LMFDB - Embedded newform 990.2.ba.i.289.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(289,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.289"); 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.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,8,2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.4
Character	$\chi$	$=$	990.289
Dual form			990.2.ba.i.829.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(1.38390 + 1.75636i) q^{5} +(-3.49179 - 1.13455i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.607489 - 2.15197i) q^{10} +(-1.59974 + 2.90531i) q^{11} +(-1.31288 - 1.80702i) q^{13} +(1.13455 + 3.49179i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.47516 - 3.40676i) q^{17} +(-2.47119 - 7.60555i) q^{19} +(-2.09805 + 0.773425i) q^{20} +(3.29075 - 0.413482i) q^{22} -0.0365882i q^{23} +(-1.16962 + 4.86127i) q^{25} +(-0.690222 + 2.12428i) q^{26} +(2.15805 - 2.97030i) q^{28} +(2.85295 - 8.78048i) q^{29} +(2.97662 - 2.16264i) q^{31} +1.00000i q^{32} -4.21099 q^{34} +(-2.83962 - 7.70297i) q^{35} +(0.824696 + 0.267960i) q^{37} +(-4.70049 + 6.46966i) q^{38} +(1.85892 + 1.24275i) q^{40} +(1.90952 + 5.87689i) q^{41} -9.60194i q^{43} +(-2.26877 - 2.41923i) q^{44} +(-0.0296005 + 0.0215060i) q^{46} +(6.50662 - 2.11413i) q^{47} +(5.24229 + 3.80875i) q^{49} +(4.62034 - 1.91114i) q^{50} +(2.12428 - 0.690222i) q^{52} +(-0.676313 - 0.930864i) q^{53} +(-7.31667 + 1.21095i) q^{55} -3.67149 q^{56} +(-8.78048 + 2.85295i) q^{58} +(3.33245 - 10.2562i) q^{59} +(-1.21498 - 0.882733i) q^{61} +(-3.49923 - 1.13697i) q^{62} +(0.809017 - 0.587785i) q^{64} +(1.35689 - 4.80664i) q^{65} -2.88670i q^{67} +(2.47516 + 3.40676i) q^{68} +(-4.56274 + 6.82499i) q^{70} +(-4.78306 - 3.47509i) q^{71} +(9.70730 + 3.15409i) q^{73} +(-0.267960 - 0.824696i) q^{74} +7.99694 q^{76} +(8.88219 - 8.32976i) q^{77} +(-6.37992 + 4.63528i) q^{79} +(-0.0872378 - 2.23437i) q^{80} +(3.63212 - 4.99918i) q^{82} +(-9.01255 + 12.4047i) q^{83} +(9.40890 - 0.367358i) q^{85} +(-7.76814 + 5.64388i) q^{86} +(-0.623653 + 3.25746i) q^{88} -4.64654 q^{89} +(2.53414 + 7.79928i) q^{91} +(0.0347975 + 0.0113064i) q^{92} +(-5.53486 - 4.02131i) q^{94} +(9.93820 - 14.8657i) q^{95} +(-8.70788 - 11.9854i) q^{97} -6.47983i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{14} - 8 q^{16} + 20 q^{19} - 2 q^{20} + 4 q^{25} + 2 q^{26} - 2 q^{29} - 24 q^{31} - 28 q^{34} - 44 q^{35} - 4 q^{40} + 34 q^{41} + 20 q^{44} - 38 q^{46} + 14 q^{49}+ \cdots + 60 q^{95}+O(q^{100}) $ 32 * q + 8 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^14 - 8 * q^16 + 20 * q^19 - 2 * q^20 + 4 * q^25 + 2 * q^26 - 2 * q^29 - 24 * q^31 - 28 * q^34 - 44 * q^35 - 4 * q^40 + 34 * q^41 + 20 * q^44 - 38 * q^46 + 14 * q^49 + 24 * q^50 + 28 * q^55 - 20 * q^56 + 4 * q^59 - 8 * q^61 + 8 * q^64 + 44 * q^65 - 10 * q^70 - 8 * q^71 - 20 * q^74 + 20 * q^76 + 2 * q^79 + 2 * q^80 - 20 * q^85 - 34 * q^86 + 132 * q^89 + 78 * q^91 + 22 * q^94 + 60 * q^95

Character values

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

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	1.38390	+	1.75636i	0.618901	+	0.785469i
$5$	1.38390	+	1.75636i	0.618901	+	0.785469i
$6$		0			0
$7$	−3.49179	−	1.13455i	−1.31977	−	0.428820i	−0.437356	−	0.899288i	$-0.644085\pi$
$7$	−3.49179	−	1.13455i	−1.31977	−	0.428820i	−0.882417	+	0.470468i	$0.844085\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$		0			0
$10$	0.607489	−	2.15197i	0.192105	−	0.680511i
$11$	−1.59974	+	2.90531i	−0.482340	+	0.875984i
$11$	−1.59974	+	2.90531i	−0.482340	+	0.875984i
$12$		0			0
$13$	−1.31288	−	1.80702i	−0.364127	−	0.501178i	0.587166	−	0.809467i	$-0.300244\pi$
$13$	−1.31288	−	1.80702i	−0.364127	−	0.501178i	−0.951293	+	0.308289i	$0.900244\pi$
$14$	1.13455	+	3.49179i	0.303222	+	0.933221i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.47516	−	3.40676i	0.600314	−	0.826262i	−0.395423	−	0.918499i	$-0.629402\pi$
$17$	2.47516	−	3.40676i	0.600314	−	0.826262i	0.995737	+	0.0922376i	$0.0294019\pi$
$18$		0			0
$19$	−2.47119	−	7.60555i	−0.566930	−	1.74483i	−0.662146	−	0.749375i	$-0.730354\pi$
$19$	−2.47119	−	7.60555i	−0.566930	−	1.74483i	0.0952153	−	0.995457i	$-0.469646\pi$
$20$	−2.09805	+	0.773425i	−0.469138	+	0.172943i
$21$		0			0
$22$	3.29075	−	0.413482i	0.701590	−	0.0881547i
$23$		−	0.0365882i		−	0.00762918i	−0.999993	−	0.00381459i	$-0.998786\pi$
$23$		−	0.0365882i		−	0.00762918i	0.999993	−	0.00381459i	$-0.00121422\pi$
$24$		0			0
$25$	−1.16962	+	4.86127i	−0.233924	+	0.972255i
$26$	−0.690222	+	2.12428i	−0.135364	+	0.416606i
$27$		0			0
$28$	2.15805	−	2.97030i	0.407832	−	0.561333i
$29$	2.85295	−	8.78048i	0.529780	−	1.63049i	−0.224887	−	0.974385i	$-0.572201\pi$
$29$	2.85295	−	8.78048i	0.529780	−	1.63049i	0.754666	−	0.656109i	$-0.227799\pi$
$30$		0			0
$31$	2.97662	−	2.16264i	0.534617	−	0.388422i	−0.287465	−	0.957791i	$-0.592813\pi$
$31$	2.97662	−	2.16264i	0.534617	−	0.388422i	0.822082	+	0.569369i	$0.192813\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−4.21099			−0.722179
$35$	−2.83962	−	7.70297i	−0.479984	−	1.30204i
$36$		0			0
$37$	0.824696	+	0.267960i	0.135579	+	0.0440523i	0.376021	−	0.926611i	$-0.377292\pi$
$37$	0.824696	+	0.267960i	0.135579	+	0.0440523i	−0.240441	+	0.970664i	$0.577292\pi$
$38$	−4.70049	+	6.46966i	−0.762520	+	1.04952i
$39$		0			0
$40$	1.85892	+	1.24275i	0.293921	+	0.196496i
$41$	1.90952	+	5.87689i	0.298217	+	0.917816i	0.982122	+	0.188246i	$0.0602801\pi$
$41$	1.90952	+	5.87689i	0.298217	+	0.917816i	−0.683905	+	0.729571i	$0.739720\pi$
$42$		0			0
$43$		−	9.60194i		−	1.46428i	−0.681153	−	0.732141i	$-0.738521\pi$
$43$		−	9.60194i		−	1.46428i	0.681153	−	0.732141i	$-0.261479\pi$
$44$	−2.26877	−	2.41923i	−0.342030	−	0.364713i
$45$		0			0
$46$	−0.0296005	+	0.0215060i	−0.00436436	+	0.00317089i
$47$	6.50662	−	2.11413i	0.949089	−	0.308378i	0.206743	−	0.978395i	$-0.433713\pi$
$47$	6.50662	−	2.11413i	0.949089	−	0.308378i	0.742345	+	0.670018i	$0.233713\pi$
$48$		0			0
$49$	5.24229	+	3.80875i	0.748898	+	0.544107i
$50$	4.62034	−	1.91114i	0.653415	−	0.270277i
$51$		0			0
$52$	2.12428	−	0.690222i	0.294585	−	0.0957165i
$53$	−0.676313	−	0.930864i	−0.0928987	−	0.127864i	0.760038	−	0.649879i	$-0.225180\pi$
$53$	−0.676313	−	0.930864i	−0.0928987	−	0.127864i	−0.852936	+	0.522015i	$0.825180\pi$
$54$		0			0
$55$	−7.31667	+	1.21095i	−0.986579	+	0.163284i
$56$	−3.67149			−0.490623
$57$		0			0
$58$	−8.78048	+	2.85295i	−1.15293	+	0.374611i
$59$	3.33245	−	10.2562i	0.433848	−	1.33525i	−0.460415	−	0.887704i	$-0.652299\pi$
$59$	3.33245	−	10.2562i	0.433848	−	1.33525i	0.894263	−	0.447542i	$-0.147701\pi$
$60$		0			0
$61$	−1.21498	−	0.882733i	−0.155562	−	0.113022i	0.507281	−	0.861780i	$-0.330650\pi$
$61$	−1.21498	−	0.882733i	−0.155562	−	0.113022i	−0.662843	+	0.748758i	$0.730650\pi$
$62$	−3.49923	−	1.13697i	−0.444402	−	0.144395i
$63$		0			0
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	1.35689	−	4.80664i	0.168301	−	0.596190i
$66$		0			0
$67$		−	2.88670i		−	0.352667i	−0.984330	−	0.176334i	$-0.943576\pi$
$67$		−	2.88670i		−	0.352667i	0.984330	−	0.176334i	$-0.0564237\pi$
$68$	2.47516	+	3.40676i	0.300157	+	0.413131i
$69$		0			0
$70$	−4.56274	+	6.82499i	−0.545352	+	0.815742i
$71$	−4.78306	−	3.47509i	−0.567644	−	0.412418i	0.266604	−	0.963806i	$-0.414098\pi$
$71$	−4.78306	−	3.47509i	−0.567644	−	0.412418i	−0.834249	+	0.551388i	$0.814098\pi$
$72$		0			0
$73$	9.70730	+	3.15409i	1.13615	+	0.369159i	0.815911	−	0.578177i	$-0.196236\pi$
$73$	9.70730	+	3.15409i	1.13615	+	0.369159i	0.320242	+	0.947336i	$0.396236\pi$
$74$	−0.267960	−	0.824696i	−0.0311497	−	0.0958689i
$75$		0			0
$76$	7.99694			0.917312
$77$	8.88219	−	8.32976i	1.01222	−	0.949264i
$78$		0			0
$79$	−6.37992	+	4.63528i	−0.717797	+	0.521510i	−0.885680	−	0.464297i	$-0.846307\pi$
$79$	−6.37992	+	4.63528i	−0.717797	+	0.521510i	0.167883	+	0.985807i	$0.446307\pi$
$80$	−0.0872378	−	2.23437i	−0.00975349	−	0.249810i
$81$		0			0
$82$	3.63212	−	4.99918i	0.401100	−	0.552067i
$83$	−9.01255	+	12.4047i	−0.989256	+	1.36159i	−0.0575655	+	0.998342i	$0.518334\pi$
$83$	−9.01255	+	12.4047i	−0.989256	+	1.36159i	−0.931691	+	0.363253i	$0.881666\pi$
$84$		0			0
$85$	9.40890	−	0.367358i	1.02054	−	0.0398455i
$86$	−7.76814	+	5.64388i	−0.837660	+	0.608595i
$87$		0			0
$88$	−0.623653	+	3.25746i	−0.0664816	+	0.347247i
$89$	−4.64654			−0.492532			−0.246266	−	0.969202i	$-0.579204\pi$
$89$	−4.64654			−0.492532			−0.246266	+	0.969202i	$0.579204\pi$
$90$		0			0
$91$	2.53414	+	7.79928i	0.265650	+	0.817587i
$92$	0.0347975	+	0.0113064i	0.00362789	+	0.00117877i
$93$		0			0
$94$	−5.53486	−	4.02131i	−0.570878	−	0.414767i
$95$	9.93820	−	14.8657i	1.01964	−	1.52518i
$96$		0			0
$97$	−8.70788	−	11.9854i	−0.884151	−	1.21693i	−0.975254	−	0.221088i	$-0.929039\pi$
$97$	−8.70788	−	11.9854i	−0.884151	−	1.21693i	0.0911028	−	0.995841i	$-0.470961\pi$
$98$		−	6.47983i		−	0.654561i
$99$		0			0
$100$	−4.26191	−	2.61459i	−0.426191	−	0.261459i
$101$	−0.652650	+	0.474178i	−0.0649411	+	0.0471825i	−0.619782	−	0.784774i	$-0.712779\pi$
$101$	−0.652650	+	0.474178i	−0.0649411	+	0.0471825i	0.554841	+	0.831956i	$0.312779\pi$
$102$		0			0
$103$	−10.8222	−	3.51635i	−1.06634	−	0.346476i	−0.277282	−	0.960789i	$-0.589433\pi$
$103$	−10.8222	−	3.51635i	−1.06634	−	0.346476i	−0.789063	+	0.614312i	$0.789433\pi$
$104$	−1.80702	−	1.31288i	−0.177193	−	0.128738i
$105$		0			0
$106$	−0.355559	+	1.09430i	−0.0345349	+	0.106287i
$107$	−18.2784	+	5.93903i	−1.76704	+	0.574148i	−0.997891	−	0.0649163i	$-0.979322\pi$
$107$	−18.2784	+	5.93903i	−1.76704	+	0.574148i	−0.769154	+	0.639064i	$0.779322\pi$
$108$		0			0
$109$	−1.84787			−0.176993			−0.0884967	−	0.996076i	$-0.528206\pi$
$109$	−1.84787			−0.176993			−0.0884967	+	0.996076i	$0.528206\pi$
$110$	5.28031	+	5.20753i	0.503457	+	0.496518i
$111$		0			0
$112$	2.15805	+	2.97030i	0.203916	+	0.280667i
$113$	−8.52947	+	2.77139i	−0.802385	+	0.260711i	−0.681369	−	0.731940i	$-0.738615\pi$
$113$	−8.52947	+	2.77139i	−0.802385	+	0.260711i	−0.121016	+	0.992651i	$0.538615\pi$
$114$		0			0
$115$	0.0642622	−	0.0506346i	0.00599248	−	0.00472170i
$116$	7.46912	+	5.42663i	0.693490	+	0.503850i
$117$		0			0
$118$	−10.2562	+	3.33245i	−0.944162	+	0.306777i
$119$	−12.5079	+	9.08752i	−1.14660	+	0.833051i
$120$		0			0
$121$	−5.88166	−	9.29548i	−0.534697	−	0.845044i
$122$			1.50179i			0.135966i
$123$		0			0
$124$	1.13697	+	3.49923i	0.102103	+	0.314240i
$125$	−10.1568	+	4.67326i	−0.908452	+	0.417989i
$126$		0			0
$127$	−3.88580	+	5.34835i	−0.344809	+	0.474589i	−0.945838	−	0.324638i	$-0.894758\pi$
$127$	−3.88580	+	5.34835i	−0.344809	+	0.474589i	0.601029	+	0.799227i	$0.294758\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$		0			0
$130$	−4.68621	+	1.72753i	−0.411008	+	0.151514i
$131$	−0.0620230			−0.00541897			−0.00270949	−	0.999996i	$-0.500862\pi$
$131$	−0.0620230			−0.00541897			−0.00270949	+	0.999996i	$0.500862\pi$
$132$		0			0
$133$			29.3607i			2.54589i
$134$	−2.33539	+	1.69676i	−0.201747	+	0.146578i
$135$		0			0
$136$	1.30127	−	4.00489i	0.111583	−	0.343417i
$137$	−0.548600	+	0.755084i	−0.0468701	+	0.0645112i	−0.831809	−	0.555062i	$-0.812694\pi$
$137$	−0.548600	+	0.755084i	−0.0468701	+	0.0645112i	0.784939	+	0.619573i	$0.212694\pi$
$138$		0			0
$139$	1.96364	−	6.04348i	0.166554	−	0.512601i	−0.832593	−	0.553885i	$-0.813145\pi$
$139$	1.96364	−	6.04348i	0.166554	−	0.512601i	0.999147	+	0.0412838i	$0.0131448\pi$
$140$	8.20345	−	0.320293i	0.693318	−	0.0270697i
$141$		0			0
$142$			5.91218i			0.496139i
$143$	7.35023	−	0.923556i	0.614657	−	0.0772316i
$144$		0			0
$145$	19.3699	−	7.14052i	1.60858	−	0.592988i
$146$	−3.15409	−	9.70730i	−0.261035	−	0.803382i
$147$		0			0
$148$	−0.509690	+	0.701528i	−0.0418963	+	0.0576653i
$149$	9.52264	+	6.91860i	0.780125	+	0.566794i	0.905016	−	0.425376i	$-0.139858\pi$
$149$	9.52264	+	6.91860i	0.780125	+	0.566794i	−0.124892	+	0.992170i	$0.539858\pi$
$150$		0			0
$151$	−7.45137	−	22.9330i	−0.606384	−	1.86626i	−0.486984	−	0.873411i	$-0.661903\pi$
$151$	−7.45137	−	22.9330i	−0.606384	−	1.86626i	−0.119400	−	0.992846i	$-0.538097\pi$
$152$	−4.70049	−	6.46966i	−0.381260	−	0.524759i
$153$		0			0
$154$	−11.9597	−	2.28973i	−0.963743	−	0.184512i
$155$	7.91774	+	2.23514i	0.635968	+	0.179531i
$156$		0			0
$157$	12.9311	−	4.20158i	1.03202	−	0.335323i	0.256430	−	0.966563i	$-0.417454\pi$
$157$	12.9311	−	4.20158i	1.03202	−	0.335323i	0.775587	+	0.631240i	$0.217454\pi$
$158$	7.50004	+	2.43691i	0.596671	+	0.193870i
$159$		0			0
$160$	−1.75636	+	1.38390i	−0.138853	+	0.109407i
$161$	−0.0415113	+	0.127759i	−0.00327155	+	0.0100688i
$162$		0			0
$163$	5.95025	+	8.18982i	0.466060	+	0.641476i	0.975752	−	0.218881i	$-0.0702406\pi$
$163$	5.95025	+	8.18982i	0.466060	+	0.641476i	−0.509692	+	0.860357i	$0.670241\pi$
$164$	−6.17933			−0.482525
$165$		0			0
$166$	15.3331			1.19008
$167$	12.4457	+	17.1301i	0.963080	+	1.32557i	0.945466	+	0.325720i	$0.105607\pi$
$167$	12.4457	+	17.1301i	0.963080	+	1.32557i	0.0176135	+	0.999845i	$0.494393\pi$
$168$		0			0
$169$	2.47554	−	7.61892i	0.190426	−	0.586071i
$170$	−5.82761	−	7.39603i	−0.446957	−	0.567249i
$171$		0			0
$172$	9.13199	+	2.96716i	0.696308	+	0.226244i
$173$	0.181614	−	0.0590099i	0.0138078	−	0.00448644i	−0.302105	−	0.953275i	$-0.597689\pi$
$173$	0.181614	−	0.0590099i	0.0138078	−	0.00448644i	0.315913	+	0.948788i	$0.397689\pi$
$174$		0			0
$175$	9.59944	−	15.6476i	0.725649	−	1.18285i
$176$	3.00192	−	1.41014i	0.226278	−	0.106293i
$177$		0			0
$178$	2.73117	+	3.75913i	0.204710	+	0.281759i
$179$	1.31305	+	4.04116i	0.0981423	+	0.302051i	0.988060	−	0.154071i	$-0.0492383\pi$
$179$	1.31305	+	4.04116i	0.0981423	+	0.302051i	−0.889918	+	0.456121i	$0.849238\pi$
$180$		0			0
$181$	18.4447	+	13.4009i	1.37098	+	0.996078i	0.997660	+	0.0683776i	$0.0217823\pi$
$181$	18.4447	+	13.4009i	1.37098	+	0.996078i	0.373325	+	0.927701i	$0.378218\pi$
$182$	4.82022	−	6.63447i	0.357299	−	0.491779i
$183$		0			0
$184$	−0.0113064	−	0.0347975i	−0.000833518	−	0.00256530i
$185$	0.670665	+	1.81930i	0.0493083	+	0.133757i
$186$		0			0
$187$	5.93810	+	12.6410i	0.434237	+	0.924405i
$188$			6.84147i			0.498965i
$189$		0			0
$190$	−17.8681	+	0.697636i	−1.29629	+	0.0506118i
$191$	3.20893	−	9.87607i	0.232190	−	0.714608i	−0.765292	−	0.643684i	$-0.777405\pi$
$191$	3.20893	−	9.87607i	0.232190	−	0.714608i	0.997482	−	0.0709239i	$-0.0225947\pi$
$192$		0			0
$193$	−3.90867	+	5.37982i	−0.281352	+	0.387248i	−0.926181	−	0.377079i	$-0.876929\pi$
$193$	−3.90867	+	5.37982i	−0.281352	+	0.387248i	0.644829	+	0.764327i	$0.276929\pi$
$194$	−4.57800	+	14.0896i	−0.328681	+	1.01158i
$195$		0			0
$196$	−5.24229	+	3.80875i	−0.374449	+	0.272053i
$197$		−	11.5464i		−	0.822650i	−0.911489	−	0.411325i	$-0.865066\pi$
$197$		−	11.5464i		−	0.822650i	0.911489	−	0.411325i	$-0.134934\pi$
$198$		0			0
$199$	−14.0999			−0.999516			−0.499758	−	0.866165i	$-0.666578\pi$
$199$	−14.0999			−0.999516			−0.499758	+	0.866165i	$0.666578\pi$
$200$	0.389842	+	4.98478i	0.0275660	+	0.352477i
$201$		0			0
$202$	0.767236	+	0.249290i	0.0539825	+	0.0175400i
$203$	−19.9238	+	27.4228i	−1.39838	+	1.92470i
$204$		0			0
$205$	−7.67936	+	11.4869i	−0.536350	+	0.802277i
$206$	3.51635	+	10.8222i	0.244996	+	0.754019i
$207$		0			0
$208$			2.23360i			0.154873i
$209$	26.0497	+	4.98731i	1.80190	+	0.344980i
$210$		0			0
$211$	−0.216945	+	0.157620i	−0.0149351	+	0.0108510i	−0.595228	−	0.803557i	$-0.702938\pi$
$211$	−0.216945	+	0.157620i	−0.0149351	+	0.0108510i	0.580293	+	0.814408i	$0.302938\pi$
$212$	1.09430	−	0.355559i	0.0751566	−	0.0244199i
$213$		0			0
$214$	15.5486	+	11.2967i	1.06288	+	0.772227i
$215$	16.8645	−	13.2882i	1.15015	−	0.906246i
$216$		0			0
$217$	−12.8474	+	4.17436i	−0.872136	+	0.283374i
$218$	1.08615	+	1.49495i	0.0735632	+	0.101251i
$219$		0			0
$220$	1.10929	−	7.33277i	0.0747886	−	0.494375i
$221$	−9.40569			−0.632695
$222$		0			0
$223$	16.8703	−	5.48149i	1.12972	−	0.367068i	0.316250	−	0.948676i	$-0.397576\pi$
$223$	16.8703	−	5.48149i	1.12972	−	0.367068i	0.813469	+	0.581608i	$0.197576\pi$
$224$	1.13455	−	3.49179i	0.0758055	−	0.233305i
$225$		0			0
$226$	7.25560	+	5.27150i	0.482635	+	0.350655i
$227$	18.0822	+	5.87528i	1.20016	+	0.389956i	0.839820	−	0.542865i	$-0.182660\pi$
$227$	18.0822	+	5.87528i	1.20016	+	0.389956i	0.360341	+	0.932821i	$0.382660\pi$
$228$		0			0
$229$	18.4855	−	13.4305i	1.22156	−	0.887513i	0.225329	−	0.974283i	$-0.427654\pi$
$229$	18.4855	−	13.4305i	1.22156	−	0.887513i	0.996228	+	0.0867697i	$0.0276544\pi$
$230$	−0.0787367	−	0.0222269i	−0.00519174	−	0.00146560i
$231$		0			0
$232$		−	9.23234i		−	0.606133i
$233$	−0.360355	−	0.495986i	−0.0236076	−	0.0324931i	0.797050	−	0.603913i	$-0.206393\pi$
$233$	−0.360355	−	0.495986i	−0.0236076	−	0.0324931i	−0.820658	+	0.571420i	$0.806393\pi$
$234$		0			0
$235$	12.7177	+	8.50224i	0.829613	+	0.554625i
$236$	8.72446	+	6.33869i	0.567914	+	0.412614i
$237$		0			0
$238$	14.7039	+	4.77759i	0.953113	+	0.309685i
$239$	−5.50559	−	16.9445i	−0.356127	−	1.09605i	−0.955353	−	0.295466i	$-0.904525\pi$
$239$	−5.50559	−	16.9445i	−0.356127	−	1.09605i	0.599226	−	0.800580i	$-0.295475\pi$
$240$		0			0
$241$	−20.1522			−1.29812			−0.649059	−	0.760738i	$-0.724837\pi$
$241$	−20.1522			−1.29812			−0.649059	+	0.760738i	$0.724837\pi$
$242$	−4.06305	+	10.2221i	−0.261183	+	0.657102i
$243$		0			0
$244$	1.21498	−	0.882733i	0.0777810	−	0.0565112i
$245$	0.565286	+	14.4783i	0.0361148	+	0.924985i
$246$		0			0
$247$	−10.4990	+	14.4507i	−0.668037	+	0.919474i
$248$	2.16264	−	2.97662i	0.137328	−	0.189016i
$249$		0			0
$250$	9.75077	+	5.47015i	0.616693	+	0.345963i
$251$	−3.30676	+	2.40250i	−0.208721	+	0.151645i	−0.687235	−	0.726435i	$-0.741176\pi$
$251$	−3.30676	+	2.40250i	−0.208721	+	0.151645i	0.478514	+	0.878080i	$0.341176\pi$
$252$		0			0
$253$	0.106300	+	0.0585317i	0.00668304	+	0.00367985i
$254$	6.61092			0.414806
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.92060	+	0.624042i	0.119804	+	0.0389267i	0.368305	−	0.929705i	$-0.379938\pi$
$257$	1.92060	+	0.624042i	0.119804	+	0.0389267i	−0.248501	+	0.968632i	$0.579938\pi$
$258$		0			0
$259$	−2.57565	−	1.87132i	−0.160043	−	0.116278i
$260$	4.15209	+	2.77581i	0.257501	+	0.172149i
$261$		0			0
$262$	0.0364562	+	0.0501776i	0.00225227	+	0.00309998i
$263$			12.2121i			0.753028i	0.926411	+	0.376514i	$0.122877\pi$
$263$			12.2121i			0.753028i	−0.926411	+	0.376514i	$0.877123\pi$
$264$		0			0
$265$	0.698984	−	2.47608i	0.0429382	−	0.152104i
$266$	23.7533	−	17.2578i	1.45641	−	1.05814i
$267$		0			0
$268$	2.74542	+	0.892041i	0.167703	+	0.0544901i
$269$	7.45881	+	5.41914i	0.454771	+	0.330411i	0.791477	−	0.611199i	$-0.209313\pi$
$269$	7.45881	+	5.41914i	0.454771	+	0.330411i	−0.336705	+	0.941610i	$0.609313\pi$
$270$		0			0
$271$	−3.93769	+	12.1190i	−0.239198	+	0.736175i	0.757339	+	0.653022i	$0.226499\pi$
$271$	−3.93769	+	12.1190i	−0.239198	+	0.736175i	−0.996537	+	0.0831529i	$0.973501\pi$
$272$	−4.00489	+	1.30127i	−0.242832	+	0.0789010i
$273$		0			0
$274$	0.933335			0.0563848
$275$	−12.2524	−	11.1749i	−0.738849	−	0.673871i
$276$		0			0
$277$	−7.81487	−	10.7563i	−0.469550	−	0.646281i	0.506905	−	0.862002i	$-0.330790\pi$
$277$	−7.81487	−	10.7563i	−0.469550	−	0.646281i	−0.976455	+	0.215722i	$0.930790\pi$
$278$	−6.04348	+	1.96364i	−0.362464	+	0.117772i
$279$		0			0
$280$	−5.08099	−	6.44846i	−0.303647	−	0.385369i
$281$	1.26883	+	0.921862i	0.0756923	+	0.0549937i	0.624988	−	0.780634i	$-0.285104\pi$
$281$	1.26883	+	0.921862i	0.0756923	+	0.0549937i	−0.549296	+	0.835628i	$0.685104\pi$
$282$		0			0
$283$	−10.2840	+	3.34148i	−0.611321	+	0.198630i	−0.598283	−	0.801285i	$-0.704150\pi$
$283$	−10.2840	+	3.34148i	−0.611321	+	0.198630i	−0.0130376	+	0.999915i	$0.504150\pi$
$284$	4.78306	−	3.47509i	0.283822	−	0.206209i
$285$		0			0
$286$	−5.06753	−	5.40361i	−0.299649	−	0.319522i
$287$		−	22.6873i		−	1.33919i
$288$		0			0
$289$	−0.226340	−	0.696603i	−0.0133141	−	0.0409767i
$290$	−17.1622	−	11.4735i	−1.00780	−	0.673747i
$291$		0			0
$292$	−5.99944	+	8.25753i	−0.351091	+	0.483235i
$293$	21.2021	+	6.88897i	1.23864	+	0.402458i	0.853836	−	0.520542i	$-0.174270\pi$
$293$	21.2021	+	6.88897i	1.23864	+	0.402458i	0.384801	+	0.922999i	$0.374270\pi$
$294$		0			0
$295$	22.6254	−	8.34064i	1.31730	−	0.485611i
$296$	0.867136			0.0504013
$297$		0			0
$298$		−	11.7706i		−	0.681854i
$299$	−0.0661158	+	0.0480360i	−0.00382358	+	0.00277799i
$300$		0			0
$301$	−10.8939	+	33.5280i	−0.627914	+	1.93252i
$302$	−14.1733	+	19.5079i	−0.815584	+	1.12256i
$303$		0			0
$304$	−2.47119	+	7.60555i	−0.141733	+	0.436208i
$305$	−0.131013	−	3.35556i	−0.00750180	−	0.192139i
$306$		0			0
$307$		−	7.11124i		−	0.405860i	−0.979193	−	0.202930i	$-0.934954\pi$
$307$		−	7.11124i		−	0.405860i	0.979193	−	0.202930i	$-0.0650464\pi$
$308$	5.17732	+	11.0215i	0.295005	+	0.628008i
$309$		0			0
$310$	−2.84567	−	7.71937i	−0.161623	−	0.438431i
$311$	−5.91086	−	18.1918i	−0.335174	−	1.03156i	−0.966636	−	0.256153i	$-0.917545\pi$
$311$	−5.91086	−	18.1918i	−0.335174	−	1.03156i	0.631462	−	0.775407i	$-0.282455\pi$
$312$		0			0
$313$	−17.6306	+	24.2665i	−0.996542	+	1.37162i	−0.0691190	+	0.997608i	$0.522019\pi$
$313$	−17.6306	+	24.2665i	−0.996542	+	1.37162i	−0.927423	+	0.374014i	$0.877981\pi$
$314$	−10.9999	−	7.99188i	−0.620759	−	0.451008i
$315$		0			0
$316$	−2.43691	−	7.50004i	−0.137087	−	0.421910i
$317$	−3.88012	−	5.34053i	−0.217929	−	0.299954i	0.686029	−	0.727574i	$-0.259352\pi$
$317$	−3.88012	−	5.34053i	−0.217929	−	0.299954i	−0.903959	+	0.427620i	$0.859352\pi$
$318$		0			0
$319$	20.9460	+	22.3352i	1.17275	+	1.25053i
$320$	2.15197	+	0.607489i	0.120299	+	0.0339597i
$321$		0			0
$322$	0.127759	−	0.0415113i	0.00711971	−	0.00231333i
$323$	−32.0269	−	10.4062i	−1.78202	−	0.579015i
$324$		0			0
$325$	10.3200	−	4.26874i	0.572451	−	0.236787i
$326$	3.12823	−	9.62771i	0.173257	−	0.533230i
$327$		0			0
$328$	3.63212	+	4.99918i	0.200550	+	0.276034i
$329$	−25.1184			−1.38482
$330$		0			0
$331$	−1.96710			−0.108122			−0.0540608	−	0.998538i	$-0.517216\pi$
$331$	−1.96710			−0.108122			−0.0540608	+	0.998538i	$0.517216\pi$
$332$	−9.01255	−	12.4047i	−0.494628	−	0.680797i
$333$		0			0
$334$	6.54311	−	20.1376i	0.358023	−	1.10188i
$335$	5.07010	−	3.99492i	0.277009	−	0.218266i
$336$		0			0
$337$	8.89720	+	2.89088i	0.484661	+	0.157476i	0.541148	−	0.840927i	$-0.317990\pi$
$337$	8.89720	+	2.89088i	0.484661	+	0.157476i	−0.0564867	+	0.998403i	$0.517990\pi$
$338$	−7.61892	+	2.47554i	−0.414415	+	0.134652i
$339$		0			0
$340$	−2.55813	+	9.06191i	−0.138734	+	0.491451i
$341$	1.52133	+	12.1077i	0.0823845	+	0.655667i
$342$		0			0
$343$	1.12256	+	1.54507i	0.0606125	+	0.0834260i
$344$	−2.96716	−	9.13199i	−0.159979	−	0.492364i
$345$		0			0
$346$	−0.154490	−	0.112243i	−0.00830542	−	0.00603424i
$347$	11.9401	−	16.4342i	0.640979	−	0.882232i	−0.357688	−	0.933841i	$-0.616435\pi$
$347$	11.9401	−	16.4342i	0.640979	−	0.882232i	0.998667	+	0.0516090i	$0.0164350\pi$
$348$		0			0
$349$	−5.08169	−	15.6398i	−0.272017	−	0.837181i	−0.989993	−	0.141114i	$-0.954932\pi$
$349$	−5.08169	−	15.6398i	−0.272017	−	0.837181i	0.717977	−	0.696067i	$-0.245068\pi$
$350$	−18.3016	+	1.43130i	−0.978259	+	0.0765063i
$351$		0			0
$352$	−2.90531	−	1.59974i	−0.154854	−	0.0852664i
$353$		−	26.1300i		−	1.39076i	−0.718643	−	0.695379i	$-0.755237\pi$
$353$		−	26.1300i		−	1.39076i	0.718643	−	0.695379i	$-0.244763\pi$
$354$		0			0
$355$	−0.515766	−	13.2100i	−0.0273740	−	0.701113i
$356$	1.43586	−	4.41912i	0.0761004	−	0.234213i
$357$		0			0
$358$	2.49758	−	3.43762i	0.132001	−	0.181684i
$359$	1.86004	−	5.72461i	0.0981692	−	0.302134i	−0.889897	−	0.456161i	$-0.849224\pi$
$359$	1.86004	−	5.72461i	0.0981692	−	0.302134i	0.988067	+	0.154027i	$0.0492243\pi$
$360$		0			0
$361$	−36.3662	+	26.4216i	−1.91401	+	1.39061i
$362$		−	22.7989i		−	1.19828i
$363$		0			0
$364$	−8.20065			−0.429831
$365$	7.89424	+	21.4145i	0.413204	+	1.12089i
$366$		0			0
$367$	2.85905	+	0.928961i	0.149241	+	0.0484914i	0.382685	−	0.923879i	$-0.374999\pi$
$367$	2.85905	+	0.928961i	0.149241	+	0.0484914i	−0.233444	+	0.972370i	$0.574999\pi$
$368$	−0.0215060	+	0.0296005i	−0.00112108	+	0.00154303i
$369$		0			0
$370$	1.07763	−	1.61193i	0.0560235	−	0.0838005i
$371$	1.30543	+	4.01770i	0.0677745	+	0.208588i
$372$		0			0
$373$			16.1368i			0.835532i	0.908555	+	0.417766i	$0.137187\pi$
$373$			16.1368i			0.835532i	−0.908555	+	0.417766i	$0.862813\pi$
$374$	6.73649	−	12.2342i	0.348336	−	0.632618i
$375$		0			0
$376$	5.53486	−	4.02131i	0.285439	−	0.207383i
$377$	−19.6121	+	6.37236i	−1.01008	+	0.328193i
$378$		0			0
$379$	20.4244	+	14.8392i	1.04913	+	0.762238i	0.972047	−	0.234786i	$-0.0754390\pi$
$379$	20.4244	+	14.8392i	1.04913	+	0.762238i	0.0770842	+	0.997025i	$0.475439\pi$
$380$	11.0670	+	14.0455i	0.567725	+	0.720521i
$381$		0			0
$382$	−9.87607	+	3.20893i	−0.505304	+	0.164183i
$383$	20.6742	+	28.4557i	1.05640	+	1.45402i	0.883122	+	0.469144i	$0.155438\pi$
$383$	20.6742	+	28.4557i	1.05640	+	1.45402i	0.173283	+	0.984872i	$0.444562\pi$
$384$		0			0
$385$	26.9222	+	4.07276i	1.37208	+	0.207567i
$386$	6.64983			0.338467
$387$		0			0
$388$	14.0896	−	4.57800i	0.715293	−	0.232413i
$389$	−0.697918	+	2.14797i	−0.0353859	+	0.108907i	−0.967189	−	0.254057i	$-0.918235\pi$
$389$	−0.697918	+	2.14797i	−0.0353859	+	0.108907i	0.931803	+	0.362963i	$0.118235\pi$
$390$		0			0
$391$	−0.124648	−	0.0905617i	−0.00630370	−	0.00457990i
$392$	6.16268	+	2.00238i	0.311262	+	0.101135i
$393$		0			0
$394$	−9.34127	+	6.78683i	−0.470606	+	0.341915i
$395$	−16.9704	−	4.79066i	−0.853875	−	0.241044i
$396$		0			0
$397$		−	18.6869i		−	0.937868i	−0.883233	−	0.468934i	$-0.844638\pi$
$397$		−	18.6869i		−	0.937868i	0.883233	−	0.468934i	$-0.155362\pi$
$398$	8.28772	+	11.4071i	0.415426	+	0.571784i
$399$		0			0
$400$	3.80363	−	3.24537i	0.190181	−	0.162268i
$401$	12.4245	+	9.02694i	0.620451	+	0.450784i	0.853079	−	0.521782i	$-0.174732\pi$
$401$	12.4245	+	9.02694i	0.620451	+	0.450784i	−0.232628	+	0.972566i	$0.574732\pi$
$402$		0			0
$403$	−7.81589	−	2.53954i	−0.389337	−	0.126503i
$404$	−0.249290	−	0.767236i	−0.0124026	−	0.0381714i
$405$		0			0
$406$	33.8964			1.68225
$407$	−2.09781	+	1.96733i	−0.103984	+	0.0975170i
$408$		0			0
$409$	−2.59071	+	1.88226i	−0.128103	+	0.0930719i	−0.649991	−	0.759942i	$-0.725228\pi$
$409$	−2.59071	+	1.88226i	−0.128103	+	0.0930719i	0.521889	+	0.853013i	$0.325228\pi$
$410$	13.8069	−	0.539071i	0.681873	−	0.0266228i
$411$		0			0
$412$	6.68850	−	9.20592i	0.329519	−	0.453543i
$413$	−23.2724	+	32.0318i	−1.14516	+	1.57618i
$414$		0			0
$415$	−34.2597	+	1.33762i	−1.68174	+	0.0656614i
$416$	1.80702	−	1.31288i	0.0885966	−	0.0643692i
$417$		0			0
$418$	−11.2768	−	24.0062i	−0.551568	−	1.17418i
$419$	0.122299			0.00597471			0.00298736	−	0.999996i	$-0.499049\pi$
$419$	0.122299			0.00597471			0.00298736	+	0.999996i	$0.499049\pi$
$420$		0			0
$421$	0.661002	+	2.03436i	0.0322153	+	0.0991485i	0.965871	−	0.259023i	$-0.0834004\pi$
$421$	0.661002	+	2.03436i	0.0322153	+	0.0991485i	−0.933656	+	0.358171i	$0.883400\pi$
$422$	0.255034	+	0.0828655i	0.0124149	+	0.00403383i
$423$		0			0
$424$	−0.930864	−	0.676313i	−0.0452068	−	0.0328446i
$425$	13.6662	+	16.0170i	0.662909	+	0.776941i
$426$		0			0
$427$	3.24094	+	4.46078i	0.156840	+	0.215872i
$428$		−	19.2191i		−	0.928990i
$429$		0			0
$430$	−20.6631	−	5.83307i	−0.996461	−	0.281296i
$431$	24.3875	−	17.7186i	1.17471	−	0.853474i	0.183141	−	0.983087i	$-0.441373\pi$
$431$	24.3875	−	17.7186i	1.17471	−	0.853474i	0.991565	+	0.129613i	$0.0413735\pi$
$432$		0			0
$433$	−25.2902	−	8.21727i	−1.21537	−	0.394897i	−0.369975	−	0.929042i	$-0.620634\pi$
$433$	−25.2902	−	8.21727i	−1.21537	−	0.394897i	−0.845393	+	0.534145i	$0.820634\pi$
$434$	10.9286	+	7.94011i	0.524591	+	0.381138i
$435$		0			0
$436$	0.571022	−	1.75742i	0.0273470	−	0.0841654i
$437$	−0.278274	+	0.0904166i	−0.0133116	+	0.00432521i
$438$		0			0
$439$	−9.60080			−0.458221			−0.229111	−	0.973400i	$-0.573582\pi$
$439$	−9.60080			−0.458221			−0.229111	+	0.973400i	$0.573582\pi$
$440$	−6.58436	+	3.41265i	−0.313897	+	0.162692i
$441$		0			0
$442$	5.52853	+	7.60936i	0.262965	+	0.361941i
$443$	13.3652	−	4.34263i	0.635001	−	0.206324i	0.0262121	−	0.999656i	$-0.491655\pi$
$443$	13.3652	−	4.34263i	0.635001	−	0.206324i	0.608789	+	0.793332i	$0.291655\pi$
$444$		0			0
$445$	−6.43036	−	8.16101i	−0.304829	−	0.386869i
$446$	−14.3507	−	10.4264i	−0.679527	−	0.493705i
$447$		0			0
$448$	−3.49179	+	1.13455i	−0.164972	+	0.0536026i
$449$	−23.0363	+	16.7369i	−1.08715	+	0.789862i	−0.978916	−	0.204263i	$-0.934520\pi$
$449$	−23.0363	+	16.7369i	−1.08715	+	0.789862i	−0.108236	+	0.994125i	$0.534520\pi$
$450$		0			0
$451$	−20.1289	−	3.85376i	−0.947834	−	0.181466i
$452$		−	8.96841i		−	0.421839i
$453$		0			0
$454$	−5.87528	−	18.0822i	−0.275740	−	0.848642i
$455$	−10.1914	+	15.2443i	−0.477778	+	0.714665i
$456$		0			0
$457$	17.1007	−	23.5372i	0.799939	−	1.10102i	−0.192859	−	0.981226i	$-0.561776\pi$
$457$	17.1007	−	23.5372i	0.799939	−	1.10102i	0.992799	−	0.119795i	$-0.0382239\pi$
$458$	−21.7310	−	7.06084i	−1.01542	−	0.329931i
$459$		0			0
$460$	0.0282983	+	0.0767640i	0.00131941	+	0.00357914i
$461$	−14.5472			−0.677533			−0.338766	−	0.940871i	$-0.610010\pi$
$461$	−14.5472			−0.677533			−0.338766	+	0.940871i	$0.610010\pi$
$462$		0			0
$463$		−	26.5659i		−	1.23462i	−0.786719	−	0.617311i	$-0.788222\pi$
$463$		−	26.5659i		−	1.23462i	0.786719	−	0.617311i	$-0.211778\pi$
$464$	−7.46912	+	5.42663i	−0.346745	+	0.251925i
$465$		0			0
$466$	−0.189450	+	0.583066i	−0.00877609	+	0.0270100i
$467$	−3.38974	+	4.66558i	−0.156858	+	0.215897i	−0.880212	−	0.474581i	$-0.842600\pi$
$467$	−3.38974	+	4.66558i	−0.156858	+	0.215897i	0.723354	+	0.690478i	$0.242600\pi$
$468$		0			0
$469$	−3.27512	+	10.0798i	−0.151231	+	0.465441i
$470$	−0.596835	−	15.2863i	−0.0275299	−	0.705106i
$471$		0			0
$472$		−	10.7840i		−	0.496375i
$473$	27.8966	+	15.3606i	1.28269	+	0.706282i
$474$		0			0
$475$	39.8630	−	3.11755i	1.82904	−	0.143043i
$476$	−4.77759	−	14.7039i	−0.218980	−	0.673953i
$477$		0			0
$478$	−10.4723	+	14.4138i	−0.478990	+	0.659273i
$479$	−9.85916	−	7.16310i	−0.450477	−	0.327291i	0.339307	−	0.940676i	$-0.389807\pi$
$479$	−9.85916	−	7.16310i	−0.450477	−	0.327291i	−0.789784	+	0.613385i	$0.789807\pi$
$480$		0			0
$481$	−0.598516	−	1.84204i	−0.0272900	−	0.0839900i
$482$	11.8452	+	16.3035i	0.539533	+	0.742603i
$483$		0			0
$484$	10.6581	−	2.72133i	0.484457	−	0.123697i
$485$	8.99978	−	31.8808i	0.408659	−	1.44763i
$486$		0			0
$487$	−5.66556	+	1.84085i	−0.256731	+	0.0834170i	−0.434555	−	0.900645i	$-0.643094\pi$
$487$	−5.66556	+	1.84085i	−0.256731	+	0.0834170i	0.177824	+	0.984062i	$0.443094\pi$
$488$	−1.42829	−	0.464080i	−0.0646557	−	0.0210079i
$489$		0			0
$490$	11.3809	−	8.96746i	0.514138	−	0.405108i
$491$	−8.86786	+	27.2925i	−0.400201	+	1.23169i	0.524635	+	0.851327i	$0.324202\pi$
$491$	−8.86786	+	27.2925i	−0.400201	+	1.23169i	−0.924836	+	0.380365i	$0.875798\pi$
$492$		0			0
$493$	−22.8515	−	31.4524i	−1.02918	−	1.41654i
$494$	17.8620			0.803650
$495$		0			0
$496$	−3.67931			−0.165206
$497$	12.7588	+	17.5609i	0.572309	+	0.787715i
$498$		0			0
$499$	3.05089	−	9.38968i	0.136577	−	0.420340i	−0.859255	−	0.511547i	$-0.829073\pi$
$499$	3.05089	−	9.38968i	0.136577	−	0.420340i	0.995832	+	0.0912073i	$0.0290726\pi$
$500$	−1.30591	−	11.1038i	−0.0584021	−	0.496577i
$501$		0			0
$502$	3.88733	+	1.26307i	0.173500	+	0.0563736i
$503$	−20.5152	+	6.66581i	−0.914730	+	0.297214i	−0.728303	−	0.685255i	$-0.759691\pi$
$503$	−20.5152	+	6.66581i	−0.914730	+	0.297214i	−0.186427	+	0.982469i	$0.559691\pi$
$504$		0			0
$505$	−1.73603	−	0.490073i	−0.0772525	−	0.0218080i
$506$	−0.0151286	−	0.120403i	−0.000672548	−	0.00535255i
$507$		0			0
$508$	−3.88580	−	5.34835i	−0.172405	−	0.237294i
$509$	6.13785	+	18.8904i	0.272056	+	0.837301i	0.989983	+	0.141183i	$0.0450907\pi$
$509$	6.13785	+	18.8904i	0.272056	+	0.837301i	−0.717928	+	0.696118i	$0.754909\pi$
$510$		0			0
$511$	−30.3174	−	22.0269i	−1.34116	−	0.974412i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$		0			0
$514$	−0.624042	−	1.92060i	−0.0275253	−	0.0847142i
$515$	−8.80092	−	23.8740i	−0.387815	−	1.05202i
$516$		0			0
$517$	−4.26670	+	22.2858i	−0.187649	+	0.980129i
$518$			3.18368i			0.139883i
$519$		0			0
$520$	−0.194855	−	4.99069i	−0.00854495	−	0.218856i
$521$	−3.34006	+	10.2796i	−0.146331	+	0.450359i	−0.997180	−	0.0750508i	$-0.976088\pi$
$521$	−3.34006	+	10.2796i	−0.146331	+	0.450359i	0.850849	+	0.525410i	$0.176088\pi$
$522$		0			0
$523$	11.3088	−	15.5652i	0.494499	−	0.680620i	−0.486711	−	0.873563i	$-0.661803\pi$
$523$	11.3088	−	15.5652i	0.494499	−	0.680620i	0.981210	+	0.192944i	$0.0618034\pi$
$524$	0.0191661	−	0.0589873i	0.000837277	−	0.00257687i
$525$		0			0
$526$	9.87976	−	7.17807i	0.430778	−	0.312979i
$527$		−	15.4935i		−	0.674909i
$528$		0			0
$529$	22.9987			0.999942
$530$	−2.41404	+	0.889912i	−0.104859	+	0.0386553i
$531$		0			0
$532$	−27.9237	−	9.07295i	−1.21064	−	0.393362i
$533$	8.11272	−	11.1662i	0.351401	−	0.483662i
$534$		0			0
$535$	−35.7267	−	23.8845i	−1.54460	−	1.03262i
$536$	−0.892041	−	2.74542i	−0.0385303	−	0.118584i
$537$		0			0
$538$		−	9.21959i		−	0.397485i
$539$	−19.4519	+	9.13748i	−0.837852	+	0.393579i
$540$		0			0
$541$	−6.18481	+	4.49353i	−0.265906	+	0.193192i	−0.712747	−	0.701422i	$-0.752549\pi$
$541$	−6.18481	+	4.49353i	−0.265906	+	0.193192i	0.446841	+	0.894614i	$0.352549\pi$
$542$	12.1190	−	3.93769i	0.520554	−	0.169138i
$543$		0			0
$544$	3.40676	+	2.47516i	0.146064	+	0.106122i
$545$	−2.55727	−	3.24552i	−0.109541	−	0.139023i
$546$		0			0
$547$	15.8930	−	5.16394i	0.679534	−	0.220794i	0.0511426	−	0.998691i	$-0.483714\pi$
$547$	15.8930	−	5.16394i	0.679534	−	0.220794i	0.628391	+	0.777897i	$0.283714\pi$
$548$	−0.548600	−	0.755084i	−0.0234351	−	0.0322556i
$549$		0			0
$550$	−1.83887	+	16.4809i	−0.0784098	+	0.702746i
$551$	−73.8305			−3.14529
$552$		0			0
$553$	27.5363	−	8.94709i	1.17096	−	0.380469i
$554$	−4.10852	+	12.6447i	−0.174554	+	0.537223i
$555$		0			0
$556$	5.14089	+	3.73507i	0.218022	+	0.158402i
$557$	6.20631	+	2.01655i	0.262970	+	0.0854441i	0.437534	−	0.899202i	$-0.355852\pi$
$557$	6.20631	+	2.01655i	0.262970	+	0.0854441i	−0.174565	+	0.984646i	$0.555852\pi$
$558$		0			0
$559$	−17.3509	+	12.6062i	−0.733867	+	0.533185i
$560$	−2.23039	+	7.90092i	−0.0942511	+	0.333875i
$561$		0			0
$562$		−	1.56837i		−	0.0661575i
$563$	−11.4827	−	15.8046i	−0.483940	−	0.666086i	0.495316	−	0.868713i	$-0.335052\pi$
$563$	−11.4827	−	15.8046i	−0.483940	−	0.666086i	−0.979256	+	0.202627i	$0.935052\pi$
$564$		0			0
$565$	−16.6715	−	11.1455i	−0.701377	−	0.468895i
$566$	8.74810	+	6.35586i	0.367710	+	0.267157i
$567$		0			0
$568$	−5.62282	−	1.82696i	−0.235928	−	0.0766577i
$569$	−3.39217	−	10.4400i	−0.142207	−	0.437669i	0.854434	−	0.519560i	$-0.173904\pi$
$569$	−3.39217	−	10.4400i	−0.142207	−	0.437669i	−0.996641	+	0.0818909i	$0.973904\pi$
$570$		0			0
$571$	−30.0076			−1.25578			−0.627889	−	0.778303i	$-0.716081\pi$
$571$	−30.0076			−1.25578			−0.627889	+	0.778303i	$0.716081\pi$
$572$	−1.39299	+	7.27588i	−0.0582440	+	0.304220i
$573$		0			0
$574$	−18.3544	+	13.3353i	−0.766100	+	0.556604i
$575$	0.177865	+	0.0427943i	0.00741750	+	0.00178465i
$576$		0			0
$577$	14.2539	−	19.6188i	0.593398	−	0.816742i	−0.401686	−	0.915777i	$-0.631576\pi$
$577$	14.2539	−	19.6188i	0.593398	−	0.816742i	0.995084	+	0.0990355i	$0.0315757\pi$
$578$	−0.430524	+	0.592566i	−0.0179075	+	0.0246475i
$579$		0			0
$580$	0.805409	+	20.6284i	0.0334428	+	0.856549i
$581$	45.5438	−	33.0895i	1.88947	−	1.37278i
$582$		0			0
$583$	3.78637	−	0.475757i	0.156816	−	0.0197039i
$584$	10.2069			0.422363
$585$		0			0
$586$	−6.88897	−	21.2021i	−0.284581	−	0.875849i
$587$	−27.6188	−	8.97388i	−1.13995	−	0.370392i	−0.322600	−	0.946535i	$-0.604557\pi$
$587$	−27.6188	−	8.97388i	−1.13995	−	0.370392i	−0.817348	+	0.576144i	$0.804557\pi$
$588$		0			0
$589$	−23.8039	−	17.2945i	−0.980821	−	0.712608i
$590$	−20.0466	−	13.4019i	−0.825306	−	0.551746i
$591$		0			0
$592$	−0.509690	−	0.701528i	−0.0209481	−	0.0288326i
$593$		−	38.5708i		−	1.58391i	−0.610579	−	0.791956i	$-0.709063\pi$
$593$		−	38.5708i		−	1.58391i	0.610579	−	0.791956i	$-0.290937\pi$
$594$		0			0
$595$	−33.2707	−	9.39215i	−1.36397	−	0.385040i
$596$	−9.52264	+	6.91860i	−0.390062	+	0.283397i
$597$		0			0
$598$	0.0777238	+	0.0252540i	0.00317836	+	0.00103271i
$599$	35.4633	+	25.7656i	1.44899	+	1.05275i	0.986066	+	0.166356i	$0.0532000\pi$
$599$	35.4633	+	25.7656i	1.44899	+	1.05275i	0.462925	+	0.886398i	$0.346800\pi$
$600$		0			0
$601$	11.9756	−	36.8572i	0.488497	−	1.50344i	−0.338355	−	0.941019i	$-0.609870\pi$
$601$	11.9756	−	36.8572i	0.488497	−	1.50344i	0.826852	−	0.562420i	$-0.190130\pi$
$602$	33.5280	−	10.8939i	1.36650	−	0.444003i
$603$		0			0
$604$	24.1131			0.981150
$605$	8.18658	−	23.1944i	0.332832	−	0.942986i
$606$		0			0
$607$	14.8661	+	20.4614i	0.603396	+	0.830503i	0.996014	−	0.0891983i	$-0.0284305\pi$
$607$	14.8661	+	20.4614i	0.603396	+	0.830503i	−0.392618	+	0.919702i	$0.628430\pi$
$608$	7.60555	−	2.47119i	0.308446	−	0.100220i
$609$		0			0
$610$	−2.63770	+	2.07834i	−0.106797	+	0.0841495i
$611$	−12.3627	−	8.98203i	−0.500141	−	0.363374i
$612$		0			0
$613$	26.0537	−	8.46535i	1.05230	−	0.341912i	0.268728	−	0.963216i	$-0.413397\pi$
$613$	26.0537	−	8.46535i	1.05230	−	0.341912i	0.783570	+	0.621304i	$0.213397\pi$
$614$	−5.75312	+	4.17988i	−0.232177	+	0.168686i
$615$		0			0
$616$	5.87343	−	10.6668i	0.236647	−	0.429778i
$617$			15.5982i			0.627961i	0.949429	+	0.313981i	$0.101663\pi$
$617$			15.5982i			0.627961i	−0.949429	+	0.313981i	$0.898337\pi$
$618$		0			0
$619$	6.43523	+	19.8056i	0.258654	+	0.796054i	0.993088	+	0.117374i	$0.0374476\pi$
$619$	6.43523	+	19.8056i	0.258654	+	0.796054i	−0.734434	+	0.678680i	$0.762552\pi$
$620$	−4.57246	+	6.83952i	−0.183634	+	0.274682i
$621$		0			0
$622$	−11.2431	+	15.4748i	−0.450808	+	0.620484i
$623$	16.2248	+	5.27174i	0.650031	+	0.211208i
$624$		0			0
$625$	−22.2640	−	11.3717i	−0.890559	−	0.454867i
$626$	29.9950			1.19884
$627$		0			0
$628$			13.5966i			0.542563i
$629$	2.95413	−	2.14630i	0.117789	−	0.0855786i
$630$		0			0
$631$	6.58817	−	20.2763i	0.262271	−	0.807187i	−0.730039	−	0.683406i	$-0.760498\pi$
$631$	6.58817	−	20.2763i	0.262271	−	0.807187i	0.992310	−	0.123781i	$-0.0395020\pi$
$632$	−4.63528	+	6.37992i	−0.184382	+	0.253779i
$633$		0			0
$634$	−2.03990	+	6.27817i	−0.0810148	+	0.249338i
$635$	−14.7712	+	0.576722i	−0.586178	+	0.0228865i
$636$		0			0
$637$		−	14.4734i		−	0.573456i
$638$	5.75777	−	30.0740i	0.227952	−	1.19064i
$639$		0			0
$640$	−0.773425	−	2.09805i	−0.0305723	−	0.0829327i
$641$	1.35758	+	4.17819i	0.0536211	+	0.165029i	0.974281	−	0.225337i	$-0.0723484\pi$
$641$	1.35758	+	4.17819i	0.0536211	+	0.165029i	−0.920660	+	0.390366i	$0.872348\pi$
$642$		0			0
$643$	−10.9094	+	15.0155i	−0.430226	+	0.592155i	−0.968005	−	0.250931i	$-0.919263\pi$
$643$	−10.9094	+	15.0155i	−0.430226	+	0.592155i	0.537779	+	0.843086i	$0.319263\pi$
$644$	−0.108678	−	0.0789591i	−0.00428251	−	0.00311143i
$645$		0			0
$646$	10.4062	+	32.0269i	0.409425	+	1.26008i
$647$	−22.4440	−	30.8915i	−0.882364	−	1.21447i	−0.975761	−	0.218841i	$-0.929772\pi$
$647$	−22.4440	−	30.8915i	−0.882364	−	1.21447i	0.0933967	−	0.995629i	$-0.470228\pi$
$648$		0			0
$649$	24.4665	+	26.0891i	0.960393	+	1.02409i
$650$	−9.51943	−	5.83996i	−0.373383	−	0.229062i
$651$		0			0
$652$	−9.62771	+	3.12823i	−0.377050	+	0.122511i
$653$	−8.58380	−	2.78905i	−0.335910	−	0.109144i	0.136205	−	0.990681i	$-0.456509\pi$
$653$	−8.58380	−	2.78905i	−0.335910	−	0.109144i	−0.472115	+	0.881537i	$0.656509\pi$
$654$		0			0
$655$	−0.0858338	−	0.108935i	−0.00335380	−	0.00425643i
$656$	1.90952	−	5.87689i	0.0745542	−	0.229454i
$657$		0			0
$658$	14.7642	+	20.3212i	0.575569	+	0.792202i
$659$	−3.25065			−0.126627			−0.0633137	−	0.997994i	$-0.520167\pi$
$659$	−3.25065			−0.126627			−0.0633137	+	0.997994i	$0.520167\pi$
$660$		0			0
$661$	32.7128			1.27238			0.636190	−	0.771532i	$-0.280509\pi$
$661$	32.7128			1.27238			0.636190	+	0.771532i	$0.280509\pi$
$662$	1.15623	+	1.59142i	0.0449382	+	0.0618522i
$663$		0			0
$664$	−4.73818	+	14.5826i	−0.183877	+	0.565915i
$665$	−51.5680	+	40.6324i	−1.99972	+	1.57566i
$666$		0			0
$667$	−0.321262	−	0.104384i	−0.0124393	−	0.00404178i
$668$	−20.1376	+	6.54311i	−0.779148	+	0.253160i
$669$		0			0
$670$	−6.21209	−	1.75364i	−0.239994	−	0.0677490i
$671$	4.50826	−	2.11774i	0.174040	−	0.0817546i
$672$		0			0
$673$	−0.454434	−	0.625475i	−0.0175171	−	0.0241103i	0.800169	−	0.599775i	$-0.204743\pi$
$673$	−0.454434	−	0.625475i	−0.0175171	−	0.0241103i	−0.817686	+	0.575665i	$0.804743\pi$
$674$	−2.89088	−	8.89720i	−0.111352	−	0.342707i
$675$		0			0
$676$	6.48104	+	4.70875i	0.249271	+	0.181106i
$677$	−21.8005	+	30.0058i	−0.837861	+	1.15322i	0.148548	+	0.988905i	$0.452540\pi$
$677$	−21.8005	+	30.0058i	−0.837861	+	1.15322i	−0.986409	+	0.164311i	$0.947460\pi$
$678$		0			0
$679$	16.8081	+	51.7300i	0.645035	+	1.98521i
$680$	8.83487	−	3.25689i	0.338802	−	0.124896i
$681$		0			0
$682$	8.90110	−	8.34749i	0.340841	−	0.319642i
$683$		−	22.7377i		−	0.870034i	−0.900422	−	0.435017i	$-0.856742\pi$
$683$		−	22.7377i		−	0.870034i	0.900422	−	0.435017i	$-0.143258\pi$
$684$		0			0
$685$	−2.08541	+	0.0814221i	−0.0796795	+	0.00311098i
$686$	0.590165	−	1.81634i	0.0225326	−	0.0693482i
$687$		0			0
$688$	−5.64388	+	7.76814i	−0.215171	+	0.296157i
$689$	−0.794177	+	2.44423i	−0.0302557	+	0.0931176i
$690$		0			0
$691$	1.36479	−	0.991577i	0.0519190	−	0.0377214i	−0.561523	−	0.827461i	$-0.689784\pi$
$691$	1.36479	−	0.991577i	0.0519190	−	0.0377214i	0.613442	+	0.789740i	$0.289784\pi$
$692$			0.190960i			0.00725921i
$693$		0			0
$694$	−20.3137			−0.771099
$695$	13.3320	−	4.91472i	0.505713	−	0.186426i
$696$		0			0
$697$	24.7475	+	8.04097i	0.937380	+	0.304573i
$698$	−9.66595	+	13.3040i	−0.365862	+	0.503565i
$699$		0			0
$700$	11.9153	+	13.9650i	0.450357	+	0.527826i
$701$	12.4806	+	38.4112i	0.471384	+	1.45077i	0.850773	+	0.525534i	$0.176134\pi$
$701$	12.4806	+	38.4112i	0.471384	+	1.45077i	−0.379388	+	0.925238i	$0.623866\pi$
$702$		0			0
$703$		−	6.93444i		−	0.261537i
$704$	0.413482	+	3.29075i	0.0155837	+	0.124025i
$705$		0			0
$706$	−21.1396	+	15.3588i	−0.795599	+	0.578036i
$707$	2.81690	−	0.915266i	0.105940	−	0.0344221i
$708$		0			0
$709$	−9.28629	−	6.74688i	−0.348754	−	0.253384i	0.399592	−	0.916693i	$-0.369152\pi$
$709$	−9.28629	−	6.74688i	−0.348754	−	0.253384i	−0.748346	+	0.663309i	$0.769152\pi$
$710$	−10.3839	+	8.18189i	−0.389702	+	0.307061i
$711$		0			0
$712$	−4.41912	+	1.43586i	−0.165614	+	0.0538111i
$713$	−0.0791273	−	0.108909i	−0.00296334	−	0.00407869i
$714$		0			0
$715$	11.7941	+	11.6316i	0.441075	+	0.434996i
$716$	−4.24913			−0.158797
$717$		0			0
$718$	−5.72461	+	1.86004i	−0.213641	+	0.0694161i
$719$	−13.7386	+	42.2830i	−0.512363	+	1.57689i	0.275667	+	0.961253i	$0.411101\pi$
$719$	−13.7386	+	42.2830i	−0.512363	+	1.57689i	−0.788030	+	0.615637i	$0.788899\pi$
$720$		0			0
$721$	33.7994	+	24.5567i	1.25876	+	0.914541i
$722$	42.7511	+	13.8907i	1.59103	+	0.516957i
$723$		0			0
$724$	−18.4447	+	13.4009i	−0.685492	+	0.498039i
$725$	39.3474	+	24.1388i	1.46133	+	0.896492i
$726$		0			0
$727$		−	24.5763i		−	0.911484i	−0.890112	−	0.455742i	$-0.849374\pi$
$727$		−	24.5763i		−	0.911484i	0.890112	−	0.455742i	$-0.150626\pi$
$728$	4.82022	+	6.63447i	0.178649	+	0.245890i
$729$		0			0
$730$	12.6846	−	18.9737i	0.469477	−	0.702248i
$731$	−32.7116	−	23.7663i	−1.20988	−	0.879030i
$732$		0			0
$733$	24.2238	+	7.87080i	0.894728	+	0.290715i	0.720059	−	0.693913i	$-0.244115\pi$
$733$	24.2238	+	7.87080i	0.894728	+	0.290715i	0.174668	+	0.984627i	$0.444115\pi$
$734$	−0.928961	−	2.85905i	−0.0342886	−	0.105529i
$735$		0			0
$736$	0.0365882			0.00134866
$737$	8.38677	+	4.61798i	0.308931	+	0.170105i
$738$		0			0
$739$	24.0114	−	17.4453i	0.883273	−	0.641735i	−0.0508427	−	0.998707i	$-0.516191\pi$
$739$	24.0114	−	17.4453i	0.883273	−	0.641735i	0.934115	+	0.356972i	$0.116191\pi$
$740$	−1.93750	+	0.0756471i	−0.0712239	+	0.00278084i
$741$		0			0
$742$	2.48307	−	3.41766i	0.0911565	−	0.125466i
$743$	23.2228	−	31.9634i	0.851962	−	1.17262i	−0.131465	−	0.991321i	$-0.541968\pi$
$743$	23.2228	−	31.9634i	0.851962	−	1.17262i	0.983427	−	0.181304i	$-0.0580319\pi$
$744$		0			0
$745$	1.02684	+	26.2999i	0.0376207	+	0.963553i
$746$	13.0549	−	9.48497i	0.477975	−	0.347269i
$747$		0			0
$748$	−13.8573	+	1.74117i	−0.506674	+	0.0636635i
$749$	70.5627			2.57830
$750$		0			0
$751$	16.4756	+	50.7066i	0.601202	+	1.85031i	0.521050	+	0.853526i	$0.325541\pi$
$751$	16.4756	+	50.7066i	0.601202	+	1.85031i	0.0801523	+	0.996783i	$0.474459\pi$
$752$	−6.50662	−	2.11413i	−0.237272	−	0.0770944i
$753$		0			0
$754$	16.6831	+	12.1210i	0.607561	+	0.441419i
$755$	29.9666	−	44.8243i	1.09060	−	1.63132i
$756$		0			0
$757$	−3.98396	−	5.48346i	−0.144800	−	0.199300i	0.730457	−	0.682959i	$-0.239307\pi$
$757$	−3.98396	−	5.48346i	−0.144800	−	0.199300i	−0.875256	+	0.483660i	$0.839307\pi$
$758$		−	25.2460i		−	0.916974i
$759$		0			0
$760$	4.85805	−	17.2092i	0.176220	−	0.624242i
$761$	−19.8050	+	14.3891i	−0.717929	+	0.521606i	−0.885722	−	0.464216i	$-0.846336\pi$
$761$	−19.8050	+	14.3891i	−0.717929	+	0.521606i	0.167793	+	0.985822i	$0.446336\pi$
$762$		0			0
$763$	6.45237	+	2.09650i	0.233591	+	0.0758984i
$764$	8.40109	+	6.10375i	0.303941	+	0.220826i
$765$		0			0
$766$	10.8691	−	33.4516i	0.392716	−	1.20866i
$767$	−22.9083	+	7.44337i	−0.827172	+	0.268765i
$768$		0			0
$769$	−21.1893			−0.764104			−0.382052	−	0.924141i	$-0.624783\pi$
$769$	−21.1893			−0.764104			−0.382052	+	0.924141i	$0.624783\pi$
$770$	−12.5295	−	24.1744i	−0.451533	−	0.871185i
$771$		0			0
$772$	−3.90867	−	5.37982i	−0.140676	−	0.193624i
$773$	39.9082	−	12.9670i	1.43540	−	0.466389i	0.514938	−	0.857227i	$-0.327815\pi$
$773$	39.9082	−	12.9670i	1.43540	−	0.466389i	0.920459	+	0.390838i	$0.127815\pi$
$774$		0			0
$775$	7.03168	+	16.9996i	0.252585	+	0.610645i
$776$	−11.9854	−	8.70788i	−0.430250	−	0.312595i
$777$		0			0
$778$	2.14797	−	0.697918i	0.0770085	−	0.0250216i
$779$	39.9782	−	29.0459i	1.43237	−	1.04068i
$780$		0			0
$781$	17.7479	−	8.33702i	0.635069	−	0.298322i
$782$			0.154073i			0.00550963i
$783$		0			0
$784$	−2.00238	−	6.16268i	−0.0715134	−	0.220096i
$785$	25.2749	+	16.8972i	0.902102	+	0.603086i
$786$		0			0
$787$	−13.2891	+	18.2909i	−0.473706	+	0.652001i	−0.977280	−	0.211951i	$-0.932018\pi$
$787$	−13.2891	+	18.2909i	−0.473706	+	0.652001i	0.503574	+	0.863952i	$0.332018\pi$
$788$	10.9813	+	3.56805i	0.391193	+	0.127106i
$789$		0			0
$790$	6.09924	+	16.5452i	0.217001	+	0.588653i
$791$	32.9274			1.17076
$792$		0			0
$793$			3.35442i			0.119119i
$794$	−15.1180	+	10.9839i	−0.536518	+	0.389803i
$795$		0			0
$796$	4.35711	−	13.4098i	0.154434	−	0.475298i
$797$	3.69554	−	5.08647i	0.130903	−	0.180172i	−0.738534	−	0.674216i	$-0.764482\pi$
$797$	3.69554	−	5.08647i	0.130903	−	0.180172i	0.869437	+	0.494044i	$0.164482\pi$
$798$		0			0
$799$	8.90258	−	27.3993i	0.314951	−	0.969319i
$800$	−4.86127	−	1.16962i	−0.171872	−	0.0413523i
$801$		0			0
$802$		−	15.3576i		−	0.542294i
$803$	−24.6928	+	23.1570i	−0.871389	+	0.817193i
$804$		0			0
$805$	−0.281838	+	0.103897i	−0.00993348	+	0.00366188i
$806$	2.53954	+	7.81589i	0.0894514	+	0.275303i
$807$		0			0
$808$	−0.474178	+	0.652650i	−0.0166815	+	0.0229601i
$809$	−21.4826	−	15.6081i	−0.755290	−	0.548750i	0.142172	−	0.989842i	$-0.454591\pi$
$809$	−21.4826	−	15.6081i	−0.755290	−	0.548750i	−0.897462	+	0.441092i	$0.854591\pi$
$810$		0			0
$811$	−8.04230	−	24.7517i	−0.282403	−	0.869148i	−0.987165	−	0.159704i	$-0.948946\pi$
$811$	−8.04230	−	24.7517i	−0.282403	−	0.869148i	0.704761	−	0.709444i	$-0.251054\pi$
$812$	−19.9238	−	27.4228i	−0.699189	−	0.962351i
$813$		0			0
$814$	2.82466	+	0.540792i	0.0990044	+	0.0189547i
$815$	−6.14971	+	21.7847i	−0.215415	+	0.763086i
$816$		0			0
$817$	−73.0280	+	23.7282i	−2.55493	+	0.830146i
$818$	3.04557	+	0.989564i	0.106486	+	0.0345993i
$819$		0			0
$820$	−8.55160	−	10.8531i	−0.298635	−	0.379008i
$821$	0.0728207	−	0.224119i	0.00254146	−	0.00782181i	−0.949778	−	0.312925i	$-0.898691\pi$
$821$	0.0728207	−	0.224119i	0.00254146	−	0.00782181i	0.952319	+	0.305103i	$0.0986911\pi$
$822$		0			0
$823$	22.3456	+	30.7561i	0.778919	+	1.07209i	0.995400	+	0.0958037i	$0.0305421\pi$
$823$	22.3456	+	30.7561i	0.778919	+	1.07209i	−0.216481	+	0.976287i	$0.569458\pi$
$824$	−11.3791			−0.396411
$825$		0			0
$826$	39.5934			1.37763
$827$	12.7394	+	17.5343i	0.442992	+	0.609726i	0.970874	−	0.239592i	$-0.0770136\pi$
$827$	12.7394	+	17.5343i	0.442992	+	0.609726i	−0.527882	+	0.849318i	$0.677014\pi$
$828$		0			0
$829$	−5.68287	+	17.4901i	−0.197374	+	0.607455i	0.802567	+	0.596563i	$0.203467\pi$
$829$	−5.68287	+	17.4901i	−0.197374	+	0.607455i	−0.999941	+	0.0108924i	$0.996533\pi$
$830$	21.2195	+	26.9304i	0.736540	+	0.934769i
$831$		0			0
$832$	−2.12428	−	0.690222i	−0.0736463	−	0.0239291i
$833$	25.9510	−	8.43199i	0.899149	−	0.292151i
$834$		0			0
$835$	−12.8629	+	45.5656i	−0.445140	+	1.57686i
$836$	−12.7930	+	23.2336i	−0.442456	+	0.803551i
$837$		0			0
$838$	−0.0718858	−	0.0989423i	−0.00248325	−	0.00341790i
$839$	−4.43832	−	13.6598i	−0.153228	−	0.471587i	0.844749	−	0.535163i	$-0.179750\pi$
$839$	−4.43832	−	13.6598i	−0.153228	−	0.471587i	−0.997977	+	0.0635754i	$0.979750\pi$
$840$		0			0
$841$	−45.4960	−	33.0548i	−1.56883	−	1.13982i
$842$	1.25730	−	1.73053i	0.0433295	−	0.0596379i
$843$		0			0
$844$	−0.0828655	−	0.255034i	−0.00285235	−	0.00877863i
$845$	16.8075	−	6.19592i	0.578196	−	0.213146i
$846$		0			0
$847$	9.99134	+	39.1310i	0.343307	+	1.34456i
$848$			1.15061i			0.0395122i
$849$		0			0
$850$	4.92526	−	20.4708i	0.168935	−	0.702142i
$851$	0.00980418	−	0.0301742i	0.000336083	−	0.00103436i
$852$		0			0
$853$	−22.3924	+	30.8205i	−0.766702	+	1.05528i	0.229924	+	0.973208i	$0.426152\pi$
$853$	−22.3924	+	30.8205i	−0.766702	+	1.05528i	−0.996627	+	0.0820669i	$0.973848\pi$
$854$	1.70386	−	5.24396i	0.0583051	−	0.179445i
$855$		0			0
$856$	−15.5486	+	11.2967i	−0.531439	+	0.386113i
$857$			11.0195i			0.376420i	0.982129	+	0.188210i	$0.0602686\pi$
$857$			11.0195i			0.376420i	−0.982129	+	0.188210i	$0.939731\pi$
$858$		0			0
$859$	−24.5275			−0.836866			−0.418433	−	0.908248i	$-0.637420\pi$
$859$	−24.5275			−0.836866			−0.418433	+	0.908248i	$0.637420\pi$
$860$	7.42638	+	20.1454i	0.253238	+	0.686951i
$861$		0			0
$862$	−28.6693	−	9.31521i	−0.976479	−	0.317277i
$863$	−3.99242	+	5.49509i	−0.135904	+	0.187055i	−0.871544	−	0.490317i	$-0.836881\pi$
$863$	−3.99242	+	5.49509i	−0.135904	+	0.187055i	0.735641	+	0.677372i	$0.236881\pi$
$864$		0			0
$865$	0.354979	+	0.237315i	0.0120696	+	0.00806897i
$866$	8.21727	+	25.2902i	0.279234	+	0.859395i
$867$		0			0
$868$		−	13.5085i		−	0.458509i
$869$	−3.26073	−	25.9509i	−0.110613	−	0.880324i
$870$		0			0
$871$	−5.21634	+	3.78990i	−0.176749	+	0.128416i
$872$	−1.75742	+	0.571022i	−0.0595139	+	0.0193372i
$873$		0			0
$874$	0.236714	+	0.171983i	0.00800696	+	0.00581740i
$875$	40.7675	−	4.79464i	1.37819	−	0.162088i
$876$		0			0
$877$	14.7567	−	4.79474i	0.498298	−	0.161907i	−0.0490757	−	0.998795i	$-0.515628\pi$
$877$	14.7567	−	4.79474i	0.498298	−	0.161907i	0.547374	+	0.836888i	$0.315628\pi$
$878$	5.64321	+	7.76721i	0.190449	+	0.262131i
$879$		0			0
$880$	6.63108	+	3.32095i	0.223534	+	0.111949i
$881$	−39.0509			−1.31566			−0.657829	−	0.753167i	$-0.728525\pi$
$881$	−39.0509			−1.31566			−0.657829	+	0.753167i	$0.728525\pi$
$882$		0			0
$883$	44.3327	−	14.4046i	1.49192	−	0.484753i	0.554267	−	0.832339i	$-0.312999\pi$
$883$	44.3327	−	14.4046i	1.49192	−	0.484753i	0.937648	+	0.347586i	$0.112999\pi$
$884$	2.90652	−	8.94534i	0.0977568	−	0.300864i
$885$		0			0
$886$	−11.3691	−	8.26017i	−0.381954	−	0.277506i
$887$	7.41261	+	2.40850i	0.248891	+	0.0808696i	0.430806	−	0.902445i	$-0.358229\pi$
$887$	7.41261	+	2.40850i	0.248891	+	0.0808696i	−0.181915	+	0.983314i	$0.558229\pi$
$888$		0			0
$889$	19.6364	−	14.2667i	0.658583	−	0.478489i
$890$	−2.82272	+	9.99919i	−0.0946178	+	0.335174i
$891$		0			0
$892$			17.7385i			0.593928i
$893$	−32.1582	−	44.2620i	−1.07613	−	1.48117i
$894$		0			0
$895$	−5.28061	+	7.89878i	−0.176511	+	0.264027i
$896$	2.97030	+	2.15805i	0.0992306	+	0.0720953i
$897$		0			0
$898$	27.0808	+	8.79910i	0.903699	+	0.293630i
$899$	−10.4969	−	32.3061i	−0.350090	−	1.07747i
$900$		0			0
$901$	−4.84522			−0.161418
$902$	8.71374	+	18.5498i	0.290136	+	0.617642i
$903$		0			0
$904$	−7.25560	+	5.27150i	−0.241318	+	0.175327i
$905$	1.98893	+	50.9411i	0.0661142	+	1.69334i
$906$		0			0
$907$	−3.44121	+	4.73642i	−0.114263	+	0.157270i	−0.862318	−	0.506367i	$-0.830988\pi$
$907$	−3.44121	+	4.73642i	−0.114263	+	0.157270i	0.748055	+	0.663637i	$0.230988\pi$
$908$	−11.1754	+	15.3817i	−0.370870	+	0.510459i
$909$		0			0
$910$	18.3233	−	0.715407i	0.607410	−	0.0237155i
$911$	4.55243	−	3.30753i	0.150829	−	0.109583i	−0.509812	−	0.860286i	$-0.670285\pi$
$911$	4.55243	−	3.30753i	0.150829	−	0.109583i	0.660640	+	0.750703i	$0.270285\pi$
$912$		0			0
$913$	−21.6218	−	46.0286i	−0.715578	−	1.52332i
$914$	−29.0935			−0.962328
$915$		0			0
$916$	7.06084	+	21.7310i	0.233297	+	0.718013i
$917$	0.216571	+	0.0703683i	0.00715181	+	0.00232377i
$918$		0			0
$919$	10.3086	+	7.48964i	0.340050	+	0.247061i	0.744683	−	0.667419i	$-0.232601\pi$
$919$	10.3086	+	7.48964i	0.340050	+	0.247061i	−0.404633	+	0.914479i	$0.632601\pi$
$920$	0.0454700	−	0.0680145i	0.00149910	−	0.00224237i
$921$		0			0
$922$	8.55065	+	11.7690i	0.281601	+	0.387590i
$923$			13.2055i			0.434664i
$924$		0			0
$925$	−2.26721	+	3.69566i	−0.0745453	+	0.121513i
$926$	−21.4923	+	15.6150i	−0.706279	+	0.513142i
$927$		0			0
$928$	8.78048	+	2.85295i	0.288233	+	0.0936527i
$929$	−14.5778	−	10.5914i	−0.478281	−	0.347492i	0.322379	−	0.946611i	$-0.395518\pi$
$929$	−14.5778	−	10.5914i	−0.478281	−	0.347492i	−0.800660	+	0.599119i	$0.795518\pi$
$930$		0			0
$931$	16.0129	−	49.2826i	0.524801	−	1.61517i
$932$	0.583066	−	0.189450i	0.0190990	−	0.00620563i
$933$		0			0
$934$	5.76697			0.188701
$935$	−13.9845	+	27.9234i	−0.457342	+	0.913194i
$936$		0			0
$937$	15.4767	+	21.3018i	0.505602	+	0.695901i	0.983170	−	0.182694i	$-0.0584816\pi$
$937$	15.4767	+	21.3018i	0.505602	+	0.695901i	−0.477568	+	0.878595i	$0.658482\pi$
$938$	10.0798	−	3.27512i	0.329116	−	0.106936i
$939$		0			0
$940$	−12.0161	+	9.46794i	−0.391922	+	0.308810i
$941$	9.66039	+	7.01869i	0.314920	+	0.228803i	0.734005	−	0.679144i	$-0.237649\pi$
$941$	9.66039	+	7.01869i	0.314920	+	0.228803i	−0.419085	+	0.907947i	$0.637649\pi$
$942$		0			0
$943$	0.215025	−	0.0698659i	0.00700218	−	0.00227515i
$944$	−8.72446	+	6.33869i	−0.283957	+	0.206307i
$945$		0			0
$946$	−3.97023	−	31.5976i	−0.129083	−	1.02733i
$947$			37.4189i			1.21595i	0.793956	+	0.607976i	$0.208018\pi$
$947$			37.4189i			1.21595i	−0.793956	+	0.607976i	$0.791982\pi$
$948$		0			0
$949$	−7.04500	−	21.6823i	−0.228690	−	0.703837i
$950$	−25.9530	−	30.4174i	−0.842028	−	0.986871i
$951$		0			0
$952$	−9.08752	+	12.5079i	−0.294528	+	0.405383i
$953$	3.68410	+	1.19704i	0.119340	+	0.0387759i	0.368078	−	0.929795i	$-0.380016\pi$
$953$	3.68410	+	1.19704i	0.119340	+	0.0387759i	−0.248738	+	0.968571i	$0.580016\pi$
$954$		0			0
$955$	21.7868	−	8.03149i	0.705005	−	0.259893i
$956$	17.8165			0.576225
$957$		0			0
$958$			12.1866i			0.393731i
$959$	2.77228	−	2.01418i	0.0895216	−	0.0650413i
$960$		0			0
$961$	−5.39627	+	16.6080i	−0.174073	+	0.535743i
$962$	−1.13845	+	1.56694i	−0.0367050	+	0.0505201i
$963$		0			0
$964$	6.22738	−	19.1659i	0.200570	−	0.617292i
$965$	−14.8581	+	0.580117i	−0.478301	+	0.0186746i
$966$		0			0
$967$			0.516048i			0.0165950i	0.999966	+	0.00829749i	$0.00264120\pi$
$967$			0.516048i			0.0165950i	−0.999966	+	0.00829749i	$0.997359\pi$
$968$	−8.46626	−	7.02300i	−0.272116	−	0.225728i
$969$		0			0
$970$	−31.0820	+	11.4581i	−0.997984	+	0.367897i
$971$	15.4723	+	47.6190i	0.496531	+	1.52817i	0.814557	+	0.580084i	$0.196980\pi$
$971$	15.4723	+	47.6190i	0.496531	+	1.52817i	−0.318026	+	0.948082i	$0.603020\pi$
$972$		0			0
$973$	−13.7133	+	18.8747i	−0.439628	+	0.605096i
$974$	4.81942	+	3.50151i	0.154424	+	0.112196i
$975$		0			0
$976$	0.464080	+	1.42829i	0.0148548	+	0.0457185i
$977$	−14.0956	−	19.4010i	−0.450960	−	0.620693i	0.521644	−	0.853163i	$-0.325319\pi$
$977$	−14.0956	−	19.4010i	−0.450960	−	0.620693i	−0.972603	+	0.232471i	$0.925319\pi$
$978$		0			0
$979$	7.43325	−	13.4996i	0.237568	−	0.431450i
$980$	−13.9444	−	3.93642i	−0.445436	−	0.125744i
$981$		0			0
$982$	27.2925	−	8.86786i	0.870938	−	0.282985i
$983$	35.0687	+	11.3945i	1.11852	+	0.363428i	0.809202	−	0.587531i	$-0.199900\pi$
$983$	35.0687	+	11.3945i	1.11852	+	0.363428i	0.309316	+	0.950959i	$0.399900\pi$
$984$		0			0
$985$	20.2797	−	15.9792i	0.646166	−	0.509139i
$986$	−12.0137	+	36.9745i	−0.382596	+	1.17751i
$987$		0			0
$988$	−10.4990	−	14.4507i	−0.334019	−	0.459737i
$989$	−0.351318			−0.0111713
$990$		0			0
$991$	8.01942			0.254745			0.127373	−	0.991855i	$-0.459346\pi$
$991$	8.01942			0.254745			0.127373	+	0.991855i	$0.459346\pi$
$992$	2.16264	+	2.97662i	0.0686639	+	0.0945078i
$993$		0			0
$994$	6.70768	−	20.6441i	0.212755	−	0.654791i
$995$	−19.5129	−	24.7645i	−0.618601	−	0.785089i
$996$		0			0
$997$	40.4649	+	13.1479i	1.28154	+	0.416397i	0.869121	−	0.494599i	$-0.164685\pi$
$997$	40.4649	+	13.1479i	1.28154	+	0.416397i	0.412416	+	0.910996i	$0.364685\pi$
$998$	−9.38968	+	3.05089i	−0.297225	+	0.0965743i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.ba.i.289.4		32
3.2	odd	2		330.2.s.c.289.5	yes	32
5.4	even	2	inner	990.2.ba.i.289.7		32
11.4	even	5	inner	990.2.ba.i.829.7		32
15.14	odd	2		330.2.s.c.289.2	yes	32
33.26	odd	10		330.2.s.c.169.2	✓	32
55.4	even	10	inner	990.2.ba.i.829.4		32
165.59	odd	10		330.2.s.c.169.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.s.c.169.2	✓	32	33.26	odd	10
330.2.s.c.169.5	yes	32	165.59	odd	10
330.2.s.c.289.2	yes	32	15.14	odd	2
330.2.s.c.289.5	yes	32	3.2	odd	2
990.2.ba.i.289.4		32	1.1	even	1	trivial
990.2.ba.i.289.7		32	5.4	even	2	inner
990.2.ba.i.829.4		32	55.4	even	10	inner
990.2.ba.i.829.7		32	11.4	even	5	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.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(1.38390 + 1.75636i) q^{5} +(-3.49179 - 1.13455i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.607489 - 2.15197i) q^{10} +(-1.59974 + 2.90531i) q^{11} +(-1.31288 - 1.80702i) q^{13} +(1.13455 + 3.49179i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.47516 - 3.40676i) q^{17} +(-2.47119 - 7.60555i) q^{19} +(-2.09805 + 0.773425i) q^{20} +(3.29075 - 0.413482i) q^{22} -0.0365882i q^{23} +(-1.16962 + 4.86127i) q^{25} +(-0.690222 + 2.12428i) q^{26} +(2.15805 - 2.97030i) q^{28} +(2.85295 - 8.78048i) q^{29} +(2.97662 - 2.16264i) q^{31} +1.00000i q^{32} -4.21099 q^{34} +(-2.83962 - 7.70297i) q^{35} +(0.824696 + 0.267960i) q^{37} +(-4.70049 + 6.46966i) q^{38} +(1.85892 + 1.24275i) q^{40} +(1.90952 + 5.87689i) q^{41} -9.60194i q^{43} +(-2.26877 - 2.41923i) q^{44} +(-0.0296005 + 0.0215060i) q^{46} +(6.50662 - 2.11413i) q^{47} +(5.24229 + 3.80875i) q^{49} +(4.62034 - 1.91114i) q^{50} +(2.12428 - 0.690222i) q^{52} +(-0.676313 - 0.930864i) q^{53} +(-7.31667 + 1.21095i) q^{55} -3.67149 q^{56} +(-8.78048 + 2.85295i) q^{58} +(3.33245 - 10.2562i) q^{59} +(-1.21498 - 0.882733i) q^{61} +(-3.49923 - 1.13697i) q^{62} +(0.809017 - 0.587785i) q^{64} +(1.35689 - 4.80664i) q^{65} -2.88670i q^{67} +(2.47516 + 3.40676i) q^{68} +(-4.56274 + 6.82499i) q^{70} +(-4.78306 - 3.47509i) q^{71} +(9.70730 + 3.15409i) q^{73} +(-0.267960 - 0.824696i) q^{74} +7.99694 q^{76} +(8.88219 - 8.32976i) q^{77} +(-6.37992 + 4.63528i) q^{79} +(-0.0872378 - 2.23437i) q^{80} +(3.63212 - 4.99918i) q^{82} +(-9.01255 + 12.4047i) q^{83} +(9.40890 - 0.367358i) q^{85} +(-7.76814 + 5.64388i) q^{86} +(-0.623653 + 3.25746i) q^{88} -4.64654 q^{89} +(2.53414 + 7.79928i) q^{91} +(0.0347975 + 0.0113064i) q^{92} +(-5.53486 - 4.02131i) q^{94} +(9.93820 - 14.8657i) q^{95} +(-8.70788 - 11.9854i) q^{97} -6.47983i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{14} - 8 q^{16} + 20 q^{19} - 2 q^{20} + 4 q^{25} + 2 q^{26} - 2 q^{29} - 24 q^{31} - 28 q^{34} - 44 q^{35} - 4 q^{40} + 34 q^{41} + 20 q^{44} - 38 q^{46} + 14 q^{49}+ \cdots + 60 q^{95}+O(q^{100}) \) 32 * q + 8 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^14 - 8 * q^16 + 20 * q^19 - 2 * q^20 + 4 * q^25 + 2 * q^26 - 2 * q^29 - 24 * q^31 - 28 * q^34 - 44 * q^35 - 4 * q^40 + 34 * q^41 + 20 * q^44 - 38 * q^46 + 14 * q^49 + 24 * q^50 + 28 * q^55 - 20 * q^56 + 4 * q^59 - 8 * q^61 + 8 * q^64 + 44 * q^65 - 10 * q^70 - 8 * q^71 - 20 * q^74 + 20 * q^76 + 2 * q^79 + 2 * q^80 - 20 * q^85 - 34 * q^86 + 132 * q^89 + 78 * q^91 + 22 * q^94 + 60 * q^95

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