LMFDB - Embedded newform 230.2.j.a.209.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(9,230)] 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("230.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			209.7
Character	$\chi$	$=$	230.209
Dual form			230.2.j.a.219.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.540641 - 0.841254i) q^{2} +(-2.56448 + 0.368717i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.88872 + 1.19697i) q^{5} +(-1.07628 + 2.35672i) q^{6} +(1.82575 + 1.58202i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(3.56212 - 1.04593i) q^{9} +(2.02807 - 0.941762i) q^{10} +(1.25768 - 0.808265i) q^{11} +(1.40072 + 2.17956i) q^{12} +(3.06511 - 2.65594i) q^{13} +(2.31795 - 0.680612i) q^{14} +(-5.28493 - 2.37320i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(5.62426 + 2.56851i) q^{17} +(1.04593 - 3.56212i) q^{18} +(0.291448 + 0.638182i) q^{19} +(0.304199 - 2.21528i) q^{20} +(-5.26540 - 3.38387i) q^{21} -1.49501i q^{22} +(-3.56194 - 3.21132i) q^{23} +2.59085 q^{24} +(2.13453 + 4.52148i) q^{25} +(-0.577190 - 4.01445i) q^{26} +(-1.67918 + 0.766856i) q^{27} +(0.680612 - 2.31795i) q^{28} +(-2.53349 + 5.54757i) q^{29} +(-4.85371 + 3.16291i) q^{30} +(-0.649873 + 4.51997i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-2.92729 + 2.53651i) q^{33} +(5.20148 - 3.34279i) q^{34} +(1.55469 + 5.17335i) q^{35} +(-2.43118 - 2.80573i) q^{36} +(-1.60042 - 5.45053i) q^{37} +(0.694442 + 0.0998457i) q^{38} +(-6.88114 + 7.94125i) q^{39} +(-1.69915 - 1.45358i) q^{40} +(-4.89061 - 1.43601i) q^{41} +(-5.69338 + 2.60008i) q^{42} +(-4.99509 + 0.718186i) q^{43} +(-1.25768 - 0.808265i) q^{44} +(7.97981 + 2.28828i) q^{45} +(-4.62726 + 1.26033i) q^{46} +4.52400i q^{47} +(1.40072 - 2.17956i) q^{48} +(-0.165637 - 1.15203i) q^{49} +(4.95772 + 0.648819i) q^{50} +(-15.3704 - 4.51315i) q^{51} +(-3.68922 - 1.68481i) q^{52} +(4.01724 + 3.48096i) q^{53} +(-0.262713 + 1.82721i) q^{54} +(3.34288 - 0.0211755i) q^{55} +(-1.58202 - 1.82575i) q^{56} +(-0.982721 - 1.52914i) q^{57} +(3.29720 + 5.13055i) q^{58} +(-9.64692 - 11.1331i) q^{59} +(0.0366970 + 5.79320i) q^{60} +(2.04923 - 14.2527i) q^{61} +(3.45109 + 2.99039i) q^{62} +(8.15822 + 3.72573i) q^{63} +(0.959493 + 0.281733i) q^{64} +(8.96822 - 1.34747i) q^{65} +(0.551236 + 3.83393i) q^{66} +(1.77215 - 2.75752i) q^{67} -6.18301i q^{68} +(10.3186 + 6.92201i) q^{69} +(5.19263 + 1.48903i) q^{70} +(9.51232 + 6.11320i) q^{71} +(-3.67472 + 0.528345i) q^{72} +(-3.05196 + 1.39378i) q^{73} +(-5.45053 - 1.60042i) q^{74} +(-7.14110 - 10.8082i) q^{75} +(0.459439 - 0.530221i) q^{76} +(3.57490 + 0.513993i) q^{77} +(2.96039 + 10.0821i) q^{78} +(1.54077 + 1.77814i) q^{79} +(-2.14146 + 0.643551i) q^{80} +(-5.34601 + 3.43567i) q^{81} +(-3.85212 + 3.33788i) q^{82} +(0.823140 + 2.80336i) q^{83} +(-0.890748 + 6.19529i) q^{84} +(7.54822 + 11.5833i) q^{85} +(-2.09637 + 4.59042i) q^{86} +(4.45160 - 15.1608i) q^{87} +(-1.35991 + 0.621051i) q^{88} +(-0.515328 - 3.58419i) q^{89} +(6.23923 - 5.47591i) q^{90} +9.79786 q^{91} +(-1.44143 + 4.57409i) q^{92} -11.8310i q^{93} +(3.80583 + 2.44586i) q^{94} +(-0.213421 + 1.55420i) q^{95} +(-1.07628 - 2.35672i) q^{96} +(3.34235 - 11.3830i) q^{97} +(-1.05870 - 0.483491i) q^{98} +(3.63464 - 4.19460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$3$	−2.56448	+	0.368717i	−1.48060	+	0.212879i	−0.834769	−	0.550600i	$-0.814399\pi$
$3$	−2.56448	+	0.368717i	−1.48060	+	0.212879i	−0.645834	+	0.763478i	$0.723490\pi$
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	1.88872	+	1.19697i	0.844661	+	0.535301i
$5$	1.88872	+	1.19697i	0.844661	+	0.535301i
$6$	−1.07628	+	2.35672i	−0.439389	+	0.962127i
$7$	1.82575	+	1.58202i	0.690067	+	0.597946i	0.927663	−	0.373418i	$-0.121814\pi$
$7$	1.82575	+	1.58202i	0.690067	+	0.597946i	−0.237596	+	0.971364i	$0.576360\pi$
$8$	−0.989821	−	0.142315i	−0.349955	−	0.0503159i
$9$	3.56212	−	1.04593i	1.18737	−	0.348645i
$10$	2.02807	−	0.941762i	0.641333	−	0.297811i
$11$	1.25768	−	0.808265i	0.379206	−	0.243701i	−0.337127	−	0.941459i	$-0.609455\pi$
$11$	1.25768	−	0.808265i	0.379206	−	0.243701i	0.716333	+	0.697758i	$0.245819\pi$
$12$	1.40072	+	2.17956i	0.404353	+	0.629185i
$13$	3.06511	−	2.65594i	0.850110	−	0.736624i	−0.116414	−	0.993201i	$-0.537140\pi$
$13$	3.06511	−	2.65594i	0.850110	−	0.736624i	0.966524	+	0.256576i	$0.0825945\pi$
$14$	2.31795	−	0.680612i	0.619498	−	0.181901i
$15$	−5.28493	−	2.37320i	−1.36456	−	0.612758i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	5.62426	+	2.56851i	1.36408	+	0.622956i	0.956907	−	0.290393i	$-0.0937861\pi$
$17$	5.62426	+	2.56851i	1.36408	+	0.622956i	0.407177	+	0.913349i	$0.366513\pi$
$18$	1.04593	−	3.56212i	0.246529	−	0.839601i
$19$	0.291448	+	0.638182i	0.0668628	+	0.146409i	0.940113	−	0.340863i	$-0.110719\pi$
$19$	0.291448	+	0.638182i	0.0668628	+	0.146409i	−0.873250	+	0.487272i	$0.837992\pi$
$20$	0.304199	−	2.21528i	0.0680210	−	0.495352i
$21$	−5.26540	−	3.38387i	−1.14901	−	0.738421i
$22$		−	1.49501i		−	0.318738i
$23$	−3.56194	−	3.21132i	−0.742716	−	0.669606i
$23$	−3.56194	−	3.21132i	−0.742716	−	0.669606i
$24$	2.59085			0.528855
$25$	2.13453	+	4.52148i	0.426905	+	0.904296i
$26$	−0.577190	−	4.01445i	−0.113196	−	0.787298i
$27$	−1.67918	+	0.766856i	−0.323159	+	0.147582i
$28$	0.680612	−	2.31795i	0.128623	−	0.438051i
$29$	−2.53349	+	5.54757i	−0.470457	+	1.03016i	0.514521	+	0.857478i	$0.327970\pi$
$29$	−2.53349	+	5.54757i	−0.470457	+	1.03016i	−0.984978	+	0.172679i	$0.944758\pi$
$30$	−4.85371	+	3.16291i	−0.886162	+	0.577466i
$31$	−0.649873	+	4.51997i	−0.116721	+	0.811810i	0.844406	+	0.535703i	$0.179953\pi$
$31$	−0.649873	+	4.51997i	−0.116721	+	0.811810i	−0.961127	+	0.276107i	$0.910956\pi$
$32$	0.281733	+	0.959493i	0.0498038	+	0.169616i
$33$	−2.92729	+	2.53651i	−0.509575	+	0.441549i
$34$	5.20148	−	3.34279i	0.892046	−	0.573283i
$35$	1.55469	+	5.17335i	0.262791	+	0.874456i
$36$	−2.43118	−	2.80573i	−0.405196	−	0.467621i
$37$	−1.60042	−	5.45053i	−0.263108	−	0.896062i	−0.980020	−	0.198899i	$-0.936263\pi$
$37$	−1.60042	−	5.45053i	−0.263108	−	0.896062i	0.716912	−	0.697163i	$-0.245555\pi$
$38$	0.694442	+	0.0998457i	0.112653	+	0.0161971i
$39$	−6.88114	+	7.94125i	−1.10186	+	1.27162i
$40$	−1.69915	−	1.45358i	−0.268659	−	0.229831i
$41$	−4.89061	−	1.43601i	−0.763785	−	0.224268i	−0.123437	−	0.992352i	$-0.539392\pi$
$41$	−4.89061	−	1.43601i	−0.763785	−	0.224268i	−0.640348	+	0.768085i	$0.721210\pi$
$42$	−5.69338	+	2.60008i	−0.878508	+	0.401201i
$43$	−4.99509	+	0.718186i	−0.761744	+	0.109522i	−0.512229	−	0.858849i	$-0.671180\pi$
$43$	−4.99509	+	0.718186i	−0.761744	+	0.109522i	−0.249515	+	0.968371i	$0.580271\pi$
$44$	−1.25768	−	0.808265i	−0.189603	−	0.121850i
$45$	7.97981	+	2.28828i	1.18956	+	0.341116i
$46$	−4.62726	+	1.26033i	−0.682253	+	0.185825i
$47$			4.52400i			0.659893i	0.944000	+	0.329947i	$0.107031\pi$
$47$			4.52400i			0.659893i	−0.944000	+	0.329947i	$0.892969\pi$
$48$	1.40072	−	2.17956i	0.202176	−	0.314593i
$49$	−0.165637	−	1.15203i	−0.0236624	−	0.164576i
$50$	4.95772	+	0.648819i	0.701128	+	0.0917569i
$51$	−15.3704	−	4.51315i	−2.15228	−	0.631967i
$52$	−3.68922	−	1.68481i	−0.511603	−	0.233641i
$53$	4.01724	+	3.48096i	0.551811	+	0.478147i	0.885566	−	0.464513i	$-0.153771\pi$
$53$	4.01724	+	3.48096i	0.551811	+	0.478147i	−0.333756	+	0.942660i	$0.608316\pi$
$54$	−0.262713	+	1.82721i	−0.0357508	+	0.248652i
$55$	3.34288	−	0.0211755i	0.450754	−	0.00285530i
$56$	−1.58202	−	1.82575i	−0.211406	−	0.243975i
$57$	−0.982721	−	1.52914i	−0.130165	−	0.202540i
$58$	3.29720	+	5.13055i	0.432944	+	0.673674i
$59$	−9.64692	−	11.1331i	−1.25592	−	1.44941i	−0.842342	−	0.538943i	$-0.818824\pi$
$59$	−9.64692	−	11.1331i	−1.25592	−	1.44941i	−0.413580	−	0.910468i	$-0.635722\pi$
$60$	0.0366970	+	5.79320i	0.00473757	+	0.747899i
$61$	2.04923	−	14.2527i	0.262377	−	1.82487i	−0.252486	−	0.967600i	$-0.581248\pi$
$61$	2.04923	−	14.2527i	0.262377	−	1.82487i	0.514864	−	0.857272i	$-0.327843\pi$
$62$	3.45109	+	2.99039i	0.438289	+	0.379779i
$63$	8.15822	+	3.72573i	1.02784	+	0.469398i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	8.96822	−	1.34747i	1.11237	−	0.167133i
$66$	0.551236	+	3.83393i	0.0678524	+	0.471924i
$67$	1.77215	−	2.75752i	0.216503	−	0.336885i	−0.715966	−	0.698135i	$-0.754014\pi$
$67$	1.77215	−	2.75752i	0.216503	−	0.336885i	0.932469	+	0.361250i	$0.117650\pi$
$68$		−	6.18301i		−	0.749800i
$69$	10.3186	+	6.92201i	1.24221	+	0.833312i
$70$	5.19263	+	1.48903i	0.620638	+	0.177973i
$71$	9.51232	+	6.11320i	1.12891	+	0.725503i	0.965331	−	0.261028i	$-0.0840614\pi$
$71$	9.51232	+	6.11320i	1.12891	+	0.725503i	0.163574	+	0.986531i	$0.447698\pi$
$72$	−3.67472	+	0.528345i	−0.433070	+	0.0622660i
$73$	−3.05196	+	1.39378i	−0.357205	+	0.163130i	−0.585931	−	0.810361i	$-0.699271\pi$
$73$	−3.05196	+	1.39378i	−0.357205	+	0.163130i	0.228726	+	0.973491i	$0.426544\pi$
$74$	−5.45053	−	1.60042i	−0.633612	−	0.186045i
$75$	−7.14110	−	10.8082i	−0.824583	−	1.24802i
$76$	0.459439	−	0.530221i	0.0527013	−	0.0608205i
$77$	3.57490	+	0.513993i	0.407398	+	0.0585749i
$78$	2.96039	+	10.0821i	0.335198	+	1.14158i
$79$	1.54077	+	1.77814i	0.173350	+	0.200057i	0.835776	−	0.549071i	$-0.185018\pi$
$79$	1.54077	+	1.77814i	0.173350	+	0.200057i	−0.662425	+	0.749128i	$0.730473\pi$
$80$	−2.14146	+	0.643551i	−0.239422	+	0.0719512i
$81$	−5.34601	+	3.43567i	−0.594001	+	0.381741i
$82$	−3.85212	+	3.33788i	−0.425395	+	0.368607i
$83$	0.823140	+	2.80336i	0.0903513	+	0.307708i	0.992253	−	0.124233i	$-0.0396470\pi$
$83$	0.823140	+	2.80336i	0.0903513	+	0.307708i	−0.901902	+	0.431941i	$0.857829\pi$
$84$	−0.890748	+	6.19529i	−0.0971886	+	0.675961i
$85$	7.54822	+	11.5833i	0.818720	+	1.25638i
$86$	−2.09637	+	4.59042i	−0.226058	+	0.494998i
$87$	4.45160	−	15.1608i	0.477262	−	1.62540i
$88$	−1.35991	+	0.621051i	−0.144967	+	0.0662042i
$89$	−0.515328	−	3.58419i	−0.0546247	−	0.379923i	−0.998735	−	0.0502921i	$-0.983985\pi$
$89$	−0.515328	−	3.58419i	−0.0546247	−	0.379923i	0.944110	−	0.329631i	$-0.106924\pi$
$90$	6.23923	−	5.47591i	0.657673	−	0.577211i
$91$	9.79786			1.02709
$92$	−1.44143	+	4.57409i	−0.150280	+	0.476882i
$93$		−	11.8310i		−	1.22682i
$94$	3.80583	+	2.44586i	0.392541	+	0.252271i
$95$	−0.213421	+	1.55420i	−0.0218965	+	0.159458i
$96$	−1.07628	−	2.35672i	−0.109847	−	0.240532i
$97$	3.34235	−	11.3830i	0.339364	−	1.15577i	−0.596267	−	0.802786i	$-0.703350\pi$
$97$	3.34235	−	11.3830i	0.339364	−	1.15577i	0.935631	−	0.352981i	$-0.114832\pi$
$98$	−1.05870	−	0.483491i	−0.106945	−	0.0488400i
$99$	3.63464	−	4.19460i	0.365295	−	0.421573i
$100$	3.22617	−	3.81993i	0.322617	−	0.381993i
$101$	−18.3614	+	5.39140i	−1.82703	+	0.536464i	−0.999682	−	0.0252253i	$-0.991970\pi$
$101$	−18.3614	+	5.39140i	−1.82703	+	0.536464i	−0.827348	+	0.561690i	$0.810151\pi$
$102$	−12.1065	+	10.4904i	−1.19873	+	1.03870i
$103$	−2.68750	−	4.18183i	−0.264807	−	0.412048i	0.683232	−	0.730201i	$-0.260574\pi$
$103$	−2.68750	−	4.18183i	−0.264807	−	0.412048i	−0.948039	+	0.318153i	$0.896937\pi$
$104$	−3.41190	+	2.19269i	−0.334564	+	0.215011i
$105$	−5.89448	−	12.6937i	−0.575243	−	1.23878i
$106$	5.10026	−	1.49757i	0.495381	−	0.145457i
$107$	−17.3483	−	2.49431i	−1.67712	−	0.241134i	−0.762949	−	0.646458i	$-0.776249\pi$
$107$	−17.3483	−	2.49431i	−1.67712	−	0.241134i	−0.914173	+	0.405325i	$0.867159\pi$
$108$	1.39511	+	1.20887i	0.134245	+	0.116324i
$109$	6.21222	−	13.6029i	0.595022	−	1.30292i	−0.337337	−	0.941384i	$-0.609526\pi$
$109$	6.21222	−	13.6029i	0.595022	−	1.30292i	0.932359	−	0.361533i	$-0.117747\pi$
$110$	1.78948	−	2.82366i	0.170621	−	0.269225i
$111$	6.11395	+	13.3877i	0.580310	+	1.27070i
$112$	−2.39122	+	0.343805i	−0.225949	+	0.0324865i
$113$	−10.2744	+	15.9873i	−0.966535	+	1.50396i	−0.106127	+	0.994353i	$0.533845\pi$
$113$	−10.2744	+	15.9873i	−0.966535	+	1.50396i	−0.860408	+	0.509606i	$0.829791\pi$
$114$	−1.81770			−0.170243
$115$	−2.88366	−	10.3288i	−0.268903	−	0.963167i
$116$	6.09869			0.566249
$117$	8.14039	−	12.6667i	0.752579	−	1.17104i
$118$	−14.5813	+	2.09648i	−1.34232	+	0.192996i
$119$	6.20504	+	13.5871i	0.568815	+	1.24553i
$120$	4.89339	+	3.10117i	0.446704	+	0.283097i
$121$	−3.64109	+	7.97287i	−0.331008	+	0.724806i
$122$	−10.8822	−	9.42952i	−0.985232	−	0.853709i
$123$	13.0714	+	1.87938i	1.17860	+	0.169458i
$124$	4.38147	−	1.28652i	0.393468	−	0.115533i
$125$	−1.38055	+	11.0948i	−0.123480	+	0.992347i
$126$	7.54495	−	4.84885i	0.672158	−	0.431970i
$127$	−7.18318	−	11.1772i	−0.637404	−	0.991820i	−0.998247	−	0.0591930i	$-0.981147\pi$
$127$	−7.18318	−	11.1772i	−0.637404	−	0.991820i	0.360843	−	0.932627i	$-0.382489\pi$
$128$	0.755750	−	0.654861i	0.0667995	−	0.0578821i
$129$	12.5450	−	3.68355i	1.10453	−	0.324318i
$130$	3.71502	−	8.27304i	0.325829	−	0.725594i
$131$	9.11394	−	10.5181i	0.796289	−	0.918966i	−0.201883	−	0.979410i	$-0.564706\pi$
$131$	9.11394	−	10.5181i	0.796289	−	0.918966i	0.998172	+	0.0604434i	$0.0192515\pi$
$132$	3.52333	+	1.60905i	0.306666	+	0.140050i
$133$	−0.477505	+	1.62623i	−0.0414050	+	0.141012i
$134$	−1.36168	−	2.98166i	−0.117631	−	0.257576i
$135$	−4.08941	−	0.561552i	−0.351960	−	0.0483307i
$136$	−5.20148	−	3.34279i	−0.446023	−	0.286642i
$137$			16.9150i			1.44514i	0.691297	+	0.722571i	$0.257040\pi$
$137$			16.9150i			1.44514i	−0.691297	+	0.722571i	$0.742960\pi$
$138$	11.4018	−	4.93823i	0.970588	−	0.420370i
$139$	17.9369			1.52139			0.760696	−	0.649109i	$-0.224858\pi$
$139$	17.9369			1.52139			0.760696	+	0.649109i	$0.224858\pi$
$140$	4.06000	−	3.56329i	0.343133	−	0.301153i
$141$	−1.66807	−	11.6017i	−0.140477	−	0.977040i
$142$	10.2855	−	4.69723i	0.863140	−	0.394183i
$143$	1.70825	−	5.81775i	0.142851	−	0.486505i
$144$	−1.54223	+	3.37702i	−0.128519	+	0.281418i
$145$	−11.4253	+	7.44529i	−0.948821	+	0.618298i
$146$	−0.477489	+	3.32101i	−0.0395173	+	0.274849i
$147$	0.849544	+	2.89328i	0.0700692	+	0.238634i
$148$	−4.29314	+	3.72003i	−0.352894	+	0.305784i
$149$	−13.3485	+	8.57858i	−1.09355	+	0.702784i	−0.957649	−	0.287937i	$-0.907030\pi$
$149$	−13.3485	+	8.57858i	−1.09355	+	0.702784i	−0.135905	+	0.990722i	$0.543394\pi$
$150$	−12.9532	+	0.164111i	−1.05763	+	0.0133996i
$151$	7.06380	+	8.15206i	0.574844	+	0.663405i	0.966488	−	0.256711i	$-0.0826390\pi$
$151$	7.06380	+	8.15206i	0.574844	+	0.663405i	−0.391644	+	0.920117i	$0.628094\pi$
$152$	−0.197659	−	0.673164i	−0.0160322	−	0.0546008i
$153$	22.7208	+	3.26676i	1.83687	+	0.264102i
$154$	2.36514	−	2.72951i	0.190588	−	0.219950i
$155$	−6.63769	+	7.75907i	−0.533152	+	0.623224i
$156$	10.0821	+	2.96039i	0.807218	+	0.237020i
$157$	2.78637	−	1.27249i	0.222377	−	0.101556i	−0.301112	−	0.953589i	$-0.597358\pi$
$157$	2.78637	−	1.27249i	0.222377	−	0.101556i	0.523488	+	0.852033i	$0.324630\pi$
$158$	2.32887	−	0.334842i	0.185275	−	0.0266386i
$159$	−11.5856	−	7.44563i	−0.918800	−	0.590477i
$160$	−0.616370	+	2.14944i	−0.0487283	+	0.169928i
$161$	−1.42284	−	11.4981i	−0.112135	−	0.906178i
$162$			6.35481i			0.499281i
$163$	1.59230	−	2.47766i	0.124718	−	0.194065i	−0.773280	−	0.634065i	$-0.781385\pi$
$163$	1.59230	−	2.47766i	0.124718	−	0.194065i	0.897998	+	0.440000i	$0.145021\pi$
$164$	0.725390	+	5.04520i	0.0566435	+	0.393964i
$165$	−8.56495	+	1.28688i	−0.666780	+	0.100183i
$166$	2.80336	+	0.823140i	0.217583	+	0.0638880i
$167$	14.0597	+	6.42086i	1.08797	+	0.496861i	0.876931	−	0.480615i	$-0.159587\pi$
$167$	14.0597	+	6.42086i	1.08797	+	0.496861i	0.211043	+	0.977477i	$0.432314\pi$
$168$	4.73023	+	4.09877i	0.364945	+	0.316227i
$169$	0.490833	−	3.41382i	0.0377564	−	0.262602i
$170$	13.8254	−	0.0875767i	1.06036	−	0.00671682i
$171$	1.70567	+	1.96845i	0.130436	+	0.150531i
$172$	2.72832	+	4.24535i	0.208033	+	0.323705i
$173$	−7.00534	−	10.9005i	−0.532606	−	0.828751i	0.465818	−	0.884881i	$-0.345760\pi$
$173$	−7.00534	−	10.9005i	−0.532606	−	0.828751i	−0.998423	+	0.0561299i	$0.982124\pi$
$174$	−10.3473	−	11.9414i	−0.784429	−	0.905279i
$175$	−3.25596	+	11.6319i	−0.246127	+	0.879291i
$176$	−0.212762	+	1.47980i	−0.0160376	+	0.111544i
$177$	28.8443	+	24.9937i	2.16807	+	1.87864i
$178$	−3.29382	−	1.50424i	−0.246882	−	0.112747i
$179$	−10.6510	−	3.12741i	−0.796092	−	0.233754i	−0.141701	−	0.989910i	$-0.545257\pi$
$179$	−10.6510	−	3.12741i	−0.796092	−	0.233754i	−0.654392	+	0.756156i	$0.727075\pi$
$180$	−1.23344	−	8.20927i	−0.0919352	−	0.611883i
$181$	0.716678	+	4.98460i	0.0532702	+	0.370503i	0.998967	+	0.0454512i	$0.0144725\pi$
$181$	0.716678	+	4.98460i	0.0532702	+	0.370503i	−0.945696	+	0.325051i	$0.894618\pi$
$182$	5.29712	−	8.24248i	0.392649	−	0.610973i
$183$			37.3064i			2.75777i
$184$	3.06867	+	3.68555i	0.226225	+	0.271702i
$185$	3.50138	−	12.2102i	0.257426	−	0.897711i
$186$	−9.95285	−	6.39631i	−0.729779	−	0.469000i
$187$	9.14959	−	1.31551i	0.669084	−	0.0961998i
$188$	4.11517	−	1.87934i	0.300130	−	0.137065i
$189$	−4.27894	−	1.25641i	−0.311247	−	0.0913903i
$190$	1.19209	+	1.01981i	0.0864836	+	0.0739845i
$191$	4.85692	−	5.60518i	0.351434	−	0.405577i	−0.552317	−	0.833634i	$-0.686256\pi$
$191$	4.85692	−	5.60518i	0.351434	−	0.405577i	0.903752	+	0.428057i	$0.140802\pi$
$192$	−2.56448	−	0.368717i	−0.185075	−	0.0266098i
$193$	−3.79451	−	12.9229i	−0.273135	−	0.930212i	−0.975795	−	0.218686i	$-0.929823\pi$
$193$	−3.79451	−	12.9229i	−0.273135	−	0.930212i	0.702660	−	0.711525i	$-0.251995\pi$
$194$	−7.76897	−	8.96587i	−0.557779	−	0.643712i
$195$	−22.5020	+	6.76229i	−1.61140	+	0.484258i
$196$	−0.979114	+	0.629238i	−0.0699367	+	0.0449456i
$197$	1.13562	−	0.984024i	0.0809099	−	0.0701088i	−0.613467	−	0.789720i	$-0.710226\pi$
$197$	1.13562	−	0.984024i	0.0809099	−	0.0701088i	0.694377	+	0.719612i	$0.255680\pi$
$198$	−1.56368	−	5.32542i	−0.111126	−	0.378461i
$199$	0.172134	−	1.19722i	0.0122022	−	0.0848684i	−0.982810	−	0.184618i	$-0.940895\pi$
$199$	0.172134	−	1.19722i	0.0122022	−	0.0848684i	0.995013	+	0.0997498i	$0.0318042\pi$
$200$	−1.46933	−	4.77923i	−0.103897	−	0.337943i
$201$	−3.52790	+	7.72503i	−0.248839	+	0.544882i
$202$	−5.39140	+	18.3614i	−0.379338	+	1.29191i
$203$	−13.4018	+	6.12042i	−0.940625	+	0.429569i
$204$	2.27978	+	15.8562i	0.159616	+	1.11016i
$205$	−7.51813	−	8.56614i	−0.525089	−	0.598285i
$206$	−4.97095			−0.346343
$207$	−16.0469	−	7.71356i	−1.11534	−	0.536129i
$208$			4.05573i			0.281214i
$209$	0.882370	+	0.567065i	0.0610348	+	0.0392247i
$210$	−13.8654	−	1.90398i	−0.956805	−	0.131387i
$211$	−2.24700	−	4.92025i	−0.154690	−	0.338724i	0.816381	−	0.577513i	$-0.195977\pi$
$211$	−2.24700	−	4.92025i	−0.154690	−	0.338724i	−0.971071	+	0.238789i	$0.923250\pi$
$212$	1.49757	−	5.10026i	0.102854	−	0.350287i
$213$	−26.6482	−	12.1698i	−1.82590	−	0.833863i
$214$	−11.4775	+	13.2458i	−0.784588	+	0.905463i
$215$	−10.2940	−	4.62252i	−0.702043	−	0.315253i
$216$	1.77122	−	0.520079i	0.120517	−	0.0353869i
$217$	−8.33717	+	7.22420i	−0.565964	+	0.490410i
$218$	−8.08487	−	12.5803i	−0.547577	−	0.852046i
$219$	7.31279	−	4.69964i	0.494152	−	0.317572i
$220$	−1.40795	−	3.03200i	−0.0949237	−	0.204417i
$221$	24.0608	−	7.06489i	1.61851	−	0.475236i
$222$	14.5679	+	2.09455i	0.977732	+	0.140577i
$223$	−4.15604	−	3.60123i	−0.278309	−	0.241156i	0.504510	−	0.863406i	$-0.331673\pi$
$223$	−4.15604	−	3.60123i	−0.278309	−	0.241156i	−0.782819	+	0.622250i	$0.786219\pi$
$224$	−1.00356	+	2.19750i	−0.0670533	+	0.146826i
$225$	12.3326	+	13.8735i	0.822175	+	0.924901i
$226$	7.89460	+	17.2868i	0.525141	+	1.14990i
$227$	2.10956	−	0.303310i	0.140017	−	0.0201314i	−0.0719501	−	0.997408i	$-0.522922\pi$
$227$	2.10956	−	0.303310i	0.140017	−	0.0201314i	0.211967	+	0.977277i	$0.432013\pi$
$228$	−0.982721	+	1.52914i	−0.0650823	+	0.101270i
$229$	−18.6710			−1.23381			−0.616906	−	0.787037i	$-0.711614\pi$
$229$	−18.6710			−1.23381			−0.616906	+	0.787037i	$0.711614\pi$
$230$	−10.2482	−	3.15829i	−0.675745	−	0.208252i
$231$	−9.35728			−0.615664
$232$	3.29720	−	5.13055i	0.216472	−	0.336837i
$233$	−12.0965	+	1.73922i	−0.792469	+	0.113940i	−0.526649	−	0.850083i	$-0.676552\pi$
$233$	−12.0965	+	1.73922i	−0.792469	+	0.113940i	−0.265820	+	0.964023i	$0.585643\pi$
$234$	−6.25487	−	13.6963i	−0.408894	−	0.895352i
$235$	−5.41509	+	8.54457i	−0.353242	+	0.557386i
$236$	−6.11958	+	13.4000i	−0.398351	+	0.872267i
$237$	−4.60691	−	3.99191i	−0.299251	−	0.259302i
$238$	14.7849	+	2.12575i	0.958364	+	0.137792i
$239$	−0.676711	+	0.198700i	−0.0437728	+	0.0128529i	−0.303546	−	0.952817i	$-0.598170\pi$
$239$	−0.676711	+	0.198700i	−0.0437728	+	0.0128529i	0.259773	+	0.965670i	$0.416352\pi$
$240$	5.25444	−	2.43996i	0.339172	−	0.157499i
$241$	7.17710	−	4.61244i	0.462318	−	0.297114i	−0.288671	−	0.957428i	$-0.593213\pi$
$241$	7.17710	−	4.61244i	0.462318	−	0.297114i	0.750989	+	0.660315i	$0.229577\pi$
$242$	4.73868	+	7.37354i	0.304614	+	0.473989i
$243$	16.6283	−	14.4085i	1.06670	−	0.924305i
$244$	−13.8160	+	4.05674i	−0.884479	+	0.259706i
$245$	1.06610	−	2.37412i	0.0681108	−	0.151677i
$246$	8.64794	−	9.98026i	0.551373	−	0.636318i
$247$	2.58829	+	1.18203i	0.164689	+	0.0752110i
$248$	1.28652	−	4.38147i	0.0816939	−	0.278224i
$249$	−3.14457	−	6.88565i	−0.199279	−	0.436360i
$250$	8.58714	+	7.15968i	0.543098	+	0.452818i
$251$	21.2403	+	13.6503i	1.34067	+	0.861599i	0.996993	−	0.0774875i	$-0.0246898\pi$
$251$	21.2403	+	13.6503i	1.34067	+	0.861599i	0.343681	+	0.939086i	$0.388326\pi$
$252$		−	8.96870i		−	0.564975i
$253$	−7.07539	−	1.15983i	−0.444826	−	0.0729181i
$254$	−13.2864			−0.833664
$255$	−23.6282	−	26.9219i	−1.47966	−	1.68592i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	5.11793	−	2.33728i	0.319247	−	0.145795i	−0.249345	−	0.968415i	$-0.580215\pi$
$257$	5.11793	−	2.33728i	0.319247	−	0.145795i	0.568593	+	0.822619i	$0.307488\pi$
$258$	3.68355	−	12.5450i	0.229328	−	0.781018i
$259$	5.70088	−	12.4832i	0.354235	−	0.775667i
$260$	−4.95124	−	7.59802i	−0.307063	−	0.471209i
$261$	−3.22221	+	22.4110i	−0.199450	+	1.38721i
$262$	−3.92098	−	13.3536i	−0.242239	−	0.824990i
$263$	−16.8925	+	14.6374i	−1.04163	+	0.902581i	−0.995348	−	0.0963471i	$-0.969284\pi$
$263$	−16.8925	+	14.6374i	−1.04163	+	0.902581i	−0.0462863	+	0.998928i	$0.514739\pi$
$264$	3.25847	−	2.09409i	0.200545	−	0.128883i
$265$	3.42084	+	11.3831i	0.210141	+	0.699257i
$266$	1.10992	+	1.28091i	0.0680533	+	0.0785377i
$267$	2.64310	+	9.00157i	0.161755	+	0.550887i
$268$	−3.24451	−	0.466490i	−0.198190	−	0.0284954i
$269$	−1.26262	+	1.45714i	−0.0769830	+	0.0888432i	−0.792934	−	0.609307i	$-0.791448\pi$
$269$	−1.26262	+	1.45714i	−0.0769830	+	0.0888432i	0.715951	+	0.698150i	$0.245993\pi$
$270$	−2.68331	+	3.13663i	−0.163301	+	0.190889i
$271$	−1.10040	−	0.323107i	−0.0668445	−	0.0196273i	0.248139	−	0.968724i	$-0.420181\pi$
$271$	−1.10040	−	0.323107i	−0.0668445	−	0.0196273i	−0.314984	+	0.949097i	$0.601999\pi$
$272$	−5.62426	+	2.56851i	−0.341021	+	0.155739i
$273$	−25.1264	+	3.61263i	−1.52072	+	0.218646i
$274$	14.2298	+	9.14492i	0.859652	+	0.552465i
$275$	6.33911	+	3.96133i	0.382263	+	0.238877i
$276$	2.00999	−	12.2616i	0.120987	−	0.738064i
$277$			15.5372i			0.933538i	0.884379	+	0.466769i	$0.154582\pi$
$277$			15.5372i			0.933538i	−0.884379	+	0.466769i	$0.845418\pi$
$278$	9.69744	−	15.0895i	0.581614	−	0.905009i
$279$	2.41266	+	16.7804i	0.144442	+	1.00462i
$280$	−0.802626	−	5.34195i	−0.0479661	−	0.319242i
$281$	−3.71420	−	1.09059i	−0.221570	−	0.0650589i	0.169063	−	0.985605i	$-0.445926\pi$
$281$	−3.71420	−	1.09059i	−0.221570	−	0.0650589i	−0.390633	+	0.920546i	$0.627744\pi$
$282$	−10.6618	−	4.86908i	−0.634901	−	0.289950i
$283$	15.8360	+	13.7220i	0.941354	+	0.815688i	0.983030	−	0.183443i	$-0.0587244\pi$
$283$	15.8360	+	13.7220i	0.941354	+	0.815688i	−0.0416763	+	0.999131i	$0.513270\pi$
$284$	1.60920	−	11.1922i	0.0954884	−	0.664137i
$285$	−0.0257460	−	4.06441i	−0.00152506	−	0.240755i
$286$	−3.97066	−	4.58238i	−0.234790	−	0.270962i
$287$	−6.65722	−	10.3588i	−0.392963	−	0.611462i
$288$	2.00713	+	3.12316i	0.118271	+	0.184034i
$289$	13.9024	+	16.0443i	0.817790	+	0.943780i
$290$	0.0863824	+	13.6368i	0.00507255	+	0.800781i
$291$	−4.37428	+	30.4238i	−0.256425	+	1.78348i
$292$	2.53566	+	2.19716i	0.148388	+	0.128579i
$293$	5.42971	+	2.47966i	0.317207	+	0.144864i	0.567655	−	0.823266i	$-0.307851\pi$
$293$	5.42971	+	2.47966i	0.317207	+	0.144864i	−0.250448	+	0.968130i	$0.580578\pi$
$294$	2.89328	+	0.849544i	0.168740	+	0.0495464i
$295$	−4.89430	−	32.5745i	−0.284957	−	1.89656i
$296$	0.808439	+	5.62282i	0.0469896	+	0.326820i
$297$	−1.49206	+	2.32169i	−0.0865779	+	0.134718i
$298$			15.8674i			0.919175i
$299$	−19.4468	−	0.382764i	−1.12464	−	0.0221358i
$300$	−6.86498	+	10.9857i	−0.396350	+	0.634258i
$301$	−10.2559	−	6.59110i	−0.591143	−	0.379905i
$302$	10.6769	−	1.53511i	0.614388	−	0.0883357i
$303$	45.0996	−	20.5963i	2.59090	−	1.18323i
$304$	−0.673164	−	0.197659i	−0.0386086	−	0.0113365i
$305$	20.9305	−	24.4665i	1.19848	−	1.40095i
$306$	15.0320	−	17.3478i	0.859321	−	0.991709i
$307$	−13.6163	−	1.95773i	−0.777123	−	0.111733i	−0.257671	−	0.966233i	$-0.582955\pi$
$307$	−13.6163	−	1.95773i	−0.777123	−	0.111733i	−0.519452	+	0.854499i	$0.673864\pi$
$308$	−1.01752	−	3.46536i	−0.0579787	−	0.197457i
$309$	8.43395	+	9.73329i	0.479790	+	0.553708i
$310$	2.93874	+	9.77885i	0.166909	+	0.555401i
$311$	23.6829	−	15.2201i	1.34293	−	0.863050i	0.345769	−	0.938320i	$-0.387618\pi$
$311$	23.6829	−	15.2201i	1.34293	−	0.863050i	0.997163	+	0.0752698i	$0.0239818\pi$
$312$	7.94125	−	6.88114i	0.449585	−	0.389568i
$313$	0.813212	+	2.76955i	0.0459655	+	0.156544i	0.979278	−	0.202522i	$-0.0649136\pi$
$313$	0.813212	+	2.76955i	0.0459655	+	0.156544i	−0.933312	+	0.359066i	$0.883095\pi$
$314$	0.435937	−	3.03201i	0.0246013	−	0.171106i
$315$	10.9490	+	16.8020i	0.616906	+	0.946686i
$316$	0.977398	−	2.14020i	0.0549829	−	0.120396i
$317$	4.75833	−	16.2054i	0.267254	−	0.910185i	−0.711073	−	0.703119i	$-0.751790\pi$
$317$	4.75833	−	16.2054i	0.267254	−	0.910185i	0.978327	−	0.207066i	$-0.0663916\pi$
$318$	−12.5273	+	5.72104i	−0.702497	+	0.320820i
$319$	1.29757	+	9.02482i	0.0726501	+	0.505293i
$320$	1.47499	+	1.68060i	0.0824543	+	0.0939483i
$321$	45.4090			2.53448
$322$	−10.4421	−	5.01938i	−0.581914	−	0.279719i
$323$			4.33789i			0.241367i
$324$	5.34601	+	3.43567i	0.297000	+	0.190871i
$325$	18.5513	+	8.18969i	1.02904	+	0.454282i
$326$	−1.22348	−	2.67905i	−0.0677623	−	0.148379i
$327$	−10.9155	+	37.1748i	−0.603629	+	2.05577i
$328$	4.63647	+	2.11740i	0.256006	+	0.116914i
$329$	−7.15704	+	8.25967i	−0.394581	+	0.455370i
$330$	−3.54797	+	7.90103i	−0.195309	+	0.434937i
$331$	−22.3968	+	6.57628i	−1.23104	+	0.361465i	−0.831641	−	0.555313i	$-0.812598\pi$
$331$	−22.3968	+	6.57628i	−1.23104	+	0.361465i	−0.399396	+	0.916778i	$0.630780\pi$
$332$	2.20808	−	1.91331i	0.121184	−	0.105007i
$333$	−11.4018	−	17.7415i	−0.624815	−	0.972231i
$334$	13.0028	−	8.35642i	0.711484	−	0.457243i
$335$	6.64777	−	3.08698i	0.363207	−	0.168660i
$336$	6.00546	−	1.76336i	0.327625	−	0.0961993i
$337$	−10.5303	−	1.51402i	−0.573620	−	0.0824741i	−0.150601	−	0.988595i	$-0.548121\pi$
$337$	−10.5303	−	1.51402i	−0.573620	−	0.0824741i	−0.423020	+	0.906121i	$0.639030\pi$
$338$	−2.60652	−	2.25857i	−0.141776	−	0.122850i
$339$	20.4537	−	44.7874i	1.11089	−	2.43252i
$340$	7.40087	−	11.6780i	0.401369	−	0.633327i
$341$	2.83599	+	6.20996i	0.153578	+	0.336288i
$342$	2.57812	−	0.370678i	0.139409	−	0.0200440i
$343$	10.6627	−	16.5915i	0.575732	−	0.895857i
$344$	5.04646			0.272087
$345$	11.2035	+	25.4248i	0.603176	+	1.36882i
$346$	−12.9575			−0.696598
$347$	7.02594	−	10.9326i	0.377172	−	0.586892i	−0.599828	−	0.800129i	$-0.704764\pi$
$347$	7.02594	−	10.9326i	0.377172	−	0.586892i	0.977000	+	0.213237i	$0.0684007\pi$
$348$	−15.6400	+	2.24869i	−0.838390	+	0.120542i
$349$	2.69252	+	5.89579i	0.144127	+	0.315594i	0.967904	−	0.251320i	$-0.0808645\pi$
$349$	2.69252	+	5.89579i	0.144127	+	0.315594i	−0.823777	+	0.566914i	$0.808137\pi$
$350$	8.02510	+	9.02779i	0.428960	+	0.482555i
$351$	−3.11016	+	6.81030i	−0.166008	+	0.363507i
$352$	1.12985	+	0.979025i	0.0602215	+	0.0521822i
$353$	17.7999	+	2.55923i	0.947391	+	0.136214i	0.598655	−	0.801007i	$-0.295702\pi$
$353$	17.7999	+	2.55923i	0.947391	+	0.136214i	0.348736	+	0.937221i	$0.386611\pi$
$354$	36.6205	−	10.7527i	1.94636	−	0.571502i
$355$	10.6488	+	22.9321i	0.565180	+	1.21711i
$356$	−3.04622	+	1.95768i	−0.161449	+	0.103757i
$357$	−20.9225	−	32.5560i	−1.10734	−	1.72305i
$358$	−8.38931	+	7.26938i	−0.443389	+	0.384198i
$359$	−20.4195	+	5.99571i	−1.07770	+	0.316441i	−0.771959	−	0.635673i	$-0.780723\pi$
$359$	−20.4195	+	5.99571i	−1.07770	+	0.316441i	−0.305742	+	0.952114i	$0.598905\pi$
$360$	−7.57293	−	3.40063i	−0.399128	−	0.179229i
$361$	12.1200	−	13.9872i	0.637896	−	0.736171i
$362$	4.58078	+	2.09197i	0.240760	+	0.109952i
$363$	6.39777	−	21.7888i	0.335796	−	1.14361i
$364$	−4.07018	−	8.91244i	−0.213335	−	0.467139i
$365$	−7.43262	−	1.02064i	−0.389041	−	0.0534226i
$366$	31.3841	+	20.1693i	1.64047	+	1.05427i
$367$			12.7296i			0.664479i	0.943195	+	0.332239i	$0.107804\pi$
$367$			12.7296i			0.664479i	−0.943195	+	0.332239i	$0.892196\pi$
$368$	4.75953	−	0.588970i	0.248108	−	0.0307022i
$369$	−18.9230			−0.985090
$370$	−8.37888	−	9.54687i	−0.435597	−	0.496318i
$371$	1.82752	+	12.7107i	0.0948802	+	0.659906i
$372$	−10.7618	+	4.91477i	−0.557975	+	0.254819i
$373$	6.44841	−	21.9613i	0.333886	−	1.13711i	−0.605955	−	0.795499i	$-0.707209\pi$
$373$	6.44841	−	21.9613i	0.333886	−	1.13711i	0.939841	−	0.341612i	$-0.110973\pi$
$374$	3.83996	−	8.40834i	0.198560	−	0.434785i
$375$	−0.550426	−	28.9614i	−0.0284239	−	1.49556i
$376$	0.643832	−	4.47795i	0.0332031	−	0.230933i
$377$	6.96855	+	23.7327i	0.358899	+	1.22230i
$378$	−3.37033	+	2.92041i	−0.173351	+	0.150209i
$379$	−17.2762	+	11.1027i	−0.887417	+	0.570308i	−0.903034	−	0.429570i	$-0.858665\pi$
$379$	−17.2762	+	11.1027i	−0.887417	+	0.570308i	0.0156170	+	0.999878i	$0.495029\pi$
$380$	1.50241	−	0.451504i	0.0770720	−	0.0231617i
$381$	22.5423	+	26.0152i	1.15488	+	1.33280i
$382$	−2.08953	−	7.11629i	−0.106910	−	0.364101i
$383$	10.6314	+	1.52857i	0.543240	+	0.0781062i	0.408472	−	0.912771i	$-0.366062\pi$
$383$	10.6314	+	1.52857i	0.543240	+	0.0781062i	0.134769	+	0.990877i	$0.456971\pi$
$384$	−1.69665	+	1.95803i	−0.0865816	+	0.0999205i
$385$	6.13675	+	5.24984i	0.312758	+	0.267556i
$386$	−12.9229	−	3.79451i	−0.657759	−	0.193135i
$387$	−17.0420	+	7.78280i	−0.866292	+	0.395622i
$388$	−11.7428	+	1.68836i	−0.596150	+	0.0857134i
$389$	−11.6149	−	7.46445i	−0.588900	−	0.378463i	0.211993	−	0.977271i	$-0.432005\pi$
$389$	−11.6149	−	7.46445i	−0.588900	−	0.378463i	−0.800892	+	0.598808i	$0.795641\pi$
$390$	−6.47668	+	22.5858i	−0.327960	+	1.14368i
$391$	−11.7850	−	27.2102i	−0.595992	−	1.37608i
$392$			1.16388i			0.0587846i
$393$	−19.4943	+	30.3338i	−0.983359	+	1.53014i
$394$	−0.213849	−	1.48735i	−0.0107736	−	0.0749317i
$395$	0.781700	+	5.20267i	0.0393316	+	0.261775i
$396$	−5.32542	−	1.56368i	−0.267612	−	0.0785781i
$397$	−28.8570	−	13.1786i	−1.44829	−	0.661413i	−0.472744	−	0.881200i	$-0.656737\pi$
$397$	−28.8570	−	13.1786i	−1.44829	−	0.661413i	−0.975548	+	0.219787i	$0.929464\pi$
$398$	−0.914100	−	0.792072i	−0.0458197	−	0.0397030i
$399$	0.624934	−	4.34651i	0.0312858	−	0.217598i
$400$	−4.81493	−	1.34777i	−0.240746	−	0.0673887i
$401$	−8.35448	−	9.64158i	−0.417203	−	0.481478i	0.507780	−	0.861487i	$-0.330466\pi$
$401$	−8.35448	−	9.64158i	−0.417203	−	0.481478i	−0.924983	+	0.380009i	$0.875921\pi$
$402$	4.59138	+	7.14433i	0.228997	+	0.356327i
$403$	10.0128	+	15.5802i	0.498774	+	0.776107i
$404$	12.5318	+	14.4625i	0.623480	+	0.719535i
$405$	−14.2095	+	0.0900101i	−0.706076	+	0.00447264i
$406$	−2.09676	+	14.5833i	−0.104061	+	0.723757i
$407$	−6.41830	−	5.56149i	−0.318143	−	0.275673i
$408$	14.5716	+	6.65464i	0.721403	+	0.329454i
$409$	−10.7737	−	3.16344i	−0.532725	−	0.156422i	0.00429653	−	0.999991i	$-0.498632\pi$
$409$	−10.7737	−	3.16344i	−0.532725	−	0.156422i	−0.537021	+	0.843569i	$0.680451\pi$
$410$	−11.2709	+	1.69345i	−0.556631	+	0.0836335i
$411$	−6.23682	−	43.3781i	−0.307640	−	2.13968i
$412$	−2.68750	+	4.18183i	−0.132404	+	0.206024i
$413$		−	35.5879i		−	1.75116i
$414$	−15.1647	+	9.32926i	−0.745303	+	0.458508i
$415$	−1.80085	+	6.28003i	−0.0884004	+	0.308275i
$416$	3.41190	+	2.19269i	0.167282	+	0.107506i
$417$	−45.9989	+	6.61364i	−2.25258	+	0.323872i
$418$	0.954090	−	0.435719i	0.0466661	−	0.0213117i
$419$	11.9348	+	3.50437i	0.583053	+	0.171200i	0.559940	−	0.828533i	$-0.310824\pi$
$419$	11.9348	+	3.50437i	0.583053	+	0.171200i	0.0231127	+	0.999733i	$0.492642\pi$
$420$	−9.09795	+	10.6350i	−0.443934	+	0.518933i
$421$	−5.76463	+	6.65273i	−0.280951	+	0.324234i	−0.878632	−	0.477499i	$-0.841543\pi$
$421$	−5.76463	+	6.65273i	−0.280951	+	0.324234i	0.597681	+	0.801734i	$0.296089\pi$
$422$	−5.35400	−	0.769790i	−0.260629	−	0.0374728i
$423$	4.73181	+	16.1151i	0.230068	+	0.783541i
$424$	−3.48096	−	4.01724i	−0.169050	−	0.195095i
$425$	0.391647	+	30.9126i	0.0189977	+	1.49948i
$426$	−24.6450	+	15.8384i	−1.19405	+	0.767372i
$427$	26.2894	−	22.7799i	1.27223	−	1.10240i
$428$	4.93784	+	16.8167i	0.238679	+	0.812867i
$429$	−2.23566	+	15.5494i	−0.107939	+	0.750731i
$430$	−9.45406	+	6.16072i	−0.455915	+	0.297096i
$431$	11.4845	−	25.1475i	0.553188	−	1.21131i	−0.402089	−	0.915601i	$-0.631716\pi$
$431$	11.4845	−	25.1475i	0.553188	−	1.21131i	0.955277	−	0.295713i	$-0.0955571\pi$
$432$	0.520079	−	1.77122i	0.0250223	−	0.0852181i
$433$	9.46083	−	4.32062i	0.454659	−	0.207636i	−0.174904	−	0.984586i	$-0.555961\pi$
$433$	9.46083	−	4.32062i	0.454659	−	0.207636i	0.629562	+	0.776950i	$0.283234\pi$
$434$	1.56997	+	10.9194i	0.0753609	+	0.524146i
$435$	26.5548	−	23.3060i	1.27320	−	1.11744i
$436$	−14.9542			−0.716178
$437$	1.01129	−	3.20910i	0.0483763	−	0.153512i
$438$		−	8.69273i		−	0.415354i
$439$	8.17338	+	5.25271i	0.390094	+	0.250698i	0.720956	−	0.692981i	$-0.243703\pi$
$439$	8.17338	+	5.25271i	0.390094	+	0.250698i	−0.330862	+	0.943679i	$0.607339\pi$
$440$	−3.31187	−	0.454782i	−0.157887	−	0.0216809i
$441$	−1.79496	−	3.93043i	−0.0854745	−	0.187163i
$442$	7.06489	−	24.0608i	0.336043	−	1.14446i
$443$	8.65078	+	3.95068i	0.411011	+	0.187702i	0.610180	−	0.792263i	$-0.291097\pi$
$443$	8.65078	+	3.95068i	0.411011	+	0.187702i	−0.199169	+	0.979965i	$0.563824\pi$
$444$	9.63804	−	11.1229i	0.457401	−	0.527869i
$445$	3.31685	−	7.38636i	0.157234	−	0.350147i
$446$	−5.27647	+	1.54931i	−0.249848	+	0.0733620i
$447$	31.0690	−	26.9214i	1.46951	−	1.27334i
$448$	1.30608	+	2.03231i	0.0617067	+	0.0960175i
$449$	13.4491	−	8.64324i	0.634704	−	0.407900i	−0.183344	−	0.983049i	$-0.558692\pi$
$449$	13.4491	−	8.64324i	0.634704	−	0.407900i	0.818049	+	0.575149i	$0.195056\pi$
$450$	18.3387	−	2.87428i	0.864493	−	0.135495i
$451$	−7.31153	+	2.14686i	−0.344286	+	0.101092i
$452$	18.8107	+	2.70457i	0.884781	+	0.127212i
$453$	−21.1208	−	18.3013i	−0.992341	−	0.859868i
$454$	0.885356	−	1.93866i	0.0415518	−	0.0909858i
$455$	18.5054	+	11.7277i	0.867547	+	0.549805i
$456$	0.755099	+	1.65344i	0.0353607	+	0.0774292i
$457$	−0.0670682	+	0.00964295i	−0.00313732	+	0.000451078i	−0.143883	−	0.989595i	$-0.545959\pi$
$457$	−0.0670682	+	0.00964295i	−0.00313732	+	0.000451078i	0.140746	+	0.990046i	$0.455050\pi$
$458$	−10.0943	+	15.7070i	−0.471675	+	0.733940i
$459$	−11.4138			−0.532752
$460$	−8.19751	+	6.91382i	−0.382211	+	0.322358i
$461$	−10.2698			−0.478315			−0.239157	−	0.970981i	$-0.576871\pi$
$461$	−10.2698			−0.478315			−0.239157	+	0.970981i	$0.576871\pi$
$462$	−5.05893	+	7.87184i	−0.235363	+	0.366231i
$463$	31.4603	−	4.52330i	1.46208	−	0.210216i	0.635094	−	0.772435i	$-0.280961\pi$
$463$	31.4603	−	4.52330i	1.46208	−	0.210216i	0.826988	+	0.562219i	$0.190052\pi$
$464$	−2.53349	−	5.54757i	−0.117614	−	0.257539i
$465$	14.1613	−	22.3454i	0.656716	−	1.03624i
$466$	−5.07675	+	11.1165i	−0.235176	+	0.514963i
$467$	−3.00482	−	2.60369i	−0.139046	−	0.120484i	0.582561	−	0.812787i	$-0.302051\pi$
$467$	−3.00482	−	2.60369i	−0.139046	−	0.120484i	−0.721607	+	0.692303i	$0.756596\pi$
$468$	−14.9037	−	2.14282i	−0.688922	−	0.0990520i
$469$	7.59795	−	2.23096i	0.350841	−	0.103016i
$470$	4.26053	+	9.17501i	0.196524	+	0.423211i
$471$	−6.67640	+	4.29066i	−0.307633	+	0.197703i
$472$	7.96432	+	12.3927i	0.366587	+	0.570421i
$473$	−5.70176	+	4.94061i	−0.262167	+	0.227169i
$474$	−5.84889	+	1.71739i	−0.268648	+	0.0788823i
$475$	−2.26343	+	2.67999i	−0.103853	+	0.122967i
$476$	9.78163	−	11.2886i	0.448340	−	0.517412i
$477$	17.9508	+	8.19785i	0.821910	+	0.375354i
$478$	−0.198700	+	0.676711i	−0.00908834	+	0.0309521i
$479$	−1.46663	−	3.21147i	−0.0670120	−	0.146736i	0.873162	−	0.487429i	$-0.162065\pi$
$479$	−1.46663	−	3.21147i	−0.0670120	−	0.146736i	−0.940174	+	0.340694i	$0.889338\pi$
$480$	0.788135	−	5.73946i	0.0359733	−	0.261969i
$481$	−19.3817	−	12.4559i	−0.883732	−	0.567940i
$482$		−	8.53144i		−	0.388596i
$483$	7.88838	+	28.9620i	0.358934	+	1.31782i
$484$	8.76494			0.398406
$485$	19.9378	−	17.4986i	0.905331	−	0.794570i
$486$	−3.13126	−	21.7784i	−0.142037	−	0.987889i
$487$	3.53050	−	1.61232i	0.159982	−	0.0730614i	−0.333815	−	0.942639i	$-0.608336\pi$
$487$	3.53050	−	1.61232i	0.159982	−	0.0730614i	0.493797	+	0.869577i	$0.335609\pi$
$488$	−4.05674	+	13.8160i	−0.183640	+	0.625421i
$489$	−3.16986	+	6.94102i	−0.143346	+	0.313884i
$490$	−1.42086	−	2.18041i	−0.0641879	−	0.0985009i
$491$	−3.74182	+	26.0250i	−0.168866	+	1.17449i	0.712367	+	0.701807i	$0.247623\pi$
$491$	−3.74182	+	26.0250i	−0.168866	+	1.17449i	−0.881233	+	0.472682i	$0.843286\pi$
$492$	−3.72050	−	12.6708i	−0.167733	−	0.571246i
$493$	−28.4980	+	24.6937i	−1.28349	+	1.11215i
$494$	2.39373	−	1.53836i	0.107699	−	0.0692139i
$495$	11.8856	−	3.57186i	0.534219	−	0.160543i
$496$	−2.99039	−	3.45109i	−0.134272	−	0.154958i
$497$	7.69589	+	26.2098i	0.345208	+	1.17567i
$498$	−7.49266	−	1.07728i	−0.335754	−	0.0482741i
$499$	11.6560	−	13.4517i	0.521793	−	0.602181i	−0.432286	−	0.901737i	$-0.642293\pi$
$499$	11.6560	−	13.4517i	0.521793	−	0.602181i	0.954079	+	0.299555i	$0.0968383\pi$
$500$	10.6657	−	3.35314i	0.476983	−	0.149957i
$501$	−38.4234	−	11.2821i	−1.71663	−	0.504048i
$502$	22.9667	−	10.4885i	1.02505	−	0.468127i
$503$	−12.5167	+	1.79963i	−0.558094	+	0.0802417i	−0.415589	−	0.909552i	$-0.636425\pi$
$503$	−12.5167	+	1.79963i	−0.558094	+	0.0802417i	−0.142504	+	0.989794i	$0.545516\pi$
$504$	−7.54495	−	4.84885i	−0.336079	−	0.215985i
$505$	−41.1329	−	11.7952i	−1.83039	−	0.524880i
$506$	−4.80096	+	5.32515i	−0.213429	+	0.236732i
$507$			8.93565i			0.396846i
$508$	−7.18318	+	11.1772i	−0.318702	+	0.495910i
$509$	0.724478	+	5.03886i	0.0321119	+	0.223343i	0.999558	−	0.0297345i	$-0.00946618\pi$
$509$	0.724478	+	5.03886i	0.0321119	+	0.223343i	−0.967446	+	0.253078i	$0.918557\pi$
$510$	−35.4225	+	5.32222i	−1.56854	+	0.235672i
$511$	−7.77710	−	2.28356i	−0.344039	−	0.101019i
$512$	−0.909632	−	0.415415i	−0.0402004	−	0.0183589i
$513$	−0.978788	−	0.848125i	−0.0432146	−	0.0374456i
$514$	0.800716	−	5.56910i	0.0353181	−	0.245643i
$515$	−0.0704090	−	11.1152i	−0.00310259	−	0.489793i
$516$	−8.56205	−	9.88114i	−0.376923	−	0.434993i
$517$	3.65659	+	5.68976i	0.160817	+	0.250235i
$518$	−7.41939	−	11.5448i	−0.325989	−	0.507249i
$519$	21.9842	+	25.3712i	0.965001	+	1.11367i
$520$	−9.06870	+	0.0574457i	−0.397689	+	0.00251916i
$521$	−0.479945	+	3.33809i	−0.0210268	+	0.146244i	−0.997630	−	0.0688037i	$-0.978082\pi$
$521$	−0.479945	+	3.33809i	−0.0210268	+	0.146244i	0.976603	+	0.215048i	$0.0689909\pi$
$522$	17.1113	+	14.8270i	0.748939	+	0.648960i
$523$	−11.6173	−	5.30545i	−0.507990	−	0.231991i	0.144897	−	0.989447i	$-0.453715\pi$
$523$	−11.6173	−	5.30545i	−0.507990	−	0.231991i	−0.652887	+	0.757456i	$0.726442\pi$
$524$	−13.3536	−	3.92098i	−0.583356	−	0.171289i
$525$	4.06096	−	31.0304i	0.177235	−	1.35428i
$526$	3.18101	+	22.1244i	0.138699	+	0.964671i
$527$	−15.2647	+	23.7523i	−0.664939	+	1.03467i
$528$		−	3.87335i		−	0.168566i
$529$	2.37487	+	22.8771i	0.103255	+	0.994655i
$530$	11.4255	+	3.27636i	0.496292	+	0.142316i
$531$	−46.0081	−	29.5676i	−1.99658	−	1.28312i
$532$	1.67764	−	0.241208i	0.0727348	−	0.0104577i
$533$	−18.8043	+	8.58761i	−0.814502	+	0.371971i
$534$	9.00157	+	2.64310i	0.389536	+	0.114378i
$535$	−29.7804	−	25.4764i	−1.28752	−	1.10144i
$536$	−2.14655	+	2.47725i	−0.0927169	+	0.107001i
$537$	28.4674	+	4.09299i	1.22846	+	0.176626i
$538$	0.543199	+	1.84997i	0.0234190	+	0.0797577i
$539$	−1.13946	−	1.31501i	−0.0490801	−	0.0566415i
$540$	1.18800	+	3.95313i	0.0511232	+	0.170116i
$541$	11.6836	−	7.50856i	0.502315	−	0.322818i	−0.264826	−	0.964296i	$-0.585315\pi$
$541$	11.6836	−	7.50856i	0.502315	−	0.322818i	0.767142	+	0.641478i	$0.221678\pi$
$542$	−0.866736	+	0.751031i	−0.0372295	+	0.0322595i
$543$	−3.67581	−	12.5187i	−0.157744	−	0.537227i
$544$	−0.879934	+	6.12007i	−0.0377269	+	0.262396i
$545$	28.0153	−	18.2561i	1.20005	−	0.782008i
$546$	−10.5452	+	23.0908i	−0.451294	+	0.988195i
$547$	−5.65506	+	19.2594i	−0.241793	+	0.823471i	0.745764	+	0.666210i	$0.232085\pi$
$547$	−5.65506	+	19.2594i	−0.241793	+	0.823471i	−0.987557	+	0.157261i	$0.949734\pi$
$548$	15.3864	−	7.02673i	0.657274	−	0.300167i
$549$	−7.60778	−	52.9133i	−0.324692	−	2.25828i
$550$	6.75967	−	3.19114i	0.288233	−	0.136071i
$551$	−4.27874			−0.182280
$552$	−9.22846	−	8.32005i	−0.392789	−	0.354125i
$553$			5.68397i			0.241707i
$554$	13.0707	+	8.40003i	0.555321	+	0.356883i
$555$	−4.47711	+	32.6038i	−0.190043	+	1.38395i
$556$	−7.45127	−	16.3160i	−0.316004	−	0.691953i
$557$	10.4569	−	35.6128i	0.443071	−	1.50896i	−0.371242	−	0.928536i	$-0.621068\pi$
$557$	10.4569	−	35.6128i	0.443071	−	1.50896i	0.814313	−	0.580425i	$-0.197114\pi$
$558$	15.4210	+	7.04252i	0.652821	+	0.298133i
$559$	−13.4031	+	15.4680i	−0.566889	+	0.654225i
$560$	−4.92787	−	2.21286i	−0.208240	−	0.0935106i
$561$	−22.9789	+	6.74721i	−0.970169	+	0.284867i
$562$	−2.92551	+	2.53496i	−0.123405	+	0.106931i
$563$	10.5256	+	16.3781i	0.443601	+	0.690257i	0.988999	−	0.147920i	$-0.0472579\pi$
$563$	10.5256	+	16.3781i	0.443601	+	0.690257i	−0.545398	+	0.838177i	$0.683622\pi$
$564$	−9.86034	+	6.33685i	−0.415195	+	0.266830i
$565$	−38.5418	+	17.8974i	−1.62147	+	0.752948i
$566$	20.1053	−	5.90344i	0.845088	−	0.248140i
$567$	−15.1957	−	2.18482i	−0.638161	−	0.0917537i
$568$	−8.54550	−	7.40472i	−0.358561	−	0.310695i
$569$	−1.96027	+	4.29239i	−0.0821787	+	0.179946i	−0.946261	−	0.323405i	$-0.895172\pi$
$569$	−1.96027	+	4.29239i	−0.0821787	+	0.179946i	0.864082	+	0.503351i	$0.167900\pi$
$570$	−3.43312	−	2.17573i	−0.143798	−	0.0911312i
$571$	15.2898	+	33.4800i	0.639858	+	1.40109i	0.900157	+	0.435566i	$0.143452\pi$
$571$	15.2898	+	33.4800i	0.639858	+	1.40109i	−0.260299	+	0.965528i	$0.583821\pi$
$572$	−6.00165	+	0.862906i	−0.250941	+	0.0360799i
$573$	−10.3887	+	16.1652i	−0.433996	+	0.675311i
$574$	−12.3136			−0.513958
$575$	6.91686	−	22.9599i	0.288453	−	0.957494i
$576$	3.71251			0.154688
$577$	−23.0160	+	35.8136i	−0.958168	+	1.49094i	−0.0892342	+	0.996011i	$0.528442\pi$
$577$	−23.0160	+	35.8136i	−0.958168	+	1.49094i	−0.868934	+	0.494928i	$0.835194\pi$
$578$	21.0135	−	3.02129i	0.874047	−	0.125669i
$579$	14.4958	+	31.7414i	0.602426	+	1.31913i
$580$	11.5187	+	7.29995i	0.478289	+	0.303114i
$581$	−2.93212	+	6.42044i	−0.121645	+	0.266365i
$582$	23.2292	+	20.1282i	0.962882	+	0.834342i
$583$	7.86596	+	1.13095i	0.325775	+	0.0468394i
$584$	3.21925	−	0.945259i	0.133214	−	0.0391151i
$585$	30.5365	−	14.1800i	1.26253	−	0.586272i
$586$	5.02155	−	3.22715i	0.207438	−	0.133312i
$587$	16.0681	+	25.0024i	0.663201	+	1.03196i	0.996034	+	0.0889750i	$0.0283591\pi$
$587$	16.0681	+	25.0024i	0.663201	+	1.03196i	−0.332833	+	0.942986i	$0.608005\pi$
$588$	2.27891	−	1.97468i	0.0939806	−	0.0814346i
$589$	−3.07397	+	0.902598i	−0.126661	+	0.0371909i
$590$	−30.0494	−	13.4937i	−1.23712	−	0.555528i
$591$	−2.54946	+	2.94223i	−0.104871	+	0.121027i
$592$	5.16729	+	2.35982i	0.212374	+	0.0969881i
$593$	12.1010	−	41.2121i	0.496927	−	1.69238i	−0.203854	−	0.979001i	$-0.565347\pi$
$593$	12.1010	−	41.2121i	0.496927	−	1.69238i	0.700781	−	0.713377i	$-0.252835\pi$
$594$	1.14646	+	2.51040i	0.0470398	+	0.103003i
$595$	−4.54381	+	33.0895i	−0.186278	+	1.35654i
$596$	13.3485	+	8.57858i	0.546777	+	0.351392i
$597$			3.13371i			0.128254i
$598$	−10.8357	+	16.1528i	−0.443107	+	0.660536i
$599$	−41.0730			−1.67820			−0.839099	−	0.543979i	$-0.816917\pi$
$599$	−41.0730			−1.67820			−0.839099	+	0.543979i	$0.816917\pi$
$600$	5.53024	+	11.7145i	0.225771	+	0.478242i
$601$	4.05076	+	28.1736i	0.165234	+	1.14923i	0.888574	+	0.458734i	$0.151697\pi$
$601$	4.05076	+	28.1736i	0.165234	+	1.14923i	−0.723340	+	0.690492i	$0.757394\pi$
$602$	−11.0896	+	5.06444i	−0.451977	+	0.206411i
$603$	3.42844	−	11.6762i	0.139617	−	0.475492i
$604$	4.48097	−	9.81195i	0.182328	−	0.399243i
$605$	−16.4203	+	10.7002i	−0.667579	+	0.435027i
$606$	7.05598	−	49.0754i	0.286629	−	1.99355i
$607$	2.04027	+	6.94851i	0.0828119	+	0.282031i	0.990480	−	0.137658i	$-0.0439573\pi$
$607$	2.04027	+	6.94851i	0.0828119	+	0.282031i	−0.907668	+	0.419689i	$0.862139\pi$
$608$	−0.530221	+	0.459439i	−0.0215033	+	0.0186327i
$609$	32.1121	−	20.6372i	1.30125	−	0.836260i
$610$	−9.26667	−	30.8354i	−0.375196	−	1.24849i
$611$	12.0155	+	13.8666i	0.486093	+	0.560982i
$612$	−6.46702	−	22.0247i	−0.261414	−	0.890294i
$613$	26.7135	+	3.84083i	1.07895	+	0.155130i	0.658795	−	0.752323i	$-0.271067\pi$
$613$	26.7135	+	3.84083i	1.07895	+	0.155130i	0.420155	+	0.907452i	$0.361976\pi$
$614$	−9.00847	+	10.3963i	−0.363552	+	0.419562i
$615$	22.4386	+	19.1956i	0.904811	+	0.774043i
$616$	−3.46536	−	1.01752i	−0.139623	−	0.0409972i
$617$	14.4775	−	6.61165i	0.582842	−	0.266175i	−0.102098	−	0.994774i	$-0.532556\pi$
$617$	14.4775	−	6.61165i	0.582842	−	0.266175i	0.684940	+	0.728599i	$0.259828\pi$
$618$	12.7479	−	1.83287i	0.512796	−	0.0737289i
$619$	−11.6323	−	7.47565i	−0.467543	−	0.300472i	0.285576	−	0.958356i	$-0.407815\pi$
$619$	−11.6323	−	7.47565i	−0.467543	−	0.300472i	−0.753119	+	0.657884i	$0.771452\pi$
$620$	9.81530	+	2.81462i	0.394192	+	0.113038i
$621$	8.44377	+	2.66089i	0.338837	+	0.106778i
$622$		−	28.1519i		−	1.12879i
$623$	4.72939	−	7.35907i	0.189479	−	0.294835i
$624$	−1.49541	−	10.4008i	−0.0598645	−	0.416366i
$625$	−15.8876	+	19.3024i	−0.635504	+	0.772098i
$626$	2.76955	+	0.813212i	0.110693	+	0.0325025i
$627$	−2.47191	−	1.12888i	−0.0987184	−	0.0450832i
$628$	−2.31500	−	2.00596i	−0.0923786	−	0.0800465i
$629$	4.99859	−	34.7659i	0.199307	−	1.38621i
$630$	20.0542	−	0.127033i	0.798980	−	0.00506114i
$631$	−23.8670	−	27.5440i	−0.950131	−	1.09651i	−0.995233	−	0.0975273i	$-0.968907\pi$
$631$	−23.8670	−	27.5440i	−0.950131	−	1.09651i	0.0451017	−	0.998982i	$-0.485639\pi$
$632$	−1.27203	−	1.97932i	−0.0505987	−	0.0787331i
$633$	7.57658	+	11.7894i	0.301142	+	0.468586i
$634$	−11.0603	−	12.7643i	−0.439260	−	0.506933i
$635$	−0.188190	−	29.7087i	−0.00746809	−	1.17895i
$636$	−1.95994	+	13.6317i	−0.0777167	+	0.540531i
$637$	−3.56741	−	3.09118i	−0.141346	−	0.122477i
$638$	8.29368	+	3.78760i	0.328350	+	0.149952i
$639$	40.2781	+	11.8267i	1.59338	+	0.467858i
$640$	2.21125	−	0.332239i	0.0874072	−	0.0131329i
$641$	0.564030	+	3.92292i	0.0222779	+	0.154946i	0.997924	−	0.0644053i	$-0.0205150\pi$
$641$	0.564030	+	3.92292i	0.0222779	+	0.154946i	−0.975646	+	0.219351i	$0.929606\pi$
$642$	24.5500	−	38.2005i	0.968910	−	1.50765i
$643$		−	24.8411i		−	0.979637i	−0.871824	−	0.489818i	$-0.837063\pi$
$643$		−	24.8411i		−	0.979637i	0.871824	−	0.489818i	$-0.162937\pi$
$644$	−9.86797	+	6.07074i	−0.388853	+	0.239221i
$645$	28.1031	+	8.05880i	1.10656	+	0.317315i
$646$	3.64927	+	2.34524i	0.143579	+	0.0922723i
$647$	−25.4353	+	3.65704i	−0.999963	+	0.143773i	−0.622806	−	0.782376i	$-0.714007\pi$
$647$	−25.4353	+	3.65704i	−0.999963	+	0.143773i	−0.377157	+	0.926149i	$0.623098\pi$
$648$	5.78054	−	2.63988i	0.227081	−	0.103704i
$649$	−21.1313	−	6.20471i	−0.829476	−	0.243556i
$650$	16.9192	−	11.1787i	0.663626	−	0.438465i
$651$	18.7168	−	21.6004i	0.733570	−	0.846585i
$652$	−2.91522	−	0.419146i	−0.114169	−	0.0164150i
$653$	12.7330	+	43.3646i	0.498280	+	1.69699i	0.697120	+	0.716955i	$0.254465\pi$
$653$	12.7330	+	43.3646i	0.498280	+	1.69699i	−0.198839	+	0.980032i	$0.563717\pi$
$654$	25.3721	+	29.2809i	0.992126	+	1.14497i
$655$	29.8035	−	8.95654i	1.16452	−	0.349961i
$656$	4.28794	−	2.75569i	0.167416	−	0.107592i
$657$	−9.41367	+	8.15699i	−0.367262	+	0.318234i
$658$	3.07909	+	10.4864i	0.120035	+	0.408803i
$659$	−1.30081	+	9.04735i	−0.0506724	+	0.352435i	0.948673	+	0.316259i	$0.102427\pi$
$659$	−1.30081	+	9.04735i	−0.0506724	+	0.352435i	−0.999345	+	0.0361759i	$0.988482\pi$
$660$	4.72859	+	7.25636i	0.184060	+	0.282453i
$661$	−14.8571	+	32.5326i	−0.577875	+	1.26537i	0.364622	+	0.931156i	$0.381198\pi$
$661$	−14.8571	+	32.5326i	−0.577875	+	1.26537i	−0.942497	+	0.334214i	$0.891529\pi$
$662$	−6.57628	+	22.3968i	−0.255595	+	0.870475i
$663$	−59.0985	+	26.9894i	−2.29520	+	1.04818i
$664$	−0.415802	−	2.89197i	−0.0161363	−	0.112230i
$665$	−2.84843	+	2.49994i	−0.110457	+	0.0969436i
$666$	−21.0894			−0.817198
$667$	26.8391	−	11.6243i	1.03922	−	0.450094i
$668$		−	15.4565i		−	0.598030i
$669$	11.9859	+	7.70287i	0.463402	+	0.297810i
$670$	0.997127	−	7.26141i	0.0385224	−	0.280533i
$671$	−8.94268	−	19.5817i	−0.345228	−	0.755944i
$672$	1.76336	−	6.00546i	0.0680232	−	0.231666i
$673$	−8.30660	−	3.79350i	−0.320196	−	0.146229i	0.248832	−	0.968547i	$-0.419953\pi$
$673$	−8.30660	−	3.79350i	−0.320196	−	0.146229i	−0.569028	+	0.822318i	$0.692680\pi$
$674$	−6.96677	+	8.04008i	−0.268350	+	0.309692i
$675$	−7.05159	−	5.95551i	−0.271416	−	0.229228i
$676$	−3.30922	+	0.971675i	−0.127278	+	0.0373721i
$677$	10.2257	−	8.86062i	0.393006	−	0.340541i	−0.435834	−	0.900027i	$-0.643547\pi$
$677$	10.2257	−	8.86062i	0.393006	−	0.340541i	0.828840	+	0.559485i	$0.189001\pi$
$678$	−26.6195	−	41.4207i	−1.02231	−	1.59075i
$679$	24.1103	−	15.4948i	0.925270	−	0.594635i
$680$	−5.82292	−	12.5396i	−0.223299	−	0.480872i
$681$	−5.29810	+	1.55566i	−0.203024	+	0.0596131i
$682$	6.75740	+	0.971568i	0.258754	+	0.0372033i
$683$	−0.226706	−	0.196442i	−0.00867466	−	0.00751664i	0.650513	−	0.759495i	$-0.274554\pi$
$683$	−0.226706	−	0.196442i	−0.00867466	−	0.00751664i	−0.659187	+	0.751979i	$0.729100\pi$
$684$	1.08200	−	2.36926i	0.0413714	−	0.0905908i
$685$	−20.2467	+	31.9476i	−0.773586	+	1.22066i
$686$	−8.19296	−	17.9401i	−0.312809	−	0.684955i
$687$	47.8813	−	6.88429i	1.82678	−	0.262652i
$688$	2.72832	−	4.24535i	0.104016	−	0.161852i
$689$	21.5585			0.821314
$690$	27.4458	+	4.32070i	1.04484	+	0.164486i
$691$	0.587233			0.0223394			0.0111697	−	0.999938i	$-0.496445\pi$
$691$	0.587233			0.0223394			0.0111697	+	0.999938i	$0.496445\pi$
$692$	−7.00534	+	10.9005i	−0.266303	+	0.414375i
$693$	13.2718	−	1.90820i	0.504156	−	0.0724866i
$694$	−5.39856	−	11.8212i	−0.204927	−	0.448727i
$695$	33.8779	+	21.4700i	1.28506	+	0.814402i
$696$	−6.56389	+	14.3729i	−0.248804	+	0.544804i
$697$	−23.8177	−	20.6381i	−0.902159	−	0.781725i
$698$	6.41553	+	0.922415i	0.242832	+	0.0349139i
$699$	30.3800	−	8.92037i	1.14908	−	0.337399i
$700$	11.9334	−	1.87035i	0.451038	−	0.0706927i
$701$	38.7268	−	24.8882i	1.46269	−	0.940016i	0.464166	−	0.885748i	$-0.346354\pi$
$701$	38.7268	−	24.8882i	1.46269	−	0.940016i	0.998526	−	0.0542674i	$-0.0172823\pi$
$702$	4.04771	+	6.29836i	0.152771	+	0.237716i
$703$	3.01199	−	2.60991i	0.113600	−	0.0984345i
$704$	1.43445	−	0.421194i	0.0540630	−	0.0158743i
$705$	10.7364	−	23.9090i	0.404355	−	0.900465i
$706$	11.7763	−	13.5906i	0.443207	−	0.511488i
$707$	−42.0526	−	19.2048i	−1.58155	−	0.722270i
$708$	10.7527	−	36.6205i	0.404113	−	1.37628i
$709$	20.8063	+	45.5594i	0.781396	+	1.71102i	0.699785	+	0.714354i	$0.253279\pi$
$709$	20.8063	+	45.5594i	0.781396	+	1.71102i	0.0816110	+	0.996664i	$0.473993\pi$
$710$	25.0489	+	3.43968i	0.940068	+	0.129089i
$711$	7.34824	+	4.72243i	0.275581	+	0.177105i
$712$			3.62104i			0.135704i
$713$	16.8299	−	14.0129i	0.630283	−	0.524788i
$714$	−38.6994			−1.44829
$715$	10.1901	−	8.94339i	0.381087	−	0.334464i
$716$	1.57979	+	10.9877i	0.0590394	+	0.410628i
$717$	1.66215	−	0.759078i	0.0620741	−	0.0283483i
$718$	−5.99571	+	20.4195i	−0.223758	+	0.762049i
$719$	12.7313	−	27.8776i	0.474797	−	1.03966i	−0.509065	−	0.860728i	$-0.670009\pi$
$719$	12.7313	−	27.8776i	0.474797	−	1.03966i	0.983862	−	0.178931i	$-0.0572640\pi$
$720$	−6.95503	+	4.53223i	−0.259199	+	0.168906i
$721$	1.70904	−	11.8866i	0.0636479	−	0.442681i
$722$	−5.21424	−	17.7581i	−0.194054	−	0.660888i
$723$	−16.7048	+	14.4748i	−0.621260	+	0.538325i
$724$	4.23644	−	2.72259i	0.157446	−	0.101184i
$725$	−30.4910	+	0.386306i	−1.13241	+	0.0143470i
$726$	−14.8710	−	17.1620i	−0.551915	−	0.636943i
$727$	2.77362	+	9.44608i	0.102868	+	0.350336i	0.994802	−	0.101830i	$-0.0324698\pi$
$727$	2.77362	+	9.44608i	0.102868	+	0.350336i	−0.891934	+	0.452166i	$0.850652\pi$
$728$	−9.69813	−	1.39438i	−0.359437	−	0.0516792i
$729$	−24.8457	+	28.6735i	−0.920211	+	1.06198i
$730$	−4.87699	+	5.70092i	−0.180506	+	0.211001i
$731$	−29.9384	−	8.79070i	−1.10731	−	0.325136i
$732$	33.9351	−	15.4976i	1.25428	−	0.572809i
$733$	29.2600	−	4.20696i	1.08074	−	0.155388i	0.421136	−	0.906997i	$-0.361631\pi$
$733$	29.2600	−	4.20696i	1.08074	−	0.155388i	0.659608	+	0.751610i	$0.270722\pi$
$734$	10.7088	+	6.88213i	0.395269	+	0.254024i
$735$	−1.85862	+	6.48148i	−0.0685562	+	0.239073i
$736$	2.07772	−	4.32239i	0.0765859	−	0.159325i
$737$		−	4.90046i		−	0.180511i
$738$	−10.2305	+	15.9190i	−0.376591	+	0.585986i
$739$	2.37446	+	16.5148i	0.0873460	+	0.607505i	0.985735	+	0.168304i	$0.0538292\pi$
$739$	2.37446	+	16.5148i	0.0873460	+	0.607505i	−0.898389	+	0.439201i	$0.855262\pi$
$740$	−12.5613	+	1.88733i	−0.461763	+	0.0693797i
$741$	−7.07346	−	2.07696i	−0.259850	−	0.0762989i
$742$	11.6810	+	5.33451i	0.428821	+	0.195836i
$743$	2.29186	+	1.98591i	0.0840803	+	0.0728560i	0.695887	−	0.718151i	$-0.255011\pi$
$743$	2.29186	+	1.98591i	0.0840803	+	0.0728560i	−0.611807	+	0.791007i	$0.709557\pi$
$744$	−1.68372	+	11.7106i	−0.0617283	+	0.429330i
$745$	−35.4799	+	0.224748i	−1.29988	+	0.00823411i
$746$	−14.9887	−	17.2979i	−0.548776	−	0.633321i
$747$	5.86425	+	9.12496i	0.214562	+	0.333865i
$748$	−4.99751	−	7.77627i	−0.182727	−	0.284329i
$749$	−27.7275	−	31.9993i	−1.01314	−	1.16923i
$750$	−24.6614	−	15.1946i	−0.900508	−	0.554830i
$751$	5.44047	−	37.8393i	0.198526	−	1.38078i	−0.610040	−	0.792371i	$-0.708847\pi$
$751$	5.44047	−	37.8393i	0.198526	−	1.38078i	0.808566	−	0.588406i	$-0.200244\pi$
$752$	−3.41901	−	2.96259i	−0.124678	−	0.108035i
$753$	−59.5033	−	27.1743i	−2.16842	−	0.990285i
$754$	23.7327	+	6.96855i	0.864294	+	0.253780i
$755$	3.58377	+	23.8521i	0.130427	+	0.868068i
$756$	0.634665	+	4.41419i	0.0230825	+	0.160543i
$757$	−4.34433	+	6.75990i	−0.157897	+	0.245693i	−0.911184	−	0.411999i	$-0.864831\pi$
$757$	−4.34433	+	6.75990i	−0.157897	+	0.245693i	0.753287	+	0.657692i	$0.228467\pi$
$758$			20.5362i			0.745909i
$759$	18.5724	+	0.365552i	0.674134	+	0.0132687i
$760$	0.432435	−	1.50801i	0.0156861	−	0.0547013i
$761$	36.9682	+	23.7580i	1.34010	+	0.861228i	0.996949	−	0.0780539i	$-0.0248706\pi$
$761$	36.9682	+	23.7580i	1.34010	+	0.861228i	0.343147	+	0.939282i	$0.388507\pi$
$762$	34.0727	−	4.89892i	1.23432	−	0.177469i
$763$	32.8619	−	15.0075i	1.18968	−	0.543309i
$764$	−7.11629	−	2.08953i	−0.257458	−	0.0755966i
$765$	39.0031	+	33.3661i	1.41016	+	1.20636i
$766$	7.03369	−	8.11732i	0.254138	−	0.293291i
$767$	−59.1378	−	8.50274i	−2.13534	−	0.307016i
$768$	0.729927	+	2.48590i	0.0263390	+	0.0897023i
$769$	10.6393	+	12.2784i	0.383663	+	0.442771i	0.914428	−	0.404748i	$-0.132641\pi$
$769$	10.6393	+	12.2784i	0.383663	+	0.442771i	−0.530765	+	0.847519i	$0.678095\pi$
$770$	7.73422	−	2.32429i	0.278722	−	0.0837615i
$771$	−12.2630	+	7.88097i	−0.441642	+	0.283826i
$772$	−10.1788	+	8.81998i	−0.366343	+	0.317438i
$773$	10.0254	+	34.1434i	0.360589	+	1.22805i	0.917586	+	0.397538i	$0.130135\pi$
$773$	10.0254	+	34.1434i	0.360589	+	1.22805i	−0.556997	+	0.830515i	$0.688046\pi$
$774$	−2.66627	+	18.5443i	−0.0958371	+	0.666562i
$775$	−21.8241	+	6.70960i	−0.783945	+	0.241016i
$776$	−4.92829	+	10.7915i	−0.176915	+	0.387391i
$777$	−10.0170	+	34.1149i	−0.359359	+	1.22386i
$778$	−12.5590	+	5.73550i	−0.450262	+	0.205628i
$779$	−0.508921	−	3.53963i	−0.0182340	−	0.126820i
$780$	15.4989	+	17.6594i	0.554948	+	0.632307i
$781$	16.9046			0.604894
$782$	−29.2621	−	4.79679i	−1.04641	−	0.171533i
$783$		−	11.2582i		−	0.402335i
$784$	0.979114	+	0.629238i	0.0349684	+	0.0224728i
$785$	6.78581	+	0.931819i	0.242196	+	0.0332581i
$786$	14.9790	+	32.7994i	0.534282	+	1.16991i
$787$	−13.2613	+	45.1638i	−0.472714	+	1.60992i	0.285820	+	0.958283i	$0.407734\pi$
$787$	−13.2613	+	45.1638i	−0.472714	+	1.60992i	−0.758534	+	0.651633i	$0.774084\pi$
$788$	−1.36686	−	0.624222i	−0.0486922	−	0.0222370i
$789$	37.9233	−	43.7659i	1.35011	−	1.55811i
$790$	4.79939	+	2.15517i	0.170754	+	0.0766775i
$791$	−44.0506	+	12.9344i	−1.56626	+	0.459896i
$792$	−4.19460	+	3.63464i	−0.149048	+	0.129151i
$793$	−31.5732	−	49.1288i	−1.12120	−	1.74462i
$794$	−26.6878	+	17.1512i	−0.947114	+	0.608673i
$795$	−12.9698	−	27.9304i	−0.459992	−	0.990588i
$796$	−1.16053	+	0.340763i	−0.0411340	+	0.0120780i
$797$	−33.9932	−	4.88748i	−1.20410	−	0.173124i	−0.489088	−	0.872235i	$-0.662670\pi$
$797$	−33.9932	−	4.88748i	−1.20410	−	0.173124i	−0.715013	+	0.699111i	$0.753579\pi$
$798$	−3.31865	−	2.87563i	−0.117479	−	0.101796i
$799$	−11.6200	+	25.4442i	−0.411085	+	0.900150i
$800$	−3.73696	+	3.32191i	−0.132122	+	0.117447i
$801$	−5.58449	−	12.2283i	−0.197318	−	0.432067i
$802$	−12.6278	+	1.81560i	−0.445903	+	0.0641111i
$803$	−2.71186	+	4.21974i	−0.0956994	+	0.148911i
$804$	8.49248			0.299507
$805$	11.0755	−	23.4198i	0.390361	−	0.825439i
$806$	18.5203			0.652348
$807$	2.70068	−	4.20234i	0.0950685	−	0.147929i
$808$	18.9418	−	2.72342i	0.666370	−	0.0958096i
$809$	4.28637	+	9.38585i	0.150701	+	0.329989i	0.969893	−	0.243530i	$-0.0783053\pi$
$809$	4.28637	+	9.38585i	0.150701	+	0.329989i	−0.819193	+	0.573519i	$0.805578\pi$
$810$	−7.60652	+	12.0025i	−0.267266	+	0.421723i
$811$	−2.70172	+	5.91594i	−0.0948703	+	0.207737i	−0.951117	−	0.308829i	$-0.900063\pi$
$811$	−2.70172	+	5.91594i	−0.0948703	+	0.207737i	0.856247	+	0.516566i	$0.172790\pi$
$812$	11.1347	+	9.64824i	0.390750	+	0.338587i
$813$	2.94109	+	0.422865i	0.103148	+	0.0148305i
$814$	−8.14861	+	2.39265i	−0.285609	+	0.0838623i
$815$	5.97309	−	2.77368i	0.209228	−	0.0971577i
$816$	13.4763	−	8.66066i	0.471763	−	0.303184i
$817$	−1.91414	−	2.97847i	−0.0669674	−	0.104203i
$818$	−8.48595	+	7.35312i	−0.296704	+	0.257096i
$819$	34.9012	−	10.2479i	1.21955	−	0.358091i
$820$	−4.66889	+	10.3972i	−0.163045	+	0.363087i
$821$	−24.1404	+	27.8595i	−0.842504	+	0.972302i	−0.999884	−	0.0152365i	$-0.995150\pi$
$821$	−24.1404	+	27.8595i	−0.842504	+	0.972302i	0.157380	+	0.987538i	$0.449695\pi$
$822$	−39.8638	−	18.2052i	−1.39041	−	0.634979i
$823$	1.55967	−	5.31173i	0.0543665	−	0.185155i	−0.927833	−	0.372996i	$-0.878331\pi$
$823$	1.55967	−	5.31173i	0.0543665	−	0.185155i	0.982200	+	0.187840i	$0.0601488\pi$
$824$	2.06501	+	4.52174i	0.0719379	+	0.157522i
$825$	−17.7171	−	7.82142i	−0.616832	−	0.272307i
$826$	−29.9384	−	19.2403i	−1.04169	−	0.669454i
$827$		−	34.5351i		−	1.20090i	−0.799661	−	0.600452i	$-0.794987\pi$
$827$		−	34.5351i		−	1.20090i	0.799661	−	0.600452i	$-0.205013\pi$
$828$	−0.350372	+	17.8011i	−0.0121763	+	0.618631i
$829$	44.1739			1.53422			0.767112	−	0.641514i	$-0.221693\pi$
$829$	44.1739			1.53422			0.767112	+	0.641514i	$0.221693\pi$
$830$	4.30948	+	4.91021i	0.149584	+	0.170436i
$831$	−5.72881	−	39.8448i	−0.198730	−	1.38220i
$832$	3.68922	−	1.68481i	0.127901	−	0.0584103i
$833$	2.02742	−	6.90475i	0.0702459	−	0.239235i
$834$	−19.3051	+	42.2724i	−0.668482	+	1.46377i
$835$	18.8693	+	28.9563i	0.653000	+	1.00207i
$836$	0.149271	−	1.03820i	0.00516263	−	0.0359069i
$837$	−2.37491	−	8.08820i	−0.0820889	−	0.279569i
$838$	9.40050	−	8.14558i	0.324735	−	0.281384i
$839$	−28.4148	+	18.2611i	−0.980988	+	0.630443i	−0.929730	−	0.368243i	$-0.879960\pi$
$839$	−28.4148	+	18.2611i	−0.980988	+	0.630443i	−0.0512585	+	0.998685i	$0.516323\pi$
$840$	4.02798	+	13.4034i	0.138979	+	0.462460i
$841$	−5.36596	−	6.19265i	−0.185033	−	0.213540i
$842$	2.48004	+	8.44625i	0.0854679	+	0.291077i
$843$	9.92710	+	1.42730i	0.341907	+	0.0491589i
$844$	−3.54218	+	4.08790i	−0.121927	+	0.140711i
$845$	5.01329	−	5.86024i	0.172462	−	0.201598i
$846$	16.1151	+	4.73181i	0.554047	+	0.162683i
$847$	−19.2609	+	8.79616i	−0.661813	+	0.302240i
$848$	−5.26147	+	0.756485i	−0.180680	+	0.0259778i
$849$	−45.6707	−	29.3508i	−1.56741	−	1.00732i
$850$	26.2170	+	16.3831i	0.899237	+	0.561936i
$851$	−11.8028	+	24.5539i	−0.404594	+	0.841699i
$852$			29.2956i			1.00365i
$853$	−2.39038	+	3.71950i	−0.0818450	+	0.127353i	−0.879763	−	0.475413i	$-0.842299\pi$
$853$	−2.39038	+	3.71950i	−0.0818450	+	0.127353i	0.797918	+	0.602767i	$0.205935\pi$
$854$	−4.95055	−	34.4318i	−0.169404	−	1.17823i
$855$	0.865361	+	5.75949i	0.0295947	+	0.196970i
$856$	16.8167	+	4.93784i	0.574784	+	0.168772i
$857$	53.1672	+	24.2807i	1.81616	+	0.829411i	0.932345	+	0.361571i	$0.117759\pi$
$857$	53.1672	+	24.2807i	1.81616	+	0.829411i	0.883813	+	0.467841i	$0.154968\pi$
$858$	11.8723	+	10.2874i	0.405313	+	0.351205i
$859$	5.70704	−	39.6933i	0.194722	−	1.35432i	−0.624582	−	0.780959i	$-0.714731\pi$
$859$	5.70704	−	39.6933i	0.194722	−	1.35432i	0.819304	−	0.573360i	$-0.194360\pi$
$860$	0.0714785	+	11.2840i	0.00243740	+	0.384781i
$861$	20.8918	+	24.1104i	0.711989	+	0.821680i
$862$	−14.9465	−	23.2571i	−0.509078	−	0.792141i
$863$	14.6706	+	22.8279i	0.499392	+	0.777070i	0.995852	−	0.0909901i	$-0.0290032\pi$
$863$	14.6706	+	22.8279i	0.499392	+	0.777070i	−0.496459	+	0.868060i	$0.665367\pi$
$864$	−1.20887	−	1.39511i	−0.0411267	−	0.0474628i
$865$	−0.183531	−	28.9732i	−0.00624023	−	0.985118i
$866$	1.48018	−	10.2949i	0.0502985	−	0.349834i
$867$	−41.5683	−	36.0191i	−1.41173	−	1.22327i
$868$	10.0347	+	4.58271i	0.340601	+	0.155547i
$869$	3.37502	+	0.990994i	0.114490	+	0.0336172i
$870$	−5.24965	−	34.9395i	−0.177980	−	1.18456i
$871$	−1.89196	−	13.1588i	−0.0641065	−	0.445871i
$872$	−8.08487	+	12.5803i	−0.273788	+	0.426023i
$873$		−	44.0435i		−	1.49065i
$874$	−2.15293	−	2.58572i	−0.0728238	−	0.0874632i
$875$	−20.0727	+	18.0722i	−0.678580	+	0.610951i
$876$	−7.31279	−	4.69964i	−0.247076	−	0.158786i
$877$	−10.3992	+	1.49519i	−0.351157	+	0.0504888i	−0.315637	−	0.948880i	$-0.602218\pi$
$877$	−10.3992	+	1.49519i	−0.351157	+	0.0504888i	−0.0355208	+	0.999369i	$0.511309\pi$
$878$	8.83772	−	4.03605i	0.298259	−	0.136210i
$879$	−14.8387	−	4.35703i	−0.500496	−	0.146959i
$880$	−2.17312	+	2.54025i	−0.0732558	+	0.0856318i
$881$	−6.23389	+	7.19429i	−0.210025	+	0.242382i	−0.850982	−	0.525195i	$-0.823992\pi$
$881$	−6.23389	+	7.19429i	−0.210025	+	0.242382i	0.640957	+	0.767577i	$0.278538\pi$
$882$	−4.27692	−	0.614928i	−0.144011	−	0.0207057i
$883$	7.52758	+	25.6366i	0.253323	+	0.862739i	0.983719	+	0.179715i	$0.0575175\pi$
$883$	7.52758	+	25.6366i	0.253323	+	0.862739i	−0.730396	+	0.683024i	$0.760664\pi$
$884$	−16.4217	−	18.9516i	−0.552321	−	0.637412i
$885$	24.5621	+	81.7319i	0.825645	+	2.74739i
$886$	8.00049	−	5.14160i	0.268782	−	0.172735i
$887$	14.6556	−	12.6992i	0.492088	−	0.426396i	−0.373140	−	0.927775i	$-0.621719\pi$
$887$	14.6556	−	12.6992i	0.492088	−	0.426396i	0.865228	+	0.501379i	$0.167174\pi$
$888$	−4.14645	−	14.1215i	−0.139146	−	0.473887i
$889$	4.56794	−	31.7707i	0.153204	−	1.06556i
$890$	−4.42057	−	6.78368i	−0.148178	−	0.227390i
$891$	−3.94666	+	8.64198i	−0.132218	+	0.289517i
$892$	−1.54931	+	5.27647i	−0.0518747	+	0.176669i
$893$	−2.88714	+	1.31851i	−0.0966143	+	0.0441223i
$894$	−5.85058	−	40.6917i	−0.195673	−	1.36093i
$895$	−16.3733	−	18.6557i	−0.547300	−	0.623592i
$896$	2.41581			0.0807065
$897$	50.0121	−	6.18877i	1.66986	−	0.206637i
$898$		−	15.9870i		−	0.533494i
$899$	−23.4284	−	15.0565i	−0.781380	−	0.502162i
$900$	7.49663	−	16.9814i	0.249888	−	0.566047i
$901$	13.6531	+	29.8962i	0.454852	+	0.995986i
$902$	−2.14686	+	7.31153i	−0.0714826	+	0.243447i
$903$	28.7314	+	13.1212i	0.956122	+	0.436646i
$904$	12.4451	−	14.3624i	0.413917	−	0.477685i
$905$	−4.61282	+	10.2724i	−0.153335	+	0.341465i
$906$	−26.8147	+	7.87352i	−0.890860	+	0.261580i
$907$	21.5552	−	18.6777i	0.715728	−	0.620182i	−0.218925	−	0.975742i	$-0.570255\pi$
$907$	21.5552	−	18.6777i	0.715728	−	0.620182i	0.934654	+	0.355559i	$0.115710\pi$
$908$	−1.15224	−	1.79293i	−0.0382386	−	0.0595004i
$909$	−59.7666	+	38.4097i	−1.98233	+	1.27397i
$910$	19.8708	−	9.22725i	0.658710	−	0.305880i
$911$	−33.3300	+	9.78657i	−1.10427	+	0.324244i	−0.782548	−	0.622590i	$-0.786080\pi$
$911$	−33.3300	+	9.78657i	−1.10427	+	0.324244i	−0.321724	+	0.946834i	$0.604262\pi$
$912$	1.79920	+	0.258685i	0.0595773	+	0.00856592i
$913$	3.30110	+	2.86042i	0.109251	+	0.0946662i
$914$	−0.0281476	+	0.0616347i	−0.000931041	+	0.00203870i
$915$	−44.6546	+	70.4613i	−1.47624	+	2.32938i
$916$	7.75619	+	16.9837i	0.256272	+	0.561157i
$917$	33.2795	−	4.78487i	1.09899	−	0.158010i
$918$	−6.17079	+	9.60193i	−0.203666	+	0.316911i
$919$	−13.5686			−0.447586			−0.223793	−	0.974637i	$-0.571844\pi$
$919$	−13.5686			−0.447586			−0.223793	+	0.974637i	$0.571844\pi$
$920$	1.38437	+	10.6341i	0.0456412	+	0.350595i
$921$	35.6406			1.17440
$922$	−5.55230	+	8.63955i	−0.182855	+	0.284528i
$923$	45.3926	−	6.52648i	1.49412	−	0.214822i
$924$	3.88715	+	8.51168i	0.127878	+	0.280014i
$925$	21.2283	−	18.8706i	0.697984	−	0.620461i
$926$	13.2035	−	28.9115i	0.433892	−	0.950092i
$927$	−13.9471	−	12.0853i	−0.458084	−	0.396932i
$928$	−6.03662	−	0.867934i	−0.198162	−	0.0284913i
$929$	−17.5627	+	5.15687i	−0.576213	+	0.169192i	−0.556839	−	0.830621i	$-0.687986\pi$
$929$	−17.5627	+	5.15687i	−0.576213	+	0.169192i	−0.0193749	+	0.999812i	$0.506168\pi$
$930$	−11.1420	−	23.9941i	−0.365359	−	0.786798i
$931$	0.686930	−	0.441463i	0.0225132	−	0.0144684i
$932$	6.60712	+	10.2809i	0.216423	+	0.336761i
$933$	−55.1223	+	47.7638i	−1.80462	+	1.56372i
$934$	−3.81489	+	1.12015i	−0.124827	+	0.0366525i
$935$	18.8556	+	8.46715i	0.616645	+	0.276905i
$936$	−9.86019	+	11.3793i	−0.322290	+	0.371943i
$937$	15.8248	+	7.22695i	0.516974	+	0.236094i	0.656776	−	0.754085i	$-0.271920\pi$
$937$	15.8248	+	7.22695i	0.516974	+	0.236094i	−0.139803	+	0.990179i	$0.544647\pi$
$938$	2.23096	−	7.59795i	0.0728434	−	0.248082i
$939$	−3.10664	−	6.80260i	−0.101382	−	0.221995i
$940$	10.0219	+	1.37620i	0.326879	+	0.0448866i
$941$	−0.870322	−	0.559322i	−0.0283717	−	0.0182334i	0.526378	−	0.850251i	$-0.323550\pi$
$941$	−0.870322	−	0.559322i	−0.0283717	−	0.0182334i	−0.554750	+	0.832017i	$0.687186\pi$
$942$			7.93626i			0.258577i
$943$	12.8086	+	20.8203i	0.417105	+	0.678003i
$944$	14.7313			0.479461
$945$	−6.57783	−	7.49477i	−0.213977	−	0.243805i
$946$	1.07370	+	7.46772i	0.0349089	+	0.242797i
$947$	−38.1652	+	17.4295i	−1.24020	+	0.566381i	−0.924030	−	0.382321i	$-0.875125\pi$
$947$	−38.1652	+	17.4295i	−1.24020	+	0.566381i	−0.316172	+	0.948702i	$0.602398\pi$
$948$	−1.71739	+	5.84889i	−0.0557782	+	0.189963i
$949$	−5.65281	+	12.3779i	−0.183498	+	0.401805i
$950$	1.03085	+	3.35303i	0.0334453	+	0.108787i
$951$	−6.22745	+	43.3128i	−0.201939	+	1.40452i
$952$	−4.20823	−	14.3319i	−0.136389	−	0.464500i
$953$	17.6476	−	15.2917i	0.571662	−	0.495348i	−0.320387	−	0.947287i	$-0.603813\pi$
$953$	17.6476	−	15.2917i	0.571662	−	0.495348i	0.892049	+	0.451939i	$0.149267\pi$
$954$	16.6014	−	10.6691i	0.537490	−	0.345424i
$955$	15.8826	−	4.77304i	0.513949	−	0.154452i
$956$	0.461860	+	0.533015i	0.0149376	+	0.0172389i
$957$	−6.65520	−	22.6655i	−0.215132	−	0.732672i
$958$	−3.49458	−	0.502445i	−0.112905	−	0.0162332i
$959$	−26.7598	+	30.8824i	−0.864118	+	0.997245i
$960$	−4.40224	−	3.76601i	−0.142082	−	0.121547i
$961$	9.73652	+	2.85890i	0.314081	+	0.0922226i
$962$	−20.9571	+	9.57080i	−0.675685	+	0.308575i
$963$	−64.4056	+	9.26013i	−2.07544	+	0.298404i
$964$	−7.17710	−	4.61244i	−0.231159	−	0.148557i
$965$	8.30157	−	28.9497i	0.267237	−	0.931923i
$966$	28.6292	+	9.02193i	0.921129	+	0.290276i
$967$		−	16.0285i		−	0.515442i	−0.966219	−	0.257721i	$-0.917028\pi$
$967$		−	16.0285i		−	0.515442i	0.966219	−	0.257721i	$-0.0829716\pi$
$968$	4.73868	−	7.37354i	0.152307	−	0.236994i
$969$	−1.59945	−	11.1244i	−0.0513818	−	0.357368i
$970$	−3.94153	−	26.2332i	−0.126555	−	0.842298i
$971$	21.5331	+	6.32268i	0.691029	+	0.202904i	0.608347	−	0.793671i	$-0.291833\pi$
$971$	21.5331	+	6.32268i	0.691029	+	0.202904i	0.0826826	+	0.996576i	$0.473651\pi$
$972$	−20.0141	−	9.14011i	−0.641951	−	0.293169i
$973$	32.7483	+	28.3765i	1.04986	+	0.909710i
$974$	0.552358	−	3.84173i	0.0176987	−	0.123097i
$975$	−50.5942	−	14.1621i	−1.62031	−	0.453550i
$976$	9.42952	+	10.8822i	0.301832	+	0.348332i
$977$	8.22441	+	12.7974i	0.263122	+	0.409426i	0.947527	−	0.319676i	$-0.103574\pi$
$977$	8.22441	+	12.7974i	0.263122	+	0.409426i	−0.684405	+	0.729102i	$0.739938\pi$
$978$	4.12540	+	6.41925i	0.131916	+	0.205265i
$979$	−3.54509	−	4.09126i	−0.113302	−	0.130757i
$980$	−2.60245	+	0.0164852i	−0.0831323	+	0.000526601i
$981$	7.90100	−	54.9526i	0.252259	−	1.75450i
$982$	19.8706	+	17.2180i	0.634096	+	0.549448i
$983$	−40.3851	−	18.4433i	−1.28809	−	0.588249i	−0.350682	−	0.936494i	$-0.614050\pi$
$983$	−40.3851	−	18.4433i	−1.28809	−	0.588249i	−0.937403	+	0.348245i	$0.886778\pi$
$984$	−12.6708	−	3.72050i	−0.403932	−	0.118605i
$985$	3.32272	−	0.499238i	0.105871	−	0.0159070i
$986$	5.36645	+	37.3245i	0.170902	+	1.18865i
$987$	15.3086	−	23.8207i	0.487279	−	0.758220i
$988$		−	2.84543i		−	0.0905252i
$989$	20.0986	+	13.4827i	0.639097	+	0.428725i
$990$	3.42101	−	11.9299i	0.108727	−	0.379157i
$991$	30.3739	+	19.5201i	0.964860	+	0.620078i	0.925339	−	0.379141i	$-0.123780\pi$
$991$	30.3739	+	19.5201i	0.964860	+	0.620078i	0.0395211	+	0.999219i	$0.487417\pi$
$992$	−4.51997	+	0.649873i	−0.143509	+	0.0206335i
$993$	55.0113	−	25.1228i	1.74573	−	0.797248i
$994$	26.2098	+	7.69589i	0.831325	+	0.244099i
$995$	1.75814	−	2.05517i	0.0557369	−	0.0651532i
$996$	−4.95710	+	5.72080i	−0.157072	+	0.181271i
$997$	27.8175	+	3.99955i	0.880988	+	0.126667i	0.567939	−	0.823070i	$-0.307741\pi$
$997$	27.8175	+	3.99955i	0.880988	+	0.126667i	0.313048	+	0.949737i	$0.398650\pi$
$998$	−5.01461	−	17.0782i	−0.158735	−	0.540600i
$999$	6.86717	+	7.92514i	0.217268	+	0.250740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.j.a.209.7	yes	120
5.4	even	2	inner	230.2.j.a.209.6	✓	120
23.12	even	11	inner	230.2.j.a.219.6	yes	120
115.104	even	22	inner	230.2.j.a.219.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.209.6	✓	120	5.4	even	2	inner
230.2.j.a.209.7	yes	120	1.1	even	1	trivial
230.2.j.a.219.6	yes	120	23.12	even	11	inner
230.2.j.a.219.7	yes	120	115.104	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 - 0.841254i) q^{2} +(-2.56448 + 0.368717i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.88872 + 1.19697i) q^{5} +(-1.07628 + 2.35672i) q^{6} +(1.82575 + 1.58202i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(3.56212 - 1.04593i) q^{9} +(2.02807 - 0.941762i) q^{10} +(1.25768 - 0.808265i) q^{11} +(1.40072 + 2.17956i) q^{12} +(3.06511 - 2.65594i) q^{13} +(2.31795 - 0.680612i) q^{14} +(-5.28493 - 2.37320i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(5.62426 + 2.56851i) q^{17} +(1.04593 - 3.56212i) q^{18} +(0.291448 + 0.638182i) q^{19} +(0.304199 - 2.21528i) q^{20} +(-5.26540 - 3.38387i) q^{21} -1.49501i q^{22} +(-3.56194 - 3.21132i) q^{23} +2.59085 q^{24} +(2.13453 + 4.52148i) q^{25} +(-0.577190 - 4.01445i) q^{26} +(-1.67918 + 0.766856i) q^{27} +(0.680612 - 2.31795i) q^{28} +(-2.53349 + 5.54757i) q^{29} +(-4.85371 + 3.16291i) q^{30} +(-0.649873 + 4.51997i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-2.92729 + 2.53651i) q^{33} +(5.20148 - 3.34279i) q^{34} +(1.55469 + 5.17335i) q^{35} +(-2.43118 - 2.80573i) q^{36} +(-1.60042 - 5.45053i) q^{37} +(0.694442 + 0.0998457i) q^{38} +(-6.88114 + 7.94125i) q^{39} +(-1.69915 - 1.45358i) q^{40} +(-4.89061 - 1.43601i) q^{41} +(-5.69338 + 2.60008i) q^{42} +(-4.99509 + 0.718186i) q^{43} +(-1.25768 - 0.808265i) q^{44} +(7.97981 + 2.28828i) q^{45} +(-4.62726 + 1.26033i) q^{46} +4.52400i q^{47} +(1.40072 - 2.17956i) q^{48} +(-0.165637 - 1.15203i) q^{49} +(4.95772 + 0.648819i) q^{50} +(-15.3704 - 4.51315i) q^{51} +(-3.68922 - 1.68481i) q^{52} +(4.01724 + 3.48096i) q^{53} +(-0.262713 + 1.82721i) q^{54} +(3.34288 - 0.0211755i) q^{55} +(-1.58202 - 1.82575i) q^{56} +(-0.982721 - 1.52914i) q^{57} +(3.29720 + 5.13055i) q^{58} +(-9.64692 - 11.1331i) q^{59} +(0.0366970 + 5.79320i) q^{60} +(2.04923 - 14.2527i) q^{61} +(3.45109 + 2.99039i) q^{62} +(8.15822 + 3.72573i) q^{63} +(0.959493 + 0.281733i) q^{64} +(8.96822 - 1.34747i) q^{65} +(0.551236 + 3.83393i) q^{66} +(1.77215 - 2.75752i) q^{67} -6.18301i q^{68} +(10.3186 + 6.92201i) q^{69} +(5.19263 + 1.48903i) q^{70} +(9.51232 + 6.11320i) q^{71} +(-3.67472 + 0.528345i) q^{72} +(-3.05196 + 1.39378i) q^{73} +(-5.45053 - 1.60042i) q^{74} +(-7.14110 - 10.8082i) q^{75} +(0.459439 - 0.530221i) q^{76} +(3.57490 + 0.513993i) q^{77} +(2.96039 + 10.0821i) q^{78} +(1.54077 + 1.77814i) q^{79} +(-2.14146 + 0.643551i) q^{80} +(-5.34601 + 3.43567i) q^{81} +(-3.85212 + 3.33788i) q^{82} +(0.823140 + 2.80336i) q^{83} +(-0.890748 + 6.19529i) q^{84} +(7.54822 + 11.5833i) q^{85} +(-2.09637 + 4.59042i) q^{86} +(4.45160 - 15.1608i) q^{87} +(-1.35991 + 0.621051i) q^{88} +(-0.515328 - 3.58419i) q^{89} +(6.23923 - 5.47591i) q^{90} +9.79786 q^{91} +(-1.44143 + 4.57409i) q^{92} -11.8310i q^{93} +(3.80583 + 2.44586i) q^{94} +(-0.213421 + 1.55420i) q^{95} +(-1.07628 - 2.35672i) q^{96} +(3.34235 - 11.3830i) q^{97} +(-1.05870 - 0.483491i) q^{98} +(3.63464 - 4.19460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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