LMFDB - Embedded newform 684.3.s.a.445.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.24
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.962094 - 2.84154i) q^{3} +(-4.17611 - 7.23323i) q^{5} +(0.352343 + 0.610277i) q^{7} +(-7.14875 - 5.46767i) q^{9} +O(q^{10})$	\(q+(0.962094 - 2.84154i) q^{3} +(-4.17611 - 7.23323i) q^{5} +(0.352343 + 0.610277i) q^{7} +(-7.14875 - 5.46767i) q^{9} +(-10.3266 - 17.8862i) q^{11} +8.59104i q^{13} +(-24.5713 + 4.90754i) q^{15} +(2.72428 - 4.71858i) q^{17} +(0.849123 + 18.9810i) q^{19} +(2.07312 - 0.414056i) q^{21} +23.7392 q^{23} +(-22.3797 + 38.7628i) q^{25} +(-22.4144 + 15.0531i) q^{27} +(-2.06106 - 1.18995i) q^{29} +(-2.32115 - 1.34012i) q^{31} +(-60.7595 + 12.1353i) q^{33} +(2.94285 - 5.09716i) q^{35} -19.8089i q^{37} +(24.4118 + 8.26539i) q^{39} +(65.3355 - 37.7215i) q^{41} +10.8967 q^{43} +(-9.69495 + 74.5421i) q^{45} +(-15.4130 + 26.6960i) q^{47} +(24.2517 - 42.0052i) q^{49} +(-10.7871 - 12.2809i) q^{51} +(-76.8522 + 44.3706i) q^{53} +(-86.2498 + 149.389i) q^{55} +(54.7523 + 15.8487i) q^{57} +(-79.2807 + 45.7727i) q^{59} +(5.04264 - 8.73410i) q^{61} +(0.817975 - 6.28921i) q^{63} +(62.1410 - 35.8771i) q^{65} -16.0987i q^{67} +(22.8393 - 67.4559i) q^{69} +(67.0947 + 38.7371i) q^{71} +(-39.6851 + 68.7366i) q^{73} +(88.6148 + 100.886i) q^{75} +(7.27700 - 12.6041i) q^{77} -90.4947i q^{79} +(21.2092 + 78.1740i) q^{81} +(-31.5302 - 54.6119i) q^{83} -45.5074 q^{85} +(-5.36424 + 4.71175i) q^{87} +(-65.0621 + 37.5636i) q^{89} +(-5.24291 + 3.02700i) q^{91} +(-6.04116 + 5.30633i) q^{93} +(133.748 - 85.4086i) q^{95} -75.6045i q^{97} +(-23.9734 + 184.326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.962094	−	2.84154i	0.320698	−	0.947181i
$3$	0.962094	−	2.84154i	0.320698	−	0.947181i
$4$		0			0
$5$	−4.17611	−	7.23323i	−0.835221	−	1.44665i	−0.893850	−	0.448365i	$-0.852006\pi$
$5$	−4.17611	−	7.23323i	−0.835221	−	1.44665i	0.0586293	−	0.998280i	$-0.481327\pi$
$6$		0			0
$7$	0.352343	+	0.610277i	0.0503348	+	0.0871824i	0.890095	−	0.455775i	$-0.150638\pi$
$7$	0.352343	+	0.610277i	0.0503348	+	0.0871824i	−0.839760	+	0.542957i	$0.817305\pi$
$8$		0			0
$9$	−7.14875	−	5.46767i	−0.794305	−	0.607519i
$10$		0			0
$11$	−10.3266	−	17.8862i	−0.938780	−	1.62601i	−0.767751	−	0.640749i	$-0.778624\pi$
$11$	−10.3266	−	17.8862i	−0.938780	−	1.62601i	−0.171029	−	0.985266i	$-0.554709\pi$
$12$		0			0
$13$			8.59104i			0.660849i	0.943832	+	0.330425i	$0.107192\pi$
$13$			8.59104i			0.660849i	−0.943832	+	0.330425i	$0.892808\pi$
$14$		0			0
$15$	−24.5713	+	4.90754i	−1.63809	+	0.327169i
$16$		0			0
$17$	2.72428	−	4.71858i	0.160251	−	0.277564i	−0.774707	−	0.632320i	$-0.782103\pi$
$17$	2.72428	−	4.71858i	0.160251	−	0.277564i	0.934959	+	0.354756i	$0.115436\pi$
$18$		0			0
$19$	0.849123	+	18.9810i	0.0446907	+	0.999001i
$19$	0.849123	+	18.9810i	0.0446907	+	0.999001i
$20$		0			0
$21$	2.07312	−	0.414056i	0.0987198	−	0.0197169i
$22$		0			0
$23$	23.7392			1.03214			0.516069	−	0.856547i	$-0.327395\pi$
$23$	23.7392			1.03214			0.516069	+	0.856547i	$0.327395\pi$
$24$		0			0
$25$	−22.3797	+	38.7628i	−0.895188	+	1.55051i
$26$		0			0
$27$	−22.4144	+	15.0531i	−0.830163	+	0.557521i
$28$		0			0
$29$	−2.06106	−	1.18995i	−0.0710711	−	0.0410329i	0.464043	−	0.885812i	$-0.346398\pi$
$29$	−2.06106	−	1.18995i	−0.0710711	−	0.0410329i	−0.535114	+	0.844780i	$0.679732\pi$
$30$		0			0
$31$	−2.32115	−	1.34012i	−0.0748757	−	0.0432295i	0.462095	−	0.886831i	$-0.347098\pi$
$31$	−2.32115	−	1.34012i	−0.0748757	−	0.0432295i	−0.536970	+	0.843601i	$0.680431\pi$
$32$		0			0
$33$	−60.7595	+	12.1353i	−1.84120	+	0.367735i
$34$		0			0
$35$	2.94285	−	5.09716i	0.0840813	−	0.145633i
$36$		0			0
$37$		−	19.8089i		−	0.535376i	−0.963506	−	0.267688i	$-0.913740\pi$
$37$		−	19.8089i		−	0.535376i	0.963506	−	0.267688i	$-0.0862596\pi$
$38$		0			0
$39$	24.4118	+	8.26539i	0.625944	+	0.211933i
$40$		0			0
$41$	65.3355	−	37.7215i	1.59355	−	0.920036i	0.600857	−	0.799356i	$-0.294826\pi$
$41$	65.3355	−	37.7215i	1.59355	−	0.920036i	0.992692	−	0.120679i	$-0.0385073\pi$
$42$		0			0
$43$	10.8967			0.253412			0.126706	−	0.991940i	$-0.459559\pi$
$43$	10.8967			0.253412			0.126706	+	0.991940i	$0.459559\pi$
$44$		0			0
$45$	−9.69495	+	74.5421i	−0.215443	+	1.65649i
$46$		0			0
$47$	−15.4130	+	26.6960i	−0.327936	+	0.568001i	−0.982102	−	0.188350i	$-0.939686\pi$
$47$	−15.4130	+	26.6960i	−0.327936	+	0.568001i	0.654167	+	0.756351i	$0.273020\pi$
$48$		0			0
$49$	24.2517	−	42.0052i	0.494933	−	0.857249i
$50$		0			0
$51$	−10.7871	−	12.2809i	−0.211511	−	0.240801i
$52$		0			0
$53$	−76.8522	+	44.3706i	−1.45004	+	0.837182i	−0.998483	−	0.0550603i	$-0.982465\pi$
$53$	−76.8522	+	44.3706i	−1.45004	+	0.837182i	−0.451558	+	0.892242i	$0.649132\pi$
$54$		0			0
$55$	−86.2498	+	149.389i	−1.56818	+	2.71616i
$56$		0			0
$57$	54.7523	+	15.8487i	0.960567	+	0.278047i
$58$		0			0
$59$	−79.2807	+	45.7727i	−1.34374	+	0.775809i	−0.987354	−	0.158529i	$-0.949325\pi$
$59$	−79.2807	+	45.7727i	−1.34374	+	0.775809i	−0.356387	+	0.934339i	$0.615991\pi$
$60$		0			0
$61$	5.04264	−	8.73410i	0.0826662	−	0.143182i	−0.821728	−	0.569880i	$-0.806990\pi$
$61$	5.04264	−	8.73410i	0.0826662	−	0.143182i	0.904394	+	0.426698i	$0.140323\pi$
$62$		0			0
$63$	0.817975	−	6.28921i	0.0129837	−	0.0998287i
$64$		0			0
$65$	62.1410	−	35.8771i	0.956015	−	0.551955i
$66$		0			0
$67$		−	16.0987i		−	0.240280i	−0.992757	−	0.120140i	$-0.961666\pi$
$67$		−	16.0987i		−	0.240280i	0.992757	−	0.120140i	$-0.0383343\pi$
$68$		0			0
$69$	22.8393	−	67.4559i	0.331004	−	0.977621i
$70$		0			0
$71$	67.0947	+	38.7371i	0.944995	+	0.545593i	0.891523	−	0.452976i	$-0.149638\pi$
$71$	67.0947	+	38.7371i	0.944995	+	0.545593i	0.0534727	+	0.998569i	$0.482971\pi$
$72$		0			0
$73$	−39.6851	+	68.7366i	−0.543631	+	0.941597i	0.455061	+	0.890460i	$0.349618\pi$
$73$	−39.6851	+	68.7366i	−0.543631	+	0.941597i	−0.998692	+	0.0511363i	$0.983716\pi$
$74$		0			0
$75$	88.6148	+	100.886i	1.18153	+	1.34515i
$76$		0			0
$77$	7.27700	−	12.6041i	0.0945065	−	0.163690i
$78$		0			0
$79$		−	90.4947i		−	1.14550i	−0.819729	−	0.572751i	$-0.805876\pi$
$79$		−	90.4947i		−	1.14550i	0.819729	−	0.572751i	$-0.194124\pi$
$80$		0			0
$81$	21.2092	+	78.1740i	0.261842	+	0.965111i
$82$		0			0
$83$	−31.5302	−	54.6119i	−0.379882	−	0.657975i	0.611163	−	0.791505i	$-0.290702\pi$
$83$	−31.5302	−	54.6119i	−0.379882	−	0.657975i	−0.991045	+	0.133530i	$0.957369\pi$
$84$		0			0
$85$	−45.5074			−0.535382
$86$		0			0
$87$	−5.36424	+	4.71175i	−0.0616580	+	0.0541580i
$88$		0			0
$89$	−65.0621	+	37.5636i	−0.731035	+	0.422063i	−0.818801	−	0.574078i	$-0.805361\pi$
$89$	−65.0621	+	37.5636i	−0.731035	+	0.422063i	0.0877659	+	0.996141i	$0.472027\pi$
$90$		0			0
$91$	−5.24291	+	3.02700i	−0.0576144	+	0.0332637i
$92$		0			0
$93$	−6.04116	+	5.30633i	−0.0649587	+	0.0570573i
$94$		0			0
$95$	133.748	−	85.4086i	1.40787	−	0.899038i
$96$		0			0
$97$		−	75.6045i		−	0.779428i	−0.920936	−	0.389714i	$-0.872574\pi$
$97$		−	75.6045i		−	0.779428i	0.920936	−	0.389714i	$-0.127426\pi$
$98$		0			0
$99$	−23.9734	+	184.326i	−0.242156	+	1.86188i
$100$		0			0
$101$	−42.4567	+	73.5371i	−0.420363	+	0.728090i	−0.995975	−	0.0896329i	$-0.971431\pi$
$101$	−42.4567	+	73.5371i	−0.420363	+	0.728090i	0.575612	+	0.817723i	$0.304764\pi$
$102$		0			0
$103$	−24.5788	−	14.1906i	−0.238629	−	0.137772i	0.375918	−	0.926653i	$-0.377328\pi$
$103$	−24.5788	−	14.1906i	−0.238629	−	0.137772i	−0.614546	+	0.788881i	$0.710661\pi$
$104$		0			0
$105$	−11.6525	−	13.2662i	−0.110976	−	0.126345i
$106$		0			0
$107$		−	148.821i		−	1.39085i	−0.718600	−	0.695423i	$-0.755217\pi$
$107$		−	148.821i		−	1.39085i	0.718600	−	0.695423i	$-0.244783\pi$
$108$		0			0
$109$	−49.6931	−	28.6903i	−0.455900	−	0.263214i	0.254419	−	0.967094i	$-0.418116\pi$
$109$	−49.6931	−	28.6903i	−0.455900	−	0.263214i	−0.710319	+	0.703880i	$0.751449\pi$
$110$		0			0
$111$	−56.2879	−	19.0580i	−0.507098	−	0.171694i
$112$		0			0
$113$	−59.1471	−	34.1486i	−0.523426	−	0.302200i	0.214909	−	0.976634i	$-0.431054\pi$
$113$	−59.1471	−	34.1486i	−0.523426	−	0.302200i	−0.738335	+	0.674434i	$0.764388\pi$
$114$		0			0
$115$	−99.1372	−	171.711i	−0.862063	−	1.49314i
$116$		0			0
$117$	46.9730	−	61.4152i	0.401478	−	0.524916i
$118$		0			0
$119$	3.83952			0.0322649
$120$		0			0
$121$	−152.776	+	264.617i	−1.26262	+	2.18691i
$122$		0			0
$123$	−44.3283	−	221.945i	−0.360393	−	1.80443i
$124$		0			0
$125$	165.035			1.32028
$126$		0			0
$127$	−45.0028	+	25.9824i	−0.354353	+	0.204586i	−0.666601	−	0.745415i	$-0.732251\pi$
$127$	−45.0028	+	25.9824i	−0.354353	+	0.204586i	0.312248	+	0.950001i	$0.398918\pi$
$128$		0			0
$129$	10.4837	−	30.9635i	0.0812689	−	0.240027i
$130$		0			0
$131$	−45.3935	−	78.6238i	−0.346515	−	0.600181i	0.639113	−	0.769113i	$-0.279302\pi$
$131$	−45.3935	−	78.6238i	−0.346515	−	0.600181i	−0.985628	+	0.168932i	$0.945968\pi$
$132$		0			0
$133$	−11.2845	+	7.20604i	−0.0848458	+	0.0541807i
$134$		0			0
$135$	202.487	+	99.2651i	1.49990	+	0.735297i
$136$		0			0
$137$	−116.094	+	201.081i	−0.847403	+	1.46774i	0.0361153	+	0.999348i	$0.488502\pi$
$137$	−116.094	+	201.081i	−0.847403	+	1.46774i	−0.883518	+	0.468397i	$0.844832\pi$
$138$		0			0
$139$	−26.3828			−0.189804			−0.0949022	−	0.995487i	$-0.530254\pi$
$139$	−26.3828			−0.189804			−0.0949022	+	0.995487i	$0.530254\pi$
$140$		0			0
$141$	61.0293	+	69.4808i	0.432832	+	0.492771i
$142$		0			0
$143$	153.661	−	88.7161i	1.07455	−	0.620392i
$144$		0			0
$145$			19.8775i			0.137086i
$146$		0			0
$147$	−96.0272	−	109.325i	−0.653246	−	0.743709i
$148$		0			0
$149$	−50.4334	−	87.3533i	−0.338479	−	0.586264i	0.645668	−	0.763619i	$-0.276579\pi$
$149$	−50.4334	−	87.3533i	−0.338479	−	0.586264i	−0.984147	+	0.177355i	$0.943246\pi$
$150$		0			0
$151$	201.351	−	116.250i	1.33345	−	0.769868i	0.347624	−	0.937634i	$-0.386988\pi$
$151$	201.351	−	116.250i	1.33345	−	0.769868i	0.985827	+	0.167765i	$0.0536551\pi$
$152$		0			0
$153$	−45.2748	+	18.8365i	−0.295914	+	0.123115i
$154$		0			0
$155$			22.3859i			0.144425i
$156$		0			0
$157$	−98.6975	−	170.949i	−0.628647	−	1.08885i	−0.987824	−	0.155578i	$-0.950276\pi$
$157$	−98.6975	−	170.949i	−0.628647	−	1.08885i	0.359177	−	0.933269i	$-0.383057\pi$
$158$		0			0
$159$	52.1421	+	261.068i	0.327937	+	1.64193i
$160$		0			0
$161$	8.36433	+	14.4875i	0.0519524	+	0.0899842i
$162$		0			0
$163$	−238.025			−1.46027			−0.730137	−	0.683301i	$-0.760544\pi$
$163$	−238.025			−1.46027			−0.730137	+	0.683301i	$0.760544\pi$
$164$		0			0
$165$	341.515	+	388.809i	2.06979	+	2.35642i
$166$		0			0
$167$		−	251.379i		−	1.50526i	−0.658443	−	0.752631i	$-0.728784\pi$
$167$		−	251.379i		−	1.50526i	0.658443	−	0.752631i	$-0.271216\pi$
$168$		0			0
$169$	95.1940			0.563278
$170$		0			0
$171$	97.7117	−	140.333i	0.571414	−	0.820662i
$172$		0			0
$173$			274.857i			1.58877i	0.607416	+	0.794384i	$0.292206\pi$
$173$			274.857i			1.58877i	−0.607416	+	0.794384i	$0.707794\pi$
$174$		0			0
$175$	−31.5414			−0.180236
$176$		0			0
$177$	53.7898	+	269.317i	0.303897	+	1.52157i
$178$		0			0
$179$		−	106.008i		−	0.592221i	−0.955154	−	0.296111i	$-0.904310\pi$
$179$		−	106.008i		−	0.592221i	0.955154	−	0.296111i	$-0.0956897\pi$
$180$		0			0
$181$	155.686	−	89.8854i	0.860144	−	0.496604i	−0.00391638	−	0.999992i	$-0.501247\pi$
$181$	155.686	−	89.8854i	0.860144	−	0.496604i	0.864061	+	0.503388i	$0.167913\pi$
$182$		0			0
$183$	−19.9668	−	22.7319i	−0.109108	−	0.124218i
$184$		0			0
$185$	−143.282	+	82.7240i	−0.774499	+	0.447157i
$186$		0			0
$187$	−112.530			−0.601763
$188$		0			0
$189$	−17.0841	−	8.37513i	−0.0903921	−	0.0443128i
$190$		0			0
$191$	−60.2220	−	104.308i	−0.315298	−	0.546113i	0.664203	−	0.747553i	$-0.268771\pi$
$191$	−60.2220	−	104.308i	−0.315298	−	0.546113i	−0.979501	+	0.201440i	$0.935438\pi$
$192$		0			0
$193$	−101.549	+	58.6291i	−0.526158	+	0.303778i	−0.739451	−	0.673211i	$-0.764915\pi$
$193$	−101.549	+	58.6291i	−0.526158	+	0.303778i	0.213292	+	0.976988i	$0.431581\pi$
$194$		0			0
$195$	−42.1609	−	211.093i	−0.216210	−	1.08253i
$196$		0			0
$197$	216.141			1.09716			0.548581	−	0.836098i	$-0.315168\pi$
$197$	216.141			1.09716			0.548581	+	0.836098i	$0.315168\pi$
$198$		0			0
$199$	129.858	+	224.920i	0.652551	+	1.13025i	0.982502	+	0.186254i	$0.0596347\pi$
$199$	129.858	+	224.920i	0.652551	+	1.13025i	−0.329950	+	0.943998i	$0.607032\pi$
$200$		0			0
$201$	−45.7453	−	15.4885i	−0.227589	−	0.0770573i
$202$		0			0
$203$		−	1.67709i		−	0.00826153i
$204$		0			0
$205$	−545.696	−	315.058i	−2.66193	−	1.53687i
$206$		0			0
$207$	−169.705	−	129.798i	−0.819832	−	0.627042i
$208$		0			0
$209$	330.729	−	211.197i	1.58244	−	1.01051i
$210$		0			0
$211$	−36.2971	+	20.9561i	−0.172024	+	0.0993182i	−0.583540	−	0.812084i	$-0.698333\pi$
$211$	−36.2971	+	20.9561i	−0.172024	+	0.0993182i	0.411516	+	0.911403i	$0.365000\pi$
$212$		0			0
$213$	174.625	−	153.384i	0.819834	−	0.720111i
$214$		0			0
$215$	−45.5059	−	78.8185i	−0.211655	−	0.366598i
$216$		0			0
$217$		−	1.88872i		−	0.00870379i
$218$		0			0
$219$	157.137	+	178.898i	0.717522	+	0.816886i
$220$		0			0
$221$	40.5375	+	23.4044i	0.183428	+	0.105902i
$222$		0			0
$223$		−	105.577i		−	0.473439i	−0.971578	−	0.236720i	$-0.923928\pi$
$223$		−	105.577i		−	0.473439i	0.971578	−	0.236720i	$-0.0760723\pi$
$224$		0			0
$225$	371.929	−	154.741i	1.65302	−	0.687736i
$226$		0			0
$227$	384.737	−	222.128i	1.69488	−	0.978537i	0.744403	−	0.667730i	$-0.232734\pi$
$227$	384.737	−	222.128i	1.69488	−	0.978537i	0.950473	−	0.310807i	$-0.100599\pi$
$228$		0			0
$229$	118.302	−	204.906i	0.516604	−	0.894784i	−0.483210	−	0.875504i	$-0.660529\pi$
$229$	118.302	−	204.906i	0.516604	−	0.894784i	0.999814	−	0.0192797i	$-0.00613729\pi$
$230$		0			0
$231$	−28.8141	−	32.8043i	−0.124736	−	0.142010i
$232$		0			0
$233$	−85.0481	+	147.308i	−0.365013	+	0.632222i	−0.988778	−	0.149390i	$-0.952269\pi$
$233$	−85.0481	+	147.308i	−0.365013	+	0.632222i	0.623765	+	0.781612i	$0.285602\pi$
$234$		0			0
$235$	257.465			1.09559
$236$		0			0
$237$	−257.145	−	87.0644i	−1.08500	−	0.367360i
$238$		0			0
$239$	221.528	−	383.698i	0.926896	−	1.60543i	0.138413	−	0.990375i	$-0.455800\pi$
$239$	221.528	−	383.698i	0.926896	−	1.60543i	0.788483	−	0.615057i	$-0.210867\pi$
$240$		0			0
$241$	−133.094	−	76.8417i	−0.552256	−	0.318845i	0.197775	−	0.980247i	$-0.436628\pi$
$241$	−133.094	−	76.8417i	−0.552256	−	0.318845i	−0.750031	+	0.661402i	$0.769962\pi$
$242$		0			0
$243$	242.540	+	14.9438i	0.998107	+	0.0614969i
$244$		0			0
$245$	−405.111			−1.65351
$246$		0			0
$247$	−163.067	+	7.29485i	−0.660189	+	0.0295338i
$248$		0			0
$249$	−185.517	+	37.0527i	−0.745049	+	0.148806i
$250$		0			0
$251$	−84.3664	−	146.127i	−0.336121	−	0.582179i	0.647578	−	0.761999i	$-0.275782\pi$
$251$	−84.3664	−	146.127i	−0.336121	−	0.582179i	−0.983700	+	0.179820i	$0.942449\pi$
$252$		0			0
$253$	−245.144	−	424.602i	−0.968950	−	1.67827i
$254$		0			0
$255$	−43.7824	+	129.311i	−0.171696	+	0.507104i
$256$		0			0
$257$		−	323.090i		−	1.25716i	−0.777744	−	0.628581i	$-0.783636\pi$
$257$		−	323.090i		−	1.25716i	0.777744	−	0.628581i	$-0.216364\pi$
$258$		0			0
$259$	12.0889	−	6.97953i	0.0466753	−	0.0269480i
$260$		0			0
$261$	8.22773	+	19.7759i	0.0315239	+	0.0757696i
$262$		0			0
$263$	214.364			0.815074			0.407537	−	0.913189i	$-0.366388\pi$
$263$	214.364			0.815074			0.407537	+	0.913189i	$0.366388\pi$
$264$		0			0
$265$	641.885	+	370.593i	2.42221	+	1.39846i
$266$		0			0
$267$	44.1428	+	221.017i	0.165329	+	0.827777i
$268$		0			0
$269$	−339.682	−	196.116i	−1.26276	−	0.729054i	−0.289152	−	0.957283i	$-0.593373\pi$
$269$	−339.682	−	196.116i	−1.26276	−	0.729054i	−0.973608	+	0.228229i	$0.926707\pi$
$270$		0			0
$271$	−89.8653	+	155.651i	−0.331606	+	0.574359i	−0.982827	−	0.184529i	$-0.940924\pi$
$271$	−89.8653	+	155.651i	−0.331606	+	0.574359i	0.651221	+	0.758888i	$0.274257\pi$
$272$		0			0
$273$	3.55717	+	17.8102i	0.0130299	+	0.0652389i
$274$		0			0
$275$	924.423			3.36154
$276$		0			0
$277$	112.854	+	195.468i	0.407414	+	0.705662i	0.994599	−	0.103791i	$-0.0330973\pi$
$277$	112.854	+	195.468i	0.407414	+	0.705662i	−0.587185	+	0.809453i	$0.699764\pi$
$278$		0			0
$279$	9.26600	+	22.2714i	0.0332115	+	0.0798259i
$280$		0			0
$281$	120.212	+	69.4045i	0.427801	+	0.246991i	0.698409	−	0.715699i	$-0.253892\pi$
$281$	120.212	+	69.4045i	0.427801	+	0.246991i	−0.270608	+	0.962689i	$0.587225\pi$
$282$		0			0
$283$	−22.9508	−	39.7520i	−0.0810984	−	0.140466i	0.822624	−	0.568586i	$-0.192509\pi$
$283$	−22.9508	−	39.7520i	−0.0810984	−	0.140466i	−0.903722	+	0.428120i	$0.859176\pi$
$284$		0			0
$285$	−114.014	−	462.222i	−0.400050	−	1.62183i
$286$		0			0
$287$	46.0411	+	26.5818i	0.160422	+	0.0926196i
$288$		0			0
$289$	129.657	+	224.572i	0.448639	+	0.777065i
$290$		0			0
$291$	−214.834	−	72.7386i	−0.738259	−	0.249961i
$292$		0			0
$293$	−357.501	−	206.404i	−1.22014	−	0.704449i	−0.255193	−	0.966890i	$-0.582139\pi$
$293$	−357.501	−	206.404i	−1.22014	−	0.704449i	−0.964948	+	0.262441i	$0.915472\pi$
$294$		0			0
$295$	662.169	+	382.304i	2.24464	+	1.29594i
$296$		0			0
$297$	500.706	+	245.461i	1.68588	+	0.826467i
$298$		0			0
$299$			203.944i			0.682087i
$300$		0			0
$301$	3.83939	+	6.65002i	0.0127555	+	0.0220931i
$302$		0			0
$303$	168.112	+	191.392i	0.554824	+	0.631657i
$304$		0			0
$305$	−84.2343			−0.276178
$306$		0			0
$307$	48.2502	+	27.8573i	0.157167	+	0.0907403i	0.576521	−	0.817083i	$-0.304410\pi$
$307$	48.2502	+	27.8573i	0.157167	+	0.0907403i	−0.419354	+	0.907823i	$0.637743\pi$
$308$		0			0
$309$	−63.9702	+	56.1890i	−0.207023	+	0.181841i
$310$		0			0
$311$	143.848	−	249.152i	0.462534	−	0.801133i	−0.536552	−	0.843867i	$-0.680274\pi$
$311$	143.848	−	249.152i	0.462534	−	0.801133i	0.999086	+	0.0427343i	$0.0136069\pi$
$312$		0			0
$313$	−253.663	+	439.358i	−0.810426	+	1.40370i	0.102141	+	0.994770i	$0.467431\pi$
$313$	−253.663	+	439.358i	−0.810426	+	1.40370i	−0.912566	+	0.408929i	$0.865903\pi$
$314$		0			0
$315$	−48.9072	+	20.3478i	−0.155261	+	0.0645962i
$316$		0			0
$317$	−43.3887	−	25.0505i	−0.136873	−	0.0790235i	0.430000	−	0.902829i	$-0.358514\pi$
$317$	−43.3887	−	25.0505i	−0.136873	−	0.0790235i	−0.566873	+	0.823805i	$0.691847\pi$
$318$		0			0
$319$			49.1526i			0.154083i
$320$		0			0
$321$	−422.880	−	143.179i	−1.31738	−	0.446042i
$322$		0			0
$323$	91.8767	+	47.7029i	0.284448	+	0.147687i
$324$		0			0
$325$	−333.013	−	192.265i	−1.02465	−	0.591585i
$326$		0			0
$327$	−129.334	+	113.602i	−0.395518	+	0.347408i
$328$		0			0
$329$	−21.7226			−0.0660262
$330$		0			0
$331$	−269.005	+	155.310i	−0.812705	+	0.469215i	−0.847894	−	0.530165i	$-0.822130\pi$
$331$	−269.005	+	155.310i	−0.812705	+	0.469215i	0.0351896	+	0.999381i	$0.488796\pi$
$332$		0			0
$333$	−108.308	+	141.609i	−0.325251	+	0.425252i
$334$		0			0
$335$	−116.446	+	67.2301i	−0.347600	+	0.200687i
$336$		0			0
$337$	−27.0500	+	15.6173i	−0.0802671	+	0.0463423i	−0.539596	−	0.841924i	$-0.681423\pi$
$337$	−27.0500	+	15.6173i	−0.0802671	+	0.0463423i	0.459329	+	0.888266i	$0.348090\pi$
$338$		0			0
$339$	−153.940	+	135.215i	−0.454100	+	0.398864i
$340$		0			0
$341$			55.3552i			0.162332i
$342$		0			0
$343$	68.7094			0.200319
$344$		0			0
$345$	−583.303	+	116.501i	−1.69073	+	0.337684i
$346$		0			0
$347$	−184.556	−	319.660i	−0.531861	−	0.921210i	−0.999308	−	0.0371889i	$-0.988160\pi$
$347$	−184.556	−	319.660i	−0.531861	−	0.921210i	0.467448	−	0.884021i	$-0.345174\pi$
$348$		0			0
$349$	182.826	+	316.663i	0.523856	+	0.907345i	0.999614	+	0.0277692i	$0.00884035\pi$
$349$	182.826	+	316.663i	0.523856	+	0.907345i	−0.475758	+	0.879576i	$0.657826\pi$
$350$		0			0
$351$	−129.322	−	192.563i	−0.368438	−	0.548612i
$352$		0			0
$353$	289.028	+	500.611i	0.818776	+	1.41816i	0.906584	+	0.422025i	$0.138681\pi$
$353$	289.028	+	500.611i	0.818776	+	1.41816i	−0.0878078	+	0.996137i	$0.527986\pi$
$354$		0			0
$355$		−	647.081i		−	1.82276i
$356$		0			0
$357$	3.69398	−	10.9102i	0.0103473	−	0.0305607i
$358$		0			0
$359$	311.123	−	538.882i	0.866639	−	1.50106i	0.00122868	−	0.999999i	$-0.499609\pi$
$359$	311.123	−	538.882i	0.866639	−	1.50106i	0.865410	−	0.501064i	$-0.167058\pi$
$360$		0			0
$361$	−359.558	+	32.2344i	−0.996005	+	0.0892921i
$362$		0			0
$363$	604.934	+	688.707i	1.66649	+	1.89727i
$364$		0			0
$365$	662.916			1.81621
$366$		0			0
$367$	−121.099	+	209.750i	−0.329970	+	0.571525i	−0.982506	−	0.186233i	$-0.940372\pi$
$367$	−121.099	+	209.750i	−0.329970	+	0.571525i	0.652536	+	0.757758i	$0.273705\pi$
$368$		0			0
$369$	−673.315	−	87.5715i	−1.82470	−	0.237321i
$370$		0			0
$371$	−54.1567	−	31.2674i	−0.145975	−	0.0842787i
$372$		0			0
$373$	290.835	+	167.914i	0.779718	+	0.450170i	0.836330	−	0.548226i	$-0.184697\pi$
$373$	290.835	+	167.914i	0.779718	+	0.450170i	−0.0566124	+	0.998396i	$0.518030\pi$
$374$		0			0
$375$	158.779	−	468.954i	0.423411	−	1.25054i
$376$		0			0
$377$	10.2229	−	17.7067i	0.0271166	−	0.0469673i
$378$		0			0
$379$		−	83.3649i		−	0.219960i	−0.993934	−	0.109980i	$-0.964921\pi$
$379$		−	83.3649i		−	0.219960i	0.993934	−	0.109980i	$-0.0350787\pi$
$380$		0			0
$381$	30.5331	+	152.875i	0.0801395	+	0.401246i
$382$		0			0
$383$	28.2753	−	16.3247i	0.0738258	−	0.0426234i	−0.462633	−	0.886550i	$-0.653095\pi$
$383$	28.2753	−	16.3247i	0.0738258	−	0.0426234i	0.536459	+	0.843927i	$0.319762\pi$
$384$		0			0
$385$	−121.558			−0.315735
$386$		0			0
$387$	−77.8980	−	59.5797i	−0.201287	−	0.153953i
$388$		0			0
$389$	126.631	−	219.331i	0.325529	−	0.563833i	−0.656090	−	0.754682i	$-0.727791\pi$
$389$	126.631	−	219.331i	0.325529	−	0.563833i	0.981619	+	0.190850i	$0.0611243\pi$
$390$		0			0
$391$	64.6720	−	112.015i	0.165402	−	0.286484i
$392$		0			0
$393$	−267.086	+	53.3440i	−0.679607	+	0.135735i
$394$		0			0
$395$	−654.568	+	377.915i	−1.65714	+	0.956747i
$396$		0			0
$397$	131.950	−	228.543i	0.332367	−	0.575676i	−0.650609	−	0.759413i	$-0.725486\pi$
$397$	131.950	−	228.543i	0.332367	−	0.575676i	0.982975	+	0.183737i	$0.0588195\pi$
$398$		0			0
$399$	9.61953	+	38.9983i	0.0241091	+	0.0977400i
$400$		0			0
$401$	−644.581	+	372.149i	−1.60743	+	0.928052i	−0.617492	+	0.786577i	$0.711851\pi$
$401$	−644.581	+	372.149i	−1.60743	+	0.928052i	−0.989942	+	0.141475i	$0.954815\pi$
$402$		0			0
$403$	11.5130	−	19.9411i	0.0285682	−	0.0494816i
$404$		0			0
$405$	476.878	−	479.874i	1.17748	−	1.18487i
$406$		0			0
$407$	−354.305	+	204.558i	−0.870529	+	0.502600i
$408$		0			0
$409$			46.9946i			0.114901i	0.998348	+	0.0574506i	$0.0182972\pi$
$409$			46.9946i			0.114901i	−0.998348	+	0.0574506i	$0.981703\pi$
$410$		0			0
$411$	459.687	+	523.346i	1.11846	+	1.27335i
$412$		0			0
$413$	−55.8681	−	32.2555i	−0.135274	−	0.0781004i
$414$		0			0
$415$	−263.347	+	456.130i	−0.634571	+	1.09911i
$416$		0			0
$417$	−25.3827	+	74.9679i	−0.0608699	+	0.179779i
$418$		0			0
$419$	−35.3570	+	61.2401i	−0.0843842	+	0.146158i	−0.905129	−	0.425138i	$-0.860226\pi$
$419$	−35.3570	+	61.2401i	−0.0843842	+	0.146158i	0.820744	+	0.571295i	$0.193559\pi$
$420$		0			0
$421$			127.574i			0.303027i	0.988455	+	0.151513i	$0.0484147\pi$
$421$			127.574i			0.303027i	−0.988455	+	0.151513i	$0.951585\pi$
$422$		0			0
$423$	256.149	−	106.570i	0.605552	−	0.251939i
$424$		0			0
$425$	121.937	+	211.201i	0.286911	+	0.496944i
$426$		0			0
$427$	7.10696			0.0166439
$428$		0			0
$429$	−104.255	−	521.987i	−0.243018	−	1.21675i
$430$		0			0
$431$	−541.149	+	312.432i	−1.25557	+	0.724901i	−0.972209	−	0.234113i	$-0.924781\pi$
$431$	−541.149	+	312.432i	−1.25557	+	0.724901i	−0.283357	+	0.959015i	$0.591448\pi$
$432$		0			0
$433$	78.5687	−	45.3617i	0.181452	−	0.104761i	−0.406523	−	0.913641i	$-0.633259\pi$
$433$	78.5687	−	45.3617i	0.181452	−	0.104761i	0.587975	+	0.808879i	$0.299925\pi$
$434$		0			0
$435$	56.4828	+	19.1240i	0.129845	+	0.0439633i
$436$		0			0
$437$	20.1575	+	450.593i	0.0461269	+	1.03111i
$438$		0			0
$439$		−	151.104i		−	0.344201i	−0.985079	−	0.172101i	$-0.944945\pi$
$439$		−	151.104i		−	0.344201i	0.985079	−	0.172101i	$-0.0550554\pi$
$440$		0			0
$441$	−403.040	+	167.684i	−0.913922	+	0.380237i
$442$		0			0
$443$	−435.614	+	754.506i	−0.983328	+	1.70317i	−0.334184	+	0.942508i	$0.608461\pi$
$443$	−435.614	+	754.506i	−0.983328	+	1.70317i	−0.649144	+	0.760666i	$0.724873\pi$
$444$		0			0
$445$	543.412	+	313.739i	1.22115	+	0.705032i
$446$		0			0
$447$	−296.740	+	59.2668i	−0.663848	+	0.132588i
$448$		0			0
$449$		−	174.763i		−	0.389228i	−0.980880	−	0.194614i	$-0.937655\pi$
$449$		−	174.763i		−	0.389228i	0.980880	−	0.194614i	$-0.0623454\pi$
$450$		0			0
$451$	−1349.38	−	779.067i	−2.99198	−	1.72742i
$452$		0			0
$453$	−136.611	−	683.992i	−0.301570	−	1.50992i
$454$		0			0
$455$	43.7899	+	25.2821i	0.0962416	+	0.0555651i
$456$		0			0
$457$	−370.554	−	641.818i	−0.810840	−	1.40442i	−0.912277	−	0.409574i	$-0.865677\pi$
$457$	−370.554	−	641.818i	−0.810840	−	1.40442i	0.101437	−	0.994842i	$-0.467656\pi$
$458$		0			0
$459$	9.96623	+	146.773i	0.0217129	+	0.319767i
$460$		0			0
$461$	−565.944			−1.22764			−0.613822	−	0.789444i	$-0.710369\pi$
$461$	−565.944			−1.22764			−0.613822	+	0.789444i	$0.710369\pi$
$462$		0			0
$463$	178.485	−	309.146i	0.385497	−	0.667701i	−0.606341	−	0.795205i	$-0.707363\pi$
$463$	178.485	−	309.146i	0.385497	−	0.667701i	0.991838	+	0.127504i	$0.0406965\pi$
$464$		0			0
$465$	63.6104	+	21.5373i	0.136797	+	0.0463168i
$466$		0			0
$467$	−427.161			−0.914691			−0.457345	−	0.889289i	$-0.651200\pi$
$467$	−427.161			−0.914691			−0.457345	+	0.889289i	$0.651200\pi$
$468$		0			0
$469$	9.82469	−	5.67229i	0.0209482	−	0.0120944i
$470$		0			0
$471$	−580.716	+	115.984i	−1.23294	+	0.246251i
$472$		0			0
$473$	−112.526	−	194.901i	−0.237898	−	0.412052i
$474$		0			0
$475$	−754.760	−	391.875i	−1.58897	−	0.825000i
$476$		0			0
$477$	792.001	+	103.008i	1.66038	+	0.215949i
$478$		0			0
$479$	164.600	−	285.096i	0.343633	−	0.595190i	−0.641471	−	0.767147i	$-0.721676\pi$
$479$	164.600	−	285.096i	0.343633	−	0.595190i	0.985104	+	0.171957i	$0.0550091\pi$
$480$		0			0
$481$	170.179			0.353803
$482$		0			0
$483$	49.2140	−	9.82933i	0.101892	−	0.0203506i
$484$		0			0
$485$	−546.864	+	315.732i	−1.12756	+	0.650994i
$486$		0			0
$487$		−	788.052i		−	1.61818i	−0.587687	−	0.809088i	$-0.699961\pi$
$487$		−	788.052i		−	1.61818i	0.587687	−	0.809088i	$-0.300039\pi$
$488$		0			0
$489$	−229.002	+	676.357i	−0.468307	+	1.38314i
$490$		0			0
$491$	390.588	+	676.518i	0.795495	+	1.37784i	0.922525	+	0.385938i	$0.126122\pi$
$491$	390.588	+	676.518i	0.795495	+	1.37784i	−0.127030	+	0.991899i	$0.540544\pi$
$492$		0			0
$493$	−11.2298	+	6.48352i	−0.0227785	+	0.0131512i
$494$		0			0
$495$	1433.39	−	596.359i	2.89573	−	1.20477i
$496$		0			0
$497$			54.5951i			0.109849i
$498$		0			0
$499$	−116.750	−	202.218i	−0.233969	−	0.405246i	0.725004	−	0.688745i	$-0.241838\pi$
$499$	−116.750	−	202.218i	−0.233969	−	0.405246i	−0.958973	+	0.283499i	$0.908505\pi$
$500$		0			0
$501$	−714.304	−	241.850i	−1.42576	−	0.482735i
$502$		0			0
$503$	402.390	+	696.960i	0.799980	+	1.38561i	0.919628	+	0.392789i	$0.128490\pi$
$503$	402.390	+	696.960i	0.799980	+	1.38561i	−0.119649	+	0.992816i	$0.538177\pi$
$504$		0			0
$505$	709.214			1.40438
$506$		0			0
$507$	91.5856	−	270.498i	0.180642	−	0.533527i
$508$		0			0
$509$			114.097i			0.224160i	0.993699	+	0.112080i	$0.0357513\pi$
$509$			114.097i			0.224160i	−0.993699	+	0.112080i	$0.964249\pi$
$510$		0			0
$511$	−55.9311			−0.109454
$512$		0			0
$513$	−304.755	−	412.666i	−0.594065	−	0.804417i
$514$		0			0
$515$			237.045i			0.460282i
$516$		0			0
$517$	636.653			1.23144
$518$		0			0
$519$	781.018	+	264.438i	1.50485	+	0.509515i
$520$		0			0
$521$		−	330.381i		−	0.634130i	−0.948404	−	0.317065i	$-0.897303\pi$
$521$		−	330.381i		−	0.634130i	0.948404	−	0.317065i	$-0.102697\pi$
$522$		0			0
$523$	223.871	−	129.252i	0.428052	−	0.247136i	−0.270464	−	0.962730i	$-0.587177\pi$
$523$	223.871	−	129.252i	0.428052	−	0.247136i	0.698517	+	0.715594i	$0.253844\pi$
$524$		0			0
$525$	−30.3458	+	89.6262i	−0.0578015	+	0.170717i
$526$		0			0
$527$	−12.6469	+	7.30169i	−0.0239979	+	0.0138552i
$528$		0			0
$529$	34.5474			0.0653070
$530$		0			0
$531$	817.028	+	106.263i	1.53866	+	0.200118i
$532$		0			0
$533$	324.067	+	561.300i	0.608005	+	1.05310i
$534$		0			0
$535$	−1076.45	+	621.490i	−2.01206	+	1.16166i
$536$		0			0
$537$	−301.225	−	101.989i	−0.560941	−	0.189924i
$538$		0			0
$539$	−1001.75			−1.85853
$540$		0			0
$541$	307.180	+	532.051i	0.567800	+	0.983458i	0.996783	+	0.0801456i	$0.0255385\pi$
$541$	307.180	+	532.051i	0.567800	+	0.983458i	−0.428983	+	0.903312i	$0.641128\pi$
$542$		0			0
$543$	−105.629	−	528.867i	−0.194528	−	0.973973i
$544$		0			0
$545$			479.255i			0.879367i
$546$		0			0
$547$	278.732	+	160.926i	0.509564	+	0.294197i	0.732654	−	0.680601i	$-0.238281\pi$
$547$	278.732	+	160.926i	0.509564	+	0.294197i	−0.223090	+	0.974798i	$0.571614\pi$
$548$		0			0
$549$	−83.8037	+	34.8664i	−0.152648	+	0.0635090i
$550$		0			0
$551$	20.8364	−	40.1314i	0.0378157	−	0.0728338i
$552$		0			0
$553$	55.2268	−	31.8852i	0.0998676	−	0.0576586i
$554$		0			0
$555$	97.2130	+	486.731i	0.175159	+	0.876993i
$556$		0			0
$557$	−257.207	−	445.496i	−0.461772	−	0.799813i	0.537277	−	0.843406i	$-0.319453\pi$
$557$	−257.207	−	445.496i	−0.461772	−	0.799813i	−0.999049	+	0.0435927i	$0.986120\pi$
$558$		0			0
$559$			93.6143i			0.167467i
$560$		0			0
$561$	−108.264	+	319.758i	−0.192984	+	0.569979i
$562$		0			0
$563$	−378.199	−	218.353i	−0.671756	−	0.387839i	0.124986	−	0.992159i	$-0.460112\pi$
$563$	−378.199	−	218.353i	−0.671756	−	0.387839i	−0.796742	+	0.604320i	$0.793445\pi$
$564$		0			0
$565$			570.433i			1.00962i
$566$		0			0
$567$	−40.2348	+	40.4876i	−0.0709609	+	0.0714067i
$568$		0			0
$569$	−734.219	+	423.901i	−1.29037	+	0.744994i	−0.978719	−	0.205204i	$-0.934214\pi$
$569$	−734.219	+	423.901i	−1.29037	+	0.744994i	−0.311648	+	0.950198i	$0.600881\pi$
$570$		0			0
$571$	−393.820	+	682.116i	−0.689702	+	1.19460i	0.282232	+	0.959346i	$0.408925\pi$
$571$	−393.820	+	682.116i	−0.689702	+	1.19460i	−0.971934	+	0.235253i	$0.924408\pi$
$572$		0			0
$573$	−354.334	+	70.7698i	−0.618383	+	0.123507i
$574$		0			0
$575$	−531.275	+	920.196i	−0.923957	+	1.60034i
$576$		0			0
$577$	291.421			0.505062			0.252531	−	0.967589i	$-0.418737\pi$
$577$	291.421			0.505062			0.252531	+	0.967589i	$0.418737\pi$
$578$		0			0
$579$	68.8979	+	344.961i	0.118995	+	0.595788i
$580$		0			0
$581$	22.2189	−	38.4843i	0.0382425	−	0.0662380i
$582$		0			0
$583$	1587.24	+	916.393i	2.72254	+	1.57186i
$584$		0			0
$585$	−640.394	−	83.2897i	−1.09469	−	0.142376i
$586$		0			0
$587$	899.053			1.53161			0.765803	−	0.643075i	$-0.222342\pi$
$587$	899.053			1.53161			0.765803	+	0.643075i	$0.222342\pi$
$588$		0			0
$589$	23.4658	−	45.1957i	0.0398401	−	0.0767329i
$590$		0			0
$591$	207.948	−	614.174i	0.351858	−	1.03921i
$592$		0			0
$593$	272.320	+	471.672i	0.459224	+	0.795400i	0.998920	−	0.0464601i	$-0.0147941\pi$
$593$	272.320	+	471.672i	0.459224	+	0.795400i	−0.539696	+	0.841860i	$0.681461\pi$
$594$		0			0
$595$	−16.0342	−	27.7721i	−0.0269483	−	0.0466758i
$596$		0			0
$597$	764.056	−	152.602i	1.27983	−	0.255615i
$598$		0			0
$599$		−	430.405i		−	0.718540i	−0.933234	−	0.359270i	$-0.883026\pi$
$599$		−	430.405i		−	0.718540i	0.933234	−	0.359270i	$-0.116974\pi$
$600$		0			0
$601$	640.942	−	370.048i	1.06646	−	0.615721i	0.139247	−	0.990258i	$-0.455532\pi$
$601$	640.942	−	370.048i	1.06646	−	0.615721i	0.927212	+	0.374537i	$0.122198\pi$
$602$		0			0
$603$	−88.0226	+	115.086i	−0.145974	+	0.190856i
$604$		0			0
$605$	2552.04			4.21825
$606$		0			0
$607$	452.418	+	261.204i	0.745334	+	0.430319i	0.824006	−	0.566582i	$-0.191734\pi$
$607$	452.418	+	261.204i	0.745334	+	0.430319i	−0.0786715	+	0.996901i	$0.525068\pi$
$608$		0			0
$609$	−4.76552	−	1.61352i	−0.00782516	−	0.00264946i
$610$		0			0
$611$	−229.347	−	132.413i	−0.375363	−	0.216716i
$612$		0			0
$613$	−129.627	+	224.520i	−0.211463	+	0.366264i	−0.952172	−	0.305561i	$-0.901156\pi$
$613$	−129.627	+	224.520i	−0.211463	+	0.366264i	0.740710	+	0.671825i	$0.234489\pi$
$614$		0			0
$615$	−1420.26	+	1247.50i	−2.30937	+	2.02846i
$616$		0			0
$617$	51.2846			0.0831193			0.0415596	−	0.999136i	$-0.486767\pi$
$617$	51.2846			0.0831193			0.0415596	+	0.999136i	$0.486767\pi$
$618$		0			0
$619$	−338.509	−	586.315i	−0.546865	−	0.947197i	−0.998487	−	0.0549882i	$-0.982488\pi$
$619$	−338.509	−	586.315i	−0.546865	−	0.947197i	0.451622	−	0.892209i	$-0.350845\pi$
$620$		0			0
$621$	−532.099	+	357.347i	−0.856842	+	0.575438i
$622$		0			0
$623$	−45.8484	−	26.4706i	−0.0735929	−	0.0424889i
$624$		0			0
$625$	−129.710	−	224.664i	−0.207536	−	0.359463i
$626$		0			0
$627$	−281.932	−	1142.97i	−0.449652	−	1.82292i
$628$		0			0
$629$	−93.4699	−	53.9649i	−0.148601	−	0.0857947i
$630$		0			0
$631$	−174.679	−	302.553i	−0.276829	−	0.479481i	0.693766	−	0.720200i	$-0.255950\pi$
$631$	−174.679	−	302.553i	−0.276829	−	0.479481i	−0.970595	+	0.240719i	$0.922617\pi$
$632$		0			0
$633$	24.6266	+	123.302i	0.0389045	+	0.194789i
$634$		0			0
$635$	375.873	+	217.010i	0.591926	+	0.341748i
$636$		0			0
$637$	360.868	+	208.347i	0.566512	+	0.327076i
$638$		0			0
$639$	−267.841	−	643.773i	−0.419157	−	1.00747i
$640$		0			0
$641$		−	334.673i		−	0.522111i	−0.965324	−	0.261056i	$-0.915929\pi$
$641$		−	334.673i		−	0.522111i	0.965324	−	0.261056i	$-0.0840706\pi$
$642$		0			0
$643$	29.5540	+	51.1890i	0.0459626	+	0.0796096i	0.888091	−	0.459667i	$-0.152031\pi$
$643$	29.5540	+	51.1890i	0.0459626	+	0.0796096i	−0.842129	+	0.539276i	$0.818698\pi$
$644$		0			0
$645$	−267.747	+	53.4762i	−0.415112	+	0.0829088i
$646$		0			0
$647$	157.684			0.243716			0.121858	−	0.992548i	$-0.461115\pi$
$647$	157.684			0.243716			0.121858	+	0.992548i	$0.461115\pi$
$648$		0			0
$649$	1637.40	+	945.352i	2.52295	+	1.45663i
$650$		0			0
$651$	−5.36689	−	1.81713i	−0.00824407	−	0.00279129i
$652$		0			0
$653$	199.103	−	344.856i	0.304905	−	0.528111i	−0.672335	−	0.740247i	$-0.734709\pi$
$653$	199.103	−	344.856i	0.304905	−	0.528111i	0.977240	+	0.212136i	$0.0680420\pi$
$654$		0			0
$655$	−379.136	+	656.682i	−0.578833	+	1.00257i
$656$		0			0
$657$	659.527	−	274.396i	1.00385	−	0.417649i
$658$		0			0
$659$	−919.880	−	531.093i	−1.39587	−	0.805908i	−0.401916	−	0.915677i	$-0.631656\pi$
$659$	−919.880	−	531.093i	−1.39587	−	0.805908i	−0.993957	+	0.109769i	$0.964989\pi$
$660$		0			0
$661$			406.874i			0.615543i	0.951460	+	0.307772i	$0.0995832\pi$
$661$			406.874i			0.615543i	−0.951460	+	0.307772i	$0.900417\pi$
$662$		0			0
$663$	105.505	−	92.6720i	0.159133	−	0.139777i
$664$		0			0
$665$	99.2481	+	51.5301i	0.149245	+	0.0774889i
$666$		0			0
$667$	−48.9278	−	28.2485i	−0.0733551	−	0.0423516i
$668$		0			0
$669$	−300.001	−	101.575i	−0.448433	−	0.151831i
$670$		0			0
$671$	−208.293			−0.310421
$672$		0			0
$673$	−376.962	+	217.639i	−0.560122	+	0.323387i	−0.753195	−	0.657798i	$-0.771488\pi$
$673$	−376.962	+	217.639i	−0.560122	+	0.323387i	0.193072	+	0.981185i	$0.438155\pi$
$674$		0			0
$675$	−81.8718	−	1205.73i	−0.121292	−	1.78626i
$676$		0			0
$677$	−396.408	+	228.866i	−0.585536	+	0.338059i	−0.763330	−	0.646008i	$-0.776437\pi$
$677$	−396.408	+	228.866i	−0.585536	+	0.338059i	0.177794	+	0.984068i	$0.443104\pi$
$678$		0			0
$679$	46.1397	−	26.6387i	0.0679524	−	0.0392323i
$680$		0			0
$681$	−261.033	−	1306.96i	−0.383309	−	1.91917i
$682$		0			0
$683$		−	332.751i		−	0.487190i	−0.969877	−	0.243595i	$-0.921673\pi$
$683$		−	332.751i		−	0.487190i	0.969877	−	0.243595i	$-0.0783267\pi$
$684$		0			0
$685$	1939.29			2.83107
$686$		0			0
$687$	−468.430	−	533.300i	−0.681849	−	0.776273i
$688$		0			0
$689$	−381.190	−	660.240i	−0.553251	−	0.958259i
$690$		0			0
$691$	42.6760	+	73.9170i	0.0617598	+	0.106971i	0.895252	−	0.445560i	$-0.146995\pi$
$691$	42.6760	+	73.9170i	0.0617598	+	0.106971i	−0.833492	+	0.552531i	$0.813662\pi$
$692$		0			0
$693$	−120.937	+	50.3156i	−0.174512	+	0.0726055i
$694$		0			0
$695$	110.177	+	190.833i	0.158529	+	0.274580i
$696$		0			0
$697$		−	411.055i		−	0.589748i
$698$		0			0
$699$	336.757	+	383.392i	0.481770	+	0.548486i
$700$		0			0
$701$	−264.113	+	457.458i	−0.376766	+	0.652579i	−0.990590	−	0.136865i	$-0.956297\pi$
$701$	−264.113	+	457.458i	−0.376766	+	0.652579i	0.613823	+	0.789443i	$0.289631\pi$
$702$		0			0
$703$	375.993	−	16.8202i	0.534841	−	0.0239263i
$704$		0			0
$705$	247.705	−	731.597i	0.351355	−	1.03773i
$706$		0			0
$707$	−59.8373			−0.0846355
$708$		0			0
$709$	601.129	−	1041.19i	0.847854	−	1.46853i	−0.0352651	−	0.999378i	$-0.511228\pi$
$709$	601.129	−	1041.19i	0.847854	−	1.46853i	0.883119	−	0.469149i	$-0.155439\pi$
$710$		0			0
$711$	−494.795	+	646.924i	−0.695914	+	0.909879i
$712$		0			0
$713$	−55.1021	−	31.8132i	−0.0772820	−	0.0446188i
$714$		0			0
$715$	−1283.41	−	740.975i	−1.79497	−	1.03633i
$716$		0			0
$717$	−877.164	−	998.636i	−1.22338	−	1.39280i
$718$		0			0
$719$	346.447	−	600.064i	0.481846	−	0.834581i	−0.517937	−	0.855419i	$-0.673300\pi$
$719$	346.447	−	600.064i	0.481846	−	0.834581i	0.999783	+	0.0208376i	$0.00663328\pi$
$720$		0			0
$721$		−	19.9998i		−	0.0277390i
$722$		0			0
$723$	−346.398	+	304.263i	−0.479112	+	0.420834i
$724$		0			0
$725$	92.2519	−	53.2616i	0.127244	−	0.0734643i
$726$		0			0
$727$	1308.09			1.79929			0.899646	−	0.436620i	$-0.143824\pi$
$727$	1308.09			1.79929			0.899646	+	0.436620i	$0.143824\pi$
$728$		0			0
$729$	275.810	−	674.811i	0.378340	−	0.925667i
$730$		0			0
$731$	29.6857	−	51.4171i	0.0406097	−	0.0703381i
$732$		0			0
$733$	−216.509	+	375.004i	−0.295374	+	0.511602i	−0.975072	−	0.221890i	$-0.928777\pi$
$733$	−216.509	+	375.004i	−0.295374	+	0.511602i	0.679698	+	0.733492i	$0.262111\pi$
$734$		0			0
$735$	−389.755	+	1151.14i	−0.530279	+	1.56618i
$736$		0			0
$737$	−287.945	+	166.245i	−0.390698	+	0.225570i
$738$		0			0
$739$	617.926	−	1070.28i	0.836165	−	1.44828i	−0.0569131	−	0.998379i	$-0.518126\pi$
$739$	617.926	−	1070.28i	0.836165	−	1.44828i	0.893078	−	0.449901i	$-0.148541\pi$
$740$		0			0
$741$	−136.157	+	470.380i	−0.183748	+	0.634790i
$742$		0			0
$743$	820.310	−	473.606i	1.10405	−	0.637424i	0.166769	−	0.985996i	$-0.446667\pi$
$743$	820.310	−	473.606i	1.10405	−	0.637424i	0.937282	+	0.348572i	$0.113333\pi$
$744$		0			0
$745$	−421.231	+	729.593i	−0.565410	+	0.979319i
$746$		0			0
$747$	−73.1983	+	562.804i	−0.0979896	+	0.753418i
$748$		0			0
$749$	90.8217	−	52.4359i	0.121257	−	0.0700079i
$750$		0			0
$751$		−	1407.77i		−	1.87453i	−0.348623	−	0.937263i	$-0.613351\pi$
$751$		−	1407.77i		−	1.87453i	0.348623	−	0.937263i	$-0.386649\pi$
$752$		0			0
$753$	−496.395	+	99.1431i	−0.659223	+	0.131664i
$754$		0			0
$755$	−1681.73	−	970.946i	−2.22745	−	1.28602i
$756$		0			0
$757$	−325.685	+	564.102i	−0.430231	+	0.745182i	−0.996893	−	0.0787687i	$-0.974901\pi$
$757$	−325.685	+	564.102i	−0.430231	+	0.745182i	0.566662	+	0.823950i	$0.308234\pi$
$758$		0			0
$759$	−1442.38	+	288.081i	−1.90037	+	0.379553i
$760$		0			0
$761$	261.899	−	453.622i	0.344151	−	0.596087i	−0.641048	−	0.767501i	$-0.721500\pi$
$761$	261.899	−	453.622i	0.344151	−	0.596087i	0.985199	+	0.171414i	$0.0548335\pi$
$762$		0			0
$763$		−	40.4354i		−	0.0529953i
$764$		0			0
$765$	325.321	+	248.820i	0.425257	+	0.325254i
$766$		0			0
$767$	−393.236	−	681.104i	−0.512693	−	0.888010i
$768$		0			0
$769$	−184.489			−0.239907			−0.119954	−	0.992779i	$-0.538275\pi$
$769$	−184.489			−0.239907			−0.119954	+	0.992779i	$0.538275\pi$
$770$		0			0
$771$	−918.076	−	310.843i	−1.19076	−	0.403169i
$772$		0			0
$773$	152.283	−	87.9206i	0.197002	−	0.113739i	−0.398254	−	0.917275i	$-0.630384\pi$
$773$	152.283	−	87.9206i	0.197002	−	0.113739i	0.595257	+	0.803536i	$0.297050\pi$
$774$		0			0
$775$	103.893	−	59.9828i	0.134056	−	0.0773971i
$776$		0			0
$777$	−8.20199	−	41.0661i	−0.0105560	−	0.0528522i
$778$		0			0
$779$	771.470	+	1208.10i	0.990333	+	1.55084i
$780$		0			0
$781$		−	1600.09i		−	2.04877i
$782$		0			0
$783$	64.1099	−	4.35321i	0.0818773	−	0.00555966i
$784$		0			0
$785$	−824.342	+	1427.80i	−1.05012	+	1.81886i
$786$		0			0
$787$	80.0272	+	46.2037i	0.101686	+	0.0587087i	0.549981	−	0.835177i	$-0.314635\pi$
$787$	80.0272	+	46.2037i	0.101686	+	0.0587087i	−0.448294	+	0.893886i	$0.647968\pi$
$788$		0			0
$789$	206.239	−	609.126i	0.261393	−	0.772023i
$790$		0			0
$791$		−	48.1281i		−	0.0608447i
$792$		0			0
$793$	75.0350	+	43.3215i	0.0946217	+	0.0546299i
$794$		0			0
$795$	1670.61	−	1467.40i	2.10140	−	1.84579i
$796$		0			0
$797$	769.440	+	444.236i	0.965420	+	0.557385i	0.897837	−	0.440328i	$-0.145138\pi$
$797$	769.440	+	444.236i	0.965420	+	0.557385i	0.0675830	+	0.997714i	$0.478471\pi$
$798$		0			0
$799$	83.9783	+	145.455i	0.105104	+	0.182046i
$800$		0			0
$801$	670.498	+	87.2050i	0.837076	+	0.108870i
$802$		0			0
$803$	1639.24			2.04140
$804$		0			0
$805$	69.8607	−	121.002i	0.0867834	−	0.150313i
$806$		0			0
$807$	−884.078	+	776.540i	−1.09551	+	0.962256i
$808$		0			0
$809$	−939.940			−1.16185			−0.580927	−	0.813956i	$-0.697310\pi$
$809$	−939.940			−1.16185			−0.580927	+	0.813956i	$0.697310\pi$
$810$		0			0
$811$	361.756	−	208.860i	0.446062	−	0.257534i	−0.260104	−	0.965581i	$-0.583757\pi$
$811$	361.756	−	208.860i	0.446062	−	0.257534i	0.706166	+	0.708047i	$0.250423\pi$
$812$		0			0
$813$	355.831	+	405.108i	0.437677	+	0.498287i
$814$		0			0
$815$	994.016	+	1721.69i	1.21965	+	2.11250i
$816$		0			0
$817$	9.25267	+	206.831i	0.0113252	+	0.253159i
$818$		0			0
$819$	54.0309	+	7.02726i	0.0659718	+	0.00858029i
$820$		0			0
$821$	280.068	−	485.091i	0.341130	−	0.590854i	−0.643513	−	0.765435i	$-0.722524\pi$
$821$	280.068	−	485.091i	0.341130	−	0.590854i	0.984643	+	0.174581i	$0.0558571\pi$
$822$		0			0
$823$	−1247.92			−1.51631			−0.758154	−	0.652076i	$-0.773898\pi$
$823$	−1247.92			−1.51631			−0.758154	+	0.652076i	$0.773898\pi$
$824$		0			0
$825$	889.382	−	2626.79i	1.07804	−	3.18399i
$826$		0			0
$827$	496.644	−	286.737i	0.600537	−	0.346720i	−0.168716	−	0.985665i	$-0.553962\pi$
$827$	496.644	−	286.737i	0.600537	−	0.346720i	0.769253	+	0.638945i	$0.220629\pi$
$828$		0			0
$829$			921.847i			1.11200i	0.831183	+	0.555999i	$0.187664\pi$
$829$			921.847i			1.11200i	−0.831183	+	0.555999i	$0.812336\pi$
$830$		0			0
$831$	664.008	−	132.620i	0.799047	−	0.159591i
$832$		0			0
$833$	−132.137	−	228.867i	−0.158627	−	0.274751i
$834$		0			0
$835$	−1818.28	+	1049.78i	−2.17758	+	1.25723i
$836$		0			0
$837$	72.2000	−	4.90255i	0.0862604	−	0.00585729i
$838$		0			0
$839$		−	498.538i		−	0.594205i	−0.954846	−	0.297102i	$-0.903980\pi$
$839$		−	498.538i		−	0.594205i	0.954846	−	0.297102i	$-0.0960203\pi$
$840$		0			0
$841$	−417.668	−	723.422i	−0.496633	−	0.860193i
$842$		0			0
$843$	312.871	−	274.814i	0.371140	−	0.325996i
$844$		0			0
$845$	−397.540	−	688.560i	−0.470462	−	0.814864i
$846$		0			0
$847$	−215.319			−0.254214
$848$		0			0
$849$	−135.038	+	26.9706i	−0.159055	+	0.0317675i
$850$		0			0
$851$		−	470.246i		−	0.552581i
$852$		0			0
$853$	1363.70			1.59872			0.799358	−	0.600855i	$-0.205173\pi$
$853$	1363.70			1.59872			0.799358	+	0.600855i	$0.205173\pi$
$854$		0			0
$855$	−1423.12	−	120.725i	−1.66446	−	0.141198i
$856$		0			0
$857$			1338.69i			1.56207i	0.624487	+	0.781036i	$0.285308\pi$
$857$			1338.69i			1.56207i	−0.624487	+	0.781036i	$0.714692\pi$
$858$		0			0
$859$	632.570			0.736403			0.368202	−	0.929746i	$-0.379974\pi$
$859$	632.570			0.736403			0.368202	+	0.929746i	$0.379974\pi$
$860$		0			0
$861$	119.829	−	105.253i	0.139175	−	0.122246i
$862$		0			0
$863$		−	731.113i		−	0.847176i	−0.905855	−	0.423588i	$-0.860770\pi$
$863$		−	731.113i		−	0.847176i	0.905855	−	0.423588i	$-0.139230\pi$
$864$		0			0
$865$	1988.10	−	1147.83i	2.29838	−	1.32697i
$866$		0			0
$867$	762.873	−	152.366i	0.879900	−	0.175739i
$868$		0			0
$869$	−1618.60	+	934.500i	−1.86260	+	1.07537i
$870$		0			0
$871$	138.305			0.158789
$872$		0			0
$873$	−413.380	+	540.478i	−0.473517	+	0.619104i
$874$		0			0
$875$	58.1489	+	100.717i	0.0664559	+	0.115105i
$876$		0			0
$877$	1002.62	−	578.861i	1.14323	−	0.660047i	0.196005	−	0.980603i	$-0.437203\pi$
$877$	1002.62	−	578.861i	1.14323	−	0.660047i	0.947230	+	0.320556i	$0.103870\pi$
$878$		0			0
$879$	−930.455	+	817.277i	−1.05854	+	0.929780i
$880$		0			0
$881$	18.0365			0.0204728			0.0102364	−	0.999948i	$-0.496742\pi$
$881$	18.0365			0.0204728			0.0102364	+	0.999948i	$0.496742\pi$
$882$		0			0
$883$	494.516	+	856.527i	0.560041	+	0.970019i	0.997492	+	0.0707772i	$0.0225479\pi$
$883$	494.516	+	856.527i	0.560041	+	0.970019i	−0.437451	+	0.899242i	$0.644119\pi$
$884$		0			0
$885$	1723.40	−	1513.77i	1.94735	−	1.71048i
$886$		0			0
$887$		−	1210.81i		−	1.36506i	−0.730859	−	0.682528i	$-0.760880\pi$
$887$		−	1210.81i		−	1.36506i	0.730859	−	0.682528i	$-0.239120\pi$
$888$		0			0
$889$	−31.7129	−	18.3094i	−0.0356725	−	0.0205955i
$890$		0			0
$891$	1179.21	−	1186.62i	1.32347	−	1.33179i
$892$		0			0
$893$	−519.806	−	269.886i	−0.582089	−	0.302224i
$894$		0			0
$895$	−766.777	+	442.699i	−0.856734	+	0.494636i
$896$		0			0
$897$	579.516	+	196.213i	0.646060	+	0.218744i
$898$		0			0
$899$	3.18935	+	5.52412i	0.00354767	+	0.00614474i
$900$		0			0
$901$			483.511i			0.536638i
$902$		0			0
$903$	22.5902	−	4.51185i	0.0250168	−	0.00499652i
$904$		0			0
$905$	−1300.32	−	750.742i	−1.43682	−	0.829549i
$906$		0			0
$907$			322.748i			0.355842i	0.984045	+	0.177921i	$0.0569371\pi$
$907$			322.748i			0.355842i	−0.984045	+	0.177921i	$0.943063\pi$
$908$		0			0
$909$	705.589	−	293.559i	0.776225	−	0.322948i
$910$		0			0
$911$	−567.038	+	327.380i	−0.622435	+	0.359363i	−0.777816	−	0.628492i	$-0.783673\pi$
$911$	−567.038	+	327.380i	−0.622435	+	0.359363i	0.155382	+	0.987855i	$0.450339\pi$
$912$		0			0
$913$	−651.198	+	1127.91i	−0.713251	+	1.23539i
$914$		0			0
$915$	−81.0414	+	239.356i	−0.0885698	+	0.261591i
$916$		0			0
$917$	31.9882	−	55.4051i	0.0348835	−	0.0604200i
$918$		0			0
$919$	−1299.09			−1.41359			−0.706796	−	0.707417i	$-0.749860\pi$
$919$	−1299.09			−1.41359			−0.706796	+	0.707417i	$0.749860\pi$
$920$		0			0
$921$	125.579	−	110.304i	0.136351	−	0.119765i
$922$		0			0
$923$	−332.792	+	576.413i	−0.360555	+	0.624500i
$924$		0			0
$925$	767.848	+	443.317i	0.830106	+	0.479262i
$926$		0			0
$927$	98.1182	+	235.833i	0.105845	+	0.254405i
$928$		0			0
$929$	521.542			0.561401			0.280701	−	0.959795i	$-0.409433\pi$
$929$	521.542			0.561401			0.280701	+	0.959795i	$0.409433\pi$
$930$		0			0
$931$	817.894	+	424.655i	0.878511	+	0.456127i
$932$		0			0
$933$	−569.582	−	648.459i	−0.610484	−	0.695026i
$934$		0			0
$935$	469.936	+	813.953i	0.502606	+	0.870538i
$936$		0			0
$937$	−625.318	−	1083.08i	−0.667362	−	1.15590i	−0.978639	−	0.205586i	$-0.934090\pi$
$937$	−625.318	−	1083.08i	−0.667362	−	1.15590i	0.311277	−	0.950319i	$-0.399243\pi$
$938$		0			0
$939$	1004.41	+	1143.50i	1.06966	+	1.21778i
$940$		0			0
$941$		−	191.045i		−	0.203023i	−0.994834	−	0.101512i	$-0.967632\pi$
$941$		−	191.045i		−	0.203023i	0.994834	−	0.101512i	$-0.0323679\pi$
$942$		0			0
$943$	1551.01	−	895.476i	1.64476	−	0.949603i
$944$		0			0
$945$	10.7658	+	158.549i	0.0113924	+	0.167776i
$946$		0			0
$947$	−584.486			−0.617198			−0.308599	−	0.951192i	$-0.599860\pi$
$947$	−584.486			−0.617198			−0.308599	+	0.951192i	$0.599860\pi$
$948$		0			0
$949$	−590.519	−	340.936i	−0.622254	−	0.359258i
$950$		0			0
$951$	−112.926	+	99.1899i	−0.118744	+	0.104301i
$952$		0			0
$953$	221.454	+	127.856i	0.232375	+	0.134162i	0.611667	−	0.791115i	$-0.290499\pi$
$953$	221.454	+	127.856i	0.232375	+	0.134162i	−0.379292	+	0.925277i	$0.623832\pi$
$954$		0			0
$955$	−502.987	+	871.198i	−0.526688	+	0.912250i
$956$		0			0
$957$	139.669	+	47.2895i	0.145945	+	0.0494143i
$958$		0			0
$959$	−163.620			−0.170615
$960$		0			0
$961$	−476.908	−	826.029i	−0.496262	−	0.859552i
$962$		0			0
$963$	−813.701	+	1063.88i	−0.844965	+	1.10476i
$964$		0			0
$965$	848.155	+	489.682i	0.878917	+	0.507443i
$966$		0			0
$967$	387.929	+	671.912i	0.401167	+	0.694842i	0.993867	−	0.110582i	$-0.0352713\pi$
$967$	387.929	+	671.912i	0.401167	+	0.694842i	−0.592700	+	0.805423i	$0.701938\pi$
$968$		0			0
$969$	223.944	−	215.177i	0.231108	−	0.222061i
$970$		0			0
$971$	618.028	+	356.819i	0.636486	+	0.367476i	0.783260	−	0.621695i	$-0.213555\pi$
$971$	618.028	+	356.819i	0.636486	+	0.367476i	−0.146773	+	0.989170i	$0.546889\pi$
$972$		0			0
$973$	−9.29581	−	16.1008i	−0.00955376	−	0.0165476i
$974$		0			0
$975$	−866.719	+	761.293i	−0.888943	+	0.780814i
$976$		0			0
$977$	749.812	+	432.904i	0.767463	+	0.443095i	0.831969	−	0.554822i	$-0.187214\pi$
$977$	749.812	+	432.904i	0.767463	+	0.443095i	−0.0645057	+	0.997917i	$0.520547\pi$
$978$		0			0
$979$	1343.74	+	775.807i	1.37256	+	0.792449i
$980$		0			0
$981$	198.374	+	476.805i	0.202216	+	0.486040i
$982$		0			0
$983$			1579.12i			1.60642i	0.595693	+	0.803212i	$0.296878\pi$
$983$			1579.12i			1.60642i	−0.595693	+	0.803212i	$0.703122\pi$
$984$		0			0
$985$	−902.627	−	1563.40i	−0.916372	−	1.58720i
$986$		0			0
$987$	−20.8992	+	61.7258i	−0.0211745	+	0.0625388i
$988$		0			0
$989$	258.679			0.261556
$990$		0			0
$991$	208.038	+	120.111i	0.209927	+	0.121202i	0.601278	−	0.799040i	$-0.294659\pi$
$991$	208.038	+	120.111i	0.209927	+	0.121202i	−0.391350	+	0.920242i	$0.627992\pi$
$992$		0			0
$993$	182.513	+	913.813i	0.183799	+	0.920255i
$994$		0			0
$995$	1084.60	−	1878.58i	1.09005	−	1.88802i
$996$		0			0
$997$	227.311	−	393.715i	0.227995	−	0.394900i	−0.729218	−	0.684281i	$-0.760116\pi$
$997$	227.311	−	393.715i	0.227995	−	0.394900i	0.957214	+	0.289381i	$0.0934495\pi$
$998$		0			0
$999$	298.185	+	444.004i	0.298483	+	0.444449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.24	✓	80
3.2	odd	2		2052.3.s.a.901.38		80
9.2	odd	6		2052.3.bl.a.1585.3		80
9.7	even	3		684.3.bl.a.673.11	yes	80
19.12	odd	6		684.3.bl.a.373.11	yes	80
57.50	even	6		2052.3.bl.a.145.3		80
171.88	odd	6	inner	684.3.s.a.601.24	yes	80
171.164	even	6		2052.3.s.a.829.38		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.24	✓	80	1.1	even	1	trivial
684.3.s.a.601.24	yes	80	171.88	odd	6	inner
684.3.bl.a.373.11	yes	80	19.12	odd	6
684.3.bl.a.673.11	yes	80	9.7	even	3
2052.3.s.a.829.38		80	171.164	even	6
2052.3.s.a.901.38		80	3.2	odd	2
2052.3.bl.a.145.3		80	57.50	even	6
2052.3.bl.a.1585.3		80	9.2	odd	6

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.962094 - 2.84154i) q^{3} +(-4.17611 - 7.23323i) q^{5} +(0.352343 + 0.610277i) q^{7} +(-7.14875 - 5.46767i) q^{9} +O(q^{10})\)	\(q+(0.962094 - 2.84154i) q^{3} +(-4.17611 - 7.23323i) q^{5} +(0.352343 + 0.610277i) q^{7} +(-7.14875 - 5.46767i) q^{9} +(-10.3266 - 17.8862i) q^{11} +8.59104i q^{13} +(-24.5713 + 4.90754i) q^{15} +(2.72428 - 4.71858i) q^{17} +(0.849123 + 18.9810i) q^{19} +(2.07312 - 0.414056i) q^{21} +23.7392 q^{23} +(-22.3797 + 38.7628i) q^{25} +(-22.4144 + 15.0531i) q^{27} +(-2.06106 - 1.18995i) q^{29} +(-2.32115 - 1.34012i) q^{31} +(-60.7595 + 12.1353i) q^{33} +(2.94285 - 5.09716i) q^{35} -19.8089i q^{37} +(24.4118 + 8.26539i) q^{39} +(65.3355 - 37.7215i) q^{41} +10.8967 q^{43} +(-9.69495 + 74.5421i) q^{45} +(-15.4130 + 26.6960i) q^{47} +(24.2517 - 42.0052i) q^{49} +(-10.7871 - 12.2809i) q^{51} +(-76.8522 + 44.3706i) q^{53} +(-86.2498 + 149.389i) q^{55} +(54.7523 + 15.8487i) q^{57} +(-79.2807 + 45.7727i) q^{59} +(5.04264 - 8.73410i) q^{61} +(0.817975 - 6.28921i) q^{63} +(62.1410 - 35.8771i) q^{65} -16.0987i q^{67} +(22.8393 - 67.4559i) q^{69} +(67.0947 + 38.7371i) q^{71} +(-39.6851 + 68.7366i) q^{73} +(88.6148 + 100.886i) q^{75} +(7.27700 - 12.6041i) q^{77} -90.4947i q^{79} +(21.2092 + 78.1740i) q^{81} +(-31.5302 - 54.6119i) q^{83} -45.5074 q^{85} +(-5.36424 + 4.71175i) q^{87} +(-65.0621 + 37.5636i) q^{89} +(-5.24291 + 3.02700i) q^{91} +(-6.04116 + 5.30633i) q^{93} +(133.748 - 85.4086i) q^{95} -75.6045i q^{97} +(-23.9734 + 184.326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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