0.126882	+	0.991918i	$0.459503\pi$
$954$		0			0
$955$	−14.7419	−	14.7419i	−0.477037	−	0.477037i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−21.4388	−	37.1331i	−0.692295	−	1.19909i
$960$		0			0
$961$	−12.7438	+	22.0728i	−0.411089	+	0.712027i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−90.2370	+	24.1789i	−2.90483	+	0.778347i
$966$		0			0
$967$	−22.1358	−	38.3403i	−0.711839	−	1.23294i	−0.964166	−	0.265299i	$-0.914529\pi$
$967$	−22.1358	−	38.3403i	−0.711839	−	1.23294i	0.252328	−	0.967642i	$-0.418804\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	28.0737	−	28.0737i	0.900928	−	0.900928i	−0.0945888	−	0.995516i	$-0.530154\pi$
$971$	28.0737	−	28.0737i	0.900928	−	0.900928i	0.995516	+	0.0945888i	$0.0301536\pi$
$972$		0			0
$973$	13.0048	+	13.0048i	0.416914	+	0.416914i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.8614	−	8.58022i	0.475458	−	0.274506i	−0.243064	−	0.970010i	$-0.578152\pi$
$977$	14.8614	−	8.58022i	0.475458	−	0.274506i	0.718522	+	0.695505i	$0.244819\pi$
$978$		0			0
$979$	7.68293	+	28.6731i	0.245547	+	0.916396i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−26.8455	−	15.4993i	−0.856240	−	0.494350i	0.00651160	−	0.999979i	$-0.497927\pi$
$983$	−26.8455	−	15.4993i	−0.856240	−	0.494350i	−0.862751	+	0.505629i	$0.831261\pi$
$984$		0			0
$985$	19.6423	−	11.3405i	0.625854	−	0.361337i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.63324	−	8.63324i	0.274521	−	0.274521i
$990$		0			0
$991$		−	37.2374i		−	1.18289i	−0.806347	−	0.591443i	$-0.798558\pi$
$991$		−	37.2374i		−	1.18289i	0.806347	−	0.591443i	$-0.201442\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	14.1008	−	52.6247i	0.447024	−	1.66832i
$996$		0			0
$997$	−3.73234	−	13.9293i	−0.118204	−	0.441145i	0.881302	−	0.472553i	$-0.156667\pi$
$997$	−3.73234	−	13.9293i	−0.118204	−	0.441145i	−0.999507	+	0.0314082i	$0.990001\pi$
$998$		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.1007.21		88
3.2	odd	2		576.2.y.a.47.1		88
4.3	odd	2		432.2.v.a.35.21		88
9.4	even	3		576.2.y.a.239.10		88
9.5	odd	6	inner	1728.2.z.a.1583.21		88
12.11	even	2		144.2.u.a.83.2	yes	88
16.5	even	4		432.2.v.a.251.14		88
16.11	odd	4	inner	1728.2.z.a.143.21		88
36.23	even	6		432.2.v.a.179.14		88
36.31	odd	6		144.2.u.a.131.9	yes	88
48.5	odd	4		144.2.u.a.11.9	✓	88
48.11	even	4		576.2.y.a.335.10		88
144.5	odd	12		432.2.v.a.395.21		88
144.59	even	12	inner	1728.2.z.a.719.21		88
144.85	even	12		144.2.u.a.59.2	yes	88
144.139	odd	12		576.2.y.a.527.1		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.9	✓	88	48.5	odd	4
144.2.u.a.59.2	yes	88	144.85	even	12
144.2.u.a.83.2	yes	88	12.11	even	2
144.2.u.a.131.9	yes	88	36.31	odd	6
432.2.v.a.35.21		88	4.3	odd	2
432.2.v.a.179.14		88	36.23	even	6
432.2.v.a.251.14		88	16.5	even	4
432.2.v.a.395.21		88	144.5	odd	12
576.2.y.a.47.1		88	3.2	odd	2
576.2.y.a.239.10		88	9.4	even	3
576.2.y.a.335.10		88	48.11	even	4
576.2.y.a.527.1		88	144.139	odd	12
1728.2.z.a.143.21		88	16.11	odd	4	inner
1728.2.z.a.719.21		88	144.59	even	12	inner
1728.2.z.a.1007.21		88	1.1	even	1	trivial
1728.2.z.a.1583.21		88	9.5	odd	6	inner

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)

\(f(q)\)	\(=\)	\(q+(0.961558 - 3.58858i) q^{5} +(1.29216 - 2.23809i) q^{7} +(-0.541286 - 2.02011i) q^{11} +(0.267433 - 0.998074i) q^{13} -4.13788i q^{17} +(-2.49279 + 2.49279i) q^{19} +(7.01915 - 4.05251i) q^{23} +(-7.62322 - 4.40127i) q^{25} +(1.88218 + 7.02439i) q^{29} +(-2.03331 + 1.17393i) q^{31} +(-6.78909 - 6.78909i) q^{35} +(-4.75590 + 4.75590i) q^{37} +(0.636217 + 1.10196i) q^{41} +(1.45505 - 0.389880i) q^{43} +(3.60814 - 6.24948i) q^{47} +(0.160635 + 0.278228i) q^{49} +(0.546616 + 0.546616i) q^{53} -7.76980 q^{55} +(-8.00411 - 2.14469i) q^{59} +(-6.77407 + 1.81511i) q^{61} +(-3.32452 - 1.91941i) q^{65} +(2.80643 + 0.751980i) q^{67} +6.59449i q^{71} +8.78699i q^{73} +(-5.22061 - 1.39886i) q^{77} +(5.64940 + 3.26168i) q^{79} +(7.71754 - 2.06791i) q^{83} +(-14.8491 - 3.97882i) q^{85} -14.1938 q^{89} +(-1.88821 - 1.88821i) q^{91} +(6.54863 + 11.3426i) q^{95} +(6.54551 - 11.3372i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) \) 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

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