LMFDB - Embedded newform 330.2.s.c.169.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [330,2,Mod(49,330)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("330.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(330, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 330 = 2 \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	330.s (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,8,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.63506326670$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.5
Character	$\chi$	$=$	330.169
Dual form			330.2.s.c.289.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.38390 + 1.75636i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-3.49179 + 1.13455i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.607489 + 2.15197i) q^{10} +(1.59974 + 2.90531i) q^{11} +1.00000i q^{12} +(-1.31288 + 1.80702i) q^{13} +(-1.13455 + 3.49179i) q^{14} +(1.85892 - 1.24275i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.47516 - 3.40676i) q^{17} +(0.951057 - 0.309017i) q^{18} +(-2.47119 + 7.60555i) q^{19} +(2.09805 + 0.773425i) q^{20} +3.67149 q^{21} +(3.29075 + 0.413482i) q^{22} -0.0365882i q^{23} +(0.809017 + 0.587785i) q^{24} +(-1.16962 - 4.86127i) q^{25} +(0.690222 + 2.12428i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(2.15805 + 2.97030i) q^{28} +(-2.85295 - 8.78048i) q^{29} +(0.0872378 - 2.23437i) q^{30} +(2.97662 + 2.16264i) q^{31} +1.00000i q^{32} +(-0.623653 - 3.25746i) q^{33} -4.21099 q^{34} +(2.83962 - 7.70297i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.824696 - 0.267960i) q^{37} +(4.70049 + 6.46966i) q^{38} +(1.80702 - 1.31288i) q^{39} +(1.85892 - 1.24275i) q^{40} +(-1.90952 + 5.87689i) q^{41} +(2.15805 - 2.97030i) q^{42} +9.60194i q^{43} +(2.26877 - 2.41923i) q^{44} +(-2.15197 + 0.607489i) q^{45} +(-0.0296005 - 0.0215060i) q^{46} +(-6.50662 - 2.11413i) q^{47} +(0.951057 - 0.309017i) q^{48} +(5.24229 - 3.80875i) q^{49} +(-4.62034 - 1.91114i) q^{50} +(1.30127 + 4.00489i) q^{51} +(2.12428 + 0.690222i) q^{52} +(0.676313 - 0.930864i) q^{53} -1.00000 q^{54} +(-7.31667 - 1.21095i) q^{55} +3.67149 q^{56} +(4.70049 - 6.46966i) q^{57} +(-8.78048 - 2.85295i) q^{58} +(-3.33245 - 10.2562i) q^{59} +(-1.75636 - 1.38390i) q^{60} +(-1.21498 + 0.882733i) q^{61} +(3.49923 - 1.13697i) q^{62} +(-3.49179 - 1.13455i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.35689 - 4.80664i) q^{65} +(-3.00192 - 1.41014i) q^{66} +2.88670i q^{67} +(-2.47516 + 3.40676i) q^{68} +(-0.0113064 + 0.0347975i) q^{69} +(-4.56274 - 6.82499i) q^{70} +(4.78306 - 3.47509i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(9.70730 - 3.15409i) q^{73} +(0.267960 - 0.824696i) q^{74} +(-0.389842 + 4.98478i) q^{75} +7.99694 q^{76} +(-8.88219 - 8.32976i) q^{77} -2.23360i q^{78} +(-6.37992 - 4.63528i) q^{79} +(0.0872378 - 2.23437i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.63212 + 4.99918i) q^{82} +(9.01255 + 12.4047i) q^{83} +(-1.13455 - 3.49179i) q^{84} +(9.40890 + 0.367358i) q^{85} +(7.76814 + 5.64388i) q^{86} +9.23234i q^{87} +(-0.623653 - 3.25746i) q^{88} +4.64654 q^{89} +(-0.773425 + 2.09805i) q^{90} +(2.53414 - 7.79928i) q^{91} +(-0.0347975 + 0.0113064i) q^{92} +(-2.16264 - 2.97662i) q^{93} +(-5.53486 + 4.02131i) q^{94} +(-9.93820 - 14.8657i) q^{95} +(0.309017 - 0.951057i) q^{96} +(-8.70788 + 11.9854i) q^{97} -6.47983i q^{98} +(-0.413482 + 3.29075i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 2 q^{5} - 8 q^{6} + 8 q^{9} + 4 q^{10} + 10 q^{14} - 4 q^{15} - 8 q^{16} + 20 q^{19} + 2 q^{20} + 20 q^{21} + 8 q^{24} + 4 q^{25} - 2 q^{26} + 2 q^{29} - 2 q^{30} - 24 q^{31} - 28 q^{34}+ \cdots - 8 q^{96}+O(q^{100}) $ 32 * q + 8 * q^4 - 2 * q^5 - 8 * q^6 + 8 * q^9 + 4 * q^10 + 10 * q^14 - 4 * q^15 - 8 * q^16 + 20 * q^19 + 2 * q^20 + 20 * q^21 + 8 * q^24 + 4 * q^25 - 2 * q^26 + 2 * q^29 - 2 * q^30 - 24 * q^31 - 28 * q^34 + 44 * q^35 - 8 * q^36 + 2 * q^39 - 4 * q^40 - 34 * q^41 - 20 * q^44 - 8 * q^45 - 38 * q^46 + 14 * q^49 - 24 * q^50 - 12 * q^51 - 32 * q^54 + 28 * q^55 + 20 * q^56 - 4 * q^59 - 6 * q^60 - 8 * q^61 + 8 * q^64 - 44 * q^65 - 10 * q^66 - 22 * q^69 - 10 * q^70 + 8 * q^71 + 20 * q^74 + 24 * q^75 + 20 * q^76 + 2 * q^79 - 2 * q^80 - 8 * q^81 + 10 * q^84 - 20 * q^85 + 34 * q^86 - 132 * q^89 + 6 * q^90 + 78 * q^91 + 22 * q^94 - 60 * q^95 - 8 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/330\mathbb{Z}\right)^\times$.

$n$	$67$	$211$	$221$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−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
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$	−3.49179	+	1.13455i	−1.31977	+	0.428820i	−0.882417	−	0.470468i	$-0.844085\pi$
$7$	−3.49179	+	1.13455i	−1.31977	+	0.428820i	−0.437356	+	0.899288i	$0.644085\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	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
$12$			1.00000i			0.288675i
$13$	−1.31288	+	1.80702i	−0.364127	+	0.501178i	−0.951293	−	0.308289i	$-0.900244\pi$
$13$	−1.31288	+	1.80702i	−0.364127	+	0.501178i	0.587166	+	0.809467i	$0.300244\pi$
$14$	−1.13455	+	3.49179i	−0.303222	+	0.933221i
$15$	1.85892	−	1.24275i	0.479970	−	0.320877i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.47516	−	3.40676i	−0.600314	−	0.826262i	0.395423	−	0.918499i	$-0.370598\pi$
$17$	−2.47516	−	3.40676i	−0.600314	−	0.826262i	−0.995737	+	0.0922376i	$0.970598\pi$
$18$	0.951057	−	0.309017i	0.224166	−	0.0728360i
$19$	−2.47119	+	7.60555i	−0.566930	+	1.74483i	0.0952153	+	0.995457i	$0.469646\pi$
$19$	−2.47119	+	7.60555i	−0.566930	+	1.74483i	−0.662146	+	0.749375i	$0.730354\pi$
$20$	2.09805	+	0.773425i	0.469138	+	0.172943i
$21$	3.67149			0.801184
$22$	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	$-0.00121422\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	−1.16962	−	4.86127i	−0.233924	−	0.972255i
$26$	0.690222	+	2.12428i	0.135364	+	0.416606i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	2.15805	+	2.97030i	0.407832	+	0.561333i
$29$	−2.85295	−	8.78048i	−0.529780	−	1.63049i	−0.754666	−	0.656109i	$-0.772201\pi$
$29$	−2.85295	−	8.78048i	−0.529780	−	1.63049i	0.224887	−	0.974385i	$-0.427799\pi$
$30$	0.0872378	−	2.23437i	0.0159274	−	0.407937i
$31$	2.97662	+	2.16264i	0.534617	+	0.388422i	0.822082	−	0.569369i	$-0.192813\pi$
$31$	2.97662	+	2.16264i	0.534617	+	0.388422i	−0.287465	+	0.957791i	$0.592813\pi$
$32$			1.00000i			0.176777i
$33$	−0.623653	−	3.25746i	−0.108564	−	0.567051i
$34$	−4.21099			−0.722179
$35$	2.83962	−	7.70297i	0.479984	−	1.30204i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	0.824696	−	0.267960i	0.135579	−	0.0440523i	−0.240441	−	0.970664i	$-0.577292\pi$
$37$	0.824696	−	0.267960i	0.135579	−	0.0440523i	0.376021	+	0.926611i	$0.377292\pi$
$38$	4.70049	+	6.46966i	0.762520	+	1.04952i
$39$	1.80702	−	1.31288i	0.289355	−	0.210229i
$40$	1.85892	−	1.24275i	0.293921	−	0.196496i
$41$	−1.90952	+	5.87689i	−0.298217	+	0.917816i	0.683905	+	0.729571i	$0.260280\pi$
$41$	−1.90952	+	5.87689i	−0.298217	+	0.917816i	−0.982122	+	0.188246i	$0.939720\pi$
$42$	2.15805	−	2.97030i	0.332994	−	0.458327i
$43$			9.60194i			1.46428i	0.681153	+	0.732141i	$0.261479\pi$
$43$			9.60194i			1.46428i	−0.681153	+	0.732141i	$0.738521\pi$
$44$	2.26877	−	2.41923i	0.342030	−	0.364713i
$45$	−2.15197	+	0.607489i	−0.320796	+	0.0905591i
$46$	−0.0296005	−	0.0215060i	−0.00436436	−	0.00317089i
$47$	−6.50662	−	2.11413i	−0.949089	−	0.308378i	−0.206743	−	0.978395i	$-0.566287\pi$
$47$	−6.50662	−	2.11413i	−0.949089	−	0.308378i	−0.742345	+	0.670018i	$0.766287\pi$
$48$	0.951057	−	0.309017i	0.137273	−	0.0446028i
$49$	5.24229	−	3.80875i	0.748898	−	0.544107i
$50$	−4.62034	−	1.91114i	−0.653415	−	0.270277i
$51$	1.30127	+	4.00489i	0.182214	+	0.560797i
$52$	2.12428	+	0.690222i	0.294585	+	0.0957165i
$53$	0.676313	−	0.930864i	0.0928987	−	0.127864i	−0.760038	−	0.649879i	$-0.774820\pi$
$53$	0.676313	−	0.930864i	0.0928987	−	0.127864i	0.852936	+	0.522015i	$0.174820\pi$
$54$	−1.00000			−0.136083
$55$	−7.31667	−	1.21095i	−0.986579	−	0.163284i
$56$	3.67149			0.490623
$57$	4.70049	−	6.46966i	0.622595	−	0.856928i
$58$	−8.78048	−	2.85295i	−1.15293	−	0.374611i
$59$	−3.33245	−	10.2562i	−0.433848	−	1.33525i	−0.894263	−	0.447542i	$-0.852299\pi$
$59$	−3.33245	−	10.2562i	−0.433848	−	1.33525i	0.460415	−	0.887704i	$-0.347701\pi$
$60$	−1.75636	−	1.38390i	−0.226745	−	0.178661i
$61$	−1.21498	+	0.882733i	−0.155562	+	0.113022i	−0.662843	−	0.748758i	$-0.730650\pi$
$61$	−1.21498	+	0.882733i	−0.155562	+	0.113022i	0.507281	+	0.861780i	$0.330650\pi$
$62$	3.49923	−	1.13697i	0.444402	−	0.144395i
$63$	−3.49179	−	1.13455i	−0.439925	−	0.142940i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−1.35689	−	4.80664i	−0.168301	−	0.596190i
$66$	−3.00192	−	1.41014i	−0.369510	−	0.173577i
$67$			2.88670i			0.352667i	0.984330	+	0.176334i	$0.0564237\pi$
$67$			2.88670i			0.352667i	−0.984330	+	0.176334i	$0.943576\pi$
$68$	−2.47516	+	3.40676i	−0.300157	+	0.413131i
$69$	−0.0113064	+	0.0347975i	−0.00136113	+	0.00418913i
$70$	−4.56274	−	6.82499i	−0.545352	−	0.815742i
$71$	4.78306	−	3.47509i	0.567644	−	0.412418i	−0.266604	−	0.963806i	$-0.585902\pi$
$71$	4.78306	−	3.47509i	0.567644	−	0.412418i	0.834249	+	0.551388i	$0.185902\pi$
$72$	−0.587785	−	0.809017i	−0.0692712	−	0.0953436i
$73$	9.70730	−	3.15409i	1.13615	−	0.369159i	0.320242	−	0.947336i	$-0.396236\pi$
$73$	9.70730	−	3.15409i	1.13615	−	0.369159i	0.815911	+	0.578177i	$0.196236\pi$
$74$	0.267960	−	0.824696i	0.0311497	−	0.0958689i
$75$	−0.389842	+	4.98478i	−0.0450151	+	0.575593i
$76$	7.99694			0.917312
$77$	−8.88219	−	8.32976i	−1.01222	−	0.949264i
$78$		−	2.23360i		−	0.252906i
$79$	−6.37992	−	4.63528i	−0.717797	−	0.521510i	0.167883	−	0.985807i	$-0.446307\pi$
$79$	−6.37992	−	4.63528i	−0.717797	−	0.521510i	−0.885680	+	0.464297i	$0.846307\pi$
$80$	0.0872378	−	2.23437i	0.00975349	−	0.249810i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	3.63212	+	4.99918i	0.401100	+	0.552067i
$83$	9.01255	+	12.4047i	0.989256	+	1.36159i	0.931691	+	0.363253i	$0.118334\pi$
$83$	9.01255	+	12.4047i	0.989256	+	1.36159i	0.0575655	+	0.998342i	$0.481666\pi$
$84$	−1.13455	−	3.49179i	−0.123790	−	0.380986i
$85$	9.40890	+	0.367358i	1.02054	+	0.0398455i
$86$	7.76814	+	5.64388i	0.837660	+	0.608595i
$87$			9.23234i			0.989811i
$88$	−0.623653	−	3.25746i	−0.0664816	−	0.347247i
$89$	4.64654			0.492532			0.246266	−	0.969202i	$-0.420796\pi$
$89$	4.64654			0.492532			0.246266	+	0.969202i	$0.420796\pi$
$90$	−0.773425	+	2.09805i	−0.0815262	+	0.221154i
$91$	2.53414	−	7.79928i	0.265650	−	0.817587i
$92$	−0.0347975	+	0.0113064i	−0.00362789	+	0.00117877i
$93$	−2.16264	−	2.97662i	−0.224255	−	0.308661i
$94$	−5.53486	+	4.02131i	−0.570878	+	0.414767i
$95$	−9.93820	−	14.8657i	−1.01964	−	1.52518i
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	−8.70788	+	11.9854i	−0.884151	+	1.21693i	0.0911028	+	0.995841i	$0.470961\pi$
$97$	−8.70788	+	11.9854i	−0.884151	+	1.21693i	−0.975254	+	0.221088i	$0.929039\pi$
$98$		−	6.47983i		−	0.654561i
$99$	−0.413482	+	3.29075i	−0.0415565	+	0.330733i
$100$	−4.26191	+	2.61459i	−0.426191	+	0.261459i
$101$	0.652650	+	0.474178i	0.0649411	+	0.0471825i	0.619782	−	0.784774i	$-0.287221\pi$
$101$	0.652650	+	0.474178i	0.0649411	+	0.0471825i	−0.554841	+	0.831956i	$0.687221\pi$
$102$	4.00489	+	1.30127i	0.396543	+	0.128845i
$103$	−10.8222	+	3.51635i	−1.06634	+	0.346476i	−0.789063	−	0.614312i	$-0.789433\pi$
$103$	−10.8222	+	3.51635i	−1.06634	+	0.346476i	−0.277282	+	0.960789i	$0.589433\pi$
$104$	1.80702	−	1.31288i	0.177193	−	0.128738i
$105$	−5.08099	+	6.44846i	−0.495854	+	0.629306i
$106$	−0.355559	−	1.09430i	−0.0345349	−	0.106287i
$107$	18.2784	+	5.93903i	1.76704	+	0.574148i	0.997891	−	0.0649163i	$-0.0206780\pi$
$107$	18.2784	+	5.93903i	1.76704	+	0.574148i	0.769154	+	0.639064i	$0.220678\pi$
$108$	−0.587785	+	0.809017i	−0.0565597	+	0.0778477i
$109$	−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
$111$	−0.867136			−0.0823050
$112$	2.15805	−	2.97030i	0.203916	−	0.280667i
$113$	8.52947	+	2.77139i	0.802385	+	0.260711i	0.681369	−	0.731940i	$-0.261385\pi$
$113$	8.52947	+	2.77139i	0.802385	+	0.260711i	0.121016	+	0.992651i	$0.461385\pi$
$114$	−2.47119	−	7.60555i	−0.231448	−	0.712325i
$115$	0.0642622	+	0.0506346i	0.00599248	+	0.00472170i
$116$	−7.46912	+	5.42663i	−0.693490	+	0.503850i
$117$	−2.12428	+	0.690222i	−0.196390	+	0.0638110i
$118$	−10.2562	−	3.33245i	−0.944162	−	0.306777i
$119$	12.5079	+	9.08752i	1.14660	+	0.833051i
$120$	−2.15197	+	0.607489i	−0.196447	+	0.0554559i
$121$	−5.88166	+	9.29548i	−0.534697	+	0.845044i
$122$			1.50179i			0.135966i
$123$	3.63212	−	4.99918i	0.327497	−	0.450761i
$124$	1.13697	−	3.49923i	0.102103	−	0.314240i
$125$	10.1568	+	4.67326i	0.908452	+	0.417989i
$126$	−2.97030	+	2.15805i	−0.264615	+	0.192254i
$127$	−3.88580	−	5.34835i	−0.344809	−	0.474589i	0.601029	−	0.799227i	$-0.294758\pi$
$127$	−3.88580	−	5.34835i	−0.344809	−	0.474589i	−0.945838	+	0.324638i	$0.894758\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	2.96716	−	9.13199i	0.261244	−	0.804027i
$130$	−4.68621	−	1.72753i	−0.411008	−	0.151514i
$131$	0.0620230			0.00541897			0.00270949	−	0.999996i	$-0.499138\pi$
$131$	0.0620230			0.00541897			0.00270949	+	0.999996i	$0.499138\pi$
$132$	−2.90531	+	1.59974i	−0.252875	+	0.139239i
$133$		−	29.3607i		−	2.54589i
$134$	2.33539	+	1.69676i	0.201747	+	0.146578i
$135$	2.23437	+	0.0872378i	0.192304	+	0.00750824i
$136$	1.30127	+	4.00489i	0.111583	+	0.343417i
$137$	0.548600	+	0.755084i	0.0468701	+	0.0645112i	0.831809	−	0.555062i	$-0.187306\pi$
$137$	0.548600	+	0.755084i	0.0468701	+	0.0645112i	−0.784939	+	0.619573i	$0.787306\pi$
$138$	0.0215060	+	0.0296005i	0.00183071	+	0.00251976i
$139$	1.96364	+	6.04348i	0.166554	+	0.512601i	0.999147	−	0.0412838i	$-0.0131448\pi$
$139$	1.96364	+	6.04348i	0.166554	+	0.512601i	−0.832593	+	0.553885i	$0.813145\pi$
$140$	−8.20345	−	0.320293i	−0.693318	−	0.0270697i
$141$	5.53486	+	4.02131i	0.466120	+	0.338656i
$142$		−	5.91218i		−	0.496139i
$143$	−7.35023	−	0.923556i	−0.614657	−	0.0772316i
$144$	−1.00000			−0.0833333
$145$	19.3699	+	7.14052i	1.60858	+	0.592988i
$146$	3.15409	−	9.70730i	0.261035	−	0.803382i
$147$	−6.16268	+	2.00238i	−0.508289	+	0.165153i
$148$	−0.509690	−	0.701528i	−0.0418963	−	0.0576653i
$149$	−9.52264	+	6.91860i	−0.780125	+	0.566794i	−0.905016	−	0.425376i	$-0.860142\pi$
$149$	−9.52264	+	6.91860i	−0.780125	+	0.566794i	0.124892	+	0.992170i	$0.460142\pi$
$150$	3.80363	+	3.24537i	0.310565	+	0.264983i
$151$	−7.45137	+	22.9330i	−0.606384	+	1.86626i	−0.119400	+	0.992846i	$0.538097\pi$
$151$	−7.45137	+	22.9330i	−0.606384	+	1.86626i	−0.486984	+	0.873411i	$0.661903\pi$
$152$	4.70049	−	6.46966i	0.381260	−	0.524759i
$153$		−	4.21099i		−	0.340439i
$154$	−11.9597	+	2.28973i	−0.963743	+	0.184512i
$155$	−7.91774	+	2.23514i	−0.635968	+	0.179531i
$156$	−1.80702	−	1.31288i	−0.144678	−	0.105115i
$157$	12.9311	+	4.20158i	1.03202	+	0.335323i	0.775587	−	0.631240i	$-0.217454\pi$
$157$	12.9311	+	4.20158i	1.03202	+	0.335323i	0.256430	+	0.966563i	$0.417454\pi$
$158$	−7.50004	+	2.43691i	−0.596671	+	0.193870i
$159$	−0.930864	+	0.676313i	−0.0738223	+	0.0536351i
$160$	−1.75636	−	1.38390i	−0.138853	−	0.109407i
$161$	0.0415113	+	0.127759i	0.00327155	+	0.0100688i
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	5.95025	−	8.18982i	0.466060	−	0.641476i	−0.509692	−	0.860357i	$-0.670241\pi$
$163$	5.95025	−	8.18982i	0.466060	−	0.641476i	0.975752	+	0.218881i	$0.0702406\pi$
$164$	6.17933			0.482525
$165$	6.58436	+	3.41265i	0.512592	+	0.265675i
$166$	15.3331			1.19008
$167$	−12.4457	+	17.1301i	−0.963080	+	1.32557i	−0.0176135	+	0.999845i	$0.505607\pi$
$167$	−12.4457	+	17.1301i	−0.963080	+	1.32557i	−0.945466	+	0.325720i	$0.894393\pi$
$168$	−3.49179	−	1.13455i	−0.269398	−	0.0875326i
$169$	2.47554	+	7.61892i	0.190426	+	0.586071i
$170$	5.82761	−	7.39603i	0.446957	−	0.567249i
$171$	−6.46966	+	4.70049i	−0.494748	+	0.359455i
$172$	9.13199	−	2.96716i	0.696308	−	0.226244i
$173$	−0.181614	−	0.0590099i	−0.0138078	−	0.00448644i	0.302105	−	0.953275i	$-0.402311\pi$
$173$	−0.181614	−	0.0590099i	−0.0138078	−	0.00448644i	−0.315913	+	0.948788i	$0.602311\pi$
$174$	7.46912	+	5.42663i	0.566233	+	0.411392i
$175$	9.59944	+	15.6476i	0.725649	+	1.18285i
$176$	−3.00192	−	1.41014i	−0.226278	−	0.106293i
$177$			10.7840i			0.810577i
$178$	2.73117	−	3.75913i	0.204710	−	0.281759i
$179$	−1.31305	+	4.04116i	−0.0981423	+	0.302051i	−0.988060	−	0.154071i	$-0.950762\pi$
$179$	−1.31305	+	4.04116i	−0.0981423	+	0.302051i	0.889918	+	0.456121i	$0.150762\pi$
$180$	1.24275	+	1.85892i	0.0926291	+	0.138555i
$181$	18.4447	−	13.4009i	1.37098	−	0.996078i	0.373325	−	0.927701i	$-0.378218\pi$
$181$	18.4447	−	13.4009i	1.37098	−	0.996078i	0.997660	−	0.0683776i	$-0.0217823\pi$
$182$	−4.82022	−	6.63447i	−0.357299	−	0.491779i
$183$	1.42829	−	0.464080i	0.105582	−	0.0343058i
$184$	−0.0113064	+	0.0347975i	−0.000833518	+	0.00256530i
$185$	−0.670665	+	1.81930i	−0.0493083	+	0.133757i
$186$	−3.67931			−0.269780
$187$	5.93810	−	12.6410i	0.434237	−	0.924405i
$188$			6.84147i			0.498965i
$189$	2.97030	+	2.15805i	0.216057	+	0.156975i
$190$	−17.8681	−	0.697636i	−1.29629	−	0.0506118i
$191$	−3.20893	−	9.87607i	−0.232190	−	0.714608i	−0.997482	−	0.0709239i	$-0.977405\pi$
$191$	−3.20893	−	9.87607i	−0.232190	−	0.714608i	0.765292	−	0.643684i	$-0.222595\pi$
$192$	−0.587785	−	0.809017i	−0.0424197	−	0.0583858i
$193$	−3.90867	−	5.37982i	−0.281352	−	0.387248i	0.644829	−	0.764327i	$-0.276929\pi$
$193$	−3.90867	−	5.37982i	−0.281352	−	0.387248i	−0.926181	+	0.377079i	$0.876929\pi$
$194$	4.57800	+	14.0896i	0.328681	+	1.01158i
$195$	−0.194855	+	4.99069i	−0.0139538	+	0.357391i
$196$	−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	$-0.134934\pi$
$198$	2.41923	+	2.26877i	0.171927	+	0.161234i
$199$	−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
$201$	0.892041	−	2.74542i	0.0629197	−	0.193647i
$202$	0.767236	−	0.249290i	0.0539825	−	0.0175400i
$203$	19.9238	+	27.4228i	1.39838	+	1.92470i
$204$	3.40676	−	2.47516i	0.238521	−	0.173296i
$205$	−7.67936	−	11.4869i	−0.536350	−	0.802277i
$206$	−3.51635	+	10.8222i	−0.244996	+	0.754019i
$207$	0.0215060	−	0.0296005i	0.00149477	−	0.00205738i
$208$		−	2.23360i		−	0.154873i
$209$	−26.0497	+	4.98731i	−1.80190	+	0.344980i
$210$	2.23039	+	7.90092i	0.153911	+	0.545215i
$211$	−0.216945	−	0.157620i	−0.0149351	−	0.0108510i	0.580293	−	0.814408i	$-0.302938\pi$
$211$	−0.216945	−	0.157620i	−0.0149351	−	0.0108510i	−0.595228	+	0.803557i	$0.702938\pi$
$212$	−1.09430	−	0.355559i	−0.0751566	−	0.0244199i
$213$	−5.62282	+	1.82696i	−0.385269	+	0.125182i
$214$	15.5486	−	11.2967i	1.06288	−	0.772227i
$215$	−16.8645	−	13.2882i	−1.15015	−	0.906246i
$216$	0.309017	+	0.951057i	0.0210259	+	0.0647112i
$217$	−12.8474	−	4.17436i	−0.872136	−	0.283374i
$218$	−1.08615	+	1.49495i	−0.0735632	+	0.101251i
$219$	−10.2069			−0.689716
$220$	1.10929	+	7.33277i	0.0747886	+	0.494375i
$221$	9.40569			0.632695
$222$	−0.509690	+	0.701528i	−0.0342082	+	0.0470835i
$223$	16.8703	+	5.48149i	1.12972	+	0.367068i	0.813469	−	0.581608i	$-0.197576\pi$
$223$	16.8703	+	5.48149i	1.12972	+	0.367068i	0.316250	+	0.948676i	$0.397576\pi$
$224$	−1.13455	−	3.49179i	−0.0758055	−	0.233305i
$225$	1.91114	−	4.62034i	0.127410	−	0.308023i
$226$	7.25560	−	5.27150i	0.482635	−	0.350655i
$227$	−18.0822	+	5.87528i	−1.20016	+	0.389956i	−0.839820	−	0.542865i	$-0.817340\pi$
$227$	−18.0822	+	5.87528i	−1.20016	+	0.389956i	−0.360341	+	0.932821i	$0.617340\pi$
$228$	−7.60555	−	2.47119i	−0.503690	−	0.163659i
$229$	18.4855	+	13.4305i	1.22156	+	0.887513i	0.996228	−	0.0867697i	$-0.0276544\pi$
$229$	18.4855	+	13.4305i	1.22156	+	0.887513i	0.225329	+	0.974283i	$0.427654\pi$
$230$	0.0787367	−	0.0222269i	0.00519174	−	0.00146560i
$231$	5.87343	+	10.6668i	0.386443	+	0.701825i
$232$			9.23234i			0.606133i
$233$	0.360355	−	0.495986i	0.0236076	−	0.0324931i	−0.797050	−	0.603913i	$-0.793607\pi$
$233$	0.360355	−	0.495986i	0.0236076	−	0.0324931i	0.820658	+	0.571420i	$0.193607\pi$
$234$	−0.690222	+	2.12428i	−0.0451212	+	0.138869i
$235$	12.7177	−	8.50224i	0.829613	−	0.554625i
$236$	−8.72446	+	6.33869i	−0.567914	+	0.412614i
$237$	4.63528	+	6.37992i	0.301094	+	0.414420i
$238$	14.7039	−	4.77759i	0.953113	−	0.309685i
$239$	5.50559	−	16.9445i	0.356127	−	1.09605i	−0.599226	−	0.800580i	$-0.704525\pi$
$239$	5.50559	−	16.9445i	0.356127	−	1.09605i	0.955353	−	0.295466i	$-0.0954750\pi$
$240$	−0.773425	+	2.09805i	−0.0499244	+	0.135429i
$241$	−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
$243$		−	1.00000i		−	0.0641500i
$244$	1.21498	+	0.882733i	0.0777810	+	0.0565112i
$245$	−0.565286	+	14.4783i	−0.0361148	+	0.924985i
$246$	−1.90952	−	5.87689i	−0.121746	−	0.374697i
$247$	−10.4990	−	14.4507i	−0.668037	−	0.919474i
$248$	−2.16264	−	2.97662i	−0.137328	−	0.189016i
$249$	−4.73818	−	14.5826i	−0.300270	−	0.924136i
$250$	9.75077	−	5.47015i	0.616693	−	0.345963i
$251$	3.30676	+	2.40250i	0.208721	+	0.151645i	0.687235	−	0.726435i	$-0.258824\pi$
$251$	3.30676	+	2.40250i	0.208721	+	0.151645i	−0.478514	+	0.878080i	$0.658824\pi$
$252$			3.67149i			0.231282i
$253$	0.106300	−	0.0585317i	0.00668304	−	0.00367985i
$254$	−6.61092			−0.414806
$255$	−8.83487	−	3.25689i	−0.553261	−	0.203954i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.92060	+	0.624042i	−0.119804	+	0.0389267i	−0.368305	−	0.929705i	$-0.620062\pi$
$257$	−1.92060	+	0.624042i	−0.119804	+	0.0389267i	0.248501	+	0.968632i	$0.420062\pi$
$258$	−5.64388	−	7.76814i	−0.351373	−	0.483623i
$259$	−2.57565	+	1.87132i	−0.160043	+	0.116278i
$260$	−4.15209	+	2.77581i	−0.257501	+	0.172149i
$261$	2.85295	−	8.78048i	0.176593	−	0.543498i
$262$	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	$0.877123\pi$
$264$	−0.413482	+	3.29075i	−0.0254481	+	0.202532i
$265$	0.698984	+	2.47608i	0.0429382	+	0.152104i
$266$	−23.7533	−	17.2578i	−1.45641	−	1.05814i
$267$	−4.41912	−	1.43586i	−0.270446	−	0.0878732i
$268$	2.74542	−	0.892041i	0.167703	−	0.0544901i
$269$	−7.45881	+	5.41914i	−0.454771	+	0.330411i	−0.791477	−	0.611199i	$-0.790687\pi$
$269$	−7.45881	+	5.41914i	−0.454771	+	0.330411i	0.336705	+	0.941610i	$0.390687\pi$
$270$	1.38390	−	1.75636i	0.0842217	−	0.106889i
$271$	−3.93769	−	12.1190i	−0.239198	−	0.736175i	−0.996537	−	0.0831529i	$-0.973501\pi$
$271$	−3.93769	−	12.1190i	−0.239198	−	0.736175i	0.757339	−	0.653022i	$-0.226499\pi$
$272$	4.00489	+	1.30127i	0.242832	+	0.0789010i
$273$	−4.82022	+	6.63447i	−0.291733	+	0.401536i
$274$	0.933335			0.0563848
$275$	12.2524	−	11.1749i	0.738849	−	0.673871i
$276$	0.0365882			0.00220235
$277$	−7.81487	+	10.7563i	−0.469550	+	0.646281i	−0.976455	−	0.215722i	$-0.930790\pi$
$277$	−7.81487	+	10.7563i	−0.469550	+	0.646281i	0.506905	+	0.862002i	$0.330790\pi$
$278$	6.04348	+	1.96364i	0.362464	+	0.117772i
$279$	1.13697	+	3.49923i	0.0680685	+	0.209493i
$280$	−5.08099	+	6.44846i	−0.303647	+	0.385369i
$281$	−1.26883	+	0.921862i	−0.0756923	+	0.0549937i	−0.624988	−	0.780634i	$-0.714896\pi$
$281$	−1.26883	+	0.921862i	−0.0756923	+	0.0549937i	0.549296	+	0.835628i	$0.314896\pi$
$282$	6.50662	−	2.11413i	0.387464	−	0.125895i
$283$	−10.2840	−	3.34148i	−0.611321	−	0.198630i	−0.0130376	−	0.999915i	$-0.504150\pi$
$283$	−10.2840	−	3.34148i	−0.611321	−	0.198630i	−0.598283	+	0.801285i	$0.704150\pi$
$284$	−4.78306	−	3.47509i	−0.283822	−	0.206209i
$285$	4.85805	+	17.2092i	0.287766	+	1.01938i
$286$	−5.06753	+	5.40361i	−0.299649	+	0.319522i
$287$		−	22.6873i		−	1.33919i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	−0.226340	+	0.696603i	−0.0133141	+	0.0409767i
$290$	17.1622	−	11.4735i	1.00780	−	0.673747i
$291$	11.9854	−	8.70788i	0.702595	−	0.510465i
$292$	−5.99944	−	8.25753i	−0.351091	−	0.483235i
$293$	−21.2021	+	6.88897i	−1.23864	+	0.402458i	−0.853836	−	0.520542i	$-0.825730\pi$
$293$	−21.2021	+	6.88897i	−1.23864	+	0.402458i	−0.384801	+	0.922999i	$0.625730\pi$
$294$	−2.00238	+	6.16268i	−0.116781	+	0.359415i
$295$	22.6254	+	8.34064i	1.31730	+	0.485611i
$296$	−0.867136			−0.0504013
$297$	1.41014	−	3.00192i	0.0818248	−	0.174189i
$298$			11.7706i			0.681854i
$299$	0.0661158	+	0.0480360i	0.00382358	+	0.00277799i
$300$	4.86127	−	1.16962i	0.280666	−	0.0675280i
$301$	−10.8939	−	33.5280i	−0.627914	−	1.93252i
$302$	14.1733	+	19.5079i	0.815584	+	1.12256i
$303$	−0.474178	−	0.652650i	−0.0272408	−	0.0374938i
$304$	−2.47119	−	7.60555i	−0.141733	−	0.436208i
$305$	0.131013	−	3.35556i	0.00750180	−	0.192139i
$306$	−3.40676	−	2.47516i	−0.194752	−	0.141495i
$307$			7.11124i			0.405860i	0.979193	+	0.202930i	$0.0650464\pi$
$307$			7.11124i			0.405860i	−0.979193	+	0.202930i	$0.934954\pi$
$308$	−5.17732	+	11.0215i	−0.295005	+	0.628008i
$309$	11.3791			0.647337
$310$	−2.84567	+	7.71937i	−0.161623	+	0.438431i
$311$	5.91086	−	18.1918i	0.335174	−	1.03156i	−0.631462	−	0.775407i	$-0.717545\pi$
$311$	5.91086	−	18.1918i	0.335174	−	1.03156i	0.966636	−	0.256153i	$-0.0824551\pi$
$312$	−2.12428	+	0.690222i	−0.120264	+	0.0390761i
$313$	−17.6306	−	24.2665i	−0.996542	−	1.37162i	−0.927423	−	0.374014i	$-0.877981\pi$
$313$	−17.6306	−	24.2665i	−0.996542	−	1.37162i	−0.0691190	−	0.997608i	$-0.522019\pi$
$314$	10.9999	−	7.99188i	0.620759	−	0.451008i
$315$	6.82499	−	4.56274i	0.384545	−	0.257081i
$316$	−2.43691	+	7.50004i	−0.137087	+	0.421910i
$317$	3.88012	−	5.34053i	0.217929	−	0.299954i	−0.686029	−	0.727574i	$-0.740648\pi$
$317$	3.88012	−	5.34053i	0.217929	−	0.299954i	0.903959	+	0.427620i	$0.140648\pi$
$318$			1.15061i			0.0645231i
$319$	20.9460	−	22.3352i	1.17275	−	1.25053i
$320$	−2.15197	+	0.607489i	−0.120299	+	0.0339597i
$321$	−15.5486	−	11.2967i	−0.867837	−	0.630520i
$322$	0.127759	+	0.0415113i	0.00711971	+	0.00231333i
$323$	32.0269	−	10.4062i	1.78202	−	0.579015i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	10.3200	+	4.26874i	0.572451	+	0.236787i
$326$	−3.12823	−	9.62771i	−0.173257	−	0.533230i
$327$	1.75742	+	0.571022i	0.0971858	+	0.0315776i
$328$	3.63212	−	4.99918i	0.200550	−	0.276034i
$329$	25.1184			1.38482
$330$	6.63108	−	3.32095i	0.365029	−	0.182812i
$331$	−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
$333$	0.824696	+	0.267960i	0.0451931	+	0.0146841i
$334$	6.54311	+	20.1376i	0.358023	+	1.10188i
$335$	−5.07010	−	3.99492i	−0.277009	−	0.218266i
$336$	−2.97030	+	2.15805i	−0.162043	+	0.117731i
$337$	8.89720	−	2.89088i	0.484661	−	0.157476i	−0.0564867	−	0.998403i	$-0.517990\pi$
$337$	8.89720	−	2.89088i	0.484661	−	0.157476i	0.541148	+	0.840927i	$0.317990\pi$
$338$	7.61892	+	2.47554i	0.414415	+	0.134652i
$339$	−7.25560	−	5.27150i	−0.394070	−	0.286309i
$340$	−2.55813	−	9.06191i	−0.138734	−	0.491451i
$341$	−1.52133	+	12.1077i	−0.0823845	+	0.655667i
$342$			7.99694i			0.432425i
$343$	1.12256	−	1.54507i	0.0606125	−	0.0834260i
$344$	2.96716	−	9.13199i	0.159979	−	0.492364i
$345$	−0.0454700	−	0.0680145i	−0.00244803	−	0.00366178i
$346$	−0.154490	+	0.112243i	−0.00830542	+	0.00603424i
$347$	−11.9401	−	16.4342i	−0.640979	−	0.882232i	0.357688	−	0.933841i	$-0.383565\pi$
$347$	−11.9401	−	16.4342i	−0.640979	−	0.882232i	−0.998667	+	0.0516090i	$0.983565\pi$
$348$	8.78048	−	2.85295i	0.470683	−	0.152934i
$349$	−5.08169	+	15.6398i	−0.272017	+	0.837181i	0.717977	+	0.696067i	$0.245068\pi$
$349$	−5.08169	+	15.6398i	−0.272017	+	0.837181i	−0.989993	+	0.141114i	$0.954932\pi$
$350$	18.3016	+	1.43130i	0.978259	+	0.0765063i
$351$	2.23360			0.119221
$352$	−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	$-0.244763\pi$
$354$	8.72446	+	6.33869i	0.463700	+	0.336898i
$355$	−0.515766	+	13.2100i	−0.0273740	+	0.701113i
$356$	−1.43586	−	4.41912i	−0.0761004	−	0.234213i
$357$	−9.08752	−	12.5079i	−0.480962	−	0.661988i
$358$	2.49758	+	3.43762i	0.132001	+	0.181684i
$359$	−1.86004	−	5.72461i	−0.0981692	−	0.302134i	0.889897	−	0.456161i	$-0.150776\pi$
$359$	−1.86004	−	5.72461i	−0.0981692	−	0.302134i	−0.988067	+	0.154027i	$0.950776\pi$
$360$	2.23437	+	0.0872378i	0.117761	+	0.00459784i
$361$	−36.3662	−	26.4216i	−1.91401	−	1.39061i
$362$		−	22.7989i		−	1.19828i
$363$	8.46626	−	7.02300i	0.444363	−	0.368612i
$364$	−8.20065			−0.429831
$365$	−7.89424	+	21.4145i	−0.413204	+	1.12089i
$366$	0.464080	−	1.42829i	0.0242579	−	0.0746580i
$367$	2.85905	−	0.928961i	0.149241	−	0.0484914i	−0.233444	−	0.972370i	$-0.574999\pi$
$367$	2.85905	−	0.928961i	0.149241	−	0.0484914i	0.382685	+	0.923879i	$0.374999\pi$
$368$	0.0215060	+	0.0296005i	0.00112108	+	0.00154303i
$369$	−4.99918	+	3.63212i	−0.260247	+	0.189081i
$370$	1.07763	+	1.61193i	0.0560235	+	0.0838005i
$371$	−1.30543	+	4.01770i	−0.0677745	+	0.208588i
$372$	−2.16264	+	2.97662i	−0.112128	+	0.154331i
$373$		−	16.1368i		−	0.835532i	−0.908555	−	0.417766i	$-0.862813\pi$
$373$		−	16.1368i		−	0.835532i	0.908555	−	0.417766i	$-0.137187\pi$
$374$	−6.73649	−	12.2342i	−0.348336	−	0.632618i
$375$	−8.21558	−	7.58316i	−0.424250	−	0.391593i
$376$	5.53486	+	4.02131i	0.285439	+	0.207383i
$377$	19.6121	+	6.37236i	1.01008	+	0.328193i
$378$	3.49179	−	1.13455i	0.179598	−	0.0583551i
$379$	20.4244	−	14.8392i	1.04913	−	0.762238i	0.0770842	−	0.997025i	$-0.475439\pi$
$379$	20.4244	−	14.8392i	1.04913	−	0.762238i	0.972047	+	0.234786i	$0.0754390\pi$
$380$	−11.0670	+	14.0455i	−0.567725	+	0.720521i
$381$	2.04289	+	6.28736i	0.104660	+	0.322111i
$382$	−9.87607	−	3.20893i	−0.505304	−	0.164183i
$383$	−20.6742	+	28.4557i	−1.05640	+	1.45402i	−0.173283	+	0.984872i	$0.555438\pi$
$383$	−20.6742	+	28.4557i	−1.05640	+	1.45402i	−0.883122	+	0.469144i	$0.844562\pi$
$384$	−1.00000			−0.0510310
$385$	26.9222	−	4.07276i	1.37208	−	0.207567i
$386$	−6.64983			−0.338467
$387$	−5.64388	+	7.76814i	−0.286895	+	0.394877i
$388$	14.0896	+	4.57800i	0.715293	+	0.232413i
$389$	0.697918	+	2.14797i	0.0353859	+	0.108907i	0.967189	−	0.254057i	$-0.0817650\pi$
$389$	0.697918	+	2.14797i	0.0353859	+	0.108907i	−0.931803	+	0.362963i	$0.881765\pi$
$390$	3.92302	+	3.09109i	0.198650	+	0.156524i
$391$	−0.124648	+	0.0905617i	−0.00630370	+	0.00457990i
$392$	−6.16268	+	2.00238i	−0.311262	+	0.101135i
$393$	−0.0589873	−	0.0191661i	−0.00297552	−	0.000966804i
$394$	−9.34127	−	6.78683i	−0.470606	−	0.341915i
$395$	16.9704	−	4.79066i	0.853875	−	0.241044i
$396$	3.25746	−	0.623653i	0.163694	−	0.0313397i
$397$			18.6869i			0.937868i	0.883233	+	0.468934i	$0.155362\pi$
$397$			18.6869i			0.937868i	−0.883233	+	0.468934i	$0.844638\pi$
$398$	−8.28772	+	11.4071i	−0.415426	+	0.571784i
$399$	−9.07295	+	27.9237i	−0.454216	+	1.39793i
$400$	3.80363	+	3.24537i	0.190181	+	0.162268i
$401$	−12.4245	+	9.02694i	−0.620451	+	0.450784i	−0.853079	−	0.521782i	$-0.825268\pi$
$401$	−12.4245	+	9.02694i	−0.620451	+	0.450784i	0.232628	+	0.972566i	$0.425268\pi$
$402$	−1.69676	−	2.33539i	−0.0846268	−	0.116479i
$403$	−7.81589	+	2.53954i	−0.389337	+	0.126503i
$404$	0.249290	−	0.767236i	0.0124026	−	0.0381714i
$405$	−2.09805	−	0.773425i	−0.104253	−	0.0384318i
$406$	33.8964			1.68225
$407$	2.09781	+	1.96733i	0.103984	+	0.0975170i
$408$		−	4.21099i		−	0.208475i
$409$	−2.59071	−	1.88226i	−0.128103	−	0.0930719i	0.521889	−	0.853013i	$-0.325228\pi$
$409$	−2.59071	−	1.88226i	−0.128103	−	0.0930719i	−0.649991	+	0.759942i	$0.725228\pi$
$410$	−13.8069	−	0.539071i	−0.681873	−	0.0266228i
$411$	−0.288416	−	0.887654i	−0.0142265	−	0.0437848i
$412$	6.68850	+	9.20592i	0.329519	+	0.453543i
$413$	23.2724	+	32.0318i	1.14516	+	1.57618i
$414$	−0.0113064	−	0.0347975i	−0.000555679	−	0.00171020i
$415$	−34.2597	−	1.33762i	−1.68174	−	0.0656614i
$416$	−1.80702	−	1.31288i	−0.0885966	−	0.0643692i
$417$		−	6.35449i		−	0.311181i
$418$	−11.2768	+	24.0062i	−0.551568	+	1.17418i
$419$	−0.122299			−0.00597471			−0.00298736	−	0.999996i	$-0.500951\pi$
$419$	−0.122299			−0.00597471			−0.00298736	+	0.999996i	$0.500951\pi$
$420$	7.70297	+	2.83962i	0.375866	+	0.138559i
$421$	0.661002	−	2.03436i	0.0322153	−	0.0991485i	−0.933656	−	0.358171i	$-0.883400\pi$
$421$	0.661002	−	2.03436i	0.0322153	−	0.0991485i	0.965871	+	0.259023i	$0.0834004\pi$
$422$	−0.255034	+	0.0828655i	−0.0124149	+	0.00403383i
$423$	−4.02131	−	5.53486i	−0.195523	−	0.269114i
$424$	−0.930864	+	0.676313i	−0.0452068	+	0.0328446i
$425$	−13.6662	+	16.0170i	−0.662909	+	0.776941i
$426$	−1.82696	+	5.62282i	−0.0885167	+	0.272426i
$427$	3.24094	−	4.46078i	0.156840	−	0.215872i
$428$		−	19.2191i		−	0.928990i
$429$	6.70509	+	3.14970i	0.323725	+	0.152069i
$430$	−20.6631	+	5.83307i	−0.996461	+	0.281296i
$431$	−24.3875	−	17.7186i	−1.17471	−	0.853474i	−0.183141	−	0.983087i	$-0.558627\pi$
$431$	−24.3875	−	17.7186i	−1.17471	−	0.853474i	−0.991565	+	0.129613i	$0.958627\pi$
$432$	0.951057	+	0.309017i	0.0457577	+	0.0148676i
$433$	−25.2902	+	8.21727i	−1.21537	+	0.394897i	−0.845393	−	0.534145i	$-0.820634\pi$
$433$	−25.2902	+	8.21727i	−1.21537	+	0.394897i	−0.369975	+	0.929042i	$0.620634\pi$
$434$	−10.9286	+	7.94011i	−0.524591	+	0.381138i
$435$	−16.2153	−	12.7767i	−0.777466	−	0.612595i
$436$	0.571022	+	1.75742i	0.0273470	+	0.0841654i
$437$	0.278274	+	0.0904166i	0.0133116	+	0.00432521i
$438$	−5.99944	+	8.25753i	−0.286664	+	0.394560i
$439$	−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
$441$	6.47983			0.308563
$442$	5.52853	−	7.60936i	0.262965	−	0.361941i
$443$	−13.3652	−	4.34263i	−0.635001	−	0.206324i	−0.0262121	−	0.999656i	$-0.508345\pi$
$443$	−13.3652	−	4.34263i	−0.635001	−	0.206324i	−0.608789	+	0.793332i	$0.708345\pi$
$444$	0.267960	+	0.824696i	0.0127168	+	0.0391383i
$445$	−6.43036	+	8.16101i	−0.304829	+	0.386869i
$446$	14.3507	−	10.4264i	0.679527	−	0.493705i
$447$	11.1945	−	3.63732i	0.529483	−	0.172040i
$448$	−3.49179	−	1.13455i	−0.164972	−	0.0536026i
$449$	23.0363	+	16.7369i	1.08715	+	0.789862i	0.978916	−	0.204263i	$-0.0654799\pi$
$449$	23.0363	+	16.7369i	1.08715	+	0.789862i	0.108236	+	0.994125i	$0.465480\pi$
$450$	−2.61459	−	4.26191i	−0.123253	−	0.200909i
$451$	−20.1289	+	3.85376i	−0.947834	+	0.181466i
$452$		−	8.96841i		−	0.421839i
$453$	14.1733	−	19.5079i	0.665922	−	0.916563i
$454$	−5.87528	+	18.0822i	−0.275740	+	0.848642i
$455$	10.1914	+	15.2443i	0.477778	+	0.714665i
$456$	−6.46966	+	4.70049i	−0.302970	+	0.220120i
$457$	17.1007	+	23.5372i	0.799939	+	1.10102i	0.992799	+	0.119795i	$0.0382239\pi$
$457$	17.1007	+	23.5372i	0.799939	+	1.10102i	−0.192859	+	0.981226i	$0.561776\pi$
$458$	21.7310	−	7.06084i	1.01542	−	0.329931i
$459$	−1.30127	+	4.00489i	−0.0607380	+	0.186932i
$460$	0.0282983	−	0.0767640i	0.00131941	−	0.00357914i
$461$	14.5472			0.677533			0.338766	−	0.940871i	$-0.389990\pi$
$461$	14.5472			0.677533			0.338766	+	0.940871i	$0.389990\pi$
$462$	12.0819	+	1.51810i	0.562103	+	0.0706282i
$463$			26.5659i			1.23462i	0.786719	+	0.617311i	$0.211778\pi$
$463$			26.5659i			1.23462i	−0.786719	+	0.617311i	$0.788222\pi$
$464$	7.46912	+	5.42663i	0.346745	+	0.251925i
$465$	8.22091	+	0.320975i	0.381236	+	0.0148848i
$466$	−0.189450	−	0.583066i	−0.00877609	−	0.0270100i
$467$	3.38974	+	4.66558i	0.156858	+	0.215897i	0.880212	−	0.474581i	$-0.157400\pi$
$467$	3.38974	+	4.66558i	0.156858	+	0.215897i	−0.723354	+	0.690478i	$0.757400\pi$
$468$	1.31288	+	1.80702i	0.0606879	+	0.0835297i
$469$	−3.27512	−	10.0798i	−0.151231	−	0.465441i
$470$	0.596835	−	15.2863i	0.0275299	−	0.705106i
$471$	−10.9999	−	7.99188i	−0.506848	−	0.368246i
$472$			10.7840i			0.496375i
$473$	−27.8966	+	15.3606i	−1.28269	+	0.706282i
$474$	7.88601			0.362216
$475$	39.8630	+	3.11755i	1.82904	+	0.143043i
$476$	4.77759	−	14.7039i	0.218980	−	0.673953i
$477$	1.09430	−	0.355559i	0.0501044	−	0.0162799i
$478$	−10.4723	−	14.4138i	−0.478990	−	0.659273i
$479$	9.85916	−	7.16310i	0.450477	−	0.327291i	−0.339307	−	0.940676i	$-0.610193\pi$
$479$	9.85916	−	7.16310i	0.450477	−	0.327291i	0.789784	+	0.613385i	$0.210193\pi$
$480$	1.24275	+	1.85892i	0.0567235	+	0.0848476i
$481$	−0.598516	+	1.84204i	−0.0272900	+	0.0839900i
$482$	−11.8452	+	16.3035i	−0.539533	+	0.742603i
$483$		−	0.134333i		−	0.00611238i
$484$	10.6581	+	2.72133i	0.484457	+	0.123697i
$485$	−8.99978	−	31.8808i	−0.408659	−	1.44763i
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	−5.66556	−	1.84085i	−0.256731	−	0.0834170i	0.177824	−	0.984062i	$-0.443094\pi$
$487$	−5.66556	−	1.84085i	−0.256731	−	0.0834170i	−0.434555	+	0.900645i	$0.643094\pi$
$488$	1.42829	−	0.464080i	0.0646557	−	0.0210079i
$489$	−8.18982	+	5.95025i	−0.370356	+	0.269080i
$490$	11.3809	+	8.96746i	0.514138	+	0.405108i
$491$	8.86786	+	27.2925i	0.400201	+	1.23169i	0.924836	+	0.380365i	$0.124202\pi$
$491$	8.86786	+	27.2925i	0.400201	+	1.23169i	−0.524635	+	0.851327i	$0.675798\pi$
$492$	−5.87689	−	1.90952i	−0.264951	−	0.0860877i
$493$	−22.8515	+	31.4524i	−1.02918	+	1.41654i
$494$	−17.8620			−0.803650
$495$	−5.20753	−	5.28031i	−0.234061	−	0.237332i
$496$	−3.67931			−0.165206
$497$	−12.7588	+	17.5609i	−0.572309	+	0.787715i
$498$	−14.5826	−	4.73818i	−0.653463	−	0.212323i
$499$	3.05089	+	9.38968i	0.136577	+	0.420340i	0.995832	−	0.0912073i	$-0.0290726\pi$
$499$	3.05089	+	9.38968i	0.136577	+	0.420340i	−0.859255	+	0.511547i	$0.829073\pi$
$500$	1.30591	−	11.1038i	0.0584021	−	0.496577i
$501$	17.1301	−	12.4457i	0.765315	−	0.556034i
$502$	3.88733	−	1.26307i	0.173500	−	0.0563736i
$503$	20.5152	+	6.66581i	0.914730	+	0.297214i	0.728303	−	0.685255i	$-0.240309\pi$
$503$	20.5152	+	6.66581i	0.914730	+	0.297214i	0.186427	+	0.982469i	$0.440309\pi$
$504$	2.97030	+	2.15805i	0.132308	+	0.0961270i
$505$	−1.73603	+	0.490073i	−0.0772525	+	0.0218080i
$506$	0.0151286	−	0.120403i	0.000672548	−	0.00535255i
$507$		−	8.01101i		−	0.355781i
$508$	−3.88580	+	5.34835i	−0.172405	+	0.237294i
$509$	−6.13785	+	18.8904i	−0.272056	+	0.837301i	0.717928	+	0.696118i	$0.245091\pi$
$509$	−6.13785	+	18.8904i	−0.272056	+	0.837301i	−0.989983	+	0.141183i	$0.954909\pi$
$510$	−7.82788	+	5.23321i	−0.346625	+	0.231730i
$511$	−30.3174	+	22.0269i	−1.34116	+	0.974412i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	7.60555	−	2.47119i	0.335793	−	0.109106i
$514$	−0.624042	+	1.92060i	−0.0275253	+	0.0847142i
$515$	8.80092	−	23.8740i	0.387815	−	1.05202i
$516$	−9.60194			−0.422702
$517$	−4.26670	−	22.2858i	−0.187649	−	0.980129i
$518$			3.18368i			0.139883i
$519$	0.154490	+	0.112243i	0.00678135	+	0.00492694i
$520$	−0.194855	+	4.99069i	−0.00854495	+	0.218856i
$521$	3.34006	+	10.2796i	0.146331	+	0.450359i	0.997180	−	0.0750508i	$-0.0239119\pi$
$521$	3.34006	+	10.2796i	0.146331	+	0.450359i	−0.850849	+	0.525410i	$0.823912\pi$
$522$	−5.42663	−	7.46912i	−0.237517	−	0.326914i
$523$	11.3088	+	15.5652i	0.494499	+	0.680620i	0.981210	−	0.192944i	$-0.0618034\pi$
$523$	11.3088	+	15.5652i	0.494499	+	0.680620i	−0.486711	+	0.873563i	$0.661803\pi$
$524$	−0.0191661	−	0.0589873i	−0.000837277	−	0.00257687i
$525$	−4.29424	−	17.8481i	−0.187416	−	0.778955i
$526$	9.87976	+	7.17807i	0.430778	+	0.312979i
$527$		−	15.4935i		−	0.674909i
$528$	2.41923	+	2.26877i	0.105284	+	0.0987355i
$529$	22.9987			0.999942
$530$	2.41404	+	0.889912i	0.104859	+	0.0386553i
$531$	3.33245	−	10.2562i	0.144616	−	0.445082i
$532$	−27.9237	+	9.07295i	−1.21064	+	0.393362i
$533$	−8.11272	−	11.1662i	−0.351401	−	0.483662i
$534$	−3.75913	+	2.73117i	−0.162673	+	0.118189i
$535$	−35.7267	+	23.8845i	−1.54460	+	1.03262i
$536$	0.892041	−	2.74542i	0.0385303	−	0.118584i
$537$	2.49758	−	3.43762i	0.107778	−	0.148344i
$538$			9.21959i			0.397485i
$539$	19.4519	+	9.13748i	0.837852	+	0.393579i
$540$	−0.607489	−	2.15197i	−0.0261422	−	0.0926059i
$541$	−6.18481	−	4.49353i	−0.265906	−	0.193192i	0.446841	−	0.894614i	$-0.352549\pi$
$541$	−6.18481	−	4.49353i	−0.265906	−	0.193192i	−0.712747	+	0.701422i	$0.752549\pi$
$542$	−12.1190	−	3.93769i	−0.520554	−	0.169138i
$543$	−21.6831	+	7.04525i	−0.930509	+	0.302341i
$544$	3.40676	−	2.47516i	0.146064	−	0.106122i
$545$	2.55727	−	3.24552i	0.109541	−	0.139023i
$546$	2.53414	+	7.79928i	0.108451	+	0.333779i
$547$	15.8930	+	5.16394i	0.679534	+	0.220794i	0.628391	−	0.777897i	$-0.283714\pi$
$547$	15.8930	+	5.16394i	0.679534	+	0.220794i	0.0511426	+	0.998691i	$0.483714\pi$
$548$	0.548600	−	0.755084i	0.0234351	−	0.0322556i
$549$	−1.50179			−0.0640950
$550$	−1.83887	−	16.4809i	−0.0784098	−	0.702746i
$551$	73.8305			3.14529
$552$	0.0215060	−	0.0296005i	0.000915357	−	0.00125988i
$553$	27.5363	+	8.94709i	1.17096	+	0.380469i
$554$	4.10852	+	12.6447i	0.174554	+	0.537223i
$555$	1.20003	−	1.52301i	0.0509386	−	0.0646480i
$556$	5.14089	−	3.73507i	0.218022	−	0.158402i
$557$	−6.20631	+	2.01655i	−0.262970	+	0.0854441i	−0.437534	−	0.899202i	$-0.644148\pi$
$557$	−6.20631	+	2.01655i	−0.262970	+	0.0854441i	0.174565	+	0.984646i	$0.444148\pi$
$558$	3.49923	+	1.13697i	0.148134	+	0.0481317i
$559$	−17.3509	−	12.6062i	−0.733867	−	0.533185i
$560$	2.23039	+	7.90092i	0.0942511	+	0.333875i
$561$	−9.55376	+	10.1874i	−0.403360	+	0.430111i
$562$			1.56837i			0.0661575i
$563$	11.4827	−	15.8046i	0.483940	−	0.666086i	−0.495316	−	0.868713i	$-0.664948\pi$
$563$	11.4827	−	15.8046i	0.483940	−	0.666086i	0.979256	+	0.202627i	$0.0649478\pi$
$564$	2.11413	−	6.50662i	0.0890209	−	0.273978i
$565$	−16.6715	+	11.1455i	−0.701377	+	0.468895i
$566$	−8.74810	+	6.35586i	−0.367710	+	0.267157i
$567$	−2.15805	−	2.97030i	−0.0906294	−	0.124741i
$568$	−5.62282	+	1.82696i	−0.235928	+	0.0766577i
$569$	3.39217	−	10.4400i	0.142207	−	0.437669i	−0.854434	−	0.519560i	$-0.826096\pi$
$569$	3.39217	−	10.4400i	0.142207	−	0.437669i	0.996641	+	0.0818909i	$0.0260959\pi$
$570$	16.7780	+	6.18504i	0.702753	+	0.259063i
$571$	−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
$573$			10.3843i			0.433811i
$574$	−18.3544	−	13.3353i	−0.766100	−	0.556604i
$575$	−0.177865	+	0.0427943i	−0.00741750	+	0.00178465i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	14.2539	+	19.6188i	0.593398	+	0.816742i	0.995084	−	0.0990355i	$-0.0315757\pi$
$577$	14.2539	+	19.6188i	0.593398	+	0.816742i	−0.401686	+	0.915777i	$0.631576\pi$
$578$	0.430524	+	0.592566i	0.0179075	+	0.0246475i
$579$	2.05491	+	6.32436i	0.0853991	+	0.262832i
$580$	0.805409	−	20.6284i	0.0334428	−	0.856549i
$581$	−45.5438	−	33.0895i	−1.88947	−	1.37278i
$582$		−	14.8147i		−	0.614090i
$583$	3.78637	+	0.475757i	0.156816	+	0.0197039i
$584$	−10.2069			−0.422363
$585$	1.72753	−	4.68621i	0.0714244	−	0.193751i
$586$	−6.88897	+	21.2021i	−0.284581	+	0.875849i
$587$	27.6188	−	8.97388i	1.13995	−	0.370392i	0.322600	−	0.946535i	$-0.395443\pi$
$587$	27.6188	−	8.97388i	1.13995	−	0.370392i	0.817348	+	0.576144i	$0.195443\pi$
$588$	3.80875	+	5.24229i	0.157070	+	0.216188i
$589$	−23.8039	+	17.2945i	−0.980821	+	0.712608i
$590$	20.0466	−	13.4019i	0.825306	−	0.551746i
$591$	−3.56805	+	10.9813i	−0.146770	+	0.451711i
$592$	−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	$-0.290937\pi$
$594$	−1.59974	−	2.90531i	−0.0656381	−	0.119206i
$595$	−33.2707	+	9.39215i	−1.36397	+	0.385040i
$596$	9.52264	+	6.91860i	0.390062	+	0.283397i
$597$	13.4098	+	4.35711i	0.548827	+	0.178325i
$598$	0.0777238	−	0.0252540i	0.00317836	−	0.00103271i
$599$	−35.4633	+	25.7656i	−1.44899	+	1.05275i	−0.462925	+	0.886398i	$0.653200\pi$
$599$	−35.4633	+	25.7656i	−1.44899	+	1.05275i	−0.986066	+	0.166356i	$0.946800\pi$
$600$	1.91114	−	4.62034i	0.0780221	−	0.188625i
$601$	11.9756	+	36.8572i	0.488497	+	1.50344i	0.826852	+	0.562420i	$0.190130\pi$
$601$	11.9756	+	36.8572i	0.488497	+	1.50344i	−0.338355	+	0.941019i	$0.609870\pi$
$602$	−33.5280	−	10.8939i	−1.36650	−	0.444003i
$603$	−1.69676	+	2.33539i	−0.0690975	+	0.0951045i
$604$	24.1131			0.981150
$605$	−8.18658	−	23.1944i	−0.332832	−	0.942986i
$606$	−0.806720			−0.0327707
$607$	14.8661	−	20.4614i	0.603396	−	0.830503i	−0.392618	−	0.919702i	$-0.628430\pi$
$607$	14.8661	−	20.4614i	0.603396	−	0.830503i	0.996014	+	0.0891983i	$0.0284305\pi$
$608$	−7.60555	−	2.47119i	−0.308446	−	0.100220i
$609$	−10.4746	−	32.2374i	−0.424451	−	1.30633i
$610$	−2.63770	−	2.07834i	−0.106797	−	0.0841495i
$611$	12.3627	−	8.98203i	0.500141	−	0.363374i
$612$	−4.00489	+	1.30127i	−0.161888	+	0.0526006i
$613$	26.0537	+	8.46535i	1.05230	+	0.341912i	0.783570	−	0.621304i	$-0.213397\pi$
$613$	26.0537	+	8.46535i	1.05230	+	0.341912i	0.268728	+	0.963216i	$0.413397\pi$
$614$	5.75312	+	4.17988i	0.232177	+	0.168686i
$615$	3.75387	+	13.2977i	0.151371	+	0.536215i
$616$	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	$0.898337\pi$
$618$	6.68850	−	9.20592i	0.269051	−	0.370317i
$619$	6.43523	−	19.8056i	0.258654	−	0.796054i	−0.734434	−	0.678680i	$-0.762552\pi$
$619$	6.43523	−	19.8056i	0.258654	−	0.796054i	0.993088	−	0.117374i	$-0.0374476\pi$
$620$	4.57246	+	6.83952i	0.183634	+	0.274682i
$621$	−0.0296005	+	0.0215060i	−0.00118783	+	0.000863007i
$622$	−11.2431	−	15.4748i	−0.450808	−	0.620484i
$623$	−16.2248	+	5.27174i	−0.650031	+	0.211208i
$624$	−0.690222	+	2.12428i	−0.0276310	+	0.0850394i
$625$	−22.2640	+	11.3717i	−0.890559	+	0.454867i
$626$	−29.9950			−1.19884
$627$	26.3159	+	3.30659i	1.05096	+	0.132053i
$628$		−	13.5966i		−	0.542563i
$629$	−2.95413	−	2.14630i	−0.117789	−	0.0855786i
$630$	0.320293	−	8.20345i	0.0127608	−	0.326833i
$631$	6.58817	+	20.2763i	0.262271	+	0.807187i	0.992310	+	0.123781i	$0.0395020\pi$
$631$	6.58817	+	20.2763i	0.262271	+	0.807187i	−0.730039	+	0.683406i	$0.760498\pi$
$632$	4.63528	+	6.37992i	0.184382	+	0.253779i
$633$	0.157620	+	0.216945i	0.00626482	+	0.00862278i
$634$	−2.03990	−	6.27817i	−0.0810148	−	0.249338i
$635$	14.7712	+	0.576722i	0.586178	+	0.0228865i
$636$	0.930864	+	0.676313i	0.0369112	+	0.0268175i
$637$			14.4734i			0.573456i
$638$	−5.75777	−	30.0740i	−0.227952	−	1.19064i
$639$	5.91218			0.233882
$640$	−0.773425	+	2.09805i	−0.0305723	+	0.0829327i
$641$	−1.35758	+	4.17819i	−0.0536211	+	0.165029i	−0.974281	−	0.225337i	$-0.927652\pi$
$641$	−1.35758	+	4.17819i	−0.0536211	+	0.165029i	0.920660	+	0.390366i	$0.127652\pi$
$642$	−18.2784	+	5.93903i	−0.721393	+	0.234395i
$643$	−10.9094	−	15.0155i	−0.430226	−	0.592155i	0.537779	−	0.843086i	$-0.319263\pi$
$643$	−10.9094	−	15.0155i	−0.430226	−	0.592155i	−0.968005	+	0.250931i	$0.919263\pi$
$644$	0.108678	−	0.0789591i	0.00428251	−	0.00311143i
$645$	11.9328	+	17.8492i	0.469854	+	0.702812i
$646$	10.4062	−	32.0269i	0.409425	−	1.26008i
$647$	22.4440	−	30.8915i	0.882364	−	1.21447i	−0.0933967	−	0.995629i	$-0.529772\pi$
$647$	22.4440	−	30.8915i	0.882364	−	1.21447i	0.975761	−	0.218841i	$-0.0702275\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	24.4665	−	26.0891i	0.960393	−	1.02409i
$650$	9.51943	−	5.83996i	0.373383	−	0.229062i
$651$	10.9286	+	7.94011i	0.428327	+	0.311198i
$652$	−9.62771	−	3.12823i	−0.377050	−	0.122511i
$653$	8.58380	−	2.78905i	0.335910	−	0.109144i	−0.136205	−	0.990681i	$-0.543491\pi$
$653$	8.58380	−	2.78905i	0.335910	−	0.109144i	0.472115	+	0.881537i	$0.343491\pi$
$654$	1.49495	−	1.08615i	0.0584574	−	0.0424718i
$655$	−0.0858338	+	0.108935i	−0.00335380	+	0.00425643i
$656$	−1.90952	−	5.87689i	−0.0745542	−	0.229454i
$657$	9.70730	+	3.15409i	0.378718	+	0.123053i
$658$	14.7642	−	20.3212i	0.575569	−	0.792202i
$659$	3.25065			0.126627			0.0633137	−	0.997994i	$-0.479833\pi$
$659$	3.25065			0.126627			0.0633137	+	0.997994i	$0.479833\pi$
$660$	1.21095	−	7.31667i	0.0471361	−	0.284801i
$661$	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
$663$	−8.94534	−	2.90652i	−0.347408	−	0.112880i
$664$	−4.73818	−	14.5826i	−0.183877	−	0.565915i
$665$	51.5680	+	40.6324i	1.99972	+	1.57566i
$666$	0.701528	−	0.509690i	0.0271837	−	0.0197501i
$667$	−0.321262	+	0.104384i	−0.0124393	+	0.00404178i
$668$	20.1376	+	6.54311i	0.779148	+	0.253160i
$669$	−14.3507	−	10.4264i	−0.554832	−	0.403109i
$670$	−6.21209	+	1.75364i	−0.239994	+	0.0677490i
$671$	−4.50826	−	2.11774i	−0.174040	−	0.0817546i
$672$			3.67149i			0.141631i
$673$	−0.454434	+	0.625475i	−0.0175171	+	0.0241103i	−0.817686	−	0.575665i	$-0.804743\pi$
$673$	−0.454434	+	0.625475i	−0.0175171	+	0.0241103i	0.800169	+	0.599775i	$0.204743\pi$
$674$	2.89088	−	8.89720i	0.111352	−	0.342707i
$675$	−3.24537	+	3.80363i	−0.124914	+	0.146402i
$676$	6.48104	−	4.70875i	0.249271	−	0.181106i
$677$	21.8005	+	30.0058i	0.837861	+	1.15322i	0.986409	+	0.164311i	$0.0525401\pi$
$677$	21.8005	+	30.0058i	0.837861	+	1.15322i	−0.148548	+	0.988905i	$0.547460\pi$
$678$	−8.52947	+	2.77139i	−0.327572	+	0.106435i
$679$	16.8081	−	51.7300i	0.645035	−	1.98521i
$680$	−8.83487	−	3.25689i	−0.338802	−	0.124896i
$681$	19.0128			0.728572
$682$	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	$-0.143258\pi$
$684$	6.46966	+	4.70049i	0.247374	+	0.179728i
$685$	−2.08541	−	0.0814221i	−0.0796795	−	0.00311098i
$686$	−0.590165	−	1.81634i	−0.0225326	−	0.0693482i
$687$	−13.4305	−	18.4855i	−0.512406	−	0.705266i
$688$	−5.64388	−	7.76814i	−0.215171	−	0.296157i
$689$	0.794177	+	2.44423i	0.0302557	+	0.0931176i
$690$	−0.0817515	−	0.00319188i	−0.00311223	−	0.000121513i
$691$	1.36479	+	0.991577i	0.0519190	+	0.0377214i	0.613442	−	0.789740i	$-0.289784\pi$
$691$	1.36479	+	0.991577i	0.0519190	+	0.0377214i	−0.561523	+	0.827461i	$0.689784\pi$
$692$			0.190960i			0.00725921i
$693$	−2.28973	−	11.9597i	−0.0869798	−	0.454313i
$694$	−20.3137			−0.771099
$695$	−13.3320	−	4.91472i	−0.505713	−	0.186426i
$696$	2.85295	−	8.78048i	0.108141	−	0.332823i
$697$	24.7475	−	8.04097i	0.937380	−	0.304573i
$698$	9.66595	+	13.3040i	0.365862	+	0.503565i
$699$	−0.495986	+	0.360355i	−0.0187599	+	0.0136299i
$700$	11.9153	−	13.9650i	0.450357	−	0.527826i
$701$	−12.4806	+	38.4112i	−0.471384	+	1.45077i	0.379388	+	0.925238i	$0.376134\pi$
$701$	−12.4806	+	38.4112i	−0.471384	+	1.45077i	−0.850773	+	0.525534i	$0.823866\pi$
$702$	1.31288	−	1.80702i	0.0495515	−	0.0682017i
$703$			6.93444i			0.261537i
$704$	−0.413482	+	3.29075i	−0.0155837	+	0.124025i
$705$	−14.7226	+	4.15612i	−0.554485	+	0.156528i
$706$	−21.1396	−	15.3588i	−0.795599	−	0.578036i
$707$	−2.81690	−	0.915266i	−0.105940	−	0.0344221i
$708$	10.2562	−	3.33245i	0.385452	−	0.125241i
$709$	−9.28629	+	6.74688i	−0.348754	+	0.253384i	−0.748346	−	0.663309i	$-0.769152\pi$
$709$	−9.28629	+	6.74688i	−0.348754	+	0.253384i	0.399592	+	0.916693i	$0.369152\pi$
$710$	10.3839	+	8.18189i	0.389702	+	0.307061i
$711$	−2.43691	−	7.50004i	−0.0913913	−	0.281274i
$712$	−4.41912	−	1.43586i	−0.165614	−	0.0538111i
$713$	0.0791273	−	0.108909i	0.00296334	−	0.00407869i
$714$	−15.4606			−0.578599
$715$	11.7941	−	11.6316i	0.441075	−	0.434996i
$716$	4.24913			0.158797
$717$	−10.4723	+	14.4138i	−0.391093	+	0.538294i
$718$	−5.72461	−	1.86004i	−0.213641	−	0.0694161i
$719$	13.7386	+	42.2830i	0.512363	+	1.57689i	0.788030	+	0.615637i	$0.211101\pi$
$719$	13.7386	+	42.2830i	0.512363	+	1.57689i	−0.275667	+	0.961253i	$0.588899\pi$
$720$	1.38390	−	1.75636i	0.0515751	−	0.0654558i
$721$	33.7994	−	24.5567i	1.25876	−	0.914541i
$722$	−42.7511	+	13.8907i	−1.59103	+	0.516957i
$723$	19.1659	+	6.22738i	0.712787	+	0.231599i
$724$	−18.4447	−	13.4009i	−0.685492	−	0.498039i
$725$	−39.3474	+	24.1388i	−1.46133	+	0.896492i
$726$	−0.705382	−	10.9774i	−0.0261792	−	0.407408i
$727$			24.5763i			0.911484i	0.890112	+	0.455742i	$0.150626\pi$
$727$			24.5763i			0.911484i	−0.890112	+	0.455742i	$0.849374\pi$
$728$	−4.82022	+	6.63447i	−0.178649	+	0.245890i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	12.6846	+	18.9737i	0.469477	+	0.702248i
$731$	32.7116	−	23.7663i	1.20988	−	0.879030i
$732$	−0.882733	−	1.21498i	−0.0326267	−	0.0449069i
$733$	24.2238	−	7.87080i	0.894728	−	0.290715i	0.174668	−	0.984627i	$-0.444115\pi$
$733$	24.2238	−	7.87080i	0.894728	−	0.290715i	0.720059	+	0.693913i	$0.244115\pi$
$734$	0.928961	−	2.85905i	0.0342886	−	0.105529i
$735$	5.01166	−	13.5950i	0.184858	−	0.501459i
$736$	0.0365882			0.00134866
$737$	−8.38677	+	4.61798i	−0.308931	+	0.170105i
$738$			6.17933i			0.227464i
$739$	24.0114	+	17.4453i	0.883273	+	0.641735i	0.934115	−	0.356972i	$-0.116191\pi$
$739$	24.0114	+	17.4453i	0.883273	+	0.641735i	−0.0508427	+	0.998707i	$0.516191\pi$
$740$	1.93750	+	0.0756471i	0.0712239	+	0.00278084i
$741$	5.51967	+	16.9878i	0.202770	+	0.624062i
$742$	2.48307	+	3.41766i	0.0911565	+	0.125466i
$743$	−23.2228	−	31.9634i	−0.851962	−	1.17262i	−0.983427	−	0.181304i	$-0.941968\pi$
$743$	−23.2228	−	31.9634i	−0.851962	−	1.17262i	0.131465	−	0.991321i	$-0.458032\pi$
$744$	1.13697	+	3.49923i	0.0416833	+	0.128288i
$745$	1.02684	−	26.2999i	0.0376207	−	0.963553i
$746$	−13.0549	−	9.48497i	−0.477975	−	0.347269i
$747$			15.3331i			0.561008i
$748$	−13.8573	−	1.74117i	−0.506674	−	0.0636635i
$749$	−70.5627			−2.57830
$750$	−10.9639	+	2.18927i	−0.400345	+	0.0799408i
$751$	16.4756	−	50.7066i	0.601202	−	1.85031i	0.0801523	−	0.996783i	$-0.474459\pi$
$751$	16.4756	−	50.7066i	0.601202	−	1.85031i	0.521050	−	0.853526i	$-0.325541\pi$
$752$	6.50662	−	2.11413i	0.237272	−	0.0770944i
$753$	−2.40250	−	3.30676i	−0.0875521	−	0.120505i
$754$	16.6831	−	12.1210i	0.607561	−	0.441419i
$755$	−29.9666	−	44.8243i	−1.09060	−	1.63132i
$756$	1.13455	−	3.49179i	0.0412633	−	0.126995i
$757$	−3.98396	+	5.48346i	−0.144800	+	0.199300i	−0.875256	−	0.483660i	$-0.839307\pi$
$757$	−3.98396	+	5.48346i	−0.144800	+	0.199300i	0.730457	+	0.682959i	$0.239307\pi$
$758$		−	25.2460i		−	0.916974i
$759$	−0.119185	+	0.0228184i	−0.00432613	+	0.000828254i
$760$	4.85805	+	17.2092i	0.176220	+	0.624242i
$761$	19.8050	+	14.3891i	0.717929	+	0.521606i	0.885722	−	0.464216i	$-0.153664\pi$
$761$	19.8050	+	14.3891i	0.717929	+	0.521606i	−0.167793	+	0.985822i	$0.553664\pi$
$762$	6.28736	+	2.04289i	0.227767	+	0.0740060i
$763$	6.45237	−	2.09650i	0.233591	−	0.0758984i
$764$	−8.40109	+	6.10375i	−0.303941	+	0.220826i
$765$	7.39603	+	5.82761i	0.267404	+	0.210698i
$766$	10.8691	+	33.4516i	0.392716	+	1.20866i
$767$	22.9083	+	7.44337i	0.827172	+	0.268765i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	−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
$771$	2.01944			0.0727284
$772$	−3.90867	+	5.37982i	−0.140676	+	0.193624i
$773$	−39.9082	−	12.9670i	−1.43540	−	0.466389i	−0.514938	−	0.857227i	$-0.672185\pi$
$773$	−39.9082	−	12.9670i	−1.43540	−	0.466389i	−0.920459	+	0.390838i	$0.872185\pi$
$774$	2.96716	+	9.13199i	0.106653	+	0.328243i
$775$	7.03168	−	16.9996i	0.252585	−	0.610645i
$776$	11.9854	−	8.70788i	0.430250	−	0.312595i
$777$	3.02786	−	0.983812i	0.108624	−	0.0352940i
$778$	2.14797	+	0.697918i	0.0770085	+	0.0250216i
$779$	−39.9782	−	29.0459i	−1.43237	−	1.04068i
$780$	4.80664	−	1.35689i	0.172105	−	0.0485844i
$781$	17.7479	+	8.33702i	0.635069	+	0.298322i
$782$			0.154073i			0.00550963i
$783$	−5.42663	+	7.46912i	−0.193932	+	0.266925i
$784$	−2.00238	+	6.16268i	−0.0715134	+	0.220096i
$785$	−25.2749	+	16.8972i	−0.902102	+	0.603086i
$786$	−0.0501776	+	0.0364562i	−0.00178978	+	0.00130035i
$787$	−13.2891	−	18.2909i	−0.473706	−	0.652001i	0.503574	−	0.863952i	$-0.332018\pi$
$787$	−13.2891	−	18.2909i	−0.473706	−	0.652001i	−0.977280	+	0.211951i	$0.932018\pi$
$788$	−10.9813	+	3.56805i	−0.391193	+	0.127106i
$789$	3.77373	−	11.6144i	0.134348	−	0.413482i
$790$	6.09924	−	16.5452i	0.217001	−	0.588653i
$791$	−32.9274			−1.17076
$792$	1.41014	−	3.00192i	0.0501072	−	0.106668i
$793$		−	3.35442i		−	0.119119i
$794$	15.1180	+	10.9839i	0.536518	+	0.389803i
$795$	0.100377	−	2.57089i	0.00356000	−	0.0911800i
$796$	4.35711	+	13.4098i	0.154434	+	0.475298i
$797$	−3.69554	−	5.08647i	−0.130903	−	0.180172i	0.738534	−	0.674216i	$-0.235518\pi$
$797$	−3.69554	−	5.08647i	−0.130903	−	0.180172i	−0.869437	+	0.494044i	$0.835518\pi$
$798$	17.2578	+	23.7533i	0.610919	+	0.840858i
$799$	8.90258	+	27.3993i	0.314951	+	0.969319i
$800$	4.86127	−	1.16962i	0.171872	−	0.0413523i
$801$	3.75913	+	2.73117i	0.132822	+	0.0965011i
$802$			15.3576i			0.542294i
$803$	24.6928	+	23.1570i	0.871389	+	0.817193i
$804$	−2.88670			−0.101806
$805$	−0.281838	−	0.103897i	−0.00993348	−	0.00366188i
$806$	−2.53954	+	7.81589i	−0.0894514	+	0.275303i
$807$	8.76835	−	2.84901i	0.308661	−	0.100290i
$808$	−0.474178	−	0.652650i	−0.0166815	−	0.0229601i
$809$	21.4826	−	15.6081i	0.755290	−	0.548750i	−0.142172	−	0.989842i	$-0.545409\pi$
$809$	21.4826	−	15.6081i	0.755290	−	0.548750i	0.897462	+	0.441092i	$0.145409\pi$
$810$	−1.85892	+	1.24275i	−0.0653157	+	0.0436658i
$811$	−8.04230	+	24.7517i	−0.282403	+	0.869148i	0.704761	+	0.709444i	$0.251054\pi$
$811$	−8.04230	+	24.7517i	−0.282403	+	0.869148i	−0.987165	+	0.159704i	$0.948946\pi$
$812$	19.9238	−	27.4228i	0.699189	−	0.962351i
$813$			12.7426i			0.446904i
$814$	2.82466	−	0.540792i	0.0990044	−	0.0189547i
$815$	6.14971	+	21.7847i	0.215415	+	0.763086i
$816$	−3.40676	−	2.47516i	−0.119261	−	0.0866479i
$817$	−73.0280	−	23.7282i	−2.55493	−	0.830146i
$818$	−3.04557	+	0.989564i	−0.106486	+	0.0345993i
$819$	6.63447	−	4.82022i	0.231827	−	0.168432i
$820$	−8.55160	+	10.8531i	−0.298635	+	0.379008i
$821$	−0.0728207	−	0.224119i	−0.00254146	−	0.00782181i	0.949778	−	0.312925i	$-0.101309\pi$
$821$	−0.0728207	−	0.224119i	−0.00254146	−	0.00782181i	−0.952319	+	0.305103i	$0.901309\pi$
$822$	−0.887654	−	0.288416i	−0.0309605	−	0.0100597i
$823$	22.3456	−	30.7561i	0.778919	−	1.07209i	−0.216481	−	0.976287i	$-0.569458\pi$
$823$	22.3456	−	30.7561i	0.778919	−	1.07209i	0.995400	−	0.0958037i	$-0.0305421\pi$
$824$	11.3791			0.396411
$825$	−15.1060	+	6.84174i	−0.525923	+	0.238199i
$826$	39.5934			1.37763
$827$	−12.7394	+	17.5343i	−0.442992	+	0.609726i	−0.970874	−	0.239592i	$-0.922986\pi$
$827$	−12.7394	+	17.5343i	−0.442992	+	0.609726i	0.527882	+	0.849318i	$0.322986\pi$
$828$	−0.0347975	−	0.0113064i	−0.00120930	−	0.000392924i
$829$	−5.68287	−	17.4901i	−0.197374	−	0.607455i	−0.999941	−	0.0108924i	$-0.996533\pi$
$829$	−5.68287	−	17.4901i	−0.197374	−	0.607455i	0.802567	−	0.596563i	$-0.203467\pi$
$830$	−21.2195	+	26.9304i	−0.736540	+	0.934769i
$831$	10.7563	−	7.81487i	0.373130	−	0.271095i
$832$	−2.12428	+	0.690222i	−0.0736463	+	0.0239291i
$833$	−25.9510	−	8.43199i	−0.899149	−	0.292151i
$834$	−5.14089	−	3.73507i	−0.178014	−	0.129335i
$835$	−12.8629	−	45.5656i	−0.445140	−	1.57686i
$836$	12.7930	+	23.2336i	0.442456	+	0.803551i
$837$		−	3.67931i		−	0.127175i
$838$	−0.0718858	+	0.0989423i	−0.00248325	+	0.00341790i
$839$	4.43832	−	13.6598i	0.153228	−	0.471587i	−0.844749	−	0.535163i	$-0.820250\pi$
$839$	4.43832	−	13.6598i	0.153228	−	0.471587i	0.997977	+	0.0635754i	$0.0202503\pi$
$840$	6.82499	−	4.56274i	0.235485	−	0.157430i
$841$	−45.4960	+	33.0548i	−1.56883	+	1.13982i
$842$	−1.25730	−	1.73053i	−0.0433295	−	0.0596379i
$843$	1.49160	−	0.484651i	0.0513736	−	0.0166923i
$844$	−0.0828655	+	0.255034i	−0.00285235	+	0.00877863i
$845$	−16.8075	−	6.19592i	−0.578196	−	0.213146i
$846$	−6.84147			−0.235215
$847$	9.99134	−	39.1310i	0.343307	−	1.34456i
$848$			1.15061i			0.0395122i
$849$	8.74810	+	6.35586i	0.300234	+	0.218133i
$850$	4.92526	+	20.4708i	0.168935	+	0.702142i
$851$	−0.00980418	−	0.0301742i	−0.000336083	−	0.00103436i
$852$	3.47509	+	4.78306i	0.119055	+	0.163865i
$853$	−22.3924	−	30.8205i	−0.766702	−	1.05528i	−0.996627	−	0.0820669i	$-0.973848\pi$
$853$	−22.3924	−	30.8205i	−0.766702	−	1.05528i	0.229924	−	0.973208i	$-0.426152\pi$
$854$	−1.70386	−	5.24396i	−0.0583051	−	0.179445i
$855$	0.697636	−	17.8681i	0.0238587	−	0.611076i
$856$	−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	$0.939731\pi$
$858$	6.48932	−	3.57319i	0.221542	−	0.121987i
$859$	−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
$861$	−7.01077	+	21.5769i	−0.238927	+	0.735340i
$862$	−28.6693	+	9.31521i	−0.976479	+	0.317277i
$863$	3.99242	+	5.49509i	0.135904	+	0.187055i	0.871544	−	0.490317i	$-0.163119\pi$
$863$	3.99242	+	5.49509i	0.135904	+	0.187055i	−0.735641	+	0.677372i	$0.763119\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	0.354979	−	0.237315i	0.0120696	−	0.00806897i
$866$	−8.21727	+	25.2902i	−0.279234	+	0.859395i
$867$	0.430524	−	0.592566i	0.0146214	−	0.0201246i
$868$			13.5085i			0.458509i
$869$	3.26073	−	25.9509i	0.110613	−	0.880324i
$870$	−19.8677	+	5.60854i	−0.673577	+	0.190147i
$871$	−5.21634	−	3.78990i	−0.176749	−	0.128416i
$872$	1.75742	+	0.571022i	0.0595139	+	0.0193372i
$873$	−14.0896	+	4.57800i	−0.476862	+	0.154942i
$874$	0.236714	−	0.171983i	0.00800696	−	0.00581740i
$875$	−40.7675	−	4.79464i	−1.37819	−	0.162088i
$876$	3.15409	+	9.70730i	0.106567	+	0.327979i
$877$	14.7567	+	4.79474i	0.498298	+	0.161907i	0.547374	−	0.836888i	$-0.315628\pi$
$877$	14.7567	+	4.79474i	0.498298	+	0.161907i	−0.0490757	+	0.998795i	$0.515628\pi$
$878$	−5.64321	+	7.76721i	−0.190449	+	0.262131i
$879$	22.2932			0.751930
$880$	6.63108	−	3.32095i	0.223534	−	0.111949i
$881$	39.0509			1.31566			0.657829	−	0.753167i	$-0.271475\pi$
$881$	39.0509			1.31566			0.657829	+	0.753167i	$0.271475\pi$
$882$	3.80875	−	5.24229i	0.128247	−	0.176517i
$883$	44.3327	+	14.4046i	1.49192	+	0.484753i	0.937648	−	0.347586i	$-0.112999\pi$
$883$	44.3327	+	14.4046i	1.49192	+	0.484753i	0.554267	+	0.832339i	$0.312999\pi$
$884$	−2.90652	−	8.94534i	−0.0977568	−	0.300864i
$885$	−18.9407	−	14.9241i	−0.636683	−	0.501667i
$886$	−11.3691	+	8.26017i	−0.381954	+	0.277506i
$887$	−7.41261	+	2.40850i	−0.248891	+	0.0808696i	−0.430806	−	0.902445i	$-0.641771\pi$
$887$	−7.41261	+	2.40850i	−0.248891	+	0.0808696i	0.181915	+	0.983314i	$0.441771\pi$
$888$	0.824696	+	0.267960i	0.0276750	+	0.00899215i
$889$	19.6364	+	14.2667i	0.658583	+	0.478489i
$890$	2.82272	+	9.99919i	0.0946178	+	0.335174i
$891$	−2.26877	+	2.41923i	−0.0760066	+	0.0810474i
$892$		−	17.7385i		−	0.593928i
$893$	32.1582	−	44.2620i	1.07613	−	1.48117i
$894$	3.63732	−	11.1945i	0.121650	−	0.374401i
$895$	−5.28061	−	7.89878i	−0.176511	−	0.264027i
$896$	−2.97030	+	2.15805i	−0.0992306	+	0.0720953i
$897$	−0.0480360	−	0.0661158i	−0.00160387	−	0.00220754i
$898$	27.0808	−	8.79910i	0.903699	−	0.293630i
$899$	10.4969	−	32.3061i	0.350090	−	1.07747i
$900$	−4.98478	−	0.389842i	−0.166159	−	0.0129947i
$901$	−4.84522			−0.161418
$902$	−8.71374	+	18.5498i	−0.290136	+	0.617642i
$903$			35.2534i			1.17316i
$904$	−7.25560	−	5.27150i	−0.241318	−	0.175327i
$905$	−1.98893	+	50.9411i	−0.0661142	+	1.69334i
$906$	−7.45137	−	22.9330i	−0.247555	−	0.761896i
$907$	−3.44121	−	4.73642i	−0.114263	−	0.157270i	0.748055	−	0.663637i	$-0.230988\pi$
$907$	−3.44121	−	4.73642i	−0.114263	−	0.157270i	−0.862318	+	0.506367i	$0.830988\pi$
$908$	11.1754	+	15.3817i	0.370870	+	0.510459i
$909$	0.249290	+	0.767236i	0.00826843	+	0.0254476i
$910$	18.3233	+	0.715407i	0.607410	+	0.0237155i
$911$	−4.55243	−	3.30753i	−0.150829	−	0.109583i	0.509812	−	0.860286i	$-0.329715\pi$
$911$	−4.55243	−	3.30753i	−0.150829	−	0.109583i	−0.660640	+	0.750703i	$0.729715\pi$
$912$			7.99694i			0.264805i
$913$	−21.6218	+	46.0286i	−0.715578	+	1.52332i
$914$	29.0935			0.962328
$915$	−1.16153	+	3.15084i	−0.0383989	+	0.104164i
$916$	7.06084	−	21.7310i	0.233297	−	0.718013i
$917$	−0.216571	+	0.0703683i	−0.00715181	+	0.00232377i
$918$	2.47516	+	3.40676i	0.0816924	+	0.112440i
$919$	10.3086	−	7.48964i	0.340050	−	0.247061i	−0.404633	−	0.914479i	$-0.632601\pi$
$919$	10.3086	−	7.48964i	0.340050	−	0.247061i	0.744683	+	0.667419i	$0.232601\pi$
$920$	−0.0454700	−	0.0680145i	−0.00149910	−	0.00224237i
$921$	2.19750	−	6.76319i	0.0724099	−	0.222855i
$922$	8.55065	−	11.7690i	0.281601	−	0.387590i
$923$			13.2055i			0.434664i
$924$	8.32976	−	8.88219i	0.274029	−	0.292203i
$925$	−2.26721	−	3.69566i	−0.0745453	−	0.121513i
$926$	21.4923	+	15.6150i	0.706279	+	0.513142i
$927$	−10.8222	−	3.51635i	−0.355448	−	0.115492i
$928$	8.78048	−	2.85295i	0.288233	−	0.0936527i
$929$	14.5778	−	10.5914i	0.478281	−	0.347492i	−0.322379	−	0.946611i	$-0.604482\pi$
$929$	14.5778	−	10.5914i	0.478281	−	0.347492i	0.800660	+	0.599119i	$0.204482\pi$
$930$	5.09181	−	6.46219i	0.166967	−	0.211904i
$931$	16.0129	+	49.2826i	0.524801	+	1.61517i
$932$	−0.583066	−	0.189450i	−0.0190990	−	0.00620563i
$933$	−11.2431	+	15.4748i	−0.368083	+	0.506623i
$934$	5.76697			0.188701
$935$	13.9845	+	27.9234i	0.457342	+	0.913194i
$936$	2.23360			0.0730076
$937$	15.4767	−	21.3018i	0.505602	−	0.695901i	−0.477568	−	0.878595i	$-0.658482\pi$
$937$	15.4767	−	21.3018i	0.505602	−	0.695901i	0.983170	+	0.182694i	$0.0584816\pi$
$938$	−10.0798	−	3.27512i	−0.329116	−	0.106936i
$939$	9.26897	+	28.5270i	0.302481	+	0.930942i
$940$	−12.0161	−	9.46794i	−0.391922	−	0.308810i
$941$	−9.66039	+	7.01869i	−0.314920	+	0.228803i	−0.734005	−	0.679144i	$-0.762351\pi$
$941$	−9.66039	+	7.01869i	−0.314920	+	0.228803i	0.419085	+	0.907947i	$0.362351\pi$
$942$	−12.9311	+	4.20158i	−0.421319	+	0.136895i
$943$	0.215025	+	0.0698659i	0.00700218	+	0.00227515i
$944$	8.72446	+	6.33869i	0.283957	+	0.206307i
$945$	−7.90092	+	2.23039i	−0.257017	+	0.0725545i
$946$	−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	$0.791982\pi$
$948$	4.63528	−	6.37992i	0.150547	−	0.207210i
$949$	−7.04500	+	21.6823i	−0.228690	+	0.703837i
$950$	25.9530	−	30.4174i	0.842028	−	0.986871i
$951$	−5.34053	+	3.88012i	−0.173179	+	0.125822i
$952$	−9.08752	−	12.5079i	−0.294528	−	0.405383i
$953$	−3.68410	+	1.19704i	−0.119340	+	0.0387759i	−0.368078	−	0.929795i	$-0.619984\pi$
$953$	−3.68410	+	1.19704i	−0.119340	+	0.0387759i	0.248738	+	0.968571i	$0.419984\pi$
$954$	0.355559	−	1.09430i	0.0115116	−	0.0354292i
$955$	21.7868	+	8.03149i	0.705005	+	0.259893i
$956$	−17.8165			−0.576225
$957$	−26.8228	+	14.7693i	−0.867059	+	0.477425i
$958$		−	12.1866i		−	0.393731i
$959$	−2.77228	−	2.01418i	−0.0895216	−	0.0650413i
$960$	2.23437	+	0.0872378i	0.0721138	+	0.00281559i
$961$	−5.39627	−	16.6080i	−0.174073	−	0.535743i
$962$	1.13845	+	1.56694i	0.0367050	+	0.0505201i
$963$	11.2967	+	15.5486i	0.364031	+	0.501046i
$964$	6.22738	+	19.1659i	0.200570	+	0.617292i
$965$	14.8581	+	0.580117i	0.478301	+	0.0186746i
$966$	−0.108678	−	0.0789591i	−0.00349665	−	0.00254047i
$967$		−	0.516048i		−	0.0165950i	−0.999966	−	0.00829749i	$-0.997359\pi$
$967$		−	0.516048i		−	0.0165950i	0.999966	−	0.00829749i	$-0.00264120\pi$
$968$	8.46626	−	7.02300i	0.272116	−	0.225728i
$969$	−33.6751			−1.08180
$970$	−31.0820	−	11.4581i	−0.997984	−	0.367897i
$971$	−15.4723	+	47.6190i	−0.496531	+	1.52817i	0.318026	+	0.948082i	$0.396980\pi$
$971$	−15.4723	+	47.6190i	−0.496531	+	1.52817i	−0.814557	+	0.580084i	$0.803020\pi$
$972$	−0.951057	+	0.309017i	−0.0305052	+	0.00991172i
$973$	−13.7133	−	18.8747i	−0.439628	−	0.605096i
$974$	−4.81942	+	3.50151i	−0.154424	+	0.112196i
$975$	−8.49580	−	7.24887i	−0.272083	−	0.232150i
$976$	0.464080	−	1.42829i	0.0148548	−	0.0457185i
$977$	14.0956	−	19.4010i	0.450960	−	0.620693i	−0.521644	−	0.853163i	$-0.674681\pi$
$977$	14.0956	−	19.4010i	0.450960	−	0.620693i	0.972603	+	0.232471i	$0.0746810\pi$
$978$			10.1232i			0.323703i
$979$	7.43325	+	13.4996i	0.237568	+	0.431450i
$980$	13.9444	−	3.93642i	0.445436	−	0.125744i
$981$	−1.49495	−	1.08615i	−0.0477302	−	0.0346780i
$982$	27.2925	+	8.86786i	0.870938	+	0.282985i
$983$	−35.0687	+	11.3945i	−1.11852	+	0.363428i	−0.809202	−	0.587531i	$-0.800100\pi$
$983$	−35.0687	+	11.3945i	−1.11852	+	0.363428i	−0.309316	+	0.950959i	$0.600100\pi$
$984$	−4.99918	+	3.63212i	−0.159368	+	0.115788i
$985$	20.2797	+	15.9792i	0.646166	+	0.509139i
$986$	12.0137	+	36.9745i	0.382596	+	1.17751i
$987$	−23.8890	−	7.76200i	−0.760395	−	0.247067i
$988$	−10.4990	+	14.4507i	−0.334019	+	0.459737i
$989$	0.351318			0.0111713
$990$	−7.33277	+	1.10929i	−0.233051	+	0.0352557i
$991$	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
$993$	1.87082	+	0.607867i	0.0593687	+	0.0192901i
$994$	6.70768	+	20.6441i	0.212755	+	0.654791i
$995$	19.5129	−	24.7645i	0.618601	−	0.785089i
$996$	−12.4047	+	9.01255i	−0.393058	+	0.285574i
$997$	40.4649	−	13.1479i	1.28154	−	0.416397i	0.412416	−	0.910996i	$-0.364685\pi$
$997$	40.4649	−	13.1479i	1.28154	−	0.416397i	0.869121	+	0.494599i	$0.164685\pi$
$998$	9.38968	+	3.05089i	0.297225	+	0.0965743i
$999$	−0.701528	−	0.509690i	−0.0221954	−	0.0161259i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.s.c.169.2	✓	32	5.4	even	2	inner
330.2.s.c.169.5	yes	32	1.1	even	1	trivial
330.2.s.c.289.2	yes	32	11.3	even	5	inner
330.2.s.c.289.5	yes	32	55.14	even	10	inner
990.2.ba.i.289.4		32	165.14	odd	10
990.2.ba.i.289.7		32	33.14	odd	10
990.2.ba.i.829.4		32	3.2	odd	2
990.2.ba.i.829.7		32	15.14	odd	2

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:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.38390 + 1.75636i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-3.49179 + 1.13455i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.607489 + 2.15197i) q^{10} +(1.59974 + 2.90531i) q^{11} +1.00000i q^{12} +(-1.31288 + 1.80702i) q^{13} +(-1.13455 + 3.49179i) q^{14} +(1.85892 - 1.24275i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.47516 - 3.40676i) q^{17} +(0.951057 - 0.309017i) q^{18} +(-2.47119 + 7.60555i) q^{19} +(2.09805 + 0.773425i) q^{20} +3.67149 q^{21} +(3.29075 + 0.413482i) q^{22} -0.0365882i q^{23} +(0.809017 + 0.587785i) q^{24} +(-1.16962 - 4.86127i) q^{25} +(0.690222 + 2.12428i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(2.15805 + 2.97030i) q^{28} +(-2.85295 - 8.78048i) q^{29} +(0.0872378 - 2.23437i) q^{30} +(2.97662 + 2.16264i) q^{31} +1.00000i q^{32} +(-0.623653 - 3.25746i) q^{33} -4.21099 q^{34} +(2.83962 - 7.70297i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.824696 - 0.267960i) q^{37} +(4.70049 + 6.46966i) q^{38} +(1.80702 - 1.31288i) q^{39} +(1.85892 - 1.24275i) q^{40} +(-1.90952 + 5.87689i) q^{41} +(2.15805 - 2.97030i) q^{42} +9.60194i q^{43} +(2.26877 - 2.41923i) q^{44} +(-2.15197 + 0.607489i) q^{45} +(-0.0296005 - 0.0215060i) q^{46} +(-6.50662 - 2.11413i) q^{47} +(0.951057 - 0.309017i) q^{48} +(5.24229 - 3.80875i) q^{49} +(-4.62034 - 1.91114i) q^{50} +(1.30127 + 4.00489i) q^{51} +(2.12428 + 0.690222i) q^{52} +(0.676313 - 0.930864i) q^{53} -1.00000 q^{54} +(-7.31667 - 1.21095i) q^{55} +3.67149 q^{56} +(4.70049 - 6.46966i) q^{57} +(-8.78048 - 2.85295i) q^{58} +(-3.33245 - 10.2562i) q^{59} +(-1.75636 - 1.38390i) q^{60} +(-1.21498 + 0.882733i) q^{61} +(3.49923 - 1.13697i) q^{62} +(-3.49179 - 1.13455i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.35689 - 4.80664i) q^{65} +(-3.00192 - 1.41014i) q^{66} +2.88670i q^{67} +(-2.47516 + 3.40676i) q^{68} +(-0.0113064 + 0.0347975i) q^{69} +(-4.56274 - 6.82499i) q^{70} +(4.78306 - 3.47509i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(9.70730 - 3.15409i) q^{73} +(0.267960 - 0.824696i) q^{74} +(-0.389842 + 4.98478i) q^{75} +7.99694 q^{76} +(-8.88219 - 8.32976i) q^{77} -2.23360i q^{78} +(-6.37992 - 4.63528i) q^{79} +(0.0872378 - 2.23437i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.63212 + 4.99918i) q^{82} +(9.01255 + 12.4047i) q^{83} +(-1.13455 - 3.49179i) q^{84} +(9.40890 + 0.367358i) q^{85} +(7.76814 + 5.64388i) q^{86} +9.23234i q^{87} +(-0.623653 - 3.25746i) q^{88} +4.64654 q^{89} +(-0.773425 + 2.09805i) q^{90} +(2.53414 - 7.79928i) q^{91} +(-0.0347975 + 0.0113064i) q^{92} +(-2.16264 - 2.97662i) q^{93} +(-5.53486 + 4.02131i) q^{94} +(-9.93820 - 14.8657i) q^{95} +(0.309017 - 0.951057i) q^{96} +(-8.70788 + 11.9854i) q^{97} -6.47983i q^{98} +(-0.413482 + 3.29075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 2 q^{5} - 8 q^{6} + 8 q^{9} + 4 q^{10} + 10 q^{14} - 4 q^{15} - 8 q^{16} + 20 q^{19} + 2 q^{20} + 20 q^{21} + 8 q^{24} + 4 q^{25} - 2 q^{26} + 2 q^{29} - 2 q^{30} - 24 q^{31} - 28 q^{34}+ \cdots - 8 q^{96}+O(q^{100}) \) 32 * q + 8 * q^4 - 2 * q^5 - 8 * q^6 + 8 * q^9 + 4 * q^10 + 10 * q^14 - 4 * q^15 - 8 * q^16 + 20 * q^19 + 2 * q^20 + 20 * q^21 + 8 * q^24 + 4 * q^25 - 2 * q^26 + 2 * q^29 - 2 * q^30 - 24 * q^31 - 28 * q^34 + 44 * q^35 - 8 * q^36 + 2 * q^39 - 4 * q^40 - 34 * q^41 - 20 * q^44 - 8 * q^45 - 38 * q^46 + 14 * q^49 - 24 * q^50 - 12 * q^51 - 32 * q^54 + 28 * q^55 + 20 * q^56 - 4 * q^59 - 6 * q^60 - 8 * q^61 + 8 * q^64 - 44 * q^65 - 10 * q^66 - 22 * q^69 - 10 * q^70 + 8 * q^71 + 20 * q^74 + 24 * q^75 + 20 * q^76 + 2 * q^79 - 2 * q^80 - 8 * q^81 + 10 * q^84 - 20 * q^85 + 34 * q^86 - 132 * q^89 + 6 * q^90 + 78 * q^91 + 22 * q^94 - 60 * q^95 - 8 * q^96

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