LMFDB - Embedded newform 684.3.m.a.353.7

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			353.7
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.64568 + 1.41435i) q^{3} -6.34957i q^{5} +(-3.73312 + 6.46596i) q^{7} +(4.99921 - 7.48384i) q^{9} +O(q^{10})$	\(q+(-2.64568 + 1.41435i) q^{3} -6.34957i q^{5} +(-3.73312 + 6.46596i) q^{7} +(4.99921 - 7.48384i) q^{9} +(-4.85076 - 2.80059i) q^{11} +(-2.59582 + 4.49610i) q^{13} +(8.98053 + 16.7989i) q^{15} +(-10.9238 - 6.30688i) q^{17} +(18.2190 - 5.39160i) q^{19} +(0.731488 - 22.3868i) q^{21} +(-22.3510 - 12.9044i) q^{23} -15.3170 q^{25} +(-2.64150 + 26.8705i) q^{27} +9.16161i q^{29} +(23.3648 + 40.4690i) q^{31} +(16.7946 + 0.548762i) q^{33} +(41.0560 + 23.7037i) q^{35} +46.3137 q^{37} +(0.508639 - 15.5666i) q^{39} -26.3532i q^{41} +(27.9247 + 48.3669i) q^{43} +(-47.5192 - 31.7428i) q^{45} +20.4907i q^{47} +(-3.37239 - 5.84114i) q^{49} +(37.8211 + 1.23580i) q^{51} +(-45.9725 + 26.5422i) q^{53} +(-17.7825 + 30.8003i) q^{55} +(-40.5759 + 40.0325i) q^{57} +20.6874i q^{59} -35.4492 q^{61} +(29.7275 + 60.2628i) q^{63} +(28.5483 + 16.4823i) q^{65} +(-53.7493 + 93.0966i) q^{67} +(77.3849 + 2.52855i) q^{69} +(74.9285 + 43.2600i) q^{71} +(-25.3385 + 43.8876i) q^{73} +(40.5239 - 21.6637i) q^{75} +(36.2170 - 20.9099i) q^{77} +(20.8830 + 36.1704i) q^{79} +(-31.0158 - 74.8266i) q^{81} +(90.2997 + 52.1346i) q^{83} +(-40.0459 + 69.3616i) q^{85} +(-12.9577 - 24.2387i) q^{87} +(32.7765 - 18.9235i) q^{89} +(-19.3810 - 33.5689i) q^{91} +(-119.053 - 74.0219i) q^{93} +(-34.2343 - 115.683i) q^{95} +(81.1072 + 140.482i) q^{97} +(-45.2092 + 22.3016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−2.64568	+	1.41435i	−0.881892	+	0.471451i
$3$	−2.64568	+	1.41435i	−0.881892	+	0.471451i
$4$		0			0
$5$		−	6.34957i		−	1.26991i	−0.772548	−	0.634957i	$-0.781018\pi$
$5$		−	6.34957i		−	1.26991i	0.772548	−	0.634957i	$-0.218982\pi$
$6$		0			0
$7$	−3.73312	+	6.46596i	−0.533303	+	0.923708i	0.465940	+	0.884816i	$0.345716\pi$
$7$	−3.73312	+	6.46596i	−0.533303	+	0.923708i	−0.999243	+	0.0388918i	$0.987617\pi$
$8$		0			0
$9$	4.99921	−	7.48384i	0.555468	−	0.831538i
$10$		0			0
$11$	−4.85076	−	2.80059i	−0.440978	−	0.254599i	0.263034	−	0.964787i	$-0.415277\pi$
$11$	−4.85076	−	2.80059i	−0.440978	−	0.254599i	−0.704013	+	0.710187i	$0.748610\pi$
$12$		0			0
$13$	−2.59582	+	4.49610i	−0.199679	+	0.345853i	−0.948424	−	0.317004i	$-0.897323\pi$
$13$	−2.59582	+	4.49610i	−0.199679	+	0.345853i	0.748746	+	0.662857i	$0.230656\pi$
$14$		0			0
$15$	8.98053	+	16.7989i	0.598702	+	1.11993i
$16$		0			0
$17$	−10.9238	−	6.30688i	−0.642578	−	0.370993i	0.143029	−	0.989719i	$-0.454316\pi$
$17$	−10.9238	−	6.30688i	−0.642578	−	0.370993i	−0.785607	+	0.618726i	$0.787649\pi$
$18$		0			0
$19$	18.2190	−	5.39160i	0.958893	−	0.283768i
$19$	18.2190	−	5.39160i	0.958893	−	0.283768i
$20$		0			0
$21$	0.731488	−	22.3868i	0.0348327	−	1.06604i
$22$		0			0
$23$	−22.3510	−	12.9044i	−0.971784	−	0.561060i	−0.0720043	−	0.997404i	$-0.522940\pi$
$23$	−22.3510	−	12.9044i	−0.971784	−	0.561060i	−0.899780	+	0.436345i	$0.856273\pi$
$24$		0			0
$25$	−15.3170			−0.612681
$26$		0			0
$27$	−2.64150	+	26.8705i	−0.0978333	+	0.995203i
$28$		0			0
$29$			9.16161i			0.315918i	0.987446	+	0.157959i	$0.0504913\pi$
$29$			9.16161i			0.315918i	−0.987446	+	0.157959i	$0.949509\pi$
$30$		0			0
$31$	23.3648	+	40.4690i	0.753703	+	1.30545i	0.946016	+	0.324119i	$0.105068\pi$
$31$	23.3648	+	40.4690i	0.753703	+	1.30545i	−0.192313	+	0.981334i	$0.561599\pi$
$32$		0			0
$33$	16.7946	+	0.548762i	0.508926	+	0.0166292i
$34$		0			0
$35$	41.0560	+	23.7037i	1.17303	+	0.677249i
$36$		0			0
$37$	46.3137			1.25172			0.625860	−	0.779935i	$-0.284748\pi$
$37$	46.3137			1.25172			0.625860	+	0.779935i	$0.284748\pi$
$38$		0			0
$39$	0.508639	−	15.5666i	0.0130420	−	0.399144i
$40$		0			0
$41$		−	26.3532i		−	0.642761i	−0.946950	−	0.321380i	$-0.895853\pi$
$41$		−	26.3532i		−	0.642761i	0.946950	−	0.321380i	$-0.104147\pi$
$42$		0			0
$43$	27.9247	+	48.3669i	0.649411	+	1.12481i	0.983264	+	0.182187i	$0.0583177\pi$
$43$	27.9247	+	48.3669i	0.649411	+	1.12481i	−0.333853	+	0.942625i	$0.608349\pi$
$44$		0			0
$45$	−47.5192	−	31.7428i	−1.05598	−	0.705396i
$46$		0			0
$47$			20.4907i			0.435972i	0.975952	+	0.217986i	$0.0699487\pi$
$47$			20.4907i			0.435972i	−0.975952	+	0.217986i	$0.930051\pi$
$48$		0			0
$49$	−3.37239	−	5.84114i	−0.0688242	−	0.119207i
$50$		0			0
$51$	37.8211	+	1.23580i	0.741590	+	0.0242314i
$52$		0			0
$53$	−45.9725	+	26.5422i	−0.867406	+	0.500797i	−0.866485	−	0.499203i	$-0.833626\pi$
$53$	−45.9725	+	26.5422i	−0.867406	+	0.500797i	−0.000920543		1.00000i	$0.500293\pi$
$54$		0			0
$55$	−17.7825	+	30.8003i	−0.323319	+	0.560005i
$56$		0			0
$57$	−40.5759	+	40.0325i	−0.711857	+	0.702324i
$58$		0			0
$59$			20.6874i			0.350634i	0.984512	+	0.175317i	$0.0560951\pi$
$59$			20.6874i			0.350634i	−0.984512	+	0.175317i	$0.943905\pi$
$60$		0			0
$61$	−35.4492			−0.581134			−0.290567	−	0.956855i	$-0.593844\pi$
$61$	−35.4492			−0.581134			−0.290567	+	0.956855i	$0.593844\pi$
$62$		0			0
$63$	29.7275	+	60.2628i	0.471866	+	0.956552i
$64$		0			0
$65$	28.5483	+	16.4823i	0.439204	+	0.253575i
$66$		0			0
$67$	−53.7493	+	93.0966i	−0.802229	+	1.38950i	0.115917	+	0.993259i	$0.463019\pi$
$67$	−53.7493	+	93.0966i	−0.802229	+	1.38950i	−0.918146	+	0.396242i	$0.870314\pi$
$68$		0			0
$69$	77.3849	+	2.52855i	1.12152	+	0.0366457i
$70$		0			0
$71$	74.9285	+	43.2600i	1.05533	+	0.609296i	0.924137	−	0.382061i	$-0.124786\pi$
$71$	74.9285	+	43.2600i	1.05533	+	0.609296i	0.131194	+	0.991357i	$0.458119\pi$
$72$		0			0
$73$	−25.3385	+	43.8876i	−0.347103	+	0.601200i	−0.985734	−	0.168313i	$-0.946168\pi$
$73$	−25.3385	+	43.8876i	−0.347103	+	0.601200i	0.638630	+	0.769514i	$0.279501\pi$
$74$		0			0
$75$	40.5239	−	21.6637i	0.540318	−	0.288849i
$76$		0			0
$77$	36.2170	−	20.9099i	0.470350	−	0.271557i
$78$		0			0
$79$	20.8830	+	36.1704i	0.264342	+	0.457853i	0.967391	−	0.253288i	$-0.0815120\pi$
$79$	20.8830	+	36.1704i	0.264342	+	0.457853i	−0.703049	+	0.711141i	$0.748179\pi$
$80$		0			0
$81$	−31.0158	−	74.8266i	−0.382911	−	0.923785i
$82$		0			0
$83$	90.2997	+	52.1346i	1.08795	+	0.628127i	0.933029	−	0.359800i	$-0.117155\pi$
$83$	90.2997	+	52.1346i	1.08795	+	0.628127i	0.154919	+	0.987927i	$0.450488\pi$
$84$		0			0
$85$	−40.0459	+	69.3616i	−0.471129	+	0.816019i
$86$		0			0
$87$	−12.9577	−	24.2387i	−0.148940	−	0.278605i
$88$		0			0
$89$	32.7765	−	18.9235i	0.368276	−	0.212624i	−0.304429	−	0.952535i	$-0.598466\pi$
$89$	32.7765	−	18.9235i	0.368276	−	0.212624i	0.672705	+	0.739911i	$0.265132\pi$
$90$		0			0
$91$	−19.3810	−	33.5689i	−0.212978	−	0.368889i
$92$		0			0
$93$	−119.053	−	74.0219i	−1.28014	−	0.795934i
$94$		0			0
$95$	−34.2343	−	115.683i	−0.360361	−	1.21771i
$96$		0			0
$97$	81.1072	+	140.482i	0.836157	+	1.44827i	0.893085	+	0.449888i	$0.148536\pi$
$97$	81.1072	+	140.482i	0.836157	+	1.44827i	−0.0569277	+	0.998378i	$0.518130\pi$
$98$		0			0
$99$	−45.2092	+	22.3016i	−0.456658	+	0.225269i
$100$		0			0
$101$			185.798i			1.83958i	0.392406	+	0.919792i	$0.371643\pi$
$101$			185.798i			1.83958i	−0.392406	+	0.919792i	$0.628357\pi$
$102$		0			0
$103$	−89.3215	−	154.709i	−0.867199	−	1.50203i	−0.864847	−	0.502035i	$-0.832585\pi$
$103$	−89.3215	−	154.709i	−0.867199	−	1.50203i	−0.00235139	−	0.999997i	$-0.500748\pi$
$104$		0			0
$105$	−142.146	−	4.64463i	−1.35378	−	0.0442346i
$106$		0			0
$107$			143.064i			1.33705i	0.743690	+	0.668524i	$0.233074\pi$
$107$			143.064i			1.33705i	−0.743690	+	0.668524i	$0.766926\pi$
$108$		0			0
$109$	−13.3471	+	23.1179i	−0.122451	+	0.212091i	−0.920734	−	0.390192i	$-0.872409\pi$
$109$	−13.3471	+	23.1179i	−0.122451	+	0.212091i	0.798283	+	0.602283i	$0.205742\pi$
$110$		0			0
$111$	−122.531	+	65.5039i	−1.10388	+	0.590125i
$112$		0			0
$113$	113.859	−	65.7363i	1.00760	−	0.581737i	0.0971109	−	0.995274i	$-0.469040\pi$
$113$	113.859	−	65.7363i	1.00760	−	0.581737i	0.910488	+	0.413536i	$0.135707\pi$
$114$		0			0
$115$	−81.9372	+	141.919i	−0.712497	+	1.23408i
$116$		0			0
$117$	20.6710	+	41.9036i	0.176675	+	0.358151i
$118$		0			0
$119$	81.5599	−	47.0887i	0.685378	−	0.395703i
$120$		0			0
$121$	−44.8134	−	77.6191i	−0.370359	−	0.641480i
$122$		0			0
$123$	37.2727	+	69.7220i	0.303030	+	0.566846i
$124$		0			0
$125$		−	61.4828i		−	0.491862i
$126$		0			0
$127$	−45.9185	−	79.5332i	−0.361563	−	0.626245i	0.626655	−	0.779297i	$-0.284423\pi$
$127$	−45.9185	−	79.5332i	−0.361563	−	0.626245i	−0.988218	+	0.153051i	$0.951090\pi$
$128$		0			0
$129$	−142.288	−	88.4679i	−1.10300	−	0.685798i
$130$		0			0
$131$			6.77581i			0.0517237i	0.999666	+	0.0258619i	$0.00823300\pi$
$131$			6.77581i			0.0517237i	−0.999666	+	0.0258619i	$0.991767\pi$
$132$		0			0
$133$	−33.1518	+	137.931i	−0.249261	+	1.03707i
$134$		0			0
$135$	170.616	+	16.7724i	1.26382	+	0.124240i
$136$		0			0
$137$		−	18.8796i		−	0.137807i	−0.997623	−	0.0689037i	$-0.978050\pi$
$137$		−	18.8796i		−	0.137807i	0.997623	−	0.0689037i	$-0.0219501\pi$
$138$		0			0
$139$	111.807	−	193.656i	0.804369	−	1.39321i	−0.112347	−	0.993669i	$-0.535837\pi$
$139$	111.807	−	193.656i	0.804369	−	1.39321i	0.916716	−	0.399539i	$-0.130830\pi$
$140$		0			0
$141$	−28.9811	−	54.2117i	−0.205539	−	0.384480i
$142$		0			0
$143$	25.1834	−	14.5397i	0.176108	−	0.101676i
$144$		0			0
$145$	58.1723			0.401188
$146$		0			0
$147$	17.1837	+	10.6840i	0.116896	+	0.0726805i
$148$		0			0
$149$		−	32.8124i		−	0.220218i	−0.993920	−	0.110109i	$-0.964880\pi$
$149$		−	32.8124i		−	0.220218i	0.993920	−	0.110109i	$-0.0351200\pi$
$150$		0			0
$151$	57.6278	−	99.8143i	0.381641	−	0.661022i	−0.609656	−	0.792666i	$-0.708692\pi$
$151$	57.6278	−	99.8143i	0.381641	−	0.661022i	0.991297	+	0.131644i	$0.0420256\pi$
$152$		0			0
$153$	−101.810	+	50.2228i	−0.665426	+	0.328254i
$154$		0			0
$155$	256.961	−	148.356i	1.65781	−	0.957138i
$156$		0			0
$157$	−17.2911			−0.110134			−0.0550672	−	0.998483i	$-0.517537\pi$
$157$	−17.2911			−0.110134			−0.0550672	+	0.998483i	$0.517537\pi$
$158$		0			0
$159$	84.0883	−	135.244i	0.528857	−	0.850588i
$160$		0			0
$161$	166.878	−	96.3472i	1.03651	−	0.598430i
$162$		0			0
$163$	−149.764			−0.918798			−0.459399	−	0.888230i	$-0.651935\pi$
$163$	−149.764			−0.918798			−0.459399	+	0.888230i	$0.651935\pi$
$164$		0			0
$165$	3.48440	−	106.638i	0.0211176	−	0.646293i
$166$		0			0
$167$	34.6487	+	20.0044i	0.207477	+	0.119787i	0.600138	−	0.799896i	$-0.295112\pi$
$167$	34.6487	+	20.0044i	0.207477	+	0.119787i	−0.392661	+	0.919683i	$0.628446\pi$
$168$		0			0
$169$	71.0234	+	123.016i	0.420257	+	0.727906i
$170$		0			0
$171$	50.7306	−	163.302i	0.296670	−	0.954980i
$172$		0			0
$173$	−44.8672	+	25.9041i	−0.259348	+	0.149735i	−0.624037	−	0.781395i	$-0.714509\pi$
$173$	−44.8672	+	25.9041i	−0.259348	+	0.149735i	0.364689	+	0.931129i	$0.381175\pi$
$174$		0			0
$175$	57.1803	−	99.0392i	0.326744	−	0.565938i
$176$		0			0
$177$	−29.2593	−	54.7322i	−0.165307	−	0.309222i
$178$		0			0
$179$		−	246.793i		−	1.37873i	−0.724413	−	0.689366i	$-0.757889\pi$
$179$		−	246.793i		−	1.37873i	0.724413	−	0.689366i	$-0.242111\pi$
$180$		0			0
$181$	−7.45828	−	12.9181i	−0.0412060	−	0.0713709i	0.844687	−	0.535261i	$-0.179787\pi$
$181$	−7.45828	−	12.9181i	−0.0412060	−	0.0713709i	−0.885893	+	0.463890i	$0.846453\pi$
$182$		0			0
$183$	93.7871	−	50.1377i	0.512498	−	0.273976i
$184$		0			0
$185$		−	294.072i		−	1.58958i
$186$		0			0
$187$	35.3259	+	61.1863i	0.188909	+	0.327200i
$188$		0			0
$189$	−163.882	−	117.391i	−0.867102	−	0.621114i
$190$		0			0
$191$	221.125	+	127.667i	1.15772	+	0.668412i	0.950758	−	0.309936i	$-0.100307\pi$
$191$	221.125	+	127.667i	1.15772	+	0.668412i	0.206967	+	0.978348i	$0.433641\pi$
$192$		0			0
$193$	110.136			0.570653			0.285326	−	0.958430i	$-0.407898\pi$
$193$	110.136			0.570653			0.285326	+	0.958430i	$0.407898\pi$
$194$		0			0
$195$	−98.8413	−	3.22964i	−0.506879	−	0.0165623i
$196$		0			0
$197$			237.875i			1.20749i	0.797178	+	0.603744i	$0.206325\pi$
$197$			237.875i			1.20749i	−0.797178	+	0.603744i	$0.793675\pi$
$198$		0			0
$199$	41.7395	+	72.2950i	0.209746	+	0.363291i	0.951635	−	0.307232i	$-0.0994029\pi$
$199$	41.7395	+	72.2950i	0.209746	+	0.363291i	−0.741888	+	0.670524i	$0.766070\pi$
$200$		0			0
$201$	10.5319	−	322.324i	0.0523977	−	1.60360i
$202$		0			0
$203$	−59.2386	−	34.2014i	−0.291816	−	0.168480i
$204$		0			0
$205$	−167.331			−0.816251
$206$		0			0
$207$	−208.312	+	102.760i	−1.00634	+	0.496425i
$208$		0			0
$209$	−103.476	−	24.8705i	−0.495098	−	0.118997i
$210$		0			0
$211$	96.3856			0.456804			0.228402	−	0.973567i	$-0.426650\pi$
$211$	96.3856			0.456804			0.228402	+	0.973567i	$0.426650\pi$
$212$		0			0
$213$	−259.421	−	8.47659i	−1.21794	−	0.0397962i
$214$		0			0
$215$	307.109	−	177.310i	1.42841	−	0.824696i
$216$		0			0
$217$	−348.895			−1.60781
$218$		0			0
$219$	4.96497	−	151.950i	0.0226711	−	0.693836i
$220$		0			0
$221$	56.7126	−	32.7430i	0.256618	−	0.148159i
$222$		0			0
$223$	−20.9762	−	36.3319i	−0.0940637	−	0.162923i	0.815154	−	0.579245i	$-0.196652\pi$
$223$	−20.9762	−	36.3319i	−0.0940637	−	0.162923i	−0.909217	+	0.416322i	$0.863319\pi$
$224$		0			0
$225$	−76.5730	+	114.630i	−0.340324	+	0.509467i
$226$		0			0
$227$	−249.167	−	143.857i	−1.09765	−	0.633731i	−0.162050	−	0.986783i	$-0.551811\pi$
$227$	−249.167	−	143.857i	−1.09765	−	0.633731i	−0.935604	+	0.353052i	$0.885144\pi$
$228$		0			0
$229$	46.6191	+	80.7466i	0.203577	+	0.352605i	0.949678	−	0.313227i	$-0.101410\pi$
$229$	46.6191	+	80.7466i	0.203577	+	0.352605i	−0.746102	+	0.665832i	$0.768077\pi$
$230$		0			0
$231$	−66.2445	+	106.544i	−0.286773	+	0.461231i
$232$		0			0
$233$	−55.4506	−	32.0144i	−0.237986	−	0.137401i	0.376265	−	0.926512i	$-0.377208\pi$
$233$	−55.4506	−	32.0144i	−0.237986	−	0.137401i	−0.614251	+	0.789111i	$0.710542\pi$
$234$		0			0
$235$	130.107			0.553647
$236$		0			0
$237$	−106.407	−	66.1593i	−0.448976	−	0.279153i
$238$		0			0
$239$	−28.1997	+	16.2811i	−0.117990	+	0.0681217i	−0.557834	−	0.829953i	$-0.688367\pi$
$239$	−28.1997	+	16.2811i	−0.117990	+	0.0681217i	0.439843	+	0.898075i	$0.355034\pi$
$240$		0			0
$241$	−27.7563			−0.115171			−0.0575857	−	0.998341i	$-0.518340\pi$
$241$	−27.7563			−0.115171			−0.0575857	+	0.998341i	$0.518340\pi$
$242$		0			0
$243$	187.889	+	154.100i	0.773206	+	0.634155i
$244$		0			0
$245$	−37.0887	+	21.4132i	−0.151383	+	0.0874008i
$246$		0			0
$247$	−23.0520	+	95.9098i	−0.0933281	+	0.388299i
$248$		0			0
$249$	−312.640	−	10.2155i	−1.25558	−	0.0410262i
$250$		0			0
$251$	−234.569	+	135.428i	−0.934537	+	0.539555i	−0.888244	−	0.459373i	$-0.848074\pi$
$251$	−234.569	+	135.428i	−0.934537	+	0.539555i	−0.0462932	+	0.998928i	$0.514741\pi$
$252$		0			0
$253$	72.2797	+	125.192i	0.285691	+	0.494831i
$254$		0			0
$255$	7.84681	−	240.147i	0.0307718	−	0.941755i
$256$		0			0
$257$	−402.613	−	232.449i	−1.56659	−	0.904469i	−0.996563	−	0.0828408i	$-0.973601\pi$
$257$	−402.613	−	232.449i	−1.56659	−	0.904469i	−0.570024	−	0.821628i	$-0.693066\pi$
$258$		0			0
$259$	−172.894	+	299.462i	−0.667546	+	1.15622i
$260$		0			0
$261$	68.5640	+	45.8008i	0.262697	+	0.175482i
$262$		0			0
$263$	−318.571	+	183.927i	−1.21130	+	0.699342i	−0.963042	−	0.269353i	$-0.913190\pi$
$263$	−318.571	+	183.927i	−1.21130	+	0.699342i	−0.248254	+	0.968695i	$0.579857\pi$
$264$		0			0
$265$	168.532	+	291.906i	0.635969	+	1.10153i
$266$		0			0
$267$	−59.9515	+	96.4232i	−0.224538	+	0.361135i
$268$		0			0
$269$	154.326	+	89.1001i	0.573702	+	0.331227i	0.758627	−	0.651526i	$-0.225871\pi$
$269$	154.326	+	89.1001i	0.573702	+	0.331227i	−0.184925	+	0.982753i	$0.559204\pi$
$270$		0			0
$271$	−127.792	+	221.342i	−0.471558	+	0.816762i	−0.999471	−	0.0325367i	$-0.989641\pi$
$271$	−127.792	+	221.342i	−0.471558	+	0.816762i	0.527913	+	0.849299i	$0.322975\pi$
$272$		0			0
$273$	98.7543	+	61.4009i	0.361737	+	0.224912i
$274$		0			0
$275$	74.2992	+	42.8967i	0.270179	+	0.155988i
$276$		0			0
$277$	148.439	−	257.103i	0.535880	−	0.928171i	−0.463241	−	0.886233i	$-0.653313\pi$
$277$	148.439	−	257.103i	0.535880	−	0.928171i	0.999120	−	0.0419380i	$-0.0133532\pi$
$278$		0			0
$279$	419.669	+	27.4547i	1.50419	+	0.0984039i
$280$		0			0
$281$		−	95.4738i		−	0.339764i	−0.985464	−	0.169882i	$-0.945661\pi$
$281$		−	95.4738i		−	0.339764i	0.985464	−	0.169882i	$-0.0543387\pi$
$282$		0			0
$283$	−169.157			−0.597727			−0.298864	−	0.954296i	$-0.596608\pi$
$283$	−169.157			−0.597727			−0.298864	+	0.954296i	$0.596608\pi$
$284$		0			0
$285$	254.189	+	257.639i	0.891891	+	0.903997i
$286$		0			0
$287$	170.399	+	98.3797i	0.593723	+	0.342786i
$288$		0			0
$289$	−64.9467	−	112.491i	−0.224729	−	0.389242i
$290$		0			0
$291$	−413.274	−	256.955i	−1.42019	−	0.883008i
$292$		0			0
$293$	25.7450	−	14.8639i	0.0878669	−	0.0507300i	−0.455423	−	0.890275i	$-0.650512\pi$
$293$	25.7450	−	14.8639i	0.0878669	−	0.0507300i	0.543290	+	0.839545i	$0.317179\pi$
$294$		0			0
$295$	131.356			0.445275
$296$		0			0
$297$	88.0665	−	122.945i	0.296520	−	0.413955i
$298$		0			0
$299$	116.039	−	66.9949i	0.388089	−	0.224063i
$300$		0			0
$301$	−416.985			−1.38533
$302$		0			0
$303$	−262.784	−	491.561i	−0.867274	−	1.62231i
$304$		0			0
$305$			225.087i			0.737990i
$306$		0			0
$307$	−175.632	+	304.203i	−0.572090	+	0.990889i	0.424261	+	0.905540i	$0.360534\pi$
$307$	−175.632	+	304.203i	−0.572090	+	0.990889i	−0.996351	+	0.0853488i	$0.972800\pi$
$308$		0			0
$309$	455.129	+	282.979i	1.47291	+	0.915789i
$310$		0			0
$311$	62.2618	−	35.9469i	0.200199	−	0.115585i	−0.396549	−	0.918013i	$-0.629792\pi$
$311$	62.2618	−	35.9469i	0.200199	−	0.115585i	0.596748	+	0.802429i	$0.296459\pi$
$312$		0			0
$313$	394.525			1.26046			0.630231	−	0.776408i	$-0.282960\pi$
$313$	394.525			1.26046			0.630231	+	0.776408i	$0.282960\pi$
$314$		0			0
$315$	382.643	−	188.757i	1.21474	−	0.599229i
$316$		0			0
$317$		−	400.928i		−	1.26476i	−0.774660	−	0.632378i	$-0.782079\pi$
$317$		−	400.928i		−	1.26476i	0.774660	−	0.632378i	$-0.217921\pi$
$318$		0			0
$319$	25.6579	−	44.4408i	0.0804323	−	0.139313i
$320$		0			0
$321$	−202.343	−	378.502i	−0.630353	−	1.17913i
$322$		0			0
$323$	−233.025	−	56.0078i	−0.721440	−	0.173399i
$324$		0			0
$325$	39.7603	−	68.8668i	0.122339	−	0.211898i
$326$		0			0
$327$	2.61531	−	80.0401i	0.00799789	−	0.244771i
$328$		0			0
$329$	−132.492	−	76.4942i	−0.402711	−	0.232505i
$330$		0			0
$331$	−67.5617	+	117.020i	−0.204114	+	0.353536i	−0.949850	−	0.312706i	$-0.898765\pi$
$331$	−67.5617	+	117.020i	−0.204114	+	0.353536i	0.745736	+	0.666241i	$0.232098\pi$
$332$		0			0
$333$	231.532	−	346.604i	0.695290	−	1.04085i
$334$		0			0
$335$	591.123	+	341.285i	1.76455	+	1.01876i
$336$		0			0
$337$	128.296			0.380701			0.190350	−	0.981716i	$-0.439038\pi$
$337$	128.296			0.380701			0.190350	+	0.981716i	$0.439038\pi$
$338$		0			0
$339$	−208.259	+	334.953i	−0.614333	+	0.988063i
$340$		0			0
$341$		−	261.741i		−	0.767569i
$342$		0			0
$343$	−315.488			−0.919789
$344$		0			0
$345$	16.0552	−	491.361i	0.0465368	−	1.42423i
$346$		0			0
$347$		−	251.966i		−	0.726127i	−0.931764	−	0.363063i	$-0.881731\pi$
$347$		−	251.966i		−	0.726127i	0.931764	−	0.363063i	$-0.118269\pi$
$348$		0			0
$349$	−69.2104	+	119.876i	−0.198310	+	0.343484i	−0.947981	−	0.318328i	$-0.896879\pi$
$349$	−69.2104	+	119.876i	−0.198310	+	0.343484i	0.749670	+	0.661812i	$0.230212\pi$
$350$		0			0
$351$	−113.955	−	81.6274i	−0.324659	−	0.232557i
$352$		0			0
$353$	105.800	+	61.0837i	0.299717	+	0.173042i	0.642316	−	0.766440i	$-0.277974\pi$
$353$	105.800	+	61.0837i	0.299717	+	0.173042i	−0.342599	+	0.939482i	$0.611307\pi$
$354$		0			0
$355$	274.682	−	475.764i	0.773753	−	1.34018i
$356$		0			0
$357$	−149.181	+	239.936i	−0.417875	+	0.672089i
$358$		0			0
$359$	469.734	+	271.201i	1.30845	+	0.755434i	0.981838	−	0.189724i	$-0.0607592\pi$
$359$	469.734	+	271.201i	1.30845	+	0.755434i	0.326613	+	0.945158i	$0.394093\pi$
$360$		0			0
$361$	302.861	−	196.459i	0.838951	−	0.544207i
$362$		0			0
$363$	228.343	+	141.973i	0.629043	+	0.391110i
$364$		0			0
$365$	278.667	+	160.889i	0.763472	+	0.440791i
$366$		0			0
$367$	24.7886			0.0675440			0.0337720	−	0.999430i	$-0.489248\pi$
$367$	24.7886			0.0675440			0.0337720	+	0.999430i	$0.489248\pi$
$368$		0			0
$369$	−197.223	−	131.745i	−0.534480	−	0.357033i
$370$		0			0
$371$		−	396.342i		−	1.06831i
$372$		0			0
$373$	328.888	+	569.650i	0.881736	+	1.52721i	0.849410	+	0.527734i	$0.176958\pi$
$373$	328.888	+	569.650i	0.881736	+	1.52721i	0.0323264	+	0.999477i	$0.489708\pi$
$374$		0			0
$375$	86.9583	+	162.663i	0.231889	+	0.433769i
$376$		0			0
$377$	−41.1915	−	23.7819i	−0.109261	−	0.0630820i
$378$		0			0
$379$	−352.306			−0.929567			−0.464784	−	0.885424i	$-0.653868\pi$
$379$	−352.306			−0.929567			−0.464784	+	0.885424i	$0.653868\pi$
$380$		0			0
$381$	233.973	+	145.474i	0.614104	+	0.381822i
$382$		0			0
$383$			665.936i			1.73874i	0.494166	+	0.869368i	$0.335474\pi$
$383$			665.936i			1.73874i	−0.494166	+	0.869368i	$0.664526\pi$
$384$		0			0
$385$	−132.769	−	229.962i	−0.344854	−	0.597304i
$386$		0			0
$387$	501.572	+	32.8127i	1.29605	+	0.0847874i
$388$		0			0
$389$			348.817i			0.896703i	0.893857	+	0.448352i	$0.147989\pi$
$389$			348.817i			0.896703i	−0.893857	+	0.448352i	$0.852011\pi$
$390$		0			0
$391$	162.773	+	281.930i	0.416298	+	0.721049i
$392$		0			0
$393$	−9.58339	−	17.9266i	−0.0243852	−	0.0456148i
$394$		0			0
$395$	229.667	−	132.598i	0.581434	−	0.335691i
$396$		0			0
$397$	−318.706	+	552.015i	−0.802787	+	1.39047i	0.114989	+	0.993367i	$0.463317\pi$
$397$	−318.706	+	552.015i	−0.802787	+	1.39047i	−0.917775	+	0.397100i	$0.870016\pi$
$398$		0			0
$399$	−107.374	−	411.808i	−0.269107	−	1.03210i
$400$		0			0
$401$		−	256.162i		−	0.638807i	−0.947619	−	0.319404i	$-0.896517\pi$
$401$		−	256.162i		−	0.638807i	0.947619	−	0.319404i	$-0.103483\pi$
$402$		0			0
$403$	−242.603			−0.601994
$404$		0			0
$405$	−475.117	+	196.937i	−1.17313	+	0.486264i
$406$		0			0
$407$	−224.657	−	129.706i	−0.551982	−	0.318687i
$408$		0			0
$409$	−261.426	+	452.803i	−0.639183	+	1.10710i	0.346429	+	0.938076i	$0.387394\pi$
$409$	−261.426	+	452.803i	−0.639183	+	1.10710i	−0.985612	+	0.169022i	$0.945939\pi$
$410$		0			0
$411$	26.7024	+	49.9493i	0.0649694	+	0.121531i
$412$		0			0
$413$	−133.764	−	77.2287i	−0.323884	−	0.186994i
$414$		0			0
$415$	331.032	−	573.364i	0.797667	−	1.38160i
$416$		0			0
$417$	−21.9081	+	670.486i	−0.0525375	+	1.60788i
$418$		0			0
$419$	69.0044	−	39.8397i	0.164688	−	0.0950828i	−0.415391	−	0.909643i	$-0.636355\pi$
$419$	69.0044	−	39.8397i	0.164688	−	0.0950828i	0.580079	+	0.814560i	$0.303022\pi$
$420$		0			0
$421$	−124.880	−	216.298i	−0.296627	−	0.513773i	0.678735	−	0.734383i	$-0.262528\pi$
$421$	−124.880	−	216.298i	−0.296627	−	0.513773i	−0.975362	+	0.220610i	$0.929195\pi$
$422$		0			0
$423$	153.349	+	102.437i	0.362527	+	0.242168i
$424$		0			0
$425$	167.320	+	96.6025i	0.393695	+	0.227300i
$426$		0			0
$427$	132.336	−	229.213i	0.309921	−	0.536798i
$428$		0			0
$429$	−46.0630	+	74.0855i	−0.107373	+	0.172694i
$430$		0			0
$431$	−362.196	+	209.114i	−0.840362	+	0.485183i	−0.857387	−	0.514672i	$-0.827914\pi$
$431$	−362.196	+	209.114i	−0.840362	+	0.485183i	0.0170255	+	0.999855i	$0.494580\pi$
$432$		0			0
$433$	43.8115	+	75.8837i	0.101181	+	0.175251i	0.912172	−	0.409808i	$-0.134404\pi$
$433$	43.8115	+	75.8837i	0.101181	+	0.175251i	−0.810990	+	0.585060i	$0.801071\pi$
$434$		0			0
$435$	−153.905	+	82.2761i	−0.353805	+	0.189140i
$436$		0			0
$437$	−476.788	−	114.597i	−1.09105	−	0.262235i
$438$		0			0
$439$	−82.6557	−	143.164i	−0.188282	−	0.326114i	0.756396	−	0.654114i	$-0.226958\pi$
$439$	−82.6557	−	143.164i	−0.188282	−	0.326114i	−0.944677	+	0.328001i	$0.893625\pi$
$440$		0			0
$441$	−60.5735	−	3.96270i	−0.137355	−	0.00898573i
$442$		0			0
$443$			772.675i			1.74419i	0.489339	+	0.872094i	$0.337238\pi$
$443$			772.675i			1.74419i	−0.489339	+	0.872094i	$0.662762\pi$
$444$		0			0
$445$	−120.156	−	208.117i	−0.270014	−	0.467678i
$446$		0			0
$447$	46.4084	+	86.8111i	0.103822	+	0.194208i
$448$		0			0
$449$		−	14.1079i		−	0.0314208i	−0.999877	−	0.0157104i	$-0.994999\pi$
$449$		−	14.1079i		−	0.0314208i	0.999877	−	0.0157104i	$-0.00500097\pi$
$450$		0			0
$451$	−73.8045	+	127.833i	−0.163646	+	0.283444i
$452$		0			0
$453$	−11.2919	+	345.583i	−0.0249269	+	0.762875i
$454$		0			0
$455$	−213.148	+	123.061i	−0.468458	+	0.270464i
$456$		0			0
$457$	337.400	−	584.395i	0.738294	−	1.27876i	−0.214969	−	0.976621i	$-0.568965\pi$
$457$	337.400	−	584.395i	0.738294	−	1.27876i	0.953263	−	0.302142i	$-0.0977016\pi$
$458$		0			0
$459$	198.324	−	276.869i	0.432078	−	0.603200i
$460$		0			0
$461$	−235.868	+	136.178i	−0.511644	+	0.295398i	−0.733509	−	0.679680i	$-0.762119\pi$
$461$	−235.868	+	136.178i	−0.511644	+	0.295398i	0.221865	+	0.975077i	$0.428785\pi$
$462$		0			0
$463$	−205.309	−	355.606i	−0.443432	−	0.768047i	0.554509	−	0.832178i	$-0.312906\pi$
$463$	−205.309	−	355.606i	−0.443432	−	0.768047i	−0.997942	+	0.0641303i	$0.979573\pi$
$464$		0			0
$465$	−470.007	+	755.936i	−1.01077	+	1.62567i
$466$		0			0
$467$			577.112i			1.23579i	0.786262	+	0.617893i	$0.212014\pi$
$467$			577.112i			1.23579i	−0.786262	+	0.617893i	$0.787986\pi$
$468$		0			0
$469$	−401.306	−	695.082i	−0.855662	−	1.48205i
$470$		0			0
$471$	45.7467	−	24.4557i	0.0971267	−	0.0519230i
$472$		0			0
$473$		−	312.822i		−	0.661357i
$474$		0			0
$475$	−279.060	+	82.5832i	−0.587495	+	0.173859i
$476$		0			0
$477$	−31.1883	+	476.741i	−0.0653843	+	0.999458i
$478$		0			0
$479$			874.756i			1.82621i	0.407722	+	0.913106i	$0.366323\pi$
$479$			874.756i			1.82621i	−0.407722	+	0.913106i	$0.633677\pi$
$480$		0			0
$481$	−120.222	+	208.231i	−0.249942	+	0.432912i
$482$		0			0
$483$	−305.237	+	490.928i	−0.631960	+	1.01641i
$484$		0			0
$485$	891.999	−	514.996i	1.83917	−	1.06185i
$486$		0			0
$487$	779.378			1.60037			0.800183	−	0.599756i	$-0.204736\pi$
$487$	779.378			1.60037			0.800183	+	0.599756i	$0.204736\pi$
$488$		0			0
$489$	396.227	−	211.819i	0.810281	−	0.433168i
$490$		0			0
$491$		−	886.844i		−	1.80620i	−0.429430	−	0.903100i	$-0.641286\pi$
$491$		−	886.844i		−	1.80620i	0.429430	−	0.903100i	$-0.358714\pi$
$492$		0			0
$493$	57.7811	−	100.080i	0.117203	−	0.203002i
$494$		0			0
$495$	141.606	+	287.059i	0.286072	+	0.579916i
$496$		0			0
$497$	−559.434	+	322.990i	−1.12562	+	0.649878i
$498$		0			0
$499$	−85.7107			−0.171765			−0.0858824	−	0.996305i	$-0.527371\pi$
$499$	−85.7107			−0.171765			−0.0858824	+	0.996305i	$0.527371\pi$
$500$		0			0
$501$	−119.962	−	3.91977i	−0.239446	−	0.00782389i
$502$		0			0
$503$	−84.7516	+	48.9314i	−0.168492	+	0.0972791i	−0.581875	−	0.813278i	$-0.697681\pi$
$503$	−84.7516	+	48.9314i	−0.168492	+	0.0972791i	0.413382	+	0.910558i	$0.364347\pi$
$504$		0			0
$505$	1179.74			2.33611
$506$		0			0
$507$	−361.893	−	225.009i	−0.713793	−	0.443804i
$508$		0			0
$509$	319.490	+	184.458i	0.627682	+	0.362392i	0.779854	−	0.625962i	$-0.215293\pi$
$509$	319.490	+	184.458i	0.627682	+	0.362392i	−0.152172	+	0.988354i	$0.548627\pi$
$510$		0			0
$511$	−189.184	−	327.676i	−0.370222	−	0.641244i
$512$		0			0
$513$	96.7494	+	503.794i	0.188595	+	0.982055i
$514$		0			0
$515$	−982.337	+	567.153i	−1.90745	+	1.10127i
$516$		0			0
$517$	57.3860	−	99.3954i	0.110998	−	0.192254i
$518$		0			0
$519$	82.0665	−	131.992i	0.158124	−	0.254320i
$520$		0			0
$521$		−	340.779i		−	0.654087i	−0.945009	−	0.327044i	$-0.893948\pi$
$521$		−	340.779i		−	0.654087i	0.945009	−	0.327044i	$-0.106052\pi$
$522$		0			0
$523$	363.130	+	628.959i	0.694321	+	1.20260i	0.970409	+	0.241467i	$0.0776284\pi$
$523$	363.130	+	628.959i	0.694321	+	1.20260i	−0.276088	+	0.961132i	$0.589038\pi$
$524$		0			0
$525$	−11.2042	+	342.899i	−0.0213414	+	0.653140i
$526$		0			0
$527$		−	589.436i		−	1.11847i
$528$		0			0
$529$	68.5457	+	118.725i	0.129576	+	0.224432i
$530$		0			0
$531$	154.821	+	103.421i	0.291566	+	0.194766i
$532$		0			0
$533$	118.486	+	68.4082i	0.222301	+	0.128346i
$534$		0			0
$535$	908.396			1.69794
$536$		0			0
$537$	349.052	+	652.935i	0.650005	+	1.21589i
$538$		0			0
$539$			37.7787i			0.0700903i
$540$		0			0
$541$	−6.83691	−	11.8419i	−0.0126375	−	0.0218889i	0.859637	−	0.510905i	$-0.170689\pi$
$541$	−6.83691	−	11.8419i	−0.0126375	−	0.0218889i	−0.872275	+	0.489016i	$0.837356\pi$
$542$		0			0
$543$	38.0030	+	23.6285i	0.0699871	+	0.0435148i
$544$		0			0
$545$	146.789	+	84.7486i	0.269337	+	0.155502i
$546$		0			0
$547$	566.818			1.03623			0.518115	−	0.855311i	$-0.326634\pi$
$547$	566.818			1.03623			0.518115	+	0.855311i	$0.326634\pi$
$548$		0			0
$549$	−177.218	+	265.296i	−0.322801	+	0.483235i
$550$		0			0
$551$	49.3957	+	166.915i	0.0896474	+	0.302931i
$552$		0			0
$553$	−311.835			−0.563897
$554$		0			0
$555$	415.921	+	778.019i	0.749408	+	1.40184i
$556$		0			0
$557$	550.401	−	317.774i	0.988153	−	0.570511i	0.0834316	−	0.996514i	$-0.473412\pi$
$557$	550.401	−	317.774i	0.988153	−	0.570511i	0.904722	+	0.426003i	$0.140079\pi$
$558$		0			0
$559$	−289.950			−0.518694
$560$		0			0
$561$	−180.000	−	111.916i	−0.320856	−	0.199494i
$562$		0			0
$563$	230.616	−	133.146i	0.409619	−	0.236494i	−0.281007	−	0.959706i	$-0.590668\pi$
$563$	230.616	−	133.146i	0.409619	−	0.236494i	0.690626	+	0.723212i	$0.257335\pi$
$564$		0			0
$565$	−417.397	−	722.953i	−0.738756	−	1.27956i
$566$		0			0
$567$	599.611	+	78.7901i	1.05752	+	0.138960i
$568$		0			0
$569$	−119.581	−	69.0401i	−0.210160	−	0.121336i	0.391226	−	0.920295i	$-0.372051\pi$
$569$	−119.581	−	69.0401i	−0.210160	−	0.121336i	−0.601386	+	0.798959i	$0.705384\pi$
$570$		0			0
$571$	−316.361	−	547.954i	−0.554048	−	0.959639i	−0.997977	−	0.0635774i	$-0.979749\pi$
$571$	−316.361	−	547.954i	−0.554048	−	0.959639i	0.443929	−	0.896062i	$-0.353584\pi$
$572$		0			0
$573$	−765.592	−	25.0157i	−1.33611	−	0.0436574i
$574$		0			0
$575$	342.351	+	197.657i	0.595393	+	0.343750i
$576$		0			0
$577$	−99.7397			−0.172859			−0.0864296	−	0.996258i	$-0.527546\pi$
$577$	−99.7397			−0.172859			−0.0864296	+	0.996258i	$0.527546\pi$
$578$		0			0
$579$	−291.384	+	155.771i	−0.503254	+	0.269035i
$580$		0			0
$581$	−674.199	+	389.249i	−1.16041	+	0.669964i
$582$		0			0
$583$	297.336			0.510010
$584$		0			0
$585$	266.070	−	131.252i	0.454821	−	0.224362i
$586$		0			0
$587$	−794.396	+	458.645i	−1.35332	+	0.781337i	−0.988712	−	0.149826i	$-0.952129\pi$
$587$	−794.396	+	458.645i	−1.35332	+	0.781337i	−0.364603	+	0.931163i	$0.618795\pi$
$588$		0			0
$589$	643.875	+	611.330i	1.09317	+	1.03791i
$590$		0			0
$591$	−336.440	−	629.341i	−0.569272	−	1.06487i
$592$		0			0
$593$	675.475	−	389.986i	1.13908	−	0.657649i	0.192878	−	0.981223i	$-0.438218\pi$
$593$	675.475	−	389.986i	1.13908	−	0.657649i	0.946203	+	0.323574i	$0.104884\pi$
$594$		0			0
$595$	−298.993	−	517.870i	−0.502509	−	0.870371i
$596$		0			0
$597$	−212.680	−	132.235i	−0.356248	−	0.221499i
$598$		0			0
$599$	−719.650	−	415.490i	−1.20142	−	0.693640i	−0.240548	−	0.970637i	$-0.577327\pi$
$599$	−719.650	−	415.490i	−1.20142	−	0.693640i	−0.960871	+	0.276997i	$0.910661\pi$
$600$		0			0
$601$	160.866	−	278.628i	0.267664	−	0.463607i	−0.700594	−	0.713560i	$-0.747082\pi$
$601$	160.866	−	278.628i	0.267664	−	0.463607i	0.968258	+	0.249953i	$0.0804151\pi$
$602$		0			0
$603$	428.016	+	867.661i	0.709811	+	1.43891i
$604$		0			0
$605$	−492.848	+	284.546i	−0.814624	+	0.470324i
$606$		0			0
$607$	353.985	+	613.121i	0.583172	+	1.01008i	0.995101	+	0.0988672i	$0.0315219\pi$
$607$	353.985	+	613.121i	0.583172	+	1.01008i	−0.411929	+	0.911216i	$0.635145\pi$
$608$		0			0
$609$	205.099	+	6.70160i	0.336780	+	0.0110043i
$610$		0			0
$611$	−92.1281	−	53.1902i	−0.150782	−	0.0870543i
$612$		0			0
$613$	−239.920	+	415.553i	−0.391386	+	0.677901i	−0.992633	−	0.121163i	$-0.961338\pi$
$613$	−239.920	+	415.553i	−0.391386	+	0.677901i	0.601246	+	0.799064i	$0.294671\pi$
$614$		0			0
$615$	442.705	−	236.666i	0.719845	−	0.384822i
$616$		0			0
$617$	616.930	+	356.185i	0.999887	+	0.577285i	0.908215	−	0.418504i	$-0.137446\pi$
$617$	616.930	+	356.185i	0.999887	+	0.577285i	0.0916720	+	0.995789i	$0.470779\pi$
$618$		0			0
$619$	−238.695	+	413.431i	−0.385613	+	0.667902i	−0.991854	−	0.127379i	$-0.959343\pi$
$619$	−238.695	+	413.431i	−0.385613	+	0.667902i	0.606241	+	0.795281i	$0.292677\pi$
$620$		0			0
$621$	405.787	−	566.496i	0.653441	−	0.912232i
$622$		0			0
$623$			282.575i			0.453572i
$624$		0			0
$625$	−773.314			−1.23730
$626$		0			0
$627$	308.938	−	80.5517i	0.492725	−	0.128472i
$628$		0			0
$629$	−505.922	−	292.094i	−0.804328	−	0.464379i
$630$		0			0
$631$	−138.225	−	239.412i	−0.219057	−	0.379417i	0.735463	−	0.677565i	$-0.236965\pi$
$631$	−138.225	−	239.412i	−0.219057	−	0.379417i	−0.954520	+	0.298147i	$0.903631\pi$
$632$		0			0
$633$	−255.005	+	136.323i	−0.402852	+	0.215361i
$634$		0			0
$635$	−505.001	+	291.563i	−0.795278	+	0.459154i
$636$		0			0
$637$	35.0165			0.0549709
$638$		0			0
$639$	698.334	−	344.487i	1.09285	−	0.539104i
$640$		0			0
$641$	578.579	−	334.043i	0.902619	−	0.521127i	0.0245700	−	0.999698i	$-0.492178\pi$
$641$	578.579	−	334.043i	0.902619	−	0.521127i	0.878049	+	0.478571i	$0.158845\pi$
$642$		0			0
$643$	−155.953			−0.242540			−0.121270	−	0.992620i	$-0.538697\pi$
$643$	−155.953			−0.242540			−0.121270	+	0.992620i	$0.538697\pi$
$644$		0			0
$645$	−561.733	+	903.465i	−0.870904	+	1.40072i
$646$		0			0
$647$			325.510i			0.503107i	0.967843	+	0.251554i	$0.0809415\pi$
$647$			325.510i			0.503107i	−0.967843	+	0.251554i	$0.919058\pi$
$648$		0			0
$649$	57.9370	−	100.350i	0.0892712	−	0.154622i
$650$		0			0
$651$	923.062	−	493.460i	1.41791	−	0.758003i
$652$		0			0
$653$	−970.469	+	560.300i	−1.48617	+	0.858040i	−0.999876	−	0.0157554i	$-0.994985\pi$
$653$	−970.469	+	560.300i	−1.48617	+	0.858040i	−0.486293	+	0.873796i	$0.661651\pi$
$654$		0			0
$655$	43.0235			0.0656847
$656$		0			0
$657$	201.775	+	409.033i	0.307116	+	0.622577i
$658$		0			0
$659$			1156.40i			1.75479i	0.479771	+	0.877394i	$0.340720\pi$
$659$			1156.40i			1.75479i	−0.479771	+	0.877394i	$0.659280\pi$
$660$		0			0
$661$	409.948	−	710.051i	0.620194	−	1.07421i	−0.369255	−	0.929328i	$-0.620387\pi$
$661$	409.948	−	710.051i	0.620194	−	1.07421i	0.989449	−	0.144880i	$-0.0462795\pi$
$662$		0			0
$663$	−103.733	+	166.839i	−0.156460	+	0.251643i
$664$		0			0
$665$	875.799	+	210.499i	1.31699	+	0.316540i
$666$		0			0
$667$	118.225	−	204.771i	0.177249	−	0.307004i
$668$		0			0
$669$	106.882	+	66.4546i	0.159764	+	0.0993342i
$670$		0			0
$671$	171.956	+	99.2786i	0.256268	+	0.147956i
$672$		0			0
$673$	307.896	−	533.292i	0.457498	−	0.792410i	−0.541330	−	0.840810i	$-0.682079\pi$
$673$	307.896	−	533.292i	0.457498	−	0.792410i	0.998828	+	0.0484006i	$0.0154124\pi$
$674$		0			0
$675$	40.4599	−	411.576i	0.0599406	−	0.609742i
$676$		0			0
$677$	−721.894	−	416.786i	−1.06631	−	0.615636i	−0.139141	−	0.990273i	$-0.544434\pi$
$677$	−721.894	−	416.786i	−1.06631	−	0.615636i	−0.927172	+	0.374636i	$0.877768\pi$
$678$		0			0
$679$	−1211.13			−1.78370
$680$		0			0
$681$	862.681	+	28.1881i	1.26679	+	0.0413922i
$682$		0			0
$683$			162.807i			0.238370i	0.992872	+	0.119185i	$0.0380282\pi$
$683$			162.807i			0.238370i	−0.992872	+	0.119185i	$0.961972\pi$
$684$		0			0
$685$	−119.877			−0.175003
$686$		0			0
$687$	−237.543	−	147.694i	−0.345769	−	0.214983i
$688$		0			0
$689$		−	275.596i		−	0.399994i
$690$		0			0
$691$	−113.291	+	196.226i	−0.163952	+	0.283974i	−0.936283	−	0.351247i	$-0.885758\pi$
$691$	−113.291	+	196.226i	−0.163952	+	0.283974i	0.772330	+	0.635221i	$0.219091\pi$
$692$		0			0
$693$	24.5700	−	375.575i	0.0354546	−	0.541955i
$694$		0			0
$695$	−1229.63	−	709.928i	−1.76925	−	1.02148i
$696$		0			0
$697$	−166.206	+	287.878i	−0.238460	+	0.413024i
$698$		0			0
$699$	191.984	+	6.27308i	0.274655	+	0.00897436i
$700$		0			0
$701$	−603.483	−	348.421i	−0.860888	−	0.497034i	0.00342124	−	0.999994i	$-0.498911\pi$
$701$	−603.483	−	348.421i	−0.860888	−	0.497034i	−0.864310	+	0.502960i	$0.832244\pi$
$702$		0			0
$703$	843.787	−	249.705i	1.20027	−	0.355199i
$704$		0			0
$705$	−344.221	+	184.017i	−0.488257	+	0.261017i
$706$		0			0
$707$	−1201.36	−	693.606i	−1.69924	−	0.981056i
$708$		0			0
$709$	−476.252			−0.671724			−0.335862	−	0.941911i	$-0.609028\pi$
$709$	−476.252			−0.671724			−0.335862	+	0.941911i	$0.609028\pi$
$710$		0			0
$711$	375.092	+	24.5385i	0.527556	+	0.0345126i
$712$		0			0
$713$		−	1206.03i		−	1.69149i
$714$		0			0
$715$	−92.3206	−	159.904i	−0.129120	−	0.223642i
$716$		0			0
$717$	51.5800	−	82.9588i	0.0719387	−	0.115703i
$718$		0			0
$719$	134.505	+	77.6567i	0.187073	+	0.108007i	0.590611	−	0.806956i	$-0.298887\pi$
$719$	134.505	+	77.6567i	0.187073	+	0.108007i	−0.403539	+	0.914963i	$0.632220\pi$
$720$		0			0
$721$	1333.79			1.84992
$722$		0			0
$723$	73.4342	−	39.2572i	0.101569	−	0.0542977i
$724$		0			0
$725$		−	140.329i		−	0.193557i
$726$		0			0
$727$	−583.550	−	1010.74i	−0.802683	−	1.39029i	−0.917844	−	0.396940i	$-0.870072\pi$
$727$	−583.550	−	1010.74i	−0.802683	−	1.39029i	0.115162	−	0.993347i	$-0.463261\pi$
$728$		0			0
$729$	−715.045	−	141.957i	−0.980857	−	0.194728i
$730$		0			0
$731$		−	704.469i		−	0.963706i
$732$		0			0
$733$	435.020	+	753.476i	0.593478	+	1.02793i	0.993760	+	0.111542i	$0.0355790\pi$
$733$	435.020	+	753.476i	0.593478	+	1.02793i	−0.400281	+	0.916392i	$0.631088\pi$
$734$		0			0
$735$	67.8390	−	109.109i	0.0922980	−	0.148448i
$736$		0			0
$737$	521.451	−	301.060i	0.707531	−	0.408493i
$738$		0			0
$739$	−264.833	+	458.704i	−0.358367	+	0.620709i	−0.987688	−	0.156436i	$-0.950000\pi$
$739$	−264.833	+	458.704i	−0.358367	+	0.620709i	0.629322	+	0.777145i	$0.283333\pi$
$740$		0			0
$741$	−74.6621	−	286.350i	−0.100759	−	0.386437i
$742$		0			0
$743$			478.400i			0.643876i	0.946761	+	0.321938i	$0.104334\pi$
$743$			478.400i			0.643876i	−0.946761	+	0.321938i	$0.895666\pi$
$744$		0			0
$745$	−208.345			−0.279658
$746$		0			0
$747$	841.594	−	415.157i	1.12663	−	0.555766i
$748$		0			0
$749$	−925.047	−	534.076i	−1.23504	−	0.713052i
$750$		0			0
$751$	380.129	−	658.403i	0.506164	−	0.876701i	−0.493811	−	0.869569i	$-0.664397\pi$
$751$	380.129	−	658.403i	0.506164	−	0.876701i	0.999975	−	0.00713180i	$-0.00227014\pi$
$752$		0			0
$753$	429.050	−	690.063i	0.569787	−	0.916418i
$754$		0			0
$755$	−633.778	−	365.912i	−0.839441	−	0.484652i
$756$		0			0
$757$	−189.020	+	327.392i	−0.249696	+	0.432486i	−0.963441	−	0.267919i	$-0.913664\pi$
$757$	−189.020	+	327.392i	−0.249696	+	0.432486i	0.713746	+	0.700405i	$0.246997\pi$
$758$		0			0
$759$	−368.295	−	228.989i	−0.485237	−	0.301698i
$760$		0			0
$761$	362.168	−	209.098i	0.475911	−	0.274767i	−0.242800	−	0.970076i	$-0.578066\pi$
$761$	362.168	−	209.098i	0.475911	−	0.274767i	0.718711	+	0.695309i	$0.244732\pi$
$762$		0			0
$763$	−99.6530	−	172.604i	−0.130607	−	0.226218i
$764$		0			0
$765$	318.893	+	646.451i	0.416854	+	0.845034i
$766$		0			0
$767$	−93.0126	−	53.7009i	−0.121268	−	0.0700142i
$768$		0			0
$769$	−650.948	+	1127.47i	−0.846486	+	1.46616i	0.0378388	+	0.999284i	$0.487953\pi$
$769$	−650.948	+	1127.47i	−0.846486	+	1.46616i	−0.884325	+	0.466873i	$0.845381\pi$
$770$		0			0
$771$	1393.95	+	45.5472i	1.80797	+	0.0590755i
$772$		0			0
$773$	0.961798	−	0.555294i	0.00124424	−	0.000718362i	−0.499378	−	0.866384i	$-0.666438\pi$
$773$	0.961798	−	0.555294i	0.00124424	−	0.000718362i	0.500622	+	0.865666i	$0.333105\pi$
$774$		0			0
$775$	−357.879	−	619.865i	−0.461779	−	0.799826i
$776$		0			0
$777$	33.8779	−	1036.81i	0.0436009	−	1.33438i
$778$		0			0
$779$	−142.086	−	480.128i	−0.182395	−	0.616339i
$780$		0			0
$781$	−242.307	−	419.688i	−0.310252	−	0.537373i
$782$		0			0
$783$	−246.177	−	24.2004i	−0.314402	−	0.0309073i
$784$		0			0
$785$			109.791i			0.139861i
$786$		0			0
$787$	−726.228	−	1257.86i	−0.922780	−	1.59830i	−0.795093	−	0.606488i	$-0.792578\pi$
$787$	−726.228	−	1257.86i	−0.922780	−	1.59830i	−0.127687	−	0.991814i	$-0.540755\pi$
$788$		0			0
$789$	582.698	−	937.183i	0.738527	−	1.18781i
$790$		0			0
$791$			981.606i			1.24097i
$792$		0			0
$793$	92.0198	−	159.383i	0.116040	−	0.200987i
$794$		0			0
$795$	−858.738	−	533.924i	−1.08017	−	0.671603i
$796$		0			0
$797$	−565.944	+	326.748i	−0.710093	+	0.409972i	−0.811095	−	0.584914i	$-0.801128\pi$
$797$	−565.944	+	326.748i	−0.710093	+	0.409972i	0.101003	+	0.994886i	$0.467795\pi$
$798$		0			0
$799$	129.232	−	223.837i	0.161742	−	0.280146i
$800$		0			0
$801$	22.2360	−	339.897i	0.0277603	−	0.424341i
$802$		0			0
$803$	245.822	−	141.926i	0.306130	−	0.176744i
$804$		0			0
$805$	−611.763	−	1059.60i	−0.759954	−	1.31628i
$806$		0			0
$807$	−534.315	−	17.4587i	−0.662101	−	0.0216341i
$808$		0			0
$809$			307.348i			0.379911i	0.981793	+	0.189956i	$0.0608344\pi$
$809$			307.348i			0.379911i	−0.981793	+	0.189956i	$0.939166\pi$
$810$		0			0
$811$	−483.368	−	837.219i	−0.596015	−	1.03233i	−0.993403	−	0.114678i	$-0.963416\pi$
$811$	−483.368	−	837.219i	−0.596015	−	1.03233i	0.397388	−	0.917651i	$-0.369917\pi$
$812$		0			0
$813$	25.0403	−	766.344i	0.0307998	−	0.942612i
$814$		0			0
$815$			950.937i			1.16679i
$816$		0			0
$817$	769.534	+	730.637i	0.941901	+	0.894292i
$818$		0			0
$819$	−348.115	−	22.7736i	−0.425048	−	0.0278066i
$820$		0			0
$821$			1061.23i			1.29261i	0.763080	+	0.646304i	$0.223686\pi$
$821$			1061.23i			1.29261i	−0.763080	+	0.646304i	$0.776314\pi$
$822$		0			0
$823$	568.833	−	985.248i	0.691170	−	1.19714i	−0.280284	−	0.959917i	$-0.590429\pi$
$823$	568.833	−	985.248i	0.691170	−	1.19714i	0.971455	−	0.237225i	$-0.0762380\pi$
$824$		0			0
$825$	−257.243	−	8.40540i	−0.311809	−	0.0101884i
$826$		0			0
$827$	1240.79	−	716.370i	1.50035	−	0.866227i	0.500349	−	0.865824i	$-0.333205\pi$
$827$	1240.79	−	716.370i	1.50035	−	0.866227i	1.00000		0.000403585i	$-0.000128465\pi$
$828$		0			0
$829$	476.786			0.575133			0.287567	−	0.957761i	$-0.407154\pi$
$829$	476.786			0.575133			0.287567	+	0.957761i	$0.407154\pi$
$830$		0			0
$831$	−29.0859	+	890.157i	−0.0350010	+	1.07119i
$832$		0			0
$833$			85.0769i			0.102133i
$834$		0			0
$835$	127.019	−	220.004i	0.152119	−	0.263478i
$836$		0			0
$837$	−1149.14	+	520.924i	−1.37293	+	0.622371i
$838$		0			0
$839$	−100.555	+	58.0553i	−0.119851	+	0.0691959i	−0.558727	−	0.829352i	$-0.688710\pi$
$839$	−100.555	+	58.0553i	−0.119851	+	0.0691959i	0.438876	+	0.898548i	$0.355377\pi$
$840$		0			0
$841$	757.065			0.900196
$842$		0			0
$843$	135.034	+	252.593i	0.160182	+	0.299635i
$844$		0			0
$845$	781.100	−	450.968i	0.924378	−	0.533690i
$846$		0			0
$847$	669.175			0.790054
$848$		0			0
$849$	447.534	−	239.247i	0.527131	−	0.281799i
$850$		0			0
$851$	−1035.16	−	597.649i	−1.21640	−	0.702290i
$852$		0			0
$853$	660.180	+	1143.47i	0.773951	+	1.34052i	0.935382	+	0.353638i	$0.115055\pi$
$853$	660.180	+	1143.47i	0.773951	+	1.34052i	−0.161432	+	0.986884i	$0.551611\pi$
$854$		0			0
$855$	−1036.89	−	322.117i	−1.21274	−	0.376745i
$856$		0			0
$857$	−59.5634	+	34.3889i	−0.0695022	+	0.0401271i	−0.534348	−	0.845264i	$-0.679443\pi$
$857$	−59.5634	+	34.3889i	−0.0695022	+	0.0401271i	0.464846	+	0.885391i	$0.346110\pi$
$858$		0			0
$859$	−33.4964	+	58.0175i	−0.0389947	+	0.0675407i	−0.884864	−	0.465849i	$-0.845749\pi$
$859$	−33.4964	+	58.0175i	−0.0389947	+	0.0675407i	0.845869	+	0.533390i	$0.179082\pi$
$860$		0			0
$861$	−589.963	−	19.2770i	−0.685207	−	0.0223891i
$862$		0			0
$863$			983.878i			1.14007i	0.821621	+	0.570034i	$0.193070\pi$
$863$			983.878i			1.14007i	−0.821621	+	0.570034i	$0.806930\pi$
$864$		0			0
$865$	164.480	+	284.887i	0.190150	+	0.329349i
$866$		0			0
$867$	330.930	+	205.757i	0.381695	+	0.237321i
$868$		0			0
$869$		−	233.939i		−	0.269205i
$870$		0			0
$871$	−279.047	−	483.324i	−0.320376	−	0.554907i
$872$		0			0
$873$	1456.82	+	95.3046i	1.66875	+	0.109169i
$874$		0			0
$875$	397.545	+	229.523i	0.454337	+	0.262312i
$876$		0			0
$877$	795.482			0.907049			0.453524	−	0.891244i	$-0.350166\pi$
$877$	795.482			0.907049			0.453524	+	0.891244i	$0.350166\pi$
$878$		0			0
$879$	−47.0902	+	75.7375i	−0.0535724	+	0.0861633i
$880$		0			0
$881$		−	1278.78i		−	1.45151i	−0.687955	−	0.725753i	$-0.741491\pi$
$881$		−	1278.78i		−	1.45151i	0.687955	−	0.725753i	$-0.258509\pi$
$882$		0			0
$883$	−423.514	−	733.548i	−0.479631	−	0.830745i	0.520096	−	0.854108i	$-0.325896\pi$
$883$	−423.514	−	733.548i	−0.479631	−	0.830745i	−0.999727	+	0.0233629i	$0.992563\pi$
$884$		0			0
$885$	−347.526	+	185.784i	−0.392685	+	0.209926i
$886$		0			0
$887$	712.045	+	411.099i	0.802756	+	0.463471i	0.844434	−	0.535660i	$-0.179937\pi$
$887$	712.045	+	411.099i	0.802756	+	0.463471i	−0.0416779	+	0.999131i	$0.513270\pi$
$888$		0			0
$889$	685.677			0.771291
$890$		0			0
$891$	−59.1084	+	449.829i	−0.0663394	+	0.504858i
$892$		0			0
$893$	110.478	+	373.319i	0.123715	+	0.418050i
$894$		0			0
$895$	−1567.03			−1.75087
$896$		0			0
$897$	−212.246	+	341.366i	−0.236618	+	0.380565i
$898$		0			0
$899$	−370.761	+	214.059i	−0.412415	+	0.238108i
$900$		0			0
$901$	669.594			0.743168
$902$		0			0
$903$	1103.21	−	589.763i	1.22171	−	0.653116i
$904$		0			0
$905$	−82.0245	+	47.3569i	−0.0906348	+	0.0523280i
$906$		0			0
$907$	375.839	+	650.973i	0.414376	+	0.717721i	0.995363	−	0.0961924i	$-0.0306664\pi$
$907$	375.839	+	650.973i	0.414376	+	0.717721i	−0.580986	+	0.813913i	$0.697333\pi$
$908$		0			0
$909$	1390.48	+	928.843i	1.52968	+	1.02183i
$910$		0			0
$911$	−1194.64	−	689.727i	−1.31135	−	0.757110i	−0.329033	−	0.944318i	$-0.606723\pi$
$911$	−1194.64	−	689.727i	−1.31135	−	0.757110i	−0.982320	+	0.187208i	$0.940056\pi$
$912$		0			0
$913$	−292.015	−	505.785i	−0.319841	−	0.553981i
$914$		0			0
$915$	−318.353	−	595.508i	−0.347926	−	0.650828i
$916$		0			0
$917$	−43.8121	−	25.2949i	−0.0477776	−	0.0275844i
$918$		0			0
$919$	149.957			0.163174			0.0815868	−	0.996666i	$-0.474001\pi$
$919$	149.957			0.163174			0.0815868	+	0.996666i	$0.474001\pi$
$920$		0			0
$921$	34.4142	−	1053.23i	0.0373661	−	1.14357i
$922$		0			0
$923$	−389.002	+	224.590i	−0.421454	+	0.243327i
$924$		0			0
$925$	−709.387			−0.766905
$926$		0			0
$927$	−1604.36	−	104.957i	−1.73070	−	0.113222i
$928$		0			0
$929$	−140.260	+	80.9793i	−0.150980	+	0.0871683i	−0.573587	−	0.819145i	$-0.694448\pi$
$929$	−140.260	+	80.9793i	−0.150980	+	0.0871683i	0.422607	+	0.906313i	$0.361115\pi$
$930$		0			0
$931$	−92.9345	−	88.2370i	−0.0998222	−	0.0947766i
$932$		0			0
$933$	−113.883	+	183.164i	−0.122061	+	0.196317i
$934$		0			0
$935$	388.507	−	224.304i	0.415515	−	0.239898i
$936$		0			0
$937$	−705.449	−	1221.87i	−0.752881	−	1.30403i	−0.946421	−	0.322935i	$-0.895330\pi$
$937$	−705.449	−	1221.87i	−0.752881	−	1.30403i	0.193540	−	0.981092i	$-0.438003\pi$
$938$		0			0
$939$	−1043.78	+	557.997i	−1.11159	+	0.594246i
$940$		0			0
$941$	−296.238	−	171.033i	−0.314812	−	0.181757i	0.334266	−	0.942479i	$-0.391512\pi$
$941$	−296.238	−	171.033i	−0.314812	−	0.181757i	−0.649078	+	0.760722i	$0.724845\pi$
$942$		0			0
$943$	−340.072	+	589.021i	−0.360627	+	0.624625i
$944$		0			0
$945$	−745.379	+	1040.58i	−0.788761	+	1.10114i
$946$		0			0
$947$	310.543	−	179.292i	0.327922	−	0.189326i	−0.326996	−	0.945026i	$-0.606036\pi$
$947$	310.543	−	179.292i	0.327922	−	0.189326i	0.654918	+	0.755700i	$0.272703\pi$
$948$		0			0
$949$	−131.549	−	227.849i	−0.138618	−	0.240094i
$950$		0			0
$951$	567.054	+	1060.73i	0.596271	+	1.11538i
$952$		0			0
$953$	−228.456	−	131.899i	−0.239723	−	0.138404i	0.375326	−	0.926893i	$-0.377531\pi$
$953$	−228.456	−	131.899i	−0.239723	−	0.138404i	−0.615050	+	0.788488i	$0.710864\pi$
$954$		0			0
$955$	810.629	−	1404.05i	0.848826	−	1.47021i
$956$		0			0
$957$	−5.02755	+	153.865i	−0.00525344	+	0.160779i
$958$		0			0
$959$	122.075	+	70.4799i	0.127294	+	0.0734931i
$960$		0			0
$961$	−611.328	+	1058.85i	−0.636137	+	1.10182i
$962$		0			0
$963$	1070.67	+	715.208i	1.11181	+	0.742687i
$964$		0			0
$965$		−	699.316i		−	0.724680i
$966$		0			0
$967$	−746.026			−0.771485			−0.385743	−	0.922606i	$-0.626055\pi$
$967$	−746.026			−0.771485			−0.385743	+	0.922606i	$0.626055\pi$
$968$		0			0
$969$	695.724	−	181.401i	0.717981	−	0.187204i
$970$		0			0
$971$	−1462.99	−	844.659i	−1.50669	−	0.869886i	−0.999970	−	0.00777358i	$-0.997526\pi$
$971$	−1462.99	−	844.659i	−1.50669	−	0.869886i	−0.506717	−	0.862112i	$-0.669141\pi$
$972$		0			0
$973$	834.781	+	1445.88i	0.857945	+	1.48600i
$974$		0			0
$975$	−7.79084	+	238.434i	−0.00799060	+	0.244548i
$976$		0			0
$977$	1140.33	−	658.373i	1.16718	−	0.673872i	0.214166	−	0.976797i	$-0.431297\pi$
$977$	1140.33	−	658.373i	1.16718	−	0.673872i	0.953014	+	0.302926i	$0.0979634\pi$
$978$		0			0
$979$	−211.988			−0.216536
$980$		0			0
$981$	106.286	+	215.459i	0.108344	+	0.219632i
$982$		0			0
$983$	−650.198	+	375.392i	−0.661442	+	0.381884i	−0.792826	−	0.609448i	$-0.791391\pi$
$983$	−650.198	+	375.392i	−0.661442	+	0.381884i	0.131384	+	0.991332i	$0.458058\pi$
$984$		0			0
$985$	1510.41			1.53341
$986$		0			0
$987$	458.720	+	14.9887i	0.464762	+	0.0151861i
$988$		0			0
$989$		−	1441.40i		−	1.45743i
$990$		0			0
$991$	−140.771	+	243.823i	−0.142050	+	0.246038i	−0.928268	−	0.371911i	$-0.878703\pi$
$991$	−140.771	+	243.823i	−0.142050	+	0.246038i	0.786219	+	0.617949i	$0.212036\pi$
$992$		0			0
$993$	13.2384	−	405.154i	0.0133317	−	0.408010i
$994$		0			0
$995$	459.042	−	265.028i	0.461349	−	0.266360i
$996$		0			0
$997$	516.351			0.517905			0.258952	−	0.965890i	$-0.416623\pi$
$997$	516.351			0.517905			0.258952	+	0.965890i	$0.416623\pi$
$998$		0			0
$999$	−122.338	+	1244.47i	−0.122460	+	1.24572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.353.7	✓	80
3.2	odd	2		2052.3.m.a.1493.35		80
9.4	even	3		2052.3.be.a.125.6		80
9.5	odd	6		684.3.be.a.581.20	yes	80
19.7	even	3		684.3.be.a.425.20	yes	80
57.26	odd	6		2052.3.be.a.197.6		80
171.121	even	3		2052.3.m.a.881.6		80
171.140	odd	6	inner	684.3.m.a.653.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.7	✓	80	1.1	even	1	trivial
684.3.m.a.653.7	yes	80	171.140	odd	6	inner
684.3.be.a.425.20	yes	80	19.7	even	3
684.3.be.a.581.20	yes	80	9.5	odd	6
2052.3.m.a.881.6		80	171.121	even	3
2052.3.m.a.1493.35		80	3.2	odd	2
2052.3.be.a.125.6		80	9.4	even	3
2052.3.be.a.197.6		80	57.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.64568 + 1.41435i) q^{3} -6.34957i q^{5} +(-3.73312 + 6.46596i) q^{7} +(4.99921 - 7.48384i) q^{9} +O(q^{10})\)	\(q+(-2.64568 + 1.41435i) q^{3} -6.34957i q^{5} +(-3.73312 + 6.46596i) q^{7} +(4.99921 - 7.48384i) q^{9} +(-4.85076 - 2.80059i) q^{11} +(-2.59582 + 4.49610i) q^{13} +(8.98053 + 16.7989i) q^{15} +(-10.9238 - 6.30688i) q^{17} +(18.2190 - 5.39160i) q^{19} +(0.731488 - 22.3868i) q^{21} +(-22.3510 - 12.9044i) q^{23} -15.3170 q^{25} +(-2.64150 + 26.8705i) q^{27} +9.16161i q^{29} +(23.3648 + 40.4690i) q^{31} +(16.7946 + 0.548762i) q^{33} +(41.0560 + 23.7037i) q^{35} +46.3137 q^{37} +(0.508639 - 15.5666i) q^{39} -26.3532i q^{41} +(27.9247 + 48.3669i) q^{43} +(-47.5192 - 31.7428i) q^{45} +20.4907i q^{47} +(-3.37239 - 5.84114i) q^{49} +(37.8211 + 1.23580i) q^{51} +(-45.9725 + 26.5422i) q^{53} +(-17.7825 + 30.8003i) q^{55} +(-40.5759 + 40.0325i) q^{57} +20.6874i q^{59} -35.4492 q^{61} +(29.7275 + 60.2628i) q^{63} +(28.5483 + 16.4823i) q^{65} +(-53.7493 + 93.0966i) q^{67} +(77.3849 + 2.52855i) q^{69} +(74.9285 + 43.2600i) q^{71} +(-25.3385 + 43.8876i) q^{73} +(40.5239 - 21.6637i) q^{75} +(36.2170 - 20.9099i) q^{77} +(20.8830 + 36.1704i) q^{79} +(-31.0158 - 74.8266i) q^{81} +(90.2997 + 52.1346i) q^{83} +(-40.0459 + 69.3616i) q^{85} +(-12.9577 - 24.2387i) q^{87} +(32.7765 - 18.9235i) q^{89} +(-19.3810 - 33.5689i) q^{91} +(-119.053 - 74.0219i) q^{93} +(-34.2343 - 115.683i) q^{95} +(81.1072 + 140.482i) q^{97} +(-45.2092 + 22.3016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more