LMFDB - Embedded newform 1386.2.bu.a.827.1

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			827.1
Character	$\chi$	$=$	1386.827
Dual form			1386.2.bu.a.1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-4.02756 + 1.30863i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-4.02756 + 1.30863i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +4.23483i q^{10} +(2.00931 + 2.63869i) q^{11} +(-0.133072 - 0.0432377i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(0.224858 + 0.692041i) q^{17} +(3.29620 + 4.53683i) q^{19} +(4.02756 + 1.30863i) q^{20} +(3.13045 - 1.09557i) q^{22} -8.26728i q^{23} +(10.4636 - 7.60227i) q^{25} +(-0.0822429 + 0.113198i) q^{26} +(-0.951057 + 0.309017i) q^{28} +(-6.86734 - 4.98941i) q^{29} +(3.04858 - 9.38256i) q^{31} +1.00000 q^{32} +0.727655 q^{34} +(-1.30863 + 4.02756i) q^{35} +(-8.44666 - 6.13685i) q^{37} +(5.33337 - 1.73292i) q^{38} +(2.48917 - 3.42605i) q^{40} +(-3.05819 + 2.22191i) q^{41} -0.646564i q^{43} +(-0.0745868 - 3.31579i) q^{44} +(-7.86265 - 2.55473i) q^{46} +(6.10602 + 8.40422i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-3.99675 - 12.3007i) q^{50} +(0.0822429 + 0.113198i) q^{52} +(-2.86903 - 0.932206i) q^{53} +(-11.5457 - 7.99801i) q^{55} +1.00000i q^{56} +(-6.86734 + 4.98941i) q^{58} +(0.186609 - 0.256846i) q^{59} +(5.69261 - 1.84964i) q^{61} +(-7.98128 - 5.79874i) q^{62} +(0.309017 - 0.951057i) q^{64} +0.592537 q^{65} +4.47223 q^{67} +(0.224858 - 0.692041i) q^{68} +(3.42605 + 2.48917i) q^{70} +(5.39970 - 1.75447i) q^{71} +(8.32039 - 11.4520i) q^{73} +(-8.44666 + 6.13685i) q^{74} -5.60783i q^{76} +(3.31579 - 0.0745868i) q^{77} +(-2.12057 - 0.689016i) q^{79} +(-2.48917 - 3.42605i) q^{80} +(1.16813 + 3.59512i) q^{82} +(-1.04414 - 3.21352i) q^{83} +(-1.81126 - 2.49298i) q^{85} +(-0.614919 - 0.199799i) q^{86} +(-3.17655 - 0.953698i) q^{88} -8.13826i q^{89} +(-0.113198 + 0.0822429i) q^{91} +(-4.85939 + 6.68837i) q^{92} +(9.87975 - 3.21013i) q^{94} +(-19.2127 - 13.9588i) q^{95} +(2.96557 - 9.12709i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−4.02756	+	1.30863i	−1.80118	+	0.585239i	−0.999915	−	0.0130713i	$-0.995839\pi$
$5$	−4.02756	+	1.30863i	−1.80118	+	0.585239i	−0.801265	+	0.598310i	$0.795839\pi$
$6$		0			0
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$			4.23483i			1.33917i
$11$	2.00931	+	2.63869i	0.605830	+	0.795594i
$11$	2.00931	+	2.63869i	0.605830	+	0.795594i
$12$		0			0
$13$	−0.133072	−	0.0432377i	−0.0369075	−	0.0119920i	0.290505	−	0.956873i	$-0.406177\pi$
$13$	−0.133072	−	0.0432377i	−0.0369075	−	0.0119920i	−0.327413	+	0.944881i	$0.606177\pi$
$14$	−0.587785	−	0.809017i	−0.157092	−	0.216219i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.224858	+	0.692041i	0.0545360	+	0.167845i	0.974615	−	0.223889i	$-0.0718754\pi$
$17$	0.224858	+	0.692041i	0.0545360	+	0.167845i	−0.920079	+	0.391734i	$0.871875\pi$
$18$		0			0
$19$	3.29620	+	4.53683i	0.756200	+	1.04082i	0.997521	+	0.0703750i	$0.0224196\pi$
$19$	3.29620	+	4.53683i	0.756200	+	1.04082i	−0.241320	+	0.970446i	$0.577580\pi$
$20$	4.02756	+	1.30863i	0.900590	+	0.292619i
$21$		0			0
$22$	3.13045	−	1.09557i	0.667414	−	0.233576i
$23$		−	8.26728i		−	1.72385i	−0.507038	−	0.861924i	$-0.669260\pi$
$23$		−	8.26728i		−	1.72385i	0.507038	−	0.861924i	$-0.330740\pi$
$24$		0			0
$25$	10.4636	−	7.60227i	2.09273	−	1.52045i
$26$	−0.0822429	+	0.113198i	−0.0161292	+	0.0221999i
$27$		0			0
$28$	−0.951057	+	0.309017i	−0.179733	+	0.0583987i
$29$	−6.86734	−	4.98941i	−1.27523	−	0.926510i	−0.275834	−	0.961205i	$-0.588954\pi$
$29$	−6.86734	−	4.98941i	−1.27523	−	0.926510i	−0.999398	+	0.0346948i	$0.988954\pi$
$30$		0			0
$31$	3.04858	−	9.38256i	0.547541	−	1.68516i	−0.167330	−	0.985901i	$-0.553515\pi$
$31$	3.04858	−	9.38256i	0.547541	−	1.68516i	0.714871	−	0.699256i	$-0.246485\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	0.727655			0.124792
$35$	−1.30863	+	4.02756i	−0.221199	+	0.680782i
$36$		0			0
$37$	−8.44666	−	6.13685i	−1.38862	−	1.00889i	−0.996015	−	0.0891862i	$-0.971573\pi$
$37$	−8.44666	−	6.13685i	−1.38862	−	1.00889i	−0.392607	−	0.919706i	$-0.628427\pi$
$38$	5.33337	−	1.73292i	0.865186	−	0.281116i
$39$		0			0
$40$	2.48917	−	3.42605i	0.393572	−	0.541706i
$41$	−3.05819	+	2.22191i	−0.477609	+	0.347004i	−0.800399	−	0.599467i	$-0.795379\pi$
$41$	−3.05819	+	2.22191i	−0.477609	+	0.347004i	0.322790	+	0.946471i	$0.395379\pi$
$42$		0			0
$43$		−	0.646564i		−	0.0986001i	−0.998784	−	0.0493001i	$-0.984301\pi$
$43$		−	0.646564i		−	0.0986001i	0.998784	−	0.0493001i	$-0.0156991\pi$
$44$	−0.0745868	−	3.31579i	−0.0112444	−	0.499874i
$45$		0			0
$46$	−7.86265	−	2.55473i	−1.15929	−	0.376675i
$47$	6.10602	+	8.40422i	0.890655	+	1.22588i	0.973354	+	0.229306i	$0.0736458\pi$
$47$	6.10602	+	8.40422i	0.890655	+	1.22588i	−0.0826996	+	0.996575i	$0.526354\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$	−3.99675	−	12.3007i	−0.565226	−	1.73959i
$51$		0			0
$52$	0.0822429	+	0.113198i	0.0114050	+	0.0156977i
$53$	−2.86903	−	0.932206i	−0.394092	−	0.128048i	0.105266	−	0.994444i	$-0.466431\pi$
$53$	−2.86903	−	0.932206i	−0.394092	−	0.128048i	−0.499358	+	0.866396i	$0.666431\pi$
$54$		0			0
$55$	−11.5457	−	7.99801i	−1.55682	−	1.07845i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−6.86734	+	4.98941i	−0.901725	+	0.655142i
$59$	0.186609	−	0.256846i	0.0242945	−	0.0334385i	−0.796697	−	0.604379i	$-0.793421\pi$
$59$	0.186609	−	0.256846i	0.0242945	−	0.0334385i	0.820991	+	0.570940i	$0.193421\pi$
$60$		0			0
$61$	5.69261	−	1.84964i	0.728864	−	0.236822i	0.0790018	−	0.996874i	$-0.474827\pi$
$61$	5.69261	−	1.84964i	0.728864	−	0.236822i	0.649862	+	0.760052i	$0.274827\pi$
$62$	−7.98128	−	5.79874i	−1.01362	−	0.736441i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.592537			0.0734952
$66$		0			0
$67$	4.47223			0.546370			0.273185	−	0.961961i	$-0.411923\pi$
$67$	4.47223			0.546370			0.273185	+	0.961961i	$0.411923\pi$
$68$	0.224858	−	0.692041i	0.0272680	−	0.0839223i
$69$		0			0
$70$	3.42605	+	2.48917i	0.409491	+	0.297513i
$71$	5.39970	−	1.75447i	0.640827	−	0.208217i	0.0294617	−	0.999566i	$-0.490621\pi$
$71$	5.39970	−	1.75447i	0.640827	−	0.208217i	0.611365	+	0.791349i	$0.290621\pi$
$72$		0			0
$73$	8.32039	−	11.4520i	0.973829	−	1.34036i	0.0337396	−	0.999431i	$-0.489258\pi$
$73$	8.32039	−	11.4520i	0.973829	−	1.34036i	0.940089	−	0.340929i	$-0.110742\pi$
$74$	−8.44666	+	6.13685i	−0.981904	+	0.713395i
$75$		0			0
$76$		−	5.60783i		−	0.643262i
$77$	3.31579	−	0.0745868i	0.377869	−	0.00849995i
$78$		0			0
$79$	−2.12057	−	0.689016i	−0.238583	−	0.0775204i	0.187285	−	0.982306i	$-0.440031\pi$
$79$	−2.12057	−	0.689016i	−0.238583	−	0.0775204i	−0.425868	+	0.904785i	$0.640031\pi$
$80$	−2.48917	−	3.42605i	−0.278298	−	0.383044i
$81$		0			0
$82$	1.16813	+	3.59512i	0.128998	+	0.397015i
$83$	−1.04414	−	3.21352i	−0.114609	−	0.352730i	0.877256	−	0.480022i	$-0.159371\pi$
$83$	−1.04414	−	3.21352i	−0.114609	−	0.352730i	−0.991865	+	0.127292i	$0.959371\pi$
$84$		0			0
$85$	−1.81126	−	2.49298i	−0.196458	−	0.270402i
$86$	−0.614919	−	0.199799i	−0.0663085	−	0.0215449i
$87$		0			0
$88$	−3.17655	−	0.953698i	−0.338621	−	0.101665i
$89$		−	8.13826i		−	0.862654i	−0.902196	−	0.431327i	$-0.858046\pi$
$89$		−	8.13826i		−	0.862654i	0.902196	−	0.431327i	$-0.141954\pi$
$90$		0			0
$91$	−0.113198	+	0.0822429i	−0.0118663	+	0.00862140i
$92$	−4.85939	+	6.68837i	−0.506626	+	0.697311i
$93$		0			0
$94$	9.87975	−	3.21013i	1.01902	−	0.331099i
$95$	−19.2127	−	13.9588i	−1.97118	−	1.43215i
$96$		0			0
$97$	2.96557	−	9.12709i	0.301108	−	0.926715i	−0.679993	−	0.733219i	$-0.738017\pi$
$97$	2.96557	−	9.12709i	0.301108	−	0.926715i	0.981101	−	0.193497i	$-0.0619829\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	−12.9338			−1.29338
$101$	−1.58140	+	4.86706i	−0.157356	+	0.484291i	−0.998392	−	0.0566879i	$-0.981946\pi$
$101$	−1.58140	+	4.86706i	−0.157356	+	0.484291i	0.841036	+	0.540979i	$0.181946\pi$
$102$		0			0
$103$	2.89436	+	2.10287i	0.285189	+	0.207202i	0.721178	−	0.692750i	$-0.243601\pi$
$103$	2.89436	+	2.10287i	0.285189	+	0.207202i	−0.435988	+	0.899952i	$0.643601\pi$
$104$	0.133072	−	0.0432377i	0.0130488	−	0.00423980i
$105$		0			0
$106$	−1.77316	+	2.44055i	−0.172225	+	0.237047i
$107$	15.2718	−	11.0956i	1.47638	−	1.07265i	0.497682	−	0.867360i	$-0.334185\pi$
$107$	15.2718	−	11.0956i	1.47638	−	1.07265i	0.978700	−	0.205295i	$-0.0658153\pi$
$108$		0			0
$109$		−	6.73203i		−	0.644812i	−0.946602	−	0.322406i	$-0.895508\pi$
$109$		−	6.73203i		−	0.644812i	0.946602	−	0.322406i	$-0.104492\pi$
$110$	−11.1744	+	8.50909i	−1.06544	+	0.811310i
$111$		0			0
$112$	0.951057	+	0.309017i	0.0898664	+	0.0291994i
$113$	−3.17677	−	4.37245i	−0.298845	−	0.411325i	0.633017	−	0.774138i	$-0.281816\pi$
$113$	−3.17677	−	4.37245i	−0.298845	−	0.411325i	−0.931862	+	0.362813i	$0.881816\pi$
$114$		0			0
$115$	10.8188	+	33.2970i	1.00886	+	3.10496i
$116$	2.62309	+	8.07304i	0.243548	+	0.749563i
$117$		0			0
$118$	−0.186609	−	0.256846i	−0.0171788	−	0.0236446i
$119$	0.692041	+	0.224858i	0.0634393	+	0.0206127i
$120$		0			0
$121$	−2.92533	+	10.6039i	−0.265939	+	0.963990i
$122$		−	5.98556i		−	0.541907i
$123$		0			0
$124$	−7.98128	+	5.79874i	−0.716740	+	0.520742i
$125$	−19.7485	+	27.1814i	−1.76636	+	2.43118i
$126$		0			0
$127$	9.53079	−	3.09674i	0.845721	−	0.274791i	0.146068	−	0.989275i	$-0.453338\pi$
$127$	9.53079	−	3.09674i	0.845721	−	0.274791i	0.699653	+	0.714483i	$0.253338\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	0.183104	−	0.563536i	0.0160593	−	0.0494254i
$131$	7.06257			0.617059			0.308530	−	0.951215i	$-0.400163\pi$
$131$	7.06257			0.617059			0.308530	+	0.951215i	$0.400163\pi$
$132$		0			0
$133$	5.60783			0.486261
$134$	1.38200	−	4.25335i	0.119386	−	0.367433i
$135$		0			0
$136$	−0.588685	−	0.427705i	−0.0504793	−	0.0366754i
$137$	14.7257	−	4.78466i	1.25810	−	0.408781i	0.397282	−	0.917697i	$-0.369954\pi$
$137$	14.7257	−	4.78466i	1.25810	−	0.408781i	0.860816	+	0.508916i	$0.169954\pi$
$138$		0			0
$139$	−9.89522	+	13.6196i	−0.839302	+	1.15520i	0.146818	+	0.989164i	$0.453097\pi$
$139$	−9.89522	+	13.6196i	−0.839302	+	1.15520i	−0.986120	+	0.166036i	$0.946903\pi$
$140$	3.42605	−	2.48917i	0.289554	−	0.210373i
$141$		0			0
$142$		−	5.67758i		−	0.476452i
$143$	−0.153292	−	0.438013i	−0.0128189	−	0.0366285i
$144$		0			0
$145$	34.1879	+	11.1083i	2.83915	+	0.922496i
$146$	−8.32039	−	11.4520i	−0.688601	−	0.947778i
$147$		0			0
$148$	3.22634	+	9.92964i	0.265203	+	0.816211i
$149$	−4.75648	−	14.6389i	−0.389666	−	1.19927i	−0.933038	−	0.359777i	$-0.882853\pi$
$149$	−4.75648	−	14.6389i	−0.389666	−	1.19927i	0.543372	−	0.839492i	$-0.317147\pi$
$150$		0			0
$151$	10.4405	+	14.3702i	0.849639	+	1.16943i	0.983942	+	0.178487i	$0.0571203\pi$
$151$	10.4405	+	14.3702i	0.849639	+	1.16943i	−0.134303	+	0.990940i	$0.542880\pi$
$152$	−5.33337	−	1.73292i	−0.432593	−	0.140558i
$153$		0			0
$154$	0.953698	−	3.17655i	0.0768512	−	0.255974i
$155$			41.7783i			3.35571i
$156$		0			0
$157$	−4.77656	+	3.47037i	−0.381211	+	0.276966i	−0.761844	−	0.647760i	$-0.775706\pi$
$157$	−4.77656	+	3.47037i	−0.381211	+	0.276966i	0.380634	+	0.924726i	$0.375706\pi$
$158$	−1.31059	+	1.80387i	−0.104265	+	0.143508i
$159$		0			0
$160$	−4.02756	+	1.30863i	−0.318407	+	0.103457i
$161$	−6.68837	−	4.85939i	−0.527118	−	0.382973i
$162$		0			0
$163$	1.21569	−	3.74151i	0.0952202	−	0.293058i	−0.892091	−	0.451856i	$-0.850762\pi$
$163$	1.21569	−	3.74151i	0.0952202	−	0.293058i	0.987311	+	0.158799i	$0.0507620\pi$
$164$	3.78013			0.295179
$165$		0			0
$166$	−3.37889			−0.262253
$167$	4.08535	−	12.5734i	0.316134	−	0.972960i	−0.659151	−	0.752010i	$-0.729084\pi$
$167$	4.08535	−	12.5734i	0.316134	−	0.972960i	0.975285	−	0.220950i	$-0.0709156\pi$
$168$		0			0
$169$	−10.5014	−	7.62970i	−0.807799	−	0.586900i
$170$	−2.93067	+	0.952233i	−0.224772	+	0.0730330i
$171$		0			0
$172$	−0.380041	+	0.523082i	−0.0289779	+	0.0398846i
$173$	−2.22772	+	1.61854i	−0.169371	+	0.123055i	−0.669241	−	0.743045i	$-0.733381\pi$
$173$	−2.22772	+	1.61854i	−0.169371	+	0.123055i	0.499871	+	0.866100i	$0.333381\pi$
$174$		0			0
$175$		−	12.9338i		−	0.977700i
$176$	−1.88863	+	2.72637i	−0.142361	+	0.205508i
$177$		0			0
$178$	−7.73994	−	2.51486i	−0.580133	−	0.188497i
$179$	3.01632	+	4.15161i	0.225450	+	0.310306i	0.906725	−	0.421722i	$-0.138574\pi$
$179$	3.01632	+	4.15161i	0.225450	+	0.310306i	−0.681275	+	0.732028i	$0.738574\pi$
$180$		0			0
$181$	5.09295	+	15.6745i	0.378556	+	1.16508i	0.941048	+	0.338273i	$0.109843\pi$
$181$	5.09295	+	15.6745i	0.378556	+	1.16508i	−0.562492	+	0.826803i	$0.690157\pi$
$182$	0.0432377	+	0.133072i	0.00320499	+	0.00986394i
$183$		0			0
$184$	4.85939	+	6.68837i	0.358239	+	0.493073i
$185$	42.0503	+	13.6630i	3.09160	+	1.00452i
$186$		0			0
$187$	−1.37427	+	1.98386i	−0.100497	+	0.145074i
$188$		−	10.3882i		−	0.757636i
$189$		0			0
$190$	−19.2127	+	13.9588i	−1.39384	+	1.01268i
$191$	9.97313	−	13.7268i	0.721631	−	0.993239i	−0.277837	−	0.960628i	$-0.589618\pi$
$191$	9.97313	−	13.7268i	0.721631	−	0.993239i	0.999468	−	0.0326113i	$-0.0103823\pi$
$192$		0			0
$193$	−11.9051	+	3.86819i	−0.856945	+	0.278438i	−0.704352	−	0.709851i	$-0.748762\pi$
$193$	−11.9051	+	3.86819i	−0.856945	+	0.278438i	−0.152593	+	0.988289i	$0.548762\pi$
$194$	−7.76396	−	5.64085i	−0.557420	−	0.404989i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	−14.9105			−1.06233			−0.531164	−	0.847269i	$-0.678245\pi$
$197$	−14.9105			−1.06233			−0.531164	+	0.847269i	$0.678245\pi$
$198$		0			0
$199$	−21.0496			−1.49216			−0.746082	−	0.665854i	$-0.768067\pi$
$199$	−21.0496			−1.49216			−0.746082	+	0.665854i	$0.768067\pi$
$200$	−3.99675	+	12.3007i	−0.282613	+	0.869793i
$201$		0			0
$202$	4.14017	+	3.00801i	0.291301	+	0.211643i
$203$	−8.07304	+	2.62309i	−0.566616	+	0.184105i
$204$		0			0
$205$	9.40939	−	12.9509i	0.657180	−	0.904531i
$206$	2.89436	−	2.10287i	0.201659	−	0.146514i
$207$		0			0
$208$		−	0.139920i		−	0.00970171i
$209$	−5.34818	+	17.8136i	−0.369941	+	1.23219i
$210$		0			0
$211$	−16.5902	−	5.39047i	−1.14211	−	0.371095i	−0.323947	−	0.946075i	$-0.605010\pi$
$211$	−16.5902	−	5.39047i	−1.14211	−	0.371095i	−0.818168	+	0.574980i	$0.805010\pi$
$212$	1.77316	+	2.44055i	0.121781	+	0.167617i
$213$		0			0
$214$	−5.83331	−	17.9531i	−0.398757	−	1.22725i
$215$	0.846116	+	2.60408i	0.0577046	+	0.177597i
$216$		0			0
$217$	−5.79874	−	7.98128i	−0.393644	−	0.541805i
$218$	−6.40254	−	2.08031i	−0.433635	−	0.140897i
$219$		0			0
$220$	4.63955	+	13.2569i	0.312798	+	0.893781i
$221$		−	0.101813i		−	0.00684872i
$222$		0			0
$223$	−6.57824	+	4.77937i	−0.440512	+	0.320051i	−0.785838	−	0.618432i	$-0.787768\pi$
$223$	−6.57824	+	4.77937i	−0.440512	+	0.320051i	0.345326	+	0.938483i	$0.387768\pi$
$224$	0.587785	−	0.809017i	0.0392731	−	0.0540547i
$225$		0			0
$226$	−5.14012	+	1.67013i	−0.341916	+	0.111095i
$227$	0.0179059	+	0.0130094i	0.00118846	+	0.000863465i	0.588379	−	0.808585i	$-0.299766\pi$
$227$	0.0179059	+	0.0130094i	0.00118846	+	0.000863465i	−0.587191	+	0.809449i	$0.699766\pi$
$228$		0			0
$229$	−0.295195	+	0.908517i	−0.0195070	+	0.0600365i	−0.960336	−	0.278845i	$-0.910048\pi$
$229$	−0.295195	+	0.908517i	−0.0195070	+	0.0600365i	0.940829	+	0.338881i	$0.110048\pi$
$230$	35.0105			2.30852
$231$		0			0
$232$	8.48849			0.557297
$233$	−4.12318	+	12.6898i	−0.270119	+	0.831340i	0.720351	+	0.693610i	$0.243981\pi$
$233$	−4.12318	+	12.6898i	−0.270119	+	0.831340i	−0.990470	+	0.137730i	$0.956019\pi$
$234$		0			0
$235$	−35.5904	−	25.8579i	−2.32166	−	1.68679i
$236$	−0.301940	+	0.0981063i	−0.0196546	+	0.00638618i
$237$		0			0
$238$	0.427705	−	0.588685i	0.0277240	−	0.0381588i
$239$	1.25149	−	0.909258i	0.0809519	−	0.0588150i	−0.546573	−	0.837411i	$-0.684068\pi$
$239$	1.25149	−	0.909258i	0.0809519	−	0.0588150i	0.627525	+	0.778596i	$0.284068\pi$
$240$		0			0
$241$			28.2376i			1.81894i	0.415768	+	0.909471i	$0.363513\pi$
$241$			28.2376i			1.81894i	−0.415768	+	0.909471i	$0.636487\pi$
$242$	9.18092	+	6.05894i	0.590172	+	0.389483i
$243$		0			0
$244$	−5.69261	−	1.84964i	−0.364432	−	0.118411i
$245$	2.48917	+	3.42605i	0.159027	+	0.218882i
$246$		0			0
$247$	−0.242470	−	0.746245i	−0.0154280	−	0.0474824i
$248$	3.04858	+	9.38256i	0.193585	+	0.595793i
$249$		0			0
$250$	19.7485	+	27.1814i	1.24900	+	1.71910i
$251$	−16.5724	−	5.38469i	−1.04604	−	0.339878i	−0.264926	−	0.964269i	$-0.585347\pi$
$251$	−16.5724	−	5.38469i	−1.04604	−	0.339878i	−0.781112	+	0.624391i	$0.785347\pi$
$252$		0			0
$253$	21.8148	−	16.6116i	1.37148	−	1.04436i
$254$		−	10.0213i		−	0.628790i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.63064	−	2.24438i	0.101716	−	0.140000i	−0.755125	−	0.655581i	$-0.772424\pi$
$257$	1.63064	−	2.24438i	0.101716	−	0.140000i	0.856841	+	0.515581i	$0.172424\pi$
$258$		0			0
$259$	−9.92964	+	3.22634i	−0.616998	+	0.200475i
$260$	−0.479372	−	0.348285i	−0.0297294	−	0.0215997i
$261$		0			0
$262$	2.18245	−	6.71690i	0.134832	−	0.414972i
$263$	7.55074			0.465599			0.232799	−	0.972525i	$-0.425211\pi$
$263$	7.55074			0.465599			0.232799	+	0.972525i	$0.425211\pi$
$264$		0			0
$265$	12.7751			0.784770
$266$	1.73292	−	5.33337i	0.106252	−	0.327010i
$267$		0			0
$268$	−3.61811	−	2.62871i	−0.221011	−	0.160574i
$269$	17.4914	−	5.68331i	1.06647	−	0.346518i	0.277359	−	0.960766i	$-0.410541\pi$
$269$	17.4914	−	5.68331i	1.06647	−	0.346518i	0.789113	+	0.614249i	$0.210541\pi$
$270$		0			0
$271$	3.28057	−	4.51531i	0.199280	−	0.274286i	−0.697668	−	0.716421i	$-0.745779\pi$
$271$	3.28057	−	4.51531i	0.199280	−	0.274286i	0.896948	+	0.442135i	$0.145779\pi$
$272$	−0.588685	+	0.427705i	−0.0356943	+	0.0259334i
$273$		0			0
$274$		−	15.4835i		−	0.935391i
$275$	41.0847	+	12.3349i	2.47750	+	0.743822i
$276$		0			0
$277$	17.1212	+	5.56301i	1.02871	+	0.334249i	0.774281	−	0.632842i	$-0.218112\pi$
$277$	17.1212	+	5.56301i	1.02871	+	0.334249i	0.254432	+	0.967091i	$0.418112\pi$
$278$	9.89522	+	13.6196i	0.593476	+	0.816850i
$279$		0			0
$280$	−1.30863	−	4.02756i	−0.0782058	−	0.240693i
$281$	−3.91648	−	12.0537i	−0.233638	−	0.719062i	−0.997299	−	0.0734458i	$-0.976600\pi$
$281$	−3.91648	−	12.0537i	−0.233638	−	0.719062i	0.763662	−	0.645617i	$-0.223400\pi$
$282$		0			0
$283$	−12.0414	−	16.5736i	−0.715786	−	0.985196i	−0.999653	−	0.0263318i	$-0.991617\pi$
$283$	−12.0414	−	16.5736i	−0.715786	−	0.985196i	0.283867	−	0.958864i	$-0.408383\pi$
$284$	−5.39970	−	1.75447i	−0.320413	−	0.104109i
$285$		0			0
$286$	−0.463945	+	0.0104362i	−0.0274336	+	0.000617104i
$287$			3.78013i			0.223134i
$288$		0			0
$289$	13.3249	−	9.68113i	0.783819	−	0.569478i
$290$	21.1293	−	29.0820i	1.24075	−	1.70775i
$291$		0			0
$292$	−13.4627	+	4.37429i	−0.787844	+	0.255986i
$293$	−7.39792	−	5.37490i	−0.432191	−	0.314005i	0.350333	−	0.936625i	$-0.386068\pi$
$293$	−7.39792	−	5.37490i	−0.432191	−	0.314005i	−0.782524	+	0.622620i	$0.786068\pi$
$294$		0			0
$295$	−0.415463	+	1.27866i	−0.0241892	+	0.0744467i
$296$	10.4406			0.606850
$297$		0			0
$298$	−15.3923			−0.891652
$299$	−0.357458	+	1.10014i	−0.0206723	+	0.0636229i
$300$		0			0
$301$	−0.523082	−	0.380041i	−0.0301499	−	0.0219052i
$302$	16.8931	−	5.48891i	0.972091	−	0.315852i
$303$		0			0
$304$	−3.29620	+	4.53683i	−0.189050	+	0.260205i
$305$	−20.5068	+	14.8991i	−1.17422	+	0.853118i
$306$		0			0
$307$		−	1.02796i		−	0.0586688i	−0.999570	−	0.0293344i	$-0.990661\pi$
$307$		−	1.02796i		−	0.0586688i	0.999570	−	0.0293344i	$-0.00933877\pi$
$308$	−2.72637	−	1.88863i	−0.155349	−	0.107615i
$309$		0			0
$310$	39.7335	+	12.9102i	2.25671	+	0.733250i
$311$	−1.94158	−	2.67236i	−0.110097	−	0.151536i	0.750413	−	0.660970i	$-0.229855\pi$
$311$	−1.94158	−	2.67236i	−0.110097	−	0.151536i	−0.860510	+	0.509434i	$0.829855\pi$
$312$		0			0
$313$	−0.0613196	−	0.188722i	−0.00346599	−	0.0106672i	0.949309	−	0.314346i	$-0.101785\pi$
$313$	−0.0613196	−	0.188722i	−0.00346599	−	0.0106672i	−0.952775	+	0.303679i	$0.901785\pi$
$314$	1.82448	+	5.61518i	0.102962	+	0.316883i
$315$		0			0
$316$	1.31059	+	1.80387i	0.0737263	+	0.101476i
$317$	32.4773	+	10.5525i	1.82410	+	0.592688i	0.999642	+	0.0267720i	$0.00852281\pi$
$317$	32.4773	+	10.5525i	1.82410	+	0.592688i	0.824463	+	0.565916i	$0.191477\pi$
$318$		0			0
$319$	−0.633129	−	28.1460i	−0.0354484	−	1.57588i
$320$			4.23483i			0.236734i
$321$		0			0
$322$	−6.68837	+	4.85939i	−0.372728	+	0.270803i
$323$	−2.39850	+	3.30125i	−0.133456	+	0.183686i
$324$		0			0
$325$	−1.72112	+	0.559225i	−0.0954705	+	0.0310202i
$326$	−3.18272	−	2.31238i	−0.176274	−	0.128071i
$327$		0			0
$328$	1.16813	−	3.59512i	0.0644989	−	0.198507i
$329$	10.3882			0.572719
$330$		0			0
$331$	2.96158			0.162783			0.0813915	−	0.996682i	$-0.474064\pi$
$331$	2.96158			0.162783			0.0813915	+	0.996682i	$0.474064\pi$
$332$	−1.04414	+	3.21352i	−0.0573044	+	0.176365i
$333$		0			0
$334$	−10.6956	−	7.77080i	−0.585236	−	0.425199i
$335$	−18.0122	+	5.85251i	−0.984111	+	0.319757i
$336$		0			0
$337$	−15.8927	+	21.8744i	−0.865731	+	1.19158i	0.114442	+	0.993430i	$0.463492\pi$
$337$	−15.8927	+	21.8744i	−0.865731	+	1.19158i	−0.980173	+	0.198146i	$0.936508\pi$
$338$	−10.5014	+	7.62970i	−0.571200	+	0.415001i
$339$		0			0
$340$			3.08149i			0.167117i
$341$	30.8832	−	10.8082i	1.67242	−	0.585299i
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.0513522	−	0.0166853i
$344$	0.380041	+	0.523082i	0.0204904	+	0.0282027i
$345$		0			0
$346$	0.850915	+	2.61885i	0.0457455	+	0.140790i
$347$	−8.54628	−	26.3027i	−0.458788	−	1.41200i	−0.866630	−	0.498952i	$-0.833718\pi$
$347$	−8.54628	−	26.3027i	−0.458788	−	1.41200i	0.407841	−	0.913053i	$-0.366282\pi$
$348$		0			0
$349$	−2.41257	−	3.32062i	−0.129142	−	0.177749i	0.739549	−	0.673102i	$-0.235039\pi$
$349$	−2.41257	−	3.32062i	−0.129142	−	0.177749i	−0.868692	+	0.495353i	$0.835039\pi$
$350$	−12.3007	−	3.99675i	−0.657502	−	0.213635i
$351$		0			0
$352$	2.00931	+	2.63869i	0.107097	+	0.140642i
$353$			3.96196i			0.210874i	0.994426	+	0.105437i	$0.0336241\pi$
$353$			3.96196i			0.210874i	−0.994426	+	0.105437i	$0.966376\pi$
$354$		0			0
$355$	−19.4517	+	14.1325i	−1.03239	+	0.750073i
$356$	−4.78355	+	6.58399i	−0.253528	+	0.348951i
$357$		0			0
$358$	4.88051	−	1.58577i	0.257943	−	0.0838108i
$359$	1.25114	+	0.909004i	0.0660324	+	0.0479754i	0.620312	−	0.784355i	$-0.287006\pi$
$359$	1.25114	+	0.909004i	0.0660324	+	0.0479754i	−0.554279	+	0.832331i	$0.687006\pi$
$360$		0			0
$361$	−3.84658	+	11.8385i	−0.202451	+	0.623081i
$362$	16.4811			0.866229
$363$		0			0
$364$	0.139920			0.00733380
$365$	−18.5244	+	57.0121i	−0.969609	+	2.98415i
$366$		0			0
$367$	4.34848	+	3.15935i	0.226989	+	0.164917i	0.695467	−	0.718558i	$-0.255198\pi$
$367$	4.34848	+	3.15935i	0.226989	+	0.164917i	−0.468478	+	0.883475i	$0.655198\pi$
$368$	7.86265	−	2.55473i	0.409869	−	0.133175i
$369$		0			0
$370$	25.9885	−	35.7701i	1.35108	−	1.85960i
$371$	−2.44055	+	1.77316i	−0.126707	+	0.0920579i
$372$		0			0
$373$			18.2659i			0.945773i	0.881123	+	0.472886i	$0.156788\pi$
$373$			18.2659i			0.945773i	−0.881123	+	0.472886i	$0.843212\pi$
$374$	1.46209	+	1.92005i	0.0756026	+	0.0992836i
$375$		0			0
$376$	−9.87975	−	3.21013i	−0.509509	−	0.165550i
$377$	0.698119	+	0.960878i	0.0359549	+	0.0494877i
$378$		0			0
$379$	−2.79256	−	8.59460i	−0.143444	−	0.441475i	0.853364	−	0.521316i	$-0.174559\pi$
$379$	−2.79256	−	8.59460i	−0.143444	−	0.441475i	−0.996808	+	0.0798410i	$0.974559\pi$
$380$	7.33860	+	22.5859i	0.376462	+	1.15863i
$381$		0			0
$382$	−9.97313	−	13.7268i	−0.510270	−	0.702326i
$383$	−28.2599	−	9.18219i	−1.44401	−	0.469188i	−0.520867	−	0.853638i	$-0.674391\pi$
$383$	−28.2599	−	9.18219i	−1.44401	−	0.469188i	−0.923146	+	0.384450i	$0.874391\pi$
$384$		0			0
$385$	−13.2569	+	4.63955i	−0.675635	+	0.236453i
$386$			12.5177i			0.637135i
$387$		0			0
$388$	−7.76396	+	5.64085i	−0.394156	+	0.286371i
$389$	8.96991	−	12.3460i	0.454793	−	0.625968i	−0.518626	−	0.855001i	$-0.673556\pi$
$389$	8.96991	−	12.3460i	0.454793	−	0.625968i	0.973419	+	0.229033i	$0.0735563\pi$
$390$		0			0
$391$	5.72130	−	1.85896i	0.289338	−	0.0940118i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$		0			0
$394$	−4.60760	+	14.1807i	−0.232127	+	0.714415i
$395$	9.44241			0.475099
$396$		0			0
$397$	−28.9797			−1.45445			−0.727226	−	0.686399i	$-0.759191\pi$
$397$	−28.9797			−1.45445			−0.727226	+	0.686399i	$0.759191\pi$
$398$	−6.50467	+	20.0193i	−0.326050	+	1.00348i
$399$		0			0
$400$	10.4636	+	7.60227i	0.523181	+	0.380114i
$401$	−28.1838	+	9.15746i	−1.40743	+	0.457302i	−0.911586	−	0.411110i	$-0.865141\pi$
$401$	−28.1838	+	9.15746i	−1.40743	+	0.457302i	−0.495844	+	0.868412i	$0.665141\pi$
$402$		0			0
$403$	−0.811360	+	1.11674i	−0.0404167	+	0.0556288i
$404$	4.14017	−	3.00801i	0.205981	−	0.149654i
$405$		0			0
$406$			8.48849i			0.421277i
$407$	−0.778734	−	34.6189i	−0.0386004	−	1.71600i
$408$		0			0
$409$	30.0631	+	9.76808i	1.48652	+	0.483001i	0.936054	−	0.351855i	$-0.114449\pi$
$409$	30.0631	+	9.76808i	1.48652	+	0.483001i	0.550469	+	0.834856i	$0.314449\pi$
$410$	−9.40939	−	12.9509i	−0.464697	−	0.639600i
$411$		0			0
$412$	−1.10555	−	3.40252i	−0.0544663	−	0.167630i
$413$	−0.0981063	−	0.301940i	−0.00482750	−	0.0148575i
$414$		0			0
$415$	8.41064	+	11.5763i	0.412862	+	0.568256i
$416$	−0.133072	−	0.0432377i	−0.00652438	−	0.00211990i
$417$		0			0
$418$	15.2890	+	10.5911i	0.747810	+	0.518028i
$419$			15.2788i			0.746420i	0.927747	+	0.373210i	$0.121743\pi$
$419$			15.2788i			0.746420i	−0.927747	+	0.373210i	$0.878257\pi$
$420$		0			0
$421$	2.73361	−	1.98608i	0.133228	−	0.0967958i	−0.519175	−	0.854668i	$-0.673761\pi$
$421$	2.73361	−	1.98608i	0.133228	−	0.0967958i	0.652403	+	0.757872i	$0.273761\pi$
$422$	−10.2533	+	14.1124i	−0.499122	+	0.686983i
$423$		0			0
$424$	2.86903	−	0.932206i	0.139333	−	0.0452719i
$425$	7.61391	+	5.53183i	0.369329	+	0.268333i
$426$		0			0
$427$	1.84964	−	5.69261i	0.0895104	−	0.275485i
$428$	−18.8770			−0.912454
$429$		0			0
$430$	2.73809			0.132042
$431$	−4.20003	+	12.9264i	−0.202308	+	0.622641i	0.797505	+	0.603313i	$0.206153\pi$
$431$	−4.20003	+	12.9264i	−0.202308	+	0.622641i	−0.999813	+	0.0193287i	$0.993847\pi$
$432$		0			0
$433$	−25.4577	−	18.4961i	−1.22342	−	0.888866i	−0.227040	−	0.973885i	$-0.572905\pi$
$433$	−25.4577	−	18.4961i	−1.22342	−	0.888866i	−0.996379	+	0.0850195i	$0.972905\pi$
$434$	−9.38256	+	3.04858i	−0.450377	+	0.146336i
$435$		0			0
$436$	−3.95699	+	5.44633i	−0.189505	+	0.260832i
$437$	37.5073	−	27.2506i	1.79422	−	1.30357i
$438$		0			0
$439$		−	0.833457i		−	0.0397787i	−0.999802	−	0.0198894i	$-0.993669\pi$
$439$		−	0.833457i		−	0.0397787i	0.999802	−	0.0198894i	$-0.00633140\pi$
$440$	14.0418	−	0.315862i	0.669416	−	0.0150581i
$441$		0			0
$442$	−0.0968304	−	0.0314621i	−0.00460575	−	0.00149650i
$443$	7.08566	+	9.75257i	0.336650	+	0.463359i	0.943459	−	0.331489i	$-0.107551\pi$
$443$	7.08566	+	9.75257i	0.336650	+	0.463359i	−0.606809	+	0.794847i	$0.707551\pi$
$444$		0			0
$445$	10.6500	+	32.7773i	0.504858	+	1.55379i
$446$	2.51267	+	7.73319i	0.118978	+	0.366177i
$447$		0			0
$448$	−0.587785	−	0.809017i	−0.0277702	−	0.0382225i
$449$	13.5835	+	4.41355i	0.641046	+	0.208288i	0.611462	−	0.791274i	$-0.290582\pi$
$449$	13.5835	+	4.41355i	0.641046	+	0.208288i	0.0295840	+	0.999562i	$0.490582\pi$
$450$		0			0
$451$	−12.0078	−	3.60511i	−0.565424	−	0.169758i
$452$			5.40464i			0.254213i
$453$		0			0
$454$	0.0179059	−	0.0130094i	0.000840366	−	0.000610562i
$455$	0.348285	−	0.479372i	0.0163278	−	0.0224733i
$456$		0			0
$457$	1.93932	−	0.630123i	0.0907175	−	0.0294759i	−0.263307	−	0.964712i	$-0.584813\pi$
$457$	1.93932	−	0.630123i	0.0907175	−	0.0294759i	0.354024	+	0.935236i	$0.384813\pi$
$458$	0.772830	+	0.561494i	0.0361120	+	0.0262369i
$459$		0			0
$460$	10.8188	−	33.2970i	0.504431	−	1.55248i
$461$	−0.898573			−0.0418507			−0.0209254	−	0.999781i	$-0.506661\pi$
$461$	−0.898573			−0.0418507			−0.0209254	+	0.999781i	$0.506661\pi$
$462$		0			0
$463$	3.56108			0.165498			0.0827488	−	0.996570i	$-0.473630\pi$
$463$	3.56108			0.165498			0.0827488	+	0.996570i	$0.473630\pi$
$464$	2.62309	−	8.07304i	0.121774	−	0.374781i
$465$		0			0
$466$	10.7946	+	7.84276i	0.500052	+	0.363309i
$467$	−17.1924	+	5.58616i	−0.795571	+	0.258497i	−0.678475	−	0.734624i	$-0.737359\pi$
$467$	−17.1924	+	5.58616i	−0.795571	+	0.258497i	−0.117096	+	0.993121i	$0.537359\pi$
$468$		0			0
$469$	2.62871	−	3.61811i	0.121383	−	0.167069i
$470$	−35.5904	+	25.8579i	−1.64166	+	1.19274i
$471$		0			0
$472$			0.317479i			0.0146131i
$473$	1.70608	−	1.29915i	0.0784457	−	0.0597350i
$474$		0			0
$475$	68.9805	+	22.4131i	3.16504	+	1.02838i
$476$	−0.427705	−	0.588685i	−0.0196038	−	0.0269823i
$477$		0			0
$478$	−0.478025	−	1.47121i	−0.0218644	−	0.0672916i
$479$	−11.2633	−	34.6650i	−0.514635	−	1.58388i	−0.783945	−	0.620830i	$-0.786796\pi$
$479$	−11.2633	−	34.6650i	−0.514635	−	1.58388i	0.269310	−	0.963054i	$-0.413204\pi$
$480$		0			0
$481$	0.858669	+	1.18186i	0.0391519	+	0.0538880i
$482$	26.8555	+	8.72589i	1.22324	+	0.397453i
$483$		0			0
$484$	8.59945	−	6.85926i	0.390884	−	0.311785i
$485$			40.6407i			1.84540i
$486$		0			0
$487$	6.94932	−	5.04898i	0.314904	−	0.228791i	−0.419094	−	0.907943i	$-0.637652\pi$
$487$	6.94932	−	5.04898i	0.314904	−	0.228791i	0.733998	+	0.679152i	$0.237652\pi$
$488$	−3.51823	+	4.84242i	−0.159263	+	0.219206i
$489$		0			0
$490$	4.02756	−	1.30863i	0.181947	−	0.0591180i
$491$	17.8445	+	12.9648i	0.805311	+	0.585092i	0.912467	−	0.409150i	$-0.134175\pi$
$491$	17.8445	+	12.9648i	0.805311	+	0.585092i	−0.107157	+	0.994242i	$0.534175\pi$
$492$		0			0
$493$	1.90870	−	5.87438i	0.0859637	−	0.264569i
$494$	−0.784648			−0.0353030
$495$		0			0
$496$	9.86541			0.442970
$497$	1.75447	−	5.39970i	0.0786987	−	0.242210i
$498$		0			0
$499$	11.9373	+	8.67299i	0.534389	+	0.388256i	0.821997	−	0.569492i	$-0.192860\pi$
$499$	11.9373	+	8.67299i	0.534389	+	0.388256i	−0.287608	+	0.957748i	$0.592860\pi$
$500$	31.9537	−	10.3824i	1.42901	−	0.464314i
$501$		0			0
$502$	−10.2423	+	14.0973i	−0.457135	+	0.629193i
$503$	14.4984	−	10.5337i	0.646450	−	0.469674i	−0.215610	−	0.976480i	$-0.569174\pi$
$503$	14.4984	−	10.5337i	0.646450	−	0.469674i	0.862060	+	0.506806i	$0.169174\pi$
$504$		0			0
$505$		−	21.6719i		−	0.964385i
$506$	−9.05739	−	25.8803i	−0.402650	−	1.15052i
$507$		0			0
$508$	−9.53079	−	3.09674i	−0.422860	−	0.137396i
$509$	−8.22592	−	11.3220i	−0.364608	−	0.501839i	0.586818	−	0.809719i	$-0.300381\pi$
$509$	−8.22592	−	11.3220i	−0.364608	−	0.501839i	−0.951425	+	0.307880i	$0.900381\pi$
$510$		0			0
$511$	−4.37429	−	13.4627i	−0.193507	−	0.595554i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	−1.63064	−	2.24438i	−0.0719243	−	0.0989953i
$515$	−14.4091	−	4.68179i	−0.634940	−	0.206304i
$516$		0			0
$517$	−9.90719	+	32.9986i	−0.435718	+	1.45128i
$518$			10.4406i			0.458735i
$519$		0			0
$520$	−0.479372	+	0.348285i	−0.0210219	+	0.0152733i
$521$	−0.940749	+	1.29483i	−0.0412150	+	0.0567275i	−0.829127	−	0.559060i	$-0.811162\pi$
$521$	−0.940749	+	1.29483i	−0.0412150	+	0.0567275i	0.787912	+	0.615788i	$0.211162\pi$
$522$		0			0
$523$	−33.2058	+	10.7892i	−1.45199	+	0.471780i	−0.925613	−	0.378471i	$-0.876450\pi$
$523$	−33.2058	+	10.7892i	−1.45199	+	0.471780i	−0.526377	+	0.850251i	$0.676450\pi$
$524$	−5.71374	−	4.15127i	−0.249606	−	0.181349i
$525$		0			0
$526$	2.33331	−	7.18118i	0.101737	−	0.313114i
$527$	7.17861			0.312705
$528$		0			0
$529$	−45.3480			−1.97165
$530$	3.94773	−	12.1499i	0.171478	−	0.527756i
$531$		0			0
$532$	−4.53683	−	3.29620i	−0.196697	−	0.142908i
$533$	0.503029	−	0.163444i	0.0217886	−	0.00707955i
$534$		0			0
$535$	−46.9880	+	64.6735i	−2.03147	+	2.79608i
$536$	−3.61811	+	2.62871i	−0.156279	+	0.113543i
$537$		0			0
$538$		−	18.3916i		−	0.792918i
$539$	1.88863	−	2.72637i	0.0813490	−	0.117433i
$540$		0			0
$541$	15.7275	+	5.11018i	0.676179	+	0.219704i	0.626922	−	0.779082i	$-0.284315\pi$
$541$	15.7275	+	5.11018i	0.676179	+	0.219704i	0.0492573	+	0.998786i	$0.484315\pi$
$542$	−3.28057	−	4.51531i	−0.140912	−	0.193949i
$543$		0			0
$544$	0.224858	+	0.692041i	0.00964069	+	0.0296710i
$545$	8.80976	+	27.1137i	0.377369	+	1.16142i
$546$		0			0
$547$	−13.1270	−	18.0677i	−0.561268	−	0.772519i	0.430219	−	0.902724i	$-0.358436\pi$
$547$	−13.1270	−	18.0677i	−0.561268	−	0.772519i	−0.991487	+	0.130206i	$0.958436\pi$
$548$	−14.7257	−	4.78466i	−0.629049	−	0.204390i
$549$		0			0
$550$	24.4271	−	35.2622i	1.04157	−	1.50358i
$551$		−	47.6021i		−	2.02792i
$552$		0			0
$553$	−1.80387	+	1.31059i	−0.0767083	+	0.0557318i
$554$	10.5815	−	14.5642i	0.449564	−	0.618772i
$555$		0			0
$556$	16.0108	−	5.20223i	0.679009	−	0.220624i
$557$	21.5518	+	15.6583i	0.913178	+	0.663463i	0.941817	−	0.336127i	$-0.109117\pi$
$557$	21.5518	+	15.6583i	0.913178	+	0.663463i	−0.0286386	+	0.999590i	$0.509117\pi$
$558$		0			0
$559$	−0.0279559	+	0.0860395i	−0.00118241	+	0.00363908i
$560$	−4.23483			−0.178954
$561$		0			0
$562$	−12.6740			−0.534620
$563$	8.46045	−	26.0386i	0.356565	−	1.09740i	−0.598531	−	0.801100i	$-0.704249\pi$
$563$	8.46045	−	26.0386i	0.356565	−	1.09740i	0.955096	−	0.296296i	$-0.0957513\pi$
$564$		0			0
$565$	18.5166	+	13.4531i	0.778998	+	0.565975i
$566$	−19.4834	+	6.33053i	−0.818948	+	0.266092i
$567$		0			0
$568$	−3.33720	+	4.59326i	−0.140026	+	0.192729i
$569$	−20.9255	+	15.2033i	−0.877244	+	0.637355i	−0.932521	−	0.361116i	$-0.882396\pi$
$569$	−20.9255	+	15.2033i	−0.877244	+	0.637355i	0.0552768	+	0.998471i	$0.482396\pi$
$570$		0			0
$571$		−	8.18982i		−	0.342733i	−0.985207	−	0.171367i	$-0.945182\pi$
$571$		−	8.18982i		−	0.342733i	0.985207	−	0.171367i	$-0.0548183\pi$
$572$	−0.133441	+	0.444463i	−0.00557947	+	0.0185839i
$573$		0			0
$574$	3.59512	+	1.16813i	0.150057	+	0.0487566i
$575$	−62.8501	−	86.5058i	−2.62103	−	3.60754i
$576$		0			0
$577$	6.82567	+	21.0073i	0.284156	+	0.874543i	0.986650	+	0.162854i	$0.0520698\pi$
$577$	6.82567	+	21.0073i	0.284156	+	0.874543i	−0.702494	+	0.711690i	$0.747930\pi$
$578$	−5.08967	−	15.6644i	−0.211702	−	0.651553i
$579$		0			0
$580$	−21.1293	−	29.0820i	−0.877346	−	1.20756i
$581$	−3.21352	−	1.04414i	−0.133319	−	0.0433181i
$582$		0			0
$583$	−3.30499	−	9.44357i	−0.136879	−	0.391113i
$584$			14.1555i			0.585759i
$585$		0			0
$586$	−7.39792	+	5.37490i	−0.305605	+	0.222035i
$587$	16.8460	−	23.1865i	0.695308	−	0.957010i	−0.304681	−	0.952454i	$-0.598550\pi$
$587$	16.8460	−	23.1865i	0.695308	−	0.957010i	0.999990	−	0.00455547i	$-0.00145006\pi$
$588$		0			0
$589$	52.6158	−	17.0959i	2.16800	−	0.704425i
$590$	1.08770	+	0.790258i	0.0447798	+	0.0325344i
$591$		0			0
$592$	3.22634	−	9.92964i	0.132602	−	0.408106i
$593$	41.9128			1.72115			0.860577	−	0.509320i	$-0.170103\pi$
$593$	41.9128			1.72115			0.860577	+	0.509320i	$0.170103\pi$
$594$		0			0
$595$	−3.08149			−0.126329
$596$	−4.75648	+	14.6389i	−0.194833	+	0.599634i
$597$		0			0
$598$	0.935837	+	0.679926i	0.0382692	+	0.0278042i
$599$	−29.1399	+	9.46814i	−1.19063	+	0.386858i	−0.836304	−	0.548266i	$-0.815288\pi$
$599$	−29.1399	+	9.46814i	−1.19063	+	0.386858i	−0.354322	+	0.935124i	$0.615288\pi$
$600$		0			0
$601$	−2.37410	+	3.26766i	−0.0968414	+	0.133291i	−0.854688	−	0.519142i	$-0.826252\pi$
$601$	−2.37410	+	3.26766i	−0.0968414	+	0.133291i	0.757847	+	0.652433i	$0.226252\pi$
$602$	−0.523082	+	0.380041i	−0.0213192	+	0.0154893i
$603$		0			0
$604$		−	17.7625i		−	0.722746i
$605$	−2.09466	−	46.5360i	−0.0851601	−	1.89196i
$606$		0			0
$607$	−1.40000	−	0.454886i	−0.0568241	−	0.0184633i	0.280467	−	0.959864i	$-0.409511\pi$
$607$	−1.40000	−	0.454886i	−0.0568241	−	0.0184633i	−0.337291	+	0.941400i	$0.609511\pi$
$608$	3.29620	+	4.53683i	0.133679	+	0.183993i
$609$		0			0
$610$	7.83291	+	24.1072i	0.317145	+	0.976072i
$611$	−0.449161	−	1.38237i	−0.0181711	−	0.0559249i
$612$		0			0
$613$	−1.12347	−	1.54633i	−0.0453767	−	0.0624556i	0.785726	−	0.618575i	$-0.212290\pi$
$613$	−1.12347	−	1.54633i	−0.0453767	−	0.0624556i	−0.831102	+	0.556119i	$0.812290\pi$
$614$	−0.977648	−	0.317657i	−0.0394547	−	0.0128196i
$615$		0			0
$616$	−2.63869	+	2.00931i	−0.106316	+	0.0809575i
$617$		−	2.44376i		−	0.0983821i	−0.998789	−	0.0491910i	$-0.984336\pi$
$617$		−	2.44376i		−	0.0983821i	0.998789	−	0.0491910i	$-0.0156643\pi$
$618$		0			0
$619$	−11.1269	+	8.08417i	−0.447228	+	0.324930i	−0.788500	−	0.615034i	$-0.789142\pi$
$619$	−11.1269	+	8.08417i	−0.447228	+	0.324930i	0.341272	+	0.939964i	$0.389142\pi$
$620$	24.5567	−	33.7993i	0.986219	−	1.35741i
$621$		0			0
$622$	−3.14155	+	1.02075i	−0.125965	+	0.0409284i
$623$	−6.58399	−	4.78355i	−0.263782	−	0.191649i
$624$		0			0
$625$	23.9838	−	73.8146i	0.959353	−	2.95258i
$626$	−0.198434			−0.00793103
$627$		0			0
$628$	5.90415			0.235601
$629$	2.34766	−	7.22535i	0.0936073	−	0.288094i
$630$		0			0
$631$	−27.4311	−	19.9298i	−1.09201	−	0.793395i	−0.112276	−	0.993677i	$-0.535814\pi$
$631$	−27.4311	−	19.9298i	−1.09201	−	0.793395i	−0.979738	+	0.200282i	$0.935814\pi$
$632$	2.12057	−	0.689016i	0.0843519	−	0.0274076i
$633$		0			0
$634$	20.0721	−	27.6268i	0.797163	−	1.09720i
$635$	−34.3333	+	24.9446i	−1.36248	+	0.989897i
$636$		0			0
$637$			0.139920i			0.00554383i
$638$	−26.9641	−	8.09546i	−1.06752	−	0.320502i
$639$		0			0
$640$	4.02756	+	1.30863i	0.159203	+	0.0517283i
$641$	0.470397	+	0.647445i	0.0185795	+	0.0255726i	0.818206	−	0.574926i	$-0.194969\pi$
$641$	0.470397	+	0.647445i	0.0185795	+	0.0255726i	−0.799626	+	0.600498i	$0.794969\pi$
$642$		0			0
$643$	−3.34875	−	10.3064i	−0.132062	−	0.406445i	0.863059	−	0.505102i	$-0.168545\pi$
$643$	−3.34875	−	10.3064i	−0.132062	−	0.406445i	−0.995121	+	0.0986573i	$0.968545\pi$
$644$	2.55473	+	7.86265i	0.100671	+	0.309832i
$645$		0			0
$646$	2.39850	+	3.30125i	0.0943676	+	0.129886i
$647$	16.0555	+	5.21674i	0.631206	+	0.205091i	0.607109	−	0.794618i	$-0.292329\pi$
$647$	16.0555	+	5.21674i	0.631206	+	0.205091i	0.0240967	+	0.999710i	$0.492329\pi$
$648$		0			0
$649$	1.05269	−	0.0236797i	0.0413218	−	0.000929510i
$650$			1.80969i			0.0709819i
$651$		0			0
$652$	−3.18272	+	2.31238i	−0.124645	+	0.0905598i
$653$	15.4996	−	21.3334i	0.606548	−	0.834841i	−0.389740	−	0.920925i	$-0.627435\pi$
$653$	15.4996	−	21.3334i	0.606548	−	0.834841i	0.996288	+	0.0860836i	$0.0274352\pi$
$654$		0			0
$655$	−28.4449	+	9.24231i	−1.11143	+	0.361127i
$656$	−3.05819	−	2.22191i	−0.119402	−	0.0867509i
$657$		0			0
$658$	3.21013	−	9.87975i	0.125144	−	0.385153i
$659$	−7.13793			−0.278054			−0.139027	−	0.990289i	$-0.544398\pi$
$659$	−7.13793			−0.278054			−0.139027	+	0.990289i	$0.544398\pi$
$660$		0			0
$661$	5.47335			0.212889			0.106444	−	0.994319i	$-0.466053\pi$
$661$	5.47335			0.212889			0.106444	+	0.994319i	$0.466053\pi$
$662$	0.915178	−	2.81663i	0.0355694	−	0.109471i
$663$		0			0
$664$	2.73358	+	1.98606i	0.106084	+	0.0770743i
$665$	−22.5859	+	7.33860i	−0.875843	+	0.284579i
$666$		0			0
$667$	−41.2489	+	56.7742i	−1.59716	+	2.19831i
$668$	−10.6956	+	7.77080i	−0.413825	+	0.300661i
$669$		0			0
$670$			18.9391i			0.731683i
$671$	16.3188	+	11.3045i	0.629982	+	0.436405i
$672$		0			0
$673$	3.33594	+	1.08391i	0.128591	+	0.0417818i	0.372606	−	0.927990i	$-0.378464\pi$
$673$	3.33594	+	1.08391i	0.128591	+	0.0417818i	−0.244014	+	0.969772i	$0.578464\pi$
$674$	15.8927	+	21.8744i	0.612164	+	0.842571i
$675$		0			0
$676$	4.01117	+	12.3451i	0.154276	+	0.474812i
$677$	11.0162	+	33.9043i	0.423386	+	1.30305i	0.904531	+	0.426408i	$0.140221\pi$
$677$	11.0162	+	33.9043i	0.423386	+	1.30305i	−0.481145	+	0.876641i	$0.659779\pi$
$678$		0			0
$679$	−5.64085	−	7.76396i	−0.216476	−	0.297954i
$680$	2.93067	+	0.952233i	0.112386	+	0.0365165i
$681$		0			0
$682$	−0.735829	−	32.7116i	−0.0281763	−	1.25259i
$683$			11.8158i			0.452117i	0.974114	+	0.226059i	$0.0725841\pi$
$683$			11.8158i			0.452117i	−0.974114	+	0.226059i	$0.927416\pi$
$684$		0			0
$685$	−53.0471	+	38.5410i	−2.02683	+	1.47257i
$686$	−0.587785	+	0.809017i	−0.0224417	+	0.0308884i
$687$		0			0
$688$	0.614919	−	0.199799i	0.0234436	−	0.00761728i
$689$	0.341481	+	0.248101i	0.0130094	+	0.00945188i
$690$		0			0
$691$	1.92397	−	5.92137i	0.0731912	−	0.225259i	−0.907768	−	0.419472i	$-0.862215\pi$
$691$	1.92397	−	5.92137i	0.0731912	−	0.225259i	0.980959	+	0.194213i	$0.0622152\pi$
$692$	2.75362			0.104677
$693$		0			0
$694$	−27.6563			−1.04982
$695$	22.0305	−	67.8030i	0.835665	−	2.57191i
$696$		0			0
$697$	−2.22531	−	1.61678i	−0.0842896	−	0.0612399i
$698$	−3.90363	+	1.26837i	−0.147754	+	0.0480083i
$699$		0			0
$700$	−7.60227	+	10.4636i	−0.287339	+	0.395488i
$701$	−36.2430	+	26.3321i	−1.36888	+	0.994550i	−0.371057	+	0.928610i	$0.621005\pi$
$701$	−36.2430	+	26.3321i	−1.36888	+	0.994550i	−0.997824	+	0.0659404i	$0.978995\pi$
$702$		0			0
$703$		−	58.5494i		−	2.20823i
$704$	3.13045	−	1.09557i	0.117983	−	0.0412909i
$705$		0			0
$706$	3.76805	+	1.22431i	0.141812	+	0.0460776i
$707$	3.00801	+	4.14017i	0.113128	+	0.155707i
$708$		0			0
$709$	−10.2476	−	31.5390i	−0.384858	−	1.18447i	−0.936583	−	0.350445i	$-0.886030\pi$
$709$	−10.2476	−	31.5390i	−0.384858	−	1.18447i	0.551725	−	0.834026i	$-0.313970\pi$
$710$	7.42988	+	22.8668i	0.278838	+	0.858176i
$711$		0			0
$712$	4.78355	+	6.58399i	0.179271	+	0.246745i
$713$	−77.5683	−	25.2035i	−2.90495	−	0.943877i
$714$		0			0
$715$	1.19059	+	1.56352i	0.0445256	+	0.0584723i
$716$		−	5.13167i		−	0.191780i
$717$		0			0
$718$	1.25114	−	0.909004i	0.0466920	−	0.0339237i
$719$	−24.2810	+	33.4199i	−0.905527	+	1.24635i	0.0631437	+	0.998004i	$0.479887\pi$
$719$	−24.2810	+	33.4199i	−0.905527	+	1.24635i	−0.968671	+	0.248347i	$0.920113\pi$
$720$		0			0
$721$	3.40252	−	1.10555i	0.126716	−	0.0411727i
$722$	10.0705	+	7.31662i	0.374784	+	0.272297i
$723$		0			0
$724$	5.09295	−	15.6745i	0.189278	−	0.582538i
$725$	−109.788			−4.07743
$726$		0			0
$727$	12.3976			0.459800			0.229900	−	0.973214i	$-0.426160\pi$
$727$	12.3976			0.459800			0.229900	+	0.973214i	$0.426160\pi$
$728$	0.0432377	−	0.133072i	0.00160249	−	0.00493197i
$729$		0			0
$730$	48.4974	+	35.2354i	1.79497	+	1.30412i
$731$	0.447449	−	0.145385i	0.0165495	−	0.00537726i
$732$		0			0
$733$	6.45484	−	8.88432i	0.238415	−	0.328150i	−0.672997	−	0.739645i	$-0.734993\pi$
$733$	6.45484	−	8.88432i	0.238415	−	0.328150i	0.911412	+	0.411495i	$0.134993\pi$
$734$	4.34848	−	3.15935i	0.160505	−	0.116614i
$735$		0			0
$736$		−	8.26728i		−	0.304736i
$737$	8.98611	+	11.8008i	0.331008	+	0.434689i
$738$		0			0
$739$	26.2244	+	8.52083i	0.964681	+	0.313444i	0.748667	−	0.662946i	$-0.230694\pi$
$739$	26.2244	+	8.52083i	0.964681	+	0.313444i	0.216014	+	0.976390i	$0.430694\pi$
$740$	−25.9885	−	35.7701i	−0.955357	−	1.31494i
$741$		0			0
$742$	0.932206	+	2.86903i	0.0342224	+	0.105326i
$743$	6.64477	+	20.4505i	0.243773	+	0.750256i	0.995836	+	0.0911648i	$0.0290590\pi$
$743$	6.64477	+	20.4505i	0.243773	+	0.750256i	−0.752063	+	0.659091i	$0.770941\pi$
$744$		0			0
$745$	38.3140	+	52.7347i	1.40372	+	1.93205i
$746$	17.3719	+	5.64448i	0.636031	+	0.206659i
$747$		0			0
$748$	2.27789	−	0.797197i	0.0832878	−	0.0291484i
$749$		−	18.8770i		−	0.689751i
$750$		0			0
$751$	0.821760	−	0.597044i	0.0299865	−	0.0217864i	−0.572691	−	0.819771i	$-0.694101\pi$
$751$	0.821760	−	0.597044i	0.0299865	−	0.0217864i	0.602678	+	0.797985i	$0.294101\pi$
$752$	−6.10602	+	8.40422i	−0.222664	+	0.306470i
$753$		0			0
$754$	1.12958	−	0.367023i	0.0411369	−	0.0133662i
$755$	−60.8552	−	44.2139i	−2.21475	−	1.60911i
$756$		0			0
$757$	8.03559	−	24.7310i	0.292059	−	0.898864i	−0.692135	−	0.721768i	$-0.743330\pi$
$757$	8.03559	−	24.7310i	0.292059	−	0.898864i	0.984194	−	0.177096i	$-0.0566703\pi$
$758$	−9.03690			−0.328235
$759$		0			0
$760$	23.7482			0.861438
$761$	8.31347	−	25.5862i	0.301363	−	0.927500i	−0.679646	−	0.733540i	$-0.737867\pi$
$761$	8.31347	−	25.5862i	0.301363	−	0.927500i	0.981009	−	0.193960i	$-0.0621332\pi$
$762$		0			0
$763$	−5.44633	−	3.95699i	−0.197170	−	0.143253i
$764$	−16.1369	+	5.24319i	−0.583811	+	0.189692i
$765$		0			0
$766$	−17.4656	+	24.0393i	−0.631057	+	0.868575i
$767$	−0.0359378	+	0.0261104i	−0.00129764	+	0.000942791i
$768$		0			0
$769$			10.5089i			0.378962i	0.981884	+	0.189481i	$0.0606805\pi$
$769$			10.5089i			0.378962i	−0.981884	+	0.189481i	$0.939319\pi$
$770$	0.315862	+	14.0418i	0.0113829	+	0.506031i
$771$		0			0
$772$	11.9051	+	3.86819i	0.428472	+	0.139219i
$773$	−4.26411	−	5.86905i	−0.153370	−	0.211095i	0.725418	−	0.688309i	$-0.241647\pi$
$773$	−4.26411	−	5.86905i	−0.153370	−	0.211095i	−0.878787	+	0.477214i	$0.841647\pi$
$774$		0			0
$775$	−39.4296	−	121.352i	−1.41635	−	4.35908i
$776$	2.96557	+	9.12709i	0.106458	+	0.327643i
$777$		0			0
$778$	−8.96991	−	12.3460i	−0.321587	−	0.442626i
$779$	−20.1608	−	6.55065i	−0.722337	−	0.234701i
$780$		0			0
$781$	15.4792	+	10.7228i	0.553889	+	0.383694i
$782$		−	6.01573i		−	0.215122i
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	14.6964	−	20.2279i	0.524538	−	0.721964i
$786$		0			0
$787$	29.8767	−	9.70752i	1.06499	−	0.346036i	0.276455	−	0.961027i	$-0.410840\pi$
$787$	29.8767	−	9.70752i	1.06499	−	0.346036i	0.788534	+	0.614991i	$0.210840\pi$
$788$	12.0628	+	8.76417i	0.429721	+	0.312211i
$789$		0			0
$790$	2.91786	−	8.98026i	0.103813	−	0.319503i
$791$	−5.40464			−0.192167
$792$		0			0
$793$	−0.837500			−0.0297405
$794$	−8.95523	+	27.5614i	−0.317809	+	0.978116i
$795$		0			0
$796$	17.0295	+	12.3726i	0.603593	+	0.438536i
$797$	−37.5675	+	12.2064i	−1.33071	+	0.432374i	−0.886159	−	0.463381i	$-0.846636\pi$
$797$	−37.5675	+	12.2064i	−1.33071	+	0.432374i	−0.444550	+	0.895754i	$0.646636\pi$
$798$		0			0
$799$	−4.44308	+	6.11537i	−0.157185	+	0.216346i
$800$	10.4636	−	7.60227i	0.369945	−	0.268781i
$801$		0			0
$802$			29.6341i			1.04642i
$803$	46.9366	−	1.05581i	1.65636	−	0.0372588i
$804$		0			0
$805$	33.2970	+	10.8188i	1.17356	+	0.381314i
$806$	0.811360	+	1.11674i	0.0285789	+	0.0393355i
$807$		0			0
$808$	−1.58140	−	4.86706i	−0.0556336	−	0.171223i
$809$	−12.0402	−	37.0558i	−0.423309	−	1.30281i	−0.904604	−	0.426253i	$-0.859833\pi$
$809$	−12.0402	−	37.0558i	−0.423309	−	1.30281i	0.481295	−	0.876559i	$-0.340167\pi$
$810$		0			0
$811$	26.8691	+	36.9821i	0.943502	+	1.29862i	0.954354	+	0.298678i	$0.0965455\pi$
$811$	26.8691	+	36.9821i	0.943502	+	1.29862i	−0.0108524	+	0.999941i	$0.503454\pi$
$812$	8.07304	+	2.62309i	0.283308	+	0.0920524i
$813$		0			0
$814$	−33.1652	−	9.95722i	−1.16244	−	0.349000i
$815$			16.6600i			0.583576i
$816$		0			0
$817$	2.93335	−	2.13121i	0.102625	−	0.0745615i
$818$	18.5800	−	25.5732i	0.649634	−	0.894145i
$819$		0			0
$820$	−15.2247	+	4.94681i	−0.531670	+	0.172750i
$821$	4.57965	+	3.32731i	0.159831	+	0.116124i	0.664826	−	0.746998i	$-0.268506\pi$
$821$	4.57965	+	3.32731i	0.159831	+	0.116124i	−0.504995	+	0.863122i	$0.668506\pi$
$822$		0			0
$823$	−0.244511	+	0.752529i	−0.00852313	+	0.0262315i	−0.955228	−	0.295872i	$-0.904390\pi$
$823$	−0.244511	+	0.752529i	−0.00852313	+	0.0262315i	0.946705	+	0.322103i	$0.104390\pi$
$824$	−3.57762			−0.124632
$825$		0			0
$826$	−0.317479			−0.0110465
$827$	−5.49993	+	16.9270i	−0.191251	+	0.588611i	0.808749	+	0.588154i	$0.200145\pi$
$827$	−5.49993	+	16.9270i	−0.191251	+	0.588611i	−1.00000		0.000456458i	$0.999855\pi$
$828$		0			0
$829$	24.4335	+	17.7520i	0.848612	+	0.616553i	0.924763	−	0.380544i	$-0.124263\pi$
$829$	24.4335	+	17.7520i	0.848612	+	0.616553i	−0.0761510	+	0.997096i	$0.524263\pi$
$830$	13.6087	−	4.42173i	0.472365	−	0.153481i
$831$		0			0
$832$	−0.0822429	+	0.113198i	−0.00285126	+	0.00392442i
$833$	0.588685	−	0.427705i	0.0203967	−	0.0148191i
$834$		0			0
$835$			55.9864i			1.93749i
$836$	14.7973	−	11.2679i	0.511776	−	0.389708i
$837$		0			0
$838$	14.5310	+	4.72142i	0.501966	+	0.163099i
$839$	−10.6867	−	14.7090i	−0.368946	−	0.507811i	0.583668	−	0.811993i	$-0.301617\pi$
$839$	−10.6867	−	14.7090i	−0.368946	−	0.507811i	−0.952614	+	0.304182i	$0.901617\pi$
$840$		0			0
$841$	13.3046	+	40.9473i	0.458779	+	1.41198i
$842$	−1.04415	−	3.21355i	−0.0359836	−	0.110746i
$843$		0			0
$844$	10.2533	+	14.1124i	0.352933	+	0.485770i
$845$	52.2794	+	16.9866i	1.79847	+	0.584357i
$846$		0			0
$847$	6.85926	+	8.59945i	0.235687	+	0.295481i
$848$		−	3.01668i		−	0.103593i
$849$		0			0
$850$	7.61391	−	5.53183i	0.261155	−	0.189740i
$851$	−50.7351	+	69.8309i	−1.73918	+	2.39377i
$852$		0			0
$853$	34.6864	−	11.2703i	1.18764	−	0.385887i	0.352440	−	0.935835i	$-0.385352\pi$
$853$	34.6864	−	11.2703i	1.18764	−	0.385887i	0.835199	+	0.549947i	$0.185352\pi$
$854$	−4.84242	−	3.51823i	−0.165704	−	0.120391i
$855$		0			0
$856$	−5.83331	+	17.9531i	−0.199379	+	0.613624i
$857$	36.2118			1.23697			0.618485	−	0.785797i	$-0.287747\pi$
$857$	36.2118			1.23697			0.618485	+	0.785797i	$0.287747\pi$
$858$		0			0
$859$	10.7079			0.365347			0.182674	−	0.983174i	$-0.441525\pi$
$859$	10.7079			0.365347			0.182674	+	0.983174i	$0.441525\pi$
$860$	0.846116	−	2.60408i	0.0288523	−	0.0887983i
$861$		0			0
$862$	10.9958	+	7.98894i	0.374519	+	0.272104i
$863$	5.92588	−	1.92544i	0.201719	−	0.0655426i	−0.206415	−	0.978465i	$-0.566180\pi$
$863$	5.92588	−	1.92544i	0.201719	−	0.0655426i	0.408134	+	0.912922i	$0.366180\pi$
$864$		0			0
$865$	6.85422	−	9.43402i	0.233050	−	0.320766i
$866$	−25.4577	+	18.4961i	−0.865088	+	0.628523i
$867$		0			0
$868$			9.86541i			0.334854i
$869$	−2.44280	−	6.97998i	−0.0828662	−	0.236780i
$870$		0			0
$871$	−0.595128	−	0.193369i	−0.0201652	−	0.00655206i
$872$	3.95699	+	5.44633i	0.134001	+	0.184436i
$873$		0			0
$874$	−14.3265	−	44.0924i	−0.484601	−	1.49145i
$875$	10.3824	+	31.9537i	0.350988	+	1.08023i
$876$		0			0
$877$	−0.0689566	−	0.0949106i	−0.00232850	−	0.00320490i	0.807851	−	0.589387i	$-0.200630\pi$
$877$	−0.0689566	−	0.0949106i	−0.00232850	−	0.00320490i	−0.810180	+	0.586182i	$0.800630\pi$
$878$	−0.792665	−	0.257552i	−0.0267511	−	0.00869197i
$879$		0			0
$880$	4.03875	−	13.4521i	0.136146	−	0.453471i
$881$		−	58.0951i		−	1.95727i	−0.205595	−	0.978637i	$-0.565913\pi$
$881$		−	58.0951i		−	1.95727i	0.205595	−	0.978637i	$-0.434087\pi$
$882$		0			0
$883$	29.9688	−	21.7736i	1.00853	−	0.732741i	0.0446305	−	0.999004i	$-0.485789\pi$
$883$	29.9688	−	21.7736i	1.00853	−	0.732741i	0.963900	+	0.266263i	$0.0857890\pi$
$884$	−0.0598445	+	0.0823688i	−0.00201279	+	0.00277036i
$885$		0			0
$886$	11.4648	−	3.72515i	0.385169	−	0.125149i
$887$	−0.855372	−	0.621464i	−0.0287206	−	0.0208667i	0.573332	−	0.819323i	$-0.305650\pi$
$887$	−0.855372	−	0.621464i	−0.0287206	−	0.0208667i	−0.602053	+	0.798456i	$0.705650\pi$
$888$		0			0
$889$	3.09674	−	9.53079i	0.103861	−	0.319652i
$890$	34.4641			1.15524
$891$		0			0
$892$	8.13116			0.272251
$893$	−18.0018	+	55.4040i	−0.602409	+	1.85402i
$894$		0			0
$895$	−17.5814	−	12.7736i	−0.587680	−	0.426974i
$896$	−0.951057	+	0.309017i	−0.0317726	+	0.0103235i
$897$		0			0
$898$	8.39508	−	11.5548i	0.280147	−	0.385590i
$899$	−67.7491	+	49.2226i	−2.25956	+	1.64166i
$900$		0			0
$901$		−	2.19510i		−	0.0731295i
$902$	−7.13927	+	10.3060i	−0.237712	+	0.343153i
$903$		0			0
$904$	5.14012	+	1.67013i	0.170958	+	0.0555476i
$905$	−41.0243	−	56.4651i	−1.36369	−	1.87696i
$906$		0			0
$907$	1.67486	+	5.15469i	0.0556128	+	0.171159i	0.975005	−	0.222184i	$-0.0713186\pi$
$907$	1.67486	+	5.15469i	0.0556128	+	0.171159i	−0.919392	+	0.393343i	$0.871319\pi$
$908$	−0.00683945	−	0.0210497i	−0.000226975	−	0.000698558i
$909$		0			0
$910$	−0.348285	−	0.479372i	−0.0115455	−	0.0158910i
$911$	43.7527	+	14.2161i	1.44959	+	0.471001i	0.924874	−	0.380275i	$-0.124171\pi$
$911$	43.7527	+	14.2161i	1.44959	+	0.471001i	0.524719	+	0.851276i	$0.324171\pi$
$912$		0			0
$913$	6.38148	−	9.21211i	0.211196	−	0.304876i
$914$		−	2.03912i		−	0.0674481i
$915$		0			0
$916$	0.772830	−	0.561494i	0.0255350	−	0.0185523i
$917$	4.15127	−	5.71374i	0.137087	−	0.188684i
$918$		0			0
$919$	−30.6289	+	9.95194i	−1.01035	+	0.328284i	−0.766996	−	0.641652i	$-0.778249\pi$
$919$	−30.6289	+	9.95194i	−1.01035	+	0.328284i	−0.243359	+	0.969936i	$0.578249\pi$
$920$	−28.3241	−	20.5787i	−0.933818	−	0.678458i
$921$		0			0
$922$	−0.277674	+	0.854594i	−0.00914472	+	0.0281446i
$923$	−0.794408			−0.0261482
$924$		0			0
$925$	−135.037			−4.43998
$926$	1.10044	−	3.38679i	0.0361626	−	0.111297i
$927$		0			0
$928$	−6.86734	−	4.98941i	−0.225431	−	0.163785i
$929$	−40.6722	+	13.2152i	−1.33441	+	0.433576i	−0.887420	−	0.460962i	$-0.847504\pi$
$929$	−40.6722	+	13.2152i	−1.33441	+	0.433576i	−0.446991	+	0.894538i	$0.647504\pi$
$930$		0			0
$931$	3.29620	−	4.53683i	0.108029	−	0.148689i
$932$	10.7946	−	7.84276i	0.353590	−	0.256898i
$933$		0			0
$934$			18.0772i			0.591504i
$935$	2.93881	−	9.78851i	0.0961095	−	0.320118i
$936$		0			0
$937$	−35.1096	−	11.4078i	−1.14698	−	0.372677i	−0.326976	−	0.945032i	$-0.606030\pi$
$937$	−35.1096	−	11.4078i	−1.14698	−	0.372677i	−0.820006	+	0.572355i	$0.806030\pi$
$938$	−2.62871	−	3.61811i	−0.0858305	−	0.118136i
$939$		0			0
$940$	13.5943	+	41.8390i	0.443398	+	1.36464i
$941$	−4.73473	−	14.5720i	−0.154348	−	0.475034i	0.843746	−	0.536742i	$-0.180345\pi$
$941$	−4.73473	−	14.5720i	−0.154348	−	0.475034i	−0.998094	+	0.0617082i	$0.980345\pi$
$942$		0			0
$943$	18.3691	+	25.2829i	0.598181	+	0.823326i
$944$	0.301940	+	0.0981063i	0.00982732	+	0.00319309i
$945$		0			0
$946$	−0.708357	−	2.02404i	−0.0230307	−	0.0658072i
$947$		−	23.0974i		−	0.750564i	−0.926911	−	0.375282i	$-0.877546\pi$
$947$		−	23.0974i		−	0.750564i	0.926911	−	0.375282i	$-0.122454\pi$
$948$		0			0
$949$	−1.60237	+	1.16419i	−0.0520151	+	0.0377912i
$950$	42.6323	−	58.6783i	1.38317	−	1.90377i
$951$		0			0
$952$	−0.692041	+	0.224858i	−0.0224292	+	0.00728768i
$953$	43.5831	+	31.6650i	1.41180	+	1.02573i	0.993058	+	0.117623i	$0.0375273\pi$
$953$	43.5831	+	31.6650i	1.41180	+	1.02573i	0.418738	+	0.908107i	$0.362473\pi$
$954$		0			0
$955$	−22.2040	+	68.3368i	−0.718504	+	2.21133i
$956$	−1.54692			−0.0500310
$957$		0			0
$958$	−36.4489			−1.17761
$959$	4.78466	−	14.7257i	0.154505	−	0.475516i
$960$		0			0
$961$	−53.6591	−	38.9856i	−1.73094	−	1.25760i
$962$	1.38936	−	0.451429i	0.0447946	−	0.0145547i
$963$		0			0
$964$	16.5976	−	22.8447i	0.534573	−	0.735777i
$965$	42.8863	−	31.1587i	1.38056	−	1.00303i
$966$		0			0
$967$		−	50.1426i		−	1.61248i	−0.591590	−	0.806239i	$-0.701500\pi$
$967$		−	50.1426i		−	1.61248i	0.591590	−	0.806239i	$-0.298500\pi$
$968$	−3.86617	−	10.2982i	−0.124263	−	0.330996i
$969$		0			0
$970$	38.6516	+	12.5587i	1.24103	+	0.403235i
$971$	−12.8570	−	17.6962i	−0.412602	−	0.567898i	0.551248	−	0.834341i	$-0.314152\pi$
$971$	−12.8570	−	17.6962i	−0.412602	−	0.567898i	−0.963851	+	0.266443i	$0.914152\pi$
$972$		0			0
$973$	5.20223	+	16.0108i	0.166776	+	0.513283i
$974$	−2.65440	−	8.16942i	−0.0850526	−	0.261765i
$975$		0			0
$976$	3.51823	+	4.84242i	0.112616	+	0.155002i
$977$	9.21680	+	2.99472i	0.294872	+	0.0958096i	0.452717	−	0.891654i	$-0.350455\pi$
$977$	9.21680	+	2.99472i	0.294872	+	0.0958096i	−0.157845	+	0.987464i	$0.550455\pi$
$978$		0			0
$979$	21.4743	−	16.3523i	0.686322	−	0.522622i
$980$		−	4.23483i		−	0.135277i
$981$		0			0
$982$	17.8445	−	12.9648i	0.569441	−	0.413723i
$983$	−11.3013	+	15.5550i	−0.360457	+	0.496126i	−0.950276	−	0.311409i	$-0.899199\pi$
$983$	−11.3013	+	15.5550i	−0.360457	+	0.496126i	0.589819	+	0.807535i	$0.299199\pi$
$984$		0			0
$985$	60.0529	−	19.5124i	1.91344	−	0.621716i
$986$	−4.99705	−	3.63057i	−0.159138	−	0.115621i
$987$		0			0
$988$	−0.242470	+	0.746245i	−0.00771398	+	0.0237412i
$989$	−5.34533			−0.169972
$990$		0			0
$991$	−33.3443			−1.05922			−0.529608	−	0.848243i	$-0.677661\pi$
$991$	−33.3443			−1.05922			−0.529608	+	0.848243i	$0.677661\pi$
$992$	3.04858	−	9.38256i	0.0967925	−	0.297897i
$993$		0			0
$994$	−4.59326	−	3.33720i	−0.145689	−	0.105850i
$995$	84.7784	−	27.5462i	2.68765	−	0.873272i
$996$		0			0
$997$	−2.56406	+	3.52912i	−0.0812045	+	0.111768i	−0.847687	−	0.530497i	$-0.822005\pi$
$997$	−2.56406	+	3.52912i	−0.0812045	+	0.111768i	0.766482	+	0.642265i	$0.222005\pi$
$998$	11.9373	−	8.67299i	0.377870	−	0.274539i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.a.827.1	✓	48
3.2	odd	2		1386.2.bu.b.827.12	yes	48
11.6	odd	10		1386.2.bu.b.1205.12	yes	48
33.17	even	10	inner	1386.2.bu.a.1205.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.827.1	✓	48	1.1	even	1	trivial
1386.2.bu.a.1205.1	yes	48	33.17	even	10	inner
1386.2.bu.b.827.12	yes	48	3.2	odd	2
1386.2.bu.b.1205.12	yes	48	11.6	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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-4.02756 + 1.30863i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-4.02756 + 1.30863i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +4.23483i q^{10} +(2.00931 + 2.63869i) q^{11} +(-0.133072 - 0.0432377i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(0.224858 + 0.692041i) q^{17} +(3.29620 + 4.53683i) q^{19} +(4.02756 + 1.30863i) q^{20} +(3.13045 - 1.09557i) q^{22} -8.26728i q^{23} +(10.4636 - 7.60227i) q^{25} +(-0.0822429 + 0.113198i) q^{26} +(-0.951057 + 0.309017i) q^{28} +(-6.86734 - 4.98941i) q^{29} +(3.04858 - 9.38256i) q^{31} +1.00000 q^{32} +0.727655 q^{34} +(-1.30863 + 4.02756i) q^{35} +(-8.44666 - 6.13685i) q^{37} +(5.33337 - 1.73292i) q^{38} +(2.48917 - 3.42605i) q^{40} +(-3.05819 + 2.22191i) q^{41} -0.646564i q^{43} +(-0.0745868 - 3.31579i) q^{44} +(-7.86265 - 2.55473i) q^{46} +(6.10602 + 8.40422i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-3.99675 - 12.3007i) q^{50} +(0.0822429 + 0.113198i) q^{52} +(-2.86903 - 0.932206i) q^{53} +(-11.5457 - 7.99801i) q^{55} +1.00000i q^{56} +(-6.86734 + 4.98941i) q^{58} +(0.186609 - 0.256846i) q^{59} +(5.69261 - 1.84964i) q^{61} +(-7.98128 - 5.79874i) q^{62} +(0.309017 - 0.951057i) q^{64} +0.592537 q^{65} +4.47223 q^{67} +(0.224858 - 0.692041i) q^{68} +(3.42605 + 2.48917i) q^{70} +(5.39970 - 1.75447i) q^{71} +(8.32039 - 11.4520i) q^{73} +(-8.44666 + 6.13685i) q^{74} -5.60783i q^{76} +(3.31579 - 0.0745868i) q^{77} +(-2.12057 - 0.689016i) q^{79} +(-2.48917 - 3.42605i) q^{80} +(1.16813 + 3.59512i) q^{82} +(-1.04414 - 3.21352i) q^{83} +(-1.81126 - 2.49298i) q^{85} +(-0.614919 - 0.199799i) q^{86} +(-3.17655 - 0.953698i) q^{88} -8.13826i q^{89} +(-0.113198 + 0.0822429i) q^{91} +(-4.85939 + 6.68837i) q^{92} +(9.87975 - 3.21013i) q^{94} +(-19.2127 - 13.9588i) q^{95} +(2.96557 - 9.12709i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) \) 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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