LMFDB - Embedded newform 444.2.r.c.397.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [444,2,Mod(85,444)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(444, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("444.85"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 444 = 2^{2} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	444.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.54535784974$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			397.1
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	444.397
Dual form			444.2.r.c.85.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(1.10436 - 0.637600i) q^{5} +(-2.29129 - 3.96863i) q^{7} +(-0.500000 + 0.866025i) q^{9} -0.791288 q^{11} +(-2.60436 + 1.50363i) q^{13} +(-1.10436 - 0.637600i) q^{15} +(-1.50000 - 0.866025i) q^{17} +(-0.395644 + 0.228425i) q^{19} +(-2.29129 + 3.96863i) q^{21} -7.48040i q^{23} +(-1.68693 + 2.92185i) q^{25} +1.00000 q^{27} -1.73205i q^{29} -2.55040i q^{31} +(0.395644 + 0.685275i) q^{33} +(-5.06080 - 2.92185i) q^{35} +(6.08258 + 0.0476751i) q^{37} +(2.60436 + 1.50363i) q^{39} +(-4.39564 - 7.61348i) q^{41} -0.456850i q^{43} +1.27520i q^{45} +0.582576 q^{47} +(-7.00000 + 12.1244i) q^{49} +1.73205i q^{51} +(6.29129 - 10.8968i) q^{53} +(-0.873864 + 0.504525i) q^{55} +(0.395644 + 0.228425i) q^{57} +(1.81307 + 1.04678i) q^{59} +(-7.58258 + 4.37780i) q^{61} +4.58258 q^{63} +(-1.91742 + 3.32108i) q^{65} +(0.895644 + 1.55130i) q^{67} +(-6.47822 + 3.74020i) q^{69} +(3.58258 + 6.20520i) q^{71} +12.7477 q^{73} +3.37386 q^{75} +(1.81307 + 3.14033i) q^{77} +(3.47822 - 2.00815i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.79129 - 10.0308i) q^{83} -2.20871 q^{85} +(-1.50000 + 0.866025i) q^{87} +(14.3739 + 8.29875i) q^{89} +(11.9347 + 6.89048i) q^{91} +(-2.20871 + 1.27520i) q^{93} +(-0.291288 + 0.504525i) q^{95} +0.552200i q^{97} +(0.395644 - 0.685275i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 9 q^{5} - 2 q^{9} + 6 q^{11} - 15 q^{13} - 9 q^{15} - 6 q^{17} + 3 q^{19} + 7 q^{25} + 4 q^{27} - 3 q^{33} + 21 q^{35} + 6 q^{37} + 15 q^{39} - 13 q^{41} - 16 q^{47} - 28 q^{49} + 16 q^{53}+ \cdots - 3 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 9 * q^5 - 2 * q^9 + 6 * q^11 - 15 * q^13 - 9 * q^15 - 6 * q^17 + 3 * q^19 + 7 * q^25 + 4 * q^27 - 3 * q^33 + 21 * q^35 + 6 * q^37 + 15 * q^39 - 13 * q^41 - 16 * q^47 - 28 * q^49 + 16 * q^53 + 24 * q^55 - 3 * q^57 + 21 * q^59 - 12 * q^61 - 26 * q^65 - q^67 - 3 * q^69 - 4 * q^71 - 4 * q^73 - 14 * q^75 + 21 * q^77 - 9 * q^79 - 2 * q^81 + 14 * q^83 - 18 * q^85 - 6 * q^87 + 30 * q^89 - 21 * q^91 - 18 * q^93 + 8 * q^95 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/444\mathbb{Z}\right)^\times$.

$n$	$149$	$223$	$409$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	1.10436	−	0.637600i	0.493883	−	0.285144i	−0.232301	−	0.972644i	$-0.574625\pi$
$5$	1.10436	−	0.637600i	0.493883	−	0.285144i	0.726184	+	0.687500i	$0.241292\pi$
$6$		0			0
$7$	−2.29129	−	3.96863i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$	−2.29129	−	3.96863i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.791288			−0.238582			−0.119291	−	0.992859i	$-0.538062\pi$
$11$	−0.791288			−0.238582			−0.119291	+	0.992859i	$0.538062\pi$
$12$		0			0
$13$	−2.60436	+	1.50363i	−0.722318	+	0.417031i	−0.815605	−	0.578609i	$-0.803596\pi$
$13$	−2.60436	+	1.50363i	−0.722318	+	0.417031i	0.0932870	+	0.995639i	$0.470263\pi$
$14$		0			0
$15$	−1.10436	−	0.637600i	−0.285144	−	0.164628i
$16$		0			0
$17$	−1.50000	−	0.866025i	−0.363803	−	0.210042i	0.306944	−	0.951727i	$-0.400693\pi$
$17$	−1.50000	−	0.866025i	−0.363803	−	0.210042i	−0.670748	+	0.741685i	$0.734027\pi$
$18$		0			0
$19$	−0.395644	+	0.228425i	−0.0907669	+	0.0524043i	−0.544696	−	0.838633i	$-0.683355\pi$
$19$	−0.395644	+	0.228425i	−0.0907669	+	0.0524043i	0.453930	+	0.891038i	$0.350022\pi$
$20$		0			0
$21$	−2.29129	+	3.96863i	−0.500000	+	0.866025i
$22$		0			0
$23$		−	7.48040i		−	1.55977i	−0.625922	−	0.779886i	$-0.715277\pi$
$23$		−	7.48040i		−	1.55977i	0.625922	−	0.779886i	$-0.284723\pi$
$24$		0			0
$25$	−1.68693	+	2.92185i	−0.337386	+	0.584370i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$		−	1.73205i		−	0.321634i	−0.986984	−	0.160817i	$-0.948587\pi$
$29$		−	1.73205i		−	0.321634i	0.986984	−	0.160817i	$-0.0514129\pi$
$30$		0			0
$31$		−	2.55040i		−	0.458066i	−0.973419	−	0.229033i	$-0.926444\pi$
$31$		−	2.55040i		−	0.458066i	0.973419	−	0.229033i	$-0.0735563\pi$
$32$		0			0
$33$	0.395644	+	0.685275i	0.0688728	+	0.119291i
$34$		0			0
$35$	−5.06080	−	2.92185i	−0.855431	−	0.493883i
$36$		0			0
$37$	6.08258	+	0.0476751i	0.999969	+	0.00783774i
$37$	6.08258	+	0.0476751i	0.999969	+	0.00783774i
$38$		0			0
$39$	2.60436	+	1.50363i	0.417031	+	0.240773i
$40$		0			0
$41$	−4.39564	−	7.61348i	−0.686484	−	1.18903i	−0.972968	−	0.230940i	$-0.925820\pi$
$41$	−4.39564	−	7.61348i	−0.686484	−	1.18903i	0.286484	−	0.958085i	$-0.407514\pi$
$42$		0			0
$43$		−	0.456850i		−	0.0696690i	−0.999393	−	0.0348345i	$-0.988910\pi$
$43$		−	0.456850i		−	0.0696690i	0.999393	−	0.0348345i	$-0.0110904\pi$
$44$		0			0
$45$			1.27520i			0.190096i
$46$		0			0
$47$	0.582576			0.0849774			0.0424887	−	0.999097i	$-0.486471\pi$
$47$	0.582576			0.0849774			0.0424887	+	0.999097i	$0.486471\pi$
$48$		0			0
$49$	−7.00000	+	12.1244i	−1.00000	+	1.73205i
$50$		0			0
$51$			1.73205i			0.242536i
$52$		0			0
$53$	6.29129	−	10.8968i	0.864175	−	1.49679i	−0.00368933	−	0.999993i	$-0.501174\pi$
$53$	6.29129	−	10.8968i	0.864175	−	1.49679i	0.867864	−	0.496802i	$-0.165492\pi$
$54$		0			0
$55$	−0.873864	+	0.504525i	−0.117832	+	0.0680302i
$56$		0			0
$57$	0.395644	+	0.228425i	0.0524043	+	0.0302556i
$58$		0			0
$59$	1.81307	+	1.04678i	0.236041	+	0.136279i	0.613356	−	0.789807i	$-0.289819\pi$
$59$	1.81307	+	1.04678i	0.236041	+	0.136279i	−0.377315	+	0.926085i	$0.623152\pi$
$60$		0			0
$61$	−7.58258	+	4.37780i	−0.970849	+	0.560520i	−0.899495	−	0.436931i	$-0.856065\pi$
$61$	−7.58258	+	4.37780i	−0.970849	+	0.560520i	−0.0713543	+	0.997451i	$0.522732\pi$
$62$		0			0
$63$	4.58258			0.577350
$64$		0			0
$65$	−1.91742	+	3.32108i	−0.237827	+	0.411929i
$66$		0			0
$67$	0.895644	+	1.55130i	0.109420	+	0.189522i	0.915536	−	0.402237i	$-0.131767\pi$
$67$	0.895644	+	1.55130i	0.109420	+	0.189522i	−0.806115	+	0.591759i	$0.798434\pi$
$68$		0			0
$69$	−6.47822	+	3.74020i	−0.779886	+	0.450267i
$70$		0			0
$71$	3.58258	+	6.20520i	0.425174	+	0.736422i	0.996437	−	0.0843449i	$-0.0268797\pi$
$71$	3.58258	+	6.20520i	0.425174	+	0.736422i	−0.571263	+	0.820767i	$0.693546\pi$
$72$		0			0
$73$	12.7477			1.49201			0.746004	−	0.665941i	$-0.231970\pi$
$73$	12.7477			1.49201			0.746004	+	0.665941i	$0.231970\pi$
$74$		0			0
$75$	3.37386			0.389580
$76$		0			0
$77$	1.81307	+	3.14033i	0.206618	+	0.357873i
$78$		0			0
$79$	3.47822	−	2.00815i	0.391330	−	0.225935i	−0.291406	−	0.956599i	$-0.594123\pi$
$79$	3.47822	−	2.00815i	0.391330	−	0.225935i	0.682736	+	0.730665i	$0.260790\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	5.79129	−	10.0308i	0.635676	−	1.10102i	−0.350695	−	0.936490i	$-0.614055\pi$
$83$	5.79129	−	10.0308i	0.635676	−	1.10102i	0.986371	−	0.164534i	$-0.0526121\pi$
$84$		0			0
$85$	−2.20871			−0.239568
$86$		0			0
$87$	−1.50000	+	0.866025i	−0.160817	+	0.0928477i
$88$		0			0
$89$	14.3739	+	8.29875i	1.52363	+	0.879666i	0.999609	+	0.0279586i	$0.00890066\pi$
$89$	14.3739	+	8.29875i	1.52363	+	0.879666i	0.524017	+	0.851708i	$0.324433\pi$
$90$		0			0
$91$	11.9347	+	6.89048i	1.25109	+	0.722318i
$92$		0			0
$93$	−2.20871	+	1.27520i	−0.229033	+	0.132232i
$94$		0			0
$95$	−0.291288	+	0.504525i	−0.0298855	+	0.0517632i
$96$		0			0
$97$			0.552200i			0.0560675i	0.999607	+	0.0280337i	$0.00892458\pi$
$97$			0.552200i			0.0560675i	−0.999607	+	0.0280337i	$0.991075\pi$
$98$		0			0
$99$	0.395644	−	0.685275i	0.0397637	−	0.0688728i
$100$		0			0
$101$	17.5390			1.74520			0.872599	−	0.488438i	$-0.162433\pi$
$101$	17.5390			1.74520			0.872599	+	0.488438i	$0.162433\pi$
$102$		0			0
$103$			9.11710i			0.898335i	0.893448	+	0.449167i	$0.148279\pi$
$103$			9.11710i			0.898335i	−0.893448	+	0.449167i	$0.851721\pi$
$104$		0			0
$105$			5.84370i			0.570287i
$106$		0			0
$107$	−3.58258	−	6.20520i	−0.346341	−	0.599880i	0.639256	−	0.768994i	$-0.279243\pi$
$107$	−3.58258	−	6.20520i	−0.346341	−	0.599880i	−0.985596	+	0.169115i	$0.945909\pi$
$108$		0			0
$109$	1.10436	+	0.637600i	0.105778	+	0.0610710i	0.551956	−	0.833873i	$-0.313882\pi$
$109$	1.10436	+	0.637600i	0.105778	+	0.0610710i	−0.446178	+	0.894944i	$0.647215\pi$
$110$		0			0
$111$	−3.00000	−	5.29150i	−0.284747	−	0.502247i
$112$		0			0
$113$	4.41742	+	2.55040i	0.415556	+	0.239922i	0.693174	−	0.720770i	$-0.256212\pi$
$113$	4.41742	+	2.55040i	0.415556	+	0.239922i	−0.277618	+	0.960692i	$0.589545\pi$
$114$		0			0
$115$	−4.76951	−	8.26103i	−0.444759	−	0.770345i
$116$		0			0
$117$		−	3.00725i		−	0.278020i
$118$		0			0
$119$			7.93725i			0.727607i
$120$		0			0
$121$	−10.3739			−0.943079
$122$		0			0
$123$	−4.39564	+	7.61348i	−0.396342	+	0.686484i
$124$		0			0
$125$			10.6784i			0.955101i
$126$		0			0
$127$	2.79129	−	4.83465i	0.247687	−	0.429006i	−0.715197	−	0.698923i	$-0.753663\pi$
$127$	2.79129	−	4.83465i	0.247687	−	0.429006i	0.962884	+	0.269917i	$0.0869963\pi$
$128$		0			0
$129$	−0.395644	+	0.228425i	−0.0348345	+	0.0201117i
$130$		0			0
$131$	−12.1652	−	7.02355i	−1.06287	−	0.613651i	−0.136648	−	0.990620i	$-0.543633\pi$
$131$	−12.1652	−	7.02355i	−1.06287	−	0.613651i	−0.926226	+	0.376969i	$0.876966\pi$
$132$		0			0
$133$	1.81307	+	1.04678i	0.157213	+	0.0907669i
$134$		0			0
$135$	1.10436	−	0.637600i	0.0950478	−	0.0548759i
$136$		0			0
$137$	−17.5390			−1.49846			−0.749230	−	0.662310i	$-0.769576\pi$
$137$	−17.5390			−1.49846			−0.749230	+	0.662310i	$0.769576\pi$
$138$		0			0
$139$	−1.41742	+	2.45505i	−0.120224	+	0.208235i	−0.919856	−	0.392256i	$-0.871695\pi$
$139$	−1.41742	+	2.45505i	−0.120224	+	0.208235i	0.799632	+	0.600491i	$0.205028\pi$
$140$		0			0
$141$	−0.291288	−	0.504525i	−0.0245309	−	0.0424887i
$142$		0			0
$143$	2.06080	−	1.18980i	0.172332	−	0.0994961i
$144$		0			0
$145$	−1.10436	−	1.91280i	−0.0917118	−	0.158849i
$146$		0			0
$147$	14.0000			1.15470
$148$		0			0
$149$	8.79129			0.720210			0.360105	−	0.932912i	$-0.382741\pi$
$149$	8.79129			0.720210			0.360105	+	0.932912i	$0.382741\pi$
$150$		0			0
$151$	−7.08258	−	12.2674i	−0.576372	−	0.998305i	−0.995891	−	0.0905589i	$-0.971135\pi$
$151$	−7.08258	−	12.2674i	−0.576372	−	0.998305i	0.419519	−	0.907746i	$-0.362199\pi$
$152$		0			0
$153$	1.50000	−	0.866025i	0.121268	−	0.0700140i
$154$		0			0
$155$	−1.62614	−	2.81655i	−0.130614	−	0.226231i
$156$		0			0
$157$	−0.604356	+	1.04678i	−0.0482329	+	0.0835418i	−0.889134	−	0.457647i	$-0.848692\pi$
$157$	−0.604356	+	1.04678i	−0.0482329	+	0.0835418i	0.840901	+	0.541189i	$0.182026\pi$
$158$		0			0
$159$	−12.5826			−0.997863
$160$		0			0
$161$	−29.6869	+	17.1398i	−2.33966	+	1.35080i
$162$		0			0
$163$	12.8739	+	7.43273i	1.00836	+	0.582176i	0.910711	−	0.413045i	$-0.135535\pi$
$163$	12.8739	+	7.43273i	1.00836	+	0.582176i	0.0976481	+	0.995221i	$0.468868\pi$
$164$		0			0
$165$	0.873864	+	0.504525i	0.0680302	+	0.0392772i
$166$		0			0
$167$	−8.29129	+	4.78698i	−0.641599	+	0.370427i	−0.785230	−	0.619204i	$-0.787455\pi$
$167$	−8.29129	+	4.78698i	−0.641599	+	0.370427i	0.143631	+	0.989631i	$0.454122\pi$
$168$		0			0
$169$	−1.97822	+	3.42638i	−0.152171	+	0.263567i
$170$		0			0
$171$		−	0.456850i		−	0.0349362i
$172$		0			0
$173$	4.10436	−	7.10895i	0.312048	−	0.540484i	−0.666757	−	0.745275i	$-0.732318\pi$
$173$	4.10436	−	7.10895i	0.312048	−	0.540484i	0.978806	+	0.204791i	$0.0656516\pi$
$174$		0			0
$175$	15.4610			1.16874
$176$		0			0
$177$		−	2.09355i		−	0.157361i
$178$		0			0
$179$		−	24.8963i		−	1.86083i	−0.366503	−	0.930417i	$-0.619445\pi$
$179$		−	24.8963i		−	1.86083i	0.366503	−	0.930417i	$-0.380555\pi$
$180$		0			0
$181$	5.00000	+	8.66025i	0.371647	+	0.643712i	0.989819	−	0.142331i	$-0.0454598\pi$
$181$	5.00000	+	8.66025i	0.371647	+	0.643712i	−0.618172	+	0.786043i	$0.712126\pi$
$182$		0			0
$183$	7.58258	+	4.37780i	0.560520	+	0.323616i
$184$		0			0
$185$	6.74773	−	3.82560i	0.496103	−	0.281264i
$186$		0			0
$187$	1.18693	+	0.685275i	0.0867970	+	0.0501123i
$188$		0			0
$189$	−2.29129	−	3.96863i	−0.166667	−	0.288675i
$190$		0			0
$191$			14.1425i			1.02331i	0.859190	+	0.511656i	$0.170968\pi$
$191$			14.1425i			1.02331i	−0.859190	+	0.511656i	$0.829032\pi$
$192$		0			0
$193$		−	23.0689i		−	1.66053i	−0.557367	−	0.830266i	$-0.688188\pi$
$193$		−	23.0689i		−	1.66053i	0.557367	−	0.830266i	$-0.311812\pi$
$194$		0			0
$195$	3.83485			0.274619
$196$		0			0
$197$	8.66515	−	15.0085i	0.617366	−	1.06931i	−0.372598	−	0.927993i	$-0.621533\pi$
$197$	8.66515	−	15.0085i	0.617366	−	1.06931i	0.989964	−	0.141317i	$-0.0451337\pi$
$198$		0			0
$199$		−	4.93000i		−	0.349479i	−0.984615	−	0.174739i	$-0.944092\pi$
$199$		−	4.93000i		−	0.349479i	0.984615	−	0.174739i	$-0.0559083\pi$
$200$		0			0
$201$	0.895644	−	1.55130i	0.0631739	−	0.109420i
$202$		0			0
$203$	−6.87386	+	3.96863i	−0.482451	+	0.278543i
$204$		0			0
$205$	−9.70871	−	5.60533i	−0.678086	−	0.391493i
$206$		0			0
$207$	6.47822	+	3.74020i	0.450267	+	0.259962i
$208$		0			0
$209$	0.313068	−	0.180750i	0.0216554	−	0.0125027i
$210$		0			0
$211$	7.00000			0.481900			0.240950	−	0.970538i	$-0.422541\pi$
$211$	7.00000			0.481900			0.240950	+	0.970538i	$0.422541\pi$
$212$		0			0
$213$	3.58258	−	6.20520i	0.245474	−	0.425174i
$214$		0			0
$215$	−0.291288	−	0.504525i	−0.0198657	−	0.0344083i
$216$		0			0
$217$	−10.1216	+	5.84370i	−0.687098	+	0.396696i
$218$		0			0
$219$	−6.37386	−	11.0399i	−0.430706	−	0.746004i
$220$		0			0
$221$	5.20871			0.350376
$222$		0			0
$223$	−16.2087			−1.08542			−0.542708	−	0.839922i	$-0.682601\pi$
$223$	−16.2087			−1.08542			−0.542708	+	0.839922i	$0.682601\pi$
$224$		0			0
$225$	−1.68693	−	2.92185i	−0.112462	−	0.194790i
$226$		0			0
$227$	−18.0826	+	10.4400i	−1.20018	+	0.692926i	−0.960596	−	0.277949i	$-0.910345\pi$
$227$	−18.0826	+	10.4400i	−1.20018	+	0.692926i	−0.239587	+	0.970875i	$0.577012\pi$
$228$		0			0
$229$	−8.39564	−	14.5417i	−0.554800	−	0.960941i	−0.997919	−	0.0644787i	$-0.979462\pi$
$229$	−8.39564	−	14.5417i	−0.554800	−	0.960941i	0.443119	−	0.896463i	$-0.353872\pi$
$230$		0			0
$231$	1.81307	−	3.14033i	0.119291	−	0.206618i
$232$		0			0
$233$	5.83485			0.382254			0.191127	−	0.981565i	$-0.438786\pi$
$233$	5.83485			0.382254			0.191127	+	0.981565i	$0.438786\pi$
$234$		0			0
$235$	0.643371	−	0.371450i	0.0419689	−	0.0242308i
$236$		0			0
$237$	−3.47822	−	2.00815i	−0.225935	−	0.130443i
$238$		0			0
$239$	2.52178	+	1.45595i	0.163120	+	0.0941776i	0.579338	−	0.815087i	$-0.303311\pi$
$239$	2.52178	+	1.45595i	0.163120	+	0.0941776i	−0.416217	+	0.909265i	$0.636645\pi$
$240$		0			0
$241$	−12.2477	+	7.07123i	−0.788945	+	0.455498i	−0.839591	−	0.543219i	$-0.817205\pi$
$241$	−12.2477	+	7.07123i	−0.788945	+	0.455498i	0.0506457	+	0.998717i	$0.483872\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$			17.8528i			1.14057i
$246$		0			0
$247$	0.686932	−	1.18980i	0.0437084	−	0.0757052i
$248$		0			0
$249$	−11.5826			−0.734016
$250$		0			0
$251$			8.58480i			0.541868i	0.962598	+	0.270934i	$0.0873325\pi$
$251$			8.58480i			0.541868i	−0.962598	+	0.270934i	$0.912667\pi$
$252$		0			0
$253$			5.91915i			0.372134i
$254$		0			0
$255$	1.10436	+	1.91280i	0.0691575	+	0.119784i
$256$		0			0
$257$	−20.6869	−	11.9436i	−1.29042	−	0.745022i	−0.311688	−	0.950185i	$-0.600894\pi$
$257$	−20.6869	−	11.9436i	−1.29042	−	0.745022i	−0.978728	+	0.205163i	$0.934228\pi$
$258$		0			0
$259$	−13.7477	−	24.2487i	−0.854242	−	1.50674i
$260$		0			0
$261$	1.50000	+	0.866025i	0.0928477	+	0.0536056i
$262$		0			0
$263$	−4.18693	−	7.25198i	−0.258177	−	0.447176i	0.707576	−	0.706637i	$-0.249789\pi$
$263$	−4.18693	−	7.25198i	−0.258177	−	0.447176i	−0.965754	+	0.259461i	$0.916455\pi$
$264$		0			0
$265$		−	16.0453i		−	0.985655i
$266$		0			0
$267$		−	16.5975i		−	1.01575i
$268$		0			0
$269$	15.5390			0.947430			0.473715	−	0.880678i	$-0.342913\pi$
$269$	15.5390			0.947430			0.473715	+	0.880678i	$0.342913\pi$
$270$		0			0
$271$	−14.9782	+	25.9430i	−0.909862	+	1.57593i	−0.0956076	+	0.995419i	$0.530479\pi$
$271$	−14.9782	+	25.9430i	−0.909862	+	1.57593i	−0.814254	+	0.580508i	$0.802854\pi$
$272$		0			0
$273$		−	13.7810i		−	0.834061i
$274$		0			0
$275$	1.33485	−	2.31203i	0.0804944	−	0.139420i
$276$		0			0
$277$	24.4782	−	14.1325i	1.47075	−	0.849140i	0.471293	−	0.881977i	$-0.343787\pi$
$277$	24.4782	−	14.1325i	1.47075	−	0.849140i	0.999461	+	0.0328367i	$0.0104541\pi$
$278$		0			0
$279$	2.20871	+	1.27520i	0.132232	+	0.0763443i
$280$		0			0
$281$	−6.24773	−	3.60713i	−0.372708	−	0.215183i	0.301933	−	0.953329i	$-0.402368\pi$
$281$	−6.24773	−	3.60713i	−0.372708	−	0.215183i	−0.674641	+	0.738146i	$0.735702\pi$
$282$		0			0
$283$	19.8956	−	11.4868i	1.18267	−	0.682817i	0.226042	−	0.974118i	$-0.427421\pi$
$283$	19.8956	−	11.4868i	1.18267	−	0.682817i	0.956631	+	0.291301i	$0.0940881\pi$
$284$		0			0
$285$	0.582576			0.0345088
$286$		0			0
$287$	−20.1434	+	34.8893i	−1.18903	+	2.05945i
$288$		0			0
$289$	−7.00000	−	12.1244i	−0.411765	−	0.713197i
$290$		0			0
$291$	0.478220	−	0.276100i	0.0280337	−	0.0161853i
$292$		0			0
$293$	7.58258	+	13.1334i	0.442979	+	0.767262i	0.997909	−	0.0646351i	$-0.0205884\pi$
$293$	7.58258	+	13.1334i	0.442979	+	0.767262i	−0.554930	+	0.831897i	$0.687255\pi$
$294$		0			0
$295$	2.66970			0.155436
$296$		0			0
$297$	−0.791288			−0.0459152
$298$		0			0
$299$	11.2477	+	19.4816i	0.650473	+	1.12665i
$300$		0			0
$301$	−1.81307	+	1.04678i	−0.104504	+	0.0603351i
$302$		0			0
$303$	−8.76951	−	15.1892i	−0.503795	−	0.872599i
$304$		0			0
$305$	−5.58258	+	9.66930i	−0.319657	+	0.553663i
$306$		0			0
$307$	−15.0000			−0.856095			−0.428048	−	0.903756i	$-0.640798\pi$
$307$	−15.0000			−0.856095			−0.428048	+	0.903756i	$0.640798\pi$
$308$		0			0
$309$	7.89564	−	4.55855i	0.449167	−	0.259327i
$310$		0			0
$311$	16.5826	+	9.57395i	0.940312	+	0.542889i	0.890058	−	0.455847i	$-0.150664\pi$
$311$	16.5826	+	9.57395i	0.940312	+	0.542889i	0.0502536	+	0.998736i	$0.483997\pi$
$312$		0			0
$313$	−6.24773	−	3.60713i	−0.353142	−	0.203887i	0.312926	−	0.949778i	$-0.398691\pi$
$313$	−6.24773	−	3.60713i	−0.353142	−	0.203887i	−0.666068	+	0.745891i	$0.732024\pi$
$314$		0			0
$315$	5.06080	−	2.92185i	0.285144	−	0.164628i
$316$		0			0
$317$	11.2695	−	19.5194i	0.632959	−	1.09632i	−0.353985	−	0.935251i	$-0.615174\pi$
$317$	11.2695	−	19.5194i	0.632959	−	1.09632i	0.986944	−	0.161065i	$-0.0514930\pi$
$318$		0			0
$319$			1.37055i			0.0767361i
$320$		0			0
$321$	−3.58258	+	6.20520i	−0.199960	+	0.346341i
$322$		0			0
$323$	0.791288			0.0440284
$324$		0			0
$325$		−	10.1461i		−	0.562802i
$326$		0			0
$327$		−	1.27520i		−	0.0705188i
$328$		0			0
$329$	−1.33485	−	2.31203i	−0.0735926	−	0.127466i
$330$		0			0
$331$	1.26951	+	0.732950i	0.0697784	+	0.0402866i	0.534483	−	0.845179i	$-0.320506\pi$
$331$	1.26951	+	0.732950i	0.0697784	+	0.0402866i	−0.464705	+	0.885466i	$0.653840\pi$
$332$		0			0
$333$	−3.08258	+	5.24383i	−0.168924	+	0.287360i
$334$		0			0
$335$	1.97822	+	1.14213i	0.108082	+	0.0624010i
$336$		0			0
$337$	4.66515	+	8.08028i	0.254127	+	0.440161i	0.964658	−	0.263505i	$-0.0848785\pi$
$337$	4.66515	+	8.08028i	0.254127	+	0.440161i	−0.710531	+	0.703666i	$0.751545\pi$
$338$		0			0
$339$		−	5.10080i		−	0.277038i
$340$		0			0
$341$			2.01810i			0.109286i
$342$		0			0
$343$	32.0780			1.73205
$344$		0			0
$345$	−4.76951	+	8.26103i	−0.256782	+	0.444759i
$346$		0			0
$347$			29.7309i			1.59604i	0.602632	+	0.798020i	$0.294119\pi$
$347$			29.7309i			1.59604i	−0.602632	+	0.798020i	$0.705881\pi$
$348$		0			0
$349$	2.29129	−	3.96863i	0.122650	−	0.212436i	−0.798162	−	0.602443i	$-0.794194\pi$
$349$	2.29129	−	3.96863i	0.122650	−	0.212436i	0.920812	+	0.390007i	$0.127527\pi$
$350$		0			0
$351$	−2.60436	+	1.50363i	−0.139010	+	0.0802576i
$352$		0			0
$353$	27.3303	+	15.7792i	1.45465	+	0.839840i	0.998740	−	0.0501884i	$-0.0159822\pi$
$353$	27.3303	+	15.7792i	1.45465	+	0.839840i	0.455905	+	0.890028i	$0.349316\pi$
$354$		0			0
$355$	7.91288	+	4.56850i	0.419972	+	0.242471i
$356$		0			0
$357$	6.87386	−	3.96863i	0.363803	−	0.210042i
$358$		0			0
$359$	−20.6261			−1.08861			−0.544303	−	0.838889i	$-0.683206\pi$
$359$	−20.6261			−1.08861			−0.544303	+	0.838889i	$0.683206\pi$
$360$		0			0
$361$	−9.39564	+	16.2737i	−0.494508	+	0.856512i
$362$		0			0
$363$	5.18693	+	8.98403i	0.272243	+	0.471539i
$364$		0			0
$365$	14.0780	−	8.12795i	0.736878	−	0.425437i
$366$		0			0
$367$	−14.5608	−	25.2200i	−0.760067	−	1.31648i	−0.942815	−	0.333315i	$-0.891833\pi$
$367$	−14.5608	−	25.2200i	−0.760067	−	1.31648i	0.182748	−	0.983160i	$-0.441501\pi$
$368$		0			0
$369$	8.79129			0.457656
$370$		0			0
$371$	−57.6606			−2.99359
$372$		0			0
$373$	13.7913	+	23.8872i	0.714086	+	1.23683i	0.963311	+	0.268387i	$0.0864907\pi$
$373$	13.7913	+	23.8872i	0.714086	+	1.23683i	−0.249225	+	0.968446i	$0.580176\pi$
$374$		0			0
$375$	9.24773	−	5.33918i	0.477551	−	0.275714i
$376$		0			0
$377$	2.60436	+	4.51088i	0.134131	+	0.232322i
$378$		0			0
$379$	−15.0000	+	25.9808i	−0.770498	+	1.33454i	0.166792	+	0.985992i	$0.446659\pi$
$379$	−15.0000	+	25.9808i	−0.770498	+	1.33454i	−0.937290	+	0.348550i	$0.886674\pi$
$380$		0			0
$381$	−5.58258			−0.286004
$382$		0			0
$383$	−22.2695	+	12.8573i	−1.13792	+	0.656978i	−0.945914	−	0.324416i	$-0.894832\pi$
$383$	−22.2695	+	12.8573i	−1.13792	+	0.656978i	−0.192004	+	0.981394i	$0.561499\pi$
$384$		0			0
$385$	4.00455	+	2.31203i	0.204091	+	0.117832i
$386$		0			0
$387$	0.395644	+	0.228425i	0.0201117	+	0.0116115i
$388$		0			0
$389$	22.8303	−	13.1811i	1.15754	−	0.668307i	0.206829	−	0.978377i	$-0.433686\pi$
$389$	22.8303	−	13.1811i	1.15754	−	0.668307i	0.950714	+	0.310070i	$0.100352\pi$
$390$		0			0
$391$	−6.47822	+	11.2206i	−0.327618	+	0.567450i
$392$		0			0
$393$			14.0471i			0.708583i
$394$		0			0
$395$	2.56080	−	4.43543i	0.128848	−	0.223171i
$396$		0			0
$397$	12.2087			0.612738			0.306369	−	0.951913i	$-0.400886\pi$
$397$	12.2087			0.612738			0.306369	+	0.951913i	$0.400886\pi$
$398$		0			0
$399$		−	2.09355i		−	0.104809i
$400$		0			0
$401$		−	0.361500i		−	0.0180525i	−0.999959	−	0.00902623i	$-0.997127\pi$
$401$		−	0.361500i		−	0.0180525i	0.999959	−	0.00902623i	$-0.00287318\pi$
$402$		0			0
$403$	3.83485	+	6.64215i	0.191027	+	0.330869i
$404$		0			0
$405$	−1.10436	−	0.637600i	−0.0548759	−	0.0316826i
$406$		0			0
$407$	−4.81307	−	0.0377247i	−0.238575	−	0.00186995i
$408$		0			0
$409$	6.87386	+	3.96863i	0.339891	+	0.196236i	0.660224	−	0.751069i	$-0.270461\pi$
$409$	6.87386	+	3.96863i	0.339891	+	0.196236i	−0.320333	+	0.947305i	$0.603795\pi$
$410$		0			0
$411$	8.76951	+	15.1892i	0.432568	+	0.749230i
$412$		0			0
$413$		−	9.59386i		−	0.472083i
$414$		0			0
$415$		−	14.7701i		−	0.725036i
$416$		0			0
$417$	2.83485			0.138823
$418$		0			0
$419$	0.291288	−	0.504525i	0.0142303	−	0.0246477i	−0.858823	−	0.512273i	$-0.828804\pi$
$419$	0.291288	−	0.504525i	0.0142303	−	0.0246477i	0.873053	+	0.487626i	$0.162137\pi$
$420$		0			0
$421$		−	35.1932i		−	1.71521i	−0.514307	−	0.857606i	$-0.671951\pi$
$421$		−	35.1932i		−	1.71521i	0.514307	−	0.857606i	$-0.328049\pi$
$422$		0			0
$423$	−0.291288	+	0.504525i	−0.0141629	+	0.0245309i
$424$		0			0
$425$	5.06080	−	2.92185i	0.245485	−	0.141731i
$426$		0			0
$427$	34.7477	+	20.0616i	1.68156	+	0.970849i
$428$		0			0
$429$	−2.06080	−	1.18980i	−0.0994961	−	0.0574441i
$430$		0			0
$431$	28.8131	−	16.6352i	1.38788	−	0.801291i	0.394801	−	0.918767i	$-0.370814\pi$
$431$	28.8131	−	16.6352i	1.38788	−	0.801291i	0.993076	+	0.117476i	$0.0374802\pi$
$432$		0			0
$433$	16.7042			0.802751			0.401376	−	0.915914i	$-0.368532\pi$
$433$	16.7042			0.802751			0.401376	+	0.915914i	$0.368532\pi$
$434$		0			0
$435$	−1.10436	+	1.91280i	−0.0529498	+	0.0917118i
$436$		0			0
$437$	1.70871	+	2.95958i	0.0817388	+	0.141576i
$438$		0			0
$439$	11.2087	−	6.47135i	0.534963	−	0.308861i	−0.208072	−	0.978113i	$-0.566719\pi$
$439$	11.2087	−	6.47135i	0.534963	−	0.308861i	0.743035	+	0.669253i	$0.233386\pi$
$440$		0			0
$441$	−7.00000	−	12.1244i	−0.333333	−	0.577350i
$442$		0			0
$443$	−9.12159			−0.433380			−0.216690	−	0.976240i	$-0.569526\pi$
$443$	−9.12159			−0.433380			−0.216690	+	0.976240i	$0.569526\pi$
$444$		0			0
$445$	21.1652			1.00332
$446$		0			0
$447$	−4.39564	−	7.61348i	−0.207907	−	0.360105i
$448$		0			0
$449$	7.64792	−	4.41553i	0.360928	−	0.208382i	−0.308560	−	0.951205i	$-0.599847\pi$
$449$	7.64792	−	4.41553i	0.360928	−	0.208382i	0.669488	+	0.742823i	$0.266514\pi$
$450$		0			0
$451$	3.47822	+	6.02445i	0.163783	+	0.283680i
$452$		0			0
$453$	−7.08258	+	12.2674i	−0.332768	+	0.576372i
$454$		0			0
$455$	17.5735			0.823858
$456$		0			0
$457$	−26.2913	+	15.1793i	−1.22985	+	0.710057i	−0.966999	−	0.254778i	$-0.917997\pi$
$457$	−26.2913	+	15.1793i	−1.22985	+	0.710057i	−0.262855	+	0.964835i	$0.584664\pi$
$458$		0			0
$459$	−1.50000	−	0.866025i	−0.0700140	−	0.0404226i
$460$		0			0
$461$	−30.0998	−	17.3781i	−1.40189	−	0.809380i	−0.407302	−	0.913294i	$-0.633530\pi$
$461$	−30.0998	−	17.3781i	−1.40189	−	0.809380i	−0.994586	+	0.103913i	$0.966864\pi$
$462$		0			0
$463$	27.0998	−	15.6461i	1.25943	−	0.727135i	0.286470	−	0.958089i	$-0.407518\pi$
$463$	27.0998	−	15.6461i	1.25943	−	0.727135i	0.972965	+	0.230954i	$0.0741847\pi$
$464$		0			0
$465$	−1.62614	+	2.81655i	−0.0754103	+	0.130614i
$466$		0			0
$467$			31.0061i			1.43479i	0.696666	+	0.717396i	$0.254666\pi$
$467$			31.0061i			1.43479i	−0.696666	+	0.717396i	$0.745334\pi$
$468$		0			0
$469$	4.10436	−	7.10895i	0.189522	−	0.328261i
$470$		0			0
$471$	1.20871			0.0556945
$472$		0			0
$473$			0.361500i			0.0166218i
$474$		0			0
$475$		−	1.54135i		−	0.0707220i
$476$		0			0
$477$	6.29129	+	10.8968i	0.288058	+	0.498932i
$478$		0			0
$479$	33.2477	+	19.1956i	1.51913	+	0.877069i	0.999746	+	0.0225259i	$0.00717084\pi$
$479$	33.2477	+	19.1956i	1.51913	+	0.877069i	0.519381	+	0.854543i	$0.326162\pi$
$480$		0			0
$481$	−15.9129	+	9.02175i	−0.725565	+	0.411357i
$482$		0			0
$483$	29.6869	+	17.1398i	1.35080	+	0.779886i
$484$		0			0
$485$	0.352083	+	0.609826i	0.0159873	+	0.0276908i
$486$		0			0
$487$			36.5638i			1.65686i	0.560091	+	0.828431i	$0.310766\pi$
$487$			36.5638i			1.65686i	−0.560091	+	0.828431i	$0.689234\pi$
$488$		0			0
$489$		−	14.8655i		−	0.672239i
$490$		0			0
$491$	9.00000			0.406164			0.203082	−	0.979162i	$-0.434904\pi$
$491$	9.00000			0.406164			0.203082	+	0.979162i	$0.434904\pi$
$492$		0			0
$493$	−1.50000	+	2.59808i	−0.0675566	+	0.117011i
$494$		0			0
$495$		−	1.00905i		−	0.0453535i
$496$		0			0
$497$	16.4174	−	28.4358i	0.736422	−	1.27552i
$498$		0			0
$499$	−1.18693	+	0.685275i	−0.0531344	+	0.0306771i	−0.526332	−	0.850279i	$-0.676433\pi$
$499$	−1.18693	+	0.685275i	−0.0531344	+	0.0306771i	0.473197	+	0.880956i	$0.343100\pi$
$500$		0			0
$501$	8.29129	+	4.78698i	0.370427	+	0.213866i
$502$		0			0
$503$	−8.68693	−	5.01540i	−0.387331	−	0.223626i	0.293672	−	0.955906i	$-0.405123\pi$
$503$	−8.68693	−	5.01540i	−0.387331	−	0.223626i	−0.681003	+	0.732281i	$0.738456\pi$
$504$		0			0
$505$	19.3693	−	11.1829i	0.861923	−	0.497632i
$506$		0			0
$507$	3.95644			0.175712
$508$		0			0
$509$	−12.6652	+	21.9367i	−0.561373	+	0.972326i	0.436004	+	0.899945i	$0.356393\pi$
$509$	−12.6652	+	21.9367i	−0.561373	+	0.972326i	−0.997377	+	0.0723818i	$0.976940\pi$
$510$		0			0
$511$	−29.2087	−	50.5910i	−1.29212	−	2.23801i
$512$		0			0
$513$	−0.395644	+	0.228425i	−0.0174681	+	0.0100852i
$514$		0			0
$515$	5.81307	+	10.0685i	0.256154	+	0.443672i
$516$		0			0
$517$	−0.460985			−0.0202741
$518$		0			0
$519$	−8.20871			−0.360322
$520$		0			0
$521$	−12.0826	−	20.9276i	−0.529347	−	0.916856i	−0.999414	−	0.0342255i	$-0.989104\pi$
$521$	−12.0826	−	20.9276i	−0.529347	−	0.916856i	0.470067	−	0.882631i	$-0.344230\pi$
$522$		0			0
$523$	−16.8303	+	9.71698i	−0.735938	+	0.424894i	−0.820590	−	0.571517i	$-0.806355\pi$
$523$	−16.8303	+	9.71698i	−0.735938	+	0.424894i	0.0846527	+	0.996411i	$0.473022\pi$
$524$		0			0
$525$	−7.73049	−	13.3896i	−0.337386	−	0.584370i
$526$		0			0
$527$	−2.20871	+	3.82560i	−0.0962130	+	0.166646i
$528$		0			0
$529$	−32.9564			−1.43289
$530$		0			0
$531$	−1.81307	+	1.04678i	−0.0786805	+	0.0454262i
$532$		0			0
$533$	22.8956	+	13.2188i	0.991720	+	0.572570i
$534$		0			0
$535$	−7.91288	−	4.56850i	−0.342104	−	0.197514i
$536$		0			0
$537$	−21.5608	+	12.4481i	−0.930417	+	0.537177i
$538$		0			0
$539$	5.53901	−	9.59386i	0.238582	−	0.413237i
$540$		0			0
$541$			41.7798i			1.79625i	0.439735	+	0.898127i	$0.355072\pi$
$541$			41.7798i			1.79625i	−0.439735	+	0.898127i	$0.644928\pi$
$542$		0			0
$543$	5.00000	−	8.66025i	0.214571	−	0.371647i
$544$		0			0
$545$	1.62614			0.0696560
$546$		0			0
$547$			18.7864i			0.803249i	0.915804	+	0.401624i	$0.131554\pi$
$547$			18.7864i			0.803249i	−0.915804	+	0.401624i	$0.868446\pi$
$548$		0			0
$549$		−	8.75560i		−	0.373680i
$550$		0			0
$551$	0.395644	+	0.685275i	0.0168550	+	0.0291937i
$552$		0			0
$553$	−15.9392	−	9.20250i	−0.677804	−	0.391330i
$554$		0			0
$555$	−6.68693	−	3.93090i	−0.283844	−	0.166858i
$556$		0			0
$557$	−25.5998	−	14.7801i	−1.08470	−	0.626251i	−0.152539	−	0.988298i	$-0.548745\pi$
$557$	−25.5998	−	14.7801i	−1.08470	−	0.626251i	−0.932160	+	0.362046i	$0.882078\pi$
$558$		0			0
$559$	0.686932	+	1.18980i	0.0290541	+	0.0503232i
$560$		0			0
$561$		−	1.37055i		−	0.0578647i
$562$		0			0
$563$		−	16.7882i		−	0.707539i	−0.935333	−	0.353769i	$-0.884900\pi$
$563$		−	16.7882i		−	0.707539i	0.935333	−	0.353769i	$-0.115100\pi$
$564$		0			0
$565$	6.50455			0.273648
$566$		0			0
$567$	−2.29129	+	3.96863i	−0.0962250	+	0.166667i
$568$		0			0
$569$			1.73205i			0.0726113i	0.999341	+	0.0363057i	$0.0115590\pi$
$569$			1.73205i			0.0726113i	−0.999341	+	0.0363057i	$0.988441\pi$
$570$		0			0
$571$	−6.79129	+	11.7629i	−0.284207	+	0.492260i	−0.972416	−	0.233251i	$-0.925063\pi$
$571$	−6.79129	+	11.7629i	−0.284207	+	0.492260i	0.688210	+	0.725512i	$0.258397\pi$
$572$		0			0
$573$	12.2477	−	7.07123i	0.511656	−	0.295405i
$574$		0			0
$575$	21.8566	+	12.6189i	0.911484	+	0.526246i
$576$		0			0
$577$	−14.2913	−	8.25108i	−0.594954	−	0.343497i	0.172100	−	0.985080i	$-0.444945\pi$
$577$	−14.2913	−	8.25108i	−0.594954	−	0.343497i	−0.767054	+	0.641583i	$0.778278\pi$
$578$		0			0
$579$	−19.9782	+	11.5344i	−0.830266	+	0.479355i
$580$		0			0
$581$	−53.0780			−2.20205
$582$		0			0
$583$	−4.97822	+	8.62253i	−0.206177	+	0.357109i
$584$		0			0
$585$	−1.91742	−	3.32108i	−0.0792757	−	0.137310i
$586$		0			0
$587$	4.96099	−	2.86423i	0.204762	−	0.118219i	−0.394113	−	0.919062i	$-0.628948\pi$
$587$	4.96099	−	2.86423i	0.204762	−	0.118219i	0.598875	+	0.800843i	$0.295615\pi$
$588$		0			0
$589$	0.582576	+	1.00905i	0.0240046	+	0.0415772i
$590$		0			0
$591$	−17.3303			−0.712873
$592$		0			0
$593$	5.53901			0.227460			0.113730	−	0.993512i	$-0.463720\pi$
$593$	5.53901			0.227460			0.113730	+	0.993512i	$0.463720\pi$
$594$		0			0
$595$	5.06080	+	8.76555i	0.207472	+	0.359353i
$596$		0			0
$597$	−4.26951	+	2.46500i	−0.174739	+	0.100886i
$598$		0			0
$599$	8.58258	+	14.8655i	0.350675	+	0.607386i	0.986368	−	0.164556i	$-0.0526190\pi$
$599$	8.58258	+	14.8655i	0.350675	+	0.607386i	−0.635693	+	0.771942i	$0.719286\pi$
$600$		0			0
$601$	−10.2913	+	17.8250i	−0.419790	+	0.727098i	−0.995918	−	0.0902614i	$-0.971230\pi$
$601$	−10.2913	+	17.8250i	−0.419790	+	0.727098i	0.576128	+	0.817360i	$0.304563\pi$
$602$		0			0
$603$	−1.79129			−0.0729469
$604$		0			0
$605$	−11.4564	+	6.61438i	−0.465770	+	0.268913i
$606$		0			0
$607$	−27.8739	−	16.0930i	−1.13137	−	0.653194i	−0.187087	−	0.982343i	$-0.559905\pi$
$607$	−27.8739	−	16.0930i	−1.13137	−	0.653194i	−0.944278	+	0.329149i	$0.893238\pi$
$608$		0			0
$609$	6.87386	+	3.96863i	0.278543	+	0.160817i
$610$		0			0
$611$	−1.51723	+	0.875976i	−0.0613807	+	0.0354382i
$612$		0			0
$613$	9.03901	−	15.6560i	0.365082	−	0.632341i	−0.623707	−	0.781658i	$-0.714374\pi$
$613$	9.03901	−	15.6560i	0.365082	−	0.632341i	0.988789	+	0.149317i	$0.0477075\pi$
$614$		0			0
$615$			11.2107i			0.452057i
$616$		0			0
$617$	11.7695	−	20.3854i	0.473823	−	0.820685i	−0.525728	−	0.850653i	$-0.676207\pi$
$617$	11.7695	−	20.3854i	0.473823	−	0.820685i	0.999551	+	0.0299678i	$0.00954049\pi$
$618$		0			0
$619$	−18.9129			−0.760173			−0.380086	−	0.924951i	$-0.624106\pi$
$619$	−18.9129			−0.760173			−0.380086	+	0.924951i	$0.624106\pi$
$620$		0			0
$621$		−	7.48040i		−	0.300178i
$622$		0			0
$623$		−	76.0593i		−	3.04725i
$624$		0			0
$625$	−1.62614	−	2.81655i	−0.0650455	−	0.112662i
$626$		0			0
$627$	−0.313068	−	0.180750i	−0.0125027	−	0.00721846i
$628$		0			0
$629$	−9.08258	−	5.33918i	−0.362146	−	0.212887i
$630$		0			0
$631$	26.0608	+	15.0462i	1.03746	+	0.598980i	0.919114	−	0.393992i	$-0.128906\pi$
$631$	26.0608	+	15.0462i	1.03746	+	0.598980i	0.118350	+	0.992972i	$0.462240\pi$
$632$		0			0
$633$	−3.50000	−	6.06218i	−0.139113	−	0.240950i
$634$		0			0
$635$		−	7.11890i		−	0.282505i
$636$		0			0
$637$		−	42.1015i		−	1.66812i
$638$		0			0
$639$	−7.16515			−0.283449
$640$		0			0
$641$	13.9564	−	24.1733i	0.551246	−	0.954786i	−0.446939	−	0.894565i	$-0.647486\pi$
$641$	13.9564	−	24.1733i	0.551246	−	0.954786i	0.998185	−	0.0602219i	$-0.0191808\pi$
$642$		0			0
$643$			14.8655i			0.586236i	0.956076	+	0.293118i	$0.0946929\pi$
$643$			14.8655i			0.586236i	−0.956076	+	0.293118i	$0.905307\pi$
$644$		0			0
$645$	−0.291288	+	0.504525i	−0.0114694	+	0.0198657i
$646$		0			0
$647$	32.6869	−	18.8718i	1.28506	−	0.741927i	0.307288	−	0.951617i	$-0.400579\pi$
$647$	32.6869	−	18.8718i	1.28506	−	0.741927i	0.977768	+	0.209689i	$0.0672452\pi$
$648$		0			0
$649$	−1.43466	−	0.828301i	−0.0563153	−	0.0325136i
$650$		0			0
$651$	10.1216	+	5.84370i	0.396696	+	0.229033i
$652$		0			0
$653$	33.2477	−	19.1956i	1.30108	−	0.751181i	0.320494	−	0.947251i	$-0.396151\pi$
$653$	33.2477	−	19.1956i	1.30108	−	0.751181i	0.980590	+	0.196069i	$0.0628177\pi$
$654$		0			0
$655$	−17.9129			−0.699914
$656$		0			0
$657$	−6.37386	+	11.0399i	−0.248668	+	0.430706i
$658$		0			0
$659$	−22.6652	−	39.2572i	−0.882909	−	1.52924i	−0.848092	−	0.529849i	$-0.822248\pi$
$659$	−22.6652	−	39.2572i	−0.882909	−	1.52924i	−0.0348172	−	0.999394i	$-0.511085\pi$
$660$		0			0
$661$	9.16515	−	5.29150i	0.356483	−	0.205816i	−0.311054	−	0.950392i	$-0.600682\pi$
$661$	9.16515	−	5.29150i	0.356483	−	0.205816i	0.667537	+	0.744577i	$0.267349\pi$
$662$		0			0
$663$	−2.60436	−	4.51088i	−0.101145	−	0.175188i
$664$		0			0
$665$	2.66970			0.103526
$666$		0			0
$667$	−12.9564			−0.501675
$668$		0			0
$669$	8.10436	+	14.0372i	0.313333	+	0.542708i
$670$		0			0
$671$	6.00000	−	3.46410i	0.231627	−	0.133730i
$672$		0			0
$673$	3.73049	+	6.46140i	0.143800	+	0.249069i	0.928925	−	0.370269i	$-0.120734\pi$
$673$	3.73049	+	6.46140i	0.143800	+	0.249069i	−0.785125	+	0.619338i	$0.787401\pi$
$674$		0			0
$675$	−1.68693	+	2.92185i	−0.0649300	+	0.112462i
$676$		0			0
$677$	−31.6606			−1.21682			−0.608408	−	0.793624i	$-0.708192\pi$
$677$	−31.6606			−1.21682			−0.608408	+	0.793624i	$0.708192\pi$
$678$		0			0
$679$	2.19148	−	1.26525i	0.0841012	−	0.0485558i
$680$		0			0
$681$	18.0826	+	10.4400i	0.692926	+	0.400061i
$682$		0			0
$683$	9.47822	+	5.47225i	0.362674	+	0.209390i	0.670253	−	0.742133i	$-0.266186\pi$
$683$	9.47822	+	5.47225i	0.362674	+	0.209390i	−0.307579	+	0.951523i	$0.599519\pi$
$684$		0			0
$685$	−19.3693	+	11.1829i	−0.740064	+	0.427276i
$686$		0			0
$687$	−8.39564	+	14.5417i	−0.320314	+	0.554800i
$688$		0			0
$689$			37.8390i			1.44155i
$690$		0			0
$691$	8.39564	−	14.5417i	0.319385	−	0.553192i	−0.660975	−	0.750408i	$-0.729857\pi$
$691$	8.39564	−	14.5417i	0.319385	−	0.553192i	0.980360	+	0.197217i	$0.0631902\pi$
$692$		0			0
$693$	−3.62614			−0.137746
$694$		0			0
$695$			3.61500i			0.137125i
$696$		0			0
$697$			15.2270i			0.576762i
$698$		0			0
$699$	−2.91742	−	5.05313i	−0.110347	−	0.191127i
$700$		0			0
$701$	−8.37386	−	4.83465i	−0.316276	−	0.182602i	0.333455	−	0.942766i	$-0.391785\pi$
$701$	−8.37386	−	4.83465i	−0.316276	−	0.182602i	−0.649732	+	0.760164i	$0.725119\pi$
$702$		0			0
$703$	−2.41742	+	1.37055i	−0.0911749	+	0.0516913i
$704$		0			0
$705$	−0.643371	−	0.371450i	−0.0242308	−	0.0139896i
$706$		0			0
$707$	−40.1869	−	69.6058i	−1.51139	−	2.61780i
$708$		0			0
$709$		−	8.12795i		−	0.305252i	−0.988284	−	0.152626i	$-0.951227\pi$
$709$		−	8.12795i		−	0.305252i	0.988284	−	0.152626i	$-0.0487729\pi$
$710$		0			0
$711$			4.01630i			0.150623i
$712$		0			0
$713$	−19.0780			−0.714478
$714$		0			0
$715$	1.51723	−	2.62793i	0.0567414	−	0.0982789i
$716$		0			0
$717$		−	2.91190i		−	0.108747i
$718$		0			0
$719$	5.08258	−	8.80328i	0.189548	−	0.328307i	−0.755552	−	0.655089i	$-0.772631\pi$
$719$	5.08258	−	8.80328i	0.189548	−	0.328307i	0.945100	+	0.326782i	$0.105964\pi$
$720$		0			0
$721$	36.1824	−	20.8899i	1.34750	−	0.777981i
$722$		0			0
$723$	12.2477	+	7.07123i	0.455498	+	0.262982i
$724$		0			0
$725$	5.06080	+	2.92185i	0.187953	+	0.108515i
$726$		0			0
$727$	−19.8131	+	11.4391i	−0.734826	+	0.424252i	−0.820185	−	0.572098i	$-0.806130\pi$
$727$	−19.8131	+	11.4391i	−0.734826	+	0.424252i	0.0853591	+	0.996350i	$0.472796\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−0.395644	+	0.685275i	−0.0146334	+	0.0253458i
$732$		0			0
$733$	−5.31307	−	9.20250i	−0.196243	−	0.339902i	0.751065	−	0.660229i	$-0.229541\pi$
$733$	−5.31307	−	9.20250i	−0.196243	−	0.339902i	−0.947307	+	0.320327i	$0.896207\pi$
$734$		0			0
$735$	15.4610	−	8.92640i	0.570287	−	0.329255i
$736$		0			0
$737$	−0.708712	−	1.22753i	−0.0261057	−	0.0452165i
$738$		0			0
$739$	28.1652			1.03607			0.518036	−	0.855359i	$-0.326663\pi$
$739$	28.1652			1.03607			0.518036	+	0.855359i	$0.326663\pi$
$740$		0			0
$741$	−1.37386			−0.0504701
$742$		0			0
$743$	−8.31307	−	14.3987i	−0.304977	−	0.528235i	0.672279	−	0.740298i	$-0.265315\pi$
$743$	−8.31307	−	14.3987i	−0.304977	−	0.528235i	−0.977256	+	0.212062i	$0.931982\pi$
$744$		0			0
$745$	9.70871	−	5.60533i	0.355700	−	0.205363i
$746$		0			0
$747$	5.79129	+	10.0308i	0.211892	+	0.367008i
$748$		0			0
$749$	−16.4174	+	28.4358i	−0.599880	+	1.03902i
$750$		0			0
$751$	−26.7042			−0.974449			−0.487224	−	0.873277i	$-0.661991\pi$
$751$	−26.7042			−0.974449			−0.487224	+	0.873277i	$0.661991\pi$
$752$		0			0
$753$	7.43466	−	4.29240i	0.270934	−	0.156424i
$754$		0			0
$755$	−15.6434	−	9.03170i	−0.569321	−	0.328697i
$756$		0			0
$757$	18.1652	+	10.4877i	0.660224	+	0.381180i	0.792362	−	0.610051i	$-0.208851\pi$
$757$	18.1652	+	10.4877i	0.660224	+	0.381180i	−0.132139	+	0.991231i	$0.542184\pi$
$758$		0			0
$759$	5.12614	−	2.95958i	0.186067	−	0.107426i
$760$		0			0
$761$	−4.58258	+	7.93725i	−0.166118	+	0.287725i	−0.937052	−	0.349190i	$-0.886457\pi$
$761$	−4.58258	+	7.93725i	−0.166118	+	0.287725i	0.770934	+	0.636916i	$0.219790\pi$
$762$		0			0
$763$		−	5.84370i		−	0.211556i
$764$		0			0
$765$	1.10436	−	1.91280i	0.0399281	−	0.0691575i
$766$		0			0
$767$	−6.29583			−0.227329
$768$		0			0
$769$			38.7726i			1.39817i	0.715036	+	0.699087i	$0.246410\pi$
$769$			38.7726i			1.39817i	−0.715036	+	0.699087i	$0.753590\pi$
$770$		0			0
$771$			23.8872i			0.860277i
$772$		0			0
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	0.613062	−	0.790034i	$-0.289937\pi$
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	−0.990721	+	0.135910i	$0.956604\pi$
$774$		0			0
$775$	7.45189	+	4.30235i	0.267680	+	0.154545i
$776$		0			0
$777$	−14.1261	+	24.0302i	−0.506772	+	0.862080i
$778$		0			0
$779$	3.47822	+	2.00815i	0.124620	+	0.0719495i
$780$		0			0
$781$	−2.83485	−	4.91010i	−0.101439	−	0.175697i
$782$		0			0
$783$		−	1.73205i		−	0.0618984i
$784$		0			0
$785$			1.54135i			0.0550132i
$786$		0			0
$787$	−16.4955			−0.587999			−0.294000	−	0.955806i	$-0.594986\pi$
$787$	−16.4955			−0.587999			−0.294000	+	0.955806i	$0.594986\pi$
$788$		0			0
$789$	−4.18693	+	7.25198i	−0.149059	+	0.258177i
$790$		0			0
$791$		−	23.3748i		−	0.831113i
$792$		0			0
$793$	13.1652	−	22.8027i	0.467508	−	0.809748i
$794$		0			0
$795$	−13.8956	+	8.02265i	−0.492828	+	0.284534i
$796$		0			0
$797$	13.6479	+	7.87963i	0.483434	+	0.279111i	0.721846	−	0.692053i	$-0.243294\pi$
$797$	13.6479	+	7.87963i	0.483434	+	0.279111i	−0.238412	+	0.971164i	$0.576627\pi$
$798$		0			0
$799$	−0.873864	−	0.504525i	−0.0309151	−	0.0178488i
$800$		0			0
$801$	−14.3739	+	8.29875i	−0.507875	+	0.293222i
$802$		0			0
$803$	−10.0871			−0.355967
$804$		0			0
$805$	−21.8566	+	37.8568i	−0.770345	+	1.33428i
$806$		0			0
$807$	−7.76951	−	13.4572i	−0.273500	−	0.473715i
$808$		0			0
$809$	−21.7087	+	12.5335i	−0.763238	+	0.440655i	−0.830457	−	0.557083i	$-0.811921\pi$
$809$	−21.7087	+	12.5335i	−0.763238	+	0.440655i	0.0672193	+	0.997738i	$0.478587\pi$
$810$		0			0
$811$	−8.95644	−	15.5130i	−0.314503	−	0.544735i	0.664829	−	0.746996i	$-0.268505\pi$
$811$	−8.95644	−	15.5130i	−0.314503	−	0.544735i	−0.979332	+	0.202261i	$0.935171\pi$
$812$		0			0
$813$	29.9564			1.05062
$814$		0			0
$815$	18.9564			0.664015
$816$		0			0
$817$	0.104356	+	0.180750i	0.00365096	+	0.00632364i
$818$		0			0
$819$	−11.9347	+	6.89048i	−0.417031	+	0.240773i
$820$		0			0
$821$	5.37386	+	9.30780i	0.187549	+	0.324845i	0.944433	−	0.328705i	$-0.106612\pi$
$821$	5.37386	+	9.30780i	0.187549	+	0.324845i	−0.756883	+	0.653550i	$0.773279\pi$
$822$		0			0
$823$	4.37386	−	7.57575i	0.152463	−	0.264074i	−0.779669	−	0.626192i	$-0.784613\pi$
$823$	4.37386	−	7.57575i	0.152463	−	0.264074i	0.932132	+	0.362117i	$0.117946\pi$
$824$		0			0
$825$	−2.66970			−0.0929469
$826$		0			0
$827$	18.3303	−	10.5830i	0.637407	−	0.368007i	−0.146208	−	0.989254i	$-0.546707\pi$
$827$	18.3303	−	10.5830i	0.637407	−	0.368007i	0.783615	+	0.621247i	$0.213374\pi$
$828$		0			0
$829$	49.3521	+	28.4934i	1.71407	+	0.989618i	0.928896	+	0.370342i	$0.120759\pi$
$829$	49.3521	+	28.4934i	1.71407	+	0.989618i	0.785173	+	0.619276i	$0.212574\pi$
$830$		0			0
$831$	−24.4782	−	14.1325i	−0.849140	−	0.490251i
$832$		0			0
$833$	21.0000	−	12.1244i	0.727607	−	0.420084i
$834$		0			0
$835$	−6.10436	+	10.5731i	−0.211250	+	0.365896i
$836$		0			0
$837$		−	2.55040i		−	0.0881548i
$838$		0			0
$839$	−10.4564	+	18.1111i	−0.360996	+	0.625264i	−0.988125	−	0.153652i	$-0.950897\pi$
$839$	−10.4564	+	18.1111i	−0.360996	+	0.625264i	0.627129	+	0.778916i	$0.284230\pi$
$840$		0			0
$841$	26.0000			0.896552
$842$		0			0
$843$			7.21425i			0.248472i
$844$		0			0
$845$			5.04525i			0.173562i
$846$		0			0
$847$	23.7695	+	41.1700i	0.816730	+	1.41462i
$848$		0			0
$849$	−19.8956	−	11.4868i	−0.682817	−	0.394224i
$850$		0			0
$851$	0.356629	−	45.5001i	0.0122251	−	1.55972i
$852$		0			0
$853$	16.2695	+	9.39320i	0.557057	+	0.321617i	0.751964	−	0.659205i	$-0.229107\pi$
$853$	16.2695	+	9.39320i	0.557057	+	0.321617i	−0.194906	+	0.980822i	$0.562440\pi$
$854$		0			0
$855$	−0.291288	−	0.504525i	−0.00996183	−	0.0172544i
$856$		0			0
$857$			17.3404i			0.592337i	0.955136	+	0.296169i	$0.0957090\pi$
$857$			17.3404i			0.592337i	−0.955136	+	0.296169i	$0.904291\pi$
$858$		0			0
$859$		−	26.0761i		−	0.889705i	−0.895604	−	0.444853i	$-0.853256\pi$
$859$		−	26.0761i		−	0.889705i	0.895604	−	0.444853i	$-0.146744\pi$
$860$		0			0
$861$	40.2867			1.37297
$862$		0			0
$863$	−5.14337	+	8.90858i	−0.175082	+	0.303252i	−0.940190	−	0.340651i	$-0.889353\pi$
$863$	−5.14337	+	8.90858i	−0.175082	+	0.303252i	0.765107	+	0.643903i	$0.222686\pi$
$864$		0			0
$865$		−	10.4678i		−	0.355914i
$866$		0			0
$867$	−7.00000	+	12.1244i	−0.237732	+	0.411765i
$868$		0			0
$869$	−2.75227	+	1.58903i	−0.0933645	+	0.0539040i
$870$		0			0
$871$	−4.66515	−	2.69343i	−0.158073	−	0.0912633i
$872$		0			0
$873$	−0.478220	−	0.276100i	−0.0161853	−	0.00934458i
$874$		0			0
$875$	42.3784	−	24.4672i	1.43265	−	0.827142i
$876$		0			0
$877$	−42.1216			−1.42235			−0.711173	−	0.703018i	$-0.751836\pi$
$877$	−42.1216			−1.42235			−0.711173	+	0.703018i	$0.751836\pi$
$878$		0			0
$879$	7.58258	−	13.1334i	0.255754	−	0.442979i
$880$		0			0
$881$	10.7477	+	18.6156i	0.362100	+	0.627176i	0.988306	−	0.152482i	$-0.0487265\pi$
$881$	10.7477	+	18.6156i	0.362100	+	0.627176i	−0.626206	+	0.779658i	$0.715393\pi$
$882$		0			0
$883$	34.6652	−	20.0139i	1.16658	−	0.673523i	0.213704	−	0.976898i	$-0.431447\pi$
$883$	34.6652	−	20.0139i	1.16658	−	0.673523i	0.952871	+	0.303376i	$0.0981138\pi$
$884$		0			0
$885$	−1.33485	−	2.31203i	−0.0448704	−	0.0777179i
$886$		0			0
$887$	51.7042			1.73606			0.868028	−	0.496515i	$-0.165387\pi$
$887$	51.7042			1.73606			0.868028	+	0.496515i	$0.165387\pi$
$888$		0			0
$889$	−25.5826			−0.858012
$890$		0			0
$891$	0.395644	+	0.685275i	0.0132546	+	0.0229576i
$892$		0			0
$893$	−0.230493	+	0.133075i	−0.00771314	+	0.00445318i
$894$		0			0
$895$	−15.8739	−	27.4943i	−0.530605	−	0.919034i
$896$		0			0
$897$	11.2477	−	19.4816i	0.375551	−	0.650473i
$898$		0			0
$899$	−4.41742			−0.147329
$900$		0			0
$901$	−18.8739	+	10.8968i	−0.628780	+	0.363026i
$902$		0			0
$903$	1.81307	+	1.04678i	0.0603351	+	0.0348345i
$904$		0			0
$905$	11.0436	+	6.37600i	0.367100	+	0.211946i
$906$		0			0
$907$	34.2867	−	19.7955i	1.13847	−	0.657297i	0.192421	−	0.981313i	$-0.438366\pi$
$907$	34.2867	−	19.7955i	1.13847	−	0.657297i	0.946052	+	0.324015i	$0.105033\pi$
$908$		0			0
$909$	−8.76951	+	15.1892i	−0.290866	+	0.503795i
$910$		0			0
$911$			23.2397i			0.769964i	0.922924	+	0.384982i	$0.125792\pi$
$911$			23.2397i			0.769964i	−0.922924	+	0.384982i	$0.874208\pi$
$912$		0			0
$913$	−4.58258	+	7.93725i	−0.151661	+	0.262685i
$914$		0			0
$915$	11.1652			0.369109
$916$		0			0
$917$			64.3719i			2.12575i
$918$		0			0
$919$			10.0308i			0.330886i	0.986219	+	0.165443i	$0.0529053\pi$
$919$			10.0308i			0.330886i	−0.986219	+	0.165443i	$0.947095\pi$
$920$		0			0
$921$	7.50000	+	12.9904i	0.247133	+	0.428048i
$922$		0			0
$923$	−18.6606	−	10.7737i	−0.614221	−	0.354621i
$924$		0			0
$925$	−10.4002	+	17.6920i	−0.341956	+	0.581708i
$926$		0			0
$927$	−7.89564	−	4.55855i	−0.259327	−	0.149722i
$928$		0			0
$929$	15.4782	+	26.8091i	0.507824	+	0.879577i	0.999959	+	0.00905796i	$0.00288328\pi$
$929$	15.4782	+	26.8091i	0.507824	+	0.879577i	−0.492135	+	0.870519i	$0.663783\pi$
$930$		0			0
$931$		−	6.39590i		−	0.209617i
$932$		0			0
$933$		−	19.1479i		−	0.626874i
$934$		0			0
$935$	1.74773			0.0571568
$936$		0			0
$937$	−7.43466	+	12.8772i	−0.242880	+	0.420680i	−0.961533	−	0.274688i	$-0.911425\pi$
$937$	−7.43466	+	12.8772i	−0.242880	+	0.420680i	0.718654	+	0.695368i	$0.244759\pi$
$938$		0			0
$939$			7.21425i			0.235428i
$940$		0			0
$941$	4.16515	−	7.21425i	0.135780	−	0.235178i	−0.790115	−	0.612958i	$-0.789979\pi$
$941$	4.16515	−	7.21425i	0.135780	−	0.235178i	0.925895	+	0.377781i	$0.123313\pi$
$942$		0			0
$943$	−56.9519	+	32.8812i	−1.85461	+	1.07076i
$944$		0			0
$945$	−5.06080	−	2.92185i	−0.164628	−	0.0950478i
$946$		0			0
$947$	25.5000	+	14.7224i	0.828639	+	0.478415i	0.853386	−	0.521279i	$-0.174545\pi$
$947$	25.5000	+	14.7224i	0.828639	+	0.478415i	−0.0247477	+	0.999694i	$0.507878\pi$
$948$		0			0
$949$	−33.1996	+	19.1678i	−1.07771	+	0.622213i
$950$		0			0
$951$	−22.5390			−0.730878
$952$		0			0
$953$	16.5390	−	28.6464i	0.535751	−	0.927948i	−0.463375	−	0.886162i	$-0.653362\pi$
$953$	16.5390	−	28.6464i	0.535751	−	0.927948i	0.999127	−	0.0417863i	$-0.0133049\pi$
$954$		0			0
$955$	9.01723	+	15.6183i	0.291791	+	0.505397i
$956$		0			0
$957$	1.18693	−	0.685275i	0.0383681	−	0.0221518i
$958$		0			0
$959$	40.1869	+	69.6058i	1.29770	+	2.24769i
$960$		0			0
$961$	24.4955			0.790176
$962$		0			0
$963$	7.16515			0.230894
$964$		0			0
$965$	−14.7087	−	25.4762i	−0.473490	−	0.820109i
$966$		0			0
$967$	39.6606	−	22.8981i	1.27540	−	0.736352i	0.299400	−	0.954128i	$-0.403213\pi$
$967$	39.6606	−	22.8981i	1.27540	−	0.736352i	0.975999	+	0.217776i	$0.0698801\pi$
$968$		0			0
$969$	−0.395644	−	0.685275i	−0.0127099	−	0.0220142i
$970$		0			0
$971$	3.87386	−	6.70973i	0.124318	−	0.215325i	−0.797148	−	0.603784i	$-0.793659\pi$
$971$	3.87386	−	6.70973i	0.124318	−	0.215325i	0.921466	+	0.388458i	$0.126992\pi$
$972$		0			0
$973$	12.9909			0.416469
$974$		0			0
$975$	−8.78674	+	5.07303i	−0.281401	+	0.162467i
$976$		0			0
$977$	−13.7305	−	7.92730i	−0.439277	−	0.253617i	0.264014	−	0.964519i	$-0.414954\pi$
$977$	−13.7305	−	7.92730i	−0.439277	−	0.253617i	−0.703291	+	0.710902i	$0.748287\pi$
$978$		0			0
$979$	−11.3739	−	6.56670i	−0.363510	−	0.209873i
$980$		0			0
$981$	−1.10436	+	0.637600i	−0.0352594	+	0.0203570i
$982$		0			0
$983$	−23.6652	+	40.9892i	−0.754801	+	1.30735i	0.190672	+	0.981654i	$0.438933\pi$
$983$	−23.6652	+	40.9892i	−0.754801	+	1.30735i	−0.945473	+	0.325700i	$0.894400\pi$
$984$		0			0
$985$		−	22.0996i		−	0.704152i
$986$		0			0
$987$	−1.33485	+	2.31203i	−0.0424887	+	0.0735926i
$988$		0			0
$989$	−3.41742			−0.108668
$990$		0			0
$991$		−	28.3803i		−	0.901529i	−0.892643	−	0.450764i	$-0.851151\pi$
$991$		−	28.3803i		−	0.901529i	0.892643	−	0.450764i	$-0.148849\pi$
$992$		0			0
$993$		−	1.46590i		−	0.0465190i
$994$		0			0
$995$	−3.14337	−	5.44448i	−0.0996516	−	0.172602i
$996$		0			0
$997$	−38.9519	−	22.4889i	−1.23362	−	0.712230i	−0.265836	−	0.964018i	$-0.585648\pi$
$997$	−38.9519	−	22.4889i	−1.23362	−	0.712230i	−0.967782	+	0.251788i	$0.918981\pi$
$998$		0			0
$999$	6.08258	+	0.0476751i	0.192444	+	0.00150837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	444.2.r.c.397.1	yes	4
3.2	odd	2		1332.2.bi.g.397.2		4
4.3	odd	2		1776.2.bz.f.1729.1		4
37.11	even	6	inner	444.2.r.c.85.1	✓	4
111.11	odd	6		1332.2.bi.g.973.2		4
148.11	odd	6		1776.2.bz.f.529.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
444.2.r.c.85.1	✓	4	37.11	even	6	inner
444.2.r.c.397.1	yes	4	1.1	even	1	trivial
1332.2.bi.g.397.2		4	3.2	odd	2
1332.2.bi.g.973.2		4	111.11	odd	6
1776.2.bz.f.529.1		4	148.11	odd	6
1776.2.bz.f.1729.1		4	4.3	odd	2

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:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.10436 - 0.637600i) q^{5} +(-2.29129 - 3.96863i) q^{7} +(-0.500000 + 0.866025i) q^{9} -0.791288 q^{11} +(-2.60436 + 1.50363i) q^{13} +(-1.10436 - 0.637600i) q^{15} +(-1.50000 - 0.866025i) q^{17} +(-0.395644 + 0.228425i) q^{19} +(-2.29129 + 3.96863i) q^{21} -7.48040i q^{23} +(-1.68693 + 2.92185i) q^{25} +1.00000 q^{27} -1.73205i q^{29} -2.55040i q^{31} +(0.395644 + 0.685275i) q^{33} +(-5.06080 - 2.92185i) q^{35} +(6.08258 + 0.0476751i) q^{37} +(2.60436 + 1.50363i) q^{39} +(-4.39564 - 7.61348i) q^{41} -0.456850i q^{43} +1.27520i q^{45} +0.582576 q^{47} +(-7.00000 + 12.1244i) q^{49} +1.73205i q^{51} +(6.29129 - 10.8968i) q^{53} +(-0.873864 + 0.504525i) q^{55} +(0.395644 + 0.228425i) q^{57} +(1.81307 + 1.04678i) q^{59} +(-7.58258 + 4.37780i) q^{61} +4.58258 q^{63} +(-1.91742 + 3.32108i) q^{65} +(0.895644 + 1.55130i) q^{67} +(-6.47822 + 3.74020i) q^{69} +(3.58258 + 6.20520i) q^{71} +12.7477 q^{73} +3.37386 q^{75} +(1.81307 + 3.14033i) q^{77} +(3.47822 - 2.00815i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.79129 - 10.0308i) q^{83} -2.20871 q^{85} +(-1.50000 + 0.866025i) q^{87} +(14.3739 + 8.29875i) q^{89} +(11.9347 + 6.89048i) q^{91} +(-2.20871 + 1.27520i) q^{93} +(-0.291288 + 0.504525i) q^{95} +0.552200i q^{97} +(0.395644 - 0.685275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 9 q^{5} - 2 q^{9} + 6 q^{11} - 15 q^{13} - 9 q^{15} - 6 q^{17} + 3 q^{19} + 7 q^{25} + 4 q^{27} - 3 q^{33} + 21 q^{35} + 6 q^{37} + 15 q^{39} - 13 q^{41} - 16 q^{47} - 28 q^{49} + 16 q^{53}+ \cdots - 3 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 9 * q^5 - 2 * q^9 + 6 * q^11 - 15 * q^13 - 9 * q^15 - 6 * q^17 + 3 * q^19 + 7 * q^25 + 4 * q^27 - 3 * q^33 + 21 * q^35 + 6 * q^37 + 15 * q^39 - 13 * q^41 - 16 * q^47 - 28 * q^49 + 16 * q^53 + 24 * q^55 - 3 * q^57 + 21 * q^59 - 12 * q^61 - 26 * q^65 - q^67 - 3 * q^69 - 4 * q^71 - 4 * q^73 - 14 * q^75 + 21 * q^77 - 9 * q^79 - 2 * q^81 + 14 * q^83 - 18 * q^85 - 6 * q^87 + 30 * q^89 - 21 * q^91 - 18 * q^93 + 8 * q^95 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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