LMFDB - Embedded newform 605.2.j.k.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.4
Character	$\chi$	$=$	605.9
Dual form			605.2.j.k.269.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92380 - 0.625081i) q^{2} +(1.71325 + 2.35809i) q^{3} +(1.69226 + 1.22950i) q^{4} +(-1.42178 + 1.72585i) q^{5} +(-1.82196 - 5.60741i) q^{6} +(-1.88754 + 2.59798i) q^{7} +(-0.109082 - 0.150138i) q^{8} +(-1.69829 + 5.22681i) q^{9} +O(q^{10})$	\(q+(-1.92380 - 0.625081i) q^{2} +(1.71325 + 2.35809i) q^{3} +(1.69226 + 1.22950i) q^{4} +(-1.42178 + 1.72585i) q^{5} +(-1.82196 - 5.60741i) q^{6} +(-1.88754 + 2.59798i) q^{7} +(-0.109082 - 0.150138i) q^{8} +(-1.69829 + 5.22681i) q^{9} +(3.81402 - 2.43146i) q^{10} +6.09692i q^{12} +(-0.617001 - 0.200476i) q^{13} +(5.25521 - 3.81813i) q^{14} +(-6.50555 - 0.395871i) q^{15} +(-1.17677 - 3.62171i) q^{16} +(1.13030 - 0.367258i) q^{17} +(6.53436 - 8.99378i) q^{18} +(-1.52982 + 1.11148i) q^{19} +(-4.52794 + 1.17250i) q^{20} -9.36008 q^{21} +4.35986i q^{23} +(0.167155 - 0.514449i) q^{24} +(-0.957090 - 4.90754i) q^{25} +(1.06168 + 0.771352i) q^{26} +(-6.91857 + 2.24798i) q^{27} +(-6.38841 + 2.07572i) q^{28} +(3.36869 + 2.44750i) q^{29} +(12.2680 + 4.82808i) q^{30} +(2.44118 - 7.51319i) q^{31} +8.07420i q^{32} -2.40405 q^{34} +(-1.80004 - 6.95136i) q^{35} +(-9.30029 + 6.75706i) q^{36} +(1.20995 - 1.66536i) q^{37} +(3.63783 - 1.18200i) q^{38} +(-0.584338 - 1.79841i) q^{39} +(0.414206 + 0.0252049i) q^{40} +(-2.67396 + 1.94275i) q^{41} +(18.0070 + 5.85081i) q^{42} -10.9313i q^{43} +(-6.60607 - 10.3624i) q^{45} +(2.72527 - 8.38752i) q^{46} +(1.71325 + 2.35809i) q^{47} +(6.52422 - 8.97981i) q^{48} +(-1.02356 - 3.15019i) q^{49} +(-1.22636 + 10.0394i) q^{50} +(2.80252 + 2.03615i) q^{51} +(-0.797640 - 1.09786i) q^{52} +(-6.10422 - 1.98338i) q^{53} +14.7151 q^{54} +0.595953 q^{56} +(-5.24191 - 1.70320i) q^{57} +(-4.95081 - 6.81421i) q^{58} +(-3.00659 - 2.18442i) q^{59} +(-10.5223 - 8.66847i) q^{60} +(2.40630 + 7.40582i) q^{61} +(-9.39272 + 12.9280i) q^{62} +(-10.3735 - 14.2779i) q^{63} +(2.69350 - 8.28974i) q^{64} +(1.22323 - 0.779817i) q^{65} +2.37993i q^{67} +(2.36431 + 0.768210i) q^{68} +(-10.2809 + 7.46954i) q^{69} +(-0.882234 + 14.4982i) q^{70} +(4.85662 + 14.9471i) q^{71} +(0.969998 - 0.315171i) q^{72} +(3.35877 - 4.62295i) q^{73} +(-3.36869 + 2.44750i) q^{74} +(9.93267 - 10.6647i) q^{75} -3.95540 q^{76} +3.82504i q^{78} +(-4.71438 + 14.5094i) q^{79} +(7.92362 + 3.11836i) q^{80} +(-3.81561 - 2.77220i) q^{81} +(6.35854 - 2.06602i) q^{82} +(-10.1161 + 3.28693i) q^{83} +(-15.8397 - 11.5082i) q^{84} +(-0.973211 + 2.47289i) q^{85} +(-6.83298 + 21.0297i) q^{86} +12.1368i q^{87} -9.00000 q^{89} +(6.23146 + 24.0645i) q^{90} +(1.68545 - 1.22455i) q^{91} +(-5.36044 + 7.37801i) q^{92} +(21.8991 - 7.11545i) q^{93} +(-1.82196 - 5.60741i) q^{94} +(0.256823 - 4.22050i) q^{95} +(-19.0397 + 13.8331i) q^{96} +(-14.3972 - 4.67793i) q^{97} +6.70015i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9}+O(q^{10}) $ 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9	$ 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9} + 32 q^{14} - 20 q^{15} - 36 q^{16} - 26 q^{20} + 10 q^{25} - 20 q^{26} - 8 q^{31} + 48 q^{34} - 92 q^{36} - 72 q^{45} + 4 q^{49} + 192 q^{56} + 32 q^{59} + 92 q^{60} - 28 q^{64} + 16 q^{69} + 12 q^{70} - 112 q^{71} - 36 q^{75} + 106 q^{80} + 20 q^{81} + 56 q^{86} - 432 q^{89} - 72 q^{91}+O(q^{100}) $ 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9 + 32 * q^14 - 20 * q^15 - 36 * q^16 - 26 * q^20 + 10 * q^25 - 20 * q^26 - 8 * q^31 + 48 * q^34 - 92 * q^36 - 72 * q^45 + 4 * q^49 + 192 * q^56 + 32 * q^59 + 92 * q^60 - 28 * q^64 + 16 * q^69 + 12 * q^70 - 112 * q^71 - 36 * q^75 + 106 * q^80 + 20 * q^81 + 56 * q^86 - 432 * q^89 - 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.92380	−	0.625081i	−1.36033	−	0.441999i	−0.464179	−	0.885741i	$-0.653651\pi$
$2$	−1.92380	−	0.625081i	−1.36033	−	0.441999i	−0.896155	+	0.443742i	$0.853651\pi$
$3$	1.71325	+	2.35809i	0.989145	+	1.36144i	0.931754	+	0.363090i	$0.118278\pi$
$3$	1.71325	+	2.35809i	0.989145	+	1.36144i	0.0573908	+	0.998352i	$0.481722\pi$
$4$	1.69226	+	1.22950i	0.846128	+	0.614748i
$5$	−1.42178	+	1.72585i	−0.635839	+	0.771822i
$5$	−1.42178	+	1.72585i	−0.635839	+	0.771822i
$6$	−1.82196	−	5.60741i	−0.743812	−	2.28922i
$7$	−1.88754	+	2.59798i	−0.713424	+	0.981943i	0.286293	+	0.958142i	$0.407577\pi$
$7$	−1.88754	+	2.59798i	−0.713424	+	0.981943i	−0.999717	+	0.0238013i	$0.992423\pi$
$8$	−0.109082	−	0.150138i	−0.0385663	−	0.0530819i
$9$	−1.69829	+	5.22681i	−0.566098	+	1.74227i
$10$	3.81402	−	2.43146i	1.20610	−	0.768895i
$11$		0			0
$11$		0			0
$12$			6.09692i			1.76003i
$13$	−0.617001	−	0.200476i	−0.171125	−	0.0556020i	0.222201	−	0.975001i	$-0.428676\pi$
$13$	−0.617001	−	0.200476i	−0.171125	−	0.0556020i	−0.393327	+	0.919399i	$0.628676\pi$
$14$	5.25521	−	3.81813i	1.40451	−	1.02044i
$15$	−6.50555	−	0.395871i	−1.67973	−	0.102213i
$16$	−1.17677	−	3.62171i	−0.294191	−	0.905428i
$17$	1.13030	−	0.367258i	0.274139	−	0.0890731i	−0.168721	−	0.985664i	$-0.553964\pi$
$17$	1.13030	−	0.367258i	0.274139	−	0.0890731i	0.442860	+	0.896591i	$0.353964\pi$
$18$	6.53436	−	8.99378i	1.54016	−	2.11985i
$19$	−1.52982	+	1.11148i	−0.350964	+	0.254990i	−0.749273	−	0.662261i	$-0.769597\pi$
$19$	−1.52982	+	1.11148i	−0.350964	+	0.254990i	0.398309	+	0.917251i	$0.369597\pi$
$20$	−4.52794	+	1.17250i	−1.01248	+	0.262180i
$21$	−9.36008			−2.04254
$22$		0			0
$23$			4.35986i			0.909095i	0.890723	+	0.454547i	$0.150199\pi$
$23$			4.35986i			0.909095i	−0.890723	+	0.454547i	$0.849801\pi$
$24$	0.167155	−	0.514449i	0.0341203	−	0.105011i
$25$	−0.957090	−	4.90754i	−0.191418	−	0.981509i
$26$	1.06168	+	0.771352i	0.208212	+	0.151275i
$27$	−6.91857	+	2.24798i	−1.33148	+	0.432624i
$28$	−6.38841	+	2.07572i	−1.20730	+	0.392274i
$29$	3.36869	+	2.44750i	0.625550	+	0.454489i	0.854856	−	0.518866i	$-0.173645\pi$
$29$	3.36869	+	2.44750i	0.625550	+	0.454489i	−0.229306	+	0.973354i	$0.573645\pi$
$30$	12.2680	+	4.82808i	2.23981	+	0.881483i
$31$	2.44118	−	7.51319i	0.438450	−	1.34941i	−0.451060	−	0.892493i	$-0.648954\pi$
$31$	2.44118	−	7.51319i	0.438450	−	1.34941i	0.889510	−	0.456916i	$-0.151046\pi$
$32$			8.07420i			1.42733i
$33$		0			0
$34$	−2.40405			−0.412291
$35$	−1.80004	−	6.95136i	−0.304263	−	1.17499i
$36$	−9.30029	+	6.75706i	−1.55005	+	1.12618i
$37$	1.20995	−	1.66536i	0.198915	−	0.273783i	−0.697894	−	0.716201i	$-0.745879\pi$
$37$	1.20995	−	1.66536i	0.198915	−	0.273783i	0.896809	+	0.442418i	$0.145879\pi$
$38$	3.63783	−	1.18200i	0.590134	−	0.191746i
$39$	−0.584338	−	1.79841i	−0.0935689	−	0.287976i
$40$	0.414206	+	0.0252049i	0.0654918	+	0.00398525i
$41$	−2.67396	+	1.94275i	−0.417602	+	0.303406i	−0.776672	−	0.629905i	$-0.783094\pi$
$41$	−2.67396	+	1.94275i	−0.417602	+	0.303406i	0.359070	+	0.933311i	$0.383094\pi$
$42$	18.0070	+	5.85081i	2.77853	+	0.902800i
$43$		−	10.9313i		−	1.66701i	−0.552509	−	0.833507i	$-0.686330\pi$
$43$		−	10.9313i		−	1.66701i	0.552509	−	0.833507i	$-0.313670\pi$
$44$		0			0
$45$	−6.60607	−	10.3624i	−0.984775	−	1.54473i
$46$	2.72527	−	8.38752i	0.401819	−	1.23667i
$47$	1.71325	+	2.35809i	0.249903	+	0.343962i	0.915477	−	0.402370i	$-0.131813\pi$
$47$	1.71325	+	2.35809i	0.249903	+	0.343962i	−0.665574	+	0.746332i	$0.731813\pi$
$48$	6.52422	−	8.97981i	0.941689	−	1.29612i
$49$	−1.02356	−	3.15019i	−0.146223	−	0.450027i
$50$	−1.22636	+	10.0394i	−0.173434	+	1.41979i
$51$	2.80252	+	2.03615i	0.392431	+	0.285118i
$52$	−0.797640	−	1.09786i	−0.110613	−	0.152245i
$53$	−6.10422	−	1.98338i	−0.838479	−	0.272438i	−0.141866	−	0.989886i	$-0.545310\pi$
$53$	−6.10422	−	1.98338i	−0.838479	−	0.272438i	−0.696613	+	0.717447i	$0.745310\pi$
$54$	14.7151			2.00248
$55$		0			0
$56$	0.595953			0.0796376
$57$	−5.24191	−	1.70320i	−0.694308	−	0.225594i
$58$	−4.95081	−	6.81421i	−0.650074	−	0.894750i
$59$	−3.00659	−	2.18442i	−0.391425	−	0.284387i	0.374614	−	0.927181i	$-0.377775\pi$
$59$	−3.00659	−	2.18442i	−0.391425	−	0.284387i	−0.766039	+	0.642794i	$0.777775\pi$
$60$	−10.5223	−	8.66847i	−1.35843	−	1.11909i
$61$	2.40630	+	7.40582i	0.308095	+	0.948218i	0.978504	+	0.206227i	$0.0661184\pi$
$61$	2.40630	+	7.40582i	0.308095	+	0.948218i	−0.670410	+	0.741991i	$0.733882\pi$
$62$	−9.39272	+	12.9280i	−1.19288	+	1.64185i
$63$	−10.3735	−	14.2779i	−1.30694	−	1.79885i
$64$	2.69350	−	8.28974i	0.336688	−	1.03622i
$65$	1.22323	−	0.779817i	0.151723	−	0.0967244i
$66$		0			0
$67$			2.37993i			0.290755i	0.989376	+	0.145377i	$0.0464396\pi$
$67$			2.37993i			0.290755i	−0.989376	+	0.145377i	$0.953560\pi$
$68$	2.36431	+	0.768210i	0.286714	+	0.0931591i
$69$	−10.2809	+	7.46954i	−1.23768	+	0.899226i
$70$	−0.882234	+	14.4982i	−0.105447	+	1.73287i
$71$	4.85662	+	14.9471i	0.576375	+	1.77390i	0.631450	+	0.775417i	$0.282460\pi$
$71$	4.85662	+	14.9471i	0.576375	+	1.77390i	−0.0550754	+	0.998482i	$0.517540\pi$
$72$	0.969998	−	0.315171i	0.114315	−	0.0371433i
$73$	3.35877	−	4.62295i	0.393114	−	0.541075i	−0.565885	−	0.824484i	$-0.691465\pi$
$73$	3.35877	−	4.62295i	0.393114	−	0.541075i	0.958999	+	0.283409i	$0.0914653\pi$
$74$	−3.36869	+	2.44750i	−0.391602	+	0.284516i
$75$	9.93267	−	10.6647i	1.14693	−	1.23146i
$76$	−3.95540			−0.453715
$77$		0			0
$78$			3.82504i			0.433100i
$79$	−4.71438	+	14.5094i	−0.530410	+	1.63243i	0.222954	+	0.974829i	$0.428430\pi$
$79$	−4.71438	+	14.5094i	−0.530410	+	1.63243i	−0.753364	+	0.657604i	$0.771570\pi$
$80$	7.92362	+	3.11836i	0.885888	+	0.348643i
$81$	−3.81561	−	2.77220i	−0.423956	−	0.308022i
$82$	6.35854	−	2.06602i	0.702184	−	0.228153i
$83$	−10.1161	+	3.28693i	−1.11039	+	0.360787i	−0.806092	−	0.591790i	$-0.798421\pi$
$83$	−10.1161	+	3.28693i	−1.11039	+	0.360787i	−0.304297	+	0.952577i	$0.598421\pi$
$84$	−15.8397	−	11.5082i	−1.72825	−	1.25565i
$85$	−0.973211	+	2.47289i	−0.105560	+	0.268222i
$86$	−6.83298	+	21.0297i	−0.736819	+	2.26770i
$87$			12.1368i			1.30121i
$88$		0			0
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$	6.23146	+	24.0645i	0.656854	+	2.53662i
$91$	1.68545	−	1.22455i	0.176683	−	0.128368i
$92$	−5.36044	+	7.37801i	−0.558864	+	0.769211i
$93$	21.8991	−	7.11545i	2.27083	−	0.737838i
$94$	−1.82196	−	5.60741i	−0.187921	−	0.578360i
$95$	0.256823	−	4.22050i	0.0263494	−	0.433014i
$96$	−19.0397	+	13.8331i	−1.94323	+	1.41184i
$97$	−14.3972	−	4.67793i	−1.46181	−	0.474971i	−0.533189	−	0.845996i	$-0.679006\pi$
$97$	−14.3972	−	4.67793i	−1.46181	−	0.474971i	−0.928623	+	0.371025i	$0.879006\pi$
$98$			6.70015i			0.676817i
$99$		0			0
$100$	4.41416	−	9.48156i	0.441416	−	0.948156i
$101$	1.72375	−	5.30516i	0.171519	−	0.527883i	−0.827938	−	0.560820i	$-0.810486\pi$
$101$	1.72375	−	5.30516i	0.171519	−	0.527883i	0.999457	+	0.0329370i	$0.0104861\pi$
$102$	−4.11873	−	5.66895i	−0.407815	−	0.561310i
$103$	−1.87043	+	2.57443i	−0.184299	+	0.253666i	−0.891163	−	0.453684i	$-0.850109\pi$
$103$	−1.87043	+	2.57443i	−0.184299	+	0.253666i	0.706864	+	0.707350i	$0.250109\pi$
$104$	0.0372046	+	0.114504i	0.00364821	+	0.0112280i
$105$	13.3080	−	16.1541i	1.29872	−	1.57648i
$106$	10.5035	+	7.63127i	1.02019	+	0.741214i
$107$	−2.33296	−	3.21104i	−0.225536	−	0.310423i	0.681221	−	0.732078i	$-0.261449\pi$
$107$	−2.33296	−	3.21104i	−0.225536	−	0.310423i	−0.906756	+	0.421655i	$0.861449\pi$
$108$	−14.4719	−	4.70220i	−1.39256	−	0.452470i
$109$	−15.4150			−1.47649			−0.738243	−	0.674535i	$-0.764344\pi$
$109$	−15.4150			−1.47649			−0.738243	+	0.674535i	$0.764344\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$	11.6303	+	3.77892i	1.09896	+	0.357074i
$113$	5.95741	+	8.19967i	0.560426	+	0.771360i	0.991381	−	0.131014i	$-0.0418231\pi$
$113$	5.95741	+	8.19967i	0.560426	+	0.771360i	−0.430955	+	0.902374i	$0.641823\pi$
$114$	9.01977	+	6.55325i	0.844779	+	0.613768i
$115$	−7.52446	−	6.19876i	−0.701659	−	0.578038i
$116$	2.69150	+	8.28359i	0.249900	+	0.769112i
$117$	2.09570	−	2.88448i	0.193747	−	0.266670i
$118$	4.41865	+	6.08175i	0.406770	+	0.559870i
$119$	−1.17937	+	3.62972i	−0.108112	+	0.332736i
$120$	0.650203	+	1.01992i	0.0593552	+	0.0931052i
$121$		0			0
$122$		−	15.7515i		−	1.42607i
$123$	−9.16232	−	2.97702i	−0.826138	−	0.268429i
$124$	13.3686	−	9.71282i	1.20053	−	0.872237i
$125$	9.83044	+	5.32565i	0.879261	+	0.476341i
$126$	11.0318	+	33.9523i	0.982787	+	3.02471i
$127$	15.6382	−	5.08117i	1.38767	−	0.450881i	0.482486	−	0.875904i	$-0.339734\pi$
$127$	15.6382	−	5.08117i	1.38767	−	0.450881i	0.905183	+	0.425023i	$0.139734\pi$
$128$	−0.871737	+	1.19984i	−0.0770514	+	0.106052i
$129$	25.7770	−	18.7281i	2.26954	−	1.64892i
$130$	−2.84070	+	0.735596i	−0.249146	+	0.0645160i
$131$	14.0007			1.22325			0.611625	−	0.791148i	$-0.290516\pi$
$131$	14.0007			1.22325			0.611625	+	0.791148i	$0.290516\pi$
$132$		0			0
$133$		−	6.07239i		−	0.526543i
$134$	1.48765	−	4.57851i	0.128513	−	0.395523i
$135$	5.95701	−	15.1365i	0.512698	−	1.30274i
$136$	−0.178435	−	0.129641i	−0.0153007	−	0.0111166i
$137$	−13.0975	+	4.25564i	−1.11900	+	0.363584i	−0.809384	−	0.587280i	$-0.800199\pi$
$137$	−13.0975	+	4.25564i	−1.11900	+	0.363584i	−0.309611	+	0.950863i	$0.600199\pi$
$138$	24.4476	−	7.94349i	2.08111	−	0.676195i
$139$	5.46468	+	3.97032i	0.463508	+	0.336758i	0.794906	−	0.606733i	$-0.207520\pi$
$139$	5.46468	+	3.97032i	0.463508	+	0.336758i	−0.331398	+	0.943491i	$0.607520\pi$
$140$	5.50053	−	13.9766i	0.464880	−	1.18124i
$141$	−2.62534	+	8.07998i	−0.221094	+	0.680457i
$142$		−	31.7911i		−	2.66785i
$143$		0			0
$144$	20.9285			1.74404
$145$	−9.01354	+	2.33404i	−0.748534	+	0.193832i
$146$	−9.35133	+	6.79414i	−0.773922	+	0.562287i
$147$	5.67480	−	7.81069i	0.468050	−	0.644215i
$148$	4.09510	−	1.33058i	0.336615	−	0.109373i
$149$	5.93216	+	18.2573i	0.485982	+	1.49570i	0.830554	+	0.556938i	$0.188024\pi$
$149$	5.93216	+	18.2573i	0.485982	+	1.49570i	−0.344572	+	0.938760i	$0.611976\pi$
$150$	−25.7748	+	14.3081i	−2.10451	+	1.16825i
$151$	2.66216	−	1.93418i	0.216644	−	0.157401i	−0.474171	−	0.880433i	$-0.657252\pi$
$151$	2.66216	−	1.93418i	0.216644	−	0.157401i	0.690815	+	0.723032i	$0.257252\pi$
$152$	0.333751	+	0.108442i	0.0270708	+	0.00879582i
$153$			6.53159i			0.528048i
$154$		0			0
$155$	9.49579	+	14.8952i	0.762720	+	1.19641i
$156$	1.22229	−	3.76181i	0.0978612	−	0.301186i
$157$	8.23746	+	11.3379i	0.657421	+	0.904863i	0.999393	−	0.0348477i	$-0.0110946\pi$
$157$	8.23746	+	11.3379i	0.657421	+	0.904863i	−0.341971	+	0.939710i	$0.611095\pi$
$158$	18.1391	−	24.9663i	1.44307	−	1.98621i
$159$	−5.78107	−	17.7923i	−0.458469	−	1.41102i
$160$	−13.9348	−	11.4797i	−1.10164	−	0.907552i
$161$	−11.3268	−	8.22942i	−0.892679	−	0.648570i
$162$	5.60762	+	7.71823i	0.440577	+	0.606402i
$163$	9.81676	+	3.18966i	0.768908	+	0.249833i	0.667097	−	0.744970i	$-0.267536\pi$
$163$	9.81676	+	3.18966i	0.768908	+	0.249833i	0.101811	+	0.994804i	$0.467536\pi$
$164$	−6.91362			−0.539863
$165$		0			0
$166$	21.5160			1.66997
$167$	13.8909	+	4.51344i	1.07491	+	0.349260i	0.792399	−	0.610003i	$-0.208832\pi$
$167$	13.8909	+	4.51344i	1.07491	+	0.349260i	0.282513	+	0.959263i	$0.408832\pi$
$168$	1.02102	+	1.40531i	0.0787731	+	0.108422i
$169$	−10.1767	−	7.39382i	−0.782825	−	0.568755i
$170$	3.41802	−	4.14902i	0.262150	−	0.318215i
$171$	−3.21140	−	9.88367i	−0.245582	−	0.755823i
$172$	13.4400	−	18.4986i	1.02479	−	1.41051i
$173$	1.29806	+	1.78662i	0.0986895	+	0.135834i	0.855506	−	0.517793i	$-0.173246\pi$
$173$	1.29806	+	1.78662i	0.0986895	+	0.135834i	−0.756816	+	0.653628i	$0.773246\pi$
$174$	7.58651	−	23.3489i	0.575132	−	1.77007i
$175$	14.5562	+	6.77669i	1.10035	+	0.512270i
$176$		0			0
$177$		−	10.8322i		−	0.814201i
$178$	17.3142	+	5.62573i	1.29776	+	0.421667i
$179$	8.74393	−	6.35284i	0.653552	−	0.474833i	−0.210927	−	0.977502i	$-0.567648\pi$
$179$	8.74393	−	6.35284i	0.653552	−	0.474833i	0.864479	+	0.502668i	$0.167648\pi$
$180$	1.56131	−	25.6579i	0.116374	−	1.91243i
$181$	−1.04045	−	3.20219i	−0.0773363	−	0.238017i	0.904913	−	0.425596i	$-0.139936\pi$
$181$	−1.04045	−	3.20219i	−0.0773363	−	0.238017i	−0.982249	+	0.187580i	$0.939936\pi$
$182$	−4.00791	+	1.30225i	−0.297086	+	0.0965291i
$183$	−13.3410	+	18.3623i	−0.986193	+	1.35738i
$184$	0.654583	−	0.475582i	0.0482565	−	0.0350604i
$185$	1.15386	+	4.45596i	0.0848338	+	0.327609i
$186$	−46.5773			−3.41521
$187$		0			0
$188$			6.09692i			0.444664i
$189$	7.21889	−	22.2175i	0.525097	−	1.61608i
$190$	−3.13223	+	7.95888i	−0.227236	+	0.577398i
$191$	−7.50382	−	5.45185i	−0.542957	−	0.394482i	0.282225	−	0.959348i	$-0.408928\pi$
$191$	−7.50382	−	5.45185i	−0.542957	−	0.394482i	−0.825182	+	0.564867i	$0.808928\pi$
$192$	24.1626	−	7.85089i	1.74378	−	0.566589i
$193$	−4.62491	+	1.50273i	−0.332908	+	0.108169i	−0.470702	−	0.882293i	$-0.655999\pi$
$193$	−4.62491	+	1.50273i	−0.332908	+	0.108169i	0.137793	+	0.990461i	$0.455999\pi$
$194$	24.7732	+	17.9988i	1.77862	+	1.29224i
$195$	3.93457	+	1.54846i	0.281761	+	0.110887i
$196$	2.14102	−	6.58939i	0.152930	−	0.470670i
$197$			11.8747i			0.846038i	0.906121	+	0.423019i	$0.139030\pi$
$197$			11.8747i			0.846038i	−0.906121	+	0.423019i	$0.860970\pi$
$198$		0			0
$199$	4.99158			0.353844			0.176922	−	0.984225i	$-0.443386\pi$
$199$	4.99158			0.353844			0.176922	+	0.984225i	$0.443386\pi$
$200$	−0.632409	+	0.679020i	−0.0447181	+	0.0480140i
$201$	−5.61208	+	4.07741i	−0.395845	+	0.287598i
$202$	−6.63231	+	9.12859i	−0.466648	+	0.642285i
$203$	−12.7171	+	4.13203i	−0.892565	+	0.290012i
$204$	2.23914	+	6.89137i	0.156771	+	0.482492i
$205$	0.448899	−	7.37700i	0.0313525	−	0.515232i
$206$	5.20757	−	3.78352i	0.362828	−	0.263610i
$207$	−22.7882	−	7.40433i	−1.58389	−	0.514636i
$208$			2.47051i			0.171299i
$209$		0			0
$210$	−35.6995	+	22.7587i	−2.46350	+	1.57050i
$211$	0.486128	−	1.49615i	0.0334665	−	0.102999i	−0.932928	−	0.360063i	$-0.882755\pi$
$211$	0.486128	−	1.49615i	0.0334665	−	0.102999i	0.966394	+	0.257064i	$0.0827551\pi$
$212$	−7.89135	−	10.8615i	−0.541980	−	0.745971i
$213$	−26.9260	+	37.0605i	−1.84494	+	2.53934i
$214$	2.48099	+	7.63570i	0.169597	+	0.521966i
$215$	18.8658	+	15.5419i	1.28664	+	1.05995i
$216$	1.09220	+	0.793530i	0.0743148	+	0.0539928i
$217$	14.9113	+	20.5236i	1.01224	+	1.39323i
$218$	29.6554	+	9.63561i	2.00852	+	0.652606i
$219$	16.6557			1.12549
$220$		0			0
$221$	−0.771025			−0.0518647
$222$	−11.5428	−	3.75049i	−0.774703	−	0.251716i
$223$	1.94836	+	2.68169i	0.130472	+	0.179579i	0.869255	−	0.494364i	$-0.164599\pi$
$223$	1.94836	+	2.68169i	0.130472	+	0.179579i	−0.738783	+	0.673943i	$0.764599\pi$
$224$	−20.9766	−	15.2404i	−1.40156	−	1.01829i
$225$	27.2762	+	3.33192i	1.81841	+	0.222128i
$226$	−6.33542	−	19.4984i	−0.421426	−	1.29702i
$227$	1.66938	−	2.29770i	0.110800	−	0.152504i	−0.750015	−	0.661421i	$-0.769954\pi$
$227$	1.66938	−	2.29770i	0.110800	−	0.152504i	0.860816	+	0.508917i	$0.169954\pi$
$228$	−6.77658	−	9.32717i	−0.448790	−	0.617707i
$229$	0.615433	−	1.89411i	0.0406690	−	0.125166i	−0.928661	−	0.370930i	$-0.879039\pi$
$229$	0.615433	−	1.89411i	0.0406690	−	0.125166i	0.969330	+	0.245764i	$0.0790389\pi$
$230$	10.6008	+	16.6286i	0.698999	+	1.09646i
$231$		0			0
$232$		−	0.772748i		−	0.0507334i
$233$	19.2623	+	6.25868i	1.26191	+	0.410020i	0.862175	−	0.506610i	$-0.169102\pi$
$233$	19.2623	+	6.25868i	1.26191	+	0.410020i	0.399737	+	0.916630i	$0.369102\pi$
$234$	−5.83474	+	4.23919i	−0.381429	+	0.277125i
$235$	−6.50555	−	0.395871i	−0.424376	−	0.0258238i
$236$	−2.40219	−	7.39318i	−0.156369	−	0.481255i
$237$	−42.2913	+	13.7413i	−2.74711	+	0.892591i
$238$	4.53774	−	6.24566i	0.294138	−	0.404846i
$239$	−1.52982	+	1.11148i	−0.0989556	+	0.0718954i	−0.636163	−	0.771555i	$-0.719479\pi$
$239$	−1.52982	+	1.11148i	−0.0989556	+	0.0718954i	0.537207	+	0.843450i	$0.319479\pi$
$240$	6.22178	+	24.0271i	0.401614	+	1.55094i
$241$	−4.00503			−0.257986			−0.128993	−	0.991645i	$-0.541175\pi$
$241$	−4.00503			−0.257986			−0.128993	+	0.991645i	$0.541175\pi$
$242$		0			0
$243$			8.07686i			0.518131i
$244$	−5.03336	+	15.4911i	−0.322228	+	0.991715i
$245$	6.89201	+	2.71237i	0.440314	+	0.173287i
$246$	15.7656	+	11.4544i	1.00518	+	0.730305i
$247$	1.16672	−	0.379091i	0.0742368	−	0.0241210i
$248$	−1.39431	+	0.453038i	−0.0885386	+	0.0287680i
$249$	−25.0823	−	18.2234i	−1.58953	−	1.15486i
$250$	−15.5829	−	16.3903i	−0.985546	−	1.03662i
$251$	7.01714	−	21.5965i	0.442918	−	1.36316i	−0.441833	−	0.897097i	$-0.645672\pi$
$251$	7.01714	−	21.5965i	0.442918	−	1.36316i	0.884751	−	0.466064i	$-0.154328\pi$
$252$		−	36.9162i		−	2.32550i
$253$		0			0
$254$	−33.2610			−2.08698
$255$	−7.49864	+	1.94176i	−0.469583	+	0.121598i
$256$	−11.6763	+	8.48333i	−0.729769	+	0.530208i
$257$	−2.38815	+	3.28701i	−0.148969	+	0.205038i	−0.876979	−	0.480528i	$-0.840445\pi$
$257$	−2.38815	+	3.28701i	−0.148969	+	0.205038i	0.728011	+	0.685566i	$0.240445\pi$
$258$	−61.2965	+	19.9164i	−3.81616	+	1.23994i
$259$	2.04272	+	6.28686i	0.126929	+	0.390646i
$260$	3.02880	+	0.184306i	0.187838	+	0.0114302i
$261$	−18.5136	+	13.4509i	−1.14596	+	0.832592i
$262$	−26.9347	−	8.75160i	−1.66403	−	0.540676i
$263$		−	12.3054i		−	0.758783i	−0.925236	−	0.379391i	$-0.876133\pi$
$263$		−	12.3054i		−	0.758783i	0.925236	−	0.379391i	$-0.123867\pi$
$264$		0			0
$265$	12.1019	−	7.71502i	0.743411	−	0.473930i
$266$	−3.79574	+	11.6821i	−0.232732	+	0.716274i
$267$	−15.4192	−	21.2228i	−0.943642	−	1.29881i
$268$	−2.92611	+	4.02745i	−0.178741	+	0.246016i
$269$	2.38188	+	7.33068i	0.145226	+	0.446959i	0.997040	−	0.0768848i	$-0.0244974\pi$
$269$	2.38188	+	7.33068i	0.145226	+	0.446959i	−0.851814	+	0.523844i	$0.824497\pi$
$270$	−20.9217	+	25.3961i	−1.27325	+	1.54556i
$271$	12.5995	+	9.15410i	0.765367	+	0.556072i	0.900552	−	0.434749i	$-0.143163\pi$
$271$	12.5995	+	9.15410i	0.765367	+	0.556072i	−0.135185	+	0.990820i	$0.543163\pi$
$272$	−2.66020	−	3.66146i	−0.161299	−	0.222008i
$273$	5.77518	+	1.87647i	0.349530	+	0.113569i
$274$	27.8571			1.68291
$275$		0			0
$276$	−26.5817			−1.60003
$277$	−19.3093	−	6.27399i	−1.16019	−	0.376967i	−0.335215	−	0.942142i	$-0.608809\pi$
$277$	−19.3093	−	6.27399i	−1.16019	−	0.376967i	−0.824971	+	0.565175i	$0.808809\pi$
$278$	−8.03120	−	11.0540i	−0.481679	−	0.662974i
$279$	35.1242	+	25.5192i	2.10283	+	1.52779i
$280$	−0.847313	+	1.02852i	−0.0506367	+	0.0614660i
$281$	−7.48425	−	23.0342i	−0.446473	−	1.37410i	−0.880860	−	0.473377i	$-0.843035\pi$
$281$	−7.48425	−	23.0342i	−0.446473	−	1.37410i	0.434387	−	0.900726i	$-0.356965\pi$
$282$	10.1013	−	13.9032i	0.601523	−	0.827925i
$283$	8.48599	+	11.6800i	0.504440	+	0.694302i	0.982969	−	0.183770i	$-0.0588300\pi$
$283$	8.48599	+	11.6800i	0.504440	+	0.694302i	−0.478529	+	0.878072i	$0.658830\pi$
$284$	−10.1588	+	31.2656i	−0.602814	+	1.85527i
$285$	10.3923	−	6.62516i	0.615587	−	0.392441i
$286$		0			0
$287$		−	10.6139i		−	0.626519i
$288$	−42.2023	−	13.7124i	−2.48679	−	0.808008i
$289$	−12.6106	+	9.16212i	−0.741799	+	0.538948i
$290$	18.7992	+	1.14396i	1.10393	+	0.0671754i
$291$	−13.6350	−	41.9642i	−0.799298	−	2.45999i
$292$	11.3678	−	3.69362i	0.665250	−	0.216153i
$293$	−8.91231	+	12.2667i	−0.520663	+	0.716631i	−0.985672	−	0.168675i	$-0.946051\pi$
$293$	−8.91231	+	12.2667i	−0.520663	+	0.716631i	0.465009	+	0.885306i	$0.346051\pi$
$294$	−15.7995	+	11.4790i	−0.921447	+	0.669470i
$295$	8.04467	−	2.08316i	0.468379	−	0.121286i
$296$	−0.382018			−0.0222043
$297$		0			0
$298$		−	38.8316i		−	2.24945i
$299$	0.874048	−	2.69004i	0.0505475	−	0.155569i
$300$	29.9209	−	5.83530i	1.72748	−	0.336901i
$301$	28.3994	+	20.6334i	1.63691	+	1.18929i
$302$	−6.33050	+	2.05690i	−0.364279	+	0.118361i
$303$	15.4632	−	5.02431i	0.888339	−	0.288639i
$304$	5.82568	+	4.23261i	0.334126	+	0.242757i
$305$	−16.2025	−	6.37654i	−0.927754	−	0.365120i
$306$	4.08278	−	12.5655i	0.233397	−	0.718321i
$307$			8.04171i			0.458965i	0.973313	+	0.229482i	$0.0737033\pi$
$307$			8.04171i			0.458965i	−0.973313	+	0.229482i	$0.926297\pi$
$308$		0			0
$309$	−9.27523			−0.527650
$310$	−8.95731	−	34.5911i	−0.508741	−	1.96464i
$311$	−18.0142	+	13.0881i	−1.02149	+	0.742158i	−0.966588	−	0.256333i	$-0.917486\pi$
$311$	−18.0142	+	13.0881i	−1.02149	+	0.742158i	−0.0549049	+	0.998492i	$0.517486\pi$
$312$	−0.206269	+	0.283905i	−0.0116777	+	0.0160730i
$313$	2.23540	−	0.726326i	0.126352	−	0.0410543i	−0.245158	−	0.969483i	$-0.578840\pi$
$313$	2.23540	−	0.726326i	0.126352	−	0.0410543i	0.371511	+	0.928429i	$0.378840\pi$
$314$	−8.76015	−	26.9610i	−0.494364	−	1.52150i
$315$	39.3904	+	2.39695i	2.21940	+	0.135053i
$316$	−25.8172	+	18.7573i	−1.45233	+	1.05518i
$317$	17.1412	+	5.56952i	0.962747	+	0.312815i	0.747885	−	0.663829i	$-0.231070\pi$
$317$	17.1412	+	5.56952i	0.962747	+	0.312815i	0.214863	+	0.976644i	$0.431070\pi$
$318$			37.8425i			2.12210i
$319$		0			0
$320$	10.4773	+	16.4347i	0.585696	+	0.918730i
$321$	3.57497	−	11.0026i	0.199535	−	0.614107i
$322$	16.6465	+	22.9120i	0.927675	+	1.27683i
$323$	−1.32096	+	1.81814i	−0.0735001	+	0.101164i
$324$	−3.04858	−	9.38255i	−0.169365	−	0.521253i
$325$	−0.393318	+	3.21983i	−0.0218174	+	0.178604i
$326$	−16.8917	−	12.2726i	−0.935546	−	0.679714i
$327$	−26.4097	−	36.3498i	−1.46046	−	2.01015i
$328$	0.583361	+	0.189546i	0.0322107	+	0.0104659i
$329$	−9.36008			−0.516038
$330$		0			0
$331$	−3.09174			−0.169938			−0.0849688	−	0.996384i	$-0.527079\pi$
$331$	−3.09174			−0.169938			−0.0849688	+	0.996384i	$0.527079\pi$
$332$	−21.1603	−	6.87541i	−1.16132	−	0.377337i
$333$	6.64964	+	9.15245i	0.364398	+	0.501551i
$334$	−23.9021	−	17.3659i	−1.30787	−	0.950221i
$335$	−4.10739	−	3.38373i	−0.224411	−	0.184873i
$336$	11.0146	+	33.8995i	0.600897	+	1.84937i
$337$	21.1284	−	29.0807i	1.15094	−	1.58413i	0.410719	−	0.911762i	$-0.365278\pi$
$337$	21.1284	−	29.0807i	1.15094	−	1.58413i	0.740218	−	0.672367i	$-0.234722\pi$
$338$	14.9563	+	20.5855i	0.813514	+	1.11971i
$339$	−9.12900	+	28.0962i	−0.495819	+	1.52597i
$340$	−4.68733	+	2.98820i	−0.254206	+	0.162058i
$341$		0			0
$342$			21.0216i			1.13672i
$343$	−11.2626	−	3.65945i	−0.608124	−	0.197592i
$344$	−1.64121	+	1.19241i	−0.0884883	+	0.0642905i
$345$	1.72594	−	28.3633i	0.0929217	−	1.52703i
$346$	−1.38042	−	4.24850i	−0.0742119	−	0.228401i
$347$	−11.6627	+	3.78944i	−0.626087	+	0.203428i	−0.604841	−	0.796346i	$-0.706763\pi$
$347$	−11.6627	+	3.78944i	−0.626087	+	0.203428i	−0.0212460	+	0.999774i	$0.506763\pi$
$348$	−14.9222	+	20.5386i	−0.799914	+	1.10099i
$349$	−14.2981	+	10.3881i	−0.765357	+	0.556065i	−0.900549	−	0.434755i	$-0.856835\pi$
$349$	−14.2981	+	10.3881i	−0.765357	+	0.556065i	0.135192	+	0.990819i	$0.456835\pi$
$350$	−23.7673	−	22.1359i	−1.27042	−	1.18321i
$351$	4.71943			0.251905
$352$		0			0
$353$			18.7202i			0.996378i	0.867068	+	0.498189i	$0.166001\pi$
$353$			18.7202i			0.996378i	−0.867068	+	0.498189i	$0.833999\pi$
$354$	−6.77104	+	20.8391i	−0.359876	+	1.10759i
$355$	−32.7015	−	12.8697i	−1.73562	−	0.683055i
$356$	−15.2303	−	11.0655i	−0.807205	−	0.586469i
$357$	−10.5797	+	3.43756i	−0.559939	+	0.181935i
$358$	−20.7926	+	6.75594i	−1.09893	+	0.357062i
$359$	−30.1495	−	21.9049i	−1.59123	−	1.15610i	−0.902159	−	0.431403i	$-0.858019\pi$
$359$	−30.1495	−	21.9049i	−1.59123	−	1.15610i	−0.689071	−	0.724694i	$-0.741981\pi$
$360$	−0.835185	+	2.12217i	−0.0440181	+	0.111848i
$361$	−4.76637	+	14.6694i	−0.250861	+	0.772072i
$362$			6.81074i			0.357965i
$363$		0			0
$364$	4.35779			0.228410
$365$	3.20307	+	12.3695i	0.167657	+	0.647451i
$366$	37.1433	−	26.9862i	1.94151	−	1.41059i
$367$	10.5794	−	14.5613i	0.552242	−	0.760096i	−0.438072	−	0.898940i	$-0.644339\pi$
$367$	10.5794	−	14.5613i	0.552242	−	0.760096i	0.990314	+	0.138844i	$0.0443385\pi$
$368$	15.7902	−	5.13054i	0.823120	−	0.267448i
$369$	−5.61319	−	17.2756i	−0.292211	−	0.899333i
$370$	0.565529	−	9.29364i	0.0294005	−	0.483154i
$371$	16.6748	−	12.1149i	0.865710	−	0.628975i
$372$	45.8073	+	14.8837i	2.37500	+	0.771684i
$373$		−	0.202607i		−	0.0104906i	−0.999986	−	0.00524531i	$-0.998330\pi$
$373$		−	0.202607i		−	0.0104906i	0.999986	−	0.00524531i	$-0.00166964\pi$
$374$		0			0
$375$	4.28365	+	32.3052i	0.221207	+	1.66823i
$376$	0.167155	−	0.514449i	0.00862034	−	0.0265307i
$377$	−1.58782	−	2.18545i	−0.0817770	−	0.112556i
$378$	−27.7754	+	38.2296i	−1.42861	+	1.96632i
$379$	10.5014	+	32.3199i	0.539419	+	1.66016i	0.733901	+	0.679256i	$0.237697\pi$
$379$	10.5014	+	32.3199i	0.539419	+	1.66016i	−0.194482	+	0.980906i	$0.562303\pi$
$380$	5.62370	−	6.82641i	0.288490	−	0.350187i
$381$	38.7740	+	28.1710i	1.98645	+	1.44324i
$382$	11.0280	+	15.1788i	0.564243	+	0.776614i
$383$	6.79248	+	2.20701i	0.347080	+	0.112773i	0.477369	−	0.878703i	$-0.341591\pi$
$383$	6.79248	+	2.20701i	0.347080	+	0.112773i	−0.130289	+	0.991476i	$0.541591\pi$
$384$	−4.32284			−0.220599
$385$		0			0
$386$	9.83675			0.500677
$387$	57.1360	+	18.5646i	2.90439	+	0.943692i
$388$	−18.6122	−	25.6175i	−0.944893	−	1.30053i
$389$	10.7331	+	7.79804i	0.544189	+	0.395376i	0.825638	−	0.564200i	$-0.190815\pi$
$389$	10.7331	+	7.79804i	0.544189	+	0.395376i	−0.281450	+	0.959576i	$0.590815\pi$
$390$	−6.60143	−	5.43836i	−0.334276	−	0.275382i
$391$	1.60119	+	4.92797i	0.0809759	+	0.249218i
$392$	−0.361312	+	0.497304i	−0.0182490	+	0.0251176i
$393$	23.9867	+	33.0149i	1.20997	+	1.66538i
$394$	7.42266	−	22.8446i	0.373948	−	1.15089i
$395$	−18.3382	−	28.7654i	−0.922692	−	1.44735i
$396$		0			0
$397$			33.5614i			1.68440i	0.539165	+	0.842200i	$0.318740\pi$
$397$			33.5614i			1.68440i	−0.539165	+	0.842200i	$0.681260\pi$
$398$	−9.60282	−	3.12015i	−0.481346	−	0.156399i
$399$	14.3192	−	10.4035i	0.716857	−	0.520827i
$400$	−16.6474	+	9.24133i	−0.832372	+	0.462067i
$401$	10.3802	+	31.9469i	0.518361	+	1.59535i	0.777082	+	0.629399i	$0.216699\pi$
$401$	10.3802	+	31.9469i	0.518361	+	1.59535i	−0.258721	+	0.965952i	$0.583301\pi$
$402$	13.3452	−	4.33613i	0.665600	−	0.216267i
$403$	−3.01243	+	4.14625i	−0.150060	+	0.206539i
$404$	9.43970	−	6.85834i	0.469642	−	0.341215i
$405$	10.2093	−	2.64369i	0.507306	−	0.131366i
$406$	27.0480			1.34237
$407$		0			0
$408$		−	0.642872i		−	0.0318269i
$409$	2.52435	−	7.76914i	0.124821	−	0.384159i	−0.869048	−	0.494729i	$-0.835267\pi$
$409$	2.52435	−	7.76914i	0.124821	−	0.384159i	0.993868	+	0.110569i	$0.0352674\pi$
$410$	−5.47482	+	13.9113i	−0.270382	+	0.687030i
$411$	−32.4745	−	23.5941i	−1.60185	−	1.16381i
$412$	−6.33050	+	2.05690i	−0.311881	+	0.101336i
$413$	11.3501	−	3.68788i	0.558503	−	0.181469i
$414$	39.2117	+	28.4889i	1.92715	+	1.40015i
$415$	8.71016	−	22.1322i	0.427565	−	1.08642i
$416$	1.61868	−	4.98179i	0.0793624	−	0.244252i
$417$			19.6883i			0.964142i
$418$		0			0
$419$	−19.5329			−0.954243			−0.477121	−	0.878837i	$-0.658320\pi$
$419$	−19.5329			−0.954243			−0.477121	+	0.878837i	$0.658320\pi$
$420$	42.3819	−	10.9747i	2.06802	−	0.535512i
$421$	19.3422	−	14.0529i	0.942680	−	0.684897i	−0.00638396	−	0.999980i	$-0.502032\pi$
$421$	19.3422	−	14.0529i	0.942680	−	0.684897i	0.949064	+	0.315082i	$0.102032\pi$
$422$	−1.87043	+	2.57443i	−0.0910511	+	0.125321i
$423$	−15.2349	+	4.95011i	−0.740744	+	0.240682i
$424$	0.368078	+	1.13283i	0.0178755	+	0.0550150i
$425$	−2.88414	−	5.19551i	−0.139901	−	0.252019i
$426$	74.9662	−	54.4661i	3.63212	−	2.63889i
$427$	−23.7821	−	7.72729i	−1.15090	−	0.373950i
$428$		−	8.30227i		−	0.401306i
$429$		0			0
$430$	−26.5791	−	41.6923i	−1.28176	−	2.01058i
$431$	2.33735	−	7.19363i	0.112586	−	0.346505i	−0.878850	−	0.477099i	$-0.841688\pi$
$431$	2.33735	−	7.19363i	0.112586	−	0.346505i	0.991436	+	0.130594i	$0.0416884\pi$
$432$	16.2831	+	22.4117i	0.783420	+	1.07829i
$433$	15.0587	−	20.7265i	0.723675	−	0.996054i	−0.275718	−	0.961238i	$-0.588916\pi$
$433$	15.0587	−	20.7265i	0.723675	−	0.996054i	0.999394	−	0.0348152i	$-0.0110843\pi$
$434$	−15.8574	−	48.8041i	−0.761181	−	2.34267i
$435$	−20.9463	−	17.2559i	−1.00430	−	0.827357i
$436$	−26.0861	−	18.9527i	−1.24930	−	0.907668i
$437$	−4.84589	−	6.66979i	−0.231810	−	0.319059i
$438$	−32.0423	−	10.4112i	−1.53104	−	0.497466i
$439$	−20.4668			−0.976827			−0.488413	−	0.872612i	$-0.662424\pi$
$439$	−20.4668			−0.976827			−0.488413	+	0.872612i	$0.662424\pi$
$440$		0			0
$441$	18.2037			0.866844
$442$	1.48330	+	0.481953i	0.0705534	+	0.0229242i
$443$	−5.97474	−	8.22353i	−0.283869	−	0.390712i	0.643142	−	0.765747i	$-0.277631\pi$
$443$	−5.97474	−	8.22353i	−0.283869	−	0.390712i	−0.927010	+	0.375035i	$0.877631\pi$
$444$	10.1535	+	7.37698i	0.481866	+	0.350096i
$445$	12.7960	−	15.5326i	0.606589	−	0.736317i
$446$	−2.07199	−	6.37692i	−0.0981114	−	0.301956i
$447$	−32.8891	+	45.2679i	−1.55560	+	2.14110i
$448$	16.4525	+	22.6449i	0.777306	+	1.06987i
$449$	4.54240	−	13.9801i	0.214369	−	0.659760i	−0.784829	−	0.619713i	$-0.787249\pi$
$449$	4.54240	−	13.9801i	0.214369	−	0.659760i	0.999198	−	0.0400475i	$-0.0127509\pi$
$450$	−50.3913	−	23.4598i	−2.37547	−	1.10591i
$451$		0			0
$452$			21.2006i			0.997190i
$453$	9.12191	+	2.96389i	0.428584	+	0.139256i
$454$	−4.64780	+	3.37683i	−0.218132	+	0.158482i
$455$	−0.282950	+	4.64986i	−0.0132649	+	0.217989i
$456$	0.316082	+	0.972801i	0.0148019	+	0.0455556i
$457$	−3.19822	+	1.03916i	−0.149606	+	0.0486101i	−0.382863	−	0.923805i	$-0.625062\pi$
$457$	−3.19822	+	1.03916i	−0.149606	+	0.0486101i	0.233256	+	0.972415i	$0.425062\pi$
$458$	−2.36794	+	3.25919i	−0.110647	+	0.152292i
$459$	−6.99450	+	5.08180i	−0.326475	+	0.237198i
$460$	−5.11195	−	19.7412i	−0.238346	−	0.920438i
$461$	1.41424			0.0658677			0.0329338	−	0.999458i	$-0.489515\pi$
$461$	1.41424			0.0658677			0.0329338	+	0.999458i	$0.489515\pi$
$462$		0			0
$463$		−	15.4595i		−	0.718465i	−0.933248	−	0.359232i	$-0.883039\pi$
$463$		−	15.4595i		−	0.718465i	0.933248	−	0.359232i	$-0.116961\pi$
$464$	4.89997	−	15.0806i	0.227475	−	0.700098i
$465$	−18.8555	+	47.9111i	−0.874403	+	2.22182i
$466$	−33.1446	−	24.0810i	−1.53539	−	1.11553i
$467$	17.7760	−	5.77576i	0.822574	−	0.267270i	0.132660	−	0.991162i	$-0.457648\pi$
$467$	17.7760	−	5.77576i	0.822574	−	0.267270i	0.689914	+	0.723891i	$0.257648\pi$
$468$	7.09292	−	2.30463i	0.327870	−	0.106531i
$469$	−6.18300	−	4.49221i	−0.285505	−	0.207431i
$470$	12.2680	+	4.82808i	0.565879	+	0.222703i
$471$	−12.6229	+	38.8493i	−0.581633	+	1.79008i
$472$			0.689685i			0.0317453i
$473$		0			0
$474$	89.9495			4.13152
$475$	6.91879	+	6.44386i	0.317456	+	0.295664i
$476$	−6.45852	+	4.69239i	−0.296026	+	0.215075i
$477$	20.7335	−	28.5372i	0.949322	−	1.30663i
$478$	3.63783	−	1.18200i	0.166390	−	0.0540635i
$479$	−9.23235	−	28.4142i	−0.421837	−	1.29828i	−0.905991	−	0.423297i	$-0.860873\pi$
$479$	−9.23235	−	28.4142i	−0.421837	−	1.29828i	0.484154	−	0.874983i	$-0.339127\pi$
$480$	3.19634	−	52.5271i	0.145892	−	2.39752i
$481$	−1.08041	+	0.784960i	−0.0492622	+	0.0357911i
$482$	7.70488	+	2.50347i	0.350948	+	0.114030i
$483$		−	40.8087i		−	1.85686i
$484$		0			0
$485$	28.5430	−	18.1963i	1.29607	−	0.826253i
$486$	5.04869	−	15.5383i	0.229013	−	0.704831i
$487$	0.549473	+	0.756284i	0.0248990	+	0.0342705i	0.821285	−	0.570518i	$-0.193258\pi$
$487$	0.549473	+	0.756284i	0.0248990	+	0.0342705i	−0.796386	+	0.604789i	$0.793258\pi$
$488$	0.849414	−	1.16912i	0.0384512	−	0.0529235i
$489$	9.29707	+	28.6134i	0.420428	+	1.29394i
$490$	−11.5634	−	9.52612i	−0.522382	−	0.430346i
$491$	−26.6121	−	19.3348i	−1.20099	−	0.872569i	−0.206607	−	0.978424i	$-0.566242\pi$
$491$	−26.6121	−	19.3348i	−1.20099	−	0.872569i	−0.994382	+	0.105855i	$0.966242\pi$
$492$	−11.8448	−	16.3029i	−0.534003	−	0.734992i
$493$	4.70651	+	1.52924i	0.211970	+	0.0688733i
$494$	−2.48151			−0.111648
$495$		0			0
$496$	−30.0833			−1.35078
$497$	−47.9994	−	15.5960i	−2.15307	−	0.699574i
$498$	36.8623	+	50.7366i	1.65184	+	2.27356i
$499$	7.27434	+	5.28512i	0.325644	+	0.236594i	0.738580	−	0.674166i	$-0.235497\pi$
$499$	7.27434	+	5.28512i	0.325644	+	0.236594i	−0.412936	+	0.910760i	$0.635497\pi$
$500$	10.0878	+	21.0989i	0.451138	+	0.943569i
$501$	13.1556	+	40.4886i	0.587747	+	1.80890i
$502$	−26.9992	+	37.1612i	−1.20503	+	1.65858i
$503$	−0.717663	−	0.987779i	−0.0319990	−	0.0440429i	0.792718	−	0.609589i	$-0.208665\pi$
$503$	−0.717663	−	0.987779i	−0.0319990	−	0.0440429i	−0.824717	+	0.565546i	$0.808665\pi$
$504$	−1.01210	+	3.11493i	−0.0450826	+	0.138750i
$505$	6.70509	+	10.5177i	0.298373	+	0.468031i
$506$		0			0
$507$		−	36.6650i		−	1.62835i
$508$	32.7112	+	10.6285i	1.45132	+	0.471564i
$509$	19.5744	−	14.2216i	0.867621	−	0.630363i	−0.0623268	−	0.998056i	$-0.519852\pi$
$509$	19.5744	−	14.2216i	0.867621	−	0.630363i	0.929947	+	0.367692i	$0.119852\pi$
$510$	15.6397	+	0.951692i	0.692536	+	0.0421416i
$511$	5.67051	+	17.4520i	0.250848	+	0.772032i
$512$	30.5867	−	9.93821i	1.35175	−	0.439211i
$513$	8.08557	−	11.1288i	0.356987	−	0.491350i
$514$	6.64897	−	4.83076i	0.293274	−	0.213076i
$515$	−1.78373	−	6.88834i	−0.0786004	−	0.303537i
$516$	66.6475			2.93399
$517$		0			0
$518$		−	13.3715i		−	0.587512i
$519$	−1.98911	+	6.12186i	−0.0873124	+	0.268720i
$520$	−0.250513	−	0.0985898i	−0.0109857	−	0.00432345i
$521$	3.92663	+	2.85286i	0.172029	+	0.124986i	0.670468	−	0.741938i	$-0.266093\pi$
$521$	3.92663	+	2.85286i	0.172029	+	0.124986i	−0.498439	+	0.866925i	$0.666093\pi$
$522$	44.0245	−	14.3044i	1.92690	−	0.626088i
$523$	−6.97451	+	2.26616i	−0.304974	+	0.0990921i	−0.457506	−	0.889206i	$-0.651257\pi$
$523$	−6.97451	+	2.26616i	−0.304974	+	0.0990921i	0.152532	+	0.988299i	$0.451257\pi$
$524$	23.6928	+	17.2139i	1.03503	+	0.751991i
$525$	8.95845	+	45.9350i	0.390979	+	2.00477i
$526$	−7.69187	+	23.6731i	−0.335382	+	1.03220i
$527$		−	9.38873i		−	0.408980i
$528$		0			0
$529$	3.99158			0.173547
$530$	−28.1041	+	7.27752i	−1.22076	+	0.316115i
$531$	16.5236	−	12.0051i	0.717063	−	0.520977i
$532$	7.46598	−	10.2760i	0.323691	−	0.445523i
$533$	2.03931	−	0.662612i	0.0883323	−	0.0287009i
$534$	16.3976	+	50.4667i	0.709595	+	2.18391i
$535$	8.85872	+	0.539064i	0.382996	+	0.0233058i
$536$	0.357319	−	0.259607i	0.0154338	−	0.0112133i
$537$	29.9611	+	9.73494i	1.29292	+	0.420094i
$538$		−	15.5917i		−	0.672204i
$539$		0			0
$540$	28.6911	−	18.2908i	1.23467	−	0.787109i
$541$	−8.67728	+	26.7059i	−0.373065	+	1.14818i	0.571710	+	0.820456i	$0.306280\pi$
$541$	−8.67728	+	26.7059i	−0.373065	+	1.14818i	−0.944775	+	0.327720i	$0.893720\pi$
$542$	−18.5170	−	25.4864i	−0.795372	−	1.09474i
$543$	5.76847	−	7.93962i	0.247549	−	0.340722i
$544$	2.96531	+	9.12629i	0.127137	+	0.391287i
$545$	21.9167	−	26.6039i	0.938807	−	1.13958i
$546$	−9.93737	−	7.21992i	−0.425280	−	0.308984i
$547$	13.7323	+	18.9009i	0.587151	+	0.808144i	0.994457	−	0.105148i	$-0.0335316\pi$
$547$	13.7323	+	18.9009i	0.587151	+	0.808144i	−0.407306	+	0.913292i	$0.633532\pi$
$548$	−27.3966	−	8.90171i	−1.17033	−	0.380262i
$549$	−42.7954			−1.82646
$550$		0			0
$551$	−7.87382			−0.335436
$552$	2.24293	+	0.728772i	0.0954654	+	0.0310186i
$553$	−28.7965	−	39.6349i	−1.22455	−	1.68545i
$554$	33.2256	+	24.1398i	1.41162	+	1.02560i
$555$	−8.53067	+	10.3551i	−0.362107	+	0.439549i
$556$	4.36615	+	13.4376i	0.185166	+	0.569882i
$557$	−0.0200153	+	0.0275487i	−0.000848077	+	0.00116728i	−0.809441	−	0.587201i	$-0.800230\pi$
$557$	−0.0200153	+	0.0275487i	−0.000848077	+	0.00116728i	0.808593	+	0.588369i	$0.200230\pi$
$558$	−51.6204	−	71.0494i	−2.18527	−	3.00776i
$559$	−2.19147	+	6.74465i	−0.0926893	+	0.285268i
$560$	−23.0576	+	14.6994i	−0.974361	+	0.621161i
$561$		0			0
$562$			48.9915i			2.06658i
$563$	22.4995	+	7.31054i	0.948242	+	0.308103i	0.742001	−	0.670399i	$-0.233877\pi$
$563$	22.4995	+	7.31054i	0.948242	+	0.308103i	0.206241	+	0.978501i	$0.433877\pi$
$564$	−14.3771	+	10.4455i	−0.605383	+	0.439837i
$565$	−22.6215	−	1.37654i	−0.951693	−	0.0579117i
$566$	−9.02445	−	27.7744i	−0.379326	−	1.16744i
$567$	14.4042	−	4.68022i	0.604921	−	0.196551i
$568$	1.71437	−	2.35963i	0.0719334	−	0.0990078i
$569$	−24.8653	+	18.0657i	−1.04241	+	0.757355i	−0.970754	−	0.240075i	$-0.922828\pi$
$569$	−24.8653	+	18.0657i	−1.04241	+	0.757355i	−0.0716547	+	0.997429i	$0.522828\pi$
$570$	−24.1340	+	6.24947i	−1.01086	+	0.261761i
$571$	28.4768			1.19172			0.595860	−	0.803089i	$-0.296812\pi$
$571$	28.4768			1.19172			0.595860	+	0.803089i	$0.296812\pi$
$572$		0			0
$573$		−	27.0350i		−	1.12940i
$574$	−6.63455	+	20.4191i	−0.276921	+	0.852275i
$575$	21.3962	−	4.17278i	0.892284	−	0.174017i
$576$	38.7545	+	28.1568i	1.61477	+	1.17320i
$577$	−36.7234	+	11.9321i	−1.52881	+	0.496742i	−0.948264	−	0.317483i	$-0.897162\pi$
$577$	−36.7234	+	11.9321i	−1.52881	+	0.496742i	−0.580550	+	0.814225i	$0.697162\pi$
$578$	29.9873	−	9.74348i	1.24731	−	0.405275i
$579$	−11.4672	−	8.33140i	−0.476560	−	0.346241i
$580$	−18.1229	−	7.13231i	−0.752513	−	0.296153i
$581$	10.5552	−	32.4857i	0.437905	−	1.34773i
$582$			89.2539i			3.69969i
$583$		0			0
$584$	−1.06046			−0.0438823
$585$	1.99855	+	7.71795i	0.0826299	+	0.319098i
$586$	24.8132	−	18.0279i	1.02503	−	0.744725i
$587$	−8.39465	+	11.5542i	−0.346484	+	0.476894i	−0.946321	−	0.323228i	$-0.895232\pi$
$587$	−8.39465	+	11.5542i	−0.346484	+	0.476894i	0.599837	+	0.800122i	$0.295232\pi$
$588$	19.2064	−	6.24055i	0.792060	−	0.257356i
$589$	4.61617	+	14.2071i	0.190206	+	0.585394i
$590$	−16.7785	−	1.02099i	−0.690760	−	0.0420336i
$591$	−28.0016	+	20.3443i	−1.15183	+	0.836854i
$592$	−7.45527	−	2.42236i	−0.306410	−	0.0995585i
$593$			36.4700i			1.49764i	0.662771	+	0.748822i	$0.269380\pi$
$593$			36.4700i			1.49764i	−0.662771	+	0.748822i	$0.730620\pi$
$594$		0			0
$595$	−4.58754	−	7.19606i	−0.188071	−	0.295010i
$596$	−12.4086	+	38.1897i	−0.508275	+	1.56431i
$597$	8.55183	+	11.7706i	0.350003	+	0.481738i
$598$	−3.36299	+	4.62876i	−0.137523	+	0.189284i
$599$	−9.37587	−	28.8560i	−0.383088	−	1.17902i	−0.937858	−	0.347019i	$-0.887194\pi$
$599$	−9.37587	−	28.8560i	−0.383088	−	1.17902i	0.554770	−	0.832004i	$-0.312806\pi$
$600$	−2.68466	−	0.327944i	−0.109601	−	0.0133883i
$601$	30.5989	+	22.2314i	1.24816	+	0.906839i	0.998113	−	0.0613962i	$-0.0195553\pi$
$601$	30.5989	+	22.2314i	1.24816	+	0.906839i	0.250043	+	0.968235i	$0.419555\pi$
$602$	−41.7373	−	57.4464i	−1.70108	−	2.34134i
$603$	−12.4394	−	4.04182i	−0.506573	−	0.164595i
$604$	6.88313			0.280071
$605$		0			0
$606$	−32.8888			−1.33602
$607$	29.5616	+	9.60513i	1.19987	+	0.389860i	0.839712	−	0.543032i	$-0.182724\pi$
$607$	29.5616	+	9.60513i	1.19987	+	0.389860i	0.360155	+	0.932893i	$0.382724\pi$
$608$	−8.97428	−	12.3520i	−0.363955	−	0.500941i
$609$	−31.5312	−	22.9088i	−1.27771	−	0.928311i
$610$	27.1846	+	22.3951i	1.10067	+	0.906751i
$611$	−0.584338	−	1.79841i	−0.0236398	−	0.0727558i
$612$	−8.03057	+	11.0531i	−0.324616	+	0.446796i
$613$	−21.3175	−	29.3410i	−0.861004	−	1.18507i	−0.981329	−	0.192336i	$-0.938394\pi$
$613$	−21.3175	−	29.3410i	−0.861004	−	1.18507i	0.120325	−	0.992735i	$-0.461606\pi$
$614$	5.02672	−	15.4707i	0.202862	−	0.624345i
$615$	18.1647	−	11.5801i	0.732470	−	0.466954i
$616$		0			0
$617$			1.28079i			0.0515626i	0.999668	+	0.0257813i	$0.00820735\pi$
$617$			1.28079i			0.0515626i	−0.999668	+	0.0257813i	$0.991793\pi$
$618$	17.8437	+	5.79778i	0.717780	+	0.233221i
$619$	6.66694	−	4.84382i	0.267967	−	0.194689i	−0.445685	−	0.895190i	$-0.647040\pi$
$619$	6.66694	−	4.84382i	0.267967	−	0.194689i	0.713652	+	0.700500i	$0.247040\pi$
$620$	−2.24429	+	36.8816i	−0.0901328	+	1.48120i
$621$	−9.80089	−	30.1640i	−0.393296	−	1.21044i
$622$	42.8370	−	13.9186i	1.71761	−	0.558084i
$623$	16.9879	−	23.3818i	0.680605	−	0.936772i
$624$	−5.82568	+	4.23261i	−0.233214	+	0.169440i
$625$	−23.1680	+	9.39392i	−0.926718	+	0.375757i
$626$	−4.75448			−0.190027
$627$		0			0
$628$			29.3146i			1.16978i
$629$	0.755998	−	2.32672i	0.0301436	−	0.0927725i
$630$	−74.2811	−	29.2335i	−2.95943	−	1.16469i
$631$	10.0378	+	7.29291i	0.399600	+	0.290326i	0.769378	−	0.638794i	$-0.220566\pi$
$631$	10.0378	+	7.29291i	0.399600	+	0.290326i	−0.369778	+	0.929120i	$0.620566\pi$
$632$	2.69267	−	0.874901i	0.107109	−	0.0348017i
$633$	4.36091	−	1.41694i	0.173331	−	0.0563185i
$634$	−29.4949	−	21.4293i	−1.17139	−	0.851067i
$635$	−13.4648	+	34.2135i	−0.534334	+	1.35772i
$636$	12.0925	−	37.2169i	0.479500	−	1.47575i
$637$			2.14887i			0.0851412i
$638$		0			0
$639$	−86.3738			−3.41689
$640$	−0.831328	−	3.21040i	−0.0328611	−	0.126902i
$641$	4.39239	−	3.19126i	0.173489	−	0.126047i	−0.497652	−	0.867377i	$-0.665804\pi$
$641$	4.39239	−	3.19126i	0.173489	−	0.126047i	0.671141	+	0.741329i	$0.265804\pi$
$642$	−13.7551	+	18.9322i	−0.542870	+	0.747196i
$643$	1.98579	−	0.645222i	0.0783119	−	0.0254451i	−0.269599	−	0.962973i	$-0.586891\pi$
$643$	1.98579	−	0.645222i	0.0783119	−	0.0254451i	0.347911	+	0.937528i	$0.386891\pi$
$644$	−9.04986	−	27.8526i	−0.356614	−	1.09755i
$645$	−4.32740	+	71.1144i	−0.170391	+	2.80013i
$646$	3.67775	−	2.67204i	0.144699	−	0.105130i
$647$	23.5511	+	7.65223i	0.925891	+	0.300840i	0.732881	−	0.680357i	$-0.238175\pi$
$647$	23.5511	+	7.65223i	0.925891	+	0.300840i	0.193010	+	0.981197i	$0.438175\pi$
$648$			0.875266i			0.0343837i
$649$		0			0
$650$	2.76932	−	5.94847i	0.108622	−	0.233318i
$651$	−22.8497	+	70.3241i	−0.895550	+	2.75622i
$652$	12.6908	+	17.4674i	0.497010	+	0.684076i
$653$	4.05522	−	5.58154i	0.158693	−	0.218422i	−0.722265	−	0.691616i	$-0.756899\pi$
$653$	4.05522	−	5.58154i	0.158693	−	0.218422i	0.880958	+	0.473194i	$0.156899\pi$
$654$	28.0854	+	86.4381i	1.09823	+	3.38000i
$655$	−19.9059	+	24.1631i	−0.777790	+	0.944131i
$656$	10.1827	+	7.39816i	0.397567	+	0.288849i
$657$	18.4591	+	25.4068i	0.720158	+	0.991213i
$658$	18.0070	+	5.85081i	0.701984	+	0.228089i
$659$	−12.4567			−0.485246			−0.242623	−	0.970121i	$-0.578008\pi$
$659$	−12.4567			−0.485246			−0.242623	+	0.970121i	$0.578008\pi$
$660$		0			0
$661$	17.8173			0.693012			0.346506	−	0.938048i	$-0.387368\pi$
$661$	17.8173			0.693012			0.346506	+	0.938048i	$0.387368\pi$
$662$	5.94791	+	1.93259i	0.231172	+	0.0751123i
$663$	−1.32096	−	1.81814i	−0.0513018	−	0.0706108i
$664$	1.59698	+	1.16027i	0.0619749	+	0.0450274i
$665$	10.4800	+	8.63359i	0.406397	+	0.334796i
$666$	−7.07158	−	21.7641i	−0.274018	−	0.843341i
$667$	−10.6708	+	14.6870i	−0.413173	+	0.568684i
$668$	17.9578	+	24.7167i	0.694807	+	0.956320i
$669$	−2.98562	+	9.18880i	−0.115431	+	0.355259i
$670$	5.78670	+	9.07709i	0.223560	+	0.350679i
$671$		0			0
$672$		−	75.5752i		−	2.91538i
$673$	−27.6539	−	8.98531i	−1.06598	−	0.346358i	−0.277060	−	0.960853i	$-0.589360\pi$
$673$	−27.6539	−	8.98531i	−1.06598	−	0.346358i	−0.788921	+	0.614494i	$0.789360\pi$
$674$	−58.8247	+	42.7386i	−2.26584	+	1.64623i
$675$	17.6538	+	31.8017i	0.679494	+	1.22405i
$676$	−8.13095	−	25.0245i	−0.312729	−	0.962480i
$677$	−38.8680	+	12.6290i	−1.49382	+	0.485371i	−0.938208	−	0.346072i	$-0.887515\pi$
$677$	−38.8680	+	12.6290i	−1.49382	+	0.485371i	−0.555610	+	0.831443i	$0.687515\pi$
$678$	35.1248	−	48.3451i	1.34896	−	1.85668i
$679$	39.3284	−	28.5738i	1.50929	−	1.09656i
$680$	0.477435	−	0.123631i	0.0183088	−	0.00474104i
$681$	8.27824			0.317223
$682$		0			0
$683$		−	17.2211i		−	0.658948i	−0.944165	−	0.329474i	$-0.893129\pi$
$683$		−	17.2211i		−	0.658948i	0.944165	−	0.329474i	$-0.106871\pi$
$684$	6.71743	−	20.6741i	0.256847	−	0.790494i
$685$	11.2772	−	28.6549i	0.430879	−	1.09485i
$686$	19.3796	+	14.0801i	0.739917	+	0.537581i
$687$	5.52086	−	1.79384i	0.210634	−	0.0684391i
$688$	−39.5902	+	12.8636i	−1.50936	+	0.490421i
$689$	3.36869	+	2.44750i	0.128337	+	0.0932422i
$690$	−21.0498	+	53.4866i	−0.801351	+	2.03620i
$691$	6.22380	−	19.1549i	0.236764	−	0.728686i	−0.760118	−	0.649785i	$-0.774859\pi$
$691$	6.22380	−	19.1549i	0.236764	−	0.728686i	0.996882	−	0.0789009i	$-0.0251411\pi$
$692$			4.61938i			0.175603i
$693$		0			0
$694$	24.8055			0.941603
$695$	−14.6217	+	3.78628i	−0.554634	+	0.143622i
$696$	1.82221	−	1.32391i	0.0690705	−	0.0501827i
$697$	−2.30890	+	3.17792i	−0.0874557	+	0.120372i
$698$	34.0001	−	11.0473i	1.28692	−	0.418146i
$699$	18.2425	+	56.1447i	0.689996	+	2.12359i
$700$	16.3010	+	29.3647i	0.616119	+	1.10988i
$701$	17.1242	−	12.4414i	0.646771	−	0.469906i	−0.215399	−	0.976526i	$-0.569105\pi$
$701$	17.1242	−	12.4414i	0.646771	−	0.469906i	0.862170	+	0.506620i	$0.169105\pi$
$702$	−9.07926	−	2.95003i	−0.342675	−	0.111342i
$703$			3.89252i			0.146809i
$704$		0			0
$705$	−10.2121	−	16.0189i	−0.384611	−	0.603306i
$706$	11.7017	−	36.0141i	0.440398	−	1.35541i
$707$	10.5290	+	14.4920i	0.395985	+	0.545026i
$708$	13.3182	−	18.3309i	0.500529	−	0.688919i
$709$	−6.35410	−	19.5559i	−0.238633	−	0.734437i	−0.996619	−	0.0821658i	$-0.973816\pi$
$709$	−6.35410	−	19.5559i	−0.238633	−	0.734437i	0.757986	−	0.652271i	$-0.226184\pi$
$710$	54.8666	+	45.1999i	2.05911	+	1.69632i
$711$	−67.8313	−	49.2824i	−2.54387	−	1.84823i
$712$	0.981738	+	1.35125i	0.0367922	+	0.0506401i
$713$	32.7565	+	10.6432i	1.22674	+	0.398592i
$714$	22.5021			0.842119
$715$		0			0
$716$	22.6078			0.844892
$717$	−5.24191	−	1.70320i	−0.195763	−	0.0636072i
$718$	44.3094	+	60.9866i	1.65361	+	2.27600i
$719$	−14.7645	−	10.7271i	−0.550625	−	0.400052i	0.277391	−	0.960757i	$-0.410530\pi$
$719$	−14.7645	−	10.7271i	−0.550625	−	0.400052i	−0.828016	+	0.560705i	$0.810530\pi$
$720$	−29.7557	+	36.1194i	−1.10893	+	1.34609i
$721$	−3.15779	−	9.71868i	−0.117602	−	0.361942i
$722$	18.3391	−	25.2416i	0.682510	−	0.939395i
$723$	−6.86161	−	9.44419i	−0.255186	−	0.351233i
$724$	2.17636	−	6.69816i	0.0808839	−	0.248935i
$725$	8.78706	−	18.8745i	0.326343	−	0.700980i
$726$		0			0
$727$			0.218345i			0.00809798i	0.999992	+	0.00404899i	$0.00128884\pi$
$727$			0.218345i			0.00809798i	−0.999992	+	0.00404899i	$0.998711\pi$
$728$	−0.367704	−	0.119474i	−0.0136280	−	0.00442801i
$729$	−30.4927	+	22.1543i	−1.12936	+	0.820529i
$730$	1.56988	−	25.7987i	0.0581040	−	0.954854i
$731$	−4.01462	−	12.3557i	−0.148486	−	0.456993i
$732$	−45.1527	+	14.6710i	−1.66889	+	0.542256i
$733$	1.02489	−	1.41065i	0.0378553	−	0.0521034i	−0.789670	−	0.613532i	$-0.789748\pi$
$733$	1.02489	−	1.41065i	0.0378553	−	0.0521034i	0.827525	+	0.561429i	$0.189748\pi$
$734$	−29.4548	+	21.4002i	−1.08720	+	0.789894i
$735$	5.41174	+	20.8989i	0.199615	+	0.770868i
$736$	−35.2024			−1.29758
$737$		0			0
$738$			36.7436i			1.35255i
$739$	9.38909	−	28.8966i	0.345383	−	1.06298i	−0.615995	−	0.787750i	$-0.711246\pi$
$739$	9.38909	−	28.8966i	0.345383	−	1.06298i	0.961378	−	0.275230i	$-0.0887540\pi$
$740$	−3.52595	+	8.95930i	−0.129617	+	0.329350i
$741$	2.89282	+	2.10175i	0.106270	+	0.0772099i
$742$	−39.6517	+	12.8836i	−1.45566	+	0.472973i
$743$	−32.9687	+	10.7122i	−1.20950	+	0.392991i	−0.843249	−	0.537524i	$-0.819360\pi$
$743$	−32.9687	+	10.7122i	−1.20950	+	0.392991i	−0.366254	+	0.930515i	$0.619360\pi$
$744$	−3.45710	−	2.51173i	−0.126743	−	0.0920845i
$745$	−39.9436	−	15.7199i	−1.46342	−	0.575932i
$746$	−0.126646	+	0.389777i	−0.00463684	+	0.0142707i
$747$		−	58.4572i		−	2.13884i
$748$		0			0
$749$	12.7458			0.465720
$750$	11.9525	−	64.8264i	0.436442	−	2.36713i
$751$	−7.73330	+	5.61857i	−0.282192	+	0.205025i	−0.719873	−	0.694106i	$-0.755800\pi$
$751$	−7.73330	+	5.61857i	−0.282192	+	0.205025i	0.437681	+	0.899130i	$0.355800\pi$
$752$	6.52422	−	8.97981i	0.237914	−	0.327460i
$753$	62.9486	−	20.4532i	2.29397	−	0.745357i
$754$	1.68857	+	5.19689i	0.0614942	+	0.189260i
$755$	−0.446919	+	7.34446i	−0.0162651	+	0.267292i
$756$	39.5325	−	28.7220i	1.43778	−	1.04461i
$757$	5.95480	+	1.93483i	0.216431	+	0.0703226i	0.415225	−	0.909719i	$-0.363703\pi$
$757$	5.95480	+	1.93483i	0.216431	+	0.0703226i	−0.198795	+	0.980041i	$0.563703\pi$
$758$		−	68.7414i		−	2.49680i
$759$		0			0
$760$	−0.661674	+	0.421822i	−0.0240014	+	0.0153011i
$761$	−8.24025	+	25.3609i	−0.298709	+	0.919331i	0.683241	+	0.730193i	$0.260570\pi$
$761$	−8.24025	+	25.3609i	−0.298709	+	0.919331i	−0.981950	+	0.189139i	$0.939430\pi$
$762$	−56.9844	−	78.4324i	−2.06433	−	2.84130i
$763$	29.0964	−	40.0478i	1.05336	−	1.44983i
$764$	−5.99537	−	18.4518i	−0.216905	−	0.667564i
$765$	−11.2725	−	9.28648i	−0.407559	−	0.335753i
$766$	−11.6878	−	8.49171i	−0.422299	−	0.306818i
$767$	1.41715	+	1.95054i	0.0511702	+	0.0704298i
$768$	−40.0088	−	12.9997i	−1.44369	−	0.469085i
$769$	42.2399			1.52321			0.761605	−	0.648042i	$-0.224412\pi$
$769$	42.2399			1.52321			0.761605	+	0.648042i	$0.224412\pi$
$770$		0			0
$771$	−11.8425			−0.426498
$772$	−9.67414	−	3.14332i	−0.348180	−	0.113130i
$773$	27.2115	+	37.4535i	0.978731	+	1.34711i	0.937510	+	0.347958i	$0.113125\pi$
$773$	27.2115	+	37.4535i	0.978731	+	1.34711i	0.0412213	+	0.999150i	$0.486875\pi$
$774$	−98.3140	−	71.4293i	−3.53382	−	2.56747i
$775$	−39.2078	−	4.78941i	−1.40838	−	0.172041i
$776$	0.868135	+	2.67185i	0.0311642	+	0.0959137i
$777$	−11.3252	+	15.5879i	−0.406291	+	0.559212i
$778$	−15.7739	−	21.7109i	−0.565522	−	0.778375i
$779$	1.93135	−	5.94409i	0.0691978	−	0.212969i
$780$	4.75448	+	7.45793i	0.170238	+	0.267037i
$781$		0			0
$782$		−	10.4813i		−	0.374811i
$783$	−28.8085	−	9.36044i	−1.02953	−	0.334515i
$784$	−10.2046	+	7.41406i	−0.364449	+	0.264788i
$785$	−31.2793	−	1.90338i	−1.11641	−	0.0679347i
$786$	−25.5088	−	78.5079i	−0.909867	−	2.80028i
$787$	46.7397	−	15.1866i	1.66609	−	0.541345i	0.683955	−	0.729524i	$-0.260258\pi$
$787$	46.7397	−	15.1866i	1.66609	−	0.541345i	0.982135	+	0.188178i	$0.0602583\pi$
$788$	−14.5999	+	20.0951i	−0.520100	+	0.715857i
$789$	29.0172	−	21.0822i	1.03304	−	0.750546i
$790$	17.2982	+	66.8019i	0.615444	+	2.37670i
$791$	−32.5474			−1.15725
$792$		0			0
$793$		−	5.05180i		−	0.179395i
$794$	20.9786	−	64.5656i	0.744504	−	2.29135i
$795$	38.9262	+	15.3195i	1.38057	+	0.543326i
$796$	8.44704	+	6.13713i	0.299397	+	0.217525i
$797$	41.5326	−	13.4948i	1.47116	−	0.478009i	0.539702	−	0.841856i	$-0.318537\pi$
$797$	41.5326	−	13.4948i	1.47116	−	0.478009i	0.931459	+	0.363847i	$0.118537\pi$
$798$	−34.0504	+	11.0636i	−1.20537	+	0.391649i
$799$	2.80252	+	2.03615i	0.0991459	+	0.0720337i
$800$	39.6245	−	7.72774i	1.40094	−	0.273217i
$801$	15.2846	−	47.0413i	0.540056	−	1.66212i
$802$		−	67.9480i		−	2.39933i
$803$		0			0
$804$	−14.5102			−0.511737
$805$	30.3070	−	7.84795i	1.06818	−	0.276604i
$806$	8.38706	−	6.09356i	0.295422	−	0.214636i
$807$	−13.2056	+	18.1760i	−0.464860	+	0.639824i
$808$	−0.984538	+	0.319896i	−0.0346359	+	0.0112539i
$809$	−12.2076	−	37.5713i	−0.429198	−	1.32094i	−0.898917	−	0.438120i	$-0.855645\pi$
$809$	−12.2076	−	37.5713i	−0.429198	−	1.32094i	0.469719	−	0.882816i	$-0.344355\pi$
$810$	−21.2933	−	1.29572i	−0.748170	−	0.0455270i
$811$	37.6818	−	27.3775i	1.32319	−	0.961352i	0.323302	−	0.946296i	$-0.395207\pi$
$811$	37.6818	−	27.3775i	1.32319	−	0.961352i	0.999887	−	0.0150565i	$-0.00479280\pi$
$812$	−26.6009	−	8.64316i	−0.933509	−	0.303315i
$813$			45.3940i			1.59204i
$814$		0			0
$815$	−19.4621	+	12.4072i	−0.681728	+	0.434606i
$816$	4.07644	−	12.5460i	0.142704	−	0.439197i
$817$	12.1499	+	16.7229i	0.425072	+	0.585062i
$818$	−9.71269	+	13.3684i	−0.339596	+	0.467414i
$819$	3.53810	+	10.8892i	0.123631	+	0.380498i
$820$	9.82964	−	11.9319i	0.343266	−	0.416678i
$821$	23.6291	+	17.1675i	0.824661	+	0.599151i	0.918044	−	0.396479i	$-0.129768\pi$
$821$	23.6291	+	17.1675i	0.824661	+	0.599151i	−0.0933826	+	0.995630i	$0.529768\pi$
$822$	47.7262	+	65.6895i	1.66464	+	2.29119i
$823$	13.2024	+	4.28972i	0.460207	+	0.149530i	0.529940	−	0.848035i	$-0.322215\pi$
$823$	13.2024	+	4.28972i	0.460207	+	0.149530i	−0.0697326	+	0.997566i	$0.522215\pi$
$824$	0.590551			0.0205728
$825$		0			0
$826$	−24.1406			−0.839960
$827$	9.08284	+	2.95119i	0.315841	+	0.102623i	0.462648	−	0.886542i	$-0.346899\pi$
$827$	9.08284	+	2.95119i	0.315841	+	0.102623i	−0.146806	+	0.989165i	$0.546899\pi$
$828$	−29.4599	−	40.5480i	−1.02380	−	1.40914i
$829$	30.1958	+	21.9386i	1.04875	+	0.761958i	0.971973	−	0.235091i	$-0.0755387\pi$
$829$	30.1958	+	21.9386i	1.04875	+	0.761958i	0.0767717	+	0.997049i	$0.475539\pi$
$830$	−30.5910	+	37.1334i	−1.06183	+	1.28892i
$831$	−18.2871	−	56.2820i	−0.634373	−	1.95240i
$832$	−3.32379	+	4.57480i	−0.115232	+	0.158603i
$833$	−2.31386	−	3.18476i	−0.0801706	−	0.110345i
$834$	12.3068	−	37.8765i	0.426150	−	1.31156i
$835$	−27.5393	+	17.5565i	−0.953038	+	0.607568i
$836$		0			0
$837$			57.4683i			1.98640i
$838$	37.5774	+	12.2096i	1.29809	+	0.421775i
$839$	−1.15908	+	0.842119i	−0.0400158	+	0.0290732i	−0.607613	−	0.794233i	$-0.707873\pi$
$839$	−1.15908	+	0.842119i	−0.0400158	+	0.0290732i	0.567598	+	0.823306i	$0.307873\pi$
$840$	−3.87700	−	0.235920i	−0.133769	−	0.00814003i
$841$	−3.60366	−	11.0909i	−0.124264	−	0.382445i
$842$	−45.9948	+	14.9446i	−1.58508	+	0.515025i
$843$	41.4941	−	57.1118i	1.42913	−	1.96703i
$844$	2.66216	−	1.93418i	0.0916355	−	0.0665771i
$845$	27.2296	−	7.05108i	0.936728	−	0.242564i
$846$	32.4031			1.11404
$847$		0			0
$848$			24.4417i			0.839332i
$849$	−13.0037	+	40.0214i	−0.446287	+	1.37353i
$850$	2.30089	+	11.7980i	0.0789199	+	0.404667i
$851$	7.26072	+	5.27523i	0.248894	+	0.180832i
$852$	−91.1315	+	29.6104i	−3.12211	+	1.01444i
$853$	26.7648	−	8.69640i	0.916408	−	0.297759i	0.187416	−	0.982281i	$-0.439989\pi$
$853$	26.7648	−	8.69640i	0.916408	−	0.297759i	0.728993	+	0.684522i	$0.239989\pi$
$854$	40.9220	+	29.7315i	1.40032	+	1.01739i
$855$	21.6236	+	8.51001i	0.739511	+	0.291036i
$856$	−0.227617	+	0.700533i	−0.00777979	+	0.0239437i
$857$			4.04561i			0.138195i	0.997610	+	0.0690977i	$0.0220120\pi$
$857$			4.04561i			0.138195i	−0.997610	+	0.0690977i	$0.977988\pi$
$858$		0			0
$859$	55.2064			1.88362			0.941808	−	0.336151i	$-0.109125\pi$
$859$	55.2064			1.88362			0.941808	+	0.336151i	$0.109125\pi$
$860$	12.8170	+	49.4964i	0.437057	+	1.68781i
$861$	25.0285	−	18.1843i	0.852968	−	0.619718i
$862$	−8.99321	+	12.3781i	−0.306310	+	0.421599i
$863$	−28.7149	+	9.33004i	−0.977467	+	0.317598i	−0.753827	−	0.657073i	$-0.771794\pi$
$863$	−28.7149	+	9.33004i	−0.977467	+	0.317598i	−0.223641	+	0.974672i	$0.571794\pi$
$864$	−18.1506	−	55.8619i	−0.617497	−	1.90046i
$865$	−4.92899	−	0.299935i	−0.167591	−	0.0101981i
$866$	−41.9258	+	30.4608i	−1.42470	+	1.03510i
$867$	−43.2101	−	14.0398i	−1.46749	−	0.476818i
$868$			53.0646i			1.80113i
$869$		0			0
$870$	29.5102	+	46.2901i	1.00049	+	1.56938i
$871$	0.477118	−	1.46842i	0.0161665	−	0.0497555i
$872$	1.68150	+	2.31438i	0.0569426	+	0.0783748i
$873$	48.9012	−	67.3068i	1.65506	−	2.27799i
$874$	5.15337	+	15.8604i	0.174315	+	0.536487i
$875$	−32.3913	+	15.4869i	−1.09502	+	0.523552i
$876$	28.1858	+	20.4782i	0.952309	+	0.691893i
$877$	18.1859	+	25.0308i	0.614096	+	0.845230i	0.996906	−	0.0785967i	$-0.0250439\pi$
$877$	18.1859	+	25.0308i	0.614096	+	0.845230i	−0.382811	+	0.923827i	$0.625044\pi$
$878$	39.3741	+	12.7934i	1.32881	+	0.431757i
$879$	−44.1951			−1.49066
$880$		0			0
$881$	−8.25840			−0.278233			−0.139116	−	0.990276i	$-0.544426\pi$
$881$	−8.25840			−0.278233			−0.139116	+	0.990276i	$0.544426\pi$
$882$	−35.0204	−	11.3788i	−1.17920	−	0.383144i
$883$	−23.5284	−	32.3840i	−0.791793	−	1.08981i	−0.993883	−	0.110442i	$-0.964773\pi$
$883$	−23.5284	−	32.3840i	−0.791793	−	1.08981i	0.202090	−	0.979367i	$-0.435227\pi$
$884$	−1.30477	−	0.947972i	−0.0438842	−	0.0318838i
$885$	18.6948	+	15.4011i	0.628418	+	0.517701i
$886$	6.35385	+	19.5551i	0.213462	+	0.656968i
$887$	22.1801	−	30.5283i	0.744735	−	1.02504i	−0.253597	−	0.967310i	$-0.581614\pi$
$887$	22.1801	−	30.5283i	0.744735	−	1.02504i	0.998332	−	0.0577299i	$-0.0183862\pi$
$888$	−0.654492	−	0.900831i	−0.0219633	−	0.0302299i
$889$	−16.3170	+	50.2187i	−0.547256	+	1.68428i
$890$	−34.3261	+	21.8831i	−1.15062	+	0.733525i
$891$		0			0
$892$			6.93360i			0.232154i
$893$	−5.24191	−	1.70320i	−0.175414	−	0.0569955i
$894$	91.5682	−	66.5282i	3.06250	−	2.22504i
$895$	−1.46791	+	24.1230i	−0.0490670	+	0.806343i
$896$	−1.47173	−	4.52951i	−0.0491669	−	0.151320i
$897$	7.84081	−	2.54763i	0.261797	−	0.0850630i
$898$	−17.4774	+	24.0555i	−0.583227	+	0.802743i
$899$	26.6121	−	19.3348i	0.887564	−	0.644853i
$900$	42.0618	+	39.1745i	1.40206	+	1.30582i
$901$	−7.62803			−0.254127
$902$		0			0
$903$			102.318i			3.40494i
$904$	0.581240	−	1.78887i	0.0193317	−	0.0594970i
$905$	7.00578	+	2.75714i	0.232880	+	0.0916504i
$906$	−15.6961	−	11.4039i	−0.521467	−	0.378868i
$907$	31.8908	−	10.3619i	1.05892	−	0.344063i	0.272754	−	0.962084i	$-0.412065\pi$
$907$	31.8908	−	10.3619i	1.05892	−	0.344063i	0.786161	+	0.618021i	$0.212065\pi$
$908$	5.65003	−	1.83581i	0.187503	−	0.0609234i
$909$	24.8016	+	18.0194i	0.822617	+	0.597666i
$910$	3.45088	−	8.76855i	0.114396	−	0.290675i
$911$	−4.25913	+	13.1083i	−0.141111	+	0.434296i	−0.996490	−	0.0837064i	$-0.973324\pi$
$911$	−4.25913	+	13.1083i	−0.141111	+	0.434296i	0.855379	+	0.518003i	$0.173324\pi$
$912$			20.9890i			0.695014i
$913$		0			0
$914$	6.80231			0.225000
$915$	−12.7225	−	49.1315i	−0.420594	−	1.62424i
$916$	3.37027	−	2.44864i	0.111357	−	0.0809055i
$917$	−26.4270	+	36.3736i	−0.872695	+	1.20116i
$918$	16.6326	−	5.40425i	0.548957	−	0.178367i
$919$	12.9209	+	39.7663i	0.426220	+	1.31177i	0.901821	+	0.432109i	$0.142231\pi$
$919$	12.9209	+	39.7663i	0.426220	+	1.31177i	−0.475601	+	0.879661i	$0.657769\pi$
$920$	−0.109890	+	1.80588i	−0.00362297	+	0.0595382i
$921$	−18.9630	+	13.7775i	−0.624853	+	0.453982i
$922$	−2.72072	−	0.884014i	−0.0896020	−	0.0291135i
$923$		−	10.1960i		−	0.335607i
$924$		0			0
$925$	−9.33084	−	4.34399i	−0.306796	−	0.142830i
$926$	−9.66346	+	29.7411i	−0.317561	+	0.977352i
$927$	−10.2795	−	14.1485i	−0.337623	−	0.464698i
$928$	−19.7616	+	27.1995i	−0.648706	+	0.892867i
$929$	−4.04898	−	12.4615i	−0.132843	−	0.408848i	0.862405	−	0.506218i	$-0.168957\pi$
$929$	−4.04898	−	12.4615i	−0.132843	−	0.408848i	−0.995248	+	0.0973699i	$0.968957\pi$
$930$	66.2226	−	80.3853i	2.17153	−	2.63594i
$931$	5.06721	+	3.68155i	0.166071	+	0.120658i
$932$	24.9016	+	34.2742i	0.815680	+	1.12269i
$933$	−61.7258	−	20.0559i	−2.02081	−	0.656601i
$934$	−37.8078			−1.23711
$935$		0			0
$936$	−0.661674			−0.0216275
$937$	−8.32692	−	2.70558i	−0.272029	−	0.0883875i	0.169826	−	0.985474i	$-0.445679\pi$
$937$	−8.32692	−	2.70558i	−0.272029	−	0.0883875i	−0.441855	+	0.897087i	$0.645679\pi$
$938$	9.08688	+	12.5070i	0.296697	+	0.408369i
$939$	5.54254	+	4.02689i	0.180874	+	0.131413i
$940$	−10.5223	−	8.66847i	−0.343201	−	0.282734i
$941$	5.45505	+	16.7889i	0.177829	+	0.547303i	0.999751	−	0.0222975i	$-0.00709809\pi$
$941$	5.45505	+	16.7889i	0.177829	+	0.547303i	−0.821922	+	0.569600i	$0.807098\pi$
$942$	48.5679	−	66.8480i	1.58243	−	2.17803i
$943$	−8.47011	−	11.6581i	−0.275825	−	0.379640i
$944$	−4.37327	+	13.4595i	−0.142338	+	0.438071i
$945$	28.0803	+	44.0470i	0.913451	+	1.43285i
$946$		0			0
$947$		−	56.2415i		−	1.82760i	−0.406159	−	0.913802i	$-0.633132\pi$
$947$		−	56.2415i		−	1.82760i	0.406159	−	0.913802i	$-0.366868\pi$
$948$	−88.4625	−	28.7432i	−2.87313	−	0.933537i
$949$	−2.99916	+	2.17901i	−0.0973567	+	0.0707338i
$950$	−9.28246	−	16.7215i	−0.301163	−	0.542518i
$951$	16.2338	+	49.9625i	0.526417	+	1.62014i
$952$	0.673608	−	0.218868i	0.0218318	−	0.00709357i
$953$	2.78838	−	3.83788i	0.0903246	−	0.124321i	−0.761463	−	0.648208i	$-0.775519\pi$
$953$	2.78838	−	3.83788i	0.0903246	−	0.124321i	0.851788	+	0.523887i	$0.175519\pi$
$954$	−57.7253	+	41.9399i	−1.86892	+	1.35785i
$955$	20.0778	−	5.19912i	0.649703	−	0.168240i
$956$	−3.95540			−0.127927
$957$		0			0
$958$			60.4344i			1.95255i
$959$	13.6660	−	42.0597i	0.441299	−	1.35818i
$960$	−20.8044	+	52.8631i	−0.671458	+	1.70615i
$961$	−25.4092	−	18.4608i	−0.819650	−	0.595511i
$962$	2.56915	−	0.834768i	0.0828327	−	0.0269140i
$963$	20.7456	−	6.74064i	0.668516	−	0.217214i
$964$	−6.77753	−	4.92416i	−0.218290	−	0.158597i
$965$	3.98213	−	10.1184i	0.128189	−	0.325724i
$966$	−25.5088	+	78.5079i	−0.820731	+	2.52595i
$967$			33.8619i			1.08892i	0.838785	+	0.544462i	$0.183266\pi$
$967$			33.8619i			1.08892i	−0.838785	+	0.544462i	$0.816734\pi$
$968$		0			0
$969$	−6.55047			−0.210431
$970$	−66.2853	+	17.1645i	−2.12829	+	0.551118i
$971$	16.0047	−	11.6281i	0.513614	−	0.373162i	−0.300579	−	0.953757i	$-0.597180\pi$
$971$	16.0047	−	11.6281i	0.513614	−	0.373162i	0.814193	+	0.580595i	$0.197180\pi$
$972$	−9.93047	+	13.6681i	−0.318520	+	0.438405i
$973$	−20.6296	+	6.70297i	−0.661356	+	0.214887i
$974$	−0.584338	−	1.79841i	−0.0187234	−	0.0576247i
$975$	−8.26649	+	4.58890i	−0.264740	+	0.146962i
$976$	23.9901	−	17.4298i	0.767904	−	0.557915i
$977$	6.33521	+	2.05844i	0.202681	+	0.0658552i	0.408598	−	0.912714i	$-0.366018\pi$
$977$	6.33521	+	2.05844i	0.202681	+	0.0658552i	−0.205917	+	0.978569i	$0.566018\pi$
$978$		−	60.8581i		−	1.94603i
$979$		0			0
$980$	8.32821	+	13.0637i	0.266035	+	0.417305i
$981$	26.1791	−	80.5711i	0.835836	−	2.57244i
$982$	39.1106	+	53.8312i	1.24807	+	1.71782i
$983$	−3.03421	+	4.17623i	−0.0967762	+	0.133201i	−0.854659	−	0.519190i	$-0.826234\pi$
$983$	−3.03421	+	4.17623i	−0.0967762	+	0.133201i	0.757883	+	0.652391i	$0.226234\pi$
$984$	0.552479	+	1.70035i	0.0176124	+	0.0542053i
$985$	−20.4939	−	16.8832i	−0.652991	−	0.537944i
$986$	−8.09849	−	5.88390i	−0.257909	−	0.187382i
$987$	−16.0362	−	22.0719i	−0.510437	−	0.702556i
$988$	2.44049	+	0.792962i	0.0776422	+	0.0252275i
$989$	47.6592			1.51547
$990$		0			0
$991$	−23.8830			−0.758669			−0.379334	−	0.925260i	$-0.623847\pi$
$991$	−23.8830			−0.758669			−0.379334	+	0.925260i	$0.623847\pi$
$992$	60.6630	+	19.7106i	1.92605	+	0.625812i
$993$	−5.29693	−	7.29060i	−0.168093	−	0.231360i
$994$	82.5926	+	60.0071i	2.61968	+	1.90331i
$995$	−7.09693	+	8.61470i	−0.224988	+	0.273104i
$996$	−20.0401	−	61.6772i	−0.634996	−	1.95432i
$997$	17.4233	−	23.9811i	0.551801	−	0.759489i	−0.438454	−	0.898753i	$-0.644474\pi$
$997$	17.4233	−	23.9811i	0.551801	−	0.759489i	0.990255	+	0.139265i	$0.0444739\pi$
$998$	−10.6908	−	14.7146i	−0.338410	−	0.465782i
$999$	−4.62745	+	14.2418i	−0.146406	+	0.450592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.k.9.4		48
5.4	even	2	inner	605.2.j.k.9.9		48
11.2	odd	10	inner	605.2.j.k.124.4		48
11.3	even	5	inner	605.2.j.k.444.3		48
11.4	even	5		605.2.b.h.364.3	✓	12
11.5	even	5	inner	605.2.j.k.269.9		48
11.6	odd	10	inner	605.2.j.k.269.3		48
11.7	odd	10		605.2.b.h.364.9	yes	12
11.8	odd	10	inner	605.2.j.k.444.9		48
11.9	even	5	inner	605.2.j.k.124.10		48
11.10	odd	2	inner	605.2.j.k.9.10		48
55.4	even	10		605.2.b.h.364.10	yes	12
55.7	even	20		3025.2.a.bo.1.3		12
55.9	even	10	inner	605.2.j.k.124.3		48
55.14	even	10	inner	605.2.j.k.444.10		48
55.18	even	20		3025.2.a.bo.1.10		12
55.19	odd	10	inner	605.2.j.k.444.4		48
55.24	odd	10	inner	605.2.j.k.124.9		48
55.29	odd	10		605.2.b.h.364.4	yes	12
55.37	odd	20		3025.2.a.bo.1.9		12
55.39	odd	10	inner	605.2.j.k.269.10		48
55.48	odd	20		3025.2.a.bo.1.4		12
55.49	even	10	inner	605.2.j.k.269.4		48
55.54	odd	2	inner	605.2.j.k.9.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.h.364.3	✓	12	11.4	even	5
605.2.b.h.364.4	yes	12	55.29	odd	10
605.2.b.h.364.9	yes	12	11.7	odd	10
605.2.b.h.364.10	yes	12	55.4	even	10
605.2.j.k.9.3		48	55.54	odd	2	inner
605.2.j.k.9.4		48	1.1	even	1	trivial
605.2.j.k.9.9		48	5.4	even	2	inner
605.2.j.k.9.10		48	11.10	odd	2	inner
605.2.j.k.124.3		48	55.9	even	10	inner
605.2.j.k.124.4		48	11.2	odd	10	inner
605.2.j.k.124.9		48	55.24	odd	10	inner
605.2.j.k.124.10		48	11.9	even	5	inner
605.2.j.k.269.3		48	11.6	odd	10	inner
605.2.j.k.269.4		48	55.49	even	10	inner
605.2.j.k.269.9		48	11.5	even	5	inner
605.2.j.k.269.10		48	55.39	odd	10	inner
605.2.j.k.444.3		48	11.3	even	5	inner
605.2.j.k.444.4		48	55.19	odd	10	inner
605.2.j.k.444.9		48	11.8	odd	10	inner
605.2.j.k.444.10		48	55.14	even	10	inner
3025.2.a.bo.1.3		12	55.7	even	20
3025.2.a.bo.1.4		12	55.48	odd	20
3025.2.a.bo.1.9		12	55.37	odd	20
3025.2.a.bo.1.10		12	55.18	even	20

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.92380 - 0.625081i) q^{2} +(1.71325 + 2.35809i) q^{3} +(1.69226 + 1.22950i) q^{4} +(-1.42178 + 1.72585i) q^{5} +(-1.82196 - 5.60741i) q^{6} +(-1.88754 + 2.59798i) q^{7} +(-0.109082 - 0.150138i) q^{8} +(-1.69829 + 5.22681i) q^{9} +O(q^{10})\)	\(q+(-1.92380 - 0.625081i) q^{2} +(1.71325 + 2.35809i) q^{3} +(1.69226 + 1.22950i) q^{4} +(-1.42178 + 1.72585i) q^{5} +(-1.82196 - 5.60741i) q^{6} +(-1.88754 + 2.59798i) q^{7} +(-0.109082 - 0.150138i) q^{8} +(-1.69829 + 5.22681i) q^{9} +(3.81402 - 2.43146i) q^{10} +6.09692i q^{12} +(-0.617001 - 0.200476i) q^{13} +(5.25521 - 3.81813i) q^{14} +(-6.50555 - 0.395871i) q^{15} +(-1.17677 - 3.62171i) q^{16} +(1.13030 - 0.367258i) q^{17} +(6.53436 - 8.99378i) q^{18} +(-1.52982 + 1.11148i) q^{19} +(-4.52794 + 1.17250i) q^{20} -9.36008 q^{21} +4.35986i q^{23} +(0.167155 - 0.514449i) q^{24} +(-0.957090 - 4.90754i) q^{25} +(1.06168 + 0.771352i) q^{26} +(-6.91857 + 2.24798i) q^{27} +(-6.38841 + 2.07572i) q^{28} +(3.36869 + 2.44750i) q^{29} +(12.2680 + 4.82808i) q^{30} +(2.44118 - 7.51319i) q^{31} +8.07420i q^{32} -2.40405 q^{34} +(-1.80004 - 6.95136i) q^{35} +(-9.30029 + 6.75706i) q^{36} +(1.20995 - 1.66536i) q^{37} +(3.63783 - 1.18200i) q^{38} +(-0.584338 - 1.79841i) q^{39} +(0.414206 + 0.0252049i) q^{40} +(-2.67396 + 1.94275i) q^{41} +(18.0070 + 5.85081i) q^{42} -10.9313i q^{43} +(-6.60607 - 10.3624i) q^{45} +(2.72527 - 8.38752i) q^{46} +(1.71325 + 2.35809i) q^{47} +(6.52422 - 8.97981i) q^{48} +(-1.02356 - 3.15019i) q^{49} +(-1.22636 + 10.0394i) q^{50} +(2.80252 + 2.03615i) q^{51} +(-0.797640 - 1.09786i) q^{52} +(-6.10422 - 1.98338i) q^{53} +14.7151 q^{54} +0.595953 q^{56} +(-5.24191 - 1.70320i) q^{57} +(-4.95081 - 6.81421i) q^{58} +(-3.00659 - 2.18442i) q^{59} +(-10.5223 - 8.66847i) q^{60} +(2.40630 + 7.40582i) q^{61} +(-9.39272 + 12.9280i) q^{62} +(-10.3735 - 14.2779i) q^{63} +(2.69350 - 8.28974i) q^{64} +(1.22323 - 0.779817i) q^{65} +2.37993i q^{67} +(2.36431 + 0.768210i) q^{68} +(-10.2809 + 7.46954i) q^{69} +(-0.882234 + 14.4982i) q^{70} +(4.85662 + 14.9471i) q^{71} +(0.969998 - 0.315171i) q^{72} +(3.35877 - 4.62295i) q^{73} +(-3.36869 + 2.44750i) q^{74} +(9.93267 - 10.6647i) q^{75} -3.95540 q^{76} +3.82504i q^{78} +(-4.71438 + 14.5094i) q^{79} +(7.92362 + 3.11836i) q^{80} +(-3.81561 - 2.77220i) q^{81} +(6.35854 - 2.06602i) q^{82} +(-10.1161 + 3.28693i) q^{83} +(-15.8397 - 11.5082i) q^{84} +(-0.973211 + 2.47289i) q^{85} +(-6.83298 + 21.0297i) q^{86} +12.1368i q^{87} -9.00000 q^{89} +(6.23146 + 24.0645i) q^{90} +(1.68545 - 1.22455i) q^{91} +(-5.36044 + 7.37801i) q^{92} +(21.8991 - 7.11545i) q^{93} +(-1.82196 - 5.60741i) q^{94} +(0.256823 - 4.22050i) q^{95} +(-19.0397 + 13.8331i) q^{96} +(-14.3972 - 4.67793i) q^{97} +6.70015i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9}+O(q^{10}) \) 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9	\( 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9} + 32 q^{14} - 20 q^{15} - 36 q^{16} - 26 q^{20} + 10 q^{25} - 20 q^{26} - 8 q^{31} + 48 q^{34} - 92 q^{36} - 72 q^{45} + 4 q^{49} + 192 q^{56} + 32 q^{59} + 92 q^{60} - 28 q^{64} + 16 q^{69} + 12 q^{70} - 112 q^{71} - 36 q^{75} + 106 q^{80} + 20 q^{81} + 56 q^{86} - 432 q^{89} - 72 q^{91}+O(q^{100}) \) 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9 + 32 * q^14 - 20 * q^15 - 36 * q^16 - 26 * q^20 + 10 * q^25 - 20 * q^26 - 8 * q^31 + 48 * q^34 - 92 * q^36 - 72 * q^45 + 4 * q^49 + 192 * q^56 + 32 * q^59 + 92 * q^60 - 28 * q^64 + 16 * q^69 + 12 * q^70 - 112 * q^71 - 36 * q^75 + 106 * q^80 + 20 * q^81 + 56 * q^86 - 432 * q^89 - 72 * q^91

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