LMFDB - Embedded newform 273.2.e.a.209.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(209,273)]

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, 0]))

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

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

chi := DirichletCharacter("273.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.e (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			209.7
Character	$\chi$	$=$	273.209
Dual form			273.2.e.a.209.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.86253i q^{2} +(-0.150306 + 1.72552i) q^{3} -1.46902 q^{4} -2.96439 q^{5} +(3.21383 + 0.279950i) q^{6} +(-2.41066 - 1.09028i) q^{7} -0.988960i q^{8} +(-2.95482 - 0.518713i) q^{9} +O(q^{10})$	\(q-1.86253i q^{2} +(-0.150306 + 1.72552i) q^{3} -1.46902 q^{4} -2.96439 q^{5} +(3.21383 + 0.279950i) q^{6} +(-2.41066 - 1.09028i) q^{7} -0.988960i q^{8} +(-2.95482 - 0.518713i) q^{9} +5.52126i q^{10} -1.31518i q^{11} +(0.220804 - 2.53483i) q^{12} +1.00000i q^{13} +(-2.03069 + 4.48993i) q^{14} +(0.445566 - 5.11510i) q^{15} -4.78002 q^{16} -5.54045 q^{17} +(-0.966118 + 5.50344i) q^{18} -0.857394i q^{19} +4.35475 q^{20} +(2.24364 - 3.99576i) q^{21} -2.44956 q^{22} +5.78874i q^{23} +(1.70647 + 0.148647i) q^{24} +3.78758 q^{25} +1.86253 q^{26} +(1.33918 - 5.02062i) q^{27} +(3.54132 + 1.60165i) q^{28} -3.98835i q^{29} +(-9.52703 - 0.829881i) q^{30} -4.64055i q^{31} +6.92501i q^{32} +(2.26936 + 0.197680i) q^{33} +10.3193i q^{34} +(7.14613 + 3.23202i) q^{35} +(4.34069 + 0.762001i) q^{36} +7.04880 q^{37} -1.59692 q^{38} +(-1.72552 - 0.150306i) q^{39} +2.93166i q^{40} -2.19314 q^{41} +(-7.44222 - 4.17885i) q^{42} +5.76280 q^{43} +1.93203i q^{44} +(8.75921 + 1.53766i) q^{45} +10.7817 q^{46} +1.48535 q^{47} +(0.718467 - 8.24800i) q^{48} +(4.62256 + 5.25661i) q^{49} -7.05449i q^{50} +(0.832766 - 9.56014i) q^{51} -1.46902i q^{52} +0.966305i q^{53} +(-9.35106 - 2.49426i) q^{54} +3.89870i q^{55} +(-1.07825 + 2.38405i) q^{56} +(1.47945 + 0.128872i) q^{57} -7.42843 q^{58} -4.53802 q^{59} +(-0.654547 + 7.51420i) q^{60} -7.77235i q^{61} -8.64318 q^{62} +(6.55751 + 4.47203i) q^{63} +3.33802 q^{64} -2.96439i q^{65} +(0.368185 - 4.22676i) q^{66} -13.2909 q^{67} +8.13906 q^{68} +(-9.98856 - 0.870084i) q^{69} +(6.01974 - 13.3099i) q^{70} -13.7948i q^{71} +(-0.512986 + 2.92219i) q^{72} +6.33668i q^{73} -13.1286i q^{74} +(-0.569298 + 6.53554i) q^{75} +1.25953i q^{76} +(-1.43392 + 3.17045i) q^{77} +(-0.279950 + 3.21383i) q^{78} -14.5466 q^{79} +14.1698 q^{80} +(8.46187 + 3.06540i) q^{81} +4.08480i q^{82} -12.7772 q^{83} +(-3.29596 + 5.86986i) q^{84} +16.4240 q^{85} -10.7334i q^{86} +(6.88197 + 0.599475i) q^{87} -1.30066 q^{88} +15.8365 q^{89} +(2.86395 - 16.3143i) q^{90} +(1.09028 - 2.41066i) q^{91} -8.50379i q^{92} +(8.00735 + 0.697505i) q^{93} -2.76652i q^{94} +2.54165i q^{95} +(-11.9492 - 1.04087i) q^{96} +0.120764i q^{97} +(9.79059 - 8.60967i) q^{98} +(-0.682200 + 3.88611i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.86253i		−	1.31701i	−0.752577	−	0.658504i	$-0.771189\pi$
$2$		−	1.86253i		−	1.31701i	0.752577	−	0.658504i	$-0.228811\pi$
$3$	−0.150306	+	1.72552i	−0.0867795	+	0.996228i
$3$	−0.150306	+	1.72552i	−0.0867795	+	0.996228i
$4$	−1.46902			−0.734512
$5$	−2.96439			−1.32571			−0.662857	−	0.748746i	$-0.730656\pi$
$5$	−2.96439			−1.32571			−0.662857	+	0.748746i	$0.730656\pi$
$6$	3.21383	+	0.279950i	1.31204	+	0.114289i
$7$	−2.41066	−	1.09028i	−0.911144	−	0.412088i
$7$	−2.41066	−	1.09028i	−0.911144	−	0.412088i
$8$		−	0.988960i		−	0.349650i
$9$	−2.95482	−	0.518713i	−0.984939	−	0.172904i
$10$			5.52126i			1.74598i
$11$		−	1.31518i		−	0.396541i	−0.980147	−	0.198271i	$-0.936467\pi$
$11$		−	1.31518i		−	0.396541i	0.980147	−	0.198271i	$-0.0635325\pi$
$12$	0.220804	−	2.53483i	0.0637405	−	0.731741i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−2.03069	+	4.48993i	−0.542724	+	1.19998i
$15$	0.445566	−	5.11510i	0.115045	−	1.32071i
$16$	−4.78002			−1.19500
$17$	−5.54045			−1.34376			−0.671879	−	0.740661i	$-0.734512\pi$
$17$	−5.54045			−1.34376			−0.671879	+	0.740661i	$0.734512\pi$
$18$	−0.966118	+	5.50344i	−0.227716	+	1.29717i
$19$		−	0.857394i		−	0.196700i	−0.995152	−	0.0983498i	$-0.968644\pi$
$19$		−	0.857394i		−	0.196700i	0.995152	−	0.0983498i	$-0.0313564\pi$
$20$	4.35475			0.973752
$21$	2.24364	−	3.99576i	0.489602	−	0.871946i
$22$	−2.44956			−0.522248
$23$			5.78874i			1.20704i	0.797350	+	0.603518i	$0.206235\pi$
$23$			5.78874i			1.20704i	−0.797350	+	0.603518i	$0.793765\pi$
$24$	1.70647	+	0.148647i	0.348331	+	0.0303425i
$25$	3.78758			0.757516
$26$	1.86253			0.365272
$27$	1.33918	−	5.02062i	0.257724	−	0.966218i
$28$	3.54132	+	1.60165i	0.669246	+	0.302684i
$29$		−	3.98835i		−	0.740618i	−0.928909	−	0.370309i	$-0.879252\pi$
$29$		−	3.98835i		−	0.740618i	0.928909	−	0.370309i	$-0.120748\pi$
$30$	−9.52703	−	0.829881i	−1.73939	−	0.151515i
$31$		−	4.64055i		−	0.833468i	−0.909028	−	0.416734i	$-0.863175\pi$
$31$		−	4.64055i		−	0.833468i	0.909028	−	0.416734i	$-0.136825\pi$
$32$			6.92501i			1.22418i
$33$	2.26936	+	0.197680i	0.395045	+	0.0344116i
$34$			10.3193i			1.76974i
$35$	7.14613	+	3.23202i	1.20792	+	0.546311i
$36$	4.34069	+	0.762001i	0.723449	+	0.127000i
$37$	7.04880			1.15882			0.579408	−	0.815038i	$-0.303284\pi$
$37$	7.04880			1.15882			0.579408	+	0.815038i	$0.303284\pi$
$38$	−1.59692			−0.259055
$39$	−1.72552	−	0.150306i	−0.276304	−	0.0240683i
$40$			2.93166i			0.463536i
$41$	−2.19314			−0.342511			−0.171256	−	0.985227i	$-0.554782\pi$
$41$	−2.19314			−0.342511			−0.171256	+	0.985227i	$0.554782\pi$
$42$	−7.44222	−	4.17885i	−1.14836	−	0.644811i
$43$	5.76280			0.878819			0.439410	−	0.898287i	$-0.355188\pi$
$43$	5.76280			0.878819			0.439410	+	0.898287i	$0.355188\pi$
$44$			1.93203i			0.291264i
$45$	8.75921	+	1.53766i	1.30575	+	0.229221i
$46$	10.7817			1.58968
$47$	1.48535			0.216661			0.108331	−	0.994115i	$-0.465450\pi$
$47$	1.48535			0.216661			0.108331	+	0.994115i	$0.465450\pi$
$48$	0.718467	−	8.24800i	0.103702	−	1.19050i
$49$	4.62256	+	5.25661i	0.660366	+	0.750944i
$50$		−	7.05449i		−	0.997656i
$51$	0.832766	−	9.56014i	0.116611	−	1.33869i
$52$		−	1.46902i		−	0.203717i
$53$			0.966305i			0.132732i	0.997795	+	0.0663661i	$0.0211405\pi$
$53$			0.966305i			0.132732i	−0.997795	+	0.0663661i	$0.978859\pi$
$54$	−9.35106	−	2.49426i	−1.27252	−	0.339425i
$55$			3.89870i			0.525700i
$56$	−1.07825	+	2.38405i	−0.144087	+	0.318582i
$57$	1.47945	+	0.128872i	0.195958	+	0.0170695i
$58$	−7.42843			−0.975400
$59$	−4.53802			−0.590800			−0.295400	−	0.955374i	$-0.595453\pi$
$59$	−4.53802			−0.590800			−0.295400	+	0.955374i	$0.595453\pi$
$60$	−0.654547	+	7.51420i	−0.0845017	+	0.970079i
$61$		−	7.77235i		−	0.995148i	−0.867422	−	0.497574i	$-0.834224\pi$
$61$		−	7.77235i		−	0.995148i	0.867422	−	0.497574i	$-0.165776\pi$
$62$	−8.64318			−1.09768
$63$	6.55751	+	4.47203i	0.826169	+	0.563422i
$64$	3.33802			0.417252
$65$		−	2.96439i		−	0.367687i
$66$	0.368185	−	4.22676i	0.0453204	−	0.520278i
$67$	−13.2909			−1.62374			−0.811868	−	0.583841i	$-0.801549\pi$
$67$	−13.2909			−1.62374			−0.811868	+	0.583841i	$0.801549\pi$
$68$	8.13906			0.987006
$69$	−9.98856	−	0.870084i	−1.20248	−	0.104746i
$70$	6.01974	−	13.3099i	0.719497	−	1.59084i
$71$		−	13.7948i		−	1.63715i	−0.574402	−	0.818573i	$-0.694765\pi$
$71$		−	13.7948i		−	1.63715i	0.574402	−	0.818573i	$-0.305235\pi$
$72$	−0.512986	+	2.92219i	−0.0604560	+	0.344384i
$73$			6.33668i			0.741652i	0.928702	+	0.370826i	$0.120925\pi$
$73$			6.33668i			0.741652i	−0.928702	+	0.370826i	$0.879075\pi$
$74$		−	13.1286i		−	1.52617i
$75$	−0.569298	+	6.53554i	−0.0657369	+	0.754659i
$76$			1.25953i			0.144478i
$77$	−1.43392	+	3.17045i	−0.163410	+	0.361306i
$78$	−0.279950	+	3.21383i	−0.0316982	+	0.363895i
$79$	−14.5466			−1.63662			−0.818308	−	0.574780i	$-0.805088\pi$
$79$	−14.5466			−1.63662			−0.818308	+	0.574780i	$0.805088\pi$
$80$	14.1698			1.58423
$81$	8.46187	+	3.06540i	0.940208	+	0.340600i
$82$			4.08480i			0.451090i
$83$	−12.7772			−1.40248			−0.701241	−	0.712924i	$-0.747370\pi$
$83$	−12.7772			−1.40248			−0.701241	+	0.712924i	$0.747370\pi$
$84$	−3.29596	+	5.86986i	−0.359619	+	0.640455i
$85$	16.4240			1.78144
$86$		−	10.7334i		−	1.15741i
$87$	6.88197	+	0.599475i	0.737824	+	0.0642704i
$88$	−1.30066			−0.138651
$89$	15.8365			1.67866			0.839330	−	0.543622i	$-0.182947\pi$
$89$	15.8365			1.67866			0.839330	+	0.543622i	$0.182947\pi$
$90$	2.86395	−	16.3143i	0.301887	−	1.71968i
$91$	1.09028	−	2.41066i	0.114293	−	0.252706i
$92$		−	8.50379i		−	0.886582i
$93$	8.00735	+	0.697505i	0.830324	+	0.0723279i
$94$		−	2.76652i		−	0.285344i
$95$			2.54165i			0.260767i
$96$	−11.9492	−	1.04087i	−1.21956	−	0.106234i
$97$			0.120764i			0.0122617i	0.999981	+	0.00613086i	$0.00195153\pi$
$97$			0.120764i			0.0122617i	−0.999981	+	0.00613086i	$0.998048\pi$
$98$	9.79059	−	8.60967i	0.988999	−	0.869708i
$99$	−0.682200	+	3.88611i	−0.0685637	+	0.390569i
$100$	−5.56405			−0.556405
$101$	−8.05426			−0.801429			−0.400715	−	0.916203i	$-0.631238\pi$
$101$	−8.05426			−0.801429			−0.400715	+	0.916203i	$0.631238\pi$
$102$	−17.8061	−	1.55105i	−1.76306	−	0.153577i
$103$		−	15.4032i		−	1.51772i	−0.651253	−	0.758861i	$-0.725756\pi$
$103$		−	15.4032i		−	1.51772i	0.651253	−	0.758861i	$-0.274244\pi$
$104$	0.988960			0.0969755
$105$	−6.65101	+	11.8450i	−0.649073	+	1.15595i
$106$	1.79977			0.174809
$107$			19.1089i			1.84733i	0.383201	+	0.923665i	$0.374822\pi$
$107$			19.1089i			1.84733i	−0.383201	+	0.923665i	$0.625178\pi$
$108$	−1.96728	+	7.37541i	−0.189302	+	0.709699i
$109$	−13.5032			−1.29337			−0.646686	−	0.762756i	$-0.723846\pi$
$109$	−13.5032			−1.29337			−0.646686	+	0.762756i	$0.723846\pi$
$110$	7.26145			0.692352
$111$	−1.05948	+	12.1628i	−0.100561	+	1.15444i
$112$	11.5230	+	5.21157i	1.08882	+	0.492447i
$113$			9.35354i			0.879907i	0.898020	+	0.439954i	$0.145005\pi$
$113$			9.35354i			0.879907i	−0.898020	+	0.439954i	$0.854995\pi$
$114$	0.240028	−	2.75552i	0.0224807	−	0.258078i
$115$		−	17.1600i		−	1.60018i
$116$			5.85898i			0.543993i
$117$	0.518713	−	2.95482i	0.0479550	−	0.273173i
$118$			8.45221i			0.778089i
$119$	13.3561	+	6.04066i	1.22436	+	0.553747i
$120$	−5.05863	−	0.440647i	−0.461787	−	0.0402254i
$121$	9.27030			0.842755
$122$	−14.4762			−1.31062
$123$	0.329643	−	3.78430i	0.0297230	−	0.341219i
$124$			6.81708i			0.612192i
$125$	3.59408			0.321464
$126$	8.32929	−	12.2136i	0.742032	−	1.08807i
$127$	−1.40422			−0.124604			−0.0623021	−	0.998057i	$-0.519844\pi$
$127$	−1.40422			−0.124604			−0.0623021	+	0.998057i	$0.519844\pi$
$128$			7.63286i			0.674656i
$129$	−0.866186	+	9.94381i	−0.0762635	+	0.875504i
$130$	−5.52126			−0.484247
$131$	−14.4756			−1.26474			−0.632371	−	0.774666i	$-0.717918\pi$
$131$	−14.4756			−1.26474			−0.632371	+	0.774666i	$0.717918\pi$
$132$	−3.33375	−	0.290396i	−0.290166	−	0.0252758i
$133$	−0.934803	+	2.06689i	−0.0810577	+	0.179222i
$134$			24.7546i			2.13847i
$135$	−3.96983	+	14.8830i	−0.341669	+	1.28093i
$136$			5.47929i			0.469845i
$137$		−	15.0963i		−	1.28977i	−0.764281	−	0.644884i	$-0.776906\pi$
$137$		−	15.0963i		−	1.28977i	0.764281	−	0.644884i	$-0.223094\pi$
$138$	−1.62056	+	18.6040i	−0.137951	+	1.58368i
$139$			11.9707i			1.01534i	0.861551	+	0.507672i	$0.169494\pi$
$139$			11.9707i			1.01534i	−0.861551	+	0.507672i	$0.830506\pi$
$140$	−10.4978	−	4.74791i	−0.887228	−	0.401272i
$141$	−0.223258	+	2.56300i	−0.0188017	+	0.215844i
$142$	−25.6933			−2.15614
$143$	1.31518			0.109981
$144$	14.1241	+	2.47945i	1.17701	+	0.206621i
$145$			11.8230i			0.981847i
$146$	11.8023			0.976763
$147$	−9.76516	+	7.18621i	−0.805417	+	0.592709i
$148$	−10.3549			−0.851164
$149$		−	1.38921i		−	0.113808i	−0.998380	−	0.0569042i	$-0.981877\pi$
$149$		−	1.38921i		−	0.113808i	0.998380	−	0.0569042i	$-0.0181230\pi$
$150$	12.1726	+	1.06034i	0.993892	+	0.0865760i
$151$	−0.0661750			−0.00538524			−0.00269262	−	0.999996i	$-0.500857\pi$
$151$	−0.0661750			−0.00538524			−0.00269262	+	0.999996i	$0.500857\pi$
$152$	−0.847928			−0.0687761
$153$	16.3710	+	2.87390i	1.32352	+	0.232341i
$154$	5.90506	+	2.67072i	0.475843	+	0.215213i
$155$			13.7564i			1.10494i
$156$	2.53483	+	0.220804i	0.202948	+	0.0176784i
$157$		−	24.3249i		−	1.94134i	−0.240416	−	0.970670i	$-0.577284\pi$
$157$		−	24.3249i		−	1.94134i	0.240416	−	0.970670i	$-0.422716\pi$
$158$			27.0934i			2.15544i
$159$	−1.66737	−	0.145242i	−0.132231	−	0.0115184i
$160$		−	20.5284i		−	1.62291i
$161$	6.31136	−	13.9547i	0.497405	−	1.09978i
$162$	5.70940	−	15.7605i	0.448573	−	1.23826i
$163$	−17.7843			−1.39297			−0.696486	−	0.717570i	$-0.745254\pi$
$163$	−17.7843			−1.39297			−0.696486	+	0.717570i	$0.745254\pi$
$164$	3.22178			0.251579
$165$	−6.72727	−	0.585999i	−0.523717	−	0.0456200i
$166$			23.7980i			1.84708i
$167$	20.0206			1.54924			0.774621	−	0.632426i	$-0.217941\pi$
$167$	20.0206			1.54924			0.774621	+	0.632426i	$0.217941\pi$
$168$	−3.95164	−	2.21887i	−0.304876	−	0.171190i
$169$	−1.00000			−0.0769231
$170$		−	30.5903i		−	2.34617i
$171$	−0.444741	+	2.53344i	−0.0340102	+	0.193737i
$172$	−8.46570			−0.645503
$173$	2.44738			0.186071			0.0930353	−	0.995663i	$-0.470343\pi$
$173$	2.44738			0.186071			0.0930353	+	0.995663i	$0.470343\pi$
$174$	1.11654	−	12.8179i	0.0846447	−	0.971721i
$175$	−9.13057	−	4.12954i	−0.690206	−	0.312164i
$176$			6.28658i			0.473869i
$177$	0.682094	−	7.83044i	0.0512693	−	0.588572i
$178$		−	29.4959i		−	2.21081i
$179$		−	18.3524i		−	1.37172i	−0.727733	−	0.685860i	$-0.759426\pi$
$179$		−	18.3524i		−	1.37172i	0.727733	−	0.685860i	$-0.240574\pi$
$180$	−12.8675	−	2.25886i	−0.959086	−	0.168366i
$181$		−	6.39638i		−	0.475439i	−0.971334	−	0.237720i	$-0.923600\pi$
$181$		−	6.39638i		−	0.475439i	0.971334	−	0.237720i	$-0.0763999\pi$
$182$	−4.48993	−	2.03069i	−0.332816	−	0.150525i
$183$	13.4113	+	1.16823i	0.991393	+	0.0863584i
$184$	5.72483			0.422040
$185$	−20.8954			−1.53626
$186$	1.29913	−	14.9139i	0.0952565	−	1.09354i
$187$			7.28669i			0.532855i
$188$	−2.18202			−0.159140
$189$	−8.70219	+	10.6429i	−0.632991	+	0.774159i
$190$	4.73390			0.343433
$191$			4.56088i			0.330014i	0.986292	+	0.165007i	$0.0527647\pi$
$191$			4.56088i			0.330014i	−0.986292	+	0.165007i	$0.947235\pi$
$192$	−0.501726	+	5.75981i	−0.0362089	+	0.415678i
$193$	−6.93137			−0.498931			−0.249465	−	0.968384i	$-0.580255\pi$
$193$	−6.93137			−0.498931			−0.249465	+	0.968384i	$0.580255\pi$
$194$	0.224927			0.0161488
$195$	5.11510	+	0.445566i	0.366300	+	0.0319077i
$196$	−6.79066	−	7.72208i	−0.485047	−	0.551577i
$197$			1.55939i			0.111102i	0.998456	+	0.0555508i	$0.0176915\pi$
$197$			1.55939i			0.111102i	−0.998456	+	0.0555508i	$0.982309\pi$
$198$	7.23801	+	1.27062i	0.514383	+	0.0902989i
$199$		−	3.97205i		−	0.281571i	−0.990040	−	0.140786i	$-0.955037\pi$
$199$		−	3.97205i		−	0.281571i	0.990040	−	0.140786i	$-0.0449628\pi$
$200$		−	3.74577i		−	0.264866i
$201$	1.99770	−	22.9336i	0.140907	−	1.61761i
$202$			15.0013i			1.05549i
$203$	−4.34843	+	9.61456i	−0.305200	+	0.674810i
$204$	−1.22335	+	14.0441i	−0.0856518	+	0.983282i
$205$	6.50132			0.454072
$206$	−28.6889			−1.99885
$207$	3.00269	−	17.1047i	0.208701	−	1.18886i
$208$		−	4.78002i		−	0.331435i
$209$	−1.12763			−0.0779996
$210$	22.0616	+	12.3877i	1.52240	+	0.854834i
$211$	2.34384			0.161357			0.0806783	−	0.996740i	$-0.474291\pi$
$211$	2.34384			0.161357			0.0806783	+	0.996740i	$0.474291\pi$
$212$		−	1.41952i		−	0.0974933i
$213$	23.8032	+	2.07345i	1.63097	+	0.142071i
$214$	35.5910			2.43295
$215$	−17.0832			−1.16506
$216$	−4.96519	−	1.32439i	−0.337838	−	0.0901134i
$217$	−5.05952	+	11.1868i	−0.343463	+	0.759409i
$218$			25.1501i			1.70338i
$219$	−10.9340	−	0.952444i	−0.738855	−	0.0643602i
$220$		−	5.72728i		−	0.386133i
$221$		−	5.54045i		−	0.372691i
$222$	22.6536	+	1.97332i	1.52041	+	0.132440i
$223$			0.958296i			0.0641723i	0.999485	+	0.0320861i	$0.0102151\pi$
$223$			0.958296i			0.0641723i	−0.999485	+	0.0320861i	$0.989785\pi$
$224$	7.55023	−	16.6938i	0.504471	−	1.11540i
$225$	−11.1916	−	1.96467i	−0.746107	−	0.130978i
$226$	17.4213			1.15885
$227$	−20.8754			−1.38555			−0.692776	−	0.721153i	$-0.743613\pi$
$227$	−20.8754			−1.38555			−0.692776	+	0.721153i	$0.743613\pi$
$228$	−2.17334	−	0.189316i	−0.143933	−	0.0125377i
$229$		−	23.4449i		−	1.54928i	−0.632401	−	0.774641i	$-0.717931\pi$
$229$		−	23.4449i		−	1.54928i	0.632401	−	0.774641i	$-0.282069\pi$
$230$	−31.9611			−2.10745
$231$	−5.25514	−	2.95079i	−0.345763	−	0.194148i
$232$	−3.94432			−0.258957
$233$			16.5147i			1.08191i	0.841051	+	0.540956i	$0.181937\pi$
$233$			16.5147i			1.08191i	−0.841051	+	0.540956i	$0.818063\pi$
$234$	−5.50344	−	0.966118i	−0.359771	−	0.0631571i
$235$	−4.40316			−0.287230
$236$	6.66646			0.433950
$237$	2.18644	−	25.1003i	0.142025	−	1.63044i
$238$	11.2509	−	24.8762i	0.729289	−	1.61249i
$239$		−	21.0545i		−	1.36191i	−0.732327	−	0.680953i	$-0.761566\pi$
$239$		−	21.0545i		−	1.36191i	0.732327	−	0.680953i	$-0.238434\pi$
$240$	−2.12981	+	24.4502i	−0.137479	+	1.57826i
$241$			12.7346i			0.820309i	0.912016	+	0.410154i	$0.134525\pi$
$241$			12.7346i			0.820309i	−0.912016	+	0.410154i	$0.865475\pi$
$242$		−	17.2662i		−	1.10992i
$243$	−6.56127	+	14.1404i	−0.420906	+	0.907104i
$244$			11.4178i			0.730948i
$245$	−13.7031	−	15.5826i	−0.875457	−	0.995536i
$246$	−7.04839	−	0.613971i	−0.449389	−	0.0391454i
$247$	0.857394			0.0545547
$248$	−4.58932			−0.291422
$249$	1.92050	−	22.0473i	0.121707	−	1.39719i
$250$		−	6.69408i		−	0.423371i
$251$	8.65771			0.546470			0.273235	−	0.961947i	$-0.411906\pi$
$251$	8.65771			0.546470			0.273235	+	0.961947i	$0.411906\pi$
$252$	−9.63314	−	6.56951i	−0.606831	−	0.413840i
$253$	7.61322			0.478639
$254$			2.61540i			0.164105i
$255$	−2.46864	+	28.3400i	−0.154592	+	1.77472i
$256$	20.8925			1.30578
$257$	17.4370			1.08769			0.543846	−	0.839185i	$-0.316968\pi$
$257$	17.4370			1.08769			0.543846	+	0.839185i	$0.316968\pi$
$258$	18.5207	+	1.61330i	1.15305	+	0.100440i
$259$	−16.9923	−	7.68519i	−1.05585	−	0.477535i
$260$			4.35475i			0.270070i
$261$	−2.06881	+	11.7848i	−0.128056	+	0.729463i
$262$			26.9613i			1.66568i
$263$			1.19304i			0.0735659i	0.999323	+	0.0367829i	$0.0117110\pi$
$263$			1.19304i			0.0735659i	−0.999323	+	0.0367829i	$0.988289\pi$
$264$	0.195497	−	2.24431i	0.0120320	−	0.138128i
$265$		−	2.86450i		−	0.175965i
$266$	3.84964	+	1.74110i	0.236037	+	0.106754i
$267$	−2.38032	+	27.3261i	−0.145673	+	1.67233i
$268$	19.5246			1.19265
$269$	29.9534			1.82629			0.913144	−	0.407636i	$-0.133647\pi$
$269$	29.9534			1.82629			0.913144	+	0.407636i	$0.133647\pi$
$270$	27.7201	+	7.39394i	1.68699	+	0.449981i
$271$			4.51014i			0.273972i	0.990573	+	0.136986i	$0.0437415\pi$
$271$			4.51014i			0.273972i	−0.990573	+	0.136986i	$0.956259\pi$
$272$	26.4835			1.60580
$273$	3.99576	+	2.24364i	0.241834	+	0.135791i
$274$	−28.1174			−1.69863
$275$		−	4.98135i		−	0.300387i
$276$	14.6734	+	1.27817i	0.883237	+	0.0769371i
$277$	4.90049			0.294442			0.147221	−	0.989104i	$-0.452967\pi$
$277$	4.90049			0.294442			0.147221	+	0.989104i	$0.452967\pi$
$278$	22.2958			1.33722
$279$	−2.40711	+	13.7120i	−0.144110	+	0.820915i
$280$	3.19634	−	7.06723i	0.191018	−	0.422348i
$281$			3.84395i			0.229311i	0.993405	+	0.114655i	$0.0365764\pi$
$281$			3.84395i			0.229311i	−0.993405	+	0.114655i	$0.963424\pi$
$282$	4.77367	+	0.415825i	0.284268	+	0.0247620i
$283$		−	0.239843i		−	0.0142572i	−0.999975	−	0.00712858i	$-0.997731\pi$
$283$		−	0.239843i		−	0.0142572i	0.999975	−	0.00712858i	$-0.00226912\pi$
$284$			20.2650i			1.20250i
$285$	−4.38565	−	0.382026i	−0.259784	−	0.0226293i
$286$		−	2.44956i		−	0.144846i
$287$	5.28692	+	2.39115i	0.312077	+	0.141145i
$288$	3.59209	−	20.4621i	0.211666	−	1.20574i
$289$	13.6966			0.805684
$290$	22.0207			1.29310
$291$	−0.208380	−	0.0181516i	−0.0122155	−	0.00106407i
$292$		−	9.30873i		−	0.544752i
$293$	−22.4664			−1.31250			−0.656252	−	0.754542i	$-0.727859\pi$
$293$	−22.4664			−1.31250			−0.656252	+	0.754542i	$0.727859\pi$
$294$	13.3845	+	18.1879i	0.780602	+	1.06074i
$295$	13.4525			0.783232
$296$		−	6.97098i		−	0.405180i
$297$	−6.60301	−	1.76125i	−0.383146	−	0.102198i
$298$	−2.58745			−0.149887
$299$	−5.78874			−0.334771
$300$	0.836312	−	9.60086i	0.0482845	−	0.554306i
$301$	−13.8922	−	6.28309i	−0.800731	−	0.362151i
$302$			0.123253i			0.00709241i
$303$	1.21061	−	13.8978i	0.0695476	−	0.798406i
$304$			4.09836i			0.235057i
$305$			23.0402i			1.31928i
$306$	5.35273	−	30.4915i	0.305995	−	1.74309i
$307$			22.2879i			1.27203i	0.771675	+	0.636017i	$0.219419\pi$
$307$			22.2879i			1.27203i	−0.771675	+	0.636017i	$0.780581\pi$
$308$	2.10646	−	4.65747i	0.120027	−	0.265384i
$309$	26.5785	+	2.31520i	1.51200	+	0.131707i
$310$	25.6217			1.45522
$311$	0.254803			0.0144485			0.00722427	−	0.999974i	$-0.497700\pi$
$311$	0.254803			0.0144485			0.00722427	+	0.999974i	$0.497700\pi$
$312$	−0.148647	+	1.70647i	−0.00841548	+	0.0966097i
$313$			15.2974i			0.864662i	0.901715	+	0.432331i	$0.142309\pi$
$313$			15.2974i			0.864662i	−0.901715	+	0.432331i	$0.857691\pi$
$314$	−45.3059			−2.55676
$315$	−19.4390	−	13.2568i	−1.09526	−	0.746937i
$316$	21.3692			1.20211
$317$			10.8849i			0.611356i	0.952135	+	0.305678i	$0.0988832\pi$
$317$			10.8849i			0.611356i	−0.952135	+	0.305678i	$0.901117\pi$
$318$	−0.270517	+	3.10554i	−0.0151699	+	0.174150i
$319$	−5.24539			−0.293686
$320$	−9.89518			−0.553157
$321$	−32.9728	−	2.87220i	−1.84036	−	0.160310i
$322$	−25.9910	−	11.7551i	−1.44842	−	0.655087i
$323$			4.75035i			0.264317i
$324$	−12.4307	−	4.50315i	−0.690594	−	0.250175i
$325$			3.78758i			0.210097i
$326$			33.1238i			1.83456i
$327$	2.02962	−	23.3000i	0.112238	−	1.28849i
$328$			2.16893i			0.119759i
$329$	−3.58068	−	1.61946i	−0.197409	−	0.0892835i
$330$	−1.09144	+	12.5297i	−0.0600819	+	0.689740i
$331$	−9.58815			−0.527012			−0.263506	−	0.964658i	$-0.584879\pi$
$331$	−9.58815			−0.527012			−0.263506	+	0.964658i	$0.584879\pi$
$332$	18.7700			1.03014
$333$	−20.8279	−	3.65630i	−1.14136	−	0.200364i
$334$		−	37.2890i		−	2.04037i
$335$	39.3992			2.15261
$336$	−10.7246	+	19.0998i	−0.585077	+	1.04198i
$337$	−6.34762			−0.345777			−0.172888	−	0.984941i	$-0.555310\pi$
$337$	−6.34762			−0.345777			−0.172888	+	0.984941i	$0.555310\pi$
$338$			1.86253i			0.101308i
$339$	−16.1397	−	1.40590i	−0.876588	−	0.0763579i
$340$	−24.1273			−1.30849
$341$	−6.10316			−0.330505
$342$	4.71861	+	0.828344i	0.255153	+	0.0447917i
$343$	−5.41224	−	17.7118i	−0.292234	−	0.956347i
$344$		−	5.69918i		−	0.307279i
$345$	29.6099	+	2.57927i	1.59415	+	0.138863i
$346$		−	4.55832i		−	0.245057i
$347$		−	5.26795i		−	0.282799i	−0.989953	−	0.141399i	$-0.954840\pi$
$347$		−	5.26795i		−	0.282799i	0.989953	−	0.141399i	$-0.0451601\pi$
$348$	−10.1098	−	0.880643i	−0.541941	−	0.0472074i
$349$		−	3.04859i		−	0.163188i	−0.996666	−	0.0815938i	$-0.973999\pi$
$349$		−	3.04859i		−	0.163188i	0.996666	−	0.0815938i	$-0.0260010\pi$
$350$	−7.69139	+	17.0060i	−0.411122	+	0.909008i
$351$	5.02062	+	1.33918i	0.267981	+	0.0714799i
$352$	9.10763			0.485438
$353$	12.0522			0.641475			0.320737	−	0.947168i	$-0.396069\pi$
$353$	12.0522			0.641475			0.320737	+	0.947168i	$0.396069\pi$
$354$	−14.5844	−	1.27042i	−0.775154	−	0.0675222i
$355$			40.8932i			2.17039i
$356$	−23.2641			−1.23300
$357$	−12.4308	+	22.1383i	−0.657907	+	1.17168i
$358$	−34.1819			−1.80657
$359$		−	15.1179i		−	0.797891i	−0.916975	−	0.398946i	$-0.869376\pi$
$359$		−	15.1179i		−	0.797891i	0.916975	−	0.398946i	$-0.130624\pi$
$360$	1.52069	−	8.66251i	0.0801473	−	0.456554i
$361$	18.2649			0.961309
$362$	−11.9135			−0.626158
$363$	−1.39339	+	15.9961i	−0.0731338	+	0.839576i
$364$	−1.60165	+	3.54132i	−0.0839494	+	0.185615i
$365$		−	18.7844i		−	0.983219i
$366$	2.17587	−	24.9790i	0.113735	−	1.30567i
$367$			11.2370i			0.586565i	0.956026	+	0.293282i	$0.0947476\pi$
$367$			11.2370i			0.586565i	−0.956026	+	0.293282i	$0.905252\pi$
$368$		−	27.6703i		−	1.44241i
$369$	6.48033	+	1.13761i	0.337353	+	0.0592216i
$370$			38.9183i			2.02327i
$371$	1.05355	−	2.32943i	0.0546974	−	0.120938i
$372$	−11.7630	−	1.02465i	−0.609883	−	0.0531257i
$373$	−5.84127			−0.302450			−0.151225	−	0.988499i	$-0.548322\pi$
$373$	−5.84127			−0.302450			−0.151225	+	0.988499i	$0.548322\pi$
$374$	13.5717			0.701775
$375$	−0.540213	+	6.20164i	−0.0278965	+	0.320251i
$376$		−	1.46895i		−	0.0757556i
$377$	3.98835			0.205410
$378$	19.8228	+	16.2081i	1.01957	+	0.833655i
$379$	−29.8839			−1.53503			−0.767516	−	0.641029i	$-0.778508\pi$
$379$	−29.8839			−1.53503			−0.767516	+	0.641029i	$0.778508\pi$
$380$		−	3.73374i		−	0.191537i
$381$	0.211063	−	2.42300i	0.0108131	−	0.124134i
$382$	8.49479			0.434631
$383$	−2.92462			−0.149441			−0.0747205	−	0.997205i	$-0.523806\pi$
$383$	−2.92462			−0.149441			−0.0747205	+	0.997205i	$0.523806\pi$
$384$	−13.1706	−	1.14727i	−0.672111	−	0.0585463i
$385$	4.25069	−	9.39843i	0.216635	−	0.478989i
$386$			12.9099i			0.657096i
$387$	−17.0280	−	2.98924i	−0.865583	−	0.151952i
$388$		−	0.177405i		−	0.00900638i
$389$		−	6.87721i		−	0.348688i	−0.984685	−	0.174344i	$-0.944219\pi$
$389$		−	6.87721i		−	0.348688i	0.984685	−	0.174344i	$-0.0557805\pi$
$390$	0.829881	−	9.52703i	0.0420227	−	0.482420i
$391$		−	32.0722i		−	1.62196i
$392$	5.19857	−	4.57153i	0.262568	−	0.230897i
$393$	2.17578	−	24.9779i	0.109754	−	1.25997i
$394$	2.90440			0.146322
$395$	43.1216			2.16968
$396$	1.00217	−	5.70879i	0.0503608	−	0.286878i
$397$			19.0462i			0.955902i	0.878387	+	0.477951i	$0.158620\pi$
$397$			19.0462i			0.955902i	−0.878387	+	0.477951i	$0.841380\pi$
$398$	−7.39807			−0.370832
$399$	−3.42594	−	1.92368i	−0.171511	−	0.0963046i
$400$	−18.1047			−0.905235
$401$		−	15.5169i		−	0.774879i	−0.921895	−	0.387440i	$-0.873360\pi$
$401$		−	15.5169i		−	0.774879i	0.921895	−	0.387440i	$-0.126640\pi$
$402$	−42.7145	−	3.72078i	−2.13041	−	0.185576i
$403$	4.64055			0.231162
$404$	11.8319			0.588659
$405$	−25.0843	−	9.08703i	−1.24645	−	0.451538i
$406$	17.9074	+	8.09909i	0.888730	+	0.401951i
$407$		−	9.27044i		−	0.459518i
$408$	−9.45460	−	0.823572i	−0.468072	−	0.0407729i
$409$		−	19.2780i		−	0.953234i	−0.879111	−	0.476617i	$-0.841863\pi$
$409$		−	19.2780i		−	0.953234i	0.879111	−	0.476617i	$-0.158137\pi$
$410$		−	12.1089i		−	0.598017i
$411$	26.0490	+	2.26908i	1.28490	+	0.111925i
$412$			22.6277i			1.11478i
$413$	10.9396	+	4.94773i	0.538304	+	0.243462i
$414$	−31.8580	−	5.59261i	−1.56573	−	0.274862i
$415$	37.8766			1.85929
$416$	−6.92501			−0.339527
$417$	−20.6557	−	1.79928i	−1.01151	−	0.0881109i
$418$			2.10024i			0.102726i
$419$	34.9258			1.70623			0.853117	−	0.521719i	$-0.174709\pi$
$419$	34.9258			1.70623			0.853117	+	0.521719i	$0.174709\pi$
$420$	9.77050	−	17.4005i	0.476751	−	0.849059i
$421$	−9.15019			−0.445953			−0.222976	−	0.974824i	$-0.571577\pi$
$421$	−9.15019			−0.445953			−0.222976	+	0.974824i	$0.571577\pi$
$422$		−	4.36548i		−	0.212508i
$423$	−4.38894	−	0.770471i	−0.213398	−	0.0374616i
$424$	0.955637			0.0464098
$425$	−20.9849			−1.01792
$426$	3.86187	−	44.3343i	0.187108	−	2.14800i
$427$	−8.47407	+	18.7365i	−0.410089	+	0.906723i
$428$		−	28.0715i		−	1.35689i
$429$	−0.197680	+	2.26936i	−0.00954407	+	0.109566i
$430$			31.8179i			1.53440i
$431$			16.2225i			0.781409i	0.920516	+	0.390704i	$0.127769\pi$
$431$			16.2225i			0.781409i	−0.920516	+	0.390704i	$0.872231\pi$
$432$	−6.40128	+	23.9986i	−0.307982	+	1.15464i
$433$		−	14.6220i		−	0.702687i	−0.936247	−	0.351344i	$-0.885725\pi$
$433$		−	14.6220i		−	0.702687i	0.936247	−	0.351344i	$-0.114275\pi$
$434$	20.8358	+	9.42351i	1.00015	+	0.452343i
$435$	−20.4008	−	1.77707i	−0.978143	−	0.0852042i
$436$	19.8365			0.949997
$437$	4.96323			0.237423
$438$	−1.77396	+	20.3650i	−0.0847629	+	0.973078i
$439$			26.2250i			1.25165i	0.779962	+	0.625827i	$0.215238\pi$
$439$			26.2250i			1.25165i	−0.779962	+	0.625827i	$0.784762\pi$
$440$	3.85566			0.183811
$441$	−10.9322	−	17.9301i	−0.520579	−	0.853814i
$442$	−10.3193			−0.490838
$443$		−	18.9263i		−	0.899214i	−0.893226	−	0.449607i	$-0.851564\pi$
$443$		−	18.9263i		−	0.899214i	0.893226	−	0.449607i	$-0.148436\pi$
$444$	1.55640	−	17.8675i	0.0738636	−	0.847953i
$445$	−46.9454			−2.22542
$446$	1.78486			0.0845154
$447$	2.39710	+	0.208807i	0.113379	+	0.00987624i
$448$	−8.04683	−	3.63939i	−0.380177	−	0.171945i
$449$			5.29640i			0.249952i	0.992160	+	0.124976i	$0.0398855\pi$
$449$			5.29640i			0.249952i	−0.992160	+	0.124976i	$0.960115\pi$
$450$	−3.65925	+	20.8447i	−0.172499	+	0.982630i
$451$			2.88438i			0.135820i
$452$		−	13.7406i		−	0.646302i
$453$	0.00994652	−	0.114186i	0.000467328	−	0.00536493i
$454$			38.8812i			1.82478i
$455$	−3.23202	+	7.14613i	−0.151519	+	0.335016i
$456$	0.127449	−	1.46311i	0.00596835	−	0.0685166i
$457$	23.9299			1.11939			0.559697	−	0.828697i	$-0.310918\pi$
$457$	23.9299			1.11939			0.559697	+	0.828697i	$0.310918\pi$
$458$	−43.6668			−2.04042
$459$	−7.41964	+	27.8165i	−0.346319	+	1.29836i
$460$			25.2085i			1.17535i
$461$	0.559266			0.0260476			0.0130238	−	0.999915i	$-0.495854\pi$
$461$	0.559266			0.0260476			0.0130238	+	0.999915i	$0.495854\pi$
$462$	−5.49594	+	9.78786i	−0.255694	+	0.455372i
$463$	13.2869			0.617493			0.308747	−	0.951144i	$-0.400091\pi$
$463$	13.2869			0.617493			0.308747	+	0.951144i	$0.400091\pi$
$464$			19.0644i			0.885042i
$465$	−23.7369	−	2.06767i	−1.10077	−	0.0958861i
$466$	30.7591			1.42489
$467$	−11.0990			−0.513601			−0.256801	−	0.966464i	$-0.582668\pi$
$467$	−11.0990			−0.513601			−0.256801	+	0.966464i	$0.582668\pi$
$468$	−0.762001	+	4.34069i	−0.0352235	+	0.200649i
$469$	32.0397	+	14.4908i	1.47946	+	0.669123i
$470$			8.20102i			0.378285i
$471$	41.9731	+	3.65619i	1.93402	+	0.168468i
$472$			4.48792i			0.206573i
$473$		−	7.57912i		−	0.348488i
$474$	−46.7502	−	4.07232i	−2.14731	−	0.187048i
$475$		−	3.24745i		−	0.149003i
$476$	−19.6205	−	8.87388i	−0.899304	−	0.406734i
$477$	0.501234	−	2.85525i	0.0229499	−	0.130733i
$478$	−39.2148			−1.79364
$479$	−11.1817			−0.510906			−0.255453	−	0.966821i	$-0.582225\pi$
$479$	−11.1817			−0.510906			−0.255453	+	0.966821i	$0.582225\pi$
$480$	35.4221	+	3.08555i	1.61679	+	0.140836i
$481$			7.04880i			0.321398i
$482$	23.7186			1.08035
$483$	23.1304	+	12.9878i	1.05247	+	0.590967i
$484$	−13.6183			−0.619014
$485$		−	0.357991i		−	0.0162555i
$486$	26.3369	+	12.2206i	1.19466	+	0.554337i
$487$	21.7612			0.986096			0.493048	−	0.870002i	$-0.335883\pi$
$487$	21.7612			0.986096			0.493048	+	0.870002i	$0.335883\pi$
$488$	−7.68654			−0.347954
$489$	2.67309	−	30.6871i	0.120881	−	1.38772i
$490$	−29.0231	+	25.5224i	−1.31113	+	1.15298i
$491$		−	35.2695i		−	1.59169i	−0.605502	−	0.795844i	$-0.707027\pi$
$491$		−	35.2695i		−	1.59169i	0.605502	−	0.795844i	$-0.292973\pi$
$492$	−0.484254	+	5.55923i	−0.0218319	+	0.250630i
$493$			22.0973i			0.995211i
$494$		−	1.59692i		−	0.0718490i
$495$	2.02230	−	11.5199i	0.0908958	−	0.517783i
$496$			22.1819i			0.995998i
$497$	−15.0403	+	33.2547i	−0.674649	+	1.49168i
$498$	−41.0638	−	3.57699i	−1.84011	−	0.160289i
$499$	−9.98195			−0.446853			−0.223427	−	0.974721i	$-0.571724\pi$
$499$	−9.98195			−0.446853			−0.223427	+	0.974721i	$0.571724\pi$
$500$	−5.27978			−0.236119
$501$	−3.00923	+	34.5459i	−0.134442	+	1.54340i
$502$		−	16.1253i		−	0.719706i
$503$	−41.0766			−1.83152			−0.915758	−	0.401730i	$-0.868409\pi$
$503$	−41.0766			−1.83152			−0.915758	+	0.401730i	$0.868409\pi$
$504$	4.42266	−	6.48512i	0.197001	−	0.288870i
$505$	23.8759			1.06247
$506$		−	14.1799i		−	0.630372i
$507$	0.150306	−	1.72552i	0.00667534	−	0.0766329i
$508$	2.06283			0.0915233
$509$	−3.93663			−0.174488			−0.0872439	−	0.996187i	$-0.527806\pi$
$509$	−3.93663			−0.174488			−0.0872439	+	0.996187i	$0.527806\pi$
$510$	52.7841	+	4.59792i	2.33732	+	0.203599i
$511$	6.90878	−	15.2756i	0.305626	−	0.675752i
$512$		−	23.6472i		−	1.04507i
$513$	−4.30465	−	1.14820i	−0.190055	−	0.0506943i
$514$		−	32.4770i		−	1.43250i
$515$			45.6610i			2.01206i
$516$	1.27245	−	14.6077i	0.0560164	−	0.643068i
$517$		−	1.95350i		−	0.0859151i
$518$	−14.3139	+	31.6486i	−0.628917	+	1.39056i
$519$	−0.367856	+	4.22299i	−0.0161471	+	0.185369i
$520$	−2.93166			−0.128562
$521$	24.5998			1.07774			0.538869	−	0.842390i	$-0.318852\pi$
$521$	24.5998			1.07774			0.538869	+	0.842390i	$0.318852\pi$
$522$	21.9496	+	3.85322i	0.960710	+	0.168651i
$523$		−	9.96762i		−	0.435854i	−0.975965	−	0.217927i	$-0.930071\pi$
$523$		−	9.96762i		−	0.435854i	0.975965	−	0.217927i	$-0.0699294\pi$
$524$	21.2650			0.928968
$525$	8.49797	−	15.1343i	0.370882	−	0.660513i
$526$	2.22207			0.0968869
$527$			25.7108i			1.11998i
$528$	−10.8476	−	0.944913i	−0.472081	−	0.0411221i
$529$	−10.5095			−0.456934
$530$	−5.33522			−0.231747
$531$	13.4090	+	2.35393i	0.581902	+	0.102152i
$532$	1.37325	−	3.03630i	0.0595378	−	0.131640i
$533$		−	2.19314i		−	0.0949956i
$534$	50.8957	+	4.43342i	2.20247	+	0.191853i
$535$		−	56.6462i		−	2.44903i
$536$			13.1441i			0.567740i
$537$	31.6673	+	2.75848i	1.36655	+	0.119037i
$538$		−	55.7891i		−	2.40524i
$539$	6.91338	−	6.07950i	0.297780	−	0.261863i
$540$	5.83178	−	21.8636i	0.250960	−	0.940857i
$541$	18.9903			0.816456			0.408228	−	0.912880i	$-0.366147\pi$
$541$	18.9903			0.816456			0.408228	+	0.912880i	$0.366147\pi$
$542$	8.40028			0.360823
$543$	11.0371	+	0.961417i	0.473646	+	0.0412584i
$544$		−	38.3677i		−	1.64500i
$545$	40.0287			1.71464
$546$	4.17885	−	7.44222i	0.178838	−	0.318498i
$547$	20.5613			0.879140			0.439570	−	0.898208i	$-0.355131\pi$
$547$	20.5613			0.879140			0.439570	+	0.898208i	$0.355131\pi$
$548$			22.1769i			0.947350i
$549$	−4.03162	+	22.9659i	−0.172065	+	0.980159i
$550$	−9.27792			−0.395612
$551$	−3.41959			−0.145679
$552$	−0.860479	+	9.87829i	−0.0366244	+	0.420448i
$553$	35.0668	+	15.8599i	1.49119	+	0.674430i
$554$		−	9.12732i		−	0.387783i
$555$	3.14071	−	36.0553i	0.133316	−	1.53046i
$556$		−	17.5853i		−	0.745782i
$557$		−	1.54123i		−	0.0653039i	−0.999467	−	0.0326519i	$-0.989605\pi$
$557$		−	1.54123i		−	0.0653039i	0.999467	−	0.0326519i	$-0.0103953\pi$
$558$	25.5390	+	4.48333i	1.08115	+	0.189794i
$559$			5.76280i			0.243741i
$560$	−34.1586	−	15.4491i	−1.44346	−	0.652844i
$561$	−12.5733	−	1.09524i	−0.530845	−	0.0462409i
$562$	7.15947			0.302004
$563$	17.8806			0.753578			0.376789	−	0.926299i	$-0.377028\pi$
$563$	17.8806			0.753578			0.376789	+	0.926299i	$0.377028\pi$
$564$	0.327971	−	3.76511i	0.0138101	−	0.158540i
$565$		−	27.7275i		−	1.16651i
$566$	−0.446714			−0.0187768
$567$	−17.0565	−	16.6155i	−0.716308	−	0.697785i
$568$	−13.6426			−0.572429
$569$			21.5058i			0.901571i	0.892632	+	0.450786i	$0.148856\pi$
$569$			21.5058i			0.901571i	−0.892632	+	0.450786i	$0.851144\pi$
$570$	−0.711535	+	8.16842i	−0.0298029	+	0.342137i
$571$	7.64404			0.319893			0.159947	−	0.987126i	$-0.448868\pi$
$571$	7.64404			0.319893			0.159947	+	0.987126i	$0.448868\pi$
$572$	−1.93203			−0.0807822
$573$	−7.86988	−	0.685530i	−0.328769	−	0.0286384i
$574$	4.45359	−	9.84706i	0.185889	−	0.411008i
$575$			21.9253i			0.914349i
$576$	−9.86323	−	1.73147i	−0.410968	−	0.0721447i
$577$			26.7494i			1.11359i	0.830649	+	0.556796i	$0.187970\pi$
$577$			26.7494i			1.11359i	−0.830649	+	0.556796i	$0.812030\pi$
$578$		−	25.5104i		−	1.06109i
$579$	1.04183	−	11.9602i	0.0432969	−	0.497049i
$580$		−	17.3683i		−	0.721179i
$581$	30.8015	+	13.9308i	1.27786	+	0.577946i
$582$	−0.0338079	+	0.388115i	−0.00140138	+	0.0160879i
$583$	1.27086			0.0526338
$584$	6.26672			0.259319
$585$	−1.53766	+	8.75921i	−0.0635746	+	0.362149i
$586$			41.8445i			1.72858i
$587$	−11.3208			−0.467260			−0.233630	−	0.972326i	$-0.575060\pi$
$587$	−11.3208			−0.467260			−0.233630	+	0.972326i	$0.575060\pi$
$588$	14.3453	−	10.5567i	0.591588	−	0.435352i
$589$	−3.97878			−0.163943
$590$		−	25.0556i		−	1.03152i
$591$	−2.69075	−	0.234386i	−0.110682	−	0.00964134i
$592$	−33.6934			−1.38479
$593$	−31.0530			−1.27520			−0.637598	−	0.770369i	$-0.720072\pi$
$593$	−31.0530			−1.27520			−0.637598	+	0.770369i	$0.720072\pi$
$594$	−3.28039	+	12.2983i	−0.134596	+	0.504606i
$595$	−39.5928	−	17.9069i	−1.62315	−	0.734110i
$596$			2.04078i			0.0835937i
$597$	6.85384	+	0.597025i	0.280509	+	0.0244346i
$598$			10.7817i			0.440897i
$599$		−	2.01683i		−	0.0824053i	−0.999151	−	0.0412027i	$-0.986881\pi$
$599$		−	2.01683i		−	0.0824053i	0.999151	−	0.0412027i	$-0.0131189\pi$
$600$	6.46338	+	0.563013i	0.263867	+	0.0229849i
$601$			25.2933i			1.03173i	0.856669	+	0.515867i	$0.172530\pi$
$601$			25.2933i			1.03173i	−0.856669	+	0.515867i	$0.827470\pi$
$602$	−11.7025	+	25.8746i	−0.476956	+	1.05457i
$603$	39.2720	+	6.89413i	1.59928	+	0.280751i
$604$	0.0972126			0.00395552
$605$	−27.4808			−1.11725
$606$	−25.8850	−	2.25480i	−1.05151	−	0.0915948i
$607$		−	0.784522i		−	0.0318428i	−0.999873	−	0.0159214i	$-0.994932\pi$
$607$		−	0.784522i		−	0.0318428i	0.999873	−	0.0159214i	$-0.00506815\pi$
$608$	5.93746			0.240796
$609$	−15.9365	−	8.94842i	−0.645779	−	0.362608i
$610$	42.9132			1.73750
$611$			1.48535i			0.0600910i
$612$	−24.0494	−	4.22183i	−0.972140	−	0.170657i
$613$	−0.440265			−0.0177821			−0.00889107	−	0.999960i	$-0.502830\pi$
$613$	−0.440265			−0.0177821			−0.00889107	+	0.999960i	$0.502830\pi$
$614$	41.5118			1.67528
$615$	−0.977190	+	11.2181i	−0.0394041	+	0.452359i
$616$	3.13545	+	1.41809i	0.126331	+	0.0571364i
$617$			9.17280i			0.369283i	0.982806	+	0.184642i	$0.0591124\pi$
$617$			9.17280i			0.369283i	−0.982806	+	0.184642i	$0.940888\pi$
$618$	4.31213	−	49.5032i	0.173459	−	1.99131i
$619$		−	19.7580i		−	0.794141i	−0.917788	−	0.397071i	$-0.870027\pi$
$619$		−	19.7580i		−	0.794141i	0.917788	−	0.397071i	$-0.129973\pi$
$620$		−	20.2085i		−	0.811592i
$621$	29.0630	+	7.75213i	1.16626	+	0.311082i
$622$		−	0.474578i		−	0.0190289i
$623$	−38.1763	−	17.2662i	−1.52950	−	0.691757i
$624$	8.24800	+	0.718467i	0.330184	+	0.0287617i
$625$	−29.5921			−1.18369
$626$	28.4919			1.13877
$627$	0.169490	−	1.94574i	0.00676876	−	0.0777053i
$628$			35.7339i			1.42594i
$629$	−39.0536			−1.55717
$630$	−24.6912	+	36.2057i	−0.983722	+	1.44247i
$631$	3.73881			0.148840			0.0744198	−	0.997227i	$-0.476290\pi$
$631$	3.73881			0.148840			0.0744198	+	0.997227i	$0.476290\pi$
$632$			14.3860i			0.572243i
$633$	−0.352294	+	4.04434i	−0.0140024	+	0.160748i
$634$	20.2735			0.805162
$635$	4.16264			0.165189
$636$	2.44941	+	0.213364i	0.0971255	+	0.00846042i
$637$	−5.25661	+	4.62256i	−0.208274	+	0.183153i
$638$			9.76971i			0.386787i
$639$	−7.15556	+	40.7612i	−0.283070	+	1.61249i
$640$		−	22.6267i		−	0.894400i
$641$			26.9317i			1.06374i	0.846827	+	0.531869i	$0.178510\pi$
$641$			26.9317i			1.06374i	−0.846827	+	0.531869i	$0.821490\pi$
$642$	−5.34955	+	61.4128i	−0.211130	+	2.42377i
$643$		−	37.3721i		−	1.47381i	−0.675996	−	0.736905i	$-0.736286\pi$
$643$		−	37.3721i		−	1.47381i	0.675996	−	0.736905i	$-0.263714\pi$
$644$	−9.27154	+	20.4998i	−0.365350	+	0.807803i
$645$	2.56771	−	29.4773i	0.101104	−	1.16067i
$646$	8.84768			0.348107
$647$	−29.5608			−1.16215			−0.581077	−	0.813848i	$-0.697369\pi$
$647$	−29.5608			−1.16215			−0.581077	+	0.813848i	$0.697369\pi$
$648$	3.03156	−	8.36846i	0.119091	−	0.328744i
$649$			5.96831i			0.234277i
$650$	7.05449			0.276700
$651$	−18.5425	−	10.4117i	−0.726739	−	0.408068i
$652$	26.1255			1.02315
$653$		−	37.7653i		−	1.47787i	−0.673777	−	0.738934i	$-0.735329\pi$
$653$		−	37.7653i		−	1.47787i	0.673777	−	0.738934i	$-0.264671\pi$
$654$	−43.3970	−	3.78023i	−1.69696	−	0.147819i
$655$	42.9113			1.67668
$656$	10.4833			0.409302
$657$	3.28692	−	18.7237i	0.128235	−	0.730482i
$658$	−3.01629	+	6.66913i	−0.117587	+	0.259990i
$659$		−	37.2984i		−	1.45294i	−0.687199	−	0.726469i	$-0.741160\pi$
$659$		−	37.2984i		−	1.45294i	0.687199	−	0.726469i	$-0.258840\pi$
$660$	9.88252	+	0.860847i	0.384676	+	0.0335084i
$661$		−	34.5667i		−	1.34449i	−0.740329	−	0.672245i	$-0.765330\pi$
$661$		−	34.5667i		−	1.34449i	0.740329	−	0.672245i	$-0.234670\pi$
$662$			17.8582i			0.694080i
$663$	9.56014	+	0.832766i	0.371285	+	0.0323419i
$664$			12.6362i			0.490378i
$665$	2.77112	−	6.12705i	0.107459	−	0.237597i
$666$	−6.80998	+	38.7926i	−0.263881	+	1.50318i
$667$	23.0875			0.893952
$668$	−29.4108			−1.13794
$669$	−1.65356	−	0.144038i	−0.0639302	−	0.00556883i
$670$		−	73.3823i		−	2.83500i
$671$	−10.2220			−0.394617
$672$	27.6707	+	15.5372i	1.06742	+	0.599362i
$673$	−6.75286			−0.260304			−0.130152	−	0.991494i	$-0.541546\pi$
$673$	−6.75286			−0.260304			−0.130152	+	0.991494i	$0.541546\pi$
$674$			11.8226i			0.455391i
$675$	5.07223	−	19.0160i	0.195230	−	0.731926i
$676$	1.46902			0.0565009
$677$	−28.3626			−1.09006			−0.545031	−	0.838416i	$-0.683482\pi$
$677$	−28.3626			−1.09006			−0.545031	+	0.838416i	$0.683482\pi$
$678$	−2.61853	+	30.0607i	−0.100564	+	1.15447i
$679$	0.131667	−	0.291121i	0.00505291	−	0.0111722i
$680$		−	16.2427i		−	0.622880i
$681$	3.13771	−	36.0209i	0.120237	−	1.38032i
$682$			11.3673i			0.435277i
$683$		−	37.9019i		−	1.45027i	−0.688604	−	0.725137i	$-0.741776\pi$
$683$		−	37.9019i		−	1.45027i	0.688604	−	0.725137i	$-0.258224\pi$
$684$	0.653335	−	3.72169i	0.0249809	−	0.142302i
$685$			44.7514i			1.70986i
$686$	−32.9888	+	10.0805i	−1.25952	+	0.384874i
$687$	40.4546	+	3.52392i	1.54344	+	0.134446i
$688$	−27.5463			−1.05019
$689$	−0.966305			−0.0368133
$690$	4.80396	−	55.1495i	0.182884	−	2.09950i
$691$			4.36255i			0.165959i	0.996551	+	0.0829796i	$0.0264436\pi$
$691$			4.36255i			0.165959i	−0.996551	+	0.0829796i	$0.973556\pi$
$692$	−3.59525			−0.136671
$693$	5.88152	−	8.62430i	0.223420	−	0.327610i
$694$	−9.81173			−0.372448
$695$		−	35.4858i		−	1.34605i
$696$	0.592857	−	6.80599i	0.0224722	−	0.257980i
$697$	12.1510			0.460252
$698$	−5.67810			−0.214919
$699$	−28.4963	−	2.48226i	−1.07783	−	0.0938877i
$700$	13.4130	+	6.06639i	0.506965	+	0.229288i
$701$			28.6905i			1.08363i	0.840499	+	0.541813i	$0.182262\pi$
$701$			28.6905i			1.08363i	−0.840499	+	0.541813i	$0.817738\pi$
$702$	2.49426	−	9.35106i	0.0941396	−	0.352933i
$703$		−	6.04360i		−	0.227939i
$704$		−	4.39009i		−	0.165458i
$705$	0.661823	−	7.59772i	0.0249257	−	0.286147i
$706$		−	22.4476i		−	0.844828i
$707$	19.4161	+	8.78143i	0.730217	+	0.330260i
$708$	−1.00201	+	11.5031i	−0.0376579	+	0.432313i
$709$	−9.72613			−0.365272			−0.182636	−	0.983181i	$-0.558463\pi$
$709$	−9.72613			−0.365272			−0.182636	+	0.983181i	$0.558463\pi$
$710$	76.1649			2.85842
$711$	42.9824	+	7.54548i	1.61197	+	0.282978i
$712$		−	15.6616i		−	0.586944i
$713$	26.8629			1.00603
$714$	41.2333	+	23.1527i	1.54312	+	0.866469i
$715$	−3.89870			−0.145803
$716$			26.9601i			1.00754i
$717$	36.3300	+	3.16463i	1.35677	+	0.118185i
$718$	−28.1575			−1.05083
$719$	−45.8148			−1.70860			−0.854302	−	0.519777i	$-0.826015\pi$
$719$	−45.8148			−1.70860			−0.854302	+	0.519777i	$0.826015\pi$
$720$	−41.8692	−	7.35006i	−1.56037	−	0.273921i
$721$	−16.7938	+	37.1319i	−0.625436	+	1.38286i
$722$		−	34.0189i		−	1.26605i
$723$	−21.9738	−	1.91409i	−0.817214	−	0.0711859i
$724$			9.39643i			0.349216i
$725$		−	15.1062i		−	0.561030i
$726$	29.7932	+	2.59523i	1.10573	+	0.0963179i
$727$		−	11.8965i		−	0.441219i	−0.975362	−	0.220609i	$-0.929195\pi$
$727$		−	11.8965i		−	0.441219i	0.975362	−	0.220609i	$-0.0708046\pi$
$728$	−2.38405	−	1.07825i	−0.0883586	−	0.0399625i
$729$	−23.4132	−	13.4470i	−0.867156	−	0.498036i
$730$	−34.9865			−1.29491
$731$	−31.9285			−1.18092
$732$	−19.7016	−	1.71616i	−0.728190	−	0.0634313i
$733$			45.3273i			1.67420i	0.547047	+	0.837102i	$0.315752\pi$
$733$			45.3273i			1.67420i	−0.547047	+	0.837102i	$0.684248\pi$
$734$	20.9292			0.772511
$735$	28.9477	−	21.3027i	1.06775	−	0.785762i
$736$	−40.0871			−1.47763
$737$			17.4799i			0.643879i
$738$	2.11884	−	12.0698i	0.0779954	−	0.444296i
$739$	9.77688			0.359648			0.179824	−	0.983699i	$-0.442447\pi$
$739$	9.77688			0.359648			0.179824	+	0.983699i	$0.442447\pi$
$740$	30.6958			1.12840
$741$	−0.128872	+	1.47945i	−0.00473423	+	0.0543489i
$742$	−4.33864	−	1.96226i	−0.159276	−	0.0720369i
$743$			1.90584i			0.0699186i	0.999389	+	0.0349593i	$0.0111302\pi$
$743$			1.90584i			0.0699186i	−0.999389	+	0.0349593i	$0.988870\pi$
$744$	0.689805	−	7.91895i	0.0252895	−	0.290323i
$745$			4.11815i			0.150877i
$746$			10.8796i			0.398329i
$747$	37.7543	+	6.62770i	1.38136	+	0.242495i
$748$		−	10.7043i		−	0.391389i
$749$	20.8341	−	46.0651i	0.761263	−	1.68318i
$750$	11.5507	+	1.00616i	0.421774	+	0.0367399i
$751$	−15.1714			−0.553612			−0.276806	−	0.960926i	$-0.589276\pi$
$751$	−15.1714			−0.553612			−0.276806	+	0.960926i	$0.589276\pi$
$752$	−7.10001			−0.258911
$753$	−1.30131	+	14.9390i	−0.0474224	+	0.544408i
$754$		−	7.42843i		−	0.270527i
$755$	0.196168			0.00713929
$756$	12.7837	−	15.6347i	0.464940	−	0.568629i
$757$	−5.75488			−0.209165			−0.104582	−	0.994516i	$-0.533351\pi$
$757$	−5.75488			−0.209165			−0.104582	+	0.994516i	$0.533351\pi$
$758$			55.6597i			2.02165i
$759$	−1.14432	+	13.1367i	−0.0415361	+	0.476834i
$760$	2.51359			0.0911774
$761$	45.2509			1.64034			0.820171	−	0.572118i	$-0.193878\pi$
$761$	45.2509			1.64034			0.820171	+	0.572118i	$0.193878\pi$
$762$	−4.51292	−	0.393112i	−0.163486	−	0.0142409i
$763$	32.5516	+	14.7223i	1.17845	+	0.532984i
$764$		−	6.70005i		−	0.242399i
$765$	−48.5300	−	8.51936i	−1.75461	−	0.308018i
$766$			5.44719i			0.196815i
$767$		−	4.53802i		−	0.163859i
$768$	−3.14027	+	36.0503i	−0.113315	+	1.30085i
$769$			21.3403i			0.769552i	0.923010	+	0.384776i	$0.125721\pi$
$769$			21.3403i			0.769552i	−0.923010	+	0.384776i	$0.874279\pi$
$770$	−17.5049	−	7.91704i	−0.630832	−	0.285310i
$771$	−2.62090	+	30.0879i	−0.0943893	+	1.08359i
$772$	10.1823			0.366471
$773$	24.0692			0.865711			0.432855	−	0.901463i	$-0.357506\pi$
$773$	24.0692			0.865711			0.432855	+	0.901463i	$0.357506\pi$
$774$	−5.56755	+	31.7152i	−0.200121	+	1.13998i
$775$		−	17.5765i		−	0.631366i
$776$	0.119431			0.00428731
$777$	15.8150	−	28.1653i	0.567359	−	1.01042i
$778$	−12.8090			−0.459226
$779$			1.88039i			0.0673719i
$780$	−7.51420	−	0.654547i	−0.269051	−	0.0234366i
$781$	−18.1427			−0.649196
$782$	−59.7355			−2.13614
$783$	−20.0240	−	5.34110i	−0.715599	−	0.190875i
$784$	−22.0959	−	25.1267i	−0.789140	−	0.897381i
$785$			72.1084i			2.57366i
$786$	−46.5222	−	4.05246i	−1.65939	−	0.144546i
$787$			8.04108i			0.286634i	0.989677	+	0.143317i	$0.0457768\pi$
$787$			8.04108i			0.286634i	−0.989677	+	0.143317i	$0.954223\pi$
$788$		−	2.29077i		−	0.0816054i
$789$	−2.05861	−	0.179321i	−0.0732883	−	0.00638401i
$790$		−	80.3153i		−	2.85749i
$791$	10.1980	−	22.5482i	0.362600	−	0.801722i
$792$	3.84321	+	0.674668i	0.136562	+	0.0239733i
$793$	7.77235			0.276004
$794$	35.4742			1.25893
$795$	4.94274	+	0.430553i	0.175301	+	0.0152701i
$796$			5.83504i			0.206818i
$797$	−16.4015			−0.580971			−0.290486	−	0.956879i	$-0.593817\pi$
$797$	−16.4015			−0.580971			−0.290486	+	0.956879i	$0.593817\pi$
$798$	−3.58292	+	6.38092i	−0.126834	+	0.225882i
$799$	−8.22953			−0.291140
$800$			26.2290i			0.927337i
$801$	−46.7938	−	8.21457i	−1.65338	−	0.290247i
$802$	−28.9008			−1.02052
$803$	8.33387			0.294096
$804$	−2.93467	+	33.6900i	−0.103498	+	1.18815i
$805$	−18.7093	+	41.3670i	−0.659417	+	1.45800i
$806$		−	8.64318i		−	0.304443i
$807$	−4.50218	+	51.6850i	−0.158484	+	1.81940i
$808$			7.96535i			0.280220i
$809$		−	9.57409i		−	0.336607i	−0.985735	−	0.168304i	$-0.946171\pi$
$809$		−	9.57409i		−	0.336607i	0.985735	−	0.168304i	$-0.0538289\pi$
$810$	−16.9249	+	46.7202i	−0.594680	+	1.64158i
$811$			13.5289i			0.475064i	0.971380	+	0.237532i	$0.0763385\pi$
$811$			13.5289i			0.475064i	−0.971380	+	0.237532i	$0.923662\pi$
$812$	6.38795	−	14.1240i	0.224173	−	0.495656i
$813$	−7.78232	−	0.677903i	−0.272938	−	0.0237751i
$814$	−17.2665			−0.605190
$815$	52.7195			1.84668
$816$	−3.98063	+	45.6977i	−0.139350	+	1.59974i
$817$		−	4.94099i		−	0.172863i
$818$	−35.9058			−1.25542
$819$	−4.47203	+	6.55751i	−0.156265	+	0.229138i
$820$	−9.55059			−0.333521
$821$		−	39.7737i		−	1.38811i	−0.719921	−	0.694057i	$-0.755822\pi$
$821$		−	39.7737i		−	1.38811i	0.719921	−	0.694057i	$-0.244178\pi$
$822$	4.22623	−	48.5171i	0.147407	−	1.69223i
$823$	25.0059			0.871652			0.435826	−	0.900031i	$-0.356456\pi$
$823$	25.0059			0.871652			0.435826	+	0.900031i	$0.356456\pi$
$824$	−15.2331			−0.530672
$825$	8.59540	+	0.748729i	0.299253	+	0.0260674i
$826$	9.21531	−	20.3754i	0.320642	−	0.708951i
$827$			21.2758i			0.739831i	0.929065	+	0.369916i	$0.120613\pi$
$827$			21.2758i			0.739831i	−0.929065	+	0.369916i	$0.879387\pi$
$828$	−4.41102	+	25.1271i	−0.153294	+	0.873228i
$829$			36.9693i			1.28400i	0.766706	+	0.641999i	$0.221895\pi$
$829$			36.9693i			1.28400i	−0.766706	+	0.641999i	$0.778105\pi$
$830$		−	70.5464i		−	2.44870i
$831$	−0.736575	+	8.45588i	−0.0255515	+	0.293331i
$832$			3.33802i			0.115725i
$833$	−25.6111	−	29.1240i	−0.887372	−	1.00909i
$834$	−3.35121	+	38.4718i	−0.116043	+	1.33217i
$835$	−59.3488			−2.05385
$836$	1.65651			0.0572916
$837$	−23.2985	−	6.21451i	−0.805312	−	0.214805i
$838$		−	65.0503i		−	2.24713i
$839$	−25.5086			−0.880654			−0.440327	−	0.897838i	$-0.645137\pi$
$839$	−25.5086			−0.880654			−0.440327	+	0.897838i	$0.645137\pi$
$840$	11.7142	+	6.57759i	0.404178	+	0.226948i
$841$	13.0931			0.451485
$842$			17.0425i			0.587324i
$843$	−6.63280	−	0.577770i	−0.228446	−	0.0198995i
$844$	−3.44316			−0.118518
$845$	2.96439			0.101978
$846$	−1.43503	+	8.17455i	−0.0493372	+	0.281047i
$847$	−22.3476	−	10.1073i	−0.767871	−	0.347290i
$848$		−	4.61895i		−	0.158615i
$849$	0.413852	+	0.0360499i	0.0142034	+	0.00123723i
$850$			39.0851i			1.34061i
$851$			40.8037i			1.39873i
$852$	−34.9675	−	3.04595i	−1.19797	−	0.104353i
$853$		−	29.4069i		−	1.00687i	−0.864032	−	0.503437i	$-0.832069\pi$
$853$		−	29.4069i		−	1.00687i	0.864032	−	0.503437i	$-0.167931\pi$
$854$	34.8973	+	15.7832i	1.19416	+	0.540090i
$855$	1.31838	−	7.51010i	0.0450878	−	0.256840i
$856$	18.8980			0.645919
$857$	5.88298			0.200959			0.100479	−	0.994939i	$-0.467962\pi$
$857$	5.88298			0.200959			0.100479	+	0.994939i	$0.467962\pi$
$858$	4.22676	+	0.368185i	0.144299	+	0.0125696i
$859$		−	21.9495i		−	0.748908i	−0.927245	−	0.374454i	$-0.877830\pi$
$859$		−	21.9495i		−	0.748908i	0.927245	−	0.374454i	$-0.122170\pi$
$860$	25.0956			0.855752
$861$	−4.92062	+	8.76327i	−0.167694	+	0.298651i
$862$	30.2149			1.02912
$863$		−	25.3924i		−	0.864368i	−0.901785	−	0.432184i	$-0.857743\pi$
$863$		−	25.3924i		−	0.864368i	0.901785	−	0.432184i	$-0.142257\pi$
$864$	34.7678	+	9.27380i	1.18283	+	0.315501i
$865$	−7.25497			−0.246676
$866$	−27.2339			−0.925445
$867$	−2.05869	+	23.6337i	−0.0699168	+	0.802644i
$868$	7.43255	−	16.4337i	0.252277	−	0.557795i
$869$			19.1313i			0.648986i
$870$	−3.30986	+	37.9971i	−0.112215	+	1.28822i
$871$		−	13.2909i		−	0.450343i
$872$			13.3541i			0.452228i
$873$	0.0626418	−	0.356835i	0.00212010	−	0.0120770i
$874$		−	9.24417i		−	0.312689i
$875$	−8.66409	−	3.91856i	−0.292900	−	0.132472i
$876$	16.0624	+	1.39916i	0.542697	+	0.0472733i
$877$	6.29840			0.212682			0.106341	−	0.994330i	$-0.466086\pi$
$877$	6.29840			0.212682			0.106341	+	0.994330i	$0.466086\pi$
$878$	48.8450			1.64844
$879$	3.37685	−	38.7662i	0.113898	−	1.30755i
$880$		−	18.6358i		−	0.628214i
$881$	−8.89391			−0.299643			−0.149822	−	0.988713i	$-0.547870\pi$
$881$	−8.89391			−0.299643			−0.149822	+	0.988713i	$0.547870\pi$
$882$	−33.3953	+	20.3615i	−1.12448	+	0.685607i
$883$	18.7262			0.630188			0.315094	−	0.949060i	$-0.397964\pi$
$883$	18.7262			0.630188			0.315094	+	0.949060i	$0.397964\pi$
$884$			8.13906i			0.273746i
$885$	−2.02199	+	23.2124i	−0.0679685	+	0.780277i
$886$	−35.2508			−1.18427
$887$	30.6401			1.02879			0.514397	−	0.857552i	$-0.328016\pi$
$887$	30.6401			1.02879			0.514397	+	0.857552i	$0.328016\pi$
$888$	12.0285	+	1.04778i	0.403652	+	0.0351613i
$889$	3.38509	+	1.53100i	0.113532	+	0.0513479i
$890$			87.4372i			2.93090i
$891$	4.03155	−	11.1289i	0.135062	−	0.372831i
$892$		−	1.40776i		−	0.0471353i
$893$		−	1.27353i		−	0.0426172i
$894$	0.388910	−	4.46468i	0.0130071	−	0.149321i
$895$			54.4035i			1.81851i
$896$	8.32198	−	18.4002i	0.278018	−	0.614708i
$897$	0.870084	−	9.98856i	0.0290513	−	0.333508i
$898$	9.86471			0.329190
$899$	−18.5082			−0.617282
$900$	16.4407	+	2.88614i	0.548025	+	0.0962047i
$901$		−	5.35377i		−	0.178360i
$902$	5.37224			0.178876
$903$	12.9297	−	23.0268i	0.430272	−	0.766283i
$904$	9.25028			0.307660
$905$			18.9613i			0.630296i
$906$	−0.212675	−	0.0185257i	−0.00706566	−	0.000615476i
$907$	−42.7521			−1.41956			−0.709780	−	0.704423i	$-0.751206\pi$
$907$	−42.7521			−1.41956			−0.709780	+	0.704423i	$0.751206\pi$
$908$	30.6665			1.01770
$909$	23.7989	+	4.17785i	0.789359	+	0.138570i
$910$	13.3099	+	6.01974i	0.441218	+	0.199552i
$911$			53.7863i			1.78202i	0.453985	+	0.891010i	$0.350002\pi$
$911$			53.7863i			1.78202i	−0.453985	+	0.891010i	$0.649998\pi$
$912$	−7.07179	−	0.616010i	−0.234170	−	0.0203981i
$913$			16.8043i			0.556142i
$914$		−	44.5702i		−	1.47425i
$915$	−39.7563	−	3.46310i	−1.31430	−	0.114486i
$916$			34.4411i			1.13797i
$917$	34.8958	+	15.7825i	1.15236	+	0.521185i
$918$	51.8091	+	13.8193i	1.70996	+	0.456105i
$919$	−8.22747			−0.271399			−0.135700	−	0.990750i	$-0.543328\pi$
$919$	−8.22747			−0.271399			−0.135700	+	0.990750i	$0.543328\pi$
$920$	−16.9706			−0.559504
$921$	−38.4581	−	3.35001i	−1.26724	−	0.110386i
$922$		−	1.04165i		−	0.0343049i
$923$	13.7948			0.454063
$924$	7.71992	+	4.33478i	0.253967	+	0.142604i
$925$	26.6979			0.877822
$926$		−	24.7472i		−	0.813244i
$927$	−7.98983	+	45.5136i	−0.262420	+	1.49486i
$928$	27.6194			0.906650
$929$	−20.3305			−0.667021			−0.333510	−	0.942746i	$-0.608233\pi$
$929$	−20.3305			−0.667021			−0.333510	+	0.942746i	$0.608233\pi$
$930$	−3.85111	+	44.2107i	−0.126283	+	1.44973i
$931$	4.50698	−	3.96336i	0.147710	−	0.129894i
$932$		−	24.2604i		−	0.794677i
$933$	−0.0382985	+	0.439666i	−0.00125384	+	0.0143940i
$934$			20.6723i			0.676417i
$935$		−	21.6006i		−	0.706414i
$936$	−2.92219	−	0.512986i	−0.0955149	−	0.0167675i
$937$		−	29.0283i		−	0.948312i	−0.880441	−	0.474156i	$-0.842753\pi$
$937$		−	29.0283i		−	0.948312i	0.880441	−	0.474156i	$-0.157247\pi$
$938$	26.9896	−	59.6750i	0.881241	−	1.94846i
$939$	−26.3960	−	2.29930i	−0.861400	−	0.0750349i
$940$	6.46835			0.210974
$941$	−18.6537			−0.608092			−0.304046	−	0.952657i	$-0.598338\pi$
$941$	−18.6537			−0.608092			−0.304046	+	0.952657i	$0.598338\pi$
$942$	6.80977	−	78.1761i	0.221874	−	2.54712i
$943$		−	12.6955i		−	0.413423i
$944$	21.6918			0.706009
$945$	25.7967	−	31.5497i	0.839165	−	1.02631i
$946$	−14.1163			−0.458962
$947$		−	8.78463i		−	0.285462i	−0.989762	−	0.142731i	$-0.954412\pi$
$947$		−	8.78463i		−	0.285462i	0.989762	−	0.142731i	$-0.0455884\pi$
$948$	−3.21193	+	36.8730i	−0.104319	+	1.19758i
$949$	−6.33668			−0.205697
$950$	−6.04848			−0.196239
$951$	−18.7821	−	1.63607i	−0.609050	−	0.0530532i
$952$	5.97398	−	13.2087i	0.193618	−	0.428096i
$953$		−	59.0999i		−	1.91443i	−0.289374	−	0.957216i	$-0.593447\pi$
$953$		−	59.0999i		−	1.91443i	0.289374	−	0.957216i	$-0.406553\pi$
$954$	−5.31800	−	0.933565i	−0.172177	−	0.0302253i
$955$		−	13.5202i		−	0.437504i
$956$			30.9296i			1.00034i
$957$	0.788417	−	9.05102i	0.0254859	−	0.292578i
$958$			20.8263i			0.672868i
$959$	−16.4593	+	36.3921i	−0.531498	+	1.17516i
$960$	1.48731	−	17.0743i	0.0480027	−	0.551070i
$961$	9.46525			0.305331
$962$	13.1286			0.423284
$963$	9.91204	−	56.4634i	0.319411	−	1.81951i
$964$		−	18.7074i		−	0.602526i
$965$	20.5472			0.661439
$966$	24.1903	−	43.0811i	0.778309	−	1.38611i
$967$	−9.92505			−0.319168			−0.159584	−	0.987184i	$-0.551015\pi$
$967$	−9.92505			−0.319168			−0.159584	+	0.987184i	$0.551015\pi$
$968$		−	9.16796i		−	0.294669i
$969$	−8.19681	−	0.714008i	−0.263320	−	0.0229373i
$970$	−0.666770			−0.0214087
$971$	−18.5347			−0.594806			−0.297403	−	0.954752i	$-0.596120\pi$
$971$	−18.5347			−0.594806			−0.297403	+	0.954752i	$0.596120\pi$
$972$	9.63867	−	20.7725i	0.309160	−	0.666279i
$973$	13.0515	−	28.8573i	0.418411	−	0.925124i
$974$		−	40.5310i		−	1.29870i
$975$	−6.53554	−	0.569298i	−0.209305	−	0.0182321i
$976$			37.1520i			1.18921i
$977$		−	50.3686i		−	1.61144i	−0.592299	−	0.805718i	$-0.701780\pi$
$977$		−	50.3686i		−	1.61144i	0.592299	−	0.805718i	$-0.298220\pi$
$978$	−57.1556	−	4.97872i	−1.82764	−	0.159202i
$979$		−	20.8278i		−	0.665658i
$980$	20.1301	+	22.8912i	0.643033	+	0.731233i
$981$	39.8995	+	7.00428i	1.27389	+	0.223630i
$982$	−65.6905			−2.09627
$983$	−30.5631			−0.974811			−0.487405	−	0.873176i	$-0.662057\pi$
$983$	−30.5631			−0.974811			−0.487405	+	0.873176i	$0.662057\pi$
$984$	−3.74253	−	0.326004i	−0.119307	−	0.0103926i
$985$		−	4.62262i		−	0.147289i
$986$	41.1569			1.31070
$987$	3.33260	−	5.93511i	0.106078	−	0.188917i
$988$	−1.25953			−0.0400711
$989$			33.3594i			1.06077i
$990$	−21.4562	−	3.76660i	−0.681924	−	0.119711i
$991$	27.3779			0.869687			0.434843	−	0.900506i	$-0.356804\pi$
$991$	27.3779			0.869687			0.434843	+	0.900506i	$0.356804\pi$
$992$	32.1359			1.02032
$993$	1.44116	−	16.5445i	0.0457338	−	0.525024i
$994$	61.9379	+	28.0130i	1.96455	+	0.888519i
$995$			11.7747i			0.373283i
$996$	−2.82126	+	32.3880i	−0.0893950	+	1.02625i
$997$			11.7329i			0.371585i	0.982589	+	0.185792i	$0.0594852\pi$
$997$			11.7329i			0.371585i	−0.982589	+	0.185792i	$0.940515\pi$
$998$			18.5917i			0.588510i
$999$	9.43958	−	35.3893i	0.298655	−	1.11967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.e.a.209.7	✓	32
3.2	odd	2	inner	273.2.e.a.209.26	yes	32
7.6	odd	2	inner	273.2.e.a.209.8	yes	32
21.20	even	2	inner	273.2.e.a.209.25	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.e.a.209.7	✓	32	1.1	even	1	trivial
273.2.e.a.209.8	yes	32	7.6	odd	2	inner
273.2.e.a.209.25	yes	32	21.20	even	2	inner
273.2.e.a.209.26	yes	32	3.2	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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.86253i q^{2} +(-0.150306 + 1.72552i) q^{3} -1.46902 q^{4} -2.96439 q^{5} +(3.21383 + 0.279950i) q^{6} +(-2.41066 - 1.09028i) q^{7} -0.988960i q^{8} +(-2.95482 - 0.518713i) q^{9} +O(q^{10})\)	\(q-1.86253i q^{2} +(-0.150306 + 1.72552i) q^{3} -1.46902 q^{4} -2.96439 q^{5} +(3.21383 + 0.279950i) q^{6} +(-2.41066 - 1.09028i) q^{7} -0.988960i q^{8} +(-2.95482 - 0.518713i) q^{9} +5.52126i q^{10} -1.31518i q^{11} +(0.220804 - 2.53483i) q^{12} +1.00000i q^{13} +(-2.03069 + 4.48993i) q^{14} +(0.445566 - 5.11510i) q^{15} -4.78002 q^{16} -5.54045 q^{17} +(-0.966118 + 5.50344i) q^{18} -0.857394i q^{19} +4.35475 q^{20} +(2.24364 - 3.99576i) q^{21} -2.44956 q^{22} +5.78874i q^{23} +(1.70647 + 0.148647i) q^{24} +3.78758 q^{25} +1.86253 q^{26} +(1.33918 - 5.02062i) q^{27} +(3.54132 + 1.60165i) q^{28} -3.98835i q^{29} +(-9.52703 - 0.829881i) q^{30} -4.64055i q^{31} +6.92501i q^{32} +(2.26936 + 0.197680i) q^{33} +10.3193i q^{34} +(7.14613 + 3.23202i) q^{35} +(4.34069 + 0.762001i) q^{36} +7.04880 q^{37} -1.59692 q^{38} +(-1.72552 - 0.150306i) q^{39} +2.93166i q^{40} -2.19314 q^{41} +(-7.44222 - 4.17885i) q^{42} +5.76280 q^{43} +1.93203i q^{44} +(8.75921 + 1.53766i) q^{45} +10.7817 q^{46} +1.48535 q^{47} +(0.718467 - 8.24800i) q^{48} +(4.62256 + 5.25661i) q^{49} -7.05449i q^{50} +(0.832766 - 9.56014i) q^{51} -1.46902i q^{52} +0.966305i q^{53} +(-9.35106 - 2.49426i) q^{54} +3.89870i q^{55} +(-1.07825 + 2.38405i) q^{56} +(1.47945 + 0.128872i) q^{57} -7.42843 q^{58} -4.53802 q^{59} +(-0.654547 + 7.51420i) q^{60} -7.77235i q^{61} -8.64318 q^{62} +(6.55751 + 4.47203i) q^{63} +3.33802 q^{64} -2.96439i q^{65} +(0.368185 - 4.22676i) q^{66} -13.2909 q^{67} +8.13906 q^{68} +(-9.98856 - 0.870084i) q^{69} +(6.01974 - 13.3099i) q^{70} -13.7948i q^{71} +(-0.512986 + 2.92219i) q^{72} +6.33668i q^{73} -13.1286i q^{74} +(-0.569298 + 6.53554i) q^{75} +1.25953i q^{76} +(-1.43392 + 3.17045i) q^{77} +(-0.279950 + 3.21383i) q^{78} -14.5466 q^{79} +14.1698 q^{80} +(8.46187 + 3.06540i) q^{81} +4.08480i q^{82} -12.7772 q^{83} +(-3.29596 + 5.86986i) q^{84} +16.4240 q^{85} -10.7334i q^{86} +(6.88197 + 0.599475i) q^{87} -1.30066 q^{88} +15.8365 q^{89} +(2.86395 - 16.3143i) q^{90} +(1.09028 - 2.41066i) q^{91} -8.50379i q^{92} +(8.00735 + 0.697505i) q^{93} -2.76652i q^{94} +2.54165i q^{95} +(-11.9492 - 1.04087i) q^{96} +0.120764i q^{97} +(9.79059 - 8.60967i) q^{98} +(-0.682200 + 3.88611i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

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