LMFDB - Embedded newform 684.3.be.a.425.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(425,684)]

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, 1, 2]))

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

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

chi := DirichletCharacter("684.425");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.be (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			425.2
Character	$\chi$	$=$	684.425
Dual form			684.3.be.a.581.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.95244 - 0.532061i) q^{3} +(-2.56758 - 1.48239i) q^{5} +(-4.97804 + 8.62221i) q^{7} +(8.43382 + 3.14176i) q^{9} +O(q^{10})$	\(q+(-2.95244 - 0.532061i) q^{3} +(-2.56758 - 1.48239i) q^{5} +(-4.97804 + 8.62221i) q^{7} +(8.43382 + 3.14176i) q^{9} +(4.82506 + 2.78575i) q^{11} +0.606341 q^{13} +(6.79191 + 5.74279i) q^{15} +(-6.44927 + 3.72349i) q^{17} +(16.1298 - 10.0414i) q^{19} +(19.2849 - 22.8080i) q^{21} +42.9104i q^{23} +(-8.10502 - 14.0383i) q^{25} +(-23.2288 - 13.7632i) q^{27} +(19.3704 - 11.1835i) q^{29} +(-17.4498 - 30.2240i) q^{31} +(-12.7635 - 10.7920i) q^{33} +(25.5630 - 14.7588i) q^{35} -28.5309 q^{37} +(-1.79019 - 0.322611i) q^{39} +(-3.63788 - 2.10033i) q^{41} -0.467266 q^{43} +(-16.9972 - 20.5690i) q^{45} +(-21.2464 + 12.2666i) q^{47} +(-25.0617 - 43.4081i) q^{49} +(21.0222 - 7.56198i) q^{51} +(-90.3257 - 52.1496i) q^{53} +(-8.25916 - 14.3053i) q^{55} +(-52.9649 + 21.0647i) q^{57} +(-62.1999 - 35.9111i) q^{59} +(11.9112 + 20.6307i) q^{61} +(-69.0728 + 57.0784i) q^{63} +(-1.55683 - 0.898836i) q^{65} +83.7885 q^{67} +(22.8310 - 126.690i) q^{69} +(-44.3939 + 25.6309i) q^{71} +(-64.3669 - 111.487i) q^{73} +(16.4604 + 45.7596i) q^{75} +(-48.0387 + 27.7351i) q^{77} +127.840 q^{79} +(61.2587 + 52.9941i) q^{81} +(-38.6456 - 22.3121i) q^{83} +22.0787 q^{85} +(-63.1402 + 22.7124i) q^{87} +(-105.771 - 61.0671i) q^{89} +(-3.01839 + 5.22800i) q^{91} +(35.4386 + 98.5190i) q^{93} +(-56.2999 + 1.87153i) q^{95} +6.37361 q^{97} +(31.9415 + 38.6537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.95244	−	0.532061i	−0.984147	−	0.177354i
$3$	−2.95244	−	0.532061i	−0.984147	−	0.177354i
$4$		0			0
$5$	−2.56758	−	1.48239i	−0.513516	−	0.296479i	0.220762	−	0.975328i	$-0.429146\pi$
$5$	−2.56758	−	1.48239i	−0.513516	−	0.296479i	−0.734278	+	0.678849i	$0.762479\pi$
$6$		0			0
$7$	−4.97804	+	8.62221i	−0.711148	+	1.23174i	0.253278	+	0.967393i	$0.418491\pi$
$7$	−4.97804	+	8.62221i	−0.711148	+	1.23174i	−0.964426	+	0.264351i	$0.914842\pi$
$8$		0			0
$9$	8.43382	+	3.14176i	0.937091	+	0.349084i
$10$		0			0
$11$	4.82506	+	2.78575i	0.438642	+	0.253250i	0.703021	−	0.711169i	$-0.251834\pi$
$11$	4.82506	+	2.78575i	0.438642	+	0.253250i	−0.264380	+	0.964419i	$0.585167\pi$
$12$		0			0
$13$	0.606341			0.0466416			0.0233208	−	0.999728i	$-0.492576\pi$
$13$	0.606341			0.0466416			0.0233208	+	0.999728i	$0.492576\pi$
$14$		0			0
$15$	6.79191	+	5.74279i	0.452794	+	0.382853i
$16$		0			0
$17$	−6.44927	+	3.72349i	−0.379369	+	0.219029i	−0.677544	−	0.735483i	$-0.736956\pi$
$17$	−6.44927	+	3.72349i	−0.379369	+	0.219029i	0.298175	+	0.954511i	$0.403622\pi$
$18$		0			0
$19$	16.1298	−	10.0414i	0.848935	−	0.528497i
$19$	16.1298	−	10.0414i	0.848935	−	0.528497i
$20$		0			0
$21$	19.2849	−	22.8080i	0.918329	−	1.08609i
$22$		0			0
$23$			42.9104i			1.86567i	0.360305	+	0.932835i	$0.382673\pi$
$23$			42.9104i			1.86567i	−0.360305	+	0.932835i	$0.617327\pi$
$24$		0			0
$25$	−8.10502	−	14.0383i	−0.324201	−	0.561532i
$26$		0			0
$27$	−23.2288	−	13.7632i	−0.860324	−	0.509747i
$28$		0			0
$29$	19.3704	−	11.1835i	0.667944	−	0.385638i	−0.127353	−	0.991857i	$-0.540648\pi$
$29$	19.3704	−	11.1835i	0.667944	−	0.385638i	0.795297	+	0.606220i	$0.207315\pi$
$30$		0			0
$31$	−17.4498	−	30.2240i	−0.562898	−	0.974968i	−0.997242	−	0.0742207i	$-0.976353\pi$
$31$	−17.4498	−	30.2240i	−0.562898	−	0.974968i	0.434344	−	0.900747i	$-0.356980\pi$
$32$		0			0
$33$	−12.7635	−	10.7920i	−0.386773	−	0.327030i
$34$		0			0
$35$	25.5630	−	14.7588i	0.730372	−	0.421681i
$36$		0			0
$37$	−28.5309			−0.771106			−0.385553	−	0.922686i	$-0.625989\pi$
$37$	−28.5309			−0.771106			−0.385553	+	0.922686i	$0.625989\pi$
$38$		0			0
$39$	−1.79019	−	0.322611i	−0.0459022	−	0.00827207i
$40$		0			0
$41$	−3.63788	−	2.10033i	−0.0887287	−	0.0512275i	0.454979	−	0.890502i	$-0.349647\pi$
$41$	−3.63788	−	2.10033i	−0.0887287	−	0.0512275i	−0.543708	+	0.839275i	$0.682980\pi$
$42$		0			0
$43$	−0.467266			−0.0108667			−0.00543333	−	0.999985i	$-0.501729\pi$
$43$	−0.467266			−0.0108667			−0.00543333	+	0.999985i	$0.501729\pi$
$44$		0			0
$45$	−16.9972	−	20.5690i	−0.377715	−	0.457088i
$46$		0			0
$47$	−21.2464	+	12.2666i	−0.452051	+	0.260992i	−0.708696	−	0.705514i	$-0.750716\pi$
$47$	−21.2464	+	12.2666i	−0.452051	+	0.260992i	0.256645	+	0.966506i	$0.417383\pi$
$48$		0			0
$49$	−25.0617	−	43.4081i	−0.511463	−	0.885880i
$50$		0			0
$51$	21.0222	−	7.56198i	0.412200	−	0.148274i
$52$		0			0
$53$	−90.3257	−	52.1496i	−1.70426	−	0.983954i	−0.941341	−	0.337458i	$-0.890433\pi$
$53$	−90.3257	−	52.1496i	−1.70426	−	0.983954i	−0.762918	−	0.646496i	$-0.776234\pi$
$54$		0			0
$55$	−8.25916	−	14.3053i	−0.150166	−	0.260096i
$56$		0			0
$57$	−52.9649	+	21.0647i	−0.929208	+	0.369557i
$58$		0			0
$59$	−62.1999	−	35.9111i	−1.05424	−	0.608663i	−0.130404	−	0.991461i	$-0.541627\pi$
$59$	−62.1999	−	35.9111i	−1.05424	−	0.608663i	−0.923832	+	0.382798i	$0.874961\pi$
$60$		0			0
$61$	11.9112	+	20.6307i	0.195265	+	0.338209i	0.946987	−	0.321271i	$-0.104110\pi$
$61$	11.9112	+	20.6307i	0.195265	+	0.338209i	−0.751722	+	0.659480i	$0.770777\pi$
$62$		0			0
$63$	−69.0728	+	57.0784i	−1.09639	+	0.906007i
$64$		0			0
$65$	−1.55683	−	0.898836i	−0.0239512	−	0.0138282i
$66$		0			0
$67$	83.7885			1.25057			0.625287	−	0.780395i	$-0.284982\pi$
$67$	83.7885			1.25057			0.625287	+	0.780395i	$0.284982\pi$
$68$		0			0
$69$	22.8310	−	126.690i	0.330883	−	1.83609i
$70$		0			0
$71$	−44.3939	+	25.6309i	−0.625267	+	0.360998i	−0.778917	−	0.627127i	$-0.784231\pi$
$71$	−44.3939	+	25.6309i	−0.625267	+	0.360998i	0.153650	+	0.988125i	$0.450897\pi$
$72$		0			0
$73$	−64.3669	−	111.487i	−0.881738	−	1.52721i	−0.849407	−	0.527738i	$-0.823040\pi$
$73$	−64.3669	−	111.487i	−0.881738	−	1.52721i	−0.0323304	−	0.999477i	$-0.510293\pi$
$74$		0			0
$75$	16.4604	+	45.7596i	0.219471	+	0.610129i
$76$		0			0
$77$	−48.0387	+	27.7351i	−0.623879	+	0.360197i
$78$		0			0
$79$	127.840			1.61823			0.809115	−	0.587651i	$-0.199947\pi$
$79$	127.840			1.61823			0.809115	+	0.587651i	$0.199947\pi$
$80$		0			0
$81$	61.2587	+	52.9941i	0.756280	+	0.654248i
$82$		0			0
$83$	−38.6456	−	22.3121i	−0.465610	−	0.268820i	0.248790	−	0.968557i	$-0.419967\pi$
$83$	−38.6456	−	22.3121i	−0.465610	−	0.268820i	−0.714400	+	0.699737i	$0.753300\pi$
$84$		0			0
$85$	22.0787			0.259749
$86$		0			0
$87$	−63.1402	+	22.7124i	−0.725750	+	0.261062i
$88$		0			0
$89$	−105.771	−	61.0671i	−1.18844	−	0.686148i	−0.230490	−	0.973075i	$-0.574033\pi$
$89$	−105.771	−	61.0671i	−1.18844	−	0.686148i	−0.957952	+	0.286927i	$0.907366\pi$
$90$		0			0
$91$	−3.01839	+	5.22800i	−0.0331691	+	0.0574506i
$92$		0			0
$93$	35.4386	+	98.5190i	0.381060	+	1.05934i
$94$		0			0
$95$	−56.2999	+	1.87153i	−0.592630	+	0.0197003i
$96$		0			0
$97$	6.37361			0.0657073			0.0328536	−	0.999460i	$-0.489540\pi$
$97$	6.37361			0.0657073			0.0328536	+	0.999460i	$0.489540\pi$
$98$		0			0
$99$	31.9415	+	38.6537i	0.322642	+	0.390441i
$100$		0			0
$101$	126.225	−	72.8763i	1.24976	−	0.721548i	0.278696	−	0.960379i	$-0.410098\pi$
$101$	126.225	−	72.8763i	1.24976	−	0.721548i	0.971061	+	0.238832i	$0.0767644\pi$
$102$		0			0
$103$	−29.4519	−	51.0122i	−0.285941	−	0.495264i	0.686896	−	0.726756i	$-0.258973\pi$
$103$	−29.4519	−	51.0122i	−0.285941	−	0.495264i	−0.972837	+	0.231491i	$0.925639\pi$
$104$		0			0
$105$	−83.3259	+	29.9735i	−0.793580	+	0.285462i
$106$		0			0
$107$		−	88.0306i		−	0.822716i	−0.911474	−	0.411358i	$-0.865055\pi$
$107$		−	88.0306i		−	0.822716i	0.911474	−	0.411358i	$-0.134945\pi$
$108$		0			0
$109$	−63.0785	−	109.255i	−0.578701	−	1.00234i	−0.995629	−	0.0934004i	$-0.970226\pi$
$109$	−63.0785	−	109.255i	−0.578701	−	1.00234i	0.416927	−	0.908940i	$-0.363107\pi$
$110$		0			0
$111$	84.2359	+	15.1802i	0.758882	+	0.136759i
$112$		0			0
$113$	41.6558	−	24.0500i	0.368635	−	0.212832i	−0.304227	−	0.952600i	$-0.598398\pi$
$113$	41.6558	−	24.0500i	0.368635	−	0.212832i	0.672862	+	0.739768i	$0.265065\pi$
$114$		0			0
$115$	63.6101	−	110.176i	0.553131	−	0.958051i
$116$		0			0
$117$	5.11377	+	1.90498i	0.0437075	+	0.0162819i
$118$		0			0
$119$		−	74.1427i		−	0.623048i
$120$		0			0
$121$	−44.9792	−	77.9062i	−0.371729	−	0.643853i
$122$		0			0
$123$	9.62311	+	8.13667i	0.0782367	+	0.0661518i
$124$		0			0
$125$			122.179i			0.977432i
$126$		0			0
$127$	29.3764	−	50.8815i	0.231311	−	0.400642i	−0.726883	−	0.686761i	$-0.759032\pi$
$127$	29.3764	−	50.8815i	0.231311	−	0.400642i	0.958194	+	0.286119i	$0.0923653\pi$
$128$		0			0
$129$	1.37958	+	0.248614i	0.0106944	+	0.00192724i
$130$		0			0
$131$	−140.928	−	81.3649i	−1.07579	−	0.621106i	−0.146030	−	0.989280i	$-0.546650\pi$
$131$	−140.928	−	81.3649i	−1.07579	−	0.621106i	−0.929757	+	0.368174i	$0.879983\pi$
$132$		0			0
$133$	6.28480	+	189.061i	0.0472541	+	1.42151i
$134$		0			0
$135$	39.2393	+	69.7722i	0.290661	+	0.516831i
$136$		0			0
$137$	1.13129	−	0.653152i	0.00825761	−	0.00476753i	−0.495866	−	0.868399i	$-0.665149\pi$
$137$	1.13129	−	0.653152i	0.00825761	−	0.00476753i	0.504123	+	0.863632i	$0.331816\pi$
$138$		0			0
$139$	245.765			1.76809			0.884047	−	0.467397i	$-0.154808\pi$
$139$	245.765			1.76809			0.884047	+	0.467397i	$0.154808\pi$
$140$		0			0
$141$	69.2553	−	24.9121i	0.491172	−	0.176681i
$142$		0			0
$143$	2.92563	+	1.68911i	0.0204590	+	0.0118120i
$144$		0			0
$145$	−66.3134			−0.457334
$146$		0			0
$147$	50.8974	+	141.494i	0.346241	+	0.962547i
$148$		0			0
$149$	60.7976	+	35.1015i	0.408037	+	0.235580i	0.689946	−	0.723861i	$-0.257634\pi$
$149$	60.7976	+	35.1015i	0.408037	+	0.235580i	−0.281909	+	0.959441i	$0.590968\pi$
$150$		0			0
$151$	−48.3016	+	83.6609i	−0.319878	+	0.554046i	−0.980462	−	0.196706i	$-0.936975\pi$
$151$	−48.3016	+	83.6609i	−0.319878	+	0.554046i	0.660584	+	0.750752i	$0.270309\pi$
$152$		0			0
$153$	−66.0903	+	11.1412i	−0.431963	+	0.0728182i
$154$		0			0
$155$			103.470i			0.667549i
$156$		0			0
$157$	−114.640	+	198.562i	−0.730191	+	1.26473i	0.226611	+	0.973985i	$0.427235\pi$
$157$	−114.640	+	198.562i	−0.730191	+	1.26473i	−0.956801	+	0.290742i	$0.906098\pi$
$158$		0			0
$159$	238.935	+	202.027i	1.50273	+	1.27061i
$160$		0			0
$161$	−369.983	−	213.610i	−2.29803	−	1.32677i
$162$		0			0
$163$	34.1035			0.209224			0.104612	−	0.994513i	$-0.466640\pi$
$163$	34.1035			0.209224			0.104612	+	0.994513i	$0.466640\pi$
$164$		0			0
$165$	16.7734	+	46.6299i	0.101657	+	0.282605i
$166$		0			0
$167$		−	9.80527i		−	0.0587142i	−0.999569	−	0.0293571i	$-0.990654\pi$
$167$		−	9.80527i		−	0.0587142i	0.999569	−	0.0293571i	$-0.00934600\pi$
$168$		0			0
$169$	−168.632			−0.997825
$170$		0			0
$171$	167.583	−	34.0118i	0.980020	−	0.198900i
$172$		0			0
$173$			255.924i			1.47933i	0.672974	+	0.739666i	$0.265017\pi$
$173$			255.924i			1.47933i	−0.672974	+	0.739666i	$0.734983\pi$
$174$		0			0
$175$	161.388			0.922219
$176$		0			0
$177$	164.535	+	139.120i	0.929574	+	0.785987i
$178$		0			0
$179$			282.690i			1.57928i	0.613573	+	0.789638i	$0.289731\pi$
$179$			282.690i			1.57928i	−0.613573	+	0.789638i	$0.710269\pi$
$180$		0			0
$181$	75.0927	−	130.064i	0.414877	−	0.718588i	−0.580539	−	0.814233i	$-0.697158\pi$
$181$	75.0927	−	130.064i	0.414877	−	0.718588i	0.995416	+	0.0956449i	$0.0304913\pi$
$182$		0			0
$183$	−24.1902	−	67.2485i	−0.132187	−	0.367478i
$184$		0			0
$185$	73.2555	+	42.2941i	0.395975	+	0.228617i
$186$		0			0
$187$	−41.4908			−0.221876
$188$		0			0
$189$	234.303	−	131.770i	1.23970	−	0.697194i
$190$		0			0
$191$	53.3278	+	30.7888i	0.279203	+	0.161198i	0.633063	−	0.774101i	$-0.281798\pi$
$191$	53.3278	+	30.7888i	0.279203	+	0.161198i	−0.353860	+	0.935299i	$0.615131\pi$
$192$		0			0
$193$	149.094	−	258.238i	0.772508	−	1.33802i	−0.163677	−	0.986514i	$-0.552335\pi$
$193$	149.094	−	258.238i	0.772508	−	1.33802i	0.936185	−	0.351509i	$-0.114331\pi$
$194$		0			0
$195$	4.11821	+	3.48209i	0.0211190	+	0.0178569i
$196$		0			0
$197$		−	45.3021i		−	0.229960i	−0.993368	−	0.114980i	$-0.963320\pi$
$197$		−	45.3021i		−	0.229960i	0.993368	−	0.114980i	$-0.0366804\pi$
$198$		0			0
$199$	18.8601	−	32.6666i	0.0947743	−	0.164154i	−0.814740	−	0.579826i	$-0.803120\pi$
$199$	18.8601	−	32.6666i	0.0947743	−	0.164154i	0.909514	+	0.415672i	$0.136454\pi$
$200$		0			0
$201$	−247.381	−	44.5806i	−1.23075	−	0.221794i
$202$		0			0
$203$			222.687i			1.09698i
$204$		0			0
$205$	6.22703	+	10.7855i	0.0303757	+	0.0526123i
$206$		0			0
$207$	−134.814	+	361.899i	−0.651276	+	1.74830i
$208$		0			0
$209$	105.800	−	3.51703i	0.506220	−	0.0168279i
$210$		0			0
$211$	−42.6993	+	73.9573i	−0.202366	+	0.350509i	−0.949290	−	0.314401i	$-0.898196\pi$
$211$	−42.6993	+	73.9573i	−0.202366	+	0.350509i	0.746924	+	0.664909i	$0.231530\pi$
$212$		0			0
$213$	144.708	−	52.0533i	0.679379	−	0.244382i
$214$		0			0
$215$	1.19974	+	0.692672i	0.00558020	+	0.00322173i
$216$		0			0
$217$	347.464			1.60122
$218$		0			0
$219$	130.722	+	363.405i	0.596903	+	1.65938i
$220$		0			0
$221$	−3.91046	+	2.25770i	−0.0176944	+	0.0102159i
$222$		0			0
$223$	17.1576			0.0769399			0.0384699	−	0.999260i	$-0.487752\pi$
$223$	17.1576			0.0769399			0.0384699	+	0.999260i	$0.487752\pi$
$224$		0			0
$225$	−24.2513	−	143.861i	−0.107784	−	0.639380i
$226$		0			0
$227$	168.668	+	97.3806i	0.743031	+	0.428989i	0.823170	−	0.567794i	$-0.192203\pi$
$227$	168.668	+	97.3806i	0.743031	+	0.428989i	−0.0801391	+	0.996784i	$0.525536\pi$
$228$		0			0
$229$	−55.2952	−	95.7741i	−0.241464	−	0.418228i	0.719668	−	0.694319i	$-0.244294\pi$
$229$	−55.2952	−	95.7741i	−0.241464	−	0.418228i	−0.961131	+	0.276091i	$0.910961\pi$
$230$		0			0
$231$	156.588	−	56.3269i	0.677871	−	0.243839i
$232$		0			0
$233$	−118.185	+	68.2343i	−0.507233	+	0.292851i	−0.731696	−	0.681632i	$-0.761271\pi$
$233$	−118.185	+	68.2343i	−0.507233	+	0.292851i	0.224462	+	0.974483i	$0.427937\pi$
$234$		0			0
$235$	72.7357			0.309514
$236$		0			0
$237$	−377.440	−	68.0187i	−1.59258	−	0.286999i
$238$		0			0
$239$	−61.0867	+	35.2684i	−0.255593	+	0.147567i	−0.622323	−	0.782761i	$-0.713811\pi$
$239$	−61.0867	+	35.2684i	−0.255593	+	0.147567i	0.366730	+	0.930328i	$0.380477\pi$
$240$		0			0
$241$	−130.602	−	226.210i	−0.541918	−	0.938630i	−0.998794	−	0.0490994i	$-0.984365\pi$
$241$	−130.602	−	226.210i	−0.541918	−	0.938630i	0.456876	−	0.889531i	$-0.348968\pi$
$242$		0			0
$243$	−152.667	−	189.055i	−0.628258	−	0.778005i
$244$		0			0
$245$			148.605i			0.606552i
$246$		0			0
$247$	9.78014	−	6.08854i	0.0395957	−	0.0246499i
$248$		0			0
$249$	102.228	+	86.4369i	0.410552	+	0.347136i
$250$		0			0
$251$	−117.712	−	67.9610i	−0.468972	−	0.270761i	0.246837	−	0.969057i	$-0.420609\pi$
$251$	−117.712	−	67.9610i	−0.468972	−	0.270761i	−0.715809	+	0.698296i	$0.753942\pi$
$252$		0			0
$253$	−119.538	+	207.045i	−0.472481	+	0.818361i
$254$		0			0
$255$	−65.1861	−	11.7472i	−0.255632	−	0.0460675i
$256$		0			0
$257$		−	408.905i		−	1.59107i	−0.605907	−	0.795535i	$-0.707190\pi$
$257$		−	408.905i		−	1.59107i	0.605907	−	0.795535i	$-0.292810\pi$
$258$		0			0
$259$	142.028	−	246.000i	0.548371	−	0.949806i
$260$		0			0
$261$	198.502	−	33.4625i	0.760545	−	0.128209i
$262$		0			0
$263$			163.495i			0.621655i	0.950466	+	0.310827i	$0.100606\pi$
$263$			163.495i			0.621655i	−0.950466	+	0.310827i	$0.899394\pi$
$264$		0			0
$265$	154.612	+	267.796i	0.583443	+	1.01055i
$266$		0			0
$267$	279.792	+	236.574i	1.04791	+	0.886045i
$268$		0			0
$269$	−163.102	+	94.1668i	−0.606326	+	0.350062i	−0.771526	−	0.636198i	$-0.780506\pi$
$269$	−163.102	+	94.1668i	−0.606326	+	0.350062i	0.165200	+	0.986260i	$0.447173\pi$
$270$		0			0
$271$	−255.583	−	442.682i	−0.943109	−	1.63351i	−0.759493	−	0.650515i	$-0.774553\pi$
$271$	−255.583	−	442.682i	−0.943109	−	1.63351i	−0.183616	−	0.982998i	$-0.558780\pi$
$272$		0			0
$273$	11.6932	−	13.8294i	0.0428324	−	0.0506572i
$274$		0			0
$275$		−	90.3142i		−	0.328415i
$276$		0			0
$277$	170.252	−	294.886i	0.614629	−	1.06457i	−0.375820	−	0.926693i	$-0.622639\pi$
$277$	170.252	−	294.886i	0.614629	−	1.06457i	0.990449	−	0.137876i	$-0.0440276\pi$
$278$		0			0
$279$	−52.2123	−	309.727i	−0.187141	−	1.11013i
$280$		0			0
$281$	−104.600	+	60.3911i	−0.372244	+	0.214915i	−0.674438	−	0.738331i	$-0.735614\pi$
$281$	−104.600	+	60.3911i	−0.372244	+	0.214915i	0.302195	+	0.953246i	$0.402281\pi$
$282$		0			0
$283$	87.3147	−	151.233i	0.308532	−	0.534394i	−0.669509	−	0.742804i	$-0.733495\pi$
$283$	87.3147	−	151.233i	0.308532	−	0.534394i	0.978042	+	0.208410i	$0.0668288\pi$
$284$		0			0
$285$	167.218	+	24.4294i	0.586729	+	0.0857171i
$286$		0			0
$287$	36.2190	−	20.9110i	0.126198	−	0.0728607i
$288$		0			0
$289$	−116.771	+	202.254i	−0.404053	+	0.699840i
$290$		0			0
$291$	−18.8177	−	3.39115i	−0.0646656	−	0.0116534i
$292$		0			0
$293$	69.1428	−	39.9196i	0.235982	−	0.136244i	−0.377346	−	0.926072i	$-0.623163\pi$
$293$	69.1428	−	39.9196i	0.235982	−	0.136244i	0.613329	+	0.789828i	$0.289830\pi$
$294$		0			0
$295$	106.469	+	184.409i	0.360911	+	0.625117i
$296$		0			0
$297$	−73.7394	−	131.118i	−0.248281	−	0.441474i
$298$		0			0
$299$			26.0183i			0.0870179i
$300$		0			0
$301$	2.32607	−	4.02887i	0.00772780	−	0.0133849i
$302$		0			0
$303$	−411.448	+	148.003i	−1.35791	+	0.488460i
$304$		0			0
$305$		−	70.6281i		−	0.231567i
$306$		0			0
$307$	78.2958	+	135.612i	0.255035	+	0.441734i	0.964905	−	0.262599i	$-0.0845797\pi$
$307$	78.2958	+	135.612i	0.255035	+	0.441734i	−0.709870	+	0.704333i	$0.751246\pi$
$308$		0			0
$309$	59.8135	+	166.281i	0.193571	+	0.538126i
$310$		0			0
$311$	−276.597	+	159.693i	−0.889378	+	0.513483i	−0.873739	−	0.486395i	$-0.838312\pi$
$311$	−276.597	+	159.693i	−0.889378	+	0.513483i	−0.0156393	+	0.999878i	$0.504978\pi$
$312$		0			0
$313$	205.296	+	355.583i	0.655897	+	1.13605i	0.981668	+	0.190598i	$0.0610428\pi$
$313$	205.296	+	355.583i	0.655897	+	1.13605i	−0.325771	+	0.945449i	$0.605624\pi$
$314$		0			0
$315$	261.963	−	44.1604i	0.831627	−	0.140192i
$316$		0			0
$317$	62.5645	−	36.1216i	0.197364	−	0.113948i	−0.398061	−	0.917359i	$-0.630317\pi$
$317$	62.5645	−	36.1216i	0.197364	−	0.113948i	0.595426	+	0.803411i	$0.296983\pi$
$318$		0			0
$319$	124.618			0.390651
$320$		0			0
$321$	−46.8377	+	259.905i	−0.145912	+	0.809673i
$322$		0			0
$323$	−66.6361	+	124.819i	−0.206304	+	0.386437i
$324$		0			0
$325$	−4.91441	−	8.51200i	−0.0151213	−	0.0261908i
$326$		0			0
$327$	128.105	+	356.131i	0.391759	+	1.08909i
$328$		0			0
$329$		−	244.254i		−	0.742414i
$330$		0			0
$331$	−198.487	+	343.789i	−0.599658	+	1.03864i	0.393213	+	0.919447i	$0.371363\pi$
$331$	−198.487	+	343.789i	−0.599658	+	1.03864i	−0.992871	+	0.119191i	$0.961970\pi$
$332$		0			0
$333$	−240.625	−	89.6373i	−0.722597	−	0.269181i
$334$		0			0
$335$	−215.134	−	124.207i	−0.642190	−	0.370769i
$336$		0			0
$337$	−74.6285	+	129.260i	−0.221449	+	0.383562i	−0.955248	−	0.295805i	$-0.904412\pi$
$337$	−74.6285	+	129.260i	−0.221449	+	0.383562i	0.733799	+	0.679367i	$0.237745\pi$
$338$		0			0
$339$	−135.782	+	48.8427i	−0.400538	+	0.144079i
$340$		0			0
$341$		−	194.444i		−	0.570216i
$342$		0			0
$343$	11.1846			0.0326082
$344$		0			0
$345$	−246.425	+	291.443i	−0.714277	+	0.844764i
$346$		0			0
$347$	−42.9799	−	24.8145i	−0.123861	−	0.0715114i	0.436789	−	0.899564i	$-0.356116\pi$
$347$	−42.9799	−	24.8145i	−0.123861	−	0.0715114i	−0.560651	+	0.828052i	$0.689449\pi$
$348$		0			0
$349$	203.047	−	351.688i	0.581797	−	1.00770i	−0.413469	−	0.910518i	$-0.635683\pi$
$349$	203.047	−	351.688i	0.581797	−	1.00770i	0.995266	−	0.0971842i	$-0.0309836\pi$
$350$		0			0
$351$	−14.0846	−	8.34518i	−0.0401269	−	0.0237754i
$352$		0			0
$353$	−266.540	−	153.887i	−0.755070	−	0.435940i	0.0724531	−	0.997372i	$-0.476917\pi$
$353$	−266.540	−	153.887i	−0.755070	−	0.435940i	−0.827523	+	0.561432i	$0.810251\pi$
$354$		0			0
$355$	151.980			0.428113
$356$		0			0
$357$	−39.4484	+	218.902i	−0.110500	+	0.613171i
$358$		0			0
$359$	−490.176	+	283.004i	−1.36539	+	0.788311i	−0.990336	−	0.138691i	$-0.955711\pi$
$359$	−490.176	+	283.004i	−1.36539	+	0.788311i	−0.375058	+	0.927001i	$0.622377\pi$
$360$		0			0
$361$	159.339	−	323.932i	0.441383	−	0.897319i
$362$		0			0
$363$	91.3476	+	253.945i	0.251646	+	0.699574i
$364$		0			0
$365$			381.668i			1.04567i
$366$		0			0
$367$	18.4982	+	32.0398i	0.0504038	+	0.0873019i	0.890127	−	0.455714i	$-0.150616\pi$
$367$	18.4982	+	32.0398i	0.0504038	+	0.0873019i	−0.839723	+	0.543015i	$0.817283\pi$
$368$		0			0
$369$	−24.0825	−	29.1431i	−0.0652641	−	0.0789786i
$370$		0			0
$371$	899.289	−	519.205i	2.42396	−	1.39947i
$372$		0			0
$373$	−295.813	−	512.363i	−0.793064	−	1.37363i	−0.924061	−	0.382244i	$-0.875151\pi$
$373$	−295.813	−	512.363i	−0.793064	−	1.37363i	0.130998	−	0.991383i	$-0.458182\pi$
$374$		0			0
$375$	65.0067	−	360.726i	0.173351	−	0.961937i
$376$		0			0
$377$	11.7451	−	6.78101i	0.0311540	−	0.0179868i
$378$		0			0
$379$	−189.548			−0.500126			−0.250063	−	0.968230i	$-0.580451\pi$
$379$	−189.548			−0.500126			−0.250063	+	0.968230i	$0.580451\pi$
$380$		0			0
$381$	−113.804	+	134.595i	−0.298699	+	0.353267i
$382$		0			0
$383$	−317.975	−	183.583i	−0.830221	−	0.479328i	0.0237075	−	0.999719i	$-0.492453\pi$
$383$	−317.975	−	183.583i	−0.830221	−	0.479328i	−0.853928	+	0.520391i	$0.825786\pi$
$384$		0			0
$385$	164.458			0.427162
$386$		0			0
$387$	−3.94084	−	1.46804i	−0.0101830	−	0.00379338i
$388$		0			0
$389$	317.165	−	183.115i	0.815333	−	0.470733i	−0.0334714	−	0.999440i	$-0.510656\pi$
$389$	317.165	−	183.115i	0.815333	−	0.470733i	0.848804	+	0.528707i	$0.177323\pi$
$390$		0			0
$391$	−159.776	−	276.741i	−0.408635	−	0.707777i
$392$		0			0
$393$	372.791	+	315.207i	0.948578	+	0.802055i
$394$		0			0
$395$	−328.240	−	189.509i	−0.830987	−	0.479770i
$396$		0			0
$397$	195.945	+	339.387i	0.493565	+	0.854880i	0.999973	−	0.00741466i	$-0.00236018\pi$
$397$	195.945	+	339.387i	0.493565	+	0.854880i	−0.506408	+	0.862294i	$0.669027\pi$
$398$		0			0
$399$	82.0365	−	561.535i	0.205605	−	1.40736i
$400$		0			0
$401$	20.3829	+	11.7681i	0.0508301	+	0.0293468i	0.525200	−	0.850979i	$-0.323991\pi$
$401$	20.3829	+	11.7681i	0.0508301	+	0.0293468i	−0.474370	+	0.880326i	$0.657324\pi$
$402$		0			0
$403$	−10.5806	−	18.3261i	−0.0262545	−	0.0454741i
$404$		0			0
$405$	−78.7286	−	226.876i	−0.194392	−	0.560188i
$406$		0			0
$407$	−137.663	−	79.4800i	−0.338239	−	0.195283i
$408$		0			0
$409$	651.723			1.59345			0.796727	−	0.604340i	$-0.206563\pi$
$409$	651.723			1.59345			0.796727	+	0.604340i	$0.206563\pi$
$410$		0			0
$411$	−3.68759	+	1.32648i	−0.00897224	+	0.00322744i
$412$		0			0
$413$	619.267	−	357.534i	1.49944	−	0.865699i
$414$		0			0
$415$	66.1505	+	114.576i	0.159399	+	0.276087i
$416$		0			0
$417$	−725.607	−	130.762i	−1.74007	−	0.313578i
$418$		0			0
$419$	−375.240	+	216.645i	−0.895561	+	0.517052i	−0.875757	−	0.482752i	$-0.839637\pi$
$419$	−375.240	+	216.645i	−0.895561	+	0.517052i	−0.0198035	+	0.999804i	$0.506304\pi$
$420$		0			0
$421$	−550.434			−1.30744			−0.653722	−	0.756734i	$-0.726794\pi$
$421$	−550.434			−1.30744			−0.653722	+	0.756734i	$0.726794\pi$
$422$		0			0
$423$	−217.727	+	36.7033i	−0.514721	+	0.0867691i
$424$		0			0
$425$	104.543	+	60.3579i	0.245983	+	0.142019i
$426$		0			0
$427$	−237.177			−0.555449
$428$		0			0
$429$	−7.73905	−	6.54363i	−0.0180397	−	0.0152532i
$430$		0			0
$431$	510.519	+	294.748i	1.18450	+	0.683870i	0.957051	−	0.289920i	$-0.0936287\pi$
$431$	510.519	+	294.748i	1.18450	+	0.683870i	0.227447	+	0.973790i	$0.426962\pi$
$432$		0			0
$433$	210.589	−	364.751i	0.486349	−	0.842381i	−0.513528	−	0.858073i	$-0.671662\pi$
$433$	210.589	−	364.751i	0.486349	−	0.842381i	0.999877	+	0.0156918i	$0.00499507\pi$
$434$		0			0
$435$	195.786	+	35.2828i	0.450084	+	0.0811098i
$436$		0			0
$437$	430.882	+	692.135i	0.986000	+	1.58383i
$438$		0			0
$439$	−110.242			−0.251122			−0.125561	−	0.992086i	$-0.540073\pi$
$439$	−110.242			−0.251122			−0.125561	+	0.992086i	$0.540073\pi$
$440$		0			0
$441$	−74.9880	−	444.834i	−0.170041	−	1.00869i
$442$		0			0
$443$	−432.115	+	249.482i	−0.975429	+	0.563164i	−0.900887	−	0.434054i	$-0.857083\pi$
$443$	−432.115	+	249.482i	−0.975429	+	0.563164i	−0.0745420	+	0.997218i	$0.523749\pi$
$444$		0			0
$445$	181.051	+	313.590i	0.406856	+	0.704696i
$446$		0			0
$447$	−160.825	−	135.983i	−0.359788	−	0.304213i
$448$		0			0
$449$		−	377.626i		−	0.841038i	−0.907284	−	0.420519i	$-0.861848\pi$
$449$		−	377.626i		−	0.841038i	0.907284	−	0.420519i	$-0.138152\pi$
$450$		0			0
$451$	−11.7020	−	20.2684i	−0.0259467	−	0.0449411i
$452$		0			0
$453$	187.121	−	221.305i	0.413070	−	0.488531i
$454$		0			0
$455$	15.4999	−	8.94888i	0.0340657	−	0.0196679i
$456$		0			0
$457$	−387.993	+	672.023i	−0.848999	+	1.47051i	0.0331026	+	0.999452i	$0.489461\pi$
$457$	−387.993	+	672.023i	−0.848999	+	1.47051i	−0.882102	+	0.471058i	$0.843872\pi$
$458$		0			0
$459$	201.056	+	2.27039i	0.438030	+	0.00494639i
$460$		0			0
$461$		−	294.660i		−	0.639175i	−0.947557	−	0.319587i	$-0.896456\pi$
$461$		−	294.660i		−	0.639175i	0.947557	−	0.319587i	$-0.103544\pi$
$462$		0			0
$463$	−370.494	−	641.715i	−0.800204	−	1.38599i	−0.919482	−	0.393133i	$-0.871391\pi$
$463$	−370.494	−	641.715i	−0.800204	−	1.38599i	0.119278	−	0.992861i	$-0.461942\pi$
$464$		0			0
$465$	55.0524	−	305.489i	0.118392	−	0.656966i
$466$		0			0
$467$		−	652.113i		−	1.39639i	−0.715909	−	0.698194i	$-0.753987\pi$
$467$		−	652.113i		−	1.39639i	0.715909	−	0.698194i	$-0.246013\pi$
$468$		0			0
$469$	−417.102	+	722.442i	−0.889343	+	1.54039i
$470$		0			0
$471$	444.115	−	525.248i	0.942919	−	1.11518i
$472$		0			0
$473$	−2.25459	−	1.30169i	−0.00476657	−	0.00275198i
$474$		0			0
$475$	−271.697	−	145.049i	−0.571993	−	0.305366i
$476$		0			0
$477$	−597.949	−	723.602i	−1.25356	−	1.51698i
$478$		0			0
$479$	118.489	−	68.4094i	0.247367	−	0.142817i	−0.371191	−	0.928556i	$-0.621051\pi$
$479$	118.489	−	68.4094i	0.247367	−	0.142817i	0.618558	+	0.785739i	$0.287717\pi$
$480$		0			0
$481$	−17.2995			−0.0359656
$482$		0			0
$483$	978.698	+	827.523i	2.02629	+	1.71330i
$484$		0			0
$485$	−16.3647	−	9.44819i	−0.0337418	−	0.0194808i
$486$		0			0
$487$	−278.411			−0.571686			−0.285843	−	0.958276i	$-0.592274\pi$
$487$	−278.411			−0.571686			−0.285843	+	0.958276i	$0.592274\pi$
$488$		0			0
$489$	−100.689	−	18.1452i	−0.205907	−	0.0371067i
$490$		0			0
$491$	379.444	+	219.072i	0.772798	+	0.446175i	0.833872	−	0.551958i	$-0.186119\pi$
$491$	379.444	+	219.072i	0.772798	+	0.446175i	−0.0610736	+	0.998133i	$0.519452\pi$
$492$		0			0
$493$	−83.2833	+	144.251i	−0.168932	+	0.292598i
$494$		0			0
$495$	−24.7125	−	146.596i	−0.0499243	−	0.296154i
$496$		0			0
$497$		−	510.365i		−	1.02689i
$498$		0			0
$499$	−161.203	+	279.212i	−0.323052	+	0.559542i	−0.981116	−	0.193419i	$-0.938042\pi$
$499$	−161.203	+	279.212i	−0.323052	+	0.559542i	0.658064	+	0.752962i	$0.271376\pi$
$500$		0			0
$501$	−5.21701	+	28.9495i	−0.0104132	+	0.0577834i
$502$		0			0
$503$	−60.7182	−	35.0556i	−0.120712	−	0.0696931i	0.438428	−	0.898766i	$-0.355535\pi$
$503$	−60.7182	−	35.0556i	−0.120712	−	0.0696931i	−0.559140	+	0.829073i	$0.688869\pi$
$504$		0			0
$505$	−432.126			−0.855694
$506$		0			0
$507$	497.877	+	89.7227i	0.982006	+	0.176968i
$508$		0			0
$509$			966.994i			1.89979i	0.312567	+	0.949896i	$0.398811\pi$
$509$			966.994i			1.89979i	−0.312567	+	0.949896i	$0.601189\pi$
$510$		0			0
$511$	1281.68			2.50818
$512$		0			0
$513$	−512.877	+	11.2533i	−0.999759	+	0.0219363i
$514$		0			0
$515$			174.637i			0.339102i
$516$		0			0
$517$	−136.687			−0.264384
$518$		0			0
$519$	136.167	−	755.602i	0.262365	−	1.45588i
$520$		0			0
$521$		−	455.105i		−	0.873523i	−0.899577	−	0.436761i	$-0.856125\pi$
$521$		−	455.105i		−	0.873523i	0.899577	−	0.436761i	$-0.143875\pi$
$522$		0			0
$523$	−86.1112	+	149.149i	−0.164649	+	0.285180i	−0.936530	−	0.350586i	$-0.885982\pi$
$523$	−86.1112	+	149.149i	−0.164649	+	0.285180i	0.771882	+	0.635766i	$0.219316\pi$
$524$		0			0
$525$	−476.490	−	85.8685i	−0.907599	−	0.163559i
$526$		0			0
$527$	225.077	+	129.949i	0.427092	+	0.246582i
$528$		0			0
$529$	−1312.30			−2.48072
$530$		0			0
$531$	−411.759	−	498.285i	−0.775440	−	0.938390i
$532$		0			0
$533$	−2.20579	−	1.27352i	−0.00413845	−	0.00238933i
$534$		0			0
$535$	−130.496	+	226.026i	−0.243918	+	0.422478i
$536$		0			0
$537$	150.409	−	834.627i	0.280090	−	1.55424i
$538$		0			0
$539$		−	279.263i		−	0.518112i
$540$		0			0
$541$	101.296	−	175.449i	0.187238	−	0.324306i	−0.757090	−	0.653310i	$-0.773380\pi$
$541$	101.296	−	175.449i	0.187238	−	0.324306i	0.944328	+	0.329004i	$0.106713\pi$
$542$		0			0
$543$	−290.909	+	344.054i	−0.535744	+	0.633616i
$544$		0			0
$545$			374.028i			0.686291i
$546$		0			0
$547$	−229.873	−	398.151i	−0.420243	−	0.727881i	0.575720	−	0.817647i	$-0.304722\pi$
$547$	−229.873	−	398.151i	−0.420243	−	0.727881i	−0.995963	+	0.0897652i	$0.971388\pi$
$548$		0			0
$549$	35.6398	+	211.418i	0.0649177	+	0.385096i
$550$		0			0
$551$	200.141	−	374.894i	0.363233	−	0.680388i
$552$		0			0
$553$	−636.393	+	1102.26i	−1.15080	+	1.99325i
$554$		0			0
$555$	−193.779	−	163.847i	−0.349152	−	0.295220i
$556$		0			0
$557$	−251.433	−	145.165i	−0.451406	−	0.260620i	0.257018	−	0.966407i	$-0.417260\pi$
$557$	−251.433	−	145.165i	−0.451406	−	0.260620i	−0.708424	+	0.705787i	$0.750593\pi$
$558$		0			0
$559$	−0.283323			−0.000506838
$560$		0			0
$561$	122.499	+	22.0757i	0.218359	+	0.0393506i
$562$		0			0
$563$	−903.269	+	521.503i	−1.60439	+	0.926292i	−0.613790	+	0.789469i	$0.710356\pi$
$563$	−903.269	+	521.503i	−1.60439	+	0.926292i	−0.990595	+	0.136823i	$0.956311\pi$
$564$		0			0
$565$	−142.606			−0.252400
$566$		0			0
$567$	−761.874	+	264.379i	−1.34369	+	0.466277i
$568$		0			0
$569$	571.454	+	329.929i	1.00431	+	0.579840i	0.909521	−	0.415657i	$-0.136448\pi$
$569$	571.454	+	329.929i	1.00431	+	0.579840i	0.0947911	+	0.995497i	$0.469782\pi$
$570$		0			0
$571$	−263.596	−	456.562i	−0.461640	−	0.799584i	0.537403	−	0.843326i	$-0.319405\pi$
$571$	−263.596	−	456.562i	−0.461640	−	0.799584i	−0.999043	+	0.0437419i	$0.986072\pi$
$572$		0			0
$573$	−141.066	−	119.276i	−0.246188	−	0.208160i
$574$		0			0
$575$	602.389	−	347.790i	1.04763	−	0.604851i
$576$		0			0
$577$	433.245			0.750859			0.375429	−	0.926851i	$-0.377495\pi$
$577$	433.245			0.750859			0.375429	+	0.926851i	$0.377495\pi$
$578$		0			0
$579$	−577.590	+	683.107i	−0.997565	+	1.17980i
$580$		0			0
$581$	384.759	−	222.140i	0.662235	−	0.382342i
$582$		0			0
$583$	−290.551	−	503.250i	−0.498373	−	0.863207i
$584$		0			0
$585$	−10.3061	−	12.4718i	−0.0176173	−	0.0213193i
$586$		0			0
$587$		−	1.07499i		−	0.00183132i	−1.00000		0.000915661i	$-0.999709\pi$
$587$		−	1.07499i		−	0.00183132i	1.00000		0.000915661i	$-0.000291464\pi$
$588$		0			0
$589$	−584.954	−	312.285i	−0.993131	−	0.530195i
$590$		0			0
$591$	−24.1035	+	133.752i	−0.0407843	+	0.226314i
$592$		0			0
$593$	−379.586	−	219.154i	−0.640111	−	0.369568i	0.144546	−	0.989498i	$-0.453828\pi$
$593$	−379.586	−	219.154i	−0.640111	−	0.369568i	−0.784657	+	0.619930i	$0.787161\pi$
$594$		0			0
$595$	−109.909	+	190.367i	−0.184720	+	0.319945i
$596$		0			0
$597$	−73.0639	+	86.4116i	−0.122385	+	0.144743i
$598$		0			0
$599$			543.477i			0.907307i	0.891178	+	0.453654i	$0.149880\pi$
$599$			543.477i			0.907307i	−0.891178	+	0.453654i	$0.850120\pi$
$600$		0			0
$601$	197.324	−	341.775i	0.328326	−	0.568678i	−0.653854	−	0.756621i	$-0.726849\pi$
$601$	197.324	−	341.775i	0.328326	−	0.568678i	0.982180	+	0.187943i	$0.0601822\pi$
$602$		0			0
$603$	706.657	+	263.243i	1.17190	+	0.436556i
$604$		0			0
$605$			266.707i			0.440839i
$606$		0			0
$607$	117.747	+	203.944i	0.193982	+	0.335987i	0.946566	−	0.322509i	$-0.104526\pi$
$607$	117.747	+	203.944i	0.193982	+	0.335987i	−0.752584	+	0.658496i	$0.771193\pi$
$608$		0			0
$609$	118.483	−	657.472i	0.194554	−	1.07959i
$610$		0			0
$611$	−12.8826	+	7.43775i	−0.0210844	+	0.0121731i
$612$		0			0
$613$	118.707	+	205.606i	0.193649	+	0.335410i	0.946457	−	0.322831i	$-0.104634\pi$
$613$	118.707	+	205.606i	0.193649	+	0.335410i	−0.752808	+	0.658240i	$0.771301\pi$
$614$		0			0
$615$	−12.6464	−	35.1568i	−0.0205632	−	0.0571655i
$616$		0			0
$617$		−	126.666i		−	0.205294i	−0.994718	−	0.102647i	$-0.967269\pi$
$617$		−	126.666i		−	0.205294i	0.994718	−	0.102647i	$-0.0327312\pi$
$618$		0			0
$619$	381.337	−	660.495i	0.616053	−	1.06704i	−0.374145	−	0.927370i	$-0.622064\pi$
$619$	381.337	−	660.495i	0.616053	−	1.06704i	0.990199	−	0.139666i	$-0.0446028\pi$
$620$		0			0
$621$	590.583	−	996.755i	0.951019	−	1.60508i
$622$		0			0
$623$	1053.07	−	607.989i	1.69032	−	0.975905i
$624$		0			0
$625$	−21.5081	+	37.2532i	−0.0344130	+	0.0596051i
$626$		0			0
$627$	−314.240	−	45.9083i	−0.501180	−	0.0732190i
$628$		0			0
$629$	184.004	−	106.235i	0.292534	−	0.168894i
$630$		0			0
$631$	−156.703	+	271.418i	−0.248341	+	0.430139i	−0.963066	−	0.269267i	$-0.913219\pi$
$631$	−156.703	+	271.418i	−0.248341	+	0.430139i	0.714725	+	0.699406i	$0.246552\pi$
$632$		0			0
$633$	165.417	−	195.636i	0.261322	−	0.309062i
$634$		0			0
$635$	−150.853	+	87.0949i	−0.237563	+	0.137157i
$636$		0			0
$637$	−15.1959	−	26.3201i	−0.0238555	−	0.0413189i
$638$		0			0
$639$	−454.937	+	76.6910i	−0.711951	+	0.120017i
$640$		0			0
$641$			296.995i			0.463331i	0.972796	+	0.231665i	$0.0744175\pi$
$641$			296.995i			0.463331i	−0.972796	+	0.231665i	$0.925583\pi$
$642$		0			0
$643$	−381.917	+	661.499i	−0.593960	+	1.02877i	0.399732	+	0.916632i	$0.369103\pi$
$643$	−381.917	+	661.499i	−0.593960	+	1.02877i	−0.993693	+	0.112138i	$0.964230\pi$
$644$		0			0
$645$	−3.17363	−	2.68341i	−0.00492035	−	0.00416033i
$646$		0			0
$647$		−	1270.63i		−	1.96388i	−0.189200	−	0.981938i	$-0.560590\pi$
$647$		−	1270.63i		−	1.96388i	0.189200	−	0.981938i	$-0.439410\pi$
$648$		0			0
$649$	−200.079	−	346.547i	−0.308288	−	0.533970i
$650$		0			0
$651$	−1025.87	−	184.872i	−1.57583	−	0.283981i
$652$		0			0
$653$	−357.463	+	206.381i	−0.547416	+	0.316051i	−0.748079	−	0.663609i	$-0.769024\pi$
$653$	−357.463	+	206.381i	−0.547416	+	0.316051i	0.200663	+	0.979660i	$0.435690\pi$
$654$		0			0
$655$	241.230	+	417.822i	0.368289	+	0.637896i
$656$		0			0
$657$	−192.594	−	1142.48i	−0.293142	−	1.73894i
$658$		0			0
$659$	386.684	−	223.252i	0.586774	−	0.338774i	−0.177047	−	0.984202i	$-0.556654\pi$
$659$	386.684	−	223.252i	0.586774	−	0.338774i	0.763821	+	0.645428i	$0.223321\pi$
$660$		0			0
$661$	312.290			0.472451			0.236225	−	0.971698i	$-0.424090\pi$
$661$	312.290			0.472451			0.236225	+	0.971698i	$0.424090\pi$
$662$		0			0
$663$	12.7466	−	4.58514i	0.0192257	−	0.00691574i
$664$		0			0
$665$	264.126	−	494.746i	0.397182	−	0.743979i
$666$		0			0
$667$	479.888	+	831.191i	0.719473	+	1.24616i
$668$		0			0
$669$	−50.6568	−	9.12889i	−0.0757202	−	0.0136456i
$670$		0			0
$671$			132.726i			0.197803i
$672$		0			0
$673$	−252.021	+	436.514i	−0.374475	+	0.648609i	−0.990248	−	0.139314i	$-0.955510\pi$
$673$	−252.021	+	436.514i	−0.374475	+	0.648609i	0.615774	+	0.787923i	$0.288844\pi$
$674$		0			0
$675$	−4.94202	+	437.643i	−0.00732151	+	0.648360i
$676$		0			0
$677$	771.602	+	445.485i	1.13974	+	0.658028i	0.946366	−	0.323098i	$-0.104724\pi$
$677$	771.602	+	445.485i	1.13974	+	0.658028i	0.193372	+	0.981125i	$0.438058\pi$
$678$		0			0
$679$	−31.7280	+	54.9546i	−0.0467276	+	0.0809346i
$680$		0			0
$681$	−446.170	−	377.252i	−0.655169	−	0.553968i
$682$		0			0
$683$			119.288i			0.174653i	0.996180	+	0.0873264i	$0.0278323\pi$
$683$			119.288i			0.174653i	−0.996180	+	0.0873264i	$0.972168\pi$
$684$		0			0
$685$	−3.87291			−0.00565389
$686$		0			0
$687$	112.298	+	312.188i	0.163462	+	0.454422i
$688$		0			0
$689$	−54.7682	−	31.6204i	−0.0794894	−	0.0458932i
$690$		0			0
$691$	379.126	−	656.665i	0.548662	−	0.950311i	−0.449704	−	0.893178i	$-0.648471\pi$
$691$	379.126	−	656.665i	0.548662	−	0.950311i	0.998367	−	0.0571336i	$-0.0181961\pi$
$692$		0			0
$693$	−492.287	+	82.9873i	−0.710370	+	0.119751i
$694$		0			0
$695$	−631.022	−	364.321i	−0.907945	−	0.524202i
$696$		0			0
$697$	31.2822			0.0448812
$698$		0			0
$699$	385.240	−	138.576i	0.551130	−	0.198249i
$700$		0			0
$701$	−411.355	+	237.496i	−0.586812	+	0.338796i	−0.763836	−	0.645410i	$-0.776686\pi$
$701$	−411.355	+	237.496i	−0.586812	+	0.338796i	0.177024	+	0.984207i	$0.443353\pi$
$702$		0			0
$703$	−460.197	+	286.492i	−0.654619	+	0.407527i
$704$		0			0
$705$	−214.748	−	38.6999i	−0.304607	−	0.0548934i
$706$		0			0
$707$			1451.12i			2.05251i
$708$		0			0
$709$	638.465	+	1105.85i	0.900515	+	1.55974i	0.826827	+	0.562456i	$0.190143\pi$
$709$	638.465	+	1105.85i	0.900515	+	1.55974i	0.0736875	+	0.997281i	$0.476523\pi$
$710$		0			0
$711$	1078.18	+	401.643i	1.51643	+	0.564898i
$712$		0			0
$713$	1296.92	−	748.779i	1.81897	−	1.05018i
$714$		0			0
$715$	−5.00787	−	8.67388i	−0.00700401	−	0.0121313i
$716$		0			0
$717$	199.120	−	71.6261i	0.277713	−	0.0998970i
$718$		0			0
$719$	−858.671	+	495.754i	−1.19426	+	0.689505i	−0.959269	−	0.282494i	$-0.908838\pi$
$719$	−858.671	+	495.754i	−1.19426	+	0.689505i	−0.234988	+	0.971998i	$0.575505\pi$
$720$		0			0
$721$	586.451			0.813386
$722$		0			0
$723$	265.238	+	737.360i	0.366858	+	1.01986i
$724$		0			0
$725$	−313.995	−	181.285i	−0.433096	−	0.250048i
$726$		0			0
$727$	23.4911			0.0323124			0.0161562	−	0.999869i	$-0.494857\pi$
$727$	23.4911			0.0323124			0.0161562	+	0.999869i	$0.494857\pi$
$728$		0			0
$729$	350.150	+	639.403i	0.480316	+	0.877095i
$730$		0			0
$731$	3.01353	−	1.73986i	0.00412247	−	0.00238011i
$732$		0			0
$733$	484.778	+	839.660i	0.661362	+	1.14551i	0.980258	+	0.197722i	$0.0633544\pi$
$733$	484.778	+	839.660i	0.661362	+	1.14551i	−0.318896	+	0.947790i	$0.603312\pi$
$734$		0			0
$735$	79.0671	−	438.748i	0.107574	−	0.596936i
$736$		0			0
$737$	404.284	+	233.414i	0.548554	+	0.316708i
$738$		0			0
$739$	420.081	+	727.602i	0.568445	+	0.984576i	0.996720	+	0.0809274i	$0.0257882\pi$
$739$	420.081	+	727.602i	0.568445	+	0.984576i	−0.428275	+	0.903649i	$0.640878\pi$
$740$		0			0
$741$	−32.1148	+	12.7724i	−0.0433398	+	0.0172367i
$742$		0			0
$743$	734.164	+	423.870i	0.988108	+	0.570484i	0.904708	−	0.426032i	$-0.140089\pi$
$743$	734.164	+	423.870i	0.988108	+	0.570484i	0.0833998	+	0.996516i	$0.473422\pi$
$744$		0			0
$745$	−104.068	−	180.252i	−0.139689	−	0.241949i
$746$		0			0
$747$	−255.831	−	309.591i	−0.342478	−	0.414446i
$748$		0			0
$749$	759.018	+	438.219i	1.01338	+	0.585073i
$750$		0			0
$751$	870.454			1.15906			0.579530	−	0.814951i	$-0.303236\pi$
$751$	870.454			1.15906			0.579530	+	0.814951i	$0.303236\pi$
$752$		0			0
$753$	311.378	+	263.281i	0.413517	+	0.349642i
$754$		0			0
$755$	248.037	−	143.204i	0.328526	−	0.189674i
$756$		0			0
$757$	403.471	+	698.831i	0.532986	+	0.923159i	0.999258	+	0.0385176i	$0.0122636\pi$
$757$	403.471	+	698.831i	0.532986	+	0.923159i	−0.466272	+	0.884642i	$0.654403\pi$
$758$		0			0
$759$	463.089	−	547.688i	0.610130	−	0.721591i
$760$		0			0
$761$	−214.937	+	124.094i	−0.282441	+	0.163067i	−0.634528	−	0.772900i	$-0.718805\pi$
$761$	−214.937	+	124.094i	−0.282441	+	0.163067i	0.352087	+	0.935967i	$0.385472\pi$
$762$		0			0
$763$	1256.03			1.64617
$764$		0			0
$765$	186.208	+	69.3660i	0.243409	+	0.0906745i
$766$		0			0
$767$	−37.7144	−	21.7744i	−0.0491713	−	0.0283890i
$768$		0			0
$769$	−446.984			−0.581253			−0.290626	−	0.956837i	$-0.593864\pi$
$769$	−446.984			−0.581253			−0.290626	+	0.956837i	$0.593864\pi$
$770$		0			0
$771$	−217.563	+	1207.27i	−0.282182	+	1.56585i
$772$		0			0
$773$	942.485	+	544.144i	1.21926	+	0.703938i	0.964759	−	0.263136i	$-0.0847567\pi$
$773$	942.485	+	544.144i	1.21926	+	0.703938i	0.254497	+	0.967074i	$0.418090\pi$
$774$		0			0
$775$	−282.862	+	489.932i	−0.364984	+	0.632171i
$776$		0			0
$777$	−550.216	+	650.732i	−0.708129	+	0.837493i
$778$		0			0
$779$	−79.7684	+	2.65168i	−0.102398	+	0.00340395i
$780$		0			0
$781$	−285.605			−0.365691
$782$		0			0
$783$	−603.870	−	6.81912i	−0.771226	−	0.00870896i
$784$		0			0
$785$	588.695	−	339.883i	0.749929	−	0.432972i
$786$		0			0
$787$	193.669	+	335.444i	0.246085	+	0.426232i	0.962436	−	0.271508i	$-0.0875224\pi$
$787$	193.669	+	335.444i	0.246085	+	0.426232i	−0.716351	+	0.697740i	$0.754189\pi$
$788$		0			0
$789$	86.9894	−	482.710i	0.110253	−	0.611800i
$790$		0			0
$791$			478.887i			0.605419i
$792$		0			0
$793$	7.22222	+	12.5093i	0.00910747	+	0.0157746i
$794$		0			0
$795$	−314.000	−	872.916i	−0.394968	−	1.09801i
$796$		0			0
$797$	1110.88	−	641.368i	1.39383	−	0.804728i	0.400093	−	0.916475i	$-0.368978\pi$
$797$	1110.88	−	641.368i	1.39383	−	0.804728i	0.993737	+	0.111747i	$0.0356445\pi$
$798$		0			0
$799$	91.3491	−	158.221i	0.114329	−	0.198024i
$800$		0			0
$801$	−700.199	−	847.338i	−0.874156	−	1.05785i
$802$		0			0
$803$		−	717.240i		−	0.893200i
$804$		0			0
$805$	633.307	+	1096.92i	0.786716	+	1.36263i
$806$		0			0
$807$	531.651	−	191.242i	0.658799	−	0.236979i
$808$		0			0
$809$			1457.66i			1.80180i	0.434026	+	0.900900i	$0.357092\pi$
$809$			1457.66i			1.80180i	−0.434026	+	0.900900i	$0.642908\pi$
$810$		0			0
$811$	573.660	−	993.608i	0.707349	−	1.22516i	−0.258489	−	0.966014i	$-0.583224\pi$
$811$	573.660	−	993.608i	0.707349	−	1.22516i	0.965837	−	0.259149i	$-0.0834422\pi$
$812$		0			0
$813$	519.059	+	1442.98i	0.638449	+	1.77488i
$814$		0			0
$815$	−87.5636	−	50.5549i	−0.107440	−	0.0620305i
$816$		0			0
$817$	−7.53689	+	4.69202i	−0.00922508	+	0.00574299i
$818$		0			0
$819$	−41.8817	+	34.6090i	−0.0511376	+	0.0422576i
$820$		0			0
$821$	−69.2711	+	39.9937i	−0.0843741	+	0.0487134i	−0.541593	−	0.840641i	$-0.682179\pi$
$821$	−69.2711	+	39.9937i	−0.0843741	+	0.0487134i	0.457219	+	0.889354i	$0.348845\pi$
$822$		0			0
$823$	−1098.35			−1.33457			−0.667283	−	0.744804i	$-0.732543\pi$
$823$	−1098.35			−1.33457			−0.667283	+	0.744804i	$0.732543\pi$
$824$		0			0
$825$	−48.0527	+	266.647i	−0.0582457	+	0.323209i
$826$		0			0
$827$	−553.001	−	319.275i	−0.668683	−	0.386064i	0.126894	−	0.991916i	$-0.459499\pi$
$827$	−553.001	−	319.275i	−0.668683	−	0.386064i	−0.795577	+	0.605852i	$0.792832\pi$
$828$		0			0
$829$	−1228.65			−1.48209			−0.741046	−	0.671454i	$-0.765670\pi$
$829$	−1228.65			−1.48209			−0.741046	+	0.671454i	$0.765670\pi$
$830$		0			0
$831$	−659.557	+	780.048i	−0.793691	+	0.938686i
$832$		0			0
$833$	323.259	+	186.634i	0.388067	+	0.224050i
$834$		0			0
$835$	−14.5353	+	25.1758i	−0.0174075	+	0.0301507i
$836$		0			0
$837$	−10.6400	+	942.231i	−0.0127121	+	1.12572i
$838$		0			0
$839$			772.087i			0.920247i	0.887855	+	0.460123i	$0.152195\pi$
$839$			772.087i			0.920247i	−0.887855	+	0.460123i	$0.847805\pi$
$840$		0			0
$841$	−170.359	+	295.070i	−0.202567	+	0.350856i
$842$		0			0
$843$	340.959	−	122.647i	0.404459	−	0.145489i
$844$		0			0
$845$	432.977	+	249.980i	0.512399	+	0.295834i
$846$		0			0
$847$	895.632			1.05742
$848$		0			0
$849$	−338.257	+	400.051i	−0.398418	+	0.471203i
$850$		0			0
$851$		−	1224.27i		−	1.43863i
$852$		0			0
$853$	−539.398			−0.632354			−0.316177	−	0.948700i	$-0.602399\pi$
$853$	−539.398			−0.632354			−0.316177	+	0.948700i	$0.602399\pi$
$854$		0			0
$855$	−480.703	−	161.096i	−0.562226	−	0.188417i
$856$		0			0
$857$			1606.36i			1.87439i	0.348800	+	0.937197i	$0.386589\pi$
$857$			1606.36i			1.87439i	−0.348800	+	0.937197i	$0.613411\pi$
$858$		0			0
$859$	−1136.34			−1.32286			−0.661431	−	0.750006i	$-0.730051\pi$
$859$	−1136.34			−1.32286			−0.661431	+	0.750006i	$0.730051\pi$
$860$		0			0
$861$	−118.060	+	42.4679i	−0.137120	+	0.0493239i
$862$		0			0
$863$			805.559i			0.933440i	0.884405	+	0.466720i	$0.154564\pi$
$863$			805.559i			0.933440i	−0.884405	+	0.466720i	$0.845436\pi$
$864$		0			0
$865$	379.381	−	657.107i	0.438590	−	0.759661i
$866$		0			0
$867$	452.372	−	535.013i	0.521767	−	0.617085i
$868$		0			0
$869$	616.836	+	356.131i	0.709823	+	0.409817i
$870$		0			0
$871$	50.8044			0.0583288
$872$		0			0
$873$	53.7539	+	20.0243i	0.0615737	+	0.0229374i
$874$		0			0
$875$	−1053.45	−	608.211i	−1.20395	−	0.695099i
$876$		0			0
$877$	87.1316	−	150.916i	0.0993519	−	0.172082i	−0.812065	−	0.583567i	$-0.801656\pi$
$877$	87.1316	−	150.916i	0.0993519	−	0.172082i	0.911417	+	0.411485i	$0.134990\pi$
$878$		0			0
$879$	−225.380	+	81.0722i	−0.256405	+	0.0922323i
$880$		0			0
$881$		−	903.562i		−	1.02561i	−0.858505	−	0.512805i	$-0.828607\pi$
$881$		−	903.562i		−	1.02561i	0.858505	−	0.512805i	$-0.171393\pi$
$882$		0			0
$883$	614.714	−	1064.72i	0.696166	−	1.20579i	−0.273621	−	0.961838i	$-0.588221\pi$
$883$	614.714	−	1064.72i	0.696166	−	1.20579i	0.969786	−	0.243956i	$-0.0784454\pi$
$884$		0			0
$885$	−216.226	−	601.106i	−0.244323	−	0.679216i
$886$		0			0
$887$			85.4803i			0.0963702i	0.998838	+	0.0481851i	$0.0153437\pi$
$887$			85.4803i			0.0963702i	−0.998838	+	0.0481851i	$0.984656\pi$
$888$		0			0
$889$	292.474	+	506.580i	0.328992	+	0.569831i
$890$		0			0
$891$	147.949	+	426.351i	0.166048	+	0.478508i
$892$		0			0
$893$	−219.525	+	411.202i	−0.245829	+	0.460472i
$894$		0			0
$895$	419.058	−	725.830i	0.468222	−	0.810983i
$896$		0			0
$897$	13.8433	−	76.8176i	0.0154329	−	0.0856384i
$898$		0			0
$899$	−676.020	−	390.300i	−0.751969	−	0.434149i
$900$		0			0
$901$	776.713			0.862057
$902$		0			0
$903$	−9.01118	+	10.6574i	−0.00997916	+	0.0118022i
$904$		0			0
$905$	−385.613	+	222.634i	−0.426092	+	0.246004i
$906$		0			0
$907$	−1116.65			−1.23115			−0.615576	−	0.788078i	$-0.711077\pi$
$907$	−1116.65			−1.23115			−0.615576	+	0.788078i	$0.711077\pi$
$908$		0			0
$909$	1293.52	−	218.056i	1.42302	−	0.239885i
$910$		0			0
$911$	−318.595	−	183.941i	−0.349720	−	0.201911i	0.314842	−	0.949144i	$-0.398049\pi$
$911$	−318.595	−	183.941i	−0.349720	−	0.201911i	−0.664562	+	0.747233i	$0.731382\pi$
$912$		0			0
$913$	−124.312	−	215.314i	−0.136157	−	0.235831i
$914$		0			0
$915$	−37.5785	+	208.525i	−0.0410694	+	0.227897i
$916$		0			0
$917$	1403.09	−	810.075i	1.53009	−	0.883397i
$918$		0			0
$919$	59.0850			0.0642927			0.0321463	−	0.999483i	$-0.489766\pi$
$919$	59.0850			0.0642927			0.0321463	+	0.999483i	$0.489766\pi$
$920$		0			0
$921$	−159.010	−	442.045i	−0.172649	−	0.479962i
$922$		0			0
$923$	−26.9179	+	15.5410i	−0.0291635	+	0.0168375i
$924$		0			0
$925$	231.244	+	400.526i	0.249993	+	0.433001i
$926$		0			0
$927$	−88.1242	−	522.759i	−0.0950638	−	0.563926i
$928$		0			0
$929$			1169.17i			1.25852i	0.777193	+	0.629262i	$0.216643\pi$
$929$			1169.17i			1.25852i	−0.777193	+	0.629262i	$0.783357\pi$
$930$		0			0
$931$	−840.120	−	448.508i	−0.902384	−	0.481749i
$932$		0			0
$933$	901.602	−	324.318i	0.966347	−	0.347608i
$934$		0			0
$935$	106.531	+	61.5058i	0.113937	+	0.0657816i
$936$		0			0
$937$	90.0611	−	155.990i	0.0961165	−	0.166479i	−0.813958	−	0.580924i	$-0.802691\pi$
$937$	90.0611	−	155.990i	0.0961165	−	0.166479i	0.910074	+	0.414446i	$0.136025\pi$
$938$		0			0
$939$	−416.932	−	1159.07i	−0.444017	−	1.23436i
$940$		0			0
$941$		−	440.875i		−	0.468518i	−0.972174	−	0.234259i	$-0.924734\pi$
$941$		−	440.875i		−	0.468518i	0.972174	−	0.234259i	$-0.0752664\pi$
$942$		0			0
$943$	90.1259	−	156.103i	0.0955736	−	0.165538i
$944$		0			0
$945$	−796.925	−	8.99916i	−0.843307	−	0.00952292i
$946$		0			0
$947$		−	1531.06i		−	1.61675i	−0.588666	−	0.808376i	$-0.700347\pi$
$947$		−	1531.06i		−	1.61675i	0.588666	−	0.808376i	$-0.299653\pi$
$948$		0			0
$949$	−39.0283	−	67.5990i	−0.0411257	−	0.0712318i
$950$		0			0
$951$	−203.937	+	73.3589i	−0.214445	+	0.0771387i
$952$		0			0
$953$	395.063	−	228.090i	0.414547	−	0.239339i	−0.278195	−	0.960525i	$-0.589736\pi$
$953$	395.063	−	228.090i	0.414547	−	0.239339i	0.692741	+	0.721186i	$0.256403\pi$
$954$		0			0
$955$	−91.2823	−	158.106i	−0.0955835	−	0.165556i
$956$		0			0
$957$	−367.926	−	66.3042i	−0.384458	−	0.0692834i
$958$		0			0
$959$			13.0057i			0.0135617i
$960$		0			0
$961$	−128.494	+	222.557i	−0.133708	+	0.231589i
$962$		0			0
$963$	276.571	−	742.434i	0.287197	−	0.770960i
$964$		0			0
$965$	−765.622	+	442.032i	−0.793390	+	0.458064i
$966$		0			0
$967$	−521.232	+	902.800i	−0.539019	+	0.933609i	0.459938	+	0.887951i	$0.347872\pi$
$967$	−521.232	+	902.800i	−0.539019	+	0.933609i	−0.998957	+	0.0456576i	$0.985462\pi$
$968$		0			0
$969$	263.151	−	333.066i	0.271569	−	0.343722i
$970$		0			0
$971$	670.304	−	387.000i	0.690324	−	0.398558i	−0.113410	−	0.993548i	$-0.536177\pi$
$971$	670.304	−	387.000i	0.690324	−	0.398558i	0.803733	+	0.594990i	$0.202844\pi$
$972$		0			0
$973$	−1223.43	+	2119.04i	−1.25738	+	2.17784i
$974$		0			0
$975$	9.98059	+	27.7460i	0.0102365	+	0.0284574i
$976$		0			0
$977$	1030.42	−	594.913i	1.05468	−	0.608918i	0.130722	−	0.991419i	$-0.458270\pi$
$977$	1030.42	−	594.913i	1.05468	−	0.608918i	0.923955	+	0.382501i	$0.124937\pi$
$978$		0			0
$979$	−340.236	−	589.305i	−0.347534	−	0.601946i
$980$		0			0
$981$	−188.739	−	1119.62i	−0.192395	−	1.14130i
$982$		0			0
$983$		−	46.1449i		−	0.0469429i	−0.999725	−	0.0234715i	$-0.992528\pi$
$983$		−	46.1449i		−	0.0469429i	0.999725	−	0.0234715i	$-0.00747189\pi$
$984$		0			0
$985$	−67.1556	+	116.317i	−0.0681782	+	0.118088i
$986$		0			0
$987$	−129.958	+	721.147i	−0.131670	+	0.730645i
$988$		0			0
$989$		−	20.0506i		−	0.0202736i
$990$		0			0
$991$	521.982	+	904.099i	0.526722	+	0.912309i	0.999515	+	0.0311359i	$0.00991246\pi$
$991$	521.982	+	904.099i	0.526722	+	0.912309i	−0.472793	+	0.881173i	$0.656754\pi$
$992$		0			0
$993$	768.938	−	909.411i	0.774358	−	0.915821i
$994$		0			0
$995$	−96.8496	+	55.9161i	−0.0973363	+	0.0561971i
$996$		0			0
$997$	412.372	+	714.249i	0.413613	+	0.716398i	0.995282	−	0.0970276i	$-0.0309335\pi$
$997$	412.372	+	714.249i	0.413613	+	0.716398i	−0.581669	+	0.813425i	$0.697600\pi$
$998$		0			0
$999$	662.738	+	392.676i	0.663401	+	0.393069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.be.a.425.2	yes	80
3.2	odd	2		2052.3.be.a.197.27		80
9.4	even	3		2052.3.m.a.881.27		80
9.5	odd	6		684.3.m.a.653.25	yes	80
19.11	even	3		684.3.m.a.353.25	✓	80
57.11	odd	6		2052.3.m.a.1493.14		80
171.49	even	3		2052.3.be.a.125.27		80
171.68	odd	6	inner	684.3.be.a.581.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.25	✓	80	19.11	even	3
684.3.m.a.653.25	yes	80	9.5	odd	6
684.3.be.a.425.2	yes	80	1.1	even	1	trivial
684.3.be.a.581.2	yes	80	171.68	odd	6	inner
2052.3.m.a.881.27		80	9.4	even	3
2052.3.m.a.1493.14		80	57.11	odd	6
2052.3.be.a.125.27		80	171.49	even	3
2052.3.be.a.197.27		80	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.95244 - 0.532061i) q^{3} +(-2.56758 - 1.48239i) q^{5} +(-4.97804 + 8.62221i) q^{7} +(8.43382 + 3.14176i) q^{9} +O(q^{10})\)	\(q+(-2.95244 - 0.532061i) q^{3} +(-2.56758 - 1.48239i) q^{5} +(-4.97804 + 8.62221i) q^{7} +(8.43382 + 3.14176i) q^{9} +(4.82506 + 2.78575i) q^{11} +0.606341 q^{13} +(6.79191 + 5.74279i) q^{15} +(-6.44927 + 3.72349i) q^{17} +(16.1298 - 10.0414i) q^{19} +(19.2849 - 22.8080i) q^{21} +42.9104i q^{23} +(-8.10502 - 14.0383i) q^{25} +(-23.2288 - 13.7632i) q^{27} +(19.3704 - 11.1835i) q^{29} +(-17.4498 - 30.2240i) q^{31} +(-12.7635 - 10.7920i) q^{33} +(25.5630 - 14.7588i) q^{35} -28.5309 q^{37} +(-1.79019 - 0.322611i) q^{39} +(-3.63788 - 2.10033i) q^{41} -0.467266 q^{43} +(-16.9972 - 20.5690i) q^{45} +(-21.2464 + 12.2666i) q^{47} +(-25.0617 - 43.4081i) q^{49} +(21.0222 - 7.56198i) q^{51} +(-90.3257 - 52.1496i) q^{53} +(-8.25916 - 14.3053i) q^{55} +(-52.9649 + 21.0647i) q^{57} +(-62.1999 - 35.9111i) q^{59} +(11.9112 + 20.6307i) q^{61} +(-69.0728 + 57.0784i) q^{63} +(-1.55683 - 0.898836i) q^{65} +83.7885 q^{67} +(22.8310 - 126.690i) q^{69} +(-44.3939 + 25.6309i) q^{71} +(-64.3669 - 111.487i) q^{73} +(16.4604 + 45.7596i) q^{75} +(-48.0387 + 27.7351i) q^{77} +127.840 q^{79} +(61.2587 + 52.9941i) q^{81} +(-38.6456 - 22.3121i) q^{83} +22.0787 q^{85} +(-63.1402 + 22.7124i) q^{87} +(-105.771 - 61.0671i) q^{89} +(-3.01839 + 5.22800i) q^{91} +(35.4386 + 98.5190i) q^{93} +(-56.2999 + 1.87153i) q^{95} +6.37361 q^{97} +(31.9415 + 38.6537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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