LMFDB - Embedded newform 1512.2.j.b.323.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.4
Root			$0.500000 + 1.19293i$ of defining polynomial
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.b.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +4.38587 q^{5} +1.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +4.38587 q^{5} +1.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.60534 + 5.99121i) q^{10} +5.11792i q^{11} +5.21068i q^{13} +(-1.36603 - 0.366025i) q^{14} +(2.00000 + 3.46410i) q^{16} -2.00000i q^{17} -6.50379 q^{19} +(-7.59655 - 4.38587i) q^{20} +(-6.99121 - 1.87329i) q^{22} -4.63929 q^{23} +14.2358 q^{25} +(-7.11792 - 1.90724i) q^{26} +(1.00000 - 1.73205i) q^{28} +1.26795 q^{29} -4.21068i q^{31} +(-5.46410 + 1.46410i) q^{32} +(2.73205 + 0.732051i) q^{34} +4.38587i q^{35} +1.98547i q^{37} +(2.38055 - 8.88434i) q^{38} +(8.77174 - 8.77174i) q^{40} +7.37134i q^{41} +3.71753 q^{43} +(5.11792 - 8.86450i) q^{44} +(1.69810 - 6.33739i) q^{46} +2.57558 q^{47} -1.00000 q^{49} +(-5.21068 + 19.4465i) q^{50} +(5.21068 - 9.02516i) q^{52} -10.2358 q^{53} +22.4465i q^{55} +(2.00000 + 2.00000i) q^{56} +(-0.464102 + 1.73205i) q^{58} -3.50379i q^{59} +4.53590i q^{61} +(5.75189 + 1.54122i) q^{62} -8.00000i q^{64} +22.8533i q^{65} +5.21068 q^{67} +(-2.00000 + 3.46410i) q^{68} +(-5.99121 - 1.60534i) q^{70} -1.36071 q^{71} +15.4465 q^{73} +(-2.71221 - 0.726734i) q^{74} +(11.2649 + 6.50379i) q^{76} -5.11792 q^{77} -3.98241i q^{79} +(8.77174 + 15.1931i) q^{80} +(-10.0694 - 2.69810i) q^{82} +11.6893i q^{83} -8.77174i q^{85} +(-1.36071 + 5.07823i) q^{86} +(10.2358 + 10.2358i) q^{88} -14.8645i q^{89} -5.21068 q^{91} +(8.03549 + 4.63929i) q^{92} +(-0.942729 + 3.51831i) q^{94} -28.5247 q^{95} +4.42136 q^{97} +(0.366025 - 1.36603i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 8 q^{5} + 16 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 + 8 * q^5 + 16 * q^8	$ 8 q + 4 q^{2} + 8 q^{5} + 16 q^{8} + 4 q^{10} - 4 q^{14} + 16 q^{16} + 16 q^{19} - 12 q^{22} - 16 q^{23} + 32 q^{25} - 16 q^{26} + 8 q^{28} + 24 q^{29} - 16 q^{32} + 8 q^{34} + 20 q^{38} + 16 q^{40} + 8 q^{43} + 4 q^{46} + 8 q^{47} - 8 q^{49} - 8 q^{50} + 8 q^{52} + 16 q^{56} + 24 q^{58} + 12 q^{62} + 8 q^{67} - 16 q^{68} - 4 q^{70} - 32 q^{71} + 8 q^{73} - 28 q^{74} + 24 q^{76} + 16 q^{80} - 36 q^{82} - 32 q^{86} - 8 q^{91} + 24 q^{92} + 40 q^{94} - 112 q^{95} - 32 q^{97} - 4 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 8 * q^5 + 16 * q^8 + 4 * q^10 - 4 * q^14 + 16 * q^16 + 16 * q^19 - 12 * q^22 - 16 * q^23 + 32 * q^25 - 16 * q^26 + 8 * q^28 + 24 * q^29 - 16 * q^32 + 8 * q^34 + 20 * q^38 + 16 * q^40 + 8 * q^43 + 4 * q^46 + 8 * q^47 - 8 * q^49 - 8 * q^50 + 8 * q^52 + 16 * q^56 + 24 * q^58 + 12 * q^62 + 8 * q^67 - 16 * q^68 - 4 * q^70 - 32 * q^71 + 8 * q^73 - 28 * q^74 + 24 * q^76 + 16 * q^80 - 36 * q^82 - 32 * q^86 - 8 * q^91 + 24 * q^92 + 40 * q^94 - 112 * q^95 - 32 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$3$		0			0
$3$		0			0
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$	4.38587			1.96142			0.980710	−	0.195469i	$-0.0626229\pi$
$5$	4.38587			1.96142			0.980710	+	0.195469i	$0.0626229\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$	−1.60534	+	5.99121i	−0.507653	+	1.89459i
$11$			5.11792i			1.54311i	0.636162	+	0.771555i	$0.280521\pi$
$11$			5.11792i			1.54311i	−0.636162	+	0.771555i	$0.719479\pi$
$12$		0			0
$13$			5.21068i			1.44518i	0.691276	+	0.722591i	$0.257049\pi$
$13$			5.21068i			1.44518i	−0.691276	+	0.722591i	$0.742951\pi$
$14$	−1.36603	−	0.366025i	−0.365086	−	0.0978244i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$		0			0
$19$	−6.50379			−1.49207			−0.746035	−	0.665906i	$-0.768045\pi$
$19$	−6.50379			−1.49207			−0.746035	+	0.665906i	$0.768045\pi$
$20$	−7.59655	−	4.38587i	−1.69864	−	0.980710i
$21$		0			0
$22$	−6.99121	−	1.87329i	−1.49053	−	0.399386i
$23$	−4.63929			−0.967359			−0.483680	−	0.875245i	$-0.660700\pi$
$23$	−4.63929			−0.967359			−0.483680	+	0.875245i	$0.660700\pi$
$24$		0			0
$25$	14.2358			2.84717
$26$	−7.11792	−	1.90724i	−1.39594	−	0.374041i
$27$		0			0
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	1.26795			0.235452			0.117726	−	0.993046i	$-0.462440\pi$
$29$	1.26795			0.235452			0.117726	+	0.993046i	$0.462440\pi$
$30$		0			0
$31$		−	4.21068i		−	0.756260i	−0.925752	−	0.378130i	$-0.876567\pi$
$31$		−	4.21068i		−	0.756260i	0.925752	−	0.378130i	$-0.123433\pi$
$32$	−5.46410	+	1.46410i	−0.965926	+	0.258819i
$33$		0			0
$34$	2.73205	+	0.732051i	0.468543	+	0.125546i
$35$			4.38587i			0.741347i
$36$		0			0
$37$			1.98547i			0.326410i	0.986592	+	0.163205i	$0.0521832\pi$
$37$			1.98547i			0.326410i	−0.986592	+	0.163205i	$0.947817\pi$
$38$	2.38055	−	8.88434i	0.386176	−	1.44123i
$39$		0			0
$40$	8.77174	−	8.77174i	1.38693	−	1.38693i
$41$			7.37134i			1.15121i	0.817728	+	0.575605i	$0.195233\pi$
$41$			7.37134i			1.15121i	−0.817728	+	0.575605i	$0.804767\pi$
$42$		0			0
$43$	3.71753			0.566917			0.283459	−	0.958984i	$-0.408518\pi$
$43$	3.71753			0.566917			0.283459	+	0.958984i	$0.408518\pi$
$44$	5.11792	−	8.86450i	0.771555	−	1.33637i
$45$		0			0
$46$	1.69810	−	6.33739i	0.250371	−	0.934397i
$47$	2.57558			0.375687			0.187844	−	0.982199i	$-0.439850\pi$
$47$	2.57558			0.375687			0.187844	+	0.982199i	$0.439850\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−5.21068	+	19.4465i	−0.736901	+	2.75015i
$51$		0			0
$52$	5.21068	−	9.02516i	0.722591	−	1.25156i
$53$	−10.2358			−1.40600			−0.703000	−	0.711190i	$-0.748157\pi$
$53$	−10.2358			−1.40600			−0.703000	+	0.711190i	$0.748157\pi$
$54$		0			0
$55$			22.4465i			3.02669i
$56$	2.00000	+	2.00000i	0.267261	+	0.267261i
$57$		0			0
$58$	−0.464102	+	1.73205i	−0.0609395	+	0.227429i
$59$		−	3.50379i		−	0.456154i	−0.973643	−	0.228077i	$-0.926756\pi$
$59$		−	3.50379i		−	0.456154i	0.973643	−	0.228077i	$-0.0732438\pi$
$60$		0			0
$61$			4.53590i			0.580762i	0.956911	+	0.290381i	$0.0937821\pi$
$61$			4.53590i			0.580762i	−0.956911	+	0.290381i	$0.906218\pi$
$62$	5.75189	+	1.54122i	0.730491	+	0.195735i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$			22.8533i			2.83461i
$66$		0			0
$67$	5.21068			0.636586			0.318293	−	0.947992i	$-0.396890\pi$
$67$	5.21068			0.636586			0.318293	+	0.947992i	$0.396890\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$		0			0
$70$	−5.99121	−	1.60534i	−0.716086	−	0.191875i
$71$	−1.36071			−0.161486			−0.0807432	−	0.996735i	$-0.525729\pi$
$71$	−1.36071			−0.161486			−0.0807432	+	0.996735i	$0.525729\pi$
$72$		0			0
$73$	15.4465			1.80788			0.903939	−	0.427662i	$-0.140662\pi$
$73$	15.4465			1.80788			0.903939	+	0.427662i	$0.140662\pi$
$74$	−2.71221	−	0.726734i	−0.315288	−	0.0844811i
$75$		0			0
$76$	11.2649	+	6.50379i	1.29217	+	0.746035i
$77$	−5.11792			−0.583241
$78$		0			0
$79$		−	3.98241i		−	0.448057i	−0.974583	−	0.224028i	$-0.928079\pi$
$79$		−	3.98241i		−	0.448057i	0.974583	−	0.224028i	$-0.0719208\pi$
$80$	8.77174	+	15.1931i	0.980710	+	1.69864i
$81$		0			0
$82$	−10.0694	−	2.69810i	−1.11198	−	0.297955i
$83$			11.6893i			1.28307i	0.767095	+	0.641534i	$0.221702\pi$
$83$			11.6893i			1.28307i	−0.767095	+	0.641534i	$0.778298\pi$
$84$		0			0
$85$		−	8.77174i		−	0.951428i
$86$	−1.36071	+	5.07823i	−0.146729	+	0.547600i
$87$		0			0
$88$	10.2358	+	10.2358i	1.09114	+	1.09114i
$89$		−	14.8645i		−	1.57563i	−0.615910	−	0.787817i	$-0.711211\pi$
$89$		−	14.8645i		−	1.57563i	0.615910	−	0.787817i	$-0.288789\pi$
$90$		0			0
$91$	−5.21068			−0.546227
$92$	8.03549	+	4.63929i	0.837758	+	0.483680i
$93$		0			0
$94$	−0.942729	+	3.51831i	−0.0972351	+	0.362886i
$95$	−28.5247			−2.92658
$96$		0			0
$97$	4.42136			0.448921			0.224460	−	0.974483i	$-0.427938\pi$
$97$	4.42136			0.448921			0.224460	+	0.974483i	$0.427938\pi$
$98$	0.366025	−	1.36603i	0.0369741	−	0.137989i
$99$		0			0
$100$	−24.6572	−	14.2358i	−2.46572	−	1.42358i
$101$	2.00000			0.199007			0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000			0.199007			0.0995037	+	0.995037i	$0.468274\pi$
$102$		0			0
$103$		−	1.67478i		−	0.165021i	−0.996590	−	0.0825105i	$-0.973706\pi$
$103$		−	1.67478i		−	0.165021i	0.996590	−	0.0825105i	$-0.0262938\pi$
$104$	10.4214	+	10.4214i	1.02190	+	1.02190i
$105$		0			0
$106$	3.74658	−	13.9824i	0.363900	−	1.35809i
$107$		−	10.2649i		−	0.992344i	−0.868224	−	0.496172i	$-0.834738\pi$
$107$		−	10.2649i		−	0.992344i	0.868224	−	0.496172i	$-0.165262\pi$
$108$		0			0
$109$		−	1.29311i		−	0.123857i	−0.998081	−	0.0619287i	$-0.980275\pi$
$109$		−	1.29311i		−	0.123857i	0.998081	−	0.0619287i	$-0.0197251\pi$
$110$	−30.6625	−	8.21599i	−2.92356	−	0.783364i
$111$		0			0
$112$	−3.46410	+	2.00000i	−0.327327	+	0.188982i
$113$		−	8.07937i		−	0.760043i	−0.924978	−	0.380022i	$-0.875917\pi$
$113$		−	8.07937i		−	0.760043i	0.924978	−	0.380022i	$-0.124083\pi$
$114$		0			0
$115$	−20.3473			−1.89740
$116$	−2.19615	−	1.26795i	−0.203908	−	0.117726i
$117$		0			0
$118$	4.78626	+	1.28247i	0.440611	+	0.118061i
$119$	2.00000			0.183340
$120$		0			0
$121$	−15.1931			−1.38119
$122$	−6.19615	−	1.66025i	−0.560973	−	0.150312i
$123$		0			0
$124$	−4.21068	+	7.29311i	−0.378130	+	0.654940i
$125$	40.5072			3.62307
$126$		0			0
$127$			13.4465i			1.19319i	0.802544	+	0.596593i	$0.203479\pi$
$127$			13.4465i			1.19319i	−0.802544	+	0.596593i	$0.796521\pi$
$128$	10.9282	+	2.92820i	0.965926	+	0.258819i
$129$		0			0
$130$	−31.2183	−	8.36491i	−2.73802	−	0.733651i
$131$			1.77480i			0.155065i	0.996990	+	0.0775323i	$0.0247041\pi$
$131$			1.77480i			0.155065i	−0.996990	+	0.0775323i	$0.975296\pi$
$132$		0			0
$133$		−	6.50379i		−	0.563950i
$134$	−1.90724	+	7.11792i	−0.164760	+	0.614895i
$135$		0			0
$136$	−4.00000	−	4.00000i	−0.342997	−	0.342997i
$137$		−	14.5756i		−	1.24528i	−0.782510	−	0.622638i	$-0.786061\pi$
$137$		−	14.5756i		−	1.24528i	0.782510	−	0.622638i	$-0.213939\pi$
$138$		0			0
$139$	15.0076			1.27293			0.636463	−	0.771307i	$-0.280397\pi$
$139$	15.0076			1.27293			0.636463	+	0.771307i	$0.280397\pi$
$140$	4.38587	−	7.59655i	0.370673	−	0.642025i
$141$		0			0
$142$	0.498054	−	1.85876i	0.0417958	−	0.155984i
$143$	−26.6678			−2.23008
$144$		0			0
$145$	5.56106			0.461821
$146$	−5.65382	+	21.1003i	−0.467913	+	1.74628i
$147$		0			0
$148$	1.98547	−	3.43894i	0.163205	−	0.282679i
$149$	−5.33669			−0.437198			−0.218599	−	0.975815i	$-0.570149\pi$
$149$	−5.33669			−0.437198			−0.218599	+	0.975815i	$0.570149\pi$
$150$		0			0
$151$			17.5725i			1.43003i	0.699108	+	0.715016i	$0.253581\pi$
$151$			17.5725i			1.43003i	−0.699108	+	0.715016i	$0.746419\pi$
$152$	−13.0076	+	13.0076i	−1.05505	+	1.05505i
$153$		0			0
$154$	1.87329	−	6.99121i	0.150954	−	0.563368i
$155$		−	18.4675i		−	1.48334i
$156$		0			0
$157$			13.8259i			1.10343i	0.834032	+	0.551715i	$0.186027\pi$
$157$			13.8259i			1.10343i	−0.834032	+	0.551715i	$0.813973\pi$
$158$	5.44008	+	1.45766i	0.432789	+	0.115966i
$159$		0			0
$160$	−23.9648	+	6.42136i	−1.89459	+	0.507653i
$161$		−	4.63929i		−	0.365627i
$162$		0			0
$163$	8.67478			0.679461			0.339731	−	0.940523i	$-0.389664\pi$
$163$	8.67478			0.679461			0.339731	+	0.940523i	$0.389664\pi$
$164$	7.37134	−	12.7675i	0.575605	−	0.996977i
$165$		0			0
$166$	−15.9679	−	4.27858i	−1.23935	−	0.332082i
$167$	−15.8855			−1.22925			−0.614627	−	0.788818i	$-0.710693\pi$
$167$	−15.8855			−1.22925			−0.614627	+	0.788818i	$0.710693\pi$
$168$		0			0
$169$	−14.1512			−1.08855
$170$	11.9824	+	3.21068i	0.919009	+	0.246248i
$171$		0			0
$172$	−6.43894	−	3.71753i	−0.490965	−	0.283459i
$173$	4.22940			0.321555			0.160778	−	0.986991i	$-0.448600\pi$
$173$	4.22940			0.321555			0.160778	+	0.986991i	$0.448600\pi$
$174$		0			0
$175$			14.2358i			1.07613i
$176$	−17.7290	+	10.2358i	−1.33637	+	0.771555i
$177$		0			0
$178$	20.3053	+	5.44078i	1.52194	+	0.407804i
$179$			6.45041i			0.482126i	0.970509	+	0.241063i	$0.0774961\pi$
$179$			6.45041i			0.482126i	−0.970509	+	0.241063i	$0.922504\pi$
$180$		0			0
$181$			10.5068i			0.780968i	0.920610	+	0.390484i	$0.127692\pi$
$181$			10.5068i			0.780968i	−0.920610	+	0.390484i	$0.872308\pi$
$182$	1.90724	−	7.11792i	0.141374	−	0.527615i
$183$		0			0
$184$	−9.27858	+	9.27858i	−0.684026	+	0.684026i
$185$			8.70803i			0.640227i
$186$		0			0
$187$	10.2358			0.748519
$188$	−4.46104	−	2.57558i	−0.325355	−	0.187844i
$189$		0			0
$190$	10.4408	−	38.9655i	0.757454	−	2.82686i
$191$	8.25986			0.597663			0.298831	−	0.954306i	$-0.403403\pi$
$191$	8.25986			0.597663			0.298831	+	0.954306i	$0.403403\pi$
$192$		0			0
$193$	−8.07937			−0.581566			−0.290783	−	0.956789i	$-0.593916\pi$
$193$	−8.07937			−0.581566			−0.290783	+	0.956789i	$0.593916\pi$
$194$	−1.61833	+	6.03969i	−0.116189	+	0.433624i
$195$		0			0
$196$	1.73205	+	1.00000i	0.123718	+	0.0714286i
$197$	7.04275			0.501775			0.250887	−	0.968016i	$-0.419278\pi$
$197$	7.04275			0.501775			0.250887	+	0.968016i	$0.419278\pi$
$198$		0			0
$199$		−	20.1336i		−	1.42723i	−0.700537	−	0.713616i	$-0.747056\pi$
$199$		−	20.1336i		−	1.42723i	0.700537	−	0.713616i	$-0.252944\pi$
$200$	28.4717	−	28.4717i	2.01325	−	2.01325i
$201$		0			0
$202$	−0.732051	+	2.73205i	−0.0515069	+	0.192226i
$203$			1.26795i			0.0889926i
$204$		0			0
$205$			32.3297i			2.25801i
$206$	2.28779	+	0.613012i	0.159398	+	0.0427106i
$207$		0			0
$208$	−18.0503	+	10.4214i	−1.25156	+	0.722591i
$209$		−	33.2859i		−	2.30243i
$210$		0			0
$211$	7.54347			0.519314			0.259657	−	0.965701i	$-0.416390\pi$
$211$	7.54347			0.519314			0.259657	+	0.965701i	$0.416390\pi$
$212$	17.7290	+	10.2358i	1.21763	+	0.703000i
$213$		0			0
$214$	14.0221	+	3.75721i	0.958531	+	0.256838i
$215$	16.3046			1.11196
$216$		0			0
$217$	4.21068			0.285839
$218$	1.76642	+	0.473311i	0.119637	+	0.0320566i
$219$		0			0
$220$	22.4465	−	38.8785i	1.51334	−	2.62119i
$221$	10.4214			0.701016
$222$		0			0
$223$		−	5.48926i		−	0.367588i	−0.982965	−	0.183794i	$-0.941162\pi$
$223$		−	5.48926i		−	0.367588i	0.982965	−	0.183794i	$-0.0588380\pi$
$224$	−1.46410	−	5.46410i	−0.0978244	−	0.365086i
$225$		0			0
$226$	11.0366	+	2.95725i	0.734145	+	0.196714i
$227$		−	0.127416i		−	0.00845689i	−0.999991	−	0.00422845i	$-0.998654\pi$
$227$		−	0.127416i		−	0.00845689i	0.999991	−	0.00422845i	$-0.00134596\pi$
$228$		0			0
$229$			6.53590i			0.431904i	0.976404	+	0.215952i	$0.0692855\pi$
$229$			6.53590i			0.431904i	−0.976404	+	0.215952i	$0.930714\pi$
$230$	7.44764	−	27.7950i	0.491083	−	1.83275i
$231$		0			0
$232$	2.53590	−	2.53590i	0.166490	−	0.166490i
$233$		−	10.5359i		−	0.690230i	−0.938560	−	0.345115i	$-0.887840\pi$
$233$		−	10.5359i		−	0.690230i	0.938560	−	0.345115i	$-0.112160\pi$
$234$		0			0
$235$	11.2962			0.736881
$236$	−3.50379	+	6.06874i	−0.228077	+	0.395041i
$237$		0			0
$238$	−0.732051	+	2.73205i	−0.0474518	+	0.177093i
$239$	24.3862			1.57741			0.788706	−	0.614771i	$-0.210752\pi$
$239$	24.3862			1.57741			0.788706	+	0.614771i	$0.210752\pi$
$240$		0			0
$241$	−10.8603			−0.699573			−0.349787	−	0.936829i	$-0.613746\pi$
$241$	−10.8603			−0.699573			−0.349787	+	0.936829i	$0.613746\pi$
$242$	5.56106	−	20.7541i	0.357478	−	1.33413i
$243$		0			0
$244$	4.53590	−	7.85641i	0.290381	−	0.502955i
$245$	−4.38587			−0.280203
$246$		0			0
$247$		−	33.8891i		−	2.15631i
$248$	−8.42136	−	8.42136i	−0.534757	−	0.534757i
$249$		0			0
$250$	−14.8267	+	55.3338i	−0.937720	+	3.49962i
$251$			3.73511i			0.235758i	0.993028	+	0.117879i	$0.0376095\pi$
$251$			3.73511i			0.235758i	−0.993028	+	0.117879i	$0.962390\pi$
$252$		0			0
$253$		−	23.7435i		−	1.49274i
$254$	−18.3683	−	4.92177i	−1.15253	−	0.308819i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		−	7.52781i		−	0.469572i	−0.972047	−	0.234786i	$-0.924561\pi$
$257$		−	7.52781i		−	0.469572i	0.972047	−	0.234786i	$-0.0754389\pi$
$258$		0			0
$259$	−1.98547			−0.123371
$260$	22.8533	−	39.5832i	1.41730	−	2.45484i
$261$		0			0
$262$	−2.42442	−	0.649620i	−0.149781	−	0.0401337i
$263$	−16.7187			−1.03092			−0.515458	−	0.856915i	$-0.672378\pi$
$263$	−16.7187			−1.03092			−0.515458	+	0.856915i	$0.672378\pi$
$264$		0			0
$265$	−44.8930			−2.75776
$266$	8.88434	+	2.38055i	0.544734	+	0.145961i
$267$		0			0
$268$	−9.02516	−	5.21068i	−0.551299	−	0.318293i
$269$	−4.11486			−0.250887			−0.125444	−	0.992101i	$-0.540035\pi$
$269$	−4.11486			−0.250887			−0.125444	+	0.992101i	$0.540035\pi$
$270$		0			0
$271$			4.31293i			0.261992i	0.991383	+	0.130996i	$0.0418175\pi$
$271$			4.31293i			0.261992i	−0.991383	+	0.130996i	$0.958182\pi$
$272$	6.92820	−	4.00000i	0.420084	−	0.242536i
$273$		0			0
$274$	19.9106	+	5.33503i	1.20284	+	0.322301i
$275$			72.8579i			4.39349i
$276$		0			0
$277$		−	27.7564i		−	1.66772i	−0.551976	−	0.833860i	$-0.686126\pi$
$277$		−	27.7564i		−	1.66772i	0.551976	−	0.833860i	$-0.313874\pi$
$278$	−5.49315	+	20.5007i	−0.329457	+	1.22955i
$279$		0			0
$280$	8.77174	+	8.77174i	0.524211	+	0.524211i
$281$			21.8961i			1.30621i	0.757267	+	0.653106i	$0.226534\pi$
$281$			21.8961i			1.30621i	−0.757267	+	0.653106i	$0.773466\pi$
$282$		0			0
$283$	15.3786			0.914164			0.457082	−	0.889425i	$-0.348895\pi$
$283$	15.3786			0.914164			0.457082	+	0.889425i	$0.348895\pi$
$284$	2.35682	+	1.36071i	0.139851	+	0.0807432i
$285$		0			0
$286$	9.76110	−	36.4289i	0.577186	−	2.15409i
$287$	−7.37134			−0.435117
$288$		0			0
$289$	13.0000			0.764706
$290$	−2.03549	+	7.59655i	−0.119528	+	0.446085i
$291$		0			0
$292$	−26.7541	−	15.4465i	−1.56567	−	0.903939i
$293$	−0.408482			−0.0238638			−0.0119319	−	0.999929i	$-0.503798\pi$
$293$	−0.408482			−0.0238638			−0.0119319	+	0.999929i	$0.503798\pi$
$294$		0			0
$295$		−	15.3671i		−	0.894710i
$296$	3.97095	+	3.97095i	0.230807	+	0.230807i
$297$		0			0
$298$	1.95336	−	7.29005i	0.113155	−	0.422301i
$299$		−	24.1739i		−	1.39801i
$300$		0			0
$301$			3.71753i			0.214275i
$302$	−24.0045	−	6.43199i	−1.38130	−	0.370119i
$303$		0			0
$304$	−13.0076	−	22.5298i	−0.746035	−	1.29217i
$305$			19.8939i			1.13912i
$306$		0			0
$307$	9.99694			0.570555			0.285278	−	0.958445i	$-0.407914\pi$
$307$	9.99694			0.570555			0.285278	+	0.958445i	$0.407914\pi$
$308$	8.86450	+	5.11792i	0.505101	+	0.291620i
$309$		0			0
$310$	25.2270	+	6.75957i	1.43280	+	0.383918i
$311$	−19.9603			−1.13185			−0.565923	−	0.824458i	$-0.691480\pi$
$311$	−19.9603			−1.13185			−0.565923	+	0.824458i	$0.691480\pi$
$312$		0			0
$313$	23.4465			1.32528			0.662638	−	0.748940i	$-0.269437\pi$
$313$	23.4465			1.32528			0.662638	+	0.748940i	$0.269437\pi$
$314$	−18.8866	−	5.06065i	−1.06583	−	0.285589i
$315$		0			0
$316$	−3.98241	+	6.89774i	−0.224028	+	0.388028i
$317$	20.7740			1.16678			0.583391	−	0.812191i	$-0.301725\pi$
$317$	20.7740			1.16678			0.583391	+	0.812191i	$0.301725\pi$
$318$		0			0
$319$			6.48926i			0.363329i
$320$		−	35.0869i		−	1.96142i
$321$		0			0
$322$	6.33739	+	1.69810i	0.353169	+	0.0946313i
$323$			13.0076i			0.723761i
$324$		0			0
$325$			74.1784i			4.11468i
$326$	−3.17519	+	11.8500i	−0.175857	+	0.656309i
$327$		0			0
$328$	14.7427	+	14.7427i	0.814029	+	0.814029i
$329$			2.57558i			0.141997i
$330$		0			0
$331$	19.0366			1.04635			0.523174	−	0.852226i	$-0.324748\pi$
$331$	19.0366			1.04635			0.523174	+	0.852226i	$0.324748\pi$
$332$	11.6893	−	20.2465i	0.641534	−	1.11117i
$333$		0			0
$334$	5.81448	−	21.6999i	0.318154	−	1.18737i
$335$	22.8533			1.24861
$336$		0			0
$337$	2.88546			0.157181			0.0785905	−	0.996907i	$-0.474958\pi$
$337$	2.88546			0.157181			0.0785905	+	0.996907i	$0.474958\pi$
$338$	5.17969	−	19.3309i	0.281738	−	1.05146i
$339$		0			0
$340$	−8.77174	+	15.1931i	−0.475714	+	0.823961i
$341$	21.5499			1.16699
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	7.43505	−	7.43505i	0.400871	−	0.400871i
$345$		0			0
$346$	−1.54807	+	5.77747i	−0.0832247	+	0.310599i
$347$		−	30.7033i		−	1.64824i	−0.566415	−	0.824120i	$-0.691670\pi$
$347$		−	30.7033i		−	1.64824i	0.566415	−	0.824120i	$-0.308330\pi$
$348$		0			0
$349$		−	26.5007i		−	1.41855i	−0.704931	−	0.709276i	$-0.749022\pi$
$349$		−	26.5007i		−	1.41855i	0.704931	−	0.709276i	$-0.250978\pi$
$350$	−19.4465	−	5.21068i	−1.03946	−	0.278522i
$351$		0			0
$352$	−7.49315	−	27.9648i	−0.399386	−	1.49053i
$353$			6.29955i			0.335291i	0.985847	+	0.167645i	$0.0536164\pi$
$353$			6.29955i			0.335291i	−0.985847	+	0.167645i	$0.946384\pi$
$354$		0			0
$355$	−5.96789			−0.316743
$356$	−14.8645	+	25.7461i	−0.787817	+	1.36454i
$357$		0			0
$358$	−8.81142	−	2.36101i	−0.465698	−	0.124783i
$359$	−1.60770			−0.0848509			−0.0424255	−	0.999100i	$-0.513508\pi$
$359$	−1.60770			−0.0848509			−0.0424255	+	0.999100i	$0.513508\pi$
$360$		0			0
$361$	23.2992			1.22628
$362$	−14.3526	−	3.84577i	−0.754357	−	0.202129i
$363$		0			0
$364$	9.02516	+	5.21068i	0.473047	+	0.273114i
$365$	67.7464			3.54601
$366$		0			0
$367$		−	17.1763i		−	0.896597i	−0.893884	−	0.448298i	$-0.852030\pi$
$367$		−	17.1763i		−	0.896597i	0.893884	−	0.448298i	$-0.147970\pi$
$368$	−9.27858	−	16.0710i	−0.483680	−	0.837758i
$369$		0			0
$370$	−11.8954	−	3.18736i	−0.618412	−	0.165703i
$371$		−	10.2358i		−	0.531418i
$372$		0			0
$373$			2.27941i			0.118024i	0.998257	+	0.0590118i	$0.0187950\pi$
$373$			2.27941i			0.118024i	−0.998257	+	0.0590118i	$0.981205\pi$
$374$	−3.74658	+	13.9824i	−0.193731	+	0.723013i
$375$		0			0
$376$	5.15117	−	5.15117i	0.265651	−	0.265651i
$377$			6.60688i			0.340271i
$378$		0			0
$379$	20.1389			1.03446			0.517232	−	0.855845i	$-0.326962\pi$
$379$	20.1389			1.03446			0.517232	+	0.855845i	$0.326962\pi$
$380$	49.4063	+	28.5247i	2.53449	+	1.46329i
$381$		0			0
$382$	−3.02332	+	11.2832i	−0.154686	+	0.577298i
$383$	−22.3068			−1.13982			−0.569912	−	0.821705i	$-0.693023\pi$
$383$	−22.3068			−1.13982			−0.569912	+	0.821705i	$0.693023\pi$
$384$		0			0
$385$	−22.4465			−1.14398
$386$	2.95725	−	11.0366i	0.150520	−	0.561749i
$387$		0			0
$388$	−7.65801	−	4.42136i	−0.388777	−	0.224460i
$389$	1.57864			0.0800404			0.0400202	−	0.999199i	$-0.487258\pi$
$389$	1.57864			0.0800404			0.0400202	+	0.999199i	$0.487258\pi$
$390$		0			0
$391$			9.27858i			0.469238i
$392$	−2.00000	+	2.00000i	−0.101015	+	0.101015i
$393$		0			0
$394$	−2.57782	+	9.62057i	−0.129869	+	0.484677i
$395$		−	17.4663i		−	0.878827i
$396$		0			0
$397$			31.4289i			1.57737i	0.614796	+	0.788686i	$0.289238\pi$
$397$			31.4289i			1.57737i	−0.614796	+	0.788686i	$0.710762\pi$
$398$	27.5030	+	7.36940i	1.37860	+	0.369395i
$399$		0			0
$400$	28.4717	+	49.3144i	1.42358	+	2.46572i
$401$		−	26.5404i		−	1.32536i	−0.748901	−	0.662682i	$-0.769418\pi$
$401$		−	26.5404i		−	1.32536i	0.748901	−	0.662682i	$-0.230582\pi$
$402$		0			0
$403$	21.9405			1.09293
$404$	−3.46410	−	2.00000i	−0.172345	−	0.0995037i
$405$		0			0
$406$	−1.73205	−	0.464102i	−0.0859602	−	0.0230330i
$407$	−10.1615			−0.503687
$408$		0			0
$409$	32.0037			1.58248			0.791240	−	0.611506i	$-0.209436\pi$
$409$	32.0037			1.58248			0.791240	+	0.611506i	$0.209436\pi$
$410$	−44.1632	−	11.8335i	−2.18107	−	0.584415i
$411$		0			0
$412$	−1.67478	+	2.90080i	−0.0825105	+	0.142912i
$413$	3.50379			0.172410
$414$		0			0
$415$			51.2678i			2.51663i
$416$	−7.62896	−	28.4717i	−0.374041	−	1.39594i
$417$		0			0
$418$	45.4693	+	12.1835i	2.22398	+	0.595913i
$419$			20.6572i			1.00917i	0.863362	+	0.504585i	$0.168354\pi$
$419$			20.6572i			1.00917i	−0.863362	+	0.504585i	$0.831646\pi$
$420$		0			0
$421$		−	32.9930i		−	1.60798i	−0.594641	−	0.803991i	$-0.702706\pi$
$421$		−	32.9930i		−	1.60798i	0.594641	−	0.803991i	$-0.297294\pi$
$422$	−2.76110	+	10.3046i	−0.134408	+	0.501619i
$423$		0			0
$424$	−20.4717	+	20.4717i	−0.994192	+	0.994192i
$425$		−	28.4717i		−	1.38108i
$426$		0			0
$427$	−4.53590			−0.219508
$428$	−10.2649	+	17.7793i	−0.496172	+	0.859395i
$429$		0			0
$430$	−5.96789	+	22.2725i	−0.287797	+	1.07407i
$431$	6.48282			0.312267			0.156133	−	0.987736i	$-0.450097\pi$
$431$	6.48282			0.312267			0.156133	+	0.987736i	$0.450097\pi$
$432$		0			0
$433$	−18.4038			−0.884429			−0.442214	−	0.896909i	$-0.645807\pi$
$433$	−18.4038			−0.884429			−0.442214	+	0.896909i	$0.645807\pi$
$434$	−1.54122	+	5.75189i	−0.0739807	+	0.276100i
$435$		0			0
$436$	−1.29311	+	2.23973i	−0.0619287	+	0.107264i
$437$	30.1730			1.44337
$438$		0			0
$439$		−	4.31293i		−	0.205845i	−0.994689	−	0.102923i	$-0.967181\pi$
$439$		−	4.31293i		−	0.205845i	0.994689	−	0.102923i	$-0.0328194\pi$
$440$	44.8930	+	44.8930i	2.14019	+	2.14019i
$441$		0			0
$442$	−3.81448	+	14.2358i	−0.181436	+	0.677130i
$443$			5.54540i			0.263470i	0.991285	+	0.131735i	$0.0420547\pi$
$443$			5.54540i			0.263470i	−0.991285	+	0.131735i	$0.957945\pi$
$444$		0			0
$445$		−	65.1937i		−	3.09048i
$446$	7.49847	+	2.00921i	0.355063	+	0.0951388i
$447$		0			0
$448$	8.00000			0.377964
$449$			30.2007i			1.42526i	0.701541	+	0.712629i	$0.252496\pi$
$449$			30.2007i			1.42526i	−0.701541	+	0.712629i	$0.747504\pi$
$450$		0			0
$451$	−37.7259			−1.77644
$452$	−8.07937	+	13.9939i	−0.380022	+	0.658217i
$453$		0			0
$454$	0.174053	+	0.0466375i	0.00816873	+	0.00218880i
$455$	−22.8533			−1.07138
$456$		0			0
$457$	−24.3205			−1.13767			−0.568833	−	0.822453i	$-0.692605\pi$
$457$	−24.3205			−1.13767			−0.568833	+	0.822453i	$0.692605\pi$
$458$	−8.92820	−	2.39230i	−0.417188	−	0.111785i
$459$		0			0
$460$	35.2426	+	20.3473i	1.64319	+	0.948699i
$461$	−37.3141			−1.73789			−0.868945	−	0.494909i	$-0.835201\pi$
$461$	−37.3141			−1.73789			−0.868945	+	0.494909i	$0.835201\pi$
$462$		0			0
$463$			35.2853i			1.63985i	0.572472	+	0.819924i	$0.305985\pi$
$463$			35.2853i			1.63985i	−0.572472	+	0.819924i	$0.694015\pi$
$464$	2.53590	+	4.39230i	0.117726	+	0.203908i
$465$		0			0
$466$	14.3923	+	3.85641i	0.666711	+	0.178645i
$467$		−	20.7824i		−	0.961693i	−0.876805	−	0.480847i	$-0.840329\pi$
$467$		−	20.7824i		−	0.961693i	0.876805	−	0.480847i	$-0.159671\pi$
$468$		0			0
$469$			5.21068i			0.240607i
$470$	−4.13468	+	15.4309i	−0.190719	+	0.711772i
$471$		0			0
$472$	−7.00757	−	7.00757i	−0.322550	−	0.322550i
$473$			19.0260i			0.874816i
$474$		0			0
$475$	−92.5868			−4.24818
$476$	−3.46410	−	2.00000i	−0.158777	−	0.0916698i
$477$		0			0
$478$	−8.92596	+	33.3121i	−0.408264	+	1.52366i
$479$	17.1640			0.784245			0.392123	−	0.919913i	$-0.371741\pi$
$479$	17.1640			0.784245			0.392123	+	0.919913i	$0.371741\pi$
$480$		0			0
$481$	−10.3457			−0.471722
$482$	3.97515	−	14.8354i	0.181063	−	0.675736i
$483$		0			0
$484$	26.3152	+	15.1931i	1.19615	+	0.690595i
$485$	19.3915			0.880522
$486$		0			0
$487$		−	38.7961i		−	1.75802i	−0.476805	−	0.879009i	$-0.658205\pi$
$487$		−	38.7961i		−	1.75802i	0.476805	−	0.879009i	$-0.341795\pi$
$488$	9.07180	+	9.07180i	0.410661	+	0.410661i
$489$		0			0
$490$	1.60534	−	5.99121i	0.0725218	−	0.270655i
$491$		−	31.1973i		−	1.40791i	−0.710243	−	0.703957i	$-0.751415\pi$
$491$		−	31.1973i		−	1.40791i	0.710243	−	0.703957i	$-0.248585\pi$
$492$		0			0
$493$		−	2.53590i		−	0.114211i
$494$	46.2934	+	12.4043i	2.08284	+	0.558095i
$495$		0			0
$496$	14.5862	−	8.42136i	0.654940	−	0.378130i
$497$		−	1.36071i		−	0.0610361i
$498$		0			0
$499$	−8.78320			−0.393190			−0.196595	−	0.980485i	$-0.562988\pi$
$499$	−8.78320			−0.393190			−0.196595	+	0.980485i	$0.562988\pi$
$500$	−70.1605	−	40.5072i	−3.13767	−	1.81154i
$501$		0			0
$502$	−5.10226	−	1.36715i	−0.227725	−	0.0610187i
$503$	11.2679			0.502413			0.251207	−	0.967934i	$-0.419173\pi$
$503$	11.2679			0.502413			0.251207	+	0.967934i	$0.419173\pi$
$504$		0			0
$505$	8.77174			0.390337
$506$	32.4342	+	8.69073i	1.44188	+	0.386350i
$507$		0			0
$508$	13.4465	−	23.2900i	0.596593	−	1.03333i
$509$	−7.99388			−0.354322			−0.177161	−	0.984182i	$-0.556691\pi$
$509$	−7.99388			−0.354322			−0.177161	+	0.984182i	$0.556691\pi$
$510$		0			0
$511$			15.4465i			0.683314i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	10.2832	+	2.75537i	0.453572	+	0.121534i
$515$		−	7.34536i		−	0.323675i
$516$		0			0
$517$			13.1816i			0.579727i
$518$	0.726734	−	2.71221i	0.0319309	−	0.119168i
$519$		0			0
$520$	45.7067	+	45.7067i	2.00437	+	2.00437i
$521$		−	15.1797i		−	0.665035i	−0.943097	−	0.332517i	$-0.892102\pi$
$521$		−	15.1797i		−	0.665035i	0.943097	−	0.332517i	$-0.107898\pi$
$522$		0			0
$523$	−5.58846			−0.244366			−0.122183	−	0.992508i	$-0.538990\pi$
$523$	−5.58846			−0.244366			−0.122183	+	0.992508i	$0.538990\pi$
$524$	1.77480	−	3.07404i	0.0775323	−	0.134290i
$525$		0			0
$526$	6.11945	−	22.8381i	0.266821	−	0.995789i
$527$	−8.42136			−0.366840
$528$		0			0
$529$	−1.47698			−0.0642163
$530$	16.4320	−	61.3250i	0.713760	−	2.66379i
$531$		0			0
$532$	−6.50379	+	11.2649i	−0.281975	+	0.488395i
$533$	−38.4097			−1.66371
$534$		0			0
$535$		−	45.0204i		−	1.94640i
$536$	10.4214	−	10.4214i	0.450134	−	0.450134i
$537$		0			0
$538$	1.50614	−	5.62100i	0.0649344	−	0.242339i
$539$		−	5.11792i		−	0.220444i
$540$		0			0
$541$		−	10.1229i		−	0.435219i	−0.976036	−	0.217610i	$-0.930174\pi$
$541$		−	10.1229i		−	0.435219i	0.976036	−	0.217610i	$-0.0698260\pi$
$542$	−5.89158	−	1.57864i	−0.253065	−	0.0678086i
$543$		0			0
$544$	2.92820	+	10.9282i	0.125546	+	0.468543i
$545$		−	5.67140i		−	0.242936i
$546$		0			0
$547$	7.03662			0.300864			0.150432	−	0.988620i	$-0.451933\pi$
$547$	7.03662			0.300864			0.150432	+	0.988620i	$0.451933\pi$
$548$	−14.5756	+	25.2457i	−0.622638	+	1.07844i
$549$		0			0
$550$	−99.5257	−	26.6678i	−4.24379	−	1.13712i
$551$	−8.24647			−0.351311
$552$		0			0
$553$	3.98241			0.169349
$554$	37.9159	+	10.1595i	1.61089	+	0.431638i
$555$		0			0
$556$	−25.9939	−	15.0076i	−1.10239	−	0.636463i
$557$	11.0427			0.467896			0.233948	−	0.972249i	$-0.424835\pi$
$557$	11.0427			0.467896			0.233948	+	0.972249i	$0.424835\pi$
$558$		0			0
$559$			19.3708i			0.819299i
$560$	−15.1931	+	8.77174i	−0.642025	+	0.370673i
$561$		0			0
$562$	−29.9106	−	8.01453i	−1.26170	−	0.338072i
$563$		−	19.1115i		−	0.805453i	−0.915320	−	0.402726i	$-0.868063\pi$
$563$		−	19.1115i		−	0.805453i	0.915320	−	0.402726i	$-0.131937\pi$
$564$		0			0
$565$		−	35.4351i		−	1.49076i
$566$	−5.62896	+	21.0076i	−0.236603	+	0.883014i
$567$		0			0
$568$	−2.72142	+	2.72142i	−0.114188	+	0.114188i
$569$		−	12.6443i		−	0.530077i	−0.964238	−	0.265039i	$-0.914615\pi$
$569$		−	12.6443i		−	0.530077i	0.964238	−	0.265039i	$-0.0853847\pi$
$570$		0			0
$571$	19.4351			0.813332			0.406666	−	0.913577i	$-0.366691\pi$
$571$	19.4351			0.813332			0.406666	+	0.913577i	$0.366691\pi$
$572$	46.1900	+	26.6678i	1.93130	+	1.11504i
$573$		0			0
$574$	2.69810	−	10.0694i	0.112616	−	0.420290i
$575$	−66.0442			−2.75423
$576$		0			0
$577$	−42.8137			−1.78236			−0.891178	−	0.453654i	$-0.850120\pi$
$577$	−42.8137			−1.78236			−0.891178	+	0.453654i	$0.850120\pi$
$578$	−4.75833	+	17.7583i	−0.197920	+	0.738649i
$579$		0			0
$580$	−9.63203	−	5.56106i	−0.399948	−	0.230910i
$581$	−11.6893			−0.484954
$582$		0			0
$583$		−	52.3862i		−	2.16961i
$584$	30.8930	−	30.8930i	1.27836	−	1.27836i
$585$		0			0
$586$	0.149515	−	0.557997i	0.00617641	−	0.0230507i
$587$		−	28.9221i		−	1.19374i	−0.802337	−	0.596871i	$-0.796410\pi$
$587$		−	28.9221i		−	1.19374i	0.802337	−	0.596871i	$-0.203590\pi$
$588$		0			0
$589$			27.3854i			1.12839i
$590$	20.9919	+	5.62477i	0.864223	+	0.231568i
$591$		0			0
$592$	−6.87788	+	3.97095i	−0.282679	+	0.163205i
$593$		−	41.9140i		−	1.72120i	−0.509280	−	0.860601i	$-0.670088\pi$
$593$		−	41.9140i		−	1.72120i	0.509280	−	0.860601i	$-0.329912\pi$
$594$		0			0
$595$	8.77174			0.359606
$596$	9.24341	+	5.33669i	0.378625	+	0.218599i
$597$		0			0
$598$	33.0221	+	8.84824i	1.35037	+	0.361832i
$599$	20.5829			0.840993			0.420496	−	0.907294i	$-0.361856\pi$
$599$	20.5829			0.840993			0.420496	+	0.907294i	$0.361856\pi$
$600$		0			0
$601$	5.44652			0.222168			0.111084	−	0.993811i	$-0.464568\pi$
$601$	5.44652			0.222168			0.111084	+	0.993811i	$0.464568\pi$
$602$	−5.07823	−	1.36071i	−0.206973	−	0.0554583i
$603$		0			0
$604$	17.5725	−	30.4365i	0.715016	−	1.23844i
$605$	−66.6349			−2.70909
$606$		0			0
$607$		−	3.40600i		−	0.138245i	−0.997608	−	0.0691226i	$-0.977980\pi$
$607$		−	3.40600i		−	0.138245i	0.997608	−	0.0691226i	$-0.0220200\pi$
$608$	35.5374	−	9.52220i	1.44123	−	0.386176i
$609$		0			0
$610$	−27.1755	−	7.28165i	−1.10030	−	0.294826i
$611$			13.4205i			0.542937i
$612$		0			0
$613$		−	23.0992i		−	0.932968i	−0.884530	−	0.466484i	$-0.845521\pi$
$613$		−	23.0992i		−	0.932968i	0.884530	−	0.466484i	$-0.154479\pi$
$614$	−3.65913	+	13.6561i	−0.147671	+	0.551114i
$615$		0			0
$616$	−10.2358	+	10.2358i	−0.412414	+	0.412414i
$617$			25.4457i			1.02440i	0.858865	+	0.512202i	$0.171170\pi$
$617$			25.4457i			1.02440i	−0.858865	+	0.512202i	$0.828830\pi$
$618$		0			0
$619$	−18.7167			−0.752287			−0.376144	−	0.926561i	$-0.622750\pi$
$619$	−18.7167			−0.752287			−0.376144	+	0.926561i	$0.622750\pi$
$620$	−18.4675	+	31.9866i	−0.741672	+	1.28461i
$621$		0			0
$622$	7.30598	−	27.2663i	0.292943	−	1.09328i
$623$	14.8645			0.595533
$624$		0			0
$625$	106.480			4.25920
$626$	−8.58202	+	32.0285i	−0.343007	+	1.28012i
$627$		0			0
$628$	13.8259	−	23.9472i	0.551715	−	0.955599i
$629$	3.97095			0.158332
$630$		0			0
$631$			31.5549i			1.25618i	0.778140	+	0.628091i	$0.216163\pi$
$631$			31.5549i			1.25618i	−0.778140	+	0.628091i	$0.783837\pi$
$632$	−7.96483	−	7.96483i	−0.316824	−	0.316824i
$633$		0			0
$634$	−7.60380	+	28.3778i	−0.301986	+	1.12703i
$635$			58.9746i			2.34034i
$636$		0			0
$637$		−	5.21068i		−	0.206455i
$638$	−8.86450	−	2.37523i	−0.350949	−	0.0940364i
$639$		0			0
$640$	47.9297	+	12.8427i	1.89459	+	0.507653i
$641$			9.53508i			0.376613i	0.982110	+	0.188306i	$0.0602998\pi$
$641$			9.53508i			0.376613i	−0.982110	+	0.188306i	$0.939700\pi$
$642$		0			0
$643$	−37.8243			−1.49164			−0.745822	−	0.666145i	$-0.767943\pi$
$643$	−37.8243			−1.49164			−0.745822	+	0.666145i	$0.767943\pi$
$644$	−4.63929	+	8.03549i	−0.182814	+	0.316643i
$645$		0			0
$646$	−17.7687	−	4.76110i	−0.699099	−	0.187323i
$647$	−19.4663			−0.765301			−0.382650	−	0.923893i	$-0.624989\pi$
$647$	−19.4663			−0.765301			−0.382650	+	0.923893i	$0.624989\pi$
$648$		0			0
$649$	17.9321			0.703896
$650$	−101.330	−	27.1512i	−3.97447	−	1.06496i
$651$		0			0
$652$	−15.0252	−	8.67478i	−0.588431	−	0.339731i
$653$	9.58928			0.375257			0.187629	−	0.982240i	$-0.439920\pi$
$653$	9.58928			0.375257			0.187629	+	0.982240i	$0.439920\pi$
$654$		0			0
$655$			7.78402i			0.304147i
$656$	−25.5351	+	14.7427i	−0.996977	+	0.575605i
$657$		0			0
$658$	−3.51831	−	0.942729i	−0.137158	−	0.0367514i
$659$			13.0615i			0.508803i	0.967099	+	0.254402i	$0.0818785\pi$
$659$			13.0615i			0.508803i	−0.967099	+	0.254402i	$0.918122\pi$
$660$		0			0
$661$		−	39.8807i		−	1.55118i	−0.631236	−	0.775591i	$-0.717452\pi$
$661$		−	39.8807i		−	1.55118i	0.631236	−	0.775591i	$-0.282548\pi$
$662$	−6.96789	+	26.0045i	−0.270815	+	1.01069i
$663$		0			0
$664$	23.3786	+	23.3786i	0.907266	+	0.907266i
$665$		−	28.5247i		−	1.10614i
$666$		0			0
$667$	−5.88239			−0.227767
$668$	27.5144	+	15.8855i	1.06456	+	0.614627i
$669$		0			0
$670$	−8.36491	+	31.2183i	−0.323164	+	1.20607i
$671$	−23.2144			−0.896180
$672$		0			0
$673$	−12.8992			−0.497226			−0.248613	−	0.968603i	$-0.579975\pi$
$673$	−12.8992			−0.497226			−0.248613	+	0.968603i	$0.579975\pi$
$674$	−1.05615	+	3.94161i	−0.0406814	+	0.151825i
$675$		0			0
$676$	24.5105	+	14.1512i	0.942713	+	0.544276i
$677$	−30.1713			−1.15958			−0.579789	−	0.814767i	$-0.696865\pi$
$677$	−30.1713			−1.15958			−0.579789	+	0.814767i	$0.696865\pi$
$678$		0			0
$679$			4.42136i			0.169676i
$680$	−17.5435	−	17.5435i	−0.672761	−	0.672761i
$681$		0			0
$682$	−7.88781	+	29.4377i	−0.302040	+	1.12723i
$683$			6.61719i			0.253200i	0.991954	+	0.126600i	$0.0404064\pi$
$683$			6.61719i			0.253200i	−0.991954	+	0.126600i	$0.959594\pi$
$684$		0			0
$685$		−	63.9266i		−	2.44251i
$686$	1.36603	+	0.366025i	0.0521551	+	0.0139749i
$687$		0			0
$688$	7.43505	+	12.8779i	0.283459	+	0.490965i
$689$		−	53.3357i		−	2.03193i
$690$		0			0
$691$	40.6701			1.54716			0.773581	−	0.633697i	$-0.218463\pi$
$691$	40.6701			1.54716			0.773581	+	0.633697i	$0.218463\pi$
$692$	−7.32554	−	4.22940i	−0.278475	−	0.160778i
$693$		0			0
$694$	41.9415	+	11.2382i	1.59208	+	0.426596i
$695$	65.8212			2.49674
$696$		0			0
$697$	14.7427			0.558419
$698$	36.2007	+	9.69994i	1.37022	+	0.367148i
$699$		0			0
$700$	14.2358	−	24.6572i	0.538064	−	0.931954i
$701$	−18.4320			−0.696167			−0.348083	−	0.937464i	$-0.613167\pi$
$701$	−18.4320			−0.696167			−0.348083	+	0.937464i	$0.613167\pi$
$702$		0			0
$703$		−	12.9131i		−	0.487027i
$704$	40.9433			1.54311
$705$		0			0
$706$	−8.60534	−	2.30579i	−0.323866	−	0.0867797i
$707$			2.00000i			0.0752177i
$708$		0			0
$709$			21.1221i			0.793258i	0.917979	+	0.396629i	$0.129820\pi$
$709$			21.1221i			0.793258i	−0.917979	+	0.396629i	$0.870180\pi$
$710$	2.18440	−	8.15229i	0.0819790	−	0.305950i
$711$		0			0
$712$	−29.7290	−	29.7290i	−1.11414	−	1.11414i
$713$			19.5346i			0.731575i
$714$		0			0
$715$	−116.962			−4.37411
$716$	6.45041	−	11.1724i	0.241063	−	0.417533i
$717$		0			0
$718$	0.588457	−	2.19615i	0.0219610	−	0.0819597i
$719$	−24.1319			−0.899969			−0.449985	−	0.893036i	$-0.648571\pi$
$719$	−24.1319			−0.899969			−0.449985	+	0.893036i	$0.648571\pi$
$720$		0			0
$721$	1.67478			0.0623721
$722$	−8.52811	+	31.8274i	−0.317384	+	1.18449i
$723$		0			0
$724$	10.5068	−	18.1984i	0.390484	−	0.676338i
$725$	18.0503			0.670372
$726$		0			0
$727$		−	18.3923i		−	0.682133i	−0.940039	−	0.341066i	$-0.889212\pi$
$727$		−	18.3923i		−	0.682133i	0.940039	−	0.341066i	$-0.110788\pi$
$728$	−10.4214	+	10.4214i	−0.386241	+	0.386241i
$729$		0			0
$730$	−24.7969	+	92.5433i	−0.917774	+	3.42518i
$731$		−	7.43505i		−	0.274995i
$732$		0			0
$733$		−	34.5602i		−	1.27651i	−0.769824	−	0.638256i	$-0.779656\pi$
$733$		−	34.5602i		−	1.27651i	0.769824	−	0.638256i	$-0.220344\pi$
$734$	23.4633	+	6.28697i	0.866046	+	0.232056i
$735$		0			0
$736$	25.3496	−	6.79239i	0.934397	−	0.250371i
$737$			26.6678i			0.982322i
$738$		0			0
$739$	45.0366			1.65670			0.828350	−	0.560212i	$-0.189280\pi$
$739$	45.0366			1.65670			0.828350	+	0.560212i	$0.189280\pi$
$740$	8.70803	−	15.0827i	0.320113	−	0.554453i
$741$		0			0
$742$	13.9824	+	3.74658i	0.513311	+	0.137541i
$743$	−7.83850			−0.287567			−0.143783	−	0.989609i	$-0.545927\pi$
$743$	−7.83850			−0.287567			−0.143783	+	0.989609i	$0.545927\pi$
$744$		0			0
$745$	−23.4060			−0.857529
$746$	−3.11374	−	0.834324i	−0.114002	−	0.0305468i
$747$		0			0
$748$	−17.7290	−	10.2358i	−0.648236	−	0.374259i
$749$	10.2649			0.375071
$750$		0			0
$751$		−	38.4328i		−	1.40243i	−0.712948	−	0.701217i	$-0.752641\pi$
$751$		−	38.4328i		−	1.40243i	0.712948	−	0.701217i	$-0.247359\pi$
$752$	5.15117	+	8.92208i	0.187844	+	0.325355i
$753$		0			0
$754$	−9.02516	−	2.41828i	−0.328677	−	0.0880687i
$755$			77.0708i			2.80489i
$756$		0			0
$757$		−	2.24423i		−	0.0815680i	−0.999168	−	0.0407840i	$-0.987014\pi$
$757$		−	2.24423i		−	0.0815680i	0.999168	−	0.0407840i	$-0.0129855\pi$
$758$	−7.37134	+	27.5102i	−0.267739	+	0.999216i
$759$		0			0
$760$	−57.0495	+	57.0495i	−2.06940	+	2.06940i
$761$			28.3946i			1.02930i	0.857400	+	0.514651i	$0.172079\pi$
$761$			28.3946i			1.02930i	−0.857400	+	0.514651i	$0.827921\pi$
$762$		0			0
$763$	1.29311			0.0468137
$764$	−14.3065	−	8.25986i	−0.517591	−	0.298831i
$765$		0			0
$766$	8.16486	−	30.4717i	0.295008	−	1.10099i
$767$	18.2571			0.659226
$768$		0			0
$769$	27.2968			0.984348			0.492174	−	0.870497i	$-0.336202\pi$
$769$	27.2968			0.984348			0.492174	+	0.870497i	$0.336202\pi$
$770$	8.21599	−	30.6625i	0.296084	−	1.10500i
$771$		0			0
$772$	13.9939	+	8.07937i	0.503651	+	0.290783i
$773$	31.6583			1.13867			0.569335	−	0.822105i	$-0.307201\pi$
$773$	31.6583			1.13867			0.569335	+	0.822105i	$0.307201\pi$
$774$		0			0
$775$		−	59.9425i		−	2.15320i
$776$	8.84271	−	8.84271i	0.317435	−	0.317435i
$777$		0			0
$778$	−0.577824	+	2.15647i	−0.0207160	+	0.0773131i
$779$		−	47.9416i		−	1.71769i
$780$		0			0
$781$		−	6.96400i		−	0.249191i
$782$	−12.6748	−	3.39620i	−0.453249	−	0.121448i
$783$		0			0
$784$	−2.00000	−	3.46410i	−0.0714286	−	0.123718i
$785$			60.6388i			2.16429i
$786$		0			0
$787$	−24.1375			−0.860408			−0.430204	−	0.902732i	$-0.641558\pi$
$787$	−24.1375			−0.860408			−0.430204	+	0.902732i	$0.641558\pi$
$788$	−12.1984	−	7.04275i	−0.434550	−	0.250887i
$789$		0			0
$790$	23.8595	+	6.39312i	0.848882	+	0.227457i
$791$	8.07937			0.287269
$792$		0			0
$793$	−23.6351			−0.839307
$794$	−42.9327	−	11.5038i	−1.52363	−	0.408254i
$795$		0			0
$796$	−20.1336	+	34.8724i	−0.713616	+	1.23602i
$797$	−23.1867			−0.821313			−0.410657	−	0.911790i	$-0.634701\pi$
$797$	−23.1867			−0.821313			−0.410657	+	0.911790i	$0.634701\pi$
$798$		0			0
$799$		−	5.15117i		−	0.182235i
$800$	−77.7861	+	20.8427i	−2.75015	+	0.736901i
$801$		0			0
$802$	36.2549	+	9.71446i	1.28020	+	0.343030i
$803$			79.0540i			2.78976i
$804$		0			0
$805$		−	20.3473i		−	0.717149i
$806$	−8.03078	+	29.9713i	−0.282872	+	1.05569i
$807$		0			0
$808$	4.00000	−	4.00000i	0.140720	−	0.140720i
$809$		−	24.2823i		−	0.853719i	−0.904318	−	0.426860i	$-0.859620\pi$
$809$		−	24.2823i		−	0.853719i	0.904318	−	0.426860i	$-0.140380\pi$
$810$		0			0
$811$	29.1610			1.02398			0.511990	−	0.858991i	$-0.328908\pi$
$811$	29.1610			1.02398			0.511990	+	0.858991i	$0.328908\pi$
$812$	1.26795	−	2.19615i	0.0444963	−	0.0770698i
$813$		0			0
$814$	3.71937	−	13.8809i	0.130364	−	0.486524i
$815$	38.0464			1.33271
$816$		0			0
$817$	−24.1780			−0.845881
$818$	−11.7142	+	43.7178i	−0.409576	+	1.52856i
$819$		0			0
$820$	32.3297	−	55.9967i	1.12900	−	1.95549i
$821$	42.6701			1.48920			0.744598	−	0.667513i	$-0.232641\pi$
$821$	42.6701			1.48920			0.744598	+	0.667513i	$0.232641\pi$
$822$		0			0
$823$		−	18.4487i		−	0.643083i	−0.946896	−	0.321541i	$-0.895799\pi$
$823$		−	18.4487i		−	0.643083i	0.946896	−	0.321541i	$-0.104201\pi$
$824$	−3.34956	−	3.34956i	−0.116687	−	0.116687i
$825$		0			0
$826$	−1.28247	+	4.78626i	−0.0446230	+	0.166535i
$827$		−	37.8393i		−	1.31580i	−0.753104	−	0.657901i	$-0.771444\pi$
$827$		−	37.8393i		−	1.31580i	0.753104	−	0.657901i	$-0.228556\pi$
$828$		0			0
$829$			46.5463i			1.61662i	0.588756	+	0.808310i	$0.299618\pi$
$829$			46.5463i			1.61662i	−0.588756	+	0.808310i	$0.700382\pi$
$830$	−70.0330	−	18.7653i	−2.43088	−	0.651353i
$831$		0			0
$832$	41.6854			1.44518
$833$			2.00000i			0.0692959i
$834$		0			0
$835$	−69.6715			−2.41108
$836$	−33.2859	+	57.6528i	−1.15122	+	1.99396i
$837$		0			0
$838$	−28.2183	−	7.56106i	−0.974783	−	0.261192i
$839$	12.9388			0.446698			0.223349	−	0.974739i	$-0.428301\pi$
$839$	12.9388			0.446698			0.223349	+	0.974739i	$0.428301\pi$
$840$		0			0
$841$	−27.3923			−0.944562
$842$	45.0693	+	12.0763i	1.55319	+	0.416177i
$843$		0			0
$844$	−13.0657	−	7.54347i	−0.449739	−	0.259657i
$845$	−62.0651			−2.13511
$846$		0			0
$847$		−	15.1931i		−	0.522041i
$848$	−20.4717	−	35.4580i	−0.703000	−	1.21763i
$849$		0			0
$850$	38.8930	+	10.4214i	1.33402	+	0.357450i
$851$		−	9.21119i		−	0.315756i
$852$		0			0
$853$			49.9509i			1.71029i	0.518391	+	0.855144i	$0.326531\pi$
$853$			49.9509i			1.71029i	−0.518391	+	0.855144i	$0.673469\pi$
$854$	1.66025	−	6.19615i	0.0568127	−	0.212028i
$855$		0			0
$856$	−20.5298	−	20.5298i	−0.701693	−	0.701693i
$857$			32.4208i			1.10747i	0.832691	+	0.553737i	$0.186799\pi$
$857$			32.4208i			1.10747i	−0.832691	+	0.553737i	$0.813201\pi$
$858$		0			0
$859$	−18.3311			−0.625450			−0.312725	−	0.949844i	$-0.601242\pi$
$859$	−18.3311			−0.625450			−0.312725	+	0.949844i	$0.601242\pi$
$860$	−28.2404	−	16.3046i	−0.962988	−	0.555981i
$861$		0			0
$862$	−2.37288	+	8.85570i	−0.0808206	+	0.301626i
$863$	−3.77704			−0.128572			−0.0642859	−	0.997932i	$-0.520477\pi$
$863$	−3.77704			−0.128572			−0.0642859	+	0.997932i	$0.520477\pi$
$864$		0			0
$865$	18.5496			0.630705
$866$	6.73625	−	25.1400i	0.228907	−	0.854293i
$867$		0			0
$868$	−7.29311	−	4.21068i	−0.247544	−	0.142920i
$869$	20.3817			0.691401
$870$		0			0
$871$			27.1512i			0.919982i
$872$	−2.58622	−	2.58622i	−0.0875804	−	0.0875804i
$873$		0			0
$874$	−11.0441	+	41.2170i	−0.373571	+	1.39419i
$875$			40.5072i			1.36939i
$876$		0			0
$877$		−	9.61218i		−	0.324580i	−0.986743	−	0.162290i	$-0.948112\pi$
$877$		−	9.61218i		−	0.324580i	0.986743	−	0.162290i	$-0.0518880\pi$
$878$	5.89158	+	1.57864i	0.198831	+	0.0532766i
$879$		0			0
$880$	−77.7570	+	44.8930i	−2.62119	+	1.51334i
$881$			22.4722i			0.757107i	0.925579	+	0.378554i	$0.123578\pi$
$881$			22.4722i			0.757107i	−0.925579	+	0.378554i	$0.876422\pi$
$882$		0			0
$883$	−9.77704			−0.329023			−0.164512	−	0.986375i	$-0.552605\pi$
$883$	−9.77704			−0.329023			−0.164512	+	0.986375i	$0.552605\pi$
$884$	−18.0503	−	10.4214i	−0.607098	−	0.350508i
$885$		0			0
$886$	−7.57515	−	2.02976i	−0.254492	−	0.0681910i
$887$	−59.1043			−1.98453			−0.992265	−	0.124141i	$-0.960383\pi$
$887$	−59.1043			−1.98453			−0.992265	+	0.124141i	$0.960383\pi$
$888$		0			0
$889$	−13.4465			−0.450982
$890$	89.0563	+	23.8626i	2.98517	+	0.799875i
$891$		0			0
$892$	−5.48926	+	9.50768i	−0.183794	+	0.318341i
$893$	−16.7510			−0.560552
$894$		0			0
$895$			28.2906i			0.945652i
$896$	−2.92820	+	10.9282i	−0.0978244	+	0.365086i
$897$		0			0
$898$	−41.2549	−	11.0542i	−1.37669	−	0.368884i
$899$		−	5.33893i		−	0.178063i
$900$		0			0
$901$			20.4717i			0.682010i
$902$	13.8086	−	51.5346i	0.459778	−	1.71591i
$903$		0			0
$904$	−16.1587	−	16.1587i	−0.537432	−	0.537432i
$905$			46.0816i			1.53181i
$906$		0			0
$907$	−31.9861			−1.06208			−0.531040	−	0.847346i	$-0.678199\pi$
$907$	−31.9861			−1.06208			−0.531040	+	0.847346i	$0.678199\pi$
$908$	−0.127416	+	0.220691i	−0.00422845	+	0.00732388i
$909$		0			0
$910$	8.36491	−	31.2183i	0.277294	−	1.03487i
$911$	26.4052			0.874843			0.437421	−	0.899257i	$-0.355892\pi$
$911$	26.4052			0.874843			0.437421	+	0.899257i	$0.355892\pi$
$912$		0			0
$913$	−59.8249			−1.97992
$914$	8.90192	−	33.2224i	0.294449	−	1.09890i
$915$		0			0
$916$	6.53590	−	11.3205i	0.215952	−	0.374040i
$917$	−1.77480			−0.0586089
$918$		0			0
$919$			46.4656i			1.53276i	0.642389	+	0.766379i	$0.277943\pi$
$919$			46.4656i			1.53276i	−0.642389	+	0.766379i	$0.722057\pi$
$920$	−40.6946	+	40.6946i	−1.34166	+	1.34166i
$921$		0			0
$922$	13.6579	−	50.9720i	0.449799	−	1.67867i
$923$		−	7.09021i		−	0.233377i
$924$		0			0
$925$			28.2649i			0.929344i
$926$	−48.2007	−	12.9153i	−1.58397	−	0.424424i
$927$		0			0
$928$	−6.92820	+	1.85641i	−0.227429	+	0.0609395i
$929$			16.7656i			0.550062i	0.961435	+	0.275031i	$0.0886881\pi$
$929$			16.7656i			0.550062i	−0.961435	+	0.275031i	$0.911312\pi$
$930$		0			0
$931$	6.50379			0.213153
$932$	−10.5359	+	18.2487i	−0.345115	+	0.597756i
$933$		0			0
$934$	28.3892	+	7.60688i	0.928924	+	0.248905i
$935$	44.8930			1.46816
$936$		0			0
$937$	−32.3923			−1.05821			−0.529105	−	0.848556i	$-0.677472\pi$
$937$	−32.3923			−1.05821			−0.529105	+	0.848556i	$0.677472\pi$
$938$	−7.11792	−	1.90724i	−0.232408	−	0.0622736i
$939$		0			0
$940$	−19.5655	−	11.2962i	−0.638157	−	0.368440i
$941$	−40.1216			−1.30793			−0.653964	−	0.756526i	$-0.726895\pi$
$941$	−40.1216			−1.30793			−0.653964	+	0.756526i	$0.726895\pi$
$942$		0			0
$943$		−	34.1978i		−	1.11363i
$944$	12.1375	−	7.00757i	0.395041	−	0.228077i
$945$		0			0
$946$	−25.9900	−	6.96400i	−0.845007	−	0.226419i
$947$			38.9905i			1.26702i	0.773734	+	0.633511i	$0.218387\pi$
$947$			38.9905i			1.26702i	−0.773734	+	0.633511i	$0.781613\pi$
$948$		0			0
$949$			80.4868i			2.61271i
$950$	33.8891	−	126.476i	1.09951	−	4.10342i
$951$		0			0
$952$	4.00000	−	4.00000i	0.129641	−	0.129641i
$953$		−	1.39764i		−	0.0452739i	−0.999744	−	0.0226370i	$-0.992794\pi$
$953$		−	1.39764i		−	0.0452739i	0.999744	−	0.0226370i	$-0.00720619\pi$
$954$		0			0
$955$	36.2267			1.17227
$956$	−42.2381	−	24.3862i	−1.36608	−	0.788706i
$957$		0			0
$958$	−6.28247	+	23.4465i	−0.202978	+	0.757523i
$959$	14.5756			0.470670
$960$		0			0
$961$	13.2702			0.428071
$962$	3.78678	−	14.1324i	0.122091	−	0.455648i
$963$		0			0
$964$	18.8106	+	10.8603i	0.605848	+	0.349787i
$965$	−35.4351			−1.14069
$966$		0			0
$967$			21.9709i			0.706538i	0.935522	+	0.353269i	$0.114930\pi$
$967$			21.9709i			0.706538i	−0.935522	+	0.353269i	$0.885070\pi$
$968$	−30.3862	+	30.3862i	−0.976649	+	0.976649i
$969$		0			0
$970$	−7.09778	+	26.4893i	−0.227896	+	0.850519i
$971$			42.7098i			1.37062i	0.728251	+	0.685311i	$0.240334\pi$
$971$			42.7098i			1.37062i	−0.728251	+	0.685311i	$0.759666\pi$
$972$		0			0
$973$			15.0076i			0.481121i
$974$	52.9964	+	14.2003i	1.69811	+	0.455009i
$975$		0			0
$976$	−15.7128	+	9.07180i	−0.502955	+	0.290381i
$977$		−	60.3885i		−	1.93200i	−0.258546	−	0.965999i	$-0.583243\pi$
$977$		−	60.3885i		−	1.93200i	0.258546	−	0.965999i	$-0.416757\pi$
$978$		0			0
$979$	76.0753			2.43138
$980$	7.59655	+	4.38587i	0.242663	+	0.140101i
$981$		0			0
$982$	42.6163	+	11.4190i	1.35994	+	0.364395i
$983$	−19.6251			−0.625943			−0.312971	−	0.949763i	$-0.601324\pi$
$983$	−19.6251			−0.625943			−0.312971	+	0.949763i	$0.601324\pi$
$984$		0			0
$985$	30.8886			0.984191
$986$	3.46410	+	0.928203i	0.110319	+	0.0295600i
$987$		0			0
$988$	−33.8891	+	58.6977i	−1.07816	+	1.86742i
$989$	−17.2467			−0.548413
$990$		0			0
$991$			7.84660i			0.249256i	0.992204	+	0.124628i	$0.0397737\pi$
$991$			7.84660i			0.249256i	−0.992204	+	0.124628i	$0.960226\pi$
$992$	6.16486	+	23.0076i	0.195735	+	0.730491i
$993$		0			0
$994$	1.85876	+	0.498054i	0.0589564	+	0.0157973i
$995$		−	88.3032i		−	2.79940i
$996$		0			0
$997$			19.9128i			0.630646i	0.948984	+	0.315323i	$0.102113\pi$
$997$			19.9128i			0.630646i	−0.948984	+	0.315323i	$0.897887\pi$
$998$	3.21487	−	11.9981i	0.101765	−	0.379792i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.b.323.4	yes	8
3.2	odd	2		1512.2.j.a.323.5	✓	8
4.3	odd	2		6048.2.j.b.5615.7		8
8.3	odd	2		1512.2.j.a.323.7	yes	8
8.5	even	2		6048.2.j.a.5615.2		8
12.11	even	2		6048.2.j.a.5615.1		8
24.5	odd	2		6048.2.j.b.5615.8		8
24.11	even	2	inner	1512.2.j.b.323.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.a.323.5	✓	8	3.2	odd	2
1512.2.j.a.323.7	yes	8	8.3	odd	2
1512.2.j.b.323.2	yes	8	24.11	even	2	inner
1512.2.j.b.323.4	yes	8	1.1	even	1	trivial
6048.2.j.a.5615.1		8	12.11	even	2
6048.2.j.a.5615.2		8	8.5	even	2
6048.2.j.b.5615.7		8	4.3	odd	2
6048.2.j.b.5615.8		8	24.5	odd	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +4.38587 q^{5} +1.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +4.38587 q^{5} +1.00000i q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.60534 + 5.99121i) q^{10} +5.11792i q^{11} +5.21068i q^{13} +(-1.36603 - 0.366025i) q^{14} +(2.00000 + 3.46410i) q^{16} -2.00000i q^{17} -6.50379 q^{19} +(-7.59655 - 4.38587i) q^{20} +(-6.99121 - 1.87329i) q^{22} -4.63929 q^{23} +14.2358 q^{25} +(-7.11792 - 1.90724i) q^{26} +(1.00000 - 1.73205i) q^{28} +1.26795 q^{29} -4.21068i q^{31} +(-5.46410 + 1.46410i) q^{32} +(2.73205 + 0.732051i) q^{34} +4.38587i q^{35} +1.98547i q^{37} +(2.38055 - 8.88434i) q^{38} +(8.77174 - 8.77174i) q^{40} +7.37134i q^{41} +3.71753 q^{43} +(5.11792 - 8.86450i) q^{44} +(1.69810 - 6.33739i) q^{46} +2.57558 q^{47} -1.00000 q^{49} +(-5.21068 + 19.4465i) q^{50} +(5.21068 - 9.02516i) q^{52} -10.2358 q^{53} +22.4465i q^{55} +(2.00000 + 2.00000i) q^{56} +(-0.464102 + 1.73205i) q^{58} -3.50379i q^{59} +4.53590i q^{61} +(5.75189 + 1.54122i) q^{62} -8.00000i q^{64} +22.8533i q^{65} +5.21068 q^{67} +(-2.00000 + 3.46410i) q^{68} +(-5.99121 - 1.60534i) q^{70} -1.36071 q^{71} +15.4465 q^{73} +(-2.71221 - 0.726734i) q^{74} +(11.2649 + 6.50379i) q^{76} -5.11792 q^{77} -3.98241i q^{79} +(8.77174 + 15.1931i) q^{80} +(-10.0694 - 2.69810i) q^{82} +11.6893i q^{83} -8.77174i q^{85} +(-1.36071 + 5.07823i) q^{86} +(10.2358 + 10.2358i) q^{88} -14.8645i q^{89} -5.21068 q^{91} +(8.03549 + 4.63929i) q^{92} +(-0.942729 + 3.51831i) q^{94} -28.5247 q^{95} +4.42136 q^{97} +(0.366025 - 1.36603i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 8 q^{5} + 16 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 + 8 * q^5 + 16 * q^8	\( 8 q + 4 q^{2} + 8 q^{5} + 16 q^{8} + 4 q^{10} - 4 q^{14} + 16 q^{16} + 16 q^{19} - 12 q^{22} - 16 q^{23} + 32 q^{25} - 16 q^{26} + 8 q^{28} + 24 q^{29} - 16 q^{32} + 8 q^{34} + 20 q^{38} + 16 q^{40} + 8 q^{43} + 4 q^{46} + 8 q^{47} - 8 q^{49} - 8 q^{50} + 8 q^{52} + 16 q^{56} + 24 q^{58} + 12 q^{62} + 8 q^{67} - 16 q^{68} - 4 q^{70} - 32 q^{71} + 8 q^{73} - 28 q^{74} + 24 q^{76} + 16 q^{80} - 36 q^{82} - 32 q^{86} - 8 q^{91} + 24 q^{92} + 40 q^{94} - 112 q^{95} - 32 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 8 * q^5 + 16 * q^8 + 4 * q^10 - 4 * q^14 + 16 * q^16 + 16 * q^19 - 12 * q^22 - 16 * q^23 + 32 * q^25 - 16 * q^26 + 8 * q^28 + 24 * q^29 - 16 * q^32 + 8 * q^34 + 20 * q^38 + 16 * q^40 + 8 * q^43 + 4 * q^46 + 8 * q^47 - 8 * q^49 - 8 * q^50 + 8 * q^52 + 16 * q^56 + 24 * q^58 + 12 * q^62 + 8 * q^67 - 16 * q^68 - 4 * q^70 - 32 * q^71 + 8 * q^73 - 28 * q^74 + 24 * q^76 + 16 * q^80 - 36 * q^82 - 32 * q^86 - 8 * q^91 + 24 * q^92 + 40 * q^94 - 112 * q^95 - 32 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more