LMFDB - Embedded newform 900.2.o.b.599.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(299,900)] 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("900.299"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 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.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,6,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			599.5
Character	$\chi$	$=$	900.599
Dual form			900.2.o.b.299.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19709 + 0.752973i) q^{2} +(0.425108 - 1.67907i) q^{3} +(0.866065 - 1.80276i) q^{4} +(0.755401 + 2.33010i) q^{6} +(1.08216 + 1.87435i) q^{7} +(0.320666 + 2.81019i) q^{8} +(-2.63857 - 1.42758i) q^{9} +(-1.44632 - 2.50510i) q^{11} +(-2.65879 - 2.22055i) q^{12} +(5.72095 + 3.30299i) q^{13} +(-2.70678 - 1.42894i) q^{14} +(-2.49986 - 3.12261i) q^{16} +5.08829 q^{17} +(4.23353 - 0.277827i) q^{18} +4.66790i q^{19} +(3.60721 - 1.02022i) q^{21} +(3.61766 + 1.90980i) q^{22} +(-2.50662 - 1.44720i) q^{23} +(4.85483 + 0.656214i) q^{24} +(-9.33557 + 0.353728i) q^{26} +(-3.51868 + 3.82347i) q^{27} +(4.31623 - 0.327557i) q^{28} +(5.99593 - 3.46175i) q^{29} +(4.51887 + 2.60897i) q^{31} +(5.34381 + 1.85572i) q^{32} +(-4.82109 + 1.36354i) q^{33} +(-6.09115 + 3.83134i) q^{34} +(-4.85874 + 3.52032i) q^{36} +4.58347i q^{37} +(-3.51480 - 5.58792i) q^{38} +(7.97798 - 8.20175i) q^{39} +(-4.18802 - 2.41795i) q^{41} +(-3.54997 + 3.93743i) q^{42} +(-2.20241 - 3.81468i) q^{43} +(-5.76870 + 0.437785i) q^{44} +(4.09035 - 0.154985i) q^{46} +(0.0167877 - 0.00969237i) q^{47} +(-6.30580 + 2.87000i) q^{48} +(1.15786 - 2.00548i) q^{49} +(2.16307 - 8.54360i) q^{51} +(10.9092 - 7.45287i) q^{52} +3.21239 q^{53} +(1.33322 - 7.22652i) q^{54} +(-4.92028 + 3.64212i) q^{56} +(7.83775 + 1.98436i) q^{57} +(-4.57108 + 8.65881i) q^{58} +(4.02651 - 6.97412i) q^{59} +(-0.321400 - 0.556681i) q^{61} +(-7.37400 + 0.279404i) q^{62} +(-0.179566 - 6.49047i) q^{63} +(-7.79435 + 1.80227i) q^{64} +(4.74459 - 5.26243i) q^{66} +(4.73363 - 8.19888i) q^{67} +(4.40678 - 9.17294i) q^{68} +(-3.49553 + 3.59357i) q^{69} -1.17635 q^{71} +(3.16566 - 7.87265i) q^{72} -2.32539i q^{73} +(-3.45123 - 5.48685i) q^{74} +(8.41509 + 4.04271i) q^{76} +(3.13030 - 5.42184i) q^{77} +(-3.37469 + 15.8255i) q^{78} +(14.6983 - 8.48606i) q^{79} +(4.92406 + 7.53350i) q^{81} +(6.83410 - 0.258947i) q^{82} +(1.64651 - 0.950613i) q^{83} +(1.28487 - 7.38650i) q^{84} +(5.50883 + 2.90817i) q^{86} +(-3.26361 - 11.5392i) q^{87} +(6.57603 - 4.86774i) q^{88} -3.72649i q^{89} +14.2974i q^{91} +(-4.77983 + 3.26545i) q^{92} +(6.30166 - 6.47842i) q^{93} +(-0.0127983 + 0.0242433i) q^{94} +(5.38759 - 8.18375i) q^{96} +(-10.0127 + 5.78082i) q^{97} +(0.123999 + 3.27258i) q^{98} +(0.239992 + 8.67461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} - 12 q^{8} - 4 q^{9} - 28 q^{12} + 30 q^{14} + 18 q^{18} - 4 q^{21} + 42 q^{22} + 28 q^{24} + 12 q^{29} + 48 q^{33} + 6 q^{34} + 42 q^{36} + 6 q^{38} - 60 q^{41} - 16 q^{42} - 12 q^{46} + 74 q^{48}+ \cdots - 84 q^{98}+O(q^{100}) $ 48 * q + 6 * q^6 - 12 * q^8 - 4 * q^9 - 28 * q^12 + 30 * q^14 + 18 * q^18 - 4 * q^21 + 42 * q^22 + 28 * q^24 + 12 * q^29 + 48 * q^33 + 6 * q^34 + 42 * q^36 + 6 * q^38 - 60 * q^41 - 16 * q^42 - 12 * q^46 + 74 * q^48 - 24 * q^49 + 90 * q^52 + 32 * q^54 - 42 * q^56 + 16 * q^57 - 84 * q^58 - 84 * q^62 + 48 * q^64 + 16 * q^66 - 6 * q^68 - 36 * q^69 + 80 * q^72 - 84 * q^74 + 6 * q^76 + 46 * q^78 - 50 * q^84 - 54 * q^86 - 114 * q^88 + 42 * q^92 + 24 * q^93 - 18 * q^94 - 18 * q^96 + 48 * q^97 - 84 * q^98

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−1.19709	+	0.752973i	−0.846473	+	0.532432i
$2$	−1.19709	+	0.752973i	−0.846473	+	0.532432i
$3$	0.425108	−	1.67907i	0.245436	−	0.969413i
$3$	0.425108	−	1.67907i	0.245436	−	0.969413i
$4$	0.866065	−	1.80276i	0.433032	−	0.901378i
$5$		0			0
$5$		0			0
$6$	0.755401	+	2.33010i	0.308391	+	0.951260i
$7$	1.08216	+	1.87435i	0.409018	+	0.708440i	0.994780	−	0.102043i	$-0.0325381\pi$
$7$	1.08216	+	1.87435i	0.409018	+	0.708440i	−0.585762	+	0.810483i	$0.699205\pi$
$8$	0.320666	+	2.81019i	0.113373	+	0.993553i
$9$	−2.63857	−	1.42758i	−0.879522	−	0.475858i
$10$		0			0
$11$	−1.44632	−	2.50510i	−0.436083	−	0.755317i	0.561301	−	0.827612i	$-0.310301\pi$
$11$	−1.44632	−	2.50510i	−0.436083	−	0.755317i	−0.997383	+	0.0722948i	$0.976968\pi$
$12$	−2.65879	−	2.22055i	−0.767526	−	0.641018i
$13$	5.72095	+	3.30299i	1.58671	+	0.916085i	0.993845	+	0.110779i	$0.0353346\pi$
$13$	5.72095	+	3.30299i	1.58671	+	0.916085i	0.592860	+	0.805306i	$0.297999\pi$
$14$	−2.70678	−	1.42894i	−0.723418	−	0.381901i
$15$		0			0
$16$	−2.49986	−	3.12261i	−0.624966	−	0.780652i
$17$	5.08829			1.23409			0.617045	−	0.786928i	$-0.288330\pi$
$17$	5.08829			1.23409			0.617045	+	0.786928i	$0.288330\pi$
$18$	4.23353	−	0.277827i	0.997854	−	0.0654844i
$19$			4.66790i			1.07089i	0.844570	+	0.535445i	$0.179856\pi$
$19$			4.66790i			1.07089i	−0.844570	+	0.535445i	$0.820144\pi$
$20$		0			0
$21$	3.60721	−	1.02022i	0.787158	−	0.222630i
$22$	3.61766	+	1.90980i	0.771287	+	0.407171i
$23$	−2.50662	−	1.44720i	−0.522666	−	0.301761i	0.215359	−	0.976535i	$-0.430908\pi$
$23$	−2.50662	−	1.44720i	−0.522666	−	0.301761i	−0.738025	+	0.674774i	$0.764241\pi$
$24$	4.85483	+	0.656214i	0.990988	+	0.133949i
$25$		0			0
$26$	−9.33557	+	0.353728i	−1.83086	+	0.0693718i
$27$	−3.51868	+	3.82347i	−0.677170	+	0.735827i
$28$	4.31623	−	0.327557i	0.815690	−	0.0619025i
$29$	5.99593	−	3.46175i	1.11342	−	0.642831i	0.173704	−	0.984798i	$-0.444427\pi$
$29$	5.99593	−	3.46175i	1.11342	−	0.642831i	0.939712	+	0.341967i	$0.111093\pi$
$30$		0			0
$31$	4.51887	+	2.60897i	0.811613	+	0.468585i	0.847516	−	0.530770i	$-0.178097\pi$
$31$	4.51887	+	2.60897i	0.811613	+	0.468585i	−0.0359024	+	0.999355i	$0.511431\pi$
$32$	5.34381	+	1.85572i	0.944661	+	0.328049i
$33$	−4.82109	+	1.36354i	−0.839245	+	0.237362i
$34$	−6.09115	+	3.83134i	−1.04462	+	0.657069i
$35$		0			0
$36$	−4.85874	+	3.52032i	−0.809790	+	0.586720i
$37$			4.58347i			0.753518i	0.926311	+	0.376759i	$0.122962\pi$
$37$			4.58347i			0.753518i	−0.926311	+	0.376759i	$0.877038\pi$
$38$	−3.51480	−	5.58792i	−0.570176	−	0.906480i
$39$	7.97798	−	8.20175i	1.27750	−	1.31333i
$40$		0			0
$41$	−4.18802	−	2.41795i	−0.654059	−	0.377621i	0.135951	−	0.990716i	$-0.456591\pi$
$41$	−4.18802	−	2.41795i	−0.654059	−	0.377621i	−0.790009	+	0.613095i	$0.789924\pi$
$42$	−3.54997	+	3.93743i	−0.547773	+	0.607559i
$43$	−2.20241	−	3.81468i	−0.335864	−	0.581733i	0.647787	−	0.761822i	$-0.275695\pi$
$43$	−2.20241	−	3.81468i	−0.335864	−	0.581733i	−0.983650	+	0.180089i	$0.942361\pi$
$44$	−5.76870	+	0.437785i	−0.869664	+	0.0659986i
$45$		0			0
$46$	4.09035	−	0.154985i	0.603089	−	0.0228513i
$47$	0.0167877	−	0.00969237i	0.00244874	−	0.00141378i	−0.498775	−	0.866731i	$-0.666217\pi$
$47$	0.0167877	−	0.00969237i	0.00244874	−	0.00141378i	0.501224	+	0.865318i	$0.332883\pi$
$48$	−6.30580	+	2.87000i	−0.910163	+	0.414249i
$49$	1.15786	−	2.00548i	0.165409	−	0.286497i
$50$		0			0
$51$	2.16307	−	8.54360i	0.302891	−	1.19634i
$52$	10.9092	−	7.45287i	1.51283	−	1.03353i
$53$	3.21239			0.441256			0.220628	−	0.975358i	$-0.429189\pi$
$53$	3.21239			0.441256			0.220628	+	0.975358i	$0.429189\pi$
$54$	1.33322	−	7.22652i	0.181428	−	0.983404i
$55$		0			0
$56$	−4.92028	+	3.64212i	−0.657501	+	0.486698i
$57$	7.83775	+	1.98436i	1.03813	+	0.262836i
$58$	−4.57108	+	8.65881i	−0.600212	+	1.13696i
$59$	4.02651	−	6.97412i	0.524207	−	0.907953i	−0.475396	−	0.879772i	$-0.657695\pi$
$59$	4.02651	−	6.97412i	0.524207	−	0.907953i	0.999603	−	0.0281811i	$-0.00897150\pi$
$60$		0			0
$61$	−0.321400	−	0.556681i	−0.0411510	−	0.0712757i	0.844716	−	0.535214i	$-0.179769\pi$
$61$	−0.321400	−	0.556681i	−0.0411510	−	0.0712757i	−0.885867	+	0.463939i	$0.846436\pi$
$62$	−7.37400	+	0.279404i	−0.936499	+	0.0354843i
$63$	−0.179566	−	6.49047i	−0.0226232	−	0.817723i
$64$	−7.79435	+	1.80227i	−0.974293	+	0.225283i
$65$		0			0
$66$	4.74459	−	5.26243i	0.584019	−	0.647761i
$67$	4.73363	−	8.19888i	0.578304	−	1.00165i	−0.417370	−	0.908737i	$-0.637048\pi$
$67$	4.73363	−	8.19888i	0.578304	−	1.00165i	0.995674	−	0.0929158i	$-0.0296187\pi$
$68$	4.40678	−	9.17294i	0.534401	−	1.11238i
$69$	−3.49553	+	3.59357i	−0.420812	+	0.432615i
$70$		0			0
$71$	−1.17635			−0.139607			−0.0698035	−	0.997561i	$-0.522237\pi$
$71$	−1.17635			−0.139607			−0.0698035	+	0.997561i	$0.522237\pi$
$72$	3.16566	−	7.87265i	0.373077	−	0.927801i
$73$		−	2.32539i		−	0.272166i	−0.990697	−	0.136083i	$-0.956549\pi$
$73$		−	2.32539i		−	0.272166i	0.990697	−	0.136083i	$-0.0434514\pi$
$74$	−3.45123	−	5.48685i	−0.401197	−	0.637833i
$75$		0			0
$76$	8.41509	+	4.04271i	0.965278	+	0.463730i
$77$	3.13030	−	5.42184i	0.356731	−	0.617876i
$78$	−3.37469	+	15.8255i	−0.382109	+	1.79188i
$79$	14.6983	−	8.48606i	1.65369	−	0.954756i	0.678148	−	0.734926i	$-0.262783\pi$
$79$	14.6983	−	8.48606i	1.65369	−	0.954756i	0.975538	−	0.219830i	$-0.0705503\pi$
$80$		0			0
$81$	4.92406	+	7.53350i	0.547118	+	0.837056i
$82$	6.83410	−	0.258947i	0.754700	−	0.0285959i
$83$	1.64651	−	0.950613i	0.180728	−	0.104343i	−0.406907	−	0.913470i	$-0.633393\pi$
$83$	1.64651	−	0.950613i	0.180728	−	0.104343i	0.587635	+	0.809126i	$0.300059\pi$
$84$	1.28487	−	7.38650i	0.140191	−	0.805933i
$85$		0			0
$86$	5.50883	+	2.90817i	0.594033	+	0.313597i
$87$	−3.26361	−	11.5392i	−0.349896	−	1.23713i
$88$	6.57603	−	4.86774i	0.701007	−	0.518903i
$89$		−	3.72649i		−	0.395007i	−0.980302	−	0.197503i	$-0.936717\pi$
$89$		−	3.72649i		−	0.395007i	0.980302	−	0.197503i	$-0.0632834\pi$
$90$		0			0
$91$			14.2974i			1.49878i
$92$	−4.77983	+	3.26545i	−0.498332	+	0.340447i
$93$	6.30166	−	6.47842i	0.653452	−	0.671780i
$94$	−0.0127983	+	0.0242433i	−0.00132005	+	0.00250051i
$95$		0			0
$96$	5.38759	−	8.18375i	0.549869	−	0.835251i
$97$	−10.0127	+	5.78082i	−1.01663	+	0.586953i	−0.913127	−	0.407675i	$-0.866339\pi$
$97$	−10.0127	+	5.78082i	−1.01663	+	0.586953i	−0.103506	+	0.994629i	$0.533006\pi$
$98$	0.123999	+	3.27258i	0.0125258	+	0.330581i
$99$	0.239992	+	8.67461i	0.0241201	+	0.871831i
$100$		0			0
$101$	−9.46327	+	5.46362i	−0.941630	+	0.543650i	−0.890471	−	0.455040i	$-0.849625\pi$
$101$	−9.46327	+	5.46362i	−0.941630	+	0.543650i	−0.0511591	+	0.998691i	$0.516292\pi$
$102$	3.84369	+	11.8562i	0.380582	+	1.17394i
$103$	−0.317664	+	0.550211i	−0.0313004	+	0.0542139i	−0.881251	−	0.472648i	$-0.843298\pi$
$103$	−0.317664	+	0.550211i	−0.0313004	+	0.0542139i	0.849951	+	0.526862i	$0.176632\pi$
$104$	−7.44752	+	17.1361i	−0.730289	+	1.68033i
$105$		0			0
$106$	−3.84553	+	2.41884i	−0.373511	+	0.234939i
$107$			18.8050i			1.81795i	0.416850	+	0.908975i	$0.363134\pi$
$107$			18.8050i			1.81795i	−0.416850	+	0.908975i	$0.636866\pi$
$108$	3.84538	+	9.65469i	0.370022	+	0.929023i
$109$	3.39053			0.324754			0.162377	−	0.986729i	$-0.448084\pi$
$109$	3.39053			0.324754			0.162377	+	0.986729i	$0.448084\pi$
$110$		0			0
$111$	7.69598	+	1.94847i	0.730470	+	0.184941i
$112$	3.14763	−	8.06479i	0.297423	−	0.762051i
$113$	−0.499103	+	0.864471i	−0.0469516	+	0.0813226i	−0.888546	−	0.458787i	$-0.848284\pi$
$113$	−0.499103	+	0.864471i	−0.0469516	+	0.0813226i	0.841595	+	0.540110i	$0.181617\pi$
$114$	−10.8767	+	3.52614i	−1.01869	+	0.330253i
$115$		0			0
$116$	−1.04783	−	13.8073i	−0.0972888	−	1.28198i
$117$	−10.3798	−	16.8822i	−0.959615	−	1.56076i
$118$	0.431213	+	11.3805i	0.0396963	+	1.04766i
$119$	5.50634	+	9.53725i	0.504765	+	0.874279i
$120$		0			0
$121$	1.31630	−	2.27991i	0.119664	−	0.207264i
$122$	0.803911	+	0.424394i	0.0727827	+	0.0384228i
$123$	−5.84028	+	6.00409i	−0.526600	+	0.541371i
$124$	8.61698	−	5.88689i	0.773828	−	0.528658i
$125$		0			0
$126$	5.10210	+	7.63449i	0.454532	+	0.680135i
$127$	8.78450			0.779498			0.389749	−	0.920921i	$-0.372562\pi$
$127$	8.78450			0.779498			0.389749	+	0.920921i	$0.372562\pi$
$128$	7.97350	−	8.02641i	0.704765	−	0.709441i
$129$	−7.34138	+	2.07635i	−0.646372	+	0.182812i
$130$		0			0
$131$	−7.06346	+	12.2343i	−0.617137	+	1.06891i	0.372868	+	0.927884i	$0.378374\pi$
$131$	−7.06346	+	12.2343i	−0.617137	+	1.06891i	−0.990005	+	0.141029i	$0.954959\pi$
$132$	−1.71725	+	9.87217i	−0.149467	+	0.859262i
$133$	−8.74931	+	5.05142i	−0.758661	+	0.438013i
$134$	0.506940	+	13.3791i	0.0437929	+	1.15578i
$135$		0			0
$136$	1.63164	+	14.2991i	0.139912	+	1.22613i
$137$	7.60127	+	13.1658i	0.649420	+	1.12483i	0.983262	+	0.182200i	$0.0583217\pi$
$137$	7.60127	+	13.1658i	0.649420	+	1.12483i	−0.333841	+	0.942629i	$0.608345\pi$
$138$	1.47861	−	6.93388i	0.125868	−	0.590251i
$139$	−2.20036	−	1.27038i	−0.186632	−	0.107752i	0.403773	−	0.914859i	$-0.367699\pi$
$139$	−2.20036	−	1.27038i	−0.186632	−	0.107752i	−0.590405	+	0.807107i	$0.701032\pi$
$140$		0			0
$141$	−0.00913761	−	0.0323080i	−0.000769525	−	0.00272083i
$142$	1.40820	−	0.885759i	0.118174	−	0.0743312i
$143$		−	19.1087i		−	1.59795i
$144$	2.13830	+	11.8080i	0.178191	+	0.983996i
$145$		0			0
$146$	1.75095	+	2.78371i	0.144910	+	0.230381i
$147$	−2.87512	−	2.79668i	−0.237136	−	0.230666i
$148$	8.26289	+	3.96959i	0.679205	+	0.326298i
$149$	−5.98481	−	3.45533i	−0.490294	−	0.283072i	0.234402	−	0.972140i	$-0.424687\pi$
$149$	−5.98481	−	3.45533i	−0.490294	−	0.283072i	−0.724697	+	0.689068i	$0.758020\pi$
$150$		0			0
$151$	18.4571	−	10.6562i	1.50202	−	0.867191i	0.502021	−	0.864855i	$-0.332590\pi$
$151$	18.4571	−	10.6562i	1.50202	−	0.867191i	0.999997	−	0.00233576i	$-0.000743497\pi$
$152$	−13.1177	+	1.49684i	−1.06399	+	0.121410i
$153$	−13.4258	−	7.26391i	−1.08541	−	0.587252i
$154$	0.335235	+	8.84748i	0.0270140	+	0.712950i
$155$		0			0
$156$	−7.87632	−	21.4856i	−0.630610	−	1.72023i
$157$	−10.1062	−	5.83484i	−0.806566	−	0.465671i	0.0391957	−	0.999232i	$-0.487520\pi$
$157$	−10.1062	−	5.83484i	−0.806566	−	0.465671i	−0.845762	+	0.533560i	$0.820854\pi$
$158$	−11.2054	+	21.2260i	−0.891457	+	1.68865i
$159$	1.36561	−	5.39384i	0.108300	−	0.427759i
$160$		0			0
$161$		−	6.26438i		−	0.493703i
$162$	−11.5671	−	5.31062i	−0.908795	−	0.417242i
$163$	0.438006			0.0343073			0.0171536	−	0.999853i	$-0.494540\pi$
$163$	0.438006			0.0343073			0.0171536	+	0.999853i	$0.494540\pi$
$164$	−7.98608	+	5.45587i	−0.623608	+	0.426032i
$165$		0			0
$166$	−1.25524	+	2.37775i	−0.0974256	+	0.184549i
$167$	3.60751	+	2.08280i	0.279157	+	0.161172i	0.633042	−	0.774118i	$-0.281806\pi$
$167$	3.60751	+	2.08280i	0.279157	+	0.161172i	−0.353884	+	0.935289i	$0.615139\pi$
$168$	4.02372	+	9.80980i	0.310437	+	0.756843i
$169$	15.3195	+	26.5341i	1.17842	+	2.04109i
$170$		0			0
$171$	6.66378	−	12.3166i	0.509592	−	0.941872i
$172$	−8.78436	+	0.666643i	−0.669801	+	0.0508311i
$173$	−4.47638	−	7.75332i	−0.340333	−	0.589474i	0.644162	−	0.764889i	$-0.277206\pi$
$173$	−4.47638	−	7.75332i	−0.340333	−	0.589474i	−0.984494	+	0.175416i	$0.943873\pi$
$174$	12.5956	+	11.3561i	0.954866	+	0.860904i
$175$		0			0
$176$	−4.20685	+	10.7787i	−0.317103	+	0.812476i
$177$	−9.99835	−	9.72556i	−0.751522	−	0.731018i
$178$	2.80594	+	4.46095i	0.210314	+	0.334363i
$179$	−10.5263			−0.786776			−0.393388	−	0.919373i	$-0.628697\pi$
$179$	−10.5263			−0.786776			−0.393388	+	0.919373i	$0.628697\pi$
$180$		0			0
$181$	−9.50854			−0.706765			−0.353382	−	0.935479i	$-0.614968\pi$
$181$	−9.50854			−0.706765			−0.353382	+	0.935479i	$0.614968\pi$
$182$	−10.7656	−	17.1154i	−0.797998	−	1.26868i
$183$	−1.07134	+	0.303004i	−0.0791955	+	0.0223987i
$184$	3.26311	−	7.50814i	0.240560	−	0.553507i
$185$		0			0
$186$	−2.66561	+	12.5002i	−0.195452	+	0.916563i
$187$	−7.35930	−	12.7467i	−0.538165	−	0.932130i
$188$	−0.00293377	−	0.0386583i	−0.000213967	−	0.00281945i
$189$	−10.9743	−	2.45765i	−0.798263	−	0.178768i
$190$		0			0
$191$	−6.08040	−	10.5316i	−0.439963	−	0.762038i	0.557723	−	0.830027i	$-0.311675\pi$
$191$	−6.08040	−	10.5316i	−0.439963	−	0.762038i	−0.997686	+	0.0679893i	$0.978342\pi$
$192$	−0.287309	+	13.8534i	−0.0207347	+	0.999785i
$193$	−12.1493	−	7.01439i	−0.874525	−	0.504907i	−0.00567551	−	0.999984i	$-0.501807\pi$
$193$	−12.1493	−	7.01439i	−0.874525	−	0.504907i	−0.868849	+	0.495077i	$0.835140\pi$
$194$	7.63331	−	14.4595i	0.548040	−	1.03813i
$195$		0			0
$196$	−2.61260	−	3.82422i	−0.186614	−	0.273158i
$197$	7.21555			0.514086			0.257043	−	0.966400i	$-0.417252\pi$
$197$	7.21555			0.514086			0.257043	+	0.966400i	$0.417252\pi$
$198$	−6.81904	−	10.2036i	−0.484608	−	0.725139i
$199$			8.63093i			0.611830i	0.952059	+	0.305915i	$0.0989624\pi$
$199$			8.63093i			0.611830i	−0.952059	+	0.305915i	$0.901038\pi$
$200$		0			0
$201$	−11.7542	−	11.4335i	−0.829078	−	0.806458i
$202$	7.21446	−	13.6660i	0.507607	−	0.961539i
$203$	12.9771	+	7.49233i	0.910814	+	0.525858i
$204$	−13.5287	−	11.2988i	−0.947196	−	0.791074i
$205$		0			0
$206$	−0.0340198	−	0.897846i	−0.00237027	−	0.0625559i
$207$	4.54789	+	7.39690i	0.316100	+	0.514120i
$208$	−3.98764	−	26.1213i	−0.276493	−	1.81119i
$209$	11.6936	−	6.75129i	0.808862	−	0.466997i
$210$		0			0
$211$	−16.1103	−	9.30130i	−1.10908	−	0.640328i	−0.170490	−	0.985359i	$-0.554535\pi$
$211$	−16.1103	−	9.30130i	−1.10908	−	0.640328i	−0.938591	+	0.345031i	$0.887868\pi$
$212$	2.78214	−	5.79116i	0.191078	−	0.397739i
$213$	−0.500076	+	1.97518i	−0.0342647	+	0.135337i
$214$	−14.1597	−	22.5114i	−0.967935	−	1.53885i
$215$		0			0
$216$	−11.8730	−	8.66210i	−0.807855	−	0.589381i
$217$			11.2933i			0.766639i
$218$	−4.05878	+	2.55298i	−0.274895	+	0.172909i
$219$	−3.90450	−	0.988543i	−0.263841	−	0.0667995i
$220$		0			0
$221$	29.1098	+	16.8066i	1.95814	+	1.13053i
$222$	−10.6800	+	3.46236i	−0.716792	+	0.232378i
$223$	−6.17187	−	10.6900i	−0.413299	−	0.715854i	0.581949	−	0.813225i	$-0.302290\pi$
$223$	−6.17187	−	10.6900i	−0.413299	−	0.715854i	−0.995248	+	0.0973706i	$0.968957\pi$
$224$	2.30457	+	12.0244i	0.153980	+	0.803413i
$225$		0			0
$226$	−0.0534506	−	1.41066i	−0.00355548	−	0.0938359i
$227$	0.644365	−	0.372024i	0.0427680	−	0.0246921i	−0.478464	−	0.878107i	$-0.658806\pi$
$227$	0.644365	−	0.372024i	0.0427680	−	0.0246921i	0.521232	+	0.853415i	$0.325473\pi$
$228$	10.3653	−	12.4110i	0.686460	−	0.821936i
$229$	−13.0783	+	22.6523i	−0.864238	+	1.49690i	0.00356308	+	0.999994i	$0.498866\pi$
$229$	−13.0783	+	22.6523i	−0.864238	+	1.49690i	−0.867801	+	0.496911i	$0.834468\pi$
$230$		0			0
$231$	−7.77295	−	7.56087i	−0.511422	−	0.497469i
$232$	11.6509	+	15.7396i	0.764917	+	1.03336i
$233$	25.8264			1.69195			0.845973	−	0.533226i	$-0.179021\pi$
$233$	25.8264			1.69195			0.845973	+	0.533226i	$0.179021\pi$
$234$	25.1375	+	12.3939i	1.64329	+	0.810214i
$235$		0			0
$236$	−9.08542	−	13.2989i	−0.591411	−	0.865682i
$237$	−8.00034	−	28.2870i	−0.519678	−	1.83744i
$238$	−13.7729	−	7.27086i	−0.892764	−	0.471300i
$239$	−4.11600	+	7.12913i	−0.266242	+	0.461145i	−0.967888	−	0.251381i	$-0.919115\pi$
$239$	−4.11600	+	7.12913i	−0.266242	+	0.461145i	0.701646	+	0.712526i	$0.252449\pi$
$240$		0			0
$241$	0.0705544	+	0.122204i	0.00454481	+	0.00787184i	0.868289	−	0.496059i	$-0.165220\pi$
$241$	0.0705544	+	0.122204i	0.00454481	+	0.00787184i	−0.863744	+	0.503931i	$0.831887\pi$
$242$	0.140967	+	3.72040i	0.00906173	+	0.239156i
$243$	14.7426	−	5.06529i	0.945735	−	0.324939i
$244$	−1.28191	+	0.0972841i	−0.0820661	+	0.00622797i
$245$		0			0
$246$	2.47044	−	11.5850i	0.157510	−	0.738634i
$247$	−15.4180	+	26.7048i	−0.981026	+	1.69919i
$248$	−5.88266	+	13.5355i	−0.373549	+	0.859505i
$249$	−0.896202	−	3.16872i	−0.0567945	−	0.200810i
$250$		0			0
$251$	−9.50499			−0.599950			−0.299975	−	0.953947i	$-0.596978\pi$
$251$	−9.50499			−0.599950			−0.299975	+	0.953947i	$0.596978\pi$
$252$	−11.8563	−	5.29746i	−0.746874	−	0.333708i
$253$			8.37244i			0.526371i
$254$	−10.5159	+	6.61449i	−0.659824	+	0.415030i
$255$		0			0
$256$	−3.50136	+	15.6122i	−0.218835	+	0.975762i
$257$	−12.9923	+	22.5033i	−0.810436	+	1.40372i	0.102123	+	0.994772i	$0.467436\pi$
$257$	−12.9923	+	22.5033i	−0.810436	+	1.40372i	−0.912559	+	0.408945i	$0.865897\pi$
$258$	7.22489	−	8.01344i	0.449802	−	0.498895i
$259$	−8.59106	+	4.96005i	−0.533822	+	0.308202i
$260$		0			0
$261$	−20.7626	+	0.574418i	−1.28517	+	0.0355556i
$262$	−0.756450	−	19.9642i	−0.0467336	−	1.23339i
$263$	−23.2758	+	13.4383i	−1.43525	+	0.828640i	−0.997514	−	0.0704654i	$-0.977552\pi$
$263$	−23.2758	+	13.4383i	−1.43525	+	0.828640i	−0.437732	+	0.899105i	$0.644218\pi$
$264$	−5.37776	−	13.1110i	−0.330979	−	0.806923i
$265$		0			0
$266$	6.67016	−	12.6350i	0.408974	−	0.774702i
$267$	−6.25704	−	1.58416i	−0.382925	−	0.0969491i
$268$	−10.6810	−	15.6343i	−0.652443	−	0.955019i
$269$		−	16.4030i		−	1.00011i	−0.865995	−	0.500053i	$-0.833314\pi$
$269$		−	16.4030i		−	1.00011i	0.865995	−	0.500053i	$-0.166686\pi$
$270$		0			0
$271$			16.0484i			0.974873i	0.873158	+	0.487437i	$0.162068\pi$
$271$			16.0484i			0.974873i	−0.873158	+	0.487437i	$0.837932\pi$
$272$	−12.7200	−	15.8887i	−0.771264	−	0.963395i
$273$	24.0064	+	6.07796i	1.45294	+	0.367855i
$274$	−19.0129	−	10.0371i	−1.14861	−	0.606365i
$275$		0			0
$276$	3.45098	+	9.41386i	0.207725	+	0.566647i
$277$	−21.0720	+	12.1659i	−1.26609	+	0.730978i	−0.974246	−	0.225488i	$-0.927602\pi$
$277$	−21.0720	+	12.1659i	−1.26609	+	0.730978i	−0.291845	+	0.956466i	$0.594269\pi$
$278$	3.59060	−	0.136049i	0.215350	−	0.00815969i
$279$	−8.19884	−	13.3350i	−0.490852	−	0.798344i
$280$		0			0
$281$	9.04166	−	5.22020i	0.539380	−	0.311411i	−0.205448	−	0.978668i	$-0.565865\pi$
$281$	9.04166	−	5.22020i	0.539380	−	0.311411i	0.744828	+	0.667257i	$0.232532\pi$
$282$	0.0352656	+	0.0317954i	0.00210004	+	0.00189339i
$283$	−7.44455	+	12.8943i	−0.442533	+	0.766489i	−0.997877	−	0.0651317i	$-0.979253\pi$
$283$	−7.44455	+	12.8943i	−0.442533	+	0.766489i	0.555344	+	0.831621i	$0.312587\pi$
$284$	−1.01880	+	2.12067i	−0.0604544	+	0.125839i
$285$		0			0
$286$	14.3884	+	22.8750i	0.850802	+	1.35262i
$287$		−	10.4664i		−	0.617815i
$288$	−11.4508	−	12.5251i	−0.674745	−	0.738051i
$289$	8.89065			0.522979
$290$		0			0
$291$	5.44994	+	19.2695i	0.319481	+	1.12960i
$292$	−4.19211	−	2.01394i	−0.245325	−	0.117857i
$293$	−13.0589	+	22.6187i	−0.762911	+	1.32140i	0.178433	+	0.983952i	$0.442897\pi$
$293$	−13.0589	+	22.6187i	−0.762911	+	1.32140i	−0.941344	+	0.337449i	$0.890436\pi$
$294$	5.54761	+	1.18300i	0.323543	+	0.0689938i
$295$		0			0
$296$	−12.8804	+	1.46976i	−0.748660	+	0.0854283i
$297$	14.6673	+	3.28469i	0.851084	+	0.190597i
$298$	9.76614	−	0.370043i	0.565737	−	0.0214360i
$299$	−9.56014	−	16.5587i	−0.552877	−	0.957612i
$300$		0			0
$301$	4.76671	−	8.25618i	0.274748	−	0.475878i
$302$	−14.0710	+	26.6542i	−0.809698	+	1.53378i
$303$	5.15090	+	18.2121i	0.295911	+	1.04626i
$304$	14.5760	−	11.6691i	0.835993	−	0.669270i
$305$		0			0
$306$	21.5414	−	1.41366i	1.23144	−	0.0808137i
$307$	28.5542			1.62967			0.814837	−	0.579690i	$-0.196826\pi$
$307$	28.5542			1.62967			0.814837	+	0.579690i	$0.196826\pi$
$308$	−7.06322	−	10.3388i	−0.402464	−	0.589110i
$309$	0.788802	+	0.767281i	0.0448734	+	0.0436491i
$310$		0			0
$311$	0.0440224	−	0.0762490i	0.00249628	−	0.00432369i	−0.864775	−	0.502160i	$-0.832539\pi$
$311$	0.0440224	−	0.0762490i	0.00249628	−	0.00432369i	0.867271	+	0.497837i	$0.165872\pi$
$312$	25.6068	+	19.7896i	1.44970	+	1.12037i
$313$	−13.1775	+	7.60804i	−0.744837	+	0.430032i	−0.823825	−	0.566844i	$-0.808164\pi$
$313$	−13.1775	+	7.60804i	−0.744837	+	0.430032i	0.0789885	+	0.996876i	$0.474831\pi$
$314$	16.4916	−	0.624873i	0.930675	−	0.0352636i
$315$		0			0
$316$	−2.56863	−	33.8469i	−0.144497	−	1.90404i
$317$	3.58277	+	6.20554i	0.201228	+	0.348538i	0.948925	−	0.315503i	$-0.102173\pi$
$317$	3.58277	+	6.20554i	0.201228	+	0.348538i	−0.747696	+	0.664041i	$0.768840\pi$
$318$	2.42664	+	7.48520i	0.136079	+	0.419749i
$319$	−17.3441	−	10.0136i	−0.971082	−	0.560655i
$320$		0			0
$321$	31.5750	+	7.99417i	1.76234	+	0.446191i
$322$	4.71691	+	7.49905i	0.262863	+	0.417906i
$323$			23.7516i			1.32158i
$324$	17.8456	−	2.35238i	0.991424	−	0.130688i
$325$		0			0
$326$	−0.524334	+	0.329807i	−0.0290402	+	0.0182663i
$327$	1.44134	−	5.69295i	0.0797065	−	0.314821i
$328$	5.45196	−	12.5445i	0.301034	−	0.692653i
$329$	0.0363339	+	0.0209774i	0.00200315	+	0.00115652i
$330$		0			0
$331$	−0.709837	+	0.409824i	−0.0390161	+	0.0225260i	−0.519381	−	0.854543i	$-0.673838\pi$
$331$	−0.709837	+	0.409824i	−0.0390161	+	0.0225260i	0.480365	+	0.877069i	$0.340504\pi$
$332$	−0.287740	−	3.79155i	−0.0157918	−	0.208088i
$333$	6.54325	−	12.0938i	0.358568	−	0.662736i
$334$	−5.88681	+	0.223054i	−0.322112	+	0.0122050i
$335$		0			0
$336$	−12.2033	−	8.71350i	−0.665744	−	0.475360i
$337$	2.65680	+	1.53390i	0.144725	+	0.0835571i	0.570614	−	0.821218i	$-0.306705\pi$
$337$	2.65680	+	1.53390i	0.144725	+	0.0835571i	−0.425889	+	0.904775i	$0.640039\pi$
$338$	−38.3183	−	20.2287i	−2.08424	−	1.10029i
$339$	1.23934	+	1.20552i	0.0673115	+	0.0654750i
$340$		0			0
$341$		−	15.0937i		−	0.817367i
$342$	1.29687	+	19.7617i	0.0701266	+	1.06859i
$343$	20.1622			1.08866
$344$	10.0137	−	7.41242i	0.539904	−	0.399651i
$345$		0			0
$346$	11.1967	+	5.91085i	0.601937	+	0.317769i
$347$	−19.3234	−	11.1564i	−1.03734	−	0.598906i	−0.118258	−	0.992983i	$-0.537731\pi$
$347$	−19.3234	−	11.1564i	−1.03734	−	0.598906i	−0.919078	+	0.394077i	$0.871064\pi$
$348$	−23.6289	−	4.11021i	−1.26664	−	0.220330i
$349$	−5.01965	−	8.69429i	−0.268696	−	0.465395i	0.699829	−	0.714310i	$-0.253259\pi$
$349$	−5.01965	−	8.69429i	−0.268696	−	0.465395i	−0.968525	+	0.248915i	$0.919926\pi$
$350$		0			0
$351$	−32.7590	+	10.2517i	−1.74855	+	0.547195i
$352$	−3.08009	−	16.0708i	−0.164169	−	0.856575i
$353$	6.36616	+	11.0265i	0.338836	+	0.586882i	0.984214	−	0.176982i	$-0.0566334\pi$
$353$	6.36616	+	11.0265i	0.338836	+	0.586882i	−0.645378	+	0.763864i	$0.723300\pi$
$354$	19.2920	+	4.11392i	1.02536	+	0.218652i
$355$		0			0
$356$	−6.71795	−	3.22738i	−0.356051	−	0.171051i
$357$	18.3545	−	5.19117i	0.971424	−	0.274746i
$358$	12.6010	−	7.92605i	0.665984	−	0.418905i
$359$	5.93304			0.313134			0.156567	−	0.987667i	$-0.449957\pi$
$359$	5.93304			0.313134			0.156567	+	0.987667i	$0.449957\pi$
$360$		0			0
$361$	−2.78932			−0.146806
$362$	11.3826	−	7.15967i	0.598257	−	0.376304i
$363$	−3.26855	−	3.17938i	−0.171555	−	0.166874i
$364$	25.7748	+	12.3825i	1.35097	+	0.649020i
$365$		0			0
$366$	1.05434	−	1.16941i	0.0551111	−	0.0611261i
$367$	−13.3004	−	23.0370i	−0.694277	−	1.20252i	−0.970424	−	0.241407i	$-0.922391\pi$
$367$	−13.3004	−	23.0370i	−0.694277	−	1.20252i	0.276147	−	0.961115i	$-0.410942\pi$
$368$	1.74717	+	11.4450i	0.0910777	+	0.596610i
$369$	7.59855	+	12.3586i	0.395565	+	0.643365i
$370$		0			0
$371$	3.47632	+	6.02116i	0.180482	+	0.312603i
$372$	−6.22136	−	16.9711i	−0.322563	−	0.879910i
$373$	−22.9141	−	13.2294i	−1.18645	−	0.684995i	−0.228949	−	0.973438i	$-0.573529\pi$
$373$	−22.9141	−	13.2294i	−1.18645	−	0.684995i	−0.957497	+	0.288444i	$0.906862\pi$
$374$	18.4077	+	9.71762i	0.951838	+	0.502486i
$375$		0			0
$376$	0.0326207	+	0.0440686i	0.00168228	+	0.00227266i
$377$	45.7365			2.35555
$378$	14.9878	−	5.32131i	0.770890	−	0.273699i
$379$			21.3357i			1.09594i	0.836497	+	0.547972i	$0.184600\pi$
$379$			21.3357i			1.09594i	−0.836497	+	0.547972i	$0.815400\pi$
$380$		0			0
$381$	3.73436	−	14.7498i	0.191317	−	0.755655i
$382$	15.2088	+	8.02889i	0.778150	+	0.410794i
$383$	−2.73103	−	1.57676i	−0.139549	−	0.0805688i	0.428600	−	0.903494i	$-0.359007\pi$
$383$	−2.73103	−	1.57676i	−0.139549	−	0.0805688i	−0.568149	+	0.822926i	$0.692340\pi$
$384$	−10.0873	−	16.8002i	−0.514766	−	0.857331i
$385$		0			0
$386$	19.8255	−	0.751195i	1.00909	−	0.0382348i
$387$	0.365451	+	13.2094i	0.0185769	+	0.671470i
$388$	1.74979	+	23.0570i	0.0888321	+	1.17054i
$389$	−12.9948	+	7.50253i	−0.658860	+	0.380393i	−0.791843	−	0.610725i	$-0.790878\pi$
$389$	−12.9948	+	7.50253i	−0.658860	+	0.380393i	0.132982	+	0.991118i	$0.457545\pi$
$390$		0			0
$391$	−12.7544	−	7.36374i	−0.645017	−	0.372400i
$392$	6.00706	+	2.61073i	0.303402	+	0.131862i
$393$	17.5395	+	17.0610i	0.884750	+	0.860611i
$394$	−8.63768	+	5.43311i	−0.435160	+	0.273716i
$395$		0			0
$396$	15.8461	+	7.08013i	0.796295	+	0.355790i
$397$		−	10.0474i		−	0.504266i	−0.967693	−	0.252133i	$-0.918868\pi$
$397$		−	10.0474i		−	0.504266i	0.967693	−	0.252133i	$-0.0811320\pi$
$398$	−6.49885	−	10.3320i	−0.325758	−	0.517898i
$399$	4.76229	+	16.8381i	0.238412	+	0.842960i
$400$		0			0
$401$	−6.85153	−	3.95573i	−0.342149	−	0.197540i	0.319073	−	0.947730i	$-0.396629\pi$
$401$	−6.85153	−	3.95573i	−0.342149	−	0.197540i	−0.661222	+	0.750190i	$0.729962\pi$
$402$	22.6800	+	4.83639i	1.13118	+	0.241217i
$403$	17.2348	+	29.8516i	0.858527	+	1.48701i
$404$	1.65378	+	21.7918i	0.0822784	+	1.08418i
$405$		0			0
$406$	−21.1763	+	0.802379i	−1.05096	+	0.0398214i
$407$	11.4821	−	6.62918i	0.569145	−	0.328596i
$408$	24.7028	+	3.33901i	1.22297	+	0.165305i
$409$	13.5824	−	23.5255i	0.671608	−	1.16326i	−0.305840	−	0.952083i	$-0.598937\pi$
$409$	13.5824	−	23.5255i	0.671608	−	1.16326i	0.977448	−	0.211177i	$-0.0677295\pi$
$410$		0			0
$411$	25.3377	−	7.16619i	1.24981	−	0.353482i
$412$	0.716778	+	1.04919i	0.0353131	+	0.0516899i
$413$	17.4293			0.857640
$414$	−11.0139	−	5.43035i	−0.541304	−	0.266887i
$415$		0			0
$416$	24.4422	+	28.2670i	1.19838	+	1.38591i
$417$	−3.06845	+	3.15452i	−0.150263	+	0.154477i
$418$	−8.91477	+	16.8869i	−0.436036	+	0.825964i
$419$	−4.28527	+	7.42230i	−0.209349	+	0.362603i	−0.951510	−	0.307619i	$-0.900468\pi$
$419$	−4.28527	+	7.42230i	−0.209349	+	0.362603i	0.742161	+	0.670222i	$0.233801\pi$
$420$		0			0
$421$	3.41504	+	5.91502i	0.166439	+	0.288280i	0.937165	−	0.348886i	$-0.113440\pi$
$421$	3.41504	+	5.91502i	0.166439	+	0.288280i	−0.770727	+	0.637166i	$0.780107\pi$
$422$	26.2892	−	0.996108i	1.27974	−	0.0484898i
$423$	−0.0581320	+	0.00160828i	−0.00282647	+	7.81974e-5i
$424$	1.03010	+	9.02743i	0.0500263	+	0.438411i
$425$		0			0
$426$	−0.888615	−	2.74101i	−0.0430536	−	0.132803i
$427$	0.695612	−	1.20483i	0.0336630	−	0.0583060i
$428$	33.9009	+	16.2864i	1.63866	+	0.787231i
$429$	−32.0850	−	8.12329i	−1.54908	−	0.392196i
$430$		0			0
$431$	26.5552			1.27912			0.639559	−	0.768742i	$-0.279117\pi$
$431$	26.5552			1.27912			0.639559	+	0.768742i	$0.279117\pi$
$432$	20.7354	+	1.42930i	0.997633	+	0.0687674i
$433$			12.4714i			0.599339i	0.954043	+	0.299669i	$0.0968763\pi$
$433$			12.4714i			0.599339i	−0.954043	+	0.299669i	$0.903124\pi$
$434$	−8.50354	−	13.5191i	−0.408183	−	0.648939i
$435$		0			0
$436$	2.93642	−	6.11230i	0.140629	−	0.292726i
$437$	6.75537	−	11.7006i	0.323153	−	0.559718i
$438$	5.41839	−	1.75660i	0.258901	−	0.0839337i
$439$	−12.8412	+	7.41389i	−0.612879	+	0.353846i	−0.774091	−	0.633074i	$-0.781793\pi$
$439$	−12.8412	+	7.41389i	−0.612879	+	0.353846i	0.161212	+	0.986920i	$0.448460\pi$
$440$		0			0
$441$	−5.91806	+	3.63865i	−0.281813	+	0.173269i
$442$	−47.5020	+	1.79987i	−2.25944	+	0.0856111i
$443$	34.2297	−	19.7625i	1.62630	−	0.938945i	0.641117	−	0.767444i	$-0.278472\pi$
$443$	34.2297	−	19.7625i	1.62630	−	0.938945i	0.985184	−	0.171501i	$-0.0548618\pi$
$444$	10.1778	−	12.1865i	0.483019	−	0.578345i
$445$		0			0
$446$	15.4376	+	8.14966i	0.730990	+	0.385898i
$447$	−8.34594	+	8.58003i	−0.394749	+	0.405822i
$448$	−11.8128	−	12.6590i	−0.558103	−	0.598083i
$449$		−	22.8395i		−	1.07786i	−0.842349	−	0.538932i	$-0.818828\pi$
$449$		−	22.8395i		−	1.07786i	0.842349	−	0.538932i	$-0.181172\pi$
$450$		0			0
$451$			13.9886i			0.658695i
$452$	1.12618	+	1.64845i	0.0529709	+	0.0775365i
$453$	−10.0463	−	35.5209i	−0.472016	−	1.66892i
$454$	−0.491241	+	0.930537i	−0.0230551	+	0.0436723i
$455$		0			0
$456$	−3.06315	+	22.6619i	−0.143445	+	1.06124i
$457$	0.720950	−	0.416241i	0.0337246	−	0.0194709i	−0.483043	−	0.875597i	$-0.660468\pi$
$457$	0.720950	−	0.416241i	0.0337246	−	0.0194709i	0.516768	+	0.856126i	$0.327135\pi$
$458$	−1.40060	−	36.9645i	−0.0654457	−	1.72724i
$459$	−17.9040	+	19.4549i	−0.835689	+	0.908077i
$460$		0			0
$461$	−30.9887	+	17.8913i	−1.44329	+	0.833281i	−0.998067	−	0.0621408i	$-0.980207\pi$
$461$	−30.9887	+	17.8913i	−1.44329	+	0.833281i	−0.445218	+	0.895422i	$0.646874\pi$
$462$	14.9981	+	3.19826i	0.697773	+	0.148796i
$463$	4.16373	−	7.21179i	0.193505	−	0.335160i	−0.752904	−	0.658130i	$-0.771348\pi$
$463$	4.16373	−	7.21179i	0.193505	−	0.335160i	0.946409	+	0.322969i	$0.104681\pi$
$464$	−25.7987	−	10.0690i	−1.19767	−	0.467443i
$465$		0			0
$466$	−30.9166	+	19.4466i	−1.43219	+	0.900846i
$467$		−	16.8607i		−	0.780220i	−0.920768	−	0.390110i	$-0.872437\pi$
$467$		−	16.8607i		−	0.780220i	0.920768	−	0.390110i	$-0.127563\pi$
$468$	−39.4242	+	4.09119i	−1.82238	+	0.189115i
$469$	20.4901			0.946147
$470$		0			0
$471$	−14.0934	+	14.4887i	−0.649388	+	0.667603i
$472$	20.8898	+	9.07890i	0.961530	+	0.417890i
$473$	−6.37077	+	11.0345i	−0.292929	+	0.507367i
$474$	30.8765	+	27.8381i	1.41820	+	1.27865i
$475$		0			0
$476$	21.9622	−	1.66671i	1.00664	−	0.0763933i
$477$	−8.47611	−	4.58593i	−0.388094	−	0.209975i
$478$	−0.440797	−	11.6335i	−0.0201616	−	0.532102i
$479$	2.64691	+	4.58458i	0.120940	+	0.209475i	0.920139	−	0.391593i	$-0.128076\pi$
$479$	2.64691	+	4.58458i	0.120940	+	0.209475i	−0.799198	+	0.601067i	$0.794742\pi$
$480$		0			0
$481$	−15.1392	+	26.2218i	−0.690287	+	1.19561i
$482$	−0.176476	−	0.0931638i	−0.00803828	−	0.00424350i
$483$	−10.5184	−	2.66304i	−0.478602	−	0.121173i
$484$	−2.97011	−	4.34752i	−0.135005	−	0.197615i
$485$		0			0
$486$	−13.8342	+	17.1644i	−0.627531	+	0.778591i
$487$	−19.8270			−0.898449			−0.449225	−	0.893419i	$-0.648300\pi$
$487$	−19.8270			−0.898449			−0.449225	+	0.893419i	$0.648300\pi$
$488$	1.46132	−	1.08170i	0.0661507	−	0.0489664i
$489$	0.186200	−	0.735444i	0.00842026	−	0.0332579i
$490$		0			0
$491$	14.2239	−	24.6365i	0.641916	−	1.11183i	−0.343089	−	0.939303i	$-0.611473\pi$
$491$	14.2239	−	24.6365i	0.641916	−	1.11183i	0.985005	−	0.172528i	$-0.0551934\pi$
$492$	5.76586	+	15.7285i	0.259945	+	0.709097i
$493$	30.5090	−	17.6144i	1.37406	−	0.793311i
$494$	−1.65117	−	43.5775i	−0.0742896	−	1.96065i
$495$		0			0
$496$	−3.14977	−	20.6327i	−0.141429	−	0.926438i
$497$	−1.27300	−	2.20490i	−0.0571018	−	0.0989031i
$498$	3.45880	+	3.11844i	0.154992	+	0.139741i
$499$	−4.89300	−	2.82497i	−0.219041	−	0.126463i	0.386465	−	0.922304i	$-0.373696\pi$
$499$	−4.89300	−	2.82497i	−0.219041	−	0.126463i	−0.605506	+	0.795841i	$0.707029\pi$
$500$		0			0
$501$	5.03075	−	5.17185i	0.224757	−	0.231061i
$502$	11.3784	−	7.15700i	0.507841	−	0.319433i
$503$			32.7730i			1.46128i	0.682765	+	0.730638i	$0.260777\pi$
$503$			32.7730i			1.46128i	−0.682765	+	0.730638i	$0.739223\pi$
$504$	18.1819	−	2.58589i	0.809886	−	0.115185i
$505$		0			0
$506$	−6.30422	−	10.0226i	−0.280257	−	0.445559i
$507$	51.0652	−	14.4426i	2.26788	−	0.641420i
$508$	7.60794	−	15.8363i	0.337548	−	0.702623i
$509$	10.8656	+	6.27327i	0.481610	+	0.278058i	0.721087	−	0.692844i	$-0.243643\pi$
$509$	10.8656	+	6.27327i	0.481610	+	0.278058i	−0.239477	+	0.970902i	$0.576976\pi$
$510$		0			0
$511$	4.35861	−	2.51644i	0.192813	−	0.111321i
$512$	−7.56409	−	21.3257i	−0.334289	−	0.942471i
$513$	−17.8476	−	16.4248i	−0.787990	−	0.725175i
$514$	−1.39139	−	36.7214i	−0.0613715	−	1.61971i
$515$		0			0
$516$	−2.61496	+	15.0330i	−0.115117	+	0.661790i
$517$	−0.0485608	−	0.0280366i	−0.00213570	−	0.00123305i
$518$	6.54952	−	12.4065i	0.287769	−	0.545109i
$519$	−14.9213	+	4.22016i	−0.654974	+	0.185245i
$520$		0			0
$521$			11.7475i			0.514665i	0.966323	+	0.257333i	$0.0828436\pi$
$521$			11.7475i			0.514665i	−0.966323	+	0.257333i	$0.917156\pi$
$522$	24.4222	−	16.3213i	1.06893	−	0.714362i
$523$	−20.5196			−0.897261			−0.448630	−	0.893717i	$-0.648088\pi$
$523$	−20.5196			−0.897261			−0.448630	+	0.893717i	$0.648088\pi$
$524$	15.9380	+	23.3294i	0.696255	+	1.01915i
$525$		0			0
$526$	17.7446	−	33.6129i	0.773703	−	1.46559i
$527$	22.9933	+	13.2752i	1.00160	+	0.578277i
$528$	16.3099	+	11.6457i	0.709796	+	0.506815i
$529$	−7.31125	−	12.6635i	−0.317881	−	0.550585i
$530$		0			0
$531$	−20.5803	+	12.6535i	−0.893109	+	0.549116i
$532$	1.52901	+	20.1477i	0.0662908	+	0.873515i
$533$	−15.9730	−	27.6660i	−0.691865	−	1.19835i
$534$	8.68309	−	2.81499i	0.375754	−	0.121817i
$535$		0			0
$536$	24.5583	+	10.6733i	1.06076	+	0.461016i
$537$	−4.47484	+	17.6745i	−0.193104	+	0.762711i
$538$	12.3510	+	19.6359i	0.532488	+	0.846562i
$539$	−6.69857			−0.288528
$540$		0			0
$541$	19.0464			0.818871			0.409435	−	0.912339i	$-0.365726\pi$
$541$	19.0464			0.818871			0.409435	+	0.912339i	$0.365726\pi$
$542$	−12.0840	−	19.2115i	−0.519054	−	0.825204i
$543$	−4.04216	+	15.9655i	−0.173466	+	0.685147i
$544$	27.1908	+	9.44246i	1.16580	+	0.404842i
$545$		0			0
$546$	−33.3145	+	10.8003i	−1.42573	+	0.462210i
$547$	12.5453	+	21.7291i	0.536399	+	0.929071i	0.999094	+	0.0425534i	$0.0135493\pi$
$547$	12.5453	+	21.7291i	0.536399	+	0.929071i	−0.462695	+	0.886518i	$0.653117\pi$
$548$	30.3179	−	2.30082i	1.29512	−	0.0982861i
$549$	0.0533308	+	1.92766i	0.00227610	+	0.0822706i
$550$		0			0
$551$	16.1591	+	27.9884i	0.688401	+	1.19235i
$552$	−11.2195	−	8.67077i	−0.477535	−	0.369052i
$553$	31.8118	+	18.3665i	1.35277	+	0.781024i
$554$	16.0645	−	30.4303i	0.682515	−	1.29286i
$555$		0			0
$556$	−4.19584	+	2.86649i	−0.177943	+	0.121566i
$557$	−4.13922			−0.175384			−0.0876922	−	0.996148i	$-0.527949\pi$
$557$	−4.13922			−0.175384			−0.0876922	+	0.996148i	$0.527949\pi$
$558$	19.8556	+	9.78971i	0.840556	+	0.414431i
$559$		−	29.0981i		−	1.23072i
$560$		0			0
$561$	−24.5311	+	6.93807i	−1.03570	+	0.292926i
$562$	−6.89304	+	13.0572i	−0.290765	+	0.550784i
$563$	−25.8656	−	14.9335i	−1.09010	−	0.629372i	−0.156500	−	0.987678i	$-0.550021\pi$
$563$	−25.8656	−	14.9335i	−1.09010	−	0.629372i	−0.933604	+	0.358306i	$0.883354\pi$
$564$	−0.0661573	−	0.0115080i	−0.00278572	−	0.000484573i
$565$		0			0
$566$	−0.797262	−	21.0413i	−0.0335114	−	0.884431i
$567$	−8.79184	+	17.3819i	−0.369223	+	0.729970i
$568$	−0.377215	−	3.30577i	−0.0158276	−	0.138707i
$569$	35.2116	−	20.3294i	1.47615	−	0.852253i	0.476507	−	0.879170i	$-0.341903\pi$
$569$	35.2116	−	20.3294i	1.47615	−	0.852253i	0.999638	+	0.0269176i	$0.00856919\pi$
$570$		0			0
$571$	−34.7953	−	20.0891i	−1.45614	−	0.840702i	−0.457320	−	0.889302i	$-0.651191\pi$
$571$	−34.7953	−	20.0891i	−1.45614	−	0.840702i	−0.998818	+	0.0486002i	$0.984524\pi$
$572$	−34.4484	−	16.5494i	−1.44036	−	0.691966i
$573$	−20.2681	+	5.73238i	−0.846712	+	0.239474i
$574$	7.88094	+	12.5293i	0.328944	+	0.522963i
$575$		0			0
$576$	23.1388	+	6.37162i	0.964115	+	0.265484i
$577$			33.5865i			1.39822i	0.715013	+	0.699112i	$0.246421\pi$
$577$			33.5865i			1.39822i	−0.715013	+	0.699112i	$0.753579\pi$
$578$	−10.6429	+	6.69441i	−0.442688	+	0.278451i
$579$	−16.9424	+	17.4176i	−0.704104	+	0.723853i
$580$		0			0
$581$	3.56357	+	2.05743i	0.147842	+	0.0853565i
$582$	−21.0335	−	18.9637i	−0.871866	−	0.786071i
$583$	−4.64615	−	8.04737i	−0.192424	−	0.333288i
$584$	6.53479	−	0.745674i	0.270412	−	0.0308562i
$585$		0			0
$586$	−1.39853	−	36.9098i	−0.0577726	−	1.52473i
$587$	−32.3717	+	18.6898i	−1.33612	+	0.771410i	−0.986230	−	0.165380i	$-0.947115\pi$
$587$	−32.3717	+	18.6898i	−1.33612	+	0.771410i	−0.349892	+	0.936790i	$0.613782\pi$
$588$	−7.53177	+	2.76104i	−0.310605	+	0.113863i
$589$	−12.1784	+	21.0937i	−0.501803	+	0.869149i
$590$		0			0
$591$	3.06739	−	12.1154i	0.126176	−	0.498362i
$592$	14.3124	−	11.4581i	0.588236	−	0.470923i
$593$	−11.3789			−0.467275			−0.233638	−	0.972324i	$-0.575063\pi$
$593$	−11.3789			−0.467275			−0.233638	+	0.972324i	$0.575063\pi$
$594$	−20.0314	+	7.11202i	−0.821900	+	0.291810i
$595$		0			0
$596$	−11.4123	+	7.79661i	−0.467468	+	0.319362i
$597$	14.4920	+	3.66908i	0.593116	+	0.150165i
$598$	23.9126	+	12.6237i	0.977859	+	0.516223i
$599$	−1.12135	+	1.94223i	−0.0458170	+	0.0793574i	−0.888024	−	0.459796i	$-0.847922\pi$
$599$	−1.12135	+	1.94223i	−0.0458170	+	0.0793574i	0.842207	+	0.539154i	$0.181256\pi$
$600$		0			0
$601$	−8.67140	−	15.0193i	−0.353714	−	0.612650i	0.633183	−	0.774002i	$-0.281748\pi$
$601$	−8.67140	−	15.0193i	−0.353714	−	0.612650i	−0.986897	+	0.161352i	$0.948415\pi$
$602$	0.510483	+	13.4726i	0.0208057	+	0.549103i
$603$	−24.1945	+	14.8757i	−0.985276	+	0.605784i
$604$	−3.22552	−	42.5027i	−0.131244	−	1.72941i
$605$		0			0
$606$	−19.8793	−	17.9231i	−0.807543	−	0.728078i
$607$	−8.50549	+	14.7319i	−0.345227	+	0.597951i	−0.985395	−	0.170284i	$-0.945531\pi$
$607$	−8.50549	+	14.7319i	−0.345227	+	0.597951i	0.640168	+	0.768235i	$0.278865\pi$
$608$	−8.66234	+	24.9444i	−0.351304	+	1.01163i
$609$	18.0968	−	18.6044i	0.733321	−	0.753889i
$610$		0			0
$611$	0.128055			0.00518056
$612$	−24.7227	+	17.9124i	−0.999354	+	0.724065i
$613$		−	6.23696i		−	0.251908i	−0.992036	−	0.125954i	$-0.959801\pi$
$613$		−	6.23696i		−	0.251908i	0.992036	−	0.125954i	$-0.0401992\pi$
$614$	−34.1821	+	21.5005i	−1.37948	+	0.867691i
$615$		0			0
$616$	16.2402	+	7.05815i	0.654336	+	0.284381i
$617$	4.18992	−	7.25716i	0.168680	−	0.292162i	−0.769276	−	0.638917i	$-0.779383\pi$
$617$	4.18992	−	7.25716i	0.168680	−	0.292162i	0.937956	+	0.346754i	$0.112716\pi$
$618$	−1.52201	−	0.324560i	−0.0612242	−	0.0130557i
$619$	31.5019	−	18.1876i	1.26617	−	0.731021i	0.291906	−	0.956447i	$-0.405711\pi$
$619$	31.5019	−	18.1876i	1.26617	−	0.731021i	0.974260	+	0.225426i	$0.0723773\pi$
$620$		0			0
$621$	14.3533	−	4.49175i	0.575977	−	0.180248i
$622$	0.00471451	+	0.124425i	0.000189034	+	0.00498898i
$623$	6.98476	−	4.03265i	0.279839	−	0.161565i
$624$	−45.5547	−	4.40884i	−1.82365	−	0.176495i
$625$		0			0
$626$	10.0461	−	19.0298i	0.401521	−	0.760585i
$627$	−6.36487	−	22.5044i	−0.254188	−	0.898739i
$628$	−19.2715	+	13.1658i	−0.769015	+	0.525371i
$629$			23.3220i			0.929910i
$630$		0			0
$631$		−	42.3747i		−	1.68691i	−0.537199	−	0.843455i	$-0.680518\pi$
$631$		−	42.3747i		−	1.68691i	0.537199	−	0.843455i	$-0.319482\pi$
$632$	28.5607	+	38.5838i	1.13608	+	1.53478i
$633$	−22.4662	+	23.0963i	−0.892951	+	0.917997i
$634$	−8.96151	−	4.73088i	−0.355907	−	0.187887i
$635$		0			0
$636$	−8.54107	−	7.13328i	−0.338675	−	0.282853i
$637$	13.2481	−	7.64881i	0.524910	−	0.303057i
$638$	28.3025	−	1.07239i	1.12051	−	0.0424564i
$639$	3.10388	+	1.67933i	0.122787	+	0.0664332i
$640$		0			0
$641$	−9.58349	+	5.53303i	−0.378525	+	0.218542i	−0.677176	−	0.735821i	$-0.736797\pi$
$641$	−9.58349	+	5.53303i	−0.378525	+	0.218542i	0.298651	+	0.954362i	$0.403463\pi$
$642$	−43.8176	+	14.2053i	−1.72934	+	0.560640i
$643$	6.09436	−	10.5557i	0.240338	−	0.416278i	−0.720472	−	0.693484i	$-0.756075\pi$
$643$	6.09436	−	10.5557i	0.240338	−	0.416278i	0.960811	+	0.277206i	$0.0894083\pi$
$644$	−11.2932	−	5.42536i	−0.445013	−	0.213789i
$645$		0			0
$646$	−17.8843	−	28.4329i	−0.703649	−	1.11868i
$647$		−	13.5692i		−	0.533460i	−0.963771	−	0.266730i	$-0.914057\pi$
$647$		−	13.5692i		−	0.533460i	0.963771	−	0.266730i	$-0.0859432\pi$
$648$	−19.5916	+	16.2533i	−0.769631	+	0.638489i
$649$	−23.2945			−0.914390
$650$		0			0
$651$	18.9623	+	4.80087i	0.743189	+	0.188161i
$652$	0.379342	−	0.789619i	0.0148562	−	0.0309239i
$653$	5.73470	−	9.93280i	0.224416	−	0.388700i	−0.731728	−	0.681597i	$-0.761286\pi$
$653$	5.73470	−	9.93280i	0.224416	−	0.388700i	0.956144	+	0.292896i	$0.0946191\pi$
$654$	2.56121	+	7.90028i	0.100151	+	0.308925i
$655$		0			0
$656$	2.91915	+	19.1221i	0.113974	+	0.746592i
$657$	−3.31967	+	6.13569i	−0.129513	+	0.239376i
$658$	−0.0592905	+	0.00224654i	−0.00231138	+	8.75792e-5i
$659$	8.46548	+	14.6626i	0.329768	+	0.571175i	0.982466	−	0.186443i	$-0.0596961\pi$
$659$	8.46548	+	14.6626i	0.329768	+	0.571175i	−0.652698	+	0.757619i	$0.726363\pi$
$660$		0			0
$661$	6.92555	−	11.9954i	0.269373	−	0.466567i	−0.699327	−	0.714802i	$-0.746517\pi$
$661$	6.92555	−	11.9954i	0.269373	−	0.466567i	0.968700	+	0.248234i	$0.0798503\pi$
$662$	0.541154	−	1.02509i	0.0210326	−	0.0398411i
$663$	40.5942	−	41.7329i	1.57655	−	1.62077i
$664$	3.19938	+	4.32218i	0.124160	+	0.167733i
$665$		0			0
$666$	1.27341	+	19.4043i	0.0493437	+	0.751901i
$667$	−20.0393			−0.775925
$668$	6.87911	−	4.69962i	0.266161	−	0.181834i
$669$	−20.5730	+	5.81860i	−0.795397	+	0.224960i
$670$		0			0
$671$	−0.929695	+	1.61028i	−0.0358905	+	0.0621642i
$672$	21.1695	+	1.24213i	0.816631	+	0.0479164i
$673$	13.3158	−	7.68786i	0.513285	−	0.296345i	−0.220898	−	0.975297i	$-0.570899\pi$
$673$	13.3158	−	7.68786i	0.513285	−	0.296345i	0.734183	+	0.678952i	$0.237565\pi$
$674$	−4.33542	+	0.164271i	−0.166994	+	0.00632748i
$675$		0			0
$676$	61.1022	−	4.63703i	2.35009	−	0.178347i
$677$	−19.8641	−	34.4057i	−0.763441	−	1.32232i	−0.941067	−	0.338221i	$-0.890175\pi$
$677$	−19.8641	−	34.4057i	−0.763441	−	1.32232i	0.177626	−	0.984098i	$-0.443158\pi$
$678$	−2.39133	−	0.509937i	−0.0918384	−	0.0195840i
$679$	−21.6706	−	12.5115i	−0.831642	−	0.480149i
$680$		0			0
$681$	−0.350731	−	1.24009i	−0.0134400	−	0.0475202i
$682$	11.3651	+	18.0685i	0.435193	+	0.691879i
$683$		−	21.6572i		−	0.828690i	−0.910120	−	0.414345i	$-0.864011\pi$
$683$		−	21.6572i		−	0.828690i	0.910120	−	0.414345i	$-0.135989\pi$
$684$	−16.4325	−	22.6801i	−0.628313	−	0.867196i
$685$		0			0
$686$	−24.1360	+	15.1816i	−0.921518	+	0.579635i
$687$	32.4751	+	31.5891i	1.23900	+	1.20520i
$688$	−6.40603	+	16.4134i	−0.244228	+	0.625756i
$689$	18.3779	+	10.6105i	0.700143	+	0.404228i
$690$		0			0
$691$	15.3770	−	8.87791i	0.584968	−	0.337732i	−0.178137	−	0.984006i	$-0.557007\pi$
$691$	15.3770	−	8.87791i	0.584968	−	0.337732i	0.763105	+	0.646274i	$0.223674\pi$
$692$	−17.8542	+	1.35495i	−0.678714	+	0.0515075i
$693$	−15.9996	+	9.83715i	−0.607774	+	0.373682i
$694$	31.5324	−	1.19477i	1.19695	−	0.0453530i
$695$		0			0
$696$	31.3809	−	12.8716i	1.18949	−	0.487897i
$697$	−21.3098	−	12.3032i	−0.807167	−	0.466018i
$698$	12.5556	+	6.62822i	0.475235	+	0.250882i
$699$	10.9790	−	43.3644i	0.415265	−	1.64019i
$700$		0			0
$701$		−	38.3642i		−	1.44900i	−0.689277	−	0.724498i	$-0.742072\pi$
$701$		−	38.3642i		−	1.44900i	0.689277	−	0.724498i	$-0.257928\pi$
$702$	31.4964	−	36.9389i	1.18875	−	1.39417i
$703$	−21.3952			−0.806936
$704$	15.7880	+	16.9190i	0.595033	+	0.637658i
$705$		0			0
$706$	−15.9235	−	8.40622i	−0.599290	−	0.316372i
$707$	−20.4815	−	11.8250i	−0.770287	−	0.444725i
$708$	−26.1920	+	9.60162i	−0.984357	+	0.360851i
$709$	1.96851	+	3.40955i	0.0739288	+	0.128049i	0.900620	−	0.434608i	$-0.143113\pi$
$709$	1.96851	+	3.40955i	0.0739288	+	0.128049i	−0.826691	+	0.562656i	$0.809780\pi$
$710$		0			0
$711$	−50.8969	+	1.40812i	−1.90878	+	0.0528085i
$712$	10.4721	−	1.19496i	0.392460	−	0.0447829i
$713$	−7.55138	−	13.0794i	−0.282802	−	0.489827i
$714$	−18.0633	+	20.0348i	−0.676001	+	0.749782i
$715$		0			0
$716$	−9.11650	+	18.9764i	−0.340699	+	0.709183i
$717$	10.2206	+	9.94172i	0.381694	+	0.371280i
$718$	−7.10240	+	4.46742i	−0.265059	+	0.166722i
$719$	25.9983			0.969573			0.484787	−	0.874632i	$-0.338897\pi$
$719$	25.9983			0.969573			0.484787	+	0.874632i	$0.338897\pi$
$720$		0			0
$721$	−1.37505			−0.0512097
$722$	3.33908	−	2.10028i	0.124268	−	0.0781644i
$723$	0.235182	−	0.0665161i	0.00874652	−	0.00247376i
$724$	−8.23501	+	17.1416i	−0.306052	+	0.637062i
$725$		0			0
$726$	6.30675	+	1.34488i	0.234065	+	0.0499132i
$727$	−13.4108	−	23.2282i	−0.497379	−	0.861486i	0.502616	−	0.864510i	$-0.332371\pi$
$727$	−13.4108	−	23.2282i	−0.497379	−	0.861486i	−0.999995	+	0.00302389i	$0.999037\pi$
$728$	−40.1786	+	4.58470i	−1.48912	+	0.169920i
$729$	−2.23781	−	26.9071i	−0.0828818	−	0.996559i
$730$		0			0
$731$	−11.2065	−	19.4102i	−0.414486	−	0.717911i
$732$	−0.381605	+	2.19378i	−0.0141045	+	0.0810845i
$733$	13.8581	+	8.00096i	0.511859	+	0.295522i	0.733598	−	0.679584i	$-0.237840\pi$
$733$	13.8581	+	8.00096i	0.511859	+	0.295522i	−0.221738	+	0.975106i	$0.571173\pi$
$734$	33.2681	+	17.5626i	1.22795	+	0.648248i
$735$		0			0
$736$	−10.7093	−	12.3851i	−0.394749	−	0.456522i
$737$	−27.3854			−1.00875
$738$	−18.4019	−	9.07295i	−0.677383	−	0.333980i
$739$			2.17451i			0.0799905i	0.999200	+	0.0399952i	$0.0127343\pi$
$739$			2.17451i			0.0799905i	−0.999200	+	0.0399952i	$0.987266\pi$
$740$		0			0
$741$	38.2850	+	37.2404i	1.40643	+	1.36806i
$742$	−8.69525	−	4.59032i	−0.319213	−	0.168516i
$743$	15.8760	+	9.16604i	0.582436	+	0.336269i	0.762101	−	0.647458i	$-0.224168\pi$
$743$	15.8760	+	9.16604i	0.582436	+	0.336269i	−0.179665	+	0.983728i	$0.557501\pi$
$744$	20.2263	+	15.6315i	0.741533	+	0.573077i
$745$		0			0
$746$	37.3917	−	1.41679i	1.36901	−	0.0518722i
$747$	−5.70150	+	0.157738i	−0.208607	+	0.00577133i
$748$	−29.3528	+	2.22758i	−1.07324	+	0.0814483i
$749$	−35.2473	+	20.3500i	−1.28791	+	0.743574i
$750$		0			0
$751$	−23.9363	−	13.8196i	−0.873449	−	0.504286i	−0.00495598	−	0.999988i	$-0.501578\pi$
$751$	−23.9363	−	13.8196i	−0.873449	−	0.504286i	−0.868493	+	0.495702i	$0.834911\pi$
$752$	−0.0722324	−	0.0281917i	−0.00263404	−	0.00102805i
$753$	−4.04065	+	15.9596i	−0.147250	+	0.581599i
$754$	−54.7509	+	34.4383i	−1.99391	+	1.25417i
$755$		0			0
$756$	−13.9350	+	17.6555i	−0.506811	+	0.642125i
$757$		−	47.4098i		−	1.72314i	−0.507640	−	0.861570i	$-0.669482\pi$
$757$		−	47.4098i		−	1.72314i	0.507640	−	0.861570i	$-0.330518\pi$
$758$	−16.0652	−	25.5409i	−0.583515	−	0.927686i
$759$	14.0579	+	3.55920i	0.510271	+	0.129191i
$760$		0			0
$761$	−19.6920	−	11.3692i	−0.713834	−	0.412132i	0.0986449	−	0.995123i	$-0.468549\pi$
$761$	−19.6920	−	11.3692i	−0.713834	−	0.412132i	−0.812479	+	0.582990i	$0.801883\pi$
$762$	6.63582	+	20.4688i	0.240390	+	0.741505i
$763$	3.66910	+	6.35506i	0.132830	+	0.230069i
$764$	−24.2519	+	1.84047i	−0.877402	+	0.0665858i
$765$		0			0
$766$	4.45656	−	0.168861i	0.161022	−	0.00610119i
$767$	46.0709	−	26.5990i	1.66352	−	0.960436i
$768$	24.7255	+	12.5159i	0.892206	+	0.451629i
$769$	17.4807	−	30.2775i	0.630371	−	1.09183i	−0.357105	−	0.934064i	$-0.616236\pi$
$769$	17.4807	−	30.2775i	0.630371	−	1.09183i	0.987476	−	0.157770i	$-0.0504305\pi$
$770$		0			0
$771$	32.2615	+	31.3813i	1.16187	+	1.13017i
$772$	−23.1673	+	15.8273i	−0.833810	+	0.569637i
$773$	−5.74824			−0.206750			−0.103375	−	0.994642i	$-0.532964\pi$
$773$	−5.74824			−0.206750			−0.103375	+	0.994642i	$0.532964\pi$
$774$	−10.3838	−	15.5377i	−0.373237	−	0.558490i
$775$		0			0
$776$	−19.4559	−	26.2838i	−0.698427	−	0.943534i
$777$	4.67615	+	16.5336i	0.167756	+	0.593138i
$778$	9.90674	−	18.7659i	0.355174	−	0.672791i
$779$	11.2868	−	19.5493i	0.404391	−	0.700425i
$780$		0			0
$781$	1.70138	+	2.94688i	0.0608802	+	0.105448i
$782$	20.8129	−	0.788608i	0.744267	−	0.0282006i
$783$	−7.86185	+	35.1060i	−0.280959	+	1.25459i
$784$	−9.15681	+	1.39787i	−0.327029	+	0.0499238i
$785$		0			0
$786$	−33.8428	−	7.21680i	−1.20713	−	0.257415i
$787$	−26.5020	+	45.9027i	−0.944693	+	1.63626i	−0.188327	+	0.982106i	$0.560306\pi$
$787$	−26.5020	+	45.9027i	−0.944693	+	1.63626i	−0.756366	+	0.654149i	$0.773027\pi$
$788$	6.24913	−	13.0079i	0.222616	−	0.463386i
$789$	12.6691	+	44.7944i	0.451032	+	1.59472i
$790$		0			0
$791$	−2.16043			−0.0768162
$792$	−24.3004	+	3.45608i	−0.863476	+	0.122806i
$793$		−	4.24632i		−	0.150791i
$794$	7.56543	+	12.0277i	0.268487	+	0.426847i
$795$		0			0
$796$	15.5595	+	7.47494i	0.551491	+	0.264942i
$797$	−6.93917	+	12.0190i	−0.245798	+	0.425735i	−0.962356	−	0.271793i	$-0.912383\pi$
$797$	−6.93917	+	12.0190i	−0.245798	+	0.425735i	0.716558	+	0.697528i	$0.245717\pi$
$798$	−18.3795	−	16.5709i	−0.650629	−	0.586604i
$799$	0.0854205	−	0.0493176i	0.00302196	−	0.00174473i
$800$		0			0
$801$	−5.31984	+	9.83258i	−0.187967	+	0.347417i
$802$	11.1805	−	0.423633i	0.394796	−	0.0149590i
$803$	−5.82534	+	3.36326i	−0.205572	+	0.118687i
$804$	−30.7917	+	11.2878i	−1.08594	+	0.398090i
$805$		0			0
$806$	−43.1091	−	22.7578i	−1.51845	−	0.801609i
$807$	−27.5417	−	6.97303i	−0.969515	−	0.245462i
$808$	−18.3884	−	24.8416i	−0.646900	−	0.873924i
$809$			46.1210i			1.62153i	0.585372	+	0.810765i	$0.300948\pi$
$809$			46.1210i			1.62153i	−0.585372	+	0.810765i	$0.699052\pi$
$810$		0			0
$811$			31.7719i			1.11566i	0.829954	+	0.557832i	$0.188367\pi$
$811$			31.7719i			1.11566i	−0.829954	+	0.557832i	$0.811633\pi$
$812$	24.7459	−	16.9057i	0.868409	−	0.593274i
$813$	26.9465	+	6.82233i	0.945055	+	0.239269i
$814$	−8.75353	+	16.5814i	−0.306811	+	0.581179i
$815$		0			0
$816$	−32.0857	+	14.6034i	−1.12322	+	0.511221i
$817$	17.8065	−	10.2806i	0.622972	−	0.359673i
$818$	1.45459	+	38.3894i	0.0508585	+	1.34225i
$819$	20.4107	−	37.7247i	0.713207	−	1.31821i
$820$		0			0
$821$	11.7695	−	6.79511i	0.410758	−	0.237151i	−0.280358	−	0.959896i	$-0.590453\pi$
$821$	11.7695	−	6.79511i	0.410758	−	0.237151i	0.691115	+	0.722745i	$0.257120\pi$
$822$	−24.9356	+	27.6572i	−0.869729	+	0.964655i
$823$	14.8238	−	25.6756i	0.516725	−	0.894995i	−0.483086	−	0.875573i	$-0.660484\pi$
$823$	14.8238	−	25.6756i	0.516725	−	0.894995i	0.999811	−	0.0194217i	$-0.00618250\pi$
$824$	−1.64806	−	0.716264i	−0.0574129	−	0.0249522i
$825$		0			0
$826$	−20.8645	+	13.1238i	−0.725969	+	0.456635i
$827$		−	24.1020i		−	0.838110i	−0.907961	−	0.419055i	$-0.862361\pi$
$827$		−	24.1020i		−	0.838110i	0.907961	−	0.419055i	$-0.137639\pi$
$828$	17.2736	−	1.79254i	0.600299	−	0.0622952i
$829$	−42.6555			−1.48149			−0.740743	−	0.671789i	$-0.765526\pi$
$829$	−42.6555			−1.48149			−0.740743	+	0.671789i	$0.765526\pi$
$830$		0			0
$831$	11.4696	+	40.5532i	0.397874	+	1.40677i
$832$	−50.5439	−	15.4340i	−1.75229	−	0.535077i
$833$	5.89153	−	10.2044i	0.204130	−	0.353563i
$834$	1.29796	−	6.08671i	0.0449446	−	0.210766i
$835$		0			0
$836$	−2.04354	−	26.9277i	−0.0706773	−	0.931315i
$837$	−25.8758	+	8.09763i	−0.894398	+	0.279895i
$838$	−0.458924	−	12.1119i	−0.0158533	−	0.418398i
$839$	−9.56807	−	16.5724i	−0.330327	−	0.572142i	0.652249	−	0.758005i	$-0.273826\pi$
$839$	−9.56807	−	16.5724i	−0.330327	−	0.572142i	−0.982576	+	0.185862i	$0.940492\pi$
$840$		0			0
$841$	9.46742	−	16.3981i	0.326463	−	0.565450i
$842$	−8.54196	−	4.50940i	−0.294376	−	0.155404i
$843$	−4.92141	−	17.4007i	−0.169502	−	0.599314i
$844$	−30.7206	+	20.9875i	−1.05745	+	0.722419i
$845$		0			0
$846$	0.0683784	−	0.0456971i	0.00235090	−	0.00157110i
$847$	5.69781			0.195779
$848$	−8.03054	−	10.0310i	−0.275770	−	0.344467i
$849$	18.4858	+	17.9814i	0.634430	+	0.617121i
$850$		0			0
$851$	6.63318	−	11.4890i	0.227383	−	0.393838i
$852$	3.12766	+	2.61215i	0.107152	+	0.0894906i
$853$	−25.0942	+	14.4881i	−0.859207	+	0.496064i	−0.863747	−	0.503926i	$-0.831888\pi$
$853$	−25.0942	+	14.4881i	−0.859207	+	0.496064i	0.00453935	+	0.999990i	$0.498555\pi$
$854$	0.0744954	+	1.96608i	0.00254918	+	0.0672777i
$855$		0			0
$856$	−52.8457	+	6.03013i	−1.80623	+	0.206106i
$857$	−8.12743	−	14.0771i	−0.277628	−	0.480865i	0.693167	−	0.720777i	$-0.256215\pi$
$857$	−8.12743	−	14.0771i	−0.277628	−	0.480865i	−0.970795	+	0.239912i	$0.922882\pi$
$858$	44.5253	−	14.4348i	1.52007	−	0.492795i
$859$	39.4268	+	22.7631i	1.34523	+	0.776666i	0.987569	−	0.157187i	$-0.0502425\pi$
$859$	39.4268	+	22.7631i	1.34523	+	0.776666i	0.357657	+	0.933853i	$0.383576\pi$
$860$		0			0
$861$	−17.5739	−	4.44937i	−0.598917	−	0.151634i
$862$	−31.7890	+	19.9953i	−1.08274	+	0.681043i
$863$		−	14.4497i		−	0.491875i	−0.969286	−	0.245937i	$-0.920904\pi$
$863$		−	14.4497i		−	0.491875i	0.969286	−	0.245937i	$-0.0790957\pi$
$864$	−25.8984	+	13.9022i	−0.881083	+	0.472962i
$865$		0			0
$866$	−9.39064	−	14.9295i	−0.319107	−	0.507324i
$867$	3.77949	−	14.9280i	0.128358	−	0.506983i
$868$	20.3591	+	9.78072i	0.691032	+	0.331979i
$869$	−42.5169	−	24.5471i	−1.44229	−	0.832705i
$870$		0			0
$871$	54.1616	−	31.2702i	1.83520	−	1.05955i
$872$	1.08723	+	9.52804i	0.0368182	+	0.322660i
$873$	34.6717	−	0.959228i	1.17346	−	0.0324650i
$874$	0.723455	+	19.0934i	0.0244712	+	0.645843i
$875$		0			0
$876$	−5.16365	+	6.18272i	−0.174464	+	0.208895i
$877$	20.7046	+	11.9538i	0.699144	+	0.403651i	0.807029	−	0.590512i	$-0.201074\pi$
$877$	20.7046	+	11.9538i	0.699144	+	0.403651i	−0.107885	+	0.994163i	$0.534408\pi$
$878$	9.78970	−	18.5442i	0.330386	−	0.625837i
$879$	32.4270	+	31.5423i	1.09374	+	1.06390i
$880$		0			0
$881$			51.7852i			1.74469i	0.488893	+	0.872344i	$0.337401\pi$
$881$			51.7852i			1.74469i	−0.488893	+	0.872344i	$0.662599\pi$
$882$	4.34467	−	8.81194i	0.146293	−	0.296713i
$883$	−17.1884			−0.578436			−0.289218	−	0.957263i	$-0.593395\pi$
$883$	−17.1884			−0.578436			−0.289218	+	0.957263i	$0.593395\pi$
$884$	55.5091	−	37.9223i	1.86697	−	1.27547i
$885$		0			0
$886$	−26.0955	+	49.4316i	−0.876695	+	1.66069i
$887$	15.4564	+	8.92377i	0.518976	+	0.299631i	0.736515	−	0.676421i	$-0.236470\pi$
$887$	15.4564	+	8.92377i	0.518976	+	0.299631i	−0.217540	+	0.976051i	$0.569803\pi$
$888$	−3.00774	+	22.2520i	−0.100933	+	0.746728i
$889$	9.50623	+	16.4653i	0.318829	+	0.552227i
$890$		0			0
$891$	11.7504	−	23.2311i	0.393654	−	0.778273i
$892$	−24.6167	+	1.86815i	−0.824227	+	0.0625504i
$893$	0.0452431	+	0.0783633i	0.00151400	+	0.00262233i
$894$	3.53034	−	16.5554i	0.118072	−	0.553694i
$895$		0			0
$896$	23.6729	+	6.25932i	0.790857	+	0.209109i
$897$	−31.8673	+	9.01295i	−1.06402	+	0.300934i
$898$	17.1975	+	27.3411i	0.573890	+	0.912383i
$899$	36.1264			1.20488
$900$		0			0
$901$	16.3456			0.544550
$902$	−10.5330	−	16.7456i	−0.350711	−	0.557568i
$903$	−11.8364	−	11.5134i	−0.393889	−	0.383142i
$904$	−2.58937	−	1.12537i	−0.0861213	−	0.0374292i
$905$		0			0
$906$	38.7726	+	34.9572i	1.28813	+	1.16138i
$907$	1.17993	+	2.04370i	0.0391790	+	0.0678600i	0.884950	−	0.465686i	$-0.154192\pi$
$907$	1.17993	+	2.04370i	0.0391790	+	0.0678600i	−0.845771	+	0.533546i	$0.820859\pi$
$908$	−0.112608	−	1.48383i	−0.00373701	−	0.0492427i
$909$	32.7692	−	0.906594i	1.08688	−	0.0300698i
$910$		0			0
$911$	18.6895	+	32.3712i	0.619212	+	1.07251i	0.989630	+	0.143641i	$0.0458810\pi$
$911$	18.6895	+	32.3712i	0.619212	+	1.07251i	−0.370418	+	0.928865i	$0.620786\pi$
$912$	−13.3969	−	29.4349i	−0.443616	−	0.974685i
$913$	−4.76277	−	2.74978i	−0.157625	−	0.0910046i
$914$	−0.549626	+	1.04113i	−0.0181800	+	0.0344377i
$915$		0			0
$916$	29.5099	+	43.1953i	0.975034	+	1.42721i
$917$	−30.5752			−1.00968
$918$	6.78380	−	36.7706i	0.223899	−	1.21361i
$919$			4.73062i			0.156049i	0.996951	+	0.0780243i	$0.0248612\pi$
$919$			4.73062i			0.156049i	−0.996951	+	0.0780243i	$0.975139\pi$
$920$		0			0
$921$	12.1386	−	47.9446i	0.399982	−	1.57983i
$922$	23.6246	−	44.7512i	0.778036	−	1.47380i
$923$	−6.72983	−	3.88547i	−0.221515	−	0.127892i
$924$	−20.3623	+	7.46452i	−0.669870	+	0.245565i
$925$		0			0
$926$	0.445908	+	11.7684i	0.0146534	+	0.386732i
$927$	1.62365	−	0.998278i	0.0533275	−	0.0327877i
$928$	38.4651	−	7.37214i	1.26268	−	0.242002i
$929$	−25.4661	+	14.7029i	−0.835517	+	0.482386i	−0.855738	−	0.517410i	$-0.826896\pi$
$929$	−25.4661	+	14.7029i	−0.835517	+	0.482386i	0.0202209	+	0.999796i	$0.493563\pi$
$930$		0			0
$931$	9.36137	+	5.40479i	0.306806	+	0.177135i
$932$	22.3674	−	46.5588i	0.732667	−	1.52508i
$933$	−0.109313	−	0.106331i	−0.00357876	−	0.00348112i
$934$	12.6956	+	20.1838i	0.415414	+	0.660435i
$935$		0			0
$936$	44.1139	−	34.5829i	1.44191	−	1.13038i
$937$			20.2810i			0.662551i	0.943534	+	0.331276i	$0.107479\pi$
$937$			20.2810i			0.662551i	−0.943534	+	0.331276i	$0.892521\pi$
$938$	−24.5286	+	15.4285i	−0.800888	+	0.503759i
$939$	7.17257	+	25.3602i	0.234068	+	0.827600i
$940$		0			0
$941$	−7.09878	−	4.09848i	−0.231413	−	0.133607i	0.379810	−	0.925064i	$-0.375989\pi$
$941$	−7.09878	−	4.09848i	−0.231413	−	0.133607i	−0.611224	+	0.791458i	$0.709323\pi$
$942$	5.96151	−	27.9562i	0.194236	−	0.910863i
$943$	6.99850	+	12.1218i	0.227903	+	0.394739i
$944$	−31.8432	+	4.86114i	−1.03641	+	0.158217i
$945$		0			0
$946$	−0.682268	−	18.0064i	−0.0221824	−	0.585437i
$947$	−36.4493	+	21.0440i	−1.18444	+	0.683839i	−0.957038	−	0.289962i	$-0.906357\pi$
$947$	−36.4493	+	21.0440i	−1.18444	+	0.683839i	−0.227405	+	0.973800i	$0.573024\pi$
$948$	−57.9233	−	10.0757i	−1.88126	−	0.327243i
$949$	7.68074	−	13.3034i	0.249327	−	0.431848i
$950$		0			0
$951$	11.9426	−	3.37770i	0.387266	−	0.109530i
$952$	−25.0358	+	18.5321i	−0.811415	+	0.600630i
$953$	−17.5687			−0.569106			−0.284553	−	0.958660i	$-0.591845\pi$
$953$	−17.5687			−0.569106			−0.284553	+	0.958660i	$0.591845\pi$
$954$	13.5998	−	0.892488i	0.440309	−	0.0288954i
$955$		0			0
$956$	9.28735	+	13.5944i	0.300375	+	0.439675i
$957$	−24.1867	+	24.8651i	−0.781845	+	0.803774i
$958$	−6.62065	−	3.49512i	−0.213904	−	0.112922i
$959$	−16.4516	+	28.4950i	−0.531249	+	0.920150i
$960$		0			0
$961$	−1.88653	−	3.26756i	−0.0608557	−	0.105405i
$962$	−1.62130	−	42.7893i	−0.0522730	−	1.37958i
$963$	26.8456	−	49.6183i	0.865087	−	1.59893i
$964$	0.281408	−	0.0213560i	0.00906356	−	0.000687831i
$965$		0			0
$966$	14.5966	−	4.73212i	0.469639	−	0.152253i
$967$	11.6316	−	20.1466i	0.374048	−	0.647870i	−0.616136	−	0.787640i	$-0.711303\pi$
$967$	11.6316	−	20.1466i	0.374048	−	0.647870i	0.990184	+	0.139770i	$0.0446362\pi$
$968$	6.82907	+	2.96798i	0.219495	+	0.0953944i
$969$	39.8807	+	10.0970i	1.28115	+	0.324363i
$970$		0			0
$971$	−25.2618			−0.810688			−0.405344	−	0.914164i	$-0.632848\pi$
$971$	−25.2618			−0.810688			−0.405344	+	0.914164i	$0.632848\pi$
$972$	3.63651	−	30.9641i	0.116641	−	0.993174i
$973$		−	5.49901i		−	0.176290i
$974$	23.7348	−	14.9292i	0.760513	−	0.478363i
$975$		0			0
$976$	−0.934840	+	2.39523i	−0.0299235	+	0.0766695i
$977$	−12.4595	+	21.5806i	−0.398616	+	0.690423i	−0.993555	−	0.113347i	$-0.963843\pi$
$977$	−12.4595	+	21.5806i	−0.398616	+	0.690423i	0.594939	+	0.803771i	$0.297176\pi$
$978$	0.330870	+	1.02060i	0.0105801	+	0.0326351i
$979$	−9.33524	+	5.38970i	−0.298355	+	0.172256i
$980$		0			0
$981$	−8.94614	−	4.84024i	−0.285628	−	0.154537i
$982$	1.52329	+	40.2024i	0.0486100	+	1.28291i
$983$	−13.8502	+	7.99642i	−0.441753	+	0.255046i	−0.704341	−	0.709862i	$-0.748757\pi$
$983$	−13.8502	+	7.99642i	−0.441753	+	0.255046i	0.262588	+	0.964908i	$0.415424\pi$
$984$	−18.7454	−	14.4870i	−0.597582	−	0.461828i
$985$		0			0
$986$	−23.2590	+	44.0585i	−0.740716	+	1.40311i
$987$	0.0506684	−	0.0520896i	0.00161279	−	0.00165803i
$988$	34.7893	+	50.9231i	1.10679	+	1.62008i
$989$			12.7492i			0.405402i
$990$		0			0
$991$			29.4708i			0.936171i	0.883683	+	0.468085i	$0.155056\pi$
$991$			29.4708i			0.936171i	−0.883683	+	0.468085i	$0.844944\pi$
$992$	19.3065	+	22.3276i	0.612981	+	0.708903i
$993$	0.386367	+	1.36609i	0.0122610	+	0.0433514i
$994$	3.18412	+	1.68093i	0.100994	+	0.0533160i
$995$		0			0
$996$	−6.48860	−	1.12868i	−0.205599	−	0.0357637i
$997$	33.5185	−	19.3519i	1.06154	−	0.612881i	0.135683	−	0.990752i	$-0.456677\pi$
$997$	33.5185	−	19.3519i	1.06154	−	0.612881i	0.925858	+	0.377871i	$0.123344\pi$
$998$	7.98451	−	0.302536i	0.252745	−	0.00957661i
$999$	−17.5248	−	16.1278i	−0.554459	−	0.510260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.o.b.599.5		48
4.3	odd	2	inner	900.2.o.b.599.21		48
5.2	odd	4		900.2.r.f.851.8		48
5.3	odd	4		180.2.q.a.131.17	yes	48
5.4	even	2		900.2.o.c.599.20		48
9.2	odd	6		900.2.o.c.299.4		48
15.8	even	4		540.2.q.a.71.8		48
20.3	even	4		180.2.q.a.131.9	yes	48
20.7	even	4		900.2.r.f.851.16		48
20.19	odd	2		900.2.o.c.599.4		48
36.11	even	6		900.2.o.c.299.20		48
45.2	even	12		900.2.r.f.551.16		48
45.13	odd	12		1620.2.e.b.971.2		48
45.23	even	12		1620.2.e.b.971.47		48
45.29	odd	6	inner	900.2.o.b.299.21		48
45.38	even	12		180.2.q.a.11.9	✓	48
45.43	odd	12		540.2.q.a.251.16		48
60.23	odd	4		540.2.q.a.71.16		48
180.23	odd	12		1620.2.e.b.971.1		48
180.43	even	12		540.2.q.a.251.8		48
180.47	odd	12		900.2.r.f.551.8		48
180.83	odd	12		180.2.q.a.11.17	yes	48
180.103	even	12		1620.2.e.b.971.48		48
180.119	even	6	inner	900.2.o.b.299.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.9	✓	48	45.38	even	12
180.2.q.a.11.17	yes	48	180.83	odd	12
180.2.q.a.131.9	yes	48	20.3	even	4
180.2.q.a.131.17	yes	48	5.3	odd	4
540.2.q.a.71.8		48	15.8	even	4
540.2.q.a.71.16		48	60.23	odd	4
540.2.q.a.251.8		48	180.43	even	12
540.2.q.a.251.16		48	45.43	odd	12
900.2.o.b.299.5		48	180.119	even	6	inner
900.2.o.b.299.21		48	45.29	odd	6	inner
900.2.o.b.599.5		48	1.1	even	1	trivial
900.2.o.b.599.21		48	4.3	odd	2	inner
900.2.o.c.299.4		48	9.2	odd	6
900.2.o.c.299.20		48	36.11	even	6
900.2.o.c.599.4		48	20.19	odd	2
900.2.o.c.599.20		48	5.4	even	2
900.2.r.f.551.8		48	180.47	odd	12
900.2.r.f.551.16		48	45.2	even	12
900.2.r.f.851.8		48	5.2	odd	4
900.2.r.f.851.16		48	20.7	even	4
1620.2.e.b.971.1		48	180.23	odd	12
1620.2.e.b.971.2		48	45.13	odd	12
1620.2.e.b.971.47		48	45.23	even	12
1620.2.e.b.971.48		48	180.103	even	12

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.19709 + 0.752973i) q^{2} +(0.425108 - 1.67907i) q^{3} +(0.866065 - 1.80276i) q^{4} +(0.755401 + 2.33010i) q^{6} +(1.08216 + 1.87435i) q^{7} +(0.320666 + 2.81019i) q^{8} +(-2.63857 - 1.42758i) q^{9} +(-1.44632 - 2.50510i) q^{11} +(-2.65879 - 2.22055i) q^{12} +(5.72095 + 3.30299i) q^{13} +(-2.70678 - 1.42894i) q^{14} +(-2.49986 - 3.12261i) q^{16} +5.08829 q^{17} +(4.23353 - 0.277827i) q^{18} +4.66790i q^{19} +(3.60721 - 1.02022i) q^{21} +(3.61766 + 1.90980i) q^{22} +(-2.50662 - 1.44720i) q^{23} +(4.85483 + 0.656214i) q^{24} +(-9.33557 + 0.353728i) q^{26} +(-3.51868 + 3.82347i) q^{27} +(4.31623 - 0.327557i) q^{28} +(5.99593 - 3.46175i) q^{29} +(4.51887 + 2.60897i) q^{31} +(5.34381 + 1.85572i) q^{32} +(-4.82109 + 1.36354i) q^{33} +(-6.09115 + 3.83134i) q^{34} +(-4.85874 + 3.52032i) q^{36} +4.58347i q^{37} +(-3.51480 - 5.58792i) q^{38} +(7.97798 - 8.20175i) q^{39} +(-4.18802 - 2.41795i) q^{41} +(-3.54997 + 3.93743i) q^{42} +(-2.20241 - 3.81468i) q^{43} +(-5.76870 + 0.437785i) q^{44} +(4.09035 - 0.154985i) q^{46} +(0.0167877 - 0.00969237i) q^{47} +(-6.30580 + 2.87000i) q^{48} +(1.15786 - 2.00548i) q^{49} +(2.16307 - 8.54360i) q^{51} +(10.9092 - 7.45287i) q^{52} +3.21239 q^{53} +(1.33322 - 7.22652i) q^{54} +(-4.92028 + 3.64212i) q^{56} +(7.83775 + 1.98436i) q^{57} +(-4.57108 + 8.65881i) q^{58} +(4.02651 - 6.97412i) q^{59} +(-0.321400 - 0.556681i) q^{61} +(-7.37400 + 0.279404i) q^{62} +(-0.179566 - 6.49047i) q^{63} +(-7.79435 + 1.80227i) q^{64} +(4.74459 - 5.26243i) q^{66} +(4.73363 - 8.19888i) q^{67} +(4.40678 - 9.17294i) q^{68} +(-3.49553 + 3.59357i) q^{69} -1.17635 q^{71} +(3.16566 - 7.87265i) q^{72} -2.32539i q^{73} +(-3.45123 - 5.48685i) q^{74} +(8.41509 + 4.04271i) q^{76} +(3.13030 - 5.42184i) q^{77} +(-3.37469 + 15.8255i) q^{78} +(14.6983 - 8.48606i) q^{79} +(4.92406 + 7.53350i) q^{81} +(6.83410 - 0.258947i) q^{82} +(1.64651 - 0.950613i) q^{83} +(1.28487 - 7.38650i) q^{84} +(5.50883 + 2.90817i) q^{86} +(-3.26361 - 11.5392i) q^{87} +(6.57603 - 4.86774i) q^{88} -3.72649i q^{89} +14.2974i q^{91} +(-4.77983 + 3.26545i) q^{92} +(6.30166 - 6.47842i) q^{93} +(-0.0127983 + 0.0242433i) q^{94} +(5.38759 - 8.18375i) q^{96} +(-10.0127 + 5.78082i) q^{97} +(0.123999 + 3.27258i) q^{98} +(0.239992 + 8.67461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} - 12 q^{8} - 4 q^{9} - 28 q^{12} + 30 q^{14} + 18 q^{18} - 4 q^{21} + 42 q^{22} + 28 q^{24} + 12 q^{29} + 48 q^{33} + 6 q^{34} + 42 q^{36} + 6 q^{38} - 60 q^{41} - 16 q^{42} - 12 q^{46} + 74 q^{48}+ \cdots - 84 q^{98}+O(q^{100}) \) 48 * q + 6 * q^6 - 12 * q^8 - 4 * q^9 - 28 * q^12 + 30 * q^14 + 18 * q^18 - 4 * q^21 + 42 * q^22 + 28 * q^24 + 12 * q^29 + 48 * q^33 + 6 * q^34 + 42 * q^36 + 6 * q^38 - 60 * q^41 - 16 * q^42 - 12 * q^46 + 74 * q^48 - 24 * q^49 + 90 * q^52 + 32 * q^54 - 42 * q^56 + 16 * q^57 - 84 * q^58 - 84 * q^62 + 48 * q^64 + 16 * q^66 - 6 * q^68 - 36 * q^69 + 80 * q^72 - 84 * q^74 + 6 * q^76 + 46 * q^78 - 50 * q^84 - 54 * q^86 - 114 * q^88 + 42 * q^92 + 24 * q^93 - 18 * q^94 - 18 * q^96 + 48 * q^97 - 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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