LMFDB - Embedded newform 110.2.k.a.73.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(7,110)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			73.6
Character	$\chi$	$=$	110.73
Dual form			110.2.k.a.107.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.156434 + 0.987688i) q^{2} +(2.86091 - 1.45771i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.90161 + 1.17638i) q^{5} +(1.88730 + 2.59765i) q^{6} +(-0.692077 + 1.35828i) q^{7} +(-0.453990 - 0.891007i) 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} +(1.04553 - 0.165595i) q^{13} +(-1.44982 - 0.471075i) q^{14} +(-3.72553 + 6.13750i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-2.19616 - 0.347837i) q^{17} +(6.51299 + 3.31853i) q^{18} +(-1.91500 + 5.89375i) q^{19} +(1.44502 - 1.70643i) q^{20} +4.89475i q^{21} +(1.47241 - 2.97187i) q^{22} +(-3.05791 - 3.05791i) q^{23} +(-2.59765 - 1.88730i) q^{24} +(2.23228 - 4.47403i) q^{25} +(0.327113 + 1.00675i) q^{26} +(2.16472 - 13.6675i) q^{27} +(0.238474 - 1.50566i) q^{28} +(1.39938 + 4.30686i) q^{29} +(-6.64474 - 2.71955i) q^{30} +(2.32781 + 1.69125i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-10.5362 - 1.54760i) q^{33} -2.22353i q^{34} +(-0.281782 - 3.39707i) q^{35} +(-2.25882 + 6.95193i) q^{36} +(1.24018 + 0.631904i) q^{37} +(-6.12076 - 0.969434i) q^{38} +(2.74977 - 1.99782i) q^{39} +(1.91147 + 1.16029i) q^{40} +(2.38365 + 0.774496i) q^{41} +(-4.83449 + 0.765708i) 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} +(-2.03678 - 3.99740i) q^{47} +(1.45771 - 2.86091i) q^{48} +(2.74855 + 3.78305i) q^{49} +(4.76815 + 1.50490i) q^{50} +(-6.79005 + 2.20622i) q^{51} +(-0.943185 + 0.480577i) q^{52} +(0.594995 + 3.75665i) q^{53} +13.8379 q^{54} +(7.40145 + 0.467516i) q^{55} +1.52443 q^{56} +(3.11273 + 19.6530i) q^{57} +(-4.03492 + 2.05589i) q^{58} +(4.27154 - 1.38791i) q^{59} +(1.64660 - 6.98836i) q^{60} +(3.48115 + 4.79140i) q^{61} +(-1.30628 + 2.56372i) q^{62} +(5.05887 + 9.92860i) 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} +(2.19616 - 0.347837i) q^{68} +(-13.2059 - 4.29086i) q^{69} +(3.31116 - 0.809731i) q^{70} +(-7.19862 + 5.23010i) q^{71} +(-7.21970 - 1.14349i) q^{72} +(-10.1633 - 5.17847i) q^{73} +(-0.430117 + 1.32376i) q^{74} +(-0.135479 - 16.0538i) q^{75} -6.19706i q^{76} +(4.47882 - 2.34584i) q^{77} +(2.40339 + 2.40339i) q^{78} +(-4.69179 - 3.40879i) q^{79} +(-0.846982 + 2.06945i) q^{80} +(-6.95367 - 21.4012i) q^{81} +(-0.392075 + 2.47546i) q^{82} +(-0.200087 + 1.26330i) q^{83} +(-1.51256 - 4.65519i) q^{84} +(4.58543 - 1.92206i) q^{85} +(7.33334 + 5.32798i) q^{86} +(10.2816 + 10.2816i) q^{87} +(-0.481987 + 3.28142i) q^{88} +10.5518i q^{89} +(-16.2890 + 1.35115i) q^{90} +(-0.498662 + 1.53472i) q^{91} +(3.85319 + 1.96330i) q^{92} +(9.12499 + 1.44526i) q^{93} +(3.62956 - 2.63703i) q^{94} +(-3.29169 - 13.4604i) q^{95} +(3.05372 + 0.992214i) q^{96} +(6.92020 - 1.09605i) 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 $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$3$	2.86091	−	1.45771i	1.65175	−	0.841606i	0.655485	−	0.755208i	$-0.272464\pi$
$3$	2.86091	−	1.45771i	1.65175	−	0.841606i	0.996261	−	0.0863983i	$-0.0275358\pi$
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	−1.90161	+	1.17638i	−0.850428	+	0.526092i
$5$	−1.90161	+	1.17638i	−0.850428	+	0.526092i
$6$	1.88730	+	2.59765i	0.770488	+	1.06049i
$7$	−0.692077	+	1.35828i	−0.261581	+	0.513381i	−0.984021	−	0.178052i	$-0.943020\pi$
$7$	−0.692077	+	1.35828i	−0.261581	+	0.513381i	0.722440	+	0.691433i	$0.243020\pi$
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	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
$13$	1.04553	−	0.165595i	0.289977	−	0.0459279i	−0.00975110	−	0.999952i	$-0.503104\pi$
$13$	1.04553	−	0.165595i	0.289977	−	0.0459279i	0.299728	+	0.954025i	$0.403104\pi$
$14$	−1.44982	−	0.471075i	−0.387481	−	0.125900i
$15$	−3.72553	+	6.13750i	−0.961929	+	1.58470i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−2.19616	−	0.347837i	−0.532646	−	0.0843629i	−0.115683	−	0.993286i	$-0.536906\pi$
$17$	−2.19616	−	0.347837i	−0.532646	−	0.0843629i	−0.416963	+	0.908923i	$0.636906\pi$
$18$	6.51299	+	3.31853i	1.53513	+	0.782186i
$19$	−1.91500	+	5.89375i	−0.439330	+	1.35212i	0.449253	+	0.893405i	$0.351690\pi$
$19$	−1.91500	+	5.89375i	−0.439330	+	1.35212i	−0.888583	+	0.458715i	$0.848310\pi$
$20$	1.44502	−	1.70643i	0.323117	−	0.381570i
$21$			4.89475i			1.06812i
$22$	1.47241	−	2.97187i	0.313919	−	0.633605i
$23$	−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
$25$	2.23228	−	4.47403i	0.446455	−	0.894806i
$26$	0.327113	+	1.00675i	0.0641522	+	0.197440i
$27$	2.16472	−	13.6675i	0.416601	−	2.63031i
$28$	0.238474	−	1.50566i	0.0450673	−	0.284544i
$29$	1.39938	+	4.30686i	0.259859	+	0.799763i	0.992833	+	0.119507i	$0.0381314\pi$
$29$	1.39938	+	4.30686i	0.259859	+	0.799763i	−0.732975	+	0.680256i	$0.761869\pi$
$30$	−6.64474	−	2.71955i	−1.21316	−	0.496520i
$31$	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
$33$	−10.5362	−	1.54760i	−1.83412	−	0.269402i
$34$		−	2.22353i		−	0.381333i
$35$	−0.281782	−	3.39707i	−0.0476299	−	0.574209i
$36$	−2.25882	+	6.95193i	−0.376470	+	1.15866i
$37$	1.24018	+	0.631904i	0.203885	+	0.103884i	0.552952	−	0.833213i	$-0.313501\pi$
$37$	1.24018	+	0.631904i	0.203885	+	0.103884i	−0.349067	+	0.937098i	$0.613501\pi$
$38$	−6.12076	−	0.969434i	−0.992919	−	0.157263i
$39$	2.74977	−	1.99782i	0.440316	−	0.319908i
$40$	1.91147	+	1.16029i	0.302231	+	0.183458i
$41$	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	$0.537299\pi$
$42$	−4.83449	+	0.765708i	−0.745978	+	0.118151i
$43$	6.40957	−	6.40957i	0.977450	−	0.977450i	−0.0223009	−	0.999751i	$-0.507099\pi$
$43$	6.40957	−	6.40957i	0.977450	−	0.977450i	0.999751	+	0.0223009i	$0.00709920\pi$
$44$	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
$47$	−2.03678	−	3.99740i	−0.297095	−	0.583081i	0.693413	−	0.720541i	$-0.256106\pi$
$47$	−2.03678	−	3.99740i	−0.297095	−	0.583081i	−0.990507	+	0.137460i	$0.956106\pi$
$48$	1.45771	−	2.86091i	0.210402	−	0.412936i
$49$	2.74855	+	3.78305i	0.392650	+	0.540436i
$50$	4.76815	+	1.50490i	0.674319	+	0.212825i
$51$	−6.79005	+	2.20622i	−0.950797	+	0.308933i
$52$	−0.943185	+	0.480577i	−0.130796	+	0.0666440i
$53$	0.594995	+	3.75665i	0.0817288	+	0.516016i	0.994258	+	0.107005i	$0.0341261\pi$
$53$	0.594995	+	3.75665i	0.0817288	+	0.516016i	−0.912530	+	0.409011i	$0.865874\pi$
$54$	13.8379			1.88310
$55$	7.40145	+	0.467516i	0.998011	+	0.0630398i
$56$	1.52443			0.203711
$57$	3.11273	+	19.6530i	0.412291	+	2.60310i
$58$	−4.03492	+	2.05589i	−0.529811	+	0.269952i
$59$	4.27154	−	1.38791i	0.556107	−	0.180690i	−0.0174620	−	0.999848i	$-0.505559\pi$
$59$	4.27154	−	1.38791i	0.556107	−	0.180690i	0.573569	+	0.819158i	$0.305559\pi$
$60$	1.64660	−	6.98836i	0.212575	−	0.902193i
$61$	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	$0.676217\pi$
$62$	−1.30628	+	2.56372i	−0.165898	+	0.325593i
$63$	5.05887	+	9.92860i	0.637358	+	1.25089i
$64$	−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	$0.0952775\pi$
$68$	2.19616	−	0.347837i	0.266323	−	0.0421814i
$69$	−13.2059	−	4.29086i	−1.58980	−	0.516559i
$70$	3.31116	−	0.809731i	0.395759	−	0.0967814i
$71$	−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	$0.477057\pi$
$72$	−7.21970	−	1.14349i	−0.850850	−	0.134761i
$73$	−10.1633	−	5.17847i	−1.18953	−	0.606094i	−0.256725	−	0.966485i	$-0.582643\pi$
$73$	−10.1633	−	5.17847i	−1.18953	−	0.606094i	−0.932801	+	0.360391i	$0.882643\pi$
$74$	−0.430117	+	1.32376i	−0.0500001	+	0.153884i
$75$	−0.135479	−	16.0538i	−0.0156438	−	1.85373i
$76$		−	6.19706i		−	0.710852i
$77$	4.47882	−	2.34584i	0.510409	−	0.267334i
$78$	2.40339	+	2.40339i	0.272130	+	0.272130i
$79$	−4.69179	−	3.40879i	−0.527868	−	0.383518i	0.291692	−	0.956512i	$-0.405782\pi$
$79$	−4.69179	−	3.40879i	−0.527868	−	0.383518i	−0.819560	+	0.572994i	$0.805782\pi$
$80$	−0.846982	+	2.06945i	−0.0946954	+	0.231372i
$81$	−6.95367	−	21.4012i	−0.772631	−	2.37791i
$82$	−0.392075	+	2.47546i	−0.0432974	+	0.273369i
$83$	−0.200087	+	1.26330i	−0.0219624	+	0.138665i	−0.996233	−	0.0867161i	$-0.972363\pi$
$83$	−0.200087	+	1.26330i	−0.0219624	+	0.138665i	0.974271	+	0.225381i	$0.0723627\pi$
$84$	−1.51256	−	4.65519i	−0.165034	−	0.507922i
$85$	4.58543	−	1.92206i	0.497360	−	0.208476i
$86$	7.33334	+	5.32798i	0.790774	+	0.574531i
$87$	10.2816	+	10.2816i	1.10231	+	1.10231i
$88$	−0.481987	+	3.28142i	−0.0513800	+	0.349800i
$89$			10.5518i			1.11849i	0.829004	+	0.559243i	$0.188908\pi$
$89$			10.5518i			1.11849i	−0.829004	+	0.559243i	$0.811092\pi$
$90$	−16.2890	+	1.35115i	−1.71701	+	0.142424i
$91$	−0.498662	+	1.53472i	−0.0522740	+	0.160883i
$92$	3.85319	+	1.96330i	0.401722	+	0.204688i
$93$	9.12499	+	1.44526i	0.946218	+	0.149866i
$94$	3.62956	−	2.63703i	0.374361	−	0.271989i
$95$	−3.29169	−	13.4604i	−0.337720	−	1.38101i
$96$	3.05372	+	0.992214i	0.311669	+	0.101267i
$97$	6.92020	−	1.09605i	0.702639	−	0.111287i	0.205116	−	0.978738i	$-0.434243\pi$
$97$	6.92020	−	1.09605i	0.702639	−	0.111287i	0.497523	+	0.867451i	$0.334243\pi$
$98$	−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	0.125136	−	0.992140i	$-0.460063\pi$
$101$	10.3519	−	14.2481i	1.03005	−	1.41774i	0.904912	−	0.425599i	$-0.139937\pi$
$102$	−3.24125	−	6.36132i	−0.320932	−	0.629865i
$103$	1.45835	−	2.86217i	0.143695	−	0.282018i	−0.807930	−	0.589278i	$-0.799412\pi$
$103$	1.45835	−	2.86217i	0.143695	−	0.282018i	0.951625	+	0.307260i	$0.0994122\pi$
$104$	−0.622206	−	0.856394i	−0.0610124	−	0.0839763i
$105$	−5.75807	−	9.30793i	−0.561930	−	0.908361i
$106$	−3.61732	+	1.17534i	−0.351345	+	0.114159i
$107$	−14.7175	+	7.49892i	−1.42279	+	0.724948i	−0.984745	−	0.174006i	$-0.944329\pi$
$107$	−14.7175	+	7.49892i	−1.42279	+	0.724948i	−0.438045	+	0.898953i	$0.644329\pi$
$108$	2.16472	+	13.6675i	0.208300	+	1.31516i
$109$	1.88801			0.180839			0.0904195	−	0.995904i	$-0.471179\pi$
$109$	1.88801			0.180839			0.0904195	+	0.995904i	$0.471179\pi$
$110$	0.696082	+	7.38346i	0.0663688	+	0.703985i
$111$	4.46917			0.424195
$112$	0.238474	+	1.50566i	0.0225336	+	0.142272i
$113$	−3.55455	+	1.81113i	−0.334384	+	0.170377i	−0.613118	−	0.789991i	$-0.710085\pi$
$113$	−3.55455	+	1.81113i	−0.334384	+	0.170377i	0.278734	+	0.960368i	$0.410085\pi$
$114$	−18.9241	+	6.14881i	−1.77240	+	0.575889i
$115$	9.41221	+	2.21771i	0.877693	+	0.206803i
$116$	−2.66178	−	3.66363i	−0.247140	−	0.340160i
$117$	3.51287	−	6.89439i	0.324765	−	0.637387i
$118$	2.03903	+	4.00183i	0.187708	+	0.368398i
$119$	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
$123$	7.94840	−	1.25890i	0.716683	−	0.113511i
$124$	−2.73650	−	0.889144i	−0.245745	−	0.0798475i
$125$	1.01821	+	11.1339i	0.0910718	+	0.995844i
$126$	−9.01498	+	6.54977i	−0.803118	+	0.583500i
$127$	−16.7564	−	2.65395i	−1.48689	−	0.235500i	−0.640456	−	0.767995i	$-0.721254\pi$
$127$	−16.7564	−	2.65395i	−1.48689	−	0.235500i	−0.846433	+	0.532495i	$0.821254\pi$
$128$	−0.891007	−	0.453990i	−0.0787546	−	0.0401275i
$129$	8.99392	−	27.6805i	0.791871	−	2.43713i
$130$	−1.80636	−	1.52964i	−0.158428	−	0.134159i
$131$		−	9.77651i		−	0.854177i	−0.904210	−	0.427089i	$-0.859539\pi$
$131$		−	9.77651i		−	0.854177i	0.904210	−	0.427089i	$-0.140461\pi$
$132$	10.4988	−	1.78401i	0.913800	−	0.155278i
$133$	−6.68003	−	6.68003i	−0.579232	−	0.579232i
$134$	6.18714	+	4.49522i	0.534488	+	0.388328i
$135$	11.9617	+	28.5369i	1.02950	+	2.45606i
$136$	0.687109	+	2.11471i	0.0589191	+	0.181334i
$137$	−0.386515	+	2.44036i	−0.0330222	+	0.208494i	−0.998683	−	0.0513136i	$-0.983659\pi$
$137$	−0.386515	+	2.44036i	−0.0330222	+	0.208494i	0.965660	+	0.259808i	$0.0836592\pi$
$138$	2.17217	−	13.7146i	0.184908	−	1.16746i
$139$	2.32161	+	7.14518i	0.196916	+	0.606046i	0.999949	+	0.0101112i	$0.00321854\pi$
$139$	2.32161	+	7.14518i	0.196916	+	0.606046i	−0.803032	+	0.595935i	$0.796781\pi$
$140$	1.31774	+	3.14373i	0.111369	+	0.265693i
$141$	−11.6541	−	8.46717i	−0.981449	−	0.713065i
$142$	−6.29183	−	6.29183i	−0.527998	−	0.527998i
$143$	−3.14590	−	1.55864i	−0.263074	−	0.130340i
$144$		−	7.30970i		−	0.609141i
$145$	−7.72757	−	6.54378i	−0.641740	−	0.543431i
$146$	3.52482	−	10.8483i	0.291716	−	0.897810i
$147$	13.3779	+	6.81639i	1.10339	+	0.562206i
$148$	−1.37475	−	0.217739i	−0.113004	−	0.0178981i
$149$	−0.0269615	+	0.0195887i	−0.00220877	+	0.00160477i	−0.588889	−	0.808214i	$-0.700435\pi$
$149$	−0.0269615	+	0.0195887i	−0.00220877	+	0.00160477i	0.586680	+	0.809819i	$0.300435\pi$
$150$	15.8349	−	2.64518i	1.29292	−	0.215978i
$151$	−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	$0.930792\pi$
$152$	6.12076	−	0.969434i	0.496459	−	0.0786315i
$153$	−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
$157$	−0.891858	−	1.75037i	−0.0711780	−	0.139695i	0.852676	−	0.522441i	$-0.174978\pi$
$157$	−0.891858	−	1.75037i	−0.0711780	−	0.139695i	−0.923854	+	0.382746i	$0.874978\pi$
$158$	2.63286	−	5.16728i	0.209459	−	0.411087i
$159$	7.17831	+	9.88010i	0.569277	+	0.783543i
$160$	−2.17647	−	0.512821i	−0.172065	−	0.0405420i
$161$	6.26979	−	2.03718i	0.494129	−	0.160552i
$162$	20.0499	−	10.2160i	1.57527	−	0.802641i
$163$	−0.340601	−	2.15047i	−0.0266779	−	0.168438i	0.970752	−	0.240084i	$-0.0771749\pi$
$163$	−0.340601	−	2.15047i	−0.0266779	−	0.168438i	−0.997430	+	0.0716458i	$0.977175\pi$
$164$	−2.50632			−0.195711
$165$	21.8564	−	9.45161i	1.70152	−	0.735807i
$166$	−1.27905			−0.0992732
$167$	−3.35583	−	21.1879i	−0.259682	−	1.63957i	−0.680735	−	0.732530i	$-0.738339\pi$
$167$	−3.35583	−	21.1879i	−0.259682	−	1.63957i	0.421053	−	0.907036i	$-0.361661\pi$
$168$	4.36126	−	2.22217i	0.336478	−	0.171444i
$169$	−11.2980	+	3.67095i	−0.869079	+	0.282381i
$170$	2.61571	+	4.22830i	0.200616	+	0.324296i
$171$	26.6259	+	36.6474i	2.03613	+	2.80249i
$172$	−4.11520	+	8.07653i	−0.313781	+	0.615830i
$173$	5.98965	+	11.7553i	0.455384	+	0.893742i	0.998535	+	0.0541069i	$0.0172312\pi$
$173$	5.98965	+	11.7553i	0.455384	+	0.893742i	−0.543151	+	0.839635i	$0.682769\pi$
$174$	−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
$178$	−10.4219	+	1.65066i	−0.781152	+	0.123722i
$179$	12.8887	+	4.18779i	0.963346	+	0.313010i	0.748127	−	0.663555i	$-0.230953\pi$
$179$	12.8887	+	4.18779i	0.963346	+	0.313010i	0.215219	+	0.976566i	$0.430953\pi$
$180$	−3.88269	−	15.8771i	−0.289398	−	1.18341i
$181$	−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	$0.521445\pi$
$182$	−1.59384	−	0.252439i	−0.118143	−	0.0187120i
$183$	16.9437	+	8.63324i	1.25251	+	0.638188i
$184$	−1.33635	+	4.11287i	−0.0985173	+	0.303205i
$185$	−3.10170	+	0.257282i	−0.228042	+	0.0189158i
$186$			9.23874i			0.677417i
$187$	5.27292	+	5.15571i	0.385594	+	0.377023i
$188$	3.17236	+	3.17236i	0.231368	+	0.231368i
$189$	17.0661	+	12.3993i	1.24138	+	0.901914i
$190$	12.7798	−	5.35683i	0.927141	−	0.388626i
$191$	−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	$-0.250571\pi$
$192$	−0.502291	+	3.17134i	−0.0362497	+	0.228872i
$193$	0.599973	−	3.78808i	0.0431870	−	0.272672i	−0.956640	−	0.291273i	$-0.905921\pi$
$193$	0.599973	−	3.78808i	0.0431870	−	0.272672i	0.999827	+	0.0186009i	$0.00592120\pi$
$194$	2.16511	+	6.66354i	0.155446	+	0.478414i
$195$	−2.87881	+	7.03386i	−0.206156	+	0.503705i
$196$	−3.78305	−	2.74855i	−0.270218	−	0.196325i
$197$	−7.40013	−	7.40013i	−0.527238	−	0.527238i	0.392510	−	0.919748i	$-0.371607\pi$
$197$	−7.40013	−	7.40013i	−0.527238	−	0.527238i	−0.919748	+	0.392510i	$0.871607\pi$
$198$	−11.2484	−	21.4761i	−0.799389	−	1.52624i
$199$		−	9.10742i		−	0.645608i	−0.946466	−	0.322804i	$-0.895375\pi$
$199$		−	9.10742i		−	0.645608i	0.946466	−	0.322804i	$-0.104625\pi$
$200$	−4.99982	+	0.0421939i	−0.353541	+	0.00298356i
$201$	7.58818	−	23.3540i	0.535229	−	1.64727i
$202$	15.6921	+	7.99551i	1.10409	+	0.562562i
$203$	−6.81839	−	1.07993i	−0.478557	−	0.0757960i
$204$	5.77596	−	4.19648i	0.404398	−	0.293812i
$205$	−5.44389	+	1.33128i	−0.380218	+	0.0929807i
$206$	3.05507	+	0.992651i	0.212857	+	0.0691613i
$207$	−31.2218	+	4.94505i	−2.17007	+	0.343705i
$208$	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	−0.0986665	+	0.995121i	$0.531458\pi$
$211$	−14.7378	+	20.2849i	−1.01459	+	1.39647i	−0.915926	+	0.401347i	$0.868542\pi$
$212$	−1.72674	−	3.38892i	−0.118593	−	0.232752i
$213$	−12.9706	+	25.4563i	−0.888734	+	1.74424i
$214$	−9.70891	−	13.3632i	−0.663687	−	0.913487i
$215$	−4.64847	+	19.7286i	−0.317023	+	1.34548i
$216$	−13.1606	+	4.27614i	−0.895466	+	0.290954i
$217$	−3.90821	+	1.99133i	−0.265307	+	0.135181i
$218$	0.295350	+	1.86477i	0.0200037	+	0.126298i
$219$	−36.6250			−2.47489
$220$	−7.18367	+	1.84254i	−0.484323	+	0.124224i
$221$	−2.35374			−0.158330
$222$	0.699133	+	4.41415i	0.0469227	+	0.296258i
$223$	4.44282	−	2.26373i	0.297513	−	0.151590i	−0.298862	−	0.954296i	$-0.596607\pi$
$223$	4.44282	−	2.26373i	0.297513	−	0.151590i	0.596375	+	0.802706i	$0.296607\pi$
$224$	−1.44982	+	0.471075i	−0.0968702	+	0.0314750i
$225$	−16.8669	−	32.4238i	−1.12446	−	2.16158i
$226$	−2.34489	−	3.22746i	−0.155980	−	0.214688i
$227$	0.926486	−	1.81833i	0.0614931	−	0.120687i	−0.858214	−	0.513292i	$-0.828426\pi$
$227$	0.926486	−	1.81833i	0.0614931	−	0.120687i	0.919707	+	0.392605i	$0.128426\pi$
$228$	−9.03349	−	17.7292i	−0.598257	−	1.17415i
$229$	−0.895888	+	1.23308i	−0.0592020	+	0.0814845i	−0.837591	−	0.546297i	$-0.816037\pi$
$229$	−0.895888	+	1.23308i	−0.0592020	+	0.0814845i	0.778389	+	0.627782i	$0.216037\pi$
$230$	−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
$233$	21.9164	−	3.47122i	1.43579	−	0.227407i	0.610457	−	0.792050i	$-0.290986\pi$
$233$	21.9164	−	3.47122i	1.43579	−	0.227407i	0.825336	+	0.564642i	$0.190986\pi$
$234$	7.35904	+	2.39110i	0.481076	+	0.156311i
$235$	8.57562	+	5.20550i	0.559412	+	0.339569i
$236$	−3.63358	+	2.63995i	−0.236526	+	0.171846i
$237$	−18.3918	−	2.91297i	−1.19468	−	0.189218i
$238$	3.02018	+	1.53886i	0.195769	+	0.0997492i
$239$	7.65870	−	23.5711i	0.495400	−	1.52468i	−0.320932	−	0.947102i	$-0.603996\pi$
$239$	7.65870	−	23.5711i	0.495400	−	1.52468i	0.816332	−	0.577583i	$-0.196004\pi$
$240$	0.593511	+	7.15515i	0.0383110	+	0.461863i
$241$			0.0562577i			0.00362387i	0.999998	+	0.00181194i	$0.000576758\pi$
$241$			0.0562577i			0.00362387i	−0.999998	+	0.00181194i	$0.999423\pi$
$242$	−9.68636	+	5.21292i	−0.622662	+	0.335099i
$243$	−21.7359	−	21.7359i	−1.39436	−	1.39436i
$244$	−4.79140	−	3.48115i	−0.306738	−	0.222858i
$245$	−9.67697	−	3.96058i	−0.618239	−	0.253032i
$246$	2.48681	+	7.65360i	0.158553	+	0.487976i
$247$	−1.02620	+	6.47920i	−0.0652958	+	0.412262i
$248$	0.450114	−	2.84191i	0.0285822	−	0.180461i
$249$	1.26909	+	3.90585i	0.0804251	+	0.247523i
$250$	−10.8375	+	2.74740i	−0.685425	+	0.173761i
$251$	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
$253$	2.40278	+	14.1402i	0.151062	+	0.888984i
$254$		−	16.9653i		−	1.06449i
$255$	10.3167	−	12.1830i	0.646057	−	0.762931i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−9.35527	−	4.76675i	−0.583566	−	0.297342i	0.137175	−	0.990547i	$-0.456198\pi$
$257$	−9.35527	−	4.76675i	−0.583566	−	0.297342i	−0.720740	+	0.693205i	$0.756198\pi$
$258$	28.7466	+	4.55302i	1.78969	+	0.283458i
$259$	−1.71660	+	1.24718i	−0.106664	+	0.0774963i
$260$	1.22823	−	2.02341i	0.0761719	−	0.125487i
$261$	31.4818	+	10.2291i	1.94868	+	0.633163i
$262$	9.65614	−	1.52938i	0.596558	−	0.0944856i
$263$	−3.20922	+	3.20922i	−0.197889	+	0.197889i	−0.799095	−	0.601205i	$-0.794687\pi$
$263$	−3.20922	+	3.20922i	−0.197889	+	0.197889i	0.601205	+	0.799095i	$0.294687\pi$
$264$	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
$267$	15.3814	+	30.1877i	0.941325	+	1.84746i
$268$	−3.47200	+	6.81417i	−0.212086	+	0.416242i
$269$	15.2248	+	20.9551i	0.928272	+	1.27766i	0.960530	+	0.278178i	$0.0897304\pi$
$269$	15.2248	+	20.9551i	0.928272	+	1.27766i	−0.0322573	+	0.999480i	$0.510270\pi$
$270$	−26.3143	+	16.2786i	−1.60144	+	0.990681i
$271$	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	$0.173586\pi$
$272$	−1.98118	+	1.00946i	−0.120127	+	0.0612077i
$273$	0.810549	+	5.11760i	0.0490566	+	0.309731i
$274$	−2.47078			−0.149265
$275$	−14.6247	+	7.81785i	−0.881901	+	0.471434i
$276$	13.8855			0.835810
$277$	2.14809	+	13.5625i	0.129066	+	0.814893i	0.964264	+	0.264943i	$0.0853531\pi$
$277$	2.14809	+	13.5625i	0.129066	+	0.814893i	−0.835198	+	0.549950i	$0.814647\pi$
$278$	−6.69403	+	3.41078i	−0.401481	+	0.204565i
$279$	20.0030	−	6.49937i	1.19755	−	0.389107i
$280$	−2.89888	+	1.79331i	−0.173241	+	0.107170i
$281$	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	$0.704522\pi$
$282$	6.53983	−	12.8351i	0.389441	−	0.764322i
$283$	−0.935154	−	1.83534i	−0.0555891	−	0.109100i	0.861541	−	0.507689i	$-0.169500\pi$
$283$	−0.935154	−	1.83534i	−0.0555891	−	0.109100i	−0.917130	+	0.398589i	$0.869500\pi$
$284$	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
$288$	7.21970	−	1.14349i	0.425425	−	0.0673807i
$289$	−11.4658	−	3.72548i	−0.674461	−	0.219146i
$290$	5.25436	−	8.65611i	0.308547	−	0.508304i
$291$	18.2003	−	13.2233i	1.06692	−	0.775164i
$292$	11.2661	+	1.78438i	0.659300	+	0.104423i
$293$	−17.5019	−	8.91767i	−1.02247	−	0.520976i	−0.139412	−	0.990234i	$-0.544521\pi$
$293$	−17.5019	−	8.91767i	−1.02247	−	0.520976i	−0.883061	+	0.469259i	$0.844521\pi$
$294$	−4.63970	+	14.2795i	−0.270593	+	0.832799i
$295$	−6.49011	+	7.66420i	−0.377869	+	0.446227i
$296$		−	1.39189i		−	0.0809018i
$297$	−32.0859	+	32.8154i	−1.86181	+	1.90414i
$298$	−0.0235652	−	0.0235652i	−0.00136510	−	0.00136510i
$299$	−3.70350	−	2.69075i	−0.214179	−	0.155610i
$300$	5.08974	+	15.2262i	0.293856	+	0.879085i
$301$	4.27006	+	13.1419i	0.246122	+	0.757486i
$302$	3.31407	−	20.9242i	0.190703	−	1.20405i
$303$	8.84616	−	55.8524i	0.508199	−	3.20864i
$304$	1.91500	+	5.89375i	0.109833	+	0.338030i
$305$	−12.2563	−	5.01624i	−0.701793	−	0.287229i
$306$	−13.1492	−	9.55348i	−0.751692	−	0.546136i
$307$	8.35315	+	8.35315i	0.476740	+	0.476740i	0.904087	−	0.427348i	$-0.140552\pi$
$307$	8.35315	+	8.35315i	0.476740	+	0.476740i	−0.427348	+	0.904087i	$0.640552\pi$
$308$	−3.53470	+	3.61506i	−0.201408	+	0.205987i
$309$		−	10.3142i		−	0.586757i
$310$	−0.531858	−	6.41189i	−0.0302075	−	0.364171i
$311$	−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	$0.971000\pi$
$312$	−3.02844	−	1.54307i	−0.171452	−	0.0873591i
$313$	29.8201	+	4.72303i	1.68553	+	0.266962i	0.924341	−	0.381569i	$-0.124616\pi$
$313$	29.8201	+	4.72303i	1.68553	+	0.266962i	0.761189	+	0.648530i	$0.224616\pi$
$314$	1.58930	−	1.15470i	0.0896895	−	0.0651633i
$315$	−21.2998	−	12.9292i	−1.20011	−	0.728480i
$316$	5.51553	+	1.79211i	0.310273	+	0.100814i
$317$	30.2851	−	4.79669i	1.70098	−	0.269409i	0.770951	−	0.636894i	$-0.219781\pi$
$317$	30.2851	−	4.79669i	1.70098	−	0.269409i	0.930029	+	0.367485i	$0.119781\pi$
$318$	−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
$322$	2.99291	+	5.87392i	0.166788	+	0.327341i
$323$	6.25570	−	12.2775i	0.348076	−	0.683139i
$324$	13.2267	+	18.2050i	0.734815	+	1.01139i
$325$	1.59303	−	5.04738i	0.0883654	−	0.279978i
$326$	2.07071	−	0.672816i	0.114686	−	0.0372638i
$327$	5.40143	−	2.75217i	0.298700	−	0.152195i
$328$	−0.392075	−	2.47546i	−0.0216487	−	0.136685i
$329$	6.83919			0.377057
$330$	12.7543	+	20.1087i	0.702103	+	1.10695i
$331$	14.2522			0.783372			0.391686	−	0.920099i	$-0.371892\pi$
$331$	14.2522			0.783372			0.391686	+	0.920099i	$0.371892\pi$
$332$	−0.200087	−	1.26330i	−0.0109812	−	0.0693325i
$333$	9.06535	−	4.61903i	0.496778	−	0.253121i
$334$	20.4020	−	6.62902i	1.11635	−	0.362724i
$335$	−3.92191	+	16.6450i	−0.214277	+	0.909415i
$336$	2.87706	+	3.95994i	0.156957	+	0.216032i
$337$	6.23713	−	12.2410i	0.339758	−	0.666812i	−0.656398	−	0.754415i	$-0.727921\pi$
$337$	6.23713	−	12.2410i	0.339758	−	0.666812i	0.996155	+	0.0876027i	$0.0279206\pi$
$338$	−5.39316	−	10.5847i	−0.293349	−	0.575730i
$339$	−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
$343$	−17.5803	+	2.78444i	−0.949246	+	0.150346i
$344$	−8.62085	−	2.80109i	−0.464805	−	0.151024i
$345$	30.1602	−	7.37556i	1.62377	−	0.397087i
$346$	−10.6736	+	7.75484i	−0.573818	+	0.416903i
$347$	17.5163	+	2.77431i	0.940326	+	0.148933i	0.607737	−	0.794139i	$-0.292078\pi$
$347$	17.5163	+	2.77431i	0.940326	+	0.148933i	0.332589	+	0.943072i	$0.392078\pi$
$348$	−12.9556	−	6.60121i	−0.694494	−	0.353862i
$349$	−5.50175	+	16.9327i	−0.294502	+	0.906384i	0.688886	+	0.724870i	$0.258100\pi$
$349$	−5.50175	+	16.9327i	−0.294502	+	0.906384i	−0.983388	+	0.181515i	$0.941900\pi$
$350$	−5.34400	+	5.43497i	−0.285649	+	0.290511i
$351$		−	14.6482i		−	0.781865i
$352$	−0.555617	−	3.26975i	−0.0296145	−	0.174278i
$353$	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
$355$	7.53643	−	18.4139i	0.399992	−	0.977310i
$356$	−3.26068	−	10.0353i	−0.172816	−	0.531872i
$357$	1.70258	−	10.7496i	0.0901099	−	0.568932i
$358$	−2.12000	+	13.3851i	−0.112045	+	0.707426i
$359$	2.37480	+	7.30888i	0.125337	+	0.385748i	0.993962	−	0.109722i	$-0.0349959\pi$
$359$	2.37480	+	7.30888i	0.125337	+	0.385748i	−0.868625	+	0.495470i	$0.834996\pi$
$360$	15.0743	−	6.31861i	0.794483	−	0.333020i
$361$	−15.6978	−	11.4051i	−0.826200	−	0.600270i
$362$	−12.1942	−	12.1942i	−0.640915	−	0.640915i
$363$	25.5297	+	24.4071i	1.33996	+	1.28104i
$364$		−	1.61370i		−	0.0845810i
$365$	25.4185	−	2.10844i	1.33047	−	0.110361i
$366$	−5.87638	+	18.0856i	−0.307163	+	0.945351i
$367$	−32.2443	−	16.4293i	−1.68314	−	0.857603i	−0.990690	−	0.136139i	$-0.956531\pi$
$367$	−32.2443	−	16.4293i	−1.68314	−	0.857603i	−0.692452	−	0.721464i	$-0.743469\pi$
$368$	−4.27129	−	0.676506i	−0.222656	−	0.0352653i
$369$	14.8215	−	10.7685i	0.771579	−	0.560585i
$370$	−0.739328	−	3.02327i	−0.0384358	−	0.157172i
$371$	−5.51436	−	1.79172i	−0.286291	−	0.0930217i
$372$	−9.12499	+	1.44526i	−0.473109	+	0.0749331i
$373$	11.5350	−	11.5350i	0.597259	−	0.597259i	−0.342323	−	0.939582i	$-0.611214\pi$
$373$	11.5350	−	11.5350i	0.597259	−	0.597259i	0.939582	+	0.342323i	$0.111214\pi$
$374$	−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
$377$	2.17629	+	4.27121i	0.112085	+	0.219978i
$378$	−9.57688	+	18.7957i	−0.492582	+	0.966746i
$379$	−3.86753	−	5.32320i	−0.198662	−	0.273434i	0.698050	−	0.716049i	$-0.254051\pi$
$379$	−3.86753	−	5.32320i	−0.198662	−	0.273434i	−0.896712	+	0.442614i	$0.854051\pi$
$380$	7.29008	+	11.7844i	0.373973	+	0.604528i
$381$	−51.8071	+	16.8332i	−2.65416	+	0.862389i
$382$	11.2202	−	5.71697i	0.574074	−	0.292505i
$383$	4.57876	+	28.9091i	0.233963	+	1.47719i	0.772731	+	0.634733i	$0.218890\pi$
$383$	4.57876	+	28.9091i	0.233963	+	1.47719i	−0.538768	+	0.842454i	$0.681110\pi$
$384$	−3.21087			−0.163854
$385$	−5.75739	+	9.72967i	−0.293424	+	0.495870i
$386$	3.83530			0.195212
$387$	−10.3652	−	65.4430i	−0.526890	−	3.32665i
$388$	−6.24280	+	3.18087i	−0.316930	+	0.161484i
$389$	4.21993	−	1.37114i	0.213959	−	0.0695195i	−0.200076	−	0.979780i	$-0.564119\pi$
$389$	4.21993	−	1.37114i	0.213959	−	0.0695195i	0.414035	+	0.910261i	$0.364119\pi$
$390$	−7.39760	−	1.74303i	−0.374592	−	0.0882617i
$391$	5.65199	+	7.77930i	0.285833	+	0.393416i
$392$	2.12291	−	4.16644i	0.107223	−	0.210437i
$393$	−14.2513	−	27.9697i	−0.718881	−	1.41088i
$394$	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	$0.174820\pi$
$398$	8.99529	−	1.42471i	0.450893	−	0.0714145i
$399$	−28.8485	−	9.37344i	−1.44423	−	0.469259i
$400$	−0.823819	−	4.93167i	−0.0411909	−	0.246583i
$401$	−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	$0.370577\pi$
$402$	24.2535	+	3.84138i	1.20966	+	0.191591i
$403$	2.71385	+	1.38278i	0.135187	+	0.0688811i
$404$	−5.44229	+	16.7496i	−0.270764	+	0.833326i
$405$	38.3991	+	32.5167i	1.90807	+	1.61577i
$406$		−	6.90338i		−	0.342609i
$407$	−2.14188	−	4.08940i	−0.106169	−	0.202704i
$408$	5.04837	+	5.04837i	0.249932	+	0.249932i
$409$	−14.0728	−	10.2245i	−0.695853	−	0.505567i	0.182726	−	0.983164i	$-0.441508\pi$
$409$	−14.0728	−	10.2245i	−0.695853	−	0.505567i	−0.878579	+	0.477597i	$0.841508\pi$
$410$	−2.16650	−	5.16861i	−0.106996	−	0.255259i
$411$	2.45154	+	7.54507i	0.120926	+	0.372171i
$412$	−0.502512	+	3.17274i	−0.0247570	+	0.156310i
$413$	−1.07107	+	6.76247i	−0.0527039	+	0.332759i
$414$	−9.76834	−	30.0639i	−0.480088	−	1.47756i
$415$	−1.10563	−	2.63768i	−0.0542731	−	0.129479i
$416$	0.856394	+	0.622206i	0.0419882	+	0.0305062i
$417$	17.0575	+	17.0575i	0.835309	+	0.835309i
$418$	14.6958	+	14.3691i	0.718796	+	0.702818i
$419$		−	16.4015i		−	0.801265i	−0.916239	−	0.400632i	$-0.868790\pi$
$419$		−	16.4015i		−	0.801265i	0.916239	−	0.400632i	$-0.131210\pi$
$420$	8.35256	+	7.07303i	0.407563	+	0.345128i
$421$	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	$-0.122184\pi$
$422$	−22.3406	−	11.3831i	−1.08752	−	0.554121i
$423$	−32.3904	−	5.13013i	−1.57487	−	0.249436i
$424$	3.07708	−	2.23563i	0.149436	−	0.108572i
$425$	−6.45866	+	9.04920i	−0.313291	+	0.438951i
$426$	−27.1720	−	8.82870i	−1.31649	−	0.427752i
$427$	−8.91727	+	1.41236i	−0.431537	+	0.0683488i
$428$	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	−0.922059	−	0.387050i	$-0.873494\pi$
$431$	−5.58501	+	7.68711i	−0.269020	+	0.370275i	0.653038	+	0.757325i	$0.273494\pi$
$432$	−6.28227	−	12.3296i	−0.302256	−	0.593210i
$433$	11.3232	−	22.2230i	0.544158	−	1.06797i	−0.441190	−	0.897414i	$-0.645443\pi$
$433$	11.3232	−	22.2230i	0.544158	−	1.06797i	0.985348	−	0.170557i	$-0.0545566\pi$
$434$	−2.57820	−	3.54858i	−0.123757	−	0.170338i
$435$	−31.6468	−	7.45663i	−1.51735	−	0.357518i
$436$	−1.79561	+	0.583428i	−0.0859940	+	0.0279411i
$437$	23.8784	−	12.1667i	1.14226	−	0.582011i
$438$	−5.72941	−	36.1741i	−0.273762	−	1.72846i
$439$	−1.69115			−0.0807143			−0.0403571	−	0.999185i	$-0.512850\pi$
$439$	−1.69115			−0.0807143			−0.0403571	+	0.999185i	$0.512850\pi$
$440$	−2.94363	−	6.80699i	−0.140332	−	0.324510i
$441$	34.1809			1.62766
$442$	−0.368207	−	2.32477i	−0.0175138	−	0.110578i
$443$	−18.0946	+	9.21964i	−0.859698	+	0.438038i	−0.827515	−	0.561444i	$-0.810246\pi$
$443$	−18.0946	+	9.21964i	−0.859698	+	0.438038i	−0.0321835	+	0.999482i	$0.510246\pi$
$444$	−4.25044	+	1.38105i	−0.201717	+	0.0655418i
$445$	−12.4129	−	20.0654i	−0.588426	−	0.951192i
$446$	2.93087	+	4.03399i	0.138781	+	0.191015i
$447$	−0.0485798	+	0.0953432i	−0.00229775	+	0.00450958i
$448$	−0.692077	−	1.35828i	−0.0326976	−	0.0641726i
$449$	−24.7166	+	34.0195i	−1.16645	+	1.60548i	−0.482643	+	0.875817i	$0.660323\pi$
$449$	−24.7166	+	34.0195i	−1.16645	+	1.60548i	−0.683806	+	0.729664i	$0.739677\pi$
$450$	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
$453$	−67.1849	+	10.6410i	−3.15662	+	0.499960i
$454$	1.94088	+	0.630630i	0.0910900	+	0.0295969i
$455$	−0.857150	−	3.50507i	−0.0401838	−	0.164320i
$456$	16.0978	−	11.6957i	0.753848	−	0.547703i
$457$	−9.99618	−	1.58324i	−0.467602	−	0.0740608i	−0.0818123	−	0.996648i	$-0.526071\pi$
$457$	−9.99618	−	1.58324i	−0.467602	−	0.0740608i	−0.385789	+	0.922587i	$0.626071\pi$
$458$	−1.35805	−	0.691961i	−0.0634575	−	0.0323332i
$459$	−9.50814	+	29.2630i	−0.443802	+	1.36588i
$460$	−9.63685	+	0.799364i	−0.449321	+	0.0372706i
$461$			27.4513i			1.27854i	0.768984	+	0.639268i	$0.220763\pi$
$461$			27.4513i			1.27854i	−0.768984	+	0.639268i	$0.779237\pi$
$462$	14.5466	+	7.20708i	0.676768	+	0.335304i
$463$	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
$465$	−19.0524	+	7.98611i	−0.883533	+	0.370347i
$466$	6.85697	+	21.1036i	0.317643	+	0.977604i
$467$	−3.41594	+	21.5674i	−0.158071	+	0.998021i	0.773324	+	0.634011i	$0.218593\pi$
$467$	−3.41594	+	21.5674i	−0.158071	+	0.998021i	−0.931395	+	0.364010i	$0.881407\pi$
$468$	−1.21045	+	7.64249i	−0.0559532	+	0.353274i
$469$	3.60265	+	11.0878i	0.166355	+	0.511988i
$470$	−3.79989	+	9.28436i	−0.175276	+	0.428255i
$471$	−5.10305	−	3.70758i	−0.235136	−	0.170836i
$472$	−3.17587	−	3.17587i	−0.146181	−	0.146181i
$473$	−29.6387	+	5.03639i	−1.36279	+	0.231573i
$474$		−	18.6210i		−	0.855293i
$475$	22.0940	+	21.7242i	1.01374	+	0.996777i
$476$	−1.04745	+	3.22372i	−0.0480098	+	0.147759i
$477$	24.7720	+	12.6220i	1.13423	+	0.577920i
$478$	24.4789	+	3.87708i	1.11964	+	0.177334i
$479$	5.27636	−	3.83350i	0.241083	−	0.175157i	−0.460683	−	0.887565i	$-0.652395\pi$
$479$	5.27636	−	3.83350i	0.241083	−	0.175157i	0.701766	+	0.712408i	$0.252395\pi$
$480$	−6.97422	+	1.70552i	−0.318328	+	0.0778458i
$481$	1.40128	+	0.455305i	0.0638931	+	0.0207601i
$482$	−0.0555650	+	0.00880064i	−0.00253092	+	0.000400858i
$483$	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
$487$	1.33144	+	2.61310i	0.0603334	+	0.118411i	0.919204	−	0.393782i	$-0.128833\pi$
$487$	1.33144	+	2.61310i	0.0603334	+	0.118411i	−0.858871	+	0.512193i	$0.828833\pi$
$488$	2.68875	−	5.27698i	0.121714	−	0.238878i
$489$	−4.10918	−	5.65580i	−0.185824	−	0.255764i
$490$	2.39801	−	10.1774i	0.108331	−	0.459768i
$491$	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	$0.302839\pi$
$492$	−7.17035	+	3.65348i	−0.323264	+	0.164711i
$493$	−1.57518	−	9.94529i	−0.0709425	−	0.447913i
$494$	−6.55996			−0.295147
$495$	34.5653	−	41.7610i	1.55359	−	1.87702i
$496$	2.87733			0.129196
$497$	−2.12193	−	13.3974i	−0.0951818	−	0.600954i
$498$	−3.65923	+	1.86447i	−0.163974	+	0.0835490i
$499$	−22.2265	+	7.22182i	−0.994994	+	0.323293i	−0.760863	−	0.648912i	$-0.775224\pi$
$499$	−22.2265	+	7.22182i	−0.994994	+	0.323293i	−0.234130	+	0.972205i	$0.575224\pi$
$500$	−4.40894	−	10.2743i	−0.197174	−	0.459481i
$501$	−40.4864	−	55.7247i	−1.80880	−	2.48960i
$502$	−3.82436	+	7.50572i	−0.170689	+	0.334997i
$503$	10.5487	+	20.7030i	0.470344	+	0.923103i	0.997316	+	0.0732197i	$0.0233274\pi$
$503$	10.5487	+	20.7030i	0.470344	+	0.923103i	−0.526972	+	0.849883i	$0.676673\pi$
$504$	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
$508$	16.7564	−	2.65395i	0.743444	−	0.117750i
$509$	21.9064	+	7.11784i	0.970986	+	0.315493i	0.751214	−	0.660059i	$-0.229469\pi$
$509$	21.9064	+	7.11784i	0.970986	+	0.315493i	0.219772	+	0.975551i	$0.429469\pi$
$510$	13.6469	+	8.28384i	0.604296	+	0.366815i
$511$	14.0676	−	10.2207i	0.622314	−	0.452138i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	76.4075	+	38.9316i	3.37347	+	1.71887i
$514$	3.24457	−	9.98577i	0.143112	−	0.440454i
$515$	0.593772	+	7.15831i	0.0261647	+	0.315433i
$516$			29.1050i			1.28127i
$517$	−2.16238	+	14.7217i	−0.0951014	+	0.647460i
$518$	−1.50037	−	1.50037i	−0.0659223	−	0.0659223i
$519$	34.2716	+	24.8998i	1.50436	+	1.09298i
$520$	2.19064	+	0.896582i	0.0960658	+	0.0393177i
$521$	−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	$-0.339025\pi$
$522$	−5.17828	+	32.6944i	−0.226647	+	1.43099i
$523$	−0.813774	+	5.13797i	−0.0355838	+	0.224668i	−0.999071	−	0.0430856i	$-0.986281\pi$
$523$	−0.813774	+	5.13797i	−0.0355838	+	0.224668i	0.963488	+	0.267753i	$0.0862812\pi$
$524$	3.02111	+	9.29801i	0.131978	+	0.406185i
$525$	21.8993	+	10.9264i	0.955762	+	0.476869i
$526$	−3.67174	−	2.66768i	−0.160096	−	0.116316i
$527$	−4.52395	−	4.52395i	−0.197067	−	0.197067i
$528$	−9.43362	+	4.94099i	−0.410546	+	0.215029i
$529$		−	4.29842i		−	0.186888i
$530$	5.49611	−	6.49037i	0.238736	−	0.281924i
$531$	10.1452	−	31.2236i	0.440263	−	1.35499i
$532$	8.41733	+	4.28884i	0.364938	+	0.185945i
$533$	2.62043	+	0.415035i	0.113503	+	0.0179772i
$534$	−27.4098	+	19.9144i	−1.18614	+	0.861781i
$535$	19.1654	−	31.5733i	0.828591	−	1.36503i
$536$	−7.27342	−	2.36328i	−0.314164	−	0.102078i
$537$	42.9779	−	6.80704i	1.85463	−	0.293745i
$538$	−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	−0.612690	−	0.790323i	$-0.709913\pi$
$541$	7.63567	−	10.5096i	0.328283	−	0.451843i	0.940974	+	0.338480i	$0.109913\pi$
$542$	9.75785	+	19.1509i	0.419135	+	0.822600i
$543$	−25.1385	+	49.3371i	−1.07880	+	2.11726i
$544$	−1.30696	−	1.79888i	−0.0560354	−	0.0771262i
$545$	−3.59027	+	2.22101i	−0.153790	+	0.0951378i
$546$	−4.92780	+	1.60114i	−0.210890	+	0.0685224i
$547$	4.19261	−	2.13624i	0.179263	−	0.0913391i	−0.362056	−	0.932156i	$-0.617925\pi$
$547$	4.19261	−	2.13624i	0.179263	−	0.0913391i	0.541319	+	0.840817i	$0.317925\pi$
$548$	−0.386515	−	2.44036i	−0.0165111	−	0.104247i
$549$	43.2916			1.84764
$550$	−10.0094	−	13.2216i	−0.426803	−	0.563773i
$551$	−28.0634			−1.19554
$552$	2.17217	+	13.7146i	0.0924538	+	0.583731i
$553$	7.87716	−	4.01362i	0.334971	−	0.170676i
$554$	−13.0595	+	4.24329i	−0.554845	+	0.180280i
$555$	−8.49865	+	5.25743i	−0.360747	+	0.223165i
$556$	−4.41597	−	6.07806i	−0.187279	−	0.257767i
$557$	−14.8729	+	29.1897i	−0.630185	+	1.23681i	0.326366	+	0.945243i	$0.394176\pi$
$557$	−14.8729	+	29.1897i	−0.630185	+	1.23681i	−0.956551	+	0.291564i	$0.905824\pi$
$558$	9.54851	+	18.7400i	0.404221	+	0.793328i
$559$	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
$563$	3.28421	−	0.520168i	0.138413	−	0.0219225i	−0.0868434	−	0.996222i	$-0.527678\pi$
$563$	3.28421	−	0.520168i	0.138413	−	0.0219225i	0.225257	+	0.974299i	$0.427678\pi$
$564$	13.7002	+	4.45146i	0.576882	+	0.187440i
$565$	4.62881	−	7.62557i	0.194735	−	0.320810i
$566$	1.66646	−	1.21075i	0.0700464	−	0.0508917i
$567$	33.8813	+	5.36627i	1.42288	+	0.225362i
$568$	7.92816	+	4.03960i	0.332658	+	0.169498i
$569$	2.18501	−	6.72478i	0.0916005	−	0.281917i	−0.894752	−	0.446563i	$-0.852648\pi$
$569$	2.18501	−	6.72478i	0.0916005	−	0.281917i	0.986353	+	0.164645i	$0.0526480\pi$
$570$	28.7530	−	33.9545i	1.20433	−	1.42220i
$571$		−	24.2620i		−	1.01533i	−0.861553	−	0.507667i	$-0.830508\pi$
$571$		−	24.2620i		−	1.01533i	0.861553	−	0.507667i	$-0.169492\pi$
$572$	3.47358	+	0.510212i	0.145238	+	0.0213330i
$573$	−28.5908	−	28.5908i	−1.19440	−	1.19440i
$574$	−3.09102	−	2.24576i	−0.129017	−	0.0937362i
$575$	−20.5073	+	6.85507i	−0.855212	+	0.285876i
$576$	2.25882	+	6.95193i	0.0941175	+	0.289664i
$577$	1.00746	−	6.36086i	0.0419412	−	0.264806i	−0.957803	−	0.287426i	$-0.907201\pi$
$577$	1.00746	−	6.36086i	0.0419412	−	0.264806i	0.999744	+	0.0226195i	$0.00720062\pi$
$578$	1.88596	−	11.9075i	0.0784455	−	0.495286i
$579$	−3.80544	−	11.7119i	−0.158149	−	0.486731i
$580$	9.37150	+	3.83555i	0.389130	+	0.159263i
$581$	−1.57744	−	1.14607i	−0.0654430	−	0.0475471i
$582$	15.9077	+	15.9077i	0.659394	+	0.659394i
$583$	5.60028	−	11.3034i	0.231940	−	0.468141i
$584$			11.4066i			0.472007i
$585$	1.43028	+	17.2429i	0.0591348	+	0.712908i
$586$	6.06998	−	18.6815i	0.250748	−	0.771724i
$587$	−4.91253	−	2.50306i	−0.202762	−	0.103312i	0.349661	−	0.936876i	$-0.386297\pi$
$587$	−4.91253	−	2.50306i	−0.202762	−	0.103312i	−0.552423	+	0.833564i	$0.686297\pi$
$588$	−14.8295	−	2.34877i	−0.611560	−	0.0968615i
$589$	−14.4256	+	10.4808i	−0.594395	+	0.431853i
$590$	−8.58511	−	5.21127i	−0.353444	−	0.214544i
$591$	−31.9583	−	10.3839i	−1.31459	−	0.427136i
$592$	1.37475	−	0.217739i	0.0565019	−	0.00894903i
$593$	11.4901	−	11.4901i	0.471841	−	0.471841i	−0.430669	−	0.902510i	$-0.641722\pi$
$593$	11.4901	−	11.4901i	0.471841	−	0.471841i	0.902510	+	0.430669i	$0.141722\pi$
$594$	−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
$597$	−13.2759	−	26.0555i	−0.543348	−	1.06638i
$598$	2.07827	−	4.07883i	0.0849867	−	0.166796i
$599$	−24.2507	−	33.3782i	−0.990856	−	1.36380i	−0.930771	−	0.365603i	$-0.880863\pi$
$599$	−24.2507	−	33.3782i	−0.990856	−	1.36380i	−0.0600854	−	0.998193i	$-0.519137\pi$
$600$	−14.2425	+	7.40898i	−0.581449	+	0.302470i
$601$	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	$0.0407609\pi$
$602$	−12.3121	+	6.27334i	−0.501804	+	0.255682i
$603$	−8.74509	−	55.2143i	−0.356127	−	2.24850i
$604$	21.1850			0.862006
$605$	−19.1233	−	15.4694i	−0.777471	−	0.628919i
$606$	56.5487			2.29713
$607$	2.64036	+	16.6706i	0.107169	+	0.676638i	0.981522	+	0.191348i	$0.0612858\pi$
$607$	2.64036	+	16.6706i	0.107169	+	0.676638i	−0.874353	+	0.485290i	$0.838714\pi$
$608$	−5.52162	+	2.81341i	−0.223931	+	0.114099i
$609$	−21.0810	+	6.84963i	−0.854245	+	0.277561i
$610$	3.03718	−	12.8901i	0.122972	−	0.521905i
$611$	−2.79146	−	3.84212i	−0.112930	−	0.155435i
$612$	7.37886	−	14.4818i	0.298273	−	0.585394i
$613$	−11.0412	−	21.6696i	−0.445949	−	0.875225i	−0.999111	−	0.0421512i	$-0.986579\pi$
$613$	−11.0412	−	21.6696i	−0.445949	−	0.875225i	0.553162	−	0.833074i	$-0.313421\pi$
$614$	−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	$0.272364\pi$
$618$	10.1873	−	1.61350i	0.409791	−	0.0649046i
$619$	28.7652	+	9.34637i	1.15617	+	0.375662i	0.823464	−	0.567369i	$-0.192038\pi$
$619$	28.7652	+	9.34637i	1.15617	+	0.375662i	0.332706	+	0.943031i	$0.392038\pi$
$620$	6.24974	−	1.52835i	0.250996	−	0.0613800i
$621$	−48.4135	+	35.1745i	−1.94277	+	1.41150i
$622$	−13.7346	−	2.17534i	−0.550706	−	0.0872233i
$623$	−14.3323	−	7.30265i	−0.574210	−	0.292574i
$624$	1.05032	−	3.23255i	0.0420464	−	0.129406i
$625$	−15.0339	−	19.9745i	−0.601355	−	0.798982i
$626$			30.1918i			1.20671i
$627$	29.2980	−	59.1342i	1.17005	−	2.36159i
$628$	1.38910	+	1.38910i	0.0554312	+	0.0554312i
$629$	−2.50383	−	1.81914i	−0.0998344	−	0.0725339i
$630$	9.43803	−	23.0601i	0.376020	−	0.918738i
$631$	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	$0.683644\pi$
$632$	−0.907222	+	5.72797i	−0.0360874	+	0.227847i
$633$	−12.5942	+	79.5165i	−0.500573	+	3.16050i
$634$	9.47527	+	29.1619i	0.376311	+	1.15817i
$635$	34.9862	−	14.6650i	1.38839	−	0.581964i
$636$	−9.88010	−	7.17831i	−0.391771	−	0.284639i
$637$	3.50014	+	3.50014i	0.138681	+	0.138681i
$638$	14.8599	+	2.18268i	0.588308	+	0.0864129i
$639$			65.0416i			2.57300i
$640$	2.22841	−	0.184844i	0.0880858	−	0.00730661i
$641$	−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	$0.130870\pi$
$642$	−47.2558	−	24.0781i	−1.86504	−	0.950285i
$643$	16.1752	+	2.56190i	0.637888	+	0.101031i	0.466998	−	0.884259i	$-0.345336\pi$
$643$	16.1752	+	2.56190i	0.637888	+	0.101031i	0.170890	+	0.985290i	$0.445336\pi$
$644$	−5.33341	+	3.87495i	−0.210166	+	0.152694i
$645$	15.4597	+	63.2178i	0.608723	+	2.48920i
$646$	13.1050	+	4.25806i	0.515608	+	0.167531i
$647$	42.4816	−	6.72843i	1.67012	−	0.264522i	0.751523	−	0.659707i	$-0.229319\pi$
$647$	42.4816	−	6.72843i	1.67012	−	0.264522i	0.918602	+	0.395185i	$0.129319\pi$
$648$	−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
$652$	0.988463	+	1.93997i	0.0387112	+	0.0759750i
$653$	1.54616	−	3.03452i	0.0605061	−	0.118750i	−0.858773	−	0.512356i	$-0.828773\pi$
$653$	1.54616	−	3.03452i	0.0605061	−	0.118750i	0.919279	+	0.393606i	$0.128773\pi$
$654$	3.56325	+	4.90440i	0.139334	+	0.191777i
$655$	11.5009	+	18.5911i	0.449376	+	0.726416i
$656$	2.38365	−	0.774496i	0.0930660	−	0.0302390i
$657$	−74.2907	+	37.8530i	−2.89836	+	1.47679i
$658$	1.06989	+	6.75499i	0.0417085	+	0.263337i
$659$	1.70430			0.0663902			0.0331951	−	0.999449i	$-0.489432\pi$
$659$	1.70430			0.0663902			0.0331951	+	0.999449i	$0.489432\pi$
$660$	−17.8659	+	15.7430i	−0.695430	+	0.612795i
$661$	−3.81557			−0.148409			−0.0742043	−	0.997243i	$-0.523642\pi$
$661$	−3.81557			−0.148409			−0.0742043	+	0.997243i	$0.523642\pi$
$662$	2.22953	+	14.0767i	0.0866533	+	0.547108i
$663$	−6.73385	+	3.43107i	−0.261521	+	0.133252i
$664$	1.21644	−	0.395247i	0.0472072	−	0.0153386i
$665$	20.5611	+	4.84461i	0.797324	+	0.187866i
$666$	5.98029	+	8.23116i	0.231732	+	0.318951i
$667$	8.89078	−	17.4491i	0.344252	−	0.675634i
$668$	9.73899	+	19.1138i	0.376813	+	0.739537i
$669$	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
$673$	−26.0401	+	4.12434i	−1.00377	+	0.158982i	−0.636619	−	0.771179i	$-0.719667\pi$
$673$	−26.0401	+	4.12434i	−1.00377	+	0.158982i	−0.367153	+	0.930161i	$0.619667\pi$
$674$	13.0660	+	4.24541i	0.503285	+	0.163527i
$675$	−56.3166	−	40.1947i	−2.16763	−	1.54709i
$676$	9.61068	−	6.98256i	0.369641	−	0.268560i
$677$	11.6875	+	1.85111i	0.449185	+	0.0711440i	0.376929	−	0.926242i	$-0.376980\pi$
$677$	11.6875	+	1.85111i	0.449185	+	0.0711440i	0.0722563	+	0.997386i	$0.476980\pi$
$678$	−11.4132	−	5.81532i	−0.438321	−	0.223336i
$679$	−3.30057	+	10.1581i	−0.126664	+	0.389832i
$680$	−3.79431	−	3.21305i	−0.145505	−	0.123215i
$681$		−	6.55262i		−	0.251097i
$682$	8.45367	−	4.42773i	0.323708	−	0.169546i
$683$	−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
$685$	−2.13578	−	5.09531i	−0.0816040	−	0.194682i
$686$	−5.50033	−	16.9283i	−0.210003	−	0.646324i
$687$	−0.765580	+	4.83368i	−0.0292087	+	0.184416i
$688$	1.41800	−	8.95290i	0.0540608	−	0.341326i
$689$	1.24417	+	3.82916i	0.0473990	+	0.145879i
$690$	12.0029	+	28.6351i	0.456941	+	1.09012i
$691$	−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
$693$	5.37084	−	36.5652i	0.204021	−	1.38900i
$694$			17.7347i			0.673199i
$695$	−12.8202	−	10.8563i	−0.486299	−	0.411803i
$696$	4.49324	−	13.8288i	0.170316	−	0.524178i
$697$	−4.96548	−	2.53004i	−0.188081	−	0.0958320i
$698$	−17.5849	−	2.78517i	−0.665596	−	0.105420i
$699$	57.6408	−	41.8785i	2.18018	−	1.58399i
$700$	−6.20404	−	4.42799i	−0.234491	−	0.167362i
$701$	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	$0.331689\pi$
$702$	14.4679	−	2.29149i	0.546055	−	0.0864867i
$703$	−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
$707$	12.1886	+	23.9215i	0.458400	+	0.899660i
$708$	−6.54708	+	12.8494i	−0.246054	+	0.482908i
$709$	−23.7291	−	32.6603i	−0.891166	−	1.22658i	−0.973201	−	0.229955i	$-0.926142\pi$
$709$	−23.7291	−	32.6603i	−0.891166	−	1.22658i	0.0820353	−	0.996629i	$-0.473858\pi$
$710$	19.3662	+	4.56307i	0.726800	+	0.171249i
$711$	−40.3169	+	13.0997i	−1.51200	+	0.491279i
$712$	9.40171	−	4.79041i	0.352344	−	0.179528i
$713$	−1.94653	−	12.2899i	−0.0728982	−	0.460261i
$714$	10.8836			0.407310
$715$	7.81584	−	0.736845i	0.292296	−	0.0275564i
$716$	−13.5520			−0.506461
$717$	−12.4488	−	78.5987i	−0.464910	−	2.93532i
$718$	−6.84740	+	3.48892i	−0.255543	+	0.130205i
$719$	−6.32991	+	2.05671i	−0.236066	+	0.0767024i	−0.424661	−	0.905353i	$-0.639607\pi$
$719$	−6.32991	+	2.05671i	−0.236066	+	0.0767024i	0.188595	+	0.982055i	$0.439607\pi$
$720$	8.59895	+	13.9002i	0.320464	+	0.518031i
$721$	2.87833	+	3.96168i	0.107195	+	0.147541i
$722$	8.80903	−	17.2887i	0.327838	−	0.643418i
$723$	0.0820071	+	0.160948i	0.00304988	+	0.00598572i
$724$	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	$0.136158\pi$
$728$	1.59384	−	0.252439i	0.0590715	−	0.00935600i
$729$	−29.6653	−	9.63884i	−1.09871	−	0.356994i
$730$	6.05881	+	24.7758i	0.224247	+	0.916992i
$731$	−16.3059	+	11.8469i	−0.603096	+	0.438175i
$732$	−18.7822	−	2.97481i	−0.694211	−	0.109952i
$733$	−24.8515	−	12.6624i	−0.917909	−	0.467698i	−0.0698250	−	0.997559i	$-0.522244\pi$
$733$	−24.8515	−	12.6624i	−0.917909	−	0.467698i	−0.848084	+	0.529861i	$0.822244\pi$
$734$	11.1829	−	34.4175i	0.412769	−	1.27037i
$735$	−33.4583	+	2.77532i	−1.23413	+	0.102369i
$736$		−	4.32453i		−	0.159404i
$737$	−25.0062	+	4.24920i	−0.921115	+	0.156521i
$738$	12.9545	+	12.9545i	0.476862	+	0.476862i
$739$	−8.88327	−	6.45407i	−0.326776	−	0.237417i	0.412285	−	0.911055i	$-0.364731\pi$
$739$	−8.88327	−	6.45407i	−0.326776	−	0.237417i	−0.739061	+	0.673638i	$0.764731\pi$
$740$	2.87039	−	1.20317i	0.105518	−	0.0442294i
$741$	6.50889	+	20.0323i	0.239110	+	0.735905i
$742$	0.907029	−	5.72675i	0.0332981	−	0.210236i
$743$	3.77987	−	23.8652i	0.138670	−	0.875527i	−0.816041	−	0.577994i	$-0.803836\pi$
$743$	3.77987	−	23.8652i	0.138670	−	0.875527i	0.954711	−	0.297534i	$-0.0961641\pi$
$744$	−2.85493	−	8.78656i	−0.104667	−	0.322131i
$745$	0.0282267	−	0.0689669i	0.00103415	−	0.00252675i
$746$	13.1974	+	9.58850i	0.483193	+	0.351060i
$747$	6.61105	+	6.61105i	0.241886	+	0.241886i
$748$	−6.60805	−	3.27395i	−0.241614	−	0.119708i
$749$		−	25.1802i		−	0.920065i
$750$	−27.0002	+	23.6580i	−0.985909	+	0.863867i
$751$	−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	$0.747746\pi$
$752$	−3.99740	−	2.03678i	−0.145770	−	0.0742737i
$753$	26.7150	+	4.23123i	0.973547	+	0.154195i
$754$	−3.87818	+	2.81766i	−0.141235	+	0.102613i
$755$	46.0152	−	11.2528i	1.67466	−	0.409532i
$756$	−20.0624	−	6.51868i	−0.729664	−	0.237082i
$757$	−49.9645	+	7.91360i	−1.81599	+	0.287625i	−0.969556	−	0.244869i	$-0.921255\pi$
$757$	−49.9645	+	7.91360i	−1.81599	+	0.287625i	−0.846434	+	0.532493i	$0.821255\pi$
$758$	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	−0.319350	−	0.947637i	$-0.603464\pi$
$761$	18.7749	−	25.8415i	0.680591	−	0.936753i	0.999941	+	0.0108837i	$0.00346445\pi$
$762$	−24.7303	−	48.5360i	−0.895886	−	1.75827i
$763$	−1.30665	+	2.56445i	−0.0473040	+	0.0928392i
$764$	7.40180	+	10.1877i	0.267788	+	0.368578i
$765$	8.33505	−	35.3749i	0.301355	−	1.27898i
$766$	−27.8369	+	9.04477i	−1.00579	+	0.326801i
$767$	4.23618	−	2.15844i	0.152960	−	0.0779368i
$768$	−0.502291	−	3.17134i	−0.0181249	−	0.114436i
$769$	41.4875			1.49608			0.748039	−	0.663655i	$-0.230996\pi$
$769$	41.4875			1.49608			0.748039	+	0.663655i	$0.230996\pi$
$770$	−10.5105	−	4.16445i	−0.378773	−	0.150076i
$771$	−33.7131			−1.21415
$772$	0.599973	+	3.78808i	0.0215935	+	0.136336i
$773$	−19.4460	+	9.90821i	−0.699422	+	0.356373i	−0.767272	−	0.641322i	$-0.778386\pi$
$773$	−19.4460	+	9.90821i	−0.699422	+	0.356373i	0.0678495	+	0.997696i	$0.478386\pi$
$774$	63.0158	−	20.4751i	2.26506	−	0.735962i
$775$	12.7630	−	6.63934i	0.458461	−	0.238492i
$776$	−4.11829	−	5.66834i	−0.147838	−	0.203482i
$777$	−3.09301	+	6.07038i	−0.110961	+	0.217774i
$778$	2.01440	+	3.95348i	0.0722197	+	0.141739i
$779$	−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
$783$	61.8933	−	9.80293i	2.21189	−	0.350328i
$784$	4.44724	+	1.44500i	0.158830	+	0.0516070i
$785$	3.75506	+	2.27937i	0.134024	+	0.0813541i
$786$	25.3959	−	18.4512i	0.905843	−	0.658134i
$787$	−29.9410	−	4.74219i	−1.06728	−	0.169041i	−0.402005	−	0.915637i	$-0.631687\pi$
$787$	−29.9410	−	4.74219i	−1.06728	−	0.169041i	−0.665277	+	0.746596i	$0.731687\pi$
$788$	9.32471	+	4.75118i	0.332179	+	0.169254i
$789$	−4.50319	+	13.8594i	−0.160318	+	0.493407i
$790$	1.07198	+	12.9234i	0.0381394	+	0.459794i
$791$		−	6.08151i		−	0.216234i
$792$	17.3343	+	16.9490i	0.615949	+	0.602257i
$793$	4.43308	+	4.43308i	0.157423	+	0.157423i
$794$	7.54381	+	5.48090i	0.267720	+	0.194510i
$795$	−25.2731	−	10.3437i	−0.896345	−	0.366855i
$796$	2.81435	+	8.66167i	0.0997519	+	0.307005i
$797$	8.39878	−	53.0278i	0.297500	−	1.87834i	−0.157004	−	0.987598i	$-0.550184\pi$
$797$	8.39878	−	53.0278i	0.297500	−	1.87834i	0.454505	−	0.890744i	$-0.349816\pi$
$798$	4.74514	−	29.9596i	0.167976	−	1.06056i
$799$	3.08264	+	9.48739i	0.109056	+	0.335640i
$800$	4.74207	−	1.58516i	0.167658	−	0.0560438i
$801$	62.3997	+	45.3361i	2.20479	+	1.60187i
$802$	−6.22783	−	6.22783i	−0.219912	−	0.219912i
$803$	17.5528	+	33.5128i	0.619424	+	1.18264i
$804$			24.5559i			0.866019i
$805$	−9.52624	+	11.2496i	−0.335756	+	0.396495i
$806$	−0.941213	+	2.89676i	−0.0331528	+	0.102034i
$807$	74.1031	+	37.7574i	2.60855	+	1.32912i
$808$	−17.3948	−	2.75506i	−0.611947	−	0.0969228i
$809$	−25.4737	+	18.5077i	−0.895608	+	0.650697i	−0.937334	−	0.348432i	$-0.886714\pi$
$809$	−25.4737	+	18.5077i	−0.895608	+	0.650697i	0.0417260	+	0.999129i	$0.486714\pi$
$810$	−26.1094	+	43.0131i	−0.917392	+	1.51133i
$811$	−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	$0.638179\pi$
$812$	6.81839	−	1.07993i	0.239279	−	0.0378980i
$813$	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
$817$	25.5021	+	50.0507i	0.892206	+	1.75105i
$818$	7.89712	−	15.4990i	0.276116	−	0.541908i
$819$	6.93333	+	9.54290i	0.242270	+	0.333456i
$820$	4.76606	−	2.94838i	0.166438	−	0.102962i
$821$	−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	$0.401266\pi$
$822$	−7.06867	+	3.60167i	−0.246548	+	0.125623i
$823$	3.59018	+	22.6675i	0.125146	+	0.790139i	0.967807	+	0.251695i	$0.0809879\pi$
$823$	3.59018	+	22.6675i	0.125146	+	0.790139i	−0.842661	+	0.538445i	$0.819012\pi$
$824$	−3.21229			−0.111905
$825$	−30.4437	+	43.6846i	−1.05991	+	1.52090i
$826$	−6.84677			−0.238229
$827$	6.32782	+	39.9523i	0.220040	+	1.38928i	0.812164	+	0.583430i	$0.198290\pi$
$827$	6.32782	+	39.9523i	0.220040	+	1.38928i	−0.592124	+	0.805847i	$0.701710\pi$
$828$	28.1656	−	14.3511i	0.978823	−	0.498735i
$829$	−25.8477	+	8.39841i	−0.897726	+	0.291689i	−0.721298	−	0.692625i	$-0.756454\pi$
$829$	−25.8477	+	8.39841i	−0.897726	+	0.291689i	−0.176428	+	0.984314i	$0.556454\pi$
$830$	2.43225	−	1.50464i	0.0844247	−	0.0522268i
$831$	25.9156	+	35.6698i	0.899004	+	1.23737i
$832$	−0.480577	+	0.943185i	−0.0166610	+	0.0326990i
$833$	−4.72036	−	9.26422i	−0.163551	−	0.320986i
$834$	−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
$838$	16.1996	−	2.56576i	0.559604	−	0.0886326i
$839$	−20.9575	−	6.80951i	−0.723533	−	0.235090i	−0.0759789	−	0.997109i	$-0.524208\pi$
$839$	−20.9575	−	6.80951i	−0.723533	−	0.235090i	−0.647554	+	0.762019i	$0.724208\pi$
$840$	−5.67932	+	9.35619i	−0.195955	+	0.322819i
$841$	6.87075	−	4.99189i	0.236922	−	0.172134i
$842$	26.0493	+	4.12580i	0.897718	+	0.142185i
$843$	28.3404	+	14.4402i	0.976096	+	0.497346i
$844$	7.74813	−	23.8463i	0.266701	−	0.820823i
$845$	17.1661	−	20.2715i	0.590531	−	0.697360i
$846$		−	32.7941i		−	1.12749i
$847$	−16.6171	−	2.25030i	−0.570969	−	0.0773212i
$848$	2.68946	+	2.68946i	0.0923566	+	0.0923566i
$849$	−5.35078	−	3.88757i	−0.183638	−	0.133421i
$850$	−9.94815	−	4.96354i	−0.341219	−	0.170248i
$851$	−1.86005	−	5.72466i	−0.0637619	−	0.196239i
$852$	4.46938	−	28.2185i	0.153118	−	0.966751i
$853$	5.72190	−	36.1266i	0.195914	−	1.23695i	−0.672118	−	0.740444i	$-0.734615\pi$
$853$	5.72190	−	36.1266i	0.195914	−	1.23695i	0.868032	−	0.496508i	$-0.165385\pi$
$854$	−2.78994	−	8.58655i	−0.0954697	−	0.293826i
$855$	−93.7432	−	38.3671i	−3.20595	−	1.31213i
$856$	13.3632	+	9.70891i	0.456744	+	0.331844i
$857$	−8.98140	−	8.98140i	−0.306799	−	0.306799i	0.536868	−	0.843666i	$-0.319607\pi$
$857$	−8.98140	−	8.98140i	−0.306799	−	0.306799i	−0.843666	+	0.536868i	$0.819607\pi$
$858$	−1.88849	−	11.1136i	−0.0644719	−	0.379411i
$859$			54.6972i			1.86624i	0.359559	+	0.933122i	$0.382927\pi$
$859$			54.6972i			1.86624i	−0.359559	+	0.933122i	$0.617073\pi$
$860$	−1.67552	−	20.1995i	−0.0571348	−	0.688796i
$861$	−3.79096	+	11.6674i	−0.129196	+	0.397624i
$862$	−8.46615	−	4.31372i	−0.288358	−	0.146926i
$863$	−14.0924	−	2.23202i	−0.479711	−	0.0759788i	−0.0881040	−	0.996111i	$-0.528081\pi$
$863$	−14.0924	−	2.23202i	−0.479711	−	0.0759788i	−0.391607	+	0.920132i	$0.628081\pi$
$864$	11.1951	−	8.13370i	0.380864	−	0.276714i
$865$	−25.2187	−	15.3081i	−0.857462	−	0.520489i
$866$	23.7208	+	7.70734i	0.806064	+	0.261906i
$867$	−38.2334	+	6.05557i	−1.29847	+	0.205658i
$868$	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
$872$	−0.857140	−	1.68223i	−0.0290264	−	0.0569676i
$873$	23.2512	−	45.6330i	0.786932	−	1.54444i
$874$	15.7523	+	21.6812i	0.532829	+	0.733376i
$875$	−15.8276	−	6.32249i	−0.535070	−	0.213739i
$876$	34.8324	−	11.3177i	1.17688	−	0.382391i
$877$	13.7086	−	6.98490i	0.462908	−	0.235863i	−0.206952	−	0.978351i	$-0.566354\pi$
$877$	13.7086	−	6.98490i	0.462908	−	0.235863i	0.669860	+	0.742488i	$0.266354\pi$
$878$	−0.264554	−	1.67033i	−0.00892828	−	0.0563710i
$879$	−63.0707			−2.12732
$880$	6.26270	−	3.97223i	0.211115	−	0.133904i
$881$	−27.4651			−0.925323			−0.462662	−	0.886535i	$-0.653106\pi$
$881$	−27.4651			−0.925323			−0.462662	+	0.886535i	$0.653106\pi$
$882$	5.34708	+	33.7601i	0.180045	+	1.13676i
$883$	−48.3824	+	24.6520i	−1.62820	+	0.829607i	−0.629584	+	0.776932i	$0.716775\pi$
$883$	−48.3824	+	24.6520i	−1.62820	+	0.829607i	−0.998612	+	0.0526752i	$0.983225\pi$
$884$	2.23854	−	0.727347i	0.0752904	−	0.0244633i
$885$	−7.39548	+	31.3872i	−0.248596	+	1.05507i
$886$	−11.9367	−	16.4295i	−0.401023	−	0.551960i
$887$	−26.8712	+	52.7376i	−0.902246	+	1.77076i	−0.351134	+	0.936325i	$0.614204\pi$
$887$	−26.8712	+	52.7376i	−0.902246	+	1.77076i	−0.551111	+	0.834432i	$0.685796\pi$
$888$	−2.02896	−	3.98206i	−0.0680875	−	0.133629i
$889$	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
$893$	27.4601	−	4.34926i	0.918918	−	0.145542i
$894$	−0.101769	−	0.0330667i	−0.00340366	−	0.00110592i
$895$	−29.4358	+	7.19839i	−0.983929	+	0.240616i
$896$	1.23329	−	0.896038i	0.0412014	−	0.0299345i
$897$	−14.5177	−	2.29938i	−0.484732	−	0.0767740i
$898$	−37.4672	−	19.0905i	−1.25030	−	0.637058i
$899$	−4.02649	+	12.3922i	−0.134291	+	0.413305i
$900$	26.0608	+	25.6247i	0.868695	+	0.854156i
$901$		−	8.45716i		−	0.281749i
$902$	5.81141	−	5.94353i	0.193499	−	0.197898i
$903$	31.3733	+	31.3733i	1.04404	+	1.04404i
$904$	3.22746	+	2.34489i	0.107344	+	0.0779899i
$905$	14.6064	−	35.6882i	0.485534	−	1.18632i
$906$	−21.0201	−	64.6931i	−0.698345	−	2.14928i
$907$	−2.36980	+	14.9623i	−0.0786880	+	0.496817i	0.916596	+	0.399814i	$0.130925\pi$
$907$	−2.36980	+	14.9623i	−0.0786880	+	0.496817i	−0.995284	+	0.0970022i	$0.969075\pi$
$908$	−0.319245	+	2.01564i	−0.0105945	+	0.0668912i
$909$	−39.7815	−	122.435i	−1.31947	−	4.06091i
$910$	3.32782	−	1.39491i	0.110316	−	0.0462408i
$911$	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
$913$	2.96573	−	3.03315i	0.0981512	−	0.100383i
$914$		−	10.1208i		−	0.334766i
$915$	−42.3763	+	3.51506i	−1.40092	+	0.116204i
$916$	0.470996	−	1.44958i	0.0155622	−	0.0478954i
$917$	13.2792	+	6.76610i	0.438518	+	0.223436i
$918$	−30.3902	−	4.81333i	−1.00302	−	0.158863i
$919$	47.2044	−	34.2960i	1.55713	−	1.13132i	0.618813	−	0.785538i	$-0.287614\pi$
$919$	47.2044	−	34.2960i	1.55713	−	1.13132i	0.938315	−	0.345782i	$-0.112386\pi$
$920$	−2.29706	−	9.39316i	−0.0757318	−	0.309683i
$921$	36.0740	+	11.7212i	1.18868	+	0.386226i
$922$	−27.1134	+	4.29433i	−0.892931	+	0.141426i
$923$	−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
$927$	−10.6601	−	20.9216i	−0.350123	−	0.687155i
$928$	−2.05589	+	4.03492i	−0.0674881	+	0.132453i
$929$	5.89306	+	8.11110i	0.193345	+	0.266117i	0.894672	−	0.446723i	$-0.147409\pi$
$929$	5.89306	+	8.11110i	0.193345	+	0.266117i	−0.701327	+	0.712839i	$0.747409\pi$
$930$	−10.8682	−	17.5685i	−0.356383	−	0.576094i
$931$	−27.5598	+	8.95473i	−0.903237	+	0.293480i
$932$	−19.7711	+	10.0739i	−0.647624	+	0.329981i
$933$	6.98475	+	44.1000i	0.228670	+	1.44377i
$934$	−21.8363			−0.714505
$935$	−16.0921	−	3.60124i	−0.526269	−	0.117773i
$936$	−7.73776			−0.252917
$937$	6.52746	+	41.2128i	0.213243	+	1.34636i	0.829363	+	0.558710i	$0.188703\pi$
$937$	6.52746	+	41.2128i	0.213243	+	1.34636i	−0.616120	+	0.787652i	$0.711297\pi$
$938$	−10.3877	+	5.29282i	−0.339172	+	0.172817i
$939$	92.1972	−	29.9567i	3.00874	−	0.977600i
$940$	−9.76448	−	2.30071i	−0.318482	−	0.0750410i
$941$	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	$0.668520\pi$
$942$	2.86364	−	5.62021i	0.0933025	−	0.183116i
$943$	−4.92065	−	9.65732i	−0.160238	−	0.314486i
$944$	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	$0.299413\pi$
$948$	18.3918	−	2.91297i	0.597338	−	0.0946090i
$949$	−11.4836	−	3.73124i	−0.372772	−	0.121121i
$950$	−18.0005	+	25.2204i	−0.584014	+	0.818259i
$951$	79.6507	−	57.8696i	2.58285	−	1.87655i
$952$	−3.34789	−	0.530254i	−0.108506	−	0.0171856i
$953$	−31.2897	−	15.9429i	−1.01357	−	0.516441i	−0.133384	−	0.991064i	$-0.542584\pi$
$953$	−31.2897	−	15.9429i	−1.01357	−	0.516441i	−0.880189	+	0.474623i	$0.842584\pi$
$954$	−8.59137	+	26.4415i	−0.278156	+	0.856076i
$955$	21.4886	+	18.1967i	0.695354	+	0.588833i
$956$			24.7841i			0.801574i
$957$	−8.07890	−	47.5436i	−0.261154	−	1.53687i
$958$	4.61171	+	4.61171i	0.148998	+	0.148998i
$959$	−3.04719	−	2.21391i	−0.0983989	−	0.0714910i
$960$	−2.77553	−	6.62155i	−0.0895797	−	0.213710i
$961$	−7.02117	−	21.6089i	−0.226489	−	0.697062i
$962$	−0.230490	+	1.45526i	−0.00743130	+	0.0469194i
$963$	−18.8879	+	119.253i	−0.608654	+	3.84289i
$964$	−0.0173846	−	0.0535042i	−0.000559919	−	0.00172325i
$965$	3.31529	+	7.90927i	0.106723	+	0.254608i
$966$	17.1249	+	12.4420i	0.550984	+	0.400313i
$967$	−43.6347	−	43.6347i	−1.40320	−	1.40320i	−0.789685	−	0.613512i	$-0.789756\pi$
$967$	−43.6347	−	43.6347i	−1.40320	−	1.40320i	−0.613512	−	0.789685i	$-0.710244\pi$
$968$	7.60139	−	7.95103i	0.244318	−	0.255556i
$969$		−	44.2438i		−	1.42131i
$970$	−11.9560	−	10.1245i	−0.383885	−	0.325078i
$971$	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	$-0.0511661\pi$
$972$	27.3888	+	13.9553i	0.878497	+	0.447617i
$973$	−11.3119	−	1.79163i	−0.362642	−	0.0574369i
$974$	−2.37265	+	1.72383i	−0.0760245	+	0.0552350i
$975$	−2.80008	−	16.7623i	−0.0896743	−	0.536822i
$976$	5.63262	+	1.83015i	0.180296	+	0.0585817i
$977$	−51.0116	+	8.07944i	−1.63201	+	0.258484i	−0.904140	−	0.427236i	$-0.859487\pi$
$977$	−51.0116	+	8.07944i	−1.63201	+	0.258484i	−0.727865	+	0.685720i	$0.759487\pi$
$978$	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
$982$	6.04634	+	11.8666i	0.192946	+	0.378679i
$983$	24.7809	−	48.6352i	0.790387	−	1.55122i	−0.0433506	−	0.999060i	$-0.513803\pi$
$983$	24.7809	−	48.6352i	0.790387	−	1.55122i	0.833737	−	0.552161i	$-0.186197\pi$
$984$	−4.73019	−	6.51054i	−0.150793	−	0.207549i
$985$	22.7775	+	5.36686i	0.725753	+	0.171002i
$986$	9.57644	−	3.11157i	0.304976	−	0.0990927i
$987$	19.5663	−	9.96952i	0.622802	−	0.317333i
$988$	−1.02620	−	6.47920i	−0.0326479	−	0.206131i
$989$	−39.1997			−1.24648
$990$	46.6541	+	27.6069i	1.48276	+	0.877404i
$991$	1.67436			0.0531879			0.0265939	−	0.999646i	$-0.491534\pi$
$991$	1.67436			0.0531879			0.0265939	+	0.999646i	$0.491534\pi$
$992$	0.450114	+	2.84191i	0.0142911	+	0.0902306i
$993$	40.7742	−	20.7755i	1.29393	−	0.659291i
$994$	12.9005	−	4.19162i	0.409178	−	0.132950i
$995$	10.7138	+	17.3188i	0.339649	+	0.549043i
$996$	−2.41395	−	3.32251i	−0.0764888	−	0.105278i
$997$	−13.5579	+	26.6089i	−0.429384	+	0.842713i	0.570389	+	0.821375i	$0.306793\pi$
$997$	−13.5579	+	26.6089i	−0.429384	+	0.842713i	−0.999772	+	0.0213379i	$0.993207\pi$
$998$	−10.6099	−	20.8231i	−0.335850	−	0.659143i
$999$	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.73.6	yes	48
3.2	odd	2		990.2.bh.c.73.2		48
4.3	odd	2		880.2.cm.c.513.1		48
5.2	odd	4	inner	110.2.k.a.7.1	✓	48
5.3	odd	4		550.2.bh.b.7.6		48
5.4	even	2		550.2.bh.b.293.1		48
11.8	odd	10	inner	110.2.k.a.63.1	yes	48
15.2	even	4		990.2.bh.c.667.6		48
20.7	even	4		880.2.cm.c.337.6		48
33.8	even	10		990.2.bh.c.613.6		48
44.19	even	10		880.2.cm.c.833.6		48
55.8	even	20		550.2.bh.b.107.1		48
55.19	odd	10		550.2.bh.b.393.6		48
55.52	even	20	inner	110.2.k.a.107.6	yes	48
165.107	odd	20		990.2.bh.c.217.2		48
220.107	odd	20		880.2.cm.c.657.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.1	✓	48	5.2	odd	4	inner
110.2.k.a.63.1	yes	48	11.8	odd	10	inner
110.2.k.a.73.6	yes	48	1.1	even	1	trivial
110.2.k.a.107.6	yes	48	55.52	even	20	inner
550.2.bh.b.7.6		48	5.3	odd	4
550.2.bh.b.107.1		48	55.8	even	20
550.2.bh.b.293.1		48	5.4	even	2
550.2.bh.b.393.6		48	55.19	odd	10
880.2.cm.c.337.6		48	20.7	even	4
880.2.cm.c.513.1		48	4.3	odd	2
880.2.cm.c.657.1		48	220.107	odd	20
880.2.cm.c.833.6		48	44.19	even	10
990.2.bh.c.73.2		48	3.2	odd	2
990.2.bh.c.217.2		48	165.107	odd	20
990.2.bh.c.613.6		48	33.8	even	10
990.2.bh.c.667.6		48	15.2	even	4

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 $\F_{q}$

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+(0.156434 + 0.987688i) q^{2} +(2.86091 - 1.45771i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.90161 + 1.17638i) q^{5} +(1.88730 + 2.59765i) q^{6} +(-0.692077 + 1.35828i) q^{7} +(-0.453990 - 0.891007i) 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} +(1.04553 - 0.165595i) q^{13} +(-1.44982 - 0.471075i) q^{14} +(-3.72553 + 6.13750i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-2.19616 - 0.347837i) q^{17} +(6.51299 + 3.31853i) q^{18} +(-1.91500 + 5.89375i) q^{19} +(1.44502 - 1.70643i) q^{20} +4.89475i q^{21} +(1.47241 - 2.97187i) q^{22} +(-3.05791 - 3.05791i) q^{23} +(-2.59765 - 1.88730i) q^{24} +(2.23228 - 4.47403i) q^{25} +(0.327113 + 1.00675i) q^{26} +(2.16472 - 13.6675i) q^{27} +(0.238474 - 1.50566i) q^{28} +(1.39938 + 4.30686i) q^{29} +(-6.64474 - 2.71955i) q^{30} +(2.32781 + 1.69125i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-10.5362 - 1.54760i) q^{33} -2.22353i q^{34} +(-0.281782 - 3.39707i) q^{35} +(-2.25882 + 6.95193i) q^{36} +(1.24018 + 0.631904i) q^{37} +(-6.12076 - 0.969434i) q^{38} +(2.74977 - 1.99782i) q^{39} +(1.91147 + 1.16029i) q^{40} +(2.38365 + 0.774496i) q^{41} +(-4.83449 + 0.765708i) 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} +(-2.03678 - 3.99740i) q^{47} +(1.45771 - 2.86091i) q^{48} +(2.74855 + 3.78305i) q^{49} +(4.76815 + 1.50490i) q^{50} +(-6.79005 + 2.20622i) q^{51} +(-0.943185 + 0.480577i) q^{52} +(0.594995 + 3.75665i) q^{53} +13.8379 q^{54} +(7.40145 + 0.467516i) q^{55} +1.52443 q^{56} +(3.11273 + 19.6530i) q^{57} +(-4.03492 + 2.05589i) q^{58} +(4.27154 - 1.38791i) q^{59} +(1.64660 - 6.98836i) q^{60} +(3.48115 + 4.79140i) q^{61} +(-1.30628 + 2.56372i) q^{62} +(5.05887 + 9.92860i) 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} +(2.19616 - 0.347837i) q^{68} +(-13.2059 - 4.29086i) q^{69} +(3.31116 - 0.809731i) q^{70} +(-7.19862 + 5.23010i) q^{71} +(-7.21970 - 1.14349i) q^{72} +(-10.1633 - 5.17847i) q^{73} +(-0.430117 + 1.32376i) q^{74} +(-0.135479 - 16.0538i) q^{75} -6.19706i q^{76} +(4.47882 - 2.34584i) q^{77} +(2.40339 + 2.40339i) q^{78} +(-4.69179 - 3.40879i) q^{79} +(-0.846982 + 2.06945i) q^{80} +(-6.95367 - 21.4012i) q^{81} +(-0.392075 + 2.47546i) q^{82} +(-0.200087 + 1.26330i) q^{83} +(-1.51256 - 4.65519i) q^{84} +(4.58543 - 1.92206i) q^{85} +(7.33334 + 5.32798i) q^{86} +(10.2816 + 10.2816i) q^{87} +(-0.481987 + 3.28142i) q^{88} +10.5518i q^{89} +(-16.2890 + 1.35115i) q^{90} +(-0.498662 + 1.53472i) q^{91} +(3.85319 + 1.96330i) q^{92} +(9.12499 + 1.44526i) q^{93} +(3.62956 - 2.63703i) q^{94} +(-3.29169 - 13.4604i) q^{95} +(3.05372 + 0.992214i) q^{96} +(6.92020 - 1.09605i) 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

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