LMFDB - Embedded newform 504.2.c.f.253.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(253,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("504.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.c (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.386672896.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 $ x^8 - x^6 - 2x^5 + 2x^4 - 4x^3 - 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			253.3
Root			$-0.835949 + 1.14070i$ of defining polynomial
Character	$\chi$	$=$	504.253
Dual form			504.2.c.f.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.835949 - 1.14070i) q^{2} +(-0.602380 + 1.90713i) q^{4} -0.467138i q^{5} +1.00000 q^{7} +(2.67901 - 0.907128i) q^{8} +O(q^{10})$	\(q+(-0.835949 - 1.14070i) q^{2} +(-0.602380 + 1.90713i) q^{4} -0.467138i q^{5} +1.00000 q^{7} +(2.67901 - 0.907128i) q^{8} +(-0.532862 + 0.390503i) q^{10} +4.87666i q^{11} +4.56279i q^{13} +(-0.835949 - 1.14070i) q^{14} +(-3.27428 - 2.29763i) q^{16} -6.09565 q^{17} -1.34379i q^{19} +(0.890891 + 0.281394i) q^{20} +(5.56279 - 4.07663i) q^{22} +4.09565 q^{23} +4.78178 q^{25} +(5.20476 - 3.81426i) q^{26} +(-0.602380 + 1.90713i) q^{28} +7.78178i q^{29} +4.40952 q^{31} +(0.116226 + 5.65566i) q^{32} +(5.09565 + 6.95329i) q^{34} -0.467138i q^{35} +4.40952i q^{37} +(-1.53286 + 1.12334i) q^{38} +(-0.423754 - 1.25147i) q^{40} +6.09565 q^{41} -4.15327i q^{43} +(-9.30041 - 2.93760i) q^{44} +(-3.42375 - 4.67190i) q^{46} +6.68759 q^{47} +1.00000 q^{49} +(-3.99732 - 5.45457i) q^{50} +(-8.70182 - 2.74853i) q^{52} -1.34379i q^{53} +2.27807 q^{55} +(2.67901 - 0.907128i) q^{56} +(8.87666 - 6.50517i) q^{58} +4.00000i q^{59} +5.49706i q^{61} +(-3.68613 - 5.02993i) q^{62} +(6.35424 - 4.86042i) q^{64} +2.13145 q^{65} -5.90658i q^{67} +(3.67190 - 11.6252i) q^{68} +(-0.532862 + 0.390503i) q^{70} +4.72339 q^{71} -12.0599 q^{73} +(5.02993 - 3.68613i) q^{74} +(2.56279 + 0.809475i) q^{76} +4.87666i q^{77} -16.1913 q^{79} +(-1.07331 + 1.52954i) q^{80} +(-5.09565 - 6.95329i) q^{82} -13.7533i q^{83} +2.84751i q^{85} +(-4.73762 + 3.47192i) q^{86} +(4.42375 + 13.0646i) q^{88} -7.96420 q^{89} +4.56279i q^{91} +(-2.46714 + 7.81093i) q^{92} +(-5.59048 - 7.62851i) q^{94} -0.627737 q^{95} -12.8789 q^{97} +(-0.835949 - 1.14070i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 8 q^{7} + 6 q^{8}+O(q^{10}) $ 8 * q + 2 * q^4 + 8 * q^7 + 6 * q^8	$ 8 q + 2 q^{4} + 8 q^{7} + 6 q^{8} - 4 q^{10} - 6 q^{16} - 4 q^{17} - 24 q^{20} - 12 q^{23} - 24 q^{25} + 28 q^{26} + 2 q^{28} + 8 q^{31} + 30 q^{32} - 4 q^{34} - 12 q^{38} + 28 q^{40} + 4 q^{41} - 16 q^{44} + 4 q^{46} + 8 q^{49} + 20 q^{50} - 12 q^{52} - 8 q^{55} + 6 q^{56} + 44 q^{58} - 12 q^{62} + 26 q^{64} + 16 q^{65} + 16 q^{68} - 4 q^{70} + 28 q^{71} - 8 q^{73} - 4 q^{74} - 24 q^{76} - 40 q^{79} + 4 q^{80} + 4 q^{82} - 24 q^{86} + 4 q^{88} - 20 q^{89} - 20 q^{92} - 72 q^{94} - 40 q^{95} + 40 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 + 8 * q^7 + 6 * q^8 - 4 * q^10 - 6 * q^16 - 4 * q^17 - 24 * q^20 - 12 * q^23 - 24 * q^25 + 28 * q^26 + 2 * q^28 + 8 * q^31 + 30 * q^32 - 4 * q^34 - 12 * q^38 + 28 * q^40 + 4 * q^41 - 16 * q^44 + 4 * q^46 + 8 * q^49 + 20 * q^50 - 12 * q^52 - 8 * q^55 + 6 * q^56 + 44 * q^58 - 12 * q^62 + 26 * q^64 + 16 * q^65 + 16 * q^68 - 4 * q^70 + 28 * q^71 - 8 * q^73 - 4 * q^74 - 24 * q^76 - 40 * q^79 + 4 * q^80 + 4 * q^82 - 24 * q^86 + 4 * q^88 - 20 * q^89 - 20 * q^92 - 72 * q^94 - 40 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.835949	−	1.14070i	−0.591105	−	0.806595i
$2$	−0.835949	−	1.14070i	−0.591105	−	0.806595i
$3$		0			0
$3$		0			0
$4$	−0.602380	+	1.90713i	−0.301190	+	0.953564i
$5$		−	0.467138i		−	0.208910i	−0.994530	−	0.104455i	$-0.966690\pi$
$5$		−	0.467138i		−	0.208910i	0.994530	−	0.104455i	$-0.0333099\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.67901	−	0.907128i	0.947175	−	0.320718i
$9$		0			0
$10$	−0.532862	+	0.390503i	−0.168506	+	0.123488i
$11$			4.87666i			1.47037i	0.677868	+	0.735184i	$0.262904\pi$
$11$			4.87666i			1.47037i	−0.677868	+	0.735184i	$0.737096\pi$
$12$		0			0
$13$			4.56279i			1.26549i	0.774360	+	0.632745i	$0.218072\pi$
$13$			4.56279i			1.26549i	−0.774360	+	0.632745i	$0.781928\pi$
$14$	−0.835949	−	1.14070i	−0.223417	−	0.304864i
$15$		0			0
$16$	−3.27428	−	2.29763i	−0.818569	−	0.574408i
$17$	−6.09565			−1.47841			−0.739206	−	0.673479i	$-0.764799\pi$
$17$	−6.09565			−1.47841			−0.739206	+	0.673479i	$0.764799\pi$
$18$		0			0
$19$		−	1.34379i		−	0.308288i	−0.988048	−	0.154144i	$-0.950738\pi$
$19$		−	1.34379i		−	0.308288i	0.988048	−	0.154144i	$-0.0492619\pi$
$20$	0.890891	+	0.281394i	0.199209	+	0.0629217i
$21$		0			0
$22$	5.56279	−	4.07663i	1.18599	−	0.869141i
$23$	4.09565			0.854002			0.427001	−	0.904251i	$-0.359570\pi$
$23$	4.09565			0.854002			0.427001	+	0.904251i	$0.359570\pi$
$24$		0			0
$25$	4.78178			0.956357
$26$	5.20476	−	3.81426i	1.02074	−	0.748037i
$27$		0			0
$28$	−0.602380	+	1.90713i	−0.113839	+	0.360413i
$29$			7.78178i			1.44504i	0.691350	+	0.722520i	$0.257016\pi$
$29$			7.78178i			1.44504i	−0.691350	+	0.722520i	$0.742984\pi$
$30$		0			0
$31$	4.40952			0.791973			0.395987	−	0.918256i	$-0.370403\pi$
$31$	4.40952			0.791973			0.395987	+	0.918256i	$0.370403\pi$
$32$	0.116226	+	5.65566i	0.0205460	+	0.999789i
$33$		0			0
$34$	5.09565	+	6.95329i	0.873897	+	1.19248i
$35$		−	0.467138i		−	0.0789607i
$36$		0			0
$37$			4.40952i			0.724921i	0.931999	+	0.362460i	$0.118063\pi$
$37$			4.40952i			0.724921i	−0.931999	+	0.362460i	$0.881937\pi$
$38$	−1.53286	+	1.12334i	−0.248663	+	0.182230i
$39$		0			0
$40$	−0.423754	−	1.25147i	−0.0670013	−	0.197874i
$41$	6.09565			0.951981			0.475990	−	0.879450i	$-0.342090\pi$
$41$	6.09565			0.951981			0.475990	+	0.879450i	$0.342090\pi$
$42$		0			0
$43$		−	4.15327i		−	0.633368i	−0.948531	−	0.316684i	$-0.897431\pi$
$43$		−	4.15327i		−	0.633368i	0.948531	−	0.316684i	$-0.102569\pi$
$44$	−9.30041	−	2.93760i	−1.40209	−	0.442860i
$45$		0			0
$46$	−3.42375	−	4.67190i	−0.504805	−	0.688834i
$47$	6.68759			0.975485			0.487743	−	0.872988i	$-0.337820\pi$
$47$	6.68759			0.975485			0.487743	+	0.872988i	$0.337820\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−3.99732	−	5.45457i	−0.565307	−	0.771392i
$51$		0			0
$52$	−8.70182	−	2.74853i	−1.20673	−	0.381153i
$53$		−	1.34379i		−	0.184584i	−0.995732	−	0.0922922i	$-0.970581\pi$
$53$		−	1.34379i		−	0.184584i	0.995732	−	0.0922922i	$-0.0294194\pi$
$54$		0			0
$55$	2.27807			0.307175
$56$	2.67901	−	0.907128i	0.357998	−	0.121220i
$57$		0			0
$58$	8.87666	−	6.50517i	1.16556	−	0.854171i
$59$			4.00000i			0.520756i	0.965507	+	0.260378i	$0.0838471\pi$
$59$			4.00000i			0.520756i	−0.965507	+	0.260378i	$0.916153\pi$
$60$		0			0
$61$			5.49706i			0.703827i	0.936033	+	0.351913i	$0.114469\pi$
$61$			5.49706i			0.703827i	−0.936033	+	0.351913i	$0.885531\pi$
$62$	−3.68613	−	5.02993i	−0.468139	−	0.638801i
$63$		0			0
$64$	6.35424	−	4.86042i	0.794280	−	0.607552i
$65$	2.13145			0.264374
$66$		0			0
$67$		−	5.90658i		−	0.721604i	−0.932642	−	0.360802i	$-0.882503\pi$
$67$		−	5.90658i		−	0.721604i	0.932642	−	0.360802i	$-0.117497\pi$
$68$	3.67190	−	11.6252i	0.445283	−	1.40976i
$69$		0			0
$70$	−0.532862	+	0.390503i	−0.0636892	+	0.0466740i
$71$	4.72339			0.560563			0.280281	−	0.959918i	$-0.409572\pi$
$71$	4.72339			0.560563			0.280281	+	0.959918i	$0.409572\pi$
$72$		0			0
$73$	−12.0599			−1.41150			−0.705749	−	0.708462i	$-0.749390\pi$
$73$	−12.0599			−1.41150			−0.705749	+	0.708462i	$0.749390\pi$
$74$	5.02993	−	3.68613i	0.584717	−	0.428504i
$75$		0			0
$76$	2.56279	+	0.809475i	0.293972	+	0.0928531i
$77$			4.87666i			0.555747i
$78$		0			0
$79$	−16.1913			−1.82166			−0.910832	−	0.412778i	$-0.864559\pi$
$79$	−16.1913			−1.82166			−0.910832	+	0.412778i	$0.864559\pi$
$80$	−1.07331	+	1.52954i	−0.120000	+	0.171008i
$81$		0			0
$82$	−5.09565	−	6.95329i	−0.562721	−	0.767863i
$83$		−	13.7533i		−	1.50962i	−0.655942	−	0.754811i	$-0.727728\pi$
$83$		−	13.7533i		−	1.50962i	0.655942	−	0.754811i	$-0.272272\pi$
$84$		0			0
$85$			2.84751i			0.308856i
$86$	−4.73762	+	3.47192i	−0.510871	+	0.374387i
$87$		0			0
$88$	4.42375	+	13.0646i	0.471574	+	1.39269i
$89$	−7.96420			−0.844204			−0.422102	−	0.906548i	$-0.638708\pi$
$89$	−7.96420			−0.844204			−0.422102	+	0.906548i	$0.638708\pi$
$90$		0			0
$91$			4.56279i			0.478310i
$92$	−2.46714	+	7.81093i	−0.257217	+	0.814346i
$93$		0			0
$94$	−5.59048	−	7.62851i	−0.576614	−	0.786821i
$95$	−0.627737			−0.0644044
$96$		0			0
$97$	−12.8789			−1.30765			−0.653827	−	0.756644i	$-0.726837\pi$
$97$	−12.8789			−1.30765			−0.653827	+	0.756644i	$0.726837\pi$
$98$	−0.835949	−	1.14070i	−0.0844436	−	0.115228i
$99$		0			0
$100$	−2.88045	+	9.11947i	−0.288045	+	0.911947i
$101$			2.22045i			0.220943i	0.993879	+	0.110472i	$0.0352361\pi$
$101$			2.22045i			0.220943i	−0.993879	+	0.110472i	$0.964764\pi$
$102$		0			0
$103$	11.0971			1.09343			0.546715	−	0.837319i	$-0.315878\pi$
$103$	11.0971			1.09343			0.546715	+	0.837319i	$0.315878\pi$
$104$	4.13903	+	12.2238i	0.405866	+	1.19864i
$105$		0			0
$106$	−1.53286	+	1.12334i	−0.148885	+	0.109109i
$107$			3.12334i			0.301945i	0.988538	+	0.150972i	$0.0482405\pi$
$107$			3.12334i			0.301945i	−0.988538	+	0.150972i	$0.951760\pi$
$108$		0			0
$109$			10.6876i			1.02369i	0.859079	+	0.511843i	$0.171037\pi$
$109$			10.6876i			1.02369i	−0.859079	+	0.511843i	$0.828963\pi$
$110$	−1.90435	−	2.59859i	−0.181573	−	0.247766i
$111$		0			0
$112$	−3.27428	−	2.29763i	−0.309390	−	0.217106i
$113$	12.0599			1.13450			0.567248	−	0.823547i	$-0.308008\pi$
$113$	12.0599			1.13450			0.567248	+	0.823547i	$0.308008\pi$
$114$		0			0
$115$		−	1.91323i		−	0.178410i
$116$	−14.8409	−	4.68759i	−1.37794	−	0.435232i
$117$		0			0
$118$	4.56279	−	3.34379i	0.420039	−	0.307821i
$119$	−6.09565			−0.558787
$120$		0			0
$121$	−12.7818			−1.16198
$122$	6.27048	−	4.59526i	0.567703	−	0.416036i
$123$		0			0
$124$	−2.65621	+	8.40952i	−0.238534	+	0.755197i
$125$		−	4.56944i		−	0.408703i
$126$		0			0
$127$	18.8789			1.67523			0.837615	−	0.546261i	$-0.183949\pi$
$127$	18.8789			1.67523			0.837615	+	0.546261i	$0.183949\pi$
$128$	−10.8561	−	3.18520i	−0.959551	−	0.281534i
$129$		0			0
$130$	−1.78178	−	2.43134i	−0.156273	−	0.213243i
$131$		−	4.93428i		−	0.431110i	−0.976492	−	0.215555i	$-0.930844\pi$
$131$		−	4.93428i		−	0.431110i	0.976492	−	0.215555i	$-0.0691560\pi$
$132$		0			0
$133$		−	1.34379i		−	0.116522i
$134$	−6.73762	+	4.93760i	−0.582042	+	0.426544i
$135$		0			0
$136$	−16.3303	+	5.52954i	−1.40031	+	0.474154i
$137$	−19.0103			−1.62416			−0.812082	−	0.583544i	$-0.801666\pi$
$137$	−19.0103			−1.62416			−0.812082	+	0.583544i	$0.801666\pi$
$138$		0			0
$139$		−	10.4380i		−	0.885339i	−0.896685	−	0.442669i	$-0.854032\pi$
$139$		−	10.4380i		−	0.885339i	0.896685	−	0.442669i	$-0.145968\pi$
$140$	0.890891	+	0.281394i	0.0752941	+	0.0237822i
$141$		0			0
$142$	−3.94851	−	5.38795i	−0.331352	−	0.452147i
$143$	−22.2512			−1.86073
$144$		0			0
$145$	3.63516			0.301884
$146$	10.0814	+	13.7566i	0.834344	+	1.13851i
$147$		0			0
$148$	−8.40952	−	2.65621i	−0.691258	−	0.218339i
$149$			6.65621i			0.545298i	0.962114	+	0.272649i	$0.0878997\pi$
$149$			6.65621i			0.545298i	−0.962114	+	0.272649i	$0.912100\pi$
$150$		0			0
$151$	−2.68759			−0.218713			−0.109356	−	0.994003i	$-0.534879\pi$
$151$	−2.68759			−0.218713			−0.109356	+	0.994003i	$0.534879\pi$
$152$	−1.21899	−	3.60004i	−0.0988735	−	0.292002i
$153$		0			0
$154$	5.56279	−	4.07663i	0.448262	−	0.328505i
$155$		−	2.05985i		−	0.165451i
$156$		0			0
$157$		−	23.1351i		−	1.84639i	−0.384338	−	0.923193i	$-0.625570\pi$
$157$		−	23.1351i		−	1.84639i	0.384338	−	0.923193i	$-0.374430\pi$
$158$	13.5351	+	18.4694i	1.07679	+	1.46934i
$159$		0			0
$160$	2.64197	−	0.0542935i	0.208866	−	0.00429228i
$161$	4.09565			0.322783
$162$		0			0
$163$			12.0380i			0.942891i	0.881895	+	0.471446i	$0.156268\pi$
$163$			12.0380i			0.942891i	−0.881895	+	0.471446i	$0.843732\pi$
$164$	−3.67190	+	11.6252i	−0.286727	+	0.907775i
$165$		0			0
$166$	−15.6884	+	11.4971i	−1.21765	+	0.892345i
$167$	−9.01034			−0.697241			−0.348621	−	0.937264i	$-0.613350\pi$
$167$	−9.01034			−0.697241			−0.348621	+	0.937264i	$0.613350\pi$
$168$		0			0
$169$	−7.81904			−0.601465
$170$	3.24814	−	2.38037i	0.249121	−	0.182566i
$171$		0			0
$172$	7.92082	+	2.50185i	0.603957	+	0.190764i
$173$			9.59271i			0.729321i	0.931141	+	0.364660i	$0.118815\pi$
$173$			9.59271i			0.729321i	−0.931141	+	0.364660i	$0.881185\pi$
$174$		0			0
$175$	4.78178			0.361469
$176$	11.2048	−	15.9675i	0.844591	−	1.20360i
$177$		0			0
$178$	6.65766	+	9.08474i	0.499013	+	0.680930i
$179$		−	7.69278i		−	0.574985i	−0.957783	−	0.287493i	$-0.907178\pi$
$179$		−	7.69278i		−	0.574985i	0.957783	−	0.287493i	$-0.0928217\pi$
$180$		0			0
$181$		−	15.2504i		−	1.13355i	−0.823872	−	0.566776i	$-0.808191\pi$
$181$		−	15.2504i		−	1.13355i	0.823872	−	0.566776i	$-0.191809\pi$
$182$	5.20476	−	3.81426i	0.385802	−	0.282732i
$183$		0			0
$184$	10.9723	−	3.71528i	0.808889	−	0.273894i
$185$	2.05985			0.151443
$186$		0			0
$187$		−	29.7264i		−	2.17381i
$188$	−4.02847	+	12.7541i	−0.293806	+	0.930188i
$189$		0			0
$190$	0.524756	+	0.716058i	0.0380698	+	0.0519483i
$191$	4.72339			0.341772			0.170886	−	0.985291i	$-0.445337\pi$
$191$	4.72339			0.341772			0.170886	+	0.985291i	$0.445337\pi$
$192$		0			0
$193$	22.3379			1.60792			0.803959	−	0.594684i	$-0.202723\pi$
$193$	22.3379			1.60792			0.803959	+	0.594684i	$0.202723\pi$
$194$	10.7661	+	14.6909i	0.772960	+	1.05475i
$195$		0			0
$196$	−0.602380	+	1.90713i	−0.0430271	+	0.136223i
$197$			1.53510i			0.109371i	0.998504	+	0.0546855i	$0.0174156\pi$
$197$			1.53510i			0.109371i	−0.998504	+	0.0546855i	$0.982584\pi$
$198$		0			0
$199$	−14.6876			−1.04118			−0.520588	−	0.853808i	$-0.674287\pi$
$199$	−14.6876			−1.04118			−0.520588	+	0.853808i	$0.674287\pi$
$200$	12.8105	−	4.33769i	0.905837	−	0.306721i
$201$		0			0
$202$	2.53286	−	1.85618i	0.178212	−	0.130601i
$203$			7.78178i			0.546174i
$204$		0			0
$205$		−	2.84751i		−	0.198879i
$206$	−9.27661	−	12.6584i	−0.646332	−	0.881955i
$207$		0			0
$208$	10.4836	−	14.9398i	0.726907	−	1.03589i
$209$	6.55322			0.453296
$210$		0			0
$211$			22.8409i			1.57243i	0.617953	+	0.786215i	$0.287962\pi$
$211$			22.8409i			1.57243i	−0.617953	+	0.786215i	$0.712038\pi$
$212$	2.56279	+	0.809475i	0.176013	+	0.0555949i
$213$		0			0
$214$	3.56279	−	2.61095i	0.243547	−	0.178481i
$215$	−1.94015			−0.132317
$216$		0			0
$217$	4.40952			0.299338
$218$	12.1913	−	8.93428i	0.825699	−	0.605105i
$219$		0			0
$220$	−1.37226	+	4.34457i	−0.0925180	+	0.292911i
$221$		−	27.8132i		−	1.87092i
$222$		0			0
$223$	21.4321			1.43520			0.717600	−	0.696455i	$-0.245240\pi$
$223$	21.4321			1.43520			0.717600	+	0.696455i	$0.245240\pi$
$224$	0.116226	+	5.65566i	0.00776567	+	0.377885i
$225$		0			0
$226$	−10.0814	−	13.7566i	−0.670606	−	0.915078i
$227$		−	29.3169i		−	1.94583i	−0.231164	−	0.972915i	$-0.574253\pi$
$227$		−	29.3169i		−	1.94583i	0.231164	−	0.972915i	$-0.425747\pi$
$228$		0			0
$229$			22.5074i			1.48733i	0.668552	+	0.743666i	$0.266914\pi$
$229$			22.5074i			1.48733i	−0.668552	+	0.743666i	$0.733086\pi$
$230$	−2.18242	+	1.59936i	−0.143904	+	0.105459i
$231$		0			0
$232$	7.05908	+	20.8475i	0.463451	+	1.36871i
$233$	0.687589			0.0450454			0.0225227	−	0.999746i	$-0.492830\pi$
$233$	0.687589			0.0450454			0.0225227	+	0.999746i	$0.492830\pi$
$234$		0			0
$235$		−	3.12402i		−	0.203789i
$236$	−7.62851	−	2.40952i	−0.496574	−	0.156846i
$237$		0			0
$238$	5.09565	+	6.95329i	0.330302	+	0.450715i
$239$	9.59936			0.620931			0.310466	−	0.950585i	$-0.399515\pi$
$239$	9.59936			0.620931			0.310466	+	0.950585i	$0.399515\pi$
$240$		0			0
$241$	0.496287			0.0319687			0.0159843	−	0.999872i	$-0.494912\pi$
$241$	0.496287			0.0319687			0.0159843	+	0.999872i	$0.494912\pi$
$242$	10.6849	+	14.5801i	0.686852	+	0.937247i
$243$		0			0
$244$	−10.4836	−	3.31132i	−0.671144	−	0.211986i
$245$		−	0.467138i		−	0.0298443i
$246$		0			0
$247$	6.13145			0.390135
$248$	11.8132	−	4.00000i	0.750137	−	0.254000i
$249$		0			0
$250$	−5.21234	+	3.81982i	−0.329658	+	0.241586i
$251$		−	22.1359i		−	1.39721i	−0.715509	−	0.698603i	$-0.753805\pi$
$251$		−	22.1359i		−	1.39721i	0.715509	−	0.698603i	$-0.246195\pi$
$252$		0			0
$253$			19.9731i			1.25570i
$254$	−15.7818	−	21.5351i	−0.990237	−	1.35123i
$255$		0			0
$256$	5.44178	+	15.0462i	0.340111	+	0.940385i
$257$	−2.28695			−0.142656			−0.0713281	−	0.997453i	$-0.522724\pi$
$257$	−2.28695			−0.142656			−0.0713281	+	0.997453i	$0.522724\pi$
$258$		0			0
$259$			4.40952i			0.273994i
$260$	−1.28394	+	4.06495i	−0.0796267	+	0.252097i
$261$		0			0
$262$	−5.62851	+	4.12480i	−0.347731	+	0.254831i
$263$	30.1555			1.85947			0.929734	−	0.368232i	$-0.120037\pi$
$263$	30.1555			1.85947			0.929734	+	0.368232i	$0.120037\pi$
$264$		0			0
$265$	−0.627737			−0.0385616
$266$	−1.53286	+	1.12334i	−0.0939858	+	0.0688766i
$267$		0			0
$268$	11.2646	+	3.55801i	0.688096	+	0.217340i
$269$		−	9.47748i		−	0.577852i	−0.957351	−	0.288926i	$-0.906702\pi$
$269$		−	9.47748i		−	0.577852i	0.957351	−	0.288926i	$-0.0932982\pi$
$270$		0			0
$271$	−13.2855			−0.807036			−0.403518	−	0.914972i	$-0.632213\pi$
$271$	−13.2855			−0.807036			−0.403518	+	0.914972i	$0.632213\pi$
$272$	19.9589	+	14.0056i	1.21018	+	0.849212i
$273$		0			0
$274$	15.8917	+	21.6850i	0.960051	+	1.31004i
$275$			23.3191i			1.40620i
$276$		0			0
$277$		−	26.8475i		−	1.61311i	−0.591159	−	0.806555i	$-0.701329\pi$
$277$		−	26.8475i		−	1.61311i	0.591159	−	0.806555i	$-0.298671\pi$
$278$	−11.9066	+	8.72562i	−0.714109	+	0.523328i
$279$		0			0
$280$	−0.423754	−	1.25147i	−0.0253241	−	0.0747895i
$281$	−11.8686			−0.708018			−0.354009	−	0.935242i	$-0.615182\pi$
$281$	−11.8686			−0.708018			−0.354009	+	0.935242i	$0.615182\pi$
$282$		0			0
$283$			2.46937i			0.146789i	0.997303	+	0.0733944i	$0.0233832\pi$
$283$			2.46937i			0.146789i	−0.997303	+	0.0733944i	$0.976617\pi$
$284$	−2.84527	+	9.00811i	−0.168836	+	0.534533i
$285$		0			0
$286$	18.6008	+	25.3818i	1.09989	+	1.50086i
$287$	6.09565			0.359815
$288$		0			0
$289$	20.1570			1.18570
$290$	−3.03881	−	4.14662i	−0.178445	−	0.243498i
$291$		0			0
$292$	7.26461	−	22.9997i	0.425129	−	1.34595i
$293$		−	22.7899i		−	1.33140i	−0.746220	−	0.665700i	$-0.768133\pi$
$293$		−	22.7899i		−	1.33140i	0.746220	−	0.665700i	$-0.231867\pi$
$294$		0			0
$295$	1.86855			0.108791
$296$	4.00000	+	11.8132i	0.232495	+	0.686626i
$297$		0			0
$298$	7.59271	−	5.56425i	0.439834	−	0.322328i
$299$			18.6876i			1.08073i
$300$		0			0
$301$		−	4.15327i		−	0.239390i
$302$	2.24669	+	3.06572i	0.129282	+	0.176413i
$303$		0			0
$304$	−3.08754	+	4.39996i	−0.177083	+	0.252355i
$305$	2.56788			0.147037
$306$		0			0
$307$			9.34379i			0.533279i	0.963796	+	0.266639i	$0.0859132\pi$
$307$			9.34379i			0.533279i	−0.963796	+	0.266639i	$0.914087\pi$
$308$	−9.30041	−	2.93760i	−0.529940	−	0.167385i
$309$		0			0
$310$	−2.34967	+	1.72193i	−0.133452	+	0.0977991i
$311$	−6.68759			−0.379218			−0.189609	−	0.981860i	$-0.560722\pi$
$311$	−6.68759			−0.379218			−0.189609	+	0.981860i	$0.560722\pi$
$312$		0			0
$313$	−15.6381			−0.883916			−0.441958	−	0.897036i	$-0.645716\pi$
$313$	−15.6381			−0.883916			−0.441958	+	0.897036i	$0.645716\pi$
$314$	−26.3902	+	19.3398i	−1.48928	+	1.09141i
$315$		0			0
$316$	9.75331	−	30.8789i	0.548667	−	1.73707i
$317$		−	9.34379i		−	0.524800i	−0.964959	−	0.262400i	$-0.915486\pi$
$317$		−	9.34379i		−	0.524800i	0.964959	−	0.262400i	$-0.0845139\pi$
$318$		0			0
$319$	−37.9491			−2.12474
$320$	−2.27048	−	2.96830i	−0.126924	−	0.165933i
$321$		0			0
$322$	−3.42375	−	4.67190i	−0.190798	−	0.260355i
$323$			8.19130i			0.455776i
$324$		0			0
$325$			21.8183i			1.21026i
$326$	13.7317	−	10.0632i	0.760531	−	0.557348i
$327$		0			0
$328$	16.3303	−	5.52954i	0.901692	−	0.305318i
$329$	6.68759			0.368699
$330$		0			0
$331$		−	5.40874i		−	0.297291i	−0.988891	−	0.148646i	$-0.952509\pi$
$331$		−	5.40874i		−	0.297291i	0.988891	−	0.148646i	$-0.0474914\pi$
$332$	26.2293	+	8.28472i	1.43952	+	0.454683i
$333$		0			0
$334$	7.53218	+	10.2781i	0.412143	+	0.562391i
$335$	−2.75919			−0.150750
$336$		0			0
$337$	−6.55614			−0.357136			−0.178568	−	0.983928i	$-0.557146\pi$
$337$	−6.55614			−0.357136			−0.178568	+	0.983928i	$0.557146\pi$
$338$	6.53631	+	8.91915i	0.355529	+	0.485138i
$339$		0			0
$340$	−5.43056	−	1.71528i	−0.294514	−	0.0930242i
$341$			21.5037i			1.16449i
$342$		0			0
$343$	1.00000			0.0539949
$344$	−3.76755	−	11.1267i	−0.203133	−	0.599910i
$345$		0			0
$346$	10.9424	−	8.01902i	0.588266	−	0.431105i
$347$			24.9964i			1.34187i	0.741514	+	0.670937i	$0.234108\pi$
$347$			24.9964i			1.34187i	−0.741514	+	0.670937i	$0.765892\pi$
$348$		0			0
$349$		−	27.1921i		−	1.45556i	−0.685811	−	0.727779i	$-0.740553\pi$
$349$		−	27.1921i		−	1.45556i	0.685811	−	0.727779i	$-0.259447\pi$
$350$	−3.99732	−	5.45457i	−0.213666	−	0.291559i
$351$		0			0
$352$	−27.5807	+	0.566794i	−1.47006	+	0.0302102i
$353$	30.2870			1.61201			0.806006	−	0.591907i	$-0.201625\pi$
$353$	30.2870			1.61201			0.806006	+	0.591907i	$0.201625\pi$
$354$		0			0
$355$		−	2.20647i		−	0.117107i
$356$	4.79747	−	15.1888i	0.254266	−	0.805002i
$357$		0			0
$358$	−8.77513	+	6.43077i	−0.463780	+	0.339877i
$359$	−6.59194			−0.347909			−0.173955	−	0.984754i	$-0.555655\pi$
$359$	−6.59194			−0.347909			−0.173955	+	0.984754i	$0.555655\pi$
$360$		0			0
$361$	17.1942			0.904959
$362$	−17.3961	+	12.7485i	−0.914317	+	0.670048i
$363$		0			0
$364$	−8.70182	−	2.74853i	−0.456099	−	0.144062i
$365$			5.63361i			0.294877i
$366$		0			0
$367$	−6.68759			−0.349089			−0.174545	−	0.984649i	$-0.555845\pi$
$367$	−6.68759			−0.349089			−0.174545	+	0.984649i	$0.555845\pi$
$368$	−13.4103	−	9.41030i	−0.699060	−	0.490546i
$369$		0			0
$370$	−1.72193	−	2.34967i	−0.0895189	−	0.122153i
$371$		−	1.34379i		−	0.0697663i
$372$		0			0
$373$		−	17.1256i		−	0.886729i	−0.896341	−	0.443364i	$-0.853785\pi$
$373$		−	17.1256i		−	0.886729i	0.896341	−	0.443364i	$-0.146215\pi$
$374$	−33.9088	+	24.8497i	−1.75338	+	1.28495i
$375$		0			0
$376$	17.9161	−	6.06650i	0.923955	−	0.312856i
$377$	−35.5066			−1.82868
$378$		0			0
$379$		−	16.7094i		−	0.858305i	−0.903232	−	0.429152i	$-0.858812\pi$
$379$		−	16.7094i		−	0.858305i	0.903232	−	0.429152i	$-0.141188\pi$
$380$	0.378136	−	1.19717i	0.0193980	−	0.0614138i
$381$		0			0
$382$	−3.94851	−	5.38795i	−0.202023	−	0.275672i
$383$	9.94015			0.507918			0.253959	−	0.967215i	$-0.418267\pi$
$383$	9.94015			0.507918			0.253959	+	0.967215i	$0.418267\pi$
$384$		0			0
$385$	2.27807			0.116101
$386$	−18.6734	−	25.4808i	−0.950449	−	1.29694i
$387$		0			0
$388$	7.75798	−	24.5617i	0.393852	−	1.24693i
$389$		−	19.2884i		−	0.977961i	−0.872295	−	0.488981i	$-0.837369\pi$
$389$		−	19.2884i		−	0.977961i	0.872295	−	0.488981i	$-0.162631\pi$
$390$		0			0
$391$	−24.9657			−1.26257
$392$	2.67901	−	0.907128i	0.135311	−	0.0458169i
$393$		0			0
$394$	1.75108	−	1.28326i	0.0882181	−	0.0646498i
$395$			7.56357i			0.380564i
$396$		0			0
$397$			23.4417i			1.17650i	0.808678	+	0.588252i	$0.200184\pi$
$397$			23.4417i			1.17650i	−0.808678	+	0.588252i	$0.799816\pi$
$398$	12.2781	+	16.7541i	0.615444	+	0.839807i
$399$		0			0
$400$	−15.6569	−	10.9868i	−0.782844	−	0.549339i
$401$	16.0029			0.799147			0.399574	−	0.916701i	$-0.369158\pi$
$401$	16.0029			0.799147			0.399574	+	0.916701i	$0.369158\pi$
$402$		0			0
$403$			20.1197i			1.00223i
$404$	−4.23469	−	1.33756i	−0.210683	−	0.0665459i
$405$		0			0
$406$	8.87666	−	6.50517i	0.440541	−	0.322846i
$407$	−21.5037			−1.06590
$408$		0			0
$409$	15.5665			0.769713			0.384856	−	0.922976i	$-0.374251\pi$
$409$	15.5665			0.769713			0.384856	+	0.922976i	$0.374251\pi$
$410$	−3.24814	+	2.38037i	−0.160414	+	0.117558i
$411$		0			0
$412$	−6.68467	+	21.1636i	−0.329330	+	1.04266i
$413$			4.00000i			0.196827i
$414$		0			0
$415$	−6.42469			−0.315376
$416$	−25.8056	+	0.530314i	−1.26522	+	0.0260008i
$417$		0			0
$418$	−5.47816	−	7.47524i	−0.267946	−	0.365626i
$419$		−	1.31241i		−	0.0641155i	−0.999486	−	0.0320577i	$-0.989794\pi$
$419$		−	1.31241i		−	0.0641155i	0.999486	−	0.0320577i	$-0.0102060\pi$
$420$		0			0
$421$		−	3.66655i		−	0.178697i	−0.996000	−	0.0893483i	$-0.971522\pi$
$421$		−	3.66655i		−	0.178697i	0.996000	−	0.0893483i	$-0.0284784\pi$
$422$	26.0545	−	19.0938i	1.26831	−	0.929471i
$423$		0			0
$424$	−1.21899	−	3.60004i	−0.0591996	−	0.174834i
$425$	−29.1481			−1.41389
$426$		0			0
$427$			5.49706i			0.266022i
$428$	−5.95662	−	1.88144i	−0.287924	−	0.0909428i
$429$		0			0
$430$	1.62186	+	2.21312i	0.0782132	+	0.106726i
$431$	−20.0957			−0.967973			−0.483987	−	0.875075i	$-0.660812\pi$
$431$	−20.0957			−0.967973			−0.483987	+	0.875075i	$0.660812\pi$
$432$		0			0
$433$	8.68759			0.417499			0.208749	−	0.977969i	$-0.433061\pi$
$433$	8.68759			0.417499			0.208749	+	0.977969i	$0.433061\pi$
$434$	−3.68613	−	5.02993i	−0.176940	−	0.241444i
$435$		0			0
$436$	−20.3826	−	6.43799i	−0.976150	−	0.308324i
$437$		−	5.50371i		−	0.263278i
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	6.10298	−	2.06650i	0.290948	−	0.0985166i
$441$		0			0
$442$	−31.7264	+	23.2504i	−1.50907	+	1.10591i
$443$			4.57012i			0.217133i	0.994089	+	0.108566i	$0.0346260\pi$
$443$			4.57012i			0.217133i	−0.994089	+	0.108566i	$0.965374\pi$
$444$		0			0
$445$			3.72038i			0.176363i
$446$	−17.9161	−	24.4476i	−0.848354	−	1.15763i
$447$		0			0
$448$	6.35424	−	4.86042i	0.300209	−	0.229633i
$449$	3.94015			0.185947			0.0929735	−	0.995669i	$-0.470363\pi$
$449$	3.94015			0.185947			0.0929735	+	0.995669i	$0.470363\pi$
$450$		0			0
$451$			29.7264i			1.39976i
$452$	−7.26461	+	22.9997i	−0.341699	+	1.08181i
$453$		0			0
$454$	−33.4417	+	24.5074i	−1.56950	+	1.15019i
$455$	2.13145			0.0999239
$456$		0			0
$457$	40.0207			1.87209			0.936044	−	0.351882i	$-0.114458\pi$
$457$	40.0207			1.87209			0.936044	+	0.351882i	$0.114458\pi$
$458$	25.6741	−	18.8150i	1.19967	−	0.879169i
$459$		0			0
$460$	3.64878	+	1.15249i	0.170125	+	0.0537352i
$461$			34.6031i			1.61162i	0.592171	+	0.805812i	$0.298271\pi$
$461$			34.6031i			1.61162i	−0.592171	+	0.805812i	$0.701729\pi$
$462$		0			0
$463$	0.191302			0.00889055			0.00444528	−	0.999990i	$-0.498585\pi$
$463$	0.191302			0.00889055			0.00444528	+	0.999990i	$0.498585\pi$
$464$	17.8797	−	25.4797i	0.830043	−	1.18287i
$465$		0			0
$466$	−0.574789	−	0.784331i	−0.0266266	−	0.0363334i
$467$		−	4.49784i		−	0.208135i	−0.994570	−	0.104068i	$-0.966814\pi$
$467$		−	4.49784i		−	0.208135i	0.994570	−	0.104068i	$-0.0331858\pi$
$468$		0			0
$469$		−	5.90658i		−	0.272741i
$470$	−3.56357	+	2.61152i	−0.164375	+	0.120461i
$471$		0			0
$472$	3.62851	+	10.7161i	0.167016	+	0.493247i
$473$	20.2541			0.931283
$474$		0			0
$475$		−	6.42573i		−	0.294833i
$476$	3.67190	−	11.6252i	0.168301	−	0.532840i
$477$		0			0
$478$	−8.02457	−	10.9500i	−0.367036	−	0.500840i
$479$	22.2512			1.01668			0.508341	−	0.861156i	$-0.330259\pi$
$479$	22.2512			1.01668			0.508341	+	0.861156i	$0.330259\pi$
$480$		0			0
$481$	−20.1197			−0.917380
$482$	−0.414870	−	0.566113i	−0.0188968	−	0.0257857i
$483$		0			0
$484$	7.69949	−	24.3765i	0.349977	−	1.10802i
$485$			6.01621i			0.273182i
$486$		0			0
$487$	−1.86855			−0.0846721			−0.0423360	−	0.999103i	$-0.513480\pi$
$487$	−1.86855			−0.0846721			−0.0423360	+	0.999103i	$0.513480\pi$
$488$	4.98654	+	14.7267i	0.225730	+	0.666647i
$489$		0			0
$490$	−0.532862	+	0.390503i	−0.0240723	+	0.0176411i
$491$			17.6374i			0.795965i	0.917393	+	0.397982i	$0.130289\pi$
$491$			17.6374i			0.795965i	−0.917393	+	0.397982i	$0.869711\pi$
$492$		0			0
$493$		−	47.4350i		−	2.13637i
$494$	−5.12558	−	6.99413i	−0.230611	−	0.314681i
$495$		0			0
$496$	−14.4380	−	10.1314i	−0.648285	−	0.454916i
$497$	4.72339			0.211873
$498$		0			0
$499$			21.5854i			0.966295i	0.875539	+	0.483147i	$0.160506\pi$
$499$			21.5854i			0.966295i	−0.875539	+	0.483147i	$0.839494\pi$
$500$	8.71450	+	2.75254i	0.389724	+	0.123097i
$501$		0			0
$502$	−25.2504	+	18.5045i	−1.12698	+	0.825896i
$503$	−5.24081			−0.233676			−0.116838	−	0.993151i	$-0.537276\pi$
$503$	−5.24081			−0.233676			−0.116838	+	0.993151i	$0.537276\pi$
$504$		0			0
$505$	1.03726			0.0461573
$506$	22.7832	−	16.6965i	1.01284	−	0.742249i
$507$		0			0
$508$	−11.3723	+	36.0045i	−0.504563	+	1.59744i
$509$		−	18.3357i		−	0.812715i	−0.913714	−	0.406358i	$-0.866799\pi$
$509$		−	18.3357i		−	0.812715i	0.913714	−	0.406358i	$-0.133201\pi$
$510$		0			0
$511$	−12.0599			−0.533496
$512$	12.6141	−	18.7852i	0.557468	−	0.830198i
$513$		0			0
$514$	1.91178	+	2.60872i	0.0843248	+	0.115066i
$515$		−	5.18388i		−	0.228429i
$516$		0			0
$517$			32.6131i			1.43432i
$518$	5.02993	−	3.68613i	0.221002	−	0.161959i
$519$		0			0
$520$	5.71018	−	1.93350i	0.250408	−	0.0847895i
$521$	−6.78033			−0.297051			−0.148526	−	0.988909i	$-0.547453\pi$
$521$	−6.78033			−0.297051			−0.148526	+	0.988909i	$0.547453\pi$
$522$		0			0
$523$			23.5066i			1.02787i	0.857828	+	0.513937i	$0.171813\pi$
$523$			23.5066i			1.02787i	−0.857828	+	0.513937i	$0.828187\pi$
$524$	9.41030	+	2.97231i	0.411091	+	0.129846i
$525$		0			0
$526$	−25.2085	−	34.3983i	−1.09914	−	1.49984i
$527$	−26.8789			−1.17086
$528$		0			0
$529$	−6.22564			−0.270680
$530$	0.524756	+	0.716058i	0.0227939	+	0.0311036i
$531$		0			0
$532$	2.56279	+	0.809475i	0.111111	+	0.0350952i
$533$			27.8132i			1.20472i
$534$		0			0
$535$	1.45903			0.0630794
$536$	−5.35803	−	15.8238i	−0.231432	−	0.683485i
$537$		0			0
$538$	−10.8109	+	7.92268i	−0.466092	+	0.341571i
$539$			4.87666i			0.210052i
$540$		0			0
$541$		−	5.21526i		−	0.224222i	−0.993696	−	0.112111i	$-0.964239\pi$
$541$		−	5.21526i		−	0.224222i	0.993696	−	0.112111i	$-0.0357611\pi$
$542$	11.1060	+	15.1547i	0.477043	+	0.650951i
$543$		0			0
$544$	−0.708473	−	34.4749i	−0.0303755	−	1.47810i
$545$	4.99257			0.213858
$546$		0			0
$547$		−	27.2951i		−	1.16705i	−0.812094	−	0.583526i	$-0.801673\pi$
$547$		−	27.2951i		−	1.16705i	0.812094	−	0.583526i	$-0.198327\pi$
$548$	11.4514	−	36.2552i	0.489182	−	1.54874i
$549$		0			0
$550$	26.6000	−	19.4936i	1.13423	−	0.831209i
$551$	10.4571			0.445488
$552$		0			0
$553$	−16.1913			−0.688524
$554$	−30.6249	+	22.4431i	−1.30113	+	0.953518i
$555$		0			0
$556$	19.9066	+	6.28763i	0.844227	+	0.266655i
$557$		−	4.78766i		−	0.202859i	−0.994843	−	0.101430i	$-0.967658\pi$
$557$		−	4.78766i		−	0.202859i	0.994843	−	0.101430i	$-0.0323417\pi$
$558$		0			0
$559$	18.9505			0.801520
$560$	−1.07331	+	1.52954i	−0.0453556	+	0.0646348i
$561$		0			0
$562$	9.92150	+	13.5384i	0.418513	+	0.571084i
$563$			18.7445i			0.789988i	0.918684	+	0.394994i	$0.129253\pi$
$563$			18.7445i			0.789988i	−0.918684	+	0.394994i	$0.870747\pi$
$564$		0			0
$565$		−	5.63361i		−	0.237008i
$566$	2.81680	−	2.06427i	0.118399	−	0.0867676i
$567$		0			0
$568$	12.6540	−	4.28472i	0.530951	−	0.179783i
$569$	−27.6950			−1.16104			−0.580518	−	0.814248i	$-0.697150\pi$
$569$	−27.6950			−1.16104			−0.580518	+	0.814248i	$0.697150\pi$
$570$		0			0
$571$			17.4132i			0.728720i	0.931258	+	0.364360i	$0.118712\pi$
$571$			17.4132i			0.728720i	−0.931258	+	0.364360i	$0.881288\pi$
$572$	13.4036	−	42.4358i	0.560435	−	1.77433i
$573$		0			0
$574$	−5.09565	−	6.95329i	−0.212688	−	0.290225i
$575$	19.5845			0.816731
$576$		0			0
$577$	−6.81904			−0.283880			−0.141940	−	0.989875i	$-0.545334\pi$
$577$	−6.81904			−0.283880			−0.141940	+	0.989875i	$0.545334\pi$
$578$	−16.8502	−	22.9930i	−0.700875	−	0.956382i
$579$		0			0
$580$	−2.18975	+	6.93272i	−0.0909244	+	0.287866i
$581$		−	13.7533i		−	0.570584i
$582$		0			0
$583$	6.55322			0.271407
$584$	−32.3085	+	10.9398i	−1.33694	+	0.452694i
$585$		0			0
$586$	−25.9964	+	19.0512i	−1.07390	+	0.786997i
$587$		−	9.81025i		−	0.404912i	−0.979291	−	0.202456i	$-0.935108\pi$
$587$		−	9.81025i		−	0.404912i	0.979291	−	0.202456i	$-0.0648924\pi$
$588$		0			0
$589$		−	5.92549i		−	0.244155i
$590$	−1.56201	−	2.13145i	−0.0643070	−	0.0877504i
$591$		0			0
$592$	10.1314	−	14.4380i	0.416400	−	0.593398i
$593$	39.0913			1.60529			0.802644	−	0.596458i	$-0.203426\pi$
$593$	39.0913			1.60529			0.802644	+	0.596458i	$0.203426\pi$
$594$		0			0
$595$			2.84751i			0.116736i
$596$	−12.6942	−	4.00956i	−0.519976	−	0.164238i
$597$		0			0
$598$	21.3169	−	15.6219i	0.871712	−	0.638826i
$599$	−22.0270			−0.899998			−0.449999	−	0.893029i	$-0.648576\pi$
$599$	−22.0270			−0.899998			−0.449999	+	0.893029i	$0.648576\pi$
$600$		0			0
$601$	−20.2512			−0.826062			−0.413031	−	0.910717i	$-0.635530\pi$
$601$	−20.2512			−0.826062			−0.413031	+	0.910717i	$0.635530\pi$
$602$	−4.73762	+	3.47192i	−0.193091	+	0.141505i
$603$		0			0
$604$	1.61895	−	5.12558i	0.0658741	−	0.208557i
$605$			5.97085i			0.242750i
$606$		0			0
$607$	44.4454			1.80398			0.901991	−	0.431755i	$-0.142105\pi$
$607$	44.4454			1.80398			0.901991	+	0.431755i	$0.142105\pi$
$608$	7.60004	−	0.156184i	0.308223	−	0.00633409i
$609$		0			0
$610$	−2.14662	−	2.92918i	−0.0869141	−	0.118599i
$611$			30.5141i			1.23447i
$612$		0			0
$613$		−	47.6263i		−	1.92361i	−0.273737	−	0.961805i	$-0.588260\pi$
$613$		−	47.6263i		−	1.92361i	0.273737	−	0.961805i	$-0.411740\pi$
$614$	10.6584	−	7.81093i	0.430140	−	0.315224i
$615$		0			0
$616$	4.42375	+	13.0646i	0.178238	+	0.526389i
$617$	3.01034			0.121192			0.0605959	−	0.998162i	$-0.480700\pi$
$617$	3.01034			0.121192			0.0605959	+	0.998162i	$0.480700\pi$
$618$		0			0
$619$			18.5141i			0.744143i	0.928204	+	0.372071i	$0.121352\pi$
$619$			18.5141i			0.744143i	−0.928204	+	0.372071i	$0.878648\pi$
$620$	3.92840	+	1.24081i	0.157768	+	0.0498323i
$621$		0			0
$622$	5.59048	+	7.62851i	0.224158	+	0.305876i
$623$	−7.96420			−0.319079
$624$		0			0
$625$	21.7744			0.870974
$626$	13.0726	+	17.8383i	0.522487	+	0.712962i
$627$		0			0
$628$	44.1217	+	13.9361i	1.76065	+	0.556113i
$629$		−	26.8789i		−	1.07173i
$630$		0			0
$631$	10.2658			0.408676			0.204338	−	0.978900i	$-0.434496\pi$
$631$	10.2658			0.408676			0.204338	+	0.978900i	$0.434496\pi$
$632$	−43.3767	+	14.6876i	−1.72543	+	0.584241i
$633$		0			0
$634$	−10.6584	+	7.81093i	−0.423301	+	0.310212i
$635$		−	8.81904i		−	0.349973i
$636$		0			0
$637$			4.56279i			0.180784i
$638$	31.7235	+	43.2884i	1.25594	+	1.71380i
$639$		0			0
$640$	−1.48793	+	5.07128i	−0.0588154	+	0.200460i
$641$	16.9358			0.668925			0.334462	−	0.942409i	$-0.391445\pi$
$641$	16.9358			0.668925			0.334462	+	0.942409i	$0.391445\pi$
$642$		0			0
$643$		−	19.5189i		−	0.769750i	−0.922969	−	0.384875i	$-0.874245\pi$
$643$		−	19.5189i		−	0.769750i	0.922969	−	0.384875i	$-0.125755\pi$
$644$	−2.46714	+	7.81093i	−0.0972188	+	0.307794i
$645$		0			0
$646$	9.34379	−	6.84751i	0.367627	−	0.269412i
$647$	23.3723			0.918858			0.459429	−	0.888214i	$-0.348054\pi$
$647$	23.3723			0.918858			0.459429	+	0.888214i	$0.348054\pi$
$648$		0			0
$649$	−19.5066			−0.765702
$650$	24.8880	−	18.2389i	0.976189	−	0.715390i
$651$		0			0
$652$	−22.9581	−	7.25147i	−0.899108	−	0.283989i
$653$		−	1.45903i		−	0.0570963i	−0.999592	−	0.0285481i	$-0.990912\pi$
$653$		−	1.45903i		−	0.0570963i	0.999592	−	0.0285481i	$-0.00908839\pi$
$654$		0			0
$655$	−2.30499			−0.0900632
$656$	−19.9589	−	14.0056i	−0.779262	−	0.546825i
$657$		0			0
$658$	−5.59048	−	7.62851i	−0.217940	−	0.297390i
$659$		−	10.8929i		−	0.424326i	−0.977234	−	0.212163i	$-0.931949\pi$
$659$		−	10.8929i		−	0.424326i	0.977234	−	0.212163i	$-0.0680508\pi$
$660$		0			0
$661$			8.69715i			0.338280i	0.985592	+	0.169140i	$0.0540990\pi$
$661$			8.69715i			0.338280i	−0.985592	+	0.169140i	$0.945901\pi$
$662$	−6.16974	+	4.52143i	−0.239794	+	0.175730i
$663$		0			0
$664$	−12.4760	−	36.8453i	−0.484164	−	1.42988i
$665$	−0.627737			−0.0243426
$666$		0			0
$667$			31.8715i			1.23407i
$668$	5.42765	−	17.1839i	0.210002	−	0.664864i
$669$		0			0
$670$	2.30654	+	3.14740i	0.0891093	+	0.121595i
$671$	−26.8073			−1.03488
$672$		0			0
$673$	18.0447			0.695571			0.347786	−	0.937574i	$-0.386934\pi$
$673$	18.0447			0.695571			0.347786	+	0.937574i	$0.386934\pi$
$674$	5.48060	+	7.47857i	0.211105	+	0.288064i
$675$		0			0
$676$	4.71003	−	14.9119i	0.181155	−	0.573535i
$677$			28.7781i			1.10603i	0.833170	+	0.553017i	$0.186524\pi$
$677$			28.7781i			1.10603i	−0.833170	+	0.553017i	$0.813476\pi$
$678$		0			0
$679$	−12.8789			−0.494246
$680$	2.58305	+	7.62851i	0.0990556	+	0.292540i
$681$		0			0
$682$	24.5292	−	17.9760i	0.939273	−	0.688337i
$683$		−	34.4431i		−	1.31793i	−0.752174	−	0.658965i	$-0.770995\pi$
$683$		−	34.4431i		−	1.31793i	0.752174	−	0.658965i	$-0.229005\pi$
$684$		0			0
$685$			8.88044i			0.339304i
$686$	−0.835949	−	1.14070i	−0.0319167	−	0.0435520i
$687$		0			0
$688$	−9.54268	+	13.5990i	−0.363811	+	0.518455i
$689$	6.13145			0.233590
$690$		0			0
$691$		−	41.5651i		−	1.58121i	−0.612325	−	0.790606i	$-0.709766\pi$
$691$		−	41.5651i		−	1.58121i	0.612325	−	0.790606i	$-0.290234\pi$
$692$	−18.2945	−	5.77846i	−0.695454	−	0.219664i
$693$		0			0
$694$	28.5133	−	20.8957i	1.08235	−	0.793189i
$695$	−4.87598			−0.184956
$696$		0			0
$697$	−37.1570			−1.40742
$698$	−31.0179	+	22.7312i	−1.17405	+	0.860388i
$699$		0			0
$700$	−2.88045	+	9.11947i	−0.108871	+	0.344684i
$701$			46.7804i			1.76687i	0.468553	+	0.883435i	$0.344775\pi$
$701$			46.7804i			1.76687i	−0.468553	+	0.883435i	$0.655225\pi$
$702$		0			0
$703$	5.92549			0.223484
$704$	23.7026	+	30.9874i	0.893325	+	1.16788i
$705$		0			0
$706$	−25.3183	−	34.5482i	−0.952868	−	1.30024i
$707$			2.22045i			0.0835087i
$708$		0			0
$709$			8.43643i			0.316837i	0.987372	+	0.158418i	$0.0506395\pi$
$709$			8.43643i			0.316837i	−0.987372	+	0.158418i	$0.949360\pi$
$710$	−2.51692	+	1.84450i	−0.0944582	+	0.0692227i
$711$		0			0
$712$	−21.3362	+	7.22455i	−0.799608	+	0.270752i
$713$	18.0599			0.676347
$714$		0			0
$715$			10.3943i			0.388727i
$716$	14.6711	+	4.63398i	0.548286	+	0.173180i
$717$		0			0
$718$	5.51052	+	7.51940i	0.205651	+	0.280622i
$719$	38.4425			1.43366			0.716831	−	0.697247i	$-0.245592\pi$
$719$	38.4425			1.43366			0.716831	+	0.697247i	$0.245592\pi$
$720$		0			0
$721$	11.0971			0.413278
$722$	−14.3735	−	19.6134i	−0.534926	−	0.729935i
$723$		0			0
$724$	29.0844	+	9.18652i	1.08091	+	0.341414i
$725$			37.2108i			1.38197i
$726$		0			0
$727$	−17.5484			−0.650834			−0.325417	−	0.945571i	$-0.605505\pi$
$727$	−17.5484			−0.650834			−0.325417	+	0.945571i	$0.605505\pi$
$728$	4.13903	+	12.2238i	0.153403	+	0.453043i
$729$		0			0
$730$	6.42624	−	4.70941i	0.237846	−	0.174303i
$731$			25.3169i			0.936379i
$732$		0			0
$733$			38.8272i			1.43412i	0.697013	+	0.717058i	$0.254512\pi$
$733$			38.8272i			1.43412i	−0.697013	+	0.717058i	$0.745488\pi$
$734$	5.59048	+	7.62851i	0.206348	+	0.281574i
$735$		0			0
$736$	0.476021	+	23.1636i	0.0175464	+	0.853822i
$737$	28.8044			1.06102
$738$		0			0
$739$			13.9066i			0.511562i	0.966735	+	0.255781i	$0.0823326\pi$
$739$			13.9066i			0.511562i	−0.966735	+	0.255781i	$0.917667\pi$
$740$	−1.24081	+	3.92840i	−0.0456132	+	0.144411i
$741$		0			0
$742$	−1.53286	+	1.12334i	−0.0562732	+	0.0412392i
$743$	−40.2300			−1.47590			−0.737948	−	0.674858i	$-0.764205\pi$
$743$	−40.2300			−1.47590			−0.737948	+	0.674858i	$0.764205\pi$
$744$		0			0
$745$	3.10936			0.113918
$746$	−19.5351	+	14.3161i	−0.715231	+	0.524150i
$747$		0			0
$748$	56.6921	+	17.9066i	2.07287	+	0.654730i
$749$			3.12334i			0.114124i
$750$		0			0
$751$	16.9957			0.620181			0.310091	−	0.950707i	$-0.399641\pi$
$751$	16.9957			0.620181			0.310091	+	0.950707i	$0.399641\pi$
$752$	−21.8970	−	15.3656i	−0.798502	−	0.560326i
$753$		0			0
$754$	29.6817	+	40.5023i	1.08094	+	1.47501i
$755$			1.25547i			0.0456914i
$756$		0			0
$757$			9.43212i			0.342816i	0.985200	+	0.171408i	$0.0548316\pi$
$757$			9.43212i			0.342816i	−0.985200	+	0.171408i	$0.945168\pi$
$758$	−19.0604	+	13.9682i	−0.692304	+	0.507348i
$759$		0			0
$760$	−1.68172	+	0.569438i	−0.0610023	+	0.0206557i
$761$	9.41098			0.341148			0.170574	−	0.985345i	$-0.445438\pi$
$761$	9.41098			0.341148			0.170574	+	0.985345i	$0.445438\pi$
$762$		0			0
$763$			10.6876i			0.386917i
$764$	−2.84527	+	9.00811i	−0.102938	+	0.325902i
$765$		0			0
$766$	−8.30945	−	11.3387i	−0.300233	−	0.409684i
$767$	−18.2512			−0.659011
$768$		0			0
$769$	27.6950			0.998708			0.499354	−	0.866398i	$-0.333571\pi$
$769$	27.6950			0.998708			0.499354	+	0.866398i	$0.333571\pi$
$770$	−1.90435	−	2.59859i	−0.0686280	−	0.0936466i
$771$		0			0
$772$	−13.4559	+	42.6013i	−0.484289	+	1.53325i
$773$		−	33.8993i		−	1.21927i	−0.792682	−	0.609636i	$-0.791316\pi$
$773$		−	33.8993i		−	1.21927i	0.792682	−	0.609636i	$-0.208684\pi$
$774$		0			0
$775$	21.0854			0.757409
$776$	−34.5027	+	11.6828i	−1.23858	+	0.419388i
$777$		0			0
$778$	−22.0022	+	16.1241i	−0.788818	+	0.578078i
$779$		−	8.19130i		−	0.293484i
$780$		0			0
$781$			23.0343i			0.824234i
$782$	20.8700	+	28.4783i	0.746310	+	1.01838i
$783$		0			0
$784$	−3.27428	−	2.29763i	−0.116938	−	0.0820583i
$785$	−10.8073			−0.385729
$786$		0			0
$787$		−	31.2001i		−	1.11216i	−0.831128	−	0.556082i	$-0.812304\pi$
$787$		−	31.2001i		−	1.11216i	0.831128	−	0.556082i	$-0.187696\pi$
$788$	−2.92763	−	0.924711i	−0.104292	−	0.0329415i
$789$		0			0
$790$	8.62774	−	6.32275i	0.306961	−	0.224953i
$791$	12.0599			0.428799
$792$		0			0
$793$	−25.0819			−0.890686
$794$	26.7399	−	19.5960i	0.948962	−	0.695437i
$795$		0			0
$796$	8.84751	−	28.0111i	0.313592	−	0.992828i
$797$		−	32.2848i		−	1.14359i	−0.820398	−	0.571793i	$-0.806248\pi$
$797$		−	32.2848i		−	1.14359i	0.820398	−	0.571793i	$-0.193752\pi$
$798$		0			0
$799$	−40.7652			−1.44217
$800$	0.555767	+	27.0441i	0.0196493	+	0.956155i
$801$		0			0
$802$	−13.3776	−	18.2545i	−0.472380	−	0.644588i
$803$		−	58.8118i		−	2.07542i
$804$		0			0
$805$		−	1.91323i		−	0.0674326i
$806$	22.9505	−	16.8190i	0.808396	−	0.592425i
$807$		0			0
$808$	2.01423	+	5.94862i	0.0708605	+	0.209272i
$809$	−8.49629			−0.298714			−0.149357	−	0.988783i	$-0.547720\pi$
$809$	−8.49629			−0.298714			−0.149357	+	0.988783i	$0.547720\pi$
$810$		0			0
$811$		−	12.3826i		−	0.434812i	−0.976081	−	0.217406i	$-0.930240\pi$
$811$		−	12.3826i		−	0.434812i	0.976081	−	0.217406i	$-0.0697596\pi$
$812$	−14.8409	−	4.68759i	−0.520812	−	0.164502i
$813$		0			0
$814$	17.9760	+	24.5292i	0.630058	+	0.859749i
$815$	5.62342			0.196980
$816$		0			0
$817$	−5.58114			−0.195259
$818$	−13.0128	−	17.7566i	−0.454981	−	0.620846i
$819$		0			0
$820$	5.43056	+	1.71528i	0.189643	+	0.0599002i
$821$			21.8999i			0.764313i	0.924098	+	0.382156i	$0.124818\pi$
$821$			21.8999i			0.764313i	−0.924098	+	0.382156i	$0.875182\pi$
$822$		0			0
$823$	−1.88321			−0.0656446			−0.0328223	−	0.999461i	$-0.510450\pi$
$823$	−1.88321			−0.0656446			−0.0328223	+	0.999461i	$0.510450\pi$
$824$	29.7293	−	10.0665i	1.03567	−	0.350683i
$825$		0			0
$826$	4.56279	−	3.34379i	0.158760	−	0.116345i
$827$		−	32.8051i		−	1.14074i	−0.821387	−	0.570372i	$-0.806799\pi$
$827$		−	32.8051i		−	1.14074i	0.821387	−	0.570372i	$-0.193201\pi$
$828$		0			0
$829$			9.63143i			0.334513i	0.985913	+	0.167257i	$0.0534909\pi$
$829$			9.63143i			0.334513i	−0.985913	+	0.167257i	$0.946509\pi$
$830$	5.37071	+	7.32862i	0.186420	+	0.254380i
$831$		0			0
$832$	22.1771	+	28.9930i	0.768851	+	1.00515i
$833$	−6.09565			−0.211202
$834$		0			0
$835$			4.20907i			0.145661i
$836$	−3.94753	+	12.4978i	−0.136528	+	0.432247i
$837$		0			0
$838$	−1.49706	+	1.09711i	−0.0517152	+	0.0378990i
$839$	48.0481			1.65880			0.829402	−	0.558652i	$-0.188681\pi$
$839$	48.0481			1.65880			0.829402	+	0.558652i	$0.188681\pi$
$840$		0			0
$841$	−31.5561			−1.08814
$842$	−4.18242	+	3.06504i	−0.144136	+	0.105628i
$843$		0			0
$844$	−43.5604	−	13.7589i	−1.49941	−	0.473600i
$845$			3.65257i			0.125652i
$846$		0			0
$847$	−12.7818			−0.439187
$848$	−3.08754	+	4.39996i	−0.106027	+	0.151095i
$849$		0			0
$850$	24.3663	+	33.2491i	0.835757	+	1.14044i
$851$			18.0599i			0.619084i
$852$		0			0
$853$			1.44013i			0.0493090i	0.999696	+	0.0246545i	$0.00784856\pi$
$853$			1.44013i			0.0493090i	−0.999696	+	0.0246545i	$0.992151\pi$
$854$	6.27048	−	4.59526i	0.214572	−	0.157247i
$855$		0			0
$856$	2.83327	+	8.36748i	0.0968393	+	0.285995i
$857$	−34.9775			−1.19481			−0.597404	−	0.801941i	$-0.703801\pi$
$857$	−34.9775			−1.19481			−0.597404	+	0.801941i	$0.703801\pi$
$858$		0			0
$859$			6.45024i			0.220079i	0.993927	+	0.110040i	$0.0350978\pi$
$859$			6.45024i			0.220079i	−0.993927	+	0.110040i	$0.964902\pi$
$860$	1.16871	−	3.70011i	0.0398525	−	0.126173i
$861$		0			0
$862$	16.7989	+	22.9231i	0.572174	+	0.780762i
$863$	34.4037			1.17112			0.585559	−	0.810630i	$-0.300875\pi$
$863$	34.4037			1.17112			0.585559	+	0.810630i	$0.300875\pi$
$864$		0			0
$865$	4.48112			0.152363
$866$	−7.26238	−	9.90991i	−0.246786	−	0.336752i
$867$		0			0
$868$	−2.65621	+	8.40952i	−0.0901575	+	0.285438i
$869$		−	78.9594i		−	2.67852i
$870$		0			0
$871$	26.9505			0.913182
$872$	9.69501	+	28.6322i	0.328315	+	0.969609i
$873$		0			0
$874$	−6.27807	+	4.60082i	−0.212359	+	0.155625i
$875$		−	4.56944i		−	0.154475i
$876$		0			0
$877$		−	40.3826i		−	1.36362i	−0.731528	−	0.681812i	$-0.761192\pi$
$877$		−	40.3826i		−	1.36362i	0.731528	−	0.681812i	$-0.238808\pi$
$878$		0			0
$879$		0			0
$880$	−7.45903	−	5.23416i	−0.251444	−	0.176444i
$881$	−15.8926			−0.535435			−0.267718	−	0.963497i	$-0.586269\pi$
$881$	−15.8926			−0.535435			−0.267718	+	0.963497i	$0.586269\pi$
$882$		0			0
$883$		−	25.3113i		−	0.851792i	−0.904772	−	0.425896i	$-0.859959\pi$
$883$		−	25.3113i		−	0.851792i	0.904772	−	0.425896i	$-0.140041\pi$
$884$	53.0433	+	16.7541i	1.78404	+	0.563501i
$885$		0			0
$886$	5.21312	−	3.82038i	0.175138	−	0.128348i
$887$	−19.6352			−0.659284			−0.329642	−	0.944106i	$-0.606928\pi$
$887$	−19.6352			−0.659284			−0.329642	+	0.944106i	$0.606928\pi$
$888$		0			0
$889$	18.8789			0.633178
$890$	4.24382	−	3.11004i	0.142253	−	0.104249i
$891$		0			0
$892$	−12.9103	+	40.8738i	−0.432268	+	1.36856i
$893$		−	8.98674i		−	0.300730i
$894$		0			0
$895$	−3.59359			−0.120120
$896$	−10.8561	−	3.18520i	−0.362676	−	0.106410i
$897$		0			0
$898$	−3.29376	−	4.49452i	−0.109914	−	0.149984i
$899$			34.3139i			1.14443i
$900$		0			0
$901$			8.19130i			0.272892i
$902$	33.9088	−	24.8497i	1.12904	−	0.827406i
$903$		0			0
$904$	32.3085	−	10.9398i	1.07457	−	0.363853i
$905$	−7.12402			−0.236811
$906$		0			0
$907$		−	4.84241i		−	0.160790i	−0.996763	−	0.0803948i	$-0.974382\pi$
$907$		−	4.84241i		−	0.160790i	0.996763	−	0.0803948i	$-0.0256181\pi$
$908$	55.9111	+	17.6599i	1.85547	+	0.586064i
$909$		0			0
$910$	−1.78178	−	2.43134i	−0.0590655	−	0.0805981i
$911$	18.9176			0.626768			0.313384	−	0.949626i	$-0.398537\pi$
$911$	18.9176			0.626768			0.313384	+	0.949626i	$0.398537\pi$
$912$		0			0
$913$	67.0702			2.21970
$914$	−33.4552	−	45.6515i	−1.10660	−	1.51002i
$915$		0			0
$916$	−42.9245	−	13.5580i	−1.41827	−	0.447969i
$917$		−	4.93428i		−	0.162944i
$918$		0			0
$919$	−9.11228			−0.300586			−0.150293	−	0.988641i	$-0.548022\pi$
$919$	−9.11228			−0.300586			−0.150293	+	0.988641i	$0.548022\pi$
$920$	−1.73555	−	5.12558i	−0.0572193	−	0.168985i
$921$		0			0
$922$	39.4716	−	28.9264i	1.29993	−	0.952639i
$923$			21.5518i			0.709387i
$924$		0			0
$925$			21.0854i			0.693282i
$926$	−0.159919	−	0.218217i	−0.00525525	−	0.00717107i
$927$		0			0
$928$	−44.0111	+	0.904445i	−1.44474	+	0.0296899i
$929$	−32.7294			−1.07382			−0.536909	−	0.843640i	$-0.680408\pi$
$929$	−32.7294			−1.07382			−0.536909	+	0.843640i	$0.680408\pi$
$930$		0			0
$931$		−	1.34379i		−	0.0440411i
$932$	−0.414190	+	1.31132i	−0.0135672	+	0.0429537i
$933$		0			0
$934$	−5.13067	+	3.75996i	−0.167881	+	0.123030i
$935$	−13.8863			−0.454131
$936$		0			0
$937$	−21.5066			−0.702591			−0.351295	−	0.936265i	$-0.614259\pi$
$937$	−21.5066			−0.702591			−0.351295	+	0.936265i	$0.614259\pi$
$938$	−6.73762	+	4.93760i	−0.219991	+	0.161218i
$939$		0			0
$940$	5.95791	+	1.88185i	0.194326	+	0.0613791i
$941$			1.85115i			0.0603456i	0.999545	+	0.0301728i	$0.00960577\pi$
$941$			1.85115i			0.0603456i	−0.999545	+	0.0301728i	$0.990394\pi$
$942$		0			0
$943$	24.9657			0.812994
$944$	9.19053	−	13.0971i	0.299126	−	0.426275i
$945$		0			0
$946$	−16.9314	−	23.1038i	−0.550486	−	0.751168i
$947$		−	45.3353i		−	1.47320i	−0.676329	−	0.736600i	$-0.736430\pi$
$947$		−	45.3353i		−	1.47320i	0.676329	−	0.736600i	$-0.263570\pi$
$948$		0			0
$949$		−	55.0266i		−	1.78624i
$950$	−7.32981	+	5.37158i	−0.237811	+	0.174277i
$951$		0			0
$952$	−16.3303	+	5.52954i	−0.529269	+	0.179213i
$953$	−40.5768			−1.31441			−0.657206	−	0.753711i	$-0.728262\pi$
$953$	−40.5768			−1.31441			−0.657206	+	0.753711i	$0.728262\pi$
$954$		0			0
$955$		−	2.20647i		−	0.0713997i
$956$	−5.78246	+	18.3072i	−0.187018	+	0.592098i
$957$		0			0
$958$	−18.6008	−	25.3818i	−0.600965	−	0.820050i
$959$	−19.0103			−0.613876
$960$		0			0
$961$	−11.5561			−0.372779
$962$	16.8190	+	22.9505i	0.542268	+	0.739953i
$963$		0			0
$964$	−0.298953	+	0.946483i	−0.00962864	+	0.0304842i
$965$		−	10.4349i		−	0.335911i
$966$		0			0
$967$	15.8715			0.510392			0.255196	−	0.966889i	$-0.417860\pi$
$967$	15.8715			0.510392			0.255196	+	0.966889i	$0.417860\pi$
$968$	−34.2426	+	11.5947i	−1.10060	+	0.372668i
$969$		0			0
$970$	6.86268	−	5.02925i	0.220347	−	0.161479i
$971$		−	14.6876i		−	0.471347i	−0.971832	−	0.235674i	$-0.924270\pi$
$971$		−	14.6876i		−	0.471347i	0.971832	−	0.235674i	$-0.0757296\pi$
$972$		0			0
$973$		−	10.4380i		−	0.334627i
$974$	1.56201	+	2.13145i	0.0500501	+	0.0682961i
$975$		0			0
$976$	12.6302	−	17.9989i	0.404284	−	0.576131i
$977$	21.2437			0.679647			0.339824	−	0.940489i	$-0.389633\pi$
$977$	21.2437			0.679647			0.339824	+	0.940489i	$0.389633\pi$
$978$		0			0
$979$		−	38.8387i		−	1.24129i
$980$	0.890891	+	0.281394i	0.0284585	+	0.00898881i
$981$		0			0
$982$	20.1189	−	14.7440i	0.642021	−	0.470499i
$983$	−11.8265			−0.377206			−0.188603	−	0.982053i	$-0.560396\pi$
$983$	−11.8265			−0.377206			−0.188603	+	0.982053i	$0.560396\pi$
$984$		0			0
$985$	0.717101			0.0228487
$986$	−54.1090	+	39.6532i	−1.72318	+	1.26282i
$987$		0			0
$988$	−3.69346	+	11.6935i	−0.117505	+	0.372019i
$989$		−	17.0103i		−	0.540897i
$990$		0			0
$991$	28.9387			0.919269			0.459635	−	0.888108i	$-0.347980\pi$
$991$	28.9387			0.919269			0.459635	+	0.888108i	$0.347980\pi$
$992$	0.512500	+	24.9387i	0.0162719	+	0.791806i
$993$		0			0
$994$	−3.94851	−	5.38795i	−0.125239	−	0.170896i
$995$			6.86112i			0.217512i
$996$		0			0
$997$			56.0548i			1.77527i	0.460546	+	0.887636i	$0.347654\pi$
$997$			56.0548i			1.77527i	−0.460546	+	0.887636i	$0.652346\pi$
$998$	24.6224	−	18.0443i	0.779408	−	0.571181i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.c.f.253.3		8
3.2	odd	2		168.2.c.b.85.6	yes	8
4.3	odd	2		2016.2.c.e.1009.4		8
8.3	odd	2		2016.2.c.e.1009.5		8
8.5	even	2	inner	504.2.c.f.253.4		8
12.11	even	2		672.2.c.b.337.2		8
21.20	even	2		1176.2.c.c.589.6		8
24.5	odd	2		168.2.c.b.85.5	✓	8
24.11	even	2		672.2.c.b.337.7		8
48.5	odd	4		5376.2.a.bp.1.3		4
48.11	even	4		5376.2.a.bl.1.3		4
48.29	odd	4		5376.2.a.bm.1.2		4
48.35	even	4		5376.2.a.bq.1.2		4
84.83	odd	2		4704.2.c.c.2353.7		8
168.83	odd	2		4704.2.c.c.2353.2		8
168.125	even	2		1176.2.c.c.589.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.c.b.85.5	✓	8	24.5	odd	2
168.2.c.b.85.6	yes	8	3.2	odd	2
504.2.c.f.253.3		8	1.1	even	1	trivial
504.2.c.f.253.4		8	8.5	even	2	inner
672.2.c.b.337.2		8	12.11	even	2
672.2.c.b.337.7		8	24.11	even	2
1176.2.c.c.589.5		8	168.125	even	2
1176.2.c.c.589.6		8	21.20	even	2
2016.2.c.e.1009.4		8	4.3	odd	2
2016.2.c.e.1009.5		8	8.3	odd	2
4704.2.c.c.2353.2		8	168.83	odd	2
4704.2.c.c.2353.7		8	84.83	odd	2
5376.2.a.bl.1.3		4	48.11	even	4
5376.2.a.bm.1.2		4	48.29	odd	4
5376.2.a.bp.1.3		4	48.5	odd	4
5376.2.a.bq.1.2		4	48.35	even	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.835949 - 1.14070i) q^{2} +(-0.602380 + 1.90713i) q^{4} -0.467138i q^{5} +1.00000 q^{7} +(2.67901 - 0.907128i) q^{8} +O(q^{10})\)	\(q+(-0.835949 - 1.14070i) q^{2} +(-0.602380 + 1.90713i) q^{4} -0.467138i q^{5} +1.00000 q^{7} +(2.67901 - 0.907128i) q^{8} +(-0.532862 + 0.390503i) q^{10} +4.87666i q^{11} +4.56279i q^{13} +(-0.835949 - 1.14070i) q^{14} +(-3.27428 - 2.29763i) q^{16} -6.09565 q^{17} -1.34379i q^{19} +(0.890891 + 0.281394i) q^{20} +(5.56279 - 4.07663i) q^{22} +4.09565 q^{23} +4.78178 q^{25} +(5.20476 - 3.81426i) q^{26} +(-0.602380 + 1.90713i) q^{28} +7.78178i q^{29} +4.40952 q^{31} +(0.116226 + 5.65566i) q^{32} +(5.09565 + 6.95329i) q^{34} -0.467138i q^{35} +4.40952i q^{37} +(-1.53286 + 1.12334i) q^{38} +(-0.423754 - 1.25147i) q^{40} +6.09565 q^{41} -4.15327i q^{43} +(-9.30041 - 2.93760i) q^{44} +(-3.42375 - 4.67190i) q^{46} +6.68759 q^{47} +1.00000 q^{49} +(-3.99732 - 5.45457i) q^{50} +(-8.70182 - 2.74853i) q^{52} -1.34379i q^{53} +2.27807 q^{55} +(2.67901 - 0.907128i) q^{56} +(8.87666 - 6.50517i) q^{58} +4.00000i q^{59} +5.49706i q^{61} +(-3.68613 - 5.02993i) q^{62} +(6.35424 - 4.86042i) q^{64} +2.13145 q^{65} -5.90658i q^{67} +(3.67190 - 11.6252i) q^{68} +(-0.532862 + 0.390503i) q^{70} +4.72339 q^{71} -12.0599 q^{73} +(5.02993 - 3.68613i) q^{74} +(2.56279 + 0.809475i) q^{76} +4.87666i q^{77} -16.1913 q^{79} +(-1.07331 + 1.52954i) q^{80} +(-5.09565 - 6.95329i) q^{82} -13.7533i q^{83} +2.84751i q^{85} +(-4.73762 + 3.47192i) q^{86} +(4.42375 + 13.0646i) q^{88} -7.96420 q^{89} +4.56279i q^{91} +(-2.46714 + 7.81093i) q^{92} +(-5.59048 - 7.62851i) q^{94} -0.627737 q^{95} -12.8789 q^{97} +(-0.835949 - 1.14070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 8 q^{7} + 6 q^{8}+O(q^{10}) \) 8 * q + 2 * q^4 + 8 * q^7 + 6 * q^8	\( 8 q + 2 q^{4} + 8 q^{7} + 6 q^{8} - 4 q^{10} - 6 q^{16} - 4 q^{17} - 24 q^{20} - 12 q^{23} - 24 q^{25} + 28 q^{26} + 2 q^{28} + 8 q^{31} + 30 q^{32} - 4 q^{34} - 12 q^{38} + 28 q^{40} + 4 q^{41} - 16 q^{44} + 4 q^{46} + 8 q^{49} + 20 q^{50} - 12 q^{52} - 8 q^{55} + 6 q^{56} + 44 q^{58} - 12 q^{62} + 26 q^{64} + 16 q^{65} + 16 q^{68} - 4 q^{70} + 28 q^{71} - 8 q^{73} - 4 q^{74} - 24 q^{76} - 40 q^{79} + 4 q^{80} + 4 q^{82} - 24 q^{86} + 4 q^{88} - 20 q^{89} - 20 q^{92} - 72 q^{94} - 40 q^{95} + 40 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 + 8 * q^7 + 6 * q^8 - 4 * q^10 - 6 * q^16 - 4 * q^17 - 24 * q^20 - 12 * q^23 - 24 * q^25 + 28 * q^26 + 2 * q^28 + 8 * q^31 + 30 * q^32 - 4 * q^34 - 12 * q^38 + 28 * q^40 + 4 * q^41 - 16 * q^44 + 4 * q^46 + 8 * q^49 + 20 * q^50 - 12 * q^52 - 8 * q^55 + 6 * q^56 + 44 * q^58 - 12 * q^62 + 26 * q^64 + 16 * q^65 + 16 * q^68 - 4 * q^70 + 28 * q^71 - 8 * q^73 - 4 * q^74 - 24 * q^76 - 40 * q^79 + 4 * q^80 + 4 * q^82 - 24 * q^86 + 4 * q^88 - 20 * q^89 - 20 * q^92 - 72 * q^94 - 40 * q^95 + 40 * q^97

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