LMFDB - Embedded newform 684.3.m.a.653.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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, 4]))

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

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (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			653.3
Character	$\chi$	$=$	684.653
Dual form			684.3.m.a.353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.88193 - 0.833354i) q^{3} +7.26979i q^{5} +(3.75776 + 6.50863i) q^{7} +(7.61104 + 4.80334i) q^{9} +O(q^{10})$	\(q+(-2.88193 - 0.833354i) q^{3} +7.26979i q^{5} +(3.75776 + 6.50863i) q^{7} +(7.61104 + 4.80334i) q^{9} +(-14.6898 + 8.48117i) q^{11} +(10.1476 + 17.5762i) q^{13} +(6.05831 - 20.9510i) q^{15} +(12.9313 - 7.46590i) q^{17} +(-17.9208 + 6.31229i) q^{19} +(-5.40560 - 21.8890i) q^{21} +(28.8029 - 16.6293i) q^{23} -27.8498 q^{25} +(-17.9316 - 20.1856i) q^{27} -30.3086i q^{29} +(-23.8575 + 41.3223i) q^{31} +(49.4028 - 12.2003i) q^{33} +(-47.3163 + 27.3181i) q^{35} +25.1099 q^{37} +(-14.5975 - 59.1098i) q^{39} +5.04512i q^{41} +(-24.8411 + 43.0261i) q^{43} +(-34.9192 + 55.3306i) q^{45} -62.4682i q^{47} +(-3.74149 + 6.48044i) q^{49} +(-43.4889 + 10.7398i) q^{51} +(47.5227 + 27.4372i) q^{53} +(-61.6563 - 106.792i) q^{55} +(56.9069 - 3.25720i) q^{57} +73.6284i q^{59} -95.3512 q^{61} +(-2.66269 + 67.5872i) q^{63} +(-127.775 + 73.7709i) q^{65} +(0.588665 + 1.01960i) q^{67} +(-96.8660 + 23.9216i) q^{69} +(-12.3658 + 7.13938i) q^{71} +(-59.5390 - 103.125i) q^{73} +(80.2611 + 23.2087i) q^{75} +(-110.401 - 63.7403i) q^{77} +(0.0750630 - 0.130013i) q^{79} +(34.8559 + 73.1168i) q^{81} +(-41.9662 + 24.2292i) q^{83} +(54.2755 + 94.0079i) q^{85} +(-25.2578 + 87.3472i) q^{87} +(67.4096 + 38.9190i) q^{89} +(-76.2645 + 132.094i) q^{91} +(103.192 - 99.2064i) q^{93} +(-45.8890 - 130.280i) q^{95} +(-47.2818 + 81.8945i) q^{97} +(-152.543 - 6.00963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−2.88193	−	0.833354i	−0.960643	−	0.277785i
$3$	−2.88193	−	0.833354i	−0.960643	−	0.277785i
$4$		0			0
$5$			7.26979i			1.45396i	0.686660	+	0.726979i	$0.259076\pi$
$5$			7.26979i			1.45396i	−0.686660	+	0.726979i	$0.740924\pi$
$6$		0			0
$7$	3.75776	+	6.50863i	0.536823	+	0.929804i	0.999073	+	0.0430544i	$0.0137089\pi$
$7$	3.75776	+	6.50863i	0.536823	+	0.929804i	−0.462250	+	0.886750i	$0.652958\pi$
$8$		0			0
$9$	7.61104	+	4.80334i	0.845671	+	0.533704i
$10$		0			0
$11$	−14.6898	+	8.48117i	−1.33544	+	0.771015i	−0.986127	−	0.165992i	$-0.946917\pi$
$11$	−14.6898	+	8.48117i	−1.33544	+	0.771015i	−0.349310	+	0.937007i	$0.613584\pi$
$12$		0			0
$13$	10.1476	+	17.5762i	0.780585	+	1.35201i	0.931601	+	0.363482i	$0.118412\pi$
$13$	10.1476	+	17.5762i	0.780585	+	1.35201i	−0.151016	+	0.988531i	$0.548255\pi$
$14$		0			0
$15$	6.05831	−	20.9510i	0.403887	−	1.39673i
$16$		0			0
$17$	12.9313	−	7.46590i	0.760666	−	0.439170i	−0.0688691	−	0.997626i	$-0.521939\pi$
$17$	12.9313	−	7.46590i	0.760666	−	0.439170i	0.829535	+	0.558455i	$0.188606\pi$
$18$		0			0
$19$	−17.9208	+	6.31229i	−0.943200	+	0.332226i
$19$	−17.9208	+	6.31229i	−0.943200	+	0.332226i
$20$		0			0
$21$	−5.40560	−	21.8890i	−0.257410	−	1.04233i
$22$		0			0
$23$	28.8029	−	16.6293i	1.25230	−	0.723015i	0.280733	−	0.959786i	$-0.409422\pi$
$23$	28.8029	−	16.6293i	1.25230	−	0.723015i	0.971565	+	0.236771i	$0.0760891\pi$
$24$		0			0
$25$	−27.8498			−1.11399
$26$		0			0
$27$	−17.9316	−	20.1856i	−0.664133	−	0.747614i
$28$		0			0
$29$		−	30.3086i		−	1.04512i	−0.852601	−	0.522562i	$-0.824976\pi$
$29$		−	30.3086i		−	1.04512i	0.852601	−	0.522562i	$-0.175024\pi$
$30$		0			0
$31$	−23.8575	+	41.3223i	−0.769596	+	1.33298i	0.168187	+	0.985755i	$0.446209\pi$
$31$	−23.8575	+	41.3223i	−0.769596	+	1.33298i	−0.937782	+	0.347224i	$0.887124\pi$
$32$		0			0
$33$	49.4028	−	12.2003i	1.49706	−	0.369706i
$34$		0			0
$35$	−47.3163	+	27.3181i	−1.35190	+	0.780517i
$36$		0			0
$37$	25.1099			0.678647			0.339324	−	0.940670i	$-0.389802\pi$
$37$	25.1099			0.678647			0.339324	+	0.940670i	$0.389802\pi$
$38$		0			0
$39$	−14.5975	−	59.1098i	−0.374295	−	1.51564i
$40$		0			0
$41$			5.04512i			0.123052i	0.998105	+	0.0615258i	$0.0195967\pi$
$41$			5.04512i			0.123052i	−0.998105	+	0.0615258i	$0.980403\pi$
$42$		0			0
$43$	−24.8411	+	43.0261i	−0.577701	+	1.00061i	0.418042	+	0.908428i	$0.362717\pi$
$43$	−24.8411	+	43.0261i	−0.577701	+	1.00061i	−0.995742	+	0.0921791i	$0.970617\pi$
$44$		0			0
$45$	−34.9192	+	55.3306i	−0.775983	+	1.22957i
$46$		0			0
$47$		−	62.4682i		−	1.32911i	−0.747239	−	0.664555i	$-0.768621\pi$
$47$		−	62.4682i		−	1.32911i	0.747239	−	0.664555i	$-0.231379\pi$
$48$		0			0
$49$	−3.74149	+	6.48044i	−0.0763569	+	0.132254i
$50$		0			0
$51$	−43.4889	+	10.7398i	−0.852723	+	0.210585i
$52$		0			0
$53$	47.5227	+	27.4372i	0.896654	+	0.517684i	0.876113	−	0.482105i	$-0.160128\pi$
$53$	47.5227	+	27.4372i	0.896654	+	0.517684i	0.0205412	+	0.999789i	$0.493461\pi$
$54$		0			0
$55$	−61.6563	−	106.792i	−1.12102	−	1.94167i
$56$		0			0
$57$	56.9069	−	3.25720i	0.998366	−	0.0571438i
$58$		0			0
$59$			73.6284i			1.24794i	0.781449	+	0.623969i	$0.214481\pi$
$59$			73.6284i			1.24794i	−0.781449	+	0.623969i	$0.785519\pi$
$60$		0			0
$61$	−95.3512			−1.56314			−0.781568	−	0.623821i	$-0.785580\pi$
$61$	−95.3512			−1.56314			−0.781568	+	0.623821i	$0.785580\pi$
$62$		0			0
$63$	−2.66269	+	67.5872i	−0.0422650	+	1.07281i
$64$		0			0
$65$	−127.775	+	73.7709i	−1.96577	+	1.13494i
$66$		0			0
$67$	0.588665	+	1.01960i	0.00878605	+	0.0152179i	0.870385	−	0.492372i	$-0.163870\pi$
$67$	0.588665	+	1.01960i	0.00878605	+	0.0152179i	−0.861599	+	0.507590i	$0.830537\pi$
$68$		0			0
$69$	−96.8660	+	23.9216i	−1.40385	+	0.346690i
$70$		0			0
$71$	−12.3658	+	7.13938i	−0.174166	+	0.100555i	−0.584549	−	0.811359i	$-0.698728\pi$
$71$	−12.3658	+	7.13938i	−0.174166	+	0.100555i	0.410383	+	0.911913i	$0.365395\pi$
$72$		0			0
$73$	−59.5390	−	103.125i	−0.815603	−	1.41267i	−0.908894	−	0.417027i	$-0.863072\pi$
$73$	−59.5390	−	103.125i	−0.815603	−	1.41267i	0.0932911	−	0.995639i	$-0.470261\pi$
$74$		0			0
$75$	80.2611	+	23.2087i	1.07015	+	0.309450i
$76$		0			0
$77$	−110.401	−	63.7403i	−1.43379	−	0.827796i
$78$		0			0
$79$	0.0750630	−	0.130013i	0.000950165	−	0.00164573i	−0.865550	−	0.500823i	$-0.833031\pi$
$79$	0.0750630	−	0.130013i	0.000950165	−	0.00164573i	0.866500	+	0.499177i	$0.166364\pi$
$80$		0			0
$81$	34.8559	+	73.1168i	0.430319	+	0.902677i
$82$		0			0
$83$	−41.9662	+	24.2292i	−0.505617	+	0.291918i	−0.731030	−	0.682345i	$-0.760960\pi$
$83$	−41.9662	+	24.2292i	−0.505617	+	0.291918i	0.225413	+	0.974263i	$0.427627\pi$
$84$		0			0
$85$	54.2755	+	94.0079i	0.638535	+	1.10598i
$86$		0			0
$87$	−25.2578	+	87.3472i	−0.290320	+	1.00399i
$88$		0			0
$89$	67.4096	+	38.9190i	0.757412	+	0.437292i	0.828366	−	0.560188i	$-0.189271\pi$
$89$	67.4096	+	38.9190i	0.757412	+	0.437292i	−0.0709540	+	0.997480i	$0.522604\pi$
$90$		0			0
$91$	−76.2645	+	132.094i	−0.838071	+	1.45158i
$92$		0			0
$93$	103.192	−	99.2064i	1.10959	−	1.06674i
$94$		0			0
$95$	−45.8890	−	130.280i	−0.483042	−	1.37137i
$96$		0			0
$97$	−47.2818	+	81.8945i	−0.487441	+	0.844273i	−0.999896	−	0.0144414i	$-0.995403\pi$
$97$	−47.2818	+	81.8945i	−0.487441	+	0.844273i	0.512455	+	0.858714i	$0.328736\pi$
$98$		0			0
$99$	−152.543	−	6.00963i	−1.54083	−	0.0607034i
$100$		0			0
$101$		−	84.7721i		−	0.839328i	−0.907680	−	0.419664i	$-0.862148\pi$
$101$		−	84.7721i		−	0.839328i	0.907680	−	0.419664i	$-0.137852\pi$
$102$		0			0
$103$	−3.50170	+	6.06512i	−0.0339971	+	0.0588846i	−0.882523	−	0.470269i	$-0.844157\pi$
$103$	−3.50170	+	6.06512i	−0.0339971	+	0.0588846i	0.848526	+	0.529153i	$0.177490\pi$
$104$		0			0
$105$	159.128	−	39.2976i	1.51550	−	0.374262i
$106$		0			0
$107$		−	97.9295i		−	0.915229i	−0.889151	−	0.457614i	$-0.848704\pi$
$107$		−	97.9295i		−	0.915229i	0.889151	−	0.457614i	$-0.151296\pi$
$108$		0			0
$109$	75.3829	+	130.567i	0.691587	+	1.19786i	0.971318	+	0.237785i	$0.0764213\pi$
$109$	75.3829	+	130.567i	0.691587	+	1.19786i	−0.279731	+	0.960078i	$0.590245\pi$
$110$		0			0
$111$	−72.3651	−	20.9255i	−0.651938	−	0.188518i
$112$		0			0
$113$	39.6676	+	22.9021i	0.351041	+	0.202674i	0.665144	−	0.746715i	$-0.268370\pi$
$113$	39.6676	+	22.9021i	0.351041	+	0.202674i	−0.314103	+	0.949389i	$0.601704\pi$
$114$		0			0
$115$	120.892	+	209.391i	1.05123	+	1.82079i
$116$		0			0
$117$	−7.19045	+	182.515i	−0.0614568	+	1.55996i
$118$		0			0
$119$	97.1855	+	56.1101i	0.816685	+	0.471513i
$120$		0			0
$121$	83.3603	−	144.384i	0.688928	−	1.19326i
$122$		0			0
$123$	4.20437	−	14.5397i	0.0341819	−	0.118209i
$124$		0			0
$125$		−	20.7173i		−	0.165739i
$126$		0			0
$127$	−14.0912	+	24.4067i	−0.110955	+	0.192179i	−0.916155	−	0.400823i	$-0.868724\pi$
$127$	−14.0912	+	24.4067i	−0.110955	+	0.192179i	0.805201	+	0.593002i	$0.202058\pi$
$128$		0			0
$129$	107.446	−	103.297i	0.832918	−	0.800750i
$130$		0			0
$131$		−	252.087i		−	1.92433i	−0.272466	−	0.962166i	$-0.587839\pi$
$131$		−	252.087i		−	1.92433i	0.272466	−	0.962166i	$-0.412161\pi$
$132$		0			0
$133$	−108.426	−	92.9197i	−0.815236	−	0.698645i
$134$		0			0
$135$	146.745	−	130.359i	1.08700	−	0.965622i
$136$		0			0
$137$			86.3432i			0.630242i	0.949051	+	0.315121i	$0.102045\pi$
$137$			86.3432i			0.630242i	−0.949051	+	0.315121i	$0.897955\pi$
$138$		0			0
$139$	−82.7671	−	143.357i	−0.595447	−	1.03134i	−0.993484	−	0.113974i	$-0.963642\pi$
$139$	−82.7671	−	143.357i	−0.595447	−	1.03134i	0.398037	−	0.917369i	$-0.369692\pi$
$140$		0			0
$141$	−52.0582	+	180.029i	−0.369207	+	1.27680i
$142$		0			0
$143$	−298.133	−	172.127i	−2.08484	−	1.20369i
$144$		0			0
$145$	220.337			1.51957
$146$		0			0
$147$	16.1832	−	15.5582i	0.110090	−	0.105838i
$148$		0			0
$149$		−	196.064i		−	1.31587i	−0.753076	−	0.657934i	$-0.771431\pi$
$149$		−	196.064i		−	1.31587i	0.753076	−	0.657934i	$-0.228569\pi$
$150$		0			0
$151$	0.412875	+	0.715121i	0.00273427	+	0.00473590i	0.867389	−	0.497630i	$-0.165796\pi$
$151$	0.412875	+	0.715121i	0.00273427	+	0.00473590i	−0.864655	+	0.502366i	$0.832463\pi$
$152$		0			0
$153$	134.282	+	5.29023i	0.877660	+	0.0345767i
$154$		0			0
$155$	−300.405	−	173.439i	−1.93809	−	1.11896i
$156$		0			0
$157$	−128.511			−0.818541			−0.409271	−	0.912413i	$-0.634217\pi$
$157$	−128.511			−0.818541			−0.409271	+	0.912413i	$0.634217\pi$
$158$		0			0
$159$	−114.092	−	118.675i	−0.717560	−	0.746386i
$160$		0			0
$161$	216.468	+	124.978i	1.34452	+	0.776261i
$162$		0			0
$163$	236.259			1.44944			0.724722	−	0.689041i	$-0.241968\pi$
$163$	236.259			1.44944			0.724722	+	0.689041i	$0.241968\pi$
$164$		0			0
$165$	88.6936	+	359.148i	0.537537	+	2.17665i
$166$		0			0
$167$	144.149	−	83.2244i	0.863167	−	0.498350i	−0.00190452	−	0.999998i	$-0.500606\pi$
$167$	144.149	−	83.2244i	0.863167	−	0.498350i	0.865072	+	0.501648i	$0.167273\pi$
$168$		0			0
$169$	−121.448	+	210.354i	−0.718626	+	1.24470i
$170$		0			0
$171$	−166.716	−	38.0366i	−0.974947	−	0.222436i
$172$		0			0
$173$	−58.6776	−	33.8776i	−0.339177	−	0.195824i	0.320731	−	0.947170i	$-0.396071\pi$
$173$	−58.6776	−	33.8776i	−0.339177	−	0.195824i	−0.659908	+	0.751346i	$0.729405\pi$
$174$		0			0
$175$	−104.653	−	181.264i	−0.598016	−	1.03579i
$176$		0			0
$177$	61.3585	−	212.192i	0.346658	−	1.19882i
$178$		0			0
$179$			60.5311i			0.338163i	0.985602	+	0.169081i	$0.0540801\pi$
$179$			60.5311i			0.338163i	−0.985602	+	0.169081i	$0.945920\pi$
$180$		0			0
$181$	83.4816	−	144.594i	0.461224	−	0.798864i	−0.537798	−	0.843074i	$-0.680744\pi$
$181$	83.4816	−	144.594i	0.461224	−	0.798864i	0.999022	+	0.0442096i	$0.0140769\pi$
$182$		0			0
$183$	274.796	+	79.4614i	1.50162	+	0.434215i
$184$		0			0
$185$			182.544i			0.986724i
$186$		0			0
$187$	−126.639	+	219.345i	−0.677214	+	1.17297i
$188$		0			0
$189$	63.9978	−	192.563i	0.338613	−	1.01885i
$190$		0			0
$191$	133.030	−	76.8050i	0.696493	−	0.402120i	−0.109547	−	0.993982i	$-0.534940\pi$
$191$	133.030	−	76.8050i	0.696493	−	0.402120i	0.806040	+	0.591861i	$0.201607\pi$
$192$		0			0
$193$	238.302			1.23473			0.617364	−	0.786678i	$-0.288201\pi$
$193$	238.302			1.23473			0.617364	+	0.786678i	$0.288201\pi$
$194$		0			0
$195$	429.716	−	106.121i	2.20367	−	0.544209i
$196$		0			0
$197$			109.602i			0.556357i	0.960529	+	0.278178i	$0.0897306\pi$
$197$			109.602i			0.556357i	−0.960529	+	0.278178i	$0.910269\pi$
$198$		0			0
$199$	−126.692	+	219.437i	−0.636643	+	1.10270i	0.349522	+	0.936928i	$0.386344\pi$
$199$	−126.692	+	219.437i	−0.636643	+	1.10270i	−0.986165	+	0.165770i	$0.946989\pi$
$200$		0			0
$201$	−0.846806	−	3.42898i	−0.00421296	−	0.0170596i
$202$		0			0
$203$	197.267	−	113.892i	0.971760	−	0.561046i
$204$		0			0
$205$	−36.6769			−0.178912
$206$		0			0
$207$	299.096	+	11.7833i	1.44491	+	0.0569242i
$208$		0			0
$209$	209.718	−	244.716i	1.00343	−	1.17089i
$210$		0			0
$211$	394.462			1.86949			0.934745	−	0.355320i	$-0.115628\pi$
$211$	394.462			1.86949			0.934745	+	0.355320i	$0.115628\pi$
$212$		0			0
$213$	41.5869	−	10.2701i	0.195244	−	0.0482165i
$214$		0			0
$215$	−312.791	−	180.590i	−1.45484	−	0.839952i
$216$		0			0
$217$	−358.602			−1.65255
$218$		0			0
$219$	85.6479	+	346.815i	0.391086	+	1.58363i
$220$		0			0
$221$	262.444	+	151.522i	1.18753	+	0.685620i
$222$		0			0
$223$	97.6081	−	169.062i	0.437705	−	0.758127i	−0.559807	−	0.828623i	$-0.689125\pi$
$223$	97.6081	−	169.062i	0.437705	−	0.758127i	0.997512	+	0.0704962i	$0.0224583\pi$
$224$		0			0
$225$	−211.966	−	133.772i	−0.942070	−	0.594542i
$226$		0			0
$227$	−253.263	+	146.222i	−1.11570	+	0.644148i	−0.940299	−	0.340349i	$-0.889455\pi$
$227$	−253.263	+	146.222i	−1.11570	+	0.644148i	−0.175398	+	0.984498i	$0.556121\pi$
$228$		0			0
$229$	−70.4763	+	122.069i	−0.307757	+	0.533050i	−0.977871	−	0.209207i	$-0.932912\pi$
$229$	−70.4763	+	122.069i	−0.307757	+	0.533050i	0.670114	+	0.742258i	$0.266245\pi$
$230$		0			0
$231$	265.051	+	275.699i	1.14741	+	1.19350i
$232$		0			0
$233$	−198.955	+	114.867i	−0.853885	+	0.492991i	−0.861960	−	0.506977i	$-0.830763\pi$
$233$	−198.955	+	114.867i	−0.853885	+	0.492991i	0.00807462	+	0.999967i	$0.497430\pi$
$234$		0			0
$235$	454.130			1.93247
$236$		0			0
$237$	−0.324673	+	0.312134i	−0.00136993	+	0.00131702i
$238$		0			0
$239$	−203.641	−	117.572i	−0.852053	−	0.491933i	0.00929033	−	0.999957i	$-0.497043\pi$
$239$	−203.641	−	117.572i	−0.852053	−	0.491933i	−0.861343	+	0.508024i	$0.830376\pi$
$240$		0			0
$241$	69.1883			0.287089			0.143544	−	0.989644i	$-0.454150\pi$
$241$	69.1883			0.287089			0.143544	+	0.989644i	$0.454150\pi$
$242$		0			0
$243$	−39.5200	−	239.765i	−0.162634	−	0.986687i
$244$		0			0
$245$	−47.1114	−	27.1998i	−0.192292	−	0.111020i
$246$		0			0
$247$	−292.799	−	250.924i	−1.18542	−	1.01589i
$248$		0			0
$249$	141.135	−	34.8542i	0.566808	−	0.139977i
$250$		0			0
$251$	−18.6371	−	10.7602i	−0.0742515	−	0.0428692i	0.462415	−	0.886664i	$-0.346983\pi$
$251$	−18.6371	−	10.7602i	−0.0742515	−	0.0428692i	−0.536666	+	0.843795i	$0.680317\pi$
$252$		0			0
$253$	−282.072	+	488.564i	−1.11491	+	1.93108i
$254$		0			0
$255$	−78.0762	−	316.155i	−0.306181	−	1.23982i
$256$		0			0
$257$	−252.333	+	145.684i	−0.981839	+	0.566865i	−0.902825	−	0.430008i	$-0.858511\pi$
$257$	−252.333	+	145.684i	−0.981839	+	0.566865i	−0.0790144	+	0.996873i	$0.525177\pi$
$258$		0			0
$259$	94.3571	+	163.431i	0.364313	+	0.631009i
$260$		0			0
$261$	145.582	−	230.680i	0.557787	−	0.883831i
$262$		0			0
$263$	−140.817	−	81.3007i	−0.535426	−	0.309128i	0.207797	−	0.978172i	$-0.433371\pi$
$263$	−140.817	−	81.3007i	−0.535426	−	0.309128i	−0.743223	+	0.669044i	$0.766704\pi$
$264$		0			0
$265$	−199.463	+	345.480i	−0.752690	+	1.30370i
$266$		0			0
$267$	−161.837	−	168.338i	−0.606129	−	0.630479i
$268$		0			0
$269$	29.2134	−	16.8664i	0.108600	−	0.0627003i	−0.444716	−	0.895672i	$-0.646695\pi$
$269$	29.2134	−	16.8664i	0.108600	−	0.0627003i	0.553316	+	0.832971i	$0.313362\pi$
$270$		0			0
$271$	−88.5330	−	153.344i	−0.326690	−	0.565844i	0.655163	−	0.755488i	$-0.272600\pi$
$271$	−88.5330	−	153.344i	−0.326690	−	0.565844i	−0.981853	+	0.189644i	$0.939267\pi$
$272$		0			0
$273$	329.870	−	317.130i	1.20831	−	1.16165i
$274$		0			0
$275$	409.108	−	236.199i	1.48767	−	0.858904i
$276$		0			0
$277$	88.8575	+	153.906i	0.320785	+	0.555616i	0.980650	−	0.195768i	$-0.0627199\pi$
$277$	88.8575	+	153.906i	0.320785	+	0.555616i	−0.659865	+	0.751384i	$0.729387\pi$
$278$		0			0
$279$	−380.065	+	199.911i	−1.36224	+	0.716525i
$280$		0			0
$281$			336.283i			1.19674i	0.801221	+	0.598369i	$0.204184\pi$
$281$			336.283i			1.19674i	−0.801221	+	0.598369i	$0.795816\pi$
$282$		0			0
$283$	31.1149			0.109947			0.0549733	−	0.998488i	$-0.482493\pi$
$283$	31.1149			0.109947			0.0549733	+	0.998488i	$0.482493\pi$
$284$		0			0
$285$	23.6791	+	413.701i	0.0830846	+	1.45158i
$286$		0			0
$287$	−32.8368	+	18.9583i	−0.114414	+	0.0660569i
$288$		0			0
$289$	−33.0207	+	57.1936i	−0.114259	+	0.197902i
$290$		0			0
$291$	204.510	−	196.612i	0.702783	−	0.675641i
$292$		0			0
$293$	180.338	+	104.118i	0.615487	+	0.355351i	0.775110	−	0.631827i	$-0.217695\pi$
$293$	180.338	+	104.118i	0.615487	+	0.355351i	−0.159623	+	0.987178i	$0.551028\pi$
$294$		0			0
$295$	−535.263			−1.81445
$296$		0			0
$297$	434.609	+	144.441i	1.46333	+	0.486335i
$298$		0			0
$299$	584.560	+	337.496i	1.95505	+	1.12875i
$300$		0			0
$301$	−373.388			−1.24049
$302$		0			0
$303$	−70.6452	+	244.307i	−0.233153	+	0.806295i
$304$		0			0
$305$		−	693.183i		−	2.27273i
$306$		0			0
$307$	251.455	+	435.532i	0.819071	+	1.41867i	0.906368	+	0.422489i	$0.138844\pi$
$307$	251.455	+	435.532i	0.819071	+	1.41867i	−0.0872974	+	0.996182i	$0.527823\pi$
$308$		0			0
$309$	15.1460	−	14.5611i	0.0490163	−	0.0471233i
$310$		0			0
$311$	241.751	+	139.575i	0.777334	+	0.448794i	0.835485	−	0.549514i	$-0.185187\pi$
$311$	241.751	+	139.575i	0.777334	+	0.448794i	−0.0581507	+	0.998308i	$0.518520\pi$
$312$		0			0
$313$	−113.259			−0.361850			−0.180925	−	0.983497i	$-0.557909\pi$
$313$	−113.259			−0.361850			−0.180925	+	0.983497i	$0.557909\pi$
$314$		0			0
$315$	−491.345	−	19.3572i	−1.55982	−	0.0614515i
$316$		0			0
$317$			109.393i			0.345089i	0.985002	+	0.172544i	$0.0551988\pi$
$317$			109.393i			0.345089i	−0.985002	+	0.172544i	$0.944801\pi$
$318$		0			0
$319$	257.052	+	445.227i	0.805806	+	1.39570i
$320$		0			0
$321$	−81.6100	+	282.226i	−0.254237	+	0.879209i
$322$		0			0
$323$	−184.613	+	215.421i	−0.571556	+	0.666938i
$324$		0			0
$325$	−282.609	−	489.492i	−0.869565	−	1.50613i
$326$		0			0
$327$	−108.440	−	439.106i	−0.331620	−	1.34283i
$328$		0			0
$329$	406.582	−	234.740i	1.23581	−	0.713497i
$330$		0			0
$331$	−50.5317	−	87.5235i	−0.152664	−	0.264422i	0.779542	−	0.626350i	$-0.215452\pi$
$331$	−50.5317	−	87.5235i	−0.152664	−	0.264422i	−0.932206	+	0.361928i	$0.882119\pi$
$332$		0			0
$333$	191.113	+	120.612i	0.573912	+	0.362197i
$334$		0			0
$335$	−7.41226	+	4.27947i	−0.0221262	+	0.0127745i
$336$		0			0
$337$	−560.509			−1.66323			−0.831616	−	0.555351i	$-0.812584\pi$
$337$	−560.509			−1.66323			−0.831616	+	0.555351i	$0.812584\pi$
$338$		0			0
$339$	−95.2337	−	99.0595i	−0.280925	−	0.292211i
$340$		0			0
$341$		−	809.357i		−	2.37348i
$342$		0			0
$343$	312.022			0.909685
$344$		0			0
$345$	−173.905	−	704.195i	−0.504072	−	2.04114i
$346$		0			0
$347$		−	106.009i		−	0.305501i	−0.988265	−	0.152751i	$-0.951187\pi$
$347$		−	106.009i		−	0.305501i	0.988265	−	0.152751i	$-0.0488132\pi$
$348$		0			0
$349$	120.332	+	208.421i	0.344791	+	0.597196i	0.985316	−	0.170742i	$-0.0546164\pi$
$349$	120.332	+	208.421i	0.344791	+	0.597196i	−0.640525	+	0.767938i	$0.721283\pi$
$350$		0			0
$351$	172.822	−	520.004i	0.492371	−	1.48149i
$352$		0			0
$353$	−438.326	+	253.068i	−1.24172	+	0.716906i	−0.969444	−	0.245314i	$-0.921109\pi$
$353$	−438.326	+	253.068i	−1.24172	+	0.716906i	−0.272274	+	0.962220i	$0.587776\pi$
$354$		0			0
$355$	−51.9018	−	89.8965i	−0.146202	−	0.253229i
$356$		0			0
$357$	−233.322	−	242.695i	−0.653564	−	0.679819i
$358$		0			0
$359$	−481.722	+	278.122i	−1.34184	+	0.774714i	−0.987078	−	0.160242i	$-0.948773\pi$
$359$	−481.722	+	278.122i	−1.34184	+	0.774714i	−0.354766	+	0.934955i	$0.615439\pi$
$360$		0			0
$361$	281.310	−	226.243i	0.779252	−	0.626711i
$362$		0			0
$363$	−360.562	+	346.637i	−0.993284	+	0.954922i
$364$		0			0
$365$	749.694	−	432.836i	2.05396	−	1.18585i
$366$		0			0
$367$	608.527			1.65811			0.829056	−	0.559165i	$-0.188878\pi$
$367$	608.527			1.65811			0.829056	+	0.559165i	$0.188878\pi$
$368$		0			0
$369$	−24.2334	+	38.3986i	−0.0656732	+	0.104061i
$370$		0			0
$371$			412.410i			1.11162i
$372$		0			0
$373$	61.6756	−	106.825i	0.165350	−	0.286395i	−0.771429	−	0.636315i	$-0.780458\pi$
$373$	61.6756	−	106.825i	0.165350	−	0.286395i	0.936780	+	0.349920i	$0.113791\pi$
$374$		0			0
$375$	−17.2649	+	59.7059i	−0.0460397	+	0.159216i
$376$		0			0
$377$	532.709	−	307.560i	1.41302	−	0.815808i
$378$		0			0
$379$	−358.690			−0.946412			−0.473206	−	0.880952i	$-0.656903\pi$
$379$	−358.690			−0.946412			−0.473206	+	0.880952i	$0.656903\pi$
$380$		0			0
$381$	60.9495	−	58.5955i	0.159972	−	0.153794i
$382$		0			0
$383$			366.840i			0.957806i	0.877868	+	0.478903i	$0.158965\pi$
$383$			366.840i			0.957806i	−0.877868	+	0.478903i	$0.841035\pi$
$384$		0			0
$385$	463.379	−	802.595i	1.20358	−	2.08466i
$386$		0			0
$387$	−395.736	+	208.153i	−1.02257	+	0.537863i
$388$		0			0
$389$		−	190.120i		−	0.488740i	−0.969682	−	0.244370i	$-0.921419\pi$
$389$		−	190.120i		−	0.488740i	0.969682	−	0.244370i	$-0.0785812\pi$
$390$		0			0
$391$	248.306	−	430.078i	0.635054	−	1.09995i
$392$		0			0
$393$	−210.078	+	726.498i	−0.534550	+	1.84860i
$394$		0			0
$395$	0.945166	+	0.545692i	0.00239283	+	0.00138150i
$396$		0			0
$397$	115.434	+	199.937i	0.290765	+	0.503619i	0.973991	−	0.226588i	$-0.0727570\pi$
$397$	115.434	+	199.937i	0.290765	+	0.503619i	−0.683226	+	0.730207i	$0.739424\pi$
$398$		0			0
$399$	235.042	+	358.146i	0.589078	+	0.897608i
$400$		0			0
$401$		−	439.408i		−	1.09578i	−0.836551	−	0.547890i	$-0.815431\pi$
$401$		−	439.408i		−	1.09578i	0.836551	−	0.547890i	$-0.184569\pi$
$402$		0			0
$403$	−968.385			−2.40294
$404$		0			0
$405$	−531.544	+	253.395i	−1.31245	+	0.625666i
$406$		0			0
$407$	−368.860	+	212.962i	−0.906291	+	0.523247i
$408$		0			0
$409$	131.307	+	227.431i	0.321045	+	0.556065i	0.980704	−	0.195499i	$-0.0626328\pi$
$409$	131.307	+	227.431i	0.321045	+	0.556065i	−0.659659	+	0.751565i	$0.729299\pi$
$410$		0			0
$411$	71.9545	−	248.835i	0.175072	−	0.605438i
$412$		0			0
$413$	−479.220	+	276.678i	−1.16034	+	0.669922i
$414$		0			0
$415$	−176.141	−	305.086i	−0.424437	−	0.735146i
$416$		0			0
$417$	119.062	+	482.119i	0.285520	+	1.15616i
$418$		0			0
$419$	490.534	+	283.210i	1.17072	+	0.675918i	0.953851	−	0.300281i	$-0.0970806\pi$
$419$	490.534	+	283.210i	1.17072	+	0.675918i	0.216874	+	0.976200i	$0.430414\pi$
$420$		0			0
$421$	239.616	−	415.027i	0.569158	−	0.985811i	−0.427491	−	0.904020i	$-0.640602\pi$
$421$	239.616	−	415.027i	0.569158	−	0.985811i	0.996649	−	0.0817918i	$-0.0260642\pi$
$422$		0			0
$423$	300.056	−	475.448i	0.709352	−	1.12399i
$424$		0			0
$425$	−360.134	+	207.924i	−0.847375	+	0.489232i
$426$		0			0
$427$	−358.307	−	620.606i	−0.839126	−	1.45341i
$428$		0			0
$429$	715.755	+	744.508i	1.66843	+	1.73545i
$430$		0			0
$431$	480.030	+	277.145i	1.11376	+	0.643029i	0.939800	−	0.341724i	$-0.111011\pi$
$431$	480.030	+	277.145i	1.11376	+	0.643029i	0.173958	+	0.984753i	$0.444344\pi$
$432$		0			0
$433$	−116.826	+	202.348i	−0.269805	+	0.467316i	−0.968811	−	0.247799i	$-0.920293\pi$
$433$	−116.826	+	202.348i	−0.269805	+	0.467316i	0.699006	+	0.715116i	$0.253626\pi$
$434$		0			0
$435$	−634.996	−	183.619i	−1.45976	−	0.422112i
$436$		0			0
$437$	−411.201	+	479.823i	−0.940964	+	1.09799i
$438$		0			0
$439$	−100.290	+	173.707i	−0.228451	+	0.395688i	−0.957349	−	0.288934i	$-0.906699\pi$
$439$	−100.290	+	173.707i	−0.228451	+	0.395688i	0.728898	+	0.684622i	$0.240033\pi$
$440$		0			0
$441$	−59.6044	+	31.3513i	−0.135157	+	0.0710914i
$442$		0			0
$443$			296.907i			0.670219i	0.942179	+	0.335110i	$0.108773\pi$
$443$			296.907i			0.670219i	−0.942179	+	0.335110i	$0.891227\pi$
$444$		0			0
$445$	−282.933	+	490.054i	−0.635804	+	1.10124i
$446$		0			0
$447$	−163.391	+	565.043i	−0.365528	+	1.26408i
$448$		0			0
$449$		−	392.134i		−	0.873349i	−0.899620	−	0.436675i	$-0.856156\pi$
$449$		−	392.134i		−	0.873349i	0.899620	−	0.436675i	$-0.143844\pi$
$450$		0			0
$451$	−42.7885	−	74.1118i	−0.0948747	−	0.164328i
$452$		0			0
$453$	−0.593928	−	2.40500i	−0.00131110	−	0.00530905i
$454$		0			0
$455$	−960.295	−	554.426i	−2.11054	−	1.21852i
$456$		0			0
$457$	101.699	+	176.148i	0.222537	+	0.385445i	0.955578	−	0.294740i	$-0.0952330\pi$
$457$	101.699	+	176.148i	0.222537	+	0.385445i	−0.733041	+	0.680184i	$0.761900\pi$
$458$		0			0
$459$	−382.583	−	127.151i	−0.833513	−	0.277017i
$460$		0			0
$461$	−121.048	−	69.8873i	−0.262578	−	0.151599i	0.362932	−	0.931816i	$-0.381776\pi$
$461$	−121.048	−	69.8873i	−0.262578	−	0.151599i	−0.625510	+	0.780216i	$0.715109\pi$
$462$		0			0
$463$	94.0240	−	162.854i	0.203076	−	0.351737i	−0.746442	−	0.665450i	$-0.768240\pi$
$463$	94.0240	−	162.854i	0.203076	−	0.351737i	0.949518	+	0.313713i	$0.101573\pi$
$464$		0			0
$465$	721.209	+	750.182i	1.55099	+	1.61329i
$466$		0			0
$467$			370.749i			0.793896i	0.917841	+	0.396948i	$0.129931\pi$
$467$			370.749i			0.793896i	−0.917841	+	0.396948i	$0.870069\pi$
$468$		0			0
$469$	−4.42412	+	7.66281i	−0.00943310	+	0.0163386i
$470$		0			0
$471$	370.360	+	107.095i	0.786326	+	0.227378i
$472$		0			0
$473$		−	842.727i		−	1.78166i
$474$		0			0
$475$	499.090	−	175.796i	1.05072	−	0.370097i
$476$		0			0
$477$	229.907	+	437.093i	0.481985	+	0.916338i
$478$		0			0
$479$			330.120i			0.689185i	0.938752	+	0.344592i	$0.111983\pi$
$479$			330.120i			0.689185i	−0.938752	+	0.344592i	$0.888017\pi$
$480$		0			0
$481$	254.806	+	441.337i	0.529742	+	0.917540i
$482$		0			0
$483$	−519.696	−	540.573i	−1.07597	−	1.11920i
$484$		0			0
$485$	−595.355	−	343.729i	−1.22754	−	0.708719i
$486$		0			0
$487$	709.032			1.45592			0.727959	−	0.685621i	$-0.240469\pi$
$487$	709.032			1.45592			0.727959	+	0.685621i	$0.240469\pi$
$488$		0			0
$489$	−680.883	−	196.888i	−1.39240	−	0.402634i
$490$		0			0
$491$			363.330i			0.739980i	0.929036	+	0.369990i	$0.120639\pi$
$491$			363.330i			0.739980i	−0.929036	+	0.369990i	$0.879361\pi$
$492$		0			0
$493$	−226.281	−	391.930i	−0.458988	−	0.794990i
$494$		0			0
$495$	43.6887	−	1108.95i	0.0882601	−	2.24031i
$496$		0			0
$497$	−92.9351	−	53.6561i	−0.186992	−	0.107960i
$498$		0			0
$499$	−743.071			−1.48912			−0.744560	−	0.667556i	$-0.767341\pi$
$499$	−743.071			−1.48912			−0.744560	+	0.667556i	$0.767341\pi$
$500$		0			0
$501$	−484.782	+	119.720i	−0.967630	+	0.238962i
$502$		0			0
$503$	−319.580	−	184.509i	−0.635348	−	0.366818i	0.147473	−	0.989066i	$-0.452886\pi$
$503$	−319.580	−	184.509i	−0.635348	−	0.366818i	−0.782820	+	0.622248i	$0.786220\pi$
$504$		0			0
$505$	616.275			1.22035
$506$		0			0
$507$	525.303	−	505.016i	1.03610	−	0.996086i
$508$		0			0
$509$	−106.451	+	61.4595i	−0.209137	+	0.120746i	−0.600910	−	0.799316i	$-0.705195\pi$
$509$	−106.451	+	61.4595i	−0.209137	+	0.120746i	0.391773	+	0.920062i	$0.371862\pi$
$510$		0			0
$511$	447.466	−	775.035i	0.875668	−	1.51670i
$512$		0			0
$513$	448.766	+	248.552i	0.874787	+	0.484507i
$514$		0			0
$515$	−44.0921	−	25.4566i	−0.0856157	−	0.0494303i
$516$		0			0
$517$	529.803	+	917.646i	1.02476	+	1.77494i
$518$		0			0
$519$	140.873	+	146.532i	0.271431	+	0.282335i
$520$		0			0
$521$			883.174i			1.69515i	0.530674	+	0.847576i	$0.321939\pi$
$521$			883.174i			1.69515i	−0.530674	+	0.847576i	$0.678061\pi$
$522$		0			0
$523$	82.8317	−	143.469i	0.158378	−	0.274319i	−0.775906	−	0.630849i	$-0.782707\pi$
$523$	82.8317	−	143.469i	0.158378	−	0.274319i	0.934284	+	0.356530i	$0.116040\pi$
$524$		0			0
$525$	150.545	+	609.603i	0.286752	+	1.16115i
$526$		0			0
$527$			712.470i			1.35193i
$528$		0			0
$529$	288.570	−	499.818i	0.545501	−	0.944835i
$530$		0			0
$531$	−353.662	+	560.389i	−0.666030	+	1.05535i
$532$		0			0
$533$	−88.6738	+	51.1959i	−0.166367	+	0.0960523i
$534$		0			0
$535$	711.926			1.33070
$536$		0			0
$537$	50.4439	−	174.446i	0.0939364	−	0.324854i
$538$		0			0
$539$		−	126.929i		−	0.235489i
$540$		0			0
$541$	−239.705	+	415.182i	−0.443079	+	0.767435i	−0.997916	−	0.0645241i	$-0.979447\pi$
$541$	−239.705	+	415.182i	−0.443079	+	0.767435i	0.554838	+	0.831959i	$0.312780\pi$
$542$		0			0
$543$	−361.087	+	347.141i	−0.664985	+	0.639302i
$544$		0			0
$545$	−949.195	+	548.018i	−1.74164	+	1.00554i
$546$		0			0
$547$	323.732			0.591831			0.295916	−	0.955214i	$-0.404375\pi$
$547$	323.732			0.591831			0.295916	+	0.955214i	$0.404375\pi$
$548$		0			0
$549$	−725.722	−	458.004i	−1.32190	−	0.834252i
$550$		0			0
$551$	191.317	+	543.154i	0.347217	+	0.985761i
$552$		0			0
$553$	1.12827			0.00204028
$554$		0			0
$555$	152.124	−	526.079i	0.274097	−	0.947890i
$556$		0			0
$557$	−139.331	−	80.4425i	−0.250145	−	0.144421i	0.369686	−	0.929157i	$-0.379465\pi$
$557$	−139.331	−	80.4425i	−0.250145	−	0.144421i	−0.619830	+	0.784736i	$0.712799\pi$
$558$		0			0
$559$	−1008.31			−1.80378
$560$		0			0
$561$	547.757	−	526.602i	0.976394	−	0.938685i
$562$		0			0
$563$	−351.195	−	202.763i	−0.623793	−	0.360147i	0.154551	−	0.987985i	$-0.450607\pi$
$563$	−351.195	−	202.763i	−0.623793	−	0.360147i	−0.778344	+	0.627838i	$0.783940\pi$
$564$		0			0
$565$	−166.493	+	288.375i	−0.294679	+	0.510398i
$566$		0			0
$567$	−344.910	+	501.619i	−0.608307	+	0.884690i
$568$		0			0
$569$	937.203	−	541.095i	1.64711	−	0.950957i	0.668892	−	0.743360i	$-0.266769\pi$
$569$	937.203	−	541.095i	1.64711	−	0.950957i	0.978214	−	0.207597i	$-0.0665644\pi$
$570$		0			0
$571$	−275.915	+	477.899i	−0.483214	+	0.836951i	−0.999814	−	0.0192758i	$-0.993864\pi$
$571$	−275.915	+	477.899i	−0.483214	+	0.836951i	0.516600	+	0.856227i	$0.327197\pi$
$572$		0			0
$573$	−447.389	+	110.485i	−0.780784	+	0.192819i
$574$		0			0
$575$	−802.154	+	463.124i	−1.39505	+	0.805432i
$576$		0			0
$577$	−7.66081			−0.0132770			−0.00663848	−	0.999978i	$-0.502113\pi$
$577$	−7.66081			−0.0132770			−0.00663848	+	0.999978i	$0.502113\pi$
$578$		0			0
$579$	−686.771	−	198.590i	−1.18613	−	0.342988i
$580$		0			0
$581$	−315.398	−	182.095i	−0.542854	−	0.313417i
$582$		0			0
$583$	−930.799			−1.59657
$584$		0			0
$585$	−1326.85	−	52.2730i	−2.26811	−	0.0893556i
$586$		0			0
$587$	−686.241	−	396.201i	−1.16906	−	0.674960i	−0.215605	−	0.976481i	$-0.569172\pi$
$587$	−686.241	−	396.201i	−1.16906	−	0.674960i	−0.953459	+	0.301521i	$0.902506\pi$
$588$		0			0
$589$	166.706	−	891.125i	0.283033	−	1.51295i
$590$		0			0
$591$	91.3376	−	315.866i	0.154547	−	0.534460i
$592$		0			0
$593$	−541.981	−	312.913i	−0.913965	−	0.527678i	−0.0322602	−	0.999480i	$-0.510271\pi$
$593$	−541.981	−	312.913i	−0.913965	−	0.527678i	−0.881705	+	0.471802i	$0.843604\pi$
$594$		0			0
$595$	−407.908	+	706.518i	−0.685560	+	1.18742i
$596$		0			0
$597$	547.986	−	526.822i	0.917899	−	0.882450i
$598$		0			0
$599$	−150.471	+	86.8742i	−0.251203	+	0.145032i	−0.620315	−	0.784353i	$-0.712995\pi$
$599$	−150.471	+	86.8742i	−0.251203	+	0.145032i	0.369112	+	0.929385i	$0.379662\pi$
$600$		0			0
$601$	−138.816	−	240.436i	−0.230975	−	0.400060i	0.727120	−	0.686510i	$-0.240858\pi$
$601$	−138.816	−	240.436i	−0.230975	−	0.400060i	−0.958095	+	0.286450i	$0.907525\pi$
$602$		0			0
$603$	−0.417120	+	10.5878i	−0.000691741	+	0.0175585i
$604$		0			0
$605$	1049.64	+	606.012i	1.73495	+	1.00167i
$606$		0			0
$607$	236.591	−	409.787i	0.389770	−	0.675102i	−0.602648	−	0.798007i	$-0.705888\pi$
$607$	236.591	−	409.787i	0.389770	−	0.675102i	0.992418	+	0.122905i	$0.0392211\pi$
$608$		0			0
$609$	−663.423	+	163.836i	−1.08937	+	0.269025i
$610$		0			0
$611$	1097.95	−	633.903i	1.79697	−	1.03748i
$612$		0			0
$613$	412.386	+	714.274i	0.672735	+	1.16521i	0.977126	+	0.212663i	$0.0682137\pi$
$613$	412.386	+	714.274i	0.672735	+	1.16521i	−0.304391	+	0.952547i	$0.598453\pi$
$614$		0			0
$615$	105.700	+	30.5649i	0.171870	+	0.0496990i
$616$		0			0
$617$	449.661	−	259.612i	0.728786	−	0.420765i	−0.0891918	−	0.996014i	$-0.528428\pi$
$617$	449.661	−	259.612i	0.728786	−	0.420765i	0.817978	+	0.575250i	$0.195095\pi$
$618$		0			0
$619$	515.153	+	892.272i	0.832235	+	1.44147i	0.896262	+	0.443525i	$0.146272\pi$
$619$	515.153	+	892.272i	0.832235	+	1.44147i	−0.0640275	+	0.997948i	$0.520395\pi$
$620$		0			0
$621$	−852.154	−	283.212i	−1.37223	−	0.456058i
$622$		0			0
$623$			584.992i			0.938992i
$624$		0			0
$625$	−545.634			−0.873015
$626$		0			0
$627$	−808.326	+	530.484i	−1.28920	+	0.846067i
$628$		0			0
$629$	324.705	−	187.468i	0.516224	−	0.298042i
$630$		0			0
$631$	282.848	−	489.908i	0.448254	−	0.776399i	−0.550018	−	0.835153i	$-0.685379\pi$
$631$	282.848	−	489.908i	0.448254	−	0.776399i	0.998273	+	0.0587536i	$0.0187126\pi$
$632$		0			0
$633$	−1136.81	−	328.727i	−1.79591	−	0.519316i
$634$		0			0
$635$	−177.432	−	102.440i	−0.279420	−	0.161323i
$636$		0			0
$637$	−151.868			−0.238412
$638$		0			0
$639$	−128.409	−	5.05886i	−0.200953	−	0.00791684i
$640$		0			0
$641$	427.649	+	246.903i	0.667159	+	0.385184i	0.794999	−	0.606610i	$-0.207471\pi$
$641$	427.649	+	246.903i	0.667159	+	0.385184i	−0.127840	+	0.991795i	$0.540805\pi$
$642$		0			0
$643$	921.506			1.43314			0.716568	−	0.697518i	$-0.245712\pi$
$643$	921.506			1.43314			0.716568	+	0.697518i	$0.245712\pi$
$644$		0			0
$645$	750.945	+	781.112i	1.16426	+	1.21103i
$646$		0			0
$647$			838.370i			1.29578i	0.761734	+	0.647890i	$0.224348\pi$
$647$			838.370i			1.29578i	−0.761734	+	0.647890i	$0.775652\pi$
$648$		0			0
$649$	−624.454	−	1081.59i	−0.962179	−	1.66654i
$650$		0			0
$651$	1033.47	+	298.843i	1.58751	+	0.459052i
$652$		0			0
$653$	671.238	+	387.539i	1.02793	+	0.593475i	0.916391	−	0.400285i	$-0.131089\pi$
$653$	671.238	+	387.539i	1.02793	+	0.593475i	0.111539	+	0.993760i	$0.464422\pi$
$654$		0			0
$655$	1832.62			2.79789
$656$		0			0
$657$	42.1885	−	1070.87i	0.0642139	−	1.62994i
$658$		0			0
$659$			82.4435i			0.125104i	0.998042	+	0.0625520i	$0.0199239\pi$
$659$			82.4435i			0.125104i	−0.998042	+	0.0625520i	$0.980076\pi$
$660$		0			0
$661$	−434.594	−	752.739i	−0.657479	−	1.13879i	−0.981266	−	0.192657i	$-0.938289\pi$
$661$	−434.594	−	752.739i	−0.657479	−	1.13879i	0.323787	−	0.946130i	$-0.395044\pi$
$662$		0			0
$663$	−630.073	−	655.384i	−0.950336	−	0.988513i
$664$		0			0
$665$	675.507	−	788.236i	1.01580	−	1.18532i
$666$		0			0
$667$	−504.012	−	872.974i	−0.755640	−	1.30881i
$668$		0			0
$669$	−422.189	+	405.883i	−0.631074	+	0.606702i
$670$		0			0
$671$	1400.69	−	808.690i	2.08747	−	1.20520i
$672$		0			0
$673$	−379.173	−	656.747i	−0.563407	−	0.975850i	−0.997196	−	0.0748351i	$-0.976157\pi$
$673$	−379.173	−	656.747i	−0.563407	−	0.975850i	0.433789	−	0.901015i	$-0.357176\pi$
$674$		0			0
$675$	499.391	+	562.164i	0.739839	+	0.832836i
$676$		0			0
$677$	910.405	−	525.622i	1.34476	−	0.776400i	0.357261	−	0.934005i	$-0.383711\pi$
$677$	910.405	−	525.622i	1.34476	−	0.776400i	0.987502	+	0.157605i	$0.0503773\pi$
$678$		0			0
$679$	−710.694			−1.04668
$680$		0			0
$681$	851.742	−	210.342i	1.25072	−	0.308873i
$682$		0			0
$683$			834.766i			1.22221i	0.791551	+	0.611103i	$0.209274\pi$
$683$			834.766i			1.22221i	−0.791551	+	0.611103i	$0.790726\pi$
$684$		0			0
$685$	−627.697			−0.916345
$686$		0			0
$687$	304.834	−	293.061i	0.443718	−	0.426581i
$688$		0			0
$689$			1113.69i			1.61638i
$690$		0			0
$691$	41.2273	+	71.4077i	0.0596632	+	0.103340i	0.894314	−	0.447439i	$-0.147664\pi$
$691$	41.2273	+	71.4077i	0.0596632	+	0.103340i	−0.834651	+	0.550779i	$0.814331\pi$
$692$		0			0
$693$	−534.104	−	1015.43i	−0.770713	−	1.46526i
$694$		0			0
$695$	1042.17	−	601.699i	1.49953	−	0.865754i
$696$		0			0
$697$	37.6663	+	65.2400i	0.0540407	+	0.0936012i
$698$		0			0
$699$	669.100	−	165.238i	0.957225	−	0.236392i
$700$		0			0
$701$	−44.1386	+	25.4834i	−0.0629652	+	0.0363530i	−0.531152	−	0.847276i	$-0.678241\pi$
$701$	−44.1386	+	25.4834i	−0.0629652	+	0.0363530i	0.468187	+	0.883629i	$0.344907\pi$
$702$		0			0
$703$	−449.990	+	158.501i	−0.640100	+	0.225464i
$704$		0			0
$705$	−1308.77	−	378.452i	−1.85641	−	0.536811i
$706$		0			0
$707$	551.750	−	318.553i	0.780410	−	0.450570i
$708$		0			0
$709$	−210.795			−0.297313			−0.148657	−	0.988889i	$-0.547495\pi$
$709$	−210.795			−0.297313			−0.148657	+	0.988889i	$0.547495\pi$
$710$		0			0
$711$	1.19580	−	0.628981i	0.00168186	−	0.000884642i
$712$		0			0
$713$			1586.94i			2.22572i
$714$		0			0
$715$	1251.33	−	2167.36i	1.75011	−	3.03127i
$716$		0			0
$717$	488.899	+	508.539i	0.681867	+	0.709259i
$718$		0			0
$719$	399.243	−	230.503i	0.555276	−	0.320589i	−0.195971	−	0.980610i	$-0.562786\pi$
$719$	399.243	−	230.503i	0.555276	−	0.320589i	0.751247	+	0.660021i	$0.229453\pi$
$720$		0			0
$721$	−52.6341			−0.0730015
$722$		0			0
$723$	−199.396	−	57.6584i	−0.275790	−	0.0797488i
$724$		0			0
$725$			844.088i			1.16426i
$726$		0			0
$727$	−267.029	+	462.507i	−0.367302	+	0.636186i	−0.989143	−	0.146958i	$-0.953052\pi$
$727$	−267.029	+	462.507i	−0.367302	+	0.636186i	0.621841	+	0.783144i	$0.286385\pi$
$728$		0			0
$729$	−85.9153	+	723.920i	−0.117854	+	0.993031i
$730$		0			0
$731$			741.845i			1.01484i
$732$		0			0
$733$	262.174	−	454.098i	0.357672	−	0.619506i	−0.629899	−	0.776677i	$-0.716904\pi$
$733$	262.174	−	454.098i	0.357672	−	0.619506i	0.987571	+	0.157171i	$0.0502372\pi$
$734$		0			0
$735$	113.105	+	117.648i	0.153884	+	0.160066i
$736$		0			0
$737$	−17.2948	−	9.98514i	−0.0234664	−	0.0135484i
$738$		0			0
$739$	−16.8402	−	29.1681i	−0.0227878	−	0.0394696i	0.854407	−	0.519605i	$-0.173921\pi$
$739$	−16.8402	−	29.1681i	−0.0227878	−	0.0394696i	−0.877194	+	0.480135i	$0.840588\pi$
$740$		0			0
$741$	634.717	+	967.152i	0.856569	+	1.30520i
$742$		0			0
$743$		−	12.7053i		−	0.0171000i	−0.999963	−	0.00855001i	$-0.997278\pi$
$743$		−	12.7053i		−	0.0171000i	0.999963	−	0.00855001i	$-0.00272159\pi$
$744$		0			0
$745$	1425.35			1.91321
$746$		0			0
$747$	−435.788	−	17.1685i	−0.583384	−	0.0229832i
$748$		0			0
$749$	637.387	−	367.995i	0.850983	−	0.491316i
$750$		0			0
$751$	734.945	+	1272.96i	0.978622	+	1.69502i	0.667424	+	0.744678i	$0.267397\pi$
$751$	734.945	+	1272.96i	0.978622	+	1.69502i	0.311197	+	0.950345i	$0.399270\pi$
$752$		0			0
$753$	44.7439	+	46.5414i	0.0594209	+	0.0618079i
$754$		0			0
$755$	−5.19877	+	3.00151i	−0.00688579	+	0.00397551i
$756$		0			0
$757$	−141.145	−	244.470i	−0.186453	−	0.322945i	0.757612	−	0.652705i	$-0.226366\pi$
$757$	−141.145	−	244.470i	−0.186453	−	0.322945i	−0.944065	+	0.329759i	$0.893032\pi$
$758$		0			0
$759$	1220.06	−	1172.94i	1.60746	−	1.54538i
$760$		0			0
$761$	917.495	+	529.716i	1.20564	+	0.696079i	0.961805	−	0.273737i	$-0.0882597\pi$
$761$	917.495	+	529.716i	1.20564	+	0.696079i	0.243839	+	0.969816i	$0.421593\pi$
$762$		0			0
$763$	−566.542	+	981.279i	−0.742519	+	1.28608i
$764$		0			0
$765$	−38.4588	+	976.201i	−0.0502730	+	1.27608i
$766$		0			0
$767$	−1294.10	+	747.152i	−1.68723	+	0.974122i
$768$		0			0
$769$	548.055	+	949.259i	0.712685	+	1.23441i	0.963845	+	0.266462i	$0.0858546\pi$
$769$	548.055	+	949.259i	0.712685	+	1.23441i	−0.251160	+	0.967946i	$0.580812\pi$
$770$		0			0
$771$	848.612	−	209.570i	1.10066	−	0.271815i
$772$		0			0
$773$	−428.849	−	247.596i	−0.554786	−	0.320306i	0.196264	−	0.980551i	$-0.437119\pi$
$773$	−428.849	−	247.596i	−0.554786	−	0.320306i	−0.751050	+	0.660245i	$0.770452\pi$
$774$		0			0
$775$	664.425	−	1150.82i	0.857323	−	1.48493i
$776$		0			0
$777$	−135.734	−	549.630i	−0.174690	−	0.707375i
$778$		0			0
$779$	−31.8462	−	90.4125i	−0.0408809	−	0.116062i
$780$		0			0
$781$	121.101	−	209.752i	0.155058	−	0.268569i
$782$		0			0
$783$	−611.797	+	543.482i	−0.781349	+	0.694102i
$784$		0			0
$785$		−	934.247i		−	1.19012i
$786$		0			0
$787$	−134.383	+	232.757i	−0.170753	+	0.295753i	−0.938683	−	0.344781i	$-0.887953\pi$
$787$	−134.383	+	232.757i	−0.170753	+	0.295753i	0.767930	+	0.640533i	$0.221287\pi$
$788$		0			0
$789$	338.072	+	351.654i	0.428482	+	0.445695i
$790$		0			0
$791$			344.242i			0.435199i
$792$		0			0
$793$	−967.587	−	1675.91i	−1.22016	−	2.11338i
$794$		0			0
$795$	862.745	−	829.425i	1.08521	−	1.04330i
$796$		0			0
$797$	1058.28	+	610.999i	1.32783	+	0.766624i	0.984964	−	0.172760i	$-0.0552684\pi$
$797$	1058.28	+	610.999i	1.32783	+	0.766624i	0.342868	+	0.939384i	$0.388602\pi$
$798$		0			0
$799$	−466.381	−	807.796i	−0.583706	−	1.01101i
$800$		0			0
$801$	326.117	+	620.005i	0.407137	+	0.774039i
$802$		0			0
$803$	1749.23	+	1009.92i	2.17837	+	1.25768i
$804$		0			0
$805$	−908.564	+	1573.68i	−1.12865	+	1.95488i
$806$		0			0
$807$	−98.2467	+	24.2626i	−0.121743	+	0.0300652i
$808$		0			0
$809$		−	1065.41i		−	1.31695i	−0.752605	−	0.658473i	$-0.771203\pi$
$809$		−	1065.41i		−	1.31695i	0.752605	−	0.658473i	$-0.228797\pi$
$810$		0			0
$811$	270.922	−	469.251i	0.334059	−	0.578608i	−0.649244	−	0.760580i	$-0.724915\pi$
$811$	270.922	−	469.251i	0.334059	−	0.578608i	0.983304	+	0.181972i	$0.0582481\pi$
$812$		0			0
$813$	127.356	+	515.705i	0.156650	+	0.634323i
$814$		0			0
$815$			1717.56i			2.10743i
$816$		0			0
$817$	173.580	−	927.866i	0.212460	−	1.13570i
$818$		0			0
$819$	−1214.94	+	639.048i	−1.48345	+	0.780279i
$820$		0			0
$821$		−	340.662i		−	0.414936i	−0.978242	−	0.207468i	$-0.933478\pi$
$821$		−	340.662i		−	0.414936i	0.978242	−	0.207468i	$-0.0665222\pi$
$822$		0			0
$823$	532.112	+	921.644i	0.646551	+	1.11986i	0.983941	+	0.178494i	$0.0571227\pi$
$823$	532.112	+	921.644i	0.646551	+	1.11986i	−0.337390	+	0.941365i	$0.609544\pi$
$824$		0			0
$825$	−1375.86	+	339.776i	−1.66771	+	0.411850i
$826$		0			0
$827$	−885.426	−	511.201i	−1.07065	−	0.618139i	−0.142289	−	0.989825i	$-0.545446\pi$
$827$	−885.426	−	511.201i	−1.07065	−	0.618139i	−0.928358	+	0.371686i	$0.878780\pi$
$828$		0			0
$829$	−671.808			−0.810384			−0.405192	−	0.914232i	$-0.632795\pi$
$829$	−671.808			−0.810384			−0.405192	+	0.914232i	$0.632795\pi$
$830$		0			0
$831$	−127.823	−	517.595i	−0.153818	−	0.622858i
$832$		0			0
$833$			111.734i			0.134135i
$834$		0			0
$835$	605.024	+	1047.93i	0.724579	+	1.25501i
$836$		0			0
$837$	1261.92	−	259.399i	1.50767	−	0.309915i
$838$		0			0
$839$	−824.312	−	475.917i	−0.982493	−	0.567243i	−0.0794712	−	0.996837i	$-0.525323\pi$
$839$	−824.312	−	475.917i	−0.982493	−	0.567243i	−0.903022	+	0.429595i	$0.858657\pi$
$840$		0			0
$841$	−77.6109			−0.0922840
$842$		0			0
$843$	280.243	−	969.145i	0.332436	−	1.14964i
$844$		0			0
$845$	−1529.23	−	882.899i	−1.80974	−	1.04485i
$846$		0			0
$847$	1252.99			1.47933
$848$		0			0
$849$	−89.6710	−	25.9297i	−0.105620	−	0.0305415i
$850$		0			0
$851$	723.238	−	417.562i	0.849869	−	0.490672i
$852$		0			0
$853$	−18.4431	+	31.9445i	−0.0216215	+	0.0374495i	−0.876634	−	0.481158i	$-0.840216\pi$
$853$	−18.4431	+	31.9445i	−0.0216215	+	0.0374495i	0.855012	+	0.518608i	$0.173550\pi$
$854$		0			0
$855$	276.518	−	1211.99i	0.323413	−	1.41753i
$856$		0			0
$857$	−393.745	−	227.329i	−0.459446	−	0.265261i	0.252365	−	0.967632i	$-0.418792\pi$
$857$	−393.745	−	227.329i	−0.459446	−	0.265261i	−0.711811	+	0.702371i	$0.752125\pi$
$858$		0			0
$859$	−261.644	−	453.180i	−0.304591	−	0.527567i	0.672579	−	0.740025i	$-0.265187\pi$
$859$	−261.644	−	453.180i	−0.304591	−	0.527567i	−0.977170	+	0.212458i	$0.931853\pi$
$860$		0			0
$861$	110.432	−	27.2719i	0.128261	−	0.0316747i
$862$		0			0
$863$		−	537.201i		−	0.622481i	−0.950331	−	0.311240i	$-0.899256\pi$
$863$		−	537.201i		−	0.622481i	0.950331	−	0.311240i	$-0.100744\pi$
$864$		0			0
$865$	246.283	−	426.574i	0.284720	−	0.493149i
$866$		0			0
$867$	142.826	−	137.310i	0.164736	−	0.158374i
$868$		0			0
$869$			2.54649i			0.00293037i
$870$		0			0
$871$	−11.9471	+	20.6930i	−0.0137165	+	0.0237577i
$872$		0			0
$873$	−753.231	+	396.192i	−0.862807	+	0.453828i
$874$		0			0
$875$	134.841	−	77.8507i	0.154104	−	0.0889722i
$876$		0			0
$877$	731.890			0.834539			0.417269	−	0.908783i	$-0.362987\pi$
$877$	731.890			0.834539			0.417269	+	0.908783i	$0.362987\pi$
$878$		0			0
$879$	−432.953	−	450.346i	−0.492552	−	0.512339i
$880$		0			0
$881$		−	520.652i		−	0.590979i	−0.955346	−	0.295489i	$-0.904517\pi$
$881$		−	520.652i		−	0.590979i	0.955346	−	0.295489i	$-0.0954827\pi$
$882$		0			0
$883$	−492.648	+	853.291i	−0.557925	+	0.966354i	0.439745	+	0.898123i	$0.355069\pi$
$883$	−492.648	+	853.291i	−0.557925	+	0.966354i	−0.997670	+	0.0682312i	$0.978264\pi$
$884$		0			0
$885$	1542.59	+	446.063i	1.74304	+	0.504027i
$886$		0			0
$887$	742.547	−	428.710i	0.837144	−	0.483325i	−0.0191484	−	0.999817i	$-0.506096\pi$
$887$	742.547	−	428.710i	0.837144	−	0.483325i	0.856292	+	0.516491i	$0.172762\pi$
$888$		0			0
$889$	−211.806			−0.238252
$890$		0			0
$891$	−1132.14	−	778.454i	−1.27064	−	0.873685i
$892$		0			0
$893$	394.317	+	1119.48i	0.441565	+	1.25362i
$894$		0			0
$895$	−440.048			−0.491674
$896$		0			0
$897$	−1403.41	−	1459.79i	−1.56456	−	1.62741i
$898$		0			0
$899$	1252.42	+	723.086i	1.39313	+	0.804323i
$900$		0			0
$901$	819.374			0.909406
$902$		0			0
$903$	1076.08	+	311.164i	1.19167	+	0.344590i
$904$		0			0
$905$	1051.17	+	606.894i	1.16151	+	0.670601i
$906$		0			0
$907$	620.439	−	1074.63i	0.684057	−	1.18482i	−0.289676	−	0.957125i	$-0.593547\pi$
$907$	620.439	−	1074.63i	0.684057	−	1.18482i	0.973732	−	0.227696i	$-0.0731192\pi$
$908$		0			0
$909$	407.189	−	645.204i	0.447953	−	0.709795i
$910$		0			0
$911$	−692.109	+	399.589i	−0.759725	+	0.438627i	−0.829197	−	0.558957i	$-0.811202\pi$
$911$	−692.109	+	399.589i	−0.759725	+	0.438627i	0.0694723	+	0.997584i	$0.477868\pi$
$912$		0			0
$913$	410.984	−	711.845i	0.450147	−	0.779677i
$914$		0			0
$915$	−577.667	+	1997.71i	−0.631330	+	2.18328i
$916$		0			0
$917$	1640.74	−	947.283i	1.78925	−	1.03302i
$918$		0			0
$919$	1507.71			1.64060			0.820299	−	0.571934i	$-0.193807\pi$
$919$	1507.71			1.64060			0.820299	+	0.571934i	$0.193807\pi$
$920$		0			0
$921$	−361.722	−	1464.72i	−0.392749	−	1.59036i
$922$		0			0
$923$	−250.966	−	144.895i	−0.271902	−	0.156983i
$924$		0			0
$925$	−699.307			−0.756007
$926$		0			0
$927$	−55.7844	+	29.3420i	−0.0601773	+	0.0316527i
$928$		0			0
$929$	−871.341	−	503.069i	−0.937934	−	0.541516i	−0.0486219	−	0.998817i	$-0.515483\pi$
$929$	−871.341	−	503.069i	−0.937934	−	0.541516i	−0.889312	+	0.457301i	$0.848816\pi$
$930$		0			0
$931$	26.1440	−	139.752i	0.0280816	−	0.150110i
$932$		0			0
$933$	−580.394	−	603.709i	−0.622072	−	0.647062i
$934$		0			0
$935$	−1594.59	−	920.639i	−1.70545	−	0.984640i
$936$		0			0
$937$	−622.963	+	1079.00i	−0.664848	+	1.15155i	0.314478	+	0.949265i	$0.398170\pi$
$937$	−622.963	+	1079.00i	−0.664848	+	1.15155i	−0.979326	+	0.202286i	$0.935163\pi$
$938$		0			0
$939$	326.405	+	94.3849i	0.347609	+	0.100516i
$940$		0			0
$941$	−952.114	+	549.703i	−1.01181	+	0.584169i	−0.911721	−	0.410809i	$-0.865246\pi$
$941$	−952.114	+	549.703i	−1.01181	+	0.584169i	−0.100090	+	0.994978i	$0.531913\pi$
$942$		0			0
$943$	83.8970	+	145.314i	0.0889682	+	0.154097i
$944$		0			0
$945$	1399.89	+	465.250i	1.48136	+	0.492328i
$946$		0			0
$947$	533.426	+	307.974i	0.563280	+	0.325210i	0.754461	−	0.656345i	$-0.227898\pi$
$947$	533.426	+	307.974i	0.563280	+	0.325210i	−0.191181	+	0.981555i	$0.561232\pi$
$948$		0			0
$949$	1208.36	−	2092.94i	1.27329	−	2.20541i
$950$		0			0
$951$	91.1632	−	315.263i	0.0958604	−	0.331507i
$952$		0			0
$953$	447.017	−	258.085i	0.469063	−	0.270814i	−0.246784	−	0.969070i	$-0.579374\pi$
$953$	447.017	−	258.085i	0.469063	−	0.270814i	0.715847	+	0.698257i	$0.246041\pi$
$954$		0			0
$955$	558.356	+	967.101i	0.584666	+	1.01267i
$956$		0			0
$957$	−369.774	−	1497.33i	−0.386389	−	1.56461i
$958$		0			0
$959$	−561.976	+	324.457i	−0.586002	+	0.338328i
$960$		0			0
$961$	−657.858	−	1139.44i	−0.684555	−	1.18568i
$962$		0			0
$963$	470.389	−	745.345i	0.488462	−	0.773983i
$964$		0			0
$965$			1732.41i			1.79524i
$966$		0			0
$967$	864.526			0.894029			0.447014	−	0.894527i	$-0.352487\pi$
$967$	864.526			0.894029			0.447014	+	0.894527i	$0.352487\pi$
$968$		0			0
$969$	711.563	−	466.981i	0.734327	−	0.481920i
$970$		0			0
$971$	−1640.42	+	947.099i	−1.68942	+	0.975386i	−0.734456	+	0.678657i	$0.762562\pi$
$971$	−1640.42	+	947.099i	−1.68942	+	0.975386i	−0.954962	+	0.296729i	$0.904104\pi$
$972$		0			0
$973$	622.037	−	1077.40i	0.639298	−	1.10730i
$974$		0			0
$975$	406.537	+	1646.20i	0.416962	+	1.68841i
$976$		0			0
$977$	−1561.64	−	901.613i	−1.59840	−	0.922838i	−0.991795	−	0.127837i	$-0.959197\pi$
$977$	−1561.64	−	901.613i	−1.59840	−	0.922838i	−0.606608	−	0.795001i	$-0.707470\pi$
$978$		0			0
$979$	−1320.31			−1.34863
$980$		0			0
$981$	−53.4153	+	1355.84i	−0.0544498	+	1.38210i
$982$		0			0
$983$	−345.988	−	199.756i	−0.351972	−	0.203211i	0.313582	−	0.949561i	$-0.398471\pi$
$983$	−345.988	−	199.756i	−0.351972	−	0.203211i	−0.665553	+	0.746350i	$0.731804\pi$
$984$		0			0
$985$	−796.785			−0.808919
$986$		0			0
$987$	−1367.36	+	337.678i	−1.38537	+	0.342126i
$988$		0			0
$989$			1652.37i			1.67074i
$990$		0			0
$991$	479.340	+	830.240i	0.483693	+	0.837780i	0.999825	−	0.0187287i	$-0.00596188\pi$
$991$	479.340	+	830.240i	0.483693	+	0.837780i	−0.516132	+	0.856509i	$0.672629\pi$
$992$		0			0
$993$	72.6908	+	294.348i	0.0732032	+	0.296423i
$994$		0			0
$995$	−1595.26	−	921.023i	−1.60328	−	0.925651i
$996$		0			0
$997$	−1169.13			−1.17265			−0.586326	−	0.810075i	$-0.699426\pi$
$997$	−1169.13			−1.17265			−0.586326	+	0.810075i	$0.699426\pi$
$998$		0			0
$999$	−450.262	−	506.859i	−0.450712	−	0.507366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.653.3	yes	80
3.2	odd	2		2052.3.m.a.881.3		80
9.2	odd	6		684.3.be.a.425.23	yes	80
9.7	even	3		2052.3.be.a.197.3		80
19.11	even	3		684.3.be.a.581.23	yes	80
57.11	odd	6		2052.3.be.a.125.3		80
171.11	odd	6	inner	684.3.m.a.353.3	✓	80
171.106	even	3		2052.3.m.a.1493.38		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.3	✓	80	171.11	odd	6	inner
684.3.m.a.653.3	yes	80	1.1	even	1	trivial
684.3.be.a.425.23	yes	80	9.2	odd	6
684.3.be.a.581.23	yes	80	19.11	even	3
2052.3.m.a.881.3		80	3.2	odd	2
2052.3.m.a.1493.38		80	171.106	even	3
2052.3.be.a.125.3		80	57.11	odd	6
2052.3.be.a.197.3		80	9.7	even	3

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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.88193 - 0.833354i) q^{3} +7.26979i q^{5} +(3.75776 + 6.50863i) q^{7} +(7.61104 + 4.80334i) q^{9} +O(q^{10})\)	\(q+(-2.88193 - 0.833354i) q^{3} +7.26979i q^{5} +(3.75776 + 6.50863i) q^{7} +(7.61104 + 4.80334i) q^{9} +(-14.6898 + 8.48117i) q^{11} +(10.1476 + 17.5762i) q^{13} +(6.05831 - 20.9510i) q^{15} +(12.9313 - 7.46590i) q^{17} +(-17.9208 + 6.31229i) q^{19} +(-5.40560 - 21.8890i) q^{21} +(28.8029 - 16.6293i) q^{23} -27.8498 q^{25} +(-17.9316 - 20.1856i) q^{27} -30.3086i q^{29} +(-23.8575 + 41.3223i) q^{31} +(49.4028 - 12.2003i) q^{33} +(-47.3163 + 27.3181i) q^{35} +25.1099 q^{37} +(-14.5975 - 59.1098i) q^{39} +5.04512i q^{41} +(-24.8411 + 43.0261i) q^{43} +(-34.9192 + 55.3306i) q^{45} -62.4682i q^{47} +(-3.74149 + 6.48044i) q^{49} +(-43.4889 + 10.7398i) q^{51} +(47.5227 + 27.4372i) q^{53} +(-61.6563 - 106.792i) q^{55} +(56.9069 - 3.25720i) q^{57} +73.6284i q^{59} -95.3512 q^{61} +(-2.66269 + 67.5872i) q^{63} +(-127.775 + 73.7709i) q^{65} +(0.588665 + 1.01960i) q^{67} +(-96.8660 + 23.9216i) q^{69} +(-12.3658 + 7.13938i) q^{71} +(-59.5390 - 103.125i) q^{73} +(80.2611 + 23.2087i) q^{75} +(-110.401 - 63.7403i) q^{77} +(0.0750630 - 0.130013i) q^{79} +(34.8559 + 73.1168i) q^{81} +(-41.9662 + 24.2292i) q^{83} +(54.2755 + 94.0079i) q^{85} +(-25.2578 + 87.3472i) q^{87} +(67.4096 + 38.9190i) q^{89} +(-76.2645 + 132.094i) q^{91} +(103.192 - 99.2064i) q^{93} +(-45.8890 - 130.280i) q^{95} +(-47.2818 + 81.8945i) q^{97} +(-152.543 - 6.00963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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