LMFDB - Embedded newform 1008.2.v.e.323.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(323,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1008.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.v (of order $4$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.11
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.153718 + 1.40583i) q^{2} +(-1.95274 + 0.432203i) q^{4} +(-0.0893433 - 0.0893433i) q^{5} +1.00000 q^{7} +(-0.907777 - 2.67879i) q^{8} +O(q^{10})$	\(q+(0.153718 + 1.40583i) q^{2} +(-1.95274 + 0.432203i) q^{4} +(-0.0893433 - 0.0893433i) q^{5} +1.00000 q^{7} +(-0.907777 - 2.67879i) q^{8} +(0.111868 - 0.139335i) q^{10} +(2.42480 - 2.42480i) q^{11} +(-3.86569 - 3.86569i) q^{13} +(0.153718 + 1.40583i) q^{14} +(3.62640 - 1.68796i) q^{16} +0.794810i q^{17} +(-2.65233 + 2.65233i) q^{19} +(0.213079 + 0.135850i) q^{20} +(3.78161 + 3.03614i) q^{22} -3.92175i q^{23} -4.98404i q^{25} +(4.84029 - 6.02874i) q^{26} +(-1.95274 + 0.432203i) q^{28} +(7.47818 - 7.47818i) q^{29} -5.55554i q^{31} +(2.93044 + 4.83865i) q^{32} +(-1.11737 + 0.122176i) q^{34} +(-0.0893433 - 0.0893433i) q^{35} +(-6.35455 + 6.35455i) q^{37} +(-4.13644 - 3.32102i) q^{38} +(-0.158228 + 0.320436i) q^{40} +6.96091 q^{41} +(-1.25316 - 1.25316i) q^{43} +(-3.68701 + 5.78302i) q^{44} +(5.51333 - 0.602842i) q^{46} +6.48295 q^{47} +1.00000 q^{49} +(7.00673 - 0.766135i) q^{50} +(9.21946 + 5.87793i) q^{52} +(-0.620687 - 0.620687i) q^{53} -0.433280 q^{55} +(-0.907777 - 2.67879i) q^{56} +(11.6626 + 9.36355i) q^{58} +(-3.39065 + 3.39065i) q^{59} +(7.51460 + 7.51460i) q^{61} +(7.81017 - 0.853985i) q^{62} +(-6.35188 + 4.86350i) q^{64} +0.690747i q^{65} +(2.22915 - 2.22915i) q^{67} +(-0.343519 - 1.55206i) q^{68} +(0.111868 - 0.139335i) q^{70} -7.95182i q^{71} +12.9376i q^{73} +(-9.91025 - 7.95663i) q^{74} +(4.03296 - 6.32565i) q^{76} +(2.42480 - 2.42480i) q^{77} -10.1941i q^{79} +(-0.474803 - 0.173186i) q^{80} +(1.07002 + 9.78589i) q^{82} +(-11.2820 - 11.2820i) q^{83} +(0.0710109 - 0.0710109i) q^{85} +(1.56910 - 1.95436i) q^{86} +(-8.69673 - 4.29437i) q^{88} +5.52785 q^{89} +(-3.86569 - 3.86569i) q^{91} +(1.69499 + 7.65816i) q^{92} +(0.996544 + 9.11395i) q^{94} +0.473935 q^{95} -4.33616 q^{97} +(0.153718 + 1.40583i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{7}+O(q^{10}) $ 40 * q + 40 * q^7	$ 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) $ 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.153718	+	1.40583i	0.108695	+	0.994075i
$2$	0.153718	+	1.40583i	0.108695	+	0.994075i
$3$		0			0
$3$		0			0
$4$	−1.95274	+	0.432203i	−0.976371	+	0.216102i
$5$	−0.0893433	−	0.0893433i	−0.0399555	−	0.0399555i	0.686847	−	0.726802i	$-0.258994\pi$
$5$	−0.0893433	−	0.0893433i	−0.0399555	−	0.0399555i	−0.726802	+	0.686847i	$0.758994\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−0.907777	−	2.67879i	−0.320948	−	0.947097i
$9$		0			0
$10$	0.111868	−	0.139335i	0.0353758	−	0.0440618i
$11$	2.42480	−	2.42480i	0.731106	−	0.731106i	−0.239733	−	0.970839i	$-0.577060\pi$
$11$	2.42480	−	2.42480i	0.731106	−	0.731106i	0.970839	+	0.239733i	$0.0770600\pi$
$12$		0			0
$13$	−3.86569	−	3.86569i	−1.07215	−	1.07215i	−0.997186	−	0.0749629i	$-0.976116\pi$
$13$	−3.86569	−	3.86569i	−1.07215	−	1.07215i	−0.0749629	−	0.997186i	$-0.523884\pi$
$14$	0.153718	+	1.40583i	0.0410828	+	0.375725i
$15$		0			0
$16$	3.62640	−	1.68796i	0.906600	−	0.421991i
$17$			0.794810i			0.192770i	0.995344	+	0.0963848i	$0.0307280\pi$
$17$			0.794810i			0.192770i	−0.995344	+	0.0963848i	$0.969272\pi$
$18$		0			0
$19$	−2.65233	+	2.65233i	−0.608485	+	0.608485i	−0.942550	−	0.334065i	$-0.891580\pi$
$19$	−2.65233	+	2.65233i	−0.608485	+	0.608485i	0.334065	+	0.942550i	$0.391580\pi$
$20$	0.213079	+	0.135850i	0.0476459	+	0.0303770i
$21$		0			0
$22$	3.78161	+	3.03614i	0.806241	+	0.647306i
$23$		−	3.92175i		−	0.817741i	−0.912592	−	0.408871i	$-0.865923\pi$
$23$		−	3.92175i		−	0.817741i	0.912592	−	0.408871i	$-0.134077\pi$
$24$		0			0
$25$		−	4.98404i		−	0.996807i
$26$	4.84029	−	6.02874i	0.949260	−	1.18233i
$27$		0			0
$28$	−1.95274	+	0.432203i	−0.369033	+	0.0816788i
$29$	7.47818	−	7.47818i	1.38866	−	1.38866i	0.560525	−	0.828138i	$-0.310599\pi$
$29$	7.47818	−	7.47818i	1.38866	−	1.38866i	0.828138	−	0.560525i	$-0.189401\pi$
$30$		0			0
$31$		−	5.55554i		−	0.997804i	−0.866658	−	0.498902i	$-0.833737\pi$
$31$		−	5.55554i		−	0.997804i	0.866658	−	0.498902i	$-0.166263\pi$
$32$	2.93044	+	4.83865i	0.518033	+	0.855360i
$33$		0			0
$34$	−1.11737	+	0.122176i	−0.191628	+	0.0209531i
$35$	−0.0893433	−	0.0893433i	−0.0151018	−	0.0151018i
$36$		0			0
$37$	−6.35455	+	6.35455i	−1.04468	+	1.04468i	−0.0457270	+	0.998954i	$0.514560\pi$
$37$	−6.35455	+	6.35455i	−1.04468	+	1.04468i	−0.998954	+	0.0457270i	$0.985440\pi$
$38$	−4.13644	−	3.32102i	−0.671019	−	0.538741i
$39$		0			0
$40$	−0.158228	+	0.320436i	−0.0250181	+	0.0506654i
$41$	6.96091			1.08711			0.543556	−	0.839373i	$-0.317078\pi$
$41$	6.96091			1.08711			0.543556	+	0.839373i	$0.317078\pi$
$42$		0			0
$43$	−1.25316	−	1.25316i	−0.191105	−	0.191105i	0.605069	−	0.796173i	$-0.293146\pi$
$43$	−1.25316	−	1.25316i	−0.191105	−	0.191105i	−0.796173	+	0.605069i	$0.793146\pi$
$44$	−3.68701	+	5.78302i	−0.555837	+	0.871823i
$45$		0			0
$46$	5.51333	−	0.602842i	0.812896	−	0.0888843i
$47$	6.48295			0.945635			0.472818	−	0.881160i	$-0.343237\pi$
$47$	6.48295			0.945635			0.472818	+	0.881160i	$0.343237\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	7.00673	−	0.766135i	0.990901	−	0.108348i
$51$		0			0
$52$	9.21946	+	5.87793i	1.27851	+	0.815122i
$53$	−0.620687	−	0.620687i	−0.0852579	−	0.0852579i	0.663192	−	0.748450i	$-0.269201\pi$
$53$	−0.620687	−	0.620687i	−0.0852579	−	0.0852579i	−0.748450	+	0.663192i	$0.769201\pi$
$54$		0			0
$55$	−0.433280			−0.0584234
$56$	−0.907777	−	2.67879i	−0.121307	−	0.357969i
$57$		0			0
$58$	11.6626	+	9.36355i	1.53138	+	1.22949i
$59$	−3.39065	+	3.39065i	−0.441425	+	0.441425i	−0.892491	−	0.451066i	$-0.851044\pi$
$59$	−3.39065	+	3.39065i	−0.441425	+	0.441425i	0.451066	+	0.892491i	$0.351044\pi$
$60$		0			0
$61$	7.51460	+	7.51460i	0.962146	+	0.962146i	0.999309	−	0.0371630i	$-0.0118321\pi$
$61$	7.51460	+	7.51460i	0.962146	+	0.962146i	−0.0371630	+	0.999309i	$0.511832\pi$
$62$	7.81017	−	0.853985i	0.991892	−	0.108456i
$63$		0			0
$64$	−6.35188	+	4.86350i	−0.793985	+	0.607937i
$65$			0.690747i			0.0856766i
$66$		0			0
$67$	2.22915	−	2.22915i	0.272334	−	0.272334i	−0.557705	−	0.830039i	$-0.688318\pi$
$67$	2.22915	−	2.22915i	0.272334	−	0.272334i	0.830039	+	0.557705i	$0.188318\pi$
$68$	−0.343519	−	1.55206i	−0.0416579	−	0.188215i
$69$		0			0
$70$	0.111868	−	0.139335i	0.0133708	−	0.0166538i
$71$		−	7.95182i		−	0.943707i	−0.881677	−	0.471853i	$-0.843585\pi$
$71$		−	7.95182i		−	0.943707i	0.881677	−	0.471853i	$-0.156415\pi$
$72$		0			0
$73$			12.9376i			1.51423i	0.653283	+	0.757114i	$0.273391\pi$
$73$			12.9376i			1.51423i	−0.653283	+	0.757114i	$0.726609\pi$
$74$	−9.91025	−	7.95663i	−1.15204	−	0.924940i
$75$		0			0
$76$	4.03296	−	6.32565i	0.462613	−	0.725602i
$77$	2.42480	−	2.42480i	0.276332	−	0.276332i
$78$		0			0
$79$		−	10.1941i		−	1.14693i	−0.819230	−	0.573465i	$-0.805599\pi$
$79$		−	10.1941i		−	1.14693i	0.819230	−	0.573465i	$-0.194401\pi$
$80$	−0.474803	−	0.173186i	−0.0530845	−	0.0193628i
$81$		0			0
$82$	1.07002	+	9.78589i	0.118163	+	1.08067i
$83$	−11.2820	−	11.2820i	−1.23836	−	1.23836i	−0.960670	−	0.277694i	$-0.910430\pi$
$83$	−11.2820	−	11.2820i	−1.23836	−	1.23836i	−0.277694	−	0.960670i	$-0.589570\pi$
$84$		0			0
$85$	0.0710109	−	0.0710109i	0.00770221	−	0.00770221i
$86$	1.56910	−	1.95436i	0.169200	−	0.210744i
$87$		0			0
$88$	−8.69673	−	4.29437i	−0.927074	−	0.457781i
$89$	5.52785			0.585951			0.292976	−	0.956120i	$-0.405355\pi$
$89$	5.52785			0.585951			0.292976	+	0.956120i	$0.405355\pi$
$90$		0			0
$91$	−3.86569	−	3.86569i	−0.405234	−	0.405234i
$92$	1.69499	+	7.65816i	0.176715	+	0.798419i
$93$		0			0
$94$	0.996544	+	9.11395i	0.102786	+	0.940032i
$95$	0.473935			0.0486247
$96$		0			0
$97$	−4.33616			−0.440270			−0.220135	−	0.975469i	$-0.570650\pi$
$97$	−4.33616			−0.440270			−0.220135	+	0.975469i	$0.570650\pi$
$98$	0.153718	+	1.40583i	0.0155278	+	0.142011i
$99$		0			0
$100$	2.15412	+	9.73253i	0.215412	+	0.973253i
$101$	9.66216	+	9.66216i	0.961421	+	0.961421i	0.999283	−	0.0378620i	$-0.0120547\pi$
$101$	9.66216	+	9.66216i	0.961421	+	0.961421i	−0.0378620	+	0.999283i	$0.512055\pi$
$102$		0			0
$103$	16.4000			1.61594			0.807969	−	0.589225i	$-0.200567\pi$
$103$	16.4000			1.61594			0.807969	+	0.589225i	$0.200567\pi$
$104$	−6.84620	+	13.8646i	−0.671325	+	1.35953i
$105$		0			0
$106$	0.777173	−	0.967994i	0.0754857	−	0.0940199i
$107$	5.48912	−	5.48912i	0.530653	−	0.530653i	−0.390114	−	0.920767i	$-0.627564\pi$
$107$	5.48912	−	5.48912i	0.530653	−	0.530653i	0.920767	+	0.390114i	$0.127564\pi$
$108$		0			0
$109$	−14.6355	−	14.6355i	−1.40183	−	1.40183i	−0.794301	−	0.607524i	$-0.792163\pi$
$109$	−14.6355	−	14.6355i	−1.40183	−	1.40183i	−0.607524	−	0.794301i	$-0.707837\pi$
$110$	−0.0666028	−	0.609119i	−0.00635032	−	0.0580773i
$111$		0			0
$112$	3.62640	−	1.68796i	0.342663	−	0.159498i
$113$			8.28264i			0.779165i	0.920992	+	0.389582i	$0.127381\pi$
$113$			8.28264i			0.779165i	−0.920992	+	0.389582i	$0.872619\pi$
$114$		0			0
$115$	−0.350382	+	0.350382i	−0.0326733	+	0.0326733i
$116$	−11.3709	+	17.8350i	−1.05576	+	1.65594i
$117$		0			0
$118$	−5.28790	−	4.24549i	−0.486790	−	0.390829i
$119$			0.794810i			0.0728601i
$120$		0			0
$121$		−	0.759336i		−	0.0690305i
$122$	−9.40916	+	11.7194i	−0.851865	+	1.06103i
$123$		0			0
$124$	2.40112	+	10.8485i	0.215627	+	0.974227i
$125$	−0.892006	+	0.892006i	−0.0797835	+	0.0797835i
$126$		0			0
$127$		−	3.39522i		−	0.301277i	−0.988589	−	0.150638i	$-0.951867\pi$
$127$		−	3.39522i		−	0.301277i	0.988589	−	0.150638i	$-0.0481329\pi$
$128$	−7.81367	−	8.18209i	−0.690637	−	0.723201i
$129$		0			0
$130$	−0.971075	+	0.106180i	−0.0851690	+	0.00931260i
$131$	−8.73455	−	8.73455i	−0.763141	−	0.763141i	0.213748	−	0.976889i	$-0.431433\pi$
$131$	−8.73455	−	8.73455i	−0.763141	−	0.763141i	−0.976889	+	0.213748i	$0.931433\pi$
$132$		0			0
$133$	−2.65233	+	2.65233i	−0.229986	+	0.229986i
$134$	3.47648	+	2.79116i	0.300322	+	0.241119i
$135$		0			0
$136$	2.12913	−	0.721510i	0.182572	−	0.0618690i
$137$	−4.84889			−0.414269			−0.207134	−	0.978313i	$-0.566414\pi$
$137$	−4.84889			−0.414269			−0.207134	+	0.978313i	$0.566414\pi$
$138$		0			0
$139$	−2.19464	−	2.19464i	−0.186147	−	0.186147i	0.607881	−	0.794028i	$-0.292020\pi$
$139$	−2.19464	−	2.19464i	−0.186147	−	0.186147i	−0.794028	+	0.607881i	$0.792020\pi$
$140$	0.213079	+	0.135850i	0.0180084	+	0.0114814i
$141$		0			0
$142$	11.1789	−	1.22234i	0.938116	−	0.102576i
$143$	−18.7471			−1.56771
$144$		0			0
$145$	−1.33625			−0.110969
$146$	−18.1881	+	1.98873i	−1.50526	+	0.164589i
$147$		0			0
$148$	9.66233	−	15.1552i	0.794239	−	1.24575i
$149$	2.83836	+	2.83836i	0.232528	+	0.232528i	0.813747	−	0.581219i	$-0.197424\pi$
$149$	2.83836	+	2.83836i	0.232528	+	0.232528i	−0.581219	+	0.813747i	$0.697424\pi$
$150$		0			0
$151$	−18.9821			−1.54474			−0.772370	−	0.635172i	$-0.780929\pi$
$151$	−18.9821			−1.54474			−0.772370	+	0.635172i	$0.780929\pi$
$152$	9.51276	+	4.69732i	0.771587	+	0.381003i
$153$		0			0
$154$	3.78161	+	3.03614i	0.304731	+	0.244659i
$155$	−0.496350	+	0.496350i	−0.0398678	+	0.0398678i
$156$		0			0
$157$	−12.3221	−	12.3221i	−0.983412	−	0.983412i	0.0164522	−	0.999865i	$-0.494763\pi$
$157$	−12.3221	−	12.3221i	−0.983412	−	0.983412i	−0.999865	+	0.0164522i	$0.994763\pi$
$158$	14.3313	−	1.56702i	1.14013	−	0.124665i
$159$		0			0
$160$	0.170486	−	0.694116i	0.0134781	−	0.0548747i
$161$		−	3.92175i		−	0.309077i
$162$		0			0
$163$	−3.50400	+	3.50400i	−0.274454	+	0.274454i	−0.830890	−	0.556436i	$-0.812168\pi$
$163$	−3.50400	+	3.50400i	−0.274454	+	0.274454i	0.556436	+	0.830890i	$0.312168\pi$
$164$	−13.5929	+	3.00853i	−1.06142	+	0.234927i
$165$		0			0
$166$	14.1264	−	17.5949i	1.09642	−	1.36563i
$167$			17.4719i			1.35202i	0.736893	+	0.676009i	$0.236292\pi$
$167$			17.4719i			1.35202i	−0.736893	+	0.676009i	$0.763708\pi$
$168$		0			0
$169$			16.8871i			1.29901i
$170$	0.110745	+	0.0889140i	0.00849377	+	0.00681939i
$171$		0			0
$172$	2.98871	+	1.90547i	0.227887	+	0.145291i
$173$	−1.45528	+	1.45528i	−0.110643	+	0.110643i	−0.760261	−	0.649618i	$-0.774929\pi$
$173$	−1.45528	+	1.45528i	−0.110643	+	0.110643i	0.649618	+	0.760261i	$0.274929\pi$
$174$		0			0
$175$		−	4.98404i		−	0.376758i
$176$	4.70033	−	12.8863i	0.354301	−	0.971340i
$177$		0			0
$178$	0.849729	+	7.77125i	0.0636899	+	0.582480i
$179$	2.22288	+	2.22288i	0.166146	+	0.166146i	0.785283	−	0.619137i	$-0.212518\pi$
$179$	2.22288	+	2.22288i	0.166146	+	0.166146i	−0.619137	+	0.785283i	$0.712518\pi$
$180$		0			0
$181$	3.13227	−	3.13227i	0.232820	−	0.232820i	−0.581049	−	0.813869i	$-0.697358\pi$
$181$	3.13227	−	3.13227i	0.232820	−	0.232820i	0.813869	+	0.581049i	$0.197358\pi$
$182$	4.84029	−	6.02874i	0.358786	−	0.446880i
$183$		0			0
$184$	−10.5056	+	3.56008i	−0.774480	+	0.262452i
$185$	1.13547			0.0834816
$186$		0			0
$187$	1.92726	+	1.92726i	0.140935	+	0.140935i
$188$	−12.6595	+	2.80195i	−0.923291	+	0.204353i
$189$		0			0
$190$	0.0728522	+	0.666274i	0.00528526	+	0.0483366i
$191$	−3.61134			−0.261308			−0.130654	−	0.991428i	$-0.541708\pi$
$191$	−3.61134			−0.261308			−0.130654	+	0.991428i	$0.541708\pi$
$192$		0			0
$193$	−3.01689			−0.217160			−0.108580	−	0.994088i	$-0.534630\pi$
$193$	−3.01689			−0.217160			−0.108580	+	0.994088i	$0.534630\pi$
$194$	−0.666545	−	6.09592i	−0.0478551	−	0.437662i
$195$		0			0
$196$	−1.95274	+	0.432203i	−0.139482	+	0.0308717i
$197$	−0.282108	−	0.282108i	−0.0200994	−	0.0200994i	0.696986	−	0.717085i	$-0.254524\pi$
$197$	−0.282108	−	0.282108i	−0.0200994	−	0.0200994i	−0.717085	+	0.696986i	$0.754524\pi$
$198$		0			0
$199$	3.40015			0.241030			0.120515	−	0.992712i	$-0.461545\pi$
$199$	3.40015			0.241030			0.120515	+	0.992712i	$0.461545\pi$
$200$	−13.3512	+	4.52440i	−0.944073	+	0.319923i
$201$		0			0
$202$	−12.0982	+	15.0686i	−0.851223	+	1.06023i
$203$	7.47818	−	7.47818i	0.524865	−	0.524865i
$204$		0			0
$205$	−0.621911	−	0.621911i	−0.0434361	−	0.0434361i
$206$	2.52097	+	23.0556i	0.175644	+	1.60636i
$207$		0			0
$208$	−20.5437	−	7.49340i	−1.42445	−	0.519574i
$209$			12.8627i			0.889734i
$210$		0			0
$211$	6.04290	−	6.04290i	0.416010	−	0.416010i	−0.467816	−	0.883826i	$-0.654959\pi$
$211$	6.04290	−	6.04290i	0.416010	−	0.416010i	0.883826	+	0.467816i	$0.154959\pi$
$212$	1.48030	+	0.943778i	0.101668	+	0.0648190i
$213$		0			0
$214$	8.56057	+	6.87302i	0.585188	+	0.469830i
$215$			0.223922i			0.0152714i
$216$		0			0
$217$		−	5.55554i		−	0.377135i
$218$	18.3253	−	22.8248i	1.24115	−	1.54589i
$219$		0			0
$220$	0.846083	−	0.187265i	0.0570429	−	0.0126254i
$221$	3.07249	−	3.07249i	0.206678	−	0.206678i
$222$		0			0
$223$		−	22.2108i		−	1.48734i	−0.668545	−	0.743672i	$-0.733082\pi$
$223$		−	22.2108i		−	1.48734i	0.668545	−	0.743672i	$-0.266918\pi$
$224$	2.93044	+	4.83865i	0.195798	+	0.323296i
$225$		0			0
$226$	−11.6440	+	1.27319i	−0.774548	+	0.0846912i
$227$	−16.1859	−	16.1859i	−1.07430	−	1.07430i	−0.997009	−	0.0772896i	$-0.975373\pi$
$227$	−16.1859	−	16.1859i	−1.07430	−	1.07430i	−0.0772896	−	0.997009i	$-0.524627\pi$
$228$		0			0
$229$	−7.75579	+	7.75579i	−0.512517	+	0.512517i	−0.915297	−	0.402780i	$-0.868044\pi$
$229$	−7.75579	+	7.75579i	−0.512517	+	0.512517i	0.402780	+	0.915297i	$0.368044\pi$
$230$	−0.546439	−	0.438719i	−0.0360311	−	0.0289283i
$231$		0			0
$232$	−26.8210	−	13.2440i	−1.76089	−	0.869510i
$233$	18.7060			1.22547			0.612734	−	0.790289i	$-0.290070\pi$
$233$	18.7060			1.22547			0.612734	+	0.790289i	$0.290070\pi$
$234$		0			0
$235$	−0.579208	−	0.579208i	−0.0377834	−	0.0377834i
$236$	5.15561	−	8.08652i	0.335602	−	0.526387i
$237$		0			0
$238$	−1.11737	+	0.122176i	−0.0724284	+	0.00791952i
$239$	20.3964			1.31933			0.659667	−	0.751558i	$-0.270697\pi$
$239$	20.3964			1.31933			0.659667	+	0.751558i	$0.270697\pi$
$240$		0			0
$241$	10.4808			0.675129			0.337565	−	0.941302i	$-0.390397\pi$
$241$	10.4808			0.675129			0.337565	+	0.941302i	$0.390397\pi$
$242$	1.06750	−	0.116723i	0.0686215	−	0.00750326i
$243$		0			0
$244$	−17.9219	−	11.4262i	−1.14733	−	0.731490i
$245$	−0.0893433	−	0.0893433i	−0.00570793	−	0.00570793i
$246$		0			0
$247$	20.5061			1.30477
$248$	−14.8821	+	5.04319i	−0.945017	+	0.320243i
$249$		0			0
$250$	−1.39113	−	1.11690i	−0.0879828	−	0.0706387i
$251$	−22.2508	+	22.2508i	−1.40446	+	1.40446i	−0.619320	+	0.785139i	$0.712592\pi$
$251$	−22.2508	+	22.2508i	−1.40446	+	1.40446i	−0.785139	+	0.619320i	$0.787408\pi$
$252$		0			0
$253$	−9.50947	−	9.50947i	−0.597855	−	0.597855i
$254$	4.77311	−	0.521905i	0.299492	−	0.0327472i
$255$		0			0
$256$	10.3016	−	12.2425i	0.643848	−	0.765154i
$257$			29.3780i			1.83255i	0.400547	+	0.916276i	$0.368820\pi$
$257$			29.3780i			1.83255i	−0.400547	+	0.916276i	$0.631180\pi$
$258$		0			0
$259$	−6.35455	+	6.35455i	−0.394852	+	0.394852i
$260$	−0.298543	−	1.34885i	−0.0185149	−	0.0836521i
$261$		0			0
$262$	10.9367	−	13.6220i	0.675670	−	0.841569i
$263$		−	8.75090i		−	0.539603i	−0.962916	−	0.269802i	$-0.913042\pi$
$263$		−	8.75090i		−	0.539603i	0.962916	−	0.269802i	$-0.0869582\pi$
$264$		0			0
$265$			0.110908i			0.00681305i
$266$	−4.13644	−	3.32102i	−0.253622	−	0.203625i
$267$		0			0
$268$	−3.38951	+	5.31640i	−0.207047	+	0.324751i
$269$	8.92219	−	8.92219i	0.543996	−	0.543996i	−0.380702	−	0.924698i	$-0.624318\pi$
$269$	8.92219	−	8.92219i	0.543996	−	0.543996i	0.924698	+	0.380702i	$0.124318\pi$
$270$		0			0
$271$			3.36141i			0.204191i	0.994775	+	0.102096i	$0.0325548\pi$
$271$			3.36141i			0.204191i	−0.994775	+	0.102096i	$0.967445\pi$
$272$	1.34161	+	2.88230i	0.0813470	+	0.174765i
$273$		0			0
$274$	−0.745361	−	6.81674i	−0.0450289	−	0.411814i
$275$	−12.0853	−	12.0853i	−0.728771	−	0.728771i
$276$		0			0
$277$	0.516082	−	0.516082i	0.0310083	−	0.0310083i	−0.691433	−	0.722441i	$-0.743020\pi$
$277$	0.516082	−	0.516082i	0.0310083	−	0.0310083i	0.722441	+	0.691433i	$0.243020\pi$
$278$	2.74795	−	3.42266i	0.164811	−	0.205277i
$279$		0			0
$280$	−0.158228	+	0.320436i	−0.00945596	+	0.0191497i
$281$	−13.0206			−0.776747			−0.388373	−	0.921502i	$-0.626963\pi$
$281$	−13.0206			−0.776747			−0.388373	+	0.921502i	$0.626963\pi$
$282$		0			0
$283$	7.04669	+	7.04669i	0.418882	+	0.418882i	0.884818	−	0.465936i	$-0.154282\pi$
$283$	7.04669	+	7.04669i	0.418882	+	0.418882i	−0.465936	+	0.884818i	$0.654282\pi$
$284$	3.43680	+	15.5278i	0.203937	+	0.921408i
$285$		0			0
$286$	−2.88176	−	26.3553i	−0.170402	−	1.55842i
$287$	6.96091			0.410890
$288$		0			0
$289$	16.3683			0.962840
$290$	−0.205405	−	1.87855i	−0.0120618	−	0.110312i
$291$		0			0
$292$	−5.59166	−	25.2637i	−0.327227	−	1.47845i
$293$	3.61446	+	3.61446i	0.211159	+	0.211159i	0.804760	−	0.593601i	$-0.202294\pi$
$293$	3.61446	+	3.61446i	0.211159	+	0.211159i	−0.593601	+	0.804760i	$0.702294\pi$
$294$		0			0
$295$	0.605864			0.0352747
$296$	22.7910	+	11.2540i	1.32470	+	0.654126i
$297$		0			0
$298$	−3.55396	+	4.42657i	−0.205875	+	0.256424i
$299$	−15.1603	+	15.1603i	−0.876741	+	0.876741i
$300$		0			0
$301$	−1.25316	−	1.25316i	−0.0722308	−	0.0722308i
$302$	−2.91788	−	26.6857i	−0.167905	−	1.53559i
$303$		0			0
$304$	−5.14137	+	14.0954i	−0.294878	+	0.808428i
$305$		−	1.34276i		−	0.0768861i
$306$		0			0
$307$	−15.5015	+	15.5015i	−0.884715	+	0.884715i	−0.994009	−	0.109295i	$-0.965141\pi$
$307$	−15.5015	+	15.5015i	−0.884715	+	0.884715i	0.109295	+	0.994009i	$0.465141\pi$
$308$	−3.68701	+	5.78302i	−0.210087	+	0.329518i
$309$		0			0
$310$	−0.774084	−	0.621488i	−0.0439650	−	0.0352982i
$311$		−	17.6216i		−	0.999227i	−0.866248	−	0.499613i	$-0.833475\pi$
$311$		−	17.6216i		−	0.999227i	0.866248	−	0.499613i	$-0.166525\pi$
$312$		0			0
$313$			18.5910i			1.05083i	0.850847	+	0.525414i	$0.176089\pi$
$313$			18.5910i			1.05083i	−0.850847	+	0.525414i	$0.823911\pi$
$314$	15.4287	−	19.2170i	0.870694	−	1.08448i
$315$		0			0
$316$	4.40594	+	19.9065i	0.247854	+	1.11983i
$317$	13.0237	−	13.0237i	0.731486	−	0.731486i	−0.239428	−	0.970914i	$-0.576960\pi$
$317$	13.0237	−	13.0237i	0.731486	−	0.731486i	0.970914	+	0.239428i	$0.0769600\pi$
$318$		0			0
$319$		−	36.2662i		−	2.03052i
$320$	1.00202	+	0.132977i	0.0560145	+	0.00743363i
$321$		0			0
$322$	5.51333	−	0.602842i	0.307246	−	0.0335951i
$323$	−2.10810	−	2.10810i	−0.117298	−	0.117298i
$324$		0			0
$325$	−19.2667	+	19.2667i	−1.06873	+	1.06873i
$326$	−5.46467	−	4.38741i	−0.302660	−	0.242996i
$327$		0			0
$328$	−6.31896	−	18.6469i	−0.348906	−	1.02960i
$329$	6.48295			0.357417
$330$		0			0
$331$	−0.844531	−	0.844531i	−0.0464196	−	0.0464196i	0.683516	−	0.729936i	$-0.260450\pi$
$331$	−0.844531	−	0.844531i	−0.0464196	−	0.0464196i	−0.729936	+	0.683516i	$0.760450\pi$
$332$	26.9070	+	17.1548i	1.47671	+	0.941490i
$333$		0			0
$334$	−24.5626	+	2.68574i	−1.34401	+	0.146957i
$335$	−0.398319			−0.0217625
$336$		0			0
$337$	24.2226			1.31949			0.659746	−	0.751489i	$-0.270664\pi$
$337$	24.2226			1.31949			0.659746	+	0.751489i	$0.270664\pi$
$338$	−23.7405	+	2.59585i	−1.29131	+	0.141195i
$339$		0			0
$340$	−0.107975	+	0.169357i	−0.00585576	+	0.00918468i
$341$	−13.4711	−	13.4711i	−0.729500	−	0.729500i
$342$		0			0
$343$	1.00000			0.0539949
$344$	−2.21936	+	4.49454i	−0.119660	+	0.242329i
$345$		0			0
$346$	−2.26959	−	1.82219i	−0.122014	−	0.0979614i
$347$	−8.75310	+	8.75310i	−0.469891	+	0.469891i	−0.901879	−	0.431988i	$-0.857812\pi$
$347$	−8.75310	+	8.75310i	−0.469891	+	0.469891i	0.431988	+	0.901879i	$0.357812\pi$
$348$		0			0
$349$	−6.87743	−	6.87743i	−0.368140	−	0.368140i	0.498658	−	0.866799i	$-0.333826\pi$
$349$	−6.87743	−	6.87743i	−0.368140	−	0.368140i	−0.866799	+	0.498658i	$0.833826\pi$
$350$	7.00673	−	0.766135i	0.374525	−	0.0409516i
$351$		0			0
$352$	18.8385	+	4.62703i	1.00410	+	0.246622i
$353$			22.8780i			1.21767i	0.793295	+	0.608837i	$0.208364\pi$
$353$			22.8780i			1.21767i	−0.793295	+	0.608837i	$0.791636\pi$
$354$		0			0
$355$	−0.710441	+	0.710441i	−0.0377063	+	0.0377063i
$356$	−10.7945	+	2.38916i	−0.572106	+	0.126625i
$357$		0			0
$358$	−2.78330	+	3.46669i	−0.147102	+	0.183220i
$359$			8.82162i			0.465587i	0.972526	+	0.232794i	$0.0747867\pi$
$359$			8.82162i			0.465587i	−0.972526	+	0.232794i	$0.925213\pi$
$360$		0			0
$361$			4.93033i			0.259491i
$362$	4.88493	+	3.92196i	0.256746	+	0.206134i
$363$		0			0
$364$	9.21946	+	5.87793i	0.483231	+	0.308087i
$365$	1.15588	−	1.15588i	0.0605017	−	0.0605017i
$366$		0			0
$367$		−	21.0160i		−	1.09703i	−0.836142	−	0.548513i	$-0.815194\pi$
$367$		−	21.0160i		−	1.09703i	0.836142	−	0.548513i	$-0.184806\pi$
$368$	−6.61977	−	14.2218i	−0.345079	−	0.741364i
$369$		0			0
$370$	0.174542	+	1.59629i	0.00907401	+	0.0829869i
$371$	−0.620687	−	0.620687i	−0.0322245	−	0.0322245i
$372$		0			0
$373$	−10.3425	+	10.3425i	−0.535516	+	0.535516i	−0.922209	−	0.386693i	$-0.873617\pi$
$373$	−10.3425	+	10.3425i	−0.535516	+	0.535516i	0.386693	+	0.922209i	$0.373617\pi$
$374$	−2.41315	+	3.00566i	−0.124781	+	0.155419i
$375$		0			0
$376$	−5.88507	−	17.3665i	−0.303500	−	0.895608i
$377$	−57.8166			−2.97771
$378$		0			0
$379$	16.1353	+	16.1353i	0.828813	+	0.828813i	0.987353	−	0.158539i	$-0.0506785\pi$
$379$	16.1353	+	16.1353i	0.828813	+	0.828813i	−0.158539	+	0.987353i	$0.550678\pi$
$380$	−0.925473	+	0.204836i	−0.0474757	+	0.0105079i
$381$		0			0
$382$	−0.555127	−	5.07695i	−0.0284028	−	0.259759i
$383$	−12.1083			−0.618704			−0.309352	−	0.950948i	$-0.600112\pi$
$383$	−12.1083			−0.618704			−0.309352	+	0.950948i	$0.600112\pi$
$384$		0			0
$385$	−0.433280			−0.0220820
$386$	−0.463749	−	4.24124i	−0.0236042	−	0.215874i
$387$		0			0
$388$	8.46740	−	1.87410i	0.429867	−	0.0951432i
$389$	12.7493	+	12.7493i	0.646414	+	0.646414i	0.952124	−	0.305711i	$-0.0988941\pi$
$389$	12.7493	+	12.7493i	0.646414	+	0.646414i	−0.305711	+	0.952124i	$0.598894\pi$
$390$		0			0
$391$	3.11704			0.157636
$392$	−0.907777	−	2.67879i	−0.0458497	−	0.135300i
$393$		0			0
$394$	0.353232	−	0.439963i	0.0177956	−	0.0221650i
$395$	−0.910778	+	0.910778i	−0.0458262	+	0.0458262i
$396$		0			0
$397$	16.1299	+	16.1299i	0.809534	+	0.809534i	0.984563	−	0.175029i	$-0.0560019\pi$
$397$	16.1299	+	16.1299i	0.809534	+	0.809534i	−0.175029	+	0.984563i	$0.556002\pi$
$398$	0.522663	+	4.78004i	0.0261987	+	0.239602i
$399$		0			0
$400$	−8.41287	−	18.0741i	−0.420643	−	0.903705i
$401$		−	1.54744i		−	0.0772755i	−0.999253	−	0.0386378i	$-0.987698\pi$
$401$		−	1.54744i		−	0.0772755i	0.999253	−	0.0386378i	$-0.0123018\pi$
$402$		0			0
$403$	−21.4760	+	21.4760i	−1.06980	+	1.06980i
$404$	−23.0437	−	14.6917i	−1.14647	−	0.730939i
$405$		0			0
$406$	11.6626	+	9.36355i	0.578805	+	0.464705i
$407$			30.8170i			1.52754i
$408$		0			0
$409$			4.58498i			0.226712i	0.993554	+	0.113356i	$0.0361601\pi$
$409$			4.58498i			0.226712i	−0.993554	+	0.113356i	$0.963840\pi$
$410$	0.778705	−	0.969902i	0.0384575	−	0.0479001i
$411$		0			0
$412$	−32.0249	+	7.08812i	−1.57775	+	0.349207i
$413$	−3.39065	+	3.39065i	−0.166843	+	0.166843i
$414$		0			0
$415$			2.01595i			0.0989589i
$416$	7.37655	−	30.0329i	0.361665	−	1.47248i
$417$		0			0
$418$	−18.0829	+	1.97723i	−0.884463	+	0.0967095i
$419$	24.8750	+	24.8750i	1.21523	+	1.21523i	0.969285	+	0.245940i	$0.0790967\pi$
$419$	24.8750	+	24.8750i	1.21523	+	1.21523i	0.245940	+	0.969285i	$0.420903\pi$
$420$		0			0
$421$	9.42104	−	9.42104i	0.459153	−	0.459153i	−0.439224	−	0.898378i	$-0.644747\pi$
$421$	9.42104	−	9.42104i	0.459153	−	0.459153i	0.898378	+	0.439224i	$0.144747\pi$
$422$	9.42421	+	7.56641i	0.458764	+	0.368327i
$423$		0			0
$424$	−1.09925	+	2.22614i	−0.0533842	+	0.108111i
$425$	3.96136			0.192154
$426$		0			0
$427$	7.51460	+	7.51460i	0.363657	+	0.363657i
$428$	−8.34641	+	13.0912i	−0.403439	+	0.632789i
$429$		0			0
$430$	−0.314798	+	0.0344208i	−0.0151809	+	0.00165992i
$431$	8.96634			0.431893			0.215947	−	0.976405i	$-0.430716\pi$
$431$	8.96634			0.431893			0.215947	+	0.976405i	$0.430716\pi$
$432$		0			0
$433$	0.679368			0.0326483			0.0163242	−	0.999867i	$-0.494804\pi$
$433$	0.679368			0.0326483			0.0163242	+	0.999867i	$0.494804\pi$
$434$	7.81017	−	0.853985i	0.374900	−	0.0409926i
$435$		0			0
$436$	34.9048	+	22.2538i	1.67164	+	1.06576i
$437$	10.4018	+	10.4018i	0.497584	+	0.497584i
$438$		0			0
$439$	35.4959			1.69413			0.847065	−	0.531490i	$-0.178368\pi$
$439$	35.4959			1.69413			0.847065	+	0.531490i	$0.178368\pi$
$440$	0.393321	+	1.16067i	0.0187509	+	0.0553326i
$441$		0			0
$442$	4.79171	+	3.84711i	0.227918	+	0.182989i
$443$	23.4369	−	23.4369i	1.11352	−	1.11352i	0.120853	−	0.992670i	$-0.461437\pi$
$443$	23.4369	−	23.4369i	1.11352	−	1.11352i	0.992670	−	0.120853i	$-0.0385628\pi$
$444$		0			0
$445$	−0.493876	−	0.493876i	−0.0234120	−	0.0234120i
$446$	31.2247	−	3.41419i	1.47853	−	0.161667i
$447$		0			0
$448$	−6.35188	+	4.86350i	−0.300098	+	0.229779i
$449$		−	4.45807i		−	0.210389i	−0.994452	−	0.105195i	$-0.966453\pi$
$449$		−	4.45807i		−	0.210389i	0.994452	−	0.105195i	$-0.0335465\pi$
$450$		0			0
$451$	16.8788	−	16.8788i	0.794793	−	0.794793i
$452$	−3.57978	−	16.1739i	−0.168379	−	0.760754i
$453$		0			0
$454$	20.2667	−	25.2428i	0.951163	−	1.18470i
$455$			0.690747i			0.0323827i
$456$		0			0
$457$			14.9134i			0.697620i	0.937193	+	0.348810i	$0.113414\pi$
$457$			14.9134i			0.697620i	−0.937193	+	0.348810i	$0.886586\pi$
$458$	−12.0956	−	9.71116i	−0.565188	−	0.453773i
$459$		0			0
$460$	0.532769	−	0.835642i	0.0248405	−	0.0389620i
$461$	−7.52217	+	7.52217i	−0.350342	+	0.350342i	−0.860237	−	0.509895i	$-0.829684\pi$
$461$	−7.52217	+	7.52217i	−0.350342	+	0.350342i	0.509895	+	0.860237i	$0.329684\pi$
$462$		0			0
$463$			40.0015i			1.85903i	0.368787	+	0.929514i	$0.379773\pi$
$463$			40.0015i			1.85903i	−0.368787	+	0.929514i	$0.620227\pi$
$464$	14.4960	−	39.7417i	0.672959	−	1.84496i
$465$		0			0
$466$	2.87544	+	26.2975i	0.133202	+	1.21821i
$467$	−18.9560	−	18.9560i	−0.877177	−	0.877177i	0.116064	−	0.993242i	$-0.462972\pi$
$467$	−18.9560	−	18.9560i	−0.877177	−	0.877177i	−0.993242	+	0.116064i	$0.962972\pi$
$468$		0			0
$469$	2.22915	−	2.22915i	0.102933	−	0.102933i
$470$	0.725236	−	0.903305i	0.0334526	−	0.0416663i
$471$		0			0
$472$	12.1608	+	6.00490i	0.559747	+	0.276398i
$473$	−6.07732			−0.279435
$474$		0			0
$475$	13.2193	+	13.2193i	0.606543	+	0.606543i
$476$	−0.343519	−	1.55206i	−0.0157452	−	0.0711385i
$477$		0			0
$478$	3.13529	+	28.6740i	0.143405	+	1.31152i
$479$	21.3112			0.973733			0.486866	−	0.873476i	$-0.338140\pi$
$479$	21.3112			0.973733			0.486866	+	0.873476i	$0.338140\pi$
$480$		0			0
$481$	49.1294			2.24011
$482$	1.61109	+	14.7343i	0.0733831	+	0.671129i
$483$		0			0
$484$	0.328187	+	1.48279i	0.0149176	+	0.0673994i
$485$	0.387407	+	0.387407i	0.0175912	+	0.0175912i
$486$		0			0
$487$	13.6167			0.617031			0.308515	−	0.951219i	$-0.400168\pi$
$487$	13.6167			0.617031			0.308515	+	0.951219i	$0.400168\pi$
$488$	13.3085	−	26.9517i	0.602447	−	1.22004i
$489$		0			0
$490$	0.111868	−	0.139335i	0.00505369	−	0.00629454i
$491$	−5.18965	+	5.18965i	−0.234206	+	0.234206i	−0.814446	−	0.580240i	$-0.802959\pi$
$491$	−5.18965	+	5.18965i	−0.234206	+	0.234206i	0.580240	+	0.814446i	$0.302959\pi$
$492$		0			0
$493$	5.94373	+	5.94373i	0.267692	+	0.267692i
$494$	3.15216	+	28.8282i	0.141822	+	1.29704i
$495$		0			0
$496$	−9.37755	−	20.1466i	−0.421064	−	0.904610i
$497$		−	7.95182i		−	0.356688i
$498$		0			0
$499$	−7.15618	+	7.15618i	−0.320355	+	0.320355i	−0.848903	−	0.528548i	$-0.822736\pi$
$499$	−7.15618	+	7.15618i	−0.320355	+	0.320355i	0.528548	+	0.848903i	$0.322736\pi$
$500$	1.35633	−	2.12739i	0.0606569	−	0.0951396i
$501$		0			0
$502$	−34.7013	−	27.8606i	−1.54879	−	1.24348i
$503$		−	33.5554i		−	1.49616i	−0.663607	−	0.748081i	$-0.730975\pi$
$503$		−	33.5554i		−	1.49616i	0.663607	−	0.748081i	$-0.269025\pi$
$504$		0			0
$505$		−	1.72650i		−	0.0768282i
$506$	11.9070	−	14.8305i	0.529329	−	0.659297i
$507$		0			0
$508$	1.46742	+	6.62998i	0.0651064	+	0.294158i
$509$	0.615168	−	0.615168i	0.0272669	−	0.0272669i	−0.693342	−	0.720609i	$-0.743862\pi$
$509$	0.615168	−	0.615168i	0.0272669	−	0.0272669i	0.720609	+	0.693342i	$0.243862\pi$
$510$		0			0
$511$			12.9376i			0.572324i
$512$	18.7944	+	12.6004i	0.830603	+	0.556865i
$513$		0			0
$514$	−41.3007	+	4.51593i	−1.82169	+	0.199189i
$515$	−1.46523	−	1.46523i	−0.0645656	−	0.0645656i
$516$		0			0
$517$	15.7199	−	15.7199i	0.691359	−	0.691359i
$518$	−9.91025	−	7.95663i	−0.435431	−	0.349594i
$519$		0			0
$520$	1.85037	−	0.627044i	0.0811440	−	0.0274977i
$521$	5.91593			0.259182			0.129591	−	0.991568i	$-0.458634\pi$
$521$	5.91593			0.259182			0.129591	+	0.991568i	$0.458634\pi$
$522$		0			0
$523$	17.7110	+	17.7110i	0.774449	+	0.774449i	0.978881	−	0.204432i	$-0.0655347\pi$
$523$	17.7110	+	17.7110i	0.774449	+	0.774449i	−0.204432	+	0.978881i	$0.565535\pi$
$524$	20.8314	+	13.2812i	0.910025	+	0.580193i
$525$		0			0
$526$	12.3023	−	1.34517i	0.536406	−	0.0586521i
$527$	4.41560			0.192346
$528$		0			0
$529$	7.61988			0.331299
$530$	−0.155919	+	0.0170486i	−0.00677268	+	0.000740543i
$531$		0			0
$532$	4.03296	−	6.32565i	0.174851	−	0.274252i
$533$	−26.9087	−	26.9087i	−1.16555	−	1.16555i
$534$		0			0
$535$	−0.980831			−0.0424050
$536$	−7.99501	−	3.94787i	−0.345332	−	0.170522i
$537$		0			0
$538$	13.9146	+	11.1716i	0.599902	+	0.481643i
$539$	2.42480	−	2.42480i	0.104444	−	0.104444i
$540$		0			0
$541$	−9.13769	−	9.13769i	−0.392860	−	0.392860i	0.482846	−	0.875706i	$-0.339603\pi$
$541$	−9.13769	−	9.13769i	−0.392860	−	0.392860i	−0.875706	+	0.482846i	$0.839603\pi$
$542$	−4.72559	+	0.516709i	−0.202981	+	0.0221945i
$543$		0			0
$544$	−3.84581	+	2.32914i	−0.164888	+	0.0998611i
$545$			2.61516i			0.112021i
$546$		0			0
$547$	−30.1099	+	30.1099i	−1.28741	+	1.28741i	−0.351052	+	0.936356i	$0.614176\pi$
$547$	−30.1099	+	30.1099i	−1.28741	+	1.28741i	−0.936356	+	0.351052i	$0.885824\pi$
$548$	9.46863	−	2.09571i	0.404480	−	0.0895242i
$549$		0			0
$550$	15.1322	−	18.8477i	0.645240	−	0.803667i
$551$			39.6691i			1.68996i
$552$		0			0
$553$		−	10.1941i		−	0.433499i
$554$	0.804856	+	0.646194i	0.0341951	+	0.0274542i
$555$		0			0
$556$	5.23410	+	3.33703i	0.221975	+	0.141522i
$557$	16.3306	−	16.3306i	0.691950	−	0.691950i	−0.270711	−	0.962661i	$-0.587259\pi$
$557$	16.3306	−	16.3306i	0.691950	−	0.691950i	0.962661	+	0.270711i	$0.0872588\pi$
$558$		0			0
$559$			9.68863i			0.409785i
$560$	−0.474803	−	0.173186i	−0.0200641	−	0.00731846i
$561$		0			0
$562$	−2.00150	−	18.3049i	−0.0844284	−	0.772145i
$563$	−0.288759	−	0.288759i	−0.0121697	−	0.0121697i	0.700996	−	0.713165i	$-0.252739\pi$
$563$	−0.288759	−	0.288759i	−0.0121697	−	0.0121697i	−0.713165	+	0.700996i	$0.752739\pi$
$564$		0			0
$565$	0.739998	−	0.739998i	0.0311319	−	0.0311319i
$566$	−8.82328	+	10.9897i	−0.370870	+	0.461931i
$567$		0			0
$568$	−21.3013	+	7.21848i	−0.893782	+	0.302881i
$569$	23.8386			0.999365			0.499683	−	0.866209i	$-0.333450\pi$
$569$	23.8386			0.999365			0.499683	+	0.866209i	$0.333450\pi$
$570$		0			0
$571$	1.86113	+	1.86113i	0.0778857	+	0.0778857i	0.744976	−	0.667091i	$-0.232461\pi$
$571$	1.86113	+	1.86113i	0.0778857	+	0.0778857i	−0.667091	+	0.744976i	$0.732461\pi$
$572$	36.6082	−	8.10255i	1.53066	−	0.338784i
$573$		0			0
$574$	1.07002	+	9.78589i	0.0446616	+	0.408455i
$575$	−19.5461			−0.815130
$576$		0			0
$577$	−32.0148			−1.33279			−0.666396	−	0.745598i	$-0.732164\pi$
$577$	−32.0148			−1.33279			−0.666396	+	0.745598i	$0.732164\pi$
$578$	2.51609	+	23.0111i	0.104656	+	0.957135i
$579$		0			0
$580$	2.60935	−	0.577531i	0.108347	−	0.0239807i
$581$	−11.2820	−	11.2820i	−0.468057	−	0.468057i
$582$		0			0
$583$	−3.01009			−0.124665
$584$	34.6571	−	11.7444i	1.43412	−	0.485988i
$585$		0			0
$586$	−4.52572	+	5.63694i	−0.186956	+	0.232860i
$587$	1.73084	−	1.73084i	0.0714394	−	0.0714394i	−0.670484	−	0.741924i	$-0.733914\pi$
$587$	1.73084	−	1.73084i	0.0714394	−	0.0714394i	0.741924	+	0.670484i	$0.233914\pi$
$588$		0			0
$589$	14.7351	+	14.7351i	0.607149	+	0.607149i
$590$	0.0931320	+	0.851744i	0.00383418	+	0.0350657i
$591$		0			0
$592$	−12.3179	+	33.7704i	−0.506262	+	1.38795i
$593$			22.8985i			0.940328i	0.882579	+	0.470164i	$0.155805\pi$
$593$			22.8985i			0.940328i	−0.882579	+	0.470164i	$0.844195\pi$
$594$		0			0
$595$	0.0710109	−	0.0710109i	0.00291116	−	0.00291116i
$596$	−6.76933	−	4.31584i	−0.277283	−	0.176784i
$597$		0			0
$598$	−23.6432	−	18.9824i	−0.966843	−	0.776249i
$599$			26.0002i			1.06234i	0.847266	+	0.531169i	$0.178247\pi$
$599$			26.0002i			1.06234i	−0.847266	+	0.531169i	$0.821753\pi$
$600$		0			0
$601$			21.0502i			0.858654i	0.903149	+	0.429327i	$0.141249\pi$
$601$			21.0502i			0.858654i	−0.903149	+	0.429327i	$0.858751\pi$
$602$	1.56910	−	1.95436i	0.0639517	−	0.0796539i
$603$		0			0
$604$	37.0671	−	8.20412i	1.50824	−	0.333821i
$605$	−0.0678415	+	0.0678415i	−0.00275815	+	0.00275815i
$606$		0			0
$607$			32.7336i			1.32861i	0.747460	+	0.664307i	$0.231273\pi$
$607$			32.7336i			1.32861i	−0.747460	+	0.664307i	$0.768727\pi$
$608$	−20.6062	−	5.06120i	−0.835690	−	0.205259i
$609$		0			0
$610$	1.88770	−	0.206406i	0.0764306	−	0.00835712i
$611$	−25.0611	−	25.0611i	−1.01386	−	1.01386i
$612$		0			0
$613$	7.14939	−	7.14939i	0.288761	−	0.288761i	−0.547829	−	0.836590i	$-0.684546\pi$
$613$	7.14939	−	7.14939i	0.288761	−	0.288761i	0.836590	+	0.547829i	$0.184546\pi$
$614$	−24.1753	−	19.4096i	−0.975637	−	0.783309i
$615$		0			0
$616$	−8.69673	−	4.29437i	−0.350401	−	0.173025i
$617$	15.8667			0.638769			0.319384	−	0.947625i	$-0.396524\pi$
$617$	15.8667			0.638769			0.319384	+	0.947625i	$0.396524\pi$
$618$		0			0
$619$	−20.4351	−	20.4351i	−0.821355	−	0.821355i	0.164947	−	0.986302i	$-0.447255\pi$
$619$	−20.4351	−	20.4351i	−0.821355	−	0.821355i	−0.986302	+	0.164947i	$0.947255\pi$
$620$	0.754719	−	1.18377i	0.0303103	−	0.0475412i
$621$		0			0
$622$	24.7730	−	2.70875i	0.993307	−	0.108611i
$623$	5.52785			0.221469
$624$		0			0
$625$	−24.7608			−0.990432
$626$	−26.1359	+	2.85777i	−1.04460	+	0.114220i
$627$		0			0
$628$	29.3876	+	18.7363i	1.17269	+	0.747658i
$629$	−5.05066	−	5.05066i	−0.201383	−	0.201383i
$630$		0			0
$631$	39.1876			1.56003			0.780017	−	0.625758i	$-0.215210\pi$
$631$	39.1876			1.56003			0.780017	+	0.625758i	$0.215210\pi$
$632$	−27.3080	+	9.25401i	−1.08625	+	0.368105i
$633$		0			0
$634$	20.3112	+	16.3072i	0.806661	+	0.647643i
$635$	−0.303340	+	0.303340i	−0.0120377	+	0.0120377i
$636$		0			0
$637$	−3.86569	−	3.86569i	−0.153164	−	0.153164i
$638$	50.9843	−	5.57476i	2.01849	−	0.220707i
$639$		0			0
$640$	−0.0329155	+	1.42911i	−0.00130110	+	0.0564907i
$641$		−	32.1293i		−	1.26903i	−0.772911	−	0.634515i	$-0.781200\pi$
$641$		−	32.1293i		−	1.26903i	0.772911	−	0.634515i	$-0.218800\pi$
$642$		0			0
$643$	13.7452	−	13.7452i	0.542059	−	0.542059i	−0.382073	−	0.924132i	$-0.624790\pi$
$643$	13.7452	−	13.7452i	0.542059	−	0.542059i	0.924132	+	0.382073i	$0.124790\pi$
$644$	1.69499	+	7.65816i	0.0667921	+	0.301774i
$645$		0			0
$646$	2.63958	−	3.28768i	0.103853	−	0.129352i
$647$		−	5.78120i		−	0.227282i	−0.993522	−	0.113641i	$-0.963749\pi$
$647$		−	5.78120i		−	0.227282i	0.993522	−	0.113641i	$-0.0362514\pi$
$648$		0			0
$649$			16.4433i			0.645457i
$650$	−30.0475	−	24.1242i	−1.17856	−	0.946229i
$651$		0			0
$652$	5.32796	−	8.35684i	0.208659	−	0.327279i
$653$	13.9854	−	13.9854i	0.547293	−	0.547293i	−0.378364	−	0.925657i	$-0.623513\pi$
$653$	13.9854	−	13.9854i	0.547293	−	0.547293i	0.925657	+	0.378364i	$0.123513\pi$
$654$		0			0
$655$			1.56075i			0.0609834i
$656$	25.2431	−	11.7498i	0.985576	−	0.458751i
$657$		0			0
$658$	0.996544	+	9.11395i	0.0388493	+	0.355299i
$659$	19.6810	+	19.6810i	0.766661	+	0.766661i	0.977517	−	0.210856i	$-0.0676251\pi$
$659$	19.6810	+	19.6810i	0.766661	+	0.766661i	−0.210856	+	0.977517i	$0.567625\pi$
$660$		0			0
$661$	12.7655	−	12.7655i	0.496519	−	0.496519i	−0.413833	−	0.910353i	$-0.635810\pi$
$661$	12.7655	−	12.7655i	0.496519	−	0.496519i	0.910353	+	0.413833i	$0.135810\pi$
$662$	1.05745	−	1.31709i	0.0410990	−	0.0511902i
$663$		0			0
$664$	−19.9807	+	40.4638i	−0.775400	+	1.57030i
$665$	0.473935			0.0183784
$666$		0			0
$667$	−29.3275	−	29.3275i	−1.13557	−	1.13557i
$668$	−7.55142	−	34.1182i	−0.292173	−	1.32007i
$669$		0			0
$670$	−0.0612288	−	0.559971i	−0.00236547	−	0.0216336i
$671$	36.4429			1.40686
$672$		0			0
$673$	43.7910			1.68802			0.844010	−	0.536328i	$-0.180189\pi$
$673$	43.7910			1.68802			0.844010	+	0.536328i	$0.180189\pi$
$674$	3.72345	+	34.0530i	0.143422	+	1.31167i
$675$		0			0
$676$	−7.29866	−	32.9762i	−0.280718	−	1.26831i
$677$	25.0415	+	25.0415i	0.962422	+	0.962422i	0.999319	−	0.0368968i	$-0.0117473\pi$
$677$	25.0415	+	25.0415i	0.962422	+	0.962422i	−0.0368968	+	0.999319i	$0.511747\pi$
$678$		0			0
$679$	−4.33616			−0.166407
$680$	−0.254686	−	0.125762i	−0.00976675	−	0.00482273i
$681$		0			0
$682$	16.8674	−	21.0089i	0.645885	−	0.804471i
$683$	12.6770	−	12.6770i	0.485071	−	0.485071i	−0.421676	−	0.906747i	$-0.638558\pi$
$683$	12.6770	−	12.6770i	0.485071	−	0.485071i	0.906747	+	0.421676i	$0.138558\pi$
$684$		0			0
$685$	0.433216	+	0.433216i	0.0165523	+	0.0165523i
$686$	0.153718	+	1.40583i	0.00586897	+	0.0536750i
$687$		0			0
$688$	−6.65973	−	2.42917i	−0.253900	−	0.0926111i
$689$			4.79877i			0.182818i
$690$		0			0
$691$	11.5147	−	11.5147i	0.438041	−	0.438041i	−0.453312	−	0.891352i	$-0.649757\pi$
$691$	11.5147	−	11.5147i	0.438041	−	0.438041i	0.891352	+	0.453312i	$0.149757\pi$
$692$	2.21282	−	3.47077i	0.0841186	−	0.131939i
$693$		0			0
$694$	−13.6509	−	10.9599i	−0.518181	−	0.416032i
$695$			0.392153i			0.0148752i
$696$		0			0
$697$			5.53260i			0.209562i
$698$	8.61135	−	10.7257i	0.325944	−	0.405974i
$699$		0			0
$700$	2.15412	+	9.73253i	0.0814180	+	0.367855i
$701$	−24.5725	+	24.5725i	−0.928089	+	0.928089i	−0.997582	−	0.0694930i	$-0.977862\pi$
$701$	−24.5725	+	24.5725i	−0.928089	+	0.928089i	0.0694930	+	0.997582i	$0.477862\pi$
$702$		0			0
$703$		−	33.7087i		−	1.27135i
$704$	−3.60903	+	27.1951i	−0.136020	+	1.02495i
$705$		0			0
$706$	−32.1627	+	3.51676i	−1.21046	+	0.132355i
$707$	9.66216	+	9.66216i	0.363383	+	0.363383i
$708$		0			0
$709$	−11.9488	+	11.9488i	−0.448745	+	0.448745i	−0.894937	−	0.446192i	$-0.852780\pi$
$709$	−11.9488	+	11.9488i	−0.448745	+	0.448745i	0.446192	+	0.894937i	$0.352780\pi$
$710$	−1.10797	−	0.889555i	−0.0415814	−	0.0333844i
$711$		0			0
$712$	−5.01806	−	14.8080i	−0.188060	−	0.554953i
$713$	−21.7874			−0.815946
$714$		0			0
$715$	1.67492	+	1.67492i	0.0626386	+	0.0626386i
$716$	−5.30144	−	3.37997i	−0.198124	−	0.126315i
$717$		0			0
$718$	−12.4017	+	1.35604i	−0.462829	+	0.0506070i
$719$	−20.8496			−0.777559			−0.388779	−	0.921331i	$-0.627103\pi$
$719$	−20.8496			−0.777559			−0.388779	+	0.921331i	$0.627103\pi$
$720$		0			0
$721$	16.4000			0.610767
$722$	−6.93123	+	0.757879i	−0.257954	+	0.0282053i
$723$		0			0
$724$	−4.76273	+	7.47028i	−0.177006	+	0.277631i
$725$	−37.2715	−	37.2715i	−1.38423	−	1.38423i
$726$		0			0
$727$	−49.4099			−1.83251			−0.916257	−	0.400592i	$-0.868805\pi$
$727$	−49.4099			−1.83251			−0.916257	+	0.400592i	$0.868805\pi$
$728$	−6.84620	+	13.8646i	−0.253737	+	0.513855i
$729$		0			0
$730$	1.80266	+	1.44730i	0.0667195	+	0.0535670i
$731$	0.996021	−	0.996021i	0.0368392	−	0.0368392i
$732$		0			0
$733$	−22.8419	−	22.8419i	−0.843686	−	0.843686i	0.145650	−	0.989336i	$-0.453473\pi$
$733$	−22.8419	−	22.8419i	−0.843686	−	0.843686i	−0.989336	+	0.145650i	$0.953473\pi$
$734$	29.5450	−	3.23053i	1.09053	−	0.119241i
$735$		0			0
$736$	18.9760	−	11.4924i	0.699463	−	0.423617i
$737$		−	10.8105i		−	0.398210i
$738$		0			0
$739$	−3.95695	+	3.95695i	−0.145559	+	0.145559i	−0.776131	−	0.630572i	$-0.782820\pi$
$739$	−3.95695	+	3.95695i	−0.145559	+	0.145559i	0.630572	+	0.776131i	$0.282820\pi$
$740$	−2.21728	+	0.490755i	−0.0815090	+	0.0180405i
$741$		0			0
$742$	0.777173	−	0.967994i	0.0285309	−	0.0355362i
$743$			1.72532i			0.0632958i	0.999499	+	0.0316479i	$0.0100755\pi$
$743$			1.72532i			0.0632958i	−0.999499	+	0.0316479i	$0.989924\pi$
$744$		0			0
$745$		−	0.507177i		−	0.0185815i
$746$	−16.1297	−	12.9501i	−0.590551	−	0.474135i
$747$		0			0
$748$	−4.59640	−	2.93047i	−0.168061	−	0.107149i
$749$	5.48912	−	5.48912i	0.200568	−	0.200568i
$750$		0			0
$751$		−	28.0700i		−	1.02429i	−0.858900	−	0.512144i	$-0.828852\pi$
$751$		−	28.0700i		−	1.02429i	0.858900	−	0.512144i	$-0.171148\pi$
$752$	23.5098	−	10.9430i	0.857313	−	0.399049i
$753$		0			0
$754$	−8.88744	−	81.2806i	−0.323661	−	2.96006i
$755$	1.69592	+	1.69592i	0.0617209	+	0.0617209i
$756$		0			0
$757$	−21.3781	+	21.3781i	−0.777001	+	0.777001i	−0.979320	−	0.202319i	$-0.935152\pi$
$757$	−21.3781	+	21.3781i	−0.777001	+	0.777001i	0.202319	+	0.979320i	$0.435152\pi$
$758$	−20.2032	+	25.1638i	−0.733815	+	0.913990i
$759$		0			0
$760$	−0.430228	−	1.26957i	−0.0156060	−	0.0460523i
$761$	−17.0483			−0.618001			−0.309001	−	0.951062i	$-0.599995\pi$
$761$	−17.0483			−0.618001			−0.309001	+	0.951062i	$0.599995\pi$
$762$		0			0
$763$	−14.6355	−	14.6355i	−0.529840	−	0.529840i
$764$	7.05202	−	1.56083i	0.255133	−	0.0564690i
$765$		0			0
$766$	−1.86126	−	17.0222i	−0.0672500	−	0.615039i
$767$	26.2144			0.946547
$768$		0			0
$769$	17.6693			0.637172			0.318586	−	0.947894i	$-0.396792\pi$
$769$	17.6693			0.637172			0.318586	+	0.947894i	$0.396792\pi$
$770$	−0.0666028	−	0.609119i	−0.00240020	−	0.0219511i
$771$		0			0
$772$	5.89120	−	1.30391i	0.212029	−	0.0469287i
$773$	3.41723	+	3.41723i	0.122909	+	0.122909i	0.765886	−	0.642977i	$-0.222301\pi$
$773$	3.41723	+	3.41723i	0.122909	+	0.122909i	−0.642977	+	0.765886i	$0.722301\pi$
$774$		0			0
$775$	−27.6890			−0.994618
$776$	3.93627	+	11.6157i	0.141304	+	0.416979i
$777$		0			0
$778$	−15.9636	+	19.8832i	−0.572322	+	0.712846i
$779$	−18.4626	+	18.4626i	−0.661492	+	0.661492i
$780$		0			0
$781$	−19.2816	−	19.2816i	−0.689949	−	0.689949i
$782$	0.479145	+	4.38205i	0.0171342	+	0.156702i
$783$		0			0
$784$	3.62640	−	1.68796i	0.129514	−	0.0602844i
$785$			2.20180i			0.0785855i
$786$		0			0
$787$	−16.5567	+	16.5567i	−0.590183	+	0.590183i	−0.937681	−	0.347498i	$-0.887031\pi$
$787$	−16.5567	+	16.5567i	−0.590183	+	0.590183i	0.347498	+	0.937681i	$0.387031\pi$
$788$	0.672813	+	0.428956i	0.0239680	+	0.0152809i
$789$		0			0
$790$	−1.42041	−	1.14040i	−0.0505358	−	0.0405736i
$791$			8.28264i			0.294497i
$792$		0			0
$793$		−	58.0982i		−	2.06313i
$794$	−20.1965	+	25.1554i	−0.716746	+	0.892730i
$795$		0			0
$796$	−6.63961	+	1.46955i	−0.235335	+	0.0520870i
$797$	−15.4377	+	15.4377i	−0.546833	+	0.546833i	−0.925523	−	0.378691i	$-0.876374\pi$
$797$	−15.4377	+	15.4377i	−0.546833	+	0.546833i	0.378691	+	0.925523i	$0.376374\pi$
$798$		0			0
$799$			5.15271i			0.182290i
$800$	24.1160	−	14.6054i	0.852629	−	0.516379i
$801$		0			0
$802$	2.17545	−	0.237869i	0.0768177	−	0.00839945i
$803$	31.3710	+	31.3710i	1.10706	+	1.10706i
$804$		0			0
$805$	−0.350382	+	0.350382i	−0.0123493	+	0.0123493i
$806$	−33.4929	−	26.8904i	−1.17974	−	0.947176i
$807$		0			0
$808$	17.1119	−	34.6540i	0.601993	−	1.21912i
$809$	−49.9730			−1.75696			−0.878478	−	0.477782i	$-0.841441\pi$
$809$	−49.9730			−1.75696			−0.878478	+	0.477782i	$0.841441\pi$
$810$		0			0
$811$	34.3832	+	34.3832i	1.20736	+	1.20736i	0.971880	+	0.235477i	$0.0756651\pi$
$811$	34.3832	+	34.3832i	1.20736	+	1.20736i	0.235477	+	0.971880i	$0.424335\pi$
$812$	−11.3709	+	17.8350i	−0.399039	+	0.625887i
$813$		0			0
$814$	−43.3237	+	4.73713i	−1.51849	+	0.166036i
$815$	0.626117			0.0219319
$816$		0			0
$817$	6.64756			0.232569
$818$	−6.44572	+	0.704792i	−0.225369	+	0.0246425i
$819$		0			0
$820$	1.48322	+	0.945639i	0.0517964	+	0.0330231i
$821$	1.59874	+	1.59874i	0.0557963	+	0.0557963i	0.734454	−	0.678658i	$-0.237438\pi$
$821$	1.59874	+	1.59874i	0.0557963	+	0.0557963i	−0.678658	+	0.734454i	$0.737438\pi$
$822$		0			0
$823$	−37.9226			−1.32190			−0.660949	−	0.750431i	$-0.729846\pi$
$823$	−37.9226			−1.32190			−0.660949	+	0.750431i	$0.729846\pi$
$824$	−14.8875	−	43.9322i	−0.518632	−	1.53045i
$825$		0			0
$826$	−5.28790	−	4.24549i	−0.183989	−	0.147720i
$827$	34.5300	−	34.5300i	1.20073	−	1.20073i	0.226779	−	0.973946i	$-0.427180\pi$
$827$	34.5300	−	34.5300i	1.20073	−	1.20073i	0.973946	−	0.226779i	$-0.0728196\pi$
$828$		0			0
$829$	−16.0890	−	16.0890i	−0.558795	−	0.558795i	0.370169	−	0.928964i	$-0.379300\pi$
$829$	−16.0890	−	16.0890i	−0.558795	−	0.558795i	−0.928964	+	0.370169i	$0.879300\pi$
$830$	−2.83409	+	0.309887i	−0.0983726	+	0.0107563i
$831$		0			0
$832$	43.3552	+	5.75362i	1.50307	+	0.199471i
$833$			0.794810i			0.0275385i
$834$		0			0
$835$	1.56100	−	1.56100i	0.0540206	−	0.0540206i
$836$	−5.55932	−	25.1176i	−0.192273	−	0.868710i
$837$		0			0
$838$	−31.1465	+	38.7939i	−1.07594	+	1.34011i
$839$			27.2955i			0.942344i	0.882041	+	0.471172i	$0.156169\pi$
$839$			27.2955i			0.942344i	−0.882041	+	0.471172i	$0.843831\pi$
$840$		0			0
$841$		−	82.8462i		−	2.85677i
$842$	14.6926	+	11.7962i	0.506341	+	0.406525i
$843$		0			0
$844$	−9.18846	+	14.4120i	−0.316280	+	0.496081i
$845$	1.50875	−	1.50875i	0.0519025	−	0.0519025i
$846$		0			0
$847$		−	0.759336i		−	0.0260911i
$848$	−3.29856	−	1.20316i	−0.113273	−	0.0413168i
$849$		0			0
$850$	0.608931	+	5.56902i	0.0208862	+	0.191016i
$851$	24.9209	+	24.9209i	0.854279	+	0.854279i
$852$		0			0
$853$	18.1407	−	18.1407i	0.621125	−	0.621125i	−0.324694	−	0.945819i	$-0.605261\pi$
$853$	18.1407	−	18.1407i	0.621125	−	0.621125i	0.945819	+	0.324694i	$0.105261\pi$
$854$	−9.40916	+	11.7194i	−0.321975	+	0.401030i
$855$		0			0
$856$	−19.6871	−	9.72132i	−0.672892	−	0.332268i
$857$	43.2364			1.47693			0.738464	−	0.674293i	$-0.235551\pi$
$857$	43.2364			1.47693			0.738464	+	0.674293i	$0.235551\pi$
$858$		0			0
$859$	5.72658	+	5.72658i	0.195388	+	0.195388i	0.798020	−	0.602631i	$-0.205881\pi$
$859$	5.72658	+	5.72658i	0.195388	+	0.195388i	−0.602631	+	0.798020i	$0.705881\pi$
$860$	−0.0967800	−	0.437262i	−0.00330017	−	0.0149105i
$861$		0			0
$862$	1.37829	+	12.6052i	0.0469446	+	0.429335i
$863$	21.7413			0.740082			0.370041	−	0.929015i	$-0.379344\pi$
$863$	21.7413			0.740082			0.370041	+	0.929015i	$0.379344\pi$
$864$		0			0
$865$	0.260040			0.00884162
$866$	0.104431	+	0.955078i	0.00354870	+	0.0324549i
$867$		0			0
$868$	2.40112	+	10.8485i	0.0814994	+	0.368223i
$869$	−24.7188	−	24.7188i	−0.838527	−	0.838527i
$870$		0			0
$871$	−17.2344			−0.583966
$872$	−25.9197	+	52.4912i	−0.877752	+	1.77758i
$873$		0			0
$874$	−13.0242	+	16.2221i	−0.440551	+	0.548720i
$875$	−0.892006	+	0.892006i	−0.0301553	+	0.0301553i
$876$		0			0
$877$	−23.9822	−	23.9822i	−0.809822	−	0.809822i	0.174785	−	0.984607i	$-0.444077\pi$
$877$	−23.9822	−	23.9822i	−0.809822	−	0.809822i	−0.984607	+	0.174785i	$0.944077\pi$
$878$	5.45636	+	49.9014i	0.184143	+	1.68409i
$879$		0			0
$880$	−1.57125	+	0.731360i	−0.0529667	+	0.0246541i
$881$		−	35.2047i		−	1.18608i	−0.805175	−	0.593038i	$-0.797929\pi$
$881$		−	35.2047i		−	1.18608i	0.805175	−	0.593038i	$-0.202071\pi$
$882$		0			0
$883$	−29.0728	+	29.0728i	−0.978377	+	0.978377i	−0.999771	−	0.0213942i	$-0.993190\pi$
$883$	−29.0728	+	29.0728i	−0.978377	+	0.978377i	0.0213942	+	0.999771i	$0.493190\pi$
$884$	−4.67184	+	7.32771i	−0.157131	+	0.246458i
$885$		0			0
$886$	36.5511	+	29.3458i	1.22796	+	0.985891i
$887$		−	26.4222i		−	0.887172i	−0.896232	−	0.443586i	$-0.853706\pi$
$887$		−	26.4222i		−	0.887172i	0.896232	−	0.443586i	$-0.146294\pi$
$888$		0			0
$889$		−	3.39522i		−	0.113872i
$890$	0.618391	−	0.770226i	0.0207285	−	0.0258180i
$891$		0			0
$892$	9.59957	+	43.3719i	0.321418	+	1.45220i
$893$	−17.1949	+	17.1949i	−0.575405	+	0.575405i
$894$		0			0
$895$		−	0.397198i		−	0.0132769i
$896$	−7.81367	−	8.18209i	−0.261036	−	0.273344i
$897$		0			0
$898$	6.26730	−	0.685284i	0.209143	−	0.0228682i
$899$	−41.5453	−	41.5453i	−1.38561	−	1.38561i
$900$		0			0
$901$	0.493328	−	0.493328i	0.0164351	−	0.0164351i
$902$	26.3234	+	21.1343i	0.876474	+	0.703694i
$903$		0			0
$904$	22.1875	−	7.51879i	0.737945	−	0.250071i
$905$	−0.559694			−0.0186049
$906$		0			0
$907$	−13.8359	−	13.8359i	−0.459413	−	0.459413i	0.439050	−	0.898463i	$-0.355315\pi$
$907$	−13.8359	−	13.8359i	−0.459413	−	0.459413i	−0.898463	+	0.439050i	$0.855315\pi$
$908$	38.6026	+	24.6113i	1.28107	+	0.816756i
$909$		0			0
$910$	−0.971075	+	0.106180i	−0.0321908	+	0.00351983i
$911$	32.8417			1.08809			0.544047	−	0.839055i	$-0.316891\pi$
$911$	32.8417			1.08809			0.544047	+	0.839055i	$0.316891\pi$
$912$		0			0
$913$	−54.7134			−1.81075
$914$	−20.9658	+	2.29246i	−0.693487	+	0.0758277i
$915$		0			0
$916$	11.7930	−	18.4971i	0.389651	−	0.611163i
$917$	−8.73455	−	8.73455i	−0.288440	−	0.288440i
$918$		0			0
$919$	1.13244			0.0373559			0.0186779	−	0.999826i	$-0.494054\pi$
$919$	1.13244			0.0373559			0.0186779	+	0.999826i	$0.494054\pi$
$920$	1.25667	+	0.620532i	0.0414312	+	0.0204583i
$921$		0			0
$922$	−11.7312	−	9.41863i	−0.386347	−	0.310186i
$923$	−30.7393	+	30.7393i	−1.01179	+	1.01179i
$924$		0			0
$925$	31.6713	+	31.6713i	1.04135	+	1.04135i
$926$	−56.2355	+	6.14894i	−1.84801	+	0.202067i
$927$		0			0
$928$	58.0986	+	14.2699i	1.90718	+	0.468433i
$929$		−	47.3464i		−	1.55338i	−0.629880	−	0.776692i	$-0.716896\pi$
$929$		−	47.3464i		−	1.55338i	0.629880	−	0.776692i	$-0.283104\pi$
$930$		0			0
$931$	−2.65233	+	2.65233i	−0.0869265	+	0.0869265i
$932$	−36.5279	+	8.08478i	−1.19651	+	0.264826i
$933$		0			0
$934$	23.7351	−	29.5628i	0.776635	−	0.967325i
$935$		−	0.344375i		−	0.0112623i
$936$		0			0
$937$			52.0425i			1.70015i	0.526658	+	0.850077i	$0.323445\pi$
$937$			52.0425i			1.70015i	−0.526658	+	0.850077i	$0.676555\pi$
$938$	3.47648	+	2.79116i	0.113511	+	0.0911346i
$939$		0			0
$940$	1.38138	+	0.880708i	0.0450556	+	0.0287255i
$941$	21.8877	−	21.8877i	0.713520	−	0.713520i	−0.253750	−	0.967270i	$-0.581664\pi$
$941$	21.8877	−	21.8877i	0.713520	−	0.713520i	0.967270	+	0.253750i	$0.0816641\pi$
$942$		0			0
$943$		−	27.2989i		−	0.888976i
$944$	−6.57256	+	18.0192i	−0.213919	+	0.586473i
$945$		0			0
$946$	−0.934191	−	8.54370i	−0.0303732	−	0.277780i
$947$	27.2385	+	27.2385i	0.885132	+	0.885132i	0.994051	−	0.108919i	$-0.0347389\pi$
$947$	27.2385	+	27.2385i	0.885132	+	0.885132i	−0.108919	+	0.994051i	$0.534739\pi$
$948$		0			0
$949$	50.0126	−	50.0126i	1.62348	−	1.62348i
$950$	−16.5521	+	20.6162i	−0.537021	+	0.668877i
$951$		0			0
$952$	2.12913	−	0.721510i	0.0690056	−	0.0233843i
$953$	−40.7540			−1.32015			−0.660076	−	0.751199i	$-0.729476\pi$
$953$	−40.7540			−1.32015			−0.660076	+	0.751199i	$0.729476\pi$
$954$		0			0
$955$	0.322649	+	0.322649i	0.0104407	+	0.0104407i
$956$	−39.8289	+	8.81540i	−1.28816	+	0.285110i
$957$		0			0
$958$	3.27591	+	29.9600i	0.105840	+	0.967963i
$959$	−4.84889			−0.156579
$960$		0			0
$961$	0.135984			0.00438657
$962$	7.55206	+	69.0678i	0.243488	+	2.22684i
$963$		0			0
$964$	−20.4663	+	4.52985i	−0.659177	+	0.145897i
$965$	0.269538	+	0.269538i	0.00867675	+	0.00867675i
$966$		0			0
$967$	28.9910			0.932287			0.466143	−	0.884709i	$-0.345643\pi$
$967$	28.9910			0.932287			0.466143	+	0.884709i	$0.345643\pi$
$968$	−2.03410	+	0.689308i	−0.0653786	+	0.0221552i
$969$		0			0
$970$	−0.485079	+	0.604181i	−0.0155749	+	0.0193991i
$971$	16.5270	−	16.5270i	0.530377	−	0.530377i	−0.390308	−	0.920685i	$-0.627631\pi$
$971$	16.5270	−	16.5270i	0.530377	−	0.530377i	0.920685	+	0.390308i	$0.127631\pi$
$972$		0			0
$973$	−2.19464	−	2.19464i	−0.0703569	−	0.0703569i
$974$	2.09313	+	19.1428i	0.0670681	+	0.613375i
$975$		0			0
$976$	39.9353	+	14.5666i	1.27830	+	0.466265i
$977$			31.6420i			1.01232i	0.862440	+	0.506159i	$0.168935\pi$
$977$			31.6420i			1.01232i	−0.862440	+	0.506159i	$0.831065\pi$
$978$		0			0
$979$	13.4040	−	13.4040i	0.428392	−	0.428392i
$980$	0.213079	+	0.135850i	0.00680655	+	0.00433956i
$981$		0			0
$982$	−8.09354	−	6.49805i	−0.258275	−	0.207361i
$983$		−	11.2993i		−	0.360390i	−0.983631	−	0.180195i	$-0.942327\pi$
$983$		−	11.2993i		−	0.360390i	0.983631	−	0.180195i	$-0.0576729\pi$
$984$		0			0
$985$			0.0504089i			0.00160616i
$986$	−7.44224	+	9.26955i	−0.237009	+	0.295203i
$987$		0			0
$988$	−40.0432	+	8.86282i	−1.27394	+	0.281964i
$989$	−4.91457	+	4.91457i	−0.156274	+	0.156274i
$990$		0			0
$991$			29.9518i			0.951451i	0.879594	+	0.475725i	$0.157814\pi$
$991$			29.9518i			0.951451i	−0.879594	+	0.475725i	$0.842186\pi$
$992$	26.8813	−	16.2802i	0.853482	−	0.516896i
$993$		0			0
$994$	11.1789	−	1.22234i	0.354574	−	0.0387701i
$995$	−0.303780	−	0.303780i	−0.00963048	−	0.00963048i
$996$		0			0
$997$	−11.9968	+	11.9968i	−0.379941	+	0.379941i	−0.871081	−	0.491139i	$-0.836581\pi$
$997$	−11.9968	+	11.9968i	−0.379941	+	0.379941i	0.491139	+	0.871081i	$0.336581\pi$
$998$	−11.1604	−	8.96037i	−0.353277	−	0.283636i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.e.323.11	yes	40
3.2	odd	2	inner	1008.2.v.e.323.10	✓	40
4.3	odd	2		4032.2.v.e.1583.10		40
12.11	even	2		4032.2.v.e.1583.11		40
16.5	even	4		4032.2.v.e.3599.11		40
16.11	odd	4	inner	1008.2.v.e.827.10	yes	40
48.5	odd	4		4032.2.v.e.3599.10		40
48.11	even	4	inner	1008.2.v.e.827.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.e.323.10	✓	40	3.2	odd	2	inner
1008.2.v.e.323.11	yes	40	1.1	even	1	trivial
1008.2.v.e.827.10	yes	40	16.11	odd	4	inner
1008.2.v.e.827.11	yes	40	48.11	even	4	inner
4032.2.v.e.1583.10		40	4.3	odd	2
4032.2.v.e.1583.11		40	12.11	even	2
4032.2.v.e.3599.10		40	48.5	odd	4
4032.2.v.e.3599.11		40	16.5	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.153718 + 1.40583i) q^{2} +(-1.95274 + 0.432203i) q^{4} +(-0.0893433 - 0.0893433i) q^{5} +1.00000 q^{7} +(-0.907777 - 2.67879i) q^{8} +O(q^{10})\)	\(q+(0.153718 + 1.40583i) q^{2} +(-1.95274 + 0.432203i) q^{4} +(-0.0893433 - 0.0893433i) q^{5} +1.00000 q^{7} +(-0.907777 - 2.67879i) q^{8} +(0.111868 - 0.139335i) q^{10} +(2.42480 - 2.42480i) q^{11} +(-3.86569 - 3.86569i) q^{13} +(0.153718 + 1.40583i) q^{14} +(3.62640 - 1.68796i) q^{16} +0.794810i q^{17} +(-2.65233 + 2.65233i) q^{19} +(0.213079 + 0.135850i) q^{20} +(3.78161 + 3.03614i) q^{22} -3.92175i q^{23} -4.98404i q^{25} +(4.84029 - 6.02874i) q^{26} +(-1.95274 + 0.432203i) q^{28} +(7.47818 - 7.47818i) q^{29} -5.55554i q^{31} +(2.93044 + 4.83865i) q^{32} +(-1.11737 + 0.122176i) q^{34} +(-0.0893433 - 0.0893433i) q^{35} +(-6.35455 + 6.35455i) q^{37} +(-4.13644 - 3.32102i) q^{38} +(-0.158228 + 0.320436i) q^{40} +6.96091 q^{41} +(-1.25316 - 1.25316i) q^{43} +(-3.68701 + 5.78302i) q^{44} +(5.51333 - 0.602842i) q^{46} +6.48295 q^{47} +1.00000 q^{49} +(7.00673 - 0.766135i) q^{50} +(9.21946 + 5.87793i) q^{52} +(-0.620687 - 0.620687i) q^{53} -0.433280 q^{55} +(-0.907777 - 2.67879i) q^{56} +(11.6626 + 9.36355i) q^{58} +(-3.39065 + 3.39065i) q^{59} +(7.51460 + 7.51460i) q^{61} +(7.81017 - 0.853985i) q^{62} +(-6.35188 + 4.86350i) q^{64} +0.690747i q^{65} +(2.22915 - 2.22915i) q^{67} +(-0.343519 - 1.55206i) q^{68} +(0.111868 - 0.139335i) q^{70} -7.95182i q^{71} +12.9376i q^{73} +(-9.91025 - 7.95663i) q^{74} +(4.03296 - 6.32565i) q^{76} +(2.42480 - 2.42480i) q^{77} -10.1941i q^{79} +(-0.474803 - 0.173186i) q^{80} +(1.07002 + 9.78589i) q^{82} +(-11.2820 - 11.2820i) q^{83} +(0.0710109 - 0.0710109i) q^{85} +(1.56910 - 1.95436i) q^{86} +(-8.69673 - 4.29437i) q^{88} +5.52785 q^{89} +(-3.86569 - 3.86569i) q^{91} +(1.69499 + 7.65816i) q^{92} +(0.996544 + 9.11395i) q^{94} +0.473935 q^{95} -4.33616 q^{97} +(0.153718 + 1.40583i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{7}+O(q^{10}) \) 40 * q + 40 * q^7	\( 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) \) 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more