LMFDB - Embedded newform 287.2.e.b.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.e (of order $3$, degree $2$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.1
Root			$1.15139 - 1.99426i$ of defining polynomial
Character	$\chi$	$=$	287.165
Dual form			287.2.e.b.247.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15139 + 1.99426i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.651388 - 1.12824i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-1.15139 - 1.99426i) q^{9} +O(q^{10})$	\(q+(-1.15139 + 1.99426i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.651388 - 1.12824i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-1.15139 - 1.99426i) q^{9} +(2.15139 - 3.72631i) q^{11} +(2.30278 + 3.98852i) q^{12} -2.30278 q^{13} +3.00000 q^{15} +(-2.00000 - 3.46410i) q^{16} +(1.95416 - 3.38471i) q^{17} +(1.80278 + 3.12250i) q^{19} -2.60555 q^{20} +(5.75694 + 1.99426i) q^{21} +(2.80278 + 4.85455i) q^{23} +(1.65139 - 2.86029i) q^{25} -1.60555 q^{27} +(-5.00000 - 1.73205i) q^{28} +5.60555 q^{29} +(1.15139 - 1.99426i) q^{31} +(4.95416 + 8.58086i) q^{33} +(-2.60555 + 2.25647i) q^{35} -4.60555 q^{36} +(-3.60555 - 6.24500i) q^{37} +(2.65139 - 4.59234i) q^{39} -1.00000 q^{41} -9.60555 q^{43} +(-4.30278 - 7.45263i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(4.50000 + 7.79423i) q^{47} +9.21110 q^{48} +(-6.50000 + 2.59808i) q^{49} +(4.50000 + 7.79423i) q^{51} +(-2.30278 + 3.98852i) q^{52} +(-4.95416 + 8.58086i) q^{53} -5.60555 q^{55} -8.30278 q^{57} +(-0.197224 + 0.341603i) q^{59} +(3.00000 - 5.19615i) q^{60} +(-3.60555 - 6.24500i) q^{61} +(-4.60555 + 3.98852i) q^{63} -8.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(3.30278 - 5.72058i) q^{67} +(-3.90833 - 6.76942i) q^{68} -12.9083 q^{69} +10.8167 q^{71} +(-4.65139 + 8.05644i) q^{73} +(3.80278 + 6.58660i) q^{75} +7.21110 q^{76} +(-10.7569 - 3.72631i) q^{77} +(8.71110 + 15.0881i) q^{79} +(-2.60555 + 4.51295i) q^{80} +(5.30278 - 9.18468i) q^{81} +11.6056 q^{83} +(9.21110 - 7.97705i) q^{84} -5.09167 q^{85} +(-6.45416 + 11.1789i) q^{87} +(-0.197224 - 0.341603i) q^{89} +(1.15139 + 5.98279i) q^{91} +11.2111 q^{92} +(2.65139 + 4.59234i) q^{93} +(2.34861 - 4.06792i) q^{95} +9.30278 q^{97} -9.90833 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 4 q^{4} + q^{5} - 2 q^{7} - q^{9}+O(q^{10}) $ 4 * q - q^3 + 4 * q^4 + q^5 - 2 * q^7 - q^9	$ 4 q - q^{3} + 4 q^{4} + q^{5} - 2 q^{7} - q^{9} + 5 q^{11} + 2 q^{12} - 2 q^{13} + 12 q^{15} - 8 q^{16} - 3 q^{17} + 4 q^{20} + 5 q^{21} + 4 q^{23} + 3 q^{25} + 8 q^{27} - 20 q^{28} + 8 q^{29} + q^{31} + 9 q^{33} + 4 q^{35} - 4 q^{36} + 7 q^{39} - 4 q^{41} - 24 q^{43} - 10 q^{44} - 6 q^{45} + 18 q^{47} + 8 q^{48} - 26 q^{49} + 18 q^{51} - 2 q^{52} - 9 q^{53} - 8 q^{55} - 26 q^{57} - 8 q^{59} + 12 q^{60} - 4 q^{63} - 32 q^{64} + 6 q^{65} + 6 q^{67} + 6 q^{68} - 30 q^{69} - 15 q^{73} + 8 q^{75} - 25 q^{77} + 6 q^{79} + 4 q^{80} + 14 q^{81} + 32 q^{83} + 8 q^{84} - 42 q^{85} - 15 q^{87} - 8 q^{89} + q^{91} + 16 q^{92} + 7 q^{93} + 13 q^{95} + 30 q^{97} - 18 q^{99}+O(q^{100}) $ 4 * q - q^3 + 4 * q^4 + q^5 - 2 * q^7 - q^9 + 5 * q^11 + 2 * q^12 - 2 * q^13 + 12 * q^15 - 8 * q^16 - 3 * q^17 + 4 * q^20 + 5 * q^21 + 4 * q^23 + 3 * q^25 + 8 * q^27 - 20 * q^28 + 8 * q^29 + q^31 + 9 * q^33 + 4 * q^35 - 4 * q^36 + 7 * q^39 - 4 * q^41 - 24 * q^43 - 10 * q^44 - 6 * q^45 + 18 * q^47 + 8 * q^48 - 26 * q^49 + 18 * q^51 - 2 * q^52 - 9 * q^53 - 8 * q^55 - 26 * q^57 - 8 * q^59 + 12 * q^60 - 4 * q^63 - 32 * q^64 + 6 * q^65 + 6 * q^67 + 6 * q^68 - 30 * q^69 - 15 * q^73 + 8 * q^75 - 25 * q^77 + 6 * q^79 + 4 * q^80 + 14 * q^81 + 32 * q^83 + 8 * q^84 - 42 * q^85 - 15 * q^87 - 8 * q^89 + q^91 + 16 * q^92 + 7 * q^93 + 13 * q^95 + 30 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	−1.15139	+	1.99426i	−0.664754	+	1.15139i	0.314598	+	0.949225i	$0.398130\pi$
$3$	−1.15139	+	1.99426i	−0.664754	+	1.15139i	−0.979352	+	0.202163i	$0.935203\pi$
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−0.651388	−	1.12824i	−0.291309	−	0.504563i	0.682810	−	0.730596i	$-0.260758\pi$
$5$	−0.651388	−	1.12824i	−0.291309	−	0.504563i	−0.974120	+	0.226033i	$0.927424\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$		0			0
$9$	−1.15139	−	1.99426i	−0.383796	−	0.664754i
$10$		0			0
$11$	2.15139	−	3.72631i	0.648668	−	1.12353i	−0.334773	−	0.942299i	$-0.608660\pi$
$11$	2.15139	−	3.72631i	0.648668	−	1.12353i	0.983441	−	0.181227i	$-0.0580069\pi$
$12$	2.30278	+	3.98852i	0.664754	+	1.15139i
$13$	−2.30278			−0.638675			−0.319338	−	0.947641i	$-0.603460\pi$
$13$	−2.30278			−0.638675			−0.319338	+	0.947641i	$0.603460\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	1.95416	−	3.38471i	0.473954	−	0.820913i	−0.525601	−	0.850731i	$-0.676160\pi$
$17$	1.95416	−	3.38471i	0.473954	−	0.820913i	0.999555	+	0.0298183i	$0.00949287\pi$
$18$		0			0
$19$	1.80278	+	3.12250i	0.413585	+	0.716350i	0.995279	−	0.0970575i	$-0.0309431\pi$
$19$	1.80278	+	3.12250i	0.413585	+	0.716350i	−0.581694	+	0.813408i	$0.697610\pi$
$20$	−2.60555			−0.582619
$21$	5.75694	+	1.99426i	1.25627	+	0.435184i
$22$		0			0
$23$	2.80278	+	4.85455i	0.584419	+	1.01224i	0.994948	+	0.100396i	$0.0320109\pi$
$23$	2.80278	+	4.85455i	0.584419	+	1.01224i	−0.410528	+	0.911848i	$0.634656\pi$
$24$		0			0
$25$	1.65139	−	2.86029i	0.330278	−	0.572058i
$26$		0			0
$27$	−1.60555			−0.308988
$28$	−5.00000	−	1.73205i	−0.944911	−	0.327327i
$29$	5.60555			1.04092			0.520462	−	0.853885i	$-0.325760\pi$
$29$	5.60555			1.04092			0.520462	+	0.853885i	$0.325760\pi$
$30$		0			0
$31$	1.15139	−	1.99426i	0.206795	−	0.358180i	−0.743908	−	0.668282i	$-0.767030\pi$
$31$	1.15139	−	1.99426i	0.206795	−	0.358180i	0.950703	+	0.310102i	$0.100363\pi$
$32$		0			0
$33$	4.95416	+	8.58086i	0.862409	+	1.49374i
$34$		0			0
$35$	−2.60555	+	2.25647i	−0.440419	+	0.381414i
$36$	−4.60555			−0.767592
$37$	−3.60555	−	6.24500i	−0.592749	−	1.02667i	−0.993860	−	0.110642i	$-0.964709\pi$
$37$	−3.60555	−	6.24500i	−0.592749	−	1.02667i	0.401111	−	0.916029i	$-0.368624\pi$
$38$		0			0
$39$	2.65139	−	4.59234i	0.424562	−	0.735363i
$40$		0			0
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$		0			0
$43$	−9.60555			−1.46483			−0.732416	−	0.680857i	$-0.761608\pi$
$43$	−9.60555			−1.46483			−0.732416	+	0.680857i	$0.761608\pi$
$44$	−4.30278	−	7.45263i	−0.648668	−	1.12353i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$		0			0
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$	9.21110			1.32951
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$	4.50000	+	7.79423i	0.630126	+	1.09141i
$52$	−2.30278	+	3.98852i	−0.319338	+	0.553109i
$53$	−4.95416	+	8.58086i	−0.680507	+	1.17867i	0.294320	+	0.955707i	$0.404907\pi$
$53$	−4.95416	+	8.58086i	−0.680507	+	1.17867i	−0.974826	+	0.222965i	$0.928426\pi$
$54$		0			0
$55$	−5.60555			−0.755852
$56$		0			0
$57$	−8.30278			−1.09973
$58$		0			0
$59$	−0.197224	+	0.341603i	−0.0256764	+	0.0444729i	−0.878578	−	0.477599i	$-0.841507\pi$
$59$	−0.197224	+	0.341603i	−0.0256764	+	0.0444729i	0.852902	+	0.522072i	$0.174841\pi$
$60$	3.00000	−	5.19615i	0.387298	−	0.670820i
$61$	−3.60555	−	6.24500i	−0.461644	−	0.799590i	0.537400	−	0.843328i	$-0.319407\pi$
$61$	−3.60555	−	6.24500i	−0.461644	−	0.799590i	−0.999043	+	0.0437377i	$0.986073\pi$
$62$		0			0
$63$	−4.60555	+	3.98852i	−0.580245	+	0.502507i
$64$	−8.00000			−1.00000
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$		0			0
$67$	3.30278	−	5.72058i	0.403498	−	0.698879i	−0.590647	−	0.806930i	$-0.701127\pi$
$67$	3.30278	−	5.72058i	0.403498	−	0.698879i	0.994145	+	0.108050i	$0.0344608\pi$
$68$	−3.90833	−	6.76942i	−0.473954	−	0.820913i
$69$	−12.9083			−1.55398
$70$		0			0
$71$	10.8167			1.28370			0.641850	−	0.766830i	$-0.278167\pi$
$71$	10.8167			1.28370			0.641850	+	0.766830i	$0.278167\pi$
$72$		0			0
$73$	−4.65139	+	8.05644i	−0.544404	+	0.942935i	0.454240	+	0.890879i	$0.349911\pi$
$73$	−4.65139	+	8.05644i	−0.544404	+	0.942935i	−0.998644	+	0.0520558i	$0.983423\pi$
$74$		0			0
$75$	3.80278	+	6.58660i	0.439107	+	0.760555i
$76$	7.21110			0.827170
$77$	−10.7569	−	3.72631i	−1.22587	−	0.424653i
$78$		0			0
$79$	8.71110	+	15.0881i	0.980076	+	1.69754i	0.662052	+	0.749458i	$0.269686\pi$
$79$	8.71110	+	15.0881i	0.980076	+	1.69754i	0.318024	+	0.948083i	$0.396981\pi$
$80$	−2.60555	+	4.51295i	−0.291309	+	0.504563i
$81$	5.30278	−	9.18468i	0.589197	−	1.02052i
$82$		0			0
$83$	11.6056			1.27387			0.636937	−	0.770916i	$-0.280201\pi$
$83$	11.6056			1.27387			0.636937	+	0.770916i	$0.280201\pi$
$84$	9.21110	−	7.97705i	1.00501	−	0.870367i
$85$	−5.09167			−0.552269
$86$		0			0
$87$	−6.45416	+	11.1789i	−0.691959	+	1.19851i
$88$		0			0
$89$	−0.197224	−	0.341603i	−0.0209057	−	0.0362098i	0.855383	−	0.517996i	$-0.173322\pi$
$89$	−0.197224	−	0.341603i	−0.0209057	−	0.0362098i	−0.876289	+	0.481786i	$0.839988\pi$
$90$		0			0
$91$	1.15139	+	5.98279i	0.120698	+	0.627166i
$92$	11.2111			1.16884
$93$	2.65139	+	4.59234i	0.274936	+	0.476203i
$94$		0			0
$95$	2.34861	−	4.06792i	0.240963	−	0.417359i
$96$		0			0
$97$	9.30278			0.944554			0.472277	−	0.881450i	$-0.343432\pi$
$97$	9.30278			0.944554			0.472277	+	0.881450i	$0.343432\pi$
$98$		0			0
$99$	−9.90833			−0.995824
$100$	−3.30278	−	5.72058i	−0.330278	−	0.572058i
$101$	5.80278	−	10.0507i	0.577398	−	1.00008i	−0.418379	−	0.908273i	$-0.637402\pi$
$101$	5.80278	−	10.0507i	0.577398	−	1.00008i	0.995777	−	0.0918096i	$-0.0292651\pi$
$102$		0			0
$103$	0.894449	+	1.54923i	0.0881327	+	0.152650i	0.906722	−	0.421729i	$-0.138577\pi$
$103$	0.894449	+	1.54923i	0.0881327	+	0.152650i	−0.818589	+	0.574379i	$0.805243\pi$
$104$		0			0
$105$	−1.50000	−	7.79423i	−0.146385	−	0.760639i
$106$		0			0
$107$	3.45416	+	5.98279i	0.333927	+	0.578378i	0.983278	−	0.182111i	$-0.0582929\pi$
$107$	3.45416	+	5.98279i	0.333927	+	0.578378i	−0.649351	+	0.760488i	$0.724960\pi$
$108$	−1.60555	+	2.78090i	−0.154494	+	0.267592i
$109$	−3.15139	+	5.45836i	−0.301848	+	0.522816i	−0.976555	−	0.215270i	$-0.930937\pi$
$109$	−3.15139	+	5.45836i	−0.301848	+	0.522816i	0.674706	+	0.738086i	$0.264270\pi$
$110$		0			0
$111$	16.6056			1.57613
$112$	−8.00000	+	6.92820i	−0.755929	+	0.654654i
$113$	−7.81665			−0.735329			−0.367664	−	0.929959i	$-0.619843\pi$
$113$	−7.81665			−0.735329			−0.367664	+	0.929959i	$0.619843\pi$
$114$		0			0
$115$	3.65139	−	6.32439i	0.340494	−	0.589752i
$116$	5.60555	−	9.70910i	0.520462	−	0.901467i
$117$	2.65139	+	4.59234i	0.245121	+	0.424562i
$118$		0			0
$119$	−9.77082	−	3.38471i	−0.895689	−	0.310276i
$120$		0			0
$121$	−3.75694	−	6.50721i	−0.341540	−	0.591564i
$122$		0			0
$123$	1.15139	−	1.99426i	0.103817	−	0.179817i
$124$	−2.30278	−	3.98852i	−0.206795	−	0.358180i
$125$	−10.8167			−0.967471
$126$		0			0
$127$	13.7250			1.21790			0.608948	−	0.793210i	$-0.291592\pi$
$127$	13.7250			1.21790			0.608948	+	0.793210i	$0.291592\pi$
$128$		0			0
$129$	11.0597	−	19.1560i	0.973754	−	1.68659i
$130$		0			0
$131$	−0.848612	−	1.46984i	−0.0741436	−	0.128420i	0.826570	−	0.562834i	$-0.190289\pi$
$131$	−0.848612	−	1.46984i	−0.0741436	−	0.128420i	−0.900714	+	0.434414i	$0.856956\pi$
$132$	19.8167			1.72482
$133$	7.21110	−	6.24500i	0.625282	−	0.541510i
$134$		0			0
$135$	1.04584	+	1.81144i	0.0900113	+	0.155904i
$136$		0			0
$137$	0.591673	−	1.02481i	0.0505500	−	0.0875552i	−0.839643	−	0.543138i	$-0.817236\pi$
$137$	0.591673	−	1.02481i	0.0505500	−	0.0875552i	0.890193	+	0.455583i	$0.150569\pi$
$138$		0			0
$139$	−4.90833			−0.416319			−0.208159	−	0.978095i	$-0.566747\pi$
$139$	−4.90833			−0.416319			−0.208159	+	0.978095i	$0.566747\pi$
$140$	1.30278	+	6.76942i	0.110105	+	0.572120i
$141$	−20.7250			−1.74536
$142$		0			0
$143$	−4.95416	+	8.58086i	−0.414288	+	0.717568i
$144$	−4.60555	+	7.97705i	−0.383796	+	0.664754i
$145$	−3.65139	−	6.32439i	−0.303231	−	0.525212i
$146$		0			0
$147$	2.30278	−	15.9541i	0.189930	−	1.31587i
$148$	−14.4222			−1.18550
$149$	0.908327	+	1.57327i	0.0744130	+	0.128887i	0.900831	−	0.434170i	$-0.142958\pi$
$149$	0.908327	+	1.57327i	0.0744130	+	0.128887i	−0.826418	+	0.563057i	$0.809625\pi$
$150$		0			0
$151$	−5.55971	+	9.62971i	−0.452443	+	0.783655i	−0.998537	−	0.0540693i	$-0.982781\pi$
$151$	−5.55971	+	9.62971i	−0.452443	+	0.783655i	0.546094	+	0.837724i	$0.316114\pi$
$152$		0			0
$153$	−9.00000			−0.727607
$154$		0			0
$155$	−3.00000			−0.240966
$156$	−5.30278	−	9.18468i	−0.424562	−	0.735363i
$157$	0.894449	−	1.54923i	0.0713848	−	0.123642i	−0.828124	−	0.560545i	$-0.810592\pi$
$157$	0.894449	−	1.54923i	0.0713848	−	0.123642i	0.899508	+	0.436903i	$0.143925\pi$
$158$		0			0
$159$	−11.4083	−	19.7598i	−0.904739	−	1.56705i
$160$		0			0
$161$	11.2111	−	9.70910i	0.883559	−	0.765184i
$162$		0			0
$163$	7.86249	+	13.6182i	0.615838	+	1.06666i	0.990237	+	0.139395i	$0.0445157\pi$
$163$	7.86249	+	13.6182i	0.615838	+	1.06666i	−0.374399	+	0.927268i	$0.622151\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$	6.45416	−	11.1789i	0.502456	−	0.870279i
$166$		0			0
$167$	4.81665			0.372724			0.186362	−	0.982481i	$-0.440330\pi$
$167$	4.81665			0.372724			0.186362	+	0.982481i	$0.440330\pi$
$168$		0			0
$169$	−7.69722			−0.592094
$170$		0			0
$171$	4.15139	−	7.19041i	0.317465	−	0.549865i
$172$	−9.60555	+	16.6373i	−0.732416	+	1.26858i
$173$	7.75694	+	13.4354i	0.589749	+	1.02148i	0.994265	+	0.106945i	$0.0341067\pi$
$173$	7.75694	+	13.4354i	0.589749	+	1.02148i	−0.404516	+	0.914531i	$0.632560\pi$
$174$		0			0
$175$	−8.25694	−	2.86029i	−0.624166	−	0.216217i
$176$	−17.2111			−1.29734
$177$	−0.454163	−	0.786634i	−0.0341370	−	0.0591270i
$178$		0			0
$179$	6.84861	−	11.8621i	0.511889	−	0.886618i	−0.488016	−	0.872835i	$-0.662279\pi$
$179$	6.84861	−	11.8621i	0.511889	−	0.886618i	0.999905	−	0.0137834i	$-0.00438754\pi$
$180$	3.00000	+	5.19615i	0.223607	+	0.387298i
$181$	21.0278			1.56298			0.781490	−	0.623917i	$-0.214460\pi$
$181$	21.0278			1.56298			0.781490	+	0.623917i	$0.214460\pi$
$182$		0			0
$183$	16.6056			1.22752
$184$		0			0
$185$	−4.69722	+	8.13583i	−0.345347	+	0.598158i
$186$		0			0
$187$	−8.40833	−	14.5636i	−0.614878	−	1.06500i
$188$	18.0000			1.31278
$189$	0.802776	+	4.17134i	0.0583933	+	0.303421i
$190$		0			0
$191$	9.65139	+	16.7167i	0.698350	+	1.20958i	0.969038	+	0.246911i	$0.0794154\pi$
$191$	9.65139	+	16.7167i	0.698350	+	1.20958i	−0.270688	+	0.962667i	$0.587251\pi$
$192$	9.21110	−	15.9541i	0.664754	−	1.15139i
$193$	3.69722	−	6.40378i	0.266132	−	0.460954i	−0.701728	−	0.712445i	$-0.747588\pi$
$193$	3.69722	−	6.40378i	0.266132	−	0.460954i	0.967860	+	0.251491i	$0.0809209\pi$
$194$		0			0
$195$	−6.90833			−0.494716
$196$	−2.00000	+	13.8564i	−0.142857	+	0.989743i
$197$	3.90833			0.278457			0.139228	−	0.990260i	$-0.455538\pi$
$197$	3.90833			0.278457			0.139228	+	0.990260i	$0.455538\pi$
$198$		0			0
$199$	9.10555	−	15.7713i	0.645475	−	1.11800i	−0.338716	−	0.940889i	$-0.609993\pi$
$199$	9.10555	−	15.7713i	0.645475	−	1.11800i	0.984191	−	0.177108i	$-0.0566741\pi$
$200$		0			0
$201$	7.60555	+	13.1732i	0.536454	+	0.929166i
$202$		0			0
$203$	−2.80278	−	14.5636i	−0.196716	−	1.02217i
$204$	18.0000			1.26025
$205$	0.651388	+	1.12824i	0.0454949	+	0.0787995i
$206$		0			0
$207$	6.45416	−	11.1789i	0.448595	−	0.776990i
$208$	4.60555	+	7.97705i	0.319338	+	0.553109i
$209$	15.5139			1.07312
$210$		0			0
$211$	−10.1194			−0.696650			−0.348325	−	0.937374i	$-0.613249\pi$
$211$	−10.1194			−0.696650			−0.348325	+	0.937374i	$0.613249\pi$
$212$	9.90833	+	17.1617i	0.680507	+	1.17867i
$213$	−12.4542	+	21.5712i	−0.853345	+	1.47804i
$214$		0			0
$215$	6.25694	+	10.8373i	0.426720	+	0.739100i
$216$		0			0
$217$	−5.75694	−	1.99426i	−0.390806	−	0.135379i
$218$		0			0
$219$	−10.7111	−	18.5522i	−0.723789	−	1.25364i
$220$	−5.60555	+	9.70910i	−0.377926	+	0.654587i
$221$	−4.50000	+	7.79423i	−0.302703	+	0.524297i
$222$		0			0
$223$	8.51388			0.570131			0.285066	−	0.958508i	$-0.407985\pi$
$223$	8.51388			0.570131			0.285066	+	0.958508i	$0.407985\pi$
$224$		0			0
$225$	−7.60555			−0.507037
$226$		0			0
$227$	−6.39445	+	11.0755i	−0.424414	+	0.735107i	−0.996366	−	0.0851803i	$-0.972853\pi$
$227$	−6.39445	+	11.0755i	−0.424414	+	0.735107i	0.571951	+	0.820288i	$0.306187\pi$
$228$	−8.30278	+	14.3808i	−0.549865	+	0.952394i
$229$	1.86249	+	3.22593i	0.123077	+	0.213175i	0.920980	−	0.389611i	$-0.127391\pi$
$229$	1.86249	+	3.22593i	0.123077	+	0.213175i	−0.797903	+	0.602786i	$0.794057\pi$
$230$		0			0
$231$	19.8167	−	17.1617i	1.30384	−	1.12916i
$232$		0			0
$233$	−11.6653	−	20.2048i	−0.764217	−	1.32366i	−0.940660	−	0.339352i	$-0.889792\pi$
$233$	−11.6653	−	20.2048i	−0.764217	−	1.32366i	0.176443	−	0.984311i	$-0.443541\pi$
$234$		0			0
$235$	5.86249	−	10.1541i	0.382427	−	0.662382i
$236$	0.394449	+	0.683205i	0.0256764	+	0.0444729i
$237$	−40.1194			−2.60604
$238$		0			0
$239$	22.8167			1.47589			0.737943	−	0.674863i	$-0.235797\pi$
$239$	22.8167			1.47589			0.737943	+	0.674863i	$0.235797\pi$
$240$	−6.00000	−	10.3923i	−0.387298	−	0.670820i
$241$	−1.90833	+	3.30532i	−0.122926	+	0.212914i	−0.920920	−	0.389751i	$-0.872561\pi$
$241$	−1.90833	+	3.30532i	−0.122926	+	0.212914i	0.797994	+	0.602665i	$0.205894\pi$
$242$		0			0
$243$	9.80278	+	16.9789i	0.628848	+	1.08920i
$244$	−14.4222			−0.923287
$245$	7.16527	+	5.64118i	0.457772	+	0.360402i
$246$		0			0
$247$	−4.15139	−	7.19041i	−0.264146	−	0.457515i
$248$		0			0
$249$	−13.3625	+	23.1445i	−0.846813	+	1.46672i
$250$		0			0
$251$	−21.9083			−1.38284			−0.691421	−	0.722452i	$-0.743015\pi$
$251$	−21.9083			−1.38284			−0.691421	+	0.722452i	$0.743015\pi$
$252$	2.30278	+	11.9656i	0.145061	+	0.753760i
$253$	24.1194			1.51638
$254$		0			0
$255$	5.86249	−	10.1541i	0.367123	−	0.635876i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−7.95416	−	13.7770i	−0.496167	−	0.859387i	0.503823	−	0.863807i	$-0.331926\pi$
$257$	−7.95416	−	13.7770i	−0.496167	−	0.859387i	−0.999990	+	0.00442023i	$0.998593\pi$
$258$		0			0
$259$	−14.4222	+	12.4900i	−0.896152	+	0.776091i
$260$	6.00000			0.372104
$261$	−6.45416	−	11.1789i	−0.399503	−	0.691959i
$262$		0			0
$263$	−8.15139	+	14.1186i	−0.502636	+	0.870591i	0.497359	+	0.867545i	$0.334303\pi$
$263$	−8.15139	+	14.1186i	−0.502636	+	0.870591i	−0.999995	+	0.00304659i	$0.999030\pi$
$264$		0			0
$265$	12.9083			0.792952
$266$		0			0
$267$	0.908327			0.0555887
$268$	−6.60555	−	11.4412i	−0.403498	−	0.698879i
$269$	−3.65139	+	6.32439i	−0.222629	+	0.385605i	−0.955605	−	0.294649i	$-0.904797\pi$
$269$	−3.65139	+	6.32439i	−0.222629	+	0.385605i	0.732976	+	0.680254i	$0.238131\pi$
$270$		0			0
$271$	−12.4083	−	21.4919i	−0.753752	−	1.30554i	−0.945992	−	0.324189i	$-0.894909\pi$
$271$	−12.4083	−	21.4919i	−0.753752	−	1.30554i	0.192240	−	0.981348i	$-0.438425\pi$
$272$	−15.6333			−0.947909
$273$	−13.2569	−	4.59234i	−0.802346	−	0.277941i
$274$		0			0
$275$	−7.10555	−	12.3072i	−0.428481	−	0.742151i
$276$	−12.9083	+	22.3579i	−0.776990	+	1.34579i
$277$	3.36249	−	5.82400i	0.202032	−	0.349930i	−0.747151	−	0.664655i	$-0.768579\pi$
$277$	3.36249	−	5.82400i	0.202032	−	0.349930i	0.949183	+	0.314724i	$0.101912\pi$
$278$		0			0
$279$	−5.30278			−0.317469
$280$		0			0
$281$	−6.51388			−0.388585			−0.194293	−	0.980944i	$-0.562241\pi$
$281$	−6.51388			−0.388585			−0.194293	+	0.980944i	$0.562241\pi$
$282$		0			0
$283$	−4.71110	+	8.15987i	−0.280046	+	0.485054i	−0.971396	−	0.237466i	$-0.923683\pi$
$283$	−4.71110	+	8.15987i	−0.280046	+	0.485054i	0.691350	+	0.722520i	$0.257016\pi$
$284$	10.8167	−	18.7350i	0.641850	−	1.11172i
$285$	5.40833	+	9.36750i	0.320362	+	0.554883i
$286$		0			0
$287$	0.500000	+	2.59808i	0.0295141	+	0.153360i
$288$		0			0
$289$	0.862490	+	1.49388i	0.0507347	+	0.0878751i
$290$		0			0
$291$	−10.7111	+	18.5522i	−0.627896	+	1.08755i
$292$	9.30278	+	16.1129i	0.544404	+	0.942935i
$293$	−15.7889			−0.922397			−0.461199	−	0.887297i	$-0.652580\pi$
$293$	−15.7889			−0.922397			−0.461199	+	0.887297i	$0.652580\pi$
$294$		0			0
$295$	0.513878			0.0299191
$296$		0			0
$297$	−3.45416	+	5.98279i	−0.200431	+	0.347156i
$298$		0			0
$299$	−6.45416	−	11.1789i	−0.373254	−	0.646495i
$300$	15.2111			0.878213
$301$	4.80278	+	24.9560i	0.276827	+	1.43844i
$302$		0			0
$303$	13.3625	+	23.1445i	0.767655	+	1.32962i
$304$	7.21110	−	12.4900i	0.413585	−	0.716350i
$305$	−4.69722	+	8.13583i	−0.268962	+	0.465856i
$306$		0			0
$307$	−32.5416			−1.85725			−0.928625	−	0.371021i	$-0.879008\pi$
$307$	−32.5416			−1.85725			−0.928625	+	0.371021i	$0.879008\pi$
$308$	−17.2111	+	14.9053i	−0.980694	+	0.849306i
$309$	−4.11943			−0.234346
$310$		0			0
$311$	−11.4083	+	19.7598i	−0.646907	+	1.12048i	0.336951	+	0.941522i	$0.390604\pi$
$311$	−11.4083	+	19.7598i	−0.646907	+	1.12048i	−0.983858	+	0.178953i	$0.942729\pi$
$312$		0			0
$313$	−9.86249	−	17.0823i	−0.557461	−	0.965551i	−0.997708	−	0.0676737i	$-0.978442\pi$
$313$	−9.86249	−	17.0823i	−0.557461	−	0.965551i	0.440247	−	0.897877i	$-0.354891\pi$
$314$		0			0
$315$	7.50000	+	2.59808i	0.422577	+	0.146385i
$316$	34.8444			1.96015
$317$	7.95416	+	13.7770i	0.446750	+	0.773794i	0.998172	−	0.0604322i	$-0.0192479\pi$
$317$	7.95416	+	13.7770i	0.446750	+	0.773794i	−0.551422	+	0.834226i	$0.685915\pi$
$318$		0			0
$319$	12.0597	−	20.8880i	0.675214	−	1.16951i
$320$	5.21110	+	9.02589i	0.291309	+	0.504563i
$321$	−15.9083			−0.887916
$322$		0			0
$323$	14.0917			0.784082
$324$	−10.6056	−	18.3694i	−0.589197	−	1.02052i
$325$	−3.80278	+	6.58660i	−0.210940	+	0.365359i
$326$		0			0
$327$	−7.25694	−	12.5694i	−0.401310	−	0.695089i
$328$		0			0
$329$	18.0000	−	15.5885i	0.992372	−	0.859419i
$330$		0			0
$331$	−0.0138782	−	0.0240377i	−0.000762814	−	0.00132123i	0.865644	−	0.500660i	$-0.166909\pi$
$331$	−0.0138782	−	0.0240377i	−0.000762814	−	0.00132123i	−0.866407	+	0.499339i	$0.833576\pi$
$332$	11.6056	−	20.1014i	0.636937	−	1.10321i
$333$	−8.30278	+	14.3808i	−0.454989	+	0.788065i
$334$		0			0
$335$	−8.60555			−0.470171
$336$	−4.60555	−	23.9311i	−0.251253	−	1.30555i
$337$	−15.7250			−0.856594			−0.428297	−	0.903638i	$-0.640886\pi$
$337$	−15.7250			−0.856594			−0.428297	+	0.903638i	$0.640886\pi$
$338$		0			0
$339$	9.00000	−	15.5885i	0.488813	−	0.846649i
$340$	−5.09167	+	8.81904i	−0.276135	+	0.478279i
$341$	−4.95416	−	8.58086i	−0.268283	−	0.464680i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	8.40833	+	14.5636i	0.452689	+	0.784081i
$346$		0			0
$347$	5.09167	−	8.81904i	0.273335	−	0.473431i	−0.696378	−	0.717675i	$-0.745206\pi$
$347$	5.09167	−	8.81904i	0.273335	−	0.473431i	0.969714	+	0.244244i	$0.0785398\pi$
$348$	12.9083	+	22.3579i	0.691959	+	1.19851i
$349$	−5.18335			−0.277458			−0.138729	−	0.990330i	$-0.544302\pi$
$349$	−5.18335			−0.277458			−0.138729	+	0.990330i	$0.544302\pi$
$350$		0			0
$351$	3.69722			0.197343
$352$		0			0
$353$	12.3167	−	21.3331i	0.655549	−	1.13544i	−0.326206	−	0.945299i	$-0.605770\pi$
$353$	12.3167	−	21.3331i	0.655549	−	1.13544i	0.981756	−	0.190146i	$-0.0608962\pi$
$354$		0			0
$355$	−7.04584	−	12.2037i	−0.373954	−	0.647708i
$356$	−0.788897			−0.0418115
$357$	18.0000	−	15.5885i	0.952661	−	0.825029i
$358$		0			0
$359$	13.8167	+	23.9311i	0.729215	+	1.26304i	0.957215	+	0.289377i	$0.0934480\pi$
$359$	13.8167	+	23.9311i	0.729215	+	1.26304i	−0.228000	+	0.973661i	$0.573219\pi$
$360$		0			0
$361$	3.00000	−	5.19615i	0.157895	−	0.273482i
$362$		0			0
$363$	17.3028			0.908160
$364$	11.5139	+	3.98852i	0.603491	+	0.209055i
$365$	12.1194			0.634360
$366$		0			0
$367$	8.39445	−	14.5396i	0.438187	−	0.758962i	−0.559363	−	0.828923i	$-0.688954\pi$
$367$	8.39445	−	14.5396i	0.438187	−	0.758962i	0.997550	+	0.0699612i	$0.0222876\pi$
$368$	11.2111	−	19.4182i	0.584419	−	1.01224i
$369$	1.15139	+	1.99426i	0.0599389	+	0.103817i
$370$		0			0
$371$	24.7708	+	8.58086i	1.28604	+	0.445496i
$372$	10.6056			0.549872
$373$	−11.1653	−	19.3388i	−0.578116	−	1.00133i	−0.995695	−	0.0926853i	$-0.970455\pi$
$373$	−11.1653	−	19.3388i	−0.578116	−	1.00133i	0.417580	−	0.908640i	$-0.362878\pi$
$374$		0			0
$375$	12.4542	−	21.5712i	0.643130	−	1.11393i
$376$		0			0
$377$	−12.9083			−0.664813
$378$		0			0
$379$	−7.78890			−0.400089			−0.200044	−	0.979787i	$-0.564109\pi$
$379$	−7.78890			−0.400089			−0.200044	+	0.979787i	$0.564109\pi$
$380$	−4.69722	−	8.13583i	−0.240963	−	0.417359i
$381$	−15.8028	+	27.3712i	−0.809601	+	1.40227i
$382$		0			0
$383$	−2.60555	−	4.51295i	−0.133137	−	0.230601i	0.791747	−	0.610849i	$-0.209172\pi$
$383$	−2.60555	−	4.51295i	−0.133137	−	0.230601i	−0.924884	+	0.380248i	$0.875839\pi$
$384$		0			0
$385$	2.80278	+	14.5636i	0.142843	+	0.742232i
$386$		0			0
$387$	11.0597	+	19.1560i	0.562197	+	0.973754i
$388$	9.30278	−	16.1129i	0.472277	−	0.818008i
$389$	0.0597147	−	0.103429i	0.00302766	−	0.00524406i	−0.864508	−	0.502620i	$-0.832370\pi$
$389$	0.0597147	−	0.103429i	0.00302766	−	0.00524406i	0.867535	+	0.497376i	$0.165703\pi$
$390$		0			0
$391$	21.9083			1.10795
$392$		0			0
$393$	3.90833			0.197149
$394$		0			0
$395$	11.3486	−	19.6564i	0.571011	−	0.989019i
$396$	−9.90833	+	17.1617i	−0.497912	+	0.862409i
$397$	18.3625	+	31.8048i	0.921587	+	1.59624i	0.796960	+	0.604032i	$0.206440\pi$
$397$	18.3625	+	31.8048i	0.921587	+	1.59624i	0.124627	+	0.992204i	$0.460227\pi$
$398$		0			0
$399$	4.15139	+	21.5712i	0.207829	+	1.07991i
$400$	−13.2111			−0.660555
$401$	−3.19722	−	5.53776i	−0.159662	−	0.276542i	0.775085	−	0.631857i	$-0.217707\pi$
$401$	−3.19722	−	5.53776i	−0.159662	−	0.276542i	−0.934747	+	0.355315i	$0.884374\pi$
$402$		0			0
$403$	−2.65139	+	4.59234i	−0.132075	+	0.228761i
$404$	−11.6056	−	20.1014i	−0.577398	−	1.00008i
$405$	−13.8167			−0.686555
$406$		0			0
$407$	−31.0278			−1.53799
$408$		0			0
$409$	14.0000	−	24.2487i	0.692255	−	1.19902i	−0.278842	−	0.960337i	$-0.589950\pi$
$409$	14.0000	−	24.2487i	0.692255	−	1.19902i	0.971097	−	0.238685i	$-0.0767162\pi$
$410$		0			0
$411$	1.36249	+	2.35990i	0.0672067	+	0.116405i
$412$	3.57779			0.176265
$413$	0.986122	+	0.341603i	0.0485239	+	0.0168092i
$414$		0			0
$415$	−7.55971	−	13.0938i	−0.371092	−	0.642750i
$416$		0			0
$417$	5.65139	−	9.78849i	0.276750	−	0.479344i
$418$		0			0
$419$	−30.1194			−1.47143			−0.735715	−	0.677291i	$-0.763154\pi$
$419$	−30.1194			−1.47143			−0.735715	+	0.677291i	$0.763154\pi$
$420$	−15.0000	−	5.19615i	−0.731925	−	0.253546i
$421$	4.09167			0.199416			0.0997080	−	0.995017i	$-0.468209\pi$
$421$	4.09167			0.199416			0.0997080	+	0.995017i	$0.468209\pi$
$422$		0			0
$423$	10.3625	−	17.9484i	0.503842	−	0.872679i
$424$		0			0
$425$	−6.45416	−	11.1789i	−0.313073	−	0.542258i
$426$		0			0
$427$	−14.4222	+	12.4900i	−0.697939	+	0.604433i
$428$	13.8167			0.667853
$429$	−11.4083	−	19.7598i	−0.550799	−	0.954012i
$430$		0			0
$431$	−2.74306	+	4.75112i	−0.132129	+	0.228853i	−0.924497	−	0.381190i	$-0.875515\pi$
$431$	−2.74306	+	4.75112i	−0.132129	+	0.228853i	0.792368	+	0.610043i	$0.208848\pi$
$432$	3.21110	+	5.56179i	0.154494	+	0.267592i
$433$	34.6056			1.66304			0.831518	−	0.555497i	$-0.187472\pi$
$433$	34.6056			1.66304			0.831518	+	0.555497i	$0.187472\pi$
$434$		0			0
$435$	16.8167			0.806297
$436$	6.30278	+	10.9167i	0.301848	+	0.522816i
$437$	−10.1056	+	17.5033i	−0.483414	+	0.837298i
$438$		0			0
$439$	−18.6056	−	32.2258i	−0.887995	−	1.53805i	−0.842243	−	0.539099i	$-0.818765\pi$
$439$	−18.6056	−	32.2258i	−0.887995	−	1.53805i	−0.0457520	−	0.998953i	$-0.514568\pi$
$440$		0			0
$441$	12.6653	+	9.97131i	0.603108	+	0.474824i
$442$		0			0
$443$	−3.05971	−	5.29958i	−0.145371	−	0.251791i	0.784140	−	0.620584i	$-0.213104\pi$
$443$	−3.05971	−	5.29958i	−0.145371	−	0.251791i	−0.929511	+	0.368793i	$0.879771\pi$
$444$	16.6056	−	28.7617i	0.788065	−	1.36497i
$445$	−0.256939	+	0.445032i	−0.0121801	+	0.0210965i
$446$		0			0
$447$	−4.18335			−0.197865
$448$	4.00000	+	20.7846i	0.188982	+	0.981981i
$449$	39.6333			1.87041			0.935206	−	0.354105i	$-0.115214\pi$
$449$	39.6333			1.87041			0.935206	+	0.354105i	$0.115214\pi$
$450$		0			0
$451$	−2.15139	+	3.72631i	−0.101305	+	0.175465i
$452$	−7.81665	+	13.5388i	−0.367664	+	0.636814i
$453$	−12.8028	−	22.1751i	−0.601527	−	1.04188i
$454$		0			0
$455$	6.00000	−	5.19615i	0.281284	−	0.243599i
$456$		0			0
$457$	10.0139	+	17.3445i	0.468429	+	0.811344i	0.999349	−	0.0360786i	$-0.0114867\pi$
$457$	10.0139	+	17.3445i	0.468429	+	0.811344i	−0.530919	+	0.847422i	$0.678153\pi$
$458$		0			0
$459$	−3.13751	+	5.43433i	−0.146446	+	0.253653i
$460$	−7.30278	−	12.6488i	−0.340494	−	0.589752i
$461$	−9.00000			−0.419172			−0.209586	−	0.977790i	$-0.567212\pi$
$461$	−9.00000			−0.419172			−0.209586	+	0.977790i	$0.567212\pi$
$462$		0			0
$463$	−14.6972			−0.683038			−0.341519	−	0.939875i	$-0.610941\pi$
$463$	−14.6972			−0.683038			−0.341519	+	0.939875i	$0.610941\pi$
$464$	−11.2111	−	19.4182i	−0.520462	−	0.901467i
$465$	3.45416	−	5.98279i	0.160183	−	0.277445i
$466$		0			0
$467$	−15.7708	−	27.3159i	−0.729786	−	1.26403i	−0.956973	−	0.290176i	$-0.906286\pi$
$467$	−15.7708	−	27.3159i	−0.729786	−	1.26403i	0.227187	−	0.973851i	$-0.427047\pi$
$468$	10.6056			0.490242
$469$	−16.5139	−	5.72058i	−0.762540	−	0.264152i
$470$		0			0
$471$	2.05971	+	3.56753i	0.0949066	+	0.164383i
$472$		0			0
$473$	−20.6653	+	35.7933i	−0.950190	+	1.64578i
$474$		0			0
$475$	11.9083			0.546392
$476$	−15.6333	+	13.5388i	−0.716551	+	0.620552i
$477$	22.8167			1.04470
$478$		0			0
$479$	−15.3764	+	26.6327i	−0.702564	+	1.21688i	0.264999	+	0.964249i	$0.414628\pi$
$479$	−15.3764	+	26.6327i	−0.702564	+	1.21688i	−0.967563	+	0.252628i	$0.918705\pi$
$480$		0			0
$481$	8.30278	+	14.3808i	0.378574	+	0.655709i
$482$		0			0
$483$	6.45416	+	33.5368i	0.293675	+	1.52598i
$484$	−15.0278			−0.683080
$485$	−6.05971	−	10.4957i	−0.275157	−	0.476587i
$486$		0			0
$487$	16.1514	−	27.9750i	0.731889	−	1.26767i	−0.224186	−	0.974546i	$-0.571972\pi$
$487$	16.1514	−	27.9750i	0.731889	−	1.26767i	0.956075	−	0.293123i	$-0.0946945\pi$
$488$		0			0
$489$	−36.2111			−1.63752
$490$		0			0
$491$	−12.1194			−0.546942			−0.273471	−	0.961880i	$-0.588172\pi$
$491$	−12.1194			−0.546942			−0.273471	+	0.961880i	$0.588172\pi$
$492$	−2.30278	−	3.98852i	−0.103817	−	0.179817i
$493$	10.9542	−	18.9732i	0.493351	−	0.854508i
$494$		0			0
$495$	6.45416	+	11.1789i	0.290093	+	0.502456i
$496$	−9.21110			−0.413591
$497$	−5.40833	−	28.1025i	−0.242597	−	1.26057i
$498$		0			0
$499$	−8.42221	−	14.5877i	−0.377030	−	0.653035i	0.613599	−	0.789618i	$-0.289721\pi$
$499$	−8.42221	−	14.5877i	−0.377030	−	0.653035i	−0.990629	+	0.136583i	$0.956388\pi$
$500$	−10.8167	+	18.7350i	−0.483735	+	0.837854i
$501$	−5.54584	+	9.60567i	−0.247770	+	0.429150i
$502$		0			0
$503$	28.8167			1.28487			0.642436	−	0.766340i	$-0.277924\pi$
$503$	28.8167			1.28487			0.642436	+	0.766340i	$0.277924\pi$
$504$		0			0
$505$	−15.1194			−0.672806
$506$		0			0
$507$	8.86249	−	15.3503i	0.393597	−	0.681730i
$508$	13.7250	−	23.7724i	0.608948	−	1.05473i
$509$	−11.8625	−	20.5464i	−0.525796	−	0.910705i	−0.999548	−	0.0300469i	$-0.990434\pi$
$509$	−11.8625	−	20.5464i	−0.525796	−	0.910705i	0.473753	−	0.880658i	$-0.342899\pi$
$510$		0			0
$511$	23.2569	+	8.05644i	1.02883	+	0.356396i
$512$		0			0
$513$	−2.89445	−	5.01333i	−0.127793	−	0.221344i
$514$		0			0
$515$	1.16527	−	2.01830i	0.0513478	−	0.0889369i
$516$	−22.1194	−	38.3120i	−0.973754	−	1.68659i
$517$	38.7250			1.70312
$518$		0			0
$519$	−35.7250			−1.56815
$520$		0			0
$521$	−22.0278	+	38.1532i	−0.965054	+	1.67152i	−0.255582	+	0.966787i	$0.582267\pi$
$521$	−22.0278	+	38.1532i	−0.965054	+	1.67152i	−0.709471	+	0.704734i	$0.751066\pi$
$522$		0			0
$523$	−8.50000	−	14.7224i	−0.371679	−	0.643767i	0.618145	−	0.786064i	$-0.287884\pi$
$523$	−8.50000	−	14.7224i	−0.371679	−	0.643767i	−0.989824	+	0.142297i	$0.954551\pi$
$524$	−3.39445			−0.148287
$525$	15.2111	−	13.1732i	0.663867	−	0.574926i
$526$		0			0
$527$	−4.50000	−	7.79423i	−0.196023	−	0.339522i
$528$	19.8167	−	34.3235i	0.862409	−	1.49374i
$529$	−4.21110	+	7.29384i	−0.183091	+	0.317124i
$530$		0			0
$531$	0.908327			0.0394180
$532$	−3.60555	−	18.7350i	−0.156320	−	0.812265i
$533$	2.30278			0.0997443
$534$		0			0
$535$	4.50000	−	7.79423i	0.194552	−	0.336974i
$536$		0			0
$537$	15.7708	+	27.3159i	0.680561	+	1.17877i
$538$		0			0
$539$	−4.30278	+	29.8105i	−0.185334	+	1.28403i
$540$	4.18335			0.180023
$541$	11.3944	+	19.7358i	0.489886	+	0.848507i	0.999932	−	0.0116400i	$-0.00370520\pi$
$541$	11.3944	+	19.7358i	0.489886	+	0.848507i	−0.510047	+	0.860147i	$0.670372\pi$
$542$		0			0
$543$	−24.2111	+	41.9349i	−1.03900	+	1.79960i
$544$		0			0
$545$	8.21110			0.351725
$546$		0			0
$547$	31.7250			1.35646			0.678231	−	0.734849i	$-0.262747\pi$
$547$	31.7250			1.35646			0.678231	+	0.734849i	$0.262747\pi$
$548$	−1.18335	−	2.04962i	−0.0505500	−	0.0875552i
$549$	−8.30278	+	14.3808i	−0.354354	+	0.613759i
$550$		0			0
$551$	10.1056	+	17.5033i	0.430511	+	0.745667i
$552$		0			0
$553$	34.8444	−	30.1761i	1.48174	−	1.28322i
$554$		0			0
$555$	−10.8167	−	18.7350i	−0.459141	−	0.795256i
$556$	−4.90833	+	8.50147i	−0.208159	+	0.360543i
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	−0.945473	−	0.325701i	$-0.894400\pi$
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	0.754802	+	0.655953i	$0.227733\pi$
$558$		0			0
$559$	22.1194			0.935552
$560$	13.0278	+	4.51295i	0.550523	+	0.190707i
$561$	38.7250			1.63497
$562$		0			0
$563$	−4.89445	+	8.47743i	−0.206276	+	0.357281i	−0.950539	−	0.310606i	$-0.899468\pi$
$563$	−4.89445	+	8.47743i	−0.206276	+	0.357281i	0.744262	+	0.667888i	$0.232801\pi$
$564$	−20.7250	+	35.8967i	−0.872679	+	1.51152i
$565$	5.09167	+	8.81904i	0.214208	+	0.371020i
$566$		0			0
$567$	−26.5139	−	9.18468i	−1.11348	−	0.385720i
$568$		0			0
$569$	18.1194	+	31.3838i	0.759606	+	1.31568i	0.943052	+	0.332646i	$0.107942\pi$
$569$	18.1194	+	31.3838i	0.759606	+	1.31568i	−0.183446	+	0.983030i	$0.558725\pi$
$570$		0			0
$571$	−12.0139	+	20.8086i	−0.502765	+	0.870815i	0.497230	+	0.867619i	$0.334351\pi$
$571$	−12.0139	+	20.8086i	−0.502765	+	0.870815i	−0.999995	+	0.00319587i	$0.998983\pi$
$572$	9.90833	+	17.1617i	0.414288	+	0.717568i
$573$	−44.4500			−1.85692
$574$		0			0
$575$	18.5139			0.772082
$576$	9.21110	+	15.9541i	0.383796	+	0.664754i
$577$	15.0278	−	26.0288i	0.625614	−	1.08359i	−0.362808	−	0.931864i	$-0.618182\pi$
$577$	15.0278	−	26.0288i	0.625614	−	1.08359i	0.988422	−	0.151731i	$-0.0484847\pi$
$578$		0			0
$579$	8.51388	+	14.7465i	0.353825	+	0.612842i
$580$	−14.6056			−0.606463
$581$	−5.80278	−	30.1521i	−0.240740	−	1.25092i
$582$		0			0
$583$	21.3167	+	36.9215i	0.882846	+	1.52913i
$584$		0			0
$585$	3.45416	−	5.98279i	0.142812	−	0.247358i
$586$		0			0
$587$	35.4500			1.46318			0.731588	−	0.681747i	$-0.238779\pi$
$587$	35.4500			1.46318			0.731588	+	0.681747i	$0.238779\pi$
$588$	−25.3305	−	19.9426i	−1.04461	−	0.822420i
$589$	8.30278			0.342110
$590$		0			0
$591$	−4.50000	+	7.79423i	−0.185105	+	0.320612i
$592$	−14.4222	+	24.9800i	−0.592749	+	1.02667i
$593$	−8.60555	−	14.9053i	−0.353388	−	0.612085i	0.633453	−	0.773781i	$-0.281637\pi$
$593$	−8.60555	−	14.9053i	−0.353388	−	0.612085i	−0.986841	+	0.161696i	$0.948304\pi$
$594$		0			0
$595$	2.54584	+	13.2286i	0.104369	+	0.542318i
$596$	3.63331			0.148826
$597$	20.9680	+	36.3177i	0.858165	+	1.48639i
$598$		0			0
$599$	3.19722	−	5.53776i	0.130635	−	0.226267i	−0.793286	−	0.608849i	$-0.791632\pi$
$599$	3.19722	−	5.53776i	0.130635	−	0.226267i	0.923922	+	0.382582i	$0.124965\pi$
$600$		0			0
$601$	15.1472			0.617867			0.308933	−	0.951084i	$-0.400028\pi$
$601$	15.1472			0.617867			0.308933	+	0.951084i	$0.400028\pi$
$602$		0			0
$603$	−15.2111			−0.619444
$604$	11.1194	+	19.2594i	0.452443	+	0.783655i
$605$	−4.89445	+	8.47743i	−0.198988	+	0.344657i
$606$		0			0
$607$	−1.90833	−	3.30532i	−0.0774566	−	0.134159i	0.824695	−	0.565577i	$-0.191347\pi$
$607$	−1.90833	−	3.30532i	−0.0774566	−	0.134159i	−0.902152	+	0.431418i	$0.858013\pi$
$608$		0			0
$609$	32.2708	+	11.1789i	1.30768	+	0.452993i
$610$		0			0
$611$	−10.3625	−	17.9484i	−0.419221	−	0.726113i
$612$	−9.00000	+	15.5885i	−0.363803	+	0.630126i
$613$	3.50000	−	6.06218i	0.141364	−	0.244849i	−0.786647	−	0.617403i	$-0.788185\pi$
$613$	3.50000	−	6.06218i	0.141364	−	0.244849i	0.928010	+	0.372554i	$0.121518\pi$
$614$		0			0
$615$	−3.00000			−0.120972
$616$		0			0
$617$	−16.5416			−0.665941			−0.332971	−	0.942937i	$-0.608051\pi$
$617$	−16.5416			−0.665941			−0.332971	+	0.942937i	$0.608051\pi$
$618$		0			0
$619$	−13.2569	+	22.9617i	−0.532841	+	0.922908i	0.466423	+	0.884562i	$0.345542\pi$
$619$	−13.2569	+	22.9617i	−0.532841	+	0.922908i	−0.999264	+	0.0383466i	$0.987791\pi$
$620$	−3.00000	+	5.19615i	−0.120483	+	0.208683i
$621$	−4.50000	−	7.79423i	−0.180579	−	0.312772i
$622$		0			0
$623$	−0.788897	+	0.683205i	−0.0316065	+	0.0273720i
$624$	−21.2111			−0.849124
$625$	−1.21110	−	2.09769i	−0.0484441	−	0.0839076i
$626$		0			0
$627$	−17.8625	+	30.9387i	−0.713359	+	1.23557i
$628$	−1.78890	−	3.09846i	−0.0713848	−	0.123642i
$629$	−28.1833			−1.12374
$630$		0			0
$631$	−42.8444			−1.70561			−0.852805	−	0.522230i	$-0.825100\pi$
$631$	−42.8444			−1.70561			−0.852805	+	0.522230i	$0.825100\pi$
$632$		0			0
$633$	11.6514	−	20.1808i	0.463101	−	0.802115i
$634$		0			0
$635$	−8.94029	−	15.4850i	−0.354784	−	0.614505i
$636$	−45.6333			−1.80948
$637$	14.9680	−	5.98279i	0.593055	−	0.237047i
$638$		0			0
$639$	−12.4542	−	21.5712i	−0.492679	−	0.853345i
$640$		0			0
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$		0			0
$643$	8.00000			0.315489			0.157745	−	0.987480i	$-0.449578\pi$
$643$	8.00000			0.315489			0.157745	+	0.987480i	$0.449578\pi$
$644$	−5.60555	−	29.1273i	−0.220890	−	1.14778i
$645$	−28.8167			−1.13465
$646$		0			0
$647$	7.81665	−	13.5388i	0.307304	−	0.532267i	−0.670467	−	0.741939i	$-0.733906\pi$
$647$	7.81665	−	13.5388i	0.307304	−	0.532267i	0.977772	+	0.209672i	$0.0672397\pi$
$648$		0			0
$649$	0.848612	+	1.46984i	0.0333109	+	0.0576962i
$650$		0			0
$651$	10.6056	−	9.18468i	0.415664	−	0.359976i
$652$	31.4500			1.23168
$653$	−18.9083	−	32.7502i	−0.739940	−	1.28161i	−0.952522	−	0.304470i	$-0.901521\pi$
$653$	−18.9083	−	32.7502i	−0.739940	−	1.28161i	0.212582	−	0.977143i	$-0.431813\pi$
$654$		0			0
$655$	−1.10555	+	1.91487i	−0.0431975	+	0.0748202i
$656$	2.00000	+	3.46410i	0.0780869	+	0.135250i
$657$	21.4222			0.835760
$658$		0			0
$659$	−30.2389			−1.17794			−0.588969	−	0.808155i	$-0.700466\pi$
$659$	−30.2389			−1.17794			−0.588969	+	0.808155i	$0.700466\pi$
$660$	−12.9083	−	22.3579i	−0.502456	−	0.870279i
$661$	−21.6056	+	37.4219i	−0.840359	+	1.45554i	0.0492333	+	0.998787i	$0.484322\pi$
$661$	−21.6056	+	37.4219i	−0.840359	+	1.45554i	−0.889592	+	0.456756i	$0.849011\pi$
$662$		0			0
$663$	−10.3625	−	17.9484i	−0.402446	−	0.697057i
$664$		0			0
$665$	−11.7431	−	4.06792i	−0.455376	−	0.157747i
$666$		0			0
$667$	15.7111	+	27.2124i	0.608336	+	1.05367i
$668$	4.81665	−	8.34269i	0.186362	−	0.322788i
$669$	−9.80278	+	16.9789i	−0.378997	+	0.656442i
$670$		0			0
$671$	−31.0278			−1.19781
$672$		0			0
$673$	−36.8444			−1.42025			−0.710124	−	0.704077i	$-0.751361\pi$
$673$	−36.8444			−1.42025			−0.710124	+	0.704077i	$0.751361\pi$
$674$		0			0
$675$	−2.65139	+	4.59234i	−0.102052	+	0.176759i
$676$	−7.69722	+	13.3320i	−0.296047	+	0.512769i
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	0.999760	+	0.0219013i	$0.00697196\pi$
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	−0.480913	+	0.876768i	$0.659695\pi$
$678$		0			0
$679$	−4.65139	−	24.1693i	−0.178504	−	0.927533i
$680$		0			0
$681$	−14.7250	−	25.5044i	−0.564262	−	0.977331i
$682$		0			0
$683$	−13.8944	+	24.0659i	−0.531656	+	0.920856i	0.467661	+	0.883908i	$0.345097\pi$
$683$	−13.8944	+	24.0659i	−0.531656	+	0.920856i	−0.999317	+	0.0369478i	$0.988236\pi$
$684$	−8.30278	−	14.3808i	−0.317465	−	0.549865i
$685$	−1.54163			−0.0589028
$686$		0			0
$687$	−8.57779			−0.327263
$688$	19.2111	+	33.2746i	0.732416	+	1.26858i
$689$	11.4083	−	19.7598i	0.434623	−	0.752788i
$690$		0			0
$691$	8.84861	+	15.3262i	0.336617	+	0.583038i	0.983794	−	0.179302i	$-0.0573839\pi$
$691$	8.84861	+	15.3262i	0.336617	+	0.583038i	−0.647177	+	0.762340i	$0.724051\pi$
$692$	31.0278			1.17950
$693$	4.95416	+	25.7426i	0.188193	+	0.977880i
$694$		0			0
$695$	3.19722	+	5.53776i	0.121278	+	0.210059i
$696$		0			0
$697$	−1.95416	+	3.38471i	−0.0740192	+	0.128205i
$698$		0			0
$699$	53.7250			2.03207
$700$	−13.2111	+	11.4412i	−0.499333	+	0.432435i
$701$	−14.8444			−0.560666			−0.280333	−	0.959903i	$-0.590445\pi$
$701$	−14.8444			−0.560666			−0.280333	+	0.959903i	$0.590445\pi$
$702$		0			0
$703$	13.0000	−	22.5167i	0.490304	−	0.849232i
$704$	−17.2111	+	29.8105i	−0.648668	+	1.12353i
$705$	13.5000	+	23.3827i	0.508439	+	0.880643i
$706$		0			0
$707$	−29.0139	−	10.0507i	−1.09118	−	0.377996i
$708$	−1.81665			−0.0682740
$709$	11.1972	+	19.3942i	0.420521	+	0.728363i	0.995990	−	0.0894600i	$-0.0285141\pi$
$709$	11.1972	+	19.3942i	0.420521	+	0.728363i	−0.575470	+	0.817823i	$0.695181\pi$
$710$		0			0
$711$	20.0597	−	34.7444i	0.752298	−	1.30302i
$712$		0			0
$713$	12.9083			0.483421
$714$		0			0
$715$	12.9083			0.482744
$716$	−13.6972	−	23.7243i	−0.511889	−	0.886618i
$717$	−26.2708	+	45.5024i	−0.981102	+	1.69932i
$718$		0			0
$719$	15.0597	+	26.0842i	0.561633	+	0.972776i	0.997354	+	0.0726947i	$0.0231599\pi$
$719$	15.0597	+	26.0842i	0.561633	+	0.972776i	−0.435722	+	0.900081i	$0.643507\pi$
$720$	12.0000			0.447214
$721$	3.57779	−	3.09846i	0.133244	−	0.115393i
$722$		0			0
$723$	−4.39445	−	7.61141i	−0.163431	−	0.283071i
$724$	21.0278	−	36.4211i	0.781490	−	1.35358i
$725$	9.25694	−	16.0335i	0.343794	−	0.595469i
$726$		0			0
$727$	−41.5416			−1.54069			−0.770347	−	0.637625i	$-0.779917\pi$
$727$	−41.5416			−1.54069			−0.770347	+	0.637625i	$0.779917\pi$
$728$		0			0
$729$	−13.3305			−0.493723
$730$		0			0
$731$	−18.7708	+	32.5120i	−0.694264	+	1.20250i
$732$	16.6056	−	28.7617i	0.613759	−	1.06306i
$733$	24.6194	+	42.6421i	0.909339	+	1.57502i	0.814984	+	0.579483i	$0.196746\pi$
$733$	24.6194	+	42.6421i	0.909339	+	1.57502i	0.0943553	+	0.995539i	$0.469921\pi$
$734$		0			0
$735$	−19.5000	+	7.79423i	−0.719268	+	0.287494i
$736$		0			0
$737$	−14.2111	−	24.6144i	−0.523473	−	0.906681i
$738$		0			0
$739$	0.894449	−	1.54923i	0.0329028	−	0.0569894i	−0.849105	−	0.528224i	$-0.822858\pi$
$739$	0.894449	−	1.54923i	0.0329028	−	0.0569894i	0.882008	+	0.471235i	$0.156191\pi$
$740$	9.39445	+	16.2717i	0.345347	+	0.598158i
$741$	19.1194			0.702370
$742$		0			0
$743$	33.3583			1.22380			0.611898	−	0.790936i	$-0.290406\pi$
$743$	33.3583			1.22380			0.611898	+	0.790936i	$0.290406\pi$
$744$		0			0
$745$	1.18335	−	2.04962i	0.0433544	−	0.0750921i
$746$		0			0
$747$	−13.3625	−	23.1445i	−0.488908	−	0.846813i
$748$	−33.6333			−1.22976
$749$	13.8167	−	11.9656i	0.504850	−	0.437213i
$750$		0			0
$751$	22.4680	+	38.9158i	0.819870	+	1.42006i	0.905777	+	0.423754i	$0.139288\pi$
$751$	22.4680	+	38.9158i	0.819870	+	1.42006i	−0.0859068	+	0.996303i	$0.527379\pi$
$752$	18.0000	−	31.1769i	0.656392	−	1.13691i
$753$	25.2250	−	43.6909i	0.919249	−	1.59219i
$754$		0			0
$755$	14.4861			0.527204
$756$	8.02776	+	2.78090i	0.291967	+	0.101140i
$757$	−42.0555			−1.52853			−0.764267	−	0.644900i	$-0.776899\pi$
$757$	−42.0555			−1.52853			−0.764267	+	0.644900i	$0.776899\pi$
$758$		0			0
$759$	−27.7708	+	48.1005i	−1.00802	+	1.74594i
$760$		0			0
$761$	−13.9542	−	24.1693i	−0.505838	−	0.876137i	−0.999977	−	0.00675435i	$-0.997850\pi$
$761$	−13.9542	−	24.1693i	−0.505838	−	0.876137i	0.494139	−	0.869383i	$-0.335483\pi$
$762$		0			0
$763$	15.7569	+	5.45836i	0.570439	+	0.197606i
$764$	38.6056			1.39670
$765$	5.86249	+	10.1541i	0.211959	+	0.367123i
$766$		0			0
$767$	0.454163	−	0.786634i	0.0163989	−	0.0284037i
$768$	−18.4222	−	31.9082i	−0.664754	−	1.15139i
$769$	6.02776			0.217366			0.108683	−	0.994076i	$-0.465337\pi$
$769$	6.02776			0.217366			0.108683	+	0.994076i	$0.465337\pi$
$770$		0			0
$771$	36.6333			1.31932
$772$	−7.39445	−	12.8076i	−0.266132	−	0.460954i
$773$	−4.89445	+	8.47743i	−0.176041	+	0.304912i	−0.940521	−	0.339735i	$-0.889662\pi$
$773$	−4.89445	+	8.47743i	−0.176041	+	0.304912i	0.764480	+	0.644647i	$0.222996\pi$
$774$		0			0
$775$	−3.80278	−	6.58660i	−0.136600	−	0.236598i
$776$		0			0
$777$	−8.30278	−	43.1425i	−0.297860	−	1.54773i
$778$		0			0
$779$	−1.80278	−	3.12250i	−0.0645911	−	0.111875i
$780$	−6.90833	+	11.9656i	−0.247358	+	0.428436i
$781$	23.2708	−	40.3062i	0.832695	−	1.44227i
$782$		0			0
$783$	−9.00000			−0.321634
$784$	22.0000	+	17.3205i	0.785714	+	0.618590i
$785$	−2.33053			−0.0831803
$786$		0			0
$787$	−12.4083	+	21.4919i	−0.442309	+	0.766102i	−0.997860	−	0.0653804i	$-0.979174\pi$
$787$	−12.4083	+	21.4919i	−0.442309	+	0.766102i	0.555551	+	0.831482i	$0.312507\pi$
$788$	3.90833	−	6.76942i	0.139228	−	0.241151i
$789$	−18.7708	−	32.5120i	−0.668259	−	1.15746i
$790$		0			0
$791$	3.90833	+	20.3083i	0.138964	+	0.722079i
$792$		0			0
$793$	8.30278	+	14.3808i	0.294840	+	0.510678i
$794$		0			0
$795$	−14.8625	+	25.7426i	−0.527118	+	0.912996i
$796$	−18.2111	−	31.5426i	−0.645475	−	1.11800i
$797$	−28.8167			−1.02074			−0.510369	−	0.859955i	$-0.670491\pi$
$797$	−28.8167			−1.02074			−0.510369	+	0.859955i	$0.670491\pi$
$798$		0			0
$799$	35.1749			1.24440
$800$		0			0
$801$	−0.454163	+	0.786634i	−0.0160471	+	0.0277944i
$802$		0			0
$803$	20.0139	+	34.6651i	0.706274	+	1.22330i
$804$	30.4222			1.07291
$805$	−18.2569	−	6.32439i	−0.643473	−	0.222905i
$806$		0			0
$807$	−8.40833	−	14.5636i	−0.295987	−	0.512665i
$808$		0			0
$809$	−17.4083	+	30.1521i	−0.612044	+	1.06009i	0.378851	+	0.925458i	$0.376319\pi$
$809$	−17.4083	+	30.1521i	−0.612044	+	1.06009i	−0.990895	+	0.134634i	$0.957014\pi$
$810$		0			0
$811$	10.3305			0.362754			0.181377	−	0.983414i	$-0.441945\pi$
$811$	10.3305			0.362754			0.181377	+	0.983414i	$0.441945\pi$
$812$	−28.0278	−	9.70910i	−0.983581	−	0.340723i
$813$	57.1472			2.00424
$814$		0			0
$815$	10.2431	−	17.7415i	0.358799	−	0.621458i
$816$	18.0000	−	31.1769i	0.630126	−	1.09141i
$817$	−17.3167	−	29.9933i	−0.605833	−	1.04933i
$818$		0			0
$819$	10.6056	−	9.18468i	0.370588	−	0.320939i
$820$	2.60555			0.0909898
$821$	−13.8764	−	24.0346i	−0.484289	−	0.838812i	0.515549	−	0.856860i	$-0.327588\pi$
$821$	−13.8764	−	24.0346i	−0.484289	−	0.838812i	−0.999837	+	0.0180479i	$0.994255\pi$
$822$		0			0
$823$	6.24306	−	10.8133i	0.217619	−	0.376928i	−0.736460	−	0.676481i	$-0.763504\pi$
$823$	6.24306	−	10.8133i	0.217619	−	0.376928i	0.954080	+	0.299553i	$0.0968375\pi$
$824$		0			0
$825$	32.7250			1.13934
$826$		0			0
$827$	−22.1833			−0.771391			−0.385695	−	0.922626i	$-0.626038\pi$
$827$	−22.1833			−0.771391			−0.385695	+	0.922626i	$0.626038\pi$
$828$	−12.9083	−	22.3579i	−0.448595	−	0.776990i
$829$	−0.408327	+	0.707243i	−0.0141818	+	0.0245636i	−0.873029	−	0.487668i	$-0.837848\pi$
$829$	−0.408327	+	0.707243i	−0.0141818	+	0.0245636i	0.858847	+	0.512231i	$0.171181\pi$
$830$		0			0
$831$	7.74306	+	13.4114i	0.268604	+	0.465235i
$832$	18.4222			0.638675
$833$	−3.90833	+	27.0777i	−0.135416	+	0.938186i
$834$		0			0
$835$	−3.13751	−	5.43433i	−0.108578	−	0.188063i
$836$	15.5139	−	26.8708i	0.536559	−	0.929347i
$837$	−1.84861	+	3.20189i	−0.0638974	+	0.110674i
$838$		0			0
$839$	−5.60555			−0.193525			−0.0967626	−	0.995307i	$-0.530849\pi$
$839$	−5.60555			−0.193525			−0.0967626	+	0.995307i	$0.530849\pi$
$840$		0			0
$841$	2.42221			0.0835243
$842$		0			0
$843$	7.50000	−	12.9904i	0.258314	−	0.447412i
$844$	−10.1194	+	17.5274i	−0.348325	+	0.603317i
$845$	5.01388	+	8.68429i	0.172483	+	0.298749i
$846$		0			0
$847$	−15.0278	+	13.0144i	−0.516360	+	0.447181i
$848$	39.6333			1.36101
$849$	−10.8486	−	18.7903i	−0.372323	−	0.644883i
$850$		0			0
$851$	20.2111	−	35.0067i	0.692828	−	1.20001i
$852$	24.9083	+	43.1425i	0.853345	+	1.47804i
$853$	−2.02776			−0.0694291			−0.0347145	−	0.999397i	$-0.511052\pi$
$853$	−2.02776			−0.0694291			−0.0347145	+	0.999397i	$0.511052\pi$
$854$		0			0
$855$	−10.8167			−0.369922
$856$		0			0
$857$	−24.2569	+	42.0143i	−0.828601	+	1.43518i	0.0705344	+	0.997509i	$0.477530\pi$
$857$	−24.2569	+	42.0143i	−0.828601	+	1.43518i	−0.899136	+	0.437670i	$0.855804\pi$
$858$		0			0
$859$	−8.24306	−	14.2774i	−0.281250	−	0.487139i	0.690443	−	0.723387i	$-0.257416\pi$
$859$	−8.24306	−	14.2774i	−0.281250	−	0.487139i	−0.971693	+	0.236248i	$0.924082\pi$
$860$	25.0278			0.853439
$861$	−5.75694	−	1.99426i	−0.196196	−	0.0679643i
$862$		0			0
$863$	8.92221	+	15.4537i	0.303715	+	0.526050i	0.976974	−	0.213356i	$-0.0684395\pi$
$863$	8.92221	+	15.4537i	0.303715	+	0.526050i	−0.673259	+	0.739407i	$0.735106\pi$
$864$		0			0
$865$	10.1056	−	17.5033i	0.343599	−	0.595131i
$866$		0			0
$867$	−3.97224			−0.134904
$868$	−9.21110	+	7.97705i	−0.312645	+	0.270759i
$869$	74.9638			2.54297
$870$		0			0
$871$	−7.60555	+	13.1732i	−0.257704	+	0.446357i
$872$		0			0
$873$	−10.7111	−	18.5522i	−0.362516	−	0.627896i
$874$		0			0
$875$	5.40833	+	28.1025i	0.182835	+	0.950038i
$876$	−42.8444			−1.44758
$877$	15.6194	+	27.0536i	0.527431	+	0.913537i	0.999489	+	0.0319693i	$0.0101779\pi$
$877$	15.6194	+	27.0536i	0.527431	+	0.913537i	−0.472058	+	0.881567i	$0.656489\pi$
$878$		0			0
$879$	18.1791	−	31.4872i	0.613167	−	1.06204i
$880$	11.2111	+	19.4182i	0.377926	+	0.654587i
$881$	45.9083			1.54669			0.773345	−	0.633985i	$-0.218582\pi$
$881$	45.9083			1.54669			0.773345	+	0.633985i	$0.218582\pi$
$882$		0			0
$883$	14.7527			0.496469			0.248235	−	0.968700i	$-0.420150\pi$
$883$	14.7527			0.496469			0.248235	+	0.968700i	$0.420150\pi$
$884$	9.00000	+	15.5885i	0.302703	+	0.524297i
$885$	−0.591673	+	1.02481i	−0.0198889	+	0.0344485i
$886$		0			0
$887$	−8.60555	−	14.9053i	−0.288946	−	0.500469i	0.684612	−	0.728907i	$-0.259972\pi$
$887$	−8.60555	−	14.9053i	−0.288946	−	0.500469i	−0.973558	+	0.228438i	$0.926638\pi$
$888$		0			0
$889$	−6.86249	−	35.6585i	−0.230161	−	1.19595i
$890$		0			0
$891$	−22.8167	−	39.5196i	−0.764387	−	1.32396i
$892$	8.51388	−	14.7465i	0.285066	−	0.493748i
$893$	−16.2250	+	28.1025i	−0.542948	+	0.940414i
$894$		0			0
$895$	−17.8444			−0.596473
$896$		0			0
$897$	29.7250			0.992488
$898$		0			0
$899$	6.45416	−	11.1789i	0.215258	−	0.372838i
$900$	−7.60555	+	13.1732i	−0.253518	+	0.439107i
$901$	19.3625	+	33.5368i	0.645058	+	1.11727i
$902$		0			0
$903$	−55.2986	−	19.1560i	−1.84022	−	0.637471i
$904$		0			0
$905$	−13.6972	−	23.7243i	−0.455311	−	0.788622i
$906$		0			0
$907$	8.98612	−	15.5644i	0.298379	−	0.516808i	−0.677386	−	0.735628i	$-0.736887\pi$
$907$	8.98612	−	15.5644i	0.298379	−	0.516808i	0.975765	+	0.218820i	$0.0702206\pi$
$908$	12.7889	+	22.1510i	0.424414	+	0.735107i
$909$	−26.7250			−0.886412
$910$		0			0
$911$	−17.6056			−0.583298			−0.291649	−	0.956525i	$-0.594204\pi$
$911$	−17.6056			−0.583298			−0.291649	+	0.956525i	$0.594204\pi$
$912$	16.6056	+	28.7617i	0.549865	+	0.952394i
$913$	24.9680	−	43.2459i	0.826322	−	1.43123i
$914$		0			0
$915$	−10.8167	−	18.7350i	−0.357588	−	0.619360i
$916$	7.44996			0.246154
$917$	−3.39445	+	2.93968i	−0.112095	+	0.0970767i
$918$		0			0
$919$	9.69722	+	16.7961i	0.319882	+	0.554052i	0.980463	−	0.196703i	$-0.0630234\pi$
$919$	9.69722	+	16.7961i	0.319882	+	0.554052i	−0.660581	+	0.750755i	$0.729690\pi$
$920$		0			0
$921$	37.4680	−	64.8966i	1.23461	−	2.13841i
$922$		0			0
$923$	−24.9083			−0.819868
$924$	−9.90833	−	51.4852i	−0.325960	−	1.69374i
$925$	−23.8167			−0.783087
$926$		0			0
$927$	2.05971	−	3.56753i	0.0676499	−	0.117173i
$928$		0			0
$929$	27.5139	+	47.6554i	0.902701	+	1.56352i	0.823974	+	0.566628i	$0.191752\pi$
$929$	27.5139	+	47.6554i	0.902701	+	1.56352i	0.0787273	+	0.996896i	$0.474914\pi$
$930$		0			0
$931$	−19.8305	−	15.6125i	−0.649919	−	0.511679i
$932$	−46.6611			−1.52843
$933$	−26.2708	−	45.5024i	−0.860068	−	1.48968i
$934$		0			0
$935$	−10.9542	+	18.9732i	−0.358239	+	0.620489i
$936$		0			0
$937$	−30.0555			−0.981871			−0.490935	−	0.871196i	$-0.663345\pi$
$937$	−30.0555			−0.981871			−0.490935	+	0.871196i	$0.663345\pi$
$938$		0			0
$939$	45.4222			1.48230
$940$	−11.7250	−	20.3083i	−0.382427	−	0.662382i
$941$	20.7250	−	35.8967i	0.675615	−	1.17020i	−0.300674	−	0.953727i	$-0.597211\pi$
$941$	20.7250	−	35.8967i	0.675615	−	1.17020i	0.976289	−	0.216473i	$-0.0694552\pi$
$942$		0			0
$943$	−2.80278	−	4.85455i	−0.0912709	−	0.158086i
$944$	1.57779			0.0513528
$945$	4.18335	−	3.62288i	0.136084	−	0.117852i
$946$		0			0
$947$	19.8944	+	34.4582i	0.646483	+	1.11974i	0.983957	+	0.178406i	$0.0570941\pi$
$947$	19.8944	+	34.4582i	0.646483	+	1.11974i	−0.337474	+	0.941335i	$0.609573\pi$
$948$	−40.1194	+	69.4889i	−1.30302	+	2.25689i
$949$	10.7111	−	18.5522i	0.347697	−	0.602229i
$950$		0			0
$951$	−36.6333			−1.18792
$952$		0			0
$953$	−19.5416			−0.633016			−0.316508	−	0.948590i	$-0.602510\pi$
$953$	−19.5416			−0.633016			−0.316508	+	0.948590i	$0.602510\pi$
$954$		0			0
$955$	12.5736	−	21.7781i	0.406872	−	0.704723i
$956$	22.8167	−	39.5196i	0.737943	−	1.27816i
$957$	27.7708	+	48.1005i	0.897703	+	1.55487i
$958$		0			0
$959$	−2.95837	−	1.02481i	−0.0955306	−	0.0330928i
$960$	−24.0000			−0.774597
$961$	12.8486	+	22.2544i	0.414471	+	0.717885i
$962$		0			0
$963$	7.95416	−	13.7770i	0.256319	−	0.443958i
$964$	3.81665	+	6.61064i	0.122926	+	0.212914i
$965$	−9.63331			−0.310107
$966$		0			0
$967$	−52.5139			−1.68873			−0.844366	−	0.535766i	$-0.820023\pi$
$967$	−52.5139			−1.68873			−0.844366	+	0.535766i	$0.820023\pi$
$968$		0			0
$969$	−16.2250	+	28.1025i	−0.521221	+	0.902782i
$970$		0			0
$971$	16.8764	+	29.2307i	0.541588	+	0.938059i	0.998813	+	0.0487075i	$0.0155102\pi$
$971$	16.8764	+	29.2307i	0.541588	+	0.938059i	−0.457225	+	0.889351i	$0.651156\pi$
$972$	39.2111			1.25770
$973$	2.45416	+	12.7522i	0.0786769	+	0.408817i
$974$		0			0
$975$	−8.75694	−	15.1675i	−0.280446	−	0.485748i
$976$	−14.4222	+	24.9800i	−0.461644	+	0.799590i
$977$	−9.31665	+	16.1369i	−0.298066	+	0.516266i	−0.975693	−	0.219140i	$-0.929675\pi$
$977$	−9.31665	+	16.1369i	−0.298066	+	0.516266i	0.677627	+	0.735405i	$0.263008\pi$
$978$		0			0
$979$	−1.69722			−0.0542435
$980$	16.9361	−	6.76942i	0.541003	−	0.216241i
$981$	14.5139			0.463392
$982$		0			0
$983$	0.729183	−	1.26298i	0.0232573	−	0.0402829i	−0.854162	−	0.520006i	$-0.825930\pi$
$983$	0.729183	−	1.26298i	0.0232573	−	0.0402829i	0.877420	+	0.479723i	$0.159263\pi$
$984$		0			0
$985$	−2.54584	−	4.40952i	−0.0811171	−	0.140499i
$986$		0			0
$987$	10.3625	+	53.8451i	0.329842	+	1.71391i
$988$	−16.6056			−0.528293
$989$	−26.9222	−	46.6306i	−0.856076	−	1.48277i
$990$		0			0
$991$	3.44029	−	5.95875i	0.109284	−	0.189286i	−0.806196	−	0.591648i	$-0.798477\pi$
$991$	3.44029	−	5.95875i	0.109284	−	0.189286i	0.915481	+	0.402362i	$0.131811\pi$
$992$		0			0
$993$	0.0639167			0.00202834
$994$		0			0
$995$	−23.7250			−0.752132
$996$	26.7250	+	46.2890i	0.846813	+	1.46672i
$997$	27.0278	−	46.8134i	0.855978	−	1.48260i	−0.0197574	−	0.999805i	$-0.506289\pi$
$997$	27.0278	−	46.8134i	0.855978	−	1.48260i	0.875735	−	0.482792i	$-0.160377\pi$
$998$		0			0
$999$	5.78890	+	10.0267i	0.183153	+	0.317230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.b.165.1	✓	4
7.2	even	3	inner	287.2.e.b.247.1	yes	4
7.3	odd	6		2009.2.a.c.1.1		2
7.4	even	3		2009.2.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.b.165.1	✓	4	1.1	even	1	trivial
287.2.e.b.247.1	yes	4	7.2	even	3	inner
2009.2.a.c.1.1		2	7.3	odd	6
2009.2.a.d.1.2		2	7.4	even	3

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15139 + 1.99426i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.651388 - 1.12824i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-1.15139 - 1.99426i) q^{9} +O(q^{10})\)	\(q+(-1.15139 + 1.99426i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.651388 - 1.12824i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-1.15139 - 1.99426i) q^{9} +(2.15139 - 3.72631i) q^{11} +(2.30278 + 3.98852i) q^{12} -2.30278 q^{13} +3.00000 q^{15} +(-2.00000 - 3.46410i) q^{16} +(1.95416 - 3.38471i) q^{17} +(1.80278 + 3.12250i) q^{19} -2.60555 q^{20} +(5.75694 + 1.99426i) q^{21} +(2.80278 + 4.85455i) q^{23} +(1.65139 - 2.86029i) q^{25} -1.60555 q^{27} +(-5.00000 - 1.73205i) q^{28} +5.60555 q^{29} +(1.15139 - 1.99426i) q^{31} +(4.95416 + 8.58086i) q^{33} +(-2.60555 + 2.25647i) q^{35} -4.60555 q^{36} +(-3.60555 - 6.24500i) q^{37} +(2.65139 - 4.59234i) q^{39} -1.00000 q^{41} -9.60555 q^{43} +(-4.30278 - 7.45263i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(4.50000 + 7.79423i) q^{47} +9.21110 q^{48} +(-6.50000 + 2.59808i) q^{49} +(4.50000 + 7.79423i) q^{51} +(-2.30278 + 3.98852i) q^{52} +(-4.95416 + 8.58086i) q^{53} -5.60555 q^{55} -8.30278 q^{57} +(-0.197224 + 0.341603i) q^{59} +(3.00000 - 5.19615i) q^{60} +(-3.60555 - 6.24500i) q^{61} +(-4.60555 + 3.98852i) q^{63} -8.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(3.30278 - 5.72058i) q^{67} +(-3.90833 - 6.76942i) q^{68} -12.9083 q^{69} +10.8167 q^{71} +(-4.65139 + 8.05644i) q^{73} +(3.80278 + 6.58660i) q^{75} +7.21110 q^{76} +(-10.7569 - 3.72631i) q^{77} +(8.71110 + 15.0881i) q^{79} +(-2.60555 + 4.51295i) q^{80} +(5.30278 - 9.18468i) q^{81} +11.6056 q^{83} +(9.21110 - 7.97705i) q^{84} -5.09167 q^{85} +(-6.45416 + 11.1789i) q^{87} +(-0.197224 - 0.341603i) q^{89} +(1.15139 + 5.98279i) q^{91} +11.2111 q^{92} +(2.65139 + 4.59234i) q^{93} +(2.34861 - 4.06792i) q^{95} +9.30278 q^{97} -9.90833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 4 q^{4} + q^{5} - 2 q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^3 + 4 * q^4 + q^5 - 2 * q^7 - q^9	\( 4 q - q^{3} + 4 q^{4} + q^{5} - 2 q^{7} - q^{9} + 5 q^{11} + 2 q^{12} - 2 q^{13} + 12 q^{15} - 8 q^{16} - 3 q^{17} + 4 q^{20} + 5 q^{21} + 4 q^{23} + 3 q^{25} + 8 q^{27} - 20 q^{28} + 8 q^{29} + q^{31} + 9 q^{33} + 4 q^{35} - 4 q^{36} + 7 q^{39} - 4 q^{41} - 24 q^{43} - 10 q^{44} - 6 q^{45} + 18 q^{47} + 8 q^{48} - 26 q^{49} + 18 q^{51} - 2 q^{52} - 9 q^{53} - 8 q^{55} - 26 q^{57} - 8 q^{59} + 12 q^{60} - 4 q^{63} - 32 q^{64} + 6 q^{65} + 6 q^{67} + 6 q^{68} - 30 q^{69} - 15 q^{73} + 8 q^{75} - 25 q^{77} + 6 q^{79} + 4 q^{80} + 14 q^{81} + 32 q^{83} + 8 q^{84} - 42 q^{85} - 15 q^{87} - 8 q^{89} + q^{91} + 16 q^{92} + 7 q^{93} + 13 q^{95} + 30 q^{97} - 18 q^{99}+O(q^{100}) \) 4 * q - q^3 + 4 * q^4 + q^5 - 2 * q^7 - q^9 + 5 * q^11 + 2 * q^12 - 2 * q^13 + 12 * q^15 - 8 * q^16 - 3 * q^17 + 4 * q^20 + 5 * q^21 + 4 * q^23 + 3 * q^25 + 8 * q^27 - 20 * q^28 + 8 * q^29 + q^31 + 9 * q^33 + 4 * q^35 - 4 * q^36 + 7 * q^39 - 4 * q^41 - 24 * q^43 - 10 * q^44 - 6 * q^45 + 18 * q^47 + 8 * q^48 - 26 * q^49 + 18 * q^51 - 2 * q^52 - 9 * q^53 - 8 * q^55 - 26 * q^57 - 8 * q^59 + 12 * q^60 - 4 * q^63 - 32 * q^64 + 6 * q^65 + 6 * q^67 + 6 * q^68 - 30 * q^69 - 15 * q^73 + 8 * q^75 - 25 * q^77 + 6 * q^79 + 4 * q^80 + 14 * q^81 + 32 * q^83 + 8 * q^84 - 42 * q^85 - 15 * q^87 - 8 * q^89 + q^91 + 16 * q^92 + 7 * q^93 + 13 * q^95 + 30 * q^97 - 18 * q^99

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