LMFDB - Embedded newform 605.2.j.k.9.9

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			9.9
Character	$\chi$	$=$	605.9
Dual form			605.2.j.k.269.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92380 + 0.625081i) q^{2} +(-1.71325 - 2.35809i) q^{3} +(1.69226 + 1.22950i) q^{4} +(2.16467 + 0.560538i) q^{5} +(-1.82196 - 5.60741i) q^{6} +(1.88754 - 2.59798i) q^{7} +(0.109082 + 0.150138i) q^{8} +(-1.69829 + 5.22681i) q^{9} +O(q^{10})$	\(q+(1.92380 + 0.625081i) q^{2} +(-1.71325 - 2.35809i) q^{3} +(1.69226 + 1.22950i) q^{4} +(2.16467 + 0.560538i) 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} +(-2.38682 - 6.06482i) 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} +(2.97400 + 3.61003i) q^{20} -9.36008 q^{21} -4.35986i q^{23} +(0.167155 - 0.514449i) q^{24} +(4.37159 + 2.42676i) 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} +(-0.800770 - 13.1595i) q^{30} +(2.44118 - 7.51319i) q^{31} -8.07420i q^{32} -2.40405 q^{34} +(5.54217 - 4.56573i) 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} +(0.151968 + 0.386145i) 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} +(6.89316 + 7.40121i) 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} +(3.41756 - 13.1978i) 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} +(13.5160 - 5.31925i) 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} +(-1.76712 - 14.4662i) q^{75} -3.95540 q^{76} -3.82504i q^{78} +(-4.71438 + 14.5094i) q^{79} +(-0.517201 - 8.49944i) 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} +(-2.65260 + 0.161414i) q^{85} +(-6.83298 + 21.0297i) q^{86} -12.1368i q^{87} -9.00000 q^{89} +(-19.1861 + 15.8058i) 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} +(-3.93457 + 1.54846i) 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	0.896155	−	0.443742i	$-0.146349\pi$
$2$	1.92380	+	0.625081i	1.36033	+	0.441999i	0.464179	+	0.885741i	$0.346349\pi$
$3$	−1.71325	−	2.35809i	−0.989145	−	1.36144i	−0.931754	−	0.363090i	$-0.881722\pi$
$3$	−1.71325	−	2.35809i	−0.989145	−	1.36144i	−0.0573908	−	0.998352i	$-0.518278\pi$
$4$	1.69226	+	1.22950i	0.846128	+	0.614748i
$5$	2.16467	+	0.560538i	0.968070	+	0.250680i
$5$	2.16467	+	0.560538i	0.968070	+	0.250680i
$6$	−1.82196	−	5.60741i	−0.743812	−	2.28922i
$7$	1.88754	−	2.59798i	0.713424	−	0.981943i	−0.286293	−	0.958142i	$-0.592423\pi$
$7$	1.88754	−	2.59798i	0.713424	−	0.981943i	0.999717	−	0.0238013i	$-0.00757690\pi$
$8$	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	0.393327	−	0.919399i	$-0.371324\pi$
$13$	0.617001	+	0.200476i	0.171125	+	0.0556020i	−0.222201	+	0.975001i	$0.571324\pi$
$14$	5.25521	−	3.81813i	1.40451	−	1.02044i
$15$	−2.38682	−	6.06482i	−0.616275	−	1.56593i
$16$	−1.17677	−	3.62171i	−0.294191	−	0.905428i
$17$	−1.13030	+	0.367258i	−0.274139	+	0.0890731i	−0.442860	−	0.896591i	$-0.646036\pi$
$17$	−1.13030	+	0.367258i	−0.274139	+	0.0890731i	0.168721	+	0.985664i	$0.446036\pi$
$18$	−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	$0.369597\pi$
$20$	2.97400	+	3.61003i	0.665006	+	0.807227i
$21$	−9.36008			−2.04254
$22$		0			0
$23$		−	4.35986i		−	0.909095i	−0.890723	−	0.454547i	$-0.849801\pi$
$23$		−	4.35986i		−	0.909095i	0.890723	−	0.454547i	$-0.150199\pi$
$24$	0.167155	−	0.514449i	0.0341203	−	0.105011i
$25$	4.37159	+	2.42676i	0.874319	+	0.485352i
$26$	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	$0.573645\pi$
$30$	−0.800770	−	13.1595i	−0.146200	−	2.40258i
$31$	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
$35$	5.54217	−	4.56573i	0.936798	−	0.771749i
$36$	−9.30029	+	6.75706i	−1.55005	+	1.12618i
$37$	−1.20995	+	1.66536i	−0.198915	+	0.273783i	−0.896809	−	0.442418i	$-0.854121\pi$
$37$	−1.20995	+	1.66536i	−0.198915	+	0.273783i	0.697894	+	0.716201i	$0.254121\pi$
$38$	−3.63783	+	1.18200i	−0.590134	+	0.191746i
$39$	−0.584338	−	1.79841i	−0.0935689	−	0.287976i
$40$	0.151968	+	0.386145i	0.0240283	+	0.0610548i
$41$	−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	$0.313670\pi$
$43$			10.9313i			1.66701i	−0.552509	+	0.833507i	$0.686330\pi$
$44$		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	0.665574	−	0.746332i	$-0.268187\pi$
$47$	−1.71325	−	2.35809i	−0.249903	−	0.343962i	−0.915477	+	0.402370i	$0.868187\pi$
$48$	−6.52422	+	8.97981i	−0.941689	+	1.29612i
$49$	−1.02356	−	3.15019i	−0.146223	−	0.450027i
$50$	6.89316	+	7.40121i	0.974840	+	1.04669i
$51$	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	0.696613	−	0.717447i	$-0.254690\pi$
$53$	6.10422	+	1.98338i	0.838479	+	0.272438i	0.141866	+	0.989886i	$0.454690\pi$
$54$	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	$0.777775\pi$
$60$	3.41756	−	13.1978i	0.441205	−	1.70383i
$61$	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	$-0.953560\pi$
$67$		−	2.37993i		−	0.290755i	0.989376	−	0.145377i	$-0.0464396\pi$
$68$	−2.36431	−	0.768210i	−0.286714	−	0.0931591i
$69$	−10.2809	+	7.46954i	−1.23768	+	0.899226i
$70$	13.5160	−	5.31925i	1.61547	−	0.635772i
$71$	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	−0.958999	−	0.283409i	$-0.908535\pi$
$73$	−3.35877	+	4.62295i	−0.393114	+	0.541075i	0.565885	+	0.824484i	$0.308535\pi$
$74$	−3.36869	+	2.44750i	−0.391602	+	0.284516i
$75$	−1.76712	−	14.4662i	−0.204049	−	1.67042i
$76$	−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	$0.771570\pi$
$80$	−0.517201	−	8.49944i	−0.0578248	−	0.950266i
$81$	−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	0.304297	−	0.952577i	$-0.401579\pi$
$83$	10.1161	−	3.28693i	1.11039	−	0.360787i	0.806092	+	0.591790i	$0.201579\pi$
$84$	−15.8397	−	11.5082i	−1.72825	−	1.25565i
$85$	−2.65260	+	0.161414i	−0.287714	+	0.0175078i
$86$	−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	$0.658275\pi$
$90$	−19.1861	+	15.8058i	−2.02239	+	1.66608i
$91$	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
$95$	−3.93457	+	1.54846i	−0.403679	+	0.158869i
$96$	−19.0397	+	13.8331i	−1.94323	+	1.41184i
$97$	14.3972	+	4.67793i	1.46181	+	0.474971i	0.928623	−	0.371025i	$-0.120994\pi$
$97$	14.3972	+	4.67793i	1.46181	+	0.474971i	0.533189	+	0.845996i	$0.320994\pi$
$98$		−	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	−0.706864	−	0.707350i	$-0.749891\pi$
$103$	1.87043	−	2.57443i	0.184299	−	0.253666i	0.891163	+	0.453684i	$0.149891\pi$
$104$	0.0372046	+	0.114504i	0.00364821	+	0.0112280i
$105$	−20.2615	−	5.24669i	−1.97732	−	0.512024i
$106$	10.5035	+	7.63127i	1.02019	+	0.741214i
$107$	2.33296	+	3.21104i	0.225536	+	0.310423i	0.906756	−	0.421655i	$-0.138551\pi$
$107$	2.33296	+	3.21104i	0.225536	+	0.310423i	−0.681221	+	0.732078i	$0.738551\pi$
$108$	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	0.430955	−	0.902374i	$-0.358177\pi$
$113$	−5.95741	−	8.19967i	−0.560426	−	0.771360i	−0.991381	+	0.131014i	$0.958177\pi$
$114$	9.01977	+	6.55325i	0.844779	+	0.613768i
$115$	2.44387	−	9.43767i	0.227892	−	0.880067i
$116$	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
$125$	8.10277	+	7.70358i	0.724733	+	0.689029i
$126$	11.0318	+	33.9523i	0.982787	+	3.02471i
$127$	−15.6382	+	5.08117i	−1.38767	+	0.450881i	−0.905183	−	0.425023i	$-0.860266\pi$
$127$	−15.6382	+	5.08117i	−1.38767	+	0.450881i	−0.482486	+	0.875904i	$0.660266\pi$
$128$	0.871737	−	1.19984i	0.0770514	−	0.106052i
$129$	25.7770	−	18.7281i	2.26954	−	1.64892i
$130$	1.86580	+	2.26483i	0.163642	+	0.198639i
$131$	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
$135$	16.2365	−	0.988011i	1.39742	−	0.0850345i
$136$	−0.178435	−	0.129641i	−0.0153007	−	0.0111166i
$137$	13.0975	−	4.25564i	1.11900	−	0.363584i	0.309611	−	0.950863i	$-0.399801\pi$
$137$	13.0975	−	4.25564i	1.11900	−	0.363584i	0.809384	+	0.587280i	$0.199801\pi$
$138$	−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	$0.607520\pi$
$140$	14.9923	−	0.912301i	1.26708	−	0.0771035i
$141$	−2.62534	+	8.07998i	−0.221094	+	0.680457i
$142$			31.7911i			2.66785i
$143$		0			0
$144$	20.9285			1.74404
$145$	5.92019	+	7.18631i	0.491645	+	0.596790i
$146$	−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	$0.611976\pi$
$150$	5.64299	−	28.9348i	0.460748	−	2.36252i
$151$	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	0.341971	−	0.939710i	$-0.388905\pi$
$157$	−8.23746	−	11.3379i	−0.657421	−	0.904863i	−0.999393	+	0.0348477i	$0.988905\pi$
$158$	−18.1391	+	24.9663i	−1.44307	+	1.98621i
$159$	−5.78107	−	17.7923i	−0.458469	−	1.41102i
$160$	4.52590	−	17.4780i	0.357804	−	1.38176i
$161$	−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	−0.101811	−	0.994804i	$-0.532464\pi$
$163$	−9.81676	−	3.18966i	−0.768908	−	0.249833i	−0.667097	+	0.744970i	$0.732464\pi$
$164$	−6.91362			−0.539863
$165$		0			0
$166$	21.5160			1.66997
$167$	−13.8909	−	4.51344i	−1.07491	−	0.349260i	−0.282513	−	0.959263i	$-0.591168\pi$
$167$	−13.8909	−	4.51344i	−1.07491	−	0.349260i	−0.792399	+	0.610003i	$0.791168\pi$
$168$	−1.02102	−	1.40531i	−0.0787731	−	0.108422i
$169$	−10.1767	−	7.39382i	−0.782825	−	0.568755i
$170$	−5.20397	−	1.34756i	−0.399126	−	0.103353i
$171$	−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	0.756816	−	0.653628i	$-0.226754\pi$
$173$	−1.29806	−	1.78662i	−0.0986895	−	0.135834i	−0.855506	+	0.517793i	$0.826754\pi$
$174$	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	$0.167648\pi$
$180$	−23.9197	+	9.41363i	−1.78287	+	0.701651i
$181$	−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
$185$	−3.55264	+	2.92672i	−0.261195	+	0.215177i
$186$	−46.5773			−3.41521
$187$		0			0
$188$		−	6.09692i		−	0.444664i
$189$	7.21889	−	22.2175i	0.525097	−	1.61608i
$190$	−8.53726	+	0.519502i	−0.619358	+	0.0376887i
$191$	−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	−0.137793	−	0.990461i	$-0.544001\pi$
$193$	4.62491	−	1.50273i	0.332908	−	0.108169i	0.470702	+	0.882293i	$0.344001\pi$
$194$	24.7732	+	17.9988i	1.77862	+	1.29224i
$195$	−0.256823	−	4.22050i	−0.0183914	−	0.302236i
$196$	2.14102	−	6.58939i	0.152930	−	0.470670i
$197$		−	11.8747i		−	0.846038i	−0.906121	−	0.423019i	$-0.860970\pi$
$197$		−	11.8747i		−	0.846038i	0.906121	−	0.423019i	$-0.139030\pi$
$198$		0			0
$199$	4.99158			0.353844			0.176922	−	0.984225i	$-0.443386\pi$
$199$	4.99158			0.353844			0.176922	+	0.984225i	$0.443386\pi$
$200$	0.112512	+	0.921060i	0.00795579	+	0.0651288i
$201$	−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
$205$	−6.87722	+	2.70655i	−0.480326	+	0.189033i
$206$	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
$215$	−6.12743	+	23.6627i	−0.417888	+	1.61379i
$216$	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	0.738783	−	0.673943i	$-0.235401\pi$
$223$	−1.94836	−	2.68169i	−0.130472	−	0.179579i	−0.869255	+	0.494364i	$0.835401\pi$
$224$	−20.9766	−	15.2404i	−1.40156	−	1.01829i
$225$	−20.1085	+	18.7281i	−1.34056	+	1.24854i
$226$	−6.33542	−	19.4984i	−0.421426	−	1.29702i
$227$	−1.66938	+	2.29770i	−0.110800	+	0.152504i	−0.860816	−	0.508917i	$-0.830046\pi$
$227$	−1.66938	+	2.29770i	−0.110800	+	0.152504i	0.750015	+	0.661421i	$0.230046\pi$
$228$	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	−0.399737	−	0.916630i	$-0.630898\pi$
$233$	−19.2623	−	6.25868i	−1.26191	−	0.410020i	−0.862175	+	0.506610i	$0.830898\pi$
$234$	−5.83474	+	4.23919i	−0.381429	+	0.277125i
$235$	−2.38682	−	6.06482i	−0.155699	−	0.395625i
$236$	−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	$0.319479\pi$
$240$	−19.1563	+	15.7813i	−1.23653	+	1.01868i
$241$	−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
$245$	−0.449864	−	7.39286i	−0.0287408	−	0.472312i
$246$	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
$250$	10.7728	+	19.8851i	0.681329	+	1.25764i
$251$	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
$255$	4.92519	+	5.97851i	0.308427	+	0.374389i
$256$	−11.6763	+	8.48333i	−0.729769	+	0.530208i
$257$	2.38815	−	3.28701i	0.148969	−	0.205038i	−0.728011	−	0.685566i	$-0.759555\pi$
$257$	2.38815	−	3.28701i	0.148969	−	0.205038i	0.876979	+	0.480528i	$0.159555\pi$
$258$	61.2965	−	19.9164i	3.81616	−	1.23994i
$259$	2.04272	+	6.28686i	0.126929	+	0.390646i
$260$	1.11124	+	2.82361i	0.0689160	+	0.175113i
$261$	−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	$0.123867\pi$
$263$			12.3054i			0.758783i	−0.925236	+	0.379391i	$0.876133\pi$
$264$		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	$0.824497\pi$
$270$	31.8534	+	8.24840i	1.93854	+	0.501982i
$271$	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	0.824971	−	0.565175i	$-0.191191\pi$
$277$	19.3093	+	6.27399i	1.16019	+	0.376967i	0.335215	+	0.942142i	$0.391191\pi$
$278$	8.03120	+	11.0540i	0.481679	+	0.662974i
$279$	35.1242	+	25.5192i	2.10283	+	1.52779i
$280$	1.29004	+	0.334055i	0.0770947	+	0.0199636i
$281$	−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	0.478529	−	0.878072i	$-0.341170\pi$
$283$	−8.48599	−	11.6800i	−0.504440	−	0.694302i	−0.982969	+	0.183770i	$0.941170\pi$
$284$	−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
$290$	6.89725	+	17.5256i	0.405021	+	1.02914i
$291$	−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	−0.465009	−	0.885306i	$-0.653949\pi$
$293$	8.91231	−	12.2667i	0.520663	−	0.716631i	0.985672	+	0.168675i	$0.0539489\pi$
$294$	−15.7995	+	11.4790i	−0.921447	+	0.669470i
$295$	−5.28383	−	6.41385i	−0.307636	−	0.373429i
$296$	−0.382018			−0.0222043
$297$		0			0
$298$			38.8316i			2.24945i
$299$	0.874048	−	2.69004i	0.0505475	−	0.155569i
$300$	14.7958	−	26.6533i	0.854234	−	1.53883i
$301$	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
$305$	1.05759	+	17.3800i	0.0605576	+	0.995175i
$306$	4.08278	−	12.5655i	0.233397	−	0.718321i
$307$		−	8.04171i		−	0.458965i	−0.973313	−	0.229482i	$-0.926297\pi$
$307$		−	8.04171i		−	0.458965i	0.973313	−	0.229482i	$-0.0737033\pi$
$308$		0			0
$309$	−9.27523			−0.527650
$310$	27.5787	−	22.7198i	1.56637	−	1.29040i
$311$	−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	−0.371511	−	0.928429i	$-0.621160\pi$
$313$	−2.23540	+	0.726326i	−0.126352	+	0.0410543i	0.245158	+	0.969483i	$0.421160\pi$
$314$	−8.76015	−	26.9610i	−0.494364	−	1.52150i
$315$	14.4519	+	36.7218i	0.814275	+	2.06904i
$316$	−25.8172	+	18.7573i	−1.45233	+	1.05518i
$317$	−17.1412	−	5.56952i	−0.962747	−	0.312815i	−0.214863	−	0.976644i	$-0.568930\pi$
$317$	−17.1412	−	5.56952i	−0.962747	−	0.312815i	−0.747885	+	0.663829i	$0.768930\pi$
$318$		−	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
$325$	2.21077	+	2.37371i	0.122632	+	0.131670i
$326$	−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
$335$	1.33404	−	5.15176i	0.0728865	−	0.281471i
$336$	11.0146	+	33.8995i	0.600897	+	1.84937i
$337$	−21.1284	+	29.0807i	−1.15094	+	1.58413i	−0.410719	+	0.911762i	$0.634722\pi$
$337$	−21.1284	+	29.0807i	−1.15094	+	1.58413i	−0.740218	+	0.672367i	$0.765278\pi$
$338$	−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
$345$	−26.4418	+	10.4062i	−1.42358	+	0.560252i
$346$	−1.38042	−	4.24850i	−0.0742119	−	0.228401i
$347$	11.6627	−	3.78944i	0.626087	−	0.203428i	0.0212460	−	0.999774i	$-0.493237\pi$
$347$	11.6627	−	3.78944i	0.626087	−	0.203428i	0.604841	+	0.796346i	$0.293237\pi$
$348$	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	$0.456835\pi$
$350$	32.2393	−	3.93819i	1.72326	−	0.210505i
$351$	4.71943			0.251905
$352$		0			0
$353$		−	18.7202i		−	0.996378i	−0.867068	−	0.498189i	$-0.833999\pi$
$353$		−	18.7202i		−	0.996378i	0.867068	−	0.498189i	$-0.166001\pi$
$354$	−6.77104	+	20.8391i	−0.359876	+	1.10759i
$355$	2.13454	+	35.0779i	0.113289	+	1.86174i
$356$	−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	$-0.741981\pi$
$360$	−2.27639	+	0.138521i	−0.119976	+	0.00730071i
$361$	−4.76637	+	14.6694i	−0.250861	+	0.772072i
$362$		−	6.81074i		−	0.357965i
$363$		0			0
$364$	4.35779			0.228410
$365$	−9.86197	+	8.12444i	−0.516199	+	0.425253i
$366$	37.1433	−	26.9862i	1.94151	−	1.41059i
$367$	−10.5794	+	14.5613i	−0.552242	+	0.760096i	−0.990314	−	0.138844i	$-0.955661\pi$
$367$	−10.5794	+	14.5613i	−0.552242	+	0.760096i	0.438072	+	0.898940i	$0.355661\pi$
$368$	−15.7902	+	5.13054i	−0.823120	+	0.267448i
$369$	−5.61319	−	17.2756i	−0.292211	−	0.899333i
$370$	−8.66402	+	3.40974i	−0.450421	+	0.177264i
$371$	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	$0.00166964\pi$
$373$			0.202607i			0.0104906i	−0.999986	+	0.00524531i	$0.998330\pi$
$374$		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	$0.562303\pi$
$380$	−8.56213	−	2.21715i	−0.439228	−	0.113738i
$381$	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	0.130289	−	0.991476i	$-0.458409\pi$
$383$	−6.79248	−	2.20701i	−0.347080	−	0.112773i	−0.477369	+	0.878703i	$0.658409\pi$
$384$	−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	$0.590815\pi$
$390$	2.14408	−	8.27995i	0.108570	−	0.419271i
$391$	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	$-0.681260\pi$
$397$		−	33.5614i		−	1.68440i	0.539165	−	0.842200i	$-0.318740\pi$
$398$	9.60282	+	3.12015i	0.481346	+	0.156399i
$399$	14.3192	−	10.4035i	0.716857	−	0.520827i
$400$	3.64469	−	18.6884i	0.182235	−	0.934419i
$401$	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
$405$	−6.70561	−	8.13969i	−0.333204	−	0.404465i
$406$	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	$0.0352674\pi$
$410$	−14.9222	+	0.908036i	−0.736957	+	0.0448447i
$411$	−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
$415$	23.7405	−	1.44464i	1.16538	−	0.0709146i
$416$	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	$0.658320\pi$
$420$	−27.8369	−	33.7902i	−1.35830	−	1.64879i
$421$	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
$425$	−5.83247	−	1.13747i	−0.282917	−	0.0551756i
$426$	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	$0.411084\pi$
$433$	−15.0587	+	20.7265i	−0.723675	+	0.996054i	−0.999394	+	0.0348152i	$0.988916\pi$
$434$	−15.8574	−	48.8041i	−0.761181	−	2.34267i
$435$	6.80316	−	26.2722i	0.326187	−	1.25966i
$436$	−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	0.927010	−	0.375035i	$-0.122369\pi$
$443$	5.97474	+	8.22353i	0.283869	+	0.390712i	−0.643142	+	0.765747i	$0.722369\pi$
$444$	10.1535	+	7.37698i	0.481866	+	0.350096i
$445$	−19.4820	−	5.04485i	−0.923537	−	0.239149i
$446$	−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
$455$	4.33484	−	1.70599i	0.203221	−	0.0799779i
$456$	0.316082	+	0.972801i	0.0148019	+	0.0455556i
$457$	3.19822	−	1.03916i	0.149606	−	0.0486101i	−0.233256	−	0.972415i	$-0.574938\pi$
$457$	3.19822	−	1.03916i	0.149606	−	0.0486101i	0.382863	+	0.923805i	$0.374938\pi$
$458$	2.36794	−	3.25919i	0.110647	−	0.152292i
$459$	−6.99450	+	5.08180i	−0.326475	+	0.237198i
$460$	15.7392	−	12.9662i	0.733846	−	0.604553i
$461$	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	$0.116961\pi$
$463$			15.4595i			0.718465i	−0.933248	+	0.359232i	$0.883039\pi$
$464$	4.89997	−	15.0806i	0.227475	−	0.700098i
$465$	−51.3928	+	3.12732i	−2.38329	+	0.145026i
$466$	−33.1446	−	24.0810i	−1.53539	−	1.11553i
$467$	−17.7760	+	5.77576i	−0.822574	+	0.267270i	−0.689914	−	0.723891i	$-0.742352\pi$
$467$	−17.7760	+	5.77576i	−0.822574	+	0.267270i	−0.132660	+	0.991162i	$0.542352\pi$
$468$	−7.09292	+	2.30463i	−0.327870	+	0.106531i
$469$	−6.18300	−	4.49221i	−0.285505	−	0.207431i
$470$	−0.800770	−	13.1595i	−0.0369368	−	0.607001i
$471$	−12.6229	+	38.8493i	−0.581633	+	1.79008i
$472$		−	0.689685i		−	0.0317453i
$473$		0			0
$474$	89.9495			4.13152
$475$	−9.38502	+	1.14643i	−0.430614	+	0.0526016i
$476$	−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	$-0.339127\pi$
$480$	−48.9686	+	19.2717i	−2.23510	+	0.879628i
$481$	−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	0.796386	−	0.604789i	$-0.206742\pi$
$487$	−0.549473	−	0.756284i	−0.0248990	−	0.0342705i	−0.821285	+	0.570518i	$0.806742\pi$
$488$	−0.849414	+	1.16912i	−0.0384512	+	0.0529235i
$489$	9.29707	+	28.6134i	0.420428	+	1.29394i
$490$	3.75569	−	14.5036i	0.169665	−	0.655206i
$491$	−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	$0.635497\pi$
$500$	4.24043	+	22.9988i	0.189638	+	1.02854i
$501$	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	0.824717	−	0.565546i	$-0.191335\pi$
$503$	0.717663	+	0.987779i	0.0319990	+	0.0440429i	−0.792718	+	0.609589i	$0.791335\pi$
$504$	−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	$0.119852\pi$
$510$	5.73803	+	14.5801i	0.254084	+	0.645618i
$511$	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
$515$	5.49193	−	4.52434i	0.242003	−	0.199366i
$516$	66.6475			2.93399
$517$		0			0
$518$			13.3715i			0.587512i
$519$	−1.98911	+	6.12186i	−0.0873124	+	0.268720i
$520$	0.0163518	+	0.268718i	0.000717074	+	0.0117841i
$521$	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	−0.152532	−	0.988299i	$-0.548743\pi$
$523$	6.97451	−	2.26616i	0.304974	−	0.0990921i	0.457506	+	0.889206i	$0.348743\pi$
$524$	23.6928	+	17.2139i	1.03503	+	0.751991i
$525$	−40.9185	−	22.7147i	−1.78583	−	0.991350i
$526$	−7.69187	+	23.6731i	−0.335382	+	1.03220i
$527$			9.38873i			0.408980i
$528$		0			0
$529$	3.99158			0.173547
$530$	18.4591	+	22.4068i	0.801811	+	0.973290i
$531$	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
$535$	3.25017	+	8.25856i	0.140517	+	0.357049i
$536$	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
$545$	−33.3683	−	8.64068i	−1.42934	−	0.370126i
$546$	−9.93737	−	7.21992i	−0.425280	−	0.308984i
$547$	−13.7323	−	18.9009i	−0.587151	−	0.808144i	0.407306	−	0.913292i	$-0.366468\pi$
$547$	−13.7323	−	18.9009i	−0.587151	−	0.808144i	−0.994457	+	0.105148i	$0.966468\pi$
$548$	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
$555$	12.9880	+	3.36323i	0.551311	+	0.142761i
$556$	4.36615	+	13.4376i	0.185166	+	0.569882i
$557$	0.0200153	−	0.0275487i	0.000848077	−	0.00116728i	−0.808593	−	0.588369i	$-0.799770\pi$
$557$	0.0200153	−	0.0275487i	0.000848077	−	0.00116728i	0.809441	+	0.587201i	$0.199770\pi$
$558$	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	−0.206241	−	0.978501i	$-0.566123\pi$
$563$	−22.4995	−	7.31054i	−0.948242	−	0.308103i	−0.742001	+	0.670399i	$0.766123\pi$
$564$	−14.3771	+	10.4455i	−0.605383	+	0.439837i
$565$	−8.29960	−	21.0889i	−0.349167	−	0.887218i
$566$	−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	$0.522828\pi$
$570$	15.8515	+	19.2415i	0.663945	+	0.805940i
$571$	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
$575$	10.5803	−	19.0596i	0.441231	−	0.794838i
$576$	38.7545	+	28.1568i	1.61477	+	1.17320i
$577$	36.7234	−	11.9321i	1.52881	−	0.496742i	0.580550	−	0.814225i	$-0.302838\pi$
$577$	36.7234	−	11.9321i	1.52881	−	0.496742i	0.948264	+	0.317483i	$0.102838\pi$
$578$	−29.9873	+	9.74348i	−1.24731	+	0.405275i
$579$	−11.4672	−	8.33140i	−0.476560	−	0.346241i
$580$	1.18294	+	19.4399i	0.0491190	+	0.807199i
$581$	10.5552	−	32.4857i	0.437905	−	1.34773i
$582$		−	89.2539i		−	3.69969i
$583$		0			0
$584$	−1.06046			−0.0438823
$585$	−6.15336	+	5.06923i	−0.254410	+	0.209587i
$586$	24.8132	−	18.0279i	1.02503	−	0.744725i
$587$	8.39465	−	11.5542i	0.346484	−	0.476894i	−0.599837	−	0.800122i	$-0.704768\pi$
$587$	8.39465	−	11.5542i	0.346484	−	0.476894i	0.946321	+	0.323228i	$0.104768\pi$
$588$	−19.2064	+	6.24055i	−0.792060	+	0.257356i
$589$	4.61617	+	14.2071i	0.190206	+	0.585394i
$590$	−6.15586	−	15.6418i	−0.253433	−	0.643963i
$591$	−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	$-0.730620\pi$
$593$		−	36.4700i		−	1.49764i	0.662771	−	0.748822i	$-0.269380\pi$
$594$		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	$-0.312806\pi$
$600$	1.97918	−	1.84332i	0.0807996	−	0.0752531i
$601$	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	−0.360155	−	0.932893i	$-0.617276\pi$
$607$	−29.5616	−	9.60513i	−1.19987	−	0.389860i	−0.839712	+	0.543032i	$0.817276\pi$
$608$	8.97428	+	12.3520i	0.363955	+	0.500941i
$609$	−31.5312	−	22.9088i	−1.27771	−	0.928311i
$610$	−8.82930	+	34.0967i	−0.357488	+	1.38054i
$611$	−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	$0.0616063\pi$
$613$	21.3175	+	29.3410i	0.861004	+	1.18507i	−0.120325	+	0.992735i	$0.538394\pi$
$614$	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	$-0.991793\pi$
$617$		−	1.28079i		−	0.0515626i	0.999668	−	0.0257813i	$-0.00820735\pi$
$618$	−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	$0.247040\pi$
$620$	34.3829	−	13.5315i	1.38085	−	0.543437i
$621$	−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
$625$	13.2217	+	21.2176i	0.528866	+	0.848705i
$626$	−4.75448			−0.190027
$627$		0			0
$628$		−	29.3146i		−	1.16978i
$629$	0.755998	−	2.32672i	0.0301436	−	0.0927725i
$630$	4.84857	+	79.6792i	0.193172	+	3.17449i
$631$	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
$635$	−36.6998	+	2.23323i	−1.45639	+	0.0886229i
$636$	12.0925	−	37.2169i	0.479500	−	1.47575i
$637$		−	2.14887i		−	0.0851412i
$638$		0			0
$639$	−86.3738			−3.41689
$640$	2.55958	−	2.10862i	0.101176	−	0.0833507i
$641$	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	−0.347911	−	0.937528i	$-0.613109\pi$
$643$	−1.98579	+	0.645222i	−0.0783119	+	0.0254451i	0.269599	+	0.962973i	$0.413109\pi$
$644$	−9.04986	−	27.8526i	−0.356614	−	1.09755i
$645$	66.2966	−	26.0912i	2.61043	−	1.02734i
$646$	3.67775	−	2.67204i	0.144699	−	0.105130i
$647$	−23.5511	−	7.65223i	−0.925891	−	0.300840i	−0.193010	−	0.981197i	$-0.561825\pi$
$647$	−23.5511	−	7.65223i	−0.925891	−	0.300840i	−0.732881	+	0.680357i	$0.761825\pi$
$648$		−	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	−0.880958	−	0.473194i	$-0.843101\pi$
$653$	−4.05522	+	5.58154i	−0.158693	+	0.218422i	0.722265	+	0.691616i	$0.243101\pi$
$654$	28.0854	+	86.4381i	1.09823	+	3.38000i
$655$	30.3070	+	7.84795i	1.18419	+	0.306645i
$656$	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
$665$	−3.40381	+	13.1447i	−0.131994	+	0.509730i
$666$	−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	0.788921	−	0.614494i	$-0.210640\pi$
$673$	27.6539	+	8.98531i	1.06598	+	0.346358i	0.277060	+	0.960853i	$0.410640\pi$
$674$	−58.8247	+	42.7386i	−2.26584	+	1.64623i
$675$	35.7005	+	6.96247i	1.37411	+	0.267985i
$676$	−8.13095	−	25.0245i	−0.312729	−	0.962480i
$677$	38.8680	−	12.6290i	1.49382	−	0.485371i	0.555610	−	0.831443i	$-0.312485\pi$
$677$	38.8680	−	12.6290i	1.49382	−	0.485371i	0.938208	+	0.346072i	$0.112485\pi$
$678$	−35.1248	+	48.3451i	−1.34896	+	1.85668i
$679$	39.3284	−	28.5738i	1.50929	−	1.09656i
$680$	−0.313585	−	0.380649i	−0.0120254	−	0.0145972i
$681$	8.27824			0.317223
$682$		0			0
$683$			17.2211i			0.658948i	0.944165	+	0.329474i	$0.106871\pi$
$683$			17.2211i			0.658948i	−0.944165	+	0.329474i	$0.893129\pi$
$684$	6.71743	−	20.6741i	0.256847	−	0.790494i
$685$	30.7372	−	1.87040i	1.17441	−	0.0714642i
$686$	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
$690$	−57.3735	+	3.49125i	−2.18417	+	0.132910i
$691$	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
$695$	9.60372	+	11.6576i	0.364290	+	0.442198i
$696$	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
$700$	32.9648	+	6.42894i	1.24595	+	0.242991i
$701$	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	$-0.226184\pi$
$710$	−17.8201	+	68.8173i	−0.668778	+	2.58267i
$711$	−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	$0.810530\pi$
$720$	45.3033	+	11.7312i	1.68835	+	0.437197i
$721$	−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	$-0.998711\pi$
$727$		−	0.218345i		−	0.00809798i	0.999992	−	0.00404899i	$-0.00128884\pi$
$728$	0.367704	+	0.119474i	0.0136280	+	0.00442801i
$729$	−30.4927	+	22.1543i	−1.12936	+	0.820529i
$730$	−24.0509	+	9.46529i	−0.890165	+	0.350326i
$731$	−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	−0.827525	−	0.561429i	$-0.810252\pi$
$733$	−1.02489	+	1.41065i	−0.0378553	+	0.0521034i	0.789670	+	0.613532i	$0.210252\pi$
$734$	−29.4548	+	21.4002i	−1.08720	+	0.789894i
$735$	−16.6623	+	13.7266i	−0.614597	+	0.506314i
$736$	−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	$-0.0887540\pi$
$740$	−9.61038	+	0.584803i	−0.353284	+	0.0214978i
$741$	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	0.366254	−	0.930515i	$-0.380640\pi$
$743$	32.9687	−	10.7122i	1.20950	−	0.392991i	0.843249	+	0.537524i	$0.180640\pi$
$744$	−3.45710	−	2.51173i	−0.126743	−	0.0920845i
$745$	2.60725	+	42.8463i	0.0955222	+	1.56977i
$746$	−0.126646	+	0.389777i	−0.00463684	+	0.0142707i
$747$			58.4572i			2.13884i
$748$		0			0
$749$	12.7458			0.465720
$750$	28.4343	−	59.4712i	1.03827	−	2.17158i
$751$	−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
$755$	6.84689	−	2.69461i	0.249184	−	0.0980668i
$756$	39.5325	−	28.7220i	1.43778	−	1.04461i
$757$	−5.95480	−	1.93483i	−0.216431	−	0.0703226i	0.198795	−	0.980041i	$-0.436297\pi$
$757$	−5.95480	−	1.93483i	−0.216431	−	0.0703226i	−0.415225	+	0.909719i	$0.636297\pi$
$758$			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
$765$	3.66121	−	14.1387i	0.132371	−	0.511187i
$766$	−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	$-0.886875\pi$
$773$	−27.2115	−	37.4535i	−0.978731	−	1.34711i	−0.0412213	−	0.999150i	$-0.513125\pi$
$774$	−98.3140	−	71.4293i	−3.53382	−	2.56747i
$775$	28.9046	−	26.9205i	1.03828	−	0.967011i
$776$	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
$785$	−11.4761	−	29.1602i	−0.409598	−	1.04077i
$786$	−25.5088	−	78.5079i	−0.909867	−	2.80028i
$787$	−46.7397	+	15.1866i	−1.66609	+	0.541345i	−0.982135	−	0.188178i	$-0.939742\pi$
$787$	−46.7397	+	15.1866i	−1.66609	+	0.541345i	−0.683955	+	0.729524i	$0.739742\pi$
$788$	14.5999	−	20.0951i	0.520100	−	0.715857i
$789$	29.0172	−	21.0822i	1.03304	−	0.750546i
$790$	−53.2597	+	43.8762i	−1.89490	+	1.56104i
$791$	−32.5474			−1.15725
$792$		0			0
$793$			5.05180i			0.179395i
$794$	20.9786	−	64.5656i	0.744504	−	2.29135i
$795$	−2.54084	−	41.7550i	−0.0901143	−	1.48090i
$796$	8.44704	+	6.13713i	0.299397	+	0.217525i
$797$	−41.5326	+	13.4948i	−1.47116	+	0.478009i	−0.931459	−	0.363847i	$-0.881463\pi$
$797$	−41.5326	+	13.4948i	−1.47116	+	0.478009i	−0.539702	+	0.841856i	$0.681463\pi$
$798$	34.0504	−	11.0636i	1.20537	−	0.391649i
$799$	2.80252	+	2.03615i	0.0991459	+	0.0720337i
$800$	19.5942	−	35.2971i	0.692758	−	1.24794i
$801$	15.2846	−	47.0413i	0.540056	−	1.66212i
$802$			67.9480i			2.39933i
$803$		0			0
$804$	−14.5102			−0.511737
$805$	−19.9059	−	24.1631i	−0.701592	−	0.851638i
$806$	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	$-0.344355\pi$
$810$	−7.81229	−	19.8507i	−0.274496	−	0.697483i
$811$	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
$820$	−14.9657	−	3.87535i	−0.522625	−	0.135333i
$821$	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	0.0697326	−	0.997566i	$-0.477785\pi$
$823$	−13.2024	−	4.28972i	−0.460207	−	0.149530i	−0.529940	+	0.848035i	$0.677785\pi$
$824$	0.590551			0.0205728
$825$		0			0
$826$	−24.1406			−0.839960
$827$	−9.08284	−	2.95119i	−0.315841	−	0.102623i	0.146806	−	0.989165i	$-0.453101\pi$
$827$	−9.08284	−	2.95119i	−0.315841	−	0.102623i	−0.462648	+	0.886542i	$0.653101\pi$
$828$	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	$0.475539\pi$
$830$	46.5751	+	12.0606i	1.61665	+	0.418628i
$831$	−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	$0.307873\pi$
$840$	−1.42243	−	3.61435i	−0.0490786	−	0.124707i
$841$	−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
$845$	−17.8847	−	21.7096i	−0.615253	−	0.746834i
$846$	32.4031			1.11404
$847$		0			0
$848$		−	24.4417i		−	0.839332i
$849$	−13.0037	+	40.0214i	−0.446287	+	1.37353i
$850$	−10.5095	−	5.83405i	−0.360473	−	0.200106i
$851$	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	−0.728993	−	0.684522i	$-0.760011\pi$
$853$	−26.7648	+	8.69640i	−0.916408	+	0.297759i	−0.187416	+	0.982281i	$0.560011\pi$
$854$	40.9220	+	29.7315i	1.40032	+	1.01739i
$855$	−1.41144	−	23.1950i	−0.0482703	−	0.793252i
$856$	−0.227617	+	0.700533i	−0.00777979	+	0.0239437i
$857$		−	4.04561i		−	0.138195i	−0.997610	−	0.0690977i	$-0.977988\pi$
$857$		−	4.04561i		−	0.138195i	0.997610	−	0.0690977i	$-0.0220120\pi$
$858$		0			0
$859$	55.2064			1.88362			0.941808	−	0.336151i	$-0.109125\pi$
$859$	55.2064			1.88362			0.941808	+	0.336151i	$0.109125\pi$
$860$	−39.4625	+	32.5098i	−1.34566	+	1.10857i
$861$	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	0.223641	−	0.974672i	$-0.428206\pi$
$863$	28.7149	−	9.33004i	0.977467	−	0.317598i	0.753827	+	0.657073i	$0.228206\pi$
$864$	−18.1506	−	55.8619i	−0.617497	−	1.90046i
$865$	−1.80840	−	4.59506i	−0.0614873	−	0.156237i
$866$	−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
$875$	35.3080	−	6.50997i	1.19363	−	0.220077i
$876$	28.1858	+	20.4782i	0.952309	+	0.691893i
$877$	−18.1859	−	25.0308i	−0.614096	−	0.845230i	0.382811	−	0.923827i	$-0.374956\pi$
$877$	−18.1859	−	25.0308i	−0.614096	−	0.845230i	−0.996906	+	0.0785967i	$0.974956\pi$
$878$	−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	$0.0352267\pi$
$883$	23.5284	+	32.3840i	0.791793	+	1.08981i	−0.202090	+	0.979367i	$0.564773\pi$
$884$	−1.30477	−	0.947972i	−0.0438842	−	0.0318838i
$885$	−6.07189	+	23.4482i	−0.204104	+	0.788204i
$886$	6.35385	+	19.5551i	0.213462	+	0.656968i
$887$	−22.1801	+	30.5283i	−0.744735	+	1.02504i	0.253597	+	0.967310i	$0.418386\pi$
$887$	−22.1801	+	30.5283i	−0.744735	+	1.02504i	−0.998332	+	0.0577299i	$0.981614\pi$
$888$	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
$895$	22.4887	−	8.85049i	0.751716	−	0.295839i
$896$	−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
$900$	−57.0549	+	6.96952i	−1.90183	+	0.232317i
$901$	−7.62803			−0.254127
$902$		0			0
$903$		−	102.318i		−	3.40494i
$904$	0.581240	−	1.78887i	0.0193317	−	0.0594970i
$905$	−0.457290	−	7.51489i	−0.0152008	−	0.249803i
$906$	−15.6961	−	11.4039i	−0.521467	−	0.378868i
$907$	−31.8908	+	10.3619i	−1.05892	+	0.344063i	−0.786161	−	0.618021i	$-0.787935\pi$
$907$	−31.8908	+	10.3619i	−1.05892	+	0.344063i	−0.272754	+	0.962084i	$0.587935\pi$
$908$	−5.65003	+	1.83581i	−0.187503	+	0.0609234i
$909$	24.8016	+	18.0194i	0.822617	+	0.597666i
$910$	9.40577	−	0.572352i	0.311798	−	0.0189733i
$911$	−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
$915$	39.1716	−	32.2701i	1.29497	−	1.06682i
$916$	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	$0.657769\pi$
$920$	1.68354	−	0.662560i	0.0555046	−	0.0218440i
$921$	−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	$0.968957\pi$
$930$	−100.825	−	26.1084i	−3.30617	−	0.856127i
$931$	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	0.441855	−	0.897087i	$-0.354321\pi$
$937$	8.32692	+	2.70558i	0.272029	+	0.0883875i	−0.169826	+	0.985474i	$0.554321\pi$
$938$	−9.08688	−	12.5070i	−0.296697	−	0.408369i
$939$	5.54254	+	4.02689i	0.180874	+	0.131413i
$940$	3.41756	−	13.1978i	0.111468	−	0.430466i
$941$	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	$0.366868\pi$
$947$			56.2415i			1.82760i	−0.406159	+	0.913802i	$0.633132\pi$
$948$	88.4625	+	28.7432i	2.87313	+	0.933537i
$949$	−2.99916	+	2.17901i	−0.0973567	+	0.0707338i
$950$	−18.7715	−	3.66091i	−0.609029	−	0.118776i
$951$	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	−0.851788	−	0.523887i	$-0.824481\pi$
$953$	−2.78838	+	3.83788i	−0.0903246	+	0.124321i	0.761463	+	0.648208i	$0.224481\pi$
$954$	−57.7253	+	41.9399i	−1.86892	+	1.35785i
$955$	−13.1873	−	16.0076i	−0.426732	−	0.517995i
$956$	−3.95540			−0.127927
$957$		0			0
$958$		−	60.4344i		−	1.95255i
$959$	13.6660	−	42.0597i	0.441299	−	1.35818i
$960$	−56.7047	+	3.45055i	−1.83014	+	0.111366i
$961$	−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
$965$	10.8537	−	0.660464i	0.349394	−	0.0212611i
$966$	−25.5088	+	78.5079i	−0.820731	+	2.52595i
$967$		−	33.8619i		−	1.08892i	−0.838785	−	0.544462i	$-0.816734\pi$
$967$		−	33.8619i		−	1.08892i	0.838785	−	0.544462i	$-0.183266\pi$
$968$		0			0
$969$	−6.55047			−0.210431
$970$	43.5369	+	52.8478i	1.39788	+	1.69684i
$971$	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
$975$	1.80982	−	9.27995i	0.0579605	−	0.297196i
$976$	23.9901	−	17.4298i	0.767904	−	0.557915i
$977$	−6.33521	−	2.05844i	−0.202681	−	0.0658552i	0.205917	−	0.978569i	$-0.433982\pi$
$977$	−6.33521	−	2.05844i	−0.202681	−	0.0658552i	−0.408598	+	0.912714i	$0.633982\pi$
$978$			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	−0.757883	−	0.652391i	$-0.773766\pi$
$983$	3.03421	−	4.17623i	0.0967762	−	0.133201i	0.854659	+	0.519190i	$0.173766\pi$
$984$	0.552479	+	1.70035i	0.0176124	+	0.0542053i
$985$	6.65623	−	25.7048i	0.212085	−	0.819024i
$986$	−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
$995$	10.8051	+	2.79797i	0.342546	+	0.0887017i
$996$	−20.0401	−	61.6772i	−0.634996	−	1.95432i
$997$	−17.4233	+	23.9811i	−0.551801	+	0.759489i	−0.990255	−	0.139265i	$-0.955526\pi$
$997$	−17.4233	+	23.9811i	−0.551801	+	0.759489i	0.438454	+	0.898753i	$0.355526\pi$
$998$	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.9.9		48
5.4	even	2	inner	605.2.j.k.9.4		48
11.2	odd	10	inner	605.2.j.k.124.9		48
11.3	even	5	inner	605.2.j.k.444.10		48
11.4	even	5		605.2.b.h.364.10	yes	12
11.5	even	5	inner	605.2.j.k.269.4		48
11.6	odd	10	inner	605.2.j.k.269.10		48
11.7	odd	10		605.2.b.h.364.4	yes	12
11.8	odd	10	inner	605.2.j.k.444.4		48
11.9	even	5	inner	605.2.j.k.124.3		48
11.10	odd	2	inner	605.2.j.k.9.3		48
55.4	even	10		605.2.b.h.364.3	✓	12
55.7	even	20		3025.2.a.bo.1.10		12
55.9	even	10	inner	605.2.j.k.124.10		48
55.14	even	10	inner	605.2.j.k.444.3		48
55.18	even	20		3025.2.a.bo.1.3		12
55.19	odd	10	inner	605.2.j.k.444.9		48
55.24	odd	10	inner	605.2.j.k.124.4		48
55.29	odd	10		605.2.b.h.364.9	yes	12
55.37	odd	20		3025.2.a.bo.1.4		12
55.39	odd	10	inner	605.2.j.k.269.3		48
55.48	odd	20		3025.2.a.bo.1.9		12
55.49	even	10	inner	605.2.j.k.269.9		48
55.54	odd	2	inner	605.2.j.k.9.10		48

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

\(f(q)\)	\(=\)	\(q+(1.92380 + 0.625081i) q^{2} +(-1.71325 - 2.35809i) q^{3} +(1.69226 + 1.22950i) q^{4} +(2.16467 + 0.560538i) q^{5} +(-1.82196 - 5.60741i) q^{6} +(1.88754 - 2.59798i) q^{7} +(0.109082 + 0.150138i) q^{8} +(-1.69829 + 5.22681i) q^{9} +O(q^{10})\)	\(q+(1.92380 + 0.625081i) q^{2} +(-1.71325 - 2.35809i) q^{3} +(1.69226 + 1.22950i) q^{4} +(2.16467 + 0.560538i) 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} +(-2.38682 - 6.06482i) 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} +(2.97400 + 3.61003i) q^{20} -9.36008 q^{21} -4.35986i q^{23} +(0.167155 - 0.514449i) q^{24} +(4.37159 + 2.42676i) 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} +(-0.800770 - 13.1595i) q^{30} +(2.44118 - 7.51319i) q^{31} -8.07420i q^{32} -2.40405 q^{34} +(5.54217 - 4.56573i) 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} +(0.151968 + 0.386145i) 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} +(6.89316 + 7.40121i) 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} +(3.41756 - 13.1978i) 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} +(13.5160 - 5.31925i) 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} +(-1.76712 - 14.4662i) q^{75} -3.95540 q^{76} -3.82504i q^{78} +(-4.71438 + 14.5094i) q^{79} +(-0.517201 - 8.49944i) 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} +(-2.65260 + 0.161414i) q^{85} +(-6.83298 + 21.0297i) q^{86} -12.1368i q^{87} -9.00000 q^{89} +(-19.1861 + 15.8058i) 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} +(-3.93457 + 1.54846i) 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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