LMFDB - Embedded newform 960.2.bi.g.353.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(353,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("960.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.bi (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			353.7
Character	$\chi$	$=$	960.353
Dual form			960.2.bi.g.737.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.805097 + 1.53356i) q^{3} +(-0.217242 - 2.22549i) q^{5} +(-2.05938 + 2.05938i) q^{7} +(-1.70364 - 2.46934i) q^{9} +O(q^{10})$	\(q+(-0.805097 + 1.53356i) q^{3} +(-0.217242 - 2.22549i) q^{5} +(-2.05938 + 2.05938i) q^{7} +(-1.70364 - 2.46934i) q^{9} +5.75898 q^{11} +(-1.13561 + 1.13561i) q^{13} +(3.58783 + 1.45858i) q^{15} +(0.823659 + 0.823659i) q^{17} +2.19523 q^{19} +(-1.50019 - 4.81619i) q^{21} +(-5.71272 + 5.71272i) q^{23} +(-4.90561 + 0.966941i) q^{25} +(5.15848 - 0.624586i) q^{27} +3.43487i q^{29} -1.39486 q^{31} +(-4.63654 + 8.83177i) q^{33} +(5.03051 + 4.13574i) q^{35} +(5.57088 + 5.57088i) q^{37} +(-0.827258 - 2.65582i) q^{39} +7.96847i q^{41} +(-5.27733 + 5.27733i) q^{43} +(-5.12538 + 4.32787i) q^{45} +(-0.188854 - 0.188854i) q^{47} -1.48209i q^{49} +(-1.92626 + 0.600009i) q^{51} +(-3.51562 - 3.51562i) q^{53} +(-1.25109 - 12.8166i) q^{55} +(-1.76737 + 3.36653i) q^{57} +11.1166i q^{59} -12.5366i q^{61} +(8.59374 + 1.57686i) q^{63} +(2.77400 + 2.28059i) q^{65} +(-4.60001 - 4.60001i) q^{67} +(-4.16153 - 13.3601i) q^{69} +6.37847i q^{71} +(-5.67732 - 5.67732i) q^{73} +(2.46662 - 8.30155i) q^{75} +(-11.8599 + 11.8599i) q^{77} +11.2490i q^{79} +(-3.19523 + 8.41371i) q^{81} +(6.98086 + 6.98086i) q^{83} +(1.65411 - 2.01198i) q^{85} +(-5.26759 - 2.76540i) q^{87} +8.46187 q^{89} -4.67732i q^{91} +(1.12300 - 2.13911i) q^{93} +(-0.476897 - 4.88546i) q^{95} +(-5.67732 + 5.67732i) q^{97} +(-9.81122 - 14.2209i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3}+O(q^{10}) $ 32 * q - 4 * q^3	$ 32 q - 4 q^{3} - 16 q^{19} + 24 q^{25} - 4 q^{27} + 24 q^{33} + 40 q^{43} + 32 q^{57} - 72 q^{67} - 48 q^{73} + 4 q^{75} - 16 q^{81} - 48 q^{97} + 48 q^{99}+O(q^{100}) $ 32 * q - 4 * q^3 - 16 * q^19 + 24 * q^25 - 4 * q^27 + 24 * q^33 + 40 * q^43 + 32 * q^57 - 72 * q^67 - 48 * q^73 + 4 * q^75 - 16 * q^81 - 48 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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			0
$2$		0			0
$3$	−0.805097	+	1.53356i	−0.464823	+	0.885404i
$3$	−0.805097	+	1.53356i	−0.464823	+	0.885404i
$4$		0			0
$5$	−0.217242	−	2.22549i	−0.0971537	−	0.995269i
$5$	−0.217242	−	2.22549i	−0.0971537	−	0.995269i
$6$		0			0
$7$	−2.05938	+	2.05938i	−0.778372	+	0.778372i	−0.979554	−	0.201182i	$-0.935522\pi$
$7$	−2.05938	+	2.05938i	−0.778372	+	0.778372i	0.201182	+	0.979554i	$0.435522\pi$
$8$		0			0
$9$	−1.70364	−	2.46934i	−0.567880	−	0.823112i
$10$		0			0
$11$	5.75898			1.73640			0.868199	−	0.496216i	$-0.165278\pi$
$11$	5.75898			1.73640			0.868199	+	0.496216i	$0.165278\pi$
$12$		0			0
$13$	−1.13561	+	1.13561i	−0.314963	+	0.314963i	−0.846829	−	0.531866i	$-0.821491\pi$
$13$	−1.13561	+	1.13561i	−0.314963	+	0.314963i	0.531866	+	0.846829i	$0.321491\pi$
$14$		0			0
$15$	3.58783	+	1.45858i	0.926375	+	0.376604i
$16$		0			0
$17$	0.823659	+	0.823659i	0.199767	+	0.199767i	0.799900	−	0.600133i	$-0.204886\pi$
$17$	0.823659	+	0.823659i	0.199767	+	0.199767i	−0.600133	+	0.799900i	$0.704886\pi$
$18$		0			0
$19$	2.19523			0.503621			0.251810	−	0.967777i	$-0.418974\pi$
$19$	2.19523			0.503621			0.251810	+	0.967777i	$0.418974\pi$
$20$		0			0
$21$	−1.50019	−	4.81619i	−0.327369	−	1.05098i
$22$		0			0
$23$	−5.71272	+	5.71272i	−1.19119	+	1.19119i	−0.214450	+	0.976735i	$0.568796\pi$
$23$	−5.71272	+	5.71272i	−1.19119	+	1.19119i	−0.976735	+	0.214450i	$0.931204\pi$
$24$		0			0
$25$	−4.90561	+	0.966941i	−0.981122	+	0.193388i
$26$		0			0
$27$	5.15848	−	0.624586i	0.992750	−	0.120202i
$28$		0			0
$29$			3.43487i			0.637839i	0.947782	+	0.318919i	$0.103320\pi$
$29$			3.43487i			0.637839i	−0.947782	+	0.318919i	$0.896680\pi$
$30$		0			0
$31$	−1.39486			−0.250525			−0.125262	−	0.992124i	$-0.539977\pi$
$31$	−1.39486			−0.250525			−0.125262	+	0.992124i	$0.539977\pi$
$32$		0			0
$33$	−4.63654	+	8.83177i	−0.807117	+	1.53741i
$34$		0			0
$35$	5.03051	+	4.13574i	0.850312	+	0.699068i
$36$		0			0
$37$	5.57088	+	5.57088i	0.915847	+	0.915847i	0.996724	−	0.0808768i	$-0.0257720\pi$
$37$	5.57088	+	5.57088i	0.915847	+	0.915847i	−0.0808768	+	0.996724i	$0.525772\pi$
$38$		0			0
$39$	−0.827258	−	2.65582i	−0.132467	−	0.425271i
$40$		0			0
$41$			7.96847i			1.24447i	0.782832	+	0.622233i	$0.213774\pi$
$41$			7.96847i			1.24447i	−0.782832	+	0.622233i	$0.786226\pi$
$42$		0			0
$43$	−5.27733	+	5.27733i	−0.804785	+	0.804785i	−0.983839	−	0.179054i	$-0.942696\pi$
$43$	−5.27733	+	5.27733i	−0.804785	+	0.804785i	0.179054	+	0.983839i	$0.442696\pi$
$44$		0			0
$45$	−5.12538	+	4.32787i	−0.764046	+	0.645161i
$46$		0			0
$47$	−0.188854	−	0.188854i	−0.0275472	−	0.0275472i	0.693199	−	0.720746i	$-0.256201\pi$
$47$	−0.188854	−	0.188854i	−0.0275472	−	0.0275472i	−0.720746	+	0.693199i	$0.756201\pi$
$48$		0			0
$49$		−	1.48209i		−	0.211727i
$50$		0			0
$51$	−1.92626	+	0.600009i	−0.269730	+	0.0840181i
$52$		0			0
$53$	−3.51562	−	3.51562i	−0.482908	−	0.482908i	0.423151	−	0.906059i	$-0.360924\pi$
$53$	−3.51562	−	3.51562i	−0.482908	−	0.482908i	−0.906059	+	0.423151i	$0.860924\pi$
$54$		0			0
$55$	−1.25109	−	12.8166i	−0.168698	−	1.72818i
$56$		0			0
$57$	−1.76737	+	3.36653i	−0.234094	+	0.445908i
$58$		0			0
$59$			11.1166i			1.44726i	0.690189	+	0.723629i	$0.257527\pi$
$59$			11.1166i			1.44726i	−0.690189	+	0.723629i	$0.742473\pi$
$60$		0			0
$61$		−	12.5366i		−	1.60515i	−0.596551	−	0.802575i	$-0.703463\pi$
$61$		−	12.5366i		−	1.60515i	0.596551	−	0.802575i	$-0.296537\pi$
$62$		0			0
$63$	8.59374	+	1.57686i	1.08271	+	0.198666i
$64$		0			0
$65$	2.77400	+	2.28059i	0.344073	+	0.282873i
$66$		0			0
$67$	−4.60001	−	4.60001i	−0.561981	−	0.561981i	0.367889	−	0.929870i	$-0.380081\pi$
$67$	−4.60001	−	4.60001i	−0.561981	−	0.561981i	−0.929870	+	0.367889i	$0.880081\pi$
$68$		0			0
$69$	−4.16153	−	13.3601i	−0.500990	−	1.60837i
$70$		0			0
$71$			6.37847i			0.756986i	0.925604	+	0.378493i	$0.123558\pi$
$71$			6.37847i			0.756986i	−0.925604	+	0.378493i	$0.876442\pi$
$72$		0			0
$73$	−5.67732	−	5.67732i	−0.664480	−	0.664480i	0.291953	−	0.956433i	$-0.405695\pi$
$73$	−5.67732	−	5.67732i	−0.664480	−	0.664480i	−0.956433	+	0.291953i	$0.905695\pi$
$74$		0			0
$75$	2.46662	−	8.30155i	0.284821	−	0.958581i
$76$		0			0
$77$	−11.8599	+	11.8599i	−1.35156	+	1.35156i
$78$		0			0
$79$			11.2490i			1.26561i	0.774313	+	0.632803i	$0.218096\pi$
$79$			11.2490i			1.26561i	−0.774313	+	0.632803i	$0.781904\pi$
$80$		0			0
$81$	−3.19523	+	8.41371i	−0.355026	+	0.934857i
$82$		0			0
$83$	6.98086	+	6.98086i	0.766248	+	0.766248i	0.977444	−	0.211195i	$-0.0677356\pi$
$83$	6.98086	+	6.98086i	0.766248	+	0.766248i	−0.211195	+	0.977444i	$0.567736\pi$
$84$		0			0
$85$	1.65411	−	2.01198i	0.179414	−	0.218230i
$86$		0			0
$87$	−5.26759	−	2.76540i	−0.564745	−	0.296482i
$88$		0			0
$89$	8.46187			0.896957			0.448478	−	0.893794i	$-0.351966\pi$
$89$	8.46187			0.896957			0.448478	+	0.893794i	$0.351966\pi$
$90$		0			0
$91$		−	4.67732i		−	0.490317i
$92$		0			0
$93$	1.12300	−	2.13911i	0.116450	−	0.221816i
$94$		0			0
$95$	−0.476897	−	4.88546i	−0.0489286	−	0.501238i
$96$		0			0
$97$	−5.67732	+	5.67732i	−0.576445	+	0.576445i	−0.933922	−	0.357477i	$-0.883637\pi$
$97$	−5.67732	+	5.67732i	−0.576445	+	0.576445i	0.357477	+	0.933922i	$0.383637\pi$
$98$		0			0
$99$	−9.81122	−	14.2209i	−0.986065	−	1.42925i
$100$		0			0
$101$	14.5306			1.44584			0.722922	−	0.690929i	$-0.242798\pi$
$101$	14.5306			1.44584			0.722922	+	0.690929i	$0.242798\pi$
$102$		0			0
$103$	6.69664	+	6.69664i	0.659839	+	0.659839i	0.955342	−	0.295503i	$-0.0954871\pi$
$103$	6.69664	+	6.69664i	0.659839	+	0.659839i	−0.295503	+	0.955342i	$0.595487\pi$
$104$		0			0
$105$	−10.3925	+	4.38494i	−1.01420	+	0.427926i
$106$		0			0
$107$	−1.48102	+	1.48102i	−0.143175	+	0.143175i	−0.775061	−	0.631886i	$-0.782281\pi$
$107$	−1.48102	+	1.48102i	−0.143175	+	0.143175i	0.631886	+	0.775061i	$0.282281\pi$
$108$		0			0
$109$	−16.1172			−1.54375			−0.771873	−	0.635777i	$-0.780680\pi$
$109$	−16.1172			−1.54375			−0.771873	+	0.635777i	$0.780680\pi$
$110$		0			0
$111$	−13.0284	+	4.05821i	−1.23660	+	0.385188i
$112$		0			0
$113$	9.23737	−	9.23737i	0.868979	−	0.868979i	−0.123381	−	0.992359i	$-0.539374\pi$
$113$	9.23737	−	9.23737i	0.868979	−	0.868979i	0.992359	+	0.123381i	$0.0393737\pi$
$114$		0			0
$115$	13.9547	+	11.4726i	1.30128	+	1.06982i
$116$		0			0
$117$	4.73889	+	0.869536i	0.438110	+	0.0803886i
$118$		0			0
$119$	−3.39246			−0.310986
$120$		0			0
$121$	22.1659			2.01508
$122$		0			0
$123$	−12.2202	−	6.41539i	−1.10185	−	0.578456i
$124$		0			0
$125$	3.21763	+	10.7073i	0.287793	+	0.957693i
$126$		0			0
$127$	6.38013	−	6.38013i	0.566145	−	0.566145i	−0.364901	−	0.931046i	$-0.618897\pi$
$127$	6.38013	−	6.38013i	0.566145	−	0.566145i	0.931046	+	0.364901i	$0.118897\pi$
$128$		0			0
$129$	−3.84436	−	12.3419i	−0.338477	−	1.08664i
$130$		0			0
$131$	−4.35021			−0.380080			−0.190040	−	0.981776i	$-0.560862\pi$
$131$	−4.35021			−0.380080			−0.190040	+	0.981776i	$0.560862\pi$
$132$		0			0
$133$	−4.52081	+	4.52081i	−0.392004	+	0.392004i
$134$		0			0
$135$	−2.51065	−	11.3445i	−0.216082	−	0.976375i
$136$		0			0
$137$	−5.83009	−	5.83009i	−0.498098	−	0.498098i	0.412747	−	0.910846i	$-0.364569\pi$
$137$	−5.83009	−	5.83009i	−0.498098	−	0.498098i	−0.910846	+	0.412747i	$0.864569\pi$
$138$		0			0
$139$	−5.67253			−0.481138			−0.240569	−	0.970632i	$-0.577334\pi$
$139$	−5.67253			−0.481138			−0.240569	+	0.970632i	$0.577334\pi$
$140$		0			0
$141$	0.441666	−	0.137574i	0.0371950	−	0.0115858i
$142$		0			0
$143$	−6.53998	+	6.53998i	−0.546901	+	0.546901i
$144$		0			0
$145$	7.64426	−	0.746199i	0.634822	−	0.0619684i
$146$		0			0
$147$	2.27288	+	1.19323i	0.187464	+	0.0984157i
$148$		0			0
$149$		−	7.46573i		−	0.611616i	−0.952093	−	0.305808i	$-0.901073\pi$
$149$		−	7.46573i		−	0.611616i	0.952093	−	0.305808i	$-0.0989266\pi$
$150$		0			0
$151$	−5.37746			−0.437612			−0.218806	−	0.975768i	$-0.570216\pi$
$151$	−5.37746			−0.437612			−0.218806	+	0.975768i	$0.570216\pi$
$152$		0			0
$153$	0.630673	−	3.43711i	0.0509869	−	0.277874i
$154$		0			0
$155$	0.303023	+	3.10425i	0.0243394	+	0.249340i
$156$		0			0
$157$	10.9897	+	10.9897i	0.877074	+	0.877074i	0.993231	−	0.116157i	$-0.0370576\pi$
$157$	10.9897	+	10.9897i	0.877074	+	0.877074i	−0.116157	+	0.993231i	$0.537058\pi$
$158$		0			0
$159$	8.22184	−	2.56102i	0.652035	−	0.203102i
$160$		0			0
$161$		−	23.5293i		−	1.85437i
$162$		0			0
$163$	7.53868	−	7.53868i	0.590475	−	0.590475i	−0.347285	−	0.937760i	$-0.612896\pi$
$163$	7.53868	−	7.53868i	0.590475	−	0.590475i	0.937760	+	0.347285i	$0.112896\pi$
$164$		0			0
$165$	20.6623	+	8.39993i	1.60856	+	0.653934i
$166$		0			0
$167$	1.84337	+	1.84337i	0.142644	+	0.142644i	0.774823	−	0.632178i	$-0.217839\pi$
$167$	1.84337	+	1.84337i	0.142644	+	0.142644i	−0.632178	+	0.774823i	$0.717839\pi$
$168$		0			0
$169$			10.4208i			0.801597i
$170$		0			0
$171$	−3.73988	−	5.42076i	−0.285996	−	0.414536i
$172$		0			0
$173$	13.3290	+	13.3290i	1.01338	+	1.01338i	0.999909	+	0.0134730i	$0.00428873\pi$
$173$	13.3290	+	13.3290i	1.01338	+	1.01338i	0.0134730	+	0.999909i	$0.495711\pi$
$174$		0			0
$175$	8.11122	−	12.0938i	0.613150	−	0.914207i
$176$		0			0
$177$	−17.0480	−	8.94994i	−1.28141	−	0.672719i
$178$		0			0
$179$		−	3.92128i		−	0.293090i	−0.989204	−	0.146545i	$-0.953185\pi$
$179$		−	3.92128i		−	0.293090i	0.989204	−	0.146545i	$-0.0468153\pi$
$180$		0			0
$181$		−	14.2604i		−	1.05997i	−0.848008	−	0.529983i	$-0.822198\pi$
$181$		−	14.2604i		−	1.05997i	0.848008	−	0.529983i	$-0.177802\pi$
$182$		0			0
$183$	19.2257	+	10.0932i	1.42121	+	0.746111i
$184$		0			0
$185$	11.1877	−	13.6082i	0.822537	−	1.00049i
$186$		0			0
$187$	4.74344	+	4.74344i	0.346875	+	0.346875i
$188$		0			0
$189$	−9.33701	+	11.9095i	−0.679167	+	0.866290i
$190$		0			0
$191$		−	24.2111i		−	1.75186i	−0.482443	−	0.875928i	$-0.660250\pi$
$191$		−	24.2111i		−	1.75186i	0.482443	−	0.875928i	$-0.339750\pi$
$192$		0			0
$193$	−7.19523	−	7.19523i	−0.517924	−	0.517924i	0.399019	−	0.916943i	$-0.369351\pi$
$193$	−7.19523	−	7.19523i	−0.517924	−	0.517924i	−0.916943	+	0.399019i	$0.869351\pi$
$194$		0			0
$195$	−5.73078	+	2.41801i	−0.410390	+	0.173157i
$196$		0			0
$197$	16.4341	−	16.4341i	1.17088	−	1.17088i	0.188879	−	0.982000i	$-0.439515\pi$
$197$	16.4341	−	16.4341i	1.17088	−	1.17088i	0.982000	−	0.188879i	$-0.0604854\pi$
$198$		0			0
$199$			13.0748i			0.926851i	0.886136	+	0.463425i	$0.153380\pi$
$199$			13.0748i			0.926851i	−0.886136	+	0.463425i	$0.846620\pi$
$200$		0			0
$201$	10.7579	−	3.35096i	0.758801	−	0.236358i
$202$		0			0
$203$	−7.07370	−	7.07370i	−0.496476	−	0.496476i
$204$		0			0
$205$	17.7337	−	1.73109i	1.23858	−	0.120904i
$206$		0			0
$207$	23.8390	+	4.37421i	1.65693	+	0.304029i
$208$		0			0
$209$	12.6423			0.874486
$210$		0			0
$211$		−	8.22720i		−	0.566384i	−0.959063	−	0.283192i	$-0.908607\pi$
$211$		−	8.22720i		−	0.566384i	0.959063	−	0.283192i	$-0.0913933\pi$
$212$		0			0
$213$	−9.78180	−	5.13529i	−0.670238	−	0.351864i
$214$		0			0
$215$	12.8911	+	10.5982i	0.879166	+	0.722790i
$216$		0			0
$217$	2.87255	−	2.87255i	0.195002	−	0.195002i
$218$		0			0
$219$	13.2773	−	4.13574i	0.897199	−	0.279468i
$220$		0			0
$221$	−1.87072			−0.125838
$222$		0			0
$223$	−4.03382	−	4.03382i	−0.270124	−	0.270124i	0.559026	−	0.829150i	$-0.311175\pi$
$223$	−4.03382	−	4.03382i	−0.270124	−	0.270124i	−0.829150	+	0.559026i	$0.811175\pi$
$224$		0			0
$225$	10.7451	+	10.4663i	0.716339	+	0.697752i
$226$		0			0
$227$	−3.83272	+	3.83272i	−0.254387	+	0.254387i	−0.822766	−	0.568380i	$-0.807570\pi$
$227$	−3.83272	+	3.83272i	−0.254387	+	0.254387i	0.568380	+	0.822766i	$0.307570\pi$
$228$		0			0
$229$	7.71902			0.510087			0.255044	−	0.966930i	$-0.417910\pi$
$229$	7.71902			0.510087			0.255044	+	0.966930i	$0.417910\pi$
$230$		0			0
$231$	−8.63957	−	27.7364i	−0.568442	−	1.82492i
$232$		0			0
$233$	10.5521	−	10.5521i	0.691290	−	0.691290i	−0.271226	−	0.962516i	$-0.587429\pi$
$233$	10.5521	−	10.5521i	0.691290	−	0.691290i	0.962516	+	0.271226i	$0.0874290\pi$
$234$		0			0
$235$	−0.379266	+	0.461321i	−0.0247406	+	0.0300933i
$236$		0			0
$237$	−17.2510	−	9.05649i	−1.12057	−	0.588283i
$238$		0			0
$239$	−21.1130			−1.36568			−0.682842	−	0.730566i	$-0.739256\pi$
$239$	−21.1130			−1.36568			−0.682842	+	0.730566i	$0.739256\pi$
$240$		0			0
$241$	2.93867			0.189296			0.0946482	−	0.995511i	$-0.469827\pi$
$241$	2.93867			0.189296			0.0946482	+	0.995511i	$0.469827\pi$
$242$		0			0
$243$	−10.3305	−	11.6739i	−0.662701	−	0.748884i
$244$		0			0
$245$	−3.29838	+	0.321973i	−0.210726	+	0.0205701i
$246$		0			0
$247$	−2.49294	+	2.49294i	−0.158622	+	0.158622i
$248$		0			0
$249$	−16.3259	+	5.08533i	−1.03461	+	0.322270i
$250$		0			0
$251$	1.05557			0.0666272			0.0333136	−	0.999445i	$-0.489394\pi$
$251$	1.05557			0.0666272			0.0333136	+	0.999445i	$0.489394\pi$
$252$		0			0
$253$	−32.8995	+	32.8995i	−2.06837	+	2.06837i
$254$		0			0
$255$	1.75378	+	4.15653i	0.109826	+	0.260292i
$256$		0			0
$257$	13.1381	+	13.1381i	0.819529	+	0.819529i	0.986040	−	0.166510i	$-0.0532500\pi$
$257$	13.1381	+	13.1381i	0.819529	+	0.819529i	−0.166510	+	0.986040i	$0.553250\pi$
$258$		0			0
$259$	−22.9451			−1.42574
$260$		0			0
$261$	8.48184	−	5.85177i	0.525013	−	0.362216i
$262$		0			0
$263$	8.86025	−	8.86025i	0.546346	−	0.546346i	−0.379036	−	0.925382i	$-0.623744\pi$
$263$	8.86025	−	8.86025i	0.546346	−	0.546346i	0.925382	+	0.379036i	$0.123744\pi$
$264$		0			0
$265$	−7.06024	+	8.58772i	−0.433707	+	0.527539i
$266$		0			0
$267$	−6.81263	+	12.9768i	−0.416926	+	0.794169i
$268$		0			0
$269$			14.2219i			0.867125i	0.901123	+	0.433563i	$0.142744\pi$
$269$			14.2219i			0.867125i	−0.901123	+	0.433563i	$0.857256\pi$
$270$		0			0
$271$	−23.7948			−1.44543			−0.722717	−	0.691144i	$-0.757107\pi$
$271$	−23.7948			−1.44543			−0.722717	+	0.691144i	$0.757107\pi$
$272$		0			0
$273$	7.17297	+	3.76570i	0.434128	+	0.227910i
$274$		0			0
$275$	−28.2513	+	5.56860i	−1.70362	+	0.335799i
$276$		0			0
$277$	0.999454	+	0.999454i	0.0600514	+	0.0600514i	0.736495	−	0.676443i	$-0.236480\pi$
$277$	0.999454	+	0.999454i	0.0600514	+	0.0600514i	−0.676443	+	0.736495i	$0.736480\pi$
$278$		0			0
$279$	2.37634	+	3.44438i	0.142268	+	0.206210i
$280$		0			0
$281$			0.773144i			0.0461219i	0.999734	+	0.0230610i	$0.00734118\pi$
$281$			0.773144i			0.0461219i	−0.999734	+	0.0230610i	$0.992659\pi$
$282$		0			0
$283$	−3.47256	+	3.47256i	−0.206422	+	0.206422i	−0.802745	−	0.596323i	$-0.796628\pi$
$283$	−3.47256	+	3.47256i	−0.206422	+	0.206422i	0.596323	+	0.802745i	$0.296628\pi$
$284$		0			0
$285$	7.87612	+	3.20192i	0.466541	+	0.189665i
$286$		0			0
$287$	−16.4101	−	16.4101i	−0.968657	−	0.968657i
$288$		0			0
$289$		−	15.6432i		−	0.920186i
$290$		0			0
$291$	−4.13574	−	13.2773i	−0.242442	−	0.778331i
$292$		0			0
$293$	1.13928	+	1.13928i	0.0665573	+	0.0665573i	0.739602	−	0.673045i	$-0.235014\pi$
$293$	1.13928	+	1.13928i	0.0665573	+	0.0665573i	−0.673045	+	0.739602i	$0.735014\pi$
$294$		0			0
$295$	24.7399	−	2.41500i	1.44041	−	0.140607i
$296$		0			0
$297$	29.7076	−	3.59698i	1.72381	−	0.208718i
$298$		0			0
$299$		−	12.9749i		−	0.750358i
$300$		0			0
$301$		−	21.7361i		−	1.25285i
$302$		0			0
$303$	−11.6985	+	22.2835i	−0.672062	+	1.28016i
$304$		0			0
$305$	−27.9001	+	2.72349i	−1.59756	+	0.155946i
$306$		0			0
$307$	−5.66134	−	5.66134i	−0.323110	−	0.323110i	0.526849	−	0.849959i	$-0.323373\pi$
$307$	−5.66134	−	5.66134i	−0.323110	−	0.323110i	−0.849959	+	0.526849i	$0.823373\pi$
$308$		0			0
$309$	−15.6612	+	4.87828i	−0.890933	+	0.277516i
$310$		0			0
$311$			4.34625i			0.246453i	0.992379	+	0.123227i	$0.0393242\pi$
$311$			4.34625i			0.246453i	−0.992379	+	0.123227i	$0.960676\pi$
$312$		0			0
$313$	−9.48209	−	9.48209i	−0.535959	−	0.535959i	0.386380	−	0.922340i	$-0.373725\pi$
$313$	−9.48209	−	9.48209i	−0.535959	−	0.535959i	−0.922340	+	0.386380i	$0.873725\pi$
$314$		0			0
$315$	1.64236	−	19.4678i	0.0925366	−	1.09689i
$316$		0			0
$317$	1.80433	−	1.80433i	0.101341	−	0.101341i	−0.654618	−	0.755960i	$-0.727171\pi$
$317$	1.80433	−	1.80433i	0.101341	−	0.101341i	0.755960	+	0.654618i	$0.227171\pi$
$318$		0			0
$319$			19.7813i			1.10754i
$320$		0			0
$321$	−1.07887	−	3.46360i	−0.0602168	−	0.193319i
$322$		0			0
$323$	1.80812	+	1.80812i	0.100607	+	0.100607i
$324$		0			0
$325$	4.47281	−	6.66895i	0.248107	−	0.369927i
$326$		0			0
$327$	12.9759	−	24.7167i	0.717568	−	1.36684i
$328$		0			0
$329$	0.777846			0.0428840
$330$		0			0
$331$		−	30.1045i		−	1.65469i	−0.561690	−	0.827347i	$-0.689849\pi$
$331$		−	30.1045i		−	1.65469i	0.561690	−	0.827347i	$-0.310151\pi$
$332$		0			0
$333$	4.26560	−	23.2471i	0.233754	−	1.27394i
$334$		0			0
$335$	−9.23796	+	11.2366i	−0.504724	+	0.613921i
$336$		0			0
$337$	−12.3546	+	12.3546i	−0.673000	+	0.673000i	−0.958407	−	0.285406i	$-0.907871\pi$
$337$	−12.3546	+	12.3546i	−0.673000	+	0.673000i	0.285406	+	0.958407i	$0.407871\pi$
$338$		0			0
$339$	6.72912	+	21.6031i	0.365476	+	1.17332i
$340$		0			0
$341$	−8.03299			−0.435011
$342$		0			0
$343$	−11.3635	−	11.3635i	−0.613570	−	0.613570i
$344$		0			0
$345$	−28.8288	+	12.1638i	−1.55209	+	0.654879i
$346$		0			0
$347$	−13.0429	+	13.0429i	−0.700177	+	0.700177i	−0.964448	−	0.264271i	$-0.914869\pi$
$347$	−13.0429	+	13.0429i	−0.700177	+	0.700177i	0.264271	+	0.964448i	$0.414869\pi$
$348$		0			0
$349$	19.8227			1.06108			0.530542	−	0.847658i	$-0.321988\pi$
$349$	19.8227			1.06108			0.530542	+	0.847658i	$0.321988\pi$
$350$		0			0
$351$	−5.14875	+	6.56733i	−0.274820	+	0.350538i
$352$		0			0
$353$	−5.83009	+	5.83009i	−0.310304	+	0.310304i	−0.845027	−	0.534723i	$-0.820416\pi$
$353$	−5.83009	+	5.83009i	−0.310304	+	0.310304i	0.534723	+	0.845027i	$0.320416\pi$
$354$		0			0
$355$	14.1952	−	1.38567i	0.753405	−	0.0735440i
$356$		0			0
$357$	2.73125	−	5.20255i	0.144553	−	0.275348i
$358$		0			0
$359$	16.0660			0.847930			0.423965	−	0.905679i	$-0.360638\pi$
$359$	16.0660			0.847930			0.423965	+	0.905679i	$0.360638\pi$
$360$		0			0
$361$	−14.1810			−0.746366
$362$		0			0
$363$	−17.8457	+	33.9928i	−0.936655	+	1.78416i
$364$		0			0
$365$	−11.4015	+	13.8682i	−0.596780	+	0.725894i
$366$		0			0
$367$	−1.42636	+	1.42636i	−0.0744556	+	0.0744556i	−0.743354	−	0.668898i	$-0.766766\pi$
$367$	−1.42636	+	1.42636i	−0.0744556	+	0.0744556i	0.668898	+	0.743354i	$0.266766\pi$
$368$		0			0
$369$	19.6768	−	13.5754i	1.02433	−	0.706706i
$370$		0			0
$371$	14.4800			0.751764
$372$		0			0
$373$	−14.7703	+	14.7703i	−0.764778	+	0.764778i	−0.977182	−	0.212404i	$-0.931871\pi$
$373$	−14.7703	+	14.7703i	−0.764778	+	0.764778i	0.212404	+	0.977182i	$0.431871\pi$
$374$		0			0
$375$	−19.0109	−	3.68600i	−0.981717	−	0.190344i
$376$		0			0
$377$	−3.90068	−	3.90068i	−0.200895	−	0.200895i
$378$		0			0
$379$	7.94034			0.407868			0.203934	−	0.978985i	$-0.434627\pi$
$379$	7.94034			0.407868			0.203934	+	0.978985i	$0.434627\pi$
$380$		0			0
$381$	4.64772	+	14.9210i	0.238110	+	0.764424i
$382$		0			0
$383$	24.2385	−	24.2385i	1.23853	−	1.23853i	0.277925	−	0.960603i	$-0.410353\pi$
$383$	24.2385	−	24.2385i	1.23853	−	1.23853i	0.960603	−	0.277925i	$-0.0896467\pi$
$384$		0			0
$385$	28.9706	+	23.8177i	1.47648	+	1.21386i
$386$		0			0
$387$	22.0222	+	4.04083i	1.11945	+	0.205407i
$388$		0			0
$389$		−	17.5309i		−	0.888854i	−0.895815	−	0.444427i	$-0.853407\pi$
$389$		−	17.5309i		−	0.888854i	0.895815	−	0.444427i	$-0.146593\pi$
$390$		0			0
$391$	−9.41068			−0.475918
$392$		0			0
$393$	3.50234	−	6.67133i	0.176670	−	0.336524i
$394$		0			0
$395$	25.0344	−	2.44375i	1.25962	−	0.122958i
$396$		0			0
$397$	−1.56857	−	1.56857i	−0.0787240	−	0.0787240i	0.666648	−	0.745372i	$-0.267728\pi$
$397$	−1.56857	−	1.56857i	−0.0787240	−	0.0787240i	−0.745372	+	0.666648i	$0.767728\pi$
$398$		0			0
$399$	−3.29327	−	10.5727i	−0.164870	−	0.529295i
$400$		0			0
$401$			34.1319i			1.70447i	0.523161	+	0.852234i	$0.324753\pi$
$401$			34.1319i			1.70447i	−0.523161	+	0.852234i	$0.675247\pi$
$402$		0			0
$403$	1.58403	−	1.58403i	0.0789060	−	0.0789060i
$404$		0			0
$405$	19.4188	+	5.28314i	0.964926	+	0.262521i
$406$		0			0
$407$	32.0826	+	32.0826i	1.59028	+	1.59028i
$408$		0			0
$409$			13.8272i			0.683709i	0.939753	+	0.341855i	$0.111055\pi$
$409$			13.8272i			0.683709i	−0.939753	+	0.341855i	$0.888945\pi$
$410$		0			0
$411$	13.6346	−	4.24703i	0.672546	−	0.209491i
$412$		0			0
$413$	−22.8933	−	22.8933i	−1.12651	−	1.12651i
$414$		0			0
$415$	14.0193	−	17.0524i	0.688180	−	0.837068i
$416$		0			0
$417$	4.56694	−	8.69920i	0.223644	−	0.426001i
$418$		0			0
$419$			4.20572i			0.205463i	0.994709	+	0.102731i	$0.0327582\pi$
$419$			4.20572i			0.205463i	−0.994709	+	0.102731i	$0.967242\pi$
$420$		0			0
$421$			17.3514i			0.845656i	0.906210	+	0.422828i	$0.138963\pi$
$421$			17.3514i			0.845656i	−0.906210	+	0.422828i	$0.861037\pi$
$422$		0			0
$423$	−0.144605	+	0.788085i	−0.00703094	+	0.0383180i
$424$		0			0
$425$	−4.83698	−	3.24412i	−0.234628	−	0.157363i
$426$		0			0
$427$	25.8177	+	25.8177i	1.24940	+	1.24940i
$428$		0			0
$429$	−4.76416	−	15.2948i	−0.230016	−	0.738440i
$430$		0			0
$431$			18.4087i			0.886717i	0.896344	+	0.443359i	$0.146213\pi$
$431$			18.4087i			0.886717i	−0.896344	+	0.443359i	$0.853787\pi$
$432$		0			0
$433$	8.06778	+	8.06778i	0.387713	+	0.387713i	0.873871	−	0.486158i	$-0.161602\pi$
$433$	8.06778	+	8.06778i	0.387713	+	0.387713i	−0.486158	+	0.873871i	$0.661602\pi$
$434$		0			0
$435$	−5.01003	+	12.3237i	−0.240212	+	0.590878i
$436$		0			0
$437$	−12.5407	+	12.5407i	−0.599905	+	0.599905i
$438$		0			0
$439$			18.7370i			0.894269i	0.894467	+	0.447134i	$0.147555\pi$
$439$			18.7370i			0.894269i	−0.894467	+	0.447134i	$0.852445\pi$
$440$		0			0
$441$	−3.65978	+	2.52495i	−0.174275	+	0.120236i
$442$		0			0
$443$	6.74659	+	6.74659i	0.320540	+	0.320540i	0.848974	−	0.528434i	$-0.177221\pi$
$443$	6.74659	+	6.74659i	0.320540	+	0.320540i	−0.528434	+	0.848974i	$0.677221\pi$
$444$		0			0
$445$	−1.83828	−	18.8318i	−0.0871427	−	0.892714i
$446$		0			0
$447$	11.4492	+	6.01063i	0.541527	+	0.284293i
$448$		0			0
$449$	−18.3076			−0.863991			−0.431995	−	0.901876i	$-0.642190\pi$
$449$	−18.3076			−0.863991			−0.431995	+	0.901876i	$0.642190\pi$
$450$		0			0
$451$			45.8902i			2.16089i
$452$		0			0
$453$	4.32938	−	8.24668i	0.203412	−	0.387463i
$454$		0			0
$455$	−10.4093	+	1.01611i	−0.487997	+	0.0476361i
$456$		0			0
$457$	10.9029	−	10.9029i	0.510014	−	0.510014i	−0.404517	−	0.914531i	$-0.632560\pi$
$457$	10.9029	−	10.9029i	0.510014	−	0.510014i	0.914531	+	0.404517i	$0.132560\pi$
$458$		0			0
$459$	4.76327	+	3.73438i	0.222331	+	0.174306i
$460$		0			0
$461$	0.581628			0.0270891			0.0135446	−	0.999908i	$-0.495689\pi$
$461$	0.581628			0.0270891			0.0135446	+	0.999908i	$0.495689\pi$
$462$		0			0
$463$	−8.74423	−	8.74423i	−0.406379	−	0.406379i	0.474095	−	0.880474i	$-0.342775\pi$
$463$	−8.74423	−	8.74423i	−0.406379	−	0.406379i	−0.880474	+	0.474095i	$0.842775\pi$
$464$		0			0
$465$	−5.00454	−	2.03452i	−0.232080	−	0.0943485i
$466$		0			0
$467$	30.0649	−	30.0649i	1.39124	−	1.39124i	0.568683	−	0.822557i	$-0.307453\pi$
$467$	30.0649	−	30.0649i	1.39124	−	1.39124i	0.822557	−	0.568683i	$-0.192547\pi$
$468$		0			0
$469$	18.9463			0.874860
$470$		0			0
$471$	−25.7012	+	8.00564i	−1.18425	+	0.368881i
$472$		0			0
$473$	−30.3921	+	30.3921i	−1.39743	+	1.39743i
$474$		0			0
$475$	−10.7690	+	2.12266i	−0.494113	+	0.0973943i
$476$		0			0
$477$	−2.69190	+	14.6706i	−0.123254	+	0.671720i
$478$		0			0
$479$	−6.00077			−0.274182			−0.137091	−	0.990558i	$-0.543775\pi$
$479$	−6.00077			−0.274182			−0.137091	+	0.990558i	$0.543775\pi$
$480$		0			0
$481$	−12.6527			−0.576916
$482$		0			0
$483$	36.0837	+	18.9434i	1.64187	+	0.861954i
$484$		0			0
$485$	13.8682	+	11.4015i	0.629722	+	0.517714i
$486$		0			0
$487$	0.644799	−	0.644799i	0.0292187	−	0.0292187i	−0.692347	−	0.721565i	$-0.743423\pi$
$487$	0.644799	−	0.644799i	0.0292187	−	0.0292187i	0.721565	+	0.692347i	$0.243423\pi$
$488$		0			0
$489$	5.49168	+	17.6304i	0.248342	+	0.797275i
$490$		0			0
$491$	−3.83193			−0.172932			−0.0864662	−	0.996255i	$-0.527557\pi$
$491$	−3.83193			−0.172932			−0.0864662	+	0.996255i	$0.527557\pi$
$492$		0			0
$493$	−2.82916	+	2.82916i	−0.127419	+	0.127419i
$494$		0			0
$495$	−29.5170	+	24.9242i	−1.32669	+	1.12026i
$496$		0			0
$497$	−13.1357	−	13.1357i	−0.589217	−	0.589217i
$498$		0			0
$499$	−31.3046			−1.40138			−0.700692	−	0.713464i	$-0.747125\pi$
$499$	−31.3046			−1.40138			−0.700692	+	0.713464i	$0.747125\pi$
$500$		0			0
$501$	−4.31102	+	1.34284i	−0.192602	+	0.0599935i
$502$		0			0
$503$	−24.4000	+	24.4000i	−1.08794	+	1.08794i	−0.0922007	+	0.995740i	$0.529390\pi$
$503$	−24.4000	+	24.4000i	−1.08794	+	1.08794i	−0.995740	+	0.0922007i	$0.970610\pi$
$504$		0			0
$505$	−3.15665	−	32.3376i	−0.140469	−	1.43900i
$506$		0			0
$507$	−15.9809	−	8.38972i	−0.709737	−	0.372601i
$508$		0			0
$509$		−	16.9760i		−	0.752446i	−0.926529	−	0.376223i	$-0.877223\pi$
$509$		−	16.9760i		−	0.752446i	0.926529	−	0.376223i	$-0.122777\pi$
$510$		0			0
$511$	23.3835			1.03443
$512$		0			0
$513$	11.3241	−	1.37111i	0.499969	−	0.0605360i
$514$		0			0
$515$	13.4485	−	16.3581i	0.592612	−	0.720824i
$516$		0			0
$517$	−1.08761	−	1.08761i	−0.0478330	−	0.0478330i
$518$		0			0
$519$	−31.1719	+	9.70972i	−1.36830	+	0.426209i
$520$		0			0
$521$		−	0.702375i		−	0.0307716i	−0.999882	−	0.0153858i	$-0.995102\pi$
$521$		−	0.702375i		−	0.0307716i	0.999882	−	0.0153858i	$-0.00489765\pi$
$522$		0			0
$523$	16.2470	−	16.2470i	0.710433	−	0.710433i	−0.256193	−	0.966626i	$-0.582468\pi$
$523$	16.2470	−	16.2470i	0.710433	−	0.710433i	0.966626	+	0.256193i	$0.0824681\pi$
$524$		0			0
$525$	12.0163	+	22.1758i	0.524436	+	0.967830i
$526$		0			0
$527$	−1.14889	−	1.14889i	−0.0500465	−	0.0500465i
$528$		0			0
$529$		−	42.2704i		−	1.83784i
$530$		0			0
$531$	27.4506	−	18.9387i	1.19126	−	0.821868i
$532$		0			0
$533$	−9.04910	−	9.04910i	−0.391960	−	0.391960i
$534$		0			0
$535$	3.61773	+	2.97425i	0.156408	+	0.128588i
$536$		0			0
$537$	6.01353	+	3.15701i	0.259503	+	0.136235i
$538$		0			0
$539$		−	8.53533i		−	0.367643i
$540$		0			0
$541$		−	26.4653i		−	1.13783i	−0.822396	−	0.568916i	$-0.807363\pi$
$541$		−	26.4653i		−	1.13783i	0.822396	−	0.568916i	$-0.192637\pi$
$542$		0			0
$543$	21.8692	+	11.4810i	0.938498	+	0.492696i
$544$		0			0
$545$	3.50133	+	35.8686i	0.149981	+	1.53644i
$546$		0			0
$547$	−9.88208	−	9.88208i	−0.422527	−	0.422527i	0.463546	−	0.886073i	$-0.346577\pi$
$547$	−9.88208	−	9.88208i	−0.422527	−	0.422527i	−0.886073	+	0.463546i	$0.846577\pi$
$548$		0			0
$549$	−30.9571	+	21.3579i	−1.32122	+	0.911532i
$550$		0			0
$551$			7.54033i			0.321229i
$552$		0			0
$553$	−23.1659	−	23.1659i	−0.985113	−	0.985113i
$554$		0			0
$555$	11.8618	+	28.1130i	0.503506	+	1.19333i
$556$		0			0
$557$	22.9741	−	22.9741i	0.973442	−	0.973442i	−0.0262143	−	0.999656i	$-0.508345\pi$
$557$	22.9741	−	22.9741i	0.973442	−	0.973442i	0.999656	+	0.0262143i	$0.00834523\pi$
$558$		0			0
$559$		−	11.9860i		−	0.506955i
$560$		0			0
$561$	−11.0933	+	3.45544i	−0.468359	+	0.145889i
$562$		0			0
$563$	−1.27004	−	1.27004i	−0.0535258	−	0.0535258i	0.679837	−	0.733363i	$-0.262050\pi$
$563$	−1.27004	−	1.27004i	−0.0535258	−	0.0535258i	−0.733363	+	0.679837i	$0.762050\pi$
$564$		0			0
$565$	−22.5644	−	18.5509i	−0.949292	−	0.780443i
$566$		0			0
$567$	−10.7468	−	23.9072i	−0.451324	−	1.00401i
$568$		0			0
$569$	−39.0855			−1.63855			−0.819275	−	0.573401i	$-0.805624\pi$
$569$	−39.0855			−1.63855			−0.819275	+	0.573401i	$0.805624\pi$
$570$		0			0
$571$			25.4496i			1.06503i	0.846420	+	0.532516i	$0.178754\pi$
$571$			25.4496i			1.06503i	−0.846420	+	0.532516i	$0.821246\pi$
$572$		0			0
$573$	37.1293	+	19.4923i	1.55110	+	0.814302i
$574$		0			0
$575$	22.5005	−	33.5483i	0.938337	−	1.39906i
$576$		0			0
$577$	−25.1611	+	25.1611i	−1.04747	+	1.04747i	−0.0486537	+	0.998816i	$0.515493\pi$
$577$	−25.1611	+	25.1611i	−1.04747	+	1.04747i	−0.998816	+	0.0486537i	$0.984507\pi$
$578$		0			0
$579$	16.8272	−	5.24149i	0.699315	−	0.217829i
$580$		0			0
$581$	−28.7525			−1.19285
$582$		0			0
$583$	−20.2464	−	20.2464i	−0.838520	−	0.838520i
$584$		0			0
$585$	0.905656	−	10.7352i	0.0374443	−	0.443848i
$586$		0			0
$587$	3.62174	−	3.62174i	0.149485	−	0.149485i	−0.628403	−	0.777888i	$-0.716291\pi$
$587$	3.62174	−	3.62174i	0.149485	−	0.149485i	0.777888	+	0.628403i	$0.216291\pi$
$588$		0			0
$589$	−3.06205			−0.126169
$590$		0			0
$591$	11.9717	+	38.4337i	0.492450	+	1.58095i
$592$		0			0
$593$	−12.2639	+	12.2639i	−0.503617	+	0.503617i	−0.912560	−	0.408943i	$-0.865898\pi$
$593$	−12.2639	+	12.2639i	−0.503617	+	0.503617i	0.408943	+	0.912560i	$0.365898\pi$
$594$		0			0
$595$	0.736985	+	7.54987i	0.0302134	+	0.309515i
$596$		0			0
$597$	−20.0511	−	10.5265i	−0.820637	−	0.430821i
$598$		0			0
$599$	−2.03222			−0.0830345			−0.0415172	−	0.999138i	$-0.513219\pi$
$599$	−2.03222			−0.0830345			−0.0415172	+	0.999138i	$0.513219\pi$
$600$		0			0
$601$	42.3723			1.72840			0.864202	−	0.503145i	$-0.167824\pi$
$601$	42.3723			1.72840			0.864202	+	0.503145i	$0.167824\pi$
$602$		0			0
$603$	−3.52221	+	19.1957i	−0.143436	+	0.781710i
$604$		0			0
$605$	−4.81537	−	49.3299i	−0.195772	−	2.00555i
$606$		0			0
$607$	−24.3337	+	24.3337i	−0.987673	+	0.987673i	−0.999925	−	0.0122524i	$-0.996100\pi$
$607$	−24.3337	+	24.3337i	−0.987673	+	0.987673i	0.0122524	+	0.999925i	$0.496100\pi$
$608$		0			0
$609$	16.5430	−	5.15296i	0.670355	−	0.208808i
$610$		0			0
$611$	0.428932			0.0173527
$612$		0			0
$613$	8.13890	−	8.13890i	0.328727	−	0.328727i	−0.523375	−	0.852102i	$-0.675327\pi$
$613$	8.13890	−	8.13890i	0.328727	−	0.328727i	0.852102	+	0.523375i	$0.175327\pi$
$614$		0			0
$615$	−11.6226	+	28.5895i	−0.468670	+	1.15284i
$616$		0			0
$617$	27.3795	+	27.3795i	1.10226	+	1.10226i	0.994138	+	0.108119i	$0.0344829\pi$
$617$	27.3795	+	27.3795i	1.10226	+	1.10226i	0.108119	+	0.994138i	$0.465517\pi$
$618$		0			0
$619$	−24.0726			−0.967558			−0.483779	−	0.875190i	$-0.660736\pi$
$619$	−24.0726			−0.967558			−0.483779	+	0.875190i	$0.660736\pi$
$620$		0			0
$621$	−25.9009	+	33.0370i	−1.03937	+	1.32573i
$622$		0			0
$623$	−17.4262	+	17.4262i	−0.698166	+	0.698166i
$624$		0			0
$625$	23.1300	−	9.48688i	0.925202	−	0.379475i
$626$		0			0
$627$	−10.1783	+	19.3878i	−0.406481	+	0.774273i
$628$		0			0
$629$			9.17702i			0.365912i
$630$		0			0
$631$	12.1892			0.485245			0.242623	−	0.970121i	$-0.421992\pi$
$631$	12.1892			0.485245			0.242623	+	0.970121i	$0.421992\pi$
$632$		0			0
$633$	12.6169	+	6.62369i	0.501478	+	0.263268i
$634$		0			0
$635$	−15.5849	−	12.8129i	−0.618470	−	0.508464i
$636$		0			0
$637$	1.68308	+	1.68308i	0.0666862	+	0.0666862i
$638$		0			0
$639$	15.7506	−	10.8666i	0.623084	−	0.429877i
$640$		0			0
$641$		−	3.78334i		−	0.149433i	−0.997205	−	0.0747165i	$-0.976195\pi$
$641$		−	3.78334i		−	0.149433i	0.997205	−	0.0747165i	$-0.0238052\pi$
$642$		0			0
$643$	8.68852	−	8.68852i	0.342642	−	0.342642i	−0.514718	−	0.857360i	$-0.672103\pi$
$643$	8.68852	−	8.68852i	0.342642	−	0.342642i	0.857360	+	0.514718i	$0.172103\pi$
$644$		0			0
$645$	−26.6316	+	11.2368i	−1.04862	+	0.442448i
$646$		0			0
$647$	2.15876	+	2.15876i	0.0848697	+	0.0848697i	0.748267	−	0.663398i	$-0.230886\pi$
$647$	2.15876	+	2.15876i	0.0848697	+	0.0848697i	−0.663398	+	0.748267i	$0.730886\pi$
$648$		0			0
$649$			64.0203i			2.51302i
$650$		0			0
$651$	2.09256	+	6.71793i	0.0820140	+	0.263296i
$652$		0			0
$653$	−8.68843	−	8.68843i	−0.340004	−	0.340004i	0.516364	−	0.856369i	$-0.327285\pi$
$653$	−8.68843	−	8.68843i	−0.340004	−	0.340004i	−0.856369	+	0.516364i	$0.827285\pi$
$654$		0			0
$655$	0.945050	+	9.68135i	0.0369262	+	0.378282i
$656$		0			0
$657$	−4.34711	+	23.6913i	−0.169597	+	0.924286i
$658$		0			0
$659$		−	21.5102i		−	0.837920i	−0.908005	−	0.418960i	$-0.862395\pi$
$659$		−	21.5102i		−	0.837920i	0.908005	−	0.418960i	$-0.137605\pi$
$660$		0			0
$661$		−	5.64786i		−	0.219676i	−0.993949	−	0.109838i	$-0.964967\pi$
$661$		−	5.64786i		−	0.219676i	0.993949	−	0.109838i	$-0.0350332\pi$
$662$		0			0
$663$	1.50611	−	2.86887i	0.0584924	−	0.111418i
$664$		0			0
$665$	11.0431	+	9.07892i	0.428235	+	0.352065i
$666$		0			0
$667$	−19.6224	−	19.6224i	−0.759784	−	0.759784i
$668$		0			0
$669$	9.43373	−	2.93851i	0.364729	−	0.113609i
$670$		0			0
$671$		−	72.1982i		−	2.78718i
$672$		0			0
$673$	−10.7793	−	10.7793i	−0.415510	−	0.415510i	0.468143	−	0.883653i	$-0.344923\pi$
$673$	−10.7793	−	10.7793i	−0.415510	−	0.415510i	−0.883653	+	0.468143i	$0.844923\pi$
$674$		0			0
$675$	−24.7015	+	8.05192i	−0.950763	+	0.309919i
$676$		0			0
$677$	−31.8336	+	31.8336i	−1.22346	+	1.22346i	−0.257073	+	0.966392i	$0.582758\pi$
$677$	−31.8336	+	31.8336i	−1.22346	+	1.22346i	−0.966392	+	0.257073i	$0.917242\pi$
$678$		0			0
$679$		−	23.3835i		−	0.897377i
$680$		0			0
$681$	−2.79201	−	8.96344i	−0.106990	−	0.343480i
$682$		0			0
$683$	−21.6675	−	21.6675i	−0.829086	−	0.829086i	0.158305	−	0.987390i	$-0.449397\pi$
$683$	−21.6675	−	21.6675i	−0.829086	−	0.829086i	−0.987390	+	0.158305i	$0.949397\pi$
$684$		0			0
$685$	−11.7083	+	14.2414i	−0.447350	+	0.544134i
$686$		0			0
$687$	−6.21456	+	11.8376i	−0.237100	+	0.451633i
$688$		0			0
$689$	7.98478			0.304196
$690$		0			0
$691$			6.09163i			0.231736i	0.993265	+	0.115868i	$0.0369650\pi$
$691$			6.09163i			0.231736i	−0.993265	+	0.115868i	$0.963035\pi$
$692$		0			0
$693$	49.4912	+	9.08111i	1.88001	+	0.344963i
$694$		0			0
$695$	1.23231	+	12.6242i	0.0467444	+	0.478862i
$696$		0			0
$697$	−6.56330	+	6.56330i	−0.248603	+	0.248603i
$698$		0			0
$699$	7.68685	+	24.6777i	0.290743	+	0.933398i
$700$		0			0
$701$	11.8298			0.446805			0.223403	−	0.974726i	$-0.428284\pi$
$701$	11.8298			0.446805			0.223403	+	0.974726i	$0.428284\pi$
$702$		0			0
$703$	12.2294	+	12.2294i	0.461240	+	0.461240i
$704$		0			0
$705$	−0.402119	−	0.953037i	−0.0151447	−	0.0358935i
$706$		0			0
$707$	−29.9239	+	29.9239i	−1.12541	+	1.12541i
$708$		0			0
$709$	11.1233			0.417743			0.208871	−	0.977943i	$-0.433021\pi$
$709$	11.1233			0.417743			0.208871	+	0.977943i	$0.433021\pi$
$710$		0			0
$711$	27.7774	−	19.1642i	1.04174	−	0.718712i
$712$		0			0
$713$	7.96847	−	7.96847i	0.298421	−	0.298421i
$714$		0			0
$715$	15.9754	+	13.1339i	0.597447	+	0.491180i
$716$		0			0
$717$	16.9980	−	32.3781i	0.634801	−	1.20918i
$718$		0			0
$719$	39.6051			1.47702			0.738511	−	0.674242i	$-0.235529\pi$
$719$	39.6051			1.47702			0.738511	+	0.674242i	$0.235529\pi$
$720$		0			0
$721$	−27.5818			−1.02720
$722$		0			0
$723$	−2.36591	+	4.50664i	−0.0879893	+	0.167604i
$724$		0			0
$725$	−3.32132	−	16.8501i	−0.123351	−	0.625798i
$726$		0			0
$727$	5.63067	−	5.63067i	0.208830	−	0.208830i	−0.594940	−	0.803770i	$-0.702824\pi$
$727$	5.63067	−	5.63067i	0.208830	−	0.208830i	0.803770	+	0.594940i	$0.202824\pi$
$728$		0			0
$729$	26.2198	−	6.44382i	0.971103	−	0.238660i
$730$		0			0
$731$	−8.69345			−0.321539
$732$		0			0
$733$	11.4227	−	11.4227i	0.421905	−	0.421905i	−0.463954	−	0.885859i	$-0.653570\pi$
$733$	11.4227	−	11.4227i	0.421905	−	0.421905i	0.885859	+	0.463954i	$0.153570\pi$
$734$		0			0
$735$	2.16175	−	5.31749i	0.0797373	−	0.196139i
$736$		0			0
$737$	−26.4914	−	26.4914i	−0.975822	−	0.975822i
$738$		0			0
$739$	39.3046			1.44584			0.722921	−	0.690931i	$-0.242799\pi$
$739$	39.3046			1.44584			0.722921	+	0.690931i	$0.242799\pi$
$740$		0			0
$741$	−1.81602	−	5.83013i	−0.0667133	−	0.214175i
$742$		0			0
$743$	9.74358	−	9.74358i	0.357457	−	0.357457i	−0.505418	−	0.862875i	$-0.668662\pi$
$743$	9.74358	−	9.74358i	0.357457	−	0.357457i	0.862875	+	0.505418i	$0.168662\pi$
$744$		0			0
$745$	−16.6149	+	1.62187i	−0.608723	+	0.0594208i
$746$		0			0
$747$	5.34522	−	29.1309i	0.195571	−	1.06584i
$748$		0			0
$749$		−	6.09995i		−	0.222887i
$750$		0			0
$751$	46.4053			1.69335			0.846677	−	0.532107i	$-0.178599\pi$
$751$	46.4053			1.69335			0.846677	+	0.532107i	$0.178599\pi$
$752$		0			0
$753$	−0.849838	+	1.61879i	−0.0309698	+	0.0589920i
$754$		0			0
$755$	1.16821	+	11.9675i	0.0425156	+	0.435542i
$756$		0			0
$757$	18.1902	+	18.1902i	0.661135	+	0.661135i	0.955648	−	0.294513i	$-0.0951573\pi$
$757$	18.1902	+	18.1902i	0.661135	+	0.661135i	−0.294513	+	0.955648i	$0.595157\pi$
$758$		0			0
$759$	−23.9662	−	76.9407i	−0.869918	−	2.79277i
$760$		0			0
$761$			31.1589i			1.12951i	0.825259	+	0.564755i	$0.191029\pi$
$761$			31.1589i			1.12951i	−0.825259	+	0.564755i	$0.808971\pi$
$762$		0			0
$763$	33.1914	−	33.1914i	1.20161	−	1.20161i
$764$		0			0
$765$	−7.78626	−	0.656871i	−0.281513	−	0.0237492i
$766$		0			0
$767$	−12.6242	−	12.6242i	−0.455832	−	0.455832i
$768$		0			0
$769$		−	3.28853i		−	0.118587i	−0.998241	−	0.0592937i	$-0.981115\pi$
$769$		−	3.28853i		−	0.118587i	0.998241	−	0.0592937i	$-0.0188848\pi$
$770$		0			0
$771$	−30.7255	+	9.57064i	−1.10655	+	0.344678i
$772$		0			0
$773$	14.5900	+	14.5900i	0.524766	+	0.524766i	0.919007	−	0.394241i	$-0.128993\pi$
$773$	14.5900	+	14.5900i	0.524766	+	0.524766i	−0.394241	+	0.919007i	$0.628993\pi$
$774$		0			0
$775$	6.84266	−	1.34875i	0.245795	−	0.0484486i
$776$		0			0
$777$	18.4730	−	35.1878i	0.662717	−	1.26236i
$778$		0			0
$779$			17.4926i			0.626738i
$780$		0			0
$781$			36.7335i			1.31443i
$782$		0			0
$783$	2.14537	+	17.7187i	0.0766692	+	0.633214i
$784$		0			0
$785$	22.0700	−	26.8449i	0.787714	−	0.958136i
$786$		0			0
$787$	−37.2838	−	37.2838i	−1.32902	−	1.32902i	−0.906223	−	0.422801i	$-0.861047\pi$
$787$	−37.2838	−	37.2838i	−1.32902	−	1.32902i	−0.422801	−	0.906223i	$-0.638953\pi$
$788$		0			0
$789$	6.45440	+	20.7211i	0.229783	+	0.737691i
$790$		0			0
$791$			38.0465i			1.35278i
$792$		0			0
$793$	14.2368	+	14.2368i	0.505563	+	0.505563i
$794$		0			0
$795$	−7.48565	−	17.7413i	−0.265489	−	0.629218i
$796$		0			0
$797$	1.83306	−	1.83306i	0.0649302	−	0.0649302i	−0.673896	−	0.738826i	$-0.735380\pi$
$797$	1.83306	−	1.83306i	0.0649302	−	0.0649302i	0.738826	+	0.673896i	$0.235380\pi$
$798$		0			0
$799$		−	0.311103i		−	0.0110060i
$800$		0			0
$801$	−14.4160	−	20.8952i	−0.509363	−	0.738296i
$802$		0			0
$803$	−32.6956	−	32.6956i	−1.15380	−	1.15380i
$804$		0			0
$805$	−52.3643	+	5.11157i	−1.84560	+	0.180159i
$806$		0			0
$807$	−21.8102	−	11.4500i	−0.767756	−	0.403060i
$808$		0			0
$809$	−40.5238			−1.42474			−0.712371	−	0.701803i	$-0.752379\pi$
$809$	−40.5238			−1.42474			−0.712371	+	0.701803i	$0.752379\pi$
$810$		0			0
$811$		−	5.82716i		−	0.204619i	−0.994753	−	0.102310i	$-0.967377\pi$
$811$		−	5.82716i		−	0.204619i	0.994753	−	0.102310i	$-0.0326233\pi$
$812$		0			0
$813$	19.1571	−	36.4909i	0.671870	−	1.27979i
$814$		0			0
$815$	−18.4150	−	15.1395i	−0.645048	−	0.530315i
$816$		0			0
$817$	−11.5850	+	11.5850i	−0.405306	+	0.405306i
$818$		0			0
$819$	−11.5499	+	7.96847i	−0.403585	+	0.278441i
$820$		0			0
$821$	23.0759			0.805355			0.402677	−	0.915342i	$-0.368080\pi$
$821$	23.0759			0.805355			0.402677	+	0.915342i	$0.368080\pi$
$822$		0			0
$823$	−21.0932	−	21.0932i	−0.735262	−	0.735262i	0.236395	−	0.971657i	$-0.424034\pi$
$823$	−21.0932	−	21.0932i	−0.735262	−	0.735262i	−0.971657	+	0.236395i	$0.924034\pi$
$824$		0			0
$825$	14.2052	−	47.8085i	0.494563	−	1.66448i
$826$		0			0
$827$	36.2396	−	36.2396i	1.26017	−	1.26017i	0.309166	−	0.951008i	$-0.399950\pi$
$827$	36.2396	−	36.2396i	1.26017	−	1.26017i	0.951008	−	0.309166i	$-0.100050\pi$
$828$		0			0
$829$	27.9918			0.972196			0.486098	−	0.873904i	$-0.338420\pi$
$829$	27.9918			0.972196			0.486098	+	0.873904i	$0.338420\pi$
$830$		0			0
$831$	−2.33738	+	0.728070i	−0.0810829	+	0.0252565i
$832$		0			0
$833$	1.22074	−	1.22074i	0.0422961	−	0.0422961i
$834$		0			0
$835$	3.70194	−	4.50286i	0.128111	−	0.155828i
$836$		0			0
$837$	−7.19537	+	0.871212i	−0.248708	+	0.0301135i
$838$		0			0
$839$	36.6863			1.26655			0.633275	−	0.773927i	$-0.281710\pi$
$839$	36.6863			1.26655			0.633275	+	0.773927i	$0.281710\pi$
$840$		0			0
$841$	17.2017			0.593162
$842$		0			0
$843$	−1.18567	−	0.622456i	−0.0408365	−	0.0214385i
$844$		0			0
$845$	23.1913	−	2.26383i	0.797805	−	0.0778781i
$846$		0			0
$847$	−45.6479	+	45.6479i	−1.56848	+	1.56848i
$848$		0			0
$849$	−2.52965	−	8.12115i	−0.0868173	−	0.278717i
$850$		0			0
$851$	−63.6498			−2.18189
$852$		0			0
$853$	−17.1487	+	17.1487i	−0.587161	+	0.587161i	−0.936862	−	0.349700i	$-0.886283\pi$
$853$	−17.1487	+	17.1487i	−0.587161	+	0.587161i	0.349700	+	0.936862i	$0.386283\pi$
$854$		0			0
$855$	−11.2514	+	9.50069i	−0.384789	+	0.324917i
$856$		0			0
$857$	−23.7407	−	23.7407i	−0.810965	−	0.810965i	0.173813	−	0.984779i	$-0.444391\pi$
$857$	−23.7407	−	23.7407i	−0.810965	−	0.810965i	−0.984779	+	0.173813i	$0.944391\pi$
$858$		0			0
$859$	15.8783			0.541760			0.270880	−	0.962613i	$-0.412685\pi$
$859$	15.8783			0.541760			0.270880	+	0.962613i	$0.412685\pi$
$860$		0			0
$861$	38.3777	−	11.9542i	1.30791	−	0.407399i
$862$		0			0
$863$	18.3158	−	18.3158i	0.623477	−	0.623477i	−0.322942	−	0.946419i	$-0.604672\pi$
$863$	18.3158	−	18.3158i	0.623477	−	0.623477i	0.946419	+	0.322942i	$0.104672\pi$
$864$		0			0
$865$	26.7679	−	32.5591i	0.910134	−	1.10704i
$866$		0			0
$867$	23.9898	+	12.5943i	0.814737	+	0.427724i
$868$		0			0
$869$			64.7825i			2.19760i
$870$		0			0
$871$	10.4477			0.354006
$872$		0			0
$873$	23.6913	+	4.34711i	0.801830	+	0.147127i
$874$		0			0
$875$	−28.6768	−	15.4241i	−0.969452	−	0.521431i
$876$		0			0
$877$	33.2732	+	33.2732i	1.12356	+	1.12356i	0.991202	+	0.132355i	$0.0422538\pi$
$877$	33.2732	+	33.2732i	1.12356	+	1.12356i	0.132355	+	0.991202i	$0.457746\pi$
$878$		0			0
$879$	−2.66439	+	0.829927i	−0.0898675	+	0.0279927i
$880$		0			0
$881$		−	46.9413i		−	1.58149i	−0.612144	−	0.790747i	$-0.709693\pi$
$881$		−	46.9413i		−	1.58149i	0.612144	−	0.790747i	$-0.290307\pi$
$882$		0			0
$883$	−18.7291	+	18.7291i	−0.630285	+	0.630285i	−0.948140	−	0.317854i	$-0.897038\pi$
$883$	−18.7291	+	18.7291i	−0.630285	+	0.630285i	0.317854	+	0.948140i	$0.397038\pi$
$884$		0			0
$885$	−16.2144	+	39.8845i	−0.545043	+	1.34070i
$886$		0			0
$887$	−20.3691	−	20.3691i	−0.683928	−	0.683928i	0.276955	−	0.960883i	$-0.410675\pi$
$887$	−20.3691	−	20.3691i	−0.683928	−	0.683928i	−0.960883	+	0.276955i	$0.910675\pi$
$888$		0			0
$889$			26.2782i			0.881343i
$890$		0			0
$891$	−18.4013	+	48.4544i	−0.616466	+	1.62328i
$892$		0			0
$893$	−0.414579	−	0.414579i	−0.0138734	−	0.0138734i
$894$		0			0
$895$	−8.72677	+	0.851868i	−0.291704	+	0.0284748i
$896$		0			0
$897$	19.8978	+	10.4460i	0.664370	+	0.348783i
$898$		0			0
$899$		−	4.79117i		−	0.159794i
$900$		0			0
$901$		−	5.79135i		−	0.192938i
$902$		0			0
$903$	33.3336	+	17.4996i	1.10927	+	0.582351i
$904$		0			0
$905$	−31.7363	+	3.09796i	−1.05495	+	0.102980i
$906$		0			0
$907$	9.52265	+	9.52265i	0.316194	+	0.316194i	0.847303	−	0.531109i	$-0.178225\pi$
$907$	9.52265	+	9.52265i	0.316194	+	0.316194i	−0.531109	+	0.847303i	$0.678225\pi$
$908$		0			0
$909$	−24.7548	−	35.8808i	−0.821066	−	1.19009i
$910$		0			0
$911$			47.3563i			1.56898i	0.620139	+	0.784492i	$0.287076\pi$
$911$			47.3563i			1.56898i	−0.620139	+	0.784492i	$0.712924\pi$
$912$		0			0
$913$	40.2026	+	40.2026i	1.33051	+	1.33051i
$914$		0			0
$915$	18.2857	−	44.9793i	0.604506	−	1.48697i
$916$		0			0
$917$	8.95874	−	8.95874i	0.295844	−	0.295844i
$918$		0			0
$919$			41.4093i			1.36597i	0.730434	+	0.682983i	$0.239318\pi$
$919$			41.4093i			1.36597i	−0.730434	+	0.682983i	$0.760682\pi$
$920$		0			0
$921$	13.2400	−	4.12410i	0.436271	−	0.135894i
$922$		0			0
$923$	−7.24349	−	7.24349i	−0.238422	−	0.238422i
$924$		0			0
$925$	−32.7153	−	21.9419i	−1.07567	−	0.721444i
$926$		0			0
$927$	5.12759	−	27.9449i	0.168412	−	0.917831i
$928$		0			0
$929$	35.5656			1.16687			0.583434	−	0.812160i	$-0.301709\pi$
$929$	35.5656			1.16687			0.583434	+	0.812160i	$0.301709\pi$
$930$		0			0
$931$		−	3.25353i		−	0.106630i
$932$		0			0
$933$	−6.66525	−	3.49915i	−0.218211	−	0.114557i
$934$		0			0
$935$	9.52600	−	11.5870i	0.311534	−	0.378934i
$936$		0			0
$937$	42.5062	−	42.5062i	1.38862	−	1.38862i	0.560388	−	0.828230i	$-0.310652\pi$
$937$	42.5062	−	42.5062i	1.38862	−	1.38862i	0.828230	−	0.560388i	$-0.189348\pi$
$938$		0			0
$939$	22.1754	−	6.90740i	0.723667	−	0.225414i
$940$		0			0
$941$	24.6806			0.804565			0.402282	−	0.915516i	$-0.368217\pi$
$941$	24.6806			0.804565			0.402282	+	0.915516i	$0.368217\pi$
$942$		0			0
$943$	−45.5216	−	45.5216i	−1.48239	−	1.48239i
$944$		0			0
$945$	28.5329	+	18.1922i	0.928176	+	0.591791i
$946$		0			0
$947$	−4.02311	+	4.02311i	−0.130733	+	0.130733i	−0.769446	−	0.638712i	$-0.779467\pi$
$947$	−4.02311	+	4.02311i	−0.130733	+	0.130733i	0.638712	+	0.769446i	$0.279467\pi$
$948$		0			0
$949$	12.8945			0.418573
$950$		0			0
$951$	1.31439	+	4.21971i	0.0426222	+	0.136834i
$952$		0			0
$953$	38.1974	−	38.1974i	1.23733	−	1.23733i	0.276247	−	0.961087i	$-0.410909\pi$
$953$	38.1974	−	38.1974i	1.23733	−	1.23733i	0.961087	−	0.276247i	$-0.0890909\pi$
$954$		0			0
$955$	−53.8816	+	5.25968i	−1.74357	+	0.170199i
$956$		0			0
$957$	−30.3360	−	15.9259i	−0.980622	−	0.514811i
$958$		0			0
$959$	24.0127			0.775412
$960$		0			0
$961$	−29.0544			−0.937237
$962$		0			0
$963$	6.18025	+	1.13401i	0.199156	+	0.0365429i
$964$		0			0
$965$	−14.4498	+	17.5760i	−0.465156	+	0.565792i
$966$		0			0
$967$	−31.1763	+	31.1763i	−1.00256	+	1.00256i	−0.00256583	+	0.999997i	$0.500817\pi$
$967$	−31.1763	+	31.1763i	−1.00256	+	1.00256i	−0.999997	+	0.00256583i	$0.999183\pi$
$968$		0			0
$969$	−4.22859	+	1.31716i	−0.135842	+	0.0423132i
$970$		0			0
$971$	16.0935			0.516463			0.258232	−	0.966083i	$-0.416860\pi$
$971$	16.0935			0.516463			0.258232	+	0.966083i	$0.416860\pi$
$972$		0			0
$973$	11.6819	−	11.6819i	0.374505	−	0.374505i
$974$		0			0
$975$	6.62623	+	12.2285i	0.212209	+	0.391625i
$976$		0			0
$977$	−9.07186	−	9.07186i	−0.290235	−	0.290235i	0.546938	−	0.837173i	$-0.315793\pi$
$977$	−9.07186	−	9.07186i	−0.290235	−	0.290235i	−0.837173	+	0.546938i	$0.815793\pi$
$978$		0			0
$979$	48.7318			1.55747
$980$		0			0
$981$	27.4578	+	39.7987i	0.876661	+	1.27067i
$982$		0			0
$983$	23.7773	−	23.7773i	0.758379	−	0.758379i	−0.217648	−	0.976027i	$-0.569838\pi$
$983$	23.7773	−	23.7773i	0.758379	−	0.758379i	0.976027	+	0.217648i	$0.0698385\pi$
$984$		0			0
$985$	−40.1440	−	33.0037i	−1.27910	−	1.05159i
$986$		0			0
$987$	−0.626241	+	1.19288i	−0.0199335	+	0.0379697i
$988$		0			0
$989$		−	60.2959i		−	1.91730i
$990$		0			0
$991$	45.1730			1.43497			0.717484	−	0.696575i	$-0.245294\pi$
$991$	45.1730			1.43497			0.717484	+	0.696575i	$0.245294\pi$
$992$		0			0
$993$	46.1672	+	24.2371i	1.46507	+	0.769140i
$994$		0			0
$995$	29.0979	−	2.84041i	0.922466	−	0.0900470i
$996$		0			0
$997$	−29.4420	−	29.4420i	−0.932438	−	0.932438i	0.0654201	−	0.997858i	$-0.479161\pi$
$997$	−29.4420	−	29.4420i	−0.932438	−	0.932438i	−0.997858	+	0.0654201i	$0.979161\pi$
$998$		0			0
$999$	32.2168	+	25.2578i	1.01929	+	0.799121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.bi.g.353.7	yes	32
3.2	odd	2	inner	960.2.bi.g.353.4	yes	32
4.3	odd	2		960.2.bi.h.353.9	yes	32
5.2	odd	4		960.2.bi.h.737.13	yes	32
8.3	odd	2	inner	960.2.bi.g.353.8	yes	32
8.5	even	2		960.2.bi.h.353.10	yes	32
12.11	even	2		960.2.bi.h.353.14	yes	32
15.2	even	4		960.2.bi.h.737.10	yes	32
20.7	even	4	inner	960.2.bi.g.737.3	yes	32
24.5	odd	2		960.2.bi.h.353.13	yes	32
24.11	even	2	inner	960.2.bi.g.353.3	✓	32
40.27	even	4		960.2.bi.h.737.14	yes	32
40.37	odd	4	inner	960.2.bi.g.737.4	yes	32
60.47	odd	4	inner	960.2.bi.g.737.8	yes	32
120.77	even	4	inner	960.2.bi.g.737.7	yes	32
120.107	odd	4		960.2.bi.h.737.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.bi.g.353.3	✓	32	24.11	even	2	inner
960.2.bi.g.353.4	yes	32	3.2	odd	2	inner
960.2.bi.g.353.7	yes	32	1.1	even	1	trivial
960.2.bi.g.353.8	yes	32	8.3	odd	2	inner
960.2.bi.g.737.3	yes	32	20.7	even	4	inner
960.2.bi.g.737.4	yes	32	40.37	odd	4	inner
960.2.bi.g.737.7	yes	32	120.77	even	4	inner
960.2.bi.g.737.8	yes	32	60.47	odd	4	inner
960.2.bi.h.353.9	yes	32	4.3	odd	2
960.2.bi.h.353.10	yes	32	8.5	even	2
960.2.bi.h.353.13	yes	32	24.5	odd	2
960.2.bi.h.353.14	yes	32	12.11	even	2
960.2.bi.h.737.9	yes	32	120.107	odd	4
960.2.bi.h.737.10	yes	32	15.2	even	4
960.2.bi.h.737.13	yes	32	5.2	odd	4
960.2.bi.h.737.14	yes	32	40.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bi (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.805097 + 1.53356i) q^{3} +(-0.217242 - 2.22549i) q^{5} +(-2.05938 + 2.05938i) q^{7} +(-1.70364 - 2.46934i) q^{9} +O(q^{10})\)	\(q+(-0.805097 + 1.53356i) q^{3} +(-0.217242 - 2.22549i) q^{5} +(-2.05938 + 2.05938i) q^{7} +(-1.70364 - 2.46934i) q^{9} +5.75898 q^{11} +(-1.13561 + 1.13561i) q^{13} +(3.58783 + 1.45858i) q^{15} +(0.823659 + 0.823659i) q^{17} +2.19523 q^{19} +(-1.50019 - 4.81619i) q^{21} +(-5.71272 + 5.71272i) q^{23} +(-4.90561 + 0.966941i) q^{25} +(5.15848 - 0.624586i) q^{27} +3.43487i q^{29} -1.39486 q^{31} +(-4.63654 + 8.83177i) q^{33} +(5.03051 + 4.13574i) q^{35} +(5.57088 + 5.57088i) q^{37} +(-0.827258 - 2.65582i) q^{39} +7.96847i q^{41} +(-5.27733 + 5.27733i) q^{43} +(-5.12538 + 4.32787i) q^{45} +(-0.188854 - 0.188854i) q^{47} -1.48209i q^{49} +(-1.92626 + 0.600009i) q^{51} +(-3.51562 - 3.51562i) q^{53} +(-1.25109 - 12.8166i) q^{55} +(-1.76737 + 3.36653i) q^{57} +11.1166i q^{59} -12.5366i q^{61} +(8.59374 + 1.57686i) q^{63} +(2.77400 + 2.28059i) q^{65} +(-4.60001 - 4.60001i) q^{67} +(-4.16153 - 13.3601i) q^{69} +6.37847i q^{71} +(-5.67732 - 5.67732i) q^{73} +(2.46662 - 8.30155i) q^{75} +(-11.8599 + 11.8599i) q^{77} +11.2490i q^{79} +(-3.19523 + 8.41371i) q^{81} +(6.98086 + 6.98086i) q^{83} +(1.65411 - 2.01198i) q^{85} +(-5.26759 - 2.76540i) q^{87} +8.46187 q^{89} -4.67732i q^{91} +(1.12300 - 2.13911i) q^{93} +(-0.476897 - 4.88546i) q^{95} +(-5.67732 + 5.67732i) q^{97} +(-9.81122 - 14.2209i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3}+O(q^{10}) \) 32 * q - 4 * q^3	\( 32 q - 4 q^{3} - 16 q^{19} + 24 q^{25} - 4 q^{27} + 24 q^{33} + 40 q^{43} + 32 q^{57} - 72 q^{67} - 48 q^{73} + 4 q^{75} - 16 q^{81} - 48 q^{97} + 48 q^{99}+O(q^{100}) \) 32 * q - 4 * q^3 - 16 * q^19 + 24 * q^25 - 4 * q^27 + 24 * q^33 + 40 * q^43 + 32 * q^57 - 72 * q^67 - 48 * q^73 + 4 * q^75 - 16 * q^81 - 48 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

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Database

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