LMFDB - Embedded newform 273.2.g.a.272.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(272,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("273.272");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.g (of order $2$, degree $1$, 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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			272.13
Character	$\chi$	$=$	273.272
Dual form			273.2.g.a.272.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.305902 q^{2} +(-1.47187 - 0.913018i) q^{3} -1.90642 q^{4} +2.05385i q^{5} +(0.450247 + 0.279294i) q^{6} +(-0.946976 - 2.47047i) q^{7} +1.19498 q^{8} +(1.33280 + 2.68769i) q^{9} +O(q^{10})$	\(q-0.305902 q^{2} +(-1.47187 - 0.913018i) q^{3} -1.90642 q^{4} +2.05385i q^{5} +(0.450247 + 0.279294i) q^{6} +(-0.946976 - 2.47047i) q^{7} +1.19498 q^{8} +(1.33280 + 2.68769i) q^{9} -0.628276i q^{10} +5.03717 q^{11} +(2.80601 + 1.74060i) q^{12} +(1.75886 + 3.14745i) q^{13} +(0.289682 + 0.755722i) q^{14} +(1.87520 - 3.02300i) q^{15} +3.44730 q^{16} -3.24764 q^{17} +(-0.407705 - 0.822167i) q^{18} +4.21149 q^{19} -3.91551i q^{20} +(-0.861760 + 4.50082i) q^{21} -1.54088 q^{22} +5.65284i q^{23} +(-1.75886 - 1.09104i) q^{24} +0.781707 q^{25} +(-0.538037 - 0.962809i) q^{26} +(0.492200 - 5.17279i) q^{27} +(1.80534 + 4.70977i) q^{28} -5.12387i q^{29} +(-0.573627 + 0.924739i) q^{30} +5.11198 q^{31} -3.44450 q^{32} +(-7.41405 - 4.59902i) q^{33} +0.993458 q^{34} +(5.07398 - 1.94495i) q^{35} +(-2.54088 - 5.12387i) q^{36} +4.85607i q^{37} -1.28830 q^{38} +(0.284868 - 6.23850i) q^{39} +2.45431i q^{40} +3.35692i q^{41} +(0.263614 - 1.37681i) q^{42} -2.44730 q^{43} -9.60298 q^{44} +(-5.52010 + 2.73736i) q^{45} -1.72921i q^{46} +7.14420i q^{47} +(-5.07398 - 3.14745i) q^{48} +(-5.20647 + 4.67896i) q^{49} -0.239125 q^{50} +(4.78010 + 2.96515i) q^{51} +(-3.35313 - 6.00037i) q^{52} +3.08346i q^{53} +(-0.150565 + 1.58236i) q^{54} +10.3456i q^{55} +(-1.13162 - 2.95217i) q^{56} +(-6.19876 - 3.84516i) q^{57} +1.56740i q^{58} -12.5550i q^{59} +(-3.57493 + 5.76311i) q^{60} -3.48120i q^{61} -1.56376 q^{62} +(5.37773 - 5.83781i) q^{63} -5.84093 q^{64} +(-6.46438 + 3.61242i) q^{65} +(2.26797 + 1.40685i) q^{66} +7.77520i q^{67} +6.19138 q^{68} +(5.16114 - 8.32024i) q^{69} +(-1.55214 + 0.594962i) q^{70} +6.61172 q^{71} +(1.59267 + 3.21173i) q^{72} +15.1278 q^{73} -1.48548i q^{74} +(-1.15057 - 0.713712i) q^{75} -8.02888 q^{76} +(-4.77008 - 12.4442i) q^{77} +(-0.0871417 + 1.90837i) q^{78} +2.15279 q^{79} +7.08024i q^{80} +(-5.44730 + 7.16428i) q^{81} -1.02689i q^{82} -0.936674i q^{83} +(1.64288 - 8.58047i) q^{84} -6.67016i q^{85} +0.748634 q^{86} +(-4.67818 + 7.54166i) q^{87} +6.01932 q^{88} -11.5084i q^{89} +(1.68861 - 0.837364i) q^{90} +(6.11009 - 7.32576i) q^{91} -10.7767i q^{92} +(-7.52417 - 4.66733i) q^{93} -2.18542i q^{94} +8.64976i q^{95} +(5.06985 + 3.14489i) q^{96} -11.4241 q^{97} +(1.59267 - 1.43130i) q^{98} +(6.71352 + 13.5383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 16 q^{16} - 16 q^{25} + 16 q^{30} - 32 q^{36} - 48 q^{42} + 48 q^{43} - 32 q^{49} - 16 q^{51} - 80 q^{64} + 32 q^{78} + 80 q^{79} - 48 q^{81} - 96 q^{88} + 32 q^{91}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^16 - 16 * q^25 + 16 * q^30 - 32 * q^36 - 48 * q^42 + 48 * q^43 - 32 * q^49 - 16 * q^51 - 80 * q^64 + 32 * q^78 + 80 * q^79 - 48 * q^81 - 96 * q^88 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.305902			−0.216305			−0.108153	−	0.994134i	$-0.534493\pi$
$2$	−0.305902			−0.216305			−0.108153	+	0.994134i	$0.534493\pi$
$3$	−1.47187	−	0.913018i	−0.849784	−	0.527131i
$3$	−1.47187	−	0.913018i	−0.849784	−	0.527131i
$4$	−1.90642			−0.953212
$5$			2.05385i			0.918509i	0.888305	+	0.459254i	$0.151883\pi$
$5$			2.05385i			0.918509i	−0.888305	+	0.459254i	$0.848117\pi$
$6$	0.450247	+	0.279294i	0.183813	+	0.114021i
$7$	−0.946976	−	2.47047i	−0.357923	−	0.933751i
$7$	−0.946976	−	2.47047i	−0.357923	−	0.933751i
$8$	1.19498			0.422490
$9$	1.33280	+	2.68769i	0.444266	+	0.895895i
$10$		−	0.628276i		−	0.198678i
$11$	5.03717			1.51876			0.759381	−	0.650646i	$-0.225502\pi$
$11$	5.03717			1.51876			0.759381	+	0.650646i	$0.225502\pi$
$12$	2.80601	+	1.74060i	0.810024	+	0.502468i
$13$	1.75886	+	3.14745i	0.487819	+	0.872945i
$13$	1.75886	+	3.14745i	0.487819	+	0.872945i
$14$	0.289682	+	0.755722i	0.0774206	+	0.201975i
$15$	1.87520	−	3.02300i	0.484175	−	0.780534i
$16$	3.44730			0.861825
$17$	−3.24764			−0.787668			−0.393834	−	0.919182i	$-0.628852\pi$
$17$	−3.24764			−0.787668			−0.393834	+	0.919182i	$0.628852\pi$
$18$	−0.407705	−	0.822167i	−0.0960970	−	0.193787i
$19$	4.21149			0.966182			0.483091	−	0.875570i	$-0.339514\pi$
$19$	4.21149			0.966182			0.483091	+	0.875570i	$0.339514\pi$
$20$		−	3.91551i		−	0.875534i
$21$	−0.861760	+	4.50082i	−0.188052	+	0.982159i
$22$	−1.54088			−0.328516
$23$			5.65284i			1.17870i	0.807879	+	0.589349i	$0.200616\pi$
$23$			5.65284i			1.17870i	−0.807879	+	0.589349i	$0.799384\pi$
$24$	−1.75886	−	1.09104i	−0.359025	−	0.222707i
$25$	0.781707			0.156341
$26$	−0.538037	−	0.962809i	−0.105518	−	0.188822i
$27$	0.492200	−	5.17279i	0.0947240	−	0.995504i
$28$	1.80534	+	4.70977i	0.341177	+	0.890063i
$29$		−	5.12387i		−	0.951478i	−0.879586	−	0.475739i	$-0.842181\pi$
$29$		−	5.12387i		−	0.951478i	0.879586	−	0.475739i	$-0.157819\pi$
$30$	−0.573627	+	0.924739i	−0.104729	+	0.168834i
$31$	5.11198			0.918139			0.459070	−	0.888400i	$-0.348183\pi$
$31$	5.11198			0.918139			0.459070	+	0.888400i	$0.348183\pi$
$32$	−3.44450			−0.608907
$33$	−7.41405	−	4.59902i	−1.29062	−	0.800587i
$34$	0.993458			0.170377
$35$	5.07398	−	1.94495i	0.857659	−	0.328756i
$36$	−2.54088	−	5.12387i	−0.423480	−	0.853978i
$37$			4.85607i			0.798333i	0.916879	+	0.399166i	$0.130700\pi$
$37$			4.85607i			0.798333i	−0.916879	+	0.399166i	$0.869300\pi$
$38$	−1.28830			−0.208990
$39$	0.284868	−	6.23850i	0.0456155	−	0.998959i
$40$			2.45431i			0.388061i
$41$			3.35692i			0.524263i	0.965032	+	0.262131i	$0.0844254\pi$
$41$			3.35692i			0.524263i	−0.965032	+	0.262131i	$0.915575\pi$
$42$	0.263614	−	1.37681i	0.0406765	−	0.212446i
$43$	−2.44730			−0.373210			−0.186605	−	0.982435i	$-0.559748\pi$
$43$	−2.44730			−0.373210			−0.186605	+	0.982435i	$0.559748\pi$
$44$	−9.60298			−1.44770
$45$	−5.52010	+	2.73736i	−0.822888	+	0.408062i
$46$		−	1.72921i		−	0.254958i
$47$			7.14420i			1.04209i	0.853530	+	0.521044i	$0.174457\pi$
$47$			7.14420i			1.04209i	−0.853530	+	0.521044i	$0.825543\pi$
$48$	−5.07398	−	3.14745i	−0.732365	−	0.454295i
$49$	−5.20647	+	4.67896i	−0.743782	+	0.668423i
$50$	−0.239125			−0.0338174
$51$	4.78010	+	2.96515i	0.669348	+	0.415204i
$52$	−3.35313	−	6.00037i	−0.464995	−	0.832102i
$53$			3.08346i			0.423545i	0.977319	+	0.211773i	$0.0679236\pi$
$53$			3.08346i			0.423545i	−0.977319	+	0.211773i	$0.932076\pi$
$54$	−0.150565	+	1.58236i	−0.0204893	+	0.215333i
$55$			10.3456i			1.39500i
$56$	−1.13162	−	2.95217i	−0.151219	−	0.394500i
$57$	−6.19876	−	3.84516i	−0.821046	−	0.509304i
$58$			1.56740i			0.205810i
$59$		−	12.5550i		−	1.63452i	−0.576271	−	0.817258i	$-0.695493\pi$
$59$		−	12.5550i		−	1.63452i	0.576271	−	0.817258i	$-0.304507\pi$
$60$	−3.57493	+	5.76311i	−0.461521	+	0.744015i
$61$		−	3.48120i		−	0.445722i	−0.974850	−	0.222861i	$-0.928460\pi$
$61$		−	3.48120i		−	0.445722i	0.974850	−	0.222861i	$-0.0715396\pi$
$62$	−1.56376			−0.198598
$63$	5.37773	−	5.83781i	0.677530	−	0.735495i
$64$	−5.84093			−0.730116
$65$	−6.46438	+	3.61242i	−0.801808	+	0.448066i
$66$	2.26797	+	1.40685i	0.279168	+	0.173171i
$67$			7.77520i			0.949892i	0.880015	+	0.474946i	$0.157532\pi$
$67$			7.77520i			0.949892i	−0.880015	+	0.474946i	$0.842468\pi$
$68$	6.19138			0.750815
$69$	5.16114	−	8.32024i	0.621328	−	1.00164i
$70$	−1.55214	+	0.594962i	−0.185516	+	0.0711116i
$71$	6.61172			0.784667			0.392333	−	0.919823i	$-0.371668\pi$
$71$	6.61172			0.784667			0.392333	+	0.919823i	$0.371668\pi$
$72$	1.59267	+	3.21173i	0.187698	+	0.378506i
$73$	15.1278			1.77057			0.885286	−	0.465046i	$-0.153962\pi$
$73$	15.1278			1.77057			0.885286	+	0.465046i	$0.153962\pi$
$74$		−	1.48548i		−	0.172683i
$75$	−1.15057	−	0.713712i	−0.132856	−	0.0824124i
$76$	−8.02888			−0.920976
$77$	−4.77008	−	12.4442i	−0.543601	−	1.41815i
$78$	−0.0871417	+	1.90837i	−0.00986686	+	0.216080i
$79$	2.15279			0.242208			0.121104	−	0.992640i	$-0.461356\pi$
$79$	2.15279			0.242208			0.121104	+	0.992640i	$0.461356\pi$
$80$			7.08024i			0.791594i
$81$	−5.44730	+	7.16428i	−0.605256	+	0.796031i
$82$		−	1.02689i		−	0.113401i
$83$		−	0.936674i		−	0.102813i	−0.998678	−	0.0514067i	$-0.983630\pi$
$83$		−	0.936674i		−	0.102813i	0.998678	−	0.0514067i	$-0.0163705\pi$
$84$	1.64288	−	8.58047i	0.179253	−	0.936206i
$85$		−	6.67016i		−	0.723480i
$86$	0.748634			0.0807272
$87$	−4.67818	+	7.54166i	−0.501554	+	0.808551i
$88$	6.01932			0.641662
$89$		−	11.5084i		−	1.21988i	−0.792446	−	0.609941i	$-0.791193\pi$
$89$		−	11.5084i		−	1.21988i	0.792446	−	0.609941i	$-0.208807\pi$
$90$	1.68861	−	0.837364i	0.177995	−	0.0882659i
$91$	6.11009	−	7.32576i	0.640511	−	0.767949i
$92$		−	10.7767i		−	1.12355i
$93$	−7.52417	−	4.66733i	−0.780220	−	0.483980i
$94$		−	2.18542i		−	0.225409i
$95$			8.64976i			0.887447i
$96$	5.06985	+	3.14489i	0.517439	+	0.320974i
$97$	−11.4241			−1.15995			−0.579973	−	0.814636i	$-0.696937\pi$
$97$	−11.4241			−1.15995			−0.579973	+	0.814636i	$0.696937\pi$
$98$	1.59267	−	1.43130i	0.160884	−	0.144583i
$99$	6.71352	+	13.5383i	0.674734	+	1.36065i
$100$	−1.49026			−0.149026
$101$	13.5884			1.35210			0.676048	−	0.736857i	$-0.263691\pi$
$101$	13.5884			1.35210			0.676048	+	0.736857i	$0.263691\pi$
$102$	−1.46224	−	0.907045i	−0.144783	−	0.0898108i
$103$		−	4.90862i		−	0.483661i	−0.970319	−	0.241830i	$-0.922252\pi$
$103$		−	4.90862i		−	0.483661i	0.970319	−	0.241830i	$-0.0777478\pi$
$104$	2.10180	+	3.76114i	0.206099	+	0.368810i
$105$	−9.24400	−	1.76993i	−0.902122	−	0.172727i
$106$		−	0.943234i		−	0.0916150i
$107$			7.75382i			0.749590i	0.927108	+	0.374795i	$0.122287\pi$
$107$			7.75382i			0.749590i	−0.927108	+	0.374795i	$0.877713\pi$
$108$	−0.938343	+	9.86153i	−0.0902921	+	0.948926i
$109$			7.69033i			0.736600i	0.929707	+	0.368300i	$0.120060\pi$
$109$			7.69033i			0.736600i	−0.929707	+	0.368300i	$0.879940\pi$
$110$		−	3.16473i		−	0.301745i
$111$	4.43368	−	7.14750i	0.420826	−	0.678410i
$112$	−3.26451	−	8.51647i	−0.308467	−	0.804730i
$113$		−	0.251502i		−	0.0236593i	−0.999930	−	0.0118297i	$-0.996234\pi$
$113$		−	0.251502i		−	0.0236593i	0.999930	−	0.0118297i	$-0.00376559\pi$
$114$	1.89621	+	1.17624i	0.177596	+	0.110165i
$115$	−11.6101			−1.08264
$116$			9.76827i			0.906961i
$117$	−6.11515	+	8.92216i	−0.565346	+	0.824854i
$118$			3.84058i			0.353554i
$119$	3.07544	+	8.02320i	0.281925	+	0.735486i
$120$	2.24083	−	3.61242i	0.204559	−	0.329768i
$121$	14.3730			1.30664
$122$			1.06490i			0.0964119i
$123$	3.06493	−	4.94095i	0.276355	−	0.445510i
$124$	−9.74561			−0.875181
$125$			11.8747i			1.06211i
$126$	−1.64505	+	1.78580i	−0.146553	+	0.159091i
$127$	6.22901			0.552735			0.276368	−	0.961052i	$-0.410869\pi$
$127$	6.22901			0.552735			0.276368	+	0.961052i	$0.410869\pi$
$128$	8.67574			0.766835
$129$	3.60211	+	2.23443i	0.317148	+	0.196731i
$130$	1.97746	−	1.10505i	0.173435	−	0.0969190i
$131$	−19.0708			−1.66623			−0.833114	−	0.553102i	$-0.813444\pi$
$131$	−19.0708			−1.66623			−0.833114	+	0.553102i	$0.813444\pi$
$132$	14.1343	+	8.76769i	1.23024	+	0.763129i
$133$	−3.98818	−	10.4044i	−0.345819	−	0.902173i
$134$		−	2.37845i		−	0.205467i
$135$	10.6241	+	1.01090i	0.914379	+	0.0870048i
$136$	−3.88087			−0.332782
$137$	−1.85183			−0.158212			−0.0791062	−	0.996866i	$-0.525207\pi$
$137$	−1.85183			−0.158212			−0.0791062	+	0.996866i	$0.525207\pi$
$138$	−1.57880	+	2.54517i	−0.134396	+	0.216660i
$139$			5.72541i			0.485623i	0.970073	+	0.242811i	$0.0780696\pi$
$139$			5.72541i			0.485623i	−0.970073	+	0.242811i	$0.921930\pi$
$140$	−9.67315	+	3.70789i	−0.817531	+	0.313374i
$141$	6.52278	−	10.5153i	0.549317	−	0.885550i
$142$	−2.02254			−0.169727
$143$	8.85965	+	15.8542i	0.740881	+	1.32580i
$144$	4.59455	+	9.26526i	0.382880	+	0.772105i
$145$	10.5236			0.873941
$146$	−4.62761			−0.382984
$147$	11.9352	−	2.13321i	0.984400	−	0.175944i
$148$		−	9.25773i		−	0.760980i
$149$	0.129937			0.0106448			0.00532241	−	0.999986i	$-0.498306\pi$
$149$	0.129937			0.0106448			0.00532241	+	0.999986i	$0.498306\pi$
$150$	0.351961	+	0.218326i	0.0287375	+	0.0178262i
$151$		−	21.8890i		−	1.78130i	−0.454688	−	0.890651i	$-0.650249\pi$
$151$		−	21.8890i		−	1.78130i	0.454688	−	0.890651i	$-0.349751\pi$
$152$	5.03265			0.408202
$153$	−4.32844	−	8.72863i	−0.349934	−	0.705668i
$154$	1.45917	+	3.80670i	0.117584	+	0.306752i
$155$			10.4992i			0.843319i
$156$	−0.543080	+	11.8932i	−0.0434812	+	0.952220i
$157$		−	10.1747i		−	0.812030i	−0.913866	−	0.406015i	$-0.866918\pi$
$157$		−	10.1747i		−	0.812030i	0.913866	−	0.406015i	$-0.133082\pi$
$158$	−0.658543			−0.0523909
$159$	2.81525	−	4.53844i	0.223264	−	0.359922i
$160$		−	7.07448i		−	0.559287i
$161$	13.9652	−	5.35310i	1.10061	−	0.421883i
$162$	1.66634	−	2.19156i	0.130920	−	0.172186i
$163$		−	10.0437i		−	0.786684i	−0.919392	−	0.393342i	$-0.871319\pi$
$163$		−	10.0437i		−	0.786684i	0.919392	−	0.393342i	$-0.128681\pi$
$164$		−	6.39971i		−	0.499734i
$165$	9.44569	−	15.2273i	0.735346	−	1.18545i
$166$			0.286530i			0.0222391i
$167$		−	10.8675i		−	0.840953i	−0.907303	−	0.420477i	$-0.861863\pi$
$167$		−	10.8675i		−	0.840953i	0.907303	−	0.420477i	$-0.138137\pi$
$168$	−1.02979	+	5.37840i	−0.0794499	+	0.414952i
$169$	−6.81285	+	11.0718i	−0.524065	+	0.851678i
$170$			2.04041i			0.156492i
$171$	5.61306	+	11.3192i	0.429242	+	0.865597i
$172$	4.66560			0.355748
$173$	−2.91530			−0.221646			−0.110823	−	0.993840i	$-0.535349\pi$
$173$	−2.91530			−0.221646			−0.110823	+	0.993840i	$0.535349\pi$
$174$	1.43106	−	2.30701i	0.108489	−	0.174894i
$175$	−0.740257	−	1.93118i	−0.0559582	−	0.145984i
$176$	17.3646			1.30891
$177$	−11.4629	+	18.4793i	−0.861605	+	1.38899i
$178$			3.52042i			0.263867i
$179$		−	14.3632i		−	1.07355i	−0.843724	−	0.536777i	$-0.819642\pi$
$179$		−	14.3632i		−	1.07355i	0.843724	−	0.536777i	$-0.180358\pi$
$180$	10.5236	−	5.21858i	0.784386	−	0.388970i
$181$			21.5491i			1.60173i	0.598844	+	0.800866i	$0.295627\pi$
$181$			21.5491i			1.60173i	−0.598844	+	0.800866i	$0.704373\pi$
$182$	−1.86909	+	2.24096i	−0.138546	+	0.166111i
$183$	−3.17840	+	5.12387i	−0.234954	+	0.378767i
$184$			6.75504i			0.497988i
$185$	−9.97363			−0.733276
$186$	2.30166	+	1.42774i	0.168766	+	0.104687i
$187$	−16.3589			−1.19628
$188$		−	13.6199i		−	0.993331i
$189$	−13.2453	+	3.68254i	−0.963456	+	0.267865i
$190$		−	2.64598i		−	0.191959i
$191$			17.6376i			1.27621i	0.769950	+	0.638104i	$0.220281\pi$
$191$			17.6376i			1.27621i	−0.769950	+	0.638104i	$0.779719\pi$
$192$	8.59708	+	5.33287i	0.620441	+	0.384867i
$193$			9.25773i			0.666386i	0.942859	+	0.333193i	$0.108126\pi$
$193$			9.25773i			0.666386i	−0.942859	+	0.333193i	$0.891874\pi$
$194$	3.49466			0.250902
$195$	12.8129	+	0.585077i	0.917553	+	0.0418982i
$196$	9.92575	−	8.92008i	0.708982	−	0.637148i
$197$	−27.4590			−1.95637			−0.978186	−	0.207729i	$-0.933393\pi$
$197$	−27.4590			−1.95637			−0.978186	+	0.207729i	$0.933393\pi$
$198$	−2.05368	−	4.14139i	−0.145949	−	0.294316i
$199$			7.53188i			0.533921i	0.963707	+	0.266960i	$0.0860193\pi$
$199$			7.53188i			0.533921i	−0.963707	+	0.266960i	$0.913981\pi$
$200$	0.934125			0.0660526
$201$	7.09890	−	11.4441i	0.500718	−	0.807203i
$202$	−4.15671			−0.292465
$203$	−12.6584	+	4.85218i	−0.888444	+	0.340556i
$204$	−9.11290	−	5.65284i	−0.638030	−	0.395778i
$205$	−6.89460			−0.481540
$206$			1.50156i			0.104618i
$207$	−15.1930	+	7.53409i	−1.05599	+	0.523655i
$208$	6.06331	+	10.8502i	0.420415	+	0.752326i
$209$	21.2140			1.46740
$210$	2.82775	+	0.541423i	0.195134	+	0.0373617i
$211$	−6.51280			−0.448360			−0.224180	−	0.974548i	$-0.571970\pi$
$211$	−6.51280			−0.448360			−0.224180	+	0.974548i	$0.571970\pi$
$212$		−	5.87837i		−	0.403728i
$213$	−9.73159	−	6.03662i	−0.666797	−	0.413622i
$214$		−	2.37191i		−	0.162140i
$215$		−	5.02639i		−	0.342797i
$216$	0.588170	−	6.18139i	0.0400199	−	0.420590i
$217$	−4.84093	−	12.6290i	−0.328623	−	0.857313i
$218$		−	2.35248i		−	0.159330i
$219$	−22.2661	−	13.8119i	−1.50460	−	0.933324i
$220$		−	19.7231i		−	1.32973i
$221$	−5.71213	−	10.2218i	−0.384239	−	0.687591i
$222$	−1.35627	+	2.18643i	−0.0910268	+	0.146744i
$223$	−5.02772			−0.336681			−0.168340	−	0.985729i	$-0.553841\pi$
$223$	−5.02772			−0.336681			−0.168340	+	0.985729i	$0.553841\pi$
$224$	3.26186	+	8.50954i	0.217942	+	0.568568i
$225$	1.04186	+	2.10098i	0.0694571	+	0.140065i
$226$			0.0769350i			0.00511764i
$227$		−	10.0833i		−	0.669255i	−0.942350	−	0.334628i	$-0.891389\pi$
$227$		−	10.0833i		−	0.669255i	0.942350	−	0.334628i	$-0.108611\pi$
$228$	11.8175	+	7.33051i	0.782631	+	0.485475i
$229$	7.00449			0.462870			0.231435	−	0.972850i	$-0.425658\pi$
$229$	7.00449			0.462870			0.231435	+	0.972850i	$0.425658\pi$
$230$	3.55154			0.234182
$231$	−4.34083	+	22.6714i	−0.285606	+	1.49167i
$232$		−	6.12293i		−	0.401990i
$233$		−	23.2904i		−	1.52580i	−0.646514	−	0.762902i	$-0.723774\pi$
$233$		−	23.2904i		−	1.52580i	0.646514	−	0.762902i	$-0.276226\pi$
$234$	1.87063	−	2.72930i	0.122287	−	0.178420i
$235$	−14.6731			−0.957167
$236$			23.9351i			1.55804i
$237$	−3.16863	−	1.96554i	−0.205825	−	0.127676i
$238$	−0.940781	−	2.45431i	−0.0609818	−	0.159089i
$239$	9.99015			0.646209			0.323105	−	0.946363i	$-0.395273\pi$
$239$	9.99015			0.646209			0.323105	+	0.946363i	$0.395273\pi$
$240$	6.46438	−	10.4212i	0.417274	−	0.672684i
$241$	−6.73574			−0.433887			−0.216944	−	0.976184i	$-0.569609\pi$
$241$	−6.73574			−0.433887			−0.216944	+	0.976184i	$0.569609\pi$
$242$	−4.39674			−0.282633
$243$	14.5588	−	5.57140i	0.933949	−	0.357405i
$244$			6.63664i			0.424867i
$245$	−9.60987	−	10.6933i	−0.613952	−	0.683170i
$246$	−0.937566	+	1.51144i	−0.0597770	+	0.0963661i
$247$	7.40740	+	13.2554i	0.471322	+	0.843423i
$248$	6.10872			0.387904
$249$	−0.855200	+	1.37866i	−0.0541961	+	0.0873691i
$250$		−	3.63251i		−	0.229740i
$251$	−7.28687			−0.459943			−0.229971	−	0.973197i	$-0.573863\pi$
$251$	−7.28687			−0.459943			−0.229971	+	0.973197i	$0.573863\pi$
$252$	−10.2522	+	11.1293i	−0.645830	+	0.701083i
$253$			28.4743i			1.79016i
$254$	−1.90546			−0.119559
$255$	−6.08997	+	9.81760i	−0.381369	+	0.614802i
$256$	9.02793			0.564245
$257$	13.3387			0.832046			0.416023	−	0.909354i	$-0.363424\pi$
$257$	13.3387			0.832046			0.416023	+	0.909354i	$0.363424\pi$
$258$	−1.10189	−	0.683516i	−0.0686007	−	0.0425538i
$259$	11.9968	−	4.59858i	0.745444	−	0.285742i
$260$	12.3238	−	6.88681i	0.764293	−	0.427102i
$261$	13.7713	−	6.82908i	0.852425	−	0.422709i
$262$	5.83380			0.360413
$263$		−	17.9410i		−	1.10629i	−0.833086	−	0.553144i	$-0.813428\pi$
$263$		−	17.9410i		−	1.10629i	0.833086	−	0.553144i	$-0.186572\pi$
$264$	−8.85965	−	5.49575i	−0.545274	−	0.338240i
$265$	−6.33295			−0.389030
$266$	1.21999	+	3.18271i	0.0748024	+	0.195145i
$267$	−10.5073	+	16.9388i	−0.643038	+	1.03664i
$268$		−	14.8228i		−	0.905449i
$269$	−29.5227			−1.80003			−0.900015	−	0.435858i	$-0.856445\pi$
$269$	−29.5227			−1.80003			−0.900015	+	0.435858i	$0.856445\pi$
$270$	−3.24994	−	0.309237i	−0.197785	−	0.0188196i
$271$	−11.1865			−0.679531			−0.339765	−	0.940510i	$-0.610348\pi$
$271$	−11.1865			−0.679531			−0.339765	+	0.940510i	$0.610348\pi$
$272$	−11.1956			−0.678832
$273$	−15.6818	+	5.20395i	−0.949106	+	0.314957i
$274$	0.566478			0.0342222
$275$	3.93759			0.237445
$276$	−9.83932	+	15.8619i	−0.592258	+	0.954774i
$277$	−17.2968			−1.03927			−0.519633	−	0.854390i	$-0.673931\pi$
$277$	−17.2968			−1.03927			−0.519633	+	0.854390i	$0.673931\pi$
$278$		−	1.75141i		−	0.105043i
$279$	6.81324	+	13.7394i	0.407898	+	0.822556i
$280$	6.06331	−	2.32417i	0.362352	−	0.138896i
$281$	−14.6332			−0.872946			−0.436473	−	0.899717i	$-0.643773\pi$
$281$	−14.6332			−0.872946			−0.436473	+	0.899717i	$0.643773\pi$
$282$	−1.99533	+	3.21665i	−0.118820	+	0.191549i
$283$		−	22.6152i		−	1.34433i	−0.740399	−	0.672167i	$-0.765364\pi$
$283$		−	22.6152i		−	1.34433i	0.740399	−	0.672167i	$-0.234636\pi$
$284$	−12.6047			−0.747954
$285$	7.89738	−	12.7313i	0.467801	−	0.754138i
$286$	−2.71018	−	4.84983i	−0.160256	−	0.286776i
$287$	8.29318	−	3.17892i	0.489531	−	0.187646i
$288$	−4.59082	−	9.25773i	−0.270517	−	0.545517i
$289$	−6.45284			−0.379579
$290$	−3.21920			−0.189038
$291$	16.8148	+	10.4304i	0.985704	+	0.611443i
$292$	−28.8400			−1.68773
$293$		−	7.02886i		−	0.410631i	−0.978696	−	0.205315i	$-0.934178\pi$
$293$		−	7.02886i		−	0.410631i	0.978696	−	0.205315i	$-0.0658220\pi$
$294$	−3.65100	+	0.652553i	−0.212931	+	0.0380577i
$295$	25.7860			1.50132
$296$			5.80291i			0.337287i
$297$	2.47930	−	26.0562i	0.143863	−	1.51193i
$298$	−0.0397478			−0.00230253
$299$	−17.7920	+	9.94253i	−1.02894	+	0.574991i
$300$	2.19347	+	1.36064i	0.126640	+	0.0785565i
$301$	2.31754	+	6.04599i	0.133581	+	0.348485i
$302$			6.69588i			0.385305i
$303$	−20.0004	−	12.4065i	−1.14899	−	0.712732i
$304$	14.5183			0.832680
$305$	7.14985			0.409399
$306$	1.32408	+	2.67010i	0.0756925	+	0.152640i
$307$	5.56810			0.317788			0.158894	−	0.987296i	$-0.449207\pi$
$307$	5.56810			0.317788			0.158894	+	0.987296i	$0.449207\pi$
$308$	9.09379	+	23.7239i	0.518167	+	1.35179i
$309$	−4.48166	+	7.22485i	−0.254953	+	0.411007i
$310$		−	3.21173i		−	0.182414i
$311$	11.4078			0.646878			0.323439	−	0.946249i	$-0.395161\pi$
$311$	11.4078			0.646878			0.323439	+	0.946249i	$0.395161\pi$
$312$	0.340413	−	7.45489i	0.0192721	−	0.422050i
$313$			30.7773i			1.73964i	0.493374	+	0.869818i	$0.335764\pi$
$313$			30.7773i			1.73964i	−0.493374	+	0.869818i	$0.664236\pi$
$314$			3.11246i			0.175646i
$315$	11.9900	+	11.0450i	0.675559	+	0.622317i
$316$	−4.10414			−0.230876
$317$	−2.17223			−0.122005			−0.0610023	−	0.998138i	$-0.519430\pi$
$317$	−2.17223			−0.122005			−0.0610023	+	0.998138i	$0.519430\pi$
$318$	−0.861189	+	1.38832i	−0.0482931	+	0.0778530i
$319$		−	25.8098i		−	1.44507i
$320$		−	11.9964i		−	0.670618i
$321$	7.07937	−	11.4126i	0.395132	−	0.636989i
$322$	−4.27197	+	1.63752i	−0.238068	+	0.0912556i
$323$	−13.6774			−0.761030
$324$	10.3849	−	13.6582i	0.576937	−	0.758786i
$325$	1.37491	+	2.46038i	0.0762663	+	0.136477i
$326$			3.07239i			0.170164i
$327$	7.02140	−	11.3192i	0.388285	−	0.625951i
$328$			4.01146i			0.221496i
$329$	17.6495	−	6.76538i	0.973051	−	0.372988i
$330$	−2.88945	+	4.65807i	−0.159059	+	0.256418i
$331$			6.75504i			0.371290i	0.982617	+	0.185645i	$0.0594375\pi$
$331$			6.75504i			0.371290i	−0.982617	+	0.185645i	$0.940563\pi$
$332$			1.78570i			0.0980029i
$333$	−13.0516	+	6.47216i	−0.715222	+	0.354672i
$334$			3.32439i			0.181902i
$335$	−15.9691			−0.872485
$336$	−2.97075	+	15.5157i	−0.162068	+	0.846450i
$337$	9.27641			0.505318			0.252659	−	0.967555i	$-0.418695\pi$
$337$	9.27641			0.505318			0.252659	+	0.967555i	$0.418695\pi$
$338$	2.08406	−	3.38689i	0.113358	−	0.184222i
$339$	−0.229626	+	0.370178i	−0.0124716	+	0.0201053i
$340$			12.7161i			0.689630i
$341$	25.7499			1.39444
$342$	−1.71704	−	3.46255i	−0.0928471	−	0.187233i
$343$	16.4896	+	8.43159i	0.890357	+	0.455263i
$344$	−2.92448			−0.157677
$345$	17.0885	+	10.6002i	0.920014	+	0.570695i
$346$	0.891795			0.0479432
$347$		−	27.7698i		−	1.49076i	−0.666639	−	0.745381i	$-0.732268\pi$
$347$		−	27.7698i		−	1.49076i	0.666639	−	0.745381i	$-0.267732\pi$
$348$	8.91860	−	14.3776i	0.478087	−	0.770721i
$349$	−3.18709			−0.170601			−0.0853006	−	0.996355i	$-0.527185\pi$
$349$	−3.18709			−0.170601			−0.0853006	+	0.996355i	$0.527185\pi$
$350$	0.226446	+	0.590753i	0.0121040	+	0.0315771i
$351$	17.1468	−	7.54902i	0.915228	−	0.402937i
$352$	−17.3505			−0.924785
$353$		−	22.2593i		−	1.18474i	−0.805664	−	0.592372i	$-0.798192\pi$
$353$		−	22.2593i		−	1.18474i	0.805664	−	0.592372i	$-0.201808\pi$
$354$	3.50652	−	5.65284i	0.186369	−	0.300445i
$355$			13.5795i			0.720723i
$356$			21.9398i			1.16281i
$357$	2.79869	−	14.6170i	0.148122	−	0.773615i
$358$			4.39372i			0.232215i
$359$	21.3887			1.12885			0.564426	−	0.825484i	$-0.309098\pi$
$359$	21.3887			1.12885			0.564426	+	0.825484i	$0.309098\pi$
$360$	−6.59641	+	3.27110i	−0.347662	+	0.172402i
$361$	−1.26336			−0.0664929
$362$		−	6.59190i		−	0.346463i
$363$	−21.1552	−	13.1228i	−1.11036	−	0.688771i
$364$	−11.6484	+	13.9660i	−0.610543	+	0.732018i
$365$			31.0702i			1.62629i
$366$	0.972276	−	1.56740i	0.0508217	−	0.0819293i
$367$		−	0.740357i		−	0.0386463i	−0.999813	−	0.0193232i	$-0.993849\pi$
$367$		−	0.740357i		−	0.0386463i	0.999813	−	0.0193232i	$-0.00615113\pi$
$368$			19.4870i			1.01583i
$369$	−9.02234	+	4.47409i	−0.469684	+	0.232912i
$370$	3.05095			0.158611
$371$	7.61759	−	2.91996i	0.395486	−	0.151597i
$372$	14.3443	+	8.89791i	0.743715	+	0.461335i
$373$	−32.7429			−1.69536			−0.847681	−	0.530506i	$-0.822002\pi$
$373$	−32.7429			−1.69536			−0.847681	+	0.530506i	$0.822002\pi$
$374$	5.00421			0.258762
$375$	10.8419	−	17.4781i	0.559871	−	0.902564i
$376$			8.53718i			0.440272i
$377$	16.1271	−	9.01215i	0.830588	−	0.464149i
$378$	4.05177	−	1.12649i	0.208401	−	0.0579406i
$379$		−	17.2796i		−	0.887594i	−0.896127	−	0.443797i	$-0.853631\pi$
$379$		−	17.2796i		−	0.887594i	0.896127	−	0.443797i	$-0.146369\pi$
$380$		−	16.4901i		−	0.845925i
$381$	−9.16828	−	5.68719i	−0.469705	−	0.291364i
$382$		−	5.39536i		−	0.276050i
$383$			20.5205i			1.04855i	0.851549	+	0.524274i	$0.175663\pi$
$383$			20.5205i			1.04855i	−0.851549	+	0.524274i	$0.824337\pi$
$384$	−12.7696	−	7.92111i	−0.651644	−	0.404222i
$385$	25.5585	−	9.79701i	1.30258	−	0.499302i
$386$		−	2.83195i		−	0.144143i
$387$	−3.26176	−	6.57758i	−0.165804	−	0.334357i
$388$	21.7793			1.10567
$389$			32.7317i			1.65956i	0.558089	+	0.829781i	$0.311535\pi$
$389$			32.7317i			1.65956i	−0.558089	+	0.829781i	$0.688465\pi$
$390$	−3.91950	−	0.178976i	−0.198471	−	0.00906280i
$391$		−	18.3584i		−	0.928423i
$392$	−6.22164	+	5.59127i	−0.314240	+	0.282402i
$393$	28.0698	+	17.4120i	1.41593	+	0.878320i
$394$	8.39975			0.423173
$395$			4.42151i			0.222471i
$396$	−12.7988	−	25.8098i	−0.643165	−	1.29699i
$397$	32.5731			1.63480			0.817399	−	0.576073i	$-0.195415\pi$
$397$	32.5731			1.63480			0.817399	+	0.576073i	$0.195415\pi$
$398$		−	2.30401i		−	0.115490i
$399$	−3.62929	+	18.9551i	−0.181692	+	0.948944i
$400$	2.69478			0.134739
$401$	26.8272			1.33968			0.669842	−	0.742503i	$-0.266362\pi$
$401$	26.8272			1.33968			0.669842	+	0.742503i	$0.266362\pi$
$402$	−2.17156	+	3.50076i	−0.108308	+	0.174602i
$403$	8.99124	+	16.0897i	0.447886	+	0.801485i
$404$	−25.9053			−1.28883
$405$	−14.7143	−	11.1879i	−0.731162	−	0.555933i
$406$	3.87222	−	1.48429i	0.192175	−	0.0736641i
$407$			24.4608i			1.21248i
$408$	5.71213	+	3.54330i	0.282793	+	0.175420i
$409$	21.6481			1.07043			0.535215	−	0.844716i	$-0.320231\pi$
$409$	21.6481			1.07043			0.535215	+	0.844716i	$0.320231\pi$
$410$	2.10907			0.104160
$411$	2.72565	+	1.69075i	0.134446	+	0.0833987i
$412$			9.35792i			0.461031i
$413$	−31.0167	+	11.8893i	−1.52623	+	0.585032i
$414$	4.64758	−	2.30469i	0.228416	−	0.113269i
$415$	1.92379			0.0944350
$416$	−6.05838	−	10.8414i	−0.297036	−	0.531542i
$417$	5.22740	−	8.42705i	0.255987	−	0.412675i
$418$	−6.48939			−0.317406
$419$	−15.2533			−0.745173			−0.372586	−	0.927998i	$-0.621529\pi$
$419$	−15.2533			−0.745173			−0.372586	+	0.927998i	$0.621529\pi$
$420$	17.6230	+	3.37423i	0.859914	+	0.164645i
$421$		−	15.6273i		−	0.761630i	−0.924651	−	0.380815i	$-0.875643\pi$
$421$		−	15.6273i		−	0.761630i	0.924651	−	0.380815i	$-0.124357\pi$
$422$	1.99228			0.0969825
$423$	−19.2013	+	9.52177i	−0.933601	+	0.462964i
$424$			3.68467i			0.178944i
$425$	−2.53870			−0.123145
$426$	2.97691	+	1.84661i	0.144232	+	0.0894686i
$427$	−8.60021	+	3.29661i	−0.416193	+	0.159534i
$428$		−	14.7821i		−	0.714518i
$429$	1.43493	−	31.4244i	0.0692791	−	1.51718i
$430$			1.53758i			0.0741487i
$431$	26.9735			1.29927			0.649634	−	0.760247i	$-0.274922\pi$
$431$	26.9735			1.29927			0.649634	+	0.760247i	$0.274922\pi$
$432$	1.69676	−	17.8322i	0.0816356	−	0.857950i
$433$			22.0774i			1.06097i	0.847693	+	0.530487i	$0.177991\pi$
$433$			22.0774i			1.06097i	−0.847693	+	0.530487i	$0.822009\pi$
$434$	1.48085	+	3.86324i	0.0710829	+	0.185441i
$435$	−15.4894	−	9.60828i	−0.742661	−	0.460682i
$436$		−	14.6610i		−	0.702136i
$437$			23.8069i			1.13884i
$438$	6.81124	+	4.22509i	0.325454	+	0.201883i
$439$		−	14.1901i		−	0.677257i	−0.940920	−	0.338628i	$-0.890037\pi$
$439$		−	14.1901i		−	0.677257i	0.940920	−	0.338628i	$-0.109963\pi$
$440$			12.3628i			0.589372i
$441$	−19.5147	−	7.75725i	−0.929273	−	0.369393i
$442$	1.74735	+	3.12686i	0.0831130	+	0.148729i
$443$		−	26.8422i		−	1.27531i	−0.770321	−	0.637657i	$-0.779904\pi$
$443$		−	26.8422i		−	1.27531i	0.770321	−	0.637657i	$-0.220096\pi$
$444$	−8.45247	+	13.6262i	−0.401136	+	0.646669i
$445$	23.6364			1.12047
$446$	1.53799			0.0728258
$447$	−0.191250	−	0.118634i	−0.00904580	−	0.00561121i
$448$	5.53122	+	14.4298i	0.261325	+	0.681746i
$449$	−2.49034			−0.117526			−0.0587631	−	0.998272i	$-0.518716\pi$
$449$	−2.49034			−0.117526			−0.0587631	+	0.998272i	$0.518716\pi$
$450$	−0.318706	−	0.642694i	−0.0150239	−	0.0302969i
$451$			16.9094i			0.796231i
$452$			0.479470i			0.0225524i
$453$	−19.9850	+	32.2177i	−0.938979	+	1.51372i
$454$			3.08451i			0.144763i
$455$	15.0460	+	12.5492i	0.705368	+	0.588315i
$456$	−7.40740	−	4.59490i	−0.346883	−	0.215176i
$457$		−	19.3863i		−	0.906853i	−0.891294	−	0.453427i	$-0.850201\pi$
$457$		−	19.3863i		−	0.906853i	0.891294	−	0.453427i	$-0.149799\pi$
$458$	−2.14268			−0.100121
$459$	−1.59849	+	16.7993i	−0.0746111	+	0.784126i
$460$	22.1337			1.03199
$461$			17.5300i			0.816452i	0.912881	+	0.408226i	$0.133853\pi$
$461$			17.5300i			0.816452i	−0.912881	+	0.408226i	$0.866147\pi$
$462$	1.32787	−	6.93521i	0.0617780	−	0.322655i
$463$			1.55946i			0.0724741i	0.999343	+	0.0362371i	$0.0115371\pi$
$463$			1.55946i			0.0724741i	−0.999343	+	0.0362371i	$0.988463\pi$
$464$		−	17.6635i		−	0.820008i
$465$	9.58599	−	15.4535i	0.444540	−	0.716639i
$466$			7.12457i			0.330039i
$467$	36.3661			1.68282			0.841412	−	0.540394i	$-0.181725\pi$
$467$	36.3661			1.68282			0.841412	+	0.540394i	$0.181725\pi$
$468$	11.6581	−	17.0094i	0.538894	−	0.786261i
$469$	19.2084	−	7.36293i	0.886963	−	0.339989i
$470$	4.48852			0.207040
$471$	−9.28968	+	14.9758i	−0.428046	+	0.690050i
$472$		−	15.0029i		−	0.690567i
$473$	−12.3275			−0.566817
$474$	0.969290	+	0.601262i	0.0445210	+	0.0276169i
$475$	3.29215			0.151054
$476$	−5.86309	−	15.2956i	−0.268734	−	0.701074i
$477$	−8.28736	+	4.10962i	−0.379452	+	0.188167i
$478$	−3.05600			−0.139778
$479$			21.0908i			0.963662i	0.876264	+	0.481831i	$0.160028\pi$
$479$			21.0908i			0.963662i	−0.876264	+	0.481831i	$0.839972\pi$
$480$	−6.45912	+	10.4127i	−0.294817	+	0.475273i
$481$	−15.2842	+	8.54113i	−0.696900	+	0.389442i
$482$	2.06047			0.0938521
$483$	−25.4424	−	4.87139i	−1.15767	−	0.221656i
$484$	−27.4011			−1.24551
$485$		−	23.4635i		−	1.06542i
$486$	−4.45357	+	1.70430i	−0.202018	+	0.0773086i
$487$			28.4284i			1.28821i	0.764936	+	0.644106i	$0.222771\pi$
$487$			28.4284i			1.28821i	−0.764936	+	0.644106i	$0.777229\pi$
$488$		−	4.15997i		−	0.188313i
$489$	−9.17008	+	14.7830i	−0.414685	+	0.668511i
$490$	2.93967	+	3.27110i	0.132801	+	0.147773i
$491$			11.0888i			0.500429i	0.968190	+	0.250215i	$0.0805012\pi$
$491$			11.0888i			0.500429i	−0.968190	+	0.250215i	$0.919499\pi$
$492$	−5.84305	+	9.41954i	−0.263425	+	0.424666i
$493$			16.6405i			0.749449i
$494$	−2.26594	−	4.05486i	−0.101949	−	0.182437i
$495$	−27.8057	+	13.7886i	−1.24977	+	0.619750i
$496$	17.6225			0.791276
$497$	−6.26114	−	16.3341i	−0.280851	−	0.732683i
$498$	0.261607	−	0.421735i	0.0117229	−	0.0188984i
$499$		−	17.7340i		−	0.793884i	−0.917844	−	0.396942i	$-0.870071\pi$
$499$		−	17.7340i		−	0.793884i	0.917844	−	0.396942i	$-0.129929\pi$
$500$		−	22.6383i		−	1.01242i
$501$	−9.92223	+	15.9956i	−0.443293	+	0.714629i
$502$	2.22906			0.0994880
$503$	−5.75154			−0.256449			−0.128224	−	0.991745i	$-0.540928\pi$
$503$	−5.75154			−0.256449			−0.128224	+	0.991745i	$0.540928\pi$
$504$	6.42628	−	6.97608i	0.286249	−	0.310739i
$505$			27.9085i			1.24191i
$506$		−	8.71033i		−	0.387221i
$507$	20.1364	−	10.0760i	0.894288	−	0.447491i
$508$	−11.8751			−0.526874
$509$		−	22.4218i		−	0.993831i	−0.867799	−	0.496915i	$-0.834466\pi$
$509$		−	22.4218i		−	0.993831i	0.867799	−	0.496915i	$-0.165534\pi$
$510$	1.86293	−	3.00322i	0.0824920	−	0.132985i
$511$	−14.3256	−	37.3728i	−0.633729	−	1.65327i
$512$	−20.1131			−0.888884
$513$	2.07290	−	21.7851i	0.0915206	−	0.961837i
$514$	−4.08034			−0.179976
$515$	10.0816			0.444247
$516$	−6.86715	−	4.25977i	−0.302309	−	0.187526i
$517$			35.9865i			1.58268i
$518$	−3.66984	+	1.40671i	−0.161243	+	0.0618074i
$519$	4.29094	+	2.66172i	0.188351	+	0.116837i
$520$	−7.72481	+	4.31678i	−0.338756	+	0.189303i
$521$	−1.51591			−0.0664132			−0.0332066	−	0.999449i	$-0.510572\pi$
$521$	−1.51591			−0.0664132			−0.0332066	+	0.999449i	$0.510572\pi$
$522$	−4.21268	+	2.08903i	−0.184384	+	0.0914342i
$523$		−	10.9151i		−	0.477282i	−0.971108	−	0.238641i	$-0.923298\pi$
$523$		−	10.9151i		−	0.477282i	0.971108	−	0.238641i	$-0.0767020\pi$
$524$	36.3571			1.58827
$525$	−0.673644	+	3.51832i	−0.0294002	+	0.153552i
$526$			5.48818i			0.239296i
$527$	−16.6019			−0.723189
$528$	−25.5585	−	15.8542i	−1.11229	−	0.689966i
$529$	−8.95456			−0.389329
$530$	1.93726			0.0841492
$531$	33.7438	−	16.7332i	1.46436	−	0.726160i
$532$	7.60316	+	19.8351i	0.329639	+	0.859962i
$533$	−10.5657	+	5.90434i	−0.457652	+	0.255745i
$534$	3.21421	−	5.18160i	0.139092	−	0.224230i
$535$	−15.9252			−0.688505
$536$			9.29123i			0.401320i
$537$	−13.1138	+	21.1407i	−0.565903	+	0.912288i
$538$	9.03104			0.389356
$539$	−26.2259	+	23.5687i	−1.12963	+	1.01518i
$540$	−20.2541	−	1.92721i	−0.871597	−	0.0829341i
$541$		−	7.42511i		−	0.319230i	−0.987179	−	0.159615i	$-0.948975\pi$
$541$		−	7.42511i		−	0.319230i	0.987179	−	0.159615i	$-0.0510253\pi$
$542$	3.42196			0.146986
$543$	19.6747	−	31.7174i	0.844322	−	1.36113i
$544$	11.1865			0.479617
$545$	−15.7948			−0.676573
$546$	4.79709	−	1.59190i	0.205296	−	0.0681269i
$547$	16.0698			0.687094			0.343547	−	0.939135i	$-0.388371\pi$
$547$	16.0698			0.687094			0.343547	+	0.939135i	$0.388371\pi$
$548$	3.53037			0.150810
$549$	9.35636	−	4.63973i	0.399320	−	0.198019i
$550$	−1.20451			−0.0513607
$551$		−	21.5791i		−	0.919301i
$552$	6.16747	−	9.94253i	0.262505	−	0.423182i
$553$	−2.03865	−	5.31842i	−0.0866920	−	0.226162i
$554$	5.29113			0.224799
$555$	14.6799	+	9.10610i	0.623126	+	0.386532i
$556$		−	10.9151i		−	0.462902i
$557$	16.8791			0.715193			0.357596	−	0.933876i	$-0.383596\pi$
$557$	16.8791			0.715193			0.357596	+	0.933876i	$0.383596\pi$
$558$	−2.08418	−	4.20290i	−0.0882304	−	0.177923i
$559$	−4.30445	−	7.70275i	−0.182059	−	0.325792i
$560$	17.4915	−	6.70481i	0.739152	−	0.283330i
$561$	24.0782	+	14.9360i	1.01658	+	0.630597i
$562$	4.47633			0.188823
$563$	0.607801			0.0256157			0.0128079	−	0.999918i	$-0.495923\pi$
$563$	0.607801			0.0256157			0.0128079	+	0.999918i	$0.495923\pi$
$564$	−12.4352	+	20.0467i	−0.523616	+	0.844117i
$565$	0.516548			0.0217313
$566$			6.91803i			0.290786i
$567$	22.8576	+	6.67301i	0.959930	+	0.280240i
$568$	7.90088			0.331514
$569$		−	5.43594i		−	0.227886i	−0.993487	−	0.113943i	$-0.963652\pi$
$569$		−	5.43594i		−	0.227886i	0.993487	−	0.113943i	$-0.0363482\pi$
$570$	−2.41582	+	3.89453i	−0.101188	+	0.163124i
$571$	−25.0656			−1.04896			−0.524482	−	0.851422i	$-0.675741\pi$
$571$	−25.0656			−1.04896			−0.524482	+	0.851422i	$0.675741\pi$
$572$	−16.8903	−	30.2249i	−0.706217	−	1.26376i
$573$	16.1034	−	25.9602i	0.672729	−	1.08450i
$574$	−2.53690	+	0.972438i	−0.105888	+	0.0405888i
$575$			4.41886i			0.184279i
$576$	−7.78477	−	15.6986i	−0.324365	−	0.654107i
$577$	−15.8303			−0.659022			−0.329511	−	0.944152i	$-0.606884\pi$
$577$	−15.8303			−0.659022			−0.329511	+	0.944152i	$0.606884\pi$
$578$	1.97394			0.0821049
$579$	8.45247	−	13.6262i	0.351273	−	0.566284i
$580$	−20.0625			−0.833051
$581$	−2.31403	+	0.887008i	−0.0960021	+	0.0367993i
$582$	−5.14369	−	3.19069i	−0.213213	−	0.132258i
$583$			15.5319i			0.643265i
$584$	18.0774			0.748049
$585$	−18.3248	−	12.5596i	−0.757636	−	0.519275i
$586$			2.15014i			0.0888215i
$587$		−	34.0187i		−	1.40410i	−0.712126	−	0.702052i	$-0.752267\pi$
$587$		−	34.0187i		−	1.40410i	0.712126	−	0.702052i	$-0.247733\pi$
$588$	−22.7536	+	4.06681i	−0.938342	+	0.167712i
$589$	21.5291			0.887089
$590$	−7.88798			−0.324743
$591$	40.4161	+	25.0706i	1.66249	+	1.03126i
$592$			16.7403i			0.688023i
$593$			0.808753i			0.0332115i	0.999862	+	0.0166058i	$0.00528602\pi$
$593$			0.808753i			0.0332115i	−0.999862	+	0.0166058i	$0.994714\pi$
$594$	−0.758420	+	7.97063i	−0.0311184	+	0.327039i
$595$	−16.4784	+	6.31648i	−0.675550	+	0.258950i
$596$	−0.247714			−0.0101468
$597$	6.87674	−	11.0859i	0.281446	−	0.453717i
$598$	5.44260	−	3.04144i	0.222565	−	0.124374i
$599$		−	0.0865332i		−	0.00353565i	−0.999998	−	0.00176783i	$-0.999437\pi$
$599$		−	0.0865332i		−	0.00353565i	0.999998	−	0.00176783i	$-0.000562717\pi$
$600$	−1.37491	−	0.852873i	−0.0561305	−	0.0348184i
$601$		−	11.1624i		−	0.455322i	−0.973740	−	0.227661i	$-0.926892\pi$
$601$		−	11.1624i		−	0.455322i	0.973740	−	0.227661i	$-0.0731079\pi$
$602$	−0.708938	−	1.84948i	−0.0288942	−	0.0753791i
$603$	−20.8973	+	10.3628i	−0.851004	+	0.422005i
$604$			41.7297i			1.69796i
$605$			29.5201i			1.20016i
$606$	6.11814	+	3.79515i	0.248532	+	0.154168i
$607$		−	16.6405i		−	0.675416i	−0.941251	−	0.337708i	$-0.890348\pi$
$607$		−	16.6405i		−	0.675416i	0.941251	−	0.337708i	$-0.109652\pi$
$608$	−14.5065			−0.588315
$609$	23.0616	+	4.41555i	0.934503	+	0.178927i
$610$	−2.18715			−0.0885552
$611$	−22.4860	+	12.5656i	−0.909685	+	0.508350i
$612$	8.25185	+	16.6405i	0.333561	+	0.672651i
$613$		−	33.9935i		−	1.37298i	−0.727137	−	0.686492i	$-0.759150\pi$
$613$		−	33.9935i		−	1.37298i	0.727137	−	0.686492i	$-0.240850\pi$
$614$	−1.70329			−0.0687392
$615$	10.1480	+	6.29489i	0.409205	+	0.253835i
$616$	−5.70015	−	14.8706i	−0.229666	−	0.599152i
$617$	8.17576			0.329144			0.164572	−	0.986365i	$-0.447376\pi$
$617$	8.17576			0.329144			0.164572	+	0.986365i	$0.447376\pi$
$618$	1.37095	−	2.21009i	0.0551476	−	0.0889030i
$619$	−35.7291			−1.43607			−0.718037	−	0.696005i	$-0.754959\pi$
$619$	−35.7291			−1.43607			−0.718037	+	0.696005i	$0.754959\pi$
$620$		−	20.0160i		−	0.803862i
$621$	29.2409	+	2.78233i	1.17340	+	0.111651i
$622$	−3.48967			−0.139923
$623$	−28.4311	+	10.8981i	−1.13907	+	0.436625i
$624$	0.982028	−	21.5060i	0.0393126	−	0.860928i
$625$	−20.4804			−0.819216
$626$		−	9.41482i		−	0.376292i
$627$	−31.2242	−	19.3687i	−1.24697	−	0.773512i
$628$			19.3973i			0.774037i
$629$		−	15.7708i		−	0.628821i
$630$	−3.66776	−	3.37869i	−0.146127	−	0.134610i
$631$		−	31.6781i		−	1.26108i	−0.776155	−	0.630542i	$-0.782833\pi$
$631$		−	31.6781i		−	1.26108i	0.776155	−	0.630542i	$-0.217167\pi$
$632$	2.57255			0.102331
$633$	9.58599	+	5.94630i	0.381009	+	0.236344i
$634$	0.664489			0.0263902
$635$			12.7934i			0.507692i
$636$	−5.36706	+	8.65220i	−0.212818	+	0.343082i
$637$	−23.8842	−	8.15748i	−0.946327	−	0.323211i
$638$			7.89525i			0.312576i
$639$	8.81208	+	17.7702i	0.348601	+	0.702979i
$640$			17.8187i			0.704345i
$641$		−	0.921906i		−	0.0364131i	−0.999834	−	0.0182065i	$-0.994204\pi$
$641$		−	0.921906i		−	0.0364131i	0.999834	−	0.0182065i	$-0.00579564\pi$
$642$	−2.16559	+	3.49113i	−0.0854691	+	0.137784i
$643$	−10.1310			−0.399528			−0.199764	−	0.979844i	$-0.564018\pi$
$643$	−10.1310			−0.399528			−0.199764	+	0.979844i	$0.564018\pi$
$644$	−26.6236	+	10.2053i	−1.04912	+	0.402144i
$645$	−4.58918	+	7.39818i	−0.180699	+	0.291303i
$646$	4.18394			0.164615
$647$	17.9763			0.706721			0.353360	−	0.935487i	$-0.385039\pi$
$647$	17.9763			0.706721			0.353360	+	0.935487i	$0.385039\pi$
$648$	−6.50942	+	8.56118i	−0.255714	+	0.336315i
$649$		−	63.2414i		−	2.48244i
$650$	−0.420587	−	0.752634i	−0.0164968	−	0.0295207i
$651$	−4.40530	+	23.0081i	−0.172657	+	0.901759i
$652$			19.1476i			0.749876i
$653$			2.78003i			0.108791i	0.998519	+	0.0543954i	$0.0173231\pi$
$653$			2.78003i			0.108791i	−0.998519	+	0.0543954i	$0.982677\pi$
$654$	−2.14786	+	3.46255i	−0.0839879	+	0.135396i
$655$		−	39.1686i		−	1.53044i
$656$			11.5723i			0.451823i
$657$	20.1623	+	40.6587i	0.786605	+	1.58625i
$658$	−5.39902	+	2.06954i	−0.210476	+	0.0806791i
$659$		−	27.7092i		−	1.07940i	−0.841858	−	0.539700i	$-0.818538\pi$
$659$		−	27.7092i		−	1.07940i	0.841858	−	0.539700i	$-0.181462\pi$
$660$	−18.0075	+	29.0298i	−0.700941	+	1.12998i
$661$	−0.0294905			−0.00114705			−0.000573524	−	1.00000i	$-0.500183\pi$
$661$	−0.0294905			−0.00114705			−0.000573524		1.00000i	$0.500183\pi$
$662$		−	2.06638i		−	0.0803120i
$663$	−0.925150	+	20.2604i	−0.0359298	+	0.786848i
$664$		−	1.11931i		−	0.0434376i
$665$	21.3690	−	8.19112i	0.828654	−	0.317638i
$666$	3.99250	−	1.97984i	0.154706	−	0.0767174i
$667$	28.9644			1.12151
$668$			20.7181i			0.801607i
$669$	7.40014	+	4.59040i	0.286106	+	0.177475i
$670$	4.88497			0.188723
$671$		−	17.5354i		−	0.676946i
$672$	2.96833	−	15.5031i	0.114506	−	0.598044i
$673$	23.4074			0.902289			0.451145	−	0.892451i	$-0.351016\pi$
$673$	23.4074			0.902289			0.451145	+	0.892451i	$0.351016\pi$
$674$	−2.83767			−0.109303
$675$	0.384756	−	4.04360i	0.0148093	−	0.155638i
$676$	12.9882	−	21.1076i	0.499545	−	0.811830i
$677$	−24.9484			−0.958844			−0.479422	−	0.877585i	$-0.659154\pi$
$677$	−24.9484			−0.958844			−0.479422	+	0.877585i	$0.659154\pi$
$678$	0.0702430	−	0.113238i	0.00269767	−	0.00434889i
$679$	10.8184	+	28.2230i	0.415172	+	1.08310i
$680$		−	7.97071i		−	0.305663i
$681$	−9.20627	+	14.8414i	−0.352785	+	0.568722i
$682$	−7.87694			−0.301624
$683$	−20.8437			−0.797561			−0.398780	−	0.917046i	$-0.630566\pi$
$683$	−20.8437			−0.797561			−0.398780	+	0.917046i	$0.630566\pi$
$684$	−10.7009	−	21.5791i	−0.409158	−	0.825098i
$685$		−	3.80338i		−	0.145320i
$686$	−5.04421	−	2.57924i	−0.192589	−	0.0984757i
$687$	−10.3097	−	6.39522i	−0.393339	−	0.243993i
$688$	−8.43659			−0.321642
$689$	−9.70501	+	5.42336i	−0.369732	+	0.206613i
$690$	−5.22740	−	3.24262i	−0.199004	−	0.123444i
$691$	−35.0440			−1.33314			−0.666569	−	0.745443i	$-0.732238\pi$
$691$	−35.0440			−1.33314			−0.666569	+	0.745443i	$0.732238\pi$
$692$	5.55780			0.211276
$693$	27.0885	−	29.4060i	1.02901	−	1.11704i
$694$			8.49483i			0.322459i
$695$	−11.7591			−0.446049
$696$	−5.59034	+	9.01215i	−0.211901	+	0.341605i
$697$		−	10.9021i		−	0.412945i
$698$	0.974937			0.0369019
$699$	−21.2645	+	34.2804i	−0.804299	+	1.29660i
$700$	1.41124	+	3.68166i	0.0533400	+	0.139154i
$701$			9.20469i			0.347656i	0.984776	+	0.173828i	$0.0556137\pi$
$701$			9.20469i			0.347656i	−0.984776	+	0.173828i	$0.944386\pi$
$702$	−5.24523	+	2.30926i	−0.197968	+	0.0871573i
$703$			20.4513i			0.771334i
$704$	−29.4217			−1.10887
$705$	21.5969	+	13.3968i	0.813385	+	0.504552i
$706$			6.80916i			0.256266i
$707$	−12.8679	−	33.5698i	−0.483947	−	1.26252i
$708$	21.8532	−	35.2293i	0.821292	−	1.32400i
$709$			16.2515i			0.610338i	0.952298	+	0.305169i	$0.0987130\pi$
$709$			16.2515i			0.610338i	−0.952298	+	0.305169i	$0.901287\pi$
$710$		−	4.15398i		−	0.155896i
$711$	2.86924	+	5.78603i	0.107605	+	0.216993i
$712$		−	13.7523i		−	0.515388i
$713$			28.8972i			1.08221i
$714$	−0.856123	+	4.47137i	−0.0320396	+	0.167337i
$715$	−32.5622	+	18.1964i	−1.21776	+	0.680506i
$716$			27.3823i			1.02332i
$717$	−14.7042	−	9.12119i	−0.549138	−	0.340637i
$718$	−6.54284			−0.244176
$719$	−50.1573			−1.87055			−0.935276	−	0.353920i	$-0.884849\pi$
$719$	−50.1573			−1.87055			−0.935276	+	0.353920i	$0.884849\pi$
$720$	−19.0294	+	9.43652i	−0.709185	+	0.351678i
$721$	−12.1266	+	4.64835i	−0.451619	+	0.173114i
$722$	0.386465			0.0143828
$723$	9.91413	+	6.14985i	0.368711	+	0.228715i
$724$		−	41.0817i		−	1.52679i
$725$		−	4.00536i		−	0.148755i
$726$	6.47142	+	4.01430i	0.240177	+	0.148985i
$727$		−	19.3029i		−	0.715903i	−0.933740	−	0.357952i	$-0.883475\pi$
$727$		−	19.3029i		−	0.715903i	0.933740	−	0.357952i	$-0.116525\pi$
$728$	7.30144	−	8.75415i	0.270609	−	0.324450i
$729$	−26.5155	−	5.09210i	−0.982055	−	0.188596i
$730$		−	9.50442i		−	0.351774i
$731$	7.94795			0.293966
$732$	6.05937	−	9.76827i	0.223961	−	0.361045i
$733$	23.6407			0.873188			0.436594	−	0.899659i	$-0.356185\pi$
$733$	23.6407			0.873188			0.436594	+	0.899659i	$0.356185\pi$
$734$			0.226476i			0.00835940i
$735$	4.38129	+	24.5131i	0.161606	+	0.904180i
$736$		−	19.4712i		−	0.717717i
$737$			39.1650i			1.44266i
$738$	2.75995	−	1.36863i	0.101595	−	0.0503801i
$739$			20.0184i			0.736389i	0.929749	+	0.368195i	$0.120024\pi$
$739$			20.0184i			0.736389i	−0.929749	+	0.368195i	$0.879976\pi$
$740$	19.0140			0.698967
$741$	1.19972	−	26.2734i	0.0440728	−	0.965176i
$742$	−2.33023	+	0.893220i	−0.0855456	+	0.0327911i
$743$	27.2916			1.00123			0.500616	−	0.865669i	$-0.333107\pi$
$743$	27.2916			1.00123			0.500616	+	0.865669i	$0.333107\pi$
$744$	−8.99124	−	5.57737i	−0.329635	−	0.204476i
$745$			0.266870i			0.00977736i
$746$	10.0161			0.366715
$747$	2.51748	−	1.24840i	0.0921100	−	0.0456765i
$748$	31.1870			1.14031
$749$	19.1556	−	7.34268i	0.699930	−	0.268296i
$750$	−3.31654	+	5.34657i	−0.121103	+	0.195229i
$751$	26.4623			0.965623			0.482812	−	0.875724i	$-0.339616\pi$
$751$	26.4623			0.965623			0.482812	+	0.875724i	$0.339616\pi$
$752$			24.6282i			0.898098i
$753$	10.7253	+	6.65304i	0.390852	+	0.242450i
$754$	−4.93331	+	2.75683i	−0.179660	+	0.100398i
$755$	44.9567			1.63614
$756$	25.2512	−	7.02048i	0.918378	−	0.255332i
$757$	−20.3911			−0.741129			−0.370564	−	0.928807i	$-0.620836\pi$
$757$	−20.3911			−0.741129			−0.370564	+	0.928807i	$0.620836\pi$
$758$			5.28586i			0.191991i
$759$	25.9975	−	41.9104i	0.943650	−	1.52125i
$760$			10.3363i			0.374937i
$761$			47.6663i			1.72790i	0.503576	+	0.863951i	$0.332017\pi$
$761$			47.6663i			1.72790i	−0.503576	+	0.863951i	$0.667983\pi$
$762$	2.80459	+	1.73972i	0.101600	+	0.0630235i
$763$	18.9987	−	7.28256i	0.687801	−	0.263646i
$764$		−	33.6247i		−	1.21650i
$765$	17.9273	−	8.88997i	0.648162	−	0.321418i
$766$		−	6.27725i		−	0.226806i
$767$	39.5161	−	22.0824i	1.42684	−	0.797348i
$768$	−13.2879	−	8.24266i	−0.479487	−	0.297431i
$769$	−16.8136			−0.606313			−0.303156	−	0.952941i	$-0.598040\pi$
$769$	−16.8136			−0.606313			−0.303156	+	0.952941i	$0.598040\pi$
$770$	−7.81838	+	2.99692i	−0.281755	+	0.108002i
$771$	−19.6328	−	12.1785i	−0.707060	−	0.438597i
$772$		−	17.6492i		−	0.635207i
$773$		−	23.0113i		−	0.827659i	−0.910354	−	0.413830i	$-0.864191\pi$
$773$		−	23.0113i		−	0.827659i	0.910354	−	0.413830i	$-0.135809\pi$
$774$	0.997777	+	2.01209i	0.0358644	+	0.0723231i
$775$	3.99607			0.143543
$776$	−13.6516			−0.490065
$777$	−21.8563	−	4.18477i	−0.784090	−	0.150128i
$778$		−	10.0127i		−	0.358972i
$779$			14.1376i			0.506533i
$780$	−24.4269	−	1.11540i	−0.874622	−	0.0399379i
$781$	33.3043			1.19172
$782$			5.61586i			0.200823i
$783$	−26.5047	−	2.52197i	−0.947200	−	0.0901278i
$784$	−17.9483	+	16.1298i	−0.641010	+	0.576064i
$785$	20.8973			0.745857
$786$	−8.58659	−	5.32636i	−0.306274	−	0.189985i
$787$	37.1096			1.32281			0.661406	−	0.750028i	$-0.269960\pi$
$787$	37.1096			1.32281			0.661406	+	0.750028i	$0.269960\pi$
$788$	52.3485			1.86484
$789$	−16.3804	+	26.4068i	−0.583159	+	0.940106i
$790$		−	1.35255i		−	0.0481215i
$791$	−0.621330	+	0.238167i	−0.0220919	+	0.00846823i
$792$	8.02254	+	16.1780i	0.285068	+	0.574862i
$793$	10.9569	−	6.12293i	0.389090	−	0.217432i
$794$	−9.96416			−0.353615
$795$	9.32127	+	5.78210i	0.330592	+	0.205070i
$796$		−	14.3590i		−	0.508940i
$797$	18.3081			0.648507			0.324254	−	0.945970i	$-0.394887\pi$
$797$	18.3081			0.648507			0.324254	+	0.945970i	$0.394887\pi$
$798$	1.11021	−	5.79841i	0.0393009	−	0.205261i
$799$		−	23.2018i		−	0.820819i
$800$	−2.69259			−0.0951973
$801$	30.9308	−	15.3383i	1.09289	−	0.541952i
$802$	−8.20647			−0.289781
$803$	76.2012			2.68908
$804$	−13.5335	+	21.8173i	−0.477290	+	0.769436i
$805$	10.9945	+	28.6824i	0.387504	+	1.01092i
$806$	−2.75044	−	4.92186i	−0.0968800	−	0.173365i
$807$	43.4535	+	26.9547i	1.52964	+	0.948852i
$808$	16.2379			0.571247
$809$			36.0180i			1.26633i	0.774019	+	0.633163i	$0.218244\pi$
$809$			36.0180i			1.26633i	−0.774019	+	0.633163i	$0.781756\pi$
$810$	4.50114	+	3.42241i	0.158154	+	0.120251i
$811$	−52.3273			−1.83746			−0.918729	−	0.394888i	$-0.870783\pi$
$811$	−52.3273			−1.83746			−0.918729	+	0.394888i	$0.870783\pi$
$812$	24.1322	−	9.25031i	0.846875	−	0.324622i
$813$	16.4650	+	10.2135i	0.577454	+	0.358202i
$814$		−	7.48261i		−	0.262265i
$815$	20.6282			0.722576
$816$	16.4784	+	10.2218i	0.576861	+	0.357834i
$817$	−10.3068			−0.360589
$818$	−6.62219			−0.231539
$819$	27.8329	+	6.65823i	0.972559	+	0.232657i
$820$	13.1440			0.459010
$821$	15.7911			0.551112			0.275556	−	0.961285i	$-0.411138\pi$
$821$	15.7911			0.551112			0.275556	+	0.961285i	$0.411138\pi$
$822$	−0.833781	−	0.517204i	−0.0290815	−	0.0180396i
$823$	−16.2290			−0.565708			−0.282854	−	0.959163i	$-0.591281\pi$
$823$	−16.2290			−0.565708			−0.282854	+	0.959163i	$0.591281\pi$
$824$		−	5.86571i		−	0.204342i
$825$	−5.79561	−	3.59509i	−0.201777	−	0.125165i
$826$	9.48806	−	3.63694i	0.330132	−	0.126545i
$827$	3.50935			0.122032			0.0610161	−	0.998137i	$-0.480566\pi$
$827$	3.50935			0.122032			0.0610161	+	0.998137i	$0.480566\pi$
$828$	28.9644	−	14.3632i	1.00658	−	0.499154i
$829$			13.6148i			0.472860i	0.971649	+	0.236430i	$0.0759774\pi$
$829$			13.6148i			0.472860i	−0.971649	+	0.236430i	$0.924023\pi$
$830$	−0.588489			−0.0204268
$831$	25.4587	+	15.7923i	0.883152	+	0.547829i
$832$	−10.2733	−	18.3840i	−0.356164	−	0.637351i
$833$	16.9087	−	15.1956i	0.585853	−	0.526495i
$834$	−1.59907	+	2.57785i	−0.0553713	+	0.0892636i
$835$	22.3202			0.772423
$836$	−40.4428			−1.39874
$837$	2.51612	−	26.4432i	0.0869698	−	0.914011i
$838$	4.66601			0.161185
$839$			11.6876i			0.403502i	0.979437	+	0.201751i	$0.0646632\pi$
$839$			11.6876i			0.403502i	−0.979437	+	0.201751i	$0.935337\pi$
$840$	−11.0464	−	2.11503i	−0.381137	−	0.0729754i
$841$	2.74598			0.0946889
$842$			4.78043i			0.164744i
$843$	21.5382	+	13.3604i	0.741816	+	0.460157i
$844$	12.4162			0.427382
$845$	−22.7398	−	13.9926i	−0.782274	−	0.481359i
$846$	5.87372	−	2.91272i	0.201943	−	0.100142i
$847$	−13.6109	−	35.5082i	−0.467677	−	1.22008i
$848$			10.6296i			0.365022i
$849$	−20.6481	+	33.2866i	−0.708640	+	1.14239i
$850$	0.776593			0.0266369
$851$	−27.4506			−0.940993
$852$	18.5525	+	11.5084i	0.635599	+	0.394270i
$853$	14.5565			0.498404			0.249202	−	0.968452i	$-0.419832\pi$
$853$	14.5565			0.498404			0.249202	+	0.968452i	$0.419832\pi$
$854$	2.63082	−	1.00844i	0.0900247	−	0.0345081i
$855$	−23.2478	+	11.5284i	−0.795059	+	0.394262i
$856$			9.26567i			0.316694i
$857$	−24.0760			−0.822420			−0.411210	−	0.911541i	$-0.634894\pi$
$857$	−24.0760			−0.822420			−0.411210	+	0.911541i	$0.634894\pi$
$858$	−0.438947	+	9.61276i	−0.0149854	+	0.328174i
$859$			9.15176i			0.312254i	0.987737	+	0.156127i	$0.0499009\pi$
$859$			9.15176i			0.312254i	−0.987737	+	0.156127i	$0.950099\pi$
$860$			9.58243i			0.326758i
$861$	−15.1089	−	2.89286i	−0.514909	−	0.0985884i
$862$	−8.25124			−0.281038
$863$	14.6037			0.497115			0.248558	−	0.968617i	$-0.420043\pi$
$863$	14.6037			0.497115			0.248558	+	0.968617i	$0.420043\pi$
$864$	−1.69538	+	17.8177i	−0.0576781	+	0.606169i
$865$		−	5.98759i		−	0.203584i
$866$		−	6.75352i		−	0.229494i
$867$	9.49774	+	5.89156i	0.322560	+	0.200088i
$868$	9.22886	+	24.0763i	0.313248	+	0.817201i
$869$	10.8440			0.367857
$870$	4.73824	+	2.93919i	0.160641	+	0.0996478i
$871$	−24.4720	+	13.6755i	−0.829204	+	0.463376i
$872$			9.18980i			0.311206i
$873$	−15.2261	−	30.7045i	−0.515324	−	1.03919i
$874$		−	7.28256i		−	0.246336i
$875$	29.3362	−	11.2451i	0.991746	−	0.380154i
$876$	42.4487	+	26.3314i	1.43421	+	0.889656i
$877$		−	23.0869i		−	0.779588i	−0.920902	−	0.389794i	$-0.872546\pi$
$877$		−	23.0869i		−	0.779588i	0.920902	−	0.389794i	$-0.127454\pi$
$878$			4.34078i			0.146494i
$879$	−6.41748	+	10.3456i	−0.216456	+	0.348947i
$880$			35.6643i			1.20224i
$881$	−49.4957			−1.66755			−0.833777	−	0.552102i	$-0.813826\pi$
$881$	−49.4957			−1.66755			−0.833777	+	0.552102i	$0.813826\pi$
$882$	5.96959	+	2.37296i	0.201007	+	0.0799016i
$883$	−43.4915			−1.46360			−0.731802	−	0.681517i	$-0.761321\pi$
$883$	−43.4915			−1.46360			−0.731802	+	0.681517i	$0.761321\pi$
$884$	10.8897	+	19.4870i	0.366262	+	0.655420i
$885$	−37.9536	−	23.5431i	−1.27580	−	0.791391i
$886$			8.21109i			0.275857i
$887$	−6.21981			−0.208841			−0.104420	−	0.994533i	$-0.533299\pi$
$887$	−6.21981			−0.208841			−0.104420	+	0.994533i	$0.533299\pi$
$888$	5.29816	−	8.54113i	0.177795	−	0.286621i
$889$	−5.89872	−	15.3886i	−0.197837	−	0.516117i
$890$	−7.23042			−0.242364
$891$	−27.4390	+	36.0877i	−0.919240	+	1.20898i
$892$	9.58496			0.320928
$893$			30.0877i			1.00685i
$894$	0.0585036	+	0.0362904i	0.00195665	+	0.00121373i
$895$	29.4998			0.986068
$896$	−8.21572	−	21.4332i	−0.274468	−	0.716033i
$897$	35.2652	+	1.61031i	1.17747	+	0.0537669i
$898$	0.761798			0.0254215
$899$		−	26.1931i		−	0.873590i
$900$	−1.98622	−	4.00536i	−0.0662074	−	0.133512i
$901$		−	10.0140i		−	0.333613i
$902$		−	5.17260i		−	0.172229i
$903$	2.10899	−	11.0149i	0.0701827	−	0.366552i
$904$		−	0.300541i		−	0.00999583i
$905$	−44.2586			−1.47120
$906$	6.11346	−	9.85546i	0.203106	−	0.327426i
$907$	−19.2141			−0.637994			−0.318997	−	0.947756i	$-0.603346\pi$
$907$	−19.2141			−0.637994			−0.318997	+	0.947756i	$0.603346\pi$
$908$			19.2231i			0.637942i
$909$	18.1106	+	36.5213i	0.600690	+	1.21134i
$910$	−4.60260	−	3.83882i	−0.152575	−	0.127256i
$911$		−	47.4651i		−	1.57259i	−0.617852	−	0.786295i	$-0.711997\pi$
$911$		−	47.4651i		−	1.57259i	0.617852	−	0.786295i	$-0.288003\pi$
$912$	−21.3690	−	13.2554i	−0.707598	−	0.438931i
$913$		−	4.71818i		−	0.156149i
$914$			5.93030i			0.196157i
$915$	−10.5236	−	6.52794i	−0.347901	−	0.215807i
$916$	−13.3535			−0.441213
$917$	18.0596	+	47.1140i	0.596382	+	1.55584i
$918$	0.488980	−	5.13895i	0.0161388	−	0.169611i
$919$	−15.5459			−0.512812			−0.256406	−	0.966569i	$-0.582538\pi$
$919$	−15.5459			−0.512812			−0.256406	+	0.966569i	$0.582538\pi$
$920$	−13.8738			−0.457406
$921$	−8.19552	−	5.08378i	−0.270051	−	0.167516i
$922$		−	5.36245i		−	0.176603i
$923$	11.6291	+	20.8100i	0.382775	+	0.684971i
$924$	8.27546	−	43.2213i	0.272243	−	1.42187i
$925$			3.79602i			0.124812i
$926$		−	0.477040i		−	0.0156765i
$927$	13.1928	−	6.54220i	0.433309	−	0.214874i
$928$			17.6492i			0.579362i
$929$			15.4941i			0.508345i	0.967159	+	0.254173i	$0.0818032\pi$
$929$			15.4941i			0.508345i	−0.967159	+	0.254173i	$0.918197\pi$
$930$	−2.93237	+	4.72725i	−0.0961562	+	0.155013i
$931$	−21.9270	+	19.7054i	−0.718628	+	0.645818i
$932$			44.4014i			1.45442i
$933$	−16.7908	−	10.4155i	−0.549707	−	0.340989i
$934$	−11.1245			−0.364003
$935$		−	33.5987i		−	1.09879i
$936$	−7.30749	+	10.6618i	−0.238853	+	0.348492i
$937$		−	29.4443i		−	0.961903i	−0.876747	−	0.480952i	$-0.840291\pi$
$937$		−	29.4443i		−	0.961903i	0.876747	−	0.480952i	$-0.159709\pi$
$938$	−5.87589	+	2.25233i	−0.191855	+	0.0735413i
$939$	28.1002	−	45.3001i	0.917016	−	1.47831i
$940$	27.9731			0.912383
$941$		−	9.88486i		−	0.322237i	−0.986935	−	0.161119i	$-0.948490\pi$
$941$		−	9.88486i		−	0.322237i	0.986935	−	0.161119i	$-0.0515102\pi$
$942$	2.84173	−	4.58113i	0.0925886	−	0.149261i
$943$	−18.9761			−0.617947
$944$		−	43.2807i		−	1.40867i
$945$	−7.56338	−	27.2039i	−0.246037	−	0.884943i
$946$	3.77099			0.122606
$947$	−51.5722			−1.67587			−0.837935	−	0.545769i	$-0.816237\pi$
$947$	−51.5722			−1.67587			−0.837935	+	0.545769i	$0.816237\pi$
$948$	6.04076	+	3.74715i	0.196195	+	0.121702i
$949$	26.6076	+	47.6139i	0.863719	+	1.54561i
$950$	−1.00707			−0.0326738
$951$	3.19724	+	1.98328i	0.103678	+	0.0643124i
$952$	3.67509	+	9.58758i	0.119110	+	0.310735i
$953$		−	21.3774i		−	0.692481i	−0.938146	−	0.346240i	$-0.887458\pi$
$953$		−	21.3774i		−	0.692481i	0.938146	−	0.346240i	$-0.112542\pi$
$954$	2.53512	−	1.25714i	0.0820774	−	0.0407014i
$955$	−36.2249			−1.17221
$956$	−19.0455			−0.615975
$957$	−23.5648	+	37.9886i	−0.761741	+	1.22800i
$958$		−	6.45170i		−	0.208445i
$959$	1.75364	+	4.57490i	0.0566279	+	0.147731i
$960$	−10.9529	+	17.6571i	−0.353503	+	0.569880i
$961$	−4.86763			−0.157020
$962$	4.67547	−	2.61274i	0.150743	−	0.0842383i
$963$	−20.8398	+	10.3343i	−0.671554	+	0.333017i
$964$	12.8412			0.413587
$965$	−19.0140			−0.612081
$966$	7.78287	+	1.49017i	0.250410	+	0.0479453i
$967$			19.6205i			0.630953i	0.948933	+	0.315476i	$0.102164\pi$
$967$			19.6205i			0.630953i	−0.948933	+	0.315476i	$0.897836\pi$
$968$	17.1755			0.552042
$969$	20.1313	+	12.4877i	0.646712	+	0.401163i
$970$			7.17751i			0.230456i
$971$	−5.81429			−0.186589			−0.0932947	−	0.995639i	$-0.529740\pi$
$971$	−5.81429			−0.186589			−0.0932947	+	0.995639i	$0.529740\pi$
$972$	−27.7553	+	10.6215i	−0.890252	+	0.340683i
$973$	14.1445	−	5.42183i	0.453451	−	0.173816i
$974$		−	8.69628i		−	0.278647i
$975$	0.222684	−	4.87667i	0.00713158	−	0.156179i
$976$		−	12.0007i		−	0.384134i
$977$	−29.0313			−0.928792			−0.464396	−	0.885628i	$-0.653729\pi$
$977$	−29.0313			−0.928792			−0.464396	+	0.885628i	$0.653729\pi$
$978$	2.80514	−	4.52215i	0.0896986	−	0.144602i
$979$		−	57.9695i		−	1.85271i
$980$	18.3205	+	20.3860i	0.585227	+	0.651206i
$981$	−20.6692	+	10.2496i	−0.659916	+	0.327246i
$982$		−	3.39207i		−	0.108245i
$983$		−	27.7980i		−	0.886619i	−0.896369	−	0.443309i	$-0.853804\pi$
$983$		−	27.7980i		−	0.886619i	0.896369	−	0.443309i	$-0.146196\pi$
$984$	3.66253	−	5.90434i	0.116757	−	0.188223i
$985$		−	56.3966i		−	1.79695i
$986$		−	5.09035i		−	0.162110i
$987$	−32.1547	−	6.15659i	−1.02350	−	0.195966i
$988$	−14.1217	−	25.2705i	−0.449270	−	0.803961i
$989$		−	13.8342i		−	0.439902i
$990$	8.50579	−	4.21794i	0.270332	−	0.134055i
$991$	22.5644			0.716781			0.358390	−	0.933572i	$-0.383326\pi$
$991$	22.5644			0.716781			0.358390	+	0.933572i	$0.383326\pi$
$992$	−17.6082			−0.559061
$993$	6.16747	−	9.94253i	0.195719	−	0.315517i
$994$	1.91529	+	4.99662i	0.0607494	+	0.158483i
$995$	−15.4693			−0.490411
$996$	1.63037	−	2.62831i	0.0516604	−	0.0832813i
$997$			20.4951i			0.649087i	0.945871	+	0.324543i	$0.105211\pi$
$997$			20.4951i			0.649087i	−0.945871	+	0.324543i	$0.894789\pi$
$998$			5.42487i			0.171721i
$999$	25.1194	+	2.39016i	0.794743	+	0.0756213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.g.a.272.13	✓	32
3.2	odd	2	inner	273.2.g.a.272.19	yes	32
7.6	odd	2	inner	273.2.g.a.272.16	yes	32
13.12	even	2	inner	273.2.g.a.272.17	yes	32
21.20	even	2	inner	273.2.g.a.272.18	yes	32
39.38	odd	2	inner	273.2.g.a.272.15	yes	32
91.90	odd	2	inner	273.2.g.a.272.20	yes	32
273.272	even	2	inner	273.2.g.a.272.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.g.a.272.13	✓	32	1.1	even	1	trivial
273.2.g.a.272.14	yes	32	273.272	even	2	inner
273.2.g.a.272.15	yes	32	39.38	odd	2	inner
273.2.g.a.272.16	yes	32	7.6	odd	2	inner
273.2.g.a.272.17	yes	32	13.12	even	2	inner
273.2.g.a.272.18	yes	32	21.20	even	2	inner
273.2.g.a.272.19	yes	32	3.2	odd	2	inner
273.2.g.a.272.20	yes	32	91.90	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.305902 q^{2} +(-1.47187 - 0.913018i) q^{3} -1.90642 q^{4} +2.05385i q^{5} +(0.450247 + 0.279294i) q^{6} +(-0.946976 - 2.47047i) q^{7} +1.19498 q^{8} +(1.33280 + 2.68769i) q^{9} +O(q^{10})\)	\(q-0.305902 q^{2} +(-1.47187 - 0.913018i) q^{3} -1.90642 q^{4} +2.05385i q^{5} +(0.450247 + 0.279294i) q^{6} +(-0.946976 - 2.47047i) q^{7} +1.19498 q^{8} +(1.33280 + 2.68769i) q^{9} -0.628276i q^{10} +5.03717 q^{11} +(2.80601 + 1.74060i) q^{12} +(1.75886 + 3.14745i) q^{13} +(0.289682 + 0.755722i) q^{14} +(1.87520 - 3.02300i) q^{15} +3.44730 q^{16} -3.24764 q^{17} +(-0.407705 - 0.822167i) q^{18} +4.21149 q^{19} -3.91551i q^{20} +(-0.861760 + 4.50082i) q^{21} -1.54088 q^{22} +5.65284i q^{23} +(-1.75886 - 1.09104i) q^{24} +0.781707 q^{25} +(-0.538037 - 0.962809i) q^{26} +(0.492200 - 5.17279i) q^{27} +(1.80534 + 4.70977i) q^{28} -5.12387i q^{29} +(-0.573627 + 0.924739i) q^{30} +5.11198 q^{31} -3.44450 q^{32} +(-7.41405 - 4.59902i) q^{33} +0.993458 q^{34} +(5.07398 - 1.94495i) q^{35} +(-2.54088 - 5.12387i) q^{36} +4.85607i q^{37} -1.28830 q^{38} +(0.284868 - 6.23850i) q^{39} +2.45431i q^{40} +3.35692i q^{41} +(0.263614 - 1.37681i) q^{42} -2.44730 q^{43} -9.60298 q^{44} +(-5.52010 + 2.73736i) q^{45} -1.72921i q^{46} +7.14420i q^{47} +(-5.07398 - 3.14745i) q^{48} +(-5.20647 + 4.67896i) q^{49} -0.239125 q^{50} +(4.78010 + 2.96515i) q^{51} +(-3.35313 - 6.00037i) q^{52} +3.08346i q^{53} +(-0.150565 + 1.58236i) q^{54} +10.3456i q^{55} +(-1.13162 - 2.95217i) q^{56} +(-6.19876 - 3.84516i) q^{57} +1.56740i q^{58} -12.5550i q^{59} +(-3.57493 + 5.76311i) q^{60} -3.48120i q^{61} -1.56376 q^{62} +(5.37773 - 5.83781i) q^{63} -5.84093 q^{64} +(-6.46438 + 3.61242i) q^{65} +(2.26797 + 1.40685i) q^{66} +7.77520i q^{67} +6.19138 q^{68} +(5.16114 - 8.32024i) q^{69} +(-1.55214 + 0.594962i) q^{70} +6.61172 q^{71} +(1.59267 + 3.21173i) q^{72} +15.1278 q^{73} -1.48548i q^{74} +(-1.15057 - 0.713712i) q^{75} -8.02888 q^{76} +(-4.77008 - 12.4442i) q^{77} +(-0.0871417 + 1.90837i) q^{78} +2.15279 q^{79} +7.08024i q^{80} +(-5.44730 + 7.16428i) q^{81} -1.02689i q^{82} -0.936674i q^{83} +(1.64288 - 8.58047i) q^{84} -6.67016i q^{85} +0.748634 q^{86} +(-4.67818 + 7.54166i) q^{87} +6.01932 q^{88} -11.5084i q^{89} +(1.68861 - 0.837364i) q^{90} +(6.11009 - 7.32576i) q^{91} -10.7767i q^{92} +(-7.52417 - 4.66733i) q^{93} -2.18542i q^{94} +8.64976i q^{95} +(5.06985 + 3.14489i) q^{96} -11.4241 q^{97} +(1.59267 - 1.43130i) q^{98} +(6.71352 + 13.5383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 16 q^{16} - 16 q^{25} + 16 q^{30} - 32 q^{36} - 48 q^{42} + 48 q^{43} - 32 q^{49} - 16 q^{51} - 80 q^{64} + 32 q^{78} + 80 q^{79} - 48 q^{81} - 96 q^{88} + 32 q^{91}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^16 - 16 * q^25 + 16 * q^30 - 32 * q^36 - 48 * q^42 + 48 * q^43 - 32 * q^49 - 16 * q^51 - 80 * q^64 + 32 * q^78 + 80 * q^79 - 48 * q^81 - 96 * q^88 + 32 * q^91

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