LMFDB - Embedded newform 550.2.bh.b.7.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(7,550)] 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("550.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.bh (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	550.7
Dual form			550.2.bh.b.393.6

$q$-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} +(1.88730 + 2.59765i) q^{6} +(1.35828 + 0.692077i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-4.29653 + 5.91367i) q^{9} +(-2.70495 - 1.91918i) q^{11} +(2.27043 + 2.27043i) q^{12} +(0.165595 + 1.04553i) q^{13} +(1.44982 + 0.471075i) q^{14} +(0.809017 - 0.587785i) q^{16} +(-0.347837 + 2.19616i) q^{17} +(-3.31853 + 6.51299i) q^{18} +(1.91500 - 5.89375i) q^{19} +4.89475i q^{21} +(-2.97187 - 1.47241i) q^{22} +(3.05791 - 3.05791i) q^{23} +(2.59765 + 1.88730i) q^{24} +(0.327113 + 1.00675i) q^{26} +(-13.6675 - 2.16472i) q^{27} +(1.50566 + 0.238474i) q^{28} +(-1.39938 - 4.30686i) q^{29} +(2.32781 + 1.69125i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.54760 - 10.5362i) q^{33} +2.22353i q^{34} +(-2.25882 + 6.95193i) q^{36} +(0.631904 - 1.24018i) q^{37} +(0.969434 - 6.12076i) q^{38} +(-2.74977 + 1.99782i) q^{39} +(2.38365 + 0.774496i) q^{41} +(0.765708 + 4.83449i) q^{42} +(6.40957 + 6.40957i) q^{43} +(-3.16562 - 0.989379i) q^{44} +(2.54190 - 3.49862i) q^{46} +(-3.99740 + 2.03678i) q^{47} +(2.86091 + 1.45771i) q^{48} +(-2.74855 - 3.78305i) q^{49} +(-6.79005 + 2.20622i) q^{51} +(0.480577 + 0.943185i) q^{52} +(-3.75665 + 0.594995i) q^{53} -13.8379 q^{54} +1.52443 q^{56} +(19.6530 - 3.11273i) q^{57} +(-2.05589 - 4.03492i) q^{58} +(-4.27154 + 1.38791i) q^{59} +(3.48115 + 4.79140i) q^{61} +(2.56372 + 1.30628i) q^{62} +(-9.92860 + 5.05887i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-0.119682 - 10.6486i) q^{66} +(-5.40776 - 5.40776i) q^{67} +(0.347837 + 2.19616i) q^{68} +(13.2059 + 4.29086i) q^{69} +(-7.19862 + 5.23010i) q^{71} +(-1.14349 + 7.21970i) q^{72} +(5.17847 - 10.1633i) q^{73} +(0.430117 - 1.32376i) q^{74} -6.19706i q^{76} +(-2.34584 - 4.47882i) q^{77} +(-2.40339 + 2.40339i) q^{78} +(4.69179 + 3.40879i) q^{79} +(-6.95367 - 21.4012i) q^{81} +(2.47546 + 0.392075i) q^{82} +(-1.26330 - 0.200087i) q^{83} +(1.51256 + 4.65519i) q^{84} +(7.33334 + 5.32798i) q^{86} +(10.2816 - 10.2816i) q^{87} +(-3.28142 - 0.481987i) q^{88} -10.5518i q^{89} +(-0.498662 + 1.53472i) q^{91} +(1.96330 - 3.85319i) q^{92} +(-1.44526 + 9.12499i) q^{93} +(-3.62956 + 2.63703i) q^{94} +(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} + 20 q^{7} + 12 q^{11} + 16 q^{12} + 12 q^{16} + 20 q^{17} + 4 q^{22} + 8 q^{23} + 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}+ \cdots - 72 q^{97}+O(q^{100}) $ 48 * q + 4 * q^3 + 20 * q^7 + 12 * q^11 + 16 * q^12 + 12 * q^16 + 20 * q^17 + 4 * q^22 + 8 * q^23 + 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 + 40 * q^46 - 40 * q^47 - 4 * q^48 + 40 * q^51 - 40 * q^52 - 8 * q^56 - 48 * q^58 + 80 * q^61 - 40 * q^62 - 100 * q^63 + 24 * q^66 - 20 * q^68 - 56 * q^71 + 20 * q^73 + 96 * q^77 - 16 * q^78 - 68 * q^81 - 56 * q^86 + 4 * q^88 - 68 * q^91 + 12 * q^92 - 76 * q^93 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{4}\right)$

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	0.755208	+	0.655485i	$0.227536\pi$
$3$	1.45771	+	2.86091i	0.841606	+	1.65175i	0.0863983	+	0.996261i	$0.472464\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$		0			0
$5$		0			0
$6$	1.88730	+	2.59765i	0.770488	+	1.06049i
$7$	1.35828	+	0.692077i	0.513381	+	0.261581i	0.691433	−	0.722440i	$-0.256980\pi$
$7$	1.35828	+	0.692077i	0.513381	+	0.261581i	−0.178052	+	0.984021i	$0.556980\pi$
$8$	0.891007	−	0.453990i	0.315018	−	0.160510i
$9$	−4.29653	+	5.91367i	−1.43218	+	1.97122i
$10$		0			0
$11$	−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	$-0.00310392\pi$
$13$	0.165595	+	1.04553i	0.0459279	+	0.289977i	−0.954025	+	0.299728i	$0.903104\pi$
$14$	1.44982	+	0.471075i	0.387481	+	0.125900i
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−0.347837	+	2.19616i	−0.0843629	+	0.532646i	0.908923	+	0.416963i	$0.136906\pi$
$17$	−0.347837	+	2.19616i	−0.0843629	+	0.532646i	−0.993286	+	0.115683i	$0.963094\pi$
$18$	−3.31853	+	6.51299i	−0.782186	+	1.53513i
$19$	1.91500	−	5.89375i	0.439330	−	1.35212i	−0.449253	−	0.893405i	$-0.648310\pi$
$19$	1.91500	−	5.89375i	0.439330	−	1.35212i	0.888583	−	0.458715i	$-0.151690\pi$
$20$		0			0
$21$			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	$-0.601116\pi$
$23$	3.05791	−	3.05791i	0.637617	−	0.637617i	0.949967	+	0.312350i	$0.101116\pi$
$24$	2.59765	+	1.88730i	0.530243	+	0.385244i
$25$		0			0
$26$	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	−0.992833	−	0.119507i	$-0.961869\pi$
$29$	−1.39938	−	4.30686i	−0.259859	−	0.799763i	0.732975	−	0.680256i	$-0.238131\pi$
$30$		0			0
$31$	2.32781	+	1.69125i	0.418087	+	0.303758i	0.776868	−	0.629664i	$-0.216807\pi$
$31$	2.32781	+	1.69125i	0.418087	+	0.303758i	−0.358781	+	0.933422i	$0.616807\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.54760	−	10.5362i	0.269402	−	1.83412i
$34$			2.22353i			0.381333i
$35$		0			0
$36$	−2.25882	+	6.95193i	−0.376470	+	1.15866i
$37$	0.631904	−	1.24018i	0.103884	−	0.203885i	−0.833213	−	0.552952i	$-0.813501\pi$
$37$	0.631904	−	1.24018i	0.103884	−	0.203885i	0.937098	+	0.349067i	$0.113501\pi$
$38$	0.969434	−	6.12076i	0.157263	−	0.992919i
$39$	−2.74977	+	1.99782i	−0.440316	+	0.319908i
$40$		0			0
$41$	2.38365	+	0.774496i	0.372264	+	0.120956i	0.489173	−	0.872187i	$-0.337299\pi$
$41$	2.38365	+	0.774496i	0.372264	+	0.120956i	−0.116909	+	0.993143i	$0.537299\pi$
$42$	0.765708	+	4.83449i	0.118151	+	0.745978i
$43$	6.40957	+	6.40957i	0.977450	+	0.977450i	0.999751	−	0.0223009i	$-0.00709920\pi$
$43$	6.40957	+	6.40957i	0.977450	+	0.977450i	−0.0223009	+	0.999751i	$0.507099\pi$
$44$	−3.16562	−	0.989379i	−0.477235	−	0.149155i
$45$		0			0
$46$	2.54190	−	3.49862i	0.374782	−	0.515843i
$47$	−3.99740	+	2.03678i	−0.583081	+	0.297095i	−0.720541	−	0.693413i	$-0.756106\pi$
$47$	−3.99740	+	2.03678i	−0.583081	+	0.297095i	0.137460	+	0.990507i	$0.456106\pi$
$48$	2.86091	+	1.45771i	0.412936	+	0.210402i
$49$	−2.74855	−	3.78305i	−0.392650	−	0.540436i
$50$		0			0
$51$	−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	$-0.634126\pi$
$53$	−3.75665	+	0.594995i	−0.516016	+	0.0817288i	−0.107005	+	0.994258i	$0.534126\pi$
$54$	−13.8379			−1.88310
$55$		0			0
$56$	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	−0.573569	−	0.819158i	$-0.694441\pi$
$59$	−4.27154	+	1.38791i	−0.556107	+	0.180690i	0.0174620	+	0.999848i	$0.494441\pi$
$60$		0			0
$61$	3.48115	+	4.79140i	0.445716	+	0.613475i	0.971470	−	0.237161i	$-0.0762169\pi$
$61$	3.48115	+	4.79140i	0.445716	+	0.613475i	−0.525754	+	0.850636i	$0.676217\pi$
$62$	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
$65$		0			0
$66$	−0.119682	−	10.6486i	−0.0147318	−	1.31075i
$67$	−5.40776	−	5.40776i	−0.660663	−	0.660663i	0.294873	−	0.955536i	$-0.404723\pi$
$67$	−5.40776	−	5.40776i	−0.660663	−	0.660663i	−0.955536	+	0.294873i	$0.904723\pi$
$68$	0.347837	+	2.19616i	0.0421814	+	0.266323i
$69$	13.2059	+	4.29086i	1.58980	+	0.516559i
$70$		0			0
$71$	−7.19862	+	5.23010i	−0.854319	+	0.620699i	−0.926334	−	0.376704i	$-0.877057\pi$
$71$	−7.19862	+	5.23010i	−0.854319	+	0.620699i	0.0720143	+	0.997404i	$0.477057\pi$
$72$	−1.14349	+	7.21970i	−0.134761	+	0.850850i
$73$	5.17847	−	10.1633i	0.606094	−	1.18953i	−0.360391	−	0.932801i	$-0.617357\pi$
$73$	5.17847	−	10.1633i	0.606094	−	1.18953i	0.966485	−	0.256725i	$-0.0826434\pi$
$74$	0.430117	−	1.32376i	0.0500001	−	0.153884i
$75$		0			0
$76$		−	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	0.819560	−	0.572994i	$-0.194218\pi$
$79$	4.69179	+	3.40879i	0.527868	+	0.383518i	−0.291692	+	0.956512i	$0.594218\pi$
$80$		0			0
$81$	−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	$-0.472363\pi$
$83$	−1.26330	−	0.200087i	−0.138665	−	0.0219624i	−0.225381	+	0.974271i	$0.572363\pi$
$84$	1.51256	+	4.65519i	0.165034	+	0.507922i
$85$		0			0
$86$	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	$-0.811092\pi$
$89$		−	10.5518i		−	1.11849i	0.829004	−	0.559243i	$-0.188908\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	3.05372	+	0.992214i	0.311669	+	0.101267i
$97$	−1.09605	−	6.92020i	−0.111287	−	0.702639i	−0.978738	−	0.205116i	$-0.934243\pi$
$97$	−1.09605	−	6.92020i	−0.111287	−	0.702639i	0.867451	−	0.497523i	$-0.165757\pi$
$98$	−3.30651	−	3.30651i	−0.334008	−	0.334008i
$99$	22.9713	−	7.75031i	2.30870	−	0.778936i
$100$		0			0
$101$	10.3519	−	14.2481i	1.03005	−	1.41774i	0.125136	−	0.992140i	$-0.460063\pi$
$101$	10.3519	−	14.2481i	1.03005	−	1.41774i	0.904912	−	0.425599i	$-0.139937\pi$
$102$	−6.36132	+	3.24125i	−0.629865	+	0.320932i
$103$	2.86217	+	1.45835i	0.282018	+	0.143695i	0.589278	−	0.807930i	$-0.299412\pi$
$103$	2.86217	+	1.45835i	0.282018	+	0.143695i	−0.307260	+	0.951625i	$0.599412\pi$
$104$	0.622206	+	0.856394i	0.0610124	+	0.0839763i
$105$		0			0
$106$	−3.61732	+	1.17534i	−0.351345	+	0.114159i
$107$	7.49892	+	14.7175i	0.724948	+	1.42279i	0.898953	+	0.438045i	$0.144329\pi$
$107$	7.49892	+	14.7175i	0.724948	+	1.42279i	−0.174006	+	0.984745i	$0.555671\pi$
$108$	−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	$0.528821\pi$
$110$		0			0
$111$	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	$-0.210085\pi$
$113$	−1.81113	−	3.55455i	−0.170377	−	0.334384i	−0.960368	+	0.278734i	$0.910085\pi$
$114$	18.9241	−	6.14881i	1.77240	−	0.575889i
$115$		0			0
$116$	−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
$120$		0			0
$121$	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
$125$		0			0
$126$	−9.01498	+	6.54977i	−0.803118	+	0.583500i
$127$	−2.65395	+	16.7564i	−0.235500	+	1.48689i	0.532495	+	0.846433i	$0.321254\pi$
$127$	−2.65395	+	16.7564i	−0.235500	+	1.48689i	−0.767995	+	0.640456i	$0.778746\pi$
$128$	0.453990	−	0.891007i	0.0401275	−	0.0787546i
$129$	−8.99392	+	27.6805i	−0.791871	+	2.43713i
$130$		0			0
$131$		−	9.77651i		−	0.854177i	−0.904210	−	0.427089i	$-0.859539\pi$
$131$		−	9.77651i		−	0.854177i	0.904210	−	0.427089i	$-0.140461\pi$
$132$	−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
$135$		0			0
$136$	0.687109	+	2.11471i	0.0589191	+	0.181334i
$137$	2.44036	+	0.386515i	0.208494	+	0.0330222i	0.259808	−	0.965660i	$-0.416341\pi$
$137$	2.44036	+	0.386515i	0.208494	+	0.0330222i	−0.0513136	+	0.998683i	$0.516341\pi$
$138$	13.7146	+	2.17217i	1.16746	+	0.184908i
$139$	−2.32161	−	7.14518i	−0.196916	−	0.606046i	−0.999949	−	0.0101112i	$-0.996781\pi$
$139$	−2.32161	−	7.14518i	−0.196916	−	0.606046i	0.803032	−	0.595935i	$-0.203219\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$	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	−0.586680	−	0.809819i	$-0.699565\pi$
$149$	0.0269615	−	0.0195887i	0.00220877	−	0.00160477i	0.588889	+	0.808214i	$0.299565\pi$
$150$		0			0
$151$	−20.1481	−	6.54653i	−1.63963	−	0.532749i	−0.663176	−	0.748463i	$-0.730792\pi$
$151$	−20.1481	−	6.54653i	−1.63963	−	0.532749i	−0.976457	+	0.215714i	$0.930792\pi$
$152$	−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
$155$		0			0
$156$	−1.99782	+	2.74977i	−0.159954	+	0.220158i
$157$	−1.75037	+	0.891858i	−0.139695	+	0.0711780i	−0.522441	−	0.852676i	$-0.674978\pi$
$157$	−1.75037	+	0.891858i	−0.139695	+	0.0711780i	0.382746	+	0.923854i	$0.374978\pi$
$158$	5.16728	+	2.63286i	0.411087	+	0.209459i
$159$	−7.17831	−	9.88010i	−0.569277	−	0.783543i
$160$		0			0
$161$	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	$-0.522825\pi$
$163$	2.15047	−	0.340601i	0.168438	−	0.0266779i	0.240084	+	0.970752i	$0.422825\pi$
$164$	2.50632			0.195711
$165$		0			0
$166$	−1.27905			−0.0992732
$167$	−21.1879	+	3.35583i	−1.63957	+	0.259682i	−0.907036	−	0.421053i	$-0.861661\pi$
$167$	−21.1879	+	3.35583i	−1.63957	+	0.259682i	−0.732530	+	0.680735i	$0.761661\pi$
$168$	2.22217	+	4.36126i	0.171444	+	0.336478i
$169$	11.2980	−	3.67095i	0.869079	−	0.282381i
$170$		0			0
$171$	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	$-0.817231\pi$
$173$	−11.7553	+	5.98965i	−0.893742	+	0.455384i	−0.0541069	+	0.998535i	$0.517231\pi$
$174$	8.54665	−	11.7634i	0.647920	−	0.891785i
$175$		0			0
$176$	−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	−0.215219	−	0.976566i	$-0.569047\pi$
$179$	−12.8887	−	4.18779i	−0.963346	−	0.313010i	−0.748127	+	0.663555i	$0.769047\pi$
$180$		0			0
$181$	−13.9517	+	10.1365i	−1.03702	+	0.753441i	−0.969702	−	0.244290i	$-0.921445\pi$
$181$	−13.9517	+	10.1365i	−1.03702	+	0.753441i	−0.0673204	+	0.997731i	$0.521445\pi$
$182$	−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			0
$186$			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
$190$		0			0
$191$	−3.89136	−	11.9764i	−0.281569	−	0.866580i	−0.987406	−	0.158206i	$-0.949429\pi$
$191$	−3.89136	−	11.9764i	−0.281569	−	0.866580i	0.705837	−	0.708374i	$-0.250571\pi$
$192$	3.17134	+	0.502291i	0.228872	+	0.0362497i
$193$	3.78808	+	0.599973i	0.272672	+	0.0431870i	0.291273	−	0.956640i	$-0.405921\pi$
$193$	3.78808	+	0.599973i	0.272672	+	0.0431870i	−0.0186009	+	0.999827i	$0.505921\pi$
$194$	−2.16511	−	6.66354i	−0.155446	−	0.478414i
$195$		0			0
$196$	−3.78305	−	2.74855i	−0.270218	−	0.196325i
$197$	−7.40013	+	7.40013i	−0.527238	+	0.527238i	−0.919748	−	0.392510i	$-0.871607\pi$
$197$	−7.40013	+	7.40013i	−0.527238	+	0.527238i	0.392510	+	0.919748i	$0.371607\pi$
$198$	21.4761	−	11.2484i	1.52624	−	0.799389i
$199$			9.10742i			0.645608i	0.946466	+	0.322804i	$0.104625\pi$
$199$			9.10742i			0.645608i	−0.946466	+	0.322804i	$0.895375\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	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
$210$		0			0
$211$	−14.7378	+	20.2849i	−1.01459	+	1.39647i	−0.0986665	+	0.995121i	$0.531458\pi$
$211$	−14.7378	+	20.2849i	−1.01459	+	1.39647i	−0.915926	+	0.401347i	$0.868542\pi$
$212$	−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
$215$		0			0
$216$	−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
$220$		0			0
$221$	−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	$-0.0966071\pi$
$223$	2.26373	+	4.44282i	0.151590	+	0.297513i	−0.802706	+	0.596375i	$0.796607\pi$
$224$	1.44982	−	0.471075i	0.0968702	−	0.0314750i
$225$		0			0
$226$	−2.34489	−	3.22746i	−0.155980	−	0.214688i
$227$	−1.81833	−	0.926486i	−0.120687	−	0.0614931i	0.392605	−	0.919707i	$-0.371574\pi$
$227$	−1.81833	−	0.926486i	−0.120687	−	0.0614931i	−0.513292	+	0.858214i	$0.671574\pi$
$228$	17.7292	−	9.03349i	1.17415	−	0.598257i
$229$	0.895888	−	1.23308i	0.0592020	−	0.0814845i	−0.778389	−	0.627782i	$-0.783963\pi$
$229$	0.895888	−	1.23308i	0.0592020	−	0.0814845i	0.837591	+	0.546297i	$0.183963\pi$
$230$		0			0
$231$	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	0.792050	+	0.610457i	$0.209014\pi$
$233$	3.47122	+	21.9164i	0.227407	+	1.43579i	−0.564642	+	0.825336i	$0.690986\pi$
$234$	−7.35904	−	2.39110i	−0.481076	−	0.156311i
$235$		0			0
$236$	−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	0.320932	+	0.947102i	$0.396004\pi$
$239$	−7.65870	+	23.5711i	−0.495400	+	1.52468i	−0.816332	+	0.577583i	$0.803996\pi$
$240$		0			0
$241$			0.0562577i			0.00362387i	0.999998	+	0.00181194i	$0.000576758\pi$
$241$			0.0562577i			0.00362387i	−0.999998	+	0.00181194i	$0.999423\pi$
$242$	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
$245$		0			0
$246$	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
$250$		0			0
$251$	6.81505	+	4.95143i	0.430162	+	0.312531i	0.781714	−	0.623637i	$-0.214346\pi$
$251$	6.81505	+	4.95143i	0.430162	+	0.312531i	−0.351551	+	0.936169i	$0.614346\pi$
$252$	−7.87938	+	7.87938i	−0.496354	+	0.496354i
$253$	−14.1402	+	2.40278i	−0.888984	+	0.151062i
$254$			16.9653i			1.06449i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.76675	+	9.35527i	−0.297342	+	0.583566i	−0.990547	−	0.137175i	$-0.956198\pi$
$257$	−4.76675	+	9.35527i	−0.297342	+	0.583566i	0.693205	+	0.720740i	$0.256198\pi$
$258$	−4.55302	+	28.7466i	−0.283458	+	1.78969i
$259$	1.71660	−	1.24718i	0.106664	−	0.0774963i
$260$		0			0
$261$	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	$-0.294687\pi$
$263$	−3.20922	−	3.20922i	−0.197889	−	0.197889i	−0.799095	+	0.601205i	$0.794687\pi$
$264$	−3.40442	−	10.0904i	−0.209527	−	0.621022i
$265$		0			0
$266$	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	−0.960530	−	0.278178i	$-0.910270\pi$
$269$	−15.2248	−	20.9551i	−0.928272	−	1.27766i	0.0322573	−	0.999480i	$-0.489730\pi$
$270$		0			0
$271$	20.4415	−	6.64186i	1.24173	−	0.403464i	0.386783	−	0.922171i	$-0.373586\pi$
$271$	20.4415	−	6.64186i	1.24173	−	0.403464i	0.854952	+	0.518707i	$0.173586\pi$
$272$	1.00946	+	1.98118i	0.0612077	+	0.120127i
$273$	−5.11760	+	0.810549i	−0.309731	+	0.0490566i
$274$	2.47078			0.149265
$275$		0			0
$276$	13.8855			0.835810
$277$	13.5625	−	2.14809i	0.814893	−	0.129066i	0.264943	−	0.964264i	$-0.414647\pi$
$277$	13.5625	−	2.14809i	0.814893	−	0.129066i	0.549950	+	0.835198i	$0.314647\pi$
$278$	−3.41078	−	6.69403i	−0.204565	−	0.401481i
$279$	−20.0030	+	6.49937i	−1.19755	+	0.389107i
$280$		0			0
$281$	5.82266	+	8.01420i	0.347351	+	0.478087i	0.946570	−	0.322498i	$-0.104522\pi$
$281$	5.82266	+	8.01420i	0.347351	+	0.478087i	−0.599220	+	0.800585i	$0.704522\pi$
$282$	−12.8351	−	6.53983i	−0.764322	−	0.389441i
$283$	1.83534	−	0.935154i	0.109100	−	0.0555891i	−0.398589	−	0.917130i	$-0.630500\pi$
$283$	1.83534	−	0.935154i	0.109100	−	0.0555891i	0.507689	+	0.861541i	$0.330500\pi$
$284$	−5.23010	+	7.19862i	−0.310350	+	0.427160i
$285$		0			0
$286$	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
$290$		0			0
$291$	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	−0.469259	−	0.883061i	$-0.655479\pi$
$293$	8.91767	−	17.5019i	0.520976	−	1.02247i	0.990234	−	0.139412i	$-0.0445212\pi$
$294$	4.63970	−	14.2795i	0.270593	−	0.832799i
$295$		0			0
$296$		−	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
$300$		0			0
$301$	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
$305$		0			0
$306$	−13.1492	−	9.55348i	−0.751692	−	0.546136i
$307$	8.35315	−	8.35315i	0.476740	−	0.476740i	−0.427348	−	0.904087i	$-0.640552\pi$
$307$	8.35315	−	8.35315i	0.476740	−	0.476740i	0.904087	+	0.427348i	$0.140552\pi$
$308$	−3.61506	−	3.53470i	−0.205987	−	0.201408i
$309$			10.3142i			0.586757i
$310$		0			0
$311$	−4.29712	+	13.2252i	−0.243667	+	0.749931i	0.752185	+	0.658952i	$0.229000\pi$
$311$	−4.29712	+	13.2252i	−0.243667	+	0.749931i	−0.995853	+	0.0909796i	$0.971000\pi$
$312$	−1.54307	+	3.02844i	−0.0873591	+	0.171452i
$313$	−4.72303	+	29.8201i	−0.266962	+	1.68553i	0.381569	+	0.924341i	$0.375384\pi$
$313$	−4.72303	+	29.8201i	−0.266962	+	1.68553i	−0.648530	+	0.761189i	$0.724616\pi$
$314$	−1.58930	+	1.15470i	−0.0896895	+	0.0651633i
$315$		0			0
$316$	5.51553	+	1.79211i	0.310273	+	0.100814i
$317$	−4.79669	−	30.2851i	−0.269409	−	1.70098i	−0.636894	−	0.770951i	$-0.719781\pi$
$317$	−4.79669	−	30.2851i	−0.269409	−	1.70098i	0.367485	−	0.930029i	$-0.380219\pi$
$318$	−8.63552	−	8.63552i	−0.484256	−	0.484256i
$319$	−4.48040	+	14.3355i	−0.250854	+	0.802633i
$320$		0			0
$321$	−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
$325$		0			0
$326$	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
$330$		0			0
$331$	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
$335$		0			0
$336$	2.87706	+	3.95994i	0.156957	+	0.216032i
$337$	−12.2410	−	6.23713i	−0.666812	−	0.339758i	0.0876027	−	0.996155i	$-0.472079\pi$
$337$	−12.2410	−	6.23713i	−0.666812	−	0.339758i	−0.754415	+	0.656398i	$0.772079\pi$
$338$	10.5847	−	5.39316i	0.575730	−	0.293349i
$339$	7.52914	−	10.3630i	0.408927	−	0.562839i
$340$		0			0
$341$	−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
$345$		0			0
$346$	−10.6736	+	7.75484i	−0.573818	+	0.416903i
$347$	2.77431	−	17.5163i	0.148933	−	0.940326i	−0.794139	−	0.607737i	$-0.792078\pi$
$347$	2.77431	−	17.5163i	0.148933	−	0.940326i	0.943072	−	0.332589i	$-0.107922\pi$
$348$	6.60121	−	12.9556i	0.353862	−	0.694494i
$349$	5.50175	−	16.9327i	0.294502	−	0.906384i	−0.688886	−	0.724870i	$-0.741900\pi$
$349$	5.50175	−	16.9327i	0.294502	−	0.906384i	0.983388	−	0.181515i	$-0.0581000\pi$
$350$		0			0
$351$		−	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	$-0.904514\pi$
$353$	−12.3974	+	12.3974i	−0.659845	+	0.659845i	0.295499	+	0.955343i	$0.404514\pi$
$354$	−11.6670	−	8.47655i	−0.620093	−	0.450524i
$355$		0			0
$356$	−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	0.868625	−	0.495470i	$-0.165004\pi$
$359$	−2.37480	−	7.30888i	−0.125337	−	0.385748i	−0.993962	+	0.109722i	$0.965004\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	−5.87638	+	18.0856i	−0.307163	+	0.945351i
$367$	−16.4293	+	32.2443i	−0.857603	+	1.68314i	−0.136139	+	0.990690i	$0.543469\pi$
$367$	−16.4293	+	32.2443i	−0.857603	+	1.68314i	−0.721464	+	0.692452i	$0.756531\pi$
$368$	0.676506	−	4.27129i	0.0352653	−	0.222656i
$369$	−14.8215	+	10.7685i	−0.771579	+	0.560585i
$370$		0			0
$371$	−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	$-0.111214\pi$
$373$	11.5350	+	11.5350i	0.597259	+	0.597259i	−0.342323	+	0.939582i	$0.611214\pi$
$374$	4.26737	−	6.01453i	0.220660	−	0.311004i
$375$		0			0
$376$	−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	0.896712	−	0.442614i	$-0.145949\pi$
$379$	3.86753	+	5.32320i	0.198662	+	0.273434i	−0.698050	+	0.716049i	$0.745949\pi$
$380$		0			0
$381$	−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	$-0.818890\pi$
$383$	−28.9091	+	4.57876i	−1.47719	+	0.233963i	−0.634733	+	0.772731i	$0.718890\pi$
$384$	3.21087			0.163854
$385$		0			0
$386$	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	−0.414035	−	0.910261i	$-0.635881\pi$
$389$	−4.21993	+	1.37114i	−0.213959	+	0.0695195i	0.200076	+	0.979780i	$0.435881\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	19.4520	−	14.4695i	0.977501	−	0.727120i
$397$	−6.59354	−	6.59354i	−0.330920	−	0.330920i	0.522016	−	0.852936i	$-0.325180\pi$
$397$	−6.59354	−	6.59354i	−0.330920	−	0.330920i	−0.852936	+	0.522016i	$0.825180\pi$
$398$	1.42471	+	8.99529i	0.0714145	+	0.450893i
$399$	28.8485	+	9.37344i	1.44423	+	0.469259i
$400$		0			0
$401$	−7.12541	+	5.17691i	−0.355826	+	0.258523i	−0.751309	−	0.659951i	$-0.770577\pi$
$401$	−7.12541	+	5.17691i	−0.355826	+	0.258523i	0.395483	+	0.918473i	$0.370577\pi$
$402$	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
$405$		0			0
$406$		−	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	0.878579	−	0.477597i	$-0.158492\pi$
$409$	14.0728	+	10.2245i	0.695853	+	0.505567i	−0.182726	+	0.983164i	$0.558492\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$	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	$0.131210\pi$
$419$			16.4015i			0.801265i	−0.916239	+	0.400632i	$0.868790\pi$
$420$		0			0
$421$	8.15001	−	25.0832i	0.397207	−	1.22248i	−0.530022	−	0.847984i	$-0.677816\pi$
$421$	8.15001	−	25.0832i	0.397207	−	1.22248i	0.927229	−	0.374494i	$-0.122184\pi$
$422$	−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
$425$		0			0
$426$	−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
$430$		0			0
$431$	−5.58501	+	7.68711i	−0.269020	+	0.370275i	−0.922059	−	0.387050i	$-0.873494\pi$
$431$	−5.58501	+	7.68711i	−0.269020	+	0.370275i	0.653038	+	0.757325i	$0.273494\pi$
$432$	−12.3296	+	6.28227i	−0.593210	+	0.302256i
$433$	22.2230	+	11.3232i	1.06797	+	0.544158i	0.897414	−	0.441190i	$-0.145443\pi$
$433$	22.2230	+	11.3232i	1.06797	+	0.544158i	0.170557	+	0.985348i	$0.445443\pi$
$434$	2.57820	+	3.54858i	0.123757	+	0.170338i
$435$		0			0
$436$	−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	$0.487150\pi$
$440$		0			0
$441$	34.1809			1.62766
$442$	−2.32477	+	0.368207i	−0.110578	+	0.0175138i
$443$	−9.21964	−	18.0946i	−0.438038	−	0.859698i	−0.999482	−	0.0321835i	$-0.989754\pi$
$443$	−9.21964	−	18.0946i	−0.438038	−	0.859698i	0.561444	−	0.827515i	$-0.310246\pi$
$444$	4.25044	−	1.38105i	0.201717	−	0.0655418i
$445$		0			0
$446$	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	0.482643	−	0.875817i	$-0.339677\pi$
$449$	24.7166	−	34.0195i	1.16645	−	1.60548i	0.683806	−	0.729664i	$-0.260323\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	16.0978	−	11.6957i	0.753848	−	0.547703i
$457$	−1.58324	+	9.99618i	−0.0740608	+	0.467602i	0.922587	+	0.385789i	$0.126071\pi$
$457$	−1.58324	+	9.99618i	−0.0740608	+	0.467602i	−0.996648	+	0.0818123i	$0.973929\pi$
$458$	0.691961	−	1.35805i	0.0323332	−	0.0634575i
$459$	9.50814	−	29.2630i	0.443802	−	1.36588i
$460$		0			0
$461$			27.4513i			1.27854i	0.768984	+	0.639268i	$0.220763\pi$
$461$			27.4513i			1.27854i	−0.768984	+	0.639268i	$0.779237\pi$
$462$	7.20708	−	14.5466i	0.335304	−	0.676768i
$463$	−12.8080	+	12.8080i	−0.595237	+	0.595237i	−0.939041	−	0.343804i	$-0.888284\pi$
$463$	−12.8080	+	12.8080i	−0.595237	+	0.595237i	0.343804	+	0.939041i	$0.388284\pi$
$464$	−3.66363	−	2.66178i	−0.170080	−	0.123570i
$465$		0			0
$466$	6.85697	+	21.1036i	0.317643	+	0.977604i
$467$	21.5674	+	3.41594i	0.998021	+	0.158071i	0.634011	−	0.773324i	$-0.281407\pi$
$467$	21.5674	+	3.41594i	0.998021	+	0.158071i	0.364010	+	0.931395i	$0.381407\pi$
$468$	−7.64249	−	1.21045i	−0.353274	−	0.0559532i
$469$	−3.60265	−	11.0878i	−0.166355	−	0.511988i
$470$		0			0
$471$	−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
$475$		0			0
$476$	−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	−0.701766	−	0.712408i	$-0.747605\pi$
$479$	−5.27636	+	3.83350i	−0.241083	+	0.175157i	0.460683	+	0.887565i	$0.347605\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	18.0681	−	24.8685i	0.819583	−	1.12806i
$487$	2.61310	−	1.33144i	0.118411	−	0.0603334i	−0.393782	−	0.919204i	$-0.628833\pi$
$487$	2.61310	−	1.33144i	0.118411	−	0.0603334i	0.512193	+	0.858871i	$0.328833\pi$
$488$	5.27698	+	2.68875i	0.238878	+	0.121714i
$489$	4.10918	+	5.65580i	0.185824	+	0.255764i
$490$		0			0
$491$	12.6664	−	4.11555i	0.571625	−	0.185732i	−0.00892018	−	0.999960i	$-0.502839\pi$
$491$	12.6664	−	4.11555i	0.571625	−	0.185732i	0.580545	+	0.814228i	$0.302839\pi$
$492$	3.65348	+	7.17035i	0.164711	+	0.323264i
$493$	9.94529	−	1.57518i	0.447913	−	0.0709425i
$494$	6.55996			0.295147
$495$		0			0
$496$	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	0.234130	−	0.972205i	$-0.424776\pi$
$499$	22.2265	−	7.22182i	0.994994	−	0.323293i	0.760863	+	0.648912i	$0.224776\pi$
$500$		0			0
$501$	−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	$-0.823327\pi$
$503$	−20.7030	+	10.5487i	−0.923103	+	0.470344i	−0.0732197	+	0.997316i	$0.523327\pi$
$504$	−6.54977	+	9.01498i	−0.291750	+	0.401559i
$505$		0			0
$506$	−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	−0.219772	−	0.975551i	$-0.570531\pi$
$509$	−21.9064	−	7.11784i	−0.970986	−	0.315493i	−0.751214	+	0.660059i	$0.770531\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$			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
$520$		0			0
$521$	−9.62530	−	29.6236i	−0.421692	−	1.29783i	−0.906127	−	0.423007i	$-0.860975\pi$
$521$	−9.62530	−	29.6236i	−0.421692	−	1.29783i	0.484435	−	0.874827i	$-0.339025\pi$
$522$	32.6944	+	5.17828i	1.43099	+	0.226647i
$523$	−5.13797	−	0.813774i	−0.224668	−	0.0355838i	0.0430856	−	0.999071i	$-0.486281\pi$
$523$	−5.13797	−	0.813774i	−0.224668	−	0.0355838i	−0.267753	+	0.963488i	$0.586281\pi$
$524$	−3.02111	−	9.29801i	−0.131978	−	0.406185i
$525$		0			0
$526$	−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
$530$		0			0
$531$	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
$535$		0			0
$536$	−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
$540$		0			0
$541$	7.63567	−	10.5096i	0.328283	−	0.451843i	−0.612690	−	0.790323i	$-0.709913\pi$
$541$	7.63567	−	10.5096i	0.328283	−	0.451843i	0.940974	+	0.338480i	$0.109913\pi$
$542$	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
$545$		0			0
$546$	−4.92780	+	1.60114i	−0.210890	+	0.0685224i
$547$	−2.13624	−	4.19261i	−0.0913391	−	0.179263i	0.840817	−	0.541319i	$-0.182075\pi$
$547$	−2.13624	−	4.19261i	−0.0913391	−	0.179263i	−0.932156	+	0.362056i	$0.882075\pi$
$548$	2.44036	−	0.386515i	0.104247	−	0.0165111i
$549$	−43.2916			−1.84764
$550$		0			0
$551$	−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
$555$		0			0
$556$	−4.41597	−	6.07806i	−0.187279	−	0.257767i
$557$	29.1897	+	14.8729i	1.23681	+	0.630185i	0.945243	−	0.326366i	$-0.105824\pi$
$557$	29.1897	+	14.8729i	1.23681	+	0.630185i	0.291564	+	0.956551i	$0.405824\pi$
$558$	−18.7400	+	9.54851i	−0.793328	+	0.404221i
$559$	−5.63999	+	7.76278i	−0.238546	+	0.328331i
$560$		0			0
$561$	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	$-0.0276780\pi$
$563$	0.520168	+	3.28421i	0.0219225	+	0.138413i	−0.974299	+	0.225257i	$0.927678\pi$
$564$	−13.7002	−	4.45146i	−0.576882	−	0.187440i
$565$		0			0
$566$	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	−0.986353	−	0.164645i	$-0.947352\pi$
$569$	−2.18501	+	6.72478i	−0.0916005	+	0.281917i	0.894752	+	0.446563i	$0.147352\pi$
$570$		0			0
$571$		−	24.2620i		−	1.01533i	−0.861553	−	0.507667i	$-0.830508\pi$
$571$		−	24.2620i		−	1.01533i	0.861553	−	0.507667i	$-0.169492\pi$
$572$	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
$575$		0			0
$576$	2.25882	+	6.95193i	0.0941175	+	0.289664i
$577$	−6.36086	−	1.00746i	−0.264806	−	0.0419412i	0.0226195	−	0.999744i	$-0.492799\pi$
$577$	−6.36086	−	1.00746i	−0.264806	−	0.0419412i	−0.287426	+	0.957803i	$0.592799\pi$
$578$	11.9075	+	1.88596i	0.495286	+	0.0784455i
$579$	3.80544	+	11.7119i	0.158149	+	0.486731i
$580$		0			0
$581$	−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
$585$		0			0
$586$	6.06998	−	18.6815i	0.250748	−	0.771724i
$587$	−2.50306	+	4.91253i	−0.103312	+	0.202762i	−0.936876	−	0.349661i	$-0.886297\pi$
$587$	−2.50306	+	4.91253i	−0.103312	+	0.202762i	0.833564	+	0.552423i	$0.186297\pi$
$588$	2.34877	−	14.8295i	0.0968615	−	0.611560i
$589$	14.4256	−	10.4808i	0.594395	−	0.431853i
$590$		0			0
$591$	−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	$-0.141722\pi$
$593$	11.4901	+	11.4901i	0.471841	+	0.471841i	−0.430669	+	0.902510i	$0.641722\pi$
$594$	37.4307	+	26.5574i	1.53580	+	1.08967i
$595$		0			0
$596$	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	0.930771	+	0.365603i	$0.119137\pi$
$599$	24.2507	+	33.3782i	0.990856	+	1.36380i	0.0600854	+	0.998193i	$0.480863\pi$
$600$		0			0
$601$	42.1453	−	13.6938i	1.71914	−	0.558583i	0.727330	−	0.686288i	$-0.240761\pi$
$601$	42.1453	−	13.6938i	1.71914	−	0.558583i	0.991812	+	0.127705i	$0.0407609\pi$
$602$	6.27334	+	12.3121i	0.255682	+	0.501804i
$603$	55.2143	−	8.74509i	2.24850	−	0.356127i
$604$	−21.1850			−0.862006
$605$		0			0
$606$	56.5487			2.29713
$607$	16.6706	−	2.64036i	0.676638	−	0.107169i	0.191348	−	0.981522i	$-0.438714\pi$
$607$	16.6706	−	2.64036i	0.676638	−	0.107169i	0.485290	+	0.874353i	$0.338714\pi$
$608$	−2.81341	−	5.52162i	−0.114099	−	0.223931i
$609$	21.0810	−	6.84963i	0.854245	−	0.277561i
$610$		0			0
$611$	−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	$-0.486579\pi$
$613$	21.6696	−	11.0412i	0.875225	−	0.445949i	0.833074	+	0.553162i	$0.186579\pi$
$614$	6.94359	−	9.55703i	0.280221	−	0.385691i
$615$		0			0
$616$	−4.12350	−	2.92567i	−0.166141	−	0.117878i
$617$	2.46606	+	2.46606i	0.0992799	+	0.0992799i	0.755002	−	0.655722i	$-0.227636\pi$
$617$	2.46606	+	2.46606i	0.0992799	+	0.0992799i	−0.655722	+	0.755002i	$0.727636\pi$
$618$	1.61350	+	10.1873i	0.0649046	+	0.409791i
$619$	−28.7652	−	9.34637i	−1.15617	−	0.375662i	−0.332706	−	0.943031i	$-0.607962\pi$
$619$	−28.7652	−	9.34637i	−1.15617	−	0.375662i	−0.823464	+	0.567369i	$0.807962\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$			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
$630$		0			0
$631$	9.75833	+	30.0330i	0.388473	+	1.19560i	0.933929	+	0.357458i	$0.116356\pi$
$631$	9.75833	+	30.0330i	0.388473	+	1.19560i	−0.545456	+	0.838139i	$0.683644\pi$
$632$	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
$635$		0			0
$636$	−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			0
$641$	−1.51513	+	4.66309i	−0.0598440	+	0.184181i	−0.976509	−	0.215474i	$-0.930870\pi$
$641$	−1.51513	+	4.66309i	−0.0598440	+	0.184181i	0.916665	+	0.399655i	$0.130870\pi$
$642$	−24.0781	+	47.2558i	−0.950285	+	1.86504i
$643$	−2.56190	+	16.1752i	−0.101031	+	0.637888i	0.884259	+	0.466998i	$0.154664\pi$
$643$	−2.56190	+	16.1752i	−0.101031	+	0.637888i	−0.985290	+	0.170890i	$0.945336\pi$
$644$	5.33341	−	3.87495i	0.210166	−	0.152694i
$645$		0			0
$646$	13.1050	+	4.25806i	0.515608	+	0.167531i
$647$	−6.72843	−	42.4816i	−0.264522	−	1.67012i	−0.659707	−	0.751523i	$-0.729319\pi$
$647$	−6.72843	−	42.4816i	−0.264522	−	1.67012i	0.395185	−	0.918602i	$-0.370681\pi$
$648$	−15.9117	−	15.9117i	−0.625071	−	0.625071i
$649$	14.2179	+	4.44366i	0.558102	+	0.174429i
$650$		0			0
$651$	−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	$-0.328773\pi$
$653$	3.03452	+	1.54616i	0.118750	+	0.0605061i	−0.393606	+	0.919279i	$0.628773\pi$
$654$	−3.56325	−	4.90440i	−0.139334	−	0.191777i
$655$		0			0
$656$	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	$0.510568\pi$
$660$		0			0
$661$	−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
$665$		0			0
$666$	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
$670$		0			0
$671$	−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	−0.930161	−	0.367153i	$-0.880333\pi$
$673$	−4.12434	−	26.0401i	−0.158982	−	1.00377i	0.771179	−	0.636619i	$-0.219667\pi$
$674$	−13.0660	−	4.24541i	−0.503285	−	0.163527i
$675$		0			0
$676$	9.61068	−	6.98256i	0.369641	−	0.268560i
$677$	1.85111	−	11.6875i	0.0711440	−	0.449185i	−0.926242	−	0.376929i	$-0.876980\pi$
$677$	1.85111	−	11.6875i	0.0711440	−	0.449185i	0.997386	−	0.0722563i	$-0.0230200\pi$
$678$	5.81532	−	11.4132i	0.223336	−	0.438321i
$679$	3.30057	−	10.1581i	0.126664	−	0.389832i
$680$		0			0
$681$		−	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	$-0.575748\pi$
$683$	19.2371	−	19.2371i	0.736087	−	0.736087i	0.971818	+	0.235731i	$0.0757484\pi$
$684$	36.6474	+	26.6259i	1.40125	+	1.01807i
$685$		0			0
$686$	−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
$690$		0			0
$691$	−2.86279	−	2.07994i	−0.108906	−	0.0791246i	0.531999	−	0.846745i	$-0.321441\pi$
$691$	−2.86279	−	2.07994i	−0.108906	−	0.0791246i	−0.640905	+	0.767620i	$0.721441\pi$
$692$	−9.32909	+	9.32909i	−0.354639	+	0.354639i
$693$	36.5652	+	5.37084i	1.38900	+	0.204021i
$694$		−	17.7347i		−	0.673199i
$695$		0			0
$696$	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
$700$		0			0
$701$	37.5991	+	12.2167i	1.42010	+	0.461418i	0.915634	−	0.402013i	$-0.131689\pi$
$701$	37.5991	+	12.2167i	1.42010	+	0.461418i	0.504466	+	0.863432i	$0.331689\pi$
$702$	−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
$705$		0			0
$706$	−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	0.973201	+	0.229955i	$0.0738580\pi$
$709$	23.7291	+	32.6603i	0.891166	+	1.22658i	−0.0820353	+	0.996629i	$0.526142\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$	−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	−0.188595	−	0.982055i	$-0.560393\pi$
$719$	6.32991	−	2.05671i	0.236066	−	0.0767024i	0.424661	+	0.905353i	$0.360393\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	−20.1129	+	29.0335i	−0.746459	+	1.07754i
$727$	−13.3487	−	13.3487i	−0.495074	−	0.495074i	0.414826	−	0.909901i	$-0.363842\pi$
$727$	−13.3487	−	13.3487i	−0.495074	−	0.495074i	−0.909901	+	0.414826i	$0.863842\pi$
$728$	0.252439	+	1.59384i	0.00935600	+	0.0590715i
$729$	29.6653	+	9.63884i	1.09871	+	0.356994i
$730$		0			0
$731$	−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	−0.529861	−	0.848084i	$-0.677756\pi$
$733$	12.6624	−	24.8515i	0.467698	−	0.917909i	0.997559	−	0.0698250i	$-0.0222441\pi$
$734$	−11.1829	+	34.4175i	−0.412769	+	1.27037i
$735$		0			0
$736$		−	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	0.739061	−	0.673638i	$-0.235269\pi$
$739$	8.88327	+	6.45407i	0.326776	+	0.237417i	−0.412285	+	0.911055i	$0.635269\pi$
$740$		0			0
$741$	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	$-0.303836\pi$
$743$	23.8652	+	3.77987i	0.875527	+	0.138670i	0.297534	+	0.954711i	$0.403836\pi$
$744$	2.85493	+	8.78656i	0.104667	+	0.322131i
$745$		0			0
$746$	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
$750$		0			0
$751$	−15.1449	+	46.6112i	−0.552645	+	1.70087i	0.149437	+	0.988771i	$0.452254\pi$
$751$	−15.1449	+	46.6112i	−0.552645	+	1.70087i	−0.702082	+	0.712096i	$0.747746\pi$
$752$	−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
$755$		0			0
$756$	−20.0624	−	6.51868i	−0.729664	−	0.237082i
$757$	7.91360	+	49.9645i	0.287625	+	1.81599i	0.532493	+	0.846434i	$0.321255\pi$
$757$	7.91360	+	49.9645i	0.287625	+	1.81599i	−0.244869	+	0.969556i	$0.578745\pi$
$758$	4.65265	+	4.65265i	0.168992	+	0.168992i
$759$	−27.4863	−	36.9511i	−0.997690	−	1.34124i
$760$		0			0
$761$	18.7749	−	25.8415i	0.680591	−	0.936753i	−0.319350	−	0.947637i	$-0.603464\pi$
$761$	18.7749	−	25.8415i	0.680591	−	0.936753i	0.999941	+	0.0108837i	$0.00346445\pi$
$762$	−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
$765$		0			0
$766$	−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	$0.769004\pi$
$770$		0			0
$771$	−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	$-0.278386\pi$
$773$	−9.90821	−	19.4460i	−0.356373	−	0.699422i	−0.997696	+	0.0678495i	$0.978386\pi$
$774$	−63.0158	+	20.4751i	−2.26506	+	0.735962i
$775$		0			0
$776$	−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			0
$781$	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
$785$		0			0
$786$	25.3959	−	18.4512i	0.905843	−	0.658134i
$787$	−4.74219	+	29.9410i	−0.169041	+	1.06728i	0.746596	+	0.665277i	$0.231687\pi$
$787$	−4.74219	+	29.9410i	−0.169041	+	1.06728i	−0.915637	+	0.402005i	$0.868313\pi$
$788$	−4.75118	+	9.32471i	−0.169254	+	0.332179i
$789$	4.50319	−	13.8594i	0.160318	−	0.493407i
$790$		0			0
$791$		−	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
$795$		0			0
$796$	2.81435	+	8.66167i	0.0997519	+	0.307005i
$797$	−53.0278	−	8.39878i	−1.87834	−	0.297500i	−0.890744	−	0.454505i	$-0.849816\pi$
$797$	−53.0278	−	8.39878i	−1.87834	−	0.297500i	−0.987598	+	0.157004i	$0.949816\pi$
$798$	29.9596	+	4.74514i	1.06056	+	0.167976i
$799$	−3.08264	−	9.48739i	−0.109056	−	0.335640i
$800$		0			0
$801$	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
$805$		0			0
$806$	−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	−0.0417260	−	0.999129i	$-0.513286\pi$
$809$	25.4737	−	18.5077i	0.895608	−	0.650697i	0.937334	+	0.348432i	$0.113286\pi$
$810$		0			0
$811$	−6.48163	−	2.10601i	−0.227601	−	0.0739520i	0.192996	−	0.981199i	$-0.438179\pi$
$811$	−6.48163	−	2.10601i	−0.227601	−	0.0739520i	−0.420597	+	0.907247i	$0.638179\pi$
$812$	−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
$815$		0			0
$816$	−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
$820$		0			0
$821$	−0.216685	+	0.0704052i	−0.00756235	+	0.00245716i	−0.312796	−	0.949820i	$-0.601266\pi$
$821$	−0.216685	+	0.0704052i	−0.00756235	+	0.00245716i	0.305233	+	0.952278i	$0.401266\pi$
$822$	3.60167	+	7.06867i	0.125623	+	0.246548i
$823$	−22.6675	+	3.59018i	−0.790139	+	0.125146i	−0.538445	−	0.842661i	$-0.680988\pi$
$823$	−22.6675	+	3.59018i	−0.790139	+	0.125146i	−0.251695	+	0.967807i	$0.580988\pi$
$824$	3.21229			0.111905
$825$		0			0
$826$	−6.84677			−0.238229
$827$	39.9523	−	6.32782i	1.38928	−	0.220040i	0.583430	−	0.812164i	$-0.301710\pi$
$827$	39.9523	−	6.32782i	1.38928	−	0.220040i	0.805847	+	0.592124i	$0.201710\pi$
$828$	14.3511	+	28.1656i	0.498735	+	0.978823i
$829$	25.8477	−	8.39841i	0.897726	−	0.291689i	0.176428	−	0.984314i	$-0.443546\pi$
$829$	25.8477	−	8.39841i	0.897726	−	0.291689i	0.721298	+	0.692625i	$0.243546\pi$
$830$		0			0
$831$	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
$835$		0			0
$836$	−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	0.647554	−	0.762019i	$-0.275792\pi$
$839$	20.9575	+	6.80951i	0.723533	+	0.235090i	0.0759789	+	0.997109i	$0.475792\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$		−	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
$850$		0			0
$851$	−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	$-0.234615\pi$
$853$	36.1266	+	5.72190i	1.23695	+	0.195914i	0.496508	+	0.868032i	$0.334615\pi$
$854$	2.78994	+	8.58655i	0.0954697	+	0.293826i
$855$		0			0
$856$	13.3632	+	9.70891i	0.456744	+	0.331844i
$857$	−8.98140	+	8.98140i	−0.306799	+	0.306799i	−0.843666	−	0.536868i	$-0.819607\pi$
$857$	−8.98140	+	8.98140i	−0.306799	+	0.306799i	0.536868	+	0.843666i	$0.319607\pi$
$858$	11.1136	−	1.88849i	0.379411	−	0.0644719i
$859$		−	54.6972i		−	1.86624i	−0.359559	−	0.933122i	$-0.617073\pi$
$859$		−	54.6972i		−	1.86624i	0.359559	−	0.933122i	$-0.382927\pi$
$860$		0			0
$861$	−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	−0.920132	−	0.391607i	$-0.871919\pi$
$863$	2.23202	−	14.0924i	0.0759788	−	0.479711i	0.996111	−	0.0881040i	$-0.0280808\pi$
$864$	−11.1951	+	8.13370i	−0.380864	+	0.276714i
$865$		0			0
$866$	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
$870$		0			0
$871$	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
$875$		0			0
$876$	34.8324	−	11.3177i	1.17688	−	0.382391i
$877$	−6.98490	−	13.7086i	−0.235863	−	0.462908i	0.742488	−	0.669860i	$-0.233646\pi$
$877$	−6.98490	−	13.7086i	−0.235863	−	0.462908i	−0.978351	+	0.206952i	$0.933646\pi$
$878$	1.67033	−	0.264554i	0.0563710	−	0.00892828i
$879$	63.0707			2.12732
$880$		0			0
$881$	−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	−0.776932	−	0.629584i	$-0.783225\pi$
$883$	−24.6520	−	48.3824i	−0.829607	−	1.62820i	−0.0526752	−	0.998612i	$-0.516775\pi$
$884$	−2.23854	+	0.727347i	−0.0752904	+	0.0244633i
$885$		0			0
$886$	−11.9367	−	16.4295i	−0.401023	−	0.551960i
$887$	52.7376	+	26.8712i	1.77076	+	0.902246i	0.936325	+	0.351134i	$0.114204\pi$
$887$	52.7376	+	26.8712i	1.77076	+	0.902246i	0.834432	+	0.551111i	$0.185796\pi$
$888$	3.98206	−	2.02896i	0.133629	−	0.0680875i
$889$	−15.2015	+	20.9231i	−0.509843	+	0.701738i
$890$		0			0
$891$	−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
$895$		0			0
$896$	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
$900$		0			0
$901$		−	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
$905$		0			0
$906$	−21.0201	−	64.6931i	−0.698345	−	2.14928i
$907$	14.9623	+	2.36980i	0.496817	+	0.0786880i	0.399814	−	0.916596i	$-0.369075\pi$
$907$	14.9623	+	2.36980i	0.496817	+	0.0786880i	0.0970022	+	0.995284i	$0.469075\pi$
$908$	−2.01564	−	0.319245i	−0.0668912	−	0.0105945i
$909$	39.7815	+	122.435i	1.31947	+	4.06091i
$910$		0			0
$911$	5.44856	+	3.95861i	0.180519	+	0.131155i	0.674375	−	0.738389i	$-0.264413\pi$
$911$	5.44856	+	3.95861i	0.180519	+	0.131155i	−0.493856	+	0.869544i	$0.664413\pi$
$912$	14.0700	−	14.0700i	0.465904	−	0.465904i
$913$	3.03315	+	2.96573i	0.100383	+	0.0981512i
$914$			10.1208i			0.334766i
$915$		0			0
$916$	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	−0.618813	+	0.785538i	$0.712386\pi$
$919$	−47.2044	+	34.2960i	−1.55713	+	1.13132i	−0.938315	+	0.345782i	$0.887614\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	−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	0.701327	−	0.712839i	$-0.252591\pi$
$929$	−5.89306	−	8.11110i	−0.193345	−	0.266117i	−0.894672	+	0.446723i	$0.852591\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	−7.73776			−0.252917
$937$	41.2128	−	6.52746i	1.34636	−	0.213243i	0.558710	−	0.829363i	$-0.311297\pi$
$937$	41.2128	−	6.52746i	1.34636	−	0.213243i	0.787652	+	0.616120i	$0.211297\pi$
$938$	−5.29282	−	10.3877i	−0.172817	−	0.339172i
$939$	−92.1972	+	29.9567i	−3.00874	+	0.977600i
$940$		0			0
$941$	14.4754	+	19.9237i	0.471885	+	0.649494i	0.976920	−	0.213605i	$-0.0685205\pi$
$941$	14.4754	+	19.9237i	0.471885	+	0.649494i	−0.505035	+	0.863099i	$0.668520\pi$
$942$	−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
$945$		0			0
$946$	−9.61089	−	28.4859i	−0.312477	−	0.926157i
$947$	6.72877	+	6.72877i	0.218656	+	0.218656i	0.807932	−	0.589276i	$-0.200587\pi$
$947$	6.72877	+	6.72877i	0.218656	+	0.218656i	−0.589276	+	0.807932i	$0.700587\pi$
$948$	2.91297	+	18.3918i	0.0946090	+	0.597338i
$949$	11.4836	+	3.73124i	0.372772	+	0.121121i
$950$		0			0
$951$	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	−0.474623	−	0.880189i	$-0.657416\pi$
$953$	15.9429	−	31.2897i	0.516441	−	1.01357i	0.991064	−	0.133384i	$-0.0425844\pi$
$954$	8.59137	−	26.4415i	0.278156	−	0.856076i
$955$		0			0
$956$			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
$960$		0			0
$961$	−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
$965$		0			0
$966$	17.1249	+	12.4420i	0.550984	+	0.400313i
$967$	−43.6347	+	43.6347i	−1.40320	+	1.40320i	−0.613512	+	0.789685i	$0.710244\pi$
$967$	−43.6347	+	43.6347i	−1.40320	+	1.40320i	−0.789685	+	0.613512i	$0.789756\pi$
$968$	7.95103	+	7.60139i	0.255556	+	0.244318i
$969$			44.2438i			1.42131i
$970$		0			0
$971$	8.80597	−	27.1020i	0.282597	−	0.869744i	−0.704512	−	0.709693i	$-0.748834\pi$
$971$	8.80597	−	27.1020i	0.282597	−	0.869744i	0.987109	−	0.160052i	$-0.0511661\pi$
$972$	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
$975$		0			0
$976$	5.63262	+	1.83015i	0.180296	+	0.0585817i
$977$	8.07944	+	51.0116i	0.258484	+	1.63201i	0.685720	+	0.727865i	$0.259487\pi$
$977$	8.07944	+	51.0116i	0.258484	+	1.63201i	−0.427236	+	0.904140i	$0.640513\pi$
$978$	4.94335	+	4.94335i	0.158071	+	0.158071i
$979$	−20.2508	+	28.5420i	−0.647219	+	0.912206i
$980$		0			0
$981$	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	$-0.0138033\pi$
$983$	48.6352	+	24.7809i	1.55122	+	0.790387i	0.552161	+	0.833737i	$0.313803\pi$
$984$	4.73019	+	6.51054i	0.150793	+	0.207549i
$985$		0			0
$986$	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
$990$		0			0
$991$	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
$995$		0			0
$996$	−2.41395	−	3.32251i	−0.0764888	−	0.105278i
$997$	26.6089	+	13.5579i	0.842713	+	0.429384i	0.821375	−	0.570389i	$-0.193207\pi$
$997$	26.6089	+	13.5579i	0.842713	+	0.429384i	0.0213379	+	0.999772i	$0.493207\pi$
$998$	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	550.2.bh.b.7.6		48
5.2	odd	4		110.2.k.a.73.6	yes	48
5.3	odd	4	inner	550.2.bh.b.293.1		48
5.4	even	2		110.2.k.a.7.1	✓	48
11.8	odd	10	inner	550.2.bh.b.107.1		48
15.2	even	4		990.2.bh.c.73.2		48
15.14	odd	2		990.2.bh.c.667.6		48
20.7	even	4		880.2.cm.c.513.1		48
20.19	odd	2		880.2.cm.c.337.6		48
55.8	even	20	inner	550.2.bh.b.393.6		48
55.19	odd	10		110.2.k.a.107.6	yes	48
55.52	even	20		110.2.k.a.63.1	yes	48
165.74	even	10		990.2.bh.c.217.2		48
165.107	odd	20		990.2.bh.c.613.6		48
220.19	even	10		880.2.cm.c.657.1		48
220.107	odd	20		880.2.cm.c.833.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.1	✓	48	5.4	even	2
110.2.k.a.63.1	yes	48	55.52	even	20
110.2.k.a.73.6	yes	48	5.2	odd	4
110.2.k.a.107.6	yes	48	55.19	odd	10
550.2.bh.b.7.6		48	1.1	even	1	trivial
550.2.bh.b.107.1		48	11.8	odd	10	inner
550.2.bh.b.293.1		48	5.3	odd	4	inner
550.2.bh.b.393.6		48	55.8	even	20	inner
880.2.cm.c.337.6		48	20.19	odd	2
880.2.cm.c.513.1		48	20.7	even	4
880.2.cm.c.657.1		48	220.19	even	10
880.2.cm.c.833.6		48	220.107	odd	20
990.2.bh.c.73.2		48	15.2	even	4
990.2.bh.c.217.2		48	165.74	even	10
990.2.bh.c.613.6		48	165.107	odd	20
990.2.bh.c.667.6		48	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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.bh (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} +(1.88730 + 2.59765i) q^{6} +(1.35828 + 0.692077i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-4.29653 + 5.91367i) q^{9} +(-2.70495 - 1.91918i) q^{11} +(2.27043 + 2.27043i) q^{12} +(0.165595 + 1.04553i) q^{13} +(1.44982 + 0.471075i) q^{14} +(0.809017 - 0.587785i) q^{16} +(-0.347837 + 2.19616i) q^{17} +(-3.31853 + 6.51299i) q^{18} +(1.91500 - 5.89375i) q^{19} +4.89475i q^{21} +(-2.97187 - 1.47241i) q^{22} +(3.05791 - 3.05791i) q^{23} +(2.59765 + 1.88730i) q^{24} +(0.327113 + 1.00675i) q^{26} +(-13.6675 - 2.16472i) q^{27} +(1.50566 + 0.238474i) q^{28} +(-1.39938 - 4.30686i) q^{29} +(2.32781 + 1.69125i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.54760 - 10.5362i) q^{33} +2.22353i q^{34} +(-2.25882 + 6.95193i) q^{36} +(0.631904 - 1.24018i) q^{37} +(0.969434 - 6.12076i) q^{38} +(-2.74977 + 1.99782i) q^{39} +(2.38365 + 0.774496i) q^{41} +(0.765708 + 4.83449i) q^{42} +(6.40957 + 6.40957i) q^{43} +(-3.16562 - 0.989379i) q^{44} +(2.54190 - 3.49862i) q^{46} +(-3.99740 + 2.03678i) q^{47} +(2.86091 + 1.45771i) q^{48} +(-2.74855 - 3.78305i) q^{49} +(-6.79005 + 2.20622i) q^{51} +(0.480577 + 0.943185i) q^{52} +(-3.75665 + 0.594995i) q^{53} -13.8379 q^{54} +1.52443 q^{56} +(19.6530 - 3.11273i) q^{57} +(-2.05589 - 4.03492i) q^{58} +(-4.27154 + 1.38791i) q^{59} +(3.48115 + 4.79140i) q^{61} +(2.56372 + 1.30628i) q^{62} +(-9.92860 + 5.05887i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-0.119682 - 10.6486i) q^{66} +(-5.40776 - 5.40776i) q^{67} +(0.347837 + 2.19616i) q^{68} +(13.2059 + 4.29086i) q^{69} +(-7.19862 + 5.23010i) q^{71} +(-1.14349 + 7.21970i) q^{72} +(5.17847 - 10.1633i) q^{73} +(0.430117 - 1.32376i) q^{74} -6.19706i q^{76} +(-2.34584 - 4.47882i) q^{77} +(-2.40339 + 2.40339i) q^{78} +(4.69179 + 3.40879i) q^{79} +(-6.95367 - 21.4012i) q^{81} +(2.47546 + 0.392075i) q^{82} +(-1.26330 - 0.200087i) q^{83} +(1.51256 + 4.65519i) q^{84} +(7.33334 + 5.32798i) q^{86} +(10.2816 - 10.2816i) q^{87} +(-3.28142 - 0.481987i) q^{88} -10.5518i q^{89} +(-0.498662 + 1.53472i) q^{91} +(1.96330 - 3.85319i) q^{92} +(-1.44526 + 9.12499i) q^{93} +(-3.62956 + 2.63703i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{3} + 20 q^{7} + 12 q^{11} + 16 q^{12} + 12 q^{16} + 20 q^{17} + 4 q^{22} + 8 q^{23} + 8 q^{26} - 8 q^{27} + 20 q^{28} + 16 q^{31} + 104 q^{33} - 4 q^{36} - 20 q^{37} + 36 q^{38} - 20 q^{41}+ \cdots - 72 q^{97}+O(q^{100}) \) 48 * q + 4 * q^3 + 20 * q^7 + 12 * q^11 + 16 * q^12 + 12 * q^16 + 20 * q^17 + 4 * q^22 + 8 * q^23 + 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 + 40 * q^46 - 40 * q^47 - 4 * q^48 + 40 * q^51 - 40 * q^52 - 8 * q^56 - 48 * q^58 + 80 * q^61 - 40 * q^62 - 100 * q^63 + 24 * q^66 - 20 * q^68 - 56 * q^71 + 20 * q^73 + 96 * q^77 - 16 * q^78 - 68 * q^81 - 56 * q^86 + 4 * q^88 - 68 * q^91 + 12 * q^92 - 76 * q^93 - 72 * q^97

Introduction

L-functions

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