LMFDB - Embedded newform 684.3.be.a.425.7

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			425.7
Character	$\chi$	$=$	684.425
Dual form			684.3.be.a.581.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66330 - 1.38089i) q^{3} +(7.06805 + 4.08074i) q^{5} +(-1.62444 + 2.81362i) q^{7} +(5.18629 + 7.35543i) q^{9} +O(q^{10})$	\(q+(-2.66330 - 1.38089i) q^{3} +(7.06805 + 4.08074i) q^{5} +(-1.62444 + 2.81362i) q^{7} +(5.18629 + 7.35543i) q^{9} +(2.31169 + 1.33465i) q^{11} +8.56878 q^{13} +(-13.1893 - 20.6284i) q^{15} +(-10.8726 + 6.27730i) q^{17} +(3.40016 + 18.6933i) q^{19} +(8.21167 - 5.25032i) q^{21} -1.01373i q^{23} +(20.8049 + 36.0351i) q^{25} +(-3.65559 - 26.7514i) q^{27} +(-38.7940 + 22.3977i) q^{29} +(-28.2502 - 48.9308i) q^{31} +(-4.31370 - 6.74676i) q^{33} +(-22.9633 + 13.2579i) q^{35} -16.1619 q^{37} +(-22.8212 - 11.8325i) q^{39} +(2.11219 + 1.21948i) q^{41} +47.1409 q^{43} +(6.64134 + 73.1524i) q^{45} +(-38.2689 + 22.0946i) q^{47} +(19.2224 + 33.2941i) q^{49} +(37.6252 - 1.70445i) q^{51} +(44.0599 + 25.4380i) q^{53} +(10.8927 + 18.8668i) q^{55} +(16.7577 - 54.4810i) q^{57} +(50.0778 + 28.9124i) q^{59} +(46.4968 + 80.5349i) q^{61} +(-29.1202 + 2.64376i) q^{63} +(60.5645 + 34.9669i) q^{65} -115.006 q^{67} +(-1.39984 + 2.69986i) q^{69} +(-14.2250 + 8.21279i) q^{71} +(33.0073 + 57.1704i) q^{73} +(-5.64905 - 124.701i) q^{75} +(-7.51041 + 4.33614i) q^{77} +4.21472 q^{79} +(-27.2048 + 76.2948i) q^{81} +(50.3676 + 29.0797i) q^{83} -102.464 q^{85} +(134.249 - 6.08156i) q^{87} +(106.211 + 61.3211i) q^{89} +(-13.9195 + 24.1093i) q^{91} +(7.67065 + 169.328i) q^{93} +(-52.2499 + 146.000i) q^{95} -116.723 q^{97} +(2.17213 + 23.9254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.66330	−	1.38089i	−0.887765	−	0.460296i
$3$	−2.66330	−	1.38089i	−0.887765	−	0.460296i
$4$		0			0
$5$	7.06805	+	4.08074i	1.41361	+	0.816148i	0.995726	−	0.0923532i	$-0.0294389\pi$
$5$	7.06805	+	4.08074i	1.41361	+	0.816148i	0.417883	+	0.908501i	$0.362772\pi$
$6$		0			0
$7$	−1.62444	+	2.81362i	−0.232063	+	0.401946i	−0.958415	−	0.285378i	$-0.907881\pi$
$7$	−1.62444	+	2.81362i	−0.232063	+	0.401946i	0.726352	+	0.687323i	$0.241214\pi$
$8$		0			0
$9$	5.18629	+	7.35543i	0.576254	+	0.817270i
$10$		0			0
$11$	2.31169	+	1.33465i	0.210153	+	0.121332i	0.601383	−	0.798961i	$-0.294617\pi$
$11$	2.31169	+	1.33465i	0.210153	+	0.121332i	−0.391229	+	0.920293i	$0.627950\pi$
$12$		0			0
$13$	8.56878			0.659137			0.329568	−	0.944132i	$-0.393097\pi$
$13$	8.56878			0.659137			0.329568	+	0.944132i	$0.393097\pi$
$14$		0			0
$15$	−13.1893	−	20.6284i	−0.879283	−	1.37523i
$16$		0			0
$17$	−10.8726	+	6.27730i	−0.639564	+	0.369253i	−0.784447	−	0.620196i	$-0.787053\pi$
$17$	−10.8726	+	6.27730i	−0.639564	+	0.369253i	0.144882	+	0.989449i	$0.453720\pi$
$18$		0			0
$19$	3.40016	+	18.6933i	0.178956	+	0.983857i
$19$	3.40016	+	18.6933i	0.178956	+	0.983857i
$20$		0			0
$21$	8.21167	−	5.25032i	0.391032	−	0.250015i
$22$		0			0
$23$		−	1.01373i		−	0.0440751i	−0.999757	−	0.0220375i	$-0.992985\pi$
$23$		−	1.01373i		−	0.0440751i	0.999757	−	0.0220375i	$-0.00701534\pi$
$24$		0			0
$25$	20.8049	+	36.0351i	0.832194	+	1.44140i
$26$		0			0
$27$	−3.65559	−	26.7514i	−0.135392	−	0.990792i
$28$		0			0
$29$	−38.7940	+	22.3977i	−1.33772	+	0.772336i	−0.986470	−	0.163944i	$-0.947578\pi$
$29$	−38.7940	+	22.3977i	−1.33772	+	0.772336i	−0.351255	+	0.936280i	$0.614245\pi$
$30$		0			0
$31$	−28.2502	−	48.9308i	−0.911297	−	1.57841i	−0.812235	−	0.583331i	$-0.801749\pi$
$31$	−28.2502	−	48.9308i	−0.911297	−	1.57841i	−0.0990618	−	0.995081i	$-0.531584\pi$
$32$		0			0
$33$	−4.31370	−	6.74676i	−0.130718	−	0.204447i
$34$		0			0
$35$	−22.9633	+	13.2579i	−0.656094	+	0.378796i
$36$		0			0
$37$	−16.1619			−0.436808			−0.218404	−	0.975858i	$-0.570085\pi$
$37$	−16.1619			−0.436808			−0.218404	+	0.975858i	$0.570085\pi$
$38$		0			0
$39$	−22.8212	−	11.8325i	−0.585159	−	0.303398i
$40$		0			0
$41$	2.11219	+	1.21948i	0.0515169	+	0.0297433i	0.525537	−	0.850771i	$-0.323864\pi$
$41$	2.11219	+	1.21948i	0.0515169	+	0.0297433i	−0.474020	+	0.880514i	$0.657198\pi$
$42$		0			0
$43$	47.1409			1.09630			0.548150	−	0.836380i	$-0.315332\pi$
$43$	47.1409			1.09630			0.548150	+	0.836380i	$0.315332\pi$
$44$		0			0
$45$	6.64134	+	73.1524i	0.147585	+	1.62561i
$46$		0			0
$47$	−38.2689	+	22.0946i	−0.814233	+	0.470097i	−0.848424	−	0.529318i	$-0.822448\pi$
$47$	−38.2689	+	22.0946i	−0.814233	+	0.470097i	0.0341910	+	0.999415i	$0.489115\pi$
$48$		0			0
$49$	19.2224	+	33.2941i	0.392293	+	0.679472i
$50$		0			0
$51$	37.6252	−	1.70445i	0.737749	−	0.0334205i
$52$		0			0
$53$	44.0599	+	25.4380i	0.831318	+	0.479962i	0.854304	−	0.519774i	$-0.173984\pi$
$53$	44.0599	+	25.4380i	0.831318	+	0.479962i	−0.0229856	+	0.999736i	$0.507317\pi$
$54$		0			0
$55$	10.8927	+	18.8668i	0.198050	+	0.343033i
$56$		0			0
$57$	16.7577	−	54.4810i	0.293995	−	0.955807i
$58$		0			0
$59$	50.0778	+	28.9124i	0.848776	+	0.490041i	0.860238	−	0.509893i	$-0.170315\pi$
$59$	50.0778	+	28.9124i	0.848776	+	0.490041i	−0.0114619	+	0.999934i	$0.503649\pi$
$60$		0			0
$61$	46.4968	+	80.5349i	0.762243	+	1.32024i	0.941692	+	0.336477i	$0.109235\pi$
$61$	46.4968	+	80.5349i	0.762243	+	1.32024i	−0.179449	+	0.983767i	$0.557431\pi$
$62$		0			0
$63$	−29.1202	+	2.64376i	−0.462226	+	0.0419644i
$64$		0			0
$65$	60.5645	+	34.9669i	0.931762	+	0.537953i
$66$		0			0
$67$	−115.006			−1.71651			−0.858257	−	0.513220i	$-0.828452\pi$
$67$	−115.006			−1.71651			−0.858257	+	0.513220i	$0.828452\pi$
$68$		0			0
$69$	−1.39984	+	2.69986i	−0.0202876	+	0.0391283i
$70$		0			0
$71$	−14.2250	+	8.21279i	−0.200352	+	0.115673i	−0.596820	−	0.802376i	$-0.703569\pi$
$71$	−14.2250	+	8.21279i	−0.200352	+	0.115673i	0.396468	+	0.918049i	$0.370236\pi$
$72$		0			0
$73$	33.0073	+	57.1704i	0.452155	+	0.783156i	0.998520	−	0.0543918i	$-0.0173220\pi$
$73$	33.0073	+	57.1704i	0.452155	+	0.783156i	−0.546365	+	0.837547i	$0.683989\pi$
$74$		0			0
$75$	−5.64905	−	124.701i	−0.0753207	−	1.66268i
$76$		0			0
$77$	−7.51041	+	4.33614i	−0.0975378	+	0.0563135i
$78$		0			0
$79$	4.21472			0.0533508			0.0266754	−	0.999644i	$-0.491508\pi$
$79$	4.21472			0.0533508			0.0266754	+	0.999644i	$0.491508\pi$
$80$		0			0
$81$	−27.2048	+	76.2948i	−0.335862	+	0.941911i
$82$		0			0
$83$	50.3676	+	29.0797i	0.606838	+	0.350358i	0.771727	−	0.635954i	$-0.219393\pi$
$83$	50.3676	+	29.0797i	0.606838	+	0.350358i	−0.164889	+	0.986312i	$0.552726\pi$
$84$		0			0
$85$	−102.464			−1.20546
$86$		0			0
$87$	134.249	−	6.08156i	1.54309	−	0.0699030i
$88$		0			0
$89$	106.211	+	61.3211i	1.19338	+	0.689001i	0.959073	−	0.283160i	$-0.0913828\pi$
$89$	106.211	+	61.3211i	1.19338	+	0.689001i	0.234312	+	0.972161i	$0.424716\pi$
$90$		0			0
$91$	−13.9195	+	24.1093i	−0.152961	+	0.264937i
$92$		0			0
$93$	7.67065	+	169.328i	0.0824802	+	1.82073i
$94$		0			0
$95$	−52.2499	+	146.000i	−0.549999	+	1.53684i
$96$		0			0
$97$	−116.723			−1.20333			−0.601665	−	0.798749i	$-0.705496\pi$
$97$	−116.723			−1.20333			−0.601665	+	0.798749i	$0.705496\pi$
$98$		0			0
$99$	2.17213	+	23.9254i	0.0219407	+	0.241670i
$100$		0			0
$101$	9.68531	−	5.59182i	0.0958942	−	0.0553645i	−0.451286	−	0.892379i	$-0.649035\pi$
$101$	9.68531	−	5.59182i	0.0958942	−	0.0553645i	0.547180	+	0.837015i	$0.315701\pi$
$102$		0			0
$103$	−2.47455	−	4.28605i	−0.0240248	−	0.0416121i	0.853763	−	0.520662i	$-0.174315\pi$
$103$	−2.47455	−	4.28605i	−0.0240248	−	0.0416121i	−0.877788	+	0.479050i	$0.840981\pi$
$104$		0			0
$105$	79.4656	−	3.59985i	0.756816	−	0.0342843i
$106$		0			0
$107$			64.7630i			0.605262i	0.953108	+	0.302631i	$0.0978650\pi$
$107$			64.7630i			0.605262i	−0.953108	+	0.302631i	$0.902135\pi$
$108$		0			0
$109$	8.24360	+	14.2783i	0.0756294	+	0.130994i	0.901360	−	0.433071i	$-0.142570\pi$
$109$	8.24360	+	14.2783i	0.0756294	+	0.130994i	−0.825730	+	0.564065i	$0.809237\pi$
$110$		0			0
$111$	43.0440	+	22.3178i	0.387783	+	0.201061i
$112$		0			0
$113$	86.5642	−	49.9779i	0.766055	−	0.442282i	−0.0654105	−	0.997858i	$-0.520836\pi$
$113$	86.5642	−	49.9779i	0.766055	−	0.442282i	0.831465	+	0.555576i	$0.187502\pi$
$114$		0			0
$115$	4.13676	−	7.16507i	0.0359718	−	0.0623050i
$116$		0			0
$117$	44.4402	+	63.0271i	0.379831	+	0.538693i
$118$		0			0
$119$		−	40.7884i		−	0.342760i
$120$		0			0
$121$	−56.9374	−	98.6185i	−0.470557	−	0.815029i
$122$		0			0
$123$	−3.94144	−	6.16453i	−0.0320442	−	0.0501181i
$124$		0			0
$125$			135.560i			1.08448i
$126$		0			0
$127$	72.3034	−	125.233i	0.569318	−	0.986087i	−0.427316	−	0.904102i	$-0.640541\pi$
$127$	72.3034	−	125.233i	0.569318	−	0.986087i	0.996634	−	0.0819849i	$-0.0261259\pi$
$128$		0			0
$129$	−125.550	−	65.0964i	−0.973257	−	0.504623i
$130$		0			0
$131$	−35.8753	−	20.7126i	−0.273857	−	0.158111i	0.356782	−	0.934188i	$-0.383874\pi$
$131$	−35.8753	−	20.7126i	−0.273857	−	0.158111i	−0.630639	+	0.776076i	$0.717207\pi$
$132$		0			0
$133$	−58.1191	−	20.7994i	−0.436986	−	0.156387i
$134$		0			0
$135$	83.3275	−	203.998i	0.617241	−	1.51109i
$136$		0			0
$137$	147.503	−	85.1607i	1.07666	−	0.621611i	0.146668	−	0.989186i	$-0.453145\pi$
$137$	147.503	−	85.1607i	1.07666	−	0.621611i	0.929994	+	0.367575i	$0.119812\pi$
$138$		0			0
$139$	−234.134			−1.68442			−0.842208	−	0.539152i	$-0.818745\pi$
$139$	−234.134			−1.68442			−0.842208	+	0.539152i	$0.818745\pi$
$140$		0			0
$141$	132.432	−	5.99925i	0.939232	−	0.0425478i
$142$		0			0
$143$	19.8083	+	11.4364i	0.138520	+	0.0799745i
$144$		0			0
$145$	−365.597			−2.52136
$146$		0			0
$147$	−5.21937	−	115.216i	−0.0355059	−	0.783783i
$148$		0			0
$149$	124.900	+	72.1109i	0.838253	+	0.483966i	0.856670	−	0.515865i	$-0.172529\pi$
$149$	124.900	+	72.1109i	0.838253	+	0.483966i	−0.0184168	+	0.999830i	$0.505863\pi$
$150$		0			0
$151$	−70.2344	+	121.650i	−0.465129	+	0.805626i	−0.999207	−	0.0398084i	$-0.987325\pi$
$151$	−70.2344	+	121.650i	−0.465129	+	0.805626i	0.534079	+	0.845435i	$0.320659\pi$
$152$		0			0
$153$	−102.561	−	47.4168i	−0.670331	−	0.309914i
$154$		0			0
$155$		−	461.127i		−	2.97501i
$156$		0			0
$157$	84.5293	−	146.409i	0.538403	−	0.932541i	−0.460587	−	0.887614i	$-0.652361\pi$
$157$	84.5293	−	146.409i	0.538403	−	0.932541i	0.998990	−	0.0449269i	$-0.0143055\pi$
$158$		0			0
$159$	−82.2174	−	128.591i	−0.517091	−	0.808746i
$160$		0			0
$161$	2.85224	+	1.64674i	0.0177158	+	0.0102282i
$162$		0			0
$163$	38.8891			0.238583			0.119292	−	0.992859i	$-0.461938\pi$
$163$	38.8891			0.238583			0.119292	+	0.992859i	$0.461938\pi$
$164$		0			0
$165$	−2.95766	−	65.2895i	−0.0179252	−	0.395694i
$166$		0			0
$167$			64.1281i			0.384000i	0.981395	+	0.192000i	$0.0614974\pi$
$167$			64.1281i			0.384000i	−0.981395	+	0.192000i	$0.938503\pi$
$168$		0			0
$169$	−95.5760			−0.565539
$170$		0			0
$171$	−119.863	+	121.958i	−0.700953	+	0.713207i
$172$		0			0
$173$		−	245.661i		−	1.42001i	−0.704199	−	0.710003i	$-0.748694\pi$
$173$		−	245.661i		−	1.42001i	0.704199	−	0.710003i	$-0.251306\pi$
$174$		0			0
$175$	−135.185			−0.772487
$176$		0			0
$177$	−93.4471	−	146.154i	−0.527950	−	0.825730i
$178$		0			0
$179$			306.886i			1.71445i	0.514945	+	0.857223i	$0.327812\pi$
$179$			306.886i			1.71445i	−0.514945	+	0.857223i	$0.672188\pi$
$180$		0			0
$181$	−21.8308	+	37.8120i	−0.120612	+	0.208906i	−0.920009	−	0.391897i	$-0.871819\pi$
$181$	−21.8308	+	37.8120i	−0.120612	+	0.208906i	0.799397	+	0.600803i	$0.205152\pi$
$182$		0			0
$183$	−12.6251	−	278.695i	−0.0689895	−	1.52292i
$184$		0			0
$185$	−114.233	−	65.9525i	−0.617477	−	0.356500i
$186$		0			0
$187$	−33.5121			−0.179209
$188$		0			0
$189$	81.2065	+	33.1707i	0.429664	+	0.175506i
$190$		0			0
$191$	−10.7711	−	6.21870i	−0.0563932	−	0.0325586i	0.471538	−	0.881846i	$-0.343699\pi$
$191$	−10.7711	−	6.21870i	−0.0563932	−	0.0325586i	−0.527932	+	0.849287i	$0.677032\pi$
$192$		0			0
$193$	25.3279	−	43.8692i	0.131232	−	0.227301i	−0.792919	−	0.609326i	$-0.791440\pi$
$193$	25.3279	−	43.8692i	0.131232	−	0.227301i	0.924152	+	0.382025i	$0.124773\pi$
$194$		0			0
$195$	−113.016	−	176.760i	−0.579568	−	0.906463i
$196$		0			0
$197$		−	183.355i		−	0.930736i	−0.885117	−	0.465368i	$-0.845922\pi$
$197$		−	183.355i		−	0.930736i	0.885117	−	0.465368i	$-0.154078\pi$
$198$		0			0
$199$	48.7803	−	84.4900i	0.245127	−	0.424573i	−0.717040	−	0.697032i	$-0.754504\pi$
$199$	48.7803	−	84.4900i	0.245127	−	0.424573i	0.962167	+	0.272459i	$0.0878369\pi$
$200$		0			0
$201$	306.296	+	158.811i	1.52386	+	0.790105i
$202$		0			0
$203$		−	145.535i		−	0.716923i
$204$		0			0
$205$	9.95272	+	17.2386i	0.0485499	+	0.0840908i
$206$		0			0
$207$	7.45640	−	5.25748i	0.0360213	−	0.0253985i
$208$		0			0
$209$	−17.0889	+	47.7511i	−0.0817653	+	0.228474i
$210$		0			0
$211$	46.8404	−	81.1299i	0.221992	−	0.384502i	−0.733421	−	0.679775i	$-0.762077\pi$
$211$	46.8404	−	81.1299i	0.221992	−	0.384502i	0.955413	+	0.295273i	$0.0954107\pi$
$212$		0			0
$213$	49.2263	−	2.22998i	0.231109	−	0.0104694i
$214$		0			0
$215$	333.194	+	192.370i	1.54974	+	0.894743i
$216$		0			0
$217$	183.563			0.845914
$218$		0			0
$219$	−8.96234	−	197.841i	−0.0409239	−	0.903384i
$220$		0			0
$221$	−93.1649	+	53.7888i	−0.421560	+	0.243388i
$222$		0			0
$223$	260.642			1.16880			0.584399	−	0.811466i	$-0.301330\pi$
$223$	260.642			1.16880			0.584399	+	0.811466i	$0.301330\pi$
$224$		0			0
$225$	−157.153	+	339.917i	−0.698460	+	1.51074i
$226$		0			0
$227$	271.118	+	156.530i	1.19435	+	0.689559i	0.959290	−	0.282421i	$-0.0911376\pi$
$227$	271.118	+	156.530i	1.19435	+	0.689559i	0.235061	+	0.971981i	$0.424471\pi$
$228$		0			0
$229$	−142.714	−	247.188i	−0.623205	−	1.07942i	−0.988885	−	0.148682i	$-0.952497\pi$
$229$	−142.714	−	247.188i	−0.623205	−	1.07942i	0.365680	−	0.930741i	$-0.380836\pi$
$230$		0			0
$231$	25.9902	−	1.17737i	0.112512	−	0.00509685i
$232$		0			0
$233$	−225.585	+	130.242i	−0.968177	+	0.558977i	−0.898680	−	0.438605i	$-0.855473\pi$
$233$	−225.585	+	130.242i	−0.968177	+	0.558977i	−0.0694970	+	0.997582i	$0.522139\pi$
$234$		0			0
$235$	−360.649			−1.53468
$236$		0			0
$237$	−11.2250	−	5.82006i	−0.0473630	−	0.0245572i
$238$		0			0
$239$	108.436	−	62.6056i	0.453708	−	0.261948i	−0.255687	−	0.966760i	$-0.582302\pi$
$239$	108.436	−	62.6056i	0.453708	−	0.261948i	0.709395	+	0.704811i	$0.248968\pi$
$240$		0			0
$241$	−69.9889	−	121.224i	−0.290410	−	0.503006i	0.683496	−	0.729954i	$-0.260459\pi$
$241$	−69.9889	−	121.224i	−0.290410	−	0.503006i	−0.973907	+	0.226948i	$0.927125\pi$
$242$		0			0
$243$	177.809	−	165.629i	0.731725	−	0.681600i
$244$		0			0
$245$			313.766i			1.28068i
$246$		0			0
$247$	29.1353	+	160.179i	0.117957	+	0.648496i
$248$		0			0
$249$	−93.9879	−	147.000i	−0.377461	−	0.590361i
$250$		0			0
$251$	−59.2403	−	34.2024i	−0.236017	−	0.136265i	0.377328	−	0.926080i	$-0.376843\pi$
$251$	−59.2403	−	34.2024i	−0.236017	−	0.136265i	−0.613345	+	0.789815i	$0.710176\pi$
$252$		0			0
$253$	1.35297	−	2.34342i	0.00534773	−	0.00926253i
$254$		0			0
$255$	272.892	+	141.491i	1.07016	+	0.554868i
$256$		0			0
$257$		−	174.834i		−	0.680287i	−0.940374	−	0.340143i	$-0.889524\pi$
$257$		−	174.834i		−	0.680287i	0.940374	−	0.340143i	$-0.110476\pi$
$258$		0			0
$259$	26.2541	−	45.4735i	0.101367	−	0.175573i
$260$		0			0
$261$	−365.942	−	169.186i	−1.40208	−	0.648221i
$262$		0			0
$263$			443.866i			1.68770i	0.536577	+	0.843852i	$0.319717\pi$
$263$			443.866i			1.68770i	−0.536577	+	0.843852i	$0.680283\pi$
$264$		0			0
$265$	207.611	+	359.594i	0.783439	+	1.35696i
$266$		0			0
$267$	−198.194	−	309.982i	−0.742301	−	1.16098i
$268$		0			0
$269$	−113.808	+	65.7072i	−0.423079	+	0.244265i	−0.696394	−	0.717660i	$-0.745213\pi$
$269$	−113.808	+	65.7072i	−0.423079	+	0.244265i	0.273315	+	0.961925i	$0.411880\pi$
$270$		0			0
$271$	123.333	+	213.619i	0.455104	+	0.788263i	0.998694	−	0.0510880i	$-0.0162689\pi$
$271$	123.333	+	213.619i	0.455104	+	0.788263i	−0.543591	+	0.839351i	$0.682936\pi$
$272$		0			0
$273$	70.3640	−	44.9889i	0.257743	−	0.164794i
$274$		0			0
$275$			111.069i			0.403888i
$276$		0			0
$277$	−144.714	+	250.651i	−0.522432	+	0.904878i	0.477228	+	0.878780i	$0.341642\pi$
$277$	−144.714	+	250.651i	−0.522432	+	0.904878i	−0.999659	+	0.0260983i	$0.991692\pi$
$278$		0			0
$279$	213.393	−	461.562i	0.764851	−	1.65434i
$280$		0			0
$281$	21.5085	−	12.4180i	0.0765428	−	0.0441920i	−0.461240	−	0.887275i	$-0.652595\pi$
$281$	21.5085	−	12.4180i	0.0765428	−	0.0441920i	0.537783	+	0.843083i	$0.319262\pi$
$282$		0			0
$283$	76.6193	−	132.708i	0.270739	−	0.468934i	−0.698312	−	0.715794i	$-0.746065\pi$
$283$	76.6193	−	132.708i	0.270739	−	0.468934i	0.969051	+	0.246859i	$0.0793985\pi$
$284$		0			0
$285$	340.767	−	316.690i	1.19567	−	1.11119i
$286$		0			0
$287$	−6.86228	+	3.96194i	−0.0239104	+	0.0138047i
$288$		0			0
$289$	−65.6911	+	113.780i	−0.227305	+	0.393704i
$290$		0			0
$291$	310.868	+	161.182i	1.06827	+	0.553888i
$292$		0			0
$293$	388.201	−	224.128i	1.32492	−	0.764941i	0.340408	−	0.940278i	$-0.389435\pi$
$293$	388.201	−	224.128i	1.32492	−	0.764941i	0.984509	+	0.175337i	$0.0561014\pi$
$294$		0			0
$295$	235.968	+	408.709i	0.799891	+	1.38545i
$296$		0			0
$297$	27.2533	−	66.7198i	0.0917618	−	0.224646i
$298$		0			0
$299$		−	8.68640i		−	0.0290515i
$300$		0			0
$301$	−76.5778	+	132.637i	−0.254411	+	0.440653i
$302$		0			0
$303$	−33.5165	+	1.51832i	−0.110616	+	0.00501096i
$304$		0			0
$305$			758.966i			2.48841i
$306$		0			0
$307$	−222.128	−	384.737i	−0.723543	−	1.25321i	−0.959571	−	0.281467i	$-0.909179\pi$
$307$	−222.128	−	384.737i	−0.723543	−	1.25321i	0.236028	−	0.971746i	$-0.424154\pi$
$308$		0			0
$309$	0.671904	+	14.8321i	0.00217445	+	0.0480003i
$310$		0			0
$311$	−332.333	+	191.872i	−1.06859	+	0.616953i	−0.927797	−	0.373085i	$-0.878300\pi$
$311$	−332.333	+	191.872i	−1.06859	+	0.616953i	−0.140797	+	0.990038i	$0.544967\pi$
$312$		0			0
$313$	48.5697	+	84.1252i	0.155175	+	0.268771i	0.933123	−	0.359558i	$-0.117073\pi$
$313$	48.5697	+	84.1252i	0.155175	+	0.268771i	−0.777948	+	0.628329i	$0.783739\pi$
$314$		0			0
$315$	−216.612	−	100.146i	−0.687656	−	0.317923i
$316$		0			0
$317$	229.781	−	132.664i	0.724861	−	0.418499i	−0.0916780	−	0.995789i	$-0.529223\pi$
$317$	229.781	−	132.664i	0.724861	−	0.418499i	0.816539	+	0.577290i	$0.195890\pi$
$318$		0			0
$319$	−119.573			−0.374837
$320$		0			0
$321$	89.4306	−	172.483i	0.278600	−	0.537331i
$322$		0			0
$323$	−154.312	−	181.901i	−0.477746	−	0.563160i
$324$		0			0
$325$	178.272	+	308.776i	0.548530	+	0.950081i
$326$		0			0
$327$	−2.23835	−	49.4109i	−0.00684511	−	0.151104i
$328$		0			0
$329$		−	143.566i		−	0.436370i
$330$		0			0
$331$	269.383	−	466.585i	0.813845	−	1.40962i	−0.0963093	−	0.995351i	$-0.530704\pi$
$331$	269.383	−	466.585i	0.813845	−	1.40962i	0.910154	−	0.414269i	$-0.135963\pi$
$332$		0			0
$333$	−83.8204	−	118.878i	−0.251713	−	0.356991i
$334$		0			0
$335$	−812.871	−	469.311i	−2.42648	−	1.40093i
$336$		0			0
$337$	277.232	−	480.181i	0.822648	−	1.42487i	−0.0810554	−	0.996710i	$-0.525829\pi$
$337$	277.232	−	480.181i	0.822648	−	1.42487i	0.903704	−	0.428159i	$-0.140838\pi$
$338$		0			0
$339$	−299.560	+	13.5703i	−0.883658	+	0.0400303i
$340$		0			0
$341$		−	150.817i		−	0.442278i
$342$		0			0
$343$	−284.098			−0.828274
$344$		0			0
$345$	−20.9116	+	13.3703i	−0.0606132	+	0.0387545i
$346$		0			0
$347$	−61.4449	−	35.4752i	−0.177075	−	0.102234i	0.408843	−	0.912605i	$-0.365932\pi$
$347$	−61.4449	−	35.4752i	−0.177075	−	0.102234i	−0.585917	+	0.810371i	$0.699266\pi$
$348$		0			0
$349$	208.342	−	360.859i	0.596969	−	1.03398i	−0.396296	−	0.918123i	$-0.629705\pi$
$349$	208.342	−	360.859i	0.596969	−	1.03398i	0.993266	−	0.115859i	$-0.0369619\pi$
$350$		0			0
$351$	−31.3239	−	229.227i	−0.0892419	−	0.653068i
$352$		0			0
$353$	−414.592	−	239.365i	−1.17448	−	0.678087i	−0.219749	−	0.975556i	$-0.570524\pi$
$353$	−414.592	−	239.365i	−1.17448	−	0.678087i	−0.954731	+	0.297470i	$0.903857\pi$
$354$		0			0
$355$	−134.057			−0.377625
$356$		0			0
$357$	−56.3243	+	108.632i	−0.157771	+	0.304290i
$358$		0			0
$359$	230.981	−	133.357i	0.643402	−	0.371468i	−0.142522	−	0.989792i	$-0.545521\pi$
$359$	230.981	−	133.357i	0.643402	−	0.371468i	0.785924	+	0.618324i	$0.212188\pi$
$360$		0			0
$361$	−337.878	+	127.120i	−0.935949	+	0.352134i
$362$		0			0
$363$	15.4600	+	341.274i	0.0425894	+	0.940150i
$364$		0			0
$365$			538.777i			1.47610i
$366$		0			0
$367$	−175.840	−	304.563i	−0.479127	−	0.829873i	0.520586	−	0.853809i	$-0.325713\pi$
$367$	−175.840	−	304.563i	−0.479127	−	0.829873i	−0.999713	+	0.0239363i	$0.992380\pi$
$368$		0			0
$369$	1.98468	+	21.8606i	0.00537853	+	0.0592430i
$370$		0			0
$371$	−143.146	+	82.6451i	−0.385837	+	0.222763i
$372$		0			0
$373$	20.1245	+	34.8566i	0.0539530	+	0.0934494i	0.891741	−	0.452547i	$-0.149485\pi$
$373$	20.1245	+	34.8566i	0.0539530	+	0.0934494i	−0.837787	+	0.545996i	$0.816151\pi$
$374$		0			0
$375$	187.193	−	361.036i	0.499181	−	0.962762i
$376$		0			0
$377$	−332.417	+	191.921i	−0.881744	+	0.509075i
$378$		0			0
$379$	−383.784			−1.01262			−0.506311	−	0.862351i	$-0.668991\pi$
$379$	−383.784			−1.01262			−0.506311	+	0.862351i	$0.668991\pi$
$380$		0			0
$381$	−365.498	+	233.690i	−0.959313	+	0.613359i
$382$		0			0
$383$	580.681	+	335.256i	1.51614	+	0.875343i	0.999820	+	0.0189465i	$0.00603123\pi$
$383$	580.681	+	335.256i	1.51614	+	0.875343i	0.516318	+	0.856397i	$0.327302\pi$
$384$		0			0
$385$	−70.7786			−0.183841
$386$		0			0
$387$	244.486	+	346.742i	0.631748	+	0.895974i
$388$		0			0
$389$	450.608	−	260.159i	1.15838	−	0.668788i	0.207461	−	0.978243i	$-0.433480\pi$
$389$	450.608	−	260.159i	1.15838	−	0.668788i	0.950914	+	0.309455i	$0.100147\pi$
$390$		0			0
$391$	6.36347	+	11.0218i	0.0162748	+	0.0281889i
$392$		0			0
$393$	66.9446	+	104.703i	0.170343	+	0.266421i
$394$		0			0
$395$	29.7898	+	17.1992i	0.0754172	+	0.0435422i
$396$		0			0
$397$	170.435	+	295.202i	0.429308	+	0.743583i	0.996812	−	0.0797877i	$-0.0254242\pi$
$397$	170.435	+	295.202i	0.429308	+	0.743583i	−0.567504	+	0.823371i	$0.692091\pi$
$398$		0			0
$399$	126.067	+	135.651i	0.315957	+	0.339978i
$400$		0			0
$401$	−55.6529	−	32.1312i	−0.138785	−	0.0801277i	0.429000	−	0.903305i	$-0.358866\pi$
$401$	−55.6529	−	32.1312i	−0.138785	−	0.0801277i	−0.567785	+	0.823177i	$0.692199\pi$
$402$		0			0
$403$	−242.070	−	419.277i	−0.600669	−	1.04039i
$404$		0			0
$405$	−503.624	+	428.240i	−1.24352	+	1.05738i
$406$		0			0
$407$	−37.3613	−	21.5706i	−0.0917968	−	0.0529989i
$408$		0			0
$409$	763.459			1.86665			0.933323	−	0.359037i	$-0.116895\pi$
$409$	763.459			1.86665			0.933323	+	0.359037i	$0.116895\pi$
$410$		0			0
$411$	−510.441	+	23.1233i	−1.24195	+	0.0562611i
$412$		0			0
$413$	−162.697	+	93.9332i	−0.393939	+	0.227441i
$414$		0			0
$415$	237.334	+	411.074i	0.571888	+	0.990539i
$416$		0			0
$417$	623.568	+	323.313i	1.49537	+	0.775331i
$418$		0			0
$419$	517.338	−	298.685i	1.23470	−	0.712853i	0.266692	−	0.963782i	$-0.414069\pi$
$419$	517.338	−	298.685i	1.23470	−	0.712853i	0.968006	+	0.250929i	$0.0807360\pi$
$420$		0			0
$421$	−421.048			−1.00011			−0.500056	−	0.865993i	$-0.666687\pi$
$421$	−421.048			−1.00011			−0.500056	+	0.865993i	$0.666687\pi$
$422$		0			0
$423$	−360.989	−	166.896i	−0.853402	−	0.394552i
$424$		0			0
$425$	−452.405	−	261.196i	−1.06448	−	0.614580i
$426$		0			0
$427$	−302.126			−0.707555
$428$		0			0
$429$	−36.9631	−	57.8115i	−0.0861612	−	0.134759i
$430$		0			0
$431$	537.045	+	310.063i	1.24604	+	0.719404i	0.970318	−	0.241832i	$-0.0777484\pi$
$431$	537.045	+	310.063i	1.24604	+	0.719404i	0.275726	+	0.961236i	$0.411082\pi$
$432$		0			0
$433$	−102.906	+	178.238i	−0.237658	+	0.411636i	−0.960042	−	0.279856i	$-0.909713\pi$
$433$	−102.906	+	178.238i	−0.237658	+	0.411636i	0.722384	+	0.691493i	$0.243047\pi$
$434$		0			0
$435$	973.693	+	504.849i	2.23838	+	1.16057i
$436$		0			0
$437$	18.9499	−	3.44684i	0.0433636	−	0.00788750i
$438$		0			0
$439$	119.386			0.271950			0.135975	−	0.990712i	$-0.456583\pi$
$439$	119.386			0.271950			0.135975	+	0.990712i	$0.456583\pi$
$440$		0			0
$441$	−145.200	+	314.062i	−0.329251	+	0.712158i
$442$		0			0
$443$	700.488	−	404.427i	1.58124	−	0.912928i	0.586559	−	0.809907i	$-0.300482\pi$
$443$	700.488	−	404.427i	1.58124	−	0.912928i	0.994679	−	0.103021i	$-0.0328509\pi$
$444$		0			0
$445$	500.471	+	866.841i	1.12465	+	1.94796i
$446$		0			0
$447$	−233.068	−	364.525i	−0.521404	−	0.815493i
$448$		0			0
$449$			113.037i			0.251752i	0.992046	+	0.125876i	$0.0401742\pi$
$449$			113.037i			0.251752i	−0.992046	+	0.125876i	$0.959826\pi$
$450$		0			0
$451$	3.25516	+	5.63809i	0.00721764	+	0.0125013i
$452$		0			0
$453$	355.040	−	227.003i	0.783752	−	0.501110i
$454$		0			0
$455$	−196.767	+	113.604i	−0.432456	+	0.249678i
$456$		0			0
$457$	196.314	−	340.026i	0.429571	−	0.744039i	−0.567264	−	0.823536i	$-0.691998\pi$
$457$	196.314	−	340.026i	0.429571	−	0.744039i	0.996835	+	0.0794971i	$0.0253315\pi$
$458$		0			0
$459$	207.672	+	267.910i	0.452445	+	0.583681i
$460$		0			0
$461$			298.147i			0.646740i	0.946273	+	0.323370i	$0.104816\pi$
$461$			298.147i			0.646740i	−0.946273	+	0.323370i	$0.895184\pi$
$462$		0			0
$463$	134.637	+	233.198i	0.290793	+	0.503668i	0.973997	−	0.226559i	$-0.0727476\pi$
$463$	134.637	+	233.198i	0.290793	+	0.503668i	−0.683204	+	0.730227i	$0.739414\pi$
$464$		0			0
$465$	−636.765	+	1228.12i	−1.36939	+	2.64111i
$466$		0			0
$467$		−	608.515i		−	1.30303i	−0.758635	−	0.651516i	$-0.774134\pi$
$467$		−	608.515i		−	1.30303i	0.758635	−	0.651516i	$-0.225866\pi$
$468$		0			0
$469$	186.821	−	323.584i	0.398340	−	0.689945i
$470$		0			0
$471$	−427.301	+	273.205i	−0.907221	+	0.580053i
$472$		0			0
$473$	108.975	+	62.9168i	0.230391	+	0.133017i
$474$		0			0
$475$	−602.874	+	511.436i	−1.26921	+	1.07671i
$476$		0			0
$477$	41.3999	+	456.008i	0.0867923	+	0.955992i
$478$		0			0
$479$	−258.222	+	149.084i	−0.539085	+	0.311241i	−0.744708	−	0.667390i	$-0.767411\pi$
$479$	−258.222	+	149.084i	−0.539085	+	0.311241i	0.205623	+	0.978631i	$0.434078\pi$
$480$		0			0
$481$	−138.488			−0.287917
$482$		0			0
$483$	−5.32239	−	8.32439i	−0.0110194	−	0.0172348i
$484$		0			0
$485$	−825.004	−	476.316i	−1.70104	−	0.982095i
$486$		0			0
$487$	−387.209			−0.795091			−0.397546	−	0.917582i	$-0.630138\pi$
$487$	−387.209			−0.795091			−0.397546	+	0.917582i	$0.630138\pi$
$488$		0			0
$489$	−103.573	−	53.7015i	−0.211806	−	0.109819i
$490$		0			0
$491$	709.934	+	409.880i	1.44589	+	0.834787i	0.998233	−	0.0594167i	$-0.0189241\pi$
$491$	709.934	+	409.880i	1.44589	+	0.834787i	0.447660	+	0.894204i	$0.352257\pi$
$492$		0			0
$493$	281.194	−	487.043i	0.570374	−	0.987917i
$494$		0			0
$495$	−82.2805	+	177.970i	−0.166223	+	0.359534i
$496$		0			0
$497$		−	53.3648i		−	0.107374i
$498$		0			0
$499$	−297.270	+	514.886i	−0.595731	+	1.03184i	0.397713	+	0.917510i	$0.369804\pi$
$499$	−297.270	+	514.886i	−0.595731	+	1.03184i	−0.993443	+	0.114326i	$0.963529\pi$
$500$		0			0
$501$	88.5538	−	170.792i	0.176754	−	0.340902i
$502$		0			0
$503$	−53.9360	−	31.1399i	−0.107229	−	0.0619084i	0.445427	−	0.895318i	$-0.353052\pi$
$503$	−53.9360	−	31.1399i	−0.107229	−	0.0619084i	−0.552655	+	0.833410i	$0.686385\pi$
$504$		0			0
$505$	91.2750			0.180743
$506$		0			0
$507$	254.547	+	131.980i	0.502066	+	0.260315i
$508$		0			0
$509$		−	759.254i		−	1.49166i	−0.666138	−	0.745829i	$-0.732054\pi$
$509$		−	759.254i		−	1.49166i	0.666138	−	0.745829i	$-0.267946\pi$
$510$		0			0
$511$	−214.474			−0.419715
$512$		0			0
$513$	487.642	−	159.294i	0.950569	−	0.310515i
$514$		0			0
$515$		−	40.3920i		−	0.0784310i
$516$		0			0
$517$	−117.954			−0.228152
$518$		0			0
$519$	−339.230	+	654.268i	−0.653623	+	1.26063i
$520$		0			0
$521$			698.857i			1.34138i	0.741740	+	0.670688i	$0.234001\pi$
$521$			698.857i			1.34138i	−0.741740	+	0.670688i	$0.765999\pi$
$522$		0			0
$523$	183.451	−	317.746i	0.350766	−	0.607545i	−0.635618	−	0.772004i	$-0.719255\pi$
$523$	183.451	−	317.746i	0.350766	−	0.607545i	0.986384	+	0.164459i	$0.0525878\pi$
$524$		0			0
$525$	360.038	+	186.676i	0.685787	+	0.355573i
$526$		0			0
$527$	614.306	+	354.670i	1.16567	+	0.672997i
$528$		0			0
$529$	527.972			0.998057
$530$		0			0
$531$	47.0545	+	518.292i	0.0886149	+	0.976067i
$532$		0			0
$533$	18.0989	+	10.4494i	0.0339567	+	0.0196049i
$534$		0			0
$535$	−264.281	+	457.748i	−0.493983	+	0.855604i
$536$		0			0
$537$	423.775	−	817.328i	0.789153	−	1.52203i
$538$		0			0
$539$			102.621i			0.190391i
$540$		0			0
$541$	23.6736	−	41.0039i	0.0437590	−	0.0757929i	−0.843316	−	0.537417i	$-0.819400\pi$
$541$	23.6736	−	41.0039i	0.0437590	−	0.0757929i	0.887075	+	0.461625i	$0.152733\pi$
$542$		0			0
$543$	110.356	−	70.5587i	0.203234	−	0.129942i
$544$		0			0
$545$			134.560i			0.246899i
$546$		0			0
$547$	−219.148	−	379.576i	−0.400637	−	0.693923i	0.593166	−	0.805080i	$-0.297878\pi$
$547$	−219.148	−	379.576i	−0.400637	−	0.693923i	−0.993803	+	0.111157i	$0.964544\pi$
$548$		0			0
$549$	−351.223	+	759.682i	−0.639750	+	1.38376i
$550$		0			0
$551$	−550.593	−	649.032i	−0.999262	−	1.17792i
$552$		0			0
$553$	−6.84657	+	11.8586i	−0.0123808	+	0.0214441i
$554$		0			0
$555$	213.164	+	333.394i	0.384078	+	0.600711i
$556$		0			0
$557$	−656.442	−	378.997i	−1.17853	−	0.680425i	−0.222857	−	0.974851i	$-0.571538\pi$
$557$	−656.442	−	378.997i	−1.17853	−	0.680425i	−0.955674	+	0.294426i	$0.904872\pi$
$558$		0			0
$559$	403.940			0.722612
$560$		0			0
$561$	89.2526	+	46.2765i	0.159095	+	0.0824892i
$562$		0			0
$563$	186.860	−	107.884i	0.331900	−	0.191623i	−0.324784	−	0.945788i	$-0.605292\pi$
$563$	186.860	−	107.884i	0.331900	−	0.191623i	0.656684	+	0.754165i	$0.271958\pi$
$564$		0			0
$565$	815.786			1.44387
$566$		0			0
$567$	−170.472	−	200.481i	−0.300656	−	0.353581i
$568$		0			0
$569$	−643.496	−	371.523i	−1.13092	−	0.652940i	−0.186757	−	0.982406i	$-0.559798\pi$
$569$	−643.496	−	371.523i	−1.13092	−	0.652940i	−0.944167	+	0.329467i	$0.893131\pi$
$570$		0			0
$571$	−198.270	−	343.415i	−0.347234	−	0.601427i	0.638523	−	0.769603i	$-0.279546\pi$
$571$	−198.270	−	343.415i	−0.347234	−	0.601427i	−0.985757	+	0.168176i	$0.946212\pi$
$572$		0			0
$573$	20.0993	+	31.4359i	0.0350773	+	0.0548620i
$574$		0			0
$575$	36.5297	−	21.0904i	0.0635299	−	0.0366790i
$576$		0			0
$577$	671.575			1.16391			0.581954	−	0.813221i	$-0.302288\pi$
$577$	671.575			1.16391			0.581954	+	0.813221i	$0.302288\pi$
$578$		0			0
$579$	−128.034	+	81.8616i	−0.221130	+	0.141384i
$580$		0			0
$581$	−163.639	+	94.4768i	−0.281650	+	0.162611i
$582$		0			0
$583$	67.9018	+	117.609i	0.116470	+	0.201731i
$584$		0			0
$585$	56.9082	+	626.827i	0.0972789	+	1.07150i
$586$		0			0
$587$			542.201i			0.923681i	0.886963	+	0.461841i	$0.152811\pi$
$587$			542.201i			0.923681i	−0.886963	+	0.461841i	$0.847189\pi$
$588$		0			0
$589$	818.621	−	694.462i	1.38985	−	1.17905i
$590$		0			0
$591$	−253.193	+	488.329i	−0.428414	+	0.826275i
$592$		0			0
$593$	613.948	+	354.463i	1.03532	+	0.597745i	0.918506	−	0.395408i	$-0.129397\pi$
$593$	613.948	+	354.463i	1.03532	+	0.597745i	0.116819	+	0.993153i	$0.462730\pi$
$594$		0			0
$595$	166.447	−	288.295i	0.279743	−	0.484529i
$596$		0			0
$597$	−246.588	+	157.662i	−0.413045	+	0.264090i
$598$		0			0
$599$		−	583.048i		−	0.973368i	−0.873578	−	0.486684i	$-0.838206\pi$
$599$		−	583.048i		−	0.973368i	0.873578	−	0.486684i	$-0.161794\pi$
$600$		0			0
$601$	−499.633	+	865.390i	−0.831337	+	1.43992i	0.0656417	+	0.997843i	$0.479091\pi$
$601$	−499.633	+	865.390i	−0.831337	+	1.43992i	−0.896978	+	0.442074i	$0.854243\pi$
$602$		0			0
$603$	−596.457	−	845.922i	−0.989149	−	1.40286i
$604$		0			0
$605$		−	929.386i		−	1.53618i
$606$		0			0
$607$	262.673	+	454.962i	0.432739	+	0.749526i	0.997108	−	0.0759964i	$-0.0242138\pi$
$607$	262.673	+	454.962i	0.432739	+	0.749526i	−0.564369	+	0.825523i	$0.690880\pi$
$608$		0			0
$609$	−200.968	+	387.604i	−0.329997	+	0.636460i
$610$		0			0
$611$	−327.918	+	189.324i	−0.536691	+	0.309859i
$612$		0			0
$613$	−52.4948	−	90.9237i	−0.0856360	−	0.148326i	0.820026	−	0.572326i	$-0.193959\pi$
$613$	−52.4948	−	90.9237i	−0.0856360	−	0.148326i	−0.905662	+	0.424000i	$0.860626\pi$
$614$		0			0
$615$	−2.70242	−	59.6551i	−0.00439418	−	0.0970002i
$616$		0			0
$617$		−	332.700i		−	0.539223i	−0.962969	−	0.269611i	$-0.913105\pi$
$617$		−	332.700i		−	0.539223i	0.962969	−	0.269611i	$-0.0868952\pi$
$618$		0			0
$619$	−473.421	+	819.989i	−0.764815	+	1.32470i	0.175529	+	0.984474i	$0.443836\pi$
$619$	−473.421	+	819.989i	−0.764815	+	1.32470i	−0.940344	+	0.340225i	$0.889497\pi$
$620$		0			0
$621$	−27.1186	+	3.70577i	−0.0436693	+	0.00596742i
$622$		0			0
$623$	−345.068	+	199.225i	−0.553882	+	0.319784i
$624$		0			0
$625$	−33.0624	+	57.2657i	−0.0528998	+	0.0916251i
$626$		0			0
$627$	111.452	−	103.577i	0.177754	−	0.165195i
$628$		0			0
$629$	175.722	−	101.453i	0.279367	−	0.161293i
$630$		0			0
$631$	246.193	−	426.419i	0.390164	−	0.675784i	−0.602307	−	0.798265i	$-0.705752\pi$
$631$	246.193	−	426.419i	0.390164	−	0.675784i	0.992471	+	0.122481i	$0.0390850\pi$
$632$		0			0
$633$	−236.781	+	151.392i	−0.374062	+	0.239165i
$634$		0			0
$635$	1022.09	−	590.102i	1.60959	−	0.929295i
$636$		0			0
$637$	164.712	+	285.290i	0.258575	+	0.447865i
$638$		0			0
$639$	−134.183	−	62.0369i	−0.209990	−	0.0970843i
$640$		0			0
$641$			1131.51i			1.76523i	0.470098	+	0.882614i	$0.344219\pi$
$641$			1131.51i			1.76523i	−0.470098	+	0.882614i	$0.655781\pi$
$642$		0			0
$643$	−97.6840	+	169.194i	−0.151919	+	0.263132i	−0.931933	−	0.362631i	$-0.881879\pi$
$643$	−97.6840	+	169.194i	−0.151919	+	0.263132i	0.780014	+	0.625762i	$0.215212\pi$
$644$		0			0
$645$	−621.753	−	972.442i	−0.963959	−	1.50766i
$646$		0			0
$647$			302.724i			0.467889i	0.972250	+	0.233945i	$0.0751634\pi$
$647$			302.724i			0.467889i	−0.972250	+	0.233945i	$0.924837\pi$
$648$		0			0
$649$	77.1761	+	133.673i	0.118915	+	0.205968i
$650$		0			0
$651$	−488.884	−	253.481i	−0.750973	−	0.389371i
$652$		0			0
$653$	362.783	−	209.453i	0.555564	−	0.320755i	−0.195799	−	0.980644i	$-0.562730\pi$
$653$	362.783	−	209.453i	0.555564	−	0.320755i	0.751363	+	0.659889i	$0.229397\pi$
$654$		0			0
$655$	−169.045	−	292.795i	−0.258084	−	0.447015i
$656$		0			0
$657$	−249.327	+	539.285i	−0.379493	+	0.820830i
$658$		0			0
$659$	−86.7017	+	50.0572i	−0.131565	+	0.0759594i	−0.564338	−	0.825544i	$-0.690869\pi$
$659$	−86.7017	+	50.0572i	−0.131565	+	0.0759594i	0.432773	+	0.901503i	$0.357535\pi$
$660$		0			0
$661$	623.512			0.943286			0.471643	−	0.881790i	$-0.343661\pi$
$661$	623.512			0.943286			0.471643	+	0.881790i	$0.343661\pi$
$662$		0			0
$663$	322.402	−	14.6050i	0.486277	−	0.0220287i
$664$		0			0
$665$	−325.912	−	384.180i	−0.490093	−	0.577715i
$666$		0			0
$667$	22.7052	+	39.3265i	0.0340408	+	0.0589603i
$668$		0			0
$669$	−694.167	−	359.918i	−1.03762	−	0.537994i
$670$		0			0
$671$			248.229i			0.369938i
$672$		0			0
$673$	230.048	−	398.455i	0.341825	−	0.592058i	−0.642947	−	0.765911i	$-0.722288\pi$
$673$	230.048	−	398.455i	0.341825	−	0.592058i	0.984772	+	0.173853i	$0.0556216\pi$
$674$		0			0
$675$	887.934	−	688.288i	1.31546	−	1.01969i
$676$		0			0
$677$	−675.976	−	390.275i	−0.998488	−	0.576477i	−0.0906873	−	0.995879i	$-0.528906\pi$
$677$	−675.976	−	390.275i	−0.998488	−	0.576477i	−0.907801	+	0.419402i	$0.862240\pi$
$678$		0			0
$679$	189.610	−	328.414i	0.279249	−	0.483673i
$680$		0			0
$681$	−505.917	−	791.269i	−0.742902	−	1.16192i
$682$		0			0
$683$		−	643.879i		−	0.942722i	−0.881940	−	0.471361i	$-0.843763\pi$
$683$		−	643.879i		−	0.942722i	0.881940	−	0.471361i	$-0.156237\pi$
$684$		0			0
$685$	1390.07			2.02931
$686$		0			0
$687$	38.7505	+	855.406i	0.0564054	+	1.24513i
$688$		0			0
$689$	377.539	+	217.972i	0.547952	+	0.316361i
$690$		0			0
$691$	12.1801	−	21.0966i	0.0176268	−	0.0305305i	−0.857077	−	0.515188i	$-0.827722\pi$
$691$	12.1801	−	21.0966i	0.0176268	−	0.0305305i	0.874704	+	0.484657i	$0.161056\pi$
$692$		0			0
$693$	−70.8454	−	32.7539i	−0.102230	−	0.0472639i
$694$		0			0
$695$	−1654.87	−	955.439i	−2.38111	−	1.37473i
$696$		0			0
$697$	−30.6200			−0.0439312
$698$		0			0
$699$	780.650	−	35.3640i	1.11681	−	0.0505922i
$700$		0			0
$701$	−475.058	+	274.275i	−0.677686	+	0.391262i	−0.798983	−	0.601354i	$-0.794628\pi$
$701$	−475.058	+	274.275i	−0.677686	+	0.391262i	0.121297	+	0.992616i	$0.461295\pi$
$702$		0			0
$703$	−54.9532	−	302.119i	−0.0781695	−	0.429757i
$704$		0			0
$705$	960.514	+	498.016i	1.36243	+	0.706406i
$706$		0			0
$707$			36.3344i			0.0513923i
$708$		0			0
$709$	−529.714	−	917.492i	−0.747129	−	1.29406i	−0.949194	−	0.314693i	$-0.898099\pi$
$709$	−529.714	−	917.492i	−0.747129	−	1.29406i	0.202065	−	0.979372i	$-0.435235\pi$
$710$		0			0
$711$	21.8587	+	31.0011i	0.0307437	+	0.0436021i
$712$		0			0
$713$	−49.6024	+	28.6380i	−0.0695687	+	0.0401655i
$714$		0			0
$715$	93.3375	+	161.665i	0.130542	+	0.226105i
$716$		0			0
$717$	−375.249	+	16.9990i	−0.523360	+	0.0237086i
$718$		0			0
$719$	−914.369	+	527.911i	−1.27172	+	0.734230i	−0.975312	−	0.220831i	$-0.929123\pi$
$719$	−914.369	+	527.911i	−1.27172	+	0.734230i	−0.296411	+	0.955061i	$0.595790\pi$
$720$		0			0
$721$	16.0791			0.0223011
$722$		0			0
$723$	19.0038	+	419.503i	0.0262846	+	0.580226i
$724$		0			0
$725$	−1614.21	−	931.963i	−2.22649	−	1.28547i
$726$		0			0
$727$	637.307			0.876625			0.438313	−	0.898823i	$-0.355576\pi$
$727$	637.307			0.876625			0.438313	+	0.898823i	$0.355576\pi$
$728$		0			0
$729$	−702.273	+	195.584i	−0.963338	+	0.268291i
$730$		0			0
$731$	−512.544	+	295.917i	−0.701155	+	0.404812i
$732$		0			0
$733$	−522.939	−	905.756i	−0.713422	−	1.23568i	−0.963565	−	0.267475i	$-0.913811\pi$
$733$	−522.939	−	905.756i	−0.713422	−	1.23568i	0.250143	−	0.968209i	$-0.419522\pi$
$734$		0			0
$735$	433.276	−	835.651i	0.589491	−	1.13694i
$736$		0			0
$737$	−265.859	−	153.494i	−0.360731	−	0.208268i
$738$		0			0
$739$	374.307	+	648.318i	0.506504	+	0.877291i	0.999972	+	0.00752661i	$0.00239582\pi$
$739$	374.307	+	648.318i	0.506504	+	0.877291i	−0.493468	+	0.869764i	$0.664271\pi$
$740$		0			0
$741$	143.593	−	466.836i	0.193783	−	0.630008i
$742$		0			0
$743$	1185.38	+	684.378i	1.59539	+	0.921101i	0.992359	+	0.123386i	$0.0393754\pi$
$743$	1185.38	+	684.378i	1.59539	+	0.921101i	0.603035	+	0.797715i	$0.293958\pi$
$744$		0			0
$745$	588.531	+	1019.37i	0.789975	+	1.36828i
$746$		0			0
$747$	47.3268	+	521.291i	0.0633559	+	0.697847i
$748$		0			0
$749$	−182.219	−	105.204i	−0.243282	−	0.140459i
$750$		0			0
$751$	1027.70			1.36845			0.684224	−	0.729272i	$-0.260141\pi$
$751$	1027.70			1.36845			0.684224	+	0.729272i	$0.260141\pi$
$752$		0			0
$753$	110.545	+	172.896i	0.146806	+	0.229609i
$754$		0			0
$755$	−992.840	+	573.216i	−1.31502	+	0.759227i
$756$		0			0
$757$	−532.061	−	921.557i	−0.702855	−	1.21738i	−0.967460	−	0.253024i	$-0.918575\pi$
$757$	−532.061	−	921.557i	−0.702855	−	1.21738i	0.264605	−	0.964357i	$-0.414759\pi$
$758$		0			0
$759$	−6.83938	+	4.37292i	−0.00901104	+	0.00576142i
$760$		0			0
$761$	−245.939	+	141.993i	−0.323179	+	0.186587i	−0.652809	−	0.757523i	$-0.726409\pi$
$761$	−245.939	+	141.993i	−0.323179	+	0.186587i	0.329630	+	0.944110i	$0.393076\pi$
$762$		0			0
$763$	−53.5651			−0.0702032
$764$		0			0
$765$	−531.408	−	753.667i	−0.694651	−	0.985186i
$766$		0			0
$767$	429.105	+	247.744i	0.559459	+	0.323004i
$768$		0			0
$769$	418.945			0.544792			0.272396	−	0.962185i	$-0.412184\pi$
$769$	418.945			0.544792			0.272396	+	0.962185i	$0.412184\pi$
$770$		0			0
$771$	−241.426	+	465.634i	−0.313133	+	0.603935i
$772$		0			0
$773$	−762.208	−	440.061i	−0.986038	−	0.569289i	−0.0819505	−	0.996636i	$-0.526115\pi$
$773$	−762.208	−	440.061i	−0.986038	−	0.569289i	−0.904088	+	0.427347i	$0.859448\pi$
$774$		0			0
$775$	1175.48	−	2035.99i	1.51675	−	2.62709i
$776$		0			0
$777$	−132.716	+	84.8553i	−0.170806	+	0.109209i
$778$		0			0
$779$	−15.6142	+	43.6302i	−0.0200439	+	0.0560080i
$780$		0			0
$781$	−43.8449			−0.0561395
$782$		0			0
$783$	740.985	+	955.917i	0.946341	+	1.22084i
$784$		0			0
$785$	1194.91	−	689.884i	1.52218	−	0.878833i
$786$		0			0
$787$	−406.165	−	703.499i	−0.516093	−	0.893899i	−0.999825	−	0.0186833i	$-0.994053\pi$
$787$	−406.165	−	703.499i	−0.516093	−	0.893899i	0.483733	−	0.875216i	$-0.339281\pi$
$788$		0			0
$789$	612.930	−	1182.15i	0.776844	−	1.49828i
$790$		0			0
$791$			324.745i			0.410550i
$792$		0			0
$793$	398.421	+	690.086i	0.502423	+	0.870221i
$794$		0			0
$795$	−56.3718	−	1244.39i	−0.0709080	−	1.56527i
$796$		0			0
$797$	121.404	−	70.0928i	0.152327	−	0.0879458i	−0.421899	−	0.906643i	$-0.638636\pi$
$797$	121.404	−	70.0928i	0.152327	−	0.0879458i	0.574226	+	0.818697i	$0.305303\pi$
$798$		0			0
$799$	277.388	−	480.451i	0.347169	−	0.601315i
$800$		0			0
$801$	99.7992	+	1099.26i	0.124593	+	1.37236i
$802$		0			0
$803$			176.213i			0.219444i
$804$		0			0
$805$	13.4398	+	23.2785i	0.0166955	+	0.0289174i
$806$		0			0
$807$	393.839	−	17.8412i	0.488029	−	0.0221080i
$808$		0			0
$809$		−	1305.92i		−	1.61423i	−0.590392	−	0.807117i	$-0.701027\pi$
$809$		−	1305.92i		−	1.61423i	0.590392	−	0.807117i	$-0.298973\pi$
$810$		0			0
$811$	−529.825	+	917.684i	−0.653298	+	1.13155i	0.329019	+	0.944323i	$0.393282\pi$
$811$	−529.825	+	917.684i	−0.653298	+	1.13155i	−0.982318	+	0.187223i	$0.940051\pi$
$812$		0			0
$813$	−33.4881	−	739.240i	−0.0411908	−	0.909275i
$814$		0			0
$815$	274.870	+	158.696i	0.337264	+	0.194719i
$816$		0			0
$817$	160.287	+	881.219i	0.196190	+	1.07860i
$818$		0			0
$819$	−249.525	+	22.6538i	−0.304670	+	0.0276603i
$820$		0			0
$821$	1195.19	−	690.042i	1.45577	−	0.840489i	0.456971	−	0.889481i	$-0.348934\pi$
$821$	1195.19	−	690.042i	1.45577	−	0.840489i	0.998799	+	0.0489920i	$0.0156009\pi$
$822$		0			0
$823$	743.239			0.903086			0.451543	−	0.892249i	$-0.350874\pi$
$823$	743.239			0.903086			0.451543	+	0.892249i	$0.350874\pi$
$824$		0			0
$825$	153.374	−	295.810i	0.185908	−	0.358557i
$826$		0			0
$827$	−262.548	−	151.582i	−0.317470	−	0.183291i	0.332794	−	0.942999i	$-0.392009\pi$
$827$	−262.548	−	151.582i	−0.317470	−	0.183291i	−0.650264	+	0.759708i	$0.725342\pi$
$828$		0			0
$829$	−1431.27			−1.72650			−0.863252	−	0.504773i	$-0.831576\pi$
$829$	−1431.27			−1.72650			−0.863252	+	0.504773i	$0.831576\pi$
$830$		0			0
$831$	731.536	−	467.725i	0.880309	−	0.562846i
$832$		0			0
$833$	−417.994	−	241.329i	−0.501794	−	0.289711i
$834$		0			0
$835$	−261.690	+	453.260i	−0.313401	+	0.542827i
$836$		0			0
$837$	−1205.69	+	934.603i	−1.44050	+	1.11661i
$838$		0			0
$839$		−	431.828i		−	0.514694i	−0.966319	−	0.257347i	$-0.917152\pi$
$839$		−	431.828i		−	0.514694i	0.966319	−	0.257347i	$-0.0828483\pi$
$840$		0			0
$841$	582.817	−	1009.47i	0.693005	−	1.20032i
$842$		0			0
$843$	−74.4314	+	3.37180i	−0.0882935	+	0.00399976i
$844$		0			0
$845$	−675.536	−	390.021i	−0.799451	−	0.461563i
$846$		0			0
$847$	369.966			0.436796
$848$		0			0
$849$	−387.315	+	247.639i	−0.456202	+	0.291683i
$850$		0			0
$851$			16.3838i			0.0192524i
$852$		0			0
$853$	476.652			0.558794			0.279397	−	0.960176i	$-0.409865\pi$
$853$	476.652			0.558794			0.279397	+	0.960176i	$0.409865\pi$
$854$		0			0
$855$	−1344.88	+	372.879i	−1.57296	+	0.436116i
$856$		0			0
$857$			912.359i			1.06460i	0.846557	+	0.532298i	$0.178671\pi$
$857$			912.359i			1.06460i	−0.846557	+	0.532298i	$0.821329\pi$
$858$		0			0
$859$	−1583.13			−1.84299			−0.921495	−	0.388389i	$-0.873032\pi$
$859$	−1583.13			−1.84299			−0.921495	+	0.388389i	$0.873032\pi$
$860$		0			0
$861$	23.7473	−	1.07577i	0.0275810	−	0.00124944i
$862$		0			0
$863$		−	375.229i		−	0.434796i	−0.976083	−	0.217398i	$-0.930243\pi$
$863$		−	375.229i		−	0.434796i	0.976083	−	0.217398i	$-0.0697570\pi$
$864$		0			0
$865$	1002.48	−	1736.34i	1.15893	−	2.00733i
$866$		0			0
$867$	332.073	−	212.319i	0.383014	−	0.244889i
$868$		0			0
$869$	9.74311	+	5.62519i	0.0112119	+	0.00647317i
$870$		0			0
$871$	−985.465			−1.13142
$872$		0			0
$873$	−605.359	−	858.548i	−0.693424	−	0.983446i
$874$		0			0
$875$	−381.413	−	220.209i	−0.435901	−	0.251667i
$876$		0			0
$877$	26.2245	−	45.4221i	0.0299025	−	0.0517926i	−0.850687	−	0.525673i	$-0.823814\pi$
$877$	26.2245	−	45.4221i	0.0299025	−	0.0517926i	0.880589	+	0.473880i	$0.157147\pi$
$878$		0			0
$879$	−1343.39	+	60.8564i	−1.52831	+	0.0692337i
$880$		0			0
$881$		−	36.6434i		−	0.0415930i	−0.999784	−	0.0207965i	$-0.993380\pi$
$881$		−	36.6434i		−	0.0415930i	0.999784	−	0.0207965i	$-0.00662021\pi$
$882$		0			0
$883$	409.206	−	708.766i	0.463427	−	0.802680i	−0.535702	−	0.844407i	$-0.679953\pi$
$883$	409.206	−	708.766i	0.463427	−	0.802680i	0.999129	+	0.0417276i	$0.0132862\pi$
$884$		0			0
$885$	−64.0714	−	1414.36i	−0.0723970	−	1.59814i
$886$		0			0
$887$		−	784.157i		−	0.884055i	−0.897002	−	0.442027i	$-0.854259\pi$
$887$		−	784.157i		−	0.884055i	0.897002	−	0.442027i	$-0.145741\pi$
$888$		0			0
$889$	234.905	+	406.868i	0.264236	+	0.457669i
$890$		0			0
$891$	−164.716	+	140.061i	−0.184867	+	0.157195i
$892$		0			0
$893$	−543.141	−	640.247i	−0.608221	−	0.716962i
$894$		0			0
$895$	−1252.32	+	2169.08i	−1.39924	+	2.42356i
$896$		0			0
$897$	−11.9950	+	23.1345i	−0.0133723	+	0.0257909i
$898$		0			0
$899$	2191.88	+	1265.48i	2.43813	+	1.40765i
$900$		0			0
$901$	−638.727			−0.708909
$902$		0			0
$903$	387.106	−	247.505i	0.428688	−	0.274092i
$904$		0			0
$905$	−308.602	+	178.171i	−0.340997	+	0.196874i
$906$		0			0
$907$	−229.553			−0.253090			−0.126545	−	0.991961i	$-0.540389\pi$
$907$	−229.553			−0.253090			−0.126545	+	0.991961i	$0.540389\pi$
$908$		0			0
$909$	91.3611	+	42.2389i	0.100507	+	0.0464674i
$910$		0			0
$911$	−464.807	−	268.356i	−0.510216	−	0.294573i	0.222706	−	0.974886i	$-0.428511\pi$
$911$	−464.807	−	268.356i	−0.510216	−	0.294573i	−0.732923	+	0.680312i	$0.761844\pi$
$912$		0			0
$913$	77.6228	+	134.447i	0.0850195	+	0.147258i
$914$		0			0
$915$	1048.05	−	2021.35i	1.14541	−	2.20913i
$916$		0			0
$917$	116.555	−	67.2928i	0.127104	−	0.0733837i
$918$		0			0
$919$	711.348			0.774046			0.387023	−	0.922070i	$-0.373503\pi$
$919$	711.348			0.774046			0.387023	+	0.922070i	$0.373503\pi$
$920$		0			0
$921$	60.3134	+	1331.40i	0.0654869	+	1.44560i
$922$		0			0
$923$	−121.891	+	70.3736i	−0.132059	+	0.0762444i
$924$		0			0
$925$	−336.246	−	582.396i	−0.363509	−	0.629617i
$926$		0			0
$927$	18.6920	−	40.4301i	0.0201640	−	0.0436139i
$928$		0			0
$929$		−	641.949i		−	0.691011i	−0.938417	−	0.345506i	$-0.887707\pi$
$929$		−	641.949i		−	0.691011i	0.938417	−	0.345506i	$-0.112293\pi$
$930$		0			0
$931$	−557.017	+	472.535i	−0.598300	+	0.507556i
$932$		0			0
$933$	1150.06	−	52.0983i	1.23264	−	0.0558395i
$934$		0			0
$935$	−236.865	−	136.754i	−0.253331	−	0.146261i
$936$		0			0
$937$	−5.47419	+	9.48158i	−0.00584226	+	0.0101191i	−0.868932	−	0.494932i	$-0.835193\pi$
$937$	−5.47419	+	9.48158i	−0.00584226	+	0.0101191i	0.863089	+	0.505051i	$0.168526\pi$
$938$		0			0
$939$	−13.1879	−	291.120i	−0.0140447	−	0.310032i
$940$		0			0
$941$		−	1295.58i		−	1.37682i	−0.725324	−	0.688408i	$-0.758310\pi$
$941$		−	1295.58i		−	1.37682i	0.725324	−	0.688408i	$-0.241690\pi$
$942$		0			0
$943$	1.23622	−	2.14119i	0.00131094	−	0.00227061i
$944$		0			0
$945$	438.610	+	565.834i	0.464138	+	0.598767i
$946$		0			0
$947$			528.516i			0.558095i	0.960277	+	0.279048i	$0.0900187\pi$
$947$			528.516i			0.558095i	−0.960277	+	0.279048i	$0.909981\pi$
$948$		0			0
$949$	282.832	+	489.880i	0.298032	+	0.516207i
$950$		0			0
$951$	−795.169	+	36.0217i	−0.836140	+	0.0378777i
$952$		0			0
$953$	1618.71	−	934.563i	1.69854	−	0.980654i	0.751396	−	0.659852i	$-0.229381\pi$
$953$	1618.71	−	934.563i	1.69854	−	0.980654i	0.947146	−	0.320802i	$-0.103952\pi$
$954$		0			0
$955$	−50.7538	−	87.9081i	−0.0531453	−	0.0920504i
$956$		0			0
$957$	318.458	+	165.117i	0.332767	+	0.172536i
$958$		0			0
$959$			553.355i			0.577013i
$960$		0			0
$961$	−1115.65	+	1932.36i	−1.16092	+	2.01078i
$962$		0			0
$963$	−476.360	+	335.880i	−0.494663	+	0.348785i
$964$		0			0
$965$	358.037	−	206.713i	0.371023	−	0.214210i
$966$		0			0
$967$	210.961	−	365.395i	0.218160	−	0.377864i	−0.736085	−	0.676889i	$-0.763328\pi$
$967$	210.961	−	365.395i	0.218160	−	0.377864i	0.954246	+	0.299024i	$0.0966612\pi$
$968$		0			0
$969$	159.794	+	697.543i	0.164906	+	0.719859i
$970$		0			0
$971$	−85.2584	+	49.2239i	−0.0878047	+	0.0506941i	−0.543259	−	0.839565i	$-0.682810\pi$
$971$	−85.2584	+	49.2239i	−0.0878047	+	0.0506941i	0.455455	+	0.890259i	$0.349477\pi$
$972$		0			0
$973$	380.337	−	658.764i	0.390891	−	0.677044i
$974$		0			0
$975$	−48.4055	−	1068.54i	−0.0496466	−	1.09594i
$976$		0			0
$977$	67.5481	−	38.9989i	0.0691383	−	0.0399170i	−0.465032	−	0.885294i	$-0.653957\pi$
$977$	67.5481	−	38.9989i	0.0691383	−	0.0399170i	0.534171	+	0.845377i	$0.320624\pi$
$978$		0			0
$979$	163.685	+	283.511i	0.167196	+	0.289592i
$980$		0			0
$981$	−62.2696	+	134.687i	−0.0634757	+	0.137295i
$982$		0			0
$983$			1280.54i			1.30268i	0.758785	+	0.651341i	$0.225793\pi$
$983$			1280.54i			1.30268i	−0.758785	+	0.651341i	$0.774207\pi$
$984$		0			0
$985$	748.224	−	1295.96i	0.759618	−	1.31570i
$986$		0			0
$987$	−198.248	+	382.358i	−0.200859	+	0.387394i
$988$		0			0
$989$		−	47.7880i		−	0.0483195i
$990$		0			0
$991$	−61.6959	−	106.860i	−0.0622562	−	0.107831i	0.833217	−	0.552946i	$-0.186496\pi$
$991$	−61.6959	−	106.860i	−0.0622562	−	0.107831i	−0.895474	+	0.445115i	$0.853163\pi$
$992$		0			0
$993$	−1361.75	+	870.665i	−1.37135	+	0.876803i
$994$		0			0
$995$	689.563	−	398.120i	0.693029	−	0.400120i
$996$		0			0
$997$	−657.001	−	1137.96i	−0.658978	−	1.14138i	−0.980881	−	0.194610i	$-0.937656\pi$
$997$	−657.001	−	1137.96i	−0.658978	−	1.14138i	0.321903	−	0.946773i	$-0.395678\pi$
$998$		0			0
$999$	59.0813	+	432.354i	0.0591404	+	0.432786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.be.a.425.7	yes	80
3.2	odd	2		2052.3.be.a.197.2		80
9.4	even	3		2052.3.m.a.881.2		80
9.5	odd	6		684.3.m.a.653.21	yes	80
19.11	even	3		684.3.m.a.353.21	✓	80
57.11	odd	6		2052.3.m.a.1493.39		80
171.49	even	3		2052.3.be.a.125.2		80
171.68	odd	6	inner	684.3.be.a.581.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.21	✓	80	19.11	even	3
684.3.m.a.653.21	yes	80	9.5	odd	6
684.3.be.a.425.7	yes	80	1.1	even	1	trivial
684.3.be.a.581.7	yes	80	171.68	odd	6	inner
2052.3.m.a.881.2		80	9.4	even	3
2052.3.m.a.1493.39		80	57.11	odd	6
2052.3.be.a.125.2		80	171.49	even	3
2052.3.be.a.197.2		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)

\(f(q)\)	\(=\)	\(q+(-2.66330 - 1.38089i) q^{3} +(7.06805 + 4.08074i) q^{5} +(-1.62444 + 2.81362i) q^{7} +(5.18629 + 7.35543i) q^{9} +O(q^{10})\)	\(q+(-2.66330 - 1.38089i) q^{3} +(7.06805 + 4.08074i) q^{5} +(-1.62444 + 2.81362i) q^{7} +(5.18629 + 7.35543i) q^{9} +(2.31169 + 1.33465i) q^{11} +8.56878 q^{13} +(-13.1893 - 20.6284i) q^{15} +(-10.8726 + 6.27730i) q^{17} +(3.40016 + 18.6933i) q^{19} +(8.21167 - 5.25032i) q^{21} -1.01373i q^{23} +(20.8049 + 36.0351i) q^{25} +(-3.65559 - 26.7514i) q^{27} +(-38.7940 + 22.3977i) q^{29} +(-28.2502 - 48.9308i) q^{31} +(-4.31370 - 6.74676i) q^{33} +(-22.9633 + 13.2579i) q^{35} -16.1619 q^{37} +(-22.8212 - 11.8325i) q^{39} +(2.11219 + 1.21948i) q^{41} +47.1409 q^{43} +(6.64134 + 73.1524i) q^{45} +(-38.2689 + 22.0946i) q^{47} +(19.2224 + 33.2941i) q^{49} +(37.6252 - 1.70445i) q^{51} +(44.0599 + 25.4380i) q^{53} +(10.8927 + 18.8668i) q^{55} +(16.7577 - 54.4810i) q^{57} +(50.0778 + 28.9124i) q^{59} +(46.4968 + 80.5349i) q^{61} +(-29.1202 + 2.64376i) q^{63} +(60.5645 + 34.9669i) q^{65} -115.006 q^{67} +(-1.39984 + 2.69986i) q^{69} +(-14.2250 + 8.21279i) q^{71} +(33.0073 + 57.1704i) q^{73} +(-5.64905 - 124.701i) q^{75} +(-7.51041 + 4.33614i) q^{77} +4.21472 q^{79} +(-27.2048 + 76.2948i) q^{81} +(50.3676 + 29.0797i) q^{83} -102.464 q^{85} +(134.249 - 6.08156i) q^{87} +(106.211 + 61.3211i) q^{89} +(-13.9195 + 24.1093i) q^{91} +(7.67065 + 169.328i) q^{93} +(-52.2499 + 146.000i) q^{95} -116.723 q^{97} +(2.17213 + 23.9254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 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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