LMFDB - Embedded newform 110.2.k.a.63.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,2,Mod(7,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			63.1
Character	$\chi$	$=$	110.63
Dual form			110.2.k.a.7.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.987688 - 0.156434i) q^{2} +(-1.45771 + 2.86091i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-1.70643 - 1.44502i) q^{5} +(1.88730 - 2.59765i) q^{6} +(-1.35828 + 0.692077i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-4.29653 - 5.91367i) q^{9} +(1.45937 + 1.69418i) q^{10} +(-2.70495 + 1.91918i) q^{11} +(-2.27043 + 2.27043i) q^{12} +(-0.165595 + 1.04553i) q^{13} +(1.44982 - 0.471075i) q^{14} +(6.62155 - 2.77553i) q^{15} +(0.809017 + 0.587785i) q^{16} +(0.347837 + 2.19616i) q^{17} +(3.31853 + 6.51299i) q^{18} +(1.91500 + 5.89375i) q^{19} +(-1.17638 - 1.90161i) q^{20} -4.89475i q^{21} +(2.97187 - 1.47241i) q^{22} +(-3.05791 - 3.05791i) q^{23} +(2.59765 - 1.88730i) q^{24} +(0.823819 + 4.93167i) q^{25} +(0.327113 - 1.00675i) q^{26} +(13.6675 - 2.16472i) q^{27} +(-1.50566 + 0.238474i) q^{28} +(-1.39938 + 4.30686i) q^{29} +(-6.97422 + 1.70552i) q^{30} +(2.32781 - 1.69125i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.54760 - 10.5362i) q^{33} -2.22353i q^{34} +(3.31788 + 0.781760i) q^{35} +(-2.25882 - 6.95193i) q^{36} +(-0.631904 - 1.24018i) q^{37} +(-0.969434 - 6.12076i) q^{38} +(-2.74977 - 1.99782i) q^{39} +(0.864415 + 2.06223i) q^{40} +(2.38365 - 0.774496i) q^{41} +(-0.765708 + 4.83449i) q^{42} +(-6.40957 + 6.40957i) q^{43} +(-3.16562 + 0.989379i) q^{44} +(-1.21365 + 16.2999i) q^{45} +(2.54190 + 3.49862i) q^{46} +(3.99740 + 2.03678i) q^{47} +(-2.86091 + 1.45771i) q^{48} +(-2.74855 + 3.78305i) q^{49} +(-0.0421939 - 4.99982i) q^{50} +(-6.79005 - 2.20622i) q^{51} +(-0.480577 + 0.943185i) q^{52} +(3.75665 + 0.594995i) q^{53} -13.8379 q^{54} +(7.38907 + 0.633749i) q^{55} +1.52443 q^{56} +(-19.6530 - 3.11273i) q^{57} +(2.05589 - 4.03492i) q^{58} +(-4.27154 - 1.38791i) q^{59} +(7.15515 - 0.593511i) q^{60} +(3.48115 - 4.79140i) q^{61} +(-2.56372 + 1.30628i) q^{62} +(9.92860 + 5.05887i) q^{63} +(0.587785 + 0.809017i) q^{64} +(1.79339 - 1.54483i) q^{65} +(-0.119682 + 10.6486i) q^{66} +(5.40776 - 5.40776i) q^{67} +(-0.347837 + 2.19616i) q^{68} +(13.2059 - 4.29086i) q^{69} +(-3.15473 - 1.29117i) q^{70} +(-7.19862 - 5.23010i) q^{71} +(1.14349 + 7.21970i) q^{72} +(-5.17847 - 10.1633i) q^{73} +(0.430117 + 1.32376i) q^{74} +(-15.3099 - 4.83204i) q^{75} +6.19706i q^{76} +(2.34584 - 4.47882i) q^{77} +(2.40339 + 2.40339i) q^{78} +(4.69179 - 3.40879i) q^{79} +(-0.531169 - 2.17206i) q^{80} +(-6.95367 + 21.4012i) q^{81} +(-2.47546 + 0.392075i) q^{82} +(1.26330 - 0.200087i) q^{83} +(1.51256 - 4.65519i) q^{84} +(2.57994 - 4.25022i) q^{85} +(7.33334 - 5.32798i) q^{86} +(-10.2816 - 10.2816i) q^{87} +(3.28142 - 0.481987i) q^{88} +10.5518i q^{89} +(3.74856 - 15.9093i) q^{90} +(-0.498662 - 1.53472i) q^{91} +(-1.96330 - 3.85319i) q^{92} +(1.44526 + 9.12499i) q^{93} +(-3.62956 - 2.63703i) q^{94} +(5.24880 - 12.8245i) q^{95} +(3.05372 - 0.992214i) q^{96} +(1.09605 - 6.92020i) q^{97} +(3.30651 - 3.30651i) q^{98} +(22.9713 + 7.75031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36}+ \cdots + 72 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−0.987688	−	0.156434i	−0.698401	−	0.110616i
$2$	−0.987688	−	0.156434i	−0.698401	−	0.110616i
$3$	−1.45771	+	2.86091i	−0.841606	+	1.65175i	−0.0863983	+	0.996261i	$0.527536\pi$
$3$	−1.45771	+	2.86091i	−0.841606	+	1.65175i	−0.755208	+	0.655485i	$0.772464\pi$
$4$	0.951057	+	0.309017i	0.475528	+	0.154508i
$5$	−1.70643	−	1.44502i	−0.763139	−	0.646234i
$5$	−1.70643	−	1.44502i	−0.763139	−	0.646234i
$6$	1.88730	−	2.59765i	0.770488	−	1.06049i
$7$	−1.35828	+	0.692077i	−0.513381	+	0.261581i	−0.691433	−	0.722440i	$-0.743020\pi$
$7$	−1.35828	+	0.692077i	−0.513381	+	0.261581i	0.178052	+	0.984021i	$0.443020\pi$
$8$	−0.891007	−	0.453990i	−0.315018	−	0.160510i
$9$	−4.29653	−	5.91367i	−1.43218	−	1.97122i
$10$	1.45937	+	1.69418i	0.461494	+	0.535746i
$11$	−2.70495	+	1.91918i	−0.815572	+	0.578656i
$11$	−2.70495	+	1.91918i	−0.815572	+	0.578656i
$12$	−2.27043	+	2.27043i	−0.655416	+	0.655416i
$13$	−0.165595	+	1.04553i	−0.0459279	+	0.289977i	−0.999952	−	0.00975110i	$-0.996896\pi$
$13$	−0.165595	+	1.04553i	−0.0459279	+	0.289977i	0.954025	+	0.299728i	$0.0968961\pi$
$14$	1.44982	−	0.471075i	0.387481	−	0.125900i
$15$	6.62155	−	2.77553i	1.70968	−	0.716638i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	0.347837	+	2.19616i	0.0843629	+	0.532646i	0.993286	+	0.115683i	$0.0369057\pi$
$17$	0.347837	+	2.19616i	0.0843629	+	0.532646i	−0.908923	+	0.416963i	$0.863094\pi$
$18$	3.31853	+	6.51299i	0.782186	+	1.53513i
$19$	1.91500	+	5.89375i	0.439330	+	1.35212i	0.888583	+	0.458715i	$0.151690\pi$
$19$	1.91500	+	5.89375i	0.439330	+	1.35212i	−0.449253	+	0.893405i	$0.648310\pi$
$20$	−1.17638	−	1.90161i	−0.263046	−	0.425214i
$21$		−	4.89475i		−	1.06812i
$22$	2.97187	−	1.47241i	0.633605	−	0.313919i
$23$	−3.05791	−	3.05791i	−0.637617	−	0.637617i	0.312350	−	0.949967i	$-0.398884\pi$
$23$	−3.05791	−	3.05791i	−0.637617	−	0.637617i	−0.949967	+	0.312350i	$0.898884\pi$
$24$	2.59765	−	1.88730i	0.530243	−	0.385244i
$25$	0.823819	+	4.93167i	0.164764	+	0.986333i
$26$	0.327113	−	1.00675i	0.0641522	−	0.197440i
$27$	13.6675	−	2.16472i	2.63031	−	0.416601i
$28$	−1.50566	+	0.238474i	−0.284544	+	0.0450673i
$29$	−1.39938	+	4.30686i	−0.259859	+	0.799763i	0.732975	+	0.680256i	$0.238131\pi$
$29$	−1.39938	+	4.30686i	−0.259859	+	0.799763i	−0.992833	+	0.119507i	$0.961869\pi$
$30$	−6.97422	+	1.70552i	−1.27331	+	0.311383i
$31$	2.32781	−	1.69125i	0.418087	−	0.303758i	−0.358781	−	0.933422i	$-0.616807\pi$
$31$	2.32781	−	1.69125i	0.418087	−	0.303758i	0.776868	+	0.629664i	$0.216807\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.54760	−	10.5362i	−0.269402	−	1.83412i
$34$		−	2.22353i		−	0.381333i
$35$	3.31788	+	0.781760i	0.560823	+	0.132142i
$36$	−2.25882	−	6.95193i	−0.376470	−	1.15866i
$37$	−0.631904	−	1.24018i	−0.103884	−	0.203885i	0.833213	−	0.552952i	$-0.186499\pi$
$37$	−0.631904	−	1.24018i	−0.103884	−	0.203885i	−0.937098	+	0.349067i	$0.886499\pi$
$38$	−0.969434	−	6.12076i	−0.157263	−	0.992919i
$39$	−2.74977	−	1.99782i	−0.440316	−	0.319908i
$40$	0.864415	+	2.06223i	0.136676	+	0.326067i
$41$	2.38365	−	0.774496i	0.372264	−	0.120956i	−0.116909	−	0.993143i	$-0.537299\pi$
$41$	2.38365	−	0.774496i	0.372264	−	0.120956i	0.489173	+	0.872187i	$0.337299\pi$
$42$	−0.765708	+	4.83449i	−0.118151	+	0.745978i
$43$	−6.40957	+	6.40957i	−0.977450	+	0.977450i	−0.999751	−	0.0223009i	$-0.992901\pi$
$43$	−6.40957	+	6.40957i	−0.977450	+	0.977450i	0.0223009	+	0.999751i	$0.492901\pi$
$44$	−3.16562	+	0.989379i	−0.477235	+	0.149155i
$45$	−1.21365	+	16.2999i	−0.180920	+	2.42984i
$46$	2.54190	+	3.49862i	0.374782	+	0.515843i
$47$	3.99740	+	2.03678i	0.583081	+	0.297095i	0.720541	−	0.693413i	$-0.243894\pi$
$47$	3.99740	+	2.03678i	0.583081	+	0.297095i	−0.137460	+	0.990507i	$0.543894\pi$
$48$	−2.86091	+	1.45771i	−0.412936	+	0.210402i
$49$	−2.74855	+	3.78305i	−0.392650	+	0.540436i
$50$	−0.0421939	−	4.99982i	−0.00596712	−	0.707082i
$51$	−6.79005	−	2.20622i	−0.950797	−	0.308933i
$52$	−0.480577	+	0.943185i	−0.0666440	+	0.130796i
$53$	3.75665	+	0.594995i	0.516016	+	0.0817288i	0.409011	−	0.912530i	$-0.365874\pi$
$53$	3.75665	+	0.594995i	0.516016	+	0.0817288i	0.107005	+	0.994258i	$0.465874\pi$
$54$	−13.8379			−1.88310
$55$	7.38907	+	0.633749i	0.996342	+	0.0854548i
$56$	1.52443			0.203711
$57$	−19.6530	−	3.11273i	−2.60310	−	0.412291i
$58$	2.05589	−	4.03492i	0.269952	−	0.529811i
$59$	−4.27154	−	1.38791i	−0.556107	−	0.180690i	0.0174620	−	0.999848i	$-0.494441\pi$
$59$	−4.27154	−	1.38791i	−0.556107	−	0.180690i	−0.573569	+	0.819158i	$0.694441\pi$
$60$	7.15515	−	0.593511i	0.923726	−	0.0766219i
$61$	3.48115	−	4.79140i	0.445716	−	0.613475i	−0.525754	−	0.850636i	$-0.676217\pi$
$61$	3.48115	−	4.79140i	0.445716	−	0.613475i	0.971470	+	0.237161i	$0.0762169\pi$
$62$	−2.56372	+	1.30628i	−0.325593	+	0.165898i
$63$	9.92860	+	5.05887i	1.25089	+	0.637358i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	1.79339	−	1.54483i	0.222443	−	0.191613i
$66$	−0.119682	+	10.6486i	−0.0147318	+	1.31075i
$67$	5.40776	−	5.40776i	0.660663	−	0.660663i	−0.294873	−	0.955536i	$-0.595277\pi$
$67$	5.40776	−	5.40776i	0.660663	−	0.660663i	0.955536	+	0.294873i	$0.0952775\pi$
$68$	−0.347837	+	2.19616i	−0.0421814	+	0.266323i
$69$	13.2059	−	4.29086i	1.58980	−	0.516559i
$70$	−3.15473	−	1.29117i	−0.377063	−	0.154324i
$71$	−7.19862	−	5.23010i	−0.854319	−	0.620699i	0.0720143	−	0.997404i	$-0.477057\pi$
$71$	−7.19862	−	5.23010i	−0.854319	−	0.620699i	−0.926334	+	0.376704i	$0.877057\pi$
$72$	1.14349	+	7.21970i	0.134761	+	0.850850i
$73$	−5.17847	−	10.1633i	−0.606094	−	1.18953i	−0.966485	−	0.256725i	$-0.917357\pi$
$73$	−5.17847	−	10.1633i	−0.606094	−	1.18953i	0.360391	−	0.932801i	$-0.382643\pi$
$74$	0.430117	+	1.32376i	0.0500001	+	0.153884i
$75$	−15.3099	−	4.83204i	−1.76784	−	0.557956i
$76$			6.19706i			0.710852i
$77$	2.34584	−	4.47882i	0.267334	−	0.510409i
$78$	2.40339	+	2.40339i	0.272130	+	0.272130i
$79$	4.69179	−	3.40879i	0.527868	−	0.383518i	−0.291692	−	0.956512i	$-0.594218\pi$
$79$	4.69179	−	3.40879i	0.527868	−	0.383518i	0.819560	+	0.572994i	$0.194218\pi$
$80$	−0.531169	−	2.17206i	−0.0593865	−	0.242844i
$81$	−6.95367	+	21.4012i	−0.772631	+	2.37791i
$82$	−2.47546	+	0.392075i	−0.273369	+	0.0432974i
$83$	1.26330	−	0.200087i	0.138665	−	0.0219624i	−0.0867161	−	0.996233i	$-0.527637\pi$
$83$	1.26330	−	0.200087i	0.138665	−	0.0219624i	0.225381	+	0.974271i	$0.427637\pi$
$84$	1.51256	−	4.65519i	0.165034	−	0.507922i
$85$	2.57994	−	4.25022i	0.279833	−	0.461002i
$86$	7.33334	−	5.32798i	0.790774	−	0.574531i
$87$	−10.2816	−	10.2816i	−1.10231	−	1.10231i
$88$	3.28142	−	0.481987i	0.349800	−	0.0513800i
$89$			10.5518i			1.11849i	0.829004	+	0.559243i	$0.188908\pi$
$89$			10.5518i			1.11849i	−0.829004	+	0.559243i	$0.811092\pi$
$90$	3.74856	−	15.9093i	0.395133	−	1.67699i
$91$	−0.498662	−	1.53472i	−0.0522740	−	0.160883i
$92$	−1.96330	−	3.85319i	−0.204688	−	0.401722i
$93$	1.44526	+	9.12499i	0.149866	+	0.946218i
$94$	−3.62956	−	2.63703i	−0.374361	−	0.271989i
$95$	5.24880	−	12.8245i	0.538515	−	1.31577i
$96$	3.05372	−	0.992214i	0.311669	−	0.101267i
$97$	1.09605	−	6.92020i	0.111287	−	0.702639i	−0.867451	−	0.497523i	$-0.834243\pi$
$97$	1.09605	−	6.92020i	0.111287	−	0.702639i	0.978738	−	0.205116i	$-0.0657572\pi$
$98$	3.30651	−	3.30651i	0.334008	−	0.334008i
$99$	22.9713	+	7.75031i	2.30870	+	0.778936i
$100$	−0.740470	+	4.94487i	−0.0740470	+	0.494487i
$101$	10.3519	+	14.2481i	1.03005	+	1.41774i	0.904912	+	0.425599i	$0.139937\pi$
$101$	10.3519	+	14.2481i	1.03005	+	1.41774i	0.125136	+	0.992140i	$0.460063\pi$
$102$	6.36132	+	3.24125i	0.629865	+	0.320932i
$103$	−2.86217	+	1.45835i	−0.282018	+	0.143695i	−0.589278	−	0.807930i	$-0.700588\pi$
$103$	−2.86217	+	1.45835i	−0.282018	+	0.143695i	0.307260	+	0.951625i	$0.400588\pi$
$104$	0.622206	−	0.856394i	0.0610124	−	0.0839763i
$105$	−7.07303	+	8.35256i	−0.690257	+	0.815127i
$106$	−3.61732	−	1.17534i	−0.351345	−	0.114159i
$107$	−7.49892	+	14.7175i	−0.724948	+	1.42279i	0.174006	+	0.984745i	$0.444329\pi$
$107$	−7.49892	+	14.7175i	−0.724948	+	1.42279i	−0.898953	+	0.438045i	$0.855671\pi$
$108$	13.6675	+	2.16472i	1.31516	+	0.208300i
$109$	−1.88801			−0.180839			−0.0904195	−	0.995904i	$-0.528821\pi$
$109$	−1.88801			−0.180839			−0.0904195	+	0.995904i	$0.528821\pi$
$110$	−7.19896	−	1.78185i	−0.686394	−	0.169893i
$111$	4.46917			0.424195
$112$	−1.50566	−	0.238474i	−0.142272	−	0.0225336i
$113$	1.81113	−	3.55455i	0.170377	−	0.334384i	−0.789991	−	0.613118i	$-0.789915\pi$
$113$	1.81113	−	3.55455i	0.170377	−	0.334384i	0.960368	+	0.278734i	$0.0899149\pi$
$114$	18.9241	+	6.14881i	1.77240	+	0.575889i
$115$	0.799364	+	9.63685i	0.0745411	+	0.898641i
$116$	−2.66178	+	3.66363i	−0.247140	+	0.340160i
$117$	6.89439	−	3.51287i	0.637387	−	0.324765i
$118$	4.00183	+	2.03903i	0.368398	+	0.187708i
$119$	−1.99237	−	2.74226i	−0.182640	−	0.251383i
$120$	−7.15991	−	0.533109i	−0.653607	−	0.0486660i
$121$	3.63346	−	10.3826i	0.330314	−	0.943871i
$122$	−4.18783	+	4.18783i	−0.379149	+	0.379149i
$123$	−1.25890	+	7.94840i	−0.113511	+	0.716683i
$124$	2.73650	−	0.889144i	0.245745	−	0.0798475i
$125$	5.72058	−	9.60599i	0.511664	−	0.859186i
$126$	−9.01498	−	6.54977i	−0.803118	−	0.583500i
$127$	2.65395	+	16.7564i	0.235500	+	1.48689i	0.767995	+	0.640456i	$0.221254\pi$
$127$	2.65395	+	16.7564i	0.235500	+	1.48689i	−0.532495	+	0.846433i	$0.678746\pi$
$128$	−0.453990	−	0.891007i	−0.0401275	−	0.0787546i
$129$	−8.99392	−	27.6805i	−0.791871	−	2.43713i
$130$	−2.01297	+	1.24527i	−0.176550	+	0.109217i
$131$			9.77651i			0.854177i	0.904210	+	0.427089i	$0.140461\pi$
$131$			9.77651i			0.854177i	−0.904210	+	0.427089i	$0.859539\pi$
$132$	1.78401	−	10.4988i	0.155278	−	0.913800i
$133$	−6.68003	−	6.68003i	−0.579232	−	0.579232i
$134$	−6.18714	+	4.49522i	−0.534488	+	0.388328i
$135$	−26.4507	−	16.0559i	−2.27652	−	1.38187i
$136$	0.687109	−	2.11471i	0.0589191	−	0.181334i
$137$	−2.44036	+	0.386515i	−0.208494	+	0.0330222i	−0.259808	−	0.965660i	$-0.583659\pi$
$137$	−2.44036	+	0.386515i	−0.208494	+	0.0330222i	0.0513136	+	0.998683i	$0.483659\pi$
$138$	−13.7146	+	2.17217i	−1.16746	+	0.184908i
$139$	−2.32161	+	7.14518i	−0.196916	+	0.606046i	0.803032	+	0.595935i	$0.203219\pi$
$139$	−2.32161	+	7.14518i	−0.196916	+	0.606046i	−0.999949	+	0.0101112i	$0.996781\pi$
$140$	2.91391	+	1.76878i	0.246270	+	0.149489i
$141$	−11.6541	+	8.46717i	−0.981449	+	0.713065i
$142$	6.29183	+	6.29183i	0.527998	+	0.527998i
$143$	−1.55864	−	3.14590i	−0.130340	−	0.263074i
$144$		−	7.30970i		−	0.609141i
$145$	8.61146	−	5.32722i	0.715143	−	0.442401i
$146$	3.52482	+	10.8483i	0.291716	+	0.897810i
$147$	−6.81639	−	13.3779i	−0.562206	−	1.10339i
$148$	−0.217739	−	1.37475i	−0.0178981	−	0.113004i
$149$	0.0269615	+	0.0195887i	0.00220877	+	0.00160477i	0.588889	−	0.808214i	$-0.299565\pi$
$149$	0.0269615	+	0.0195887i	0.00220877	+	0.00160477i	−0.586680	+	0.809819i	$0.699565\pi$
$150$	14.3655	+	7.16755i	1.17294	+	0.585228i
$151$	−20.1481	+	6.54653i	−1.63963	+	0.532749i	−0.976457	−	0.215714i	$-0.930792\pi$
$151$	−20.1481	+	6.54653i	−1.63963	+	0.532749i	−0.663176	+	0.748463i	$0.730792\pi$
$152$	0.969434	−	6.12076i	0.0786315	−	0.496459i
$153$	11.4929	−	11.4929i	0.929142	−	0.929142i
$154$	−3.01760	+	4.05671i	−0.243165	+	0.326899i
$155$	−6.41615	−	0.477730i	−0.515357	−	0.0383722i
$156$	−1.99782	−	2.74977i	−0.159954	−	0.220158i
$157$	1.75037	+	0.891858i	0.139695	+	0.0711780i	0.522441	−	0.852676i	$-0.325022\pi$
$157$	1.75037	+	0.891858i	0.139695	+	0.0711780i	−0.382746	+	0.923854i	$0.625022\pi$
$158$	−5.16728	+	2.63286i	−0.411087	+	0.209459i
$159$	−7.17831	+	9.88010i	−0.569277	+	0.783543i
$160$	0.184844	+	2.22841i	0.0146132	+	0.176172i
$161$	6.26979	+	2.03718i	0.494129	+	0.160552i
$162$	10.2160	−	20.0499i	0.802641	−	1.57527i
$163$	−2.15047	−	0.340601i	−0.168438	−	0.0266779i	0.0716458	−	0.997430i	$-0.477175\pi$
$163$	−2.15047	−	0.340601i	−0.168438	−	0.0266779i	−0.240084	+	0.970752i	$0.577175\pi$
$164$	2.50632			0.195711
$165$	−12.5842	+	20.2156i	−0.979677	+	1.57378i
$166$	−1.27905			−0.0992732
$167$	21.1879	+	3.35583i	1.63957	+	0.259682i	0.907036	−	0.421053i	$-0.138339\pi$
$167$	21.1879	+	3.35583i	1.63957	+	0.259682i	0.732530	+	0.680735i	$0.238339\pi$
$168$	−2.22217	+	4.36126i	−0.171444	+	0.336478i
$169$	11.2980	+	3.67095i	0.869079	+	0.282381i
$170$	−3.21305	+	3.79431i	−0.246430	+	0.291010i
$171$	26.6259	−	36.6474i	2.03613	−	2.80249i
$172$	−8.07653	+	4.11520i	−0.615830	+	0.313781i
$173$	11.7553	+	5.98965i	0.893742	+	0.455384i	0.839635	−	0.543151i	$-0.182769\pi$
$173$	11.7553	+	5.98965i	0.893742	+	0.455384i	0.0541069	+	0.998535i	$0.482769\pi$
$174$	8.54665	+	11.7634i	0.647920	+	0.891785i
$175$	−4.53207	−	6.12843i	−0.342592	−	0.463266i
$176$	−3.31642	−	0.0372739i	−0.249984	−	0.00280962i
$177$	10.1973	−	10.1973i	0.766477	−	0.766477i
$178$	1.65066	−	10.4219i	0.123722	−	0.781152i
$179$	−12.8887	+	4.18779i	−0.963346	+	0.313010i	−0.748127	−	0.663555i	$-0.769047\pi$
$179$	−12.8887	+	4.18779i	−0.963346	+	0.313010i	−0.215219	+	0.976566i	$0.569047\pi$
$180$	−6.19118	+	15.1270i	−0.461463	+	1.12750i
$181$	−13.9517	−	10.1365i	−1.03702	−	0.753441i	−0.0673204	−	0.997731i	$-0.521445\pi$
$181$	−13.9517	−	10.1365i	−1.03702	−	0.753441i	−0.969702	+	0.244290i	$0.921445\pi$
$182$	0.252439	+	1.59384i	0.0187120	+	0.118143i
$183$	8.63324	+	16.9437i	0.638188	+	1.25251i
$184$	1.33635	+	4.11287i	0.0985173	+	0.303205i
$185$	−0.713789	+	3.02940i	−0.0524788	+	0.222726i
$186$		−	9.23874i		−	0.677417i
$187$	−5.15571	−	5.27292i	−0.377023	−	0.385594i
$188$	3.17236	+	3.17236i	0.231368	+	0.231368i
$189$	−17.0661	+	12.3993i	−1.24138	+	0.901914i
$190$	−7.19037	+	11.8455i	−0.521644	+	0.859364i
$191$	−3.89136	+	11.9764i	−0.281569	+	0.866580i	0.705837	+	0.708374i	$0.250571\pi$
$191$	−3.89136	+	11.9764i	−0.281569	+	0.866580i	−0.987406	+	0.158206i	$0.949429\pi$
$192$	−3.17134	+	0.502291i	−0.228872	+	0.0362497i
$193$	−3.78808	+	0.599973i	−0.272672	+	0.0431870i	−0.291273	−	0.956640i	$-0.594079\pi$
$193$	−3.78808	+	0.599973i	−0.272672	+	0.0431870i	0.0186009	+	0.999827i	$0.494079\pi$
$194$	−2.16511	+	6.66354i	−0.155446	+	0.478414i
$195$	1.80539	+	7.38263i	0.129287	+	0.528681i
$196$	−3.78305	+	2.74855i	−0.270218	+	0.196325i
$197$	7.40013	+	7.40013i	0.527238	+	0.527238i	0.919748	−	0.392510i	$-0.128393\pi$
$197$	7.40013	+	7.40013i	0.527238	+	0.527238i	−0.392510	+	0.919748i	$0.628393\pi$
$198$	−21.4761	−	11.2484i	−1.52624	−	0.799389i
$199$		−	9.10742i		−	0.645608i	−0.946466	−	0.322804i	$-0.895375\pi$
$199$		−	9.10742i		−	0.645608i	0.946466	−	0.322804i	$-0.104625\pi$
$200$	1.50490	−	4.76815i	0.106413	−	0.337159i
$201$	7.58818	+	23.3540i	0.535229	+	1.64727i
$202$	−7.99551	−	15.6921i	−0.562562	−	1.10409i
$203$	−1.07993	−	6.81839i	−0.0757960	−	0.478557i
$204$	−5.77596	−	4.19648i	−0.404398	−	0.293812i
$205$	−5.18670	−	2.12281i	−0.362255	−	0.148263i
$206$	3.05507	−	0.992651i	0.212857	−	0.0691613i
$207$	−4.94505	+	31.2218i	−0.343705	+	2.17007i
$208$	−0.748516	+	0.748516i	−0.0519002	+	0.0519002i
$209$	−16.4912	−	12.2671i	−1.14072	−	0.848530i
$210$	8.29258	−	7.14326i	0.572242	−	0.492932i
$211$	−14.7378	−	20.2849i	−1.01459	−	1.39647i	−0.915926	−	0.401347i	$-0.868542\pi$
$211$	−14.7378	−	20.2849i	−1.01459	−	1.39647i	−0.0986665	−	0.995121i	$-0.531458\pi$
$212$	3.38892	+	1.72674i	0.232752	+	0.118593i
$213$	25.4563	−	12.9706i	1.74424	−	0.888734i
$214$	9.70891	−	13.3632i	0.663687	−	0.913487i
$215$	20.1995	−	1.67552i	1.37759	−	0.114270i
$216$	−13.1606	−	4.27614i	−0.895466	−	0.290954i
$217$	−1.99133	+	3.90821i	−0.135181	+	0.265307i
$218$	1.86477	+	0.295350i	0.126298	+	0.0200037i
$219$	36.6250			2.47489
$220$	6.83158	+	2.88608i	0.460585	+	0.194579i
$221$	−2.35374			−0.158330
$222$	−4.41415	−	0.699133i	−0.296258	−	0.0469227i
$223$	−2.26373	+	4.44282i	−0.151590	+	0.297513i	−0.954296	−	0.298862i	$-0.903393\pi$
$223$	−2.26373	+	4.44282i	−0.151590	+	0.297513i	0.802706	+	0.596375i	$0.203393\pi$
$224$	1.44982	+	0.471075i	0.0968702	+	0.0314750i
$225$	25.6247	−	26.0608i	1.70831	−	1.73739i
$226$	−2.34489	+	3.22746i	−0.155980	+	0.214688i
$227$	1.81833	−	0.926486i	0.120687	−	0.0614931i	−0.392605	−	0.919707i	$-0.628426\pi$
$227$	1.81833	−	0.926486i	0.120687	−	0.0614931i	0.513292	+	0.858214i	$0.328426\pi$
$228$	−17.7292	−	9.03349i	−1.17415	−	0.598257i
$229$	0.895888	+	1.23308i	0.0592020	+	0.0814845i	0.837591	−	0.546297i	$-0.183963\pi$
$229$	0.895888	+	1.23308i	0.0592020	+	0.0814845i	−0.778389	+	0.627782i	$0.783963\pi$
$230$	0.718013	−	9.64325i	0.0473444	−	0.635857i
$231$	9.39394	+	13.2400i	0.618076	+	0.871131i
$232$	3.20213	−	3.20213i	0.210230	−	0.210230i
$233$	−3.47122	+	21.9164i	−0.227407	+	1.43579i	0.564642	+	0.825336i	$0.309014\pi$
$233$	−3.47122	+	21.9164i	−0.227407	+	1.43579i	−0.792050	+	0.610457i	$0.790986\pi$
$234$	−7.35904	+	2.39110i	−0.481076	+	0.156311i
$235$	−3.87810	−	9.25196i	−0.252980	−	0.603531i
$236$	−3.63358	−	2.63995i	−0.236526	−	0.171846i
$237$	2.91297	+	18.3918i	0.189218	+	1.19468i
$238$	1.53886	+	3.02018i	0.0997492	+	0.195769i
$239$	−7.65870	−	23.5711i	−0.495400	−	1.52468i	−0.816332	−	0.577583i	$-0.803996\pi$
$239$	−7.65870	−	23.5711i	−0.495400	−	1.52468i	0.320932	−	0.947102i	$-0.396004\pi$
$240$	6.98836	+	1.64660i	0.451097	+	0.106288i
$241$		−	0.0562577i		−	0.00362387i	−0.999998	−	0.00181194i	$-0.999423\pi$
$241$		−	0.0562577i		−	0.00362387i	0.999998	−	0.00181194i	$-0.000576758\pi$
$242$	−5.21292	+	9.68636i	−0.335099	+	0.622662i
$243$	−21.7359	−	21.7359i	−1.39436	−	1.39436i
$244$	4.79140	−	3.48115i	0.306738	−	0.222858i
$245$	10.1568	−	2.48381i	0.648895	−	0.158685i
$246$	2.48681	−	7.65360i	0.158553	−	0.487976i
$247$	−6.47920	+	1.02620i	−0.412262	+	0.0652958i
$248$	−2.84191	+	0.450114i	−0.180461	+	0.0285822i
$249$	−1.26909	+	3.90585i	−0.0804251	+	0.247523i
$250$	−7.15286	+	8.59283i	−0.452386	+	0.543458i
$251$	6.81505	−	4.95143i	0.430162	−	0.312531i	−0.351551	−	0.936169i	$-0.614346\pi$
$251$	6.81505	−	4.95143i	0.430162	−	0.312531i	0.781714	+	0.623637i	$0.214346\pi$
$252$	7.87938	+	7.87938i	0.496354	+	0.496354i
$253$	14.1402	+	2.40278i	0.888984	+	0.151062i
$254$		−	16.9653i		−	1.06449i
$255$	8.39871	+	13.5765i	0.525948	+	0.850196i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	4.76675	+	9.35527i	0.297342	+	0.583566i	0.990547	−	0.137175i	$-0.0438021\pi$
$257$	4.76675	+	9.35527i	0.297342	+	0.583566i	−0.693205	+	0.720740i	$0.743802\pi$
$258$	4.55302	+	28.7466i	0.283458	+	1.78969i
$259$	1.71660	+	1.24718i	0.106664	+	0.0774963i
$260$	2.18299	−	0.915036i	0.135384	−	0.0567481i
$261$	31.4818	−	10.2291i	1.94868	−	0.633163i
$262$	1.52938	−	9.65614i	0.0944856	−	0.596558i
$263$	3.20922	−	3.20922i	0.197889	−	0.197889i	−0.601205	−	0.799095i	$-0.705313\pi$
$263$	3.20922	−	3.20922i	0.197889	−	0.197889i	0.799095	+	0.601205i	$0.205313\pi$
$264$	−3.40442	+	10.0904i	−0.209527	+	0.621022i
$265$	−5.55069	−	6.44376i	−0.340976	−	0.395837i
$266$	5.55280	+	7.64278i	0.340464	+	0.468609i
$267$	−30.1877	−	15.3814i	−1.84746	−	0.941325i
$268$	6.81417	−	3.47200i	0.416242	−	0.212086i
$269$	−15.2248	+	20.9551i	−0.928272	+	1.27766i	0.0322573	+	0.999480i	$0.489730\pi$
$269$	−15.2248	+	20.9551i	−0.928272	+	1.27766i	−0.960530	+	0.278178i	$0.910270\pi$
$270$	23.6134	+	19.9960i	1.43707	+	1.21692i
$271$	20.4415	+	6.64186i	1.24173	+	0.403464i	0.854952	−	0.518707i	$-0.173586\pi$
$271$	20.4415	+	6.64186i	1.24173	+	0.403464i	0.386783	+	0.922171i	$0.373586\pi$
$272$	−1.00946	+	1.98118i	−0.0612077	+	0.120127i
$273$	5.11760	+	0.810549i	0.309731	+	0.0490566i
$274$	2.47078			0.149265
$275$	−11.6932	−	11.7588i	−0.705124	−	0.709084i
$276$	13.8855			0.835810
$277$	−13.5625	−	2.14809i	−0.814893	−	0.129066i	−0.264943	−	0.964264i	$-0.585353\pi$
$277$	−13.5625	−	2.14809i	−0.814893	−	0.129066i	−0.549950	+	0.835198i	$0.685353\pi$
$278$	3.41078	−	6.69403i	0.204565	−	0.401481i
$279$	−20.0030	−	6.49937i	−1.19755	−	0.389107i
$280$	−2.60134	−	2.20284i	−0.155460	−	0.131645i
$281$	5.82266	−	8.01420i	0.347351	−	0.478087i	−0.599220	−	0.800585i	$-0.704522\pi$
$281$	5.82266	−	8.01420i	0.347351	−	0.478087i	0.946570	+	0.322498i	$0.104522\pi$
$282$	12.8351	−	6.53983i	0.764322	−	0.389441i
$283$	−1.83534	−	0.935154i	−0.109100	−	0.0555891i	0.398589	−	0.917130i	$-0.369500\pi$
$283$	−1.83534	−	0.935154i	−0.109100	−	0.0555891i	−0.507689	+	0.861541i	$0.669500\pi$
$284$	−5.23010	−	7.19862i	−0.310350	−	0.427160i
$285$	29.0385	+	33.7107i	1.72009	+	1.99685i
$286$	1.04732	+	3.35100i	0.0619292	+	0.198149i
$287$	−2.70165	+	2.70165i	−0.159473	+	0.159473i
$288$	−1.14349	+	7.21970i	−0.0673807	+	0.425425i
$289$	11.4658	−	3.72548i	0.674461	−	0.219146i
$290$	−9.33880	+	3.91450i	−0.548393	+	0.229867i
$291$	18.2003	+	13.2233i	1.06692	+	0.775164i
$292$	−1.78438	−	11.2661i	−0.104423	−	0.659300i
$293$	−8.91767	−	17.5019i	−0.520976	−	1.02247i	−0.990234	−	0.139412i	$-0.955479\pi$
$293$	−8.91767	−	17.5019i	−0.520976	−	1.02247i	0.469259	−	0.883061i	$-0.344521\pi$
$294$	4.63970	+	14.2795i	0.270593	+	0.832799i
$295$	5.28353	+	8.54083i	0.307619	+	0.497266i
$296$			1.39189i			0.0809018i
$297$	−32.8154	+	32.0859i	−1.90414	+	1.86181i
$298$	−0.0235652	−	0.0235652i	−0.00136510	−	0.00136510i
$299$	3.70350	−	2.69075i	0.214179	−	0.155610i
$300$	−13.0674	−	9.32657i	−0.754448	−	0.538470i
$301$	4.27006	−	13.1419i	0.246122	−	0.757486i
$302$	20.9242	−	3.31407i	1.20405	−	0.190703i
$303$	−55.8524	+	8.84616i	−3.20864	+	0.508199i
$304$	−1.91500	+	5.89375i	−0.109833	+	0.338030i
$305$	−12.8640	+	3.14584i	−0.736592	+	0.180131i
$306$	−13.1492	+	9.55348i	−0.751692	+	0.546136i
$307$	−8.35315	−	8.35315i	−0.476740	−	0.476740i	0.427348	−	0.904087i	$-0.359448\pi$
$307$	−8.35315	−	8.35315i	−0.476740	−	0.476740i	−0.904087	+	0.427348i	$0.859448\pi$
$308$	3.61506	−	3.53470i	0.205987	−	0.201408i
$309$		−	10.3142i		−	0.586757i
$310$	6.26242	+	1.47555i	0.355681	+	0.0838059i
$311$	−4.29712	−	13.2252i	−0.243667	−	0.749931i	−0.995853	−	0.0909796i	$-0.971000\pi$
$311$	−4.29712	−	13.2252i	−0.243667	−	0.749931i	0.752185	−	0.658952i	$-0.229000\pi$
$312$	1.54307	+	3.02844i	0.0873591	+	0.171452i
$313$	4.72303	+	29.8201i	0.266962	+	1.68553i	0.648530	+	0.761189i	$0.275384\pi$
$313$	4.72303	+	29.8201i	0.266962	+	1.68553i	−0.381569	+	0.924341i	$0.624616\pi$
$314$	−1.58930	−	1.15470i	−0.0896895	−	0.0651633i
$315$	−9.63229	−	22.9797i	−0.542718	−	1.29476i
$316$	5.51553	−	1.79211i	0.310273	−	0.100814i
$317$	4.79669	−	30.2851i	0.269409	−	1.70098i	−0.367485	−	0.930029i	$-0.619781\pi$
$317$	4.79669	−	30.2851i	0.269409	−	1.70098i	0.636894	−	0.770951i	$-0.280219\pi$
$318$	8.63552	−	8.63552i	0.484256	−	0.484256i
$319$	−4.48040	−	14.3355i	−0.250854	−	0.802633i
$320$	0.166032	−	2.22990i	0.00928150	−	0.124655i
$321$	−31.1741	−	42.9074i	−1.73997	−	2.39486i
$322$	−5.87392	−	2.99291i	−0.327341	−	0.166788i
$323$	−12.2775	+	6.25570i	−0.683139	+	0.348076i
$324$	−13.2267	+	18.2050i	−0.734815	+	1.01139i
$325$	−5.29262	+	0.0446648i	−0.293581	+	0.00247756i
$326$	2.07071	+	0.672816i	0.114686	+	0.0372638i
$327$	2.75217	−	5.40143i	0.152195	−	0.298700i
$328$	−2.47546	−	0.392075i	−0.136685	−	0.0216487i
$329$	−6.83919			−0.377057
$330$	15.5917	−	17.9981i	0.858293	−	0.990765i
$331$	14.2522			0.783372			0.391686	−	0.920099i	$-0.371892\pi$
$331$	14.2522			0.783372			0.391686	+	0.920099i	$0.371892\pi$
$332$	1.26330	+	0.200087i	0.0693325	+	0.0109812i
$333$	−4.61903	+	9.06535i	−0.253121	+	0.496778i
$334$	−20.4020	−	6.62902i	−1.11635	−	0.362724i
$335$	−17.0423	+	1.41364i	−0.931121	+	0.0772353i
$336$	2.87706	−	3.95994i	0.156957	−	0.216032i
$337$	12.2410	−	6.23713i	0.666812	−	0.339758i	−0.0876027	−	0.996155i	$-0.527921\pi$
$337$	12.2410	−	6.23713i	0.666812	−	0.339758i	0.754415	+	0.656398i	$0.227921\pi$
$338$	−10.5847	−	5.39316i	−0.575730	−	0.293349i
$339$	7.52914	+	10.3630i	0.408927	+	0.562839i
$340$	3.76706	−	3.24496i	0.204297	−	0.175983i
$341$	−3.05077	+	9.04224i	−0.165208	+	0.489665i
$342$	−32.0310	+	32.0310i	−1.73204	+	1.73204i
$343$	2.78444	−	17.5803i	0.150346	−	0.949246i
$344$	8.62085	−	2.80109i	0.464805	−	0.151024i
$345$	−28.7354	−	11.7608i	−1.54706	−	0.633179i
$346$	−10.6736	−	7.75484i	−0.573818	−	0.416903i
$347$	−2.77431	−	17.5163i	−0.148933	−	0.940326i	−0.943072	−	0.332589i	$-0.892078\pi$
$347$	−2.77431	−	17.5163i	−0.148933	−	0.940326i	0.794139	−	0.607737i	$-0.207922\pi$
$348$	−6.60121	−	12.9556i	−0.353862	−	0.694494i
$349$	5.50175	+	16.9327i	0.294502	+	0.906384i	0.983388	+	0.181515i	$0.0581000\pi$
$349$	5.50175	+	16.9327i	0.294502	+	0.906384i	−0.688886	+	0.724870i	$0.741900\pi$
$350$	3.51757	+	6.76195i	0.188022	+	0.361441i
$351$			14.6482i			0.781865i
$352$	3.26975	+	0.555617i	0.174278	+	0.0296145i
$353$	12.3974	+	12.3974i	0.659845	+	0.659845i	0.955343	−	0.295499i	$-0.0954858\pi$
$353$	12.3974	+	12.3974i	0.659845	+	0.659845i	−0.295499	+	0.955343i	$0.595486\pi$
$354$	−11.6670	+	8.47655i	−0.620093	+	0.450524i
$355$	4.72634	+	19.3270i	0.250848	+	1.02577i
$356$	−3.26068	+	10.0353i	−0.172816	+	0.531872i
$357$	10.7496	−	1.70258i	0.568932	−	0.0901099i
$358$	13.3851	−	2.12000i	0.707426	−	0.112045i
$359$	−2.37480	+	7.30888i	−0.125337	+	0.385748i	−0.993962	−	0.109722i	$-0.965004\pi$
$359$	−2.37480	+	7.30888i	−0.125337	+	0.385748i	0.868625	+	0.495470i	$0.165004\pi$
$360$	8.48135	−	13.9723i	0.447006	−	0.736405i
$361$	−15.6978	+	11.4051i	−0.826200	+	0.600270i
$362$	12.1942	+	12.1942i	0.640915	+	0.640915i
$363$	24.4071	+	25.5297i	1.28104	+	1.33996i
$364$		−	1.61370i		−	0.0845810i
$365$	−5.84952	+	24.8260i	−0.306178	+	1.29945i
$366$	−5.87638	−	18.0856i	−0.307163	−	0.945351i
$367$	16.4293	+	32.2443i	0.857603	+	1.68314i	0.721464	+	0.692452i	$0.243469\pi$
$367$	16.4293	+	32.2443i	0.857603	+	1.68314i	0.136139	+	0.990690i	$0.456531\pi$
$368$	−0.676506	−	4.27129i	−0.0352653	−	0.222656i
$369$	−14.8215	−	10.7685i	−0.771579	−	0.560585i
$370$	1.17890	−	2.88044i	0.0612883	−	0.149747i
$371$	−5.51436	+	1.79172i	−0.286291	+	0.0930217i
$372$	−1.44526	+	9.12499i	−0.0749331	+	0.473109i
$373$	−11.5350	+	11.5350i	−0.597259	+	0.597259i	−0.939582	−	0.342323i	$-0.888786\pi$
$373$	−11.5350	+	11.5350i	−0.597259	+	0.597259i	0.342323	+	0.939582i	$0.388786\pi$
$374$	4.26737	+	6.01453i	0.220660	+	0.311004i
$375$	19.1429	+	30.3687i	0.988536	+	1.56823i
$376$	−2.63703	−	3.62956i	−0.135995	−	0.187181i
$377$	−4.27121	−	2.17629i	−0.219978	−	0.112085i
$378$	18.7957	−	9.57688i	0.966746	−	0.492582i
$379$	3.86753	−	5.32320i	0.198662	−	0.273434i	−0.698050	−	0.716049i	$-0.745949\pi$
$379$	3.86753	−	5.32320i	0.198662	−	0.273434i	0.896712	+	0.442614i	$0.145949\pi$
$380$	8.95489	−	10.5749i	0.459376	−	0.542479i
$381$	−51.8071	−	16.8332i	−2.65416	−	0.862389i
$382$	5.71697	−	11.2202i	0.292505	−	0.574074i
$383$	28.9091	+	4.57876i	1.47719	+	0.233963i	0.842454	−	0.538768i	$-0.181110\pi$
$383$	28.9091	+	4.57876i	1.47719	+	0.233963i	0.634733	+	0.772731i	$0.281110\pi$
$384$	3.21087			0.163854
$385$	−10.4750	+	4.25300i	−0.533856	+	0.216753i
$386$	3.83530			0.195212
$387$	65.4430	+	10.3652i	3.32665	+	0.526890i
$388$	3.18087	−	6.24280i	0.161484	−	0.316930i
$389$	−4.21993	−	1.37114i	−0.213959	−	0.0695195i	0.200076	−	0.979780i	$-0.435881\pi$
$389$	−4.21993	−	1.37114i	−0.213959	−	0.0695195i	−0.414035	+	0.910261i	$0.635881\pi$
$390$	−0.628267	−	7.57417i	−0.0318136	−	0.383533i
$391$	5.65199	−	7.77930i	0.285833	−	0.393416i
$392$	4.16644	−	2.12291i	0.210437	−	0.107223i
$393$	−27.9697	−	14.2513i	−1.41088	−	0.718881i
$394$	−6.15139	−	8.46666i	−0.309903	−	0.426544i
$395$	−12.9320	−	0.962884i	−0.650679	−	0.0484480i
$396$	19.4520	+	14.4695i	0.977501	+	0.727120i
$397$	6.59354	−	6.59354i	0.330920	−	0.330920i	−0.522016	−	0.852936i	$-0.674820\pi$
$397$	6.59354	−	6.59354i	0.330920	−	0.330920i	0.852936	+	0.522016i	$0.174820\pi$
$398$	−1.42471	+	8.99529i	−0.0714145	+	0.450893i
$399$	28.8485	−	9.37344i	1.44423	−	0.469259i
$400$	−2.23228	+	4.47403i	−0.111614	+	0.223701i
$401$	−7.12541	−	5.17691i	−0.355826	−	0.258523i	0.395483	−	0.918473i	$-0.370577\pi$
$401$	−7.12541	−	5.17691i	−0.355826	−	0.258523i	−0.751309	+	0.659951i	$0.770577\pi$
$402$	−3.84138	−	24.2535i	−0.191591	−	1.20966i
$403$	1.38278	+	2.71385i	0.0688811	+	0.135187i
$404$	5.44229	+	16.7496i	0.270764	+	0.833326i
$405$	42.7912	−	26.4715i	2.12631	−	1.31538i
$406$			6.90338i			0.342609i
$407$	4.08940	+	2.14188i	0.202704	+	0.106169i
$408$	5.04837	+	5.04837i	0.249932	+	0.249932i
$409$	14.0728	−	10.2245i	0.695853	−	0.505567i	−0.182726	−	0.983164i	$-0.558492\pi$
$409$	14.0728	−	10.2245i	0.695853	−	0.505567i	0.878579	+	0.477597i	$0.158492\pi$
$410$	4.79077	+	2.90805i	0.236599	+	0.143618i
$411$	2.45154	−	7.54507i	0.120926	−	0.372171i
$412$	−3.17274	+	0.502512i	−0.156310	+	0.0247570i
$413$	6.76247	−	1.07107i	0.332759	−	0.0527039i
$414$	9.76834	−	30.0639i	0.480088	−	1.47756i
$415$	−2.44486	−	1.48406i	−0.120014	−	0.0728497i
$416$	0.856394	−	0.622206i	0.0419882	−	0.0305062i
$417$	−17.0575	−	17.0575i	−0.835309	−	0.835309i
$418$	14.3691	+	14.6958i	0.702818	+	0.718796i
$419$		−	16.4015i		−	0.801265i	−0.916239	−	0.400632i	$-0.868790\pi$
$419$		−	16.4015i		−	0.801265i	0.916239	−	0.400632i	$-0.131210\pi$
$420$	−9.30793	+	5.75807i	−0.454181	+	0.280965i
$421$	8.15001	+	25.0832i	0.397207	+	1.22248i	0.927229	+	0.374494i	$0.122184\pi$
$421$	8.15001	+	25.0832i	0.397207	+	1.22248i	−0.530022	+	0.847984i	$0.677816\pi$
$422$	11.3831	+	22.3406i	0.554121	+	1.08752i
$423$	−5.13013	−	32.3904i	−0.249436	−	1.57487i
$424$	−3.07708	−	2.23563i	−0.149436	−	0.108572i
$425$	−10.5442	+	3.52465i	−0.511467	+	0.170971i
$426$	−27.1720	+	8.82870i	−1.31649	+	0.427752i
$427$	−1.41236	+	8.91727i	−0.0683488	+	0.431537i
$428$	−11.6798	+	11.6798i	−0.564566	+	0.564566i
$429$	11.2722	+	0.126690i	0.544226	+	0.00611667i
$430$	−20.2129	−	1.50500i	−0.974752	−	0.0725776i
$431$	−5.58501	−	7.68711i	−0.269020	−	0.370275i	0.653038	−	0.757325i	$-0.273494\pi$
$431$	−5.58501	−	7.68711i	−0.269020	−	0.370275i	−0.922059	+	0.387050i	$0.873494\pi$
$432$	12.3296	+	6.28227i	0.593210	+	0.302256i
$433$	−22.2230	+	11.3232i	−1.06797	+	0.544158i	−0.897414	−	0.441190i	$-0.854557\pi$
$433$	−22.2230	+	11.3232i	−1.06797	+	0.544158i	−0.170557	+	0.985348i	$0.554557\pi$
$434$	2.57820	−	3.54858i	0.123757	−	0.170338i
$435$	2.68771	+	32.4021i	0.128866	+	1.55356i
$436$	−1.79561	−	0.583428i	−0.0859940	−	0.0279411i
$437$	12.1667	−	23.8784i	0.582011	−	1.14226i
$438$	−36.1741	−	5.72941i	−1.72846	−	0.273762i
$439$	1.69115			0.0807143			0.0403571	−	0.999185i	$-0.487150\pi$
$439$	1.69115			0.0807143			0.0403571	+	0.999185i	$0.487150\pi$
$440$	−6.29599	−	3.91924i	−0.300150	−	0.186843i
$441$	34.1809			1.62766
$442$	2.32477	+	0.368207i	0.110578	+	0.0175138i
$443$	9.21964	−	18.0946i	0.438038	−	0.859698i	−0.561444	−	0.827515i	$-0.689754\pi$
$443$	9.21964	−	18.0946i	0.438038	−	0.859698i	0.999482	−	0.0321835i	$-0.0102461\pi$
$444$	4.25044	+	1.38105i	0.201717	+	0.0655418i
$445$	15.2476	−	18.0059i	0.722804	−	0.853561i
$446$	2.93087	−	4.03399i	0.138781	−	0.191015i
$447$	−0.0953432	+	0.0485798i	−0.00450958	+	0.00229775i
$448$	−1.35828	−	0.692077i	−0.0641726	−	0.0326976i
$449$	24.7166	+	34.0195i	1.16645	+	1.60548i	0.683806	+	0.729664i	$0.260323\pi$
$449$	24.7166	+	34.0195i	1.16645	+	1.60548i	0.482643	+	0.875817i	$0.339677\pi$
$450$	−29.3860	+	21.7314i	−1.38527	+	1.02443i
$451$	−4.96125	+	6.66964i	−0.233616	+	0.314061i
$452$	2.82091	−	2.82091i	0.132684	−	0.132684i
$453$	10.6410	−	67.1849i	0.499960	−	3.15662i
$454$	−1.94088	+	0.630630i	−0.0910900	+	0.0295969i
$455$	−1.36678	+	3.33948i	−0.0640755	+	0.156557i
$456$	16.0978	+	11.6957i	0.753848	+	0.547703i
$457$	1.58324	+	9.99618i	0.0740608	+	0.467602i	0.996648	+	0.0818123i	$0.0260708\pi$
$457$	1.58324	+	9.99618i	0.0740608	+	0.467602i	−0.922587	+	0.385789i	$0.873929\pi$
$458$	−0.691961	−	1.35805i	−0.0323332	−	0.0634575i
$459$	9.50814	+	29.2630i	0.443802	+	1.36588i
$460$	−2.21771	+	9.41221i	−0.103401	+	0.438846i
$461$		−	27.4513i		−	1.27854i	−0.768984	−	0.639268i	$-0.779237\pi$
$461$		−	27.4513i		−	1.27854i	0.768984	−	0.639268i	$-0.220763\pi$
$462$	−7.20708	−	14.5466i	−0.335304	−	0.676768i
$463$	12.8080	+	12.8080i	0.595237	+	0.595237i	0.939041	−	0.343804i	$-0.111716\pi$
$463$	12.8080	+	12.8080i	0.595237	+	0.595237i	−0.343804	+	0.939041i	$0.611716\pi$
$464$	−3.66363	+	2.66178i	−0.170080	+	0.123570i
$465$	10.7196	−	17.6596i	0.497109	−	0.818945i
$466$	6.85697	−	21.1036i	0.317643	−	0.977604i
$467$	−21.5674	+	3.41594i	−0.998021	+	0.158071i	−0.634011	−	0.773324i	$-0.718593\pi$
$467$	−21.5674	+	3.41594i	−0.998021	+	0.158071i	−0.364010	+	0.931395i	$0.618593\pi$
$468$	7.64249	−	1.21045i	0.353274	−	0.0559532i
$469$	−3.60265	+	11.0878i	−0.166355	+	0.511988i
$470$	2.38303	+	9.74472i	0.109921	+	0.449490i
$471$	−5.10305	+	3.70758i	−0.235136	+	0.170836i
$472$	3.17587	+	3.17587i	0.146181	+	0.146181i
$473$	5.03639	−	29.6387i	0.231573	−	1.36279i
$474$		−	18.6210i		−	0.855293i
$475$	−27.4884	+	14.2995i	−1.26125	+	0.656106i
$476$	−1.04745	−	3.22372i	−0.0480098	−	0.147759i
$477$	−12.6220	−	24.7720i	−0.577920	−	1.13423i
$478$	3.87708	+	24.4789i	0.177334	+	1.11964i
$479$	−5.27636	−	3.83350i	−0.241083	−	0.175157i	0.460683	−	0.887565i	$-0.347605\pi$
$479$	−5.27636	−	3.83350i	−0.241083	−	0.175157i	−0.701766	+	0.712408i	$0.747605\pi$
$480$	−6.64474	−	2.71955i	−0.303289	−	0.124130i
$481$	1.40128	−	0.455305i	0.0638931	−	0.0207601i
$482$	−0.00880064	+	0.0555650i	−0.000400858	+	0.00253092i
$483$	−14.9677	+	14.9677i	−0.681054	+	0.681054i
$484$	6.66402	−	8.75162i	0.302910	−	0.397801i
$485$	−11.8702	+	10.2250i	−0.538997	+	0.464294i
$486$	18.0681	+	24.8685i	0.819583	+	1.12806i
$487$	−2.61310	−	1.33144i	−0.118411	−	0.0603334i	0.393782	−	0.919204i	$-0.371167\pi$
$487$	−2.61310	−	1.33144i	−0.118411	−	0.0603334i	−0.512193	+	0.858871i	$0.671167\pi$
$488$	−5.27698	+	2.68875i	−0.238878	+	0.121714i
$489$	4.10918	−	5.65580i	0.185824	−	0.255764i
$490$	−10.4203	+	0.864351i	−0.470742	+	0.0390474i
$491$	12.6664	+	4.11555i	0.571625	+	0.185732i	0.580545	−	0.814228i	$-0.302839\pi$
$491$	12.6664	+	4.11555i	0.571625	+	0.185732i	−0.00892018	+	0.999960i	$0.502839\pi$
$492$	−3.65348	+	7.17035i	−0.164711	+	0.323264i
$493$	−9.94529	−	1.57518i	−0.447913	−	0.0709425i
$494$	6.55996			0.295147
$495$	−27.9996	−	46.4194i	−1.25849	−	2.08640i
$496$	2.87733			0.129196
$497$	13.3974	+	2.12193i	0.600954	+	0.0951818i
$498$	1.86447	−	3.65923i	0.0835490	−	0.163974i
$499$	22.2265	+	7.22182i	0.994994	+	0.323293i	0.760863	−	0.648912i	$-0.224776\pi$
$499$	22.2265	+	7.22182i	0.994994	+	0.323293i	0.234130	+	0.972205i	$0.424776\pi$
$500$	8.40901	−	7.36808i	0.376062	−	0.329511i
$501$	−40.4864	+	55.7247i	−1.80880	+	2.48960i
$502$	−7.50572	+	3.82436i	−0.334997	+	0.170689i
$503$	20.7030	+	10.5487i	0.923103	+	0.470344i	0.849883	−	0.526972i	$-0.176673\pi$
$503$	20.7030	+	10.5487i	0.923103	+	0.470344i	0.0732197	+	0.997316i	$0.476673\pi$
$504$	−6.54977	−	9.01498i	−0.291750	−	0.401559i
$505$	2.92410	−	39.2721i	0.130121	−	1.74758i
$506$	−13.5902	−	4.58521i	−0.604158	−	0.203837i
$507$	−26.9714	+	26.9714i	−1.19784	+	1.19784i
$508$	−2.65395	+	16.7564i	−0.117750	+	0.743444i
$509$	−21.9064	+	7.11784i	−0.970986	+	0.315493i	−0.751214	−	0.660059i	$-0.770531\pi$
$509$	−21.9064	+	7.11784i	−0.970986	+	0.315493i	−0.219772	+	0.975551i	$0.570531\pi$
$510$	−6.17147	−	14.7232i	−0.273277	−	0.651956i
$511$	14.0676	+	10.2207i	0.622314	+	0.452138i
$512$	−0.156434	−	0.987688i	−0.00691349	−	0.0436501i
$513$	38.9316	+	76.4075i	1.71887	+	3.37347i
$514$	−3.24457	−	9.98577i	−0.143112	−	0.440454i
$515$	6.99144	+	1.64733i	0.308080	+	0.0725899i
$516$		−	29.1050i		−	1.28127i
$517$	−14.7217	+	2.16238i	−0.647460	+	0.0951014i
$518$	−1.50037	−	1.50037i	−0.0659223	−	0.0659223i
$519$	−34.2716	+	24.8998i	−1.50436	+	1.09298i
$520$	−2.29926	+	0.562275i	−0.100829	+	0.0246574i
$521$	−9.62530	+	29.6236i	−0.421692	+	1.29783i	0.484435	+	0.874827i	$0.339025\pi$
$521$	−9.62530	+	29.6236i	−0.421692	+	1.29783i	−0.906127	+	0.423007i	$0.860975\pi$
$522$	−32.6944	+	5.17828i	−1.43099	+	0.226647i
$523$	5.13797	−	0.813774i	0.224668	−	0.0355838i	−0.0430856	−	0.999071i	$-0.513719\pi$
$523$	5.13797	−	0.813774i	0.224668	−	0.0355838i	0.267753	+	0.963488i	$0.413719\pi$
$524$	−3.02111	+	9.29801i	−0.131978	+	0.406185i
$525$	24.1393	−	4.03239i	1.05352	−	0.175988i
$526$	−3.67174	+	2.66768i	−0.160096	+	0.116316i
$527$	4.52395	+	4.52395i	0.197067	+	0.197067i
$528$	4.94099	−	9.43362i	0.215029	−	0.410546i
$529$		−	4.29842i		−	0.186888i
$530$	4.47432	+	7.23275i	0.194352	+	0.314170i
$531$	10.1452	+	31.2236i	0.440263	+	1.35499i
$532$	−4.28884	−	8.41733i	−0.185945	−	0.364938i
$533$	0.415035	+	2.62043i	0.0179772	+	0.113503i
$534$	27.4098	+	19.9144i	1.18614	+	0.861781i
$535$	34.0634	−	14.2782i	1.47269	−	0.617301i
$536$	−7.27342	+	2.36328i	−0.314164	+	0.102078i
$537$	6.80704	−	42.9779i	0.293745	−	1.85463i
$538$	18.3155	−	18.3155i	0.789636	−	0.789636i
$539$	0.174297	−	15.5079i	0.00750749	−	0.667973i
$540$	−20.1946	−	23.4438i	−0.869037	−	1.00886i
$541$	7.63567	+	10.5096i	0.328283	+	0.451843i	0.940974	−	0.338480i	$-0.109913\pi$
$541$	7.63567	+	10.5096i	0.328283	+	0.451843i	−0.612690	+	0.790323i	$0.709913\pi$
$542$	−19.1509	−	9.75785i	−0.822600	−	0.419135i
$543$	49.3371	−	25.1385i	2.11726	−	1.07880i
$544$	1.30696	−	1.79888i	0.0560354	−	0.0771262i
$545$	3.22177	+	2.72822i	0.138005	+	0.116864i
$546$	−4.92780	−	1.60114i	−0.210890	−	0.0685224i
$547$	2.13624	−	4.19261i	0.0913391	−	0.179263i	−0.840817	−	0.541319i	$-0.817925\pi$
$547$	2.13624	−	4.19261i	0.0913391	−	0.179263i	0.932156	+	0.362056i	$0.117925\pi$
$548$	−2.44036	−	0.386515i	−0.104247	−	0.0165111i
$549$	−43.2916			−1.84764
$550$	9.70971	+	13.4433i	0.414024	+	0.573223i
$551$	−28.0634			−1.19554
$552$	−13.7146	−	2.17217i	−0.583731	−	0.0924538i
$553$	−4.01362	+	7.87716i	−0.170676	+	0.334971i
$554$	13.0595	+	4.24329i	0.554845	+	0.180280i
$555$	−7.62634	−	6.45806i	−0.323720	−	0.274129i
$556$	−4.41597	+	6.07806i	−0.187279	+	0.257767i
$557$	−29.1897	+	14.8729i	−1.23681	+	0.630185i	−0.945243	−	0.326366i	$-0.894176\pi$
$557$	−29.1897	+	14.8729i	−1.23681	+	0.630185i	−0.291564	+	0.956551i	$0.594176\pi$
$558$	18.7400	+	9.54851i	0.793328	+	0.404221i
$559$	−5.63999	−	7.76278i	−0.238546	−	0.328331i
$560$	2.22471	+	2.58266i	0.0940112	+	0.109137i
$561$	22.6008	−	7.06365i	0.954209	−	0.298228i
$562$	−7.00467	+	7.00467i	−0.295474	+	0.295474i
$563$	−0.520168	+	3.28421i	−0.0219225	+	0.138413i	−0.996222	−	0.0868434i	$-0.972322\pi$
$563$	−0.520168	+	3.28421i	−0.0219225	+	0.138413i	0.974299	+	0.225257i	$0.0723220\pi$
$564$	−13.7002	+	4.45146i	−0.576882	+	0.187440i
$565$	−8.22698	+	3.44847i	−0.346112	+	0.145078i
$566$	1.66646	+	1.21075i	0.0700464	+	0.0508917i
$567$	−5.36627	−	33.8813i	−0.225362	−	1.42288i
$568$	4.03960	+	7.92816i	0.169498	+	0.332658i
$569$	−2.18501	−	6.72478i	−0.0916005	−	0.281917i	0.894752	−	0.446563i	$-0.147352\pi$
$569$	−2.18501	−	6.72478i	−0.0916005	−	0.281917i	−0.986353	+	0.164645i	$0.947352\pi$
$570$	−23.4075	−	37.8383i	−0.980432	−	1.58487i
$571$			24.2620i			1.01533i	0.861553	+	0.507667i	$0.169492\pi$
$571$			24.2620i			1.01533i	−0.861553	+	0.507667i	$0.830508\pi$
$572$	−0.510212	−	3.47358i	−0.0213330	−	0.145238i
$573$	−28.5908	−	28.5908i	−1.19440	−	1.19440i
$574$	3.09102	−	2.24576i	0.129017	−	0.0937362i
$575$	12.5614	−	17.5997i	0.523847	−	0.733959i
$576$	2.25882	−	6.95193i	0.0941175	−	0.289664i
$577$	6.36086	−	1.00746i	0.264806	−	0.0419412i	−0.0226195	−	0.999744i	$-0.507201\pi$
$577$	6.36086	−	1.00746i	0.264806	−	0.0419412i	0.287426	+	0.957803i	$0.407201\pi$
$578$	−11.9075	+	1.88596i	−0.495286	+	0.0784455i
$579$	3.80544	−	11.7119i	0.158149	−	0.486731i
$580$	9.83618	−	2.40540i	0.408425	−	0.0998787i
$581$	−1.57744	+	1.14607i	−0.0654430	+	0.0475471i
$582$	−15.9077	−	15.9077i	−0.659394	−	0.659394i
$583$	−11.3034	+	5.60028i	−0.468141	+	0.231940i
$584$			11.4066i			0.472007i
$585$	−16.8410	−	3.96808i	−0.696289	−	0.164060i
$586$	6.06998	+	18.6815i	0.250748	+	0.771724i
$587$	2.50306	+	4.91253i	0.103312	+	0.202762i	0.936876	−	0.349661i	$-0.113703\pi$
$587$	2.50306	+	4.91253i	0.103312	+	0.202762i	−0.833564	+	0.552423i	$0.813703\pi$
$588$	−2.34877	−	14.8295i	−0.0968615	−	0.611560i
$589$	14.4256	+	10.4808i	0.594395	+	0.431853i
$590$	−3.88240	−	9.26221i	−0.159836	−	0.381319i
$591$	−31.9583	+	10.3839i	−1.31459	+	0.427136i
$592$	0.217739	−	1.37475i	0.00894903	−	0.0565019i
$593$	−11.4901	+	11.4901i	−0.471841	+	0.471841i	−0.902510	−	0.430669i	$-0.858278\pi$
$593$	−11.4901	+	11.4901i	−0.471841	+	0.471841i	0.430669	+	0.902510i	$0.358278\pi$
$594$	37.4307	−	26.5574i	1.53580	−	1.08967i
$595$	−0.562787	+	7.55850i	−0.0230720	+	0.309868i
$596$	0.0195887	+	0.0269615i	0.000802383	+	0.00110439i
$597$	26.0555	+	13.2759i	1.06638	+	0.543348i
$598$	−4.07883	+	2.07827i	−0.166796	+	0.0849867i
$599$	24.2507	−	33.3782i	0.990856	−	1.36380i	0.0600854	−	0.998193i	$-0.480863\pi$
$599$	24.2507	−	33.3782i	0.990856	−	1.36380i	0.930771	−	0.365603i	$-0.119137\pi$
$600$	11.4475	+	11.2559i	0.467344	+	0.459522i
$601$	42.1453	+	13.6938i	1.71914	+	0.558583i	0.991812	−	0.127705i	$-0.0407609\pi$
$601$	42.1453	+	13.6938i	1.71914	+	0.558583i	0.727330	+	0.686288i	$0.240761\pi$
$602$	−6.27334	+	12.3121i	−0.255682	+	0.501804i
$603$	−55.2143	−	8.74509i	−2.24850	−	0.356127i
$604$	−21.1850			−0.862006
$605$	−21.2033	+	12.4667i	−0.862037	+	0.506845i
$606$	56.5487			2.29713
$607$	−16.6706	−	2.64036i	−0.676638	−	0.107169i	−0.191348	−	0.981522i	$-0.561286\pi$
$607$	−16.6706	−	2.64036i	−0.676638	−	0.107169i	−0.485290	+	0.874353i	$0.661286\pi$
$608$	2.81341	−	5.52162i	0.114099	−	0.223931i
$609$	21.0810	+	6.84963i	0.854245	+	0.277561i
$610$	13.1978	−	1.09474i	0.534362	−	0.0443246i
$611$	−2.79146	+	3.84212i	−0.112930	+	0.155435i
$612$	14.4818	−	7.37886i	0.585394	−	0.298273i
$613$	−21.6696	−	11.0412i	−0.875225	−	0.445949i	−0.0421512	−	0.999111i	$-0.513421\pi$
$613$	−21.6696	−	11.0412i	−0.875225	−	0.445949i	−0.833074	+	0.553162i	$0.813421\pi$
$614$	6.94359	+	9.55703i	0.280221	+	0.385691i
$615$	13.6338	−	11.7443i	0.549770	−	0.473574i
$616$	−4.12350	+	2.92567i	−0.166141	+	0.117878i
$617$	−2.46606	+	2.46606i	−0.0992799	+	0.0992799i	−0.755002	−	0.655722i	$-0.772364\pi$
$617$	−2.46606	+	2.46606i	−0.0992799	+	0.0992799i	0.655722	+	0.755002i	$0.272364\pi$
$618$	−1.61350	+	10.1873i	−0.0649046	+	0.409791i
$619$	−28.7652	+	9.34637i	−1.15617	+	0.375662i	−0.823464	−	0.567369i	$-0.807962\pi$
$619$	−28.7652	+	9.34637i	−1.15617	+	0.375662i	−0.332706	+	0.943031i	$0.607962\pi$
$620$	−5.95449	−	2.43705i	−0.239138	−	0.0978741i
$621$	−48.4135	−	35.1745i	−1.94277	−	1.41150i
$622$	2.17534	+	13.7346i	0.0872233	+	0.550706i
$623$	−7.30265	−	14.3323i	−0.292574	−	0.574210i
$624$	−1.05032	−	3.23255i	−0.0420464	−	0.129406i
$625$	−23.6426	+	8.12560i	−0.945706	+	0.325024i
$626$		−	30.1918i		−	1.20671i
$627$	59.1342	−	29.2980i	2.36159	−	1.17005i
$628$	1.38910	+	1.38910i	0.0554312	+	0.0554312i
$629$	2.50383	−	1.81914i	0.0998344	−	0.0725339i
$630$	5.91889	+	24.2036i	0.235814	+	0.964294i
$631$	9.75833	−	30.0330i	0.388473	−	1.19560i	−0.545456	−	0.838139i	$-0.683644\pi$
$631$	9.75833	−	30.0330i	0.388473	−	1.19560i	0.933929	−	0.357458i	$-0.116356\pi$
$632$	−5.72797	+	0.907222i	−0.227847	+	0.0360874i
$633$	79.5165	−	12.5942i	3.16050	−	0.500573i
$634$	−9.47527	+	29.1619i	−0.376311	+	1.15817i
$635$	19.6846	−	32.4286i	0.781158	−	1.28689i
$636$	−9.88010	+	7.17831i	−0.391771	+	0.284639i
$637$	−3.50014	−	3.50014i	−0.138681	−	0.138681i
$638$	2.18268	+	14.8599i	0.0864129	+	0.588308i
$639$			65.0416i			2.57300i
$640$	−0.512821	+	2.17647i	−0.0202710	+	0.0860325i
$641$	−1.51513	−	4.66309i	−0.0598440	−	0.184181i	0.916665	−	0.399655i	$-0.130870\pi$
$641$	−1.51513	−	4.66309i	−0.0598440	−	0.184181i	−0.976509	+	0.215474i	$0.930870\pi$
$642$	24.0781	+	47.2558i	0.950285	+	1.86504i
$643$	2.56190	+	16.1752i	0.101031	+	0.637888i	0.985290	+	0.170890i	$0.0546643\pi$
$643$	2.56190	+	16.1752i	0.101031	+	0.637888i	−0.884259	+	0.466998i	$0.845336\pi$
$644$	5.33341	+	3.87495i	0.210166	+	0.152694i
$645$	−24.6514	+	60.2312i	−0.970646	+	2.37160i
$646$	13.1050	−	4.25806i	0.515608	−	0.167531i
$647$	6.72843	−	42.4816i	0.264522	−	1.67012i	−0.395185	−	0.918602i	$-0.629319\pi$
$647$	6.72843	−	42.4816i	0.264522	−	1.67012i	0.659707	−	0.751523i	$-0.270681\pi$
$648$	15.9117	−	15.9117i	0.625071	−	0.625071i
$649$	14.2179	−	4.44366i	0.558102	−	0.174429i
$650$	5.23444	+	0.783833i	0.205312	+	0.0307444i
$651$	−8.27826	−	11.3940i	−0.324451	−	0.446568i
$652$	−1.93997	−	0.988463i	−0.0759750	−	0.0387112i
$653$	−3.03452	+	1.54616i	−0.118750	+	0.0605061i	−0.512356	−	0.858773i	$-0.671227\pi$
$653$	−3.03452	+	1.54616i	−0.118750	+	0.0605061i	0.393606	+	0.919279i	$0.371227\pi$
$654$	−3.56325	+	4.90440i	−0.139334	+	0.191777i
$655$	14.1273	−	16.6829i	0.551998	−	0.651856i
$656$	2.38365	+	0.774496i	0.0930660	+	0.0302390i
$657$	−37.8530	+	74.2907i	−1.47679	+	2.89836i
$658$	6.75499	+	1.06989i	0.263337	+	0.0417085i
$659$	−1.70430			−0.0663902			−0.0331951	−	0.999449i	$-0.510568\pi$
$659$	−1.70430			−0.0663902			−0.0331951	+	0.999449i	$0.510568\pi$
$660$	−18.2152	+	15.3375i	−0.709027	+	0.597010i
$661$	−3.81557			−0.148409			−0.0742043	−	0.997243i	$-0.523642\pi$
$661$	−3.81557			−0.148409			−0.0742043	+	0.997243i	$0.523642\pi$
$662$	−14.0767	−	2.22953i	−0.547108	−	0.0866533i
$663$	3.43107	−	6.73385i	0.133252	−	0.261521i
$664$	−1.21644	−	0.395247i	−0.0472072	−	0.0153386i
$665$	1.74622	+	21.0518i	0.0677156	+	0.816354i
$666$	5.98029	−	8.23116i	0.231732	−	0.318951i
$667$	17.4491	−	8.89078i	0.675634	−	0.344252i
$668$	19.1138	+	9.73899i	0.739537	+	0.376813i
$669$	−9.41064	−	12.9526i	−0.363836	−	0.500778i
$670$	17.0536	+	1.26977i	0.658839	+	0.0490555i
$671$	−0.220754	+	19.6414i	−0.00852212	+	0.758249i
$672$	−3.46111	+	3.46111i	−0.133515	+	0.133515i
$673$	4.12434	−	26.0401i	0.158982	−	1.00377i	−0.771179	−	0.636619i	$-0.780333\pi$
$673$	4.12434	−	26.0401i	0.158982	−	1.00377i	0.930161	−	0.367153i	$-0.119667\pi$
$674$	−13.0660	+	4.24541i	−0.503285	+	0.163527i
$675$	21.9352	+	65.6203i	0.844288	+	2.52572i
$676$	9.61068	+	6.98256i	0.369641	+	0.268560i
$677$	−1.85111	−	11.6875i	−0.0711440	−	0.449185i	−0.997386	−	0.0722563i	$-0.976980\pi$
$677$	−1.85111	−	11.6875i	−0.0711440	−	0.449185i	0.926242	−	0.376929i	$-0.123020\pi$
$678$	−5.81532	−	11.4132i	−0.223336	−	0.438321i
$679$	3.30057	+	10.1581i	0.126664	+	0.389832i
$680$	−4.22830	+	2.61571i	−0.162148	+	0.100308i
$681$			6.55262i			0.251097i
$682$	4.42773	−	8.45367i	0.169546	−	0.323708i
$683$	−19.2371	−	19.2371i	−0.736087	−	0.736087i	0.235731	−	0.971818i	$-0.424252\pi$
$683$	−19.2371	−	19.2371i	−0.736087	−	0.736087i	−0.971818	+	0.235731i	$0.924252\pi$
$684$	36.6474	−	26.6259i	1.40125	−	1.01807i
$685$	4.72283	+	2.86681i	0.180450	+	0.109535i
$686$	−5.50033	+	16.9283i	−0.210003	+	0.646324i
$687$	−4.83368	+	0.765580i	−0.184416	+	0.0292087i
$688$	−8.95290	+	1.41800i	−0.341326	+	0.0540608i
$689$	−1.24417	+	3.82916i	−0.0473990	+	0.145879i
$690$	26.5418	+	16.1112i	1.01043	+	0.613342i
$691$	−2.86279	+	2.07994i	−0.108906	+	0.0791246i	−0.640905	−	0.767620i	$-0.721441\pi$
$691$	−2.86279	+	2.07994i	−0.108906	+	0.0791246i	0.531999	+	0.846745i	$0.321441\pi$
$692$	9.32909	+	9.32909i	0.354639	+	0.354639i
$693$	−36.5652	+	5.37084i	−1.38900	+	0.204021i
$694$			17.7347i			0.673199i
$695$	14.2866	−	8.83799i	0.541922	−	0.335244i
$696$	4.49324	+	13.8288i	0.170316	+	0.524178i
$697$	2.53004	+	4.96548i	0.0958320	+	0.188081i
$698$	−2.78517	−	17.5849i	−0.105420	−	0.665596i
$699$	−57.6408	−	41.8785i	−2.18018	−	1.58399i
$700$	−2.41647	−	7.22897i	−0.0913338	−	0.273229i
$701$	37.5991	−	12.2167i	1.42010	−	0.461418i	0.504466	−	0.863432i	$-0.331689\pi$
$701$	37.5991	−	12.2167i	1.42010	−	0.461418i	0.915634	+	0.402013i	$0.131689\pi$
$702$	2.29149	−	14.4679i	0.0864867	−	0.546055i
$703$	6.09923	−	6.09923i	0.230037	−	0.230037i
$704$	−3.14258	−	1.06028i	−0.118440	−	0.0399607i
$705$	32.1221	+	2.39173i	1.20979	+	0.0900779i
$706$	−10.3053	−	14.1841i	−0.387847	−	0.533826i
$707$	−23.9215	−	12.1886i	−0.899660	−	0.458400i
$708$	12.8494	−	6.54708i	0.482908	−	0.246054i
$709$	23.7291	−	32.6603i	0.891166	−	1.22658i	−0.0820353	−	0.996629i	$-0.526142\pi$
$709$	23.7291	−	32.6603i	0.891166	−	1.22658i	0.973201	−	0.229955i	$-0.0738580\pi$
$710$	−1.64474	−	19.8284i	−0.0617260	−	0.744147i
$711$	−40.3169	−	13.0997i	−1.51200	−	0.491279i
$712$	4.79041	−	9.40171i	0.179528	−	0.352344i
$713$	−12.2899	−	1.94653i	−0.460261	−	0.0728982i
$714$	−10.8836			−0.407310
$715$	−1.88620	+	7.62054i	−0.0705398	+	0.284992i
$716$	−13.5520			−0.506461
$717$	78.5987	+	12.4488i	2.93532	+	0.464910i
$718$	3.48892	−	6.84740i	0.130205	−	0.255543i
$719$	6.32991	+	2.05671i	0.236066	+	0.0767024i	0.424661	−	0.905353i	$-0.360393\pi$
$719$	6.32991	+	2.05671i	0.236066	+	0.0767024i	−0.188595	+	0.982055i	$0.560393\pi$
$720$	−10.5627	+	12.4735i	−0.393648	+	0.464860i
$721$	2.87833	−	3.96168i	0.107195	−	0.147541i
$722$	17.2887	−	8.80903i	0.643418	−	0.327838i
$723$	0.160948	+	0.0820071i	0.00598572	+	0.00304988i
$724$	−10.1365	−	13.9517i	−0.376720	−	0.518511i
$725$	−22.3928	−	3.35322i	−0.831648	−	0.124535i
$726$	−20.1129	−	29.0335i	−0.746459	−	1.07754i
$727$	13.3487	−	13.3487i	0.495074	−	0.495074i	−0.414826	−	0.909901i	$-0.636158\pi$
$727$	13.3487	−	13.3487i	0.495074	−	0.495074i	0.909901	+	0.414826i	$0.136158\pi$
$728$	−0.252439	+	1.59384i	−0.00935600	+	0.0590715i
$729$	29.6653	−	9.63884i	1.09871	−	0.356994i
$730$	9.66115	−	23.6053i	0.357575	−	0.873671i
$731$	−16.3059	−	11.8469i	−0.603096	−	0.438175i
$732$	2.97481	+	18.7822i	0.109952	+	0.694211i
$733$	−12.6624	−	24.8515i	−0.467698	−	0.917909i	−0.997559	−	0.0698250i	$-0.977756\pi$
$733$	−12.6624	−	24.8515i	−0.467698	−	0.917909i	0.529861	−	0.848084i	$-0.322244\pi$
$734$	−11.1829	−	34.4175i	−0.412769	−	1.27037i
$735$	−7.69969	+	32.6783i	−0.284007	+	1.20536i
$736$			4.32453i			0.159404i
$737$	−4.24920	+	25.0062i	−0.156521	+	0.921115i
$738$	12.9545	+	12.9545i	0.476862	+	0.476862i
$739$	8.88327	−	6.45407i	0.326776	−	0.237417i	−0.412285	−	0.911055i	$-0.635269\pi$
$739$	8.88327	−	6.45407i	0.326776	−	0.237417i	0.739061	+	0.673638i	$0.235269\pi$
$740$	−1.61499	+	2.66056i	−0.0593682	+	0.0978041i
$741$	6.50889	−	20.0323i	0.239110	−	0.735905i
$742$	5.72675	−	0.907029i	0.210236	−	0.0332981i
$743$	−23.8652	+	3.77987i	−0.875527	+	0.138670i	−0.577994	−	0.816041i	$-0.696164\pi$
$743$	−23.8652	+	3.77987i	−0.875527	+	0.138670i	−0.297534	+	0.954711i	$0.596164\pi$
$744$	2.85493	−	8.78656i	0.104667	−	0.322131i
$745$	−0.0177019	−	0.0723867i	−0.000648546	−	0.00265204i
$746$	13.1974	−	9.58850i	0.483193	−	0.351060i
$747$	−6.61105	−	6.61105i	−0.241886	−	0.241886i
$748$	−3.27395	−	6.60805i	−0.119708	−	0.241614i
$749$		−	25.1802i		−	0.920065i
$750$	−14.1565	−	32.9895i	−0.516923	−	1.20460i
$751$	−15.1449	−	46.6112i	−0.552645	−	1.70087i	−0.702082	−	0.712096i	$-0.747746\pi$
$751$	−15.1449	−	46.6112i	−0.552645	−	1.70087i	0.149437	−	0.988771i	$-0.452254\pi$
$752$	2.03678	+	3.99740i	0.0742737	+	0.145770i
$753$	4.23123	+	26.7150i	0.154195	+	0.973547i
$754$	3.87818	+	2.81766i	0.141235	+	0.102613i
$755$	43.8413	+	17.9433i	1.59555	+	0.653024i
$756$	−20.0624	+	6.51868i	−0.729664	+	0.237082i
$757$	−7.91360	+	49.9645i	−0.287625	+	1.81599i	0.244869	+	0.969556i	$0.421255\pi$
$757$	−7.91360	+	49.9645i	−0.287625	+	1.81599i	−0.532493	+	0.846434i	$0.678745\pi$
$758$	−4.65265	+	4.65265i	−0.168992	+	0.168992i
$759$	−27.4863	+	36.9511i	−0.997690	+	1.34124i
$760$	−10.4989	+	9.04381i	−0.380836	+	0.328054i
$761$	18.7749	+	25.8415i	0.680591	+	0.936753i	0.999941	−	0.0108837i	$-0.00346445\pi$
$761$	18.7749	+	25.8415i	0.680591	+	0.936753i	−0.319350	+	0.947637i	$0.603464\pi$
$762$	48.5360	+	24.7303i	1.75827	+	0.895886i
$763$	2.56445	−	1.30665i	0.0928392	−	0.0473040i
$764$	−7.40180	+	10.1877i	−0.267788	+	0.368578i
$765$	−36.2192	+	3.00434i	−1.30951	+	0.108622i
$766$	−27.8369	−	9.04477i	−1.00579	−	0.326801i
$767$	2.15844	−	4.23618i	0.0779368	−	0.152960i
$768$	−3.17134	−	0.502291i	−0.114436	−	0.0181249i
$769$	−41.4875			−1.49608			−0.748039	−	0.663655i	$-0.769004\pi$
$769$	−41.4875			−1.49608			−0.748039	+	0.663655i	$0.769004\pi$
$770$	11.0114	−	2.56198i	0.396822	−	0.0923275i
$771$	−33.7131			−1.21415
$772$	−3.78808	−	0.599973i	−0.136336	−	0.0215935i
$773$	9.90821	−	19.4460i	0.356373	−	0.699422i	−0.641322	−	0.767272i	$-0.721614\pi$
$773$	9.90821	−	19.4460i	0.356373	−	0.699422i	0.997696	+	0.0678495i	$0.0216138\pi$
$774$	−63.0158	−	20.4751i	−2.26506	−	0.735962i
$775$	10.2584	+	10.0867i	0.368492	+	0.362325i
$776$	−4.11829	+	5.66834i	−0.147838	+	0.203482i
$777$	−6.07038	+	3.09301i	−0.217774	+	0.110961i
$778$	3.95348	+	2.01440i	0.141739	+	0.0722197i
$779$	9.12937	+	12.5655i	0.327094	+	0.450206i
$780$	−0.564328	+	7.57920i	−0.0202062	+	0.271379i
$781$	29.5094	+	0.331662i	1.05593	+	0.0118678i
$782$	−6.79935	+	6.79935i	−0.243144	+	0.243144i
$783$	−9.80293	+	61.8933i	−0.350328	+	2.21189i
$784$	−4.44724	+	1.44500i	−0.158830	+	0.0516070i
$785$	−1.69813	−	4.05122i	−0.0606089	−	0.144594i
$786$	25.3959	+	18.4512i	0.905843	+	0.658134i
$787$	4.74219	+	29.9410i	0.169041	+	1.06728i	0.915637	+	0.402005i	$0.131687\pi$
$787$	4.74219	+	29.9410i	0.169041	+	1.06728i	−0.746596	+	0.665277i	$0.768313\pi$
$788$	4.75118	+	9.32471i	0.169254	+	0.332179i
$789$	4.50319	+	13.8594i	0.160318	+	0.493407i
$790$	12.6222	+	2.97404i	0.449076	+	0.105812i
$791$			6.08151i			0.216234i
$792$	−16.9490	−	17.3343i	−0.602257	−	0.615949i
$793$	4.43308	+	4.43308i	0.157423	+	0.157423i
$794$	−7.54381	+	5.48090i	−0.267720	+	0.194510i
$795$	26.5263	−	6.48689i	0.940790	−	0.230066i
$796$	2.81435	−	8.66167i	0.0997519	−	0.307005i
$797$	53.0278	−	8.39878i	1.87834	−	0.297500i	0.890744	−	0.454505i	$-0.150184\pi$
$797$	53.0278	−	8.39878i	1.87834	−	0.297500i	0.987598	+	0.157004i	$0.0501837\pi$
$798$	−29.9596	+	4.74514i	−1.06056	+	0.167976i
$799$	−3.08264	+	9.48739i	−0.109056	+	0.335640i
$800$	2.90469	−	4.06974i	0.102696	−	0.143887i
$801$	62.3997	−	45.3361i	2.20479	−	1.60187i
$802$	6.22783	+	6.22783i	0.219912	+	0.219912i
$803$	33.5128	+	17.5528i	1.18264	+	0.619424i
$804$			24.5559i			0.866019i
$805$	−7.75521	−	12.5363i	−0.273335	−	0.441847i
$806$	−0.941213	−	2.89676i	−0.0331528	−	0.102034i
$807$	−37.7574	−	74.1031i	−1.32912	−	2.60855i
$808$	−2.75506	−	17.3948i	−0.0969228	−	0.611947i
$809$	25.4737	+	18.5077i	0.895608	+	0.650697i	0.937334	−	0.348432i	$-0.113286\pi$
$809$	25.4737	+	18.5077i	0.895608	+	0.650697i	−0.0417260	+	0.999129i	$0.513286\pi$
$810$	−46.4054	+	19.4516i	−1.63052	+	0.683458i
$811$	−6.48163	+	2.10601i	−0.227601	+	0.0739520i	−0.420597	−	0.907247i	$-0.638179\pi$
$811$	−6.48163	+	2.10601i	−0.227601	+	0.0739520i	0.192996	+	0.981199i	$0.438179\pi$
$812$	1.07993	−	6.81839i	0.0378980	−	0.239279i
$813$	−48.7995	+	48.7995i	−1.71147	+	1.71147i
$814$	−3.70399	−	2.75524i	−0.129825	−	0.0965710i
$815$	3.17746	+	3.68869i	0.111301	+	0.129209i
$816$	−4.19648	−	5.77596i	−0.146906	−	0.202199i
$817$	−50.0507	−	25.5021i	−1.75105	−	0.892206i
$818$	−15.4990	+	7.89712i	−0.541908	+	0.276116i
$819$	−6.93333	+	9.54290i	−0.242270	+	0.333456i
$820$	−4.27686	−	3.62169i	−0.149355	−	0.126475i
$821$	−0.216685	−	0.0704052i	−0.00756235	−	0.00245716i	0.305233	−	0.952278i	$-0.401266\pi$
$821$	−0.216685	−	0.0704052i	−0.00756235	−	0.00245716i	−0.312796	+	0.949820i	$0.601266\pi$
$822$	−3.60167	+	7.06867i	−0.125623	+	0.246548i
$823$	22.6675	+	3.59018i	0.790139	+	0.125146i	0.538445	−	0.842661i	$-0.319012\pi$
$823$	22.6675	+	3.59018i	0.790139	+	0.125146i	0.251695	+	0.967807i	$0.419012\pi$
$824$	3.21229			0.111905
$825$	50.6861	−	16.3122i	1.76466	−	0.567916i
$826$	−6.84677			−0.238229
$827$	−39.9523	−	6.32782i	−1.38928	−	0.220040i	−0.583430	−	0.812164i	$-0.698290\pi$
$827$	−39.9523	−	6.32782i	−1.38928	−	0.220040i	−0.805847	+	0.592124i	$0.798290\pi$
$828$	−14.3511	+	28.1656i	−0.498735	+	0.978823i
$829$	25.8477	+	8.39841i	0.897726	+	0.291689i	0.721298	−	0.692625i	$-0.243546\pi$
$829$	25.8477	+	8.39841i	0.897726	+	0.291689i	0.176428	+	0.984314i	$0.443546\pi$
$830$	2.18260	+	1.84825i	0.0757593	+	0.0641537i
$831$	25.9156	−	35.6698i	0.899004	−	1.23737i
$832$	−0.943185	+	0.480577i	−0.0326990	+	0.0166610i
$833$	−9.26422	−	4.72036i	−0.320986	−	0.163551i
$834$	14.1791	+	19.5159i	0.490982	+	0.675779i
$835$	−31.3064	−	36.3434i	−1.08340	−	1.25772i
$836$	−11.8933	−	16.7627i	−0.411338	−	0.579750i
$837$	28.1543	−	28.1543i	0.973154	−	0.973154i
$838$	−2.56576	+	16.1996i	−0.0886326	+	0.559604i
$839$	20.9575	−	6.80951i	0.723533	−	0.235090i	0.0759789	−	0.997109i	$-0.475792\pi$
$839$	20.9575	−	6.80951i	0.723533	−	0.235090i	0.647554	+	0.762019i	$0.275792\pi$
$840$	10.0941	−	4.23110i	0.348279	−	0.145987i
$841$	6.87075	+	4.99189i	0.236922	+	0.172134i
$842$	−4.12580	−	26.0493i	−0.142185	−	0.897718i
$843$	14.4402	+	28.3404i	0.497346	+	0.976096i
$844$	−7.74813	−	23.8463i	−0.266701	−	0.820823i
$845$	−13.9747	−	22.5901i	−0.480744	−	0.777124i
$846$			32.7941i			1.12749i
$847$	2.25030	+	16.6171i	0.0773212	+	0.570969i
$848$	2.68946	+	2.68946i	0.0923566	+	0.0923566i
$849$	5.35078	−	3.88757i	0.183638	−	0.133421i
$850$	10.9657	−	1.83179i	0.376121	−	0.0628298i
$851$	−1.86005	+	5.72466i	−0.0637619	+	0.196239i
$852$	28.2185	−	4.46938i	0.966751	−	0.153118i
$853$	−36.1266	+	5.72190i	−1.23695	+	0.195914i	−0.740444	−	0.672118i	$-0.765385\pi$
$853$	−36.1266	+	5.72190i	−1.23695	+	0.195914i	−0.496508	+	0.868032i	$0.665385\pi$
$854$	2.78994	−	8.58655i	0.0954697	−	0.293826i
$855$	−98.3915	+	24.0612i	−3.36492	+	0.822877i
$856$	13.3632	−	9.70891i	0.456744	−	0.331844i
$857$	8.98140	+	8.98140i	0.306799	+	0.306799i	0.843666	−	0.536868i	$-0.180393\pi$
$857$	8.98140	+	8.98140i	0.306799	+	0.306799i	−0.536868	+	0.843666i	$0.680393\pi$
$858$	−11.1136	−	1.88849i	−0.379411	−	0.0644719i
$859$			54.6972i			1.86624i	0.359559	+	0.933122i	$0.382927\pi$
$859$			54.6972i			1.86624i	−0.359559	+	0.933122i	$0.617073\pi$
$860$	19.7286	+	4.64847i	0.672740	+	0.158511i
$861$	−3.79096	−	11.6674i	−0.129196	−	0.397624i
$862$	4.31372	+	8.46615i	0.146926	+	0.288358i
$863$	−2.23202	−	14.0924i	−0.0759788	−	0.479711i	−0.996111	−	0.0881040i	$-0.971919\pi$
$863$	−2.23202	−	14.0924i	−0.0759788	−	0.479711i	0.920132	−	0.391607i	$-0.128081\pi$
$864$	−11.1951	−	8.13370i	−0.380864	−	0.276714i
$865$	−11.4045	−	27.2077i	−0.387765	−	0.925088i
$866$	23.7208	−	7.70734i	0.806064	−	0.261906i
$867$	−6.05557	+	38.2334i	−0.205658	+	1.29847i
$868$	−3.10158	+	3.10158i	−0.105274	+	0.105274i
$869$	−6.14895	+	18.2250i	−0.208589	+	0.618241i
$870$	2.41418	−	32.4236i	0.0818484	−	1.09926i
$871$	4.75846	+	6.54946i	0.161234	+	0.221920i
$872$	1.68223	+	0.857140i	0.0569676	+	0.0290264i
$873$	−45.6330	+	23.2512i	−1.54444	+	0.786932i
$874$	−15.7523	+	21.6812i	−0.532829	+	0.733376i
$875$	−1.12205	+	17.0067i	−0.0379322	+	0.574931i
$876$	34.8324	+	11.3177i	1.17688	+	0.382391i
$877$	6.98490	−	13.7086i	0.235863	−	0.462908i	−0.742488	−	0.669860i	$-0.766354\pi$
$877$	6.98490	−	13.7086i	0.235863	−	0.462908i	0.978351	+	0.206952i	$0.0663543\pi$
$878$	−1.67033	−	0.264554i	−0.0563710	−	0.00892828i
$879$	63.0707			2.12732
$880$	5.60537	+	4.85590i	0.188957	+	0.163692i
$881$	−27.4651			−0.925323			−0.462662	−	0.886535i	$-0.653106\pi$
$881$	−27.4651			−0.925323			−0.462662	+	0.886535i	$0.653106\pi$
$882$	−33.7601	−	5.34708i	−1.13676	−	0.180045i
$883$	24.6520	−	48.3824i	0.829607	−	1.62820i	0.0526752	−	0.998612i	$-0.483225\pi$
$883$	24.6520	−	48.3824i	0.829607	−	1.62820i	0.776932	−	0.629584i	$-0.216775\pi$
$884$	−2.23854	−	0.727347i	−0.0752904	−	0.0244633i
$885$	−32.1364	+	2.66567i	−1.08025	+	0.0896055i
$886$	−11.9367	+	16.4295i	−0.401023	+	0.551960i
$887$	−52.7376	+	26.8712i	−1.77076	+	0.902246i	−0.834432	+	0.551111i	$0.814204\pi$
$887$	−52.7376	+	26.8712i	−1.77076	+	0.902246i	−0.936325	+	0.351134i	$0.885796\pi$
$888$	−3.98206	−	2.02896i	−0.133629	−	0.0680875i
$889$	−15.2015	−	20.9231i	−0.509843	−	0.701738i
$890$	−17.8766	+	15.3990i	−0.599224	+	0.516175i
$891$	−22.2636	−	71.2345i	−0.745858	−	2.38645i
$892$	−3.52584	+	3.52584i	−0.118054	+	0.118054i
$893$	−4.34926	+	27.4601i	−0.145542	+	0.918918i
$894$	0.101769	−	0.0330667i	0.00340366	−	0.00110592i
$895$	28.0451	+	11.4783i	0.937446	+	0.383677i
$896$	1.23329	+	0.896038i	0.0412014	+	0.0299345i
$897$	2.29938	+	14.5177i	0.0767740	+	0.484732i
$898$	−19.0905	−	37.4672i	−0.637058	−	1.25030i
$899$	4.02649	+	12.3922i	0.134291	+	0.413305i
$900$	32.4238	−	16.8669i	1.08079	−	0.562229i
$901$			8.45716i			0.281749i
$902$	5.94353	−	5.81141i	0.197898	−	0.193499i
$903$	31.3733	+	31.3733i	1.04404	+	1.04404i
$904$	−3.22746	+	2.34489i	−0.107344	+	0.0779899i
$905$	9.16015	+	37.4578i	0.304494	+	1.24514i
$906$	−21.0201	+	64.6931i	−0.698345	+	2.14928i
$907$	−14.9623	+	2.36980i	−0.496817	+	0.0786880i	−0.399814	−	0.916596i	$-0.630925\pi$
$907$	−14.9623	+	2.36980i	−0.496817	+	0.0786880i	−0.0970022	+	0.995284i	$0.530925\pi$
$908$	2.01564	−	0.319245i	0.0668912	−	0.0105945i
$909$	39.7815	−	122.435i	1.31947	−	4.06091i
$910$	1.87236	−	3.08455i	0.0620681	−	0.102252i
$911$	5.44856	−	3.95861i	0.180519	−	0.131155i	−0.493856	−	0.869544i	$-0.664413\pi$
$911$	5.44856	−	3.95861i	0.180519	−	0.131155i	0.674375	+	0.738389i	$0.264413\pi$
$912$	−14.0700	−	14.0700i	−0.465904	−	0.465904i
$913$	−3.03315	+	2.96573i	−0.100383	+	0.0981512i
$914$		−	10.1208i		−	0.334766i
$915$	9.75198	−	41.3885i	0.322391	−	1.36826i
$916$	0.470996	+	1.44958i	0.0155622	+	0.0478954i
$917$	−6.76610	−	13.2792i	−0.223436	−	0.438518i
$918$	−4.81333	−	30.3902i	−0.158863	−	1.00302i
$919$	−47.2044	−	34.2960i	−1.55713	−	1.13132i	−0.938315	−	0.345782i	$-0.887614\pi$
$919$	−47.2044	−	34.2960i	−1.55713	−	1.13132i	−0.618813	−	0.785538i	$-0.712386\pi$
$920$	3.66280	−	8.94940i	0.120759	−	0.295053i
$921$	36.0740	−	11.7212i	1.18868	−	0.386226i
$922$	−4.29433	+	27.1134i	−0.141426	+	0.892931i
$923$	6.66028	−	6.66028i	0.219226	−	0.219226i
$924$	4.84277	+	15.4949i	0.159315	+	0.509745i
$925$	5.59558	−	4.13802i	0.183982	−	0.136057i
$926$	−10.6467	−	14.6539i	−0.349872	−	0.481557i
$927$	20.9216	+	10.6601i	0.687155	+	0.350123i
$928$	4.03492	−	2.05589i	0.132453	−	0.0674881i
$929$	−5.89306	+	8.11110i	−0.193345	+	0.266117i	−0.894672	−	0.446723i	$-0.852591\pi$
$929$	−5.89306	+	8.11110i	−0.193345	+	0.266117i	0.701327	+	0.712839i	$0.252591\pi$
$930$	−13.3502	+	15.7653i	−0.437770	+	0.516964i
$931$	−27.5598	−	8.95473i	−0.903237	−	0.293480i
$932$	−10.0739	+	19.7711i	−0.329981	+	0.647624i
$933$	44.1000	+	6.98475i	1.44377	+	0.228670i
$934$	21.8363			0.714505
$935$	1.17838	+	16.4480i	0.0385371	+	0.537907i
$936$	−7.73776			−0.252917
$937$	−41.2128	−	6.52746i	−1.34636	−	0.213243i	−0.558710	−	0.829363i	$-0.688703\pi$
$937$	−41.2128	−	6.52746i	−1.34636	−	0.213243i	−0.787652	+	0.616120i	$0.788703\pi$
$938$	5.29282	−	10.3877i	0.172817	−	0.339172i
$939$	−92.1972	−	29.9567i	−3.00874	−	0.977600i
$940$	−0.829283	−	9.99754i	−0.0270482	−	0.326084i
$941$	14.4754	−	19.9237i	0.471885	−	0.649494i	−0.505035	−	0.863099i	$-0.668520\pi$
$941$	14.4754	−	19.9237i	0.471885	−	0.649494i	0.976920	+	0.213605i	$0.0685205\pi$
$942$	5.62021	−	2.86364i	0.183116	−	0.0933025i
$943$	−9.65732	−	4.92065i	−0.314486	−	0.160238i
$944$	−2.63995	−	3.63358i	−0.0859232	−	0.118263i
$945$	47.0394	+	3.50244i	1.53019	+	0.113934i
$946$	−9.61089	+	28.4859i	−0.312477	+	0.926157i
$947$	−6.72877	+	6.72877i	−0.218656	+	0.218656i	−0.807932	−	0.589276i	$-0.799413\pi$
$947$	−6.72877	+	6.72877i	−0.218656	+	0.218656i	0.589276	+	0.807932i	$0.299413\pi$
$948$	−2.91297	+	18.3918i	−0.0946090	+	0.597338i
$949$	11.4836	−	3.73124i	0.372772	−	0.121121i
$950$	29.3869	−	9.82332i	0.953438	−	0.318711i
$951$	79.6507	+	57.8696i	2.58285	+	1.87655i
$952$	0.530254	+	3.34789i	0.0171856	+	0.108506i
$953$	−15.9429	−	31.2897i	−0.516441	−	1.01357i	−0.991064	−	0.133384i	$-0.957416\pi$
$953$	−15.9429	−	31.2897i	−0.516441	−	1.01357i	0.474623	−	0.880189i	$-0.342584\pi$
$954$	8.59137	+	26.4415i	0.278156	+	0.856076i
$955$	23.9465	−	14.8138i	0.774889	−	0.479362i
$956$		−	24.7841i		−	0.801574i
$957$	47.5436	+	8.07890i	1.53687	+	0.261154i
$958$	4.61171	+	4.61171i	0.148998	+	0.148998i
$959$	3.04719	−	2.21391i	0.0983989	−	0.0714910i
$960$	6.13750	+	3.72553i	0.198087	+	0.120241i
$961$	−7.02117	+	21.6089i	−0.226489	+	0.697062i
$962$	−1.45526	+	0.230490i	−0.0469194	+	0.00743130i
$963$	119.253	−	18.8879i	3.84289	−	0.608654i
$964$	0.0173846	−	0.0535042i	0.000559919	−	0.00172325i
$965$	7.33108	+	4.45005i	0.235996	+	0.143252i
$966$	17.1249	−	12.4420i	0.550984	−	0.400313i
$967$	43.6347	+	43.6347i	1.40320	+	1.40320i	0.789685	+	0.613512i	$0.210244\pi$
$967$	43.6347	+	43.6347i	1.40320	+	1.40320i	0.613512	+	0.789685i	$0.289756\pi$
$968$	−7.95103	+	7.60139i	−0.255556	+	0.244318i
$969$		−	44.2438i		−	1.42131i
$970$	13.3236	−	8.24223i	0.427794	−	0.264642i
$971$	8.80597	+	27.1020i	0.282597	+	0.869744i	0.987109	+	0.160052i	$0.0511661\pi$
$971$	8.80597	+	27.1020i	0.282597	+	0.869744i	−0.704512	+	0.709693i	$0.748834\pi$
$972$	−13.9553	−	27.3888i	−0.447617	−	0.878497i
$973$	−1.79163	−	11.3119i	−0.0574369	−	0.362642i
$974$	2.37265	+	1.72383i	0.0760245	+	0.0552350i
$975$	7.58729	−	15.2068i	0.242988	−	0.487007i
$976$	5.63262	−	1.83015i	0.180296	−	0.0585817i
$977$	−8.07944	+	51.0116i	−0.258484	+	1.63201i	0.427236	+	0.904140i	$0.359487\pi$
$977$	−8.07944	+	51.0116i	−0.258484	+	1.63201i	−0.685720	+	0.727865i	$0.740513\pi$
$978$	−4.94335	+	4.94335i	−0.158071	+	0.158071i
$979$	−20.2508	−	28.5420i	−0.647219	−	0.912206i
$980$	10.4272	+	0.776386i	0.333086	+	0.0248007i
$981$	8.11191	+	11.1651i	0.258993	+	0.356474i
$982$	−11.8666	−	6.04634i	−0.378679	−	0.192946i
$983$	−48.6352	+	24.7809i	−1.55122	+	0.790387i	−0.999060	−	0.0433506i	$-0.986197\pi$
$983$	−48.6352	+	24.7809i	−1.55122	+	0.790387i	−0.552161	+	0.833737i	$0.686197\pi$
$984$	4.73019	−	6.51054i	0.150793	−	0.207549i
$985$	−1.93446	−	23.3212i	−0.0616371	−	0.743075i
$986$	9.57644	+	3.11157i	0.304976	+	0.0990927i
$987$	9.96952	−	19.5663i	0.317333	−	0.622802i
$988$	−6.47920	−	1.02620i	−0.206131	−	0.0326479i
$989$	39.1997			1.24648
$990$	20.3933	+	50.2280i	0.648141	+	1.59635i
$991$	1.67436			0.0531879			0.0265939	−	0.999646i	$-0.491534\pi$
$991$	1.67436			0.0531879			0.0265939	+	0.999646i	$0.491534\pi$
$992$	−2.84191	−	0.450114i	−0.0902306	−	0.0142911i
$993$	−20.7755	+	40.7742i	−0.659291	+	1.29393i
$994$	−12.9005	−	4.19162i	−0.409178	−	0.132950i
$995$	−13.1604	+	15.5412i	−0.417214	+	0.492689i
$996$	−2.41395	+	3.32251i	−0.0764888	+	0.105278i
$997$	−26.6089	+	13.5579i	−0.842713	+	0.429384i	−0.821375	−	0.570389i	$-0.806793\pi$
$997$	−26.6089	+	13.5579i	−0.842713	+	0.429384i	−0.0213379	+	0.999772i	$0.506793\pi$
$998$	−20.8231	−	10.6099i	−0.659143	−	0.335850i
$999$	−11.3212	−	15.5823i	−0.358187	−	0.493002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.63.1	yes	48
3.2	odd	2		990.2.bh.c.613.6		48
4.3	odd	2		880.2.cm.c.833.6		48
5.2	odd	4	inner	110.2.k.a.107.6	yes	48
5.3	odd	4		550.2.bh.b.107.1		48
5.4	even	2		550.2.bh.b.393.6		48
11.7	odd	10	inner	110.2.k.a.73.6	yes	48
15.2	even	4		990.2.bh.c.217.2		48
20.7	even	4		880.2.cm.c.657.1		48
33.29	even	10		990.2.bh.c.73.2		48
44.7	even	10		880.2.cm.c.513.1		48
55.7	even	20	inner	110.2.k.a.7.1	✓	48
55.18	even	20		550.2.bh.b.7.6		48
55.29	odd	10		550.2.bh.b.293.1		48
165.62	odd	20		990.2.bh.c.667.6		48
220.7	odd	20		880.2.cm.c.337.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.1	✓	48	55.7	even	20	inner
110.2.k.a.63.1	yes	48	1.1	even	1	trivial
110.2.k.a.73.6	yes	48	11.7	odd	10	inner
110.2.k.a.107.6	yes	48	5.2	odd	4	inner
550.2.bh.b.7.6		48	55.18	even	20
550.2.bh.b.107.1		48	5.3	odd	4
550.2.bh.b.293.1		48	55.29	odd	10
550.2.bh.b.393.6		48	5.4	even	2
880.2.cm.c.337.6		48	220.7	odd	20
880.2.cm.c.513.1		48	44.7	even	10
880.2.cm.c.657.1		48	20.7	even	4
880.2.cm.c.833.6		48	4.3	odd	2
990.2.bh.c.73.2		48	33.29	even	10
990.2.bh.c.217.2		48	15.2	even	4
990.2.bh.c.613.6		48	3.2	odd	2
990.2.bh.c.667.6		48	165.62	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 - 0.156434i) q^{2} +(-1.45771 + 2.86091i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-1.70643 - 1.44502i) q^{5} +(1.88730 - 2.59765i) q^{6} +(-1.35828 + 0.692077i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-4.29653 - 5.91367i) q^{9} +(1.45937 + 1.69418i) q^{10} +(-2.70495 + 1.91918i) q^{11} +(-2.27043 + 2.27043i) q^{12} +(-0.165595 + 1.04553i) q^{13} +(1.44982 - 0.471075i) q^{14} +(6.62155 - 2.77553i) q^{15} +(0.809017 + 0.587785i) q^{16} +(0.347837 + 2.19616i) q^{17} +(3.31853 + 6.51299i) q^{18} +(1.91500 + 5.89375i) q^{19} +(-1.17638 - 1.90161i) q^{20} -4.89475i q^{21} +(2.97187 - 1.47241i) q^{22} +(-3.05791 - 3.05791i) q^{23} +(2.59765 - 1.88730i) q^{24} +(0.823819 + 4.93167i) q^{25} +(0.327113 - 1.00675i) q^{26} +(13.6675 - 2.16472i) q^{27} +(-1.50566 + 0.238474i) q^{28} +(-1.39938 + 4.30686i) q^{29} +(-6.97422 + 1.70552i) q^{30} +(2.32781 - 1.69125i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.54760 - 10.5362i) q^{33} -2.22353i q^{34} +(3.31788 + 0.781760i) q^{35} +(-2.25882 - 6.95193i) q^{36} +(-0.631904 - 1.24018i) q^{37} +(-0.969434 - 6.12076i) q^{38} +(-2.74977 - 1.99782i) q^{39} +(0.864415 + 2.06223i) q^{40} +(2.38365 - 0.774496i) q^{41} +(-0.765708 + 4.83449i) q^{42} +(-6.40957 + 6.40957i) q^{43} +(-3.16562 + 0.989379i) q^{44} +(-1.21365 + 16.2999i) q^{45} +(2.54190 + 3.49862i) q^{46} +(3.99740 + 2.03678i) q^{47} +(-2.86091 + 1.45771i) q^{48} +(-2.74855 + 3.78305i) q^{49} +(-0.0421939 - 4.99982i) q^{50} +(-6.79005 - 2.20622i) q^{51} +(-0.480577 + 0.943185i) q^{52} +(3.75665 + 0.594995i) q^{53} -13.8379 q^{54} +(7.38907 + 0.633749i) q^{55} +1.52443 q^{56} +(-19.6530 - 3.11273i) q^{57} +(2.05589 - 4.03492i) q^{58} +(-4.27154 - 1.38791i) q^{59} +(7.15515 - 0.593511i) q^{60} +(3.48115 - 4.79140i) q^{61} +(-2.56372 + 1.30628i) q^{62} +(9.92860 + 5.05887i) q^{63} +(0.587785 + 0.809017i) q^{64} +(1.79339 - 1.54483i) q^{65} +(-0.119682 + 10.6486i) q^{66} +(5.40776 - 5.40776i) q^{67} +(-0.347837 + 2.19616i) q^{68} +(13.2059 - 4.29086i) q^{69} +(-3.15473 - 1.29117i) q^{70} +(-7.19862 - 5.23010i) q^{71} +(1.14349 + 7.21970i) q^{72} +(-5.17847 - 10.1633i) q^{73} +(0.430117 + 1.32376i) q^{74} +(-15.3099 - 4.83204i) q^{75} +6.19706i q^{76} +(2.34584 - 4.47882i) q^{77} +(2.40339 + 2.40339i) q^{78} +(4.69179 - 3.40879i) q^{79} +(-0.531169 - 2.17206i) q^{80} +(-6.95367 + 21.4012i) q^{81} +(-2.47546 + 0.392075i) q^{82} +(1.26330 - 0.200087i) q^{83} +(1.51256 - 4.65519i) q^{84} +(2.57994 - 4.25022i) q^{85} +(7.33334 - 5.32798i) q^{86} +(-10.2816 - 10.2816i) q^{87} +(3.28142 - 0.481987i) q^{88} +10.5518i q^{89} +(3.74856 - 15.9093i) q^{90} +(-0.498662 - 1.53472i) q^{91} +(-1.96330 - 3.85319i) q^{92} +(1.44526 + 9.12499i) q^{93} +(-3.62956 - 2.63703i) q^{94} +(5.24880 - 12.8245i) q^{95} +(3.05372 - 0.992214i) q^{96} +(1.09605 - 6.92020i) q^{97} +(3.30651 - 3.30651i) q^{98} +(22.9713 + 7.75031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36}+ \cdots + 72 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more