LMFDB - Embedded newform 990.2.o.a.659.49

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(329,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.329"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.o (of order $6$, degree $2$, 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			659.49
Character	$\chi$	$=$	990.659
Dual form			990.2.o.a.329.49

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.782108 + 1.54542i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.55321 + 1.60859i) q^{5} +(-1.45003 + 0.947315i) q^{6} +(0.781159 - 1.35301i) q^{7} +1.00000i q^{8} +(-1.77662 - 2.41736i) q^{9} +(0.540822 + 2.16968i) q^{10} +(-3.27747 - 0.508147i) q^{11} +(-1.72942 + 0.0953825i) q^{12} +(0.963278 + 1.66845i) q^{13} +(1.35301 - 0.781159i) q^{14} +(-3.70071 + 1.14226i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.99714i q^{17} +(-0.329913 - 2.98180i) q^{18} +8.51458i q^{19} +(-0.616475 + 2.14941i) q^{20} +(1.48001 + 2.26541i) q^{21} +(-2.58430 - 2.07880i) q^{22} +(-1.87842 - 3.25352i) q^{23} +(-1.54542 - 0.782108i) q^{24} +(-0.175105 + 4.99693i) q^{25} +1.92656i q^{26} +(5.12533 - 0.854971i) q^{27} +1.56232 q^{28} +(-1.40314 + 2.43031i) q^{29} +(-3.77604 - 0.861129i) q^{30} +(-2.55600 - 4.42712i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.34863 - 4.66762i) q^{33} +(-2.49857 + 4.32765i) q^{34} +(3.38973 - 0.844936i) q^{35} +(1.20519 - 2.74727i) q^{36} +8.22038i q^{37} +(-4.25729 + 7.37384i) q^{38} +(-3.33183 + 0.183760i) q^{39} +(-1.60859 + 1.55321i) q^{40} +(-3.08008 - 5.33486i) q^{41} +(0.149018 + 2.70191i) q^{42} +(2.57524 - 4.46044i) q^{43} +(-1.19866 - 3.09244i) q^{44} +(1.12909 - 6.61250i) q^{45} -3.75684i q^{46} +(4.50310 - 7.79960i) q^{47} +(-0.947315 - 1.45003i) q^{48} +(2.27958 + 3.94835i) q^{49} +(-2.65011 + 4.23992i) q^{50} +(-7.72265 - 3.90830i) q^{51} +(-0.963278 + 1.66845i) q^{52} -1.72928 q^{53} +(4.86615 + 1.82224i) q^{54} +(-4.27318 - 6.06135i) q^{55} +(1.35301 + 0.781159i) q^{56} +(-13.1586 - 6.65932i) q^{57} +(-2.43031 + 1.40314i) q^{58} +(5.43524 - 3.13803i) q^{59} +(-2.83958 - 2.63378i) q^{60} +(-1.87075 - 1.08008i) q^{61} -5.11200i q^{62} +(-4.65853 + 0.515429i) q^{63} -1.00000 q^{64} +(-1.18767 + 4.14096i) q^{65} +(5.23381 - 2.36796i) q^{66} +(-3.28496 + 1.89657i) q^{67} +(-4.32765 + 2.49857i) q^{68} +(6.49716 - 0.358337i) q^{69} +(3.35806 + 0.963129i) q^{70} -2.80687i q^{71} +(2.41736 - 1.77662i) q^{72} +12.2059 q^{73} +(-4.11019 + 7.11906i) q^{74} +(-7.58538 - 4.17875i) q^{75} +(-7.37384 + 4.25729i) q^{76} +(-3.24775 + 4.03749i) q^{77} +(-2.97733 - 1.50677i) q^{78} +(3.89217 + 2.24715i) q^{79} +(-2.16968 + 0.540822i) q^{80} +(-2.68728 + 8.58944i) q^{81} -6.16017i q^{82} +(10.7488 + 6.20584i) q^{83} +(-1.22190 + 2.41443i) q^{84} +(-8.03833 + 7.76158i) q^{85} +(4.46044 - 2.57524i) q^{86} +(-2.65844 - 4.06921i) q^{87} +(0.508147 - 3.27747i) q^{88} -9.55852i q^{89} +(4.28407 - 5.16205i) q^{90} +3.00989 q^{91} +(1.87842 - 3.25352i) q^{92} +(8.84081 - 0.487595i) q^{93} +(7.79960 - 4.50310i) q^{94} +(-13.6964 + 13.2249i) q^{95} +(-0.0953825 - 1.72942i) q^{96} +(-2.52109 - 1.45555i) q^{97} +4.55916i q^{98} +(4.59442 + 8.82560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.782108	+	1.54542i	−0.451550	+	0.892246i
$3$	−0.782108	+	1.54542i	−0.451550	+	0.892246i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.55321	+	1.60859i	0.694615	+	0.719382i
$5$	1.55321	+	1.60859i	0.694615	+	0.719382i
$6$	−1.45003	+	0.947315i	−0.591973	+	0.386740i
$7$	0.781159	−	1.35301i	0.295250	−	0.511389i	−0.679793	−	0.733404i	$-0.737930\pi$
$7$	0.781159	−	1.35301i	0.295250	−	0.511389i	0.975043	+	0.222016i	$0.0712636\pi$
$8$			1.00000i			0.353553i
$9$	−1.77662	−	2.41736i	−0.592205	−	0.805787i
$10$	0.540822	+	2.16968i	0.171023	+	0.686113i
$11$	−3.27747	−	0.508147i	−0.988193	−	0.153212i
$11$	−3.27747	−	0.508147i	−0.988193	−	0.153212i
$12$	−1.72942	+	0.0953825i	−0.499241	+	0.0275346i
$13$	0.963278	+	1.66845i	0.267165	+	0.462744i	0.968129	−	0.250453i	$-0.0805797\pi$
$13$	0.963278	+	1.66845i	0.267165	+	0.462744i	−0.700963	+	0.713197i	$0.747246\pi$
$14$	1.35301	−	0.781159i	0.361606	−	0.208774i
$15$	−3.70071	+	1.14226i	−0.955519	+	0.294930i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			4.99714i			1.21198i	0.795471	+	0.605992i	$0.207224\pi$
$17$			4.99714i			1.21198i	−0.795471	+	0.605992i	$0.792776\pi$
$18$	−0.329913	−	2.98180i	−0.0777613	−	0.702818i
$19$			8.51458i			1.95338i	0.214659	+	0.976689i	$0.431136\pi$
$19$			8.51458i			1.95338i	−0.214659	+	0.976689i	$0.568864\pi$
$20$	−0.616475	+	2.14941i	−0.137848	+	0.480622i
$21$	1.48001	+	2.26541i	0.322964	+	0.494353i
$22$	−2.58430	−	2.07880i	−0.550974	−	0.443202i
$23$	−1.87842	−	3.25352i	−0.391677	−	0.678405i	0.600994	−	0.799254i	$-0.294772\pi$
$23$	−1.87842	−	3.25352i	−0.391677	−	0.678405i	−0.992671	+	0.120849i	$0.961438\pi$
$24$	−1.54542	−	0.782108i	−0.315457	−	0.159647i
$25$	−0.175105	+	4.99693i	−0.0350210	+	0.999387i
$26$			1.92656i			0.377829i
$27$	5.12533	−	0.854971i	0.986371	−	0.164539i
$28$	1.56232			0.295250
$29$	−1.40314	+	2.43031i	−0.260557	+	0.451298i	−0.966390	−	0.257080i	$-0.917240\pi$
$29$	−1.40314	+	2.43031i	−0.260557	+	0.451298i	0.705833	+	0.708378i	$0.250573\pi$
$30$	−3.77604	−	0.861129i	−0.689407	−	0.157220i
$31$	−2.55600	−	4.42712i	−0.459071	−	0.795134i	0.539841	−	0.841767i	$-0.318484\pi$
$31$	−2.55600	−	4.42712i	−0.459071	−	0.795134i	−0.998912	+	0.0466325i	$0.985151\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.34863	−	4.66762i	0.582922	−	0.812528i
$34$	−2.49857	+	4.32765i	−0.428501	+	0.742185i
$35$	3.38973	−	0.844936i	0.572969	−	0.142820i
$36$	1.20519	−	2.74727i	0.200865	−	0.457879i
$37$			8.22038i			1.35142i	0.737167	+	0.675711i	$0.236163\pi$
$37$			8.22038i			1.35142i	−0.737167	+	0.675711i	$0.763837\pi$
$38$	−4.25729	+	7.37384i	−0.690623	+	1.19619i
$39$	−3.33183	+	0.183760i	−0.533520	+	0.0294251i
$40$	−1.60859	+	1.55321i	−0.254340	+	0.245583i
$41$	−3.08008	−	5.33486i	−0.481028	−	0.833166i	0.518735	−	0.854935i	$-0.326403\pi$
$41$	−3.08008	−	5.33486i	−0.481028	−	0.833166i	−0.999763	+	0.0217697i	$0.993070\pi$
$42$	0.149018	+	2.70191i	0.0229939	+	0.416913i
$43$	2.57524	−	4.46044i	0.392720	−	0.680211i	−0.600087	−	0.799934i	$-0.704868\pi$
$43$	2.57524	−	4.46044i	0.392720	−	0.680211i	0.992807	+	0.119724i	$0.0382009\pi$
$44$	−1.19866	−	3.09244i	−0.180705	−	0.466203i
$45$	1.12909	−	6.61250i	0.168315	−	0.985733i
$46$		−	3.75684i		−	0.553916i
$47$	4.50310	−	7.79960i	0.656845	−	1.13769i	−0.324583	−	0.945857i	$-0.605224\pi$
$47$	4.50310	−	7.79960i	0.656845	−	1.13769i	0.981428	−	0.191831i	$-0.0614426\pi$
$48$	−0.947315	−	1.45003i	−0.136733	−	0.209294i
$49$	2.27958	+	3.94835i	0.325654	+	0.564050i
$50$	−2.65011	+	4.23992i	−0.374782	+	0.599615i
$51$	−7.72265	−	3.90830i	−1.08139	−	0.547271i
$52$	−0.963278	+	1.66845i	−0.133583	+	0.231372i
$53$	−1.72928			−0.237534			−0.118767	−	0.992922i	$-0.537894\pi$
$53$	−1.72928			−0.237534			−0.118767	+	0.992922i	$0.537894\pi$
$54$	4.86615	+	1.82224i	0.662200	+	0.247975i
$55$	−4.27318	−	6.06135i	−0.576195	−	0.817312i
$56$	1.35301	+	0.781159i	0.180803	+	0.104387i
$57$	−13.1586	−	6.65932i	−1.74289	−	0.882048i
$58$	−2.43031	+	1.40314i	−0.319116	+	0.184242i
$59$	5.43524	−	3.13803i	0.707607	−	0.408537i	−0.102567	−	0.994726i	$-0.532706\pi$
$59$	5.43524	−	3.13803i	0.707607	−	0.408537i	0.810174	+	0.586189i	$0.199372\pi$
$60$	−2.83958	−	2.63378i	−0.366588	−	0.340019i
$61$	−1.87075	−	1.08008i	−0.239524	−	0.138290i	0.375434	−	0.926849i	$-0.377494\pi$
$61$	−1.87075	−	1.08008i	−0.239524	−	0.138290i	−0.614958	+	0.788560i	$0.710827\pi$
$62$		−	5.11200i		−	0.649225i
$63$	−4.65853	+	0.515429i	−0.586919	+	0.0649380i
$64$	−1.00000			−0.125000
$65$	−1.18767	+	4.14096i	−0.147313	+	0.513623i
$66$	5.23381	−	2.36796i	0.644237	−	0.291476i
$67$	−3.28496	+	1.89657i	−0.401322	+	0.231703i	−0.687054	−	0.726606i	$-0.741097\pi$
$67$	−3.28496	+	1.89657i	−0.401322	+	0.231703i	0.285732	+	0.958310i	$0.407763\pi$
$68$	−4.32765	+	2.49857i	−0.524804	+	0.302996i
$69$	6.49716	−	0.358337i	0.782166	−	0.0431386i
$70$	3.35806	+	0.963129i	0.401365	+	0.115116i
$71$		−	2.80687i		−	0.333114i	−0.986032	−	0.166557i	$-0.946735\pi$
$71$		−	2.80687i		−	0.333114i	0.986032	−	0.166557i	$-0.0532650\pi$
$72$	2.41736	−	1.77662i	0.284889	−	0.209376i
$73$	12.2059			1.42859			0.714297	−	0.699842i	$-0.246746\pi$
$73$	12.2059			1.42859			0.714297	+	0.699842i	$0.246746\pi$
$74$	−4.11019	+	7.11906i	−0.477800	+	0.827574i
$75$	−7.58538	−	4.17875i	−0.875885	−	0.482520i
$76$	−7.37384	+	4.25729i	−0.845837	+	0.488345i
$77$	−3.24775	+	4.03749i	−0.370115	+	0.460115i
$78$	−2.97733	−	1.50677i	−0.337116	−	0.170609i
$79$	3.89217	+	2.24715i	0.437904	+	0.252824i	0.702708	−	0.711478i	$-0.251974\pi$
$79$	3.89217	+	2.24715i	0.437904	+	0.252824i	−0.264804	+	0.964302i	$0.585307\pi$
$80$	−2.16968	+	0.540822i	−0.242578	+	0.0604657i
$81$	−2.68728	+	8.58944i	−0.298586	+	0.954383i
$82$		−	6.16017i		−	0.680277i
$83$	10.7488	+	6.20584i	1.17984	+	0.681179i	0.955977	−	0.293442i	$-0.0948007\pi$
$83$	10.7488	+	6.20584i	1.17984	+	0.681179i	0.223860	+	0.974621i	$0.428134\pi$
$84$	−1.22190	+	2.41443i	−0.133320	+	0.263436i
$85$	−8.03833	+	7.76158i	−0.871879	+	0.841862i
$86$	4.46044	−	2.57524i	0.480982	−	0.277695i
$87$	−2.65844	−	4.06921i	−0.285014	−	0.436265i
$88$	0.508147	−	3.27747i	0.0541687	−	0.349379i
$89$		−	9.55852i		−	1.01320i	−0.862181	−	0.506601i	$-0.830902\pi$
$89$		−	9.55852i		−	1.01320i	0.862181	−	0.506601i	$-0.169098\pi$
$90$	4.28407	−	5.16205i	0.451581	−	0.544128i
$91$	3.00989			0.315523
$92$	1.87842	−	3.25352i	0.195839	−	0.339203i
$93$	8.84081	−	0.487595i	0.916749	−	0.0505613i
$94$	7.79960	−	4.50310i	0.804467	−	0.464459i
$95$	−13.6964	+	13.2249i	−1.40523	+	1.35684i
$96$	−0.0953825	−	1.72942i	−0.00973493	−	0.176508i
$97$	−2.52109	−	1.45555i	−0.255978	−	0.147789i	0.366520	−	0.930410i	$-0.380549\pi$
$97$	−2.52109	−	1.45555i	−0.255978	−	0.147789i	−0.622499	+	0.782621i	$0.713882\pi$
$98$			4.55916i			0.460545i
$99$	4.59442	+	8.82560i	0.461757	+	0.887007i
$100$	−4.41502	+	2.34682i	−0.441502	+	0.234682i
$101$	−2.80713	+	4.86209i	−0.279320	+	0.483796i	−0.971216	−	0.238201i	$-0.923442\pi$
$101$	−2.80713	+	4.86209i	−0.279320	+	0.483796i	0.691896	+	0.721997i	$0.256776\pi$
$102$	−4.73386	−	7.24601i	−0.468722	−	0.717462i
$103$	1.86132	−	1.07463i	0.183401	−	0.105887i	−0.405489	−	0.914100i	$-0.632899\pi$
$103$	1.86132	−	1.07463i	0.183401	−	0.105887i	0.588890	+	0.808214i	$0.299565\pi$
$104$	−1.66845	+	0.963278i	−0.163605	+	0.0944572i
$105$	−1.34536	+	5.89937i	−0.131293	+	0.575720i
$106$	−1.49760	−	0.864638i	−0.145459	−	0.0839810i
$107$			6.90410i			0.667444i	0.942672	+	0.333722i	$0.108305\pi$
$107$			6.90410i			0.667444i	−0.942672	+	0.333722i	$0.891695\pi$
$108$	3.30309	+	4.01118i	0.317840	+	0.385976i
$109$			3.18235i			0.304814i	0.988318	+	0.152407i	$0.0487025\pi$
$109$			3.18235i			0.304814i	−0.988318	+	0.152407i	$0.951298\pi$
$110$	−0.670008	−	7.38587i	−0.0638828	−	0.704215i
$111$	−12.7039	−	6.42922i	−1.20580	−	0.610235i
$112$	0.781159	+	1.35301i	0.0738126	+	0.127847i
$113$	−1.90511	−	3.29974i	−0.179217	−	0.310413i	0.762395	−	0.647111i	$-0.224023\pi$
$113$	−1.90511	−	3.29974i	−0.179217	−	0.310413i	−0.941613	+	0.336698i	$0.890690\pi$
$114$	−8.06599	−	12.3464i	−0.755449	−	1.15635i
$115$	2.31599	−	8.07498i	0.215968	−	0.752996i
$116$	−2.80629			−0.260557
$117$	2.32186	−	5.29278i	0.214656	−	0.489318i
$118$	6.27607			0.577759
$119$	6.76116	+	3.90356i	0.619795	+	0.357839i
$120$	−1.14226	−	3.70071i	−0.104274	−	0.337827i
$121$	10.4836	+	3.33087i	0.953052	+	0.302807i
$122$	−1.08008	−	1.87075i	−0.0977854	−	0.169369i
$123$	10.6535	−	0.587572i	0.960597	−	0.0529796i
$124$	2.55600	−	4.42712i	0.229536	−	0.397567i
$125$	−8.30998	+	7.47959i	−0.743267	+	0.668995i
$126$	−4.29212	−	1.88289i	−0.382372	−	0.167741i
$127$	19.1252			1.69709			0.848544	−	0.529125i	$-0.177480\pi$
$127$	19.1252			1.69709			0.848544	+	0.529125i	$0.177480\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	4.87912	+	7.46835i	0.429582	+	0.657552i
$130$	−3.09903	+	2.99234i	−0.271803	+	0.262445i
$131$	0.944775	+	1.63640i	0.0825454	+	0.142973i	0.904343	−	0.426807i	$-0.140362\pi$
$131$	0.944775	+	1.63640i	0.0825454	+	0.142973i	−0.821797	+	0.569780i	$0.807028\pi$
$132$	5.71659	+	0.566189i	0.497566	+	0.0492804i
$133$	11.5203	+	6.65124i	0.998935	+	0.576736i
$134$	−3.79315			−0.327678
$135$	9.33599	+	6.91660i	0.803514	+	0.595286i
$136$	−4.99714			−0.428501
$137$	4.05886	−	7.03016i	0.346772	−	0.600627i	−0.638902	−	0.769288i	$-0.720611\pi$
$137$	4.05886	−	7.03016i	0.346772	−	0.600627i	0.985674	+	0.168661i	$0.0539444\pi$
$138$	5.80587	+	2.93825i	0.494229	+	0.250121i
$139$	6.95382	−	4.01479i	0.589815	−	0.340530i	−0.175209	−	0.984531i	$-0.556060\pi$
$139$	6.95382	−	4.01479i	0.589815	−	0.340530i	0.765024	+	0.644001i	$0.222727\pi$
$140$	2.42660	+	2.51312i	0.205085	+	0.212398i
$141$	8.53171	+	13.0593i	0.718499	+	1.09979i
$142$	1.40343	−	2.43082i	0.117774	−	0.203990i
$143$	−2.30929	−	5.95777i	−0.193113	−	0.498213i
$144$	2.98180	−	0.329913i	0.248484	−	0.0274928i
$145$	−6.08874	+	1.51770i	−0.505643	+	0.126038i
$146$	10.5706	+	6.10296i	0.874832	+	0.505084i
$147$	−7.88472	+	0.434864i	−0.650321	+	0.0358670i
$148$	−7.11906	+	4.11019i	−0.585183	+	0.337856i
$149$	−1.85977	−	3.22122i	−0.152358	−	0.263893i	0.779736	−	0.626109i	$-0.215353\pi$
$149$	−1.85977	−	3.22122i	−0.152358	−	0.263893i	−0.932094	+	0.362216i	$0.882020\pi$
$150$	−4.47976	−	7.41160i	−0.365771	−	0.605154i
$151$	−16.4184	−	9.47914i	−1.33611	−	0.771402i	−0.349879	−	0.936795i	$-0.613777\pi$
$151$	−16.4184	−	9.47914i	−1.33611	−	0.771402i	−0.986228	+	0.165393i	$0.947111\pi$
$152$	−8.51458			−0.690623
$153$	12.0799	−	8.87799i	0.976601	−	0.717743i
$154$	−4.83138	+	1.87270i	−0.389324	+	0.150906i
$155$	3.15142	−	10.9878i	0.253128	−	0.882560i
$156$	−1.82506	−	2.79357i	−0.146121	−	0.223665i
$157$	15.0733	−	8.70255i	1.20298	−	0.694539i	0.241762	−	0.970336i	$-0.422275\pi$
$157$	15.0733	−	8.70255i	1.20298	−	0.694539i	0.961216	+	0.275796i	$0.0889415\pi$
$158$	2.24715	+	3.89217i	0.178773	+	0.309645i
$159$	1.35248	−	2.67245i	0.107259	−	0.211939i
$160$	−2.14941	−	0.616475i	−0.169926	−	0.0487366i
$161$	−5.86938			−0.462572
$162$	−6.62197	+	6.09504i	−0.520271	+	0.478872i
$163$			14.3680i			1.12539i	0.826664	+	0.562696i	$0.190236\pi$
$163$			14.3680i			1.12539i	−0.826664	+	0.562696i	$0.809764\pi$
$164$	3.08008	−	5.33486i	0.240514	−	0.416583i
$165$	12.7094	−	1.86321i	0.989424	−	0.145051i
$166$	6.20584	+	10.7488i	0.481667	+	0.834271i
$167$	−9.01381	+	5.20413i	−0.697510	+	0.402707i	−0.806419	−	0.591344i	$-0.798597\pi$
$167$	−9.01381	+	5.20413i	−0.697510	+	0.402707i	0.108910	+	0.994052i	$0.465264\pi$
$168$	−2.26541	+	1.48001i	−0.174780	+	0.114185i
$169$	4.64419	−	8.04397i	0.357245	−	0.618767i
$170$	−10.8422	+	2.70256i	−0.831558	+	0.207277i
$171$	20.5828	−	15.1271i	1.57401	−	1.15680i
$172$	5.15047			0.392720
$173$	0.790309	+	0.456285i	0.0600861	+	0.0346907i	0.529742	−	0.848159i	$-0.322289\pi$
$173$	0.790309	+	0.456285i	0.0600861	+	0.0346907i	−0.469656	+	0.882850i	$0.655622\pi$
$174$	−0.267670	−	4.85325i	−0.0202920	−	0.367924i
$175$	6.62410	+	4.14032i	0.500735	+	0.312979i
$176$	2.07880	−	2.58430i	0.156696	−	0.194799i
$177$	0.598627	+	10.8540i	0.0449956	+	0.815835i
$178$	4.77926	−	8.27792i	0.358221	−	0.620456i
$179$		−	6.04154i		−	0.451566i	−0.974178	−	0.225783i	$-0.927506\pi$
$179$		−	6.04154i		−	0.451566i	0.974178	−	0.225783i	$-0.0724940\pi$
$180$	6.29114	−	2.32843i	0.468914	−	0.173551i
$181$	1.76607			0.131271			0.0656355	−	0.997844i	$-0.479093\pi$
$181$	1.76607			0.131271			0.0656355	+	0.997844i	$0.479093\pi$
$182$	2.60664	+	1.50495i	0.193217	+	0.111554i
$183$	3.13229	−	2.04634i	0.231545	−	0.151270i
$184$	3.25352	−	1.87842i	0.239852	−	0.138479i
$185$	−13.2232	+	12.7679i	−0.972189	+	0.938718i
$186$	7.90016	+	3.99813i	0.579268	+	0.293157i
$187$	2.53928	−	16.3779i	0.185691	−	1.19767i
$188$	9.00620			0.656845
$189$	2.84692	−	7.60248i	0.207083	−	0.552999i
$190$	−18.4739	+	4.60487i	−1.34024	+	0.334072i
$191$	−9.69403	−	5.59685i	−0.701435	−	0.404974i	0.106446	−	0.994318i	$-0.466053\pi$
$191$	−9.69403	−	5.59685i	−0.701435	−	0.404974i	−0.807882	+	0.589345i	$0.799386\pi$
$192$	0.782108	−	1.54542i	0.0564438	−	0.111531i
$193$	11.7100	+	20.2824i	0.842907	+	1.45996i	0.887426	+	0.460949i	$0.152491\pi$
$193$	11.7100	+	20.2824i	0.842907	+	1.45996i	−0.0445193	+	0.999009i	$0.514176\pi$
$194$	−1.45555	−	2.52109i	−0.104503	−	0.181004i
$195$	−5.47061	−	5.07412i	−0.391759	−	0.363365i
$196$	−2.27958	+	3.94835i	−0.162827	+	0.282025i
$197$			13.3394i			0.950391i	0.879880	+	0.475195i	$0.157623\pi$
$197$			13.3394i			0.950391i	−0.879880	+	0.475195i	$0.842377\pi$
$198$	−0.433917	+	9.94041i	−0.0308371	+	0.706434i
$199$	17.7710			1.25975			0.629875	−	0.776697i	$-0.283106\pi$
$199$	17.7710			1.25975			0.629875	+	0.776697i	$0.283106\pi$
$200$	−4.99693	−	0.175105i	−0.353337	−	0.0123818i
$201$	−0.361800	−	6.55996i	−0.0255194	−	0.462704i
$202$	−4.86209	+	2.80713i	−0.342095	+	0.197509i
$203$	2.19216	+	3.79692i	0.153859	+	0.266492i
$204$	−0.476639	−	8.64216i	−0.0333714	−	0.605072i
$205$	3.79759	−	13.2407i	0.265235	−	0.924772i
$206$	2.14926			0.149746
$207$	−4.52770	+	10.3211i	−0.314697	+	0.717364i
$208$	−1.92656			−0.133583
$209$	4.32666	−	27.9062i	0.299281	−	1.93032i
$210$	−4.11480	+	4.43633i	−0.283948	+	0.306136i
$211$	14.8966	−	8.60055i	1.02552	−	0.592086i	0.109824	−	0.993951i	$-0.464971\pi$
$211$	14.8966	−	8.60055i	1.02552	−	0.592086i	0.915699	+	0.401865i	$0.131638\pi$
$212$	−0.864638	−	1.49760i	−0.0593836	−	0.102855i
$213$	4.33778	+	2.19527i	0.297220	+	0.150418i
$214$	−3.45205	+	5.97912i	−0.235977	+	0.408724i
$215$	11.1749	−	2.78549i	0.762120	−	0.189969i
$216$	0.854971	+	5.12533i	0.0581734	+	0.348735i
$217$	−7.98657			−0.542164
$218$	−1.59118	+	2.75600i	−0.107768	+	0.186660i
$219$	−9.54634	+	18.8632i	−0.645082	+	1.27466i
$220$	3.11269	−	6.73136i	0.209858	−	0.453828i
$221$	−8.33746	+	4.81363i	−0.560838	+	0.323800i
$222$	−7.78729	−	11.9198i	−0.522649	−	0.800006i
$223$	−6.78637	−	3.91811i	−0.454449	−	0.262376i	0.255258	−	0.966873i	$-0.417839\pi$
$223$	−6.78637	−	3.91811i	−0.454449	−	0.262376i	−0.709707	+	0.704497i	$0.751173\pi$
$224$			1.56232i			0.104387i
$225$	12.3905	−	8.45434i	0.826033	−	0.563622i
$226$		−	3.81021i		−	0.253451i
$227$	−7.46942	−	4.31247i	−0.495763	−	0.286229i	0.231199	−	0.972906i	$-0.425735\pi$
$227$	−7.46942	−	4.31247i	−0.495763	−	0.286229i	−0.726962	+	0.686678i	$0.759068\pi$
$228$	−0.812142	−	14.7253i	−0.0537854	−	0.975207i
$229$	−1.23368	−	2.13680i	−0.0815241	−	0.141204i	0.822381	−	0.568938i	$-0.192645\pi$
$229$	−1.23368	−	2.13680i	−0.0815241	−	0.141204i	−0.903905	+	0.427734i	$0.859312\pi$
$230$	6.04320	−	5.83514i	0.398477	−	0.384758i
$231$	−3.69951	−	8.17687i	−0.243410	−	0.537999i
$232$	−2.43031	−	1.40314i	−0.159558	−	0.0921208i
$233$			0.170555i			0.0111734i	0.999984	+	0.00558672i	$0.00177832\pi$
$233$			0.170555i			0.0111734i	−0.999984	+	0.00558672i	$0.998222\pi$
$234$	4.65718	−	3.42275i	0.304450	−	0.223752i
$235$	19.5406	−	4.87075i	1.27469	−	0.317733i
$236$	5.43524	+	3.13803i	0.353804	+	0.204269i
$237$	−6.51687	+	4.25751i	−0.423316	+	0.276555i
$238$	3.90356	+	6.76116i	0.253030	+	0.438261i
$239$	−13.3345	−	23.0960i	−0.862536	−	1.49396i	−0.869473	−	0.493981i	$-0.835541\pi$
$239$	−13.3345	−	23.0960i	−0.862536	−	1.49396i	0.00693675	−	0.999976i	$-0.497792\pi$
$240$	0.861129	−	3.77604i	0.0555856	−	0.243742i
$241$	4.28737	+	2.47532i	0.276174	+	0.159449i	0.631690	−	0.775221i	$-0.282362\pi$
$241$	4.28737	+	2.47532i	0.276174	+	0.159449i	−0.355516	+	0.934670i	$0.615695\pi$
$242$	7.41360	+	8.12641i	0.476565	+	0.522385i
$243$	−11.1725	−	10.8708i	−0.716717	−	0.697364i
$244$		−	2.16015i		−	0.138290i
$245$	−2.81061	+	9.79950i	−0.179563	+	0.626067i
$246$	9.52002	+	4.81791i	0.606974	+	0.307179i
$247$	−14.2061	+	8.20191i	−0.903914	+	0.521875i
$248$	4.42712	−	2.55600i	0.281122	−	0.162306i
$249$	−17.9973	+	11.7578i	−1.14054	+	0.745118i
$250$	−10.9364	+	2.32253i	−0.691682	+	0.146890i
$251$		−	31.2319i		−	1.97134i	−0.168690	−	0.985669i	$-0.553954\pi$
$251$		−	31.2319i		−	1.97134i	0.168690	−	0.985669i	$-0.446046\pi$
$252$	−2.77564	−	3.77669i	−0.174849	−	0.237909i
$253$	4.50319	+	11.6178i	0.283113	+	0.730405i
$254$	16.5629	+	9.56260i	1.03925	+	0.600011i
$255$	−5.70802	−	18.4929i	−0.357450	−	1.15807i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.4395	+	21.5458i	0.775952	+	1.34399i	0.934258	+	0.356598i	$0.116063\pi$
$257$	12.4395	+	21.5458i	0.775952	+	1.34399i	−0.158306	+	0.987390i	$0.550603\pi$
$258$	0.491265	+	8.90734i	0.0305848	+	0.554547i
$259$	11.1222	+	6.42143i	0.691102	+	0.399008i
$260$	−4.18001	+	1.04192i	−0.259233	+	0.0646174i
$261$	8.36779	−	0.925831i	0.517953	−	0.0573075i
$262$			1.88955i			0.116737i
$263$	21.8880	+	12.6370i	1.34967	+	0.779233i	0.988203	−	0.153152i	$-0.0489424\pi$
$263$	21.8880	+	12.6370i	1.34967	+	0.779233i	0.361468	+	0.932385i	$0.382276\pi$
$264$	4.66762	+	3.34863i	0.287272	+	0.206094i
$265$	−2.68592	−	2.78169i	−0.164995	−	0.170878i
$266$	6.65124	+	11.5203i	0.407814	+	0.706354i
$267$	14.7719	+	7.47579i	0.904024	+	0.457511i
$268$	−3.28496	−	1.89657i	−0.200661	−	0.115852i
$269$			25.9780i			1.58391i	0.610581	+	0.791954i	$0.290936\pi$
$269$			25.9780i			1.58391i	−0.610581	+	0.791954i	$0.709064\pi$
$270$	4.62691	+	10.6579i	0.281585	+	0.648622i
$271$			25.3367i			1.53910i	0.638588	+	0.769549i	$0.279519\pi$
$271$			25.3367i			1.53910i	−0.638588	+	0.769549i	$0.720481\pi$
$272$	−4.32765	−	2.49857i	−0.262402	−	0.151498i
$273$	−2.35406	+	4.65154i	−0.142474	+	0.281524i
$274$	7.03016	−	4.05886i	0.424708	−	0.245205i
$275$	3.11308	−	16.2883i	0.187726	−	0.982221i
$276$	3.55891	+	5.44754i	0.214221	+	0.327903i
$277$	−15.6188	+	27.0525i	−0.938442	+	1.62543i	−0.170064	+	0.985433i	$0.554397\pi$
$277$	−15.6188	+	27.0525i	−0.938442	+	1.62543i	−0.768378	+	0.639996i	$0.778936\pi$
$278$	8.02958			0.481582
$279$	−6.16093	+	14.0441i	−0.368845	+	0.840796i
$280$	0.844936	+	3.38973i	0.0504946	+	0.202575i
$281$	9.56150	−	16.5610i	0.570391	−	0.987947i	−0.426134	−	0.904660i	$-0.640125\pi$
$281$	9.56150	−	16.5610i	0.570391	−	0.987947i	0.996526	−	0.0832868i	$-0.0265418\pi$
$282$	0.859034	+	15.5755i	0.0511547	+	0.927509i
$283$	−5.82131	−	10.0828i	−0.346041	−	0.599360i	0.639501	−	0.768790i	$-0.279141\pi$
$283$	−5.82131	−	10.0828i	−0.346041	−	0.599360i	−0.985542	+	0.169430i	$0.945807\pi$
$284$	2.43082	−	1.40343i	0.144243	−	0.0832785i
$285$	−9.72585	−	31.5100i	−0.576110	−	1.86649i
$286$	0.978975	−	6.31422i	0.0578880	−	0.373368i
$287$	−9.62414			−0.568095
$288$	2.74727	+	1.20519i	0.161885	+	0.0710164i
$289$	−7.97138			−0.468905
$290$	−6.03186	−	1.73000i	−0.354203	−	0.101589i
$291$	4.22120	−	2.75773i	0.247451	−	0.161661i
$292$	6.10296	+	10.5706i	0.357149	+	0.618600i
$293$	−4.12881	+	2.38377i	−0.241208	+	0.139261i	−0.615732	−	0.787956i	$-0.711139\pi$
$293$	−4.12881	+	2.38377i	−0.241208	+	0.139261i	0.374524	+	0.927217i	$0.377806\pi$
$294$	−7.04580	−	3.56576i	−0.410919	−	0.207959i
$295$	13.4898	+	3.86904i	0.785409	+	0.225264i
$296$	−8.22038			−0.477800
$297$	−17.2326	+	0.197715i	−0.999934	+	0.0114726i
$298$		−	3.71954i		−	0.215467i
$299$	3.61888	−	6.26808i	0.209285	−	0.362493i
$300$	−0.173789	−	8.65851i	−0.0100337	−	0.499899i
$301$	−4.02334	−	6.96863i	−0.231901	−	0.401665i
$302$	−9.47914	−	16.4184i	−0.545463	−	0.944770i
$303$	−5.31847	−	8.14085i	−0.305538	−	0.467680i
$304$	−7.37384	−	4.25729i	−0.422919	−	0.244172i
$305$	−1.16826	−	4.68684i	−0.0668942	−	0.268367i
$306$	14.9005	−	1.64862i	0.851804	−	0.0942454i
$307$	−22.2797			−1.27157			−0.635786	−	0.771865i	$-0.719324\pi$
$307$	−22.2797			−1.27157			−0.635786	+	0.771865i	$0.719324\pi$
$308$	−5.12045	−	0.793888i	−0.291764	−	0.0452360i
$309$	0.205002	+	3.71698i	0.0116622	+	0.211452i
$310$	8.22310	−	7.93999i	0.467041	−	0.450961i
$311$	−27.9924	+	16.1614i	−1.58730	+	0.916430i	−0.593555	+	0.804793i	$0.702276\pi$
$311$	−27.9924	+	16.1614i	−1.58730	+	0.916430i	−0.993749	+	0.111637i	$0.964391\pi$
$312$	−0.183760	−	3.33183i	−0.0104033	−	0.188628i
$313$	26.6716	+	15.3989i	1.50757	+	0.870396i	0.999961	+	0.00880746i	$0.00280354\pi$
$313$	26.6716	+	15.3989i	1.50757	+	0.870396i	0.507608	+	0.861588i	$0.330530\pi$
$314$	17.4051			0.982227
$315$	−8.06476	−	6.69308i	−0.454398	−	0.377112i
$316$			4.49429i			0.252824i
$317$	6.75419	−	11.6986i	0.379353	−	0.657059i	−0.611615	−	0.791156i	$-0.709480\pi$
$317$	6.75419	−	11.6986i	0.379353	−	0.657059i	0.990968	+	0.134096i	$0.0428132\pi$
$318$	2.50751	−	1.63817i	0.140614	−	0.0918639i
$319$	5.83371	−	7.25227i	0.326625	−	0.406049i
$320$	−1.55321	−	1.60859i	−0.0868268	−	0.0899228i
$321$	−10.6697	−	5.39975i	−0.595524	−	0.301384i
$322$	−5.08303	−	2.93469i	−0.283266	−	0.163544i
$323$	−42.5485			−2.36746
$324$	−8.78231	+	1.96747i	−0.487906	+	0.109304i
$325$	−8.50579	+	4.52128i	−0.471816	+	0.250796i
$326$	−7.18402	+	12.4431i	−0.397886	+	0.689159i
$327$	−4.91806	−	2.48894i	−0.271969	−	0.137639i
$328$	5.33486	−	3.08008i	0.294569	−	0.170069i
$329$	−7.03528	−	12.1855i	−0.387867	−	0.671806i
$330$	11.9383	+	4.74111i	0.657179	+	0.260989i
$331$	11.5860	−	20.0675i	0.636823	−	1.10301i	−0.349303	−	0.937010i	$-0.613582\pi$
$331$	11.5860	−	20.0675i	0.636823	−	1.10301i	0.986126	−	0.166000i	$-0.0530851\pi$
$332$			12.4117i			0.681179i
$333$	19.8716	−	14.6045i	1.08896	−	0.800319i
$334$	−10.4083			−0.569514
$335$	−8.15303	−	2.33838i	−0.445447	−	0.127759i
$336$	−2.70191	+	0.149018i	−0.147401	+	0.00812959i
$337$	−6.73508	−	11.6655i	−0.366883	−	0.635461i	0.622193	−	0.782864i	$-0.286242\pi$
$337$	−6.73508	−	11.6655i	−0.366883	−	0.635461i	−0.989077	+	0.147403i	$0.952909\pi$
$338$	8.04397	−	4.64419i	0.437534	−	0.252611i
$339$	6.58946	−	0.363427i	0.357891	−	0.0197387i
$340$	−10.7409	−	3.08061i	−0.582507	−	0.167069i
$341$	6.12757	+	15.8086i	0.331827	+	0.856082i
$342$	25.3888	−	2.80907i	1.37287	−	0.151897i
$343$	18.0591			0.975099
$344$	4.46044	+	2.57524i	0.240491	+	0.138847i
$345$	10.6678	+	9.89468i	0.574337	+	0.532712i
$346$	0.456285	+	0.790309i	0.0245300	+	0.0424873i
$347$	8.43631	−	4.87070i	0.452885	−	0.261473i	−0.256163	−	0.966634i	$-0.582458\pi$
$347$	8.43631	−	4.87070i	0.452885	−	0.261473i	0.709048	+	0.705161i	$0.249125\pi$
$348$	2.19482	−	4.33688i	0.117655	−	0.232481i
$349$	3.72855	+	2.15268i	0.199585	+	0.115230i	0.596462	−	0.802641i	$-0.296573\pi$
$349$	3.72855	+	2.15268i	0.199585	+	0.115230i	−0.396877	+	0.917872i	$0.629906\pi$
$350$	3.66648	+	6.89767i	0.195982	+	0.368696i
$351$	6.36359	+	7.72777i	0.339664	+	0.412478i
$352$	3.09244	−	1.19866i	0.164828	−	0.0638890i
$353$	−3.93697	+	6.81904i	−0.209544	+	0.362941i	−0.951571	−	0.307429i	$-0.900531\pi$
$353$	−3.93697	+	6.81904i	−0.209544	+	0.362941i	0.742027	+	0.670370i	$0.233865\pi$
$354$	−4.90856	+	9.69913i	−0.260887	+	0.515503i
$355$	4.51509	−	4.35964i	0.239636	−	0.231386i
$356$	8.27792	−	4.77926i	0.438729	−	0.253300i
$357$	−11.3206	+	7.39580i	−0.599148	+	0.391427i
$358$	3.02077	−	5.23213i	0.159653	−	0.276527i
$359$	−32.0999			−1.69417			−0.847085	−	0.531457i	$-0.821645\pi$
$359$	−32.0999			−1.69417			−0.847085	+	0.531457i	$0.821645\pi$
$360$	6.61250	+	1.12909i	0.348509	+	0.0595082i
$361$	−53.4980			−2.81569
$362$	1.52946	+	0.883035i	0.0803867	+	0.0464113i
$363$	−13.3469	+	13.5964i	−0.700529	+	0.713624i
$364$	1.50495	+	2.60664i	0.0788807	+	0.136625i
$365$	18.9583	+	19.6343i	0.992323	+	1.02771i
$366$	3.73581	−	0.206041i	0.195274	−	0.0107699i
$367$	−22.5045	−	12.9930i	−1.17473	−	0.678228i	−0.219937	−	0.975514i	$-0.570585\pi$
$367$	−22.5045	−	12.9930i	−1.17473	−	0.678228i	−0.954789	+	0.297286i	$0.903919\pi$
$368$	3.75684			0.195839
$369$	−7.42417	+	16.9237i	−0.386487	+	0.881011i
$370$	−17.8356	+	4.44576i	−0.927228	+	0.231124i
$371$	−1.35084	+	2.33972i	−0.0701321	+	0.121472i
$372$	4.84267	+	7.41257i	0.251081	+	0.384324i
$373$	−1.73837	−	3.01094i	−0.0900093	−	0.155901i	0.817505	−	0.575921i	$-0.195356\pi$
$373$	−1.73837	−	3.01094i	−0.0900093	−	0.155901i	−0.907515	+	0.420020i	$0.862023\pi$
$374$	10.3881	−	12.9141i	0.537154	−	0.667771i
$375$	−5.05978	−	18.6922i	−0.261286	−	0.965261i
$376$	7.79960	+	4.50310i	0.402234	+	0.232230i
$377$	−5.40647			−0.278447
$378$	6.26674	−	5.16048i	0.322326	−	0.265427i
$379$	9.35898			0.480738			0.240369	−	0.970682i	$-0.422731\pi$
$379$	9.35898			0.480738			0.240369	+	0.970682i	$0.422731\pi$
$380$	−18.3013	−	5.24902i	−0.938837	−	0.269269i
$381$	−14.9580	+	29.5564i	−0.766320	+	1.51422i
$382$	−5.59685	−	9.69403i	−0.286360	−	0.495990i
$383$	9.29140	+	16.0932i	0.474768	+	0.822323i	0.999582	−	0.0288939i	$-0.00919850\pi$
$383$	9.29140	+	16.0932i	0.474768	+	0.822323i	−0.524814	+	0.851217i	$0.675865\pi$
$384$	1.45003	−	0.947315i	0.0739967	−	0.0483425i
$385$	−11.5391	+	1.04677i	−0.588086	+	0.0533481i
$386$			23.4201i			1.19205i
$387$	−15.3577	+	1.69921i	−0.780676	+	0.0863756i
$388$		−	2.91111i		−	0.147789i
$389$	−4.97144	−	2.87026i	−0.252062	−	0.145528i	0.368646	−	0.929570i	$-0.379821\pi$
$389$	−4.97144	−	2.87026i	−0.252062	−	0.145528i	−0.620708	+	0.784042i	$0.713155\pi$
$390$	−2.20063	−	7.12962i	−0.111433	−	0.361023i
$391$	16.2583	−	9.38672i	0.822216	−	0.474707i
$392$	−3.94835	+	2.27958i	−0.199422	+	0.115136i
$393$	−3.26783	+	0.180230i	−0.164840	+	0.00909140i
$394$	−6.66969	+	11.5522i	−0.336014	+	0.581993i
$395$	2.43061	+	9.75118i	0.122297	+	0.490635i
$396$	−5.34599	+	8.39169i	−0.268646	+	0.421698i
$397$		−	22.3459i		−	1.12151i	−0.827982	−	0.560755i	$-0.810511\pi$
$397$		−	22.3459i		−	1.12151i	0.827982	−	0.560755i	$-0.189489\pi$
$398$	15.3901	+	8.88548i	0.771436	+	0.445389i
$399$	−19.2890	+	12.6016i	−0.965659	+	0.630871i
$400$	−4.23992	−	2.65011i	−0.211996	−	0.132506i
$401$	−19.1343	+	11.0472i	−0.955520	+	0.551670i	−0.894791	−	0.446484i	$-0.852676\pi$
$401$	−19.1343	+	11.0472i	−0.955520	+	0.551670i	−0.0607288	+	0.998154i	$0.519342\pi$
$402$	2.96665	−	5.86199i	0.147963	−	0.292369i
$403$	4.92428	−	8.52910i	0.245296	−	0.424865i
$404$	−5.61425			−0.279320
$405$	−17.9908	+	9.01846i	−0.893968	+	0.448131i
$406$			4.38431i			0.217590i
$407$	4.17717	−	26.9420i	0.207054	−	1.33547i
$408$	3.90830	−	7.72265i	0.193490	−	0.382328i
$409$	32.5585	−	18.7977i	1.60991	−	0.929485i	0.620527	−	0.784185i	$-0.286919\pi$
$409$	32.5585	−	18.7977i	1.60991	−	0.929485i	0.989388	−	0.145300i	$-0.0464146\pi$
$410$	9.90917	−	9.56801i	0.489379	−	0.472530i
$411$	7.69005	+	11.7710i	0.379322	+	0.580619i
$412$	1.86132	+	1.07463i	0.0917004	+	0.0529433i
$413$		−	9.80522i		−	0.482483i
$414$	−9.08164	+	6.67446i	−0.446338	+	0.328032i
$415$	6.71251	+	26.9294i	0.329504	+	1.32191i
$416$	−1.66845	−	0.963278i	−0.0818023	−	0.0472286i
$417$	0.765881	+	13.8865i	0.0375054	+	0.680026i
$418$	17.7001	−	22.0042i	0.865741	−	1.07626i
$419$	−6.45874	+	3.72896i	−0.315530	+	0.182171i	−0.649398	−	0.760448i	$-0.724979\pi$
$419$	−6.45874	+	3.72896i	−0.315530	+	0.182171i	0.333868	+	0.942620i	$0.391646\pi$
$420$	−5.78168	+	1.78457i	−0.282117	+	0.0870782i
$421$	16.1355	−	27.9475i	0.786395	−	1.36208i	−0.141767	−	0.989900i	$-0.545278\pi$
$421$	16.1355	−	27.9475i	0.786395	−	1.36208i	0.928162	−	0.372176i	$-0.121388\pi$
$422$	17.2011			0.837336
$423$	−26.8547	+	2.97126i	−1.30572	+	0.144468i
$424$		−	1.72928i		−	0.0839810i
$425$	−24.9704	−	0.875024i	−1.21124	−	0.0424449i
$426$	2.65899	+	4.07005i	0.128828	+	0.197195i
$427$	−2.92270	+	1.68742i	−0.141439	+	0.0816601i
$428$	−5.97912	+	3.45205i	−0.289012	+	0.166861i
$429$	11.0133	+	1.09079i	0.531729	+	0.0526641i
$430$	11.0705	+	3.17514i	0.533866	+	0.153119i
$431$	26.5809			1.28036			0.640178	−	0.768226i	$-0.278860\pi$
$431$	26.5809			1.28036			0.640178	+	0.768226i	$0.278860\pi$
$432$	−1.82224	+	4.86615i	−0.0876725	+	0.234123i
$433$			0.552031i			0.0265289i	0.999912	+	0.0132645i	$0.00422233\pi$
$433$			0.552031i			0.0265289i	−0.999912	+	0.0132645i	$0.995778\pi$
$434$	−6.91657	−	3.99328i	−0.332006	−	0.191684i
$435$	2.41657	−	10.5966i	0.115866	−	0.508070i
$436$	−2.75600	+	1.59118i	−0.131988	+	0.0762035i
$437$	27.7023	−	15.9939i	1.32518	−	0.765094i
$438$	−17.6990	+	11.5628i	−0.845690	+	0.552494i
$439$	−15.1560	−	8.75031i	−0.723356	−	0.417630i	0.0926307	−	0.995701i	$-0.470472\pi$
$439$	−15.1560	−	8.75031i	−0.723356	−	0.417630i	−0.815987	+	0.578071i	$0.803806\pi$
$440$	6.06135	−	4.27318i	0.288963	−	0.203716i
$441$	5.49465	−	12.5253i	0.261650	−	0.596441i
$442$	−9.62727			−0.457922
$443$	6.00312	−	10.3977i	0.285217	−	0.494010i	−0.687445	−	0.726236i	$-0.741268\pi$
$443$	6.00312	−	10.3977i	0.285217	−	0.494010i	0.972662	+	0.232227i	$0.0746011\pi$
$444$	−0.784080	−	14.2165i	−0.0372108	−	0.674686i
$445$	15.3757	−	14.8463i	0.728879	−	0.703784i
$446$	−3.91811	−	6.78637i	−0.185528	−	0.321344i
$447$	6.43266	−	0.354779i	0.304255	−	0.0167805i
$448$	−0.781159	+	1.35301i	−0.0369063	+	0.0639236i
$449$		−	17.8969i		−	0.844606i	−0.906455	−	0.422303i	$-0.861222\pi$
$449$		−	17.8969i		−	0.844606i	0.906455	−	0.422303i	$-0.138778\pi$
$450$	14.9576	−	1.12643i	0.705110	−	0.0531002i
$451$	7.38398	+	19.0500i	0.347698	+	0.897028i
$452$	1.90511	−	3.29974i	0.0896086	−	0.155207i
$453$	27.4901	−	17.9595i	1.29160	−	0.843809i
$454$	−4.31247	−	7.46942i	−0.202394	−	0.350557i
$455$	4.67498	+	4.84168i	0.219167	+	0.226981i
$456$	6.65932	−	13.1586i	0.311851	−	0.616206i
$457$	18.4855	−	32.0178i	0.864714	−	1.49773i	−0.00261671	−	0.999997i	$-0.500833\pi$
$457$	18.4855	−	32.0178i	0.864714	−	1.49773i	0.867331	−	0.497732i	$-0.165834\pi$
$458$		−	2.46737i		−	0.115293i
$459$	4.27241	+	25.6120i	0.199419	+	1.19547i
$460$	8.15114	−	2.03178i	0.380049	−	0.0947322i
$461$	−13.4847	+	23.3562i	−0.628044	+	1.08780i	0.359899	+	0.932991i	$0.382811\pi$
$461$	−13.4847	+	23.3562i	−0.628044	+	1.08780i	−0.987944	+	0.154814i	$0.950522\pi$
$462$	0.884567	−	8.93114i	0.0411538	−	0.415514i
$463$	−17.9965	+	10.3903i	−0.836366	+	0.482876i	−0.856027	−	0.516930i	$-0.827075\pi$
$463$	−17.9965	+	10.3903i	−0.836366	+	0.482876i	0.0196612	+	0.999807i	$0.493741\pi$
$464$	−1.40314	−	2.43031i	−0.0651393	−	0.112825i
$465$	14.5159	+	13.4639i	0.673160	+	0.624372i
$466$	−0.0852775	+	0.147705i	−0.00395040	+	0.00684230i
$467$	11.3976			0.527420			0.263710	−	0.964602i	$-0.415054\pi$
$467$	11.3976			0.527420			0.263710	+	0.964602i	$0.415054\pi$
$468$	5.74461	−	0.635596i	0.265545	−	0.0293805i
$469$			5.92610i			0.273642i
$470$	19.3580	+	5.55209i	0.892918	+	0.256099i
$471$	1.66014	+	30.1008i	0.0764953	+	1.38697i
$472$	3.13803	+	5.43524i	0.144440	+	0.250177i
$473$	−10.7068	+	13.3103i	−0.492300	+	0.612010i
$474$	−7.77253	+	0.428677i	−0.357004	+	0.0196898i
$475$	−42.5468	−	1.49095i	−1.95218	−	0.0684093i
$476$			7.80712i			0.357839i
$477$	3.07226	+	4.18028i	0.140669	+	0.191402i
$478$		−	26.6690i		−	1.21981i
$479$	1.99498	−	3.45541i	0.0911531	−	0.157882i	−0.816843	−	0.576859i	$-0.804278\pi$
$479$	1.99498	−	3.45541i	0.0911531	−	0.157882i	0.907997	+	0.418978i	$0.137611\pi$
$480$	2.63378	−	2.83958i	0.120215	−	0.129608i
$481$	−13.7153	+	7.91851i	−0.625362	+	0.361053i
$482$	2.47532	+	4.28737i	0.112748	+	0.195285i
$483$	4.59048	−	9.07062i	0.208874	−	0.412728i
$484$	2.35717	+	10.7445i	0.107144	+	0.488385i
$485$	−1.57439	−	6.31617i	−0.0714894	−	0.286802i
$486$	−4.24027	−	15.0007i	−0.192343	−	0.680444i
$487$		−	23.9436i		−	1.08499i	−0.840060	−	0.542493i	$-0.817480\pi$
$487$		−	23.9436i		−	1.08499i	0.840060	−	0.542493i	$-0.182520\pi$
$488$	1.08008	−	1.87075i	0.0488927	−	0.0846847i
$489$	−22.2046	−	11.2373i	−1.00413	−	0.508170i
$490$	−7.33381	+	7.08132i	−0.331308	+	0.319901i
$491$	14.6412	+	25.3593i	0.660748	+	1.14445i	0.980420	+	0.196920i	$0.0630940\pi$
$491$	14.6412	+	25.3593i	0.660748	+	1.14445i	−0.319672	+	0.947528i	$0.603573\pi$
$492$	5.83562	+	8.93245i	0.263090	+	0.402706i
$493$	−12.1446	−	7.01170i	−0.546966	−	0.315791i
$494$	−16.4038			−0.738042
$495$	−7.06067	+	21.0985i	−0.317354	+	0.948307i
$496$	5.11200			0.229536
$497$	−3.79771	−	2.19261i	−0.170351	−	0.0983521i
$498$	−21.4650	+	1.18386i	−0.961871	+	0.0530499i
$499$	16.2480	+	28.1424i	0.727362	+	1.25983i	0.957995	+	0.286787i	$0.0925870\pi$
$499$	16.2480	+	28.1424i	0.727362	+	1.25983i	−0.230633	+	0.973041i	$0.574080\pi$
$500$	−10.6325	−	3.45685i	−0.475500	−	0.154595i
$501$	−0.992765	−	18.0003i	−0.0443535	−	0.804192i
$502$	15.6159	−	27.0476i	0.696973	−	1.20719i
$503$		−	36.5008i		−	1.62749i	−0.581222	−	0.813745i	$-0.697425\pi$
$503$		−	36.5008i		−	1.62749i	0.581222	−	0.813745i	$-0.302575\pi$
$504$	−0.515429	−	4.65853i	−0.0229591	−	0.207507i
$505$	−12.1811	+	3.03631i	−0.542053	+	0.135114i
$506$	−1.90903	+	12.3129i	−0.0848666	+	0.547376i
$507$	8.79902	+	13.4685i	0.390778	+	0.598155i
$508$	9.56260	+	16.5629i	0.424272	+	0.734861i
$509$	17.5586	−	10.1375i	0.778273	−	0.449336i	−0.0575449	−	0.998343i	$-0.518327\pi$
$509$	17.5586	−	10.1375i	0.778273	−	0.449336i	0.835818	+	0.549007i	$0.184994\pi$
$510$	4.30318	−	18.8694i	0.190548	−	0.835550i
$511$	9.53476	−	16.5147i	0.421793	−	0.730567i
$512$		−	1.00000i		−	0.0441942i
$513$	7.27972	+	43.6400i	0.321407	+	1.92675i
$514$			24.8789i			1.09736i
$515$	4.61964	+	1.32497i	0.203566	+	0.0583849i
$516$	−4.02822	+	7.95962i	−0.177333	+	0.350403i
$517$	−18.7221	+	23.2747i	−0.823397	+	1.02362i
$518$	6.42143	+	11.1222i	0.282141	+	0.488683i
$519$	−1.32326	+	0.864492i	−0.0580845	+	0.0379470i
$520$	−4.14096	−	1.18767i	−0.181593	−	0.0520829i
$521$		−	11.8500i		−	0.519159i	−0.965722	−	0.259579i	$-0.916416\pi$
$521$		−	11.8500i		−	0.519159i	0.965722	−	0.259579i	$-0.0835839\pi$
$522$	7.70964	+	3.38210i	0.337442	+	0.148031i
$523$	−32.8998			−1.43861			−0.719304	−	0.694695i	$-0.755539\pi$
$523$	−32.8998			−1.43861			−0.719304	+	0.694695i	$0.755539\pi$
$524$	−0.944775	+	1.63640i	−0.0412727	+	0.0714864i
$525$	−11.5793	+	6.99881i	−0.505361	+	0.305453i
$526$	12.6370	+	21.8880i	0.551001	+	0.954361i
$527$	22.1229	−	12.7727i	0.963690	−	0.556387i
$528$	2.36796	+	5.23381i	0.103052	+	0.227772i
$529$	4.44308	−	7.69565i	0.193178	−	0.334593i
$530$	−0.935230	−	3.75197i	−0.0406238	−	0.162975i
$531$	−17.2421	−	7.56385i	−0.748243	−	0.328243i
$532$			13.3025i			0.576736i
$533$	5.93396	−	10.2779i	0.257028	−	0.445186i
$534$	9.05493	+	13.8602i	0.391845	+	0.599788i
$535$	−11.1058	+	10.7235i	−0.480147	+	0.463616i
$536$	−1.89657	−	3.28496i	−0.0819195	−	0.141889i
$537$	9.33669	+	4.72514i	0.402908	+	0.203905i
$538$	−12.9890	+	22.4976i	−0.559996	+	0.969941i
$539$	−5.46491	−	14.0989i	−0.235390	−	0.607285i
$540$	−1.32195	+	11.5435i	−0.0568878	+	0.496753i
$541$		−	14.9083i		−	0.640958i	−0.947256	−	0.320479i	$-0.896156\pi$
$541$		−	14.9083i		−	0.640958i	0.947256	−	0.320479i	$-0.103844\pi$
$542$	−12.6684	+	21.9423i	−0.544153	+	0.942501i
$543$	−1.38126	+	2.72931i	−0.0592754	+	0.117126i
$544$	−2.49857	−	4.32765i	−0.107125	−	0.185546i
$545$	−5.11909	+	4.94285i	−0.219278	+	0.211728i
$546$	−4.36444	+	2.85132i	−0.186781	+	0.122025i
$547$	−7.60028	+	13.1641i	−0.324965	+	0.562855i	−0.981505	−	0.191436i	$-0.938686\pi$
$547$	−7.60028	+	13.1641i	−0.324965	+	0.562855i	0.656541	+	0.754291i	$0.272019\pi$
$548$	8.11773			0.346772
$549$	0.712662	+	6.44115i	0.0304157	+	0.274901i
$550$	10.8402	−	12.5495i	0.462226	−	0.535114i
$551$	−20.6931	−	11.9472i	−0.881556	−	0.508966i
$552$	0.358337	+	6.49716i	0.0152518	+	0.276537i
$553$	6.08081	−	3.51076i	0.258582	−	0.149293i
$554$	−27.0525	+	15.6188i	−1.14935	+	0.663579i
$555$	−9.38980	−	30.4212i	−0.398575	−	1.29131i
$556$	6.95382	+	4.01479i	0.294908	+	0.170265i
$557$		−	2.09640i		−	0.0888274i	−0.999013	−	0.0444137i	$-0.985858\pi$
$557$		−	2.09640i		−	0.0888274i	0.999013	−	0.0444137i	$-0.0141420\pi$
$558$	−12.3576	+	9.08206i	−0.523137	+	0.384474i
$559$	9.92268			0.419684
$560$	−0.963129	+	3.35806i	−0.0406996	+	0.141904i
$561$	23.3247	+	16.7336i	0.984771	+	0.706492i
$562$	16.5610	−	9.56150i	0.698584	−	0.403328i
$563$	27.5638	−	15.9140i	1.16168	−	0.670695i	0.209972	−	0.977707i	$-0.432663\pi$
$563$	27.5638	−	15.9140i	1.16168	−	0.670695i	0.951705	+	0.307013i	$0.0993294\pi$
$564$	−7.04382	+	13.9183i	−0.296598	+	0.586067i
$565$	2.34890	−	8.18970i	0.0988189	−	0.344543i
$566$		−	11.6426i		−	0.489376i
$567$	9.52239	+	10.3456i	0.399903	+	0.434475i
$568$	2.80687			0.117774
$569$	−17.7076	+	30.6704i	−0.742339	+	1.28577i	0.209088	+	0.977897i	$0.432950\pi$
$569$	−17.7076	+	30.6704i	−0.742339	+	1.28577i	−0.951428	+	0.307873i	$0.900383\pi$
$570$	7.33215	−	32.1514i	0.307110	−	1.34667i
$571$	−31.5428	+	18.2113i	−1.32003	+	0.762117i	−0.983732	−	0.179640i	$-0.942507\pi$
$571$	−31.5428	+	18.2113i	−1.32003	+	0.762117i	−0.336293	+	0.941757i	$0.609173\pi$
$572$	4.00493	−	4.97879i	0.167454	−	0.208174i
$573$	16.2312	−	10.6040i	0.678069	−	0.442987i
$574$	−8.33475	−	4.81207i	−0.347886	−	0.200852i
$575$	16.5865	−	8.81663i	0.691706	−	0.367679i
$576$	1.77662	+	2.41736i	0.0740256	+	0.100723i
$577$			29.2087i			1.21597i	0.793948	+	0.607986i	$0.208022\pi$
$577$			29.2087i			1.21597i	−0.793948	+	0.607986i	$0.791978\pi$
$578$	−6.90342	−	3.98569i	−0.287144	−	0.165783i
$579$	−40.5032	+	2.23387i	−1.68326	+	0.0928363i
$580$	−4.35874	−	4.51415i	−0.180987	−	0.187440i
$581$	16.7931	−	9.69550i	0.696695	−	0.402237i
$582$	5.03453	−	0.277669i	0.208688	−	0.0115097i
$583$	5.66764	+	0.878727i	0.234730	+	0.0363932i
$584$			12.2059i			0.505084i
$585$	12.1202	−	4.48585i	0.501110	−	0.185467i
$586$	−4.76754			−0.196945
$587$	4.67437	−	8.09624i	0.192932	−	0.334168i	−0.753289	−	0.657690i	$-0.771534\pi$
$587$	4.67437	−	8.09624i	0.192932	−	0.334168i	0.946221	+	0.323522i	$0.104867\pi$
$588$	−4.31896	−	6.61093i	−0.178111	−	0.272630i
$589$	37.6951	−	21.7633i	1.55320	−	0.896739i
$590$	9.74803	+	10.0956i	0.401320	+	0.415629i
$591$	−20.6149	−	10.4328i	−0.847982	−	0.429149i
$592$	−7.11906	−	4.11019i	−0.292592	−	0.168928i
$593$		−	19.0488i		−	0.782240i	−0.920340	−	0.391120i	$-0.872088\pi$
$593$		−	19.0488i		−	0.782240i	0.920340	−	0.391120i	$-0.127912\pi$
$594$	−15.0227	−	8.44505i	−0.616388	−	0.346505i
$595$	4.22226	+	16.9389i	0.173096	+	0.694429i
$596$	1.85977	−	3.22122i	0.0761792	−	0.131946i
$597$	−13.8988	+	27.4635i	−0.568840	+	1.12401i
$598$	6.26808	−	3.61888i	0.256321	−	0.147987i
$599$	−11.0401	+	6.37402i	−0.451087	+	0.260435i	−0.708289	−	0.705922i	$-0.750533\pi$
$599$	−11.0401	+	6.37402i	−0.451087	+	0.260435i	0.257202	+	0.966358i	$0.417199\pi$
$600$	4.17875	−	7.58538i	0.170597	−	0.309672i
$601$	−31.9092	−	18.4228i	−1.30160	−	0.751481i	−0.320925	−	0.947105i	$-0.603994\pi$
$601$	−31.9092	−	18.4228i	−1.30160	−	0.751481i	−0.980679	+	0.195623i	$0.937327\pi$
$602$		−	8.04668i		−	0.327958i
$603$	10.4208	+	4.57146i	0.424369	+	0.186164i
$604$		−	18.9583i		−	0.771402i
$605$	10.9251	+	22.0373i	0.444170	+	0.895942i
$606$	−0.535501	−	9.70942i	−0.0217533	−	0.394418i
$607$	−13.1028	−	22.6948i	−0.531828	−	0.921153i	−0.999310	−	0.0371504i	$-0.988172\pi$
$607$	−13.1028	−	22.6948i	−0.531828	−	0.921153i	0.467482	−	0.884003i	$-0.345161\pi$
$608$	−4.25729	−	7.37384i	−0.172656	−	0.299049i
$609$	−7.58233	+	0.418186i	−0.307251	+	0.0169458i
$610$	1.33168	−	4.64305i	0.0539181	−	0.187992i
$611$	17.3510			0.701944
$612$	13.7285	+	6.02249i	0.554942	+	0.243445i
$613$	−25.9621			−1.04860			−0.524300	−	0.851533i	$-0.675673\pi$
$613$	−25.9621			−1.04860			−0.524300	+	0.851533i	$0.675673\pi$
$614$	−19.2948	−	11.1399i	−0.778676	−	0.449569i
$615$	17.4923	+	16.2245i	0.705357	+	0.654236i
$616$	−4.03749	−	3.24775i	−0.162675	−	0.130856i
$617$	3.22832	+	5.59161i	0.129967	+	0.225110i	0.923664	−	0.383204i	$-0.125179\pi$
$617$	3.22832	+	5.59161i	0.129967	+	0.225110i	−0.793696	+	0.608314i	$0.791846\pi$
$618$	−1.68095	+	3.32150i	−0.0676179	+	0.133610i
$619$	−22.7138	+	39.3414i	−0.912944	+	1.58127i	−0.103060	+	0.994675i	$0.532863\pi$
$619$	−22.7138	+	39.3414i	−0.912944	+	1.58127i	−0.809884	+	0.586590i	$0.800470\pi$
$620$	11.0914	−	2.76468i	0.445441	−	0.111032i
$621$	−12.4092	−	15.0694i	−0.497963	−	0.604713i
$622$	−32.3229			−1.29603
$623$	−12.9327	−	7.46672i	−0.518140	−	0.299148i
$624$	1.50677	−	2.97733i	0.0603193	−	0.119189i
$625$	−24.9387	−	1.74998i	−0.997547	−	0.0699991i
$626$	15.3989	+	26.6716i	0.615463	+	1.06601i
$627$	39.7428	+	28.5122i	1.58718	+	1.13867i
$628$	15.0733	+	8.70255i	0.601489	+	0.347270i
$629$	−41.0784			−1.63790
$630$	−3.63775	−	9.82876i	−0.144931	−	0.391587i
$631$	−14.2563			−0.567535			−0.283768	−	0.958893i	$-0.591584\pi$
$631$	−14.2563			−0.567535			−0.283768	+	0.958893i	$0.591584\pi$
$632$	−2.24715	+	3.89217i	−0.0893867	+	0.154822i
$633$	1.64068	+	29.7480i	0.0652113	+	1.18237i
$634$	11.6986	−	6.75419i	0.464611	−	0.268243i
$635$	29.7054	+	30.7646i	1.17882	+	1.22085i
$636$	2.99065	−	0.164943i	0.118587	−	0.00654040i
$637$	−4.39174	+	7.60672i	−0.174007	+	0.301389i
$638$	8.67828	−	3.36380i	0.343576	−	0.133174i
$639$	−6.78522	+	4.98673i	−0.268419	+	0.197272i
$640$	−0.540822	−	2.16968i	−0.0213779	−	0.0857641i
$641$	5.38808	+	3.11081i	0.212816	+	0.122870i	0.602620	−	0.798029i	$-0.294124\pi$
$641$	5.38808	+	3.11081i	0.212816	+	0.122870i	−0.389803	+	0.920898i	$0.627457\pi$
$642$	−6.54035	−	10.0112i	−0.258127	−	0.395109i
$643$	−18.9335	+	10.9313i	−0.746664	+	0.431087i	−0.824487	−	0.565881i	$-0.808536\pi$
$643$	−18.9335	+	10.9313i	−0.746664	+	0.431087i	0.0778233	+	0.996967i	$0.475203\pi$
$644$	−2.93469	−	5.08303i	−0.115643	−	0.200299i
$645$	−4.43522	+	19.4484i	−0.174637	+	0.765779i
$646$	−36.8481	−	21.2743i	−1.44977	−	0.837024i
$647$	−2.59057			−0.101846			−0.0509229	−	0.998703i	$-0.516216\pi$
$647$	−2.59057			−0.101846			−0.0509229	+	0.998703i	$0.516216\pi$
$648$	−8.58944	−	2.68728i	−0.337425	−	0.105566i
$649$	−19.4084	+	7.52290i	−0.761846	+	0.295300i
$650$	−9.62687	−	0.337350i	−0.377597	−	0.0132319i
$651$	6.24636	−	12.3426i	0.244814	−	0.483743i
$652$	−12.4431	+	7.18402i	−0.487309	+	0.281348i
$653$	−11.0044	−	19.0603i	−0.430637	−	0.745885i	0.566291	−	0.824205i	$-0.308378\pi$
$653$	−11.0044	−	19.0603i	−0.430637	−	0.745885i	−0.996928	+	0.0783199i	$0.975044\pi$
$654$	−3.01469	−	4.61452i	−0.117884	−	0.180442i
$655$	−1.16486	+	4.06142i	−0.0455148	+	0.158693i
$656$	6.16017			0.240514
$657$	−21.6852	−	29.5061i	−0.846021	−	1.15114i
$658$		−	14.0706i		−	0.548527i
$659$	17.4775	−	30.2718i	0.680825	−	1.17922i	−0.293905	−	0.955835i	$-0.594955\pi$
$659$	17.4775	−	30.2718i	0.680825	−	1.17922i	0.974729	−	0.223388i	$-0.0717118\pi$
$660$	7.96828	+	10.0750i	0.310165	+	0.392171i
$661$	0.402443	+	0.697052i	0.0156532	+	0.0271122i	0.873746	−	0.486383i	$-0.161684\pi$
$661$	0.402443	+	0.697052i	0.0156532	+	0.0271122i	−0.858093	+	0.513495i	$0.828351\pi$
$662$	20.0675	−	11.5860i	0.779946	−	0.450302i
$663$	−0.918273	−	16.6496i	−0.0356628	−	0.646617i
$664$	−6.20584	+	10.7488i	−0.240833	+	0.417136i
$665$	7.19427	+	28.8621i	0.278982	+	1.11923i
$666$	24.5116	−	2.71201i	0.949804	−	0.105088i
$667$	10.5428			0.408217
$668$	−9.01381	−	5.20413i	−0.348755	−	0.201354i
$669$	11.3628	−	7.42337i	0.439311	−	0.287004i
$670$	−5.89154	−	6.10161i	−0.227610	−	0.235726i
$671$	5.58247	+	4.49053i	0.215509	+	0.173355i
$672$	−2.41443	−	1.22190i	−0.0931387	−	0.0471359i
$673$	−18.9391	+	32.8034i	−0.730048	+	1.26448i	0.226815	+	0.973938i	$0.427169\pi$
$673$	−18.9391	+	32.8034i	−0.730048	+	1.26448i	−0.956862	+	0.290542i	$0.906165\pi$
$674$		−	13.4702i		−	0.518852i
$675$	3.37476	+	25.7606i	0.129895	+	0.991528i
$676$	9.28838			0.357245
$677$	−37.0817	−	21.4092i	−1.42517	−	0.822821i	−0.428433	−	0.903574i	$-0.640934\pi$
$677$	−37.0817	−	21.4092i	−1.42517	−	0.822821i	−0.996734	+	0.0807531i	$0.974267\pi$
$678$	5.88836	+	2.97999i	0.226141	+	0.114446i
$679$	−3.93875	+	2.27404i	−0.151155	+	0.0872695i
$680$	−7.76158	−	8.03833i	−0.297643	−	0.308256i
$681$	12.5065	−	8.17054i	0.479248	−	0.313096i
$682$	−2.59765	+	16.7544i	−0.0994691	+	0.641559i
$683$	−24.3909			−0.933292			−0.466646	−	0.884444i	$-0.654538\pi$
$683$	−24.3909			−0.933292			−0.466646	+	0.884444i	$0.654538\pi$
$684$	23.3919	+	10.2617i	0.894411	+	0.392365i
$685$	17.6129	−	4.39025i	0.672953	−	0.167743i
$686$	15.6396	+	9.02954i	0.597124	+	0.344750i
$687$	4.26712	−	0.235344i	0.162801	−	0.00897892i
$688$	2.57524	+	4.46044i	0.0981800	+	0.170053i
$689$	−1.66577	−	2.88520i	−0.0634609	−	0.109918i
$690$	4.29128	+	13.9030i	0.163366	+	0.529277i
$691$	−4.22812	+	7.32332i	−0.160845	+	0.278592i	−0.935172	−	0.354194i	$-0.884755\pi$
$691$	−4.22812	+	7.32332i	−0.160845	+	0.278592i	0.774327	+	0.632786i	$0.218089\pi$
$692$			0.912571i			0.0346907i
$693$	15.5301	+	0.677916i	0.589939	+	0.0257519i
$694$	9.74141			0.369779
$695$	17.2588	+	4.95003i	0.654665	+	0.187765i
$696$	4.06921	−	2.65844i	0.154243	−	0.100768i
$697$	26.6590	−	15.3916i	1.00978	−	0.582999i
$698$	2.15268	+	3.72855i	0.0814801	+	0.141128i
$699$	−0.263578	−	0.133392i	−0.00996945	−	0.00504536i
$700$	−0.273570	+	7.80680i	−0.0103400	+	0.295069i
$701$	15.8462			0.598503			0.299251	−	0.954174i	$-0.403263\pi$
$701$	15.8462			0.598503			0.299251	+	0.954174i	$0.403263\pi$
$702$	1.64715	+	9.87424i	0.0621677	+	0.372679i
$703$	−69.9931			−2.63984
$704$	3.27747	+	0.508147i	0.123524	+	0.0191515i
$705$	−7.75550	+	34.0077i	−0.292089	+	1.28081i
$706$	−6.81904	+	3.93697i	−0.256638	+	0.148170i
$707$	4.38563	+	7.59613i	0.164938	+	0.285682i
$708$	−9.10050	+	5.94541i	−0.342018	+	0.223442i
$709$	−1.46258	+	2.53326i	−0.0549282	+	0.0951385i	−0.892182	−	0.451676i	$-0.850826\pi$
$709$	−1.46258	+	2.53326i	−0.0549282	+	0.0951385i	0.837254	+	0.546814i	$0.184160\pi$
$710$	6.09001	−	1.51802i	0.228554	−	0.0569701i
$711$	−1.48273	−	13.4011i	−0.0556066	−	0.502581i
$712$	9.55852			0.358221
$713$	−9.60248	+	16.6320i	−0.359616	+	0.622872i
$714$	−13.5018	+	0.744662i	−0.505292	+	0.0278683i
$715$	5.99678	−	12.9683i	0.224267	−	0.484988i
$716$	5.23213	−	3.02077i	0.195534	−	0.112891i
$717$	46.1219	−	2.54375i	1.72245	−	0.0949982i
$718$	−27.7994	−	16.0500i	−1.03746	−	0.598980i
$719$			13.1216i			0.489352i	0.969605	+	0.244676i	$0.0786817\pi$
$719$			13.1216i			0.489352i	−0.969605	+	0.244676i	$0.921318\pi$
$720$	5.16205	+	4.28407i	0.192378	+	0.159658i
$721$		−	3.35783i		−	0.125052i
$722$	−46.3307	−	26.7490i	−1.72425	−	0.995495i
$723$	−7.17858	+	4.68981i	−0.266974	+	0.174416i
$724$	0.883035	+	1.52946i	0.0328177	+	0.0568420i
$725$	−11.8984	−	7.43697i	−0.441896	−	0.276202i
$726$	−18.3569	+	5.10137i	−0.681289	+	0.189330i
$727$	−29.0177	−	16.7534i	−1.07621	−	0.621348i	−0.146336	−	0.989235i	$-0.546748\pi$
$727$	−29.0177	−	16.7534i	−1.07621	−	0.621348i	−0.929871	+	0.367887i	$0.880081\pi$
$728$			3.00989i			0.111554i
$729$	25.5380	−	8.76402i	0.945854	−	0.324593i
$730$	6.60123	+	26.4829i	0.244322	+	0.980177i
$731$	22.2894	+	12.8688i	0.824404	+	0.475970i
$732$	3.33833	+	1.68947i	0.123388	+	0.0624446i
$733$	−7.71974	−	13.3710i	−0.285135	−	0.493868i	0.687507	−	0.726178i	$-0.258705\pi$
$733$	−7.71974	−	13.3710i	−0.285135	−	0.493868i	−0.972642	+	0.232310i	$0.925372\pi$
$734$	−12.9930	−	22.5045i	−0.479580	−	0.830657i
$735$	−12.9461	−	12.0078i	−0.477524	−	0.442915i
$736$	3.25352	+	1.87842i	0.119926	+	0.0692394i
$737$	11.7301	−	4.54671i	0.432084	−	0.167480i
$738$	−14.8914	+	10.9443i	−0.548158	+	0.402863i
$739$			31.3928i			1.15480i	0.816461	+	0.577401i	$0.195933\pi$
$739$			31.3928i			1.15480i	−0.816461	+	0.577401i	$0.804067\pi$
$740$	−17.6690	−	5.06766i	−0.649524	−	0.186291i
$741$	−1.56464	−	28.3691i	−0.0574784	−	1.04217i
$742$	−2.33972	+	1.35084i	−0.0858939	+	0.0495909i
$743$	−22.3828	+	12.9227i	−0.821145	+	0.474088i	−0.850811	−	0.525472i	$-0.823889\pi$
$743$	−22.3828	+	12.9227i	−0.821145	+	0.474088i	0.0296662	+	0.999560i	$0.490556\pi$
$744$	0.487595	+	8.84081i	0.0178761	+	0.324120i
$745$	2.29300	−	7.99482i	0.0840092	−	0.292908i
$746$		−	3.47674i		−	0.127292i
$747$	−4.09478	−	37.0092i	−0.149820	−	1.35410i
$748$	15.4534	−	5.98989i	0.565031	−	0.219012i
$749$	9.34129	+	5.39320i	0.341323	+	0.197063i
$750$	4.96421	−	18.7178i	0.181267	−	0.683478i
$751$	20.7918	+	36.0124i	0.758703	+	1.31411i	0.943512	+	0.331338i	$0.107500\pi$
$751$	20.7918	+	36.0124i	0.758703	+	1.31411i	−0.184809	+	0.982774i	$0.559167\pi$
$752$	4.50310	+	7.79960i	0.164211	+	0.284422i
$753$	48.2662	+	24.4267i	1.75892	+	0.890158i
$754$	−4.68214	−	2.70323i	−0.170513	−	0.0984460i
$755$	−10.2531	−	41.1334i	−0.373147	−	1.49700i
$756$	8.00740	−	1.33574i	0.291226	−	0.0485803i
$757$		−	53.5181i		−	1.94515i	−0.232590	−	0.972575i	$-0.574720\pi$
$757$		−	53.5181i		−	1.94515i	0.232590	−	0.972575i	$-0.425280\pi$
$758$	8.10511	+	4.67949i	0.294391	+	0.169967i
$759$	−21.4763	−	2.12708i	−0.779541	−	0.0772081i
$760$	−13.2249	−	13.6964i	−0.479717	−	0.496822i
$761$	−8.73083	−	15.1222i	−0.316492	−	0.548181i	0.663261	−	0.748388i	$-0.269172\pi$
$761$	−8.73083	−	15.1222i	−0.316492	−	0.548181i	−0.979754	+	0.200207i	$0.935839\pi$
$762$	−27.7322	+	18.1176i	−1.00463	+	0.656331i
$763$	4.30575	+	2.48592i	0.155879	+	0.0899965i
$764$		−	11.1937i		−	0.404974i
$765$	33.0436	+	5.64221i	1.19469	+	0.203994i
$766$			18.5828i			0.671424i
$767$	10.4713	+	6.04560i	0.378096	+	0.218294i
$768$	1.72942	−	0.0953825i	0.0624052	−	0.00344182i
$769$	28.1988	−	16.2806i	1.01688	−	0.587093i	0.103678	−	0.994611i	$-0.466939\pi$
$769$	28.1988	−	16.2806i	1.01688	−	0.587093i	0.913197	+	0.407518i	$0.133606\pi$
$770$	−10.5165	−	4.86301i	−0.378989	−	0.175251i
$771$	−43.0262	+	2.37301i	−1.54955	+	0.0854620i
$772$	−11.7100	+	20.2824i	−0.421454	+	0.729979i
$773$	35.1109			1.26285			0.631425	−	0.775437i	$-0.282470\pi$
$773$	35.1109			1.26285			0.631425	+	0.775437i	$0.282470\pi$
$774$	−14.1498	−	6.20729i	−0.508603	−	0.223117i
$775$	22.5696	−	11.9969i	0.810724	−	0.430943i
$776$	1.45555	−	2.52109i	0.0522513	−	0.0905019i
$777$	−18.6226	+	12.1662i	−0.668080	+	0.436461i
$778$	−2.87026	−	4.97144i	−0.102904	−	0.178235i
$779$	45.4241	−	26.2256i	1.62749	−	0.939630i
$780$	1.65901	−	7.27475i	0.0594022	−	0.260478i
$781$	−1.42630	+	9.19942i	−0.0510371	+	0.329181i
$782$	18.7734			0.671337
$783$	−5.11372	+	13.6558i	−0.182750	+	0.488019i
$784$	−4.55916			−0.162827
$785$	37.4107	+	10.7298i	1.33525	+	0.382963i
$786$	−2.92014	−	1.47783i	−0.104158	−	0.0527125i
$787$	−1.62532	−	2.81513i	−0.0579363	−	0.100349i	0.835603	−	0.549334i	$-0.185119\pi$
$787$	−1.62532	−	2.81513i	−0.0579363	−	0.100349i	−0.893539	+	0.448986i	$0.851785\pi$
$788$	−11.5522	+	6.66969i	−0.411531	+	0.237598i
$789$	−36.6482	+	23.9425i	−1.30471	+	0.852375i
$790$	−2.77062	+	9.66008i	−0.0985742	+	0.343690i
$791$	−5.95276			−0.211656
$792$	−8.82560	+	4.59442i	−0.313604	+	0.163256i
$793$		−	4.16165i		−	0.147785i
$794$	11.1730	−	19.3521i	0.396513	−	0.686781i
$795$	6.39954	−	1.97528i	0.226968	−	0.0700560i
$796$	8.88548	+	15.3901i	0.314937	+	0.545488i
$797$	−1.43985	−	2.49389i	−0.0510021	−	0.0883382i	0.839397	−	0.543518i	$-0.182908\pi$
$797$	−1.43985	−	2.49389i	−0.0510021	−	0.0883382i	−0.890399	+	0.455180i	$0.849575\pi$
$798$	−23.0056	+	1.26882i	−0.814390	+	0.0449159i
$799$	38.9757	+	22.5026i	1.37886	+	0.796085i
$800$	−2.34682	−	4.41502i	−0.0829727	−	0.156095i
$801$	−23.1064	+	16.9818i	−0.816425	+	0.600023i
$802$	−22.0944			−0.780179
$803$	−40.0045	−	6.20241i	−1.41173	−	0.218878i
$804$	5.50019	−	3.59331i	0.193977	−	0.126726i
$805$	−9.11635	−	9.44140i	−0.321309	−	0.332766i
$806$	8.52910	−	4.92428i	0.300425	−	0.173450i
$807$	−40.1468	−	20.3176i	−1.41323	−	0.715213i
$808$	−4.86209	−	2.80713i	−0.171048	−	0.0987544i
$809$	30.7061			1.07957			0.539785	−	0.841803i	$-0.318505\pi$
$809$	30.7061			1.07957			0.539785	+	0.841803i	$0.318505\pi$
$810$	−20.0897	−	1.18517i	−0.705880	−	0.0416426i
$811$		−	39.8278i		−	1.39854i	−0.714856	−	0.699272i	$-0.753508\pi$
$811$		−	39.8278i		−	1.39854i	0.714856	−	0.699272i	$-0.246492\pi$
$812$	−2.19216	+	3.79692i	−0.0769296	+	0.133246i
$813$	−39.1558	−	19.8161i	−1.37325	−	0.694980i
$814$	17.0885	−	21.2439i	0.598953	−	0.744598i
$815$	−23.1122	+	22.3165i	−0.809586	+	0.781713i
$816$	7.24601	−	4.73386i	0.253661	−	0.165718i
$817$	37.9788	+	21.9270i	1.32871	+	0.767130i
$818$	37.5953			1.31449
$819$	−5.34742	−	7.27600i	−0.186854	−	0.254244i
$820$	13.3656	−	3.33155i	0.466747	−	0.116343i
$821$	20.3724	−	35.2861i	0.711003	−	1.23149i	−0.253478	−	0.967341i	$-0.581575\pi$
$821$	20.3724	−	35.2861i	0.711003	−	1.23149i	0.964481	−	0.264152i	$-0.0850920\pi$
$822$	0.774289	+	14.0390i	0.0270064	+	0.489666i
$823$	20.9042	−	12.0691i	0.728676	−	0.420701i	−0.0892616	−	0.996008i	$-0.528451\pi$
$823$	20.9042	−	12.0691i	0.728676	−	0.420701i	0.817938	+	0.575307i	$0.195117\pi$
$824$	1.07463	+	1.86132i	0.0374365	+	0.0648420i
$825$	22.7374	+	17.5502i	0.791615	+	0.611020i
$826$	4.90261	−	8.49157i	0.170584	−	0.295459i
$827$			17.2100i			0.598450i	0.954183	+	0.299225i	$0.0967281\pi$
$827$			17.2100i			0.598450i	−0.954183	+	0.299225i	$0.903272\pi$
$828$	−11.2022	+	1.23943i	−0.389302	+	0.0430732i
$829$	−39.6190			−1.37602			−0.688012	−	0.725699i	$-0.741517\pi$
$829$	−39.6190			−1.37602			−0.688012	+	0.725699i	$0.741517\pi$
$830$	−7.65148	+	26.6778i	−0.265587	+	0.925999i
$831$	−29.5918	−	45.2955i	−1.02653	−	1.57128i
$832$	−0.963278	−	1.66845i	−0.0333957	−	0.0578430i
$833$	−19.7304	+	11.3914i	−0.683619	+	0.394688i
$834$	−6.27999	+	12.4090i	−0.217458	+	0.429690i
$835$	−22.3716	−	6.41642i	−0.774201	−	0.222049i
$836$	26.3308	−	10.2061i	0.910671	−	0.352986i
$837$	−16.8854	−	20.5052i	−0.583645	−	0.708762i
$838$	−7.45791			−0.257629
$839$	−17.0978	−	9.87143i	−0.590282	−	0.340799i	0.174927	−	0.984581i	$-0.444031\pi$
$839$	−17.0978	−	9.87143i	−0.590282	−	0.340799i	−0.765209	+	0.643782i	$0.777364\pi$
$840$	−5.89937	−	1.34536i	−0.203548	−	0.0464192i
$841$	10.5624	+	18.2946i	0.364220	+	0.630848i
$842$	27.9475	−	16.1355i	0.963133	−	0.556065i
$843$	18.1155	+	27.7290i	0.623931	+	0.955037i
$844$	14.8966	+	8.60055i	0.512761	+	0.296043i
$845$	20.1528	−	5.02336i	0.693278	−	0.172809i
$846$	−24.7425	−	10.8542i	−0.850665	−	0.373174i
$847$	12.6960	−	11.5824i	0.436241	−	0.397976i
$848$	0.864638	−	1.49760i	0.0296918	−	0.0514277i
$849$	20.1350	−	1.11050i	0.691032	−	0.0381123i
$850$	−21.1875	−	13.2430i	−0.726724	−	0.454230i
$851$	26.7451	−	15.4413i	0.916812	−	0.529322i
$852$	0.267726	+	4.85426i	0.00917215	+	0.166304i
$853$	14.9607	−	25.9127i	0.512245	−	0.887234i	−0.487654	−	0.873037i	$-0.662147\pi$
$853$	14.9607	−	25.9127i	0.512245	−	0.887234i	0.999899	−	0.0141974i	$-0.00451931\pi$
$854$	−3.37484			−0.115485
$855$	56.3026	+	9.61371i	1.92551	+	0.328782i
$856$	−6.90410			−0.235977
$857$	42.9573	+	24.8014i	1.46739	+	0.847200i	0.999334	−	0.0364961i	$-0.0116197\pi$
$857$	42.9573	+	24.8014i	1.46739	+	0.847200i	0.468060	+	0.883697i	$0.344953\pi$
$858$	8.99243	+	6.45132i	0.306997	+	0.220245i
$859$	19.5831	+	33.9189i	0.668166	+	1.15730i	0.978416	+	0.206643i	$0.0662539\pi$
$859$	19.5831	+	33.9189i	0.668166	+	1.15730i	−0.310250	+	0.950655i	$0.600413\pi$
$860$	7.99974	+	8.28498i	0.272789	+	0.282516i
$861$	7.52712	−	14.8733i	0.256523	−	0.506881i
$862$	23.0197	+	13.2904i	0.784055	+	0.452674i
$863$	3.37269			0.114808			0.0574038	−	0.998351i	$-0.481718\pi$
$863$	3.37269			0.114808			0.0574038	+	0.998351i	$0.481718\pi$
$864$	−4.01118	+	3.30309i	−0.136463	+	0.112373i
$865$	0.493538	+	1.97999i	0.0167808	+	0.0673215i
$866$	−0.276016	+	0.478073i	−0.00937939	+	0.0162456i
$867$	6.23448	−	12.3191i	0.211734	−	0.418378i
$868$	−3.99328	−	6.91657i	−0.135541	−	0.234764i
$869$	−11.6146	−	9.34275i	−0.393998	−	0.316931i
$870$	7.39113	−	7.96867i	0.250583	−	0.270163i
$871$	−6.32867	−	3.65386i	−0.214439	−	0.123806i
$872$	−3.18235			−0.107768
$873$	0.960412	+	8.68035i	0.0325050	+	0.293785i
$874$	31.9879			1.08201
$875$	3.62853	+	17.0862i	0.122667	+	0.577619i
$876$	−21.1092	+	1.16423i	−0.713213	+	0.0393357i
$877$	19.3253	+	33.4725i	0.652570	+	1.13029i	0.982497	+	0.186278i	$0.0596426\pi$
$877$	19.3253	+	33.4725i	0.652570	+	1.13029i	−0.329927	+	0.944007i	$0.607024\pi$
$878$	−8.75031	−	15.1560i	−0.295309	−	0.511490i
$879$	−0.454740	−	8.24509i	−0.0153380	−	0.278100i
$880$	7.38587	−	0.670008i	0.248978	−	0.0225860i
$881$			39.8388i			1.34220i	0.741365	+	0.671102i	$0.234179\pi$
$881$			39.8388i			1.34220i	−0.741365	+	0.671102i	$0.765821\pi$
$882$	11.0211	−	8.09988i	0.371101	−	0.272737i
$883$			44.8898i			1.51066i	0.655344	+	0.755330i	$0.272524\pi$
$883$			44.8898i			1.51066i	−0.655344	+	0.755330i	$0.727476\pi$
$884$	−8.33746	−	4.81363i	−0.280419	−	0.161900i
$885$	−16.5298	+	17.8214i	−0.555642	+	0.599060i
$886$	10.3977	−	6.00312i	0.349318	−	0.201679i
$887$	−0.478423	+	0.276218i	−0.0160639	+	0.00927448i	−0.508010	−	0.861351i	$-0.669619\pi$
$887$	−0.478423	+	0.276218i	−0.0160639	+	0.00927448i	0.491947	+	0.870625i	$0.336286\pi$
$888$	6.42922	−	12.7039i	0.215751	−	0.426315i
$889$	14.9398	−	25.8765i	0.501066	−	0.867871i
$890$	20.7389	−	5.16946i	0.695171	−	0.173281i
$891$	13.1722	−	26.7861i	0.441284	−	0.897368i
$892$		−	7.83623i		−	0.262376i
$893$	66.4103	+	38.3420i	2.22234	+	1.28307i
$894$	5.74824	+	2.90908i	0.192250	+	0.0972943i
$895$	9.71834	−	9.38375i	0.324848	−	0.313664i
$896$	−1.35301	+	0.781159i	−0.0452008	+	0.0260967i
$897$	6.85644	+	10.4950i	0.228930	+	0.350417i
$898$	8.94844	−	15.4992i	0.298613	−	0.517214i
$899$	14.3457			0.478457
$900$	13.5169	+	6.50331i	0.450564	+	0.216777i
$901$		−	8.64143i		−	0.287888i
$902$	−3.13027	+	20.1897i	−0.104227	+	0.672245i
$903$	13.9161	−	0.767512i	0.463099	−	0.0255412i
$904$	3.29974	−	1.90511i	0.109748	−	0.0633629i
$905$	2.74307	+	2.84088i	0.0911827	+	0.0944339i
$906$	32.7869	−	1.80829i	1.08927	−	0.0600764i
$907$	−0.483241	−	0.278999i	−0.0160458	−	0.00926402i	0.491956	−	0.870620i	$-0.336282\pi$
$907$	−0.483241	−	0.278999i	−0.0160458	−	0.00926402i	−0.508001	+	0.861356i	$0.669616\pi$
$908$		−	8.62494i		−	0.286229i
$909$	16.7406	−	1.85222i	0.555251	−	0.0614341i
$910$	1.62782	+	6.53051i	0.0539616	+	0.216484i
$911$	7.89727	+	4.55949i	0.261648	+	0.151063i	0.625086	−	0.780556i	$-0.285064\pi$
$911$	7.89727	+	4.55949i	0.261648	+	0.151063i	−0.363438	+	0.931618i	$0.618397\pi$
$912$	12.3464	−	8.06599i	0.408831	−	0.267091i
$913$	−32.0754	−	25.8014i	−1.06154	−	0.853902i
$914$	32.0178	−	18.4855i	1.05905	−	0.611445i
$915$	8.15681	+	1.86017i	0.269656	+	0.0614953i
$916$	1.23368	−	2.13680i	0.0407621	−	0.0706020i
$917$	2.95208			0.0974863
$918$	−9.10598	+	24.3168i	−0.300542	+	0.802575i
$919$		−	49.0954i		−	1.61951i	−0.586770	−	0.809753i	$-0.699601\pi$
$919$		−	49.0954i		−	1.61951i	0.586770	−	0.809753i	$-0.300399\pi$
$920$	8.07498	+	2.31599i	0.266224	+	0.0763561i
$921$	17.4252	−	34.4314i	0.574178	−	1.13455i
$922$	−23.3562	+	13.4847i	−0.769194	+	0.444094i
$923$	4.68311	−	2.70380i	0.154147	−	0.0889965i
$924$	5.23163	−	7.29231i	0.172108	−	0.239899i
$925$	−41.0767	−	1.43943i	−1.35059	−	0.0473282i
$926$	−20.7805			−0.682890
$927$	−5.90461	−	2.59027i	−0.193933	−	0.0850755i
$928$		−	2.80629i		−	0.0921208i
$929$	19.0798	+	11.0157i	0.625987	+	0.361414i	0.779196	−	0.626780i	$-0.215627\pi$
$929$	19.0798	+	11.0157i	0.625987	+	0.361414i	−0.153209	+	0.988194i	$0.548961\pi$
$930$	5.83923	+	18.9180i	0.191476	+	0.620346i
$931$	−33.6185	+	19.4097i	−1.10180	+	0.636126i
$932$	−0.147705	+	0.0852775i	−0.00483824	+	0.00279336i
$933$	−3.08303	−	55.8999i	−0.100934	−	1.83008i
$934$	9.87065	+	5.69882i	0.322977	+	0.186471i
$935$	30.2894	−	21.3537i	0.990569	−	0.698340i
$936$	5.29278	+	2.32186i	0.173000	+	0.0758925i
$937$	−6.78304			−0.221592			−0.110796	−	0.993843i	$-0.535340\pi$
$937$	−6.78304			−0.221592			−0.110796	+	0.993843i	$0.535340\pi$
$938$	−2.96305	+	5.13216i	−0.0967471	+	0.167571i
$939$	−44.6577	+	29.1752i	−1.45735	+	0.952095i
$940$	13.9885	+	14.4873i	0.456254	+	0.472522i
$941$	−2.67272	−	4.62928i	−0.0871281	−	0.150910i	0.819168	−	0.573554i	$-0.194436\pi$
$941$	−2.67272	−	4.62928i	−0.0871281	−	0.150910i	−0.906296	+	0.422643i	$0.861102\pi$
$942$	−13.6127	+	26.8981i	−0.443525	+	0.876388i
$943$	−11.5714	+	20.0422i	−0.376816	+	0.652664i
$944$			6.27607i			0.204269i
$945$	16.6511	−	7.22870i	0.541660	−	0.235150i
$946$	−15.9275	+	6.17369i	−0.517849	+	0.200724i
$947$	−15.7134	+	27.2164i	−0.510617	+	0.884415i	0.489307	+	0.872112i	$0.337250\pi$
$947$	−15.7134	+	27.2164i	−0.510617	+	0.884415i	−0.999924	+	0.0123034i	$0.996084\pi$
$948$	−6.94555	−	3.51502i	−0.225581	−	0.114163i
$949$	11.7577	+	20.3649i	0.381671	+	0.661073i
$950$	−36.1011	−	22.5646i	−1.17127	−	0.732092i
$951$	12.7967	+	19.5876i	0.414961	+	0.635171i
$952$	−3.90356	+	6.76116i	−0.126515	+	0.219131i
$953$		−	33.4588i		−	1.08384i	−0.840431	−	0.541919i	$-0.817698\pi$
$953$		−	33.4588i		−	1.08384i	0.840431	−	0.541919i	$-0.182302\pi$
$954$	0.570511	+	5.15636i	0.0184710	+	0.166943i
$955$	−6.05380	−	24.2868i	−0.195896	−	0.785901i
$956$	13.3345	−	23.0960i	0.431268	−	0.746978i
$957$	6.64518	+	14.6876i	0.214808	+	0.474781i
$958$	3.45541	−	1.99498i	0.111639	−	0.0644550i
$959$	−6.34124	−	10.9833i	−0.204769	−	0.354671i
$960$	3.70071	−	1.14226i	0.119440	−	0.0368663i
$961$	2.43373	−	4.21534i	0.0785074	−	0.135979i
$962$	−15.8370			−0.510606
$963$	16.6897	−	12.2659i	0.537818	−	0.395264i
$964$			4.95063i			0.159449i
$965$	−14.4379	+	50.3393i	−0.464772	+	1.62048i
$966$	8.51079	−	5.56015i	0.273830	−	0.178895i
$967$	9.51316	+	16.4773i	0.305923	+	0.529873i	0.977466	−	0.211091i	$-0.0677018\pi$
$967$	9.51316	+	16.4773i	0.305923	+	0.529873i	−0.671544	+	0.740965i	$0.734368\pi$
$968$	−3.33087	+	10.4836i	−0.107058	+	0.336955i
$969$	33.2775	−	65.7551i	1.06903	−	2.11236i
$970$	1.79462	−	6.25716i	0.0576219	−	0.200905i
$971$		−	57.6587i		−	1.85036i	−0.379532	−	0.925178i	$-0.623915\pi$
$971$		−	57.6587i		−	1.85036i	0.379532	−	0.925178i	$-0.376085\pi$
$972$	3.82815	−	15.1111i	0.122788	−	0.484689i
$973$		−	12.5448i		−	0.402166i
$974$	11.9718	−	20.7357i	0.383601	−	0.664416i
$975$	−0.334815	−	16.6811i	−0.0107226	−	0.534223i
$976$	1.87075	−	1.08008i	0.0598811	−	0.0345724i
$977$	7.66591	+	13.2777i	0.245254	+	0.424793i	0.962203	−	0.272333i	$-0.0877953\pi$
$977$	7.66591	+	13.2777i	0.245254	+	0.424793i	−0.716949	+	0.697126i	$0.754462\pi$
$978$	−13.6111	−	20.8341i	−0.435233	−	0.666202i
$979$	−4.85714	+	31.3277i	−0.155235	+	1.00124i
$980$	−9.89192	+	2.46569i	−0.315986	+	0.0787637i
$981$	7.69290	−	5.65382i	0.245615	−	0.180513i
$982$			29.2824i			0.934438i
$983$	11.0525	−	19.1435i	0.352520	−	0.610582i	−0.634170	−	0.773193i	$-0.718658\pi$
$983$	11.0525	−	19.1435i	0.352520	−	0.610582i	0.986690	+	0.162611i	$0.0519916\pi$
$984$	0.587572	+	10.6535i	0.0187311	+	0.339622i
$985$	−21.4575	+	20.7188i	−0.683694	+	0.660155i
$986$	−7.01170	−	12.1446i	−0.223298	−	0.386763i
$987$	24.3339	−	1.34208i	0.774557	−	0.0427190i
$988$	−14.2061	−	8.20191i	−0.451957	−	0.260937i
$989$	−19.3495			−0.615278
$990$	−16.6640	+	14.7415i	−0.529616	+	0.468516i
$991$	−22.7982			−0.724210			−0.362105	−	0.932137i	$-0.617942\pi$
$991$	−22.7982			−0.724210			−0.362105	+	0.932137i	$0.617942\pi$
$992$	4.42712	+	2.55600i	0.140561	+	0.0811531i
$993$	21.9511	+	33.6001i	0.696598	+	1.06627i
$994$	−2.19261	−	3.79771i	−0.0695454	−	0.120456i
$995$	27.6019	+	28.5861i	0.875041	+	0.906241i
$996$	−19.1812	−	9.70727i	−0.607780	−	0.307587i
$997$	2.45146	−	4.24606i	0.0776386	−	0.134474i	−0.824592	−	0.565728i	$-0.808595\pi$
$997$	2.45146	−	4.24606i	0.0776386	−	0.134474i	0.902231	+	0.431254i	$0.141929\pi$
$998$			32.4961i			1.02864i
$999$	7.02819	+	42.1322i	0.222362	+	1.33300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.o.a.659.49	yes	144
5.4	even	2	inner	990.2.o.a.659.24	yes	144
9.5	odd	6	inner	990.2.o.a.329.60	yes	144
11.10	odd	2	inner	990.2.o.a.659.13	yes	144
45.14	odd	6	inner	990.2.o.a.329.13	✓	144
55.54	odd	2	inner	990.2.o.a.659.60	yes	144
99.32	even	6	inner	990.2.o.a.329.24	yes	144
495.329	even	6	inner	990.2.o.a.329.49	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.o.a.329.13	✓	144	45.14	odd	6	inner
990.2.o.a.329.24	yes	144	99.32	even	6	inner
990.2.o.a.329.49	yes	144	495.329	even	6	inner
990.2.o.a.329.60	yes	144	9.5	odd	6	inner
990.2.o.a.659.13	yes	144	11.10	odd	2	inner
990.2.o.a.659.24	yes	144	5.4	even	2	inner
990.2.o.a.659.49	yes	144	1.1	even	1	trivial
990.2.o.a.659.60	yes	144	55.54	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.782108 + 1.54542i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.55321 + 1.60859i) q^{5} +(-1.45003 + 0.947315i) q^{6} +(0.781159 - 1.35301i) q^{7} +1.00000i q^{8} +(-1.77662 - 2.41736i) q^{9} +(0.540822 + 2.16968i) q^{10} +(-3.27747 - 0.508147i) q^{11} +(-1.72942 + 0.0953825i) q^{12} +(0.963278 + 1.66845i) q^{13} +(1.35301 - 0.781159i) q^{14} +(-3.70071 + 1.14226i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.99714i q^{17} +(-0.329913 - 2.98180i) q^{18} +8.51458i q^{19} +(-0.616475 + 2.14941i) q^{20} +(1.48001 + 2.26541i) q^{21} +(-2.58430 - 2.07880i) q^{22} +(-1.87842 - 3.25352i) q^{23} +(-1.54542 - 0.782108i) q^{24} +(-0.175105 + 4.99693i) q^{25} +1.92656i q^{26} +(5.12533 - 0.854971i) q^{27} +1.56232 q^{28} +(-1.40314 + 2.43031i) q^{29} +(-3.77604 - 0.861129i) q^{30} +(-2.55600 - 4.42712i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.34863 - 4.66762i) q^{33} +(-2.49857 + 4.32765i) q^{34} +(3.38973 - 0.844936i) q^{35} +(1.20519 - 2.74727i) q^{36} +8.22038i q^{37} +(-4.25729 + 7.37384i) q^{38} +(-3.33183 + 0.183760i) q^{39} +(-1.60859 + 1.55321i) q^{40} +(-3.08008 - 5.33486i) q^{41} +(0.149018 + 2.70191i) q^{42} +(2.57524 - 4.46044i) q^{43} +(-1.19866 - 3.09244i) q^{44} +(1.12909 - 6.61250i) q^{45} -3.75684i q^{46} +(4.50310 - 7.79960i) q^{47} +(-0.947315 - 1.45003i) q^{48} +(2.27958 + 3.94835i) q^{49} +(-2.65011 + 4.23992i) q^{50} +(-7.72265 - 3.90830i) q^{51} +(-0.963278 + 1.66845i) q^{52} -1.72928 q^{53} +(4.86615 + 1.82224i) q^{54} +(-4.27318 - 6.06135i) q^{55} +(1.35301 + 0.781159i) q^{56} +(-13.1586 - 6.65932i) q^{57} +(-2.43031 + 1.40314i) q^{58} +(5.43524 - 3.13803i) q^{59} +(-2.83958 - 2.63378i) q^{60} +(-1.87075 - 1.08008i) q^{61} -5.11200i q^{62} +(-4.65853 + 0.515429i) q^{63} -1.00000 q^{64} +(-1.18767 + 4.14096i) q^{65} +(5.23381 - 2.36796i) q^{66} +(-3.28496 + 1.89657i) q^{67} +(-4.32765 + 2.49857i) q^{68} +(6.49716 - 0.358337i) q^{69} +(3.35806 + 0.963129i) q^{70} -2.80687i q^{71} +(2.41736 - 1.77662i) q^{72} +12.2059 q^{73} +(-4.11019 + 7.11906i) q^{74} +(-7.58538 - 4.17875i) q^{75} +(-7.37384 + 4.25729i) q^{76} +(-3.24775 + 4.03749i) q^{77} +(-2.97733 - 1.50677i) q^{78} +(3.89217 + 2.24715i) q^{79} +(-2.16968 + 0.540822i) q^{80} +(-2.68728 + 8.58944i) q^{81} -6.16017i q^{82} +(10.7488 + 6.20584i) q^{83} +(-1.22190 + 2.41443i) q^{84} +(-8.03833 + 7.76158i) q^{85} +(4.46044 - 2.57524i) q^{86} +(-2.65844 - 4.06921i) q^{87} +(0.508147 - 3.27747i) q^{88} -9.55852i q^{89} +(4.28407 - 5.16205i) q^{90} +3.00989 q^{91} +(1.87842 - 3.25352i) q^{92} +(8.84081 - 0.487595i) q^{93} +(7.79960 - 4.50310i) q^{94} +(-13.6964 + 13.2249i) q^{95} +(-0.0953825 - 1.72942i) q^{96} +(-2.52109 - 1.45555i) q^{97} +4.55916i q^{98} +(4.59442 + 8.82560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Introduction

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