LMFDB - Embedded newform 900.2.bf.c.43.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(7,900)] 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("900.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 8, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.162447943996702457856.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 $ x^16 - x^12 - 15x^8 - 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.3
Root			$-0.825348 - 1.14839i$ of defining polynomial
Character	$\chi$	$=$	900.43
Dual form			900.2.bf.c.607.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.140577 - 1.40721i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-1.96048 - 0.395644i) q^{4} +(0.395644 + 2.41733i) q^{6} +(3.86370 - 1.03528i) q^{7} +(-0.832353 + 2.70318i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-2.29129 - 1.32288i) q^{11} +(3.45730 - 0.216932i) q^{12} +(-1.36954 + 5.11120i) q^{13} +(-0.913701 - 5.58258i) q^{14} +(3.68693 + 1.55130i) q^{16} +(-5.61249 + 5.61249i) q^{17} +(-1.74558 - 3.86690i) q^{18} +2.64575 q^{19} +(-6.00000 + 3.46410i) q^{21} +(-2.18367 + 3.03835i) q^{22} +(3.86370 + 1.03528i) q^{23} +(0.180750 - 4.89564i) q^{24} +(7.00000 + 2.64575i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-7.98430 + 0.500983i) q^{28} +(1.73205 + 1.00000i) q^{29} +(4.58258 - 2.64575i) q^{31} +(2.70130 - 4.97021i) q^{32} +(4.42643 + 1.18606i) q^{33} +(7.10895 + 8.68693i) q^{34} +(-5.68693 + 1.91280i) q^{36} +(3.74166 - 3.74166i) q^{37} +(0.371933 - 3.72313i) q^{38} -9.16515i q^{39} +(3.50000 + 6.06218i) q^{41} +(4.03125 + 8.93023i) q^{42} +(0.258819 + 0.965926i) q^{43} +(3.96863 + 3.50000i) q^{44} +(2.00000 - 5.29150i) q^{46} +(5.79555 - 1.55291i) q^{47} +(-6.86379 - 0.942570i) q^{48} +(7.79423 - 4.50000i) q^{49} +(6.87386 - 11.9059i) q^{51} +(4.70717 - 9.47853i) q^{52} +(3.74166 + 3.74166i) q^{53} +(4.65390 + 5.68693i) q^{54} +(-0.417424 + 11.3060i) q^{56} +(-4.42643 + 1.18606i) q^{57} +(1.65070 - 2.29678i) q^{58} +(-1.32288 - 2.29129i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-3.07892 - 6.82058i) q^{62} +(8.48528 - 8.48528i) q^{63} +(-6.61438 - 4.50000i) q^{64} +(2.29129 - 6.06218i) q^{66} +(-2.32937 + 8.69333i) q^{67} +(13.2237 - 8.78260i) q^{68} -6.92820 q^{69} +(1.89226 + 8.27160i) q^{72} +(9.35414 + 9.35414i) q^{73} +(-4.73930 - 5.79129i) q^{74} +(-5.18693 - 1.04678i) q^{76} +(-10.2224 - 2.73908i) q^{77} +(-12.8973 - 1.28841i) q^{78} +(5.29150 - 9.16515i) q^{79} +(4.50000 - 7.79423i) q^{81} +(9.02277 - 4.07303i) q^{82} +(13.1334 - 4.41742i) q^{84} +(1.39564 - 0.228425i) q^{86} +(-3.34607 - 0.896575i) q^{87} +(5.48313 - 5.09267i) q^{88} +6.00000i q^{89} +21.1660i q^{91} +(-7.16510 - 3.55828i) q^{92} +(-6.48074 + 6.48074i) q^{93} +(-1.37055 - 8.37386i) q^{94} +(-2.29129 + 9.52628i) q^{96} +(0.684771 + 2.55560i) q^{97} +(-5.23675 - 11.6007i) q^{98} -7.93725 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{6} + 4 q^{16} - 96 q^{21} + 112 q^{26} - 36 q^{36} + 56 q^{41} + 32 q^{46} - 80 q^{56} + 48 q^{61} - 28 q^{76} + 72 q^{81} + 4 q^{86}+O(q^{100}) $ 16 * q - 12 * q^6 + 4 * q^16 - 96 * q^21 + 112 * q^26 - 36 * q^36 + 56 * q^41 + 32 * q^46 - 80 * q^56 + 48 * q^61 - 28 * q^76 + 72 * q^81 + 4 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.140577	−	1.40721i	0.0994033	−	0.995047i
$2$	0.140577	−	1.40721i	0.0994033	−	0.995047i
$3$	−1.67303	+	0.448288i	−0.965926	+	0.258819i
$3$	−1.67303	+	0.448288i	−0.965926	+	0.258819i
$4$	−1.96048	−	0.395644i	−0.980238	−	0.197822i
$5$		0			0
$5$		0			0
$6$	0.395644	+	2.41733i	0.161521	+	0.986869i
$7$	3.86370	−	1.03528i	1.46034	−	0.391298i	0.560734	−	0.827996i	$-0.310519\pi$
$7$	3.86370	−	1.03528i	1.46034	−	0.391298i	0.899608	+	0.436698i	$0.143852\pi$
$8$	−0.832353	+	2.70318i	−0.294281	+	0.955719i
$9$	2.59808	−	1.50000i	0.866025	−	0.500000i
$10$		0			0
$11$	−2.29129	−	1.32288i	−0.690849	−	0.398862i	0.113081	−	0.993586i	$-0.463928\pi$
$11$	−2.29129	−	1.32288i	−0.690849	−	0.398862i	−0.803930	+	0.594724i	$0.797261\pi$
$12$	3.45730	−	0.216932i	0.998037	−	0.0626229i
$13$	−1.36954	+	5.11120i	−0.379843	+	1.41759i	0.466296	+	0.884629i	$0.345588\pi$
$13$	−1.36954	+	5.11120i	−0.379843	+	1.41759i	−0.846139	+	0.532963i	$0.821079\pi$
$14$	−0.913701	−	5.58258i	−0.244197	−	1.49201i
$15$		0			0
$16$	3.68693	+	1.55130i	0.921733	+	0.387825i
$17$	−5.61249	+	5.61249i	−1.36123	+	1.36123i	−0.488873	+	0.872355i	$0.662592\pi$
$17$	−5.61249	+	5.61249i	−1.36123	+	1.36123i	−0.872355	+	0.488873i	$0.837408\pi$
$18$	−1.74558	−	3.86690i	−0.411438	−	0.911438i
$19$	2.64575			0.606977			0.303488	−	0.952835i	$-0.401849\pi$
$19$	2.64575			0.606977			0.303488	+	0.952835i	$0.401849\pi$
$20$		0			0
$21$	−6.00000	+	3.46410i	−1.30931	+	0.755929i
$22$	−2.18367	+	3.03835i	−0.465559	+	0.647779i
$23$	3.86370	+	1.03528i	0.805638	+	0.215870i	0.638058	−	0.769988i	$-0.279738\pi$
$23$	3.86370	+	1.03528i	0.805638	+	0.215870i	0.167580	+	0.985858i	$0.446405\pi$
$24$	0.180750	−	4.89564i	0.0368954	−	0.999319i
$25$		0			0
$26$	7.00000	+	2.64575i	1.37281	+	0.518875i
$27$	−3.67423	+	3.67423i	−0.707107	+	0.707107i
$28$	−7.98430	+	0.500983i	−1.50889	+	0.0946769i
$29$	1.73205	+	1.00000i	0.321634	+	0.185695i	0.652121	−	0.758115i	$-0.273880\pi$
$29$	1.73205	+	1.00000i	0.321634	+	0.185695i	−0.330487	+	0.943811i	$0.607213\pi$
$30$		0			0
$31$	4.58258	−	2.64575i	0.823055	−	0.475191i	−0.0284139	−	0.999596i	$-0.509046\pi$
$31$	4.58258	−	2.64575i	0.823055	−	0.475191i	0.851469	+	0.524405i	$0.175712\pi$
$32$	2.70130	−	4.97021i	0.477528	−	0.878617i
$33$	4.42643	+	1.18606i	0.770542	+	0.206466i
$34$	7.10895	+	8.68693i	1.21918	+	1.48980i
$35$		0			0
$36$	−5.68693	+	1.91280i	−0.947822	+	0.318800i
$37$	3.74166	−	3.74166i	0.615125	−	0.615125i	−0.329152	−	0.944277i	$-0.606763\pi$
$37$	3.74166	−	3.74166i	0.615125	−	0.615125i	0.944277	+	0.329152i	$0.106763\pi$
$38$	0.371933	−	3.72313i	0.0603355	−	0.603971i
$39$		−	9.16515i		−	1.46760i
$40$		0			0
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	0.998504	+	0.0546823i	$0.0174146\pi$
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	−0.451896	+	0.892071i	$0.649252\pi$
$42$	4.03125	+	8.93023i	0.622036	+	1.37796i
$43$	0.258819	+	0.965926i	0.0394695	+	0.147302i	0.982849	−	0.184414i	$-0.0590389\pi$
$43$	0.258819	+	0.965926i	0.0394695	+	0.147302i	−0.943379	+	0.331717i	$0.892372\pi$
$44$	3.96863	+	3.50000i	0.598293	+	0.527645i
$45$		0			0
$46$	2.00000	−	5.29150i	0.294884	−	0.780189i
$47$	5.79555	−	1.55291i	0.845369	−	0.226516i	0.189961	−	0.981792i	$-0.439164\pi$
$47$	5.79555	−	1.55291i	0.845369	−	0.226516i	0.655407	+	0.755276i	$0.272497\pi$
$48$	−6.86379	−	0.942570i	−0.990702	−	0.136048i
$49$	7.79423	−	4.50000i	1.11346	−	0.642857i
$50$		0			0
$51$	6.87386	−	11.9059i	0.962533	−	1.66716i
$52$	4.70717	−	9.47853i	0.652767	−	1.31444i
$53$	3.74166	+	3.74166i	0.513956	+	0.513956i	0.915736	−	0.401780i	$-0.131608\pi$
$53$	3.74166	+	3.74166i	0.513956	+	0.513956i	−0.401780	+	0.915736i	$0.631608\pi$
$54$	4.65390	+	5.68693i	0.633316	+	0.773893i
$55$		0			0
$56$	−0.417424	+	11.3060i	−0.0557807	+	1.51083i
$57$	−4.42643	+	1.18606i	−0.586295	+	0.157097i
$58$	1.65070	−	2.29678i	0.216747	−	0.301582i
$59$	−1.32288	−	2.29129i	−0.172224	−	0.298300i	0.766973	−	0.641679i	$-0.221762\pi$
$59$	−1.32288	−	2.29129i	−0.172224	−	0.298300i	−0.939197	+	0.343379i	$0.888429\pi$
$60$		0			0
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	−0.607535	−	0.794293i	$-0.707841\pi$
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	0.991645	+	0.128994i	$0.0411748\pi$
$62$	−3.07892	−	6.82058i	−0.391023	−	0.866214i
$63$	8.48528	−	8.48528i	1.06904	−	1.06904i
$64$	−6.61438	−	4.50000i	−0.826797	−	0.562500i
$65$		0			0
$66$	2.29129	−	6.06218i	0.282038	−	0.746203i
$67$	−2.32937	+	8.69333i	−0.284578	+	1.06206i	0.664569	+	0.747227i	$0.268615\pi$
$67$	−2.32937	+	8.69333i	−0.284578	+	1.06206i	−0.949147	+	0.314833i	$0.898052\pi$
$68$	13.2237	−	8.78260i	1.60361	−	1.06505i
$69$	−6.92820			−0.834058
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	1.89226	+	8.27160i	0.223005	+	0.974817i
$73$	9.35414	+	9.35414i	1.09482	+	1.09482i	0.995006	+	0.0998135i	$0.0318246\pi$
$73$	9.35414	+	9.35414i	1.09482	+	1.09482i	0.0998135	+	0.995006i	$0.468175\pi$
$74$	−4.73930	−	5.79129i	−0.550933	−	0.673224i
$75$		0			0
$76$	−5.18693	−	1.04678i	−0.594982	−	0.120073i
$77$	−10.2224	−	2.73908i	−1.16495	−	0.312148i
$78$	−12.8973	−	1.28841i	−1.46033	−	0.145884i
$79$	5.29150	−	9.16515i	0.595341	−	1.03116i	−0.398158	−	0.917317i	$-0.630350\pi$
$79$	5.29150	−	9.16515i	0.595341	−	1.03116i	0.993499	−	0.113843i	$-0.0363162\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	9.02277	−	4.07303i	0.996399	−	0.449791i
$83$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$83$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$84$	13.1334	−	4.41742i	1.43297	−	0.481981i
$85$		0			0
$86$	1.39564	−	0.228425i	0.150496	−	0.0246317i
$87$	−3.34607	−	0.896575i	−0.358736	−	0.0961230i
$88$	5.48313	−	5.09267i	0.584504	−	0.542880i
$89$			6.00000i			0.635999i	0.948091	+	0.317999i	$0.103011\pi$
$89$			6.00000i			0.635999i	−0.948091	+	0.317999i	$0.896989\pi$
$90$		0			0
$91$			21.1660i			2.21880i
$92$	−7.16510	−	3.55828i	−0.747013	−	0.370977i
$93$	−6.48074	+	6.48074i	−0.672022	+	0.672022i
$94$	−1.37055	−	8.37386i	−0.141362	−	0.863698i
$95$		0			0
$96$	−2.29129	+	9.52628i	−0.233854	+	0.972272i
$97$	0.684771	+	2.55560i	0.0695279	+	0.259482i	0.991937	−	0.126733i	$-0.0404491\pi$
$97$	0.684771	+	2.55560i	0.0695279	+	0.259482i	−0.922409	+	0.386215i	$0.873782\pi$
$98$	−5.23675	−	11.6007i	−0.528991	−	1.17185i
$99$	−7.93725			−0.797724
$100$		0			0
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$	−15.7878	−	11.3467i	−1.56322	−	1.12349i
$103$	5.79555	+	1.55291i	0.571053	+	0.153013i	0.532779	−	0.846254i	$-0.321148\pi$
$103$	5.79555	+	1.55291i	0.571053	+	0.153013i	0.0382735	+	0.999267i	$0.487814\pi$
$104$	−12.6766	−	7.95644i	−1.24304	−	0.780193i
$105$		0			0
$106$	5.79129	−	4.73930i	0.562500	−	0.460322i
$107$	−9.19239	−	9.19239i	−0.888662	−	0.888662i	0.105733	−	0.994395i	$-0.466281\pi$
$107$	−9.19239	−	9.19239i	−0.888662	−	0.888662i	−0.994395	+	0.105733i	$0.966281\pi$
$108$	8.65694	−	5.74956i	0.833014	−	0.553252i
$109$			4.00000i			0.383131i	0.981480	+	0.191565i	$0.0613564\pi$
$109$			4.00000i			0.383131i	−0.981480	+	0.191565i	$0.938644\pi$
$110$		0			0
$111$	−4.58258	+	7.93725i	−0.434959	+	0.753371i
$112$	15.8512	+	2.17677i	1.49780	+	0.205686i
$113$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$113$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$114$	1.04678	+	6.39564i	0.0980395	+	0.599007i
$115$		0			0
$116$	−3.00000	−	2.64575i	−0.278543	−	0.245652i
$117$	4.10862	+	15.3336i	0.379843	+	1.41759i
$118$	−3.41029	+	1.53946i	−0.313942	+	0.141719i
$119$	−15.8745	+	27.4955i	−1.45521	+	2.52050i
$120$		0			0
$121$	−2.00000	−	3.46410i	−0.181818	−	0.314918i
$122$	−6.89034	−	4.95209i	−0.623822	−	0.448341i
$123$	−8.57321	−	8.57321i	−0.773021	−	0.773021i
$124$	−10.0308	+	3.37386i	−0.900793	+	0.302982i
$125$		0			0
$126$	−10.7477	−	13.1334i	−0.957484	−	1.17002i
$127$	5.65685	+	5.65685i	0.501965	+	0.501965i	0.912048	−	0.410083i	$-0.134500\pi$
$127$	5.65685	+	5.65685i	0.501965	+	0.501965i	−0.410083	+	0.912048i	$0.634500\pi$
$128$	−7.26227	+	8.67522i	−0.641900	+	0.766788i
$129$	−0.866025	−	1.50000i	−0.0762493	−	0.132068i
$130$		0			0
$131$	−13.7477	+	7.93725i	−1.20114	+	0.693481i	−0.960810	−	0.277209i	$-0.910591\pi$
$131$	−13.7477	+	7.93725i	−1.20114	+	0.693481i	−0.240335	+	0.970690i	$0.577257\pi$
$132$	−8.20865	−	4.07653i	−0.714471	−	0.354816i
$133$	10.2224	−	2.73908i	0.886394	−	0.237509i
$134$	11.9059	+	4.50000i	1.02851	+	0.388741i
$135$		0			0
$136$	−10.5000	−	19.8431i	−0.900368	−	1.70153i
$137$	−2.05431	−	7.66680i	−0.175512	−	0.655019i	−0.996464	−	0.0840218i	$-0.973223\pi$
$137$	−2.05431	−	7.66680i	−0.175512	−	0.655019i	0.820952	−	0.570997i	$-0.193443\pi$
$138$	−0.973949	+	9.74943i	−0.0829081	+	0.829927i
$139$	9.26013	+	16.0390i	0.785434	+	1.36041i	0.928739	+	0.370733i	$0.120894\pi$
$139$	9.26013	+	16.0390i	0.785434	+	1.36041i	−0.143306	+	0.989678i	$0.545773\pi$
$140$		0			0
$141$	−9.00000	+	5.19615i	−0.757937	+	0.437595i
$142$		0			0
$143$	9.89949	−	9.89949i	0.827837	−	0.827837i
$144$	11.9059	−	1.50000i	0.992157	−	0.125000i
$145$		0			0
$146$	14.4782	−	11.8483i	1.19823	−	0.980569i
$147$	−11.0227	+	11.0227i	−0.909137	+	0.909137i
$148$	−8.81579	+	5.85507i	−0.724654	+	0.481283i
$149$	8.66025	−	5.00000i	0.709476	−	0.409616i	−0.101391	−	0.994847i	$-0.532329\pi$
$149$	8.66025	−	5.00000i	0.709476	−	0.409616i	0.810867	+	0.585231i	$0.198996\pi$
$150$		0			0
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$	−2.20220	+	7.15195i	−0.178622	+	0.580099i
$153$	−6.16294	+	23.0004i	−0.498244	+	1.85947i
$154$	−5.29150	+	14.0000i	−0.426401	+	1.12815i
$155$		0			0
$156$	−3.62614	+	17.9681i	−0.290323	+	1.43860i
$157$	−20.4448	−	5.47817i	−1.63167	−	0.437205i	−0.677271	−	0.735733i	$-0.736838\pi$
$157$	−20.4448	−	5.47817i	−1.63167	−	0.437205i	−0.954401	+	0.298528i	$0.903504\pi$
$158$	−12.1534	−	8.73467i	−0.966874	−	0.694893i
$159$	−7.93725	−	4.58258i	−0.629465	−	0.363422i
$160$		0			0
$161$	16.0000			1.26098
$162$	−10.3355	−	7.42813i	−0.812035	−	0.583609i
$163$	−14.1421	+	14.1421i	−1.10770	+	1.10770i	−0.114245	+	0.993453i	$0.536445\pi$
$163$	−14.1421	+	14.1421i	−1.10770	+	1.10770i	−0.993453	+	0.114245i	$0.963555\pi$
$164$	−4.46320	−	13.2695i	−0.348518	−	1.03617i
$165$		0			0
$166$		0			0
$167$	3.10583	−	11.5911i	0.240336	−	0.896947i	−0.735334	−	0.677705i	$-0.762975\pi$
$167$	3.10583	−	11.5911i	0.240336	−	0.896947i	0.975670	−	0.219242i	$-0.0703585\pi$
$168$	−4.36998	−	19.1024i	−0.337151	−	1.47379i
$169$	−12.9904	−	7.50000i	−0.999260	−	0.576923i
$170$		0			0
$171$	6.87386	−	3.96863i	0.525657	−	0.303488i
$172$	−0.125246	−	1.99607i	−0.00954990	−	0.152199i
$173$	5.11120	−	1.36954i	0.388597	−	0.104124i	−0.0592301	−	0.998244i	$-0.518865\pi$
$173$	5.11120	−	1.36954i	0.388597	−	0.104124i	0.447827	+	0.894120i	$0.352198\pi$
$174$	−1.73205	+	4.58258i	−0.131306	+	0.347404i
$175$		0			0
$176$	−6.39564	−	8.43183i	−0.482090	−	0.635573i
$177$	3.24037	+	3.24037i	0.243561	+	0.243561i
$178$	8.44326	+	0.843465i	0.632849	+	0.0632204i
$179$	5.29150			0.395505			0.197753	−	0.980252i	$-0.436636\pi$
$179$	5.29150			0.395505			0.197753	+	0.980252i	$0.436636\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$	29.7850	+	2.97546i	2.20781	+	0.220556i
$183$	−2.68973	+	10.0382i	−0.198830	+	0.742045i
$184$	−6.01450	+	9.58258i	−0.443395	+	0.706437i
$185$		0			0
$186$	8.20871	+	10.0308i	0.601892	+	0.735494i
$187$	20.2844	−	5.43520i	1.48335	−	0.397461i
$188$	−11.9764	+	0.751475i	−0.873472	+	0.0548069i
$189$	−10.3923	+	18.0000i	−0.755929	+	1.30931i
$190$		0			0
$191$	−9.16515	−	5.29150i	−0.663167	−	0.382880i	0.130316	−	0.991473i	$-0.458401\pi$
$191$	−9.16515	−	5.29150i	−0.663167	−	0.382880i	−0.793483	+	0.608593i	$0.791734\pi$
$192$	13.0834	+	4.56350i	0.944211	+	0.329342i
$193$	2.05431	−	7.66680i	0.147873	−	0.551868i	−0.851738	−	0.523968i	$-0.824451\pi$
$193$	2.05431	−	7.66680i	0.147873	−	0.551868i	0.999611	−	0.0279004i	$-0.00888213\pi$
$194$	3.69253	−	0.604356i	0.265108	−	0.0433902i
$195$		0			0
$196$	−17.0608	+	5.73840i	−1.21863	+	0.409886i
$197$	7.48331	−	7.48331i	0.533164	−	0.533164i	−0.388348	−	0.921513i	$-0.626954\pi$
$197$	7.48331	−	7.48331i	0.533164	−	0.533164i	0.921513	+	0.388348i	$0.126954\pi$
$198$	−1.11580	+	11.1694i	−0.0792964	+	0.793773i
$199$	21.1660			1.50042			0.750209	−	0.661200i	$-0.229953\pi$
$199$	21.1660			1.50042			0.750209	+	0.661200i	$0.229953\pi$
$200$		0			0
$201$		−	15.5885i		−	1.09952i
$202$	11.4839	+	8.25348i	0.808005	+	0.580713i
$203$	7.72741	+	2.07055i	0.542358	+	0.145324i
$204$	−18.1865	+	20.6216i	−1.27331	+	1.44380i
$205$		0			0
$206$	3.00000	−	7.93725i	0.209020	−	0.553015i
$207$	11.5911	−	3.10583i	0.805638	−	0.215870i
$208$	−12.9784	+	16.7201i	−0.899891	+	1.15933i
$209$	−6.06218	−	3.50000i	−0.419330	−	0.242100i
$210$		0			0
$211$	−4.58258	+	2.64575i	−0.315478	+	0.182141i	−0.649375	−	0.760468i	$-0.724969\pi$
$211$	−4.58258	+	2.64575i	−0.315478	+	0.182141i	0.333897	+	0.942609i	$0.391636\pi$
$212$	−5.85507	−	8.81579i	−0.402128	−	0.605471i
$213$		0			0
$214$	−14.2279	+	11.6434i	−0.972596	+	0.795924i
$215$		0			0
$216$	−6.87386	−	12.9904i	−0.467707	−	0.883883i
$217$	14.9666	−	14.9666i	1.01600	−	1.01600i
$218$	5.62884	+	0.562310i	0.381233	+	0.0380844i
$219$	−19.8431	−	11.4564i	−1.34087	−	0.774154i
$220$		0			0
$221$	−21.0000	−	36.3731i	−1.41261	−	2.44672i
$222$	10.5252	+	7.56444i	0.706403	+	0.507692i
$223$	−4.14110	−	15.4548i	−0.277309	−	1.03493i	−0.954278	−	0.298920i	$-0.903374\pi$
$223$	−4.14110	−	15.4548i	−0.277309	−	1.03493i	0.676969	−	0.736011i	$-0.263293\pi$
$224$	5.29150	−	22.0000i	0.353553	−	1.46994i
$225$		0			0
$226$		0			0
$227$	−6.76148	+	1.81173i	−0.448775	+	0.120249i	−0.476126	−	0.879377i	$-0.657959\pi$
$227$	−6.76148	+	1.81173i	−0.448775	+	0.120249i	0.0273510	+	0.999626i	$0.491293\pi$
$228$	9.14716	−	0.573948i	0.605786	−	0.0380107i
$229$	−17.3205	+	10.0000i	−1.14457	+	0.660819i	−0.947559	−	0.319582i	$-0.896457\pi$
$229$	−17.3205	+	10.0000i	−1.14457	+	0.660819i	−0.197013	+	0.980401i	$0.563124\pi$
$230$		0			0
$231$	18.3303			1.20605
$232$	−4.14486	+	3.84969i	−0.272123	+	0.252745i
$233$	−9.35414	−	9.35414i	−0.612810	−	0.612810i	0.330867	−	0.943677i	$-0.392659\pi$
$233$	−9.35414	−	9.35414i	−0.612810	−	0.612810i	−0.943677	+	0.330867i	$0.892659\pi$
$234$	22.1552	−	3.62614i	1.44833	−	0.237048i
$235$		0			0
$236$	1.68693	+	5.01540i	0.109810	+	0.326475i
$237$	−4.74423	+	17.7057i	−0.308171	+	1.15011i
$238$	36.4603	+	26.2040i	2.36337	+	1.69855i
$239$	10.5830	+	18.3303i	0.684558	+	1.18569i	0.973576	+	0.228365i	$0.0733380\pi$
$239$	10.5830	+	18.3303i	0.684558	+	1.18569i	−0.289018	+	0.957324i	$0.593329\pi$
$240$		0			0
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	0.450910	+	0.892570i	$0.351100\pi$
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	−5.15587	+	2.32744i	−0.331432	+	0.149614i
$243$	−4.03459	+	15.0573i	−0.258819	+	0.965926i
$244$	−7.93725	+	9.00000i	−0.508131	+	0.576166i
$245$		0			0
$246$	−13.2695	+	10.8591i	−0.846033	+	0.692351i
$247$	−3.62347	+	13.5230i	−0.230556	+	0.860445i
$248$	3.33763	+	14.5897i	0.211940	+	0.926449i
$249$		0			0
$250$		0			0
$251$		−	29.1033i		−	1.83698i	−0.395442	−	0.918491i	$-0.629409\pi$
$251$		−	29.1033i		−	1.83698i	0.395442	−	0.918491i	$-0.370591\pi$
$252$	−19.9923	+	13.2780i	−1.25940	+	0.836438i
$253$	−7.48331	−	7.48331i	−0.470472	−	0.470472i
$254$	8.75560	−	7.16515i	0.549375	−	0.449582i
$255$		0			0
$256$	11.1869	+	11.4391i	0.699183	+	0.714943i
$257$	2.55560	+	0.684771i	0.159414	+	0.0427148i	0.337643	−	0.941274i	$-0.390370\pi$
$257$	2.55560	+	0.684771i	0.159414	+	0.0427148i	−0.178229	+	0.983989i	$0.557037\pi$
$258$	−2.23256	+	1.00781i	−0.138993	+	0.0627437i
$259$	10.5830	−	18.3303i	0.657596	−	1.13899i
$260$		0			0
$261$	6.00000			0.371391
$262$	9.23676	+	20.4617i	0.570649	+	1.26413i
$263$	3.10583	+	11.5911i	0.191514	+	0.714738i	0.993142	+	0.116916i	$0.0373007\pi$
$263$	3.10583	+	11.5911i	0.191514	+	0.714738i	−0.801628	+	0.597823i	$0.796033\pi$
$264$	−6.89048	+	10.9782i	−0.424080	+	0.675663i
$265$		0			0
$266$	−2.41742	−	14.7701i	−0.148222	−	0.905613i
$267$	−2.68973	−	10.0382i	−0.164609	−	0.614328i
$268$	8.00614	−	16.1215i	0.489053	−	0.984775i
$269$			18.0000i			1.09748i	0.835993	+	0.548740i	$0.184892\pi$
$269$			18.0000i			1.09748i	−0.835993	+	0.548740i	$0.815108\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	−29.3995	+	11.9862i	−1.78261	+	0.726770i
$273$	−9.48846	−	35.4114i	−0.574268	−	2.14320i
$274$	−11.0776	+	1.81307i	−0.669221	+	0.109531i
$275$		0			0
$276$	13.5826	+	2.74110i	0.817575	+	0.164995i
$277$	5.47817	+	20.4448i	0.329151	+	1.22841i	0.910073	+	0.414449i	$0.136026\pi$
$277$	5.47817	+	20.4448i	0.329151	+	1.22841i	−0.580921	+	0.813960i	$0.697308\pi$
$278$	23.8720	−	10.7762i	1.43175	−	0.646314i
$279$	7.93725	−	13.7477i	0.475191	−	0.823055i
$280$		0			0
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	0.325385	+	0.945582i	$0.394506\pi$
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	−0.981590	+	0.190999i	$0.938827\pi$
$282$	6.04688	+	13.3953i	0.360086	+	0.797681i
$283$	3.86370	+	1.03528i	0.229673	+	0.0615408i	0.371820	−	0.928305i	$-0.378734\pi$
$283$	3.86370	+	1.03528i	0.229673	+	0.0615408i	−0.142147	+	0.989846i	$0.545400\pi$
$284$		0			0
$285$		0			0
$286$	−12.5390	−	15.3223i	−0.741447	−	0.906027i
$287$	19.7990	+	19.7990i	1.16870	+	1.16870i
$288$	−0.437115	−	16.9649i	−0.0257572	−	0.999668i
$289$		−	46.0000i		−	2.70588i
$290$		0			0
$291$	−2.29129	−	3.96863i	−0.134318	−	0.232645i
$292$	−14.6377	−	22.0395i	−0.856604	−	1.28976i
$293$	1.36954	−	5.11120i	0.0800095	−	0.298599i	−0.914313	−	0.405008i	$-0.867269\pi$
$293$	1.36954	−	5.11120i	0.0800095	−	0.298599i	0.994322	+	0.106409i	$0.0339353\pi$
$294$	13.9617	+	17.0608i	0.814263	+	0.995006i
$295$		0			0
$296$	7.00000	+	13.2288i	0.406867	+	0.768906i
$297$	13.2793	−	3.55817i	0.770542	−	0.206466i
$298$	−5.81861	−	12.8897i	−0.337063	−	0.746679i
$299$	−10.5830	+	18.3303i	−0.612031	+	1.06007i
$300$		0			0
$301$	2.00000	+	3.46410i	0.115278	+	0.199667i
$302$		0			0
$303$	4.48288	−	16.7303i	0.257535	−	0.961132i
$304$	9.75470	+	4.10436i	0.559471	+	0.235401i
$305$		0			0
$306$	31.5000	+	11.9059i	1.80074	+	0.680614i
$307$	−14.8492	−	14.8492i	−0.847491	−	0.847491i	0.142328	−	0.989819i	$-0.454541\pi$
$307$	−14.8492	−	14.8492i	−0.847491	−	0.847491i	−0.989819	+	0.142328i	$0.954541\pi$
$308$	18.9571	+	9.41434i	1.08018	+	0.536432i
$309$	−10.3923			−0.591198
$310$		0			0
$311$	−13.7477	+	7.93725i	−0.779562	+	0.450080i	−0.836275	−	0.548310i	$-0.815271\pi$
$311$	−13.7477	+	7.93725i	−0.779562	+	0.450080i	0.0567130	+	0.998391i	$0.481938\pi$
$312$	24.7751	+	7.62864i	1.40261	+	0.431887i
$313$	−28.1116	+	7.53248i	−1.58896	+	0.425761i	−0.941685	−	0.336495i	$-0.890759\pi$
$313$	−28.1116	+	7.53248i	−1.58896	+	0.425761i	−0.647276	+	0.762256i	$0.724092\pi$
$314$	−10.5830	+	28.0000i	−0.597234	+	1.58013i
$315$		0			0
$316$	−14.0000	+	15.8745i	−0.787562	+	0.893011i
$317$	4.10862	+	15.3336i	0.230763	+	0.861221i	0.980013	+	0.198933i	$0.0637476\pi$
$317$	4.10862	+	15.3336i	0.230763	+	0.861221i	−0.749250	+	0.662288i	$0.769586\pi$
$318$	−7.56444	+	10.5252i	−0.424193	+	0.590222i
$319$	−2.64575	−	4.58258i	−0.148134	−	0.256575i
$320$		0			0
$321$	19.5000	+	11.2583i	1.08838	+	0.628379i
$322$	2.24924	−	22.5153i	0.125345	−	1.25473i
$323$	−14.8492	+	14.8492i	−0.826234	+	0.826234i
$324$	−11.9059	+	13.5000i	−0.661438	+	0.750000i
$325$		0			0
$326$	17.9129	+	21.8890i	0.992103	+	1.21232i
$327$	−1.79315	−	6.69213i	−0.0991615	−	0.370076i
$328$	−19.3004	+	4.41527i	−1.06569	+	0.243792i
$329$	20.7846	−	12.0000i	1.14589	−	0.661581i
$330$		0			0
$331$	4.58258	+	2.64575i	0.251881	+	0.145424i	0.620625	−	0.784107i	$-0.286879\pi$
$331$	4.58258	+	2.64575i	0.251881	+	0.145424i	−0.368744	+	0.929531i	$0.620212\pi$
$332$		0			0
$333$	4.10862	−	15.3336i	0.225151	−	0.840276i
$334$	−15.8745	−	6.00000i	−0.868614	−	0.328305i
$335$		0			0
$336$	−27.4955	+	3.46410i	−1.50000	+	0.188982i
$337$	2.55560	+	0.684771i	0.139212	+	0.0373018i	0.327752	−	0.944764i	$-0.393709\pi$
$337$	2.55560	+	0.684771i	0.139212	+	0.0373018i	−0.188540	+	0.982066i	$0.560376\pi$
$338$	−12.3802	+	17.2259i	−0.673395	+	0.936963i
$339$		0			0
$340$		0			0
$341$	−14.0000			−0.758143
$342$	−4.61838	−	10.2309i	−0.249733	−	0.553222i
$343$	5.65685	−	5.65685i	0.305441	−	0.305441i
$344$	−2.82650	−	0.104356i	−0.152395	−	0.00562650i
$345$		0			0
$346$	−1.20871	−	7.38505i	−0.0649808	−	0.397023i
$347$	2.32937	−	8.69333i	0.125047	−	0.466683i	−0.874794	−	0.484495i	$-0.839003\pi$
$347$	2.32937	−	8.69333i	0.125047	−	0.466683i	0.999841	+	0.0178123i	$0.00567012\pi$
$348$	6.20516	+	3.08157i	0.332631	+	0.165189i
$349$	13.8564	+	8.00000i	0.741716	+	0.428230i	0.822693	−	0.568486i	$-0.192471\pi$
$349$	13.8564	+	8.00000i	0.741716	+	0.428230i	−0.0809766	+	0.996716i	$0.525804\pi$
$350$		0			0
$351$	−13.7477	−	23.8118i	−0.733799	−	1.27098i
$352$	−12.7644	+	7.81468i	−0.680346	+	0.416524i
$353$	2.55560	−	0.684771i	0.136021	−	0.0364467i	−0.190166	−	0.981752i	$-0.560903\pi$
$353$	2.55560	−	0.684771i	0.136021	−	0.0364467i	0.326187	+	0.945305i	$0.394236\pi$
$354$	5.01540	−	4.10436i	0.266566	−	0.218144i
$355$		0			0
$356$	2.37386	−	11.7629i	0.125815	−	0.623430i
$357$	14.2327	−	53.1171i	0.753274	−	2.81126i
$358$	0.743866	−	7.44625i	0.0393146	−	0.393547i
$359$	−10.5830			−0.558550			−0.279275	−	0.960211i	$-0.590094\pi$
$359$	−10.5830			−0.558550			−0.279275	+	0.960211i	$0.590094\pi$
$360$		0			0
$361$	−12.0000			−0.631579
$362$	1.96808	−	19.7009i	0.103440	−	1.03546i
$363$	4.89898	+	4.89898i	0.257130	+	0.257130i
$364$	8.37420	−	41.4955i	0.438928	−	2.17495i
$365$		0			0
$366$	13.7477	+	5.19615i	0.718605	+	0.271607i
$367$	−17.3867	+	4.65874i	−0.907577	+	0.243184i	−0.682267	−	0.731103i	$-0.739006\pi$
$367$	−17.3867	+	4.65874i	−0.907577	+	0.243184i	−0.225309	+	0.974287i	$0.572339\pi$
$368$	12.6392	+	9.81076i	0.658863	+	0.511421i
$369$	18.1865	+	10.5000i	0.946753	+	0.546608i
$370$		0			0
$371$	18.3303	+	10.5830i	0.951662	+	0.549442i
$372$	15.2694	−	10.1413i	0.791682	−	0.525800i
$373$	2.73908	−	10.2224i	0.141824	−	0.529296i	−0.858052	−	0.513563i	$-0.828325\pi$
$373$	2.73908	−	10.2224i	0.141824	−	0.529296i	0.999876	−	0.0157327i	$-0.00500808\pi$
$374$	−4.79693	−	29.3085i	−0.248043	−	1.51551i
$375$		0			0
$376$	−0.626136	+	16.9590i	−0.0322905	+	0.874594i
$377$	−7.48331	+	7.48331i	−0.385410	+	0.385410i
$378$	23.8688	+	17.1545i	1.22768	+	0.882334i
$379$	29.1033			1.49493			0.747467	−	0.664299i	$-0.231270\pi$
$379$	29.1033			1.49493			0.747467	+	0.664299i	$0.231270\pi$
$380$		0			0
$381$	−12.0000	−	6.92820i	−0.614779	−	0.354943i
$382$	−8.73467	+	12.1534i	−0.446904	+	0.621823i
$383$	−32.8415	−	8.79985i	−1.67812	−	0.449651i	−0.710839	−	0.703355i	$-0.751685\pi$
$383$	−32.8415	−	8.79985i	−1.67812	−	0.449651i	−0.967282	+	0.253703i	$0.918351\pi$
$384$	8.26103	−	17.7695i	0.421569	−	0.906796i
$385$		0			0
$386$	−10.5000	−	3.96863i	−0.534436	−	0.201998i
$387$	2.12132	+	2.12132i	0.107833	+	0.107833i
$388$	−0.331369	−	5.28112i	−0.0168227	−	0.268108i
$389$	10.3923	+	6.00000i	0.526911	+	0.304212i	0.739758	−	0.672874i	$-0.234940\pi$
$389$	10.3923	+	6.00000i	0.526911	+	0.304212i	−0.212847	+	0.977086i	$0.568274\pi$
$390$		0			0
$391$	−27.4955	+	15.8745i	−1.39050	+	0.802808i
$392$	5.67677	+	24.8148i	0.286720	+	1.25334i
$393$	19.4422	−	19.4422i	0.980730	−	0.980730i
$394$	−9.47860	−	11.5826i	−0.477525	−	0.583522i
$395$		0			0
$396$	15.5608	+	3.14033i	0.781959	+	0.157807i
$397$	26.1916	−	26.1916i	1.31452	−	1.31452i	0.396472	−	0.918047i	$-0.370234\pi$
$397$	26.1916	−	26.1916i	1.31452	−	1.31452i	0.918047	−	0.396472i	$-0.129766\pi$
$398$	2.97546	−	29.7850i	0.149147	−	1.49299i
$399$	−15.8745	+	9.16515i	−0.794719	+	0.458831i
$400$		0			0
$401$	12.5000	+	21.6506i	0.624220	+	1.08118i	0.988691	+	0.149966i	$0.0479165\pi$
$401$	12.5000	+	21.6506i	0.624220	+	1.08118i	−0.364471	+	0.931215i	$0.618750\pi$
$402$	−21.9362	−	2.19139i	−1.09408	−	0.109296i
$403$	7.24693	+	27.0459i	0.360995	+	1.34725i
$404$	13.2288	−	15.0000i	0.658155	−	0.746278i
$405$		0			0
$406$	4.00000	−	10.5830i	0.198517	−	0.525226i
$407$	−13.5230	+	3.62347i	−0.670308	+	0.179609i
$408$	26.4623	+	28.4912i	1.31008	+	1.41052i
$409$	9.52628	−	5.50000i	0.471044	−	0.271957i	−0.245633	−	0.969363i	$-0.578996\pi$
$409$	9.52628	−	5.50000i	0.471044	−	0.271957i	0.716677	+	0.697406i	$0.245662\pi$
$410$		0			0
$411$	6.87386	+	11.9059i	0.339063	+	0.587274i
$412$	−10.7476	−	5.33743i	−0.529498	−	0.262956i
$413$	−7.48331	−	7.48331i	−0.368230	−	0.368230i
$414$	−2.74110	−	16.7477i	−0.134718	−	0.823106i
$415$		0			0
$416$	21.7042	+	20.6138i	1.06413	+	1.01068i
$417$	−22.6826	−	22.6826i	−1.11077	−	1.11077i
$418$	−5.77744	+	8.03873i	−0.282584	+	0.393187i
$419$	7.93725	+	13.7477i	0.387760	+	0.671620i	0.992148	−	0.125070i	$-0.0399155\pi$
$419$	7.93725	+	13.7477i	0.387760	+	0.671620i	−0.604388	+	0.796690i	$0.706582\pi$
$420$		0			0
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	−0.751935	−	0.659237i	$-0.770879\pi$
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	0.946883	+	0.321577i	$0.104213\pi$
$422$	3.07892	+	6.82058i	0.149879	+	0.332020i
$423$	12.7279	−	12.7279i	0.618853	−	0.618853i
$424$	−13.2288	+	7.00000i	−0.642445	+	0.339950i
$425$		0			0
$426$		0			0
$427$	6.21166	−	23.1822i	0.300603	−	1.12187i
$428$	14.3845	+	21.6584i	0.695303	+	1.04690i
$429$	−12.1244	+	21.0000i	−0.585369	+	1.01389i
$430$		0			0
$431$		−	21.1660i		−	1.01953i	−0.860313	−	0.509765i	$-0.829732\pi$
$431$		−	21.1660i		−	1.01953i	0.860313	−	0.509765i	$-0.170268\pi$
$432$	−19.2465	+	7.84681i	−0.925997	+	0.377530i
$433$	1.87083	+	1.87083i	0.0899063	+	0.0899063i	0.750630	−	0.660723i	$-0.229750\pi$
$433$	1.87083	+	1.87083i	0.0899063	+	0.0899063i	−0.660723	+	0.750630i	$0.729750\pi$
$434$	−18.9572	−	23.1652i	−0.909975	−	1.11196i
$435$		0			0
$436$	1.58258	−	7.84190i	0.0757916	−	0.375559i
$437$	10.2224	+	2.73908i	0.489004	+	0.131028i
$438$	−18.9111	+	26.3129i	−0.903608	+	1.25728i
$439$	−2.64575	+	4.58258i	−0.126275	+	0.218714i	−0.922231	−	0.386640i	$-0.873635\pi$
$439$	−2.64575	+	4.58258i	−0.126275	+	0.218714i	0.795956	+	0.605355i	$0.206969\pi$
$440$		0			0
$441$	13.5000	−	23.3827i	0.642857	−	1.11346i
$442$	−54.1366	+	24.4382i	−2.57502	+	1.16240i
$443$	−7.50575	−	28.0118i	−0.356609	−	1.33088i	−0.878448	−	0.477839i	$-0.841420\pi$
$443$	−7.50575	−	28.0118i	−0.356609	−	1.33088i	0.521838	−	0.853044i	$-0.325246\pi$
$444$	12.1244	−	13.7477i	0.575396	−	0.652438i
$445$		0			0
$446$	−22.3303	+	3.65480i	−1.05737	+	0.173060i
$447$	−12.2474	+	12.2474i	−0.579284	+	0.579284i
$448$	−30.2147	−	10.5390i	−1.42751	−	0.497919i
$449$		−	29.0000i		−	1.36859i	−0.729203	−	0.684297i	$-0.760109\pi$
$449$		−	29.0000i		−	1.36859i	0.729203	−	0.684297i	$-0.239891\pi$
$450$		0			0
$451$		−	18.5203i		−	0.872085i
$452$		0			0
$453$		0			0
$454$	1.59898	+	9.76951i	0.0750437	+	0.458506i
$455$		0			0
$456$	0.478220	−	12.9527i	0.0223947	−	0.606564i
$457$	4.79340	+	17.8892i	0.224226	+	0.836821i	0.982713	+	0.185134i	$0.0592719\pi$
$457$	4.79340	+	17.8892i	0.224226	+	0.836821i	−0.758488	+	0.651687i	$0.774061\pi$
$458$	11.6372	+	25.7794i	0.543772	+	1.20459i
$459$		−	41.2432i		−	1.92507i
$460$		0			0
$461$	1.00000	−	1.73205i	0.0465746	−	0.0806696i	−0.841798	−	0.539792i	$-0.818503\pi$
$461$	1.00000	−	1.73205i	0.0465746	−	0.0806696i	0.888373	+	0.459123i	$0.151836\pi$
$462$	2.57683	−	25.7946i	0.119885	−	1.20007i
$463$	−21.2504	−	5.69402i	−0.987588	−	0.264624i	−0.271351	−	0.962480i	$-0.587470\pi$
$463$	−21.2504	−	5.69402i	−0.987588	−	0.264624i	−0.716237	+	0.697857i	$0.754137\pi$
$464$	4.83465	+	6.37386i	0.224443	+	0.295899i
$465$		0			0
$466$	−14.4782	+	11.8483i	−0.670691	+	0.548860i
$467$	−19.0919	−	19.0919i	−0.883467	−	0.883467i	0.110418	−	0.993885i	$-0.464781\pi$
$467$	−19.0919	−	19.0919i	−0.883467	−	0.883467i	−0.993885	+	0.110418i	$0.964781\pi$
$468$	−1.98822	−	31.6867i	−0.0919053	−	1.46472i
$469$			36.0000i			1.66233i
$470$		0			0
$471$	36.6606			1.68923
$472$	7.29487	−	1.66881i	0.335773	−	0.0768134i
$473$	0.684771	−	2.55560i	0.0314858	−	0.117507i
$474$	24.2487	+	9.16515i	1.11378	+	0.420969i
$475$		0			0
$476$	42.0000	−	47.6235i	1.92507	−	2.18282i
$477$	15.3336	+	4.10862i	0.702077	+	0.188121i
$478$	27.2823	−	12.3157i	1.24786	−	0.563306i
$479$	13.2288	−	22.9129i	0.604437	−	1.04692i	−0.387703	−	0.921784i	$-0.626731\pi$
$479$	13.2288	−	22.9129i	0.604437	−	1.04692i	0.992140	−	0.125132i	$-0.0399353\pi$
$480$		0			0
$481$	14.0000	+	24.2487i	0.638345	+	1.10565i
$482$	19.5226	+	14.0309i	0.889232	+	0.639091i
$483$	−26.7685	+	7.17260i	−1.21801	+	0.326365i
$484$	2.55040	+	7.58258i	0.115927	+	0.344663i
$485$		0			0
$486$	20.6216	+	7.79423i	0.935414	+	0.353553i
$487$	−26.8701	−	26.8701i	−1.21760	−	1.21760i	−0.968471	−	0.249128i	$-0.919856\pi$
$487$	−26.8701	−	26.8701i	−1.21760	−	1.21760i	−0.249128	−	0.968471i	$-0.580144\pi$
$488$	11.5491	+	12.4346i	0.522802	+	0.562887i
$489$	17.3205	−	30.0000i	0.783260	−	1.35665i
$490$		0			0
$491$	−6.87386	+	3.96863i	−0.310213	+	0.179102i	−0.647022	−	0.762471i	$-0.723986\pi$
$491$	−6.87386	+	3.96863i	−0.310213	+	0.179102i	0.336809	+	0.941573i	$0.390652\pi$
$492$	13.4156	+	20.1995i	0.604824	+	0.910665i
$493$	−15.3336	+	4.10862i	−0.690590	+	0.185043i
$494$	18.5203	+	7.00000i	0.833266	+	0.314945i
$495$		0			0
$496$	21.0000	−	2.64575i	0.942928	−	0.118798i
$497$		0			0
$498$		0			0
$499$	−11.9059	−	20.6216i	−0.532980	−	0.923149i	−0.999258	−	0.0385108i	$-0.987739\pi$
$499$	−11.9059	−	20.6216i	−0.532980	−	0.923149i	0.466278	−	0.884638i	$-0.345595\pi$
$500$		0			0
$501$			20.7846i			0.928588i
$502$	−40.9544	−	4.09126i	−1.82788	−	0.182602i
$503$	−9.89949	+	9.89949i	−0.441397	+	0.441397i	−0.892481	−	0.451085i	$-0.851037\pi$
$503$	−9.89949	+	9.89949i	−0.441397	+	0.441397i	0.451085	+	0.892481i	$0.351037\pi$
$504$	15.8745	+	30.0000i	0.707107	+	1.33631i
$505$		0			0
$506$	−11.5826	+	9.47860i	−0.514908	+	0.421375i
$507$	25.0955	+	6.72432i	1.11453	+	0.298637i
$508$	−8.85203	−	13.3282i	−0.392745	−	0.591344i
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$	45.8258	+	26.4575i	2.02721	+	1.17041i
$512$	17.6698	−	14.1343i	0.780903	−	0.624653i
$513$	−9.72111	+	9.72111i	−0.429198	+	0.429198i
$514$	1.32288	−	3.50000i	0.0583495	−	0.154378i
$515$		0			0
$516$	1.10436	+	3.28335i	0.0486166	+	0.144541i
$517$	−15.3336	−	4.10862i	−0.674371	−	0.180697i
$518$	−24.3068	−	17.4693i	−1.06798	−	0.767558i
$519$	−7.93725	+	4.58258i	−0.348407	+	0.201153i
$520$		0			0
$521$	25.0000			1.09527			0.547635	−	0.836717i	$-0.315528\pi$
$521$	25.0000			1.09527			0.547635	+	0.836717i	$0.315528\pi$
$522$	0.843465	−	8.44326i	0.0369175	−	0.369551i
$523$	25.4558	−	25.4558i	1.11311	−	1.11311i	0.120378	−	0.992728i	$-0.461589\pi$
$523$	25.4558	−	25.4558i	1.11311	−	1.11311i	0.992728	−	0.120378i	$-0.0384107\pi$
$524$	30.0924	−	10.1216i	1.31459	−	0.442164i
$525$		0			0
$526$	16.7477	−	2.74110i	0.730236	−	0.119518i
$527$	−10.8704	+	40.5689i	−0.473522	+	1.76721i
$528$	14.4800	+	11.2396i	0.630161	+	0.489142i
$529$	−6.06218	−	3.50000i	−0.263573	−	0.152174i
$530$		0			0
$531$	−6.87386	−	3.96863i	−0.298300	−	0.172224i
$532$	−21.1245	+	1.32548i	−0.915862	+	0.0574667i
$533$	−35.7784	+	9.58679i	−1.54973	+	0.415250i
$534$	−14.5040	+	2.37386i	−0.627648	+	0.102727i
$535$		0			0
$536$	−21.5608	−	13.5326i	−0.931285	−	0.584521i
$537$	−8.85286	+	2.37212i	−0.382029	+	0.102364i
$538$	25.3298	+	2.53039i	1.09204	+	0.109093i
$539$	−23.8118			−1.02565
$540$		0			0
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$		0			0
$543$	−23.4225	+	6.27603i	−1.00515	+	0.269330i
$544$	12.7342	+	43.0562i	0.545974	+	1.84602i
$545$		0			0
$546$	−51.1652	+	8.37420i	−2.18967	+	0.358383i
$547$	18.3526	−	4.91756i	0.784700	−	0.210260i	0.155844	−	0.987782i	$-0.450190\pi$
$547$	18.3526	−	4.91756i	0.784700	−	0.210260i	0.628856	+	0.777522i	$0.283524\pi$
$548$	0.994108	+	15.8434i	0.0424662	+	0.676794i
$549$		−	18.0000i		−	0.768221i
$550$		0			0
$551$	4.58258	+	2.64575i	0.195224	+	0.112713i
$552$	5.76671	−	18.7282i	0.245447	−	0.797125i
$553$	10.9563	−	40.8896i	0.465911	−	1.73880i
$554$	29.5402	−	4.83485i	1.25504	−	0.205413i
$555$		0			0
$556$	−11.8085	−	35.1078i	−0.500793	−	1.48890i
$557$	22.4499	−	22.4499i	0.951235	−	0.951235i	−0.0476304	−	0.998865i	$-0.515167\pi$
$557$	22.4499	−	22.4499i	0.951235	−	0.951235i	0.998865	+	0.0476304i	$0.0151670\pi$
$558$	−18.2301	−	13.1020i	−0.771743	−	0.554652i
$559$	−5.29150			−0.223807
$560$		0			0
$561$	−31.5000	+	18.1865i	−1.32993	+	0.767836i
$562$	25.2646	+	18.1577i	1.06572	+	0.765935i
$563$	29.9437	+	8.02339i	1.26198	+	0.338146i	0.826952	−	0.562273i	$-0.190073\pi$
$563$	29.9437	+	8.02339i	1.26198	+	0.338146i	0.435025	+	0.900418i	$0.356740\pi$
$564$	19.7001	−	6.62614i	0.829524	−	0.279011i
$565$		0			0
$566$	2.00000	−	5.29150i	0.0840663	−	0.222418i
$567$	9.31749	−	34.7733i	0.391298	−	1.46034i
$568$		0			0
$569$	12.9904	+	7.50000i	0.544585	+	0.314416i	0.746935	−	0.664897i	$-0.231525\pi$
$569$	12.9904	+	7.50000i	0.544585	+	0.314416i	−0.202350	+	0.979313i	$0.564858\pi$
$570$		0			0
$571$	16.0390	−	9.26013i	0.671212	−	0.387524i	−0.125324	−	0.992116i	$-0.539997\pi$
$571$	16.0390	−	9.26013i	0.671212	−	0.387524i	0.796536	+	0.604592i	$0.206664\pi$
$572$	−23.3244	+	15.4910i	−0.975242	+	0.647713i
$573$	17.7057	+	4.74423i	0.739667	+	0.198193i
$574$	30.6446	−	25.0780i	1.27908	−	1.04674i
$575$		0			0
$576$	−23.9347	−	1.76978i	−0.997277	−	0.0737406i
$577$	−16.8375	+	16.8375i	−0.700953	+	0.700953i	−0.964615	−	0.263662i	$-0.915069\pi$
$577$	−16.8375	+	16.8375i	−0.700953	+	0.700953i	0.263662	+	0.964615i	$0.415069\pi$
$578$	−64.7316	−	6.46656i	−2.69248	−	0.268974i
$579$			13.7477i			0.571336i
$580$		0			0
$581$		0			0
$582$	−5.90679	+	2.66642i	−0.244844	+	0.110527i
$583$	−3.62347	−	13.5230i	−0.150069	−	0.560064i
$584$	−33.0719	+	17.5000i	−1.36852	+	0.724155i
$585$		0			0
$586$	−7.00000	−	2.64575i	−0.289167	−	0.109295i
$587$	18.3526	−	4.91756i	0.757492	−	0.202969i	0.140654	−	0.990059i	$-0.455080\pi$
$587$	18.3526	−	4.91756i	0.757492	−	0.202969i	0.616839	+	0.787089i	$0.288413\pi$
$588$	25.9708	−	17.2487i	1.07102	−	0.711324i
$589$	12.1244	−	7.00000i	0.499575	−	0.288430i
$590$		0			0
$591$	−9.16515	+	15.8745i	−0.377004	+	0.652990i
$592$	19.5997	−	7.99080i	0.805542	−	0.328420i
$593$	7.48331	+	7.48331i	0.307303	+	0.307303i	0.843862	−	0.536560i	$-0.180276\pi$
$593$	7.48331	+	7.48331i	0.307303	+	0.307303i	−0.536560	+	0.843862i	$0.680276\pi$
$594$	−3.14033	−	19.1869i	−0.128849	−	0.787249i
$595$		0			0
$596$	−18.9564	+	6.37600i	−0.776486	+	0.261171i
$597$	−35.4114	+	9.48846i	−1.44929	+	0.388337i
$598$	24.3068	+	17.4693i	0.993981	+	0.714374i
$599$	−23.8118	−	41.2432i	−0.972922	−	1.68515i	−0.686628	−	0.727009i	$-0.740910\pi$
$599$	−23.8118	−	41.2432i	−0.972922	−	1.68515i	−0.286294	−	0.958142i	$-0.592423\pi$
$600$		0			0
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$	5.15587	−	2.32744i	0.210138	−	0.0948595i
$603$	6.98811	+	26.0800i	0.284578	+	1.06206i
$604$		0			0
$605$		0			0
$606$	−22.9129	−	8.66025i	−0.930772	−	0.351799i
$607$	−7.24693	+	27.0459i	−0.294144	+	1.09776i	0.647751	+	0.761852i	$0.275710\pi$
$607$	−7.24693	+	27.0459i	−0.294144	+	1.09776i	−0.941895	+	0.335908i	$0.890957\pi$
$608$	7.14698	−	13.1499i	0.289848	−	0.533300i
$609$	−13.8564			−0.561490
$610$		0			0
$611$			31.7490i			1.28443i
$612$	21.1823	−	42.6534i	0.856242	−	1.72416i
$613$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$613$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$614$	−22.9835	+	18.8085i	−0.927537	+	0.759050i
$615$		0			0
$616$	15.9129	−	25.3531i	0.641148	−	1.02151i
$617$	43.4452	+	11.6411i	1.74904	+	0.468653i	0.984420	−	0.175831i	$-0.0562614\pi$
$617$	43.4452	+	11.6411i	1.74904	+	0.468653i	0.764617	+	0.644485i	$0.222928\pi$
$618$	−1.46092	+	14.6241i	−0.0587670	+	0.588269i
$619$	−9.26013	+	16.0390i	−0.372196	+	0.644662i	−0.989903	−	0.141746i	$-0.954728\pi$
$619$	−9.26013	+	16.0390i	−0.372196	+	0.644662i	0.617707	+	0.786408i	$0.288062\pi$
$620$		0			0
$621$	−18.0000	+	10.3923i	−0.722315	+	0.417029i
$622$	9.23676	+	20.4617i	0.370360	+	0.820441i
$623$	6.21166	+	23.1822i	0.248865	+	0.928776i
$624$	14.2179	−	33.7913i	0.569172	−	1.35273i
$625$		0			0
$626$	6.64792	+	40.6178i	0.265704	+	1.62341i
$627$	11.7112	+	3.13801i	0.467701	+	0.125320i
$628$	37.9141	+	18.8287i	1.51294	+	0.751346i
$629$			42.0000i			1.67465i
$630$		0			0
$631$			10.5830i			0.421303i	0.977561	+	0.210651i	$0.0675585\pi$
$631$			10.5830i			0.421303i	−0.977561	+	0.210651i	$0.932442\pi$
$632$	20.3707	+	21.9325i	0.810302	+	0.872429i
$633$	6.48074	−	6.48074i	0.257586	−	0.257586i
$634$	22.1552	−	3.62614i	0.879894	−	0.144012i
$635$		0			0
$636$	13.7477	+	12.1244i	0.545133	+	0.480762i
$637$	12.3259	+	46.0008i	0.488369	+	1.82262i
$638$	−6.82058	+	3.07892i	−0.270029	+	0.121896i
$639$		0			0
$640$		0			0
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$	18.5841	−	25.8579i	0.733455	−	1.02053i
$643$	−8.69333	−	2.32937i	−0.342832	−	0.0918614i	0.0832952	−	0.996525i	$-0.473456\pi$
$643$	−8.69333	−	2.32937i	−0.342832	−	0.0918614i	−0.426127	+	0.904663i	$0.640122\pi$
$644$	−31.3676	−	6.33030i	−1.23606	−	0.249449i
$645$		0			0
$646$	18.8085	+	22.9835i	0.740011	+	0.904272i
$647$	29.6985	+	29.6985i	1.16757	+	1.16757i	0.982778	+	0.184790i	$0.0591604\pi$
$647$	29.6985	+	29.6985i	1.16757	+	1.16757i	0.184790	+	0.982778i	$0.440840\pi$
$648$	17.3236	+	18.6519i	0.680536	+	0.732714i
$649$			7.00000i			0.274774i
$650$		0			0
$651$	−18.3303	+	31.7490i	−0.718421	+	1.24434i
$652$	33.3206	−	22.1301i	1.30493	−	0.866680i
$653$	4.10862	−	15.3336i	0.160783	−	0.600050i	−0.837758	−	0.546042i	$-0.816134\pi$
$653$	4.10862	−	15.3336i	0.160783	−	0.600050i	0.998541	−	0.0540077i	$-0.0171996\pi$
$654$	−9.66930	+	1.58258i	−0.378100	+	0.0618836i
$655$		0			0
$656$	3.50000	+	27.7804i	0.136652	+	1.08464i
$657$	38.3340	+	10.2716i	1.49555	+	0.400732i
$658$	−13.9647	−	30.9352i	−0.544399	−	1.20598i
$659$	−7.93725	+	13.7477i	−0.309192	+	0.535535i	−0.978186	−	0.207732i	$-0.933392\pi$
$659$	−7.93725	+	13.7477i	−0.309192	+	0.535535i	0.668994	+	0.743268i	$0.266725\pi$
$660$		0			0
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	0.636200	−	0.771524i	$-0.280505\pi$
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	−0.986260	+	0.165203i	$0.947172\pi$
$662$	4.36733	−	6.07671i	0.169741	−	0.236178i
$663$	51.4393	+	51.4393i	1.99774	+	1.99774i
$664$		0			0
$665$		0			0
$666$	−21.0000	−	7.93725i	−0.813733	−	0.307562i
$667$	5.65685	+	5.65685i	0.219034	+	0.219034i
$668$	−10.6749	+	21.4953i	−0.413023	+	0.831678i
$669$	13.8564	+	24.0000i	0.535720	+	0.927894i
$670$		0			0
$671$	−13.7477	+	7.93725i	−0.530725	+	0.306414i
$672$	1.00947	+	39.1788i	0.0389413	+	1.51136i
$673$	−10.2224	+	2.73908i	−0.394044	+	0.105584i	−0.450400	−	0.892827i	$-0.648719\pi$
$673$	−10.2224	+	2.73908i	−0.394044	+	0.105584i	0.0563556	+	0.998411i	$0.482052\pi$
$674$	1.32288	−	3.50000i	0.0509553	−	0.134815i
$675$		0			0
$676$	22.5000	+	19.8431i	0.865385	+	0.763197i
$677$	−2.73908	−	10.2224i	−0.105272	−	0.392879i	0.893104	−	0.449850i	$-0.148522\pi$
$677$	−2.73908	−	10.2224i	−0.105272	−	0.392879i	−0.998376	+	0.0569710i	$0.981856\pi$
$678$		0			0
$679$	5.29150	+	9.16515i	0.203069	+	0.351726i
$680$		0			0
$681$	10.5000	−	6.06218i	0.402361	−	0.232303i
$682$	−1.96808	+	19.7009i	−0.0753619	+	0.754388i
$683$	6.36396	−	6.36396i	0.243510	−	0.243510i	−0.574790	−	0.818301i	$-0.694916\pi$
$683$	6.36396	−	6.36396i	0.243510	−	0.243510i	0.818301	+	0.574790i	$0.194916\pi$
$684$	−15.0462	+	5.06080i	−0.575306	+	0.193504i
$685$		0			0
$686$	−7.16515	−	8.75560i	−0.273567	−	0.334291i
$687$	24.4949	−	24.4949i	0.934539	−	0.934539i
$688$	−0.544193	+	3.96281i	−0.0207472	+	0.151081i
$689$	−24.2487	+	14.0000i	−0.923802	+	0.533358i
$690$		0			0
$691$	−22.9129	−	13.2288i	−0.871647	−	0.503246i	−0.00375178	−	0.999993i	$-0.501194\pi$
$691$	−22.9129	−	13.2288i	−0.871647	−	0.503246i	−0.867895	+	0.496747i	$0.834528\pi$
$692$	−10.5622	+	0.662739i	−0.401516	+	0.0251935i
$693$	−30.6672	+	8.21725i	−1.16495	+	0.312148i
$694$	−11.9059	−	4.50000i	−0.451941	−	0.170818i
$695$		0			0
$696$	5.20871	−	8.29875i	0.197436	−	0.314563i
$697$	−53.6676	−	14.3802i	−2.03280	−	0.544688i
$698$	13.2056	−	18.3742i	0.499838	−	0.695475i
$699$	19.8431	+	11.4564i	0.750536	+	0.433322i
$700$		0			0
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$	−35.4408	+	15.9985i	−1.33763	+	0.603826i
$703$	9.89949	−	9.89949i	0.373367	−	0.373367i
$704$	9.20250	+	19.0608i	0.346832	+	0.718381i
$705$		0			0
$706$	−0.604356	−	3.69253i	−0.0227452	−	0.138970i
$707$	−10.3528	+	38.6370i	−0.389356	+	1.45310i
$708$	−5.07064	−	7.63470i	−0.190566	−	0.286930i
$709$	−8.66025	−	5.00000i	−0.325243	−	0.187779i	0.328484	−	0.944509i	$-0.393462\pi$
$709$	−8.66025	−	5.00000i	−0.325243	−	0.187779i	−0.653727	+	0.756730i	$0.726796\pi$
$710$		0			0
$711$		−	31.7490i		−	1.19068i
$712$	−16.2191	−	4.99412i	−0.607836	−	0.187162i
$713$	20.4448	−	5.47817i	0.765664	−	0.205159i
$714$	−72.7461	−	27.4955i	−2.72246	−	1.02899i
$715$		0			0
$716$	−10.3739	−	2.09355i	−0.387689	−	0.0782397i
$717$	−25.9230	−	25.9230i	−0.968111	−	0.968111i
$718$	−1.48773	+	14.8925i	−0.0555217	+	0.555783i
$719$	47.6235			1.77606			0.888029	−	0.459788i	$-0.152074\pi$
$719$	47.6235			1.77606			0.888029	+	0.459788i	$0.152074\pi$
$720$		0			0
$721$	24.0000			0.893807
$722$	−1.68693	+	16.8865i	−0.0627810	+	0.628451i
$723$	7.62089	−	28.4416i	0.283424	−	1.05775i
$724$	−27.4467	−	5.53901i	−1.02005	−	0.205856i
$725$		0			0
$726$	7.58258	−	6.20520i	0.281416	−	0.230297i
$727$	−28.9778	+	7.76457i	−1.07473	+	0.287972i	−0.752434	−	0.658668i	$-0.771120\pi$
$727$	−28.9778	+	7.76457i	−1.07473	+	0.287972i	−0.322293	+	0.946640i	$0.604453\pi$
$728$	−57.2156	−	17.6176i	−2.12055	−	0.652951i
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	−6.87386	−	3.96863i	−0.254239	−	0.146785i
$732$	9.24470	−	18.6155i	0.341694	−	0.688047i
$733$	2.73908	−	10.2224i	0.101170	−	0.377573i	−0.896712	−	0.442614i	$-0.854051\pi$
$733$	2.73908	−	10.2224i	0.101170	−	0.377573i	0.997883	+	0.0650411i	$0.0207179\pi$
$734$	4.11165	+	25.1216i	0.151764	+	0.927255i
$735$		0			0
$736$	15.5826	−	16.4068i	0.574381	−	0.604763i
$737$	16.8375	−	16.8375i	0.620216	−	0.620216i
$738$	17.3323	−	24.1162i	0.638011	−	0.887729i
$739$	−34.3948			−1.26523			−0.632616	−	0.774466i	$-0.718019\pi$
$739$	−34.3948			−1.26523			−0.632616	+	0.774466i	$0.718019\pi$
$740$		0			0
$741$		−	24.2487i		−	0.890799i
$742$	17.4693	−	24.3068i	0.641319	−	0.892332i
$743$	−28.9778	−	7.76457i	−1.06309	−	0.284854i	−0.315440	−	0.948946i	$-0.602152\pi$
$743$	−28.9778	−	7.76457i	−1.06309	−	0.284854i	−0.747652	+	0.664091i	$0.768819\pi$
$744$	−12.1244	−	22.9129i	−0.444500	−	0.840027i
$745$		0			0
$746$	−14.0000	−	5.29150i	−0.512576	−	0.193736i
$747$		0			0
$748$	−41.9176	+	2.63016i	−1.53266	+	0.0961683i
$749$	−45.0333	−	26.0000i	−1.64548	−	0.950019i
$750$		0			0
$751$	−4.58258	+	2.64575i	−0.167221	+	0.0965448i	−0.581275	−	0.813707i	$-0.697446\pi$
$751$	−4.58258	+	2.64575i	−0.167221	+	0.0965448i	0.414054	+	0.910252i	$0.364112\pi$
$752$	23.7769	+	3.26516i	0.867053	+	0.119068i
$753$	13.0466	+	48.6907i	0.475446	+	1.77439i
$754$	9.47860	+	11.5826i	0.345190	+	0.421813i
$755$		0			0
$756$	27.4955	−	31.1769i	1.00000	−	1.13389i
$757$	−11.2250	+	11.2250i	−0.407979	+	0.407979i	−0.881033	−	0.473055i	$-0.843151\pi$
$757$	−11.2250	+	11.2250i	−0.407979	+	0.407979i	0.473055	+	0.881033i	$0.343151\pi$
$758$	4.09126	−	40.9544i	0.148601	−	1.48753i
$759$	15.8745	+	9.16515i	0.576208	+	0.332674i
$760$		0			0
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	0.806514	−	0.591215i	$-0.201351\pi$
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	−0.915264	+	0.402854i	$0.868018\pi$
$762$	−11.4364	+	15.9126i	−0.414296	+	0.576451i
$763$	4.14110	+	15.4548i	0.149918	+	0.559502i
$764$	15.8745	+	14.0000i	0.574320	+	0.506502i
$765$		0			0
$766$	−17.0000	+	44.9778i	−0.614235	+	1.62511i
$767$	13.5230	−	3.62347i	0.488286	−	0.130836i
$768$	−23.8441	−	14.1230i	−0.860400	−	0.509620i
$769$	22.5167	−	13.0000i	0.811972	−	0.468792i	−0.0356685	−	0.999364i	$-0.511356\pi$
$769$	22.5167	−	13.0000i	0.811972	−	0.468792i	0.847640	+	0.530572i	$0.178023\pi$
$770$		0			0
$771$	−4.58258			−0.165037
$772$	−7.06075	+	14.2178i	−0.254122	+	0.511710i
$773$	29.9333	+	29.9333i	1.07662	+	1.07662i	0.996810	+	0.0798148i	$0.0254329\pi$
$773$	29.9333	+	29.9333i	1.07662	+	1.07662i	0.0798148	+	0.996810i	$0.474567\pi$
$774$	3.28335	−	2.68693i	0.118018	−	0.0965798i
$775$		0			0
$776$	−7.47822	−	0.276100i	−0.268452	−	0.00991142i
$777$	−9.48846	+	35.4114i	−0.340397	+	1.27038i
$778$	9.90418	−	13.7807i	0.355082	−	0.494061i
$779$	9.26013	+	16.0390i	0.331779	+	0.574657i
$780$		0			0
$781$		0			0
$782$	18.4735	+	40.9235i	0.660611	+	1.46342i
$783$	−10.0382	+	2.68973i	−0.358736	+	0.0961230i
$784$	35.7176	−	4.50000i	1.27563	−	0.160714i
$785$		0			0
$786$	−24.6261	−	30.0924i	−0.878385	−	1.07336i
$787$	1.03528	−	3.86370i	0.0369036	−	0.137726i	−0.945016	−	0.327024i	$-0.893954\pi$
$787$	1.03528	−	3.86370i	0.0369036	−	0.137726i	0.981920	+	0.189297i	$0.0606210\pi$
$788$	−17.6316	+	11.7101i	−0.628099	+	0.417156i
$789$	−10.3923	−	18.0000i	−0.369976	−	0.640817i
$790$		0			0
$791$		0			0
$792$	6.60659	−	21.4558i	0.234755	−	0.762400i
$793$	22.4499	+	22.4499i	0.797221	+	0.797221i
$794$	−33.1751	−	40.5390i	−1.17734	−	1.43868i
$795$		0			0
$796$	−41.4955	−	8.37420i	−1.47077	−	0.296816i
$797$	−15.3336	−	4.10862i	−0.543144	−	0.145535i	−0.0231928	−	0.999731i	$-0.507383\pi$
$797$	−15.3336	−	4.10862i	−0.543144	−	0.145535i	−0.519951	+	0.854196i	$0.674050\pi$
$798$	10.6657	+	23.6272i	0.377561	+	0.836393i
$799$	−23.8118	+	41.2432i	−0.842400	+	1.45908i
$800$		0			0
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$	32.2242	−	14.5465i	1.13788	−	0.513656i
$803$	−9.05867	−	33.8074i	−0.319673	−	1.19304i
$804$	−6.16748	+	30.5608i	−0.217510	+	1.07780i
$805$		0			0
$806$	39.0780	−	6.39590i	1.37646	−	0.225286i
$807$	−8.06918	−	30.1146i	−0.284049	−	1.06008i
$808$	−19.2485	−	20.7243i	−0.677159	−	0.729078i
$809$		−	9.00000i		−	0.316423i	−0.987405	−	0.158212i	$-0.949427\pi$
$809$		−	9.00000i		−	0.316423i	0.987405	−	0.158212i	$-0.0505728\pi$
$810$		0			0
$811$		−	18.5203i		−	0.650334i	−0.945657	−	0.325167i	$-0.894579\pi$
$811$		−	18.5203i		−	0.650334i	0.945657	−	0.325167i	$-0.105421\pi$
$812$	−14.3302	−	7.11657i	−0.502891	−	0.249743i
$813$		0			0
$814$	3.19795	+	19.5390i	0.112088	+	0.684842i
$815$		0			0
$816$	43.8131	−	33.2327i	1.53376	−	1.16338i
$817$	0.684771	+	2.55560i	0.0239571	+	0.0894091i
$818$	−6.40047	−	14.1786i	−0.223787	−	0.495745i
$819$	31.7490	+	54.9909i	1.10940	+	1.92154i
$820$		0			0
$821$	−26.0000	+	45.0333i	−0.907406	+	1.57167i	−0.0897520	+	0.995964i	$0.528607\pi$
$821$	−26.0000	+	45.0333i	−0.907406	+	1.57167i	−0.817654	+	0.575710i	$0.804726\pi$
$822$	17.7204	−	7.99927i	0.618069	−	0.279006i
$823$	−9.65926	−	2.58819i	−0.336701	−	0.0902186i	0.0865074	−	0.996251i	$-0.472429\pi$
$823$	−9.65926	−	2.58819i	−0.336701	−	0.0902186i	−0.423208	+	0.906033i	$0.639096\pi$
$824$	−9.02175	+	14.3739i	−0.314288	+	0.500737i
$825$		0			0
$826$	−11.5826	+	9.47860i	−0.403009	+	0.329803i
$827$	−31.1127	−	31.1127i	−1.08189	−	1.08189i	−0.996333	−	0.0855616i	$-0.972732\pi$
$827$	−31.1127	−	31.1127i	−1.08189	−	1.08189i	−0.0855616	−	0.996333i	$-0.527268\pi$
$828$	−23.9529	+	1.50295i	−0.832421	+	0.0522311i
$829$			4.00000i			0.138926i	0.997585	+	0.0694629i	$0.0221285\pi$
$829$			4.00000i			0.138926i	−0.997585	+	0.0694629i	$0.977871\pi$
$830$		0			0
$831$	−18.3303	−	31.7490i	−0.635871	−	1.10136i
$832$	32.0591	−	27.6445i	1.11145	−	0.958399i
$833$	−18.4888	+	69.0012i	−0.640599	+	2.39075i
$834$	−35.1078	+	28.7305i	−1.21568	+	0.994856i
$835$		0			0
$836$	10.5000	+	9.26013i	0.363150	+	0.320268i
$837$	−7.11635	+	26.5586i	−0.245977	+	0.917998i
$838$	20.4617	−	9.23676i	0.706839	−	0.319078i
$839$	7.93725	−	13.7477i	0.274024	−	0.474624i	−0.695864	−	0.718173i	$-0.744978\pi$
$839$	7.93725	−	13.7477i	0.274024	−	0.474624i	0.969889	+	0.243549i	$0.0783117\pi$
$840$		0			0
$841$	−12.5000	−	21.6506i	−0.431034	−	0.746574i
$842$	−9.18712	−	6.60279i	−0.316609	−	0.227547i
$843$	9.86233	−	36.8067i	0.339677	−	1.26769i
$844$	10.0308	−	3.37386i	0.345275	−	0.116133i
$845$		0			0
$846$	−16.1216	−	19.7001i	−0.554272	−	0.677304i
$847$	−11.3137	−	11.3137i	−0.388744	−	0.388744i
$848$	7.99080	+	19.5997i	0.274405	+	0.673055i
$849$	−6.92820			−0.237775
$850$		0			0
$851$	18.3303	−	10.5830i	0.628355	−	0.362781i
$852$		0			0
$853$	−15.3336	+	4.10862i	−0.525012	+	0.140677i	−0.511584	−	0.859233i	$-0.670941\pi$
$853$	−15.3336	+	4.10862i	−0.525012	+	0.140677i	−0.0134282	+	0.999910i	$0.504274\pi$
$854$	−31.7490	−	12.0000i	−1.08643	−	0.410632i
$855$		0			0
$856$	32.5000	−	17.1974i	1.11083	−	0.587794i
$857$	−5.47817	−	20.4448i	−0.187131	−	0.698381i	−0.994164	−	0.107876i	$-0.965595\pi$
$857$	−5.47817	−	20.4448i	−0.187131	−	0.698381i	0.807034	−	0.590505i	$-0.201072\pi$
$858$	27.8470	+	20.0136i	0.950680	+	0.683254i
$859$	−1.32288	−	2.29129i	−0.0451359	−	0.0781777i	0.842575	−	0.538579i	$-0.181039\pi$
$859$	−1.32288	−	2.29129i	−0.0451359	−	0.0781777i	−0.887711	+	0.460402i	$0.847705\pi$
$860$		0			0
$861$	−42.0000	−	24.2487i	−1.43136	−	0.826394i
$862$	−29.7850	−	2.97546i	−1.01448	−	0.101345i
$863$	2.82843	−	2.82843i	0.0962808	−	0.0962808i	−0.657326	−	0.753607i	$-0.728312\pi$
$863$	2.82843	−	2.82843i	0.0962808	−	0.0962808i	0.753607	+	0.657326i	$0.228312\pi$
$864$	8.33648	+	28.1869i	0.283613	+	0.958939i
$865$		0			0
$866$	2.89564	−	2.36965i	0.0983980	−	0.0805240i
$867$	20.6212	+	76.9595i	0.700334	+	2.61368i
$868$	−35.2632	+	23.4203i	−1.19691	+	0.794935i
$869$	−24.2487	+	14.0000i	−0.822581	+	0.474917i
$870$		0			0
$871$	−41.2432	−	23.8118i	−1.39747	−	0.806831i
$872$	−10.8127	−	3.32941i	−0.366165	−	0.112748i
$873$	5.61249	+	5.61249i	0.189954	+	0.189954i
$874$	5.29150	−	14.0000i	0.178988	−	0.473557i
$875$		0			0
$876$	34.3693	+	30.3109i	1.16123	+	1.02411i
$877$	−25.5560	−	6.84771i	−0.862965	−	0.231231i	−0.199922	−	0.979812i	$-0.564069\pi$
$877$	−25.5560	−	6.84771i	−0.862965	−	0.231231i	−0.663043	+	0.748581i	$0.730735\pi$
$878$	6.07671	+	4.36733i	0.205079	+	0.147390i
$879$			9.16515i			0.309133i
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$	−31.0065	−	22.2844i	−1.04404	−	0.750355i
$883$	9.19239	−	9.19239i	0.309348	−	0.309348i	−0.535308	−	0.844657i	$-0.679805\pi$
$883$	9.19239	−	9.19239i	0.309348	−	0.309348i	0.844657	+	0.535308i	$0.179805\pi$
$884$	26.7792	+	79.6170i	0.900682	+	2.67781i
$885$		0			0
$886$	−40.4737	+	6.62433i	−1.35974	+	0.222549i
$887$	12.4233	−	46.3644i	0.417134	−	1.55677i	−0.363388	−	0.931638i	$-0.618380\pi$
$887$	12.4233	−	46.3644i	0.417134	−	1.55677i	0.780522	−	0.625128i	$-0.214953\pi$
$888$	−17.6415	−	18.9941i	−0.592011	−	0.637401i
$889$	27.7128	+	16.0000i	0.929458	+	0.536623i
$890$		0			0
$891$	−20.6216	+	11.9059i	−0.690849	+	0.398862i
$892$	2.00393	+	31.9372i	0.0670966	+	1.06934i
$893$	15.3336	−	4.10862i	0.513119	−	0.137490i
$894$	15.5130	+	18.9564i	0.518833	+	0.633998i
$895$		0			0
$896$	−19.0780	+	41.0369i	−0.637352	+	1.37095i
$897$	9.48846	−	35.4114i	0.316811	−	1.18235i
$898$	−40.8091	−	4.07675i	−1.36182	−	0.136043i
$899$	10.5830			0.352963
$900$		0			0
$901$	−42.0000			−1.39922
$902$	−26.0619	−	2.60353i	−0.867766	−	0.0866881i
$903$	−4.89898	−	4.89898i	−0.163028	−	0.163028i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	16.4207	−	4.39992i	0.545242	−	0.146097i	0.0243242	−	0.999704i	$-0.492257\pi$
$907$	16.4207	−	4.39992i	0.545242	−	0.146097i	0.520917	+	0.853607i	$0.325590\pi$
$908$	13.9725	−	0.876721i	0.463694	−	0.0290950i
$909$			30.0000i			0.995037i
$910$		0			0
$911$	32.0780	+	18.5203i	1.06279	+	0.613604i	0.926203	−	0.377024i	$-0.123053\pi$
$911$	32.0780	+	18.5203i	1.06279	+	0.613604i	0.136589	+	0.990628i	$0.456386\pi$
$912$	−18.1599	−	2.49381i	−0.601333	−	0.0825782i
$913$		0			0
$914$	25.8477	−	4.23049i	0.854966	−	0.139932i
$915$		0			0
$916$	37.9129	−	12.7520i	1.25268	−	0.421338i
$917$	−44.8999	+	44.8999i	−1.48272	+	1.48272i
$918$	−58.0378	−	5.79786i	−1.91553	−	0.191358i
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$	31.5000	+	18.1865i	1.03796	+	0.599267i
$922$	−2.29678	−	1.65070i	−0.0756404	−	0.0543628i
$923$		0			0
$924$	−35.9361	−	7.25227i	−1.18221	−	0.238582i
$925$		0			0
$926$	−11.0000	+	29.1033i	−0.361482	+	0.956393i
$927$	17.3867	−	4.65874i	0.571053	−	0.153013i
$928$	9.64900	−	5.90735i	0.316744	−	0.193918i
$929$	−29.4449	−	17.0000i	−0.966055	−	0.557752i	−0.0680235	−	0.997684i	$-0.521669\pi$
$929$	−29.4449	−	17.0000i	−0.966055	−	0.557752i	−0.898031	+	0.439932i	$0.855003\pi$
$930$		0			0
$931$	20.6216	−	11.9059i	0.675845	−	0.390199i
$932$	14.6377	+	22.0395i	0.479473	+	0.721927i
$933$	19.4422	−	19.4422i	0.636510	−	0.636510i
$934$	−29.5502	+	24.1824i	−0.966911	+	0.791272i
$935$		0			0
$936$	−44.8693	−	1.65660i	−1.46660	−	0.0541477i
$937$	14.9666	−	14.9666i	0.488938	−	0.488938i	−0.419033	−	0.907971i	$-0.637631\pi$
$937$	14.9666	−	14.9666i	0.488938	−	0.488938i	0.907971	+	0.419033i	$0.137631\pi$
$938$	50.6595	+	5.06079i	1.65409	+	0.165241i
$939$	43.6549	−	25.2042i	1.42462	−	0.822507i
$940$		0			0
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	0.601418	−	0.798935i	$-0.294603\pi$
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	−0.992607	+	0.121376i	$0.961269\pi$
$942$	5.15366	−	51.5891i	0.167915	−	1.68087i
$943$	7.24693	+	27.0459i	0.235993	+	0.880736i
$944$	−1.32288	−	10.5000i	−0.0430559	−	0.341746i
$945$		0			0
$946$	−3.50000	−	1.32288i	−0.113795	−	0.0430104i
$947$	−51.1941	+	13.7174i	−1.66358	+	0.445756i	−0.963370	−	0.268177i	$-0.913579\pi$
$947$	−51.1941	+	13.7174i	−1.66358	+	0.445756i	−0.700214	+	0.713933i	$0.746912\pi$
$948$	16.3061	−	32.8346i	0.529598	−	1.06642i
$949$	−60.6218	+	35.0000i	−1.96787	+	1.13615i
$950$		0			0
$951$	−13.7477	−	23.8118i	−0.445801	−	0.772149i
$952$	−61.1120	−	65.7976i	−1.98065	−	2.13251i
$953$	5.61249	+	5.61249i	0.181806	+	0.181806i	0.792142	−	0.610336i	$-0.208966\pi$
$953$	5.61249	+	5.61249i	0.181806	+	0.181806i	−0.610336	+	0.792142i	$0.708966\pi$
$954$	7.93725	−	21.0000i	0.256978	−	0.679900i
$955$		0			0
$956$	−13.4955	−	40.1232i	−0.436474	−	1.29768i
$957$	6.48074	+	6.48074i	0.209493	+	0.209493i
$958$	−30.3835	−	21.8367i	−0.981648	−	0.705511i
$959$	−15.8745	−	27.4955i	−0.512615	−	0.887875i
$960$		0			0
$961$	−1.50000	+	2.59808i	−0.0483871	+	0.0838089i
$962$	36.0911	−	16.2921i	1.16362	−	0.525279i
$963$	−37.6711	−	10.0939i	−1.21393	−	0.325273i
$964$	22.4889	−	25.5000i	0.724318	−	0.821300i
$965$		0			0
$966$	6.33030	+	38.6772i	0.203674	+	1.24442i
$967$	1.55291	−	5.79555i	0.0499384	−	0.186372i	−0.936451	−	0.350798i	$-0.885910\pi$
$967$	1.55291	−	5.79555i	0.0499384	−	0.186372i	0.986389	+	0.164426i	$0.0525770\pi$
$968$	11.0288	−	2.52301i	0.354479	−	0.0810926i
$969$	18.1865	−	31.5000i	0.584236	−	1.01193i
$970$		0			0
$971$		−	15.8745i		−	0.509437i	−0.967015	−	0.254719i	$-0.918017\pi$
$971$		−	15.8745i		−	0.509437i	0.967015	−	0.254719i	$-0.0819828\pi$
$972$	13.8670	−	27.9232i	0.444786	−	0.895637i
$973$	52.3832	+	52.3832i	1.67933	+	1.67933i
$974$	−41.5891	+	34.0345i	−1.33260	+	1.09053i
$975$		0			0
$976$	19.1216	−	14.5040i	0.612067	−	0.464260i
$977$	−28.1116	−	7.53248i	−0.899370	−	0.240985i	−0.220624	−	0.975359i	$-0.570809\pi$
$977$	−28.1116	−	7.53248i	−0.899370	−	0.240985i	−0.678746	+	0.734374i	$0.737476\pi$
$978$	−39.7814	−	28.5909i	−1.27207	−	0.914236i
$979$	7.93725	−	13.7477i	0.253676	−	0.439379i
$980$		0			0
$981$	6.00000	+	10.3923i	0.191565	+	0.331801i
$982$	4.61838	+	10.2309i	0.147378	+	0.326480i
$983$	10.8704	+	40.5689i	0.346712	+	1.29395i	0.890600	+	0.454788i	$0.150285\pi$
$983$	10.8704	+	40.5689i	0.346712	+	1.29395i	−0.543888	+	0.839158i	$0.683048\pi$
$984$	30.3109	−	16.0390i	0.966276	−	0.511305i
$985$		0			0
$986$	3.62614	+	22.1552i	0.115480	+	0.705564i
$987$	−29.3939	+	29.3939i	−0.935617	+	0.935617i
$988$	12.4540	−	25.0778i	0.396214	−	0.797832i
$989$			4.00000i			0.127193i
$990$		0			0
$991$		−	31.7490i		−	1.00854i	−0.863546	−	0.504270i	$-0.831762\pi$
$991$		−	31.7490i		−	1.00854i	0.863546	−	0.504270i	$-0.168238\pi$
$992$	−0.770998	−	29.9233i	−0.0244792	−	0.950067i
$993$	−8.85286	−	2.37212i	−0.280937	−	0.0752768i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−4.10862	−	15.3336i	−0.130121	−	0.485620i	0.869849	−	0.493318i	$-0.164216\pi$
$997$	−4.10862	−	15.3336i	−0.130121	−	0.485620i	−0.999970	+	0.00769834i	$0.997550\pi$
$998$	−30.6926	+	13.8551i	−0.971557	+	0.438577i
$999$			27.4955i			0.869918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bf.c.43.3	yes	16
4.3	odd	2	inner	900.2.bf.c.43.1	yes	16
5.2	odd	4	inner	900.2.bf.c.7.4	yes	16
5.3	odd	4	inner	900.2.bf.c.7.1	✓	16
5.4	even	2	inner	900.2.bf.c.43.2	yes	16
9.4	even	3	inner	900.2.bf.c.643.3	yes	16
20.3	even	4	inner	900.2.bf.c.7.2	yes	16
20.7	even	4	inner	900.2.bf.c.7.3	yes	16
20.19	odd	2	inner	900.2.bf.c.43.4	yes	16
36.31	odd	6	inner	900.2.bf.c.643.4	yes	16
45.4	even	6	inner	900.2.bf.c.643.2	yes	16
45.13	odd	12	inner	900.2.bf.c.607.4	yes	16
45.22	odd	12	inner	900.2.bf.c.607.1	yes	16
180.67	even	12	inner	900.2.bf.c.607.3	yes	16
180.103	even	12	inner	900.2.bf.c.607.2	yes	16
180.139	odd	6	inner	900.2.bf.c.643.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.bf.c.7.1	✓	16	5.3	odd	4	inner
900.2.bf.c.7.2	yes	16	20.3	even	4	inner
900.2.bf.c.7.3	yes	16	20.7	even	4	inner
900.2.bf.c.7.4	yes	16	5.2	odd	4	inner
900.2.bf.c.43.1	yes	16	4.3	odd	2	inner
900.2.bf.c.43.2	yes	16	5.4	even	2	inner
900.2.bf.c.43.3	yes	16	1.1	even	1	trivial
900.2.bf.c.43.4	yes	16	20.19	odd	2	inner
900.2.bf.c.607.1	yes	16	45.22	odd	12	inner
900.2.bf.c.607.2	yes	16	180.103	even	12	inner
900.2.bf.c.607.3	yes	16	180.67	even	12	inner
900.2.bf.c.607.4	yes	16	45.13	odd	12	inner
900.2.bf.c.643.1	yes	16	180.139	odd	6	inner
900.2.bf.c.643.2	yes	16	45.4	even	6	inner
900.2.bf.c.643.3	yes	16	9.4	even	3	inner
900.2.bf.c.643.4	yes	16	36.31	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.140577 - 1.40721i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-1.96048 - 0.395644i) q^{4} +(0.395644 + 2.41733i) q^{6} +(3.86370 - 1.03528i) q^{7} +(-0.832353 + 2.70318i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-2.29129 - 1.32288i) q^{11} +(3.45730 - 0.216932i) q^{12} +(-1.36954 + 5.11120i) q^{13} +(-0.913701 - 5.58258i) q^{14} +(3.68693 + 1.55130i) q^{16} +(-5.61249 + 5.61249i) q^{17} +(-1.74558 - 3.86690i) q^{18} +2.64575 q^{19} +(-6.00000 + 3.46410i) q^{21} +(-2.18367 + 3.03835i) q^{22} +(3.86370 + 1.03528i) q^{23} +(0.180750 - 4.89564i) q^{24} +(7.00000 + 2.64575i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-7.98430 + 0.500983i) q^{28} +(1.73205 + 1.00000i) q^{29} +(4.58258 - 2.64575i) q^{31} +(2.70130 - 4.97021i) q^{32} +(4.42643 + 1.18606i) q^{33} +(7.10895 + 8.68693i) q^{34} +(-5.68693 + 1.91280i) q^{36} +(3.74166 - 3.74166i) q^{37} +(0.371933 - 3.72313i) q^{38} -9.16515i q^{39} +(3.50000 + 6.06218i) q^{41} +(4.03125 + 8.93023i) q^{42} +(0.258819 + 0.965926i) q^{43} +(3.96863 + 3.50000i) q^{44} +(2.00000 - 5.29150i) q^{46} +(5.79555 - 1.55291i) q^{47} +(-6.86379 - 0.942570i) q^{48} +(7.79423 - 4.50000i) q^{49} +(6.87386 - 11.9059i) q^{51} +(4.70717 - 9.47853i) q^{52} +(3.74166 + 3.74166i) q^{53} +(4.65390 + 5.68693i) q^{54} +(-0.417424 + 11.3060i) q^{56} +(-4.42643 + 1.18606i) q^{57} +(1.65070 - 2.29678i) q^{58} +(-1.32288 - 2.29129i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-3.07892 - 6.82058i) q^{62} +(8.48528 - 8.48528i) q^{63} +(-6.61438 - 4.50000i) q^{64} +(2.29129 - 6.06218i) q^{66} +(-2.32937 + 8.69333i) q^{67} +(13.2237 - 8.78260i) q^{68} -6.92820 q^{69} +(1.89226 + 8.27160i) q^{72} +(9.35414 + 9.35414i) q^{73} +(-4.73930 - 5.79129i) q^{74} +(-5.18693 - 1.04678i) q^{76} +(-10.2224 - 2.73908i) q^{77} +(-12.8973 - 1.28841i) q^{78} +(5.29150 - 9.16515i) q^{79} +(4.50000 - 7.79423i) q^{81} +(9.02277 - 4.07303i) q^{82} +(13.1334 - 4.41742i) q^{84} +(1.39564 - 0.228425i) q^{86} +(-3.34607 - 0.896575i) q^{87} +(5.48313 - 5.09267i) q^{88} +6.00000i q^{89} +21.1660i q^{91} +(-7.16510 - 3.55828i) q^{92} +(-6.48074 + 6.48074i) q^{93} +(-1.37055 - 8.37386i) q^{94} +(-2.29129 + 9.52628i) q^{96} +(0.684771 + 2.55560i) q^{97} +(-5.23675 - 11.6007i) q^{98} -7.93725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{6} + 4 q^{16} - 96 q^{21} + 112 q^{26} - 36 q^{36} + 56 q^{41} + 32 q^{46} - 80 q^{56} + 48 q^{61} - 28 q^{76} + 72 q^{81} + 4 q^{86}+O(q^{100}) \) 16 * q - 12 * q^6 + 4 * q^16 - 96 * q^21 + 112 * q^26 - 36 * q^36 + 56 * q^41 + 32 * q^46 - 80 * q^56 + 48 * q^61 - 28 * q^76 + 72 * q^81 + 4 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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