LMFDB - Embedded newform 1386.2.bu.a.701.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.2
Character	$\chi$	$=$	1386.701
Dual form			1386.2.bu.a.953.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-2.22800 + 3.06659i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-2.22800 + 3.06659i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} -3.79051i q^{10} +(1.49456 + 2.96079i) q^{11} +(1.70940 + 2.35278i) q^{13} +(-0.951057 + 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(5.61780 + 4.08157i) q^{17} +(7.19497 - 2.33779i) q^{19} +(2.22800 + 3.06659i) q^{20} +(-2.94943 - 1.51685i) q^{22} -7.90260i q^{23} +(-2.89485 - 8.90945i) q^{25} +(-2.76586 - 0.898683i) q^{26} +(0.587785 - 0.809017i) q^{28} +(-0.983541 + 3.02703i) q^{29} +(-2.88026 + 2.09263i) q^{31} +1.00000 q^{32} -6.94398 q^{34} +(-3.06659 + 2.22800i) q^{35} +(-1.62080 + 4.98830i) q^{37} +(-4.44673 + 6.12040i) q^{38} +(-3.60499 - 1.17133i) q^{40} +(0.236715 + 0.728533i) q^{41} +1.48480i q^{43} +(3.27773 - 0.506474i) q^{44} +(4.64503 + 6.39334i) q^{46} +(-7.03352 + 2.28533i) q^{47} +(0.809017 + 0.587785i) q^{49} +(7.57883 + 5.50634i) q^{50} +(2.76586 - 0.898683i) q^{52} +(2.22124 + 3.05727i) q^{53} +(-12.4094 - 2.01347i) q^{55} +1.00000i q^{56} +(-0.983541 - 3.02703i) q^{58} +(4.46174 + 1.44971i) q^{59} +(-7.07645 + 9.73989i) q^{61} +(1.10016 - 3.38595i) q^{62} +(-0.809017 + 0.587785i) q^{64} -11.0236 q^{65} +6.51017 q^{67} +(5.61780 - 4.08157i) q^{68} +(1.17133 - 3.60499i) q^{70} +(-0.922925 + 1.27030i) q^{71} +(9.04940 + 2.94033i) q^{73} +(-1.62080 - 4.98830i) q^{74} -7.56524i q^{76} +(0.506474 + 3.27773i) q^{77} +(-6.86292 - 9.44600i) q^{79} +(3.60499 - 1.17133i) q^{80} +(-0.619727 - 0.450258i) q^{82} +(-10.7827 - 7.83409i) q^{83} +(-25.0330 + 8.13370i) q^{85} +(-0.872744 - 1.20123i) q^{86} +(-2.35404 + 2.33634i) q^{88} +1.72515i q^{89} +(0.898683 + 2.76586i) q^{91} +(-7.51582 - 2.44204i) q^{92} +(4.34695 - 5.98307i) q^{94} +(-8.86140 + 27.2726i) q^{95} +(0.0144784 - 0.0105192i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−2.22800	+	3.06659i	−0.996394	+	1.37142i	−0.0688820	+	0.997625i	$0.521943\pi$
$5$	−2.22800	+	3.06659i	−0.996394	+	1.37142i	−0.927512	+	0.373794i	$0.878057\pi$
$6$		0			0
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$		−	3.79051i		−	1.19866i
$11$	1.49456	+	2.96079i	0.450626	+	0.892713i
$11$	1.49456	+	2.96079i	0.450626	+	0.892713i
$12$		0			0
$13$	1.70940	+	2.35278i	0.474101	+	0.652545i	0.977358	−	0.211592i	$-0.0678649\pi$
$13$	1.70940	+	2.35278i	0.474101	+	0.652545i	−0.503257	+	0.864137i	$0.667865\pi$
$14$	−0.951057	+	0.309017i	−0.254181	+	0.0825883i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	5.61780	+	4.08157i	1.36252	+	0.989926i	0.998280	+	0.0586199i	$0.0186700\pi$
$17$	5.61780	+	4.08157i	1.36252	+	0.989926i	0.364236	+	0.931307i	$0.381330\pi$
$18$		0			0
$19$	7.19497	−	2.33779i	1.65064	−	0.536325i	0.671760	−	0.740769i	$-0.265539\pi$
$19$	7.19497	−	2.33779i	1.65064	−	0.536325i	0.978878	+	0.204444i	$0.0655385\pi$
$20$	2.22800	+	3.06659i	0.498197	+	0.685709i
$21$		0			0
$22$	−2.94943	−	1.51685i	−0.628821	−	0.323394i
$23$		−	7.90260i		−	1.64781i	−0.566731	−	0.823903i	$-0.691792\pi$
$23$		−	7.90260i		−	1.64781i	0.566731	−	0.823903i	$-0.308208\pi$
$24$		0			0
$25$	−2.89485	−	8.90945i	−0.578971	−	1.78189i
$26$	−2.76586	−	0.898683i	−0.542430	−	0.176246i
$27$		0			0
$28$	0.587785	−	0.809017i	0.111081	−	0.152890i
$29$	−0.983541	+	3.02703i	−0.182639	+	0.562105i	−0.999900	−	0.0141630i	$-0.995492\pi$
$29$	−0.983541	+	3.02703i	−0.182639	+	0.562105i	0.817261	+	0.576268i	$0.195492\pi$
$30$		0			0
$31$	−2.88026	+	2.09263i	−0.517310	+	0.375847i	−0.815589	−	0.578631i	$-0.803587\pi$
$31$	−2.88026	+	2.09263i	−0.517310	+	0.375847i	0.298280	+	0.954478i	$0.403587\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−6.94398			−1.19088
$35$	−3.06659	+	2.22800i	−0.518347	+	0.376601i
$36$		0			0
$37$	−1.62080	+	4.98830i	−0.266457	+	0.820071i	0.724897	+	0.688857i	$0.241887\pi$
$37$	−1.62080	+	4.98830i	−0.266457	+	0.820071i	−0.991354	+	0.131214i	$0.958113\pi$
$38$	−4.44673	+	6.12040i	−0.721355	+	0.992861i
$39$		0			0
$40$	−3.60499	−	1.17133i	−0.569998	−	0.185204i
$41$	0.236715	+	0.728533i	0.0369686	+	0.113778i	0.967838	−	0.251575i	$-0.0809485\pi$
$41$	0.236715	+	0.728533i	0.0369686	+	0.113778i	−0.930869	+	0.365353i	$0.880948\pi$
$42$		0			0
$43$			1.48480i			0.226430i	0.993571	+	0.113215i	$0.0361149\pi$
$43$			1.48480i			0.226430i	−0.993571	+	0.113215i	$0.963885\pi$
$44$	3.27773	−	0.506474i	0.494136	−	0.0763538i
$45$		0			0
$46$	4.64503	+	6.39334i	0.684872	+	0.942646i
$47$	−7.03352	+	2.28533i	−1.02594	+	0.333349i	−0.773185	−	0.634180i	$-0.781338\pi$
$47$	−7.03352	+	2.28533i	−1.02594	+	0.333349i	−0.252758	+	0.967529i	$0.581338\pi$
$48$		0			0
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	7.57883	+	5.50634i	1.07181	+	0.778714i
$51$		0			0
$52$	2.76586	−	0.898683i	0.383556	−	0.124625i
$53$	2.22124	+	3.05727i	0.305111	+	0.419949i	0.933849	−	0.357668i	$-0.116428\pi$
$53$	2.22124	+	3.05727i	0.305111	+	0.419949i	−0.628738	+	0.777617i	$0.716428\pi$
$54$		0			0
$55$	−12.4094	−	2.01347i	−1.67328	−	0.271496i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−0.983541	−	3.02703i	−0.129145	−	0.397468i
$59$	4.46174	+	1.44971i	0.580868	+	0.188736i	0.584690	−	0.811257i	$-0.301216\pi$
$59$	4.46174	+	1.44971i	0.580868	+	0.188736i	−0.00382114	+	0.999993i	$0.501216\pi$
$60$		0			0
$61$	−7.07645	+	9.73989i	−0.906046	+	1.24707i	0.0624530	+	0.998048i	$0.480108\pi$
$61$	−7.07645	+	9.73989i	−0.906046	+	1.24707i	−0.968499	+	0.249017i	$0.919892\pi$
$62$	1.10016	−	3.38595i	0.139721	−	0.430016i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−11.0236			−1.36730
$66$		0			0
$67$	6.51017			0.795344			0.397672	−	0.917528i	$-0.369818\pi$
$67$	6.51017			0.795344			0.397672	+	0.917528i	$0.369818\pi$
$68$	5.61780	−	4.08157i	0.681258	−	0.494963i
$69$		0			0
$70$	1.17133	−	3.60499i	0.140001	−	0.430878i
$71$	−0.922925	+	1.27030i	−0.109531	+	0.150757i	−0.860263	−	0.509850i	$-0.829701\pi$
$71$	−0.922925	+	1.27030i	−0.109531	+	0.150757i	0.750732	+	0.660607i	$0.229701\pi$
$72$		0			0
$73$	9.04940	+	2.94033i	1.05915	+	0.344139i	0.786254	−	0.617904i	$-0.212018\pi$
$73$	9.04940	+	2.94033i	1.05915	+	0.344139i	0.272898	+	0.962043i	$0.412018\pi$
$74$	−1.62080	−	4.98830i	−0.188414	−	0.579878i
$75$		0			0
$76$		−	7.56524i		−	0.867792i
$77$	0.506474	+	3.27773i	0.0577181	+	0.373531i
$78$		0			0
$79$	−6.86292	−	9.44600i	−0.772139	−	1.06276i	−0.996106	−	0.0881617i	$-0.971901\pi$
$79$	−6.86292	−	9.44600i	−0.772139	−	1.06276i	0.223967	−	0.974597i	$-0.428099\pi$
$80$	3.60499	−	1.17133i	0.403050	−	0.130959i
$81$		0			0
$82$	−0.619727	−	0.450258i	−0.0684374	−	0.0497227i
$83$	−10.7827	−	7.83409i	−1.18355	−	0.859903i	−0.190986	−	0.981593i	$-0.561169\pi$
$83$	−10.7827	−	7.83409i	−1.18355	−	0.859903i	−0.992568	+	0.121690i	$0.961169\pi$
$84$		0			0
$85$	−25.0330	+	8.13370i	−2.71521	+	0.882224i
$86$	−0.872744	−	1.20123i	−0.0941104	−	0.129532i
$87$		0			0
$88$	−2.35404	+	2.33634i	−0.250941	+	0.249055i
$89$			1.72515i			0.182866i	0.995811	+	0.0914328i	$0.0291447\pi$
$89$			1.72515i			0.182866i	−0.995811	+	0.0914328i	$0.970855\pi$
$90$		0			0
$91$	0.898683	+	2.76586i	0.0942076	+	0.289941i
$92$	−7.51582	−	2.44204i	−0.783578	−	0.254600i
$93$		0			0
$94$	4.34695	−	5.98307i	0.448354	−	0.617106i
$95$	−8.86140	+	27.2726i	−0.909160	+	2.79811i
$96$		0			0
$97$	0.0144784	−	0.0105192i	0.00147006	−	0.00106806i	−0.587050	−	0.809551i	$-0.699711\pi$
$97$	0.0144784	−	0.0105192i	0.00147006	−	0.00106806i	0.588520	+	0.808483i	$0.299711\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	−9.36795			−0.936795
$101$	11.6034	−	8.43039i	1.15458	−	0.838855i	0.165501	−	0.986210i	$-0.447076\pi$
$101$	11.6034	−	8.43039i	1.15458	−	0.838855i	0.989084	+	0.147355i	$0.0470760\pi$
$102$		0			0
$103$	3.32300	−	10.2271i	0.327425	−	1.00771i	−0.642909	−	0.765943i	$-0.722273\pi$
$103$	3.32300	−	10.2271i	0.327425	−	1.00771i	0.970334	−	0.241768i	$-0.0777273\pi$
$104$	−1.70940	+	2.35278i	−0.167620	+	0.230709i
$105$		0			0
$106$	−3.59404	−	1.16777i	−0.349084	−	0.113424i
$107$	2.47137	+	7.60610i	0.238916	+	0.735309i	0.996578	+	0.0826612i	$0.0263419\pi$
$107$	2.47137	+	7.60610i	0.238916	+	0.735309i	−0.757661	+	0.652648i	$0.773658\pi$
$108$		0			0
$109$			8.22095i			0.787424i	0.919234	+	0.393712i	$0.128809\pi$
$109$			8.22095i			0.787424i	−0.919234	+	0.393712i	$0.871191\pi$
$110$	11.2229	−	5.66513i	1.07006	−	0.540149i
$111$		0			0
$112$	−0.587785	−	0.809017i	−0.0555405	−	0.0764449i
$113$	−13.9335	+	4.52727i	−1.31075	+	0.425890i	−0.879310	−	0.476250i	$-0.841996\pi$
$113$	−13.9335	+	4.52727i	−1.31075	+	0.425890i	−0.431444	+	0.902140i	$0.641996\pi$
$114$		0			0
$115$	24.2340	+	17.6070i	2.25983	+	1.64186i
$116$	2.57494	+	1.87081i	0.239078	+	0.173700i
$117$		0			0
$118$	−4.46174	+	1.44971i	−0.410736	+	0.133456i
$119$	4.08157	+	5.61780i	0.374157	+	0.514983i
$120$		0			0
$121$	−6.53259	+	8.85016i	−0.593872	+	0.804560i
$122$		−	12.0392i		−	1.08998i
$123$		0			0
$124$	1.10016	+	3.38595i	0.0987973	+	0.304067i
$125$	15.7464	+	5.11631i	1.40840	+	0.457617i
$126$		0			0
$127$	2.20370	−	3.03314i	0.195547	−	0.269147i	−0.699972	−	0.714170i	$-0.746804\pi$
$127$	2.20370	−	3.03314i	0.195547	−	0.269147i	0.895519	+	0.445023i	$0.146804\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	8.91824	−	6.47948i	0.782182	−	0.568288i
$131$	−3.84957			−0.336338			−0.168169	−	0.985758i	$-0.553785\pi$
$131$	−3.84957			−0.336338			−0.168169	+	0.985758i	$0.553785\pi$
$132$		0			0
$133$	7.56524			0.655989
$134$	−5.26684	+	3.82658i	−0.454986	+	0.330566i
$135$		0			0
$136$	−2.14581	+	6.60412i	−0.184002	+	0.566299i
$137$	−2.91445	+	4.01140i	−0.248998	+	0.342717i	−0.915160	−	0.403090i	$-0.867936\pi$
$137$	−2.91445	+	4.01140i	−0.248998	+	0.342717i	0.666162	+	0.745807i	$0.267936\pi$
$138$		0			0
$139$	−4.69175	−	1.52444i	−0.397949	−	0.129302i	0.103204	−	0.994660i	$-0.467091\pi$
$139$	−4.69175	−	1.52444i	−0.397949	−	0.129302i	−0.501153	+	0.865359i	$0.667091\pi$
$140$	1.17133	+	3.60499i	0.0989956	+	0.304677i
$141$		0			0
$142$		−	1.57017i		−	0.131766i
$143$	−4.41131	+	8.57754i	−0.368892	+	0.717290i
$144$		0			0
$145$	−7.09131	−	9.76035i	−0.588901	−	0.810553i
$146$	−9.04940	+	2.94033i	−0.748934	+	0.243343i
$147$		0			0
$148$	4.24330	+	3.08294i	0.348797	+	0.253416i
$149$	6.20493	+	4.50815i	0.508328	+	0.369322i	0.812189	−	0.583395i	$-0.198276\pi$
$149$	6.20493	+	4.50815i	0.508328	+	0.369322i	−0.303861	+	0.952716i	$0.598276\pi$
$150$		0			0
$151$	−9.33470	+	3.03303i	−0.759647	+	0.246824i	−0.663127	−	0.748507i	$-0.730771\pi$
$151$	−9.33470	+	3.03303i	−0.759647	+	0.246824i	−0.0965197	+	0.995331i	$0.530771\pi$
$152$	4.44673	+	6.12040i	0.360678	+	0.496430i
$153$		0			0
$154$	−2.33634	−	2.35404i	−0.188268	−	0.189694i
$155$		−	13.4949i		−	1.08394i
$156$		0			0
$157$	−3.72581	−	11.4669i	−0.297352	−	0.915156i	−0.982421	−	0.186678i	$-0.940228\pi$
$157$	−3.72581	−	11.4669i	−0.297352	−	0.915156i	0.685069	−	0.728478i	$-0.259772\pi$
$158$	11.1044	+	3.60805i	0.883422	+	0.287041i
$159$		0			0
$160$	−2.22800	+	3.06659i	−0.176139	+	0.242435i
$161$	2.44204	−	7.51582i	0.192459	−	0.592329i
$162$		0			0
$163$	6.72402	−	4.88529i	0.526666	−	0.382645i	−0.292443	−	0.956283i	$-0.594468\pi$
$163$	6.72402	−	4.88529i	0.526666	−	0.382645i	0.819109	+	0.573638i	$0.194468\pi$
$164$	0.766024			0.0598165
$165$		0			0
$166$	13.3281			1.03446
$167$	7.35488	−	5.34364i	0.569138	−	0.413503i	−0.265654	−	0.964068i	$-0.585588\pi$
$167$	7.35488	−	5.34364i	0.569138	−	0.413503i	0.834792	+	0.550565i	$0.185588\pi$
$168$		0			0
$169$	1.40367	−	4.32005i	0.107975	−	0.332312i
$170$	15.4712	−	21.2943i	1.18659	−	1.63320i
$171$		0			0
$172$	1.41213	+	0.458829i	0.107674	+	0.0349854i
$173$	−4.92128	−	15.1461i	−0.374158	−	1.15154i	−0.944045	−	0.329817i	$-0.893013\pi$
$173$	−4.92128	−	15.1461i	−0.374158	−	1.15154i	0.569887	−	0.821723i	$-0.306987\pi$
$174$		0			0
$175$		−	9.36795i		−	0.708150i
$176$	0.531187	−	3.27381i	0.0400398	−	0.246773i
$177$		0			0
$178$	−1.01402	−	1.39568i	−0.0760038	−	0.104610i
$179$	−13.1143	+	4.26110i	−0.980210	+	0.318489i	−0.754930	−	0.655805i	$-0.772329\pi$
$179$	−13.1143	+	4.26110i	−0.980210	+	0.318489i	−0.225279	+	0.974294i	$0.572329\pi$
$180$		0			0
$181$	5.63667	+	4.09528i	0.418971	+	0.304400i	0.777223	−	0.629225i	$-0.216627\pi$
$181$	5.63667	+	4.09528i	0.418971	+	0.304400i	−0.358253	+	0.933625i	$0.616627\pi$
$182$	−2.35278	−	1.70940i	−0.174400	−	0.126709i
$183$		0			0
$184$	7.51582	−	2.44204i	0.554073	−	0.180029i
$185$	−11.6859	−	16.0843i	−0.859164	−	1.18254i
$186$		0			0
$187$	−3.68856	+	22.7333i	−0.269734	+	1.66242i
$188$			7.39548i			0.539371i
$189$		0			0
$190$	−8.86140	−	27.2726i	−0.642873	−	1.97856i
$191$	−22.3836	−	7.27287i	−1.61962	−	0.526246i	−0.647768	−	0.761838i	$-0.724297\pi$
$191$	−22.3836	−	7.27287i	−1.61962	−	0.526246i	−0.971852	+	0.235591i	$0.924297\pi$
$192$		0			0
$193$	−2.41417	+	3.32281i	−0.173775	+	0.239181i	−0.887017	−	0.461737i	$-0.847226\pi$
$193$	−2.41417	+	3.32281i	−0.173775	+	0.239181i	0.713241	+	0.700918i	$0.247226\pi$
$194$	−0.00553026	+	0.0170204i	−0.000397049	+	0.00122199i
$195$		0			0
$196$	0.809017	−	0.587785i	0.0577869	−	0.0419847i
$197$	−24.9996			−1.78115			−0.890573	−	0.454841i	$-0.849696\pi$
$197$	−24.9996			−1.78115			−0.890573	+	0.454841i	$0.849696\pi$
$198$		0			0
$199$	21.7178			1.53953			0.769766	−	0.638326i	$-0.220373\pi$
$199$	21.7178			1.53953			0.769766	+	0.638326i	$0.220373\pi$
$200$	7.57883	−	5.50634i	0.535904	−	0.389357i
$201$		0			0
$202$	−4.43212	+	13.6406i	−0.311843	+	0.959753i
$203$	−1.87081	+	2.57494i	−0.131305	+	0.180726i
$204$		0			0
$205$	−2.76151	−	0.897268i	−0.192872	−	0.0626679i
$206$	3.32300	+	10.2271i	0.231524	+	0.712559i
$207$		0			0
$208$		−	2.90820i		−	0.201647i
$209$	17.6750	+	17.8088i	1.22261	+	1.23186i
$210$		0			0
$211$	6.21743	+	8.55756i	0.428025	+	0.589127i	0.967499	−	0.252876i	$-0.0813766\pi$
$211$	6.21743	+	8.55756i	0.428025	+	0.589127i	−0.539473	+	0.842003i	$0.681377\pi$
$212$	3.59404	−	1.16777i	0.246840	−	0.0802031i
$213$		0			0
$214$	−6.47013	−	4.70083i	−0.442289	−	0.321342i
$215$	−4.55327	−	3.30814i	−0.310530	−	0.225613i
$216$		0			0
$217$	−3.38595	+	1.10016i	−0.229853	+	0.0746838i
$218$	−4.83215	−	6.65089i	−0.327275	−	0.450455i
$219$		0			0
$220$	−5.74964	+	11.1799i	−0.387641	+	0.753745i
$221$			20.1945i			1.35843i
$222$		0			0
$223$	6.94376	+	21.3707i	0.464988	+	1.43109i	0.858997	+	0.511980i	$0.171088\pi$
$223$	6.94376	+	21.3707i	0.464988	+	1.43109i	−0.394009	+	0.919107i	$0.628912\pi$
$224$	0.951057	+	0.309017i	0.0635451	+	0.0206471i
$225$		0			0
$226$	8.61138	−	11.8525i	0.572820	−	0.788420i
$227$	6.05719	−	18.6421i	0.402030	−	1.23732i	−0.521320	−	0.853361i	$-0.674560\pi$
$227$	6.05719	−	18.6421i	0.402030	−	1.23732i	0.923350	−	0.383960i	$-0.125440\pi$
$228$		0			0
$229$	−22.8966	+	16.6354i	−1.51305	+	1.09930i	−0.548252	+	0.836313i	$0.684707\pi$
$229$	−22.8966	+	16.6354i	−1.51305	+	1.09930i	−0.964800	+	0.262984i	$0.915293\pi$
$230$	−29.9549			−1.97516
$231$		0			0
$232$	−3.18281			−0.208961
$233$	13.5168	−	9.82056i	0.885518	−	0.643366i	−0.0491879	−	0.998790i	$-0.515663\pi$
$233$	13.5168	−	9.82056i	0.885518	−	0.643366i	0.934705	+	0.355423i	$0.115663\pi$
$234$		0			0
$235$	8.66255	−	26.6606i	0.565083	−	1.73915i
$236$	2.75750	−	3.79538i	0.179498	−	0.247058i
$237$		0			0
$238$	−6.60412	−	2.14581i	−0.428082	−	0.139092i
$239$	−7.14098	−	21.9777i	−0.461911	−	1.42162i	−0.862826	−	0.505501i	$-0.831308\pi$
$239$	−7.14098	−	21.9777i	−0.461911	−	1.42162i	0.400914	−	0.916116i	$-0.368692\pi$
$240$		0			0
$241$			6.35471i			0.409343i	0.978831	+	0.204672i	$0.0656126\pi$
$241$			6.35471i			0.409343i	−0.978831	+	0.204672i	$0.934387\pi$
$242$	0.0829859	−	10.9997i	0.00533454	−	0.707087i
$243$		0			0
$244$	7.07645	+	9.73989i	0.453023	+	0.623533i
$245$	−3.60499	+	1.17133i	−0.230314	+	0.0748336i
$246$		0			0
$247$	17.7994	+	12.9320i	1.13255	+	0.822843i
$248$	−2.88026	−	2.09263i	−0.182897	−	0.132882i
$249$		0			0
$250$	−15.7464	+	5.11631i	−0.995889	+	0.323584i
$251$	−3.02162	−	4.15891i	−0.190723	−	0.262508i	0.702937	−	0.711252i	$-0.251871\pi$
$251$	−3.02162	−	4.15891i	−0.190723	−	0.262508i	−0.893660	+	0.448744i	$0.851871\pi$
$252$		0			0
$253$	23.3980	−	11.8109i	1.47102	−	0.742545i
$254$			3.74916i			0.235243i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−12.9486	−	4.20726i	−0.807712	−	0.262441i	−0.124083	−	0.992272i	$-0.539599\pi$
$257$	−12.9486	−	4.20726i	−0.807712	−	0.262441i	−0.683628	+	0.729830i	$0.739599\pi$
$258$		0			0
$259$	−3.08294	+	4.24330i	−0.191564	+	0.263666i
$260$	−3.40647	+	10.4840i	−0.211260	+	0.650192i
$261$		0			0
$262$	3.11436	−	2.26272i	0.192406	−	0.139791i
$263$	1.64816			0.101630			0.0508151	−	0.998708i	$-0.483818\pi$
$263$	1.64816			0.101630			0.0508151	+	0.998708i	$0.483818\pi$
$264$		0			0
$265$	−14.3243			−0.879936
$266$	−6.12040	+	4.44673i	−0.375266	+	0.272647i
$267$		0			0
$268$	2.01175	−	6.19154i	0.122887	−	0.378209i
$269$	16.5222	−	22.7408i	1.00737	−	1.38653i	0.0866833	−	0.996236i	$-0.472373\pi$
$269$	16.5222	−	22.7408i	1.00737	−	1.38653i	0.920690	−	0.390295i	$-0.127627\pi$
$270$		0			0
$271$	4.16065	+	1.35188i	0.252742	+	0.0821207i	0.432648	−	0.901563i	$-0.357579\pi$
$271$	4.16065	+	1.35188i	0.252742	+	0.0821207i	−0.179906	+	0.983684i	$0.557579\pi$
$272$	−2.14581	−	6.60412i	−0.130109	−	0.400434i
$273$		0			0
$274$		−	4.95836i		−	0.299546i
$275$	22.0525	−	21.8868i	1.32982	−	1.31982i
$276$		0			0
$277$	−9.74456	−	13.4122i	−0.585494	−	0.805863i	0.408790	−	0.912628i	$-0.365951\pi$
$277$	−9.74456	−	13.4122i	−0.585494	−	0.805863i	−0.994284	+	0.106765i	$0.965951\pi$
$278$	4.69175	−	1.52444i	0.281393	−	0.0914300i
$279$		0			0
$280$	−3.06659	−	2.22800i	−0.183264	−	0.133149i
$281$	23.2147	+	16.8665i	1.38487	+	1.00617i	0.996406	+	0.0847054i	$0.0269949\pi$
$281$	23.2147	+	16.8665i	1.38487	+	1.00617i	0.388466	+	0.921463i	$0.373005\pi$
$282$		0			0
$283$	8.29439	−	2.69501i	0.493050	−	0.160202i	−0.0519298	−	0.998651i	$-0.516537\pi$
$283$	8.29439	−	2.69501i	0.493050	−	0.160202i	0.544980	+	0.838449i	$0.316537\pi$
$284$	0.922925	+	1.27030i	0.0547655	+	0.0753783i
$285$		0			0
$286$	−1.47293	−	9.53228i	−0.0870961	−	0.563656i
$287$			0.766024i			0.0452170i
$288$		0			0
$289$	9.64717	+	29.6909i	0.567481	+	1.74653i
$290$	11.4740	+	3.72812i	0.673775	+	0.218923i
$291$		0			0
$292$	5.59284	−	7.69788i	0.327296	−	0.450484i
$293$	9.72590	−	29.9332i	0.568193	−	1.74872i	−0.0900757	−	0.995935i	$-0.528711\pi$
$293$	9.72590	−	29.9332i	0.568193	−	1.74872i	0.658269	−	0.752783i	$-0.271289\pi$
$294$		0			0
$295$	−14.3864	+	10.4523i	−0.837609	+	0.608559i
$296$	−5.24501			−0.304860
$297$		0			0
$298$	−7.66972			−0.444295
$299$	18.5931	−	13.5087i	1.07527	−	0.781227i
$300$		0			0
$301$	−0.458829	+	1.41213i	−0.0264464	+	0.0813938i
$302$	5.76916	−	7.94057i	0.331978	−	0.456928i
$303$		0			0
$304$	−7.19497	−	2.33779i	−0.412660	−	0.134081i
$305$	−14.1019	−	43.4010i	−0.807470	−	2.48514i
$306$		0			0
$307$		−	12.1181i		−	0.691616i	−0.938305	−	0.345808i	$-0.887605\pi$
$307$		−	12.1181i		−	0.691616i	0.938305	−	0.345808i	$-0.112395\pi$
$308$	3.27381	+	0.531187i	0.186543	+	0.0302672i
$309$		0			0
$310$	7.93213	+	10.9176i	0.450515	+	0.620080i
$311$	2.06450	−	0.670798i	0.117067	−	0.0380375i	−0.249898	−	0.968272i	$-0.580397\pi$
$311$	2.06450	−	0.670798i	0.117067	−	0.0380375i	0.366965	+	0.930235i	$0.380397\pi$
$312$		0			0
$313$	7.67230	+	5.57425i	0.433664	+	0.315075i	0.783112	−	0.621880i	$-0.213631\pi$
$313$	7.67230	+	5.57425i	0.433664	+	0.315075i	−0.349448	+	0.936956i	$0.613631\pi$
$314$	9.75431	+	7.08692i	0.550467	+	0.399938i
$315$		0			0
$316$	−11.1044	+	3.60805i	−0.624674	+	0.202969i
$317$	15.8978	+	21.8814i	0.892909	+	1.22898i	0.972675	+	0.232171i	$0.0745828\pi$
$317$	15.8978	+	21.8814i	0.892909	+	1.22898i	−0.0797658	+	0.996814i	$0.525417\pi$
$318$		0			0
$319$	−10.4324	+	1.61201i	−0.584100	+	0.0902552i
$320$		−	3.79051i		−	0.211896i
$321$		0			0
$322$	2.44204	+	7.51582i	0.136089	+	0.418840i
$323$	49.9617	+	16.2335i	2.77994	+	0.903259i
$324$		0			0
$325$	16.0135	−	22.0408i	0.888272	−	1.22260i
$326$	−2.56835	+	7.90456i	−0.142248	+	0.437793i
$327$		0			0
$328$	−0.619727	+	0.450258i	−0.0342187	+	0.0248613i
$329$	−7.39548			−0.407726
$330$		0			0
$331$	34.8004			1.91280			0.956401	−	0.292056i	$-0.0943394\pi$
$331$	34.8004			1.91280			0.956401	+	0.292056i	$0.0943394\pi$
$332$	−10.7827	+	7.83409i	−0.591777	+	0.429951i
$333$		0			0
$334$	−2.80932	+	8.64618i	−0.153719	+	0.473098i
$335$	−14.5047	+	19.9640i	−0.792476	+	1.09075i
$336$		0			0
$337$	−29.1899	−	9.48439i	−1.59008	−	0.516648i	−0.625450	−	0.780264i	$-0.715085\pi$
$337$	−29.1899	−	9.48439i	−1.59008	−	0.516648i	−0.964628	+	0.263617i	$0.915085\pi$
$338$	1.40367	+	4.32005i	0.0763496	+	0.234980i
$339$		0			0
$340$			26.3212i			1.42747i
$341$	−10.5006	−	5.40029i	−0.568637	−	0.292442i
$342$		0			0
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	−1.41213	+	0.458829i	−0.0761369	+	0.0247384i
$345$		0			0
$346$	12.8841	+	9.36084i	0.692653	+	0.503242i
$347$	18.3389	+	13.3240i	0.984485	+	0.715270i	0.958706	−	0.284398i	$-0.0917936\pi$
$347$	18.3389	+	13.3240i	0.984485	+	0.715270i	0.0257782	+	0.999668i	$0.491794\pi$
$348$		0			0
$349$	6.36807	−	2.06911i	0.340875	−	0.110757i	−0.133577	−	0.991038i	$-0.542646\pi$
$349$	6.36807	−	2.06911i	0.340875	−	0.110757i	0.474452	+	0.880282i	$0.342646\pi$
$350$	5.50634	+	7.57883i	0.294326	+	0.405105i
$351$		0			0
$352$	1.49456	+	2.96079i	0.0796602	+	0.157811i
$353$		−	23.3555i		−	1.24309i	−0.783380	−	0.621543i	$-0.786506\pi$
$353$		−	23.3555i		−	1.24309i	0.783380	−	0.621543i	$-0.213494\pi$
$354$		0			0
$355$	−1.83919	−	5.66046i	−0.0976143	−	0.300426i
$356$	1.64071	+	0.533101i	0.0869577	+	0.0282543i
$357$		0			0
$358$	8.10509	−	11.1557i	0.428367	−	0.589597i
$359$	0.207471	−	0.638529i	0.0109499	−	0.0337002i	−0.945432	−	0.325819i	$-0.894360\pi$
$359$	0.207471	−	0.638529i	0.0109499	−	0.0337002i	0.956382	+	0.292118i	$0.0943601\pi$
$360$		0			0
$361$	30.9310	−	22.4727i	1.62795	−	1.18277i
$362$	−6.96731			−0.366194
$363$		0			0
$364$	2.90820			0.152431
$365$	−29.1789	+	21.1997i	−1.52729	+	1.10964i
$366$		0			0
$367$	−5.99620	+	18.4544i	−0.312999	+	0.963312i	0.663571	+	0.748113i	$0.269040\pi$
$367$	−5.99620	+	18.4544i	−0.312999	+	0.963312i	−0.976570	+	0.215199i	$0.930960\pi$
$368$	−4.64503	+	6.39334i	−0.242139	+	0.333276i
$369$		0			0
$370$	18.9082	+	6.14364i	0.982989	+	0.319393i
$371$	1.16777	+	3.59404i	0.0606278	+	0.186593i
$372$		0			0
$373$			6.34581i			0.328573i	0.986413	+	0.164287i	$0.0525322\pi$
$373$			6.34581i			0.328573i	−0.986413	+	0.164287i	$0.947468\pi$
$374$	−10.3782	−	20.5597i	−0.536643	−	1.06312i
$375$		0			0
$376$	−4.34695	−	5.98307i	−0.224177	−	0.308553i
$377$	−8.80321	+	2.86033i	−0.453388	+	0.147315i
$378$		0			0
$379$	13.7553	+	9.99381i	0.706562	+	0.513347i	0.882063	−	0.471132i	$-0.156154\pi$
$379$	13.7553	+	9.99381i	0.706562	+	0.513347i	−0.175501	+	0.984479i	$0.556154\pi$
$380$	23.1994	+	16.8554i	1.19011	+	0.864663i
$381$		0			0
$382$	22.3836	−	7.27287i	1.14524	−	0.372112i
$383$	11.7874	+	16.2240i	0.602309	+	0.829008i	0.995917	−	0.0902706i	$-0.0287732\pi$
$383$	11.7874	+	16.2240i	0.602309	+	0.829008i	−0.393608	+	0.919278i	$0.628773\pi$
$384$		0			0
$385$	−11.1799	−	5.74964i	−0.569778	−	0.293029i
$386$		−	4.10722i		−	0.209052i
$387$		0			0
$388$	−0.00553026	−	0.0170204i	−0.000280756	−	0.000864079i
$389$	−22.8749	−	7.43252i	−1.15980	−	0.376843i	−0.334976	−	0.942226i	$-0.608728\pi$
$389$	−22.8749	−	7.43252i	−1.15980	−	0.376843i	−0.824829	+	0.565383i	$0.808728\pi$
$390$		0			0
$391$	32.2550	−	44.3952i	1.63121	−	2.24516i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$		0			0
$394$	20.2251	−	14.6944i	1.01892	−	0.740292i
$395$	44.2576			2.22684
$396$		0			0
$397$	5.18572			0.260264			0.130132	−	0.991497i	$-0.458460\pi$
$397$	5.18572			0.260264			0.130132	+	0.991497i	$0.458460\pi$
$398$	−17.5701	+	12.7654i	−0.880707	+	0.639871i
$399$		0			0
$400$	−2.89485	+	8.90945i	−0.144743	+	0.445472i
$401$	−22.1684	+	30.5121i	−1.10703	+	1.52370i	−0.281321	+	0.959614i	$0.590773\pi$
$401$	−22.1684	+	30.5121i	−1.10703	+	1.52370i	−0.825714	+	0.564089i	$0.809227\pi$
$402$		0			0
$403$	−9.84701	−	3.19949i	−0.490514	−	0.159378i
$404$	−4.43212	−	13.6406i	−0.220506	−	0.678648i
$405$		0			0
$406$		−	3.18281i		−	0.157960i
$407$	−17.1917	+	2.65646i	−0.852160	+	0.131676i
$408$		0			0
$409$	16.9565	+	23.3386i	0.838445	+	1.15402i	0.986292	+	0.165010i	$0.0527657\pi$
$409$	16.9565	+	23.3386i	0.838445	+	1.15402i	−0.147847	+	0.989010i	$0.547234\pi$
$410$	2.76151	−	0.897268i	0.136381	−	0.0443129i
$411$		0			0
$412$	−8.69973	−	6.32072i	−0.428605	−	0.311400i
$413$	3.79538	+	2.75750i	0.186758	+	0.135688i
$414$		0			0
$415$	48.0478	−	15.6117i	2.35857	−	0.766347i
$416$	1.70940	+	2.35278i	0.0838101	+	0.115355i
$417$		0			0
$418$	−24.7672	−	4.01856i	−1.21140	−	0.196554i
$419$			14.0236i			0.685099i	0.939500	+	0.342550i	$0.111291\pi$
$419$			14.0236i			0.685099i	−0.939500	+	0.342550i	$0.888709\pi$
$420$		0			0
$421$	−4.60555	−	14.1744i	−0.224461	−	0.690820i	−0.998346	−	0.0574936i	$-0.981689\pi$
$421$	−4.60555	−	14.1744i	−0.224461	−	0.690820i	0.773885	−	0.633326i	$-0.218311\pi$
$422$	−10.0600	−	3.26870i	−0.489714	−	0.159118i
$423$		0			0
$424$	−2.22124	+	3.05727i	−0.107873	+	0.148474i
$425$	20.1018	−	61.8671i	0.975082	−	3.00099i
$426$		0			0
$427$	−9.73989	+	7.07645i	−0.471346	+	0.342453i
$428$	7.99752			0.386575
$429$		0			0
$430$	5.62815			0.271413
$431$	−3.03251	+	2.20325i	−0.146071	+	0.106127i	−0.658421	−	0.752650i	$-0.728775\pi$
$431$	−3.03251	+	2.20325i	−0.146071	+	0.106127i	0.512350	+	0.858777i	$0.328775\pi$
$432$		0			0
$433$	5.18999	−	15.9731i	0.249415	−	0.767620i	−0.745464	−	0.666546i	$-0.767772\pi$
$433$	5.18999	−	15.9731i	0.249415	−	0.767620i	0.994879	−	0.101074i	$-0.0322279\pi$
$434$	2.09263	−	2.88026i	0.100449	−	0.138257i
$435$		0			0
$436$	7.81859	+	2.54041i	0.374442	+	0.121664i
$437$	−18.4746	−	56.8589i	−0.883759	−	2.71993i
$438$		0			0
$439$			21.3609i			1.01950i	0.860323	+	0.509749i	$0.170262\pi$
$439$			21.3609i			1.01950i	−0.860323	+	0.509749i	$0.829738\pi$
$440$	−1.91979	−	12.4242i	−0.0915226	−	0.592303i
$441$		0			0
$442$	−11.8700	−	16.3377i	−0.564600	−	0.777105i
$443$	9.49059	−	3.08368i	0.450911	−	0.146510i	−0.0747529	−	0.997202i	$-0.523817\pi$
$443$	9.49059	−	3.08368i	0.450911	−	0.146510i	0.525664	+	0.850692i	$0.323817\pi$
$444$		0			0
$445$	−5.29032	−	3.84364i	−0.250785	−	0.182206i
$446$	−18.1790	−	13.2078i	−0.860800	−	0.625408i
$447$		0			0
$448$	−0.951057	+	0.309017i	−0.0449332	+	0.0145997i
$449$	2.23434	+	3.07531i	0.105445	+	0.145133i	0.858479	−	0.512850i	$-0.171410\pi$
$449$	2.23434	+	3.07531i	0.105445	+	0.145133i	−0.753033	+	0.657982i	$0.771410\pi$
$450$		0			0
$451$	−1.80325	+	1.78970i	−0.0849117	+	0.0842736i
$452$			14.6506i			0.689104i
$453$		0			0
$454$	6.05719	+	18.6421i	0.284278	+	0.874918i
$455$	−10.4840	−	3.40647i	−0.491499	−	0.159698i
$456$		0			0
$457$	6.65801	−	9.16396i	0.311449	−	0.428672i	−0.624384	−	0.781118i	$-0.714650\pi$
$457$	6.65801	−	9.16396i	0.311449	−	0.428672i	0.935832	+	0.352446i	$0.114650\pi$
$458$	8.74574	−	26.9166i	0.408661	−	1.25773i
$459$		0			0
$460$	24.2340	−	17.6070i	1.12992	−	0.820932i
$461$	22.6846			1.05653			0.528263	−	0.849081i	$-0.322844\pi$
$461$	22.6846			1.05653			0.528263	+	0.849081i	$0.322844\pi$
$462$		0			0
$463$	1.32867			0.0617487			0.0308743	−	0.999523i	$-0.490171\pi$
$463$	1.32867			0.0617487			0.0308743	+	0.999523i	$0.490171\pi$
$464$	2.57494	−	1.87081i	0.119539	−	0.0868500i
$465$		0			0
$466$	−5.16297	+	15.8900i	−0.239170	+	0.736090i
$467$	−7.96877	+	10.9681i	−0.368751	+	0.507542i	−0.952561	−	0.304348i	$-0.901561\pi$
$467$	−7.96877	+	10.9681i	−0.368751	+	0.507542i	0.583810	+	0.811890i	$0.301561\pi$
$468$		0			0
$469$	6.19154	+	2.01175i	0.285899	+	0.0928942i
$470$	8.66255	+	26.6606i	0.399574	+	1.22976i
$471$		0			0
$472$			4.69135i			0.215937i
$473$	−4.39619	+	2.21912i	−0.202137	+	0.102035i
$474$		0			0
$475$	−41.6568	−	57.3356i	−1.91134	−	2.63074i
$476$	6.60412	−	2.14581i	0.302699	−	0.0983530i
$477$		0			0
$478$	18.6953	+	13.5829i	0.855104	+	0.621269i
$479$	29.8666	+	21.6994i	1.36464	+	0.991469i	0.998135	+	0.0610532i	$0.0194459\pi$
$479$	29.8666	+	21.6994i	1.36464	+	0.991469i	0.366506	+	0.930416i	$0.380554\pi$
$480$		0			0
$481$	−14.5070	+	4.71360i	−0.661461	+	0.214922i
$482$	−3.73521	−	5.14107i	−0.170134	−	0.234169i
$483$		0			0
$484$	6.39832	+	8.94771i	0.290833	+	0.406714i
$485$			0.0678360i			0.00308027i
$486$		0			0
$487$	−11.2192	−	34.5291i	−0.508389	−	1.56466i	−0.794997	−	0.606614i	$-0.792527\pi$
$487$	−11.2192	−	34.5291i	−0.508389	−	1.56466i	0.286607	−	0.958048i	$-0.407473\pi$
$488$	−11.4499	−	3.72031i	−0.518314	−	0.168410i
$489$		0			0
$490$	2.22800	−	3.06659i	0.100651	−	0.138534i
$491$	−12.3440	+	37.9909i	−0.557077	+	1.71451i	0.133318	+	0.991073i	$0.457437\pi$
$491$	−12.3440	+	37.9909i	−0.557077	+	1.71451i	−0.690395	+	0.723433i	$0.742563\pi$
$492$		0			0
$493$	−17.8804	+	12.9909i	−0.805291	+	0.585078i
$494$	−22.0012			−0.989882
$495$		0			0
$496$	3.56019			0.159857
$497$	−1.27030	+	0.922925i	−0.0569806	+	0.0413988i
$498$		0			0
$499$	−0.820335	+	2.52473i	−0.0367232	+	0.113023i	−0.967738	−	0.251960i	$-0.918925\pi$
$499$	−0.820335	+	2.52473i	−0.0367232	+	0.113023i	0.931014	+	0.364982i	$0.118925\pi$
$500$	9.73181	−	13.3947i	0.435220	−	0.599028i
$501$		0			0
$502$	4.88909	+	1.58856i	0.218211	+	0.0709009i
$503$	7.12032	+	21.9141i	0.317479	+	0.977101i	0.974722	+	0.223422i	$0.0717226\pi$
$503$	7.12032	+	21.9141i	0.317479	+	0.977101i	−0.657243	+	0.753679i	$0.728277\pi$
$504$		0			0
$505$			54.3658i			2.41925i
$506$	−11.9871	+	23.3082i	−0.532891	+	1.03618i
$507$		0			0
$508$	−2.20370	−	3.03314i	−0.0977735	−	0.134574i
$509$	23.1259	−	7.51406i	1.02504	−	0.333055i	0.252211	−	0.967672i	$-0.418842\pi$
$509$	23.1259	−	7.51406i	1.02504	−	0.333055i	0.772827	+	0.634617i	$0.218842\pi$
$510$		0			0
$511$	7.69788	+	5.59284i	0.340534	+	0.247412i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	12.9486	−	4.20726i	0.571138	−	0.185574i
$515$	23.9588	+	32.9764i	1.05575	+	1.45311i
$516$		0			0
$517$	−17.2784	−	17.4092i	−0.759902	−	0.765657i
$518$		−	5.24501i		−	0.230452i
$519$		0			0
$520$	−3.40647	−	10.4840i	−0.149383	−	0.459755i
$521$	32.5954	+	10.5909i	1.42803	+	0.463995i	0.918144	−	0.396247i	$-0.129688\pi$
$521$	32.5954	+	10.5909i	1.42803	+	0.463995i	0.509886	+	0.860242i	$0.329688\pi$
$522$		0			0
$523$	−14.0256	+	19.3046i	−0.613297	+	0.844131i	−0.996844	−	0.0793906i	$-0.974703\pi$
$523$	−14.0256	+	19.3046i	−0.613297	+	0.844131i	0.383547	+	0.923522i	$0.374703\pi$
$524$	−1.18958	+	3.66115i	−0.0519671	+	0.159938i
$525$		0			0
$526$	−1.33339	+	0.968766i	−0.0581387	+	0.0422402i
$527$	−24.7219			−1.07690
$528$		0			0
$529$	−39.4511			−1.71526
$530$	11.5886	−	8.41962i	0.503377	−	0.365725i
$531$		0			0
$532$	2.33779	−	7.19497i	0.101356	−	0.311941i
$533$	−1.30944	+	1.80229i	−0.0567181	+	0.0780658i
$534$		0			0
$535$	−28.8310	−	9.36775i	−1.24647	−	0.405003i
$536$	2.01175	+	6.19154i	0.0868945	+	0.267434i
$537$		0			0
$538$			28.1092i			1.21187i
$539$	−0.531187	+	3.27381i	−0.0228799	+	0.141013i
$540$		0			0
$541$	−12.9377	−	17.8073i	−0.556237	−	0.765594i	0.434605	−	0.900621i	$-0.356888\pi$
$541$	−12.9377	−	17.8073i	−0.556237	−	0.765594i	−0.990842	+	0.135027i	$0.956888\pi$
$542$	−4.16065	+	1.35188i	−0.178715	+	0.0580681i
$543$		0			0
$544$	5.61780	+	4.08157i	0.240861	+	0.174996i
$545$	−25.2102	−	18.3163i	−1.07989	−	0.784585i
$546$		0			0
$547$	7.40729	−	2.40678i	0.316713	−	0.102906i	−0.146347	−	0.989233i	$-0.546752\pi$
$547$	7.40729	−	2.40678i	0.316713	−	0.102906i	0.463060	+	0.886327i	$0.346752\pi$
$548$	2.91445	+	4.01140i	0.124499	+	0.171359i
$549$		0			0
$550$	−4.97614	+	30.6689i	−0.212183	+	1.30773i
$551$			24.0787i			1.02579i
$552$		0			0
$553$	−3.60805	−	11.1044i	−0.153430	−	0.472209i
$554$	15.7670	+	5.12302i	0.669877	+	0.217656i
$555$		0			0
$556$	−2.89966	+	3.99104i	−0.122973	+	0.169258i
$557$	−2.89672	+	8.91518i	−0.122738	+	0.377748i	−0.993482	−	0.113988i	$-0.963638\pi$
$557$	−2.89672	+	8.91518i	−0.122738	+	0.377748i	0.870744	+	0.491736i	$0.163638\pi$
$558$		0			0
$559$	−3.49341	+	2.53811i	−0.147756	+	0.107351i
$560$	3.79051			0.160178
$561$		0			0
$562$	−28.6949			−1.21042
$563$	−18.9148	+	13.7424i	−0.797163	+	0.579173i	−0.910081	−	0.414431i	$-0.863981\pi$
$563$	−18.9148	+	13.7424i	−0.797163	+	0.579173i	0.112917	+	0.993604i	$0.463981\pi$
$564$		0			0
$565$	17.1607	−	52.8151i	0.721954	−	2.22195i
$566$	−5.12622	+	7.05563i	−0.215471	+	0.296570i
$567$		0			0
$568$	−1.49332	−	0.485210i	−0.0626585	−	0.0203590i
$569$	−11.0318	−	33.9525i	−0.462479	−	1.42336i	−0.862126	−	0.506694i	$-0.830867\pi$
$569$	−11.0318	−	33.9525i	−0.462479	−	1.42336i	0.399647	−	0.916669i	$-0.369133\pi$
$570$		0			0
$571$			24.9304i			1.04330i	0.853159	+	0.521652i	$0.174684\pi$
$571$			24.9304i			1.04330i	−0.853159	+	0.521652i	$0.825316\pi$
$572$	6.79456	+	6.84601i	0.284095	+	0.286246i
$573$		0			0
$574$	−0.450258	−	0.619727i	−0.0187934	−	0.0258669i
$575$	−70.4078	+	22.8769i	−2.93621	+	0.954032i
$576$		0			0
$577$	−17.9915	−	13.0716i	−0.748997	−	0.544178i	0.146519	−	0.989208i	$-0.453193\pi$
$577$	−17.9915	−	13.0716i	−0.748997	−	0.544178i	−0.895516	+	0.445030i	$0.853193\pi$
$578$	−25.2566	−	18.3500i	−1.05054	−	0.763260i
$579$		0			0
$580$	−11.4740	+	3.72812i	−0.476431	+	0.154802i
$581$	−7.83409	−	10.7827i	−0.325013	−	0.447342i
$582$		0			0
$583$	−5.73218	+	11.1459i	−0.237403	+	0.461616i
$584$			9.51510i			0.393738i
$585$		0			0
$586$	9.72590	+	29.9332i	0.401773	+	1.23653i
$587$	13.0687	+	4.24627i	0.539402	+	0.175262i	0.566033	−	0.824383i	$-0.308478\pi$
$587$	13.0687	+	4.24627i	0.539402	+	0.175262i	−0.0266302	+	0.999645i	$0.508478\pi$
$588$		0			0
$589$	−15.8312	+	21.7898i	−0.652315	+	0.897834i
$590$	5.49512	−	16.9122i	0.226231	−	0.696266i
$591$		0			0
$592$	4.24330	−	3.08294i	0.174398	−	0.126708i
$593$	−17.1753			−0.705305			−0.352652	−	0.935754i	$-0.614720\pi$
$593$	−17.1753			−0.705305			−0.352652	+	0.935754i	$0.614720\pi$
$594$		0			0
$595$	−26.3212			−1.07906
$596$	6.20493	−	4.50815i	0.254164	−	0.184661i
$597$		0			0
$598$	−7.10193	+	21.8575i	−0.290420	+	0.893820i
$599$	8.33335	−	11.4699i	0.340492	−	0.468647i	−0.604093	−	0.796914i	$-0.706465\pi$
$599$	8.33335	−	11.4699i	0.340492	−	0.468647i	0.944585	+	0.328267i	$0.106465\pi$
$600$		0			0
$601$	−16.2410	−	5.27701i	−0.662483	−	0.215254i	−0.0415726	−	0.999135i	$-0.513237\pi$
$601$	−16.2410	−	5.27701i	−0.662483	−	0.215254i	−0.620910	+	0.783882i	$0.713237\pi$
$602$	−0.458829	−	1.41213i	−0.0187005	−	0.0575541i
$603$		0			0
$604$			9.81508i			0.399370i
$605$	−12.5851	−	39.7509i	−0.511658	−	1.61611i
$606$		0			0
$607$	−10.5711	−	14.5499i	−0.429069	−	0.590563i	0.538670	−	0.842517i	$-0.318927\pi$
$607$	−10.5711	−	14.5499i	−0.429069	−	0.590563i	−0.967739	+	0.251954i	$0.918927\pi$
$608$	7.19497	−	2.33779i	0.291794	−	0.0948098i
$609$		0			0
$610$	36.9191	+	26.8233i	1.49481	+	1.08604i
$611$	−17.4000	−	12.6418i	−0.703927	−	0.511433i
$612$		0			0
$613$	−20.1219	+	6.53799i	−0.812715	+	0.264067i	−0.685747	−	0.727840i	$-0.740524\pi$
$613$	−20.1219	+	6.53799i	−0.812715	+	0.264067i	−0.126968	+	0.991907i	$0.540524\pi$
$614$	7.12283	+	9.80374i	0.287454	+	0.395647i
$615$		0			0
$616$	−2.96079	+	1.49456i	−0.119294	+	0.0602175i
$617$		−	16.0402i		−	0.645754i	−0.946441	−	0.322877i	$-0.895350\pi$
$617$		−	16.0402i		−	0.645754i	0.946441	−	0.322877i	$-0.104650\pi$
$618$		0			0
$619$	−6.62709	−	20.3961i	−0.266365	−	0.819788i	−0.991376	−	0.131050i	$-0.958165\pi$
$619$	−6.62709	−	20.3961i	−0.266365	−	0.819788i	0.725010	−	0.688738i	$-0.241835\pi$
$620$	−12.8345	−	4.17017i	−0.515444	−	0.167478i
$621$		0			0
$622$	−1.27593	+	1.75617i	−0.0511603	+	0.0704161i
$623$	−0.533101	+	1.64071i	−0.0213582	+	0.0657339i
$624$		0			0
$625$	−12.8785	+	9.35678i	−0.515140	+	0.374271i
$626$	−9.48348			−0.379036
$627$		0			0
$628$	−12.0570			−0.481126
$629$	−29.4654	+	21.4079i	−1.17486	+	0.853587i
$630$		0			0
$631$	−6.73698	+	20.7343i	−0.268195	+	0.825419i	0.722745	+	0.691114i	$0.242880\pi$
$631$	−6.73698	+	20.7343i	−0.268195	+	0.825419i	−0.990940	+	0.134304i	$0.957120\pi$
$632$	6.86292	−	9.44600i	0.272992	−	0.375742i
$633$		0			0
$634$	−25.7232	−	8.35797i	−1.02160	−	0.331937i
$635$	4.39151	+	13.5157i	0.174272	+	0.536353i
$636$		0			0
$637$			2.90820i			0.115227i
$638$	7.49245	−	7.43613i	0.296629	−	0.294399i
$639$		0			0
$640$	2.22800	+	3.06659i	0.0880696	+	0.121217i
$641$	24.1734	−	7.85440i	0.954791	−	0.310230i	0.210130	−	0.977673i	$-0.432611\pi$
$641$	24.1734	−	7.85440i	0.954791	−	0.310230i	0.744661	+	0.667443i	$0.232611\pi$
$642$		0			0
$643$	35.9395	+	26.1116i	1.41732	+	1.02974i	0.992207	+	0.124600i	$0.0397647\pi$
$643$	35.9395	+	26.1116i	1.41732	+	1.02974i	0.425110	+	0.905142i	$0.360235\pi$
$644$	−6.39334	−	4.64503i	−0.251933	−	0.183040i
$645$		0			0
$646$	−49.9617	+	16.2335i	−1.96572	+	0.638700i
$647$	−6.93774	−	9.54898i	−0.272751	−	0.375409i	0.650565	−	0.759450i	$-0.274532\pi$
$647$	−6.93774	−	9.54898i	−0.272751	−	0.375409i	−0.923316	+	0.384041i	$0.874532\pi$
$648$		0			0
$649$	2.37605	+	15.3769i	0.0932679	+	0.603598i
$650$			27.2439i			1.06859i
$651$		0			0
$652$	−2.56835	−	7.90456i	−0.100584	−	0.309566i
$653$	35.0551	+	11.3901i	1.37181	+	0.445729i	0.899970	−	0.435953i	$-0.143588\pi$
$653$	35.0551	+	11.3901i	1.37181	+	0.445729i	0.471844	+	0.881682i	$0.343588\pi$
$654$		0			0
$655$	8.57685	−	11.8050i	0.335125	−	0.461260i
$656$	0.236715	−	0.728533i	0.00924215	−	0.0284444i
$657$		0			0
$658$	5.98307	−	4.34695i	0.233244	−	0.169462i
$659$	32.5650			1.26855			0.634276	−	0.773107i	$-0.281298\pi$
$659$	32.5650			1.26855			0.634276	+	0.773107i	$0.281298\pi$
$660$		0			0
$661$	16.3230			0.634890			0.317445	−	0.948277i	$-0.397175\pi$
$661$	16.3230			0.634890			0.317445	+	0.948277i	$0.397175\pi$
$662$	−28.1541	+	20.4552i	−1.09424	+	0.795012i
$663$		0			0
$664$	4.11862	−	12.6758i	0.159834	−	0.491917i
$665$	−16.8554	+	23.1994i	−0.653624	+	0.899636i
$666$		0			0
$667$	23.9214	+	7.77253i	0.926240	+	0.300954i
$668$	−2.80932	−	8.64618i	−0.108696	−	0.334531i
$669$		0			0
$670$		−	24.6769i		−	0.953350i
$671$	−39.4140	−	6.39505i	−1.52156	−	0.246878i
$672$		0			0
$673$	−22.9949	−	31.6497i	−0.886387	−	1.22001i	−0.974611	−	0.223907i	$-0.928119\pi$
$673$	−22.9949	−	31.6497i	−0.886387	−	1.22001i	0.0882232	−	0.996101i	$-0.471881\pi$
$674$	29.1899	−	9.48439i	1.12435	−	0.365325i
$675$		0			0
$676$	−3.67486	−	2.66994i	−0.141341	−	0.102690i
$677$	−6.94512	−	5.04592i	−0.266923	−	0.193931i	0.446271	−	0.894898i	$-0.352752\pi$
$677$	−6.94512	−	5.04592i	−0.266923	−	0.193931i	−0.713193	+	0.700967i	$0.752752\pi$
$678$		0			0
$679$	0.0170204	−	0.00553026i	0.000653182	−	0.000212232i
$680$	−15.4712	−	21.2943i	−0.593294	−	0.816600i
$681$		0			0
$682$	11.6693	−	1.80315i	0.446842	−	0.0690460i
$683$		−	9.05494i		−	0.346478i	−0.984880	−	0.173239i	$-0.944577\pi$
$683$		−	9.05494i		−	0.346478i	0.984880	−	0.173239i	$-0.0554233\pi$
$684$		0			0
$685$	−5.80789	−	17.8748i	−0.221908	−	0.682962i
$686$	−0.951057	−	0.309017i	−0.0363115	−	0.0117983i
$687$		0			0
$688$	0.872744	−	1.20123i	0.0332731	−	0.0457964i
$689$	−3.39612	+	10.4522i	−0.129382	+	0.398197i
$690$		0			0
$691$	−4.25373	+	3.09052i	−0.161820	+	0.117569i	−0.665748	−	0.746177i	$-0.731887\pi$
$691$	−4.25373	+	3.09052i	−0.161820	+	0.117569i	0.503929	+	0.863745i	$0.331887\pi$
$692$	−15.9256			−0.605401
$693$		0			0
$694$	−22.6681			−0.860471
$695$	15.1281	−	10.9912i	0.573841	−	0.416920i
$696$		0			0
$697$	−1.64374	+	5.05892i	−0.0622612	+	0.191620i
$698$	−3.93568	+	5.41700i	−0.148968	+	0.205037i
$699$		0			0
$700$	−8.90945	−	2.89485i	−0.336745	−	0.109415i
$701$	6.98581	+	21.5001i	0.263850	+	0.812048i	0.991956	+	0.126583i	$0.0404010\pi$
$701$	6.98581	+	21.5001i	0.263850	+	0.812048i	−0.728106	+	0.685465i	$0.759599\pi$
$702$		0			0
$703$			39.6797i			1.49655i
$704$	−2.94943	−	1.51685i	−0.111161	−	0.0571685i
$705$		0			0
$706$	13.7280	+	18.8950i	0.516660	+	0.711121i
$707$	13.6406	−	4.43212i	0.513009	−	0.166687i
$708$		0			0
$709$	−21.1590	−	15.3729i	−0.794644	−	0.577343i	0.114694	−	0.993401i	$-0.463411\pi$
$709$	−21.1590	−	15.3729i	−0.794644	−	0.577343i	−0.909338	+	0.416058i	$0.863411\pi$
$710$	4.81507	+	3.49835i	0.180706	+	0.131291i
$711$		0			0
$712$	−1.64071	+	0.533101i	−0.0614884	+	0.0199788i
$713$	16.5372	+	22.7615i	0.619323	+	0.852425i
$714$		0			0
$715$	−16.4753	−	32.6385i	−0.616143	−	1.22061i
$716$			13.7892i			0.515327i
$717$		0			0
$718$	0.207471	+	0.638529i	0.00774273	+	0.0238297i
$719$	4.87714	+	1.58468i	0.181887	+	0.0590986i	0.398544	−	0.917149i	$-0.369516\pi$
$719$	4.87714	+	1.58468i	0.181887	+	0.0590986i	−0.216658	+	0.976248i	$0.569516\pi$
$720$		0			0
$721$	6.32072	−	8.69973i	0.235396	−	0.323995i
$722$	−11.8146	+	36.3615i	−0.439693	+	1.35324i
$723$		0			0
$724$	5.63667	−	4.09528i	0.209485	−	0.152200i
$725$	29.8164			1.10735
$726$		0			0
$727$	−30.2332			−1.12129			−0.560644	−	0.828057i	$-0.689446\pi$
$727$	−30.2332			−1.12129			−0.560644	+	0.828057i	$0.689446\pi$
$728$	−2.35278	+	1.70940i	−0.0872000	+	0.0633545i
$729$		0			0
$730$	11.1453	−	34.3018i	0.412507	−	1.26957i
$731$	−6.06032	+	8.34132i	−0.224149	+	0.308515i
$732$		0			0
$733$	19.9564	+	6.48422i	0.737105	+	0.239500i	0.653424	−	0.756992i	$-0.273332\pi$
$733$	19.9564	+	6.48422i	0.737105	+	0.239500i	0.0836818	+	0.996493i	$0.473332\pi$
$734$	−5.99620	−	18.4544i	−0.221324	−	0.681165i
$735$		0			0
$736$		−	7.90260i		−	0.291294i
$737$	9.72983	+	19.2753i	0.358403	+	0.710014i
$738$		0			0
$739$	−14.2548	−	19.6200i	−0.524370	−	0.721733i	0.461890	−	0.886937i	$-0.347172\pi$
$739$	−14.2548	−	19.6200i	−0.524370	−	0.721733i	−0.986259	+	0.165204i	$0.947172\pi$
$740$	−18.9082	+	6.14364i	−0.695078	+	0.225845i
$741$		0			0
$742$	−3.05727	−	2.22124i	−0.112236	−	0.0815443i
$743$	−28.6830	−	20.8394i	−1.05228	−	0.764524i	−0.0796328	−	0.996824i	$-0.525375\pi$
$743$	−28.6830	−	20.8394i	−1.05228	−	0.764524i	−0.972644	+	0.232300i	$0.925375\pi$
$744$		0			0
$745$	−27.6492	+	8.98378i	−1.01299	+	0.329140i
$746$	−3.72997	−	5.13386i	−0.136564	−	0.187964i
$747$		0			0
$748$	20.4808	+	10.5330i	0.748853	+	0.385125i
$749$			7.99752i			0.292223i
$750$		0			0
$751$	10.0654	+	30.9780i	0.367291	+	1.13041i	0.948534	+	0.316675i	$0.102567\pi$
$751$	10.0654	+	30.9780i	0.367291	+	1.13041i	−0.581243	+	0.813730i	$0.697433\pi$
$752$	7.03352	+	2.28533i	0.256486	+	0.0833373i
$753$		0			0
$754$	5.44068	−	7.48845i	0.198138	−	0.272713i
$755$	11.4967	−	35.3832i	0.418408	−	1.28773i
$756$		0			0
$757$	24.6777	−	17.9294i	0.896927	−	0.651656i	−0.0407477	−	0.999169i	$-0.512974\pi$
$757$	24.6777	−	17.9294i	0.896927	−	0.651656i	0.937675	+	0.347514i	$0.112974\pi$
$758$	−17.0025			−0.617558
$759$		0			0
$760$	−28.6761			−1.04019
$761$	4.76064	−	3.45881i	0.172573	−	0.125382i	−0.498146	−	0.867093i	$-0.665986\pi$
$761$	4.76064	−	3.45881i	0.172573	−	0.125382i	0.670719	+	0.741711i	$0.265986\pi$
$762$		0			0
$763$	−2.54041	+	7.81859i	−0.0919691	+	0.283052i
$764$	−13.8338	+	19.0406i	−0.500490	+	0.688866i
$765$		0			0
$766$	−19.0725	−	6.19702i	−0.689116	−	0.223907i
$767$	4.21603	+	12.9756i	0.152232	+	0.468522i
$768$		0			0
$769$			7.71768i			0.278307i	0.990271	+	0.139153i	$0.0444381\pi$
$769$			7.71768i			0.278307i	−0.990271	+	0.139153i	$0.955562\pi$
$770$	12.4242	−	1.91979i	0.447739	−	0.0691846i
$771$		0			0
$772$	2.41417	+	3.32281i	0.0868877	+	0.119591i
$773$	−1.41295	+	0.459094i	−0.0508201	+	0.0165125i	−0.334317	−	0.942461i	$-0.608506\pi$
$773$	−1.41295	+	0.459094i	−0.0508201	+	0.0165125i	0.283497	+	0.958973i	$0.408506\pi$
$774$		0			0
$775$	26.9821	+	19.6036i	0.969226	+	0.704184i
$776$	0.0144784	+	0.0105192i	0.000519744	+	0.000377616i
$777$		0			0
$778$	22.8749	−	7.43252i	0.820106	−	0.266469i
$779$	3.40631	+	4.68838i	0.122044	+	0.167979i
$780$		0			0
$781$	−5.14045	−	0.834056i	−0.183940	−	0.0298449i
$782$			54.8755i			1.96234i
$783$		0			0
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	43.4653	+	14.1227i	1.55134	+	0.504062i
$786$		0			0
$787$	24.9230	−	34.3036i	0.888410	−	1.22279i	−0.0856097	−	0.996329i	$-0.527284\pi$
$787$	24.9230	−	34.3036i	0.888410	−	1.22279i	0.974020	−	0.226463i	$-0.0727162\pi$
$788$	−7.72529	+	23.7760i	−0.275202	+	0.846985i
$789$		0			0
$790$	−35.8051	+	26.0140i	−1.27389	+	0.925535i
$791$	−14.6506			−0.520914
$792$		0			0
$793$	−35.0123			−1.24332
$794$	−4.19533	+	3.04809i	−0.148887	+	0.108173i
$795$		0			0
$796$	6.71116	−	20.6548i	0.237871	−	0.732091i
$797$	−7.27973	+	10.0197i	−0.257861	+	0.354916i	−0.918245	−	0.396013i	$-0.870394\pi$
$797$	−7.27973	+	10.0197i	−0.257861	+	0.354916i	0.660384	+	0.750928i	$0.270394\pi$
$798$		0			0
$799$	−48.8406	−	15.8693i	−1.72786	−	0.561415i
$800$	−2.89485	−	8.90945i	−0.102349	−	0.314997i
$801$		0			0
$802$		−	37.7151i		−	1.33177i
$803$	4.81915	+	31.1879i	0.170064	+	1.10060i
$804$		0			0
$805$	17.6070	+	24.2340i	0.620566	+	0.854136i
$806$	9.84701	−	3.19949i	0.346846	−	0.112697i
$807$		0			0
$808$	11.6034	+	8.43039i	0.408207	+	0.296580i
$809$	6.61201	+	4.80391i	0.232466	+	0.168896i	0.697920	−	0.716176i	$-0.254109\pi$
$809$	6.61201	+	4.80391i	0.232466	+	0.168896i	−0.465454	+	0.885072i	$0.654109\pi$
$810$		0			0
$811$	30.4393	−	9.89031i	1.06887	−	0.347296i	0.278821	−	0.960343i	$-0.410056\pi$
$811$	30.4393	−	9.89031i	1.06887	−	0.347296i	0.790046	+	0.613047i	$0.210056\pi$
$812$	1.87081	+	2.57494i	0.0656524	+	0.0903628i
$813$		0			0
$814$	12.3469	−	12.2541i	0.432760	−	0.429507i
$815$			31.5042i			1.10354i
$816$		0			0
$817$	3.47115	+	10.6831i	0.121440	+	0.373754i
$818$	−27.4362	−	8.91456i	−0.959284	−	0.311690i
$819$		0			0
$820$	−1.70671	+	2.34908i	−0.0596008	+	0.0820334i
$821$	15.4179	−	47.4513i	0.538087	−	1.65606i	−0.198795	−	0.980041i	$-0.563703\pi$
$821$	15.4179	−	47.4513i	0.538087	−	1.65606i	0.736882	−	0.676021i	$-0.236297\pi$
$822$		0			0
$823$	−9.71057	+	7.05514i	−0.338489	+	0.245927i	−0.744024	−	0.668153i	$-0.767085\pi$
$823$	−9.71057	+	7.05514i	−0.338489	+	0.245927i	0.405535	+	0.914080i	$0.367085\pi$
$824$	10.7535			0.374614
$825$		0			0
$826$	−4.69135			−0.163233
$827$	27.7348	−	20.1505i	0.964435	−	0.700703i	0.0102584	−	0.999947i	$-0.496735\pi$
$827$	27.7348	−	20.1505i	0.964435	−	0.700703i	0.954176	+	0.299244i	$0.0967346\pi$
$828$		0			0
$829$	10.5245	−	32.3911i	0.365531	−	1.12499i	−0.584116	−	0.811670i	$-0.698559\pi$
$829$	10.5245	−	32.3911i	0.365531	−	1.12499i	0.949648	−	0.313320i	$-0.101441\pi$
$830$	−29.6952	+	40.8719i	−1.03073	+	1.41868i
$831$		0			0
$832$	−2.76586	−	0.898683i	−0.0958890	−	0.0311562i
$833$	2.14581	+	6.60412i	0.0743479	+	0.228819i
$834$		0			0
$835$			34.4600i			1.19254i
$836$	22.3991	−	11.3067i	0.774689	−	0.391050i
$837$		0			0
$838$	−8.24289	−	11.3454i	−0.284746	−	0.391919i
$839$	54.7253	−	17.7813i	1.88933	−	0.613879i	0.908892	−	0.417031i	$-0.136930\pi$
$839$	54.7253	−	17.7813i	1.88933	−	0.613879i	0.980434	−	0.196848i	$-0.0630705\pi$
$840$		0			0
$841$	15.2659	+	11.0914i	0.526412	+	0.382461i
$842$	12.0575	+	8.76029i	0.415529	+	0.301899i
$843$		0			0
$844$	10.0600	−	3.26870i	0.346280	−	0.112513i
$845$	10.1204	+	13.9296i	0.348153	+	0.479192i
$846$		0			0
$847$	−8.94771	+	6.39832i	−0.307447	+	0.219849i
$848$		−	3.77900i		−	0.129771i
$849$		0			0
$850$	20.1018	+	61.8671i	0.689487	+	2.12202i
$851$	39.4205	+	12.8085i	1.35132	+	0.439070i
$852$		0			0
$853$	−5.58016	+	7.68043i	−0.191061	+	0.262973i	−0.893791	−	0.448484i	$-0.851964\pi$
$853$	−5.58016	+	7.68043i	−0.191061	+	0.262973i	0.702730	+	0.711457i	$0.251964\pi$
$854$	3.72031	−	11.4499i	0.127306	−	0.391809i
$855$		0			0
$856$	−6.47013	+	4.70083i	−0.221145	+	0.160671i
$857$	−19.9220			−0.680524			−0.340262	−	0.940331i	$-0.610516\pi$
$857$	−19.9220			−0.680524			−0.340262	+	0.940331i	$0.610516\pi$
$858$		0			0
$859$	−25.0382			−0.854292			−0.427146	−	0.904183i	$-0.640481\pi$
$859$	−25.0382			−0.854292			−0.427146	+	0.904183i	$0.640481\pi$
$860$	−4.55327	+	3.30814i	−0.155265	+	0.112807i
$861$		0			0
$862$	1.15832	−	3.56493i	0.0394524	−	0.121422i
$863$	3.07297	−	4.22958i	0.104605	−	0.143977i	−0.753505	−	0.657442i	$-0.771638\pi$
$863$	3.07297	−	4.22958i	0.104605	−	0.143977i	0.858110	+	0.513465i	$0.171638\pi$
$864$		0			0
$865$	57.4116	+	18.6542i	1.95205	+	0.634260i
$866$	5.18999	+	15.9731i	0.176363	+	0.542789i
$867$		0			0
$868$			3.56019i			0.120841i
$869$	17.7106	−	34.4373i	0.600792	−	1.16821i
$870$		0			0
$871$	11.1285	+	15.3170i	0.377074	+	0.518998i
$872$	−7.81859	+	2.54041i	−0.264771	+	0.0860292i
$873$		0			0
$874$	48.3671	+	35.1407i	1.63604	+	1.18865i
$875$	13.3947	+	9.73181i	0.452823	+	0.328995i
$876$		0			0
$877$	−36.1606	+	11.7493i	−1.22106	+	0.396745i	−0.847466	−	0.530850i	$-0.821873\pi$
$877$	−36.1606	+	11.7493i	−1.22106	+	0.396745i	−0.373589	+	0.927594i	$0.621873\pi$
$878$	−12.5556	−	17.2813i	−0.423731	−	0.583216i
$879$		0			0
$880$	8.85593	+	8.92300i	0.298533	+	0.300794i
$881$			57.8710i			1.94972i	0.222810	+	0.974862i	$0.428477\pi$
$881$			57.8710i			1.94972i	−0.222810	+	0.974862i	$0.571523\pi$
$882$		0			0
$883$	−17.7730	−	54.6996i	−0.598109	−	1.84079i	−0.538600	−	0.842561i	$-0.681047\pi$
$883$	−17.7730	−	54.6996i	−0.598109	−	1.84079i	−0.0595084	−	0.998228i	$-0.518953\pi$
$884$	19.2061	+	6.24044i	0.645971	+	0.209889i
$885$		0			0
$886$	−5.86551	+	8.07318i	−0.197056	+	0.271224i
$887$	−0.823406	+	2.53418i	−0.0276473	+	0.0850895i	−0.963928	−	0.266163i	$-0.914244\pi$
$887$	−0.823406	+	2.53418i	−0.0276473	+	0.0850895i	0.936281	+	0.351252i	$0.114244\pi$
$888$		0			0
$889$	3.03314	−	2.20370i	0.101728	−	0.0739098i
$890$	6.53919			0.219194
$891$		0			0
$892$	22.4705			0.752367
$893$	−45.2633	+	32.8857i	−1.51468	+	1.10048i
$894$		0			0
$895$	16.1517	−	49.7099i	0.539893	−	1.66162i
$896$	0.587785	−	0.809017i	0.0196365	−	0.0270274i
$897$		0			0
$898$	−3.61524	−	1.17466i	−0.120642	−	0.0391990i
$899$	−3.50160	−	10.7768i	−0.116785	−	0.359427i
$900$		0			0
$901$			26.2413i			0.874224i
$902$	0.406903	−	2.50782i	0.0135484	−	0.0835013i
$903$		0			0
$904$	−8.61138	−	11.8525i	−0.286410	−	0.394210i
$905$	−25.1171	+	8.16103i	−0.834919	+	0.271282i
$906$		0			0
$907$	16.9775	+	12.3349i	0.563730	+	0.409574i	0.832822	−	0.553541i	$-0.186724\pi$
$907$	16.9775	+	12.3349i	0.563730	+	0.409574i	−0.269092	+	0.963114i	$0.586724\pi$
$908$	−15.8579	−	11.5215i	−0.526264	−	0.382353i
$909$		0			0
$910$	10.4840	−	3.40647i	0.347542	−	0.112923i
$911$	−18.6100	−	25.6145i	−0.616578	−	0.848647i	0.380520	−	0.924773i	$-0.375745\pi$
$911$	−18.6100	−	25.6145i	−0.616578	−	0.848647i	−0.997098	+	0.0761255i	$0.975745\pi$
$912$		0			0
$913$	7.07974	−	43.6338i	0.234305	−	1.44407i
$914$			11.3273i			0.374673i
$915$		0			0
$916$	8.74574	+	26.9166i	0.288967	+	0.889350i
$917$	−3.66115	−	1.18958i	−0.120902	−	0.0392834i
$918$		0			0
$919$	−15.2045	+	20.9272i	−0.501551	+	0.690326i	−0.982466	−	0.186441i	$-0.940305\pi$
$919$	−15.2045	+	20.9272i	−0.501551	+	0.690326i	0.480915	+	0.876767i	$0.340305\pi$
$920$	−9.25656	+	28.4888i	−0.305180	+	0.939247i
$921$		0			0
$922$	−18.3522	+	13.3337i	−0.604398	+	0.439121i
$923$	−4.56638			−0.150304
$924$		0			0
$925$	49.1349			1.61555
$926$	−1.07492	+	0.780974i	−0.0353240	+	0.0256644i
$927$		0			0
$928$	−0.983541	+	3.02703i	−0.0322863	+	0.0993671i
$929$	−11.5210	+	15.8573i	−0.377992	+	0.520261i	−0.955051	−	0.296441i	$-0.904200\pi$
$929$	−11.5210	+	15.8573i	−0.377992	+	0.520261i	0.577060	+	0.816702i	$0.304200\pi$
$930$		0			0
$931$	7.19497	+	2.33779i	0.235805	+	0.0766179i
$932$	−5.16297	−	15.8900i	−0.169119	−	0.520494i
$933$		0			0
$934$		−	13.5573i		−	0.443608i
$935$	−61.4955	−	61.9611i	−2.01112	−	2.02635i
$936$		0			0
$937$	−14.6615	−	20.1798i	−0.478970	−	0.659245i	0.499337	−	0.866408i	$-0.333577\pi$
$937$	−14.6615	−	20.1798i	−0.478970	−	0.659245i	−0.978306	+	0.207163i	$0.933577\pi$
$938$	−6.19154	+	2.01175i	−0.202161	+	0.0656861i
$939$		0			0
$940$	−22.6789	−	16.4772i	−0.739703	−	0.537426i
$941$	11.8943	+	8.64168i	0.387742	+	0.281711i	0.764529	−	0.644589i	$-0.222971\pi$
$941$	11.8943	+	8.64168i	0.387742	+	0.281711i	−0.376788	+	0.926300i	$0.622971\pi$
$942$		0			0
$943$	5.75730	−	1.87066i	0.187483	−	0.0609171i
$944$	−2.75750	−	3.79538i	−0.0897491	−	0.123529i
$945$		0			0
$946$	2.25222	−	4.37932i	0.0732261	−	0.142384i
$947$		−	39.7249i		−	1.29089i	−0.763808	−	0.645443i	$-0.776673\pi$
$947$		−	39.7249i		−	1.29089i	0.763808	−	0.645443i	$-0.223327\pi$
$948$		0			0
$949$	8.55106	+	26.3175i	0.277579	+	0.854301i
$950$	67.4021	+	21.9003i	2.18681	+	0.710538i
$951$		0			0
$952$	−4.08157	+	5.61780i	−0.132284	+	0.182074i
$953$	−9.12777	+	28.0924i	−0.295677	+	0.910002i	0.687316	+	0.726359i	$0.258789\pi$
$953$	−9.12777	+	28.0924i	−0.295677	+	0.910002i	−0.982993	+	0.183643i	$0.941211\pi$
$954$		0			0
$955$	72.1736	−	52.4372i	2.33548	−	1.69683i
$956$	−23.1087			−0.747388
$957$		0			0
$958$	−36.9172			−1.19274
$959$	−4.01140	+	2.91445i	−0.129535	+	0.0941126i
$960$		0			0
$961$	−5.66274	+	17.4281i	−0.182669	+	0.562198i
$962$	8.96580	−	12.3404i	0.289069	−	0.397869i
$963$		0			0
$964$	6.04369	+	1.96371i	0.194654	+	0.0632470i
$965$	−4.81092	−	14.8065i	−0.154869	−	0.476638i
$966$		0			0
$967$		−	26.8746i		−	0.864229i	−0.901819	−	0.432115i	$-0.857768\pi$
$967$		−	26.8746i		−	0.864229i	0.901819	−	0.432115i	$-0.142232\pi$
$968$	−10.4357	−	3.47801i	−0.335415	−	0.111788i
$969$		0			0
$970$	−0.0398730	−	0.0548805i	−0.00128025	−	0.00176211i
$971$	26.5225	−	8.61770i	0.851149	−	0.276555i	0.149222	−	0.988804i	$-0.452323\pi$
$971$	26.5225	−	8.61770i	0.851149	−	0.276555i	0.701927	+	0.712249i	$0.252323\pi$
$972$		0			0
$973$	−3.99104	−	2.89966i	−0.127947	−	0.0929589i
$974$	29.3722	+	21.3401i	0.941146	+	0.683782i
$975$		0			0
$976$	11.4499	−	3.72031i	0.366503	−	0.119084i
$977$	18.9072	+	26.0236i	0.604896	+	0.832568i	0.996145	−	0.0877170i	$-0.0279571\pi$
$977$	18.9072	+	26.0236i	0.604896	+	0.832568i	−0.391250	+	0.920285i	$0.627957\pi$
$978$		0			0
$979$	−5.10781	+	2.57834i	−0.163246	+	0.0824040i
$980$			3.79051i			0.121083i
$981$		0			0
$982$	−12.3440	−	37.9909i	−0.393913	−	1.21234i
$983$	−0.175583	−	0.0570505i	−0.00560024	−	0.00181963i	0.306216	−	0.951962i	$-0.400937\pi$
$983$	−0.175583	−	0.0570505i	−0.00560024	−	0.00181963i	−0.311816	+	0.950143i	$0.600937\pi$
$984$		0			0
$985$	55.6992	−	76.6633i	1.77472	−	2.44270i
$986$	6.82969	−	21.0196i	0.217502	−	0.669402i
$987$		0			0
$988$	17.7994	−	12.9320i	0.566273	−	0.411421i
$989$	11.7338			0.373113
$990$		0			0
$991$	6.72640			0.213671			0.106835	−	0.994277i	$-0.465928\pi$
$991$	6.72640			0.213671			0.106835	+	0.994277i	$0.465928\pi$
$992$	−2.88026	+	2.09263i	−0.0914483	+	0.0664411i
$993$		0			0
$994$	0.485210	−	1.49332i	0.0153899	−	0.0473654i
$995$	−48.3873	+	66.5994i	−1.53398	+	2.11134i
$996$		0			0
$997$	−39.5867	−	12.8625i	−1.25372	−	0.407359i	−0.394469	−	0.918909i	$-0.629071\pi$
$997$	−39.5867	−	12.8625i	−1.25372	−	0.407359i	−0.859253	+	0.511550i	$0.829071\pi$
$998$	−0.820335	−	2.52473i	−0.0259673	−	0.0799190i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.a.701.2	✓	48
3.2	odd	2		1386.2.bu.b.701.11	yes	48
11.7	odd	10		1386.2.bu.b.953.11	yes	48
33.29	even	10	inner	1386.2.bu.a.953.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.701.2	✓	48	1.1	even	1	trivial
1386.2.bu.a.953.2	yes	48	33.29	even	10	inner
1386.2.bu.b.701.11	yes	48	3.2	odd	2
1386.2.bu.b.953.11	yes	48	11.7	odd	10

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-2.22800 + 3.06659i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-2.22800 + 3.06659i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} -3.79051i q^{10} +(1.49456 + 2.96079i) q^{11} +(1.70940 + 2.35278i) q^{13} +(-0.951057 + 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(5.61780 + 4.08157i) q^{17} +(7.19497 - 2.33779i) q^{19} +(2.22800 + 3.06659i) q^{20} +(-2.94943 - 1.51685i) q^{22} -7.90260i q^{23} +(-2.89485 - 8.90945i) q^{25} +(-2.76586 - 0.898683i) q^{26} +(0.587785 - 0.809017i) q^{28} +(-0.983541 + 3.02703i) q^{29} +(-2.88026 + 2.09263i) q^{31} +1.00000 q^{32} -6.94398 q^{34} +(-3.06659 + 2.22800i) q^{35} +(-1.62080 + 4.98830i) q^{37} +(-4.44673 + 6.12040i) q^{38} +(-3.60499 - 1.17133i) q^{40} +(0.236715 + 0.728533i) q^{41} +1.48480i q^{43} +(3.27773 - 0.506474i) q^{44} +(4.64503 + 6.39334i) q^{46} +(-7.03352 + 2.28533i) q^{47} +(0.809017 + 0.587785i) q^{49} +(7.57883 + 5.50634i) q^{50} +(2.76586 - 0.898683i) q^{52} +(2.22124 + 3.05727i) q^{53} +(-12.4094 - 2.01347i) q^{55} +1.00000i q^{56} +(-0.983541 - 3.02703i) q^{58} +(4.46174 + 1.44971i) q^{59} +(-7.07645 + 9.73989i) q^{61} +(1.10016 - 3.38595i) q^{62} +(-0.809017 + 0.587785i) q^{64} -11.0236 q^{65} +6.51017 q^{67} +(5.61780 - 4.08157i) q^{68} +(1.17133 - 3.60499i) q^{70} +(-0.922925 + 1.27030i) q^{71} +(9.04940 + 2.94033i) q^{73} +(-1.62080 - 4.98830i) q^{74} -7.56524i q^{76} +(0.506474 + 3.27773i) q^{77} +(-6.86292 - 9.44600i) q^{79} +(3.60499 - 1.17133i) q^{80} +(-0.619727 - 0.450258i) q^{82} +(-10.7827 - 7.83409i) q^{83} +(-25.0330 + 8.13370i) q^{85} +(-0.872744 - 1.20123i) q^{86} +(-2.35404 + 2.33634i) q^{88} +1.72515i q^{89} +(0.898683 + 2.76586i) q^{91} +(-7.51582 - 2.44204i) q^{92} +(4.34695 - 5.98307i) q^{94} +(-8.86140 + 27.2726i) q^{95} +(0.0144784 - 0.0105192i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

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