LMFDB - Embedded newform 588.3.g.h.295.19

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)

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")

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);

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			295.19
Character	$\chi$	$=$	588.295
Dual form			588.3.g.h.295.18

$q$-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	$-0.403568\pi$
$5$	2.98338			0.596677			0.298338	+	0.954460i	$0.403568\pi$
$6$	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	$-0.889074\pi$
$11$		−	7.51244i		−	0.682949i	0.939891	−	0.341474i	$-0.110926\pi$
$12$	6.12564	−	3.23675i	0.510470	−	0.269729i
$13$	23.3458			1.79583			0.897916	−	0.440166i	$-0.145081\pi$
$13$	23.3458			1.79583			0.897916	+	0.440166i	$0.145081\pi$
$14$		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	$-0.401928\pi$
$17$	10.3105			0.606499			0.303250	+	0.952911i	$0.401928\pi$
$18$	−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	$0.204671\pi$
$23$			27.5813i			1.19919i	−0.800305	+	0.599593i	$0.795329\pi$
$24$	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	$-0.376078\pi$
$41$	31.1234			0.759107			0.379553	+	0.925170i	$0.376078\pi$
$42$		0			0
$43$		−	15.2200i		−	0.353954i	−0.984215	−	0.176977i	$-0.943368\pi$
$43$		−	15.2200i		−	0.353954i	0.984215	−	0.176977i	$-0.0566318\pi$
$44$	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	$-0.491369\pi$
$61$	3.30747			0.0542209			0.0271104	+	0.999632i	$0.491369\pi$
$62$	−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	$-0.756149\pi$
$67$		−	92.9042i		−	1.38663i	0.720634	−	0.693315i	$-0.243851\pi$
$68$	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	$0.170791\pi$
$71$			72.5872i			1.02236i	−0.859475	+	0.511178i	$0.829209\pi$
$72$	1.34914	−	23.9620i	0.0187380	−	0.332806i
$73$	−69.3610			−0.950151			−0.475075	−	0.879945i	$-0.657579\pi$
$73$	−69.3610			−0.950151			−0.475075	+	0.879945i	$0.657579\pi$
$74$	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	$0.450588\pi$
$79$			156.100i			1.97595i	−0.154610	+	0.987976i	$0.549412\pi$
$80$	−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	$-0.530844\pi$
$89$	−17.2213			−0.193498			−0.0967492	+	0.995309i	$0.530844\pi$
$90$	−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	$-0.693544\pi$
$97$	−110.824			−1.14251			−0.571256	+	0.820772i	$0.693544\pi$
$98$		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	$-0.508790\pi$
$101$	−5.57758			−0.0552236			−0.0276118	+	0.999619i	$0.508790\pi$
$102$	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	$0.0467293\pi$
$107$			31.3034i			0.292555i	−0.989244	+	0.146278i	$0.953271\pi$
$108$	−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	$0.0751491\pi$
$127$			59.4108i			0.467802i	−0.972260	+	0.233901i	$0.924851\pi$
$128$	−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	$-0.877368\pi$
$151$		−	113.491i		−	0.751597i	0.926701	−	0.375798i	$-0.122632\pi$
$152$	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	$-0.625423\pi$
$157$	−120.548			−0.767823			−0.383911	+	0.923370i	$0.625423\pi$
$158$	−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	$-0.796235\pi$
$163$		−	194.724i		−	1.19463i	0.802008	−	0.597313i	$-0.203765\pi$
$164$	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	$-0.846448\pi$
$173$	−306.516			−1.77177			−0.885885	+	0.463906i	$0.846448\pi$
$174$	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	$0.210326\pi$
$179$			219.711i			1.22743i	−0.789526	+	0.613717i	$0.789674\pi$
$180$	−16.7255	−	31.6535i	−0.0929193	−	0.175853i
$181$	10.3397			0.0571255			0.0285627	−	0.999592i	$-0.490907\pi$
$181$	10.3397			0.0571255			0.0285627	+	0.999592i	$0.490907\pi$
$182$		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	$0.0259751\pi$
$191$			31.1378i			0.163025i	−0.996672	+	0.0815126i	$0.974025\pi$
$192$	−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	$-0.739314\pi$
$211$		−	308.247i		−	1.46089i	0.682974	−	0.730443i	$-0.260686\pi$
$212$	−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	$-0.290185\pi$
$229$	280.501			1.22489			0.612447	+	0.790512i	$0.290185\pi$
$230$	−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	$0.314943\pi$
$239$			399.469i			1.67142i	−0.549173	+	0.835709i	$0.685057\pi$
$240$	68.3028	+	46.5872i	0.284595	+	0.194114i
$241$	42.8635			0.177857			0.0889284	−	0.996038i	$-0.471656\pi$
$241$	42.8635			0.177857			0.0889284	+	0.996038i	$0.471656\pi$
$242$	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	$-0.447442\pi$
$257$	84.4840			0.328732			0.164366	+	0.986399i	$0.447442\pi$
$258$	−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	$0.00288132\pi$
$263$			4.76125i			0.0181036i	−0.999959	+	0.00905180i	$0.997119\pi$
$264$	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	$-0.565821\pi$
$269$	−110.458			−0.410626			−0.205313	+	0.978696i	$0.565821\pi$
$270$	−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	$-0.416848\pi$
$293$	151.346			0.516538			0.258269	+	0.966073i	$0.416848\pi$
$294$		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	$-0.347620\pi$
$313$	288.360			0.921279			0.460640	+	0.887587i	$0.347620\pi$
$314$	−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	$-0.861877\pi$
$331$		−	278.329i		−	0.840874i	0.907322	−	0.420437i	$-0.138123\pi$
$332$	−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	$0.333602\pi$
$347$			601.315i			1.73290i	−0.499268	+	0.866448i	$0.666398\pi$
$348$	120.537	−	63.6910i	0.346371	−	0.183020i
$349$	−146.665			−0.420244			−0.210122	−	0.977675i	$-0.567386\pi$
$349$	−146.665			−0.420244			−0.210122	+	0.977675i	$0.567386\pi$
$350$		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	$-0.477566\pi$
$353$	49.7171			0.140842			0.0704208	+	0.997517i	$0.477566\pi$
$354$	−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	$0.0773249\pi$
$359$			172.708i			0.481082i	−0.970639	+	0.240541i	$0.922675\pi$
$360$	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	$-0.902412\pi$
$379$		−	228.766i		−	0.603605i	0.953370	−	0.301803i	$-0.0975884\pi$
$380$	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	$-0.337135\pi$
$397$	388.759			0.979242			0.489621	+	0.871935i	$0.337135\pi$
$398$	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	$-0.416422\pi$
$409$	212.321			0.519123			0.259561	+	0.965727i	$0.416422\pi$
$410$	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	$-0.892158\pi$
$431$		−	286.486i		−	0.664701i	0.943156	−	0.332351i	$-0.107842\pi$
$432$	−68.6832	−	46.8467i	−0.158989	−	0.108441i
$433$	158.782			0.366702			0.183351	−	0.983047i	$-0.441305\pi$
$433$	158.782			0.366702			0.183351	+	0.983047i	$0.441305\pi$
$434$		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	$-0.732320\pi$
$443$		−	660.309i		−	1.49054i	0.666763	−	0.745270i	$-0.267680\pi$
$444$	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	$-0.403704\pi$
$461$	274.690			0.595856			0.297928	+	0.954588i	$0.403704\pi$
$462$		0			0
$463$			28.3801i			0.0612961i	0.999530	+	0.0306481i	$0.00975711\pi$
$463$			28.3801i			0.0612961i	−0.999530	+	0.0306481i	$0.990243\pi$
$464$	−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	$-0.977889\pi$
$487$		−	67.6020i		−	0.138813i	0.997588	−	0.0694066i	$-0.0221106\pi$
$488$	−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	$-0.895134\pi$
$491$		−	317.695i		−	0.647036i	0.946222	−	0.323518i	$-0.104866\pi$
$492$	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	$-0.883139\pi$
$499$		−	358.220i		−	0.717876i	0.933361	−	0.358938i	$-0.116861\pi$
$500$	−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	$-0.492871\pi$
$509$	22.7983			0.0447904			0.0223952	+	0.999749i	$0.492871\pi$
$510$	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	$-0.422540\pi$
$521$	251.073			0.481906			0.240953	+	0.970537i	$0.422540\pi$
$522$	−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	$0.0603980\pi$
$547$			206.339i			0.377219i	−0.982052	+	0.188610i	$0.939602\pi$
$548$	−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	$0.278653\pi$
$571$			876.837i			1.53562i	−0.640680	+	0.767808i	$0.721347\pi$
$572$	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	$-0.434300\pi$
$577$	236.500			0.409879			0.204940	+	0.978775i	$0.434300\pi$
$578$	−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	$-0.790632\pi$
$593$	−938.566			−1.58274			−0.791371	+	0.611337i	$0.790632\pi$
$594$	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	$0.00571764\pi$
$599$			21.5179i			0.0359230i	−0.999839	+	0.0179615i	$0.994282\pi$
$600$	−222.727	−	12.5402i	−0.371212	−	0.0209004i
$601$	−796.035			−1.32452			−0.662258	−	0.749275i	$-0.730402\pi$
$601$	−796.035			−1.32452			−0.662258	+	0.749275i	$0.730402\pi$
$602$		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	$0.258229\pi$
$631$			915.136i			1.45030i	−0.688593	+	0.725148i	$0.741771\pi$
$632$	−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	$0.0377456\pi$
$659$			155.924i			0.236607i	−0.992977	+	0.118304i	$0.962254\pi$
$660$	−72.5435	−	137.291i	−0.109914	−	0.208016i
$661$	−789.862			−1.19495			−0.597475	−	0.801888i	$-0.703829\pi$
$661$	−789.862			−1.19495			−0.597475	+	0.801888i	$0.703829\pi$
$662$	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	$-0.342919\pi$
$677$	641.385			0.947393			0.473696	+	0.880688i	$0.342919\pi$
$678$	−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	$-0.924289\pi$
$683$		−	321.852i		−	0.471232i	0.971846	−	0.235616i	$-0.0757108\pi$
$684$	−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	$-0.785263\pi$
$733$	−1144.87			−1.56189			−0.780946	+	0.624599i	$0.785263\pi$
$734$	−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	$0.0689460\pi$
$739$			317.638i			0.429821i	−0.976634	+	0.214911i	$0.931054\pi$
$740$	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	$0.277868\pi$
$743$			1138.61i			1.53245i	−0.642570	+	0.766227i	$0.722132\pi$
$744$	−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	$0.0277885\pi$
$751$			130.959i			0.174379i	−0.996192	+	0.0871894i	$0.972211\pi$
$752$	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	$-0.741871\pi$
$761$	−1048.39			−1.37764			−0.688821	+	0.724931i	$0.741871\pi$
$762$	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	$-0.297908\pi$
$769$	912.173			1.18618			0.593091	+	0.805136i	$0.297908\pi$
$770$		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	$-0.758241\pi$
$773$	−1121.12			−1.45035			−0.725174	+	0.688566i	$0.758241\pi$
$774$	−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	$-0.646159\pi$
$797$	−706.469			−0.886410			−0.443205	+	0.896420i	$0.646159\pi$
$798$		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	$-0.795048\pi$
$823$		−	988.093i		−	1.20060i	0.799775	−	0.600299i	$-0.204952\pi$
$824$	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	$0.0296773\pi$
$827$			153.986i			0.186198i	−0.995657	+	0.0930991i	$0.970323\pi$
$828$	292.635	−	154.626i	0.353424	−	0.186747i
$829$	1239.01			1.49458			0.747292	−	0.664495i	$-0.231353\pi$
$829$	1239.01			1.49458			0.747292	+	0.664495i	$0.231353\pi$
$830$	−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	$-0.504223\pi$
$853$	−22.6308			−0.0265308			−0.0132654	+	0.999912i	$0.504223\pi$
$854$		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	$-0.126271\pi$
$857$	1580.90			1.84469			0.922344	+	0.386370i	$0.126271\pi$
$858$	−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	$0.118759\pi$
$863$			629.122i			0.728994i	−0.931205	+	0.364497i	$0.881241\pi$
$864$	−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	$-0.558222\pi$
$881$	−320.493			−0.363784			−0.181892	+	0.983319i	$0.558222\pi$
$882$		0			0
$883$			1221.53i			1.38339i	0.722189	+	0.691696i	$0.243136\pi$
$883$			1221.53i			1.38339i	−0.722189	+	0.691696i	$0.756864\pi$
$884$	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	$-0.877138\pi$
$907$		−	682.918i		−	0.752941i	0.926429	−	0.376471i	$-0.122862\pi$
$908$	−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	$-0.869089\pi$
$911$		−	728.384i		−	0.799543i	0.916615	−	0.399772i	$-0.130911\pi$
$912$	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	$-0.989331\pi$
$919$		−	61.5914i		−	0.0670200i	0.999438	−	0.0335100i	$-0.0106686\pi$
$920$	−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	$-0.599523\pi$
$929$	−571.504			−0.615181			−0.307591	+	0.951519i	$0.599523\pi$
$930$	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	$-0.194355\pi$
$937$	1535.39			1.63863			0.819314	+	0.573345i	$0.194355\pi$
$938$		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	$-0.681506\pi$
$941$	−1015.93			−1.07963			−0.539815	+	0.841783i	$0.681506\pi$
$942$	−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	$0.149059\pi$
$947$			854.866i			0.902710i	−0.892345	+	0.451355i	$0.850941\pi$
$948$	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	$0.0512095\pi$
$967$			309.800i			0.320372i	−0.987087	+	0.160186i	$0.948791\pi$
$968$	−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	$-0.867543\pi$
$991$		−	801.163i		−	0.808439i	0.914662	−	0.404219i	$-0.132457\pi$
$992$	−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	$-0.415418\pi$
$997$	523.638			0.525214			0.262607	+	0.964903i	$0.415418\pi$
$998$	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.295.19	yes	24
4.3	odd	2	inner	588.3.g.h.295.18	yes	24
7.6	odd	2	inner	588.3.g.h.295.20	yes	24
28.27	even	2	inner	588.3.g.h.295.17	✓	24

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