LMFDB - Embedded newform 504.2.bk.c.451.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(19,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.3
Character	$\chi$	$=$	504.451
Dual form			504.2.bk.c.19.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34597 - 0.434022i) q^{2} +(1.62325 + 1.16836i) q^{4} +(-1.44142 - 2.49662i) q^{5} +(-2.63862 - 0.194181i) q^{7} +(-1.67775 - 2.27710i) q^{8} +(0.856518 + 3.98597i) q^{10} +(-2.91340 + 5.04616i) q^{11} +1.04841 q^{13} +(3.46721 + 1.40658i) q^{14} +(1.26988 + 3.79307i) q^{16} +(5.91062 + 3.41250i) q^{17} +(-0.589961 + 0.340614i) q^{19} +(0.577155 - 5.73673i) q^{20} +(6.11148 - 5.52748i) q^{22} +(1.85937 - 1.07351i) q^{23} +(-1.65540 + 2.86723i) q^{25} +(-1.41112 - 0.455033i) q^{26} +(-4.05626 - 3.39805i) q^{28} +6.61515i q^{29} +(-1.91558 + 3.31788i) q^{31} +(-0.0629331 - 5.65650i) q^{32} +(-6.47439 - 7.15845i) q^{34} +(3.31857 + 6.86751i) q^{35} +(-2.06185 + 1.19041i) q^{37} +(0.941902 - 0.202399i) q^{38} +(-3.26670 + 7.47095i) q^{40} -1.19919i q^{41} +1.34319 q^{43} +(-10.6249 + 4.78728i) q^{44} +(-2.96857 + 0.637896i) q^{46} +(5.52670 + 9.57253i) q^{47} +(6.92459 + 1.02474i) q^{49} +(3.47255 - 3.14072i) q^{50} +(1.70183 + 1.22492i) q^{52} +(-6.99615 - 4.03923i) q^{53} +16.7978 q^{55} +(3.98476 + 6.33417i) q^{56} +(2.87112 - 8.90377i) q^{58} +(-6.81625 - 3.93537i) q^{59} +(1.63471 + 2.83140i) q^{61} +(4.01834 - 3.63435i) q^{62} +(-2.37034 + 7.64078i) q^{64} +(-1.51120 - 2.61747i) q^{65} +(-6.65629 + 11.5290i) q^{67} +(5.60739 + 12.4451i) q^{68} +(-1.48603 - 10.6838i) q^{70} +1.08533i q^{71} +(4.88878 + 2.82254i) q^{73} +(3.29184 - 0.707361i) q^{74} +(-1.35561 - 0.136384i) q^{76} +(8.66721 - 12.7491i) q^{77} +(-10.9630 + 6.32946i) q^{79} +(7.63942 - 8.63782i) q^{80} +(-0.520474 + 1.61406i) q^{82} +0.482042i q^{83} -19.6754i q^{85} +(-1.80789 - 0.582976i) q^{86} +(16.3785 - 1.83207i) q^{88} +(-10.7308 + 6.19543i) q^{89} +(-2.76635 - 0.203581i) q^{91} +(4.27246 + 0.429839i) q^{92} +(-3.28406 - 15.2830i) q^{94} +(1.70077 + 0.981939i) q^{95} +3.63532i q^{97} +(-8.87550 - 4.38468i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44}+ \cdots - 60 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34597	−	0.434022i	−0.951742	−	0.306900i
$2$	−1.34597	−	0.434022i	−0.951742	−	0.306900i
$3$		0			0
$3$		0			0
$4$	1.62325	+	1.16836i	0.811625	+	0.584179i
$5$	−1.44142	−	2.49662i	−0.644624	−	1.11652i	−0.984388	−	0.176010i	$-0.943681\pi$
$5$	−1.44142	−	2.49662i	−0.644624	−	1.11652i	0.339765	−	0.940511i	$-0.389653\pi$
$6$		0			0
$7$	−2.63862	−	0.194181i	−0.997303	−	0.0733933i
$7$	−2.63862	−	0.194181i	−0.997303	−	0.0733933i
$8$	−1.67775	−	2.27710i	−0.593172	−	0.805075i
$9$		0			0
$10$	0.856518	+	3.98597i	0.270855	+	1.26047i
$11$	−2.91340	+	5.04616i	−0.878423	+	1.52147i	−0.0253527	+	0.999679i	$0.508071\pi$
$11$	−2.91340	+	5.04616i	−0.878423	+	1.52147i	−0.853071	+	0.521795i	$0.825262\pi$
$12$		0			0
$13$	1.04841			0.290776			0.145388	−	0.989375i	$-0.453557\pi$
$13$	1.04841			0.290776			0.145388	+	0.989375i	$0.453557\pi$
$14$	3.46721	+	1.40658i	0.926651	+	0.375924i
$15$		0			0
$16$	1.26988	+	3.79307i	0.317469	+	0.948269i
$17$	5.91062	+	3.41250i	1.43354	+	0.827652i	0.997388	−	0.0722232i	$-0.0230094\pi$
$17$	5.91062	+	3.41250i	1.43354	+	0.827652i	0.436147	+	0.899875i	$0.356343\pi$
$18$		0			0
$19$	−0.589961	+	0.340614i	−0.135346	+	0.0781423i	−0.566144	−	0.824306i	$-0.691566\pi$
$19$	−0.589961	+	0.340614i	−0.135346	+	0.0781423i	0.430798	+	0.902448i	$0.358232\pi$
$20$	0.577155	−	5.73673i	0.129056	−	1.28277i
$21$		0			0
$22$	6.11148	−	5.52748i	1.30297	−	1.17846i
$23$	1.85937	−	1.07351i	0.387705	−	0.223841i	−0.293460	−	0.955971i	$-0.594807\pi$
$23$	1.85937	−	1.07351i	0.387705	−	0.223841i	0.681165	+	0.732130i	$0.261474\pi$
$24$		0			0
$25$	−1.65540	+	2.86723i	−0.331079	+	0.573446i
$26$	−1.41112	−	0.455033i	−0.276744	−	0.0892393i
$27$		0			0
$28$	−4.05626	−	3.39805i	−0.766561	−	0.642172i
$29$			6.61515i			1.22840i	0.789149	+	0.614201i	$0.210522\pi$
$29$			6.61515i			1.22840i	−0.789149	+	0.614201i	$0.789478\pi$
$30$		0			0
$31$	−1.91558	+	3.31788i	−0.344048	+	0.595909i	−0.985180	−	0.171522i	$-0.945132\pi$
$31$	−1.91558	+	3.31788i	−0.344048	+	0.595909i	0.641132	+	0.767430i	$0.278465\pi$
$32$	−0.0629331	−	5.65650i	−0.0111251	−	0.999938i
$33$		0			0
$34$	−6.47439	−	7.15845i	−1.11035	−	1.22766i
$35$	3.31857	+	6.86751i	0.560940	+	1.16082i
$36$		0			0
$37$	−2.06185	+	1.19041i	−0.338966	+	0.195702i	−0.659814	−	0.751429i	$-0.729365\pi$
$37$	−2.06185	+	1.19041i	−0.338966	+	0.195702i	0.320849	+	0.947130i	$0.396032\pi$
$38$	0.941902	−	0.202399i	0.152797	−	0.0328335i
$39$		0			0
$40$	−3.26670	+	7.47095i	−0.516511	+	1.18126i
$41$		−	1.19919i		−	0.187281i	−0.995606	−	0.0936407i	$-0.970149\pi$
$41$		−	1.19919i		−	0.187281i	0.995606	−	0.0936407i	$-0.0298505\pi$
$42$		0			0
$43$	1.34319			0.204835			0.102418	−	0.994741i	$-0.467342\pi$
$43$	1.34319			0.204835			0.102418	+	0.994741i	$0.467342\pi$
$44$	−10.6249	+	4.78728i	−1.60176	+	0.721709i
$45$		0			0
$46$	−2.96857	+	0.637896i	−0.437692	+	0.0940526i
$47$	5.52670	+	9.57253i	0.806152	+	1.39630i	0.915511	+	0.402294i	$0.131787\pi$
$47$	5.52670	+	9.57253i	0.806152	+	1.39630i	−0.109359	+	0.994002i	$0.534880\pi$
$48$		0			0
$49$	6.92459	+	1.02474i	0.989227	+	0.146391i
$50$	3.47255	−	3.14072i	0.491093	−	0.444165i
$51$		0			0
$52$	1.70183	+	1.22492i	0.236001	+	0.169865i
$53$	−6.99615	−	4.03923i	−0.960995	−	0.554830i	−0.0645156	−	0.997917i	$-0.520550\pi$
$53$	−6.99615	−	4.03923i	−0.960995	−	0.554830i	−0.896479	+	0.443086i	$0.853884\pi$
$54$		0			0
$55$	16.7978			2.26501
$56$	3.98476	+	6.33417i	0.532486	+	0.846439i
$57$		0			0
$58$	2.87112	−	8.90377i	0.376997	−	1.16912i
$59$	−6.81625	−	3.93537i	−0.887400	−	0.512341i	−0.0143092	−	0.999898i	$-0.504555\pi$
$59$	−6.81625	−	3.93537i	−0.887400	−	0.512341i	−0.873091	+	0.487557i	$0.837888\pi$
$60$		0			0
$61$	1.63471	+	2.83140i	0.209303	+	0.362524i	0.951495	−	0.307663i	$-0.0995471\pi$
$61$	1.63471	+	2.83140i	0.209303	+	0.362524i	−0.742192	+	0.670187i	$0.766214\pi$
$62$	4.01834	−	3.63435i	0.510329	−	0.461563i
$63$		0			0
$64$	−2.37034	+	7.64078i	−0.296293	+	0.955097i
$65$	−1.51120	−	2.61747i	−0.187441	−	0.324658i
$66$		0			0
$67$	−6.65629	+	11.5290i	−0.813195	+	1.40850i	0.0974214	+	0.995243i	$0.468941\pi$
$67$	−6.65629	+	11.5290i	−0.813195	+	1.40850i	−0.910617	+	0.413252i	$0.864393\pi$
$68$	5.60739	+	12.4451i	0.679996	+	1.50918i
$69$		0			0
$70$	−1.48603	−	10.6838i	−0.177614	−	1.27695i
$71$			1.08533i			0.128805i	0.997924	+	0.0644027i	$0.0205142\pi$
$71$			1.08533i			0.128805i	−0.997924	+	0.0644027i	$0.979486\pi$
$72$		0			0
$73$	4.88878	+	2.82254i	0.572188	+	0.330353i	0.758023	−	0.652228i	$-0.226166\pi$
$73$	4.88878	+	2.82254i	0.572188	+	0.330353i	−0.185835	+	0.982581i	$0.559499\pi$
$74$	3.29184	−	0.707361i	0.382669	−	0.0822291i
$75$		0			0
$76$	−1.35561	−	0.136384i	−0.155500	−	0.0156444i
$77$	8.66721	−	12.7491i	0.987720	−	1.45290i
$78$		0			0
$79$	−10.9630	+	6.32946i	−1.23343	+	0.712120i	−0.967743	−	0.251939i	$-0.918932\pi$
$79$	−10.9630	+	6.32946i	−1.23343	+	0.712120i	−0.265686	+	0.964060i	$0.585598\pi$
$80$	7.63942	−	8.63782i	0.854114	−	0.965738i
$81$		0			0
$82$	−0.520474	+	1.61406i	−0.0574767	+	0.178244i
$83$			0.482042i			0.0529110i	0.999650	+	0.0264555i	$0.00842203\pi$
$83$			0.482042i			0.0529110i	−0.999650	+	0.0264555i	$0.991578\pi$
$84$		0			0
$85$		−	19.6754i		−	2.13410i
$86$	−1.80789	−	0.582976i	−0.194950	−	0.0628639i
$87$		0			0
$88$	16.3785	−	1.83207i	1.74596	−	0.195299i
$89$	−10.7308	+	6.19543i	−1.13746	+	0.656714i	−0.945801	−	0.324747i	$-0.894721\pi$
$89$	−10.7308	+	6.19543i	−1.13746	+	0.656714i	−0.191661	+	0.981461i	$0.561388\pi$
$90$		0			0
$91$	−2.76635	−	0.203581i	−0.289992	−	0.0213410i
$92$	4.27246	+	0.429839i	0.445434	+	0.0448138i
$93$		0			0
$94$	−3.28406	−	15.2830i	−0.338725	−	1.57632i
$95$	1.70077	+	0.981939i	0.174495	+	0.100745i
$96$		0			0
$97$			3.63532i			0.369111i	0.982822	+	0.184556i	$0.0590846\pi$
$97$			3.63532i			0.369111i	−0.982822	+	0.184556i	$0.940915\pi$
$98$	−8.87550	−	4.38468i	−0.896561	−	0.442920i
$99$		0			0
$100$	−6.03708	+	2.72014i	−0.603708	+	0.272014i
$101$	1.25234	−	2.16911i	0.124612	−	0.215835i	−0.796969	−	0.604020i	$-0.793565\pi$
$101$	1.25234	−	2.16911i	0.124612	−	0.215835i	0.921581	+	0.388185i	$0.126898\pi$
$102$		0			0
$103$	2.31322	+	4.00661i	0.227928	+	0.394783i	0.957194	−	0.289447i	$-0.0934715\pi$
$103$	2.31322	+	4.00661i	0.227928	+	0.394783i	−0.729266	+	0.684231i	$0.760138\pi$
$104$	−1.75896	−	2.38733i	−0.172480	−	0.234097i
$105$		0			0
$106$	7.66346	+	8.47315i	0.744341	+	0.822985i
$107$	−3.03473	−	5.25631i	−0.293378	−	0.508146i	0.681228	−	0.732071i	$-0.261446\pi$
$107$	−3.03473	−	5.25631i	−0.293378	−	0.508146i	−0.974606	+	0.223925i	$0.928113\pi$
$108$		0			0
$109$	−12.6132	−	7.28224i	−1.20813	−	0.697513i	−0.245777	−	0.969326i	$-0.579043\pi$
$109$	−12.6132	−	7.28224i	−1.20813	−	0.697513i	−0.962350	+	0.271814i	$0.912377\pi$
$110$	−22.6092	−	7.29060i	−2.15570	−	0.695132i
$111$		0			0
$112$	−2.61418	−	10.2551i	−0.247017	−	0.969011i
$113$	3.82875			0.360179			0.180089	−	0.983650i	$-0.442361\pi$
$113$	3.82875			0.360179			0.180089	+	0.983650i	$0.442361\pi$
$114$		0			0
$115$	−5.36027	−	3.09475i	−0.499847	−	0.288587i
$116$	−7.72887	+	10.7380i	−0.717607	+	0.997002i
$117$		0			0
$118$	7.46641	+	8.25527i	0.687339	+	0.759959i
$119$	−14.9332	−	10.1520i	−1.36893	−	0.930632i
$120$		0			0
$121$	−11.4758	−	19.8767i	−1.04326	−	1.80697i
$122$	−0.971374	−	4.52047i	−0.0879441	−	0.409265i
$123$		0			0
$124$	−6.98593	+	3.14766i	−0.627355	+	0.282668i
$125$	−4.86972			−0.435561
$126$		0			0
$127$		−	0.550415i		−	0.0488415i	−0.999702	−	0.0244207i	$-0.992226\pi$
$127$		−	0.550415i		−	0.0488415i	0.999702	−	0.0244207i	$-0.00777413\pi$
$128$	6.50667	−	9.25545i	0.575114	−	0.818074i
$129$		0			0
$130$	0.897981	+	4.17893i	0.0787582	+	0.366516i
$131$	2.42818	−	1.40191i	0.212151	−	0.122486i	−0.390159	−	0.920747i	$-0.627580\pi$
$131$	2.42818	−	1.40191i	0.212151	−	0.122486i	0.602311	+	0.798262i	$0.294247\pi$
$132$		0			0
$133$	1.62282	−	0.784192i	0.140717	−	0.0679980i
$134$	13.9630	−	12.6287i	1.20622	−	1.09095i
$135$		0			0
$136$	−2.14592	−	19.1844i	−0.184011	−	1.64504i
$137$	6.38148	−	11.0530i	0.545206	−	0.944325i	−0.453387	−	0.891314i	$-0.649785\pi$
$137$	6.38148	−	11.0530i	0.545206	−	0.944325i	0.998594	−	0.0530118i	$-0.0168821\pi$
$138$		0			0
$139$		−	6.11761i		−	0.518889i	−0.965758	−	0.259444i	$-0.916461\pi$
$139$		−	6.11761i		−	0.518889i	0.965758	−	0.259444i	$-0.0835394\pi$
$140$	−2.63685	+	15.0250i	−0.222855	+	1.26984i
$141$		0			0
$142$	0.471059	−	1.46082i	0.0395304	−	0.122589i
$143$	−3.05443	+	5.29044i	−0.255425	+	0.442408i
$144$		0			0
$145$	16.5155	−	9.53522i	1.37154	−	0.791857i
$146$	−5.35508	−	5.92087i	−0.443190	−	0.490015i
$147$		0			0
$148$	−4.73771	−	0.476647i	−0.389438	−	0.0391802i
$149$	−1.75163	+	1.01130i	−0.143499	+	0.0828491i	−0.570030	−	0.821624i	$-0.693069\pi$
$149$	−1.75163	+	1.01130i	−0.143499	+	0.0828491i	0.426532	+	0.904473i	$0.359735\pi$
$150$		0			0
$151$	12.1833	+	7.03404i	0.991464	+	0.572422i	0.905712	−	0.423895i	$-0.139337\pi$
$151$	12.1833	+	7.03404i	0.991464	+	0.572422i	0.0857523	+	0.996316i	$0.472671\pi$
$152$	1.76542	+	0.771935i	0.143194	+	0.0626122i
$153$		0			0
$154$	−17.1992	+	13.3982i	−1.38595	+	1.07965i
$155$	11.0446			0.887126
$156$		0			0
$157$	2.61739	−	4.53344i	0.208890	−	0.361808i	−0.742475	−	0.669874i	$-0.766348\pi$
$157$	2.61739	−	4.53344i	0.208890	−	0.361808i	0.951365	+	0.308065i	$0.0996816\pi$
$158$	17.5029	−	3.76108i	1.39246	−	0.299215i
$159$		0			0
$160$	−14.0314	+	8.31053i	−1.10928	+	0.657005i
$161$	−5.11461	+	2.47152i	−0.403088	+	0.194783i
$162$		0			0
$163$	−0.488212	−	0.845609i	−0.0382397	−	0.0662332i	0.846272	−	0.532751i	$-0.178842\pi$
$163$	−0.488212	−	0.845609i	−0.0382397	−	0.0662332i	−0.884512	+	0.466518i	$0.845508\pi$
$164$	1.40108	−	1.94658i	0.109406	−	0.152002i
$165$		0			0
$166$	0.209217	−	0.648813i	0.0162384	−	0.0503576i
$167$	2.08267			0.161162			0.0805808	−	0.996748i	$-0.474322\pi$
$167$	2.08267			0.161162			0.0805808	+	0.996748i	$0.474322\pi$
$168$		0			0
$169$	−11.9008			−0.915449
$170$	−8.53956	+	26.4824i	−0.654954	+	2.03111i
$171$		0			0
$172$	2.18034	+	1.56933i	0.166249	+	0.119660i
$173$	10.6732	+	18.4864i	0.811465	+	1.40550i	0.911839	+	0.410548i	$0.134663\pi$
$173$	10.6732	+	18.4864i	0.811465	+	1.40550i	−0.100374	+	0.994950i	$0.532004\pi$
$174$		0			0
$175$	4.92472	−	7.24408i	0.372274	−	0.547601i
$176$	−22.8401	−	4.64274i	−1.72164	−	0.349960i
$177$		0			0
$178$	17.1322	−	3.68143i	1.28412	−	0.275935i
$179$	−3.47487	+	6.01865i	−0.259724	+	0.449855i	−0.966168	−	0.257914i	$-0.916965\pi$
$179$	−3.47487	+	6.01865i	−0.259724	+	0.449855i	0.706444	+	0.707769i	$0.250298\pi$
$180$		0			0
$181$	−7.67619			−0.570566			−0.285283	−	0.958443i	$-0.592088\pi$
$181$	−7.67619			−0.570566			−0.285283	+	0.958443i	$0.592088\pi$
$182$	3.63505	+	1.47467i	0.269448	+	0.109310i
$183$		0			0
$184$	−5.56402	−	2.43289i	−0.410185	−	0.179355i
$185$	5.94398	+	3.43176i	0.437010	+	0.252308i
$186$		0			0
$187$	−34.4400	+	19.8839i	−2.51850	+	1.45406i
$188$	−2.21293	+	21.9958i	−0.161394	+	1.60421i
$189$		0			0
$190$	−1.86299	−	2.05983i	−0.135156	−	0.149436i
$191$	15.4238	−	8.90495i	1.11603	−	0.644340i	0.175645	−	0.984454i	$-0.443799\pi$
$191$	15.4238	−	8.90495i	1.11603	−	0.644340i	0.940384	+	0.340114i	$0.110466\pi$
$192$		0			0
$193$	6.89797	−	11.9476i	0.496527	−	0.860010i	−0.503465	−	0.864016i	$-0.667942\pi$
$193$	6.89797	−	11.9476i	0.496527	−	0.860010i	0.999992	+	0.00400574i	$0.00127507\pi$
$194$	1.57781	−	4.89302i	0.113280	−	0.351299i
$195$		0			0
$196$	10.0431	+	9.75380i	0.717362	+	0.696700i
$197$			1.13180i			0.0806374i	0.999187	+	0.0403187i	$0.0128373\pi$
$197$			1.13180i			0.0806374i	−0.999187	+	0.0403187i	$0.987163\pi$
$198$		0			0
$199$	−4.26593	+	7.38881i	−0.302404	+	0.523779i	−0.976680	−	0.214701i	$-0.931122\pi$
$199$	−4.26593	+	7.38881i	−0.302404	+	0.523779i	0.674276	+	0.738479i	$0.264456\pi$
$200$	9.30630	−	1.04098i	0.658055	−	0.0736087i
$201$		0			0
$202$	−2.62705	+	2.37601i	−0.184838	+	0.167175i
$203$	1.28453	−	17.4548i	0.0901566	−	1.22509i
$204$		0			0
$205$	−2.99391	+	1.72853i	−0.209104	+	0.120726i
$206$	−1.37456	−	6.39676i	−0.0957698	−	0.445683i
$207$		0			0
$208$	1.33135	+	3.97669i	0.0923125	+	0.275734i
$209$		−	3.96939i		−	0.274568i
$210$		0			0
$211$	21.2436			1.46247			0.731237	−	0.682124i	$-0.238944\pi$
$211$	21.2436			1.46247			0.731237	+	0.682124i	$0.238944\pi$
$212$	−6.63723	−	14.7307i	−0.455846	−	1.01171i
$213$		0			0
$214$	1.80329	+	8.39195i	0.123270	+	0.573662i
$215$	−1.93611	−	3.35344i	−0.132042	−	0.228703i
$216$		0			0
$217$	5.69874	−	8.38264i	0.386856	−	0.569051i
$218$	13.8163	+	15.2761i	0.935758	+	1.03463i
$219$		0			0
$220$	27.2670	+	19.6258i	1.83834	+	1.32317i
$221$	6.19674	+	3.57769i	0.416838	+	0.240662i
$222$		0			0
$223$	3.12207			0.209069			0.104535	−	0.994521i	$-0.466665\pi$
$223$	3.12207			0.209069			0.104535	+	0.994521i	$0.466665\pi$
$224$	−0.932327	+	14.9376i	−0.0622937	+	0.998058i
$225$		0			0
$226$	−5.15337	−	1.66176i	−0.342797	−	0.110539i
$227$	−4.52649	−	2.61337i	−0.300434	−	0.173456i	0.342204	−	0.939626i	$-0.388827\pi$
$227$	−4.52649	−	2.61337i	−0.300434	−	0.173456i	−0.642638	+	0.766170i	$0.722160\pi$
$228$		0			0
$229$	14.2129	+	24.6175i	0.939215	+	1.62677i	0.766939	+	0.641720i	$0.221779\pi$
$229$	14.2129	+	24.6175i	0.939215	+	1.62677i	0.172276	+	0.985049i	$0.444888\pi$
$230$	5.87154	+	6.49190i	0.387158	+	0.428063i
$231$		0			0
$232$	15.0633	−	11.0985i	0.988957	−	0.728655i
$233$	3.05971	+	5.29957i	0.200448	+	0.347186i	0.948673	−	0.316259i	$-0.102427\pi$
$233$	3.05971	+	5.29957i	0.200448	+	0.347186i	−0.748225	+	0.663445i	$0.769094\pi$
$234$		0			0
$235$	15.9326	−	27.5961i	1.03933	−	1.80017i
$236$	−6.46656	−	14.3519i	−0.420937	−	0.934229i
$237$		0			0
$238$	15.6934	+	20.1456i	1.01725	+	1.30584i
$239$			8.83528i			0.571507i	0.958303	+	0.285753i	$0.0922439\pi$
$239$			8.83528i			0.571507i	−0.958303	+	0.285753i	$0.907756\pi$
$240$		0			0
$241$	5.15757	+	2.97772i	0.332228	+	0.191812i	0.656830	−	0.754039i	$-0.271897\pi$
$241$	5.15757	+	2.97772i	0.332228	+	0.191812i	−0.324602	+	0.945851i	$0.605230\pi$
$242$	6.81913	+	31.7341i	0.438350	+	2.03994i
$243$		0			0
$244$	−0.654550	+	6.50600i	−0.0419032	+	0.416504i
$245$	−7.42288	−	18.7651i	−0.474231	−	1.19886i
$246$		0			0
$247$	−0.618521	+	0.357103i	−0.0393555	+	0.0227219i
$248$	10.7690	−	1.20460i	0.683831	−	0.0764920i
$249$		0			0
$250$	6.55448	+	2.11357i	0.414541	+	0.133674i
$251$		−	2.13955i		−	0.135047i	−0.997718	−	0.0675235i	$-0.978490\pi$
$251$		−	2.13955i		−	0.135047i	0.997718	−	0.0675235i	$-0.0215098\pi$
$252$		0			0
$253$			12.5102i			0.786510i
$254$	−0.238892	+	0.740840i	−0.0149894	+	0.0464845i
$255$		0			0
$256$	−12.7748	+	9.63348i	−0.798426	+	0.602092i
$257$	16.7030	−	9.64346i	1.04190	−	0.601543i	0.121531	−	0.992588i	$-0.461220\pi$
$257$	16.7030	−	9.64346i	1.04190	−	0.601543i	0.920372	+	0.391045i	$0.127886\pi$
$258$		0			0
$259$	5.67158	−	2.74066i	0.352415	−	0.170296i
$260$	0.605095	−	6.01444i	0.0375264	−	0.373000i
$261$		0			0
$262$	−3.87672	+	0.833041i	−0.239504	+	0.0514655i
$263$	−21.0740	−	12.1671i	−1.29948	−	0.750254i	−0.319164	−	0.947699i	$-0.603402\pi$
$263$	−21.0740	−	12.1671i	−1.29948	−	0.750254i	−0.980314	+	0.197446i	$0.936735\pi$
$264$		0			0
$265$			23.2889i			1.43063i
$266$	−2.52462	+	0.351154i	−0.154794	+	0.0215306i
$267$		0			0
$268$	−24.2749	+	10.9376i	−1.48282	+	0.668118i
$269$	−10.4505	+	18.1007i	−0.637176	+	1.10362i	0.348873	+	0.937170i	$0.386564\pi$
$269$	−10.4505	+	18.1007i	−0.637176	+	1.10362i	−0.986050	+	0.166452i	$0.946769\pi$
$270$		0			0
$271$	−9.99697	−	17.3153i	−0.607273	−	1.05183i	−0.991688	−	0.128667i	$-0.958930\pi$
$271$	−9.99697	−	17.3153i	−0.607273	−	1.05183i	0.384415	−	0.923160i	$-0.374403\pi$
$272$	−5.43810	+	26.7529i	−0.329733	+	1.62213i
$273$		0			0
$274$	−13.3865	+	12.1073i	−0.808709	+	0.731430i
$275$	−9.64567	−	16.7068i	−0.581656	−	1.00746i
$276$		0			0
$277$	−13.2433	−	7.64600i	−0.795710	−	0.459404i	0.0462586	−	0.998929i	$-0.485270\pi$
$277$	−13.2433	−	7.64600i	−0.795710	−	0.459404i	−0.841969	+	0.539526i	$0.818604\pi$
$278$	−2.65518	+	8.23409i	−0.159247	+	0.493848i
$279$		0			0
$280$	10.0703	−	19.0786i	0.601814	−	1.14017i
$281$	−5.59802			−0.333950			−0.166975	−	0.985961i	$-0.553400\pi$
$281$	−5.59802			−0.333950			−0.166975	+	0.985961i	$0.553400\pi$
$282$		0			0
$283$	9.72911	+	5.61710i	0.578335	+	0.333902i	0.760472	−	0.649371i	$-0.224968\pi$
$283$	9.72911	+	5.61710i	0.578335	+	0.333902i	−0.182136	+	0.983273i	$0.558301\pi$
$284$	−1.26806	+	1.76177i	−0.0752454	+	0.104542i
$285$		0			0
$286$	6.40733	−	5.79505i	0.378874	−	0.342669i
$287$	−0.232859	+	3.16419i	−0.0137452	+	0.186776i
$288$		0			0
$289$	14.7903	+	25.6175i	0.870016	+	1.50691i
$290$	−26.3678	+	5.66600i	−1.54837	+	0.332719i
$291$		0			0
$292$	4.63797	+	10.2935i	0.271417	+	0.602383i
$293$	17.7212			1.03528			0.517642	−	0.855598i	$-0.326810\pi$
$293$	17.7212			1.03528			0.517642	+	0.855598i	$0.326810\pi$
$294$		0			0
$295$			22.6901i			1.32107i
$296$	6.16993	+	2.69782i	0.358620	+	0.156808i
$297$		0			0
$298$	2.79656	−	0.600933i	0.162000	−	0.0348111i
$299$	1.94938	−	1.12547i	0.112735	−	0.0650878i
$300$		0			0
$301$	−3.54417	−	0.260822i	−0.204283	−	0.0150335i
$302$	−13.3454	−	14.7554i	−0.767941	−	0.849078i
$303$		0			0
$304$	−2.04115	−	1.80523i	−0.117068	−	0.103537i
$305$	4.71262	−	8.16250i	0.269844	−	0.467383i
$306$		0			0
$307$		−	20.3724i		−	1.16271i	−0.813649	−	0.581357i	$-0.802522\pi$
$307$		−	20.3724i		−	1.16271i	0.813649	−	0.581357i	$-0.197478\pi$
$308$	28.9646	−	10.5686i	1.65041	−	0.602204i
$309$		0			0
$310$	−14.8657	−	4.79362i	−0.844315	−	0.272259i
$311$	−14.4363	+	25.0045i	−0.818610	+	1.41787i	0.0880964	+	0.996112i	$0.471922\pi$
$311$	−14.4363	+	25.0045i	−0.818610	+	1.41787i	−0.906706	+	0.421762i	$0.861412\pi$
$312$		0			0
$313$	−4.08718	+	2.35974i	−0.231021	+	0.133380i	−0.611043	−	0.791597i	$-0.709250\pi$
$313$	−4.08718	+	2.35974i	−0.231021	+	0.133380i	0.380022	+	0.924978i	$0.375916\pi$
$314$	−5.49053	+	4.96586i	−0.309848	+	0.280240i
$315$		0			0
$316$	−25.1907	−	2.53436i	−1.41709	−	0.142569i
$317$	−22.0349	+	12.7218i	−1.23760	+	0.714529i	−0.968603	−	0.248612i	$-0.920026\pi$
$317$	−22.0349	+	12.7218i	−1.23760	+	0.714529i	−0.268998	+	0.963141i	$0.586692\pi$
$318$		0			0
$319$	−33.3811	−	19.2726i	−1.86898	−	1.07906i
$320$	22.4928	−	5.09575i	1.25738	−	0.284861i
$321$		0			0
$322$	7.95678	−	1.10672i	0.443414	−	0.0616753i
$323$	−4.64938			−0.258699
$324$		0			0
$325$	−1.73553	+	3.00603i	−0.0962700	+	0.166745i
$326$	0.290104	+	1.35006i	0.0160674	+	0.0747727i
$327$		0			0
$328$	−2.73066	+	2.01193i	−0.150776	+	0.111090i
$329$	−12.7240	−	26.3314i	−0.701499	−	1.45170i
$330$		0			0
$331$	9.85929	+	17.0768i	0.541916	+	0.938625i	0.998794	+	0.0490963i	$0.0156341\pi$
$331$	9.85929	+	17.0768i	0.541916	+	0.938625i	−0.456878	+	0.889529i	$0.651033\pi$
$332$	−0.563198	+	0.782475i	−0.0309095	+	0.0429439i
$333$		0			0
$334$	−2.80320	−	0.903924i	−0.153384	−	0.0494605i
$335$	38.3781			2.09682
$336$		0			0
$337$	−24.7720			−1.34942			−0.674709	−	0.738084i	$-0.735731\pi$
$337$	−24.7720			−1.34942			−0.674709	+	0.738084i	$0.735731\pi$
$338$	16.0181	+	5.16523i	0.871271	+	0.280951i
$339$		0			0
$340$	22.9879	−	31.9381i	1.24669	−	1.73209i
$341$	−11.1617	−	19.3326i	−0.604440	−	1.04692i
$342$		0			0
$343$	−18.0723	−	4.04850i	−0.975815	−	0.218599i
$344$	−2.25354	−	3.05858i	−0.121503	−	0.164908i
$345$		0			0
$346$	−6.34217	−	29.5145i	−0.340957	−	1.58671i
$347$	−7.49413	+	12.9802i	−0.402306	+	0.696815i	−0.994004	−	0.109345i	$-0.965125\pi$
$347$	−7.49413	+	12.9802i	−0.402306	+	0.696815i	0.591698	+	0.806160i	$0.298458\pi$
$348$		0			0
$349$	27.4546			1.46961			0.734806	−	0.678278i	$-0.237273\pi$
$349$	27.4546			1.46961			0.734806	+	0.678278i	$0.237273\pi$
$350$	−9.77259	+	7.61285i	−0.522367	+	0.406924i
$351$		0			0
$352$	28.7270	+	16.1621i	1.53115	+	0.861442i
$353$	−20.7884	−	12.0022i	−1.10645	−	0.638811i	−0.168544	−	0.985694i	$-0.553907\pi$
$353$	−20.7884	−	12.0022i	−1.10645	−	0.638811i	−0.937908	+	0.346883i	$0.887240\pi$
$354$		0			0
$355$	2.70966	−	1.56442i	0.143814	−	0.0830310i
$356$	−24.6572	−	2.48069i	−1.30683	−	0.131476i
$357$		0			0
$358$	7.28928	−	6.59273i	0.385251	−	0.348437i
$359$	11.8249	−	6.82714i	0.624097	−	0.360322i	−0.154366	−	0.988014i	$-0.549333\pi$
$359$	11.8249	−	6.82714i	0.624097	−	0.360322i	0.778462	+	0.627691i	$0.216000\pi$
$360$		0			0
$361$	−9.26796	+	16.0526i	−0.487788	+	0.844873i
$362$	10.3319	+	3.33164i	0.543032	+	0.175107i
$363$		0			0
$364$	−4.25262	−	3.56255i	−0.222898	−	0.186728i
$365$		−	16.2739i		−	0.851813i
$366$		0			0
$367$	17.3424	−	30.0379i	0.905264	−	1.56796i	0.0847016	−	0.996406i	$-0.473006\pi$
$367$	17.3424	−	30.0379i	0.905264	−	1.56796i	0.820562	−	0.571557i	$-0.193660\pi$
$368$	6.43305	+	5.68950i	0.335346	+	0.296585i
$369$		0			0
$370$	−6.51094	−	7.19885i	−0.338488	−	0.374251i
$371$	17.6758	+	12.0165i	0.917682	+	0.623865i
$372$		0			0
$373$	5.26744	−	3.04116i	0.272738	−	0.157465i	−0.357393	−	0.933954i	$-0.616334\pi$
$373$	5.26744	−	3.04116i	0.272738	−	0.157465i	0.630131	+	0.776489i	$0.283001\pi$
$374$	54.9851	−	11.8154i	2.84321	−	0.610959i
$375$		0			0
$376$	12.5252	−	28.6451i	0.645937	−	1.47726i
$377$			6.93538i			0.357190i
$378$		0			0
$379$	19.0628			0.979189			0.489594	−	0.871950i	$-0.337145\pi$
$379$	19.0628			0.979189			0.489594	+	0.871950i	$0.337145\pi$
$380$	1.61351	+	3.58104i	0.0827715	+	0.183703i
$381$		0			0
$382$	−24.6249	+	5.29148i	−1.25992	+	0.270736i
$383$	4.12501	+	7.14473i	0.210778	+	0.365079i	0.951958	−	0.306228i	$-0.0990668\pi$
$383$	4.12501	+	7.14473i	0.210778	+	0.365079i	−0.741180	+	0.671306i	$0.765733\pi$
$384$		0			0
$385$	−44.3228	−	3.26180i	−2.25890	−	0.166237i
$386$	−14.4700	+	13.0872i	−0.736502	+	0.666123i
$387$		0			0
$388$	−4.24736	+	5.90104i	−0.215627	+	0.299580i
$389$	−16.9926	−	9.81070i	−0.861560	−	0.497422i	0.00297421	−	0.999996i	$-0.499053\pi$
$389$	−16.9926	−	9.81070i	−0.861560	−	0.497422i	−0.864534	+	0.502574i	$0.832387\pi$
$390$		0			0
$391$	14.6533			0.741051
$392$	−9.28427	−	17.4872i	−0.468926	−	0.883237i
$393$		0			0
$394$	0.491226	−	1.52336i	0.0247476	−	0.0767460i
$395$	31.6045	+	18.2469i	1.59019	+	0.918099i
$396$		0			0
$397$	15.6816	+	27.1613i	0.787035	+	1.36318i	0.927776	+	0.373138i	$0.121718\pi$
$397$	15.6816	+	27.1613i	0.787035	+	1.36318i	−0.140741	+	0.990047i	$0.544948\pi$
$398$	8.94870	−	8.09358i	0.448558	−	0.405694i
$399$		0			0
$400$	−12.9778	−	2.63801i	−0.648889	−	0.131901i
$401$	17.4562	+	30.2350i	0.871722	+	1.50987i	0.860215	+	0.509932i	$0.170330\pi$
$401$	17.4562	+	30.2350i	0.871722	+	1.50987i	0.0115069	+	0.999934i	$0.496337\pi$
$402$		0			0
$403$	−2.00831	+	3.47849i	−0.100041	+	0.173276i
$404$	4.56716	−	2.05783i	0.227225	−	0.102381i
$405$		0			0
$406$	−9.30473	+	22.9361i	−0.461786	+	1.13830i
$407$		−	13.8725i		−	0.687636i
$408$		0			0
$409$	11.8182	+	6.82325i	0.584373	+	0.337388i	0.762869	−	0.646553i	$-0.223790\pi$
$409$	11.8182	+	6.82325i	0.584373	+	0.337388i	−0.178496	+	0.983941i	$0.557123\pi$
$410$	4.77992	−	1.02713i	0.236064	−	0.0507261i
$411$		0			0
$412$	−0.926229	+	9.20640i	−0.0456320	+	0.453567i
$413$	17.2213	+	11.7075i	0.847405	+	0.576088i
$414$		0			0
$415$	1.20348	−	0.694827i	0.0590763	−	0.0341077i
$416$	−0.0659796	−	5.93033i	−0.00323492	−	0.290758i
$417$		0			0
$418$	−1.72280	+	5.34266i	−0.0842650	+	0.261318i
$419$		−	4.22322i		−	0.206318i	−0.994665	−	0.103159i	$-0.967105\pi$
$419$		−	4.22322i		−	0.206318i	0.994665	−	0.103159i	$-0.0328950\pi$
$420$		0			0
$421$		−	11.6892i		−	0.569697i	−0.958573	−	0.284849i	$-0.908057\pi$
$421$		−	11.6892i		−	0.569697i	0.958573	−	0.284849i	$-0.0919433\pi$
$422$	−28.5932	−	9.22022i	−1.39190	−	0.448833i
$423$		0			0
$424$	2.54004	+	22.7077i	0.123355	+	1.10278i
$425$	−19.5688	+	11.2981i	−0.949228	+	0.548037i
$426$		0			0
$427$	−3.76357	−	7.78842i	−0.182132	−	0.376908i
$428$	1.21513	−	12.0779i	0.0587354	−	0.583810i
$429$		0			0
$430$	1.15047	+	5.35393i	0.0554806	+	0.258190i
$431$	−29.7064	−	17.1510i	−1.43091	−	0.826136i	−0.433719	−	0.901048i	$-0.642799\pi$
$431$	−29.7064	−	17.1510i	−1.43091	−	0.826136i	−0.997190	+	0.0749129i	$0.976132\pi$
$432$		0			0
$433$		−	14.1884i		−	0.681853i	−0.940090	−	0.340926i	$-0.889259\pi$
$433$		−	14.1884i		−	0.681853i	0.940090	−	0.340926i	$-0.110741\pi$
$434$	−11.3086	+	8.80937i	−0.542829	+	0.422863i
$435$		0			0
$436$	−11.9661	−	26.5577i	−0.573073	−	1.27188i
$437$	−0.731303	+	1.26665i	−0.0349830	+	0.0605923i
$438$		0			0
$439$	−14.0252	−	24.2923i	−0.669386	−	1.15941i	−0.978076	−	0.208247i	$-0.933224\pi$
$439$	−14.0252	−	24.2923i	−0.669386	−	1.15941i	0.308691	−	0.951163i	$-0.400109\pi$
$440$	−28.1824	−	38.2501i	−1.34354	−	1.82350i
$441$		0			0
$442$	−6.78781	−	7.50498i	−0.322863	−	0.356975i
$443$	5.51040	+	9.54430i	0.261807	+	0.453463i	0.966722	−	0.255828i	$-0.0823482\pi$
$443$	5.51040	+	9.54430i	0.261807	+	0.453463i	−0.704915	+	0.709292i	$0.749015\pi$
$444$		0			0
$445$	30.9352	+	17.8605i	1.46647	+	0.846667i
$446$	−4.20220	−	1.35505i	−0.198980	−	0.0641634i
$447$		0			0
$448$	7.73811	−	19.7008i	0.365592	−	0.930775i
$449$	−30.2270			−1.42650			−0.713250	−	0.700910i	$-0.752778\pi$
$449$	−30.2270			−1.42650			−0.713250	+	0.700910i	$0.752778\pi$
$450$		0			0
$451$	6.05128	+	3.49371i	0.284944	+	0.164512i
$452$	6.21502	+	4.47335i	0.292330	+	0.210409i
$453$		0			0
$454$	4.95825	+	5.48211i	0.232702	+	0.257288i
$455$	3.47921	+	7.19996i	0.163108	+	0.337539i
$456$		0			0
$457$	−12.7386	−	22.0639i	−0.595887	−	1.03211i	−0.993421	−	0.114519i	$-0.963467\pi$
$457$	−12.7386	−	22.0639i	−0.595887	−	1.03211i	0.397534	−	0.917587i	$-0.369866\pi$
$458$	−8.44556	−	39.3030i	−0.394635	−	1.83651i
$459$		0			0
$460$	−5.08527	−	11.2863i	−0.237102	−	0.526225i
$461$	27.9292			1.30079			0.650395	−	0.759596i	$-0.274603\pi$
$461$	27.9292			1.30079			0.650395	+	0.759596i	$0.274603\pi$
$462$		0			0
$463$			19.4232i			0.902674i	0.892354	+	0.451337i	$0.149053\pi$
$463$			19.4232i			0.902674i	−0.892354	+	0.451337i	$0.850947\pi$
$464$	−25.0918	+	8.40043i	−1.16486	+	0.389980i
$465$		0			0
$466$	−1.81813	−	8.46102i	−0.0842233	−	0.391949i
$467$	1.30760	−	0.754943i	0.0605085	−	0.0349346i	−0.469441	−	0.882964i	$-0.655544\pi$
$467$	1.30760	−	0.754943i	0.0605085	−	0.0349346i	0.529949	+	0.848029i	$0.322211\pi$
$468$		0			0
$469$	19.8021	−	29.1282i	0.914376	−	1.34501i
$470$	−33.4221	+	30.2283i	−1.54165	+	1.39433i
$471$		0			0
$472$	2.47473	+	22.1238i	0.113908	+	1.01833i
$473$	−3.91326	+	6.77797i	−0.179932	+	0.311651i
$474$		0			0
$475$		−	2.25541i		−	0.103485i
$476$	−12.3792	−	33.9266i	−0.567398	−	1.55502i
$477$		0			0
$478$	3.83471	−	11.8920i	0.175396	−	0.543927i
$479$	7.12030	−	12.3327i	0.325335	−	0.563496i	−0.656245	−	0.754548i	$-0.727856\pi$
$479$	7.12030	−	12.3327i	0.325335	−	0.563496i	0.981580	+	0.191051i	$0.0611897\pi$
$480$		0			0
$481$	−2.16166	+	1.24803i	−0.0985631	+	0.0569054i
$482$	−5.64951	−	6.24641i	−0.257328	−	0.284516i
$483$		0			0
$484$	4.59499	−	45.6727i	0.208863	−	2.07603i
$485$	9.07601	−	5.24004i	0.412120	−	0.237938i
$486$		0			0
$487$	6.40076	+	3.69548i	0.290046	+	0.167458i	0.637963	−	0.770067i	$-0.279777\pi$
$487$	6.40076	+	3.69548i	0.290046	+	0.167458i	−0.347916	+	0.937526i	$0.613111\pi$
$488$	3.70475	−	8.47277i	0.167706	−	0.383544i
$489$		0			0
$490$	1.84647	+	28.4789i	0.0834150	+	1.28655i
$491$	−14.0578			−0.634420			−0.317210	−	0.948355i	$-0.602746\pi$
$491$	−14.0578			−0.634420			−0.317210	+	0.948355i	$0.602746\pi$
$492$		0			0
$493$	−22.5742	+	39.0996i	−1.01669	+	1.76096i
$494$	0.987499	−	0.212197i	0.0444297	−	0.00954719i
$495$		0			0
$496$	−15.0175	−	3.05263i	−0.674306	−	0.137067i
$497$	0.210751	−	2.86378i	0.00945346	−	0.128458i
$498$		0			0
$499$	−13.4960	−	23.3757i	−0.604162	−	1.04644i	−0.992183	−	0.124789i	$-0.960175\pi$
$499$	−13.4960	−	23.3757i	−0.604162	−	1.04644i	0.388021	−	0.921651i	$-0.373159\pi$
$500$	−7.90477	−	5.68958i	−0.353512	−	0.254446i
$501$		0			0
$502$	−0.928611	+	2.87976i	−0.0414459	+	0.128530i
$503$	3.15505			0.140677			0.0703384	−	0.997523i	$-0.477592\pi$
$503$	3.15505			0.140677			0.0703384	+	0.997523i	$0.477592\pi$
$504$		0			0
$505$	−7.22059			−0.321312
$506$	5.42971	−	16.8383i	0.241380	−	0.748555i
$507$		0			0
$508$	0.643082	−	0.893461i	0.0285322	−	0.0396409i
$509$	10.8815	+	18.8473i	0.482315	+	0.835394i	0.999794	−	0.0203019i	$-0.00646275\pi$
$509$	10.8815	+	18.8473i	0.482315	+	0.835394i	−0.517479	+	0.855696i	$0.673129\pi$
$510$		0			0
$511$	−12.3515	−	8.39689i	−0.546399	−	0.371457i
$512$	21.3756	−	7.42178i	0.944678	−	0.327999i
$513$		0			0
$514$	−26.6671	+	5.73031i	−1.17624	+	0.252753i
$515$	6.66865	−	11.5504i	0.293856	−	0.508973i
$516$		0			0
$517$	−64.4060			−2.83257
$518$	−8.82325	+	1.22724i	−0.387672	+	0.0539220i
$519$		0			0
$520$	−3.42484	+	7.83260i	−0.150189	+	0.343482i
$521$	34.9828	+	20.1973i	1.53262	+	0.884860i	0.999240	+	0.0389867i	$0.0124130\pi$
$521$	34.9828	+	20.1973i	1.53262	+	0.884860i	0.533383	+	0.845874i	$0.320920\pi$
$522$		0			0
$523$	25.4468	−	14.6917i	1.11271	−	0.642424i	0.173181	−	0.984890i	$-0.444595\pi$
$523$	25.4468	−	14.6917i	1.11271	−	0.642424i	0.939530	+	0.342466i	$0.111262\pi$
$524$	5.57949	+	0.561335i	0.243741	+	0.0245221i
$525$		0			0
$526$	23.0841	+	25.5230i	1.00651	+	1.11286i
$527$	−22.6445	+	13.0738i	−0.986410	+	0.569504i
$528$		0			0
$529$	−9.19517	+	15.9265i	−0.399790	+	0.692457i
$530$	10.1079	−	31.3461i	0.439060	−	1.36159i
$531$		0			0
$532$	3.55046	+	0.623100i	0.153932	+	0.0270148i
$533$		−	1.25724i		−	0.0544570i
$534$		0			0
$535$	−8.74866	+	15.1531i	−0.378237	+	0.655126i
$536$	37.4203	−	4.18576i	1.61631	−	0.180797i
$537$		0			0
$538$	21.9221	−	19.8272i	0.945129	−	0.854813i
$539$	−25.3451	+	31.9571i	−1.09169	+	1.37649i
$540$		0			0
$541$	26.5848	−	15.3487i	1.14297	−	0.659893i	0.195805	−	0.980643i	$-0.437268\pi$
$541$	26.5848	−	15.3487i	1.14297	−	0.659893i	0.947164	+	0.320749i	$0.103935\pi$
$542$	5.94038	+	27.6447i	0.255161	+	1.18744i
$543$		0			0
$544$	18.9308	−	33.6482i	0.811653	−	1.44265i
$545$			41.9872i			1.79853i
$546$		0			0
$547$	−15.7691			−0.674240			−0.337120	−	0.941462i	$-0.609453\pi$
$547$	−15.7691			−0.674240			−0.337120	+	0.941462i	$0.609453\pi$
$548$	23.2726	−	10.4860i	0.994158	−	0.447939i
$549$		0			0
$550$	5.73163	+	26.6732i	0.244397	+	1.13735i
$551$	−2.25322	−	3.90268i	−0.0959902	−	0.166260i
$552$		0			0
$553$	30.1561	−	14.5722i	1.28237	−	0.619674i
$554$	14.5064	+	16.0391i	0.616320	+	0.681437i
$555$		0			0
$556$	7.14756	−	9.93041i	0.303124	−	0.421143i
$557$	19.2427	+	11.1098i	0.815340	+	0.470737i	0.848807	−	0.528703i	$-0.177321\pi$
$557$	19.2427	+	11.1098i	0.815340	+	0.470737i	−0.0334668	+	0.999440i	$0.510655\pi$
$558$		0			0
$559$	1.40822			0.0595612
$560$	−21.8348	+	21.3085i	−0.922689	+	0.900447i
$561$		0			0
$562$	7.53475	+	2.42967i	0.317834	+	0.102489i
$563$	−20.7809	−	11.9978i	−0.875809	−	0.505648i	−0.00653450	−	0.999979i	$-0.502080\pi$
$563$	−20.7809	−	11.9978i	−0.875809	−	0.505648i	−0.869274	+	0.494330i	$0.835413\pi$
$564$		0			0
$565$	−5.51885	−	9.55893i	−0.232180	−	0.402147i
$566$	−10.6571	−	11.7831i	−0.447951	−	0.495280i
$567$		0			0
$568$	2.47141	−	1.82091i	0.103698	−	0.0764038i
$569$	0.631897	+	1.09448i	0.0264905	+	0.0458829i	0.878967	−	0.476883i	$-0.158233\pi$
$569$	0.631897	+	1.09448i	0.0264905	+	0.0458829i	−0.852476	+	0.522766i	$0.824900\pi$
$570$		0			0
$571$	−10.3555	+	17.9363i	−0.433365	+	0.750611i	−0.997161	−	0.0753037i	$-0.976007\pi$
$571$	−10.3555	+	17.9363i	−0.433365	+	0.750611i	0.563795	+	0.825915i	$0.309341\pi$
$572$	−11.1392	+	5.01902i	−0.465755	+	0.209856i
$573$		0			0
$574$	1.68675	−	4.15783i	0.0704036	−	0.173544i
$575$			7.10831i			0.296437i
$576$		0			0
$577$	−27.2402	−	15.7271i	−1.13402	−	0.654728i	−0.189079	−	0.981962i	$-0.560550\pi$
$577$	−27.2402	−	15.7271i	−1.13402	−	0.654728i	−0.944943	+	0.327234i	$0.893884\pi$
$578$	−8.78864	−	40.8996i	−0.365559	−	1.70120i
$579$		0			0
$580$	37.9493	+	3.81797i	1.57576	+	0.158533i
$581$	0.0936032	−	1.27192i	0.00388332	−	0.0527683i
$582$		0			0
$583$	40.7652	−	23.5358i	1.68832	−	0.974752i
$584$	−1.77493	−	15.8677i	−0.0734472	−	0.656611i
$585$		0			0
$586$	−23.8521	−	7.69139i	−0.985322	−	0.317728i
$587$		−	5.93391i		−	0.244919i	−0.992474	−	0.122459i	$-0.960922\pi$
$587$		−	5.93391i		−	0.244919i	0.992474	−	0.122459i	$-0.0390781\pi$
$588$		0			0
$589$		−	2.60989i		−	0.107539i
$590$	9.84801	−	30.5401i	0.405436	−	1.25732i
$591$		0			0
$592$	−7.13360	−	6.30907i	−0.293189	−	0.259301i
$593$	13.6001	−	7.85199i	0.558487	−	0.322443i	−0.194051	−	0.980991i	$-0.562163\pi$
$593$	13.6001	−	7.85199i	0.558487	−	0.322443i	0.752538	+	0.658549i	$0.228829\pi$
$594$		0			0
$595$	−3.82058	+	51.9158i	−0.156628	+	2.12834i
$596$	−4.02489	−	0.404932i	−0.164866	−	0.0165867i
$597$		0			0
$598$	−3.11227	+	0.668776i	−0.127270	+	0.0273483i
$599$	−15.0452	−	8.68632i	−0.614728	−	0.354914i	0.160085	−	0.987103i	$-0.448823\pi$
$599$	−15.0452	−	8.68632i	−0.614728	−	0.354914i	−0.774814	+	0.632190i	$0.782156\pi$
$600$		0			0
$601$			43.6846i			1.78193i	0.454069	+	0.890966i	$0.349972\pi$
$601$			43.6846i			1.78193i	−0.454069	+	0.890966i	$0.650028\pi$
$602$	4.65713	+	1.88931i	0.189811	+	0.0770024i
$603$		0			0
$604$	11.5583	+	25.6525i	0.470300	+	1.04378i
$605$	−33.0830	+	57.3014i	−1.34501	+	2.32963i
$606$		0			0
$607$	9.60046	+	16.6285i	0.389671	+	0.674929i	0.992405	−	0.123012i	$-0.0392555\pi$
$607$	9.60046	+	16.6285i	0.389671	+	0.674929i	−0.602734	+	0.797942i	$0.705922\pi$
$608$	1.96382	+	3.31568i	0.0796432	+	0.134469i
$609$		0			0
$610$	−9.88573	+	8.94106i	−0.400262	+	0.362013i
$611$	5.79424	+	10.0359i	0.234410	+	0.406010i
$612$		0			0
$613$	14.8672	+	8.58358i	0.600480	+	0.346688i	0.769231	−	0.638971i	$-0.220640\pi$
$613$	14.8672	+	8.58358i	0.600480	+	0.346688i	−0.168750	+	0.985659i	$0.553973\pi$
$614$	−8.84207	+	27.4205i	−0.356837	+	1.10660i
$615$		0			0
$616$	−43.5724	+	1.65374i	−1.75558	+	0.0666310i
$617$	16.8150			0.676946			0.338473	−	0.940976i	$-0.390090\pi$
$617$	16.8150			0.676946			0.338473	+	0.940976i	$0.390090\pi$
$618$		0			0
$619$	−30.1572	−	17.4113i	−1.21212	−	0.699818i	−0.248899	−	0.968529i	$-0.580069\pi$
$619$	−30.1572	−	17.4113i	−1.21212	−	0.699818i	−0.963221	+	0.268712i	$0.913402\pi$
$620$	17.9282	+	12.9041i	0.720013	+	0.518241i
$621$		0			0
$622$	30.2833	−	27.3895i	1.21425	−	1.09822i
$623$	29.5175	−	14.2636i	1.18259	−	0.571461i
$624$		0			0
$625$	15.2963	+	26.4940i	0.611852	+	1.05976i
$626$	6.52539	−	1.40220i	0.260807	−	0.0560430i
$627$		0			0
$628$	9.54536	−	4.30087i	0.380901	−	0.171623i
$629$	−16.2491			−0.647892
$630$		0			0
$631$		−	11.8869i		−	0.473210i	−0.971606	−	0.236605i	$-0.923965\pi$
$631$		−	11.8869i		−	0.473210i	0.971606	−	0.236605i	$-0.0760346\pi$
$632$	32.8058	+	14.3445i	1.30495	+	0.570593i
$633$		0			0
$634$	35.1797	−	7.55953i	1.39717	−	0.300227i
$635$	−1.37418	+	0.793381i	−0.0545325	+	0.0314844i
$636$		0			0
$637$	7.25980	+	1.07434i	0.287644	+	0.0425670i
$638$	36.5651	+	40.4284i	1.44763	+	1.60057i
$639$		0			0
$640$	−32.4862	−	2.90365i	−1.28413	−	0.114777i
$641$	−18.4447	+	31.9472i	−0.728523	+	1.26184i	0.228984	+	0.973430i	$0.426460\pi$
$641$	−18.4447	+	31.9472i	−0.728523	+	1.26184i	−0.957507	+	0.288409i	$0.906874\pi$
$642$		0			0
$643$		−	10.0475i		−	0.396235i	−0.980178	−	0.198117i	$-0.936517\pi$
$643$		−	10.0475i		−	0.396235i	0.980178	−	0.198117i	$-0.0634827\pi$
$644$	−11.1899	−	1.96381i	−0.440944	−	0.0773849i
$645$		0			0
$646$	6.25791	+	2.01794i	0.246214	+	0.0793946i
$647$	19.5824	−	33.9177i	0.769862	−	1.33344i	−0.167775	−	0.985825i	$-0.553658\pi$
$647$	19.5824	−	33.9177i	0.769862	−	1.33344i	0.937637	−	0.347615i	$-0.113008\pi$
$648$		0			0
$649$	39.7169	−	22.9306i	1.55903	−	0.900104i
$650$	3.64065	−	3.29276i	0.142798	−	0.129153i
$651$		0			0
$652$	0.195484	−	1.94304i	0.00765573	−	0.0760954i
$653$	35.9422	−	20.7512i	1.40653	−	0.812058i	0.411475	−	0.911421i	$-0.365014\pi$
$653$	35.9422	−	20.7512i	1.40653	−	0.812058i	0.995051	+	0.0993632i	$0.0316806\pi$
$654$		0			0
$655$	−7.00008	−	4.04150i	−0.273516	−	0.157914i
$656$	4.54860	−	1.52282i	0.177593	−	0.0594561i
$657$		0			0
$658$	5.69772	+	40.9637i	0.222120	+	1.59693i
$659$	35.4347			1.38034			0.690170	−	0.723647i	$-0.257536\pi$
$659$	35.4347			1.38034			0.690170	+	0.723647i	$0.257536\pi$
$660$		0			0
$661$	−11.8165	+	20.4668i	−0.459610	+	0.796067i	−0.998940	−	0.0460268i	$-0.985344\pi$
$661$	−11.8165	+	20.4668i	−0.459610	+	0.796067i	0.539330	+	0.842094i	$0.318677\pi$
$662$	−5.85856	−	27.2639i	−0.227700	−	1.05964i
$663$		0			0
$664$	1.09766	−	0.808744i	0.0425974	−	0.0313854i
$665$	−4.29700	−	2.92121i	−0.166630	−	0.113280i
$666$		0			0
$667$	7.10140	+	12.3000i	0.274967	+	0.476257i
$668$	3.38069	+	2.43330i	0.130803	+	0.0941472i
$669$		0			0
$670$	−51.6556	−	16.6569i	−1.99563	−	0.643514i
$671$	−19.0503			−0.735428
$672$		0			0
$673$	8.69720			0.335253			0.167626	−	0.985851i	$-0.446390\pi$
$673$	8.69720			0.335253			0.167626	+	0.985851i	$0.446390\pi$
$674$	33.3423	+	10.7516i	1.28430	+	0.414137i
$675$		0			0
$676$	−19.3180	−	13.9044i	−0.743001	−	0.534786i
$677$	−5.45947	−	9.45608i	−0.209825	−	0.363427i	0.741835	−	0.670583i	$-0.233956\pi$
$677$	−5.45947	−	9.45608i	−0.209825	−	0.363427i	−0.951659	+	0.307156i	$0.900623\pi$
$678$		0			0
$679$	0.705909	−	9.59223i	0.0270903	−	0.368116i
$680$	−44.8028	+	33.0103i	−1.71811	+	1.26589i
$681$		0			0
$682$	6.63247	+	30.8655i	0.253971	+	1.18190i
$683$	18.2758	−	31.6547i	0.699305	−	1.21123i	−0.269402	−	0.963028i	$-0.586826\pi$
$683$	18.2758	−	31.6547i	0.699305	−	1.21123i	0.968708	−	0.248204i	$-0.0798405\pi$
$684$		0			0
$685$	−36.7936			−1.40581
$686$	22.5676	+	13.2929i	0.861636	+	0.507527i
$687$		0			0
$688$	1.70569	+	5.09484i	0.0650289	+	0.194239i
$689$	−7.33482	−	4.23476i	−0.279434	−	0.161332i
$690$		0			0
$691$	−4.59821	+	2.65478i	−0.174924	+	0.100993i	−0.584906	−	0.811101i	$-0.698869\pi$
$691$	−4.59821	+	2.65478i	−0.174924	+	0.100993i	0.409981	+	0.912094i	$0.365535\pi$
$692$	−4.27360	+	42.4782i	−0.162458	+	1.61478i
$693$		0			0
$694$	15.7206	−	14.2183i	0.596744	−	0.539720i
$695$	−15.2733	+	8.81806i	−0.579350	+	0.334488i
$696$		0			0
$697$	4.09222	−	7.08793i	0.155004	−	0.268475i
$698$	−36.9530	−	11.9159i	−1.39869	−	0.451024i
$699$		0			0
$700$	16.4577	−	6.00511i	0.622044	−	0.226972i
$701$			6.16681i			0.232917i	0.993196	+	0.116459i	$0.0371542\pi$
$701$			6.16681i			0.232917i	−0.993196	+	0.116459i	$0.962846\pi$
$702$		0			0
$703$	0.810940	−	1.40459i	0.0305852	−	0.0529751i
$704$	−31.6508	−	34.2218i	−1.19288	−	1.28978i
$705$		0			0
$706$	22.7712	+	25.1771i	0.857006	+	0.947553i
$707$	−3.72564	+	5.48028i	−0.140117	+	0.206107i
$708$		0			0
$709$	1.73062	−	0.999172i	0.0649947	−	0.0375247i	−0.467151	−	0.884178i	$-0.654719\pi$
$709$	1.73062	−	0.999172i	0.0649947	−	0.0375247i	0.532145	+	0.846653i	$0.321386\pi$
$710$	−4.32611	+	0.929608i	−0.162356	+	0.0348876i
$711$		0			0
$712$	32.1111	+	14.0407i	1.20342	+	0.526198i
$713$			8.22554i			0.308049i
$714$		0			0
$715$	17.6109			0.658611
$716$	−12.6725	+	5.70988i	−0.473594	+	0.213388i
$717$		0			0
$718$	−18.8791	+	4.05680i	−0.704562	+	0.151399i
$719$	−6.72446	−	11.6471i	−0.250780	−	0.434364i	0.712961	−	0.701204i	$-0.247354\pi$
$719$	−6.72446	−	11.6471i	−0.250780	−	0.434364i	−0.963741	+	0.266840i	$0.914020\pi$
$720$		0			0
$721$	−5.32569	−	11.0211i	−0.198339	−	0.410447i
$722$	19.4415	−	17.5837i	0.723539	−	0.654399i
$723$		0			0
$724$	−12.4604	−	8.96854i	−0.463086	−	0.333313i
$725$	−18.9672	−	10.9507i	−0.704423	−	0.406699i
$726$		0			0
$727$	−19.6532			−0.728897			−0.364448	−	0.931224i	$-0.618742\pi$
$727$	−19.6532			−0.728897			−0.364448	+	0.931224i	$0.618742\pi$
$728$	4.17765	+	6.64080i	0.154834	+	0.246124i
$729$		0			0
$730$	−7.06322	+	21.9041i	−0.261421	+	0.810706i
$731$	7.93911	+	4.58365i	0.293639	+	0.169532i
$732$		0			0
$733$	−12.6139	−	21.8480i	−0.465907	−	0.806974i	0.533335	−	0.845904i	$-0.320938\pi$
$733$	−12.6139	−	21.8480i	−0.465907	−	0.806974i	−0.999242	+	0.0389298i	$0.987605\pi$
$734$	−36.3793	+	32.9030i	−1.34279	+	1.21447i
$735$		0			0
$736$	−6.18931	−	10.4500i	−0.228141	−	0.385190i
$737$	−38.7849	−	67.1774i	−1.42866	−	2.47451i
$738$		0			0
$739$	−3.35478	+	5.81064i	−0.123407	+	0.213748i	−0.921109	−	0.389304i	$-0.872716\pi$
$739$	−3.35478	+	5.81064i	−0.123407	+	0.213748i	0.797702	+	0.603052i	$0.206049\pi$
$740$	5.63904	+	12.5153i	0.207295	+	0.460072i
$741$		0			0
$742$	−18.5756	−	23.8455i	−0.681932	−	0.875395i
$743$			26.0661i			0.956273i	0.878286	+	0.478137i	$0.158688\pi$
$743$			26.0661i			0.956273i	−0.878286	+	0.478137i	$0.841312\pi$
$744$		0			0
$745$	5.04967	+	2.91543i	0.185005	+	0.106813i
$746$	−8.40973	+	1.80711i	−0.307902	+	0.0661630i
$747$		0			0
$748$	−79.1363	−	7.96167i	−2.89351	−	0.291107i
$749$	6.98682	+	14.4587i	0.255293	+	0.528308i
$750$		0			0
$751$	4.94762	−	2.85651i	0.180541	−	0.104236i	−0.407006	−	0.913426i	$-0.633427\pi$
$751$	4.94762	−	2.85651i	0.180541	−	0.104236i	0.587547	+	0.809190i	$0.300094\pi$
$752$	−29.2911	+	33.1191i	−1.06814	+	1.20773i
$753$		0			0
$754$	3.01011	−	9.33479i	0.109622	−	0.339953i
$755$		−	40.5561i		−	1.47599i
$756$		0			0
$757$		−	4.75364i		−	0.172774i	−0.996262	−	0.0863869i	$-0.972468\pi$
$757$		−	4.75364i		−	0.172774i	0.996262	−	0.0863869i	$-0.0275321\pi$
$758$	−25.6578	−	8.27366i	−0.931935	−	0.300513i
$759$		0			0
$760$	−0.617485	−	5.52026i	−0.0223985	−	0.200241i
$761$	23.6671	−	13.6642i	0.857931	−	0.495327i	−0.00538774	−	0.999985i	$-0.501715\pi$
$761$	23.6671	−	13.6642i	0.857931	−	0.495327i	0.863319	+	0.504659i	$0.168382\pi$
$762$		0			0
$763$	31.8674	+	21.6643i	1.15368	+	0.784300i
$764$	35.4409	+	3.56560i	1.28221	+	0.128999i
$765$		0			0
$766$	−2.45116	−	11.4069i	−0.0885639	−	0.412149i
$767$	−7.14622	−	4.12587i	−0.258035	−	0.148977i
$768$		0			0
$769$			22.7151i			0.819127i	0.912282	+	0.409564i	$0.134319\pi$
$769$			22.7151i			0.819127i	−0.912282	+	0.409564i	$0.865681\pi$
$770$	58.2414	+	23.6274i	2.09887	+	0.851471i
$771$		0			0
$772$	25.1563	−	11.3347i	0.905393	−	0.407945i
$773$	9.05937	−	15.6913i	0.325843	−	0.564376i	−0.655840	−	0.754900i	$-0.727685\pi$
$773$	9.05937	−	15.6913i	0.325843	−	0.564376i	0.981683	+	0.190524i	$0.0610187\pi$
$774$		0			0
$775$	−6.34209	−	10.9848i	−0.227814	−	0.394586i
$776$	8.27799	−	6.09915i	0.297162	−	0.218947i
$777$		0			0
$778$	18.6134	+	20.5800i	0.667324	+	0.737830i
$779$	0.408460	+	0.707474i	0.0146346	+	0.0253479i
$780$		0			0
$781$	−5.47676	−	3.16201i	−0.195974	−	0.113146i
$782$	−19.7229	−	6.35988i	−0.705290	−	0.227429i
$783$		0			0
$784$	4.90648	+	27.5668i	0.175231	+	0.984527i
$785$	−15.0910			−0.538622
$786$		0			0
$787$	4.25358	+	2.45581i	0.151624	+	0.0875400i	0.573892	−	0.818931i	$-0.305433\pi$
$787$	4.25358	+	2.45581i	0.151624	+	0.0875400i	−0.422269	+	0.906471i	$0.638766\pi$
$788$	−1.32235	+	1.83719i	−0.0471067	+	0.0654473i
$789$		0			0
$790$	−34.6190	−	38.2767i	−1.23169	−	1.36182i
$791$	−10.1026	−	0.743469i	−0.359207	−	0.0264347i
$792$		0			0
$793$	1.71385	+	2.96847i	0.0608604	+	0.105413i
$794$	−9.31826	−	43.3643i	−0.330693	−	1.53894i
$795$		0			0
$796$	−15.5574	+	7.00974i	−0.551419	+	0.248454i
$797$	−23.8384			−0.844398			−0.422199	−	0.906503i	$-0.638742\pi$
$797$	−23.8384			−0.844398			−0.422199	+	0.906503i	$0.638742\pi$
$798$		0			0
$799$			75.4394i			2.66885i
$800$	16.3227	+	9.18332i	0.577094	+	0.324679i
$801$		0			0
$802$	−10.3728	−	48.2717i	−0.366276	−	1.70453i
$803$	−28.4859	+	16.4464i	−1.00525	+	0.580379i
$804$		0			0
$805$	13.5427	+	9.20672i	0.477319	+	0.324494i
$806$	4.21286	−	3.81028i	0.148392	−	0.134211i
$807$		0			0
$808$	−7.04038	+	0.787523i	−0.247680	+	0.0277050i
$809$	−0.597915	+	1.03562i	−0.0210216	+	0.0364104i	−0.876345	−	0.481684i	$-0.840025\pi$
$809$	−0.597915	+	1.03562i	−0.0210216	+	0.0364104i	0.855323	+	0.518095i	$0.173359\pi$
$810$		0			0
$811$			6.44559i			0.226335i	0.993576	+	0.113168i	$0.0360997\pi$
$811$			6.44559i			0.226335i	−0.993576	+	0.113168i	$0.963900\pi$
$812$	22.4786	−	26.8328i	0.788845	−	0.941645i
$813$		0			0
$814$	−6.02099	+	18.6720i	−0.211036	+	0.654452i
$815$	−1.40744	+	2.43776i	−0.0493005	+	0.0853910i
$816$		0			0
$817$	−0.792433	+	0.457511i	−0.0277237	+	0.0160063i
$818$	−12.9455	−	14.3132i	−0.452628	−	0.500450i
$819$		0			0
$820$	−6.87941	−	0.692117i	−0.240239	−	0.0241698i
$821$	1.87701	−	1.08369i	0.0655079	−	0.0378210i	−0.466888	−	0.884316i	$-0.654625\pi$
$821$	1.87701	−	1.08369i	0.0655079	−	0.0378210i	0.532396	+	0.846495i	$0.321292\pi$
$822$		0			0
$823$	5.19529	+	2.99950i	0.181096	+	0.104556i	0.587808	−	0.809001i	$-0.299991\pi$
$823$	5.19529	+	2.99950i	0.181096	+	0.104556i	−0.406711	+	0.913557i	$0.633325\pi$
$824$	5.24246	−	11.9895i	0.182630	−	0.417674i
$825$		0			0
$826$	−18.0980	−	23.2323i	−0.629709	−	0.808356i
$827$	−21.0143			−0.730738			−0.365369	−	0.930863i	$-0.619057\pi$
$827$	−21.0143			−0.730738			−0.365369	+	0.930863i	$0.619057\pi$
$828$		0			0
$829$	6.59891	−	11.4296i	0.229190	−	0.396968i	−0.728379	−	0.685175i	$-0.759726\pi$
$829$	6.59891	−	11.4296i	0.229190	−	0.396968i	0.957568	+	0.288207i	$0.0930591\pi$
$830$	−1.92141	+	0.412878i	−0.0666930	+	0.0143312i
$831$		0			0
$832$	−2.48509	+	8.01066i	−0.0861549	+	0.277720i
$833$	37.4317	+	29.6870i	1.29693	+	1.02859i
$834$		0			0
$835$	−3.00200	−	5.19962i	−0.103889	−	0.179940i
$836$	4.63766	−	6.44330i	0.160397	−	0.222846i
$837$		0			0
$838$	−1.83297	+	5.68430i	−0.0633189	+	0.196361i
$839$	33.8661			1.16919			0.584594	−	0.811326i	$-0.301254\pi$
$839$	33.8661			1.16919			0.584594	+	0.811326i	$0.301254\pi$
$840$		0			0
$841$	−14.7602			−0.508973
$842$	−5.07338	+	15.7333i	−0.174840	+	0.542205i
$843$		0			0
$844$	34.4837	+	24.8202i	1.18698	+	0.854346i
$845$	17.1541	+	29.7118i	0.590120	+	1.02212i
$846$		0			0
$847$	26.4206	+	54.6753i	0.907822	+	1.87867i
$848$	6.43684	−	31.6662i	0.221042	−	1.08742i
$849$		0			0
$850$	31.2426	−	6.71351i	1.07161	−	0.230272i
$851$	−2.55582	+	4.42681i	−0.0876124	+	0.151749i
$852$		0			0
$853$	50.0832			1.71482			0.857408	−	0.514638i	$-0.172074\pi$
$853$	50.0832			1.71482			0.857408	+	0.514638i	$0.172074\pi$
$854$	1.68530	+	12.1164i	0.0576696	+	0.414615i
$855$		0			0
$856$	−6.87762	+	15.7291i	−0.235072	+	0.537610i
$857$	−42.6628	−	24.6314i	−1.45734	−	0.841393i	−0.458455	−	0.888717i	$-0.651597\pi$
$857$	−42.6628	−	24.6314i	−1.45734	−	0.841393i	−0.998880	+	0.0473246i	$0.984930\pi$
$858$		0			0
$859$	−3.38667	+	1.95530i	−0.115552	+	0.0667139i	−0.556662	−	0.830739i	$-0.687918\pi$
$859$	−3.38667	+	1.95530i	−0.115552	+	0.0667139i	0.441110	+	0.897453i	$0.354585\pi$
$860$	0.775232	−	7.70554i	0.0264352	−	0.262757i
$861$		0			0
$862$	32.5399	+	35.9779i	1.10831	+	1.22541i
$863$	−37.4230	+	21.6062i	−1.27390	+	0.735484i	−0.975719	−	0.219027i	$-0.929712\pi$
$863$	−37.4230	+	21.6062i	−1.27390	+	0.735484i	−0.298176	+	0.954511i	$0.596378\pi$
$864$		0			0
$865$	30.7690	−	53.2935i	1.04618	−	1.81203i
$866$	−6.15810	+	19.0972i	−0.209261	+	0.648948i
$867$		0			0
$868$	19.0444	−	6.94894i	0.646409	−	0.235862i
$869$		−	73.7611i		−	2.50217i
$870$		0			0
$871$	−6.97851	+	12.0871i	−0.236458	+	0.409557i
$872$	4.57939	+	40.9393i	0.155078	+	1.38638i
$873$		0			0
$874$	1.53407	−	1.38747i	0.0518905	−	0.0469319i
$875$	12.8493	+	0.945604i	0.434386	+	0.0319673i
$876$		0			0
$877$	−18.3069	+	10.5695i	−0.618182	+	0.356907i	−0.776161	−	0.630535i	$-0.782835\pi$
$877$	−18.3069	+	10.5695i	−0.618182	+	0.356907i	0.157979	+	0.987442i	$0.449502\pi$
$878$	8.33401	+	38.7839i	0.281259	+	1.30889i
$879$		0			0
$880$	21.3311	+	63.7152i	0.719071	+	2.14784i
$881$		−	49.1167i		−	1.65478i	−0.561625	−	0.827392i	$-0.689823\pi$
$881$		−	49.1167i		−	1.65478i	0.561625	−	0.827392i	$-0.310177\pi$
$882$		0			0
$883$	37.8457			1.27361			0.636804	−	0.771025i	$-0.280256\pi$
$883$	37.8457			1.27361			0.636804	+	0.771025i	$0.280256\pi$
$884$	5.87883	+	13.0475i	0.197727	+	0.438835i
$885$		0			0
$886$	−3.27438	−	15.2379i	−0.110005	−	0.511929i
$887$	−8.97039	−	15.5372i	−0.301196	−	0.521687i	0.675211	−	0.737625i	$-0.264053\pi$
$887$	−8.97039	−	15.5372i	−0.301196	−	0.521687i	−0.976407	+	0.215937i	$0.930719\pi$
$888$		0			0
$889$	−0.106880	+	1.45233i	−0.00358464	+	0.0487097i
$890$	−33.8859	−	37.4662i	−1.13586	−	1.25587i
$891$		0			0
$892$	5.06790	+	3.64770i	0.169686	+	0.122134i
$893$	−6.52108	−	3.76495i	−0.218220	−	0.125989i
$894$		0			0
$895$	20.0350			0.669697
$896$	−18.9658	+	23.1581i	−0.633604	+	0.773658i
$897$		0			0
$898$	40.6845	+	13.1192i	1.35766	+	0.437793i
$899$	−21.9483	−	12.6718i	−0.732016	−	0.422629i
$900$		0			0
$901$	−27.5677	−	47.7487i	−0.918413	−	1.59074i
$902$	−6.62848	−	7.32881i	−0.220704	−	0.244023i
$903$		0			0
$904$	−6.42367	−	8.71844i	−0.213648	−	0.289971i
$905$	11.0646	+	19.1645i	0.367801	+	0.637049i
$906$		0			0
$907$	−11.0887	+	19.2062i	−0.368194	+	0.637730i	−0.989283	−	0.146009i	$-0.953357\pi$
$907$	−11.0887	+	19.2062i	−0.368194	+	0.637730i	0.621089	+	0.783740i	$0.286690\pi$
$908$	−4.29427	−	9.53072i	−0.142510	−	0.316288i
$909$		0			0
$910$	−1.55796	−	11.2010i	−0.0516459	−	0.371308i
$911$			35.2495i			1.16787i	0.811801	+	0.583934i	$0.198487\pi$
$911$			35.2495i			1.16787i	−0.811801	+	0.583934i	$0.801513\pi$
$912$		0			0
$913$	−2.43246	−	1.40438i	−0.0805027	−	0.0464783i
$914$	7.56951	+	35.2261i	0.250377	+	1.16518i
$915$		0			0
$916$	−5.69094	+	56.5661i	−0.188034	+	1.86900i
$917$	−6.67927	+	3.22760i	−0.220569	+	0.106585i
$918$		0			0
$919$	−15.1837	+	8.76632i	−0.500864	+	0.289174i	−0.729070	−	0.684439i	$-0.760047\pi$
$919$	−15.1837	+	8.76632i	−0.500864	+	0.289174i	0.228206	+	0.973613i	$0.426714\pi$
$920$	1.94611	+	17.3980i	0.0641614	+	0.573597i
$921$		0			0
$922$	−37.5917	−	12.1219i	−1.23802	−	0.399213i
$923$			1.13787i			0.0374535i
$924$		0			0
$925$		−	7.88239i		−	0.259171i
$926$	8.43011	−	26.1430i	0.277031	−	0.859113i
$927$		0			0
$928$	37.4186	−	0.416312i	1.22833	−	0.0136661i
$929$	44.9106	−	25.9292i	1.47347	−	0.850708i	0.473916	−	0.880570i	$-0.342840\pi$
$929$	44.9106	−	25.9292i	1.47347	−	0.850708i	0.999554	+	0.0298619i	$0.00950676\pi$
$930$		0			0
$931$	−4.43428	+	1.75406i	−0.145328	+	0.0574870i
$932$	−1.22513	+	12.1774i	−0.0401304	+	0.398882i
$933$		0			0
$934$	−2.08765	+	0.448600i	−0.0683098	+	0.0146786i
$935$	99.2852	+	57.3223i	3.24697	+	1.87464i
$936$		0			0
$937$		−	36.9665i		−	1.20764i	−0.797120	−	0.603821i	$-0.793644\pi$
$937$		−	36.9665i		−	1.20764i	0.797120	−	0.603821i	$-0.206356\pi$
$938$	−39.2952	+	30.6110i	−1.28303	+	0.999484i
$939$		0			0
$940$	58.1048	−	26.1804i	1.89517	−	0.853909i
$941$	26.2751	−	45.5098i	0.856544	−	1.48358i	−0.0186621	−	0.999826i	$-0.505941\pi$
$941$	26.2751	−	45.5098i	0.856544	−	1.48358i	0.875206	−	0.483751i	$-0.160726\pi$
$942$		0			0
$943$	−1.28733	−	2.22973i	−0.0419214	−	0.0726099i
$944$	6.27133	−	30.8520i	0.204114	−	1.00415i
$945$		0			0
$946$	8.20891	−	7.42448i	0.266895	−	0.241391i
$947$	13.4671	+	23.3256i	0.437621	+	0.757982i	0.997505	−	0.0705889i	$-0.0224879\pi$
$947$	13.4671	+	23.3256i	0.437621	+	0.757982i	−0.559885	+	0.828571i	$0.689155\pi$
$948$		0			0
$949$	5.12543	+	2.95917i	0.166379	+	0.0960588i
$950$	−0.978897	+	3.03570i	−0.0317596	+	0.0984912i
$951$		0			0
$952$	1.93704	+	51.0368i	0.0627798	+	1.65411i
$953$	31.5488			1.02196			0.510982	−	0.859591i	$-0.329282\pi$
$953$	31.5488			1.02196			0.510982	+	0.859591i	$0.329282\pi$
$954$		0			0
$955$	−44.4645	−	25.6716i	−1.43884	−	0.830713i
$956$	−10.3228	+	14.3419i	−0.333862	+	0.463849i
$957$		0			0
$958$	−14.9364	+	13.5091i	−0.482572	+	0.436458i
$959$	−18.9846	+	27.9256i	−0.613043	+	0.901764i
$960$		0			0
$961$	8.16112	+	14.1355i	0.263262	+	0.455983i
$962$	3.45119	−	0.741604i	0.111271	−	0.0239103i
$963$		0			0
$964$	4.89297	+	10.8595i	0.157592	+	0.349760i
$965$	−39.7716			−1.28029
$966$		0			0
$967$		−	60.7635i		−	1.95402i	−0.213187	−	0.977011i	$-0.568384\pi$
$967$		−	60.7635i		−	1.95402i	0.213187	−	0.977011i	$-0.431616\pi$
$968$	−26.0077	+	59.4795i	−0.835918	+	1.91174i
$969$		0			0
$970$	−14.4903	+	3.11372i	−0.465255	+	0.0999756i
$971$	13.9382	−	8.04723i	0.447299	−	0.258248i	−0.259390	−	0.965773i	$-0.583521\pi$
$971$	13.9382	−	8.04723i	0.447299	−	0.258248i	0.706689	+	0.707525i	$0.250188\pi$
$972$		0			0
$973$	−1.18792	+	16.1420i	−0.0380830	+	0.517489i
$974$	−7.01129	−	7.75207i	−0.224656	−	0.248392i
$975$		0			0
$976$	−8.66384	+	9.79612i	−0.277323	+	0.313566i
$977$	−16.3583	+	28.3334i	−0.523349	+	0.906467i	0.476282	+	0.879293i	$0.341984\pi$
$977$	−16.3583	+	28.3334i	−0.523349	+	0.906467i	−0.999631	+	0.0271741i	$0.991349\pi$
$978$		0			0
$979$		−	72.1991i		−	2.30749i
$980$	9.87519	−	39.1331i	0.315451	−	1.25006i
$981$		0			0
$982$	18.9213	+	6.10140i	0.603804	+	0.194704i
$983$	−18.5785	+	32.1789i	−0.592561	+	1.02635i	0.401325	+	0.915936i	$0.368550\pi$
$983$	−18.5785	+	32.1789i	−0.592561	+	1.02635i	−0.993886	+	0.110410i	$0.964783\pi$
$984$		0			0
$985$	2.82567	−	1.63140i	0.0900333	−	0.0519808i
$986$	47.3542	−	42.8291i	1.50806	−	1.36396i
$987$		0			0
$988$	−1.42124	−	0.142987i	−0.0452156	−	0.00454901i
$989$	2.49749	−	1.44193i	0.0794156	−	0.0458506i
$990$		0			0
$991$	−38.2912	−	22.1074i	−1.21636	−	0.702266i	−0.252223	−	0.967669i	$-0.581162\pi$
$991$	−38.2912	−	22.1074i	−1.21636	−	0.702266i	−0.964137	+	0.265403i	$0.914495\pi$
$992$	18.8882	+	10.6267i	0.599699	+	0.337397i
$993$		0			0
$994$	−1.52661	+	3.76308i	−0.0484210	+	0.119358i
$995$	24.5960			0.779747
$996$		0			0
$997$	13.3432	−	23.1110i	0.422582	−	0.731934i	−0.573609	−	0.819129i	$-0.694457\pi$
$997$	13.3432	−	23.1110i	0.422582	−	0.731934i	0.996191	+	0.0871953i	$0.0277904\pi$
$998$	8.01954	+	37.3204i	0.253854	+	1.18136i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.c.451.3		32
3.2	odd	2		168.2.t.a.115.14	yes	32
4.3	odd	2		2016.2.bs.c.1711.3		32
7.5	odd	6	inner	504.2.bk.c.19.8		32
8.3	odd	2	inner	504.2.bk.c.451.8		32
8.5	even	2		2016.2.bs.c.1711.14		32
12.11	even	2		672.2.bb.a.367.15		32
21.5	even	6		168.2.t.a.19.9	✓	32
21.11	odd	6		1176.2.p.a.979.8		32
21.17	even	6		1176.2.p.a.979.7		32
24.5	odd	2		672.2.bb.a.367.10		32
24.11	even	2		168.2.t.a.115.9	yes	32
28.19	even	6		2016.2.bs.c.271.14		32
56.5	odd	6		2016.2.bs.c.271.3		32
56.19	even	6	inner	504.2.bk.c.19.3		32
84.11	even	6		4704.2.p.a.3919.25		32
84.47	odd	6		672.2.bb.a.271.10		32
84.59	odd	6		4704.2.p.a.3919.30		32
168.5	even	6		672.2.bb.a.271.15		32
168.11	even	6		1176.2.p.a.979.5		32
168.53	odd	6		4704.2.p.a.3919.29		32
168.59	odd	6		1176.2.p.a.979.6		32
168.101	even	6		4704.2.p.a.3919.26		32
168.131	odd	6		168.2.t.a.19.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.9	✓	32	21.5	even	6
168.2.t.a.19.14	yes	32	168.131	odd	6
168.2.t.a.115.9	yes	32	24.11	even	2
168.2.t.a.115.14	yes	32	3.2	odd	2
504.2.bk.c.19.3		32	56.19	even	6	inner
504.2.bk.c.19.8		32	7.5	odd	6	inner
504.2.bk.c.451.3		32	1.1	even	1	trivial
504.2.bk.c.451.8		32	8.3	odd	2	inner
672.2.bb.a.271.10		32	84.47	odd	6
672.2.bb.a.271.15		32	168.5	even	6
672.2.bb.a.367.10		32	24.5	odd	2
672.2.bb.a.367.15		32	12.11	even	2
1176.2.p.a.979.5		32	168.11	even	6
1176.2.p.a.979.6		32	168.59	odd	6
1176.2.p.a.979.7		32	21.17	even	6
1176.2.p.a.979.8		32	21.11	odd	6
2016.2.bs.c.271.3		32	56.5	odd	6
2016.2.bs.c.271.14		32	28.19	even	6
2016.2.bs.c.1711.3		32	4.3	odd	2
2016.2.bs.c.1711.14		32	8.5	even	2
4704.2.p.a.3919.25		32	84.11	even	6
4704.2.p.a.3919.26		32	168.101	even	6
4704.2.p.a.3919.29		32	168.53	odd	6
4704.2.p.a.3919.30		32	84.59	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34597 - 0.434022i) q^{2} +(1.62325 + 1.16836i) q^{4} +(-1.44142 - 2.49662i) q^{5} +(-2.63862 - 0.194181i) q^{7} +(-1.67775 - 2.27710i) q^{8} +(0.856518 + 3.98597i) q^{10} +(-2.91340 + 5.04616i) q^{11} +1.04841 q^{13} +(3.46721 + 1.40658i) q^{14} +(1.26988 + 3.79307i) q^{16} +(5.91062 + 3.41250i) q^{17} +(-0.589961 + 0.340614i) q^{19} +(0.577155 - 5.73673i) q^{20} +(6.11148 - 5.52748i) q^{22} +(1.85937 - 1.07351i) q^{23} +(-1.65540 + 2.86723i) q^{25} +(-1.41112 - 0.455033i) q^{26} +(-4.05626 - 3.39805i) q^{28} +6.61515i q^{29} +(-1.91558 + 3.31788i) q^{31} +(-0.0629331 - 5.65650i) q^{32} +(-6.47439 - 7.15845i) q^{34} +(3.31857 + 6.86751i) q^{35} +(-2.06185 + 1.19041i) q^{37} +(0.941902 - 0.202399i) q^{38} +(-3.26670 + 7.47095i) q^{40} -1.19919i q^{41} +1.34319 q^{43} +(-10.6249 + 4.78728i) q^{44} +(-2.96857 + 0.637896i) q^{46} +(5.52670 + 9.57253i) q^{47} +(6.92459 + 1.02474i) q^{49} +(3.47255 - 3.14072i) q^{50} +(1.70183 + 1.22492i) q^{52} +(-6.99615 - 4.03923i) q^{53} +16.7978 q^{55} +(3.98476 + 6.33417i) q^{56} +(2.87112 - 8.90377i) q^{58} +(-6.81625 - 3.93537i) q^{59} +(1.63471 + 2.83140i) q^{61} +(4.01834 - 3.63435i) q^{62} +(-2.37034 + 7.64078i) q^{64} +(-1.51120 - 2.61747i) q^{65} +(-6.65629 + 11.5290i) q^{67} +(5.60739 + 12.4451i) q^{68} +(-1.48603 - 10.6838i) q^{70} +1.08533i q^{71} +(4.88878 + 2.82254i) q^{73} +(3.29184 - 0.707361i) q^{74} +(-1.35561 - 0.136384i) q^{76} +(8.66721 - 12.7491i) q^{77} +(-10.9630 + 6.32946i) q^{79} +(7.63942 - 8.63782i) q^{80} +(-0.520474 + 1.61406i) q^{82} +0.482042i q^{83} -19.6754i q^{85} +(-1.80789 - 0.582976i) q^{86} +(16.3785 - 1.83207i) q^{88} +(-10.7308 + 6.19543i) q^{89} +(-2.76635 - 0.203581i) q^{91} +(4.27246 + 0.429839i) q^{92} +(-3.28406 - 15.2830i) q^{94} +(1.70077 + 0.981939i) q^{95} +3.63532i q^{97} +(-8.87550 - 4.38468i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44}+ \cdots - 60 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

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