LMFDB - Embedded newform 900.2.bf.e.607.28

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 = [128,2] 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:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			607.28
Character	$\chi$	$=$	900.607
Dual form			900.2.bf.e.43.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25060 + 0.660305i) q^{2} +(1.72686 + 0.133985i) q^{3} +(1.12799 + 1.65155i) q^{4} +(2.07114 + 1.30782i) q^{6} +(-2.46165 - 0.659597i) q^{7} +(0.320139 + 2.81025i) q^{8} +(2.96410 + 0.462748i) q^{9} +(3.01796 - 1.74242i) q^{11} +(1.72661 + 3.00314i) q^{12} +(1.36518 + 5.09493i) q^{13} +(-2.64300 - 2.45033i) q^{14} +(-1.45526 + 3.72589i) q^{16} +(-2.16382 - 2.16382i) q^{17} +(3.40134 + 2.53592i) q^{18} +3.88577 q^{19} +(-4.16255 - 1.46886i) q^{21} +(4.92478 - 0.186294i) q^{22} +(-3.70190 + 0.991920i) q^{23} +(0.176303 + 4.89581i) q^{24} +(-1.65691 + 7.27315i) q^{26} +(5.05658 + 1.19625i) q^{27} +(-1.68737 - 4.80957i) q^{28} +(3.85118 - 2.22348i) q^{29} +(-1.86992 - 1.07960i) q^{31} +(-4.28016 + 3.69867i) q^{32} +(5.44505 - 2.60455i) q^{33} +(-1.27729 - 4.13484i) q^{34} +(2.57923 + 5.41734i) q^{36} +(-3.67542 - 3.67542i) q^{37} +(4.85954 + 2.56579i) q^{38} +(1.67483 + 8.98115i) q^{39} +(-4.04792 + 7.01121i) q^{41} +(-4.23579 - 4.58550i) q^{42} +(1.36185 - 5.08248i) q^{43} +(6.28194 + 3.01888i) q^{44} +(-5.28456 - 1.20389i) q^{46} +(0.231550 + 0.0620436i) q^{47} +(-3.01224 + 6.23910i) q^{48} +(-0.437526 - 0.252606i) q^{49} +(-3.44669 - 4.02653i) q^{51} +(-6.87463 + 8.00173i) q^{52} +(-0.265818 + 0.265818i) q^{53} +(5.53386 + 4.83491i) q^{54} +(1.06556 - 7.12902i) q^{56} +(6.71018 + 0.520636i) q^{57} +(6.28446 - 0.237728i) q^{58} +(5.69158 - 9.85810i) q^{59} +(-4.61792 - 7.99848i) q^{61} +(-1.62566 - 2.58487i) q^{62} +(-6.99134 - 3.09423i) q^{63} +(-7.79502 + 1.79934i) q^{64} +(8.52937 + 0.338146i) q^{66} +(-0.192807 - 0.719566i) q^{67} +(1.13289 - 6.01443i) q^{68} +(-6.52556 + 1.21691i) q^{69} -2.06980i q^{71} +(-0.351515 + 8.47800i) q^{72} +(-8.97449 + 8.97449i) q^{73} +(-2.16958 - 7.02337i) q^{74} +(4.38312 + 6.41755i) q^{76} +(-8.57845 + 2.29859i) q^{77} +(-3.83576 + 12.3377i) q^{78} +(-7.56173 - 13.0973i) q^{79} +(8.57173 + 2.74326i) q^{81} +(-9.69186 + 6.09534i) q^{82} +(4.01723 - 14.9925i) q^{83} +(-2.26944 - 8.53154i) q^{84} +(5.05911 - 5.45691i) q^{86} +(6.94837 - 3.32364i) q^{87} +(5.86280 + 7.92340i) q^{88} -3.61495i q^{89} -13.4424i q^{91} +(-5.81393 - 4.99500i) q^{92} +(-3.08444 - 2.11486i) q^{93} +(0.248608 + 0.230485i) q^{94} +(-7.88682 + 5.81362i) q^{96} +(0.818990 - 3.05651i) q^{97} +(-0.380373 - 0.604809i) q^{98} +(9.75182 - 3.76814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 2 q^{2} - 8 q^{6} + 8 q^{8} - 2 q^{12} + 4 q^{13} - 4 q^{16} + 16 q^{17} + 36 q^{18} - 24 q^{21} + 10 q^{22} - 48 q^{26} - 8 q^{28} - 18 q^{32} + 20 q^{33} - 40 q^{36} + 16 q^{37} + 34 q^{38} - 8 q^{41}+ \cdots - 164 q^{98}+O(q^{100}) $ 128 * q + 2 * q^2 - 8 * q^6 + 8 * q^8 - 2 * q^12 + 4 * q^13 - 4 * q^16 + 16 * q^17 + 36 * q^18 - 24 * q^21 + 10 * q^22 - 48 * q^26 - 8 * q^28 - 18 * q^32 + 20 * q^33 - 40 * q^36 + 16 * q^37 + 34 * q^38 - 8 * q^41 - 34 * q^42 - 40 * q^46 + 22 * q^48 + 18 * q^52 + 64 * q^53 - 32 * q^56 + 48 * q^57 + 10 * q^58 - 8 * q^61 - 44 * q^62 - 36 * q^66 - 58 * q^68 - 78 * q^72 + 16 * q^73 - 32 * q^76 + 60 * q^77 - 114 * q^78 + 24 * q^81 + 32 * q^86 + 10 * q^88 - 52 * q^92 + 68 * q^93 + 52 * q^96 + 4 * q^97 - 164 * q^98

Character values

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

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

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 $

$2$	1.25060	+	0.660305i	0.884307	+	0.466906i
$2$	1.25060	+	0.660305i	0.884307	+	0.466906i
$3$	1.72686	+	0.133985i	0.997003	+	0.0773565i
$3$	1.72686	+	0.133985i	0.997003	+	0.0773565i
$4$	1.12799	+	1.65155i	0.563997	+	0.825777i
$5$		0			0
$5$		0			0
$6$	2.07114	+	1.30782i	0.845539	+	0.533914i
$7$	−2.46165	−	0.659597i	−0.930416	−	0.249304i	−0.238384	−	0.971171i	$-0.576618\pi$
$7$	−2.46165	−	0.659597i	−0.930416	−	0.249304i	−0.692032	+	0.721867i	$0.743284\pi$
$8$	0.320139	+	2.81025i	0.113186	+	0.993574i
$9$	2.96410	+	0.462748i	0.988032	+	0.154249i
$10$		0			0
$11$	3.01796	−	1.74242i	0.909948	−	0.525359i	0.0295338	−	0.999564i	$-0.490598\pi$
$11$	3.01796	−	1.74242i	0.909948	−	0.525359i	0.880415	+	0.474205i	$0.157264\pi$
$12$	1.72661	+	3.00314i	0.498428	+	0.866931i
$13$	1.36518	+	5.09493i	0.378634	+	1.41308i	0.847962	+	0.530057i	$0.177829\pi$
$13$	1.36518	+	5.09493i	0.378634	+	1.41308i	−0.469329	+	0.883024i	$0.655504\pi$
$14$	−2.64300	−	2.45033i	−0.706372	−	0.654879i
$15$		0			0
$16$	−1.45526	+	3.72589i	−0.363814	+	0.931472i
$17$	−2.16382	−	2.16382i	−0.524802	−	0.524802i	0.394216	−	0.919018i	$-0.371016\pi$
$17$	−2.16382	−	2.16382i	−0.524802	−	0.524802i	−0.919018	+	0.394216i	$0.871016\pi$
$18$	3.40134	+	2.53592i	0.801703	+	0.597722i
$19$	3.88577			0.891456			0.445728	−	0.895168i	$-0.352945\pi$
$19$	3.88577			0.891456			0.445728	+	0.895168i	$0.352945\pi$
$20$		0			0
$21$	−4.16255	−	1.46886i	−0.908343	−	0.320531i
$22$	4.92478	−	0.186294i	1.04997	−	0.0397180i
$23$	−3.70190	+	0.991920i	−0.771899	+	0.206830i	−0.623210	−	0.782054i	$-0.714172\pi$
$23$	−3.70190	+	0.991920i	−0.771899	+	0.206830i	−0.148689	+	0.988884i	$0.547505\pi$
$24$	0.176303	+	4.89581i	0.0359878	+	0.999352i
$25$		0			0
$26$	−1.65691	+	7.27315i	−0.324947	+	1.42638i
$27$	5.05658	+	1.19625i	0.973139	+	0.230218i
$28$	−1.68737	−	4.80957i	−0.318883	−	0.908923i
$29$	3.85118	−	2.22348i	0.715147	−	0.412890i	−0.0978169	−	0.995204i	$-0.531186\pi$
$29$	3.85118	−	2.22348i	0.715147	−	0.412890i	0.812964	+	0.582314i	$0.197853\pi$
$30$		0			0
$31$	−1.86992	−	1.07960i	−0.335848	−	0.193902i	0.322586	−	0.946540i	$-0.395448\pi$
$31$	−1.86992	−	1.07960i	−0.335848	−	0.193902i	−0.658434	+	0.752638i	$0.728781\pi$
$32$	−4.28016	+	3.69867i	−0.756633	+	0.653840i
$33$	5.44505	−	2.60455i	0.947862	−	0.453394i
$34$	−1.27729	−	4.13484i	−0.219053	−	0.709120i
$35$		0			0
$36$	2.57923	+	5.41734i	0.429872	+	0.902890i
$37$	−3.67542	−	3.67542i	−0.604235	−	0.604235i	0.337198	−	0.941434i	$-0.390521\pi$
$37$	−3.67542	−	3.67542i	−0.604235	−	0.604235i	−0.941434	+	0.337198i	$0.890521\pi$
$38$	4.85954	+	2.56579i	0.788321	+	0.416226i
$39$	1.67483	+	8.98115i	0.268188	+	1.43814i
$40$		0			0
$41$	−4.04792	+	7.01121i	−0.632179	+	1.09497i	0.354926	+	0.934894i	$0.384506\pi$
$41$	−4.04792	+	7.01121i	−0.632179	+	1.09497i	−0.987105	+	0.160072i	$0.948827\pi$
$42$	−4.23579	−	4.58550i	−0.653596	−	0.707559i
$43$	1.36185	−	5.08248i	0.207680	−	0.775071i	−0.780936	−	0.624611i	$-0.785258\pi$
$43$	1.36185	−	5.08248i	0.207680	−	0.775071i	0.988616	−	0.150461i	$-0.0480757\pi$
$44$	6.28194	+	3.01888i	0.947037	+	0.455113i
$45$		0			0
$46$	−5.28456	−	1.20389i	−0.779165	−	0.177503i
$47$	0.231550	+	0.0620436i	0.0337750	+	0.00904999i	0.275667	−	0.961253i	$-0.411101\pi$
$47$	0.231550	+	0.0620436i	0.0337750	+	0.00904999i	−0.241892	+	0.970303i	$0.577768\pi$
$48$	−3.01224	+	6.23910i	−0.434780	+	0.900537i
$49$	−0.437526	−	0.252606i	−0.0625037	−	0.0360865i
$50$		0			0
$51$	−3.44669	−	4.02653i	−0.482633	−	0.563827i
$52$	−6.87463	+	8.00173i	−0.953340	+	1.10964i
$53$	−0.265818	+	0.265818i	−0.0365129	+	0.0365129i	−0.725127	−	0.688615i	$-0.758219\pi$
$53$	−0.265818	+	0.265818i	−0.0365129	+	0.0365129i	0.688615	+	0.725127i	$0.258219\pi$
$54$	5.53386	+	4.83491i	0.753063	+	0.657948i
$55$		0			0
$56$	1.06556	−	7.12902i	0.142392	−	0.952655i
$57$	6.71018	+	0.520636i	0.888785	+	0.0689600i
$58$	6.28446	−	0.237728i	0.825190	−	0.0312152i
$59$	5.69158	−	9.85810i	0.740980	−	1.28342i	−0.211069	−	0.977471i	$-0.567695\pi$
$59$	5.69158	−	9.85810i	0.740980	−	1.28342i	0.952049	−	0.305944i	$-0.0989722\pi$
$60$		0			0
$61$	−4.61792	−	7.99848i	−0.591264	−	1.02410i	−0.994062	−	0.108811i	$-0.965296\pi$
$61$	−4.61792	−	7.99848i	−0.591264	−	1.02410i	0.402798	−	0.915289i	$-0.368038\pi$
$62$	−1.62566	−	2.58487i	−0.206459	−	0.328278i
$63$	−6.99134	−	3.09423i	−0.880826	−	0.389837i
$64$	−7.79502	+	1.79934i	−0.974378	+	0.224918i
$65$		0			0
$66$	8.52937	+	0.338146i	1.04989	+	0.0416228i
$67$	−0.192807	−	0.719566i	−0.0235551	−	0.0879089i	0.953148	−	0.302505i	$-0.0978230\pi$
$67$	−0.192807	−	0.719566i	−0.0235551	−	0.0879089i	−0.976703	+	0.214596i	$0.931156\pi$
$68$	1.13289	−	6.01443i	0.137383	−	0.729357i
$69$	−6.52556	+	1.21691i	−0.785585	+	0.146498i
$70$		0			0
$71$		−	2.06980i		−	0.245640i	−0.992429	−	0.122820i	$-0.960806\pi$
$71$		−	2.06980i		−	0.245640i	0.992429	−	0.122820i	$-0.0391938\pi$
$72$	−0.351515	+	8.47800i	−0.0414265	+	0.999142i
$73$	−8.97449	+	8.97449i	−1.05038	+	1.05038i	−0.0517232	+	0.998661i	$0.516471\pi$
$73$	−8.97449	+	8.97449i	−1.05038	+	1.05038i	−0.998661	+	0.0517232i	$0.983529\pi$
$74$	−2.16958	−	7.02337i	−0.252208	−	0.816451i
$75$		0			0
$76$	4.38312	+	6.41755i	0.502779	+	0.736144i
$77$	−8.57845	+	2.29859i	−0.977605	+	0.261948i
$78$	−3.83576	+	12.3377i	−0.434314	+	1.39697i
$79$	−7.56173	−	13.0973i	−0.850761	−	1.47356i	−0.880523	−	0.474004i	$-0.842808\pi$
$79$	−7.56173	−	13.0973i	−0.850761	−	1.47356i	0.0297623	−	0.999557i	$-0.490525\pi$
$80$		0			0
$81$	8.57173	+	2.74326i	0.952414	+	0.304807i
$82$	−9.69186	+	6.09534i	−1.07029	+	0.673118i
$83$	4.01723	−	14.9925i	0.440949	−	1.64564i	−0.285468	−	0.958388i	$-0.592149\pi$
$83$	4.01723	−	14.9925i	0.440949	−	1.64564i	0.726417	−	0.687255i	$-0.241184\pi$
$84$	−2.26944	−	8.53154i	−0.247616	−	0.930867i
$85$		0			0
$86$	5.05911	−	5.45691i	0.545538	−	0.588434i
$87$	6.94837	−	3.32364i	0.744944	−	0.356332i
$88$	5.86280	+	7.92340i	0.624977	+	0.844637i
$89$		−	3.61495i		−	0.383184i	−0.981475	−	0.191592i	$-0.938635\pi$
$89$		−	3.61495i		−	0.383184i	0.981475	−	0.191592i	$-0.0613650\pi$
$90$		0			0
$91$		−	13.4424i		−	1.40915i
$92$	−5.81393	−	4.99500i	−0.606144	−	0.520765i
$93$	−3.08444	−	2.11486i	−0.319842	−	0.219301i
$94$	0.248608	+	0.230485i	0.0256420	+	0.0237727i
$95$		0			0
$96$	−7.88682	+	5.81362i	−0.804945	+	0.593350i
$97$	0.818990	−	3.05651i	0.0831559	−	0.310342i	−0.911803	−	0.410629i	$-0.865309\pi$
$97$	0.818990	−	3.05651i	0.0831559	−	0.310342i	0.994959	+	0.100287i	$0.0319760\pi$
$98$	−0.380373	−	0.604809i	−0.0384234	−	0.0610949i
$99$	9.75182	−	3.76814i	0.980094	−	0.378712i
$100$		0			0
$101$	2.15969	+	3.74069i	0.214897	+	0.372213i	0.953241	−	0.302212i	$-0.0977250\pi$
$101$	2.15969	+	3.74069i	0.214897	+	0.372213i	−0.738344	+	0.674425i	$0.764392\pi$
$102$	−1.65169	−	7.31144i	−0.163541	−	0.723940i
$103$	−1.31939	+	0.353529i	−0.130003	+	0.0348342i	−0.323234	−	0.946319i	$-0.604770\pi$
$103$	−1.31939	+	0.353529i	−0.130003	+	0.0348342i	0.193231	+	0.981153i	$0.438103\pi$
$104$	−13.8810	+	5.46760i	−1.36114	+	0.536142i
$105$		0			0
$106$	−0.507952	+	0.156910i	−0.0493366	+	0.0152405i
$107$	5.32781	−	5.32781i	0.515059	−	0.515059i	−0.401013	−	0.916072i	$-0.631342\pi$
$107$	5.32781	−	5.32781i	0.515059	−	0.515059i	0.916072	+	0.401013i	$0.131342\pi$
$108$	3.72813	+	9.70057i	0.358739	+	0.933438i
$109$			14.1851i			1.35869i	0.733820	+	0.679344i	$0.237736\pi$
$109$			14.1851i			1.35869i	−0.733820	+	0.679344i	$0.762264\pi$
$110$		0			0
$111$	−5.85449	−	6.83939i	−0.555683	−	0.649166i
$112$	6.03992	−	8.21194i	0.570719	−	0.775956i
$113$	0.117242	+	0.437551i	0.0110292	+	0.0411614i	0.971221	−	0.238180i	$-0.0765507\pi$
$113$	0.117242	+	0.437551i	0.0110292	+	0.0411614i	−0.960192	+	0.279341i	$0.909884\pi$
$114$	8.04796	+	5.08187i	0.753761	+	0.475961i
$115$		0			0
$116$	8.01631	+	3.85236i	0.744296	+	0.357683i
$117$	1.68886	+	15.7336i	0.156135	+	1.45457i
$118$	13.6272	−	8.57035i	1.25449	−	0.788965i
$119$	3.89931	+	6.75380i	0.357449	+	0.619120i
$120$		0			0
$121$	0.572043	−	0.990808i	0.0520040	−	0.0900735i
$122$	−0.493734	−	13.0521i	−0.0447005	−	1.18168i
$123$	−7.92960	+	11.5650i	−0.714988	+	1.04278i
$124$	−0.326245	−	4.30606i	−0.0292976	−	0.386696i
$125$		0			0
$126$	−6.70022	−	8.48606i	−0.596903	−	0.755998i
$127$	−2.66261	+	2.66261i	−0.236269	+	0.236269i	−0.815303	−	0.579034i	$-0.803430\pi$
$127$	−2.66261	+	2.66261i	−0.236269	+	0.236269i	0.579034	+	0.815303i	$0.303430\pi$
$128$	−10.9366	−	2.89683i	−0.966664	−	0.256046i
$129$	3.03270	−	8.59427i	0.267014	−	0.756683i
$130$		0			0
$131$	10.6177	+	6.13011i	0.927670	+	0.535590i	0.886074	−	0.463544i	$-0.153422\pi$
$131$	10.6177	+	6.13011i	0.927670	+	0.535590i	0.0415959	+	0.999135i	$0.486756\pi$
$132$	10.4435	+	6.05487i	0.908994	+	0.527009i
$133$	−9.56540	−	2.56304i	−0.829425	−	0.222244i
$134$	0.234009	−	1.02720i	0.0202153	−	0.0887365i
$135$		0			0
$136$	5.38814	−	6.77359i	0.462029	−	0.580830i
$137$	−2.39423	+	8.93538i	−0.204553	+	0.763401i	0.785033	+	0.619454i	$0.212646\pi$
$137$	−2.39423	+	8.93538i	−0.204553	+	0.763401i	−0.989585	+	0.143947i	$0.954021\pi$
$138$	−8.96439	−	2.78700i	−0.763099	−	0.237245i
$139$	−8.95460	+	15.5098i	−0.759520	+	1.31553i	0.183576	+	0.983005i	$0.441233\pi$
$139$	−8.95460	+	15.5098i	−0.759520	+	1.31553i	−0.943096	+	0.332521i	$0.892101\pi$
$140$		0			0
$141$	0.391542	+	0.138165i	0.0329738	+	0.0116356i
$142$	1.36670	−	2.58849i	0.114691	−	0.217221i
$143$	12.9976	+	12.9976i	1.08691	+	1.08691i
$144$	−6.03767	+	10.3705i	−0.503139	+	0.864205i
$145$		0			0
$146$	−17.1494	+	5.29759i	−1.41929	+	0.438431i
$147$	−0.721701	−	0.494837i	−0.0595249	−	0.0408135i
$148$	1.92430	−	10.2160i	0.158176	−	0.839751i
$149$	−2.39752	−	1.38421i	−0.196413	−	0.113399i	0.398568	−	0.917139i	$-0.369507\pi$
$149$	−2.39752	−	1.38421i	−0.196413	−	0.113399i	−0.594981	+	0.803740i	$0.702840\pi$
$150$		0			0
$151$	6.51667	−	3.76240i	0.530319	−	0.306180i	−0.210827	−	0.977523i	$-0.567616\pi$
$151$	6.51667	−	3.76240i	0.530319	−	0.306180i	0.741146	+	0.671343i	$0.234282\pi$
$152$	1.24399	+	10.9200i	0.100901	+	0.885728i
$153$	−5.41246	−	7.41506i	−0.437571	−	0.599472i
$154$	−12.2460	−	2.78978i	−0.986808	−	0.224807i
$155$		0			0
$156$	−12.9437	+	12.8968i	−1.03632	+	1.03257i
$157$	3.61744	−	0.969291i	0.288703	−	0.0773578i	−0.111561	−	0.993758i	$-0.535585\pi$
$157$	3.61744	−	0.969291i	0.288703	−	0.0773578i	0.400264	+	0.916400i	$0.368918\pi$
$158$	−0.808476	−	21.3725i	−0.0643189	−	1.70031i
$159$	−0.494646	+	0.423414i	−0.0392279	+	0.0335789i
$160$		0			0
$161$	9.76704			0.769751
$162$	8.90840	+	9.09067i	0.699910	+	0.714231i
$163$	−6.76935	−	6.76935i	−0.530216	−	0.530216i	0.390420	−	0.920637i	$-0.372330\pi$
$163$	−6.76935	−	6.76935i	−0.530216	−	0.530216i	−0.920637	+	0.390420i	$0.872330\pi$
$164$	−16.1454	+	1.22324i	−1.26074	+	0.0955192i
$165$		0			0
$166$	14.9236	−	16.0970i	1.15829	−	1.24937i
$167$	−0.957423	−	3.57315i	−0.0740876	−	0.276499i	0.918937	−	0.394404i	$-0.129049\pi$
$167$	−0.957423	−	3.57315i	−0.0740876	−	0.276499i	−0.993025	+	0.117905i	$0.962382\pi$
$168$	2.79526	−	12.1680i	0.215659	−	0.938785i
$169$	−12.8363	+	7.41103i	−0.987406	+	0.570079i
$170$		0			0
$171$	11.5178	+	1.79813i	0.880787	+	0.137507i
$172$	9.93015	−	3.48385i	0.757167	−	0.265641i
$173$	22.3985	+	6.00167i	1.70293	+	0.456299i	0.973674	−	0.227943i	$-0.0732000\pi$
$173$	22.3985	+	6.00167i	1.70293	+	0.456299i	0.729255	+	0.684242i	$0.239867\pi$
$174$	10.8842	+	0.431504i	0.825132	+	0.0327122i
$175$		0			0
$176$	2.10015	+	13.7802i	0.158305	+	1.03872i
$177$	11.1494	−	16.2610i	0.838041	−	1.22225i
$178$	2.38697	−	4.52085i	0.178911	−	0.338852i
$179$	10.0185			0.748819			0.374410	−	0.927263i	$-0.377845\pi$
$179$	10.0185			0.748819			0.374410	+	0.927263i	$0.377845\pi$
$180$		0			0
$181$	−19.9811			−1.48518			−0.742590	−	0.669746i	$-0.766403\pi$
$181$	−19.9811			−1.48518			−0.742590	+	0.669746i	$0.766403\pi$
$182$	8.87609	−	16.8111i	0.657940	−	1.24612i
$183$	−6.90283	−	14.4310i	−0.510272	−	1.06677i
$184$	−3.97267	−	10.0857i	−0.292869	−	0.743528i
$185$		0			0
$186$	−2.46095	−	4.68152i	−0.180446	−	0.343266i
$187$	−10.3006	−	2.76003i	−0.753253	−	0.201833i
$188$	0.158719	+	0.452402i	0.0115758	+	0.0329948i
$189$	−11.6585	−	6.28005i	−0.848030	−	0.456806i
$190$		0			0
$191$	−13.5705	+	7.83490i	−0.981923	+	0.566914i	−0.902850	−	0.429955i	$-0.858529\pi$
$191$	−13.5705	+	7.83490i	−0.981923	+	0.566914i	−0.0790731	+	0.996869i	$0.525196\pi$
$192$	−13.7020	+	2.06280i	−0.988857	+	0.148870i
$193$	−5.58592	−	20.8469i	−0.402083	−	1.50060i	−0.809372	−	0.587296i	$-0.800193\pi$
$193$	−5.58592	−	20.8469i	−0.402083	−	1.50060i	0.407289	−	0.913299i	$-0.366474\pi$
$194$	3.04246	−	3.28169i	0.218436	−	0.235611i
$195$		0			0
$196$	−0.0763350	−	1.00754i	−0.00545250	−	0.0719668i
$197$	9.44630	+	9.44630i	0.673021	+	0.673021i	0.958411	−	0.285390i	$-0.0921232\pi$
$197$	9.44630	+	9.44630i	0.673021	+	0.673021i	−0.285390	+	0.958411i	$0.592123\pi$
$198$	14.6837	+	1.72674i	1.04353	+	0.122714i
$199$	2.06079			0.146085			0.0730427	−	0.997329i	$-0.476729\pi$
$199$	2.06079			0.146085			0.0730427	+	0.997329i	$0.476729\pi$
$200$		0			0
$201$	−0.236540	−	1.26842i	−0.0166842	−	0.0894677i
$202$	0.230907	+	6.10416i	0.0162466	+	0.429487i
$203$	−10.9469	+	2.93320i	−0.768320	+	0.205871i
$204$	2.76218	−	10.2343i	0.193391	−	0.716544i
$205$		0			0
$206$	−1.88346	−	0.429076i	−0.131227	−	0.0298951i
$207$	−11.4318	+	1.22710i	−0.794564	+	0.0852893i
$208$	−20.9698	−	2.32792i	−1.45400	−	0.161412i
$209$	11.7271	−	6.77063i	0.811179	−	0.468335i
$210$		0			0
$211$	1.99458	+	1.15157i	0.137313	+	0.0792776i	0.567083	−	0.823661i	$-0.308072\pi$
$211$	1.99458	+	1.15157i	0.137313	+	0.0792776i	−0.429770	+	0.902938i	$0.641405\pi$
$212$	−0.738853	−	0.139171i	−0.0507446	−	0.00955831i
$213$	0.277323	−	3.57425i	0.0190019	−	0.244904i
$214$	10.1809	−	3.14497i	0.695954	−	0.214986i
$215$		0			0
$216$	−1.74295	+	14.5932i	−0.118592	+	0.992943i
$217$	3.89099	+	3.89099i	0.264138	+	0.264138i
$218$	−9.36651	+	17.7399i	−0.634380	+	1.20150i
$219$	−16.7001	+	14.2952i	−1.12849	+	0.965983i
$220$		0			0
$221$	8.07049	−	13.9785i	0.542880	−	0.940296i
$222$	−2.80553	−	12.4191i	−0.188295	−	0.833514i
$223$	−4.32002	+	16.1225i	−0.289290	+	1.07964i	0.656357	+	0.754450i	$0.272096\pi$
$223$	−4.32002	+	16.1225i	−0.289290	+	1.07964i	−0.945647	+	0.325194i	$0.894570\pi$
$224$	12.9759	−	6.28166i	0.866989	−	0.419711i
$225$		0			0
$226$	−0.142295	+	0.624617i	−0.00946534	+	0.0415489i
$227$	−4.86933	−	1.30473i	−0.323189	−	0.0865981i	0.0935772	−	0.995612i	$-0.470170\pi$
$227$	−4.86933	−	1.30473i	−0.323189	−	0.0865981i	−0.416766	+	0.909014i	$0.636836\pi$
$228$	6.70919	+	11.6695i	0.444327	+	0.772831i
$229$	6.71866	+	3.87902i	0.443981	+	0.256333i	0.705285	−	0.708924i	$-0.250819\pi$
$229$	6.71866	+	3.87902i	0.443981	+	0.256333i	−0.261304	+	0.965257i	$0.584152\pi$
$230$		0			0
$231$	−15.1218	+	2.81995i	−0.994939	+	0.185539i
$232$	7.48146	+	10.1110i	0.491182	+	0.663818i
$233$	4.15335	−	4.15335i	0.272095	−	0.272095i	−0.557848	−	0.829943i	$-0.688373\pi$
$233$	4.15335	−	4.15335i	0.272095	−	0.272095i	0.829943	+	0.557848i	$0.188373\pi$
$234$	−8.27689	+	20.7916i	−0.541077	+	1.35919i
$235$		0			0
$236$	22.7012	−	1.71994i	1.47773	−	0.111959i
$237$	−11.3032	−	23.6304i	−0.734222	−	1.53496i
$238$	0.416902	+	11.0210i	0.0270237	+	0.714388i
$239$	1.28058	−	2.21802i	0.0828335	−	0.143472i	−0.821632	−	0.570018i	$-0.806936\pi$
$239$	1.28058	−	2.21802i	0.0828335	−	0.143472i	0.904466	+	0.426546i	$0.140270\pi$
$240$		0			0
$241$	6.89420	+	11.9411i	0.444094	+	0.769194i	0.997989	−	0.0633929i	$-0.0201921\pi$
$241$	6.89420	+	11.9411i	0.444094	+	0.769194i	−0.553894	+	0.832587i	$0.686859\pi$
$242$	1.36963	−	0.861381i	0.0880433	−	0.0553716i
$243$	14.4346	+	5.88572i	0.925981	+	0.377569i
$244$	8.00092	−	16.6490i	0.512206	−	1.06584i
$245$		0			0
$246$	−17.5532	+	9.22724i	−1.11915	+	0.588307i
$247$	5.30478	+	19.7977i	0.337535	+	1.25970i
$248$	2.43531	−	5.60057i	0.154642	−	0.355637i
$249$	8.94598	−	25.3517i	0.566929	−	1.60660i
$250$		0			0
$251$		−	11.4799i		−	0.724602i	−0.932061	−	0.362301i	$-0.881991\pi$
$251$		−	11.4799i		−	0.724602i	0.932061	−	0.362301i	$-0.118009\pi$
$252$	−2.77590	−	15.0368i	−0.174865	−	0.947232i
$253$	−9.44382	+	9.44382i	−0.593728	+	0.593728i
$254$	−5.08799	+	1.57172i	−0.319249	+	0.0986187i
$255$		0			0
$256$	−11.7645	−	10.8442i	−0.735278	−	0.677765i
$257$	−14.1728	+	3.79760i	−0.884077	+	0.236888i	−0.672165	−	0.740401i	$-0.734636\pi$
$257$	−14.1728	+	3.79760i	−0.884077	+	0.236888i	−0.211912	+	0.977289i	$0.567969\pi$
$258$	9.46753	−	8.74548i	0.589423	−	0.544470i
$259$	6.62330	+	11.4719i	0.411552	+	0.712829i
$260$		0			0
$261$	12.4442	−	4.80848i	0.770276	−	0.297638i
$262$	9.23070	+	14.6772i	0.570274	+	0.906761i
$263$	0.474777	−	1.77189i	0.0292760	−	0.109259i	−0.949742	−	0.313034i	$-0.898654\pi$
$263$	0.474777	−	1.77189i	0.0292760	−	0.109259i	0.979018	+	0.203775i	$0.0653211\pi$
$264$	9.06262	+	14.4681i	0.557766	+	0.890452i
$265$		0			0
$266$	−10.2701	−	9.52142i	−0.629700	−	0.583796i
$267$	0.484351	−	6.24252i	0.0296418	−	0.382036i
$268$	0.970916	−	1.13010i	0.0593081	−	0.0690317i
$269$			13.4031i			0.817201i	0.912713	+	0.408600i	$0.133983\pi$
$269$			13.4031i			0.817201i	−0.912713	+	0.408600i	$0.866017\pi$
$270$		0			0
$271$			19.1919i			1.16582i	0.812536	+	0.582911i	$0.198086\pi$
$271$			19.1919i			1.16582i	−0.812536	+	0.582911i	$0.801914\pi$
$272$	11.2110	−	4.91322i	0.679769	−	0.297908i
$273$	1.80109	−	23.2132i	0.109007	−	1.40493i
$274$	−8.89430	+	9.59366i	−0.537324	+	0.579574i
$275$		0			0
$276$	−9.37058	−	9.40465i	−0.564043	−	0.566093i
$277$	1.93430	−	7.21889i	0.116221	−	0.433741i	−0.883155	−	0.469082i	$-0.844585\pi$
$277$	1.93430	−	7.21889i	0.116221	−	0.433741i	0.999375	+	0.0353406i	$0.0112516\pi$
$278$	−21.4398	+	13.4838i	−1.28588	+	0.808705i
$279$	−5.04305	−	4.06534i	−0.301919	−	0.243386i
$280$		0			0
$281$	−6.99536	−	12.1163i	−0.417308	−	0.722799i	0.578360	−	0.815782i	$-0.303693\pi$
$281$	−6.99536	−	12.1163i	−0.417308	−	0.722799i	−0.995668	+	0.0929831i	$0.970360\pi$
$282$	0.398430	+	0.431326i	0.0237262	+	0.0256851i
$283$	1.79491	−	0.480944i	0.106696	−	0.0285891i	−0.205076	−	0.978746i	$-0.565744\pi$
$283$	1.79491	−	0.480944i	0.106696	−	0.0285891i	0.311772	+	0.950157i	$0.399077\pi$
$284$	3.41838	−	2.33472i	0.202844	−	0.138540i
$285$		0			0
$286$	7.67238	+	24.8371i	0.453677	+	1.46865i
$287$	14.5891	−	14.5891i	0.861170	−	0.861170i
$288$	−14.3984	+	8.98259i	−0.848432	+	0.529304i
$289$		−	7.63580i		−	0.449165i
$290$		0			0
$291$	1.82381	−	5.16844i	0.106914	−	0.302979i
$292$	−24.9450	−	4.69867i	−1.45980	−	0.274969i
$293$	6.82756	+	25.4808i	0.398870	+	1.48860i	0.815087	+	0.579339i	$0.196689\pi$
$293$	6.82756	+	25.4808i	0.398870	+	1.48860i	−0.416217	+	0.909266i	$0.636644\pi$
$294$	−0.575815	−	1.09539i	−0.0335822	−	0.0638842i
$295$		0			0
$296$	9.15221	−	11.5055i	0.531961	−	0.668744i
$297$	17.3449	−	5.20045i	1.00645	−	0.301761i
$298$	−2.08434	−	3.31419i	−0.120742	−	0.191986i
$299$	−10.1075	−	17.5068i	−0.584534	−	1.01244i
$300$		0			0
$301$	−6.70478	+	11.6130i	−0.386457	+	0.669363i
$302$	10.6341	−	0.402264i	0.611922	−	0.0231477i
$303$	3.22828	+	6.74902i	0.185460	+	0.387721i
$304$	−5.65479	+	14.4779i	−0.324325	+	0.830366i
$305$		0			0
$306$	−1.87261	−	12.8471i	−0.107050	−	0.734422i
$307$	13.9421	−	13.9421i	0.795717	−	0.795717i	−0.186700	−	0.982417i	$-0.559779\pi$
$307$	13.9421	−	13.9421i	0.795717	−	0.795717i	0.982417	+	0.186700i	$0.0597792\pi$
$308$	−13.4727	−	11.5750i	−0.767677	−	0.659545i
$309$	−2.32577	+	0.433717i	−0.132308	+	0.0246733i
$310$		0			0
$311$	0.701482	+	0.405001i	0.0397774	+	0.0229655i	0.519757	−	0.854314i	$-0.326023\pi$
$311$	0.701482	+	0.405001i	0.0397774	+	0.0229655i	−0.479979	+	0.877280i	$0.659356\pi$
$312$	−24.7031	+	7.58193i	−1.39854	+	0.429242i
$313$	−6.11329	−	1.63805i	−0.345544	−	0.0925882i	0.0818732	−	0.996643i	$-0.473910\pi$
$313$	−6.11329	−	1.63805i	−0.345544	−	0.0925882i	−0.427417	+	0.904055i	$0.640576\pi$
$314$	5.16400	+	1.17642i	0.291421	+	0.0663893i
$315$		0			0
$316$	13.1013	−	27.2623i	0.737005	−	1.53362i
$317$	5.23297	−	19.5297i	0.293913	−	1.09690i	−0.648164	−	0.761501i	$-0.724463\pi$
$317$	5.23297	−	19.5297i	0.293913	−	1.09690i	0.942077	−	0.335397i	$-0.108871\pi$
$318$	−0.898186	+	0.202904i	−0.0503678	+	0.0113783i
$319$	7.74847	−	13.4207i	0.433831	−	0.751418i
$320$		0			0
$321$	9.91424	−	8.48654i	0.553359	−	0.473672i
$322$	12.2146	+	6.44923i	0.680696	+	0.359401i
$323$	−8.40809	−	8.40809i	−0.467838	−	0.467838i
$324$	5.13822	+	17.2510i	0.285457	+	0.958392i
$325$		0			0
$326$	−3.99590	−	12.9356i	−0.221313	−	0.716435i
$327$	−1.90060	+	24.4957i	−0.105103	+	1.35462i
$328$	−20.9991	−	9.13111i	−1.15948	−	0.504181i
$329$	−0.529071	−	0.305459i	−0.0291686	−	0.0168405i
$330$		0			0
$331$	−16.9166	+	9.76680i	−0.929821	+	0.536832i	−0.886755	−	0.462240i	$-0.847046\pi$
$331$	−16.9166	+	9.76680i	−0.929821	+	0.536832i	−0.0430657	+	0.999072i	$0.513712\pi$
$332$	29.2924	−	10.2768i	1.60763	−	0.564013i
$333$	−9.19350	−	12.5951i	−0.503801	−	0.690207i
$334$	1.16202	−	5.10077i	0.0635828	−	0.279102i
$335$		0			0
$336$	11.5304	−	13.3716i	0.629034	−	0.729482i
$337$	−9.77024	+	2.61793i	−0.532219	+	0.142608i	−0.514913	−	0.857243i	$-0.672176\pi$
$337$	−9.77024	+	2.61793i	−0.532219	+	0.142608i	−0.0173061	+	0.999850i	$0.505509\pi$
$338$	−20.9466	+	0.792364i	−1.13934	+	0.0430989i
$339$	0.143834	+	0.771299i	0.00781201	+	0.0418912i
$340$		0			0
$341$	−7.52446			−0.407472
$342$	13.2168	+	9.85400i	0.714684	+	0.532843i
$343$	13.5248	+	13.5248i	0.730270	+	0.730270i
$344$	14.7190	+	2.20003i	0.793597	+	0.118618i
$345$		0			0
$346$	24.0487	+	22.2956i	1.29286	+	1.19862i
$347$	6.50347	+	24.2713i	0.349125	+	1.30295i	0.887719	+	0.460386i	$0.152289\pi$
$347$	6.50347	+	24.2713i	0.349125	+	1.30295i	−0.538594	+	0.842565i	$0.681044\pi$
$348$	13.3269	+	7.72656i	0.714397	+	0.414187i
$349$	−15.0315	+	8.67844i	−0.804617	+	0.464546i	−0.845083	−	0.534635i	$-0.820449\pi$
$349$	−15.0315	+	8.67844i	−0.804617	+	0.464546i	0.0404658	+	0.999181i	$0.487116\pi$
$350$		0			0
$351$	0.808354	+	27.3960i	0.0431467	+	1.46229i
$352$	−6.47271	+	18.6203i	−0.344997	+	0.992464i
$353$	28.8445	+	7.72886i	1.53524	+	0.411366i	0.924723	−	0.380640i	$-0.124296\pi$
$353$	28.8445	+	7.72886i	1.53524	+	0.411366i	0.610514	+	0.792006i	$0.290963\pi$
$354$	24.6806	−	12.9740i	1.31176	−	0.689558i
$355$		0			0
$356$	5.97028	−	4.07764i	0.316424	−	0.216115i
$357$	5.82865	+	12.1853i	0.308485	+	0.644916i
$358$	12.5291	+	6.61528i	0.662186	+	0.349628i
$359$	−26.1394			−1.37959			−0.689794	−	0.724006i	$-0.742299\pi$
$359$	−26.1394			−1.37959			−0.689794	+	0.724006i	$0.742299\pi$
$360$		0			0
$361$	−3.90081			−0.205306
$362$	−24.9883	−	13.1936i	−1.31336	−	0.693440i
$363$	1.12059	−	1.63434i	0.0588159	−	0.0857807i
$364$	22.2009	−	15.1630i	1.16364	−	0.794755i
$365$		0			0
$366$	0.896186	−	22.6054i	0.0468444	−	1.18160i
$367$	−22.2128	−	5.95191i	−1.15950	−	0.310687i	−0.372734	−	0.927938i	$-0.621580\pi$
$367$	−22.2128	−	5.95191i	−1.15950	−	0.310687i	−0.786766	+	0.617251i	$0.788246\pi$
$368$	1.69143	−	15.2363i	0.0881718	−	0.794249i
$369$	−15.2429	+	18.9087i	−0.793511	+	0.984348i
$370$		0			0
$371$	0.829682	−	0.479017i	0.0430750	−	0.0248693i
$372$	0.0135702	−	7.47968i	0.000703581	−	0.387803i
$373$	3.44016	+	12.8388i	0.178125	+	0.664770i	0.995998	+	0.0893722i	$0.0284861\pi$
$373$	3.44016	+	12.8388i	0.178125	+	0.664770i	−0.817874	+	0.575398i	$0.804847\pi$
$374$	−11.0594	−	10.2532i	−0.571869	−	0.530181i
$375$		0			0
$376$	−0.100230	+	0.670576i	−0.00516896	+	0.0345823i
$377$	16.5861	+	16.5861i	0.854226	+	0.854226i
$378$	−10.4333	−	15.5520i	−0.536633	−	0.799907i
$379$	12.7657			0.655730			0.327865	−	0.944725i	$-0.393671\pi$
$379$	12.7657			0.655730			0.327865	+	0.944725i	$0.393671\pi$
$380$		0			0
$381$	−4.95471	+	4.24121i	−0.253838	+	0.217284i
$382$	−22.1446	+	0.837683i	−1.13302	+	0.0428596i
$383$	33.9365	−	9.09327i	1.73408	−	0.464644i	0.752960	−	0.658066i	$-0.228625\pi$
$383$	33.9365	−	9.09327i	1.73408	−	0.464644i	0.981116	+	0.193422i	$0.0619586\pi$
$384$	−18.4978	−	6.46777i	−0.943961	−	0.330057i
$385$		0			0
$386$	6.77959	−	29.7596i	0.345072	−	1.51472i
$387$	6.38856	−	14.4348i	0.324749	−	0.733761i
$388$	5.97181	−	2.09512i	0.303173	−	0.106364i
$389$	15.4675	−	8.93019i	0.784236	−	0.452779i	−0.0536937	−	0.998557i	$-0.517099\pi$
$389$	15.4675	−	8.93019i	0.784236	−	0.452779i	0.837929	+	0.545779i	$0.183766\pi$
$390$		0			0
$391$	10.1566	+	5.86389i	0.513639	+	0.296550i
$392$	0.569816	−	1.31043i	0.0287801	−	0.0661865i
$393$	17.5139	+	12.0085i	0.883459	+	0.605747i
$394$	5.57609	+	18.0510i	0.280919	+	0.909395i
$395$		0			0
$396$	17.2233	+	11.8552i	0.865502	+	0.595746i
$397$	−22.9050	−	22.9050i	−1.14957	−	1.14957i	−0.986637	−	0.162934i	$-0.947904\pi$
$397$	−22.9050	−	22.9050i	−1.14957	−	1.14957i	−0.162934	−	0.986637i	$-0.552096\pi$
$398$	2.57722	+	1.36075i	0.129184	+	0.0682082i
$399$	−16.1747	−	5.70764i	−0.809748	−	0.285739i
$400$		0			0
$401$	−15.2608	+	26.4324i	−0.762087	+	1.31997i	0.179686	+	0.983724i	$0.442492\pi$
$401$	−15.2608	+	26.4324i	−0.762087	+	1.31997i	−0.941773	+	0.336249i	$0.890841\pi$
$402$	0.541730	−	1.74248i	0.0270190	−	0.0869068i
$403$	2.94770	−	11.0010i	0.146836	−	0.547998i
$404$	−3.74183	+	7.78632i	−0.186163	+	0.387384i
$405$		0			0
$406$	−15.6270	−	3.56001i	−0.775553	−	0.176680i
$407$	−17.4964	−	4.68814i	−0.867263	−	0.232383i
$408$	10.2121	−	10.9751i	0.505576	−	0.543349i
$409$	14.2191	+	8.20942i	0.703091	+	0.405930i	0.808498	−	0.588499i	$-0.200281\pi$
$409$	14.2191	+	8.20942i	0.703091	+	0.405930i	−0.105407	+	0.994429i	$0.533614\pi$
$410$		0			0
$411$	−5.33171	+	15.1094i	−0.262994	+	0.745290i
$412$	−2.07213	−	1.78026i	−0.102087	−	0.0877072i
$413$	−20.5130	+	20.5130i	−1.00938	+	1.00938i
$414$	−15.1068	−	6.01386i	−0.742460	−	0.295565i
$415$		0			0
$416$	−24.6877	−	16.7578i	−1.21041	−	0.821618i
$417$	−17.5414	+	25.5835i	−0.859008	+	1.25283i
$418$	19.1366	−	0.723895i	0.936000	−	0.0354068i
$419$	−5.01036	+	8.67820i	−0.244772	+	0.423958i	−0.962068	−	0.272811i	$-0.912047\pi$
$419$	−5.01036	+	8.67820i	−0.244772	+	0.423958i	0.717295	+	0.696769i	$0.245380\pi$
$420$		0			0
$421$	−3.68335	−	6.37975i	−0.179515	−	0.310930i	0.762199	−	0.647342i	$-0.224120\pi$
$421$	−3.68335	−	6.37975i	−0.179515	−	0.310930i	−0.941715	+	0.336413i	$0.890786\pi$
$422$	1.73403	+	2.75719i	0.0844115	+	0.134218i
$423$	0.657626	+	0.291053i	0.0319749	+	0.0141515i
$424$	−0.832113	−	0.661915i	−0.0404110	−	0.0321455i
$425$		0			0
$426$	2.70692	−	4.28684i	0.131151	−	0.207698i
$427$	6.09194	+	22.7354i	0.294810	+	1.10024i
$428$	14.8089	+	2.78942i	0.715816	+	0.134832i
$429$	20.7035	+	24.1865i	0.999575	+	1.16773i
$430$		0			0
$431$			16.4473i			0.792237i	0.918199	+	0.396119i	$0.129643\pi$
$431$			16.4473i			0.792237i	−0.918199	+	0.396119i	$0.870357\pi$
$432$	−11.8157	+	17.0994i	−0.568483	+	0.822695i
$433$	3.78112	−	3.78112i	0.181709	−	0.181709i	−0.610391	−	0.792100i	$-0.708988\pi$
$433$	3.78112	−	3.78112i	0.181709	−	0.181709i	0.792100	+	0.610391i	$0.208988\pi$
$434$	2.29683	+	7.43531i	0.110251	+	0.356906i
$435$		0			0
$436$	−23.4275	+	16.0007i	−1.12197	+	0.766297i
$437$	−14.3847	+	3.85437i	−0.688114	+	0.184380i
$438$	−30.3244	+	6.85042i	−1.44896	+	0.327326i
$439$	−18.4104	−	31.8878i	−0.878683	−	1.52192i	−0.852787	−	0.522258i	$-0.825090\pi$
$439$	−18.4104	−	31.8878i	−0.878683	−	1.52192i	−0.0258954	−	0.999665i	$-0.508244\pi$
$440$		0			0
$441$	−1.17998	−	0.951212i	−0.0561893	−	0.0452958i
$442$	19.3230	−	12.1525i	0.919102	−	0.578036i
$443$	−3.13302	+	11.6926i	−0.148854	+	0.555532i	0.850699	+	0.525653i	$0.176179\pi$
$443$	−3.13302	+	11.6926i	−0.148854	+	0.555532i	−0.999554	+	0.0298790i	$0.990488\pi$
$444$	4.69179	−	17.3838i	0.222663	−	0.824998i
$445$		0			0
$446$	−16.0484	+	17.3103i	−0.759914	+	0.819666i
$447$	−3.95472	−	2.71157i	−0.187052	−	0.128253i
$448$	20.3755	+	0.712219i	0.962650	+	0.0336492i
$449$		−	1.04828i		−	0.0494715i	−0.999694	−	0.0247357i	$-0.992126\pi$
$449$		−	1.04828i		−	0.0494715i	0.999694	−	0.0247357i	$-0.00787443\pi$
$450$		0			0
$451$			28.2127i			1.32848i
$452$	−0.590392	+	0.687186i	−0.0277697	+	0.0323225i
$453$	11.7575	−	5.62401i	0.552415	−	0.264239i
$454$	−5.22805	−	4.84694i	−0.245365	−	0.227478i
$455$		0			0
$456$	0.685074	+	19.0240i	0.0320815	+	0.890879i
$457$	−3.52188	+	13.1438i	−0.164747	+	0.614843i	0.833326	+	0.552782i	$0.186434\pi$
$457$	−3.52188	+	13.1438i	−0.164747	+	0.614843i	−0.998072	+	0.0620609i	$0.980233\pi$
$458$	5.84101	+	9.28746i	0.272932	+	0.433974i
$459$	−8.35305	−	13.5300i	−0.389887	−	0.631525i
$460$		0			0
$461$	5.72422	+	9.91464i	0.266604	+	0.461771i	0.967983	−	0.251018i	$-0.0807652\pi$
$461$	5.72422	+	9.91464i	0.266604	+	0.461771i	−0.701379	+	0.712789i	$0.747432\pi$
$462$	−20.7733	−	6.45834i	−0.966461	−	0.300469i
$463$	−4.53841	+	1.21606i	−0.210918	+	0.0565153i	−0.362731	−	0.931894i	$-0.618156\pi$
$463$	−4.53841	+	1.21606i	−0.210918	+	0.0565153i	0.151813	+	0.988409i	$0.451489\pi$
$464$	2.67998	+	17.5848i	0.124415	+	0.816354i
$465$		0			0
$466$	7.93664	−	2.45169i	0.367658	−	0.113573i
$467$	−25.5411	+	25.5411i	−1.18190	+	1.18190i	−0.202651	+	0.979251i	$0.564956\pi$
$467$	−25.5411	+	25.5411i	−1.18190	+	1.18190i	−0.979251	+	0.202651i	$0.935044\pi$
$468$	−24.0799	+	20.5367i	−1.11309	+	0.949308i
$469$			1.89849i			0.0876643i
$470$		0			0
$471$	6.37669	−	1.18915i	0.293822	−	0.0547929i
$472$	29.5258	+	12.8388i	1.35904	+	0.590953i
$473$	−4.74581	−	17.7116i	−0.218213	−	0.814381i
$474$	1.46748	−	37.0157i	0.0674036	−	1.70019i
$475$		0			0
$476$	−6.75587	+	14.0582i	−0.309655	+	0.644355i
$477$	−0.910915	+	0.664902i	−0.0417080	+	0.0304438i
$478$	3.06606	−	1.92828i	0.140238	−	0.0881977i
$479$	6.06234	+	10.5003i	0.276995	+	0.479770i	0.970637	−	0.240551i	$-0.0773280\pi$
$479$	6.06234	+	10.5003i	0.276995	+	0.479770i	−0.693641	+	0.720321i	$0.743995\pi$
$480$		0			0
$481$	13.7084	−	23.7436i	0.625049	−	1.08262i
$482$	0.737106	+	19.4858i	0.0335743	+	0.887554i
$483$	16.8663	+	1.30864i	0.767444	+	0.0595452i
$484$	2.28163	−	0.172866i	0.103711	−	0.00785755i
$485$		0			0
$486$	14.1656	+	16.8919i	0.642562	+	0.766233i
$487$	12.5621	−	12.5621i	0.569243	−	0.569243i	−0.362673	−	0.931916i	$-0.618136\pi$
$487$	12.5621	−	12.5621i	0.569243	−	0.569243i	0.931916	+	0.362673i	$0.118136\pi$
$488$	20.9994	−	15.5382i	0.950596	−	0.703379i
$489$	−10.7827	−	12.5967i	−0.487612	−	0.569643i
$490$		0			0
$491$	−0.109289	−	0.0630982i	−0.00493215	−	0.00284758i	0.497532	−	0.867446i	$-0.334240\pi$
$491$	−0.109289	−	0.0630982i	−0.00493215	−	0.00284758i	−0.502464	+	0.864598i	$0.667573\pi$
$492$	−28.0448	−	0.0508809i	−1.26436	−	0.00229389i
$493$	−13.1445	−	3.52205i	−0.591997	−	0.158625i
$494$	−6.43838	+	28.2618i	−0.289677	+	1.27156i
$495$		0			0
$496$	6.74369	−	5.39602i	0.302800	−	0.242289i
$497$	−1.36523	+	5.09512i	−0.0612391	+	0.228547i
$498$	27.9277	−	25.7978i	1.25147	−	1.15603i
$499$	−20.2868	+	35.1377i	−0.908161	+	1.57298i	−0.0915430	+	0.995801i	$0.529180\pi$
$499$	−20.2868	+	35.1377i	−0.908161	+	1.57298i	−0.816618	+	0.577179i	$0.804153\pi$
$500$		0			0
$501$	−1.17459	−	6.29862i	−0.0524766	−	0.281401i
$502$	7.58021	−	14.3567i	0.338321	−	0.640771i
$503$	6.97397	+	6.97397i	0.310954	+	0.310954i	0.845279	−	0.534325i	$-0.179434\pi$
$503$	6.97397	+	6.97397i	0.310954	+	0.310954i	−0.534325	+	0.845279i	$0.679434\pi$
$504$	6.45737	−	20.6380i	0.287634	−	0.919290i
$505$		0			0
$506$	−18.0462	+	5.57463i	−0.802253	+	0.247823i
$507$	−23.1594	+	11.0779i	−1.02855	+	0.491989i
$508$	−7.40086	−	1.39403i	−0.328360	−	0.0618503i
$509$	27.6387	+	15.9572i	1.22507	+	0.707292i	0.965994	−	0.258566i	$-0.0832499\pi$
$509$	27.6387	+	15.9572i	1.22507	+	0.707292i	0.259072	+	0.965858i	$0.416583\pi$
$510$		0			0
$511$	28.0116	−	16.1725i	1.23916	−	0.715430i
$512$	−7.55210	−	21.3299i	−0.333759	−	0.942658i
$513$	19.6487	+	4.64834i	0.867511	+	0.205229i
$514$	−20.2321	−	4.60912i	−0.892400	−	0.203300i
$515$		0			0
$516$	17.6148	−	4.68563i	0.775447	−	0.206273i
$517$	0.806914	−	0.216212i	0.0354880	−	0.00950899i
$518$	0.708142	+	18.7201i	0.0311140	+	0.822516i
$519$	37.8750	+	13.3651i	1.66253	+	0.586664i
$520$		0			0
$521$	34.5815			1.51504			0.757521	−	0.652811i	$-0.226410\pi$
$521$	34.5815			1.51504			0.757521	+	0.652811i	$0.226410\pi$
$522$	18.7378	+	2.20348i	0.820129	+	0.0964436i
$523$	31.6445	+	31.6445i	1.38372	+	1.38372i	0.837915	+	0.545801i	$0.183775\pi$
$523$	31.6445	+	31.6445i	1.38372	+	1.38372i	0.545801	+	0.837915i	$0.316225\pi$
$524$	1.85246	+	24.4504i	0.0809251	+	1.06812i
$525$		0			0
$526$	1.76374	−	1.90243i	0.0769028	−	0.0829497i
$527$	1.71011	+	6.38222i	0.0744936	+	0.278014i
$528$	1.78031	+	24.0779i	0.0774782	+	1.04786i
$529$	−7.19846	+	4.15603i	−0.312976	+	0.180697i
$530$		0			0
$531$	21.4322	−	26.5866i	0.930078	−	1.15376i
$532$	−6.55672	−	18.6889i	−0.284270	−	0.810265i
$533$	−41.2478	−	11.0523i	−1.78664	−	0.478729i
$534$	4.72769	−	7.48706i	0.204587	−	0.323997i
$535$		0			0
$536$	1.96044	−	0.772198i	0.0846779	−	0.0333539i
$537$	17.3006	+	1.34234i	0.746575	+	0.0579261i
$538$	−8.85013	+	16.7619i	−0.381556	+	0.722656i
$539$	−1.76058			−0.0758335
$540$		0			0
$541$	35.6814			1.53407			0.767033	−	0.641608i	$-0.221732\pi$
$541$	35.6814			1.53407			0.767033	+	0.641608i	$0.221732\pi$
$542$	−12.6725	+	24.0013i	−0.544330	+	1.03094i
$543$	−34.5045	−	2.67717i	−1.48073	−	0.114888i
$544$	17.2647	+	1.25824i	0.740220	+	0.0539464i
$545$		0			0
$546$	17.5802	−	27.8411i	0.752364	−	1.19149i
$547$	15.9487	+	4.27345i	0.681919	+	0.182720i	0.583118	−	0.812388i	$-0.301833\pi$
$547$	15.9487	+	4.27345i	0.681919	+	0.182720i	0.0988010	+	0.995107i	$0.468499\pi$
$548$	−17.4579	+	6.12487i	−0.745766	+	0.261641i
$549$	−9.98668	−	25.8452i	−0.426221	−	1.10305i
$550$		0			0
$551$	14.9648	−	8.63994i	0.637522	−	0.368074i
$552$	−5.50890	−	17.9489i	−0.234475	−	0.763955i
$553$	9.97538	+	37.2286i	0.424197	+	1.58312i
$554$	7.18570	−	7.75071i	0.305291	−	0.329296i
$555$		0			0
$556$	−35.7161	+	2.70599i	−1.51470	+	0.114760i
$557$	−1.96120	−	1.96120i	−0.0830989	−	0.0830989i	0.664336	−	0.747434i	$-0.268715\pi$
$557$	−1.96120	−	1.96120i	−0.0830989	−	0.0830989i	−0.747434	+	0.664336i	$0.768715\pi$
$558$	−3.62246	−	8.41406i	−0.153351	−	0.356196i
$559$	27.7541			1.17387
$560$		0			0
$561$	−17.4179	−	6.14632i	−0.735383	−	0.259498i
$562$	−0.747922	−	19.7717i	−0.0315492	−	0.834020i
$563$	−12.8024	+	3.43039i	−0.539557	+	0.144574i	−0.518298	−	0.855200i	$-0.673434\pi$
$563$	−12.8024	+	3.43039i	−0.539557	+	0.144574i	−0.0212589	+	0.999774i	$0.506767\pi$
$564$	0.213470	+	0.802501i	0.00898870	+	0.0337914i
$565$		0			0
$566$	2.56228	+	0.583718i	0.107701	+	0.0245355i
$567$	−19.2911	−	12.4068i	−0.810152	−	0.521038i
$568$	5.81665	−	0.662624i	0.244061	−	0.0278031i
$569$	−9.89594	+	5.71342i	−0.414859	+	0.239519i	−0.692876	−	0.721057i	$-0.743656\pi$
$569$	−9.89594	+	5.71342i	−0.414859	+	0.239519i	0.278016	+	0.960576i	$0.410323\pi$
$570$		0			0
$571$	−32.2228	−	18.6038i	−1.34848	−	0.778546i	−0.360447	−	0.932780i	$-0.617376\pi$
$571$	−32.2228	−	18.6038i	−1.34848	−	0.778546i	−0.988034	+	0.154234i	$0.950709\pi$
$572$	−6.80499	+	36.1274i	−0.284531	+	1.51056i
$573$	−24.4840	+	11.7115i	−1.02284	+	0.489257i
$574$	27.8784	−	8.61188i	1.16362	−	0.359453i
$575$		0			0
$576$	−23.9378	+	1.72629i	−0.997410	+	0.0719289i
$577$	8.63696	+	8.63696i	0.359561	+	0.359561i	0.863651	−	0.504090i	$-0.168172\pi$
$577$	8.63696	+	8.63696i	0.359561	+	0.359561i	−0.504090	+	0.863651i	$0.668172\pi$
$578$	5.04196	−	9.54932i	0.209718	−	0.397199i
$579$	−6.85292	−	36.7482i	−0.284798	−	1.52720i
$580$		0			0
$581$	−19.7780	+	34.2566i	−0.820532	+	1.42120i
$582$	5.69360	−	5.25937i	0.236007	−	0.218008i
$583$	−0.339061	+	1.26539i	−0.0140425	+	0.0524072i
$584$	−28.0937	−	22.3475i	−1.16252	−	0.924745i
$585$		0			0
$586$	−8.28656	+	36.3745i	−0.342315	+	1.50262i
$587$	7.66180	+	2.05297i	0.316236	+	0.0847352i	0.413446	−	0.910529i	$-0.364325\pi$
$587$	7.66180	+	2.05297i	0.316236	+	0.0847352i	−0.0972097	+	0.995264i	$0.530992\pi$
$588$	0.00317516	−	1.75010i	0.000130941	−	0.0721729i
$589$	−7.26609	−	4.19508i	−0.299394	−	0.172855i
$590$		0			0
$591$	15.0468	+	17.5781i	0.618942	+	0.723067i
$592$	19.0429	−	8.34552i	0.782657	−	0.342999i
$593$	17.4824	−	17.4824i	0.717918	−	0.717918i	−0.250261	−	0.968178i	$-0.580516\pi$
$593$	17.4824	−	17.4824i	0.717918	−	0.717918i	0.968178	+	0.250261i	$0.0805164\pi$
$594$	25.1254	+	4.94925i	1.03091	+	0.203070i
$595$		0			0
$596$	−0.418295	−	5.52102i	−0.0171340	−	0.226150i
$597$	3.55869	+	0.276116i	0.145648	+	0.0113007i
$598$	−1.08067	−	28.5680i	−0.0441917	−	1.16823i
$599$	−15.1365	+	26.2172i	−0.618461	+	1.07121i	0.371305	+	0.928511i	$0.378910\pi$
$599$	−15.1365	+	26.2172i	−0.618461	+	1.07121i	−0.989767	+	0.142696i	$0.954423\pi$
$600$		0			0
$601$	−1.15030	−	1.99238i	−0.0469219	−	0.0812710i	0.841611	−	0.540085i	$-0.181608\pi$
$601$	−1.15030	−	1.99238i	−0.0469219	−	0.0812710i	−0.888532	+	0.458814i	$0.848275\pi$
$602$	−16.0531	+	10.0960i	−0.654277	+	0.411483i
$603$	−0.238521	−	2.22208i	−0.00971331	−	0.0904902i
$604$	13.5646	+	6.51866i	0.551935	+	0.265241i
$605$		0			0
$606$	−0.419124	+	10.5720i	−0.0170257	+	0.429457i
$607$	−11.3362	−	42.3071i	−0.460120	−	1.71719i	−0.672581	−	0.740023i	$-0.734815\pi$
$607$	−11.3362	−	42.3071i	−0.460120	−	1.71719i	0.212461	−	0.977170i	$-0.431852\pi$
$608$	−16.6317	+	14.3722i	−0.674506	+	0.582869i
$609$	−19.2967	+	3.59851i	−0.781943	+	0.145819i
$610$		0			0
$611$			1.26443i			0.0511535i
$612$	6.14115	−	17.3031i	0.248241	−	0.699437i
$613$	−5.01756	+	5.01756i	−0.202657	+	0.202657i	−0.801138	−	0.598480i	$-0.795772\pi$
$613$	−5.01756	+	5.01756i	−0.202657	+	0.202657i	0.598480	+	0.801138i	$0.295772\pi$
$614$	26.6420	−	8.22993i	1.07518	−	0.332133i
$615$		0			0
$616$	−9.20591	−	23.3717i	−0.370917	−	0.941674i
$617$	6.92773	−	1.85628i	0.278900	−	0.0747310i	−0.116658	−	0.993172i	$-0.537218\pi$
$617$	6.92773	−	1.85628i	0.278900	−	0.0747310i	0.395558	+	0.918441i	$0.370551\pi$
$618$	−3.19499	−	0.993311i	−0.128521	−	0.0399568i
$619$	6.11352	+	10.5889i	0.245723	+	0.425605i	0.962335	−	0.271868i	$-0.0876413\pi$
$619$	6.11352	+	10.5889i	0.245723	+	0.425605i	−0.716612	+	0.697473i	$0.754308\pi$
$620$		0			0
$621$	−19.9055	+	0.587337i	−0.798781	+	0.0235690i
$622$	0.609848	+	0.969686i	0.0244527	+	0.0388809i
$623$	−2.38441	+	8.89874i	−0.0955294	+	0.356521i
$624$	−35.9001	−	6.82965i	−1.43715	−	0.273405i
$625$		0			0
$626$	−6.56366	−	6.08519i	−0.262337	−	0.243213i
$627$	21.1582	−	10.1207i	0.844977	−	0.404181i
$628$	5.68129	+	4.88105i	0.226708	+	0.194775i
$629$			15.9059i			0.634208i
$630$		0			0
$631$			8.53598i			0.339812i	0.985460	+	0.169906i	$0.0543464\pi$
$631$			8.53598i			0.339812i	−0.985460	+	0.169906i	$0.945654\pi$
$632$	34.3859	−	25.4433i	1.36780	−	1.01208i
$633$	3.29008	+	2.25585i	0.130769	+	0.0896621i
$634$	19.4399	−	20.9685i	0.772058	−	0.832765i
$635$		0			0
$636$	−1.25725	−	0.339325i	−0.0498532	−	0.0134551i
$637$	0.689706	−	2.57402i	0.0273272	−	0.101986i
$638$	18.5520	−	11.6676i	0.734481	−	0.461925i
$639$	0.957796	−	6.13508i	0.0378898	−	0.242700i
$640$		0			0
$641$	5.32828	+	9.22886i	0.210454	+	0.364518i	0.951857	−	0.306543i	$-0.0991723\pi$
$641$	5.32828	+	9.22886i	0.210454	+	0.364518i	−0.741402	+	0.671061i	$0.765839\pi$
$642$	18.0024	−	4.06683i	0.710500	−	0.160505i
$643$	0.317383	−	0.0850425i	0.0125164	−	0.00335375i	−0.252555	−	0.967582i	$-0.581271\pi$
$643$	0.317383	−	0.0850425i	0.0125164	−	0.00335375i	0.265072	+	0.964229i	$0.414604\pi$
$644$	11.0172	+	16.1308i	0.434137	+	0.635642i
$645$		0			0
$646$	−4.96324	−	16.0670i	−0.195276	−	0.632149i
$647$	−1.08970	+	1.08970i	−0.0428405	+	0.0428405i	−0.728203	−	0.685362i	$-0.759644\pi$
$647$	−1.08970	+	1.08970i	−0.0428405	+	0.0428405i	0.685362	+	0.728203i	$0.259644\pi$
$648$	−4.96511	+	24.9669i	−0.195048	+	0.980794i
$649$		−	39.6684i		−	1.55712i
$650$		0			0
$651$	6.19787	+	7.24054i	0.242914	+	0.283779i
$652$	3.54415	−	18.8157i	0.138800	−	0.736881i
$653$	−5.92931	−	22.1285i	−0.232032	−	0.865954i	−0.979465	−	0.201617i	$-0.935380\pi$
$653$	−5.92931	−	22.1285i	−0.232032	−	0.865954i	0.747433	−	0.664337i	$-0.231286\pi$
$654$	−18.5515	+	29.3794i	−0.725423	+	1.14882i
$655$		0			0
$656$	−20.2322	−	25.2852i	−0.789934	−	0.987221i
$657$	−30.7542	+	22.4483i	−1.19983	+	0.875792i
$658$	−0.459959	−	0.731356i	−0.0179311	−	0.0285112i
$659$	−6.24819	−	10.8222i	−0.243395	−	0.421572i	0.718284	−	0.695750i	$-0.244928\pi$
$659$	−6.24819	−	10.8222i	−0.243395	−	0.421572i	−0.961679	+	0.274177i	$0.911594\pi$
$660$		0			0
$661$	−2.84081	+	4.92043i	−0.110495	+	0.191382i	−0.915970	−	0.401247i	$-0.868577\pi$
$661$	−2.84081	+	4.92043i	−0.110495	+	0.191382i	0.805475	+	0.592630i	$0.201910\pi$
$662$	−27.6050	+	1.04424i	−1.07290	+	0.0405854i
$663$	15.8095	−	23.0576i	0.613991	−	0.895483i
$664$	43.4188	+	6.48974i	1.68498	+	0.251851i
$665$		0			0
$666$	−3.18078	−	21.8219i	−0.123253	−	0.845582i
$667$	−12.0512	+	12.0512i	−0.466623	+	0.466623i
$668$	4.82128	−	5.61173i	0.186541	−	0.217124i
$669$	−9.62026	+	27.2625i	−0.371941	+	1.05403i
$670$		0			0
$671$	−27.8734	−	16.0927i	−1.07604	−	0.621252i
$672$	23.2492	−	9.10897i	0.896858	−	0.351386i
$673$	28.9286	+	7.75138i	1.11511	+	0.298794i	0.768905	−	0.639363i	$-0.220802\pi$
$673$	28.9286	+	7.75138i	1.11511	+	0.298794i	0.346209	+	0.938157i	$0.387469\pi$
$674$	−13.9473	−	3.17736i	−0.537229	−	0.122387i
$675$		0			0
$676$	−26.7190	−	12.8402i	−1.02765	−	0.493854i
$677$	0.688499	−	2.56951i	0.0264612	−	0.0987544i	−0.951432	−	0.307858i	$-0.900388\pi$
$677$	0.688499	−	2.56951i	0.0264612	−	0.0987544i	0.977894	+	0.209103i	$0.0670545\pi$
$678$	−0.329414	+	1.05956i	−0.0126511	+	0.0406922i
$679$	−4.03213	+	6.98386i	−0.154739	+	0.268016i
$680$		0			0
$681$	−8.23384	−	2.90551i	−0.315521	−	0.111339i
$682$	−9.41008	−	4.96844i	−0.360331	−	0.190251i
$683$	−31.3443	−	31.3443i	−1.19936	−	1.19936i	−0.974359	−	0.224999i	$-0.927762\pi$
$683$	−31.3443	−	31.3443i	−1.19936	−	1.19936i	−0.224999	−	0.974359i	$-0.572238\pi$
$684$	10.0223	+	21.0505i	0.383212	+	0.804887i
$685$		0			0
$686$	7.98360	+	25.8446i	0.304815	+	0.986750i
$687$	11.0825	+	7.59873i	0.422822	+	0.289909i
$688$	16.9549	+	12.4704i	0.646400	+	0.475430i
$689$	−1.71721	−	0.991433i	−0.0654206	−	0.0377706i
$690$		0			0
$691$	1.44150	−	0.832251i	0.0548373	−	0.0316603i	−0.472331	−	0.881421i	$-0.656587\pi$
$691$	1.44150	−	0.832251i	0.0548373	−	0.0316603i	0.527168	+	0.849761i	$0.323254\pi$
$692$	15.3534	+	43.7622i	0.583647	+	1.66359i
$693$	−26.4910	+	2.84357i	−1.00631	+	0.108018i
$694$	−7.89322	+	34.6479i	−0.299623	+	1.31522i
$695$		0			0
$696$	11.5647	+	18.4626i	0.438359	+	0.699825i
$697$	23.9299	−	6.41200i	0.906410	−	0.242872i
$698$	−24.5288	+	0.927871i	−0.928428	+	0.0351204i
$699$	7.72874	−	6.61576i	0.292328	−	0.250231i
$700$		0			0
$701$	−6.95642			−0.262740			−0.131370	−	0.991333i	$-0.541938\pi$
$701$	−6.95642			−0.262740			−0.131370	+	0.991333i	$0.541938\pi$
$702$	−17.0788	+	34.7952i	−0.644598	+	1.31326i
$703$	−14.2818	−	14.2818i	−0.538649	−	0.538649i
$704$	−20.3898	+	19.0125i	−0.768471	+	0.716562i
$705$		0			0
$706$	30.9695	+	28.7119i	1.16555	+	1.08059i
$707$	−2.84905	−	10.6328i	−0.107150	−	0.399888i
$708$	39.4323	+	0.0715410i	1.48196	+	0.00268868i
$709$	41.5369	−	23.9814i	1.55995	−	0.900639i	0.562693	−	0.826666i	$-0.309765\pi$
$709$	41.5369	−	23.9814i	1.55995	−	0.900639i	0.997260	−	0.0739729i	$-0.0235678\pi$
$710$		0			0
$711$	−16.3529	−	42.3208i	−0.613283	−	1.58715i
$712$	10.1589	−	1.15729i	0.380722	−	0.0433712i
$713$	7.99314	+	2.14175i	0.299345	+	0.0802093i
$714$	−0.756727	+	19.0876i	−0.0283198	+	0.714337i
$715$		0			0
$716$	11.3008	+	16.5461i	0.422332	+	0.618357i
$717$	2.50856	−	3.65864i	0.0936838	−	0.136634i
$718$	−32.6900	−	17.2600i	−1.21998	−	0.644138i
$719$	27.9555			1.04257			0.521283	−	0.853384i	$-0.325454\pi$
$719$	27.9555			1.04257			0.521283	+	0.853384i	$0.325454\pi$
$720$		0			0
$721$	3.48106			0.129641
$722$	−4.87834	−	2.57572i	−0.181553	−	0.0958584i
$723$	10.3054	+	21.5443i	0.383261	+	0.801243i
$724$	−22.5385	−	32.9998i	−0.837638	−	1.22643i
$725$		0			0
$726$	2.48058	−	1.30397i	0.0920629	−	0.0483950i
$727$	32.2018	+	8.62843i	1.19430	+	0.320011i	0.800583	−	0.599222i	$-0.204523\pi$
$727$	32.2018	+	8.62843i	1.19430	+	0.320011i	0.393714	+	0.919233i	$0.371190\pi$
$728$	37.7766	−	4.30345i	1.40009	−	0.159496i
$729$	24.1380	+	12.0978i	0.893999	+	0.448068i
$730$		0			0
$731$	−13.9443	+	8.05077i	−0.515750	+	0.297768i
$732$	16.0472	−	27.6785i	0.593122	−	1.02303i
$733$	0.439391	+	1.63983i	0.0162293	+	0.0605685i	0.973566	−	0.228408i	$-0.0733519\pi$
$733$	0.439391	+	1.63983i	0.0162293	+	0.0605685i	−0.957336	+	0.288976i	$0.906685\pi$
$734$	−23.8493	−	22.1107i	−0.880293	−	0.816121i
$735$		0			0
$736$	12.1759	−	17.9377i	0.448811	−	0.661192i
$737$	−1.83567	−	1.83567i	−0.0676177	−	0.0676177i
$738$	−31.5482	+	13.5823i	−1.16131	+	0.499971i
$739$	48.7588			1.79362			0.896811	−	0.442414i	$-0.145878\pi$
$739$	48.7588			1.79362			0.896811	+	0.442414i	$0.145878\pi$
$740$		0			0
$741$	6.50802	+	34.8987i	0.239078	+	1.28204i
$742$	1.35390	−	0.0512150i	0.0497031	−	0.00188016i
$743$	−20.5756	+	5.51322i	−0.754846	+	0.202260i	−0.615667	−	0.788007i	$-0.711113\pi$
$743$	−20.5756	+	5.51322i	−0.754846	+	0.202260i	−0.139179	+	0.990267i	$0.544446\pi$
$744$	4.95584	−	9.34512i	0.181690	−	0.342609i
$745$		0			0
$746$	−4.17530	+	18.3278i	−0.152868	+	0.671028i
$747$	18.8452	−	42.5803i	0.689511	−	1.55793i
$748$	−7.06065	−	20.1253i	−0.258163	−	0.735852i
$749$	−16.6294	+	9.60100i	−0.607626	+	0.350813i
$750$		0			0
$751$	−30.0558	−	17.3527i	−1.09675	−	0.633209i	−0.161385	−	0.986892i	$-0.551596\pi$
$751$	−30.0558	−	17.3527i	−1.09675	−	0.633209i	−0.935366	+	0.353682i	$0.884929\pi$
$752$	−0.568132	+	0.772440i	−0.0207177	+	0.0281680i
$753$	1.53813	−	19.8241i	0.0560527	−	0.722431i
$754$	9.79065	+	31.6944i	0.356554	+	1.15424i
$755$		0			0
$756$	−2.77887	−	26.3385i	−0.101067	−	0.957921i
$757$	−21.6732	−	21.6732i	−0.787727	−	0.787727i	0.193394	−	0.981121i	$-0.438050\pi$
$757$	−21.6732	−	21.6732i	−0.787727	−	0.787727i	−0.981121	+	0.193394i	$0.938050\pi$
$758$	15.9648	+	8.42926i	0.579867	+	0.306165i
$759$	−17.5735	+	15.0428i	−0.637878	+	0.546020i
$760$		0			0
$761$	13.2539	−	22.9564i	0.480452	−	0.832167i	−0.519297	−	0.854594i	$-0.673806\pi$
$761$	13.2539	−	22.9564i	0.480452	−	0.832167i	0.999748	+	0.0224270i	$0.00713933\pi$
$762$	−8.99685	+	2.03243i	−0.325921	+	0.0736271i
$763$	9.35647	−	34.9188i	0.338727	−	1.26415i
$764$	−28.2472	−	13.5746i	−1.02195	−	0.491112i
$765$		0			0
$766$	48.4453	+	11.0364i	1.75040	+	0.398763i
$767$	57.9964	+	15.5401i	2.09413	+	0.561120i
$768$	−18.8626	−	20.3028i	−0.680646	−	0.732613i
$769$	10.2142	+	5.89716i	0.368333	+	0.212657i	0.672730	−	0.739888i	$-0.265122\pi$
$769$	10.2142	+	5.89716i	0.368333	+	0.212657i	−0.304397	+	0.952545i	$0.598455\pi$
$770$		0			0
$771$	−24.9833	+	4.65897i	−0.899753	+	0.167789i
$772$	28.1289	−	32.7407i	1.01238	−	1.17836i
$773$	−7.36402	+	7.36402i	−0.264865	+	0.264865i	−0.827027	−	0.562162i	$-0.809970\pi$
$773$	−7.36402	+	7.36402i	−0.264865	+	0.264865i	0.562162	+	0.827027i	$0.309970\pi$
$774$	17.5209	−	13.8337i	0.629775	−	0.497242i
$775$		0			0
$776$	8.85176	+	1.32306i	0.317760	+	0.0474950i
$777$	9.90045	+	20.6978i	0.355177	+	0.742529i
$778$	25.2403	−	0.954788i	0.904910	−	0.0342308i
$779$	−15.7293	+	27.2439i	−0.563560	+	0.976115i
$780$		0			0
$781$	−3.60645	−	6.24656i	−0.129049	−	0.223520i
$782$	8.82982	+	14.0398i	0.315754	+	0.502062i
$783$	22.1337	−	6.63624i	0.790992	−	0.237160i
$784$	1.57789	−	1.26257i	0.0563533	−	0.0450916i
$785$		0			0
$786$	13.9736	+	26.5823i	0.498422	+	0.948158i
$787$	7.95656	+	29.6943i	0.283621	+	1.05849i	0.949841	+	0.312733i	$0.101244\pi$
$787$	7.95656	+	29.6943i	0.283621	+	1.05849i	−0.666220	+	0.745755i	$0.732089\pi$
$788$	−4.94570	+	26.2565i	−0.176183	+	0.935347i
$789$	1.05728	−	2.99619i	0.0376402	−	0.106667i
$790$		0			0
$791$		−	1.15443i		−	0.0410468i
$792$	13.7114	+	26.1987i	0.487212	+	0.930931i
$793$	34.4474	−	34.4474i	1.22326	−	1.22326i
$794$	−13.5207	−	43.7693i	−0.479832	−	1.55332i
$795$		0			0
$796$	2.32456	+	3.40350i	0.0823918	+	0.120634i
$797$	17.8210	−	4.77511i	0.631251	−	0.169143i	0.0710135	−	0.997475i	$-0.477377\pi$
$797$	17.8210	−	4.77511i	0.631251	−	0.169143i	0.560237	+	0.828332i	$0.310710\pi$
$798$	−16.4593	−	17.8182i	−0.582652	−	0.630758i
$799$	−0.366781	−	0.635283i	−0.0129758	−	0.0224747i
$800$		0			0
$801$	1.67281	−	10.7151i	0.0591059	−	0.378598i
$802$	−36.5386	+	22.9796i	−1.29022	+	0.811438i
$803$	−11.4473	+	42.7219i	−0.403967	+	1.50762i
$804$	1.82805	−	1.82143i	0.0644705	−	0.0642370i
$805$		0			0
$806$	10.9504	−	11.8114i	0.385711	−	0.416040i
$807$	−1.79582	+	23.1453i	−0.0632158	+	0.814752i
$808$	−9.82088	+	7.26681i	−0.345497	+	0.255646i
$809$		−	45.3459i		−	1.59428i	−0.603798	−	0.797138i	$-0.706347\pi$
$809$		−	45.3459i		−	1.59428i	0.603798	−	0.797138i	$-0.293653\pi$
$810$		0			0
$811$			32.6505i			1.14652i	0.819375	+	0.573258i	$0.194321\pi$
$811$			32.6505i			1.14652i	−0.819375	+	0.573258i	$0.805679\pi$
$812$	−17.1924	−	14.7707i	−0.603333	−	0.518350i
$813$	−2.57143	+	33.1417i	−0.0901840	+	1.16233i
$814$	−18.7853	−	17.4159i	−0.658426	−	0.610428i
$815$		0			0
$816$	20.0182	−	6.98234i	0.700777	−	0.244431i
$817$	5.29182	−	19.7493i	0.185137	−	0.690942i
$818$	12.3617	+	19.6557i	0.432217	+	0.687244i
$819$	6.22045	−	39.8446i	0.217360	−	1.39228i
$820$		0			0
$821$	−14.0278	−	24.2968i	−0.489572	−	0.847964i	0.510356	−	0.859963i	$-0.329514\pi$
$821$	−14.0278	−	24.2968i	−0.489572	−	0.847964i	−0.999928	+	0.0119995i	$0.996180\pi$
$822$	−16.6446	+	15.3752i	−0.580548	+	0.536272i
$823$	−33.5290	+	8.98407i	−1.16875	+	0.313165i	−0.790454	−	0.612521i	$-0.790156\pi$
$823$	−33.5290	+	8.98407i	−1.16875	+	0.313165i	−0.378293	+	0.925686i	$0.623489\pi$
$824$	−1.41589	−	3.59463i	−0.0493250	−	0.125225i
$825$		0			0
$826$	−39.1985	+	12.1087i	−1.36389	+	0.421316i
$827$	−0.244245	+	0.244245i	−0.00849323	+	0.00849323i	−0.711341	−	0.702847i	$-0.751912\pi$
$827$	−0.244245	+	0.244245i	−0.00849323	+	0.00849323i	0.702847	+	0.711341i	$0.251912\pi$
$828$	−14.9216	−	17.4960i	−0.518562	−	0.608029i
$829$			24.5821i			0.853771i	0.904306	+	0.426885i	$0.140389\pi$
$829$			24.5821i			0.853771i	−0.904306	+	0.426885i	$0.859611\pi$
$830$		0			0
$831$	4.30749	−	12.2069i	0.149425	−	0.423451i
$832$	−19.8092	−	37.2587i	−0.686759	−	1.29171i
$833$	0.400133	+	1.49332i	0.0138638	+	0.0517404i
$834$	−38.8302	+	20.4120i	−1.34458	+	0.706811i
$835$		0			0
$836$	24.4101	+	11.7307i	0.844243	+	0.405713i
$837$	−8.16394	−	7.69597i	−0.282187	−	0.266012i
$838$	−11.9962	+	7.54458i	−0.414402	+	0.260623i
$839$	−4.08967	−	7.08351i	−0.141191	−	0.244550i	0.786754	−	0.617266i	$-0.211760\pi$
$839$	−4.08967	−	7.08351i	−0.141191	−	0.244550i	−0.927945	+	0.372716i	$0.878426\pi$
$840$		0			0
$841$	−4.61225	+	7.98866i	−0.159043	+	0.275471i
$842$	−0.393812	−	10.4106i	−0.0135717	−	0.358774i
$843$	−10.4566	−	21.8605i	−0.360144	−	0.752914i
$844$	0.347994	+	4.59313i	0.0119785	+	0.158102i
$845$		0			0
$846$	0.630242	+	0.798224i	0.0216682	+	0.0274435i
$847$	−2.06171	+	2.06171i	−0.0708410	+	0.0708410i
$848$	−0.603573	−	1.37724i	−0.0207268	−	0.0472946i
$849$	3.16399	−	0.590032i	0.108588	−	0.0202498i
$850$		0			0
$851$	17.2517	+	9.96030i	0.591382	+	0.341435i
$852$	6.21589	−	3.57372i	0.212953	−	0.122434i
$853$	−26.9342	−	7.21700i	−0.922210	−	0.247105i	−0.233680	−	0.972314i	$-0.575077\pi$
$853$	−26.9342	−	7.21700i	−0.922210	−	0.247105i	−0.688530	+	0.725208i	$0.741743\pi$
$854$	−7.39374	+	32.4554i	−0.253009	+	1.11060i
$855$		0			0
$856$	16.6781	+	13.2668i	0.570047	+	0.453451i
$857$	11.3944	−	42.5245i	0.389226	−	1.45261i	−0.442171	−	0.896931i	$-0.645792\pi$
$857$	11.3944	−	42.5245i	0.389226	−	1.45261i	0.831397	−	0.555679i	$-0.187542\pi$
$858$	9.92133	+	43.9182i	0.338708	+	1.49934i
$859$	−1.47011	+	2.54630i	−0.0501593	+	0.0868785i	−0.890015	−	0.455931i	$-0.849306\pi$
$859$	−1.47011	+	2.54630i	−0.0501593	+	0.0868785i	0.839856	+	0.542810i	$0.182640\pi$
$860$		0			0
$861$	27.1481	−	23.2387i	0.925206	−	0.791972i
$862$	−10.8602	+	20.5689i	−0.369900	+	0.700581i
$863$	−7.13386	−	7.13386i	−0.242839	−	0.242839i	0.575184	−	0.818024i	$-0.304930\pi$
$863$	−7.13386	−	7.13386i	−0.242839	−	0.242839i	−0.818024	+	0.575184i	$0.804930\pi$
$864$	−26.0675	+	13.5825i	−0.886835	+	0.462086i
$865$		0			0
$866$	7.22536	−	2.23197i	0.245528	−	0.0758455i
$867$	1.02309	−	13.1860i	0.0347458	−	0.447819i
$868$	−2.03716	+	10.8152i	−0.0691459	+	0.367092i
$869$	−45.6419	−	26.3514i	−1.54830	−	0.893909i
$870$		0			0
$871$	3.40292	−	1.96468i	0.115304	−	0.0665706i
$872$	−39.8638	+	4.54122i	−1.34996	+	0.153785i
$873$	3.84196	−	8.68081i	0.130031	−	0.293801i
$874$	−20.5346	−	4.67802i	−0.694592	−	0.158237i
$875$		0			0
$876$	−42.4470	−	11.4562i	−1.43415	−	0.387070i
$877$	22.5386	−	6.03921i	0.761076	−	0.203930i	0.142650	−	0.989773i	$-0.454438\pi$
$877$	22.5386	−	6.03921i	0.761076	−	0.203930i	0.618426	+	0.785843i	$0.287771\pi$
$878$	−1.96839	−	52.0354i	−0.0664298	−	1.75611i
$879$	8.37619	+	44.9166i	0.282522	+	1.51500i
$880$		0			0
$881$	−42.4590			−1.43048			−0.715241	−	0.698878i	$-0.753683\pi$
$881$	−42.4590			−1.43048			−0.715241	+	0.698878i	$0.753683\pi$
$882$	−0.847586	−	1.96873i	−0.0285397	−	0.0662905i
$883$	−7.64008	−	7.64008i	−0.257109	−	0.257109i	0.566768	−	0.823877i	$-0.308193\pi$
$883$	−7.64008	−	7.64008i	−0.257109	−	0.257109i	−0.823877	+	0.566768i	$0.808193\pi$
$884$	32.1897	−	2.43882i	1.08266	−	0.0820265i
$885$		0			0
$886$	−11.6388	+	12.5540i	−0.391014	+	0.421759i
$887$	−1.25685	−	4.69064i	−0.0422010	−	0.157496i	0.941610	−	0.336706i	$-0.109313\pi$
$887$	−1.25685	−	4.69064i	−0.0422010	−	0.157496i	−0.983811	+	0.179209i	$0.942646\pi$
$888$	17.3462	−	18.6421i	0.582099	−	0.625589i
$889$	8.31067	−	4.79817i	0.278731	−	0.160925i
$890$		0			0
$891$	30.6490	−	6.65649i	1.02678	−	0.223001i
$892$	−31.5002	+	11.0514i	−1.05470	+	0.370028i
$893$	0.899750	+	0.241087i	0.0301090	+	0.00806768i
$894$	−3.15531	−	6.00241i	−0.105529	−	0.200751i
$895$		0			0
$896$	25.0112	+	14.3447i	0.835567	+	0.479223i
$897$	−15.1086	−	31.5860i	−0.504463	−	1.05463i
$898$	0.692186	−	1.31098i	0.0230985	−	0.0437480i
$899$	−9.60189			−0.320241
$900$		0			0
$901$	1.15036			0.0383241
$902$	−18.6290	+	35.2828i	−0.620277	+	1.17479i
$903$	−13.1342	+	19.1557i	−0.437079	+	0.637463i
$904$	−1.19210	+	0.469556i	−0.0396485	+	0.0156172i
$905$		0			0
$906$	18.4175	+	0.730157i	0.611879	+	0.0242579i
$907$	−58.1113	−	15.5709i	−1.92955	−	0.517022i	−0.977399	−	0.211402i	$-0.932197\pi$
$907$	−58.1113	−	15.5709i	−1.92955	−	0.517022i	−0.952154	−	0.305620i	$-0.901136\pi$
$908$	−3.33774	−	9.51369i	−0.110767	−	0.315723i
$909$	4.67053	+	12.0872i	0.154912	+	0.400906i
$910$		0			0
$911$	2.72513	−	1.57335i	0.0902875	−	0.0521275i	−0.454176	−	0.890912i	$-0.650066\pi$
$911$	2.72513	−	1.57335i	0.0902875	−	0.0521275i	0.544464	+	0.838784i	$0.316733\pi$
$912$	−11.7049	+	24.2437i	−0.387587	+	0.802789i
$913$	−13.9994	−	52.2465i	−0.463313	−	1.72911i
$914$	−13.0834	+	14.1122i	−0.432761	+	0.466789i
$915$		0			0
$916$	1.17220	+	15.4717i	0.0387306	+	0.511200i
$917$	−22.0936	−	22.0936i	−0.729594	−	0.729594i
$918$	−1.51240	−	22.4361i	−0.0499168	−	0.740502i
$919$	−31.3326			−1.03357			−0.516783	−	0.856116i	$-0.672871\pi$
$919$	−31.3326			−1.03357			−0.516783	+	0.856116i	$0.672871\pi$
$920$		0			0
$921$	25.9441	−	22.2080i	0.854887	−	0.731779i
$922$	0.612016	+	16.1790i	0.0201557	+	0.532826i
$923$	10.5455	−	2.82565i	0.347109	−	0.0930075i
$924$	−21.7146	−	21.7935i	−0.714357	−	0.716954i
$925$		0			0
$926$	−6.47871	−	1.47593i	−0.212904	−	0.0485020i
$927$	−4.07439	+	0.437349i	−0.133820	+	0.0143644i
$928$	−8.25976	+	23.7611i	−0.271140	+	0.779998i
$929$	−10.8495	+	6.26399i	−0.355962	+	0.205515i	−0.667308	−	0.744782i	$-0.732554\pi$
$929$	−10.8495	+	6.26399i	−0.355962	+	0.205515i	0.311346	+	0.950297i	$0.399220\pi$
$930$		0			0
$931$	−1.70012	−	0.981567i	−0.0557193	−	0.0321696i
$932$	11.5444	+	2.17452i	0.378150	+	0.0712288i
$933$	1.15710	+	0.793368i	0.0378817	+	0.0259737i
$934$	−48.8066	+	15.0768i	−1.59700	+	0.493327i
$935$		0			0
$936$	−43.6747	+	9.78307i	−1.42755	+	0.319770i
$937$	27.1824	+	27.1824i	0.888011	+	0.888011i	0.994332	−	0.106321i	$-0.0339070\pi$
$937$	27.1824	+	27.1824i	0.888011	+	0.888011i	−0.106321	+	0.994332i	$0.533907\pi$
$938$	−1.25359	+	2.37425i	−0.0409310	+	0.0775221i
$939$	−10.3373	−	3.64778i	−0.337346	−	0.119041i
$940$		0			0
$941$	12.5030	−	21.6558i	0.407585	−	0.705957i	−0.587034	−	0.809562i	$-0.699704\pi$
$941$	12.5030	−	21.6558i	0.407585	−	0.705957i	0.994619	+	0.103605i	$0.0330378\pi$
$942$	8.75988	+	2.72342i	0.285412	+	0.0887337i
$943$	8.03043	−	29.9700i	0.261507	−	0.975956i
$944$	28.4475	+	35.5522i	0.925886	+	1.15713i
$945$		0			0
$946$	5.75996	−	25.2838i	0.187273	−	0.822048i
$947$	−58.2038	−	15.5957i	−1.89137	−	0.506791i	−0.998392	−	0.0566928i	$-0.981944\pi$
$947$	−58.2038	−	15.5957i	−1.89137	−	0.506791i	−0.892979	−	0.450098i	$-0.851389\pi$
$948$	26.2769	−	45.3228i	0.853433	−	1.47201i
$949$	−57.9762	−	33.4726i	−1.88199	−	1.08657i
$950$		0			0
$951$	11.6533	−	33.0240i	0.377885	−	1.07088i
$952$	−17.7316	+	13.1202i	−0.574683	+	0.425228i
$953$	−7.86673	+	7.86673i	−0.254828	+	0.254828i	−0.822947	−	0.568118i	$-0.807672\pi$
$953$	−7.86673	+	7.86673i	−0.254828	+	0.254828i	0.568118	+	0.822947i	$0.307672\pi$
$954$	−1.57823	+	0.230044i	−0.0510970	+	0.00744794i
$955$		0			0
$956$	5.10766	−	0.386977i	0.165194	−	0.0125157i
$957$	15.1787	−	22.1376i	0.490658	−	0.715606i
$958$	0.648166	+	17.1346i	0.0209413	+	0.553595i
$959$	11.7875	−	20.4166i	0.380638	−	0.659285i
$960$		0			0
$961$	−13.1689	−	22.8092i	−0.424804	−	0.735782i
$962$	32.8218	−	20.6420i	1.05822	−	0.665526i
$963$	18.2576	−	13.3267i	0.588342	−	0.429447i
$964$	−11.9448	+	24.8556i	−0.384715	+	0.800546i
$965$		0			0
$966$	20.2289	+	12.7735i	0.650854	+	0.410981i
$967$	−4.17163	−	15.5687i	−0.134151	−	0.500657i	−1.00000		0.000352232i	$-0.999888\pi$
$967$	−4.17163	−	15.5687i	−0.134151	−	0.500657i	0.865849	−	0.500305i	$-0.166779\pi$
$968$	2.96755	+	1.29039i	0.0953808	+	0.0414747i
$969$	−13.3930	−	15.6462i	−0.430246	−	0.502627i
$970$		0			0
$971$		−	51.3038i		−	1.64642i	−0.567739	−	0.823209i	$-0.692182\pi$
$971$		−	51.3038i		−	1.64642i	0.567739	−	0.823209i	$-0.307818\pi$
$972$	6.56160	+	30.4786i	0.210463	+	0.977602i
$973$	32.2733	−	32.2733i	1.03464	−	1.03464i
$974$	24.0050	−	7.41533i	0.769169	−	0.237602i
$975$		0			0
$976$	36.5217	−	5.56601i	1.16903	−	0.178164i
$977$	−1.37730	+	0.369048i	−0.0440639	+	0.0118069i	−0.280784	−	0.959771i	$-0.590594\pi$
$977$	−1.37730	+	0.369048i	−0.0440639	+	0.0118069i	0.236720	+	0.971578i	$0.423928\pi$
$978$	−5.16719	−	22.8733i	−0.165229	−	0.731408i
$979$	−6.29876	−	10.9098i	−0.201309	−	0.348678i
$980$		0			0
$981$	−6.56414	+	42.0461i	−0.209577	+	1.34243i
$982$	−0.0950129	−	0.151075i	−0.00303198	−	0.00482099i
$983$	11.8993	−	44.4088i	0.379529	−	1.41642i	−0.467085	−	0.884212i	$-0.654696\pi$
$983$	11.8993	−	44.4088i	0.379529	−	1.41642i	0.846614	−	0.532208i	$-0.178638\pi$
$984$	−35.0392	−	18.5817i	−1.11701	−	0.592364i
$985$		0			0
$986$	−14.1128	−	13.0840i	−0.449444	−	0.416680i
$987$	−0.872705	−	0.598374i	−0.0277785	−	0.0190464i
$988$	−26.7132	+	31.0929i	−0.849861	+	0.989196i
$989$			20.1657i			0.641231i
$990$		0			0
$991$		−	47.4822i		−	1.50832i	−0.656689	−	0.754161i	$-0.728044\pi$
$991$		−	47.4822i		−	1.50832i	0.656689	−	0.754161i	$-0.271956\pi$
$992$	11.9967	−	2.29537i	0.380895	−	0.0728780i
$993$	−30.5212	+	14.5993i	−0.968562	+	0.463296i
$994$	−5.07169	+	5.47048i	−0.160864	+	0.173513i
$995$		0			0
$996$	51.9608	−	13.8219i	1.64644	−	0.437962i
$997$	−14.6874	+	54.8142i	−0.465156	+	1.73598i	0.191218	+	0.981548i	$0.438756\pi$
$997$	−14.6874	+	54.8142i	−0.465156	+	1.73598i	−0.656373	+	0.754436i	$0.727910\pi$
$998$	−48.5722	+	30.5477i	−1.53753	+	0.966971i
$999$	−14.1883	−	22.9818i	−0.448899	−	0.727111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bf.e.607.28		128
4.3	odd	2	inner	900.2.bf.e.607.1		128
5.2	odd	4		180.2.x.a.103.12	yes	128
5.3	odd	4	inner	900.2.bf.e.643.21		128
5.4	even	2		180.2.x.a.67.5	yes	128
9.7	even	3	inner	900.2.bf.e.7.15		128
15.2	even	4		540.2.y.a.523.21		128
15.14	odd	2		540.2.y.a.307.28		128
20.3	even	4	inner	900.2.bf.e.643.15		128
20.7	even	4		180.2.x.a.103.18	yes	128
20.19	odd	2		180.2.x.a.67.32	yes	128
36.7	odd	6	inner	900.2.bf.e.7.21		128
45.2	even	12		540.2.y.a.343.1		128
45.7	odd	12		180.2.x.a.43.32	yes	128
45.29	odd	6		540.2.y.a.127.15		128
45.34	even	6		180.2.x.a.7.18	yes	128
45.43	odd	12	inner	900.2.bf.e.43.1		128
60.47	odd	4		540.2.y.a.523.15		128
60.59	even	2		540.2.y.a.307.1		128
180.7	even	12		180.2.x.a.43.5	yes	128
180.43	even	12	inner	900.2.bf.e.43.28		128
180.47	odd	12		540.2.y.a.343.28		128
180.79	odd	6		180.2.x.a.7.12	✓	128
180.119	even	6		540.2.y.a.127.21		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.x.a.7.12	✓	128	180.79	odd	6
180.2.x.a.7.18	yes	128	45.34	even	6
180.2.x.a.43.5	yes	128	180.7	even	12
180.2.x.a.43.32	yes	128	45.7	odd	12
180.2.x.a.67.5	yes	128	5.4	even	2
180.2.x.a.67.32	yes	128	20.19	odd	2
180.2.x.a.103.12	yes	128	5.2	odd	4
180.2.x.a.103.18	yes	128	20.7	even	4
540.2.y.a.127.15		128	45.29	odd	6
540.2.y.a.127.21		128	180.119	even	6
540.2.y.a.307.1		128	60.59	even	2
540.2.y.a.307.28		128	15.14	odd	2
540.2.y.a.343.1		128	45.2	even	12
540.2.y.a.343.28		128	180.47	odd	12
540.2.y.a.523.15		128	60.47	odd	4
540.2.y.a.523.21		128	15.2	even	4
900.2.bf.e.7.15		128	9.7	even	3	inner
900.2.bf.e.7.21		128	36.7	odd	6	inner
900.2.bf.e.43.1		128	45.43	odd	12	inner
900.2.bf.e.43.28		128	180.43	even	12	inner
900.2.bf.e.607.1		128	4.3	odd	2	inner
900.2.bf.e.607.28		128	1.1	even	1	trivial
900.2.bf.e.643.15		128	20.3	even	4	inner
900.2.bf.e.643.21		128	5.3	odd	4	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+(1.25060 + 0.660305i) q^{2} +(1.72686 + 0.133985i) q^{3} +(1.12799 + 1.65155i) q^{4} +(2.07114 + 1.30782i) q^{6} +(-2.46165 - 0.659597i) q^{7} +(0.320139 + 2.81025i) q^{8} +(2.96410 + 0.462748i) q^{9} +(3.01796 - 1.74242i) q^{11} +(1.72661 + 3.00314i) q^{12} +(1.36518 + 5.09493i) q^{13} +(-2.64300 - 2.45033i) q^{14} +(-1.45526 + 3.72589i) q^{16} +(-2.16382 - 2.16382i) q^{17} +(3.40134 + 2.53592i) q^{18} +3.88577 q^{19} +(-4.16255 - 1.46886i) q^{21} +(4.92478 - 0.186294i) q^{22} +(-3.70190 + 0.991920i) q^{23} +(0.176303 + 4.89581i) q^{24} +(-1.65691 + 7.27315i) q^{26} +(5.05658 + 1.19625i) q^{27} +(-1.68737 - 4.80957i) q^{28} +(3.85118 - 2.22348i) q^{29} +(-1.86992 - 1.07960i) q^{31} +(-4.28016 + 3.69867i) q^{32} +(5.44505 - 2.60455i) q^{33} +(-1.27729 - 4.13484i) q^{34} +(2.57923 + 5.41734i) q^{36} +(-3.67542 - 3.67542i) q^{37} +(4.85954 + 2.56579i) q^{38} +(1.67483 + 8.98115i) q^{39} +(-4.04792 + 7.01121i) q^{41} +(-4.23579 - 4.58550i) q^{42} +(1.36185 - 5.08248i) q^{43} +(6.28194 + 3.01888i) q^{44} +(-5.28456 - 1.20389i) q^{46} +(0.231550 + 0.0620436i) q^{47} +(-3.01224 + 6.23910i) q^{48} +(-0.437526 - 0.252606i) q^{49} +(-3.44669 - 4.02653i) q^{51} +(-6.87463 + 8.00173i) q^{52} +(-0.265818 + 0.265818i) q^{53} +(5.53386 + 4.83491i) q^{54} +(1.06556 - 7.12902i) q^{56} +(6.71018 + 0.520636i) q^{57} +(6.28446 - 0.237728i) q^{58} +(5.69158 - 9.85810i) q^{59} +(-4.61792 - 7.99848i) q^{61} +(-1.62566 - 2.58487i) q^{62} +(-6.99134 - 3.09423i) q^{63} +(-7.79502 + 1.79934i) q^{64} +(8.52937 + 0.338146i) q^{66} +(-0.192807 - 0.719566i) q^{67} +(1.13289 - 6.01443i) q^{68} +(-6.52556 + 1.21691i) q^{69} -2.06980i q^{71} +(-0.351515 + 8.47800i) q^{72} +(-8.97449 + 8.97449i) q^{73} +(-2.16958 - 7.02337i) q^{74} +(4.38312 + 6.41755i) q^{76} +(-8.57845 + 2.29859i) q^{77} +(-3.83576 + 12.3377i) q^{78} +(-7.56173 - 13.0973i) q^{79} +(8.57173 + 2.74326i) q^{81} +(-9.69186 + 6.09534i) q^{82} +(4.01723 - 14.9925i) q^{83} +(-2.26944 - 8.53154i) q^{84} +(5.05911 - 5.45691i) q^{86} +(6.94837 - 3.32364i) q^{87} +(5.86280 + 7.92340i) q^{88} -3.61495i q^{89} -13.4424i q^{91} +(-5.81393 - 4.99500i) q^{92} +(-3.08444 - 2.11486i) q^{93} +(0.248608 + 0.230485i) q^{94} +(-7.88682 + 5.81362i) q^{96} +(0.818990 - 3.05651i) q^{97} +(-0.380373 - 0.604809i) q^{98} +(9.75182 - 3.76814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 2 q^{2} - 8 q^{6} + 8 q^{8} - 2 q^{12} + 4 q^{13} - 4 q^{16} + 16 q^{17} + 36 q^{18} - 24 q^{21} + 10 q^{22} - 48 q^{26} - 8 q^{28} - 18 q^{32} + 20 q^{33} - 40 q^{36} + 16 q^{37} + 34 q^{38} - 8 q^{41}+ \cdots - 164 q^{98}+O(q^{100}) \) 128 * q + 2 * q^2 - 8 * q^6 + 8 * q^8 - 2 * q^12 + 4 * q^13 - 4 * q^16 + 16 * q^17 + 36 * q^18 - 24 * q^21 + 10 * q^22 - 48 * q^26 - 8 * q^28 - 18 * q^32 + 20 * q^33 - 40 * q^36 + 16 * q^37 + 34 * q^38 - 8 * q^41 - 34 * q^42 - 40 * q^46 + 22 * q^48 + 18 * q^52 + 64 * q^53 - 32 * q^56 + 48 * q^57 + 10 * q^58 - 8 * q^61 - 44 * q^62 - 36 * q^66 - 58 * q^68 - 78 * q^72 + 16 * q^73 - 32 * q^76 + 60 * q^77 - 114 * q^78 + 24 * q^81 + 32 * q^86 + 10 * q^88 - 52 * q^92 + 68 * q^93 + 52 * q^96 + 4 * q^97 - 164 * q^98

Introduction

L-functions

Modular forms

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Database

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