LMFDB - Embedded newform 175.2.x.a.3.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] 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("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	175.3
Dual form			175.2.x.a.117.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.863911 + 1.33031i) q^{2} +(-0.702377 + 1.82975i) q^{3} +(-0.209899 - 0.471441i) q^{4} +(-2.03789 - 0.920336i) q^{5} +(-1.82734 - 2.51512i) q^{6} +(-2.08368 - 1.63042i) q^{7} +(-2.32486 - 0.368222i) q^{8} +(-0.625235 - 0.562964i) q^{9} +(2.98488 - 1.91592i) q^{10} +(1.39398 + 1.54818i) q^{11} +(1.01005 - 0.0529345i) q^{12} +(1.94768 + 0.992394i) q^{13} +(3.96908 - 1.36339i) q^{14} +(3.11535 - 3.08241i) q^{15} +(3.18894 - 3.54168i) q^{16} +(-3.18817 + 3.93706i) q^{17} +(1.28906 - 0.345403i) q^{18} +(-6.86927 - 3.05840i) q^{19} +(-0.00613384 + 1.15392i) q^{20} +(4.44680 - 2.66745i) q^{21} +(-3.26382 + 0.516939i) q^{22} +(-1.68435 - 1.09383i) q^{23} +(2.30669 - 3.99530i) q^{24} +(3.30596 + 3.75108i) q^{25} +(-3.00281 + 1.73368i) q^{26} +(-3.76970 + 1.92076i) q^{27} +(-0.331286 + 1.32456i) q^{28} +(-4.12547 + 5.67823i) q^{29} +(1.40916 + 6.80730i) q^{30} +(6.31745 - 0.663990i) q^{31} +(0.738117 + 2.75469i) q^{32} +(-3.81188 + 1.46324i) q^{33} +(-2.48320 - 7.64252i) q^{34} +(2.74576 + 5.24030i) q^{35} +(-0.134168 + 0.412927i) q^{36} +(0.138578 + 2.64422i) q^{37} +(10.0030 - 6.49605i) q^{38} +(-3.18385 + 2.86675i) q^{39} +(4.39892 + 2.89005i) q^{40} +(-8.47974 + 2.75523i) q^{41} +(-0.293115 + 8.22005i) q^{42} +(0.986332 + 0.986332i) q^{43} +(0.437278 - 0.982142i) q^{44} +(0.756041 + 1.72268i) q^{45} +(2.91025 - 1.29573i) q^{46} +(2.04177 - 1.65339i) q^{47} +(4.24056 + 8.32258i) q^{48} +(1.68344 + 6.79456i) q^{49} +(-7.84614 + 1.15734i) q^{50} +(-4.96456 - 8.59887i) q^{51} +(0.0590385 - 1.12652i) q^{52} +(8.62323 + 3.31015i) q^{53} +(0.701489 - 6.67422i) q^{54} +(-1.41594 - 4.43794i) q^{55} +(4.24391 + 4.55777i) q^{56} +(10.4209 - 10.4209i) q^{57} +(-3.98974 - 10.3936i) q^{58} +(-10.2924 - 2.18773i) q^{59} +(-2.10709 - 0.821712i) q^{60} +(1.78346 + 8.39053i) q^{61} +(-4.57440 + 8.97777i) q^{62} +(0.384920 + 2.19243i) q^{63} +(4.76284 + 1.54754i) q^{64} +(-3.05582 - 3.81491i) q^{65} +(1.34656 - 6.33508i) q^{66} +(-2.55191 - 2.06649i) q^{67} +(2.52529 + 0.676649i) q^{68} +(3.18448 - 2.31366i) q^{69} +(-9.34330 - 0.874447i) q^{70} +(5.41526 + 3.93442i) q^{71} +(1.24629 + 1.53904i) q^{72} +(8.26979 + 0.433401i) q^{73} +(-3.63734 - 2.10002i) q^{74} +(-9.18559 + 3.41443i) q^{75} +3.88041i q^{76} +(-0.380434 - 5.49868i) q^{77} +(-1.06309 - 6.71211i) q^{78} +(-2.65691 - 0.279252i) q^{79} +(-9.75824 + 4.28264i) q^{80} +(-1.13060 - 10.7569i) q^{81} +(3.66043 - 13.6609i) q^{82} +(-0.456772 + 2.88395i) q^{83} +(-2.19093 - 1.53651i) q^{84} +(10.1206 - 5.08910i) q^{85} +(-2.16423 + 0.460021i) q^{86} +(-7.49212 - 11.5369i) q^{87} +(-2.67075 - 4.11259i) q^{88} +(12.3861 - 2.63274i) q^{89} +(-2.94485 - 0.482478i) q^{90} +(-2.44033 - 5.24338i) q^{91} +(-0.162132 + 1.02366i) q^{92} +(-3.22229 + 12.0258i) q^{93} +(0.435611 + 4.14456i) q^{94} +(11.1840 + 12.5547i) q^{95} +(-5.55884 - 0.584258i) q^{96} +(-0.527619 - 3.33125i) q^{97} +(-10.4932 - 3.63040i) q^{98} -1.75274i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	−0.863911	+	1.33031i	−0.610877	+	0.940669i	0.388934	+	0.921265i	$0.372843\pi$
$2$	−0.863911	+	1.33031i	−0.610877	+	0.940669i	−0.999812	+	0.0194031i	$0.993823\pi$
$3$	−0.702377	+	1.82975i	−0.405518	+	1.05641i	0.567028	+	0.823698i	$0.308093\pi$
$3$	−0.702377	+	1.82975i	−0.405518	+	1.05641i	−0.972546	+	0.232711i	$0.925240\pi$
$4$	−0.209899	−	0.471441i	−0.104950	−	0.235721i
$5$	−2.03789	−	0.920336i	−0.911371	−	0.411587i
$5$	−2.03789	−	0.920336i	−0.911371	−	0.411587i
$6$	−1.82734	−	2.51512i	−0.746010	−	1.02679i
$7$	−2.08368	−	1.63042i	−0.787557	−	0.616242i
$7$	−2.08368	−	1.63042i	−0.787557	−	0.616242i
$8$	−2.32486	−	0.368222i	−0.821963	−	0.130186i
$9$	−0.625235	−	0.562964i	−0.208412	−	0.187655i
$10$	2.98488	−	1.91592i	0.943902	−	0.605868i
$11$	1.39398	+	1.54818i	0.420302	+	0.466792i	0.915694	−	0.401877i	$-0.131642\pi$
$11$	1.39398	+	1.54818i	0.420302	+	0.466792i	−0.495392	+	0.868670i	$0.664975\pi$
$12$	1.01005	−	0.0529345i	0.291576	−	0.0152809i
$13$	1.94768	+	0.992394i	0.540190	+	0.275241i	0.702724	−	0.711462i	$-0.251967\pi$
$13$	1.94768	+	0.992394i	0.540190	+	0.275241i	−0.162534	+	0.986703i	$0.551967\pi$
$14$	3.96908	−	1.36339i	1.06078	−	0.364382i
$15$	3.11535	−	3.08241i	0.804381	−	0.795875i
$16$	3.18894	−	3.54168i	0.797235	−	0.885420i
$17$	−3.18817	+	3.93706i	−0.773245	+	0.954878i	−0.999817	−	0.0191163i	$-0.993915\pi$
$17$	−3.18817	+	3.93706i	−0.773245	+	0.954878i	0.226572	+	0.973994i	$0.427248\pi$
$18$	1.28906	−	0.345403i	0.303835	−	0.0814123i
$19$	−6.86927	−	3.05840i	−1.57592	−	0.701644i	−0.582148	−	0.813083i	$-0.697788\pi$
$19$	−6.86927	−	3.05840i	−1.57592	−	0.701644i	−0.993771	+	0.111438i	$0.964454\pi$
$20$	−0.00613384	+	1.15392i	−0.00137157	+	0.258025i
$21$	4.44680	−	2.66745i	0.970372	−	0.582086i
$22$	−3.26382	+	0.516939i	−0.695850	+	0.110212i
$23$	−1.68435	−	1.09383i	−0.351210	−	0.228079i	0.356961	−	0.934119i	$-0.383813\pi$
$23$	−1.68435	−	1.09383i	−0.351210	−	0.228079i	−0.708171	+	0.706041i	$0.750480\pi$
$24$	2.30669	−	3.99530i	0.470851	−	0.815537i
$25$	3.30596	+	3.75108i	0.661192	+	0.750216i
$26$	−3.00281	+	1.73368i	−0.588900	+	0.340002i
$27$	−3.76970	+	1.92076i	−0.725479	+	0.369650i
$28$	−0.331286	+	1.32456i	−0.0626072	+	0.250318i
$29$	−4.12547	+	5.67823i	−0.766081	+	1.05442i	0.230603	+	0.973048i	$0.425930\pi$
$29$	−4.12547	+	5.67823i	−0.766081	+	1.05442i	−0.996684	+	0.0813721i	$0.974070\pi$
$30$	1.40916	+	6.80730i	0.257276	+	1.24284i
$31$	6.31745	−	0.663990i	1.13465	−	0.119256i	0.481471	−	0.876462i	$-0.340103\pi$
$31$	6.31745	−	0.663990i	1.13465	−	0.119256i	0.653176	+	0.757206i	$0.273436\pi$
$32$	0.738117	+	2.75469i	0.130482	+	0.486965i
$33$	−3.81188	+	1.46324i	−0.663564	+	0.254718i
$34$	−2.48320	−	7.64252i	−0.425866	−	1.31068i
$35$	2.74576	+	5.24030i	0.464119	+	0.885773i
$36$	−0.134168	+	0.412927i	−0.0223614	+	0.0688212i
$37$	0.138578	+	2.64422i	0.0227820	+	0.434707i	0.986080	+	0.166272i	$0.0531730\pi$
$37$	0.138578	+	2.64422i	0.0227820	+	0.434707i	−0.963298	+	0.268435i	$0.913494\pi$
$38$	10.0030	−	6.49605i	1.62271	−	1.05380i
$39$	−3.18385	+	2.86675i	−0.509823	+	0.459047i
$40$	4.39892	+	2.89005i	0.695530	+	0.456957i
$41$	−8.47974	+	2.75523i	−1.32431	+	0.430295i	−0.883974	−	0.467536i	$-0.845142\pi$
$41$	−8.47974	+	2.75523i	−1.32431	+	0.430295i	−0.440339	+	0.897832i	$0.645142\pi$
$42$	−0.293115	+	8.22005i	−0.0452287	+	1.26838i
$43$	0.986332	+	0.986332i	0.150414	+	0.150414i	0.778303	−	0.627889i	$-0.216081\pi$
$43$	0.986332	+	0.986332i	0.150414	+	0.150414i	−0.627889	+	0.778303i	$0.716081\pi$
$44$	0.437278	−	0.982142i	0.0659221	−	0.148063i
$45$	0.756041	+	1.72268i	0.112704	+	0.256802i
$46$	2.91025	−	1.29573i	0.429093	−	0.191044i
$47$	2.04177	−	1.65339i	0.297822	−	0.241172i	−0.468748	−	0.883332i	$-0.655295\pi$
$47$	2.04177	−	1.65339i	0.297822	−	0.241172i	0.766571	+	0.642160i	$0.221962\pi$
$48$	4.24056	+	8.32258i	0.612073	+	1.20126i
$49$	1.68344	+	6.79456i	0.240492	+	0.970651i
$50$	−7.84614	+	1.15734i	−1.10961	+	0.163673i
$51$	−4.96456	−	8.59887i	−0.695178	−	1.20408i
$52$	0.0590385	−	1.12652i	0.00818716	−	0.156220i
$53$	8.62323	+	3.31015i	1.18449	+	0.454684i	0.869271	−	0.494335i	$-0.164588\pi$
$53$	8.62323	+	3.31015i	1.18449	+	0.454684i	0.315220	+	0.949019i	$0.397922\pi$
$54$	0.701489	−	6.67422i	0.0954606	−	0.908247i
$55$	−1.41594	−	4.43794i	−0.190925	−	0.598412i
$56$	4.24391	+	4.55777i	0.567117	+	0.609057i
$57$	10.4209	−	10.4209i	1.38029	−	1.38029i
$58$	−3.98974	−	10.3936i	−0.523878	−	1.36475i
$59$	−10.2924	−	2.18773i	−1.33996	−	0.284818i	−0.518498	−	0.855079i	$-0.673509\pi$
$59$	−10.2924	−	2.18773i	−1.33996	−	0.284818i	−0.821464	+	0.570261i	$0.806842\pi$
$60$	−2.10709	−	0.821712i	−0.272024	−	0.106083i
$61$	1.78346	+	8.39053i	0.228349	+	1.07430i	0.931637	+	0.363391i	$0.118381\pi$
$61$	1.78346	+	8.39053i	0.228349	+	1.07430i	−0.703288	+	0.710905i	$0.748285\pi$
$62$	−4.57440	+	8.97777i	−0.580949	+	1.14018i
$63$	0.384920	+	2.19243i	0.0484953	+	0.276221i
$64$	4.76284	+	1.54754i	0.595355	+	0.193443i
$65$	−3.05582	−	3.81491i	−0.379028	−	0.473181i
$66$	1.34656	−	6.33508i	0.165751	−	0.779795i
$67$	−2.55191	−	2.06649i	−0.311765	−	0.252462i	0.460648	−	0.887583i	$-0.347617\pi$
$67$	−2.55191	−	2.06649i	−0.311765	−	0.252462i	−0.772413	+	0.635121i	$0.780950\pi$
$68$	2.52529	+	0.676649i	0.306236	+	0.0820558i
$69$	3.18448	−	2.31366i	0.383366	−	0.278532i
$70$	−9.34330	−	0.874447i	−1.11674	−	0.104516i
$71$	5.41526	+	3.93442i	0.642673	+	0.466930i	0.860768	−	0.508998i	$-0.169984\pi$
$71$	5.41526	+	3.93442i	0.642673	+	0.466930i	−0.218094	+	0.975928i	$0.569984\pi$
$72$	1.24629	+	1.53904i	0.146877	+	0.181378i
$73$	8.26979	+	0.433401i	0.967906	+	0.0507258i	0.529733	−	0.848165i	$-0.322292\pi$
$73$	8.26979	+	0.433401i	0.967906	+	0.0507258i	0.438173	+	0.898891i	$0.355626\pi$
$74$	−3.63734	−	2.10002i	−0.422832	−	0.244122i
$75$	−9.18559	+	3.41443i	−1.06066	+	0.394264i
$76$			3.88041i			0.445114i
$77$	−0.380434	−	5.49868i	−0.0433545	−	0.626633i
$78$	−1.06309	−	6.71211i	−0.120372	−	0.759996i
$79$	−2.65691	−	0.279252i	−0.298926	−	0.0314184i	−0.0461216	−	0.998936i	$-0.514686\pi$
$79$	−2.65691	−	0.279252i	−0.298926	−	0.0314184i	−0.252804	+	0.967517i	$0.581353\pi$
$80$	−9.75824	+	4.28264i	−1.09100	+	0.478814i
$81$	−1.13060	−	10.7569i	−0.125622	−	1.19521i
$82$	3.66043	−	13.6609i	0.404227	−	1.50860i
$83$	−0.456772	+	2.88395i	−0.0501373	+	0.316554i	0.949855	+	0.312690i	$0.101230\pi$
$83$	−0.456772	+	2.88395i	−0.0501373	+	0.316554i	−0.999993	+	0.00386431i	$0.998770\pi$
$84$	−2.19093	−	1.53651i	−0.239050	−	0.167647i
$85$	10.1206	−	5.08910i	1.09773	−	0.551990i
$86$	−2.16423	+	0.460021i	−0.233375	+	0.0496053i
$87$	−7.49212	−	11.5369i	−0.803240	−	1.23688i
$88$	−2.67075	−	4.11259i	−0.284703	−	0.438404i
$89$	12.3861	−	2.63274i	1.31292	−	0.279070i	0.502327	−	0.864678i	$-0.332477\pi$
$89$	12.3861	−	2.63274i	1.31292	−	0.279070i	0.810595	+	0.585608i	$0.199144\pi$
$90$	−2.94485	−	0.482478i	−0.310414	−	0.0508577i
$91$	−2.44033	−	5.24338i	−0.255816	−	0.549656i
$92$	−0.162132	+	1.02366i	−0.0169035	+	0.106724i
$93$	−3.22229	+	12.0258i	−0.334136	+	1.24701i
$94$	0.435611	+	4.14456i	0.0449298	+	0.427479i
$95$	11.1840	+	12.5547i	1.14746	+	1.28809i
$96$	−5.55884	−	0.584258i	−0.567347	−	0.0596306i
$97$	−0.527619	−	3.33125i	−0.0535716	−	0.338237i	−0.999888	−	0.0149946i	$-0.995227\pi$
$97$	−0.527619	−	3.33125i	−0.0535716	−	0.338237i	0.946316	−	0.323243i	$-0.104773\pi$
$98$	−10.4932	−	3.63040i	−1.05997	−	0.366726i
$99$		−	1.75274i		−	0.176157i
$100$	1.07450	−	2.34592i	0.107450	−	0.234592i
$101$	−2.45915	−	1.41979i	−0.244695	−	0.141275i	0.372638	−	0.927977i	$-0.378453\pi$
$101$	−2.45915	−	1.41979i	−0.244695	−	0.141275i	−0.617333	+	0.786702i	$0.711787\pi$
$102$	15.7281	+	0.824274i	1.55731	+	0.0816152i
$103$	−4.59308	−	5.67198i	−0.452570	−	0.558877i	0.498884	−	0.866669i	$-0.333743\pi$
$103$	−4.59308	−	5.67198i	−0.452570	−	0.558877i	−0.951454	+	0.307792i	$0.900410\pi$
$104$	−4.16268	−	3.02436i	−0.408184	−	0.296563i
$105$	−11.5170	+	1.34341i	−1.12395	+	0.131103i
$106$	−11.8532	+	8.61186i	−1.15129	+	0.836458i
$107$	11.2003	+	3.00110i	1.08277	+	0.290127i	0.755730	−	0.654883i	$-0.227282\pi$
$107$	11.2003	+	3.00110i	1.08277	+	0.290127i	0.327040	+	0.945011i	$0.393949\pi$
$108$	1.69678	+	1.37403i	0.163273	+	0.132216i
$109$	−2.03244	+	9.56186i	−0.194672	+	0.915860i	0.766998	+	0.641650i	$0.221750\pi$
$109$	−2.03244	+	9.56186i	−0.194672	+	0.915860i	−0.961670	+	0.274210i	$0.911584\pi$
$110$	7.12706	+	1.95035i	0.679539	+	0.185959i
$111$	−4.93560	−	1.60367i	−0.468467	−	0.152214i
$112$	−12.4192	+	2.18040i	−1.17350	+	0.206028i
$113$	4.16132	−	8.16704i	0.391464	−	0.768291i	−0.608212	−	0.793775i	$-0.708113\pi$
$113$	4.16132	−	8.16704i	0.391464	−	0.768291i	0.999675	+	0.0254843i	$0.00811278\pi$
$114$	4.86028	+	22.8658i	0.455207	+	2.14158i
$115$	2.42582	+	3.77926i	0.226209	+	0.352418i
$116$	3.54288	+	0.753063i	0.328949	+	0.0699202i
$117$	−0.659077	−	1.71696i	−0.0609317	−	0.158733i
$118$	11.8021	−	11.8021i	1.08647	−	1.08647i
$119$	13.0622	−	3.00551i	1.19741	−	0.275515i
$120$	−8.37779	+	6.01904i	−0.764784	+	0.549460i
$121$	0.696156	−	6.62348i	0.0632869	−	0.602135i
$122$	−12.7027	−	4.87612i	−1.15005	−	0.441463i
$123$	0.914571	−	17.4511i	0.0824641	−	1.57351i
$124$	−1.63906	−	2.83893i	−0.147192	−	0.254944i
$125$	−3.28492	−	10.6869i	−0.293812	−	0.955863i
$126$	−3.24914	−	1.38201i	−0.289457	−	0.123119i
$127$	1.11576	+	2.18980i	0.0990074	+	0.194313i	0.935197	−	0.354127i	$-0.115222\pi$
$127$	1.11576	+	2.18980i	0.0990074	+	0.194313i	−0.836190	+	0.548440i	$0.815222\pi$
$128$	−10.6060	+	8.58857i	−0.937447	+	0.759130i
$129$	−2.49752	+	1.11197i	−0.219895	+	0.0979034i
$130$	7.71496	−	0.769435i	0.676646	−	0.0674839i
$131$	2.26610	−	5.08975i	0.197990	−	0.444693i	−0.787079	−	0.616852i	$-0.788408\pi$
$131$	2.26610	−	5.08975i	0.197990	−	0.444693i	0.985069	+	0.172159i	$0.0550742\pi$
$132$	1.48995	+	1.48995i	0.129683	+	0.129683i
$133$	9.32688	+	17.5725i	0.808743	+	1.52373i
$134$	4.95369	−	1.60955i	0.427934	−	0.139044i
$135$	9.44997	−	0.444895i	0.813324	−	0.0382905i
$136$	8.86178	−	7.97918i	0.759891	−	0.684209i
$137$	−7.61653	+	4.94623i	−0.650724	+	0.422585i	−0.827345	−	0.561694i	$-0.810150\pi$
$137$	−7.61653	+	4.94623i	−0.650724	+	0.422585i	0.176621	+	0.984279i	$0.443483\pi$
$138$	0.326769	+	6.23513i	0.0278165	+	0.530770i
$139$	−5.50579	+	16.9451i	−0.466995	+	1.43726i	0.389461	+	0.921043i	$0.372661\pi$
$139$	−5.50579	+	16.9451i	−0.466995	+	1.43726i	−0.856456	+	0.516220i	$0.827339\pi$
$140$	1.89416	−	2.39440i	0.160086	−	0.202364i
$141$	1.59121	+	4.89724i	0.134004	+	0.412422i
$142$	−9.91229	+	3.80497i	−0.831821	+	0.319306i
$143$	1.17864	+	4.39874i	0.0985627	+	0.367841i
$144$	−3.98768	+	0.419122i	−0.332306	+	0.0349268i
$145$	13.6331	−	7.77476i	1.13217	−	0.645658i
$146$	−7.72092	+	10.6269i	−0.638988	+	0.879491i
$147$	−13.6148	−	1.69206i	−1.12293	−	0.139559i
$148$	1.21751	−	0.620350i	0.100078	−	0.0509925i
$149$	12.6781	−	7.31970i	1.03863	−	0.599653i	0.119185	−	0.992872i	$-0.461972\pi$
$149$	12.6781	−	7.31970i	1.03863	−	0.599653i	0.919445	+	0.393219i	$0.128638\pi$
$150$	3.39330	−	15.1694i	0.277062	−	1.23858i
$151$	−8.05257	+	13.9475i	−0.655309	+	1.13503i	0.326508	+	0.945195i	$0.394128\pi$
$151$	−8.05257	+	13.9475i	−0.655309	+	1.13503i	−0.981816	+	0.189833i	$0.939205\pi$
$152$	14.8440	+	9.63977i	1.20400	+	0.781889i
$153$	4.20978	−	0.666764i	0.340341	−	0.0539047i
$154$	7.64359	+	4.24428i	0.615938	+	0.342014i
$155$	−13.4853	−	4.46104i	−1.08317	−	0.358319i
$156$	2.01979	+	0.899269i	0.161713	+	0.0719991i
$157$	−4.14906	+	1.11174i	−0.331131	+	0.0887263i	−0.420554	−	0.907267i	$-0.638164\pi$
$157$	−4.14906	+	1.11174i	−0.331131	+	0.0887263i	0.0894230	+	0.995994i	$0.471498\pi$
$158$	2.66682	−	3.29325i	0.212161	−	0.261997i
$159$	−12.1135	+	13.4534i	−0.960664	+	1.06693i
$160$	1.03104	−	6.29306i	0.0815110	−	0.497510i
$161$	1.72624	+	5.02538i	0.136046	+	0.396055i
$162$	15.2867	+	7.78897i	1.20104	+	0.611959i
$163$	−15.2329	+	0.798321i	−1.19313	+	0.0625294i	−0.638537	−	0.769591i	$-0.720460\pi$
$163$	−15.2329	+	0.798321i	−1.19313	+	0.0625294i	−0.554595	+	0.832121i	$0.687127\pi$
$164$	3.07882	+	3.41938i	0.240416	+	0.267009i
$165$	9.11486	+	0.526288i	0.709591	+	0.0409714i
$166$	−3.44192	−	3.09912i	−0.267145	−	0.240538i
$167$	16.7023	+	2.64539i	1.29246	+	0.204706i	0.764535	−	0.644583i	$-0.222969\pi$
$167$	16.7023	+	2.64539i	1.29246	+	0.204706i	0.527929	+	0.849289i	$0.322969\pi$
$168$	−11.3204	+	4.56405i	−0.873390	+	0.352124i
$169$	−4.83258	−	6.65148i	−0.371737	−	0.511652i
$170$	−1.97320	+	17.8600i	−0.151337	+	1.36980i
$171$	2.57314	+	5.77937i	0.196773	+	0.441959i
$172$	0.257967	−	0.672028i	0.0196698	−	0.0512417i
$173$	−10.2096	+	15.7214i	−0.776219	+	1.19527i	0.200277	+	0.979739i	$0.435816\pi$
$173$	−10.2096	+	15.7214i	−0.776219	+	1.19527i	−0.976496	+	0.215533i	$0.930851\pi$
$174$	21.8201			1.65418
$175$	−0.772716	−	13.2062i	−0.0584118	−	0.998293i
$176$	9.92847			0.748387
$177$	11.2322	−	17.2960i	0.844262	−	1.30005i
$178$	−7.19811	+	18.7517i	−0.539521	+	1.40550i
$179$	−3.98974	−	8.96111i	−0.298207	−	0.669785i	0.700845	−	0.713314i	$-0.252807\pi$
$179$	−3.98974	−	8.96111i	−0.298207	−	0.669785i	−0.999052	+	0.0435289i	$0.986140\pi$
$180$	0.653451	−	0.718019i	0.0487054	−	0.0535180i
$181$	−0.493376	−	0.679074i	−0.0366723	−	0.0504751i	0.790287	−	0.612737i	$-0.209931\pi$
$181$	−0.493376	−	0.679074i	−0.0366723	−	0.0504751i	−0.826959	+	0.562262i	$0.809931\pi$
$182$	9.08353	+	1.28343i	0.673316	+	0.0951344i
$183$	−16.6053	−	2.63002i	−1.22750	−	0.194416i
$184$	3.51310	+	3.16321i	0.258989	+	0.233195i
$185$	2.15116	−	5.51615i	0.158157	−	0.405555i
$186$	−13.2142	−	14.6758i	−0.968909	−	1.07608i
$187$	−10.5395	+	0.552353i	−0.770726	+	0.0403920i
$188$	−1.20804	−	0.615528i	−0.0881055	−	0.0448920i
$189$	10.9865	+	2.14396i	0.799150	+	0.155950i
$190$	−26.3636	+	4.03205i	−1.91262	+	0.292516i
$191$	−1.82056	+	2.02194i	−0.131731	+	0.146302i	−0.805401	−	0.592730i	$-0.798050\pi$
$191$	−1.82056	+	2.02194i	−0.131731	+	0.146302i	0.673670	+	0.739032i	$0.264717\pi$
$192$	−6.17693	+	7.62788i	−0.445782	+	0.550494i
$193$	−6.77095	+	1.81427i	−0.487384	+	0.130594i	−0.494139	−	0.869383i	$-0.664517\pi$
$193$	−6.77095	+	1.81427i	−0.487384	+	0.130594i	0.00675479	+	0.999977i	$0.497850\pi$
$194$	4.88740	+	2.17601i	0.350895	+	0.156229i
$195$	9.12669	−	2.91190i	0.653576	−	0.208525i
$196$	2.84988	−	2.21982i	0.203563	−	0.158558i
$197$	14.6392	−	2.31863i	1.04300	−	0.165195i	0.388650	−	0.921385i	$-0.372942\pi$
$197$	14.6392	−	2.31863i	1.04300	−	0.165195i	0.654352	+	0.756190i	$0.272942\pi$
$198$	2.33167	+	1.51421i	0.165705	+	0.107610i
$199$	10.5072	−	18.1990i	0.744835	−	1.29009i	−0.205437	−	0.978670i	$-0.565862\pi$
$199$	10.5072	−	18.1990i	0.744835	−	1.29009i	0.950272	−	0.311422i	$-0.100805\pi$
$200$	−6.30468	−	9.93808i	−0.445808	−	0.702728i
$201$	5.57358	−	3.21791i	0.393130	−	0.226974i
$202$	4.01325	−	2.04485i	0.282371	−	0.143875i
$203$	17.8541	−	5.10534i	1.25311	−	0.358324i
$204$	−3.01181	+	4.14540i	−0.210869	+	0.290236i
$205$	19.8165	+	2.18936i	1.38404	+	0.152911i
$206$	11.5135	−	1.21012i	0.802183	−	0.0843128i
$207$	0.437326	+	1.63212i	0.0303963	+	0.113440i
$208$	9.72579	−	3.73338i	0.674362	−	0.258863i
$209$	−4.84072	−	14.8982i	−0.334839	−	1.03053i
$210$	8.16255	−	16.4818i	0.563269	−	1.13735i
$211$	−7.71478	+	23.7437i	−0.531108	+	1.63458i	0.220805	+	0.975318i	$0.429132\pi$
$211$	−7.71478	+	23.7437i	−0.531108	+	1.63458i	−0.751912	+	0.659263i	$0.770868\pi$
$212$	−0.249468	−	4.76014i	−0.0171336	−	0.326928i
$213$	−11.0026	+	7.14516i	−0.753884	+	0.489578i
$214$	−13.6684	+	12.3071i	−0.934353	+	0.841295i
$215$	−1.10228	−	2.91779i	−0.0751746	−	0.198992i
$216$	9.47131	−	3.07741i	0.644441	−	0.209392i
$217$	−14.2461	−	8.91657i	−0.967090	−	0.605296i
$218$	−10.9644	−	10.9644i	−0.742600	−	0.742600i
$219$	−6.60153	+	14.8273i	−0.446090	+	1.00193i
$220$	−1.79502	+	1.59905i	−0.121020	+	0.107808i
$221$	−10.1167	+	4.50423i	−0.680521	+	0.302987i
$222$	6.39730	−	5.18043i	0.429359	−	0.347688i
$223$	−5.91390	−	11.6067i	−0.396024	−	0.777241i	0.603778	−	0.797153i	$-0.293661\pi$
$223$	−5.91390	−	11.6067i	−0.396024	−	0.777241i	−0.999802	+	0.0199118i	$0.993661\pi$
$224$	2.95331	−	6.94333i	0.197326	−	0.463921i
$225$	0.0447212	−	4.20644i	0.00298141	−	0.280430i
$226$	7.26966	+	12.5914i	0.483571	+	0.837569i
$227$	0.162101	−	3.09307i	0.0107590	−	0.205294i	−0.987961	−	0.154706i	$-0.950557\pi$
$227$	0.162101	−	3.09307i	0.0107590	−	0.205294i	0.998720	−	0.0505884i	$-0.0161097\pi$
$228$	−7.10021	−	2.72551i	−0.470223	−	0.180502i
$229$	0.0558012	−	0.530913i	0.00368745	−	0.0350837i	−0.992523	−	0.122054i	$-0.961052\pi$
$229$	0.0558012	−	0.530913i	0.00368745	−	0.0350837i	0.996211	+	0.0869703i	$0.0277185\pi$
$230$	−7.12326	−	0.0378647i	−0.469694	−	0.00249673i
$231$	10.3285	+	3.16605i	0.679562	+	0.208311i
$232$	11.6820	−	11.6820i	0.766961	−	0.766961i
$233$	−8.89443	−	23.1708i	−0.582694	−	1.51797i	−0.834960	−	0.550311i	$-0.814509\pi$
$233$	−8.89443	−	23.1708i	−0.582694	−	1.51797i	0.252266	−	0.967658i	$-0.418824\pi$
$234$	2.85346	+	0.606522i	0.186537	+	0.0396496i
$235$	−5.68257	+	1.49031i	−0.370690	+	0.0972171i
$236$	1.12899	+	5.31148i	0.0734910	+	0.345748i
$237$	2.37712	−	4.66535i	0.154410	−	0.303047i
$238$	−7.28633	+	19.9732i	−0.472303	+	1.29467i
$239$	−25.9462	−	8.43043i	−1.67832	−	0.545320i	−0.693736	−	0.720229i	$-0.744037\pi$
$239$	−25.9462	−	8.43043i	−1.67832	−	0.545320i	−0.984585	+	0.174910i	$0.944037\pi$
$240$	−0.982219	−	20.8632i	−0.0634020	−	1.34671i
$241$	−3.97979	+	18.7235i	−0.256361	+	1.20608i	0.641958	+	0.766740i	$0.278122\pi$
$241$	−3.97979	+	18.7235i	−0.256361	+	1.20608i	−0.898319	+	0.439344i	$0.855211\pi$
$242$	8.20984	+	6.64820i	0.527749	+	0.427362i
$243$	8.21660	+	2.20163i	0.527095	+	0.141235i
$244$	3.58129	−	2.60196i	0.229269	−	0.166574i
$245$	2.82262	−	15.3959i	0.180330	−	0.983606i
$246$	22.4251	+	16.2928i	1.42977	+	1.03879i
$247$	−10.3440	−	12.7738i	−0.658175	−	0.812779i
$248$	−14.9317	−	0.782537i	−0.948164	−	0.0496912i
$249$	−4.95609	−	2.86140i	−0.314079	−	0.181334i
$250$	17.0547	+	4.86256i	1.07863	+	0.307535i
$251$			7.49714i			0.473215i	0.971605	+	0.236608i	$0.0760356\pi$
$251$			7.49714i			0.473215i	−0.971605	+	0.236608i	$0.923964\pi$
$252$	0.952810	−	0.641657i	0.0600214	−	0.0404206i
$253$	−0.654514	−	4.13244i	−0.0411489	−	0.259804i
$254$	−3.87701	−	0.407490i	−0.243265	−	0.0255682i
$255$	2.20336	+	22.0926i	0.137980	+	1.38349i
$256$	−1.21584	−	11.5680i	−0.0759901	−	0.722998i
$257$	−3.54307	+	13.2229i	−0.221011	+	0.824824i	0.762953	+	0.646454i	$0.223749\pi$
$257$	−3.54307	+	13.2229i	−0.221011	+	0.824824i	−0.983964	+	0.178369i	$0.942918\pi$
$258$	0.678378	−	4.28311i	0.0422340	−	0.266655i
$259$	4.02244	−	5.73564i	0.249942	−	0.356395i
$260$	−1.15709	+	2.24139i	−0.0717598	+	0.139005i
$261$	5.77603	−	1.22773i	0.357527	−	0.0759947i
$262$	4.81321	+	7.41170i	0.297361	+	0.457896i
$263$	−10.6570	−	16.4103i	−0.657137	−	1.01190i	−0.997435	−	0.0715841i	$-0.977195\pi$
$263$	−10.6570	−	16.4103i	−0.657137	−	1.01190i	0.340298	−	0.940318i	$-0.389472\pi$
$264$	9.40091	−	1.99822i	0.578586	−	0.122982i
$265$	−14.5267	−	14.6820i	−0.892369	−	0.901906i
$266$	−31.4345	−	2.77350i	−1.92737	−	0.170054i
$267$	−3.88242	+	24.5127i	−0.237600	+	1.50015i
$268$	−0.438587	+	1.63683i	−0.0267910	+	0.0999853i
$269$	0.965195	+	9.18322i	0.0588490	+	0.559911i	0.983730	+	0.179654i	$0.0574978\pi$
$269$	0.965195	+	9.18322i	0.0588490	+	0.559911i	−0.924881	+	0.380257i	$0.875836\pi$
$270$	−7.57208	+	12.9557i	−0.460822	+	0.788459i
$271$	1.10014	+	0.115630i	0.0668289	+	0.00702400i	0.137884	−	0.990448i	$-0.455970\pi$
$271$	1.10014	+	0.115630i	0.0668289	+	0.00702400i	−0.0710550	+	0.997472i	$0.522637\pi$
$272$	3.77692	+	23.8465i	0.229010	+	1.44591i
$273$	11.3081	−	0.782368i	0.684399	−	0.0473511i
$274$		−	14.4054i		−	0.870263i
$275$	−1.19888	+	10.3472i	−0.0722949	+	0.623957i
$276$	−1.75918	−	1.01566i	−0.105890	−	0.0611356i
$277$	−19.4143	−	1.01746i	−1.16649	−	0.0611331i	−0.540763	−	0.841175i	$-0.681864\pi$
$277$	−19.4143	−	1.01746i	−1.16649	−	0.0611331i	−0.625727	+	0.780042i	$0.715198\pi$
$278$	−17.7856	−	21.9634i	−1.06671	−	1.31728i
$279$	−4.32369	−	3.14135i	−0.258853	−	0.188067i
$280$	−4.45393	−	13.1940i	−0.266173	−	0.788495i
$281$	−1.38801	+	1.00845i	−0.0828017	+	0.0601589i	−0.628416	−	0.777878i	$-0.716296\pi$
$281$	−1.38801	+	1.00845i	−0.0828017	+	0.0601589i	0.545614	+	0.838036i	$0.316296\pi$
$282$	−7.88949	−	2.11398i	−0.469812	−	0.125886i
$283$	20.5156	+	16.6132i	1.21953	+	0.987553i	0.999928	+	0.0119625i	$0.00380787\pi$
$283$	20.5156	+	16.6132i	1.21953	+	0.987553i	0.219598	+	0.975590i	$0.429525\pi$
$284$	0.718188	−	3.37881i	0.0426166	−	0.200495i
$285$	−30.8275	+	11.6459i	−1.82606	+	0.689845i
$286$	−6.86990	−	2.23217i	−0.406226	−	0.131991i
$287$	22.1613	+	8.08454i	1.30814	+	0.477215i
$288$	1.08929	−	2.13786i	0.0641873	−	0.125975i
$289$	−1.80153	−	8.47555i	−0.105973	−	0.498562i
$290$	−1.43500	+	24.8529i	−0.0842659	+	1.45941i
$291$	6.46596	+	1.37438i	0.379041	+	0.0805678i
$292$	−1.53150	−	3.98969i	−0.0896242	−	0.233479i
$293$	−4.33790	+	4.33790i	−0.253423	+	0.253423i	−0.822372	−	0.568950i	$-0.807350\pi$
$293$	−4.33790	+	4.33790i	−0.253423	+	0.253423i	0.568950	+	0.822372i	$0.307350\pi$
$294$	14.0129	−	16.6500i	0.817250	−	0.971051i
$295$	18.9614	+	13.9308i	1.10397	+	0.811085i
$296$	0.651485	−	6.19847i	0.0378668	−	0.360279i
$297$	−8.22857	−	3.15865i	−0.477470	−	0.183284i
$298$	−1.21530	+	23.1893i	−0.0704005	+	1.34332i
$299$	−2.19506	−	3.80196i	−0.126944	−	0.219873i
$300$	3.53775	+	3.61378i	0.204252	+	0.208642i
$301$	−0.447061	−	3.66334i	−0.0257682	−	0.211151i
$302$	−11.5977	−	22.7617i	−0.667372	−	1.30979i
$303$	4.32512	−	3.50242i	0.248472	−	0.201209i
$304$	−32.7376	+	14.5757i	−1.87763	+	0.835974i
$305$	4.08761	−	18.7403i	0.234056	−	1.07307i
$306$	−2.74988	+	6.17632i	−0.157200	+	0.353077i
$307$	12.5574	+	12.5574i	0.716687	+	0.716687i	0.967925	−	0.251239i	$-0.0808379\pi$
$307$	12.5574	+	12.5574i	0.716687	+	0.716687i	−0.251239	+	0.967925i	$0.580838\pi$
$308$	−2.51245	+	1.33352i	−0.143160	+	0.0759844i
$309$	13.6044	−	4.42034i	0.773928	−	0.251464i
$310$	17.5847	−	14.0857i	0.998742	−	0.800013i
$311$	4.72615	−	4.25544i	0.267995	−	0.241304i	−0.524166	−	0.851616i	$-0.675623\pi$
$311$	4.72615	−	4.25544i	0.267995	−	0.241304i	0.792161	+	0.610312i	$0.208956\pi$
$312$	8.45761	−	5.49244i	0.478818	−	0.310948i
$313$	0.399757	+	7.62782i	0.0225956	+	0.431150i	0.986382	+	0.164473i	$0.0525924\pi$
$313$	0.399757	+	7.62782i	0.0225956	+	0.431150i	−0.963786	+	0.266677i	$0.914074\pi$
$314$	2.10547	−	6.47997i	0.118818	−	0.365686i
$315$	1.23335	−	4.82219i	0.0694916	−	0.271699i
$316$	0.426032	+	1.31119i	0.0239662	+	0.0737603i
$317$	13.1753	−	5.05753i	0.740000	−	0.284059i	0.0409785	−	0.999160i	$-0.486952\pi$
$317$	13.1753	−	5.05753i	0.740000	−	0.284059i	0.699021	+	0.715101i	$0.253619\pi$
$318$	−7.43217	−	27.7372i	−0.416775	−	1.55543i
$319$	−14.5417	+	1.52840i	−0.814181	+	0.0855738i
$320$	−8.28187	−	7.53713i	−0.462971	−	0.421338i
$321$	−13.3581	+	18.3858i	−0.745575	+	1.02620i
$322$	−8.17661	−	2.04506i	−0.455665	−	0.113967i
$323$	33.9415	−	17.2941i	1.88856	−	0.962268i
$324$	−4.83394	+	2.79088i	−0.268552	+	0.155049i
$325$	2.71642	+	10.5867i	0.150680	+	0.587247i
$326$	12.0978	−	20.9541i	0.670037	−	1.16054i
$327$	−16.0683	−	10.4349i	−0.888580	−	0.577051i
$328$	20.7288	−	3.28311i	1.14455	−	0.181280i
$329$	−6.95011	+	0.116192i	−0.383172	+	0.00640585i
$330$	−8.57455	+	11.6709i	−0.472014	+	0.642461i
$331$	−9.40598	−	4.18781i	−0.516999	−	0.230183i	0.131614	−	0.991301i	$-0.457984\pi$
$331$	−9.40598	−	4.18781i	−0.516999	−	0.230183i	−0.648613	+	0.761118i	$0.724651\pi$
$332$	1.45549	−	0.389997i	0.0798802	−	0.0214038i
$333$	1.40196	−	1.73127i	0.0768267	−	0.0948730i
$334$	−17.9485	+	19.9338i	−0.982097	+	1.09073i
$335$	3.29863	+	6.55989i	0.180223	+	0.358405i
$336$	4.73334	−	24.2555i	0.258225	−	1.32325i
$337$	22.9028	+	11.6695i	1.24759	+	0.635681i	0.947965	−	0.318375i	$-0.103137\pi$
$337$	22.9028	+	11.6695i	1.24759	+	0.635681i	0.299629	+	0.954056i	$0.403137\pi$
$338$	13.0234	−	0.682529i	0.708381	−	0.0371247i
$339$	12.0209	+	13.3505i	0.652884	+	0.725101i
$340$	−4.52351	−	3.70305i	−0.245322	−	0.200826i
$341$	9.83439	+	8.85492i	0.532562	+	0.479521i
$342$	−9.91130	−	1.56980i	−0.535942	−	0.0848848i
$343$	7.57025	−	16.9024i	0.408755	−	0.912644i
$344$	−1.92990	−	2.65628i	−0.104053	−	0.143217i
$345$	−8.61896	+	1.78418i	−0.464029	+	0.0960573i
$346$	−12.0941	−	27.1637i	−0.650181	−	1.46033i
$347$	1.63539	−	4.26035i	0.0877926	−	0.228707i	−0.882654	−	0.470023i	$-0.844246\pi$
$347$	1.63539	−	4.26035i	0.0877926	−	0.228707i	0.970447	+	0.241316i	$0.0775789\pi$
$348$	−3.86636	+	5.95367i	−0.207259	+	0.319150i
$349$	35.4204			1.89601			0.948005	−	0.318256i	$-0.103097\pi$
$349$	35.4204			1.89601			0.948005	+	0.318256i	$0.103097\pi$
$350$	18.2358	+	10.3810i	0.974745	+	0.554888i
$351$	−9.24834			−0.493640
$352$	−3.23582	+	4.98272i	−0.172470	+	0.265580i
$353$	−3.83210	+	9.98297i	−0.203962	+	0.531340i	−0.996963	−	0.0778814i	$-0.975184\pi$
$353$	−3.83210	+	9.98297i	−0.203962	+	0.531340i	0.793000	+	0.609221i	$0.208518\pi$
$354$	13.3054	+	29.8845i	0.707175	+	1.58834i
$355$	−7.41470	−	13.0018i	−0.393532	−	0.690062i
$356$	−3.84101	−	5.28670i	−0.203573	−	0.280194i
$357$	−3.67525	+	26.0116i	−0.194515	+	1.37668i
$358$	15.3678	+	2.43402i	0.812214	+	0.128642i
$359$	−2.83659	−	2.55408i	−0.149710	−	0.134799i	0.590873	−	0.806765i	$-0.298784\pi$
$359$	−2.83659	−	2.55408i	−0.149710	−	0.134799i	−0.740582	+	0.671966i	$0.765450\pi$
$360$	−1.12336	−	4.28339i	−0.0592064	−	0.225755i
$361$	25.1196	+	27.8982i	1.32209	+	1.46833i
$362$	1.32961	−	0.0696818i	0.0698827	−	0.00366240i
$363$	11.6304	+	5.92598i	0.610437	+	0.311033i
$364$	−1.95972	+	2.25105i	−0.102717	+	0.117987i
$365$	−16.4540	−	8.49421i	−0.861243	−	0.444607i
$366$	17.8442	−	19.8180i	0.932731	−	1.03590i
$367$	5.24006	−	6.47094i	0.273529	−	0.337780i	−0.621808	−	0.783170i	$-0.713601\pi$
$367$	5.24006	−	6.47094i	0.273529	−	0.337780i	0.895337	+	0.445390i	$0.146935\pi$
$368$	−9.24526	+	2.47726i	−0.481943	+	0.129136i
$369$	6.85293	+	3.05112i	0.356749	+	0.158835i
$370$	5.47976	+	7.62717i	0.284879	+	0.396518i
$371$	−12.5711	−	20.9568i	−0.652659	−	1.08802i
$372$	6.34579	−	1.00507i	0.329014	−	0.0521107i
$373$	−14.6190	−	9.49367i	−0.756941	−	0.491563i	0.107557	−	0.994199i	$-0.465697\pi$
$373$	−14.6190	−	9.49367i	−0.756941	−	0.491563i	−0.864498	+	0.502635i	$0.832364\pi$
$374$	8.37041	−	14.4980i	0.432824	−	0.749672i
$375$	21.8616	+	1.49562i	1.12893	+	0.0772335i
$376$	−5.35564	+	3.09208i	−0.276196	+	0.159462i
$377$	−13.6702	+	6.96529i	−0.704049	+	0.358731i
$378$	−12.3435	+	12.7632i	−0.634880	+	0.656469i
$379$	−6.41691	+	8.83212i	−0.329614	+	0.453675i	−0.941372	−	0.337370i	$-0.890463\pi$
$379$	−6.41691	+	8.83212i	−0.329614	+	0.453675i	0.611758	+	0.791045i	$0.290463\pi$
$380$	3.57129	−	7.90784i	0.183203	−	0.405664i
$381$	−4.79047	+	0.503499i	−0.245423	+	0.0257950i
$382$	−1.11699	−	4.16868i	−0.0571504	−	0.213288i
$383$	15.4910	−	5.94645i	0.791555	−	0.303849i	0.0712062	−	0.997462i	$-0.477315\pi$
$383$	15.4910	−	5.94645i	0.791555	−	0.303849i	0.720349	+	0.693612i	$0.243982\pi$
$384$	−8.26557	−	25.4388i	−0.421800	−	1.29817i
$385$	−4.28536	+	11.5558i	−0.218402	+	0.588939i
$386$	3.43596	−	10.5748i	0.174886	−	0.538244i
$387$	−0.0614198	−	1.17196i	−0.00312214	−	0.0595740i
$388$	−1.45974	+	0.947969i	−0.0741072	+	0.0481258i
$389$	14.2859	−	12.8631i	0.724323	−	0.652183i	−0.222133	−	0.975016i	$-0.571302\pi$
$389$	14.2859	−	12.8631i	0.724323	−	0.652183i	0.946456	+	0.322833i	$0.104635\pi$
$390$	−4.01093	+	14.6569i	−0.203101	+	0.742182i
$391$	9.67645	−	3.14407i	0.489359	−	0.159002i
$392$	−1.41186	−	16.4163i	−0.0713099	−	0.829148i
$393$	7.72133	+	7.72133i	0.389490	+	0.389490i
$394$	−9.56251	+	21.4777i	−0.481752	+	1.08203i
$395$	5.15747	+	3.01434i	0.259501	+	0.151668i
$396$	−0.826312	+	0.367898i	−0.0415237	+	0.0184876i
$397$	0.945508	−	0.765657i	0.0474537	−	0.0384272i	−0.605300	−	0.795997i	$-0.706947\pi$
$397$	0.945508	−	0.765657i	0.0474537	−	0.0384272i	0.652754	+	0.757570i	$0.273614\pi$
$398$	15.1329	+	29.7001i	0.758546	+	1.48873i
$399$	−38.7044	+	4.72336i	−1.93765	+	0.236464i
$400$	23.8276	+	0.253326i	1.19138	+	0.0126663i
$401$	2.37174	+	4.10797i	0.118439	+	0.205142i	0.919149	−	0.393910i	$-0.128878\pi$
$401$	2.37174	+	4.10797i	0.118439	+	0.205142i	−0.800710	+	0.599052i	$0.795544\pi$
$402$	−0.534274	+	10.1945i	−0.0266471	+	0.508458i
$403$	12.9633	+	4.97615i	0.645749	+	0.247880i
$404$	−0.153175	+	1.45736i	−0.00762072	+	0.0725063i
$405$	−7.59595	+	22.9619i	−0.377446	+	1.14099i
$406$	−8.63267	+	28.1619i	−0.428432	+	1.39765i
$407$	−3.90054	+	3.90054i	−0.193342	+	0.193342i
$408$	8.37563	+	21.8193i	0.414656	+	1.08021i
$409$	24.2503	+	5.15456i	1.19910	+	0.254877i	0.763827	−	0.645421i	$-0.223318\pi$
$409$	24.2503	+	5.15456i	1.19910	+	0.254877i	0.435274	+	0.900298i	$0.356651\pi$
$410$	−20.0322	+	24.4706i	−0.989319	+	1.20852i
$411$	−3.70072	−	17.4105i	−0.182543	−	0.858797i
$412$	−1.70992	+	3.35591i	−0.0842419	+	0.165334i
$413$	17.8792	+	21.3396i	0.879779	+	1.05005i
$414$	−2.54904	−	0.828232i	−0.125278	−	0.0407054i
$415$	3.58505	−	5.45677i	0.175983	−	0.267862i
$416$	−1.29612	+	6.09776i	−0.0635475	+	0.298968i
$417$	−27.1382	−	21.9761i	−1.32896	−	1.07617i
$418$	24.0011	+	6.43108i	1.17393	+	0.314554i
$419$	−19.6973	+	14.3109i	−0.962276	+	0.699135i	−0.953678	−	0.300828i	$-0.902737\pi$
$419$	−19.6973	+	14.3109i	−0.962276	+	0.699135i	−0.00859807	+	0.999963i	$0.502737\pi$
$420$	3.05075	+	5.14762i	0.148862	+	0.251178i
$421$	−6.00083	−	4.35986i	−0.292463	−	0.212486i	0.431872	−	0.901935i	$-0.357853\pi$
$421$	−6.00083	−	4.35986i	−0.292463	−	0.212486i	−0.724335	+	0.689448i	$0.757853\pi$
$422$	−24.9215	−	30.7754i	−1.21316	−	1.49812i
$423$	−2.20738	−	0.115684i	−0.107327	−	0.00562475i
$424$	−18.8290	−	10.8709i	−0.914415	−	0.527938i
$425$	−25.3082	+	1.05669i	−1.22763	+	0.0512571i
$426$		−	20.8096i		−	1.00823i
$427$	9.96394	−	20.3910i	0.482189	−	0.986788i
$428$	−0.936083	−	5.91019i	−0.0452473	−	0.285680i
$429$	−8.87646	−	0.932953i	−0.428559	−	0.0450434i
$430$	4.83382	+	1.05435i	0.233108	+	0.0508451i
$431$	−1.88691	−	17.9528i	−0.0908895	−	0.864756i	−0.941058	−	0.338245i	$-0.890167\pi$
$431$	−1.88691	−	17.9528i	−0.0908895	−	0.864756i	0.850169	−	0.526511i	$-0.176500\pi$
$432$	−5.21865	+	19.4763i	−0.251082	+	0.937052i
$433$	−3.94891	+	24.9324i	−0.189773	+	1.19818i	0.690366	+	0.723460i	$0.257449\pi$
$433$	−3.94891	+	24.9324i	−0.189773	+	1.19818i	−0.880139	+	0.474717i	$0.842551\pi$
$434$	24.1691	−	11.2486i	1.16016	−	0.539949i
$435$	4.65031	+	30.4061i	0.222965	+	1.45786i
$436$	4.93446	−	1.04885i	0.236318	−	0.0502309i
$437$	8.22487	+	12.6652i	0.393449	+	0.605858i
$438$	−14.0217	−	21.5915i	−0.669982	−	1.03168i
$439$	27.2854	−	5.79968i	1.30226	−	0.276804i	0.495977	−	0.868335i	$-0.334810\pi$
$439$	27.2854	−	5.79968i	1.30226	−	0.276804i	0.806282	+	0.591532i	$0.201477\pi$
$440$	1.65771	+	10.8390i	0.0790284	+	0.516728i
$441$	2.77255	−	5.19591i	0.132026	−	0.247424i
$442$	2.74789	−	17.3495i	0.130704	−	0.825232i
$443$	−7.92554	+	29.5785i	−0.376554	+	1.40532i	0.474507	+	0.880252i	$0.342626\pi$
$443$	−7.92554	+	29.5785i	−0.376554	+	1.40532i	−0.851061	+	0.525066i	$0.824040\pi$
$444$	0.279941	+	2.66346i	0.0132854	+	0.126402i
$445$	−27.6644	−	6.03413i	−1.31142	−	0.286045i
$446$	20.5495	+	2.15984i	0.973048	+	0.102271i
$447$	4.48846	+	28.3390i	0.212297	+	1.34039i
$448$	−7.40109	−	10.9900i	−0.349669	−	0.519230i
$449$			30.4224i			1.43572i	0.696187	+	0.717861i	$0.254879\pi$
$449$			30.4224i			1.43572i	−0.696187	+	0.717861i	$0.745121\pi$
$450$	5.55722	+	3.69349i	0.261970	+	0.174113i
$451$	−16.0862	−	9.28737i	−0.757469	−	0.437325i
$452$	−4.72374	−	0.247561i	−0.222186	−	0.0116443i
$453$	−19.8645	−	24.5306i	−0.933315	−	1.15255i
$454$	3.97469	+	2.88778i	0.186541	+	0.135530i
$455$	0.147434	+	12.9313i	0.00691180	+	0.606230i
$456$	−28.0645	+	20.3900i	−1.31424	+	0.954851i
$457$	−38.9922	−	10.4479i	−1.82398	−	0.488733i	−0.826710	−	0.562628i	$-0.809790\pi$
$457$	−38.9922	−	10.4479i	−1.82398	−	0.488733i	−0.997266	+	0.0738955i	$0.976457\pi$
$458$	0.658070	+	0.532894i	0.0307496	+	0.0249005i
$459$	4.45630	−	20.9653i	0.208002	−	0.978575i
$460$	1.27252	−	1.93689i	0.0593316	−	0.0903081i
$461$	−16.9923	−	5.52114i	−0.791411	−	0.257145i	−0.114706	−	0.993399i	$-0.536593\pi$
$461$	−16.9923	−	5.52114i	−0.791411	−	0.257145i	−0.676705	+	0.736255i	$0.736593\pi$
$462$	−13.1347	+	11.0048i	−0.611080	+	0.511990i
$463$	−15.5311	+	30.4814i	−0.721790	+	1.41659i	0.179668	+	0.983727i	$0.442498\pi$
$463$	−15.5311	+	30.4814i	−0.721790	+	1.41659i	−0.901458	+	0.432866i	$0.857502\pi$
$464$	6.95456	+	32.7186i	0.322857	+	1.51892i
$465$	17.6344	−	21.5415i	0.817776	−	0.998964i
$466$	38.5083	+	8.18518i	1.78386	+	0.379171i
$467$	2.39302	+	6.23404i	0.110736	+	0.288477i	0.977739	−	0.209826i	$-0.0672899\pi$
$467$	2.39302	+	6.23404i	0.110736	+	0.288477i	−0.867003	+	0.498303i	$0.833957\pi$
$468$	−0.671104	+	0.671104i	−0.0310218	+	0.0310218i
$469$	1.94810	+	8.46660i	0.0899548	+	0.390951i
$470$	2.92666	−	8.84705i	0.134997	−	0.408084i
$471$	0.879999	−	8.37263i	0.0405482	−	0.385790i
$472$	23.1230	+	8.87607i	1.06432	+	0.408554i
$473$	−0.152085	+	2.90195i	−0.00699285	+	0.133432i
$474$	4.15273	+	7.19274i	0.190741	+	0.330374i
$475$	−11.2373	−	35.8782i	−0.515601	−	1.64620i
$476$	−4.15867	−	5.52721i	−0.190612	−	0.253339i
$477$	−3.52805	−	6.92419i	−0.161538	−	0.317037i
$478$	33.6303	−	27.2333i	1.53821	−	1.24562i
$479$	4.62700	−	2.06007i	0.211413	−	0.0941271i	−0.298298	−	0.954473i	$-0.596419\pi$
$479$	4.62700	−	2.06007i	0.211413	−	0.0941271i	0.509711	+	0.860346i	$0.329752\pi$
$480$	10.7906	+	6.30665i	0.492520	+	0.287858i
$481$	−2.35420	+	5.28762i	−0.107342	+	0.241095i
$482$	−21.4697	−	21.4697i	−0.977920	−	0.977920i
$483$	−10.4077	−	0.371123i	−0.473566	−	0.0168867i
$484$	−3.26870	+	1.06207i	−0.148577	+	0.0482758i
$485$	−1.99065	+	7.27430i	−0.0903906	+	0.330309i
$486$	−10.0272	+	9.02858i	−0.454845	+	0.409544i
$487$	15.7690	−	10.2405i	0.714563	−	0.464043i	−0.135464	−	0.990782i	$-0.543252\pi$
$487$	15.7690	−	10.2405i	0.714563	−	0.464043i	0.850027	+	0.526740i	$0.176586\pi$
$488$	−1.05673	−	20.1635i	−0.0478357	−	0.912760i
$489$	9.23849	−	28.4332i	0.417779	−	1.28579i
$490$	18.0427	+	17.0556i	0.815088	+	0.770494i
$491$	−8.10726	−	24.9516i	−0.365876	−	1.12605i	−0.949431	−	0.313976i	$-0.898339\pi$
$491$	−8.10726	−	24.9516i	−0.365876	−	1.12605i	0.583555	−	0.812073i	$-0.301661\pi$
$492$	−8.41912	+	3.23180i	−0.379563	+	0.145701i
$493$	−9.20282	−	34.3454i	−0.414474	−	1.54684i
$494$	25.9294	−	2.72529i	1.16662	−	0.122617i
$495$	−1.61311	+	3.57188i	−0.0725037	+	0.160544i
$496$	17.7943	−	24.4918i	0.798989	−	1.09971i
$497$	−4.86891	−	17.0272i	−0.218400	−	0.763776i
$498$	8.08815	−	4.12112i	0.362439	−	0.184672i
$499$	2.61768	−	1.51132i	0.117183	−	0.0676558i	−0.440263	−	0.897869i	$-0.645115\pi$
$499$	2.61768	−	1.51132i	0.117183	−	0.0676558i	0.557446	+	0.830213i	$0.311781\pi$
$500$	−4.34873	+	3.79181i	−0.194481	+	0.169575i
$501$	−16.5717	+	28.7031i	−0.740370	+	1.28236i
$502$	−9.97349	−	6.47686i	−0.445139	−	0.289076i
$503$	13.8594	−	2.19511i	0.617958	−	0.0978750i	0.160396	−	0.987053i	$-0.448723\pi$
$503$	13.8594	−	2.19511i	0.617958	−	0.0978750i	0.457562	+	0.889178i	$0.348723\pi$
$504$	−0.0875827	−	5.23885i	−0.00390124	−	0.233357i
$505$	3.70479	+	5.15662i	0.164861	+	0.229467i
$506$	6.06285	+	2.69935i	0.269527	+	0.120001i
$507$	15.5649	−	4.17060i	0.691260	−	0.185223i
$508$	0.798164	−	0.985650i	0.0354128	−	0.0437311i
$509$	−15.1783	+	16.8573i	−0.672768	+	0.747185i	−0.978796	−	0.204838i	$-0.934333\pi$
$509$	−15.1783	+	16.8573i	−0.672768	+	0.747185i	0.306028	+	0.952023i	$0.401000\pi$
$510$	−31.2934	−	16.1549i	−1.38570	−	0.715351i
$511$	−16.5250	−	14.3863i	−0.731022	−	0.636414i
$512$	−7.88049	−	4.01531i	−0.348272	−	0.177453i
$513$	31.7696	−	1.66497i	1.40266	−	0.0735103i
$514$	−14.5296	−	16.1368i	−0.640875	−	0.711764i
$515$	4.14005	+	15.7860i	0.182432	+	0.695616i
$516$	1.04846	+	0.944034i	0.0461557	+	0.0415588i
$517$	5.40593	+	0.856215i	0.237752	+	0.0376563i
$518$	4.15513	+	10.3062i	0.182566	+	0.452827i
$519$	−21.5953	−	29.7233i	−0.947927	−	1.30471i
$520$	5.69963	+	9.99437i	0.249945	+	0.438282i
$521$	−17.0862	−	38.3763i	−0.748562	−	1.68130i	−0.731877	−	0.681437i	$-0.761355\pi$
$521$	−17.0862	−	38.3763i	−0.748562	−	1.68130i	−0.0166856	−	0.999861i	$-0.505311\pi$
$522$	−3.35671	+	8.74454i	−0.146919	+	0.382738i
$523$	14.3920	−	22.1618i	0.629320	−	0.969068i	−0.369880	−	0.929079i	$-0.620601\pi$
$523$	14.3920	−	22.1618i	0.629320	−	0.969068i	0.999200	−	0.0399883i	$-0.0127321\pi$
$524$	−2.87517			−0.125602
$525$	24.7068	+	7.86183i	1.07829	+	0.343118i
$526$	31.0374			1.35329
$527$	−17.5269	+	26.9891i	−0.763485	+	1.17566i
$528$	−6.97353	+	18.1667i	−0.303484	+	0.790603i
$529$	−7.71438	−	17.3268i	−0.335408	−	0.753338i
$530$	32.0813	−	6.64105i	1.39352	−	0.288469i
$531$	5.20358	+	7.16212i	0.225816	+	0.310809i
$532$	6.32672	−	8.08554i	0.274298	−	0.350553i
$533$	−19.2501	−	3.04892i	−0.833815	−	0.132063i
$534$	−29.2553	−	26.3416i	−1.26600	−	1.13991i
$535$	−20.0628	−	16.4239i	−0.867392	−	0.710067i
$536$	5.17191	+	5.74398i	0.223392	+	0.248102i
$537$	19.1989	−	1.00617i	0.828496	−	0.0434196i
$538$	−13.0503	−	6.64948i	−0.562640	−	0.286679i
$539$	−8.17248	+	12.0778i	−0.352014	+	0.520226i
$540$	−2.19328	−	4.36172i	−0.0943839	−	0.187699i
$541$	−3.31932	+	3.68648i	−0.142709	+	0.158494i	−0.810262	−	0.586068i	$-0.800675\pi$
$541$	−3.31932	+	3.68648i	−0.142709	+	0.158494i	0.667553	+	0.744562i	$0.267342\pi$
$542$	−1.10425	+	1.36363i	−0.0474315	+	0.0585731i
$543$	1.58907	−	0.425791i	0.0681937	−	0.0182724i
$544$	−13.1986	−	5.87641i	−0.565886	−	0.251949i
$545$	12.9420	−	17.6155i	0.554374	−	0.754563i
$546$	−8.72843	+	15.7192i	−0.373542	+	0.672718i
$547$	−17.1842	+	2.72171i	−0.734743	+	0.116372i	−0.512582	−	0.858638i	$-0.671311\pi$
$547$	−17.1842	+	2.72171i	−0.734743	+	0.116372i	−0.222161	+	0.975010i	$0.571311\pi$
$548$	3.93056	+	2.55254i	0.167905	+	0.109039i
$549$	3.60848	−	6.25007i	0.154006	−	0.266747i
$550$	−12.7292	−	10.5339i	−0.542773	−	0.449167i
$551$	45.7053	−	26.3880i	1.94711	−	1.12416i
$552$	−8.25542	+	4.20635i	−0.351374	+	0.179034i
$553$	5.08085	+	4.91376i	0.216060	+	0.208954i
$554$	18.1257	−	24.9479i	0.770088	−	1.05994i
$555$	8.58228	+	7.81052i	0.364297	+	0.331538i
$556$	9.14427	−	0.961102i	0.387804	−	0.0407598i
$557$	2.83348	+	10.5747i	0.120058	+	0.448064i	0.999615	−	0.0277296i	$-0.00882774\pi$
$557$	2.83348	+	10.5747i	0.120058	+	0.448064i	−0.879557	+	0.475793i	$0.842161\pi$
$558$	7.91423	−	3.03799i	0.335036	−	0.128608i
$559$	0.942233	+	2.89989i	0.0398522	+	0.122652i
$560$	27.3156	+	6.98641i	1.15429	+	0.295230i
$561$	6.39205	−	19.6727i	0.269872	−	0.830582i
$562$	−0.142428	−	2.71769i	−0.00600796	−	0.114639i
$563$	−1.67086	+	1.08507i	−0.0704183	+	0.0457302i	−0.579368	−	0.815066i	$-0.696701\pi$
$563$	−1.67086	+	1.08507i	−0.0704183	+	0.0457302i	0.508950	+	0.860796i	$0.330034\pi$
$564$	1.97477	−	1.77809i	0.0831527	−	0.0748710i
$565$	−15.9967	+	12.8137i	−0.672987	+	0.539076i
$566$	−39.8243	+	12.9397i	−1.67394	+	0.543896i
$567$	−15.1825	+	24.2573i	−0.637606	+	1.01871i
$568$	−11.1410	−	11.1410i	−0.467466	−	0.467466i
$569$	12.9886	−	29.1729i	0.544511	−	1.22299i	−0.406447	−	0.913674i	$-0.633232\pi$
$569$	12.9886	−	29.1729i	0.544511	−	1.22299i	0.950959	−	0.309318i	$-0.100101\pi$
$570$	11.1395	−	51.0710i	0.466584	−	2.13913i
$571$	−13.4872	+	6.00488i	−0.564421	+	0.251297i	−0.669053	−	0.743214i	$-0.733300\pi$
$571$	−13.4872	+	6.00488i	−0.564421	+	0.251297i	0.104632	+	0.994511i	$0.466634\pi$
$572$	1.82635	−	1.47895i	0.0763636	−	0.0618380i
$573$	−2.42093	−	4.75134i	−0.101136	−	0.198490i
$574$	−29.9003	+	22.4969i	−1.24801	+	0.939004i
$575$	−1.46535	−	9.93427i	−0.0611093	−	0.414288i
$576$	−2.10668	−	3.64889i	−0.0877785	−	0.152037i
$577$	0.424978	−	8.10906i	0.0176921	−	0.337585i	−0.975415	−	0.220375i	$-0.929272\pi$
$577$	0.424978	−	8.10906i	0.0176921	−	0.337585i	0.993107	−	0.117209i	$-0.0373949\pi$
$578$	12.8314	+	4.92553i	0.533718	+	0.204875i
$579$	1.43609	−	13.6635i	0.0596819	−	0.567835i
$580$	−6.52692	−	4.79530i	−0.271016	−	0.199114i
$581$	5.65382	−	5.26449i	0.234560	−	0.218408i
$582$	−7.41437	+	7.41437i	−0.307335	+	0.307335i
$583$	6.89595	+	17.9646i	0.285601	+	0.744016i
$584$	−19.0665	−	4.05272i	−0.788979	−	0.167703i
$585$	−0.237051	+	4.10553i	−0.00980087	+	0.169743i
$586$	−2.02318	−	9.51830i	−0.0835767	−	0.393197i
$587$	3.16940	−	6.22031i	0.130815	−	0.256739i	−0.816303	−	0.577624i	$-0.803980\pi$
$587$	3.16940	−	6.22031i	0.130815	−	0.256739i	0.947118	+	0.320884i	$0.103980\pi$
$588$	2.06003	+	6.77373i	0.0849541	+	0.279344i
$589$	−45.4270	−	14.7601i	−1.87179	−	0.608181i
$590$	−34.9132	+	13.1894i	−1.43736	+	0.543000i
$591$	−6.03974	+	28.4148i	−0.248442	+	1.16883i
$592$	9.80688	+	7.94146i	0.403060	+	0.326392i
$593$	8.18799	+	2.19397i	0.336240	+	0.0900954i	0.422989	−	0.906135i	$-0.360981\pi$
$593$	8.18799	+	2.19397i	0.336240	+	0.0900954i	−0.0867484	+	0.996230i	$0.527648\pi$
$594$	11.3107	−	8.21773i	0.464085	−	0.337177i
$595$	−29.3854	−	5.89673i	−1.20468	−	0.241742i
$596$	−6.11193	−	4.44058i	−0.250355	−	0.181893i
$597$	25.9197	+	32.0081i	1.06082	+	1.31001i
$598$	6.95412	+	0.364450i	0.284375	+	0.0149035i
$599$	20.6751	+	11.9368i	0.844762	+	0.487723i	0.858880	−	0.512177i	$-0.171161\pi$
$599$	20.6751	+	11.9368i	0.844762	+	0.487723i	−0.0141183	+	0.999900i	$0.504494\pi$
$600$	22.6125	−	4.55574i	0.923152	−	0.185987i
$601$			9.32470i			0.380362i	0.981749	+	0.190181i	$0.0609075\pi$
$601$			9.32470i			0.380362i	−0.981749	+	0.190181i	$0.939092\pi$
$602$	5.25958	+	2.57007i	0.214365	+	0.104748i
$603$	0.432180	+	2.72868i	0.0175997	+	0.111120i
$604$	8.26564	+	0.868753i	0.336324	+	0.0353491i
$605$	−7.51452	+	12.8572i	−0.305509	+	0.522720i
$606$	0.922764	+	8.77952i	0.0374847	+	0.356643i
$607$	−5.76957	+	21.5323i	−0.234180	+	0.873971i	0.744337	+	0.667804i	$0.232766\pi$
$607$	−5.76957	+	21.5323i	−0.234180	+	0.873971i	−0.978517	+	0.206167i	$0.933901\pi$
$608$	3.35461	−	21.1802i	0.136047	−	0.858969i
$609$	−3.19878	+	36.2545i	−0.129621	+	1.46910i
$610$	21.3990	+	21.6277i	0.866421	+	0.875682i
$611$	5.61753	−	1.19404i	0.227261	−	0.0483058i
$612$	−1.19797	−	1.84471i	−0.0484250	−	0.0745680i
$613$	11.2408	+	17.3094i	0.454013	+	0.699118i	0.989356	−	0.145516i	$-0.0464843\pi$
$613$	11.2408	+	17.3094i	0.454013	+	0.699118i	−0.535343	+	0.844635i	$0.679818\pi$
$614$	−27.5536	+	5.85669i	−1.11197	+	0.236357i
$615$	−17.9246	+	34.7216i	−0.722791	+	1.40011i
$616$	−1.14028	+	12.9238i	−0.0459432	+	0.520714i
$617$	−1.89563	+	11.9685i	−0.0763151	+	0.481835i	0.919698	+	0.392627i	$0.128434\pi$
$617$	−1.89563	+	11.9685i	−0.0763151	+	0.481835i	−0.996013	+	0.0892079i	$0.971566\pi$
$618$	−5.87259	+	21.9168i	−0.236230	+	0.881624i
$619$	1.68698	+	16.0505i	0.0678054	+	0.645125i	0.974662	+	0.223685i	$0.0718086\pi$
$619$	1.68698	+	16.0505i	0.0678054	+	0.645125i	−0.906856	+	0.421440i	$0.861525\pi$
$620$	0.727443	+	7.29391i	0.0292148	+	0.292931i
$621$	8.45046	+	0.888179i	0.339105	+	0.0356414i
$622$	1.57807	+	9.96354i	0.0632749	+	0.399502i
$623$	−30.1011	−	14.7088i	−1.20597	−	0.589294i
$624$			20.4181i			0.817376i
$625$	−3.14123	+	24.8019i	−0.125649	+	0.992075i
$626$	−10.4927	−	6.05796i	−0.419372	−	0.242125i
$627$	30.6600	+	1.60683i	1.22444	+	0.0641704i
$628$	1.39500	+	1.72269i	0.0556667	+	0.0687427i
$629$	−10.8523	−	7.88463i	−0.432708	−	0.314381i
$630$	5.34948	+	5.80668i	0.213128	+	0.231344i
$631$	32.3943	−	23.5358i	1.28960	−	0.936947i	0.289799	−	0.957087i	$-0.406411\pi$
$631$	32.3943	−	23.5358i	1.28960	−	0.936947i	0.999797	+	0.0201409i	$0.00641148\pi$
$632$	6.07412	+	1.62756i	0.241616	+	0.0647407i
$633$	−38.0264	−	30.7932i	−1.51141	−	1.22392i
$634$	−4.65424	+	21.8965i	−0.184843	+	0.869620i
$635$	−0.258437	−	5.48942i	−0.0102557	−	0.217841i
$636$	8.88511	+	2.88695i	0.352318	+	0.114475i
$637$	−3.46407	+	14.9043i	−0.137251	+	0.590529i
$638$	10.5295	−	20.6654i	0.416868	−	0.818149i
$639$	−1.17088	−	5.50853i	−0.0463191	−	0.217914i
$640$	29.5182	−	7.74144i	1.16681	−	0.306007i
$641$	36.0927	+	7.67174i	1.42558	+	0.303015i	0.855170	−	0.518348i	$-0.173453\pi$
$641$	36.0927	+	7.67174i	1.42558	+	0.303015i	0.570406	+	0.821363i	$0.306786\pi$
$642$	−12.9186	−	33.6541i	−0.509856	−	1.32822i
$643$	15.3835	−	15.3835i	0.606667	−	0.606667i	−0.335406	−	0.942074i	$-0.608874\pi$
$643$	15.3835	−	15.3835i	0.606667	−	0.606667i	0.942074	+	0.335406i	$0.108874\pi$
$644$	2.00684	−	1.86864i	0.0790804	−	0.0736348i
$645$	6.11305	+	0.0324948i	0.240701	+	0.00127948i
$646$	−6.31604	+	60.0932i	−0.248501	+	2.36433i
$647$	32.8659	+	12.6160i	1.29209	+	0.495987i	0.904747	−	0.425949i	$-0.140060\pi$
$647$	32.8659	+	12.6160i	1.29209	+	0.495987i	0.387343	+	0.921936i	$0.373393\pi$
$648$	−1.33245	+	25.4247i	−0.0523436	+	0.998775i
$649$	−10.9605	−	18.9842i	−0.430238	−	0.745193i
$650$	−16.4303	−	5.53233i	−0.644451	−	0.216996i
$651$	26.3213	−	19.8041i	1.03161	−	0.776184i
$652$	3.57373	+	7.01384i	0.139958	+	0.274683i
$653$	−24.0920	+	19.5093i	−0.942794	+	0.763459i	−0.971723	−	0.236122i	$-0.924124\pi$
$653$	−24.0920	+	19.5093i	−0.942794	+	0.763459i	0.0289295	+	0.999581i	$0.490790\pi$
$654$	27.7632	−	12.3610i	1.08563	−	0.483352i
$655$	−9.30234	+	8.28675i	−0.363472	+	0.323790i
$656$	−17.2832	+	38.8188i	−0.674797	+	1.51562i
$657$	−4.92657	−	4.92657i	−0.192204	−	0.192204i
$658$	5.84971	−	9.34616i	0.228045	−	0.364351i
$659$	6.75492	−	2.19481i	0.263134	−	0.0854976i	−0.174479	−	0.984661i	$-0.555824\pi$
$659$	6.75492	−	2.19481i	0.263134	−	0.0854976i	0.437613	+	0.899163i	$0.355824\pi$
$660$	−1.66509	−	4.40759i	−0.0648135	−	0.171565i
$661$	3.56987	−	3.21432i	0.138852	−	0.125023i	−0.596778	−	0.802406i	$-0.703553\pi$
$661$	3.56987	−	3.21432i	0.138852	−	0.125023i	0.735630	+	0.677383i	$0.236886\pi$
$662$	13.6970	−	8.89494i	0.532349	−	0.345712i
$663$	−1.13592	−	21.6747i	−0.0441156	−	0.841775i
$664$	2.12387	−	6.53659i	0.0824220	−	0.253669i
$665$	−2.83448	−	44.3947i	−0.109916	−	1.72155i
$666$	1.09196	+	3.36069i	0.0423124	+	0.130224i
$667$	13.1597	−	5.05154i	0.509546	−	0.195596i
$668$	−2.25866	−	8.42942i	−0.0873901	−	0.326144i
$669$	25.3912	−	2.66872i	0.981679	−	0.103179i
$670$	−11.5764	−	1.27898i	−0.447235	−	0.0494112i
$671$	−10.5039	+	14.4574i	−0.405498	+	0.558120i
$672$	10.6303	+	10.2807i	0.410071	+	0.396585i
$673$	−11.7311	+	5.97729i	−0.452201	+	0.230408i	−0.665231	−	0.746638i	$-0.731667\pi$
$673$	−11.7311	+	5.97729i	−0.452201	+	0.230408i	0.213030	+	0.977046i	$0.431667\pi$
$674$	−35.3100	+	20.3863i	−1.36009	+	0.785249i
$675$	−19.6674	−	7.79050i	−0.756999	−	0.299857i
$676$	−2.12143	+	3.67442i	−0.0815934	+	0.141324i
$677$	39.7955	+	25.8435i	1.52947	+	0.993247i	0.988333	+	0.152311i	$0.0486714\pi$
$677$	39.7955	+	25.8435i	1.52947	+	0.993247i	0.541134	+	0.840937i	$0.317995\pi$
$678$	−28.1453	+	4.45777i	−1.08091	+	0.171200i
$679$	−4.33196	+	7.80151i	−0.166245	+	0.299394i
$680$	−25.4028	+	8.10485i	−0.974154	+	0.310807i
$681$	5.54570	+	2.46911i	0.212512	+	0.0946164i
$682$	−20.2758	+	5.43288i	−0.776400	+	0.208036i
$683$	−11.2348	+	13.8738i	−0.429886	+	0.530865i	−0.945355	−	0.326043i	$-0.894284\pi$
$683$	−11.2348	+	13.8738i	−0.429886	+	0.530865i	0.515469	+	0.856908i	$0.327618\pi$
$684$	2.18453	−	2.42617i	0.0835277	−	0.0927669i
$685$	20.0738	−	3.07009i	0.766981	−	0.117302i
$686$	15.9453	+	24.6729i	0.608796	+	0.942017i
$687$	0.932248	+	0.475004i	0.0355675	+	0.0181225i
$688$	6.63863	−	0.347916i	0.253095	−	0.0132642i
$689$	13.5103	+	15.0048i	0.514703	+	0.571636i
$690$	5.07250	−	13.0072i	0.193107	−	0.495177i
$691$	−5.84754	−	5.26515i	−0.222451	−	0.200296i	0.550368	−	0.834922i	$-0.314487\pi$
$691$	−5.84754	−	5.26515i	−0.222451	−	0.200296i	−0.772819	+	0.634626i	$0.781154\pi$
$692$	9.55468	+	1.51331i	0.363214	+	0.0575275i
$693$	−2.85770	+	3.65214i	−0.108555	+	0.138733i
$694$	4.25473	+	5.85614i	0.161507	+	0.222296i
$695$	26.8154	−	29.4650i	1.01716	−	1.11767i
$696$	13.1700	+	29.5804i	0.499209	+	1.12124i
$697$	16.1873	−	42.1694i	0.613139	−	1.59728i
$698$	−30.6001	+	47.1199i	−1.15823	+	1.78352i
$699$	48.6441			1.83989
$700$	−6.06374	+	3.13625i	−0.229188	+	0.118539i
$701$	21.0860			0.796406			0.398203	−	0.917297i	$-0.369634\pi$
$701$	21.0860			0.796406			0.398203	+	0.917297i	$0.369634\pi$
$702$	7.98974	−	12.3031i	0.301553	−	0.464351i
$703$	7.13514	−	18.5877i	0.269107	−	0.701047i
$704$	4.24346	+	9.53096i	0.159931	+	0.359212i
$705$	1.26440	−	11.4445i	0.0476201	−	0.431023i
$706$	−9.96981	−	13.7223i	−0.375219	−	0.516444i
$707$	2.80922	+	6.96785i	0.105652	+	0.262053i
$708$	−10.5117	−	1.66489i	−0.395054	−	0.0625703i
$709$	2.13303	+	1.92059i	0.0801077	+	0.0721293i	0.708212	−	0.706000i	$-0.249502\pi$
$709$	2.13303	+	1.92059i	0.0801077	+	0.0721293i	−0.628104	+	0.778129i	$0.716169\pi$
$710$	23.7020	+	1.36854i	0.889519	+	0.0513604i
$711$	1.50398	+	1.67034i	0.0564038	+	0.0626427i
$712$	−29.7654	+	1.55994i	−1.11550	+	0.0584611i
$713$	−11.3671	−	5.79180i	−0.425699	−	0.216905i
$714$	−31.4284	−	27.3609i	−1.17618	−	1.02396i
$715$	1.64639	−	10.0489i	0.0615714	−	0.375806i
$716$	−3.38719	+	3.76186i	−0.126585	+	0.140587i
$717$	33.6497	−	41.5539i	1.25667	−	1.55186i
$718$	5.84827	−	1.56704i	0.218256	−	0.0584814i
$719$	5.18872	+	2.31017i	0.193507	+	0.0861547i	0.501202	−	0.865330i	$-0.332891\pi$
$719$	5.18872	+	2.31017i	0.193507	+	0.0861547i	−0.307696	+	0.951485i	$0.599558\pi$
$720$	8.51216	+	2.81588i	0.317230	+	0.104942i
$721$	0.322778	+	19.3073i	0.0120209	+	0.719040i
$722$	−58.8143	+	9.31526i	−2.18884	+	0.346678i
$723$	−31.4640	−	20.4330i	−1.17016	−	0.759911i
$724$	−0.216584	+	0.375135i	−0.00804929	+	0.0139418i
$725$	−34.9381	+	3.29701i	−1.29757	+	0.122448i
$726$	−17.9310	+	10.3525i	−0.665481	+	0.384216i
$727$	−37.1735	+	18.9408i	−1.37869	+	0.702477i	−0.976988	−	0.213294i	$-0.931581\pi$
$727$	−37.1735	+	18.9408i	−1.37869	+	0.702477i	−0.401701	+	0.915771i	$0.631581\pi$
$728$	3.74270	+	13.0887i	0.138714	+	0.485100i
$729$	9.27315	−	12.7634i	0.343450	−	0.472718i
$730$	25.5147	−	14.5506i	0.944342	−	0.538543i
$731$	−7.02785	+	0.738657i	−0.259934	+	0.0273202i
$732$	2.24553	+	8.38045i	0.0829973	+	0.309750i
$733$	−32.2848	+	12.3930i	−1.19247	+	0.457745i	−0.871996	−	0.489513i	$-0.837175\pi$
$733$	−32.2848	+	12.3930i	−1.19247	+	0.457745i	−0.320471	+	0.947258i	$0.603841\pi$
$734$	4.08138	+	12.5612i	0.150647	+	0.463642i
$735$	26.1881	+	15.9784i	0.965964	+	0.589372i
$736$	1.76991	−	5.44722i	0.0652397	−	0.200787i
$737$	−0.358021	−	6.83146i	−0.0131879	−	0.251640i
$738$	−9.97924	+	6.48059i	−0.367341	+	0.238554i
$739$	6.17964	−	5.56417i	0.227322	−	0.204681i	−0.547597	−	0.836742i	$-0.684457\pi$
$739$	6.17964	−	5.56417i	0.227322	−	0.204681i	0.774919	+	0.632061i	$0.217791\pi$
$740$	−3.05207	+	0.143688i	−0.112196	+	0.00528209i
$741$	30.6384	−	9.95501i	1.12553	−	0.365706i
$742$	38.7393	+	1.38139i	1.42216	+	0.0507123i
$743$	10.0390	+	10.0390i	0.368295	+	0.368295i	0.866855	−	0.498560i	$-0.166138\pi$
$743$	10.0390	+	10.0390i	0.368295	+	0.368295i	−0.498560	+	0.866855i	$0.666138\pi$
$744$	11.9195	−	26.7717i	0.436991	−	0.981498i
$745$	−32.5731	+	3.24861i	−1.19339	+	0.119020i
$746$	25.2590	−	11.2460i	0.924797	−	0.411746i
$747$	1.90915	−	1.54600i	0.0698521	−	0.0565651i
$748$	2.47264	+	4.85283i	0.0904086	+	0.177437i
$749$	−18.4447	−	24.5145i	−0.673954	−	0.895740i
$750$	−20.8761	+	27.7906i	−0.762288	+	1.01477i
$751$	19.9959	+	34.6339i	0.729661	+	1.26381i	0.957026	+	0.290000i	$0.0936555\pi$
$751$	19.9959	+	34.6339i	0.729661	+	1.26381i	−0.227365	+	0.973810i	$0.573011\pi$
$752$	0.655299	−	12.5039i	0.0238963	−	0.455968i
$753$	−13.7179	−	5.26582i	−0.499909	−	0.191897i
$754$	2.54383	−	24.2029i	0.0926407	−	0.881417i
$755$	29.2466	−	21.0123i	1.06439	−	0.764715i
$756$	−1.29531	−	5.62951i	−0.0471098	−	0.204743i
$757$	12.1964	−	12.1964i	0.443287	−	0.443287i	−0.449828	−	0.893115i	$-0.648515\pi$
$757$	12.1964	−	12.1964i	0.443287	−	0.443287i	0.893115	+	0.449828i	$0.148515\pi$
$758$	−6.20578	−	16.1666i	−0.225404	−	0.587198i
$759$	8.02106	+	1.70493i	0.291146	+	0.0618850i
$760$	−21.3785	−	33.3062i	−0.775478	−	1.20814i
$761$	−2.08132	−	9.79185i	−0.0754479	−	0.354954i	0.924188	−	0.381938i	$-0.124743\pi$
$761$	−2.08132	−	9.79185i	−0.0754479	−	0.354954i	−0.999636	+	0.0269835i	$0.991410\pi$
$762$	3.46873	−	6.80777i	0.125659	−	0.246619i
$763$	19.8248	−	16.6101i	0.717707	−	0.601327i
$764$	1.33536	+	0.433884i	0.0483116	+	0.0156974i
$765$	−9.19270	−	2.51563i	−0.332363	−	0.0909526i
$766$	−5.47227	+	25.7450i	−0.197721	+	0.930205i
$767$	−17.8753	−	14.4752i	−0.645441	−	0.522668i
$768$	22.0205	+	5.90038i	0.794597	+	0.212912i
$769$	−33.7752	+	24.5391i	−1.21796	+	0.884902i	−0.995929	−	0.0901368i	$-0.971270\pi$
$769$	−33.7752	+	24.5391i	−1.21796	+	0.884902i	−0.222034	+	0.975039i	$0.571270\pi$
$770$	−11.6706	−	15.6840i	−0.420580	−	0.565213i
$771$	−21.7061	−	15.7704i	−0.781728	−	0.567959i
$772$	2.27654	+	2.81129i	0.0819345	+	0.101181i
$773$	28.5404	+	1.49574i	1.02653	+	0.0537980i	0.558158	−	0.829735i	$-0.311508\pi$
$773$	28.5404	+	1.49574i	1.02653	+	0.0537980i	0.468370	+	0.883533i	$0.344842\pi$
$774$	1.61213	+	0.930761i	0.0579466	+	0.0334555i
$775$	23.3759	+	21.5021i	0.839688	+	0.772379i
$776$			7.93899i			0.284993i
$777$	7.66955	+	11.3887i	0.275143	+	0.408566i
$778$	4.77008	+	30.1171i	0.171016	+	1.07975i
$779$	66.6762	+	7.00795i	2.38892	+	0.251086i
$780$	−3.28847	−	3.69149i	−0.117746	−	0.132177i
$781$	1.45762	+	13.8683i	0.0521576	+	0.496246i
$782$	−4.17702	+	15.5888i	−0.149370	+	0.557456i
$783$	4.64530	−	29.3293i	0.166009	−	1.04814i
$784$	29.4325	+	15.7052i	1.05116	+	0.560902i
$785$	9.47849	+	1.55294i	0.338302	+	0.0554267i
$786$	−16.9423	+	3.60119i	−0.604311	+	0.128450i
$787$	−18.8075	−	28.9611i	−0.670416	−	1.03235i	−0.996216	−	0.0869114i	$-0.972300\pi$
$787$	−18.8075	−	28.9611i	−0.670416	−	1.03235i	0.325800	−	0.945439i	$-0.394366\pi$
$788$	−4.16586	−	6.41486i	−0.148403	−	0.228520i
$789$	37.5120	−	7.97342i	1.33546	−	0.283861i
$790$	−8.46559	+	4.25690i	−0.301192	+	0.151454i
$791$	−21.9866	+	10.2328i	−0.781753	+	0.363836i
$792$	−0.645396	+	4.07487i	−0.0229332	+	0.144794i
$793$	−4.85309	+	18.1120i	−0.172338	+	0.643175i
$794$	0.201724	+	1.91927i	0.00715891	+	0.0681125i
$795$	37.0676	−	16.2680i	1.31465	−	0.576968i
$796$	−10.7852	−	1.13357i	−0.382271	−	0.0401783i
$797$	−7.35212	−	46.4194i	−0.260425	−	1.64426i	−0.677597	−	0.735433i	$-0.736979\pi$
$797$	−7.35212	−	46.4194i	−0.260425	−	1.64426i	0.417172	−	0.908828i	$-0.363021\pi$
$798$	27.1537	−	55.5693i	0.961230	−	1.96713i
$799$			13.3099i			0.470869i
$800$	−7.89288	+	11.8756i	−0.279055	+	0.419867i
$801$	−9.22634	−	5.32683i	−0.325997	−	0.188214i
$802$	−7.51383	−	0.393783i	−0.265322	−	0.0139050i
$803$	10.8570	+	13.4072i	0.383134	+	0.473131i
$804$	−2.68694	−	1.95218i	−0.0947612	−	0.0688480i
$805$	1.10717	−	11.8299i	0.0390225	−	0.416948i
$806$	−17.8190	+	12.9462i	−0.627646	+	0.456012i
$807$	−17.4810	−	4.68401i	−0.615359	−	0.164885i
$808$	5.19439	+	4.20634i	0.182738	+	0.147978i
$809$	−6.74211	+	31.7191i	−0.237040	+	1.11519i	0.685136	+	0.728415i	$0.259743\pi$
$809$	−6.74211	+	31.7191i	−0.237040	+	1.11519i	−0.922176	+	0.386770i	$0.873591\pi$
$810$	−23.9841	−	29.9420i	−0.842716	−	1.05205i
$811$	8.85993	+	2.87877i	0.311114	+	0.101087i	0.460413	−	0.887705i	$-0.347701\pi$
$811$	8.85993	+	2.87877i	0.311114	+	0.101087i	−0.149298	+	0.988792i	$0.547701\pi$
$812$	−6.15442	−	7.34554i	−0.215978	−	0.257778i
$813$	−0.984289	+	1.93178i	−0.0345205	+	0.0677503i
$814$	−1.81919	−	8.55862i	−0.0637626	−	0.299980i
$815$	31.7776	+	12.3925i	1.11312	+	0.434090i
$816$	−46.2862	−	9.83843i	−1.62034	−	0.344414i
$817$	−3.75879	−	9.79198i	−0.131503	−	0.342578i
$818$	−27.8073	+	27.8073i	−0.972258	+	0.972258i
$819$	−1.42606	+	4.65216i	−0.0498305	+	0.162560i
$820$	−3.12731	−	9.80185i	−0.109210	−	0.342296i
$821$	3.88835	−	36.9952i	0.135704	−	1.29114i	−0.688661	−	0.725083i	$-0.741801\pi$
$821$	3.88835	−	36.9952i	0.135704	−	1.29114i	0.824366	−	0.566058i	$-0.191532\pi$
$822$	26.3584	+	10.1180i	0.919354	+	0.352907i
$823$	−1.56075	+	29.7808i	−0.0544042	+	1.03809i	0.825940	+	0.563758i	$0.190645\pi$
$823$	−1.56075	+	29.7808i	−0.0544042	+	1.03809i	−0.880344	+	0.474335i	$0.842688\pi$
$824$	8.58974	+	14.8779i	0.299238	+	0.518295i
$825$	−18.0907	−	9.46125i	−0.629837	−	0.329399i
$826$	−43.8342	+	5.34938i	−1.52519	+	0.186129i
$827$	13.1390	+	25.7867i	0.456887	+	0.896691i	0.998430	+	0.0560176i	$0.0178403\pi$
$827$	13.1390	+	25.7867i	0.456887	+	0.896691i	−0.541543	+	0.840673i	$0.682160\pi$
$828$	0.677656	−	0.548755i	0.0235502	−	0.0190706i
$829$	8.61441	−	3.83538i	0.299191	−	0.133208i	−0.251651	−	0.967818i	$-0.580973\pi$
$829$	8.61441	−	3.83538i	0.299191	−	0.133208i	0.550842	+	0.834610i	$0.314307\pi$
$830$	4.16201	+	9.48338i	0.144466	+	0.329173i
$831$	15.4978	−	34.8087i	0.537614	−	1.20750i
$832$	7.74074	+	7.74074i	0.268362	+	0.268362i
$833$	−32.1177	−	15.0344i	−1.11281	−	0.520911i
$834$	52.6799	−	17.1167i	1.82416	−	0.592704i
$835$	−31.6028	−	20.7627i	−1.09366	−	0.718524i
$836$	−6.00756	+	5.40923i	−0.207776	+	0.187082i
$837$	−22.5395	+	14.6373i	−0.779080	+	0.505940i
$838$	−2.02120	−	38.5668i	−0.0698212	−	1.33227i
$839$	−16.9096	+	52.0423i	−0.583784	+	1.79670i	0.0203179	+	0.999794i	$0.493532\pi$
$839$	−16.9096	+	52.0423i	−0.583784	+	1.79670i	−0.604101	+	0.796907i	$0.706468\pi$
$840$	27.2702	+	1.11759i	0.940911	+	0.0385604i
$841$	−6.26123	−	19.2701i	−0.215905	−	0.664486i
$842$	10.9841	−	4.21641i	0.378538	−	0.145307i
$843$	−0.870306	−	3.24803i	−0.0299749	−	0.111868i
$844$	12.8131	−	1.34671i	0.441044	−	0.0463556i
$845$	3.72666	+	18.0026i	0.128201	+	0.619307i
$846$	2.06088	−	2.83656i	0.0708544	−	0.0975228i
$847$	−12.2496	+	12.6662i	−0.420903	+	0.435215i
$848$	39.2224	−	19.9848i	1.34690	−	0.686282i
$849$	−44.8078	+	25.8698i	−1.53780	+	0.887849i
$850$	20.4583	−	34.5806i	0.701715	−	1.18610i
$851$	2.65890	−	4.60535i	0.0911460	−	0.157870i
$852$	5.67796	+	3.68731i	0.194524	+	0.126325i
$853$	−57.0510	+	9.03599i	−1.95339	+	0.309386i	−0.953419	+	0.301650i	$0.902462\pi$
$853$	−57.0510	+	9.03599i	−1.95339	+	0.309386i	−0.999970	+	0.00773601i	$0.997538\pi$
$854$	18.5183	+	30.8711i	0.633682	+	1.05639i
$855$	0.0751944	−	14.1459i	0.00257159	−	0.483778i
$856$	−24.9340	−	11.1013i	−0.852226	−	0.379436i
$857$	−13.6104	+	3.64690i	−0.464923	+	0.124576i	−0.483674	−	0.875248i	$-0.660698\pi$
$857$	−13.6104	+	3.64690i	−0.464923	+	0.124576i	0.0187505	+	0.999824i	$0.494031\pi$
$858$	8.90958	−	11.0024i	0.304168	−	0.375616i
$859$	−14.0269	+	15.5785i	−0.478592	+	0.531530i	−0.933294	−	0.359113i	$-0.883079\pi$
$859$	−14.0269	+	15.5785i	−0.478592	+	0.531530i	0.454702	+	0.890644i	$0.349746\pi$
$860$	−1.14420	+	1.13210i	−0.0390169	+	0.0386043i
$861$	−30.3583	+	34.8713i	−1.03461	+	1.18841i
$862$	25.5128	+	12.9994i	0.868971	+	0.442763i
$863$	−15.2735	+	0.800451i	−0.519916	+	0.0272477i	−0.310490	−	0.950577i	$-0.600493\pi$
$863$	−15.2735	+	0.800451i	−0.519916	+	0.0272477i	−0.209427	+	0.977824i	$0.567160\pi$
$864$	−8.07357	−	8.96661i	−0.274669	−	0.305050i
$865$	35.2749	−	22.6421i	1.19938	−	0.769855i
$866$	−29.7563	−	26.7927i	−1.01116	−	0.910452i
$867$	16.7735	+	2.65667i	0.569659	+	0.0902252i
$868$	−1.21339	+	8.58779i	−0.0411851	+	0.291489i
$869$	−3.27136	−	4.50263i	−0.110973	−	0.152741i
$870$	−44.4669	−	20.0818i	−1.50757	−	0.680837i
$871$	−2.91953	−	6.55737i	−0.0989245	−	0.222188i
$872$	8.24602	−	21.4816i	0.279246	−	0.727460i
$873$	−1.54549	+	2.37985i	−0.0523069	+	0.0805456i
$874$	−23.9541			−0.810261
$875$	−10.5794	+	27.6238i	−0.357649	+	0.933856i
$876$	8.37585			0.282994
$877$	8.15148	−	12.5522i	0.275256	−	0.423857i	−0.673824	−	0.738892i	$-0.735350\pi$
$877$	8.15148	−	12.5522i	0.275256	−	0.423857i	0.949080	+	0.315035i	$0.102016\pi$
$878$	−15.8568	+	41.3083i	−0.535140	+	1.39409i
$879$	−4.89045	−	10.9841i	−0.164951	−	0.370486i
$880$	−20.2331	−	9.13753i	−0.682058	−	0.308026i
$881$	10.0697	+	13.8597i	0.339257	+	0.466947i	0.944224	−	0.329303i	$-0.106814\pi$
$881$	10.0697	+	13.8597i	0.339257	+	0.466947i	−0.604967	+	0.796250i	$0.706814\pi$
$882$	4.51692	+	8.17714i	0.152093	+	0.275339i
$883$	26.9691	+	4.27148i	0.907581	+	0.143747i	0.592736	−	0.805397i	$-0.298048\pi$
$883$	26.9691	+	4.27148i	0.907581	+	0.143747i	0.314845	+	0.949143i	$0.398048\pi$
$884$	4.24696	+	3.82398i	0.142841	+	0.128614i
$885$	−38.8081	+	24.9100i	−1.30452	+	0.837340i
$886$	−32.5015	−	36.0966i	−1.09191	−	1.21269i
$887$	−31.6840	+	1.66049i	−1.06384	+	0.0557537i	−0.576216	−	0.817298i	$-0.695471\pi$
$887$	−31.6840	+	1.66049i	−1.06384	+	0.0557537i	−0.487628	+	0.873051i	$0.662138\pi$
$888$	10.8841	+	5.54572i	0.365246	+	0.186102i
$889$	1.24541	−	6.38199i	0.0417698	−	0.214045i
$890$	31.9268	−	31.5892i	1.07019	−	1.05887i
$891$	15.0775	−	16.7453i	0.505117	−	0.560989i
$892$	−4.23055	+	5.22429i	−0.141649	+	0.174922i
$893$	−19.0822	+	5.11306i	−0.638561	+	0.171102i
$894$	−41.5772	−	18.5114i	−1.39055	−	0.619112i
$895$	−0.116591	+	21.9336i	−0.00389722	+	0.733161i
$896$	36.1025	−	0.603560i	1.20610	−	0.0201635i
$897$	8.49842	−	1.34602i	0.283754	−	0.0449422i
$898$	−40.4711	−	26.2822i	−1.35054	−	0.877050i
$899$	−22.2922	+	38.6112i	−0.743485	+	1.28775i
$900$	−1.99248	+	0.861846i	−0.0664160	+	0.0287282i
$901$	−40.5246	+	23.3969i	−1.35007	+	0.779463i
$902$	26.2521	−	13.3761i	0.874099	−	0.445376i
$903$	7.01702	+	1.75503i	0.233512	+	0.0584038i
$904$	−12.6818	+	17.4550i	−0.421790	+	0.580544i
$905$	0.380468	+	1.83795i	0.0126472	+	0.0610954i
$906$	49.7944	−	5.23360i	1.65431	−	0.173875i
$907$	−3.31110	−	12.3572i	−0.109943	−	0.410314i	0.888916	−	0.458071i	$-0.151459\pi$
$907$	−3.31110	−	12.3572i	−0.109943	−	0.410314i	−0.998859	+	0.0477567i	$0.984793\pi$
$908$	−1.49223	+	0.572812i	−0.0495212	+	0.0190094i
$909$	0.738256	+	2.27212i	0.0244864	+	0.0753614i
$910$	−17.3300	−	10.9754i	−0.574484	−	0.363831i
$911$	−2.87409	+	8.84554i	−0.0952228	+	0.293066i	−0.987312	−	0.158794i	$-0.949239\pi$
$911$	−2.87409	+	8.84554i	−0.0952228	+	0.293066i	0.892089	+	0.451860i	$0.149239\pi$
$912$	−3.67585	−	70.1394i	−0.121720	−	2.32255i
$913$	−5.10159	+	3.31301i	−0.168838	+	0.109645i
$914$	47.5847	−	42.8454i	1.57396	−	1.41720i
$915$	31.4191	+	20.6421i	1.03868	+	0.682407i
$916$	−0.262007	+	0.0851313i	−0.00865696	+	0.00281282i
$917$	−13.0203	+	6.91070i	−0.429967	+	0.228211i
$918$	24.0404	+	24.0404i	0.793450	+	0.793450i
$919$	19.7932	−	44.4563i	0.652917	−	1.46648i	−0.218451	−	0.975848i	$-0.570101\pi$
$919$	19.7932	−	44.4563i	0.652917	−	1.46648i	0.871369	−	0.490629i	$-0.163233\pi$
$920$	−4.24808	−	9.67950i	−0.140055	−	0.319124i
$921$	−31.7969	+	14.1569i	−1.04774	+	0.466485i
$922$	22.0246	−	17.8352i	0.725343	−	0.587371i
$923$	6.64272	+	13.0371i	0.218648	+	0.429121i
$924$	−0.675327	−	5.53381i	−0.0222166	−	0.182049i
$925$	−9.46054	+	9.26150i	−0.311061	+	0.304516i
$926$	−27.1322	−	46.9943i	−0.891619	−	1.54433i
$927$	−0.321368	+	6.13206i	−0.0105551	+	0.201403i
$928$	−18.6868	−	7.17320i	−0.613425	−	0.235472i
$929$	−0.0493594	+	0.469623i	−0.00161943	+	0.0154078i	−0.995302	−	0.0968214i	$-0.969132\pi$
$929$	−0.0493594	+	0.469623i	−0.00161943	+	0.0154078i	0.993682	+	0.112229i	$0.0357991\pi$
$930$	13.4223	+	42.0691i	0.440134	+	1.37950i
$931$	9.21644	−	51.8223i	0.302057	−	1.69841i
$932$	−9.05674	+	9.05674i	−0.296663	+	0.296663i
$933$	4.46688	+	11.6366i	0.146239	+	0.380966i
$934$	−10.3605	−	2.20220i	−0.339007	−	0.0720582i
$935$	21.9867	+	8.57427i	0.719042	+	0.280409i
$936$	0.900044	+	4.23437i	0.0294189	+	0.138405i
$937$	15.7304	−	30.8727i	0.513890	−	1.00857i	−0.477624	−	0.878565i	$-0.658502\pi$
$937$	15.7304	−	30.8727i	0.513890	−	1.00857i	0.991514	−	0.130002i	$-0.0414983\pi$
$938$	−12.9462	−	4.72282i	−0.422707	−	0.154206i
$939$	−14.2378	−	4.62615i	−0.464634	−	0.150969i
$940$	1.89536	+	2.36618i	0.0618198	+	0.0771763i
$941$	2.33096	−	10.9663i	0.0759873	−	0.357492i	−0.923683	−	0.383157i	$-0.874837\pi$
$941$	2.33096	−	10.9663i	0.0759873	−	0.357492i	0.999671	+	0.0256647i	$0.00817023\pi$
$942$	10.3779	+	8.40387i	0.338131	+	0.273813i
$943$	17.2966	+	4.63460i	0.563253	+	0.150923i
$944$	−40.5702	+	29.4760i	−1.32045	+	0.959362i
$945$	−20.4161	−	14.4804i	−0.664135	−	0.471048i
$946$	−3.72909	−	2.70934i	−0.121243	−	0.0880883i
$947$	36.0736	+	44.5472i	1.17224	+	1.44759i	0.869096	+	0.494644i	$0.164701\pi$
$947$	36.0736	+	44.5472i	1.17224	+	1.44759i	0.303139	+	0.952946i	$0.401965\pi$
$948$	−2.69839	−	0.141417i	−0.0876398	−	0.00459301i
$949$	15.6768	+	9.05102i	0.508892	+	0.293809i
$950$	57.4369	+	16.0465i	1.86350	+	0.520618i
$951$			27.6599i			0.896934i
$952$	−31.4745	+	2.17761i	−1.02010	+	0.0705767i
$953$	−2.70486	−	17.0778i	−0.0876189	−	0.553204i	−0.991976	−	0.126427i	$-0.959649\pi$
$953$	−2.70486	−	17.0778i	−0.0876189	−	0.553204i	0.904357	−	0.426777i	$-0.140351\pi$
$954$	12.2592	+	1.28849i	0.396906	+	0.0417165i
$955$	5.57096	−	2.44495i	0.180272	−	0.0791167i
$956$	1.47163	+	14.0017i	0.0475960	+	0.452846i
$957$	7.41718	−	27.6813i	0.239764	−	0.894810i
$958$	−1.25679	+	7.93504i	−0.0406050	+	0.256370i
$959$	23.9349	+	2.11180i	0.772897	+	0.0681937i
$960$	19.6081	−	9.85989i	0.632849	−	0.318227i
$961$	9.14667	−	1.94419i	0.295054	−	0.0627156i
$962$	−5.00034	−	7.69984i	−0.161217	−	0.248253i
$963$	−5.31328	−	8.18173i	−0.171218	−	0.263653i
$964$	9.66237	−	2.05380i	0.311204	−	0.0661484i
$965$	15.4682	+	2.53428i	0.497938	+	0.0815812i
$966$	9.48502	−	13.5248i	0.305175	−	0.435153i
$967$	−2.21053	+	13.9567i	−0.0710859	+	0.448819i	0.926314	+	0.376753i	$0.122959\pi$
$967$	−2.21053	+	13.9567i	−0.0710859	+	0.448819i	−0.997400	+	0.0720662i	$0.977041\pi$
$968$	−4.05738	+	15.1423i	−0.130409	+	0.486693i
$969$	7.80416	+	74.2516i	0.250706	+	2.38531i
$970$	−7.95731	−	8.93252i	−0.255494	−	0.286806i
$971$	−10.3623	−	1.08912i	−0.332542	−	0.0349516i	−0.0632139	−	0.998000i	$-0.520135\pi$
$971$	−10.3623	−	1.08912i	−0.332542	−	0.0349516i	−0.269328	+	0.963048i	$0.586802\pi$
$972$	−0.686717	−	4.33576i	−0.0220265	−	0.139070i
$973$	39.1000	−	26.3314i	1.25349	−	0.844144i
$974$			29.8245i			0.955640i
$975$	−21.2791	−	2.46551i	−0.681476	−	0.0789594i
$976$	35.4039	+	20.4405i	1.13325	+	0.654283i
$977$	−24.8821	−	1.30401i	−0.796048	−	0.0417191i	−0.350025	−	0.936740i	$-0.613827\pi$
$977$	−24.8821	−	1.30401i	−0.796048	−	0.0417191i	−0.446023	+	0.895021i	$0.647160\pi$
$978$	29.8436	+	36.8537i	0.954292	+	1.17845i
$979$	21.3419	+	15.5058i	0.682091	+	0.495568i
$980$	−7.85071	+	1.90088i	−0.250782	+	0.0607215i
$981$	6.65373	−	4.83422i	0.212437	−	0.154345i
$982$	40.1972	+	10.7708i	1.28274	+	0.343710i
$983$	9.08311	+	7.35536i	0.289706	+	0.234600i	0.763145	−	0.646227i	$-0.223654\pi$
$983$	9.08311	+	7.35536i	0.289706	+	0.234600i	−0.473439	+	0.880827i	$0.656987\pi$
$984$	−8.55212	+	40.2346i	−0.272632	+	1.28263i
$985$	−31.9670	−	8.74792i	−1.01855	−	0.278732i
$986$	53.6403	+	17.4288i	1.70826	+	0.555046i
$987$	4.66900	−	12.7986i	0.148616	−	0.407384i
$988$	−3.85090	+	7.55782i	−0.122513	+	0.240446i
$989$	−0.582448	−	2.74020i	−0.0185208	−	0.0871333i
$990$	−3.35811	−	5.23171i	−0.106728	−	0.166275i
$991$	10.5500	+	2.24247i	0.335132	+	0.0712345i	0.372404	−	0.928071i	$-0.378533\pi$
$991$	10.5500	+	2.24247i	0.335132	+	0.0712345i	−0.0372721	+	0.999305i	$0.511867\pi$
$992$	6.49210	+	16.9125i	0.206124	+	0.536972i
$993$	14.2692	−	14.2692i	0.452820	−	0.452820i
$994$	26.8577	+	8.23288i	0.851876	+	0.261131i
$995$	−38.1616	+	27.4173i	−1.20981	+	0.869187i
$996$	−0.308703	+	2.93711i	−0.00978162	+	0.0930659i
$997$	−11.5636	−	4.43884i	−0.366222	−	0.140580i	0.168296	−	0.985737i	$-0.446174\pi$
$997$	−11.5636	−	4.43884i	−0.366222	−	0.140580i	−0.534518	+	0.845157i	$0.679507\pi$
$998$	−0.250926	+	4.78795i	−0.00794293	+	0.151560i
$999$	−5.60130	−	9.70173i	−0.177217	−	0.306949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.3.5	✓	288
5.2	odd	4		875.2.bb.b.507.5		288
5.3	odd	4		875.2.bb.a.507.14		288
5.4	even	2		875.2.bb.c.493.14		288
7.5	odd	6	inner	175.2.x.a.103.14	yes	288
25.6	even	5		875.2.bb.b.143.5		288
25.8	odd	20		875.2.bb.c.857.5		288
25.17	odd	20	inner	175.2.x.a.17.14	yes	288
25.19	even	10		875.2.bb.a.143.14		288
35.12	even	12		875.2.bb.b.257.5		288
35.19	odd	6		875.2.bb.c.243.5		288
35.33	even	12		875.2.bb.a.257.14		288
175.19	odd	30		875.2.bb.a.768.14		288
175.33	even	60		875.2.bb.c.607.14		288
175.117	even	60	inner	175.2.x.a.117.5	yes	288
175.131	odd	30		875.2.bb.b.768.5		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.5	✓	288	1.1	even	1	trivial
175.2.x.a.17.14	yes	288	25.17	odd	20	inner
175.2.x.a.103.14	yes	288	7.5	odd	6	inner
175.2.x.a.117.5	yes	288	175.117	even	60	inner
875.2.bb.a.143.14		288	25.19	even	10
875.2.bb.a.257.14		288	35.33	even	12
875.2.bb.a.507.14		288	5.3	odd	4
875.2.bb.a.768.14		288	175.19	odd	30
875.2.bb.b.143.5		288	25.6	even	5
875.2.bb.b.257.5		288	35.12	even	12
875.2.bb.b.507.5		288	5.2	odd	4
875.2.bb.b.768.5		288	175.131	odd	30
875.2.bb.c.243.5		288	35.19	odd	6
875.2.bb.c.493.14		288	5.4	even	2
875.2.bb.c.607.14		288	175.33	even	60
875.2.bb.c.857.5		288	25.8	odd	20

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.863911 + 1.33031i) q^{2} +(-0.702377 + 1.82975i) q^{3} +(-0.209899 - 0.471441i) q^{4} +(-2.03789 - 0.920336i) q^{5} +(-1.82734 - 2.51512i) q^{6} +(-2.08368 - 1.63042i) q^{7} +(-2.32486 - 0.368222i) q^{8} +(-0.625235 - 0.562964i) q^{9} +(2.98488 - 1.91592i) q^{10} +(1.39398 + 1.54818i) q^{11} +(1.01005 - 0.0529345i) q^{12} +(1.94768 + 0.992394i) q^{13} +(3.96908 - 1.36339i) q^{14} +(3.11535 - 3.08241i) q^{15} +(3.18894 - 3.54168i) q^{16} +(-3.18817 + 3.93706i) q^{17} +(1.28906 - 0.345403i) q^{18} +(-6.86927 - 3.05840i) q^{19} +(-0.00613384 + 1.15392i) q^{20} +(4.44680 - 2.66745i) q^{21} +(-3.26382 + 0.516939i) q^{22} +(-1.68435 - 1.09383i) q^{23} +(2.30669 - 3.99530i) q^{24} +(3.30596 + 3.75108i) q^{25} +(-3.00281 + 1.73368i) q^{26} +(-3.76970 + 1.92076i) q^{27} +(-0.331286 + 1.32456i) q^{28} +(-4.12547 + 5.67823i) q^{29} +(1.40916 + 6.80730i) q^{30} +(6.31745 - 0.663990i) q^{31} +(0.738117 + 2.75469i) q^{32} +(-3.81188 + 1.46324i) q^{33} +(-2.48320 - 7.64252i) q^{34} +(2.74576 + 5.24030i) q^{35} +(-0.134168 + 0.412927i) q^{36} +(0.138578 + 2.64422i) q^{37} +(10.0030 - 6.49605i) q^{38} +(-3.18385 + 2.86675i) q^{39} +(4.39892 + 2.89005i) q^{40} +(-8.47974 + 2.75523i) q^{41} +(-0.293115 + 8.22005i) q^{42} +(0.986332 + 0.986332i) q^{43} +(0.437278 - 0.982142i) q^{44} +(0.756041 + 1.72268i) q^{45} +(2.91025 - 1.29573i) q^{46} +(2.04177 - 1.65339i) q^{47} +(4.24056 + 8.32258i) q^{48} +(1.68344 + 6.79456i) q^{49} +(-7.84614 + 1.15734i) q^{50} +(-4.96456 - 8.59887i) q^{51} +(0.0590385 - 1.12652i) q^{52} +(8.62323 + 3.31015i) q^{53} +(0.701489 - 6.67422i) q^{54} +(-1.41594 - 4.43794i) q^{55} +(4.24391 + 4.55777i) q^{56} +(10.4209 - 10.4209i) q^{57} +(-3.98974 - 10.3936i) q^{58} +(-10.2924 - 2.18773i) q^{59} +(-2.10709 - 0.821712i) q^{60} +(1.78346 + 8.39053i) q^{61} +(-4.57440 + 8.97777i) q^{62} +(0.384920 + 2.19243i) q^{63} +(4.76284 + 1.54754i) q^{64} +(-3.05582 - 3.81491i) q^{65} +(1.34656 - 6.33508i) q^{66} +(-2.55191 - 2.06649i) q^{67} +(2.52529 + 0.676649i) q^{68} +(3.18448 - 2.31366i) q^{69} +(-9.34330 - 0.874447i) q^{70} +(5.41526 + 3.93442i) q^{71} +(1.24629 + 1.53904i) q^{72} +(8.26979 + 0.433401i) q^{73} +(-3.63734 - 2.10002i) q^{74} +(-9.18559 + 3.41443i) q^{75} +3.88041i q^{76} +(-0.380434 - 5.49868i) q^{77} +(-1.06309 - 6.71211i) q^{78} +(-2.65691 - 0.279252i) q^{79} +(-9.75824 + 4.28264i) q^{80} +(-1.13060 - 10.7569i) q^{81} +(3.66043 - 13.6609i) q^{82} +(-0.456772 + 2.88395i) q^{83} +(-2.19093 - 1.53651i) q^{84} +(10.1206 - 5.08910i) q^{85} +(-2.16423 + 0.460021i) q^{86} +(-7.49212 - 11.5369i) q^{87} +(-2.67075 - 4.11259i) q^{88} +(12.3861 - 2.63274i) q^{89} +(-2.94485 - 0.482478i) q^{90} +(-2.44033 - 5.24338i) q^{91} +(-0.162132 + 1.02366i) q^{92} +(-3.22229 + 12.0258i) q^{93} +(0.435611 + 4.14456i) q^{94} +(11.1840 + 12.5547i) q^{95} +(-5.55884 - 0.584258i) q^{96} +(-0.527619 - 3.33125i) q^{97} +(-10.4932 - 3.63040i) q^{98} -1.75274i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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