LMFDB - Embedded newform 273.2.g.a.272.19

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			272.19
Character	$\chi$	$=$	273.272
Dual form			273.2.g.a.272.20

$q$-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} +(-3.64941 - 2.77161i) 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} +(5.46248 + 3.02676i) q^{39} +2.45431i q^{40} -3.35692i q^{41} +(-1.11636 - 0.847839i) 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} +(-7.90198 - 0.747467i) 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} +(1.67098 + 0.925892i) q^{78} +2.15279 q^{79} -7.08024i q^{80} +(-5.44730 - 7.16428i) q^{81} -1.02689i q^{82} +0.936674i q^{83} +(6.95732 + 5.28386i) 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	$-0.465507\pi$
$2$	0.305902			0.216305			0.108153	+	0.994134i	$0.465507\pi$
$3$	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	$-0.848117\pi$
$5$		−	2.05385i		−	0.918509i	0.888305	−	0.459254i	$-0.151883\pi$
$6$	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	$-0.774498\pi$
$11$	−5.03717			−1.51876			−0.759381	+	0.650646i	$0.774498\pi$
$12$	−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	$-0.371148\pi$
$17$	3.24764			0.787668			0.393834	+	0.919182i	$0.371148\pi$
$18$	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
$21$	−3.64941	−	2.77161i	−0.796367	−	0.604814i
$22$	−1.54088			−0.328516
$23$		−	5.65284i		−	1.17870i	−0.807879	−	0.589349i	$-0.799384\pi$
$23$		−	5.65284i		−	1.17870i	0.807879	−	0.589349i	$-0.200616\pi$
$24$	−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	$0.157819\pi$
$29$			5.12387i			0.951478i	−0.879586	+	0.475739i	$0.842181\pi$
$30$	−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
$39$	5.46248	+	3.02676i	0.874697	+	0.484670i
$40$			2.45431i			0.388061i
$41$		−	3.35692i		−	0.524263i	−0.965032	−	0.262131i	$-0.915575\pi$
$41$		−	3.35692i		−	0.524263i	0.965032	−	0.262131i	$-0.0844254\pi$
$42$	−1.11636	−	0.847839i	−0.172258	−	0.130824i
$43$	−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	$-0.825543\pi$
$47$		−	7.14420i		−	1.04209i	0.853530	−	0.521044i	$-0.174457\pi$
$48$	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	$-0.932076\pi$
$53$		−	3.08346i		−	0.423545i	0.977319	−	0.211773i	$-0.0679236\pi$
$54$	−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	$0.304507\pi$
$59$			12.5550i			1.63452i	−0.576271	+	0.817258i	$0.695493\pi$
$60$	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
$63$	−7.90198	−	0.747467i	−0.995556	−	0.0941719i
$64$	−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	$-0.628332\pi$
$71$	−6.61172			−0.784667			−0.392333	+	0.919823i	$0.628332\pi$
$72$	−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
$78$	1.67098	+	0.925892i	0.189201	+	0.104837i
$79$	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	$0.0163705\pi$
$83$			0.936674i			0.102813i	−0.998678	+	0.0514067i	$0.983630\pi$
$84$	6.95732	+	5.28386i	0.759106	+	0.576516i
$85$		−	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	$0.208807\pi$
$89$			11.5084i			1.21988i	−0.792446	+	0.609941i	$0.791193\pi$
$90$	−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	$-0.736309\pi$
$101$	−13.5884			−1.35210			−0.676048	+	0.736857i	$0.736309\pi$
$102$	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
$105$	−5.69246	+	7.49534i	−0.555527	+	0.731470i
$106$		−	0.943234i		−	0.0916150i
$107$		−	7.75382i		−	0.749590i	−0.927108	−	0.374795i	$-0.877713\pi$
$107$		−	7.75382i		−	0.749590i	0.927108	−	0.374795i	$-0.122287\pi$
$108$	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	$0.00376559\pi$
$113$			0.251502i			0.0236593i	−0.999930	+	0.0118297i	$0.996234\pi$
$114$	1.89621	−	1.17624i	0.177596	−	0.110165i
$115$	−11.6101			−1.08264
$116$		−	9.76827i		−	0.906961i
$117$	10.8035	−	0.532342i	0.998788	−	0.0492150i
$118$			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
$126$	−2.41723	−	0.228651i	−0.215344	−	0.0203699i
$127$	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	$-0.186556\pi$
$131$	19.0708			1.66623			0.833114	+	0.553102i	$0.186556\pi$
$132$	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	$-0.474793\pi$
$137$	1.85183			0.158212			0.0791062	+	0.996866i	$0.474793\pi$
$138$	−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
$147$	−3.39128	+	11.6404i	−0.279708	+	0.960085i
$148$		−	9.25773i		−	0.760980i
$149$	−0.129937			−0.0106448			−0.00532241	−	0.999986i	$-0.501694\pi$
$149$	−0.129937			−0.0106448			−0.00532241	+	0.999986i	$0.501694\pi$
$150$	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
$156$	−10.4138	−	5.77030i	−0.833772	−	0.461993i
$157$		−	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	$0.138137\pi$
$167$			10.8675i			0.840953i	−0.907303	+	0.420477i	$0.861863\pi$
$168$	4.36098	+	3.31202i	0.336457	+	0.255528i
$169$	−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	$-0.464651\pi$
$173$	2.91530			0.221646			0.110823	+	0.993840i	$0.464651\pi$
$174$	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	$0.180358\pi$
$179$			14.3632i			1.07355i	−0.843724	+	0.536777i	$0.819642\pi$
$180$	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
$189$	−12.3131	+	6.11447i	−0.895649	+	0.444763i
$190$		−	2.64598i		−	0.191959i
$191$		−	17.6376i		−	1.27621i	−0.769950	−	0.638104i	$-0.779719\pi$
$191$		−	17.6376i		−	1.27621i	0.769950	−	0.638104i	$-0.220281\pi$
$192$	−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
$195$	6.21651	−	11.2191i	0.445174	−	0.803417i
$196$	9.92575	−	8.92008i	0.708982	−	0.637148i
$197$	27.4590			1.95637			0.978186	−	0.207729i	$-0.0666072\pi$
$197$	27.4590			1.95637			0.978186	+	0.207729i	$0.0666072\pi$
$198$	−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
$210$	−1.74133	+	2.29284i	−0.120163	+	0.158221i
$211$	−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	$0.108611\pi$
$227$			10.0833i			0.669255i	−0.942350	+	0.334628i	$0.891389\pi$
$228$	−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
$231$	18.3827	+	13.9610i	1.20949	+	0.918569i
$232$		−	6.12293i		−	0.401990i
$233$			23.2904i			1.52580i	0.646514	+	0.762902i	$0.276226\pi$
$233$			23.2904i			1.52580i	−0.646514	+	0.762902i	$0.723774\pi$
$234$	3.30482	−	0.162844i	0.216043	−	0.0106455i
$235$	−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	$-0.604727\pi$
$239$	−9.99015			−0.646209			−0.323105	+	0.946363i	$0.604727\pi$
$240$	−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	$-0.426137\pi$
$251$	7.28687			0.459943			0.229971	+	0.973197i	$0.426137\pi$
$252$	15.0645	+	1.42499i	0.948976	+	0.0897658i
$253$			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	$-0.636576\pi$
$257$	−13.3387			−0.832046			−0.416023	+	0.909354i	$0.636576\pi$
$258$	−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	$0.186572\pi$
$263$			17.9410i			1.10629i	−0.833086	+	0.553144i	$0.813428\pi$
$264$	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	$-0.143555\pi$
$269$	29.5227			1.80003			0.900015	+	0.435858i	$0.143555\pi$
$270$	−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
$273$	2.30470	−	16.3612i	0.139487	−	0.990224i
$274$	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	$-0.356227\pi$
$281$	14.6332			0.872946			0.436473	+	0.899717i	$0.356227\pi$
$282$	−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	$0.0658220\pi$
$293$			7.02886i			0.410631i	−0.978696	+	0.205315i	$0.934178\pi$
$294$	−1.03740	+	3.56082i	−0.0605022	+	0.207671i
$295$	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	$-0.604839\pi$
$311$	−11.4078			−0.646878			−0.323439	+	0.946249i	$0.604839\pi$
$312$	−6.52756	−	3.61693i	−0.369551	−	0.204768i
$313$			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
$315$	−1.53518	+	16.2295i	−0.0864978	+	0.914427i
$316$	−4.10414			−0.230876
$317$	2.17223			0.122005			0.0610023	−	0.998138i	$-0.480570\pi$
$317$	2.17223			0.122005			0.0610023	+	0.998138i	$0.480570\pi$
$318$	−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
$336$	−12.5806	−	9.55456i	−0.686329	−	0.521244i
$337$	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	$0.267732\pi$
$347$			27.7698i			1.49076i	−0.666639	+	0.745381i	$0.732268\pi$
$348$	−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
$351$	15.4154	−	10.6474i	0.822812	−	0.568314i
$352$	−17.3505			−0.924785
$353$			22.2593i			1.18474i	0.805664	+	0.592372i	$0.201808\pi$
$353$			22.2593i			1.18474i	−0.805664	+	0.592372i	$0.798192\pi$
$354$	3.50652	+	5.65284i	0.186369	+	0.300445i
$355$			13.5795i			0.720723i
$356$		−	21.9398i		−	1.16281i
$357$	−11.8520	−	9.00118i	−0.627273	−	0.476393i
$358$			4.39372i			0.232215i
$359$	−21.3887			−1.12885			−0.564426	−	0.825484i	$-0.690902\pi$
$359$	−21.3887			−1.12885			−0.564426	+	0.825484i	$0.690902\pi$
$360$	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
$378$	−3.76661	+	1.87043i	−0.193733	+	0.0962044i
$379$		−	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	$-0.824337\pi$
$383$		−	20.5205i		−	1.04855i	0.851549	−	0.524274i	$-0.175663\pi$
$384$	−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	$-0.688465\pi$
$389$		−	32.7317i		−	1.65956i	0.558089	−	0.829781i	$-0.311535\pi$
$390$	1.90164	−	3.43194i	0.0962934	−	0.173783i
$391$		−	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
$399$	−15.3694	−	11.6726i	−0.769435	−	0.584360i
$400$	2.69478			0.134739
$401$	−26.8272			−1.33968			−0.669842	−	0.742503i	$-0.733638\pi$
$401$	−26.8272			−1.33968			−0.669842	+	0.742503i	$0.733638\pi$
$402$	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	$-0.378471\pi$
$419$	15.2533			0.745173			0.372586	+	0.927998i	$0.378471\pi$
$420$	10.8522	−	14.2893i	0.529535	−	0.697246i
$421$		−	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
$429$	−27.5154	−	15.2463i	−1.32846	−	0.736099i
$430$			1.53758i			0.0741487i
$431$	−26.9735			−1.29927			−0.649634	−	0.760247i	$-0.725078\pi$
$431$	−26.9735			−1.29927			−0.649634	+	0.760247i	$0.725078\pi$
$432$	−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
$441$	5.63639	+	20.2295i	0.268400	+	0.963308i
$442$	1.74735	+	3.12686i	0.0831130	+	0.148729i
$443$			26.8422i			1.27531i	0.770321	+	0.637657i	$0.220096\pi$
$443$			26.8422i			1.27531i	−0.770321	+	0.637657i	$0.779904\pi$
$444$	−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	$-0.481284\pi$
$449$	2.49034			0.117526			0.0587631	+	0.998272i	$0.481284\pi$
$450$	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	$-0.866147\pi$
$461$		−	17.5300i		−	0.816452i	0.912881	−	0.408226i	$-0.133853\pi$
$462$	5.62329	+	4.27071i	0.261619	+	0.198691i
$463$			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	$-0.818275\pi$
$467$	−36.3661			−1.68282			−0.841412	+	0.540394i	$0.818275\pi$
$468$	−20.5961	+	1.01487i	−0.952057	+	0.0469124i
$469$	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	$-0.839972\pi$
$479$		−	21.0908i		−	0.963662i	0.876264	−	0.481831i	$-0.160028\pi$
$480$	−6.45912	−	10.4127i	−0.294817	−	0.475273i
$481$	−15.2842	+	8.54113i	−0.696900	+	0.389442i
$482$	−2.06047			−0.0938521
$483$	−15.6674	+	20.6295i	−0.712893	+	0.938676i
$484$	−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	$-0.919499\pi$
$491$		−	11.0888i		−	0.500429i	0.968190	−	0.250215i	$-0.0805012\pi$
$492$	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	$-0.459072\pi$
$503$	5.75154			0.256449			0.128224	+	0.991745i	$0.459072\pi$
$504$	9.44272	+	0.893209i	0.420612	+	0.0397867i
$505$			27.9085i			1.24191i
$506$			8.71033i			0.387221i
$507$	0.0811417	+	22.5165i	0.00360363	+	0.999994i
$508$	−11.8751			−0.526874
$509$			22.4218i			0.993831i	0.867799	+	0.496915i	$0.165534\pi$
$509$			22.4218i			0.993831i	−0.867799	+	0.496915i	$0.834466\pi$
$510$	−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	$-0.489428\pi$
$521$	1.51591			0.0664132			0.0332066	+	0.999449i	$0.489428\pi$
$522$	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
$525$	−2.85277	−	2.16658i	−0.124505	−	0.0945575i
$526$			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
$546$	0.705011	−	5.00491i	0.0301717	−	0.214191i
$547$	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	$-0.616404\pi$
$557$	−16.8791			−0.715193			−0.357596	+	0.933876i	$0.616404\pi$
$558$	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	$-0.504077\pi$
$563$	−0.607801			−0.0256157			−0.0128079	+	0.999918i	$0.504077\pi$
$564$	12.4352	+	20.0467i	0.523616	+	0.844117i
$565$	0.516548			0.0217313
$566$		−	6.91803i		−	0.290786i
$567$	−12.5407	+	20.2418i	−0.526660	+	0.850076i
$568$	7.90088			0.331514
$569$			5.43594i			0.227886i	0.993487	+	0.113943i	$0.0363482\pi$
$569$			5.43594i			0.227886i	−0.993487	+	0.113943i	$0.963652\pi$
$570$	−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
$585$	−1.09335	−	22.1888i	−0.0452045	−	0.917396i
$586$			2.15014i			0.0888215i
$587$			34.0187i			1.40410i	0.712126	+	0.702052i	$0.247733\pi$
$587$			34.0187i			1.40410i	−0.712126	+	0.702052i	$0.752267\pi$
$588$	6.46521	−	22.1916i	0.266621	−	0.915165i
$589$	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	$-0.994714\pi$
$593$		−	0.808753i		−	0.0332115i	0.999862	−	0.0166058i	$-0.00528602\pi$
$594$	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	$0.000562717\pi$
$599$			0.0865332i			0.00353565i	−0.999998	+	0.00176783i	$0.999437\pi$
$600$	−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
$609$	14.2013	−	18.6991i	0.575468	−	0.757726i
$610$	−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	$-0.552624\pi$
$617$	−8.17576			−0.329144			−0.164572	+	0.986365i	$0.552624\pi$
$618$	−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
$624$	18.8308	+	10.4342i	0.753836	+	0.417701i
$625$	−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
$630$	−0.469615	+	4.96462i	−0.0187099	+	0.197795i
$631$		−	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	$0.00579564\pi$
$641$			0.921906i			0.0364131i	−0.999834	+	0.0182065i	$0.994204\pi$
$642$	−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	$-0.614961\pi$
$647$	−17.9763			−0.706721			−0.353360	+	0.935487i	$0.614961\pi$
$648$	6.50942	+	8.56118i	0.255714	+	0.336315i
$649$		−	63.2414i		−	2.48244i
$650$	0.420587	+	0.752634i	0.0164968	+	0.0295207i
$651$	−18.6557	−	14.1684i	−0.731175	−	0.555304i
$652$			19.1476i			0.749876i
$653$		−	2.78003i		−	0.108791i	−0.998519	−	0.0543954i	$-0.982677\pi$
$653$		−	2.78003i		−	0.108791i	0.998519	−	0.0543954i	$-0.0173231\pi$
$654$	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	$0.181462\pi$
$659$			27.7092i			1.07940i	−0.841858	+	0.539700i	$0.818538\pi$
$660$	−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
$663$	17.7402	+	9.82983i	0.688971	+	0.381759i
$664$		−	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
$672$	−12.5704	−	9.54679i	−0.484913	−	0.368276i
$673$	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	$-0.340846\pi$
$677$	24.9484			0.958844			0.479422	+	0.877585i	$0.340846\pi$
$678$	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	$-0.369434\pi$
$683$	20.8437			0.797561			0.398780	+	0.917046i	$0.369434\pi$
$684$	−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
$693$	39.8036	+	3.76511i	1.51201	+	0.143025i
$694$			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	$-0.944386\pi$
$701$		−	9.20469i		−	0.347656i	0.984776	−	0.173828i	$-0.0556137\pi$
$702$	4.71559	−	3.25705i	0.177978	−	0.122929i
$703$			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
$714$	−3.62554	−	2.75347i	−0.135682	−	0.103046i
$715$	−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	$-0.115151\pi$
$719$	50.1573			1.87055			0.935276	+	0.353920i	$0.115151\pi$
$720$	−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
$735$	23.9076	+	6.96517i	0.881847	+	0.256914i
$736$		−	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
$741$	23.0052	+	12.7472i	0.845116	+	0.468279i
$742$	−2.33023	+	0.893220i	−0.0855456	+	0.0327911i
$743$	−27.2916			−1.00123			−0.500616	−	0.865669i	$-0.666893\pi$
$743$	−27.2916			−1.00123			−0.500616	+	0.865669i	$0.666893\pi$
$744$	−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
$756$	23.4741	−	11.6568i	0.853743	−	0.423953i
$757$	−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	$-0.667983\pi$
$761$		−	47.6663i		−	1.72790i	0.503576	−	0.863951i	$-0.332017\pi$
$762$	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	$0.135809\pi$
$773$			23.0113i			0.827659i	−0.910354	+	0.413830i	$0.864191\pi$
$774$	−0.997777	+	2.01209i	−0.0358644	+	0.0723231i
$775$	3.99607			0.143543
$776$	13.6516			0.490065
$777$	13.4591	−	17.7218i	0.482843	−	0.635766i
$778$		−	10.0127i		−	0.358972i
$779$		−	14.1376i		−	0.506533i
$780$	−11.8513	+	21.3884i	−0.424345	+	0.765827i
$781$	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	$-0.605113\pi$
$797$	−18.3081			−0.648507			−0.324254	+	0.945970i	$0.605113\pi$
$798$	−4.70154	−	3.57066i	−0.166433	−	0.126400i
$799$		−	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	$-0.781756\pi$
$809$		−	36.0180i		−	1.26633i	0.774019	−	0.633163i	$-0.218244\pi$
$810$	−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
$819$	−11.5458	−	26.1858i	−0.403444	−	0.915004i
$820$	13.1440			0.459010
$821$	−15.7911			−0.551112			−0.275556	−	0.961285i	$-0.588862\pi$
$821$	−15.7911			−0.551112			−0.275556	+	0.961285i	$0.588862\pi$
$822$	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	$-0.519434\pi$
$827$	−3.50935			−0.122032			−0.0610161	+	0.998137i	$0.519434\pi$
$828$	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	$-0.935337\pi$
$839$		−	11.6876i		−	0.403502i	0.979437	−	0.201751i	$-0.0646632\pi$
$840$	6.80238	−	8.95679i	0.234705	−	0.309039i
$841$	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	$-0.365106\pi$
$857$	24.0760			0.822420			0.411210	+	0.911541i	$0.365106\pi$
$858$	−8.41701	−	4.66387i	−0.287352	−	0.159222i
$859$			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
$861$	−9.30406	+	12.2508i	−0.317082	+	0.417505i
$862$	−8.25124			−0.281038
$863$	−14.6037			−0.497115			−0.248558	−	0.968617i	$-0.579957\pi$
$863$	−14.6037			−0.497115			−0.248558	+	0.968617i	$0.579957\pi$
$864$	−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	$-0.186174\pi$
$881$	49.4957			1.66755			0.833777	+	0.552102i	$0.186174\pi$
$882$	1.72418	+	6.18822i	0.0580562	+	0.208368i
$883$	−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	$-0.466701\pi$
$887$	6.21981			0.208841			0.104420	+	0.994533i	$0.466701\pi$
$888$	−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
$897$	17.1098	−	30.8785i	0.571280	−	1.03100i
$898$	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
$903$	8.93121	+	6.78296i	0.297212	+	0.225723i
$904$		−	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	$0.288003\pi$
$911$			47.4651i			1.57259i	−0.617852	+	0.786295i	$0.711997\pi$
$912$	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
$924$	−35.0452	−	26.6157i	−1.15290	−	0.875591i
$925$			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	$-0.918197\pi$
$929$		−	15.4941i		−	0.508345i	0.967159	−	0.254173i	$-0.0818032\pi$
$930$	−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
$936$	−12.9100	+	0.636139i	−0.421978	+	0.0207929i
$937$		−	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	$0.0515102\pi$
$941$			9.88486i			0.322237i	−0.986935	+	0.161119i	$0.948490\pi$
$942$	−2.84173	−	4.58113i	−0.0925886	−	0.149261i
$943$	−18.9761			−0.617947
$944$			43.2807i			1.40867i
$945$	12.5582	+	25.2893i	0.408518	+	0.822661i
$946$	3.77099			0.122606
$947$	51.5722			1.67587			0.837935	−	0.545769i	$-0.183763\pi$
$947$	51.5722			1.67587			0.837935	+	0.545769i	$0.183763\pi$
$948$	−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	$0.112542\pi$
$953$			21.3774i			0.692481i	−0.938146	+	0.346240i	$0.887458\pi$
$954$	−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
$966$	−4.79270	+	6.31060i	−0.154202	+	0.203040i
$967$			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	$-0.470260\pi$
$971$	5.81429			0.186589			0.0932947	+	0.995639i	$0.470260\pi$
$972$	27.7553	+	10.6215i	0.890252	+	0.340683i
$973$	14.1445	−	5.42183i	0.453451	−	0.173816i
$974$			8.69628i			0.278647i
$975$	4.27006	+	2.36604i	0.136751	+	0.0757740i
$976$		−	12.0007i		−	0.384134i
$977$	29.0313			0.928792			0.464396	−	0.885628i	$-0.346271\pi$
$977$	29.0313			0.928792			0.464396	+	0.885628i	$0.346271\pi$
$978$	−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	$0.146196\pi$
$983$			27.7980i			0.886619i	−0.896369	+	0.443309i	$0.853804\pi$
$984$	3.66253	+	5.90434i	0.116757	+	0.188223i
$985$		−	56.3966i		−	1.79695i
$986$			5.09035i			0.162110i
$987$	−19.8009	+	26.0721i	−0.630270	+	0.829884i
$988$	−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.272.19	yes	32
3.2	odd	2	inner	273.2.g.a.272.13	✓	32
7.6	odd	2	inner	273.2.g.a.272.18	yes	32
13.12	even	2	inner	273.2.g.a.272.15	yes	32
21.20	even	2	inner	273.2.g.a.272.16	yes	32
39.38	odd	2	inner	273.2.g.a.272.17	yes	32
91.90	odd	2	inner	273.2.g.a.272.14	yes	32
273.272	even	2	inner	273.2.g.a.272.20	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.g.a.272.13	✓	32	3.2	odd	2	inner
273.2.g.a.272.14	yes	32	91.90	odd	2	inner
273.2.g.a.272.15	yes	32	13.12	even	2	inner
273.2.g.a.272.16	yes	32	21.20	even	2	inner
273.2.g.a.272.17	yes	32	39.38	odd	2	inner
273.2.g.a.272.18	yes	32	7.6	odd	2	inner
273.2.g.a.272.19	yes	32	1.1	even	1	trivial
273.2.g.a.272.20	yes	32	273.272	even	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} +(-3.64941 - 2.77161i) 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} +(5.46248 + 3.02676i) q^{39} +2.45431i q^{40} -3.35692i q^{41} +(-1.11636 - 0.847839i) 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} +(-7.90198 - 0.747467i) 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} +(1.67098 + 0.925892i) q^{78} +2.15279 q^{79} -7.08024i q^{80} +(-5.44730 - 7.16428i) q^{81} -1.02689i q^{82} +0.936674i q^{83} +(6.95732 + 5.28386i) 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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