LMFDB - Embedded newform 900.2.bf.c.7.1

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			7.1
Root			$-1.14839 + 0.825348i$ of defining polynomial
Character	$\chi$	$=$	900.7
Dual form			900.2.bf.c.643.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40721 - 0.140577i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(1.96048 + 0.395644i) q^{4} +(0.395644 + 2.41733i) q^{6} +(-1.03528 - 3.86370i) q^{7} +(-2.70318 - 0.832353i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(-2.29129 - 1.32288i) q^{11} +(-0.216932 - 3.45730i) q^{12} +(-5.11120 - 1.36954i) q^{13} +(0.913701 + 5.58258i) q^{14} +(3.68693 + 1.55130i) q^{16} +(5.61249 + 5.61249i) q^{17} +(3.86690 - 1.74558i) q^{18} -2.64575 q^{19} +(-6.00000 + 3.46410i) q^{21} +(3.03835 + 2.18367i) q^{22} +(-1.03528 + 3.86370i) q^{23} +(-0.180750 + 4.89564i) q^{24} +(7.00000 + 2.64575i) q^{26} +(3.67423 + 3.67423i) q^{27} +(-0.500983 - 7.98430i) q^{28} +(-1.73205 - 1.00000i) q^{29} +(4.58258 - 2.64575i) q^{31} +(-4.97021 - 2.70130i) q^{32} +(-1.18606 + 4.42643i) q^{33} +(-7.10895 - 8.68693i) q^{34} +(-5.68693 + 1.91280i) q^{36} +(-3.74166 - 3.74166i) q^{37} +(3.72313 + 0.371933i) q^{38} +9.16515i q^{39} +(3.50000 + 6.06218i) q^{41} +(8.93023 - 4.03125i) q^{42} +(-0.965926 + 0.258819i) q^{43} +(-3.96863 - 3.50000i) q^{44} +(2.00000 - 5.29150i) q^{46} +(-1.55291 - 5.79555i) q^{47} +(0.942570 - 6.86379i) q^{48} +(-7.79423 + 4.50000i) q^{49} +(6.87386 - 11.9059i) q^{51} +(-9.47853 - 4.70717i) q^{52} +(-3.74166 + 3.74166i) q^{53} +(-4.65390 - 5.68693i) q^{54} +(-0.417424 + 11.3060i) q^{56} +(1.18606 + 4.42643i) q^{57} +(2.29678 + 1.65070i) q^{58} +(1.32288 + 2.29129i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-6.82058 + 3.07892i) q^{62} +(8.48528 + 8.48528i) q^{63} +(6.61438 + 4.50000i) q^{64} +(2.29129 - 6.06218i) q^{66} +(8.69333 + 2.32937i) q^{67} +(8.78260 + 13.2237i) q^{68} +6.92820 q^{69} +(8.27160 - 1.89226i) q^{72} +(-9.35414 + 9.35414i) q^{73} +(4.73930 + 5.79129i) q^{74} +(-5.18693 - 1.04678i) q^{76} +(-2.73908 + 10.2224i) q^{77} +(1.28841 - 12.8973i) q^{78} +(-5.29150 + 9.16515i) q^{79} +(4.50000 - 7.79423i) q^{81} +(-4.07303 - 9.02277i) q^{82} +(-13.1334 + 4.41742i) q^{84} +(1.39564 - 0.228425i) q^{86} +(-0.896575 + 3.34607i) q^{87} +(5.09267 + 5.48313i) q^{88} -6.00000i q^{89} +21.1660i q^{91} +(-3.55828 + 7.16510i) q^{92} +(-6.48074 - 6.48074i) q^{93} +(1.37055 + 8.37386i) q^{94} +(-2.29129 + 9.52628i) q^{96} +(2.55560 - 0.684771i) q^{97} +(11.6007 - 5.23675i) 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.40721	−	0.140577i	−0.995047	−	0.0994033i
$2$	−1.40721	−	0.140577i	−0.995047	−	0.0994033i
$3$	−0.448288	−	1.67303i	−0.258819	−	0.965926i
$3$	−0.448288	−	1.67303i	−0.258819	−	0.965926i
$4$	1.96048	+	0.395644i	0.980238	+	0.197822i
$5$		0			0
$5$		0			0
$6$	0.395644	+	2.41733i	0.161521	+	0.986869i
$7$	−1.03528	−	3.86370i	−0.391298	−	1.46034i	−0.827996	−	0.560734i	$-0.810519\pi$
$7$	−1.03528	−	3.86370i	−0.391298	−	1.46034i	0.436698	−	0.899608i	$-0.356148\pi$
$8$	−2.70318	−	0.832353i	−0.955719	−	0.294281i
$9$	−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	$0.797261\pi$
$12$	−0.216932	−	3.45730i	−0.0626229	−	0.998037i
$13$	−5.11120	−	1.36954i	−1.41759	−	0.379843i	−0.532963	−	0.846139i	$-0.678921\pi$
$13$	−5.11120	−	1.36954i	−1.41759	−	0.379843i	−0.884629	+	0.466296i	$0.845588\pi$
$14$	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	0.872355	+	0.488873i	$0.162592\pi$
$17$	5.61249	+	5.61249i	1.36123	+	1.36123i	0.488873	+	0.872355i	$0.337408\pi$
$18$	3.86690	−	1.74558i	0.911438	−	0.411438i
$19$	−2.64575			−0.606977			−0.303488	−	0.952835i	$-0.598151\pi$
$19$	−2.64575			−0.606977			−0.303488	+	0.952835i	$0.598151\pi$
$20$		0			0
$21$	−6.00000	+	3.46410i	−1.30931	+	0.755929i
$22$	3.03835	+	2.18367i	0.647779	+	0.465559i
$23$	−1.03528	+	3.86370i	−0.215870	+	0.805638i	0.769988	+	0.638058i	$0.220262\pi$
$23$	−1.03528	+	3.86370i	−0.215870	+	0.805638i	−0.985858	+	0.167580i	$0.946405\pi$
$24$	−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
$28$	−0.500983	−	7.98430i	−0.0946769	−	1.50889i
$29$	−1.73205	−	1.00000i	−0.321634	−	0.185695i	0.330487	−	0.943811i	$-0.392787\pi$
$29$	−1.73205	−	1.00000i	−0.321634	−	0.185695i	−0.652121	+	0.758115i	$0.726120\pi$
$30$		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	$0.175712\pi$
$32$	−4.97021	−	2.70130i	−0.878617	−	0.477528i
$33$	−1.18606	+	4.42643i	−0.206466	+	0.770542i
$34$	−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	$-0.393237\pi$
$37$	−3.74166	−	3.74166i	−0.615125	−	0.615125i	−0.944277	+	0.329152i	$0.893237\pi$
$38$	3.72313	+	0.371933i	0.603971	+	0.0603355i
$39$			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	$0.649252\pi$
$42$	8.93023	−	4.03125i	1.37796	−	0.622036i
$43$	−0.965926	+	0.258819i	−0.147302	+	0.0394695i	−0.331717	−	0.943379i	$-0.607628\pi$
$43$	−0.965926	+	0.258819i	−0.147302	+	0.0394695i	0.184414	+	0.982849i	$0.440961\pi$
$44$	−3.96863	−	3.50000i	−0.598293	−	0.527645i
$45$		0			0
$46$	2.00000	−	5.29150i	0.294884	−	0.780189i
$47$	−1.55291	−	5.79555i	−0.226516	−	0.845369i	−0.981792	−	0.189961i	$-0.939164\pi$
$47$	−1.55291	−	5.79555i	−0.226516	−	0.845369i	0.755276	−	0.655407i	$-0.227503\pi$
$48$	0.942570	−	6.86379i	0.136048	−	0.990702i
$49$	−7.79423	+	4.50000i	−1.11346	+	0.642857i
$50$		0			0
$51$	6.87386	−	11.9059i	0.962533	−	1.66716i
$52$	−9.47853	−	4.70717i	−1.31444	−	0.652767i
$53$	−3.74166	+	3.74166i	−0.513956	+	0.513956i	−0.915736	−	0.401780i	$-0.868392\pi$
$53$	−3.74166	+	3.74166i	−0.513956	+	0.513956i	0.401780	+	0.915736i	$0.368392\pi$
$54$	−4.65390	−	5.68693i	−0.633316	−	0.773893i
$55$		0			0
$56$	−0.417424	+	11.3060i	−0.0557807	+	1.51083i
$57$	1.18606	+	4.42643i	0.157097	+	0.586295i
$58$	2.29678	+	1.65070i	0.301582	+	0.216747i
$59$	1.32288	+	2.29129i	0.172224	+	0.298300i	0.939197	−	0.343379i	$-0.111571\pi$
$59$	1.32288	+	2.29129i	0.172224	+	0.298300i	−0.766973	+	0.641679i	$0.778238\pi$
$60$		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	$0.0411748\pi$
$62$	−6.82058	+	3.07892i	−0.866214	+	0.391023i
$63$	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
$67$	8.69333	+	2.32937i	1.06206	+	0.284578i	0.747227	−	0.664569i	$-0.231385\pi$
$67$	8.69333	+	2.32937i	1.06206	+	0.284578i	0.314833	+	0.949147i	$0.398052\pi$
$68$	8.78260	+	13.2237i	1.06505	+	1.60361i
$69$	6.92820			0.834058
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	8.27160	−	1.89226i	0.974817	−	0.223005i
$73$	−9.35414	+	9.35414i	−1.09482	+	1.09482i	−0.0998135	+	0.995006i	$0.531825\pi$
$73$	−9.35414	+	9.35414i	−1.09482	+	1.09482i	−0.995006	+	0.0998135i	$0.968175\pi$
$74$	4.73930	+	5.79129i	0.550933	+	0.673224i
$75$		0			0
$76$	−5.18693	−	1.04678i	−0.594982	−	0.120073i
$77$	−2.73908	+	10.2224i	−0.312148	+	1.16495i
$78$	1.28841	−	12.8973i	0.145884	−	1.46033i
$79$	−5.29150	+	9.16515i	−0.595341	+	1.03116i	0.398158	+	0.917317i	$0.369650\pi$
$79$	−5.29150	+	9.16515i	−0.595341	+	1.03116i	−0.993499	+	0.113843i	$0.963684\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	−4.07303	−	9.02277i	−0.449791	−	0.996399i
$83$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$83$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$84$	−13.1334	+	4.41742i	−1.43297	+	0.481981i
$85$		0			0
$86$	1.39564	−	0.228425i	0.150496	−	0.0246317i
$87$	−0.896575	+	3.34607i	−0.0961230	+	0.358736i
$88$	5.09267	+	5.48313i	0.542880	+	0.584504i
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$		0			0
$91$			21.1660i			2.21880i
$92$	−3.55828	+	7.16510i	−0.370977	+	0.747013i
$93$	−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
$97$	2.55560	−	0.684771i	0.259482	−	0.0695279i	−0.126733	−	0.991937i	$-0.540449\pi$
$97$	2.55560	−	0.684771i	0.259482	−	0.0695279i	0.386215	+	0.922409i	$0.373782\pi$
$98$	11.6007	−	5.23675i	1.17185	−	0.528991i
$99$	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	$0.332422\pi$
$102$	−11.3467	+	15.7878i	−1.12349	+	1.56322i
$103$	−1.55291	+	5.79555i	−0.153013	+	0.571053i	0.846254	+	0.532779i	$0.178852\pi$
$103$	−1.55291	+	5.79555i	−0.153013	+	0.571053i	−0.999267	+	0.0382735i	$0.987814\pi$
$104$	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	−0.994395	−	0.105733i	$-0.966281\pi$
$107$	−9.19239	+	9.19239i	−0.888662	+	0.888662i	0.105733	+	0.994395i	$0.466281\pi$
$108$	5.74956	+	8.65694i	0.553252	+	0.833014i
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$	−4.58258	+	7.93725i	−0.434959	+	0.753371i
$112$	2.17677	−	15.8512i	0.205686	−	1.49780i
$113$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$113$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$114$	−1.04678	−	6.39564i	−0.0980395	−	0.599007i
$115$		0			0
$116$	−3.00000	−	2.64575i	−0.278543	−	0.245652i
$117$	15.3336	−	4.10862i	1.41759	−	0.379843i
$118$	−1.53946	−	3.41029i	−0.141719	−	0.313942i
$119$	15.8745	−	27.4955i	1.45521	−	2.52050i
$120$		0			0
$121$	−2.00000	−	3.46410i	−0.181818	−	0.314918i
$122$	−4.95209	+	6.89034i	−0.448341	+	0.623822i
$123$	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	−0.410083	−	0.912048i	$-0.634500\pi$
$127$	5.65685	−	5.65685i	0.501965	−	0.501965i	0.912048	+	0.410083i	$0.134500\pi$
$128$	−8.67522	−	7.26227i	−0.766788	−	0.641900i
$129$	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	$0.577257\pi$
$132$	−4.07653	+	8.20865i	−0.354816	+	0.714471i
$133$	2.73908	+	10.2224i	0.237509	+	0.886394i
$134$	−11.9059	−	4.50000i	−1.02851	−	0.388741i
$135$		0			0
$136$	−10.5000	−	19.8431i	−0.900368	−	1.70153i
$137$	−7.66680	+	2.05431i	−0.655019	+	0.175512i	−0.570997	−	0.820952i	$-0.693443\pi$
$137$	−7.66680	+	2.05431i	−0.655019	+	0.175512i	−0.0840218	+	0.996464i	$0.526777\pi$
$138$	−9.74943	−	0.973949i	−0.829927	−	0.0829081i
$139$	−9.26013	−	16.0390i	−0.785434	−	1.36041i	−0.928739	−	0.370733i	$-0.879106\pi$
$139$	−9.26013	−	16.0390i	−0.785434	−	1.36041i	0.143306	−	0.989678i	$-0.454227\pi$
$140$		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
$148$	−5.85507	−	8.81579i	−0.481283	−	0.724654i
$149$	−8.66025	+	5.00000i	−0.709476	+	0.409616i	−0.810867	−	0.585231i	$-0.801004\pi$
$149$	−8.66025	+	5.00000i	−0.709476	+	0.409616i	0.101391	+	0.994847i	$0.467671\pi$
$150$		0			0
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$	7.15195	+	2.20220i	0.580099	+	0.178622i
$153$	−23.0004	−	6.16294i	−1.85947	−	0.498244i
$154$	5.29150	−	14.0000i	0.426401	−	1.12815i
$155$		0			0
$156$	−3.62614	+	17.9681i	−0.290323	+	1.43860i
$157$	−5.47817	+	20.4448i	−0.437205	+	1.63167i	0.298528	+	0.954401i	$0.403504\pi$
$157$	−5.47817	+	20.4448i	−0.437205	+	1.63167i	−0.735733	+	0.677271i	$0.763162\pi$
$158$	8.73467	−	12.1534i	0.694893	−	0.966874i
$159$	7.93725	+	4.58258i	0.629465	+	0.363422i
$160$		0			0
$161$	16.0000			1.26098
$162$	−7.42813	+	10.3355i	−0.583609	+	0.812035i
$163$	−14.1421	−	14.1421i	−1.10770	−	1.10770i	−0.993453	−	0.114245i	$-0.963555\pi$
$163$	−14.1421	−	14.1421i	−1.10770	−	1.10770i	−0.114245	−	0.993453i	$-0.536445\pi$
$164$	4.46320	+	13.2695i	0.348518	+	1.03617i
$165$		0			0
$166$		0			0
$167$	−11.5911	−	3.10583i	−0.896947	−	0.240336i	−0.219242	−	0.975670i	$-0.570359\pi$
$167$	−11.5911	−	3.10583i	−0.896947	−	0.240336i	−0.677705	+	0.735334i	$0.737025\pi$
$168$	19.1024	−	4.36998i	1.47379	−	0.337151i
$169$	12.9904	+	7.50000i	0.999260	+	0.576923i
$170$		0			0
$171$	6.87386	−	3.96863i	0.525657	−	0.303488i
$172$	−1.99607	+	0.125246i	−0.152199	+	0.00954990i
$173$	1.36954	+	5.11120i	0.104124	+	0.388597i	0.998244	−	0.0592301i	$-0.0188646\pi$
$173$	1.36954	+	5.11120i	0.104124	+	0.388597i	−0.894120	+	0.447827i	$0.852198\pi$
$174$	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
$178$	−0.843465	+	8.44326i	−0.0632204	+	0.632849i
$179$	−5.29150			−0.395505			−0.197753	−	0.980252i	$-0.563364\pi$
$179$	−5.29150			−0.395505			−0.197753	+	0.980252i	$0.563364\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$	2.97546	−	29.7850i	0.220556	−	2.20781i
$183$	−10.0382	−	2.68973i	−0.742045	−	0.198830i
$184$	6.01450	−	9.58258i	0.443395	−	0.706437i
$185$		0			0
$186$	8.20871	+	10.0308i	0.601892	+	0.735494i
$187$	−5.43520	−	20.2844i	−0.397461	−	1.48335i
$188$	−0.751475	−	11.9764i	−0.0548069	−	0.873472i
$189$	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	$0.791734\pi$
$192$	4.56350	−	13.0834i	0.329342	−	0.944211i
$193$	7.66680	+	2.05431i	0.551868	+	0.147873i	0.523968	−	0.851738i	$-0.324451\pi$
$193$	7.66680	+	2.05431i	0.551868	+	0.147873i	0.0279004	+	0.999611i	$0.491118\pi$
$194$	−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	$-0.373046\pi$
$197$	−7.48331	−	7.48331i	−0.533164	−	0.533164i	−0.921513	+	0.388348i	$0.873046\pi$
$198$	−11.1694	−	1.11580i	−0.793773	−	0.0792964i
$199$	−21.1660			−1.50042			−0.750209	−	0.661200i	$-0.770047\pi$
$199$	−21.1660			−1.50042			−0.750209	+	0.661200i	$0.770047\pi$
$200$		0			0
$201$		−	15.5885i		−	1.09952i
$202$	8.25348	−	11.4839i	0.580713	−	0.808005i
$203$	−2.07055	+	7.72741i	−0.145324	+	0.542358i
$204$	18.1865	−	20.6216i	1.27331	−	1.44380i
$205$		0			0
$206$	3.00000	−	7.93725i	0.209020	−	0.553015i
$207$	−3.10583	−	11.5911i	−0.215870	−	0.805638i
$208$	−16.7201	−	12.9784i	−1.15933	−	0.899891i
$209$	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	$0.391636\pi$
$212$	−8.81579	+	5.85507i	−0.605471	+	0.402128i
$213$		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
$218$	−0.562310	+	5.62884i	−0.0380844	+	0.381233i
$219$	19.8431	+	11.4564i	1.34087	+	0.774154i
$220$		0			0
$221$	−21.0000	−	36.3731i	−1.41261	−	2.44672i
$222$	7.56444	−	10.5252i	0.507692	−	0.706403i
$223$	15.4548	−	4.14110i	1.03493	−	0.277309i	0.298920	−	0.954278i	$-0.403374\pi$
$223$	15.4548	−	4.14110i	1.03493	−	0.277309i	0.736011	+	0.676969i	$0.236707\pi$
$224$	−5.29150	+	22.0000i	−0.353553	+	1.46994i
$225$		0			0
$226$		0			0
$227$	1.81173	+	6.76148i	0.120249	+	0.448775i	0.999626	−	0.0273510i	$-0.00870719\pi$
$227$	1.81173	+	6.76148i	0.120249	+	0.448775i	−0.879377	+	0.476126i	$0.842041\pi$
$228$	0.573948	+	9.14716i	0.0380107	+	0.605786i
$229$	17.3205	−	10.0000i	1.14457	−	0.660819i	0.197013	−	0.980401i	$-0.436876\pi$
$229$	17.3205	−	10.0000i	1.14457	−	0.660819i	0.947559	+	0.319582i	$0.103543\pi$
$230$		0			0
$231$	18.3303			1.20605
$232$	3.84969	+	4.14486i	0.252745	+	0.272123i
$233$	9.35414	−	9.35414i	0.612810	−	0.612810i	−0.330867	−	0.943677i	$-0.607341\pi$
$233$	9.35414	−	9.35414i	0.612810	−	0.612810i	0.943677	+	0.330867i	$0.107341\pi$
$234$	−22.1552	+	3.62614i	−1.44833	+	0.237048i
$235$		0			0
$236$	1.68693	+	5.01540i	0.109810	+	0.326475i
$237$	17.7057	+	4.74423i	1.15011	+	0.308171i
$238$	−26.2040	+	36.4603i	−1.69855	+	2.36337i
$239$	−10.5830	−	18.3303i	−0.684558	−	1.18569i	−0.973576	−	0.228365i	$-0.926662\pi$
$239$	−10.5830	−	18.3303i	−0.684558	−	1.18569i	0.289018	−	0.957324i	$-0.406671\pi$
$240$		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	$0.982234\pi$
$242$	2.32744	+	5.15587i	0.149614	+	0.331432i
$243$	−15.0573	−	4.03459i	−0.965926	−	0.258819i
$244$	7.93725	−	9.00000i	0.508131	−	0.576166i
$245$		0			0
$246$	−13.2695	+	10.8591i	−0.846033	+	0.692351i
$247$	13.5230	+	3.62347i	0.860445	+	0.230556i
$248$	−14.5897	+	3.33763i	−0.926449	+	0.211940i
$249$		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	$-0.370591\pi$
$252$	13.2780	+	19.9923i	0.836438	+	1.25940i
$253$	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
$257$	0.684771	−	2.55560i	0.0427148	−	0.159414i	−0.941274	−	0.337643i	$-0.890370\pi$
$257$	0.684771	−	2.55560i	0.0427148	−	0.159414i	0.983989	+	0.178229i	$0.0570369\pi$
$258$	−1.00781	−	2.23256i	−0.0627437	−	0.138993i
$259$	−10.5830	+	18.3303i	−0.657596	+	1.13899i
$260$		0			0
$261$	6.00000			0.371391
$262$	20.4617	−	9.23676i	1.26413	−	0.570649i
$263$	−11.5911	+	3.10583i	−0.714738	+	0.191514i	−0.597823	−	0.801628i	$-0.703967\pi$
$263$	−11.5911	+	3.10583i	−0.714738	+	0.191514i	−0.116916	+	0.993142i	$0.537301\pi$
$264$	6.89048	−	10.9782i	0.424080	−	0.675663i
$265$		0			0
$266$	−2.41742	−	14.7701i	−0.148222	−	0.905613i
$267$	−10.0382	+	2.68973i	−0.614328	+	0.164609i
$268$	16.1215	+	8.00614i	0.984775	+	0.489053i
$269$		−	18.0000i		−	1.09748i	−0.835993	−	0.548740i	$-0.815108\pi$
$269$		−	18.0000i		−	1.09748i	0.835993	−	0.548740i	$-0.184892\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	11.9862	+	29.3995i	0.726770	+	1.78261i
$273$	35.4114	−	9.48846i	2.14320	−	0.574268i
$274$	11.0776	−	1.81307i	0.669221	−	0.109531i
$275$		0			0
$276$	13.5826	+	2.74110i	0.817575	+	0.164995i
$277$	20.4448	−	5.47817i	1.22841	−	0.329151i	0.414449	−	0.910073i	$-0.363974\pi$
$277$	20.4448	−	5.47817i	1.22841	−	0.329151i	0.813960	+	0.580921i	$0.197308\pi$
$278$	10.7762	+	23.8720i	0.646314	+	1.43175i
$279$	−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	$0.938827\pi$
$282$	13.3953	−	6.04688i	0.797681	−	0.360086i
$283$	−1.03528	+	3.86370i	−0.0615408	+	0.229673i	−0.989846	−	0.142147i	$-0.954600\pi$
$283$	−1.03528	+	3.86370i	−0.0615408	+	0.229673i	0.928305	+	0.371820i	$0.121266\pi$
$284$		0			0
$285$		0			0
$286$	−12.5390	−	15.3223i	−0.741447	−	0.906027i
$287$	19.7990	−	19.7990i	1.16870	−	1.16870i
$288$	16.9649	−	0.437115i	0.999668	−	0.0257572i
$289$			46.0000i			2.70588i
$290$		0			0
$291$	−2.29129	−	3.96863i	−0.134318	−	0.232645i
$292$	−22.0395	+	14.6377i	−1.28976	+	0.856604i
$293$	5.11120	+	1.36954i	0.298599	+	0.0800095i	0.405008	−	0.914313i	$-0.367269\pi$
$293$	5.11120	+	1.36954i	0.298599	+	0.0800095i	−0.106409	+	0.994322i	$0.533935\pi$
$294$	−13.9617	−	17.0608i	−0.814263	−	0.995006i
$295$		0			0
$296$	7.00000	+	13.2288i	0.406867	+	0.768906i
$297$	−3.55817	−	13.2793i	−0.206466	−	0.770542i
$298$	12.8897	−	5.81861i	0.746679	−	0.337063i
$299$	10.5830	−	18.3303i	0.612031	−	1.06007i
$300$		0			0
$301$	2.00000	+	3.46410i	0.115278	+	0.199667i
$302$		0			0
$303$	16.7303	+	4.48288i	0.961132	+	0.257535i
$304$	−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	−0.989819	−	0.142328i	$-0.954541\pi$
$307$	−14.8492	+	14.8492i	−0.847491	+	0.847491i	0.142328	+	0.989819i	$0.454541\pi$
$308$	−9.41434	+	18.9571i	−0.536432	+	1.08018i
$309$	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	$0.481938\pi$
$312$	7.62864	−	24.7751i	0.431887	−	1.40261i
$313$	−7.53248	−	28.1116i	−0.425761	−	1.58896i	−0.762256	−	0.647276i	$-0.775908\pi$
$313$	−7.53248	−	28.1116i	−0.425761	−	1.58896i	0.336495	−	0.941685i	$-0.390759\pi$
$314$	10.5830	−	28.0000i	0.597234	−	1.58013i
$315$		0			0
$316$	−14.0000	+	15.8745i	−0.787562	+	0.893011i
$317$	15.3336	−	4.10862i	0.861221	−	0.230763i	0.198933	−	0.980013i	$-0.436252\pi$
$317$	15.3336	−	4.10862i	0.861221	−	0.230763i	0.662288	+	0.749250i	$0.269586\pi$
$318$	−10.5252	−	7.56444i	−0.590222	−	0.424193i
$319$	2.64575	+	4.58258i	0.148134	+	0.256575i
$320$		0			0
$321$	19.5000	+	11.2583i	1.08838	+	0.628379i
$322$	−22.5153	−	2.24924i	−1.25473	−	0.125345i
$323$	−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
$327$	−6.69213	+	1.79315i	−0.370076	+	0.0991615i
$328$	−4.41527	−	19.3004i	−0.243792	−	1.06569i
$329$	−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
$333$	15.3336	+	4.10862i	0.840276	+	0.225151i
$334$	15.8745	+	6.00000i	0.868614	+	0.328305i
$335$		0			0
$336$	−27.4955	+	3.46410i	−1.50000	+	0.188982i
$337$	0.684771	−	2.55560i	0.0373018	−	0.139212i	−0.944764	−	0.327752i	$-0.893709\pi$
$337$	0.684771	−	2.55560i	0.0373018	−	0.139212i	0.982066	+	0.188540i	$0.0603755\pi$
$338$	−17.2259	−	12.3802i	−0.936963	−	0.673395i
$339$		0			0
$340$		0			0
$341$	−14.0000			−0.758143
$342$	−10.2309	+	4.61838i	−0.553222	+	0.249733i
$343$	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
$347$	−8.69333	−	2.32937i	−0.466683	−	0.125047i	0.0178123	−	0.999841i	$-0.494330\pi$
$347$	−8.69333	−	2.32937i	−0.466683	−	0.125047i	−0.484495	+	0.874794i	$0.660997\pi$
$348$	−3.08157	+	6.20516i	−0.165189	+	0.332631i
$349$	−13.8564	−	8.00000i	−0.741716	−	0.428230i	0.0809766	−	0.996716i	$-0.474196\pi$
$349$	−13.8564	−	8.00000i	−0.741716	−	0.428230i	−0.822693	+	0.568486i	$0.807529\pi$
$350$		0			0
$351$	−13.7477	−	23.8118i	−0.733799	−	1.27098i
$352$	7.81468	+	12.7644i	0.416524	+	0.680346i
$353$	0.684771	+	2.55560i	0.0364467	+	0.136021i	0.981752	−	0.190166i	$-0.0609027\pi$
$353$	0.684771	+	2.55560i	0.0364467	+	0.136021i	−0.945305	+	0.326187i	$0.894236\pi$
$354$	−5.01540	+	4.10436i	−0.266566	+	0.218144i
$355$		0			0
$356$	2.37386	−	11.7629i	0.125815	−	0.623430i
$357$	−53.1171	−	14.2327i	−2.81126	−	0.753274i
$358$	7.44625	+	0.743866i	0.393547	+	0.0393146i
$359$	10.5830			0.558550			0.279275	−	0.960211i	$-0.409906\pi$
$359$	10.5830			0.558550			0.279275	+	0.960211i	$0.409906\pi$
$360$		0			0
$361$	−12.0000			−0.631579
$362$	−19.7009	−	1.96808i	−1.03546	−	0.103440i
$363$	−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
$367$	4.65874	+	17.3867i	0.243184	+	0.907577i	0.974287	+	0.225309i	$0.0723393\pi$
$367$	4.65874	+	17.3867i	0.243184	+	0.907577i	−0.731103	+	0.682267i	$0.760994\pi$
$368$	−9.81076	+	12.6392i	−0.511421	+	0.658863i
$369$	−18.1865	−	10.5000i	−0.946753	−	0.546608i
$370$		0			0
$371$	18.3303	+	10.5830i	0.951662	+	0.549442i
$372$	−10.1413	−	15.2694i	−0.525800	−	0.791682i
$373$	10.2224	+	2.73908i	0.529296	+	0.141824i	0.513563	−	0.858052i	$-0.328325\pi$
$373$	10.2224	+	2.73908i	0.529296	+	0.141824i	0.0157327	+	0.999876i	$0.494992\pi$
$374$	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
$378$	−17.1545	+	23.8688i	−0.882334	+	1.22768i
$379$	−29.1033			−1.49493			−0.747467	−	0.664299i	$-0.768730\pi$
$379$	−29.1033			−1.49493			−0.747467	+	0.664299i	$0.768730\pi$
$380$		0			0
$381$	−12.0000	−	6.92820i	−0.614779	−	0.354943i
$382$	12.1534	+	8.73467i	0.621823	+	0.446904i
$383$	8.79985	−	32.8415i	0.449651	−	1.67812i	−0.253703	−	0.967282i	$-0.581649\pi$
$383$	8.79985	−	32.8415i	0.449651	−	1.67812i	0.703355	−	0.710839i	$-0.251685\pi$
$384$	−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
$388$	5.28112	−	0.331369i	0.268108	−	0.0168227i
$389$	−10.3923	−	6.00000i	−0.526911	−	0.304212i	0.212847	−	0.977086i	$-0.431726\pi$
$389$	−10.3923	−	6.00000i	−0.526911	−	0.304212i	−0.739758	+	0.672874i	$0.765060\pi$
$390$		0			0
$391$	−27.4955	+	15.8745i	−1.39050	+	0.802808i
$392$	24.8148	−	5.67677i	1.25334	−	0.286720i
$393$	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	−0.918047	−	0.396472i	$-0.870234\pi$
$397$	−26.1916	−	26.1916i	−1.31452	−	1.31452i	−0.396472	−	0.918047i	$-0.629766\pi$
$398$	29.7850	+	2.97546i	1.49299	+	0.149147i
$399$	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	$0.618750\pi$
$402$	−2.19139	+	21.9362i	−0.109296	+	1.09408i
$403$	−27.0459	+	7.24693i	−1.34725	+	0.360995i
$404$	−13.2288	+	15.0000i	−0.658155	+	0.746278i
$405$		0			0
$406$	4.00000	−	10.5830i	0.198517	−	0.525226i
$407$	3.62347	+	13.5230i	0.179609	+	0.670308i
$408$	−28.4912	+	26.4623i	−1.41052	+	1.31008i
$409$	−9.52628	+	5.50000i	−0.471044	+	0.271957i	−0.716677	−	0.697406i	$-0.754338\pi$
$409$	−9.52628	+	5.50000i	−0.471044	+	0.271957i	0.245633	+	0.969363i	$0.421004\pi$
$410$		0			0
$411$	6.87386	+	11.9059i	0.339063	+	0.587274i
$412$	−5.33743	+	10.7476i	−0.262956	+	0.529498i
$413$	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
$418$	−8.03873	−	5.77744i	−0.393187	−	0.282584i
$419$	−7.93725	−	13.7477i	−0.387760	−	0.671620i	0.604388	−	0.796690i	$-0.293418\pi$
$419$	−7.93725	−	13.7477i	−0.387760	−	0.671620i	−0.992148	+	0.125070i	$0.960084\pi$
$420$		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	$0.104213\pi$
$422$	6.82058	−	3.07892i	0.332020	−	0.149879i
$423$	12.7279	+	12.7279i	0.618853	+	0.618853i
$424$	13.2288	−	7.00000i	0.642445	−	0.339950i
$425$		0			0
$426$		0			0
$427$	−23.1822	−	6.21166i	−1.12187	−	0.300603i
$428$	−21.6584	+	14.3845i	−1.04690	+	0.695303i
$429$	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	$-0.170268\pi$
$432$	7.84681	+	19.2465i	0.377530	+	0.925997i
$433$	−1.87083	+	1.87083i	−0.0899063	+	0.0899063i	−0.750630	−	0.660723i	$-0.770250\pi$
$433$	−1.87083	+	1.87083i	−0.0899063	+	0.0899063i	0.660723	+	0.750630i	$0.270250\pi$
$434$	18.9572	+	23.1652i	0.909975	+	1.11196i
$435$		0			0
$436$	1.58258	−	7.84190i	0.0757916	−	0.375559i
$437$	2.73908	−	10.2224i	0.131028	−	0.489004i
$438$	−26.3129	−	18.9111i	−1.25728	−	0.903608i
$439$	2.64575	−	4.58258i	0.126275	−	0.218714i	−0.795956	−	0.605355i	$-0.793031\pi$
$439$	2.64575	−	4.58258i	0.126275	−	0.218714i	0.922231	+	0.386640i	$0.126365\pi$
$440$		0			0
$441$	13.5000	−	23.3827i	0.642857	−	1.11346i
$442$	24.4382	+	54.1366i	1.16240	+	2.57502i
$443$	28.0118	−	7.50575i	1.33088	−	0.356609i	0.477839	−	0.878448i	$-0.341420\pi$
$443$	28.0118	−	7.50575i	1.33088	−	0.356609i	0.853044	+	0.521838i	$0.174754\pi$
$444$	−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
$448$	10.5390	−	30.2147i	0.497919	−	1.42751i
$449$			29.0000i			1.36859i	0.729203	+	0.684297i	$0.239891\pi$
$449$			29.0000i			1.36859i	−0.729203	+	0.684297i	$0.760109\pi$
$450$		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
$457$	17.8892	−	4.79340i	0.836821	−	0.224226i	0.185134	−	0.982713i	$-0.440728\pi$
$457$	17.8892	−	4.79340i	0.836821	−	0.224226i	0.651687	+	0.758488i	$0.274061\pi$
$458$	−25.7794	+	11.6372i	−1.20459	+	0.543772i
$459$			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	$0.151836\pi$
$462$	−25.7946	−	2.57683i	−1.20007	−	0.119885i
$463$	5.69402	−	21.2504i	0.264624	−	0.987588i	−0.697857	−	0.716237i	$-0.745863\pi$
$463$	5.69402	−	21.2504i	0.264624	−	0.987588i	0.962480	−	0.271351i	$-0.0874705\pi$
$464$	−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	−0.993885	−	0.110418i	$-0.964781\pi$
$467$	−19.0919	+	19.0919i	−0.883467	+	0.883467i	0.110418	+	0.993885i	$0.464781\pi$
$468$	31.6867	−	1.98822i	1.46472	−	0.0919053i
$469$		−	36.0000i		−	1.66233i
$470$		0			0
$471$	36.6606			1.68923
$472$	−1.66881	−	7.29487i	−0.0768134	−	0.335773i
$473$	2.55560	+	0.684771i	0.117507	+	0.0314858i
$474$	−24.2487	−	9.16515i	−1.11378	−	0.420969i
$475$		0			0
$476$	42.0000	−	47.6235i	1.92507	−	2.18282i
$477$	4.10862	−	15.3336i	0.188121	−	0.702077i
$478$	12.3157	+	27.2823i	0.563306	+	1.24786i
$479$	−13.2288	+	22.9129i	−0.604437	+	1.04692i	0.387703	+	0.921784i	$0.373269\pi$
$479$	−13.2288	+	22.9129i	−0.604437	+	1.04692i	−0.992140	+	0.125132i	$0.960065\pi$
$480$		0			0
$481$	14.0000	+	24.2487i	0.638345	+	1.10565i
$482$	14.0309	−	19.5226i	0.639091	−	0.889232i
$483$	−7.17260	−	26.7685i	−0.326365	−	1.21801i
$484$	−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	−0.249128	+	0.968471i	$0.580144\pi$
$487$	−26.8701	+	26.8701i	−1.21760	+	1.21760i	−0.968471	+	0.249128i	$0.919856\pi$
$488$	−12.4346	+	11.5491i	−0.562887	+	0.522802i
$489$	−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	$0.390652\pi$
$492$	20.1995	−	13.4156i	0.910665	−	0.604824i
$493$	−4.10862	−	15.3336i	−0.185043	−	0.690590i
$494$	−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	$0.0122614\pi$
$499$	11.9059	+	20.6216i	0.532980	+	0.923149i	−0.466278	+	0.884638i	$0.654405\pi$
$500$		0			0
$501$			20.7846i			0.928588i
$502$	−4.09126	+	40.9544i	−0.182602	+	1.82788i
$503$	−9.89949	−	9.89949i	−0.441397	−	0.441397i	0.451085	−	0.892481i	$-0.351037\pi$
$503$	−9.89949	−	9.89949i	−0.441397	−	0.441397i	−0.892481	+	0.451085i	$0.851037\pi$
$504$	−15.8745	−	30.0000i	−0.707107	−	1.33631i
$505$		0			0
$506$	−11.5826	+	9.47860i	−0.514908	+	0.421375i
$507$	6.72432	−	25.0955i	0.298637	−	1.11453i
$508$	13.3282	−	8.85203i	0.591344	−	0.392745i
$509$		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
$512$	−14.1343	−	17.6698i	−0.624653	−	0.780903i
$513$	−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
$517$	−4.10862	+	15.3336i	−0.180697	+	0.674371i
$518$	17.4693	−	24.3068i	0.767558	−	1.06798i
$519$	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	$0.315528\pi$
$522$	−8.44326	−	0.843465i	−0.369551	−	0.0369175i
$523$	25.4558	+	25.4558i	1.11311	+	1.11311i	0.992728	+	0.120378i	$0.0384107\pi$
$523$	25.4558	+	25.4558i	1.11311	+	1.11311i	0.120378	+	0.992728i	$0.461589\pi$
$524$	−30.0924	+	10.1216i	−1.31459	+	0.442164i
$525$		0			0
$526$	16.7477	−	2.74110i	0.730236	−	0.119518i
$527$	40.5689	+	10.8704i	1.76721	+	0.473522i
$528$	−11.2396	+	14.4800i	−0.489142	+	0.630161i
$529$	6.06218	+	3.50000i	0.263573	+	0.152174i
$530$		0			0
$531$	−6.87386	−	3.96863i	−0.298300	−	0.172224i
$532$	1.32548	+	21.1245i	0.0574667	+	0.915862i
$533$	−9.58679	−	35.7784i	−0.415250	−	1.54973i
$534$	14.5040	−	2.37386i	0.627648	−	0.102727i
$535$		0			0
$536$	−21.5608	−	13.5326i	−0.931285	−	0.584521i
$537$	2.37212	+	8.85286i	0.102364	+	0.382029i
$538$	−2.53039	+	25.3298i	−0.109093	+	1.09204i
$539$	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
$543$	−6.27603	−	23.4225i	−0.269330	−	1.00515i
$544$	−12.7342	−	43.0562i	−0.545974	−	1.84602i
$545$		0			0
$546$	−51.1652	+	8.37420i	−2.18967	+	0.358383i
$547$	−4.91756	−	18.3526i	−0.210260	−	0.784700i	−0.987782	−	0.155844i	$-0.950190\pi$
$547$	−4.91756	−	18.3526i	−0.210260	−	0.784700i	0.777522	−	0.628856i	$-0.216476\pi$
$548$	−15.8434	+	0.994108i	−0.676794	+	0.0424662i
$549$			18.0000i			0.768221i
$550$		0			0
$551$	4.58258	+	2.64575i	0.195224	+	0.112713i
$552$	−18.7282	−	5.76671i	−0.797125	−	0.245447i
$553$	40.8896	+	10.9563i	1.73880	+	0.465911i
$554$	−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	$-0.484833\pi$
$557$	−22.4499	−	22.4499i	−0.951235	−	0.951235i	−0.998865	+	0.0476304i	$0.984833\pi$
$558$	13.1020	−	18.2301i	0.554652	−	0.771743i
$559$	5.29150			0.223807
$560$		0			0
$561$	−31.5000	+	18.1865i	−1.32993	+	0.767836i
$562$	18.1577	−	25.2646i	0.765935	−	1.06572i
$563$	−8.02339	+	29.9437i	−0.338146	+	1.26198i	0.562273	+	0.826952i	$0.309927\pi$
$563$	−8.02339	+	29.9437i	−0.338146	+	1.26198i	−0.900418	+	0.435025i	$0.856740\pi$
$564$	−19.7001	+	6.62614i	−0.829524	+	0.279011i
$565$		0			0
$566$	2.00000	−	5.29150i	0.0840663	−	0.222418i
$567$	−34.7733	−	9.31749i	−1.46034	−	0.391298i
$568$		0			0
$569$	−12.9904	−	7.50000i	−0.544585	−	0.314416i	0.202350	−	0.979313i	$-0.435142\pi$
$569$	−12.9904	−	7.50000i	−0.544585	−	0.314416i	−0.746935	+	0.664897i	$0.768475\pi$
$570$		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	$0.206664\pi$
$572$	15.4910	+	23.3244i	0.647713	+	0.975242i
$573$	−4.74423	+	17.7057i	−0.198193	+	0.739667i
$574$	−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	$-0.0849305\pi$
$577$	16.8375	+	16.8375i	0.700953	+	0.700953i	−0.263662	+	0.964615i	$0.584931\pi$
$578$	6.46656	−	64.7316i	0.268974	−	2.69248i
$579$		−	13.7477i		−	0.571336i
$580$		0			0
$581$		0			0
$582$	2.66642	+	5.90679i	0.110527	+	0.244844i
$583$	13.5230	−	3.62347i	0.560064	−	0.150069i
$584$	33.0719	−	17.5000i	1.36852	−	0.724155i
$585$		0			0
$586$	−7.00000	−	2.64575i	−0.289167	−	0.109295i
$587$	−4.91756	−	18.3526i	−0.202969	−	0.757492i	−0.990059	−	0.140654i	$-0.955080\pi$
$587$	−4.91756	−	18.3526i	−0.202969	−	0.757492i	0.787089	−	0.616839i	$-0.211587\pi$
$588$	17.2487	+	25.9708i	0.711324	+	1.07102i
$589$	−12.1244	+	7.00000i	−0.499575	+	0.288430i
$590$		0			0
$591$	−9.16515	+	15.8745i	−0.377004	+	0.652990i
$592$	−7.99080	−	19.5997i	−0.328420	−	0.805542i
$593$	−7.48331	+	7.48331i	−0.307303	+	0.307303i	−0.843862	−	0.536560i	$-0.819724\pi$
$593$	−7.48331	+	7.48331i	−0.307303	+	0.307303i	0.536560	+	0.843862i	$0.319724\pi$
$594$	3.14033	+	19.1869i	0.128849	+	0.787249i
$595$		0			0
$596$	−18.9564	+	6.37600i	−0.776486	+	0.261171i
$597$	9.48846	+	35.4114i	0.388337	+	1.44929i
$598$	−17.4693	+	24.3068i	−0.714374	+	0.993981i
$599$	23.8118	+	41.2432i	0.972922	+	1.68515i	0.686628	+	0.727009i	$0.259090\pi$
$599$	23.8118	+	41.2432i	0.972922	+	1.68515i	0.286294	+	0.958142i	$0.407577\pi$
$600$		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	$-0.0863789\pi$
$602$	−2.32744	−	5.15587i	−0.0948595	−	0.210138i
$603$	−26.0800	+	6.98811i	−1.06206	+	0.284578i
$604$		0			0
$605$		0			0
$606$	−22.9129	−	8.66025i	−0.930772	−	0.351799i
$607$	27.0459	+	7.24693i	1.09776	+	0.294144i	0.761852	−	0.647751i	$-0.224290\pi$
$607$	27.0459	+	7.24693i	1.09776	+	0.294144i	0.335908	+	0.941895i	$0.390957\pi$
$608$	13.1499	+	7.14698i	0.533300	+	0.289848i
$609$	13.8564			0.561490
$610$		0			0
$611$			31.7490i			1.28443i
$612$	−42.6534	−	21.1823i	−1.72416	−	0.856242i
$613$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$613$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$614$	22.9835	−	18.8085i	0.927537	−	0.759050i
$615$		0			0
$616$	15.9129	−	25.3531i	0.641148	−	1.02151i
$617$	11.6411	−	43.4452i	0.468653	−	1.74904i	−0.175831	−	0.984420i	$-0.556261\pi$
$617$	11.6411	−	43.4452i	0.468653	−	1.74904i	0.644485	−	0.764617i	$-0.277072\pi$
$618$	−14.6241	−	1.46092i	−0.588269	−	0.0587670i
$619$	9.26013	−	16.0390i	0.372196	−	0.644662i	−0.617707	−	0.786408i	$-0.711938\pi$
$619$	9.26013	−	16.0390i	0.372196	−	0.644662i	0.989903	+	0.141746i	$0.0452716\pi$
$620$		0			0
$621$	−18.0000	+	10.3923i	−0.722315	+	0.417029i
$622$	20.4617	−	9.23676i	0.820441	−	0.370360i
$623$	−23.1822	+	6.21166i	−0.928776	+	0.248865i
$624$	−14.2179	+	33.7913i	−0.569172	+	1.35273i
$625$		0			0
$626$	6.64792	+	40.6178i	0.265704	+	1.62341i
$627$	3.13801	−	11.7112i	0.125320	−	0.467701i
$628$	−18.8287	+	37.9141i	−0.751346	+	1.51294i
$629$		−	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	$0.932442\pi$
$632$	21.9325	−	20.3707i	0.872429	−	0.810302i
$633$	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
$637$	46.0008	−	12.3259i	1.82262	−	0.488369i
$638$	−3.07892	−	6.82058i	−0.121896	−	0.270029i
$639$		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	$0.109788\pi$
$642$	−25.8579	−	18.5841i	−1.02053	−	0.733455i
$643$	2.32937	−	8.69333i	0.0918614	−	0.342832i	−0.904663	−	0.426127i	$-0.859878\pi$
$643$	2.32937	−	8.69333i	0.0918614	−	0.342832i	0.996525	+	0.0832952i	$0.0265444\pi$
$644$	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	0.184790	−	0.982778i	$-0.440840\pi$
$647$	29.6985	−	29.6985i	1.16757	−	1.16757i	0.982778	−	0.184790i	$-0.0591604\pi$
$648$	−18.6519	+	17.3236i	−0.732714	+	0.680536i
$649$		−	7.00000i		−	0.274774i
$650$		0			0
$651$	−18.3303	+	31.7490i	−0.718421	+	1.24434i
$652$	−22.1301	−	33.3206i	−0.866680	−	1.30493i
$653$	15.3336	+	4.10862i	0.600050	+	0.160783i	0.546042	−	0.837758i	$-0.316134\pi$
$653$	15.3336	+	4.10862i	0.600050	+	0.160783i	0.0540077	+	0.998541i	$0.482800\pi$
$654$	9.66930	−	1.58258i	0.378100	−	0.0618836i
$655$		0			0
$656$	3.50000	+	27.7804i	0.136652	+	1.08464i
$657$	10.2716	−	38.3340i	0.400732	−	1.49555i
$658$	30.9352	−	13.9647i	1.20598	−	0.544399i
$659$	7.93725	−	13.7477i	0.309192	−	0.535535i	−0.668994	−	0.743268i	$-0.733275\pi$
$659$	7.93725	−	13.7477i	0.309192	−	0.535535i	0.978186	+	0.207732i	$0.0666083\pi$
$660$		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	$0.947172\pi$
$662$	−6.07671	−	4.36733i	−0.236178	−	0.169741i
$663$	−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
$668$	−21.4953	−	10.6749i	−0.831678	−	0.413023i
$669$	−13.8564	−	24.0000i	−0.535720	−	0.927894i
$670$		0			0
$671$	−13.7477	+	7.93725i	−0.530725	+	0.306414i
$672$	39.1788	−	1.00947i	1.51136	−	0.0389413i
$673$	−2.73908	−	10.2224i	−0.105584	−	0.394044i	0.892827	−	0.450400i	$-0.148719\pi$
$673$	−2.73908	−	10.2224i	−0.105584	−	0.394044i	−0.998411	+	0.0563556i	$0.982052\pi$
$674$	−1.32288	+	3.50000i	−0.0509553	+	0.134815i
$675$		0			0
$676$	22.5000	+	19.8431i	0.865385	+	0.763197i
$677$	−10.2224	+	2.73908i	−0.392879	+	0.105272i	−0.449850	−	0.893104i	$-0.648522\pi$
$677$	−10.2224	+	2.73908i	−0.392879	+	0.105272i	0.0569710	+	0.998376i	$0.481856\pi$
$678$		0			0
$679$	−5.29150	−	9.16515i	−0.203069	−	0.351726i
$680$		0			0
$681$	10.5000	−	6.06218i	0.402361	−	0.232303i
$682$	19.7009	+	1.96808i	0.754388	+	0.0753619i
$683$	6.36396	+	6.36396i	0.243510	+	0.243510i	0.818301	−	0.574790i	$-0.194916\pi$
$683$	6.36396	+	6.36396i	0.243510	+	0.243510i	−0.574790	+	0.818301i	$0.694916\pi$
$684$	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
$688$	−3.96281	−	0.544193i	−0.151081	−	0.0207472i
$689$	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	$0.834528\pi$
$692$	0.662739	+	10.5622i	0.0251935	+	0.401516i
$693$	−8.21725	−	30.6672i	−0.312148	−	1.16495i
$694$	11.9059	+	4.50000i	0.451941	+	0.170818i
$695$		0			0
$696$	5.20871	−	8.29875i	0.197436	−	0.314563i
$697$	−14.3802	+	53.6676i	−0.544688	+	2.03280i
$698$	18.3742	+	13.2056i	0.695475	+	0.499838i
$699$	−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	$0.427233\pi$
$702$	15.9985	+	35.4408i	0.603826	+	1.33763i
$703$	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
$707$	38.6370	+	10.3528i	1.45310	+	0.389356i
$708$	7.63470	−	5.07064i	0.286930	−	0.190566i
$709$	8.66025	+	5.00000i	0.325243	+	0.187779i	0.653727	−	0.756730i	$-0.273204\pi$
$709$	8.66025	+	5.00000i	0.325243	+	0.187779i	−0.328484	+	0.944509i	$0.606538\pi$
$710$		0			0
$711$		−	31.7490i		−	1.19068i
$712$	−4.99412	+	16.2191i	−0.187162	+	0.607836i
$713$	5.47817	+	20.4448i	0.205159	+	0.765664i
$714$	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
$718$	−14.8925	−	1.48773i	−0.555783	−	0.0555217i
$719$	−47.6235			−1.77606			−0.888029	−	0.459788i	$-0.847926\pi$
$719$	−47.6235			−1.77606			−0.888029	+	0.459788i	$0.847926\pi$
$720$		0			0
$721$	24.0000			0.893807
$722$	16.8865	+	1.68693i	0.628451	+	0.0627810i
$723$	28.4416	+	7.62089i	1.05775	+	0.283424i
$724$	27.4467	+	5.53901i	1.02005	+	0.205856i
$725$		0			0
$726$	7.58258	−	6.20520i	0.281416	−	0.230297i
$727$	7.76457	+	28.9778i	0.287972	+	1.07473i	0.946640	+	0.322293i	$0.104453\pi$
$727$	7.76457	+	28.9778i	0.287972	+	1.07473i	−0.658668	+	0.752434i	$0.728880\pi$
$728$	17.6176	−	57.2156i	0.652951	−	2.12055i
$729$			27.0000i			1.00000i
$730$		0			0
$731$	−6.87386	−	3.96863i	−0.254239	−	0.146785i
$732$	−18.6155	−	9.24470i	−0.688047	−	0.341694i
$733$	10.2224	+	2.73908i	0.377573	+	0.101170i	0.442614	−	0.896712i	$-0.354051\pi$
$733$	10.2224	+	2.73908i	0.377573	+	0.101170i	−0.0650411	+	0.997883i	$0.520718\pi$
$734$	−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
$738$	24.1162	+	17.3323i	0.887729	+	0.638011i
$739$	34.3948			1.26523			0.632616	−	0.774466i	$-0.281981\pi$
$739$	34.3948			1.26523			0.632616	+	0.774466i	$0.281981\pi$
$740$		0			0
$741$		−	24.2487i		−	0.890799i
$742$	−24.3068	−	17.4693i	−0.892332	−	0.641319i
$743$	7.76457	−	28.9778i	0.284854	−	1.06309i	−0.664091	−	0.747652i	$-0.731181\pi$
$743$	7.76457	−	28.9778i	0.284854	−	1.06309i	0.948946	−	0.315440i	$-0.102152\pi$
$744$	12.1244	+	22.9129i	0.444500	+	0.840027i
$745$		0			0
$746$	−14.0000	−	5.29150i	−0.512576	−	0.193736i
$747$		0			0
$748$	−2.63016	−	41.9176i	−0.0961683	−	1.53266i
$749$	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	$0.364112\pi$
$752$	3.26516	−	23.7769i	0.119068	−	0.867053i
$753$	−48.6907	+	13.0466i	−1.77439	+	0.475446i
$754$	−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	$-0.156849\pi$
$757$	11.2250	+	11.2250i	0.407979	+	0.407979i	−0.473055	+	0.881033i	$0.656849\pi$
$758$	40.9544	+	4.09126i	1.48753	+	0.148601i
$759$	−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	$0.868018\pi$
$762$	15.9126	+	11.4364i	0.576451	+	0.414296i
$763$	−15.4548	+	4.14110i	−0.559502	+	0.149918i
$764$	−15.8745	−	14.0000i	−0.574320	−	0.506502i
$765$		0			0
$766$	−17.0000	+	44.9778i	−0.614235	+	1.62511i
$767$	−3.62347	−	13.5230i	−0.130836	−	0.488286i
$768$	14.1230	−	23.8441i	0.509620	−	0.860400i
$769$	−22.5167	+	13.0000i	−0.811972	+	0.468792i	−0.847640	−	0.530572i	$-0.821977\pi$
$769$	−22.5167	+	13.0000i	−0.811972	+	0.468792i	0.0356685	+	0.999364i	$0.488644\pi$
$770$		0			0
$771$	−4.58258			−0.165037
$772$	14.2178	+	7.06075i	0.511710	+	0.254122i
$773$	−29.9333	+	29.9333i	−1.07662	+	1.07662i	−0.0798148	+	0.996810i	$0.525433\pi$
$773$	−29.9333	+	29.9333i	−1.07662	+	1.07662i	−0.996810	+	0.0798148i	$0.974567\pi$
$774$	−3.28335	+	2.68693i	−0.118018	+	0.0965798i
$775$		0			0
$776$	−7.47822	−	0.276100i	−0.268452	−	0.00991142i
$777$	35.4114	+	9.48846i	1.27038	+	0.340397i
$778$	13.7807	+	9.90418i	0.494061	+	0.355082i
$779$	−9.26013	−	16.0390i	−0.331779	−	0.574657i
$780$		0			0
$781$		0			0
$782$	40.9235	−	18.4735i	1.46342	−	0.660611i
$783$	−2.68973	−	10.0382i	−0.0961230	−	0.358736i
$784$	−35.7176	+	4.50000i	−1.27563	+	0.160714i
$785$		0			0
$786$	−24.6261	−	30.0924i	−0.878385	−	1.07336i
$787$	−3.86370	−	1.03528i	−0.137726	−	0.0369036i	0.189297	−	0.981920i	$-0.439379\pi$
$787$	−3.86370	−	1.03528i	−0.137726	−	0.0369036i	−0.327024	+	0.945016i	$0.606046\pi$
$788$	−11.7101	−	17.6316i	−0.417156	−	0.628099i
$789$	10.3923	+	18.0000i	0.369976	+	0.640817i
$790$		0			0
$791$		0			0
$792$	−21.4558	−	6.60659i	−0.762400	−	0.234755i
$793$	−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
$797$	−4.10862	+	15.3336i	−0.145535	+	0.543144i	0.854196	+	0.519951i	$0.174050\pi$
$797$	−4.10862	+	15.3336i	−0.145535	+	0.543144i	−0.999731	+	0.0231928i	$0.992617\pi$
$798$	−23.6272	+	10.6657i	−0.836393	+	0.377561i
$799$	23.8118	−	41.2432i	0.842400	−	1.45908i
$800$		0			0
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$	−14.5465	−	32.2242i	−0.513656	−	1.13788i
$803$	33.8074	−	9.05867i	1.19304	−	0.319673i
$804$	6.16748	−	30.5608i	0.217510	−	1.07780i
$805$		0			0
$806$	39.0780	−	6.39590i	1.37646	−	0.225286i
$807$	−30.1146	+	8.06918i	−1.06008	+	0.284049i
$808$	20.7243	−	19.2485i	0.729078	−	0.677159i
$809$			9.00000i			0.316423i	0.987405	+	0.158212i	$0.0505728\pi$
$809$			9.00000i			0.316423i	−0.987405	+	0.158212i	$0.949427\pi$
$810$		0			0
$811$		−	18.5203i		−	0.650334i	−0.945657	−	0.325167i	$-0.894579\pi$
$811$		−	18.5203i		−	0.650334i	0.945657	−	0.325167i	$-0.105421\pi$
$812$	−7.11657	+	14.3302i	−0.249743	+	0.502891i
$813$		0			0
$814$	−3.19795	−	19.5390i	−0.112088	−	0.684842i
$815$		0			0
$816$	43.8131	−	33.2327i	1.53376	−	1.16338i
$817$	2.55560	−	0.684771i	0.0894091	−	0.0239571i
$818$	14.1786	−	6.40047i	0.495745	−	0.223787i
$819$	−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	$0.804726\pi$
$822$	−7.99927	−	17.7204i	−0.279006	−	0.618069i
$823$	2.58819	−	9.65926i	0.0902186	−	0.336701i	−0.906033	−	0.423208i	$-0.860904\pi$
$823$	2.58819	−	9.65926i	0.0902186	−	0.336701i	0.996251	+	0.0865074i	$0.0275706\pi$
$824$	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	−0.0855616	+	0.996333i	$0.527268\pi$
$827$	−31.1127	+	31.1127i	−1.08189	+	1.08189i	−0.996333	+	0.0855616i	$0.972732\pi$
$828$	−1.50295	−	23.9529i	−0.0522311	−	0.832421i
$829$		−	4.00000i		−	0.138926i	−0.997585	−	0.0694629i	$-0.977871\pi$
$829$		−	4.00000i		−	0.138926i	0.997585	−	0.0694629i	$-0.0221285\pi$
$830$		0			0
$831$	−18.3303	−	31.7490i	−0.635871	−	1.10136i
$832$	−27.6445	−	32.0591i	−0.958399	−	1.11145i
$833$	−69.0012	−	18.4888i	−2.39075	−	0.640599i
$834$	35.1078	−	28.7305i	1.21568	−	0.994856i
$835$		0			0
$836$	10.5000	+	9.26013i	0.363150	+	0.320268i
$837$	26.5586	+	7.11635i	0.917998	+	0.245977i
$838$	9.23676	+	20.4617i	0.319078	+	0.706839i
$839$	−7.93725	+	13.7477i	−0.274024	+	0.474624i	−0.969889	−	0.243549i	$-0.921688\pi$
$839$	−7.93725	+	13.7477i	−0.274024	+	0.474624i	0.695864	+	0.718173i	$0.255022\pi$
$840$		0			0
$841$	−12.5000	−	21.6506i	−0.431034	−	0.746574i
$842$	−6.60279	+	9.18712i	−0.227547	+	0.316609i
$843$	36.8067	+	9.86233i	1.26769	+	0.339677i
$844$	−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
$848$	−19.5997	+	7.99080i	−0.673055	+	0.274405i
$849$	6.92820			0.237775
$850$		0			0
$851$	18.3303	−	10.5830i	0.628355	−	0.362781i
$852$		0			0
$853$	−4.10862	−	15.3336i	−0.140677	−	0.525012i	−0.999910	−	0.0134282i	$-0.995726\pi$
$853$	−4.10862	−	15.3336i	−0.140677	−	0.525012i	0.859233	−	0.511584i	$-0.170941\pi$
$854$	31.7490	+	12.0000i	1.08643	+	0.410632i
$855$		0			0
$856$	32.5000	−	17.1974i	1.11083	−	0.587794i
$857$	−20.4448	+	5.47817i	−0.698381	+	0.187131i	−0.590505	−	0.807034i	$-0.701072\pi$
$857$	−20.4448	+	5.47817i	−0.698381	+	0.187131i	−0.107876	+	0.994164i	$0.534405\pi$
$858$	−20.0136	+	27.8470i	−0.683254	+	0.950680i
$859$	1.32288	+	2.29129i	0.0451359	+	0.0781777i	0.887711	−	0.460402i	$-0.152295\pi$
$859$	1.32288	+	2.29129i	0.0451359	+	0.0781777i	−0.842575	+	0.538579i	$0.818961\pi$
$860$		0			0
$861$	−42.0000	−	24.2487i	−1.43136	−	0.826394i
$862$	−2.97546	+	29.7850i	−0.101345	+	1.01448i
$863$	2.82843	+	2.82843i	0.0962808	+	0.0962808i	0.753607	−	0.657326i	$-0.228312\pi$
$863$	2.82843	+	2.82843i	0.0962808	+	0.0962808i	−0.657326	+	0.753607i	$0.728312\pi$
$864$	−8.33648	−	28.1869i	−0.283613	−	0.958939i
$865$		0			0
$866$	2.89564	−	2.36965i	0.0983980	−	0.0805240i
$867$	76.9595	−	20.6212i	2.61368	−	0.700334i
$868$	−23.4203	−	35.2632i	−0.794935	−	1.19691i
$869$	24.2487	−	14.0000i	0.822581	−	0.474917i
$870$		0			0
$871$	−41.2432	−	23.8118i	−1.39747	−	0.806831i
$872$	−3.32941	+	10.8127i	−0.112748	+	0.366165i
$873$	−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
$877$	−6.84771	+	25.5560i	−0.231231	+	0.862965i	0.748581	+	0.663043i	$0.230735\pi$
$877$	−6.84771	+	25.5560i	−0.231231	+	0.862965i	−0.979812	+	0.199922i	$0.935931\pi$
$878$	−4.36733	+	6.07671i	−0.147390	+	0.205079i
$879$		−	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	$0.489274\pi$
$882$	−22.2844	+	31.0065i	−0.750355	+	1.04404i
$883$	9.19239	+	9.19239i	0.309348	+	0.309348i	0.844657	−	0.535308i	$-0.179805\pi$
$883$	9.19239	+	9.19239i	0.309348	+	0.309348i	−0.535308	+	0.844657i	$0.679805\pi$
$884$	−26.7792	−	79.6170i	−0.900682	−	2.67781i
$885$		0			0
$886$	−40.4737	+	6.62433i	−1.35974	+	0.222549i
$887$	−46.3644	−	12.4233i	−1.55677	−	0.417134i	−0.625128	−	0.780522i	$-0.714953\pi$
$887$	−46.3644	−	12.4233i	−1.55677	−	0.417134i	−0.931638	+	0.363388i	$0.881620\pi$
$888$	18.9941	−	17.6415i	0.637401	−	0.592011i
$889$	−27.7128	−	16.0000i	−0.929458	−	0.536623i
$890$		0			0
$891$	−20.6216	+	11.9059i	−0.690849	+	0.398862i
$892$	31.9372	−	2.00393i	1.06934	−	0.0670966i
$893$	4.10862	+	15.3336i	0.137490	+	0.513119i
$894$	−15.5130	−	18.9564i	−0.518833	−	0.633998i
$895$		0			0
$896$	−19.0780	+	41.0369i	−0.637352	+	1.37095i
$897$	−35.4114	−	9.48846i	−1.18235	−	0.316811i
$898$	4.07675	−	40.8091i	0.136043	−	1.36182i
$899$	−10.5830			−0.352963
$900$		0			0
$901$	−42.0000			−1.39922
$902$	−2.60353	+	26.0619i	−0.0866881	+	0.867766i
$903$	4.89898	−	4.89898i	0.163028	−	0.163028i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−4.39992	−	16.4207i	−0.146097	−	0.545242i	−0.999704	−	0.0243242i	$-0.992257\pi$
$907$	−4.39992	−	16.4207i	−0.146097	−	0.545242i	0.853607	−	0.520917i	$-0.174410\pi$
$908$	0.876721	+	13.9725i	0.0290950	+	0.463694i
$909$		−	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	$0.456386\pi$
$912$	−2.49381	+	18.1599i	−0.0825782	+	0.601333i
$913$		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
$918$	5.79786	−	58.0378i	0.191358	−	1.91553i
$919$		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
$922$	−1.65070	+	2.29678i	−0.0543628	+	0.0756404i
$923$		0			0
$924$	35.9361	+	7.25227i	1.18221	+	0.238582i
$925$		0			0
$926$	−11.0000	+	29.1033i	−0.361482	+	0.956393i
$927$	−4.65874	−	17.3867i	−0.153013	−	0.571053i
$928$	5.90735	+	9.64900i	0.193918	+	0.316744i
$929$	29.4449	+	17.0000i	0.966055	+	0.557752i	0.898031	−	0.439932i	$-0.144997\pi$
$929$	29.4449	+	17.0000i	0.966055	+	0.557752i	0.0680235	+	0.997684i	$0.478331\pi$
$930$		0			0
$931$	20.6216	−	11.9059i	0.675845	−	0.390199i
$932$	22.0395	−	14.6377i	0.721927	−	0.479473i
$933$	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	$-0.362369\pi$
$937$	−14.9666	−	14.9666i	−0.488938	−	0.488938i	−0.907971	+	0.419033i	$0.862369\pi$
$938$	−5.06079	+	50.6595i	−0.165241	+	1.65409i
$939$	−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	$0.961269\pi$
$942$	−51.5891	−	5.15366i	−1.68087	−	0.167915i
$943$	−27.0459	+	7.24693i	−0.880736	+	0.235993i
$944$	1.32288	+	10.5000i	0.0430559	+	0.341746i
$945$		0			0
$946$	−3.50000	−	1.32288i	−0.113795	−	0.0430104i
$947$	13.7174	+	51.1941i	0.445756	+	1.66358i	0.713933	+	0.700214i	$0.246912\pi$
$947$	13.7174	+	51.1941i	0.445756	+	1.66358i	−0.268177	+	0.963370i	$0.586421\pi$
$948$	32.8346	+	16.3061i	1.06642	+	0.529598i
$949$	60.6218	−	35.0000i	1.96787	−	1.13615i
$950$		0			0
$951$	−13.7477	−	23.8118i	−0.445801	−	0.772149i
$952$	−65.7976	+	61.1120i	−2.13251	+	1.98065i
$953$	−5.61249	+	5.61249i	−0.181806	+	0.181806i	−0.792142	−	0.610336i	$-0.791034\pi$
$953$	−5.61249	+	5.61249i	−0.181806	+	0.181806i	0.610336	+	0.792142i	$0.291034\pi$
$954$	−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
$958$	21.8367	−	30.3835i	0.705511	−	0.981648i
$959$	15.8745	+	27.4955i	0.512615	+	0.887875i
$960$		0			0
$961$	−1.50000	+	2.59808i	−0.0483871	+	0.0838089i
$962$	−16.2921	−	36.0911i	−0.525279	−	1.16362i
$963$	10.0939	−	37.6711i	0.325273	−	1.21393i
$964$	−22.4889	+	25.5000i	−0.724318	+	0.821300i
$965$		0			0
$966$	6.33030	+	38.6772i	0.203674	+	1.24442i
$967$	−5.79555	−	1.55291i	−0.186372	−	0.0499384i	0.164426	−	0.986389i	$-0.447423\pi$
$967$	−5.79555	−	1.55291i	−0.186372	−	0.0499384i	−0.350798	+	0.936451i	$0.614090\pi$
$968$	2.52301	+	11.0288i	0.0810926	+	0.354479i
$969$	−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	$-0.0819828\pi$
$972$	−27.9232	−	13.8670i	−0.895637	−	0.444786i
$973$	−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
$977$	−7.53248	+	28.1116i	−0.240985	+	0.899370i	0.734374	+	0.678746i	$0.237476\pi$
$977$	−7.53248	+	28.1116i	−0.240985	+	0.899370i	−0.975359	+	0.220624i	$0.929191\pi$
$978$	28.5909	−	39.7814i	0.914236	−	1.27207i
$979$	−7.93725	+	13.7477i	−0.253676	+	0.439379i
$980$		0			0
$981$	6.00000	+	10.3923i	0.191565	+	0.331801i
$982$	10.2309	−	4.61838i	0.326480	−	0.147378i
$983$	−40.5689	+	10.8704i	−1.29395	+	0.346712i	−0.839158	−	0.543888i	$-0.816952\pi$
$983$	−40.5689	+	10.8704i	−1.29395	+	0.346712i	−0.454788	+	0.890600i	$0.650285\pi$
$984$	−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
$988$	25.0778	+	12.4540i	0.797832	+	0.396214i
$989$		−	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	$-0.168238\pi$
$992$	−29.9233	+	0.770998i	−0.950067	+	0.0244792i
$993$	2.37212	−	8.85286i	0.0752768	−	0.280937i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−15.3336	+	4.10862i	−0.485620	+	0.130121i	−0.493318	−	0.869849i	$-0.664216\pi$
$997$	−15.3336	+	4.10862i	−0.485620	+	0.130121i	0.00769834	+	0.999970i	$0.497550\pi$
$998$	−13.8551	−	30.6926i	−0.438577	−	0.971557i
$999$		−	27.4955i		−	0.869918i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.bf.c.7.1	✓	16	1.1	even	1	trivial
900.2.bf.c.7.2	yes	16	4.3	odd	2	inner
900.2.bf.c.7.3	yes	16	20.19	odd	2	inner
900.2.bf.c.7.4	yes	16	5.4	even	2	inner
900.2.bf.c.43.1	yes	16	20.7	even	4	inner
900.2.bf.c.43.2	yes	16	5.3	odd	4	inner
900.2.bf.c.43.3	yes	16	5.2	odd	4	inner
900.2.bf.c.43.4	yes	16	20.3	even	4	inner
900.2.bf.c.607.1	yes	16	45.4	even	6	inner
900.2.bf.c.607.2	yes	16	36.31	odd	6	inner
900.2.bf.c.607.3	yes	16	180.139	odd	6	inner
900.2.bf.c.607.4	yes	16	9.4	even	3	inner
900.2.bf.c.643.1	yes	16	180.103	even	12	inner
900.2.bf.c.643.2	yes	16	45.13	odd	12	inner
900.2.bf.c.643.3	yes	16	45.22	odd	12	inner
900.2.bf.c.643.4	yes	16	180.67	even	12	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+(-1.40721 - 0.140577i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(1.96048 + 0.395644i) q^{4} +(0.395644 + 2.41733i) q^{6} +(-1.03528 - 3.86370i) q^{7} +(-2.70318 - 0.832353i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(-2.29129 - 1.32288i) q^{11} +(-0.216932 - 3.45730i) q^{12} +(-5.11120 - 1.36954i) q^{13} +(0.913701 + 5.58258i) q^{14} +(3.68693 + 1.55130i) q^{16} +(5.61249 + 5.61249i) q^{17} +(3.86690 - 1.74558i) q^{18} -2.64575 q^{19} +(-6.00000 + 3.46410i) q^{21} +(3.03835 + 2.18367i) q^{22} +(-1.03528 + 3.86370i) q^{23} +(-0.180750 + 4.89564i) q^{24} +(7.00000 + 2.64575i) q^{26} +(3.67423 + 3.67423i) q^{27} +(-0.500983 - 7.98430i) q^{28} +(-1.73205 - 1.00000i) q^{29} +(4.58258 - 2.64575i) q^{31} +(-4.97021 - 2.70130i) q^{32} +(-1.18606 + 4.42643i) q^{33} +(-7.10895 - 8.68693i) q^{34} +(-5.68693 + 1.91280i) q^{36} +(-3.74166 - 3.74166i) q^{37} +(3.72313 + 0.371933i) q^{38} +9.16515i q^{39} +(3.50000 + 6.06218i) q^{41} +(8.93023 - 4.03125i) q^{42} +(-0.965926 + 0.258819i) q^{43} +(-3.96863 - 3.50000i) q^{44} +(2.00000 - 5.29150i) q^{46} +(-1.55291 - 5.79555i) q^{47} +(0.942570 - 6.86379i) q^{48} +(-7.79423 + 4.50000i) q^{49} +(6.87386 - 11.9059i) q^{51} +(-9.47853 - 4.70717i) q^{52} +(-3.74166 + 3.74166i) q^{53} +(-4.65390 - 5.68693i) q^{54} +(-0.417424 + 11.3060i) q^{56} +(1.18606 + 4.42643i) q^{57} +(2.29678 + 1.65070i) q^{58} +(1.32288 + 2.29129i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-6.82058 + 3.07892i) q^{62} +(8.48528 + 8.48528i) q^{63} +(6.61438 + 4.50000i) q^{64} +(2.29129 - 6.06218i) q^{66} +(8.69333 + 2.32937i) q^{67} +(8.78260 + 13.2237i) q^{68} +6.92820 q^{69} +(8.27160 - 1.89226i) q^{72} +(-9.35414 + 9.35414i) q^{73} +(4.73930 + 5.79129i) q^{74} +(-5.18693 - 1.04678i) q^{76} +(-2.73908 + 10.2224i) q^{77} +(1.28841 - 12.8973i) q^{78} +(-5.29150 + 9.16515i) q^{79} +(4.50000 - 7.79423i) q^{81} +(-4.07303 - 9.02277i) q^{82} +(-13.1334 + 4.41742i) q^{84} +(1.39564 - 0.228425i) q^{86} +(-0.896575 + 3.34607i) q^{87} +(5.09267 + 5.48313i) q^{88} -6.00000i q^{89} +21.1660i q^{91} +(-3.55828 + 7.16510i) q^{92} +(-6.48074 - 6.48074i) q^{93} +(1.37055 + 8.37386i) q^{94} +(-2.29129 + 9.52628i) q^{96} +(2.55560 - 0.684771i) q^{97} +(11.6007 - 5.23675i) 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

Related objects

Downloads

Learn more