LMFDB - Embedded newform 504.2.bs.a.257.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(257,504)]

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, 0, 5, 5]))

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

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

chi := DirichletCharacter("504.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bs (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.17
Character	$\chi$	$=$	504.257
Dual form			504.2.bs.a.353.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.872943 + 1.49598i) q^{3} +(-2.09905 - 3.63567i) q^{5} +(-2.61186 + 0.422135i) q^{7} +(-1.47594 + 2.61182i) q^{9} +O(q^{10})$	\(q+(0.872943 + 1.49598i) q^{3} +(-2.09905 - 3.63567i) q^{5} +(-2.61186 + 0.422135i) q^{7} +(-1.47594 + 2.61182i) q^{9} +(1.44513 + 0.834345i) q^{11} +(-5.64000 - 3.25626i) q^{13} +(3.60655 - 6.31388i) q^{15} +(-1.45558 - 2.52114i) q^{17} +(-2.39558 - 1.38309i) q^{19} +(-2.91151 - 3.53880i) q^{21} +(-1.92146 + 1.10935i) q^{23} +(-6.31205 + 10.9328i) q^{25} +(-5.19565 + 0.0719817i) q^{27} +(5.69309 - 3.28691i) q^{29} -0.478324i q^{31} +(0.0133465 + 2.89023i) q^{33} +(7.01717 + 8.60976i) q^{35} +(-0.378300 + 0.655234i) q^{37} +(-0.0520883 - 11.2799i) q^{39} +(0.769875 - 1.33346i) q^{41} +(-4.79971 - 8.31334i) q^{43} +(12.5938 - 0.116314i) q^{45} +8.11745 q^{47} +(6.64360 - 2.20511i) q^{49} +(2.50095 - 4.37835i) q^{51} +(-7.11119 + 4.10565i) q^{53} -7.00534i q^{55} +(-0.0221244 - 4.79111i) q^{57} +0.853729 q^{59} +4.50254i q^{61} +(2.75241 - 7.44475i) q^{63} +27.3402i q^{65} +15.3897 q^{67} +(-3.33690 - 1.90607i) q^{69} +1.89916i q^{71} +(-6.22280 + 3.59274i) q^{73} +(-21.8654 + 0.100970i) q^{75} +(-4.12668 - 1.56915i) q^{77} -11.0590 q^{79} +(-4.64319 - 7.70978i) q^{81} +(-0.162143 - 0.280840i) q^{83} +(-6.11070 + 10.5840i) q^{85} +(9.88691 + 5.64750i) q^{87} +(2.86206 - 4.95723i) q^{89} +(16.1055 + 6.12404i) q^{91} +(0.715565 - 0.417549i) q^{93} +11.6127i q^{95} +(-4.22671 + 2.44029i) q^{97} +(-4.31208 + 2.54297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.872943	+	1.49598i	0.503994	+	0.863707i
$3$	0.872943	+	1.49598i	0.503994	+	0.863707i
$4$		0			0
$5$	−2.09905	−	3.63567i	−0.938725	−	1.62592i	−0.767852	−	0.640627i	$-0.778674\pi$
$5$	−2.09905	−	3.63567i	−0.938725	−	1.62592i	−0.170873	−	0.985293i	$-0.554659\pi$
$6$		0			0
$7$	−2.61186	+	0.422135i	−0.987190	+	0.159552i
$7$	−2.61186	+	0.422135i	−0.987190	+	0.159552i
$8$		0			0
$9$	−1.47594	+	2.61182i	−0.491981	+	0.870606i
$10$		0			0
$11$	1.44513	+	0.834345i	0.435722	+	0.251564i	0.701782	−	0.712392i	$-0.252388\pi$
$11$	1.44513	+	0.834345i	0.435722	+	0.251564i	−0.266059	+	0.963957i	$0.585722\pi$
$12$		0			0
$13$	−5.64000	−	3.25626i	−1.56426	−	0.903123i	−0.996818	−	0.0797060i	$-0.974602\pi$
$13$	−5.64000	−	3.25626i	−1.56426	−	0.903123i	−0.567437	−	0.823417i	$-0.692065\pi$
$14$		0			0
$15$	3.60655	−	6.31388i	0.931207	−	1.63024i
$16$		0			0
$17$	−1.45558	−	2.52114i	−0.353031	−	0.611467i	0.633748	−	0.773539i	$-0.281516\pi$
$17$	−1.45558	−	2.52114i	−0.353031	−	0.611467i	−0.986779	+	0.162072i	$0.948182\pi$
$18$		0			0
$19$	−2.39558	−	1.38309i	−0.549584	−	0.317302i	0.199370	−	0.979924i	$-0.436110\pi$
$19$	−2.39558	−	1.38309i	−0.549584	−	0.317302i	−0.748954	+	0.662622i	$0.769444\pi$
$20$		0			0
$21$	−2.91151	−	3.53880i	−0.635344	−	0.772230i
$22$		0			0
$23$	−1.92146	+	1.10935i	−0.400652	+	0.231316i	−0.686765	−	0.726879i	$-0.740970\pi$
$23$	−1.92146	+	1.10935i	−0.400652	+	0.231316i	0.286113	+	0.958196i	$0.407637\pi$
$24$		0			0
$25$	−6.31205	+	10.9328i	−1.26241	+	2.18656i
$26$		0			0
$27$	−5.19565	+	0.0719817i	−0.999904	+	0.0138529i
$28$		0			0
$29$	5.69309	−	3.28691i	1.05718	−	0.610364i	0.132530	−	0.991179i	$-0.457690\pi$
$29$	5.69309	−	3.28691i	1.05718	−	0.610364i	0.924651	+	0.380815i	$0.124357\pi$
$30$		0			0
$31$		−	0.478324i		−	0.0859094i	−0.999077	−	0.0429547i	$-0.986323\pi$
$31$		−	0.478324i		−	0.0859094i	0.999077	−	0.0429547i	$-0.0136771\pi$
$32$		0			0
$33$	0.0133465	+	2.89023i	0.00232333	+	0.503124i
$34$		0			0
$35$	7.01717	+	8.60976i	1.18612	+	1.45532i
$36$		0			0
$37$	−0.378300	+	0.655234i	−0.0621921	+	0.107720i	−0.895445	−	0.445172i	$-0.853142\pi$
$37$	−0.378300	+	0.655234i	−0.0621921	+	0.107720i	0.833253	+	0.552892i	$0.186476\pi$
$38$		0			0
$39$	−0.0520883	−	11.2799i	−0.00834080	−	1.80623i
$40$		0			0
$41$	0.769875	−	1.33346i	0.120234	−	0.208252i	−0.799626	−	0.600499i	$-0.794969\pi$
$41$	0.769875	−	1.33346i	0.120234	−	0.208252i	0.919860	+	0.392247i	$0.128302\pi$
$42$		0			0
$43$	−4.79971	−	8.31334i	−0.731948	−	1.26777i	−0.956049	−	0.293206i	$-0.905278\pi$
$43$	−4.79971	−	8.31334i	−0.731948	−	1.26777i	0.224101	−	0.974566i	$-0.428055\pi$
$44$		0			0
$45$	12.5938	−	0.116314i	1.87737	−	0.0173390i
$46$		0			0
$47$	8.11745			1.18405			0.592026	−	0.805919i	$-0.298328\pi$
$47$	8.11745			1.18405			0.592026	+	0.805919i	$0.298328\pi$
$48$		0			0
$49$	6.64360	−	2.20511i	0.949086	−	0.315016i
$50$		0			0
$51$	2.50095	−	4.37835i	0.350203	−	0.613091i
$52$		0			0
$53$	−7.11119	+	4.10565i	−0.976797	+	0.563954i	−0.901302	−	0.433192i	$-0.857387\pi$
$53$	−7.11119	+	4.10565i	−0.976797	+	0.563954i	−0.0754956	+	0.997146i	$0.524054\pi$
$54$		0			0
$55$		−	7.00534i		−	0.944600i
$56$		0			0
$57$	−0.0221244	−	4.79111i	−0.00293045	−	0.634598i
$58$		0			0
$59$	0.853729			0.111146			0.0555730	−	0.998455i	$-0.482301\pi$
$59$	0.853729			0.111146			0.0555730	+	0.998455i	$0.482301\pi$
$60$		0			0
$61$			4.50254i			0.576491i	0.957557	+	0.288246i	$0.0930719\pi$
$61$			4.50254i			0.576491i	−0.957557	+	0.288246i	$0.906928\pi$
$62$		0			0
$63$	2.75241	−	7.44475i	0.346771	−	0.937950i
$64$		0			0
$65$			27.3402i			3.39114i
$66$		0			0
$67$	15.3897			1.88015			0.940074	−	0.340970i	$-0.110756\pi$
$67$	15.3897			1.88015			0.940074	+	0.340970i	$0.110756\pi$
$68$		0			0
$69$	−3.33690	−	1.90607i	−0.401715	−	0.229464i
$70$		0			0
$71$			1.89916i			0.225389i	0.993630	+	0.112694i	$0.0359481\pi$
$71$			1.89916i			0.225389i	−0.993630	+	0.112694i	$0.964052\pi$
$72$		0			0
$73$	−6.22280	+	3.59274i	−0.728324	+	0.420498i	−0.817809	−	0.575490i	$-0.804811\pi$
$73$	−6.22280	+	3.59274i	−0.728324	+	0.420498i	0.0894848	+	0.995988i	$0.471478\pi$
$74$		0			0
$75$	−21.8654	+	0.100970i	−2.52480	+	0.0116590i
$76$		0			0
$77$	−4.12668	−	1.56915i	−0.470278	−	0.178821i
$78$		0			0
$79$	−11.0590			−1.24424			−0.622118	−	0.782924i	$-0.713727\pi$
$79$	−11.0590			−1.24424			−0.622118	+	0.782924i	$0.713727\pi$
$80$		0			0
$81$	−4.64319	−	7.70978i	−0.515910	−	0.856643i
$82$		0			0
$83$	−0.162143	−	0.280840i	−0.0177975	−	0.0308262i	0.856989	−	0.515334i	$-0.172332\pi$
$83$	−0.162143	−	0.280840i	−0.0177975	−	0.0308262i	−0.874787	+	0.484508i	$0.838999\pi$
$84$		0			0
$85$	−6.11070	+	10.5840i	−0.662798	+	1.14800i
$86$		0			0
$87$	9.88691	+	5.64750i	1.05999	+	0.605475i
$88$		0			0
$89$	2.86206	−	4.95723i	0.303378	−	0.525466i	−0.673521	−	0.739168i	$-0.735219\pi$
$89$	2.86206	−	4.95723i	0.303378	−	0.525466i	0.976899	+	0.213702i	$0.0685522\pi$
$90$		0			0
$91$	16.1055	+	6.12404i	1.68831	+	0.641973i
$92$		0			0
$93$	0.715565	−	0.417549i	0.0742006	−	0.0432978i
$94$		0			0
$95$			11.6127i			1.19144i
$96$		0			0
$97$	−4.22671	+	2.44029i	−0.429158	+	0.247774i	−0.698988	−	0.715134i	$-0.746366\pi$
$97$	−4.22671	+	2.44029i	−0.429158	+	0.247774i	0.269830	+	0.962908i	$0.413032\pi$
$98$		0			0
$99$	−4.31208	+	2.54297i	−0.433381	+	0.255578i
$100$		0			0
$101$	3.06514	−	5.30897i	0.304992	−	0.528262i	−0.672267	−	0.740309i	$-0.734679\pi$
$101$	3.06514	−	5.30897i	0.304992	−	0.528262i	0.977260	+	0.212046i	$0.0680128\pi$
$102$		0			0
$103$	−9.99325	+	5.76961i	−0.984665	+	0.568496i	−0.903675	−	0.428219i	$-0.859141\pi$
$103$	−9.99325	+	5.76961i	−0.984665	+	0.568496i	−0.0809894	+	0.996715i	$0.525808\pi$
$104$		0			0
$105$	−6.75449	+	18.0134i	−0.659170	+	1.75793i
$106$		0			0
$107$	1.03912	+	0.599935i	0.100455	+	0.0579979i	0.549386	−	0.835569i	$-0.314862\pi$
$107$	1.03912	+	0.599935i	0.100455	+	0.0579979i	−0.448931	+	0.893567i	$0.648195\pi$
$108$		0			0
$109$	−2.59691	−	4.49798i	−0.248739	−	0.430828i	0.714437	−	0.699699i	$-0.246683\pi$
$109$	−2.59691	−	4.49798i	−0.248739	−	0.430828i	−0.963176	+	0.268871i	$0.913349\pi$
$110$		0			0
$111$	−1.31045	+	0.00605143i	−0.124383	+	0.000574376i
$112$		0			0
$113$	3.83161	+	2.21218i	0.360447	+	0.208104i	0.669277	−	0.743013i	$-0.266604\pi$
$113$	3.83161	+	2.21218i	0.360447	+	0.208104i	−0.308830	+	0.951117i	$0.599937\pi$
$114$		0			0
$115$	8.06649	+	4.65719i	0.752204	+	0.434285i
$116$		0			0
$117$	16.8291	−	9.92462i	1.55585	−	0.917531i
$118$		0			0
$119$	4.86604	+	5.97042i	0.446069	+	0.547307i
$120$		0			0
$121$	−4.10774	−	7.11481i	−0.373431	−	0.646801i
$122$		0			0
$123$	2.66690	−	0.0123152i	0.240466	−	0.00111043i
$124$		0			0
$125$	32.0068			2.86278
$126$		0			0
$127$	−4.97205			−0.441198			−0.220599	−	0.975365i	$-0.570801\pi$
$127$	−4.97205			−0.441198			−0.220599	+	0.975365i	$0.570801\pi$
$128$		0			0
$129$	8.24676	−	14.4374i	0.726086	−	1.27114i
$130$		0			0
$131$	−2.77083	−	4.79923i	−0.242089	−	0.419310i	0.719220	−	0.694782i	$-0.244499\pi$
$131$	−2.77083	−	4.79923i	−0.242089	−	0.419310i	−0.961309	+	0.275472i	$0.911166\pi$
$132$		0			0
$133$	6.84077	+	2.60117i	0.593170	+	0.225550i
$134$		0			0
$135$	11.1677	+	18.7386i	0.961159	+	1.61276i
$136$		0			0
$137$	−18.2355	−	10.5282i	−1.55796	−	0.899489i	−0.997452	−	0.0713403i	$-0.977272\pi$
$137$	−18.2355	−	10.5282i	−1.55796	−	0.899489i	−0.560509	−	0.828149i	$-0.689394\pi$
$138$		0			0
$139$	11.3650	+	6.56161i	0.963971	+	0.556549i	0.897393	−	0.441233i	$-0.145459\pi$
$139$	11.3650	+	6.56161i	0.963971	+	0.556549i	0.0665778	+	0.997781i	$0.478792\pi$
$140$		0			0
$141$	7.08607	+	12.1436i	0.596755	+	1.02267i
$142$		0			0
$143$	−5.43368	−	9.41141i	−0.454387	−	0.787022i
$144$		0			0
$145$	−23.9002	−	13.7988i	−1.98480	−	1.14593i
$146$		0			0
$147$	9.09830	+	8.01379i	0.750415	+	0.660966i
$148$		0			0
$149$	7.00200	−	4.04261i	0.573626	−	0.331183i	−0.184970	−	0.982744i	$-0.559219\pi$
$149$	7.00200	−	4.04261i	0.573626	−	0.331183i	0.758596	+	0.651561i	$0.225886\pi$
$150$		0			0
$151$	−9.63783	+	16.6932i	−0.784316	+	1.35847i	0.145091	+	0.989418i	$0.453652\pi$
$151$	−9.63783	+	16.6932i	−0.784316	+	1.35847i	−0.929407	+	0.369057i	$0.879681\pi$
$152$		0			0
$153$	8.73313	−	0.0806575i	0.706031	−	0.00652077i
$154$		0			0
$155$	−1.73903	+	1.00403i	−0.139682	+	0.0806454i
$156$		0			0
$157$		−	9.12706i		−	0.728419i	−0.931317	−	0.364209i	$-0.881339\pi$
$157$		−	9.12706i		−	0.728419i	0.931317	−	0.364209i	$-0.118661\pi$
$158$		0			0
$159$	−12.3497	−	7.05424i	−0.979391	−	0.559438i
$160$		0			0
$161$	4.55028	−	3.70859i	0.358612	−	0.292278i
$162$		0			0
$163$	2.74203	−	4.74934i	0.214772	−	0.371997i	−0.738430	−	0.674330i	$-0.764432\pi$
$163$	2.74203	−	4.74934i	0.214772	−	0.371997i	0.953202	+	0.302334i	$0.0977657\pi$
$164$		0			0
$165$	10.4799	−	6.11526i	0.815858	−	0.476072i
$166$		0			0
$167$	7.64279	−	13.2377i	0.591417	−	1.02436i	−0.402625	−	0.915365i	$-0.631902\pi$
$167$	7.64279	−	13.2377i	0.591417	−	1.02436i	0.994042	−	0.108999i	$-0.0347646\pi$
$168$		0			0
$169$	14.7064	+	25.4723i	1.13126	+	1.95940i
$170$		0			0
$171$	7.14812	−	4.21546i	0.546630	−	0.322365i
$172$		0			0
$173$	−14.8377			−1.12809			−0.564046	−	0.825744i	$-0.690756\pi$
$173$	−14.8377			−1.12809			−0.564046	+	0.825744i	$0.690756\pi$
$174$		0			0
$175$	11.8711	−	31.2195i	0.897369	−	2.35997i
$176$		0			0
$177$	0.745257	+	1.27717i	0.0560169	+	0.0959977i
$178$		0			0
$179$	11.2034	−	6.46826i	0.837378	−	0.483460i	−0.0189941	−	0.999820i	$-0.506046\pi$
$179$	11.2034	−	6.46826i	0.837378	−	0.483460i	0.856372	+	0.516359i	$0.172713\pi$
$180$		0			0
$181$			7.63582i			0.567566i	0.958888	+	0.283783i	$0.0915896\pi$
$181$			7.63582i			0.567566i	−0.958888	+	0.283783i	$0.908410\pi$
$182$		0			0
$183$	−6.73573	+	3.93046i	−0.497920	+	0.290548i
$184$		0			0
$185$	3.17629			0.233525
$186$		0			0
$187$		−	4.85783i		−	0.355240i
$188$		0			0
$189$	13.5399	−	2.38127i	0.984885	−	0.173212i
$190$		0			0
$191$		−	0.419088i		−	0.0303241i	−0.999885	−	0.0151621i	$-0.995174\pi$
$191$		−	0.419088i		−	0.0303241i	0.999885	−	0.0151621i	$-0.00482642\pi$
$192$		0			0
$193$	0.916454			0.0659678			0.0329839	−	0.999456i	$-0.489499\pi$
$193$	0.916454			0.0659678			0.0329839	+	0.999456i	$0.489499\pi$
$194$		0			0
$195$	−40.9006	+	23.8665i	−2.92895	+	1.70911i
$196$		0			0
$197$		−	15.9509i		−	1.13646i	−0.822871	−	0.568228i	$-0.807629\pi$
$197$		−	15.9509i		−	1.13646i	0.822871	−	0.568228i	$-0.192371\pi$
$198$		0			0
$199$	−8.13289	+	4.69553i	−0.576525	+	0.332857i	−0.759751	−	0.650214i	$-0.774679\pi$
$199$	−8.13289	+	4.69553i	−0.576525	+	0.332857i	0.183226	+	0.983071i	$0.441346\pi$
$200$		0			0
$201$	13.4343	+	23.0227i	0.947583	+	1.62390i
$202$		0			0
$203$	−13.4820	+	10.9882i	−0.946253	+	0.771220i
$204$		0			0
$205$	−6.46404			−0.451468
$206$		0			0
$207$	−0.0614721	−	6.65584i	−0.00427260	−	0.462613i
$208$		0			0
$209$	−2.30795	−	3.99748i	−0.159644	−	0.276512i
$210$		0			0
$211$	−2.03425	+	3.52343i	−0.140044	+	0.242563i	−0.927513	−	0.373791i	$-0.878058\pi$
$211$	−2.03425	+	3.52343i	−0.140044	+	0.242563i	0.787469	+	0.616354i	$0.211391\pi$
$212$		0			0
$213$	−2.84111	+	1.65786i	−0.194670	+	0.113594i
$214$		0			0
$215$	−20.1497	+	34.9003i	−1.37420	+	2.38018i
$216$		0			0
$217$	0.201917	+	1.24931i	0.0137070	+	0.0848089i
$218$		0			0
$219$	−10.8068	−	6.17296i	−0.730258	−	0.417130i
$220$		0			0
$221$			18.9590i			1.27532i
$222$		0			0
$223$	5.94398	−	3.43176i	0.398038	−	0.229808i	−0.287599	−	0.957751i	$-0.592857\pi$
$223$	5.94398	−	3.43176i	0.398038	−	0.229808i	0.685637	+	0.727943i	$0.259524\pi$
$224$		0			0
$225$	−19.2383	−	32.6221i	−1.28255	−	2.17481i
$226$		0			0
$227$	3.36619	−	5.83040i	0.223422	−	0.386978i	−0.732423	−	0.680850i	$-0.761611\pi$
$227$	3.36619	−	5.83040i	0.223422	−	0.386978i	0.955845	+	0.293872i	$0.0949440\pi$
$228$		0			0
$229$	−2.90924	+	1.67965i	−0.192248	+	0.110994i	−0.593035	−	0.805177i	$-0.702070\pi$
$229$	−2.90924	+	1.67965i	−0.192248	+	0.110994i	0.400787	+	0.916171i	$0.368737\pi$
$230$		0			0
$231$	−1.25492	−	7.54322i	−0.0825680	−	0.496308i
$232$		0			0
$233$	−17.7165	−	10.2286i	−1.16065	−	0.670101i	−0.209190	−	0.977875i	$-0.567083\pi$
$233$	−17.7165	−	10.2286i	−1.16065	−	0.670101i	−0.951459	+	0.307774i	$0.900416\pi$
$234$		0			0
$235$	−17.0390	−	29.5123i	−1.11150	−	1.92517i
$236$		0			0
$237$	−9.65388	−	16.5441i	−0.627087	−	1.07465i
$238$		0			0
$239$	24.7890	+	14.3120i	1.60347	+	0.925764i	0.990786	+	0.135436i	$0.0432434\pi$
$239$	24.7890	+	14.3120i	1.60347	+	0.925764i	0.612684	+	0.790328i	$0.290090\pi$
$240$		0			0
$241$	−24.2422	−	13.9962i	−1.56158	−	0.901576i	−0.997098	−	0.0761270i	$-0.975745\pi$
$241$	−24.2422	−	13.9962i	−1.56158	−	0.901576i	−0.564477	−	0.825449i	$-0.690922\pi$
$242$		0			0
$243$	7.48048	−	13.6763i	0.479873	−	0.877338i
$244$		0			0
$245$	−21.9623	−	19.5253i	−1.40312	−	1.24742i
$246$		0			0
$247$	9.00739	+	15.6013i	0.573126	+	0.992684i
$248$		0			0
$249$	0.278591	−	0.487721i	0.0176550	−	0.0309081i
$250$		0			0
$251$	−25.7333			−1.62427			−0.812135	−	0.583469i	$-0.801695\pi$
$251$	−25.7333			−1.62427			−0.812135	+	0.583469i	$0.801695\pi$
$252$		0			0
$253$	−3.70234			−0.232764
$254$		0			0
$255$	−21.1678	+	0.0977490i	−1.32558	+	0.00612128i
$256$		0			0
$257$	−4.56808	−	7.91215i	−0.284949	−	0.493547i	0.687648	−	0.726045i	$-0.258643\pi$
$257$	−4.56808	−	7.91215i	−0.284949	−	0.493547i	−0.972597	+	0.232498i	$0.925310\pi$
$258$		0			0
$259$	0.711468	−	1.87107i	0.0442085	−	0.116263i
$260$		0			0
$261$	0.182136	+	19.7206i	0.0112739	+	1.22068i
$262$		0			0
$263$	3.37444	+	1.94824i	0.208077	+	0.120133i	0.600417	−	0.799687i	$-0.295001\pi$
$263$	3.37444	+	1.94824i	0.208077	+	0.120133i	−0.392340	+	0.919820i	$0.628334\pi$
$264$		0			0
$265$	29.8535	+	17.2360i	1.83389	+	1.05880i
$266$		0			0
$267$	9.91436	−	0.0457826i	0.606749	−	0.00280185i
$268$		0			0
$269$	−12.8010	−	22.1720i	−0.780492	−	1.35185i	−0.931656	−	0.363342i	$-0.881636\pi$
$269$	−12.8010	−	22.1720i	−0.780492	−	1.35185i	0.151164	−	0.988509i	$-0.451698\pi$
$270$		0			0
$271$	14.7398	+	8.51005i	0.895382	+	0.516949i	0.875699	−	0.482857i	$-0.160401\pi$
$271$	14.7398	+	8.51005i	0.895382	+	0.516949i	0.0196827	+	0.999806i	$0.493734\pi$
$272$		0			0
$273$	4.89768	+	29.4395i	0.296421	+	1.78176i
$274$		0			0
$275$	−18.2435	+	10.5329i	−1.10012	+	0.635156i
$276$		0			0
$277$	11.1258	−	19.2704i	0.668482	−	1.15784i	−0.309847	−	0.950787i	$-0.600278\pi$
$277$	11.1258	−	19.2704i	0.668482	−	1.15784i	0.978329	−	0.207058i	$-0.0663890\pi$
$278$		0			0
$279$	1.24929	+	0.705978i	0.0747933	+	0.0422658i
$280$		0			0
$281$	15.2400	−	8.79879i	0.909140	−	0.524892i	0.0289854	−	0.999580i	$-0.490772\pi$
$281$	15.2400	−	8.79879i	0.909140	−	0.524892i	0.880154	+	0.474688i	$0.157439\pi$
$282$		0			0
$283$		−	3.41435i		−	0.202962i	−0.994837	−	0.101481i	$-0.967642\pi$
$283$		−	3.41435i		−	0.202962i	0.994837	−	0.101481i	$-0.0323581\pi$
$284$		0			0
$285$	−17.3724	+	10.1372i	−1.02905	+	0.600478i
$286$		0			0
$287$	−1.44790	+	3.80781i	−0.0854670	+	0.224768i
$288$		0			0
$289$	4.26256	−	7.38296i	0.250739	−	0.434292i
$290$		0			0
$291$	−7.34032	−	4.19286i	−0.430297	−	0.245790i
$292$		0			0
$293$	8.43057	−	14.6022i	0.492519	−	0.853069i	−0.507443	−	0.861685i	$-0.669409\pi$
$293$	8.43057	−	14.6022i	0.492519	−	0.853069i	0.999963	+	0.00861641i	$0.00274272\pi$
$294$		0			0
$295$	−1.79202	−	3.10388i	−0.104336	−	0.180715i
$296$		0			0
$297$	−7.56844	−	4.23095i	−0.439166	−	0.245504i
$298$		0			0
$299$	14.4494			0.835628
$300$		0			0
$301$	16.0455	+	19.6871i	0.924847	+	1.13475i
$302$		0			0
$303$	10.6178	−	0.0490311i	0.609978	−	0.00281676i
$304$		0			0
$305$	16.3697	−	9.45107i	0.937328	−	0.541167i
$306$		0			0
$307$		−	10.3026i		−	0.588002i	−0.955805	−	0.294001i	$-0.905013\pi$
$307$		−	10.3026i		−	0.588002i	0.955805	−	0.294001i	$-0.0949869\pi$
$308$		0			0
$309$	−17.3548	−	9.91322i	−0.987279	−	0.563943i
$310$		0			0
$311$	−3.53883			−0.200669			−0.100334	−	0.994954i	$-0.531991\pi$
$311$	−3.53883			−0.200669			−0.100334	+	0.994954i	$0.531991\pi$
$312$		0			0
$313$		−	7.47549i		−	0.422540i	−0.977428	−	0.211270i	$-0.932240\pi$
$313$		−	7.47549i		−	0.422540i	0.977428	−	0.211270i	$-0.0677599\pi$
$314$		0			0
$315$	−32.8441	+	5.62007i	−1.85055	+	0.316655i
$316$		0			0
$317$			21.8080i			1.22486i	0.790526	+	0.612429i	$0.209807\pi$
$317$			21.8080i			1.22486i	−0.790526	+	0.612429i	$0.790193\pi$
$318$		0			0
$319$	10.9697			0.614183
$320$		0			0
$321$	0.00959679	+	2.07821i	0.000535641	+	0.115995i
$322$		0			0
$323$			8.05281i			0.448070i
$324$		0			0
$325$	71.2000	−	41.1073i	3.94947	−	2.28022i
$326$		0			0
$327$	4.46195	−	7.81141i	0.246747	−	0.431972i
$328$		0			0
$329$	−21.2016	+	3.42666i	−1.16888	+	0.188918i
$330$		0			0
$331$	13.8805			0.762943			0.381471	−	0.924381i	$-0.375418\pi$
$331$	13.8805			0.762943			0.381471	+	0.924381i	$0.375418\pi$
$332$		0			0
$333$	−1.15301	−	1.95514i	−0.0631843	−	0.107141i
$334$		0			0
$335$	−32.3038	−	55.9518i	−1.76494	−	3.05697i
$336$		0			0
$337$	5.72982	−	9.92434i	0.312123	−	0.540613i	−0.666699	−	0.745327i	$-0.732293\pi$
$337$	5.72982	−	9.92434i	0.312123	−	0.540613i	0.978822	+	0.204714i	$0.0656265\pi$
$338$		0			0
$339$	0.0353868	+	7.66313i	0.00192195	+	0.416204i
$340$		0			0
$341$	0.399087	−	0.691239i	0.0216118	−	0.0374327i
$342$		0			0
$343$	−16.4213	+	8.56394i	−0.886667	+	0.462409i
$344$		0			0
$345$	0.0744981	+	16.1328i	0.00401084	+	0.868561i
$346$		0			0
$347$			7.15705i			0.384211i	0.981374	+	0.192105i	$0.0615315\pi$
$347$			7.15705i			0.384211i	−0.981374	+	0.192105i	$0.938468\pi$
$348$		0			0
$349$	2.23155	−	1.28838i	0.119452	−	0.0689656i	−0.439084	−	0.898446i	$-0.644697\pi$
$349$	2.23155	−	1.28838i	0.119452	−	0.0689656i	0.558535	+	0.829481i	$0.311363\pi$
$350$		0			0
$351$	29.5379	+	16.5124i	1.57662	+	0.881367i
$352$		0			0
$353$	−13.1314	+	22.7442i	−0.698912	+	1.21055i	0.269932	+	0.962879i	$0.412999\pi$
$353$	−13.1314	+	22.7442i	−0.698912	+	1.21055i	−0.968844	+	0.247671i	$0.920335\pi$
$354$		0			0
$355$	6.90471	−	3.98643i	0.366464	−	0.211578i
$356$		0			0
$357$	−4.68388	+	12.4914i	−0.247897	+	0.661113i
$358$		0			0
$359$	−20.9327	−	12.0855i	−1.10478	−	0.637848i	−0.167311	−	0.985904i	$-0.553508\pi$
$359$	−20.9327	−	12.0855i	−1.10478	−	0.637848i	−0.937474	+	0.348057i	$0.886842\pi$
$360$		0			0
$361$	−5.67413	−	9.82788i	−0.298638	−	0.517257i
$362$		0			0
$363$	7.05783	−	12.3559i	0.370440	−	0.648518i
$364$		0			0
$365$	26.1240	+	15.0827i	1.36739	+	0.789464i
$366$		0			0
$367$	−2.09517	−	1.20965i	−0.109367	−	0.0631430i	0.444319	−	0.895869i	$-0.353446\pi$
$367$	−2.09517	−	1.20965i	−0.109367	−	0.0631430i	−0.553686	+	0.832726i	$0.686779\pi$
$368$		0			0
$369$	2.34647	+	3.97889i	0.122152	+	0.207133i
$370$		0			0
$371$	16.8403	−	13.7253i	0.874304	−	0.712580i
$372$		0			0
$373$	−1.95866	−	3.39249i	−0.101415	−	0.175657i	0.810853	−	0.585250i	$-0.199004\pi$
$373$	−1.95866	−	3.39249i	−0.101415	−	0.175657i	−0.912268	+	0.409594i	$0.865670\pi$
$374$		0			0
$375$	27.9401	+	47.8817i	1.44282	+	2.47260i
$376$		0			0
$377$	−42.8121			−2.20493
$378$		0			0
$379$	−25.2195			−1.29544			−0.647719	−	0.761880i	$-0.724277\pi$
$379$	−25.2195			−1.29544			−0.647719	+	0.761880i	$0.724277\pi$
$380$		0			0
$381$	−4.34032	−	7.43811i	−0.222361	−	0.381066i
$382$		0			0
$383$	−15.2413	−	26.3987i	−0.778793	−	1.34891i	−0.932638	−	0.360813i	$-0.882499\pi$
$383$	−15.2413	−	26.3987i	−0.778793	−	1.34891i	0.153845	−	0.988095i	$-0.450834\pi$
$384$		0			0
$385$	2.95720	+	18.2970i	0.150713	+	0.932499i
$386$		0			0
$387$	28.7970	−	0.265964i	1.46383	−	0.0135197i
$388$		0			0
$389$	−13.3652	−	7.71638i	−0.677640	−	0.391236i	0.121325	−	0.992613i	$-0.461286\pi$
$389$	−13.3652	−	7.71638i	−0.677640	−	0.391236i	−0.798965	+	0.601377i	$0.794619\pi$
$390$		0			0
$391$	5.59368	+	3.22951i	0.282885	+	0.163324i
$392$		0			0
$393$	4.76079	−	8.33458i	0.240150	−	0.420424i
$394$		0			0
$395$	23.2134	+	40.2069i	1.16800	+	2.02303i
$396$		0			0
$397$	2.88696	+	1.66679i	0.144892	+	0.0836537i	0.570694	−	0.821163i	$-0.306674\pi$
$397$	2.88696	+	1.66679i	0.144892	+	0.0836537i	−0.425801	+	0.904817i	$0.640008\pi$
$398$		0			0
$399$	2.08028	+	12.5044i	0.104144	+	0.626001i
$400$		0			0
$401$	10.1951	−	5.88617i	0.509121	−	0.293941i	−0.223351	−	0.974738i	$-0.571700\pi$
$401$	10.1951	−	5.88617i	0.509121	−	0.293941i	0.732472	+	0.680797i	$0.238366\pi$
$402$		0			0
$403$	−1.55754	+	2.69775i	−0.0775868	+	0.134384i
$404$		0			0
$405$	−18.2839	+	33.0644i	−0.908535	+	1.64298i
$406$		0			0
$407$	−1.09338	+	0.631265i	−0.0541970	+	0.0312906i
$408$		0			0
$409$			29.2934i			1.44847i	0.689556	+	0.724233i	$0.257806\pi$
$409$			29.2934i			1.44847i	−0.689556	+	0.724233i	$0.742194\pi$
$410$		0			0
$411$	−0.168414	−	36.4705i	−0.00830724	−	1.79896i
$412$		0			0
$413$	−2.22982	+	0.360389i	−0.109722	+	0.0177336i
$414$		0			0
$415$	−0.680694	+	1.17900i	−0.0334140	+	0.0578747i
$416$		0			0
$417$	0.104962	+	22.7298i	0.00514001	+	1.11309i
$418$		0			0
$419$	5.91159	−	10.2392i	0.288800	−	0.500216i	−0.684724	−	0.728803i	$-0.740077\pi$
$419$	5.91159	−	10.2392i	0.288800	−	0.500216i	0.973524	+	0.228587i	$0.0734104\pi$
$420$		0			0
$421$	−1.03025	−	1.78444i	−0.0502111	−	0.0869682i	0.839827	−	0.542853i	$-0.182656\pi$
$421$	−1.03025	−	1.78444i	−0.0502111	−	0.0869682i	−0.890039	+	0.455885i	$0.849323\pi$
$422$		0			0
$423$	−11.9809	+	21.2013i	−0.582530	+	1.03084i
$424$		0			0
$425$	36.7509			1.78268
$426$		0			0
$427$	−1.90068	−	11.7600i	−0.0919803	−	0.569106i
$428$		0			0
$429$	9.33604	−	16.3443i	0.450748	−	0.789112i
$430$		0			0
$431$	20.1480	−	11.6325i	0.970495	−	0.560316i	0.0711080	−	0.997469i	$-0.477347\pi$
$431$	20.1480	−	11.6325i	0.970495	−	0.560316i	0.899387	+	0.437153i	$0.144013\pi$
$432$		0			0
$433$			21.8314i			1.04915i	0.851364	+	0.524575i	$0.175776\pi$
$433$			21.8314i			1.04915i	−0.851364	+	0.524575i	$0.824224\pi$
$434$		0			0
$435$	−0.220731	−	47.7999i	−0.0105832	−	2.29183i
$436$		0			0
$437$	6.13734			0.293589
$438$		0			0
$439$			31.7755i			1.51656i	0.651929	+	0.758280i	$0.273960\pi$
$439$			31.7755i			1.51656i	−0.651929	+	0.758280i	$0.726040\pi$
$440$		0			0
$441$	−4.04621	+	20.6065i	−0.192677	+	0.981262i
$442$		0			0
$443$			24.7405i			1.17545i	0.809059	+	0.587727i	$0.199977\pi$
$443$			24.7405i			1.17545i	−0.809059	+	0.587727i	$0.800023\pi$
$444$		0			0
$445$	−24.0305			−1.13915
$446$		0			0
$447$	12.1600	+	6.94592i	0.575149	+	0.328531i
$448$		0			0
$449$			23.0496i			1.08778i	0.839158	+	0.543888i	$0.183048\pi$
$449$			23.0496i			1.08778i	−0.839158	+	0.543888i	$0.816952\pi$
$450$		0			0
$451$	2.22514	−	1.28468i	0.104778	−	0.0604934i
$452$		0			0
$453$	−33.3861	+	0.154170i	−1.56862	+	0.00724356i
$454$		0			0
$455$	−11.5413	−	71.4088i	−0.541063	−	3.34770i
$456$		0			0
$457$	5.99084			0.280240			0.140120	−	0.990135i	$-0.455251\pi$
$457$	5.99084			0.280240			0.140120	+	0.990135i	$0.455251\pi$
$458$		0			0
$459$	7.74418	+	12.9942i	0.361467	+	0.606518i
$460$		0			0
$461$	−5.75499	−	9.96794i	−0.268037	−	0.464253i	0.700318	−	0.713831i	$-0.253042\pi$
$461$	−5.75499	−	9.96794i	−0.268037	−	0.464253i	−0.968355	+	0.249578i	$0.919708\pi$
$462$		0			0
$463$	−18.6834	+	32.3606i	−0.868292	+	1.50393i	−0.00455057	+	0.999990i	$0.501448\pi$
$463$	−18.6834	+	32.3606i	−0.868292	+	1.50393i	−0.863741	+	0.503936i	$0.831885\pi$
$464$		0			0
$465$	−3.02008	−	1.72510i	−0.140053	−	0.0799995i
$466$		0			0
$467$	−1.06192	+	1.83930i	−0.0491397	+	0.0851125i	−0.889549	−	0.456840i	$-0.848981\pi$
$467$	−1.06192	+	1.83930i	−0.0491397	+	0.0851125i	0.840409	+	0.541952i	$0.182315\pi$
$468$		0			0
$469$	−40.1956	+	6.49652i	−1.85606	+	0.299982i
$470$		0			0
$471$	13.6539	−	7.96740i	0.629141	−	0.367119i
$472$		0			0
$473$		−	16.0184i		−	0.736529i
$474$		0			0
$475$	30.2421	−	17.4603i	1.38760	−	0.801132i
$476$		0			0
$477$	−0.227504	−	24.6328i	−0.0104167	−	1.12786i
$478$		0			0
$479$	2.23301	−	3.86768i	0.102029	−	0.176719i	−0.810492	−	0.585750i	$-0.800800\pi$
$479$	2.23301	−	3.86768i	0.102029	−	0.176719i	0.912520	+	0.409031i	$0.134133\pi$
$480$		0			0
$481$	4.26722	−	2.46368i	0.194569	−	0.112334i
$482$		0			0
$483$	9.52013	+	3.56976i	0.433181	+	0.162430i
$484$		0			0
$485$	17.7442	+	10.2446i	0.805723	+	0.465184i
$486$		0			0
$487$	−7.26260	−	12.5792i	−0.329100	−	0.570018i	0.653234	−	0.757156i	$-0.273412\pi$
$487$	−7.26260	−	12.5792i	−0.329100	−	0.570018i	−0.982334	+	0.187139i	$0.940079\pi$
$488$		0			0
$489$	9.49857	−	0.0438625i	0.429540	−	0.00198353i
$490$		0			0
$491$	−0.984470	−	0.568384i	−0.0444285	−	0.0256508i	0.477621	−	0.878566i	$-0.341499\pi$
$491$	−0.984470	−	0.568384i	−0.0444285	−	0.0256508i	−0.522050	+	0.852915i	$0.674832\pi$
$492$		0			0
$493$	−16.5735	−	9.56874i	−0.746435	−	0.430954i
$494$		0			0
$495$	18.2967	+	10.3395i	0.822375	+	0.464725i
$496$		0			0
$497$	−0.801701	−	4.96033i	−0.0359612	−	0.222501i
$498$		0			0
$499$	−10.4650	−	18.1260i	−0.468480	−	0.811431i	0.530871	−	0.847453i	$-0.321865\pi$
$499$	−10.4650	−	18.1260i	−0.468480	−	0.811431i	−0.999351	+	0.0360215i	$0.988532\pi$
$500$		0			0
$501$	26.4751	−	0.122257i	1.18282	−	0.00546204i
$502$		0			0
$503$	24.1806			1.07816			0.539080	−	0.842254i	$-0.318772\pi$
$503$	24.1806			1.07816			0.539080	+	0.842254i	$0.318772\pi$
$504$		0			0
$505$	−25.7355			−1.14522
$506$		0			0
$507$	−25.2683	+	44.2364i	−1.12220	+	1.96461i
$508$		0			0
$509$	12.4101	+	21.4949i	0.550067	+	0.952744i	0.998269	+	0.0588116i	$0.0187311\pi$
$509$	12.4101	+	21.4949i	0.550067	+	0.952744i	−0.448202	+	0.893932i	$0.647936\pi$
$510$		0			0
$511$	14.7365	−	12.0106i	0.651902	−	0.531317i
$512$		0			0
$513$	12.5462	+	7.01362i	0.553927	+	0.309659i
$514$		0			0
$515$	41.9528	+	24.2214i	1.84866	+	1.06732i
$516$		0			0
$517$	11.7308	+	6.77275i	0.515918	+	0.297865i
$518$		0			0
$519$	−12.9525	−	22.1970i	−0.568551	−	0.974341i
$520$		0			0
$521$	12.9623	+	22.4513i	0.567887	+	0.983609i	0.996775	+	0.0802510i	$0.0255722\pi$
$521$	12.9623	+	22.4513i	0.567887	+	0.983609i	−0.428888	+	0.903358i	$0.641094\pi$
$522$		0			0
$523$	12.4620	+	7.19495i	0.544926	+	0.314613i	0.747073	−	0.664742i	$-0.231459\pi$
$523$	12.4620	+	7.19495i	0.544926	+	0.314613i	−0.202147	+	0.979355i	$0.564792\pi$
$524$		0			0
$525$	57.0666	−	9.49386i	2.49059	−	0.414346i
$526$		0			0
$527$	−1.20592	+	0.696240i	−0.0525308	+	0.0303287i
$528$		0			0
$529$	−9.03867	+	15.6554i	−0.392986	+	0.680671i
$530$		0			0
$531$	−1.26005	+	2.22979i	−0.0546817	+	0.0967645i
$532$		0			0
$533$	−8.68419	+	5.01382i	−0.376154	+	0.217173i
$534$		0			0
$535$		−	5.03719i		−	0.217777i
$536$		0			0
$537$	19.4563	+	11.1136i	0.839602	+	0.479588i
$538$		0			0
$539$	11.4407	+	2.35639i	0.492785	+	0.101497i
$540$		0			0
$541$	5.81246	−	10.0675i	0.249897	−	0.432835i	−0.713600	−	0.700553i	$-0.752937\pi$
$541$	5.81246	−	10.0675i	0.249897	−	0.432835i	0.963497	+	0.267719i	$0.0862698\pi$
$542$		0			0
$543$	−11.4231	+	6.66564i	−0.490211	+	0.286050i
$544$		0			0
$545$	−10.9021	+	18.8830i	−0.466995	+	0.808858i
$546$		0			0
$547$	11.0062	+	19.0633i	0.470590	+	0.815086i	0.999434	−	0.0336331i	$-0.0107078\pi$
$547$	11.0062	+	19.0633i	0.470590	+	0.815086i	−0.528844	+	0.848719i	$0.677374\pi$
$548$		0			0
$549$	−11.7598	−	6.64549i	−0.501897	−	0.283622i
$550$		0			0
$551$	−18.1843			−0.774679
$552$		0			0
$553$	28.8845	−	4.66839i	1.22830	−	0.198520i
$554$		0			0
$555$	2.77272	+	4.75168i	0.117695	+	0.201697i
$556$		0			0
$557$	−28.9226	+	16.6984i	−1.22549	+	0.707536i	−0.966083	−	0.258233i	$-0.916860\pi$
$557$	−28.9226	+	16.6984i	−1.22549	+	0.707536i	−0.259405	+	0.965768i	$0.583527\pi$
$558$		0			0
$559$			62.5163i			2.64416i
$560$		0			0
$561$	7.26725	−	4.24061i	0.306823	−	0.179039i
$562$		0			0
$563$	−40.1123			−1.69053			−0.845265	−	0.534347i	$-0.820558\pi$
$563$	−40.1123			−1.69053			−0.845265	+	0.534347i	$0.820558\pi$
$564$		0			0
$565$		−	18.5739i		−	0.781411i
$566$		0			0
$567$	15.3819	+	18.1768i	0.645980	+	0.763354i
$568$		0			0
$569$		−	21.2457i		−	0.890664i	−0.895365	−	0.445332i	$-0.853086\pi$
$569$		−	21.2457i		−	0.890664i	0.895365	−	0.445332i	$-0.146914\pi$
$570$		0			0
$571$	−26.6527			−1.11538			−0.557690	−	0.830050i	$-0.688312\pi$
$571$	−26.6527			−1.11538			−0.557690	+	0.830050i	$0.688312\pi$
$572$		0			0
$573$	0.626949	−	0.365840i	0.0261912	−	0.0152832i
$574$		0			0
$575$		−	28.0092i		−	1.16807i
$576$		0			0
$577$	8.26696	−	4.77293i	0.344158	−	0.198700i	−0.317951	−	0.948107i	$-0.602995\pi$
$577$	8.26696	−	4.77293i	0.344158	−	0.198700i	0.662109	+	0.749407i	$0.269661\pi$
$578$		0			0
$579$	0.800012	+	1.37100i	0.0332474	+	0.0569769i
$580$		0			0
$581$	0.542047	+	0.665068i	0.0224879	+	0.0275917i
$582$		0			0
$583$	−13.7021			−0.567483
$584$		0			0
$585$	−71.4077	−	40.3526i	−2.95235	−	1.66837i
$586$		0			0
$587$	14.4269	+	24.9881i	0.595462	+	1.03137i	0.993481	+	0.113994i	$0.0363645\pi$
$587$	14.4269	+	24.9881i	0.595462	+	1.03137i	−0.398019	+	0.917377i	$0.630302\pi$
$588$		0			0
$589$	−0.661564	+	1.14586i	−0.0272593	+	0.0472144i
$590$		0			0
$591$	23.8623	−	13.9242i	0.981565	−	0.572766i
$592$		0			0
$593$	−8.81985	+	15.2764i	−0.362188	+	0.627328i	−0.988321	−	0.152389i	$-0.951303\pi$
$593$	−8.81985	+	15.2764i	−0.362188	+	0.627328i	0.626133	+	0.779717i	$0.284637\pi$
$594$		0			0
$595$	11.4924	−	30.2235i	0.471141	−	1.23904i
$596$		0			0
$597$	−14.1240	−	8.06775i	−0.578056	−	0.330191i
$598$		0			0
$599$		−	25.7384i		−	1.05164i	−0.850595	−	0.525821i	$-0.823758\pi$
$599$		−	25.7384i		−	1.05164i	0.850595	−	0.525821i	$-0.176242\pi$
$600$		0			0
$601$	34.9110	−	20.1559i	1.42405	−	0.822175i	0.427407	−	0.904059i	$-0.359427\pi$
$601$	34.9110	−	20.1559i	1.42405	−	0.822175i	0.996642	+	0.0818843i	$0.0260938\pi$
$602$		0			0
$603$	−22.7143	+	40.1950i	−0.924996	+	1.63687i
$604$		0			0
$605$	−17.2447	+	29.8687i	−0.701098	+	1.21434i
$606$		0			0
$607$	21.1428	−	12.2068i	0.858159	−	0.495458i	−0.00523634	−	0.999986i	$-0.501667\pi$
$607$	21.1428	−	12.2068i	0.858159	−	0.495458i	0.863395	+	0.504528i	$0.168333\pi$
$608$		0			0
$609$	−28.2072	−	10.5768i	−1.14301	−	0.428596i
$610$		0			0
$611$	−45.7824	−	26.4325i	−1.85216	−	1.06934i
$612$		0			0
$613$	7.90021	+	13.6836i	0.319087	+	0.552674i	0.980298	−	0.197526i	$-0.0632906\pi$
$613$	7.90021	+	13.6836i	0.319087	+	0.552674i	−0.661211	+	0.750200i	$0.729957\pi$
$614$		0			0
$615$	−5.64273	−	9.67010i	−0.227537	−	0.389936i
$616$		0			0
$617$	15.4940	+	8.94544i	0.623763	+	0.360130i	0.778333	−	0.627852i	$-0.216066\pi$
$617$	15.4940	+	8.94544i	0.623763	+	0.360130i	−0.154570	+	0.987982i	$0.549399\pi$
$618$		0			0
$619$	28.0527	+	16.1962i	1.12753	+	0.650982i	0.943313	−	0.331903i	$-0.107691\pi$
$619$	28.0527	+	16.1962i	1.12753	+	0.650982i	0.184220	+	0.982885i	$0.441024\pi$
$620$		0			0
$621$	9.90338	−	5.90213i	0.397409	−	0.236844i
$622$		0			0
$623$	−5.38267	+	14.1558i	−0.215652	+	0.567139i
$624$		0			0
$625$	−35.6238	−	61.7022i	−1.42495	−	2.46809i
$626$		0			0
$627$	3.96547	−	6.94223i	0.158365	−	0.277246i
$628$		0			0
$629$	2.20259			0.0878229
$630$		0			0
$631$	34.0138			1.35407			0.677034	−	0.735951i	$-0.263265\pi$
$631$	34.0138			1.35407			0.677034	+	0.735951i	$0.263265\pi$
$632$		0			0
$633$	−7.04679	+	0.0325407i	−0.280085	+	0.00129338i
$634$		0			0
$635$	10.4366	+	18.0767i	0.414164	+	0.717353i
$636$		0			0
$637$	−44.6504	−	9.19643i	−1.76911	−	0.364376i
$638$		0			0
$639$	−4.96025	−	2.80305i	−0.196225	−	0.110887i
$640$		0			0
$641$	21.1416	+	12.2061i	0.835041	+	0.482111i	0.855576	−	0.517678i	$-0.173203\pi$
$641$	21.1416	+	12.2061i	0.835041	+	0.482111i	−0.0205343	+	0.999789i	$0.506537\pi$
$642$		0			0
$643$	−12.7714	−	7.37357i	−0.503655	−	0.290785i	0.226567	−	0.973996i	$-0.427250\pi$
$643$	−12.7714	−	7.37357i	−0.503655	−	0.290785i	−0.730222	+	0.683210i	$0.760583\pi$
$644$		0			0
$645$	−69.7998	+	0.322322i	−2.74837	+	0.0126914i
$646$		0			0
$647$	−1.14288	−	1.97952i	−0.0449311	−	0.0778230i	0.842685	−	0.538407i	$-0.180974\pi$
$647$	−1.14288	−	1.97952i	−0.0449311	−	0.0778230i	−0.887616	+	0.460584i	$0.847640\pi$
$648$		0			0
$649$	1.23375	+	0.712305i	0.0484288	+	0.0279604i
$650$		0			0
$651$	−1.69269	+	1.39264i	−0.0663418	+	0.0545820i
$652$		0			0
$653$	−27.6066	+	15.9387i	−1.08033	+	0.623729i	−0.930986	−	0.365056i	$-0.881050\pi$
$653$	−27.6066	+	15.9387i	−1.08033	+	0.623729i	−0.149345	+	0.988785i	$0.547717\pi$
$654$		0			0
$655$	−11.6323	+	20.1477i	−0.454510	+	0.787235i
$656$		0			0
$657$	−0.199082	−	21.5555i	−0.00776695	−	0.840960i
$658$		0			0
$659$	22.1391	−	12.7820i	0.862416	−	0.497916i	−0.00240490	−	0.999997i	$-0.500766\pi$
$659$	22.1391	−	12.7820i	0.862416	−	0.497916i	0.864820	+	0.502081i	$0.167432\pi$
$660$		0			0
$661$		−	4.16823i		−	0.162125i	−0.996709	−	0.0810626i	$-0.974169\pi$
$661$		−	4.16823i		−	0.162125i	0.996709	−	0.0810626i	$-0.0258314\pi$
$662$		0			0
$663$	−28.3624	+	16.5501i	−1.10150	+	0.642754i
$664$		0			0
$665$	−4.90214	−	30.3308i	−0.190097	−	1.17618i
$666$		0			0
$667$	−7.29269	+	12.6313i	−0.282374	+	0.489086i
$668$		0			0
$669$	10.3226	+	5.89638i	0.399095	+	0.227967i
$670$		0			0
$671$	−3.75667	+	6.50675i	−0.145025	+	0.251190i
$672$		0			0
$673$	−7.96201	−	13.7906i	−0.306913	−	0.531589i	0.670772	−	0.741663i	$-0.265963\pi$
$673$	−7.96201	−	13.7906i	−0.306913	−	0.531589i	−0.977685	+	0.210074i	$0.932629\pi$
$674$		0			0
$675$	32.0083	−	57.2574i	1.23200	−	2.20384i
$676$		0			0
$677$	36.4485			1.40083			0.700415	−	0.713736i	$-0.252998\pi$
$677$	36.4485			1.40083			0.700415	+	0.713736i	$0.252998\pi$
$678$		0			0
$679$	10.0094	−	8.15795i	0.384127	−	0.313073i
$680$		0			0
$681$	11.6607	−	0.0538468i	0.446838	−	0.00206341i
$682$		0			0
$683$	15.5858	−	8.99846i	0.596374	−	0.344317i	−0.171240	−	0.985229i	$-0.554777\pi$
$683$	15.5858	−	8.99846i	0.596374	−	0.344317i	0.767614	+	0.640913i	$0.221444\pi$
$684$		0			0
$685$			88.3974i			3.37749i
$686$		0			0
$687$	−5.05233	−	2.88594i	−0.192758	−	0.110105i
$688$		0			0
$689$	53.4762			2.03728
$690$		0			0
$691$		−	30.1670i		−	1.14761i	−0.818992	−	0.573804i	$-0.805467\pi$
$691$		−	30.1670i		−	1.14761i	0.818992	−	0.573804i	$-0.194533\pi$
$692$		0			0
$693$	10.1891	−	8.46215i	0.387051	−	0.321451i
$694$		0			0
$695$		−	55.0927i		−	2.08979i
$696$		0			0
$697$	−4.48247			−0.169786
$698$		0			0
$699$	−0.163621	−	35.4327i	−0.00618873	−	1.34019i
$700$		0			0
$701$			14.6302i			0.552574i	0.961075	+	0.276287i	$0.0891040\pi$
$701$			14.6302i			0.552574i	−0.961075	+	0.276287i	$0.910896\pi$
$702$		0			0
$703$	1.81250	−	1.04644i	0.0683596	−	0.0394674i
$704$		0			0
$705$	29.2760	−	51.2526i	1.10260	−	1.93029i
$706$		0			0
$707$	−5.76460	+	15.1602i	−0.216800	+	0.570157i
$708$		0			0
$709$	36.3383			1.36471			0.682356	−	0.731020i	$-0.260955\pi$
$709$	36.3383			1.36471			0.682356	+	0.731020i	$0.260955\pi$
$710$		0			0
$711$	16.3224	−	28.8841i	0.612140	−	1.08324i
$712$		0			0
$713$	0.530630	+	0.919078i	0.0198723	+	0.0344198i
$714$		0			0
$715$	−22.8112	+	39.5101i	−0.853090	+	1.47760i
$716$		0			0
$717$	0.228940	+	49.5776i	0.00854990	+	1.85151i
$718$		0			0
$719$	−16.6780	+	28.8871i	−0.621983	+	1.07731i	0.367133	+	0.930168i	$0.380339\pi$
$719$	−16.6780	+	28.8871i	−0.621983	+	1.07731i	−0.989116	+	0.147138i	$0.952994\pi$
$720$		0			0
$721$	23.6654	−	19.2879i	0.881346	−	0.718319i
$722$		0			0
$723$	−0.223889	−	48.4838i	−0.00832651	−	1.80313i
$724$		0			0
$725$			82.9886i			3.08212i
$726$		0			0
$727$	−30.9908	+	17.8926i	−1.14939	+	0.663598i	−0.948737	−	0.316065i	$-0.897638\pi$
$727$	−30.9908	+	17.8926i	−1.14939	+	0.663598i	−0.200648	+	0.979663i	$0.564305\pi$
$728$		0			0
$729$	26.9896	−	0.747983i	0.999616	−	0.0277031i
$730$		0			0
$731$	−13.9727	+	24.2015i	−0.516801	+	0.895125i
$732$		0			0
$733$	−2.53412	+	1.46308i	−0.0936000	+	0.0540400i	−0.546069	−	0.837740i	$-0.683877\pi$
$733$	−2.53412	+	1.46308i	−0.0936000	+	0.0540400i	0.452469	+	0.891780i	$0.350543\pi$
$734$		0			0
$735$	10.0377	−	49.8998i	0.370245	−	1.84058i
$736$		0			0
$737$	22.2401	+	12.8403i	0.819223	+	0.472979i
$738$		0			0
$739$	−24.4998	−	42.4350i	−0.901241	−	1.56100i	−0.825885	−	0.563839i	$-0.809324\pi$
$739$	−24.4998	−	42.4350i	−0.901241	−	1.56100i	−0.0753563	−	0.997157i	$-0.524009\pi$
$740$		0			0
$741$	−15.4763	+	27.0939i	−0.568536	+	0.995320i
$742$		0			0
$743$	−15.0792	−	8.70600i	−0.553203	−	0.319392i	0.197210	−	0.980361i	$-0.436812\pi$
$743$	−15.0792	−	8.70600i	−0.553203	−	0.319392i	−0.750413	+	0.660969i	$0.770145\pi$
$744$		0			0
$745$	−29.3952	−	16.9713i	−1.07696	−	0.621780i
$746$		0			0
$747$	0.972817	−	0.00898475i	0.0355935	−	0.000328735i
$748$		0			0
$749$	−2.96728	−	1.12830i	−0.108422	−	0.0412271i
$750$		0			0
$751$	−16.3237	−	28.2734i	−0.595659	−	1.03171i	−0.993453	−	0.114238i	$-0.963557\pi$
$751$	−16.3237	−	28.2734i	−0.595659	−	1.03171i	0.397794	−	0.917475i	$-0.369776\pi$
$752$		0			0
$753$	−22.4637	−	38.4966i	−0.818622	−	1.40289i
$754$		0			0
$755$	80.9213			2.94503
$756$		0			0
$757$	−11.9818			−0.435485			−0.217742	−	0.976006i	$-0.569869\pi$
$757$	−11.9818			−0.435485			−0.217742	+	0.976006i	$0.569869\pi$
$758$		0			0
$759$	−3.23193	−	5.53864i	−0.117312	−	0.201040i
$760$		0			0
$761$	0.813311	+	1.40870i	0.0294825	+	0.0510652i	0.880390	−	0.474250i	$-0.157281\pi$
$761$	0.813311	+	1.40870i	0.0294825	+	0.0510652i	−0.850908	+	0.525315i	$0.823947\pi$
$762$		0			0
$763$	8.68151	+	10.6518i	0.314292	+	0.385622i
$764$		0			0
$765$	−18.6245	−	31.5814i	−0.673372	−	1.14183i
$766$		0			0
$767$	−4.81503	−	2.77996i	−0.173861	−	0.100379i
$768$		0			0
$769$	−6.18483	−	3.57081i	−0.223031	−	0.128767i	0.384322	−	0.923199i	$-0.374435\pi$
$769$	−6.18483	−	3.57081i	−0.223031	−	0.128767i	−0.607353	+	0.794432i	$0.707769\pi$
$770$		0			0
$771$	7.84879	−	13.7406i	0.282667	−	0.494857i
$772$		0			0
$773$	−11.3318	−	19.6273i	−0.407577	−	0.705943i	0.587041	−	0.809557i	$-0.300293\pi$
$773$	−11.3318	−	19.6273i	−0.407577	−	0.705943i	−0.994618	+	0.103614i	$0.966959\pi$
$774$		0			0
$775$	5.22942	+	3.01920i	0.187846	+	0.108453i
$776$		0			0
$777$	3.42017	−	0.568995i	0.122698	−	0.0204126i
$778$		0			0
$779$	−3.68860	+	2.12961i	−0.132158	+	0.0763013i
$780$		0			0
$781$	−1.58455	+	2.74453i	−0.0566997	+	0.0982068i
$782$		0			0
$783$	−29.3427	+	17.4874i	−1.04862	+	0.624950i
$784$		0			0
$785$	−33.1830	+	19.1582i	−1.18435	+	0.683785i
$786$		0			0
$787$			31.9497i			1.13888i	0.822032	+	0.569441i	$0.192840\pi$
$787$			31.9497i			1.13888i	−0.822032	+	0.569441i	$0.807160\pi$
$788$		0			0
$789$	0.0311647	+	6.74881i	0.00110949	+	0.240264i
$790$		0			0
$791$	−10.9414	−	4.16044i	−0.389033	−	0.147928i
$792$		0			0
$793$	14.6614	−	25.3943i	0.520642	−	0.901779i
$794$		0			0
$795$	0.275713	+	59.7065i	0.00977853	+	2.11757i
$796$		0			0
$797$	18.3232	−	31.7366i	0.649040	−	1.12417i	−0.334313	−	0.942462i	$-0.608504\pi$
$797$	18.3232	−	31.7366i	0.649040	−	1.12417i	0.983353	−	0.181707i	$-0.0581624\pi$
$798$		0			0
$799$	−11.8156	−	20.4653i	−0.418007	−	0.724009i
$800$		0			0
$801$	8.72316	+	14.7918i	0.308218	+	0.522642i
$802$		0			0
$803$	−11.9903			−0.423129
$804$		0			0
$805$	−23.0345	−	8.75877i	−0.811859	−	0.308706i
$806$		0			0
$807$	21.9944	−	38.5050i	0.774241	−	1.35544i
$808$		0			0
$809$	−4.23692	+	2.44618i	−0.148962	+	0.0860033i	−0.572628	−	0.819815i	$-0.694076\pi$
$809$	−4.23692	+	2.44618i	−0.148962	+	0.0860033i	0.423666	+	0.905818i	$0.360743\pi$
$810$		0			0
$811$			13.3463i			0.468652i	0.972158	+	0.234326i	$0.0752883\pi$
$811$			13.3463i			0.468652i	−0.972158	+	0.234326i	$0.924712\pi$
$812$		0			0
$813$	0.136130	+	29.4794i	0.00477429	+	1.03389i
$814$		0			0
$815$	−23.0227			−0.806449
$816$		0			0
$817$			26.5537i			0.928996i
$818$		0			0
$819$	−39.7656	+	33.0258i	−1.38952	+	1.15402i
$820$		0			0
$821$			47.1094i			1.64413i	0.569394	+	0.822064i	$0.307178\pi$
$821$			47.1094i			1.64413i	−0.569394	+	0.822064i	$0.692822\pi$
$822$		0			0
$823$	−31.2752			−1.09019			−0.545093	−	0.838376i	$-0.683506\pi$
$823$	−31.2752			−1.09019			−0.545093	+	0.838376i	$0.683506\pi$
$824$		0			0
$825$	−31.6825	−	18.0973i	−1.10304	−	0.630069i
$826$		0			0
$827$		−	19.4190i		−	0.675264i	−0.941278	−	0.337632i	$-0.890374\pi$
$827$		−	19.4190i		−	0.675264i	0.941278	−	0.337632i	$-0.109626\pi$
$828$		0			0
$829$	−26.2979	+	15.1831i	−0.913363	+	0.527330i	−0.881512	−	0.472162i	$-0.843474\pi$
$829$	−26.2979	+	15.1831i	−0.913363	+	0.527330i	−0.0318512	+	0.999493i	$0.510140\pi$
$830$		0			0
$831$	38.5404	−	0.177972i	1.33695	−	0.00617377i
$832$		0			0
$833$	−15.2297	−	13.5398i	−0.527679	−	0.469125i
$834$		0			0
$835$	−64.1705			−2.22071
$836$		0			0
$837$	0.0344305	+	2.48520i	0.00119009	+	0.0859012i
$838$		0			0
$839$	3.47828	+	6.02456i	0.120084	+	0.207991i	0.919800	−	0.392386i	$-0.128350\pi$
$839$	3.47828	+	6.02456i	0.120084	+	0.207991i	−0.799717	+	0.600377i	$0.795017\pi$
$840$		0			0
$841$	7.10753	−	12.3106i	0.245087	−	0.424504i
$842$		0			0
$843$	26.4665	+	15.1179i	0.911554	+	0.520688i
$844$		0			0
$845$	61.7391	−	106.935i	2.12389	−	3.67869i
$846$		0			0
$847$	13.7322	+	16.8488i	0.471845	+	0.578933i
$848$		0			0
$849$	5.10781	−	2.98053i	0.175300	−	0.102291i
$850$		0			0
$851$		−	1.67867i		−	0.0575442i
$852$		0			0
$853$	−0.707858	+	0.408682i	−0.0242366	+	0.0139930i	−0.512069	−	0.858944i	$-0.671121\pi$
$853$	−0.707858	+	0.408682i	−0.0242366	+	0.0139930i	0.487833	+	0.872937i	$0.337788\pi$
$854$		0			0
$855$	−30.3303	−	17.1397i	−1.03727	−	0.586165i
$856$		0			0
$857$	10.7663	−	18.6478i	0.367770	−	0.636996i	−0.621447	−	0.783457i	$-0.713455\pi$
$857$	10.7663	−	18.6478i	0.367770	−	0.636996i	0.989217	+	0.146460i	$0.0467880\pi$
$858$		0			0
$859$	−41.4317	+	23.9206i	−1.41363	+	0.816161i	−0.995728	−	0.0923302i	$-0.970568\pi$
$859$	−41.4317	+	23.9206i	−1.41363	+	0.816161i	−0.417904	+	0.908491i	$0.637235\pi$
$860$		0			0
$861$	−6.96036	+	1.15796i	−0.237208	+	0.0394631i
$862$		0			0
$863$	35.4144	+	20.4465i	1.20552	+	0.696007i	0.961777	−	0.273832i	$-0.0882914\pi$
$863$	35.4144	+	20.4465i	1.20552	+	0.696007i	0.243743	+	0.969840i	$0.421625\pi$
$864$		0			0
$865$	31.1452	+	53.9451i	1.05897	+	1.83419i
$866$		0			0
$867$	14.7658	−	0.0681854i	0.501472	−	0.00231570i
$868$		0			0
$869$	−15.9817	−	9.22702i	−0.542141	−	0.313005i
$870$		0			0
$871$	−86.7978	−	50.1127i	−2.94103	−	1.69801i
$872$		0			0
$873$	−0.135223	−	14.6411i	−0.00457660	−	0.495528i
$874$		0			0
$875$	−83.5973	+	13.5112i	−2.82610	+	0.456762i
$876$		0			0
$877$	−13.2611	−	22.9690i	−0.447797	−	0.775607i	0.550445	−	0.834871i	$-0.314458\pi$
$877$	−13.2611	−	22.9690i	−0.447797	−	0.775607i	−0.998242	+	0.0592639i	$0.981125\pi$
$878$		0			0
$879$	29.2041	−	0.134859i	0.985028	−	0.00454867i
$880$		0			0
$881$	−18.8167			−0.633952			−0.316976	−	0.948433i	$-0.602668\pi$
$881$	−18.8167			−0.633952			−0.316976	+	0.948433i	$0.602668\pi$
$882$		0			0
$883$	6.54732			0.220335			0.110167	−	0.993913i	$-0.464861\pi$
$883$	6.54732			0.220335			0.110167	+	0.993913i	$0.464861\pi$
$884$		0			0
$885$	3.07902	−	5.39035i	0.103500	−	0.181195i
$886$		0			0
$887$	21.9971	+	38.1000i	0.738589	+	1.27927i	0.953131	+	0.302559i	$0.0978408\pi$
$887$	21.9971	+	38.1000i	0.738589	+	1.27927i	−0.214542	+	0.976715i	$0.568826\pi$
$888$		0			0
$889$	12.9863	−	2.09888i	0.435546	−	0.0703941i
$890$		0			0
$891$	−0.277387	−	15.0156i	−0.00929281	−	0.503043i
$892$		0			0
$893$	−19.4460	−	11.2272i	−0.650736	−	0.375702i
$894$		0			0
$895$	−47.0329	−	27.1545i	−1.57214	−	0.907673i
$896$		0			0
$897$	12.6135	+	21.6160i	0.421152	+	0.721738i
$898$		0			0
$899$	−1.57221	−	2.72314i	−0.0524360	−	0.0908218i
$900$		0			0
$901$	20.7019	+	11.9522i	0.689679	+	0.398186i
$902$		0			0
$903$	−15.4448	+	41.1896i	−0.513972	+	1.37070i
$904$		0			0
$905$	27.7613	−	16.0280i	0.922818	−	0.532789i
$906$		0			0
$907$	−11.5668	+	20.0342i	−0.384068	+	0.665225i	−0.991639	−	0.129040i	$-0.958811\pi$
$907$	−11.5668	+	20.0342i	−0.384068	+	0.665225i	0.607571	+	0.794265i	$0.292144\pi$
$908$		0			0
$909$	9.34211	+	15.8413i	0.309858	+	0.525423i
$910$		0			0
$911$	36.3839	−	21.0062i	1.20545	−	0.695968i	0.243689	−	0.969853i	$-0.421642\pi$
$911$	36.3839	−	21.0062i	1.20545	−	0.695968i	0.961762	+	0.273886i	$0.0883091\pi$
$912$		0			0
$913$		−	0.541133i		−	0.0179089i
$914$		0			0
$915$	28.4285	+	16.2386i	0.939817	+	0.536833i
$916$		0			0
$917$	9.26295	+	11.3652i	0.305890	+	0.375313i
$918$		0			0
$919$	−9.86391	+	17.0848i	−0.325380	+	0.563576i	−0.981589	−	0.191004i	$-0.938826\pi$
$919$	−9.86391	+	17.0848i	−0.325380	+	0.563576i	0.656209	+	0.754579i	$0.272159\pi$
$920$		0			0
$921$	15.4126	−	8.99360i	0.507862	−	0.296349i
$922$		0			0
$923$	6.18414	−	10.7113i	0.203554	−	0.352565i
$924$		0			0
$925$	−4.77570	−	8.27175i	−0.157024	−	0.271974i
$926$		0			0
$927$	−0.319708	−	34.6162i	−0.0105006	−	1.13694i
$928$		0			0
$929$	−4.35843			−0.142995			−0.0714976	−	0.997441i	$-0.522778\pi$
$929$	−4.35843			−0.142995			−0.0714976	+	0.997441i	$0.522778\pi$
$930$		0			0
$931$	−18.9652	−	3.90617i	−0.621558	−	0.128019i
$932$		0			0
$933$	−3.08920	−	5.29404i	−0.101136	−	0.173319i
$934$		0			0
$935$	−17.6615	+	10.1969i	−0.577592	+	0.333473i
$936$		0			0
$937$		−	47.1729i		−	1.54107i	−0.637398	−	0.770535i	$-0.719989\pi$
$937$		−	47.1729i		−	1.54107i	0.637398	−	0.770535i	$-0.280011\pi$
$938$		0			0
$939$	11.1832	−	6.52568i	0.364951	−	0.212957i
$940$		0			0
$941$	−49.3536			−1.60888			−0.804440	−	0.594034i	$-0.797535\pi$
$941$	−49.3536			−1.60888			−0.804440	+	0.594034i	$0.797535\pi$
$942$		0			0
$943$			3.41626i			0.111249i
$944$		0			0
$945$	−37.0786	−	44.2282i	−1.20617	−	1.43874i
$946$		0			0
$947$			15.3360i			0.498354i	0.968458	+	0.249177i	$0.0801602\pi$
$947$			15.3360i			0.498354i	−0.968458	+	0.249177i	$0.919840\pi$
$948$		0			0
$949$	46.7955			1.51905
$950$		0			0
$951$	−32.6244	+	19.0371i	−1.05792	+	0.617321i
$952$		0			0
$953$		−	7.66556i		−	0.248312i	−0.992263	−	0.124156i	$-0.960378\pi$
$953$		−	7.66556i		−	0.248312i	0.992263	−	0.124156i	$-0.0396223\pi$
$954$		0			0
$955$	−1.52366	+	0.879688i	−0.0493046	+	0.0284660i
$956$		0			0
$957$	9.57589	+	16.4104i	0.309544	+	0.530474i
$958$		0			0
$959$	52.0728	+	19.8005i	1.68152	+	0.639390i
$960$		0			0
$961$	30.7712			0.992620
$962$		0			0
$963$	−3.10060	+	1.82852i	−0.0999154	+	0.0589232i
$964$		0			0
$965$	−1.92369	−	3.33192i	−0.0619257	−	0.107258i
$966$		0			0
$967$	−29.4620	+	51.0298i	−0.947435	+	1.64101i	−0.196636	+	0.980477i	$0.563002\pi$
$967$	−29.4620	+	51.0298i	−0.947435	+	1.64101i	−0.750800	+	0.660530i	$0.770332\pi$
$968$		0			0
$969$	−12.0469	+	7.02964i	−0.387001	+	0.225825i
$970$		0			0
$971$	2.00021	−	3.46446i	0.0641897	−	0.111180i	−0.832145	−	0.554559i	$-0.812887\pi$
$971$	2.00021	−	3.46446i	0.0641897	−	0.111180i	0.896334	+	0.443379i	$0.146220\pi$
$972$		0			0
$973$	−32.4538	−	12.3404i	−1.04042	−	0.395615i
$974$		0			0
$975$	123.649	+	70.6298i	3.95995	+	2.26196i
$976$		0			0
$977$		−	26.5664i		−	0.849935i	−0.905209	−	0.424967i	$-0.860286\pi$
$977$		−	26.5664i		−	0.849935i	0.905209	−	0.424967i	$-0.139714\pi$
$978$		0			0
$979$	8.27209	−	4.77589i	0.264377	−	0.152638i
$980$		0			0
$981$	15.5808	−	0.143901i	0.497456	−	0.00459441i
$982$		0			0
$983$	−12.1640	+	21.0687i	−0.387973	+	0.671988i	−0.992177	−	0.124841i	$-0.960158\pi$
$983$	−12.1640	+	21.0687i	−0.387973	+	0.671988i	0.604204	+	0.796830i	$0.293491\pi$
$984$		0			0
$985$	−57.9922	+	33.4818i	−1.84779	+	1.06682i
$986$		0			0
$987$	−23.6340	−	28.7260i	−0.752280	−	0.914359i
$988$		0			0
$989$	18.4449	+	10.6491i	0.586513	+	0.338623i
$990$		0			0
$991$	4.60564	+	7.97720i	0.146303	+	0.253404i	0.929858	−	0.367918i	$-0.119929\pi$
$991$	4.60564	+	7.97720i	0.146303	+	0.253404i	−0.783555	+	0.621322i	$0.786596\pi$
$992$		0			0
$993$	12.1169	+	20.7651i	0.384518	+	0.658959i
$994$		0			0
$995$	34.1427	+	19.7123i	1.08240	+	0.624923i
$996$		0			0
$997$	30.7809	+	17.7714i	0.974841	+	0.562825i	0.900709	−	0.434424i	$-0.143048\pi$
$997$	30.7809	+	17.7714i	0.974841	+	0.562825i	0.0741325	+	0.997248i	$0.476381\pi$
$998$		0			0
$999$	1.91835	−	3.43160i	0.0606939	−	0.108571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.257.17	✓	48
3.2	odd	2		1512.2.bs.a.1097.24		48
4.3	odd	2		1008.2.ca.e.257.8		48
7.3	odd	6		504.2.cx.a.185.9	yes	48
9.2	odd	6		504.2.cx.a.425.9	yes	48
9.7	even	3		1512.2.cx.a.89.24		48
12.11	even	2		3024.2.ca.e.2609.24		48
21.17	even	6		1512.2.cx.a.17.24		48
28.3	even	6		1008.2.df.e.689.16		48
36.7	odd	6		3024.2.df.e.1601.24		48
36.11	even	6		1008.2.df.e.929.16		48
63.38	even	6	inner	504.2.bs.a.353.17	yes	48
63.52	odd	6		1512.2.bs.a.521.24		48
84.59	odd	6		3024.2.df.e.17.24		48
252.115	even	6		3024.2.ca.e.2033.24		48
252.227	odd	6		1008.2.ca.e.353.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.17	✓	48	1.1	even	1	trivial
504.2.bs.a.353.17	yes	48	63.38	even	6	inner
504.2.cx.a.185.9	yes	48	7.3	odd	6
504.2.cx.a.425.9	yes	48	9.2	odd	6
1008.2.ca.e.257.8		48	4.3	odd	2
1008.2.ca.e.353.8		48	252.227	odd	6
1008.2.df.e.689.16		48	28.3	even	6
1008.2.df.e.929.16		48	36.11	even	6
1512.2.bs.a.521.24		48	63.52	odd	6
1512.2.bs.a.1097.24		48	3.2	odd	2
1512.2.cx.a.17.24		48	21.17	even	6
1512.2.cx.a.89.24		48	9.7	even	3
3024.2.ca.e.2033.24		48	252.115	even	6
3024.2.ca.e.2609.24		48	12.11	even	2
3024.2.df.e.17.24		48	84.59	odd	6
3024.2.df.e.1601.24		48	36.7	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.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.872943 + 1.49598i) q^{3} +(-2.09905 - 3.63567i) q^{5} +(-2.61186 + 0.422135i) q^{7} +(-1.47594 + 2.61182i) q^{9} +O(q^{10})\)	\(q+(0.872943 + 1.49598i) q^{3} +(-2.09905 - 3.63567i) q^{5} +(-2.61186 + 0.422135i) q^{7} +(-1.47594 + 2.61182i) q^{9} +(1.44513 + 0.834345i) q^{11} +(-5.64000 - 3.25626i) q^{13} +(3.60655 - 6.31388i) q^{15} +(-1.45558 - 2.52114i) q^{17} +(-2.39558 - 1.38309i) q^{19} +(-2.91151 - 3.53880i) q^{21} +(-1.92146 + 1.10935i) q^{23} +(-6.31205 + 10.9328i) q^{25} +(-5.19565 + 0.0719817i) q^{27} +(5.69309 - 3.28691i) q^{29} -0.478324i q^{31} +(0.0133465 + 2.89023i) q^{33} +(7.01717 + 8.60976i) q^{35} +(-0.378300 + 0.655234i) q^{37} +(-0.0520883 - 11.2799i) q^{39} +(0.769875 - 1.33346i) q^{41} +(-4.79971 - 8.31334i) q^{43} +(12.5938 - 0.116314i) q^{45} +8.11745 q^{47} +(6.64360 - 2.20511i) q^{49} +(2.50095 - 4.37835i) q^{51} +(-7.11119 + 4.10565i) q^{53} -7.00534i q^{55} +(-0.0221244 - 4.79111i) q^{57} +0.853729 q^{59} +4.50254i q^{61} +(2.75241 - 7.44475i) q^{63} +27.3402i q^{65} +15.3897 q^{67} +(-3.33690 - 1.90607i) q^{69} +1.89916i q^{71} +(-6.22280 + 3.59274i) q^{73} +(-21.8654 + 0.100970i) q^{75} +(-4.12668 - 1.56915i) q^{77} -11.0590 q^{79} +(-4.64319 - 7.70978i) q^{81} +(-0.162143 - 0.280840i) q^{83} +(-6.11070 + 10.5840i) q^{85} +(9.88691 + 5.64750i) q^{87} +(2.86206 - 4.95723i) q^{89} +(16.1055 + 6.12404i) q^{91} +(0.715565 - 0.417549i) q^{93} +11.6127i q^{95} +(-4.22671 + 2.44029i) q^{97} +(-4.31208 + 2.54297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more