LMFDB - Embedded newform 900.2.bf.e.607.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(7,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.7"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

sage:traces = [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			607.1
Character	$\chi$	$=$	900.607
Dual form			900.2.bf.e.43.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41320 - 0.0534584i) q^{2} +(-1.72686 - 0.133985i) q^{3} +(1.99428 + 0.151095i) q^{4} +(2.43324 + 0.281664i) q^{6} +(2.46165 + 0.659597i) q^{7} +(-2.81025 - 0.320139i) q^{8} +(2.96410 + 0.462748i) q^{9} +(-3.01796 + 1.74242i) q^{11} +(-3.42361 - 0.528125i) q^{12} +(1.36518 + 5.09493i) q^{13} +(-3.44355 - 1.06374i) q^{14} +(3.95434 + 0.602653i) q^{16} +(-2.16382 - 2.16382i) q^{17} +(-4.16413 - 0.812413i) q^{18} -3.88577 q^{19} +(-4.16255 - 1.46886i) q^{21} +(4.35813 - 2.30106i) q^{22} +(3.70190 - 0.991920i) q^{23} +(4.81002 + 0.929369i) q^{24} +(-1.65691 - 7.27315i) q^{26} +(-5.05658 - 1.19625i) q^{27} +(4.80957 + 1.68737i) q^{28} +(3.85118 - 2.22348i) q^{29} +(1.86992 + 1.07960i) q^{31} +(-5.55607 - 1.06306i) q^{32} +(5.44505 - 2.60455i) q^{33} +(2.94224 + 3.17359i) q^{34} +(5.84133 + 1.37071i) q^{36} +(-3.67542 - 3.67542i) q^{37} +(5.49138 + 0.207727i) q^{38} +(-1.67483 - 8.98115i) q^{39} +(-4.04792 + 7.01121i) q^{41} +(5.80400 + 2.29832i) 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} +(-6.74785 - 1.57052i) q^{48} +(-0.437526 - 0.252606i) q^{49} +(3.44669 + 4.02653i) q^{51} +(1.95274 + 10.3670i) q^{52} +(-0.265818 + 0.265818i) q^{53} +(7.08202 + 1.96086i) q^{54} +(-6.70669 - 2.64170i) q^{56} +(6.71018 + 0.520636i) q^{57} +(-5.56137 + 2.93635i) q^{58} +(-5.69158 + 9.85810i) q^{59} +(-4.61792 - 7.99848i) q^{61} +(-2.58487 - 1.62566i) q^{62} +(6.99134 + 3.09423i) q^{63} +(7.79502 + 1.79934i) q^{64} +(-7.83420 + 3.38968i) q^{66} +(0.192807 + 0.719566i) q^{67} +(-3.98832 - 4.64221i) q^{68} +(-6.52556 + 1.21691i) q^{69} +2.06980i q^{71} +(-8.18171 - 2.24936i) q^{72} +(-8.97449 + 8.97449i) q^{73} +(4.99763 + 5.39060i) q^{74} +(-7.74933 - 0.587121i) q^{76} +(-8.57845 + 2.29859i) q^{77} +(1.88676 + 12.7817i) q^{78} +(7.56173 + 13.0973i) q^{79} +(8.57173 + 2.74326i) q^{81} +(6.09534 - 9.69186i) q^{82} +(-4.01723 + 14.9925i) q^{83} +(-8.07937 - 3.55826i) q^{84} +(2.19627 - 7.10978i) q^{86} +(-6.94837 + 3.32364i) q^{87} +(9.03903 - 3.93047i) q^{88} -3.61495i q^{89} +13.4424i q^{91} +(7.53251 - 1.41883i) q^{92} +(-3.08444 - 2.11486i) q^{93} +(0.323910 + 0.100059i) q^{94} +(9.45212 + 2.58020i) q^{96} +(0.818990 - 3.05651i) q^{97} +(0.604809 + 0.380373i) 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 $

$2$	−1.41320	−	0.0534584i	−0.999285	−	0.0378008i
$2$	−1.41320	−	0.0534584i	−0.999285	−	0.0378008i
$3$	−1.72686	−	0.133985i	−0.997003	−	0.0773565i
$3$	−1.72686	−	0.133985i	−0.997003	−	0.0773565i
$4$	1.99428	+	0.151095i	0.997142	+	0.0755476i
$5$		0			0
$5$		0			0
$6$	2.43324	+	0.281664i	0.993367	+	0.114989i
$7$	2.46165	+	0.659597i	0.930416	+	0.249304i	0.692032	−	0.721867i	$-0.256716\pi$
$7$	2.46165	+	0.659597i	0.930416	+	0.249304i	0.238384	+	0.971171i	$0.423382\pi$
$8$	−2.81025	−	0.320139i	−0.993574	−	0.113186i
$9$	2.96410	+	0.462748i	0.988032	+	0.154249i
$10$		0			0
$11$	−3.01796	+	1.74242i	−0.909948	+	0.525359i	−0.880415	−	0.474205i	$-0.842736\pi$
$11$	−3.01796	+	1.74242i	−0.909948	+	0.525359i	−0.0295338	+	0.999564i	$0.509402\pi$
$12$	−3.42361	−	0.528125i	−0.988310	−	0.152457i
$13$	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	$0.655504\pi$
$14$	−3.44355	−	1.06374i	−0.920327	−	0.284297i
$15$		0			0
$16$	3.95434	+	0.602653i	0.988585	+	0.150663i
$17$	−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	$0.871016\pi$
$18$	−4.16413	−	0.812413i	−0.981495	−	0.191488i
$19$	−3.88577			−0.891456			−0.445728	−	0.895168i	$-0.647055\pi$
$19$	−3.88577			−0.891456			−0.445728	+	0.895168i	$0.647055\pi$
$20$		0			0
$21$	−4.16255	−	1.46886i	−0.908343	−	0.320531i
$22$	4.35813	−	2.30106i	0.929157	−	0.490587i
$23$	3.70190	−	0.991920i	0.771899	−	0.206830i	0.148689	−	0.988884i	$-0.452495\pi$
$23$	3.70190	−	0.991920i	0.771899	−	0.206830i	0.623210	+	0.782054i	$0.285828\pi$
$24$	4.81002	+	0.929369i	0.981841	+	0.189707i
$25$		0			0
$26$	−1.65691	−	7.27315i	−0.324947	−	1.42638i
$27$	−5.05658	−	1.19625i	−0.973139	−	0.230218i
$28$	4.80957	+	1.68737i	0.908923	+	0.318883i
$29$	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	0.658434	−	0.752638i	$-0.271219\pi$
$31$	1.86992	+	1.07960i	0.335848	+	0.193902i	−0.322586	+	0.946540i	$0.604552\pi$
$32$	−5.55607	−	1.06306i	−0.982183	−	0.187925i
$33$	5.44505	−	2.60455i	0.947862	−	0.453394i
$34$	2.94224	+	3.17359i	0.504589	+	0.544265i
$35$		0			0
$36$	5.84133	+	1.37071i	0.973555	+	0.228452i
$37$	−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	$0.890521\pi$
$38$	5.49138	+	0.207727i	0.890819	+	0.0336978i
$39$	−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	$0.948827\pi$
$42$	5.80400	+	2.29832i	0.895577	+	0.354638i
$43$	−1.36185	+	5.08248i	−0.207680	+	0.775071i	0.780936	+	0.624611i	$0.214742\pi$
$43$	−1.36185	+	5.08248i	−0.207680	+	0.775071i	−0.988616	+	0.150461i	$0.951924\pi$
$44$	−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	0.241892	−	0.970303i	$-0.422232\pi$
$47$	−0.231550	−	0.0620436i	−0.0337750	−	0.00904999i	−0.275667	+	0.961253i	$0.588899\pi$
$48$	−6.74785	−	1.57052i	−0.973968	−	0.226685i
$49$	−0.437526	−	0.252606i	−0.0625037	−	0.0360865i
$50$		0			0
$51$	3.44669	+	4.02653i	0.482633	+	0.563827i
$52$	1.95274	+	10.3670i	0.270797	+	1.43765i
$53$	−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	$0.258219\pi$
$54$	7.08202	+	1.96086i	0.963741	+	0.266839i
$55$		0			0
$56$	−6.70669	−	2.64170i	−0.896219	−	0.353013i
$57$	6.71018	+	0.520636i	0.888785	+	0.0689600i
$58$	−5.56137	+	2.93635i	−0.730243	+	0.385562i
$59$	−5.69158	+	9.85810i	−0.740980	+	1.28342i	0.211069	+	0.977471i	$0.432305\pi$
$59$	−5.69158	+	9.85810i	−0.740980	+	1.28342i	−0.952049	+	0.305944i	$0.901028\pi$
$60$		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	$-0.368038\pi$
$62$	−2.58487	−	1.62566i	−0.328278	−	0.206459i
$63$	6.99134	+	3.09423i	0.880826	+	0.389837i
$64$	7.79502	+	1.79934i	0.974378	+	0.224918i
$65$		0			0
$66$	−7.83420	+	3.38968i	−0.964323	+	0.417240i
$67$	0.192807	+	0.719566i	0.0235551	+	0.0879089i	0.976703	−	0.214596i	$-0.0688436\pi$
$67$	0.192807	+	0.719566i	0.0235551	+	0.0879089i	−0.953148	+	0.302505i	$0.902177\pi$
$68$	−3.98832	−	4.64221i	−0.483655	−	0.562950i
$69$	−6.52556	+	1.21691i	−0.785585	+	0.146498i
$70$		0			0
$71$			2.06980i			0.245640i	0.992429	+	0.122820i	$0.0391938\pi$
$71$			2.06980i			0.245640i	−0.992429	+	0.122820i	$0.960806\pi$
$72$	−8.18171	−	2.24936i	−0.964224	−	0.265090i
$73$	−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	$0.983529\pi$
$74$	4.99763	+	5.39060i	0.580963	+	0.626644i
$75$		0			0
$76$	−7.74933	−	0.587121i	−0.888909	−	0.0673474i
$77$	−8.57845	+	2.29859i	−0.977605	+	0.261948i
$78$	1.88676	+	12.7817i	0.213634	+	1.44725i
$79$	7.56173	+	13.0973i	0.850761	+	1.47356i	0.880523	+	0.474004i	$0.157192\pi$
$79$	7.56173	+	13.0973i	0.850761	+	1.47356i	−0.0297623	+	0.999557i	$0.509475\pi$
$80$		0			0
$81$	8.57173	+	2.74326i	0.952414	+	0.304807i
$82$	6.09534	−	9.69186i	0.673118	−	1.07029i
$83$	−4.01723	+	14.9925i	−0.440949	+	1.64564i	0.285468	+	0.958388i	$0.407851\pi$
$83$	−4.01723	+	14.9925i	−0.440949	+	1.64564i	−0.726417	+	0.687255i	$0.758816\pi$
$84$	−8.07937	−	3.55826i	−0.881532	−	0.388238i
$85$		0			0
$86$	2.19627	−	7.10978i	0.236830	−	0.766667i
$87$	−6.94837	+	3.32364i	−0.744944	+	0.356332i
$88$	9.03903	−	3.93047i	0.963564	−	0.418989i
$89$		−	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
$92$	7.53251	−	1.41883i	0.785318	−	0.147923i
$93$	−3.08444	−	2.11486i	−0.319842	−	0.219301i
$94$	0.323910	+	0.100059i	0.0334088	+	0.0103203i
$95$		0			0
$96$	9.45212	+	2.58020i	0.964703	+	0.263340i
$97$	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	$0.0319760\pi$
$98$	0.604809	+	0.380373i	0.0610949	+	0.0384234i
$99$	−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	$0.764392\pi$
$102$	−4.65562	−	5.87456i	−0.460975	−	0.581668i
$103$	1.31939	−	0.353529i	0.130003	−	0.0348342i	−0.193231	−	0.981153i	$-0.561897\pi$
$103$	1.31939	−	0.353529i	0.130003	−	0.0348342i	0.323234	+	0.946319i	$0.395230\pi$
$104$	−2.20542	−	14.7551i	−0.216259	−	1.44686i
$105$		0			0
$106$	0.389864	−	0.361444i	0.0378670	−	0.0351065i
$107$	−5.32781	+	5.32781i	−0.515059	+	0.515059i	−0.916072	−	0.401013i	$-0.868658\pi$
$107$	−5.32781	+	5.32781i	−0.515059	+	0.515059i	0.401013	+	0.916072i	$0.368658\pi$
$108$	−9.90351	−	3.14968i	−0.952966	−	0.303078i
$109$			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
$112$	9.33669	+	4.09179i	0.882235	+	0.386638i
$113$	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	$0.909884\pi$
$114$	−9.45501	−	1.09448i	−0.885543	−	0.102507i
$115$		0			0
$116$	8.01631	−	3.85236i	0.744296	−	0.357683i
$117$	1.68886	+	15.7336i	0.156135	+	1.45457i
$118$	8.57035	−	13.6272i	0.788965	−	1.25449i
$119$	−3.89931	−	6.75380i	−0.357449	−	0.619120i
$120$		0			0
$121$	0.572043	−	0.990808i	0.0520040	−	0.0900735i
$122$	6.09848	+	11.5503i	0.552130	+	1.04572i
$123$	7.92960	−	11.5650i	0.714988	−	1.04278i
$124$	3.56603	+	2.43557i	0.320239	+	0.218720i
$125$		0			0
$126$	−9.71477	−	4.74653i	−0.865460	−	0.422854i
$127$	2.66261	−	2.66261i	0.236269	−	0.236269i	−0.579034	−	0.815303i	$-0.696570\pi$
$127$	2.66261	−	2.66261i	0.236269	−	0.236269i	0.815303	+	0.579034i	$0.196570\pi$
$128$	−10.9198	−	2.95955i	−0.965179	−	0.261590i
$129$	3.03270	−	8.59427i	0.267014	−	0.756683i
$130$		0			0
$131$	−10.6177	−	6.13011i	−0.927670	−	0.535590i	−0.0415959	−	0.999135i	$-0.513244\pi$
$131$	−10.6177	−	6.13011i	−0.927670	−	0.535590i	−0.886074	+	0.463544i	$0.846578\pi$
$132$	11.2525	−	4.37150i	0.979406	−	0.380490i
$133$	−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	$0.954021\pi$
$138$	9.28700	−	1.37089i	0.790562	−	0.116698i
$139$	8.95460	−	15.5098i	0.759520	−	1.31553i	−0.183576	−	0.983005i	$-0.558767\pi$
$139$	8.95460	−	15.5098i	0.759520	−	1.31553i	0.943096	−	0.332521i	$-0.107899\pi$
$140$		0			0
$141$	0.391542	+	0.138165i	0.0329738	+	0.0116356i
$142$	0.110648	−	2.92504i	0.00928539	−	0.245464i
$143$	−12.9976	−	12.9976i	−1.08691	−	1.08691i
$144$	11.4422	+	3.61619i	0.953514	+	0.301349i
$145$		0			0
$146$	13.1625	−	12.2030i	1.08934	−	1.00993i
$147$	0.721701	+	0.494837i	0.0595249	+	0.0408135i
$148$	−6.77450	−	7.88517i	−0.556860	−	0.648157i
$149$	−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	−0.741146	−	0.671343i	$-0.765718\pi$
$151$	−6.51667	+	3.76240i	−0.530319	+	0.306180i	0.210827	+	0.977523i	$0.432384\pi$
$152$	10.9200	+	1.24399i	0.885728	+	0.100901i
$153$	−5.41246	−	7.41506i	−0.437571	−	0.599472i
$154$	12.2460	−	2.78978i	0.986808	−	0.224807i
$155$		0			0
$156$	−1.98309	−	18.1640i	−0.158774	−	1.45429i
$157$	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	$0.368918\pi$
$158$	−9.98609	−	18.9134i	−0.794451	−	1.50467i
$159$	0.494646	−	0.423414i	0.0392279	−	0.0335789i
$160$		0			0
$161$	9.76704			0.769751
$162$	−11.9669	−	4.33502i	−0.940212	−	0.340591i
$163$	6.76935	+	6.76935i	0.530216	+	0.530216i	0.920637	−	0.390420i	$-0.127670\pi$
$163$	6.76935	+	6.76935i	0.530216	+	0.530216i	−0.390420	+	0.920637i	$0.627670\pi$
$164$	−9.13207	+	13.3707i	−0.713095	+	1.04408i
$165$		0			0
$166$	6.47864	−	20.9727i	0.502840	−	1.62780i
$167$	0.957423	+	3.57315i	0.0740876	+	0.276499i	0.993025	−	0.117905i	$-0.0376178\pi$
$167$	0.957423	+	3.57315i	0.0740876	+	0.276499i	−0.918937	+	0.394404i	$0.870951\pi$
$168$	11.2276	+	5.46045i	0.866226	+	0.421283i
$169$	−12.8363	+	7.41103i	−0.987406	+	0.570079i
$170$		0			0
$171$	−11.5178	−	1.79813i	−0.880787	−	0.137507i
$172$	−3.48385	+	9.93015i	−0.265641	+	0.757167i
$173$	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	$0.239867\pi$
$174$	9.99714	−	4.32553i	0.757881	−	0.327918i
$175$		0			0
$176$	−12.9841	+	5.07133i	−0.978714	+	0.382266i
$177$	11.1494	−	16.2610i	0.838041	−	1.22225i
$178$	−0.193249	+	5.10866i	−0.0144847	+	0.382910i
$179$	−10.0185			−0.748819			−0.374410	−	0.927263i	$-0.622155\pi$
$179$	−10.0185			−0.748819			−0.374410	+	0.927263i	$0.622155\pi$
$180$		0			0
$181$	−19.9811			−1.48518			−0.742590	−	0.669746i	$-0.766403\pi$
$181$	−19.9811			−1.48518			−0.742590	+	0.669746i	$0.766403\pi$
$182$	0.718610	−	18.9969i	0.0532669	−	1.40814i
$183$	6.90283	+	14.4310i	0.510272	+	1.06677i
$184$	−10.7208	+	1.60242i	−0.790349	+	0.118132i
$185$		0			0
$186$	4.24589	+	3.15362i	0.311324	+	0.231234i
$187$	10.3006	+	2.76003i	0.753253	+	0.201833i
$188$	−0.452402	−	0.158719i	−0.0329948	−	0.0115758i
$189$	−11.6585	−	6.28005i	−0.848030	−	0.456806i
$190$		0			0
$191$	13.5705	−	7.83490i	0.981923	−	0.566914i	0.0790731	−	0.996869i	$-0.474804\pi$
$191$	13.5705	−	7.83490i	0.981923	−	0.566914i	0.902850	+	0.429955i	$0.141471\pi$
$192$	−13.2198	−	4.15164i	−0.954059	−	0.299619i
$193$	−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	$-0.366474\pi$
$194$	−1.32080	+	4.27569i	−0.0948276	+	0.306977i
$195$		0			0
$196$	−0.834384	−	0.569876i	−0.0595988	−	0.0407054i
$197$	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	$0.592123\pi$
$198$	13.9827	−	4.80383i	0.993709	−	0.341393i
$199$	−2.06079			−0.146085			−0.0730427	−	0.997329i	$-0.523271\pi$
$199$	−2.06079			−0.146085			−0.0730427	+	0.997329i	$0.523271\pi$
$200$		0			0
$201$	−0.236540	−	1.26842i	−0.0166842	−	0.0894677i
$202$	−2.85211	−	5.40181i	−0.200674	−	0.380070i
$203$	10.9469	−	2.93320i	0.768320	−	0.205871i
$204$	6.26529	+	8.55082i	0.438658	+	0.598677i
$205$		0			0
$206$	−1.88346	+	0.429076i	−0.131227	+	0.0298951i
$207$	11.4318	−	1.22710i	0.794564	−	0.0852893i
$208$	2.32792	+	20.9698i	0.161412	+	1.45400i
$209$	11.7271	−	6.77063i	0.811179	−	0.468335i
$210$		0			0
$211$	−1.99458	−	1.15157i	−0.137313	−	0.0792776i	0.429770	−	0.902938i	$-0.358595\pi$
$211$	−1.99458	−	1.15157i	−0.137313	−	0.0792776i	−0.567083	+	0.823661i	$0.691928\pi$
$212$	−0.570280	+	0.489952i	−0.0391670	+	0.0336500i
$213$	0.277323	−	3.57425i	0.0190019	−	0.244904i
$214$	7.81409	−	7.24446i	0.534161	−	0.495221i
$215$		0			0
$216$	13.8273	+	4.98057i	0.940828	+	0.338885i
$217$	3.89099	+	3.89099i	0.264138	+	0.264138i
$218$	0.758314	−	20.0465i	0.0513595	−	1.35772i
$219$	16.7001	−	14.2952i	1.12849	−	0.965983i
$220$		0			0
$221$	8.07049	−	13.9785i	0.542880	−	0.940296i
$222$	−7.90795	−	9.97842i	−0.530747	−	0.669708i
$223$	4.32002	−	16.1225i	0.289290	−	1.07964i	−0.656357	−	0.754450i	$-0.727904\pi$
$223$	4.32002	−	16.1225i	0.289290	−	1.07964i	0.945647	−	0.325194i	$-0.105430\pi$
$224$	−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	0.416766	−	0.909014i	$-0.363164\pi$
$227$	4.86933	+	1.30473i	0.323189	+	0.0865981i	−0.0935772	+	0.995612i	$0.529830\pi$
$228$	13.3033	+	2.05217i	0.881035	+	0.135908i
$229$	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
$232$	−11.5346	+	5.01563i	−0.757285	+	0.329292i
$233$	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	$0.188373\pi$
$234$	−1.54561	−	22.3251i	−0.101040	−	1.45943i
$235$		0			0
$236$	−12.8401	+	18.7999i	−0.835822	+	1.22377i
$237$	−11.3032	−	23.6304i	−0.734222	−	1.53496i
$238$	5.14947	+	9.75295i	0.333791	+	0.632190i
$239$	−1.28058	+	2.21802i	−0.0828335	+	0.143472i	−0.904466	−	0.426546i	$-0.859730\pi$
$239$	−1.28058	+	2.21802i	−0.0828335	+	0.143472i	0.821632	+	0.570018i	$0.193064\pi$
$240$		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	$0.686859\pi$
$242$	−0.861381	+	1.36963i	−0.0553716	+	0.0880433i
$243$	−14.4346	−	5.88572i	−0.925981	−	0.377569i
$244$	−8.00092	−	16.6490i	−0.512206	−	1.06584i
$245$		0			0
$246$	−11.8244	+	15.9198i	−0.753895	+	1.01501i
$247$	−5.30478	−	19.7977i	−0.337535	−	1.25970i
$248$	−4.90933	−	3.63258i	−0.311743	−	0.230669i
$249$	8.94598	−	25.3517i	0.566929	−	1.60660i
$250$		0			0
$251$			11.4799i			0.724602i	0.932061	+	0.362301i	$0.118009\pi$
$251$			11.4799i			0.724602i	−0.932061	+	0.362301i	$0.881991\pi$
$252$	13.4752	+	7.22714i	0.848857	+	0.455267i
$253$	−9.44382	+	9.44382i	−0.593728	+	0.593728i
$254$	−3.90515	+	3.62047i	−0.245031	+	0.227169i
$255$		0			0
$256$	15.2736	+	4.76619i	0.954601	+	0.297887i
$257$	−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	$0.567969\pi$
$258$	−4.74525	+	11.9833i	−0.295427	+	0.746049i
$259$	−6.62330	−	11.4719i	−0.411552	−	0.712829i
$260$		0			0
$261$	12.4442	−	4.80848i	0.770276	−	0.297638i
$262$	14.6772	+	9.23070i	0.906761	+	0.570274i
$263$	−0.474777	+	1.77189i	−0.0292760	+	0.109259i	−0.979018	−	0.203775i	$-0.934679\pi$
$263$	−0.474777	+	1.77189i	−0.0292760	+	0.109259i	0.949742	+	0.313034i	$0.101346\pi$
$264$	−16.1358	+	5.57627i	−0.993088	+	0.343196i
$265$		0			0
$266$	13.3808	+	4.13345i	0.820432	+	0.253438i
$267$	−0.484351	+	6.24252i	−0.0296418	+	0.382036i
$268$	0.275789	+	1.46415i	0.0168465	+	0.0894372i
$269$			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	$-0.801914\pi$
$271$		−	19.1919i		−	1.16582i	0.812536	−	0.582911i	$-0.198086\pi$
$272$	−7.25243	−	9.86050i	−0.439743	−	0.597880i
$273$	1.80109	−	23.2132i	0.109007	−	1.40493i
$274$	3.86120	−	12.4995i	0.233264	−	0.755123i
$275$		0			0
$276$	−13.1977	+	1.44088i	−0.794408	+	0.0867307i
$277$	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	$0.0112516\pi$
$278$	−13.4838	+	21.4398i	−0.808705	+	1.28588i
$279$	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	$0.970360\pi$
$282$	−0.545942	−	0.216186i	−0.0325104	−	0.0128737i
$283$	−1.79491	+	0.480944i	−0.106696	+	0.0285891i	−0.311772	−	0.950157i	$-0.600923\pi$
$283$	−1.79491	+	0.480944i	−0.106696	+	0.0285891i	0.205076	+	0.978746i	$0.434256\pi$
$284$	−0.312737	+	4.12777i	−0.0185575	+	0.244938i
$285$		0			0
$286$	17.6734	+	19.0630i	1.04505	+	1.12722i
$287$	−14.5891	+	14.5891i	−0.861170	+	0.861170i
$288$	−15.9768	−	5.72209i	−0.941441	−	0.337177i
$289$		−	7.63580i		−	0.449165i
$290$		0			0
$291$	−1.82381	+	5.16844i	−0.106914	+	0.302979i
$292$	−19.2537	+	16.5417i	−1.12674	+	0.968029i
$293$	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	$0.636644\pi$
$294$	−0.993456	−	0.737886i	−0.0579396	−	0.0430344i
$295$		0			0
$296$	9.15221	+	11.5055i	0.531961	+	0.668744i
$297$	17.3449	−	5.20045i	1.00645	−	0.301761i
$298$	3.31419	+	2.08434i	0.191986	+	0.120742i
$299$	10.1075	+	17.5068i	0.584534	+	1.01244i
$300$		0			0
$301$	−6.70478	+	11.6130i	−0.386457	+	0.669363i
$302$	9.41051	−	4.96867i	0.541514	−	0.285915i
$303$	−3.22828	−	6.74902i	−0.185460	−	0.387721i
$304$	−15.3657	−	2.34177i	−0.881280	−	0.134310i
$305$		0			0
$306$	7.25250	+	10.7683i	0.414598	+	0.615584i
$307$	−13.9421	+	13.9421i	−0.795717	+	0.795717i	−0.982417	−	0.186700i	$-0.940221\pi$
$307$	−13.9421	+	13.9421i	−0.795717	+	0.795717i	0.186700	+	0.982417i	$0.440221\pi$
$308$	−17.4552	+	3.28788i	−0.994601	+	0.187344i
$309$	−2.32577	+	0.433717i	−0.132308	+	0.0246733i
$310$		0			0
$311$	−0.701482	−	0.405001i	−0.0397774	−	0.0229655i	0.479979	−	0.877280i	$-0.340644\pi$
$311$	−0.701482	−	0.405001i	−0.0397774	−	0.0229655i	−0.519757	+	0.854314i	$0.673977\pi$
$312$	1.83148	+	25.7755i	0.103687	+	1.45925i
$313$	−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	$-0.108871\pi$
$318$	−0.721670	+	0.571927i	−0.0404692	+	0.0320721i
$319$	−7.74847	+	13.4207i	−0.433831	+	0.751418i
$320$		0			0
$321$	9.91424	−	8.48654i	0.553359	−	0.473672i
$322$	−13.8028	−	0.522130i	−0.769200	−	0.0290972i
$323$	8.40809	+	8.40809i	0.467838	+	0.467838i
$324$	16.6800	+	6.76599i	0.926665	+	0.375888i
$325$		0			0
$326$	−9.20458	−	9.92834i	−0.509795	−	0.549880i
$327$	1.90060	−	24.4957i	0.105103	−	1.35462i
$328$	13.6202	−	18.4073i	0.752052	−	1.01638i
$329$	−0.529071	−	0.305459i	−0.0291686	−	0.0168405i
$330$		0			0
$331$	16.9166	−	9.76680i	0.929821	−	0.536832i	0.0430657	−	0.999072i	$-0.486288\pi$
$331$	16.9166	−	9.76680i	0.929821	−	0.536832i	0.886755	+	0.462240i	$0.152954\pi$
$332$	−10.2768	+	29.2924i	−0.564013	+	1.60763i
$333$	−9.19350	−	12.5951i	−0.503801	−	0.690207i
$334$	−1.16202	−	5.10077i	−0.0635828	−	0.279102i
$335$		0			0
$336$	−15.5749	−	8.31694i	−0.849682	−	0.453726i
$337$	−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	$0.505509\pi$
$338$	18.5365	−	9.78708i	1.00825	−	0.532347i
$339$	−0.143834	−	0.771299i	−0.00781201	−	0.0418912i
$340$		0			0
$341$	−7.52446			−0.407472
$342$	16.1808	+	3.15685i	0.874960	+	0.170703i
$343$	−13.5248	−	13.5248i	−0.730270	−	0.730270i
$344$	5.45423	−	13.8471i	0.294073	−	0.746584i
$345$		0			0
$346$	−31.3328	−	9.67897i	−1.68446	−	0.520345i
$347$	−6.50347	−	24.2713i	−0.349125	−	1.30295i	−0.887719	−	0.460386i	$-0.847711\pi$
$347$	−6.50347	−	24.2713i	−0.349125	−	1.30295i	0.538594	−	0.842565i	$-0.318956\pi$
$348$	−14.3592	+	5.57842i	−0.769735	+	0.299035i
$349$	−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
$352$	18.6203	−	6.47271i	0.992464	−	0.344997i
$353$	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	$0.290963\pi$
$354$	−16.6257	+	22.3840i	−0.883644	+	1.18970i
$355$		0			0
$356$	0.546201	−	7.20924i	0.0289486	−	0.382089i
$357$	5.82865	+	12.1853i	0.308485	+	0.644916i
$358$	14.1582	+	0.535574i	0.748284	+	0.0283060i
$359$	26.1394			1.37959			0.689794	−	0.724006i	$-0.257701\pi$
$359$	26.1394			1.37959			0.689794	+	0.724006i	$0.257701\pi$
$360$		0			0
$361$	−3.90081			−0.205306
$362$	28.2373	+	1.06816i	1.48412	+	0.0561410i
$363$	−1.12059	+	1.63434i	−0.0588159	+	0.0857807i
$364$	−2.03108	+	26.8080i	−0.106458	+	1.40512i
$365$		0			0
$366$	−8.98364	−	20.7629i	−0.469582	−	1.08530i
$367$	22.2128	+	5.95191i	1.15950	+	0.310687i	0.786766	−	0.617251i	$-0.211754\pi$
$367$	22.2128	+	5.95191i	1.15950	+	0.310687i	0.372734	+	0.927938i	$0.378420\pi$
$368$	15.2363	−	1.69143i	0.794249	−	0.0881718i
$369$	−15.2429	+	18.9087i	−0.793511	+	0.984348i
$370$		0			0
$371$	−0.829682	+	0.479017i	−0.0430750	+	0.0248693i
$372$	−5.83172	−	4.68368i	−0.302360	−	0.242838i
$373$	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	$0.804847\pi$
$374$	−14.4093	−	4.45114i	−0.745085	−	0.230163i
$375$		0			0
$376$	0.630851	+	0.248486i	0.0325337	+	0.0128147i
$377$	16.5861	+	16.5861i	0.854226	+	0.854226i
$378$	16.1401	+	9.49823i	0.830156	+	0.488536i
$379$	−12.7657			−0.655730			−0.327865	−	0.944725i	$-0.606329\pi$
$379$	−12.7657			−0.655730			−0.327865	+	0.944725i	$0.606329\pi$
$380$		0			0
$381$	−4.95471	+	4.24121i	−0.253838	+	0.217284i
$382$	−19.5966	+	10.3469i	−1.00265	+	0.529391i
$383$	−33.9365	+	9.09327i	−1.73408	+	0.464644i	−0.981116	−	0.193422i	$-0.938041\pi$
$383$	−33.9365	+	9.09327i	−1.73408	+	0.464644i	−0.752960	+	0.658066i	$0.771375\pi$
$384$	18.4604	+	6.57381i	0.942051	+	0.335469i
$385$		0			0
$386$	6.77959	+	29.7596i	0.345072	+	1.51472i
$387$	−6.38856	+	14.4348i	−0.324749	+	0.733761i
$388$	2.09512	−	5.97181i	0.106364	−	0.303173i
$389$	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
$392$	1.14869	+	0.849955i	0.0580175	+	0.0429292i
$393$	17.5139	+	12.0085i	0.883459	+	0.605747i
$394$	−12.8446	−	13.8545i	−0.647099	−	0.697981i
$395$		0			0
$396$	−20.0172	+	6.04129i	−1.00590	+	0.303586i
$397$	−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	$-0.552096\pi$
$398$	2.91231	+	0.110166i	0.145981	+	0.00552215i
$399$	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	$0.890841\pi$
$402$	0.266471	+	1.80518i	0.0132903	+	0.0900344i
$403$	−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
$408$	−8.39701	−	12.4190i	−0.415714	−	0.614831i
$409$	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
$412$	2.68465	−	0.505684i	0.132263	−	0.0249133i
$413$	−20.5130	+	20.5130i	−1.00938	+	1.00938i
$414$	−16.2210	+	1.12302i	−0.797220	+	0.0551932i
$415$		0			0
$416$	−2.16881	−	29.7591i	−0.106335	−	1.45906i
$417$	−17.5414	+	25.5835i	−0.859008	+	1.25283i
$418$	−16.9347	+	8.94137i	−0.828303	+	0.437337i
$419$	5.01036	−	8.67820i	0.244772	−	0.423958i	−0.717295	−	0.696769i	$-0.754620\pi$
$419$	5.01036	−	8.67820i	0.244772	−	0.423958i	0.962068	+	0.272811i	$0.0879535\pi$
$420$		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	$0.890786\pi$
$422$	2.75719	+	1.73403i	0.134218	+	0.0844115i
$423$	−0.657626	−	0.291053i	−0.0319749	−	0.0141515i
$424$	0.832113	−	0.661915i	0.0404110	−	0.0321455i
$425$		0			0
$426$	−0.582987	+	5.03632i	−0.0282458	+	0.244010i
$427$	−6.09194	−	22.7354i	−0.294810	−	1.10024i
$428$	−11.4302	+	9.82017i	−0.552499	+	0.474676i
$429$	20.7035	+	24.1865i	0.999575	+	1.16773i
$430$		0			0
$431$		−	16.4473i		−	0.792237i	−0.918199	−	0.396119i	$-0.870357\pi$
$431$		−	16.4473i		−	0.792237i	0.918199	−	0.396119i	$-0.129643\pi$
$432$	−19.2745	−	7.77774i	−0.927345	−	0.374206i
$433$	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	$0.208988\pi$
$434$	−5.29076	−	5.70677i	−0.253964	−	0.273934i
$435$		0			0
$436$	−2.14330	+	28.2892i	−0.102646	+	1.35481i
$437$	−14.3847	+	3.85437i	−0.688114	+	0.184380i
$438$	−24.3649	+	19.3093i	−1.16420	+	0.922635i
$439$	18.4104	+	31.8878i	0.878683	+	1.52192i	0.852787	+	0.522258i	$0.174910\pi$
$439$	18.4104	+	31.8878i	0.878683	+	1.52192i	0.0258954	+	0.999665i	$0.491756\pi$
$440$		0			0
$441$	−1.17998	−	0.951212i	−0.0561893	−	0.0452958i
$442$	−12.1525	+	19.3230i	−0.578036	+	0.919102i
$443$	3.13302	−	11.6926i	0.148854	−	0.555532i	−0.850699	−	0.525653i	$-0.823821\pi$
$443$	3.13302	−	11.6926i	0.148854	−	0.555532i	0.999554	−	0.0298790i	$-0.00951219\pi$
$444$	10.6421	+	14.5243i	0.505052	+	0.689292i
$445$		0			0
$446$	−6.96695	+	22.5535i	−0.329895	+	1.06794i
$447$	3.95472	+	2.71157i	0.187052	+	0.128253i
$448$	18.0018	+	9.57093i	0.850504	+	0.452184i
$449$		−	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
$452$	0.167701	+	0.890317i	0.00788800	+	0.0418770i
$453$	11.7575	−	5.62401i	0.552415	−	0.264239i
$454$	−6.81160	−	2.10416i	−0.319684	−	0.0987530i
$455$		0			0
$456$	−18.6906	−	3.61131i	−0.875268	−	0.169115i
$457$	−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	$0.980233\pi$
$458$	−9.28746	−	5.84101i	−0.433974	−	0.272932i
$459$	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	$0.747432\pi$
$462$	−21.5209	+	3.17678i	−1.00124	+	0.147797i
$463$	4.53841	−	1.21606i	0.210918	−	0.0565153i	−0.151813	−	0.988409i	$-0.548511\pi$
$463$	4.53841	−	1.21606i	0.210918	−	0.0565153i	0.362731	+	0.931894i	$0.381844\pi$
$464$	16.5689	−	6.47148i	0.769191	−	0.300431i
$465$		0			0
$466$	−6.09155	+	5.64749i	−0.282186	+	0.261615i
$467$	25.5411	−	25.5411i	1.18190	−	1.18190i	0.202651	−	0.979251i	$-0.435044\pi$
$467$	25.5411	−	25.5411i	1.18190	−	1.18190i	0.979251	−	0.202651i	$-0.0649557\pi$
$468$	0.990798	+	31.6325i	0.0457997	+	1.46221i
$469$			1.89849i			0.0876643i
$470$		0			0
$471$	−6.37669	+	1.18915i	−0.293822	+	0.0547929i
$472$	19.1507	−	25.8816i	0.881484	−	1.19130i
$473$	−4.74581	−	17.7116i	−0.218213	−	0.814381i
$474$	14.7105	+	33.9987i	0.675674	+	1.56161i
$475$		0			0
$476$	−6.75587	−	14.0582i	−0.309655	−	0.644355i
$477$	−0.910915	+	0.664902i	−0.0417080	+	0.0304438i
$478$	1.92828	−	3.06606i	0.0881977	−	0.140238i
$479$	−6.06234	−	10.5003i	−0.276995	−	0.479770i	0.693641	−	0.720321i	$-0.256005\pi$
$479$	−6.06234	−	10.5003i	−0.276995	−	0.479770i	−0.970637	+	0.240551i	$0.922672\pi$
$480$		0			0
$481$	13.7084	−	23.7436i	0.625049	−	1.08262i
$482$	−9.10455	−	17.2438i	−0.414701	−	0.785431i
$483$	−16.8663	−	1.30864i	−0.767444	−	0.0595452i
$484$	1.29052	−	1.88952i	0.0586602	−	0.0858873i
$485$		0			0
$486$	20.0844	+	9.08936i	0.911047	+	0.412302i
$487$	−12.5621	+	12.5621i	−0.569243	+	0.569243i	−0.931916	−	0.362673i	$-0.881864\pi$
$487$	−12.5621	+	12.5621i	−0.569243	+	0.569243i	0.362673	+	0.931916i	$0.381864\pi$
$488$	10.4169	+	23.9561i	0.471551	+	1.08444i
$489$	−10.7827	−	12.5967i	−0.487612	−	0.569643i
$490$		0			0
$491$	0.109289	+	0.0630982i	0.00493215	+	0.00284758i	0.502464	−	0.864598i	$-0.332427\pi$
$491$	0.109289	+	0.0630982i	0.00493215	+	0.00284758i	−0.497532	+	0.867446i	$0.665760\pi$
$492$	17.5613	−	21.8658i	0.791724	−	0.985786i
$493$	−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
$498$	−13.9978	+	35.3489i	−0.627254	+	1.58402i
$499$	20.2868	−	35.1377i	0.908161	−	1.57298i	0.0915430	−	0.995801i	$-0.470820\pi$
$499$	20.2868	−	35.1377i	0.908161	−	1.57298i	0.816618	−	0.577179i	$-0.195847\pi$
$500$		0			0
$501$	−1.17459	−	6.29862i	−0.0524766	−	0.281401i
$502$	0.613695	−	16.2234i	0.0273905	−	0.724084i
$503$	−6.97397	−	6.97397i	−0.310954	−	0.310954i	0.534325	−	0.845279i	$-0.320566\pi$
$503$	−6.97397	−	6.97397i	−0.310954	−	0.310954i	−0.845279	+	0.534325i	$0.820566\pi$
$504$	−18.6568	−	10.9338i	−0.831041	−	0.487029i
$505$		0			0
$506$	13.8509	−	12.8412i	0.615747	−	0.570860i
$507$	23.1594	−	11.0779i	1.02855	−	0.491989i
$508$	5.71231	−	4.90770i	0.253443	−	0.217744i
$509$	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
$512$	−21.3299	−	7.55210i	−0.942658	−	0.333759i
$513$	19.6487	+	4.64834i	0.867511	+	0.205229i
$514$	20.2321	−	4.60912i	0.892400	−	0.203300i
$515$		0			0
$516$	7.34662	−	16.6812i	0.323417	−	0.734349i
$517$	0.806914	−	0.216212i	0.0354880	−	0.00950899i
$518$	8.74680	+	16.5662i	0.384312	+	0.727876i
$519$	−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	$0.226410\pi$
$522$	−17.8432	+	6.13012i	−0.780977	+	0.268308i
$523$	−31.6445	−	31.6445i	−1.38372	−	1.38372i	−0.837915	−	0.545801i	$-0.816225\pi$
$523$	−31.6445	−	31.6445i	−1.38372	−	1.38372i	−0.545801	−	0.837915i	$-0.683775\pi$
$524$	−20.2484	−	13.8295i	−0.884556	−	0.604143i
$525$		0			0
$526$	0.765678	−	2.47866i	0.0333851	−	0.108075i
$527$	−1.71011	−	6.38222i	−0.0744936	−	0.278014i
$528$	23.1012	−	7.01780i	1.00535	−	0.305411i
$529$	−7.19846	+	4.15603i	−0.312976	+	0.180697i
$530$		0			0
$531$	−21.4322	+	26.5866i	−0.930078	+	1.15376i
$532$	−18.6889	−	6.55672i	−0.810265	−	0.284270i
$533$	−41.2478	−	11.0523i	−1.78664	−	0.478729i
$534$	1.01820	−	8.79605i	0.0440619	−	0.380642i
$535$		0			0
$536$	−0.311475	−	2.08389i	−0.0134537	−	0.0900101i
$537$	17.3006	+	1.34234i	0.746575	+	0.0579261i
$538$	0.716508	−	18.9413i	0.0308908	−	0.816617i
$539$	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	$0.221732\pi$
$542$	−1.02597	+	27.1220i	−0.0440690	+	1.16499i
$543$	34.5045	+	2.67717i	1.48073	+	0.114888i
$544$	9.72203	+	14.3226i	0.416829	+	0.614076i
$545$		0			0
$546$	−3.78624	+	32.7086i	−0.162036	+	1.39980i
$547$	−15.9487	−	4.27345i	−0.681919	−	0.182720i	−0.0988010	−	0.995107i	$-0.531501\pi$
$547$	−15.9487	−	4.27345i	−0.681919	−	0.182720i	−0.583118	+	0.812388i	$0.698167\pi$
$548$	−6.12487	+	17.4579i	−0.261641	+	0.745766i
$549$	−9.98668	−	25.8452i	−0.426221	−	1.10305i
$550$		0			0
$551$	−14.9648	+	8.63994i	−0.637522	+	0.368074i
$552$	18.7280	−	1.33073i	0.797119	−	0.0566395i
$553$	9.97538	+	37.2286i	0.424197	+	1.58312i
$554$	−3.11946	+	10.0984i	−0.132533	+	0.429038i
$555$		0			0
$556$	20.2015	−	29.5780i	0.856734	−	1.25439i
$557$	−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	$0.768715\pi$
$558$	−6.90952	−	6.01475i	−0.292503	−	0.254625i
$559$	−27.7541			−1.17387
$560$		0			0
$561$	−17.4179	−	6.14632i	−0.735383	−	0.259498i
$562$	9.23814	+	17.4968i	0.389687	+	0.738057i
$563$	12.8024	−	3.43039i	0.539557	−	0.144574i	0.0212589	−	0.999774i	$-0.493233\pi$
$563$	12.8024	−	3.43039i	0.539557	−	0.144574i	0.518298	+	0.855200i	$0.326566\pi$
$564$	0.759969	+	0.334700i	0.0320005	+	0.0140934i
$565$		0			0
$566$	2.56228	−	0.583718i	0.107701	−	0.0245355i
$567$	19.2911	+	12.4068i	0.810152	+	0.521038i
$568$	0.662624	−	5.81665i	0.0278031	−	0.244061i
$569$	−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	0.988034	−	0.154234i	$-0.0492908\pi$
$571$	32.2228	+	18.6038i	1.34848	+	0.778546i	0.360447	+	0.932780i	$0.382624\pi$
$572$	−23.9570	−	27.8847i	−1.00169	−	1.16592i
$573$	−24.4840	+	11.7115i	−1.02284	+	0.489257i
$574$	21.3973	−	19.8375i	0.893107	−	0.828001i
$575$		0			0
$576$	22.2725	+	8.94056i	0.928023	+	0.372523i
$577$	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	$0.668172\pi$
$578$	−0.408198	+	10.7909i	−0.0169788	+	0.448844i
$579$	6.85292	+	36.7482i	0.284798	+	1.52720i
$580$		0			0
$581$	−19.7780	+	34.2566i	−0.820532	+	1.42120i
$582$	2.85371	−	7.20655i	0.118290	−	0.298721i
$583$	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	0.0972097	−	0.995264i	$-0.469008\pi$
$587$	−7.66180	−	2.05297i	−0.316236	−	0.0847352i	−0.413446	+	0.910529i	$0.635675\pi$
$588$	1.36451	+	1.09589i	0.0562714	+	0.0451938i
$589$	−7.26609	−	4.19508i	−0.299394	−	0.172855i
$590$		0			0
$591$	−15.0468	−	17.5781i	−0.618942	−	0.723067i
$592$	−12.3189	−	16.7489i	−0.506302	−	0.688374i
$593$	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	$0.0805164\pi$
$594$	−24.7899	+	6.42206i	−1.01714	+	0.263500i
$595$		0			0
$596$	−4.57219	−	3.12276i	−0.187284	−	0.127913i
$597$	3.55869	+	0.276116i	0.145648	+	0.0113007i
$598$	−13.3481	−	25.2809i	−0.545845	−	1.03381i
$599$	15.1365	−	26.2172i	0.618461	−	1.07121i	−0.371305	−	0.928511i	$-0.621090\pi$
$599$	15.1365	−	26.2172i	0.618461	−	1.07121i	0.989767	−	0.142696i	$-0.0455770\pi$
$600$		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	$0.848275\pi$
$602$	10.0960	−	16.0531i	0.411483	−	0.654277i
$603$	0.238521	+	2.22208i	0.00971331	+	0.0904902i
$604$	−13.5646	+	6.51866i	−0.551935	+	0.265241i
$605$		0			0
$606$	4.20143	+	9.71031i	0.170671	+	0.394455i
$607$	11.3362	+	42.3071i	0.460120	+	1.71719i	0.672581	+	0.740023i	$0.265185\pi$
$607$	11.3362	+	42.3071i	0.460120	+	1.71719i	−0.212461	+	0.977170i	$0.568148\pi$
$608$	21.5896	+	4.13082i	0.875574	+	0.167527i
$609$	−19.2967	+	3.59851i	−0.781943	+	0.145819i
$610$		0			0
$611$		−	1.26443i		−	0.0511535i
$612$	−9.67360	−	15.6055i	−0.391032	−	0.630816i
$613$	−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	$0.295772\pi$
$614$	20.4483	−	18.9577i	0.825227	−	0.765070i
$615$		0			0
$616$	24.8435	−	3.71331i	1.00097	−	0.149614i
$617$	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	$0.370551\pi$
$618$	3.30997	−	0.488598i	0.133146	−	0.0196543i
$619$	−6.11352	−	10.5889i	−0.245723	−	0.425605i	0.716612	−	0.697473i	$-0.245692\pi$
$619$	−6.11352	−	10.5889i	−0.245723	−	0.425605i	−0.962335	+	0.271868i	$0.912359\pi$
$620$		0			0
$621$	−19.9055	+	0.587337i	−0.798781	+	0.0235690i
$622$	0.969686	+	0.609848i	0.0388809	+	0.0244527i
$623$	2.38441	−	8.89874i	0.0955294	−	0.356521i
$624$	−1.21034	−	36.5239i	−0.0484524	−	1.46213i
$625$		0			0
$626$	8.55176	+	2.64171i	0.341797	+	0.105584i
$627$	−21.1582	+	10.1207i	−0.844977	+	0.404181i
$628$	7.36066	−	1.38646i	0.293723	−	0.0553259i
$629$			15.9059i			0.634208i
$630$		0			0
$631$		−	8.53598i		−	0.339812i	−0.985460	−	0.169906i	$-0.945654\pi$
$631$		−	8.53598i		−	0.339812i	0.985460	−	0.169906i	$-0.0543464\pi$
$632$	−17.0574	−	39.2275i	−0.678506	−	1.56039i
$633$	3.29008	+	2.25585i	0.130769	+	0.0896621i
$634$	−8.43928	+	27.3197i	−0.335167	+	1.08500i
$635$		0			0
$636$	1.05044	−	0.769670i	0.0416527	−	0.0305194i
$637$	0.689706	−	2.57402i	0.0273272	−	0.101986i
$638$	11.6676	−	18.5520i	0.461925	−	0.734481i
$639$	−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	$0.765839\pi$
$642$	−14.4645	+	11.4632i	−0.570869	+	0.452416i
$643$	−0.317383	+	0.0850425i	−0.0125164	+	0.00335375i	−0.265072	−	0.964229i	$-0.585396\pi$
$643$	−0.317383	+	0.0850425i	−0.0125164	+	0.00335375i	0.252555	+	0.967582i	$0.418729\pi$
$644$	19.4783	+	1.47575i	0.767551	+	0.0581528i
$645$		0			0
$646$	−11.4328	−	12.3318i	−0.449819	−	0.485189i
$647$	1.08970	−	1.08970i	0.0428405	−	0.0428405i	−0.685362	−	0.728203i	$-0.740356\pi$
$647$	1.08970	−	1.08970i	0.0428405	−	0.0428405i	0.728203	+	0.685362i	$0.240356\pi$
$648$	−23.2105	−	10.4534i	−0.911794	−	0.410648i
$649$		−	39.6684i		−	1.55712i
$650$		0			0
$651$	−6.19787	−	7.24054i	−0.242914	−	0.283779i
$652$	12.4772	+	14.5228i	0.488644	+	0.568758i
$653$	−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	$-0.231286\pi$
$654$	−3.99544	+	34.5158i	−0.156234	+	1.34968i
$655$		0			0
$656$	−20.2322	+	25.2852i	−0.789934	+	0.987221i
$657$	−30.7542	+	22.4483i	−1.19983	+	0.875792i
$658$	0.731356	+	0.459959i	0.0285112	+	0.0179311i
$659$	6.24819	+	10.8222i	0.243395	+	0.421572i	0.961679	−	0.274177i	$-0.0884055\pi$
$659$	6.24819	+	10.8222i	0.243395	+	0.421572i	−0.718284	+	0.695750i	$0.755072\pi$
$660$		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	$0.201910\pi$
$662$	−24.4287	+	12.8981i	−0.949449	+	0.501300i
$663$	−15.8095	+	23.0576i	−0.613991	+	0.895483i
$664$	16.0891	−	40.8467i	0.624379	−	1.58516i
$665$		0			0
$666$	12.3190	+	18.2909i	0.477350	+	0.708758i
$667$	12.0512	−	12.0512i	0.466623	−	0.466623i
$668$	1.36949	+	7.27054i	0.0529871	+	0.281306i
$669$	−9.62026	+	27.2625i	−0.371941	+	1.05403i
$670$		0			0
$671$	27.8734	+	16.0927i	1.07604	+	0.621252i
$672$	21.5659	+	12.5861i	0.831924	+	0.485521i
$673$	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	$0.0670545\pi$
$678$	0.162035	+	1.09769i	0.00622290	+	0.0421566i
$679$	4.03213	−	6.98386i	0.154739	−	0.268016i
$680$		0			0
$681$	−8.23384	−	2.90551i	−0.315521	−	0.111339i
$682$	10.6336	+	0.402246i	0.407181	+	0.0154028i
$683$	31.3443	+	31.3443i	1.19936	+	1.19936i	0.974359	+	0.224999i	$0.0722379\pi$
$683$	31.3443	+	31.3443i	1.19936	+	1.19936i	0.224999	+	0.974359i	$0.427762\pi$
$684$	−22.6981	−	5.32627i	−0.867882	−	0.203655i
$685$		0			0
$686$	18.3903	+	19.8363i	0.702143	+	0.757353i
$687$	−11.0825	−	7.59873i	−0.422822	−	0.289909i
$688$	−8.44818	+	19.2771i	−0.322084	+	0.734934i
$689$	−1.71721	−	0.991433i	−0.0654206	−	0.0377706i
$690$		0			0
$691$	−1.44150	+	0.832251i	−0.0548373	+	0.0316603i	−0.527168	−	0.849761i	$-0.676746\pi$
$691$	−1.44150	+	0.832251i	−0.0548373	+	0.0316603i	0.472331	+	0.881421i	$0.343413\pi$
$692$	43.7622	+	15.3534i	1.66359	+	0.583647i
$693$	−26.4910	+	2.84357i	−1.00631	+	0.108018i
$694$	7.89322	+	34.6479i	0.299623	+	1.31522i
$695$		0			0
$696$	20.5907	−	7.11582i	0.780488	−	0.269724i
$697$	23.9299	−	6.41200i	0.906410	−	0.242872i
$698$	21.7065	−	11.4608i	0.821603	−	0.433799i
$699$	−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	$0.541938\pi$
$702$	−0.322180	+	38.7594i	−0.0121599	+	1.46288i
$703$	14.2818	+	14.2818i	0.538649	+	0.538649i
$704$	−26.6603	+	8.15185i	−1.00480	+	0.307234i
$705$		0			0
$706$	−40.3499	−	12.4644i	−1.51859	−	0.469105i
$707$	2.84905	+	10.6328i	0.107150	+	0.399888i
$708$	24.6920	−	30.7444i	0.927984	−	1.15545i
$709$	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
$712$	−1.15729	+	10.1589i	−0.0433712	+	0.380722i
$713$	7.99314	+	2.14175i	0.299345	+	0.0802093i
$714$	−7.58566	−	17.5319i	−0.283886	−	0.656116i
$715$		0			0
$716$	−19.9798	−	1.51375i	−0.746679	−	0.0565715i
$717$	2.50856	−	3.65864i	0.0936838	−	0.136634i
$718$	−36.9403	−	1.39737i	−1.37860	−	0.0521495i
$719$	−27.9555			−1.04257			−0.521283	−	0.853384i	$-0.674546\pi$
$719$	−27.9555			−1.04257			−0.521283	+	0.853384i	$0.674546\pi$
$720$		0			0
$721$	3.48106			0.129641
$722$	5.51263	+	0.208531i	0.205159	+	0.00776072i
$723$	−10.3054	−	21.5443i	−0.383261	−	0.801243i
$724$	−39.8479	−	3.01904i	−1.48094	−	0.112202i
$725$		0			0
$726$	1.67100	−	2.24975i	0.0620164	−	0.0834961i
$727$	−32.2018	−	8.62843i	−1.19430	−	0.320011i	−0.393714	−	0.919233i	$-0.628810\pi$
$727$	−32.2018	−	8.62843i	−1.19430	−	0.320011i	−0.800583	+	0.599222i	$0.795477\pi$
$728$	4.30345	−	37.7766i	0.159496	−	1.40009i
$729$	24.1380	+	12.0978i	0.893999	+	0.448068i
$730$		0			0
$731$	13.9443	−	8.05077i	0.515750	−	0.297768i
$732$	11.5858	+	29.8225i	0.428222	+	1.10227i
$733$	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	$0.906685\pi$
$734$	−31.0731	−	9.59872i	−1.14693	−	0.354295i
$735$		0			0
$736$	−21.6225	+	1.57582i	−0.797014	+	0.0580856i
$737$	−1.83567	−	1.83567i	−0.0676177	−	0.0676177i
$738$	22.5521	−	25.9070i	0.830153	−	0.953650i
$739$	−48.7588			−1.79362			−0.896811	−	0.442414i	$-0.854122\pi$
$739$	−48.7588			−1.79362			−0.896811	+	0.442414i	$0.854122\pi$
$740$		0			0
$741$	6.50802	+	34.8987i	0.239078	+	1.28204i
$742$	1.19812	−	0.632595i	0.0439843	−	0.0232233i
$743$	20.5756	−	5.51322i	0.754846	−	0.202260i	0.139179	−	0.990267i	$-0.455554\pi$
$743$	20.5756	−	5.51322i	0.754846	−	0.202260i	0.615667	+	0.788007i	$0.288887\pi$
$744$	7.99101	+	6.93074i	0.292965	+	0.254093i
$745$		0			0
$746$	−4.17530	−	18.3278i	−0.152868	−	0.671028i
$747$	−18.8452	+	42.5803i	−0.689511	+	1.55793i
$748$	20.1253	+	7.06065i	0.735852	+	0.258163i
$749$	−16.6294	+	9.60100i	−0.607626	+	0.350813i
$750$		0			0
$751$	30.0558	+	17.3527i	1.09675	+	0.633209i	0.935366	−	0.353682i	$-0.115071\pi$
$751$	30.0558	+	17.3527i	1.09675	+	0.633209i	0.161385	+	0.986892i	$0.448404\pi$
$752$	−0.878237	−	0.384886i	−0.0320260	−	0.0140354i
$753$	1.53813	−	19.8241i	0.0560527	−	0.722431i
$754$	−22.5528	−	24.3261i	−0.821325	−	0.885906i
$755$		0			0
$756$	−22.3015	−	14.2857i	−0.811096	−	0.519567i
$757$	−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	$0.938050\pi$
$758$	18.0405	+	0.682434i	0.655262	+	0.0247871i
$759$	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	$0.00713933\pi$
$762$	7.22874	−	5.72882i	0.261870	−	0.207533i
$763$	−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
$768$	−25.7368	−	10.2770i	−0.928697	−	0.370839i
$769$	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
$772$	−7.99004	−	42.4187i	−0.287568	−	1.52668i
$773$	−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	$0.309970\pi$
$774$	9.79998	−	20.0577i	0.352253	−	0.720960i
$775$		0			0
$776$	−3.28008	+	8.32738i	−0.117748	+	0.298935i
$777$	9.90045	+	20.6978i	0.355177	+	0.742529i
$778$	−22.3362	+	11.7933i	−0.800791	+	0.422810i
$779$	15.7293	−	27.2439i	0.563560	−	0.976115i
$780$		0			0
$781$	−3.60645	−	6.24656i	−0.129049	−	0.223520i
$782$	14.0398	+	8.82982i	0.502062	+	0.315754i
$783$	−22.1337	+	6.63624i	−0.790992	+	0.237160i
$784$	−1.57789	−	1.26257i	−0.0563533	−	0.0450916i
$785$		0			0
$786$	−24.1087	−	17.9067i	−0.859929	−	0.638709i
$787$	−7.95656	−	29.6943i	−0.283621	−	1.05849i	−0.949841	−	0.312733i	$-0.898756\pi$
$787$	−7.95656	−	29.6943i	−0.283621	−	1.05849i	0.666220	−	0.745755i	$-0.267911\pi$
$788$	17.4113	+	20.2659i	0.620253	+	0.721943i
$789$	1.05728	−	2.99619i	0.0376402	−	0.106667i
$790$		0			0
$791$			1.15443i			0.0410468i
$792$	28.6114	−	7.46748i	1.01666	−	0.265345i
$793$	34.4474	−	34.4474i	1.22326	−	1.22326i
$794$	31.1450	+	33.5939i	1.10529	+	1.19220i
$795$		0			0
$796$	−4.10980	−	0.311375i	−0.145668	−	0.0110364i
$797$	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	$0.310710\pi$
$798$	−22.5530	−	8.93073i	−0.798368	−	0.316144i
$799$	0.366781	+	0.635283i	0.0129758	+	0.0224747i
$800$		0			0
$801$	1.67281	−	10.7151i	0.0591059	−	0.378598i
$802$	22.9796	−	36.5386i	0.811438	−	1.29022i
$803$	11.4473	−	42.7219i	0.403967	−	1.50762i
$804$	−0.280075	−	2.56534i	−0.00987747	−	0.0904724i
$805$		0			0
$806$	4.75380	−	15.3890i	0.167445	−	0.542056i
$807$	1.79582	−	23.1453i	0.0632158	−	0.814752i
$808$	−4.87173	−	11.2037i	−0.171387	−	0.394144i
$809$		−	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	$-0.805679\pi$
$811$		−	32.6505i		−	1.14652i	0.819375	−	0.573258i	$-0.194321\pi$
$812$	22.2744	−	4.19563i	0.781677	−	0.147238i
$813$	−2.57143	+	33.1417i	−0.0901840	+	1.16233i
$814$	−24.4753	−	7.56062i	−0.857859	−	0.265000i
$815$		0			0
$816$	11.2028	+	17.9994i	0.392176	+	0.630106i
$817$	5.29182	−	19.7493i	0.185137	−	0.690942i
$818$	−19.6557	−	12.3617i	−0.687244	−	0.432217i
$819$	−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	$0.996180\pi$
$822$	−8.34251	+	21.0676i	−0.290978	+	0.734816i
$823$	33.5290	−	8.98407i	1.16875	−	0.313165i	0.378293	−	0.925686i	$-0.376511\pi$
$823$	33.5290	−	8.98407i	1.16875	−	0.313165i	0.790454	+	0.612521i	$0.209844\pi$
$824$	−3.82099	+	0.571117i	−0.133111	+	0.0198958i
$825$		0			0
$826$	30.0857	−	27.8925i	1.04682	−	0.970504i
$827$	0.244245	−	0.244245i	0.00849323	−	0.00849323i	−0.702847	−	0.711341i	$-0.748088\pi$
$827$	0.244245	−	0.244245i	0.00849323	−	0.00849323i	0.711341	+	0.702847i	$0.248088\pi$
$828$	22.9836	−	0.719898i	0.798737	−	0.0250182i
$829$			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
$832$	1.47409	+	42.1715i	0.0511050	+	1.46204i
$833$	0.400133	+	1.49332i	0.0138638	+	0.0517404i
$834$	26.1573	−	35.2170i	0.905752	−	1.21946i
$835$		0			0
$836$	24.4101	−	11.7307i	0.844243	−	0.405713i
$837$	−8.16394	−	7.69597i	−0.282187	−	0.266012i
$838$	−7.54458	+	11.9962i	−0.260623	+	0.414402i
$839$	4.08967	+	7.08351i	0.141191	+	0.244550i	0.927945	−	0.372716i	$-0.121574\pi$
$839$	4.08967	+	7.08351i	0.141191	+	0.244550i	−0.786754	+	0.617266i	$0.788240\pi$
$840$		0			0
$841$	−4.61225	+	7.98866i	−0.159043	+	0.275471i
$842$	4.86427	+	9.21278i	0.167634	+	0.317493i
$843$	10.4566	+	21.8605i	0.360144	+	0.752914i
$844$	−3.80377	−	2.59794i	−0.130931	−	0.0894247i
$845$		0			0
$846$	0.913799	+	0.446472i	0.0314171	+	0.0153500i
$847$	2.06171	−	2.06171i	0.0708410	−	0.0708410i
$848$	−1.21133	+	0.890937i	−0.0415972	+	0.0305949i
$849$	3.16399	−	0.590032i	0.108588	−	0.0202498i
$850$		0			0
$851$	−17.2517	−	9.96030i	−0.591382	−	0.341435i
$852$	1.09311	−	7.08618i	0.0374494	−	0.242768i
$853$	−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	$-0.187542\pi$
$858$	−27.9653	−	35.2872i	−0.954719	−	1.20468i
$859$	1.47011	−	2.54630i	0.0501593	−	0.0868785i	−0.839856	−	0.542810i	$-0.817360\pi$
$859$	1.47011	−	2.54630i	0.0501593	−	0.0868785i	0.890015	+	0.455931i	$0.150694\pi$
$860$		0			0
$861$	27.1481	−	23.2387i	0.925206	−	0.791972i
$862$	−0.879245	+	23.2433i	−0.0299472	+	0.791671i
$863$	7.13386	+	7.13386i	0.242839	+	0.242839i	0.818024	−	0.575184i	$-0.195070\pi$
$863$	7.13386	+	7.13386i	0.242839	+	0.242839i	−0.575184	+	0.818024i	$0.695070\pi$
$864$	26.8230	+	12.0219i	0.912537	+	0.408993i
$865$		0			0
$866$	−5.54562	+	5.14136i	−0.188448	+	0.174710i
$867$	−1.02309	+	13.1860i	−0.0347458	+	0.447819i
$868$	7.17184	+	8.34766i	0.243428	+	0.283338i
$869$	−45.6419	−	26.3514i	−1.54830	−	0.893909i
$870$		0			0
$871$	−3.40292	+	1.96468i	−0.115304	+	0.0665706i
$872$	4.54122	−	39.8638i	0.153785	−	1.34996i
$873$	3.84196	−	8.68081i	0.130031	−	0.293801i
$874$	20.5346	−	4.67802i	0.694592	−	0.158237i
$875$		0			0
$876$	35.4648	−	25.9855i	1.19824	−	0.877968i
$877$	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	$0.287771\pi$
$878$	−24.3130	−	46.0482i	−0.820525	−	1.55405i
$879$	−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	$0.753683\pi$
$882$	1.61669	+	1.40734i	0.0544370	+	0.0473874i
$883$	7.64008	+	7.64008i	0.257109	+	0.257109i	0.823877	−	0.566768i	$-0.191807\pi$
$883$	7.64008	+	7.64008i	0.257109	+	0.257109i	−0.566768	+	0.823877i	$0.691807\pi$
$884$	18.2069	−	26.6577i	0.612366	−	0.896595i
$885$		0			0
$886$	−5.05266	+	16.3565i	−0.169747	+	0.549508i
$887$	1.25685	+	4.69064i	0.0422010	+	0.157496i	0.983811	−	0.179209i	$-0.0573539\pi$
$887$	1.25685	+	4.69064i	0.0422010	+	0.157496i	−0.941610	+	0.336706i	$0.890687\pi$
$888$	−14.2630	−	21.0947i	−0.478636	−	0.707890i
$889$	8.31067	−	4.79817i	0.278731	−	0.160925i
$890$		0			0
$891$	−30.6490	+	6.65649i	−1.02678	+	0.223001i
$892$	11.0514	−	31.5002i	0.370028	−	1.05470i
$893$	0.899750	+	0.241087i	0.0301090	+	0.00806768i
$894$	−5.44387	−	4.04341i	−0.182070	−	0.135232i
$895$		0			0
$896$	−24.9285	−	14.4880i	−0.832803	−	0.484010i
$897$	−15.1086	−	31.5860i	−0.504463	−	1.05463i
$898$	−0.0560395	+	1.48143i	−0.00187006	+	0.0494361i
$899$	9.60189			0.320241
$900$		0			0
$901$	1.15036			0.0383241
$902$	−1.50821	+	39.8703i	−0.0502178	+	1.32753i
$903$	13.1342	−	19.1557i	0.437079	−	0.637463i
$904$	−0.189401	−	1.26716i	−0.00629938	−	0.0421452i
$905$		0			0
$906$	−16.9164	+	7.31932i	−0.562009	+	0.243168i
$907$	58.1113	+	15.5709i	1.92955	+	0.517022i	0.977399	+	0.211402i	$0.0678030\pi$
$907$	58.1113	+	15.5709i	1.92955	+	0.517022i	0.952154	+	0.305620i	$0.0988636\pi$
$908$	9.51369	+	3.33774i	0.315723	+	0.110767i
$909$	4.67053	+	12.0872i	0.154912	+	0.400906i
$910$		0			0
$911$	−2.72513	+	1.57335i	−0.0902875	+	0.0521275i	−0.544464	−	0.838784i	$-0.683267\pi$
$911$	−2.72513	+	1.57335i	−0.0902875	+	0.0521275i	0.454176	+	0.890912i	$0.349934\pi$
$912$	26.2206	+	6.10269i	0.868250	+	0.202080i
$913$	−13.9994	−	52.2465i	−0.463313	−	1.72911i
$914$	5.67979	−	18.3867i	0.187871	−	0.608176i
$915$		0			0
$916$	12.8128	+	8.75102i	0.423347	+	0.289142i
$917$	−22.0936	−	22.0936i	−0.729594	−	0.729594i
$918$	−11.0813	−	19.5671i	−0.365736	−	0.645811i
$919$	31.3326			1.03357			0.516783	−	0.856116i	$-0.327129\pi$
$919$	31.3326			1.03357			0.516783	+	0.856116i	$0.327129\pi$
$920$		0			0
$921$	25.9441	−	22.2080i	0.854887	−	0.731779i
$922$	−7.55947	−	14.3174i	−0.248958	−	0.471519i
$923$	−10.5455	+	2.82565i	−0.347109	+	0.0930075i
$924$	30.5832	−	3.33897i	1.00611	−	0.109844i
$925$		0			0
$926$	−6.47871	+	1.47593i	−0.212904	+	0.0485020i
$927$	4.07439	−	0.437349i	0.133820	−	0.0143644i
$928$	−23.7611	+	8.25976i	−0.779998	+	0.271140i
$929$	−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
$932$	8.91050	−	7.65540i	0.291873	−	0.250761i
$933$	1.15710	+	0.793368i	0.0378817	+	0.0259737i
$934$	−37.4602	+	34.7294i	−1.22573	+	1.13638i
$935$		0			0
$936$	0.290822	−	44.7561i	0.00950583	−	1.46290i
$937$	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	$0.533907\pi$
$938$	0.101490	−	2.68296i	0.00331378	−	0.0876016i
$939$	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	$0.0330378\pi$
$942$	9.07513	−	1.33962i	0.295684	−	0.0436471i
$943$	−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	$0.0180556\pi$
$947$	58.2038	+	15.5957i	1.89137	+	0.506791i	0.892979	+	0.450098i	$0.148611\pi$
$948$	−18.9714	−	48.8335i	−0.616161	−	1.58604i
$949$	−57.9762	−	33.4726i	−1.88199	−	1.08657i
$950$		0			0
$951$	−11.6533	+	33.0240i	−0.377885	+	1.07088i
$952$	8.79588	+	20.2282i	0.285076	+	0.655600i
$953$	−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	$0.307672\pi$
$954$	1.32285	−	0.890945i	0.0428289	−	0.0288454i
$955$		0			0
$956$	−2.88896	+	4.22988i	−0.0934357	+	0.136804i
$957$	15.1787	−	22.1376i	0.490658	−	0.715606i
$958$	8.00599	+	15.1631i	0.258662	+	0.489898i
$959$	−11.7875	+	20.4166i	−0.380638	+	0.659285i
$960$		0			0
$961$	−13.1689	−	22.8092i	−0.424804	−	0.735782i
$962$	−20.6420	+	32.8218i	−0.665526	+	1.05822i
$963$	−18.2576	+	13.3267i	−0.588342	+	0.429447i
$964$	11.9448	+	24.8556i	0.384715	+	0.800546i
$965$		0			0
$966$	23.7656	+	2.75102i	0.764645	+	0.0885127i
$967$	4.17163	+	15.5687i	0.134151	+	0.500657i	1.00000		0.000352232i	$0.000112119\pi$
$967$	4.17163	+	15.5687i	0.134151	+	0.500657i	−0.865849	+	0.500305i	$0.833221\pi$
$968$	−1.92478	+	2.60129i	−0.0618649	+	0.0836085i
$969$	−13.3930	−	15.6462i	−0.430246	−	0.502627i
$970$		0			0
$971$			51.3038i			1.64642i	0.567739	+	0.823209i	$0.307818\pi$
$971$			51.3038i			1.64642i	−0.567739	+	0.823209i	$0.692182\pi$
$972$	−27.8974	−	13.9188i	−0.894811	−	0.446446i
$973$	32.2733	−	32.2733i	1.03464	−	1.03464i
$974$	18.4243	−	17.0812i	0.590354	−	0.547318i
$975$		0			0
$976$	−13.4405	−	34.4117i	−0.430221	−	1.10149i
$977$	−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	$0.423928\pi$
$978$	14.5648	+	18.3781i	0.465730	+	0.587668i
$979$	6.29876	+	10.9098i	0.201309	+	0.348678i
$980$		0			0
$981$	−6.56414	+	42.0461i	−0.209577	+	1.34243i
$982$	−0.151075	−	0.0950129i	−0.00482099	−	0.00303198i
$983$	−11.8993	+	44.4088i	−0.379529	+	1.41642i	0.467085	+	0.884212i	$0.345304\pi$
$983$	−11.8993	+	44.4088i	−0.379529	+	1.41642i	−0.846614	+	0.532208i	$0.821362\pi$
$984$	−25.9866	+	29.9620i	−0.828422	+	0.955154i
$985$		0			0
$986$	18.3875	+	5.68005i	0.585577	+	0.180890i
$987$	0.872705	+	0.598374i	0.0277785	+	0.0190464i
$988$	−7.58791	−	40.2838i	−0.241404	−	1.28160i
$989$			20.1657i			0.641231i
$990$		0			0
$991$			47.4822i			1.50832i	0.656689	+	0.754161i	$0.271956\pi$
$991$			47.4822i			1.50832i	−0.656689	+	0.754161i	$0.728044\pi$
$992$	−9.24173	−	7.98618i	−0.293425	−	0.253561i
$993$	−30.5212	+	14.5993i	−0.968562	+	0.463296i
$994$	2.20173	−	7.12745i	0.0698346	−	0.226069i
$995$		0			0
$996$	21.6714	−	49.2069i	0.686683	−	1.55918i
$997$	−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	$0.727910\pi$
$998$	−30.5477	+	48.5722i	−0.966971	+	1.53753i
$999$	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.607.1		128
4.3	odd	2	inner	900.2.bf.e.607.28		128
5.2	odd	4		180.2.x.a.103.18	yes	128
5.3	odd	4	inner	900.2.bf.e.643.15		128
5.4	even	2		180.2.x.a.67.32	yes	128
9.7	even	3	inner	900.2.bf.e.7.21		128
15.2	even	4		540.2.y.a.523.15		128
15.14	odd	2		540.2.y.a.307.1		128
20.3	even	4	inner	900.2.bf.e.643.21		128
20.7	even	4		180.2.x.a.103.12	yes	128
20.19	odd	2		180.2.x.a.67.5	yes	128
36.7	odd	6	inner	900.2.bf.e.7.15		128
45.2	even	12		540.2.y.a.343.28		128
45.7	odd	12		180.2.x.a.43.5	yes	128
45.29	odd	6		540.2.y.a.127.21		128
45.34	even	6		180.2.x.a.7.12	✓	128
45.43	odd	12	inner	900.2.bf.e.43.28		128
60.47	odd	4		540.2.y.a.523.21		128
60.59	even	2		540.2.y.a.307.28		128
180.7	even	12		180.2.x.a.43.32	yes	128
180.43	even	12	inner	900.2.bf.e.43.1		128
180.47	odd	12		540.2.y.a.343.1		128
180.79	odd	6		180.2.x.a.7.18	yes	128
180.119	even	6		540.2.y.a.127.15		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.x.a.7.12	✓	128	45.34	even	6
180.2.x.a.7.18	yes	128	180.79	odd	6
180.2.x.a.43.5	yes	128	45.7	odd	12
180.2.x.a.43.32	yes	128	180.7	even	12
180.2.x.a.67.5	yes	128	20.19	odd	2
180.2.x.a.67.32	yes	128	5.4	even	2
180.2.x.a.103.12	yes	128	20.7	even	4
180.2.x.a.103.18	yes	128	5.2	odd	4
540.2.y.a.127.15		128	180.119	even	6
540.2.y.a.127.21		128	45.29	odd	6
540.2.y.a.307.1		128	15.14	odd	2
540.2.y.a.307.28		128	60.59	even	2
540.2.y.a.343.1		128	180.47	odd	12
540.2.y.a.343.28		128	45.2	even	12
540.2.y.a.523.15		128	15.2	even	4
540.2.y.a.523.21		128	60.47	odd	4
900.2.bf.e.7.15		128	36.7	odd	6	inner
900.2.bf.e.7.21		128	9.7	even	3	inner
900.2.bf.e.43.1		128	180.43	even	12	inner
900.2.bf.e.43.28		128	45.43	odd	12	inner
900.2.bf.e.607.1		128	1.1	even	1	trivial
900.2.bf.e.607.28		128	4.3	odd	2	inner
900.2.bf.e.643.15		128	5.3	odd	4	inner
900.2.bf.e.643.21		128	20.3	even	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+(-1.41320 - 0.0534584i) q^{2} +(-1.72686 - 0.133985i) q^{3} +(1.99428 + 0.151095i) q^{4} +(2.43324 + 0.281664i) q^{6} +(2.46165 + 0.659597i) q^{7} +(-2.81025 - 0.320139i) q^{8} +(2.96410 + 0.462748i) q^{9} +(-3.01796 + 1.74242i) q^{11} +(-3.42361 - 0.528125i) q^{12} +(1.36518 + 5.09493i) q^{13} +(-3.44355 - 1.06374i) q^{14} +(3.95434 + 0.602653i) q^{16} +(-2.16382 - 2.16382i) q^{17} +(-4.16413 - 0.812413i) q^{18} -3.88577 q^{19} +(-4.16255 - 1.46886i) q^{21} +(4.35813 - 2.30106i) q^{22} +(3.70190 - 0.991920i) q^{23} +(4.81002 + 0.929369i) q^{24} +(-1.65691 - 7.27315i) q^{26} +(-5.05658 - 1.19625i) q^{27} +(4.80957 + 1.68737i) q^{28} +(3.85118 - 2.22348i) q^{29} +(1.86992 + 1.07960i) q^{31} +(-5.55607 - 1.06306i) q^{32} +(5.44505 - 2.60455i) q^{33} +(2.94224 + 3.17359i) q^{34} +(5.84133 + 1.37071i) q^{36} +(-3.67542 - 3.67542i) q^{37} +(5.49138 + 0.207727i) q^{38} +(-1.67483 - 8.98115i) q^{39} +(-4.04792 + 7.01121i) q^{41} +(5.80400 + 2.29832i) 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} +(-6.74785 - 1.57052i) q^{48} +(-0.437526 - 0.252606i) q^{49} +(3.44669 + 4.02653i) q^{51} +(1.95274 + 10.3670i) q^{52} +(-0.265818 + 0.265818i) q^{53} +(7.08202 + 1.96086i) q^{54} +(-6.70669 - 2.64170i) q^{56} +(6.71018 + 0.520636i) q^{57} +(-5.56137 + 2.93635i) q^{58} +(-5.69158 + 9.85810i) q^{59} +(-4.61792 - 7.99848i) q^{61} +(-2.58487 - 1.62566i) q^{62} +(6.99134 + 3.09423i) q^{63} +(7.79502 + 1.79934i) q^{64} +(-7.83420 + 3.38968i) q^{66} +(0.192807 + 0.719566i) q^{67} +(-3.98832 - 4.64221i) q^{68} +(-6.52556 + 1.21691i) q^{69} +2.06980i q^{71} +(-8.18171 - 2.24936i) q^{72} +(-8.97449 + 8.97449i) q^{73} +(4.99763 + 5.39060i) q^{74} +(-7.74933 - 0.587121i) q^{76} +(-8.57845 + 2.29859i) q^{77} +(1.88676 + 12.7817i) q^{78} +(7.56173 + 13.0973i) q^{79} +(8.57173 + 2.74326i) q^{81} +(6.09534 - 9.69186i) q^{82} +(-4.01723 + 14.9925i) q^{83} +(-8.07937 - 3.55826i) q^{84} +(2.19627 - 7.10978i) q^{86} +(-6.94837 + 3.32364i) q^{87} +(9.03903 - 3.93047i) q^{88} -3.61495i q^{89} +13.4424i q^{91} +(7.53251 - 1.41883i) q^{92} +(-3.08444 - 2.11486i) q^{93} +(0.323910 + 0.100059i) q^{94} +(9.45212 + 2.58020i) q^{96} +(0.818990 - 3.05651i) q^{97} +(0.604809 + 0.380373i) 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

Varieties

Fields

Representations

Groups

Database

Properties

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