LMFDB - Embedded newform 684.3.t.a.265.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(265,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("684.265");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.t (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			265.19
Character	$\chi$	$=$	684.265
Dual form			684.3.t.a.493.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.775474 + 2.89804i) q^{3} +(-0.775683 + 1.34352i) q^{5} +(-0.749140 - 1.29755i) q^{7} +(-7.79728 - 4.49471i) q^{9} +O(q^{10})$	\(q+(-0.775474 + 2.89804i) q^{3} +(-0.775683 + 1.34352i) q^{5} +(-0.749140 - 1.29755i) q^{7} +(-7.79728 - 4.49471i) q^{9} +(8.70899 + 15.0844i) q^{11} +(-17.4081 - 10.0506i) q^{13} +(-3.29206 - 3.28983i) q^{15} -5.81212 q^{17} +(-13.2990 - 13.5697i) q^{19} +(4.34129 - 1.16482i) q^{21} +(15.3936 - 26.6626i) q^{23} +(11.2966 + 19.5663i) q^{25} +(19.0724 - 19.1113i) q^{27} +(-14.3623 + 8.29210i) q^{29} +(-36.1004 - 20.8426i) q^{31} +(-50.4689 + 13.5414i) q^{33} +2.32438 q^{35} +34.5858i q^{37} +(42.6265 - 42.6554i) q^{39} +(-16.0819 - 9.28488i) q^{41} +(18.1752 + 31.4804i) q^{43} +(12.0870 - 6.98935i) q^{45} +(-33.5510 - 58.1120i) q^{47} +(23.3776 - 40.4912i) q^{49} +(4.50715 - 16.8438i) q^{51} -91.9886i q^{53} -27.0217 q^{55} +(49.6386 - 28.0181i) q^{57} +(-2.26445 - 1.30738i) q^{59} +(-16.9517 - 29.3612i) q^{61} +(0.00914934 + 13.4845i) q^{63} +(27.0063 - 15.5921i) q^{65} +(27.4441 + 15.8449i) q^{67} +(65.3318 + 65.2875i) q^{69} -5.45516i q^{71} +121.153 q^{73} +(-65.4643 + 17.5649i) q^{75} +(13.0485 - 22.6007i) q^{77} +(-9.83846 + 5.68024i) q^{79} +(40.5952 + 70.0930i) q^{81} +(-72.7825 - 126.063i) q^{83} +(4.50836 - 7.80871i) q^{85} +(-12.8932 - 48.0530i) q^{87} -102.417i q^{89} +30.1171i q^{91} +(88.3977 - 88.4577i) q^{93} +(28.5470 - 7.34171i) q^{95} +(-140.473 + 81.1019i) q^{97} +(-0.106364 - 156.762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 2 * q^7 + 4 * q^9	$ 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) $ 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.775474	+	2.89804i	−0.258491	+	0.966014i
$3$	−0.775474	+	2.89804i	−0.258491	+	0.966014i
$4$		0			0
$5$	−0.775683	+	1.34352i	−0.155137	+	0.268704i	−0.933109	−	0.359594i	$-0.882915\pi$
$5$	−0.775683	+	1.34352i	−0.155137	+	0.268704i	0.777972	+	0.628299i	$0.216248\pi$
$6$		0			0
$7$	−0.749140	−	1.29755i	−0.107020	−	0.185364i	0.807542	−	0.589810i	$-0.200798\pi$
$7$	−0.749140	−	1.29755i	−0.107020	−	0.185364i	−0.914562	+	0.404446i	$0.867464\pi$
$8$		0			0
$9$	−7.79728	−	4.49471i	−0.866364	−	0.499412i
$10$		0			0
$11$	8.70899	+	15.0844i	0.791727	+	1.37131i	0.924897	+	0.380218i	$0.124151\pi$
$11$	8.70899	+	15.0844i	0.791727	+	1.37131i	−0.133170	+	0.991093i	$0.542516\pi$
$12$		0			0
$13$	−17.4081	−	10.0506i	−1.33908	−	0.773121i	−0.352413	−	0.935845i	$-0.614639\pi$
$13$	−17.4081	−	10.0506i	−1.33908	−	0.773121i	−0.986672	+	0.162724i	$0.947972\pi$
$14$		0			0
$15$	−3.29206	−	3.28983i	−0.219471	−	0.219322i
$16$		0			0
$17$	−5.81212			−0.341890			−0.170945	−	0.985281i	$-0.554682\pi$
$17$	−5.81212			−0.341890			−0.170945	+	0.985281i	$0.554682\pi$
$18$		0			0
$19$	−13.2990	−	13.5697i	−0.699947	−	0.714195i
$19$	−13.2990	−	13.5697i	−0.699947	−	0.714195i
$20$		0			0
$21$	4.34129	−	1.16482i	0.206728	−	0.0554678i
$22$		0			0
$23$	15.3936	−	26.6626i	0.669288	−	1.15924i	−0.308815	−	0.951122i	$-0.599932\pi$
$23$	15.3936	−	26.6626i	0.669288	−	1.15924i	0.978103	−	0.208119i	$-0.0667343\pi$
$24$		0			0
$25$	11.2966	+	19.5663i	0.451865	+	0.782654i
$26$		0			0
$27$	19.0724	−	19.1113i	0.706387	−	0.707826i
$28$		0			0
$29$	−14.3623	+	8.29210i	−0.495253	+	0.285935i	−0.726751	−	0.686901i	$-0.758971\pi$
$29$	−14.3623	+	8.29210i	−0.495253	+	0.285935i	0.231498	+	0.972835i	$0.425637\pi$
$30$		0			0
$31$	−36.1004	−	20.8426i	−1.16453	−	0.672342i	−0.212145	−	0.977238i	$-0.568045\pi$
$31$	−36.1004	−	20.8426i	−1.16453	−	0.672342i	−0.952386	+	0.304896i	$0.901378\pi$
$32$		0			0
$33$	−50.4689	+	13.5414i	−1.52936	+	0.410347i
$34$		0			0
$35$	2.32438			0.0664109
$36$		0			0
$37$			34.5858i			0.934752i	0.884059	+	0.467376i	$0.154801\pi$
$37$			34.5858i			0.934752i	−0.884059	+	0.467376i	$0.845199\pi$
$38$		0			0
$39$	42.6265	−	42.6554i	1.09299	−	1.09373i
$40$		0			0
$41$	−16.0819	−	9.28488i	−0.392241	−	0.226461i	0.290890	−	0.956757i	$-0.406049\pi$
$41$	−16.0819	−	9.28488i	−0.392241	−	0.226461i	−0.683131	+	0.730296i	$0.739382\pi$
$42$		0			0
$43$	18.1752	+	31.4804i	0.422680	+	0.732103i	0.996201	−	0.0870882i	$-0.0277562\pi$
$43$	18.1752	+	31.4804i	0.422680	+	0.732103i	−0.573521	+	0.819191i	$0.694423\pi$
$44$		0			0
$45$	12.0870	−	6.98935i	0.268599	−	0.155319i
$46$		0			0
$47$	−33.5510	−	58.1120i	−0.713851	−	1.23643i	−0.963401	−	0.268064i	$-0.913616\pi$
$47$	−33.5510	−	58.1120i	−0.713851	−	1.23643i	0.249550	−	0.968362i	$-0.419717\pi$
$48$		0			0
$49$	23.3776	−	40.4912i	0.477093	−	0.826350i
$50$		0			0
$51$	4.50715	−	16.8438i	0.0883755	−	0.330270i
$52$		0			0
$53$		−	91.9886i		−	1.73563i	−0.496885	−	0.867817i	$-0.665523\pi$
$53$		−	91.9886i		−	1.73563i	0.496885	−	0.867817i	$-0.334477\pi$
$54$		0			0
$55$	−27.0217			−0.491303
$56$		0			0
$57$	49.6386	−	28.0181i	0.870852	−	0.491545i
$58$		0			0
$59$	−2.26445	−	1.30738i	−0.0383805	−	0.0221590i	0.480687	−	0.876892i	$-0.340387\pi$
$59$	−2.26445	−	1.30738i	−0.0383805	−	0.0221590i	−0.519068	+	0.854733i	$0.673721\pi$
$60$		0			0
$61$	−16.9517	−	29.3612i	−0.277897	−	0.481331i	0.692965	−	0.720971i	$-0.256304\pi$
$61$	−16.9517	−	29.3612i	−0.277897	−	0.481331i	−0.970862	+	0.239640i	$0.922971\pi$
$62$		0			0
$63$	0.00914934	+	13.4845i	0.000145228	+	0.214040i
$64$		0			0
$65$	27.0063	−	15.5921i	0.415482	−	0.239879i
$66$		0			0
$67$	27.4441	+	15.8449i	0.409614	+	0.236491i	0.690624	−	0.723214i	$-0.257336\pi$
$67$	27.4441	+	15.8449i	0.409614	+	0.236491i	−0.281010	+	0.959705i	$0.590669\pi$
$68$		0			0
$69$	65.3318	+	65.2875i	0.946838	+	0.946196i
$70$		0			0
$71$		−	5.45516i		−	0.0768333i	−0.999262	−	0.0384166i	$-0.987769\pi$
$71$		−	5.45516i		−	0.0768333i	0.999262	−	0.0384166i	$-0.0122314\pi$
$72$		0			0
$73$	121.153			1.65963			0.829815	−	0.558039i	$-0.188446\pi$
$73$	121.153			1.65963			0.829815	+	0.558039i	$0.188446\pi$
$74$		0			0
$75$	−65.4643	+	17.5649i	−0.872857	+	0.234199i
$76$		0			0
$77$	13.0485	−	22.6007i	0.169461	−	0.293515i
$78$		0			0
$79$	−9.83846	+	5.68024i	−0.124537	+	0.0719017i	−0.560975	−	0.827833i	$-0.689573\pi$
$79$	−9.83846	+	5.68024i	−0.124537	+	0.0719017i	0.436437	+	0.899735i	$0.356240\pi$
$80$		0			0
$81$	40.5952	+	70.0930i	0.501175	+	0.865346i
$82$		0			0
$83$	−72.7825	−	126.063i	−0.876897	−	1.51883i	−0.854728	−	0.519076i	$-0.826276\pi$
$83$	−72.7825	−	126.063i	−0.876897	−	1.51883i	−0.0221693	−	0.999754i	$-0.507057\pi$
$84$		0			0
$85$	4.50836	−	7.80871i	0.0530395	−	0.0918672i
$86$		0			0
$87$	−12.8932	−	48.0530i	−0.148198	−	0.552333i
$88$		0			0
$89$		−	102.417i		−	1.15076i	−0.817887	−	0.575378i	$-0.804855\pi$
$89$		−	102.417i		−	1.15076i	0.817887	−	0.575378i	$-0.195145\pi$
$90$		0			0
$91$			30.1171i			0.330958i
$92$		0			0
$93$	88.3977	−	88.4577i	0.950512	−	0.951158i
$94$		0			0
$95$	28.5470	−	7.34171i	0.300495	−	0.0772811i
$96$		0			0
$97$	−140.473	+	81.1019i	−1.44817	+	0.836102i	−0.998373	−	0.0570274i	$-0.981838\pi$
$97$	−140.473	+	81.1019i	−1.44817	+	0.836102i	−0.449799	+	0.893130i	$0.648504\pi$
$98$		0			0
$99$	−0.106364	−	156.762i	−0.00107438	−	1.58345i
$100$		0			0
$101$	61.0334	+	105.713i	0.604291	+	1.04666i	0.992163	+	0.124950i	$0.0398769\pi$
$101$	61.0334	+	105.713i	0.604291	+	1.04666i	−0.387872	+	0.921713i	$0.626790\pi$
$102$		0			0
$103$	−139.624	−	80.6118i	−1.35557	−	0.782639i	−0.366547	−	0.930399i	$-0.619460\pi$
$103$	−139.624	−	80.6118i	−1.35557	−	0.782639i	−0.989023	+	0.147761i	$0.952793\pi$
$104$		0			0
$105$	−1.80250	+	6.73615i	−0.0171666	+	0.0641538i
$106$		0			0
$107$			86.0891i			0.804571i	0.915514	+	0.402286i	$0.131784\pi$
$107$			86.0891i			0.804571i	−0.915514	+	0.402286i	$0.868216\pi$
$108$		0			0
$109$		−	187.205i		−	1.71748i	−0.512412	−	0.858740i	$-0.671248\pi$
$109$		−	187.205i		−	1.71748i	0.512412	−	0.858740i	$-0.328752\pi$
$110$		0			0
$111$	−100.231	−	26.8204i	−0.902983	−	0.241625i
$112$		0			0
$113$	53.2005	+	30.7153i	0.470801	+	0.271817i	0.716575	−	0.697510i	$-0.245709\pi$
$113$	53.2005	+	30.7153i	0.470801	+	0.271817i	−0.245774	+	0.969327i	$0.579042\pi$
$114$		0			0
$115$	23.8811	+	41.3634i	0.207662	+	0.359681i
$116$		0			0
$117$	90.5614	+	156.611i	0.774029	+	1.33856i
$118$		0			0
$119$	4.35409	+	7.54151i	0.0365890	+	0.0633741i
$120$		0			0
$121$	−91.1932	+	157.951i	−0.753663	+	1.30538i
$122$		0			0
$123$	39.3791	−	39.4058i	0.320155	−	0.320372i
$124$		0			0
$125$	−73.8345			−0.590676
$126$		0			0
$127$			11.4726i			0.0903355i	0.998979	+	0.0451678i	$0.0143822\pi$
$127$			11.4726i			0.0903355i	−0.998979	+	0.0451678i	$0.985618\pi$
$128$		0			0
$129$	−105.326	+	28.2603i	−0.816480	+	0.219072i
$130$		0			0
$131$	−59.8966	+	103.744i	−0.457226	+	0.791938i	−0.998813	−	0.0487062i	$-0.984490\pi$
$131$	−59.8966	+	103.744i	−0.457226	+	0.791938i	0.541587	+	0.840644i	$0.317824\pi$
$132$		0			0
$133$	−7.64454	+	27.4217i	−0.0574777	+	0.206178i
$134$		0			0
$135$	10.8823	+	40.4485i	0.0806095	+	0.299619i
$136$		0			0
$137$	−81.3798	−	140.954i	−0.594013	−	1.02886i	−0.993685	−	0.112203i	$-0.964209\pi$
$137$	−81.3798	−	140.954i	−0.594013	−	1.02886i	0.399672	−	0.916658i	$-0.369124\pi$
$138$		0			0
$139$	−2.58212	+	4.47237i	−0.0185764	+	0.0321753i	−0.875164	−	0.483826i	$-0.839247\pi$
$139$	−2.58212	+	4.47237i	−0.0185764	+	0.0321753i	0.856588	+	0.516001i	$0.172580\pi$
$140$		0			0
$141$	194.429	−	52.1678i	1.37893	−	0.369984i
$142$		0			0
$143$		−	350.121i		−	2.44840i
$144$		0			0
$145$		−	25.7282i		−	0.177436i
$146$		0			0
$147$	99.2163	+	99.1490i	0.674941	+	0.674483i
$148$		0			0
$149$	−117.757	+	203.961i	−0.790315	+	1.36887i	0.135457	+	0.990783i	$0.456750\pi$
$149$	−117.757	+	203.961i	−0.790315	+	1.36887i	−0.925772	+	0.378082i	$0.876584\pi$
$150$		0			0
$151$	−78.4083	+	45.2691i	−0.519260	+	0.299795i	−0.736632	−	0.676294i	$-0.763585\pi$
$151$	−78.4083	+	45.2691i	−0.519260	+	0.299795i	0.217372	+	0.976089i	$0.430252\pi$
$152$		0			0
$153$	45.3187	+	26.1238i	0.296201	+	0.170744i
$154$		0			0
$155$	56.0050	−	32.3345i	0.361322	−	0.208610i
$156$		0			0
$157$	−144.554	+	250.375i	−0.920725	+	1.59474i	−0.122429	+	0.992477i	$0.539068\pi$
$157$	−144.554	+	250.375i	−0.920725	+	1.59474i	−0.798296	+	0.602265i	$0.794265\pi$
$158$		0			0
$159$	266.587	+	71.3347i	1.67665	+	0.448646i
$160$		0			0
$161$	−46.1280			−0.286509
$162$		0			0
$163$	−39.1297			−0.240060			−0.120030	−	0.992770i	$-0.538299\pi$
$163$	−39.1297			−0.240060			−0.120030	+	0.992770i	$0.538299\pi$
$164$		0			0
$165$	20.9546	−	78.3099i	0.126998	−	0.474605i
$166$		0			0
$167$	−108.100	−	62.4118i	−0.647308	−	0.373724i	0.140116	−	0.990135i	$-0.455252\pi$
$167$	−108.100	−	62.4118i	−0.647308	−	0.373724i	−0.787424	+	0.616411i	$0.788586\pi$
$168$		0			0
$169$	117.528	+	203.564i	0.695431	+	1.20452i
$170$		0			0
$171$	42.7041	+	165.582i	0.249732	+	0.968315i
$172$		0			0
$173$	−52.4480	+	30.2809i	−0.303168	+	0.175034i	−0.643865	−	0.765139i	$-0.722670\pi$
$173$	−52.4480	+	30.2809i	−0.303168	+	0.175034i	0.340697	+	0.940173i	$0.389337\pi$
$174$		0			0
$175$	16.9255	−	29.3159i	0.0967173	−	0.167519i
$176$		0			0
$177$	5.54487	−	5.54863i	0.0313270	−	0.0313482i
$178$		0			0
$179$			204.210i			1.14084i	0.821354	+	0.570419i	$0.193219\pi$
$179$			204.210i			1.14084i	−0.821354	+	0.570419i	$0.806781\pi$
$180$		0			0
$181$			209.010i			1.15475i	0.816478	+	0.577376i	$0.195923\pi$
$181$			209.010i			1.15475i	−0.816478	+	0.577376i	$0.804077\pi$
$182$		0			0
$183$	98.2355	−	26.3579i	0.536806	−	0.144032i
$184$		0			0
$185$	−46.4668	−	26.8276i	−0.251172	−	0.145014i
$186$		0			0
$187$	−50.6177	−	87.6725i	−0.270683	−	0.468837i
$188$		0			0
$189$	−39.0858	−	10.4304i	−0.206803	−	0.0551872i
$190$		0			0
$191$	−120.215	−	208.219i	−0.629399	−	1.09015i	−0.987672	−	0.156535i	$-0.949968\pi$
$191$	−120.215	−	208.219i	−0.629399	−	1.09015i	0.358273	−	0.933617i	$-0.383366\pi$
$192$		0			0
$193$	219.115	+	126.506i	1.13531	+	0.655471i	0.945265	−	0.326304i	$-0.105803\pi$
$193$	219.115	+	126.506i	1.13531	+	0.655471i	0.190045	+	0.981775i	$0.439137\pi$
$194$		0			0
$195$	24.2439	+	90.3567i	0.124327	+	0.463368i
$196$		0			0
$197$	39.0812			0.198382			0.0991909	−	0.995068i	$-0.468375\pi$
$197$	39.0812			0.198382			0.0991909	+	0.995068i	$0.468375\pi$
$198$		0			0
$199$	−125.480			−0.630553			−0.315277	−	0.949000i	$-0.602097\pi$
$199$	−125.480			−0.630553			−0.315277	+	0.949000i	$0.602097\pi$
$200$		0			0
$201$	−67.2013	+	67.2469i	−0.334335	+	0.334562i
$202$		0			0
$203$	21.5188	+	12.4239i	0.106004	+	0.0612015i
$204$		0			0
$205$	24.9489	−	14.4042i	0.121702	−	0.0702646i
$206$		0			0
$207$	−239.869	+	138.705i	−1.15879	+	0.670075i
$208$		0			0
$209$	88.8702	−	318.786i	0.425216	−	1.52529i
$210$		0			0
$211$	−278.670	−	160.890i	−1.32071	−	0.762513i	−0.336869	−	0.941552i	$-0.609368\pi$
$211$	−278.670	−	160.890i	−1.32071	−	0.762513i	−0.983842	+	0.179039i	$0.942701\pi$
$212$		0			0
$213$	15.8093	+	4.23034i	0.0742220	+	0.0198607i
$214$		0			0
$215$	−56.3928			−0.262292
$216$		0			0
$217$			62.4561i			0.287816i
$218$		0			0
$219$	−93.9510	+	351.106i	−0.429000	+	1.60322i
$220$		0			0
$221$	101.178	+	58.4151i	0.457819	+	0.264322i
$222$		0			0
$223$	−86.9311	+	50.1897i	−0.389826	+	0.225066i	−0.682085	−	0.731273i	$-0.738926\pi$
$223$	−86.9311	+	50.1897i	−0.389826	+	0.225066i	0.292259	+	0.956339i	$0.405593\pi$
$224$		0			0
$225$	−0.137967	−	203.339i	−0.000613188	−	0.903730i
$226$		0			0
$227$	317.008	−	183.025i	1.39651	−	0.806276i	0.402486	−	0.915426i	$-0.368146\pi$
$227$	317.008	−	183.025i	1.39651	−	0.806276i	0.994025	+	0.109150i	$0.0348130\pi$
$228$		0			0
$229$	−88.2418	+	152.839i	−0.385335	+	0.667420i	−0.991816	−	0.127678i	$-0.959248\pi$
$229$	−88.2418	+	152.839i	−0.385335	+	0.667420i	0.606480	+	0.795099i	$0.292581\pi$
$230$		0			0
$231$	55.3789	+	55.3414i	0.239736	+	0.239573i
$232$		0			0
$233$	−298.357			−1.28050			−0.640250	−	0.768166i	$-0.721169\pi$
$233$	−298.357			−1.28050			−0.640250	+	0.768166i	$0.721169\pi$
$234$		0			0
$235$	104.100			0.442977
$236$		0			0
$237$	−8.83209	−	32.9171i	−0.0372662	−	0.138891i
$238$		0			0
$239$	−19.5215	+	33.8122i	−0.0816799	+	0.141474i	−0.903972	−	0.427592i	$-0.859362\pi$
$239$	−19.5215	+	33.8122i	−0.0816799	+	0.141474i	0.822292	+	0.569066i	$0.192695\pi$
$240$		0			0
$241$	−213.426	+	123.222i	−0.885585	+	0.511293i	−0.872496	−	0.488622i	$-0.837500\pi$
$241$	−213.426	+	123.222i	−0.885585	+	0.511293i	−0.0130891	+	0.999914i	$0.504167\pi$
$242$		0			0
$243$	−234.613	+	63.2911i	−0.965485	+	0.260457i
$244$		0			0
$245$	36.2672	+	62.8166i	0.148029	+	0.256394i
$246$		0			0
$247$	95.1270	+	369.885i	0.385129	+	1.49751i
$248$		0			0
$249$	421.776	−	113.168i	1.69388	−	0.454490i
$250$		0			0
$251$	78.4174			0.312420			0.156210	−	0.987724i	$-0.450072\pi$
$251$	78.4174			0.312420			0.156210	+	0.987724i	$0.450072\pi$
$252$		0			0
$253$	536.252			2.11957
$254$		0			0
$255$	19.1338	+	19.1209i	0.0750347	+	0.0749838i
$256$		0			0
$257$	310.826	+	179.455i	1.20944	+	0.698270i	0.962637	−	0.270796i	$-0.0872869\pi$
$257$	310.826	+	179.455i	1.20944	+	0.698270i	0.246802	+	0.969066i	$0.420620\pi$
$258$		0			0
$259$	44.8768	−	25.9096i	0.173270	−	0.100037i
$260$		0			0
$261$	149.258	−	0.101273i	0.571869	−	0.000388017i
$262$		0			0
$263$	−46.2374	−	80.0855i	−0.175808	−	0.304508i	0.764633	−	0.644466i	$-0.222920\pi$
$263$	−46.2374	−	80.0855i	−0.175808	−	0.304508i	−0.940440	+	0.339958i	$0.889587\pi$
$264$		0			0
$265$	123.589	+	71.3539i	0.466372	+	0.269260i
$266$		0			0
$267$	296.810	+	79.4220i	1.11165	+	0.297461i
$268$		0			0
$269$		−	394.275i		−	1.46570i	−0.680388	−	0.732852i	$-0.738189\pi$
$269$		−	394.275i		−	1.46570i	0.680388	−	0.732852i	$-0.261811\pi$
$270$		0			0
$271$	−375.694			−1.38632			−0.693162	−	0.720782i	$-0.743783\pi$
$271$	−375.694			−1.38632			−0.693162	+	0.720782i	$0.743783\pi$
$272$		0			0
$273$	−87.2807	−	23.3551i	−0.319710	−	0.0855497i
$274$		0			0
$275$	−196.765	+	340.806i	−0.715508	+	1.23930i
$276$		0			0
$277$	194.097	+	336.186i	0.700712	+	1.21367i	0.968217	+	0.250113i	$0.0804676\pi$
$277$	194.097	+	336.186i	0.700712	+	1.21367i	−0.267505	+	0.963557i	$0.586199\pi$
$278$		0			0
$279$	187.804	+	324.777i	0.673132	+	1.16407i
$280$		0			0
$281$	126.365	−	72.9571i	0.449699	−	0.259634i	−0.258004	−	0.966144i	$-0.583065\pi$
$281$	126.365	−	72.9571i	0.449699	−	0.259634i	0.707703	+	0.706510i	$0.249731\pi$
$282$		0			0
$283$	144.253	−	249.854i	0.509729	−	0.882877i	−0.490207	−	0.871606i	$-0.663079\pi$
$283$	144.253	−	249.854i	0.509729	−	0.882877i	0.999936	−	0.0112708i	$-0.00358769\pi$
$284$		0			0
$285$	−0.860882	+	88.4236i	−0.00302064	+	0.310258i
$286$		0			0
$287$			27.8227i			0.0969433i
$288$		0			0
$289$	−255.219			−0.883112
$290$		0			0
$291$	−126.104	−	469.988i	−0.433346	−	1.61508i
$292$		0			0
$293$	402.264	+	232.247i	1.37291	+	0.792653i	0.991294	−	0.131667i	$-0.0420328\pi$
$293$	402.264	+	232.247i	1.37291	+	0.792653i	0.381620	+	0.924319i	$0.375366\pi$
$294$		0			0
$295$	3.51299	−	2.02823i	0.0119084	−	0.00687535i
$296$		0			0
$297$	454.385	+	121.257i	1.52991	+	0.408271i
$298$		0			0
$299$	−535.948	+	309.430i	−1.79247	+	1.03488i
$300$		0			0
$301$	27.2316	−	47.1665i	0.0904704	−	0.156699i
$302$		0			0
$303$	−353.690	+	94.8996i	−1.16729	+	0.313200i
$304$		0			0
$305$	52.5965			0.172448
$306$		0			0
$307$			78.7537i			0.256527i	0.991740	+	0.128263i	$0.0409403\pi$
$307$			78.7537i			0.256527i	−0.991740	+	0.128263i	$0.959060\pi$
$308$		0			0
$309$	341.891	−	342.123i	1.10644	−	1.10719i
$310$		0			0
$311$	66.2776	−	114.796i	0.213111	−	0.369119i	−0.739575	−	0.673074i	$-0.764974\pi$
$311$	66.2776	−	114.796i	0.213111	−	0.369119i	0.952687	+	0.303954i	$0.0983070\pi$
$312$		0			0
$313$	156.846	+	271.665i	0.501105	+	0.867940i	0.999999	+	0.00127682i	$0.000406425\pi$
$313$	156.846	+	271.665i	0.501105	+	0.867940i	−0.498894	+	0.866663i	$0.666260\pi$
$314$		0			0
$315$	−18.1238	−	10.4474i	−0.0575360	−	0.0331664i
$316$		0			0
$317$	−325.071	+	187.680i	−1.02546	+	0.592049i	−0.915681	−	0.401907i	$-0.868348\pi$
$317$	−325.071	+	187.680i	−1.02546	+	0.592049i	−0.109779	+	0.993956i	$0.535014\pi$
$318$		0			0
$319$	−250.163	−	144.432i	−0.784211	−	0.452764i
$320$		0			0
$321$	−249.490	−	66.7599i	−0.777227	−	0.207975i
$322$		0			0
$323$	77.2954	+	78.8688i	0.239305	+	0.244176i
$324$		0			0
$325$		−	454.150i		−	1.39739i
$326$		0			0
$327$	542.528	+	145.173i	1.65911	+	0.443954i
$328$		0			0
$329$	−50.2688	+	87.0681i	−0.152793	+	0.264645i
$330$		0			0
$331$	107.188	−	61.8848i	0.323830	−	0.186963i	−0.329269	−	0.944236i	$-0.606802\pi$
$331$	107.188	−	61.8848i	0.323830	−	0.186963i	0.653098	+	0.757273i	$0.273469\pi$
$332$		0			0
$333$	155.453	−	269.675i	0.466827	−	0.809836i
$334$		0			0
$335$	−42.5758	+	24.5812i	−0.127092	+	0.0733766i
$336$		0			0
$337$	−433.884	−	250.503i	−1.28749	−	0.743332i	−0.309283	−	0.950970i	$-0.600089\pi$
$337$	−433.884	−	250.503i	−1.28749	−	0.743332i	−0.978206	+	0.207638i	$0.933422\pi$
$338$		0			0
$339$	−130.270	+	130.358i	−0.384277	+	0.384538i
$340$		0			0
$341$		−	726.072i		−	2.12924i
$342$		0			0
$343$	−143.468			−0.418274
$344$		0			0
$345$	−138.392	+	37.1323i	−0.401136	+	0.107630i
$346$		0			0
$347$	196.520	−	340.382i	0.566339	−	0.980928i	−0.430585	−	0.902550i	$-0.641693\pi$
$347$	196.520	−	340.382i	0.566339	−	0.980928i	0.996924	−	0.0783777i	$-0.0249740\pi$
$348$		0			0
$349$	−156.324	−	270.761i	−0.447919	−	0.775819i	0.550331	−	0.834947i	$-0.314501\pi$
$349$	−156.324	−	270.761i	−0.447919	−	0.775819i	−0.998250	+	0.0591275i	$0.981168\pi$
$350$		0			0
$351$	−524.094	+	141.003i	−1.49315	+	0.401717i
$352$		0			0
$353$	−24.7463	−	42.8619i	−0.0701029	−	0.121422i	0.828843	−	0.559481i	$-0.188999\pi$
$353$	−24.7463	−	42.8619i	−0.0701029	−	0.121422i	−0.898946	+	0.438059i	$0.855666\pi$
$354$		0			0
$355$	7.32913	+	4.23147i	0.0206454	+	0.0119196i
$356$		0			0
$357$	−25.2321	+	6.77010i	−0.0706781	+	0.0189639i
$358$		0			0
$359$	87.4889			0.243702			0.121851	−	0.992548i	$-0.461117\pi$
$359$	87.4889			0.243702			0.121851	+	0.992548i	$0.461117\pi$
$360$		0			0
$361$	−7.27353	+	360.927i	−0.0201483	+	0.999797i
$362$		0			0
$363$	−387.031	−	386.769i	−1.06620	−	1.06548i
$364$		0			0
$365$	−93.9762	+	162.772i	−0.257469	+	0.445950i
$366$		0			0
$367$	−272.981	−	472.817i	−0.743817	−	1.28833i	−0.950745	−	0.309973i	$-0.899680\pi$
$367$	−272.981	−	472.817i	−0.743817	−	1.28833i	0.206928	−	0.978356i	$-0.433653\pi$
$368$		0			0
$369$	83.6621	+	144.680i	0.226727	+	0.392088i
$370$		0			0
$371$	−119.360	+	68.9123i	−0.321724	+	0.185747i
$372$		0			0
$373$	−297.949	−	172.021i	−0.798791	−	0.461182i	0.0442573	−	0.999020i	$-0.485908\pi$
$373$	−297.949	−	172.021i	−0.798791	−	0.461182i	−0.843048	+	0.537838i	$0.819241\pi$
$374$		0			0
$375$	57.2568	−	213.975i	0.152685	−	0.570601i
$376$		0			0
$377$	333.361			0.884248
$378$		0			0
$379$			201.866i			0.532627i	0.963886	+	0.266314i	$0.0858057\pi$
$379$			201.866i			0.532627i	−0.963886	+	0.266314i	$0.914194\pi$
$380$		0			0
$381$	−33.2481	−	8.89671i	−0.0872653	−	0.0233509i
$382$		0			0
$383$	595.776	+	343.971i	1.55555	+	0.898098i	0.997673	+	0.0681747i	$0.0217175\pi$
$383$	595.776	+	343.971i	1.55555	+	0.898098i	0.557878	+	0.829923i	$0.311616\pi$
$384$		0			0
$385$	20.2430	+	35.0619i	0.0525792	+	0.0910699i
$386$		0			0
$387$	−0.221976	−	327.154i	−0.000573582	−	0.845359i
$388$		0			0
$389$	201.187	+	348.465i	0.517189	+	0.895798i	0.999801	+	0.0199632i	$0.00635491\pi$
$389$	201.187	+	348.465i	0.517189	+	0.895798i	−0.482612	+	0.875834i	$0.660312\pi$
$390$		0			0
$391$	−89.4697	+	154.966i	−0.228823	+	0.396333i
$392$		0			0
$393$	−254.206	−	254.033i	−0.646834	−	0.646396i
$394$		0			0
$395$		−	17.6242i		−	0.0446183i
$396$		0			0
$397$	−59.2042			−0.149129			−0.0745645	−	0.997216i	$-0.523757\pi$
$397$	−59.2042			−0.149129			−0.0745645	+	0.997216i	$0.523757\pi$
$398$		0			0
$399$	−73.5411	−	43.4190i	−0.184313	−	0.108820i
$400$		0			0
$401$	−584.250	−	337.317i	−1.45698	−	0.841189i	−0.458120	−	0.888890i	$-0.651477\pi$
$401$	−584.250	−	337.317i	−1.45698	−	0.841189i	−0.998862	+	0.0477019i	$0.984810\pi$
$402$		0			0
$403$	418.960	+	725.660i	1.03960	+	1.80065i
$404$		0			0
$405$	−125.660	+	0.170523i	−0.310273	+	0.000421045i
$406$		0			0
$407$	−521.707	+	301.208i	−1.28184	+	0.740068i
$408$		0			0
$409$	195.808	+	113.050i	0.478749	+	0.276406i	0.719895	−	0.694083i	$-0.244190\pi$
$409$	195.808	+	113.050i	0.478749	+	0.276406i	−0.241146	+	0.970489i	$0.577523\pi$
$410$		0			0
$411$	471.598	−	126.536i	1.14744	−	0.307873i
$412$		0			0
$413$			3.91765i			0.00948584i
$414$		0			0
$415$	225.824			0.544155
$416$		0			0
$417$	−10.9587	−	10.9513i	−0.0262799	−	0.0262621i
$418$		0			0
$419$	252.860	−	437.966i	0.603484	−	1.04526i	−0.388805	−	0.921320i	$-0.627112\pi$
$419$	252.860	−	437.966i	0.603484	−	1.04526i	0.992289	−	0.123945i	$-0.0395545\pi$
$420$		0			0
$421$	362.556	−	209.322i	0.861179	−	0.497202i	−0.00322821	−	0.999995i	$-0.501028\pi$
$421$	362.556	−	209.322i	0.861179	−	0.497202i	0.864407	+	0.502793i	$0.167694\pi$
$422$		0			0
$423$	0.409762	+	603.918i	0.000968706	+	1.42770i
$424$		0			0
$425$	−65.6574	−	113.722i	−0.154488	−	0.267581i
$426$		0			0
$427$	−25.3984	+	43.9913i	−0.0594810	+	0.103024i
$428$		0			0
$429$	1014.67	+	271.510i	2.36519	+	0.632891i
$430$		0			0
$431$		−	313.017i		−	0.726257i	−0.931739	−	0.363129i	$-0.881709\pi$
$431$		−	313.017i		−	0.726257i	0.931739	−	0.363129i	$-0.118291\pi$
$432$		0			0
$433$			439.155i			1.01421i	0.861883	+	0.507107i	$0.169285\pi$
$433$			439.155i			1.01421i	−0.861883	+	0.507107i	$0.830715\pi$
$434$		0			0
$435$	74.5613	+	19.9515i	0.171405	+	0.0458656i
$436$		0			0
$437$	−566.523	+	145.698i	−1.29639	+	0.333405i
$438$		0			0
$439$	−145.713	+	84.1275i	−0.331921	+	0.191635i	−0.656694	−	0.754158i	$-0.728045\pi$
$439$	−145.713	+	84.1275i	−0.331921	+	0.191635i	0.324773	+	0.945792i	$0.394712\pi$
$440$		0			0
$441$	−364.278	+	210.645i	−0.826026	+	0.477654i
$442$		0			0
$443$	−118.109	−	204.571i	−0.266612	−	0.461786i	0.701372	−	0.712795i	$-0.252571\pi$
$443$	−118.109	−	204.571i	−0.266612	−	0.461786i	−0.967985	+	0.251009i	$0.919238\pi$
$444$		0			0
$445$	137.600	+	79.4434i	0.309213	+	0.178524i
$446$		0			0
$447$	−499.770	−	499.431i	−1.11805	−	1.11729i
$448$		0			0
$449$			128.160i			0.285435i	0.989763	+	0.142718i	$0.0455841\pi$
$449$			128.160i			0.285435i	−0.989763	+	0.142718i	$0.954416\pi$
$450$		0			0
$451$		−	323.448i		−	0.717180i
$452$		0			0
$453$	−70.3880	−	262.336i	−0.155382	−	0.579107i
$454$		0			0
$455$	−40.4630	−	23.3613i	−0.0889297	−	0.0513436i
$456$		0			0
$457$	−105.345	−	182.463i	−0.230515	−	0.399263i	0.727445	−	0.686166i	$-0.240708\pi$
$457$	−105.345	−	182.463i	−0.230515	−	0.399263i	−0.957960	+	0.286903i	$0.907374\pi$
$458$		0			0
$459$	−110.851	+	111.077i	−0.241506	+	0.241998i
$460$		0			0
$461$	−433.506	−	750.855i	−0.940361	−	1.62875i	−0.764784	−	0.644287i	$-0.777154\pi$
$461$	−433.506	−	750.855i	−0.940361	−	1.62875i	−0.175577	−	0.984466i	$-0.556179\pi$
$462$		0			0
$463$	223.388	−	386.919i	0.482479	−	0.835678i	−0.517319	−	0.855793i	$-0.673070\pi$
$463$	223.388	−	386.919i	0.482479	−	0.835678i	0.999798	+	0.0201149i	$0.00640321\pi$
$464$		0			0
$465$	50.2762	+	187.379i	0.108121	+	0.402966i
$466$		0			0
$467$	321.260			0.687922			0.343961	−	0.938984i	$-0.388231\pi$
$467$	321.260			0.687922			0.343961	+	0.938984i	$0.388231\pi$
$468$		0			0
$469$		−	47.4801i		−	0.101237i
$470$		0			0
$471$	−613.498	−	613.082i	−1.30254	−	1.30166i
$472$		0			0
$473$	−316.576	+	548.325i	−0.669294	+	1.15925i
$474$		0			0
$475$	115.276	−	413.505i	0.242685	−	0.870536i
$476$		0			0
$477$	−413.462	+	717.261i	−0.866796	+	1.50369i
$478$		0			0
$479$	−142.239	−	246.365i	−0.296950	−	0.514333i	0.678486	−	0.734613i	$-0.262636\pi$
$479$	−142.239	−	246.365i	−0.296950	−	0.514333i	−0.975437	+	0.220280i	$0.929303\pi$
$480$		0			0
$481$	347.607	−	602.074i	0.722676	−	1.25171i
$482$		0			0
$483$	35.7710	−	133.681i	0.0740601	−	0.276772i
$484$		0			0
$485$		−	251.637i		−	0.518840i
$486$		0			0
$487$		−	1.29990i		−	0.00266919i	−0.999999	−	0.00133460i	$-0.999575\pi$
$487$		−	1.29990i		−	0.00266919i	0.999999	−	0.00133460i	$-0.000424815\pi$
$488$		0			0
$489$	30.3441	−	113.400i	0.0620534	−	0.231901i
$490$		0			0
$491$	−58.2447	+	100.883i	−0.118625	+	0.205464i	−0.919223	−	0.393738i	$-0.871182\pi$
$491$	−58.2447	+	100.883i	−0.118625	+	0.205464i	0.800598	+	0.599202i	$0.204515\pi$
$492$		0			0
$493$	83.4757	−	48.1947i	0.169322	−	0.0977581i
$494$		0			0
$495$	210.695	+	121.455i	0.425647	+	0.245363i
$496$		0			0
$497$	−7.07834	+	4.08668i	−0.0142421	+	0.00822270i
$498$		0			0
$499$	188.028	−	325.674i	0.376809	−	0.652653i	−0.613787	−	0.789472i	$-0.710354\pi$
$499$	188.028	−	325.674i	0.376809	−	0.652653i	0.990596	+	0.136819i	$0.0436878\pi$
$500$		0			0
$501$	264.701	−	264.881i	0.528346	−	0.528704i
$502$		0			0
$503$	−115.968			−0.230552			−0.115276	−	0.993334i	$-0.536775\pi$
$503$	−115.968			−0.230552			−0.115276	+	0.993334i	$0.536775\pi$
$504$		0			0
$505$	−189.370			−0.374990
$506$		0			0
$507$	−681.078	+	182.742i	−1.34335	+	0.360438i
$508$		0			0
$509$	−410.351	−	236.917i	−0.806191	−	0.465455i	0.0394401	−	0.999222i	$-0.487443\pi$
$509$	−410.351	−	236.917i	−0.806191	−	0.465455i	−0.845632	+	0.533767i	$0.820776\pi$
$510$		0			0
$511$	−90.7606	−	157.202i	−0.177614	−	0.307636i
$512$		0			0
$513$	−512.979	−	4.64621i	−0.999959	−	0.00905695i
$514$		0			0
$515$	216.607	−	125.058i	0.420597	−	0.242832i
$516$		0			0
$517$	584.391	−	1012.19i	1.13035	−	1.95782i
$518$		0			0
$519$	−47.0831	−	175.479i	−0.0907190	−	0.338109i
$520$		0			0
$521$			279.583i			0.536628i	0.963331	+	0.268314i	$0.0864665\pi$
$521$			279.583i			0.536628i	−0.963331	+	0.268314i	$0.913533\pi$
$522$		0			0
$523$		−	242.691i		−	0.464036i	−0.972711	−	0.232018i	$-0.925467\pi$
$523$		−	242.691i		−	0.464036i	0.972711	−	0.232018i	$-0.0745328\pi$
$524$		0			0
$525$	71.8333	+	71.7846i	0.136825	+	0.136732i
$526$		0			0
$527$	209.820	+	121.140i	0.398141	+	0.229867i
$528$		0			0
$529$	−209.428	−	362.740i	−0.395894	−	0.685708i
$530$		0			0
$531$	11.7803	+	20.3721i	0.0221851	+	0.0383655i
$532$		0			0
$533$	186.637	+	323.264i	0.350163	+	0.606500i
$534$		0			0
$535$	−115.663	−	66.7778i	−0.216192	−	0.124818i
$536$		0			0
$537$	−591.808	−	158.359i	−1.10206	−	0.294896i
$538$		0			0
$539$	814.381			1.51091
$540$		0			0
$541$	−85.1975			−0.157482			−0.0787408	−	0.996895i	$-0.525090\pi$
$541$	−85.1975			−0.157482			−0.0787408	+	0.996895i	$0.525090\pi$
$542$		0			0
$543$	−605.720	−	162.082i	−1.11551	−	0.298494i
$544$		0			0
$545$	251.514	+	145.212i	0.461494	+	0.266444i
$546$		0			0
$547$	−198.566	+	114.642i	−0.363008	+	0.209583i	−0.670400	−	0.742000i	$-0.733877\pi$
$547$	−198.566	+	114.642i	−0.363008	+	0.209583i	0.307391	+	0.951583i	$0.400544\pi$
$548$		0			0
$549$	0.207033	+	305.130i	0.000377110	+	0.555793i
$550$		0			0
$551$	303.526	+	84.6161i	0.550864	+	0.153568i
$552$		0			0
$553$	14.7408	+	8.51059i	0.0266560	+	0.0153899i
$554$		0			0
$555$	113.781	−	113.859i	0.205011	−	0.205151i
$556$		0			0
$557$	840.648			1.50924			0.754621	−	0.656161i	$-0.227821\pi$
$557$	840.648			1.50924			0.754621	+	0.656161i	$0.227821\pi$
$558$		0			0
$559$		−	730.686i		−	1.30713i
$560$		0			0
$561$	293.331	−	78.7045i	0.522872	−	0.140293i
$562$		0			0
$563$	276.643	+	159.720i	0.491374	+	0.283695i	0.725144	−	0.688597i	$-0.241773\pi$
$563$	276.643	+	159.720i	0.491374	+	0.283695i	−0.233771	+	0.972292i	$0.575106\pi$
$564$		0			0
$565$	−82.5334	+	47.6507i	−0.146077	+	0.0843374i
$566$		0			0
$567$	60.5377	−	105.184i	0.106768	−	0.185509i
$568$		0			0
$569$	−797.982	+	460.715i	−1.40243	+	0.809693i	−0.994642	−	0.103384i	$-0.967033\pi$
$569$	−797.982	+	460.715i	−1.40243	+	0.809693i	−0.407788	+	0.913077i	$0.633700\pi$
$570$		0			0
$571$	89.3788	−	154.809i	0.156530	−	0.271118i	−0.777085	−	0.629396i	$-0.783302\pi$
$571$	89.3788	−	154.809i	0.156530	−	0.271118i	0.933615	+	0.358277i	$0.116636\pi$
$572$		0			0
$573$	696.651	−	186.920i	1.21580	−	0.326213i
$574$		0			0
$575$	695.585			1.20971
$576$		0			0
$577$	847.332			1.46851			0.734257	−	0.678872i	$-0.237531\pi$
$577$	847.332			1.46851			0.734257	+	0.678872i	$0.237531\pi$
$578$		0			0
$579$	−536.537	+	536.901i	−0.926662	+	0.927291i
$580$		0			0
$581$	−109.049	+	188.878i	−0.187691	+	0.325091i
$582$		0			0
$583$	1387.59	−	801.128i	2.38009	−	1.37415i
$584$		0			0
$585$	−280.658	+	0.190428i	−0.479757	+	0.000325519i
$586$		0			0
$587$	114.883	+	198.983i	0.195712	+	0.338983i	0.947134	−	0.320839i	$-0.103965\pi$
$587$	114.883	+	198.983i	0.195712	+	0.338983i	−0.751422	+	0.659822i	$0.770632\pi$
$588$		0			0
$589$	197.272	+	767.058i	0.334926	+	1.30231i
$590$		0			0
$591$	−30.3065	+	113.259i	−0.0512800	+	0.191640i
$592$		0			0
$593$	1005.52			1.69564			0.847821	−	0.530282i	$-0.177914\pi$
$593$	1005.52			1.69564			0.847821	+	0.530282i	$0.177914\pi$
$594$		0			0
$595$	−13.5096			−0.0227052
$596$		0			0
$597$	97.3065	−	363.646i	0.162993	−	0.609123i
$598$		0			0
$599$	777.097	+	448.657i	1.29732	+	0.749010i	0.979941	−	0.199288i	$-0.0638628\pi$
$599$	777.097	+	448.657i	1.29732	+	0.749010i	0.317382	+	0.948298i	$0.397196\pi$
$600$		0			0
$601$	−249.174	+	143.861i	−0.414600	+	0.239369i	−0.692764	−	0.721164i	$-0.743607\pi$
$601$	−249.174	+	143.861i	−0.414600	+	0.239369i	0.278165	+	0.960533i	$0.410274\pi$
$602$		0			0
$603$	−142.771	−	246.900i	−0.236768	−	0.409453i
$604$		0			0
$605$	−141.474	−	245.040i	−0.233841	−	0.405025i
$606$		0			0
$607$	331.532	+	191.410i	0.546181	+	0.315338i	0.747580	−	0.664171i	$-0.231215\pi$
$607$	331.532	+	191.410i	0.546181	+	0.315338i	−0.201399	+	0.979509i	$0.564549\pi$
$608$		0			0
$609$	−52.6922	+	52.7280i	−0.0865226	+	0.0865813i
$610$		0			0
$611$			1348.83i			2.20757i
$612$		0			0
$613$	47.2763			0.0771229			0.0385615	−	0.999256i	$-0.487722\pi$
$613$	47.2763			0.0771229			0.0385615	+	0.999256i	$0.487722\pi$
$614$		0			0
$615$	22.3969	+	83.4730i	0.0364177	+	0.135728i
$616$		0			0
$617$	−170.506	+	295.324i	−0.276346	+	0.478646i	−0.970474	−	0.241206i	$-0.922457\pi$
$617$	−170.506	+	295.324i	−0.276346	+	0.478646i	0.694128	+	0.719852i	$0.255790\pi$
$618$		0			0
$619$	−534.402	−	925.611i	−0.863330	−	1.49533i	−0.868695	−	0.495347i	$-0.835041\pi$
$619$	−534.402	−	925.611i	−0.863330	−	1.49533i	0.00536509	−	0.999986i	$-0.498292\pi$
$620$		0			0
$621$	−215.962	−	802.712i	−0.347765	−	1.29261i
$622$		0			0
$623$	−132.892	+	76.7250i	−0.213309	+	0.123154i
$624$		0			0
$625$	−225.144	+	389.960i	−0.360230	+	0.623936i
$626$		0			0
$627$	854.938	+	504.760i	1.36354	+	0.805040i
$628$		0			0
$629$		−	201.017i		−	0.319582i
$630$		0			0
$631$	−547.868			−0.868253			−0.434126	−	0.900852i	$-0.642943\pi$
$631$	−547.868			−0.868253			−0.434126	+	0.900852i	$0.642943\pi$
$632$		0			0
$633$	682.368	−	682.831i	1.07799	−	1.07872i
$634$		0			0
$635$	−15.4137	−	8.89910i	−0.0242735	−	0.0140143i
$636$		0			0
$637$	−813.918	+	469.916i	−1.27774	+	0.737702i
$638$		0			0
$639$	−24.5194	+	42.5354i	−0.0383715	+	0.0665656i
$640$		0			0
$641$	−118.114	+	68.1929i	−0.184265	+	0.106385i	−0.589295	−	0.807918i	$-0.700594\pi$
$641$	−118.114	+	68.1929i	−0.184265	+	0.106385i	0.405030	+	0.914303i	$0.367261\pi$
$642$		0			0
$643$	−432.221	+	748.629i	−0.672195	+	1.16428i	0.305086	+	0.952325i	$0.401315\pi$
$643$	−432.221	+	748.629i	−0.672195	+	1.16428i	−0.977280	+	0.211951i	$0.932018\pi$
$644$		0			0
$645$	43.7312	−	163.429i	0.0678003	−	0.253378i
$646$		0			0
$647$	−157.540			−0.243493			−0.121746	−	0.992561i	$-0.538849\pi$
$647$	−157.540			−0.243493			−0.121746	+	0.992561i	$0.538849\pi$
$648$		0			0
$649$		−	45.5439i		−	0.0701756i
$650$		0			0
$651$	−181.000	−	48.4331i	−0.278034	−	0.0743980i
$652$		0			0
$653$	391.071	−	677.355i	0.598884	−	1.03730i	−0.394102	−	0.919067i	$-0.628944\pi$
$653$	391.071	−	677.355i	0.598884	−	1.03730i	0.992986	−	0.118231i	$-0.0377222\pi$
$654$		0			0
$655$	−92.9215	−	160.945i	−0.141865	−	0.245717i
$656$		0			0
$657$	−944.664	−	544.548i	−1.43784	−	0.828839i
$658$		0			0
$659$	−788.598	+	455.297i	−1.19666	+	0.690891i	−0.959809	−	0.280655i	$-0.909448\pi$
$659$	−788.598	+	455.297i	−1.19666	+	0.690891i	−0.236850	+	0.971546i	$0.576115\pi$
$660$		0			0
$661$	381.101	+	220.029i	0.576553	+	0.332873i	0.759762	−	0.650201i	$-0.225315\pi$
$661$	381.101	+	220.029i	0.576553	+	0.332873i	−0.183209	+	0.983074i	$0.558649\pi$
$662$		0			0
$663$	−247.750	+	247.919i	−0.373681	+	0.373934i
$664$		0			0
$665$	−30.9119	−	31.5411i	−0.0464841	−	0.0474303i
$666$		0			0
$667$			510.582i			0.765491i
$668$		0			0
$669$	−78.0390	−	290.851i	−0.116650	−	0.434754i
$670$		0			0
$671$	295.264	−	511.413i	0.440036	−	0.762165i
$672$		0			0
$673$	354.716	−	204.796i	0.527068	−	0.304303i	−0.212754	−	0.977106i	$-0.568243\pi$
$673$	354.716	−	204.796i	0.527068	−	0.304303i	0.739822	+	0.672803i	$0.234910\pi$
$674$		0			0
$675$	589.393	+	157.285i	0.873174	+	0.233014i
$676$		0			0
$677$	−197.879	+	114.245i	−0.292288	+	0.168753i	−0.638973	−	0.769229i	$-0.720641\pi$
$677$	−197.879	+	114.245i	−0.292288	+	0.168753i	0.346685	+	0.937982i	$0.387307\pi$
$678$		0			0
$679$	210.467	+	121.513i	0.309967	+	0.178959i
$680$		0			0
$681$	284.581	+	1060.63i	0.417888	+	1.55746i
$682$		0			0
$683$		−	540.331i		−	0.791114i	−0.918441	−	0.395557i	$-0.870552\pi$
$683$		−	540.331i		−	0.791114i	0.918441	−	0.395557i	$-0.129448\pi$
$684$		0			0
$685$	252.500			0.368613
$686$		0			0
$687$	−374.505	−	374.251i	−0.545131	−	0.544762i
$688$		0			0
$689$	−924.537	+	1601.35i	−1.34185	+	2.32416i
$690$		0			0
$691$	−334.419	−	579.231i	−0.483964	−	0.838251i	0.515866	−	0.856669i	$-0.327470\pi$
$691$	−334.419	−	579.231i	−0.483964	−	0.838251i	−0.999830	+	0.0184185i	$0.994137\pi$
$692$		0			0
$693$	−203.326	+	117.575i	−0.293400	+	0.169660i
$694$		0			0
$695$	−4.00582	−	6.93828i	−0.00576376	−	0.00998313i
$696$		0			0
$697$	93.4699	+	53.9649i	0.134103	+	0.0774245i
$698$		0			0
$699$	231.368	−	864.649i	0.330998	−	1.23698i
$700$		0			0
$701$	−419.280			−0.598117			−0.299059	−	0.954235i	$-0.596673\pi$
$701$	−419.280			−0.598117			−0.299059	+	0.954235i	$0.596673\pi$
$702$		0			0
$703$	469.319	−	459.957i	0.667595	−	0.654277i
$704$		0			0
$705$	−80.7266	+	301.685i	−0.114506	+	0.427922i
$706$		0			0
$707$	91.4451	−	158.388i	0.129342	−	0.224028i
$708$		0			0
$709$	211.497	+	366.323i	0.298303	+	0.516676i	0.975748	−	0.218897i	$-0.0702460\pi$
$709$	211.497	+	366.323i	0.298303	+	0.516676i	−0.677445	+	0.735574i	$0.736913\pi$
$710$		0			0
$711$	102.244	−	0.0693735i	0.143803	−	9.75717e-5i
$712$		0			0
$713$	−1111.43	+	641.687i	−1.55881	+	0.899981i
$714$		0			0
$715$	470.396	+	271.583i	0.657896	+	0.379836i
$716$		0			0
$717$	−82.8508	−	82.7946i	−0.115552	−	0.115474i
$718$		0			0
$719$	457.789			0.636703			0.318351	−	0.947973i	$-0.396871\pi$
$719$	457.789			0.636703			0.318351	+	0.947973i	$0.396871\pi$
$720$		0			0
$721$			241.558i			0.335032i
$722$		0			0
$723$	−191.595	−	714.072i	−0.265000	−	0.987652i
$724$		0			0
$725$	−324.492	−	187.346i	−0.447576	−	0.258408i
$726$		0			0
$727$	−4.60676	−	7.97915i	−0.00633667	−	0.0109754i	0.862840	−	0.505478i	$-0.168684\pi$
$727$	−4.60676	−	7.97915i	−0.00633667	−	0.0109754i	−0.869176	+	0.494502i	$0.835350\pi$
$728$		0			0
$729$	−1.48389	−	728.998i	−0.00203552	−	0.999998i
$730$		0			0
$731$	−105.637	−	182.968i	−0.144510	−	0.250298i
$732$		0			0
$733$	156.219	−	270.580i	0.213123	−	0.369140i	−0.739567	−	0.673083i	$-0.764970\pi$
$733$	156.219	−	270.580i	0.213123	−	0.369140i	0.952690	+	0.303942i	$0.0983031\pi$
$734$		0			0
$735$	−210.169	+	56.3911i	−0.285944	+	0.0767226i
$736$		0			0
$737$			551.971i			0.748943i
$738$		0			0
$739$	−1131.33			−1.53090			−0.765448	−	0.643498i	$-0.777483\pi$
$739$	−1131.33			−1.53090			−0.765448	+	0.643498i	$0.777483\pi$
$740$		0			0
$741$	−1145.71	−	11.1545i	−1.54617	−	0.0150533i
$742$		0			0
$743$	344.392	+	198.835i	0.463516	+	0.267611i	0.713522	−	0.700633i	$-0.247099\pi$
$743$	344.392	+	198.835i	0.463516	+	0.267611i	−0.250005	+	0.968244i	$0.580432\pi$
$744$		0			0
$745$	−182.684	−	316.418i	−0.245213	−	0.424722i
$746$		0			0
$747$	0.888902	+	1310.08i	0.00118996	+	1.75379i
$748$		0			0
$749$	111.705	−	64.4928i	0.149139	−	0.0861052i
$750$		0			0
$751$	36.9611	+	21.3395i	0.0492158	+	0.0284148i	0.524406	−	0.851468i	$-0.324287\pi$
$751$	36.9611	+	21.3395i	0.0492158	+	0.0284148i	−0.475190	+	0.879883i	$0.657621\pi$
$752$		0			0
$753$	−60.8107	+	227.257i	−0.0807579	+	0.301802i
$754$		0			0
$755$		−	140.458i		−	0.186037i
$756$		0			0
$757$	594.354			0.785144			0.392572	−	0.919721i	$-0.371585\pi$
$757$	594.354			0.785144			0.392572	+	0.919721i	$0.371585\pi$
$758$		0			0
$759$	−415.850	+	1554.08i	−0.547892	+	2.04754i
$760$		0			0
$761$	−249.226	+	431.672i	−0.327498	+	0.567244i	−0.982015	−	0.188804i	$-0.939539\pi$
$761$	−249.226	+	431.672i	−0.327498	+	0.567244i	0.654516	+	0.756048i	$0.272872\pi$
$762$		0			0
$763$	−242.908	+	140.243i	−0.318359	+	0.183805i
$764$		0			0
$765$	−70.2509	+	40.6229i	−0.0918312	+	0.0531019i
$766$		0			0
$767$	26.2799	+	45.5181i	0.0342632	+	0.0593456i
$768$		0			0
$769$	−515.606	+	893.056i	−0.670489	+	1.16132i	0.307277	+	0.951620i	$0.400582\pi$
$769$	−515.606	+	893.056i	−0.670489	+	1.16132i	−0.977766	+	0.209701i	$0.932751\pi$
$770$		0			0
$771$	−761.106	+	761.623i	−0.987167	+	0.987838i
$772$		0			0
$773$		−	127.121i		−	0.164451i	−0.996614	−	0.0822255i	$-0.973797\pi$
$773$		−	127.121i		−	0.164451i	0.996614	−	0.0822255i	$-0.0262028\pi$
$774$		0			0
$775$		−	941.805i		−	1.21523i
$776$		0			0
$777$	40.2864	+	150.147i	0.0518486	+	0.193239i
$778$		0			0
$779$	87.8799	+	341.706i	0.112811	+	0.438647i
$780$		0			0
$781$	82.2879	−	47.5090i	0.105362	−	0.0608309i
$782$		0			0
$783$	−115.452	+	432.634i	−0.147448	+	0.552534i
$784$		0			0
$785$	−224.256	−	388.422i	−0.285676	−	0.494805i
$786$		0			0
$787$	1176.39	+	679.191i	1.49478	+	0.863013i	0.999982	−	0.00599305i	$-0.00190766\pi$
$787$	1176.39	+	679.191i	1.49478	+	0.863013i	0.494801	+	0.869006i	$0.335241\pi$
$788$		0			0
$789$	267.947	−	71.8936i	0.339603	−	0.0911199i
$790$		0			0
$791$		−	92.0403i		−	0.116359i
$792$		0			0
$793$			681.497i			0.859390i
$794$		0			0
$795$	−302.626	+	302.832i	−0.380662	+	0.380920i
$796$		0			0
$797$	1269.61	+	733.012i	1.59299	+	0.919714i	0.992790	+	0.119866i	$0.0382464\pi$
$797$	1269.61	+	733.012i	1.59299	+	0.919714i	0.600202	+	0.799849i	$0.295087\pi$
$798$		0			0
$799$	195.002	+	337.754i	0.244058	+	0.422721i
$800$		0			0
$801$	−460.336	+	798.577i	−0.574702	+	0.996975i
$802$		0			0
$803$	1055.12	+	1827.52i	1.31397	+	2.27587i
$804$		0			0
$805$	35.7807	−	61.9739i	0.0444480	−	0.0769862i
$806$		0			0
$807$	1142.62	+	305.750i	1.41589	+	0.378872i
$808$		0			0
$809$	−360.344			−0.445419			−0.222710	−	0.974885i	$-0.571490\pi$
$809$	−360.344			−0.445419			−0.222710	+	0.974885i	$0.571490\pi$
$810$		0			0
$811$		−	4.81998i		−	0.00594326i	−0.999996	−	0.00297163i	$-0.999054\pi$
$811$		−	4.81998i		−	0.00594326i	0.999996	−	0.00297163i	$-0.000945900\pi$
$812$		0			0
$813$	291.341	−	1088.78i	0.358353	−	1.33921i
$814$		0			0
$815$	30.3523	−	52.5717i	0.0372420	−	0.0645051i
$816$		0			0
$817$	185.468	−	665.290i	0.227010	−	0.814309i
$818$		0			0
$819$	135.368	−	234.832i	0.165284	−	0.286730i
$820$		0			0
$821$	−67.7106	−	117.278i	−0.0824734	−	0.142848i	0.821838	−	0.569721i	$-0.192949\pi$
$821$	−67.7106	−	117.278i	−0.0824734	−	0.142848i	−0.904312	+	0.426873i	$0.859615\pi$
$822$		0			0
$823$	1.22876	−	2.12828i	0.00149303	−	0.00258600i	−0.865278	−	0.501292i	$-0.832858\pi$
$823$	1.22876	−	2.12828i	0.00149303	−	0.00258600i	0.866771	+	0.498706i	$0.166191\pi$
$824$		0			0
$825$	−835.085	−	834.518i	−1.01222	−	1.01154i
$826$		0			0
$827$		−	191.271i		−	0.231283i	−0.993291	−	0.115642i	$-0.963108\pi$
$827$		−	191.271i		−	0.231283i	0.993291	−	0.115642i	$-0.0368924\pi$
$828$		0			0
$829$			566.616i			0.683493i	0.939792	+	0.341746i	$0.111018\pi$
$829$			566.616i			0.683493i	−0.939792	+	0.341746i	$0.888982\pi$
$830$		0			0
$831$	−1124.80	+	301.798i	−1.35355	+	0.363175i
$832$		0			0
$833$	−135.873	+	235.340i	−0.163113	+	0.282520i
$834$		0			0
$835$	167.703	−	96.8236i	0.200842	−	0.115956i
$836$		0			0
$837$	−1086.85	+	292.407i	−1.29851	+	0.349352i
$838$		0			0
$839$	1006.54	−	581.125i	1.19969	−	0.692640i	0.239202	−	0.970970i	$-0.423114\pi$
$839$	1006.54	−	581.125i	1.19969	−	0.692640i	0.960486	+	0.278330i	$0.0897807\pi$
$840$		0			0
$841$	−282.982	+	490.139i	−0.336483	+	0.582805i
$842$		0			0
$843$	113.440	+	422.788i	0.134567	+	0.501528i
$844$		0			0
$845$	−364.657			−0.431547
$846$		0			0
$847$	273.266			0.322628
$848$		0			0
$849$	612.223	+	611.807i	0.721110	+	0.720621i
$850$		0			0
$851$	922.147	+	532.402i	1.08360	+	0.625619i
$852$		0			0
$853$	680.123	+	1178.01i	0.797330	+	1.38102i	0.921349	+	0.388737i	$0.127089\pi$
$853$	680.123	+	1178.01i	0.797330	+	1.38102i	−0.124018	+	0.992280i	$0.539578\pi$
$854$		0			0
$855$	−255.588	−	71.0651i	−0.298933	−	0.0831171i
$856$		0			0
$857$	−84.9168	+	49.0267i	−0.0990861	+	0.0572074i	−0.548724	−	0.836003i	$-0.684886\pi$
$857$	−84.9168	+	49.0267i	−0.0990861	+	0.0572074i	0.449638	+	0.893211i	$0.351553\pi$
$858$		0			0
$859$	768.235	−	1330.62i	0.894337	−	1.54904i	0.0597134	−	0.998216i	$-0.480981\pi$
$859$	768.235	−	1330.62i	0.894337	−	1.54904i	0.834623	−	0.550821i	$-0.185685\pi$
$860$		0			0
$861$	−80.6314	−	21.5758i	−0.0936485	−	0.0250590i
$862$		0			0
$863$			23.1798i			0.0268596i	0.999910	+	0.0134298i	$0.00427497\pi$
$863$			23.1798i			0.0268596i	−0.999910	+	0.0134298i	$0.995725\pi$
$864$		0			0
$865$		−	93.9534i		−	0.108617i
$866$		0			0
$867$	197.916	−	739.636i	0.228277	−	0.853098i
$868$		0			0
$869$	−171.366	−	98.9383i	−0.197199	−	0.113853i
$870$		0			0
$871$	−318.500	−	551.658i	−0.365671	−	0.633362i
$872$		0			0
$873$	1459.83	−	0.990508i	1.67220	−	0.00113460i
$874$		0			0
$875$	55.3124	+	95.8039i	0.0632142	+	0.109490i
$876$		0			0
$877$	515.722	+	297.752i	0.588052	+	0.339512i	0.764327	−	0.644829i	$-0.223071\pi$
$877$	515.722	+	297.752i	0.588052	+	0.339512i	−0.176275	+	0.984341i	$0.556405\pi$
$878$		0			0
$879$	−985.007	+	985.676i	−1.12060	+	1.12136i
$880$		0			0
$881$	−474.861			−0.539002			−0.269501	−	0.963000i	$-0.586859\pi$
$881$	−474.861			−0.539002			−0.269501	+	0.963000i	$0.586859\pi$
$882$		0			0
$883$	−978.093			−1.10769			−0.553846	−	0.832619i	$-0.686840\pi$
$883$	−978.093			−1.10769			−0.553846	+	0.832619i	$0.686840\pi$
$884$		0			0
$885$	3.15365	+	11.7536i	0.00356345	+	0.0132809i
$886$		0			0
$887$	60.6342	+	35.0072i	0.0683588	+	0.0394670i	0.533790	−	0.845617i	$-0.320767\pi$
$887$	60.6342	+	35.0072i	0.0683588	+	0.0394670i	−0.465431	+	0.885084i	$0.654101\pi$
$888$		0			0
$889$	14.8863	−	8.59459i	0.0167450	−	0.00966771i
$890$		0			0
$891$	−703.770	+	1222.79i	−0.789865	+	1.37238i
$892$		0			0
$893$	−342.368	+	1228.11i	−0.383391	+	1.37526i
$894$		0			0
$895$	−274.360	−	158.402i	−0.306548	−	0.176985i
$896$		0			0
$897$	−481.126	−	1793.15i	−0.536372	−	1.99906i
$898$		0			0
$899$	691.316			0.768983
$900$		0			0
$901$			534.649i			0.593395i
$902$		0			0
$903$	115.573	+	115.495i	0.127988	+	0.127901i
$904$		0			0
$905$	−280.810	−	162.126i	−0.310287	−	0.179144i
$906$		0			0
$907$	1257.30	−	725.905i	1.38622	−	0.800336i	0.393336	−	0.919395i	$-0.371321\pi$
$907$	1257.30	−	725.905i	1.38622	−	0.800336i	0.992887	+	0.119058i	$0.0379876\pi$
$908$		0			0
$909$	−0.745409	−	1098.60i	−0.000820031	−	1.20858i
$910$		0			0
$911$	−606.867	+	350.375i	−0.666155	+	0.384605i	−0.794618	−	0.607110i	$-0.792329\pi$
$911$	−606.867	+	350.375i	−0.666155	+	0.384605i	0.128463	+	0.991714i	$0.458996\pi$
$912$		0			0
$913$	1267.72	−	2195.76i	1.38853	−	2.40500i
$914$		0			0
$915$	−40.7872	+	152.427i	−0.0445762	+	0.166587i
$916$		0			0
$917$	179.484			0.195729
$918$		0			0
$919$	383.036			0.416796			0.208398	−	0.978044i	$-0.433175\pi$
$919$	383.036			0.416796			0.208398	+	0.978044i	$0.433175\pi$
$920$		0			0
$921$	−228.232	−	61.0715i	−0.247808	−	0.0663100i
$922$		0			0
$923$	−54.8275	+	94.9640i	−0.0594014	+	0.102886i
$924$		0			0
$925$	−676.718	+	390.703i	−0.731587	+	0.422382i
$926$		0			0
$927$	726.359	+	1256.12i	0.783558	+	1.35504i
$928$		0			0
$929$	−712.404	−	1233.92i	−0.766851	−	1.32822i	−0.939263	−	0.343199i	$-0.888489\pi$
$929$	−712.404	−	1233.92i	−0.766851	−	1.32822i	0.172412	−	0.985025i	$-0.444844\pi$
$930$		0			0
$931$	−860.351	+	221.265i	−0.924115	+	0.237664i
$932$		0			0
$933$	281.287	+	281.096i	0.301487	+	0.301282i
$934$		0			0
$935$	157.053			0.167971
$936$		0			0
$937$	−997.228			−1.06428			−0.532139	−	0.846657i	$-0.678612\pi$
$937$	−997.228			−1.06428			−0.532139	+	0.846657i	$0.678612\pi$
$938$		0			0
$939$	−908.927	+	243.877i	−0.967973	+	0.259720i
$940$		0			0
$941$	131.794	+	76.0915i	0.140058	+	0.0808623i	0.568391	−	0.822758i	$-0.307566\pi$
$941$	131.794	+	76.0915i	0.140058	+	0.0808623i	−0.428334	+	0.903621i	$0.640899\pi$
$942$		0			0
$943$	−495.117	+	285.856i	−0.525045	+	0.303135i
$944$		0			0
$945$	44.3316	−	44.4219i	0.0469117	−	0.0470073i
$946$		0			0
$947$	28.5333	+	49.4211i	0.0301302	+	0.0521871i	0.880697	−	0.473679i	$-0.157074\pi$
$947$	28.5333	+	49.4211i	0.0301302	+	0.0521871i	−0.850567	+	0.525867i	$0.823741\pi$
$948$		0			0
$949$	−2109.04	−	1217.66i	−2.22238	−	1.28309i
$950$		0			0
$951$	−291.819	−	1087.61i	−0.306855	−	1.14365i
$952$		0			0
$953$		−	914.890i		−	0.960010i	−0.877266	−	0.480005i	$-0.840635\pi$
$953$		−	914.890i		−	0.960010i	0.877266	−	0.480005i	$-0.159365\pi$
$954$		0			0
$955$	372.995			0.390571
$956$		0			0
$957$	612.564	−	612.980i	0.640088	−	0.640522i
$958$		0			0
$959$	−121.930	+	211.189i	−0.127143	+	0.220217i
$960$		0			0
$961$	388.328	+	672.604i	0.404087	+	0.699900i
$962$		0			0
$963$	386.946	−	671.261i	0.401813	−	0.697052i
$964$		0			0
$965$	−339.927	+	196.257i	−0.352256	+	0.203375i
$966$		0			0
$967$	−462.264	+	800.664i	−0.478039	+	0.827988i	−0.999683	−	0.0251756i	$-0.991986\pi$
$967$	−462.264	+	800.664i	−0.478039	+	0.827988i	0.521644	+	0.853163i	$0.325319\pi$
$968$		0			0
$969$	−288.505	+	162.844i	−0.297735	+	0.168054i
$970$		0			0
$971$		−	144.724i		−	0.149046i	−0.997219	−	0.0745231i	$-0.976257\pi$
$971$		−	144.724i		−	0.149046i	0.997219	−	0.0745231i	$-0.0237435\pi$
$972$		0			0
$973$	7.73749			0.00795220
$974$		0			0
$975$	1316.15	+	352.182i	1.34989	+	0.361212i
$976$		0			0
$977$	823.892	+	475.674i	0.843288	+	0.486872i	0.858380	−	0.513014i	$-0.171471\pi$
$977$	823.892	+	475.674i	0.843288	+	0.486872i	−0.0150928	+	0.999886i	$0.504804\pi$
$978$		0			0
$979$	1544.91	−	891.952i	1.57805	−	0.911085i
$980$		0			0
$981$	−841.433	+	1459.69i	−0.857730	+	1.48796i
$982$		0			0
$983$	148.775	−	85.8951i	0.151348	−	0.0873805i	−0.422414	−	0.906403i	$-0.638817\pi$
$983$	148.775	−	85.8951i	0.151348	−	0.0873805i	0.573761	+	0.819023i	$0.305484\pi$
$984$		0			0
$985$	−30.3146	+	52.5065i	−0.0307763	+	0.0533060i
$986$		0			0
$987$	−213.345	−	213.200i	−0.216155	−	0.216008i
$988$		0			0
$989$	1119.13			1.13158
$990$		0			0
$991$			419.864i			0.423677i	0.977305	+	0.211839i	$0.0679451\pi$
$991$			419.864i			0.423677i	−0.977305	+	0.211839i	$0.932055\pi$
$992$		0			0
$993$	96.2235	+	358.624i	0.0969018	+	0.361152i
$994$		0			0
$995$	97.3327	−	168.585i	0.0978218	−	0.169432i
$996$		0			0
$997$	−576.294	−	998.171i	−0.578028	−	1.00117i	−0.995705	−	0.0925787i	$-0.970489\pi$
$997$	−576.294	−	998.171i	−0.578028	−	1.00117i	0.417677	−	0.908596i	$-0.362844\pi$
$998$		0			0
$999$	660.980	+	659.636i	0.661642	+	0.660297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.t.a.265.19	✓	80
3.2	odd	2		2052.3.t.a.37.24		80
9.2	odd	6		2052.3.t.a.721.23		80
9.7	even	3	inner	684.3.t.a.493.22	yes	80
19.18	odd	2	inner	684.3.t.a.265.22	yes	80
57.56	even	2		2052.3.t.a.37.23		80
171.56	even	6		2052.3.t.a.721.24		80
171.151	odd	6	inner	684.3.t.a.493.19	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.t.a.265.19	✓	80	1.1	even	1	trivial
684.3.t.a.265.22	yes	80	19.18	odd	2	inner
684.3.t.a.493.19	yes	80	171.151	odd	6	inner
684.3.t.a.493.22	yes	80	9.7	even	3	inner
2052.3.t.a.37.23		80	57.56	even	2
2052.3.t.a.37.24		80	3.2	odd	2
2052.3.t.a.721.23		80	9.2	odd	6
2052.3.t.a.721.24		80	171.56	even	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.775474 + 2.89804i) q^{3} +(-0.775683 + 1.34352i) q^{5} +(-0.749140 - 1.29755i) q^{7} +(-7.79728 - 4.49471i) q^{9} +O(q^{10})\)	\(q+(-0.775474 + 2.89804i) q^{3} +(-0.775683 + 1.34352i) q^{5} +(-0.749140 - 1.29755i) q^{7} +(-7.79728 - 4.49471i) q^{9} +(8.70899 + 15.0844i) q^{11} +(-17.4081 - 10.0506i) q^{13} +(-3.29206 - 3.28983i) q^{15} -5.81212 q^{17} +(-13.2990 - 13.5697i) q^{19} +(4.34129 - 1.16482i) q^{21} +(15.3936 - 26.6626i) q^{23} +(11.2966 + 19.5663i) q^{25} +(19.0724 - 19.1113i) q^{27} +(-14.3623 + 8.29210i) q^{29} +(-36.1004 - 20.8426i) q^{31} +(-50.4689 + 13.5414i) q^{33} +2.32438 q^{35} +34.5858i q^{37} +(42.6265 - 42.6554i) q^{39} +(-16.0819 - 9.28488i) q^{41} +(18.1752 + 31.4804i) q^{43} +(12.0870 - 6.98935i) q^{45} +(-33.5510 - 58.1120i) q^{47} +(23.3776 - 40.4912i) q^{49} +(4.50715 - 16.8438i) q^{51} -91.9886i q^{53} -27.0217 q^{55} +(49.6386 - 28.0181i) q^{57} +(-2.26445 - 1.30738i) q^{59} +(-16.9517 - 29.3612i) q^{61} +(0.00914934 + 13.4845i) q^{63} +(27.0063 - 15.5921i) q^{65} +(27.4441 + 15.8449i) q^{67} +(65.3318 + 65.2875i) q^{69} -5.45516i q^{71} +121.153 q^{73} +(-65.4643 + 17.5649i) q^{75} +(13.0485 - 22.6007i) q^{77} +(-9.83846 + 5.68024i) q^{79} +(40.5952 + 70.0930i) q^{81} +(-72.7825 - 126.063i) q^{83} +(4.50836 - 7.80871i) q^{85} +(-12.8932 - 48.0530i) q^{87} -102.417i q^{89} +30.1171i q^{91} +(88.3977 - 88.4577i) q^{93} +(28.5470 - 7.34171i) q^{95} +(-140.473 + 81.1019i) q^{97} +(-0.106364 - 156.762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 2 * q^7 + 4 * q^9	\( 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) \) 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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