LMFDB - Embedded newform 588.3.g.h.295.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,3,Mod(295,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.295"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,4,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			295.17
Character	$\chi$	$=$	588.295
Dual form			588.3.g.h.295.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71300 - 1.03229i) q^{2} -1.73205i q^{3} +(1.86874 - 3.53664i) q^{4} -2.98338 q^{5} +(-1.78799 - 2.96700i) q^{6} +(-0.449712 - 7.98735i) q^{8} -3.00000 q^{9} +(-5.11054 + 3.07973i) q^{10} +7.51244i q^{11} +(-6.12564 - 3.23675i) q^{12} -23.3458 q^{13} +5.16737i q^{15} +(-9.01565 - 13.2181i) q^{16} -10.3105 q^{17} +(-5.13900 + 3.09688i) q^{18} -15.5324i q^{19} +(-5.57516 + 10.5512i) q^{20} +(7.75505 + 12.8688i) q^{22} -27.5813i q^{23} +(-13.8345 + 0.778924i) q^{24} -16.0994 q^{25} +(-39.9914 + 24.0998i) q^{26} +5.19615i q^{27} +19.6775 q^{29} +(5.33425 + 8.85171i) q^{30} +28.5622i q^{31} +(-29.0888 - 13.3358i) q^{32} +13.0119 q^{33} +(-17.6619 + 10.6435i) q^{34} +(-5.60621 + 10.6099i) q^{36} +53.4171 q^{37} +(-16.0341 - 26.6071i) q^{38} +40.4361i q^{39} +(1.34166 + 23.8293i) q^{40} -31.1234 q^{41} +15.2200i q^{43} +(26.5688 + 14.0388i) q^{44} +8.95015 q^{45} +(-28.4720 - 47.2467i) q^{46} -3.62503i q^{47} +(-22.8944 + 15.6156i) q^{48} +(-27.5783 + 16.6193i) q^{50} +17.8583i q^{51} +(-43.6272 + 82.5658i) q^{52} -68.8586 q^{53} +(5.36396 + 8.90101i) q^{54} -22.4125i q^{55} -26.9030 q^{57} +(33.7075 - 20.3130i) q^{58} -113.268i q^{59} +(18.2751 + 9.65645i) q^{60} -3.30747 q^{61} +(29.4846 + 48.9270i) q^{62} +(-63.5955 + 7.18401i) q^{64} +69.6496 q^{65} +(22.2894 - 13.4321i) q^{66} +92.9042i q^{67} +(-19.2676 + 36.4645i) q^{68} -47.7721 q^{69} -72.5872i q^{71} +(1.34914 + 23.9620i) q^{72} +69.3610 q^{73} +(91.5034 - 55.1422i) q^{74} +27.8850i q^{75} +(-54.9327 - 29.0260i) q^{76} +(41.7420 + 69.2671i) q^{78} -156.100i q^{79} +(26.8972 + 39.4346i) q^{80} +9.00000 q^{81} +(-53.3143 + 32.1285i) q^{82} +85.1194i q^{83} +30.7602 q^{85} +(15.7115 + 26.0719i) q^{86} -34.0824i q^{87} +(60.0045 - 3.37843i) q^{88} +17.2213 q^{89} +(15.3316 - 9.23919i) q^{90} +(-97.5450 - 51.5421i) q^{92} +49.4711 q^{93} +(-3.74210 - 6.20967i) q^{94} +46.3392i q^{95} +(-23.0982 + 50.3832i) q^{96} +110.824 q^{97} -22.5373i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 12 q^{4} - 20 q^{8} - 72 q^{9} - 60 q^{16} - 12 q^{18} + 168 q^{22} + 120 q^{25} + 64 q^{29} - 236 q^{32} - 36 q^{36} - 192 q^{37} - 360 q^{44} - 72 q^{46} + 532 q^{50} + 432 q^{53} + 240 q^{58}+ \cdots - 96 q^{93}+O(q^{100}) $ 24 * q + 4 * q^2 + 12 * q^4 - 20 * q^8 - 72 * q^9 - 60 * q^16 - 12 * q^18 + 168 * q^22 + 120 * q^25 + 64 * q^29 - 236 * q^32 - 36 * q^36 - 192 * q^37 - 360 * q^44 - 72 * q^46 + 532 * q^50 + 432 * q^53 + 240 * q^58 + 72 * q^60 - 372 * q^64 - 560 * q^65 + 60 * q^72 + 96 * q^74 + 216 * q^78 + 216 * q^81 + 144 * q^85 + 816 * q^86 - 72 * q^88 - 504 * q^92 - 96 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.71300	−	1.03229i	0.856500	−	0.516147i
$2$	1.71300	−	1.03229i	0.856500	−	0.516147i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	1.86874	−	3.53664i	0.467184	−	0.884160i
$5$	−2.98338			−0.596677			−0.298338	−	0.954460i	$-0.596432\pi$
$5$	−2.98338			−0.596677			−0.298338	+	0.954460i	$0.596432\pi$
$6$	−1.78799	−	2.96700i	−0.297998	−	0.494500i
$7$		0			0
$7$		0			0
$8$	−0.449712	−	7.98735i	−0.0562140	−	0.998419i
$9$	−3.00000			−0.333333
$10$	−5.11054	+	3.07973i	−0.511054	+	0.307973i
$11$			7.51244i			0.682949i	0.939891	+	0.341474i	$0.110926\pi$
$11$			7.51244i			0.682949i	−0.939891	+	0.341474i	$0.889074\pi$
$12$	−6.12564	−	3.23675i	−0.510470	−	0.269729i
$13$	−23.3458			−1.79583			−0.897916	−	0.440166i	$-0.854919\pi$
$13$	−23.3458			−1.79583			−0.897916	+	0.440166i	$0.854919\pi$
$14$		0			0
$15$			5.16737i			0.344492i
$16$	−9.01565	−	13.2181i	−0.563478	−	0.826131i
$17$	−10.3105			−0.606499			−0.303250	−	0.952911i	$-0.598072\pi$
$17$	−10.3105			−0.606499			−0.303250	+	0.952911i	$0.598072\pi$
$18$	−5.13900	+	3.09688i	−0.285500	+	0.172049i
$19$		−	15.5324i		−	0.817497i	−0.912647	−	0.408748i	$-0.865965\pi$
$19$		−	15.5324i		−	0.817497i	0.912647	−	0.408748i	$-0.134035\pi$
$20$	−5.57516	+	10.5512i	−0.278758	+	0.527558i
$21$		0			0
$22$	7.75505	+	12.8688i	0.352502	+	0.584946i
$23$		−	27.5813i		−	1.19919i	−0.800305	−	0.599593i	$-0.795329\pi$
$23$		−	27.5813i		−	1.19919i	0.800305	−	0.599593i	$-0.204671\pi$
$24$	−13.8345	+	0.778924i	−0.576437	+	0.0324551i
$25$	−16.0994			−0.643977
$26$	−39.9914	+	24.0998i	−1.53813	+	0.926914i
$27$			5.19615i			0.192450i
$28$		0			0
$29$	19.6775			0.678534			0.339267	−	0.940690i	$-0.389821\pi$
$29$	19.6775			0.678534			0.339267	+	0.940690i	$0.389821\pi$
$30$	5.33425	+	8.85171i	0.177808	+	0.295057i
$31$			28.5622i			0.921360i	0.887566	+	0.460680i	$0.152394\pi$
$31$			28.5622i			0.921360i	−0.887566	+	0.460680i	$0.847606\pi$
$32$	−29.0888	−	13.3358i	−0.909024	−	0.416743i
$33$	13.0119			0.394301
$34$	−17.6619	+	10.6435i	−0.519467	+	0.313043i
$35$		0			0
$36$	−5.60621	+	10.6099i	−0.155728	+	0.294720i
$37$	53.4171			1.44371			0.721853	−	0.692047i	$-0.243291\pi$
$37$	53.4171			1.44371			0.721853	+	0.692047i	$0.243291\pi$
$38$	−16.0341	−	26.6071i	−0.421949	−	0.700186i
$39$			40.4361i			1.03682i
$40$	1.34166	+	23.8293i	0.0335416	+	0.595733i
$41$	−31.1234			−0.759107			−0.379553	−	0.925170i	$-0.623922\pi$
$41$	−31.1234			−0.759107			−0.379553	+	0.925170i	$0.623922\pi$
$42$		0			0
$43$			15.2200i			0.353954i	0.984215	+	0.176977i	$0.0566318\pi$
$43$			15.2200i			0.353954i	−0.984215	+	0.176977i	$0.943368\pi$
$44$	26.5688	+	14.0388i	0.603836	+	0.319063i
$45$	8.95015			0.198892
$46$	−28.4720	−	47.2467i	−0.618956	−	1.02710i
$47$		−	3.62503i		−	0.0771282i	−0.999256	−	0.0385641i	$-0.987722\pi$
$47$		−	3.62503i		−	0.0771282i	0.999256	−	0.0385641i	$-0.0122784\pi$
$48$	−22.8944	+	15.6156i	−0.476967	+	0.325324i
$49$		0			0
$50$	−27.5783	+	16.6193i	−0.551566	+	0.332387i
$51$			17.8583i			0.350163i
$52$	−43.6272	+	82.5658i	−0.838984	+	1.58780i
$53$	−68.8586			−1.29922			−0.649610	−	0.760268i	$-0.725068\pi$
$53$	−68.8586			−1.29922			−0.649610	+	0.760268i	$0.725068\pi$
$54$	5.36396	+	8.90101i	0.0993326	+	0.164833i
$55$		−	22.4125i		−	0.407500i
$56$		0			0
$57$	−26.9030			−0.471982
$58$	33.7075	−	20.3130i	0.581164	−	0.350223i
$59$		−	113.268i		−	1.91979i	−0.280359	−	0.959895i	$-0.590453\pi$
$59$		−	113.268i		−	1.91979i	0.280359	−	0.959895i	$-0.409547\pi$
$60$	18.2751	+	9.65645i	0.304586	+	0.160941i
$61$	−3.30747			−0.0542209			−0.0271104	−	0.999632i	$-0.508631\pi$
$61$	−3.30747			−0.0542209			−0.0271104	+	0.999632i	$0.508631\pi$
$62$	29.4846	+	48.9270i	0.475558	+	0.789145i
$63$		0			0
$64$	−63.5955	+	7.18401i	−0.993680	+	0.112250i
$65$	69.6496			1.07153
$66$	22.2894	−	13.4321i	0.337718	−	0.203517i
$67$			92.9042i			1.38663i	0.720634	+	0.693315i	$0.243851\pi$
$67$			92.9042i			1.38663i	−0.720634	+	0.693315i	$0.756149\pi$
$68$	−19.2676	+	36.4645i	−0.283347	+	0.536243i
$69$	−47.7721			−0.692350
$70$		0			0
$71$		−	72.5872i		−	1.02236i	−0.859475	−	0.511178i	$-0.829209\pi$
$71$		−	72.5872i		−	1.02236i	0.859475	−	0.511178i	$-0.170791\pi$
$72$	1.34914	+	23.9620i	0.0187380	+	0.332806i
$73$	69.3610			0.950151			0.475075	−	0.879945i	$-0.342421\pi$
$73$	69.3610			0.950151			0.475075	+	0.879945i	$0.342421\pi$
$74$	91.5034	−	55.1422i	1.23653	−	0.745164i
$75$			27.8850i			0.371800i
$76$	−54.9327	−	29.0260i	−0.722798	−	0.381921i
$77$		0			0
$78$	41.7420	+	69.2671i	0.535154	+	0.888040i
$79$		−	156.100i		−	1.97595i	−0.154610	−	0.987976i	$-0.549412\pi$
$79$		−	156.100i		−	1.97595i	0.154610	−	0.987976i	$-0.450588\pi$
$80$	26.8972	+	39.4346i	0.336215	+	0.492933i
$81$	9.00000			0.111111
$82$	−53.3143	+	32.1285i	−0.650175	+	0.391811i
$83$			85.1194i			1.02554i	0.858527	+	0.512768i	$0.171380\pi$
$83$			85.1194i			1.02554i	−0.858527	+	0.512768i	$0.828620\pi$
$84$		0			0
$85$	30.7602			0.361884
$86$	15.7115	+	26.0719i	0.182692	+	0.303161i
$87$		−	34.0824i		−	0.391752i
$88$	60.0045	−	3.37843i	0.681869	−	0.0383913i
$89$	17.2213			0.193498			0.0967492	−	0.995309i	$-0.469156\pi$
$89$	17.2213			0.193498			0.0967492	+	0.995309i	$0.469156\pi$
$90$	15.3316	−	9.23919i	0.170351	−	0.102658i
$91$		0			0
$92$	−97.5450	−	51.5421i	−1.06027	−	0.560240i
$93$	49.4711			0.531948
$94$	−3.74210	−	6.20967i	−0.0398095	−	0.0660603i
$95$			46.3392i			0.487781i
$96$	−23.0982	+	50.3832i	−0.240607	+	0.524825i
$97$	110.824			1.14251			0.571256	−	0.820772i	$-0.306456\pi$
$97$	110.824			1.14251			0.571256	+	0.820772i	$0.306456\pi$
$98$		0			0
$99$		−	22.5373i		−	0.227650i
$100$	−30.0856	+	56.9379i	−0.300856	+	0.569379i
$101$	5.57758			0.0552236			0.0276118	−	0.999619i	$-0.491210\pi$
$101$	5.57758			0.0552236			0.0276118	+	0.999619i	$0.491210\pi$
$102$	18.4350	+	30.5913i	0.180736	+	0.299914i
$103$		−	189.953i		−	1.84420i	−0.386951	−	0.922100i	$-0.626472\pi$
$103$		−	189.953i		−	1.84420i	0.386951	−	0.922100i	$-0.373528\pi$
$104$	10.4989	+	186.471i	0.100951	+	1.79299i
$105$		0			0
$106$	−117.955	+	71.0824i	−1.11278	+	0.670589i
$107$		−	31.3034i		−	0.292555i	−0.989244	−	0.146278i	$-0.953271\pi$
$107$		−	31.3034i		−	0.292555i	0.989244	−	0.146278i	$-0.0467293\pi$
$108$	18.3769	+	9.71024i	0.170157	+	0.0899096i
$109$	27.0700			0.248349			0.124174	−	0.992260i	$-0.460372\pi$
$109$	27.0700			0.248349			0.124174	+	0.992260i	$0.460372\pi$
$110$	−23.1363	−	38.3926i	−0.210330	−	0.349023i
$111$		−	92.5211i		−	0.833523i
$112$		0			0
$113$	−162.124			−1.43472			−0.717362	−	0.696701i	$-0.754650\pi$
$113$	−162.124			−1.43472			−0.717362	+	0.696701i	$0.754650\pi$
$114$	−46.0848	+	27.7718i	−0.404253	+	0.243612i
$115$			82.2855i			0.715526i
$116$	36.7720	−	69.5922i	0.317000	−	0.599932i
$117$	70.0375			0.598611
$118$	−116.926	−	194.027i	−0.990895	−	1.64430i
$119$		0			0
$120$	41.2736	−	2.32383i	0.343947	−	0.0193652i
$121$	64.5633			0.533581
$122$	−5.66570	+	3.41429i	−0.0464402	+	0.0279860i
$123$			53.9073i			0.438271i
$124$	101.014	+	53.3751i	0.814630	+	0.430445i
$125$	122.615			0.980923
$126$		0			0
$127$		−	59.4108i		−	0.467802i	−0.972260	−	0.233901i	$-0.924851\pi$
$127$		−	59.4108i		−	0.467802i	0.972260	−	0.233901i	$-0.0751491\pi$
$128$	−101.523	+	77.9555i	−0.793149	+	0.609027i
$129$	26.3618			0.204355
$130$	119.310	−	71.8989i	0.917767	−	0.553068i
$131$		−	210.537i		−	1.60715i	−0.595202	−	0.803576i	$-0.702928\pi$
$131$		−	210.537i		−	1.60715i	0.595202	−	0.803576i	$-0.297072\pi$
$132$	24.3158	−	46.0185i	0.184211	−	0.348625i
$133$		0			0
$134$	95.9045	+	159.145i	0.715706	+	1.18765i
$135$		−	15.5021i		−	0.114831i
$136$	4.63675	+	82.3535i	0.0340937	+	0.605540i
$137$	−203.528			−1.48561			−0.742804	−	0.669509i	$-0.766504\pi$
$137$	−203.528			−1.48561			−0.742804	+	0.669509i	$0.766504\pi$
$138$	−81.8337	+	49.3149i	−0.592998	+	0.357355i
$139$		−	81.6255i		−	0.587233i	−0.955923	−	0.293617i	$-0.905141\pi$
$139$		−	81.6255i		−	0.587233i	0.955923	−	0.293617i	$-0.0948589\pi$
$140$		0			0
$141$	−6.27873			−0.0445300
$142$	−74.9314	−	124.342i	−0.527686	−	0.875647i
$143$		−	175.384i		−	1.22646i
$144$	27.0470	+	39.6543i	0.187826	+	0.275377i
$145$	−58.7055			−0.404865
$146$	118.815	−	71.6010i	0.813804	−	0.490418i
$147$		0			0
$148$	99.8224	−	188.917i	0.674476	−	1.27647i
$149$	−242.330			−1.62638			−0.813188	−	0.582001i	$-0.802270\pi$
$149$	−242.330			−1.62638			−0.813188	+	0.582001i	$0.802270\pi$
$150$	28.7855	+	47.7670i	0.191904	+	0.318447i
$151$			113.491i			0.751597i	0.926701	+	0.375798i	$0.122632\pi$
$151$			113.491i			0.751597i	−0.926701	+	0.375798i	$0.877368\pi$
$152$	−124.063	+	6.98512i	−0.816204	+	0.0459547i
$153$	30.9315			0.202166
$154$		0			0
$155$		−	85.2119i		−	0.549754i
$156$	143.008	+	75.5645i	0.916719	+	0.484388i
$157$	120.548			0.767823			0.383911	−	0.923370i	$-0.374577\pi$
$157$	120.548			0.767823			0.383911	+	0.923370i	$0.374577\pi$
$158$	−161.141	−	267.399i	−1.01988	−	1.69240i
$159$			119.267i			0.750105i
$160$	86.7830	+	39.7857i	0.542394	+	0.248661i
$161$		0			0
$162$	15.4170	−	9.29065i	0.0951666	−	0.0573497i
$163$			194.724i			1.19463i	0.802008	+	0.597313i	$0.203765\pi$
$163$			194.724i			1.19463i	−0.802008	+	0.597313i	$0.796235\pi$
$164$	−58.1614	+	110.072i	−0.354643	+	0.671172i
$165$	−38.8196			−0.235270
$166$	87.8683	+	145.810i	0.529327	+	0.878371i
$167$			150.495i			0.901165i	0.892735	+	0.450583i	$0.148784\pi$
$167$			150.495i			0.901165i	−0.892735	+	0.450583i	$0.851216\pi$
$168$		0			0
$169$	376.027			2.22501
$170$	52.6921	−	31.7535i	0.309954	−	0.186786i
$171$			46.5973i			0.272499i
$172$	53.8277	+	28.4422i	0.312952	+	0.165362i
$173$	306.516			1.77177			0.885885	−	0.463906i	$-0.153552\pi$
$173$	306.516			1.77177			0.885885	+	0.463906i	$0.153552\pi$
$174$	−35.1831	−	58.3831i	−0.202202	−	0.335535i
$175$		0			0
$176$	99.3001	−	67.7295i	0.564205	−	0.384827i
$177$	−196.185			−1.10839
$178$	29.5002	−	17.7775i	0.165731	−	0.0998736i
$179$		−	219.711i		−	1.22743i	−0.789526	−	0.613717i	$-0.789674\pi$
$179$		−	219.711i		−	1.22743i	0.789526	−	0.613717i	$-0.210326\pi$
$180$	16.7255	−	31.6535i	0.0929193	−	0.175853i
$181$	−10.3397			−0.0571255			−0.0285627	−	0.999592i	$-0.509093\pi$
$181$	−10.3397			−0.0571255			−0.0285627	+	0.999592i	$0.509093\pi$
$182$		0			0
$183$			5.72871i			0.0313044i
$184$	−220.301	+	12.4036i	−1.19729	+	0.0674110i
$185$	−159.364			−0.861425
$186$	84.7440	−	51.0688i	0.455613	−	0.274563i
$187$		−	77.4569i		−	0.414208i
$188$	−12.8204	−	6.77422i	−0.0681937	−	0.0360331i
$189$		0			0
$190$	47.8357	+	79.3791i	0.251767	+	0.417785i
$191$		−	31.1378i		−	0.163025i	−0.996672	−	0.0815126i	$-0.974025\pi$
$191$		−	31.1378i		−	0.163025i	0.996672	−	0.0815126i	$-0.0259751\pi$
$192$	12.4431	+	110.151i	0.0648077	+	0.573701i
$193$	−68.2099			−0.353419			−0.176709	−	0.984263i	$-0.556545\pi$
$193$	−68.2099			−0.353419			−0.176709	+	0.984263i	$0.556545\pi$
$194$	189.841	−	114.403i	0.978561	−	0.589704i
$195$		−	120.637i		−	0.618649i
$196$		0			0
$197$	113.365			0.575456			0.287728	−	0.957712i	$-0.407100\pi$
$197$	113.365			0.575456			0.287728	+	0.957712i	$0.407100\pi$
$198$	−23.2651	−	38.6064i	−0.117501	−	0.194982i
$199$		−	154.567i		−	0.776720i	−0.921508	−	0.388360i	$-0.873042\pi$
$199$		−	154.567i		−	0.776720i	0.921508	−	0.388360i	$-0.126958\pi$
$200$	7.24010	+	128.592i	0.0362005	+	0.642958i
$201$	160.915			0.800571
$202$	9.55440	−	5.75771i	0.0472990	−	0.0285035i
$203$		0			0
$204$	63.1584	+	33.3724i	0.309600	+	0.163590i
$205$	92.8530			0.452942
$206$	−196.087	−	325.389i	−0.951879	−	1.57956i
$207$			82.7438i			0.399728i
$208$	210.478	+	308.587i	1.01191	+	1.48359i
$209$	116.686			0.558308
$210$		0			0
$211$			308.247i			1.46089i	0.682974	+	0.730443i	$0.260686\pi$
$211$			308.247i			1.46089i	−0.682974	+	0.730443i	$0.739314\pi$
$212$	−128.679	+	243.528i	−0.606974	+	1.14872i
$213$	−125.725			−0.590257
$214$	−32.3144	−	53.6228i	−0.151002	−	0.250574i
$215$		−	45.4072i		−	0.211196i
$216$	41.5035	−	2.33677i	0.192146	−	0.0108184i
$217$		0			0
$218$	46.3710	−	27.9443i	0.212711	−	0.128185i
$219$		−	120.137i		−	0.548570i
$220$	−79.2649	−	41.8830i	−0.360295	−	0.190377i
$221$	240.707			1.08917
$222$	−95.5090	−	158.489i	−0.430221	−	0.713913i
$223$		−	79.3494i		−	0.355827i	−0.984046	−	0.177913i	$-0.943065\pi$
$223$		−	79.3494i		−	0.355827i	0.984046	−	0.177913i	$-0.0569347\pi$
$224$		0			0
$225$	48.2983			0.214659
$226$	−277.718	+	167.359i	−1.22884	+	0.740529i
$227$			228.474i			1.00649i	0.864142	+	0.503247i	$0.167862\pi$
$227$			228.474i			1.00649i	−0.864142	+	0.503247i	$0.832138\pi$
$228$	−50.2745	+	95.1462i	−0.220502	+	0.417308i
$229$	−280.501			−1.22489			−0.612447	−	0.790512i	$-0.709815\pi$
$229$	−280.501			−1.22489			−0.612447	+	0.790512i	$0.709815\pi$
$230$	84.9429	+	140.955i	0.369317	+	0.612848i
$231$		0			0
$232$	−8.84919	−	157.171i	−0.0381431	−	0.677461i
$233$	−47.6232			−0.204392			−0.102196	−	0.994764i	$-0.532587\pi$
$233$	−47.6232			−0.204392			−0.102196	+	0.994764i	$0.532587\pi$
$234$	119.974	−	72.2993i	0.512710	−	0.308971i
$235$			10.8148i			0.0460206i
$236$	−400.587	−	211.667i	−1.69740	−	0.896895i
$237$	−270.373			−1.14082
$238$		0			0
$239$		−	399.469i		−	1.67142i	−0.549173	−	0.835709i	$-0.685057\pi$
$239$		−	399.469i		−	1.67142i	0.549173	−	0.835709i	$-0.314943\pi$
$240$	68.3028	−	46.5872i	0.284595	−	0.194114i
$241$	−42.8635			−0.177857			−0.0889284	−	0.996038i	$-0.528344\pi$
$241$	−42.8635			−0.177857			−0.0889284	+	0.996038i	$0.528344\pi$
$242$	110.597	−	66.6483i	0.457012	−	0.275406i
$243$		−	15.5885i		−	0.0641500i
$244$	−6.18079	+	11.6973i	−0.0253311	+	0.0479399i
$245$		0			0
$246$	55.6482	+	92.3432i	0.226212	+	0.375379i
$247$			362.618i			1.46809i
$248$	228.136	−	12.8447i	0.919903	−	0.0517933i
$249$	147.431			0.592093
$250$	210.040	−	126.575i	0.840160	−	0.506301i
$251$		−	134.620i		−	0.536335i	−0.963372	−	0.268168i	$-0.913582\pi$
$251$		−	134.620i		−	0.536335i	0.963372	−	0.268168i	$-0.0864181\pi$
$252$		0			0
$253$	207.202			0.818982
$254$	−61.3295	−	101.771i	−0.241455	−	0.400672i
$255$		−	53.2782i		−	0.208934i
$256$	−93.4359	+	238.340i	−0.364984	+	0.931014i
$257$	−84.4840			−0.328732			−0.164366	−	0.986399i	$-0.552558\pi$
$257$	−84.4840			−0.328732			−0.164366	+	0.986399i	$0.552558\pi$
$258$	45.1578	−	27.2132i	0.175030	−	0.105477i
$259$		0			0
$260$	130.157	−	246.325i	0.500602	−	0.947406i
$261$	−59.0324			−0.226178
$262$	−217.336	−	360.650i	−0.829527	−	1.37653i
$263$		−	4.76125i		−	0.0181036i	−0.999959	−	0.00905180i	$-0.997119\pi$
$263$		−	4.76125i		−	0.0181036i	0.999959	−	0.00905180i	$-0.00288132\pi$
$264$	−5.85161	−	103.931i	−0.0221652	−	0.393677i
$265$	205.432			0.775214
$266$		0			0
$267$		−	29.8283i		−	0.111716i
$268$	328.569	+	173.613i	1.22600	+	0.647811i
$269$	110.458			0.410626			0.205313	−	0.978696i	$-0.434179\pi$
$269$	110.458			0.410626			0.205313	+	0.978696i	$0.434179\pi$
$270$	−16.0028	−	26.5551i	−0.0592695	−	0.0983523i
$271$			169.430i			0.625202i	0.949885	+	0.312601i	$0.101200\pi$
$271$			169.430i			0.625202i	−0.949885	+	0.312601i	$0.898800\pi$
$272$	92.9558	+	136.285i	0.341749	+	0.501048i
$273$		0			0
$274$	−348.644	+	210.101i	−1.27242	+	0.766792i
$275$		−	120.946i		−	0.439803i
$276$	−89.2735	+	168.953i	−0.323455	+	0.612148i
$277$	368.077			1.32880			0.664398	−	0.747379i	$-0.268688\pi$
$277$	368.077			1.32880			0.664398	+	0.747379i	$0.268688\pi$
$278$	−84.2615	−	139.824i	−0.303099	−	0.502965i
$279$		−	85.6865i		−	0.307120i
$280$		0			0
$281$	−395.717			−1.40825			−0.704123	−	0.710078i	$-0.748659\pi$
$281$	−395.717			−1.40825			−0.704123	+	0.710078i	$0.748659\pi$
$282$	−10.7555	+	6.48150i	−0.0381399	+	0.0229840i
$283$			96.9072i			0.342428i	0.985234	+	0.171214i	$0.0547690\pi$
$283$			96.9072i			0.342428i	−0.985234	+	0.171214i	$0.945231\pi$
$284$	−256.715	−	135.646i	−0.903926	−	0.477628i
$285$	80.2619			0.281621
$286$	−181.048	−	300.433i	−0.633035	−	1.05046i
$287$		0			0
$288$	87.2663	+	40.0073i	0.303008	+	0.138914i
$289$	−182.694			−0.632158
$290$	−100.562	+	60.6013i	−0.346767	+	0.208970i
$291$		−	191.952i		−	0.659629i
$292$	129.617	−	245.305i	0.443895	−	0.840086i
$293$	−151.346			−0.516538			−0.258269	−	0.966073i	$-0.583152\pi$
$293$	−151.346			−0.516538			−0.258269	+	0.966073i	$0.583152\pi$
$294$		0			0
$295$			337.921i			1.14549i
$296$	−24.0223	−	426.661i	−0.0811564	−	1.44142i
$297$	−39.0358			−0.131434
$298$	−415.111	+	250.156i	−1.39299	+	0.839450i
$299$			643.907i			2.15354i
$300$	98.6193	+	52.1097i	0.328731	+	0.173699i
$301$		0			0
$302$	117.156	+	194.410i	0.387935	+	0.643743i
$303$		−	9.66066i		−	0.0318834i
$304$	−205.309	+	140.035i	−0.675359	+	0.460642i
$305$	9.86747			0.0323523
$306$	52.9856	−	31.9304i	0.173156	−	0.104348i
$307$			514.328i			1.67533i	0.546181	+	0.837667i	$0.316081\pi$
$307$			514.328i			1.67533i	−0.546181	+	0.837667i	$0.683919\pi$
$308$		0			0
$309$	−329.008			−1.06475
$310$	−87.9638	−	145.968i	−0.283754	−	0.470865i
$311$		−	135.081i		−	0.434344i	−0.976133	−	0.217172i	$-0.930317\pi$
$311$		−	135.081i		−	0.434344i	0.976133	−	0.217172i	$-0.0696832\pi$
$312$	322.978	−	18.1846i	1.03518	−	0.0582840i
$313$	−288.360			−0.921279			−0.460640	−	0.887587i	$-0.652380\pi$
$313$	−288.360			−0.921279			−0.460640	+	0.887587i	$0.652380\pi$
$314$	206.499	−	124.441i	0.657640	−	0.396310i
$315$		0			0
$316$	−552.070	−	291.710i	−1.74706	−	0.923133i
$317$	159.576			0.503395			0.251698	−	0.967806i	$-0.419011\pi$
$317$	159.576			0.503395			0.251698	+	0.967806i	$0.419011\pi$
$318$	123.118	+	204.304i	0.387165	+	0.642465i
$319$			147.826i			0.463404i
$320$	189.730	−	21.4327i	0.592906	−	0.0669771i
$321$	−54.2191			−0.168907
$322$		0			0
$323$			160.147i			0.495811i
$324$	16.8186	−	31.8298i	0.0519093	−	0.0982400i
$325$	375.854			1.15647
$326$	201.013	+	333.562i	0.616603	+	1.02320i
$327$		−	46.8867i		−	0.143384i
$328$	13.9966	+	248.593i	0.0426724	+	0.757907i
$329$		0			0
$330$	−66.4979	+	40.0732i	−0.201509	+	0.121434i
$331$			278.329i			0.840874i	0.907322	+	0.420437i	$0.138123\pi$
$331$			278.329i			0.840874i	−0.907322	+	0.420437i	$0.861877\pi$
$332$	301.037	+	159.066i	0.906738	+	0.479114i
$333$	−160.251			−0.481235
$334$	155.355	+	257.797i	0.465134	+	0.771848i
$335$		−	277.169i		−	0.827370i
$336$		0			0
$337$	123.224			0.365651			0.182825	−	0.983145i	$-0.441476\pi$
$337$	123.224			0.365651			0.182825	+	0.983145i	$0.441476\pi$
$338$	644.135	−	388.171i	1.90572	−	1.14843i
$339$			280.807i			0.828338i
$340$	57.4826	−	108.788i	0.169066	−	0.319964i
$341$	−214.571			−0.629242
$342$	48.1022	+	79.8212i	0.140650	+	0.233395i
$343$		0			0
$344$	121.568	−	6.84462i	0.353394	−	0.0198972i
$345$	142.523			0.413109
$346$	525.062	−	316.415i	1.51752	−	0.914494i
$347$		−	601.315i		−	1.73290i	−0.499268	−	0.866448i	$-0.666398\pi$
$347$		−	601.315i		−	1.73290i	0.499268	−	0.866448i	$-0.333602\pi$
$348$	−120.537	−	63.6910i	−0.346371	−	0.183020i
$349$	146.665			0.420244			0.210122	−	0.977675i	$-0.432614\pi$
$349$	146.665			0.420244			0.210122	+	0.977675i	$0.432614\pi$
$350$		0			0
$351$		−	121.308i		−	0.345608i
$352$	100.184	−	218.528i	0.284614	−	0.620817i
$353$	−49.7171			−0.140842			−0.0704208	−	0.997517i	$-0.522434\pi$
$353$	−49.7171			−0.140842			−0.0704208	+	0.997517i	$0.522434\pi$
$354$	−336.065	+	202.521i	−0.949337	+	0.572093i
$355$			216.556i			0.610016i
$356$	32.1821	−	60.9057i	0.0903993	−	0.171083i
$357$		0			0
$358$	−226.806	−	376.364i	−0.633537	−	1.05130i
$359$		−	172.708i		−	0.481082i	−0.970639	−	0.240541i	$-0.922675\pi$
$359$		−	172.708i		−	0.481082i	0.970639	−	0.240541i	$-0.0773249\pi$
$360$	−4.02499	−	71.4880i	−0.0111805	−	0.198578i
$361$	119.743			0.331699
$362$	−17.7119	+	10.6736i	−0.0489279	+	0.0294851i
$363$		−	111.827i		−	0.308063i
$364$		0			0
$365$	−206.931			−0.566933
$366$	5.91372	+	9.81328i	0.0161577	+	0.0268122i
$367$			396.276i			1.07977i	0.841738	+	0.539886i	$0.181533\pi$
$367$			396.276i			1.07977i	−0.841738	+	0.539886i	$0.818467\pi$
$368$	−364.572	+	248.663i	−0.990684	+	0.675715i
$369$	93.3702			0.253036
$370$	−272.990	+	164.510i	−0.737811	+	0.444622i
$371$		0			0
$372$	92.4485	−	174.962i	0.248517	−	0.470327i
$373$	568.935			1.52530			0.762648	−	0.646814i	$-0.223899\pi$
$373$	568.935			1.52530			0.762648	+	0.646814i	$0.223899\pi$
$374$	−79.9584	−	132.684i	−0.213792	−	0.354769i
$375$		−	212.376i		−	0.566336i
$376$	−28.9544	+	1.63022i	−0.0770063	+	0.00433568i
$377$	−459.387			−1.21853
$378$		0			0
$379$			228.766i			0.603605i	0.953370	+	0.301803i	$0.0975884\pi$
$379$			228.766i			0.603605i	−0.953370	+	0.301803i	$0.902412\pi$
$380$	163.885	+	86.5958i	0.431277	+	0.227884i
$381$	−102.903			−0.270085
$382$	−32.1434	−	53.3391i	−0.0841451	−	0.139631i
$383$			59.1583i			0.154460i	0.997013	+	0.0772301i	$0.0246076\pi$
$383$			59.1583i			0.154460i	−0.997013	+	0.0772301i	$0.975392\pi$
$384$	135.023	+	175.843i	0.351622	+	0.457925i
$385$		0			0
$386$	−116.843	+	70.4127i	−0.302703	+	0.182416i
$387$		−	45.6601i		−	0.117985i
$388$	207.100	−	391.943i	0.533763	−	1.01016i
$389$	123.606			0.317752			0.158876	−	0.987299i	$-0.449213\pi$
$389$	123.606			0.317752			0.158876	+	0.987299i	$0.449213\pi$
$390$	−124.532	−	206.650i	−0.319314	−	0.529873i
$391$			284.376i			0.727305i
$392$		0			0
$393$	−364.661			−0.927890
$394$	194.194	−	117.026i	0.492878	−	0.297020i
$395$			465.707i			1.17900i
$396$	−79.7064	−	42.1163i	−0.201279	−	0.106354i
$397$	−388.759			−0.979242			−0.489621	−	0.871935i	$-0.662865\pi$
$397$	−388.759			−0.979242			−0.489621	+	0.871935i	$0.662865\pi$
$398$	−159.559	−	264.774i	−0.400902	−	0.665260i
$399$		0			0
$400$	145.147	+	212.804i	0.362867	+	0.532009i
$401$	−85.5616			−0.213371			−0.106685	−	0.994293i	$-0.534024\pi$
$401$	−85.5616			−0.213371			−0.106685	+	0.994293i	$0.534024\pi$
$402$	275.647	−	166.112i	0.685689	−	0.413213i
$403$		−	666.807i		−	1.65461i
$404$	10.4230	−	19.7259i	0.0257996	−	0.0488265i
$405$	−26.8505			−0.0662974
$406$		0			0
$407$			401.292i			0.985977i
$408$	142.640	−	8.03108i	0.349609	−	0.0196840i
$409$	−212.321			−0.519123			−0.259561	−	0.965727i	$-0.583578\pi$
$409$	−212.321			−0.519123			−0.259561	+	0.965727i	$0.583578\pi$
$410$	159.057	−	95.8517i	0.387944	−	0.233785i
$411$			352.521i			0.857716i
$412$	−671.794	−	354.971i	−1.63057	−	0.861581i
$413$		0			0
$414$	85.4160	+	141.740i	0.206319	+	0.342367i
$415$		−	253.944i		−	0.611913i
$416$	679.101	+	311.335i	1.63246	+	0.748401i
$417$	−141.379			−0.339039
$418$	199.884	−	120.455i	0.478191	−	0.288169i
$419$			411.422i			0.981914i	0.871184	+	0.490957i	$0.163353\pi$
$419$			411.422i			0.981914i	−0.871184	+	0.490957i	$0.836647\pi$
$420$		0			0
$421$	−307.278			−0.729876			−0.364938	−	0.931032i	$-0.618910\pi$
$421$	−307.278			−0.729876			−0.364938	+	0.931032i	$0.618910\pi$
$422$	318.201	+	528.027i	0.754032	+	1.25125i
$423$			10.8751i			0.0257094i
$424$	30.9665	+	549.998i	0.0730343	+	1.29717i
$425$	165.993			0.390572
$426$	−215.366	+	129.785i	−0.505555	+	0.304660i
$427$		0			0
$428$	−110.709	−	58.4978i	−0.258666	−	0.136677i
$429$	−303.774			−0.708098
$430$	−46.8736	−	77.7825i	−0.109008	−	0.180889i
$431$			286.486i			0.664701i	0.943156	+	0.332351i	$0.107842\pi$
$431$			286.486i			0.664701i	−0.943156	+	0.332351i	$0.892158\pi$
$432$	68.6832	−	46.8467i	0.158989	−	0.108441i
$433$	−158.782			−0.366702			−0.183351	−	0.983047i	$-0.558695\pi$
$433$	−158.782			−0.366702			−0.183351	+	0.983047i	$0.558695\pi$
$434$		0			0
$435$			101.681i			0.233749i
$436$	50.5867	−	95.7370i	0.116025	−	0.219580i
$437$	−428.404			−0.980330
$438$	−124.017	−	205.794i	−0.283143	−	0.469850i
$439$		−	662.533i		−	1.50919i	−0.656193	−	0.754593i	$-0.727834\pi$
$439$		−	662.533i		−	1.50919i	0.656193	−	0.754593i	$-0.272166\pi$
$440$	−179.016	+	10.0792i	−0.406855	+	0.0229072i
$441$		0			0
$442$	412.331	−	248.480i	0.932875	−	0.562173i
$443$			660.309i			1.49054i	0.666763	+	0.745270i	$0.267680\pi$
$443$			660.309i			1.49054i	−0.666763	+	0.745270i	$0.732320\pi$
$444$	−327.214	−	172.897i	−0.736968	−	0.389409i
$445$	−51.3779			−0.115456
$446$	−81.9119	−	135.925i	−0.183659	−	0.304766i
$447$			419.728i			0.938989i
$448$		0			0
$449$	−334.712			−0.745462			−0.372731	−	0.927940i	$-0.621578\pi$
$449$	−334.712			−0.745462			−0.372731	+	0.927940i	$0.621578\pi$
$450$	82.7349	−	49.8580i	0.183855	−	0.110796i
$451$		−	233.812i		−	0.518431i
$452$	−302.966	+	573.373i	−0.670280	+	1.26853i
$453$	196.572			0.433935
$454$	235.853	+	391.376i	0.519500	+	0.862063i
$455$		0			0
$456$	12.0986	+	214.883i	0.0265320	+	0.471236i
$457$	393.880			0.861883			0.430941	−	0.902380i	$-0.358182\pi$
$457$	393.880			0.861883			0.430941	+	0.902380i	$0.358182\pi$
$458$	−480.498	+	289.559i	−1.04912	+	0.632226i
$459$		−	53.5749i		−	0.116721i
$460$	291.014	+	153.770i	0.632640	+	0.334282i
$461$	−274.690			−0.595856			−0.297928	−	0.954588i	$-0.596296\pi$
$461$	−274.690			−0.595856			−0.297928	+	0.954588i	$0.596296\pi$
$462$		0			0
$463$		−	28.3801i		−	0.0612961i	−0.999530	−	0.0306481i	$-0.990243\pi$
$463$		−	28.3801i		−	0.0612961i	0.999530	−	0.0306481i	$-0.00975711\pi$
$464$	−177.405	−	260.099i	−0.382339	−	0.560558i
$465$	−147.591			−0.317401
$466$	−81.5786	+	49.1612i	−0.175061	+	0.105496i
$467$			658.235i			1.40950i	0.709457	+	0.704749i	$0.248940\pi$
$467$			658.235i			1.40950i	−0.709457	+	0.704749i	$0.751060\pi$
$468$	130.882	−	247.697i	0.279661	−	0.529268i
$469$		0			0
$470$	11.1641	+	18.5258i	0.0237534	+	0.0394167i
$471$		−	208.796i		−	0.443303i
$472$	−904.708	+	50.9378i	−1.91675	+	0.107919i
$473$	−114.339			−0.241732
$474$	−463.149	+	279.105i	−0.977109	+	0.588829i
$475$			250.063i			0.526449i
$476$		0			0
$477$	206.576			0.433073
$478$	−412.370	−	684.290i	−0.862698	−	1.43157i
$479$			48.9758i			0.102246i	0.998692	+	0.0511230i	$0.0162800\pi$
$479$			48.9758i			0.102246i	−0.998692	+	0.0511230i	$0.983720\pi$
$480$	68.9109	−	150.313i	0.143564	−	0.313151i
$481$	−1247.07			−2.59265
$482$	−73.4251	+	44.2477i	−0.152334	+	0.0918003i
$483$		0			0
$484$	120.652	−	228.337i	0.249280	−	0.471771i
$485$	−330.629			−0.681710
$486$	−16.0919	−	26.7030i	−0.0331109	−	0.0549445i
$487$			67.6020i			0.138813i	0.997588	+	0.0694066i	$0.0221106\pi$
$487$			67.6020i			0.138813i	−0.997588	+	0.0694066i	$0.977889\pi$
$488$	1.48741	+	26.4180i	0.00304797	+	0.0541351i
$489$	337.272			0.689718
$490$		0			0
$491$			317.695i			0.647036i	0.946222	+	0.323518i	$0.104866\pi$
$491$			317.695i			0.647036i	−0.946222	+	0.323518i	$0.895134\pi$
$492$	190.651	+	100.738i	0.387501	+	0.204753i
$493$	−202.884			−0.411530
$494$	374.328	+	621.164i	0.757749	+	1.25742i
$495$			67.2375i			0.135833i
$496$	377.537	−	257.507i	0.761164	−	0.519167i
$497$		0			0
$498$	252.550	−	152.192i	0.507128	−	0.305607i
$499$			358.220i			0.717876i	0.933361	+	0.358938i	$0.116861\pi$
$499$			358.220i			0.717876i	−0.933361	+	0.358938i	$0.883139\pi$
$500$	229.136	−	433.646i	0.458271	−	0.867293i
$501$	260.664			0.520288
$502$	−138.968	−	230.604i	−0.276828	−	0.459371i
$503$		−	326.404i		−	0.648914i	−0.945900	−	0.324457i	$-0.894818\pi$
$503$		−	326.404i		−	0.648914i	0.945900	−	0.324457i	$-0.105182\pi$
$504$		0			0
$505$	−16.6401			−0.0329506
$506$	354.938	−	213.894i	0.701458	−	0.422715i
$507$		−	651.298i		−	1.28461i
$508$	−210.115	−	111.023i	−0.413612	−	0.218549i
$509$	−22.7983			−0.0447904			−0.0223952	−	0.999749i	$-0.507129\pi$
$509$	−22.7983			−0.0447904			−0.0223952	+	0.999749i	$0.507129\pi$
$510$	−54.9988	−	91.2655i	−0.107841	−	0.178952i
$511$		0			0
$512$	85.9808	+	504.729i	0.167931	+	0.985799i
$513$	80.7089			0.157327
$514$	−144.721	+	87.2124i	−0.281559	+	0.169674i
$515$			566.702i			1.10039i
$516$	49.2633	−	93.2324i	0.0954715	−	0.180683i
$517$	27.2328			0.0526746
$518$		0			0
$519$		−	530.901i		−	1.02293i
$520$	−31.3222	−	556.315i	−0.0602350	−	1.06984i
$521$	−251.073			−0.481906			−0.240953	−	0.970537i	$-0.577460\pi$
$521$	−251.073			−0.481906			−0.240953	+	0.970537i	$0.577460\pi$
$522$	−101.123	+	60.9389i	−0.193721	+	0.116741i
$523$			574.271i			1.09803i	0.835811	+	0.549017i	$0.184998\pi$
$523$			574.271i			1.09803i	−0.835811	+	0.549017i	$0.815002\pi$
$524$	−744.593	−	393.438i	−1.42098	−	0.750835i
$525$		0			0
$526$	−4.91501	−	8.15602i	−0.00934413	−	0.0155057i
$527$		−	294.490i		−	0.558805i
$528$	−117.311	−	171.993i	−0.222180	−	0.325744i
$529$	−231.726			−0.438045
$530$	351.905	−	212.066i	0.663971	−	0.400125i
$531$			339.803i			0.639930i
$532$		0			0
$533$	726.601			1.36323
$534$	−30.7915	−	51.0958i	−0.0576621	−	0.0956850i
$535$			93.3901i			0.174561i
$536$	742.059	−	41.7801i	1.38444	−	0.0779480i
$537$	−380.550			−0.708659
$538$	189.215	−	114.026i	0.351701	−	0.211943i
$539$		0			0
$540$	−54.8254	−	28.9694i	−0.101529	−	0.0536470i
$541$	−350.497			−0.647869			−0.323934	−	0.946080i	$-0.605006\pi$
$541$	−350.497			−0.647869			−0.323934	+	0.946080i	$0.605006\pi$
$542$	174.901	+	290.233i	0.322696	+	0.535485i
$543$			17.9089i			0.0329814i
$544$	299.920	+	137.498i	0.551323	+	0.252754i
$545$	−80.7603			−0.148184
$546$		0			0
$547$		−	206.339i		−	0.377219i	−0.982052	−	0.188610i	$-0.939602\pi$
$547$		−	206.339i		−	0.377219i	0.982052	−	0.188610i	$-0.0603980\pi$
$548$	−380.340	+	719.806i	−0.694052	+	1.31351i
$549$	9.92242			0.0180736
$550$	−124.852	−	207.180i	−0.227003	−	0.376691i
$551$		−	305.639i		−	0.554699i
$552$	21.4837	+	381.573i	0.0389197	+	0.691255i
$553$		0			0
$554$	630.515	−	379.963i	1.13811	−	0.685855i
$555$			276.026i			0.497344i
$556$	−288.680	−	152.536i	−0.519208	−	0.274346i
$557$	−189.749			−0.340662			−0.170331	−	0.985387i	$-0.554484\pi$
$557$	−189.749			−0.340662			−0.170331	+	0.985387i	$0.554484\pi$
$558$	−88.4537	−	146.781i	−0.158519	−	0.263048i
$559$		−	355.324i		−	0.635642i
$560$		0			0
$561$	−134.159			−0.239143
$562$	−677.863	+	408.496i	−1.20616	+	0.726862i
$563$		−	121.571i		−	0.215934i	−0.994154	−	0.107967i	$-0.965566\pi$
$563$		−	121.571i		−	0.215934i	0.994154	−	0.107967i	$-0.0344341\pi$
$564$	−11.7333	+	22.2056i	−0.0208037	+	0.0393717i
$565$	483.677			0.856066
$566$	100.037	+	166.002i	0.176744	+	0.293290i
$567$		0			0
$568$	−579.779	+	32.6433i	−1.02074	+	0.0574706i
$569$	−411.249			−0.722757			−0.361379	−	0.932419i	$-0.617694\pi$
$569$	−411.249			−0.722757			−0.361379	+	0.932419i	$0.617694\pi$
$570$	137.489	−	82.8539i	0.241208	−	0.145358i
$571$		−	876.837i		−	1.53562i	−0.640680	−	0.767808i	$-0.721347\pi$
$571$		−	876.837i		−	1.53562i	0.640680	−	0.767808i	$-0.278653\pi$
$572$	−620.270	−	327.746i	−1.08439	−	0.572983i
$573$	−53.9323			−0.0941227
$574$		0			0
$575$			444.042i			0.772247i
$576$	190.787	−	21.5520i	0.331227	−	0.0374167i
$577$	−236.500			−0.409879			−0.204940	−	0.978775i	$-0.565700\pi$
$577$	−236.500			−0.409879			−0.204940	+	0.978775i	$0.565700\pi$
$578$	−312.954	+	188.594i	−0.541444	+	0.326287i
$579$			118.143i			0.204047i
$580$	−109.705	+	207.620i	−0.189147	+	0.357966i
$581$		0			0
$582$	−198.151	−	328.814i	−0.340466	−	0.564972i
$583$		−	517.296i		−	0.887300i
$584$	−31.1925	−	554.011i	−0.0534117	−	0.948648i
$585$	−208.949			−0.357177
$586$	−259.255	+	156.233i	−0.442414	+	0.266610i
$587$		−	1015.68i		−	1.73030i	−0.501516	−	0.865149i	$-0.667224\pi$
$587$		−	1015.68i		−	1.73030i	0.501516	−	0.865149i	$-0.332776\pi$
$588$		0			0
$589$	443.640			0.753209
$590$	348.834	+	578.858i	0.591244	+	0.981116i
$591$		−	196.354i		−	0.332239i
$592$	−481.590	−	706.072i	−0.813497	−	1.19269i
$593$	938.566			1.58274			0.791371	−	0.611337i	$-0.209368\pi$
$593$	938.566			1.58274			0.791371	+	0.611337i	$0.209368\pi$
$594$	−66.8683	+	40.2964i	−0.112573	+	0.0678391i
$595$		0			0
$596$	−452.851	+	857.034i	−0.759817	+	1.43798i
$597$	−267.718			−0.448439
$598$	664.702	+	1103.01i	1.11154	+	1.84450i
$599$		−	21.5179i		−	0.0359230i	−0.999839	−	0.0179615i	$-0.994282\pi$
$599$		−	21.5179i		−	0.0359230i	0.999839	−	0.0179615i	$-0.00571764\pi$
$600$	222.727	−	12.5402i	0.371212	−	0.0209004i
$601$	796.035			1.32452			0.662258	−	0.749275i	$-0.269598\pi$
$601$	796.035			1.32452			0.662258	+	0.749275i	$0.269598\pi$
$602$		0			0
$603$		−	278.713i		−	0.462210i
$604$	401.377	+	212.085i	0.664532	+	0.351134i
$605$	−192.617			−0.318375
$606$	−9.97265	−	16.5487i	−0.0164565	−	0.0273081i
$607$		−	1036.00i		−	1.70675i	−0.521296	−	0.853376i	$-0.674551\pi$
$607$		−	1036.00i		−	1.70675i	0.521296	−	0.853376i	$-0.325449\pi$
$608$	−207.137	+	451.820i	−0.340686	+	0.743125i
$609$		0			0
$610$	16.9030	−	10.1861i	0.0277098	−	0.0166986i
$611$			84.6292i			0.138509i
$612$	57.8027	−	109.394i	0.0944489	−	0.178748i
$613$	−302.872			−0.494081			−0.247041	−	0.969005i	$-0.579458\pi$
$613$	−302.872			−0.494081			−0.247041	+	0.969005i	$0.579458\pi$
$614$	530.938	+	881.043i	0.864719	+	1.43492i
$615$		−	160.826i		−	0.261506i
$616$		0			0
$617$	634.576			1.02849			0.514243	−	0.857644i	$-0.328073\pi$
$617$	634.576			1.02849			0.514243	+	0.857644i	$0.328073\pi$
$618$	−563.590	+	339.633i	−0.911958	+	0.549568i
$619$			912.748i			1.47455i	0.675591	+	0.737276i	$0.263888\pi$
$619$			912.748i			1.47455i	−0.675591	+	0.737276i	$0.736112\pi$
$620$	−301.364	−	159.239i	−0.486071	−	0.256836i
$621$	143.316			0.230783
$622$	−139.443	−	231.394i	−0.224185	−	0.372015i
$623$		0			0
$624$	534.489	−	364.558i	0.856552	−	0.584228i
$625$	36.6767			0.0586828
$626$	−493.961	+	297.673i	−0.789076	+	0.475516i
$627$		−	202.107i		−	0.322340i
$628$	225.273	−	426.336i	0.358714	−	0.678878i
$629$	−550.756			−0.875606
$630$		0			0
$631$		−	915.136i		−	1.45030i	−0.688593	−	0.725148i	$-0.741771\pi$
$631$		−	915.136i		−	1.45030i	0.688593	−	0.725148i	$-0.258229\pi$
$632$	−1246.83	+	70.2001i	−1.97283	+	0.111076i
$633$	533.899			0.843442
$634$	273.354	−	164.730i	0.431158	−	0.259826i
$635$			177.245i			0.279126i
$636$	421.803	+	222.878i	0.663213	+	0.350437i
$637$		0			0
$638$	152.600	+	253.226i	0.239185	+	0.396905i
$639$			217.762i			0.340785i
$640$	302.882	−	232.571i	0.473254	−	0.363393i
$641$	1107.74			1.72815			0.864074	−	0.503365i	$-0.167905\pi$
$641$	1107.74			1.72815			0.864074	+	0.503365i	$0.167905\pi$
$642$	−92.8773	+	55.9701i	−0.144669	+	0.0871809i
$643$		−	160.376i		−	0.249418i	−0.992193	−	0.124709i	$-0.960200\pi$
$643$		−	160.376i		−	0.249418i	0.992193	−	0.124709i	$-0.0397998\pi$
$644$		0			0
$645$	−78.6475			−0.121934
$646$	165.319	+	274.332i	0.255912	+	0.424662i
$647$			13.8092i			0.0213434i	0.999943	+	0.0106717i	$0.00339697\pi$
$647$			13.8092i			0.0213434i	−0.999943	+	0.0106717i	$0.996603\pi$
$648$	−4.04741	−	71.8861i	−0.00624600	−	0.110935i
$649$	850.916			1.31112
$650$	643.838	−	387.992i	0.990520	−	0.596911i
$651$		0			0
$652$	688.669	+	363.888i	1.05624	+	0.558110i
$653$	903.251			1.38323			0.691617	−	0.722265i	$-0.256899\pi$
$653$	903.251			1.38323			0.691617	+	0.722265i	$0.256899\pi$
$654$	−48.4009	−	80.3169i	−0.0740074	−	0.122809i
$655$			628.112i			0.958950i
$656$	280.598	+	411.392i	0.427740	+	0.627122i
$657$	−208.083			−0.316717
$658$		0			0
$659$		−	155.924i		−	0.236607i	−0.992977	−	0.118304i	$-0.962254\pi$
$659$		−	155.924i		−	0.236607i	0.992977	−	0.118304i	$-0.0377456\pi$
$660$	−72.5435	+	137.291i	−0.109914	+	0.208016i
$661$	789.862			1.19495			0.597475	−	0.801888i	$-0.296171\pi$
$661$	789.862			1.19495			0.597475	+	0.801888i	$0.296171\pi$
$662$	287.318	+	476.778i	0.434015	+	0.720208i
$663$		−	416.917i		−	0.628833i
$664$	679.879	−	38.2792i	1.02391	−	0.0576494i
$665$		0			0
$666$	−274.510	+	165.427i	−0.412178	+	0.248388i
$667$		−	542.730i		−	0.813687i
$668$	532.245	+	281.235i	0.796774	+	0.421010i
$669$	−137.437			−0.205437
$670$	−286.120	−	474.790i	−0.427045	−	0.708643i
$671$		−	24.8472i		−	0.0370301i
$672$		0			0
$673$	788.072			1.17098			0.585491	−	0.810679i	$-0.300902\pi$
$673$	788.072			1.17098			0.585491	+	0.810679i	$0.300902\pi$
$674$	211.083	−	127.204i	0.313180	−	0.188730i
$675$		−	83.6550i		−	0.123933i
$676$	702.696	−	1329.87i	1.03949	−	1.96727i
$677$	−641.385			−0.947393			−0.473696	−	0.880688i	$-0.657081\pi$
$677$	−641.385			−0.947393			−0.473696	+	0.880688i	$0.657081\pi$
$678$	289.875	+	481.022i	0.427544	+	0.709471i
$679$		0			0
$680$	−13.8332	−	245.692i	−0.0203429	−	0.361312i
$681$	395.729			0.581100
$682$	−367.561	+	221.501i	−0.538946	+	0.324782i
$683$			321.852i			0.471232i	0.971846	+	0.235616i	$0.0757108\pi$
$683$			321.852i			0.471232i	−0.971846	+	0.235616i	$0.924289\pi$
$684$	164.798	+	87.0781i	0.240933	+	0.127307i
$685$	607.203			0.886427
$686$		0			0
$687$			485.842i			0.707193i
$688$	201.180	−	137.218i	0.292412	−	0.199445i
$689$	1607.56			2.33318
$690$	244.141	−	147.125i	0.353828	−	0.213225i
$691$			242.318i			0.350678i	0.984508	+	0.175339i	$0.0561021\pi$
$691$			242.318i			0.350678i	−0.984508	+	0.175339i	$0.943898\pi$
$692$	572.798	−	1084.04i	0.827742	−	1.56653i
$693$		0			0
$694$	−620.734	−	1030.05i	−0.894429	−	1.48422i
$695$			243.520i			0.350389i
$696$	−272.228	+	15.3272i	−0.391132	+	0.0220219i
$697$	320.897			0.460398
$698$	251.238	−	151.402i	0.359939	−	0.216908i
$699$			82.4858i			0.118006i
$700$		0			0
$701$	−460.014			−0.656225			−0.328112	−	0.944639i	$-0.606412\pi$
$701$	−460.014			−0.656225			−0.328112	+	0.944639i	$0.606412\pi$
$702$	−125.226	−	207.801i	−0.178385	−	0.296013i
$703$		−	829.698i		−	1.18022i
$704$	−53.9694	−	477.757i	−0.0766611	−	0.678633i
$705$	18.7319			0.0265700
$706$	−85.1654	+	51.3227i	−0.120631	+	0.0726950i
$707$		0			0
$708$	−366.618	+	693.837i	−0.517823	+	0.979996i
$709$	−1039.84			−1.46663			−0.733314	−	0.679890i	$-0.762027\pi$
$709$	−1039.84			−1.46663			−0.733314	+	0.679890i	$0.762027\pi$
$710$	223.549	+	370.960i	0.314858	+	0.522478i
$711$			468.300i			0.658650i
$712$	−7.74464	−	137.553i	−0.0108773	−	0.193192i
$713$	787.781			1.10488
$714$		0			0
$715$			523.238i			0.731801i
$716$	−777.038	−	410.581i	−1.08525	−	0.573437i
$717$	−691.900			−0.964994
$718$	−178.286	−	295.850i	−0.248309	−	0.412047i
$719$		−	951.072i		−	1.32277i	−0.750047	−	0.661385i	$-0.769969\pi$
$719$		−	951.072i		−	1.32277i	0.750047	−	0.661385i	$-0.230031\pi$
$720$	−80.6915	−	118.304i	−0.112072	−	0.164311i
$721$		0			0
$722$	205.120	−	123.610i	0.284100	−	0.171205i
$723$			74.2417i			0.102686i
$724$	−19.3222	+	36.5678i	−0.0266881	+	0.0505081i
$725$	−316.796			−0.436960
$726$	−115.438	−	191.559i	−0.159006	−	0.263856i
$727$			531.386i			0.730930i	0.930825	+	0.365465i	$0.119090\pi$
$727$			531.386i			0.730930i	−0.930825	+	0.365465i	$0.880910\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	−354.472	+	213.613i	−0.485578	+	0.292621i
$731$		−	156.926i		−	0.214673i
$732$	20.2604	+	10.7054i	0.0276781	+	0.0146249i
$733$	1144.87			1.56189			0.780946	−	0.624599i	$-0.214737\pi$
$733$	1144.87			1.56189			0.780946	+	0.624599i	$0.214737\pi$
$734$	409.074	+	678.821i	0.557321	+	0.924824i
$735$		0			0
$736$	−367.818	+	802.305i	−0.499752	+	1.09009i
$737$	−697.937			−0.946998
$738$	159.943	−	96.3855i	0.216725	−	0.130604i
$739$		−	317.638i		−	0.429821i	−0.976634	−	0.214911i	$-0.931054\pi$
$739$		−	317.638i		−	0.429821i	0.976634	−	0.214911i	$-0.0689460\pi$
$740$	−297.809	+	563.612i	−0.402444	+	0.761638i
$741$	628.072			0.847601
$742$		0			0
$743$		−	1138.61i		−	1.53245i	−0.642570	−	0.766227i	$-0.722132\pi$
$743$		−	1138.61i		−	1.53245i	0.642570	−	0.766227i	$-0.277868\pi$
$744$	−22.2477	−	395.143i	−0.0299029	−	0.531107i
$745$	722.964			0.970421
$746$	974.586	−	587.309i	1.30642	−	0.787277i
$747$		−	255.358i		−	0.341845i
$748$	−273.937	−	144.746i	−0.366226	−	0.193511i
$749$		0			0
$750$	−219.235	−	363.800i	−0.292313	−	0.485067i
$751$		−	130.959i		−	0.174379i	−0.996192	−	0.0871894i	$-0.972211\pi$
$751$		−	130.959i		−	0.174379i	0.996192	−	0.0871894i	$-0.0277885\pi$
$752$	−47.9159	+	32.6820i	−0.0637180	+	0.0434601i
$753$	−233.169			−0.309653
$754$	−786.929	+	474.223i	−1.04367	+	0.628942i
$755$		−	338.588i		−	0.448461i
$756$		0			0
$757$	−899.105			−1.18772			−0.593861	−	0.804568i	$-0.702397\pi$
$757$	−899.105			−1.18772			−0.593861	+	0.804568i	$0.702397\pi$
$758$	236.154	+	391.877i	0.311549	+	0.516988i
$759$		−	358.885i		−	0.472839i
$760$	370.128	−	20.8393i	0.487010	−	0.0274201i
$761$	1048.39			1.37764			0.688821	−	0.724931i	$-0.258129\pi$
$761$	1048.39			1.37764			0.688821	+	0.724931i	$0.258129\pi$
$762$	−176.272	+	106.226i	−0.231328	+	0.139404i
$763$		0			0
$764$	−110.123	−	58.1884i	−0.144140	−	0.0761628i
$765$	−92.2805			−0.120628
$766$	61.0688	+	101.338i	0.0797243	+	0.132295i
$767$			2644.33i			3.44762i
$768$	412.816	+	161.836i	0.537521	+	0.210724i
$769$	−912.173			−1.18618			−0.593091	−	0.805136i	$-0.702092\pi$
$769$	−912.173			−1.18618			−0.593091	+	0.805136i	$0.702092\pi$
$770$		0			0
$771$			146.331i			0.189793i
$772$	−127.466	+	241.234i	−0.165112	+	0.312479i
$773$	1121.12			1.45035			0.725174	−	0.688566i	$-0.241759\pi$
$773$	1121.12			1.45035			0.725174	+	0.688566i	$0.241759\pi$
$774$	−47.1346	−	78.2157i	−0.0608975	−	0.101054i
$775$		−	459.834i		−	0.593335i
$776$	−49.8387	−	885.187i	−0.0642251	−	1.14070i
$777$		0			0
$778$	211.736	−	127.597i	0.272154	−	0.164007i
$779$			483.422i			0.620568i
$780$	−426.648	−	225.438i	−0.546985	−	0.289023i
$781$	545.307			0.698216
$782$	293.560	+	487.137i	0.375397	+	0.622937i
$783$			102.247i			0.130584i
$784$		0			0
$785$	−359.642			−0.458142
$786$	−624.663	+	376.437i	−0.794737	+	0.478928i
$787$			306.423i			0.389356i	0.980867	+	0.194678i	$0.0623662\pi$
$787$			306.423i			0.389356i	−0.980867	+	0.194678i	$0.937634\pi$
$788$	211.849	−	400.930i	0.268844	−	0.508795i
$789$	−8.24673			−0.0104521
$790$	480.747	+	797.755i	0.608540	+	1.00982i
$791$		0			0
$792$	−180.013	+	10.1353i	−0.227290	+	0.0127971i
$793$	77.2157			0.0973716
$794$	−665.944	+	401.314i	−0.838720	+	0.505433i
$795$		−	355.818i		−	0.447570i
$796$	−546.649	−	288.845i	−0.686745	−	0.362871i
$797$	706.469			0.886410			0.443205	−	0.896420i	$-0.353841\pi$
$797$	706.469			0.886410			0.443205	+	0.896420i	$0.353841\pi$
$798$		0			0
$799$			37.3758i			0.0467782i
$800$	468.312	+	214.698i	0.585391	+	0.268373i
$801$	−51.6640			−0.0644994
$802$	−146.567	+	88.3248i	−0.182752	+	0.110131i
$803$			521.070i			0.648904i
$804$	300.707	−	569.098i	0.374014	−	0.707833i
$805$		0			0
$806$	−688.342	−	1142.24i	−0.854022	−	1.41717i
$807$		−	191.320i		−	0.237075i
$808$	−2.50830	−	44.5501i	−0.00310434	−	0.0551363i
$809$	−84.0475			−0.103891			−0.0519453	−	0.998650i	$-0.516542\pi$
$809$	−84.0475			−0.103891			−0.0519453	+	0.998650i	$0.516542\pi$
$810$	−45.9948	+	27.7176i	−0.0567837	+	0.0342192i
$811$		−	1393.50i		−	1.71825i	−0.511763	−	0.859126i	$-0.671008\pi$
$811$		−	1393.50i		−	1.71825i	0.511763	−	0.859126i	$-0.328992\pi$
$812$		0			0
$813$	293.461			0.360961
$814$	414.252	+	687.414i	0.508909	+	0.844489i
$815$		−	580.937i		−	0.712806i
$816$	236.053	−	161.004i	0.289280	−	0.197309i
$817$	236.404			0.289356
$818$	−363.706	+	219.178i	−0.444628	+	0.267944i
$819$		0			0
$820$	173.518	−	328.388i	0.211607	−	0.400473i
$821$	999.637			1.21758			0.608792	−	0.793330i	$-0.291654\pi$
$821$	999.637			1.21758			0.608792	+	0.793330i	$0.291654\pi$
$822$	363.906	+	603.869i	0.442708	+	0.734633i
$823$			988.093i			1.20060i	0.799775	+	0.600299i	$0.204952\pi$
$823$			988.093i			1.20060i	−0.799775	+	0.600299i	$0.795048\pi$
$824$	−1517.22	+	85.4239i	−1.84128	+	0.103670i
$825$	−209.484			−0.253920
$826$		0			0
$827$		−	153.986i		−	0.186198i	−0.995657	−	0.0930991i	$-0.970323\pi$
$827$		−	153.986i		−	0.186198i	0.995657	−	0.0930991i	$-0.0296773\pi$
$828$	292.635	+	154.626i	0.353424	+	0.186747i
$829$	−1239.01			−1.49458			−0.747292	−	0.664495i	$-0.768647\pi$
$829$	−1239.01			−1.49458			−0.747292	+	0.664495i	$0.768647\pi$
$830$	−262.145	−	435.006i	−0.315837	−	0.524104i
$831$		−	637.527i		−	0.767181i
$832$	1484.69	−	167.717i	1.78448	−	0.201582i
$833$		0			0
$834$	−242.183	+	145.945i	−0.290387	+	0.174994i
$835$		−	448.983i		−	0.537704i
$836$	218.056	−	412.678i	0.260833	−	0.493634i
$837$	−148.413			−0.177316
$838$	424.709	+	704.766i	0.506812	+	0.841009i
$839$		−	629.209i		−	0.749951i	−0.927035	−	0.374976i	$-0.877651\pi$
$839$		−	629.209i		−	0.749951i	0.927035	−	0.374976i	$-0.122349\pi$
$840$		0			0
$841$	−453.797			−0.539592
$842$	−526.367	+	317.201i	−0.625139	+	0.376724i
$843$			685.402i			0.813051i
$844$	1090.16	+	576.032i	1.29166	+	0.682502i
$845$	−1121.83			−1.32761
$846$	11.2263	+	18.6290i	0.0132698	+	0.0220201i
$847$		0			0
$848$	620.806	+	910.180i	0.732082	+	1.07333i
$849$	167.848			0.197701
$850$	284.346	−	171.354i	0.334524	−	0.201592i
$851$		−	1473.31i		−	1.73127i
$852$	−234.946	+	444.643i	−0.275759	+	0.521882i
$853$	22.6308			0.0265308			0.0132654	−	0.999912i	$-0.495777\pi$
$853$	22.6308			0.0265308			0.0132654	+	0.999912i	$0.495777\pi$
$854$		0			0
$855$		−	139.018i		−	0.162594i
$856$	−250.031	+	14.0775i	−0.292093	+	0.0164457i
$857$	−1580.90			−1.84469			−0.922344	−	0.386370i	$-0.873729\pi$
$857$	−1580.90			−1.84469			−0.922344	+	0.386370i	$0.873729\pi$
$858$	−520.365	+	313.584i	−0.606486	+	0.365483i
$859$		−	1559.88i		−	1.81593i	−0.419050	−	0.907963i	$-0.637637\pi$
$859$		−	1559.88i		−	1.81593i	0.419050	−	0.907963i	$-0.362363\pi$
$860$	−160.589	−	84.8540i	−0.186731	−	0.0986674i
$861$		0			0
$862$	295.738	+	490.751i	0.343084	+	0.569317i
$863$		−	629.122i		−	0.728994i	−0.931205	−	0.364497i	$-0.881241\pi$
$863$		−	629.122i		−	0.728994i	0.931205	−	0.364497i	$-0.118759\pi$
$864$	69.2947	−	151.150i	0.0802022	−	0.174942i
$865$	−914.455			−1.05717
$866$	−271.994	+	163.910i	−0.314081	+	0.189272i
$867$			316.435i			0.364977i
$868$		0			0
$869$	1172.69			1.34947
$870$	104.965	+	174.179i	0.120649	+	0.200206i
$871$		−	2168.93i		−	2.49016i
$872$	−12.1737	−	216.218i	−0.0139607	−	0.247956i
$873$	−332.471			−0.380837
$874$	−733.856	+	442.239i	−0.839653	+	0.505995i
$875$		0			0
$876$	−424.881	−	224.504i	−0.485024	−	0.256283i
$877$	531.113			0.605602			0.302801	−	0.953054i	$-0.402078\pi$
$877$	531.113			0.605602			0.302801	+	0.953054i	$0.402078\pi$
$878$	−683.929	−	1134.92i	−0.778962	−	1.29262i
$879$			262.138i			0.298223i
$880$	−296.250	+	202.063i	−0.336648	+	0.229617i
$881$	320.493			0.363784			0.181892	−	0.983319i	$-0.441778\pi$
$881$	320.493			0.363784			0.181892	+	0.983319i	$0.441778\pi$
$882$		0			0
$883$		−	1221.53i		−	1.38339i	−0.722189	−	0.691696i	$-0.756864\pi$
$883$		−	1221.53i		−	1.38339i	0.722189	−	0.691696i	$-0.243136\pi$
$884$	449.818	−	851.294i	0.508843	−	0.963002i
$885$	585.296			0.661352
$886$	681.634	+	1131.11i	0.769338	+	1.27665i
$887$		−	584.356i		−	0.658800i	−0.944190	−	0.329400i	$-0.893154\pi$
$887$		−	584.356i		−	0.658800i	0.944190	−	0.329400i	$-0.106846\pi$
$888$	−738.998	+	41.6078i	−0.832205	+	0.0468557i
$889$		0			0
$890$	−88.0103	+	53.0371i	−0.0988880	+	0.0595923i
$891$			67.6119i			0.0758832i
$892$	−280.630	−	148.283i	−0.314608	−	0.166237i
$893$	−56.3055			−0.0630521
$894$	433.283	+	718.994i	0.484657	+	0.804244i
$895$			655.481i			0.732381i
$896$		0			0
$897$	1115.28			1.24334
$898$	−573.362	+	345.522i	−0.638488	+	0.384768i
$899$			562.031i			0.625174i
$900$	90.2567	−	170.814i	0.100285	−	0.189793i
$901$	709.966			0.787976
$902$	−241.363	−	400.521i	−0.267587	−	0.444036i
$903$		0			0
$904$	72.9090	+	1294.94i	0.0806515	+	1.43245i
$905$	30.8473			0.0340854
$906$	336.729	−	202.921i	0.371665	−	0.223974i
$907$			682.918i			0.752941i	0.926429	+	0.376471i	$0.122862\pi$
$907$			682.918i			0.752941i	−0.926429	+	0.376471i	$0.877138\pi$
$908$	808.032	+	426.958i	0.889903	+	0.470218i
$909$	−16.7328			−0.0184079
$910$		0			0
$911$			728.384i			0.799543i	0.916615	+	0.399772i	$0.130911\pi$
$911$			728.384i			0.799543i	−0.916615	+	0.399772i	$0.869089\pi$
$912$	242.548	+	355.606i	0.265952	+	0.389919i
$913$	−639.454			−0.700388
$914$	674.717	−	406.601i	0.738202	−	0.444858i
$915$		−	17.0910i		−	0.0186786i
$916$	−524.182	+	992.030i	−0.572251	+	1.08300i
$917$		0			0
$918$	−55.3051	−	91.7738i	−0.0602452	−	0.0999714i
$919$			61.5914i			0.0670200i	0.999438	+	0.0335100i	$0.0106686\pi$
$919$			61.5914i			0.0670200i	−0.999438	+	0.0335100i	$0.989331\pi$
$920$	657.243	−	37.0047i	0.714395	−	0.0402226i
$921$	890.842			0.967255
$922$	−470.544	+	283.561i	−0.510351	+	0.307550i
$923$			1694.61i			1.83598i
$924$		0			0
$925$	−859.984			−0.929712
$926$	−29.2966	−	48.6151i	−0.0316378	−	0.0525001i
$927$			569.858i			0.614734i
$928$	−572.394	−	262.414i	−0.616804	−	0.282774i
$929$	571.504			0.615181			0.307591	−	0.951519i	$-0.400477\pi$
$929$	571.504			0.615181			0.307591	+	0.951519i	$0.400477\pi$
$930$	−252.824	+	152.358i	−0.271854	+	0.163826i
$931$		0			0
$932$	−88.9952	+	168.426i	−0.0954884	+	0.180715i
$933$	−233.967			−0.250769
$934$	679.493	+	1127.56i	0.727508	+	1.20723i
$935$			231.084i			0.247148i
$936$	−31.4967	−	559.414i	−0.0336503	−	0.597664i
$937$	−1535.39			−1.63863			−0.819314	−	0.573345i	$-0.805645\pi$
$937$	−1535.39			−1.63863			−0.819314	+	0.573345i	$0.805645\pi$
$938$		0			0
$939$			499.455i			0.531901i
$940$	38.2482	+	20.2101i	0.0406896	+	0.0215001i
$941$	1015.93			1.07963			0.539815	−	0.841783i	$-0.318494\pi$
$941$	1015.93			1.07963			0.539815	+	0.841783i	$0.318494\pi$
$942$	−215.539	−	357.667i	−0.228809	−	0.379689i
$943$			858.422i			0.910310i
$944$	−1497.18	+	1021.18i	−1.58600	+	1.08176i
$945$		0			0
$946$	−195.863	+	118.032i	−0.207044	+	0.124770i
$947$		−	854.866i		−	0.902710i	−0.892345	−	0.451355i	$-0.850941\pi$
$947$		−	854.866i		−	0.902710i	0.892345	−	0.451355i	$-0.149059\pi$
$948$	−505.256	+	956.213i	−0.532971	+	1.00866i
$949$	−1619.29			−1.70631
$950$	258.139	+	428.358i	0.271725	+	0.450903i
$951$		−	276.394i		−	0.290635i
$952$		0			0
$953$	451.850			0.474134			0.237067	−	0.971493i	$-0.423814\pi$
$953$	451.850			0.474134			0.237067	+	0.971493i	$0.423814\pi$
$954$	353.864	−	213.247i	0.370927	−	0.223530i
$955$			92.8961i			0.0972734i
$956$	−1412.78	−	746.502i	−1.47780	−	0.780859i
$957$	256.042			0.267546
$958$	50.5575	+	83.8955i	0.0527740	+	0.0875736i
$959$		0			0
$960$	−37.1225	−	328.622i	−0.0386692	−	0.342314i
$961$	145.202			0.151095
$962$	−2136.22	+	1287.34i	−2.22061	+	1.33819i
$963$			93.9103i			0.0975185i
$964$	−80.1005	+	151.593i	−0.0830918	+	0.157254i
$965$	203.496			0.210877
$966$		0			0
$967$		−	309.800i		−	0.320372i	−0.987087	−	0.160186i	$-0.948791\pi$
$967$		−	309.800i		−	0.320372i	0.987087	−	0.160186i	$-0.0512095\pi$
$968$	−29.0349	−	515.690i	−0.0299947	−	0.532737i
$969$	277.383			0.286257
$970$	−566.368	+	341.307i	−0.583885	+	0.351863i
$971$		−	613.433i		−	0.631754i	−0.948800	−	0.315877i	$-0.897701\pi$
$971$		−	613.433i		−	0.631754i	0.948800	−	0.315877i	$-0.102299\pi$
$972$	−55.1308	−	29.1307i	−0.0567189	−	0.0299699i
$973$		0			0
$974$	69.7852	+	115.802i	0.0716481	+	0.118894i
$975$		−	650.998i		−	0.667691i
$976$	29.8190	+	43.7185i	0.0305523	+	0.0447935i
$977$	−1430.43			−1.46411			−0.732054	−	0.681246i	$-0.761438\pi$
$977$	−1430.43			−1.46411			−0.732054	+	0.681246i	$0.761438\pi$
$978$	577.747	−	348.164i	0.590743	−	0.355996i
$979$			129.374i			0.132149i
$980$		0			0
$981$	−81.2101			−0.0827830
$982$	327.954	+	544.211i	0.333966	+	0.554186i
$983$		−	686.757i		−	0.698633i	−0.937005	−	0.349317i	$-0.886414\pi$
$983$		−	686.757i		−	0.698633i	0.937005	−	0.349317i	$-0.113586\pi$
$984$	430.576	−	24.2427i	0.437578	−	0.0246369i
$985$	−338.211			−0.343361
$986$	−347.541	+	209.437i	−0.352476	+	0.212410i
$987$		0			0
$988$	1282.45	+	677.636i	1.29802	+	0.685867i
$989$	419.787			0.424456
$990$	69.4089	+	115.178i	0.0701100	+	0.116341i
$991$			801.163i			0.808439i	0.914662	+	0.404219i	$0.132457\pi$
$991$			801.163i			0.808439i	−0.914662	+	0.404219i	$0.867543\pi$
$992$	380.899	−	830.839i	0.383970	−	0.837539i
$993$	482.080			0.485479
$994$		0			0
$995$			461.133i			0.463451i
$996$	275.510	−	521.411i	0.276616	−	0.523505i
$997$	−523.638			−0.525214			−0.262607	−	0.964903i	$-0.584582\pi$
$997$	−523.638			−0.525214			−0.262607	+	0.964903i	$0.584582\pi$
$998$	369.789	+	613.631i	0.370530	+	0.614861i
$999$			277.563i			0.277841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.g.h.295.17	✓	24
4.3	odd	2	inner	588.3.g.h.295.20	yes	24
7.6	odd	2	inner	588.3.g.h.295.18	yes	24
28.27	even	2	inner	588.3.g.h.295.19	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.3.g.h.295.17	✓	24	1.1	even	1	trivial
588.3.g.h.295.18	yes	24	7.6	odd	2	inner
588.3.g.h.295.19	yes	24	28.27	even	2	inner
588.3.g.h.295.20	yes	24	4.3	odd	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71300 - 1.03229i) q^{2} -1.73205i q^{3} +(1.86874 - 3.53664i) q^{4} -2.98338 q^{5} +(-1.78799 - 2.96700i) q^{6} +(-0.449712 - 7.98735i) q^{8} -3.00000 q^{9} +(-5.11054 + 3.07973i) q^{10} +7.51244i q^{11} +(-6.12564 - 3.23675i) q^{12} -23.3458 q^{13} +5.16737i q^{15} +(-9.01565 - 13.2181i) q^{16} -10.3105 q^{17} +(-5.13900 + 3.09688i) q^{18} -15.5324i q^{19} +(-5.57516 + 10.5512i) q^{20} +(7.75505 + 12.8688i) q^{22} -27.5813i q^{23} +(-13.8345 + 0.778924i) q^{24} -16.0994 q^{25} +(-39.9914 + 24.0998i) q^{26} +5.19615i q^{27} +19.6775 q^{29} +(5.33425 + 8.85171i) q^{30} +28.5622i q^{31} +(-29.0888 - 13.3358i) q^{32} +13.0119 q^{33} +(-17.6619 + 10.6435i) q^{34} +(-5.60621 + 10.6099i) q^{36} +53.4171 q^{37} +(-16.0341 - 26.6071i) q^{38} +40.4361i q^{39} +(1.34166 + 23.8293i) q^{40} -31.1234 q^{41} +15.2200i q^{43} +(26.5688 + 14.0388i) q^{44} +8.95015 q^{45} +(-28.4720 - 47.2467i) q^{46} -3.62503i q^{47} +(-22.8944 + 15.6156i) q^{48} +(-27.5783 + 16.6193i) q^{50} +17.8583i q^{51} +(-43.6272 + 82.5658i) q^{52} -68.8586 q^{53} +(5.36396 + 8.90101i) q^{54} -22.4125i q^{55} -26.9030 q^{57} +(33.7075 - 20.3130i) q^{58} -113.268i q^{59} +(18.2751 + 9.65645i) q^{60} -3.30747 q^{61} +(29.4846 + 48.9270i) q^{62} +(-63.5955 + 7.18401i) q^{64} +69.6496 q^{65} +(22.2894 - 13.4321i) q^{66} +92.9042i q^{67} +(-19.2676 + 36.4645i) q^{68} -47.7721 q^{69} -72.5872i q^{71} +(1.34914 + 23.9620i) q^{72} +69.3610 q^{73} +(91.5034 - 55.1422i) q^{74} +27.8850i q^{75} +(-54.9327 - 29.0260i) q^{76} +(41.7420 + 69.2671i) q^{78} -156.100i q^{79} +(26.8972 + 39.4346i) q^{80} +9.00000 q^{81} +(-53.3143 + 32.1285i) q^{82} +85.1194i q^{83} +30.7602 q^{85} +(15.7115 + 26.0719i) q^{86} -34.0824i q^{87} +(60.0045 - 3.37843i) q^{88} +17.2213 q^{89} +(15.3316 - 9.23919i) q^{90} +(-97.5450 - 51.5421i) q^{92} +49.4711 q^{93} +(-3.74210 - 6.20967i) q^{94} +46.3392i q^{95} +(-23.0982 + 50.3832i) q^{96} +110.824 q^{97} -22.5373i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 12 q^{4} - 20 q^{8} - 72 q^{9} - 60 q^{16} - 12 q^{18} + 168 q^{22} + 120 q^{25} + 64 q^{29} - 236 q^{32} - 36 q^{36} - 192 q^{37} - 360 q^{44} - 72 q^{46} + 532 q^{50} + 432 q^{53} + 240 q^{58}+ \cdots - 96 q^{93}+O(q^{100}) \) 24 * q + 4 * q^2 + 12 * q^4 - 20 * q^8 - 72 * q^9 - 60 * q^16 - 12 * q^18 + 168 * q^22 + 120 * q^25 + 64 * q^29 - 236 * q^32 - 36 * q^36 - 192 * q^37 - 360 * q^44 - 72 * q^46 + 532 * q^50 + 432 * q^53 + 240 * q^58 + 72 * q^60 - 372 * q^64 - 560 * q^65 + 60 * q^72 + 96 * q^74 + 216 * q^78 + 216 * q^81 + 144 * q^85 + 816 * q^86 - 72 * q^88 - 504 * q^92 - 96 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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