LMFDB - Embedded newform 273.2.g.a.272.1

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			272.1
Character	$\chi$	$=$	273.272
Dual form			273.2.g.a.272.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35085 q^{2} +(-0.813690 - 1.52902i) q^{3} +3.52651 q^{4} -0.514868i q^{5} +(1.91287 + 3.59451i) q^{6} +(-1.49028 + 2.18611i) q^{7} -3.58861 q^{8} +(-1.67582 + 2.48830i) q^{9} +O(q^{10})$	\(q-2.35085 q^{2} +(-0.813690 - 1.52902i) q^{3} +3.52651 q^{4} -0.514868i q^{5} +(1.91287 + 3.59451i) q^{6} +(-1.49028 + 2.18611i) q^{7} -3.58861 q^{8} +(-1.67582 + 2.48830i) q^{9} +1.21038i q^{10} +2.08851 q^{11} +(-2.86949 - 5.39212i) q^{12} +(-2.92002 + 2.11506i) q^{13} +(3.50342 - 5.13923i) q^{14} +(-0.787245 + 0.418943i) q^{15} +1.38328 q^{16} +0.359522 q^{17} +(3.93960 - 5.84963i) q^{18} +3.55174 q^{19} -1.81569i q^{20} +(4.55523 + 0.499847i) q^{21} -4.90979 q^{22} +1.93858i q^{23} +(2.92002 + 5.48707i) q^{24} +4.73491 q^{25} +(6.86454 - 4.97220i) q^{26} +(5.16826 + 0.537655i) q^{27} +(-5.25548 + 7.70935i) q^{28} +8.77503i q^{29} +(1.85070 - 0.984875i) q^{30} +7.37747 q^{31} +3.92534 q^{32} +(-1.69940 - 3.19338i) q^{33} -0.845183 q^{34} +(1.12556 + 0.767296i) q^{35} +(-5.90979 + 8.77503i) q^{36} +2.76971i q^{37} -8.34962 q^{38} +(5.60997 + 2.74377i) q^{39} +1.84766i q^{40} -5.37332i q^{41} +(-10.7087 - 1.17507i) q^{42} -0.383277 q^{43} +7.36518 q^{44} +(1.28115 + 0.862825i) q^{45} -4.55733i q^{46} +6.90164i q^{47} +(-1.12556 - 2.11506i) q^{48} +(-2.55816 - 6.51581i) q^{49} -11.1311 q^{50} +(-0.292539 - 0.549717i) q^{51} +(-10.2975 + 7.45880i) q^{52} -9.21019i q^{53} +(-12.1498 - 1.26395i) q^{54} -1.07531i q^{55} +(5.34802 - 7.84511i) q^{56} +(-2.89002 - 5.43069i) q^{57} -20.6288i q^{58} -1.01344i q^{59} +(-2.77623 + 1.47741i) q^{60} +10.7842i q^{61} -17.3434 q^{62} +(-2.94227 - 7.37177i) q^{63} -11.9945 q^{64} +(1.08898 + 1.50343i) q^{65} +(3.99505 + 7.50718i) q^{66} +3.71944i q^{67} +1.26786 q^{68} +(2.96414 - 1.57741i) q^{69} +(-2.64603 - 1.80380i) q^{70} +2.79049 q^{71} +(6.01386 - 8.92955i) q^{72} -6.83815 q^{73} -6.51119i q^{74} +(-3.85275 - 7.23978i) q^{75} +12.5253 q^{76} +(-3.11246 + 4.56572i) q^{77} +(-13.1882 - 6.45020i) q^{78} +9.78607 q^{79} -0.712206i q^{80} +(-3.38328 - 8.33987i) q^{81} +12.6319i q^{82} +14.8929i q^{83} +(16.0641 + 1.76272i) q^{84} -0.185106i q^{85} +0.901029 q^{86} +(13.4172 - 7.14015i) q^{87} -7.49487 q^{88} +15.0466i q^{89} +(-3.01179 - 2.02838i) q^{90} +(-0.272125 - 9.53551i) q^{91} +6.83644i q^{92} +(-6.00298 - 11.2803i) q^{93} -16.2247i q^{94} -1.82868i q^{95} +(-3.19401 - 6.00194i) q^{96} -8.34372 q^{97} +(6.01386 + 15.3177i) q^{98} +(-3.49997 + 5.19685i) 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 $

$2$	−2.35085			−1.66230			−0.831152	−	0.556045i	$-0.812318\pi$
$2$	−2.35085			−1.66230			−0.831152	+	0.556045i	$0.812318\pi$
$3$	−0.813690	−	1.52902i	−0.469784	−	0.882781i
$3$	−0.813690	−	1.52902i	−0.469784	−	0.882781i
$4$	3.52651			1.76326
$5$		−	0.514868i		−	0.230256i	−0.993351	−	0.115128i	$-0.963272\pi$
$5$		−	0.514868i		−	0.230256i	0.993351	−	0.115128i	$-0.0367278\pi$
$6$	1.91287	+	3.59451i	0.780925	+	1.46745i
$7$	−1.49028	+	2.18611i	−0.563271	+	0.826272i
$7$	−1.49028	+	2.18611i	−0.563271	+	0.826272i
$8$	−3.58861			−1.26877
$9$	−1.67582	+	2.48830i	−0.558606	+	0.829433i
$10$			1.21038i			0.382756i
$11$	2.08851			0.629711			0.314855	−	0.949140i	$-0.398044\pi$
$11$	2.08851			0.629711			0.314855	+	0.949140i	$0.398044\pi$
$12$	−2.86949	−	5.39212i	−0.828351	−	1.55657i
$13$	−2.92002	+	2.11506i	−0.809868	+	0.586613i
$13$	−2.92002	+	2.11506i	−0.809868	+	0.586613i
$14$	3.50342	−	5.13923i	0.936328	−	1.37352i
$15$	−0.787245	+	0.418943i	−0.203266	+	0.108171i
$16$	1.38328			0.345819
$17$	0.359522			0.0871968			0.0435984	−	0.999049i	$-0.486118\pi$
$17$	0.359522			0.0871968			0.0435984	+	0.999049i	$0.486118\pi$
$18$	3.93960	−	5.84963i	0.928573	−	1.37877i
$19$	3.55174			0.814825			0.407412	−	0.913244i	$-0.366431\pi$
$19$	3.55174			0.814825			0.407412	+	0.913244i	$0.366431\pi$
$20$		−	1.81569i		−	0.406001i
$21$	4.55523	+	0.499847i	0.994033	+	0.109076i
$22$	−4.90979			−1.04677
$23$			1.93858i			0.404223i	0.979363	+	0.202111i	$0.0647803\pi$
$23$			1.93858i			0.404223i	−0.979363	+	0.202111i	$0.935220\pi$
$24$	2.92002	+	5.48707i	0.596047	+	1.12004i
$25$	4.73491			0.946982
$26$	6.86454	−	4.97220i	1.34625	−	0.975129i
$27$	5.16826	+	0.537655i	0.994632	+	0.103472i
$28$	−5.25548	+	7.70935i	−0.993192	+	1.45693i
$29$			8.77503i			1.62948i	0.579825	+	0.814741i	$0.303121\pi$
$29$			8.77503i			1.62948i	−0.579825	+	0.814741i	$0.696879\pi$
$30$	1.85070	−	0.984875i	0.337890	−	0.179813i
$31$	7.37747			1.32503			0.662517	−	0.749047i	$-0.269488\pi$
$31$	7.37747			1.32503			0.662517	+	0.749047i	$0.269488\pi$
$32$	3.92534			0.693909
$33$	−1.69940	−	3.19338i	−0.295828	−	0.555897i
$34$	−0.845183			−0.144948
$35$	1.12556	+	0.767296i	0.190254	+	0.129697i
$36$	−5.90979	+	8.77503i	−0.984965	+	1.46250i
$37$			2.76971i			0.455338i	0.973739	+	0.227669i	$0.0731104\pi$
$37$			2.76971i			0.455338i	−0.973739	+	0.227669i	$0.926890\pi$
$38$	−8.34962			−1.35449
$39$	5.60997	+	2.74377i	0.898314	+	0.439355i
$40$			1.84766i			0.292141i
$41$		−	5.37332i		−	0.839172i	−0.907716	−	0.419586i	$-0.862175\pi$
$41$		−	5.37332i		−	0.839172i	0.907716	−	0.419586i	$-0.137825\pi$
$42$	−10.7087	−	1.17507i	−1.65239	−	0.181317i
$43$	−0.383277			−0.0584492			−0.0292246	−	0.999573i	$-0.509304\pi$
$43$	−0.383277			−0.0584492			−0.0292246	+	0.999573i	$0.509304\pi$
$44$	7.36518			1.11034
$45$	1.28115	+	0.862825i	0.190982	+	0.128622i
$46$		−	4.55733i		−	0.671941i
$47$			6.90164i			1.00671i	0.864081	+	0.503354i	$0.167901\pi$
$47$			6.90164i			1.00671i	−0.864081	+	0.503354i	$0.832099\pi$
$48$	−1.12556	−	2.11506i	−0.162460	−	0.305283i
$49$	−2.55816	−	6.51581i	−0.365451	−	0.930830i
$50$	−11.1311			−1.57417
$51$	−0.292539	−	0.549717i	−0.0409637	−	0.0769757i
$52$	−10.2975	+	7.45880i	−1.42801	+	1.03435i
$53$		−	9.21019i		−	1.26512i	−0.774513	−	0.632558i	$-0.782005\pi$
$53$		−	9.21019i		−	1.26512i	0.774513	−	0.632558i	$-0.217995\pi$
$54$	−12.1498	−	1.26395i	−1.65338	−	0.172002i
$55$		−	1.07531i		−	0.144995i
$56$	5.34802	−	7.84511i	0.714660	−	1.04835i
$57$	−2.89002	−	5.43069i	−0.382792	−	0.719312i
$58$		−	20.6288i		−	2.70870i
$59$		−	1.01344i		−	0.131939i	−0.997822	−	0.0659696i	$-0.978986\pi$
$59$		−	1.01344i		−	0.131939i	0.997822	−	0.0659696i	$-0.0210140\pi$
$60$	−2.77623	+	1.47741i	−0.358410	+	0.190733i
$61$			10.7842i			1.38078i	0.723437	+	0.690390i	$0.242561\pi$
$61$			10.7842i			1.38078i	−0.723437	+	0.690390i	$0.757439\pi$
$62$	−17.3434			−2.20261
$63$	−2.94227	−	7.37177i	−0.370691	−	0.928756i
$64$	−11.9945			−1.49931
$65$	1.08898	+	1.50343i	0.135071	+	0.186477i
$66$	3.99505	+	7.50718i	0.491757	+	0.924070i
$67$			3.71944i			0.454402i	0.973848	+	0.227201i	$0.0729574\pi$
$67$			3.71944i			0.454402i	−0.973848	+	0.227201i	$0.927043\pi$
$68$	1.26786			0.153750
$69$	2.96414	−	1.57741i	0.356840	−	0.189897i
$70$	−2.64603	−	1.80380i	−0.316261	−	0.215595i
$71$	2.79049			0.331170			0.165585	−	0.986196i	$-0.447049\pi$
$71$	2.79049			0.331170			0.165585	+	0.986196i	$0.447049\pi$
$72$	6.01386	−	8.92955i	0.708740	−	1.05236i
$73$	−6.83815			−0.800345			−0.400173	−	0.916440i	$-0.631050\pi$
$73$	−6.83815			−0.800345			−0.400173	+	0.916440i	$0.631050\pi$
$74$		−	6.51119i		−	0.756911i
$75$	−3.85275	−	7.23978i	−0.444877	−	0.835978i
$76$	12.5253			1.43675
$77$	−3.11246	+	4.56572i	−0.354698	+	0.520312i
$78$	−13.1882	−	6.45020i	−1.49327	−	0.730342i
$79$	9.78607			1.10102			0.550509	−	0.834829i	$-0.314433\pi$
$79$	9.78607			1.10102			0.550509	+	0.834829i	$0.314433\pi$
$80$		−	0.712206i		−	0.0796270i
$81$	−3.38328	−	8.33987i	−0.375920	−	0.926652i
$82$			12.6319i			1.39496i
$83$			14.8929i			1.63471i	0.576136	+	0.817354i	$0.304560\pi$
$83$			14.8929i			1.63471i	−0.576136	+	0.817354i	$0.695440\pi$
$84$	16.0641	+	1.76272i	1.75274	+	0.192328i
$85$		−	0.185106i		−	0.0200776i
$86$	0.901029			0.0971605
$87$	13.4172	−	7.14015i	1.43848	−	0.765505i
$88$	−7.49487			−0.798956
$89$			15.0466i			1.59494i	0.603358	+	0.797470i	$0.293829\pi$
$89$			15.0466i			1.59494i	−0.603358	+	0.797470i	$0.706171\pi$
$90$	−3.01179	−	2.02838i	−0.317471	−	0.213810i
$91$	−0.272125	−	9.53551i	−0.0285265	−	0.999593i
$92$			6.83644i			0.712749i
$93$	−6.00298	−	11.2803i	−0.622480	−	1.16971i
$94$		−	16.2247i		−	1.67345i
$95$		−	1.82868i		−	0.187618i
$96$	−3.19401	−	6.00194i	−0.325988	−	0.612570i
$97$	−8.34372			−0.847176			−0.423588	−	0.905855i	$-0.639230\pi$
$97$	−8.34372			−0.847176			−0.423588	+	0.905855i	$0.639230\pi$
$98$	6.01386	+	15.3177i	0.607491	+	1.54732i
$99$	−3.49997	+	5.19685i	−0.351760	+	0.522303i
$100$	16.6977			1.66977
$101$	−16.8574			−1.67738			−0.838688	−	0.544612i	$-0.816677\pi$
$101$	−16.8574			−1.67738			−0.838688	+	0.544612i	$0.816677\pi$
$102$	0.687717	+	1.29230i	0.0680941	+	0.127957i
$103$		−	3.69533i		−	0.364111i	−0.983288	−	0.182056i	$-0.941725\pi$
$103$		−	3.69533i		−	0.364111i	0.983288	−	0.182056i	$-0.0582751\pi$
$104$	10.4788	−	7.59014i	1.02753	−	0.744274i
$105$	0.257355	−	2.34535i	0.0251153	−	0.228882i
$106$			21.6518i			2.10301i
$107$			13.7205i			1.32641i	0.748439	+	0.663204i	$0.230804\pi$
$107$			13.7205i			1.32641i	−0.748439	+	0.663204i	$0.769196\pi$
$108$	18.2260	+	1.89605i	1.75379	+	0.182447i
$109$			10.8614i			1.04033i	0.854065	+	0.520166i	$0.174130\pi$
$109$			10.8614i			1.04033i	−0.854065	+	0.520166i	$0.825870\pi$
$110$			2.52790i			0.241025i
$111$	4.23495	−	2.25369i	0.401964	−	0.213911i
$112$	−2.06146	+	3.02400i	−0.194790	+	0.285741i
$113$		−	13.7516i		−	1.29364i	−0.762641	−	0.646822i	$-0.776098\pi$
$113$		−	13.7516i		−	1.29364i	0.762641	−	0.646822i	$-0.223902\pi$
$114$	6.79400	+	12.7668i	0.636317	+	1.19572i
$115$	0.998115			0.0930747
$116$			30.9453i			2.87320i
$117$	−0.369491	−	10.8103i	−0.0341594	−	0.999416i
$118$			2.38246i			0.219323i
$119$	−0.535786	+	0.785954i	−0.0491155	+	0.0720483i
$120$	2.82512	−	1.50343i	0.257897	−	0.137243i
$121$	−6.63811			−0.603464
$122$		−	25.3522i		−	2.29528i
$123$	−8.21593	+	4.37222i	−0.740806	+	0.394230i
$124$	26.0168			2.33637
$125$		−	5.01220i		−	0.448305i
$126$	6.91685	+	17.3300i	0.616202	+	1.54388i
$127$	8.11819			0.720373			0.360186	−	0.932880i	$-0.382713\pi$
$127$	8.11819			0.720373			0.360186	+	0.932880i	$0.382713\pi$
$128$	20.3466			1.79840
$129$	0.311869	+	0.586039i	0.0274585	+	0.0515979i
$130$	−2.56003	−	3.53433i	−0.224529	−	0.309982i
$131$	16.9323			1.47939			0.739693	−	0.672945i	$-0.234971\pi$
$131$	16.9323			1.47939			0.739693	+	0.672945i	$0.234971\pi$
$132$	−5.99297	−	11.2615i	−0.521621	−	0.980189i
$133$	−5.29307	+	7.76450i	−0.458967	+	0.673267i
$134$		−	8.74386i		−	0.755355i
$135$	0.276822	−	2.66097i	0.0238250	−	0.229020i
$136$	−1.29018			−0.110632
$137$	9.93920			0.849163			0.424582	−	0.905390i	$-0.360421\pi$
$137$	9.93920			0.849163			0.424582	+	0.905390i	$0.360421\pi$
$138$	−6.96825	+	3.70825i	−0.593177	+	0.315667i
$139$		−	1.24868i		−	0.105912i	−0.998597	−	0.0529559i	$-0.983136\pi$
$139$		−	1.24868i		−	0.105912i	0.998597	−	0.0529559i	$-0.0168643\pi$
$140$	3.96930	+	2.70588i	0.335467	+	0.228689i
$141$	10.5528	−	5.61579i	0.888702	−	0.472935i
$142$	−6.56003			−0.550505
$143$	−6.09850	+	4.41734i	−0.509982	+	0.369396i
$144$	−2.31812	+	3.44201i	−0.193177	+	0.286834i
$145$	4.51798			0.375198
$146$	16.0755			1.33042
$147$	−7.88127	+	9.21333i	−0.650036	+	0.759903i
$148$			9.76744i			0.802878i
$149$	−14.5206			−1.18958			−0.594789	−	0.803882i	$-0.702764\pi$
$149$	−14.5206			−1.18958			−0.594789	+	0.803882i	$0.702764\pi$
$150$	9.05725	+	17.0197i	0.739522	+	1.38965i
$151$			3.27828i			0.266783i	0.991063	+	0.133391i	$0.0425867\pi$
$151$			3.27828i			0.266783i	−0.991063	+	0.133391i	$0.957413\pi$
$152$	−12.7458			−1.03382
$153$	−0.602492	+	0.894598i	−0.0487086	+	0.0723240i
$154$	7.31694	−	10.7333i	0.589616	−	0.864918i
$155$		−	3.79843i		−	0.305097i
$156$	19.7836	+	9.67594i	1.58396	+	0.774696i
$157$			17.9756i			1.43461i	0.696758	+	0.717306i	$0.254625\pi$
$157$			17.9756i			1.43461i	−0.696758	+	0.717306i	$0.745375\pi$
$158$	−23.0056			−1.83023
$159$	−14.0826	+	7.49424i	−1.11682	+	0.594332i
$160$		−	2.02104i		−	0.159777i
$161$	−4.23796	−	2.88902i	−0.333998	−	0.227687i
$162$	7.95359	+	19.6058i	0.624893	+	1.54038i
$163$		−	16.4417i		−	1.28781i	−0.765104	−	0.643907i	$-0.777313\pi$
$163$		−	16.4417i		−	1.28781i	0.765104	−	0.643907i	$-0.222687\pi$
$164$		−	18.9491i		−	1.47968i
$165$	−1.64417	+	0.874969i	−0.127999	+	0.0681163i
$166$		−	35.0110i		−	2.71738i
$167$		−	11.5628i		−	0.894753i	−0.894346	−	0.447376i	$-0.852358\pi$
$167$		−	11.5628i		−	0.894753i	0.894346	−	0.447376i	$-0.147642\pi$
$168$	−16.3470	−	1.79376i	−1.26120	−	0.138391i
$169$	4.05303	−	12.3520i	0.311772	−	0.950157i
$170$			0.435158i			0.0333751i
$171$	−5.95206	+	8.83779i	−0.455166	+	0.675843i
$172$	−1.35163			−0.103061
$173$	−12.6080			−0.958570			−0.479285	−	0.877659i	$-0.659104\pi$
$173$	−12.6080			−0.958570			−0.479285	+	0.877659i	$0.659104\pi$
$174$	−31.5419	+	16.7855i	−2.39119	+	1.27250i
$175$	−7.05632	+	10.3510i	−0.533408	+	0.782465i
$176$	2.88899			0.217766
$177$	−1.54958	+	0.824630i	−0.116473	+	0.0619830i
$178$		−	35.3725i		−	2.65128i
$179$		−	11.4566i		−	0.856309i	−0.903706	−	0.428154i	$-0.859164\pi$
$179$		−	11.4566i		−	0.856309i	0.903706	−	0.428154i	$-0.140836\pi$
$180$	4.51798	+	3.04277i	0.336751	+	0.226794i
$181$			6.85014i			0.509167i	0.967051	+	0.254583i	$0.0819384\pi$
$181$			6.85014i			0.509167i	−0.967051	+	0.254583i	$0.918062\pi$
$182$	0.639726	+	22.4166i	0.0474197	+	1.66163i
$183$	16.4893	−	8.77503i	1.21893	−	0.648669i
$184$		−	6.95683i		−	0.512864i
$185$	1.42604			0.104844
$186$	14.1121	+	26.5184i	1.03475	+	1.94442i
$187$	0.750866			0.0549088
$188$			24.3387i			1.77508i
$189$	−8.87751	+	10.4971i	−0.645744	+	0.763554i
$190$			4.29896i			0.311879i
$191$			4.65135i			0.336560i	0.985739	+	0.168280i	$0.0538212\pi$
$191$			4.65135i			0.336560i	−0.985739	+	0.168280i	$0.946179\pi$
$192$	9.75978	+	18.3398i	0.704351	+	1.32356i
$193$		−	9.76744i		−	0.703075i	−0.936174	−	0.351538i	$-0.885659\pi$
$193$		−	9.76744i		−	0.703075i	0.936174	−	0.351538i	$-0.114341\pi$
$194$	19.6149			1.40827
$195$	1.41268	−	2.88839i	0.101164	−	0.206842i
$196$	−9.02139	−	22.9781i	−0.644385	−	1.64129i
$197$	20.0181			1.42623			0.713116	−	0.701046i	$-0.247283\pi$
$197$	20.0181			1.42623			0.713116	+	0.701046i	$0.247283\pi$
$198$	8.22791	−	12.2170i	0.584732	−	0.868227i
$199$		−	16.0897i		−	1.14057i	−0.821448	−	0.570283i	$-0.806833\pi$
$199$		−	16.0897i		−	1.14057i	0.821448	−	0.570283i	$-0.193167\pi$
$200$	−16.9918			−1.20150
$201$	5.68711	−	3.02647i	0.401138	−	0.213471i
$202$	39.6293			2.78831
$203$	−19.1832	−	13.0772i	−1.34640	−	0.917840i
$204$	−1.03164	−	1.93858i	−0.0722295	−	0.135728i
$205$	−2.76655			−0.193225
$206$			8.68718i			0.605264i
$207$	−4.82378	−	3.24871i	−0.335276	−	0.225801i
$208$	−4.03920	+	2.92572i	−0.280068	+	0.202862i
$209$	7.41786			0.513104
$210$	−0.605005	+	5.51357i	−0.0417493	+	0.380472i
$211$	7.13770			0.491380			0.245690	−	0.969348i	$-0.420986\pi$
$211$	7.13770			0.491380			0.245690	+	0.969348i	$0.420986\pi$
$212$		−	32.4799i		−	2.23073i
$213$	−2.27059	−	4.26672i	−0.155578	−	0.292351i
$214$		−	32.2548i		−	2.20489i
$215$			0.197337i			0.0134583i
$216$	−18.5469	−	1.92944i	−1.26196	−	0.131281i
$217$	−10.9945	+	16.1280i	−0.746353	+	1.09484i
$218$		−	25.5335i		−	1.72935i
$219$	5.56414	+	10.4557i	0.375990	+	0.706530i
$220$		−	3.79210i		−	0.255663i
$221$	−1.04981	+	0.760411i	−0.0706179	+	0.0511507i
$222$	−9.95576	+	5.29809i	−0.668187	+	0.355585i
$223$	13.7655			0.921806			0.460903	−	0.887450i	$-0.347526\pi$
$223$	13.7655			0.921806			0.460903	+	0.887450i	$0.347526\pi$
$224$	−5.84984	+	8.58124i	−0.390859	+	0.573358i
$225$	−7.93484	+	11.7819i	−0.528989	+	0.785459i
$226$			32.3281i			2.15043i
$227$		−	16.6621i		−	1.10591i	−0.833213	−	0.552953i	$-0.813501\pi$
$227$		−	16.6621i		−	1.10591i	0.833213	−	0.552953i	$-0.186499\pi$
$228$	−10.1917	−	19.1514i	−0.674961	−	1.26833i
$229$	−24.1786			−1.59777			−0.798883	−	0.601486i	$-0.794576\pi$
$229$	−24.1786			−1.59777			−0.798883	+	0.601486i	$0.794576\pi$
$230$	−2.34642			−0.154719
$231$	9.51367	+	1.04394i	0.625954	+	0.0686861i
$232$		−	31.4902i		−	2.06743i
$233$		−	6.58993i		−	0.431721i	−0.976424	−	0.215860i	$-0.930744\pi$
$233$		−	6.58993i		−	0.431721i	0.976424	−	0.215860i	$-0.0692556\pi$
$234$	0.868619	+	25.4135i	0.0567834	+	1.66133i
$235$	3.55343			0.231801
$236$		−	3.57393i		−	0.232643i
$237$	−7.96283	−	14.9631i	−0.517241	−	0.971959i
$238$	1.25956	−	1.84766i	0.0816449	−	0.119766i
$239$	−5.44285			−0.352069			−0.176034	−	0.984384i	$-0.556327\pi$
$239$	−5.44285			−0.352069			−0.176034	+	0.984384i	$0.556327\pi$
$240$	−1.08898	+	0.579515i	−0.0702932	+	0.0374075i
$241$	1.44312			0.0929593			0.0464797	−	0.998919i	$-0.485200\pi$
$241$	1.44312			0.0929593			0.0464797	+	0.998919i	$0.485200\pi$
$242$	15.6052			1.00314
$243$	−9.99891	+	11.9592i	−0.641430	+	0.767181i
$244$			38.0308i			2.43467i
$245$	−3.35479	+	1.31712i	−0.214329	+	0.0841474i
$246$	19.3145	−	10.2785i	1.23144	−	0.655330i
$247$	−10.3711	+	7.51215i	−0.659900	+	0.477986i
$248$	−26.4749			−1.68116
$249$	22.7716	−	12.1182i	1.44309	−	0.767960i
$250$			11.7829i			0.745219i
$251$	−28.3665			−1.79048			−0.895239	−	0.445587i	$-0.852995\pi$
$251$	−28.3665			−1.79048			−0.895239	+	0.445587i	$0.852995\pi$
$252$	−10.3760	−	25.9967i	−0.653624	−	1.63764i
$253$			4.04876i			0.254543i
$254$	−19.0847			−1.19748
$255$	−0.283032	+	0.150619i	−0.0177241	+	0.00943214i
$256$	−23.8428			−1.49018
$257$	23.8529			1.48790			0.743951	−	0.668234i	$-0.232950\pi$
$257$	23.8529			1.48790			0.743951	+	0.668234i	$0.232950\pi$
$258$	−0.733159	−	1.37769i	−0.0456445	−	0.0857714i
$259$	−6.05490	−	4.12764i	−0.376233	−	0.256479i
$260$	3.84030	+	5.30185i	0.238165	+	0.328807i
$261$	−21.8349	−	14.7053i	−1.35155	−	0.910238i
$262$	−39.8055			−2.45919
$263$			15.1763i			0.935812i	0.883778	+	0.467906i	$0.154991\pi$
$263$			15.1763i			0.935812i	−0.883778	+	0.467906i	$0.845009\pi$
$264$	6.09850	+	11.4598i	0.375337	+	0.705303i
$265$	−4.74203			−0.291301
$266$	12.4432	−	18.2532i	0.762944	−	1.11918i
$267$	23.0066	−	12.2433i	1.40798	−	0.749278i
$268$			13.1167i			0.801228i
$269$	16.6681			1.01627			0.508137	−	0.861276i	$-0.330334\pi$
$269$	16.6681			1.01627			0.508137	+	0.861276i	$0.330334\pi$
$270$	−0.650767	+	6.25556i	−0.0396044	+	0.380701i
$271$	−1.41125			−0.0857271			−0.0428636	−	0.999081i	$-0.513648\pi$
$271$	−1.41125			−0.0857271			−0.0428636	+	0.999081i	$0.513648\pi$
$272$	0.497318			0.0301543
$273$	−14.3586	+	8.17504i	−0.869021	+	0.494776i
$274$	−23.3656			−1.41157
$275$	9.88893			0.596325
$276$	10.4531	−	5.56275i	0.629201	−	0.334838i
$277$	−2.02977			−0.121957			−0.0609787	−	0.998139i	$-0.519422\pi$
$277$	−2.02977			−0.121957			−0.0609787	+	0.998139i	$0.519422\pi$
$278$			2.93547i			0.176058i
$279$	−12.3633	+	18.3574i	−0.740171	+	1.09903i
$280$	−4.03920	−	2.75353i	−0.241388	−	0.164555i
$281$	15.9966			0.954279			0.477139	−	0.878828i	$-0.341674\pi$
$281$	15.9966			0.954279			0.477139	+	0.878828i	$0.341674\pi$
$282$	−24.8080	+	13.2019i	−1.47729	+	0.786162i
$283$			30.3700i			1.80531i	0.430367	+	0.902654i	$0.358384\pi$
$283$			30.3700i			1.80531i	−0.430367	+	0.902654i	$0.641616\pi$
$284$	9.84070			0.583938
$285$	−2.79609	+	1.48798i	−0.165626	+	0.0881402i
$286$	14.3367	−	10.3845i	0.847746	−	0.614049i
$287$	11.7467	+	8.00773i	0.693385	+	0.472682i
$288$	−6.57816	+	9.76744i	−0.387622	+	0.575552i
$289$	−16.8707			−0.992397
$290$	−10.6211			−0.623694
$291$	6.78920	+	12.7577i	0.397990	+	0.747871i
$292$	−24.1149			−1.41122
$293$		−	24.4561i		−	1.42874i	−0.699769	−	0.714369i	$-0.746714\pi$
$293$		−	24.4561i		−	1.42874i	0.699769	−	0.714369i	$-0.253286\pi$
$294$	18.5277	−	21.6592i	1.08056	−	1.26319i
$295$	−0.521790			−0.0303798
$296$		−	9.93943i		−	0.577718i
$297$	10.7940	+	1.12290i	0.626331	+	0.0651573i
$298$	34.1359			1.97744
$299$	−4.10022	−	5.66070i	−0.237122	−	0.327367i
$300$	−13.5868	−	25.5312i	−0.784433	−	1.47404i
$301$	0.571189	−	0.837887i	0.0329228	−	0.0482950i
$302$		−	7.70676i		−	0.443474i
$303$	13.7167	+	25.7754i	0.788005	+	1.48076i
$304$	4.91304			0.281782
$305$	5.55246			0.317933
$306$	1.41637	−	2.10307i	0.0809686	−	0.120224i
$307$	9.83678			0.561415			0.280707	−	0.959793i	$-0.409431\pi$
$307$	9.83678			0.561415			0.280707	+	0.959793i	$0.409431\pi$
$308$	−10.9761	+	16.1011i	−0.625424	+	0.917445i
$309$	−5.65024	+	3.00685i	−0.321431	+	0.171054i
$310$			8.92955i			0.507164i
$311$	21.5814			1.22377			0.611884	−	0.790948i	$-0.290412\pi$
$311$	21.5814			1.22377			0.611884	+	0.790948i	$0.290412\pi$
$312$	−20.1320	−	9.84633i	−1.13975	−	0.557439i
$313$		−	9.13704i		−	0.516456i	−0.966084	−	0.258228i	$-0.916861\pi$
$313$		−	9.13704i		−	0.516456i	0.966084	−	0.258228i	$-0.0831386\pi$
$314$		−	42.2581i		−	2.38476i
$315$	−3.79549	+	1.51488i	−0.213852	+	0.0853540i
$316$	34.5107			1.94138
$317$	−0.763354			−0.0428743			−0.0214371	−	0.999770i	$-0.506824\pi$
$317$	−0.763354			−0.0428743			−0.0214371	+	0.999770i	$0.506824\pi$
$318$	33.1061	−	17.6179i	1.85650	−	0.987961i
$319$			18.3268i			1.02610i
$320$			6.17557i			0.345225i
$321$	20.9789	−	11.1642i	1.17093	−	0.623125i
$322$	9.96282	+	6.79167i	0.555206	+	0.378485i
$323$	1.27693			0.0710501
$324$	−11.9312	−	29.4107i	−0.662843	−	1.63393i
$325$	−13.8260	+	10.0146i	−0.766930	+	0.555512i
$326$			38.6520i			2.14074i
$327$	16.6073	−	8.83779i	0.918385	−	0.488731i
$328$			19.2828i			1.06471i
$329$	−15.0877	−	10.2853i	−0.831814	−	0.567049i
$330$	3.86521	−	2.05692i	0.212773	−	0.113230i
$331$		−	6.95683i		−	0.382382i	−0.981553	−	0.191191i	$-0.938765\pi$
$331$		−	6.95683i		−	0.382382i	0.981553	−	0.191191i	$-0.0612350\pi$
$332$			52.5200i			2.88241i
$333$	−6.89188	−	4.64153i	−0.377673	−	0.254354i
$334$			27.1824i			1.48735i
$335$	1.91502			0.104629
$336$	6.30115	+	0.691427i	0.343756	+	0.0377204i
$337$	14.6708			0.799170			0.399585	−	0.916696i	$-0.369154\pi$
$337$	14.6708			0.799170			0.399585	+	0.916696i	$0.369154\pi$
$338$	−9.52808	+	29.0378i	−0.518259	+	1.57945i
$339$	−21.0265	+	11.1896i	−1.14201	+	0.607734i
$340$		−	0.652780i		−	0.0354020i
$341$	15.4080			0.834388
$342$	13.9924	−	20.7764i	0.756624	−	1.12346i
$343$	18.0566	+	4.11794i	0.974967	+	0.222348i
$344$	1.37543			0.0741584
$345$	−0.812157	−	1.52614i	−0.0437250	−	0.0821646i
$346$	29.6396			1.59344
$347$		−	27.1157i		−	1.45565i	−0.685765	−	0.727823i	$-0.740532\pi$
$347$		−	27.1157i		−	1.45565i	0.685765	−	0.727823i	$-0.259468\pi$
$348$	47.3160	−	25.1799i	2.53640	−	1.34978i
$349$	8.10159			0.433668			0.216834	−	0.976208i	$-0.430427\pi$
$349$	8.10159			0.433668			0.216834	+	0.976208i	$0.430427\pi$
$350$	16.5884	−	24.3338i	0.886686	−	1.30070i
$351$	−16.2286	+	9.36123i	−0.866219	+	0.499665i
$352$	8.19814			0.436962
$353$			25.1410i			1.33812i	0.743209	+	0.669059i	$0.233303\pi$
$353$			25.1410i			1.33812i	−0.743209	+	0.669059i	$0.766697\pi$
$354$	3.64283	−	1.93858i	0.193614	−	0.103035i
$355$		−	1.43673i		−	0.0762539i
$356$			53.0622i			2.81229i
$357$	1.63771	+	0.179706i	0.0866766	+	0.00951104i
$358$			26.9329i			1.42345i
$359$	−6.28685			−0.331807			−0.165904	−	0.986142i	$-0.553054\pi$
$359$	−6.28685			−0.331807			−0.165904	+	0.986142i	$0.553054\pi$
$360$	−4.59754	−	3.09635i	−0.242312	−	0.163192i
$361$	−6.38515			−0.336060
$362$		−	16.1037i		−	0.846391i
$363$	5.40136	+	10.1498i	0.283498	+	0.532727i
$364$	−0.959653	−	33.6271i	−0.0502995	−	1.76254i
$365$			3.52075i			0.184284i
$366$	−38.7640	+	20.6288i	−2.02623	+	1.07829i
$367$		−	22.3791i		−	1.16818i	−0.811689	−	0.584091i	$-0.801451\pi$
$367$		−	22.3791i		−	1.16818i	0.811689	−	0.584091i	$-0.198549\pi$
$368$			2.68160i			0.139788i
$369$	13.3704	+	9.00471i	0.696038	+	0.468766i
$370$	−3.35241			−0.174283
$371$	20.1345	+	13.7257i	1.04533	+	0.712604i
$372$	−21.1696	−	39.7802i	−1.09759	−	2.06251i
$373$	27.3311			1.41515			0.707576	−	0.706637i	$-0.249789\pi$
$373$	27.3311			1.41515			0.707576	+	0.706637i	$0.249789\pi$
$374$	−1.76518			−0.0912751
$375$	−7.66376	+	4.07838i	−0.395755	+	0.210606i
$376$		−	24.7673i		−	1.27728i
$377$	−18.5597	−	25.6233i	−0.955874	−	1.31966i
$378$	20.8697	−	24.6772i	1.07342	−	1.26926i
$379$		−	11.9962i		−	0.616204i	−0.951353	−	0.308102i	$-0.900306\pi$
$379$		−	11.9962i		−	0.616204i	0.951353	−	0.308102i	$-0.0996938\pi$
$380$		−	6.44886i		−	0.330820i
$381$	−6.60569	−	12.4129i	−0.338420	−	0.635932i
$382$		−	10.9346i		−	0.559465i
$383$			10.5766i			0.540440i	0.962799	+	0.270220i	$0.0870964\pi$
$383$			10.5766i			0.540440i	−0.962799	+	0.270220i	$0.912904\pi$
$384$	−16.5558	−	31.1103i	−0.844859	−	1.58759i
$385$	2.35075	+	1.60251i	0.119805	+	0.0816714i
$386$			22.9618i			1.16873i
$387$	0.642303	−	0.953709i	0.0326501	−	0.0484798i
$388$	−29.4242			−1.49379
$389$		−	18.6357i		−	0.944868i	−0.881366	−	0.472434i	$-0.843375\pi$
$389$		−	18.6357i		−	0.944868i	0.881366	−	0.472434i	$-0.156625\pi$
$390$	−3.32100	+	6.79019i	−0.168166	+	0.343835i
$391$			0.696963i			0.0352469i
$392$	9.18024	+	23.3827i	0.463672	+	1.18101i
$393$	−13.7777	−	25.8899i	−0.694992	−	1.30597i
$394$	−47.0597			−2.37083
$395$		−	5.03854i		−	0.253516i
$396$	−12.3427	+	18.3268i	−0.620243	+	0.920955i
$397$	−13.1051			−0.657727			−0.328864	−	0.944377i	$-0.606666\pi$
$397$	−13.1051			−0.657727			−0.328864	+	0.944377i	$0.606666\pi$
$398$			37.8245i			1.89597i
$399$	16.1790	+	1.77533i	0.809963	+	0.0888775i
$400$	6.54969			0.327485
$401$	2.36431			0.118068			0.0590341	−	0.998256i	$-0.481198\pi$
$401$	2.36431			0.118068			0.0590341	+	0.998256i	$0.481198\pi$
$402$	−13.3696	+	7.11480i	−0.666813	+	0.354854i
$403$	−21.5424	+	15.6038i	−1.07310	+	0.777281i
$404$	−59.4479			−2.95765
$405$	−4.29394	+	1.74194i	−0.213367	+	0.0865578i
$406$	45.0969	+	30.7426i	2.23812	+	1.52573i
$407$			5.78459i			0.286731i
$408$	1.04981	+	1.97272i	0.0519734	+	0.0976642i
$409$	23.0987			1.14216			0.571078	−	0.820896i	$-0.306525\pi$
$409$	23.0987			1.14216			0.571078	+	0.820896i	$0.306525\pi$
$410$	6.50377			0.321198
$411$	−8.08743	−	15.1973i	−0.398924	−	0.749626i
$412$		−	13.0316i		−	0.642022i
$413$	2.21550	+	1.51031i	0.109018	+	0.0743175i
$414$	11.3400	+	7.63725i	0.557331	+	0.375350i
$415$	7.66788			0.376402
$416$	−11.4621	+	8.30234i	−0.561975	+	0.407056i
$417$	−1.90926	+	1.01604i	−0.0934970	+	0.0497557i
$418$	−17.4383			−0.852935
$419$	−5.80253			−0.283472			−0.141736	−	0.989904i	$-0.545268\pi$
$419$	−5.80253			−0.283472			−0.141736	+	0.989904i	$0.545268\pi$
$420$	0.907568	−	8.27090i	0.0442848	−	0.403578i
$421$		−	39.7670i		−	1.93812i	−0.246820	−	0.969061i	$-0.579386\pi$
$421$		−	39.7670i		−	1.93812i	0.246820	−	0.969061i	$-0.420614\pi$
$422$	−16.7797			−0.816823
$423$	−17.1733	−	11.5659i	−0.834997	−	0.562352i
$424$			33.0518i			1.60514i
$425$	1.70230			0.0825738
$426$	5.33783	+	10.0304i	0.258619	+	0.485976i
$427$	−23.5755	−	16.0715i	−1.14090	−	0.777754i
$428$			48.3854i			2.33880i
$429$	11.7165	+	5.73040i	0.565678	+	0.276666i
$430$		−	0.463911i		−	0.0223718i
$431$	−36.2007			−1.74372			−0.871862	−	0.489751i	$-0.837088\pi$
$431$	−36.2007			−1.74372			−0.871862	+	0.489751i	$0.837088\pi$
$432$	7.14914	+	0.743726i	0.343963	+	0.0357825i
$433$		−	1.61582i		−	0.0776516i	−0.999246	−	0.0388258i	$-0.987638\pi$
$433$		−	1.61582i		−	0.0776516i	0.999246	−	0.0388258i	$-0.0123617\pi$
$434$	25.8464	−	37.9145i	1.24067	−	1.81995i
$435$	−3.67624	−	6.90810i	−0.176262	−	0.331218i
$436$			38.3028i			1.83437i
$437$			6.88534i			0.329371i
$438$	−13.0805	−	24.5798i	−0.625009	−	1.17447i
$439$		−	17.9868i		−	0.858465i	−0.903194	−	0.429233i	$-0.858784\pi$
$439$		−	17.9868i		−	0.858465i	0.903194	−	0.429233i	$-0.141216\pi$
$440$			3.85887i			0.183964i
$441$	20.5003	+	4.55384i	0.976205	+	0.216850i
$442$	2.46795	−	1.78761i	0.117388	−	0.0850281i
$443$			3.25336i			0.154572i	0.997009	+	0.0772860i	$0.0246255\pi$
$443$			3.25336i			0.154572i	−0.997009	+	0.0772860i	$0.975375\pi$
$444$	14.9346	−	7.94767i	0.708766	−	0.377180i
$445$	7.74704			0.367245
$446$	−32.3607			−1.53232
$447$	11.8153	+	22.2024i	0.558845	+	1.05014i
$448$	17.8751	−	26.2212i	0.844517	−	1.23884i
$449$	−40.1506			−1.89482			−0.947411	−	0.320019i	$-0.896311\pi$
$449$	−40.1506			−1.89482			−0.947411	+	0.320019i	$0.896311\pi$
$450$	18.6537	−	27.6975i	0.879342	−	1.30567i
$451$		−	11.2223i		−	0.528436i
$452$		−	48.4953i		−	2.28103i
$453$	5.01256	−	2.66751i	0.235511	−	0.125330i
$454$			39.1703i			1.83835i
$455$	−4.90953	+	0.140109i	−0.230162	+	0.00656839i
$456$	10.3711	+	19.4886i	0.485674	+	0.912639i
$457$			0.467674i			0.0218769i	0.999940	+	0.0109384i	$0.00348188\pi$
$457$			0.467674i			0.0218769i	−0.999940	+	0.0109384i	$0.996518\pi$
$458$	56.8403			2.65598
$459$	1.85810	+	0.193299i	0.0867288	+	0.00902241i
$460$	3.51987			0.164115
$461$			25.9844i			1.21021i	0.796144	+	0.605107i	$0.206870\pi$
$461$			25.9844i			1.21021i	−0.796144	+	0.605107i	$0.793130\pi$
$462$	−22.3653	−	2.45415i	−1.04053	−	0.114177i
$463$			18.8412i			0.875625i	0.899066	+	0.437812i	$0.144247\pi$
$463$			18.8412i			0.875625i	−0.899066	+	0.437812i	$0.855753\pi$
$464$			12.1383i			0.563506i
$465$	−5.80788	+	3.09074i	−0.269334	+	0.143330i
$466$			15.4920i			0.717652i
$467$	7.90380			0.365744			0.182872	−	0.983137i	$-0.441461\pi$
$467$	7.90380			0.365744			0.182872	+	0.983137i	$0.441461\pi$
$468$	−1.30301	−	38.1228i	−0.0602319	−	1.76223i
$469$	−8.13111	−	5.54299i	−0.375460	−	0.255952i
$470$	−8.35361			−0.385323
$471$	27.4851	−	14.6266i	1.26645	−	0.673958i
$472$			3.63686i			0.167400i
$473$	−0.800480			−0.0368061
$474$	18.7194	+	35.1761i	0.859813	+	1.61569i
$475$	16.8172			0.771625
$476$	−1.88946	+	2.77168i	−0.0866032	+	0.127040i
$477$	22.9177	+	15.4346i	1.04933	+	0.706701i
$478$	12.7953			0.585245
$479$		−	14.3507i		−	0.655701i	−0.944730	−	0.327851i	$-0.893676\pi$
$479$		−	14.3507i		−	0.655701i	0.944730	−	0.327851i	$-0.106324\pi$
$480$	−3.09021	+	1.64450i	−0.141048	+	0.0750607i
$481$	−5.85811	−	8.08762i	−0.267107	−	0.368764i
$482$	−3.39256			−0.154527
$483$	−0.968995	+	8.83070i	−0.0440908	+	0.401811i
$484$	−23.4094			−1.06406
$485$			4.29592i			0.195068i
$486$	23.5060	−	28.1143i	1.06625	−	1.27529i
$487$			31.9722i			1.44880i	0.689380	+	0.724400i	$0.257883\pi$
$487$			31.9722i			1.44880i	−0.689380	+	0.724400i	$0.742117\pi$
$488$		−	38.7005i		−	1.75189i
$489$	−25.1397	+	13.3784i	−1.13686	+	0.604994i
$490$	7.88661	−	3.09635i	0.356281	−	0.139879i
$491$			18.2619i			0.824148i	0.911150	+	0.412074i	$0.135196\pi$
$491$			18.2619i			0.824148i	−0.911150	+	0.412074i	$0.864804\pi$
$492$	−28.9736	+	15.4187i	−1.30623	+	0.695129i
$493$			3.15481i			0.142086i
$494$	24.3811	−	17.6600i	1.09696	−	0.794559i
$495$	2.67569	+	1.80202i	0.120264	+	0.0809949i
$496$	10.2051			0.458222
$497$	−4.15859	+	6.10031i	−0.186538	+	0.273636i
$498$	−53.5326	+	28.4881i	−2.39885	+	1.27658i
$499$		−	27.3031i		−	1.22225i	−0.791533	−	0.611127i	$-0.790717\pi$
$499$		−	27.3031i		−	1.22225i	0.791533	−	0.611127i	$-0.209283\pi$
$500$		−	17.6756i		−	0.790476i
$501$	−17.6797	+	9.40850i	−0.789871	+	0.420341i
$502$	66.6855			2.97632
$503$	−0.0424911			−0.00189459			−0.000947293	−	1.00000i	$-0.500302\pi$
$503$	−0.0424911			−0.00189459			−0.000947293		1.00000i	$0.500302\pi$
$504$	10.5587	+	26.4544i	0.470321	+	1.17837i
$505$			8.67935i			0.386226i
$506$		−	9.51804i		−	0.423129i
$507$	−22.1845	+	3.85356i	−0.985246	+	0.171143i
$508$	28.6289			1.27020
$509$		−	19.8553i		−	0.880069i	−0.897981	−	0.440034i	$-0.854966\pi$
$509$		−	19.8553i		−	0.880069i	0.897981	−	0.440034i	$-0.145034\pi$
$510$	0.665366	−	0.354084i	0.0294629	−	0.0156791i
$511$	10.1907	−	14.9490i	0.450811	−	0.661303i
$512$	15.3579			0.678731
$513$	18.3563	+	1.90961i	0.810451	+	0.0843114i
$514$	−56.0746			−2.47335
$515$	−1.90261			−0.0838389
$516$	1.09981	+	2.06668i	0.0484165	+	0.0909804i
$517$			14.4142i			0.633934i
$518$	14.2342	+	9.70347i	0.625414	+	0.426346i
$519$	10.2590	+	19.2779i	0.450321	+	0.846208i
$520$	−3.90792	−	5.39521i	−0.171374	−	0.236596i
$521$	12.5037			0.547798			0.273899	−	0.961759i	$-0.411687\pi$
$521$	12.5037			0.547798			0.273899	+	0.961759i	$0.411687\pi$
$522$	51.3307	+	34.5701i	2.24668	+	1.51309i
$523$		−	4.40349i		−	0.192551i	−0.995355	−	0.0962757i	$-0.969307\pi$
$523$		−	4.40349i		−	0.192551i	0.995355	−	0.0962757i	$-0.0306930\pi$
$524$	59.7122			2.60854
$525$	21.5686	+	2.36673i	0.941332	+	0.103293i
$526$		−	35.6773i		−	1.55560i
$527$	2.65236			0.115539
$528$	−2.35075	−	4.41734i	−0.102303	−	0.192240i
$529$	19.2419			0.836604
$530$	11.1478			0.484231
$531$	2.52175	+	1.69835i	0.109435	+	0.0737020i
$532$	−18.6661	+	27.3816i	−0.809278	+	1.18714i
$533$	11.3649	+	15.6902i	0.492269	+	0.679619i
$534$	−54.0853	+	28.7822i	−2.34050	+	1.24553i
$535$	7.06423			0.305413
$536$		−	13.3476i		−	0.576530i
$537$	−17.5174	+	9.32214i	−0.755933	+	0.402280i
$538$	−39.1843			−1.68936
$539$	−5.34275	−	13.6084i	−0.230129	−	0.586154i
$540$	0.976215	−	9.38397i	0.0420096	−	0.403822i
$541$			33.8573i			1.45564i	0.685768	+	0.727820i	$0.259466\pi$
$541$			33.8573i			1.45564i	−0.685768	+	0.727820i	$0.740534\pi$
$542$	3.31763			0.142505
$543$	10.4740	−	5.57389i	0.449483	−	0.239199i
$544$	1.41125			0.0605067
$545$	5.59218			0.239543
$546$	33.7549	−	19.2183i	1.44458	−	0.822468i
$547$	−25.7777			−1.10217			−0.551087	−	0.834448i	$-0.685787\pi$
$547$	−25.7777			−1.10217			−0.551087	+	0.834448i	$0.685787\pi$
$548$	35.0507			1.49729
$549$	−26.8344	−	18.0724i	−1.14527	−	0.771311i
$550$	−23.2474			−0.991274
$551$			31.1666i			1.32774i
$552$	−10.6371	+	5.66070i	−0.452747	+	0.240936i
$553$	−14.5839	+	21.3934i	−0.620172	+	0.909741i
$554$	4.77170			0.202730
$555$	−1.16035	−	2.18044i	−0.0492542	−	0.0925547i
$556$		−	4.40349i		−	0.186750i
$557$	−13.2935			−0.563265			−0.281633	−	0.959522i	$-0.590876\pi$
$557$	−13.2935			−0.563265			−0.281633	+	0.959522i	$0.590876\pi$
$558$	29.0643	−	43.1555i	1.23039	−	1.82692i
$559$	1.11918	−	0.810655i	0.0473362	−	0.0342871i
$560$	1.55696	+	1.06138i	0.0657936	+	0.0448516i
$561$	−0.610972	−	1.14809i	−0.0257953	−	0.0484724i
$562$	−37.6057			−1.58630
$563$	−3.97380			−0.167476			−0.0837379	−	0.996488i	$-0.526686\pi$
$563$	−3.97380			−0.167476			−0.0837379	+	0.996488i	$0.526686\pi$
$564$	37.2144	−	19.8042i	1.56701	−	0.833906i
$565$	−7.08028			−0.297870
$566$		−	71.3954i		−	3.00097i
$567$	23.2739	+	5.03248i	0.977412	+	0.211344i
$568$	−10.0140			−0.420177
$569$		−	16.3233i		−	0.684309i	−0.939644	−	0.342155i	$-0.888843\pi$
$569$		−	16.3233i		−	0.684309i	0.939644	−	0.342155i	$-0.111157\pi$
$570$	6.57320	−	3.49802i	0.275321	−	0.146516i
$571$	−22.2039			−0.929205			−0.464603	−	0.885519i	$-0.653803\pi$
$571$	−22.2039			−0.929205			−0.464603	+	0.885519i	$0.653803\pi$
$572$	−21.5065	+	15.5778i	−0.899230	+	0.651341i
$573$	7.11201	−	3.78476i	0.297109	−	0.158110i
$574$	−27.6147	−	18.8250i	−1.15262	−	0.785741i
$575$			9.17902i			0.382792i
$576$	20.1005	−	29.8458i	0.837522	−	1.24358i
$577$	23.2603			0.968338			0.484169	−	0.874975i	$-0.339122\pi$
$577$	23.2603			0.968338			0.484169	+	0.874975i	$0.339122\pi$
$578$	39.6607			1.64967
$579$	−14.9346	+	7.94767i	−0.620662	+	0.330294i
$580$	15.9327			0.661571
$581$	−32.5575	−	22.1945i	−1.35071	−	0.920784i
$582$	−15.9604	−	29.9916i	−0.661581	−	1.24319i
$583$		−	19.2356i		−	0.796657i
$584$	24.5395			1.01545
$585$	−5.56590	+	0.190239i	−0.230122	+	0.00786542i
$586$			57.4926i			2.37500i
$587$			12.5987i			0.520006i	0.965608	+	0.260003i	$0.0837235\pi$
$587$			12.5987i			0.520006i	−0.965608	+	0.260003i	$0.916277\pi$
$588$	−27.7934	+	32.4910i	−1.14618	+	1.33990i
$589$	26.2029			1.07967
$590$	1.22665			0.0505005
$591$	−16.2885	−	30.6081i	−0.670021	−	1.25905i
$592$			3.83128i			0.157465i
$593$		−	30.1206i		−	1.23690i	−0.785823	−	0.618452i	$-0.787760\pi$
$593$		−	30.1206i		−	1.23690i	0.785823	−	0.618452i	$-0.212240\pi$
$594$	−25.3751	−	2.63977i	−1.04115	−	0.108311i
$595$	0.404663	+	0.275859i	0.0165896	+	0.0113091i
$596$	−51.2073			−2.09753
$597$	−24.6015	+	13.0920i	−1.00687	+	0.535820i
$598$	9.63903	+	13.3075i	0.394169	+	0.544184i
$599$			5.44292i			0.222392i	0.993799	+	0.111196i	$0.0354681\pi$
$599$			5.44292i			0.222392i	−0.993799	+	0.111196i	$0.964532\pi$
$600$	13.8260	+	25.9808i	0.564445	+	1.06066i
$601$			6.01932i			0.245533i	0.992436	+	0.122767i	$0.0391766\pi$
$601$			6.01932i			0.245533i	−0.992436	+	0.122767i	$0.960823\pi$
$602$	−1.34278	+	1.96975i	−0.0547277	+	0.0802810i
$603$	−9.25509	−	6.23310i	−0.376896	−	0.253831i
$604$			11.5609i			0.470407i
$605$			3.41775i			0.138951i
$606$	−32.2460	−	60.5941i	−1.30990	−	2.46147i
$607$		−	3.15481i		−	0.128050i	−0.997948	−	0.0640250i	$-0.979606\pi$
$607$		−	3.15481i		−	0.128050i	0.997948	−	0.0640250i	$-0.0203937\pi$
$608$	13.9418			0.565415
$609$	−4.38617	+	39.9723i	−0.177737	+	1.61976i
$610$	−13.0530			−0.528502
$611$	−14.5974	−	20.1529i	−0.590547	−	0.815300i
$612$	−2.12470	+	3.15481i	−0.0858858	+	0.127526i
$613$		−	28.6230i		−	1.15607i	−0.816011	−	0.578036i	$-0.803819\pi$
$613$		−	28.6230i		−	1.15607i	0.816011	−	0.578036i	$-0.196181\pi$
$614$	−23.1248			−0.933242
$615$	2.25112	+	4.23012i	0.0907739	+	0.170575i
$616$	11.1694	−	16.3846i	0.450029	−	0.660155i
$617$	−4.18768			−0.168590			−0.0842949	−	0.996441i	$-0.526864\pi$
$617$	−4.18768			−0.168590			−0.0842949	+	0.996441i	$0.526864\pi$
$618$	13.2829	−	7.06867i	0.534316	−	0.284344i
$619$	−8.46124			−0.340086			−0.170043	−	0.985437i	$-0.554391\pi$
$619$	−8.46124			−0.340086			−0.170043	+	0.985437i	$0.554391\pi$
$620$		−	13.3952i		−	0.537965i
$621$	−1.04229	+	10.0191i	−0.0418256	+	0.402053i
$622$	−50.7347			−2.03428
$623$	−32.8936	−	22.4236i	−1.31786	−	0.898384i
$624$	7.76014	+	3.79539i	0.310654	+	0.151937i
$625$	21.0939			0.843757
$626$			21.4799i			0.858508i
$627$	−6.03584	−	11.3421i	−0.241048	−	0.452959i
$628$			63.3913i			2.52959i
$629$			0.995772i			0.0397040i
$630$	8.92265	−	3.56127i	0.355487	−	0.141884i
$631$		−	34.5892i		−	1.37698i	−0.725248	−	0.688488i	$-0.758275\pi$
$631$		−	34.5892i		−	1.37698i	0.725248	−	0.688488i	$-0.241725\pi$
$632$	−35.1184			−1.39694
$633$	−5.80788	−	10.9137i	−0.230842	−	0.433781i
$634$	1.79453			0.0712701
$635$		−	4.17980i		−	0.165870i
$636$	−49.6624	+	26.4285i	−1.96924	+	1.04796i
$637$	21.2512	+	13.6156i	0.842004	+	0.539471i
$638$		−	43.0836i		−	1.70569i
$639$	−4.67635	+	6.94357i	−0.184993	+	0.274683i
$640$		−	10.4758i		−	0.414092i
$641$			32.3388i			1.27731i	0.769495	+	0.638653i	$0.220508\pi$
$641$			32.3388i			1.27731i	−0.769495	+	0.638653i	$0.779492\pi$
$642$	−49.3183	+	26.2454i	−1.94644	+	1.03582i
$643$	−19.4259			−0.766081			−0.383041	−	0.923731i	$-0.625123\pi$
$643$	−19.4259			−0.766081			−0.383041	+	0.923731i	$0.625123\pi$
$644$	−14.9452	−	10.1882i	−0.588924	−	0.401471i
$645$	0.301733	−	0.160571i	0.0118807	−	0.00632250i
$646$	−3.00187			−0.118107
$647$	19.2229			0.755731			0.377865	−	0.925861i	$-0.376658\pi$
$647$	19.2229			0.755731			0.377865	+	0.925861i	$0.376658\pi$
$648$	12.1413	+	29.9286i	0.476954	+	1.17571i
$649$		−	2.11659i		−	0.0830835i
$650$	32.5030	−	23.5429i	1.27487	−	0.923430i
$651$	33.6061	+	3.68761i	1.31713	+	0.144529i
$652$		−	57.9819i		−	2.27075i
$653$			10.6175i			0.415494i	0.978183	+	0.207747i	$0.0666131\pi$
$653$			10.6175i			0.415494i	−0.978183	+	0.207747i	$0.933387\pi$
$654$	−39.0413	+	20.7764i	−1.52664	+	0.812420i
$655$		−	8.71793i		−	0.340638i
$656$		−	7.43280i		−	0.290202i
$657$	11.4595	−	17.0154i	0.447077	−	0.663833i
$658$	35.4691	+	24.1793i	1.38273	+	0.942608i
$659$		−	15.7690i		−	0.614271i	−0.951666	−	0.307136i	$-0.900629\pi$
$659$		−	15.7690i		−	0.614271i	0.951666	−	0.307136i	$-0.0993705\pi$
$660$	−5.79820	+	3.08559i	−0.225695	+	0.120106i
$661$	22.0381			0.857183			0.428591	−	0.903498i	$-0.359010\pi$
$661$	22.0381			0.857183			0.428591	+	0.903498i	$0.359010\pi$
$662$			16.3545i			0.635635i
$663$	2.01690	+	0.986445i	0.0783301	+	0.0383103i
$664$		−	53.4449i		−	2.07406i
$665$	3.99769	+	2.72523i	0.155024	+	0.105680i
$666$	16.2018	+	10.9116i	0.627807	+	0.422815i
$667$	−17.0111			−0.658673
$668$		−	40.7762i		−	1.57768i
$669$	−11.2009	−	21.0478i	−0.433050	−	0.813753i
$670$	−4.50194			−0.173925
$671$			22.5230i			0.869492i
$672$	17.8809	+	1.96207i	0.689769	+	0.0756886i
$673$	5.62885			0.216976			0.108488	−	0.994098i	$-0.465399\pi$
$673$	5.62885			0.216976			0.108488	+	0.994098i	$0.465399\pi$
$674$	−34.4889			−1.32846
$675$	24.4713	+	2.54575i	0.941899	+	0.0979859i
$676$	14.2931	−	43.5597i	0.549733	−	1.67537i
$677$	25.1231			0.965560			0.482780	−	0.875742i	$-0.339627\pi$
$677$	25.1231			0.965560			0.482780	+	0.875742i	$0.339627\pi$
$678$	49.4303	−	26.3050i	1.89836	−	1.01024i
$679$	12.4344	−	18.2403i	0.477190	−	0.699998i
$680$			0.664275i			0.0254738i
$681$	−25.4768	+	13.5578i	−0.976273	+	0.519537i
$682$	−36.2219			−1.38701
$683$	19.7688			0.756432			0.378216	−	0.925717i	$-0.376538\pi$
$683$	19.7688			0.756432			0.378216	+	0.925717i	$0.376538\pi$
$684$	−20.9900	+	31.1666i	−0.802574	+	1.19169i
$685$		−	5.11738i		−	0.195525i
$686$	−42.4485	−	9.68067i	−1.62069	−	0.369610i
$687$	19.6739	+	36.9696i	0.750606	+	1.41048i
$688$	−0.530179			−0.0202129
$689$	19.4801	+	26.8939i	0.742133	+	1.02458i
$690$	1.90926	+	3.58773i	0.0726844	+	0.136583i
$691$	26.7444			1.01741			0.508703	−	0.860942i	$-0.330125\pi$
$691$	26.7444			1.01741			0.508703	+	0.860942i	$0.330125\pi$
$692$	−44.4624			−1.69021
$693$	−6.14498	−	15.3961i	−0.233428	−	0.584848i
$694$			63.7450i			2.41973i
$695$	−0.642907			−0.0243868
$696$	−48.1492	+	25.6233i	−1.82509	+	0.971247i
$697$		−	1.93183i		−	0.0731732i
$698$	−19.0457			−0.720889
$699$	−10.0762	+	5.36216i	−0.381115	+	0.202816i
$700$	−24.8842	+	36.5031i	−0.940535	+	1.37969i
$701$		−	7.90471i		−	0.298557i	−0.988795	−	0.149278i	$-0.952305\pi$
$701$		−	7.90471i		−	0.298557i	0.988795	−	0.149278i	$-0.0476951\pi$
$702$	38.1511	−	22.0069i	1.43992	−	0.830596i
$703$			9.83730i			0.371021i
$704$	−25.0506			−0.944131
$705$	−2.89139	−	5.43328i	−0.108896	−	0.204629i
$706$		−	59.1028i		−	2.22436i
$707$	25.1222	−	36.8522i	0.944818	−	1.38597i
$708$	−5.46461	+	2.90807i	−0.205373	+	0.109292i
$709$			40.7899i			1.53190i	0.642901	+	0.765949i	$0.277731\pi$
$709$			40.7899i			1.53190i	−0.642901	+	0.765949i	$0.722269\pi$
$710$			3.37755i			0.126757i
$711$	−16.3997	+	24.3507i	−0.615035	+	0.913222i
$712$		−	53.9966i		−	2.02361i
$713$			14.3018i			0.535608i
$714$	−3.85001	−	0.422462i	−0.144083	−	0.0158103i
$715$	2.27435	+	3.13993i	0.0850557	+	0.117427i
$716$		−	40.4020i		−	1.50989i
$717$	4.42879	+	8.32224i	0.165396	+	0.310800i
$718$	14.7795			0.551565
$719$	16.2571			0.606288			0.303144	−	0.952945i	$-0.401964\pi$
$719$	16.2571			0.606288			0.303144	+	0.952945i	$0.401964\pi$
$720$	1.77218	+	1.19353i	0.0660453	+	0.0444801i
$721$	8.07839	+	5.50706i	0.300855	+	0.205093i
$722$	15.0105			0.558635
$723$	−1.17425	−	2.20656i	−0.0436708	−	0.0820628i
$724$			24.1571i			0.897792i
$725$			41.5490i			1.54309i
$726$	−12.6978	−	23.8607i	−0.471260	−	0.885555i
$727$		−	19.1679i		−	0.710897i	−0.934696	−	0.355449i	$-0.884328\pi$
$727$		−	19.1679i		−	0.710897i	0.934696	−	0.355449i	$-0.115672\pi$
$728$	0.976552	+	34.2193i	0.0361934	+	1.26825i
$729$	26.4219	+	5.55748i	0.978587	+	0.205833i
$730$		−	8.27677i		−	0.306337i
$731$	−0.137797			−0.00509659
$732$	58.1499	−	30.9453i	2.14928	−	1.14377i
$733$	−31.3124			−1.15655			−0.578274	−	0.815842i	$-0.696274\pi$
$733$	−31.3124			−1.15655			−0.578274	+	0.815842i	$0.696274\pi$
$734$			52.6101i			1.94187i
$735$	4.74365	+	4.05782i	0.174972	+	0.149675i
$736$			7.60961i			0.280494i
$737$			7.76811i			0.286142i
$738$	−31.4320	−	21.1688i	−1.15703	−	0.779232i
$739$		−	38.9147i		−	1.43150i	−0.698357	−	0.715750i	$-0.746085\pi$
$739$		−	38.9147i		−	1.43150i	0.698357	−	0.715750i	$-0.253915\pi$
$740$	5.02894			0.184868
$741$	19.9251	+	9.74515i	0.731968	+	0.357997i
$742$	−47.3332	−	32.2671i	−1.73766	−	1.18456i
$743$	3.18656			0.116903			0.0584517	−	0.998290i	$-0.481384\pi$
$743$	3.18656			0.116903			0.0584517	+	0.998290i	$0.481384\pi$
$744$	21.5424	+	40.4807i	0.789781	+	1.48409i
$745$			7.47622i			0.273907i
$746$	−64.2515			−2.35241
$747$	−37.0580	−	24.9578i	−1.35588	−	0.913157i
$748$	2.64794			0.0968183
$749$	−29.9945	−	20.4473i	−1.09597	−	0.747127i
$750$	18.0164	−	9.58767i	0.657865	−	0.350092i
$751$	−0.0203251			−0.000741673			−0.000370837	−	1.00000i	$-0.500118\pi$
$751$	−0.0203251			−0.000741673			−0.000370837		1.00000i	$0.500118\pi$
$752$			9.54688i			0.348139i
$753$	23.0815	+	43.3730i	0.841138	+	1.58060i
$754$	43.6312	+	60.2365i	1.58895	+	2.19369i
$755$	1.68788			0.0614284
$756$	−31.3067	+	37.0183i	−1.13861	+	1.34634i
$757$	15.7117			0.571052			0.285526	−	0.958371i	$-0.407832\pi$
$757$	15.7117			0.571052			0.285526	+	0.958371i	$0.407832\pi$
$758$			28.2013i			1.02432i
$759$	6.19064	−	3.29444i	0.224706	−	0.119580i
$760$			6.56242i			0.238044i
$761$			27.8139i			1.00825i	0.863629	+	0.504127i	$0.168186\pi$
$761$			27.8139i			1.00825i	−0.863629	+	0.504127i	$0.831814\pi$
$762$	15.5290	+	29.1809i	0.562557	+	1.05711i
$763$	−23.7442	−	16.1864i	−0.859597	−	0.585988i
$764$			16.4030i			0.593441i
$765$	0.460600	+	0.310204i	0.0166530	+	0.0112155i
$766$		−	24.8641i		−	0.898376i
$767$	2.14350	+	2.95928i	0.0773972	+	0.106853i
$768$	19.4007	+	36.4562i	0.700062	+	1.31550i
$769$	32.8282			1.18381			0.591907	−	0.806006i	$-0.298375\pi$
$769$	32.8282			1.18381			0.591907	+	0.806006i	$0.298375\pi$
$770$	−5.52626	−	3.76726i	−0.199153	−	0.135763i
$771$	−19.4089	−	36.4716i	−0.698993	−	1.31349i
$772$		−	34.4450i		−	1.23970i
$773$		−	18.4141i		−	0.662310i	−0.943576	−	0.331155i	$-0.892562\pi$
$773$		−	18.4141i		−	0.662310i	0.943576	−	0.331155i	$-0.107438\pi$
$774$	−1.50996	+	2.24203i	−0.0542744	+	0.0805881i
$775$	34.9317			1.25478
$776$	29.9424			1.07487
$777$	−1.38443	+	12.6167i	−0.0496663	+	0.452621i
$778$			43.8099i			1.57066i
$779$		−	19.0846i		−	0.683778i
$780$	4.98184	−	10.1860i	0.178378	−	0.364716i
$781$	5.82797			0.208541
$782$		−	1.63846i		−	0.0585911i
$783$	−4.71794	+	45.3516i	−0.168605	+	1.62074i
$784$	−3.53864	−	9.01318i	−0.126380	−	0.321899i
$785$	9.25509			0.330328
$786$	32.3893	+	60.8634i	1.15529	+	2.17093i
$787$	45.4288			1.61936			0.809682	−	0.586869i	$-0.199640\pi$
$787$	45.4288			1.61936			0.809682	+	0.586869i	$0.199640\pi$
$788$	70.5942			2.51481
$789$	23.2049	−	12.3488i	0.826117	−	0.439630i
$790$			11.8449i			0.421421i
$791$	30.0626	+	20.4937i	1.06890	+	0.728673i
$792$	12.5600	−	18.6495i	0.446301	−	0.662681i
$793$	−22.8093	−	31.4902i	−0.809983	−	1.11825i
$794$	30.8082			1.09334
$795$	3.85855	+	7.25067i	0.136849	+	0.257155i
$796$		−	56.7405i		−	2.01111i
$797$	24.1920			0.856925			0.428463	−	0.903559i	$-0.359055\pi$
$797$	24.1920			0.856925			0.428463	+	0.903559i	$0.359055\pi$
$798$	−38.0345	−	4.17353i	−1.34641	−	0.147741i
$799$			2.48129i			0.0877817i
$800$	18.5862			0.657120
$801$	−37.4406	−	25.2154i	−1.32290	−	0.890943i
$802$	−5.55816			−0.196265
$803$	−14.2816			−0.503986
$804$	20.0557	−	10.6729i	0.707309	−	0.376404i
$805$	−1.48747	+	2.18199i	−0.0524263	+	0.0769051i
$806$	50.6430	−	36.6823i	1.78382	−	1.29208i
$807$	−13.5627	−	25.4859i	−0.477429	−	0.897147i
$808$	60.4948			2.12820
$809$			23.4134i			0.823171i	0.911371	+	0.411585i	$0.135025\pi$
$809$			23.4134i			0.823171i	−0.911371	+	0.411585i	$0.864975\pi$
$810$	10.0944	−	4.09505i	0.354682	−	0.143885i
$811$	−7.01299			−0.246259			−0.123130	−	0.992391i	$-0.539293\pi$
$811$	−7.01299			−0.246259			−0.123130	+	0.992391i	$0.539293\pi$
$812$	−67.6498	−	46.1170i	−2.37404	−	1.61839i
$813$	1.14832	+	2.15783i	0.0402732	+	0.0756783i
$814$		−	13.5987i		−	0.476635i
$815$	−8.46531			−0.296527
$816$	−0.404663	−	0.760411i	−0.0141660	−	0.0266197i
$817$	−1.36130			−0.0476259
$818$	−54.3016			−1.89861
$819$	24.1832	+	15.3026i	0.845031	+	0.534717i
$820$	−9.75630			−0.340705
$821$	44.6315			1.55765			0.778824	−	0.627242i	$-0.215816\pi$
$821$	44.6315			1.55765			0.778824	+	0.627242i	$0.215816\pi$
$822$	19.0124	+	35.7265i	0.663133	+	1.24611i
$823$	−18.1182			−0.631560			−0.315780	−	0.948832i	$-0.602266\pi$
$823$	−18.1182			−0.631560			−0.315780	+	0.948832i	$0.602266\pi$
$824$			13.2611i			0.461972i
$825$	−8.04652	−	15.1204i	−0.280144	−	0.526424i
$826$	−5.20832	−	3.55052i	−0.181221	−	0.123538i
$827$	19.6905			0.684704			0.342352	−	0.939572i	$-0.388776\pi$
$827$	19.6905			0.684704			0.342352	+	0.939572i	$0.388776\pi$
$828$	−17.0111	−	11.4566i	−0.591178	−	0.398145i
$829$		−	42.7046i		−	1.48319i	−0.670846	−	0.741597i	$-0.734069\pi$
$829$		−	42.7046i		−	1.48319i	0.670846	−	0.741597i	$-0.265931\pi$
$830$	−18.0261			−0.625694
$831$	1.65161	+	3.10357i	0.0572936	+	0.107662i
$832$	35.0241	−	25.3690i	1.21424	−	0.879513i
$833$	−0.919714	−	2.34258i	−0.0318662	−	0.0811655i
$834$	4.48840	−	2.38856i	0.155420	−	0.0827091i
$835$	−5.95330			−0.206022
$836$	26.1592			0.904734
$837$	38.1287	+	3.96653i	1.31792	+	0.137104i
$838$	13.6409			0.471217
$839$		−	24.9872i		−	0.862655i	−0.902195	−	0.431327i	$-0.858045\pi$
$839$		−	24.9872i		−	0.862655i	0.902195	−	0.431327i	$-0.141955\pi$
$840$	−0.923549	+	8.41654i	−0.0318655	+	0.290398i
$841$	−48.0011			−1.65521
$842$			93.4863i			3.22175i
$843$	−13.0163	−	24.4592i	−0.448305	−	0.842419i
$844$	25.1712			0.866429
$845$	−6.35968	−	2.08678i	−0.218779	−	0.0717873i
$846$	40.3720	+	27.1897i	1.38802	+	0.934801i
$847$	9.89261	−	14.5116i	0.339914	−	0.498626i
$848$		−	12.7402i		−	0.437502i
$849$	46.4364	−	24.7118i	1.59369	−	0.848105i
$850$	−4.00187			−0.137263
$851$	−5.36932			−0.184058
$852$	−8.00728	−	15.0466i	−0.274325	−	0.515489i
$853$	−42.9390			−1.47020			−0.735101	−	0.677958i	$-0.762865\pi$
$853$	−42.9390			−1.47020			−0.735101	+	0.677958i	$0.762865\pi$
$854$	55.4226	+	37.7817i	1.89652	+	1.29286i
$855$	4.55030	+	3.06453i	0.155617	+	0.104805i
$856$		−	49.2374i		−	1.68290i
$857$	−44.5564			−1.52202			−0.761008	−	0.648742i	$-0.775295\pi$
$857$	−44.5564			−1.52202			−0.761008	+	0.648742i	$0.775295\pi$
$858$	−27.5438	−	13.4713i	−0.940329	−	0.459904i
$859$			11.3360i			0.386778i	0.981122	+	0.193389i	$0.0619479\pi$
$859$			11.3360i			0.386778i	−0.981122	+	0.193389i	$0.938052\pi$
$860$			0.695913i			0.0237304i
$861$	2.68584	−	24.4767i	0.0915332	−	0.834165i
$862$	85.1025			2.89860
$863$	45.8518			1.56081			0.780407	−	0.625272i	$-0.215012\pi$
$863$	45.8518			1.56081			0.780407	+	0.625272i	$0.215012\pi$
$864$	20.2872	+	2.11048i	0.690185	+	0.0718000i
$865$			6.49147i			0.220717i
$866$			3.79857i			0.129081i
$867$	13.7276	+	25.7957i	0.466212	+	0.876069i
$868$	−38.7721	+	56.8755i	−1.31601	+	1.93048i
$869$	20.4383			0.693323
$870$	8.64230	+	16.2399i	0.293001	+	0.550585i
$871$	−7.86685	−	10.8608i	−0.266558	−	0.368006i
$872$		−	38.9773i		−	1.31994i
$873$	13.9825	−	20.7617i	0.473237	−	0.702676i
$874$		−	16.1864i		−	0.547514i
$875$	10.9572	+	7.46955i	0.370422	+	0.252517i
$876$	19.6220	+	36.8721i	0.662967	+	1.24579i
$877$			46.3559i			1.56533i	0.622445	+	0.782664i	$0.286139\pi$
$877$			46.3559i			1.56533i	−0.622445	+	0.782664i	$0.713861\pi$
$878$			42.2844i			1.42703i
$879$	−37.3939	+	19.8997i	−1.26126	+	0.671199i
$880$		−	1.48745i		−	0.0501420i
$881$	−30.1838			−1.01692			−0.508460	−	0.861086i	$-0.669785\pi$
$881$	−30.1838			−1.01692			−0.508460	+	0.861086i	$0.669785\pi$
$882$	−48.1932	−	10.7054i	−1.62275	−	0.360470i
$883$	−26.8810			−0.904618			−0.452309	−	0.891861i	$-0.649400\pi$
$883$	−26.8810			−0.904618			−0.452309	+	0.891861i	$0.649400\pi$
$884$	−3.70217	+	2.68160i	−0.124518	+	0.0901919i
$885$	0.424576	+	0.797829i	0.0142720	+	0.0268187i
$886$		−	7.64818i		−	0.256946i
$887$	9.71279			0.326123			0.163062	−	0.986616i	$-0.447863\pi$
$887$	9.71279			0.326123			0.163062	+	0.986616i	$0.447863\pi$
$888$	−15.1976	+	8.08762i	−0.509998	+	0.271403i
$889$	−12.0983	+	17.7473i	−0.405765	+	0.595224i
$890$	−18.2122			−0.610473
$891$	−7.06602	−	17.4179i	−0.236721	−	0.583523i
$892$	48.5442			1.62538
$893$			24.5128i			0.820290i
$894$	−27.7761	−	52.1946i	−0.928970	−	1.74565i
$895$	−5.89865			−0.197170
$896$	−30.3220	+	44.4798i	−1.01299	+	1.48597i
$897$	−5.31903	+	10.8754i	−0.177597	+	0.363119i
$898$	94.3881			3.14977
$899$			64.7375i			2.15912i
$900$	−27.9823	+	41.5490i	−0.932745	+	1.38497i
$901$		−	3.31126i		−	0.110314i
$902$			26.3819i			0.878421i
$903$	−1.74592	−	0.191580i	−0.0581005	−	0.00637538i
$904$			49.3493i			1.64133i
$905$	3.52692			0.117239
$906$	−11.7838	+	6.27092i	−0.391491	+	0.208337i
$907$	−54.2467			−1.80123			−0.900616	−	0.434616i	$-0.856884\pi$
$907$	−54.2467			−1.80123			−0.900616	+	0.434616i	$0.856884\pi$
$908$		−	58.7593i		−	1.95000i
$909$	28.2499	−	41.9463i	0.936992	−	1.39127i
$910$	11.5416	−	0.329375i	0.382600	−	0.0109187i
$911$			29.5135i			0.977825i	0.872333	+	0.488913i	$0.162606\pi$
$911$			29.5135i			0.977825i	−0.872333	+	0.488913i	$0.837394\pi$
$912$	−3.99769	−	7.51215i	−0.132377	−	0.248752i
$913$			31.1040i			1.02939i
$914$		−	1.09943i		−	0.0363660i
$915$	−4.51798	−	8.48984i	−0.149360	−	0.280665i
$916$	−85.2662			−2.81727
$917$	−25.2339	+	37.0160i	−0.833295	+	1.22238i
$918$	−4.36813	−	0.454417i	−0.144170	−	0.0149980i
$919$	37.6149			1.24080			0.620401	−	0.784285i	$-0.286970\pi$
$919$	37.6149			1.24080			0.620401	+	0.784285i	$0.286970\pi$
$920$	−3.58185			−0.118090
$921$	−8.00409	−	15.0407i	−0.263744	−	0.495606i
$922$		−	61.0855i		−	2.01174i
$923$	−8.14828	+	5.90205i	−0.268204	+	0.194268i
$924$	33.5501	+	3.68146i	1.10372	+	0.121111i
$925$			13.1143i			0.431197i
$926$		−	44.2929i		−	1.45556i
$927$	9.19508	+	6.19269i	0.302006	+	0.203395i
$928$			34.4450i			1.13071i
$929$			10.7740i			0.353482i	0.984257	+	0.176741i	$0.0565555\pi$
$929$			10.7740i			0.353482i	−0.984257	+	0.176741i	$0.943445\pi$
$930$	13.6535	−	7.26589i	0.447715	−	0.238258i
$931$	−9.08591	−	23.1425i	−0.297779	−	0.758464i
$932$		−	23.2395i		−	0.761235i
$933$	−17.5606	−	32.9984i	−0.574907	−	1.08032i
$934$	−18.5807			−0.607978
$935$		−	0.386597i		−	0.0126431i
$936$	1.32596	+	38.7941i	0.0433404	+	1.26803i
$937$		−	20.6069i		−	0.673197i	−0.941648	−	0.336598i	$-0.890724\pi$
$937$		−	20.6069i		−	0.673197i	0.941648	−	0.336598i	$-0.109276\pi$
$938$	19.1151	+	13.0308i	0.624129	+	0.425469i
$939$	−13.9707	+	7.43472i	−0.455918	+	0.242623i
$940$	12.5312			0.408724
$941$		−	3.11651i		−	0.101595i	−0.998709	−	0.0507977i	$-0.983824\pi$
$941$		−	3.11651i		−	0.101595i	0.998709	−	0.0507977i	$-0.0161764\pi$
$942$	−64.6136	+	34.3850i	−2.10522	+	1.12032i
$943$	10.4166			0.339212
$944$		−	1.40187i		−	0.0456271i
$945$	5.40464	+	4.57075i	0.175813	+	0.148686i
$946$	1.88181			0.0611830
$947$	18.1393			0.589449			0.294724	−	0.955582i	$-0.404772\pi$
$947$	18.1393			0.589449			0.294724	+	0.955582i	$0.404772\pi$
$948$	−28.0810	−	52.7677i	−0.912030	−	1.71381i
$949$	19.9675	−	14.4631i	0.648174	−	0.469493i
$950$	−39.5347			−1.28268
$951$	0.621134	+	1.16719i	0.0201416	+	0.0378486i
$952$	1.92273	−	2.82049i	0.0623160	−	0.0914125i
$953$		−	14.9948i		−	0.485728i	−0.970060	−	0.242864i	$-0.921913\pi$
$953$		−	14.9948i		−	0.485728i	0.970060	−	0.242864i	$-0.0780869\pi$
$954$	−53.8762	−	36.2845i	−1.74431	−	1.17475i
$955$	2.39483			0.0774949
$956$	−19.1943			−0.620788
$957$	28.0220	−	14.9123i	0.905824	−	0.482047i
$958$			33.7365i			1.08998i
$959$	−14.8121	+	21.7282i	−0.478309	+	0.701640i
$960$	9.44258	−	5.02500i	0.304758	−	0.162181i
$961$	23.4271			0.755713
$962$	13.7716	+	19.0128i	0.444013	+	0.612998i
$963$	−34.1406	−	22.9930i	−1.10017	−	0.740938i
$964$	5.08917			0.163911
$965$	−5.02894			−0.161887
$966$	2.27797	−	20.7597i	0.0732924	−	0.667932i
$967$		−	16.0005i		−	0.514543i	−0.966339	−	0.257271i	$-0.917177\pi$
$967$		−	16.0005i		−	0.514543i	0.966339	−	0.257271i	$-0.0828234\pi$
$968$	23.8216			0.765655
$969$	−1.03902	−	1.95245i	−0.0333782	−	0.0627217i
$970$		−	10.0991i		−	0.324262i
$971$	−4.89419			−0.157062			−0.0785310	−	0.996912i	$-0.525023\pi$
$971$	−4.89419			−0.157062			−0.0785310	+	0.996912i	$0.525023\pi$
$972$	−35.2613	+	42.1742i	−1.13101	+	1.35274i
$973$	2.72976	+	1.86088i	0.0875120	+	0.0596571i
$974$		−	75.1621i		−	2.40835i
$975$	26.5627	+	12.9915i	0.850687	+	0.416061i
$976$			14.9176i			0.477500i
$977$	−9.36851			−0.299725			−0.149863	−	0.988707i	$-0.547883\pi$
$977$	−9.36851			−0.299725			−0.149863	+	0.988707i	$0.547883\pi$
$978$	59.0998	−	31.4508i	1.88980	−	1.00568i
$979$			31.4251i			1.00435i
$980$	−11.8307	+	4.64483i	−0.377918	+	0.148374i
$981$	−27.0264	−	18.2017i	−0.862885	−	0.581135i
$982$		−	42.9311i		−	1.36999i
$983$			15.8015i			0.503989i	0.967729	+	0.251994i	$0.0810865\pi$
$983$			15.8015i			0.503989i	−0.967729	+	0.251994i	$0.918914\pi$
$984$	29.4838	−	15.6902i	0.939909	−	0.500186i
$985$		−	10.3067i		−	0.328399i
$986$		−	7.41651i		−	0.236190i
$987$	−3.44976	+	31.4386i	−0.109807	+	1.00070i
$988$	−36.5740	+	26.4917i	−1.16357	+	0.842813i
$989$		−	0.743015i		−	0.0236265i
$990$	−6.29017	−	4.23629i	−0.199915	−	0.134638i
$991$	−26.5667			−0.843918			−0.421959	−	0.906615i	$-0.638657\pi$
$991$	−26.5667			−0.843918			−0.421959	+	0.906615i	$0.638657\pi$
$992$	28.9591			0.919453
$993$	−10.6371	+	5.66070i	−0.337560	+	0.179637i
$994$	9.77625	−	14.3409i	0.310084	−	0.454867i
$995$	−8.28406			−0.262622
$996$	80.3043	−	42.7350i	2.54454	−	1.35411i
$997$			60.4042i			1.91302i	0.291700	+	0.956510i	$0.405779\pi$
$997$			60.4042i			1.91302i	−0.291700	+	0.956510i	$0.594221\pi$
$998$			64.1855i			2.03176i
$999$	−1.48915	+	14.3146i	−0.0471146	+	0.452894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.g.a.272.1	✓	32
3.2	odd	2	inner	273.2.g.a.272.31	yes	32
7.6	odd	2	inner	273.2.g.a.272.4	yes	32
13.12	even	2	inner	273.2.g.a.272.29	yes	32
21.20	even	2	inner	273.2.g.a.272.30	yes	32
39.38	odd	2	inner	273.2.g.a.272.3	yes	32
91.90	odd	2	inner	273.2.g.a.272.32	yes	32
273.272	even	2	inner	273.2.g.a.272.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.g.a.272.1	✓	32	1.1	even	1	trivial
273.2.g.a.272.2	yes	32	273.272	even	2	inner
273.2.g.a.272.3	yes	32	39.38	odd	2	inner
273.2.g.a.272.4	yes	32	7.6	odd	2	inner
273.2.g.a.272.29	yes	32	13.12	even	2	inner
273.2.g.a.272.30	yes	32	21.20	even	2	inner
273.2.g.a.272.31	yes	32	3.2	odd	2	inner
273.2.g.a.272.32	yes	32	91.90	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.35085 q^{2} +(-0.813690 - 1.52902i) q^{3} +3.52651 q^{4} -0.514868i q^{5} +(1.91287 + 3.59451i) q^{6} +(-1.49028 + 2.18611i) q^{7} -3.58861 q^{8} +(-1.67582 + 2.48830i) q^{9} +O(q^{10})\)	\(q-2.35085 q^{2} +(-0.813690 - 1.52902i) q^{3} +3.52651 q^{4} -0.514868i q^{5} +(1.91287 + 3.59451i) q^{6} +(-1.49028 + 2.18611i) q^{7} -3.58861 q^{8} +(-1.67582 + 2.48830i) q^{9} +1.21038i q^{10} +2.08851 q^{11} +(-2.86949 - 5.39212i) q^{12} +(-2.92002 + 2.11506i) q^{13} +(3.50342 - 5.13923i) q^{14} +(-0.787245 + 0.418943i) q^{15} +1.38328 q^{16} +0.359522 q^{17} +(3.93960 - 5.84963i) q^{18} +3.55174 q^{19} -1.81569i q^{20} +(4.55523 + 0.499847i) q^{21} -4.90979 q^{22} +1.93858i q^{23} +(2.92002 + 5.48707i) q^{24} +4.73491 q^{25} +(6.86454 - 4.97220i) q^{26} +(5.16826 + 0.537655i) q^{27} +(-5.25548 + 7.70935i) q^{28} +8.77503i q^{29} +(1.85070 - 0.984875i) q^{30} +7.37747 q^{31} +3.92534 q^{32} +(-1.69940 - 3.19338i) q^{33} -0.845183 q^{34} +(1.12556 + 0.767296i) q^{35} +(-5.90979 + 8.77503i) q^{36} +2.76971i q^{37} -8.34962 q^{38} +(5.60997 + 2.74377i) q^{39} +1.84766i q^{40} -5.37332i q^{41} +(-10.7087 - 1.17507i) q^{42} -0.383277 q^{43} +7.36518 q^{44} +(1.28115 + 0.862825i) q^{45} -4.55733i q^{46} +6.90164i q^{47} +(-1.12556 - 2.11506i) q^{48} +(-2.55816 - 6.51581i) q^{49} -11.1311 q^{50} +(-0.292539 - 0.549717i) q^{51} +(-10.2975 + 7.45880i) q^{52} -9.21019i q^{53} +(-12.1498 - 1.26395i) q^{54} -1.07531i q^{55} +(5.34802 - 7.84511i) q^{56} +(-2.89002 - 5.43069i) q^{57} -20.6288i q^{58} -1.01344i q^{59} +(-2.77623 + 1.47741i) q^{60} +10.7842i q^{61} -17.3434 q^{62} +(-2.94227 - 7.37177i) q^{63} -11.9945 q^{64} +(1.08898 + 1.50343i) q^{65} +(3.99505 + 7.50718i) q^{66} +3.71944i q^{67} +1.26786 q^{68} +(2.96414 - 1.57741i) q^{69} +(-2.64603 - 1.80380i) q^{70} +2.79049 q^{71} +(6.01386 - 8.92955i) q^{72} -6.83815 q^{73} -6.51119i q^{74} +(-3.85275 - 7.23978i) q^{75} +12.5253 q^{76} +(-3.11246 + 4.56572i) q^{77} +(-13.1882 - 6.45020i) q^{78} +9.78607 q^{79} -0.712206i q^{80} +(-3.38328 - 8.33987i) q^{81} +12.6319i q^{82} +14.8929i q^{83} +(16.0641 + 1.76272i) q^{84} -0.185106i q^{85} +0.901029 q^{86} +(13.4172 - 7.14015i) q^{87} -7.49487 q^{88} +15.0466i q^{89} +(-3.01179 - 2.02838i) q^{90} +(-0.272125 - 9.53551i) q^{91} +6.83644i q^{92} +(-6.00298 - 11.2803i) q^{93} -16.2247i q^{94} -1.82868i q^{95} +(-3.19401 - 6.00194i) q^{96} -8.34372 q^{97} +(6.01386 + 15.3177i) q^{98} +(-3.49997 + 5.19685i) 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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