LMFDB - Embedded newform 399.2.ck.a.10.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(10,399)] 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("399.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.ck (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [78] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			10.7
Character	$\chi$	$=$	399.10
Dual form			399.2.ck.a.40.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.137026 - 0.163301i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.339405 - 1.92486i) q^{4} +(2.98443 - 0.526235i) q^{5} +(-0.137026 + 0.163301i) q^{6} +(-0.181283 - 2.63953i) q^{7} +(-0.730069 + 0.421505i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.494879 - 0.415253i) q^{10} +1.47301 q^{11} -1.95456 q^{12} +(3.17945 + 2.66787i) q^{13} +(-0.406198 + 0.391288i) q^{14} +(-1.03648 - 2.84771i) q^{15} +(-3.50449 - 1.27553i) q^{16} +(-1.26471 + 3.47476i) q^{17} +(0.184615 + 0.106587i) q^{18} +(-4.31729 + 0.600840i) q^{19} -5.92322i q^{20} +(-2.56795 + 0.636879i) q^{21} +(-0.201841 - 0.240545i) q^{22} +(0.106754 + 0.0895772i) q^{23} +(0.541877 + 0.645784i) q^{24} +(3.93142 - 1.43092i) q^{25} -0.884776i q^{26} +(0.500000 + 0.866025i) q^{27} +(-5.14227 - 0.546926i) q^{28} +(3.71169 + 0.654470i) q^{29} +(-0.323009 + 0.559468i) q^{30} +(0.616770 + 1.06828i) q^{31} +(0.848564 + 2.33141i) q^{32} +(-0.255786 - 1.45063i) q^{33} +(0.740730 - 0.269604i) q^{34} +(-1.93004 - 7.78210i) q^{35} +(0.339405 + 1.92486i) q^{36} +(-4.18463 + 2.41600i) q^{37} +(0.689699 + 0.622688i) q^{38} +(2.07524 - 3.59442i) q^{39} +(-1.95703 + 1.64214i) q^{40} +(6.94865 - 5.83061i) q^{41} +(0.455879 + 0.332081i) q^{42} +(-1.43983 - 0.524056i) q^{43} +(0.499948 - 2.83535i) q^{44} +(-2.62446 + 1.51523i) q^{45} -0.0297075i q^{46} +(-3.68693 - 10.1298i) q^{47} +(-0.647604 + 3.67275i) q^{48} +(-6.93427 + 0.957006i) q^{49} +(-0.772377 - 0.445932i) q^{50} +(3.64158 + 0.642109i) q^{51} +(6.21441 - 5.21451i) q^{52} +(4.21495 + 0.743210i) q^{53} +(0.0729100 - 0.200319i) q^{54} +(4.39610 - 0.775151i) q^{55} +(1.24493 + 1.85063i) q^{56} +(1.34140 + 4.14737i) q^{57} +(-0.401722 - 0.695802i) q^{58} +(5.23397 + 1.90501i) q^{59} +(-5.83323 + 1.02856i) q^{60} +(-5.19105 + 6.18645i) q^{61} +(0.0899374 - 0.247101i) q^{62} +(1.07312 + 2.41835i) q^{63} +(-3.46496 + 6.00148i) q^{64} +(10.8928 + 6.28894i) q^{65} +(-0.201841 + 0.240545i) q^{66} +(-6.08581 + 7.25279i) q^{67} +(6.25918 + 3.61374i) q^{68} +(0.0696787 - 0.120687i) q^{69} +(-1.00636 + 1.38153i) q^{70} +(-2.60170 + 7.14811i) q^{71} +(0.541877 - 0.645784i) q^{72} +(12.6785 - 2.23555i) q^{73} +(0.967938 + 0.352301i) q^{74} +(-2.09186 - 3.62322i) q^{75} +(-0.308776 + 8.51412i) q^{76} +(-0.267032 - 3.88807i) q^{77} +(-0.871334 + 0.153640i) q^{78} +(0.251597 - 0.691258i) q^{79} +(-11.1301 - 1.96254i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.90429 - 0.335778i) q^{82} +(13.1405 + 7.58668i) q^{83} +(0.354328 + 5.15912i) q^{84} +(-1.94589 + 11.0357i) q^{85} +(0.111715 + 0.306935i) q^{86} -3.76894i q^{87} +(-1.07540 + 0.620883i) q^{88} +(-1.16146 + 6.58694i) q^{89} +(0.607059 + 0.220951i) q^{90} +(6.46556 - 8.87590i) q^{91} +(0.208657 - 0.175084i) q^{92} +(0.944946 - 0.792904i) q^{93} +(-1.14900 + 1.99012i) q^{94} +(-12.5685 + 4.06507i) q^{95} +(2.14864 - 1.24052i) q^{96} +(2.19807 + 12.4659i) q^{97} +(1.10646 + 1.00124i) q^{98} +(-1.38418 + 0.503800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 6 q^{7} + 12 q^{10} + 6 q^{11} + 72 q^{12} + 3 q^{13} - 15 q^{14} + 18 q^{19} + 9 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{24} + 18 q^{25} + 39 q^{27} - 9 q^{28} - 6 q^{29} - 18 q^{31} - 51 q^{32} - 12 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) $ 78 * q - 6 * q^7 + 12 * q^10 + 6 * q^11 + 72 * q^12 + 3 * q^13 - 15 * q^14 + 18 * q^19 + 9 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^24 + 18 * q^25 + 39 * q^27 - 9 * q^28 - 6 * q^29 - 18 * q^31 - 51 * q^32 - 12 * q^33 + 30 * q^34 + 33 * q^35 + 18 * q^37 - 57 * q^38 - 18 * q^40 - 63 * q^41 - 27 * q^42 - 51 * q^43 - 36 * q^44 + 9 * q^45 - 84 * q^47 + 18 * q^49 - 27 * q^50 - 18 * q^51 + 18 * q^52 - 45 * q^53 + 30 * q^55 + 33 * q^56 - 6 * q^57 - 18 * q^58 - 24 * q^59 + 66 * q^61 + 171 * q^62 + 6 * q^63 + 18 * q^64 - 99 * q^65 - 12 * q^66 - 24 * q^67 - 12 * q^69 - 150 * q^70 - 66 * q^71 - 9 * q^72 + 3 * q^73 + 18 * q^74 - 36 * q^75 - 12 * q^76 + 21 * q^77 + 75 * q^78 + 45 * q^79 + 78 * q^80 - 24 * q^82 - 72 * q^83 - 9 * q^84 + 60 * q^85 - 9 * q^86 - 108 * q^88 + 48 * q^89 - 33 * q^90 - 54 * q^91 - 102 * q^92 + 9 * q^93 - 66 * q^94 - 84 * q^95 + 75 * q^97 - 39 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.137026	−	0.163301i	−0.0968920	−	0.115471i	0.715420	−	0.698695i	$-0.246236\pi$
$2$	−0.137026	−	0.163301i	−0.0968920	−	0.115471i	−0.812312	+	0.583224i	$0.801791\pi$
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	0.339405	−	1.92486i	0.169703	−	0.962431i
$5$	2.98443	−	0.526235i	1.33468	−	0.235339i	0.539637	−	0.841898i	$-0.318561\pi$
$5$	2.98443	−	0.526235i	1.33468	−	0.235339i	0.795039	+	0.606558i	$0.207450\pi$
$6$	−0.137026	+	0.163301i	−0.0559406	+	0.0666674i
$7$	−0.181283	−	2.63953i	−0.0685186	−	0.997650i
$7$	−0.181283	−	2.63953i	−0.0685186	−	0.997650i
$8$	−0.730069	+	0.421505i	−0.258118	+	0.149025i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−0.494879	−	0.415253i	−0.156494	−	0.131314i
$11$	1.47301			0.444130			0.222065	−	0.975032i	$-0.428720\pi$
$11$	1.47301			0.444130			0.222065	+	0.975032i	$0.428720\pi$
$12$	−1.95456			−0.564232
$13$	3.17945	+	2.66787i	0.881820	+	0.739935i	0.966553	−	0.256469i	$-0.0825590\pi$
$13$	3.17945	+	2.66787i	0.881820	+	0.739935i	−0.0847321	+	0.996404i	$0.527003\pi$
$14$	−0.406198	+	0.391288i	−0.108561	+	0.104576i
$15$	−1.03648	−	2.84771i	−0.267618	−	0.735275i
$16$	−3.50449	−	1.27553i	−0.876124	−	0.318883i
$17$	−1.26471	+	3.47476i	−0.306737	+	0.842753i	0.686551	+	0.727082i	$0.259124\pi$
$17$	−1.26471	+	3.47476i	−0.306737	+	0.842753i	−0.993288	+	0.115671i	$0.963098\pi$
$18$	0.184615	+	0.106587i	0.0435141	+	0.0251229i
$19$	−4.31729	+	0.600840i	−0.990454	+	0.137842i
$19$	−4.31729	+	0.600840i	−0.990454	+	0.137842i
$20$		−	5.92322i		−	1.32447i
$21$	−2.56795	+	0.636879i	−0.560373	+	0.138978i
$22$	−0.201841	−	0.240545i	−0.0430326	−	0.0512843i
$23$	0.106754	+	0.0895772i	0.0222597	+	0.0186781i	0.653850	−	0.756625i	$-0.273153\pi$
$23$	0.106754	+	0.0895772i	0.0222597	+	0.0186781i	−0.631590	+	0.775303i	$0.717597\pi$
$24$	0.541877	+	0.645784i	0.110610	+	0.131820i
$25$	3.93142	−	1.43092i	0.786284	−	0.286184i
$26$		−	0.884776i		−	0.173519i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−5.14227	−	0.546926i	−0.971797	−	0.103359i
$29$	3.71169	+	0.654470i	0.689243	+	0.121532i	0.507290	−	0.861775i	$-0.330647\pi$
$29$	3.71169	+	0.654470i	0.689243	+	0.121532i	0.181952	+	0.983307i	$0.441758\pi$
$30$	−0.323009	+	0.559468i	−0.0589731	+	0.102144i
$31$	0.616770	+	1.06828i	0.110775	+	0.191868i	0.916083	−	0.400989i	$-0.131333\pi$
$31$	0.616770	+	1.06828i	0.110775	+	0.191868i	−0.805308	+	0.592857i	$0.798000\pi$
$32$	0.848564	+	2.33141i	0.150006	+	0.412139i
$33$	−0.255786	−	1.45063i	−0.0445266	−	0.252523i
$34$	0.740730	−	0.269604i	0.127034	−	0.0462367i
$35$	−1.93004	−	7.78210i	−0.326237	−	1.31541i
$36$	0.339405	+	1.92486i	0.0565675	+	0.320810i
$37$	−4.18463	+	2.41600i	−0.687949	+	0.397187i	−0.802843	−	0.596190i	$-0.796680\pi$
$37$	−4.18463	+	2.41600i	−0.687949	+	0.397187i	0.114894	+	0.993378i	$0.463347\pi$
$38$	0.689699	+	0.622688i	0.111884	+	0.101013i
$39$	2.07524	−	3.59442i	0.332304	−	0.575567i
$40$	−1.95703	+	1.64214i	−0.309433	+	0.259645i
$41$	6.94865	−	5.83061i	1.08520	−	0.910589i	0.0888554	−	0.996045i	$-0.471679\pi$
$41$	6.94865	−	5.83061i	1.08520	−	0.910589i	0.996342	+	0.0854558i	$0.0272346\pi$
$42$	0.455879	+	0.332081i	0.0703437	+	0.0512412i
$43$	−1.43983	−	0.524056i	−0.219572	−	0.0799178i	0.229892	−	0.973216i	$-0.426163\pi$
$43$	−1.43983	−	0.524056i	−0.219572	−	0.0799178i	−0.449464	+	0.893298i	$0.648385\pi$
$44$	0.499948	−	2.83535i	0.0753700	−	0.427445i
$45$	−2.62446	+	1.51523i	−0.391232	+	0.225878i
$46$		−	0.0297075i		−	0.00438013i
$47$	−3.68693	−	10.1298i	−0.537794	−	1.47758i	−0.849598	−	0.527431i	$-0.823155\pi$
$47$	−3.68693	−	10.1298i	−0.537794	−	1.47758i	0.311804	−	0.950147i	$-0.399067\pi$
$48$	−0.647604	+	3.67275i	−0.0934736	+	0.530115i
$49$	−6.93427	+	0.957006i	−0.990610	+	0.136715i
$50$	−0.772377	−	0.445932i	−0.109231	−	0.0630643i
$51$	3.64158	+	0.642109i	0.509924	+	0.0899133i
$52$	6.21441	−	5.21451i	0.861784	−	0.723123i
$53$	4.21495	+	0.743210i	0.578968	+	0.102088i	0.455461	−	0.890256i	$-0.349475\pi$
$53$	4.21495	+	0.743210i	0.578968	+	0.102088i	0.123508	+	0.992344i	$0.460586\pi$
$54$	0.0729100	−	0.200319i	0.00992179	−	0.0272599i
$55$	4.39610	−	0.775151i	0.592770	−	0.104521i
$56$	1.24493	+	1.85063i	0.166360	+	0.247301i
$57$	1.34140	+	4.14737i	0.177673	+	0.549332i
$58$	−0.401722	−	0.695802i	−0.0527486	−	0.0913633i
$59$	5.23397	+	1.90501i	0.681405	+	0.248011i	0.659451	−	0.751748i	$-0.270789\pi$
$59$	5.23397	+	1.90501i	0.681405	+	0.248011i	0.0219543	+	0.999759i	$0.493011\pi$
$60$	−5.83323	+	1.02856i	−0.753067	+	0.132786i
$61$	−5.19105	+	6.18645i	−0.664645	+	0.792093i	−0.988044	−	0.154169i	$-0.950730\pi$
$61$	−5.19105	+	6.18645i	−0.664645	+	0.792093i	0.323399	+	0.946263i	$0.395174\pi$
$62$	0.0899374	−	0.247101i	0.0114221	−	0.0313818i
$63$	1.07312	+	2.41835i	0.135201	+	0.304683i
$64$	−3.46496	+	6.00148i	−0.433120	+	0.750185i
$65$	10.8928	+	6.28894i	1.35108	+	0.780047i
$66$	−0.201841	+	0.240545i	−0.0248449	+	0.0296090i
$67$	−6.08581	+	7.25279i	−0.743500	+	0.886069i	−0.996686	−	0.0813489i	$-0.974077\pi$
$67$	−6.08581	+	7.25279i	−0.743500	+	0.886069i	0.253186	+	0.967418i	$0.418522\pi$
$68$	6.25918	+	3.61374i	0.759037	+	0.438230i
$69$	0.0696787	−	0.120687i	0.00838833	−	0.0145290i
$70$	−1.00636	+	1.38153i	−0.120283	+	0.165124i
$71$	−2.60170	+	7.14811i	−0.308765	+	0.848325i	0.684133	+	0.729357i	$0.260181\pi$
$71$	−2.60170	+	7.14811i	−0.308765	+	0.848325i	−0.992898	+	0.118968i	$0.962042\pi$
$72$	0.541877	−	0.645784i	0.0638608	−	0.0761063i
$73$	12.6785	−	2.23555i	1.48390	−	0.261652i	0.627765	−	0.778403i	$-0.283970\pi$
$73$	12.6785	−	2.23555i	1.48390	−	0.261652i	0.856136	+	0.516751i	$0.172859\pi$
$74$	0.967938	+	0.352301i	0.112521	+	0.0409541i
$75$	−2.09186	−	3.62322i	−0.241548	−	0.418373i
$76$	−0.308776	+	8.51412i	−0.0354191	+	0.976636i
$77$	−0.267032	−	3.88807i	−0.0304312	−	0.443086i
$78$	−0.871334	+	0.153640i	−0.0986592	+	0.0173963i
$79$	0.251597	−	0.691258i	0.0283069	−	0.0777726i	−0.924734	−	0.380613i	$-0.875713\pi$
$79$	0.251597	−	0.691258i	0.0283069	−	0.0777726i	0.953041	+	0.302841i	$0.0979351\pi$
$80$	−11.1301	−	1.96254i	−1.24439	−	0.219419i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−1.90429	−	0.335778i	−0.210294	−	0.0370805i
$83$	13.1405	+	7.58668i	1.44236	+	0.832746i	0.998007	−	0.0631063i	$-0.0201007\pi$
$83$	13.1405	+	7.58668i	1.44236	+	0.832746i	0.444352	+	0.895852i	$0.353434\pi$
$84$	0.354328	+	5.15912i	0.0386604	+	0.562906i
$85$	−1.94589	+	11.0357i	−0.211062	+	1.19699i
$86$	0.111715	+	0.306935i	0.0120466	+	0.0330977i
$87$		−	3.76894i		−	0.404073i
$88$	−1.07540	+	0.620883i	−0.114638	+	0.0661863i
$89$	−1.16146	+	6.58694i	−0.123114	+	0.698214i	0.859296	+	0.511478i	$0.170902\pi$
$89$	−1.16146	+	6.58694i	−0.123114	+	0.698214i	−0.982410	+	0.186736i	$0.940209\pi$
$90$	0.607059	+	0.220951i	0.0639896	+	0.0232903i
$91$	6.46556	−	8.87590i	0.677775	−	0.930447i
$92$	0.208657	−	0.175084i	0.0217540	−	0.0182537i
$93$	0.944946	−	0.792904i	0.0979864	−	0.0822203i
$94$	−1.14900	+	1.99012i	−0.118510	+	0.205265i
$95$	−12.5685	+	4.06507i	−1.28950	+	0.417068i
$96$	2.14864	−	1.24052i	0.219295	−	0.126610i
$97$	2.19807	+	12.4659i	0.223180	+	1.26572i	0.866134	+	0.499812i	$0.166597\pi$
$97$	2.19807	+	12.4659i	0.223180	+	1.26572i	−0.642954	+	0.765905i	$0.722291\pi$
$98$	1.10646	+	1.00124i	0.111769	+	0.101141i
$99$	−1.38418	+	0.503800i	−0.139115	+	0.0506338i
$100$	−1.41998	−	8.05310i	−0.141998	−	0.805310i
$101$	−4.30219	−	11.8202i	−0.428084	−	1.17615i	−0.946974	−	0.321311i	$-0.895877\pi$
$101$	−4.30219	−	11.8202i	−0.428084	−	1.17615i	0.518889	−	0.854841i	$-0.326346\pi$
$102$	−0.394134	−	0.682660i	−0.0390251	−	0.0675935i
$103$	6.66257	−	11.5399i	0.656482	−	1.13706i	−0.325038	−	0.945701i	$-0.605377\pi$
$103$	6.66257	−	11.5399i	0.656482	−	1.13706i	0.981520	−	0.191360i	$-0.0612897\pi$
$104$	−3.44574	−	0.607577i	−0.337883	−	0.0595778i
$105$	−7.32872	+	3.25207i	−0.715210	+	0.317369i
$106$	−0.456191	−	0.790146i	−0.0443092	−	0.0767457i
$107$			11.4878i			1.11056i	0.831662	+	0.555282i	$0.187390\pi$
$107$			11.4878i			1.11056i	−0.831662	+	0.555282i	$0.812610\pi$
$108$	1.83668	−	0.668498i	0.176735	−	0.0643262i
$109$	−7.69660	−	9.17245i	−0.737201	−	0.878561i	0.258980	−	0.965883i	$-0.416614\pi$
$109$	−7.69660	−	9.17245i	−0.737201	−	0.878561i	−0.996180	+	0.0873213i	$0.972169\pi$
$110$	−0.728963	−	0.611672i	−0.0695039	−	0.0583207i
$111$	3.10595	+	3.70152i	0.294803	+	0.351333i
$112$	−2.73150	+	9.48146i	−0.258103	+	0.895914i
$113$			14.7011i			1.38296i	0.722396	+	0.691480i	$0.243041\pi$
$113$			14.7011i			1.38296i	−0.722396	+	0.691480i	$0.756959\pi$
$114$	0.493463	−	0.787349i	0.0462170	−	0.0737420i
$115$	0.365738	+	0.211159i	0.0341053	+	0.0196907i
$116$	2.51953	−	6.92235i	0.233933	−	0.642724i
$117$	−3.90017	−	1.41955i	−0.360571	−	0.131237i
$118$	−0.406100	−	1.11575i	−0.0373845	−	0.102713i
$119$	9.40101	+	2.70833i	0.861789	+	0.248272i
$120$	1.95703	+	1.64214i	0.178651	+	0.149906i
$121$	−8.83023			−0.802749
$122$	1.72156			0.155863
$123$	−6.94865	−	5.83061i	−0.626539	−	0.525729i
$124$	2.26562	−	0.824618i	0.203459	−	0.0740529i
$125$	−2.14227	+	1.23684i	−0.191611	+	0.110627i
$126$	0.247873	−	0.506619i	0.0220823	−	0.0451332i
$127$	8.16526	−	9.73098i	0.724550	−	0.863485i	−0.270514	−	0.962716i	$-0.587194\pi$
$127$	8.16526	−	9.73098i	0.724550	−	0.863485i	0.995064	+	0.0992308i	$0.0316382\pi$
$128$	6.34153	−	1.11818i	0.560517	−	0.0988343i
$129$	−0.266070	+	1.50896i	−0.0234262	+	0.132856i
$130$	−0.465600	−	2.64055i	−0.0408358	−	0.231591i
$131$	−14.5330	−	17.3198i	−1.26976	−	1.51324i	−0.754684	−	0.656089i	$-0.772210\pi$
$131$	−14.5330	−	17.3198i	−1.26976	−	1.51324i	−0.515072	−	0.857147i	$-0.672235\pi$
$132$	−2.87909			−0.250592
$133$	2.36859	+	11.2867i	0.205383	+	0.978682i
$134$	2.01830			0.174355
$135$	1.94795	+	2.32147i	0.167653	+	0.199801i
$136$	−0.541305	−	3.06989i	−0.0464165	−	0.263241i
$137$	−0.0672848	+	0.381591i	−0.00574853	+	0.0326015i	−0.987547	−	0.157324i	$-0.949713\pi$
$137$	−0.0672848	+	0.381591i	−0.00574853	+	0.0326015i	0.981799	+	0.189925i	$0.0608245\pi$
$138$	−0.0292561	+	0.00515865i	−0.00249045	+	0.000439133i
$139$	11.9896	−	14.2886i	1.01694	−	1.21195i	0.0398356	−	0.999206i	$-0.487317\pi$
$139$	11.9896	−	14.2886i	1.01694	−	1.21195i	0.977109	−	0.212741i	$-0.0682390\pi$
$140$	−15.6345	+	1.07378i	−1.32136	+	0.0907509i
$141$	−9.33564	+	5.38993i	−0.786203	+	0.453914i
$142$	1.52380	−	0.554616i	0.127874	−	0.0465423i
$143$	4.68337	+	3.92981i	0.391643	+	0.328627i
$144$	3.72940			0.310784
$145$	11.4217			0.948517
$146$	−2.10235	−	1.76408i	−0.173991	−	0.145996i
$147$	2.14659	+	6.66274i	0.177048	+	0.549534i
$148$	3.23018	+	8.87484i	0.265519	+	0.729507i
$149$	10.3823	+	3.77886i	0.850554	+	0.309576i	0.730266	−	0.683163i	$-0.239396\pi$
$149$	10.3823	+	3.77886i	0.850554	+	0.309576i	0.120288	+	0.992739i	$0.461618\pi$
$150$	−0.305036	+	0.838078i	−0.0249061	+	0.0684288i
$151$	−4.34534	−	2.50878i	−0.353618	−	0.204162i	0.312659	−	0.949865i	$-0.398780\pi$
$151$	−4.34534	−	2.50878i	−0.353618	−	0.204162i	−0.666278	+	0.745704i	$0.732113\pi$
$152$	2.89866	−	2.25842i	0.235112	−	0.183182i
$153$		−	3.69776i		−	0.298946i
$154$	−0.598335	+	0.576373i	−0.0482152	+	0.0464454i
$155$	2.40287	+	2.86363i	0.193003	+	0.230012i
$156$	−6.21441	−	5.21451i	−0.497551	−	0.417495i
$157$	−2.24778	−	2.67880i	−0.179392	−	0.213792i	0.668853	−	0.743394i	$-0.266785\pi$
$157$	−2.24778	−	2.67880i	−0.179392	−	0.213792i	−0.848246	+	0.529603i	$0.822341\pi$
$158$	−0.147359	+	0.0536341i	−0.0117232	+	0.00426690i
$159$		−	4.27997i		−	0.339424i
$160$	3.75935	+	6.51138i	0.297203	+	0.514770i
$161$	0.217089	−	0.298020i	0.0171090	−	0.0234872i
$162$	−0.209936	−	0.0370174i	−0.0164941	−	0.00290836i
$163$	−4.28632	+	7.42412i	−0.335730	+	0.581502i	−0.983625	−	0.180228i	$-0.942316\pi$
$163$	−4.28632	+	7.42412i	−0.335730	+	0.581502i	0.647895	+	0.761730i	$0.275650\pi$
$164$	−8.86472	−	15.3541i	−0.692218	−	1.19896i
$165$	−1.52675	−	4.19471i	−0.118857	−	0.326558i
$166$	−0.561678	−	3.18543i	−0.0435946	−	0.247238i
$167$	13.4145	−	4.88248i	1.03804	−	0.377817i	0.233906	−	0.972259i	$-0.424849\pi$
$167$	13.4145	−	4.88248i	1.03804	−	0.377817i	0.804139	+	0.594442i	$0.202627\pi$
$168$	1.60633	−	1.54737i	0.123931	−	0.119382i
$169$	0.733915	+	4.16224i	0.0564550	+	0.320172i
$170$	2.06878	−	1.19441i	0.158668	−	0.0916071i
$171$	3.85143	−	2.04120i	0.294526	−	0.156095i
$172$	−1.49742	+	2.59361i	−0.114177	+	0.197761i
$173$	4.22029	−	3.54124i	0.320863	−	0.269236i	−0.468102	−	0.883674i	$-0.655062\pi$
$173$	4.22029	−	3.54124i	0.320863	−	0.269236i	0.788964	+	0.614439i	$0.210618\pi$
$174$	−0.615473	+	0.516443i	−0.0466589	+	0.0391515i
$175$	−4.48966	−	10.1177i	−0.339386	−	0.764827i
$176$	−5.16216	−	1.87887i	−0.389113	−	0.141625i
$177$	0.967199	−	5.48526i	0.0726991	−	0.412297i
$178$	1.23480	−	0.712915i	0.0925525	−	0.0534352i
$179$			10.4643i			0.782141i	0.920361	+	0.391070i	$0.127895\pi$
$179$			10.4643i			0.782141i	−0.920361	+	0.391070i	$0.872105\pi$
$180$	2.02586	+	5.56600i	0.150999	+	0.414866i
$181$	2.59135	−	14.6963i	0.192614	−	1.09237i	−0.723163	−	0.690678i	$-0.757312\pi$
$181$	2.59135	−	14.6963i	0.192614	−	1.09237i	0.915776	−	0.401688i	$-0.131577\pi$
$182$	−2.33540	+	0.160395i	−0.173111	+	0.0118893i
$183$	6.99388	+	4.03792i	0.517002	+	0.298491i
$184$	−0.115695	−	0.0204002i	−0.00852915	−	0.00150392i
$185$	−11.2173	+	9.41246i	−0.824715	+	0.692018i
$186$	−0.258964	−	0.0456624i	−0.0189882	−	0.00334813i
$187$	−1.86293	+	5.11836i	−0.136231	+	0.374292i
$188$	−20.7498	+	3.65874i	−1.51333	+	0.266841i
$189$	2.19526	−	1.47676i	0.159682	−	0.107419i
$190$	2.38604	+	1.49542i	0.173101	+	0.108489i
$191$	3.08726	+	5.34729i	0.223386	+	0.386916i	0.955834	−	0.293907i	$-0.0949556\pi$
$191$	3.08726	+	5.34729i	0.223386	+	0.386916i	−0.732448	+	0.680823i	$0.761622\pi$
$192$	6.51199	+	2.37017i	0.469962	+	0.171052i
$193$	14.0614	−	2.47940i	1.01216	−	0.178471i	0.357115	−	0.934061i	$-0.383761\pi$
$193$	14.0614	−	2.47940i	1.01216	−	0.178471i	0.655045	+	0.755589i	$0.272649\pi$
$194$	1.73450	−	2.06709i	0.124530	−	0.148409i
$195$	4.30189	−	11.8193i	0.308065	−	0.846400i
$196$	−0.511424	+	13.6723i	−0.0365303	+	0.976595i
$197$	−2.35790	+	4.08400i	−0.167993	+	0.290973i	−0.937714	−	0.347408i	$-0.887062\pi$
$197$	−2.35790	+	4.08400i	−0.167993	+	0.290973i	0.769721	+	0.638381i	$0.220395\pi$
$198$	0.271940	+	0.157004i	0.0193259	+	0.0111578i
$199$	4.64758	−	5.53877i	0.329458	−	0.392633i	−0.575733	−	0.817638i	$-0.695283\pi$
$199$	4.64758	−	5.53877i	0.329458	−	0.392633i	0.905191	+	0.425005i	$0.139728\pi$
$200$	−2.26707	+	2.70178i	−0.160306	+	0.191045i
$201$	8.19939	+	4.73392i	0.578340	+	0.333905i
$202$	−1.34074	+	2.32223i	−0.0943339	+	0.163391i
$203$	1.05463	−	9.91576i	0.0740205	−	0.695950i
$204$	2.47194	−	6.79161i	0.173071	−	0.475508i
$205$	17.6695	−	21.0577i	1.23409	−	1.47073i
$206$	−2.79743	+	0.493262i	−0.194906	+	0.0343672i
$207$	−0.130953	−	0.0476631i	−0.00910187	−	0.00331281i
$208$	−7.73940	−	13.4050i	−0.536631	−	0.929472i
$209$	−6.35942	+	0.885045i	−0.439890	+	0.0612198i
$210$	1.53529	+	0.751171i	0.105945	+	0.0518357i
$211$	−26.2421	+	4.62720i	−1.80658	+	0.318549i	−0.972467	−	0.233039i	$-0.925133\pi$
$211$	−26.2421	+	4.62720i	−1.80658	+	0.318549i	−0.834116	+	0.551589i	$0.814022\pi$
$212$	2.86115	−	7.86095i	0.196505	−	0.539893i
$213$	7.49129	+	1.32092i	0.513295	+	0.0905078i
$214$	1.87597	−	1.57412i	0.128238	−	0.107605i
$215$	−4.57285	−	0.806317i	−0.311866	−	0.0549903i
$216$	−0.730069	−	0.421505i	−0.0496749	−	0.0286798i
$217$	2.70794	−	1.82165i	0.183827	−	0.123661i
$218$	−0.443238	+	2.51373i	−0.0300199	+	0.170251i
$219$	−4.40318	−	12.0976i	−0.297539	−	0.817483i
$220$		−	8.72497i		−	0.588238i
$221$	−13.2913	+	7.67373i	−0.894069	+	0.516191i
$222$	0.178868	−	1.01441i	0.0120048	−	0.0680827i
$223$	−23.0280	−	8.38151i	−1.54207	−	0.561267i	−0.575529	−	0.817781i	$-0.695204\pi$
$223$	−23.0280	−	8.38151i	−1.54207	−	0.561267i	−0.966540	+	0.256514i	$0.917426\pi$
$224$	6.00001	−	2.66246i	0.400892	−	0.177893i
$225$	−3.20492	+	2.68925i	−0.213661	+	0.179283i
$226$	2.40070	−	2.01443i	0.159692	−	0.133998i
$227$	−4.16464	+	7.21337i	−0.276417	+	0.478768i	−0.970492	−	0.241135i	$-0.922480\pi$
$227$	−4.16464	+	7.21337i	−0.276417	+	0.478768i	0.694075	+	0.719903i	$0.255814\pi$
$228$	8.43839	−	1.17438i	0.558846	−	0.0777749i
$229$	−10.6664	+	6.15824i	−0.704855	+	0.406948i	−0.809153	−	0.587598i	$-0.800074\pi$
$229$	−10.6664	+	6.15824i	−0.704855	+	0.406948i	0.104298	+	0.994546i	$0.466740\pi$
$230$	−0.0156331	−	0.0886598i	−0.00103082	−	0.00584605i
$231$	−3.78263	+	0.938131i	−0.248879	+	0.0617245i
$232$	−2.98565	+	1.08669i	−0.196017	+	0.0713445i
$233$	−1.82023	−	10.3230i	−0.119247	−	0.676285i	−0.984559	−	0.175051i	$-0.943991\pi$
$233$	−1.82023	−	10.3230i	−0.119247	−	0.676285i	0.865312	−	0.501234i	$-0.167120\pi$
$234$	0.302611	+	0.831417i	0.0197823	+	0.0543514i
$235$	−16.3340	−	28.2913i	−1.06551	−	1.84552i
$236$	5.44332	−	9.42810i	0.354330	−	0.613717i
$237$	−0.724445	−	0.127739i	−0.0470578	−	0.00829756i
$238$	−0.845910	−	1.90631i	−0.0548322	−	0.123568i
$239$	−1.83253	−	3.17404i	−0.118537	−	0.205312i	0.800651	−	0.599131i	$-0.204487\pi$
$239$	−1.83253	−	3.17404i	−0.118537	−	0.205312i	−0.919188	+	0.393819i	$0.871154\pi$
$240$			11.3018i			0.729530i
$241$	−13.8376	+	5.03647i	−0.891358	+	0.324428i	−0.746784	−	0.665066i	$-0.768403\pi$
$241$	−13.8376	+	5.03647i	−0.891358	+	0.324428i	−0.144574	+	0.989494i	$0.546181\pi$
$242$	1.20997	+	1.44199i	0.0777799	+	0.0926945i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	10.1462	+	12.0918i	0.649543	+	0.774096i
$245$	−20.1912	+	6.50517i	−1.28997	+	0.415600i
$246$			1.93367i			0.123286i
$247$	−15.3296	−	9.60765i	−0.975397	−	0.611320i
$248$	−0.900569	−	0.519944i	−0.0571862	−	0.0330165i
$249$	5.18959	−	14.2583i	0.328877	−	0.903582i
$250$	0.495525	+	0.180356i	0.0313397	+	0.0114067i
$251$	0.593091	+	1.62951i	0.0374356	+	0.102853i	0.957002	−	0.290081i	$-0.0936822\pi$
$251$	0.593091	+	1.62951i	0.0374356	+	0.102853i	−0.919567	+	0.392934i	$0.871460\pi$
$252$	5.01921	−	1.24482i	0.316181	−	0.0784161i
$253$	0.157250	+	0.131948i	0.00988622	+	0.00829552i
$254$	−2.70793			−0.169911
$255$	11.2059			0.701743
$256$	9.56569	+	8.02657i	0.597856	+	0.501661i
$257$	4.34368	−	1.58097i	0.270951	−	0.0986181i	−0.202971	−	0.979185i	$-0.565060\pi$
$257$	4.34368	−	1.58097i	0.270951	−	0.0986181i	0.473923	+	0.880567i	$0.342838\pi$
$258$	0.282873	−	0.163317i	0.0176109	−	0.0101677i
$259$	7.13571	+	10.6075i	0.443391	+	0.659117i
$260$	15.8024	−	18.8326i	0.980023	−	1.16795i
$261$	−3.71169	+	0.654470i	−0.229748	+	0.0405107i
$262$	−0.836939	+	4.74652i	−0.0517063	+	0.293241i
$263$	1.95154	+	11.0677i	0.120337	+	0.682466i	0.983969	+	0.178342i	$0.0570734\pi$
$263$	1.95154	+	11.0677i	0.120337	+	0.682466i	−0.863631	+	0.504124i	$0.831815\pi$
$264$	0.798191	+	0.951247i	0.0491253	+	0.0585452i
$265$	12.9703			0.796760
$266$	1.51857	−	1.93337i	0.0931098	−	0.118542i
$267$	6.68855			0.409333
$268$	11.8951	+	14.1760i	0.726606	+	0.865936i
$269$	0.405471	+	2.29954i	0.0247220	+	0.140205i	0.994670	−	0.103105i	$-0.0328777\pi$
$269$	0.405471	+	2.29954i	0.0247220	+	0.140205i	−0.969948	+	0.243310i	$0.921767\pi$
$270$	0.112180	−	0.636204i	0.00682705	−	0.0387181i
$271$	19.5684	−	3.45043i	1.18869	−	0.209599i	0.455889	−	0.890037i	$-0.349321\pi$
$271$	19.5684	−	3.45043i	1.18869	−	0.209599i	0.732806	+	0.680438i	$0.238210\pi$
$272$	8.86433	−	10.5641i	0.537479	−	0.640542i
$273$	−9.86379	−	4.82605i	−0.596984	−	0.292086i
$274$	0.0715340	−	0.0413002i	0.00432153	−	0.00249504i
$275$	5.79103	−	2.10776i	0.349212	−	0.127103i
$276$	−0.208657	−	0.175084i	−0.0125597	−	0.0105388i
$277$	−5.09050			−0.305858			−0.152929	−	0.988237i	$-0.548871\pi$
$277$	−5.09050			−0.305858			−0.152929	+	0.988237i	$0.548871\pi$
$278$	−3.97624			−0.238479
$279$	−0.944946	−	0.792904i	−0.0565724	−	0.0474699i
$280$	4.68926	+	4.86794i	0.280237	+	0.290915i
$281$	−10.5450	−	28.9720i	−0.629059	−	1.72833i	−0.683642	−	0.729817i	$-0.739605\pi$
$281$	−10.5450	−	28.9720i	−0.629059	−	1.72833i	0.0545831	−	0.998509i	$-0.482617\pi$
$282$	2.15941	+	0.785960i	0.128591	+	0.0468032i
$283$	−9.46628	+	26.0084i	−0.562712	+	1.54604i	0.252932	+	0.967484i	$0.418605\pi$
$283$	−9.46628	+	26.0084i	−0.562712	+	1.54604i	−0.815644	+	0.578554i	$0.803617\pi$
$284$	12.8761	+	7.43402i	0.764056	+	0.441128i
$285$	6.18580	+	11.6716i	0.366415	+	0.691367i
$286$		−	1.30329i		−	0.0770649i
$287$	−16.6498	−	17.2842i	−0.982805	−	1.02025i
$288$	−1.59478	−	1.90058i	−0.0939733	−	0.111993i
$289$	2.54830	+	2.13828i	0.149900	+	0.125781i
$290$	−1.56506	−	1.86517i	−0.0919037	−	0.109527i
$291$	11.8948	−	4.32935i	0.697285	−	0.253791i
$292$		−	25.1630i		−	1.47256i
$293$	16.8530	+	29.1903i	0.984564	+	1.70532i	0.643856	+	0.765147i	$0.277334\pi$
$293$	16.8530	+	29.1903i	0.984564	+	1.70532i	0.340708	+	0.940169i	$0.389333\pi$
$294$	0.793895	−	1.26351i	0.0463009	−	0.0736894i
$295$	16.6229	+	2.93106i	0.967822	+	0.170653i
$296$	2.03671	−	3.52769i	0.118381	−	0.205043i
$297$	0.736506	+	1.27567i	0.0427364	+	0.0740217i
$298$	−0.805557	−	2.21325i	−0.0466646	−	0.128210i
$299$	0.100438	+	0.569613i	0.00580848	+	0.0329415i
$300$	−7.68418	+	2.79681i	−0.443646	+	0.161474i
$301$	−1.12225	+	3.89549i	−0.0646852	+	0.224532i
$302$	0.185737	+	1.05337i	0.0106880	+	0.0606144i
$303$	−10.8935	+	6.28939i	−0.625817	+	0.361316i
$304$	15.8963	+	3.40120i	0.911716	+	0.195072i
$305$	−12.2368	+	21.1947i	−0.700676	+	1.21361i
$306$	−0.603849	+	0.506689i	−0.0345197	+	0.0289655i
$307$	11.5543	−	9.69518i	0.659437	−	0.553333i	−0.250481	−	0.968122i	$-0.580589\pi$
$307$	11.5543	−	9.69518i	0.659437	−	0.553333i	0.909918	+	0.414788i	$0.136144\pi$
$308$	−7.57462	−	0.805629i	−0.431604	−	0.0459050i
$309$	−12.5215	−	4.55746i	−0.712325	−	0.259265i
$310$	0.138378	−	0.784783i	0.00785936	−	0.0445727i
$311$	−26.3547	+	15.2159i	−1.49444	+	0.862815i	−0.999980	−	0.00638577i	$-0.997967\pi$
$311$	−26.3547	+	15.2159i	−1.49444	+	0.862815i	−0.494460	+	0.869201i	$0.664634\pi$
$312$			3.49890i			0.198086i
$313$	2.87074	+	7.88730i	0.162264	+	0.445817i	0.994003	−	0.109350i	$-0.0348768\pi$
$313$	2.87074	+	7.88730i	0.162264	+	0.445817i	−0.831739	+	0.555166i	$0.812655\pi$
$314$	−0.129447	+	0.734130i	−0.00730512	+	0.0414294i
$315$	4.47528	+	6.65267i	0.252153	+	0.374835i
$316$	−1.24518	−	0.718906i	−0.0700470	−	0.0404416i
$317$	−27.2005	−	4.79618i	−1.52773	−	0.269380i	−0.654265	−	0.756265i	$-0.727022\pi$
$317$	−27.2005	−	4.79618i	−1.52773	−	0.269380i	−0.873466	+	0.486885i	$0.838133\pi$
$318$	−0.698925	+	0.586468i	−0.0391938	+	0.0328875i
$319$	5.46736	+	0.964043i	0.306113	+	0.0539760i
$320$	−7.18272	+	19.7344i	−0.401526	+	1.10318i
$321$	11.3132	−	1.99483i	0.631444	−	0.111341i
$322$	−0.0784138	+	0.00538546i	−0.00436983	+	0.000300120i
$323$	3.37234	−	15.7614i	0.187642	−	0.876989i
$324$	−0.977278	−	1.69270i	−0.0542932	−	0.0940386i
$325$	16.3173	+	5.93900i	0.905119	+	0.329436i
$326$	1.79970	−	0.317336i	0.0996764	−	0.0175756i
$327$	−7.69660	+	9.17245i	−0.425623	+	0.507238i
$328$	−2.61536	+	7.18564i	−0.144409	+	0.396761i
$329$	−26.0695	+	11.5681i	−1.43726	+	0.637772i
$330$	−0.475797	+	0.824104i	−0.0261917	+	0.0453654i
$331$	−1.21321	−	0.700445i	−0.0666838	−	0.0384999i	0.466287	−	0.884633i	$-0.345591\pi$
$331$	−1.21321	−	0.700445i	−0.0666838	−	0.0384999i	−0.532971	+	0.846133i	$0.678925\pi$
$332$	19.0633	−	22.7187i	1.04623	−	1.24685i
$333$	3.10595	−	3.70152i	0.170205	−	0.202842i
$334$	−2.63545	−	1.52158i	−0.144205	−	0.0832570i
$335$	−14.3460	+	24.8480i	−0.783805	+	1.35759i
$336$	9.81174	+	1.04357i	0.535274	+	0.0569312i
$337$	−5.17233	+	14.2109i	−0.281755	+	0.774115i	0.715399	+	0.698716i	$0.246245\pi$
$337$	−5.17233	+	14.2109i	−0.281755	+	0.774115i	−0.997153	+	0.0753983i	$0.975977\pi$
$338$	0.579133	−	0.690184i	0.0315007	−	0.0375411i
$339$	14.4777	−	2.55281i	0.786322	−	0.138650i
$340$	20.5818	+	7.49115i	1.11620	+	0.406264i
$341$	0.908510	+	1.57358i	0.0491985	+	0.0852144i
$342$	−0.861077	−	0.349244i	−0.0465617	−	0.0188850i
$343$	3.78312	+	18.1298i	0.204269	+	0.978915i
$344$	1.27207	−	0.224300i	0.0685853	−	0.0120934i
$345$	0.144441	−	0.396849i	0.00777646	−	0.0213656i
$346$	−1.15658	−	0.203936i	−0.0621780	−	0.0109637i
$347$	−20.3404	+	17.0676i	−1.09193	+	0.916237i	−0.996856	−	0.0792333i	$-0.974753\pi$
$347$	−20.3404	+	17.0676i	−1.09193	+	0.916237i	−0.0950727	+	0.995470i	$0.530308\pi$
$348$	−7.25470	−	1.27920i	−0.388893	−	0.0685723i
$349$	−19.0083	−	10.9744i	−1.01749	−	0.587447i	−0.104113	−	0.994565i	$-0.533200\pi$
$349$	−19.0083	−	10.9744i	−1.01749	−	0.587447i	−0.913376	+	0.407118i	$0.866534\pi$
$350$	−1.03703	+	2.11956i	−0.0554318	+	0.113295i
$351$	−0.720723	+	4.08742i	−0.0384693	+	0.218170i
$352$	1.24995	+	3.43420i	0.0666223	+	0.183043i
$353$			0.980433i			0.0521832i	0.999660	+	0.0260916i	$0.00830615\pi$
$353$			0.980433i			0.0521832i	−0.999660	+	0.0260916i	$0.991694\pi$
$354$	−1.02828	+	0.593678i	−0.0546525	+	0.0315536i
$355$	−4.00300	+	22.7021i	−0.212457	+	1.20490i
$356$	12.2848	+	4.47128i	0.651090	+	0.236978i
$357$	1.03471	−	9.72848i	0.0547627	−	0.514886i
$358$	1.70884	−	1.43389i	0.0903149	−	0.0757832i
$359$	−7.78003	+	6.52822i	−0.410614	+	0.344546i	−0.824579	−	0.565747i	$-0.808588\pi$
$359$	−7.78003	+	6.52822i	−0.410614	+	0.344546i	0.413965	+	0.910293i	$0.364144\pi$
$360$	1.27736	−	2.21245i	0.0673227	−	0.116606i
$361$	18.2780	−	5.18800i	0.961999	−	0.273053i
$362$	−2.75500	+	1.59060i	−0.144800	+	0.0836002i
$363$	1.53335	+	8.69608i	0.0804802	+	0.456426i
$364$	−14.8904	−	15.4578i	−0.780471	−	0.810211i
$365$	36.6615	−	13.3437i	1.91895	−	0.698441i
$366$	−0.298946	−	1.69541i	−0.0156262	−	0.0886204i
$367$	−6.45475	−	17.7343i	−0.336935	−	0.925722i	−0.986258	−	0.165210i	$-0.947170\pi$
$367$	−6.45475	−	17.7343i	−0.336935	−	0.925722i	0.649323	−	0.760513i	$-0.275052\pi$
$368$	−0.259860	−	0.450091i	−0.0135461	−	0.0234626i
$369$	−4.53541	+	7.85556i	−0.236104	+	0.408944i
$370$	3.07413	+	0.542053i	0.159817	+	0.0281800i
$371$	1.19763	−	11.2602i	0.0621777	−	0.584602i
$372$	−1.20551	−	2.08801i	−0.0625029	−	0.108258i
$373$			18.6092i			0.963550i	0.876295	+	0.481775i	$0.160008\pi$
$373$			18.6092i			0.963550i	−0.876295	+	0.481775i	$0.839992\pi$
$374$	1.09110	−	0.397130i	0.0564197	−	0.0205351i
$375$	1.59005	+	1.89495i	0.0821100	+	0.0978549i
$376$	6.96146	+	5.84136i	0.359010	+	0.301245i
$377$	10.0551	+	11.9832i	0.517862	+	0.617164i
$378$	−0.541965	−	0.156134i	−0.0278757	−	0.00803067i
$379$		−	17.5049i		−	0.899167i	−0.893238	−	0.449584i	$-0.851572\pi$
$379$		−	17.5049i		−	0.899167i	0.893238	−	0.449584i	$-0.148428\pi$
$380$	3.55891	+	25.5723i	0.182568	+	1.31183i
$381$	−11.0010	−	6.35145i	−0.563600	−	0.325395i
$382$	0.450184	−	1.23687i	0.0230334	−	0.0632838i
$383$	2.71432	+	0.987932i	0.138695	+	0.0504810i	0.410435	−	0.911890i	$-0.365377\pi$
$383$	2.71432	+	0.987932i	0.138695	+	0.0504810i	−0.271740	+	0.962371i	$0.587599\pi$
$384$	−2.20239	−	6.05101i	−0.112390	−	0.308789i
$385$	−2.84297	−	11.4631i	−0.144891	−	0.584215i
$386$	−2.33166	−	1.95650i	−0.118679	−	0.0995831i
$387$	1.53224			0.0778880
$388$	24.7411			1.25604
$389$	11.6541	+	9.77894i	0.590885	+	0.495812i	0.888501	−	0.458874i	$-0.151747\pi$
$389$	11.6541	+	9.77894i	0.590885	+	0.495812i	−0.297616	+	0.954686i	$0.596191\pi$
$390$	−2.51958	+	0.917053i	−0.127584	+	0.0464368i
$391$	−0.446272	+	0.257655i	−0.0225689	+	0.0130302i
$392$	4.65911	−	3.62151i	0.235321	−	0.182914i
$393$	−14.5330	+	17.3198i	−0.733094	+	0.873667i
$394$	0.990015	−	0.174566i	0.0498763	−	0.00879453i
$395$	0.387110	−	2.19541i	0.0194776	−	0.110463i
$396$	0.499948	+	2.83535i	0.0251233	+	0.142482i
$397$	−4.45714	−	5.31181i	−0.223698	−	0.266592i	0.642509	−	0.766278i	$-0.277893\pi$
$397$	−4.45714	−	5.31181i	−0.223698	−	0.266592i	−0.866207	+	0.499685i	$0.833449\pi$
$398$	−1.54133			−0.0772598
$399$	10.7039	−	4.29252i	0.535867	−	0.214895i
$400$	−15.6028			−0.780141
$401$	−14.3836	−	17.1418i	−0.718285	−	0.856018i	0.276178	−	0.961106i	$-0.410932\pi$
$401$	−14.3836	−	17.1418i	−0.718285	−	0.856018i	−0.994463	+	0.105088i	$0.966488\pi$
$402$	−0.350475	−	1.98764i	−0.0174801	−	0.0991345i
$403$	−0.889040	+	5.04200i	−0.0442862	+	0.251160i
$404$	−24.2124	+	4.26930i	−1.20461	+	0.212406i
$405$	1.94795	−	2.32147i	0.0967942	−	0.115355i
$406$	−1.76377	+	1.18649i	−0.0875343	+	0.0588847i
$407$	−6.16401	+	3.55879i	−0.305539	+	0.176403i
$408$	−2.92926	+	1.06616i	−0.145020	+	0.0527829i
$409$	−13.9269	−	11.6861i	−0.688642	−	0.577839i	0.229876	−	0.973220i	$-0.426168\pi$
$409$	−13.9269	−	11.6861i	−0.688642	−	0.577839i	−0.918517	+	0.395381i	$0.870613\pi$
$410$	−5.85992			−0.289401
$411$	0.387478			0.0191129
$412$	−19.9514	−	16.7412i	−0.982936	−	0.824781i
$413$	4.07951	−	14.1606i	0.200739	−	0.696797i
$414$	0.0101606	+	0.0279159i	0.000499364	+	0.00137199i
$415$	43.2093	+	15.7269i	2.12106	+	0.772003i
$416$	−3.52195	+	9.67647i	−0.172678	+	0.474428i
$417$	−16.1535	−	9.32625i	−0.791042	−	0.456708i
$418$	1.01593	+	0.917227i	0.0496910	+	0.0448630i
$419$		−	33.3897i		−	1.63119i	−0.578620	−	0.815597i	$-0.696409\pi$
$419$		−	33.3897i		−	1.63119i	0.578620	−	0.815597i	$-0.303591\pi$
$420$	3.77237	+	15.2105i	0.184073	+	0.742199i
$421$	−4.21702	−	5.02565i	−0.205525	−	0.244935i	0.653429	−	0.756988i	$-0.273330\pi$
$421$	−4.21702	−	5.02565i	−0.205525	−	0.244935i	−0.858954	+	0.512053i	$0.828885\pi$
$422$	4.35148	+	3.65133i	0.211827	+	0.177744i
$423$	6.92917	+	8.25786i	0.336908	+	0.401511i
$424$	−3.39047	+	1.23403i	−0.164656	+	0.0599298i
$425$			15.4704i			0.750426i
$426$	−0.810794	−	1.40434i	−0.0392831	−	0.0680404i
$427$	17.2704	+	12.5804i	0.835772	+	0.608810i
$428$	22.1124	+	3.89901i	1.06884	+	0.188466i
$429$	3.05685	−	5.29462i	0.147586	−	0.255627i
$430$	0.494927	+	0.857238i	0.0238675	+	0.0413397i
$431$	1.47060	+	4.04044i	0.0708363	+	0.194621i	0.970059	−	0.242871i	$-0.0780891\pi$
$431$	1.47060	+	4.04044i	0.0708363	+	0.194621i	−0.899222	+	0.437492i	$0.855867\pi$
$432$	−0.647604	−	3.67275i	−0.0311579	−	0.176705i
$433$	−27.6852	+	10.0766i	−1.33047	+	0.484251i	−0.906798	−	0.421566i	$-0.861481\pi$
$433$	−27.6852	+	10.0766i	−1.33047	+	0.484251i	−0.423670	+	0.905817i	$0.639258\pi$
$434$	−0.668535	−	0.192597i	−0.0320907	−	0.00924497i
$435$	−1.98335	−	11.2481i	−0.0950944	−	0.539307i
$436$	−20.2680	+	11.7017i	−0.970660	+	0.560411i
$437$	−0.514710	−	0.322589i	−0.0246219	−	0.0154315i
$438$	−1.37221	+	2.37674i	−0.0655667	+	0.113565i
$439$	10.7018	−	8.97985i	0.510768	−	0.428585i	−0.350632	−	0.936514i	$-0.614033\pi$
$439$	10.7018	−	8.97985i	0.510768	−	0.428585i	0.861399	+	0.507928i	$0.169589\pi$
$440$	−2.88272	+	2.41889i	−0.137428	+	0.115316i
$441$	6.18877	−	3.27095i	0.294703	−	0.155760i
$442$	3.07438	+	1.11898i	0.146233	+	0.0532246i
$443$	1.23964	−	7.03036i	0.0588972	−	0.334023i	−0.941094	−	0.338144i	$-0.890201\pi$
$443$	1.23964	−	7.03036i	0.0588972	−	0.334023i	0.999992	+	0.00412155i	$0.00131193\pi$
$444$	8.17909	−	4.72220i	0.388163	−	0.224106i
$445$			20.2694i			0.960864i
$446$	1.78672	+	4.90898i	0.0846039	+	0.232447i
$447$	1.91858	−	10.8808i	0.0907456	−	0.514644i
$448$	16.4693	+	8.05790i	0.778099	+	0.380700i
$449$	26.1054	+	15.0720i	1.23199	+	0.711290i	0.967445	−	0.253083i	$-0.0814444\pi$
$449$	26.1054	+	15.0720i	1.23199	+	0.711290i	0.264546	+	0.964373i	$0.414778\pi$
$450$	0.878315	+	0.154871i	0.0414042	+	0.00730067i
$451$	10.2355	−	8.58856i	0.481969	−	0.404420i
$452$	28.2975	+	4.98962i	1.33100	+	0.234692i
$453$	−1.71611	+	4.71497i	−0.0806297	+	0.221528i
$454$	1.74862	−	0.308328i	0.0820666	−	0.0144706i
$455$	14.6252	−	29.8919i	0.685640	−	1.40135i
$456$	−2.72745	−	2.46245i	−0.127725	−	0.115315i
$457$	−10.4451	−	18.0915i	−0.488602	−	0.846283i	0.511312	−	0.859395i	$-0.329160\pi$
$457$	−10.4451	−	18.0915i	−0.488602	−	0.846283i	−0.999914	+	0.0131117i	$0.995826\pi$
$458$	2.46722	+	0.897995i	0.115286	+	0.0419605i
$459$	−3.64158	+	0.642109i	−0.169975	+	0.0299711i
$460$	0.530586	−	0.632327i	0.0247387	−	0.0294824i
$461$	−3.65740	+	10.0486i	−0.170342	+	0.468011i	−0.995261	−	0.0972402i	$-0.968998\pi$
$461$	−3.65740	+	10.0486i	−0.170342	+	0.468011i	0.824919	+	0.565251i	$0.191221\pi$
$462$	0.671516	+	0.489159i	0.0312418	+	0.0227577i
$463$	−11.7521	+	20.3552i	−0.546166	+	0.945987i	0.452367	+	0.891832i	$0.350580\pi$
$463$	−11.7521	+	20.3552i	−0.546166	+	0.945987i	−0.998533	+	0.0541548i	$0.982754\pi$
$464$	−12.1728	−	7.02796i	−0.565107	−	0.326265i
$465$	2.40287	−	2.86363i	0.111430	−	0.132798i
$466$	−1.43635	+	1.71177i	−0.0665375	+	0.0792963i
$467$	23.2945	+	13.4491i	1.07794	+	0.622349i	0.930340	−	0.366698i	$-0.119512\pi$
$467$	23.2945	+	13.4491i	1.07794	+	0.622349i	0.147601	+	0.989047i	$0.452845\pi$
$468$	−4.05617	+	7.02549i	−0.187497	+	0.324754i
$469$	20.2472	+	14.7489i	0.934930	+	0.681040i
$470$	−2.38183	+	6.54401i	−0.109865	+	0.301853i
$471$	−2.24778	+	2.67880i	−0.103572	+	0.123433i
$472$	−4.62413	+	0.815359i	−0.212843	+	0.0375299i
$473$	−2.12089	−	0.771941i	−0.0975186	−	0.0354939i
$474$	0.0784078	+	0.135806i	0.00360139	+	0.00623779i
$475$	−16.1133	+	8.53985i	−0.739330	+	0.391835i
$476$	8.40391	−	17.1764i	0.385192	−	0.787281i
$477$	−4.21495	+	0.743210i	−0.192989	+	0.0340292i
$478$	−0.267220	+	0.734181i	−0.0122224	+	0.0335807i
$479$	−30.5927	−	5.39433i	−1.39782	−	0.246473i	−0.576572	−	0.817047i	$-0.695610\pi$
$479$	−30.5927	−	5.39433i	−1.39782	−	0.246473i	−0.821246	+	0.570574i	$0.806721\pi$
$480$	5.75966	−	4.83292i	0.262891	−	0.220592i
$481$	−19.7504	−	3.48253i	−0.900540	−	0.158790i
$482$	2.71857	+	1.56957i	0.123828	+	0.0714919i
$483$	−0.331189	−	0.162041i	−0.0150696	−	0.00737311i
$484$	−2.99703	+	16.9970i	−0.136229	+	0.772590i
$485$	13.1199	+	36.0468i	0.595746	+	1.63680i
$486$			0.213175i			0.00966979i
$487$	−27.0781	+	15.6335i	−1.22702	+	0.708423i	−0.966406	−	0.257020i	$-0.917260\pi$
$487$	−27.0781	+	15.6335i	−1.22702	+	0.708423i	−0.260618	+	0.965442i	$0.583926\pi$
$488$	1.18220	−	6.70459i	0.0535157	−	0.303502i
$489$	8.05564	+	2.93201i	0.364289	+	0.132590i
$490$	3.82902	+	2.40587i	0.172978	+	0.108686i
$491$	−0.417594	+	0.350403i	−0.0188458	+	0.0158135i	−0.652162	−	0.758080i	$-0.726138\pi$
$491$	−0.417594	+	0.350403i	−0.0188458	+	0.0158135i	0.633316	+	0.773893i	$0.281693\pi$
$492$	−13.5815	+	11.3963i	−0.612303	+	0.513783i
$493$	−6.96833	+	12.0695i	−0.313838	+	0.543583i
$494$	0.531609	+	3.81983i	0.0239182	+	0.171862i
$495$	−3.86586	+	2.23196i	−0.173758	+	0.100319i
$496$	−0.798846	−	4.53048i	−0.0358692	−	0.203424i
$497$	19.3393	+	5.57144i	0.867487	+	0.249913i
$498$	−3.03950	+	1.10629i	−0.136203	+	0.0495740i
$499$	−4.49710	−	25.5043i	−0.201318	−	1.14173i	−0.903130	−	0.429368i	$-0.858736\pi$
$499$	−4.49710	−	25.5043i	−0.201318	−	1.14173i	0.701812	−	0.712362i	$-0.252375\pi$
$500$	1.65365	+	4.54337i	0.0739536	+	0.203186i
$501$	−7.13770	−	12.3629i	−0.318889	−	0.552332i
$502$	0.184831	−	0.320137i	0.00824942	−	0.0142884i
$503$	20.3290	+	3.58454i	0.906423	+	0.159827i	0.607379	−	0.794412i	$-0.292221\pi$
$503$	20.3290	+	3.58454i	0.906423	+	0.159827i	0.299044	+	0.954239i	$0.403332\pi$
$504$	−1.80280	−	1.31323i	−0.0803031	−	0.0584960i
$505$	−19.0598	−	33.0125i	−0.848149	−	1.46904i
$506$		−	0.0437595i		−	0.00194535i
$507$	3.97156	−	1.44553i	0.176383	−	0.0641983i
$508$	−15.9595	−	19.0198i	−0.708087	−	0.843865i
$509$	26.3350	+	22.0977i	1.16728	+	0.979464i	0.999979	−	0.00644227i	$-0.00205065\pi$
$509$	26.3350	+	22.0977i	1.16728	+	0.979464i	0.167300	+	0.985906i	$0.446495\pi$
$510$	−1.53550	−	1.82994i	−0.0679933	−	0.0810312i
$511$	−8.19921	−	33.0599i	−0.362712	−	1.46249i
$512$		−	15.5406i		−	0.686806i
$513$	−2.67899	−	3.43846i	−0.118280	−	0.151812i
$514$	−0.853371	−	0.492694i	−0.0376406	−	0.0217318i
$515$	13.8112	−	37.9461i	0.608596	−	1.67210i
$516$	2.81423	+	1.02430i	0.123890	+	0.0450922i
$517$	−5.43090	−	14.9213i	−0.238851	−	0.656236i
$518$	0.754438	−	2.61877i	0.0331481	−	0.115062i
$519$	−4.22029	−	3.54124i	−0.185250	−	0.155443i
$520$	−10.6033			−0.464985
$521$	−4.50208			−0.197240			−0.0986198	−	0.995125i	$-0.531443\pi$
$521$	−4.50208			−0.197240			−0.0986198	+	0.995125i	$0.531443\pi$
$522$	0.615473	+	0.516443i	0.0269385	+	0.0226041i
$523$	−6.90340	+	2.51263i	−0.301865	+	0.109870i	−0.488512	−	0.872557i	$-0.662460\pi$
$523$	−6.90340	+	2.51263i	−0.301865	+	0.109870i	0.186647	+	0.982427i	$0.440238\pi$
$524$	−38.2708	+	22.0956i	−1.67187	+	0.965252i
$525$	−9.18438	+	6.17837i	−0.400839	+	0.269646i
$526$	1.53996	−	1.83526i	0.0671456	−	0.0800210i
$527$	−4.49204	+	0.792067i	−0.195676	+	0.0345030i
$528$	−0.953929	+	5.41000i	−0.0415144	+	0.235440i
$529$	−3.99054	−	22.6315i	−0.173502	−	0.983976i
$530$	−1.77727	−	2.11807i	−0.0771997	−	0.0920030i
$531$	−5.56988			−0.241712
$532$	22.5293	−	0.728440i	0.976768	−	0.0315819i
$533$	37.6482			1.63073
$534$	−0.916506	−	1.09225i	−0.0396611	−	0.0472662i
$535$	6.04527	+	34.2844i	0.261360	+	1.48224i
$536$	1.38597	−	7.86023i	0.0598648	−	0.339510i
$537$	10.3054	−	1.81711i	0.444709	−	0.0784142i
$538$	0.319958	−	0.381311i	0.0137944	−	0.0164395i
$539$	−10.2143	+	1.40968i	−0.439960	+	0.0607193i
$540$	5.12966	−	2.96161i	0.220745	−	0.127447i
$541$	10.1567	−	3.69672i	0.436669	−	0.158935i	−0.114326	−	0.993443i	$-0.536471\pi$
$541$	10.1567	−	3.69672i	0.436669	−	0.158935i	0.550995	+	0.834509i	$0.314248\pi$
$542$	−3.24484	−	2.72274i	−0.139378	−	0.116952i
$543$	−14.9230			−0.640407
$544$	−9.17428			−0.393344
$545$	−27.7968	−	23.3243i	−1.19068	−	0.999103i
$546$	0.563495	+	2.27206i	0.0241154	+	0.0972353i
$547$	−9.79652	−	26.9157i	−0.418869	−	1.15083i	−0.952346	−	0.305018i	$-0.901337\pi$
$547$	−9.79652	−	26.9157i	−0.418869	−	1.15083i	0.533478	−	0.845814i	$-0.320885\pi$
$548$	0.711674	+	0.259028i	0.0304012	+	0.0110651i
$549$	2.76210	−	7.58880i	0.117883	−	0.323882i
$550$	−1.13772	−	0.656864i	−0.0485126	−	0.0280088i
$551$	−16.4177	−	0.595409i	−0.699416	−	0.0253653i
$552$			0.117480i			0.00500027i
$553$	−1.87021	−	0.538786i	−0.0795293	−	0.0229115i
$554$	0.697530	+	0.831284i	0.0296352	+	0.0353179i
$555$	11.2173	+	9.41246i	0.476150	+	0.399537i
$556$	−23.4343	−	27.9280i	−0.993838	−	1.18441i
$557$	40.3340	−	14.6804i	1.70901	−	0.622028i	0.712209	−	0.701968i	$-0.247695\pi$
$557$	40.3340	−	14.6804i	1.70901	−	0.622028i	0.996800	+	0.0799397i	$0.0254728\pi$
$558$			0.262959i			0.0111320i
$559$	−3.17976	−	5.50750i	−0.134489	−	0.232942i
$560$	−3.16249	+	29.7341i	−0.133640	+	1.25650i
$561$	5.36410	+	0.945835i	0.226472	+	0.0399332i
$562$	−3.28623	+	5.69192i	−0.138621	+	0.240099i
$563$	1.27793	+	2.21343i	0.0538581	+	0.0932850i	0.891698	−	0.452632i	$-0.149515\pi$
$563$	1.27793	+	2.21343i	0.0538581	+	0.0932850i	−0.837839	+	0.545917i	$0.816181\pi$
$564$	7.20632	+	19.7992i	0.303441	+	0.833696i
$565$	7.73621	+	43.8742i	0.325465	+	1.84580i
$566$	5.54433	−	2.01797i	0.233045	−	0.0848216i
$567$	−1.83553	−	1.90547i	−0.0770850	−	0.0800224i
$568$	−1.11355	−	6.31524i	−0.0467234	−	0.264982i
$569$	−31.8354	+	18.3802i	−1.33461	+	0.770537i	−0.986002	−	0.166732i	$-0.946679\pi$
$569$	−31.8354	+	18.3802i	−1.33461	+	0.770537i	−0.348607	+	0.937269i	$0.613345\pi$
$570$	1.05837	−	2.60946i	0.0443304	−	0.109298i
$571$	13.2643	−	22.9744i	0.555093	−	0.961449i	−0.442804	−	0.896619i	$-0.646016\pi$
$571$	13.2643	−	22.9744i	0.555093	−	0.961449i	0.997896	−	0.0648302i	$-0.0206506\pi$
$572$	9.15391	−	7.68104i	0.382744	−	0.321160i
$573$	4.72995	−	3.96890i	0.197597	−	0.165803i
$574$	−0.541081	+	5.08731i	−0.0225843	+	0.212340i
$575$	0.547873	+	0.199409i	0.0228479	+	0.00831594i
$576$	1.20337	−	6.82463i	0.0501403	−	0.284360i
$577$	−2.87274	+	1.65858i	−0.119594	+	0.0690475i	−0.558604	−	0.829435i	$-0.688663\pi$
$577$	−2.87274	+	1.65858i	−0.119594	+	0.0690475i	0.439010	+	0.898482i	$0.355329\pi$
$578$		−	0.709139i		−	0.0294963i
$579$	−4.88347	−	13.4172i	−0.202950	−	0.557600i
$580$	3.87657	−	21.9851i	0.160966	−	0.912883i
$581$	17.6431	−	36.0602i	0.731961	−	1.49603i
$582$	−2.33688	−	1.34920i	−0.0968669	−	0.0559261i
$583$	6.20868	+	1.09476i	0.257137	+	0.0453402i
$584$	−8.31384	+	6.97614i	−0.344029	+	0.288675i
$585$	−12.3868	−	2.18413i	−0.512131	−	0.0903025i
$586$	2.45751	−	6.75195i	0.101519	−	0.278920i
$587$	−1.54602	+	0.272606i	−0.0638112	+	0.0112516i	−0.205463	−	0.978665i	$-0.565870\pi$
$587$	−1.54602	+	0.272606i	−0.0638112	+	0.0112516i	0.141651	+	0.989917i	$0.454759\pi$
$588$	13.5534	−	1.87052i	0.558934	−	0.0771390i
$589$	−3.30464	−	4.24148i	−0.136165	−	0.174767i
$590$	−1.79912	−	3.11617i	−0.0740686	−	0.128291i
$591$	4.43140	+	1.61290i	0.182283	+	0.0663457i
$592$	17.7467	−	3.12922i	0.729384	−	0.128610i
$593$	27.7604	−	33.0836i	1.13998	−	1.35858i	0.215890	−	0.976418i	$-0.430735\pi$
$593$	27.7604	−	33.0836i	1.13998	−	1.35858i	0.924095	−	0.382163i	$-0.124821\pi$
$594$	0.107397	−	0.295072i	0.00440657	−	0.0121069i
$595$	29.4818	+	3.13566i	1.20864	+	0.128549i
$596$	10.7976	−	18.7020i	0.442287	−	0.766064i
$597$	−6.26167	−	3.61518i	−0.256273	−	0.147959i
$598$	0.0792558	−	0.0944534i	0.00324101	−	0.00386249i
$599$	−23.6276	+	28.1583i	−0.965397	+	1.15052i	0.0231693	+	0.999732i	$0.492624\pi$
$599$	−23.6276	+	28.1583i	−0.965397	+	1.15052i	−0.988567	+	0.150784i	$0.951820\pi$
$600$	3.05441	+	1.76346i	0.124696	+	0.0719931i
$601$	−8.27057	+	14.3250i	−0.337364	+	0.584331i	−0.983936	−	0.178522i	$-0.942869\pi$
$601$	−8.27057	+	14.3250i	−0.337364	+	0.584331i	0.646572	+	0.762853i	$0.276202\pi$
$602$	0.789914	−	0.350519i	0.0321945	−	0.0142861i
$603$	3.23819	−	8.89686i	0.131869	−	0.362308i
$604$	−6.30389	+	7.51268i	−0.256502	+	0.305687i
$605$	−26.3532	+	4.64678i	−1.07141	+	0.188918i
$606$	2.51976	+	0.917118i	0.102358	+	0.0372554i
$607$	−3.58105	−	6.20256i	−0.145350	−	0.251754i	0.784153	−	0.620567i	$-0.213098\pi$
$607$	−3.58105	−	6.20256i	−0.145350	−	0.251754i	−0.929504	+	0.368813i	$0.879764\pi$
$608$	−5.06430	−	9.55553i	−0.205385	−	0.387528i
$609$	−9.94825	+	0.683246i	−0.403124	+	0.0276865i
$610$	5.13788	−	0.905946i	0.208027	−	0.0366807i
$611$	15.3025	−	42.0433i	0.619074	−	1.70089i
$612$	−7.11768	−	1.25504i	−0.287715	−	0.0507319i
$613$	−0.692191	+	0.580817i	−0.0279573	+	0.0234590i	−0.656659	−	0.754187i	$-0.728031\pi$
$613$	−0.692191	+	0.580817i	−0.0279573	+	0.0234590i	0.628702	+	0.777646i	$0.283587\pi$
$614$	−3.16647	−	0.558334i	−0.127788	−	0.0225325i
$615$	−23.8060	−	13.7444i	−0.959952	−	0.554228i
$616$	1.83379	+	2.72600i	0.0738856	+	0.109834i
$617$	2.99425	−	16.9812i	0.120544	−	0.683638i	−0.863311	−	0.504672i	$-0.831614\pi$
$617$	2.99425	−	16.9812i	0.120544	−	0.683638i	0.983855	−	0.178966i	$-0.0572753\pi$
$618$	0.971536	+	2.66927i	0.0390809	+	0.107374i
$619$			35.8326i			1.44023i	0.693854	+	0.720116i	$0.255911\pi$
$619$			35.8326i			1.44023i	−0.693854	+	0.720116i	$0.744089\pi$
$620$	6.32764	−	3.65326i	0.254124	−	0.146719i
$621$	−0.0241992	+	0.137240i	−0.000971079	+	0.00550726i
$622$	6.09606	+	2.21878i	0.244430	+	0.0889651i
$623$	17.5970	+	1.87160i	0.705009	+	0.0749840i
$624$	−11.8575	+	9.94958i	−0.474678	+	0.398302i
$625$	−21.7672	+	18.2648i	−0.870688	+	0.730594i
$626$	0.894639	−	1.54956i	0.0357570	−	0.0619329i
$627$	1.97590	+	6.10912i	0.0789099	+	0.243975i
$628$	−5.91923	+	3.41747i	−0.236203	+	0.136372i
$629$	−3.10267	−	17.5961i	−0.123711	−	0.701603i
$630$	0.473159	−	1.64241i	0.0188511	−	0.0654350i
$631$	20.3581	−	7.40973i	0.810442	−	0.294977i	0.0966355	−	0.995320i	$-0.469192\pi$
$631$	20.3581	−	7.40973i	0.810442	−	0.294977i	0.713806	+	0.700343i	$0.246970\pi$
$632$	0.107686	+	0.610715i	0.00428350	+	0.0242929i
$633$	9.11380	+	25.0400i	0.362241	+	0.995249i
$634$	2.94395	+	5.09907i	0.116919	+	0.202510i
$635$	19.2479	−	33.3383i	0.763828	−	1.32299i
$636$	−8.23836	−	1.45265i	−0.326672	−	0.0576011i
$637$	−24.6003	−	15.4570i	−0.974701	−	0.612429i
$638$	−0.591741	−	1.02493i	−0.0234272	−	0.0405772i
$639$		−	7.60686i		−	0.300923i
$640$	18.3374	−	6.67427i	0.724849	−	0.263823i
$641$	−7.67362	−	9.14506i	−0.303090	−	0.361208i	0.592905	−	0.805272i	$-0.297981\pi$
$641$	−7.67362	−	9.14506i	−0.303090	−	0.361208i	−0.895995	+	0.444064i	$0.853536\pi$
$642$	−1.87597	−	1.57412i	−0.0740385	−	0.0621257i
$643$	11.4641	+	13.6624i	0.452100	+	0.538792i	0.943162	−	0.332333i	$-0.107836\pi$
$643$	11.4641	+	13.6624i	0.452100	+	0.538792i	−0.491062	+	0.871124i	$0.663391\pi$
$644$	−0.499965	−	0.519017i	−0.0197014	−	0.0204521i
$645$			4.64339i			0.182833i
$646$	−3.03596	+	1.60902i	−0.119448	+	0.0633059i
$647$	−35.0852	−	20.2564i	−1.37934	−	0.796363i	−0.387261	−	0.921970i	$-0.626579\pi$
$647$	−35.0852	−	20.2564i	−1.37934	−	0.796363i	−0.992080	+	0.125608i	$0.959912\pi$
$648$	−0.288327	+	0.792171i	−0.0113265	+	0.0311194i
$649$	7.70970	+	2.80610i	0.302632	+	0.110149i
$650$	−1.26604	−	3.47842i	−0.0496583	−	0.136435i
$651$	−2.26420	−	2.35048i	−0.0887410	−	0.0921225i
$652$	12.8356	+	10.7704i	0.502681	+	0.421800i
$653$	37.9121			1.48362			0.741808	−	0.670613i	$-0.233969\pi$
$653$	37.9121			1.48362			0.741808	+	0.670613i	$0.233969\pi$
$654$	2.55251			0.0998109
$655$	−52.4870	−	44.0418i	−2.05084	−	1.72086i
$656$	−31.7886	+	11.5701i	−1.24114	+	0.451737i
$657$	−11.1492	+	6.43702i	−0.434973	+	0.251132i
$658$	5.46128	+	2.67204i	0.212903	+	0.104167i
$659$	9.85601	−	11.7459i	0.383936	−	0.457557i	−0.539117	−	0.842231i	$-0.681242\pi$
$659$	9.85601	−	11.7459i	0.383936	−	0.457557i	0.923052	+	0.384674i	$0.125686\pi$
$660$	−8.59242	+	1.51508i	−0.334460	+	0.0589742i
$661$	−0.862166	+	4.88959i	−0.0335344	+	0.190183i	−0.996973	−	0.0777453i	$-0.975228\pi$
$661$	−0.862166	+	4.88959i	−0.0335344	+	0.190183i	0.963439	+	0.267928i	$0.0863390\pi$
$662$	0.0518572	+	0.294097i	0.00201549	+	0.0114304i
$663$	9.86516	+	11.7568i	0.383131	+	0.456598i
$664$	−12.7913			−0.496399
$665$	13.0083	+	32.4379i	0.504442	+	1.25789i
$666$	−1.03006			−0.0399139
$667$	0.337612	+	0.402350i	0.0130724	+	0.0155791i
$668$	−4.84515	−	27.4782i	−0.187464	−	1.06316i
$669$	−4.25540	+	24.1336i	−0.164523	+	0.933059i
$670$	6.02348	−	1.06210i	0.232707	−	0.0410326i
$671$	−7.64647	+	9.11271i	−0.295189	+	0.351792i
$672$	−3.66390	−	5.44652i	−0.141338	−	0.210104i
$673$	−31.3858	+	18.1206i	−1.20983	+	0.698498i	−0.962723	−	0.270489i	$-0.912815\pi$
$673$	−31.3858	+	18.1206i	−1.20983	+	0.698498i	−0.247111	+	0.968987i	$0.579481\pi$
$674$	3.02939	−	1.10261i	0.116688	−	0.0424709i
$675$	3.20492	+	2.68925i	0.123357	+	0.103509i
$676$	8.26083			0.317724
$677$	4.46385			0.171560			0.0857799	−	0.996314i	$-0.472662\pi$
$677$	4.46385			0.171560			0.0857799	+	0.996314i	$0.472662\pi$
$678$	−2.40070	−	2.01443i	−0.0921983	−	0.0773636i
$679$	32.5056	−	8.06172i	1.24745	−	0.309381i
$680$	−3.23097	−	8.87702i	−0.123902	−	0.340418i
$681$	7.82696	+	2.84878i	0.299930	+	0.109166i
$682$	0.132479	−	0.363983i	0.00507288	−	0.0139376i
$683$	2.39388	+	1.38211i	0.0915991	+	0.0528848i	0.545100	−	0.838371i	$-0.316492\pi$
$683$	2.39388	+	1.38211i	0.0915991	+	0.0528848i	−0.453501	+	0.891256i	$0.649825\pi$
$684$	−2.62184	−	8.10626i	−0.100249	−	0.309951i
$685$			1.17424i			0.0448653i
$686$	2.44223	−	3.10203i	0.0932446	−	0.118436i
$687$	7.91688	+	9.43497i	0.302048	+	0.359967i
$688$	4.37743	+	3.67310i	0.166888	+	0.140036i
$689$	11.4184	+	13.6080i	0.435008	+	0.518422i
$690$	−0.0845982	+	0.0307912i	−0.00322060	+	0.00117220i
$691$			28.3399i			1.07810i	0.842273	+	0.539051i	$0.181217\pi$
$691$			28.3399i			1.07810i	−0.842273	+	0.539051i	$0.818783\pi$
$692$	−5.38402	−	9.32539i	−0.204670	−	0.354498i
$693$	1.58072	+	3.56226i	0.0600468	+	0.135319i
$694$	5.57432	+	0.982903i	0.211598	+	0.0373105i
$695$	28.2629	−	48.9528i	1.07207	−	1.85688i
$696$	1.58863	+	2.75159i	0.0602169	+	0.104299i
$697$	11.4719	+	31.5189i	0.434531	+	1.19386i
$698$	0.812489	+	4.60785i	0.0307532	+	0.174410i
$699$	−9.85013	+	3.58516i	−0.372566	+	0.135603i
$700$	−20.9990	+	5.20797i	−0.793688	+	0.196843i
$701$	2.77178	+	15.7196i	0.104689	+	0.593720i	0.991344	+	0.131289i	$0.0419116\pi$
$701$	2.77178	+	15.7196i	0.104689	+	0.593720i	−0.886655	+	0.462431i	$0.846977\pi$
$702$	0.766238	−	0.442388i	0.0289198	−	0.0166969i
$703$	16.6146	−	12.9449i	0.626633	−	0.488224i
$704$	−5.10393	+	8.84026i	−0.192361	+	0.333180i
$705$	−25.0252	+	20.9986i	−0.942502	+	0.790853i
$706$	0.160106	−	0.134345i	0.00602566	−	0.00505613i
$707$	−30.4198	+	13.4986i	−1.14406	+	0.507667i
$708$	−10.2301	−	3.72345i	−0.384470	−	0.139936i
$709$	0.925022	−	5.24606i	0.0347399	−	0.197020i	−0.962498	−	0.271287i	$-0.912551\pi$
$709$	0.925022	−	5.24606i	0.0347399	−	0.197020i	0.997238	+	0.0742673i	$0.0236618\pi$
$710$	4.25580	−	2.45709i	0.159717	−	0.0922128i
$711$			0.735621i			0.0275879i
$712$	−1.92849	−	5.29848i	−0.0722732	−	0.198569i
$713$	−0.0298506	+	0.169291i	−0.00111792	+	0.00634001i
$714$	−1.73046	+	1.16409i	−0.0647607	+	0.0435648i
$715$	16.0452	+	9.26369i	0.600055	+	0.346442i
$716$	20.1424	+	3.55165i	0.752757	+	0.132731i
$717$	−2.80760	+	2.35586i	−0.104852	+	0.0879812i
$718$	2.13213	+	0.375952i	0.0795705	+	0.0140304i
$719$	9.71000	−	26.6780i	0.362122	−	0.994922i	−0.616156	−	0.787624i	$-0.711311\pi$
$719$	9.71000	−	26.6780i	0.362122	−	0.994922i	0.978278	−	0.207298i	$-0.0664668\pi$
$720$	11.1301	−	1.96254i	0.414796	−	0.0731397i
$721$	−31.6678	−	15.4941i	−1.17937	−	0.577030i
$722$	−3.35176	−	2.27393i	−0.124740	−	0.0846267i
$723$	7.36283	+	12.7528i	0.273827	+	0.474282i
$724$	−27.4088	−	9.97599i	−1.01864	−	0.370755i
$725$	15.5287	−	2.73813i	0.576721	−	0.101691i
$726$	1.20997	−	1.44199i	0.0449063	−	0.0535172i
$727$	10.3257	−	28.3696i	0.382959	−	1.05217i	−0.587145	−	0.809482i	$-0.699748\pi$
$727$	10.3257	−	28.3696i	0.382959	−	1.05217i	0.970104	−	0.242689i	$-0.0780295\pi$
$728$	−0.979065	+	9.20529i	−0.0362866	+	0.341171i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−7.20262	−	4.15843i	−0.266581	−	0.153910i
$731$	3.64193	−	4.34029i	0.134702	−	0.160531i
$732$	10.1462	−	12.0918i	0.375014	−	0.446924i
$733$	11.3819	+	6.57137i	0.420401	+	0.242719i	0.695249	−	0.718769i	$-0.255294\pi$
$733$	11.3819	+	6.57137i	0.420401	+	0.242719i	−0.274848	+	0.961488i	$0.588627\pi$
$734$	−2.01156	+	3.48413i	−0.0742481	+	0.128601i
$735$	9.91251	+	18.7549i	0.365629	+	0.691783i
$736$	−0.118254	+	0.324900i	−0.00435889	+	0.0119760i
$737$	−8.96447	+	10.6834i	−0.330211	+	0.393530i
$738$	1.90429	−	0.335778i	0.0700980	−	0.0123602i
$739$	18.2766	+	6.65215i	0.672316	+	0.244703i	0.655545	−	0.755156i	$-0.272439\pi$
$739$	18.2766	+	6.65215i	0.672316	+	0.244703i	0.0167715	+	0.999859i	$0.494661\pi$
$740$	14.3105	+	24.7865i	0.526064	+	0.911169i
$741$	−6.79973	+	16.7650i	−0.249794	+	0.615879i
$742$	−2.00292	+	1.34737i	−0.0735294	+	0.0494635i
$743$	−27.2277	+	4.80097i	−0.998887	+	0.176131i	−0.649104	−	0.760700i	$-0.724856\pi$
$743$	−27.2277	+	4.80097i	−0.998887	+	0.176131i	−0.349783	+	0.936831i	$0.613745\pi$
$744$	−0.355662	+	0.977174i	−0.0130392	+	0.0358250i
$745$	32.9739	+	5.81418i	1.20807	+	0.213015i
$746$	3.03891	−	2.54995i	0.111262	−	0.0933603i
$747$	−14.9428	−	2.63483i	−0.546730	−	0.0964032i
$748$	9.21985	+	5.32309i	0.337111	+	0.194631i
$749$	30.3223	−	2.08254i	1.10795	−	0.0760943i
$750$	0.0915693	−	0.519315i	0.00334364	−	0.0189627i
$751$	8.79091	+	24.1528i	0.320785	+	0.881350i	0.990349	+	0.138595i	$0.0442587\pi$
$751$	8.79091	+	24.1528i	0.320785	+	0.881350i	−0.669564	+	0.742754i	$0.733519\pi$
$752$			40.2025i			1.46603i
$753$	1.50176	−	0.867042i	0.0547272	−	0.0315967i
$754$	0.579060	−	3.28401i	0.0210881	−	0.119597i
$755$	−14.2885	−	5.20061i	−0.520013	−	0.189269i
$756$	−2.09748	−	4.72680i	−0.0762847	−	0.171912i
$757$	17.6108	−	14.7772i	0.640077	−	0.537088i	−0.263965	−	0.964532i	$-0.585030\pi$
$757$	17.6108	−	14.7772i	0.640077	−	0.537088i	0.904042	+	0.427444i	$0.140586\pi$
$758$	−2.85857	+	2.39863i	−0.103828	+	0.0871221i
$759$	0.102638	−	0.177774i	0.00372551	−	0.00645277i
$760$	7.46239	−	8.26545i	0.270689	−	0.299820i
$761$	16.9600	−	9.79186i	0.614799	−	0.354954i	−0.160042	−	0.987110i	$-0.551163\pi$
$761$	16.9600	−	9.79186i	0.614799	−	0.354954i	0.774841	+	0.632156i	$0.217830\pi$
$762$	0.470228	+	2.66679i	0.0170346	+	0.0966078i
$763$	−22.8157	+	21.9782i	−0.825985	+	0.795666i
$764$	11.3406	−	4.12765i	0.410289	−	0.149333i
$765$	−1.94589	−	11.0357i	−0.0703538	−	0.398996i
$766$	−0.210602	−	0.578624i	−0.00760936	−	0.0209065i
$767$	11.5588	+	20.0205i	0.417365	+	0.722897i
$768$	6.24356	−	10.8142i	0.225295	−	0.390223i
$769$	−25.4110	−	4.48064i	−0.916344	−	0.161576i	−0.304461	−	0.952525i	$-0.598476\pi$
$769$	−25.4110	−	4.48064i	−0.916344	−	0.161576i	−0.611883	+	0.790949i	$0.709587\pi$
$770$	−1.48238	+	2.03501i	−0.0534213	+	0.0733366i
$771$	−2.31122	−	4.00315i	−0.0832366	−	0.144170i
$772$		−	27.9077i		−	1.00442i
$773$	−40.2503	+	14.6499i	−1.44770	+	0.526921i	−0.941949	−	0.335756i	$-0.891008\pi$
$773$	−40.2503	+	14.6499i	−1.44770	+	0.526921i	−0.505755	+	0.862677i	$0.668786\pi$
$774$	−0.209956	−	0.250216i	−0.00754672	−	0.00899383i
$775$	3.95340	+	3.31729i	0.142010	+	0.119161i
$776$	−6.85917	−	8.17444i	−0.246230	−	0.293445i
$777$	9.20724	−	8.86927i	0.330308	−	0.318183i
$778$		−	3.24309i		−	0.116271i
$779$	−26.4961	+	29.3475i	−0.949321	+	1.05148i
$780$	−21.2905	−	12.2921i	−0.762323	−	0.440127i
$781$	−3.83234	+	10.5293i	−0.137132	+	0.376766i
$782$	0.103226	+	0.0375713i	0.00369136	+	0.00134355i
$783$	1.28905	+	3.54165i	0.0460671	+	0.126568i
$784$	25.5218	+	5.49106i	0.911493	+	0.196109i
$785$	−8.11802	−	6.81182i	−0.289744	−	0.243124i
$786$	4.81974			0.171914
$787$	18.2444			0.650341			0.325171	−	0.945655i	$-0.394578\pi$
$787$	18.2444			0.650341			0.325171	+	0.945655i	$0.394578\pi$
$788$	7.06086	+	5.92476i	0.251533	+	0.211061i
$789$	10.5607	−	3.84379i	0.375971	−	0.136842i
$790$	−0.411557	+	0.237612i	−0.0146425	+	0.00845387i
$791$	38.8039	−	2.66505i	1.37971	−	0.0947584i
$792$	0.798191	−	0.951247i	0.0283625	−	0.0338011i
$793$	−33.0093	+	5.82044i	−1.17220	+	0.206690i
$794$	−0.256681	+	1.45571i	−0.00910928	+	0.0516613i
$795$	−2.25227	−	12.7733i	−0.0798799	−	0.453021i
$796$	−9.08396	−	10.8258i	−0.321972	−	0.383712i
$797$	40.6566			1.44013			0.720066	−	0.693906i	$-0.244112\pi$
$797$	40.6566			1.44013			0.720066	+	0.693906i	$0.244112\pi$
$798$	−2.16769	−	1.15978i	−0.0767354	−	0.0410557i
$799$	39.8614			1.41019
$800$	6.67212	+	7.95153i	0.235895	+	0.281129i
$801$	−1.16146	−	6.58694i	−0.0410380	−	0.232738i
$802$	−0.828337	+	4.69773i	−0.0292496	+	0.165883i
$803$	18.6755	−	3.29300i	0.659045	−	0.116207i
$804$	11.8951	−	14.1760i	0.419506	−	0.499948i
$805$	0.491059	−	1.00366i	0.0173076	−	0.0353743i
$806$	0.945185	−	0.545703i	0.0332927	−	0.0192216i
$807$	2.19420	−	0.798622i	0.0772394	−	0.0281128i
$808$	8.12317	+	6.81615i	0.285772	+	0.239791i
$809$	−46.0951			−1.62062			−0.810309	−	0.586003i	$-0.800701\pi$
$809$	−46.0951			−1.62062			−0.810309	+	0.586003i	$0.800701\pi$
$810$	−0.646018			−0.0226988
$811$	18.8216	+	15.7932i	0.660914	+	0.554573i	0.910361	−	0.413816i	$-0.135804\pi$
$811$	18.8216	+	15.7932i	0.660914	+	0.554573i	−0.249446	+	0.968389i	$0.580249\pi$
$812$	−18.7285	−	5.39548i	−0.657243	−	0.189344i
$813$	−6.79603	−	18.6719i	−0.238347	−	0.654853i
$814$	1.42578	+	0.518943i	0.0499737	+	0.0181889i
$815$	−8.88537	+	24.4123i	−0.311241	+	0.855127i
$816$	−11.9429	−	6.89522i	−0.418084	−	0.241381i
$817$	6.53104	+	1.39739i	0.228492	+	0.0488886i
$818$			3.87558i			0.135506i
$819$	−3.03990	+	10.5520i	−0.106223	+	0.368716i
$820$	−34.5360	−	41.1584i	−1.20605	−	1.43731i
$821$	−5.05992	−	4.24577i	−0.176592	−	0.148179i	0.550207	−	0.835028i	$-0.314549\pi$
$821$	−5.05992	−	4.24577i	−0.176592	−	0.148179i	−0.726800	+	0.686850i	$0.758993\pi$
$822$	−0.0530945	−	0.0632756i	−0.00185188	−	0.00220699i
$823$	−11.5826	+	4.21573i	−0.403745	+	0.146951i	−0.535907	−	0.844277i	$-0.680030\pi$
$823$	−11.5826	+	4.21573i	−0.403745	+	0.146951i	0.132162	+	0.991228i	$0.457808\pi$
$824$			11.2332i			0.391328i
$825$	−3.08134	−	5.33704i	−0.107279	−	0.185812i
$826$	−2.87144	+	1.27418i	−0.0999101	+	0.0443344i
$827$	−46.8260	−	8.25668i	−1.62830	−	0.287113i	−0.716449	−	0.697639i	$-0.754234\pi$
$827$	−46.8260	−	8.25668i	−1.62830	−	0.287113i	−0.911849	+	0.410526i	$0.865345\pi$
$828$	−0.136191	+	0.235890i	−0.00473297	+	0.00819774i
$829$	−16.8385	−	29.1651i	−0.584825	−	1.01295i	−0.994897	−	0.100894i	$-0.967830\pi$
$829$	−16.8385	−	29.1651i	−0.584825	−	1.01295i	0.410072	−	0.912053i	$-0.365504\pi$
$830$	−3.35257	−	9.21112i	−0.116369	−	0.319723i
$831$	0.883956	+	5.01316i	0.0306641	+	0.173905i
$832$	−27.0279	+	9.83734i	−0.937022	+	0.341048i
$833$	5.44447	−	25.3053i	0.188640	−	0.876775i
$834$	0.690467	+	3.91583i	0.0239089	+	0.135594i
$835$	37.4652	−	21.6306i	1.29654	−	0.748557i
$836$	−0.454832	+	12.5414i	−0.0157307	+	0.433753i
$837$	−0.616770	+	1.06828i	−0.0213187	+	0.0369250i
$838$	−5.45258	+	4.57526i	−0.188356	+	0.158050i
$839$	−9.21966	+	7.73621i	−0.318298	+	0.267084i	−0.787912	−	0.615788i	$-0.788838\pi$
$839$	−9.21966	+	7.73621i	−0.318298	+	0.267084i	0.469614	+	0.882872i	$0.344393\pi$
$840$	3.97971	−	5.46333i	0.137313	−	0.188503i
$841$	−13.9028	−	5.06021i	−0.479407	−	0.174490i
$842$	−0.242853	+	1.37729i	−0.00836927	+	0.0474645i
$843$	−26.7008	+	15.4157i	−0.919623	+	0.530945i
$844$			52.0830i			1.79277i
$845$	4.38063	+	12.0357i	0.150698	+	0.414040i
$846$	0.399042	−	2.26308i	0.0137194	−	0.0778064i
$847$	1.60077	+	23.3077i	0.0550032	+	0.800862i
$848$	−13.8233	−	7.98088i	−0.474694	−	0.274065i
$849$	27.2571	+	4.80616i	0.935460	+	0.164947i
$850$	2.52634	−	2.11985i	0.0866527	−	0.0727103i
$851$	−0.663144	−	0.116930i	−0.0227323	−	0.00400832i
$852$	5.08517	−	13.9714i	0.174215	−	0.478652i
$853$	14.2421	−	2.51127i	0.487641	−	0.0859843i	0.0755785	−	0.997140i	$-0.475920\pi$
$853$	14.2421	−	2.51127i	0.487641	−	0.0859843i	0.412062	+	0.911156i	$0.364809\pi$
$854$	−0.312090	−	4.54412i	−0.0106795	−	0.155497i
$855$	10.4201	−	8.11858i	0.356361	−	0.277650i
$856$	−4.84216	−	8.38686i	−0.165501	−	0.286657i
$857$	35.2949	+	12.8463i	1.20565	+	0.438820i	0.865193	−	0.501440i	$-0.167196\pi$
$857$	35.2949	+	12.8463i	1.20565	+	0.438820i	0.340457	+	0.940260i	$0.389418\pi$
$858$	−1.28349	+	0.226313i	−0.0438175	+	0.00772620i
$859$	−29.1603	+	34.7519i	−0.994937	+	1.18572i	−0.0123493	+	0.999924i	$0.503931\pi$
$859$	−29.1603	+	34.7519i	−0.994937	+	1.18572i	−0.982588	+	0.185797i	$0.940513\pi$
$860$	−3.10410	+	8.52844i	−0.105849	+	0.290817i
$861$	−14.1304	+	19.3982i	−0.481564	+	0.661089i
$862$	0.458298	−	0.793796i	0.0156097	−	0.0270368i
$863$	8.12423	+	4.69053i	0.276552	+	0.159667i	0.631861	−	0.775081i	$-0.282291\pi$
$863$	8.12423	+	4.69053i	0.276552	+	0.159667i	−0.355309	+	0.934749i	$0.615624\pi$
$864$	−1.59478	+	1.90058i	−0.0542555	+	0.0646592i
$865$	10.7316	−	12.7894i	0.364886	−	0.434854i
$866$	5.43912	+	3.14028i	0.184829	+	0.106711i
$867$	1.66328	−	2.88089i	0.0564881	−	0.0978402i
$868$	−2.58733	−	5.83069i	−0.0878196	−	0.197907i
$869$	0.370606	−	1.01823i	0.0125719	−	0.0345411i
$870$	−1.56506	+	1.86517i	−0.0530606	+	0.0632352i
$871$	−38.6990	+	6.82368i	−1.31127	+	0.231212i
$872$	9.48529	+	3.45236i	0.321212	+	0.116912i
$873$	−6.32908	−	10.9623i	−0.214207	−	0.371017i
$874$	0.0178494	+	0.128256i	0.000603766	+	0.00433831i
$875$	3.65304	+	5.43038i	0.123495	+	0.183580i
$876$	−24.7808	+	4.36952i	−0.837264	+	0.147632i
$877$	−0.492190	+	1.35228i	−0.0166201	+	0.0456632i	−0.947725	−	0.319088i	$-0.896624\pi$
$877$	−0.492190	+	1.35228i	−0.0166201	+	0.0456632i	0.931105	+	0.364751i	$0.118846\pi$
$878$	−2.93284	−	0.517139i	−0.0989786	−	0.0174526i
$879$	25.8203	−	21.6658i	0.870898	−	0.730771i
$880$	−16.3948	−	2.89085i	−0.552670	−	0.0974506i
$881$	25.9635	+	14.9900i	0.874732	+	0.505027i	0.868918	−	0.494956i	$-0.164816\pi$
$881$	25.9635	+	14.9900i	0.874732	+	0.505027i	0.00581411	+	0.999983i	$0.498149\pi$
$882$	−1.38217	−	0.562428i	−0.0465402	−	0.0189379i
$883$	9.42350	−	53.4434i	0.317126	−	1.79851i	−0.242915	−	0.970047i	$-0.578104\pi$
$883$	9.42350	−	53.4434i	0.317126	−	1.79851i	0.560042	−	0.828465i	$-0.310785\pi$
$884$	10.2597	+	28.1884i	0.345073	+	0.948079i
$885$		−	16.8793i		−	0.567392i
$886$	−1.31793	+	0.760907i	−0.0442767	+	0.0255632i
$887$	−4.99202	+	28.3112i	−0.167616	+	0.950596i	0.778711	+	0.627383i	$0.215874\pi$
$887$	−4.99202	+	28.3112i	−0.167616	+	0.950596i	−0.946326	+	0.323213i	$0.895237\pi$
$888$	−3.82777	−	1.39319i	−0.128451	−	0.0467525i
$889$	−27.1655	−	19.7884i	−0.911101	−	0.663682i
$890$	3.31002	−	2.77744i	0.110952	−	0.0931000i
$891$	1.12839	−	0.946834i	0.0378026	−	0.0317201i
$892$	−23.9491	+	41.4810i	−0.801874	+	1.38889i
$893$	22.0039	+	41.5179i	0.736333	+	1.38934i
$894$	−2.03974	+	1.17765i	−0.0682192	+	0.0393863i
$895$	5.50670	+	31.2300i	0.184069	+	1.04390i
$896$	−4.10109	−	16.5360i	−0.137008	−	0.552428i
$897$	0.543518	−	0.197824i	0.0181475	−	0.00660516i
$898$	−1.11585	−	6.32830i	−0.0372364	−	0.211178i
$899$	1.59010	+	4.36876i	0.0530328	+	0.145706i
$900$	4.08867	+	7.08178i	0.136289	+	0.236059i
$901$	−7.91316	+	13.7060i	−0.263626	+	0.456613i
$902$	−2.80505	−	0.494605i	−0.0933978	−	0.0164686i
$903$	4.03118	+	0.428752i	0.134149	+	0.0142680i
$904$	−6.19658	−	10.7328i	−0.206095	−	0.356967i
$905$		−	45.2236i		−	1.50328i
$906$	1.00511	−	0.365830i	0.0333926	−	0.0121539i
$907$	−1.69405	−	2.01889i	−0.0562500	−	0.0670362i	0.737186	−	0.675690i	$-0.236154\pi$
$907$	−1.69405	−	2.01889i	−0.0562500	−	0.0670362i	−0.793436	+	0.608654i	$0.791710\pi$
$908$	12.4712	+	10.4646i	0.413873	+	0.347280i
$909$	8.08548	+	9.63590i	0.268178	+	0.319603i
$910$	−6.88541	+	1.70765i	−0.228249	+	0.0566082i
$911$			33.9502i			1.12482i	0.826859	+	0.562410i	$0.190126\pi$
$911$			33.9502i			1.12482i	−0.826859	+	0.562410i	$0.809874\pi$
$912$	0.589163	−	16.2454i	0.0195091	−	0.537940i
$913$	19.3561	+	11.1753i	0.640595	+	0.369847i
$914$	−1.52311	+	4.18470i	−0.0503799	+	0.138418i
$915$	22.9976	+	8.37045i	0.760277	+	0.276718i
$916$	8.23354	+	22.6215i	0.272044	+	0.747434i
$917$	−43.0815	+	41.5002i	−1.42268	+	1.37046i
$918$	0.603849	+	0.506689i	0.0199300	+	0.0167232i
$919$	17.3874			0.573556			0.286778	−	0.957997i	$-0.407416\pi$
$919$	17.3874			0.573556			0.286778	+	0.957997i	$0.407416\pi$
$920$	−0.356019			−0.0117376
$921$	−11.5543	−	9.69518i	−0.380726	−	0.319467i
$922$	2.14211	−	0.779664i	0.0705466	−	0.0256769i
$923$	−27.3422	+	15.7860i	−0.899980	+	0.519604i
$924$	0.521930	+	7.59944i	0.0171702	+	0.250003i
$925$	−12.9944	+	15.4862i	−0.427254	+	0.509182i
$926$	4.93437	−	0.870063i	0.162153	−	0.0285920i
$927$	−2.31389	+	13.1227i	−0.0759980	+	0.431006i
$928$	1.62376	+	9.20883i	0.0533027	+	0.302294i
$929$	−33.9961	−	40.5149i	−1.11537	−	1.32925i	−0.938603	−	0.345000i	$-0.887879\pi$
$929$	−33.9961	−	40.5149i	−1.11537	−	1.32925i	−0.176772	−	0.984252i	$-0.556566\pi$
$930$	−0.796889			−0.0261310
$931$	29.3623	−	8.29806i	0.962309	−	0.271958i
$932$	−20.4882			−0.671114
$933$	19.5612	+	23.3121i	0.640405	+	0.763205i
$934$	−0.995700	−	5.64689i	−0.0325803	−	0.184772i
$935$	−2.86632	+	16.2557i	−0.0937387	+	0.531619i
$936$	3.44574	−	0.607577i	0.112628	−	0.0198593i
$937$	0.188292	−	0.224398i	0.00615123	−	0.00733075i	−0.762960	−	0.646446i	$-0.776255\pi$
$937$	0.188292	−	0.224398i	0.00615123	−	0.00733075i	0.769111	+	0.639115i	$0.220699\pi$
$938$	−0.365884	−	5.32738i	−0.0119465	−	0.173945i
$939$	7.26898	−	4.19675i	0.237214	−	0.136956i
$940$	−60.0008	+	21.8385i	−1.95701	+	0.712293i
$941$	20.2968	+	17.0310i	0.661657	+	0.555196i	0.910583	−	0.413326i	$-0.135633\pi$
$941$	20.2968	+	17.0310i	0.661657	+	0.555196i	−0.248926	+	0.968523i	$0.580078\pi$
$942$	0.745456			0.0242883
$943$	1.26409			0.0411643
$944$	−15.9125	−	13.3522i	−0.517908	−	0.434577i
$945$	5.77447	−	5.56251i	0.187844	−	0.180949i
$946$	0.164558	+	0.452120i	0.00535025	+	0.0146997i
$947$	14.5095	+	5.28104i	0.471497	+	0.171611i	0.566830	−	0.823835i	$-0.308170\pi$
$947$	14.5095	+	5.28104i	0.471497	+	0.171611i	−0.0953336	+	0.995445i	$0.530392\pi$
$948$	−0.491761	+	1.35110i	−0.0159717	+	0.0438818i
$949$	46.2747	+	26.7167i	1.50214	+	0.867260i
$950$	3.60251	+	1.46114i	0.116881	+	0.0474058i
$951$			27.6201i			0.895643i
$952$	−8.00496	+	1.98531i	−0.259442	+	0.0643444i
$953$	1.76461	+	2.10298i	0.0571613	+	0.0681222i	0.793867	−	0.608091i	$-0.208064\pi$
$953$	1.76461	+	2.10298i	0.0571613	+	0.0681222i	−0.736706	+	0.676213i	$0.763620\pi$
$954$	0.698925	+	0.586468i	0.0226285	+	0.0189876i
$955$	12.0276	+	14.3340i	0.389205	+	0.463836i
$956$	−6.73156	+	2.45009i	−0.217714	+	0.0792415i
$957$		−	5.55170i		−	0.179461i
$958$	3.31110	+	5.73499i	0.106977	+	0.185289i
$959$	1.01942	+	0.108424i	0.0329188	+	0.00350121i
$960$	20.6818	+	3.64676i	0.667503	+	0.117699i
$961$	14.7392	−	25.5290i	0.475458	−	0.823517i
$962$	2.13762	+	3.70246i	0.0689195	+	0.119372i
$963$	−3.92905	−	10.7950i	−0.126612	−	0.347863i
$964$	4.99797	+	28.3449i	0.160974	+	0.912927i
$965$	40.6604	−	14.7992i	1.30890	−	0.476402i
$966$	0.0189201	+	0.0762874i	0.000608743	+	0.00245451i
$967$	−1.48648	−	8.43023i	−0.0478019	−	0.271098i	0.951534	−	0.307544i	$-0.0995073\pi$
$967$	−1.48648	−	8.43023i	−0.0478019	−	0.271098i	−0.999336	+	0.0364465i	$0.988396\pi$
$968$	6.44668	−	3.72199i	0.207204	−	0.119629i
$969$	−16.1076	−	0.584164i	−0.517450	−	0.0187660i
$970$	4.08870	−	7.08184i	0.131280	−	0.227384i
$971$	−20.8209	+	17.4708i	−0.668175	+	0.560665i	−0.912525	−	0.409022i	$-0.865870\pi$
$971$	−20.8209	+	17.4708i	−0.668175	+	0.560665i	0.244350	+	0.969687i	$0.421426\pi$
$972$	−1.49728	+	1.25636i	−0.0480252	+	0.0402979i
$973$	−39.8889	−	29.0566i	−1.27878	−	0.931513i
$974$	6.26337	+	2.27968i	0.200691	+	0.0730457i
$975$	3.01531	−	17.1007i	0.0965671	−	0.547659i
$976$	26.0830	−	15.0590i	0.834896	−	0.482028i
$977$		−	2.71980i		−	0.0870142i	−0.999053	−	0.0435071i	$-0.986147\pi$
$977$		−	2.71980i		−	0.0870142i	0.999053	−	0.0435071i	$-0.0138531\pi$
$978$	−0.625031	−	1.71726i	−0.0199863	−	0.0549118i
$979$	−1.71084	+	9.70264i	−0.0546786	+	0.310098i
$980$	5.66855	+	41.0732i	0.181075	+	1.31204i
$981$	10.3696	+	5.98689i	0.331076	+	0.191147i
$982$	0.114442	+	0.0201793i	0.00365201	+	0.000643947i
$983$	38.1706	−	32.0289i	1.21745	−	1.02156i	0.218499	−	0.975837i	$-0.429884\pi$
$983$	38.1706	−	32.0289i	1.21745	−	1.02156i	0.998954	−	0.0457275i	$-0.0145606\pi$
$984$	7.53063	+	1.32785i	0.240068	+	0.0423304i
$985$	−4.88783	+	13.4292i	−0.155739	+	0.427890i
$986$	2.92580	−	0.515898i	0.0931766	−	0.0164295i
$987$	15.9193	+	23.6646i	0.506717	+	0.753253i
$988$	−23.6963	+	26.2464i	−0.753881	+	0.835010i
$989$	−0.106764	−	0.184921i	−0.00339491	−	0.00588015i
$990$	0.894205	+	0.325464i	0.0284197	+	0.0103439i
$991$	−16.0421	+	2.82865i	−0.509593	+	0.0898550i	−0.422532	−	0.906348i	$-0.638859\pi$
$991$	−16.0421	+	2.82865i	−0.509593	+	0.0898550i	−0.0870610	+	0.996203i	$0.527748\pi$
$992$	−1.96722	+	2.34445i	−0.0624594	+	0.0744362i
$993$	−0.479132	+	1.31641i	−0.0152048	+	0.0417749i
$994$	−1.74017	−	3.92157i	−0.0551947	−	0.124385i
$995$	10.9557	−	18.9758i	0.347318	−	0.601573i
$996$	−25.6839	−	14.8286i	−0.813825	−	0.469862i
$997$	28.1507	−	33.5487i	0.891541	−	1.06250i	−0.106134	−	0.994352i	$-0.533847\pi$
$997$	28.1507	−	33.5487i	0.891541	−	1.06250i	0.997675	−	0.0681455i	$-0.0217082\pi$
$998$	−3.54867	+	4.22913i	−0.112331	+	0.133871i
$999$	−4.18463	−	2.41600i	−0.132396	−	0.0764388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.ck.a.10.7	yes	78
7.5	odd	6		399.2.cd.a.124.7	✓	78
19.2	odd	18		399.2.cd.a.325.7	yes	78
133.40	even	18	inner	399.2.ck.a.40.7	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.cd.a.124.7	✓	78	7.5	odd	6
399.2.cd.a.325.7	yes	78	19.2	odd	18
399.2.ck.a.10.7	yes	78	1.1	even	1	trivial
399.2.ck.a.40.7	yes	78	133.40	even	18	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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.137026 - 0.163301i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.339405 - 1.92486i) q^{4} +(2.98443 - 0.526235i) q^{5} +(-0.137026 + 0.163301i) q^{6} +(-0.181283 - 2.63953i) q^{7} +(-0.730069 + 0.421505i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.494879 - 0.415253i) q^{10} +1.47301 q^{11} -1.95456 q^{12} +(3.17945 + 2.66787i) q^{13} +(-0.406198 + 0.391288i) q^{14} +(-1.03648 - 2.84771i) q^{15} +(-3.50449 - 1.27553i) q^{16} +(-1.26471 + 3.47476i) q^{17} +(0.184615 + 0.106587i) q^{18} +(-4.31729 + 0.600840i) q^{19} -5.92322i q^{20} +(-2.56795 + 0.636879i) q^{21} +(-0.201841 - 0.240545i) q^{22} +(0.106754 + 0.0895772i) q^{23} +(0.541877 + 0.645784i) q^{24} +(3.93142 - 1.43092i) q^{25} -0.884776i q^{26} +(0.500000 + 0.866025i) q^{27} +(-5.14227 - 0.546926i) q^{28} +(3.71169 + 0.654470i) q^{29} +(-0.323009 + 0.559468i) q^{30} +(0.616770 + 1.06828i) q^{31} +(0.848564 + 2.33141i) q^{32} +(-0.255786 - 1.45063i) q^{33} +(0.740730 - 0.269604i) q^{34} +(-1.93004 - 7.78210i) q^{35} +(0.339405 + 1.92486i) q^{36} +(-4.18463 + 2.41600i) q^{37} +(0.689699 + 0.622688i) q^{38} +(2.07524 - 3.59442i) q^{39} +(-1.95703 + 1.64214i) q^{40} +(6.94865 - 5.83061i) q^{41} +(0.455879 + 0.332081i) q^{42} +(-1.43983 - 0.524056i) q^{43} +(0.499948 - 2.83535i) q^{44} +(-2.62446 + 1.51523i) q^{45} -0.0297075i q^{46} +(-3.68693 - 10.1298i) q^{47} +(-0.647604 + 3.67275i) q^{48} +(-6.93427 + 0.957006i) q^{49} +(-0.772377 - 0.445932i) q^{50} +(3.64158 + 0.642109i) q^{51} +(6.21441 - 5.21451i) q^{52} +(4.21495 + 0.743210i) q^{53} +(0.0729100 - 0.200319i) q^{54} +(4.39610 - 0.775151i) q^{55} +(1.24493 + 1.85063i) q^{56} +(1.34140 + 4.14737i) q^{57} +(-0.401722 - 0.695802i) q^{58} +(5.23397 + 1.90501i) q^{59} +(-5.83323 + 1.02856i) q^{60} +(-5.19105 + 6.18645i) q^{61} +(0.0899374 - 0.247101i) q^{62} +(1.07312 + 2.41835i) q^{63} +(-3.46496 + 6.00148i) q^{64} +(10.8928 + 6.28894i) q^{65} +(-0.201841 + 0.240545i) q^{66} +(-6.08581 + 7.25279i) q^{67} +(6.25918 + 3.61374i) q^{68} +(0.0696787 - 0.120687i) q^{69} +(-1.00636 + 1.38153i) q^{70} +(-2.60170 + 7.14811i) q^{71} +(0.541877 - 0.645784i) q^{72} +(12.6785 - 2.23555i) q^{73} +(0.967938 + 0.352301i) q^{74} +(-2.09186 - 3.62322i) q^{75} +(-0.308776 + 8.51412i) q^{76} +(-0.267032 - 3.88807i) q^{77} +(-0.871334 + 0.153640i) q^{78} +(0.251597 - 0.691258i) q^{79} +(-11.1301 - 1.96254i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.90429 - 0.335778i) q^{82} +(13.1405 + 7.58668i) q^{83} +(0.354328 + 5.15912i) q^{84} +(-1.94589 + 11.0357i) q^{85} +(0.111715 + 0.306935i) q^{86} -3.76894i q^{87} +(-1.07540 + 0.620883i) q^{88} +(-1.16146 + 6.58694i) q^{89} +(0.607059 + 0.220951i) q^{90} +(6.46556 - 8.87590i) q^{91} +(0.208657 - 0.175084i) q^{92} +(0.944946 - 0.792904i) q^{93} +(-1.14900 + 1.99012i) q^{94} +(-12.5685 + 4.06507i) q^{95} +(2.14864 - 1.24052i) q^{96} +(2.19807 + 12.4659i) q^{97} +(1.10646 + 1.00124i) q^{98} +(-1.38418 + 0.503800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 6 q^{7} + 12 q^{10} + 6 q^{11} + 72 q^{12} + 3 q^{13} - 15 q^{14} + 18 q^{19} + 9 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{24} + 18 q^{25} + 39 q^{27} - 9 q^{28} - 6 q^{29} - 18 q^{31} - 51 q^{32} - 12 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) \) 78 * q - 6 * q^7 + 12 * q^10 + 6 * q^11 + 72 * q^12 + 3 * q^13 - 15 * q^14 + 18 * q^19 + 9 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^24 + 18 * q^25 + 39 * q^27 - 9 * q^28 - 6 * q^29 - 18 * q^31 - 51 * q^32 - 12 * q^33 + 30 * q^34 + 33 * q^35 + 18 * q^37 - 57 * q^38 - 18 * q^40 - 63 * q^41 - 27 * q^42 - 51 * q^43 - 36 * q^44 + 9 * q^45 - 84 * q^47 + 18 * q^49 - 27 * q^50 - 18 * q^51 + 18 * q^52 - 45 * q^53 + 30 * q^55 + 33 * q^56 - 6 * q^57 - 18 * q^58 - 24 * q^59 + 66 * q^61 + 171 * q^62 + 6 * q^63 + 18 * q^64 - 99 * q^65 - 12 * q^66 - 24 * q^67 - 12 * q^69 - 150 * q^70 - 66 * q^71 - 9 * q^72 + 3 * q^73 + 18 * q^74 - 36 * q^75 - 12 * q^76 + 21 * q^77 + 75 * q^78 + 45 * q^79 + 78 * q^80 - 24 * q^82 - 72 * q^83 - 9 * q^84 + 60 * q^85 - 9 * q^86 - 108 * q^88 + 48 * q^89 - 33 * q^90 - 54 * q^91 - 102 * q^92 + 9 * q^93 - 66 * q^94 - 84 * q^95 + 75 * q^97 - 39 * q^98 - 6 * q^99

Introduction

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