LMFDB - Embedded newform 990.2.o.a.659.60

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			659.60
Character	$\chi$	$=$	990.659
Dual form			990.2.o.a.329.60

$q$-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} +(-0.616475 - 2.14941i) 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} +(-2.07880 - 2.58430i) q^{11} +(1.72942 - 0.0953825i) q^{12} +(0.963278 + 1.66845i) q^{13} +(1.35301 - 0.781159i) q^{14} +(-3.80388 - 0.728360i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.99714i q^{17} +(-0.329913 - 2.98180i) q^{18} -8.51458i q^{19} +(1.55321 - 1.60859i) q^{20} +(-1.48001 - 2.26541i) q^{21} +(-0.508147 - 3.27747i) q^{22} +(1.87842 + 3.25352i) q^{23} +(1.54542 + 0.782108i) q^{24} +(-4.23992 + 2.65011i) q^{25} +1.92656i q^{26} +(-5.12533 + 0.854971i) q^{27} +1.56232 q^{28} +(1.40314 - 2.43031i) q^{29} +(-2.93008 - 2.53272i) q^{30} +(-2.55600 - 4.42712i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.61966 + 1.19141i) 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} +(2.14941 - 0.616475i) 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} +(-4.10066 + 5.30892i) q^{45} +3.75684i q^{46} +(-4.50310 + 7.79960i) q^{47} +(0.947315 + 1.45003i) q^{48} +(2.27958 + 3.94835i) q^{49} +(-4.99693 + 0.175105i) 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} +(-1.27116 - 3.65844i) q^{60} +(1.87075 + 1.08008i) q^{61} -5.11200i q^{62} +(-4.65853 + 0.515429i) q^{63} -1.00000 q^{64} +(2.99234 - 3.09903i) q^{65} +(-5.46247 - 1.77803i) q^{66} +(3.28496 - 1.89657i) q^{67} +(-4.32765 + 2.49857i) q^{68} +(6.49716 - 0.358337i) q^{69} +(-2.51312 - 2.42660i) q^{70} -2.80687i q^{71} +(2.41736 - 1.77662i) q^{72} +12.2059 q^{73} +(4.11019 - 7.11906i) q^{74} +(0.779451 + 8.62511i) q^{75} +(7.37384 - 4.25729i) q^{76} +(-5.12045 + 0.793888i) 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} +(10.7409 - 3.08061i) q^{85} +(4.46044 - 2.57524i) q^{86} +(-2.65844 - 4.06921i) q^{87} +(2.58430 - 2.07880i) q^{88} -9.55852i q^{89} +(-6.20573 + 2.54732i) q^{90} +3.00989 q^{91} +(-1.87842 + 3.25352i) q^{92} +(-8.84081 + 0.487595i) q^{93} +(-7.79960 + 4.50310i) q^{94} +(-18.3013 + 5.24902i) q^{95} +(0.0953825 + 1.72942i) q^{96} +(2.52109 + 1.45555i) q^{97} +4.55916i q^{98} +(-2.55395 + 9.61652i) 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
$5$	−0.616475	−	2.14941i	−0.275696	−	0.961245i
$5$	−0.616475	−	2.14941i	−0.275696	−	0.961245i
$6$	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
$11$	−2.07880	−	2.58430i	−0.626782	−	0.779194i
$11$	−2.07880	−	2.58430i	−0.626782	−	0.779194i
$12$	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
$15$	−3.80388	−	0.728360i	−0.982157	−	0.188062i
$16$	−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	$-0.568864\pi$
$19$		−	8.51458i		−	1.95338i	0.214659	−	0.976689i	$-0.431136\pi$
$20$	1.55321	−	1.60859i	0.347307	−	0.359691i
$21$	−1.48001	−	2.26541i	−0.322964	−	0.494353i
$22$	−0.508147	−	3.27747i	−0.108337	−	0.698758i
$23$	1.87842	+	3.25352i	0.391677	+	0.678405i	0.992671	−	0.120849i	$-0.0385616\pi$
$23$	1.87842	+	3.25352i	0.391677	+	0.678405i	−0.600994	+	0.799254i	$0.705228\pi$
$24$	1.54542	+	0.782108i	0.315457	+	0.159647i
$25$	−4.23992	+	2.65011i	−0.847984	+	0.530022i
$26$			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	−0.705833	−	0.708378i	$-0.749427\pi$
$29$	1.40314	−	2.43031i	0.260557	−	0.451298i	0.966390	+	0.257080i	$0.0827604\pi$
$30$	−2.93008	−	2.53272i	−0.534956	−	0.462409i
$31$	−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
$33$	−5.61966	+	1.19141i	−0.978257	+	0.207399i
$34$	−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	$-0.763837\pi$
$37$		−	8.22038i		−	1.35142i	0.737167	−	0.675711i	$-0.236163\pi$
$38$	4.25729	−	7.37384i	0.690623	−	1.19619i
$39$	3.33183	−	0.183760i	0.533520	−	0.0294251i
$40$	2.14941	−	0.616475i	0.339851	−	0.0974732i
$41$	3.08008	+	5.33486i	0.481028	+	0.833166i	0.999763	−	0.0217697i	$-0.00693006\pi$
$41$	3.08008	+	5.33486i	0.481028	+	0.833166i	−0.518735	+	0.854935i	$0.673597\pi$
$42$	−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
$45$	−4.10066	+	5.30892i	−0.611290	+	0.791406i
$46$			3.75684i			0.553916i
$47$	−4.50310	+	7.79960i	−0.656845	+	1.13769i	0.324583	+	0.945857i	$0.394776\pi$
$47$	−4.50310	+	7.79960i	−0.656845	+	1.13769i	−0.981428	+	0.191831i	$0.938557\pi$
$48$	0.947315	+	1.45003i	0.136733	+	0.209294i
$49$	2.27958	+	3.94835i	0.325654	+	0.564050i
$50$	−4.99693	+	0.175105i	−0.706673	+	0.0247636i
$51$	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	$-0.462106\pi$
$53$	1.72928			0.237534			0.118767	+	0.992922i	$0.462106\pi$
$54$	−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	$0.199372\pi$
$60$	−1.27116	−	3.65844i	−0.164106	−	0.472302i
$61$	1.87075	+	1.08008i	0.239524	+	0.138290i	0.614958	−	0.788560i	$-0.289173\pi$
$61$	1.87075	+	1.08008i	0.239524	+	0.138290i	−0.375434	+	0.926849i	$0.622506\pi$
$62$		−	5.11200i		−	0.649225i
$63$	−4.65853	+	0.515429i	−0.586919	+	0.0649380i
$64$	−1.00000			−0.125000
$65$	2.99234	−	3.09903i	0.371154	−	0.384388i
$66$	−5.46247	−	1.77803i	−0.672384	−	0.218861i
$67$	3.28496	−	1.89657i	0.401322	−	0.231703i	−0.285732	−	0.958310i	$-0.592237\pi$
$67$	3.28496	−	1.89657i	0.401322	−	0.231703i	0.687054	+	0.726606i	$0.258903\pi$
$68$	−4.32765	+	2.49857i	−0.524804	+	0.302996i
$69$	6.49716	−	0.358337i	0.782166	−	0.0431386i
$70$	−2.51312	−	2.42660i	−0.300376	−	0.290034i
$71$		−	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
$75$	0.779451	+	8.62511i	0.0900032	+	0.995941i
$76$	7.37384	−	4.25729i	0.845837	−	0.488345i
$77$	−5.12045	+	0.793888i	−0.583529	+	0.0904719i
$78$	2.97733	+	1.50677i	0.337116	+	0.170609i
$79$	−3.89217	−	2.24715i	−0.437904	−	0.252824i	0.264804	−	0.964302i	$-0.414693\pi$
$79$	−3.89217	−	2.24715i	−0.437904	−	0.252824i	−0.702708	+	0.711478i	$0.748026\pi$
$80$	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
$85$	10.7409	−	3.08061i	1.16501	−	0.334139i
$86$	4.46044	−	2.57524i	0.480982	−	0.277695i
$87$	−2.65844	−	4.06921i	−0.285014	−	0.436265i
$88$	2.58430	−	2.07880i	0.275487	−	0.221601i
$89$		−	9.55852i		−	1.01320i	−0.862181	−	0.506601i	$-0.830902\pi$
$89$		−	9.55852i		−	1.01320i	0.862181	−	0.506601i	$-0.169098\pi$
$90$	−6.20573	+	2.54732i	−0.654142	+	0.268512i
$91$	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
$95$	−18.3013	+	5.24902i	−1.87767	+	0.538538i
$96$	0.0953825	+	1.72942i	0.00973493	+	0.176508i
$97$	2.52109	+	1.45555i	0.255978	+	0.147789i	0.622499	−	0.782621i	$-0.286118\pi$
$97$	2.52109	+	1.45555i	0.255978	+	0.147789i	−0.366520	+	0.930410i	$0.619451\pi$
$98$			4.55916i			0.460545i
$99$	−2.55395	+	9.61652i	−0.256681	+	0.966496i
$100$	−4.41502	−	2.34682i	−0.441502	−	0.234682i
$101$	2.80713	−	4.86209i	0.279320	−	0.483796i	−0.691896	−	0.721997i	$-0.743224\pi$
$101$	2.80713	−	4.86209i	0.279320	−	0.483796i	0.971216	+	0.238201i	$0.0765578\pi$
$102$	4.73386	+	7.24601i	0.468722	+	0.717462i
$103$	−1.86132	+	1.07463i	−0.183401	+	0.105887i	−0.588890	−	0.808214i	$-0.700435\pi$
$103$	−1.86132	+	1.07463i	−0.183401	+	0.105887i	0.405489	+	0.914100i	$0.367101\pi$
$104$	−1.66845	+	0.963278i	−0.163605	+	0.0944572i
$105$	−3.95691	+	4.57771i	−0.386155	+	0.446739i
$106$	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	$-0.951298\pi$
$109$		−	3.18235i		−	0.304814i	0.988318	−	0.152407i	$-0.0487025\pi$
$110$	−6.73136	+	3.11269i	−0.641810	+	0.296783i
$111$	−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	0.941613	−	0.336698i	$-0.109310\pi$
$113$	1.90511	+	3.29974i	0.179217	+	0.310413i	−0.762395	+	0.647111i	$0.775977\pi$
$114$	−8.06599	−	12.3464i	−0.755449	−	1.15635i
$115$	5.83514	−	6.04320i	0.544130	−	0.563531i
$116$	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
$120$	0.728360	−	3.80388i	0.0664899	−	0.347245i
$121$	−2.35717	+	10.7445i	−0.214288	+	0.976771i
$122$	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
$130$	4.14096	−	1.18767i	0.363186	−	0.104166i
$131$	−0.944775	−	1.63640i	−0.0825454	−	0.142973i	0.821797	−	0.569780i	$-0.192972\pi$
$131$	−0.944775	−	1.63640i	−0.0825454	−	0.142973i	−0.904343	+	0.426807i	$0.859638\pi$
$132$	−3.84162	−	4.27106i	−0.334370	−	0.371748i
$133$	−11.5203	−	6.65124i	−0.998935	−	0.576736i
$134$	3.79315			0.327678
$135$	4.99732	+	10.4894i	0.430101	+	0.902781i
$136$	−4.99714			−0.428501
$137$	−4.05886	+	7.03016i	−0.346772	+	0.600627i	−0.985674	−	0.168661i	$-0.946056\pi$
$137$	−4.05886	+	7.03016i	−0.346772	+	0.600627i	0.638902	+	0.769288i	$0.279389\pi$
$138$	5.80587	+	2.93825i	0.494229	+	0.250121i
$139$	−6.95382	+	4.01479i	−0.589815	+	0.340530i	−0.765024	−	0.644001i	$-0.777273\pi$
$139$	−6.95382	+	4.01479i	−0.589815	+	0.340530i	0.175209	+	0.984531i	$0.443940\pi$
$140$	−0.963129	−	3.35806i	−0.0813993	−	0.283808i
$141$	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	0.932094	−	0.362216i	$-0.117980\pi$
$149$	1.85977	+	3.22122i	0.152358	+	0.263893i	−0.779736	+	0.626109i	$0.784647\pi$
$150$	−3.63753	+	7.85929i	−0.297003	+	0.641708i
$151$	16.4184	+	9.47914i	1.33611	+	0.771402i	0.986228	−	0.165393i	$-0.0528892\pi$
$151$	16.4184	+	9.47914i	1.33611	+	0.771402i	0.349879	+	0.936795i	$0.386223\pi$
$152$	8.51458			0.690623
$153$	12.0799	−	8.87799i	0.976601	−	0.717743i
$154$	−4.83138	−	1.87270i	−0.389324	−	0.150906i
$155$	−7.93999	+	8.22310i	−0.637755	+	0.660495i
$156$	1.82506	+	2.79357i	0.146121	+	0.223665i
$157$	−15.0733	+	8.70255i	−1.20298	+	0.694539i	−0.961216	−	0.275796i	$-0.911059\pi$
$157$	−15.0733	+	8.70255i	−1.20298	+	0.694539i	−0.241762	+	0.970336i	$0.577725\pi$
$158$	−2.24715	−	3.89217i	−0.178773	−	0.309645i
$159$	1.35248	−	2.67245i	0.107259	−	0.211939i
$160$	1.60859	+	1.55321i	0.127170	+	0.122792i
$161$	5.86938			0.462572
$162$	−6.62197	+	6.09504i	−0.520271	+	0.478872i
$163$		−	14.3680i		−	1.12539i	−0.826664	−	0.562696i	$-0.809764\pi$
$163$		−	14.3680i		−	1.12539i	0.826664	−	0.562696i	$-0.190236\pi$
$164$	−3.08008	+	5.33486i	−0.240514	+	0.416583i
$165$	6.02521	+	11.3445i	0.469062	+	0.883165i
$166$	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
$175$	0.273570	+	7.80680i	0.0206799	+	0.590139i
$176$	3.27747	−	0.508147i	0.247048	−	0.0383031i
$177$	−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	$-0.0724940\pi$
$180$	−6.64799	−	0.896819i	−0.495512	−	0.0668449i
$181$	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
$185$	−17.6690	+	5.06766i	−1.29905	+	0.372581i
$186$	−7.90016	−	3.99813i	−0.579268	−	0.293157i
$187$	12.9141	−	10.3881i	0.944371	−	0.759650i
$188$	−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
$195$	−2.44896	−	7.04818i	−0.175374	−	0.504731i
$196$	−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	$0.842377\pi$
$198$	−7.02004	+	7.05117i	−0.498892	+	0.501105i
$199$	17.7710			1.25975			0.629875	−	0.776697i	$-0.283106\pi$
$199$	17.7710			1.25975			0.629875	+	0.776697i	$0.283106\pi$
$200$	−2.65011	−	4.23992i	−0.187391	−	0.299807i
$201$	−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
$205$	9.56801	−	9.90917i	0.668259	−	0.692086i
$206$	−2.14926			−0.149746
$207$	4.52770	−	10.3211i	0.314697	−	0.717364i
$208$	−1.92656			−0.133583
$209$	−22.0042	+	17.7001i	−1.52206	+	1.22434i
$210$	−5.71564	+	1.98596i	−0.394417	+	0.137044i
$211$	−14.8966	+	8.60055i	−1.02552	+	0.592086i	−0.915699	−	0.401865i	$-0.868362\pi$
$211$	−14.8966	+	8.60055i	−1.02552	+	0.592086i	−0.109824	+	0.993951i	$0.535029\pi$
$212$	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
$220$	−7.38587	−	0.670008i	−0.497955	−	0.0451719i
$221$	−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	0.709707	−	0.704497i	$-0.248827\pi$
$223$	6.78637	+	3.91811i	0.454449	+	0.262376i	−0.255258	+	0.966873i	$0.582161\pi$
$224$			1.56232i			0.104387i
$225$	13.9390	+	5.54119i	0.929266	+	0.369412i
$226$			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	$0.859312\pi$
$230$	8.07498	−	2.31599i	0.532448	−	0.152712i
$231$	−2.77785	+	8.53412i	−0.182769	+	0.561504i
$232$	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	$0.164459\pi$
$239$	13.3345	+	23.0960i	0.862536	+	1.49396i	−0.00693675	+	0.999976i	$0.502208\pi$
$240$	2.53272	−	2.93008i	0.163486	−	0.189136i
$241$	−4.28737	−	2.47532i	−0.276174	−	0.159449i	0.355516	−	0.934670i	$-0.384305\pi$
$241$	−4.28737	−	2.47532i	−0.276174	−	0.159449i	−0.631690	+	0.775221i	$0.717638\pi$
$242$	−7.41360	+	8.12641i	−0.476565	+	0.522385i
$243$	11.1725	+	10.8708i	0.716717	+	0.697364i
$244$			2.16015i			0.138290i
$245$	7.08132	−	7.33381i	0.452409	−	0.468540i
$246$	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
$250$	3.45685	+	10.6325i	0.218631	+	0.672459i
$251$		−	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
$255$	3.63972	−	19.0085i	0.227928	−	1.19036i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.4395	−	21.5458i	−0.775952	−	1.34399i	−0.934258	−	0.356598i	$-0.883937\pi$
$257$	−12.4395	−	21.5458i	−0.775952	−	1.34399i	0.158306	−	0.987390i	$-0.449397\pi$
$258$	−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	$0.382276\pi$
$264$	−1.19141	−	5.61966i	−0.0733265	−	0.345866i
$265$	−1.06605	−	3.71692i	−0.0654872	−	0.228329i
$266$	−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	$0.709064\pi$
$270$	−0.916877	+	11.5827i	−0.0557994	+	0.704902i
$271$		−	25.3367i		−	1.53910i	−0.638588	−	0.769549i	$-0.720481\pi$
$271$		−	25.3367i		−	1.53910i	0.638588	−	0.769549i	$-0.279519\pi$
$272$	−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
$275$	15.6626	+	5.44814i	0.944492	+	0.328535i
$276$	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	$0.359875\pi$
$281$	−9.56150	+	16.5610i	−0.570391	+	0.987947i	−0.996526	+	0.0832868i	$0.973458\pi$
$282$	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
$285$	−6.20168	+	32.3884i	−0.367356	+	1.91852i
$286$	4.97879	−	4.00493i	0.294402	−	0.236816i
$287$	9.62414			0.568095
$288$	2.74727	+	1.20519i	0.161885	+	0.0710164i
$289$	−7.97138			−0.468905
$290$	−4.51415	−	4.35874i	−0.265080	−	0.255954i
$291$	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
$295$	−10.0956	−	9.74803i	−0.587789	−	0.567552i
$296$	8.22038			0.477800
$297$	12.8640	+	11.4681i	0.746448	+	0.665444i
$298$			3.71954i			0.215467i
$299$	−3.61888	+	6.26808i	−0.209285	+	0.362493i
$300$	−7.07984	+	4.98758i	−0.408755	+	0.287958i
$301$	−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	$0.719324\pi$
$308$	−3.24775	−	4.03749i	−0.185058	−	0.230057i
$309$	0.205002	+	3.71698i	0.0116622	+	0.211452i
$310$	−10.9878	+	3.15142i	−0.624064	+	0.178988i
$311$	−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	$-0.997196\pi$
$313$	−26.6716	−	15.3989i	−1.50757	−	0.870396i	−0.507608	−	0.861588i	$-0.669470\pi$
$314$	−17.4051			−0.982227
$315$	3.97973	+	9.69533i	0.224232	+	0.546270i
$316$		−	4.49429i		−	0.252824i
$317$	−6.75419	+	11.6986i	−0.379353	+	0.657059i	−0.990968	−	0.134096i	$-0.957187\pi$
$317$	−6.75419	+	11.6986i	−0.379353	+	0.657059i	0.611615	+	0.791156i	$0.290520\pi$
$318$	2.50751	−	1.63817i	0.140614	−	0.0918639i
$319$	−9.19751	+	1.42601i	−0.514962	+	0.0798411i
$320$	0.616475	+	2.14941i	0.0344620	+	0.120156i
$321$	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
$330$	−0.454245	+	12.8372i	−0.0250053	+	0.706665i
$331$	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
$335$	−6.10161	−	5.89154i	−0.333367	−	0.321889i
$336$	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
$340$	8.03833	+	7.76158i	0.435940	+	0.420931i
$341$	−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
$345$	−4.77555	−	13.7441i	−0.257107	−	0.739960i
$346$	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	0.396877	−	0.917872i	$-0.370094\pi$
$349$	−3.72855	−	2.15268i	−0.199585	−	0.115230i	−0.596462	+	0.802641i	$0.703427\pi$
$350$	−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	−0.742027	−	0.670370i	$-0.766135\pi$
$353$	3.93697	−	6.81904i	0.209544	−	0.362941i	0.951571	+	0.307429i	$0.0994688\pi$
$354$	4.90856	−	9.69913i	0.260887	−	0.515503i
$355$	−6.03311	+	1.73036i	−0.320204	+	0.0918382i
$356$	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	$-0.178355\pi$
$359$	32.0999			1.69417			0.847085	+	0.531457i	$0.178355\pi$
$360$	−5.30892	−	4.10066i	−0.279804	−	0.216124i
$361$	−53.4980			−2.81569
$362$	1.52946	+	0.883035i	0.0803867	+	0.0464113i
$363$	14.7611	+	12.0461i	0.774758	+	0.632258i
$364$	1.50495	+	2.60664i	0.0788807	+	0.136625i
$365$	−7.52464	−	26.2355i	−0.393858	−	1.37323i
$366$	3.73581	−	0.206041i	0.195274	−	0.0107699i
$367$	22.5045	+	12.9930i	1.17473	+	0.678228i	0.954789	−	0.297286i	$-0.0960814\pi$
$367$	22.5045	+	12.9930i	1.17473	+	0.678228i	0.219937	+	0.975514i	$0.429415\pi$
$368$	−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	$0.862023\pi$
$374$	16.3779	−	2.53928i	0.846884	−	0.131303i
$375$	18.0584	−	6.99252i	0.932530	−	0.361092i
$376$	−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	$0.422731\pi$
$380$	−13.6964	−	13.2249i	−0.702613	−	0.678422i
$381$	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	0.524814	−	0.851217i	$-0.324135\pi$
$383$	−9.29140	−	16.0932i	−0.474768	−	0.822323i	−0.999582	+	0.0288939i	$0.990801\pi$
$384$	−1.45003	+	0.947315i	−0.0739967	+	0.0483425i
$385$	4.86301	+	10.5165i	0.247842	+	0.535971i
$386$			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	$0.713155\pi$
$390$	1.40323	−	7.32839i	0.0710551	−	0.371087i
$391$	−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
$396$	−9.60512	+	2.59648i	−0.482675	+	0.130478i
$397$			22.3459i			1.12151i	0.827982	+	0.560755i	$0.189489\pi$
$397$			22.3459i			1.12151i	−0.827982	+	0.560755i	$0.810511\pi$
$398$	15.3901	+	8.88548i	0.771436	+	0.445389i
$399$	−19.2890	+	12.6016i	−0.965659	+	0.630871i
$400$	−0.175105	−	4.99693i	−0.00875525	−	0.249847i
$401$	−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
$405$	20.1189	+	0.480880i	0.999714	+	0.0238951i
$406$		−	4.38431i		−	0.217590i
$407$	−21.2439	+	17.0885i	−1.05302	+	0.847048i
$408$	−3.90830	+	7.72265i	−0.193490	+	0.382328i
$409$	−32.5585	+	18.7977i	−1.60991	+	0.929485i	−0.620527	+	0.784185i	$0.713081\pi$
$409$	−32.5585	+	18.7977i	−1.60991	+	0.929485i	−0.989388	+	0.145300i	$0.953585\pi$
$410$	13.2407	−	3.79759i	0.653913	−	0.187549i
$411$	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
$418$	−27.9062	+	4.32666i	−1.36494	+	0.211624i
$419$	−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	$0.391646\pi$
$420$	−5.94287	−	1.13793i	−0.289982	−	0.0555253i
$421$	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
$425$	−13.2430	−	21.1875i	−0.642379	−	1.02774i
$426$	−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
$429$	−7.40110	−	8.22843i	−0.357329	−	0.397272i
$430$	−8.28498	−	7.99974i	−0.399537	−	0.385782i
$431$	−26.5809			−1.28036			−0.640178	−	0.768226i	$-0.721140\pi$
$431$	−26.5809			−1.28036			−0.640178	+	0.768226i	$0.721140\pi$
$432$	1.82224	−	4.86615i	0.0876725	−	0.234123i
$433$		−	0.552031i		−	0.0265289i	−0.999912	−	0.0132645i	$-0.995778\pi$
$433$		−	0.552031i		−	0.0265289i	0.999912	−	0.0132645i	$-0.00422233\pi$
$434$	−6.91657	−	3.99328i	−0.332006	−	0.191684i
$435$	−7.10753	+	8.22263i	−0.340780	+	0.394245i
$436$	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	0.815987	−	0.578071i	$-0.196194\pi$
$439$	15.1560	+	8.75031i	0.723356	+	0.417630i	−0.0926307	+	0.995701i	$0.529528\pi$
$440$	−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	−0.972662	−	0.232227i	$-0.925399\pi$
$443$	−6.00312	+	10.3977i	−0.285217	+	0.494010i	0.687445	+	0.726236i	$0.258732\pi$
$444$	−0.784080	−	14.2165i	−0.0372108	−	0.674686i
$445$	−20.5452	+	5.89258i	−0.973934	+	0.279335i
$446$	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	$-0.138778\pi$
$450$	9.30092	+	11.7683i	0.438450	+	0.554763i
$451$	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
$455$	−1.85552	−	6.46949i	−0.0869883	−	0.303295i
$456$	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	$-0.617189\pi$
$461$	13.4847	−	23.3562i	0.628044	−	1.08780i	0.987944	−	0.154814i	$-0.0494777\pi$
$462$	−6.67275	+	6.00184i	−0.310444	+	0.279231i
$463$	17.9965	−	10.3903i	0.836366	−	0.482876i	−0.0196612	−	0.999807i	$-0.506259\pi$
$463$	17.9965	−	10.3903i	0.836366	−	0.482876i	0.856027	+	0.516930i	$0.172925\pi$
$464$	1.40314	+	2.43031i	0.0651393	+	0.112825i
$465$	6.49817	+	18.7019i	0.301346	+	0.867281i
$466$	−0.0852775	+	0.147705i	−0.00395040	+	0.00684230i
$467$	−11.3976			−0.527420			−0.263710	−	0.964602i	$-0.584946\pi$
$467$	−11.3976			−0.527420			−0.263710	+	0.964602i	$0.584946\pi$
$468$	5.74461	−	0.635596i	0.265545	−	0.0293805i
$469$		−	5.92610i		−	0.273642i
$470$	14.4873	+	13.9885i	0.668247	+	0.645241i
$471$	1.66014	+	30.1008i	0.0764953	+	1.38697i
$472$	3.13803	+	5.43524i	0.144440	+	0.250177i
$473$	−16.8805	+	2.61720i	−0.776166	+	0.120339i
$474$	−7.77253	+	0.428677i	−0.357004	+	0.0196898i
$475$	22.5646	+	36.1011i	1.03533	+	1.65643i
$476$			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	−0.907997	−	0.418978i	$-0.862389\pi$
$479$	−1.99498	+	3.45541i	−0.0911531	+	0.157882i	0.816843	+	0.576859i	$0.195722\pi$
$480$	3.65844	−	1.27116i	0.166984	−	0.0580203i
$481$	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
$484$	−10.4836	+	3.33087i	−0.476526	+	0.151403i
$485$	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	$0.182520\pi$
$487$			23.9436i			1.08499i	−0.840060	+	0.542493i	$0.817480\pi$
$488$	−1.08008	+	1.87075i	−0.0488927	+	0.0846847i
$489$	−22.2046	−	11.2373i	−1.00413	−	0.508170i
$490$	9.79950	−	2.81061i	0.442696	−	0.126970i
$491$	−14.6412	−	25.3593i	−0.660748	−	1.14445i	−0.980420	−	0.196920i	$-0.936906\pi$
$491$	−14.6412	−	25.3593i	−0.660748	−	1.14445i	0.319672	−	0.947528i	$-0.396427\pi$
$492$	5.83562	+	8.93245i	0.263090	+	0.402706i
$493$	12.1446	+	7.01170i	0.546966	+	0.315791i
$494$	16.4038			0.738042
$495$	22.2443	−	0.438863i	0.999805	−	0.0197254i
$496$	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	$0.574080\pi$
$500$	−2.32253	+	10.9364i	−0.103867	+	0.489093i
$501$	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
$506$	9.70878	−	7.80972i	0.431608	−	0.347184i
$507$	−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	$0.184994\pi$
$510$	12.6563	−	14.6420i	0.560432	−	0.648358i
$511$	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
$515$	3.45727	+	3.33824i	0.152346	+	0.147101i
$516$	4.02822	−	7.95962i	0.177333	−	0.350403i
$517$	29.5175	−	4.57648i	1.29818	−	0.201273i
$518$	−6.42143	−	11.1222i	−0.282141	−	0.488683i
$519$	1.32326	−	0.864492i	0.0580845	−	0.0379470i
$520$	3.09903	+	2.99234i	0.135902	+	0.131223i
$521$		−	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
$525$	12.2787	+	5.68298i	0.535887	+	0.248025i
$526$	12.6370	+	21.8880i	0.551001	+	0.954361i
$527$	22.1229	−	12.7727i	0.963690	−	0.556387i
$528$	1.77803	−	5.46247i	0.0773789	−	0.237724i
$529$	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
$535$	14.8397	−	4.25620i	0.641577	−	0.184012i
$536$	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
$540$	−6.58540	+	9.57249i	−0.283390	+	0.411934i
$541$			14.9083i			0.640958i	0.947256	+	0.320479i	$0.103844\pi$
$541$			14.9083i			0.640958i	−0.947256	+	0.320479i	$0.896156\pi$
$542$	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
$545$	−6.84018	+	1.96184i	−0.293001	+	0.0840360i
$546$	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
$555$	−5.98740	+	31.2693i	−0.254151	+	1.32731i
$556$	−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
$560$	2.42660	−	2.51312i	0.102543	−	0.106199i
$561$	−5.95366	−	28.0822i	−0.251364	−	1.18563i
$562$	−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
$565$	5.91804	−	6.12906i	0.248974	−	0.257851i
$566$		−	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	$-0.567050\pi$
$569$	17.7076	−	30.6704i	0.742339	−	1.28577i	0.951428	−	0.307873i	$-0.0996171\pi$
$570$	−21.5650	+	24.9484i	−0.903259	+	1.04497i
$571$	31.5428	−	18.2113i	1.32003	−	0.762117i	0.336293	−	0.941757i	$-0.390827\pi$
$571$	31.5428	−	18.2113i	1.32003	−	0.762117i	0.983732	+	0.179640i	$0.0574933\pi$
$572$	6.31422	−	0.978975i	0.264011	−	0.0409330i
$573$	−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	$-0.791978\pi$
$577$		−	29.2087i		−	1.21597i	0.793948	−	0.607986i	$-0.208022\pi$
$578$	−6.90342	−	3.98569i	−0.287144	−	0.165783i
$579$	40.5032	−	2.23387i	1.68326	−	0.0928363i
$580$	−1.73000	−	6.03186i	−0.0718345	−	0.250459i
$581$	16.7931	−	9.69550i	0.696695	−	0.402237i
$582$	5.03453	−	0.277669i	0.208688	−	0.0115097i
$583$	−3.59482	−	4.46896i	−0.148882	−	0.185085i
$584$			12.2059i			0.505084i
$585$	−12.8077	−	1.72777i	−0.529534	−	0.0714346i
$586$	−4.76754			−0.196945
$587$	−4.67437	+	8.09624i	−0.192932	+	0.334168i	−0.946221	−	0.323522i	$-0.895133\pi$
$587$	−4.67437	+	8.09624i	−0.192932	+	0.334168i	0.753289	+	0.657690i	$0.228466\pi$
$588$	4.31896	+	6.61093i	0.178111	+	0.272630i
$589$	−37.6951	+	21.7633i	−1.55320	+	0.896739i
$590$	−3.86904	−	13.4898i	−0.159286	−	0.555368i
$591$	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	$-0.127912\pi$
$594$	5.40656	+	16.3637i	0.221834	+	0.671409i
$595$	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	$0.417199\pi$
$600$	−8.62511	+	0.779451i	−0.352118	+	0.0318209i
$601$	31.9092	+	18.4228i	1.30160	+	0.751481i	0.980679	−	0.195623i	$-0.0626730\pi$
$601$	31.9092	+	18.4228i	1.30160	+	0.751481i	0.320925	+	0.947105i	$0.396006\pi$
$602$		−	8.04668i		−	0.327958i
$603$	−10.4208	−	4.57146i	−0.424369	−	0.186164i
$604$			18.9583i			0.771402i
$605$	24.5474	−	1.55718i	0.997994	−	0.0633085i
$606$	−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
$610$	3.35516	−	3.47479i	0.135846	−	0.140690i
$611$	−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
$615$	−7.83057	−	22.5366i	−0.315759	−	0.908763i
$616$	−0.793888	−	5.12045i	−0.0319867	−	0.206309i
$617$	−3.22832	−	5.59161i	−0.129967	−	0.225110i	0.793696	−	0.608314i	$-0.208154\pi$
$617$	−3.22832	−	5.59161i	−0.129967	−	0.225110i	−0.923664	+	0.383204i	$0.874821\pi$
$618$	−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
$625$	10.9538	−	22.4725i	0.438153	−	0.898901i
$626$	−15.3989	−	26.6716i	−0.615463	−	1.06601i
$627$	10.1444	+	47.8490i	0.405128	+	1.91090i
$628$	−15.0733	−	8.70255i	−0.601489	−	0.347270i
$629$	41.0784			1.63790
$630$	−1.40112	+	10.3863i	−0.0558218	+	0.413799i
$631$	−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
$635$	−11.7902	−	41.1079i	−0.467880	−	1.63132i
$636$	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	−0.0778233	−	0.996967i	$-0.524797\pi$
$643$	18.9335	−	10.9313i	0.746664	−	0.431087i	0.824487	+	0.565881i	$0.191464\pi$
$644$	2.93469	+	5.08303i	0.115643	+	0.200299i
$645$	−13.0447	+	15.0913i	−0.513634	+	0.594218i
$646$	36.8481	+	21.2743i	1.44977	+	0.837024i
$647$	2.59057			0.101846			0.0509229	−	0.998703i	$-0.483784\pi$
$647$	2.59057			0.101846			0.0509229	+	0.998703i	$0.483784\pi$
$648$	−8.58944	−	2.68728i	−0.337425	−	0.105566i
$649$	−19.4084	−	7.52290i	−0.761846	−	0.295300i
$650$	−5.10559	−	8.16844i	−0.200258	−	0.320393i
$651$	−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	0.996928	−	0.0783199i	$-0.0249556\pi$
$653$	11.0044	+	19.0603i	0.430637	+	0.745885i	−0.566291	+	0.824205i	$0.691622\pi$
$654$	−3.01469	−	4.61452i	−0.117884	−	0.180442i
$655$	−2.93486	+	3.03951i	−0.114675	+	0.118763i
$656$	−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	$0.405045\pi$
$659$	−17.4775	+	30.2718i	−0.680825	+	1.17922i	−0.974729	+	0.223388i	$0.928288\pi$
$660$	−6.81199	+	10.8902i	−0.265156	+	0.423901i
$661$	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
$670$	−2.33838	−	8.15303i	−0.0903395	−	0.314979i
$671$	−1.09768	−	7.07982i	−0.0423753	−	0.273314i
$672$	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
$675$	19.4652	−	17.2077i	0.749217	−	0.662325i
$676$	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
$680$	3.08061	+	10.7409i	0.118136	+	0.411894i
$681$	−12.5065	+	8.17054i	−0.479248	+	0.313096i
$682$	−13.2109	+	10.6268i	−0.505872	+	0.406923i
$683$	24.3909			0.933292			0.466646	−	0.884444i	$-0.345462\pi$
$683$	24.3909			0.933292			0.466646	+	0.884444i	$0.345462\pi$
$684$	−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
$690$	2.73633	−	14.2906i	0.104170	−	0.544032i
$691$	−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
$693$	11.0162	+	10.9675i	0.418470	+	0.416622i
$694$	9.74141			0.369779
$695$	12.9163	+	12.4716i	0.489942	+	0.473074i
$696$	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
$700$	−6.62410	+	4.14032i	−0.250367	+	0.156489i
$701$	−15.8462			−0.598503			−0.299251	−	0.954174i	$-0.596737\pi$
$701$	−15.8462			−0.598503			−0.299251	+	0.954174i	$0.596737\pi$
$702$	−1.64715	−	9.87424i	−0.0621677	−	0.372679i
$703$	−69.9931			−2.63984
$704$	2.07880	+	2.58430i	0.0783478	+	0.0973993i
$705$	22.8102	−	26.3888i	0.859080	−	0.993861i
$706$	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
$715$	−14.2293	−	1.29081i	−0.532146	−	0.0482735i
$716$	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	$0.921318\pi$
$720$	−2.54732	−	6.20573i	−0.0949332	−	0.231274i
$721$			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
$725$	0.491395	+	14.0228i	0.0182499	+	0.520794i
$726$	6.76043	+	17.8128i	0.250903	+	0.661096i
$727$	29.0177	+	16.7534i	1.07621	+	0.621348i	0.929871	−	0.367887i	$-0.119919\pi$
$727$	29.0177	+	16.7534i	1.07621	+	0.621348i	0.146336	+	0.989235i	$0.453252\pi$
$728$			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
$735$	−5.79543	−	16.6794i	−0.213768	−	0.615229i
$736$	−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	$-0.804067\pi$
$739$		−	31.3928i		−	1.15480i	0.816461	−	0.577401i	$-0.195933\pi$
$740$	−13.2232	−	12.7679i	−0.486094	−	0.469359i
$741$	−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
$745$	5.77722	−	5.98321i	0.211661	−	0.219208i
$746$		−	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
$750$	19.1353	+	2.97349i	0.698721	+	0.108576i
$751$	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	$0.425280\pi$
$757$			53.5181i			1.94515i	−0.232590	+	0.972575i	$0.574720\pi$
$758$	8.10511	+	4.67949i	0.294391	+	0.169967i
$759$	−14.4324	−	16.0457i	−0.523861	−	0.582421i
$760$	−5.24902	−	18.3013i	−0.190402	−	0.663858i
$761$	8.73083	+	15.1222i	0.316492	+	0.548181i	0.979754	−	0.200207i	$-0.0641615\pi$
$761$	8.73083	+	15.1222i	0.316492	+	0.548181i	−0.663261	+	0.748388i	$0.730828\pi$
$762$	27.7322	−	18.1176i	1.00463	−	0.656331i
$763$	−4.30575	−	2.48592i	−0.155879	−	0.0899965i
$764$		−	11.1937i		−	0.404974i
$765$	−26.5294	−	20.4916i	−0.959172	−	0.740874i
$766$		−	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	−0.913197	−	0.407518i	$-0.866394\pi$
$769$	−28.1988	+	16.2806i	−1.01688	+	0.587093i	−0.103678	+	0.994611i	$0.533061\pi$
$770$	−1.04677	+	11.5391i	−0.0377228	+	0.415840i
$771$	−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	$-0.717530\pi$
$773$	−35.1109			−1.26285			−0.631425	+	0.775437i	$0.717530\pi$
$774$	−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
$780$	4.87942	−	5.64496i	0.174711	−	0.202122i
$781$	−7.25378	+	5.83492i	−0.259561	+	0.208790i
$782$	−18.7734			−0.671337
$783$	−5.11372	+	13.6558i	−0.182750	+	0.488019i
$784$	−4.55916			−0.162827
$785$	27.9976	+	27.0337i	0.999278	+	0.964875i
$786$	−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
$790$	−6.98056	+	7.22946i	−0.248357	+	0.257213i
$791$	5.95276			0.211656
$792$	−9.61652	−	2.55395i	−0.341708	−	0.0907505i
$793$			4.16165i			0.147785i
$794$	−11.1730	+	19.3521i	−0.396513	+	0.686781i
$795$	−6.57795	−	1.25954i	−0.233296	−	0.0446711i
$796$	8.88548	+	15.3901i	0.314937	+	0.545488i
$797$	1.43985	+	2.49389i	0.0510021	+	0.0883382i	0.890399	−	0.455180i	$-0.150425\pi$
$797$	1.43985	+	2.49389i	0.0510021	+	0.0883382i	−0.839397	+	0.543518i	$0.817092\pi$
$798$	−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
$803$	−25.3737	−	31.5437i	−0.895418	−	1.11315i
$804$	5.50019	−	3.59331i	0.193977	−	0.126726i
$805$	−3.61832	−	12.6157i	−0.127529	−	0.444645i
$806$	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	$-0.681495\pi$
$809$	−30.7061			−1.07957			−0.539785	+	0.841803i	$0.681495\pi$
$810$	17.1830	+	10.4759i	0.603749	+	0.368085i
$811$			39.8278i			1.39854i	0.714856	+	0.699272i	$0.246492\pi$
$811$			39.8278i			1.39854i	−0.714856	+	0.699272i	$0.753508\pi$
$812$	2.19216	−	3.79692i	0.0769296	−	0.133246i
$813$	−39.1558	−	19.8161i	−1.37325	−	0.694980i
$814$	−26.9420	+	4.17717i	−0.944317	+	0.146410i
$815$	−30.8828	+	8.85753i	−1.08178	+	0.310266i
$816$	−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	$0.418425\pi$
$821$	−20.3724	+	35.2861i	−0.711003	+	1.23149i	−0.964481	+	0.264152i	$0.914908\pi$
$822$	0.774289	+	14.0390i	0.0270064	+	0.489666i
$823$	−20.9042	+	12.0691i	−0.728676	+	0.420701i	−0.817938	−	0.575307i	$-0.804883\pi$
$823$	−20.9042	+	12.0691i	−0.728676	+	0.420701i	0.0892616	+	0.996008i	$0.471549\pi$
$824$	−1.07463	−	1.86132i	−0.0374365	−	0.0648420i
$825$	20.6695	−	19.9442i	0.719620	−	0.694369i
$826$	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	$0.741517\pi$
$830$	19.2779	−	19.9653i	0.669145	−	0.693005i
$831$	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
$835$	16.7426	+	16.1662i	0.579401	+	0.559453i
$836$	−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	$0.777364\pi$
$840$	−4.57771	−	3.95691i	−0.157946	−	0.136526i
$841$	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
$850$	−0.875024	−	24.9704i	−0.0300131	−	0.856476i
$851$	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
$855$	45.2032	+	34.9154i	1.54592	+	1.19408i
$856$	−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	$0.344953\pi$
$858$	−2.29533	−	10.8266i	−0.0783612	−	0.369613i
$859$	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	$0.600413\pi$
$860$	−3.17514	−	11.0705i	−0.108271	−	0.377500i
$861$	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	$-0.518282\pi$
$863$	−3.37269			−0.114808			−0.0574038	+	0.998351i	$0.518282\pi$
$864$	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
$869$	2.28376	+	14.7299i	0.0774714	+	0.499678i
$870$	−10.2666	+	3.56724i	−0.348071	+	0.120941i
$871$	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
$875$	16.6114	−	5.40071i	0.561566	−	0.182577i
$876$	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
$880$	−3.11269	−	6.73136i	−0.104929	−	0.226914i
$881$			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	$-0.727476\pi$
$883$		−	44.8898i		−	1.51066i	0.655344	−	0.755330i	$-0.272524\pi$
$884$	−8.33746	−	4.81363i	−0.280419	−	0.161900i
$885$	−22.9606	+	7.97789i	−0.771812	+	0.268174i
$886$	−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
$891$	27.7840	−	10.9110i	0.930798	−	0.365534i
$892$			7.83623i			0.262376i
$893$	66.4103	+	38.3420i	2.22234	+	1.28307i
$894$	5.74824	+	2.90908i	0.192250	+	0.0972943i
$895$	−12.9857	+	3.72446i	−0.434065	+	0.124495i
$896$	−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
$900$	2.17068	+	14.8421i	0.0723561	+	0.494737i
$901$			8.64143i			0.287888i
$902$	15.9197	−	12.8058i	0.530068	−	0.426386i
$903$	−13.9161	+	0.767512i	−0.463099	+	0.0255412i
$904$	−3.29974	+	1.90511i	−0.109748	+	0.0633629i
$905$	−1.08874	−	3.79601i	−0.0361908	−	0.126184i
$906$	32.7869	−	1.80829i	1.08927	−	0.0600764i
$907$	0.483241	+	0.278999i	0.0160458	+	0.00926402i	0.508001	−	0.861356i	$-0.330384\pi$
$907$	0.483241	+	0.278999i	0.0160458	+	0.00926402i	−0.491956	+	0.870620i	$0.663718\pi$
$908$		−	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
$913$	−6.30696	−	40.6789i	−0.208730	−	1.34627i
$914$	32.0178	−	18.4855i	1.05905	−	0.611445i
$915$	−6.32941	−	5.47105i	−0.209244	−	0.180867i
$916$	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	$0.300399\pi$
$919$			49.0954i			1.61951i	−0.586770	+	0.809753i	$0.699601\pi$
$920$	6.04320	+	5.83514i	0.199238	+	0.192379i
$921$	−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
$924$	−8.77969	+	1.86137i	−0.288831	+	0.0612345i
$925$	21.7849	+	34.8537i	0.716284	+	1.14598i
$926$	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	$0.548961\pi$
$930$	−3.72338	+	19.4454i	−0.122094	+	0.637641i
$931$	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
$940$	5.55209	+	19.3580i	0.181089	+	0.631389i
$941$	2.67272	+	4.62928i	0.0871281	+	0.150910i	0.906296	−	0.422643i	$-0.138898\pi$
$941$	2.67272	+	4.62928i	0.0871281	+	0.150910i	−0.819168	+	0.573554i	$0.805564\pi$
$942$	−13.6127	+	26.8981i	−0.443525	+	0.876388i
$943$	−11.5714	+	20.0422i	−0.376816	+	0.652664i
$944$			6.27607i			0.204269i
$945$	18.0959	+	1.43245i	0.588659	+	0.0465977i
$946$	−15.9275	−	6.17369i	−0.517849	−	0.200724i
$947$	15.7134	−	27.2164i	0.510617	−	0.884415i	−0.489307	−	0.872112i	$-0.662750\pi$
$947$	15.7134	−	27.2164i	0.510617	−	0.884415i	0.999924	−	0.0123034i	$-0.00391640\pi$
$948$	−6.94555	−	3.51502i	−0.225581	−	0.114163i
$949$	11.7577	+	20.3649i	0.381671	+	0.661073i
$950$	1.49095	+	42.5468i	0.0483727	+	1.38040i
$951$	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
$957$	−4.98967	+	15.3293i	−0.161293	+	0.495524i
$958$	−3.45541	+	1.99498i	−0.111639	+	0.0644550i
$959$	6.34124	+	10.9833i	0.204769	+	0.354671i
$960$	3.80388	+	0.728360i	0.122770	+	0.0235077i
$961$	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
$965$	36.3762	−	37.6732i	1.17099	−	1.21274i
$966$	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	$0.734368\pi$
$968$	−10.7445	−	2.35717i	−0.345341	−	0.0757622i
$969$	33.2775	−	65.7551i	1.06903	−	2.11236i
$970$	4.52155	−	4.68277i	0.145178	−	0.150355i
$971$		−	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
$975$	−13.6397	+	9.60885i	−0.436820	+	0.307729i
$976$	−1.87075	+	1.08008i	−0.0598811	+	0.0345724i
$977$	−7.66591	−	13.2777i	−0.245254	−	0.424793i	0.716949	−	0.697126i	$-0.245538\pi$
$977$	−7.66591	−	13.2777i	−0.245254	−	0.424793i	−0.962203	+	0.272333i	$0.912205\pi$
$978$	−13.6111	−	20.8341i	−0.435233	−	0.666202i
$979$	−24.7020	+	19.8703i	−0.789481	+	0.635057i
$980$	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	−0.986690	−	0.162611i	$-0.948008\pi$
$983$	−11.0525	+	19.1435i	−0.352520	+	0.610582i	0.634170	+	0.773193i	$0.281342\pi$
$984$	0.587572	+	10.6535i	0.0187311	+	0.339622i
$985$	28.6718	−	8.22338i	0.913558	−	0.262019i
$986$	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
$990$	19.4835	+	10.7421i	0.619227	+	0.341405i
$991$	−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
$995$	−10.9553	−	38.1971i	−0.347308	−	1.21093i
$996$	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.659.60	yes	144
5.4	even	2	inner	990.2.o.a.659.13	yes	144
9.5	odd	6	inner	990.2.o.a.329.49	yes	144
11.10	odd	2	inner	990.2.o.a.659.24	yes	144
45.14	odd	6	inner	990.2.o.a.329.24	yes	144
55.54	odd	2	inner	990.2.o.a.659.49	yes	144
99.32	even	6	inner	990.2.o.a.329.13	✓	144
495.329	even	6	inner	990.2.o.a.329.60	yes	144

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

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} +(-0.616475 - 2.14941i) 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} +(-2.07880 - 2.58430i) q^{11} +(1.72942 - 0.0953825i) q^{12} +(0.963278 + 1.66845i) q^{13} +(1.35301 - 0.781159i) q^{14} +(-3.80388 - 0.728360i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.99714i q^{17} +(-0.329913 - 2.98180i) q^{18} -8.51458i q^{19} +(1.55321 - 1.60859i) q^{20} +(-1.48001 - 2.26541i) q^{21} +(-0.508147 - 3.27747i) q^{22} +(1.87842 + 3.25352i) q^{23} +(1.54542 + 0.782108i) q^{24} +(-4.23992 + 2.65011i) q^{25} +1.92656i q^{26} +(-5.12533 + 0.854971i) q^{27} +1.56232 q^{28} +(1.40314 - 2.43031i) q^{29} +(-2.93008 - 2.53272i) q^{30} +(-2.55600 - 4.42712i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.61966 + 1.19141i) 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} +(2.14941 - 0.616475i) 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} +(-4.10066 + 5.30892i) q^{45} +3.75684i q^{46} +(-4.50310 + 7.79960i) q^{47} +(0.947315 + 1.45003i) q^{48} +(2.27958 + 3.94835i) q^{49} +(-4.99693 + 0.175105i) 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} +(-1.27116 - 3.65844i) q^{60} +(1.87075 + 1.08008i) q^{61} -5.11200i q^{62} +(-4.65853 + 0.515429i) q^{63} -1.00000 q^{64} +(2.99234 - 3.09903i) q^{65} +(-5.46247 - 1.77803i) q^{66} +(3.28496 - 1.89657i) q^{67} +(-4.32765 + 2.49857i) q^{68} +(6.49716 - 0.358337i) q^{69} +(-2.51312 - 2.42660i) q^{70} -2.80687i q^{71} +(2.41736 - 1.77662i) q^{72} +12.2059 q^{73} +(4.11019 - 7.11906i) q^{74} +(0.779451 + 8.62511i) q^{75} +(7.37384 - 4.25729i) q^{76} +(-5.12045 + 0.793888i) 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} +(10.7409 - 3.08061i) q^{85} +(4.46044 - 2.57524i) q^{86} +(-2.65844 - 4.06921i) q^{87} +(2.58430 - 2.07880i) q^{88} -9.55852i q^{89} +(-6.20573 + 2.54732i) q^{90} +3.00989 q^{91} +(-1.87842 + 3.25352i) q^{92} +(-8.84081 + 0.487595i) q^{93} +(-7.79960 + 4.50310i) q^{94} +(-18.3013 + 5.24902i) q^{95} +(0.0953825 + 1.72942i) q^{96} +(2.52109 + 1.45555i) q^{97} +4.55916i q^{98} +(-2.55395 + 9.61652i) 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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