LMFDB - Embedded newform 1344.2.s.c.239.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, 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("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (of order $4$, degree $2$, not 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.7
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.c.911.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.985133 + 1.42461i) q^{3} +(0.766553 + 0.766553i) q^{5} +1.00000 q^{7} +(-1.05903 - 2.80686i) q^{9} +O(q^{10})$	\(q+(-0.985133 + 1.42461i) q^{3} +(0.766553 + 0.766553i) q^{5} +1.00000 q^{7} +(-1.05903 - 2.80686i) q^{9} +(3.09355 - 3.09355i) q^{11} +(0.262549 + 0.262549i) q^{13} +(-1.84720 + 0.336883i) q^{15} +2.68766i q^{17} +(2.44019 - 2.44019i) q^{19} +(-0.985133 + 1.42461i) q^{21} -3.24607i q^{23} -3.82479i q^{25} +(5.04196 + 1.25643i) q^{27} +(3.28972 - 3.28972i) q^{29} -3.76875i q^{31} +(1.35954 + 7.45466i) q^{33} +(0.766553 + 0.766553i) q^{35} +(4.88595 - 4.88595i) q^{37} +(-0.632675 + 0.115384i) q^{39} -11.2823 q^{41} +(0.938292 + 0.938292i) q^{43} +(1.33981 - 2.96341i) q^{45} +0.764222 q^{47} +1.00000 q^{49} +(-3.82887 - 2.64770i) q^{51} +(4.14619 + 4.14619i) q^{53} +4.74274 q^{55} +(1.07241 + 5.88023i) q^{57} +(-2.63246 + 2.63246i) q^{59} +(10.7072 + 10.7072i) q^{61} +(-1.05903 - 2.80686i) q^{63} +0.402516i q^{65} +(8.41087 - 8.41087i) q^{67} +(4.62439 + 3.19781i) q^{69} +13.7602i q^{71} +6.79488i q^{73} +(5.44884 + 3.76793i) q^{75} +(3.09355 - 3.09355i) q^{77} +3.83558i q^{79} +(-6.75693 + 5.94508i) q^{81} +(-0.107522 - 0.107522i) q^{83} +(-2.06023 + 2.06023i) q^{85} +(1.44576 + 7.92738i) q^{87} -9.00266 q^{89} +(0.262549 + 0.262549i) q^{91} +(5.36900 + 3.71272i) q^{93} +3.74107 q^{95} +18.1447 q^{97} +(-11.9593 - 5.40701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 40 * q^7	$ 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) $ 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.985133	+	1.42461i	−0.568767	+	0.822499i
$3$	−0.985133	+	1.42461i	−0.568767	+	0.822499i
$4$		0			0
$5$	0.766553	+	0.766553i	0.342813	+	0.342813i	0.857424	−	0.514611i	$-0.172064\pi$
$5$	0.766553	+	0.766553i	0.342813	+	0.342813i	−0.514611	+	0.857424i	$0.672064\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		0			0
$9$	−1.05903	−	2.80686i	−0.353009	−	0.935620i
$10$		0			0
$11$	3.09355	−	3.09355i	0.932741	−	0.932741i	−0.0651356	−	0.997876i	$-0.520748\pi$
$11$	3.09355	−	3.09355i	0.932741	−	0.932741i	0.997876	+	0.0651356i	$0.0207480\pi$
$12$		0			0
$13$	0.262549	+	0.262549i	0.0728180	+	0.0728180i	0.742578	−	0.669760i	$-0.233603\pi$
$13$	0.262549	+	0.262549i	0.0728180	+	0.0728180i	−0.669760	+	0.742578i	$0.733603\pi$
$14$		0			0
$15$	−1.84720	+	0.336883i	−0.476944	+	0.0869827i
$16$		0			0
$17$			2.68766i			0.651853i	0.945395	+	0.325927i	$0.105676\pi$
$17$			2.68766i			0.651853i	−0.945395	+	0.325927i	$0.894324\pi$
$18$		0			0
$19$	2.44019	−	2.44019i	0.559818	−	0.559818i	−0.369438	−	0.929255i	$-0.620450\pi$
$19$	2.44019	−	2.44019i	0.559818	−	0.559818i	0.929255	+	0.369438i	$0.120450\pi$
$20$		0			0
$21$	−0.985133	+	1.42461i	−0.214974	+	0.310875i
$22$		0			0
$23$		−	3.24607i		−	0.676853i	−0.940993	−	0.338427i	$-0.890105\pi$
$23$		−	3.24607i		−	0.676853i	0.940993	−	0.338427i	$-0.109895\pi$
$24$		0			0
$25$		−	3.82479i		−	0.764958i
$26$		0			0
$27$	5.04196	+	1.25643i	0.970326	+	0.241800i
$28$		0			0
$29$	3.28972	−	3.28972i	0.610886	−	0.610886i	−0.332291	−	0.943177i	$-0.607822\pi$
$29$	3.28972	−	3.28972i	0.610886	−	0.610886i	0.943177	+	0.332291i	$0.107822\pi$
$30$		0			0
$31$		−	3.76875i		−	0.676888i	−0.940987	−	0.338444i	$-0.890099\pi$
$31$		−	3.76875i		−	0.676888i	0.940987	−	0.338444i	$-0.109901\pi$
$32$		0			0
$33$	1.35954	+	7.45466i	0.236666	+	1.29769i
$34$		0			0
$35$	0.766553	+	0.766553i	0.129571	+	0.129571i
$36$		0			0
$37$	4.88595	−	4.88595i	0.803245	−	0.803245i	−0.180357	−	0.983601i	$-0.557725\pi$
$37$	4.88595	−	4.88595i	0.803245	−	0.803245i	0.983601	+	0.180357i	$0.0577252\pi$
$38$		0			0
$39$	−0.632675	+	0.115384i	−0.101309	+	0.0184763i
$40$		0			0
$41$	−11.2823			−1.76200			−0.880998	−	0.473120i	$-0.843128\pi$
$41$	−11.2823			−1.76200			−0.880998	+	0.473120i	$0.843128\pi$
$42$		0			0
$43$	0.938292	+	0.938292i	0.143088	+	0.143088i	0.775022	−	0.631934i	$-0.217739\pi$
$43$	0.938292	+	0.938292i	0.143088	+	0.143088i	−0.631934	+	0.775022i	$0.717739\pi$
$44$		0			0
$45$	1.33981	−	2.96341i	0.199727	−	0.441759i
$46$		0			0
$47$	0.764222			0.111473			0.0557366	−	0.998446i	$-0.482249\pi$
$47$	0.764222			0.111473			0.0557366	+	0.998446i	$0.482249\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	−3.82887	−	2.64770i	−0.536149	−	0.370752i
$52$		0			0
$53$	4.14619	+	4.14619i	0.569523	+	0.569523i	0.931995	−	0.362471i	$-0.118067\pi$
$53$	4.14619	+	4.14619i	0.569523	+	0.569523i	−0.362471	+	0.931995i	$0.618067\pi$
$54$		0			0
$55$	4.74274			0.639512
$56$		0			0
$57$	1.07241	+	5.88023i	0.142044	+	0.778855i
$58$		0			0
$59$	−2.63246	+	2.63246i	−0.342717	+	0.342717i	−0.857388	−	0.514671i	$-0.827914\pi$
$59$	−2.63246	+	2.63246i	−0.342717	+	0.342717i	0.514671	+	0.857388i	$0.327914\pi$
$60$		0			0
$61$	10.7072	+	10.7072i	1.37092	+	1.37092i	0.859087	+	0.511830i	$0.171032\pi$
$61$	10.7072	+	10.7072i	1.37092	+	1.37092i	0.511830	+	0.859087i	$0.328968\pi$
$62$		0			0
$63$	−1.05903	−	2.80686i	−0.133425	−	0.353631i
$64$		0			0
$65$			0.402516i			0.0499259i
$66$		0			0
$67$	8.41087	−	8.41087i	1.02755	−	1.02755i	0.0279421	−	0.999610i	$-0.491105\pi$
$67$	8.41087	−	8.41087i	1.02755	−	1.02755i	0.999610	−	0.0279421i	$-0.00889542\pi$
$68$		0			0
$69$	4.62439	+	3.19781i	0.556711	+	0.384971i
$70$		0			0
$71$			13.7602i			1.63303i	0.577322	+	0.816516i	$0.304098\pi$
$71$			13.7602i			1.63303i	−0.577322	+	0.816516i	$0.695902\pi$
$72$		0			0
$73$			6.79488i			0.795281i	0.917541	+	0.397641i	$0.130171\pi$
$73$			6.79488i			0.795281i	−0.917541	+	0.397641i	$0.869829\pi$
$74$		0			0
$75$	5.44884	+	3.76793i	0.629177	+	0.435083i
$76$		0			0
$77$	3.09355	−	3.09355i	0.352543	−	0.352543i
$78$		0			0
$79$			3.83558i			0.431536i	0.976445	+	0.215768i	$0.0692255\pi$
$79$			3.83558i			0.431536i	−0.976445	+	0.215768i	$0.930775\pi$
$80$		0			0
$81$	−6.75693	+	5.94508i	−0.750770	+	0.660564i
$82$		0			0
$83$	−0.107522	−	0.107522i	−0.0118021	−	0.0118021i	0.701181	−	0.712983i	$-0.252656\pi$
$83$	−0.107522	−	0.107522i	−0.0118021	−	0.0118021i	−0.712983	+	0.701181i	$0.752656\pi$
$84$		0			0
$85$	−2.06023	+	2.06023i	−0.223464	+	0.223464i
$86$		0			0
$87$	1.44576	+	7.92738i	0.155001	+	0.849905i
$88$		0			0
$89$	−9.00266			−0.954280			−0.477140	−	0.878827i	$-0.658326\pi$
$89$	−9.00266			−0.954280			−0.477140	+	0.878827i	$0.658326\pi$
$90$		0			0
$91$	0.262549	+	0.262549i	0.0275226	+	0.0275226i
$92$		0			0
$93$	5.36900	+	3.71272i	0.556739	+	0.384991i
$94$		0			0
$95$	3.74107			0.383826
$96$		0			0
$97$	18.1447			1.84232			0.921160	−	0.389185i	$-0.127243\pi$
$97$	18.1447			1.84232			0.921160	+	0.389185i	$0.127243\pi$
$98$		0			0
$99$	−11.9593	−	5.40701i	−1.20196	−	0.543425i
$100$		0			0
$101$	−7.24602	−	7.24602i	−0.721006	−	0.721006i	0.247804	−	0.968810i	$-0.420291\pi$
$101$	−7.24602	−	7.24602i	−0.721006	−	0.721006i	−0.968810	+	0.247804i	$0.920291\pi$
$102$		0			0
$103$	17.2202			1.69676			0.848378	−	0.529390i	$-0.177579\pi$
$103$	17.2202			1.69676			0.848378	+	0.529390i	$0.177579\pi$
$104$		0			0
$105$	−1.84720	+	0.336883i	−0.180268	+	0.0328764i
$106$		0			0
$107$	−7.02957	+	7.02957i	−0.679574	+	0.679574i	−0.959904	−	0.280330i	$-0.909556\pi$
$107$	−7.02957	+	7.02957i	−0.679574	+	0.679574i	0.280330	+	0.959904i	$0.409556\pi$
$108$		0			0
$109$	−1.85810	−	1.85810i	−0.177973	−	0.177973i	0.612498	−	0.790472i	$-0.290165\pi$
$109$	−1.85810	−	1.85810i	−0.177973	−	0.177973i	−0.790472	+	0.612498i	$0.790165\pi$
$110$		0			0
$111$	2.14726	+	11.7739i	0.203809	+	1.11753i
$112$		0			0
$113$		−	15.6715i		−	1.47425i	−0.675755	−	0.737126i	$-0.736182\pi$
$113$		−	15.6715i		−	1.47425i	0.675755	−	0.737126i	$-0.263818\pi$
$114$		0			0
$115$	2.48829	−	2.48829i	0.232034	−	0.232034i
$116$		0			0
$117$	0.458892	−	1.01498i	0.0424246	−	0.0938353i
$118$		0			0
$119$			2.68766i			0.246377i
$120$		0			0
$121$		−	8.14012i		−	0.740011i
$122$		0			0
$123$	11.1145	−	16.0728i	1.00216	−	1.44924i
$124$		0			0
$125$	6.76467	−	6.76467i	0.605051	−	0.605051i
$126$		0			0
$127$		−	0.874680i		−	0.0776153i	−0.999247	−	0.0388076i	$-0.987644\pi$
$127$		−	0.874680i		−	0.0776153i	0.999247	−	0.0388076i	$-0.0123560\pi$
$128$		0			0
$129$	−2.26104	+	0.412358i	−0.199074	+	0.0363061i
$130$		0			0
$131$	2.96129	+	2.96129i	0.258729	+	0.258729i	0.824537	−	0.565808i	$-0.191436\pi$
$131$	2.96129	+	2.96129i	0.258729	+	0.258729i	−0.565808	+	0.824537i	$0.691436\pi$
$132$		0			0
$133$	2.44019	−	2.44019i	0.211591	−	0.211591i
$134$		0			0
$135$	2.90181	+	4.82805i	0.249748	+	0.415533i
$136$		0			0
$137$	−13.5561			−1.15817			−0.579086	−	0.815266i	$-0.696590\pi$
$137$	−13.5561			−1.15817			−0.579086	+	0.815266i	$0.696590\pi$
$138$		0			0
$139$	−0.262462	−	0.262462i	−0.0222618	−	0.0222618i	0.695888	−	0.718150i	$-0.255011\pi$
$139$	−0.262462	−	0.262462i	−0.0222618	−	0.0222618i	−0.718150	+	0.695888i	$0.755011\pi$
$140$		0			0
$141$	−0.752860	+	1.08872i	−0.0634022	+	0.0916866i
$142$		0			0
$143$	1.62442			0.135841
$144$		0			0
$145$	5.04350			0.418839
$146$		0			0
$147$	−0.985133	+	1.42461i	−0.0812524	+	0.117500i
$148$		0			0
$149$	14.9894	+	14.9894i	1.22798	+	1.22798i	0.964726	+	0.263254i	$0.0847959\pi$
$149$	14.9894	+	14.9894i	1.22798	+	1.22798i	0.263254	+	0.964726i	$0.415204\pi$
$150$		0			0
$151$	−13.2687			−1.07979			−0.539895	−	0.841733i	$-0.681536\pi$
$151$	−13.2687			−1.07979			−0.539895	+	0.841733i	$0.681536\pi$
$152$		0			0
$153$	7.54389	−	2.84630i	0.609887	−	0.230110i
$154$		0			0
$155$	2.88895	−	2.88895i	0.232046	−	0.232046i
$156$		0			0
$157$	−7.89825	−	7.89825i	−0.630349	−	0.630349i	0.317807	−	0.948156i	$-0.397054\pi$
$157$	−7.89825	−	7.89825i	−0.630349	−	0.630349i	−0.948156	+	0.317807i	$0.897054\pi$
$158$		0			0
$159$	−9.99126	+	1.82216i	−0.792358	+	0.144506i
$160$		0			0
$161$		−	3.24607i		−	0.255826i
$162$		0			0
$163$	−2.20835	+	2.20835i	−0.172971	+	0.172971i	−0.788283	−	0.615312i	$-0.789030\pi$
$163$	−2.20835	+	2.20835i	−0.172971	+	0.172971i	0.615312	+	0.788283i	$0.289030\pi$
$164$		0			0
$165$	−4.67223	+	6.75656i	−0.363733	+	0.525998i
$166$		0			0
$167$			18.4786i			1.42992i	0.699166	+	0.714959i	$0.253555\pi$
$167$			18.4786i			1.42992i	−0.699166	+	0.714959i	$0.746445\pi$
$168$		0			0
$169$		−	12.8621i		−	0.989395i
$170$		0			0
$171$	−9.43349	−	4.26504i	−0.721397	−	0.326156i
$172$		0			0
$173$	0.866535	−	0.866535i	0.0658814	−	0.0658814i	−0.673398	−	0.739280i	$-0.735166\pi$
$173$	0.866535	−	0.866535i	0.0658814	−	0.0658814i	0.739280	+	0.673398i	$0.235166\pi$
$174$		0			0
$175$		−	3.82479i		−	0.289127i
$176$		0			0
$177$	−1.15690	−	6.34355i	−0.0869583	−	0.476810i
$178$		0			0
$179$	−12.2237	−	12.2237i	−0.913642	−	0.913642i	0.0829148	−	0.996557i	$-0.473577\pi$
$179$	−12.2237	−	12.2237i	−0.913642	−	0.913642i	−0.996557	+	0.0829148i	$0.973577\pi$
$180$		0			0
$181$	3.58486	−	3.58486i	0.266461	−	0.266461i	−0.561212	−	0.827672i	$-0.689665\pi$
$181$	3.58486	−	3.58486i	0.266461	−	0.266461i	0.827672	+	0.561212i	$0.189665\pi$
$182$		0			0
$183$	−25.8016	+	4.70557i	−1.90731	+	0.347846i
$184$		0			0
$185$	7.49068			0.550725
$186$		0			0
$187$	8.31441	+	8.31441i	0.608010	+	0.608010i
$188$		0			0
$189$	5.04196	+	1.25643i	0.366749	+	0.0913919i
$190$		0			0
$191$	22.9268			1.65892			0.829461	−	0.558564i	$-0.188648\pi$
$191$	22.9268			1.65892			0.829461	+	0.558564i	$0.188648\pi$
$192$		0			0
$193$	−3.43127			−0.246989			−0.123494	−	0.992345i	$-0.539410\pi$
$193$	−3.43127			−0.246989			−0.123494	+	0.992345i	$0.539410\pi$
$194$		0			0
$195$	−0.573428	−	0.396531i	−0.0410640	−	0.0283962i
$196$		0			0
$197$	8.61873	+	8.61873i	0.614059	+	0.614059i	0.944001	−	0.329942i	$-0.107029\pi$
$197$	8.61873	+	8.61873i	0.614059	+	0.614059i	−0.329942	+	0.944001i	$0.607029\pi$
$198$		0			0
$199$	−13.4959			−0.956701			−0.478351	−	0.878169i	$-0.658765\pi$
$199$	−13.4959			−0.956701			−0.478351	+	0.878169i	$0.658765\pi$
$200$		0			0
$201$	3.69639	+	20.2680i	0.260723	+	1.42960i
$202$		0			0
$203$	3.28972	−	3.28972i	0.230893	−	0.230893i
$204$		0			0
$205$	−8.64847	−	8.64847i	−0.604035	−	0.604035i
$206$		0			0
$207$	−9.11127	+	3.43768i	−0.633277	+	0.238935i
$208$		0			0
$209$		−	15.0977i		−	1.04433i
$210$		0			0
$211$	−8.78164	+	8.78164i	−0.604553	+	0.604553i	−0.941517	−	0.336964i	$-0.890600\pi$
$211$	−8.78164	+	8.78164i	−0.604553	+	0.604553i	0.336964	+	0.941517i	$0.390600\pi$
$212$		0			0
$213$	−19.6029	−	13.5556i	−1.34317	−	0.928815i
$214$		0			0
$215$			1.43850i			0.0981050i
$216$		0			0
$217$		−	3.76875i		−	0.255839i
$218$		0			0
$219$	−9.68006	−	6.69386i	−0.654118	−	0.452329i
$220$		0			0
$221$	−0.705642	+	0.705642i	−0.0474666	+	0.0474666i
$222$		0			0
$223$		−	10.6418i		−	0.712629i	−0.934366	−	0.356314i	$-0.884033\pi$
$223$		−	10.6418i		−	0.712629i	0.934366	−	0.356314i	$-0.115967\pi$
$224$		0			0
$225$	−10.7357	+	4.05056i	−0.715710	+	0.270037i
$226$		0			0
$227$	−1.76217	−	1.76217i	−0.116960	−	0.116960i	0.646205	−	0.763164i	$-0.276355\pi$
$227$	−1.76217	−	1.76217i	−0.116960	−	0.116960i	−0.763164	+	0.646205i	$0.776355\pi$
$228$		0			0
$229$	2.67283	−	2.67283i	0.176626	−	0.176626i	−0.613257	−	0.789883i	$-0.710141\pi$
$229$	2.67283	−	2.67283i	0.176626	−	0.176626i	0.789883	+	0.613257i	$0.210141\pi$
$230$		0			0
$231$	1.35954	+	7.45466i	0.0894515	+	0.490481i
$232$		0			0
$233$	0.740966			0.0485423			0.0242712	−	0.999705i	$-0.492273\pi$
$233$	0.740966			0.0485423			0.0242712	+	0.999705i	$0.492273\pi$
$234$		0			0
$235$	0.585817	+	0.585817i	0.0382145	+	0.0382145i
$236$		0			0
$237$	−5.46420	−	3.77855i	−0.354938	−	0.245443i
$238$		0			0
$239$	4.05725			0.262441			0.131221	−	0.991353i	$-0.458110\pi$
$239$	4.05725			0.262441			0.131221	+	0.991353i	$0.458110\pi$
$240$		0			0
$241$	−22.5065			−1.44977			−0.724885	−	0.688870i	$-0.758107\pi$
$241$	−22.5065			−1.44977			−0.724885	+	0.688870i	$0.758107\pi$
$242$		0			0
$243$	−1.81295	−	15.4827i	−0.116301	−	0.993214i
$244$		0			0
$245$	0.766553	+	0.766553i	0.0489733	+	0.0489733i
$246$		0			0
$247$	1.28134			0.0815296
$248$		0			0
$249$	0.259100	−	0.0472534i	0.0164198	−	0.00299456i
$250$		0			0
$251$	−19.1167	+	19.1167i	−1.20664	+	1.20664i	−0.234526	+	0.972110i	$0.575354\pi$
$251$	−19.1167	+	19.1167i	−1.20664	+	1.20664i	−0.972110	+	0.234526i	$0.924646\pi$
$252$		0			0
$253$	−10.0419	−	10.0419i	−0.631328	−	0.631328i
$254$		0			0
$255$	−0.905426	−	4.96464i	−0.0567000	−	0.310898i
$256$		0			0
$257$			7.40089i			0.461655i	0.972995	+	0.230827i	$0.0741433\pi$
$257$			7.40089i			0.461655i	−0.972995	+	0.230827i	$0.925857\pi$
$258$		0			0
$259$	4.88595	−	4.88595i	0.303598	−	0.303598i
$260$		0			0
$261$	−12.7177	−	5.74989i	−0.787205	−	0.355909i
$262$		0			0
$263$		−	16.5931i		−	1.02317i	−0.859232	−	0.511586i	$-0.829058\pi$
$263$		−	16.5931i		−	1.02317i	0.859232	−	0.511586i	$-0.170942\pi$
$264$		0			0
$265$			6.35656i			0.390480i
$266$		0			0
$267$	8.86881	−	12.8253i	0.542762	−	0.784894i
$268$		0			0
$269$	13.9816	−	13.9816i	0.852471	−	0.852471i	−0.137966	−	0.990437i	$-0.544056\pi$
$269$	13.9816	−	13.9816i	0.852471	−	0.852471i	0.990437	+	0.137966i	$0.0440565\pi$
$270$		0			0
$271$			7.27474i			0.441909i	0.975284	+	0.220955i	$0.0709173\pi$
$271$			7.27474i			0.441909i	−0.975284	+	0.220955i	$0.929083\pi$
$272$		0			0
$273$	−0.632675	+	0.115384i	−0.0382913	+	0.00698337i
$274$		0			0
$275$	−11.8322	−	11.8322i	−0.713508	−	0.713508i
$276$		0			0
$277$	−3.36999	+	3.36999i	−0.202483	+	0.202483i	−0.801063	−	0.598580i	$-0.795732\pi$
$277$	−3.36999	+	3.36999i	−0.202483	+	0.202483i	0.598580	+	0.801063i	$0.295732\pi$
$278$		0			0
$279$	−10.5784	+	3.99121i	−0.633310	+	0.238947i
$280$		0			0
$281$	−23.9375			−1.42799			−0.713997	−	0.700149i	$-0.753117\pi$
$281$	−23.9375			−1.42799			−0.713997	+	0.700149i	$0.753117\pi$
$282$		0			0
$283$	−17.1984	−	17.1984i	−1.02234	−	1.02234i	−0.999745	−	0.0225944i	$-0.992807\pi$
$283$	−17.1984	−	17.1984i	−1.02234	−	1.02234i	−0.0225944	−	0.999745i	$-0.507193\pi$
$284$		0			0
$285$	−3.68545	+	5.32956i	−0.218307	+	0.315696i
$286$		0			0
$287$	−11.2823			−0.665972
$288$		0			0
$289$	9.77648			0.575087
$290$		0			0
$291$	−17.8750	+	25.8492i	−1.04785	+	1.51531i
$292$		0			0
$293$	11.3212	+	11.3212i	0.661394	+	0.661394i	0.955708	−	0.294315i	$-0.0950915\pi$
$293$	11.3212	+	11.3212i	0.661394	+	0.661394i	−0.294315	+	0.955708i	$0.595091\pi$
$294$		0			0
$295$	−4.03584			−0.234976
$296$		0			0
$297$	19.4844	−	11.7107i	1.13060	−	0.679526i
$298$		0			0
$299$	0.852253	−	0.852253i	0.0492871	−	0.0492871i
$300$		0			0
$301$	0.938292	+	0.938292i	0.0540822	+	0.0540822i
$302$		0			0
$303$	17.4610	−	3.18446i	1.00311	−	0.182942i
$304$		0			0
$305$			16.4153i			0.939936i
$306$		0			0
$307$	19.0113	−	19.0113i	1.08503	−	1.08503i	0.0890009	−	0.996032i	$-0.471633\pi$
$307$	19.0113	−	19.0113i	1.08503	−	1.08503i	0.996032	−	0.0890009i	$-0.0283674\pi$
$308$		0			0
$309$	−16.9642	+	24.5321i	−0.965059	+	1.39558i
$310$		0			0
$311$		−	28.7635i		−	1.63103i	−0.578737	−	0.815514i	$-0.696454\pi$
$311$		−	28.7635i		−	1.63103i	0.578737	−	0.815514i	$-0.303546\pi$
$312$		0			0
$313$		−	20.0305i		−	1.13219i	−0.824339	−	0.566096i	$-0.808453\pi$
$313$		−	20.0305i		−	1.13219i	0.824339	−	0.566096i	$-0.191547\pi$
$314$		0			0
$315$	1.33981	−	2.96341i	0.0754896	−	0.166969i
$316$		0			0
$317$	−22.5290	+	22.5290i	−1.26535	+	1.26535i	−0.316891	+	0.948462i	$0.602639\pi$
$317$	−22.5290	+	22.5290i	−1.26535	+	1.26535i	−0.948462	+	0.316891i	$0.897361\pi$
$318$		0			0
$319$		−	20.3539i		−	1.13960i
$320$		0			0
$321$	−3.08933	−	16.9395i	−0.172430	−	0.945468i
$322$		0			0
$323$	6.55840	+	6.55840i	0.364919	+	0.364919i
$324$		0			0
$325$	1.00420	−	1.00420i	0.0557027	−	0.0557027i
$326$		0			0
$327$	4.47754	−	0.816591i	0.247608	−	0.0451576i
$328$		0			0
$329$	0.764222			0.0421329
$330$		0			0
$331$	10.9663	+	10.9663i	0.602763	+	0.602763i	0.941045	−	0.338282i	$-0.109846\pi$
$331$	10.9663	+	10.9663i	0.602763	+	0.602763i	−0.338282	+	0.941045i	$0.609846\pi$
$332$		0			0
$333$	−18.8885	−	8.53982i	−1.03508	−	0.467979i
$334$		0			0
$335$	12.8948			0.704516
$336$		0			0
$337$	−31.9429			−1.74004			−0.870020	−	0.493016i	$-0.835894\pi$
$337$	−31.9429			−1.74004			−0.870020	+	0.493016i	$0.835894\pi$
$338$		0			0
$339$	22.3258	+	15.4385i	1.21257	+	0.838505i
$340$		0			0
$341$	−11.6588	−	11.6588i	−0.631361	−	0.631361i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	1.09355	+	5.99613i	0.0588745	+	0.322821i
$346$		0			0
$347$	17.8392	−	17.8392i	0.957656	−	0.957656i	−0.0414832	−	0.999139i	$-0.513208\pi$
$347$	17.8392	−	17.8392i	0.957656	−	0.957656i	0.999139	+	0.0414832i	$0.0132083\pi$
$348$		0			0
$349$	18.9731	+	18.9731i	1.01561	+	1.01561i	0.999876	+	0.0157305i	$0.00500739\pi$
$349$	18.9731	+	18.9731i	1.01561	+	1.01561i	0.0157305	+	0.999876i	$0.494993\pi$
$350$		0			0
$351$	0.993887	+	1.65364i	0.0530498	+	0.0882646i
$352$		0			0
$353$			23.1220i			1.23066i	0.788271	+	0.615329i	$0.210977\pi$
$353$			23.1220i			1.23066i	−0.788271	+	0.615329i	$0.789023\pi$
$354$		0			0
$355$	−10.5479	+	10.5479i	−0.559825	+	0.559825i
$356$		0			0
$357$	−3.82887	−	2.64770i	−0.202645	−	0.140131i
$358$		0			0
$359$		−	30.5132i		−	1.61043i	−0.592986	−	0.805213i	$-0.702051\pi$
$359$		−	30.5132i		−	1.61043i	0.592986	−	0.805213i	$-0.297949\pi$
$360$		0			0
$361$			7.09096i			0.373208i
$362$		0			0
$363$	11.5965	+	8.01910i	0.608658	+	0.420894i
$364$		0			0
$365$	−5.20864	+	5.20864i	−0.272633	+	0.272633i
$366$		0			0
$367$			24.0298i			1.25434i	0.778881	+	0.627172i	$0.215788\pi$
$367$			24.0298i			1.25434i	−0.778881	+	0.627172i	$0.784212\pi$
$368$		0			0
$369$	11.9482	+	31.6678i	0.622000	+	1.64856i
$370$		0			0
$371$	4.14619	+	4.14619i	0.215260	+	0.215260i
$372$		0			0
$373$	−1.44743	+	1.44743i	−0.0749453	+	0.0749453i	−0.743586	−	0.668641i	$-0.766877\pi$
$373$	−1.44743	+	1.44743i	−0.0749453	+	0.0749453i	0.668641	+	0.743586i	$0.266877\pi$
$374$		0			0
$375$	2.97292	+	16.3011i	0.153521	+	0.841786i
$376$		0			0
$377$	1.72743			0.0889670
$378$		0			0
$379$	−17.3532	−	17.3532i	−0.891372	−	0.891372i	0.103280	−	0.994652i	$-0.467066\pi$
$379$	−17.3532	−	17.3532i	−0.891372	−	0.891372i	−0.994652	+	0.103280i	$0.967066\pi$
$380$		0			0
$381$	1.24608	+	0.861676i	0.0638385	+	0.0441450i
$382$		0			0
$383$	3.29068			0.168146			0.0840729	−	0.996460i	$-0.473207\pi$
$383$	3.29068			0.168146			0.0840729	+	0.996460i	$0.473207\pi$
$384$		0			0
$385$	4.74274			0.241713
$386$		0			0
$387$	1.63998	−	3.62733i	0.0833648	−	0.184388i
$388$		0			0
$389$	15.9506	+	15.9506i	0.808728	+	0.808728i	0.984441	−	0.175713i	$-0.0562231\pi$
$389$	15.9506	+	15.9506i	0.808728	+	0.808728i	−0.175713	+	0.984441i	$0.556223\pi$
$390$		0			0
$391$	8.72434			0.441209
$392$		0			0
$393$	−7.13594	+	1.30142i	−0.359960	+	0.0656478i
$394$		0			0
$395$	−2.94017	+	2.94017i	−0.147936	+	0.147936i
$396$		0			0
$397$	0.355551	+	0.355551i	0.0178446	+	0.0178446i	0.715973	−	0.698128i	$-0.245983\pi$
$397$	0.355551	+	0.355551i	0.0178446	+	0.0178446i	−0.698128	+	0.715973i	$0.745983\pi$
$398$		0			0
$399$	1.07241	+	5.88023i	0.0536875	+	0.294380i
$400$		0			0
$401$		−	21.6901i		−	1.08315i	−0.840652	−	0.541576i	$-0.817828\pi$
$401$		−	21.6901i		−	1.08315i	0.840652	−	0.541576i	$-0.182172\pi$
$402$		0			0
$403$	0.989482	−	0.989482i	0.0492896	−	0.0492896i
$404$		0			0
$405$	−9.73676	−	0.622325i	−0.483824	−	0.0309236i
$406$		0			0
$407$		−	30.2299i		−	1.49844i
$408$		0			0
$409$			13.8029i			0.682508i	0.939971	+	0.341254i	$0.110852\pi$
$409$			13.8029i			0.682508i	−0.939971	+	0.341254i	$0.889148\pi$
$410$		0			0
$411$	13.3545	−	19.3121i	0.658730	−	0.952595i
$412$		0			0
$413$	−2.63246	+	2.63246i	−0.129535	+	0.129535i
$414$		0			0
$415$		−	0.164843i		−	0.00809180i
$416$		0			0
$417$	0.632466	−	0.115346i	0.0309720	−	0.00564852i
$418$		0			0
$419$	−8.43616	−	8.43616i	−0.412133	−	0.412133i	0.470348	−	0.882481i	$-0.344128\pi$
$419$	−8.43616	−	8.43616i	−0.412133	−	0.412133i	−0.882481	+	0.470348i	$0.844128\pi$
$420$		0			0
$421$	−5.33124	+	5.33124i	−0.259829	+	0.259829i	−0.824984	−	0.565155i	$-0.808816\pi$
$421$	−5.33124	+	5.33124i	−0.259829	+	0.259829i	0.565155	+	0.824984i	$0.308816\pi$
$422$		0			0
$423$	−0.809331	−	2.14506i	−0.0393510	−	0.104297i
$424$		0			0
$425$	10.2797			0.498641
$426$		0			0
$427$	10.7072	+	10.7072i	0.518158	+	0.518158i
$428$		0			0
$429$	−1.60027	+	2.31416i	−0.0772616	+	0.111729i
$430$		0			0
$431$	−25.7527			−1.24046			−0.620232	−	0.784419i	$-0.712961\pi$
$431$	−25.7527			−1.24046			−0.620232	+	0.784419i	$0.712961\pi$
$432$		0			0
$433$	6.76490			0.325101			0.162550	−	0.986700i	$-0.448028\pi$
$433$	6.76490			0.325101			0.162550	+	0.986700i	$0.448028\pi$
$434$		0			0
$435$	−4.96851	+	7.18501i	−0.238222	+	0.344495i
$436$		0			0
$437$	−7.92103	−	7.92103i	−0.378914	−	0.378914i
$438$		0			0
$439$	2.54261			0.121352			0.0606762	−	0.998158i	$-0.480674\pi$
$439$	2.54261			0.121352			0.0606762	+	0.998158i	$0.480674\pi$
$440$		0			0
$441$	−1.05903	−	2.80686i	−0.0504298	−	0.133660i
$442$		0			0
$443$	−24.5321	+	24.5321i	−1.16555	+	1.16555i	−0.182313	+	0.983240i	$0.558359\pi$
$443$	−24.5321	+	24.5321i	−1.16555	+	1.16555i	−0.983240	+	0.182313i	$0.941641\pi$
$444$		0			0
$445$	−6.90102	−	6.90102i	−0.327140	−	0.327140i
$446$		0			0
$447$	−36.1206	+	6.58750i	−1.70845	+	0.311578i
$448$		0			0
$449$		−	27.7538i		−	1.30978i	−0.755724	−	0.654891i	$-0.772715\pi$
$449$		−	27.7538i		−	1.30978i	0.755724	−	0.654891i	$-0.227285\pi$
$450$		0			0
$451$	−34.9023	+	34.9023i	−1.64349	+	1.64349i
$452$		0			0
$453$	13.0714	−	18.9027i	0.614148	−	0.888126i
$454$		0			0
$455$			0.402516i			0.0188702i
$456$		0			0
$457$			25.1096i			1.17458i	0.809378	+	0.587288i	$0.199804\pi$
$457$			25.1096i			1.17458i	−0.809378	+	0.587288i	$0.800196\pi$
$458$		0			0
$459$	−3.37686	+	13.5511i	−0.157618	+	0.632510i
$460$		0			0
$461$	1.51791	−	1.51791i	0.0706959	−	0.0706959i	−0.670875	−	0.741571i	$-0.734081\pi$
$461$	1.51791	−	1.51791i	0.0706959	−	0.0706959i	0.741571	+	0.670875i	$0.234081\pi$
$462$		0			0
$463$		−	10.9075i		−	0.506915i	−0.967347	−	0.253457i	$-0.918432\pi$
$463$		−	10.9075i		−	0.506915i	0.967347	−	0.253457i	$-0.0815678\pi$
$464$		0			0
$465$	1.26963	+	6.96162i	0.0588775	+	0.322838i
$466$		0			0
$467$	26.0440	+	26.0440i	1.20517	+	1.20517i	0.972572	+	0.232601i	$0.0747237\pi$
$467$	26.0440	+	26.0440i	1.20517	+	1.20517i	0.232601	+	0.972572i	$0.425276\pi$
$468$		0			0
$469$	8.41087	−	8.41087i	0.388378	−	0.388378i
$470$		0			0
$471$	19.0327	−	3.47110i	0.876983	−	0.159940i
$472$		0			0
$473$	5.80531			0.266928
$474$		0			0
$475$	−9.33321	−	9.33321i	−0.428237	−	0.428237i
$476$		0			0
$477$	7.24686	−	16.0287i	0.331811	−	0.733904i
$478$		0			0
$479$	−17.6724			−0.807473			−0.403737	−	0.914875i	$-0.632289\pi$
$479$	−17.6724			−0.807473			−0.403737	+	0.914875i	$0.632289\pi$
$480$		0			0
$481$	2.56560			0.116981
$482$		0			0
$483$	4.62439	+	3.19781i	0.210417	+	0.145506i
$484$		0			0
$485$	13.9089	+	13.9089i	0.631571	+	0.631571i
$486$		0			0
$487$	7.46608			0.338321			0.169160	−	0.985589i	$-0.445894\pi$
$487$	7.46608			0.338321			0.169160	+	0.985589i	$0.445894\pi$
$488$		0			0
$489$	−0.970518	−	5.32155i	−0.0438883	−	0.240649i
$490$		0			0
$491$	−21.8771	+	21.8771i	−0.987300	+	0.987300i	−0.999920	−	0.0126204i	$-0.995983\pi$
$491$	−21.8771	+	21.8771i	−0.987300	+	0.987300i	0.0126204	+	0.999920i	$0.495983\pi$
$492$		0			0
$493$	8.84165	+	8.84165i	0.398208	+	0.398208i
$494$		0			0
$495$	−5.02269	−	13.3122i	−0.225753	−	0.598340i
$496$		0			0
$497$			13.7602i			0.617228i
$498$		0			0
$499$	18.1129	−	18.1129i	0.810843	−	0.810843i	−0.173917	−	0.984760i	$-0.555643\pi$
$499$	18.1129	−	18.1129i	0.810843	−	0.810843i	0.984760	+	0.173917i	$0.0556426\pi$
$500$		0			0
$501$	−26.3248	−	18.2039i	−1.17611	−	0.813290i
$502$		0			0
$503$		−	8.65417i		−	0.385871i	−0.981211	−	0.192935i	$-0.938199\pi$
$503$		−	8.65417i		−	0.385871i	0.981211	−	0.192935i	$-0.0618007\pi$
$504$		0			0
$505$		−	11.1089i		−	0.494340i
$506$		0			0
$507$	18.3235	+	12.6709i	0.813776	+	0.562735i
$508$		0			0
$509$	−0.578725	+	0.578725i	−0.0256515	+	0.0256515i	−0.719816	−	0.694165i	$-0.755774\pi$
$509$	−0.578725	+	0.578725i	−0.0256515	+	0.0256515i	0.694165	+	0.719816i	$0.255774\pi$
$510$		0			0
$511$			6.79488i			0.300588i
$512$		0			0
$513$	15.3693	−	9.23741i	0.678570	−	0.407842i
$514$		0			0
$515$	13.2002	+	13.2002i	0.581670	+	0.581670i
$516$		0			0
$517$	2.36416	−	2.36416i	0.103976	−	0.103976i
$518$		0			0
$519$	0.380822	+	2.08813i	0.0167162	+	0.0916586i
$520$		0			0
$521$	13.3576			0.585206			0.292603	−	0.956234i	$-0.405478\pi$
$521$	13.3576			0.585206			0.292603	+	0.956234i	$0.405478\pi$
$522$		0			0
$523$	7.10147	+	7.10147i	0.310526	+	0.310526i	0.845113	−	0.534588i	$-0.179533\pi$
$523$	7.10147	+	7.10147i	0.310526	+	0.310526i	−0.534588	+	0.845113i	$0.679533\pi$
$524$		0			0
$525$	5.44884	+	3.76793i	0.237807	+	0.164446i
$526$		0			0
$527$	10.1291			0.441231
$528$		0			0
$529$	12.4630			0.541870
$530$		0			0
$531$	10.1768	+	4.60110i	0.441635	+	0.199671i
$532$		0			0
$533$	−2.96215	−	2.96215i	−0.128305	−	0.128305i
$534$		0			0
$535$	−10.7771			−0.465934
$536$		0			0
$537$	29.4560	−	5.37203i	1.27112	−	0.231820i
$538$		0			0
$539$	3.09355	−	3.09355i	0.133249	−	0.133249i
$540$		0			0
$541$	14.0412	+	14.0412i	0.603678	+	0.603678i	0.941287	−	0.337609i	$-0.109618\pi$
$541$	14.0412	+	14.0412i	0.603678	+	0.603678i	−0.337609	+	0.941287i	$0.609618\pi$
$542$		0			0
$543$	1.57547	+	8.63860i	0.0676097	+	0.370718i
$544$		0			0
$545$		−	2.84866i		−	0.122023i
$546$		0			0
$547$	−7.03679	+	7.03679i	−0.300871	+	0.300871i	−0.841355	−	0.540483i	$-0.818241\pi$
$547$	−7.03679	+	7.03679i	−0.300871	+	0.300871i	0.540483	+	0.841355i	$0.318241\pi$
$548$		0			0
$549$	18.7144	−	41.3928i	0.798711	−	1.76660i
$550$		0			0
$551$		−	16.0551i		−	0.683970i
$552$		0			0
$553$			3.83558i			0.163105i
$554$		0			0
$555$	−7.37931	+	10.6713i	−0.313234	+	0.452971i
$556$		0			0
$557$	15.3000	−	15.3000i	0.648280	−	0.648280i	−0.304297	−	0.952577i	$-0.598422\pi$
$557$	15.3000	−	15.3000i	0.648280	−	0.648280i	0.952577	+	0.304297i	$0.0984216\pi$
$558$		0			0
$559$			0.492695i			0.0208388i
$560$		0			0
$561$	−20.0356	+	3.65399i	−0.845904	+	0.154272i
$562$		0			0
$563$	18.1230	+	18.1230i	0.763793	+	0.763793i	0.977006	−	0.213213i	$-0.0683928\pi$
$563$	18.1230	+	18.1230i	0.763793	+	0.763793i	−0.213213	+	0.977006i	$0.568393\pi$
$564$		0			0
$565$	12.0131	−	12.0131i	0.505393	−	0.505393i
$566$		0			0
$567$	−6.75693	+	5.94508i	−0.283764	+	0.249670i
$568$		0			0
$569$	4.23430			0.177511			0.0887555	−	0.996053i	$-0.471711\pi$
$569$	4.23430			0.177511			0.0887555	+	0.996053i	$0.471711\pi$
$570$		0			0
$571$	0.713850	+	0.713850i	0.0298737	+	0.0298737i	0.721886	−	0.692012i	$-0.243276\pi$
$571$	0.713850	+	0.713850i	0.0298737	+	0.0298737i	−0.692012	+	0.721886i	$0.743276\pi$
$572$		0			0
$573$	−22.5859	+	32.6617i	−0.943540	+	1.36446i
$574$		0			0
$575$	−12.4156			−0.517764
$576$		0			0
$577$	−11.2780			−0.469508			−0.234754	−	0.972055i	$-0.575428\pi$
$577$	−11.2780			−0.469508			−0.234754	+	0.972055i	$0.575428\pi$
$578$		0			0
$579$	3.38026	−	4.88823i	0.140479	−	0.203148i
$580$		0			0
$581$	−0.107522	−	0.107522i	−0.00446076	−	0.00446076i
$582$		0			0
$583$	25.6529			1.06244
$584$		0			0
$585$	1.12980	−	0.426275i	0.0467117	−	0.0176243i
$586$		0			0
$587$	1.93378	−	1.93378i	0.0798157	−	0.0798157i	−0.666072	−	0.745888i	$-0.732026\pi$
$587$	1.93378	−	1.93378i	0.0798157	−	0.0798157i	0.745888	+	0.666072i	$0.232026\pi$
$588$		0			0
$589$	−9.19646	−	9.19646i	−0.378934	−	0.378934i
$590$		0			0
$591$	−20.7689	+	3.78773i	−0.854319	+	0.155807i
$592$		0			0
$593$		−	5.46475i		−	0.224410i	−0.993685	−	0.112205i	$-0.964209\pi$
$593$		−	5.46475i		−	0.224410i	0.993685	−	0.112205i	$-0.0357914\pi$
$594$		0			0
$595$	−2.06023	+	2.06023i	−0.0844614	+	0.0844614i
$596$		0			0
$597$	13.2953	−	19.2264i	0.544140	−	0.786886i
$598$		0			0
$599$			2.30973i			0.0943728i	0.998886	+	0.0471864i	$0.0150255\pi$
$599$			2.30973i			0.0943728i	−0.998886	+	0.0471864i	$0.984975\pi$
$600$		0			0
$601$			9.20218i			0.375365i	0.982230	+	0.187682i	$0.0600975\pi$
$601$			9.20218i			0.375365i	−0.982230	+	0.187682i	$0.939902\pi$
$602$		0			0
$603$	−32.5155	−	14.7008i	−1.32413	−	0.598663i
$604$		0			0
$605$	6.23984	−	6.23984i	0.253685	−	0.253685i
$606$		0			0
$607$		−	17.5119i		−	0.710784i	−0.934717	−	0.355392i	$-0.884347\pi$
$607$		−	17.5119i		−	0.710784i	0.934717	−	0.355392i	$-0.115653\pi$
$608$		0			0
$609$	1.44576	+	7.92738i	0.0585850	+	0.321234i
$610$		0			0
$611$	0.200646	+	0.200646i	0.00811725	+	0.00811725i
$612$		0			0
$613$	12.0484	−	12.0484i	0.486629	−	0.486629i	−0.420611	−	0.907241i	$-0.638184\pi$
$613$	12.0484	−	12.0484i	0.486629	−	0.486629i	0.907241	+	0.420611i	$0.138184\pi$
$614$		0			0
$615$	20.8406	−	3.80080i	0.840374	−	0.153263i
$616$		0			0
$617$	17.2962			0.696320			0.348160	−	0.937435i	$-0.386807\pi$
$617$	17.2962			0.696320			0.348160	+	0.937435i	$0.386807\pi$
$618$		0			0
$619$	8.03863	+	8.03863i	0.323100	+	0.323100i	0.849955	−	0.526855i	$-0.176629\pi$
$619$	8.03863	+	8.03863i	0.323100	+	0.323100i	−0.526855	+	0.849955i	$0.676629\pi$
$620$		0			0
$621$	4.07847	−	16.3666i	0.163663	−	0.656768i
$622$		0			0
$623$	−9.00266			−0.360684
$624$		0			0
$625$	−8.75299			−0.350120
$626$		0			0
$627$	21.5083	+	14.8732i	0.858960	+	0.593980i
$628$		0			0
$629$	13.1318	+	13.1318i	0.523598	+	0.523598i
$630$		0			0
$631$	−32.3346			−1.28722			−0.643610	−	0.765353i	$-0.722564\pi$
$631$	−32.3346			−1.28722			−0.643610	+	0.765353i	$0.722564\pi$
$632$		0			0
$633$	−3.85933	−	21.1615i	−0.153395	−	0.841094i
$634$		0			0
$635$	0.670489	−	0.670489i	0.0266075	−	0.0266075i
$636$		0			0
$637$	0.262549	+	0.262549i	0.0104026	+	0.0104026i
$638$		0			0
$639$	38.6229	−	14.5724i	1.52790	−	0.576475i
$640$		0			0
$641$			26.9406i			1.06409i	0.846717	+	0.532044i	$0.178576\pi$
$641$			26.9406i			1.06409i	−0.846717	+	0.532044i	$0.821424\pi$
$642$		0			0
$643$	2.08209	−	2.08209i	0.0821098	−	0.0821098i	−0.664859	−	0.746969i	$-0.731508\pi$
$643$	2.08209	−	2.08209i	0.0821098	−	0.0821098i	0.746969	+	0.664859i	$0.231508\pi$
$644$		0			0
$645$	−2.04930	−	1.41712i	−0.0806912	−	0.0557989i
$646$		0			0
$647$		−	0.704788i		−	0.0277081i	−0.999904	−	0.0138540i	$-0.995590\pi$
$647$		−	0.704788i		−	0.0277081i	0.999904	−	0.0138540i	$-0.00441002\pi$
$648$		0			0
$649$			16.2873i			0.639332i
$650$		0			0
$651$	5.36900	+	3.71272i	0.210428	+	0.145513i
$652$		0			0
$653$	−28.0029	+	28.0029i	−1.09584	+	1.09584i	−0.100947	+	0.994892i	$0.532187\pi$
$653$	−28.0029	+	28.0029i	−1.09584	+	1.09584i	−0.994892	+	0.100947i	$0.967813\pi$
$654$		0			0
$655$			4.53997i			0.177391i
$656$		0			0
$657$	19.0723	−	7.19596i	0.744081	−	0.280741i
$658$		0			0
$659$	7.83856	+	7.83856i	0.305347	+	0.305347i	0.843101	−	0.537755i	$-0.180727\pi$
$659$	7.83856	+	7.83856i	0.305347	+	0.305347i	−0.537755	+	0.843101i	$0.680727\pi$
$660$		0			0
$661$	−26.4193	+	26.4193i	−1.02759	+	1.02759i	−0.0279814	+	0.999608i	$0.508908\pi$
$661$	−26.4193	+	26.4193i	−1.02759	+	1.02759i	−0.999608	+	0.0279814i	$0.991092\pi$
$662$		0			0
$663$	−0.310114	−	1.70042i	−0.0120438	−	0.0660387i
$664$		0			0
$665$	3.74107			0.145072
$666$		0			0
$667$	−10.6787	−	10.6787i	−0.413480	−	0.413480i
$668$		0			0
$669$	15.1604	+	10.4836i	0.586136	+	0.405319i
$670$		0			0
$671$	66.2466			2.55742
$672$		0			0
$673$	32.2415			1.24282			0.621410	−	0.783486i	$-0.286560\pi$
$673$	32.2415			1.24282			0.621410	+	0.783486i	$0.286560\pi$
$674$		0			0
$675$	4.80558	−	19.2845i	0.184967	−	0.742259i
$676$		0			0
$677$	−32.8347	−	32.8347i	−1.26194	−	1.26194i	−0.950151	−	0.311789i	$-0.899072\pi$
$677$	−32.8347	−	32.8347i	−1.26194	−	1.26194i	−0.311789	−	0.950151i	$-0.600928\pi$
$678$		0			0
$679$	18.1447			0.696331
$680$		0			0
$681$	4.24638	−	0.774435i	0.162722	−	0.0296764i
$682$		0			0
$683$	−15.6297	+	15.6297i	−0.598056	+	0.598056i	−0.939795	−	0.341739i	$-0.888984\pi$
$683$	−15.6297	+	15.6297i	−0.598056	+	0.598056i	0.341739	+	0.939795i	$0.388984\pi$
$684$		0			0
$685$	−10.3914	−	10.3914i	−0.397036	−	0.397036i
$686$		0			0
$687$	1.17465	+	6.44084i	0.0448156	+	0.245733i
$688$		0			0
$689$			2.17716i			0.0829431i
$690$		0			0
$691$	16.0088	−	16.0088i	0.609003	−	0.609003i	−0.333682	−	0.942686i	$-0.608291\pi$
$691$	16.0088	−	16.0088i	0.609003	−	0.609003i	0.942686	+	0.333682i	$0.108291\pi$
$692$		0			0
$693$	−11.9593	−	5.40701i	−0.454297	−	0.205395i
$694$		0			0
$695$		−	0.402383i		−	0.0152632i
$696$		0			0
$697$		−	30.3229i		−	1.14856i
$698$		0			0
$699$	−0.729950	+	1.05559i	−0.0276093	+	0.0399260i
$700$		0			0
$701$	−6.13145	+	6.13145i	−0.231582	+	0.231582i	−0.813353	−	0.581771i	$-0.802360\pi$
$701$	−6.13145	+	6.13145i	−0.231582	+	0.231582i	0.581771	+	0.813353i	$0.302360\pi$
$702$		0			0
$703$		−	23.8453i		−	0.899341i
$704$		0			0
$705$	−1.41167	+	0.257453i	−0.0531665	+	0.00969624i
$706$		0			0
$707$	−7.24602	−	7.24602i	−0.272515	−	0.272515i
$708$		0			0
$709$	−28.7473	+	28.7473i	−1.07963	+	1.07963i	−0.0830852	+	0.996542i	$0.526477\pi$
$709$	−28.7473	+	28.7473i	−1.07963	+	1.07963i	−0.996542	+	0.0830852i	$0.973523\pi$
$710$		0			0
$711$	10.7659	−	4.06198i	0.403754	−	0.152336i
$712$		0			0
$713$	−12.2336			−0.458153
$714$		0			0
$715$	1.24520	+	1.24520i	0.0465679	+	0.0465679i
$716$		0			0
$717$	−3.99693	+	5.77999i	−0.149268	+	0.215858i
$718$		0			0
$719$	−37.8458			−1.41141			−0.705706	−	0.708505i	$-0.749370\pi$
$719$	−37.8458			−1.41141			−0.705706	+	0.708505i	$0.749370\pi$
$720$		0			0
$721$	17.2202			0.641314
$722$		0			0
$723$	22.1719	−	32.0630i	0.824581	−	1.19243i
$724$		0			0
$725$	−12.5825	−	12.5825i	−0.467302	−	0.467302i
$726$		0			0
$727$	26.7204			0.991005			0.495503	−	0.868606i	$-0.334984\pi$
$727$	26.7204			0.991005			0.495503	+	0.868606i	$0.334984\pi$
$728$		0			0
$729$	23.8428	+	12.6697i	0.883065	+	0.469250i
$730$		0			0
$731$	−2.52181	+	2.52181i	−0.0932725	+	0.0932725i
$732$		0			0
$733$	−19.2237	−	19.2237i	−0.710045	−	0.710045i	0.256500	−	0.966544i	$-0.417431\pi$
$733$	−19.2237	−	19.2237i	−0.710045	−	0.710045i	−0.966544	+	0.256500i	$0.917431\pi$
$734$		0			0
$735$	−1.84720	+	0.336883i	−0.0681349	+	0.0124261i
$736$		0			0
$737$		−	52.0389i		−	1.91688i
$738$		0			0
$739$	−2.40651	+	2.40651i	−0.0885250	+	0.0885250i	−0.749983	−	0.661458i	$-0.769938\pi$
$739$	−2.40651	+	2.40651i	−0.0885250	+	0.0885250i	0.661458	+	0.749983i	$0.269938\pi$
$740$		0			0
$741$	−1.26229	+	1.82541i	−0.0463713	+	0.0670580i
$742$		0			0
$743$		−	2.79821i		−	0.102656i	−0.998682	−	0.0513282i	$-0.983655\pi$
$743$		−	2.79821i		−	0.102656i	0.998682	−	0.0513282i	$-0.0163455\pi$
$744$		0			0
$745$			22.9804i			0.841936i
$746$		0			0
$747$	−0.187930	+	0.415667i	−0.00687601	+	0.0152085i
$748$		0			0
$749$	−7.02957	+	7.02957i	−0.256855	+	0.256855i
$750$		0			0
$751$			51.0005i			1.86104i	0.366246	+	0.930518i	$0.380643\pi$
$751$			51.0005i			1.86104i	−0.366246	+	0.930518i	$0.619357\pi$
$752$		0			0
$753$	−8.40135	−	46.0663i	−0.306162	−	1.67875i
$754$		0			0
$755$	−10.1711	−	10.1711i	−0.370166	−	0.370166i
$756$		0			0
$757$	−6.19243	+	6.19243i	−0.225068	+	0.225068i	−0.810629	−	0.585561i	$-0.800874\pi$
$757$	−6.19243	+	6.19243i	−0.225068	+	0.225068i	0.585561	+	0.810629i	$0.300874\pi$
$758$		0			0
$759$	24.1984	−	4.41318i	0.878346	−	0.160188i
$760$		0			0
$761$	11.4162			0.413837			0.206919	−	0.978358i	$-0.433656\pi$
$761$	11.4162			0.413837			0.206919	+	0.978358i	$0.433656\pi$
$762$		0			0
$763$	−1.85810	−	1.85810i	−0.0672677	−	0.0672677i
$764$		0			0
$765$	7.96463	+	3.60095i	0.287962	+	0.130193i
$766$		0			0
$767$	−1.38230			−0.0499119
$768$		0			0
$769$	−3.36949			−0.121507			−0.0607535	−	0.998153i	$-0.519350\pi$
$769$	−3.36949			−0.121507			−0.0607535	+	0.998153i	$0.519350\pi$
$770$		0			0
$771$	−10.5434	−	7.29086i	−0.379711	−	0.262574i
$772$		0			0
$773$	−11.1451	−	11.1451i	−0.400860	−	0.400860i	0.477676	−	0.878536i	$-0.341479\pi$
$773$	−11.1451	−	11.1451i	−0.400860	−	0.400860i	−0.878536	+	0.477676i	$0.841479\pi$
$774$		0			0
$775$	−14.4147			−0.517791
$776$		0			0
$777$	2.14726	+	11.7739i	0.0770326	+	0.422385i
$778$		0			0
$779$	−27.5309	+	27.5309i	−0.986397	+	0.986397i
$780$		0			0
$781$	42.5678	+	42.5678i	1.52320	+	1.52320i
$782$		0			0
$783$	20.7200	−	12.4533i	0.740471	−	0.445046i
$784$		0			0
$785$		−	12.1089i		−	0.432184i
$786$		0			0
$787$	−7.85840	+	7.85840i	−0.280122	+	0.280122i	−0.833158	−	0.553036i	$-0.813469\pi$
$787$	−7.85840	+	7.85840i	−0.280122	+	0.280122i	0.553036	+	0.833158i	$0.313469\pi$
$788$		0			0
$789$	23.6386	+	16.3464i	0.841557	+	0.581946i
$790$		0			0
$791$		−	15.6715i		−	0.557215i
$792$		0			0
$793$			5.62233i			0.199655i
$794$		0			0
$795$	−9.05561	−	6.26205i	−0.321170	−	0.222092i
$796$		0			0
$797$	−24.9703	+	24.9703i	−0.884494	+	0.884494i	−0.993987	−	0.109494i	$-0.965077\pi$
$797$	−24.9703	+	24.9703i	−0.884494	+	0.884494i	0.109494	+	0.993987i	$0.465077\pi$
$798$		0			0
$799$			2.05397i			0.0726642i
$800$		0			0
$801$	9.53405	+	25.2692i	0.336869	+	0.892843i
$802$		0			0
$803$	21.0203	+	21.0203i	0.741791	+	0.741791i
$804$		0			0
$805$	2.48829	−	2.48829i	0.0877006	−	0.0877006i
$806$		0			0
$807$	6.14458	+	33.6920i	0.216299	+	1.18601i
$808$		0			0
$809$	16.3328			0.574232			0.287116	−	0.957896i	$-0.407303\pi$
$809$	16.3328			0.574232			0.287116	+	0.957896i	$0.407303\pi$
$810$		0			0
$811$	21.0730	+	21.0730i	0.739973	+	0.739973i	0.972573	−	0.232599i	$-0.0747231\pi$
$811$	21.0730	+	21.0730i	0.739973	+	0.739973i	−0.232599	+	0.972573i	$0.574723\pi$
$812$		0			0
$813$	−10.3637	−	7.16659i	−0.363470	−	0.251343i
$814$		0			0
$815$	−3.38563			−0.118594
$816$		0			0
$817$	4.57922			0.160207
$818$		0			0
$819$	0.458892	−	1.01498i	0.0160350	−	0.0354664i
$820$		0			0
$821$	32.3716	+	32.3716i	1.12978	+	1.12978i	0.990213	+	0.139565i	$0.0445704\pi$
$821$	32.3716	+	32.3716i	1.12978	+	1.12978i	0.139565	+	0.990213i	$0.455430\pi$
$822$		0			0
$823$	−15.8594			−0.552824			−0.276412	−	0.961039i	$-0.589146\pi$
$823$	−15.8594			−0.552824			−0.276412	+	0.961039i	$0.589146\pi$
$824$		0			0
$825$	28.5125	−	5.19998i	0.992679	−	0.181040i
$826$		0			0
$827$	11.4655	−	11.4655i	0.398693	−	0.398693i	−0.479079	−	0.877772i	$-0.659029\pi$
$827$	11.4655	−	11.4655i	0.398693	−	0.398693i	0.877772	+	0.479079i	$0.159029\pi$
$828$		0			0
$829$	−14.1050	−	14.1050i	−0.489888	−	0.489888i	0.418383	−	0.908271i	$-0.362597\pi$
$829$	−14.1050	−	14.1050i	−0.489888	−	0.489888i	−0.908271	+	0.418383i	$0.862597\pi$
$830$		0			0
$831$	−1.48103	−	8.12081i	−0.0513765	−	0.281708i
$832$		0			0
$833$			2.68766i			0.0931219i
$834$		0			0
$835$	−14.1649	+	14.1649i	−0.490195	+	0.490195i
$836$		0			0
$837$	4.73517	−	19.0019i	0.163672	−	0.656802i
$838$		0			0
$839$		−	9.65631i		−	0.333373i	−0.986010	−	0.166686i	$-0.946693\pi$
$839$		−	9.65631i		−	0.333373i	0.986010	−	0.166686i	$-0.0533067\pi$
$840$		0			0
$841$			7.35545i			0.253636i
$842$		0			0
$843$	23.5817	−	34.1017i	0.812195	−	1.17452i
$844$		0			0
$845$	9.85951	−	9.85951i	0.339178	−	0.339178i
$846$		0			0
$847$		−	8.14012i		−	0.279698i
$848$		0			0
$849$	41.4437	−	7.55830i	1.42235	−	0.259400i
$850$		0			0
$851$	−15.8601	−	15.8601i	−0.543679	−	0.543679i
$852$		0			0
$853$	21.2847	−	21.2847i	0.728773	−	0.728773i	−0.241602	−	0.970375i	$-0.577673\pi$
$853$	21.2847	−	21.2847i	0.728773	−	0.728773i	0.970375	+	0.241602i	$0.0776729\pi$
$854$		0			0
$855$	−3.96189	−	10.5007i	−0.135494	−	0.359115i
$856$		0			0
$857$	−4.52066			−0.154423			−0.0772115	−	0.997015i	$-0.524602\pi$
$857$	−4.52066			−0.154423			−0.0772115	+	0.997015i	$0.524602\pi$
$858$		0			0
$859$	−13.1351	−	13.1351i	−0.448164	−	0.448164i	0.446579	−	0.894744i	$-0.352642\pi$
$859$	−13.1351	−	13.1351i	−0.448164	−	0.448164i	−0.894744	+	0.446579i	$0.852642\pi$
$860$		0			0
$861$	11.1145	−	16.0728i	0.378783	−	0.547761i
$862$		0			0
$863$	9.02247			0.307128			0.153564	−	0.988139i	$-0.450925\pi$
$863$	9.02247			0.307128			0.153564	+	0.988139i	$0.450925\pi$
$864$		0			0
$865$	1.32849			0.0451700
$866$		0			0
$867$	−9.63114	+	13.9277i	−0.327091	+	0.473009i
$868$		0			0
$869$	11.8655	+	11.8655i	0.402511	+	0.402511i
$870$		0			0
$871$	4.41653			0.149648
$872$		0			0
$873$	−19.2158	−	50.9297i	−0.650355	−	1.72371i
$874$		0			0
$875$	6.76467	−	6.76467i	0.228688	−	0.228688i
$876$		0			0
$877$	2.14142	+	2.14142i	0.0723106	+	0.0723106i	0.742337	−	0.670027i	$-0.233717\pi$
$877$	2.14142	+	2.14142i	0.0723106	+	0.0723106i	−0.670027	+	0.742337i	$0.733717\pi$
$878$		0			0
$879$	−27.2813	+	4.97542i	−0.920174	+	0.167817i
$880$		0			0
$881$			12.6375i			0.425768i	0.977077	+	0.212884i	$0.0682856\pi$
$881$			12.6375i			0.425768i	−0.977077	+	0.212884i	$0.931714\pi$
$882$		0			0
$883$	23.7761	−	23.7761i	0.800128	−	0.800128i	−0.182987	−	0.983115i	$-0.558577\pi$
$883$	23.7761	−	23.7761i	0.800128	−	0.800128i	0.983115	+	0.182987i	$0.0585767\pi$
$884$		0			0
$885$	3.97584	−	5.74950i	0.133646	−	0.193267i
$886$		0			0
$887$			47.8477i			1.60657i	0.595596	+	0.803284i	$0.296916\pi$
$887$			47.8477i			1.60657i	−0.595596	+	0.803284i	$0.703084\pi$
$888$		0			0
$889$		−	0.874680i		−	0.0293358i
$890$		0			0
$891$	−2.51149	+	39.2943i	−0.0841382	+	1.31641i
$892$		0			0
$893$	1.86484	−	1.86484i	0.0624047	−	0.0624047i
$894$		0			0
$895$		−	18.7402i		−	0.626417i
$896$		0			0
$897$	0.374546	+	2.05371i	0.0125057	+	0.0685714i
$898$		0			0
$899$	−12.3981	−	12.3981i	−0.413501	−	0.413501i
$900$		0			0
$901$	−11.1436	+	11.1436i	−0.371246	+	0.371246i
$902$		0			0
$903$	−2.26104	+	0.412358i	−0.0752428	+	0.0137224i
$904$		0			0
$905$	5.49598			0.182693
$906$		0			0
$907$	25.2932	+	25.2932i	0.839848	+	0.839848i	0.988839	−	0.148991i	$-0.0476025\pi$
$907$	25.2932	+	25.2932i	0.839848	+	0.839848i	−0.148991	+	0.988839i	$0.547602\pi$
$908$		0			0
$909$	−12.6648	+	28.0123i	−0.420066	+	0.929109i
$910$		0			0
$911$	37.1786			1.23178			0.615892	−	0.787831i	$-0.288796\pi$
$911$	37.1786			1.23178			0.615892	+	0.787831i	$0.288796\pi$
$912$		0			0
$913$	−0.665249			−0.0220165
$914$		0			0
$915$	−23.3854	−	16.1712i	−0.773097	−	0.534605i
$916$		0			0
$917$	2.96129	+	2.96129i	0.0977903	+	0.0977903i
$918$		0			0
$919$	−40.7166			−1.34312			−0.671558	−	0.740952i	$-0.734375\pi$
$919$	−40.7166			−1.34312			−0.671558	+	0.740952i	$0.734375\pi$
$920$		0			0
$921$	8.35503	+	45.8124i	0.275308	+	1.50957i
$922$		0			0
$923$	−3.61272	+	3.61272i	−0.118914	+	0.118914i
$924$		0			0
$925$	−18.6877	−	18.6877i	−0.614449	−	0.614449i
$926$		0			0
$927$	−18.2366	−	48.3347i	−0.598970	−	1.58752i
$928$		0			0
$929$		−	20.4674i		−	0.671513i	−0.941949	−	0.335756i	$-0.891008\pi$
$929$		−	20.4674i		−	0.671513i	0.941949	−	0.335756i	$-0.108992\pi$
$930$		0			0
$931$	2.44019	−	2.44019i	0.0799740	−	0.0799740i
$932$		0			0
$933$	40.9768	+	28.3359i	1.34152	+	0.927674i
$934$		0			0
$935$			12.7469i			0.416868i
$936$		0			0
$937$		−	15.4186i		−	0.503704i	−0.967766	−	0.251852i	$-0.918960\pi$
$937$		−	15.4186i		−	0.503704i	0.967766	−	0.251852i	$-0.0810396\pi$
$938$		0			0
$939$	28.5357	+	19.7327i	0.931227	+	0.643954i
$940$		0			0
$941$	−21.0694	+	21.0694i	−0.686844	+	0.686844i	−0.961533	−	0.274689i	$-0.911425\pi$
$941$	−21.0694	+	21.0694i	−0.686844	+	0.686844i	0.274689	+	0.961533i	$0.411425\pi$
$942$		0			0
$943$			36.6231i			1.19261i
$944$		0			0
$945$	2.90181	+	4.82805i	0.0943960	+	0.157057i
$946$		0			0
$947$	2.08628	+	2.08628i	0.0677949	+	0.0677949i	0.740191	−	0.672396i	$-0.234735\pi$
$947$	2.08628	+	2.08628i	0.0677949	+	0.0677949i	−0.672396	+	0.740191i	$0.734735\pi$
$948$		0			0
$949$	−1.78399	+	1.78399i	−0.0579108	+	0.0579108i
$950$		0			0
$951$	−9.90096	−	54.2890i	−0.321061	−	1.76044i
$952$		0			0
$953$	9.74445			0.315654			0.157827	−	0.987467i	$-0.449551\pi$
$953$	9.74445			0.315654			0.157827	+	0.987467i	$0.449551\pi$
$954$		0			0
$955$	17.5746	+	17.5746i	0.568700	+	0.568700i
$956$		0			0
$957$	28.9963	+	20.0512i	0.937317	+	0.648165i
$958$		0			0
$959$	−13.5561			−0.437748
$960$		0			0
$961$	16.7965			0.541823
$962$		0			0
$963$	27.1755	+	12.2865i	0.875719	+	0.395928i
$964$		0			0
$965$	−2.63026	−	2.63026i	−0.0846709	−	0.0846709i
$966$		0			0
$967$	18.2255			0.586091			0.293046	−	0.956098i	$-0.405331\pi$
$967$	18.2255			0.586091			0.293046	+	0.956098i	$0.405331\pi$
$968$		0			0
$969$	−15.8041	+	2.88226i	−0.507699	+	0.0925917i
$970$		0			0
$971$	2.70601	−	2.70601i	0.0868399	−	0.0868399i	−0.662352	−	0.749192i	$-0.730442\pi$
$971$	2.70601	−	2.70601i	0.0868399	−	0.0868399i	0.749192	+	0.662352i	$0.230442\pi$
$972$		0			0
$973$	−0.262462	−	0.262462i	−0.00841415	−	0.00841415i
$974$		0			0
$975$	0.441321	+	2.41985i	0.0141336	+	0.0774973i
$976$		0			0
$977$			4.09093i			0.130880i	0.997856	+	0.0654402i	$0.0208452\pi$
$977$			4.09093i			0.130880i	−0.997856	+	0.0654402i	$0.979155\pi$
$978$		0			0
$979$	−27.8502	+	27.8502i	−0.890096	+	0.890096i
$980$		0			0
$981$	−3.24765	+	7.18319i	−0.103689	+	0.229342i
$982$		0			0
$983$			37.9997i			1.21200i	0.795464	+	0.606001i	$0.207227\pi$
$983$			37.9997i			1.21200i	−0.795464	+	0.606001i	$0.792773\pi$
$984$		0			0
$985$			13.2134i			0.421015i
$986$		0			0
$987$	−0.752860	+	1.08872i	−0.0239638	+	0.0346543i
$988$		0			0
$989$	3.04576	−	3.04576i	0.0968497	−	0.0968497i
$990$		0			0
$991$			37.3664i			1.18698i	0.804841	+	0.593491i	$0.202251\pi$
$991$			37.3664i			1.18698i	−0.804841	+	0.593491i	$0.797749\pi$
$992$		0			0
$993$	−26.4260	+	4.81944i	−0.838604	+	0.152940i
$994$		0			0
$995$	−10.3454	−	10.3454i	−0.327970	−	0.327970i
$996$		0			0
$997$	−22.5704	+	22.5704i	−0.714813	+	0.714813i	−0.967538	−	0.252725i	$-0.918673\pi$
$997$	−22.5704	+	22.5704i	−0.714813	+	0.714813i	0.252725	+	0.967538i	$0.418673\pi$
$998$		0			0
$999$	30.7736	−	18.4959i	0.973634	−	0.585185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.c.239.7		40
3.2	odd	2	inner	1344.2.s.c.239.4		40
4.3	odd	2		336.2.s.c.323.19	yes	40
12.11	even	2		336.2.s.c.323.2	yes	40
16.5	even	4		336.2.s.c.155.2	✓	40
16.11	odd	4	inner	1344.2.s.c.911.4		40
48.5	odd	4		336.2.s.c.155.19	yes	40
48.11	even	4	inner	1344.2.s.c.911.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.2	✓	40	16.5	even	4
336.2.s.c.155.19	yes	40	48.5	odd	4
336.2.s.c.323.2	yes	40	12.11	even	2
336.2.s.c.323.19	yes	40	4.3	odd	2
1344.2.s.c.239.4		40	3.2	odd	2	inner
1344.2.s.c.239.7		40	1.1	even	1	trivial
1344.2.s.c.911.4		40	16.11	odd	4	inner
1344.2.s.c.911.7		40	48.11	even	4	inner

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.985133 + 1.42461i) q^{3} +(0.766553 + 0.766553i) q^{5} +1.00000 q^{7} +(-1.05903 - 2.80686i) q^{9} +O(q^{10})\)	\(q+(-0.985133 + 1.42461i) q^{3} +(0.766553 + 0.766553i) q^{5} +1.00000 q^{7} +(-1.05903 - 2.80686i) q^{9} +(3.09355 - 3.09355i) q^{11} +(0.262549 + 0.262549i) q^{13} +(-1.84720 + 0.336883i) q^{15} +2.68766i q^{17} +(2.44019 - 2.44019i) q^{19} +(-0.985133 + 1.42461i) q^{21} -3.24607i q^{23} -3.82479i q^{25} +(5.04196 + 1.25643i) q^{27} +(3.28972 - 3.28972i) q^{29} -3.76875i q^{31} +(1.35954 + 7.45466i) q^{33} +(0.766553 + 0.766553i) q^{35} +(4.88595 - 4.88595i) q^{37} +(-0.632675 + 0.115384i) q^{39} -11.2823 q^{41} +(0.938292 + 0.938292i) q^{43} +(1.33981 - 2.96341i) q^{45} +0.764222 q^{47} +1.00000 q^{49} +(-3.82887 - 2.64770i) q^{51} +(4.14619 + 4.14619i) q^{53} +4.74274 q^{55} +(1.07241 + 5.88023i) q^{57} +(-2.63246 + 2.63246i) q^{59} +(10.7072 + 10.7072i) q^{61} +(-1.05903 - 2.80686i) q^{63} +0.402516i q^{65} +(8.41087 - 8.41087i) q^{67} +(4.62439 + 3.19781i) q^{69} +13.7602i q^{71} +6.79488i q^{73} +(5.44884 + 3.76793i) q^{75} +(3.09355 - 3.09355i) q^{77} +3.83558i q^{79} +(-6.75693 + 5.94508i) q^{81} +(-0.107522 - 0.107522i) q^{83} +(-2.06023 + 2.06023i) q^{85} +(1.44576 + 7.92738i) q^{87} -9.00266 q^{89} +(0.262549 + 0.262549i) q^{91} +(5.36900 + 3.71272i) q^{93} +3.74107 q^{95} +18.1447 q^{97} +(-11.9593 - 5.40701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 40 * q^7	\( 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) \) 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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