LMFDB - Embedded newform 684.2.c.b.647.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(647,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("684.647"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			647.13
Character	$\chi$	$=$	684.647
Dual form			684.2.c.b.647.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.647279 - 1.25739i) q^{2} +(-1.16206 + 1.62776i) q^{4} +1.07823i q^{5} -3.32412i q^{7} +(2.79891 + 0.407546i) q^{8} +(1.35575 - 0.697914i) q^{10} -1.96175 q^{11} +5.47134 q^{13} +(-4.17972 + 2.15163i) q^{14} +(-1.29923 - 3.78312i) q^{16} +3.80151i q^{17} +1.00000i q^{19} +(-1.75510 - 1.25297i) q^{20} +(1.26980 + 2.46668i) q^{22} -0.563522 q^{23} +3.83743 q^{25} +(-3.54148 - 6.87961i) q^{26} +(5.41088 + 3.86283i) q^{28} -10.2866i q^{29} -7.19699i q^{31} +(-3.91589 + 4.08238i) q^{32} +(4.77998 - 2.46064i) q^{34} +3.58416 q^{35} +4.71282 q^{37} +(1.25739 - 0.647279i) q^{38} +(-0.439427 + 3.01786i) q^{40} -2.44045i q^{41} -11.9618i q^{43} +(2.27967 - 3.19326i) q^{44} +(0.364756 + 0.708567i) q^{46} +4.38837 q^{47} -4.04978 q^{49} +(-2.48388 - 4.82514i) q^{50} +(-6.35802 + 8.90605i) q^{52} -3.92349i q^{53} -2.11521i q^{55} +(1.35473 - 9.30392i) q^{56} +(-12.9342 + 6.65829i) q^{58} +12.4430 q^{59} -6.74286 q^{61} +(-9.04943 + 4.65846i) q^{62} +(7.66781 + 2.28137i) q^{64} +5.89935i q^{65} +3.40676i q^{67} +(-6.18796 - 4.41758i) q^{68} +(-2.31995 - 4.50669i) q^{70} -0.390266 q^{71} +6.10952 q^{73} +(-3.05051 - 5.92585i) q^{74} +(-1.62776 - 1.16206i) q^{76} +6.52108i q^{77} +8.10895i q^{79} +(4.07906 - 1.40087i) q^{80} +(-3.06859 + 1.57965i) q^{82} -11.1298 q^{83} -4.09889 q^{85} +(-15.0407 + 7.74264i) q^{86} +(-5.49075 - 0.799501i) q^{88} +11.2732i q^{89} -18.1874i q^{91} +(0.654846 - 0.917281i) q^{92} +(-2.84050 - 5.51790i) q^{94} -1.07823 q^{95} -9.56020 q^{97} +(2.62133 + 5.09215i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94}+ \cdots - 128 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.647279	−	1.25739i	−0.457695	−	0.889109i
$2$	−0.647279	−	1.25739i	−0.457695	−	0.889109i
$3$		0			0
$3$		0			0
$4$	−1.16206	+	1.62776i	−0.581030	+	0.813882i
$5$			1.07823i			0.482198i	0.970501	+	0.241099i	$0.0775079\pi$
$5$			1.07823i			0.482198i	−0.970501	+	0.241099i	$0.922492\pi$
$6$		0			0
$7$		−	3.32412i		−	1.25640i	−0.778052	−	0.628200i	$-0.783792\pi$
$7$		−	3.32412i		−	1.25640i	0.778052	−	0.628200i	$-0.216208\pi$
$8$	2.79891	+	0.407546i	0.989565	+	0.144089i
$9$		0			0
$10$	1.35575	−	0.697914i	0.428727	−	0.220700i
$11$	−1.96175			−0.591489			−0.295744	−	0.955267i	$-0.595568\pi$
$11$	−1.96175			−0.591489			−0.295744	+	0.955267i	$0.595568\pi$
$12$		0			0
$13$	5.47134			1.51748			0.758738	−	0.651396i	$-0.225816\pi$
$13$	5.47134			1.51748			0.758738	+	0.651396i	$0.225816\pi$
$14$	−4.17972	+	2.15163i	−1.11708	+	0.575048i
$15$		0			0
$16$	−1.29923	−	3.78312i	−0.324808	−	0.945780i
$17$			3.80151i			0.922001i	0.887400	+	0.461001i	$0.152509\pi$
$17$			3.80151i			0.922001i	−0.887400	+	0.461001i	$0.847491\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−1.75510	−	1.25297i	−0.392452	−	0.280172i
$21$		0			0
$22$	1.26980	+	2.46668i	0.270722	+	0.525898i
$23$	−0.563522			−0.117502			−0.0587512	−	0.998273i	$-0.518712\pi$
$23$	−0.563522			−0.117502			−0.0587512	+	0.998273i	$0.518712\pi$
$24$		0			0
$25$	3.83743			0.767485
$26$	−3.54148	−	6.87961i	−0.694542	−	1.34920i
$27$		0			0
$28$	5.41088	+	3.86283i	1.02256	+	0.730006i
$29$		−	10.2866i		−	1.91017i	−0.296332	−	0.955085i	$-0.595763\pi$
$29$		−	10.2866i		−	1.91017i	0.296332	−	0.955085i	$-0.404237\pi$
$30$		0			0
$31$		−	7.19699i		−	1.29262i	−0.763076	−	0.646309i	$-0.776312\pi$
$31$		−	7.19699i		−	1.29262i	0.763076	−	0.646309i	$-0.223688\pi$
$32$	−3.91589	+	4.08238i	−0.692238	+	0.721669i
$33$		0			0
$34$	4.77998	−	2.46064i	0.819760	−	0.421996i
$35$	3.58416			0.605833
$36$		0			0
$37$	4.71282			0.774783			0.387391	−	0.921915i	$-0.373376\pi$
$37$	4.71282			0.774783			0.387391	+	0.921915i	$0.373376\pi$
$38$	1.25739	−	0.647279i	0.203976	−	0.105002i
$39$		0			0
$40$	−0.439427	+	3.01786i	−0.0694795	+	0.477166i
$41$		−	2.44045i		−	0.381134i	−0.981674	−	0.190567i	$-0.938967\pi$
$41$		−	2.44045i		−	0.381134i	0.981674	−	0.190567i	$-0.0610326\pi$
$42$		0			0
$43$		−	11.9618i		−	1.82416i	−0.410009	−	0.912082i	$-0.634474\pi$
$43$		−	11.9618i		−	1.82416i	0.410009	−	0.912082i	$-0.365526\pi$
$44$	2.27967	−	3.19326i	0.343673	−	0.481402i
$45$		0			0
$46$	0.364756	+	0.708567i	0.0537803	+	0.104473i
$47$	4.38837			0.640110			0.320055	−	0.947399i	$-0.396299\pi$
$47$	4.38837			0.640110			0.320055	+	0.947399i	$0.396299\pi$
$48$		0			0
$49$	−4.04978			−0.578539
$50$	−2.48388	−	4.82514i	−0.351274	−	0.682378i
$51$		0			0
$52$	−6.35802	+	8.90605i	−0.881699	+	1.23505i
$53$		−	3.92349i		−	0.538933i	−0.963010	−	0.269467i	$-0.913153\pi$
$53$		−	3.92349i		−	0.538933i	0.963010	−	0.269467i	$-0.0868474\pi$
$54$		0			0
$55$		−	2.11521i		−	0.285215i
$56$	1.35473	−	9.30392i	0.181034	−	1.24329i
$57$		0			0
$58$	−12.9342	+	6.65829i	−1.69835	+	0.874276i
$59$	12.4430			1.61995			0.809973	−	0.586468i	$-0.199482\pi$
$59$	12.4430			1.61995			0.809973	+	0.586468i	$0.199482\pi$
$60$		0			0
$61$	−6.74286			−0.863335			−0.431668	−	0.902033i	$-0.642075\pi$
$61$	−6.74286			−0.863335			−0.431668	+	0.902033i	$0.642075\pi$
$62$	−9.04943	+	4.65846i	−1.14928	+	0.591625i
$63$		0			0
$64$	7.66781	+	2.28137i	0.958477	+	0.285171i
$65$			5.89935i			0.731724i
$66$		0			0
$67$			3.40676i			0.416202i	0.978107	+	0.208101i	$0.0667283\pi$
$67$			3.40676i			0.416202i	−0.978107	+	0.208101i	$0.933272\pi$
$68$	−6.18796	−	4.41758i	−0.750400	−	0.535710i
$69$		0			0
$70$	−2.31995	−	4.50669i	−0.277287	−	0.538652i
$71$	−0.390266			−0.0463161			−0.0231580	−	0.999732i	$-0.507372\pi$
$71$	−0.390266			−0.0463161			−0.0231580	+	0.999732i	$0.507372\pi$
$72$		0			0
$73$	6.10952			0.715065			0.357533	−	0.933901i	$-0.383618\pi$
$73$	6.10952			0.715065			0.357533	+	0.933901i	$0.383618\pi$
$74$	−3.05051	−	5.92585i	−0.354614	−	0.688866i
$75$		0			0
$76$	−1.62776	−	1.16206i	−0.186717	−	0.133297i
$77$			6.52108i			0.743146i
$78$		0			0
$79$			8.10895i			0.912328i	0.889896	+	0.456164i	$0.150777\pi$
$79$			8.10895i			0.912328i	−0.889896	+	0.456164i	$0.849223\pi$
$80$	4.07906	−	1.40087i	0.456053	−	0.156622i
$81$		0			0
$82$	−3.06859	+	1.57965i	−0.338869	+	0.174443i
$83$	−11.1298			−1.22166			−0.610830	−	0.791762i	$-0.709164\pi$
$83$	−11.1298			−1.22166			−0.610830	+	0.791762i	$0.709164\pi$
$84$		0			0
$85$	−4.09889			−0.444587
$86$	−15.0407	+	7.74264i	−1.62188	+	0.834911i
$87$		0			0
$88$	−5.49075	−	0.799501i	−0.585316	−	0.0852271i
$89$			11.2732i			1.19495i	0.801887	+	0.597476i	$0.203830\pi$
$89$			11.2732i			1.19495i	−0.801887	+	0.597476i	$0.796170\pi$
$90$		0			0
$91$		−	18.1874i		−	1.90656i
$92$	0.654846	−	0.917281i	0.0682725	−	0.0956331i
$93$		0			0
$94$	−2.84050	−	5.51790i	−0.292975	−	0.569128i
$95$	−1.07823			−0.110624
$96$		0			0
$97$	−9.56020			−0.970691			−0.485345	−	0.874323i	$-0.661306\pi$
$97$	−9.56020			−0.970691			−0.485345	+	0.874323i	$0.661306\pi$
$98$	2.62133	+	5.09215i	0.264795	+	0.514385i
$99$		0			0
$100$	−4.45932	+	6.24642i	−0.445932	+	0.624642i
$101$		−	0.547862i		−	0.0545143i	−0.999628	−	0.0272571i	$-0.991323\pi$
$101$		−	0.547862i		−	0.0545143i	0.999628	−	0.0272571i	$-0.00867729\pi$
$102$		0			0
$103$			12.7223i			1.25357i	0.779194	+	0.626783i	$0.215629\pi$
$103$			12.7223i			1.25357i	−0.779194	+	0.626783i	$0.784371\pi$
$104$	15.3138	+	2.22982i	1.50164	+	0.218652i
$105$		0			0
$106$	−4.93336	+	2.53959i	−0.479170	+	0.246667i
$107$	−5.79148			−0.559883			−0.279942	−	0.960017i	$-0.590315\pi$
$107$	−5.79148			−0.559883			−0.279942	+	0.960017i	$0.590315\pi$
$108$		0			0
$109$	13.7901			1.32085			0.660424	−	0.750893i	$-0.270377\pi$
$109$	13.7901			1.32085			0.660424	+	0.750893i	$0.270377\pi$
$110$	−2.65964	+	1.36913i	−0.253587	+	0.130541i
$111$		0			0
$112$	−12.5755	+	4.31880i	−1.18828	+	0.408089i
$113$		−	5.13667i		−	0.483218i	−0.970374	−	0.241609i	$-0.922325\pi$
$113$		−	5.13667i		−	0.483218i	0.970374	−	0.241609i	$-0.0776751\pi$
$114$		0			0
$115$		−	0.607605i		−	0.0566595i
$116$	16.7441	+	11.9536i	1.55465	+	1.10987i
$117$		0			0
$118$	−8.05411	−	15.6458i	−0.741441	−	1.44031i
$119$	12.6367			1.15840
$120$		0			0
$121$	−7.15155			−0.650141
$122$	4.36451	+	8.47841i	0.395144	+	0.767599i
$123$		0			0
$124$	11.7150	+	8.36334i	1.05204	+	0.751050i
$125$			9.52876i			0.852278i
$126$		0			0
$127$		−	4.00490i		−	0.355377i	−0.984087	−	0.177689i	$-0.943138\pi$
$127$		−	4.00490i		−	0.355377i	0.984087	−	0.177689i	$-0.0568620\pi$
$128$	−2.09464	−	11.1181i	−0.185142	−	0.982712i
$129$		0			0
$130$	7.41778	−	3.81852i	0.650583	−	0.334907i
$131$	18.9380			1.65462			0.827308	−	0.561748i	$-0.189871\pi$
$131$	18.9380			1.65462			0.827308	+	0.561748i	$0.189871\pi$
$132$		0			0
$133$	3.32412			0.288238
$134$	4.28363	−	2.20512i	0.370049	−	0.190494i
$135$		0			0
$136$	−1.54929	+	10.6401i	−0.132850	+	0.912380i
$137$			1.57895i			0.134899i	0.997723	+	0.0674496i	$0.0214862\pi$
$137$			1.57895i			0.134899i	−0.997723	+	0.0674496i	$0.978514\pi$
$138$		0			0
$139$		−	1.09687i		−	0.0930353i	−0.998917	−	0.0465177i	$-0.985188\pi$
$139$		−	1.09687i		−	0.0930353i	0.998917	−	0.0465177i	$-0.0148124\pi$
$140$	−4.16501	+	5.83416i	−0.352007	+	0.493077i
$141$		0			0
$142$	0.252611	+	0.490717i	0.0211987	+	0.0411800i
$143$	−10.7334			−0.897570
$144$		0			0
$145$	11.0913			0.921080
$146$	−3.95456	−	7.68205i	−0.327282	−	0.635771i
$147$		0			0
$148$	−5.47658	+	7.67136i	−0.450172	+	0.630582i
$149$		−	3.63911i		−	0.298127i	−0.988828	−	0.149064i	$-0.952374\pi$
$149$		−	3.63911i		−	0.298127i	0.988828	−	0.149064i	$-0.0476259\pi$
$150$		0			0
$151$			13.9298i			1.13359i	0.823857	+	0.566797i	$0.191818\pi$
$151$			13.9298i			1.13359i	−0.823857	+	0.566797i	$0.808182\pi$
$152$	−0.407546	+	2.79891i	−0.0330563	+	0.227022i
$153$		0			0
$154$	8.19954	−	4.22096i	0.660738	−	0.340134i
$155$	7.76000			0.623298
$156$		0			0
$157$	−6.52169			−0.520487			−0.260244	−	0.965543i	$-0.583803\pi$
$157$	−6.52169			−0.520487			−0.260244	+	0.965543i	$0.583803\pi$
$158$	10.1961	−	5.24875i	0.811159	−	0.417568i
$159$		0			0
$160$	−4.40173	−	4.22222i	−0.347987	−	0.333796i
$161$			1.87321i			0.147630i
$162$		0			0
$163$		−	4.21662i		−	0.330271i	−0.986271	−	0.165136i	$-0.947194\pi$
$163$		−	4.21662i		−	0.330271i	0.986271	−	0.165136i	$-0.0528062\pi$
$164$	3.97247	+	2.83594i	0.310198	+	0.221450i
$165$		0			0
$166$	7.20411	+	13.9946i	0.559148	+	1.08619i
$167$	17.8978			1.38497			0.692486	−	0.721431i	$-0.256515\pi$
$167$	17.8978			1.38497			0.692486	+	0.721431i	$0.256515\pi$
$168$		0			0
$169$	16.9355			1.30273
$170$	2.65313	+	5.15391i	0.203485	+	0.395286i
$171$		0			0
$172$	19.4711	+	13.9004i	1.48465	+	1.05989i
$173$			11.5422i			0.877535i	0.898601	+	0.438767i	$0.144585\pi$
$173$			11.5422i			0.877535i	−0.898601	+	0.438767i	$0.855415\pi$
$174$		0			0
$175$		−	12.7561i		−	0.964268i
$176$	2.54876	+	7.42152i	0.192120	+	0.559418i
$177$		0			0
$178$	14.1748	−	7.29687i	1.06244	−	0.546924i
$179$	−23.9339			−1.78890			−0.894451	−	0.447167i	$-0.852433\pi$
$179$	−23.9339			−1.78890			−0.894451	+	0.447167i	$0.852433\pi$
$180$		0			0
$181$	−12.2682			−0.911886			−0.455943	−	0.890009i	$-0.650698\pi$
$181$	−12.2682			−0.911886			−0.455943	+	0.890009i	$0.650698\pi$
$182$	−22.8686	+	11.7723i	−1.69514	+	0.872622i
$183$		0			0
$184$	−1.57725	−	0.229661i	−0.116276	−	0.0169308i
$185$			5.08149i			0.373599i
$186$		0			0
$187$		−	7.45759i		−	0.545353i
$188$	−5.09955	+	7.14324i	−0.371923	+	0.520974i
$189$		0			0
$190$	0.697914	+	1.35575i	0.0506320	+	0.0983566i
$191$	20.5274			1.48531			0.742657	−	0.669672i	$-0.233565\pi$
$191$	20.5274			1.48531			0.742657	+	0.669672i	$0.233565\pi$
$192$		0			0
$193$	−18.6621			−1.34333			−0.671663	−	0.740857i	$-0.734420\pi$
$193$	−18.6621			−1.34333			−0.671663	+	0.740857i	$0.734420\pi$
$194$	6.18811	+	12.0209i	0.444281	+	0.863050i
$195$		0			0
$196$	4.70608	−	6.59208i	0.336149	−	0.470863i
$197$		−	14.8835i		−	1.06041i	−0.847871	−	0.530203i	$-0.822116\pi$
$197$		−	14.8835i		−	1.06041i	0.847871	−	0.530203i	$-0.177884\pi$
$198$		0			0
$199$			23.4995i			1.66584i	0.553397	+	0.832918i	$0.313331\pi$
$199$			23.4995i			1.66584i	−0.553397	+	0.832918i	$0.686669\pi$
$200$	10.7406	+	1.56393i	0.759476	+	0.110586i
$201$		0			0
$202$	−0.688876	+	0.354619i	−0.0484692	+	0.0249509i
$203$	−34.1938			−2.39994
$204$		0			0
$205$	2.63136			0.183782
$206$	15.9969	−	8.23488i	1.11456	−	0.573751i
$207$		0			0
$208$	−7.10854	−	20.6987i	−0.492889	−	1.43520i
$209$		−	1.96175i		−	0.135697i
$210$		0			0
$211$			8.83240i			0.608047i	0.952664	+	0.304024i	$0.0983302\pi$
$211$			8.83240i			0.608047i	−0.952664	+	0.304024i	$0.901670\pi$
$212$	6.38652	+	4.55933i	0.438628	+	0.313136i
$213$		0			0
$214$	3.74870	+	7.28215i	0.256256	+	0.497798i
$215$	12.8976			0.879608
$216$		0			0
$217$	−23.9237			−1.62404
$218$	−8.92601	−	17.3395i	−0.604546	−	1.17438i
$219$		0			0
$220$	3.44306	+	2.45800i	0.232131	+	0.165718i
$221$			20.7993i			1.39911i
$222$		0			0
$223$			26.5423i			1.77741i	0.458484	+	0.888703i	$0.348393\pi$
$223$			26.5423i			1.77741i	−0.458484	+	0.888703i	$0.651607\pi$
$224$	13.5703	+	13.0169i	0.906704	+	0.869728i
$225$		0			0
$226$	−6.45880	+	3.32486i	−0.429633	+	0.221166i
$227$	−11.7947			−0.782840			−0.391420	−	0.920212i	$-0.628016\pi$
$227$	−11.7947			−0.782840			−0.391420	+	0.920212i	$0.628016\pi$
$228$		0			0
$229$	6.84691			0.452457			0.226228	−	0.974074i	$-0.427360\pi$
$229$	6.84691			0.452457			0.226228	+	0.974074i	$0.427360\pi$
$230$	−0.763996	+	0.393290i	−0.0503764	+	0.0259328i
$231$		0			0
$232$	4.19225	−	28.7912i	0.275235	−	1.89024i
$233$		−	17.5158i		−	1.14750i	−0.819031	−	0.573749i	$-0.805489\pi$
$233$		−	17.5158i		−	1.14750i	0.819031	−	0.573749i	$-0.194511\pi$
$234$		0			0
$235$			4.73166i			0.308660i
$236$	−14.4596	+	20.2543i	−0.941237	+	1.31844i
$237$		0			0
$238$	−8.17945	−	15.8892i	−0.530195	−	1.02995i
$239$	−12.9244			−0.836012			−0.418006	−	0.908444i	$-0.637271\pi$
$239$	−12.9244			−0.836012			−0.418006	+	0.908444i	$0.637271\pi$
$240$		0			0
$241$	−11.7444			−0.756520			−0.378260	−	0.925699i	$-0.623478\pi$
$241$	−11.7444			−0.756520			−0.378260	+	0.925699i	$0.623478\pi$
$242$	4.62905	+	8.99229i	0.297567	+	0.578046i
$243$		0			0
$244$	7.83561	−	10.9758i	0.501624	−	0.702653i
$245$		−	4.36658i		−	0.278971i
$246$		0			0
$247$			5.47134i			0.348133i
$248$	2.93310	−	20.1438i	0.186252	−	1.27913i
$249$		0			0
$250$	11.9814	−	6.16776i	0.757768	−	0.390084i
$251$	−17.3203			−1.09325			−0.546623	−	0.837379i	$-0.684087\pi$
$251$	−17.3203			−1.09325			−0.546623	+	0.837379i	$0.684087\pi$
$252$		0			0
$253$	1.10549			0.0695014
$254$	−5.03572	+	2.59229i	−0.315969	+	0.162655i
$255$		0			0
$256$	−12.6240	+	9.83030i	−0.788999	+	0.614394i
$257$			19.5964i			1.22239i	0.791479	+	0.611196i	$0.209311\pi$
$257$			19.5964i			1.22239i	−0.791479	+	0.611196i	$0.790689\pi$
$258$		0			0
$259$		−	15.6660i		−	0.973436i
$260$	−9.60275	−	6.85540i	−0.595537	−	0.425154i
$261$		0			0
$262$	−12.2581	−	23.8124i	−0.757310	−	1.47113i
$263$	20.1348			1.24156			0.620781	−	0.783984i	$-0.286815\pi$
$263$	20.1348			1.24156			0.620781	+	0.783984i	$0.286815\pi$
$264$		0			0
$265$	4.23042			0.259872
$266$	−2.15163	−	4.17972i	−0.131925	−	0.256275i
$267$		0			0
$268$	−5.54540	−	3.95886i	−0.338739	−	0.241826i
$269$		−	11.7206i		−	0.714620i	−0.933986	−	0.357310i	$-0.883694\pi$
$269$		−	11.7206i		−	0.714620i	0.933986	−	0.357310i	$-0.116306\pi$
$270$		0			0
$271$		−	14.1065i		−	0.856907i	−0.903564	−	0.428454i	$-0.859059\pi$
$271$		−	14.1065i		−	0.856907i	0.903564	−	0.428454i	$-0.140941\pi$
$272$	14.3816	−	4.93904i	0.872010	−	0.299473i
$273$		0			0
$274$	1.98536	−	1.02202i	0.119940	−	0.0617427i
$275$	−7.52805			−0.453959
$276$		0			0
$277$	14.1942			0.852845			0.426423	−	0.904524i	$-0.359774\pi$
$277$	14.1942			0.852845			0.426423	+	0.904524i	$0.359774\pi$
$278$	−1.37919	+	0.709981i	−0.0827185	+	0.0425818i
$279$		0			0
$280$	10.0317	+	1.46071i	0.599511	+	0.0872940i
$281$		−	23.8492i		−	1.42272i	−0.702826	−	0.711362i	$-0.748079\pi$
$281$		−	23.8492i		−	1.42272i	0.702826	−	0.711362i	$-0.251921\pi$
$282$		0			0
$283$			14.2442i			0.846729i	0.905959	+	0.423364i	$0.139151\pi$
$283$			14.2442i			0.846729i	−0.905959	+	0.423364i	$0.860849\pi$
$284$	0.453513	−	0.635261i	0.0269110	−	0.0376958i
$285$		0			0
$286$	6.94749	+	13.4960i	0.410814	+	0.798038i
$287$	−8.11233			−0.478856
$288$		0			0
$289$	2.54854			0.149914
$290$	−7.17915	−	13.9461i	−0.421574	−	0.818941i
$291$		0			0
$292$	−7.09963	+	9.94486i	−0.415475	+	0.581979i
$293$		−	12.9038i		−	0.753850i	−0.926244	−	0.376925i	$-0.876981\pi$
$293$		−	12.9038i		−	0.753850i	0.926244	−	0.376925i	$-0.123019\pi$
$294$		0			0
$295$			13.4164i			0.781134i
$296$	13.1908	+	1.92069i	0.766698	+	0.111638i
$297$		0			0
$298$	−4.57578	+	2.35552i	−0.265068	+	0.136451i
$299$	−3.08322			−0.178307
$300$		0			0
$301$	−39.7626			−2.29188
$302$	17.5152	−	9.01649i	1.00789	−	0.518841i
$303$		0			0
$304$	3.78312	−	1.29923i	0.216977	−	0.0745161i
$305$		−	7.27034i		−	0.416298i
$306$		0			0
$307$			11.9638i			0.682813i	0.939916	+	0.341406i	$0.110903\pi$
$307$			11.9638i			0.682813i	−0.939916	+	0.341406i	$0.889097\pi$
$308$	−10.6148	−	7.57789i	−0.604833	−	0.431790i
$309$		0			0
$310$	−5.02288	−	9.75735i	−0.285281	−	0.554180i
$311$	6.69344			0.379550			0.189775	−	0.981828i	$-0.439224\pi$
$311$	6.69344			0.379550			0.189775	+	0.981828i	$0.439224\pi$
$312$		0			0
$313$	27.9071			1.57740			0.788701	−	0.614777i	$-0.210754\pi$
$313$	27.9071			1.57740			0.788701	+	0.614777i	$0.210754\pi$
$314$	4.22135	+	8.20031i	0.238225	+	0.462770i
$315$		0			0
$316$	−13.1995	−	9.42309i	−0.742527	−	0.530090i
$317$			14.6011i			0.820079i	0.912068	+	0.410039i	$0.134485\pi$
$317$			14.6011i			0.820079i	−0.912068	+	0.410039i	$0.865515\pi$
$318$		0			0
$319$			20.1797i			1.12984i
$320$	−2.45983	+	8.26765i	−0.137509	+	0.462176i
$321$		0			0
$322$	2.35536	−	1.21249i	0.131259	−	0.0675696i
$323$	−3.80151			−0.211522
$324$		0			0
$325$	20.9959			1.16464
$326$	−5.30194	+	2.72933i	−0.293647	+	0.151164i
$327$		0			0
$328$	0.994593	−	6.83059i	0.0549172	−	0.377156i
$329$		−	14.5875i		−	0.804234i
$330$		0			0
$331$			6.60254i			0.362909i	0.983399	+	0.181454i	$0.0580805\pi$
$331$			6.60254i			0.362909i	−0.983399	+	0.181454i	$0.941920\pi$
$332$	12.9335	−	18.1168i	0.709821	−	0.994286i
$333$		0			0
$334$	−11.5849	−	22.5045i	−0.633895	−	1.23139i
$335$	−3.67326			−0.200692
$336$		0			0
$337$	13.0810			0.712568			0.356284	−	0.934378i	$-0.384044\pi$
$337$	13.0810			0.712568			0.356284	+	0.934378i	$0.384044\pi$
$338$	−10.9620	−	21.2946i	−0.596255	−	1.15827i
$339$		0			0
$340$	4.76316	−	6.67203i	0.258318	−	0.361842i
$341$			14.1187i			0.764569i
$342$		0			0
$343$		−	9.80690i		−	0.529523i
$344$	4.87500	−	33.4801i	0.262842	−	1.80513i
$345$		0			0
$346$	14.5130	−	7.47100i	0.780224	−	0.401644i
$347$	−9.56551			−0.513504			−0.256752	−	0.966477i	$-0.582652\pi$
$347$	−9.56551			−0.513504			−0.256752	+	0.966477i	$0.582652\pi$
$348$		0			0
$349$	−14.4091			−0.771304			−0.385652	−	0.922644i	$-0.626023\pi$
$349$	−14.4091			−0.771304			−0.385652	+	0.922644i	$0.626023\pi$
$350$	−16.0393	+	8.25673i	−0.857339	+	0.441341i
$351$		0			0
$352$	7.68199	−	8.00858i	0.409451	−	0.426859i
$353$		−	10.3693i		−	0.551901i	−0.961172	−	0.275950i	$-0.911007\pi$
$353$		−	10.3693i		−	0.551901i	0.961172	−	0.275950i	$-0.0889925\pi$
$354$		0			0
$355$		−	0.420796i		−	0.0223335i
$356$	−18.3500	−	13.1001i	−0.972550	−	0.694303i
$357$		0			0
$358$	15.4919	+	30.0942i	0.818772	+	1.59053i
$359$	−24.5107			−1.29363			−0.646813	−	0.762649i	$-0.723898\pi$
$359$	−24.5107			−1.29363			−0.646813	+	0.762649i	$0.723898\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	7.94093	+	15.4259i	0.417366	+	0.810767i
$363$		0			0
$364$	29.6048	+	21.1348i	1.55171	+	1.10777i
$365$			6.58745i			0.344803i
$366$		0			0
$367$		−	0.293849i		−	0.0153388i	−0.999971	−	0.00766940i	$-0.997559\pi$
$367$		−	0.293849i		−	0.0153388i	0.999971	−	0.00766940i	$-0.00244127\pi$
$368$	0.732146	+	2.13187i	0.0381658	+	0.111131i
$369$		0			0
$370$	6.38942	−	3.28914i	0.332170	−	0.170994i
$371$	−13.0422			−0.677115
$372$		0			0
$373$	−33.5282			−1.73602			−0.868012	−	0.496544i	$-0.834602\pi$
$373$	−33.5282			−1.73602			−0.868012	+	0.496544i	$0.834602\pi$
$374$	−9.37711	+	4.82714i	−0.484879	+	0.249606i
$375$		0			0
$376$	12.2827	+	1.78846i	0.633430	+	0.0922329i
$377$		−	56.2814i		−	2.89864i
$378$		0			0
$379$			1.30352i			0.0669572i	0.999439	+	0.0334786i	$0.0106586\pi$
$379$			1.30352i			0.0669572i	−0.999439	+	0.0334786i	$0.989341\pi$
$380$	1.25297	−	1.75510i	0.0642758	−	0.0900347i
$381$		0			0
$382$	−13.2870	−	25.8110i	−0.679821	−	1.32061i
$383$	−12.3689			−0.632020			−0.316010	−	0.948756i	$-0.602343\pi$
$383$	−12.3689			−0.632020			−0.316010	+	0.948756i	$0.602343\pi$
$384$		0			0
$385$	−7.03121			−0.358344
$386$	12.0796	+	23.4655i	0.614834	+	1.19436i
$387$		0			0
$388$	11.1095	−	15.5617i	0.564001	−	0.790028i
$389$		−	9.18330i		−	0.465612i	−0.972523	−	0.232806i	$-0.925209\pi$
$389$		−	9.18330i		−	0.465612i	0.972523	−	0.232806i	$-0.0747907\pi$
$390$		0			0
$391$		−	2.14223i		−	0.108337i
$392$	−11.3350	−	1.65047i	−0.572502	−	0.0833612i
$393$		0			0
$394$	−18.7144	+	9.63377i	−0.942816	+	0.485342i
$395$	−8.74329			−0.439923
$396$		0			0
$397$	−20.4486			−1.02629			−0.513143	−	0.858303i	$-0.671519\pi$
$397$	−20.4486			−1.02629			−0.513143	+	0.858303i	$0.671519\pi$
$398$	29.5480	−	15.2107i	1.48111	−	0.762445i
$399$		0			0
$400$	−4.98571	−	14.5174i	−0.249285	−	0.725872i
$401$		−	20.3860i		−	1.01803i	−0.860758	−	0.509014i	$-0.830010\pi$
$401$		−	20.3860i		−	1.01803i	0.860758	−	0.509014i	$-0.169990\pi$
$402$		0			0
$403$		−	39.3772i		−	1.96152i
$404$	0.891790	+	0.636648i	0.0443682	+	0.0316744i
$405$		0			0
$406$	22.1329	+	42.9950i	1.09844	+	2.13381i
$407$	−9.24535			−0.458275
$408$		0			0
$409$	18.0275			0.891403			0.445701	−	0.895182i	$-0.352954\pi$
$409$	18.0275			0.891403			0.445701	+	0.895182i	$0.352954\pi$
$410$	−1.70322	−	3.30864i	−0.0841161	−	0.163402i
$411$		0			0
$412$	−20.7089	−	14.7841i	−1.02025	−	0.728359i
$413$		−	41.3622i		−	2.03530i
$414$		0			0
$415$		−	12.0005i		−	0.589082i
$416$	−21.4252	+	22.3361i	−1.05046	+	1.09512i
$417$		0			0
$418$	−2.46668	+	1.26980i	−0.120649	+	0.0621078i
$419$	−10.0028			−0.488669			−0.244334	−	0.969691i	$-0.578569\pi$
$419$	−10.0028			−0.488669			−0.244334	+	0.969691i	$0.578569\pi$
$420$		0			0
$421$	13.7949			0.672322			0.336161	−	0.941805i	$-0.390871\pi$
$421$	13.7949			0.672322			0.336161	+	0.941805i	$0.390871\pi$
$422$	11.1058	−	5.71702i	0.540620	−	0.278300i
$423$		0			0
$424$	1.59900	−	10.9815i	0.0776544	−	0.533309i
$425$			14.5880i			0.707622i
$426$		0			0
$427$			22.4141i			1.08469i
$428$	6.73005	−	9.42716i	0.325309	−	0.455679i
$429$		0			0
$430$	−8.34833	−	16.2173i	−0.402592	−	0.782067i
$431$	−9.29350			−0.447652			−0.223826	−	0.974629i	$-0.571855\pi$
$431$	−9.29350			−0.447652			−0.223826	+	0.974629i	$0.571855\pi$
$432$		0			0
$433$	7.48297			0.359608			0.179804	−	0.983702i	$-0.442454\pi$
$433$	7.48297			0.359608			0.179804	+	0.983702i	$0.442454\pi$
$434$	15.4853	+	30.0814i	0.743318	+	1.44395i
$435$		0			0
$436$	−16.0249	+	22.4470i	−0.767452	+	1.07501i
$437$		−	0.563522i		−	0.0269569i
$438$		0			0
$439$		−	16.3437i		−	0.780044i	−0.920806	−	0.390022i	$-0.872467\pi$
$439$		−	16.3437i		−	0.780044i	0.920806	−	0.390022i	$-0.127533\pi$
$440$	0.862044	−	5.92028i	0.0410963	−	0.282238i
$441$		0			0
$442$	26.1529	−	13.4630i	1.24397	−	0.640368i
$443$	33.7560			1.60379			0.801897	−	0.597462i	$-0.203824\pi$
$443$	33.7560			1.60379			0.801897	+	0.597462i	$0.203824\pi$
$444$		0			0
$445$	−12.1550			−0.576203
$446$	33.3741	−	17.1803i	1.58031	−	0.813510i
$447$		0			0
$448$	7.58354	−	25.4887i	0.358289	−	1.20423i
$449$			31.3987i			1.48180i	0.671616	+	0.740899i	$0.265600\pi$
$449$			31.3987i			1.48180i	−0.671616	+	0.740899i	$0.734400\pi$
$450$		0			0
$451$			4.78753i			0.225436i
$452$	8.36130	+	5.96912i	0.393282	+	0.280764i
$453$		0			0
$454$	7.63444	+	14.8305i	0.358302	+	0.696030i
$455$	19.6101			0.919338
$456$		0			0
$457$	−27.1757			−1.27123			−0.635613	−	0.772007i	$-0.719253\pi$
$457$	−27.1757			−1.27123			−0.635613	+	0.772007i	$0.719253\pi$
$458$	−4.43186	−	8.60924i	−0.207087	−	0.402283i
$459$		0			0
$460$	0.989038	+	0.706073i	0.0461141	+	0.0329208i
$461$			20.7663i			0.967182i	0.875294	+	0.483591i	$0.160668\pi$
$461$			20.7663i			0.967182i	−0.875294	+	0.483591i	$0.839332\pi$
$462$		0			0
$463$			26.1728i			1.21635i	0.793802	+	0.608177i	$0.208099\pi$
$463$			26.1728i			1.21635i	−0.793802	+	0.608177i	$0.791901\pi$
$464$	−38.9154	+	13.3647i	−1.80660	+	0.620439i
$465$		0			0
$466$	−22.0242	+	11.3376i	−1.02025	+	0.525204i
$467$	−31.1792			−1.44280			−0.721401	−	0.692518i	$-0.756501\pi$
$467$	−31.1792			−1.44280			−0.721401	+	0.692518i	$0.756501\pi$
$468$		0			0
$469$	11.3245			0.522916
$470$	5.94955	−	3.06271i	0.274432	−	0.141272i
$471$		0			0
$472$	34.8270	+	5.07111i	1.60304	+	0.233417i
$473$			23.4661i			1.07897i
$474$		0			0
$475$			3.83743i			0.176073i
$476$	−14.6846	+	20.5695i	−0.673066	+	0.942802i
$477$		0			0
$478$	8.36571	+	16.2510i	0.382639	+	0.743306i
$479$	23.1488			1.05770			0.528848	−	0.848716i	$-0.322624\pi$
$479$	23.1488			1.05770			0.528848	+	0.848716i	$0.322624\pi$
$480$		0			0
$481$	25.7854			1.17571
$482$	7.60187	+	14.7672i	0.346256	+	0.672629i
$483$		0			0
$484$	8.31053	−	11.6410i	0.377752	−	0.529138i
$485$		−	10.3081i		−	0.468065i
$486$		0			0
$487$			24.6821i			1.11845i	0.829015	+	0.559227i	$0.188902\pi$
$487$			24.6821i			1.11845i	−0.829015	+	0.559227i	$0.811098\pi$
$488$	−18.8727	−	2.74802i	−0.854326	−	0.124397i
$489$		0			0
$490$	−5.49049	+	2.82639i	−0.248035	+	0.127684i
$491$	39.6452			1.78916			0.894581	−	0.446905i	$-0.147474\pi$
$491$	39.6452			1.78916			0.894581	+	0.446905i	$0.147474\pi$
$492$		0			0
$493$	39.1045			1.76118
$494$	6.87961	−	3.54148i	0.309528	−	0.159339i
$495$		0			0
$496$	−27.2271	+	9.35057i	−1.22253	+	0.419853i
$497$			1.29729i			0.0581915i
$498$		0			0
$499$		−	16.8060i		−	0.752340i	−0.926551	−	0.376170i	$-0.877241\pi$
$499$		−	16.8060i		−	0.752340i	0.926551	−	0.376170i	$-0.122759\pi$
$500$	−15.5106	−	11.0730i	−0.693654	−	0.495199i
$501$		0			0
$502$	11.2111	+	21.7784i	0.500374	+	0.972015i
$503$	9.42278			0.420141			0.210070	−	0.977686i	$-0.432631\pi$
$503$	9.42278			0.420141			0.210070	+	0.977686i	$0.432631\pi$
$504$		0			0
$505$	0.590720			0.0262867
$506$	−0.715558	−	1.39003i	−0.0318105	−	0.0617943i
$507$		0			0
$508$	6.51903	+	4.65394i	0.289235	+	0.206485i
$509$			33.7698i			1.49682i	0.663236	+	0.748410i	$0.269183\pi$
$509$			33.7698i			1.49682i	−0.663236	+	0.748410i	$0.730817\pi$
$510$		0			0
$511$		−	20.3088i		−	0.898408i
$512$	20.5318	+	9.51033i	0.907385	+	0.420301i
$513$		0			0
$514$	24.6404	−	12.6844i	1.08684	−	0.559483i
$515$	−13.7175			−0.604467
$516$		0			0
$517$	−8.60887			−0.378618
$518$	−19.6982	+	10.1403i	−0.865491	+	0.445537i
$519$		0			0
$520$	−2.40425	+	16.5118i	−0.105434	+	0.724088i
$521$			6.21098i			0.272108i	0.990701	+	0.136054i	$0.0434420\pi$
$521$			6.21098i			0.272108i	−0.990701	+	0.136054i	$0.956558\pi$
$522$		0			0
$523$		−	4.62567i		−	0.202267i	−0.994873	−	0.101133i	$-0.967753\pi$
$523$		−	4.62567i		−	0.202267i	0.994873	−	0.101133i	$-0.0322468\pi$
$524$	−22.0070	+	30.8265i	−0.961382	+	1.34666i
$525$		0			0
$526$	−13.0328	−	25.3173i	−0.568257	−	1.10388i
$527$	27.3594			1.19180
$528$		0			0
$529$	−22.6824			−0.986193
$530$	−2.73826	−	5.31929i	−0.118942	−	0.231055i
$531$		0			0
$532$	−3.86283	+	5.41088i	−0.167475	+	0.234592i
$533$		−	13.3525i		−	0.578361i
$534$		0			0
$535$		−	6.24453i		−	0.269975i
$536$	−1.38841	+	9.53522i	−0.0599702	+	0.411859i
$537$		0			0
$538$	−14.7374	+	7.58652i	−0.635375	+	0.327078i
$539$	7.94463			0.342200
$540$		0			0
$541$	45.8653			1.97191			0.985953	−	0.167025i	$-0.0534161\pi$
$541$	45.8653			1.97191			0.985953	+	0.167025i	$0.0534161\pi$
$542$	−17.7373	+	9.13082i	−0.761884	+	0.392202i
$543$		0			0
$544$	−15.5192	−	14.8863i	−0.665380	−	0.638245i
$545$			14.8688i			0.636910i
$546$		0			0
$547$		−	0.755289i		−	0.0322938i	−0.999870	−	0.0161469i	$-0.994860\pi$
$547$		−	0.755289i		−	0.0322938i	0.999870	−	0.0161469i	$-0.00513995\pi$
$548$	−2.57016	−	1.83484i	−0.109792	−	0.0783804i
$549$		0			0
$550$	4.87275	+	9.46570i	0.207775	+	0.403619i
$551$	10.2866			0.438223
$552$		0			0
$553$	26.9551			1.14625
$554$	−9.18759	−	17.8476i	−0.390343	−	0.758272i
$555$		0			0
$556$	1.78545	+	1.27463i	0.0757198	+	0.0540563i
$557$			12.3000i			0.521169i	0.965451	+	0.260585i	$0.0839153\pi$
$557$			12.3000i			0.521169i	−0.965451	+	0.260585i	$0.916085\pi$
$558$		0			0
$559$		−	65.4473i		−	2.76812i
$560$	−4.65665	−	13.5593i	−0.196780	−	0.572985i
$561$		0			0
$562$	−29.9877	+	15.4371i	−1.26496	+	0.651174i
$563$	−36.3248			−1.53091			−0.765455	−	0.643490i	$-0.777486\pi$
$563$	−36.3248			−1.53091			−0.765455	+	0.643490i	$0.777486\pi$
$564$		0			0
$565$	5.53850			0.233007
$566$	17.9105	−	9.21996i	0.752834	−	0.387544i
$567$		0			0
$568$	−1.09232	−	0.159051i	−0.0458328	−	0.00667364i
$569$			42.8218i			1.79518i	0.440829	+	0.897591i	$0.354685\pi$
$569$			42.8218i			1.79518i	−0.440829	+	0.897591i	$0.645315\pi$
$570$		0			0
$571$			6.91400i			0.289342i	0.989480	+	0.144671i	$0.0462124\pi$
$571$			6.91400i			0.289342i	−0.989480	+	0.144671i	$0.953788\pi$
$572$	12.4728	−	17.4714i	0.521515	−	0.730516i
$573$		0			0
$574$	5.25094	+	10.2004i	0.219170	+	0.425755i
$575$	−2.16247			−0.0901814
$576$		0			0
$577$	−32.8663			−1.36824			−0.684121	−	0.729369i	$-0.739814\pi$
$577$	−32.8663			−1.36824			−0.684121	+	0.729369i	$0.739814\pi$
$578$	−1.64961	−	3.20450i	−0.0686149	−	0.133290i
$579$		0			0
$580$	−12.8887	+	18.0540i	−0.535175	+	0.749651i
$581$			36.9969i			1.53489i
$582$		0			0
$583$			7.69690i			0.318773i
$584$	17.1000	+	2.48991i	0.707604	+	0.103033i
$585$		0			0
$586$	−16.2252	+	8.35238i	−0.670255	+	0.345034i
$587$	−36.3279			−1.49941			−0.749707	−	0.661770i	$-0.769806\pi$
$587$	−36.3279			−1.49941			−0.749707	+	0.661770i	$0.769806\pi$
$588$		0			0
$589$	7.19699			0.296547
$590$	16.8697	−	8.68417i	0.694514	−	0.357522i
$591$		0			0
$592$	−6.12305	−	17.8292i	−0.251656	−	0.732774i
$593$		−	7.98112i		−	0.327745i	−0.986481	−	0.163873i	$-0.947601\pi$
$593$		−	7.98112i		−	0.327745i	0.986481	−	0.163873i	$-0.0523986\pi$
$594$		0			0
$595$			13.6252i			0.558579i
$596$	5.92361	+	4.22886i	0.242640	+	0.173221i
$597$		0			0
$598$	1.99570	+	3.87681i	0.0816104	+	0.158535i
$599$	44.9807			1.83786			0.918932	−	0.394417i	$-0.129053\pi$
$599$	44.9807			1.83786			0.918932	+	0.394417i	$0.129053\pi$
$600$		0			0
$601$	20.6878			0.843874			0.421937	−	0.906625i	$-0.361350\pi$
$601$	20.6878			0.843874			0.421937	+	0.906625i	$0.361350\pi$
$602$	25.7375	+	49.9971i	1.04898	+	2.03773i
$603$		0			0
$604$	−22.6745	−	16.1873i	−0.922612	−	0.658652i
$605$		−	7.71100i		−	0.313497i
$606$		0			0
$607$			20.7915i			0.843900i	0.906619	+	0.421950i	$0.138654\pi$
$607$			20.7915i			0.843900i	−0.906619	+	0.421950i	$0.861346\pi$
$608$	−4.08238	−	3.91589i	−0.165562	−	0.158810i
$609$		0			0
$610$	−9.14165	+	4.70594i	−0.370135	+	0.190538i
$611$	24.0103			0.971352
$612$		0			0
$613$	−19.5535			−0.789760			−0.394880	−	0.918733i	$-0.629214\pi$
$613$	−19.5535			−0.789760			−0.394880	+	0.918733i	$0.629214\pi$
$614$	15.0432	−	7.74395i	0.607095	−	0.312520i
$615$		0			0
$616$	−2.65764	+	18.2519i	−0.107079	+	0.735391i
$617$			11.2359i			0.452341i	0.974088	+	0.226171i	$0.0726207\pi$
$617$			11.2359i			0.452341i	−0.974088	+	0.226171i	$0.927379\pi$
$618$		0			0
$619$		−	6.49897i		−	0.261216i	−0.991434	−	0.130608i	$-0.958307\pi$
$619$		−	6.49897i		−	0.261216i	0.991434	−	0.130608i	$-0.0416929\pi$
$620$	−9.01758	+	12.6314i	−0.362155	+	0.507291i
$621$		0			0
$622$	−4.33252	−	8.41627i	−0.173718	−	0.337462i
$623$	37.4733			1.50134
$624$		0			0
$625$	8.91296			0.356518
$626$	−18.0637	−	35.0901i	−0.721969	−	1.40248i
$627$		0			0
$628$	7.57859	−	10.6158i	0.302419	−	0.423615i
$629$			17.9158i			0.714351i
$630$		0			0
$631$			23.9091i			0.951805i	0.879498	+	0.475902i	$0.157878\pi$
$631$			23.9091i			0.951805i	−0.879498	+	0.475902i	$0.842122\pi$
$632$	−3.30477	+	22.6962i	−0.131457	+	0.902808i
$633$		0			0
$634$	18.3593	−	9.45097i	0.729139	−	0.375346i
$635$	4.31819			0.171362
$636$		0			0
$637$	−22.1577			−0.877920
$638$	25.3737	−	13.0619i	1.00455	−	0.517124i
$639$		0			0
$640$	11.9879	−	2.25850i	0.473862	−	0.0892751i
$641$			38.3200i			1.51355i	0.653675	+	0.756775i	$0.273226\pi$
$641$			38.3200i			1.51355i	−0.653675	+	0.756775i	$0.726774\pi$
$642$		0			0
$643$		−	42.5273i		−	1.67711i	−0.544814	−	0.838557i	$-0.683400\pi$
$643$		−	42.5273i		−	1.67711i	0.544814	−	0.838557i	$-0.316600\pi$
$644$	−3.04915	−	2.17679i	−0.120153	−	0.0857775i
$645$		0			0
$646$	2.46064	+	4.77998i	0.0968124	+	0.188066i
$647$	−5.85813			−0.230307			−0.115153	−	0.993348i	$-0.536736\pi$
$647$	−5.85813			−0.230307			−0.115153	+	0.993348i	$0.536736\pi$
$648$		0			0
$649$	−24.4101			−0.958179
$650$	−13.5902	−	26.4000i	−0.533050	−	1.03549i
$651$		0			0
$652$	6.86366	+	4.89997i	0.268802	+	0.191897i
$653$		−	47.2139i		−	1.84762i	−0.382847	−	0.923812i	$-0.625056\pi$
$653$		−	47.2139i		−	1.84762i	0.382847	−	0.923812i	$-0.374944\pi$
$654$		0			0
$655$			20.4194i			0.797853i
$656$	−9.23250	+	3.17071i	−0.360468	+	0.123795i
$657$		0			0
$658$	−18.3422	+	9.44217i	−0.715052	+	0.368094i
$659$	−10.3713			−0.404009			−0.202004	−	0.979385i	$-0.564746\pi$
$659$	−10.3713			−0.404009			−0.202004	+	0.979385i	$0.564746\pi$
$660$		0			0
$661$	−6.14135			−0.238871			−0.119435	−	0.992842i	$-0.538108\pi$
$661$	−6.14135			−0.238871			−0.119435	+	0.992842i	$0.538108\pi$
$662$	8.30197	−	4.27369i	0.322665	−	0.166102i
$663$		0			0
$664$	−31.1515	−	4.53592i	−1.20891	−	0.176028i
$665$			3.58416i			0.138988i
$666$		0			0
$667$			5.79671i			0.224450i
$668$	−20.7983	+	29.1334i	−0.804710	+	1.12720i
$669$		0			0
$670$	2.37763	+	4.61872i	0.0918557	+	0.178437i
$671$	13.2278			0.510653
$672$		0			0
$673$	−20.2087			−0.778986			−0.389493	−	0.921029i	$-0.627350\pi$
$673$	−20.2087			−0.778986			−0.389493	+	0.921029i	$0.627350\pi$
$674$	−8.46706	−	16.4479i	−0.326139	−	0.633551i
$675$		0			0
$676$	−19.6801	+	27.5671i	−0.756928	+	1.06027i
$677$			12.3735i			0.475551i	0.971320	+	0.237776i	$0.0764183\pi$
$677$			12.3735i			0.475551i	−0.971320	+	0.237776i	$0.923582\pi$
$678$		0			0
$679$			31.7792i			1.21958i
$680$	−11.4724	−	1.67049i	−0.439948	−	0.0640602i
$681$		0			0
$682$	17.7527	−	9.13872i	0.679785	−	0.349940i
$683$	9.84657			0.376769			0.188384	−	0.982095i	$-0.439675\pi$
$683$	9.84657			0.376769			0.188384	+	0.982095i	$0.439675\pi$
$684$		0			0
$685$	−1.70247			−0.0650481
$686$	−12.3311	+	6.34780i	−0.470804	+	0.242360i
$687$		0			0
$688$	−45.2531	+	15.5412i	−1.72526	+	0.592503i
$689$		−	21.4668i		−	0.817818i
$690$		0			0
$691$		−	43.1590i		−	1.64185i	−0.571040	−	0.820923i	$-0.693460\pi$
$691$		−	43.1590i		−	1.64185i	0.571040	−	0.820923i	$-0.306540\pi$
$692$	−18.7879	−	13.4127i	−0.714210	−	0.509874i
$693$		0			0
$694$	6.19155	+	12.0276i	0.235028	+	0.456561i
$695$	1.18268			0.0448614
$696$		0			0
$697$	9.27737			0.351406
$698$	9.32673	+	18.1179i	0.353022	+	0.685773i
$699$		0			0
$700$	20.7639	+	14.8233i	0.784800	+	0.560269i
$701$		−	30.9785i		−	1.17004i	−0.811019	−	0.585020i	$-0.801087\pi$
$701$		−	30.9785i		−	1.17004i	0.811019	−	0.585020i	$-0.198913\pi$
$702$		0			0
$703$			4.71282i			0.177747i
$704$	−15.0423	−	4.47547i	−0.566928	−	0.168675i
$705$		0			0
$706$	−13.0382	+	6.71181i	−0.490700	+	0.252602i
$707$	−1.82116			−0.0684917
$708$		0			0
$709$	−23.6140			−0.886841			−0.443420	−	0.896314i	$-0.646235\pi$
$709$	−23.6140			−0.886841			−0.443420	+	0.896314i	$0.646235\pi$
$710$	−0.529105	+	0.272372i	−0.0198569	+	0.0102219i
$711$		0			0
$712$	−4.59432	+	31.5526i	−0.172180	+	1.18248i
$713$			4.05566i			0.151886i
$714$		0			0
$715$		−	11.5730i		−	0.432807i
$716$	27.8126	−	38.9587i	1.03941	−	1.45595i
$717$		0			0
$718$	15.8653	+	30.8195i	0.592086	+	1.15017i
$719$	26.8975			1.00311			0.501554	−	0.865126i	$-0.332762\pi$
$719$	26.8975			1.00311			0.501554	+	0.865126i	$0.332762\pi$
$720$		0			0
$721$	42.2905			1.57498
$722$	0.647279	+	1.25739i	0.0240892	+	0.0467952i
$723$		0			0
$724$	14.2564	−	19.9697i	0.529833	−	0.742168i
$725$		−	39.4740i		−	1.46603i
$726$		0			0
$727$			34.8029i			1.29077i	0.763859	+	0.645383i	$0.223302\pi$
$727$			34.8029i			1.29077i	−0.763859	+	0.645383i	$0.776698\pi$
$728$	7.41219	−	50.9049i	0.274714	−	1.88666i
$729$		0			0
$730$	8.28300	−	4.26392i	0.306568	−	0.157815i
$731$	45.4730			1.68188
$732$		0			0
$733$	−17.7355			−0.655075			−0.327537	−	0.944838i	$-0.606219\pi$
$733$	−17.7355			−0.655075			−0.327537	+	0.944838i	$0.606219\pi$
$734$	−0.369483	+	0.190202i	−0.0136379	+	0.00702050i
$735$		0			0
$736$	2.20669	−	2.30051i	0.0813397	−	0.0847979i
$737$		−	6.68320i		−	0.246179i
$738$		0			0
$739$			20.4077i			0.750710i	0.926881	+	0.375355i	$0.122479\pi$
$739$			20.4077i			0.750710i	−0.926881	+	0.375355i	$0.877521\pi$
$740$	−8.27147	−	5.90500i	−0.304065	−	0.217072i
$741$		0			0
$742$	8.44191	+	16.3991i	0.309912	+	0.602029i
$743$	−16.0882			−0.590219			−0.295110	−	0.955463i	$-0.595356\pi$
$743$	−16.0882			−0.590219			−0.295110	+	0.955463i	$0.595356\pi$
$744$		0			0
$745$	3.92379			0.143756
$746$	21.7021	+	42.1580i	0.794570	+	1.54351i
$747$		0			0
$748$	12.1392	+	8.66617i	0.443853	+	0.316867i
$749$			19.2516i			0.703437i
$750$		0			0
$751$		−	51.9976i		−	1.89742i	−0.316148	−	0.948710i	$-0.602389\pi$
$751$		−	51.9976i		−	1.89742i	0.316148	−	0.948710i	$-0.397611\pi$
$752$	−5.70152	−	16.6017i	−0.207913	−	0.605403i
$753$		0			0
$754$	−70.7676	+	36.4297i	−2.57721	+	1.32669i
$755$	−15.0195			−0.546617
$756$		0			0
$757$	7.09089			0.257723			0.128861	−	0.991663i	$-0.458868\pi$
$757$	7.09089			0.257723			0.128861	+	0.991663i	$0.458868\pi$
$758$	1.63903	−	0.843740i	0.0595323	−	0.0306460i
$759$		0			0
$760$	−3.01786	−	0.439427i	−0.109469	−	0.0159397i
$761$		−	37.6919i		−	1.36633i	−0.730264	−	0.683165i	$-0.760603\pi$
$761$		−	37.6919i		−	1.36633i	0.730264	−	0.683165i	$-0.239397\pi$
$762$		0			0
$763$		−	45.8398i		−	1.65951i
$764$	−23.8541	+	33.4138i	−0.863012	+	1.20887i
$765$		0			0
$766$	8.00611	+	15.5525i	0.289273	+	0.561935i
$767$	68.0801			2.45823
$768$		0			0
$769$	10.3608			0.373619			0.186810	−	0.982396i	$-0.440185\pi$
$769$	10.3608			0.373619			0.186810	+	0.982396i	$0.440185\pi$
$770$	4.55115	+	8.84097i	0.164012	+	0.318607i
$771$		0			0
$772$	21.6865	−	30.3775i	0.780513	−	1.09331i
$773$			30.3425i			1.09134i	0.837999	+	0.545672i	$0.183725\pi$
$773$			30.3425i			1.09134i	−0.837999	+	0.545672i	$0.816275\pi$
$774$		0			0
$775$		−	27.6179i		−	0.992065i
$776$	−26.7581	−	3.89622i	−0.960561	−	0.139866i
$777$		0			0
$778$	−11.5470	+	5.94416i	−0.413980	+	0.213108i
$779$	2.44045			0.0874380
$780$		0			0
$781$	0.765603			0.0273954
$782$	−2.69362	+	1.38662i	−0.0963238	+	0.0495855i
$783$		0			0
$784$	5.26160	+	15.3208i	0.187914	+	0.547171i
$785$		−	7.03186i		−	0.250978i
$786$		0			0
$787$		−	47.3060i		−	1.68628i	−0.537698	−	0.843138i	$-0.680706\pi$
$787$		−	47.3060i		−	1.68628i	0.537698	−	0.843138i	$-0.319294\pi$
$788$	24.2268	+	17.2955i	0.863045	+	0.616127i
$789$		0			0
$790$	5.65935	+	10.9937i	0.201351	+	0.391139i
$791$	−17.0749			−0.607114
$792$		0			0
$793$	−36.8925			−1.31009
$794$	13.2359	+	25.7119i	0.469726	+	0.912480i
$795$		0			0
$796$	−38.2517	−	27.3078i	−1.35579	−	0.967901i
$797$		−	20.8231i		−	0.737591i	−0.929511	−	0.368795i	$-0.879770\pi$
$797$		−	20.8231i		−	0.737591i	0.929511	−	0.368795i	$-0.120230\pi$
$798$		0			0
$799$			16.6824i			0.590182i
$800$	−15.0269	+	15.6658i	−0.531283	+	0.553870i
$801$		0			0
$802$	−25.6332	+	13.1954i	−0.905138	+	0.465947i
$803$	−11.9853			−0.422953
$804$		0			0
$805$	−2.01975			−0.0711869
$806$	−49.5125	+	25.4880i	−1.74400	+	0.897777i
$807$		0			0
$808$	0.223279	−	1.53342i	0.00785492	−	0.0539454i
$809$			31.9587i			1.12361i	0.827270	+	0.561804i	$0.189893\pi$
$809$			31.9587i			1.12361i	−0.827270	+	0.561804i	$0.810107\pi$
$810$		0			0
$811$		−	38.1734i		−	1.34045i	−0.742159	−	0.670224i	$-0.766198\pi$
$811$		−	38.1734i		−	1.34045i	0.742159	−	0.670224i	$-0.233802\pi$
$812$	39.7353	−	55.6595i	1.39444	−	1.95327i
$813$		0			0
$814$	5.98432	+	11.6250i	0.209750	+	0.407457i
$815$	4.54648			0.159256
$816$		0			0
$817$	11.9618			0.418492
$818$	−11.6688	−	22.6676i	−0.407991	−	0.792554i
$819$		0			0
$820$	−3.05779	+	4.28323i	−0.106783	+	0.149577i
$821$			52.2726i			1.82433i	0.409827	+	0.912163i	$0.365589\pi$
$821$			52.2726i			1.82433i	−0.409827	+	0.912163i	$0.634411\pi$
$822$		0			0
$823$		−	11.6243i		−	0.405198i	−0.979262	−	0.202599i	$-0.935061\pi$
$823$		−	11.6243i		−	0.405198i	0.979262	−	0.202599i	$-0.0649387\pi$
$824$	−5.18492	+	35.6086i	−0.180625	+	1.24048i
$825$		0			0
$826$	−52.0084	+	26.7728i	−1.80960	+	0.931546i
$827$	−25.0618			−0.871485			−0.435742	−	0.900071i	$-0.643514\pi$
$827$	−25.0618			−0.871485			−0.435742	+	0.900071i	$0.643514\pi$
$828$		0			0
$829$	38.6763			1.34328			0.671642	−	0.740875i	$-0.265589\pi$
$829$	38.6763			1.34328			0.671642	+	0.740875i	$0.265589\pi$
$830$	−15.0893	+	7.76767i	−0.523758	+	0.269620i
$831$		0			0
$832$	41.9532	+	12.4821i	1.45447	+	0.432740i
$833$		−	15.3953i		−	0.533414i
$834$		0			0
$835$			19.2979i			0.667831i
$836$	3.19326	+	2.27967i	0.110441	+	0.0788439i
$837$		0			0
$838$	6.47460	+	12.5774i	0.223661	+	0.434480i
$839$	10.7634			0.371592			0.185796	−	0.982588i	$-0.440514\pi$
$839$	10.7634			0.371592			0.185796	+	0.982588i	$0.440514\pi$
$840$		0			0
$841$	−76.8138			−2.64875
$842$	−8.92914	−	17.3456i	−0.307719	−	0.597767i
$843$		0			0
$844$	−14.3771	−	10.2638i	−0.494879	−	0.353294i
$845$			18.2604i			0.628176i
$846$		0			0
$847$			23.7726i			0.816837i
$848$	−14.8430	+	5.09753i	−0.509712	+	0.175050i
$849$		0			0
$850$	18.3428	−	9.44251i	0.629153	−	0.323875i
$851$	−2.65578			−0.0910389
$852$		0			0
$853$	44.6869			1.53005			0.765025	−	0.644000i	$-0.222726\pi$
$853$	44.6869			1.53005			0.765025	+	0.644000i	$0.222726\pi$
$854$	28.1833	−	14.5082i	0.964411	−	0.496459i
$855$		0			0
$856$	−16.2098	−	2.36029i	−0.554041	−	0.0806731i
$857$			33.1559i			1.13258i	0.824205	+	0.566292i	$0.191622\pi$
$857$			33.1559i			1.13258i	−0.824205	+	0.566292i	$0.808378\pi$
$858$		0			0
$859$		−	1.48402i		−	0.0506342i	−0.999679	−	0.0253171i	$-0.991940\pi$
$859$		−	1.48402i		−	0.0506342i	0.999679	−	0.0253171i	$-0.00805955\pi$
$860$	−14.9878	+	20.9942i	−0.511079	+	0.715897i
$861$		0			0
$862$	6.01549	+	11.6856i	0.204888	+	0.398012i
$863$	−52.7184			−1.79456			−0.897278	−	0.441466i	$-0.854458\pi$
$863$	−52.7184			−1.79456			−0.897278	+	0.441466i	$0.854458\pi$
$864$		0			0
$865$	−12.4451			−0.423146
$866$	−4.84357	−	9.40901i	−0.164591	−	0.319731i
$867$		0			0
$868$	27.8007	−	38.9421i	0.943619	−	1.32178i
$869$		−	15.9077i		−	0.539632i
$870$		0			0
$871$			18.6395i			0.631577i
$872$	38.5971	+	5.62008i	1.30706	+	0.190320i
$873$		0			0
$874$	−0.708567	+	0.364756i	−0.0239676	+	0.0123381i
$875$	31.6747			1.07080
$876$		0			0
$877$	−12.3112			−0.415718			−0.207859	−	0.978159i	$-0.566650\pi$
$877$	−12.3112			−0.415718			−0.207859	+	0.978159i	$0.566650\pi$
$878$	−20.5504	+	10.5790i	−0.693544	+	0.357022i
$879$		0			0
$880$	−8.00209	+	2.74815i	−0.269750	+	0.0926400i
$881$			9.90718i			0.333781i	0.985975	+	0.166891i	$0.0533727\pi$
$881$			9.90718i			0.333781i	−0.985975	+	0.166891i	$0.946627\pi$
$882$		0			0
$883$		−	18.0076i		−	0.606006i	−0.952990	−	0.303003i	$-0.902011\pi$
$883$		−	18.0076i		−	0.606006i	0.952990	−	0.303003i	$-0.0979891\pi$
$884$	−33.8564	−	24.1701i	−1.13871	−	0.812928i
$885$		0			0
$886$	−21.8495	−	42.4444i	−0.734049	−	1.42595i
$887$	17.2920			0.580608			0.290304	−	0.956935i	$-0.406244\pi$
$887$	17.2920			0.580608			0.290304	+	0.956935i	$0.406244\pi$
$888$		0			0
$889$	−13.3128			−0.446496
$890$	7.86769	+	15.2836i	0.263726	+	0.512308i
$891$		0			0
$892$	−43.2046	−	30.8438i	−1.44660	−	1.03273i
$893$			4.38837i			0.146851i
$894$		0			0
$895$		−	25.8062i		−	0.862605i
$896$	−36.9580	+	6.96284i	−1.23468	+	0.232612i
$897$		0			0
$898$	39.4805	−	20.3237i	1.31748	−	0.678212i
$899$	−74.0325			−2.46912
$900$		0			0
$901$	14.9152			0.496897
$902$	6.01980	−	3.09887i	0.200437	−	0.103181i
$903$		0			0
$904$	2.09343	−	14.3771i	0.0696264	−	0.478175i
$905$		−	13.2279i		−	0.439710i
$906$		0			0
$907$			14.6923i			0.487851i	0.969794	+	0.243925i	$0.0784352\pi$
$907$			14.6923i			0.487851i	−0.969794	+	0.243925i	$0.921565\pi$
$908$	13.7061	−	19.1990i	0.454854	−	0.637140i
$909$		0			0
$910$	−12.6932	−	24.6576i	−0.420777	−	0.817392i
$911$	−37.4076			−1.23937			−0.619684	−	0.784851i	$-0.712739\pi$
$911$	−37.4076			−1.23937			−0.619684	+	0.784851i	$0.712739\pi$
$912$		0			0
$913$	21.8339			0.722598
$914$	17.5903	+	34.1705i	0.581835	+	1.13026i
$915$		0			0
$916$	−7.95652	+	11.1452i	−0.262891	+	0.368246i
$917$		−	62.9520i		−	2.07886i
$918$		0			0
$919$		−	8.25183i		−	0.272203i	−0.990695	−	0.136101i	$-0.956543\pi$
$919$		−	8.25183i		−	0.272203i	0.990695	−	0.136101i	$-0.0434573\pi$
$920$	0.247627	−	1.70063i	0.00816401	−	0.0560682i
$921$		0			0
$922$	26.1113	−	13.4416i	0.859930	−	0.442675i
$923$	−2.13528			−0.0702836
$924$		0			0
$925$	18.0851			0.594634
$926$	32.9094	−	16.9411i	1.08147	−	0.556719i
$927$		0			0
$928$	41.9937	+	40.2811i	1.37851	+	1.32229i
$929$			5.56369i			0.182539i	0.995826	+	0.0912694i	$0.0290924\pi$
$929$			5.56369i			0.182539i	−0.995826	+	0.0912694i	$0.970908\pi$
$930$		0			0
$931$		−	4.04978i		−	0.132726i
$932$	28.5116	+	20.3544i	0.933928	+	0.666731i
$933$		0			0
$934$	20.1816	+	39.2044i	0.660363	+	1.28281i
$935$	8.04098			0.262968
$936$		0			0
$937$	38.9005			1.27082			0.635411	−	0.772174i	$-0.280831\pi$
$937$	38.9005			1.27082			0.635411	+	0.772174i	$0.280831\pi$
$938$	−7.33010	−	14.2393i	−0.239336	−	0.464929i
$939$		0			0
$940$	−7.70203	−	5.49848i	−0.251213	−	0.179341i
$941$			2.70718i			0.0882516i	0.999026	+	0.0441258i	$0.0140502\pi$
$941$			2.70718i			0.0882516i	−0.999026	+	0.0441258i	$0.985950\pi$
$942$		0			0
$943$			1.37524i			0.0447841i
$944$	−16.1664	−	47.0735i	−0.526171	−	1.53211i
$945$		0			0
$946$	29.5060	−	15.1891i	0.959324	−	0.493840i
$947$	−21.7767			−0.707648			−0.353824	−	0.935312i	$-0.615119\pi$
$947$	−21.7767			−0.707648			−0.353824	+	0.935312i	$0.615119\pi$
$948$		0			0
$949$	33.4273			1.08509
$950$	4.82514	−	2.48388i	0.156548	−	0.0805878i
$951$		0			0
$952$	35.3689	+	5.15002i	1.14631	+	0.166913i
$953$		−	33.7212i		−	1.09234i	−0.837676	−	0.546168i	$-0.816086\pi$
$953$		−	33.7212i		−	1.09234i	0.837676	−	0.546168i	$-0.183914\pi$
$954$		0			0
$955$			22.1333i			0.716215i
$956$	15.0190	−	21.0379i	0.485748	−	0.680415i
$957$		0			0
$958$	−14.9837	−	29.1071i	−0.484103	−	0.940408i
$959$	5.24863			0.169487
$960$		0			0
$961$	−20.7967			−0.670862
$962$	−16.6904	−	32.4223i	−0.538119	−	1.04534i
$963$		0			0
$964$	13.6476	−	19.1170i	0.439561	−	0.615718i
$965$		−	20.1220i		−	0.647749i
$966$		0			0
$967$			32.3424i			1.04006i	0.854147	+	0.520031i	$0.174080\pi$
$967$			32.3424i			1.04006i	−0.854147	+	0.520031i	$0.825920\pi$
$968$	−20.0166	−	2.91458i	−0.643357	−	0.0936783i
$969$		0			0
$970$	−12.9613	+	6.67219i	−0.416161	+	0.214231i
$971$	36.3523			1.16660			0.583301	−	0.812256i	$-0.301761\pi$
$971$	36.3523			1.16660			0.583301	+	0.812256i	$0.301761\pi$
$972$		0			0
$973$	−3.64613			−0.116889
$974$	31.0351	−	15.9762i	0.994428	−	0.511911i
$975$		0			0
$976$	8.76055	+	25.5091i	0.280418	+	0.816525i
$977$			31.0762i			0.994215i	0.867689	+	0.497107i	$0.165604\pi$
$977$			31.0762i			0.994215i	−0.867689	+	0.497107i	$0.834396\pi$
$978$		0			0
$979$		−	22.1151i		−	0.706800i
$980$	7.10776	+	5.07423i	0.227049	+	0.162090i
$981$		0			0
$982$	−25.6615	−	49.8495i	−0.818891	−	1.59076i
$983$	1.99707			0.0636967			0.0318483	−	0.999493i	$-0.489861\pi$
$983$	1.99707			0.0636967			0.0318483	+	0.999493i	$0.489861\pi$
$984$		0			0
$985$	16.0478			0.511325
$986$	−25.3115	−	49.1696i	−0.806083	−	1.56588i
$987$		0			0
$988$	−8.90605	−	6.35802i	−0.283339	−	0.202276i
$989$			6.74076i			0.214344i
$990$		0			0
$991$		−	27.4432i		−	0.871762i	−0.900004	−	0.435881i	$-0.856437\pi$
$991$		−	27.4432i		−	0.871762i	0.900004	−	0.435881i	$-0.143563\pi$
$992$	29.3808	+	28.1827i	0.932842	+	0.894800i
$993$		0			0
$994$	1.63120	−	0.839710i	0.0517386	−	0.0266340i
$995$	−25.3378			−0.803263
$996$		0			0
$997$	22.3996			0.709401			0.354701	−	0.934980i	$-0.384583\pi$
$997$	22.3996			0.709401			0.354701	+	0.934980i	$0.384583\pi$
$998$	−21.1317	+	10.8782i	−0.668912	+	0.344342i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.c.b.647.13	✓	32
3.2	odd	2	inner	684.2.c.b.647.20	yes	32
4.3	odd	2	inner	684.2.c.b.647.19	yes	32
12.11	even	2	inner	684.2.c.b.647.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.c.b.647.13	✓	32	1.1	even	1	trivial
684.2.c.b.647.14	yes	32	12.11	even	2	inner
684.2.c.b.647.19	yes	32	4.3	odd	2	inner
684.2.c.b.647.20	yes	32	3.2	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.647279 - 1.25739i) q^{2} +(-1.16206 + 1.62776i) q^{4} +1.07823i q^{5} -3.32412i q^{7} +(2.79891 + 0.407546i) q^{8} +(1.35575 - 0.697914i) q^{10} -1.96175 q^{11} +5.47134 q^{13} +(-4.17972 + 2.15163i) q^{14} +(-1.29923 - 3.78312i) q^{16} +3.80151i q^{17} +1.00000i q^{19} +(-1.75510 - 1.25297i) q^{20} +(1.26980 + 2.46668i) q^{22} -0.563522 q^{23} +3.83743 q^{25} +(-3.54148 - 6.87961i) q^{26} +(5.41088 + 3.86283i) q^{28} -10.2866i q^{29} -7.19699i q^{31} +(-3.91589 + 4.08238i) q^{32} +(4.77998 - 2.46064i) q^{34} +3.58416 q^{35} +4.71282 q^{37} +(1.25739 - 0.647279i) q^{38} +(-0.439427 + 3.01786i) q^{40} -2.44045i q^{41} -11.9618i q^{43} +(2.27967 - 3.19326i) q^{44} +(0.364756 + 0.708567i) q^{46} +4.38837 q^{47} -4.04978 q^{49} +(-2.48388 - 4.82514i) q^{50} +(-6.35802 + 8.90605i) q^{52} -3.92349i q^{53} -2.11521i q^{55} +(1.35473 - 9.30392i) q^{56} +(-12.9342 + 6.65829i) q^{58} +12.4430 q^{59} -6.74286 q^{61} +(-9.04943 + 4.65846i) q^{62} +(7.66781 + 2.28137i) q^{64} +5.89935i q^{65} +3.40676i q^{67} +(-6.18796 - 4.41758i) q^{68} +(-2.31995 - 4.50669i) q^{70} -0.390266 q^{71} +6.10952 q^{73} +(-3.05051 - 5.92585i) q^{74} +(-1.62776 - 1.16206i) q^{76} +6.52108i q^{77} +8.10895i q^{79} +(4.07906 - 1.40087i) q^{80} +(-3.06859 + 1.57965i) q^{82} -11.1298 q^{83} -4.09889 q^{85} +(-15.0407 + 7.74264i) q^{86} +(-5.49075 - 0.799501i) q^{88} +11.2732i q^{89} -18.1874i q^{91} +(0.654846 - 0.917281i) q^{92} +(-2.84050 - 5.51790i) q^{94} -1.07823 q^{95} -9.56020 q^{97} +(2.62133 + 5.09215i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94}+ \cdots - 128 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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