LMFDB - Embedded newform 504.2.ch.b.269.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(269,504)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			269.3
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39540 + 0.229930i) q^{2} +(1.89426 - 0.641688i) q^{4} +(-3.16007 + 1.82447i) q^{5} +(-1.64838 + 2.06951i) q^{7} +(-2.49571 + 1.33096i) q^{8} +O(q^{10})$	\(q+(-1.39540 + 0.229930i) q^{2} +(1.89426 - 0.641688i) q^{4} +(-3.16007 + 1.82447i) q^{5} +(-1.64838 + 2.06951i) q^{7} +(-2.49571 + 1.33096i) q^{8} +(3.99006 - 3.27246i) q^{10} +(0.200123 - 0.346624i) q^{11} -0.581419 q^{13} +(1.82430 - 3.26679i) q^{14} +(3.17647 - 2.43105i) q^{16} +(2.27603 - 3.94220i) q^{17} +(-2.43222 - 4.21272i) q^{19} +(-4.81528 + 5.48381i) q^{20} +(-0.199552 + 0.529692i) q^{22} +(6.21119 - 3.58603i) q^{23} +(4.15738 - 7.20080i) q^{25} +(0.811310 - 0.133686i) q^{26} +(-1.79448 + 4.97793i) q^{28} -6.69007 q^{29} +(-2.85749 - 1.64978i) q^{31} +(-3.87347 + 4.12265i) q^{32} +(-2.26954 + 6.02426i) q^{34} +(1.43324 - 9.54721i) q^{35} +(-1.93278 + 1.11589i) q^{37} +(4.36254 + 5.31918i) q^{38} +(5.45833 - 8.75927i) q^{40} -4.51491 q^{41} +4.09678i q^{43} +(0.156662 - 0.785014i) q^{44} +(-7.84253 + 6.43207i) q^{46} +(2.86389 + 4.96040i) q^{47} +(-1.56571 - 6.82265i) q^{49} +(-4.14552 + 11.0039i) q^{50} +(-1.10136 + 0.373089i) q^{52} +(6.74170 - 11.6770i) q^{53} +1.46048i q^{55} +(1.35944 - 7.35880i) q^{56} +(9.33530 - 1.53825i) q^{58} +(-7.72158 - 4.45806i) q^{59} +(-6.42386 - 11.1265i) q^{61} +(4.36667 + 1.64507i) q^{62} +(4.45710 - 6.64336i) q^{64} +(1.83733 - 1.06078i) q^{65} +(8.30513 + 4.79497i) q^{67} +(1.78174 - 8.92807i) q^{68} +(0.195254 + 13.6517i) q^{70} -6.42019i q^{71} +(-6.18408 - 3.57038i) q^{73} +(2.44042 - 2.00151i) q^{74} +(-7.31051 - 6.41929i) q^{76} +(0.387462 + 0.985523i) q^{77} +(4.15037 + 7.18866i) q^{79} +(-5.60251 + 13.4777i) q^{80} +(6.30010 - 1.03812i) q^{82} +10.3852i q^{83} +16.6102i q^{85} +(-0.941975 - 5.71664i) q^{86} +(-0.0381076 + 1.13143i) q^{88} +(-5.25986 - 9.11034i) q^{89} +(0.958396 - 1.20325i) q^{91} +(9.46452 - 10.7785i) q^{92} +(-5.13681 - 6.26323i) q^{94} +(15.3720 + 8.87501i) q^{95} -4.00635i q^{97} +(3.75352 + 9.16030i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) $ 56 * q - 8 * q^4 - 20 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	−1.39540	+	0.229930i	−0.986695	+	0.162585i
$2$	−1.39540	+	0.229930i	−0.986695	+	0.162585i
$3$		0			0
$3$		0			0
$4$	1.89426	−	0.641688i	0.947132	−	0.320844i
$5$	−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
$10$	3.99006	−	3.27246i	1.26177	−	1.03484i
$11$	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	$-0.525693\pi$
$13$	−0.581419			−0.161256			−0.0806282	+	0.996744i	$0.525693\pi$
$14$	1.82430	−	3.26679i	0.487564	−	0.873087i
$15$		0			0
$16$	3.17647	−	2.43105i	0.794118	−	0.607763i
$17$	2.27603	−	3.94220i	0.552019	−	0.956124i	−0.446110	−	0.894978i	$-0.647191\pi$
$17$	2.27603	−	3.94220i	0.552019	−	0.956124i	0.998129	−	0.0611464i	$-0.0194756\pi$
$18$		0			0
$19$	−2.43222	−	4.21272i	−0.557989	−	0.966465i	−0.997664	−	0.0683081i	$-0.978240\pi$
$19$	−2.43222	−	4.21272i	−0.557989	−	0.966465i	0.439676	−	0.898157i	$-0.355093\pi$
$20$	−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	0.315565	−	0.948904i	$-0.397806\pi$
$23$	6.21119	−	3.58603i	1.29512	−	0.747739i	0.979557	+	0.201165i	$0.0644728\pi$
$24$		0			0
$25$	4.15738	−	7.20080i	0.831476	−	1.44016i
$26$	0.811310	−	0.133686i	0.159111	−	0.0262179i
$27$		0			0
$28$	−1.79448	+	4.97793i	−0.339125	+	0.940741i
$29$	−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	$0.762422\pi$
$32$	−3.87347	+	4.12265i	−0.684739	+	0.728788i
$33$		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	−0.650388	−	0.759602i	$-0.725394\pi$
$37$	−1.93278	+	1.11589i	−0.317747	+	0.183451i	0.332641	+	0.943054i	$0.392060\pi$
$38$	4.36254	+	5.31918i	0.707697	+	0.862885i
$39$		0			0
$40$	5.45833	−	8.75927i	0.863037	−	1.38496i
$41$	−4.51491			−0.705111			−0.352556	−	0.935791i	$-0.614687\pi$
$41$	−4.51491			−0.705111			−0.352556	+	0.935791i	$0.614687\pi$
$42$		0			0
$43$			4.09678i			0.624754i	0.949958	+	0.312377i	$0.101125\pi$
$43$			4.09678i			0.624754i	−0.949958	+	0.312377i	$0.898875\pi$
$44$	0.156662	−	0.785014i	0.0236177	−	0.118345i
$45$		0			0
$46$	−7.84253	+	6.43207i	−1.15632	+	0.948358i
$47$	2.86389	+	4.96040i	0.417741	+	0.723549i	0.995712	−	0.0925088i	$-0.0294886\pi$
$47$	2.86389	+	4.96040i	0.417741	+	0.723549i	−0.577971	+	0.816057i	$0.696155\pi$
$48$		0			0
$49$	−1.56571	−	6.82265i	−0.223673	−	0.974664i
$50$	−4.14552	+	11.0039i	−0.586265	+	1.55618i
$51$		0			0
$52$	−1.10136	+	0.373089i	−0.152731	+	0.0517382i
$53$	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
$56$	1.35944	−	7.35880i	0.181663	−	0.983361i
$57$		0			0
$58$	9.33530	−	1.53825i	1.22579	−	0.201982i
$59$	−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	$-0.859250\pi$
$61$	−6.42386	−	11.1265i	−0.822491	−	1.42460i	0.0813302	−	0.996687i	$-0.474083\pi$
$62$	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	0.912545	−	0.408977i	$-0.134114\pi$
$67$	8.30513	+	4.79497i	1.01463	+	0.585798i	0.102088	+	0.994775i	$0.467448\pi$
$68$	1.78174	−	8.92807i	0.216068	−	1.08269i
$69$		0			0
$70$	0.195254	+	13.6517i	0.0233373	+	1.63169i
$71$		−	6.42019i		−	0.761937i	−0.924588	−	0.380968i	$-0.875591\pi$
$71$		−	6.42019i		−	0.761937i	0.924588	−	0.380968i	$-0.124409\pi$
$72$		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	$0.803894\pi$
$74$	2.44042	−	2.00151i	0.283693	−	0.232671i
$75$		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	$0.678685\pi$
$80$	−5.60251	+	13.4777i	−0.626380	+	1.50685i
$81$		0			0
$82$	6.30010	−	1.03812i	0.695729	−	0.114641i
$83$			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
$86$	−0.941975	−	5.71664i	−0.101576	−	0.616441i
$87$		0			0
$88$	−0.0381076	+	1.13143i	−0.00406228	+	0.120610i
$89$	−5.25986	−	9.11034i	−0.557544	−	0.965694i	−0.997701	−	0.0677734i	$-0.978411\pi$
$89$	−5.25986	−	9.11034i	−0.557544	−	0.965694i	0.440157	−	0.897921i	$-0.354923\pi$
$90$		0			0
$91$	0.958396	−	1.20325i	0.100467	−	0.126135i
$92$	9.46452	−	10.7785i	0.986744	−	1.12374i
$93$		0			0
$94$	−5.13681	−	6.26323i	−0.529821	−	0.646003i
$95$	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	$-0.0651964\pi$
$98$	3.75352	+	9.16030i	0.379163	+	0.925330i
$99$		0			0
$100$	3.25452	−	16.3080i	0.325452	−	1.63080i
$101$	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	$-0.984592\pi$
$109$	−16.0796	−	9.28357i	−1.54015	−	0.889205i	−0.541319	−	0.840817i	$-0.682075\pi$
$110$	−0.335808	−	2.03794i	−0.0320180	−	0.194310i
$111$		0			0
$112$	−0.204945	+	10.5810i	−0.0193655	+	0.999812i
$113$			3.44494i			0.324073i	0.986785	+	0.162037i	$0.0518063\pi$
$113$			3.44494i			0.324073i	−0.986785	+	0.162037i	$0.948194\pi$
$114$		0			0
$115$	−13.0852	+	22.6642i	−1.22020	+	2.11345i
$116$	−12.6728	+	4.29294i	−1.17664	+	0.398589i
$117$		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
$122$	11.5221	+	14.0488i	1.04317	+	1.27192i
$123$		0			0
$124$	−6.47149	−	1.29149i	−0.581157	−	0.115979i
$125$			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	$0.554236\pi$
$128$	−4.69192	+	10.2949i	−0.414711	+	0.909953i
$129$		0			0
$130$	−2.31989	+	1.90267i	−0.203468	+	0.166875i
$131$	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
$136$	−0.433403	+	12.8679i	−0.0371640	+	1.10341i
$137$	−13.2672	−	7.65983i	−1.13350	−	0.654424i	−0.188684	−	0.982038i	$-0.560422\pi$
$137$	−13.2672	−	7.65983i	−1.13350	−	0.654424i	−0.944812	+	0.327614i	$0.893755\pi$
$138$		0			0
$139$	10.5472			0.894602			0.447301	−	0.894383i	$-0.352385\pi$
$139$	10.5472			0.894602			0.447301	+	0.894383i	$0.352385\pi$
$140$	−3.41139	−	19.0046i	−0.288315	−	1.60618i
$141$		0			0
$142$	1.47620	+	8.95872i	0.123880	+	0.751799i
$143$	−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	$0.119872\pi$
$152$	11.6771	+	7.27654i	0.947134	+	0.590206i
$153$		0			0
$154$	−0.767264	−	1.28611i	−0.0618279	−	0.103637i
$155$	12.0399			0.967065
$156$		0			0
$157$	−0.359090	+	0.621963i	−0.0286585	+	0.0496380i	−0.879999	−	0.474976i	$-0.842457\pi$
$157$	−0.359090	+	0.621963i	−0.0286585	+	0.0496380i	0.851340	+	0.524614i	$0.175790\pi$
$158$	−7.44431	−	9.07673i	−0.592237	−	0.722106i
$159$		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	0.497011	−	0.867744i	$-0.334431\pi$
$163$	19.1125	−	11.0346i	1.49700	−	0.864296i	0.999994	+	0.00344810i	$0.00109757\pi$
$164$	−8.55244	+	2.89717i	−0.667833	+	0.226231i
$165$		0			0
$166$	−2.38786	−	14.4914i	−0.185334	−	1.12475i
$167$	−13.4882			−1.04375			−0.521875	−	0.853022i	$-0.674767\pi$
$167$	−13.4882			−1.04375			−0.521875	+	0.853022i	$0.674767\pi$
$168$		0			0
$169$	−12.6620			−0.973996
$170$	−3.81919	−	23.1778i	−0.292918	−	1.77766i
$171$		0			0
$172$	2.62886	+	7.76039i	0.200448	+	0.591724i
$173$	−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
$178$	9.43433	+	11.5031i	0.707133	+	0.862197i
$179$	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	$-0.385787\pi$
$181$	9.44875			0.702320			0.351160	+	0.936315i	$0.385787\pi$
$182$	−1.06068	+	1.89937i	−0.0786228	+	0.140791i
$183$		0			0
$184$	−10.7284	+	17.2165i	−0.790912	+	1.26922i
$185$	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	−0.957742	−	0.287630i	$-0.907133\pi$
$191$	−16.4118	+	9.47537i	−1.18752	+	0.685614i	−0.229776	+	0.973244i	$0.573799\pi$
$192$		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	$0.105174\pi$
$194$	0.921181	+	5.59045i	0.0661369	+	0.401371i
$195$		0			0
$196$	−7.34388	−	11.9192i	−0.524563	−	0.851372i
$197$	−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	$0.751594\pi$
$200$	−0.791650	+	23.5044i	−0.0559781	+	1.66201i
$201$		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
$206$	22.0773	−	18.1068i	1.53820	−	1.26156i
$207$		0			0
$208$	−1.84686	+	1.41346i	−0.128057	+	0.0980057i
$209$	−1.94697			−0.134675
$210$		0			0
$211$		−	24.6986i		−	1.70032i	−0.526521	−	0.850162i	$-0.676504\pi$
$211$		−	24.6986i		−	1.70032i	0.526521	−	0.850162i	$-0.323496\pi$
$212$	5.27759	−	26.4453i	0.362466	−	1.81627i
$213$		0			0
$214$	−3.76511	−	4.59074i	−0.257377	−	0.313816i
$215$	−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
$220$	0.937169	+	2.76653i	0.0631840	+	0.186519i
$221$	−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	$-0.0862019\pi$
$224$	−2.14692	−	14.8118i	−0.143447	−	0.989658i
$225$		0			0
$226$	−0.792097	−	4.80706i	−0.0526895	−	0.319761i
$227$	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	0.986581	−	0.163271i	$-0.0522045\pi$
$229$	5.32512	+	9.22338i	0.351894	+	0.609498i	−0.634687	+	0.772769i	$0.718871\pi$
$230$	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	−0.853744	−	0.520693i	$-0.825673\pi$
$233$	−12.6645	+	7.31188i	−0.829682	+	0.479017i	0.0240618	+	0.999710i	$0.492340\pi$
$234$		0			0
$235$	−18.1002	−	10.4502i	−1.18073	−	0.681693i
$236$	−17.4874	−	3.48989i	−1.13833	−	0.227173i
$237$		0			0
$238$	−8.72621	−	14.6271i	−0.565636	−	0.948132i
$239$		−	11.5819i		−	0.749168i	−0.927193	−	0.374584i	$-0.877786\pi$
$239$		−	11.5819i		−	0.749168i	0.927193	−	0.374584i	$-0.122214\pi$
$240$		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	$0.650478\pi$
$242$	−9.72139	−	11.8531i	−0.624915	−	0.761949i
$243$		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
$248$	9.32725	+	0.314151i	0.592281	+	0.0199486i
$249$		0			0
$250$	−2.78109	−	16.8778i	−0.175892	−	1.06745i
$251$			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
$254$	5.33292	−	0.878745i	0.334617	−	0.0551374i
$255$		0			0
$256$	4.17997	−	15.4443i	0.261248	−	0.965272i
$257$	−3.71744	−	6.43879i	−0.231887	−	0.401640i	0.726476	−	0.687192i	$-0.241157\pi$
$257$	−3.71744	−	6.43879i	−0.231887	−	0.401640i	−0.958363	+	0.285551i	$0.907823\pi$
$258$		0			0
$259$	0.876604	−	5.83931i	0.0544695	−	0.362837i
$260$	2.79969	−	3.18839i	0.173629	−	0.197735i
$261$		0			0
$262$	−0.202751	+	0.166286i	−0.0125260	+	0.0102732i
$263$	7.28419	+	4.20553i	0.449162	+	0.259324i	0.707476	−	0.706737i	$-0.249834\pi$
$263$	7.28419	+	4.20553i	0.449162	+	0.259324i	−0.258314	+	0.966061i	$0.583167\pi$
$264$		0			0
$265$			49.2001i			3.02234i
$266$	−18.1992	+	0.260295i	−1.11586	+	0.0159597i
$267$		0			0
$268$	18.8090	+	3.75364i	1.14894	+	0.229290i
$269$	−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	−0.0313266	−	0.999509i	$-0.509973\pi$
$277$	−15.1885	−	8.76910i	−0.912590	−	0.526884i	−0.881264	+	0.472625i	$0.843307\pi$
$278$	−14.7175	+	2.42512i	−0.882699	+	0.145449i
$279$		0			0
$280$	9.12998	+	25.7346i	0.545621	+	1.53794i
$281$			14.8388i			0.885208i	0.896717	+	0.442604i	$0.145945\pi$
$281$			14.8388i			0.885208i	−0.896717	+	0.442604i	$0.854055\pi$
$282$		0			0
$283$	0.293271	−	0.507960i	0.0174331	−	0.0301951i	−0.857177	−	0.515022i	$-0.827784\pi$
$283$	0.293271	−	0.507960i	0.0174331	−	0.0301951i	0.874610	+	0.484826i	$0.161117\pi$
$284$	−4.11976	−	12.1615i	−0.244463	−	0.721655i
$285$		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
$290$	−26.6938	+	21.8930i	−1.56751	+	1.28560i
$291$		0			0
$292$	−14.0053	−	2.79499i	−0.819601	−	0.163565i
$293$		−	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
$296$	3.33845	−	5.35738i	0.194043	−	0.311392i
$297$		0			0
$298$	8.23494	+	10.0407i	0.477037	+	0.581644i
$299$	−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
$304$	−17.9672	−	7.46876i	−1.03049	−	0.428363i
$305$	40.5998	+	23.4403i	2.32474	+	1.34219i
$306$		0			0
$307$	−19.0443			−1.08691			−0.543457	−	0.839437i	$-0.682885\pi$
$307$	−19.0443			−1.08691			−0.543457	+	0.839437i	$0.682885\pi$
$308$	1.36635	+	1.61821i	0.0778551	+	0.0922061i
$309$		0			0
$310$	−16.8004	+	2.76833i	−0.954198	+	0.157230i
$311$	−4.52301	+	7.83409i	−0.256476	+	0.444230i	−0.965295	−	0.261160i	$-0.915895\pi$
$311$	−4.52301	+	7.83409i	−0.256476	+	0.444230i	0.708819	+	0.705390i	$0.249228\pi$
$312$		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
$320$	−1.96417	+	29.1254i	−0.109800	+	1.62816i
$321$		0			0
$322$	−0.383775	−	26.8326i	−0.0213870	−	1.49533i
$323$	−22.1432			−1.23208
$324$		0			0
$325$	−2.41718	+	4.18668i	−0.134081	+	0.232235i
$326$	−24.1323	+	19.7922i	−1.33656	+	1.09619i
$327$		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	−0.343140	−	0.939284i	$-0.611490\pi$
$331$	5.43500	−	3.13790i	0.298735	−	0.172475i	0.641874	+	0.766810i	$0.278157\pi$
$332$	6.66402	+	19.6722i	0.365736	+	1.07965i
$333$		0			0
$334$	18.8214	−	3.10135i	1.02986	−	0.169698i
$335$	−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	$0.684745\pi$
$338$	17.6684	−	2.91137i	0.961037	−	0.158357i
$339$		0			0
$340$	10.6586	+	31.4641i	0.578042	+	1.70638i
$341$	−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
$346$	17.6894	−	14.5080i	0.950989	−	0.779956i
$347$	−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	$-0.472316\pi$
$349$	3.24549			0.173727			0.0868635	+	0.996220i	$0.472316\pi$
$350$	−15.9392	−	26.7177i	−0.851987	−	1.42812i
$351$		0			0
$352$	0.653837	+	2.16767i	0.0348496	+	0.115537i
$353$	14.6032	−	25.2934i	0.777248	−	1.34623i	−0.156274	−	0.987714i	$-0.549948\pi$
$353$	14.6032	−	25.2934i	0.777248	−	1.34623i	0.933522	−	0.358519i	$-0.116718\pi$
$354$		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	−0.247136	−	0.968981i	$-0.579490\pi$
$359$	8.87600	−	5.12456i	0.468457	−	0.270464i	0.715594	+	0.698517i	$0.246156\pi$
$360$		0			0
$361$	−2.33135	+	4.03802i	−0.122703	+	0.212528i
$362$	−13.1848	+	2.17255i	−0.692975	+	0.114187i
$363$		0			0
$364$	1.04335	−	2.89426i	0.0546862	−	0.151701i
$365$	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	$0.962768\pi$
$368$	11.0118	−	26.4907i	0.574032	−	1.38092i
$369$		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	0.0280346	−	0.999607i	$-0.491075\pi$
$373$	17.5313	−	10.1217i	0.907737	−	0.524082i	0.879702	+	0.475525i	$0.157742\pi$
$374$	1.63397	+	1.99227i	0.0844904	+	0.103018i
$375$		0			0
$376$	−13.7495	−	8.56799i	−0.709077	−	0.441860i
$377$	3.88973			0.200331
$378$		0			0
$379$			15.4020i			0.791146i	0.918435	+	0.395573i	$0.129454\pi$
$379$			15.4020i			0.791146i	−0.918435	+	0.395573i	$0.870546\pi$
$380$	34.8136	+	6.94761i	1.78590	+	0.356405i
$381$		0			0
$382$	20.7223	−	16.9955i	1.06025	−	0.869564i
$383$	1.96494	+	3.40338i	0.100404	+	0.173905i	0.911851	−	0.410521i	$-0.134653\pi$
$383$	1.96494	+	3.40338i	0.100404	+	0.173905i	−0.811447	+	0.584426i	$0.801320\pi$
$384$		0			0
$385$	−3.02246	−	2.40741i	−0.154039	−	0.122693i
$386$	−2.65954	+	7.05950i	−0.135367	+	0.359319i
$387$		0			0
$388$	−2.57082	−	7.58908i	−0.130514	−	0.385277i
$389$	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
$392$	12.9882	+	14.9434i	0.656004	+	0.754757i
$393$		0			0
$394$	3.91372	−	0.644894i	0.197171	−	0.0324893i
$395$	−26.2310	−	15.1445i	−1.31982	−	0.762001i
$396$		0			0
$397$	4.40738	+	7.63380i	0.221200	+	0.383129i	0.955173	−	0.296050i	$-0.0956693\pi$
$397$	4.40738	+	7.63380i	0.221200	+	0.383129i	−0.733973	+	0.679179i	$0.762336\pi$
$398$	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	−0.136224	−	0.990678i	$-0.543497\pi$
$401$	13.0887	−	7.55674i	0.653616	−	0.377365i	0.789840	+	0.613313i	$0.210163\pi$
$402$		0			0
$403$	1.66140	+	0.959210i	0.0827602	+	0.0477816i
$404$	27.6019	+	5.50842i	1.37325	+	0.274054i
$405$		0			0
$406$	−12.2047	+	21.8551i	−0.605708	+	1.08465i
$407$			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	$0.720117\pi$
$410$	−18.0148	+	14.7749i	−0.889686	+	0.729678i
$411$		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
$416$	2.25211	−	2.39698i	0.110419	−	0.117522i
$417$		0			0
$418$	2.71680	−	0.447668i	0.132883	−	0.0218962i
$419$		−	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	$-0.947628\pi$
$421$		−	6.72143i		−	0.327582i	0.986495	−	0.163791i	$-0.0523723\pi$
$422$	5.67896	+	34.4644i	0.276448	+	1.67770i
$423$		0			0
$424$	−1.28376	+	38.1152i	−0.0623447	+	1.85104i
$425$	−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
$430$	13.4065	+	16.3464i	0.646521	+	0.788294i
$431$	1.32418	+	0.764518i	0.0637837	+	0.0368255i	0.531553	−	0.847025i	$-0.321609\pi$
$431$	1.32418	+	0.764518i	0.0637837	+	0.0368255i	−0.467769	+	0.883851i	$0.654942\pi$
$432$		0			0
$433$			19.9225i			0.957416i	0.877974	+	0.478708i	$0.158895\pi$
$433$			19.9225i			0.957416i	−0.877974	+	0.478708i	$0.841105\pi$
$434$	−10.6024	+	6.32517i	−0.508931	+	0.303618i
$435$		0			0
$436$	−36.4162	−	7.26744i	−1.74402	−	0.348047i
$437$	−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
$446$	1.83706	+	11.1487i	0.0869873	+	0.527907i
$447$		0			0
$448$	6.40149	+	20.1748i	0.302442	+	0.953168i
$449$			38.5884i			1.82110i	0.413397	+	0.910551i	$0.364342\pi$
$449$			38.5884i			1.82110i	−0.413397	+	0.910551i	$0.635658\pi$
$450$		0			0
$451$	−0.903540	+	1.56498i	−0.0425460	+	0.0736919i
$452$	2.21058	+	6.52563i	0.103977	+	0.306940i
$453$		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	$0.714426\pi$
$458$	−9.55139	−	11.6459i	−0.446307	−	0.544176i
$459$		0			0
$460$	−10.2435	+	51.3287i	−0.477604	+	2.39321i
$461$		−	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	$0.385544\pi$
$464$	−21.2508	+	16.2639i	−0.986545	+	0.755033i
$465$		0			0
$466$	15.9908	−	13.1149i	0.740762	−	0.607538i
$467$	−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
$472$	25.2043	+	0.848905i	1.16012	+	0.0390740i
$473$	1.42004	+	0.819862i	0.0652936	+	0.0376973i
$474$		0			0
$475$	−40.4466			−1.85582
$476$	15.5397	+	18.4041i	0.712262	+	0.843553i
$477$		0			0
$478$	2.66302	+	16.1613i	0.121804	+	0.739200i
$479$	15.2782	−	26.4626i	0.698077	−	1.20911i	−0.271055	−	0.962564i	$-0.587373\pi$
$479$	15.2782	−	26.4626i	0.698077	−	1.20911i	0.969132	−	0.246541i	$-0.0792941\pi$
$480$		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	$0.00217610\pi$
$488$	30.8409	+	19.2185i	1.39610	+	0.869980i
$489$		0			0
$490$	−28.5741	−	22.0990i	−1.29085	−	0.998333i
$491$	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
$494$	−2.53646	−	3.09267i	−0.114121	−	0.139146i
$495$		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	$0.712774\pi$
$499$	−35.9490	+	20.7552i	−1.60930	+	0.929128i	−0.989528	+	0.144344i	$0.953893\pi$
$500$	7.76145	+	22.9118i	0.347103	+	1.02465i
$501$		0			0
$502$	−4.13343	−	25.0849i	−0.184484	−	1.11959i
$503$	−18.4870			−0.824295			−0.412147	−	0.911117i	$-0.635221\pi$
$503$	−18.4870			−0.824295			−0.412147	+	0.911117i	$0.635221\pi$
$504$		0			0
$505$	−51.3519			−2.28513
$506$	0.660036	+	4.00562i	0.0293422	+	0.178071i
$507$		0			0
$508$	−7.23948	+	2.45240i	−0.321200	+	0.108808i
$509$	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
$514$	6.66777	+	8.12991i	0.294103	+	0.358595i
$515$	36.8359	−	63.8016i	1.62318	−	2.81144i
$516$		0			0
$517$	2.29252			0.100825
$518$	0.119422	+	8.34971i	0.00524711	+	0.366865i
$519$		0			0
$520$	−3.17357	+	5.09280i	−0.139170	+	0.223334i
$521$	−3.54303	+	6.13671i	−0.155223	+	0.268854i	−0.933140	−	0.359513i	$-0.882943\pi$
$521$	−3.54303	+	6.13671i	−0.155223	+	0.268854i	0.777917	+	0.628367i	$0.216276\pi$
$522$		0			0
$523$	12.3169	+	21.3336i	0.538583	+	0.932852i	0.998981	+	0.0451399i	$0.0143733\pi$
$523$	12.3169	+	21.3336i	0.538583	+	0.932852i	−0.460398	+	0.887713i	$0.652293\pi$
$524$	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
$530$	−11.3126	−	68.6537i	−0.491387	−	2.98212i
$531$		0			0
$532$	25.3352	−	4.54776i	1.09842	−	0.197170i
$533$	2.62505			0.113704
$534$		0			0
$535$	−13.2668	−	7.65962i	−0.573576	−	0.331154i
$536$	−27.1091	−	0.913060i	−1.17093	−	0.0394382i
$537$		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	−0.869048	−	0.494728i	$-0.835268\pi$
$541$	−20.3549	+	11.7519i	−0.875125	+	0.505254i	−0.00607698	+	0.999982i	$0.501934\pi$
$542$	−20.3256	+	16.6701i	−0.873060	+	0.716042i
$543$		0			0
$544$	7.43618	+	24.6533i	0.318824	+	1.05700i
$545$	67.7504			2.90211
$546$		0			0
$547$		−	16.9894i		−	0.726412i	−0.931709	−	0.363206i	$-0.881682\pi$
$547$		−	16.9894i		−	0.726412i	0.931709	−	0.363206i	$-0.118318\pi$
$548$	−30.0468	−	5.99634i	−1.28354	−	0.256151i
$549$		0			0
$550$	2.98459	+	3.63907i	0.127263	+	0.155170i
$551$	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
$556$	19.9792	−	6.76801i	0.847307	−	0.287028i
$557$	−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
$560$	−18.6571	−	33.8107i	−0.788407	−	1.42876i
$561$		0			0
$562$	−3.41189	−	20.7060i	−0.143922	−	0.873430i
$563$	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	−0.170903	−	0.985288i	$-0.554668\pi$
$569$	14.2390	−	8.22089i	0.596930	−	0.344638i	0.767833	+	0.640650i	$0.221335\pi$
$570$		0			0
$571$	−33.2026	−	19.1696i	−1.38949	−	0.802221i	−0.396230	−	0.918151i	$-0.629682\pi$
$571$	−33.2026	−	19.1696i	−1.38949	−	0.802221i	−0.993257	+	0.115931i	$0.963015\pi$
$572$	−0.0910863	+	0.456421i	−0.00380851	+	0.0190839i
$573$		0			0
$574$	−8.23654	+	14.7493i	−0.343787	+	0.615624i
$575$		−	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	$0.513818\pi$
$578$	3.33733	+	4.06916i	0.138815	+	0.169255i
$579$		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
$584$	20.1857	+	0.679873i	0.835289	+	0.0281333i
$585$		0			0
$586$	1.39661	+	8.47572i	0.0576934	+	0.350129i
$587$			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
$590$	−45.3984	+	7.48063i	−1.86902	+	0.307973i
$591$		0			0
$592$	−3.42663	+	8.24328i	−0.140834	+	0.338797i
$593$	19.4634	+	33.7116i	0.799267	+	1.38437i	0.920094	+	0.391697i	$0.128112\pi$
$593$	19.4634	+	33.7116i	0.799267	+	1.38437i	−0.120827	+	0.992674i	$0.538555\pi$
$594$		0			0
$595$	−34.3749	−	27.3799i	−1.40923	−	1.12246i
$596$	−13.7997	−	12.1173i	−0.565257	−	0.496346i
$597$		0			0
$598$	4.55979	−	3.73973i	0.186464	−	0.152929i
$599$	−8.92743	−	5.15425i	−0.364765	−	0.210597i	0.306404	−	0.951902i	$-0.400874\pi$
$599$	−8.92743	−	5.15425i	−0.364765	−	0.210597i	−0.671169	+	0.741304i	$0.734207\pi$
$600$		0			0
$601$			16.1379i			0.658277i	0.944282	+	0.329139i	$0.106758\pi$
$601$			16.1379i			0.658277i	−0.944282	+	0.329139i	$0.893242\pi$
$602$	13.3834	+	7.47375i	0.545465	+	0.304607i
$603$		0			0
$604$	1.40908	−	7.06074i	0.0573349	−	0.287297i
$605$	−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	0.526704	−	0.850049i	$-0.323428\pi$
$613$	1.33431	+	0.770363i	0.0538922	+	0.0311147i	−0.472812	+	0.881163i	$0.656761\pi$
$614$	26.5743	−	4.37885i	1.07245	−	0.176716i
$615$		0			0
$616$	−2.27868	−	1.94388i	−0.0918106	−	0.0783212i
$617$		−	40.1412i		−	1.61602i	−0.589165	−	0.808012i	$-0.700543\pi$
$617$		−	40.1412i		−	1.61602i	0.589165	−	0.808012i	$-0.299457\pi$
$618$		0			0
$619$	18.4948	−	32.0339i	0.743368	−	1.28755i	−0.207586	−	0.978217i	$-0.566561\pi$
$619$	18.4948	−	32.0339i	0.743368	−	1.28755i	0.950953	−	0.309334i	$-0.100106\pi$
$620$	22.8067	−	7.72583i	0.915938	−	0.310277i
$621$		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
$626$	8.15233	−	6.68615i	0.325832	−	0.267232i
$627$		0			0
$628$	−0.281106	+	1.40859i	−0.0112174	+	0.0562087i
$629$			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	$0.287488\pi$
$632$	−19.9259	−	12.4168i	−0.792610	−	0.493914i
$633$		0			0
$634$	4.31789	+	5.26474i	0.171485	+	0.209089i
$635$	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
$640$	−3.95601	−	41.0931i	−0.156375	−	1.62435i
$641$	3.44022	+	1.98621i	0.135881	+	0.0784507i	0.566399	−	0.824131i	$-0.308336\pi$
$641$	3.44022	+	1.98621i	0.135881	+	0.0784507i	−0.430519	+	0.902582i	$0.641669\pi$
$642$		0			0
$643$	47.5503			1.87520			0.937600	−	0.347717i	$-0.113043\pi$
$643$	47.5503			1.87520			0.937600	+	0.347717i	$0.113043\pi$
$644$	6.70516	+	37.3540i	0.264220	+	1.47195i
$645$		0			0
$646$	30.8986	−	5.09139i	1.21569	−	0.200318i
$647$	20.9097	−	36.2166i	0.822044	−	1.42382i	−0.0821142	−	0.996623i	$-0.526167\pi$
$647$	20.9097	−	36.2166i	0.822044	−	1.42382i	0.904158	−	0.427199i	$-0.140499\pi$
$648$		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
$656$	−14.3415	+	10.9760i	−0.559942	+	0.428541i
$657$		0			0
$658$	21.4292	−	0.306492i	0.835397	−	0.0119483i
$659$	−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	−0.533440	−	0.845838i	$-0.679101\pi$
$661$	11.9756	−	20.7423i	0.465797	−	0.806784i	0.999237	+	0.0390540i	$0.0124344\pi$
$662$	−6.86249	+	5.62829i	−0.266718	+	0.218750i
$663$		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
$668$	−25.5503	+	8.65524i	−0.988570	+	0.334881i
$669$		0			0
$670$	48.8292	−	8.04597i	1.88644	−	0.310843i
$671$	−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	$0.516004\pi$
$674$	28.0933	−	4.62915i	1.08211	−	0.178308i
$675$		0			0
$676$	−23.9851	+	8.12502i	−0.922503	+	0.312501i
$677$	−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
$682$	1.44409	−	1.18438i	0.0552971	−	0.0453521i
$683$	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
$686$	−25.1445	−	7.33167i	−0.960022	−	0.279925i
$687$		0			0
$688$	9.95950	+	13.0133i	0.379702	+	0.496128i
$689$	−3.91975	+	6.78920i	−0.149330	+	0.258648i
$690$		0			0
$691$	−12.6075	−	21.8368i	−0.479611	−	0.830710i	0.520116	−	0.854096i	$-0.325889\pi$
$691$	−12.6075	−	21.8368i	−0.479611	−	0.830710i	−0.999727	+	0.0233857i	$0.992555\pi$
$692$	−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
$698$	−4.52874	+	0.746236i	−0.171415	+	0.0282454i
$699$		0			0
$700$	28.3847	+	33.6169i	1.07284	+	1.27060i
$701$	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
$704$	−1.41078	−	2.87443i	−0.0531706	−	0.108334i
$705$		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	−0.970244	−	0.242130i	$-0.922154\pi$
$709$	−33.1687	+	19.1499i	−1.24568	+	0.719191i	−0.275431	+	0.961321i	$0.588821\pi$
$710$	−21.0098	−	25.6169i	−0.788484	−	0.961387i
$711$		0			0
$712$	25.2525	+	15.7361i	0.946379	+	0.589735i
$713$	−23.6646			−0.886245
$714$		0			0
$715$		−	0.849148i		−	0.0317563i
$716$	0.682646	−	3.42065i	0.0255117	−	0.127836i
$717$		0			0
$718$	−11.2073	+	9.19166i	−0.418251	+	0.343030i
$719$	−3.40747	−	5.90191i	−0.127077	−	0.220104i	0.795466	−	0.605998i	$-0.207226\pi$
$719$	−3.40747	−	5.90191i	−0.127077	−	0.220104i	−0.922543	+	0.385894i	$0.873893\pi$
$720$		0			0
$721$	7.93024	−	52.8256i	0.295338	−	1.96733i
$722$	2.32470	−	6.17069i	0.0865164	−	0.229649i
$723$		0			0
$724$	17.8984	−	6.06315i	0.665190	−	0.225335i
$725$	−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	$-0.307188\pi$
$728$	−0.790402	+	4.27854i	−0.0292943	+	0.158573i
$729$		0			0
$730$	−36.3587	+	5.99111i	−1.34570	+	0.221741i
$731$	16.1504	+	9.32441i	0.597342	+	0.344876i
$732$		0			0
$733$	4.98689	+	8.63755i	0.184195	+	0.319035i	0.943305	−	0.331927i	$-0.107699\pi$
$733$	4.98689	+	8.63755i	0.184195	+	0.319035i	−0.759110	+	0.650962i	$0.774366\pi$
$734$	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	0.990485	−	0.137619i	$-0.0439450\pi$
$739$	37.1489	+	21.4480i	1.36655	+	0.788976i	0.376061	+	0.926595i	$0.377278\pi$
$740$	3.18753	−	15.9723i	0.117176	−	0.587154i
$741$		0			0
$742$	−25.8474	−	43.3260i	−0.948887	−	1.59055i
$743$			11.2075i			0.411165i	0.978640	+	0.205582i	$0.0659088\pi$
$743$			11.2075i			0.411165i	−0.978640	+	0.205582i	$0.934091\pi$
$744$		0			0
$745$	29.0169	+	16.7529i	1.06310	+	0.613778i
$746$	−22.1359	+	18.1548i	−0.810451	+	0.664694i
$747$		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	$0.596563\pi$
$752$	21.1561	+	8.79432i	0.771482	+	0.320696i
$753$		0			0
$754$	−5.42772	+	0.894367i	−0.197666	+	0.0325709i
$755$			13.1361i			0.478073i
$756$		0			0
$757$		−	20.8257i		−	0.756924i	−0.925617	−	0.378462i	$-0.876453\pi$
$757$		−	20.8257i		−	0.756924i	0.925617	−	0.378462i	$-0.123547\pi$
$758$	−3.54138	−	21.4918i	−0.128629	−	0.780619i
$759$		0			0
$760$	−50.1762	−	1.68998i	−1.82008	−	0.0613022i
$761$	−7.26978	−	12.5916i	−0.263529	−	0.456446i	0.703648	−	0.710549i	$-0.251553\pi$
$761$	−7.26978	−	12.5916i	−0.263529	−	0.456446i	−0.967177	+	0.254103i	$0.918220\pi$
$762$		0			0
$763$	45.7177	−	17.9740i	1.65509	−	0.650704i
$764$	−25.0081	+	28.4801i	−0.904761	+	1.03037i
$765$		0			0
$766$	−3.52442	−	4.29727i	−0.127342	−	0.155267i
$767$	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	$0.987853\pi$
$770$	4.77107	+	2.66434i	0.171938	+	0.0960162i
$771$		0			0
$772$	2.08792	−	10.4623i	0.0751460	−	0.376547i
$773$	−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
$782$	7.50669	+	45.5565i	0.268439	+	1.62910i
$783$		0			0
$784$	−21.5597	−	17.8656i	−0.769988	−	0.638058i
$785$		−	2.62060i		−	0.0935331i
$786$		0			0
$787$	−15.1516	+	26.2433i	−0.540096	+	0.935473i	0.458802	+	0.888538i	$0.348279\pi$
$787$	−15.1516	+	26.2433i	−0.540096	+	0.935473i	−0.998898	+	0.0469348i	$0.985055\pi$
$788$	−5.31292	+	1.79977i	−0.189265	+	0.0641140i
$789$		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
$794$	−7.90528	−	9.63879i	−0.280548	−	0.342068i
$795$		0			0
$796$	−14.5894	−	2.91156i	−0.517109	−	0.103197i
$797$		−	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
$800$	13.5829	+	45.0315i	0.480227	+	1.59210i
$801$		0			0
$802$	−16.5263	+	13.5541i	−0.583565	+	0.478613i
$803$	−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
$808$	−39.7822	−	1.33990i	−1.39953	−	0.0471377i
$809$	−31.3922	−	18.1243i	−1.10369	−	0.637216i	−0.166502	−	0.986041i	$-0.553247\pi$
$809$	−31.3922	−	18.1243i	−1.10369	−	0.637216i	−0.937188	+	0.348825i	$0.886581\pi$
$810$		0			0
$811$	5.48133			0.192475			0.0962377	−	0.995358i	$-0.469319\pi$
$811$	5.48133			0.192475			0.0962377	+	0.995358i	$0.469319\pi$
$812$	12.0052	−	33.3027i	0.421301	−	1.16870i
$813$		0			0
$814$	−0.205388	−	1.24646i	−0.00719885	−	0.0436883i
$815$	−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	$0.905359\pi$
$824$	30.2014	−	48.4658i	1.05212	−	1.68839i
$825$		0			0
$826$	−28.6500	+	17.0920i	−0.996861	+	0.594707i
$827$	−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	−0.707009	−	0.707205i	$-0.749956\pi$
$829$	7.45588	−	12.9140i	0.258953	−	0.448520i	0.965962	+	0.258685i	$0.0832891\pi$
$830$	33.9850	+	41.4373i	1.17963	+	1.43831i
$831$		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
$836$	−3.68808	+	1.24935i	−0.127555	+	0.0432096i
$837$		0			0
$838$	2.55233	+	15.4896i	0.0881689	+	0.535078i
$839$	28.4322			0.981587			0.490794	−	0.871276i	$-0.336707\pi$
$839$	28.4322			0.981587			0.490794	+	0.871276i	$0.336707\pi$
$840$		0			0
$841$	15.7571			0.543347
$842$	1.54546	+	9.37906i	0.0532601	+	0.323224i
$843$		0			0
$844$	−15.8488	−	46.7858i	−0.545539	−	1.61043i
$845$	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
$850$	33.9442	+	41.3876i	1.16428	+	1.41958i
$851$	−8.00324	+	13.8620i	−0.274347	+	0.475184i
$852$		0			0
$853$	9.45822			0.323843			0.161922	−	0.986804i	$-0.448231\pi$
$853$	9.45822			0.323843			0.161922	+	0.986804i	$0.448231\pi$
$854$	−48.0669	+	0.687479i	−1.64481	+	0.0235250i
$855$		0			0
$856$	−10.0779	−	6.28005i	−0.344457	−	0.214648i
$857$	19.8068	−	34.3064i	0.676588	−	1.17188i	−0.299415	−	0.954123i	$-0.596791\pi$
$857$	19.8068	−	34.3064i	0.676588	−	1.17188i	0.976002	−	0.217761i	$-0.0698753\pi$
$858$		0			0
$859$	17.1446	+	29.6953i	0.584965	+	1.01319i	0.994880	+	0.101066i	$0.0322253\pi$
$859$	17.1446	+	29.6953i	0.584965	+	1.01319i	−0.409914	+	0.912124i	$0.634441\pi$
$860$	−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	0.129627	−	0.991563i	$-0.458622\pi$
$863$	30.9385	−	17.8623i	1.05316	−	0.608041i	0.923532	+	0.383522i	$0.125289\pi$
$864$		0			0
$865$	29.5147	−	51.1209i	1.00353	−	1.73816i
$866$	−4.58079	−	27.7998i	−0.155662	−	0.944677i
$867$		0			0
$868$	13.3402	−	11.2639i	0.452796	−	0.382323i
$869$	3.32235			0.112703
$870$		0			0
$871$	−4.82875	−	2.78788i	−0.163616	−	0.0944638i
$872$	52.4860	+	1.76778i	1.77740	+	0.0598646i
$873$		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	−0.257003	−	0.966411i	$-0.582735\pi$
$877$	13.3688	−	7.71847i	0.451431	−	0.260634i	0.708435	+	0.705777i	$0.249402\pi$
$878$	18.8977	−	15.4990i	0.637768	−	0.523067i
$879$		0			0
$880$	3.55049	+	4.63916i	0.119687	+	0.156386i
$881$	2.47237			0.0832962			0.0416481	−	0.999132i	$-0.486739\pi$
$881$	2.47237			0.0832962			0.0416481	+	0.999132i	$0.486739\pi$
$882$		0			0
$883$			22.3515i			0.752187i	0.926582	+	0.376094i	$0.122733\pi$
$883$			22.3515i			0.752187i	−0.926582	+	0.376094i	$0.877267\pi$
$884$	−1.03594	+	5.19095i	−0.0348424	+	0.174590i
$885$		0			0
$886$	1.19467	+	1.45664i	0.0401358	+	0.0489369i
$887$	11.2912	+	19.5570i	0.379122	+	0.656658i	0.990935	−	0.134344i	$-0.0428928\pi$
$887$	11.2912	+	19.5570i	0.379122	+	0.656658i	−0.611813	+	0.791003i	$0.709559\pi$
$888$		0			0
$889$	6.29975	−	7.90922i	0.211287	−	0.265267i
$890$	−50.8003	−	19.1381i	−1.70283	−	0.641512i
$891$		0			0
$892$	−5.12686	−	15.1345i	−0.171660	−	0.506740i
$893$	13.9312	−	24.1295i	0.466189	−	0.807464i
$894$		0			0
$895$			6.36394i			0.212723i
$896$	−13.5714	−	26.6799i	−0.453389	−	0.891313i
$897$		0			0
$898$	−8.87265	−	53.8462i	−0.296084	−	1.79687i
$899$	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	0.347514	−	0.937675i	$-0.387026\pi$
$907$	−8.75724	−	5.05599i	−0.290779	−	0.167882i	−0.638293	+	0.769793i	$0.720359\pi$
$908$	4.62727	+	0.923447i	0.153561	+	0.0306457i
$909$		0			0
$910$	−0.113524	−	7.93734i	−0.00376329	−	0.263120i
$911$			28.5297i			0.945230i	0.881269	+	0.472615i	$0.156690\pi$
$911$			28.5297i			0.945230i	−0.881269	+	0.472615i	$0.843310\pi$
$912$		0			0
$913$	3.59974	+	2.07831i	0.119134	+	0.0687820i
$914$	−13.9928	−	17.0613i	−0.462842	−	0.564336i
$915$		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	$0.686804\pi$
$920$	2.49169	−	73.9792i	0.0821486	−	2.43902i
$921$		0			0
$922$	4.06094	+	24.6449i	0.133740	+	0.811638i
$923$			3.73282i			0.122867i
$924$		0			0
$925$			18.5567i			0.610142i
$926$	−21.1304	+	3.48183i	−0.694390	+	0.114420i
$927$		0			0
$928$	25.9138	−	27.5808i	0.850662	−	0.905385i
$929$	−11.2786	−	19.5350i	−0.370038	−	0.640924i	0.619533	−	0.784970i	$-0.287322\pi$
$929$	−11.2786	−	19.5350i	−0.370038	−	0.640924i	−0.989571	+	0.144046i	$0.953989\pi$
$930$		0			0
$931$	−24.9338	+	23.1901i	−0.817171	+	0.760024i
$932$	−19.2981	+	21.9773i	−0.632129	+	0.719891i
$933$		0			0
$934$	15.2013	−	12.4674i	0.497402	−	0.407945i
$935$	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	$0.862436\pi$
$938$	30.8152	−	18.3837i	1.00615	−	0.600249i
$939$		0			0
$940$	−40.9923	−	8.18068i	−1.33702	−	0.266824i
$941$	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
$950$	56.4391	−	9.29990i	1.83113	−	0.301729i
$951$		0			0
$952$	−25.9158	−	22.1080i	−0.839934	−	0.716526i
$953$			31.4456i			1.01862i	0.860582	+	0.509312i	$0.170100\pi$
$953$			31.4456i			1.01862i	−0.860582	+	0.509312i	$0.829900\pi$
$954$		0			0
$955$	34.5750	−	59.8857i	1.11882	−	1.93786i
$956$	−7.43194	−	21.9391i	−0.240366	−	0.709561i
$957$		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
$962$	−1.41890	+	1.16372i	−0.0457473	+	0.0375198i
$963$		0			0
$964$	3.09568	+	0.617793i	0.0997051	+	0.0198978i
$965$			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	$0.487445\pi$
$968$	−26.0209	−	16.2149i	−0.836344	−	0.521167i
$969$		0			0
$970$	−13.1106	−	15.9856i	−0.420956	−	0.513265i
$971$	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
$976$	−47.4542	−	19.7261i	−1.51897	−	0.631419i
$977$	−8.83921	−	5.10332i	−0.282791	−	0.163270i	0.351895	−	0.936039i	$-0.385537\pi$
$977$	−8.83921	−	5.10332i	−0.282791	−	0.163270i	−0.634686	+	0.772770i	$0.718871\pi$
$978$		0			0
$979$	−4.21048			−0.134568
$980$	44.9534	+	24.2669i	1.43599	+	0.775177i
$981$		0			0
$982$	−4.72826	+	0.779111i	−0.150885	+	0.0248624i
$983$	−2.76849	+	4.79516i	−0.0883010	+	0.152942i	−0.906793	−	0.421576i	$-0.861477\pi$
$983$	−2.76849	+	4.79516i	−0.0883010	+	0.152942i	0.818492	+	0.574518i	$0.194810\pi$
$984$		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	$0.233276\pi$
$992$	17.8699	−	5.39010i	0.567369	−	0.171136i
$993$		0			0
$994$	−20.9734	−	11.7123i	−0.665237	−	0.371493i
$995$	27.1429			0.860487
$996$		0			0
$997$	−3.01429	+	5.22091i	−0.0954636	+	0.165348i	−0.909802	−	0.415043i	$-0.863767\pi$
$997$	−3.01429	+	5.22091i	−0.0954636	+	0.165348i	0.814338	+	0.580390i	$0.197100\pi$
$998$	45.3908	−	37.2274i	1.43682	−	1.17841i
$999$		0			0

Twists

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

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

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

\(f(q)\)	\(=\)	\(q+(-1.39540 + 0.229930i) q^{2} +(1.89426 - 0.641688i) q^{4} +(-3.16007 + 1.82447i) q^{5} +(-1.64838 + 2.06951i) q^{7} +(-2.49571 + 1.33096i) q^{8} +O(q^{10})\)	\(q+(-1.39540 + 0.229930i) q^{2} +(1.89426 - 0.641688i) q^{4} +(-3.16007 + 1.82447i) q^{5} +(-1.64838 + 2.06951i) q^{7} +(-2.49571 + 1.33096i) q^{8} +(3.99006 - 3.27246i) q^{10} +(0.200123 - 0.346624i) q^{11} -0.581419 q^{13} +(1.82430 - 3.26679i) q^{14} +(3.17647 - 2.43105i) q^{16} +(2.27603 - 3.94220i) q^{17} +(-2.43222 - 4.21272i) q^{19} +(-4.81528 + 5.48381i) q^{20} +(-0.199552 + 0.529692i) q^{22} +(6.21119 - 3.58603i) q^{23} +(4.15738 - 7.20080i) q^{25} +(0.811310 - 0.133686i) q^{26} +(-1.79448 + 4.97793i) q^{28} -6.69007 q^{29} +(-2.85749 - 1.64978i) q^{31} +(-3.87347 + 4.12265i) q^{32} +(-2.26954 + 6.02426i) q^{34} +(1.43324 - 9.54721i) q^{35} +(-1.93278 + 1.11589i) q^{37} +(4.36254 + 5.31918i) q^{38} +(5.45833 - 8.75927i) q^{40} -4.51491 q^{41} +4.09678i q^{43} +(0.156662 - 0.785014i) q^{44} +(-7.84253 + 6.43207i) q^{46} +(2.86389 + 4.96040i) q^{47} +(-1.56571 - 6.82265i) q^{49} +(-4.14552 + 11.0039i) q^{50} +(-1.10136 + 0.373089i) q^{52} +(6.74170 - 11.6770i) q^{53} +1.46048i q^{55} +(1.35944 - 7.35880i) q^{56} +(9.33530 - 1.53825i) q^{58} +(-7.72158 - 4.45806i) q^{59} +(-6.42386 - 11.1265i) q^{61} +(4.36667 + 1.64507i) q^{62} +(4.45710 - 6.64336i) q^{64} +(1.83733 - 1.06078i) q^{65} +(8.30513 + 4.79497i) q^{67} +(1.78174 - 8.92807i) q^{68} +(0.195254 + 13.6517i) q^{70} -6.42019i q^{71} +(-6.18408 - 3.57038i) q^{73} +(2.44042 - 2.00151i) q^{74} +(-7.31051 - 6.41929i) q^{76} +(0.387462 + 0.985523i) q^{77} +(4.15037 + 7.18866i) q^{79} +(-5.60251 + 13.4777i) q^{80} +(6.30010 - 1.03812i) q^{82} +10.3852i q^{83} +16.6102i q^{85} +(-0.941975 - 5.71664i) q^{86} +(-0.0381076 + 1.13143i) q^{88} +(-5.25986 - 9.11034i) q^{89} +(0.958396 - 1.20325i) q^{91} +(9.46452 - 10.7785i) q^{92} +(-5.13681 - 6.26323i) q^{94} +(15.3720 + 8.87501i) q^{95} -4.00635i q^{97} +(3.75352 + 9.16030i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 56 * q - 8 * q^4 - 20 * q^7	\( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) \) 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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