LMFDB - Embedded newform 504.2.ch.b.269.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(269,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.269"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.21
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.896824 - 1.09348i) q^{2} +(-0.391414 - 1.96132i) q^{4} +(-3.16007 + 1.82447i) q^{5} +(-1.64838 + 2.06951i) q^{7} +(-2.49571 - 1.33096i) q^{8} +(-0.839002 + 5.09172i) q^{10} +(0.200123 - 0.346624i) q^{11} +0.581419 q^{13} +(0.784669 + 3.65846i) q^{14} +(-3.69359 + 1.53538i) q^{16} +(-2.27603 + 3.94220i) q^{17} +(2.43222 + 4.21272i) q^{19} +(4.81528 + 5.48381i) q^{20} +(-0.199552 - 0.529692i) q^{22} +(-6.21119 + 3.58603i) q^{23} +(4.15738 - 7.20080i) q^{25} +(0.521430 - 0.635772i) q^{26} +(4.70417 + 2.42297i) q^{28} -6.69007 q^{29} +(-2.85749 - 1.64978i) q^{31} +(-1.63359 + 5.41585i) q^{32} +(2.26954 + 6.02426i) q^{34} +(1.43324 - 9.54721i) q^{35} +(1.93278 - 1.11589i) q^{37} +(6.78781 + 1.11848i) q^{38} +(10.3149 - 0.347416i) q^{40} +4.51491 q^{41} -4.09678i q^{43} +(-0.758173 - 0.256833i) q^{44} +(-1.64907 + 10.0079i) q^{46} +(-2.86389 - 4.96040i) q^{47} +(-1.56571 - 6.82265i) q^{49} +(-4.14552 - 11.0039i) q^{50} +(-0.227575 - 1.14035i) q^{52} +(6.74170 - 11.6770i) q^{53} +1.46048i q^{55} +(6.86829 - 2.97096i) q^{56} +(-5.99982 + 7.31549i) q^{58} +(-7.72158 - 4.45806i) q^{59} +(6.42386 + 11.1265i) q^{61} +(-4.36667 + 1.64507i) q^{62} +(4.45710 + 6.64336i) q^{64} +(-1.83733 + 1.06078i) q^{65} +(-8.30513 - 4.79497i) q^{67} +(8.62281 + 2.92100i) q^{68} +(-9.15435 - 10.1294i) q^{70} +6.42019i q^{71} +(-6.18408 - 3.57038i) q^{73} +(0.513154 - 3.11422i) q^{74} +(7.31051 - 6.41929i) q^{76} +(0.387462 + 0.985523i) q^{77} +(4.15037 + 7.18866i) q^{79} +(8.87076 - 11.5908i) q^{80} +(4.04908 - 4.93699i) q^{82} +10.3852i q^{83} -16.6102i q^{85} +(-4.47977 - 3.67409i) q^{86} +(-0.960790 + 0.598715i) q^{88} +(5.25986 + 9.11034i) q^{89} +(-0.958396 + 1.20325i) q^{91} +(9.46452 + 10.7785i) q^{92} +(-7.99252 - 1.31699i) q^{94} +(-15.3720 - 8.87501i) q^{95} -4.00635i q^{97} +(-8.86463 - 4.40663i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82}+ \cdots - 180 q^{94}+O(q^{100}) $ 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

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 $

$2$	0.896824	−	1.09348i	0.634150	−	0.773210i
$2$	0.896824	−	1.09348i	0.634150	−	0.773210i
$3$		0			0
$3$		0			0
$4$	−0.391414	−	1.96132i	−0.195707	−	0.980662i
$5$	−3.16007	+	1.82447i	−1.41323	+	0.815928i	−0.995691	−	0.0927320i	$-0.970440\pi$
$5$	−3.16007	+	1.82447i	−1.41323	+	0.815928i	−0.417537	+	0.908660i	$0.637107\pi$
$6$		0			0
$7$	−1.64838	+	2.06951i	−0.623028	+	0.782200i
$7$	−1.64838	+	2.06951i	−0.623028	+	0.782200i
$8$	−2.49571	−	1.33096i	−0.882366	−	0.470565i
$9$		0			0
$10$	−0.839002	+	5.09172i	−0.265316	+	1.61014i
$11$	0.200123	−	0.346624i	0.0603394	−	0.104511i	−0.834278	−	0.551344i	$-0.814115\pi$
$11$	0.200123	−	0.346624i	0.0603394	−	0.104511i	0.894617	+	0.446833i	$0.147448\pi$
$12$		0			0
$13$	0.581419			0.161256			0.0806282	−	0.996744i	$-0.474307\pi$
$13$	0.581419			0.161256			0.0806282	+	0.996744i	$0.474307\pi$
$14$	0.784669	+	3.65846i	0.209712	+	0.977763i
$15$		0			0
$16$	−3.69359	+	1.53538i	−0.923397	+	0.383845i
$17$	−2.27603	+	3.94220i	−0.552019	+	0.956124i	0.446110	+	0.894978i	$0.352809\pi$
$17$	−2.27603	+	3.94220i	−0.552019	+	0.956124i	−0.998129	+	0.0611464i	$0.980524\pi$
$18$		0			0
$19$	2.43222	+	4.21272i	0.557989	+	0.966465i	0.997664	+	0.0683081i	$0.0217601\pi$
$19$	2.43222	+	4.21272i	0.557989	+	0.966465i	−0.439676	+	0.898157i	$0.644907\pi$
$20$	4.81528	+	5.48381i	1.07673	+	1.22622i
$21$		0			0
$22$	−0.199552	−	0.529692i	−0.0425447	−	0.112931i
$23$	−6.21119	+	3.58603i	−1.29512	+	0.747739i	−0.979557	−	0.201165i	$-0.935527\pi$
$23$	−6.21119	+	3.58603i	−1.29512	+	0.747739i	−0.315565	+	0.948904i	$0.602194\pi$
$24$		0			0
$25$	4.15738	−	7.20080i	0.831476	−	1.44016i
$26$	0.521430	−	0.635772i	0.102261	−	0.124685i
$27$		0			0
$28$	4.70417	+	2.42297i	0.889005	+	0.457898i
$29$	−6.69007			−1.24232			−0.621158	−	0.783686i	$-0.713337\pi$
$29$	−6.69007			−1.24232			−0.621158	+	0.783686i	$0.713337\pi$
$30$		0			0
$31$	−2.85749	−	1.64978i	−0.513221	−	0.296308i	0.220936	−	0.975288i	$-0.429089\pi$
$31$	−2.85749	−	1.64978i	−0.513221	−	0.296308i	−0.734157	+	0.678980i	$0.762422\pi$
$32$	−1.63359	+	5.41585i	−0.288780	+	0.957396i
$33$		0			0
$34$	2.26954	+	6.02426i	0.389222	+	1.03315i
$35$	1.43324	−	9.54721i	0.242262	−	1.61377i
$36$		0			0
$37$	1.93278	−	1.11589i	0.317747	−	0.183451i	−0.332641	−	0.943054i	$-0.607940\pi$
$37$	1.93278	−	1.11589i	0.317747	−	0.183451i	0.650388	+	0.759602i	$0.274606\pi$
$38$	6.78781	+	1.11848i	1.10113	+	0.181441i
$39$		0			0
$40$	10.3149	−	0.347416i	1.63093	−	0.0549314i
$41$	4.51491			0.705111			0.352556	−	0.935791i	$-0.385313\pi$
$41$	4.51491			0.705111			0.352556	+	0.935791i	$0.385313\pi$
$42$		0			0
$43$		−	4.09678i		−	0.624754i	−0.949958	−	0.312377i	$-0.898875\pi$
$43$		−	4.09678i		−	0.624754i	0.949958	−	0.312377i	$-0.101125\pi$
$44$	−0.758173	−	0.256833i	−0.114299	−	0.0387191i
$45$		0			0
$46$	−1.64907	+	10.0079i	−0.243143	+	1.47558i
$47$	−2.86389	−	4.96040i	−0.417741	−	0.723549i	0.577971	−	0.816057i	$-0.303845\pi$
$47$	−2.86389	−	4.96040i	−0.417741	−	0.723549i	−0.995712	+	0.0925088i	$0.970511\pi$
$48$		0			0
$49$	−1.56571	−	6.82265i	−0.223673	−	0.974664i
$50$	−4.14552	−	11.0039i	−0.586265	−	1.55618i
$51$		0			0
$52$	−0.227575	−	1.14035i	−0.0315590	−	0.158138i
$53$	6.74170	−	11.6770i	0.926043	−	1.60395i	0.136169	−	0.990686i	$-0.456521\pi$
$53$	6.74170	−	11.6770i	0.926043	−	1.60395i	0.789875	−	0.613268i	$-0.210146\pi$
$54$		0			0
$55$			1.46048i			0.196931i
$56$	6.86829	−	2.97096i	0.917814	−	0.397011i
$57$		0			0
$58$	−5.99982	+	7.31549i	−0.787814	+	0.960570i
$59$	−7.72158	−	4.45806i	−1.00526	−	0.580390i	−0.0954627	−	0.995433i	$-0.530433\pi$
$59$	−7.72158	−	4.45806i	−1.00526	−	0.580390i	−0.909802	+	0.415043i	$0.863766\pi$
$60$		0			0
$61$	6.42386	+	11.1265i	0.822491	+	1.42460i	0.903822	+	0.427910i	$0.140750\pi$
$61$	6.42386	+	11.1265i	0.822491	+	1.42460i	−0.0813302	+	0.996687i	$0.525917\pi$
$62$	−4.36667	+	1.64507i	−0.554568	+	0.208924i
$63$		0			0
$64$	4.45710	+	6.64336i	0.557138	+	0.830420i
$65$	−1.83733	+	1.06078i	−0.227892	+	0.131574i
$66$		0			0
$67$	−8.30513	−	4.79497i	−1.01463	−	0.585798i	−0.102088	−	0.994775i	$-0.532552\pi$
$67$	−8.30513	−	4.79497i	−1.01463	−	0.585798i	−0.912545	+	0.408977i	$0.865886\pi$
$68$	8.62281	+	2.92100i	1.04567	+	0.354224i
$69$		0			0
$70$	−9.15435	−	10.1294i	−1.09415	−	1.21069i
$71$			6.42019i			0.761937i	0.924588	+	0.380968i	$0.124409\pi$
$71$			6.42019i			0.761937i	−0.924588	+	0.380968i	$0.875591\pi$
$72$		0			0
$73$	−6.18408	−	3.57038i	−0.723791	−	0.417881i	0.0923551	−	0.995726i	$-0.470561\pi$
$73$	−6.18408	−	3.57038i	−0.723791	−	0.417881i	−0.816147	+	0.577845i	$0.803894\pi$
$74$	0.513154	−	3.11422i	0.0596529	−	0.362021i
$75$		0			0
$76$	7.31051	−	6.41929i	0.838573	−	0.736343i
$77$	0.387462	+	0.985523i	0.0441553	+	0.112311i
$78$		0			0
$79$	4.15037	+	7.18866i	0.466953	+	0.808787i	0.999287	−	0.0377474i	$-0.0120182\pi$
$79$	4.15037	+	7.18866i	0.466953	+	0.808787i	−0.532334	+	0.846535i	$0.678685\pi$
$80$	8.87076	−	11.5908i	0.991782	−	1.29589i
$81$		0			0
$82$	4.04908	−	4.93699i	0.447146	−	0.545199i
$83$			10.3852i			1.13992i	0.821673	+	0.569959i	$0.193041\pi$
$83$			10.3852i			1.13992i	−0.821673	+	0.569959i	$0.806959\pi$
$84$		0			0
$85$		−	16.6102i		−	1.80163i
$86$	−4.47977	−	3.67409i	−0.483066	−	0.396188i
$87$		0			0
$88$	−0.960790	+	0.598715i	−0.102421	+	0.0638233i
$89$	5.25986	+	9.11034i	0.557544	+	0.965694i	0.997701	+	0.0677734i	$0.0215895\pi$
$89$	5.25986	+	9.11034i	0.557544	+	0.965694i	−0.440157	+	0.897921i	$0.645077\pi$
$90$		0			0
$91$	−0.958396	+	1.20325i	−0.100467	+	0.126135i
$92$	9.46452	+	10.7785i	0.986744	+	1.12374i
$93$		0			0
$94$	−7.99252	−	1.31699i	−0.824365	−	0.135837i
$95$	−15.3720	−	8.87501i	−1.57713	−	0.910557i
$96$		0			0
$97$		−	4.00635i		−	0.406783i	−0.979097	−	0.203392i	$-0.934804\pi$
$97$		−	4.00635i		−	0.406783i	0.979097	−	0.203392i	$-0.0651964\pi$
$98$	−8.86463	−	4.40663i	−0.895462	−	0.445137i
$99$		0			0
$100$	−15.7504	−	5.33548i	−1.57504	−	0.533548i
$101$	12.1877	+	7.03656i	1.21272	+	0.700164i	0.963351	−	0.268245i	$-0.0864437\pi$
$101$	12.1877	+	7.03656i	1.21272	+	0.700164i	0.249368	+	0.968409i	$0.419777\pi$
$102$		0			0
$103$	−17.4850	+	10.0950i	−1.72285	+	0.994686i	−0.809943	+	0.586508i	$0.800502\pi$
$103$	−17.4850	+	10.0950i	−1.72285	+	0.994686i	−0.912903	+	0.408177i	$0.866165\pi$
$104$	−1.45105	−	0.773843i	−0.142287	−	0.0758816i
$105$		0			0
$106$	−6.72246	−	17.8441i	−0.652943	−	1.73317i
$107$	2.09913	+	3.63581i	0.202931	+	0.351487i	0.949472	−	0.313853i	$-0.101620\pi$
$107$	2.09913	+	3.63581i	0.202931	+	0.351487i	−0.746541	+	0.665340i	$0.768287\pi$
$108$		0			0
$109$	16.0796	+	9.28357i	1.54015	+	0.889205i	0.998829	+	0.0483874i	$0.0154082\pi$
$109$	16.0796	+	9.28357i	1.54015	+	0.889205i	0.541319	+	0.840817i	$0.317925\pi$
$110$	1.59701	+	1.30979i	0.152269	+	0.124884i
$111$		0			0
$112$	2.91095	−	10.1748i	0.275058	−	0.961428i
$113$		−	3.44494i		−	0.324073i	−0.986785	−	0.162037i	$-0.948194\pi$
$113$		−	3.44494i		−	0.324073i	0.986785	−	0.162037i	$-0.0518063\pi$
$114$		0			0
$115$	13.0852	−	22.6642i	1.22020	−	2.11345i
$116$	2.61859	+	13.1214i	0.243130	+	1.21829i
$117$		0			0
$118$	−11.7997	+	4.44533i	−1.08625	+	0.409226i
$119$	−4.40666	−	11.2085i	−0.403958	−	1.02748i
$120$		0			0
$121$	5.41990	+	9.38754i	0.492718	+	0.853413i
$122$	17.9277	+	2.95408i	1.62310	+	0.267450i
$123$		0			0
$124$	−2.11728	+	6.25022i	−0.190137	+	0.561286i
$125$			12.0954i			1.08184i
$126$		0			0
$127$	−3.82179			−0.339129			−0.169565	−	0.985519i	$-0.554236\pi$
$127$	−3.82179			−0.339129			−0.169565	+	0.985519i	$0.554236\pi$
$128$	11.2616	+	1.08415i	0.995398	+	0.0958264i
$129$		0			0
$130$	−0.487811	+	2.96042i	−0.0427839	+	0.259646i
$131$	0.160576	−	0.0927085i	0.0140296	−	0.00809998i	−0.492969	−	0.870047i	$-0.664088\pi$
$131$	0.160576	−	0.0927085i	0.0140296	−	0.00809998i	0.506998	+	0.861947i	$0.330755\pi$
$132$		0			0
$133$	−12.7275	−	1.91066i	−1.10361	−	0.165676i
$134$	−12.6915	+	4.78128i	−1.09637	+	0.413040i
$135$		0			0
$136$	10.9272	−	6.80928i	0.937001	−	0.583891i
$137$	13.2672	+	7.65983i	1.13350	+	0.654424i	0.944812	−	0.327614i	$-0.106245\pi$
$137$	13.2672	+	7.65983i	1.13350	+	0.654424i	0.188684	+	0.982038i	$0.439578\pi$
$138$		0			0
$139$	−10.5472			−0.894602			−0.447301	−	0.894383i	$-0.647615\pi$
$139$	−10.5472			−0.894602			−0.447301	+	0.894383i	$0.647615\pi$
$140$	−19.2862	+	0.925864i	−1.62998	+	0.0782498i
$141$		0			0
$142$	7.02038	+	5.75778i	0.589137	+	0.483182i
$143$	0.116355	−	0.201533i	0.00973013	−	0.0168531i
$144$		0			0
$145$	21.1411	−	12.2058i	1.75567	−	1.01364i
$146$	−9.45018	+	3.56019i	−0.782102	+	0.294643i
$147$		0			0
$148$	−2.94514	−	3.35403i	−0.242089	−	0.275700i
$149$	−4.59117	−	7.95213i	−0.376123	−	0.651464i	0.614371	−	0.789017i	$-0.289410\pi$
$149$	−4.59117	−	7.95213i	−0.376123	−	0.651464i	−0.990494	+	0.137553i	$0.956076\pi$
$150$		0			0
$151$	1.79999	−	3.11768i	0.146481	−	0.253713i	−0.783443	−	0.621463i	$-0.786539\pi$
$151$	1.79999	−	3.11768i	0.146481	−	0.253713i	0.929925	+	0.367750i	$0.119872\pi$
$152$	−0.463144	−	13.7509i	−0.0375659	−	1.11534i
$153$		0			0
$154$	1.42514	+	0.460157i	0.114841	+	0.0370805i
$155$	12.0399			0.967065
$156$		0			0
$157$	0.359090	−	0.621963i	0.0286585	−	0.0496380i	−0.851340	−	0.524614i	$-0.824210\pi$
$157$	0.359090	−	0.621963i	0.0286585	−	0.0496380i	0.879999	+	0.474976i	$0.157543\pi$
$158$	11.5828	+	1.90859i	0.921481	+	0.151839i
$159$		0			0
$160$	−4.71880	−	20.0949i	−0.373054	−	1.58864i
$161$	2.81706	−	18.7652i	0.222015	−	1.47891i
$162$		0			0
$163$	−19.1125	+	11.0346i	−1.49700	+	0.864296i	−0.999994	−	0.00344810i	$-0.998902\pi$
$163$	−19.1125	+	11.0346i	−1.49700	+	0.864296i	−0.497011	+	0.867744i	$0.665569\pi$
$164$	−1.76720	−	8.85521i	−0.137995	−	0.691476i
$165$		0			0
$166$	11.3560	+	9.31365i	0.881396	+	0.722879i
$167$	13.4882			1.04375			0.521875	−	0.853022i	$-0.325233\pi$
$167$	13.4882			1.04375			0.521875	+	0.853022i	$0.325233\pi$
$168$		0			0
$169$	−12.6620			−0.973996
$170$	−18.1630	−	14.8964i	−1.39304	−	1.14250i
$171$		0			0
$172$	−8.03512	+	1.60354i	−0.612673	+	0.122269i
$173$	−14.0098	+	8.08856i	−1.06514	+	0.614962i	−0.926851	−	0.375430i	$-0.877495\pi$
$173$	−14.0098	+	8.08856i	−1.06514	+	0.614962i	−0.138294	+	0.990391i	$0.544162\pi$
$174$		0			0
$175$	8.04917	+	20.4733i	0.608460	+	1.54764i
$176$	−0.206974	+	1.58755i	−0.0156013	+	0.119666i
$177$		0			0
$178$	14.6792	+	2.41880i	1.10025	+	0.181297i
$179$	0.872025	−	1.51039i	0.0651782	−	0.112892i	−0.831595	−	0.555383i	$-0.812572\pi$
$179$	0.872025	−	1.51039i	0.0651782	−	0.112892i	0.896773	+	0.442491i	$0.145905\pi$
$180$		0			0
$181$	−9.44875			−0.702320			−0.351160	−	0.936315i	$-0.614213\pi$
$181$	−9.44875			−0.702320			−0.351160	+	0.936315i	$0.614213\pi$
$182$	0.456221	+	2.12709i	0.0338174	+	0.157671i
$183$		0			0
$184$	20.2742	−	0.682853i	1.49463	−	0.0503406i
$185$	−4.07182	+	7.05260i	−0.299366	+	0.518517i
$186$		0			0
$187$	0.910974	+	1.57785i	0.0666170	+	0.115384i
$188$	−8.60799	+	7.55858i	−0.627802	+	0.551266i
$189$		0			0
$190$	−23.4906	+	8.84968i	−1.70419	+	0.642023i
$191$	16.4118	−	9.47537i	1.18752	−	0.685614i	0.229776	−	0.973244i	$-0.426201\pi$
$191$	16.4118	−	9.47537i	1.18752	−	0.685614i	0.957742	+	0.287630i	$0.0928673\pi$
$192$		0			0
$193$	2.66715	−	4.61965i	0.191986	−	0.332529i	−0.753922	−	0.656964i	$-0.771841\pi$
$193$	2.66715	−	4.61965i	0.191986	−	0.332529i	0.945908	+	0.324434i	$0.105174\pi$
$194$	−4.38088	−	3.59299i	−0.314529	−	0.257962i
$195$		0			0
$196$	−12.7686	+	5.74135i	−0.912042	+	0.410097i
$197$	−2.80474			−0.199829			−0.0999147	−	0.994996i	$-0.531857\pi$
$197$	−2.80474			−0.199829			−0.0999147	+	0.994996i	$0.531857\pi$
$198$		0			0
$199$	−6.44198	−	3.71928i	−0.456660	−	0.263653i	0.253979	−	0.967210i	$-0.418261\pi$
$199$	−6.44198	−	3.71928i	−0.456660	−	0.263653i	−0.710639	+	0.703557i	$0.751594\pi$
$200$	−19.9596	+	12.4378i	−1.41135	+	0.879484i
$201$		0			0
$202$	18.6246	−	7.01647i	1.31042	−	0.493677i
$203$	11.0278	−	13.8451i	0.773997	−	0.971739i
$204$		0			0
$205$	−14.2675	+	8.23733i	−0.996483	+	0.575320i
$206$	−4.64227	+	28.1729i	−0.323442	+	1.96290i
$207$		0			0
$208$	−2.14752	+	0.892699i	−0.148904	+	0.0618975i
$209$	1.94697			0.134675
$210$		0			0
$211$			24.6986i			1.70032i	0.526521	+	0.850162i	$0.323496\pi$
$211$			24.6986i			1.70032i	−0.526521	+	0.850162i	$0.676504\pi$
$212$	−25.5411	−	8.65213i	−1.75417	−	0.594231i
$213$		0			0
$214$	5.85825	+	0.965309i	0.400462	+	0.0659872i
$215$	7.47446	+	12.9461i	0.509754	+	0.882920i
$216$		0			0
$217$	8.12445	−	3.19415i	0.551523	−	0.216833i
$218$	24.5720	−	9.25707i	1.66423	−	0.626968i
$219$		0			0
$220$	2.86447	−	0.571651i	0.193122	−	0.0385407i
$221$	−1.32333	+	2.29207i	−0.0890166	+	0.154181i
$222$		0			0
$223$		−	7.98964i		−	0.535026i	−0.963554	−	0.267513i	$-0.913798\pi$
$223$		−	7.98964i		−	0.535026i	0.963554	−	0.267513i	$-0.0862019\pi$
$224$	−8.51537	−	12.3081i	−0.568957	−	0.822367i
$225$		0			0
$226$	−3.76699	−	3.08951i	−0.250577	−	0.205511i
$227$	2.04318	+	1.17963i	0.135610	+	0.0782947i	0.566270	−	0.824220i	$-0.308386\pi$
$227$	2.04318	+	1.17963i	0.135610	+	0.0782947i	−0.430660	+	0.902514i	$0.641719\pi$
$228$		0			0
$229$	−5.32512	−	9.22338i	−0.351894	−	0.609498i	0.634687	−	0.772769i	$-0.281129\pi$
$229$	−5.32512	−	9.22338i	−0.351894	−	0.609498i	−0.986581	+	0.163271i	$0.947796\pi$
$230$	−13.0479	−	34.6343i	−0.860351	−	2.28372i
$231$		0			0
$232$	16.6965	+	8.90420i	1.09618	+	0.584589i
$233$	12.6645	−	7.31188i	0.829682	−	0.479017i	−0.0240618	−	0.999710i	$-0.507660\pi$
$233$	12.6645	−	7.31188i	0.829682	−	0.479017i	0.853744	+	0.520693i	$0.174327\pi$
$234$		0			0
$235$	18.1002	+	10.4502i	1.18073	+	0.681693i
$236$	−5.72136	+	16.8895i	−0.372429	+	1.09941i
$237$		0			0
$238$	−16.2083	−	5.23344i	−1.05063	−	0.339233i
$239$			11.5819i			0.749168i	0.927193	+	0.374584i	$0.122214\pi$
$239$			11.5819i			0.749168i	−0.927193	+	0.374584i	$0.877786\pi$
$240$		0			0
$241$	1.36690	+	0.789180i	0.0880498	+	0.0508356i	0.543378	−	0.839488i	$-0.317145\pi$
$241$	1.36690	+	0.789180i	0.0880498	+	0.0508356i	−0.455329	+	0.890323i	$0.650478\pi$
$242$	15.1258	+	2.49240i	0.972325	+	0.160217i
$243$		0			0
$244$	19.3082	−	16.9543i	1.23608	−	1.08539i
$245$	17.3955	+	18.7035i	1.11136	+	1.19492i
$246$		0			0
$247$	1.41414	+	2.44935i	0.0899793	+	0.155849i
$248$	4.93569	+	7.92056i	0.313416	+	0.502956i
$249$		0			0
$250$	13.2261	+	10.8474i	0.836492	+	0.686051i
$251$			17.9769i			1.13469i	0.823480	+	0.567345i	$0.192029\pi$
$251$			17.9769i			1.13469i	−0.823480	+	0.567345i	$0.807971\pi$
$252$		0			0
$253$			2.87059i			0.180473i
$254$	−3.42747	+	4.17907i	−0.215059	+	0.262218i
$255$		0			0
$256$	11.2852	−	11.3421i	0.705326	−	0.708883i
$257$	3.71744	+	6.43879i	0.231887	+	0.401640i	0.958363	−	0.285551i	$-0.0921766\pi$
$257$	3.71744	+	6.43879i	0.231887	+	0.401640i	−0.726476	+	0.687192i	$0.758843\pi$
$258$		0			0
$259$	−0.876604	+	5.83931i	−0.0544695	+	0.362837i
$260$	2.79969	+	3.18839i	0.173629	+	0.197735i
$261$		0			0
$262$	0.0426330	−	0.258730i	0.00263388	−	0.0159844i
$263$	−7.28419	−	4.20553i	−0.449162	−	0.259324i	0.258314	−	0.966061i	$-0.416833\pi$
$263$	−7.28419	−	4.20553i	−0.449162	−	0.259324i	−0.707476	+	0.706737i	$0.750166\pi$
$264$		0			0
$265$			49.2001i			3.02234i
$266$	−13.5036	+	12.2037i	−0.827957	+	0.748260i
$267$		0			0
$268$	−6.15374	+	18.1659i	−0.375900	+	1.10966i
$269$	−11.9259	−	6.88541i	−0.727134	−	0.419811i	0.0902390	−	0.995920i	$-0.471237\pi$
$269$	−11.9259	−	6.88541i	−0.727134	−	0.419811i	−0.817373	+	0.576109i	$0.804570\pi$
$270$		0			0
$271$	16.0976	−	9.29397i	0.977861	−	0.564568i	0.0762374	−	0.997090i	$-0.475709\pi$
$271$	16.0976	−	9.29397i	0.977861	−	0.564568i	0.901624	+	0.432521i	$0.142376\pi$
$272$	2.35395	−	18.0555i	0.142729	−	1.09477i
$273$		0			0
$274$	20.2743	−	7.63797i	1.22481	−	0.461427i
$275$	−1.66398	−	2.88209i	−0.100342	−	0.173797i
$276$		0			0
$277$	15.1885	+	8.76910i	0.912590	+	0.526884i	0.881264	−	0.472625i	$-0.156693\pi$
$277$	15.1885	+	8.76910i	0.912590	+	0.526884i	0.0313266	+	0.999509i	$0.490027\pi$
$278$	−9.45898	+	11.5332i	−0.567312	+	0.691715i
$279$		0			0
$280$	−16.2839	+	21.9194i	−0.973148	+	1.30994i
$281$		−	14.8388i		−	0.885208i	−0.896717	−	0.442604i	$-0.854055\pi$
$281$		−	14.8388i		−	0.885208i	0.896717	−	0.442604i	$-0.145945\pi$
$282$		0			0
$283$	−0.293271	+	0.507960i	−0.0174331	+	0.0301951i	−0.874610	−	0.484826i	$-0.838883\pi$
$283$	−0.293271	+	0.507960i	−0.0174331	+	0.0301951i	0.857177	+	0.515022i	$0.172216\pi$
$284$	12.5921	−	2.51295i	0.747203	−	0.149116i
$285$		0			0
$286$	−0.116023	−	0.307973i	−0.00686060	−	0.0182108i
$287$	−7.44228	+	9.34364i	−0.439304	+	0.551538i
$288$		0			0
$289$	−1.86064	−	3.22272i	−0.109449	−	0.189572i
$290$	5.61298	−	34.0640i	0.329606	−	2.00030i
$291$		0			0
$292$	−4.58214	+	13.5265i	−0.268149	+	0.791577i
$293$		−	6.07405i		−	0.354850i	−0.984134	−	0.177425i	$-0.943223\pi$
$293$		−	6.07405i		−	0.354850i	0.984134	−	0.177425i	$-0.0567767\pi$
$294$		0			0
$295$	32.5344			1.89422
$296$	−6.30885	+	0.212488i	−0.366695	+	0.0123506i
$297$		0			0
$298$	−12.8130	−	2.11130i	−0.742237	−	0.122304i
$299$	−3.61130	+	2.08498i	−0.208847	+	0.120578i
$300$		0			0
$301$	8.47832	+	6.75304i	0.488682	+	0.389239i
$302$	−1.79485	−	4.76427i	−0.103282	−	0.274153i
$303$		0			0
$304$	−15.4517	−	11.8257i	−0.886218	−	0.678250i
$305$	−40.5998	−	23.4403i	−2.32474	−	1.34219i
$306$		0			0
$307$	19.0443			1.08691			0.543457	−	0.839437i	$-0.317115\pi$
$307$	19.0443			1.08691			0.543457	+	0.839437i	$0.317115\pi$
$308$	1.78127	−	1.14569i	0.101497	−	0.0652815i
$309$		0			0
$310$	10.7976	−	13.1654i	0.613264	−	0.747744i
$311$	4.52301	−	7.83409i	0.256476	−	0.444230i	−0.708819	−	0.705390i	$-0.750772\pi$
$311$	4.52301	−	7.83409i	0.256476	−	0.444230i	0.965295	+	0.261160i	$0.0841051\pi$
$312$		0			0
$313$	−6.45654	+	3.72768i	−0.364945	+	0.210701i	−0.671248	−	0.741233i	$-0.734241\pi$
$313$	−6.45654	+	3.72768i	−0.364945	+	0.210701i	0.306303	+	0.951934i	$0.400908\pi$
$314$	−0.358065	−	0.950450i	−0.0202068	−	0.0536370i
$315$		0			0
$316$	12.4748	−	10.9540i	0.701761	−	0.616209i
$317$	−2.40732	−	4.16961i	−0.135209	−	0.234188i	0.790468	−	0.612503i	$-0.209837\pi$
$317$	−2.40732	−	4.16961i	−0.135209	−	0.234188i	−0.925677	+	0.378314i	$0.876504\pi$
$318$		0			0
$319$	−1.33884	+	2.31894i	−0.0749606	+	0.129836i
$320$	−26.2054	−	12.8617i	−1.46493	−	0.718989i
$321$		0			0
$322$	−17.9931	−	19.9095i	−1.00271	−	1.10951i
$323$	−22.1432			−1.23208
$324$		0			0
$325$	2.41718	−	4.18668i	0.134081	−	0.232235i
$326$	−5.07437	+	30.7953i	−0.281044	+	1.70559i
$327$		0			0
$328$	−11.2679	−	6.00916i	−0.622166	−	0.331800i
$329$	14.9863	+	2.24977i	0.826224	+	0.124034i
$330$		0			0
$331$	−5.43500	+	3.13790i	−0.298735	+	0.172475i	−0.641874	−	0.766810i	$-0.721843\pi$
$331$	−5.43500	+	3.13790i	−0.298735	+	0.172475i	0.343140	+	0.939284i	$0.388510\pi$
$332$	20.3687	−	4.06490i	1.11788	−	0.223090i
$333$		0			0
$334$	12.0966	−	14.7492i	0.661895	−	0.807039i
$335$	34.9931			1.91188
$336$		0			0
$337$	−20.1329			−1.09671			−0.548353	−	0.836247i	$-0.684745\pi$
$337$	−20.1329			−1.09671			−0.548353	+	0.836247i	$0.684745\pi$
$338$	−11.3555	+	13.8456i	−0.617660	+	0.753104i
$339$		0			0
$340$	−32.5780	+	6.50147i	−1.76679	+	0.352592i
$341$	−1.14370	+	0.660317i	−0.0619350	+	0.0357582i
$342$		0			0
$343$	16.7004	+	8.00604i	0.901737	+	0.432285i
$344$	−5.45265	+	10.2244i	−0.293987	+	0.551261i
$345$		0			0
$346$	−3.71961	+	22.5735i	−0.199967	+	1.21356i
$347$	−9.04269	+	15.6624i	−0.485437	+	0.840802i	−0.999860	−	0.0167350i	$-0.994673\pi$
$347$	−9.04269	+	15.6624i	−0.485437	+	0.840802i	0.514423	+	0.857537i	$0.328006\pi$
$348$		0			0
$349$	−3.24549			−0.173727			−0.0868635	−	0.996220i	$-0.527684\pi$
$349$	−3.24549			−0.173727			−0.0868635	+	0.996220i	$0.527684\pi$
$350$	29.6060	+	9.55935i	1.58251	+	0.510969i
$351$		0			0
$352$	1.55034	+	1.65008i	0.0826335	+	0.0879494i
$353$	−14.6032	+	25.2934i	−0.777248	+	1.34623i	0.156274	+	0.987714i	$0.450052\pi$
$353$	−14.6032	+	25.2934i	−0.777248	+	1.34623i	−0.933522	+	0.358519i	$0.883282\pi$
$354$		0			0
$355$	−11.7135	−	20.2883i	−0.621685	−	1.07679i
$356$	15.8096	−	13.8822i	0.837905	−	0.735756i
$357$		0			0
$358$	−0.869536	−	2.30810i	−0.0459564	−	0.121987i
$359$	−8.87600	+	5.12456i	−0.468457	+	0.270464i	−0.715594	−	0.698517i	$-0.753844\pi$
$359$	−8.87600	+	5.12456i	−0.468457	+	0.270464i	0.247136	+	0.968981i	$0.420510\pi$
$360$		0			0
$361$	−2.33135	+	4.03802i	−0.122703	+	0.212528i
$362$	−8.47386	+	10.3321i	−0.445376	+	0.543041i
$363$		0			0
$364$	2.73509	+	1.40876i	0.143358	+	0.0738390i
$365$	26.0562			1.36384
$366$		0			0
$367$	−26.6034	−	15.3595i	−1.38869	−	0.801758i	−0.395518	−	0.918458i	$-0.629435\pi$
$367$	−26.6034	−	15.3595i	−1.38869	−	0.801758i	−0.993167	+	0.116700i	$0.962768\pi$
$368$	17.4357	−	22.7819i	0.908896	−	1.18759i
$369$		0			0
$370$	4.06020	+	10.7774i	0.211080	+	0.560291i
$371$	13.0527	+	33.2000i	0.677662	+	1.72366i
$372$		0			0
$373$	−17.5313	+	10.1217i	−0.907737	+	0.524082i	−0.879702	−	0.475525i	$-0.842258\pi$
$373$	−17.5313	+	10.1217i	−0.907737	+	0.524082i	−0.0280346	+	0.999607i	$0.508925\pi$
$374$	2.54234	+	0.418921i	0.131461	+	0.0216619i
$375$		0			0
$376$	0.545343	+	16.1914i	0.0281239	+	0.835008i
$377$	−3.88973			−0.200331
$378$		0			0
$379$		−	15.4020i		−	0.791146i	−0.918435	−	0.395573i	$-0.870546\pi$
$379$		−	15.4020i		−	0.791146i	0.918435	−	0.395573i	$-0.129454\pi$
$380$	−11.3900	+	33.6232i	−0.584293	+	1.72484i
$381$		0			0
$382$	4.35735	−	26.4438i	0.222941	−	1.35298i
$383$	−1.96494	−	3.40338i	−0.100404	−	0.173905i	0.811447	−	0.584426i	$-0.198680\pi$
$383$	−1.96494	−	3.40338i	−0.100404	−	0.173905i	−0.911851	+	0.410521i	$0.865347\pi$
$384$		0			0
$385$	−3.02246	−	2.40741i	−0.154039	−	0.122693i
$386$	−2.65954	−	7.05950i	−0.135367	−	0.359319i
$387$		0			0
$388$	−7.85775	+	1.56814i	−0.398917	+	0.0796103i
$389$	6.94490	−	12.0289i	0.352121	−	0.609891i	−0.634500	−	0.772923i	$-0.718794\pi$
$389$	6.94490	−	12.0289i	0.352121	−	0.609891i	0.986621	+	0.163032i	$0.0521273\pi$
$390$		0			0
$391$		−	32.6477i		−	1.65106i
$392$	−5.17310	+	19.1112i	−0.261281	+	0.965263i
$393$		0			0
$394$	−2.51536	+	3.06694i	−0.126722	+	0.154510i
$395$	−26.2310	−	15.1445i	−1.31982	−	0.762001i
$396$		0			0
$397$	−4.40738	−	7.63380i	−0.221200	−	0.383129i	0.733973	−	0.679179i	$-0.237664\pi$
$397$	−4.40738	−	7.63380i	−0.221200	−	0.383129i	−0.955173	+	0.296050i	$0.904331\pi$
$398$	−9.84430	+	3.70867i	−0.493450	+	0.185899i
$399$		0			0
$400$	−4.29970	+	32.9800i	−0.214985	+	1.64900i
$401$	−13.0887	+	7.55674i	−0.653616	+	0.377365i	−0.789840	−	0.613313i	$-0.789837\pi$
$401$	−13.0887	+	7.55674i	−0.653616	+	0.377365i	0.136224	+	0.990678i	$0.456503\pi$
$402$		0			0
$403$	−1.66140	−	0.959210i	−0.0827602	−	0.0477816i
$404$	9.03054	−	26.6582i	0.449286	−	1.32629i
$405$		0			0
$406$	−5.24949	−	24.4753i	−0.260528	−	1.21469i
$407$		−	0.893263i		−	0.0442774i
$408$		0			0
$409$	−5.85435	−	3.38001i	−0.289479	−	0.167131i	0.348228	−	0.937410i	$-0.386784\pi$
$409$	−5.85435	−	3.38001i	−0.289479	−	0.167131i	−0.637707	+	0.770279i	$0.720117\pi$
$410$	−3.78802	+	22.9887i	−0.187077	+	1.13533i
$411$		0			0
$412$	26.6434	+	30.3424i	1.31262	+	1.49486i
$413$	21.9540	−	8.63131i	1.08029	−	0.424719i
$414$		0			0
$415$	−18.9474	−	32.8179i	−0.930091	−	1.61097i
$416$	−0.949797	+	3.14887i	−0.0465676	+	0.154386i
$417$		0			0
$418$	1.74609	−	2.12898i	0.0854041	−	0.104132i
$419$		−	11.1005i		−	0.542293i	−0.962538	−	0.271147i	$-0.912597\pi$
$419$		−	11.1005i		−	0.542293i	0.962538	−	0.271147i	$-0.0874029\pi$
$420$		0			0
$421$			6.72143i			0.327582i	0.986495	+	0.163791i	$0.0523723\pi$
$421$			6.72143i			0.327582i	−0.986495	+	0.163791i	$0.947628\pi$
$422$	27.0076	+	22.1503i	1.31471	+	1.07826i
$423$		0			0
$424$	−32.3668	+	20.1694i	−1.57187	+	0.979511i
$425$	18.9247	+	32.7785i	0.917981	+	1.58999i
$426$		0			0
$427$	−33.6152	−	5.04636i	−1.62675	−	0.244210i
$428$	6.30937	−	5.54019i	0.304975	−	0.267795i
$429$		0			0
$430$	20.8597	+	3.43721i	1.00594	+	0.165757i
$431$	−1.32418	−	0.764518i	−0.0637837	−	0.0368255i	0.467769	−	0.883851i	$-0.345058\pi$
$431$	−1.32418	−	0.764518i	−0.0637837	−	0.0368255i	−0.531553	+	0.847025i	$0.678391\pi$
$432$		0			0
$433$			19.9225i			0.957416i	0.877974	+	0.478708i	$0.158895\pi$
$433$			19.9225i			0.957416i	−0.877974	+	0.478708i	$0.841105\pi$
$434$	3.79344	−	11.7485i	0.182091	−	0.563948i
$435$		0			0
$436$	11.9143	−	35.1711i	0.570592	−	1.68439i
$437$	−30.2139	−	17.4440i	−1.44533	−	0.834460i
$438$		0			0
$439$	−14.9668	+	8.64107i	−0.714325	+	0.412416i	−0.812660	−	0.582738i	$-0.801982\pi$
$439$	−14.9668	+	8.64107i	−0.714325	+	0.412416i	0.0983355	+	0.995153i	$0.468648\pi$
$440$	1.94383	−	3.64492i	0.0926685	−	0.173765i
$441$		0			0
$442$	1.31955	+	3.50262i	0.0627646	+	0.166603i
$443$	−0.666057	−	1.15364i	−0.0316453	−	0.0548113i	0.849769	−	0.527155i	$-0.176741\pi$
$443$	−0.666057	−	1.15364i	−0.0316453	−	0.0548113i	−0.881414	+	0.472344i	$0.843408\pi$
$444$		0			0
$445$	−33.2431	−	19.1929i	−1.57587	−	0.909831i
$446$	−8.73655	−	7.16530i	−0.413688	−	0.339287i
$447$		0			0
$448$	−21.0955	−	1.72675i	−0.996667	−	0.0815813i
$449$		−	38.5884i		−	1.82110i	−0.413397	−	0.910551i	$-0.635658\pi$
$449$		−	38.5884i		−	1.82110i	0.413397	−	0.910551i	$-0.364342\pi$
$450$		0			0
$451$	0.903540	−	1.56498i	0.0425460	−	0.0736919i
$452$	−6.75666	+	1.34840i	−0.317806	+	0.0634234i
$453$		0			0
$454$	3.12228	−	1.17626i	0.146536	−	0.0552047i
$455$	0.833312	−	5.55092i	0.0390663	−	0.260231i
$456$		0			0
$457$	7.80133	+	13.5123i	0.364931	+	0.632079i	0.988765	−	0.149478i	$-0.0477593\pi$
$457$	7.80133	+	13.5123i	0.364931	+	0.632079i	−0.623834	+	0.781557i	$0.714426\pi$
$458$	−14.8613	−	2.44881i	−0.694423	−	0.114425i
$459$		0			0
$460$	−49.5737	−	16.7932i	−2.31139	−	0.782989i
$461$		−	17.6616i		−	0.822583i	−0.911504	−	0.411291i	$-0.865078\pi$
$461$		−	17.6616i		−	0.822583i	0.911504	−	0.411291i	$-0.134922\pi$
$462$		0			0
$463$	15.1430			0.703753			0.351877	−	0.936046i	$-0.385544\pi$
$463$	15.1430			0.703753			0.351877	+	0.936046i	$0.385544\pi$
$464$	24.7104	−	10.2718i	1.14715	−	0.476857i
$465$		0			0
$466$	3.36244	−	20.4059i	0.155762	−	0.945287i
$467$	−12.0392	+	6.95086i	−0.557110	+	0.321647i	−0.751985	−	0.659181i	$-0.770903\pi$
$467$	−12.0392	+	6.95086i	−0.557110	+	0.321647i	0.194875	+	0.980828i	$0.437570\pi$
$468$		0			0
$469$	23.6132	−	9.28360i	1.09036	−	0.428677i
$470$	27.6598	−	10.4203i	1.27585	−	0.480654i
$471$		0			0
$472$	13.3373	+	21.4031i	0.613900	+	0.985158i
$473$	−1.42004	−	0.819862i	−0.0652936	−	0.0376973i
$474$		0			0
$475$	40.4466			1.85582
$476$	−20.2587	+	13.0300i	−0.928554	+	0.597231i
$477$		0			0
$478$	12.6646	+	10.3869i	0.579264	+	0.475085i
$479$	−15.2782	+	26.4626i	−0.698077	+	1.20911i	0.271055	+	0.962564i	$0.412627\pi$
$479$	−15.2782	+	26.4626i	−0.698077	+	1.20911i	−0.969132	+	0.246541i	$0.920706\pi$
$480$		0			0
$481$	1.12375	−	0.648799i	0.0512388	−	0.0295827i
$482$	2.08882	−	0.786928i	0.0951434	−	0.0358436i
$483$		0			0
$484$	16.2906	−	14.3046i	0.740482	−	0.650209i
$485$	7.30946	+	12.6604i	0.331906	+	0.574877i
$486$		0			0
$487$	10.9031	−	18.8848i	0.494068	−	0.855751i	−0.505909	−	0.862587i	$-0.668843\pi$
$487$	10.9031	−	18.8848i	0.494068	−	0.855751i	0.999977	+	0.00683637i	$0.00217610\pi$
$488$	−1.22323	−	36.3183i	−0.0553732	−	1.64405i
$489$		0			0
$490$	36.0526	−	2.24796i	1.62869	−	0.101552i
$491$	3.38847			0.152919			0.0764597	−	0.997073i	$-0.475638\pi$
$491$	3.38847			0.152919			0.0764597	+	0.997073i	$0.475638\pi$
$492$		0			0
$493$	15.2268	−	26.3736i	0.685781	−	1.18781i
$494$	3.94656	+	0.650305i	0.177564	+	0.0292586i
$495$		0			0
$496$	13.0874	+	1.70625i	0.587644	+	0.0766129i
$497$	−13.2866	−	10.5829i	−0.595987	−	0.474708i
$498$		0			0
$499$	35.9490	−	20.7552i	1.60930	−	0.929128i	0.619770	−	0.784784i	$-0.287226\pi$
$499$	35.9490	−	20.7552i	1.60930	−	0.929128i	0.989528	−	0.144344i	$-0.0461073\pi$
$500$	23.7230	−	4.73430i	1.06092	−	0.211724i
$501$		0			0
$502$	19.6574	+	16.1221i	0.877354	+	0.719564i
$503$	18.4870			0.824295			0.412147	−	0.911117i	$-0.364779\pi$
$503$	18.4870			0.824295			0.412147	+	0.911117i	$0.364779\pi$
$504$		0			0
$505$	−51.3519			−2.28513
$506$	3.13895	+	2.57442i	0.139543	+	0.114447i
$507$		0			0
$508$	1.49590	+	7.49577i	0.0663700	+	0.332571i
$509$	5.71745	−	3.30097i	0.253422	−	0.146313i	−0.367908	−	0.929862i	$-0.619926\pi$
$509$	5.71745	−	3.30097i	0.253422	−	0.146313i	0.621330	+	0.783549i	$0.286593\pi$
$510$		0			0
$511$	17.5826	−	6.91266i	0.777809	−	0.305798i
$512$	−2.28159	−	22.5121i	−0.100833	−	0.994903i
$513$		0			0
$514$	10.3746	+	1.70950i	0.457604	+	0.0754029i
$515$	36.8359	−	63.8016i	1.62318	−	2.81144i
$516$		0			0
$517$	−2.29252			−0.100825
$518$	5.59903	+	6.19538i	0.246007	+	0.272209i
$519$		0			0
$520$	5.99728	−	0.201994i	0.262998	−	0.00885804i
$521$	3.54303	−	6.13671i	0.155223	−	0.268854i	−0.777917	−	0.628367i	$-0.783724\pi$
$521$	3.54303	−	6.13671i	0.155223	−	0.268854i	0.933140	+	0.359513i	$0.117057\pi$
$522$		0			0
$523$	−12.3169	−	21.3336i	−0.538583	−	0.932852i	−0.998981	−	0.0451399i	$-0.985627\pi$
$523$	−12.3169	−	21.3336i	−0.538583	−	0.932852i	0.460398	−	0.887713i	$-0.347707\pi$
$524$	−0.244683	−	0.278654i	−0.0106890	−	0.0121731i
$525$		0			0
$526$	−11.1313	+	4.19352i	−0.485348	+	0.182846i
$527$	13.0075	−	7.50988i	0.566615	−	0.327136i
$528$		0			0
$529$	14.2192	−	24.6284i	0.618227	−	1.07080i
$530$	53.7995	+	44.1238i	2.33690	+	1.91662i
$531$		0			0
$532$	1.23428	+	25.7105i	0.0535127	+	1.11469i
$533$	2.62505			0.113704
$534$		0			0
$535$	−13.2668	−	7.65962i	−0.573576	−	0.331154i
$536$	14.3453	+	23.0206i	0.619621	+	0.994338i
$537$		0			0
$538$	−18.2245	+	6.86576i	−0.785714	+	0.296004i
$539$	−2.67823	−	0.822658i	−0.115359	−	0.0354344i
$540$		0			0
$541$	20.3549	−	11.7519i	0.875125	−	0.505254i	0.00607698	−	0.999982i	$-0.498066\pi$
$541$	20.3549	−	11.7519i	0.875125	−	0.505254i	0.869048	+	0.494728i	$0.164732\pi$
$542$	4.27393	−	25.9375i	0.183581	−	1.11411i
$543$		0			0
$544$	−17.6323	−	18.7666i	−0.755977	−	0.804610i
$545$	−67.7504			−2.90211
$546$		0			0
$547$			16.9894i			0.726412i	0.931709	+	0.363206i	$0.118318\pi$
$547$			16.9894i			0.726412i	−0.931709	+	0.363206i	$0.881682\pi$
$548$	9.83044	−	29.0195i	0.419936	−	1.23965i
$549$		0			0
$550$	−4.64382	−	0.765198i	−0.198013	−	0.0326281i
$551$	−16.2717	−	28.1834i	−0.693198	−	1.20065i
$552$		0			0
$553$	−21.7183	−	3.26039i	−0.923558	−	0.138646i
$554$	23.2103	−	8.74407i	0.986111	−	0.371500i
$555$		0			0
$556$	4.12833	+	20.6865i	0.175080	+	0.877303i
$557$	−2.69847	+	4.67389i	−0.114338	+	0.198039i	−0.917515	−	0.397701i	$-0.869808\pi$
$557$	−2.69847	+	4.67389i	−0.114338	+	0.198039i	0.803177	+	0.595740i	$0.203141\pi$
$558$		0			0
$559$		−	2.38195i		−	0.100746i
$560$	9.36480	+	37.4640i	0.395735	+	1.58314i
$561$		0			0
$562$	−16.2260	−	13.3078i	−0.684452	−	0.561355i
$563$	29.2646	+	16.8959i	1.23336	+	0.712078i	0.967728	−	0.251997i	$-0.0810874\pi$
$563$	29.2646	+	16.8959i	1.23336	+	0.712078i	0.265628	+	0.964076i	$0.414421\pi$
$564$		0			0
$565$	6.28520	+	10.8863i	0.264420	+	0.457989i
$566$	0.292434	+	0.776237i	0.0122919	+	0.0326277i
$567$		0			0
$568$	8.54501	−	16.0229i	0.358540	−	0.672307i
$569$	−14.2390	+	8.22089i	−0.596930	+	0.344638i	−0.767833	−	0.640650i	$-0.778665\pi$
$569$	−14.2390	+	8.22089i	−0.596930	+	0.344638i	0.170903	+	0.985288i	$0.445332\pi$
$570$		0			0
$571$	33.2026	+	19.1696i	1.38949	+	0.802221i	0.993257	−	0.115931i	$-0.0369850\pi$
$571$	33.2026	+	19.1696i	1.38949	+	0.802221i	0.396230	+	0.918151i	$0.370318\pi$
$572$	−0.440816	−	0.149328i	−0.0184314	−	0.00624370i
$573$		0			0
$574$	3.54271	+	16.5176i	0.147870	+	0.689432i
$575$			59.6340i			2.48691i
$576$		0			0
$577$	19.2194	+	11.0963i	0.800113	+	0.461946i	0.843511	−	0.537112i	$-0.180485\pi$
$577$	19.2194	+	11.0963i	0.800113	+	0.461946i	−0.0433975	+	0.999058i	$0.513818\pi$
$578$	−5.19266	−	0.855634i	−0.215986	−	0.0355897i
$579$		0			0
$580$	−32.2145	−	36.6871i	−1.33764	−	1.52335i
$581$	−21.4921	−	17.1186i	−0.891644	−	0.710201i
$582$		0			0
$583$	−2.69834	−	4.67366i	−0.111754	−	0.193563i
$584$	10.6816	+	17.1414i	0.442009	+	0.709315i
$585$		0			0
$586$	−6.64188	−	5.44736i	−0.274374	−	0.225028i
$587$			3.25736i			0.134445i	0.997738	+	0.0672227i	$0.0214138\pi$
$587$			3.25736i			0.134445i	−0.997738	+	0.0672227i	$0.978586\pi$
$588$		0			0
$589$		−	16.0504i		−	0.661347i
$590$	29.1776	−	35.5758i	1.20122	−	1.46463i
$591$		0			0
$592$	−5.42558	+	7.08919i	−0.222990	+	0.291364i
$593$	−19.4634	−	33.7116i	−0.799267	−	1.38437i	−0.920094	−	0.391697i	$-0.871888\pi$
$593$	−19.4634	−	33.7116i	−0.799267	−	1.38437i	0.120827	−	0.992674i	$-0.461445\pi$
$594$		0			0
$595$	34.3749	+	27.3799i	1.40923	+	1.12246i
$596$	−13.7997	+	12.1173i	−0.565257	+	0.496346i
$597$		0			0
$598$	−0.958802	+	5.81876i	−0.0392083	+	0.237947i
$599$	8.92743	+	5.15425i	0.364765	+	0.210597i	0.671169	−	0.741304i	$-0.265793\pi$
$599$	8.92743	+	5.15425i	0.364765	+	0.210597i	−0.306404	+	0.951902i	$0.599126\pi$
$600$		0			0
$601$			16.1379i			0.658277i	0.944282	+	0.329139i	$0.106758\pi$
$601$			16.1379i			0.658277i	−0.944282	+	0.329139i	$0.893242\pi$
$602$	14.9879	−	3.21462i	0.610861	−	0.131018i
$603$		0			0
$604$	−6.81932	−	2.31007i	−0.277474	−	0.0939953i
$605$	−34.2546	−	19.7769i	−1.39265	−	0.804045i
$606$		0			0
$607$	−31.3010	+	18.0717i	−1.27047	+	0.733506i	−0.975076	−	0.221870i	$-0.928784\pi$
$607$	−31.3010	+	18.0717i	−1.27047	+	0.733506i	−0.295393	+	0.955376i	$0.595451\pi$
$608$	−26.7887	+	6.29067i	−1.08642	+	0.255120i
$609$		0			0
$610$	−62.0424	+	23.3734i	−2.51202	+	0.946361i
$611$	−1.66512	−	2.88407i	−0.0673634	−	0.116677i
$612$		0			0
$613$	−1.33431	−	0.770363i	−0.0538922	−	0.0311147i	0.472812	−	0.881163i	$-0.343239\pi$
$613$	−1.33431	−	0.770363i	−0.0538922	−	0.0311147i	−0.526704	+	0.850049i	$0.676572\pi$
$614$	17.0794	−	20.8246i	0.689267	−	0.840413i
$615$		0			0
$616$	0.344699	−	2.97527i	0.0138883	−	0.119877i
$617$			40.1412i			1.61602i	0.589165	+	0.808012i	$0.299457\pi$
$617$			40.1412i			1.61602i	−0.589165	+	0.808012i	$0.700543\pi$
$618$		0			0
$619$	−18.4948	+	32.0339i	−0.743368	+	1.28755i	0.207586	+	0.978217i	$0.433439\pi$
$619$	−18.4948	+	32.0339i	−0.743368	+	1.28755i	−0.950953	+	0.309334i	$0.899894\pi$
$620$	−4.71257	−	23.6141i	−0.189261	−	0.948364i
$621$		0			0
$622$	−4.51010	−	11.9716i	−0.180839	−	0.480019i
$623$	−27.5241	−	4.13196i	−1.10273	−	0.165543i
$624$		0			0
$625$	−1.28074	−	2.21830i	−0.0512295	−	0.0887321i
$626$	−1.71421	+	10.4032i	−0.0685138	+	0.415795i
$627$		0			0
$628$	−1.36042	−	0.460848i	−0.0542868	−	0.0183898i
$629$			10.1592i			0.405074i
$630$		0			0
$631$	31.1044			1.23825			0.619123	−	0.785294i	$-0.287488\pi$
$631$	31.1044			1.23825			0.619123	+	0.785294i	$0.287488\pi$
$632$	−0.790316	−	23.4648i	−0.0314371	−	0.933378i
$633$		0			0
$634$	−6.71834	−	1.10703i	−0.266819	−	0.0439659i
$635$	12.0771	−	6.97274i	0.479267	−	0.276705i
$636$		0			0
$637$	−0.910334	−	3.96681i	−0.0360688	−	0.157171i
$638$	1.33502	+	3.54368i	0.0528539	+	0.140296i
$639$		0			0
$640$	−37.5656	+	17.1205i	−1.48491	+	0.676748i
$641$	−3.44022	−	1.98621i	−0.135881	−	0.0784507i	0.430519	−	0.902582i	$-0.358331\pi$
$641$	−3.44022	−	1.98621i	−0.135881	−	0.0784507i	−0.566399	+	0.824131i	$0.691664\pi$
$642$		0			0
$643$	−47.5503			−1.87520			−0.937600	−	0.347717i	$-0.886957\pi$
$643$	−47.5503			−1.87520			−0.937600	+	0.347717i	$0.886957\pi$
$644$	−37.9073	+	1.81980i	−1.49376	+	0.0717103i
$645$		0			0
$646$	−19.8586	+	24.2132i	−0.781324	+	0.952657i
$647$	−20.9097	+	36.2166i	−0.822044	+	1.42382i	0.0821142	+	0.996623i	$0.473833\pi$
$647$	−20.9097	+	36.2166i	−0.822044	+	1.42382i	−0.904158	+	0.427199i	$0.859501\pi$
$648$		0			0
$649$	−3.09054	+	1.78432i	−0.121314	+	0.0700408i
$650$	−2.41028	−	6.39786i	−0.0945390	−	0.250945i
$651$		0			0
$652$	29.1233	+	33.1667i	1.14056	+	1.29891i
$653$	10.6456	+	18.4388i	0.416596	+	0.721565i	0.995595	−	0.0937632i	$-0.0298896\pi$
$653$	10.6456	+	18.4388i	0.416596	+	0.721565i	−0.578999	+	0.815329i	$0.696556\pi$
$654$		0			0
$655$	−0.338288	+	0.585932i	−0.0132180	+	0.0228943i
$656$	−16.6762	+	6.93211i	−0.651098	+	0.270654i
$657$		0			0
$658$	15.9002	−	14.3697i	0.619854	−	0.560188i
$659$	−50.0936			−1.95137			−0.975685	−	0.219179i	$-0.929662\pi$
$659$	−50.0936			−1.95137			−0.975685	+	0.219179i	$0.929662\pi$
$660$		0			0
$661$	−11.9756	+	20.7423i	−0.465797	+	0.806784i	−0.999237	−	0.0390540i	$-0.987566\pi$
$661$	−11.9756	+	20.7423i	−0.465797	+	0.806784i	0.533440	+	0.845838i	$0.320899\pi$
$662$	−1.44300	+	8.75723i	−0.0560836	+	0.340359i
$663$		0			0
$664$	13.8222	−	25.9183i	0.536405	−	1.00582i
$665$	43.7057	−	17.1830i	1.69483	−	0.666330i
$666$		0			0
$667$	41.5533	−	23.9908i	1.60895	−	0.928927i
$668$	−5.27949	−	26.4548i	−0.204269	−	1.02357i
$669$		0			0
$670$	31.3826	−	38.2644i	1.21242	−	1.47828i
$671$	5.14226			0.198515
$672$		0			0
$673$	−2.60756			−0.100514			−0.0502570	−	0.998736i	$-0.516004\pi$
$673$	−2.60756			−0.100514			−0.0502570	+	0.998736i	$0.516004\pi$
$674$	−18.0556	+	22.0150i	−0.695477	+	0.847985i
$675$		0			0
$676$	4.95607	+	24.8342i	0.190618	+	0.955162i
$677$	−13.5947	+	7.84890i	−0.522486	+	0.301658i	−0.737951	−	0.674854i	$-0.764207\pi$
$677$	−13.5947	+	7.84890i	−0.522486	+	0.301658i	0.215465	+	0.976512i	$0.430873\pi$
$678$		0			0
$679$	8.29116	+	6.60397i	0.318186	+	0.253437i
$680$	−22.1075	+	41.4542i	−0.847783	+	1.58970i
$681$		0			0
$682$	−0.303654	+	1.84281i	−0.0116275	+	0.0705648i
$683$	10.7229	−	18.5726i	0.410300	−	0.710661i	−0.584622	−	0.811306i	$-0.698757\pi$
$683$	10.7229	−	18.5726i	0.410300	−	0.710661i	0.994922	+	0.100645i	$0.0320905\pi$
$684$		0			0
$685$	−55.9005			−2.13585
$686$	23.7318	−	11.0816i	0.906084	−	0.423098i
$687$		0			0
$688$	6.29012	+	15.1318i	0.239809	+	0.576896i
$689$	3.91975	−	6.78920i	0.149330	−	0.258648i
$690$		0			0
$691$	12.6075	+	21.8368i	0.479611	+	0.830710i	0.999727	−	0.0233857i	$-0.00744459\pi$
$691$	12.6075	+	21.8368i	0.479611	+	0.830710i	−0.520116	+	0.854096i	$0.674111\pi$
$692$	21.3479	+	24.3118i	0.811526	+	0.924195i
$693$		0			0
$694$	9.01688	+	23.9344i	0.342276	+	0.908539i
$695$	33.3300	−	19.2431i	1.26428	−	0.729931i
$696$		0			0
$697$	−10.2761	+	17.7987i	−0.389235	+	0.674174i
$698$	−2.91063	+	3.54889i	−0.110169	+	0.134327i
$699$		0			0
$700$	37.0043	−	23.8006i	1.39863	−	0.899578i
$701$	33.6820			1.27215			0.636076	−	0.771626i	$-0.280556\pi$
$701$	33.6820			1.27215			0.636076	+	0.771626i	$0.280556\pi$
$702$		0			0
$703$	9.40187	+	5.42818i	0.354598	+	0.204727i
$704$	3.19472	−	0.215447i	0.120405	−	0.00811996i
$705$		0			0
$706$	14.5615	+	38.6521i	0.548029	+	1.45469i
$707$	−34.6521	+	13.6236i	−1.30323	+	0.512367i
$708$		0			0
$709$	33.1687	−	19.1499i	1.24568	−	0.719191i	0.275431	−	0.961321i	$-0.411179\pi$
$709$	33.1687	−	19.1499i	1.24568	−	0.719191i	0.970244	+	0.242130i	$0.0778460\pi$
$710$	−32.6898	−	5.38655i	−1.22683	−	0.202154i
$711$		0			0
$712$	−1.00158	−	29.7374i	−0.0375360	−	1.11446i
$713$	23.6646			0.886245
$714$		0			0
$715$			0.849148i			0.0317563i
$716$	−3.30369	−	1.11914i	−0.123465	−	0.0418241i
$717$		0			0
$718$	−2.35658	+	14.3016i	−0.0879469	+	0.533731i
$719$	3.40747	+	5.90191i	0.127077	+	0.220104i	0.922543	−	0.385894i	$-0.126107\pi$
$719$	3.40747	+	5.90191i	0.127077	+	0.220104i	−0.795466	+	0.605998i	$0.792774\pi$
$720$		0			0
$721$	7.93024	−	52.8256i	0.295338	−	1.96733i
$722$	2.32470	+	6.17069i	0.0865164	+	0.229649i
$723$		0			0
$724$	3.69837	+	18.5321i	0.137449	+	0.688739i
$725$	−27.8132	+	48.1738i	−1.03296	+	1.78913i
$726$		0			0
$727$		−	44.3315i		−	1.64416i	−0.569369	−	0.822082i	$-0.692812\pi$
$727$		−	44.3315i		−	1.64416i	0.569369	−	0.822082i	$-0.307188\pi$
$728$	3.99335	−	1.72737i	0.148003	−	0.0640207i
$729$		0			0
$730$	23.3678	−	28.4920i	0.864882	−	1.05454i
$731$	16.1504	+	9.32441i	0.597342	+	0.344876i
$732$		0			0
$733$	−4.98689	−	8.63755i	−0.184195	−	0.319035i	0.759110	−	0.650962i	$-0.225634\pi$
$733$	−4.98689	−	8.63755i	−0.184195	−	0.319035i	−0.943305	+	0.331927i	$0.892301\pi$
$734$	−40.6539	+	15.3156i	−1.50056	+	0.565310i
$735$		0			0
$736$	−9.27489	−	39.4969i	−0.341877	−	1.45588i
$737$	−3.32410	+	1.91917i	−0.122445	+	0.0706935i
$738$		0			0
$739$	−37.1489	−	21.4480i	−1.36655	−	0.788976i	−0.376061	−	0.926595i	$-0.622722\pi$
$739$	−37.1489	−	21.4480i	−1.36655	−	0.788976i	−0.990485	+	0.137619i	$0.956055\pi$
$740$	15.4262	+	5.22567i	0.567078	+	0.192100i
$741$		0			0
$742$	48.0096	+	15.5016i	1.76249	+	0.569083i
$743$		−	11.2075i		−	0.411165i	−0.978640	−	0.205582i	$-0.934091\pi$
$743$		−	11.2075i		−	0.411165i	0.978640	−	0.205582i	$-0.0659088\pi$
$744$		0			0
$745$	29.0169	+	16.7529i	1.06310	+	0.613778i
$746$	−4.65457	+	28.2476i	−0.170416	+	1.03422i
$747$		0			0
$748$	2.73811	−	2.40431i	0.100115	−	0.0879103i
$749$	−10.9845	−	1.64901i	−0.401365	−	0.0602534i
$750$		0			0
$751$	18.5560	+	32.1399i	0.677117	+	1.17280i	0.975845	+	0.218462i	$0.0701041\pi$
$751$	18.5560	+	32.1399i	0.677117	+	1.17280i	−0.298729	+	0.954338i	$0.596563\pi$
$752$	18.1941	+	13.9245i	0.663472	+	0.507775i
$753$		0			0
$754$	−3.48840	+	4.25336i	−0.127040	+	0.154898i
$755$			13.1361i			0.478073i
$756$		0			0
$757$			20.8257i			0.756924i	0.925617	+	0.378462i	$0.123547\pi$
$757$			20.8257i			0.756924i	−0.925617	+	0.378462i	$0.876453\pi$
$758$	−16.8418	−	13.8128i	−0.611722	−	0.501705i
$759$		0			0
$760$	26.5517	+	42.6089i	0.963130	+	1.54559i
$761$	7.26978	+	12.5916i	0.263529	+	0.456446i	0.967177	−	0.254103i	$-0.0817801\pi$
$761$	7.26978	+	12.5916i	0.263529	+	0.456446i	−0.703648	+	0.710549i	$0.748447\pi$
$762$		0			0
$763$	−45.7177	+	17.9740i	−1.65509	+	0.650704i
$764$	−25.0081	−	28.4801i	−0.904761	−	1.03037i
$765$		0			0
$766$	−5.48376	−	0.903600i	−0.198136	−	0.0326484i
$767$	−4.48947	−	2.59200i	−0.162105	−	0.0935916i
$768$		0			0
$769$			2.11604i			0.0763063i	0.999272	+	0.0381532i	$0.0121475\pi$
$769$			2.11604i			0.0763063i	−0.999272	+	0.0381532i	$0.987853\pi$
$770$	−5.34309	+	1.14599i	−0.192551	+	0.0412986i
$771$		0			0
$772$	−10.1046	−	3.42296i	−0.363672	−	0.123195i
$773$	−18.3194	−	10.5767i	−0.658902	−	0.380417i	0.132957	−	0.991122i	$-0.457553\pi$
$773$	−18.3194	−	10.5767i	−0.658902	−	0.380417i	−0.791858	+	0.610705i	$0.790886\pi$
$774$		0			0
$775$	−23.7594	+	13.7175i	−0.853462	+	0.492747i
$776$	−5.33228	+	9.99867i	−0.191418	+	0.358931i
$777$		0			0
$778$	−6.92508	−	18.3820i	−0.248276	−	0.659026i
$779$	10.9812	+	19.0201i	0.393444	+	0.681465i
$780$		0			0
$781$	2.22539	+	1.28483i	0.0796308	+	0.0459748i
$782$	−35.6997	−	29.2792i	−1.27662	−	1.04702i
$783$		0			0
$784$	16.2585	+	22.7961i	0.580659	+	0.814147i
$785$			2.62060i			0.0935331i
$786$		0			0
$787$	15.1516	−	26.2433i	0.540096	−	0.935473i	−0.458802	−	0.888538i	$-0.651721\pi$
$787$	15.1516	−	26.2433i	0.540096	−	0.935473i	0.998898	−	0.0469348i	$-0.0149453\pi$
$788$	1.09781	+	5.50100i	0.0391080	+	0.195965i
$789$		0			0
$790$	−40.0848	+	15.1012i	−1.42615	+	0.537278i
$791$	7.12933	+	5.67856i	0.253490	+	0.201906i
$792$		0			0
$793$	3.73495	+	6.46913i	0.132632	+	0.229725i
$794$	−12.3001	−	2.02678i	−0.436513	−	0.0719277i
$795$		0			0
$796$	−4.77323	+	14.0906i	−0.169183	+	0.499428i
$797$		−	12.8964i		−	0.456812i	−0.973566	−	0.228406i	$-0.926649\pi$
$797$		−	12.8964i		−	0.456812i	0.973566	−	0.228406i	$-0.0733514\pi$
$798$		0			0
$799$	26.0732			0.922403
$800$	32.2070	+	34.2789i	1.13869	+	1.21194i
$801$		0			0
$802$	−3.47504	+	21.0893i	−0.122708	+	0.744689i
$803$	−2.47516	+	1.42903i	−0.0873463	+	0.0504294i
$804$		0			0
$805$	25.3345	+	64.4391i	0.892922	+	2.27118i
$806$	−2.53886	+	0.956472i	−0.0894277	+	0.0336903i
$807$		0			0
$808$	−21.0515	−	33.7825i	−0.740589	−	1.18846i
$809$	31.3922	+	18.1243i	1.10369	+	0.637216i	0.937188	−	0.348825i	$-0.113419\pi$
$809$	31.3922	+	18.1243i	1.10369	+	0.637216i	0.166502	+	0.986041i	$0.446753\pi$
$810$		0			0
$811$	−5.48133			−0.192475			−0.0962377	−	0.995358i	$-0.530681\pi$
$811$	−5.48133			−0.192475			−0.0962377	+	0.995358i	$0.530681\pi$
$812$	−31.4712	−	16.2098i	−1.10442	−	0.568853i
$813$		0			0
$814$	−0.976769	−	0.801099i	−0.0342357	−	0.0280785i
$815$	40.2646	−	69.7403i	1.41041	−	2.44290i
$816$		0			0
$817$	17.2586	−	9.96427i	0.603803	−	0.348606i
$818$	−8.94631	+	3.37036i	−0.312800	+	0.117842i
$819$		0			0
$820$	21.7406	+	24.7589i	0.759213	+	0.864619i
$821$	5.95824	+	10.3200i	0.207944	+	0.360169i	0.951067	−	0.308986i	$-0.0999895\pi$
$821$	5.95824	+	10.3200i	0.207944	+	0.360169i	−0.743123	+	0.669155i	$0.766656\pi$
$822$		0			0
$823$	−20.9931	+	36.3612i	−0.731775	+	1.26747i	0.224349	+	0.974509i	$0.427975\pi$
$823$	−20.9931	+	36.3612i	−0.731775	+	1.26747i	−0.956124	+	0.292963i	$0.905359\pi$
$824$	57.0733	−	1.92229i	1.98824	−	0.0669660i
$825$		0			0
$826$	10.2507	−	31.7472i	0.356668	−	1.10463i
$827$	−18.7749			−0.652869			−0.326434	−	0.945220i	$-0.605847\pi$
$827$	−18.7749			−0.652869			−0.326434	+	0.945220i	$0.605847\pi$
$828$		0			0
$829$	−7.45588	+	12.9140i	−0.258953	+	0.448520i	−0.965962	−	0.258685i	$-0.916711\pi$
$829$	−7.45588	+	12.9140i	−0.258953	+	0.448520i	0.707009	+	0.707205i	$0.250044\pi$
$830$	−52.8783	−	8.71316i	−1.83543	−	0.302438i
$831$		0			0
$832$	2.59144	+	3.86257i	0.0898421	+	0.133911i
$833$	30.4599	+	9.35621i	1.05537	+	0.324173i
$834$		0			0
$835$	−42.6238	+	24.6089i	−1.47506	+	0.851625i
$836$	−0.762073	−	3.81865i	−0.0263568	−	0.132071i
$837$		0			0
$838$	−12.1382	−	9.95517i	−0.419307	−	0.343895i
$839$	−28.4322			−0.981587			−0.490794	−	0.871276i	$-0.663293\pi$
$839$	−28.4322			−0.981587			−0.490794	+	0.871276i	$0.663293\pi$
$840$		0			0
$841$	15.7571			0.543347
$842$	7.34977	+	6.02794i	0.253290	+	0.207736i
$843$		0			0
$844$	48.4421	−	9.66740i	1.66744	−	0.332766i
$845$	40.0127	−	23.1014i	1.37648	−	0.794711i
$846$		0			0
$847$	−28.3616	−	4.25768i	−0.974517	−	0.146296i
$848$	−6.97248	+	53.4810i	−0.239436	+	1.83654i
$849$		0			0
$850$	52.8148	+	8.70270i	1.81153	+	0.298500i
$851$	−8.00324	+	13.8620i	−0.274347	+	0.475184i
$852$		0			0
$853$	−9.45822			−0.323843			−0.161922	−	0.986804i	$-0.551769\pi$
$853$	−9.45822			−0.323843			−0.161922	+	0.986804i	$0.551769\pi$
$854$	−35.6650	+	32.2320i	−1.22043	+	1.10296i
$855$		0			0
$856$	−0.399718	−	11.8678i	−0.0136621	−	0.405632i
$857$	−19.8068	+	34.3064i	−0.676588	+	1.17188i	0.299415	+	0.954123i	$0.403209\pi$
$857$	−19.8068	+	34.3064i	−0.676588	+	1.17188i	−0.976002	+	0.217761i	$0.930125\pi$
$858$		0			0
$859$	−17.1446	−	29.6953i	−0.584965	−	1.01319i	−0.994880	−	0.101066i	$-0.967775\pi$
$859$	−17.1446	−	29.6953i	−0.584965	−	1.01319i	0.409914	−	0.912124i	$-0.365559\pi$
$860$	22.4660	−	19.7271i	0.766084	−	0.672690i
$861$		0			0
$862$	−2.02355	+	0.762336i	−0.0689223	+	0.0259653i
$863$	−30.9385	+	17.8623i	−1.05316	+	0.608041i	−0.923532	−	0.383522i	$-0.874711\pi$
$863$	−30.9385	+	17.8623i	−1.05316	+	0.608041i	−0.129627	+	0.991563i	$0.541378\pi$
$864$		0			0
$865$	29.5147	−	51.1209i	1.00353	−	1.73816i
$866$	21.7850	+	17.8670i	0.740283	+	0.607145i
$867$		0			0
$868$	−9.44479	−	14.6844i	−0.320577	−	0.498422i
$869$	3.32235			0.112703
$870$		0			0
$871$	−4.82875	−	2.78788i	−0.163616	−	0.0944638i
$872$	−27.7740	−	44.5704i	−0.940545	−	1.50934i
$873$		0			0
$874$	−46.1713	+	17.3942i	−1.56177	+	0.588368i
$875$	−25.0315	−	19.9377i	−0.846218	−	0.674018i
$876$		0			0
$877$	−13.3688	+	7.71847i	−0.451431	+	0.260634i	−0.708435	−	0.705777i	$-0.750598\pi$
$877$	−13.3688	+	7.71847i	−0.451431	+	0.260634i	0.257003	+	0.966411i	$0.417265\pi$
$878$	−3.97369	+	24.1154i	−0.134105	+	0.813857i
$879$		0			0
$880$	−2.24239	−	5.39440i	−0.0755908	−	0.181845i
$881$	−2.47237			−0.0832962			−0.0416481	−	0.999132i	$-0.513261\pi$
$881$	−2.47237			−0.0832962			−0.0416481	+	0.999132i	$0.513261\pi$
$882$		0			0
$883$		−	22.3515i		−	0.752187i	−0.926582	−	0.376094i	$-0.877267\pi$
$883$		−	22.3515i		−	0.752187i	0.926582	−	0.376094i	$-0.122733\pi$
$884$	5.01346	+	1.69833i	0.168621	+	0.0571209i
$885$		0			0
$886$	−1.85883	−	0.306293i	−0.0624485	−	0.0102901i
$887$	−11.2912	−	19.5570i	−0.379122	−	0.656658i	0.611813	−	0.791003i	$-0.290441\pi$
$887$	−11.2912	−	19.5570i	−0.379122	−	0.656658i	−0.990935	+	0.134344i	$0.957107\pi$
$888$		0			0
$889$	6.29975	−	7.90922i	0.211287	−	0.265267i
$890$	−50.8003	+	19.1381i	−1.70283	+	0.641512i
$891$		0			0
$892$	−15.6703	+	3.12726i	−0.524680	+	0.104708i
$893$	13.9312	−	24.1295i	0.466189	−	0.807464i
$894$		0			0
$895$			6.36394i			0.212723i
$896$	−20.8071	+	21.5190i	−0.695116	+	0.718898i
$897$		0			0
$898$	−42.1958	−	34.6070i	−1.40809	−	1.15485i
$899$	19.1168	+	11.0371i	0.637582	+	0.368108i
$900$		0			0
$901$	30.6886	+	53.1543i	1.02239	+	1.77083i
$902$	−0.900961	−	2.39151i	−0.0299987	−	0.0796287i
$903$		0			0
$904$	−4.58508	+	8.59757i	−0.152497	+	0.285951i
$905$	29.8588	−	17.2390i	0.992539	−	0.573042i
$906$		0			0
$907$	8.75724	+	5.05599i	0.290779	+	0.167882i	0.638293	−	0.769793i	$-0.279641\pi$
$907$	8.75724	+	5.05599i	0.290779	+	0.167882i	−0.347514	+	0.937675i	$0.612974\pi$
$908$	1.51391	−	4.46906i	0.0502408	−	0.148311i
$909$		0			0
$910$	−5.32251	−	5.88941i	−0.176440	−	0.195232i
$911$		−	28.5297i		−	0.945230i	−0.881269	−	0.472615i	$-0.843310\pi$
$911$		−	28.5297i		−	0.945230i	0.881269	−	0.472615i	$-0.156690\pi$
$912$		0			0
$913$	3.59974	+	2.07831i	0.119134	+	0.0687820i
$914$	21.7719	+	3.58752i	0.720151	+	0.118665i
$915$		0			0
$916$	−16.0057	+	14.0544i	−0.528844	+	0.464372i
$917$	−0.0728286	+	0.485131i	−0.00240501	+	0.0160204i
$918$		0			0
$919$	13.4674	+	23.3263i	0.444249	+	0.769463i	0.998000	−	0.0632203i	$-0.0201371\pi$
$919$	13.4674	+	23.3263i	0.444249	+	0.769463i	−0.553750	+	0.832683i	$0.686804\pi$
$920$	−62.8220	+	39.1475i	−2.07118	+	1.29065i
$921$		0			0
$922$	−19.3127	−	15.8393i	−0.636029	−	0.521641i
$923$			3.73282i			0.122867i
$924$		0			0
$925$		−	18.5567i		−	0.610142i
$926$	13.5806	−	16.5586i	0.446285	−	0.544149i
$927$		0			0
$928$	10.9288	−	36.2324i	0.358755	−	1.18939i
$929$	11.2786	+	19.5350i	0.370038	+	0.640924i	0.989571	−	0.144046i	$-0.0460114\pi$
$929$	11.2786	+	19.5350i	0.370038	+	0.640924i	−0.619533	+	0.784970i	$0.712678\pi$
$930$		0			0
$931$	24.9338	−	23.1901i	0.817171	−	0.760024i
$932$	−19.2981	−	21.9773i	−0.632129	−	0.719891i
$933$		0			0
$934$	−3.19642	+	19.3984i	−0.104590	+	0.634735i
$935$	−5.75749	−	3.32409i	−0.188290	−	0.108709i
$936$		0			0
$937$			25.6419i			0.837684i	0.908059	+	0.418842i	$0.137564\pi$
$937$			25.6419i			0.837684i	−0.908059	+	0.418842i	$0.862436\pi$
$938$	11.0254	−	34.1464i	0.359992	−	1.11492i
$939$		0			0
$940$	13.4115	−	39.5907i	0.437434	−	1.29131i
$941$	49.1787	+	28.3933i	1.60318	+	0.925596i	0.990846	+	0.134996i	$0.0431022\pi$
$941$	49.1787	+	28.3933i	1.60318	+	0.925596i	0.612333	+	0.790600i	$0.290231\pi$
$942$		0			0
$943$	−28.0430	+	16.1906i	−0.913205	+	0.527239i
$944$	35.3652	+	4.61067i	1.15104	+	0.150064i
$945$		0			0
$946$	−2.17003	+	0.817522i	−0.0705539	+	0.0265799i
$947$	5.32282	+	9.21939i	0.172968	+	0.299590i	0.939456	−	0.342669i	$-0.111331\pi$
$947$	5.32282	+	9.21939i	0.172968	+	0.299590i	−0.766488	+	0.642259i	$0.777998\pi$
$948$		0			0
$949$	−3.59554	−	2.07588i	−0.116716	−	0.0673861i
$950$	36.2735	−	44.2277i	1.17687	−	1.43494i
$951$		0			0
$952$	−3.92031	+	33.8382i	−0.127058	+	1.09670i
$953$		−	31.4456i		−	1.01862i	−0.860582	−	0.509312i	$-0.829900\pi$
$953$		−	31.4456i		−	1.01862i	0.860582	−	0.509312i	$-0.170100\pi$
$954$		0			0
$955$	−34.5750	+	59.8857i	−1.11882	+	1.93786i
$956$	22.7158	−	4.53330i	0.734681	−	0.146617i
$957$		0			0
$958$	15.2346	+	40.4387i	0.492206	+	1.30651i
$959$	−37.7214	+	14.8303i	−1.21809	+	0.478896i
$960$		0			0
$961$	−10.0565	−	17.4183i	−0.324403	−	0.561882i
$962$	0.298357	−	1.81067i	0.00961942	−	0.0583782i
$963$		0			0
$964$	1.01281	−	2.98983i	0.0326206	−	0.0962960i
$965$			19.4646i			0.626587i
$966$		0			0
$967$	2.45245			0.0788655			0.0394327	−	0.999222i	$-0.487445\pi$
$967$	2.45245			0.0788655			0.0394327	+	0.999222i	$0.487445\pi$
$968$	−1.03206	−	30.6422i	−0.0331717	−	0.984878i
$969$		0			0
$970$	20.3992	+	3.36133i	0.654979	+	0.107926i
$971$	28.2257	−	16.2961i	0.905807	−	0.522968i	0.0267274	−	0.999643i	$-0.491491\pi$
$971$	28.2257	−	16.2961i	0.905807	−	0.522968i	0.879080	+	0.476675i	$0.158158\pi$
$972$		0			0
$973$	17.3858	−	21.8275i	0.557362	−	0.699758i
$974$	−10.8720	−	28.8587i	−0.348362	−	0.924693i
$975$		0			0
$976$	−40.8105	−	31.2335i	−1.30631	−	0.999760i
$977$	8.83921	+	5.10332i	0.282791	+	0.163270i	0.634686	−	0.772770i	$-0.281129\pi$
$977$	8.83921	+	5.10332i	0.282791	+	0.163270i	−0.351895	+	0.936039i	$0.614463\pi$
$978$		0			0
$979$	4.21048			0.134568
$980$	29.8748	−	41.4390i	0.954315	−	1.32372i
$981$		0			0
$982$	3.03886	−	3.70524i	0.0969739	−	0.118239i
$983$	2.76849	−	4.79516i	0.0883010	−	0.152942i	−0.818492	−	0.574518i	$-0.805190\pi$
$983$	2.76849	−	4.79516i	0.0883010	−	0.152942i	0.906793	+	0.421576i	$0.138523\pi$
$984$		0			0
$985$	8.86318	−	5.11716i	0.282405	−	0.163046i
$986$	−15.1834	−	40.3028i	−0.483536	−	1.28350i
$987$		0			0
$988$	4.25047	−	3.73229i	0.135225	−	0.118740i
$989$	14.6912	+	25.4459i	0.467153	+	0.809132i
$990$		0			0
$991$	−6.53951	+	11.3268i	−0.207734	+	0.359806i	−0.951000	−	0.309189i	$-0.899942\pi$
$991$	−6.53951	+	11.3268i	−0.207734	+	0.359806i	0.743266	+	0.668996i	$0.233276\pi$
$992$	13.6029	−	12.7807i	0.431892	−	0.405788i
$993$		0			0
$994$	−23.4880	+	5.03773i	−0.744994	+	0.159787i
$995$	27.1429			0.860487
$996$		0			0
$997$	3.01429	−	5.22091i	0.0954636	−	0.165348i	−0.814338	−	0.580390i	$-0.802900\pi$
$997$	3.01429	−	5.22091i	0.0954636	−	0.165348i	0.909802	+	0.415043i	$0.136233\pi$
$998$	9.54447	−	57.9233i	0.302125	−	1.83353i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ch.b.269.21	yes	56
3.2	odd	2	inner	504.2.ch.b.269.8	yes	56
4.3	odd	2		2016.2.cp.b.17.4		56
7.5	odd	6	inner	504.2.ch.b.341.3	yes	56
8.3	odd	2		2016.2.cp.b.17.25		56
8.5	even	2	inner	504.2.ch.b.269.26	yes	56
12.11	even	2		2016.2.cp.b.17.26		56
21.5	even	6	inner	504.2.ch.b.341.26	yes	56
24.5	odd	2	inner	504.2.ch.b.269.3	✓	56
24.11	even	2		2016.2.cp.b.17.3		56
28.19	even	6		2016.2.cp.b.593.3		56
56.5	odd	6	inner	504.2.ch.b.341.8	yes	56
56.19	even	6		2016.2.cp.b.593.26		56
84.47	odd	6		2016.2.cp.b.593.25		56
168.5	even	6	inner	504.2.ch.b.341.21	yes	56
168.131	odd	6		2016.2.cp.b.593.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.3	✓	56	24.5	odd	2	inner
504.2.ch.b.269.8	yes	56	3.2	odd	2	inner
504.2.ch.b.269.21	yes	56	1.1	even	1	trivial
504.2.ch.b.269.26	yes	56	8.5	even	2	inner
504.2.ch.b.341.3	yes	56	7.5	odd	6	inner
504.2.ch.b.341.8	yes	56	56.5	odd	6	inner
504.2.ch.b.341.21	yes	56	168.5	even	6	inner
504.2.ch.b.341.26	yes	56	21.5	even	6	inner
2016.2.cp.b.17.3		56	24.11	even	2
2016.2.cp.b.17.4		56	4.3	odd	2
2016.2.cp.b.17.25		56	8.3	odd	2
2016.2.cp.b.17.26		56	12.11	even	2
2016.2.cp.b.593.3		56	28.19	even	6
2016.2.cp.b.593.4		56	168.131	odd	6
2016.2.cp.b.593.25		56	84.47	odd	6
2016.2.cp.b.593.26		56	56.19	even	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.ch (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.896824 - 1.09348i) q^{2} +(-0.391414 - 1.96132i) q^{4} +(-3.16007 + 1.82447i) q^{5} +(-1.64838 + 2.06951i) q^{7} +(-2.49571 - 1.33096i) q^{8} +(-0.839002 + 5.09172i) q^{10} +(0.200123 - 0.346624i) q^{11} +0.581419 q^{13} +(0.784669 + 3.65846i) q^{14} +(-3.69359 + 1.53538i) q^{16} +(-2.27603 + 3.94220i) q^{17} +(2.43222 + 4.21272i) q^{19} +(4.81528 + 5.48381i) q^{20} +(-0.199552 - 0.529692i) q^{22} +(-6.21119 + 3.58603i) q^{23} +(4.15738 - 7.20080i) q^{25} +(0.521430 - 0.635772i) q^{26} +(4.70417 + 2.42297i) q^{28} -6.69007 q^{29} +(-2.85749 - 1.64978i) q^{31} +(-1.63359 + 5.41585i) q^{32} +(2.26954 + 6.02426i) q^{34} +(1.43324 - 9.54721i) q^{35} +(1.93278 - 1.11589i) q^{37} +(6.78781 + 1.11848i) q^{38} +(10.3149 - 0.347416i) q^{40} +4.51491 q^{41} -4.09678i q^{43} +(-0.758173 - 0.256833i) q^{44} +(-1.64907 + 10.0079i) q^{46} +(-2.86389 - 4.96040i) q^{47} +(-1.56571 - 6.82265i) q^{49} +(-4.14552 - 11.0039i) q^{50} +(-0.227575 - 1.14035i) q^{52} +(6.74170 - 11.6770i) q^{53} +1.46048i q^{55} +(6.86829 - 2.97096i) q^{56} +(-5.99982 + 7.31549i) q^{58} +(-7.72158 - 4.45806i) q^{59} +(6.42386 + 11.1265i) q^{61} +(-4.36667 + 1.64507i) q^{62} +(4.45710 + 6.64336i) q^{64} +(-1.83733 + 1.06078i) q^{65} +(-8.30513 - 4.79497i) q^{67} +(8.62281 + 2.92100i) q^{68} +(-9.15435 - 10.1294i) q^{70} +6.42019i q^{71} +(-6.18408 - 3.57038i) q^{73} +(0.513154 - 3.11422i) q^{74} +(7.31051 - 6.41929i) q^{76} +(0.387462 + 0.985523i) q^{77} +(4.15037 + 7.18866i) q^{79} +(8.87076 - 11.5908i) q^{80} +(4.04908 - 4.93699i) q^{82} +10.3852i q^{83} -16.6102i q^{85} +(-4.47977 - 3.67409i) q^{86} +(-0.960790 + 0.598715i) q^{88} +(5.25986 + 9.11034i) q^{89} +(-0.958396 + 1.20325i) q^{91} +(9.46452 + 10.7785i) q^{92} +(-7.99252 - 1.31699i) q^{94} +(-15.3720 - 8.87501i) q^{95} -4.00635i q^{97} +(-8.86463 - 4.40663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82}+ \cdots - 180 q^{94}+O(q^{100}) \) 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

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