LMFDB - Embedded newform 273.2.cg.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	273.19
Dual form			273.2.cg.a.115.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50246 - 0.402582i) q^{2} -1.00000i q^{3} +(0.363252 + 0.209723i) q^{4} +(2.78312 - 0.745735i) q^{5} +(-0.402582 + 1.50246i) q^{6} +(0.599883 + 2.57685i) q^{7} +(1.73841 + 1.73841i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.50246 - 0.402582i) q^{2} -1.00000i q^{3} +(0.363252 + 0.209723i) q^{4} +(2.78312 - 0.745735i) q^{5} +(-0.402582 + 1.50246i) q^{6} +(0.599883 + 2.57685i) q^{7} +(1.73841 + 1.73841i) q^{8} -1.00000 q^{9} -4.48173 q^{10} +(3.87160 + 3.87160i) q^{11} +(0.209723 - 0.363252i) q^{12} +(0.662549 - 3.54415i) q^{13} +(0.136094 - 4.11310i) q^{14} +(-0.745735 - 2.78312i) q^{15} +(-2.33148 - 4.03824i) q^{16} +(-2.18233 + 3.77990i) q^{17} +(1.50246 + 0.402582i) q^{18} +(-1.02111 - 1.02111i) q^{19} +(1.16737 + 0.312796i) q^{20} +(2.57685 - 0.599883i) q^{21} +(-4.25828 - 7.37555i) q^{22} +(7.25058 - 4.18612i) q^{23} +(1.73841 - 1.73841i) q^{24} +(2.85951 - 1.65094i) q^{25} +(-2.42226 + 5.05821i) q^{26} +1.00000i q^{27} +(-0.322517 + 1.06185i) q^{28} +(0.882488 - 1.52851i) q^{29} +4.48173i q^{30} +(0.206540 - 0.770818i) q^{31} +(0.604618 + 2.25647i) q^{32} +(3.87160 - 3.87160i) q^{33} +(4.80057 - 4.80057i) q^{34} +(3.59119 + 6.72432i) q^{35} +(-0.363252 - 0.209723i) q^{36} +(1.41417 - 5.27775i) q^{37} +(1.12309 + 1.94525i) q^{38} +(-3.54415 - 0.662549i) q^{39} +(6.13459 + 3.54181i) q^{40} +(-3.88124 + 1.03997i) q^{41} +(-4.11310 - 0.136094i) q^{42} +(-5.58033 + 3.22180i) q^{43} +(0.594400 + 2.21833i) q^{44} +(-2.78312 + 0.745735i) q^{45} +(-12.5789 + 3.37051i) q^{46} +(-2.28374 - 8.52304i) q^{47} +(-4.03824 + 2.33148i) q^{48} +(-6.28028 + 3.09161i) q^{49} +(-4.96092 + 1.32927i) q^{50} +(3.77990 + 2.18233i) q^{51} +(0.983964 - 1.14847i) q^{52} +(0.139208 + 0.241116i) q^{53} +(0.402582 - 1.50246i) q^{54} +(13.6623 + 7.88795i) q^{55} +(-3.43677 + 5.52246i) q^{56} +(-1.02111 + 1.02111i) q^{57} +(-1.94125 + 1.94125i) q^{58} +(1.89004 + 7.05373i) q^{59} +(0.312796 - 1.16737i) q^{60} +4.74239i q^{61} +(-0.620634 + 1.07497i) q^{62} +(-0.599883 - 2.57685i) q^{63} +5.69226i q^{64} +(-0.799046 - 10.3579i) q^{65} +(-7.37555 + 4.25828i) q^{66} +(-1.37307 + 1.37307i) q^{67} +(-1.58547 + 0.915370i) q^{68} +(-4.18612 - 7.25058i) q^{69} +(-2.68852 - 11.5487i) q^{70} +(11.3490 + 3.04095i) q^{71} +(-1.73841 - 1.73841i) q^{72} +(-13.9107 - 3.72736i) q^{73} +(-4.24945 + 7.36027i) q^{74} +(-1.65094 - 2.85951i) q^{75} +(-0.156769 - 0.585069i) q^{76} +(-7.65402 + 12.2990i) q^{77} +(5.05821 + 2.42226i) q^{78} +(-0.431242 + 0.746933i) q^{79} +(-9.50024 - 9.50024i) q^{80} +1.00000 q^{81} +6.25006 q^{82} +(-4.29551 - 4.29551i) q^{83} +(1.06185 + 0.322517i) q^{84} +(-3.25487 + 12.1473i) q^{85} +(9.68124 - 2.59408i) q^{86} +(-1.52851 - 0.882488i) q^{87} +13.4609i q^{88} +(5.75757 + 1.54274i) q^{89} +4.48173 q^{90} +(9.53019 - 0.418792i) q^{91} +3.51171 q^{92} +(-0.770818 - 0.206540i) q^{93} +13.7249i q^{94} +(-3.60334 - 2.08039i) q^{95} +(2.25647 - 0.604618i) q^{96} +(0.575652 - 2.14836i) q^{97} +(10.6805 - 2.11669i) q^{98} +(-3.87160 - 3.87160i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.50246	−	0.402582i	−1.06240	−	0.284668i	−0.315031	−	0.949081i	$-0.602015\pi$
$2$	−1.50246	−	0.402582i	−1.06240	−	0.284668i	−0.747366	+	0.664413i	$0.768682\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.363252	+	0.209723i	0.181626	+	0.104862i
$5$	2.78312	−	0.745735i	1.24465	−	0.333503i	0.424382	−	0.905483i	$-0.360491\pi$
$5$	2.78312	−	0.745735i	1.24465	−	0.333503i	0.820267	+	0.571981i	$0.193825\pi$
$6$	−0.402582	+	1.50246i	−0.164353	+	0.613375i
$7$	0.599883	+	2.57685i	0.226735	+	0.973957i
$7$	0.599883	+	2.57685i	0.226735	+	0.973957i
$8$	1.73841	+	1.73841i	0.614621	+	0.614621i
$9$	−1.00000			−0.333333
$10$	−4.48173			−1.41725
$11$	3.87160	+	3.87160i	1.16733	+	1.16733i	0.982833	+	0.184500i	$0.0590665\pi$
$11$	3.87160	+	3.87160i	1.16733	+	1.16733i	0.184500	+	0.982833i	$0.440934\pi$
$12$	0.209723	−	0.363252i	0.0605420	−	0.104862i
$13$	0.662549	−	3.54415i	0.183758	−	0.982972i
$13$	0.662549	−	3.54415i	0.183758	−	0.982972i
$14$	0.136094	−	4.11310i	0.0363725	−	1.09927i
$15$	−0.745735	−	2.78312i	−0.192548	−	0.718598i
$16$	−2.33148	−	4.03824i	−0.582870	−	1.00956i
$17$	−2.18233	+	3.77990i	−0.529292	+	0.916760i	0.470125	+	0.882600i	$0.344209\pi$
$17$	−2.18233	+	3.77990i	−0.529292	+	0.916760i	−0.999416	+	0.0341600i	$0.989124\pi$
$18$	1.50246	+	0.402582i	0.354132	+	0.0948895i
$19$	−1.02111	−	1.02111i	−0.234258	−	0.234258i	0.580209	−	0.814467i	$-0.302971\pi$
$19$	−1.02111	−	1.02111i	−0.234258	−	0.234258i	−0.814467	+	0.580209i	$0.802971\pi$
$20$	1.16737	+	0.312796i	0.261032	+	0.0699433i
$21$	2.57685	−	0.599883i	0.562314	−	0.130905i
$22$	−4.25828	−	7.37555i	−0.907868	−	1.57247i
$23$	7.25058	−	4.18612i	1.51185	−	0.872867i	0.511946	−	0.859018i	$-0.328925\pi$
$23$	7.25058	−	4.18612i	1.51185	−	0.872867i	0.999904	−	0.0138492i	$-0.00440848\pi$
$24$	1.73841	−	1.73841i	0.354851	−	0.354851i
$25$	2.85951	−	1.65094i	0.571901	−	0.330187i
$26$	−2.42226	+	5.05821i	−0.475045	+	0.991996i
$27$			1.00000i			0.192450i
$28$	−0.322517	+	1.06185i	−0.0609499	+	0.200671i
$29$	0.882488	−	1.52851i	0.163874	−	0.283838i	−0.772381	−	0.635160i	$-0.780934\pi$
$29$	0.882488	−	1.52851i	0.163874	−	0.283838i	0.936255	+	0.351322i	$0.114268\pi$
$30$			4.48173i			0.818249i
$31$	0.206540	−	0.770818i	0.0370957	−	0.138443i	−0.944894	−	0.327375i	$-0.893836\pi$
$31$	0.206540	−	0.770818i	0.0370957	−	0.138443i	0.981990	+	0.188932i	$0.0605026\pi$
$32$	0.604618	+	2.25647i	0.106882	+	0.398891i
$33$	3.87160	−	3.87160i	0.673960	−	0.673960i
$34$	4.80057	−	4.80057i	0.823290	−	0.823290i
$35$	3.59119	+	6.72432i	0.607022	+	1.13662i
$36$	−0.363252	−	0.209723i	−0.0605420	−	0.0349539i
$37$	1.41417	−	5.27775i	0.232488	−	0.867657i	−0.746777	−	0.665074i	$-0.768400\pi$
$37$	1.41417	−	5.27775i	0.232488	−	0.867657i	0.979265	−	0.202583i	$-0.0649334\pi$
$38$	1.12309	+	1.94525i	0.182189	+	0.315561i
$39$	−3.54415	−	0.662549i	−0.567519	−	0.106093i
$40$	6.13459	+	3.54181i	0.969965	+	0.560009i
$41$	−3.88124	+	1.03997i	−0.606147	+	0.162417i	−0.548823	−	0.835939i	$-0.684924\pi$
$41$	−3.88124	+	1.03997i	−0.606147	+	0.162417i	−0.0573248	+	0.998356i	$0.518257\pi$
$42$	−4.11310	−	0.136094i	−0.634665	−	0.0209997i
$43$	−5.58033	+	3.22180i	−0.850992	+	0.491320i	−0.860985	−	0.508630i	$-0.830152\pi$
$43$	−5.58033	+	3.22180i	−0.850992	+	0.491320i	0.00999354	+	0.999950i	$0.496819\pi$
$44$	0.594400	+	2.21833i	0.0896092	+	0.334426i
$45$	−2.78312	+	0.745735i	−0.414883	+	0.111168i
$46$	−12.5789	+	3.37051i	−1.85466	+	0.496955i
$47$	−2.28374	−	8.52304i	−0.333118	−	1.24321i	−0.905895	−	0.423502i	$-0.860800\pi$
$47$	−2.28374	−	8.52304i	−0.333118	−	1.24321i	0.572777	−	0.819711i	$-0.305866\pi$
$48$	−4.03824	+	2.33148i	−0.582870	+	0.336520i
$49$	−6.28028	+	3.09161i	−0.897183	+	0.441659i
$50$	−4.96092	+	1.32927i	−0.701580	+	0.187988i
$51$	3.77990	+	2.18233i	0.529292	+	0.305587i
$52$	0.983964	−	1.14847i	0.136451	−	0.159264i
$53$	0.139208	+	0.241116i	0.0191217	+	0.0331198i	0.875428	−	0.483349i	$-0.160580\pi$
$53$	0.139208	+	0.241116i	0.0191217	+	0.0331198i	−0.856306	+	0.516468i	$0.827246\pi$
$54$	0.402582	−	1.50246i	0.0547845	−	0.204458i
$55$	13.6623	+	7.88795i	1.84223	+	1.06361i
$56$	−3.43677	+	5.52246i	−0.459258	+	0.737970i
$57$	−1.02111	+	1.02111i	−0.135249	+	0.135249i
$58$	−1.94125	+	1.94125i	−0.254899	+	0.254899i
$59$	1.89004	+	7.05373i	0.246062	+	0.918318i	0.972846	+	0.231451i	$0.0743475\pi$
$59$	1.89004	+	7.05373i	0.246062	+	0.918318i	−0.726784	+	0.686866i	$0.758986\pi$
$60$	0.312796	−	1.16737i	0.0403818	−	0.150707i
$61$			4.74239i			0.607200i	0.952800	+	0.303600i	$0.0981887\pi$
$61$			4.74239i			0.607200i	−0.952800	+	0.303600i	$0.901811\pi$
$62$	−0.620634	+	1.07497i	−0.0788207	+	0.136521i
$63$	−0.599883	−	2.57685i	−0.0755782	−	0.324652i
$64$			5.69226i			0.711533i
$65$	−0.799046	−	10.3579i	−0.0991094	−	1.28474i
$66$	−7.37555	+	4.25828i	−0.907868	+	0.524158i
$67$	−1.37307	+	1.37307i	−0.167748	+	0.167748i	−0.785989	−	0.618241i	$-0.787846\pi$
$67$	−1.37307	+	1.37307i	−0.167748	+	0.167748i	0.618241	+	0.785989i	$0.287846\pi$
$68$	−1.58547	+	0.915370i	−0.192266	+	0.111005i
$69$	−4.18612	−	7.25058i	−0.503950	−	0.872867i
$70$	−2.68852	−	11.5487i	−0.321339	−	1.38034i
$71$	11.3490	+	3.04095i	1.34688	+	0.360894i	0.858981	−	0.512008i	$-0.171098\pi$
$71$	11.3490	+	3.04095i	1.34688	+	0.360894i	0.487895	+	0.872902i	$0.337765\pi$
$72$	−1.73841	−	1.73841i	−0.204874	−	0.204874i
$73$	−13.9107	−	3.72736i	−1.62812	−	0.436254i	−0.674749	−	0.738047i	$-0.735748\pi$
$73$	−13.9107	−	3.72736i	−1.62812	−	0.436254i	−0.953373	+	0.301793i	$0.902415\pi$
$74$	−4.24945	+	7.36027i	−0.493989	+	0.855614i
$75$	−1.65094	−	2.85951i	−0.190634	−	0.330187i
$76$	−0.156769	−	0.585069i	−0.0179826	−	0.0671121i
$77$	−7.65402	+	12.2990i	−0.872256	+	1.40161i
$78$	5.05821	+	2.42226i	0.572729	+	0.274267i
$79$	−0.431242	+	0.746933i	−0.0485185	+	0.0840365i	−0.889265	−	0.457393i	$-0.848783\pi$
$79$	−0.431242	+	0.746933i	−0.0485185	+	0.0840365i	0.840746	+	0.541429i	$0.182117\pi$
$80$	−9.50024	−	9.50024i	−1.06216	−	1.06216i
$81$	1.00000			0.111111
$82$	6.25006			0.690204
$83$	−4.29551	−	4.29551i	−0.471494	−	0.471494i	0.430904	−	0.902398i	$-0.358195\pi$
$83$	−4.29551	−	4.29551i	−0.471494	−	0.471494i	−0.902398	+	0.430904i	$0.858195\pi$
$84$	1.06185	+	0.322517i	0.115858	+	0.0351895i
$85$	−3.25487	+	12.1473i	−0.353040	+	1.31756i
$86$	9.68124	−	2.59408i	1.04395	−	0.279727i
$87$	−1.52851	−	0.882488i	−0.163874	−	0.0946127i
$88$			13.4609i			1.43493i
$89$	5.75757	+	1.54274i	0.610301	+	0.163530i	0.550715	−	0.834693i	$-0.314355\pi$
$89$	5.75757	+	1.54274i	0.610301	+	0.163530i	0.0595865	+	0.998223i	$0.481022\pi$
$90$	4.48173			0.472416
$91$	9.53019	−	0.418792i	0.999036	−	0.0439013i
$92$	3.51171			0.366121
$93$	−0.770818	−	0.206540i	−0.0799301	−	0.0214172i
$94$			13.7249i			1.41561i
$95$	−3.60334	−	2.08039i	−0.369695	−	0.213443i
$96$	2.25647	−	0.604618i	0.230300	−	0.0617086i
$97$	0.575652	−	2.14836i	0.0584486	−	0.218133i	−0.930524	−	0.366230i	$-0.880648\pi$
$97$	0.575652	−	2.14836i	0.0584486	−	0.218133i	0.988973	+	0.148097i	$0.0473149\pi$
$98$	10.6805	−	2.11669i	1.07889	−	0.213818i
$99$	−3.87160	−	3.87160i	−0.389111	−	0.389111i
$100$	1.38496			0.138496
$101$	−15.8444			−1.57657			−0.788287	−	0.615308i	$-0.789032\pi$
$101$	−15.8444			−1.57657			−0.788287	+	0.615308i	$0.789032\pi$
$102$	−4.80057	−	4.80057i	−0.475327	−	0.475327i
$103$	5.32654	−	9.22583i	0.524839	−	0.909048i	−0.474742	−	0.880125i	$-0.657459\pi$
$103$	5.32654	−	9.22583i	0.524839	−	0.909048i	0.999582	−	0.0289234i	$-0.00920788\pi$
$104$	7.31297	−	5.00941i	0.717096	−	0.491213i
$105$	6.72432	−	3.59119i	0.656226	−	0.350464i
$106$	−0.112085	−	0.418309i	−0.0108867	−	0.0406297i
$107$	7.27563	+	12.6018i	0.703361	+	1.21826i	0.967280	+	0.253712i	$0.0816517\pi$
$107$	7.27563	+	12.6018i	0.703361	+	1.21826i	−0.263918	+	0.964545i	$0.585015\pi$
$108$	−0.209723	+	0.363252i	−0.0201807	+	0.0349539i
$109$	8.31237	+	2.22729i	0.796181	+	0.213336i	0.633906	−	0.773410i	$-0.281450\pi$
$109$	8.31237	+	2.22729i	0.796181	+	0.213336i	0.162274	+	0.986746i	$0.448117\pi$
$110$	−17.3515	−	17.3515i	−1.65440	−	1.65440i
$111$	−5.27775	−	1.41417i	−0.500942	−	0.134227i
$112$	9.00731	−	8.43034i	0.851111	−	0.796592i
$113$	−6.81406	−	11.8023i	−0.641013	−	1.11027i	−0.985207	−	0.171368i	$-0.945181\pi$
$113$	−6.81406	−	11.8023i	−0.641013	−	1.11027i	0.344195	−	0.938898i	$-0.388152\pi$
$114$	1.94525	−	1.12309i	0.182189	−	0.105187i
$115$	17.0575	−	17.0575i	1.59062	−	1.59062i
$116$	0.641131	−	0.370157i	0.0595275	−	0.0343682i
$117$	−0.662549	+	3.54415i	−0.0612527	+	0.327657i
$118$		−	11.3588i		−	1.04566i
$119$	−11.0494	−	3.35602i	−1.01289	−	0.307646i
$120$	3.54181	−	6.13459i	0.323322	−	0.560009i
$121$			18.9786i			1.72533i
$122$	1.90920	−	7.12523i	0.172851	−	0.645088i
$123$	1.03997	+	3.88124i	0.0937713	+	0.349959i
$124$	0.236685	−	0.236685i	0.0212549	−	0.0212549i
$125$	−3.45974	+	3.45974i	−0.309448	+	0.309448i
$126$	−0.136094	+	4.11310i	−0.0121242	+	0.366424i
$127$	3.01715	+	1.74195i	0.267728	+	0.154573i	0.627855	−	0.778330i	$-0.283933\pi$
$127$	3.01715	+	1.74195i	0.267728	+	0.154573i	−0.360126	+	0.932904i	$0.617266\pi$
$128$	3.50084	−	13.0653i	0.309433	−	1.15482i
$129$	3.22180	+	5.58033i	0.283664	+	0.491320i
$130$	−2.96937	+	15.8840i	−0.260431	+	1.39312i
$131$	−5.01539	−	2.89564i	−0.438197	−	0.252993i	0.264636	−	0.964348i	$-0.414748\pi$
$131$	−5.01539	−	2.89564i	−0.438197	−	0.252993i	−0.702832	+	0.711356i	$0.748082\pi$
$132$	2.21833	−	0.594400i	0.193081	−	0.0517359i
$133$	2.01869	−	3.24378i	0.175043	−	0.281272i
$134$	2.61576	−	1.51021i	0.225967	−	0.130462i
$135$	0.745735	+	2.78312i	0.0641826	+	0.239533i
$136$	−10.3648	+	2.77724i	−0.888773	+	0.238146i
$137$	3.31077	−	0.887118i	0.282858	−	0.0757916i	−0.114601	−	0.993412i	$-0.536559\pi$
$137$	3.31077	−	0.887118i	0.282858	−	0.0757916i	0.397459	+	0.917620i	$0.369892\pi$
$138$	3.37051	+	12.5789i	0.286917	+	1.07079i
$139$	16.1580	−	9.32882i	1.37050	−	0.791260i	0.379512	−	0.925187i	$-0.376092\pi$
$139$	16.1580	−	9.32882i	1.37050	−	0.791260i	0.990991	+	0.133927i	$0.0427586\pi$
$140$	−0.105741	+	3.19578i	−0.00893677	+	0.270092i
$141$	−8.52304	+	2.28374i	−0.717770	+	0.192326i
$142$	−15.8271	−	9.13779i	−1.32818	−	0.766826i
$143$	16.2867	−	11.1564i	1.36196	−	0.932948i
$144$	2.33148	+	4.03824i	0.194290	+	0.336520i
$145$	1.31620	−	4.91214i	0.109305	−	0.407931i
$146$	19.3996	+	11.2004i	1.60552	+	0.926950i
$147$	3.09161	+	6.28028i	0.254992	+	0.517989i
$148$	1.62057	−	1.62057i	0.133210	−	0.133210i
$149$	−10.1083	+	10.1083i	−0.828106	+	0.828106i	−0.987255	−	0.159149i	$-0.949125\pi$
$149$	−10.1083	+	10.1083i	−0.828106	+	0.828106i	0.159149	+	0.987255i	$0.449125\pi$
$150$	1.32927	+	4.96092i	0.108535	+	0.405058i
$151$	0.00532352	−	0.0198676i	0.000433222	−	0.00161681i	−0.965709	−	0.259627i	$-0.916400\pi$
$151$	0.00532352	−	0.0198676i	0.000433222	−	0.00161681i	0.966142	+	0.258011i	$0.0830669\pi$
$152$		−	3.55021i		−	0.287960i
$153$	2.18233	−	3.77990i	0.176431	−	0.305587i
$154$	16.4512	−	15.3974i	1.32568	−	1.24076i
$155$		−	2.29930i		−	0.184684i
$156$	−1.14847	−	0.983964i	−0.0919510	−	0.0787802i
$157$	5.26575	−	3.04018i	0.420253	−	0.242633i	−0.274933	−	0.961463i	$-0.588656\pi$
$157$	5.26575	−	3.04018i	0.420253	−	0.242633i	0.695185	+	0.718830i	$0.255322\pi$
$158$	0.948624	−	0.948624i	0.0754685	−	0.0754685i
$159$	0.241116	−	0.139208i	0.0191217	−	0.0110399i
$160$	3.36545	+	5.82913i	0.266062	+	0.460833i
$161$	15.1365	+	16.1724i	1.19292	+	1.27457i
$162$	−1.50246	−	0.402582i	−0.118044	−	0.0316298i
$163$	−10.0711	−	10.0711i	−0.788827	−	0.788827i	0.192475	−	0.981302i	$-0.438349\pi$
$163$	−10.0711	−	10.0711i	−0.788827	−	0.788827i	−0.981302	+	0.192475i	$0.938349\pi$
$164$	−1.62797	−	0.436214i	−0.127123	−	0.0340626i
$165$	7.88795	−	13.6623i	0.614076	−	1.06361i
$166$	4.72452	+	8.18312i	0.366694	+	0.635133i
$167$	0.579671	+	2.16336i	0.0448563	+	0.167406i	0.984720	−	0.174142i	$-0.0557153\pi$
$167$	0.579671	+	2.16336i	0.0448563	+	0.167406i	−0.939864	+	0.341548i	$0.889049\pi$
$168$	5.52246	+	3.43677i	0.426067	+	0.265153i
$169$	−12.1221	−	4.69635i	−0.932466	−	0.361258i
$170$	9.78060	−	16.9405i	0.750138	−	1.29928i
$171$	1.02111	+	1.02111i	0.0780861	+	0.0780861i
$172$	−2.70275			−0.206083
$173$	−3.24988			−0.247084			−0.123542	−	0.992339i	$-0.539425\pi$
$173$	−3.24988			−0.247084			−0.123542	+	0.992339i	$0.539425\pi$
$174$	1.94125	+	1.94125i	0.147166	+	0.147166i
$175$	5.96958	+	6.37814i	0.451258	+	0.482142i
$176$	6.60790	−	24.6610i	0.498089	−	1.85889i
$177$	7.05373	−	1.89004i	0.530191	−	0.142064i
$178$	−8.02942	−	4.63579i	−0.601831	−	0.347467i
$179$			21.1701i			1.58233i	0.611603	+	0.791165i	$0.290525\pi$
$179$			21.1701i			1.58233i	−0.611603	+	0.791165i	$0.709475\pi$
$180$	−1.16737	−	0.312796i	−0.0870107	−	0.0233144i
$181$	−18.5217			−1.37671			−0.688353	−	0.725376i	$-0.741666\pi$
$181$	−18.5217			−1.37671			−0.688353	+	0.725376i	$0.741666\pi$
$182$	−14.4873	−	3.20747i	−1.07387	−	0.237753i
$183$	4.74239			0.350567
$184$	19.8817	+	5.32728i	1.46570	+	0.392732i
$185$		−	15.7432i		−	1.15746i
$186$	1.07497	+	0.620634i	0.0788207	+	0.0455071i
$187$	−23.0834	+	6.18517i	−1.68802	+	0.452304i
$188$	0.957909	−	3.57496i	0.0698627	−	0.260731i
$189$	−2.57685	+	0.599883i	−0.187438	+	0.0436351i
$190$	4.57633	+	4.57633i	0.332002	+	0.332002i
$191$	−27.4180			−1.98390			−0.991948	−	0.126649i	$-0.959578\pi$
$191$	−27.4180			−1.98390			−0.991948	+	0.126649i	$0.959578\pi$
$192$	5.69226			0.410804
$193$	−13.4853	−	13.4853i	−0.970695	−	0.970695i	0.0288876	−	0.999583i	$-0.490804\pi$
$193$	−13.4853	−	13.4853i	−0.970695	−	0.970695i	−0.999583	+	0.0288876i	$0.990804\pi$
$194$	−1.72978	+	2.99607i	−0.124191	+	0.215105i
$195$	−10.3579	+	0.799046i	−0.741744	+	0.0572208i
$196$	−2.92971	−	0.194088i	−0.209265	−	0.0138634i
$197$	1.20155	+	4.48424i	0.0856068	+	0.319489i	0.995428	−	0.0955106i	$-0.0304484\pi$
$197$	1.20155	+	4.48424i	0.0856068	+	0.319489i	−0.909822	+	0.415000i	$0.863782\pi$
$198$	4.25828	+	7.37555i	0.302623	+	0.524158i
$199$	−0.223560	+	0.387218i	−0.0158478	+	0.0274492i	−0.873841	−	0.486213i	$-0.838378\pi$
$199$	−0.223560	+	0.387218i	−0.0158478	+	0.0274492i	0.857993	+	0.513662i	$0.171711\pi$
$200$	7.84100	+	2.10099i	0.554442	+	0.148562i
$201$	1.37307	+	1.37307i	0.0968491	+	0.0968491i
$202$	23.8055	+	6.37866i	1.67495	+	0.448801i
$203$	4.46814	+	1.35711i	0.313602	+	0.0952502i
$204$	0.915370	+	1.58547i	0.0640887	+	0.111005i
$205$	−10.0264	+	5.78875i	−0.700274	+	0.404303i
$206$	−11.7170	+	11.7170i	−0.816365	+	0.816365i
$207$	−7.25058	+	4.18612i	−0.503950	+	0.290956i
$208$	−15.8569	+	5.58759i	−1.09948	+	0.387430i
$209$		−	7.90665i		−	0.546914i
$210$	−11.5487	+	2.68852i	−0.796939	+	0.185525i
$211$	−14.3795	+	24.9060i	−0.989924	+	1.71460i	−0.372331	+	0.928100i	$0.621442\pi$
$211$	−14.3795	+	24.9060i	−0.989924	+	1.71460i	−0.617592	+	0.786498i	$0.711892\pi$
$212$			0.116781i			0.00802055i
$213$	3.04095	−	11.3490i	0.208362	−	0.777619i
$214$	−5.85807	−	21.8626i	−0.400449	−	1.49450i
$215$	−13.1281	+	13.1281i	−0.895329	+	0.895329i
$216$	−1.73841	+	1.73841i	−0.118284	+	0.118284i
$217$	2.11018	+	0.0698212i	0.143248	+	0.00473977i
$218$	−11.5923	−	6.69282i	−0.785130	−	0.453295i
$219$	−3.72736	+	13.9107i	−0.251871	+	0.939997i
$220$	3.30857	+	5.73062i	0.223064	+	0.386358i
$221$	11.9506	+	10.2389i	0.803887	+	0.688741i
$222$	7.36027	+	4.24945i	0.493989	+	0.285205i
$223$	−14.0758	+	3.77160i	−0.942586	+	0.252565i	−0.697213	−	0.716864i	$-0.745577\pi$
$223$	−14.0758	+	3.77160i	−0.942586	+	0.252565i	−0.245372	+	0.969429i	$0.578910\pi$
$224$	−5.45187	+	2.91163i	−0.364268	+	0.194541i
$225$	−2.85951	+	1.65094i	−0.190634	+	0.110062i
$226$	5.48643	+	20.4756i	0.364952	+	1.36202i
$227$	17.3155	−	4.63969i	1.14927	−	0.307947i	0.366599	−	0.930379i	$-0.380522\pi$
$227$	17.3155	−	4.63969i	1.14927	−	0.307947i	0.782674	+	0.622432i	$0.213855\pi$
$228$	−0.585069	+	0.156769i	−0.0387472	+	0.0103823i
$229$	−1.77229	−	6.61427i	−0.117116	−	0.437083i	0.882320	−	0.470649i	$-0.155980\pi$
$229$	−1.77229	−	6.61427i	−0.117116	−	0.437083i	−0.999437	+	0.0335661i	$0.989314\pi$
$230$	−32.4952	+	18.7611i	−2.14267	+	1.23707i
$231$	12.2990	+	7.65402i	0.809217	+	0.503597i
$232$	4.19131	−	1.12306i	0.275173	−	0.0737324i
$233$	−6.74247	−	3.89276i	−0.441714	−	0.255023i	0.262611	−	0.964902i	$-0.415417\pi$
$233$	−6.74247	−	3.89276i	−0.441714	−	0.255023i	−0.704324	+	0.709878i	$0.748750\pi$
$234$	2.42226	−	5.05821i	0.158348	−	0.330665i
$235$	−12.7119	−	22.0176i	−0.829230	−	1.43627i
$236$	−0.792772	+	2.95867i	−0.0516051	+	0.192593i
$237$	0.746933	+	0.431242i	0.0485185	+	0.0280122i
$238$	15.2501	+	9.49055i	0.988518	+	0.615181i
$239$	−2.22428	+	2.22428i	−0.143877	+	0.143877i	−0.775376	−	0.631499i	$-0.782440\pi$
$239$	−2.22428	+	2.22428i	−0.143877	+	0.143877i	0.631499	+	0.775376i	$0.282440\pi$
$240$	−9.50024	+	9.50024i	−0.613238	+	0.613238i
$241$	−2.32406	−	8.67353i	−0.149706	−	0.558711i	−0.999501	−	0.0315969i	$-0.989941\pi$
$241$	−2.32406	−	8.67353i	−0.149706	−	0.558711i	0.849795	−	0.527114i	$-0.176726\pi$
$242$	7.64045	−	28.5146i	0.491147	−	1.83298i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.994590	+	1.72268i	−0.0636721	+	0.110283i
$245$	−15.1732	+	13.2878i	−0.969383	+	0.848924i
$246$		−	6.25006i		−	0.398489i
$247$	−4.29550	+	2.94243i	−0.273316	+	0.187222i
$248$	1.69905	−	0.980946i	0.107890	−	0.0622901i
$249$	−4.29551	+	4.29551i	−0.272217	+	0.272217i
$250$	6.59093	−	3.80527i	0.416847	−	0.240667i
$251$	−12.3486	−	21.3883i	−0.779434	−	1.35002i	−0.932269	−	0.361767i	$-0.882174\pi$
$251$	−12.3486	−	21.3883i	−0.779434	−	1.35002i	0.152835	−	0.988252i	$-0.451160\pi$
$252$	0.322517	−	1.06185i	0.0203166	−	0.0668905i
$253$	44.2784	+	11.8644i	2.78376	+	0.745905i
$254$	−3.83185	−	3.83185i	−0.240432	−	0.240432i
$255$	12.1473	+	3.25487i	0.760696	+	0.203828i
$256$	−4.82745	+	8.36139i	−0.301716	+	0.522587i
$257$	−3.07554	−	5.32699i	−0.191847	−	0.332288i	0.754015	−	0.656857i	$-0.228114\pi$
$257$	−3.07554	−	5.32699i	−0.191847	−	0.332288i	−0.945862	+	0.324568i	$0.894781\pi$
$258$	−2.59408	−	9.68124i	−0.161500	−	0.602727i
$259$	14.4483	+	0.478063i	0.897773	+	0.0297054i
$260$	1.88204	−	3.93010i	0.116719	−	0.243734i
$261$	−0.882488	+	1.52851i	−0.0546247	+	0.0946127i
$262$	6.36967	+	6.36967i	0.393520	+	0.393520i
$263$	17.1492			1.05747			0.528733	−	0.848788i	$-0.322667\pi$
$263$	17.1492			1.05747			0.528733	+	0.848788i	$0.322667\pi$
$264$	13.4609			0.828459
$265$	0.567242	+	0.567242i	0.0348454	+	0.0348454i
$266$	−4.33889	+	4.06095i	−0.266034	+	0.248993i
$267$	1.54274	−	5.75757i	0.0944140	−	0.352358i
$268$	−0.786737	+	0.210806i	−0.0480576	+	0.0128770i
$269$	2.00185	+	1.15577i	0.122055	+	0.0704685i	0.559785	−	0.828638i	$-0.310884\pi$
$269$	2.00185	+	1.15577i	0.122055	+	0.0704685i	−0.437729	+	0.899107i	$0.644217\pi$
$270$		−	4.48173i		−	0.272750i
$271$	−6.25936	−	1.67719i	−0.380229	−	0.101882i	0.0636420	−	0.997973i	$-0.479728\pi$
$271$	−6.25936	−	1.67719i	−0.380229	−	0.101882i	−0.443871	+	0.896091i	$0.646395\pi$
$272$	20.3522			1.23403
$273$	−0.418792	−	9.53019i	−0.0253464	−	0.576794i
$274$	−5.33142			−0.322083
$275$	17.4627	+	4.67910i	1.05304	+	0.282161i
$276$		−	3.51171i		−	0.211380i
$277$	−20.9378	−	12.0884i	−1.25803	−	0.726323i	−0.285337	−	0.958427i	$-0.592105\pi$
$277$	−20.9378	−	12.0884i	−1.25803	−	0.726323i	−0.972691	+	0.232105i	$0.925439\pi$
$278$	−28.0323	+	7.51123i	−1.68127	+	0.450494i
$279$	−0.206540	+	0.770818i	−0.0123652	+	0.0461476i
$280$	−5.44666	+	17.9326i	−0.325500	+	1.07168i
$281$	18.6196	+	18.6196i	1.11075	+	1.11075i	0.993049	+	0.117703i	$0.0375532\pi$
$281$	18.6196	+	18.6196i	1.11075	+	1.11075i	0.117703	+	0.993049i	$0.462447\pi$
$282$	13.7249			0.817306
$283$	−12.5046			−0.743322			−0.371661	−	0.928369i	$-0.621212\pi$
$283$	−12.5046			−0.743322			−0.371661	+	0.928369i	$0.621212\pi$
$284$	3.48478	+	3.48478i	0.206783	+	0.206783i
$285$	−2.08039	+	3.60334i	−0.123232	+	0.213443i
$286$	−28.9614	+	10.2053i	−1.71252	+	0.603454i
$287$	−5.00814	−	9.37749i	−0.295621	−	0.553536i
$288$	−0.604618	−	2.25647i	−0.0356275	−	0.132964i
$289$	−1.02509	−	1.77550i	−0.0602992	−	0.104441i
$290$	−3.95508	+	6.85040i	−0.232250	+	0.402269i
$291$	−2.14836	−	0.575652i	−0.125939	−	0.0337453i
$292$	−4.27137	−	4.27137i	−0.249963	−	0.249963i
$293$	0.0851383	+	0.0228127i	0.00497383	+	0.00133274i	0.261305	−	0.965256i	$-0.415847\pi$
$293$	0.0851383	+	0.0228127i	0.00497383	+	0.00133274i	−0.256331	+	0.966589i	$0.582514\pi$
$294$	−2.11669	−	10.6805i	−0.123448	−	0.622898i
$295$	10.5204	+	18.2219i	0.612523	+	1.06092i
$296$	11.6333	−	6.71649i	0.676172	−	0.390388i
$297$	−3.87160	+	3.87160i	−0.224653	+	0.224653i
$298$	19.2567	−	11.1179i	1.11551	−	0.644042i
$299$	−10.0324	−	28.4707i	−0.580189	−	1.64650i
$300$		−	1.38496i		−	0.0799608i
$301$	−11.6496	−	12.4469i	−0.671474	−	0.717430i
$302$	−0.0159967	+	0.0277071i	−0.000920507	+	0.00159436i
$303$			15.8444i			0.910235i
$304$	−1.74279	+	6.50417i	−0.0999557	+	0.373040i
$305$	3.53656	+	13.1986i	0.202503	+	0.755751i
$306$	−4.80057	+	4.80057i	−0.274430	+	0.274430i
$307$	7.58728	−	7.58728i	0.433029	−	0.433029i	−0.456628	−	0.889658i	$-0.650943\pi$
$307$	7.58728	−	7.58728i	0.433029	−	0.433029i	0.889658	+	0.456628i	$0.150943\pi$
$308$	−5.35973	+	2.86242i	−0.305399	+	0.163101i
$309$	−9.22583	−	5.32654i	−0.524839	−	0.303016i
$310$	−0.925657	+	3.45460i	−0.0525738	+	0.196208i
$311$	15.1148	+	26.1796i	0.857082	+	1.48451i	0.874700	+	0.484665i	$0.161059\pi$
$311$	15.1148	+	26.1796i	0.857082	+	1.48451i	−0.0176172	+	0.999845i	$0.505608\pi$
$312$	−5.00941	−	7.31297i	−0.283602	−	0.414016i
$313$	24.9891	+	14.4275i	1.41247	+	0.815489i	0.995621	−	0.0934866i	$-0.0298012\pi$
$313$	24.9891	+	14.4275i	1.41247	+	0.815489i	0.416849	+	0.908976i	$0.363135\pi$
$314$	−9.13548	+	2.44784i	−0.515545	+	0.138140i
$315$	−3.59119	−	6.72432i	−0.202341	−	0.378872i
$316$	−0.313299	+	0.180883i	−0.0176244	+	0.0101755i
$317$	−4.34297	−	16.2082i	−0.243926	−	0.910343i	−0.973920	−	0.226890i	$-0.927144\pi$
$317$	−4.34297	−	16.2082i	−0.243926	−	0.910343i	0.729995	−	0.683453i	$-0.239523\pi$
$318$	−0.418309	+	0.112085i	−0.0234576	+	0.00628544i
$319$	9.33445	−	2.50116i	0.522629	−	0.140038i
$320$	4.24492	+	15.8423i	0.237298	+	0.885609i
$321$	12.6018	−	7.27563i	0.703361	−	0.406086i
$322$	−16.2312	−	30.3921i	−0.904529	−	1.69368i
$323$	6.08807	−	1.63129i	0.338749	−	0.0907676i
$324$	0.363252	+	0.209723i	0.0201807	+	0.0116513i
$325$	−3.95661	−	11.2284i	−0.219473	−	0.622837i
$326$	11.0769	+	19.1858i	0.613493	+	1.06260i
$327$	2.22729	−	8.31237i	0.123170	−	0.459675i
$328$	−8.55508	−	4.93928i	−0.472375	−	0.272726i
$329$	20.5926	−	10.9977i	1.13531	−	0.606322i
$330$	−17.3515	+	17.3515i	−0.955169	+	0.955169i
$331$	4.44970	−	4.44970i	0.244577	−	0.244577i	−0.574163	−	0.818741i	$-0.694673\pi$
$331$	4.44970	−	4.44970i	0.244577	−	0.244577i	0.818741	+	0.574163i	$0.194673\pi$
$332$	−0.659482	−	2.46122i	−0.0361938	−	0.135077i
$333$	−1.41417	+	5.27775i	−0.0774960	+	0.289219i
$334$		−	3.48372i		−	0.190621i
$335$	−2.79748	+	4.84538i	−0.152843	+	0.264731i
$336$	−8.43034	−	9.00731i	−0.459913	−	0.491389i
$337$		−	17.1415i		−	0.933758i	−0.884321	−	0.466879i	$-0.845378\pi$
$337$		−	17.1415i		−	0.933758i	0.884321	−	0.466879i	$-0.154622\pi$
$338$	16.3222	+	11.9362i	0.887810	+	0.649243i
$339$	−11.8023	+	6.81406i	−0.641013	+	0.370089i
$340$	−3.72992	+	3.72992i	−0.202283	+	0.202283i
$341$	3.78394	−	2.18466i	0.204912	−	0.118306i
$342$	−1.12309	−	1.94525i	−0.0607298	−	0.105187i
$343$	−11.7341	−	14.3287i	−0.633579	−	0.773678i
$344$	−15.3017	−	4.10008i	−0.825013	−	0.221062i
$345$	−17.0575	−	17.0575i	−0.918344	−	0.918344i
$346$	4.88281	+	1.30834i	0.262501	+	0.0703370i
$347$	−2.11487	+	3.66307i	−0.113532	+	0.196644i	−0.917192	−	0.398445i	$-0.869550\pi$
$347$	−2.11487	+	3.66307i	−0.113532	+	0.196644i	0.803660	+	0.595089i	$0.202883\pi$
$348$	−0.370157	−	0.641131i	−0.0198425	−	0.0343682i
$349$	−4.82352	−	18.0016i	−0.258197	−	0.963605i	−0.966284	−	0.257479i	$-0.917108\pi$
$349$	−4.82352	−	18.0016i	−0.258197	−	0.963605i	0.708087	−	0.706125i	$-0.249559\pi$
$350$	−6.40131	−	11.9861i	−0.342165	−	0.640685i
$351$	3.54415	+	0.662549i	0.189173	+	0.0353642i
$352$	−6.39530	+	11.0770i	−0.340871	+	0.590405i
$353$	3.14985	+	3.14985i	0.167650	+	0.167650i	0.785945	−	0.618296i	$-0.212177\pi$
$353$	3.14985	+	3.14985i	0.167650	+	0.167650i	−0.618296	+	0.785945i	$0.712177\pi$
$354$	−11.3588			−0.603714
$355$	33.8533			1.79675
$356$	1.76790	+	1.76790i	0.0936985	+	0.0936985i
$357$	−3.35602	+	11.0494i	−0.177619	+	0.584794i
$358$	8.52271	−	31.8072i	0.450439	−	1.68106i
$359$	15.8524	−	4.24764i	0.836657	−	0.224182i	0.185041	−	0.982731i	$-0.440758\pi$
$359$	15.8524	−	4.24764i	0.836657	−	0.224182i	0.651616	+	0.758549i	$0.274091\pi$
$360$	−6.13459	−	3.54181i	−0.323322	−	0.186670i
$361$		−	16.9147i		−	0.890246i
$362$	27.8280	+	7.45649i	1.46261	+	0.391905i
$363$	18.9786			0.996119
$364$	3.54969	+	1.84658i	0.186054	+	0.0967870i
$365$	−41.4947			−2.17193
$366$	−7.12523	−	1.90920i	−0.372442	−	0.0997955i
$367$			27.9299i			1.45793i	0.684552	+	0.728964i	$0.259998\pi$
$367$			27.9299i			1.45793i	−0.684552	+	0.728964i	$0.740002\pi$
$368$	−33.8091	−	19.5197i	−1.76242	−	1.01754i
$369$	3.88124	−	1.03997i	0.202049	−	0.0541389i
$370$	−6.33793	+	23.6535i	−0.329493	+	1.22969i
$371$	−0.537810	+	0.503360i	−0.0279217	+	0.0261331i
$372$	−0.236685	−	0.236685i	−0.0122715	−	0.0122715i
$373$	−5.84813			−0.302805			−0.151402	−	0.988472i	$-0.548379\pi$
$373$	−5.84813			−0.302805			−0.151402	+	0.988472i	$0.548379\pi$
$374$	37.1718			1.92211
$375$	3.45974	+	3.45974i	0.178660	+	0.178660i
$376$	10.8465	−	18.7866i	0.559364	−	0.968846i
$377$	−4.83260	−	4.14039i	−0.248892	−	0.213241i
$378$	4.11310	+	0.136094i	0.211555	+	0.00699990i
$379$	−0.411597	−	1.53610i	−0.0211423	−	0.0789043i	0.954549	−	0.298055i	$-0.0963380\pi$
$379$	−0.411597	−	1.53610i	−0.0211423	−	0.0789043i	−0.975691	+	0.219151i	$0.929671\pi$
$380$	−0.872613	−	1.51141i	−0.0447641	−	0.0775337i
$381$	1.74195	−	3.01715i	0.0892428	−	0.154573i
$382$	41.1943	+	11.0380i	2.10768	+	0.564752i
$383$	−9.95949	−	9.95949i	−0.508906	−	0.508906i	0.405285	−	0.914191i	$-0.367172\pi$
$383$	−9.95949	−	9.95949i	−0.508906	−	0.508906i	−0.914191	+	0.405285i	$0.867172\pi$
$384$	−13.0653	−	3.50084i	−0.666736	−	0.178651i
$385$	−12.1302	+	39.9376i	−0.618214	+	2.03541i
$386$	14.8322	+	25.6901i	0.754937	+	1.30759i
$387$	5.58033	−	3.22180i	0.283664	−	0.163773i
$388$	0.659668	−	0.659668i	0.0334896	−	0.0334896i
$389$	−0.216783	+	0.125160i	−0.0109913	+	0.00634584i	−0.505486	−	0.862835i	$-0.668687\pi$
$389$	−0.216783	+	0.125160i	−0.0109913	+	0.00634584i	0.494494	+	0.869181i	$0.335353\pi$
$390$	15.8840	+	2.96937i	0.804315	+	0.150360i
$391$			36.5419i			1.84800i
$392$	−16.2922	−	5.54321i	−0.822880	−	0.279974i
$393$	−2.89564	+	5.01539i	−0.146066	+	0.252993i
$394$		−	7.22110i		−	0.363794i
$395$	−0.643184	+	2.40040i	−0.0323621	+	0.120777i
$396$	−0.594400	−	2.21833i	−0.0298697	−	0.111475i
$397$	−4.76132	+	4.76132i	−0.238964	+	0.238964i	−0.816421	−	0.577457i	$-0.804045\pi$
$397$	−4.76132	+	4.76132i	−0.238964	+	0.238964i	0.577457	+	0.816421i	$0.304045\pi$
$398$	0.491777	−	0.491777i	0.0246505	−	0.0246505i
$399$	−3.24378	−	2.01869i	−0.162392	−	0.101061i
$400$	−13.3338	−	7.69825i	−0.666688	−	0.384913i
$401$	−7.46297	+	27.8522i	−0.372683	+	1.39087i	0.484018	+	0.875058i	$0.339177\pi$
$401$	−7.46297	+	27.8522i	−0.372683	+	1.39087i	−0.856701	+	0.515813i	$0.827490\pi$
$402$	−1.51021	−	2.61576i	−0.0753223	−	0.130462i
$403$	−2.59505	−	1.24271i	−0.129269	−	0.0619040i
$404$	−5.75549	−	3.32294i	−0.286347	−	0.165322i
$405$	2.78312	−	0.745735i	0.138294	−	0.0370559i
$406$	−6.16683	−	3.83779i	−0.306055	−	0.190466i
$407$	25.9085	−	14.9583i	1.28423	−	0.741453i
$408$	2.77724	+	10.3648i	0.137494	+	0.513133i
$409$	26.0399	−	6.97737i	1.28759	−	0.345009i	0.450846	−	0.892602i	$-0.351123\pi$
$409$	26.0399	−	6.97737i	1.28759	−	0.345009i	0.836745	+	0.547593i	$0.184456\pi$
$410$	17.3947	−	4.66089i	0.859062	−	0.230185i
$411$	−0.887118	−	3.31077i	−0.0437583	−	0.163308i
$412$	3.86975	−	2.23420i	0.190649	−	0.110071i
$413$	−17.0426	+	9.10176i	−0.838611	+	0.447869i
$414$	12.5789	−	3.37051i	0.618221	−	0.165652i
$415$	−15.1582	−	8.75161i	−0.744089	−	0.429600i
$416$	8.39786	−	0.647841i	0.411739	−	0.0317630i
$417$	−9.32882	−	16.1580i	−0.456834	−	0.791260i
$418$	−3.18307	+	11.8794i	−0.155689	+	0.581040i
$419$	−12.0707	−	6.96900i	−0.589691	−	0.340458i	0.175284	−	0.984518i	$-0.443916\pi$
$419$	−12.0707	−	6.96900i	−0.589691	−	0.340458i	−0.764975	+	0.644060i	$0.777249\pi$
$420$	3.19578	+	0.105741i	0.155938	+	0.00515965i
$421$	15.9864	−	15.9864i	0.779131	−	0.779131i	−0.200552	−	0.979683i	$-0.564274\pi$
$421$	15.9864	−	15.9864i	0.779131	−	0.779131i	0.979683	+	0.200552i	$0.0642735\pi$
$422$	31.6312	−	31.6312i	1.53978	−	1.53978i
$423$	2.28374	+	8.52304i	0.111039	+	0.414405i
$424$	−0.177157	+	0.661159i	−0.00860351	+	0.0321087i
$425$			14.4115i			0.699062i
$426$	−9.13779	+	15.8271i	−0.442727	+	0.766826i
$427$	−12.2204	+	2.84488i	−0.591387	+	0.137673i
$428$			6.10348i			0.295023i
$429$	−11.1564	−	16.2867i	−0.538638	−	0.786329i
$430$	25.0095	−	14.4393i	1.20607	−	0.696323i
$431$	−2.27636	+	2.27636i	−0.109648	+	0.109648i	−0.759802	−	0.650154i	$-0.774704\pi$
$431$	−2.27636	+	2.27636i	−0.109648	+	0.109648i	0.650154	+	0.759802i	$0.274704\pi$
$432$	4.03824	−	2.33148i	0.194290	−	0.112173i
$433$	5.34137	+	9.25152i	0.256690	+	0.444600i	0.965353	−	0.260947i	$-0.0840348\pi$
$433$	5.34137	+	9.25152i	0.256690	+	0.444600i	−0.708663	+	0.705547i	$0.750701\pi$
$434$	−3.14234	−	0.954423i	−0.150837	−	0.0458138i
$435$	−4.91214	−	1.31620i	−0.235519	−	0.0631072i
$436$	2.55237	+	2.55237i	0.122236	+	0.122236i
$437$	−11.6781	−	3.12914i	−0.558639	−	0.149687i
$438$	11.2004	−	19.3996i	0.535175	−	0.926950i
$439$	7.28052	+	12.6102i	0.347480	+	0.601854i	0.985801	−	0.167917i	$-0.0537040\pi$
$439$	7.28052	+	12.6102i	0.347480	+	0.601854i	−0.638321	+	0.769770i	$0.720371\pi$
$440$	10.0382	+	37.4632i	0.478554	+	1.78599i
$441$	6.28028	−	3.09161i	0.299061	−	0.147220i
$442$	−13.8333	−	20.1946i	−0.657985	−	0.960557i
$443$	−2.49941	+	4.32911i	−0.118751	+	0.205682i	−0.919273	−	0.393621i	$-0.871222\pi$
$443$	−2.49941	+	4.32911i	−0.118751	+	0.205682i	0.800522	+	0.599303i	$0.204556\pi$
$444$	−1.62057	−	1.62057i	−0.0769087	−	0.0769087i
$445$	17.1745			0.814149
$446$	22.6667			1.07330
$447$	10.1083	+	10.1083i	0.478107	+	0.478107i
$448$	−14.6681	+	3.41469i	−0.693002	+	0.161329i
$449$	6.89362	−	25.7273i	0.325330	−	1.21415i	−0.588650	−	0.808388i	$-0.700340\pi$
$449$	6.89362	−	25.7273i	0.325330	−	1.21415i	0.913980	−	0.405760i	$-0.132993\pi$
$450$	4.96092	−	1.32927i	0.233860	−	0.0626626i
$451$	−19.0530	−	11.0002i	−0.897170	−	0.517981i
$452$		−	5.71627i		−	0.268871i
$453$	−0.0198676	−	0.00532352i	−0.000933463	−	0.000250121i
$454$	−27.8837			−1.30865
$455$	26.2114	−	8.27254i	1.22881	−	0.387823i
$456$	−3.55021			−0.166254
$457$	12.0928	+	3.24025i	0.565676	+	0.151572i	0.530313	−	0.847802i	$-0.322075\pi$
$457$	12.0928	+	3.24025i	0.565676	+	0.151572i	0.0353630	+	0.999375i	$0.488741\pi$
$458$			10.6511i			0.497695i
$459$	−3.77990	−	2.18233i	−0.176431	−	0.101862i
$460$	9.77352	−	2.61881i	0.455693	−	0.122102i
$461$	−2.58295	+	9.63971i	−0.120300	+	0.448966i	−0.999629	−	0.0272495i	$-0.991325\pi$
$461$	−2.58295	+	9.63971i	−0.120300	+	0.448966i	0.879329	+	0.476216i	$0.157992\pi$
$462$	−15.3974	−	16.4512i	−0.716352	−	0.765379i
$463$	−8.87215	−	8.87215i	−0.412324	−	0.412324i	0.470224	−	0.882547i	$-0.344173\pi$
$463$	−8.87215	−	8.87215i	−0.412324	−	0.412324i	−0.882547	+	0.470224i	$0.844173\pi$
$464$	−8.23001			−0.382069
$465$	−2.29930			−0.106628
$466$	8.56310	+	8.56310i	0.396678	+	0.396678i
$467$	−7.33629	+	12.7068i	−0.339483	+	0.588002i	−0.984336	−	0.176305i	$-0.943585\pi$
$467$	−7.33629	+	12.7068i	−0.339483	+	0.588002i	0.644853	+	0.764307i	$0.276919\pi$
$468$	−0.983964	+	1.14847i	−0.0454838	+	0.0530880i
$469$	−4.36188	−	2.71452i	−0.201413	−	0.125345i
$470$	10.2351	+	38.1980i	0.472111	+	1.76194i
$471$	−3.04018	−	5.26575i	−0.140084	−	0.242633i
$472$	−8.97661	+	15.5479i	−0.413182	+	0.715652i
$473$	−34.0784	−	9.13127i	−1.56692	−	0.419856i
$474$	−0.948624	−	0.948624i	−0.0435717	−	0.0435717i
$475$	−4.60565	−	1.23408i	−0.211322	−	0.0566235i
$476$	−3.30986	−	3.53639i	−0.151707	−	0.162090i
$477$	−0.139208	−	0.241116i	−0.00637391	−	0.0110399i
$478$	4.23734	−	2.44643i	0.193811	−	0.111897i
$479$	9.76842	−	9.76842i	0.446330	−	0.446330i	−0.447802	−	0.894133i	$-0.647793\pi$
$479$	9.76842	−	9.76842i	0.446330	−	0.446330i	0.894133	+	0.447802i	$0.147793\pi$
$480$	5.82913	−	3.36545i	0.266062	−	0.153611i
$481$	−17.7682	−	8.50880i	−0.810160	−	0.387968i
$482$			13.9672i			0.636189i
$483$	16.1724	−	15.1365i	0.735872	−	0.688735i
$484$	−3.98026	+	6.89402i	−0.180921	+	0.313364i
$485$		−	6.40843i		−	0.290992i
$486$	−0.402582	+	1.50246i	−0.0182615	+	0.0681528i
$487$	7.78069	+	29.0379i	0.352577	+	1.31583i	0.883507	+	0.468418i	$0.155176\pi$
$487$	7.78069	+	29.0379i	0.352577	+	1.31583i	−0.530930	+	0.847415i	$0.678157\pi$
$488$	−8.24421	+	8.24421i	−0.373198	+	0.373198i
$489$	−10.0711	+	10.0711i	−0.455430	+	0.455430i
$490$	28.1465	−	13.8558i	1.27153	−	0.625941i
$491$	27.2827	+	15.7517i	1.23125	+	0.710863i	0.967291	−	0.253670i	$-0.0816377\pi$
$491$	27.2827	+	15.7517i	1.23125	+	0.710863i	0.263961	+	0.964533i	$0.414971\pi$
$492$	−0.436214	+	1.62797i	−0.0196660	+	0.0733947i
$493$	3.85175	+	6.67143i	0.173474	+	0.300466i
$494$	7.63836	−	2.69158i	0.343666	−	0.121100i
$495$	−13.6623	−	7.88795i	−0.614076	−	0.354537i
$496$	−3.59429	+	0.963087i	−0.161388	+	0.0432439i
$497$	−1.02800	+	31.0688i	−0.0461121	+	1.39363i
$498$	8.18312	−	4.72452i	0.366694	−	0.211711i
$499$	6.05231	+	22.5875i	0.270938	+	1.01116i	0.958515	+	0.285044i	$0.0920081\pi$
$499$	6.05231	+	22.5875i	0.270938	+	1.01116i	−0.687576	+	0.726112i	$0.741325\pi$
$500$	−1.98234	+	0.531167i	−0.0886531	+	0.0237545i
$501$	2.16336	−	0.579671i	0.0966519	−	0.0258978i
$502$	9.94261	+	37.1063i	0.443760	+	1.65614i
$503$	7.16456	−	4.13646i	0.319452	−	0.184436i	−0.331696	−	0.943386i	$-0.607621\pi$
$503$	7.16456	−	4.13646i	0.319452	−	0.184436i	0.651148	+	0.758951i	$0.274288\pi$
$504$	3.43677	−	5.52246i	0.153086	−	0.245990i
$505$	−44.0968	+	11.8157i	−1.96228	+	0.525792i
$506$	−61.7499	−	35.6513i	−2.74512	−	1.58490i
$507$	−4.69635	+	12.1221i	−0.208572	+	0.538359i
$508$	0.730656	+	1.26553i	0.0324176	+	0.0561489i
$509$	2.38441	−	8.89874i	0.105687	−	0.394430i	−0.892735	−	0.450582i	$-0.851217\pi$
$509$	2.38441	−	8.89874i	0.105687	−	0.394430i	0.998422	+	0.0561523i	$0.0178832\pi$
$510$	−16.9405	−	9.78060i	−0.750138	−	0.433092i
$511$	1.26004	−	38.0817i	0.0557409	−	1.68463i
$512$	−8.50976	+	8.50976i	−0.376082	+	0.376082i
$513$	1.02111	−	1.02111i	0.0450830	−	0.0450830i
$514$	2.47631	+	9.24172i	0.109225	+	0.407635i
$515$	7.94436	−	29.6488i	0.350071	−	1.30648i
$516$			2.70275i			0.118982i
$517$	24.1561	−	41.8396i	1.06238	−	1.84010i
$518$	−21.5155	−	6.53489i	−0.945335	−	0.287127i
$519$			3.24988i			0.142654i
$520$	16.6172	−	19.3953i	0.728712	−	0.850541i
$521$	5.78613	−	3.34062i	0.253495	−	0.146355i	−0.367869	−	0.929878i	$-0.619912\pi$
$521$	5.78613	−	3.34062i	0.253495	−	0.146355i	0.621364	+	0.783522i	$0.286579\pi$
$522$	1.94125	−	1.94125i	0.0849663	−	0.0849663i
$523$	27.8150	−	16.0590i	1.21627	−	0.702211i	0.252148	−	0.967689i	$-0.418863\pi$
$523$	27.8150	−	16.0590i	1.21627	−	0.702211i	0.964117	+	0.265477i	$0.0855296\pi$
$524$	−1.21457	−	2.10369i	−0.0530586	−	0.0919001i
$525$	6.37814	−	5.96958i	0.278365	−	0.260534i
$526$	−25.7659	−	6.90396i	−1.12345	−	0.301027i
$527$	2.46287	+	2.46287i	0.107285	+	0.107285i
$528$	−24.6610	−	6.60790i	−1.07323	−	0.287572i
$529$	23.5472	−	40.7850i	1.02379	−	1.77326i
$530$	−0.623895	−	1.08062i	−0.0271003	−	0.0469390i
$531$	−1.89004	−	7.05373i	−0.0820208	−	0.306106i
$532$	1.41359	−	0.754943i	0.0612869	−	0.0327309i
$533$	1.11432	+	14.4447i	0.0482665	+	0.625671i
$534$	−4.63579	+	8.02942i	−0.200610	+	0.347467i
$535$	29.6465	+	29.6465i	1.28173	+	1.28173i
$536$	−4.77393			−0.206202
$537$	21.1701			0.913558
$538$	−2.54240	−	2.54240i	−0.109611	−	0.109611i
$539$	−36.2843	−	12.3452i	−1.56287	−	0.531747i
$540$	−0.312796	+	1.16737i	−0.0134606	+	0.0502356i
$541$	6.05418	−	1.62221i	0.260289	−	0.0697443i	−0.126314	−	0.991990i	$-0.540315\pi$
$541$	6.05418	−	1.62221i	0.260289	−	0.0697443i	0.386604	+	0.922246i	$0.373648\pi$
$542$	8.72920	+	5.03981i	0.374951	+	0.216478i
$543$			18.5217i			0.794841i
$544$	−9.84869	−	2.63895i	−0.422259	−	0.113144i
$545$	24.7953			1.06211
$546$	−3.20747	+	14.4873i	−0.137267	+	0.619999i
$547$	−17.9848			−0.768973			−0.384487	−	0.923131i	$-0.625622\pi$
$547$	−17.9848			−0.768973			−0.384487	+	0.923131i	$0.625622\pi$
$548$	1.38869	+	0.372099i	0.0593220	+	0.0158953i
$549$		−	4.74239i		−	0.202400i
$550$	−24.3531	−	14.0603i	−1.03842	−	0.599533i
$551$	−2.46189	+	0.659662i	−0.104880	+	0.0281026i
$552$	5.32728	−	19.8817i	0.226744	−	0.846220i
$553$	−2.18343	−	0.663172i	−0.0928488	−	0.0282009i
$554$	26.5915	+	26.5915i	1.12976	+	1.12976i
$555$	−15.7432			−0.668262
$556$	7.82589			0.331892
$557$	26.7133	+	26.7133i	1.13188	+	1.13188i	0.989865	+	0.142012i	$0.0453572\pi$
$557$	26.7133	+	26.7133i	1.13188	+	1.13188i	0.142012	+	0.989865i	$0.454643\pi$
$558$	0.620634	−	1.07497i	0.0262736	−	0.0455071i
$559$	7.72133	+	21.9121i	0.326577	+	0.926785i
$560$	18.7816	−	30.1797i	0.793669	−	1.27533i
$561$	6.18517	+	23.0834i	0.261138	+	0.974580i
$562$	−20.4792	−	35.4711i	−0.863864	−	1.49626i
$563$	−3.18658	+	5.51931i	−0.134298	+	0.232611i	−0.925329	−	0.379165i	$-0.876211\pi$
$563$	−3.18658	+	5.51931i	−0.134298	+	0.232611i	0.791031	+	0.611776i	$0.209545\pi$
$564$	−3.57496	−	0.957909i	−0.150533	−	0.0403352i
$565$	−27.7657	−	27.7657i	−1.16811	−	1.16811i
$566$	18.7876	+	5.03413i	0.789703	+	0.211600i
$567$	0.599883	+	2.57685i	0.0251927	+	0.108217i
$568$	14.4428	+	25.0156i	0.606005	+	1.04963i
$569$	−3.81617	+	2.20327i	−0.159982	+	0.0923657i	−0.577854	−	0.816140i	$-0.696110\pi$
$569$	−3.81617	+	2.20327i	−0.159982	+	0.0923657i	0.417872	+	0.908506i	$0.362776\pi$
$570$	4.57633	−	4.57633i	0.191682	−	0.191682i
$571$	−12.2682	+	7.08302i	−0.513406	+	0.296415i	−0.734233	−	0.678898i	$-0.762458\pi$
$571$	−12.2682	+	7.08302i	−0.513406	+	0.296415i	0.220826	+	0.975313i	$0.429125\pi$
$572$	8.25593	−	0.636893i	0.345198	−	0.0266298i
$573$			27.4180i			1.14540i
$574$	3.74931	+	16.1055i	0.156493	+	0.672229i
$575$	13.8221	−	23.9405i	0.576419	−	0.998388i
$576$		−	5.69226i		−	0.237178i
$577$	2.40718	−	8.98371i	0.100212	−	0.373997i	−0.897546	−	0.440921i	$-0.854652\pi$
$577$	2.40718	−	8.98371i	0.100212	−	0.373997i	0.997758	+	0.0669241i	$0.0213186\pi$
$578$	0.825363	+	3.08030i	0.0343306	+	0.128123i
$579$	−13.4853	+	13.4853i	−0.560431	+	0.560431i
$580$	1.50830	−	1.50830i	0.0626289	−	0.0626289i
$581$	8.49207	−	13.6457i	0.352311	−	0.566118i
$582$	2.99607	+	1.72978i	0.124191	+	0.0717018i
$583$	−0.394546	+	1.47246i	−0.0163404	+	0.0609832i
$584$	−17.7028	−	30.6621i	−0.732547	−	1.26881i
$585$	0.799046	+	10.3579i	0.0330365	+	0.428246i
$586$	−0.118733	−	0.0685503i	−0.00490480	−	0.00283179i
$587$	10.0172	−	2.68411i	0.413455	−	0.110785i	−0.0460944	−	0.998937i	$-0.514678\pi$
$587$	10.0172	−	2.68411i	0.413455	−	0.110785i	0.459550	+	0.888152i	$0.348011\pi$
$588$	−0.194088	+	2.92971i	−0.00800404	+	0.120819i
$589$	−0.997987	+	0.576188i	−0.0411213	+	0.0237414i
$590$	−8.47066	−	31.6130i	−0.348732	−	1.30148i
$591$	4.48424	−	1.20155i	0.184457	−	0.0494251i
$592$	−24.6099	+	6.59421i	−1.01146	+	0.271020i
$593$	3.11158	+	11.6126i	0.127777	+	0.476871i	0.999923	−	0.0123741i	$-0.00393891\pi$
$593$	3.11158	+	11.6126i	0.127777	+	0.476871i	−0.872146	+	0.489245i	$0.837272\pi$
$594$	7.37555	−	4.25828i	0.302623	−	0.174719i
$595$	−33.2544	−	1.10032i	−1.36330	−	0.0451085i
$596$	−5.79182	+	1.55191i	−0.237242	+	0.0635688i
$597$	0.387218	+	0.223560i	0.0158478	+	0.00914972i
$598$	3.61147	+	46.8148i	0.147684	+	1.91440i
$599$	−9.16962	−	15.8822i	−0.374660	−	0.648931i	0.615616	−	0.788046i	$-0.288907\pi$
$599$	−9.16962	−	15.8822i	−0.374660	−	0.648931i	−0.990276	+	0.139116i	$0.955574\pi$
$600$	2.10099	−	7.84100i	0.0857725	−	0.320107i
$601$	−29.4396	−	16.9969i	−1.20086	−	0.693319i	−0.240117	−	0.970744i	$-0.577186\pi$
$601$	−29.4396	−	16.9969i	−1.20086	−	0.693319i	−0.960747	+	0.277424i	$0.910519\pi$
$602$	12.4922	+	23.3909i	0.509142	+	0.953343i
$603$	1.37307	−	1.37307i	0.0559159	−	0.0559159i
$604$	0.00610049	−	0.00610049i	0.000248225	−	0.000248225i
$605$	14.1530	+	52.8198i	0.575402	+	2.14743i
$606$	6.37866	−	23.8055i	0.259115	−	0.967031i
$607$			41.0442i			1.66593i	0.553325	+	0.832965i	$0.313359\pi$
$607$			41.0442i			1.66593i	−0.553325	+	0.832965i	$0.686641\pi$
$608$	1.68672	−	2.92148i	0.0684053	−	0.118482i
$609$	1.35711	−	4.46814i	0.0549927	−	0.181058i
$610$		−	21.2541i		−	0.860554i
$611$	−31.7201	+	2.44700i	−1.28326	+	0.0989951i
$612$	1.58547	−	0.915370i	0.0640887	−	0.0370016i
$613$	18.9601	−	18.9601i	0.765790	−	0.765790i	−0.211572	−	0.977362i	$-0.567858\pi$
$613$	18.9601	−	18.9601i	0.765790	−	0.765790i	0.977362	+	0.211572i	$0.0678583\pi$
$614$	−14.4541	+	8.34506i	−0.583319	+	0.336779i
$615$	5.78875	+	10.0264i	0.233425	+	0.404303i
$616$	−34.6866	+	8.07495i	−1.39756	+	0.325349i
$617$	−10.2681	−	2.75133i	−0.413378	−	0.110764i	0.0461351	−	0.998935i	$-0.485310\pi$
$617$	−10.2681	−	2.75133i	−0.413378	−	0.110764i	−0.459513	+	0.888171i	$0.651976\pi$
$618$	11.7170	+	11.7170i	0.471328	+	0.471328i
$619$	−27.0153	−	7.23874i	−1.08584	−	0.290949i	−0.328853	−	0.944381i	$-0.606662\pi$
$619$	−27.0153	−	7.23874i	−1.08584	−	0.290949i	−0.756985	+	0.653432i	$0.773329\pi$
$620$	0.482217	−	0.835225i	0.0193663	−	0.0335434i
$621$	4.18612	+	7.25058i	0.167983	+	0.290956i
$622$	−12.1699	−	45.4187i	−0.487969	−	1.82112i
$623$	−0.521525	+	15.7618i	−0.0208945	+	0.631485i
$624$	5.58759	+	15.8569i	0.223683	+	0.634783i
$625$	−15.3035	+	26.5064i	−0.612140	+	1.06026i
$626$	−31.7368	−	31.7368i	−1.26846	−	1.26846i
$627$	−7.90665			−0.315761
$628$	2.55039			0.101772
$629$	16.8632	+	16.8632i	0.672379	+	0.672379i
$630$	2.68852	+	11.5487i	0.107113	+	0.460113i
$631$	−0.748324	+	2.79278i	−0.0297903	+	0.111179i	−0.979220	−	0.202801i	$-0.934996\pi$
$631$	−0.748324	+	2.79278i	−0.0297903	+	0.111179i	0.949430	+	0.313980i	$0.101662\pi$
$632$	−2.04815	+	0.548800i	−0.0814711	+	0.0218301i
$633$	24.9060	+	14.3795i	0.989924	+	0.571533i
$634$			26.1005i			1.03658i
$635$	9.69611	+	2.59807i	0.384779	+	0.103101i
$636$	0.116781			0.00463067
$637$	6.79617	+	24.3066i	0.269274	+	0.963064i
$638$	−15.0315			−0.595103
$639$	−11.3490	−	3.04095i	−0.448959	−	0.120298i
$640$		−	38.9730i		−	1.54054i
$641$	−13.0554	−	7.53755i	−0.515658	−	0.297715i	0.219498	−	0.975613i	$-0.429558\pi$
$641$	−13.0554	−	7.53755i	−0.515658	−	0.297715i	−0.735156	+	0.677898i	$0.762891\pi$
$642$	−21.8626	+	5.85807i	−0.862849	+	0.231200i
$643$	−10.7996	+	40.3048i	−0.425896	+	1.58946i	0.336063	+	0.941839i	$0.390904\pi$
$643$	−10.7996	+	40.3048i	−0.425896	+	1.58946i	−0.761959	+	0.647625i	$0.775762\pi$
$644$	2.10662	+	9.04915i	0.0830124	+	0.356586i
$645$	13.1281	+	13.1281i	0.516919	+	0.516919i
$646$	−9.80379			−0.385725
$647$	−0.428217			−0.0168349			−0.00841747	−	0.999965i	$-0.502679\pi$
$647$	−0.428217			−0.0168349			−0.00841747	+	0.999965i	$0.502679\pi$
$648$	1.73841	+	1.73841i	0.0682912	+	0.0682912i
$649$	−19.9918	+	34.6267i	−0.784745	+	1.35922i
$650$	1.42430	+	18.4630i	0.0558657	+	0.724178i
$651$	0.0698212	−	2.11018i	0.00273651	−	0.0827044i
$652$	−1.54619	−	5.77047i	−0.0605536	−	0.225989i
$653$	8.19250	+	14.1898i	0.320597	+	0.555291i	0.980611	−	0.195962i	$-0.0627831\pi$
$653$	8.19250	+	14.1898i	0.320597	+	0.555291i	−0.660014	+	0.751253i	$0.729450\pi$
$654$	−6.69282	+	11.5923i	−0.261710	+	0.453295i
$655$	−16.1178	−	4.31875i	−0.629775	−	0.168748i
$656$	13.2487	+	13.2487i	0.517274	+	0.517274i
$657$	13.9107	+	3.72736i	0.542707	+	0.145418i
$658$	−35.3670	+	8.23334i	−1.37875	+	0.320969i
$659$	−13.2020	−	22.8666i	−0.514278	−	0.890755i	−0.999863	−	0.0165659i	$-0.994727\pi$
$659$	−13.2020	−	22.8666i	−0.514278	−	0.890755i	0.485585	−	0.874190i	$-0.338607\pi$
$660$	5.73062	−	3.30857i	0.223064	−	0.128786i
$661$	19.5788	−	19.5788i	0.761529	−	0.761529i	−0.215070	−	0.976599i	$-0.568998\pi$
$661$	19.5788	−	19.5788i	0.761529	−	0.761529i	0.976599	+	0.215070i	$0.0689979\pi$
$662$	−8.47684	+	4.89411i	−0.329462	+	0.190215i
$663$	10.2389	−	11.9506i	0.397645	−	0.464125i
$664$		−	14.9347i		−	0.579580i
$665$	3.19926	−	10.5332i	0.124062	−	0.408462i
$666$	4.24945	−	7.36027i	0.164663	−	0.285205i
$667$		−	14.7768i		−	0.572161i
$668$	−0.243141	+	0.907416i	−0.00940742	+	0.0351090i
$669$	3.77160	+	14.0758i	0.145819	+	0.544202i
$670$	6.15375	−	6.15375i	0.237740	−	0.237740i
$671$	−18.3606	+	18.3606i	−0.708805	+	0.708805i
$672$	2.91163	+	5.45187i	0.112318	+	0.210310i
$673$	−16.8918	−	9.75249i	−0.651131	−	0.375931i	0.137758	−	0.990466i	$-0.456010\pi$
$673$	−16.8918	−	9.75249i	−0.651131	−	0.375931i	−0.788889	+	0.614535i	$0.789344\pi$
$674$	−6.90086	+	25.7544i	−0.265811	+	0.992021i
$675$	1.65094	+	2.85951i	0.0635446	+	0.110062i
$676$	−3.41842	−	4.24824i	−0.131478	−	0.163394i
$677$	−1.91182	−	1.10379i	−0.0734772	−	0.0424221i	0.462811	−	0.886457i	$-0.346841\pi$
$677$	−1.91182	−	1.10379i	−0.0734772	−	0.0424221i	−0.536288	+	0.844035i	$0.680174\pi$
$678$	20.4756	−	5.48643i	0.786362	−	0.210705i
$679$	5.88132	+	0.194600i	0.225704	+	0.00746807i
$680$	−26.7754	+	15.4588i	−1.02679	+	0.592816i
$681$	−4.63969	−	17.3155i	−0.177793	−	0.663533i
$682$	−6.56471	+	1.75901i	−0.251376	+	0.0673559i
$683$	12.6252	−	3.38292i	0.483091	−	0.129444i	−0.00905031	−	0.999959i	$-0.502881\pi$
$683$	12.6252	−	3.38292i	0.483091	−	0.129444i	0.492142	+	0.870515i	$0.336214\pi$
$684$	0.156769	+	0.585069i	0.00599421	+	0.0223707i
$685$	8.55271	−	4.93791i	0.326782	−	0.188668i
$686$	11.8614	+	26.2522i	0.452871	+	1.00231i
$687$	−6.61427	+	1.77229i	−0.252350	+	0.0676170i
$688$	26.0208	+	15.0231i	0.992035	+	0.572752i
$689$	0.946784	−	0.333625i	0.0360696	−	0.0127101i
$690$	18.7611	+	32.4952i	0.714223	+	1.23707i
$691$	13.1517	−	49.0829i	0.500315	−	1.86720i	0.00236284	−	0.999997i	$-0.499248\pi$
$691$	13.1517	−	49.0829i	0.500315	−	1.86720i	0.497952	−	0.867204i	$-0.334085\pi$
$692$	−1.18053	−	0.681577i	−0.0448768	−	0.0259097i
$693$	7.65402	−	12.2990i	0.290752	−	0.467202i
$694$	4.65219	−	4.65219i	0.176595	−	0.176595i
$695$	38.0128	−	38.0128i	1.44191	−	1.44191i
$696$	−1.12306	−	4.19131i	−0.0425694	−	0.158871i
$697$	4.53912	−	16.9402i	0.171932	−	0.641657i
$698$			28.9885i			1.09723i
$699$	−3.89276	+	6.74247i	−0.147238	+	0.255023i
$700$	0.830815	+	3.56883i	0.0314019	+	0.134889i
$701$		−	12.9407i		−	0.488765i	−0.969679	−	0.244383i	$-0.921415\pi$
$701$		−	12.9407i		−	0.488765i	0.969679	−	0.244383i	$-0.0785853\pi$
$702$	−5.05821	−	2.42226i	−0.190910	−	0.0914224i
$703$	−6.83317	+	3.94513i	−0.257718	+	0.148793i
$704$	−22.0382	+	22.0382i	−0.830596	+	0.830596i
$705$	−22.0176	+	12.7119i	−0.829230	+	0.478756i
$706$	−3.46444	−	6.00059i	−0.130386	−	0.225835i
$707$	−9.50477	−	40.8285i	−0.357464	−	1.53551i
$708$	2.95867	+	0.792772i	0.111193	+	0.0297942i
$709$	17.4540	+	17.4540i	0.655497	+	0.655497i	0.954311	−	0.298814i	$-0.0965911\pi$
$709$	17.4540	+	17.4540i	0.655497	+	0.655497i	−0.298814	+	0.954311i	$0.596591\pi$
$710$	−50.8631	−	13.6287i	−1.90886	−	0.511477i
$711$	0.431242	−	0.746933i	0.0161728	−	0.0280122i
$712$	7.32711	+	12.6909i	0.274595	+	0.475613i
$713$	−1.72920	−	6.45347i	−0.0647592	−	0.241684i
$714$	9.49055	−	15.2501i	0.355175	−	0.570721i
$715$	37.0081	−	43.1952i	1.38402	−	1.61541i
$716$	−4.43987	+	7.69008i	−0.165926	+	0.287392i
$717$	2.22428	+	2.22428i	0.0830673	+	0.0830673i
$718$	−25.5276			−0.952680
$719$	−14.9323			−0.556880			−0.278440	−	0.960454i	$-0.589817\pi$
$719$	−14.9323			−0.556880			−0.278440	+	0.960454i	$0.589817\pi$
$720$	9.50024	+	9.50024i	0.354053	+	0.354053i
$721$	26.9689	+	8.19125i	1.00437	+	0.305058i
$722$	−6.80954	+	25.4136i	−0.253425	+	0.945795i
$723$	−8.67353	+	2.32406i	−0.322572	+	0.0864329i
$724$	−6.72803	−	3.88443i	−0.250045	−	0.144364i
$725$		−	5.82773i		−	0.216436i
$726$	−28.5146	−	7.64045i	−1.05827	−	0.283564i
$727$	−8.06701			−0.299189			−0.149595	−	0.988747i	$-0.547797\pi$
$727$	−8.06701			−0.299189			−0.149595	+	0.988747i	$0.547797\pi$
$728$	17.2954	+	15.8394i	0.641011	+	0.587045i
$729$	−1.00000			−0.0370370
$730$	62.3440	+	16.7050i	2.30745	+	0.618281i
$731$		−	28.1241i		−	1.04021i
$732$	1.72268	+	0.994590i	0.0636721	+	0.0367611i
$733$	3.69987	−	0.991378i	0.136658	−	0.0366174i	−0.189842	−	0.981815i	$-0.560797\pi$
$733$	3.69987	−	0.991378i	0.136658	−	0.0366174i	0.326500	+	0.945197i	$0.394131\pi$
$734$	11.2441	−	41.9635i	0.415026	−	1.54890i
$735$	13.2878	+	15.1732i	0.490126	+	0.559674i
$736$	13.8297	+	13.8297i	0.509769	+	0.509769i
$737$	−10.6320			−0.391634
$738$	−6.25006			−0.230068
$739$	13.5656	+	13.5656i	0.499018	+	0.499018i	0.911132	−	0.412114i	$-0.135210\pi$
$739$	13.5656	+	13.5656i	0.499018	+	0.499018i	−0.412114	+	0.911132i	$0.635210\pi$
$740$	3.30172	−	5.71875i	0.121374	−	0.210225i
$741$	2.94243	+	4.29550i	0.108093	+	0.157799i
$742$	1.01068	−	0.539764i	0.0371032	−	0.0198153i
$743$	2.24541	+	8.37997i	0.0823759	+	0.307431i	0.994804	−	0.101805i	$-0.0324618\pi$
$743$	2.24541	+	8.37997i	0.0823759	+	0.307431i	−0.912428	+	0.409236i	$0.865795\pi$
$744$	−0.980946	−	1.69905i	−0.0359632	−	0.0622901i
$745$	−20.5945	+	35.6708i	−0.754526	+	1.30688i
$746$	8.78656	+	2.35435i	0.321699	+	0.0861989i
$747$	4.29551	+	4.29551i	0.157165	+	0.157165i
$748$	−9.68225	−	2.59435i	−0.354018	−	0.0948588i
$749$	−28.1083	+	26.3078i	−1.02705	+	0.961264i
$750$	−3.80527	−	6.59093i	−0.138949	−	0.240667i
$751$	26.0916	−	15.0640i	0.952094	−	0.549692i	0.0583635	−	0.998295i	$-0.481412\pi$
$751$	26.0916	−	15.0640i	0.952094	−	0.549692i	0.893731	+	0.448603i	$0.148078\pi$
$752$	−29.0936	+	29.0936i	−1.06093	+	1.06093i
$753$	−21.3883	+	12.3486i	−0.779434	+	0.450006i
$754$	5.59392	+	8.16627i	0.203719	+	0.297398i
$755$		−	0.0592640i		−	0.00215684i
$756$	−1.06185	−	0.322517i	−0.0386192	−	0.0117298i
$757$	−0.444897	+	0.770584i	−0.0161700	+	0.0280073i	−0.873997	−	0.485931i	$-0.838481\pi$
$757$	−0.444897	+	0.770584i	−0.0161700	+	0.0280073i	0.857827	+	0.513938i	$0.171814\pi$
$758$			2.47363i			0.0898462i
$759$	11.8644	−	44.2784i	0.430649	−	1.60720i
$760$	−2.64751	−	9.88065i	−0.0960354	−	0.358409i
$761$	33.9171	−	33.9171i	1.22949	−	1.22949i	0.265338	−	0.964155i	$-0.414516\pi$
$761$	33.9171	−	33.9171i	1.22949	−	1.22949i	0.964155	−	0.265338i	$-0.0854836\pi$
$762$	−3.83185	+	3.83185i	−0.138813	+	0.138813i
$763$	−0.752941	+	22.7558i	−0.0272583	+	0.823816i
$764$	−9.95963	−	5.75019i	−0.360327	−	0.208035i
$765$	3.25487	−	12.1473i	0.117680	−	0.439188i
$766$	10.9542	+	18.9732i	0.395791	+	0.685530i
$767$	26.2518	−	2.02516i	0.947896	−	0.0731242i
$768$	8.36139	+	4.82745i	0.301716	+	0.174196i
$769$	−4.85396	+	1.30061i	−0.175038	+	0.0469013i	−0.345274	−	0.938502i	$-0.612214\pi$
$769$	−4.85396	+	1.30061i	−0.175038	+	0.0469013i	0.170235	+	0.985403i	$0.445547\pi$
$770$	34.3033	−	55.1210i	1.23620	−	1.98642i
$771$	−5.32699	+	3.07554i	−0.191847	+	0.110763i
$772$	−2.07038	−	7.72676i	−0.0745146	−	0.278092i
$773$	12.5079	−	3.35148i	0.449878	−	0.120544i	−0.0267645	−	0.999642i	$-0.508520\pi$
$773$	12.5079	−	3.35148i	0.449878	−	0.120544i	0.476642	+	0.879097i	$0.341854\pi$
$774$	−9.68124	+	2.59408i	−0.347985	+	0.0932423i
$775$	−0.681969	−	2.54514i	−0.0244970	−	0.0914242i
$776$	4.73545	−	2.73401i	0.169993	−	0.0981454i
$777$	0.478063	−	14.4483i	0.0171504	−	0.518330i
$778$	0.376093	−	0.100774i	0.0134836	−	0.00361292i
$779$	5.02509	+	2.90123i	0.180042	+	0.103948i
$780$	−3.93010	−	1.88204i	−0.140720	−	0.0673878i
$781$	32.1654	+	55.7121i	1.15097	+	1.99354i
$782$	14.7111	−	54.9026i	0.526069	−	1.96331i
$783$	1.52851	+	0.882488i	0.0546247	+	0.0315376i
$784$	27.1270	+	18.1532i	0.968822	+	0.648330i
$785$	12.3880	−	12.3880i	0.442148	−	0.442148i
$786$	6.36967	−	6.36967i	0.227199	−	0.227199i
$787$	−0.598619	−	2.23408i	−0.0213385	−	0.0796363i	0.954436	−	0.298417i	$-0.0964587\pi$
$787$	−0.598619	−	2.23408i	−0.0213385	−	0.0796363i	−0.975774	+	0.218781i	$0.929792\pi$
$788$	−0.503986	+	1.88090i	−0.0179538	+	0.0670043i
$789$		−	17.1492i		−	0.610528i
$790$	1.93271	−	3.34756i	0.0687628	−	0.119101i
$791$	26.3251	−	24.6388i	0.936011	−	0.876054i
$792$		−	13.4609i		−	0.478311i
$793$	16.8078	+	3.14206i	0.596861	+	0.111578i
$794$	9.07049	−	5.23685i	0.321900	−	0.185849i
$795$	0.567242	−	0.567242i	0.0201180	−	0.0201180i
$796$	−0.162417	+	0.0937717i	−0.00575673	+	0.00332365i
$797$	−22.4781	−	38.9332i	−0.796216	−	1.37909i	−0.922064	−	0.387037i	$-0.873499\pi$
$797$	−22.4781	−	38.9332i	−0.796216	−	1.37909i	0.125848	−	0.992049i	$-0.459835\pi$
$798$	4.06095	+	4.33889i	0.143756	+	0.153595i
$799$	37.2001	+	9.96774i	1.31605	+	0.352633i
$800$	5.45420	+	5.45420i	0.192835	+	0.192835i
$801$	−5.75757	−	1.54274i	−0.203434	−	0.0545099i
$802$	22.4256	−	38.8422i	0.791874	−	1.37157i
$803$	−39.4258	−	68.2875i	−1.39131	−	2.40981i
$804$	0.210806	+	0.786737i	0.00743454	+	0.0277461i
$805$	54.1870	+	33.7220i	1.90984	+	1.18855i
$806$	3.39866	+	2.91184i	0.119713	+	0.102565i
$807$	1.15577	−	2.00185i	0.0406850	−	0.0704685i
$808$	−27.5440	−	27.5440i	−0.968995	−	0.968995i
$809$	−14.3965			−0.506155			−0.253078	−	0.967446i	$-0.581443\pi$
$809$	−14.3965			−0.506155			−0.253078	+	0.967446i	$0.581443\pi$
$810$	−4.48173			−0.157472
$811$	−15.3043	−	15.3043i	−0.537406	−	0.537406i	0.385360	−	0.922766i	$-0.374077\pi$
$811$	−15.3043	−	15.3043i	−0.537406	−	0.537406i	−0.922766	+	0.385360i	$0.874077\pi$
$812$	1.33844	+	1.43004i	0.0469701	+	0.0501847i
$813$	−1.67719	+	6.25936i	−0.0588216	+	0.219525i
$814$	−44.9482	+	12.0438i	−1.57544	+	0.422137i
$815$	−35.5393	−	20.5186i	−1.24489	−	0.718737i
$816$		−	20.3522i		−	0.712469i
$817$	8.98792	+	2.40831i	0.314448	+	0.0842560i
$818$	−41.9328			−1.46615
$819$	−9.53019	+	0.418792i	−0.333012	+	0.0146338i
$820$	−4.85614			−0.169584
$821$	35.4952	+	9.51091i	1.23879	+	0.331933i	0.817997	−	0.575223i	$-0.195085\pi$
$821$	35.4952	+	9.51091i	1.23879	+	0.331933i	0.420795	+	0.907156i	$0.361751\pi$
$822$			5.33142i			0.185955i
$823$	−28.0981	−	16.2225i	−0.979439	−	0.565480i	−0.0773384	−	0.997005i	$-0.524642\pi$
$823$	−28.0981	−	16.2225i	−0.979439	−	0.565480i	−0.902101	+	0.431525i	$0.857976\pi$
$824$	25.2980	−	6.77857i	0.881297	−	0.236143i
$825$	4.67910	−	17.4627i	0.162905	−	0.607971i
$826$	29.2699	−	6.81397i	1.01843	−	0.237088i
$827$	−32.5966	−	32.5966i	−1.13349	−	1.13349i	−0.989592	−	0.143901i	$-0.954035\pi$
$827$	−32.5966	−	32.5966i	−1.13349	−	1.13349i	−0.143901	−	0.989592i	$-0.545965\pi$
$828$	−3.51171			−0.122040
$829$	47.4214			1.64701			0.823507	−	0.567307i	$-0.192015\pi$
$829$	47.4214			1.64701			0.823507	+	0.567307i	$0.192015\pi$
$830$	19.2513	+	19.2513i	0.668224	+	0.668224i
$831$	−12.0884	+	20.9378i	−0.419343	+	0.726323i
$832$	20.1743	+	3.77140i	0.699417	+	0.130750i
$833$	2.01962	−	30.4857i	0.0699758	−	1.05627i
$834$	7.51123	+	28.0323i	0.260093	+	0.970679i
$835$	3.22659	+	5.58862i	0.111661	+	0.193402i
$836$	1.65821	−	2.87210i	0.0573504	−	0.0993338i
$837$	0.770818	+	0.206540i	0.0266434	+	0.00713906i
$838$	15.3301	+	15.3301i	0.529568	+	0.529568i
$839$	3.74709	+	1.00403i	0.129364	+	0.0346629i	0.322920	−	0.946426i	$-0.395336\pi$
$839$	3.74709	+	1.00403i	0.129364	+	0.0346629i	−0.193556	+	0.981089i	$0.562002\pi$
$840$	17.9326	+	5.44666i	0.618733	+	0.187928i
$841$	12.9424	+	22.4169i	0.446291	+	0.772998i
$842$	−30.4548	+	17.5831i	−1.04954	+	0.605953i
$843$	18.6196	−	18.6196i	0.641293	−	0.641293i
$844$	−10.4467	+	6.03143i	−0.359591	+	0.207610i
$845$	−37.2394	−	4.03067i	−1.28107	−	0.138659i
$846$		−	13.7249i		−	0.471872i
$847$	−48.9050	+	11.3850i	−1.68040	+	0.391192i
$848$	0.649122	−	1.12431i	0.0222910	−	0.0386091i
$849$			12.5046i			0.429157i
$850$	5.80182	−	21.6527i	0.199001	−	0.742681i
$851$	−11.8398	−	44.1866i	−0.405862	−	1.51470i
$852$	3.48478	−	3.48478i	0.119387	−	0.119387i
$853$	23.3977	−	23.3977i	0.801122	−	0.801122i	−0.182149	−	0.983271i	$-0.558305\pi$
$853$	23.3977	−	23.3977i	0.801122	−	0.801122i	0.983271	+	0.182149i	$0.0583054\pi$
$854$	19.5059	+	0.645409i	0.667479	+	0.0220854i
$855$	3.60334	+	2.08039i	0.123232	+	0.0711478i
$856$	−9.25899	+	34.5550i	−0.316466	+	1.18107i
$857$	7.09899	+	12.2958i	0.242497	+	0.420017i	0.961425	−	0.275068i	$-0.0887003\pi$
$857$	7.09899	+	12.2958i	0.242497	+	0.420017i	−0.718928	+	0.695084i	$0.755367\pi$
$858$	10.2053	+	28.9614i	0.348404	+	0.988726i
$859$	−41.7926	−	24.1290i	−1.42595	−	0.823270i	−0.429148	−	0.903234i	$-0.641186\pi$
$859$	−41.7926	−	24.1290i	−1.42595	−	0.823270i	−0.996798	+	0.0799637i	$0.974520\pi$
$860$	−7.52208	+	2.01553i	−0.256501	+	0.0687292i
$861$	−9.37749	+	5.00814i	−0.319584	+	0.170677i
$862$	4.33655	−	2.50371i	0.147703	−	0.0852766i
$863$	10.6866	+	39.8830i	0.363776	+	1.35763i	0.869072	+	0.494686i	$0.164717\pi$
$863$	10.6866	+	39.8830i	0.363776	+	1.35763i	−0.505296	+	0.862946i	$0.668617\pi$
$864$	−2.25647	+	0.604618i	−0.0767666	+	0.0205695i
$865$	−9.04481	+	2.42355i	−0.307533	+	0.0824032i
$866$	−4.30068	−	16.0503i	−0.146143	−	0.545413i
$867$	−1.77550	+	1.02509i	−0.0602992	+	0.0348138i
$868$	0.751883	+	0.467917i	0.0255206	+	0.0158821i
$869$	−4.56143	+	1.22223i	−0.154736	+	0.0414613i
$870$	6.85040	+	3.95508i	0.232250	+	0.134090i
$871$	3.95666	+	5.77611i	0.134066	+	0.195716i
$872$	10.5784	+	18.3223i	0.358228	+	0.620470i
$873$	−0.575652	+	2.14836i	−0.0194829	+	0.0727110i
$874$	16.2861	+	9.40279i	0.550886	+	0.318054i
$875$	−10.9906	−	6.83977i	−0.371552	−	0.231226i
$876$	−4.27137	+	4.27137i	−0.144316	+	0.144316i
$877$	13.9970	−	13.9970i	0.472644	−	0.472644i	−0.430125	−	0.902769i	$-0.641531\pi$
$877$	13.9970	−	13.9970i	0.472644	−	0.472644i	0.902769	+	0.430125i	$0.141531\pi$
$878$	−5.86201	−	21.8773i	−0.197833	−	0.738324i
$879$	0.0228127	−	0.0851383i	0.000769455	−	0.00287164i
$880$		−	73.5623i		−	2.47979i
$881$	−4.58892	+	7.94824i	−0.154605	+	0.267783i	−0.932915	−	0.360097i	$-0.882744\pi$
$881$	−4.58892	+	7.94824i	−0.154605	+	0.267783i	0.778310	+	0.627880i	$0.216077\pi$
$882$	−10.6805	+	2.11669i	−0.359630	+	0.0712726i
$883$			2.23790i			0.0753113i	0.999291	+	0.0376556i	$0.0119890\pi$
$883$			2.23790i			0.0753113i	−0.999291	+	0.0376556i	$0.988011\pi$
$884$	2.19376	+	6.22562i	0.0737842	+	0.209390i
$885$	18.2219	−	10.5204i	0.612523	−	0.353640i
$886$	5.49808	−	5.49808i	0.184711	−	0.184711i
$887$	−8.83171	+	5.09899i	−0.296540	+	0.171207i	−0.640887	−	0.767635i	$-0.721433\pi$
$887$	−8.83171	+	5.09899i	−0.296540	+	0.171207i	0.344348	+	0.938842i	$0.388100\pi$
$888$	−6.71649	−	11.6333i	−0.225391	−	0.390388i
$889$	−2.67880	+	8.81969i	−0.0898442	+	0.295803i
$890$	−25.8039	−	6.91414i	−0.864949	−	0.231762i
$891$	3.87160	+	3.87160i	0.129704	+	0.129704i
$892$	−5.90405	−	1.58199i	−0.197682	−	0.0529688i
$893$	−6.37100	+	11.0349i	−0.213197	+	0.369269i
$894$	−11.1179	−	19.2567i	−0.371838	−	0.644042i
$895$	15.7873	+	58.9190i	0.527711	+	1.96944i
$896$	35.7674	+	1.18347i	1.19491	+	0.0395368i
$897$	−28.4707	+	10.0324i	−0.950608	+	0.334972i
$898$	−20.7147	+	35.8790i	−0.691259	+	1.19730i
$899$	−0.995937	−	0.995937i	−0.0332164	−	0.0332164i
$900$	−1.38496			−0.0461654
$901$	−1.21519			−0.0404839
$902$	24.1978	+	24.1978i	0.805697	+	0.805697i
$903$	−12.4469	+	11.6496i	−0.414208	+	0.387676i
$904$	8.67160	−	32.3628i	0.288413	−	1.07637i
$905$	−51.5480	+	13.8123i	−1.71351	+	0.459135i
$906$	0.0277071	+	0.0159967i	0.000920507	+	0.000531455i
$907$			40.9715i			1.36044i	0.733009	+	0.680219i	$0.238115\pi$
$907$			40.9715i			1.36044i	−0.733009	+	0.680219i	$0.761885\pi$
$908$	7.26295	+	1.94610i	0.241030	+	0.0645837i
$909$	15.8444			0.525525
$910$	−42.7118	+	1.87691i	−1.41588	+	0.0622191i
$911$	45.1869			1.49711			0.748554	−	0.663074i	$-0.230748\pi$
$911$	45.1869			1.49711			0.748554	+	0.663074i	$0.230748\pi$
$912$	6.50417	+	1.74279i	0.215375	+	0.0577094i
$913$		−	33.2610i		−	1.10078i
$914$	−16.8644	−	9.73665i	−0.557824	−	0.322060i
$915$	13.1986	−	3.53656i	0.436333	−	0.116915i
$916$	0.743381	−	2.77433i	0.0245620	−	0.0916666i
$917$	4.45296	−	14.6609i	0.147050	−	0.484147i
$918$	4.80057	+	4.80057i	0.158442	+	0.158442i
$919$	20.8241			0.686925			0.343463	−	0.939166i	$-0.388400\pi$
$919$	20.8241			0.686925			0.343463	+	0.939166i	$0.388400\pi$
$920$	59.3058			1.95525
$921$	−7.58728	−	7.58728i	−0.250010	−	0.250010i
$922$	7.76155	−	13.4434i	0.255613	−	0.442735i
$923$	18.2968	−	38.2078i	0.602248	−	1.25762i
$924$	2.86242	+	5.35973i	0.0941667	+	0.176322i
$925$	−4.66941	−	17.4265i	−0.153529	−	0.572979i
$926$	9.75824	+	16.9018i	0.320676	+	0.555427i
$927$	−5.32654	+	9.22583i	−0.174946	+	0.303016i
$928$	3.98261	+	1.06714i	0.130736	+	0.0350305i
$929$	39.7163	+	39.7163i	1.30305	+	1.30305i	0.926325	+	0.376725i	$0.122950\pi$
$929$	39.7163	+	39.7163i	1.30305	+	1.30305i	0.376725	+	0.926325i	$0.377050\pi$
$930$	3.45460	+	0.925657i	0.113281	+	0.0303535i
$931$	9.56971	+	3.25597i	0.313635	+	0.106710i
$932$	−1.63281	−	2.82811i	−0.0534844	−	0.0926377i
$933$	26.1796	−	15.1148i	0.857082	−	0.494837i
$934$	16.1380	−	16.1380i	0.528051	−	0.528051i
$935$	−59.6313	+	34.4281i	−1.95015	+	1.12592i
$936$	−7.31297	+	5.00941i	−0.239032	+	0.163738i
$937$		−	12.6449i		−	0.413092i	−0.978437	−	0.206546i	$-0.933778\pi$
$937$		−	12.6449i		−	0.413092i	0.978437	−	0.206546i	$-0.0662223\pi$
$938$	5.46072	+	5.83446i	0.178299	+	0.190502i
$939$	14.4275	−	24.9891i	0.470823	−	0.815489i
$940$		−	10.6639i		−	0.347818i
$941$	−0.310180	+	1.15761i	−0.0101116	+	0.0377369i	−0.970797	−	0.239901i	$-0.922885\pi$
$941$	−0.310180	+	1.15761i	−0.0101116	+	0.0377369i	0.960686	+	0.277638i	$0.0895516\pi$
$942$	2.44784	+	9.13548i	0.0797551	+	0.297650i
$943$	−23.7877	+	23.7877i	−0.774636	+	0.774636i
$944$	24.0781	−	24.0781i	0.783674	−	0.783674i
$945$	−6.72432	+	3.59119i	−0.218742	+	0.116821i
$946$	47.5252	+	27.4387i	1.54518	+	0.892108i
$947$	8.25863	−	30.8216i	0.268370	−	1.00157i	−0.691786	−	0.722103i	$-0.743176\pi$
$947$	8.25863	−	30.8216i	0.268370	−	1.00157i	0.960156	−	0.279466i	$-0.0901575\pi$
$948$	0.180883	+	0.313299i	0.00587481	+	0.0101755i
$949$	−22.4268	+	46.8321i	−0.728006	+	1.52023i
$950$	6.42297	+	3.70830i	0.208389	+	0.120313i
$951$	−16.2082	+	4.34297i	−0.525587	+	0.140831i
$952$	−13.3742	−	25.0425i	−0.433460	−	0.811631i
$953$	9.16224	−	5.28982i	0.296794	−	0.171354i	−0.344208	−	0.938894i	$-0.611852\pi$
$953$	9.16224	−	5.28982i	0.296794	−	0.171354i	0.641002	+	0.767539i	$0.278519\pi$
$954$	0.112085	+	0.418309i	0.00362890	+	0.0135432i
$955$	−76.3075	+	20.4465i	−2.46925	+	0.661634i
$956$	−1.27446	+	0.341490i	−0.0412189	+	0.0110446i
$957$	−2.50116	−	9.33445i	−0.0808509	−	0.301740i
$958$	−18.6092	+	10.7440i	−0.601236	+	0.347124i
$959$	4.27204	+	7.99918i	0.137951	+	0.258307i
$960$	15.8423	−	4.24492i	0.511307	−	0.137004i
$961$	26.2953	+	15.1816i	0.848235	+	0.489729i
$962$	23.2705	+	19.9373i	0.750270	+	0.642803i
$963$	−7.27563	−	12.6018i	−0.234454	−	0.406086i
$964$	0.974822	−	3.63808i	0.0313969	−	0.117175i
$965$	−47.5878	−	27.4748i	−1.53190	−	0.884445i
$966$	−30.3921	+	16.2312i	−0.977849	+	0.522230i
$967$	23.9761	−	23.9761i	0.771021	−	0.771021i	−0.207264	−	0.978285i	$-0.566456\pi$
$967$	23.9761	−	23.9761i	0.771021	−	0.771021i	0.978285	+	0.207264i	$0.0664560\pi$
$968$	−32.9926	+	32.9926i	−1.06042	+	1.06042i
$969$	−1.63129	−	6.08807i	−0.0524047	−	0.195577i
$970$	−2.57992	+	9.62838i	−0.0828362	+	0.309149i
$971$			24.9712i			0.801364i	0.916217	+	0.400682i	$0.131227\pi$
$971$			24.9712i			0.801364i	−0.916217	+	0.400682i	$0.868773\pi$
$972$	0.209723	−	0.363252i	0.00672688	−	0.0116513i
$973$	33.7319	+	36.0405i	1.08139	+	1.15540i
$974$		−	46.7606i		−	1.49831i
$975$	−11.2284	+	3.95661i	−0.359595	+	0.126713i
$976$	19.1509	−	11.0568i	0.613005	−	0.353919i
$977$	−11.9691	+	11.9691i	−0.382925	+	0.382925i	−0.872155	−	0.489230i	$-0.837278\pi$
$977$	−11.9691	+	11.9691i	−0.382925	+	0.382925i	0.489230	+	0.872155i	$0.337278\pi$
$978$	19.1858	−	11.0769i	0.613493	−	0.354201i
$979$	16.3182	+	28.2639i	0.521531	+	0.903318i
$980$	−8.29846	+	1.64461i	−0.265085	+	0.0525353i
$981$	−8.31237	−	2.22729i	−0.265394	−	0.0711120i
$982$	−34.6497	−	34.6497i	−1.10572	−	1.10572i
$983$	−26.7546	−	7.16888i	−0.853340	−	0.228652i	−0.194470	−	0.980908i	$-0.562299\pi$
$983$	−26.7546	−	7.16888i	−0.853340	−	0.228652i	−0.658870	+	0.752257i	$0.728965\pi$
$984$	−4.93928	+	8.55508i	−0.157458	+	0.272726i
$985$	6.68811	+	11.5841i	0.213101	+	0.369101i
$986$	−3.10129	−	11.5742i	−0.0987653	−	0.368597i
$987$	−10.9977	−	20.5926i	−0.350060	−	0.655470i
$988$	−2.17744	+	0.167976i	−0.0692737	+	0.00534403i
$989$	−26.9737	+	46.7199i	−0.857715	+	1.48561i
$990$	17.3515	+	17.3515i	0.551467	+	0.551467i
$991$	12.3125			0.391120			0.195560	−	0.980692i	$-0.437348\pi$
$991$	12.3125			0.391120			0.195560	+	0.980692i	$0.437348\pi$
$992$	1.86420			0.0591885
$993$	−4.44970	−	4.44970i	−0.141207	−	0.141207i
$994$	14.0523	−	46.2657i	0.445711	−	1.46746i
$995$	−0.333433	+	1.24439i	−0.0105706	+	0.0394498i
$996$	−2.46122	+	0.659482i	−0.0779868	+	0.0208965i
$997$	10.8856	+	6.28478i	0.344749	+	0.199041i	0.662370	−	0.749177i	$-0.269551\pi$
$997$	10.8856	+	6.28478i	0.344749	+	0.199041i	−0.317621	+	0.948218i	$0.602884\pi$
$998$		−	36.3733i		−	1.15138i
$999$	5.27775	+	1.41417i	0.166981	+	0.0447423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.19.3	yes	36
3.2	odd	2		819.2.gh.c.19.7		36
7.3	odd	6		273.2.bt.a.136.7	✓	36
13.11	odd	12		273.2.bt.a.271.7	yes	36
21.17	even	6		819.2.et.c.136.3		36
39.11	even	12		819.2.et.c.271.3		36
91.24	even	12	inner	273.2.cg.a.115.3	yes	36
273.206	odd	12		819.2.gh.c.388.7		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.7	✓	36	7.3	odd	6
273.2.bt.a.271.7	yes	36	13.11	odd	12
273.2.cg.a.19.3	yes	36	1.1	even	1	trivial
273.2.cg.a.115.3	yes	36	91.24	even	12	inner
819.2.et.c.136.3		36	21.17	even	6
819.2.et.c.271.3		36	39.11	even	12
819.2.gh.c.19.7		36	3.2	odd	2
819.2.gh.c.388.7		36	273.206	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50246 - 0.402582i) q^{2} -1.00000i q^{3} +(0.363252 + 0.209723i) q^{4} +(2.78312 - 0.745735i) q^{5} +(-0.402582 + 1.50246i) q^{6} +(0.599883 + 2.57685i) q^{7} +(1.73841 + 1.73841i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.50246 - 0.402582i) q^{2} -1.00000i q^{3} +(0.363252 + 0.209723i) q^{4} +(2.78312 - 0.745735i) q^{5} +(-0.402582 + 1.50246i) q^{6} +(0.599883 + 2.57685i) q^{7} +(1.73841 + 1.73841i) q^{8} -1.00000 q^{9} -4.48173 q^{10} +(3.87160 + 3.87160i) q^{11} +(0.209723 - 0.363252i) q^{12} +(0.662549 - 3.54415i) q^{13} +(0.136094 - 4.11310i) q^{14} +(-0.745735 - 2.78312i) q^{15} +(-2.33148 - 4.03824i) q^{16} +(-2.18233 + 3.77990i) q^{17} +(1.50246 + 0.402582i) q^{18} +(-1.02111 - 1.02111i) q^{19} +(1.16737 + 0.312796i) q^{20} +(2.57685 - 0.599883i) q^{21} +(-4.25828 - 7.37555i) q^{22} +(7.25058 - 4.18612i) q^{23} +(1.73841 - 1.73841i) q^{24} +(2.85951 - 1.65094i) q^{25} +(-2.42226 + 5.05821i) q^{26} +1.00000i q^{27} +(-0.322517 + 1.06185i) q^{28} +(0.882488 - 1.52851i) q^{29} +4.48173i q^{30} +(0.206540 - 0.770818i) q^{31} +(0.604618 + 2.25647i) q^{32} +(3.87160 - 3.87160i) q^{33} +(4.80057 - 4.80057i) q^{34} +(3.59119 + 6.72432i) q^{35} +(-0.363252 - 0.209723i) q^{36} +(1.41417 - 5.27775i) q^{37} +(1.12309 + 1.94525i) q^{38} +(-3.54415 - 0.662549i) q^{39} +(6.13459 + 3.54181i) q^{40} +(-3.88124 + 1.03997i) q^{41} +(-4.11310 - 0.136094i) q^{42} +(-5.58033 + 3.22180i) q^{43} +(0.594400 + 2.21833i) q^{44} +(-2.78312 + 0.745735i) q^{45} +(-12.5789 + 3.37051i) q^{46} +(-2.28374 - 8.52304i) q^{47} +(-4.03824 + 2.33148i) q^{48} +(-6.28028 + 3.09161i) q^{49} +(-4.96092 + 1.32927i) q^{50} +(3.77990 + 2.18233i) q^{51} +(0.983964 - 1.14847i) q^{52} +(0.139208 + 0.241116i) q^{53} +(0.402582 - 1.50246i) q^{54} +(13.6623 + 7.88795i) q^{55} +(-3.43677 + 5.52246i) q^{56} +(-1.02111 + 1.02111i) q^{57} +(-1.94125 + 1.94125i) q^{58} +(1.89004 + 7.05373i) q^{59} +(0.312796 - 1.16737i) q^{60} +4.74239i q^{61} +(-0.620634 + 1.07497i) q^{62} +(-0.599883 - 2.57685i) q^{63} +5.69226i q^{64} +(-0.799046 - 10.3579i) q^{65} +(-7.37555 + 4.25828i) q^{66} +(-1.37307 + 1.37307i) q^{67} +(-1.58547 + 0.915370i) q^{68} +(-4.18612 - 7.25058i) q^{69} +(-2.68852 - 11.5487i) q^{70} +(11.3490 + 3.04095i) q^{71} +(-1.73841 - 1.73841i) q^{72} +(-13.9107 - 3.72736i) q^{73} +(-4.24945 + 7.36027i) q^{74} +(-1.65094 - 2.85951i) q^{75} +(-0.156769 - 0.585069i) q^{76} +(-7.65402 + 12.2990i) q^{77} +(5.05821 + 2.42226i) q^{78} +(-0.431242 + 0.746933i) q^{79} +(-9.50024 - 9.50024i) q^{80} +1.00000 q^{81} +6.25006 q^{82} +(-4.29551 - 4.29551i) q^{83} +(1.06185 + 0.322517i) q^{84} +(-3.25487 + 12.1473i) q^{85} +(9.68124 - 2.59408i) q^{86} +(-1.52851 - 0.882488i) q^{87} +13.4609i q^{88} +(5.75757 + 1.54274i) q^{89} +4.48173 q^{90} +(9.53019 - 0.418792i) q^{91} +3.51171 q^{92} +(-0.770818 - 0.206540i) q^{93} +13.7249i q^{94} +(-3.60334 - 2.08039i) q^{95} +(2.25647 - 0.604618i) q^{96} +(0.575652 - 2.14836i) q^{97} +(10.6805 - 2.11669i) q^{98} +(-3.87160 - 3.87160i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

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